Properties

Label 429.2.s.b.166.9
Level $429$
Weight $2$
Character 429.166
Analytic conductor $3.426$
Analytic rank $0$
Dimension $28$
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] = [429,2,Mod(166,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.166");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.s (of order \(6\), 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: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 166.9
Character \(\chi\) \(=\) 429.166
Dual form 429.2.s.b.199.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.813989 - 0.469957i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.558281 + 0.966972i) q^{4} -0.163878i q^{5} +(-0.813989 - 0.469957i) q^{6} +(2.40248 + 1.38708i) q^{7} +2.92930i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.813989 - 0.469957i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.558281 + 0.966972i) q^{4} -0.163878i q^{5} +(-0.813989 - 0.469957i) q^{6} +(2.40248 + 1.38708i) q^{7} +2.92930i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.0770155 - 0.133395i) q^{10} +(0.866025 - 0.500000i) q^{11} +1.11656 q^{12} +(3.59344 - 0.295291i) q^{13} +2.60746 q^{14} +(-0.141922 + 0.0819389i) q^{15} +(0.260081 + 0.450474i) q^{16} +(-1.03931 + 1.80013i) q^{17} +0.939913i q^{18} +(2.48517 + 1.43482i) q^{19} +(0.158465 + 0.0914899i) q^{20} -2.77415i q^{21} +(0.469957 - 0.813989i) q^{22} +(0.745923 + 1.29198i) q^{23} +(2.53685 - 1.46465i) q^{24} +4.97314 q^{25} +(2.78625 - 1.92912i) q^{26} +1.00000 q^{27} +(-2.68252 + 1.54876i) q^{28} +(-0.213005 - 0.368936i) q^{29} +(-0.0770155 + 0.133395i) q^{30} -6.48317i q^{31} +(-4.65029 - 2.68485i) q^{32} +(-0.866025 - 0.500000i) q^{33} +1.95372i q^{34} +(0.227311 - 0.393714i) q^{35} +(-0.558281 - 0.966972i) q^{36} +(2.52192 - 1.45603i) q^{37} +2.69721 q^{38} +(-2.05245 - 2.96436i) q^{39} +0.480047 q^{40} +(-3.97665 + 2.29592i) q^{41} +(-1.30373 - 2.25813i) q^{42} +(-3.72486 + 6.45165i) q^{43} +1.11656i q^{44} +(0.141922 + 0.0819389i) q^{45} +(1.21435 + 0.701103i) q^{46} -2.71471i q^{47} +(0.260081 - 0.450474i) q^{48} +(0.347955 + 0.602676i) q^{49} +(4.04808 - 2.33716i) q^{50} +2.07861 q^{51} +(-1.72061 + 3.63961i) q^{52} -5.71174 q^{53} +(0.813989 - 0.469957i) q^{54} +(-0.0819389 - 0.141922i) q^{55} +(-4.06316 + 7.03760i) q^{56} -2.86963i q^{57} +(-0.346767 - 0.200206i) q^{58} +(2.07066 + 1.19550i) q^{59} -0.182980i q^{60} +(-2.65604 + 4.60039i) q^{61} +(-3.04681 - 5.27723i) q^{62} +(-2.40248 + 1.38708i) q^{63} -6.08737 q^{64} +(-0.0483916 - 0.588885i) q^{65} -0.939913 q^{66} +(-8.10306 + 4.67830i) q^{67} +(-1.16045 - 2.00996i) q^{68} +(0.745923 - 1.29198i) q^{69} -0.427305i q^{70} +(-11.3570 - 6.55696i) q^{71} +(-2.53685 - 1.46465i) q^{72} -2.42783i q^{73} +(1.36854 - 2.37039i) q^{74} +(-2.48657 - 4.30687i) q^{75} +(-2.77485 + 1.60206i) q^{76} +2.77415 q^{77} +(-3.06379 - 1.44840i) q^{78} +7.41437 q^{79} +(0.0738227 - 0.0426216i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.15797 + 3.73771i) q^{82} -7.48093i q^{83} +(2.68252 + 1.54876i) q^{84} +(0.295002 + 0.170319i) q^{85} +7.00209i q^{86} +(-0.213005 + 0.368936i) q^{87} +(1.46465 + 2.53685i) q^{88} +(7.56642 - 4.36847i) q^{89} +0.154031 q^{90} +(9.04277 + 4.27494i) q^{91} -1.66574 q^{92} +(-5.61459 + 3.24158i) q^{93} +(-1.27579 - 2.20974i) q^{94} +(0.235135 - 0.407265i) q^{95} +5.36969i q^{96} +(8.31993 + 4.80351i) q^{97} +(0.566463 + 0.327048i) q^{98} +1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 14 q^{3} + 18 q^{4} - 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 14 q^{3} + 18 q^{4} - 14 q^{9} - 36 q^{12} - 6 q^{13} - 4 q^{14} + 6 q^{15} - 22 q^{16} + 2 q^{17} + 12 q^{19} + 18 q^{20} - 6 q^{22} + 2 q^{23} - 40 q^{25} - 18 q^{26} + 28 q^{27} - 18 q^{28} - 30 q^{32} + 2 q^{35} + 18 q^{36} + 20 q^{38} + 6 q^{39} + 20 q^{40} + 18 q^{41} + 2 q^{42} - 2 q^{43} - 6 q^{45} + 48 q^{46} - 22 q^{48} + 10 q^{49} + 24 q^{50} - 4 q^{51} - 28 q^{52} + 16 q^{53} - 12 q^{55} - 10 q^{56} - 48 q^{58} - 12 q^{59} - 4 q^{61} - 6 q^{62} - 32 q^{64} + 6 q^{65} + 12 q^{66} + 12 q^{67} - 22 q^{68} + 2 q^{69} - 18 q^{71} + 48 q^{74} + 20 q^{75} + 96 q^{76} - 24 q^{77} + 6 q^{78} - 48 q^{79} + 66 q^{80} - 14 q^{81} + 46 q^{82} + 18 q^{84} - 66 q^{85} + 12 q^{88} + 8 q^{91} + 72 q^{92} + 6 q^{93} + 50 q^{94} - 60 q^{95} - 36 q^{97} + 18 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.813989 0.469957i 0.575577 0.332310i −0.183797 0.982964i \(-0.558839\pi\)
0.759374 + 0.650655i \(0.225505\pi\)
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) −0.558281 + 0.966972i −0.279141 + 0.483486i
\(5\) 0.163878i 0.0732884i −0.999328 0.0366442i \(-0.988333\pi\)
0.999328 0.0366442i \(-0.0116668\pi\)
\(6\) −0.813989 0.469957i −0.332310 0.191859i
\(7\) 2.40248 + 1.38708i 0.908054 + 0.524265i 0.879804 0.475336i \(-0.157673\pi\)
0.0282494 + 0.999601i \(0.491007\pi\)
\(8\) 2.92930i 1.03566i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −0.0770155 0.133395i −0.0243544 0.0421831i
\(11\) 0.866025 0.500000i 0.261116 0.150756i
\(12\) 1.11656 0.322324
\(13\) 3.59344 0.295291i 0.996641 0.0818989i
\(14\) 2.60746 0.696873
\(15\) −0.141922 + 0.0819389i −0.0366442 + 0.0211565i
\(16\) 0.260081 + 0.450474i 0.0650203 + 0.112619i
\(17\) −1.03931 + 1.80013i −0.252069 + 0.436596i −0.964095 0.265556i \(-0.914444\pi\)
0.712026 + 0.702153i \(0.247778\pi\)
\(18\) 0.939913i 0.221540i
\(19\) 2.48517 + 1.43482i 0.570138 + 0.329169i 0.757205 0.653178i \(-0.226565\pi\)
−0.187066 + 0.982347i \(0.559898\pi\)
\(20\) 0.158465 + 0.0914899i 0.0354339 + 0.0204578i
\(21\) 2.77415i 0.605369i
\(22\) 0.469957 0.813989i 0.100195 0.173543i
\(23\) 0.745923 + 1.29198i 0.155536 + 0.269396i 0.933254 0.359217i \(-0.116956\pi\)
−0.777718 + 0.628613i \(0.783623\pi\)
\(24\) 2.53685 1.46465i 0.517832 0.298970i
\(25\) 4.97314 0.994629
\(26\) 2.78625 1.92912i 0.546428 0.378332i
\(27\) 1.00000 0.192450
\(28\) −2.68252 + 1.54876i −0.506949 + 0.292687i
\(29\) −0.213005 0.368936i −0.0395540 0.0685096i 0.845571 0.533864i \(-0.179260\pi\)
−0.885125 + 0.465354i \(0.845927\pi\)
\(30\) −0.0770155 + 0.133395i −0.0140610 + 0.0243544i
\(31\) 6.48317i 1.16441i −0.813042 0.582205i \(-0.802190\pi\)
0.813042 0.582205i \(-0.197810\pi\)
\(32\) −4.65029 2.68485i −0.822063 0.474618i
\(33\) −0.866025 0.500000i −0.150756 0.0870388i
\(34\) 1.95372i 0.335060i
\(35\) 0.227311 0.393714i 0.0384226 0.0665498i
\(36\) −0.558281 0.966972i −0.0930469 0.161162i
\(37\) 2.52192 1.45603i 0.414601 0.239370i −0.278164 0.960534i \(-0.589726\pi\)
0.692765 + 0.721164i \(0.256392\pi\)
\(38\) 2.69721 0.437545
\(39\) −2.05245 2.96436i −0.328655 0.474678i
\(40\) 0.480047 0.0759021
\(41\) −3.97665 + 2.29592i −0.621049 + 0.358563i −0.777277 0.629158i \(-0.783400\pi\)
0.156228 + 0.987721i \(0.450066\pi\)
\(42\) −1.30373 2.25813i −0.201170 0.348437i
\(43\) −3.72486 + 6.45165i −0.568036 + 0.983867i 0.428724 + 0.903435i \(0.358963\pi\)
−0.996760 + 0.0804316i \(0.974370\pi\)
\(44\) 1.11656i 0.168328i
\(45\) 0.141922 + 0.0819389i 0.0211565 + 0.0122147i
\(46\) 1.21435 + 0.701103i 0.179045 + 0.103372i
\(47\) 2.71471i 0.395981i −0.980204 0.197990i \(-0.936559\pi\)
0.980204 0.197990i \(-0.0634414\pi\)
\(48\) 0.260081 0.450474i 0.0375395 0.0650203i
\(49\) 0.347955 + 0.602676i 0.0497079 + 0.0860966i
\(50\) 4.04808 2.33716i 0.572486 0.330525i
\(51\) 2.07861 0.291064
\(52\) −1.72061 + 3.63961i −0.238606 + 0.504723i
\(53\) −5.71174 −0.784568 −0.392284 0.919844i \(-0.628315\pi\)
−0.392284 + 0.919844i \(0.628315\pi\)
\(54\) 0.813989 0.469957i 0.110770 0.0639530i
\(55\) −0.0819389 0.141922i −0.0110486 0.0191368i
\(56\) −4.06316 + 7.03760i −0.542962 + 0.940438i
\(57\) 2.86963i 0.380092i
\(58\) −0.346767 0.200206i −0.0455328 0.0262884i
\(59\) 2.07066 + 1.19550i 0.269578 + 0.155641i 0.628696 0.777651i \(-0.283589\pi\)
−0.359118 + 0.933292i \(0.616922\pi\)
\(60\) 0.182980i 0.0236226i
\(61\) −2.65604 + 4.60039i −0.340071 + 0.589020i −0.984446 0.175690i \(-0.943784\pi\)
0.644375 + 0.764710i \(0.277118\pi\)
\(62\) −3.04681 5.27723i −0.386945 0.670208i
\(63\) −2.40248 + 1.38708i −0.302685 + 0.174755i
\(64\) −6.08737 −0.760921
\(65\) −0.0483916 0.588885i −0.00600224 0.0730422i
\(66\) −0.939913 −0.115695
\(67\) −8.10306 + 4.67830i −0.989946 + 0.571545i −0.905258 0.424862i \(-0.860323\pi\)
−0.0846877 + 0.996408i \(0.526989\pi\)
\(68\) −1.16045 2.00996i −0.140725 0.243744i
\(69\) 0.745923 1.29198i 0.0897985 0.155536i
\(70\) 0.427305i 0.0510727i
\(71\) −11.3570 6.55696i −1.34783 0.778167i −0.359884 0.932997i \(-0.617184\pi\)
−0.987941 + 0.154830i \(0.950517\pi\)
\(72\) −2.53685 1.46465i −0.298970 0.172611i
\(73\) 2.42783i 0.284156i −0.989855 0.142078i \(-0.954622\pi\)
0.989855 0.142078i \(-0.0453783\pi\)
\(74\) 1.36854 2.37039i 0.159090 0.275552i
\(75\) −2.48657 4.30687i −0.287125 0.497314i
\(76\) −2.77485 + 1.60206i −0.318298 + 0.183769i
\(77\) 2.77415 0.316144
\(78\) −3.06379 1.44840i −0.346906 0.163999i
\(79\) 7.41437 0.834182 0.417091 0.908865i \(-0.363050\pi\)
0.417091 + 0.908865i \(0.363050\pi\)
\(80\) 0.0738227 0.0426216i 0.00825363 0.00476524i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −2.15797 + 3.73771i −0.238308 + 0.412761i
\(83\) 7.48093i 0.821139i −0.911829 0.410570i \(-0.865330\pi\)
0.911829 0.410570i \(-0.134670\pi\)
\(84\) 2.68252 + 1.54876i 0.292687 + 0.168983i
\(85\) 0.295002 + 0.170319i 0.0319974 + 0.0184737i
\(86\) 7.00209i 0.755055i
\(87\) −0.213005 + 0.368936i −0.0228365 + 0.0395540i
\(88\) 1.46465 + 2.53685i 0.156132 + 0.270429i
\(89\) 7.56642 4.36847i 0.802039 0.463057i −0.0421447 0.999112i \(-0.513419\pi\)
0.844184 + 0.536054i \(0.180086\pi\)
\(90\) 0.154031 0.0162363
\(91\) 9.04277 + 4.27494i 0.947940 + 0.448135i
\(92\) −1.66574 −0.173665
\(93\) −5.61459 + 3.24158i −0.582205 + 0.336136i
\(94\) −1.27579 2.20974i −0.131588 0.227917i
\(95\) 0.235135 0.407265i 0.0241243 0.0417845i
\(96\) 5.36969i 0.548042i
\(97\) 8.31993 + 4.80351i 0.844761 + 0.487723i 0.858880 0.512178i \(-0.171161\pi\)
−0.0141189 + 0.999900i \(0.504494\pi\)
\(98\) 0.566463 + 0.327048i 0.0572214 + 0.0330368i
\(99\) 1.00000i 0.100504i
\(100\) −2.77641 + 4.80889i −0.277641 + 0.480889i
\(101\) −2.94671 5.10385i −0.293208 0.507852i 0.681358 0.731950i \(-0.261390\pi\)
−0.974567 + 0.224098i \(0.928056\pi\)
\(102\) 1.69197 0.976859i 0.167530 0.0967234i
\(103\) −5.05671 −0.498253 −0.249126 0.968471i \(-0.580143\pi\)
−0.249126 + 0.968471i \(0.580143\pi\)
\(104\) 0.864994 + 10.5263i 0.0848197 + 1.03218i
\(105\) −0.454622 −0.0443665
\(106\) −4.64930 + 2.68427i −0.451580 + 0.260720i
\(107\) −4.19490 7.26577i −0.405536 0.702409i 0.588848 0.808244i \(-0.299582\pi\)
−0.994384 + 0.105835i \(0.966248\pi\)
\(108\) −0.558281 + 0.966972i −0.0537206 + 0.0930469i
\(109\) 11.4104i 1.09292i 0.837484 + 0.546461i \(0.184025\pi\)
−0.837484 + 0.546461i \(0.815975\pi\)
\(110\) −0.133395 0.0770155i −0.0127187 0.00734314i
\(111\) −2.52192 1.45603i −0.239370 0.138200i
\(112\) 1.44301i 0.136352i
\(113\) 4.67346 8.09467i 0.439642 0.761483i −0.558019 0.829828i \(-0.688439\pi\)
0.997662 + 0.0683451i \(0.0217719\pi\)
\(114\) −1.34860 2.33585i −0.126308 0.218772i
\(115\) 0.211726 0.122240i 0.0197436 0.0113990i
\(116\) 0.475667 0.0441646
\(117\) −1.54099 + 3.25965i −0.142465 + 0.301355i
\(118\) 2.24733 0.206884
\(119\) −4.99384 + 2.88319i −0.457784 + 0.264302i
\(120\) −0.240024 0.415733i −0.0219111 0.0379511i
\(121\) 0.500000 0.866025i 0.0454545 0.0787296i
\(122\) 4.99289i 0.452035i
\(123\) 3.97665 + 2.29592i 0.358563 + 0.207016i
\(124\) 6.26904 + 3.61943i 0.562976 + 0.325034i
\(125\) 1.63438i 0.146183i
\(126\) −1.30373 + 2.25813i −0.116146 + 0.201170i
\(127\) −7.19603 12.4639i −0.638545 1.10599i −0.985752 0.168204i \(-0.946203\pi\)
0.347208 0.937788i \(-0.387130\pi\)
\(128\) 4.34552 2.50889i 0.384094 0.221757i
\(129\) 7.44972 0.655911
\(130\) −0.316141 0.456604i −0.0277274 0.0400468i
\(131\) −8.12560 −0.709937 −0.354969 0.934878i \(-0.615508\pi\)
−0.354969 + 0.934878i \(0.615508\pi\)
\(132\) 0.966972 0.558281i 0.0841641 0.0485922i
\(133\) 3.98040 + 6.89425i 0.345144 + 0.597807i
\(134\) −4.39720 + 7.61617i −0.379860 + 0.657937i
\(135\) 0.163878i 0.0141044i
\(136\) −5.27313 3.04444i −0.452167 0.261059i
\(137\) −15.7332 9.08356i −1.34418 0.776061i −0.356760 0.934196i \(-0.616118\pi\)
−0.987417 + 0.158135i \(0.949452\pi\)
\(138\) 1.40221i 0.119364i
\(139\) 5.46987 9.47409i 0.463948 0.803582i −0.535205 0.844722i \(-0.679766\pi\)
0.999153 + 0.0411403i \(0.0130991\pi\)
\(140\) 0.253807 + 0.439606i 0.0214506 + 0.0371535i
\(141\) −2.35100 + 1.35735i −0.197990 + 0.114310i
\(142\) −12.3259 −1.03437
\(143\) 2.96436 2.05245i 0.247893 0.171634i
\(144\) −0.520163 −0.0433469
\(145\) −0.0604604 + 0.0349068i −0.00502096 + 0.00289885i
\(146\) −1.14097 1.97622i −0.0944276 0.163553i
\(147\) 0.347955 0.602676i 0.0286989 0.0497079i
\(148\) 3.25150i 0.267272i
\(149\) 13.8777 + 8.01230i 1.13691 + 0.656394i 0.945663 0.325149i \(-0.105414\pi\)
0.191244 + 0.981542i \(0.438748\pi\)
\(150\) −4.04808 2.33716i −0.330525 0.190829i
\(151\) 16.5728i 1.34868i −0.738422 0.674339i \(-0.764428\pi\)
0.738422 0.674339i \(-0.235572\pi\)
\(152\) −4.20301 + 7.27982i −0.340909 + 0.590471i
\(153\) −1.03931 1.80013i −0.0840230 0.145532i
\(154\) 2.25813 1.30373i 0.181965 0.105058i
\(155\) −1.06245 −0.0853378
\(156\) 4.01230 0.329710i 0.321241 0.0263980i
\(157\) 21.1013 1.68407 0.842035 0.539423i \(-0.181358\pi\)
0.842035 + 0.539423i \(0.181358\pi\)
\(158\) 6.03521 3.48443i 0.480136 0.277207i
\(159\) 2.85587 + 4.94652i 0.226485 + 0.392284i
\(160\) −0.439987 + 0.762079i −0.0347840 + 0.0602477i
\(161\) 4.13860i 0.326168i
\(162\) −0.813989 0.469957i −0.0639530 0.0369233i
\(163\) −10.1609 5.86639i −0.795863 0.459491i 0.0461598 0.998934i \(-0.485302\pi\)
−0.842022 + 0.539443i \(0.818635\pi\)
\(164\) 5.12708i 0.400358i
\(165\) −0.0819389 + 0.141922i −0.00637894 + 0.0110486i
\(166\) −3.51572 6.08940i −0.272872 0.472629i
\(167\) 18.4503 10.6523i 1.42772 0.824297i 0.430783 0.902456i \(-0.358237\pi\)
0.996941 + 0.0781589i \(0.0249042\pi\)
\(168\) 8.12632 0.626959
\(169\) 12.8256 2.12222i 0.986585 0.163247i
\(170\) 0.320171 0.0245560
\(171\) −2.48517 + 1.43482i −0.190046 + 0.109723i
\(172\) −4.15904 7.20367i −0.317124 0.549275i
\(173\) −1.17798 + 2.04032i −0.0895600 + 0.155122i −0.907325 0.420429i \(-0.861879\pi\)
0.817765 + 0.575552i \(0.195213\pi\)
\(174\) 0.400413i 0.0303552i
\(175\) 11.9479 + 6.89812i 0.903177 + 0.521449i
\(176\) 0.450474 + 0.260081i 0.0339558 + 0.0196044i
\(177\) 2.39100i 0.179718i
\(178\) 4.10599 7.11178i 0.307757 0.533050i
\(179\) −7.96439 13.7947i −0.595286 1.03107i −0.993506 0.113776i \(-0.963705\pi\)
0.398220 0.917290i \(-0.369628\pi\)
\(180\) −0.158465 + 0.0914899i −0.0118113 + 0.00681926i
\(181\) −19.0296 −1.41446 −0.707230 0.706984i \(-0.750055\pi\)
−0.707230 + 0.706984i \(0.750055\pi\)
\(182\) 9.36975 0.769959i 0.694532 0.0570731i
\(183\) 5.31207 0.392680
\(184\) −3.78458 + 2.18503i −0.279003 + 0.161083i
\(185\) −0.238611 0.413287i −0.0175431 0.0303855i
\(186\) −3.04681 + 5.27723i −0.223403 + 0.386945i
\(187\) 2.07861i 0.152003i
\(188\) 2.62504 + 1.51557i 0.191451 + 0.110534i
\(189\) 2.40248 + 1.38708i 0.174755 + 0.100895i
\(190\) 0.442012i 0.0320670i
\(191\) −4.53853 + 7.86097i −0.328397 + 0.568800i −0.982194 0.187870i \(-0.939842\pi\)
0.653797 + 0.756670i \(0.273175\pi\)
\(192\) 3.04369 + 5.27182i 0.219659 + 0.380461i
\(193\) 0.989480 0.571277i 0.0712243 0.0411214i −0.463965 0.885854i \(-0.653574\pi\)
0.535189 + 0.844732i \(0.320240\pi\)
\(194\) 9.02977 0.648300
\(195\) −0.485794 + 0.336351i −0.0347884 + 0.0240866i
\(196\) −0.777027 −0.0555020
\(197\) −15.0212 + 8.67251i −1.07022 + 0.617891i −0.928241 0.371979i \(-0.878679\pi\)
−0.141977 + 0.989870i \(0.545346\pi\)
\(198\) 0.469957 + 0.813989i 0.0333984 + 0.0578477i
\(199\) −0.475891 + 0.824267i −0.0337350 + 0.0584307i −0.882400 0.470500i \(-0.844074\pi\)
0.848665 + 0.528931i \(0.177407\pi\)
\(200\) 14.5678i 1.03010i
\(201\) 8.10306 + 4.67830i 0.571545 + 0.329982i
\(202\) −4.79717 2.76965i −0.337528 0.194872i
\(203\) 1.18182i 0.0829472i
\(204\) −1.16045 + 2.00996i −0.0812478 + 0.140725i
\(205\) 0.376251 + 0.651685i 0.0262785 + 0.0455157i
\(206\) −4.11611 + 2.37644i −0.286783 + 0.165574i
\(207\) −1.49185 −0.103690
\(208\) 1.06761 + 1.54195i 0.0740252 + 0.106915i
\(209\) 2.86963 0.198497
\(210\) −0.370057 + 0.213653i −0.0255364 + 0.0147434i
\(211\) −4.98172 8.62859i −0.342956 0.594017i 0.642025 0.766684i \(-0.278095\pi\)
−0.984980 + 0.172667i \(0.944761\pi\)
\(212\) 3.18876 5.52309i 0.219005 0.379328i
\(213\) 13.1139i 0.898550i
\(214\) −6.82920 3.94284i −0.466834 0.269527i
\(215\) 1.05728 + 0.610422i 0.0721060 + 0.0416304i
\(216\) 2.92930i 0.199314i
\(217\) 8.99264 15.5757i 0.610460 1.05735i
\(218\) 5.36241 + 9.28797i 0.363189 + 0.629061i
\(219\) −2.10256 + 1.21391i −0.142078 + 0.0820286i
\(220\) 0.182980 0.0123365
\(221\) −3.20312 + 6.77556i −0.215465 + 0.455774i
\(222\) −2.73709 −0.183701
\(223\) −10.1997 + 5.88882i −0.683025 + 0.394345i −0.800994 0.598673i \(-0.795695\pi\)
0.117969 + 0.993017i \(0.462362\pi\)
\(224\) −7.44816 12.9006i −0.497651 0.861958i
\(225\) −2.48657 + 4.30687i −0.165771 + 0.287125i
\(226\) 8.78530i 0.584389i
\(227\) 11.7824 + 6.80259i 0.782028 + 0.451504i 0.837149 0.546976i \(-0.184221\pi\)
−0.0551205 + 0.998480i \(0.517554\pi\)
\(228\) 2.77485 + 1.60206i 0.183769 + 0.106099i
\(229\) 19.3966i 1.28176i 0.767641 + 0.640881i \(0.221431\pi\)
−0.767641 + 0.640881i \(0.778569\pi\)
\(230\) 0.114895 0.199004i 0.00757597 0.0131220i
\(231\) −1.38708 2.40248i −0.0912628 0.158072i
\(232\) 1.08072 0.623955i 0.0709529 0.0409647i
\(233\) 28.5050 1.86742 0.933712 0.358026i \(-0.116550\pi\)
0.933712 + 0.358026i \(0.116550\pi\)
\(234\) 0.277548 + 3.37752i 0.0181439 + 0.220796i
\(235\) −0.444880 −0.0290208
\(236\) −2.31203 + 1.33485i −0.150500 + 0.0868913i
\(237\) −3.70718 6.42103i −0.240807 0.417091i
\(238\) −2.70995 + 4.69378i −0.175660 + 0.304252i
\(239\) 2.55682i 0.165387i 0.996575 + 0.0826936i \(0.0263523\pi\)
−0.996575 + 0.0826936i \(0.973648\pi\)
\(240\) −0.0738227 0.0426216i −0.00476524 0.00275121i
\(241\) 6.57793 + 3.79777i 0.423722 + 0.244636i 0.696668 0.717393i \(-0.254665\pi\)
−0.272947 + 0.962029i \(0.587998\pi\)
\(242\) 0.939913i 0.0604199i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −2.96563 5.13662i −0.189855 0.328839i
\(245\) 0.0987652 0.0570221i 0.00630988 0.00364301i
\(246\) 4.31593 0.275174
\(247\) 9.35401 + 4.42208i 0.595182 + 0.281370i
\(248\) 18.9911 1.20594
\(249\) −6.47868 + 3.74047i −0.410570 + 0.237042i
\(250\) −0.768087 1.33037i −0.0485781 0.0841397i
\(251\) −1.62987 + 2.82301i −0.102876 + 0.178187i −0.912869 0.408254i \(-0.866138\pi\)
0.809992 + 0.586441i \(0.199471\pi\)
\(252\) 3.09751i 0.195125i
\(253\) 1.29198 + 0.745923i 0.0812258 + 0.0468957i
\(254\) −11.7150 6.76365i −0.735063 0.424389i
\(255\) 0.340639i 0.0213316i
\(256\) 8.44551 14.6281i 0.527844 0.914253i
\(257\) 11.0734 + 19.1798i 0.690742 + 1.19640i 0.971595 + 0.236650i \(0.0760495\pi\)
−0.280853 + 0.959751i \(0.590617\pi\)
\(258\) 6.06399 3.50105i 0.377528 0.217966i
\(259\) 8.07850 0.501974
\(260\) 0.596451 + 0.281970i 0.0369903 + 0.0174871i
\(261\) 0.426010 0.0263694
\(262\) −6.61415 + 3.81868i −0.408624 + 0.235919i
\(263\) −12.5479 21.7336i −0.773738 1.34015i −0.935501 0.353324i \(-0.885051\pi\)
0.161763 0.986830i \(-0.448282\pi\)
\(264\) 1.46465 2.53685i 0.0901430 0.156132i
\(265\) 0.936028i 0.0574998i
\(266\) 6.48000 + 3.74123i 0.397314 + 0.229389i
\(267\) −7.56642 4.36847i −0.463057 0.267346i
\(268\) 10.4472i 0.638166i
\(269\) −3.12969 + 5.42078i −0.190820 + 0.330511i −0.945522 0.325557i \(-0.894448\pi\)
0.754702 + 0.656068i \(0.227781\pi\)
\(270\) −0.0770155 0.133395i −0.00468701 0.00811815i
\(271\) −7.51874 + 4.34095i −0.456731 + 0.263694i −0.710669 0.703527i \(-0.751608\pi\)
0.253938 + 0.967221i \(0.418274\pi\)
\(272\) −1.08122 −0.0655584
\(273\) −0.819180 9.96874i −0.0495791 0.603336i
\(274\) −17.0755 −1.03157
\(275\) 4.30687 2.48657i 0.259714 0.149946i
\(276\) 0.832869 + 1.44257i 0.0501328 + 0.0868326i
\(277\) 15.0094 25.9971i 0.901829 1.56201i 0.0767120 0.997053i \(-0.475558\pi\)
0.825117 0.564961i \(-0.191109\pi\)
\(278\) 10.2824i 0.616698i
\(279\) 5.61459 + 3.24158i 0.336136 + 0.194068i
\(280\) 1.15331 + 0.665862i 0.0689232 + 0.0397928i
\(281\) 26.5273i 1.58248i 0.611503 + 0.791242i \(0.290565\pi\)
−0.611503 + 0.791242i \(0.709435\pi\)
\(282\) −1.27579 + 2.20974i −0.0759724 + 0.131588i
\(283\) 0.322563 + 0.558696i 0.0191744 + 0.0332110i 0.875453 0.483303i \(-0.160563\pi\)
−0.856279 + 0.516514i \(0.827230\pi\)
\(284\) 12.6808 7.32125i 0.752466 0.434436i
\(285\) −0.470269 −0.0278563
\(286\) 1.44840 3.06379i 0.0856455 0.181166i
\(287\) −12.7385 −0.751928
\(288\) 4.65029 2.68485i 0.274021 0.158206i
\(289\) 6.33968 + 10.9807i 0.372922 + 0.645921i
\(290\) −0.0328094 + 0.0568275i −0.00192663 + 0.00333703i
\(291\) 9.60702i 0.563174i
\(292\) 2.34764 + 1.35541i 0.137385 + 0.0793194i
\(293\) 15.0751 + 8.70364i 0.880699 + 0.508472i 0.870889 0.491480i \(-0.163544\pi\)
0.00981048 + 0.999952i \(0.496877\pi\)
\(294\) 0.654095i 0.0381476i
\(295\) 0.195916 0.339336i 0.0114067 0.0197569i
\(296\) 4.26515 + 7.38746i 0.247907 + 0.429387i
\(297\) 0.866025 0.500000i 0.0502519 0.0290129i
\(298\) 15.0617 0.872504
\(299\) 3.06194 + 4.42237i 0.177076 + 0.255752i
\(300\) 5.55283 0.320593
\(301\) −17.8978 + 10.3333i −1.03161 + 0.595603i
\(302\) −7.78852 13.4901i −0.448179 0.776269i
\(303\) −2.94671 + 5.10385i −0.169284 + 0.293208i
\(304\) 1.49268i 0.0856108i
\(305\) 0.753902 + 0.435266i 0.0431683 + 0.0249232i
\(306\) −1.69197 0.976859i −0.0967234 0.0558433i
\(307\) 7.60069i 0.433794i −0.976194 0.216897i \(-0.930406\pi\)
0.976194 0.216897i \(-0.0695937\pi\)
\(308\) −1.54876 + 2.68252i −0.0882486 + 0.152851i
\(309\) 2.52836 + 4.37924i 0.143833 + 0.249126i
\(310\) −0.864820 + 0.499304i −0.0491185 + 0.0283586i
\(311\) −8.88702 −0.503937 −0.251968 0.967735i \(-0.581078\pi\)
−0.251968 + 0.967735i \(0.581078\pi\)
\(312\) 8.68351 6.01224i 0.491607 0.340376i
\(313\) 17.2887 0.977213 0.488606 0.872504i \(-0.337505\pi\)
0.488606 + 0.872504i \(0.337505\pi\)
\(314\) 17.1762 9.91671i 0.969312 0.559632i
\(315\) 0.227311 + 0.393714i 0.0128075 + 0.0221833i
\(316\) −4.13930 + 7.16948i −0.232854 + 0.403315i
\(317\) 10.7911i 0.606086i 0.952977 + 0.303043i \(0.0980026\pi\)
−0.952977 + 0.303043i \(0.901997\pi\)
\(318\) 4.64930 + 2.68427i 0.260720 + 0.150527i
\(319\) −0.368936 0.213005i −0.0206564 0.0119260i
\(320\) 0.997585i 0.0557667i
\(321\) −4.19490 + 7.26577i −0.234136 + 0.405536i
\(322\) 1.94496 + 3.36878i 0.108389 + 0.187735i
\(323\) −5.16572 + 2.98243i −0.287428 + 0.165947i
\(324\) 1.11656 0.0620313
\(325\) 17.8707 1.46852i 0.991287 0.0814590i
\(326\) −11.0278 −0.610774
\(327\) 9.88173 5.70522i 0.546461 0.315499i
\(328\) −6.72544 11.6488i −0.371350 0.643198i
\(329\) 3.76550 6.52204i 0.207599 0.359572i
\(330\) 0.154031i 0.00847913i
\(331\) −20.5365 11.8568i −1.12879 0.651706i −0.185159 0.982709i \(-0.559280\pi\)
−0.943630 + 0.331002i \(0.892613\pi\)
\(332\) 7.23385 + 4.17647i 0.397009 + 0.229213i
\(333\) 2.91206i 0.159580i
\(334\) 10.0122 17.3416i 0.547843 0.948893i
\(335\) 0.766670 + 1.32791i 0.0418877 + 0.0725515i
\(336\) 1.24968 0.721505i 0.0681758 0.0393613i
\(337\) −15.0119 −0.817753 −0.408876 0.912590i \(-0.634079\pi\)
−0.408876 + 0.912590i \(0.634079\pi\)
\(338\) 9.44255 7.75494i 0.513607 0.421813i
\(339\) −9.34692 −0.507655
\(340\) −0.329388 + 0.190172i −0.0178636 + 0.0103135i
\(341\) −3.24158 5.61459i −0.175542 0.304047i
\(342\) −1.34860 + 2.33585i −0.0729241 + 0.126308i
\(343\) 17.4885i 0.944290i
\(344\) −18.8988 10.9112i −1.01896 0.588294i
\(345\) −0.211726 0.122240i −0.0113990 0.00658119i
\(346\) 2.21440i 0.119047i
\(347\) −12.1188 + 20.9905i −0.650574 + 1.12683i 0.332410 + 0.943135i \(0.392138\pi\)
−0.982984 + 0.183692i \(0.941195\pi\)
\(348\) −0.237833 0.411940i −0.0127492 0.0220823i
\(349\) −16.8523 + 9.72970i −0.902085 + 0.520819i −0.877876 0.478888i \(-0.841040\pi\)
−0.0242087 + 0.999707i \(0.507707\pi\)
\(350\) 12.9673 0.693130
\(351\) 3.59344 0.295291i 0.191804 0.0157614i
\(352\) −5.36969 −0.286205
\(353\) −28.4220 + 16.4094i −1.51275 + 0.873386i −0.512860 + 0.858472i \(0.671414\pi\)
−0.999889 + 0.0149134i \(0.995253\pi\)
\(354\) −1.12367 1.94625i −0.0597221 0.103442i
\(355\) −1.07454 + 1.86116i −0.0570307 + 0.0987800i
\(356\) 9.75535i 0.517033i
\(357\) 4.99384 + 2.88319i 0.264302 + 0.152595i
\(358\) −12.9658 7.48584i −0.685266 0.395639i
\(359\) 26.5319i 1.40030i 0.713996 + 0.700149i \(0.246883\pi\)
−0.713996 + 0.700149i \(0.753117\pi\)
\(360\) −0.240024 + 0.415733i −0.0126504 + 0.0219111i
\(361\) −5.38260 9.32294i −0.283295 0.490681i
\(362\) −15.4899 + 8.94309i −0.814131 + 0.470039i
\(363\) −1.00000 −0.0524864
\(364\) −9.18216 + 6.35749i −0.481276 + 0.333223i
\(365\) −0.397867 −0.0208253
\(366\) 4.32397 2.49644i 0.226017 0.130491i
\(367\) 6.99940 + 12.1233i 0.365366 + 0.632832i 0.988835 0.149016i \(-0.0476107\pi\)
−0.623469 + 0.781848i \(0.714277\pi\)
\(368\) −0.388001 + 0.672038i −0.0202260 + 0.0350324i
\(369\) 4.59184i 0.239042i
\(370\) −0.388454 0.224274i −0.0201948 0.0116594i
\(371\) −13.7224 7.92262i −0.712430 0.411322i
\(372\) 7.23886i 0.375317i
\(373\) 16.6872 28.9031i 0.864030 1.49654i −0.00397769 0.999992i \(-0.501266\pi\)
0.868007 0.496551i \(-0.165401\pi\)
\(374\) 0.976859 + 1.69197i 0.0505122 + 0.0874896i
\(375\) −1.41541 + 0.817189i −0.0730916 + 0.0421994i
\(376\) 7.95219 0.410103
\(377\) −0.874364 1.26285i −0.0450320 0.0650400i
\(378\) 2.60746 0.134113
\(379\) −10.9640 + 6.33009i −0.563185 + 0.325155i −0.754423 0.656389i \(-0.772083\pi\)
0.191238 + 0.981544i \(0.438750\pi\)
\(380\) 0.262543 + 0.454737i 0.0134681 + 0.0233275i
\(381\) −7.19603 + 12.4639i −0.368664 + 0.638545i
\(382\) 8.53166i 0.436518i
\(383\) 24.9991 + 14.4332i 1.27739 + 0.737504i 0.976369 0.216112i \(-0.0693375\pi\)
0.301026 + 0.953616i \(0.402671\pi\)
\(384\) −4.34552 2.50889i −0.221757 0.128031i
\(385\) 0.454622i 0.0231697i
\(386\) 0.536951 0.930026i 0.0273301 0.0473371i
\(387\) −3.72486 6.45165i −0.189345 0.327956i
\(388\) −9.28972 + 5.36342i −0.471614 + 0.272287i
\(389\) −34.6650 −1.75759 −0.878793 0.477203i \(-0.841651\pi\)
−0.878793 + 0.477203i \(0.841651\pi\)
\(390\) −0.237360 + 0.502088i −0.0120192 + 0.0254242i
\(391\) −3.10097 −0.156823
\(392\) −1.76542 + 1.01926i −0.0891671 + 0.0514806i
\(393\) 4.06280 + 7.03698i 0.204941 + 0.354969i
\(394\) −8.15141 + 14.1187i −0.410662 + 0.711288i
\(395\) 1.21505i 0.0611358i
\(396\) −0.966972 0.558281i −0.0485922 0.0280547i
\(397\) −23.0989 13.3362i −1.15930 0.669322i −0.208164 0.978094i \(-0.566749\pi\)
−0.951136 + 0.308772i \(0.900082\pi\)
\(398\) 0.894592i 0.0448419i
\(399\) 3.98040 6.89425i 0.199269 0.345144i
\(400\) 1.29342 + 2.24027i 0.0646711 + 0.112014i
\(401\) 14.5178 8.38188i 0.724986 0.418571i −0.0915990 0.995796i \(-0.529198\pi\)
0.816585 + 0.577225i \(0.195864\pi\)
\(402\) 8.79440 0.438625
\(403\) −1.91442 23.2969i −0.0953639 1.16050i
\(404\) 6.58037 0.327386
\(405\) −0.141922 + 0.0819389i −0.00705218 + 0.00407158i
\(406\) −0.555402 0.961985i −0.0275642 0.0477425i
\(407\) 1.45603 2.52192i 0.0721728 0.125007i
\(408\) 6.08888i 0.301445i
\(409\) −20.6351 11.9137i −1.02034 0.589095i −0.106139 0.994351i \(-0.533849\pi\)
−0.914203 + 0.405256i \(0.867182\pi\)
\(410\) 0.612528 + 0.353643i 0.0302506 + 0.0174652i
\(411\) 18.1671i 0.896118i
\(412\) 2.82307 4.88970i 0.139083 0.240898i
\(413\) 3.31649 + 5.74433i 0.163194 + 0.282660i
\(414\) −1.21435 + 0.701103i −0.0596818 + 0.0344573i
\(415\) −1.22596 −0.0601800
\(416\) −17.5033 8.27464i −0.858172 0.405698i
\(417\) −10.9397 −0.535721
\(418\) 2.33585 1.34860i 0.114250 0.0659623i
\(419\) −9.06959 15.7090i −0.443078 0.767434i 0.554838 0.831959i \(-0.312780\pi\)
−0.997916 + 0.0645244i \(0.979447\pi\)
\(420\) 0.253807 0.439606i 0.0123845 0.0214506i
\(421\) 20.8542i 1.01637i 0.861247 + 0.508186i \(0.169684\pi\)
−0.861247 + 0.508186i \(0.830316\pi\)
\(422\) −8.11013 4.68238i −0.394795 0.227935i
\(423\) 2.35100 + 1.35735i 0.114310 + 0.0659968i
\(424\) 16.7314i 0.812549i
\(425\) −5.16862 + 8.95232i −0.250715 + 0.434251i
\(426\) 6.16297 + 10.6746i 0.298597 + 0.517185i
\(427\) −12.7622 + 7.36825i −0.617605 + 0.356574i
\(428\) 9.36773 0.452806
\(429\) −3.25965 1.54099i −0.157378 0.0743997i
\(430\) 1.14749 0.0553368
\(431\) 11.0792 6.39656i 0.533665 0.308112i −0.208843 0.977949i \(-0.566970\pi\)
0.742508 + 0.669838i \(0.233636\pi\)
\(432\) 0.260081 + 0.450474i 0.0125132 + 0.0216734i
\(433\) 2.25122 3.89923i 0.108187 0.187385i −0.806849 0.590758i \(-0.798829\pi\)
0.915036 + 0.403373i \(0.132162\pi\)
\(434\) 16.9046i 0.811447i
\(435\) 0.0604604 + 0.0349068i 0.00289885 + 0.00167365i
\(436\) −11.0336 6.37024i −0.528412 0.305079i
\(437\) 4.28105i 0.204790i
\(438\) −1.14097 + 1.97622i −0.0545178 + 0.0944276i
\(439\) 14.3923 + 24.9282i 0.686908 + 1.18976i 0.972833 + 0.231507i \(0.0743657\pi\)
−0.285925 + 0.958252i \(0.592301\pi\)
\(440\) 0.415733 0.240024i 0.0198193 0.0114427i
\(441\) −0.695910 −0.0331386
\(442\) 0.576914 + 7.02056i 0.0274410 + 0.333934i
\(443\) −8.71939 −0.414271 −0.207135 0.978312i \(-0.566414\pi\)
−0.207135 + 0.978312i \(0.566414\pi\)
\(444\) 2.81588 1.62575i 0.133636 0.0771547i
\(445\) −0.715896 1.23997i −0.0339367 0.0587801i
\(446\) −5.53498 + 9.58687i −0.262089 + 0.453951i
\(447\) 16.0246i 0.757938i
\(448\) −14.6248 8.44364i −0.690957 0.398924i
\(449\) 16.2711 + 9.39411i 0.767879 + 0.443335i 0.832118 0.554599i \(-0.187128\pi\)
−0.0642383 + 0.997935i \(0.520462\pi\)
\(450\) 4.67433i 0.220350i
\(451\) −2.29592 + 3.97665i −0.108111 + 0.187253i
\(452\) 5.21821 + 9.03821i 0.245444 + 0.425122i
\(453\) −14.3525 + 8.28642i −0.674339 + 0.389330i
\(454\) 12.7877 0.600157
\(455\) 0.700568 1.48191i 0.0328431 0.0694730i
\(456\) 8.40601 0.393648
\(457\) −11.1189 + 6.41951i −0.520121 + 0.300292i −0.736984 0.675910i \(-0.763751\pi\)
0.216863 + 0.976202i \(0.430417\pi\)
\(458\) 9.11555 + 15.7886i 0.425942 + 0.737752i
\(459\) −1.03931 + 1.80013i −0.0485107 + 0.0840230i
\(460\) 0.272978i 0.0127276i
\(461\) 11.3477 + 6.55160i 0.528515 + 0.305138i 0.740412 0.672154i \(-0.234631\pi\)
−0.211897 + 0.977292i \(0.567964\pi\)
\(462\) −2.25813 1.30373i −0.105058 0.0606550i
\(463\) 5.97803i 0.277823i −0.990305 0.138911i \(-0.955640\pi\)
0.990305 0.138911i \(-0.0443603\pi\)
\(464\) 0.110797 0.191906i 0.00514363 0.00890903i
\(465\) 0.531224 + 0.920106i 0.0246349 + 0.0426689i
\(466\) 23.2027 13.3961i 1.07485 0.620563i
\(467\) −29.5922 −1.36936 −0.684682 0.728842i \(-0.740059\pi\)
−0.684682 + 0.728842i \(0.740059\pi\)
\(468\) −2.29169 3.30990i −0.105933 0.153000i
\(469\) −25.9566 −1.19857
\(470\) −0.362128 + 0.209074i −0.0167037 + 0.00964388i
\(471\) −10.5507 18.2743i −0.486149 0.842035i
\(472\) −3.50197 + 6.06560i −0.161191 + 0.279192i
\(473\) 7.44972i 0.342539i
\(474\) −6.03521 3.48443i −0.277207 0.160045i
\(475\) 12.3591 + 7.13555i 0.567076 + 0.327401i
\(476\) 6.43853i 0.295110i
\(477\) 2.85587 4.94652i 0.130761 0.226485i
\(478\) 1.20160 + 2.08123i 0.0549598 + 0.0951931i
\(479\) 7.03802 4.06340i 0.321575 0.185661i −0.330519 0.943799i \(-0.607224\pi\)
0.652094 + 0.758138i \(0.273891\pi\)
\(480\) 0.879973 0.0401651
\(481\) 8.63241 5.97686i 0.393604 0.272521i
\(482\) 7.13915 0.325179
\(483\) 3.58413 2.06930i 0.163084 0.0941565i
\(484\) 0.558281 + 0.966972i 0.0253764 + 0.0439533i
\(485\) 0.787189 1.36345i 0.0357444 0.0619112i
\(486\) 0.939913i 0.0426353i
\(487\) −3.72481 2.15052i −0.168787 0.0974494i 0.413227 0.910628i \(-0.364402\pi\)
−0.582014 + 0.813179i \(0.697735\pi\)
\(488\) −13.4759 7.78033i −0.610026 0.352199i
\(489\) 11.7328i 0.530575i
\(490\) 0.0535959 0.0928308i 0.00242122 0.00419367i
\(491\) −10.9243 18.9214i −0.493006 0.853911i 0.506962 0.861969i \(-0.330769\pi\)
−0.999968 + 0.00805728i \(0.997435\pi\)
\(492\) −4.44018 + 2.56354i −0.200179 + 0.115573i
\(493\) 0.885510 0.0398814
\(494\) 9.69225 0.796460i 0.436075 0.0358344i
\(495\) 0.163878 0.00736576
\(496\) 2.92050 1.68615i 0.131134 0.0757104i
\(497\) −18.1900 31.5060i −0.815932 1.41324i
\(498\) −3.51572 + 6.08940i −0.157543 + 0.272872i
\(499\) 33.9761i 1.52098i 0.649349 + 0.760490i \(0.275041\pi\)
−0.649349 + 0.760490i \(0.724959\pi\)
\(500\) 1.58040 + 0.912442i 0.0706775 + 0.0408057i
\(501\) −18.4503 10.6523i −0.824297 0.475908i
\(502\) 3.06387i 0.136747i
\(503\) 13.3026 23.0407i 0.593132 1.02733i −0.400676 0.916220i \(-0.631225\pi\)
0.993808 0.111115i \(-0.0354420\pi\)
\(504\) −4.06316 7.03760i −0.180987 0.313479i
\(505\) −0.836408 + 0.482900i −0.0372196 + 0.0214888i
\(506\) 1.40221 0.0623356
\(507\) −8.25070 10.0462i −0.366426 0.446167i
\(508\) 16.0696 0.712975
\(509\) −15.3229 + 8.84669i −0.679176 + 0.392123i −0.799545 0.600607i \(-0.794926\pi\)
0.120368 + 0.992729i \(0.461592\pi\)
\(510\) −0.160086 0.277276i −0.00708871 0.0122780i
\(511\) 3.36758 5.83282i 0.148973 0.258029i
\(512\) 5.84054i 0.258118i
\(513\) 2.48517 + 1.43482i 0.109723 + 0.0633487i
\(514\) 18.0273 + 10.4081i 0.795151 + 0.459081i
\(515\) 0.828683i 0.0365161i
\(516\) −4.15904 + 7.20367i −0.183092 + 0.317124i
\(517\) −1.35735 2.35100i −0.0596963 0.103397i
\(518\) 6.57581 3.79655i 0.288924 0.166811i
\(519\) 2.35596 0.103415
\(520\) 1.72502 0.141753i 0.0756472 0.00621630i
\(521\) −33.6991 −1.47638 −0.738191 0.674591i \(-0.764320\pi\)
−0.738191 + 0.674591i \(0.764320\pi\)
\(522\) 0.346767 0.200206i 0.0151776 0.00876279i
\(523\) 7.65910 + 13.2660i 0.334909 + 0.580080i 0.983467 0.181085i \(-0.0579610\pi\)
−0.648558 + 0.761165i \(0.724628\pi\)
\(524\) 4.53637 7.85723i 0.198172 0.343245i
\(525\) 13.7962i 0.602118i
\(526\) −20.4277 11.7940i −0.890692 0.514241i
\(527\) 11.6706 + 6.73800i 0.508377 + 0.293512i
\(528\) 0.520163i 0.0226372i
\(529\) 10.3872 17.9912i 0.451617 0.782224i
\(530\) 0.439893 + 0.761917i 0.0191077 + 0.0330956i
\(531\) −2.07066 + 1.19550i −0.0898592 + 0.0518802i
\(532\) −8.88872 −0.385375
\(533\) −13.6119 + 9.42452i −0.589597 + 0.408221i
\(534\) −8.21198 −0.355367
\(535\) −1.19070 + 0.687451i −0.0514784 + 0.0297211i
\(536\) −13.7041 23.7363i −0.591929 1.02525i
\(537\) −7.96439 + 13.7947i −0.343689 + 0.595286i
\(538\) 5.88327i 0.253646i
\(539\) 0.602676 + 0.347955i 0.0259591 + 0.0149875i
\(540\) 0.158465 + 0.0914899i 0.00681926 + 0.00393710i
\(541\) 24.9462i 1.07252i 0.844052 + 0.536261i \(0.180164\pi\)
−0.844052 + 0.536261i \(0.819836\pi\)
\(542\) −4.08011 + 7.06697i −0.175256 + 0.303552i
\(543\) 9.51481 + 16.4801i 0.408319 + 0.707230i
\(544\) 9.66615 5.58076i 0.414433 0.239273i
\(545\) 1.86992 0.0800985
\(546\) −5.35168 7.72946i −0.229031 0.330791i
\(547\) 25.6012 1.09463 0.547315 0.836927i \(-0.315650\pi\)
0.547315 + 0.836927i \(0.315650\pi\)
\(548\) 17.5671 10.1424i 0.750429 0.433260i
\(549\) −2.65604 4.60039i −0.113357 0.196340i
\(550\) 2.33716 4.04808i 0.0996569 0.172611i
\(551\) 1.22249i 0.0520799i
\(552\) 3.78458 + 2.18503i 0.161083 + 0.0930011i
\(553\) 17.8129 + 10.2843i 0.757482 + 0.437332i
\(554\) 28.2151i 1.19875i
\(555\) −0.238611 + 0.413287i −0.0101285 + 0.0175431i
\(556\) 6.10745 + 10.5784i 0.259014 + 0.448625i
\(557\) 7.86475 4.54072i 0.333240 0.192396i −0.324038 0.946044i \(-0.605041\pi\)
0.657279 + 0.753648i \(0.271707\pi\)
\(558\) 6.09361 0.257963
\(559\) −11.4799 + 24.2835i −0.485550 + 1.02708i
\(560\) 0.236477 0.00999299
\(561\) 1.80013 1.03931i 0.0760017 0.0438796i
\(562\) 12.4667 + 21.5929i 0.525875 + 0.910842i
\(563\) 8.38486 14.5230i 0.353380 0.612072i −0.633459 0.773776i \(-0.718366\pi\)
0.986839 + 0.161704i \(0.0516990\pi\)
\(564\) 3.03114i 0.127634i
\(565\) −1.32654 0.765877i −0.0558079 0.0322207i
\(566\) 0.525126 + 0.303181i 0.0220727 + 0.0127437i
\(567\) 2.77415i 0.116503i
\(568\) 19.2073 33.2680i 0.805920 1.39589i
\(569\) −12.5298 21.7023i −0.525278 0.909807i −0.999567 0.0294382i \(-0.990628\pi\)
0.474289 0.880369i \(-0.342705\pi\)
\(570\) −0.382794 + 0.221006i −0.0160335 + 0.00925693i
\(571\) −8.44547 −0.353432 −0.176716 0.984262i \(-0.556547\pi\)
−0.176716 + 0.984262i \(0.556547\pi\)
\(572\) 0.329710 + 4.01230i 0.0137859 + 0.167763i
\(573\) 9.07707 0.379200
\(574\) −10.3690 + 5.98653i −0.432792 + 0.249873i
\(575\) 3.70958 + 6.42518i 0.154700 + 0.267949i
\(576\) 3.04369 5.27182i 0.126820 0.219659i
\(577\) 22.5888i 0.940383i 0.882564 + 0.470192i \(0.155815\pi\)
−0.882564 + 0.470192i \(0.844185\pi\)
\(578\) 10.3209 + 5.95875i 0.429291 + 0.247851i
\(579\) −0.989480 0.571277i −0.0411214 0.0237414i
\(580\) 0.0779513i 0.00323675i
\(581\) 10.3766 17.9728i 0.430495 0.745639i
\(582\) −4.51489 7.82001i −0.187148 0.324150i
\(583\) −4.94652 + 2.85587i −0.204864 + 0.118278i
\(584\) 7.11183 0.294290
\(585\) 0.534185 + 0.252534i 0.0220858 + 0.0104410i
\(586\) 16.3613 0.675881
\(587\) 13.9083 8.02998i 0.574058 0.331433i −0.184710 0.982793i \(-0.559135\pi\)
0.758769 + 0.651360i \(0.225801\pi\)
\(588\) 0.388514 + 0.672925i 0.0160220 + 0.0277510i
\(589\) 9.30215 16.1118i 0.383288 0.663875i
\(590\) 0.368288i 0.0151622i
\(591\) 15.0212 + 8.67251i 0.617891 + 0.356740i
\(592\) 1.31181 + 0.757373i 0.0539150 + 0.0311278i
\(593\) 18.7915i 0.771673i 0.922567 + 0.385837i \(0.126087\pi\)
−0.922567 + 0.385837i \(0.873913\pi\)
\(594\) 0.469957 0.813989i 0.0192826 0.0333984i
\(595\) 0.472492 + 0.818380i 0.0193703 + 0.0335503i
\(596\) −15.4953 + 8.94624i −0.634714 + 0.366452i
\(597\) 0.951782 0.0389538
\(598\) 4.57071 + 2.16078i 0.186910 + 0.0883611i
\(599\) 29.3796 1.20042 0.600208 0.799844i \(-0.295084\pi\)
0.600208 + 0.799844i \(0.295084\pi\)
\(600\) 12.6161 7.28391i 0.515050 0.297365i
\(601\) −8.10907 14.0453i −0.330776 0.572921i 0.651888 0.758315i \(-0.273977\pi\)
−0.982664 + 0.185394i \(0.940644\pi\)
\(602\) −9.71243 + 16.8224i −0.395849 + 0.685631i
\(603\) 9.35660i 0.381030i
\(604\) 16.0255 + 9.25231i 0.652067 + 0.376471i
\(605\) −0.141922 0.0819389i −0.00576997 0.00333129i
\(606\) 5.53930i 0.225019i
\(607\) −3.67343 + 6.36256i −0.149100 + 0.258249i −0.930895 0.365287i \(-0.880971\pi\)
0.781795 + 0.623535i \(0.214304\pi\)
\(608\) −7.70452 13.3446i −0.312460 0.541196i
\(609\) −1.02348 + 0.590908i −0.0414736 + 0.0239448i
\(610\) 0.818224 0.0331289
\(611\) −0.801627 9.75513i −0.0324304 0.394650i
\(612\) 2.32090 0.0938169
\(613\) 25.7402 14.8611i 1.03964 0.600236i 0.119908 0.992785i \(-0.461740\pi\)
0.919731 + 0.392549i \(0.128407\pi\)
\(614\) −3.57200 6.18688i −0.144154 0.249682i
\(615\) 0.376251 0.651685i 0.0151719 0.0262785i
\(616\) 8.12632i 0.327419i
\(617\) 8.75194 + 5.05294i 0.352340 + 0.203424i 0.665715 0.746206i \(-0.268127\pi\)
−0.313375 + 0.949629i \(0.601460\pi\)
\(618\) 4.11611 + 2.37644i 0.165574 + 0.0955943i
\(619\) 32.8446i 1.32014i 0.751205 + 0.660069i \(0.229473\pi\)
−0.751205 + 0.660069i \(0.770527\pi\)
\(620\) 0.593144 1.02736i 0.0238213 0.0412596i
\(621\) 0.745923 + 1.29198i 0.0299328 + 0.0518452i
\(622\) −7.23394 + 4.17652i −0.290054 + 0.167463i
\(623\) 24.2376 0.971059
\(624\) 0.801566 1.69555i 0.0320883 0.0678764i
\(625\) 24.5979 0.983915
\(626\) 14.0728 8.12492i 0.562461 0.324737i
\(627\) −1.43482 2.48517i −0.0573010 0.0992483i
\(628\) −11.7805 + 20.4044i −0.470092 + 0.814224i
\(629\) 6.05305i 0.241351i
\(630\) 0.370057 + 0.213653i 0.0147434 + 0.00851212i
\(631\) 4.96406 + 2.86600i 0.197616 + 0.114094i 0.595543 0.803323i \(-0.296937\pi\)
−0.397927 + 0.917417i \(0.630270\pi\)
\(632\) 21.7189i 0.863932i
\(633\) −4.98172 + 8.62859i −0.198006 + 0.342956i
\(634\) 5.07133 + 8.78380i 0.201408 + 0.348849i
\(635\) −2.04256 + 1.17927i −0.0810564 + 0.0467979i
\(636\) −6.37752 −0.252885
\(637\) 1.42832 + 2.06293i 0.0565921 + 0.0817363i
\(638\) −0.400413 −0.0158525
\(639\) 11.3570 6.55696i 0.449275 0.259389i
\(640\) −0.411152 0.712135i −0.0162522 0.0281496i
\(641\) 12.1383 21.0242i 0.479436 0.830407i −0.520286 0.853992i \(-0.674175\pi\)
0.999722 + 0.0235847i \(0.00750794\pi\)
\(642\) 7.88568i 0.311223i
\(643\) 7.88538 + 4.55263i 0.310969 + 0.179538i 0.647360 0.762184i \(-0.275873\pi\)
−0.336391 + 0.941722i \(0.609206\pi\)
\(644\) −4.00191 2.31050i −0.157697 0.0910466i
\(645\) 1.22084i 0.0480707i
\(646\) −2.80323 + 4.85533i −0.110291 + 0.191030i
\(647\) 19.6739 + 34.0761i 0.773459 + 1.33967i 0.935657 + 0.352912i \(0.114808\pi\)
−0.162198 + 0.986758i \(0.551858\pi\)
\(648\) 2.53685 1.46465i 0.0996568 0.0575369i
\(649\) 2.39100 0.0938548
\(650\) 13.8564 9.59381i 0.543493 0.376300i
\(651\) −17.9853 −0.704899
\(652\) 11.3453 6.55020i 0.444315 0.256525i
\(653\) 12.8895 + 22.3253i 0.504406 + 0.873657i 0.999987 + 0.00509498i \(0.00162179\pi\)
−0.495581 + 0.868562i \(0.665045\pi\)
\(654\) 5.36241 9.28797i 0.209687 0.363189i
\(655\) 1.33161i 0.0520302i
\(656\) −2.06851 1.19425i −0.0807616 0.0466277i
\(657\) 2.10256 + 1.21391i 0.0820286 + 0.0473593i
\(658\) 7.07849i 0.275948i
\(659\) 5.08437 8.80639i 0.198059 0.343048i −0.749840 0.661619i \(-0.769870\pi\)
0.947899 + 0.318571i \(0.103203\pi\)
\(660\) −0.0914899 0.158465i −0.00356124 0.00616825i
\(661\) 26.3447 15.2101i 1.02469 0.591605i 0.109231 0.994016i \(-0.465161\pi\)
0.915459 + 0.402411i \(0.131828\pi\)
\(662\) −22.2887 −0.866273
\(663\) 7.46937 0.613795i 0.290086 0.0238378i
\(664\) 21.9139 0.850424
\(665\) 1.12981 0.652299i 0.0438123 0.0252951i
\(666\) 1.36854 + 2.37039i 0.0530300 + 0.0918506i
\(667\) 0.317770 0.550395i 0.0123041 0.0213114i
\(668\) 23.7878i 0.920379i
\(669\) 10.1997 + 5.88882i 0.394345 + 0.227675i
\(670\) 1.24812 + 0.720603i 0.0482192 + 0.0278393i
\(671\) 5.31207i 0.205070i
\(672\) −7.44816 + 12.9006i −0.287319 + 0.497651i
\(673\) −8.09316 14.0178i −0.311968 0.540345i 0.666820 0.745219i \(-0.267655\pi\)
−0.978788 + 0.204874i \(0.934322\pi\)
\(674\) −12.2196 + 7.05497i −0.470680 + 0.271747i
\(675\) 4.97314 0.191416
\(676\) −5.10817 + 13.5868i −0.196468 + 0.522569i
\(677\) 37.7024 1.44902 0.724511 0.689263i \(-0.242066\pi\)
0.724511 + 0.689263i \(0.242066\pi\)
\(678\) −7.60829 + 4.39265i −0.292195 + 0.168699i
\(679\) 13.3257 + 23.0807i 0.511392 + 0.885757i
\(680\) −0.498917 + 0.864149i −0.0191326 + 0.0331386i
\(681\) 13.6052i 0.521352i
\(682\) −5.27723 3.04681i −0.202075 0.116668i
\(683\) −22.8738 13.2062i −0.875240 0.505320i −0.00615421 0.999981i \(-0.501959\pi\)
−0.869086 + 0.494661i \(0.835292\pi\)
\(684\) 3.20412i 0.122513i
\(685\) −1.48859 + 2.57832i −0.0568763 + 0.0985126i
\(686\) −8.21884 14.2354i −0.313797 0.543512i
\(687\) 16.7979 9.69828i 0.640881 0.370013i
\(688\) −3.87507 −0.147736
\(689\) −20.5248 + 1.68662i −0.781933 + 0.0642553i
\(690\) −0.229790 −0.00874797
\(691\) −7.30038 + 4.21488i −0.277720 + 0.160341i −0.632391 0.774650i \(-0.717926\pi\)
0.354671 + 0.934991i \(0.384593\pi\)
\(692\) −1.31529 2.27814i −0.0499997 0.0866020i
\(693\) −1.38708 + 2.40248i −0.0526906 + 0.0912628i
\(694\) 22.7813i 0.864768i
\(695\) −1.55259 0.896390i −0.0588932 0.0340020i
\(696\) −1.08072 0.623955i −0.0409647 0.0236510i
\(697\) 9.54467i 0.361530i
\(698\) −9.14507 + 15.8397i −0.346146 + 0.599543i
\(699\) −14.2525 24.6860i −0.539079 0.933712i
\(700\) −13.3406 + 7.70219i −0.504227 + 0.291115i
\(701\) −22.6008 −0.853622 −0.426811 0.904341i \(-0.640363\pi\)
−0.426811 + 0.904341i \(0.640363\pi\)
\(702\) 2.78625 1.92912i 0.105160 0.0728101i
\(703\) 8.35655 0.315173
\(704\) −5.27182 + 3.04369i −0.198689 + 0.114713i
\(705\) 0.222440 + 0.385278i 0.00837758 + 0.0145104i
\(706\) −15.4234 + 26.7142i −0.580469 + 1.00540i
\(707\) 16.3492i 0.614876i
\(708\) 2.31203 + 1.33485i 0.0868913 + 0.0501667i
\(709\) 39.1916 + 22.6273i 1.47187 + 0.849786i 0.999500 0.0316131i \(-0.0100645\pi\)
0.472372 + 0.881399i \(0.343398\pi\)
\(710\) 2.01995i 0.0758073i
\(711\) −3.70718 + 6.42103i −0.139030 + 0.240807i
\(712\) 12.7966 + 22.1643i 0.479572 + 0.830643i
\(713\) 8.37609 4.83594i 0.313687 0.181107i
\(714\) 5.41991 0.202835
\(715\) −0.336351 0.485794i −0.0125788 0.0181677i
\(716\) 17.7855 0.664675
\(717\) 2.21427 1.27841i 0.0826936 0.0477432i
\(718\) 12.4688 + 21.5967i 0.465333 + 0.805980i
\(719\) 23.0880 39.9896i 0.861037 1.49136i −0.00989249 0.999951i \(-0.503149\pi\)
0.870929 0.491408i \(-0.163518\pi\)
\(720\) 0.0852431i 0.00317682i
\(721\) −12.1487 7.01404i −0.452440 0.261217i
\(722\) −8.76276 5.05918i −0.326116 0.188283i
\(723\) 7.59554i 0.282481i
\(724\) 10.6239 18.4011i 0.394833 0.683871i
\(725\) −1.05930 1.83477i −0.0393416 0.0681416i
\(726\) −0.813989 + 0.469957i −0.0302100 + 0.0174417i
\(727\) −35.2721 −1.30817 −0.654086 0.756420i \(-0.726946\pi\)
−0.654086 + 0.756420i \(0.726946\pi\)
\(728\) −12.5226 + 26.4890i −0.464118 + 0.981747i
\(729\) 1.00000 0.0370370
\(730\) −0.323859 + 0.186980i −0.0119866 + 0.00692045i
\(731\) −7.74255 13.4105i −0.286368 0.496005i
\(732\) −2.96563 + 5.13662i −0.109613 + 0.189855i
\(733\) 31.3865i 1.15929i 0.814870 + 0.579644i \(0.196808\pi\)
−0.814870 + 0.579644i \(0.803192\pi\)
\(734\) 11.3949 + 6.57883i 0.420592 + 0.242829i
\(735\) −0.0987652 0.0570221i −0.00364301 0.00210329i
\(736\) 8.01075i 0.295280i
\(737\) −4.67830 + 8.10306i −0.172327 + 0.298480i
\(738\) −2.15797 3.73771i −0.0794359 0.137587i
\(739\) −36.6626 + 21.1672i −1.34866 + 0.778647i −0.988059 0.154075i \(-0.950760\pi\)
−0.360596 + 0.932722i \(0.617427\pi\)
\(740\) 0.532849 0.0195879
\(741\) −0.847375 10.3118i −0.0311291 0.378815i
\(742\) −14.8932 −0.546745
\(743\) 40.2960 23.2649i 1.47832 0.853507i 0.478618 0.878023i \(-0.341138\pi\)
0.999699 + 0.0245164i \(0.00780459\pi\)
\(744\) −9.49557 16.4468i −0.348124 0.602969i
\(745\) 1.31304 2.27425i 0.0481060 0.0833221i
\(746\) 31.3690i 1.14850i
\(747\) 6.47868 + 3.74047i 0.237042 + 0.136857i
\(748\) −2.00996 1.16045i −0.0734914 0.0424303i
\(749\) 23.2745i 0.850433i
\(750\) −0.768087 + 1.33037i −0.0280466 + 0.0485781i
\(751\) −16.5675 28.6958i −0.604558 1.04713i −0.992121 0.125282i \(-0.960016\pi\)
0.387563 0.921843i \(-0.373317\pi\)
\(752\) 1.22290 0.706044i 0.0445947 0.0257468i
\(753\) 3.25973 0.118791
\(754\) −1.30521 0.617032i −0.0475328 0.0224710i
\(755\) −2.71592 −0.0988425
\(756\) −2.68252 + 1.54876i −0.0975625 + 0.0563277i
\(757\) 5.57461 + 9.65551i 0.202613 + 0.350935i 0.949369 0.314162i \(-0.101723\pi\)
−0.746757 + 0.665097i \(0.768390\pi\)
\(758\) −5.94974 + 10.3053i −0.216104 + 0.374304i
\(759\) 1.49185i 0.0541505i
\(760\) 1.19300 + 0.688780i 0.0432747 + 0.0249847i
\(761\) 34.9378 + 20.1713i 1.26649 + 0.731210i 0.974323 0.225156i \(-0.0722891\pi\)
0.292171 + 0.956366i \(0.405622\pi\)
\(762\) 13.5273i 0.490042i
\(763\) −15.8271 + 27.4134i −0.572981 + 0.992432i
\(764\) −5.06756 8.77727i −0.183338 0.317550i
\(765\) −0.295002 + 0.170319i −0.0106658 + 0.00615791i
\(766\) 27.1320 0.980319
\(767\) 7.79383 + 3.68450i 0.281419 + 0.133040i
\(768\) −16.8910 −0.609502
\(769\) 2.87354 1.65904i 0.103623 0.0598265i −0.447293 0.894387i \(-0.647612\pi\)
0.550916 + 0.834561i \(0.314279\pi\)
\(770\) −0.213653 0.370057i −0.00769950 0.0133359i
\(771\) 11.0734 19.1798i 0.398800 0.690742i
\(772\) 1.27573i 0.0459146i
\(773\) −22.3406 12.8983i −0.803535 0.463921i 0.0411707 0.999152i \(-0.486891\pi\)
−0.844706 + 0.535231i \(0.820225\pi\)
\(774\) −6.06399 3.50105i −0.217966 0.125843i
\(775\) 32.2417i 1.15816i
\(776\) −14.0709 + 24.3716i −0.505117 + 0.874888i
\(777\) −4.03925 6.99619i −0.144907 0.250987i
\(778\) −28.2169 + 16.2911i −1.01163 + 0.584063i
\(779\) −13.1769 −0.472112
\(780\) −0.0540322 0.657527i −0.00193466 0.0235432i
\(781\) −13.1139 −0.469253
\(782\) −2.52416 + 1.45732i −0.0902636 + 0.0521137i
\(783\) −0.213005 0.368936i −0.00761218 0.0131847i
\(784\) −0.180993 + 0.313490i −0.00646405 + 0.0111961i
\(785\) 3.45804i 0.123423i
\(786\) 6.61415 + 3.81868i 0.235919 + 0.136208i
\(787\) −29.0089 16.7483i −1.03406 0.597012i −0.115912 0.993259i \(-0.536979\pi\)
−0.918144 + 0.396247i \(0.870312\pi\)
\(788\) 19.3668i 0.689914i
\(789\) −12.5479 + 21.7336i −0.446718 + 0.773738i
\(790\) −0.571021 0.989038i −0.0203160 0.0351884i
\(791\) 22.4558 12.9649i 0.798438 0.460978i
\(792\) −2.92930 −0.104088
\(793\) −8.18585 + 17.3155i −0.290688 + 0.614892i
\(794\) −25.0697 −0.889689
\(795\) 0.810624 0.468014i 0.0287499 0.0165988i
\(796\) −0.531362 0.920346i −0.0188336 0.0326208i
\(797\) 2.69109 4.66111i 0.0953234 0.165105i −0.814420 0.580276i \(-0.802945\pi\)
0.909744 + 0.415171i \(0.136278\pi\)
\(798\) 7.48246i 0.264876i
\(799\) 4.88683 + 2.82141i 0.172884 + 0.0998144i
\(800\) −23.1266 13.3521i −0.817647 0.472069i
\(801\) 8.73695i 0.308705i
\(802\) 7.87824 13.6455i 0.278190 0.481840i
\(803\) −1.21391 2.10256i −0.0428381 0.0741977i
\(804\) −9.04757 + 5.22362i −0.319083 + 0.184223i
\(805\) 0.678225 0.0239043
\(806\) −12.5068 18.0637i −0.440534 0.636266i
\(807\) 6.25938 0.220341
\(808\) 14.9507 8.63179i 0.525964 0.303665i
\(809\) 10.8061 + 18.7168i 0.379924 + 0.658048i 0.991051 0.133485i \(-0.0426168\pi\)
−0.611127 + 0.791533i \(0.709284\pi\)
\(810\) −0.0770155 + 0.133395i −0.00270605 + 0.00468701i
\(811\) 19.2028i 0.674301i −0.941451 0.337151i \(-0.890537\pi\)
0.941451 0.337151i \(-0.109463\pi\)
\(812\) 1.14278 + 0.659786i 0.0401038 + 0.0231539i
\(813\) 7.51874 + 4.34095i 0.263694 + 0.152244i
\(814\) 2.73709i 0.0959348i
\(815\) −0.961372 + 1.66515i −0.0336754 + 0.0583275i
\(816\) 0.540609 + 0.936362i 0.0189251 + 0.0327792i
\(817\) −18.5139 + 10.6890i −0.647718 + 0.373960i
\(818\) −22.3957 −0.783048
\(819\) −8.22359 + 5.69380i −0.287356 + 0.198958i
\(820\) −0.840215 −0.0293416
\(821\) 9.85527 5.68994i 0.343951 0.198580i −0.318067 0.948068i \(-0.603034\pi\)
0.662018 + 0.749488i \(0.269700\pi\)
\(822\) 8.53776 + 14.7878i 0.297789 + 0.515785i
\(823\) 16.8531 29.1903i 0.587460 1.01751i −0.407103 0.913382i \(-0.633461\pi\)
0.994564 0.104129i \(-0.0332056\pi\)
\(824\) 14.8126i 0.516022i
\(825\) −4.30687 2.48657i −0.149946 0.0865713i
\(826\) 5.39918 + 3.11722i 0.187861 + 0.108462i
\(827\) 31.2953i 1.08824i 0.839006 + 0.544122i \(0.183137\pi\)
−0.839006 + 0.544122i \(0.816863\pi\)
\(828\) 0.832869 1.44257i 0.0289442 0.0501328i
\(829\) −3.68138 6.37633i −0.127859 0.221459i 0.794988 0.606626i \(-0.207477\pi\)
−0.922847 + 0.385167i \(0.874144\pi\)
\(830\) −0.997917 + 0.576148i −0.0346382 + 0.0199984i
\(831\) −30.0189 −1.04134
\(832\) −21.8746 + 1.79754i −0.758365 + 0.0623186i
\(833\) −1.44653 −0.0501193
\(834\) −8.90482 + 5.14120i −0.308349 + 0.178025i
\(835\) −1.74567 3.02359i −0.0604114 0.104636i
\(836\) −1.60206 + 2.77485i −0.0554085 + 0.0959703i
\(837\) 6.48317i 0.224091i
\(838\) −14.7651 8.52463i −0.510051 0.294478i
\(839\) −7.04747 4.06886i −0.243306 0.140473i 0.373389 0.927675i \(-0.378196\pi\)
−0.616695 + 0.787202i \(0.711529\pi\)
\(840\) 1.33172i 0.0459488i
\(841\) 14.4093 24.9576i 0.496871 0.860606i
\(842\) 9.80057 + 16.9751i 0.337750 + 0.585000i
\(843\) 22.9733 13.2636i 0.791242 0.456824i
\(844\) 11.1248 0.382931
\(845\) −0.347784 2.10183i −0.0119641 0.0723053i
\(846\) 2.55159 0.0877254
\(847\) 2.40248 1.38708i 0.0825504 0.0476605i
\(848\) −1.48552 2.57299i −0.0510129 0.0883569i
\(849\) 0.322563 0.558696i 0.0110703 0.0191744i
\(850\) 9.71612i 0.333260i
\(851\) 3.76231 + 2.17217i 0.128970 + 0.0744611i
\(852\) −12.6808 7.32125i −0.434436 0.250822i
\(853\) 31.8425i 1.09027i −0.838349 0.545134i \(-0.816479\pi\)
0.838349 0.545134i \(-0.183521\pi\)
\(854\) −6.92551 + 11.9953i −0.236986 + 0.410472i
\(855\) 0.235135 + 0.407265i 0.00804143 + 0.0139282i
\(856\) 21.2836 12.2881i 0.727459 0.419999i
\(857\) −10.4553 −0.357146 −0.178573 0.983927i \(-0.557148\pi\)
−0.178573 + 0.983927i \(0.557148\pi\)
\(858\) −3.37752 + 0.277548i −0.115307 + 0.00947532i
\(859\) 38.4561 1.31210 0.656052 0.754715i \(-0.272225\pi\)
0.656052 + 0.754715i \(0.272225\pi\)
\(860\) −1.18052 + 0.681575i −0.0402555 + 0.0232415i
\(861\) 6.36923 + 11.0318i 0.217063 + 0.375964i
\(862\) 6.01221 10.4135i 0.204777 0.354684i
\(863\) 22.3930i 0.762266i −0.924520 0.381133i \(-0.875534\pi\)
0.924520 0.381133i \(-0.124466\pi\)
\(864\) −4.65029 2.68485i −0.158206 0.0913403i
\(865\) 0.334363 + 0.193045i 0.0113687 + 0.00656371i
\(866\) 4.23191i 0.143806i
\(867\) 6.33968 10.9807i 0.215307 0.372922i
\(868\) 10.0408 + 17.3913i 0.340808 + 0.590298i
\(869\) 6.42103 3.70718i 0.217819 0.125758i
\(870\) 0.0656188 0.00222468
\(871\) −27.7364 + 19.2039i −0.939811 + 0.650701i
\(872\) −33.4246 −1.13190
\(873\) −8.31993 + 4.80351i −0.281587 + 0.162574i
\(874\) 2.01191 + 3.48473i 0.0680538 + 0.117873i
\(875\) 2.26700 3.92657i 0.0766387 0.132742i
\(876\) 2.71082i 0.0915901i
\(877\) −10.3935 6.00070i −0.350964 0.202629i 0.314146 0.949375i \(-0.398282\pi\)
−0.665110 + 0.746745i \(0.731615\pi\)
\(878\) 23.4304 + 13.5275i 0.790737 + 0.456532i
\(879\) 17.4073i 0.587133i
\(880\) 0.0426216 0.0738227i 0.00143677 0.00248856i
\(881\) 5.32032 + 9.21506i 0.179246 + 0.310463i 0.941622 0.336671i \(-0.109301\pi\)
−0.762377 + 0.647134i \(0.775968\pi\)
\(882\) −0.566463 + 0.327048i −0.0190738 + 0.0110123i
\(883\) −36.8559 −1.24030 −0.620149 0.784484i \(-0.712928\pi\)
−0.620149 + 0.784484i \(0.712928\pi\)
\(884\) −4.76353 6.88000i −0.160215 0.231399i
\(885\) −0.391831 −0.0131713
\(886\) −7.09749 + 4.09774i −0.238445 + 0.137666i
\(887\) 24.6627 + 42.7171i 0.828093 + 1.43430i 0.899532 + 0.436854i \(0.143908\pi\)
−0.0714390 + 0.997445i \(0.522759\pi\)
\(888\) 4.26515 7.38746i 0.143129 0.247907i
\(889\) 39.9258i 1.33907i
\(890\) −1.16546 0.672880i −0.0390664 0.0225550i
\(891\) −0.866025 0.500000i −0.0290129 0.0167506i
\(892\) 13.1505i 0.440310i
\(893\) 3.89510 6.74652i 0.130345 0.225764i
\(894\) −7.53087 13.0439i −0.251870 0.436252i
\(895\) −2.26065 + 1.30519i −0.0755652 + 0.0436276i
\(896\) 13.9201 0.465037
\(897\) 2.29892 4.86290i 0.0767587 0.162367i
\(898\) 17.6593 0.589298
\(899\) −2.39187 + 1.38095i −0.0797733 + 0.0460572i
\(900\) −2.77641 4.80889i −0.0925471 0.160296i
\(901\) 5.93626 10.2819i 0.197765 0.342540i
\(902\) 4.31593i 0.143705i
\(903\) 17.8978 + 10.3333i 0.595603 + 0.343871i
\(904\) 23.7117 + 13.6900i 0.788640 + 0.455322i
\(905\) 3.11853i 0.103664i
\(906\) −7.78852 + 13.4901i −0.258756 + 0.448179i
\(907\) 12.9497 + 22.4295i 0.429986 + 0.744758i 0.996872 0.0790386i \(-0.0251850\pi\)
−0.566885 + 0.823797i \(0.691852\pi\)
\(908\) −13.1558 + 7.59552i −0.436592 + 0.252066i
\(909\) 5.89342 0.195472
\(910\) −0.126179 1.53550i −0.00418280 0.0509012i
\(911\) −30.9025 −1.02385 −0.511923 0.859031i \(-0.671067\pi\)
−0.511923 + 0.859031i \(0.671067\pi\)
\(912\) 1.29270 0.746338i 0.0428054 0.0247137i
\(913\) −3.74047 6.47868i −0.123791 0.214413i
\(914\) −6.03378 + 10.4508i −0.199580 + 0.345682i
\(915\) 0.870531i 0.0287789i
\(916\) −18.7559 10.8287i −0.619713 0.357792i
\(917\) −19.5216 11.2708i −0.644661 0.372195i
\(918\) 1.95372i 0.0644823i
\(919\) −26.3110 + 45.5719i −0.867918 + 1.50328i −0.00379808 + 0.999993i \(0.501209\pi\)
−0.864120 + 0.503286i \(0.832124\pi\)
\(920\) 0.358078 + 0.620209i 0.0118055 + 0.0204477i
\(921\) −6.58239 + 3.80035i −0.216897 + 0.125226i
\(922\) 12.3159 0.405601
\(923\) −42.7468 20.2084i −1.40703 0.665168i
\(924\) 3.09751 0.101901
\(925\) 12.5419 7.24105i 0.412374 0.238084i
\(926\) −2.80942 4.86605i −0.0923232 0.159908i
\(927\) 2.52836 4.37924i 0.0830421 0.143833i
\(928\) 2.28754i 0.0750922i
\(929\) −23.7545 13.7147i −0.779360 0.449963i 0.0568437 0.998383i \(-0.481896\pi\)
−0.836203 + 0.548420i \(0.815230\pi\)
\(930\) 0.864820 + 0.499304i 0.0283586 + 0.0163728i
\(931\) 1.99701i 0.0654493i
\(932\) −15.9138 + 27.5635i −0.521274 + 0.902873i
\(933\) 4.44351 + 7.69639i 0.145474 + 0.251968i
\(934\) −24.0877 + 13.9071i −0.788175 + 0.455053i
\(935\) 0.340639 0.0111401
\(936\) −9.54850 4.51402i −0.312103 0.147545i
\(937\) −3.29578 −0.107668 −0.0538342 0.998550i \(-0.517144\pi\)
−0.0538342 + 0.998550i \(0.517144\pi\)
\(938\) −21.1284 + 12.1985i −0.689867 + 0.398295i
\(939\) −8.64433 14.9724i −0.282097 0.488606i
\(940\) 0.248368 0.430186i 0.00810088 0.0140311i
\(941\) 52.3176i 1.70550i 0.522316 + 0.852752i \(0.325068\pi\)
−0.522316 + 0.852752i \(0.674932\pi\)
\(942\) −17.1762 9.91671i −0.559632 0.323104i
\(943\) −5.93255 3.42516i −0.193190 0.111539i
\(944\) 1.24371i 0.0404792i
\(945\) 0.227311 0.393714i 0.00739442 0.0128075i
\(946\) 3.50105 + 6.06399i 0.113829 + 0.197157i
\(947\) 46.9640 27.1147i 1.52612 0.881108i 0.526605 0.850110i \(-0.323465\pi\)
0.999519 0.0309981i \(-0.00986859\pi\)
\(948\) 8.27861 0.268877
\(949\) −0.716914 8.72425i −0.0232720 0.283201i
\(950\) 13.4136 0.435195
\(951\) 9.34533 5.39553i 0.303043 0.174962i
\(952\) −8.44574 14.6284i −0.273728 0.474111i
\(953\) −19.8929 + 34.4554i −0.644393 + 1.11612i 0.340048 + 0.940408i \(0.389557\pi\)
−0.984441 + 0.175713i \(0.943777\pi\)
\(954\) 5.36855i 0.173813i
\(955\) 1.28824 + 0.743765i 0.0416864 + 0.0240677i
\(956\) −2.47238 1.42743i −0.0799624 0.0461663i
\(957\) 0.426010i 0.0137709i
\(958\) 3.81924 6.61513i 0.123394 0.213725i
\(959\) −25.1992 43.6462i −0.813723 1.40941i
\(960\) 0.863934 0.498793i 0.0278834 0.0160985i
\(961\) −11.0314 −0.355853
\(962\) 4.21782 8.92196i 0.135988 0.287655i
\(963\) 8.38979 0.270357
\(964\) −7.34467 + 4.24045i −0.236556 + 0.136576i
\(965\) −0.0936196 0.162154i −0.00301372 0.00521992i
\(966\) 1.94496 3.36878i 0.0625782 0.108389i
\(967\) 26.4697i 0.851207i −0.904910 0.425603i \(-0.860062\pi\)
0.904910 0.425603i \(-0.139938\pi\)
\(968\) 2.53685 + 1.46465i 0.0815374 + 0.0470756i
\(969\) 5.16572 + 2.98243i 0.165947 + 0.0958094i
\(970\) 1.47978i 0.0475129i
\(971\) −26.8047 + 46.4272i −0.860205 + 1.48992i 0.0115258 + 0.999934i \(0.496331\pi\)
−0.871731 + 0.489985i \(0.837002\pi\)
\(972\) −0.558281 0.966972i −0.0179069 0.0310156i
\(973\) 26.2825 15.1742i 0.842580 0.486464i
\(974\) −4.04261 −0.129533
\(975\) −10.2071 14.7422i −0.326890 0.472129i
\(976\) −2.76314 −0.0884460
\(977\) 5.53223 3.19404i 0.176992 0.102186i −0.408887 0.912585i \(-0.634083\pi\)
0.585879 + 0.810399i \(0.300750\pi\)
\(978\) 5.51390 + 9.55036i 0.176315 + 0.305387i
\(979\) 4.36847 7.56642i 0.139617 0.241824i
\(980\) 0.127338i 0.00406765i
\(981\) −9.88173 5.70522i −0.315499 0.182154i
\(982\) −17.7845 10.2679i −0.567526 0.327661i
\(983\) 33.0630i 1.05455i 0.849696 + 0.527273i \(0.176786\pi\)
−0.849696 + 0.527273i \(0.823214\pi\)
\(984\) −6.72544 + 11.6488i −0.214399 + 0.371350i
\(985\) 1.42123 + 2.46165i 0.0452842 + 0.0784346i
\(986\) 0.720796 0.416152i 0.0229548 0.0132530i
\(987\) −7.53100 −0.239714
\(988\) −9.49819 + 6.57630i −0.302178 + 0.209220i
\(989\) −11.1138 −0.353399
\(990\) 0.133395 0.0770155i 0.00423956 0.00244771i
\(991\) 21.8087 + 37.7738i 0.692777 + 1.19992i 0.970924 + 0.239386i \(0.0769463\pi\)
−0.278147 + 0.960538i \(0.589720\pi\)
\(992\) −17.4063 + 30.1486i −0.552650 + 0.957219i
\(993\) 23.7135i 0.752526i
\(994\) −29.6129 17.0970i −0.939264 0.542284i
\(995\) 0.135079 + 0.0779880i 0.00428230 + 0.00247238i
\(996\) 8.35293i 0.264673i
\(997\) 18.1905 31.5069i 0.576100 0.997834i −0.419821 0.907607i \(-0.637907\pi\)
0.995921 0.0902275i \(-0.0287594\pi\)
\(998\) 15.9673 + 27.6562i 0.505436 + 0.875442i
\(999\) 2.52192 1.45603i 0.0797900 0.0460668i
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 429.2.s.b.166.9 28
13.2 odd 12 5577.2.a.bf.1.11 14
13.4 even 6 inner 429.2.s.b.199.9 yes 28
13.11 odd 12 5577.2.a.bg.1.4 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.s.b.166.9 28 1.1 even 1 trivial
429.2.s.b.199.9 yes 28 13.4 even 6 inner
5577.2.a.bf.1.11 14 13.2 odd 12
5577.2.a.bg.1.4 14 13.11 odd 12