Properties

Label 441.2.f.e.148.3
Level $441$
Weight $2$
Character 441.148
Analytic conductor $3.521$
Analytic rank $0$
Dimension $10$
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] = [441,2,Mod(148,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.148");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.f (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.991381711347.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 148.3
Root \(0.247934 + 0.429435i\) of defining polynomial
Character \(\chi\) \(=\) 441.148
Dual form 441.2.f.e.295.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.247934 + 0.429435i) q^{2} +(-1.37706 - 1.05058i) q^{3} +(0.877057 - 1.51911i) q^{4} +(1.84629 - 3.19787i) q^{5} +(0.109735 - 0.851830i) q^{6} +1.86155 q^{8} +(0.792574 + 2.89341i) q^{9} +O(q^{10})\) \(q+(0.247934 + 0.429435i) q^{2} +(-1.37706 - 1.05058i) q^{3} +(0.877057 - 1.51911i) q^{4} +(1.84629 - 3.19787i) q^{5} +(0.109735 - 0.851830i) q^{6} +1.86155 q^{8} +(0.792574 + 2.89341i) q^{9} +1.83103 q^{10} +(0.446284 + 0.772987i) q^{11} +(-2.80370 + 1.17048i) q^{12} +(0.598355 - 1.03638i) q^{13} +(-5.90205 + 2.46398i) q^{15} +(-1.29257 - 2.23880i) q^{16} +0.249983 q^{17} +(-1.04602 + 1.05773i) q^{18} -2.80827 q^{19} +(-3.23860 - 5.60943i) q^{20} +(-0.221298 + 0.383300i) q^{22} +(-1.23886 + 2.14576i) q^{23} +(-2.56346 - 1.95570i) q^{24} +(-4.31757 - 7.47825i) q^{25} +0.593411 q^{26} +(1.94833 - 4.81705i) q^{27} +(2.07128 + 3.58755i) q^{29} +(-2.52144 - 1.92364i) q^{30} +(-1.79257 + 3.10483i) q^{31} +(2.50249 - 4.33444i) q^{32} +(0.197524 - 1.53330i) q^{33} +(0.0619793 + 0.107351i) q^{34} +(5.09054 + 1.33368i) q^{36} +4.73136 q^{37} +(-0.696267 - 1.20597i) q^{38} +(-1.91277 + 0.798539i) q^{39} +(3.43695 - 5.95298i) q^{40} +(-2.39093 + 4.14121i) q^{41} +(-4.98928 - 8.64169i) q^{43} +1.56567 q^{44} +(10.7161 + 2.80753i) q^{45} -1.22862 q^{46} +(5.08653 + 8.81013i) q^{47} +(-0.572088 + 4.44091i) q^{48} +(2.14095 - 3.70823i) q^{50} +(-0.344241 - 0.262626i) q^{51} +(-1.04958 - 1.81793i) q^{52} +9.88929 q^{53} +(2.55167 - 0.357630i) q^{54} +3.29588 q^{55} +(3.86715 + 2.95031i) q^{57} +(-1.02708 + 1.77895i) q^{58} +(-0.906186 + 1.56956i) q^{59} +(-1.43339 + 11.1269i) q^{60} +(-5.40205 - 9.35663i) q^{61} -1.77776 q^{62} -2.68848 q^{64} +(-2.20948 - 3.82692i) q^{65} +(0.707426 - 0.295335i) q^{66} +(-0.514685 + 0.891460i) q^{67} +(0.219249 - 0.379751i) q^{68} +(3.96027 - 1.65332i) q^{69} -4.94533 q^{71} +(1.47541 + 5.38622i) q^{72} +1.83052 q^{73} +(1.17306 + 2.03181i) q^{74} +(-1.91094 + 14.8339i) q^{75} +(-2.46302 + 4.26607i) q^{76} +(-0.817161 - 0.623424i) q^{78} +(0.899562 + 1.55809i) q^{79} -9.54586 q^{80} +(-7.74365 + 4.58648i) q^{81} -2.37117 q^{82} +(6.16156 + 10.6721i) q^{83} +(0.461541 - 0.799412i) q^{85} +(2.47403 - 4.28514i) q^{86} +(0.916739 - 7.11630i) q^{87} +(0.830779 + 1.43895i) q^{88} +2.40741 q^{89} +(1.45123 + 5.29793i) q^{90} +(2.17310 + 3.76392i) q^{92} +(5.73034 - 2.39229i) q^{93} +(-2.52225 + 4.36867i) q^{94} +(-5.18489 + 8.98049i) q^{95} +(-7.99975 + 3.33972i) q^{96} +(5.52210 + 9.56456i) q^{97} +(-1.88286 + 1.90393i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 2 q^{2} - q^{3} - 4 q^{4} + 4 q^{5} - 2 q^{6} - 6 q^{8} - 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 2 q^{2} - q^{3} - 4 q^{4} + 4 q^{5} - 2 q^{6} - 6 q^{8} - 7 q^{9} + 14 q^{10} + 4 q^{11} - 2 q^{12} - 8 q^{13} - 19 q^{15} + 2 q^{16} - 24 q^{17} - 2 q^{18} - 2 q^{19} + 5 q^{20} - q^{22} + 3 q^{23} - 9 q^{24} - q^{25} - 22 q^{26} - 7 q^{27} + 7 q^{29} + 10 q^{30} - 3 q^{31} - 2 q^{32} - 13 q^{33} + 3 q^{34} + 34 q^{36} + 20 q^{38} - 22 q^{39} - 3 q^{40} + 5 q^{41} - 7 q^{43} + 20 q^{44} + 17 q^{45} - 6 q^{46} + 27 q^{47} - 5 q^{48} + 19 q^{50} - 15 q^{51} - 10 q^{52} + 42 q^{53} + 52 q^{54} + 4 q^{55} - 4 q^{57} - 10 q^{58} + 30 q^{59} + 31 q^{60} - 14 q^{61} - 12 q^{62} - 50 q^{64} - 11 q^{65} + 22 q^{66} - 2 q^{67} + 27 q^{68} + 15 q^{69} - 6 q^{71} - 12 q^{72} - 30 q^{73} - 36 q^{74} - 17 q^{75} + 5 q^{76} - 20 q^{78} - 4 q^{79} - 40 q^{80} - 31 q^{81} + 10 q^{82} + 9 q^{83} - 6 q^{85} - 8 q^{86} - 34 q^{87} - 18 q^{88} - 56 q^{89} + 28 q^{90} + 27 q^{92} + 18 q^{93} - 3 q^{94} - 14 q^{95} - 58 q^{96} - 12 q^{97} + 35 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(199\) \(344\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.247934 + 0.429435i 0.175316 + 0.303656i 0.940271 0.340428i \(-0.110572\pi\)
−0.764955 + 0.644084i \(0.777239\pi\)
\(3\) −1.37706 1.05058i −0.795044 0.606551i
\(4\) 0.877057 1.51911i 0.438529 0.759554i
\(5\) 1.84629 3.19787i 0.825686 1.43013i −0.0757082 0.997130i \(-0.524122\pi\)
0.901394 0.433000i \(-0.142545\pi\)
\(6\) 0.109735 0.851830i 0.0447990 0.347758i
\(7\) 0 0
\(8\) 1.86155 0.658156
\(9\) 0.792574 + 2.89341i 0.264191 + 0.964470i
\(10\) 1.83103 0.579023
\(11\) 0.446284 + 0.772987i 0.134560 + 0.233064i 0.925429 0.378921i \(-0.123705\pi\)
−0.790869 + 0.611985i \(0.790371\pi\)
\(12\) −2.80370 + 1.17048i −0.809358 + 0.337889i
\(13\) 0.598355 1.03638i 0.165954 0.287441i −0.771040 0.636787i \(-0.780263\pi\)
0.936994 + 0.349346i \(0.113596\pi\)
\(14\) 0 0
\(15\) −5.90205 + 2.46398i −1.52390 + 0.636196i
\(16\) −1.29257 2.23880i −0.323143 0.559701i
\(17\) 0.249983 0.0606298 0.0303149 0.999540i \(-0.490349\pi\)
0.0303149 + 0.999540i \(0.490349\pi\)
\(18\) −1.04602 + 1.05773i −0.246550 + 0.249310i
\(19\) −2.80827 −0.644262 −0.322131 0.946695i \(-0.604399\pi\)
−0.322131 + 0.946695i \(0.604399\pi\)
\(20\) −3.23860 5.60943i −0.724174 1.25431i
\(21\) 0 0
\(22\) −0.221298 + 0.383300i −0.0471809 + 0.0817198i
\(23\) −1.23886 + 2.14576i −0.258320 + 0.447423i −0.965792 0.259318i \(-0.916502\pi\)
0.707472 + 0.706741i \(0.249835\pi\)
\(24\) −2.56346 1.95570i −0.523263 0.399205i
\(25\) −4.31757 7.47825i −0.863514 1.49565i
\(26\) 0.593411 0.116377
\(27\) 1.94833 4.81705i 0.374957 0.927042i
\(28\) 0 0
\(29\) 2.07128 + 3.58755i 0.384626 + 0.666192i 0.991717 0.128440i \(-0.0409970\pi\)
−0.607091 + 0.794632i \(0.707664\pi\)
\(30\) −2.52144 1.92364i −0.460349 0.351207i
\(31\) −1.79257 + 3.10483i −0.321956 + 0.557644i −0.980892 0.194555i \(-0.937674\pi\)
0.658936 + 0.752199i \(0.271007\pi\)
\(32\) 2.50249 4.33444i 0.442382 0.766229i
\(33\) 0.197524 1.53330i 0.0343845 0.266914i
\(34\) 0.0619793 + 0.107351i 0.0106294 + 0.0184106i
\(35\) 0 0
\(36\) 5.09054 + 1.33368i 0.848423 + 0.222280i
\(37\) 4.73136 0.777830 0.388915 0.921274i \(-0.372850\pi\)
0.388915 + 0.921274i \(0.372850\pi\)
\(38\) −0.696267 1.20597i −0.112949 0.195634i
\(39\) −1.91277 + 0.798539i −0.306288 + 0.127869i
\(40\) 3.43695 5.95298i 0.543430 0.941249i
\(41\) −2.39093 + 4.14121i −0.373400 + 0.646748i −0.990086 0.140461i \(-0.955142\pi\)
0.616686 + 0.787209i \(0.288475\pi\)
\(42\) 0 0
\(43\) −4.98928 8.64169i −0.760859 1.31785i −0.942408 0.334464i \(-0.891445\pi\)
0.181550 0.983382i \(-0.441889\pi\)
\(44\) 1.56567 0.236033
\(45\) 10.7161 + 2.80753i 1.59746 + 0.418522i
\(46\) −1.22862 −0.181150
\(47\) 5.08653 + 8.81013i 0.741947 + 1.28509i 0.951608 + 0.307316i \(0.0994308\pi\)
−0.209661 + 0.977774i \(0.567236\pi\)
\(48\) −0.572088 + 4.44091i −0.0825738 + 0.640990i
\(49\) 0 0
\(50\) 2.14095 3.70823i 0.302776 0.524423i
\(51\) −0.344241 0.262626i −0.0482034 0.0367751i
\(52\) −1.04958 1.81793i −0.145551 0.252102i
\(53\) 9.88929 1.35840 0.679199 0.733954i \(-0.262327\pi\)
0.679199 + 0.733954i \(0.262327\pi\)
\(54\) 2.55167 0.357630i 0.347238 0.0486673i
\(55\) 3.29588 0.444416
\(56\) 0 0
\(57\) 3.86715 + 2.95031i 0.512217 + 0.390778i
\(58\) −1.02708 + 1.77895i −0.134862 + 0.233588i
\(59\) −0.906186 + 1.56956i −0.117975 + 0.204339i −0.918965 0.394339i \(-0.870974\pi\)
0.800990 + 0.598678i \(0.204307\pi\)
\(60\) −1.43339 + 11.1269i −0.185050 + 1.43648i
\(61\) −5.40205 9.35663i −0.691662 1.19799i −0.971293 0.237886i \(-0.923545\pi\)
0.279631 0.960108i \(-0.409788\pi\)
\(62\) −1.77776 −0.225776
\(63\) 0 0
\(64\) −2.68848 −0.336060
\(65\) −2.20948 3.82692i −0.274052 0.474671i
\(66\) 0.707426 0.295335i 0.0870781 0.0363532i
\(67\) −0.514685 + 0.891460i −0.0628787 + 0.108909i −0.895751 0.444556i \(-0.853361\pi\)
0.832872 + 0.553465i \(0.186695\pi\)
\(68\) 0.219249 0.379751i 0.0265879 0.0460516i
\(69\) 3.96027 1.65332i 0.476761 0.199037i
\(70\) 0 0
\(71\) −4.94533 −0.586903 −0.293451 0.955974i \(-0.594804\pi\)
−0.293451 + 0.955974i \(0.594804\pi\)
\(72\) 1.47541 + 5.38622i 0.173879 + 0.634772i
\(73\) 1.83052 0.214247 0.107123 0.994246i \(-0.465836\pi\)
0.107123 + 0.994246i \(0.465836\pi\)
\(74\) 1.17306 + 2.03181i 0.136366 + 0.236193i
\(75\) −1.91094 + 14.8339i −0.220656 + 1.71287i
\(76\) −2.46302 + 4.26607i −0.282527 + 0.489352i
\(77\) 0 0
\(78\) −0.817161 0.623424i −0.0925253 0.0705889i
\(79\) 0.899562 + 1.55809i 0.101209 + 0.175298i 0.912183 0.409783i \(-0.134396\pi\)
−0.810974 + 0.585082i \(0.801062\pi\)
\(80\) −9.54586 −1.06726
\(81\) −7.74365 + 4.58648i −0.860406 + 0.509609i
\(82\) −2.37117 −0.261852
\(83\) 6.16156 + 10.6721i 0.676319 + 1.17142i 0.976082 + 0.217405i \(0.0697591\pi\)
−0.299763 + 0.954014i \(0.596908\pi\)
\(84\) 0 0
\(85\) 0.461541 0.799412i 0.0500611 0.0867084i
\(86\) 2.47403 4.28514i 0.266781 0.462079i
\(87\) 0.916739 7.11630i 0.0982847 0.762948i
\(88\) 0.830779 + 1.43895i 0.0885613 + 0.153393i
\(89\) 2.40741 0.255185 0.127592 0.991827i \(-0.459275\pi\)
0.127592 + 0.991827i \(0.459275\pi\)
\(90\) 1.45123 + 5.29793i 0.152973 + 0.558451i
\(91\) 0 0
\(92\) 2.17310 + 3.76392i 0.226561 + 0.392416i
\(93\) 5.73034 2.39229i 0.594209 0.248069i
\(94\) −2.52225 + 4.36867i −0.260150 + 0.450593i
\(95\) −5.18489 + 8.98049i −0.531958 + 0.921379i
\(96\) −7.99975 + 3.33972i −0.816471 + 0.340858i
\(97\) 5.52210 + 9.56456i 0.560684 + 0.971134i 0.997437 + 0.0715522i \(0.0227952\pi\)
−0.436752 + 0.899582i \(0.643871\pi\)
\(98\) 0 0
\(99\) −1.88286 + 1.90393i −0.189234 + 0.191352i
\(100\) −15.1470 −1.51470
\(101\) 1.29982 + 2.25136i 0.129337 + 0.224018i 0.923420 0.383791i \(-0.125382\pi\)
−0.794083 + 0.607810i \(0.792048\pi\)
\(102\) 0.0274318 0.212943i 0.00271615 0.0210845i
\(103\) −4.85578 + 8.41045i −0.478454 + 0.828706i −0.999695 0.0247032i \(-0.992136\pi\)
0.521241 + 0.853409i \(0.325469\pi\)
\(104\) 1.11387 1.92927i 0.109224 0.189181i
\(105\) 0 0
\(106\) 2.45189 + 4.24680i 0.238149 + 0.412486i
\(107\) 10.9005 1.05379 0.526896 0.849930i \(-0.323356\pi\)
0.526896 + 0.849930i \(0.323356\pi\)
\(108\) −5.60882 7.18456i −0.539709 0.691335i
\(109\) 2.12193 0.203244 0.101622 0.994823i \(-0.467597\pi\)
0.101622 + 0.994823i \(0.467597\pi\)
\(110\) 0.817161 + 1.41536i 0.0779132 + 0.134950i
\(111\) −6.51535 4.97066i −0.618410 0.471794i
\(112\) 0 0
\(113\) 7.91318 13.7060i 0.744409 1.28935i −0.206061 0.978539i \(-0.566065\pi\)
0.950470 0.310816i \(-0.100602\pi\)
\(114\) −0.308165 + 2.39217i −0.0288623 + 0.224047i
\(115\) 4.57458 + 7.92341i 0.426582 + 0.738861i
\(116\) 7.26651 0.674679
\(117\) 3.47292 + 0.909879i 0.321072 + 0.0841183i
\(118\) −0.898698 −0.0827318
\(119\) 0 0
\(120\) −10.9869 + 4.58681i −1.00297 + 0.418716i
\(121\) 5.10166 8.83634i 0.463787 0.803303i
\(122\) 2.67871 4.63966i 0.242519 0.420055i
\(123\) 7.64311 3.19083i 0.689156 0.287707i
\(124\) 3.14438 + 5.44623i 0.282374 + 0.489086i
\(125\) −13.4230 −1.20059
\(126\) 0 0
\(127\) −1.26946 −0.112647 −0.0563233 0.998413i \(-0.517938\pi\)
−0.0563233 + 0.998413i \(0.517938\pi\)
\(128\) −5.67155 9.82342i −0.501299 0.868275i
\(129\) −2.20824 + 17.1417i −0.194425 + 1.50925i
\(130\) 1.09561 1.89765i 0.0960912 0.166435i
\(131\) 7.51444 13.0154i 0.656540 1.13716i −0.324965 0.945726i \(-0.605353\pi\)
0.981505 0.191435i \(-0.0613140\pi\)
\(132\) −2.15601 1.64485i −0.187657 0.143166i
\(133\) 0 0
\(134\) −0.510432 −0.0440946
\(135\) −11.8071 15.1242i −1.01619 1.30168i
\(136\) 0.465355 0.0399038
\(137\) 0.244246 + 0.423047i 0.0208674 + 0.0361433i 0.876271 0.481819i \(-0.160024\pi\)
−0.855403 + 0.517963i \(0.826691\pi\)
\(138\) 1.69188 + 1.29076i 0.144022 + 0.109877i
\(139\) −4.93487 + 8.54745i −0.418570 + 0.724985i −0.995796 0.0915997i \(-0.970802\pi\)
0.577226 + 0.816585i \(0.304135\pi\)
\(140\) 0 0
\(141\) 2.25128 17.4759i 0.189592 1.47173i
\(142\) −1.22612 2.12370i −0.102893 0.178217i
\(143\) 1.06815 0.0893229
\(144\) 5.45332 5.51436i 0.454443 0.459530i
\(145\) 15.2967 1.27032
\(146\) 0.453849 + 0.786090i 0.0375609 + 0.0650573i
\(147\) 0 0
\(148\) 4.14967 7.18744i 0.341101 0.590804i
\(149\) −10.5120 + 18.2073i −0.861175 + 1.49160i 0.00962096 + 0.999954i \(0.496938\pi\)
−0.870796 + 0.491645i \(0.836396\pi\)
\(150\) −6.84399 + 2.85721i −0.558809 + 0.233290i
\(151\) −0.749191 1.29764i −0.0609683 0.105600i 0.833930 0.551870i \(-0.186086\pi\)
−0.894898 + 0.446270i \(0.852752\pi\)
\(152\) −5.22773 −0.424025
\(153\) 0.198130 + 0.723303i 0.0160179 + 0.0584756i
\(154\) 0 0
\(155\) 6.61922 + 11.4648i 0.531669 + 0.920877i
\(156\) −0.464542 + 3.60607i −0.0371931 + 0.288716i
\(157\) 8.33982 14.4450i 0.665590 1.15284i −0.313535 0.949577i \(-0.601513\pi\)
0.979125 0.203259i \(-0.0651534\pi\)
\(158\) −0.446064 + 0.772606i −0.0354870 + 0.0614652i
\(159\) −13.6181 10.3895i −1.07999 0.823938i
\(160\) −9.24065 16.0053i −0.730538 1.26533i
\(161\) 0 0
\(162\) −3.88951 2.18825i −0.305589 0.171925i
\(163\) 6.68269 0.523429 0.261714 0.965145i \(-0.415712\pi\)
0.261714 + 0.965145i \(0.415712\pi\)
\(164\) 4.19396 + 7.26416i 0.327494 + 0.567236i
\(165\) −4.53861 3.46258i −0.353331 0.269561i
\(166\) −3.05532 + 5.29197i −0.237139 + 0.410737i
\(167\) 8.81549 15.2689i 0.682163 1.18154i −0.292156 0.956371i \(-0.594373\pi\)
0.974319 0.225170i \(-0.0722939\pi\)
\(168\) 0 0
\(169\) 5.78394 + 10.0181i 0.444919 + 0.770622i
\(170\) 0.457727 0.0351061
\(171\) −2.22576 8.12549i −0.170208 0.621372i
\(172\) −17.5036 −1.33463
\(173\) 1.94342 + 3.36611i 0.147756 + 0.255920i 0.930398 0.366552i \(-0.119462\pi\)
−0.782642 + 0.622472i \(0.786128\pi\)
\(174\) 3.28328 1.37070i 0.248905 0.103912i
\(175\) 0 0
\(176\) 1.15371 1.99829i 0.0869642 0.150626i
\(177\) 2.89681 1.20936i 0.217738 0.0909007i
\(178\) 0.596879 + 1.03382i 0.0447380 + 0.0774884i
\(179\) −7.33516 −0.548256 −0.274128 0.961693i \(-0.588389\pi\)
−0.274128 + 0.961693i \(0.588389\pi\)
\(180\) 13.6635 13.8165i 1.01842 1.02982i
\(181\) 11.2566 0.836693 0.418346 0.908288i \(-0.362610\pi\)
0.418346 + 0.908288i \(0.362610\pi\)
\(182\) 0 0
\(183\) −2.39093 + 18.5599i −0.176743 + 1.37199i
\(184\) −2.30619 + 3.99444i −0.170015 + 0.294474i
\(185\) 8.73545 15.1302i 0.642243 1.11240i
\(186\) 2.44808 + 1.86768i 0.179502 + 0.136945i
\(187\) 0.111563 + 0.193234i 0.00815833 + 0.0141306i
\(188\) 17.8447 1.30146
\(189\) 0 0
\(190\) −5.14204 −0.373043
\(191\) 11.9230 + 20.6512i 0.862715 + 1.49427i 0.869298 + 0.494288i \(0.164571\pi\)
−0.00658302 + 0.999978i \(0.502095\pi\)
\(192\) 3.70219 + 2.82446i 0.267183 + 0.203838i
\(193\) −2.96728 + 5.13948i −0.213589 + 0.369948i −0.952835 0.303488i \(-0.901849\pi\)
0.739246 + 0.673436i \(0.235182\pi\)
\(194\) −2.73823 + 4.74276i −0.196594 + 0.340510i
\(195\) −0.977905 + 7.59112i −0.0700293 + 0.543611i
\(196\) 0 0
\(197\) −15.4682 −1.10206 −0.551032 0.834484i \(-0.685766\pi\)
−0.551032 + 0.834484i \(0.685766\pi\)
\(198\) −1.28444 0.336513i −0.0912811 0.0239150i
\(199\) −15.4964 −1.09851 −0.549254 0.835655i \(-0.685088\pi\)
−0.549254 + 0.835655i \(0.685088\pi\)
\(200\) −8.03736 13.9211i −0.568327 0.984371i
\(201\) 1.64530 0.686875i 0.116050 0.0484485i
\(202\) −0.644540 + 1.11638i −0.0453497 + 0.0785480i
\(203\) 0 0
\(204\) −0.700877 + 0.292600i −0.0490712 + 0.0204861i
\(205\) 8.82870 + 15.2917i 0.616623 + 1.06802i
\(206\) −4.81565 −0.335522
\(207\) −7.19047 1.88385i −0.499772 0.130936i
\(208\) −3.09367 −0.214508
\(209\) −1.25329 2.17076i −0.0866918 0.150155i
\(210\) 0 0
\(211\) 0.771898 1.33697i 0.0531397 0.0920406i −0.838232 0.545314i \(-0.816410\pi\)
0.891372 + 0.453273i \(0.149744\pi\)
\(212\) 8.67347 15.0229i 0.595697 1.03178i
\(213\) 6.81001 + 5.19545i 0.466614 + 0.355987i
\(214\) 2.70261 + 4.68105i 0.184746 + 0.319990i
\(215\) −36.8467 −2.51292
\(216\) 3.62691 8.96717i 0.246780 0.610138i
\(217\) 0 0
\(218\) 0.526098 + 0.911229i 0.0356319 + 0.0617162i
\(219\) −2.52074 1.92311i −0.170336 0.129952i
\(220\) 2.89068 5.00680i 0.194889 0.337558i
\(221\) 0.149579 0.259078i 0.0100617 0.0174275i
\(222\) 0.519194 4.03031i 0.0348460 0.270497i
\(223\) −2.72171 4.71414i −0.182259 0.315682i 0.760390 0.649466i \(-0.225008\pi\)
−0.942649 + 0.333784i \(0.891674\pi\)
\(224\) 0 0
\(225\) 18.2157 18.4196i 1.21438 1.22797i
\(226\) 7.84779 0.522027
\(227\) 8.03818 + 13.9225i 0.533513 + 0.924072i 0.999234 + 0.0391399i \(0.0124618\pi\)
−0.465721 + 0.884932i \(0.654205\pi\)
\(228\) 7.87356 3.28703i 0.521439 0.217689i
\(229\) 4.98420 8.63289i 0.329365 0.570477i −0.653021 0.757340i \(-0.726499\pi\)
0.982386 + 0.186863i \(0.0598319\pi\)
\(230\) −2.26839 + 3.92897i −0.149573 + 0.259068i
\(231\) 0 0
\(232\) 3.85578 + 6.67840i 0.253144 + 0.438458i
\(233\) −16.5409 −1.08363 −0.541815 0.840498i \(-0.682263\pi\)
−0.541815 + 0.840498i \(0.682263\pi\)
\(234\) 0.470322 + 1.71698i 0.0307459 + 0.112243i
\(235\) 37.5648 2.45046
\(236\) 1.58955 + 2.75319i 0.103471 + 0.179217i
\(237\) 0.398143 3.09063i 0.0258621 0.200758i
\(238\) 0 0
\(239\) −11.0119 + 19.0732i −0.712303 + 1.23375i 0.251687 + 0.967809i \(0.419015\pi\)
−0.963990 + 0.265937i \(0.914319\pi\)
\(240\) 13.1452 + 10.0287i 0.848519 + 0.647348i
\(241\) −8.36004 14.4800i −0.538517 0.932739i −0.998984 0.0450623i \(-0.985651\pi\)
0.460467 0.887677i \(-0.347682\pi\)
\(242\) 5.05950 0.325237
\(243\) 15.4819 + 1.81946i 0.993165 + 0.116718i
\(244\) −18.9516 −1.21325
\(245\) 0 0
\(246\) 3.26524 + 2.49110i 0.208184 + 0.158827i
\(247\) −1.68035 + 2.91045i −0.106918 + 0.185187i
\(248\) −3.33696 + 5.77978i −0.211897 + 0.367017i
\(249\) 2.72708 21.1693i 0.172822 1.34155i
\(250\) −3.32803 5.76432i −0.210483 0.364568i
\(251\) −8.53099 −0.538471 −0.269236 0.963074i \(-0.586771\pi\)
−0.269236 + 0.963074i \(0.586771\pi\)
\(252\) 0 0
\(253\) −2.21153 −0.139038
\(254\) −0.314743 0.545151i −0.0197488 0.0342058i
\(255\) −1.47541 + 0.615952i −0.0923939 + 0.0385724i
\(256\) 0.123861 0.214533i 0.00774131 0.0134083i
\(257\) 8.55986 14.8261i 0.533950 0.924828i −0.465264 0.885172i \(-0.654041\pi\)
0.999213 0.0396557i \(-0.0126261\pi\)
\(258\) −7.90875 + 3.30173i −0.492377 + 0.205557i
\(259\) 0 0
\(260\) −7.75135 −0.480718
\(261\) −8.73863 + 8.83645i −0.540908 + 0.546963i
\(262\) 7.45235 0.460408
\(263\) −10.2763 17.7991i −0.633666 1.09754i −0.986796 0.161967i \(-0.948216\pi\)
0.353130 0.935574i \(-0.385117\pi\)
\(264\) 0.367700 2.85432i 0.0226303 0.175671i
\(265\) 18.2585 31.6246i 1.12161 1.94269i
\(266\) 0 0
\(267\) −3.31514 2.52917i −0.202883 0.154783i
\(268\) 0.902816 + 1.56372i 0.0551483 + 0.0955196i
\(269\) −19.8453 −1.20999 −0.604996 0.796229i \(-0.706825\pi\)
−0.604996 + 0.796229i \(0.706825\pi\)
\(270\) 3.56746 8.82018i 0.217109 0.536779i
\(271\) −10.6411 −0.646402 −0.323201 0.946330i \(-0.604759\pi\)
−0.323201 + 0.946330i \(0.604759\pi\)
\(272\) −0.323121 0.559663i −0.0195921 0.0339345i
\(273\) 0 0
\(274\) −0.121114 + 0.209776i −0.00731676 + 0.0126730i
\(275\) 3.85373 6.67485i 0.232388 0.402509i
\(276\) 0.961806 7.46614i 0.0578939 0.449409i
\(277\) 12.4407 + 21.5479i 0.747487 + 1.29469i 0.949024 + 0.315205i \(0.102073\pi\)
−0.201536 + 0.979481i \(0.564593\pi\)
\(278\) −4.89409 −0.293528
\(279\) −10.4043 2.72585i −0.622889 0.163192i
\(280\) 0 0
\(281\) −6.83733 11.8426i −0.407881 0.706470i 0.586771 0.809753i \(-0.300399\pi\)
−0.994652 + 0.103282i \(0.967065\pi\)
\(282\) 8.06290 3.36608i 0.480139 0.200447i
\(283\) −3.16089 + 5.47483i −0.187896 + 0.325445i −0.944548 0.328372i \(-0.893500\pi\)
0.756653 + 0.653817i \(0.226833\pi\)
\(284\) −4.33734 + 7.51249i −0.257374 + 0.445784i
\(285\) 16.5746 6.91952i 0.981794 0.409877i
\(286\) 0.264830 + 0.458699i 0.0156597 + 0.0271234i
\(287\) 0 0
\(288\) 14.5247 + 3.80537i 0.855878 + 0.224234i
\(289\) −16.9375 −0.996324
\(290\) 3.79257 + 6.56893i 0.222708 + 0.385741i
\(291\) 2.44406 18.9723i 0.143273 1.11218i
\(292\) 1.60547 2.78076i 0.0939533 0.162732i
\(293\) −1.31508 + 2.27778i −0.0768277 + 0.133069i −0.901880 0.431987i \(-0.857812\pi\)
0.825052 + 0.565057i \(0.191146\pi\)
\(294\) 0 0
\(295\) 3.34616 + 5.79573i 0.194821 + 0.337440i
\(296\) 8.80764 0.511934
\(297\) 4.59303 0.643739i 0.266515 0.0373535i
\(298\) −10.4251 −0.603911
\(299\) 1.48255 + 2.56786i 0.0857384 + 0.148503i
\(300\) 20.8583 + 15.9131i 1.20426 + 0.918745i
\(301\) 0 0
\(302\) 0.371500 0.643457i 0.0213774 0.0370268i
\(303\) 0.575296 4.46581i 0.0330499 0.256554i
\(304\) 3.62990 + 6.28717i 0.208189 + 0.360594i
\(305\) −39.8950 −2.28438
\(306\) −0.261488 + 0.264415i −0.0149483 + 0.0151156i
\(307\) −2.79496 −0.159517 −0.0797583 0.996814i \(-0.525415\pi\)
−0.0797583 + 0.996814i \(0.525415\pi\)
\(308\) 0 0
\(309\) 15.5225 6.48030i 0.883045 0.368652i
\(310\) −3.28226 + 5.68504i −0.186420 + 0.322889i
\(311\) 7.55013 13.0772i 0.428129 0.741541i −0.568578 0.822629i \(-0.692506\pi\)
0.996707 + 0.0810885i \(0.0258396\pi\)
\(312\) −3.56071 + 1.48652i −0.201585 + 0.0841574i
\(313\) 12.7392 + 22.0650i 0.720064 + 1.24719i 0.960974 + 0.276640i \(0.0892209\pi\)
−0.240910 + 0.970548i \(0.577446\pi\)
\(314\) 8.27090 0.466754
\(315\) 0 0
\(316\) 3.15587 0.177531
\(317\) −16.2605 28.1639i −0.913278 1.58184i −0.809403 0.587253i \(-0.800209\pi\)
−0.103875 0.994590i \(-0.533124\pi\)
\(318\) 1.08520 8.42399i 0.0608549 0.472394i
\(319\) −1.84875 + 3.20214i −0.103510 + 0.179285i
\(320\) −4.96372 + 8.59741i −0.277480 + 0.480610i
\(321\) −15.0106 11.4518i −0.837811 0.639179i
\(322\) 0 0
\(323\) −0.702021 −0.0390615
\(324\) 0.175735 + 15.7861i 0.00976303 + 0.877003i
\(325\) −10.3338 −0.573214
\(326\) 1.65687 + 2.86978i 0.0917654 + 0.158942i
\(327\) −2.92201 2.22925i −0.161588 0.123278i
\(328\) −4.45083 + 7.70906i −0.245756 + 0.425661i
\(329\) 0 0
\(330\) 0.361672 2.80753i 0.0199094 0.154549i
\(331\) −9.04741 15.6706i −0.497291 0.861333i 0.502704 0.864458i \(-0.332338\pi\)
−0.999995 + 0.00312545i \(0.999005\pi\)
\(332\) 21.6162 1.18634
\(333\) 3.74995 + 13.6898i 0.205496 + 0.750194i
\(334\) 8.74264 0.478376
\(335\) 1.90051 + 3.29179i 0.103836 + 0.179850i
\(336\) 0 0
\(337\) −12.5086 + 21.6656i −0.681389 + 1.18020i 0.293168 + 0.956061i \(0.405290\pi\)
−0.974557 + 0.224139i \(0.928043\pi\)
\(338\) −2.86807 + 4.96765i −0.156003 + 0.270204i
\(339\) −25.2961 + 10.5606i −1.37390 + 0.573572i
\(340\) −0.809596 1.40226i −0.0439065 0.0760483i
\(341\) −3.19999 −0.173289
\(342\) 2.93752 2.97041i 0.158843 0.160621i
\(343\) 0 0
\(344\) −9.28778 16.0869i −0.500764 0.867348i
\(345\) 2.02469 15.7169i 0.109006 0.846171i
\(346\) −0.963682 + 1.66915i −0.0518078 + 0.0897338i
\(347\) −5.37444 + 9.30881i −0.288515 + 0.499723i −0.973456 0.228876i \(-0.926495\pi\)
0.684940 + 0.728599i \(0.259828\pi\)
\(348\) −10.0064 7.63403i −0.536399 0.409227i
\(349\) −1.64301 2.84577i −0.0879482 0.152331i 0.818695 0.574228i \(-0.194698\pi\)
−0.906644 + 0.421897i \(0.861364\pi\)
\(350\) 0 0
\(351\) −3.82651 4.90153i −0.204244 0.261624i
\(352\) 4.46729 0.238107
\(353\) −8.40960 14.5658i −0.447598 0.775262i 0.550631 0.834748i \(-0.314387\pi\)
−0.998229 + 0.0594866i \(0.981054\pi\)
\(354\) 1.23756 + 0.944152i 0.0657755 + 0.0501811i
\(355\) −9.13051 + 15.8145i −0.484597 + 0.839347i
\(356\) 2.11144 3.65711i 0.111906 0.193827i
\(357\) 0 0
\(358\) −1.81864 3.14997i −0.0961180 0.166481i
\(359\) −23.7842 −1.25528 −0.627642 0.778502i \(-0.715980\pi\)
−0.627642 + 0.778502i \(0.715980\pi\)
\(360\) 19.9485 + 5.22634i 1.05138 + 0.275453i
\(361\) −11.1136 −0.584926
\(362\) 2.79088 + 4.83395i 0.146686 + 0.254067i
\(363\) −16.3085 + 6.80845i −0.855976 + 0.357351i
\(364\) 0 0
\(365\) 3.37968 5.85377i 0.176900 0.306401i
\(366\) −8.56305 + 3.57488i −0.447598 + 0.186862i
\(367\) 0.344992 + 0.597544i 0.0180084 + 0.0311915i 0.874889 0.484323i \(-0.160934\pi\)
−0.856881 + 0.515515i \(0.827601\pi\)
\(368\) 6.40526 0.333897
\(369\) −13.8772 3.63573i −0.722419 0.189268i
\(370\) 8.66327 0.450382
\(371\) 0 0
\(372\) 1.39169 10.8032i 0.0721558 0.560119i
\(373\) 1.88006 3.25636i 0.0973457 0.168608i −0.813239 0.581929i \(-0.802298\pi\)
0.910585 + 0.413321i \(0.135631\pi\)
\(374\) −0.0553208 + 0.0958184i −0.00286057 + 0.00495465i
\(375\) 18.4843 + 14.1020i 0.954525 + 0.728222i
\(376\) 9.46882 + 16.4005i 0.488317 + 0.845790i
\(377\) 4.95744 0.255321
\(378\) 0 0
\(379\) 32.8735 1.68860 0.844300 0.535872i \(-0.180017\pi\)
0.844300 + 0.535872i \(0.180017\pi\)
\(380\) 9.09489 + 15.7528i 0.466558 + 0.808102i
\(381\) 1.74812 + 1.33367i 0.0895591 + 0.0683260i
\(382\) −5.91222 + 10.2403i −0.302495 + 0.523937i
\(383\) 0.536335 0.928960i 0.0274055 0.0474676i −0.851997 0.523546i \(-0.824609\pi\)
0.879403 + 0.476078i \(0.157942\pi\)
\(384\) −2.51021 + 19.4858i −0.128099 + 0.994381i
\(385\) 0 0
\(386\) −2.94276 −0.149782
\(387\) 21.0496 21.2852i 1.07001 1.08199i
\(388\) 19.3728 0.983505
\(389\) 11.8718 + 20.5626i 0.601925 + 1.04256i 0.992529 + 0.122006i \(0.0389326\pi\)
−0.390605 + 0.920559i \(0.627734\pi\)
\(390\) −3.50234 + 1.46215i −0.177348 + 0.0740389i
\(391\) −0.309693 + 0.536405i −0.0156619 + 0.0271271i
\(392\) 0 0
\(393\) −24.0215 + 10.0284i −1.21172 + 0.505868i
\(394\) −3.83510 6.64258i −0.193209 0.334648i
\(395\) 6.64340 0.334266
\(396\) 1.24091 + 4.53012i 0.0623579 + 0.227647i
\(397\) 0.0320978 0.00161094 0.000805471 1.00000i \(-0.499744\pi\)
0.000805471 1.00000i \(0.499744\pi\)
\(398\) −3.84208 6.65467i −0.192586 0.333569i
\(399\) 0 0
\(400\) −11.1616 + 19.3324i −0.558078 + 0.966619i
\(401\) −12.2628 + 21.2398i −0.612374 + 1.06066i 0.378465 + 0.925616i \(0.376452\pi\)
−0.990839 + 0.135048i \(0.956881\pi\)
\(402\) 0.702894 + 0.536248i 0.0350571 + 0.0267456i
\(403\) 2.14519 + 3.71558i 0.106860 + 0.185086i
\(404\) 4.56007 0.226872
\(405\) 0.369938 + 33.2312i 0.0183824 + 1.65127i
\(406\) 0 0
\(407\) 2.11153 + 3.65728i 0.104665 + 0.181284i
\(408\) −0.640820 0.488891i −0.0317253 0.0242037i
\(409\) −13.3948 + 23.2006i −0.662333 + 1.14719i 0.317669 + 0.948202i \(0.397100\pi\)
−0.980001 + 0.198992i \(0.936233\pi\)
\(410\) −4.37787 + 7.58269i −0.216208 + 0.374483i
\(411\) 0.108103 0.839160i 0.00533230 0.0413927i
\(412\) 8.51759 + 14.7529i 0.419631 + 0.726823i
\(413\) 0 0
\(414\) −0.973773 3.55490i −0.0478583 0.174714i
\(415\) 45.5041 2.23371
\(416\) −2.99476 5.18708i −0.146830 0.254317i
\(417\) 15.7754 6.58586i 0.772522 0.322511i
\(418\) 0.621466 1.07641i 0.0303969 0.0526490i
\(419\) −10.5262 + 18.2320i −0.514240 + 0.890689i 0.485624 + 0.874168i \(0.338593\pi\)
−0.999864 + 0.0165215i \(0.994741\pi\)
\(420\) 0 0
\(421\) −7.44533 12.8957i −0.362863 0.628498i 0.625568 0.780170i \(-0.284867\pi\)
−0.988431 + 0.151672i \(0.951534\pi\)
\(422\) 0.765520 0.0372649
\(423\) −21.4599 + 21.7001i −1.04342 + 1.05510i
\(424\) 18.4094 0.894038
\(425\) −1.07932 1.86944i −0.0523547 0.0906809i
\(426\) −0.542675 + 4.21258i −0.0262927 + 0.204100i
\(427\) 0 0
\(428\) 9.56037 16.5590i 0.462118 0.800412i
\(429\) −1.47090 1.12217i −0.0710157 0.0541789i
\(430\) −9.13554 15.8232i −0.440555 0.763064i
\(431\) 15.9038 0.766061 0.383031 0.923736i \(-0.374880\pi\)
0.383031 + 0.923736i \(0.374880\pi\)
\(432\) −13.3028 + 1.86446i −0.640031 + 0.0897040i
\(433\) −16.3658 −0.786490 −0.393245 0.919434i \(-0.628648\pi\)
−0.393245 + 0.919434i \(0.628648\pi\)
\(434\) 0 0
\(435\) −21.0644 16.0704i −1.00996 0.770515i
\(436\) 1.86105 3.22344i 0.0891282 0.154375i
\(437\) 3.47905 6.02590i 0.166426 0.288258i
\(438\) 0.200872 1.55930i 0.00959804 0.0745060i
\(439\) 7.77236 + 13.4621i 0.370954 + 0.642512i 0.989713 0.143070i \(-0.0456973\pi\)
−0.618758 + 0.785582i \(0.712364\pi\)
\(440\) 6.13543 0.292495
\(441\) 0 0
\(442\) 0.148343 0.00705594
\(443\) −0.895027 1.55023i −0.0425240 0.0736537i 0.843980 0.536375i \(-0.180207\pi\)
−0.886504 + 0.462721i \(0.846873\pi\)
\(444\) −13.2653 + 5.53797i −0.629543 + 0.262820i
\(445\) 4.44477 7.69857i 0.210702 0.364947i
\(446\) 1.34961 2.33759i 0.0639058 0.110688i
\(447\) 33.6038 14.0288i 1.58940 0.663540i
\(448\) 0 0
\(449\) 13.5666 0.640250 0.320125 0.947375i \(-0.396275\pi\)
0.320125 + 0.947375i \(0.396275\pi\)
\(450\) 12.4263 + 3.25559i 0.585781 + 0.153470i
\(451\) −4.26814 −0.200979
\(452\) −13.8806 24.0419i −0.652890 1.13084i
\(453\) −0.331589 + 2.57400i −0.0155794 + 0.120937i
\(454\) −3.98588 + 6.90375i −0.187067 + 0.324009i
\(455\) 0 0
\(456\) 7.19889 + 5.49214i 0.337119 + 0.257193i
\(457\) −1.28459 2.22497i −0.0600905 0.104080i 0.834415 0.551136i \(-0.185806\pi\)
−0.894506 + 0.447057i \(0.852472\pi\)
\(458\) 4.94301 0.230972
\(459\) 0.487050 1.20418i 0.0227335 0.0562064i
\(460\) 16.0487 0.748274
\(461\) 18.0934 + 31.3388i 0.842695 + 1.45959i 0.887608 + 0.460600i \(0.152366\pi\)
−0.0449122 + 0.998991i \(0.514301\pi\)
\(462\) 0 0
\(463\) 8.19224 14.1894i 0.380726 0.659436i −0.610440 0.792062i \(-0.709008\pi\)
0.991166 + 0.132626i \(0.0423409\pi\)
\(464\) 5.35455 9.27436i 0.248579 0.430551i
\(465\) 2.92964 22.7417i 0.135859 1.05462i
\(466\) −4.10105 7.10323i −0.189978 0.329051i
\(467\) 8.70044 0.402608 0.201304 0.979529i \(-0.435482\pi\)
0.201304 + 0.979529i \(0.435482\pi\)
\(468\) 4.42815 4.47772i 0.204692 0.206983i
\(469\) 0 0
\(470\) 9.31361 + 16.1316i 0.429605 + 0.744097i
\(471\) −26.6600 + 11.1300i −1.22843 + 0.512841i
\(472\) −1.68691 + 2.92181i −0.0776462 + 0.134487i
\(473\) 4.45328 7.71330i 0.204762 0.354658i
\(474\) 1.42594 0.595297i 0.0654955 0.0273429i
\(475\) 12.1249 + 21.0010i 0.556330 + 0.963591i
\(476\) 0 0
\(477\) 7.83799 + 28.6138i 0.358877 + 1.31014i
\(478\) −10.9209 −0.499513
\(479\) 8.88370 + 15.3870i 0.405907 + 0.703051i 0.994427 0.105432i \(-0.0336224\pi\)
−0.588520 + 0.808483i \(0.700289\pi\)
\(480\) −4.08988 + 31.7482i −0.186677 + 1.44910i
\(481\) 2.83103 4.90349i 0.129084 0.223580i
\(482\) 4.14548 7.18018i 0.188821 0.327048i
\(483\) 0 0
\(484\) −8.94890 15.4999i −0.406768 0.704543i
\(485\) 40.7816 1.85180
\(486\) 3.05716 + 7.09957i 0.138675 + 0.322043i
\(487\) −16.6553 −0.754722 −0.377361 0.926066i \(-0.623168\pi\)
−0.377361 + 0.926066i \(0.623168\pi\)
\(488\) −10.0562 17.4178i −0.455222 0.788467i
\(489\) −9.20245 7.02068i −0.416149 0.317486i
\(490\) 0 0
\(491\) −3.21021 + 5.56025i −0.144875 + 0.250930i −0.929326 0.369260i \(-0.879611\pi\)
0.784451 + 0.620190i \(0.212945\pi\)
\(492\) 1.85623 14.4092i 0.0836854 0.649619i
\(493\) 0.517784 + 0.896827i 0.0233198 + 0.0403911i
\(494\) −1.66646 −0.0749776
\(495\) 2.61223 + 9.53633i 0.117411 + 0.428626i
\(496\) 9.26814 0.416152
\(497\) 0 0
\(498\) 9.76698 4.07750i 0.437669 0.182717i
\(499\) −5.57296 + 9.65264i −0.249480 + 0.432112i −0.963382 0.268134i \(-0.913593\pi\)
0.713902 + 0.700246i \(0.246926\pi\)
\(500\) −11.7728 + 20.3911i −0.526495 + 0.911916i
\(501\) −28.1806 + 11.7648i −1.25901 + 0.525611i
\(502\) −2.11512 3.66350i −0.0944026 0.163510i
\(503\) −17.7223 −0.790200 −0.395100 0.918638i \(-0.629290\pi\)
−0.395100 + 0.918638i \(0.629290\pi\)
\(504\) 0 0
\(505\) 9.59939 0.427167
\(506\) −0.548314 0.949708i −0.0243755 0.0422197i
\(507\) 2.55995 19.8719i 0.113691 0.882544i
\(508\) −1.11339 + 1.92845i −0.0493988 + 0.0855612i
\(509\) −15.5411 + 26.9180i −0.688848 + 1.19312i 0.283362 + 0.959013i \(0.408550\pi\)
−0.972211 + 0.234107i \(0.924783\pi\)
\(510\) −0.630316 0.480878i −0.0279109 0.0212936i
\(511\) 0 0
\(512\) −22.5634 −0.997169
\(513\) −5.47145 + 13.5276i −0.241571 + 0.597258i
\(514\) 8.48913 0.374439
\(515\) 17.9303 + 31.0563i 0.790105 + 1.36850i
\(516\) 24.1034 + 18.3888i 1.06109 + 0.809524i
\(517\) −4.54008 + 7.86365i −0.199672 + 0.345843i
\(518\) 0 0
\(519\) 0.860152 6.67704i 0.0377565 0.293089i
\(520\) −4.11304 7.12399i −0.180369 0.312408i
\(521\) 4.75971 0.208527 0.104263 0.994550i \(-0.466751\pi\)
0.104263 + 0.994550i \(0.466751\pi\)
\(522\) −5.96128 1.56181i −0.260918 0.0683586i
\(523\) −40.2515 −1.76008 −0.880038 0.474904i \(-0.842483\pi\)
−0.880038 + 0.474904i \(0.842483\pi\)
\(524\) −13.1812 22.8305i −0.575823 0.997355i
\(525\) 0 0
\(526\) 5.09571 8.82602i 0.222183 0.384833i
\(527\) −0.448113 + 0.776154i −0.0195201 + 0.0338098i
\(528\) −3.68808 + 1.53969i −0.160503 + 0.0670064i
\(529\) 8.43046 + 14.6020i 0.366542 + 0.634869i
\(530\) 18.1076 0.786545
\(531\) −5.25960 1.37798i −0.228247 0.0597991i
\(532\) 0 0
\(533\) 2.86125 + 4.95583i 0.123935 + 0.214661i
\(534\) 0.264176 2.05070i 0.0114320 0.0887426i
\(535\) 20.1255 34.8584i 0.870101 1.50706i
\(536\) −0.958109 + 1.65949i −0.0413840 + 0.0716792i
\(537\) 10.1009 + 7.70616i 0.435888 + 0.332545i
\(538\) −4.92033 8.52227i −0.212131 0.367421i
\(539\) 0 0
\(540\) −33.3308 + 4.67150i −1.43433 + 0.201029i
\(541\) −24.1094 −1.03655 −0.518273 0.855215i \(-0.673425\pi\)
−0.518273 + 0.855215i \(0.673425\pi\)
\(542\) −2.63830 4.56966i −0.113325 0.196284i
\(543\) −15.5009 11.8259i −0.665208 0.507497i
\(544\) 0.625580 1.08354i 0.0268215 0.0464563i
\(545\) 3.91769 6.78564i 0.167815 0.290665i
\(546\) 0 0
\(547\) −6.17751 10.6998i −0.264131 0.457489i 0.703204 0.710988i \(-0.251752\pi\)
−0.967336 + 0.253499i \(0.918419\pi\)
\(548\) 0.856872 0.0366038
\(549\) 22.7911 23.0462i 0.972699 0.983587i
\(550\) 3.82188 0.162966
\(551\) −5.81671 10.0748i −0.247800 0.429203i
\(552\) 7.37223 3.07774i 0.313783 0.130997i
\(553\) 0 0
\(554\) −6.16893 + 10.6849i −0.262093 + 0.453958i
\(555\) −27.9247 + 11.6579i −1.18534 + 0.494852i
\(556\) 8.65633 + 14.9932i 0.367110 + 0.635853i
\(557\) −8.07689 −0.342229 −0.171114 0.985251i \(-0.554737\pi\)
−0.171114 + 0.985251i \(0.554737\pi\)
\(558\) −1.40901 5.14379i −0.0596480 0.217754i
\(559\) −11.9415 −0.505070
\(560\) 0 0
\(561\) 0.0493776 0.383300i 0.00208472 0.0161829i
\(562\) 3.39041 5.87237i 0.143016 0.247711i
\(563\) −22.6064 + 39.1554i −0.952744 + 1.65020i −0.213296 + 0.976988i \(0.568420\pi\)
−0.739448 + 0.673214i \(0.764913\pi\)
\(564\) −24.5732 18.7473i −1.03472 0.789402i
\(565\) −29.2200 50.6106i −1.22930 2.12920i
\(566\) −3.13477 −0.131764
\(567\) 0 0
\(568\) −9.20596 −0.386274
\(569\) −11.2149 19.4248i −0.470155 0.814332i 0.529263 0.848458i \(-0.322468\pi\)
−0.999418 + 0.0341263i \(0.989135\pi\)
\(570\) 7.08089 + 5.40211i 0.296586 + 0.226270i
\(571\) 10.9134 18.9026i 0.456713 0.791050i −0.542072 0.840332i \(-0.682360\pi\)
0.998785 + 0.0492820i \(0.0156933\pi\)
\(572\) 0.936826 1.62263i 0.0391706 0.0678455i
\(573\) 5.27706 40.9638i 0.220452 1.71129i
\(574\) 0 0
\(575\) 21.3954 0.892251
\(576\) −2.13082 7.77888i −0.0887842 0.324120i
\(577\) 32.2044 1.34068 0.670342 0.742052i \(-0.266147\pi\)
0.670342 + 0.742052i \(0.266147\pi\)
\(578\) −4.19939 7.27355i −0.174671 0.302540i
\(579\) 9.48553 3.96000i 0.394205 0.164572i
\(580\) 13.4161 23.2373i 0.557072 0.964878i
\(581\) 0 0
\(582\) 8.75335 3.65433i 0.362838 0.151477i
\(583\) 4.41343 + 7.64429i 0.182786 + 0.316594i
\(584\) 3.40761 0.141008
\(585\) 9.32169 9.42604i 0.385404 0.389719i
\(586\) −1.30421 −0.0538765
\(587\) −9.72304 16.8408i −0.401313 0.695094i 0.592572 0.805518i \(-0.298113\pi\)
−0.993885 + 0.110424i \(0.964779\pi\)
\(588\) 0 0
\(589\) 5.03404 8.71921i 0.207424 0.359269i
\(590\) −1.65926 + 2.87392i −0.0683105 + 0.118317i
\(591\) 21.3006 + 16.2505i 0.876190 + 0.668458i
\(592\) −6.11563 10.5926i −0.251351 0.435352i
\(593\) 28.8405 1.18434 0.592168 0.805815i \(-0.298272\pi\)
0.592168 + 0.805815i \(0.298272\pi\)
\(594\) 1.41521 + 1.81280i 0.0580669 + 0.0743801i
\(595\) 0 0
\(596\) 18.4392 + 31.9377i 0.755300 + 1.30822i
\(597\) 21.3394 + 16.2801i 0.873363 + 0.666301i
\(598\) −0.735152 + 1.27332i −0.0300626 + 0.0520699i
\(599\) 23.4994 40.7022i 0.960161 1.66305i 0.238072 0.971247i \(-0.423484\pi\)
0.722089 0.691800i \(-0.243182\pi\)
\(600\) −3.55730 + 27.6140i −0.145226 + 1.12734i
\(601\) −7.80843 13.5246i −0.318512 0.551680i 0.661665 0.749799i \(-0.269850\pi\)
−0.980178 + 0.198119i \(0.936517\pi\)
\(602\) 0 0
\(603\) −2.98729 0.782646i −0.121652 0.0318718i
\(604\) −2.62833 −0.106945
\(605\) −18.8383 32.6289i −0.765885 1.32655i
\(606\) 2.06041 0.860175i 0.0836984 0.0349422i
\(607\) 14.3266 24.8144i 0.581500 1.00719i −0.413802 0.910367i \(-0.635800\pi\)
0.995302 0.0968200i \(-0.0308671\pi\)
\(608\) −7.02769 + 12.1723i −0.285010 + 0.493652i
\(609\) 0 0
\(610\) −9.89134 17.1323i −0.400489 0.693667i
\(611\) 12.1742 0.492516
\(612\) 1.27255 + 0.333398i 0.0514397 + 0.0134768i
\(613\) −29.3468 −1.18531 −0.592653 0.805458i \(-0.701920\pi\)
−0.592653 + 0.805458i \(0.701920\pi\)
\(614\) −0.692965 1.20025i −0.0279658 0.0484382i
\(615\) 3.90755 30.3328i 0.157568 1.22314i
\(616\) 0 0
\(617\) 2.06401 3.57497i 0.0830938 0.143923i −0.821484 0.570232i \(-0.806853\pi\)
0.904577 + 0.426310i \(0.140187\pi\)
\(618\) 6.63143 + 5.05921i 0.266755 + 0.203511i
\(619\) −11.3565 19.6700i −0.456456 0.790605i 0.542315 0.840175i \(-0.317548\pi\)
−0.998771 + 0.0495708i \(0.984215\pi\)
\(620\) 23.2217 0.932608
\(621\) 7.92256 + 10.1483i 0.317921 + 0.407238i
\(622\) 7.48774 0.300231
\(623\) 0 0
\(624\) 4.26017 + 3.25014i 0.170543 + 0.130110i
\(625\) −3.19498 + 5.53387i −0.127799 + 0.221355i
\(626\) −6.31698 + 10.9413i −0.252477 + 0.437304i
\(627\) −0.554701 + 4.30594i −0.0221526 + 0.171963i
\(628\) −14.6290 25.3382i −0.583761 1.01110i
\(629\) 1.18276 0.0471597
\(630\) 0 0
\(631\) −38.6411 −1.53828 −0.769138 0.639082i \(-0.779314\pi\)
−0.769138 + 0.639082i \(0.779314\pi\)
\(632\) 1.67458 + 2.90045i 0.0666110 + 0.115374i
\(633\) −2.46754 + 1.03014i −0.0980757 + 0.0409444i
\(634\) 8.06304 13.9656i 0.320224 0.554645i
\(635\) −2.34380 + 4.05958i −0.0930107 + 0.161099i
\(636\) −27.7266 + 11.5752i −1.09943 + 0.458988i
\(637\) 0 0
\(638\) −1.83348 −0.0725881
\(639\) −3.91954 14.3089i −0.155055 0.566050i
\(640\) −41.8853 −1.65566
\(641\) 14.2363 + 24.6580i 0.562301 + 0.973933i 0.997295 + 0.0735002i \(0.0234169\pi\)
−0.434995 + 0.900433i \(0.643250\pi\)
\(642\) 1.19616 9.28538i 0.0472088 0.366465i
\(643\) −8.52125 + 14.7592i −0.336045 + 0.582048i −0.983685 0.179899i \(-0.942423\pi\)
0.647640 + 0.761947i \(0.275756\pi\)
\(644\) 0 0
\(645\) 50.7400 + 38.7103i 1.99788 + 1.52422i
\(646\) −0.174055 0.301472i −0.00684810 0.0118613i
\(647\) −3.37618 −0.132731 −0.0663657 0.997795i \(-0.521140\pi\)
−0.0663657 + 0.997795i \(0.521140\pi\)
\(648\) −14.4152 + 8.53795i −0.566281 + 0.335402i
\(649\) −1.61767 −0.0634989
\(650\) −2.56209 4.43768i −0.100494 0.174060i
\(651\) 0 0
\(652\) 5.86110 10.1517i 0.229538 0.397572i
\(653\) 9.17255 15.8873i 0.358950 0.621719i −0.628836 0.777538i \(-0.716468\pi\)
0.987786 + 0.155819i \(0.0498017\pi\)
\(654\) 0.232849 1.80752i 0.00910512 0.0706797i
\(655\) −27.7477 48.0604i −1.08419 1.87787i
\(656\) 12.3618 0.482648
\(657\) 1.45083 + 5.29646i 0.0566021 + 0.206635i
\(658\) 0 0
\(659\) −13.9248 24.1184i −0.542432 0.939519i −0.998764 0.0497098i \(-0.984170\pi\)
0.456332 0.889810i \(-0.349163\pi\)
\(660\) −9.24065 + 3.85777i −0.359692 + 0.150163i
\(661\) −19.5071 + 33.7872i −0.758737 + 1.31417i 0.184758 + 0.982784i \(0.440850\pi\)
−0.943495 + 0.331387i \(0.892484\pi\)
\(662\) 4.48633 7.77054i 0.174366 0.302011i
\(663\) −0.478160 + 0.199621i −0.0185702 + 0.00775264i
\(664\) 11.4700 + 19.8667i 0.445123 + 0.770976i
\(665\) 0 0
\(666\) −4.94911 + 5.00452i −0.191774 + 0.193921i
\(667\) −10.2641 −0.397426
\(668\) −15.4634 26.7834i −0.598296 1.03628i
\(669\) −1.20462 + 9.35100i −0.0465732 + 0.361531i
\(670\) −0.942405 + 1.63229i −0.0364083 + 0.0630610i
\(671\) 4.82170 8.35143i 0.186140 0.322404i
\(672\) 0 0
\(673\) 24.6154 + 42.6352i 0.948856 + 1.64347i 0.747841 + 0.663878i \(0.231090\pi\)
0.201014 + 0.979588i \(0.435576\pi\)
\(674\) −12.4053 −0.477833
\(675\) −44.4352 + 6.22784i −1.71031 + 0.239710i
\(676\) 20.2914 0.780438
\(677\) 11.6958 + 20.2577i 0.449505 + 0.778565i 0.998354 0.0573564i \(-0.0182671\pi\)
−0.548849 + 0.835922i \(0.684934\pi\)
\(678\) −10.8069 8.24471i −0.415035 0.316636i
\(679\) 0 0
\(680\) 0.859180 1.48814i 0.0329480 0.0570677i
\(681\) 3.55767 27.6169i 0.136330 1.05828i
\(682\) −0.793387 1.37419i −0.0303803 0.0526203i
\(683\) 30.3264 1.16041 0.580204 0.814471i \(-0.302973\pi\)
0.580204 + 0.814471i \(0.302973\pi\)
\(684\) −14.2956 3.74535i −0.546607 0.143207i
\(685\) 1.80380 0.0689196
\(686\) 0 0
\(687\) −15.9330 + 6.65169i −0.607884 + 0.253778i
\(688\) −12.8980 + 22.3401i −0.491733 + 0.851707i
\(689\) 5.91731 10.2491i 0.225432 0.390459i
\(690\) 7.25139 3.02729i 0.276056 0.115247i
\(691\) 2.05665 + 3.56223i 0.0782387 + 0.135513i 0.902490 0.430711i \(-0.141737\pi\)
−0.824251 + 0.566224i \(0.808404\pi\)
\(692\) 6.81797 0.259180
\(693\) 0 0
\(694\) −5.33003 −0.202325
\(695\) 18.2224 + 31.5621i 0.691215 + 1.19722i
\(696\) 1.70655 13.2473i 0.0646867 0.502139i
\(697\) −0.597691 + 1.03523i −0.0226392 + 0.0392122i
\(698\) 0.814716 1.41113i 0.0308375 0.0534120i
\(699\) 22.7778 + 17.3775i 0.861534 + 0.657277i
\(700\) 0 0
\(701\) 29.1835 1.10225 0.551123 0.834424i \(-0.314200\pi\)
0.551123 + 0.834424i \(0.314200\pi\)
\(702\) 1.15616 2.85849i 0.0436365 0.107887i
\(703\) −13.2869 −0.501127
\(704\) −1.19983 2.07816i −0.0452202 0.0783236i
\(705\) −51.7289 39.4648i −1.94822 1.48633i
\(706\) 4.17005 7.22274i 0.156942 0.271831i
\(707\) 0 0
\(708\) 0.703531 5.46125i 0.0264403 0.205246i
\(709\) 21.2309 + 36.7729i 0.797342 + 1.38104i 0.921341 + 0.388755i \(0.127095\pi\)
−0.123999 + 0.992282i \(0.539572\pi\)
\(710\) −9.05507 −0.339831
\(711\) −3.79522 + 3.83770i −0.142332 + 0.143925i
\(712\) 4.48150 0.167951
\(713\) −4.44149 7.69288i −0.166335 0.288101i
\(714\) 0 0
\(715\) 1.97211 3.41579i 0.0737526 0.127743i
\(716\) −6.43336 + 11.1429i −0.240426 + 0.416430i
\(717\) 35.2020 14.6961i 1.31464 0.548834i
\(718\) −5.89692 10.2138i −0.220071 0.381175i
\(719\) 11.1425 0.415546 0.207773 0.978177i \(-0.433379\pi\)
0.207773 + 0.978177i \(0.433379\pi\)
\(720\) −7.56580 27.6201i −0.281961 1.02934i
\(721\) 0 0
\(722\) −2.75544 4.77256i −0.102547 0.177616i
\(723\) −3.70012 + 28.7227i −0.137609 + 1.06821i
\(724\) 9.87264 17.0999i 0.366914 0.635513i
\(725\) 17.8858 30.9790i 0.664260 1.15053i
\(726\) −6.96723 5.31540i −0.258578 0.197273i
\(727\) −14.3410 24.8393i −0.531878 0.921239i −0.999308 0.0372089i \(-0.988153\pi\)
0.467430 0.884030i \(-0.345180\pi\)
\(728\) 0 0
\(729\) −19.4080 18.7704i −0.718815 0.695202i
\(730\) 3.35175 0.124054
\(731\) −1.24724 2.16028i −0.0461307 0.0799007i
\(732\) 26.0975 + 19.9102i 0.964591 + 0.735901i
\(733\) 12.5264 21.6964i 0.462674 0.801375i −0.536419 0.843952i \(-0.680223\pi\)
0.999093 + 0.0425768i \(0.0135567\pi\)
\(734\) −0.171071 + 0.296303i −0.00631433 + 0.0109367i
\(735\) 0 0
\(736\) 6.20047 + 10.7395i 0.228552 + 0.395864i
\(737\) −0.918782 −0.0338438
\(738\) −1.87933 6.86077i −0.0691790 0.252549i
\(739\) −27.5216 −1.01240 −0.506198 0.862417i \(-0.668950\pi\)
−0.506198 + 0.862417i \(0.668950\pi\)
\(740\) −15.3230 26.5402i −0.563284 0.975637i
\(741\) 5.37158 2.24252i 0.197330 0.0823809i
\(742\) 0 0
\(743\) −7.00608 + 12.1349i −0.257028 + 0.445186i −0.965444 0.260609i \(-0.916077\pi\)
0.708416 + 0.705795i \(0.249410\pi\)
\(744\) 10.6673 4.45336i 0.391082 0.163268i
\(745\) 38.8163 + 67.2318i 1.42212 + 2.46318i
\(746\) 1.86452 0.0682650
\(747\) −25.9954 + 26.2864i −0.951121 + 0.961768i
\(748\) 0.391390 0.0143106
\(749\) 0 0
\(750\) −1.47297 + 11.4342i −0.0537854 + 0.417516i
\(751\) 26.1297 45.2580i 0.953486 1.65149i 0.215692 0.976461i \(-0.430799\pi\)
0.737795 0.675025i \(-0.235867\pi\)
\(752\) 13.1494 22.7755i 0.479511 0.830537i
\(753\) 11.7477 + 8.96246i 0.428109 + 0.326610i
\(754\) 1.22912 + 2.12889i 0.0447618 + 0.0775298i
\(755\) −5.53289 −0.201363
\(756\) 0 0
\(757\) −43.3447 −1.57539 −0.787694 0.616066i \(-0.788725\pi\)
−0.787694 + 0.616066i \(0.788725\pi\)
\(758\) 8.15047 + 14.1170i 0.296038 + 0.512753i
\(759\) 3.04540 + 2.32338i 0.110541 + 0.0843335i
\(760\) −9.65191 + 16.7176i −0.350112 + 0.606411i
\(761\) 8.62550 14.9398i 0.312674 0.541568i −0.666266 0.745714i \(-0.732109\pi\)
0.978940 + 0.204146i \(0.0654419\pi\)
\(762\) −0.139304 + 1.08137i −0.00504646 + 0.0391738i
\(763\) 0 0
\(764\) 41.8285 1.51330
\(765\) 2.67883 + 0.701834i 0.0968534 + 0.0253749i
\(766\) 0.531903 0.0192184
\(767\) 1.08444 + 1.87831i 0.0391570 + 0.0678218i
\(768\) −0.395948 + 0.165299i −0.0142875 + 0.00596472i
\(769\) −10.6727 + 18.4856i −0.384867 + 0.666609i −0.991751 0.128182i \(-0.959086\pi\)
0.606884 + 0.794790i \(0.292419\pi\)
\(770\) 0 0
\(771\) −27.3634 + 11.4236i −0.985469 + 0.411411i
\(772\) 5.20495 + 9.01523i 0.187330 + 0.324465i
\(773\) 13.1471 0.472870 0.236435 0.971647i \(-0.424021\pi\)
0.236435 + 0.971647i \(0.424021\pi\)
\(774\) 14.3595 + 3.76209i 0.516143 + 0.135225i
\(775\) 30.9583 1.11205
\(776\) 10.2796 + 17.8049i 0.369018 + 0.639158i
\(777\) 0 0
\(778\) −5.88685 + 10.1963i −0.211054 + 0.365556i
\(779\) 6.71439 11.6297i 0.240568 0.416676i
\(780\) 10.6740 + 8.14339i 0.382192 + 0.291580i
\(781\) −2.20702 3.82268i −0.0789735 0.136786i
\(782\) −0.307134 −0.0109831
\(783\) 21.3170 2.98769i 0.761807 0.106771i
\(784\) 0 0
\(785\) −30.7954 53.3393i −1.09914 1.90376i
\(786\) −10.2623 7.82927i −0.366045 0.279261i
\(787\) 14.0650 24.3614i 0.501364 0.868389i −0.498634 0.866812i \(-0.666165\pi\)
0.999999 0.00157623i \(-0.000501728\pi\)
\(788\) −13.5665 + 23.4979i −0.483287 + 0.837077i
\(789\) −4.54827 + 35.3065i −0.161923 + 1.25694i
\(790\) 1.64713 + 2.85291i 0.0586021 + 0.101502i
\(791\) 0 0
\(792\) −3.50502 + 3.54426i −0.124546 + 0.125940i
\(793\) −12.9294 −0.459136
\(794\) 0.00795814 + 0.0137839i 0.000282424 + 0.000489172i
\(795\) −58.3671 + 24.3670i −2.07007 + 0.864208i
\(796\) −13.5912 + 23.5406i −0.481727 + 0.834376i
\(797\) 12.8683 22.2885i 0.455817 0.789499i −0.542917 0.839786i \(-0.682680\pi\)
0.998735 + 0.0502873i \(0.0160137\pi\)
\(798\) 0 0
\(799\) 1.27155 + 2.20238i 0.0449841 + 0.0779147i
\(800\) −43.2188 −1.52801
\(801\) 1.90805 + 6.96562i 0.0674176 + 0.246118i
\(802\) −12.1615 −0.429436
\(803\) 0.816934 + 1.41497i 0.0288290 + 0.0499333i
\(804\) 0.399583 3.10181i 0.0140922 0.109393i
\(805\) 0 0
\(806\) −1.06373 + 1.84244i −0.0374684 + 0.0648972i
\(807\) 27.3282 + 20.8491i 0.961997 + 0.733922i
\(808\) 2.41968 + 4.19100i 0.0851240 + 0.147439i
\(809\) −31.8705 −1.12051 −0.560254 0.828321i \(-0.689296\pi\)
−0.560254 + 0.828321i \(0.689296\pi\)
\(810\) −14.1789 + 8.39800i −0.498195 + 0.295076i
\(811\) 43.3860 1.52349 0.761744 0.647878i \(-0.224343\pi\)
0.761744 + 0.647878i \(0.224343\pi\)
\(812\) 0 0
\(813\) 14.6534 + 11.1793i 0.513918 + 0.392076i
\(814\) −1.04704 + 1.81353i −0.0366987 + 0.0635641i
\(815\) 12.3382 21.3704i 0.432188 0.748571i
\(816\) −0.143012 + 1.11015i −0.00500643 + 0.0388631i
\(817\) 14.0113 + 24.2682i 0.490193 + 0.849039i
\(818\) −13.2842 −0.464470
\(819\) 0 0
\(820\) 30.9731 1.08163
\(821\) 8.19677 + 14.1972i 0.286069 + 0.495487i 0.972868 0.231361i \(-0.0743179\pi\)
−0.686799 + 0.726848i \(0.740985\pi\)
\(822\) 0.387166 0.161633i 0.0135040 0.00563761i
\(823\) 13.1890 22.8440i 0.459739 0.796292i −0.539208 0.842173i \(-0.681276\pi\)
0.998947 + 0.0458812i \(0.0146096\pi\)
\(824\) −9.03925 + 15.6564i −0.314897 + 0.545418i
\(825\) −12.3193 + 5.14301i −0.428901 + 0.179057i
\(826\) 0 0
\(827\) 36.7225 1.27697 0.638484 0.769635i \(-0.279562\pi\)
0.638484 + 0.769635i \(0.279562\pi\)
\(828\) −9.16822 + 9.27085i −0.318618 + 0.322184i
\(829\) −24.3158 −0.844522 −0.422261 0.906474i \(-0.638763\pi\)
−0.422261 + 0.906474i \(0.638763\pi\)
\(830\) 11.2820 + 19.5410i 0.391604 + 0.678279i
\(831\) 5.50619 42.7425i 0.191008 1.48272i
\(832\) −1.60867 + 2.78629i −0.0557705 + 0.0965974i
\(833\) 0 0
\(834\) 6.73944 + 5.14162i 0.233368 + 0.178040i
\(835\) −32.5519 56.3815i −1.12650 1.95116i
\(836\) −4.39682 −0.152067
\(837\) 11.4636 + 14.6842i 0.396240 + 0.507559i
\(838\) −10.4392 −0.360618
\(839\) −12.8405 22.2404i −0.443303 0.767824i 0.554629 0.832098i \(-0.312860\pi\)
−0.997932 + 0.0642741i \(0.979527\pi\)
\(840\) 0 0
\(841\) 5.91963 10.2531i 0.204125 0.353555i
\(842\) 3.69190 6.39456i 0.127231 0.220371i
\(843\) −3.02618 + 23.4911i −0.104227 + 0.809076i
\(844\) −1.35400 2.34519i −0.0466065 0.0807249i
\(845\) 42.7153 1.46945
\(846\) −14.6394 3.83542i −0.503313 0.131864i
\(847\) 0 0
\(848\) −12.7826 22.1402i −0.438958 0.760297i
\(849\) 10.1045 4.21839i 0.346784 0.144775i
\(850\) 0.535200 0.926994i 0.0183572 0.0317956i
\(851\) −5.86148 + 10.1524i −0.200929 + 0.348019i
\(852\) 13.8652 5.78842i 0.475015 0.198308i
\(853\) 14.4872 + 25.0925i 0.496031 + 0.859150i 0.999990 0.00457743i \(-0.00145705\pi\)
−0.503959 + 0.863728i \(0.668124\pi\)
\(854\) 0 0
\(855\) −30.0937 7.88431i −1.02918 0.269638i
\(856\) 20.2918 0.693559
\(857\) 12.6934 + 21.9856i 0.433598 + 0.751015i 0.997180 0.0750458i \(-0.0239103\pi\)
−0.563582 + 0.826060i \(0.690577\pi\)
\(858\) 0.117213 0.909879i 0.00400158 0.0310628i
\(859\) 2.97891 5.15963i 0.101639 0.176044i −0.810721 0.585433i \(-0.800925\pi\)
0.912360 + 0.409388i \(0.134258\pi\)
\(860\) −32.3166 + 55.9740i −1.10199 + 1.90870i
\(861\) 0 0
\(862\) 3.94310 + 6.82966i 0.134303 + 0.232619i
\(863\) −16.3909 −0.557953 −0.278977 0.960298i \(-0.589995\pi\)
−0.278977 + 0.960298i \(0.589995\pi\)
\(864\) −16.0036 20.4996i −0.544452 0.697410i
\(865\) 14.3525 0.487999
\(866\) −4.05764 7.02804i −0.137884 0.238822i
\(867\) 23.3239 + 17.7942i 0.792122 + 0.604322i
\(868\) 0 0
\(869\) −0.802920 + 1.39070i −0.0272372 + 0.0471762i
\(870\) 1.67858 13.0302i 0.0569092 0.441765i
\(871\) 0.615929 + 1.06682i 0.0208700 + 0.0361478i
\(872\) 3.95006 0.133766
\(873\) −23.2975 + 23.5583i −0.788502 + 0.797329i
\(874\) 3.45030 0.116708
\(875\) 0 0
\(876\) −5.13224 + 2.14260i −0.173402 + 0.0723916i
\(877\) −17.6270 + 30.5308i −0.595220 + 1.03095i 0.398295 + 0.917257i \(0.369602\pi\)
−0.993516 + 0.113695i \(0.963731\pi\)
\(878\) −3.85407 + 6.67544i −0.130068 + 0.225285i
\(879\) 4.20392 1.75504i 0.141795 0.0591962i
\(880\) −4.26017 7.37883i −0.143610 0.248740i
\(881\) 26.2582 0.884661 0.442331 0.896852i \(-0.354152\pi\)
0.442331 + 0.896852i \(0.354152\pi\)
\(882\) 0 0
\(883\) 10.0087 0.336821 0.168410 0.985717i \(-0.446137\pi\)
0.168410 + 0.985717i \(0.446137\pi\)
\(884\) −0.262378 0.454452i −0.00882473 0.0152849i
\(885\) 1.48100 11.4965i 0.0497833 0.386449i
\(886\) 0.443815 0.768711i 0.0149103 0.0258253i
\(887\) 7.95282 13.7747i 0.267030 0.462509i −0.701064 0.713099i \(-0.747291\pi\)
0.968093 + 0.250590i \(0.0806245\pi\)
\(888\) −12.1286 9.25311i −0.407010 0.310514i
\(889\) 0 0
\(890\) 4.40804 0.147758
\(891\) −7.00116 3.93887i −0.234548 0.131957i
\(892\) −9.54838 −0.319703
\(893\) −14.2844 24.7413i −0.478009 0.827935i
\(894\) 14.3560 + 10.9524i 0.480136 + 0.366303i
\(895\) −13.5428 + 23.4569i −0.452687 + 0.784077i
\(896\) 0 0
\(897\) 0.656173 5.09363i 0.0219090 0.170071i
\(898\) 3.36364 + 5.82599i 0.112246 + 0.194416i
\(899\) −14.8517 −0.495331
\(900\) −12.0051 43.8266i −0.400171 1.46089i
\(901\) 2.47215 0.0823594
\(902\) −1.05822 1.83288i −0.0352348 0.0610284i
\(903\) 0 0
\(904\) 14.7307 25.5144i 0.489937 0.848597i
\(905\) 20.7829 35.9970i 0.690846 1.19658i
\(906\) −1.18758 + 0.495787i −0.0394546 + 0.0164714i
\(907\) 8.54624 + 14.8025i 0.283773 + 0.491510i 0.972311 0.233691i \(-0.0750804\pi\)
−0.688538 + 0.725201i \(0.741747\pi\)
\(908\) 28.1998 0.935843
\(909\) −5.48390 + 5.54528i −0.181889 + 0.183925i
\(910\) 0 0
\(911\) 14.9435 + 25.8829i 0.495099 + 0.857537i 0.999984 0.00564955i \(-0.00179832\pi\)
−0.504885 + 0.863187i \(0.668465\pi\)
\(912\) 1.60658 12.4713i 0.0531992 0.412966i
\(913\) −5.49961 + 9.52561i −0.182011 + 0.315252i
\(914\) 0.636986 1.10329i 0.0210696 0.0364937i
\(915\) 54.9377 + 41.9128i 1.81619 + 1.38560i
\(916\) −8.74286 15.1431i −0.288872 0.500341i
\(917\) 0 0
\(918\) 0.637873 0.0894015i 0.0210530 0.00295069i
\(919\) −23.6567 −0.780362 −0.390181 0.920738i \(-0.627588\pi\)
−0.390181 + 0.920738i \(0.627588\pi\)
\(920\) 8.51579 + 14.7498i 0.280757 + 0.486286i
\(921\) 3.84882 + 2.93632i 0.126823 + 0.0967550i
\(922\) −8.97196 + 15.5399i −0.295476 + 0.511779i
\(923\) −2.95907 + 5.12525i −0.0973989 + 0.168700i
\(924\) 0 0
\(925\) −20.4280 35.3823i −0.671667 1.16336i
\(926\) 8.12454 0.266989
\(927\) −28.1834 7.38385i −0.925666 0.242518i
\(928\) 20.7334 0.680607
\(929\) −6.30880 10.9272i −0.206985 0.358509i 0.743778 0.668426i \(-0.233032\pi\)
−0.950763 + 0.309918i \(0.899698\pi\)
\(930\) 10.4924 4.38036i 0.344061 0.143638i
\(931\) 0 0
\(932\) −14.5073 + 25.1274i −0.475203 + 0.823075i
\(933\) −24.1356 + 10.0761i −0.790164 + 0.329876i
\(934\) 2.15714 + 3.73627i 0.0705836 + 0.122254i
\(935\) 0.823914 0.0269449
\(936\) 6.46500 + 1.69378i 0.211315 + 0.0553630i
\(937\) −26.3440 −0.860622 −0.430311 0.902681i \(-0.641596\pi\)
−0.430311 + 0.902681i \(0.641596\pi\)
\(938\) 0 0
\(939\) 5.63834 43.7683i 0.184000 1.42833i
\(940\) 32.9465 57.0651i 1.07460 1.86126i
\(941\) −25.4699 + 44.1151i −0.830294 + 1.43811i 0.0675118 + 0.997718i \(0.478494\pi\)
−0.897805 + 0.440392i \(0.854839\pi\)
\(942\) −11.3895 8.68923i −0.371090 0.283110i
\(943\) −5.92404 10.2607i −0.192913 0.334136i
\(944\) 4.68525 0.152492
\(945\) 0 0
\(946\) 4.41648 0.143592
\(947\) −13.8399 23.9714i −0.449737 0.778967i 0.548632 0.836064i \(-0.315149\pi\)
−0.998369 + 0.0570968i \(0.981816\pi\)
\(948\) −4.34581 3.31548i −0.141145 0.107682i
\(949\) 1.09530 1.89712i 0.0355551 0.0615832i
\(950\) −6.01236 + 10.4137i −0.195067 + 0.337866i
\(951\) −7.19682 + 55.8662i −0.233373 + 1.81159i
\(952\) 0 0
\(953\) −27.4017 −0.887628 −0.443814 0.896119i \(-0.646375\pi\)
−0.443814 + 0.896119i \(0.646375\pi\)
\(954\) −10.3444 + 10.4602i −0.334914 + 0.338663i
\(955\) 88.0530 2.84933
\(956\) 19.3162 + 33.4567i 0.624731 + 1.08207i
\(957\) 5.90994 2.46727i 0.191041 0.0797554i
\(958\) −4.40515 + 7.62994i −0.142324 + 0.246512i
\(959\) 0 0
\(960\) 15.8676 6.62436i 0.512123 0.213800i
\(961\) 9.07336 + 15.7155i 0.292689 + 0.506952i
\(962\) 2.80764 0.0905219
\(963\) 8.63946 + 31.5396i 0.278403 + 1.01635i
\(964\) −29.3289 −0.944621
\(965\) 10.9569 + 18.9779i 0.352715 + 0.610921i
\(966\) 0 0
\(967\) 9.09069 15.7455i 0.292337 0.506342i −0.682025 0.731329i \(-0.738900\pi\)
0.974362 + 0.224986i \(0.0722338\pi\)
\(968\) 9.49698 16.4492i 0.305244 0.528699i
\(969\) 0.966723 + 0.737527i 0.0310556 + 0.0236928i
\(970\) 10.1111 + 17.5130i 0.324649 + 0.562309i
\(971\) −39.4832 −1.26708 −0.633538 0.773712i \(-0.718398\pi\)
−0.633538 + 0.773712i \(0.718398\pi\)
\(972\) 16.3425 21.9229i 0.524185 0.703178i
\(973\) 0 0
\(974\) −4.12941 7.15234i −0.132315 0.229176i
\(975\) 14.2302 + 10.8564i 0.455731 + 0.347684i
\(976\) −13.9651 + 24.1883i −0.447012 + 0.774248i
\(977\) −5.95782 + 10.3193i −0.190608 + 0.330142i −0.945452 0.325762i \(-0.894379\pi\)
0.754844 + 0.655904i \(0.227712\pi\)
\(978\) 0.733323 5.69252i 0.0234491 0.182027i
\(979\) 1.07439 + 1.86090i 0.0343376 + 0.0594745i
\(980\) 0 0
\(981\) 1.68178 + 6.13961i 0.0536952 + 0.196023i
\(982\) −3.18368 −0.101595
\(983\) 9.23896 + 16.0024i 0.294677 + 0.510396i 0.974910 0.222601i \(-0.0714546\pi\)
−0.680233 + 0.732996i \(0.738121\pi\)
\(984\) 14.2280 5.93987i 0.453572 0.189356i
\(985\) −28.5588 + 49.4653i −0.909959 + 1.57609i
\(986\) −0.256752 + 0.444708i −0.00817666 + 0.0141624i
\(987\) 0 0
\(988\) 2.94752 + 5.10525i 0.0937731 + 0.162420i
\(989\) 24.7241 0.786179
\(990\) −3.44757 + 3.48616i −0.109571 + 0.110798i
\(991\) 12.6970 0.403334 0.201667 0.979454i \(-0.435364\pi\)
0.201667 + 0.979454i \(0.435364\pi\)
\(992\) 8.97181 + 15.5396i 0.284855 + 0.493384i
\(993\) −4.00435 + 31.0843i −0.127074 + 0.986430i
\(994\) 0 0
\(995\) −28.6108 + 49.5553i −0.907023 + 1.57101i
\(996\) −29.7667 22.7094i −0.943194 0.719576i
\(997\) −20.9767 36.3327i −0.664338 1.15067i −0.979464 0.201617i \(-0.935380\pi\)
0.315127 0.949050i \(-0.397953\pi\)
\(998\) −5.52690 −0.174951
\(999\) 9.21826 22.7912i 0.291653 0.721081i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 441.2.f.e.148.3 10
3.2 odd 2 1323.2.f.e.442.3 10
7.2 even 3 63.2.g.b.4.3 10
7.3 odd 6 441.2.h.f.373.3 10
7.4 even 3 63.2.h.b.58.3 yes 10
7.5 odd 6 441.2.g.f.67.3 10
7.6 odd 2 441.2.f.f.148.3 10
9.2 odd 6 1323.2.f.e.883.3 10
9.4 even 3 3969.2.a.z.1.3 5
9.5 odd 6 3969.2.a.bc.1.3 5
9.7 even 3 inner 441.2.f.e.295.3 10
21.2 odd 6 189.2.g.b.172.3 10
21.5 even 6 1323.2.g.f.361.3 10
21.11 odd 6 189.2.h.b.37.3 10
21.17 even 6 1323.2.h.f.226.3 10
21.20 even 2 1323.2.f.f.442.3 10
28.11 odd 6 1008.2.q.i.625.3 10
28.23 odd 6 1008.2.t.i.193.1 10
63.2 odd 6 189.2.h.b.46.3 10
63.4 even 3 567.2.e.f.163.3 10
63.11 odd 6 189.2.g.b.100.3 10
63.13 odd 6 3969.2.a.ba.1.3 5
63.16 even 3 63.2.h.b.25.3 yes 10
63.20 even 6 1323.2.f.f.883.3 10
63.23 odd 6 567.2.e.e.487.3 10
63.25 even 3 63.2.g.b.16.3 yes 10
63.32 odd 6 567.2.e.e.163.3 10
63.34 odd 6 441.2.f.f.295.3 10
63.38 even 6 1323.2.g.f.667.3 10
63.41 even 6 3969.2.a.bb.1.3 5
63.47 even 6 1323.2.h.f.802.3 10
63.52 odd 6 441.2.g.f.79.3 10
63.58 even 3 567.2.e.f.487.3 10
63.61 odd 6 441.2.h.f.214.3 10
84.11 even 6 3024.2.q.i.2305.1 10
84.23 even 6 3024.2.t.i.1873.5 10
252.11 even 6 3024.2.t.i.289.5 10
252.79 odd 6 1008.2.q.i.529.3 10
252.151 odd 6 1008.2.t.i.961.1 10
252.191 even 6 3024.2.q.i.2881.1 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.g.b.4.3 10 7.2 even 3
63.2.g.b.16.3 yes 10 63.25 even 3
63.2.h.b.25.3 yes 10 63.16 even 3
63.2.h.b.58.3 yes 10 7.4 even 3
189.2.g.b.100.3 10 63.11 odd 6
189.2.g.b.172.3 10 21.2 odd 6
189.2.h.b.37.3 10 21.11 odd 6
189.2.h.b.46.3 10 63.2 odd 6
441.2.f.e.148.3 10 1.1 even 1 trivial
441.2.f.e.295.3 10 9.7 even 3 inner
441.2.f.f.148.3 10 7.6 odd 2
441.2.f.f.295.3 10 63.34 odd 6
441.2.g.f.67.3 10 7.5 odd 6
441.2.g.f.79.3 10 63.52 odd 6
441.2.h.f.214.3 10 63.61 odd 6
441.2.h.f.373.3 10 7.3 odd 6
567.2.e.e.163.3 10 63.32 odd 6
567.2.e.e.487.3 10 63.23 odd 6
567.2.e.f.163.3 10 63.4 even 3
567.2.e.f.487.3 10 63.58 even 3
1008.2.q.i.529.3 10 252.79 odd 6
1008.2.q.i.625.3 10 28.11 odd 6
1008.2.t.i.193.1 10 28.23 odd 6
1008.2.t.i.961.1 10 252.151 odd 6
1323.2.f.e.442.3 10 3.2 odd 2
1323.2.f.e.883.3 10 9.2 odd 6
1323.2.f.f.442.3 10 21.20 even 2
1323.2.f.f.883.3 10 63.20 even 6
1323.2.g.f.361.3 10 21.5 even 6
1323.2.g.f.667.3 10 63.38 even 6
1323.2.h.f.226.3 10 21.17 even 6
1323.2.h.f.802.3 10 63.47 even 6
3024.2.q.i.2305.1 10 84.11 even 6
3024.2.q.i.2881.1 10 252.191 even 6
3024.2.t.i.289.5 10 252.11 even 6
3024.2.t.i.1873.5 10 84.23 even 6
3969.2.a.z.1.3 5 9.4 even 3
3969.2.a.ba.1.3 5 63.13 odd 6
3969.2.a.bb.1.3 5 63.41 even 6
3969.2.a.bc.1.3 5 9.5 odd 6