Properties

Label 406.2.e.a.291.5
Level $406$
Weight $2$
Character 406.291
Analytic conductor $3.242$
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] = [406,2,Mod(233,406)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(406, 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("406.233");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 406 = 2 \cdot 7 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 406.e (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: \(3.24192632206\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.3118758597603.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 4x^{8} - 16x^{6} - 34x^{5} + 43x^{4} + 155x^{3} + 199x^{2} + 124x + 43 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 291.5
Root \(-1.80582 + 0.194943i\) of defining polynomial
Character \(\chi\) \(=\) 406.291
Dual form 406.2.e.a.233.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(1.22122 - 2.11522i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.07173 - 3.58835i) q^{5} -2.44245 q^{6} +(-0.335903 + 2.62434i) q^{7} +1.00000 q^{8} +(-1.48277 - 2.56824i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(1.22122 - 2.11522i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.07173 - 3.58835i) q^{5} -2.44245 q^{6} +(-0.335903 + 2.62434i) q^{7} +1.00000 q^{8} +(-1.48277 - 2.56824i) q^{9} +(-2.07173 + 3.58835i) q^{10} +(2.35349 - 4.07636i) q^{11} +(1.22122 + 2.11522i) q^{12} -1.91061 q^{13} +(2.44070 - 1.02127i) q^{14} -10.1202 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.38357 + 2.39642i) q^{17} +(-1.48277 + 2.56824i) q^{18} +(-2.02020 - 3.49909i) q^{19} +4.14347 q^{20} +(5.14085 + 3.91542i) q^{21} -4.70697 q^{22} +(1.08634 + 1.88160i) q^{23} +(1.22122 - 2.11522i) q^{24} +(-6.08417 + 10.5381i) q^{25} +(0.955306 + 1.65464i) q^{26} +0.0841506 q^{27} +(-2.10480 - 1.60307i) q^{28} -1.00000 q^{29} +(5.06010 + 8.76435i) q^{30} +(0.484522 - 0.839217i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-5.74826 - 9.95629i) q^{33} +2.76714 q^{34} +(10.1130 - 4.23160i) q^{35} +2.96555 q^{36} +(0.736701 + 1.27600i) q^{37} +(-2.02020 + 3.49909i) q^{38} +(-2.33328 + 4.04137i) q^{39} +(-2.07173 - 3.58835i) q^{40} +10.4741 q^{41} +(0.820425 - 6.40982i) q^{42} +7.84520 q^{43} +(2.35349 + 4.07636i) q^{44} +(-6.14382 + 10.6414i) q^{45} +(1.08634 - 1.88160i) q^{46} +(-5.86469 - 10.1579i) q^{47} -2.44245 q^{48} +(-6.77434 - 1.76305i) q^{49} +12.1683 q^{50} +(3.37930 + 5.85312i) q^{51} +(0.955306 - 1.65464i) q^{52} +(1.39041 - 2.40826i) q^{53} +(-0.0420753 - 0.0728765i) q^{54} -19.5032 q^{55} +(-0.335903 + 2.62434i) q^{56} -9.86847 q^{57} +(0.500000 + 0.866025i) q^{58} +(-1.70836 + 2.95897i) q^{59} +(5.06010 - 8.76435i) q^{60} +(-5.70959 - 9.88930i) q^{61} -0.969044 q^{62} +(7.23800 - 3.02862i) q^{63} +1.00000 q^{64} +(3.95828 + 6.85594i) q^{65} +(-5.74826 + 9.95629i) q^{66} +(1.13788 - 1.97086i) q^{67} +(-1.38357 - 2.39642i) q^{68} +5.30667 q^{69} +(-8.72115 - 6.64228i) q^{70} -6.24653 q^{71} +(-1.48277 - 2.56824i) q^{72} +(6.76148 - 11.7112i) q^{73} +(0.736701 - 1.27600i) q^{74} +(14.8603 + 25.7387i) q^{75} +4.04040 q^{76} +(9.90721 + 7.54561i) q^{77} +4.66657 q^{78} +(2.23146 + 3.86501i) q^{79} +(-2.07173 + 3.58835i) q^{80} +(4.55109 - 7.88271i) q^{81} +(-5.23706 - 9.07085i) q^{82} -6.06003 q^{83} +(-5.96128 + 2.49440i) q^{84} +11.4656 q^{85} +(-3.92260 - 6.79415i) q^{86} +(-1.22122 + 2.11522i) q^{87} +(2.35349 - 4.07636i) q^{88} +(-6.63308 - 11.4888i) q^{89} +12.2876 q^{90} +(0.641780 - 5.01410i) q^{91} -2.17268 q^{92} +(-1.18342 - 2.04974i) q^{93} +(-5.86469 + 10.1579i) q^{94} +(-8.37064 + 14.4984i) q^{95} +(1.22122 + 2.11522i) q^{96} +16.8452 q^{97} +(1.86032 + 6.74827i) q^{98} -13.9587 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 5 q^{2} - 3 q^{3} - 5 q^{4} - 7 q^{5} + 6 q^{6} - 3 q^{7} + 10 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 5 q^{2} - 3 q^{3} - 5 q^{4} - 7 q^{5} + 6 q^{6} - 3 q^{7} + 10 q^{8} - 8 q^{9} - 7 q^{10} - 3 q^{12} + 20 q^{13} + 3 q^{14} - 20 q^{15} - 5 q^{16} - 8 q^{17} - 8 q^{18} - 2 q^{19} + 14 q^{20} + 19 q^{21} - q^{23} - 3 q^{24} - 12 q^{25} - 10 q^{26} + 30 q^{27} - 10 q^{29} + 10 q^{30} - 11 q^{31} - 5 q^{32} - 9 q^{33} + 16 q^{34} + 10 q^{35} + 16 q^{36} + 8 q^{37} - 2 q^{38} - 18 q^{39} - 7 q^{40} + 46 q^{41} - 8 q^{42} - 6 q^{43} - 4 q^{45} - q^{46} - 16 q^{47} + 6 q^{48} - 11 q^{49} + 24 q^{50} - 7 q^{51} - 10 q^{52} - 7 q^{53} - 15 q^{54} + 12 q^{55} - 3 q^{56} - 68 q^{57} + 5 q^{58} + 9 q^{59} + 10 q^{60} - 15 q^{61} + 22 q^{62} - 3 q^{63} + 10 q^{64} - 5 q^{65} - 9 q^{66} + 4 q^{67} - 8 q^{68} + 28 q^{69} + 4 q^{70} - 44 q^{71} - 8 q^{72} + 8 q^{74} + 34 q^{75} + 4 q^{76} + 39 q^{77} + 36 q^{78} + 13 q^{79} - 7 q^{80} - 17 q^{81} - 23 q^{82} + 56 q^{83} - 11 q^{84} - 14 q^{85} + 3 q^{86} + 3 q^{87} - 17 q^{89} + 8 q^{90} + 6 q^{91} + 2 q^{92} - 17 q^{93} - 16 q^{94} + 9 q^{95} - 3 q^{96} + 84 q^{97} - 20 q^{98} - 84 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/406\mathbb{Z}\right)^\times\).

\(n\) \(59\) \(379\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 1.22122 2.11522i 0.705074 1.22122i −0.261591 0.965179i \(-0.584247\pi\)
0.966665 0.256045i \(-0.0824194\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −2.07173 3.58835i −0.926508 1.60476i −0.789118 0.614241i \(-0.789462\pi\)
−0.137390 0.990517i \(-0.543871\pi\)
\(6\) −2.44245 −0.997125
\(7\) −0.335903 + 2.62434i −0.126959 + 0.991908i
\(8\) 1.00000 0.353553
\(9\) −1.48277 2.56824i −0.494258 0.856080i
\(10\) −2.07173 + 3.58835i −0.655140 + 1.13474i
\(11\) 2.35349 4.07636i 0.709603 1.22907i −0.255402 0.966835i \(-0.582208\pi\)
0.965005 0.262233i \(-0.0844589\pi\)
\(12\) 1.22122 + 2.11522i 0.352537 + 0.610612i
\(13\) −1.91061 −0.529908 −0.264954 0.964261i \(-0.585357\pi\)
−0.264954 + 0.964261i \(0.585357\pi\)
\(14\) 2.44070 1.02127i 0.652304 0.272946i
\(15\) −10.1202 −2.61302
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.38357 + 2.39642i −0.335565 + 0.581216i −0.983593 0.180400i \(-0.942261\pi\)
0.648028 + 0.761617i \(0.275594\pi\)
\(18\) −1.48277 + 2.56824i −0.349493 + 0.605340i
\(19\) −2.02020 3.49909i −0.463466 0.802747i 0.535665 0.844431i \(-0.320061\pi\)
−0.999131 + 0.0416840i \(0.986728\pi\)
\(20\) 4.14347 0.926508
\(21\) 5.14085 + 3.91542i 1.12183 + 0.854414i
\(22\) −4.70697 −1.00353
\(23\) 1.08634 + 1.88160i 0.226518 + 0.392341i 0.956774 0.290833i \(-0.0939324\pi\)
−0.730256 + 0.683174i \(0.760599\pi\)
\(24\) 1.22122 2.11522i 0.249281 0.431768i
\(25\) −6.08417 + 10.5381i −1.21683 + 2.10762i
\(26\) 0.955306 + 1.65464i 0.187351 + 0.324501i
\(27\) 0.0841506 0.0161948
\(28\) −2.10480 1.60307i −0.397769 0.302952i
\(29\) −1.00000 −0.185695
\(30\) 5.06010 + 8.76435i 0.923844 + 1.60014i
\(31\) 0.484522 0.839217i 0.0870227 0.150728i −0.819229 0.573467i \(-0.805598\pi\)
0.906251 + 0.422739i \(0.138931\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −5.74826 9.95629i −1.00064 1.73317i
\(34\) 2.76714 0.474561
\(35\) 10.1130 4.23160i 1.70940 0.715271i
\(36\) 2.96555 0.494258
\(37\) 0.736701 + 1.27600i 0.121113 + 0.209774i 0.920207 0.391432i \(-0.128020\pi\)
−0.799094 + 0.601206i \(0.794687\pi\)
\(38\) −2.02020 + 3.49909i −0.327720 + 0.567628i
\(39\) −2.33328 + 4.04137i −0.373625 + 0.647137i
\(40\) −2.07173 3.58835i −0.327570 0.567368i
\(41\) 10.4741 1.63578 0.817891 0.575373i \(-0.195143\pi\)
0.817891 + 0.575373i \(0.195143\pi\)
\(42\) 0.820425 6.40982i 0.126594 0.989056i
\(43\) 7.84520 1.19638 0.598191 0.801353i \(-0.295886\pi\)
0.598191 + 0.801353i \(0.295886\pi\)
\(44\) 2.35349 + 4.07636i 0.354801 + 0.614534i
\(45\) −6.14382 + 10.6414i −0.915867 + 1.58633i
\(46\) 1.08634 1.88160i 0.160172 0.277427i
\(47\) −5.86469 10.1579i −0.855453 1.48169i −0.876224 0.481904i \(-0.839945\pi\)
0.0207706 0.999784i \(-0.493388\pi\)
\(48\) −2.44245 −0.352537
\(49\) −6.77434 1.76305i −0.967763 0.251864i
\(50\) 12.1683 1.72086
\(51\) 3.37930 + 5.85312i 0.473197 + 0.819601i
\(52\) 0.955306 1.65464i 0.132477 0.229457i
\(53\) 1.39041 2.40826i 0.190988 0.330800i −0.754590 0.656196i \(-0.772164\pi\)
0.945578 + 0.325396i \(0.105498\pi\)
\(54\) −0.0420753 0.0728765i −0.00572572 0.00991724i
\(55\) −19.5032 −2.62981
\(56\) −0.335903 + 2.62434i −0.0448869 + 0.350692i
\(57\) −9.86847 −1.30711
\(58\) 0.500000 + 0.866025i 0.0656532 + 0.113715i
\(59\) −1.70836 + 2.95897i −0.222410 + 0.385226i −0.955539 0.294864i \(-0.904726\pi\)
0.733129 + 0.680089i \(0.238059\pi\)
\(60\) 5.06010 8.76435i 0.653256 1.13147i
\(61\) −5.70959 9.88930i −0.731038 1.26620i −0.956440 0.291929i \(-0.905703\pi\)
0.225402 0.974266i \(-0.427631\pi\)
\(62\) −0.969044 −0.123069
\(63\) 7.23800 3.02862i 0.911903 0.381571i
\(64\) 1.00000 0.125000
\(65\) 3.95828 + 6.85594i 0.490964 + 0.850375i
\(66\) −5.74826 + 9.95629i −0.707562 + 1.22553i
\(67\) 1.13788 1.97086i 0.139014 0.240779i −0.788110 0.615535i \(-0.788940\pi\)
0.927124 + 0.374756i \(0.122273\pi\)
\(68\) −1.38357 2.39642i −0.167783 0.290608i
\(69\) 5.30667 0.638848
\(70\) −8.72115 6.64228i −1.04238 0.793904i
\(71\) −6.24653 −0.741327 −0.370664 0.928767i \(-0.620870\pi\)
−0.370664 + 0.928767i \(0.620870\pi\)
\(72\) −1.48277 2.56824i −0.174747 0.302670i
\(73\) 6.76148 11.7112i 0.791371 1.37070i −0.133747 0.991016i \(-0.542701\pi\)
0.925118 0.379680i \(-0.123966\pi\)
\(74\) 0.736701 1.27600i 0.0856398 0.148332i
\(75\) 14.8603 + 25.7387i 1.71591 + 2.97205i
\(76\) 4.04040 0.463466
\(77\) 9.90721 + 7.54561i 1.12903 + 0.859902i
\(78\) 4.66657 0.528385
\(79\) 2.23146 + 3.86501i 0.251059 + 0.434847i 0.963818 0.266562i \(-0.0858877\pi\)
−0.712758 + 0.701410i \(0.752554\pi\)
\(80\) −2.07173 + 3.58835i −0.231627 + 0.401190i
\(81\) 4.55109 7.88271i 0.505676 0.875857i
\(82\) −5.23706 9.07085i −0.578336 1.00171i
\(83\) −6.06003 −0.665175 −0.332587 0.943072i \(-0.607922\pi\)
−0.332587 + 0.943072i \(0.607922\pi\)
\(84\) −5.96128 + 2.49440i −0.650428 + 0.272161i
\(85\) 11.4656 1.24362
\(86\) −3.92260 6.79415i −0.422985 0.732632i
\(87\) −1.22122 + 2.11522i −0.130929 + 0.226775i
\(88\) 2.35349 4.07636i 0.250882 0.434541i
\(89\) −6.63308 11.4888i −0.703105 1.21781i −0.967371 0.253364i \(-0.918463\pi\)
0.264266 0.964450i \(-0.414870\pi\)
\(90\) 12.2876 1.29523
\(91\) 0.641780 5.01410i 0.0672768 0.525620i
\(92\) −2.17268 −0.226518
\(93\) −1.18342 2.04974i −0.122715 0.212548i
\(94\) −5.86469 + 10.1579i −0.604897 + 1.04771i
\(95\) −8.37064 + 14.4984i −0.858810 + 1.48750i
\(96\) 1.22122 + 2.11522i 0.124641 + 0.215884i
\(97\) 16.8452 1.71037 0.855186 0.518322i \(-0.173443\pi\)
0.855186 + 0.518322i \(0.173443\pi\)
\(98\) 1.86032 + 6.74827i 0.187921 + 0.681679i
\(99\) −13.9587 −1.40291
\(100\) −6.08417 10.5381i −0.608417 1.05381i
\(101\) 6.21303 10.7613i 0.618219 1.07079i −0.371591 0.928396i \(-0.621188\pi\)
0.989811 0.142391i \(-0.0454790\pi\)
\(102\) 3.37930 5.85312i 0.334601 0.579545i
\(103\) 8.08592 + 14.0052i 0.796729 + 1.37998i 0.921736 + 0.387819i \(0.126771\pi\)
−0.125007 + 0.992156i \(0.539895\pi\)
\(104\) −1.91061 −0.187351
\(105\) 3.39941 26.5589i 0.331748 2.59188i
\(106\) −2.78082 −0.270097
\(107\) −5.31229 9.20116i −0.513558 0.889509i −0.999876 0.0157273i \(-0.994994\pi\)
0.486318 0.873782i \(-0.338340\pi\)
\(108\) −0.0420753 + 0.0728765i −0.00404870 + 0.00701255i
\(109\) −3.04942 + 5.28175i −0.292081 + 0.505900i −0.974302 0.225247i \(-0.927681\pi\)
0.682220 + 0.731147i \(0.261014\pi\)
\(110\) 9.75159 + 16.8903i 0.929778 + 1.61042i
\(111\) 3.59871 0.341574
\(112\) 2.44070 1.02127i 0.230624 0.0965010i
\(113\) 14.5875 1.37228 0.686139 0.727471i \(-0.259304\pi\)
0.686139 + 0.727471i \(0.259304\pi\)
\(114\) 4.93423 + 8.54635i 0.462133 + 0.800439i
\(115\) 4.50123 7.79635i 0.419741 0.727014i
\(116\) 0.500000 0.866025i 0.0464238 0.0804084i
\(117\) 2.83300 + 4.90691i 0.261911 + 0.453644i
\(118\) 3.41673 0.314535
\(119\) −5.82427 4.43593i −0.533910 0.406641i
\(120\) −10.1202 −0.923844
\(121\) −5.57779 9.66102i −0.507072 0.878274i
\(122\) −5.70959 + 9.88930i −0.516922 + 0.895335i
\(123\) 12.7912 22.1551i 1.15335 1.99766i
\(124\) 0.484522 + 0.839217i 0.0435114 + 0.0753639i
\(125\) 29.7018 2.65661
\(126\) −6.24187 4.75398i −0.556070 0.423518i
\(127\) 5.46381 0.484835 0.242418 0.970172i \(-0.422060\pi\)
0.242418 + 0.970172i \(0.422060\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 9.58075 16.5943i 0.843538 1.46105i
\(130\) 3.95828 6.85594i 0.347164 0.601306i
\(131\) 6.70909 + 11.6205i 0.586176 + 1.01529i 0.994728 + 0.102551i \(0.0327005\pi\)
−0.408552 + 0.912735i \(0.633966\pi\)
\(132\) 11.4965 1.00064
\(133\) 9.86140 4.12634i 0.855092 0.357799i
\(134\) −2.27575 −0.196595
\(135\) −0.174338 0.301962i −0.0150046 0.0259887i
\(136\) −1.38357 + 2.39642i −0.118640 + 0.205491i
\(137\) −8.55161 + 14.8118i −0.730613 + 1.26546i 0.226008 + 0.974125i \(0.427432\pi\)
−0.956621 + 0.291334i \(0.905901\pi\)
\(138\) −2.65333 4.59571i −0.225867 0.391213i
\(139\) −3.90711 −0.331397 −0.165699 0.986176i \(-0.552988\pi\)
−0.165699 + 0.986176i \(0.552988\pi\)
\(140\) −1.39180 + 10.8739i −0.117629 + 0.919010i
\(141\) −28.6484 −2.41263
\(142\) 3.12327 + 5.40966i 0.262099 + 0.453968i
\(143\) −4.49660 + 7.78834i −0.376024 + 0.651293i
\(144\) −1.48277 + 2.56824i −0.123564 + 0.214020i
\(145\) 2.07173 + 3.58835i 0.172048 + 0.297996i
\(146\) −13.5230 −1.11917
\(147\) −12.0022 + 12.1761i −0.989926 + 1.00427i
\(148\) −1.47340 −0.121113
\(149\) 3.74913 + 6.49369i 0.307141 + 0.531984i 0.977736 0.209840i \(-0.0672943\pi\)
−0.670595 + 0.741824i \(0.733961\pi\)
\(150\) 14.8603 25.7387i 1.21333 2.10156i
\(151\) −4.70909 + 8.15638i −0.383220 + 0.663757i −0.991521 0.129950i \(-0.958518\pi\)
0.608300 + 0.793707i \(0.291852\pi\)
\(152\) −2.02020 3.49909i −0.163860 0.283814i
\(153\) 8.20609 0.663423
\(154\) 1.58109 12.3527i 0.127408 0.995409i
\(155\) −4.01520 −0.322509
\(156\) −2.33328 4.04137i −0.186812 0.323568i
\(157\) −8.91431 + 15.4400i −0.711439 + 1.23225i 0.252878 + 0.967498i \(0.418623\pi\)
−0.964317 + 0.264751i \(0.914710\pi\)
\(158\) 2.23146 3.86501i 0.177526 0.307484i
\(159\) −3.39600 5.88205i −0.269321 0.466477i
\(160\) 4.14347 0.327570
\(161\) −5.30287 + 2.21890i −0.417925 + 0.174874i
\(162\) −9.10217 −0.715134
\(163\) 5.43945 + 9.42141i 0.426051 + 0.737942i 0.996518 0.0833788i \(-0.0265711\pi\)
−0.570467 + 0.821320i \(0.693238\pi\)
\(164\) −5.23706 + 9.07085i −0.408945 + 0.708314i
\(165\) −23.8178 + 41.2536i −1.85421 + 3.21159i
\(166\) 3.03002 + 5.24814i 0.235175 + 0.407335i
\(167\) 16.0326 1.24064 0.620318 0.784350i \(-0.287003\pi\)
0.620318 + 0.784350i \(0.287003\pi\)
\(168\) 5.14085 + 3.91542i 0.396625 + 0.302081i
\(169\) −9.34956 −0.719197
\(170\) −5.73279 9.92948i −0.439685 0.761556i
\(171\) −5.99100 + 10.3767i −0.458143 + 0.793528i
\(172\) −3.92260 + 6.79415i −0.299096 + 0.518049i
\(173\) 3.09439 + 5.35964i 0.235262 + 0.407486i 0.959349 0.282223i \(-0.0910719\pi\)
−0.724087 + 0.689709i \(0.757739\pi\)
\(174\) 2.44245 0.185161
\(175\) −25.6118 19.5067i −1.93607 1.47457i
\(176\) −4.70697 −0.354801
\(177\) 4.17259 + 7.22714i 0.313631 + 0.543225i
\(178\) −6.63308 + 11.4888i −0.497170 + 0.861124i
\(179\) −0.602699 + 1.04391i −0.0450479 + 0.0780252i −0.887670 0.460480i \(-0.847677\pi\)
0.842622 + 0.538505i \(0.181011\pi\)
\(180\) −6.14382 10.6414i −0.457934 0.793164i
\(181\) 6.95105 0.516668 0.258334 0.966056i \(-0.416827\pi\)
0.258334 + 0.966056i \(0.416827\pi\)
\(182\) −4.66323 + 1.95125i −0.345661 + 0.144636i
\(183\) −27.8907 −2.06174
\(184\) 1.08634 + 1.88160i 0.0800862 + 0.138713i
\(185\) 3.05250 5.28708i 0.224424 0.388714i
\(186\) −1.18342 + 2.04974i −0.0867725 + 0.150294i
\(187\) 6.51243 + 11.2799i 0.476236 + 0.824865i
\(188\) 11.7294 0.855453
\(189\) −0.0282664 + 0.220840i −0.00205608 + 0.0160637i
\(190\) 16.7413 1.21454
\(191\) 3.40424 + 5.89631i 0.246322 + 0.426642i 0.962502 0.271273i \(-0.0874446\pi\)
−0.716181 + 0.697915i \(0.754111\pi\)
\(192\) 1.22122 2.11522i 0.0881342 0.152653i
\(193\) 1.94832 3.37459i 0.140243 0.242908i −0.787345 0.616513i \(-0.788545\pi\)
0.927588 + 0.373604i \(0.121878\pi\)
\(194\) −8.42260 14.5884i −0.604708 1.04738i
\(195\) 19.3358 1.38466
\(196\) 4.91401 4.98523i 0.351001 0.356088i
\(197\) 15.5624 1.10877 0.554386 0.832260i \(-0.312953\pi\)
0.554386 + 0.832260i \(0.312953\pi\)
\(198\) 6.97937 + 12.0886i 0.496002 + 0.859101i
\(199\) −12.2868 + 21.2813i −0.870986 + 1.50859i −0.0100081 + 0.999950i \(0.503186\pi\)
−0.860978 + 0.508642i \(0.830148\pi\)
\(200\) −6.08417 + 10.5381i −0.430216 + 0.745155i
\(201\) −2.77920 4.81372i −0.196030 0.339533i
\(202\) −12.4261 −0.874294
\(203\) 0.335903 2.62434i 0.0235758 0.184193i
\(204\) −6.75860 −0.473197
\(205\) −21.6996 37.5848i −1.51556 2.62504i
\(206\) 8.08592 14.0052i 0.563372 0.975790i
\(207\) 3.22160 5.57997i 0.223917 0.387835i
\(208\) 0.955306 + 1.65464i 0.0662386 + 0.114729i
\(209\) −19.0181 −1.31551
\(210\) −24.7004 + 10.3355i −1.70449 + 0.713215i
\(211\) 8.65646 0.595935 0.297968 0.954576i \(-0.403691\pi\)
0.297968 + 0.954576i \(0.403691\pi\)
\(212\) 1.39041 + 2.40826i 0.0954938 + 0.165400i
\(213\) −7.62841 + 13.2128i −0.522690 + 0.905326i
\(214\) −5.31229 + 9.20116i −0.363141 + 0.628978i
\(215\) −16.2532 28.1513i −1.10846 1.91990i
\(216\) 0.0841506 0.00572572
\(217\) 2.03964 + 1.55345i 0.138460 + 0.105455i
\(218\) 6.09884 0.413065
\(219\) −16.5146 28.6040i −1.11595 1.93288i
\(220\) 9.75159 16.8903i 0.657452 1.13874i
\(221\) 2.64347 4.57862i 0.177819 0.307991i
\(222\) −1.79935 3.11657i −0.120765 0.209171i
\(223\) −10.9191 −0.731194 −0.365597 0.930773i \(-0.619135\pi\)
−0.365597 + 0.930773i \(0.619135\pi\)
\(224\) −2.10480 1.60307i −0.140633 0.107110i
\(225\) 36.0858 2.40572
\(226\) −7.29376 12.6332i −0.485173 0.840345i
\(227\) 5.24754 9.08901i 0.348292 0.603259i −0.637655 0.770322i \(-0.720095\pi\)
0.985946 + 0.167064i \(0.0534286\pi\)
\(228\) 4.93423 8.54635i 0.326778 0.565996i
\(229\) 3.75763 + 6.50840i 0.248311 + 0.430087i 0.963057 0.269297i \(-0.0867912\pi\)
−0.714746 + 0.699384i \(0.753458\pi\)
\(230\) −9.00245 −0.593604
\(231\) 28.0596 11.7411i 1.84618 0.772505i
\(232\) −1.00000 −0.0656532
\(233\) −2.57131 4.45364i −0.168452 0.291767i 0.769424 0.638739i \(-0.220543\pi\)
−0.937876 + 0.346971i \(0.887210\pi\)
\(234\) 2.83300 4.90691i 0.185199 0.320775i
\(235\) −24.3002 + 42.0891i −1.58517 + 2.74559i
\(236\) −1.70836 2.95897i −0.111205 0.192613i
\(237\) 10.9005 0.708061
\(238\) −0.929492 + 7.26193i −0.0602500 + 0.470721i
\(239\) 0.749673 0.0484923 0.0242462 0.999706i \(-0.492281\pi\)
0.0242462 + 0.999706i \(0.492281\pi\)
\(240\) 5.06010 + 8.76435i 0.326628 + 0.565737i
\(241\) 4.50979 7.81119i 0.290501 0.503163i −0.683427 0.730019i \(-0.739511\pi\)
0.973928 + 0.226856i \(0.0728446\pi\)
\(242\) −5.57779 + 9.66102i −0.358554 + 0.621034i
\(243\) −10.9896 19.0345i −0.704981 1.22106i
\(244\) 11.4192 0.731038
\(245\) 7.70820 + 27.9613i 0.492459 + 1.78638i
\(246\) −25.5825 −1.63108
\(247\) 3.85982 + 6.68541i 0.245595 + 0.425382i
\(248\) 0.484522 0.839217i 0.0307672 0.0532903i
\(249\) −7.40065 + 12.8183i −0.468997 + 0.812327i
\(250\) −14.8509 25.7225i −0.939252 1.62683i
\(251\) −29.1169 −1.83784 −0.918921 0.394441i \(-0.870938\pi\)
−0.918921 + 0.394441i \(0.870938\pi\)
\(252\) −0.996136 + 7.78261i −0.0627507 + 0.490258i
\(253\) 10.2268 0.642951
\(254\) −2.73191 4.73180i −0.171415 0.296900i
\(255\) 14.0020 24.2522i 0.876841 1.51873i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 11.6138 + 20.1156i 0.724447 + 1.25478i 0.959201 + 0.282725i \(0.0912383\pi\)
−0.234754 + 0.972055i \(0.575428\pi\)
\(258\) −19.1615 −1.19294
\(259\) −3.59613 + 1.50474i −0.223453 + 0.0935001i
\(260\) −7.91656 −0.490964
\(261\) 1.48277 + 2.56824i 0.0917814 + 0.158970i
\(262\) 6.70909 11.6205i 0.414489 0.717916i
\(263\) 10.2517 17.7564i 0.632145 1.09491i −0.354968 0.934879i \(-0.615508\pi\)
0.987112 0.160028i \(-0.0511585\pi\)
\(264\) −5.74826 9.95629i −0.353781 0.612767i
\(265\) −11.5222 −0.707806
\(266\) −8.50422 6.47705i −0.521427 0.397134i
\(267\) −32.4019 −1.98296
\(268\) 1.13788 + 1.97086i 0.0695068 + 0.120389i
\(269\) 5.69760 9.86853i 0.347389 0.601695i −0.638396 0.769708i \(-0.720402\pi\)
0.985785 + 0.168013i \(0.0537351\pi\)
\(270\) −0.174338 + 0.301962i −0.0106098 + 0.0183768i
\(271\) −8.98753 15.5669i −0.545954 0.945620i −0.998546 0.0539021i \(-0.982834\pi\)
0.452592 0.891717i \(-0.350499\pi\)
\(272\) 2.76714 0.167783
\(273\) −9.82217 7.48084i −0.594465 0.452761i
\(274\) 17.1032 1.03324
\(275\) 28.6380 + 49.6025i 1.72694 + 2.99114i
\(276\) −2.65333 + 4.59571i −0.159712 + 0.276629i
\(277\) 1.04016 1.80161i 0.0624971 0.108248i −0.833084 0.553147i \(-0.813427\pi\)
0.895581 + 0.444898i \(0.146760\pi\)
\(278\) 1.95356 + 3.38366i 0.117167 + 0.202938i
\(279\) −2.87375 −0.172047
\(280\) 10.1130 4.23160i 0.604365 0.252887i
\(281\) 7.35741 0.438906 0.219453 0.975623i \(-0.429573\pi\)
0.219453 + 0.975623i \(0.429573\pi\)
\(282\) 14.3242 + 24.8102i 0.852994 + 1.47743i
\(283\) 3.04027 5.26590i 0.180725 0.313025i −0.761403 0.648279i \(-0.775489\pi\)
0.942128 + 0.335254i \(0.108822\pi\)
\(284\) 3.12327 5.40966i 0.185332 0.321004i
\(285\) 20.4448 + 35.4115i 1.21105 + 2.09760i
\(286\) 8.99320 0.531779
\(287\) −3.51829 + 27.4877i −0.207678 + 1.62255i
\(288\) 2.96555 0.174747
\(289\) 4.67146 + 8.09120i 0.274792 + 0.475953i
\(290\) 2.07173 3.58835i 0.121656 0.210715i
\(291\) 20.5718 35.6313i 1.20594 2.08875i
\(292\) 6.76148 + 11.7112i 0.395686 + 0.685348i
\(293\) 13.7159 0.801291 0.400646 0.916233i \(-0.368786\pi\)
0.400646 + 0.916233i \(0.368786\pi\)
\(294\) 16.5460 + 4.30615i 0.964980 + 0.251140i
\(295\) 14.1571 0.824259
\(296\) 0.736701 + 1.27600i 0.0428199 + 0.0741662i
\(297\) 0.198047 0.343028i 0.0114919 0.0199045i
\(298\) 3.74913 6.49369i 0.217181 0.376169i
\(299\) −2.07558 3.59501i −0.120034 0.207905i
\(300\) −29.7205 −1.71591
\(301\) −2.63523 + 20.5885i −0.151892 + 1.18670i
\(302\) 9.41817 0.541955
\(303\) −15.1750 26.2839i −0.871780 1.50997i
\(304\) −2.02020 + 3.49909i −0.115867 + 0.200687i
\(305\) −23.6575 + 40.9760i −1.35463 + 2.34628i
\(306\) −4.10305 7.10668i −0.234556 0.406262i
\(307\) 7.64494 0.436320 0.218160 0.975913i \(-0.429995\pi\)
0.218160 + 0.975913i \(0.429995\pi\)
\(308\) −11.4883 + 4.80709i −0.654606 + 0.273909i
\(309\) 39.4988 2.24701
\(310\) 2.00760 + 3.47727i 0.114024 + 0.197496i
\(311\) −12.2126 + 21.1528i −0.692512 + 1.19947i 0.278500 + 0.960436i \(0.410163\pi\)
−0.971012 + 0.239030i \(0.923171\pi\)
\(312\) −2.33328 + 4.04137i −0.132096 + 0.228797i
\(313\) 9.13225 + 15.8175i 0.516185 + 0.894059i 0.999823 + 0.0187912i \(0.00598179\pi\)
−0.483638 + 0.875268i \(0.660685\pi\)
\(314\) 17.8286 1.00613
\(315\) −25.8630 19.6980i −1.45721 1.10986i
\(316\) −4.46293 −0.251059
\(317\) 5.21086 + 9.02547i 0.292671 + 0.506921i 0.974440 0.224646i \(-0.0721227\pi\)
−0.681770 + 0.731567i \(0.738789\pi\)
\(318\) −3.39600 + 5.88205i −0.190438 + 0.329849i
\(319\) −2.35349 + 4.07636i −0.131770 + 0.228232i
\(320\) −2.07173 3.58835i −0.115813 0.200595i
\(321\) −25.9500 −1.44839
\(322\) 4.57306 + 3.48297i 0.254846 + 0.194098i
\(323\) 11.1804 0.622093
\(324\) 4.55109 + 7.88271i 0.252838 + 0.437929i
\(325\) 11.6245 20.1342i 0.644810 1.11684i
\(326\) 5.43945 9.42141i 0.301263 0.521804i
\(327\) 7.44804 + 12.9004i 0.411878 + 0.713393i
\(328\) 10.4741 0.578336
\(329\) 28.6279 11.9789i 1.57831 0.660417i
\(330\) 47.6355 2.62225
\(331\) −2.34176 4.05604i −0.128715 0.222940i 0.794464 0.607311i \(-0.207752\pi\)
−0.923179 + 0.384371i \(0.874418\pi\)
\(332\) 3.03002 5.24814i 0.166294 0.288029i
\(333\) 2.18472 3.78405i 0.119722 0.207365i
\(334\) −8.01628 13.8846i −0.438631 0.759731i
\(335\) −9.42950 −0.515189
\(336\) 0.820425 6.40982i 0.0447579 0.349684i
\(337\) −25.3719 −1.38210 −0.691048 0.722809i \(-0.742851\pi\)
−0.691048 + 0.722809i \(0.742851\pi\)
\(338\) 4.67478 + 8.09696i 0.254275 + 0.440416i
\(339\) 17.8146 30.8558i 0.967557 1.67586i
\(340\) −5.73279 + 9.92948i −0.310904 + 0.538501i
\(341\) −2.28063 3.95017i −0.123503 0.213914i
\(342\) 11.9820 0.647913
\(343\) 6.90236 17.1860i 0.372692 0.927955i
\(344\) 7.84520 0.422985
\(345\) −10.9940 19.0422i −0.591897 1.02520i
\(346\) 3.09439 5.35964i 0.166355 0.288136i
\(347\) 0.965287 1.67193i 0.0518193 0.0897537i −0.838952 0.544205i \(-0.816831\pi\)
0.890772 + 0.454451i \(0.150165\pi\)
\(348\) −1.22122 2.11522i −0.0654644 0.113388i
\(349\) 1.95782 0.104800 0.0523998 0.998626i \(-0.483313\pi\)
0.0523998 + 0.998626i \(0.483313\pi\)
\(350\) −4.08738 + 31.9339i −0.218480 + 1.70694i
\(351\) −0.160779 −0.00858175
\(352\) 2.35349 + 4.07636i 0.125441 + 0.217271i
\(353\) 8.16649 14.1448i 0.434658 0.752850i −0.562609 0.826723i \(-0.690202\pi\)
0.997268 + 0.0738726i \(0.0235358\pi\)
\(354\) 4.17259 7.22714i 0.221771 0.384118i
\(355\) 12.9412 + 22.4147i 0.686845 + 1.18965i
\(356\) 13.2662 0.703105
\(357\) −16.4957 + 6.90236i −0.873045 + 0.365312i
\(358\) 1.20540 0.0637073
\(359\) 5.89004 + 10.2019i 0.310865 + 0.538433i 0.978550 0.206010i \(-0.0660481\pi\)
−0.667685 + 0.744444i \(0.732715\pi\)
\(360\) −6.14382 + 10.6414i −0.323808 + 0.560852i
\(361\) 1.33757 2.31674i 0.0703985 0.121934i
\(362\) −3.47553 6.01979i −0.182670 0.316393i
\(363\) −27.2469 −1.43009
\(364\) 4.02145 + 3.06285i 0.210781 + 0.160537i
\(365\) −56.0320 −2.93285
\(366\) 13.9454 + 24.1541i 0.728936 + 1.26255i
\(367\) −17.8219 + 30.8684i −0.930295 + 1.61132i −0.147478 + 0.989065i \(0.547116\pi\)
−0.782816 + 0.622253i \(0.786218\pi\)
\(368\) 1.08634 1.88160i 0.0566295 0.0980852i
\(369\) −15.5307 26.9000i −0.808498 1.40036i
\(370\) −6.10500 −0.317384
\(371\) 5.85306 + 4.45785i 0.303876 + 0.231440i
\(372\) 2.36684 0.122715
\(373\) −8.87414 15.3705i −0.459486 0.795852i 0.539448 0.842019i \(-0.318633\pi\)
−0.998934 + 0.0461665i \(0.985300\pi\)
\(374\) 6.51243 11.2799i 0.336750 0.583268i
\(375\) 36.2725 62.8258i 1.87310 3.24431i
\(376\) −5.86469 10.1579i −0.302448 0.523856i
\(377\) 1.91061 0.0984015
\(378\) 0.205386 0.0859405i 0.0105639 0.00442030i
\(379\) −15.2263 −0.782124 −0.391062 0.920364i \(-0.627892\pi\)
−0.391062 + 0.920364i \(0.627892\pi\)
\(380\) −8.37064 14.4984i −0.429405 0.743751i
\(381\) 6.67254 11.5572i 0.341844 0.592092i
\(382\) 3.40424 5.89631i 0.174176 0.301681i
\(383\) 7.90588 + 13.6934i 0.403971 + 0.699699i 0.994201 0.107536i \(-0.0342962\pi\)
−0.590230 + 0.807235i \(0.700963\pi\)
\(384\) −2.44245 −0.124641
\(385\) 6.55118 51.1830i 0.333879 2.60853i
\(386\) −3.89664 −0.198334
\(387\) −11.6327 20.1484i −0.591321 1.02420i
\(388\) −8.42260 + 14.5884i −0.427593 + 0.740612i
\(389\) 10.8586 18.8076i 0.550552 0.953584i −0.447683 0.894193i \(-0.647751\pi\)
0.998235 0.0593917i \(-0.0189161\pi\)
\(390\) −9.66789 16.7453i −0.489553 0.847930i
\(391\) −6.01213 −0.304047
\(392\) −6.77434 1.76305i −0.342156 0.0890474i
\(393\) 32.7732 1.65319
\(394\) −7.78118 13.4774i −0.392010 0.678981i
\(395\) 9.24600 16.0145i 0.465217 0.805779i
\(396\) 6.97937 12.0886i 0.350727 0.607476i
\(397\) −0.630167 1.09148i −0.0316272 0.0547798i 0.849779 0.527140i \(-0.176736\pi\)
−0.881406 + 0.472360i \(0.843402\pi\)
\(398\) 24.5735 1.23176
\(399\) 3.31485 25.8982i 0.165950 1.29653i
\(400\) 12.1683 0.608417
\(401\) 0.955905 + 1.65568i 0.0477356 + 0.0826806i 0.888906 0.458090i \(-0.151466\pi\)
−0.841170 + 0.540770i \(0.818133\pi\)
\(402\) −2.77920 + 4.81372i −0.138614 + 0.240086i
\(403\) −0.925734 + 1.60342i −0.0461141 + 0.0798719i
\(404\) 6.21303 + 10.7613i 0.309110 + 0.535394i
\(405\) −37.7146 −1.87405
\(406\) −2.44070 + 1.02127i −0.121130 + 0.0506848i
\(407\) 6.93526 0.343768
\(408\) 3.37930 + 5.85312i 0.167300 + 0.289773i
\(409\) 1.50907 2.61379i 0.0746189 0.129244i −0.826302 0.563228i \(-0.809559\pi\)
0.900921 + 0.433984i \(0.142893\pi\)
\(410\) −21.6996 + 37.5848i −1.07167 + 1.85618i
\(411\) 20.8869 + 36.1771i 1.03027 + 1.78448i
\(412\) −16.1718 −0.796729
\(413\) −7.19151 5.47726i −0.353871 0.269518i
\(414\) −6.44320 −0.316666
\(415\) 12.5548 + 21.7455i 0.616290 + 1.06744i
\(416\) 0.955306 1.65464i 0.0468377 0.0811253i
\(417\) −4.77146 + 8.26441i −0.233659 + 0.404710i
\(418\) 9.50903 + 16.4701i 0.465102 + 0.805580i
\(419\) 4.64504 0.226925 0.113463 0.993542i \(-0.463806\pi\)
0.113463 + 0.993542i \(0.463806\pi\)
\(420\) 21.3010 + 16.2234i 1.03938 + 0.791621i
\(421\) −26.6202 −1.29739 −0.648695 0.761048i \(-0.724685\pi\)
−0.648695 + 0.761048i \(0.724685\pi\)
\(422\) −4.32823 7.49671i −0.210695 0.364934i
\(423\) −17.3920 + 30.1239i −0.845629 + 1.46467i
\(424\) 1.39041 2.40826i 0.0675243 0.116956i
\(425\) −16.8358 29.1604i −0.816654 1.41449i
\(426\) 15.2568 0.739196
\(427\) 27.8708 11.6621i 1.34876 0.564367i
\(428\) 10.6246 0.513558
\(429\) 10.9827 + 19.0226i 0.530250 + 0.918420i
\(430\) −16.2532 + 28.1513i −0.783798 + 1.35758i
\(431\) 4.81935 8.34735i 0.232140 0.402078i −0.726298 0.687380i \(-0.758761\pi\)
0.958438 + 0.285302i \(0.0920940\pi\)
\(432\) −0.0420753 0.0728765i −0.00202435 0.00350627i
\(433\) −3.16466 −0.152084 −0.0760420 0.997105i \(-0.524228\pi\)
−0.0760420 + 0.997105i \(0.524228\pi\)
\(434\) 0.325505 2.54310i 0.0156247 0.122073i
\(435\) 10.1202 0.485227
\(436\) −3.04942 5.28175i −0.146041 0.252950i
\(437\) 4.38926 7.60242i 0.209967 0.363673i
\(438\) −16.5146 + 28.6040i −0.789096 + 1.36675i
\(439\) −6.94499 12.0291i −0.331467 0.574117i 0.651333 0.758792i \(-0.274210\pi\)
−0.982800 + 0.184675i \(0.940877\pi\)
\(440\) −19.5032 −0.929778
\(441\) 5.51688 + 20.0123i 0.262709 + 0.952968i
\(442\) −5.28694 −0.251474
\(443\) −10.1854 17.6416i −0.483923 0.838179i 0.515907 0.856645i \(-0.327455\pi\)
−0.999829 + 0.0184661i \(0.994122\pi\)
\(444\) −1.79935 + 3.11657i −0.0853936 + 0.147906i
\(445\) −27.4840 + 47.6036i −1.30286 + 2.25663i
\(446\) 5.45953 + 9.45618i 0.258516 + 0.447763i
\(447\) 18.3141 0.866228
\(448\) −0.335903 + 2.62434i −0.0158699 + 0.123988i
\(449\) 33.1442 1.56417 0.782086 0.623170i \(-0.214156\pi\)
0.782086 + 0.623170i \(0.214156\pi\)
\(450\) −18.0429 31.2512i −0.850550 1.47320i
\(451\) 24.6507 42.6962i 1.16076 2.01049i
\(452\) −7.29376 + 12.6332i −0.343069 + 0.594214i
\(453\) 11.5017 + 19.9215i 0.540397 + 0.935995i
\(454\) −10.4951 −0.492559
\(455\) −19.3219 + 8.08495i −0.905826 + 0.379028i
\(456\) −9.86847 −0.462133
\(457\) 9.10435 + 15.7692i 0.425883 + 0.737652i 0.996502 0.0835631i \(-0.0266300\pi\)
−0.570619 + 0.821215i \(0.693297\pi\)
\(458\) 3.75763 6.50840i 0.175582 0.304117i
\(459\) −0.116428 + 0.201660i −0.00543441 + 0.00941267i
\(460\) 4.50123 + 7.79635i 0.209871 + 0.363507i
\(461\) −3.52484 −0.164168 −0.0820841 0.996625i \(-0.526158\pi\)
−0.0820841 + 0.996625i \(0.526158\pi\)
\(462\) −24.1978 18.4298i −1.12579 0.857430i
\(463\) 10.7653 0.500304 0.250152 0.968207i \(-0.419519\pi\)
0.250152 + 0.968207i \(0.419519\pi\)
\(464\) 0.500000 + 0.866025i 0.0232119 + 0.0402042i
\(465\) −4.90346 + 8.49305i −0.227393 + 0.393856i
\(466\) −2.57131 + 4.45364i −0.119114 + 0.206311i
\(467\) −6.00994 10.4095i −0.278107 0.481695i 0.692807 0.721123i \(-0.256374\pi\)
−0.970914 + 0.239427i \(0.923040\pi\)
\(468\) −5.66601 −0.261911
\(469\) 4.78999 + 3.64819i 0.221181 + 0.168458i
\(470\) 48.6003 2.24177
\(471\) 21.7727 + 37.7115i 1.00323 + 1.73765i
\(472\) −1.70836 + 2.95897i −0.0786338 + 0.136198i
\(473\) 18.4636 31.9798i 0.848956 1.47043i
\(474\) −5.45023 9.44008i −0.250337 0.433597i
\(475\) 49.1650 2.25584
\(476\) 6.75376 2.82600i 0.309558 0.129530i
\(477\) −8.24666 −0.377588
\(478\) −0.374837 0.649236i −0.0171446 0.0296954i
\(479\) −4.14601 + 7.18110i −0.189436 + 0.328113i −0.945062 0.326890i \(-0.893999\pi\)
0.755626 + 0.655003i \(0.227333\pi\)
\(480\) 5.06010 8.76435i 0.230961 0.400036i
\(481\) −1.40755 2.43795i −0.0641788 0.111161i
\(482\) −9.01959 −0.410831
\(483\) −1.78253 + 13.9265i −0.0811077 + 0.633678i
\(484\) 11.1556 0.507072
\(485\) −34.8988 60.4465i −1.58467 2.74473i
\(486\) −10.9896 + 19.0345i −0.498497 + 0.863421i
\(487\) −3.94673 + 6.83593i −0.178843 + 0.309766i −0.941485 0.337056i \(-0.890569\pi\)
0.762641 + 0.646822i \(0.223902\pi\)
\(488\) −5.70959 9.88930i −0.258461 0.447668i
\(489\) 26.5711 1.20159
\(490\) 20.3611 20.6561i 0.919819 0.933149i
\(491\) −37.7250 −1.70250 −0.851252 0.524757i \(-0.824156\pi\)
−0.851252 + 0.524757i \(0.824156\pi\)
\(492\) 12.7912 + 22.1551i 0.576673 + 0.998828i
\(493\) 1.38357 2.39642i 0.0623129 0.107929i
\(494\) 3.85982 6.68541i 0.173662 0.300791i
\(495\) 28.9188 + 50.0888i 1.29980 + 2.25133i
\(496\) −0.969044 −0.0435114
\(497\) 2.09823 16.3930i 0.0941184 0.735328i
\(498\) 14.8013 0.663262
\(499\) 4.23971 + 7.34340i 0.189796 + 0.328736i 0.945182 0.326544i \(-0.105884\pi\)
−0.755386 + 0.655280i \(0.772551\pi\)
\(500\) −14.8509 + 25.7225i −0.664152 + 1.15034i
\(501\) 19.5793 33.9124i 0.874740 1.51509i
\(502\) 14.5584 + 25.2160i 0.649775 + 1.12544i
\(503\) −25.2796 −1.12716 −0.563581 0.826061i \(-0.690577\pi\)
−0.563581 + 0.826061i \(0.690577\pi\)
\(504\) 7.23800 3.02862i 0.322406 0.134906i
\(505\) −51.4870 −2.29114
\(506\) −5.11338 8.85664i −0.227318 0.393726i
\(507\) −11.4179 + 19.7764i −0.507087 + 0.878300i
\(508\) −2.73191 + 4.73180i −0.121209 + 0.209940i
\(509\) −2.48482 4.30383i −0.110138 0.190764i 0.805688 0.592340i \(-0.201796\pi\)
−0.915826 + 0.401576i \(0.868462\pi\)
\(510\) −28.0041 −1.24004
\(511\) 28.4631 + 21.6783i 1.25913 + 0.958990i
\(512\) 1.00000 0.0441942
\(513\) −0.170001 0.294451i −0.00750573 0.0130003i
\(514\) 11.6138 20.1156i 0.512262 0.887263i
\(515\) 33.5037 58.0302i 1.47635 2.55712i
\(516\) 9.58075 + 16.5943i 0.421769 + 0.730525i
\(517\) −55.2099 −2.42813
\(518\) 3.10121 + 2.36197i 0.136259 + 0.103779i
\(519\) 15.1158 0.663508
\(520\) 3.95828 + 6.85594i 0.173582 + 0.300653i
\(521\) −13.4814 + 23.3505i −0.590631 + 1.02300i 0.403517 + 0.914972i \(0.367788\pi\)
−0.994148 + 0.108030i \(0.965546\pi\)
\(522\) 1.48277 2.56824i 0.0648992 0.112409i
\(523\) 5.24494 + 9.08451i 0.229345 + 0.397238i 0.957614 0.288054i \(-0.0930082\pi\)
−0.728269 + 0.685291i \(0.759675\pi\)
\(524\) −13.4182 −0.586176
\(525\) −72.5388 + 30.3527i −3.16585 + 1.32470i
\(526\) −20.5033 −0.893988
\(527\) 1.34074 + 2.32223i 0.0584036 + 0.101158i
\(528\) −5.74826 + 9.95629i −0.250161 + 0.433292i
\(529\) 9.13972 15.8305i 0.397379 0.688281i
\(530\) 5.76112 + 9.97856i 0.250247 + 0.433441i
\(531\) 10.1325 0.439712
\(532\) −1.35718 + 10.6034i −0.0588414 + 0.459716i
\(533\) −20.0120 −0.866815
\(534\) 16.2009 + 28.0609i 0.701084 + 1.21431i
\(535\) −22.0113 + 38.1247i −0.951632 + 1.64827i
\(536\) 1.13788 1.97086i 0.0491487 0.0851281i
\(537\) 1.47206 + 2.54968i 0.0635241 + 0.110027i
\(538\) −11.3952 −0.491282
\(539\) −23.1301 + 23.4653i −0.996285 + 1.01072i
\(540\) 0.348675 0.0150046
\(541\) 22.2847 + 38.5982i 0.958093 + 1.65947i 0.727125 + 0.686505i \(0.240856\pi\)
0.230968 + 0.972961i \(0.425811\pi\)
\(542\) −8.98753 + 15.5669i −0.386048 + 0.668654i
\(543\) 8.48879 14.7030i 0.364289 0.630967i
\(544\) −1.38357 2.39642i −0.0593201 0.102746i
\(545\) 25.2703 1.08246
\(546\) −1.56751 + 12.2467i −0.0670834 + 0.524109i
\(547\) 34.8005 1.48796 0.743980 0.668202i \(-0.232936\pi\)
0.743980 + 0.668202i \(0.232936\pi\)
\(548\) −8.55161 14.8118i −0.365307 0.632730i
\(549\) −16.9321 + 29.3272i −0.722643 + 1.25165i
\(550\) 28.6380 49.6025i 1.22113 2.11506i
\(551\) 2.02020 + 3.49909i 0.0860635 + 0.149066i
\(552\) 5.30667 0.225867
\(553\) −10.8927 + 4.55786i −0.463203 + 0.193820i
\(554\) −2.08032 −0.0883843
\(555\) −7.45557 12.9134i −0.316471 0.548144i
\(556\) 1.95356 3.38366i 0.0828493 0.143499i
\(557\) 16.8832 29.2426i 0.715365 1.23905i −0.247453 0.968900i \(-0.579594\pi\)
0.962818 0.270149i \(-0.0870731\pi\)
\(558\) 1.43687 + 2.48874i 0.0608277 + 0.105357i
\(559\) −14.9891 −0.633973
\(560\) −8.72115 6.64228i −0.368536 0.280687i
\(561\) 31.8125 1.34313
\(562\) −3.67871 6.37170i −0.155177 0.268774i
\(563\) −20.6204 + 35.7156i −0.869047 + 1.50523i −0.00607459 + 0.999982i \(0.501934\pi\)
−0.862972 + 0.505252i \(0.831400\pi\)
\(564\) 14.3242 24.8102i 0.603158 1.04470i
\(565\) −30.2215 52.3451i −1.27143 2.20217i
\(566\) −6.08053 −0.255584
\(567\) 19.1582 + 14.5914i 0.804569 + 0.612783i
\(568\) −6.24653 −0.262099
\(569\) 12.9593 + 22.4461i 0.543281 + 0.940990i 0.998713 + 0.0507193i \(0.0161514\pi\)
−0.455432 + 0.890270i \(0.650515\pi\)
\(570\) 20.4448 35.4115i 0.856340 1.48323i
\(571\) −7.94763 + 13.7657i −0.332598 + 0.576077i −0.983020 0.183496i \(-0.941259\pi\)
0.650422 + 0.759573i \(0.274592\pi\)
\(572\) −4.49660 7.78834i −0.188012 0.325647i
\(573\) 16.6293 0.694700
\(574\) 25.5642 10.6969i 1.06703 0.446480i
\(575\) −26.4380 −1.10254
\(576\) −1.48277 2.56824i −0.0617822 0.107010i
\(577\) 5.13613 8.89603i 0.213820 0.370347i −0.739087 0.673610i \(-0.764743\pi\)
0.952907 + 0.303263i \(0.0980761\pi\)
\(578\) 4.67146 8.09120i 0.194307 0.336550i
\(579\) −4.75867 8.24225i −0.197763 0.342536i
\(580\) −4.14347 −0.172048
\(581\) 2.03558 15.9036i 0.0844502 0.659792i
\(582\) −41.1435 −1.70545
\(583\) −6.54462 11.3356i −0.271051 0.469473i
\(584\) 6.76148 11.7112i 0.279792 0.484614i
\(585\) 11.7385 20.3316i 0.485326 0.840609i
\(586\) −6.85795 11.8783i −0.283299 0.490689i
\(587\) −23.9902 −0.990183 −0.495091 0.868841i \(-0.664865\pi\)
−0.495091 + 0.868841i \(0.664865\pi\)
\(588\) −4.54374 16.4823i −0.187381 0.679719i
\(589\) −3.91533 −0.161328
\(590\) −7.07855 12.2604i −0.291419 0.504753i
\(591\) 19.0051 32.9178i 0.781766 1.35406i
\(592\) 0.736701 1.27600i 0.0302782 0.0524434i
\(593\) 7.76833 + 13.4551i 0.319007 + 0.552536i 0.980281 0.197608i \(-0.0633173\pi\)
−0.661274 + 0.750144i \(0.729984\pi\)
\(594\) −0.396094 −0.0162519
\(595\) −3.85132 + 30.0896i −0.157889 + 1.23355i
\(596\) −7.49827 −0.307141
\(597\) 30.0098 + 51.9785i 1.22822 + 2.12734i
\(598\) −2.07558 + 3.59501i −0.0848767 + 0.147011i
\(599\) 10.4154 18.0400i 0.425561 0.737094i −0.570911 0.821012i \(-0.693410\pi\)
0.996473 + 0.0839180i \(0.0267434\pi\)
\(600\) 14.8603 + 25.7387i 0.606667 + 1.05078i
\(601\) 17.7149 0.722606 0.361303 0.932448i \(-0.382332\pi\)
0.361303 + 0.932448i \(0.382332\pi\)
\(602\) 19.1478 8.01207i 0.780405 0.326548i
\(603\) −6.74884 −0.274834
\(604\) −4.70909 8.15638i −0.191610 0.331878i
\(605\) −23.1114 + 40.0301i −0.939612 + 1.62746i
\(606\) −15.1750 + 26.2839i −0.616442 + 1.06771i
\(607\) 1.22259 + 2.11758i 0.0496233 + 0.0859501i 0.889770 0.456409i \(-0.150865\pi\)
−0.840147 + 0.542359i \(0.817531\pi\)
\(608\) 4.04040 0.163860
\(609\) −5.14085 3.91542i −0.208318 0.158661i
\(610\) 47.3150 1.91573
\(611\) 11.2052 + 19.4079i 0.453312 + 0.785159i
\(612\) −4.10305 + 7.10668i −0.165856 + 0.287271i
\(613\) 0.903050 1.56413i 0.0364739 0.0631746i −0.847212 0.531255i \(-0.821721\pi\)
0.883686 + 0.468080i \(0.155054\pi\)
\(614\) −3.82247 6.62071i −0.154262 0.267190i
\(615\) −106.000 −4.27434
\(616\) 9.90721 + 7.54561i 0.399173 + 0.304021i
\(617\) −15.0917 −0.607567 −0.303784 0.952741i \(-0.598250\pi\)
−0.303784 + 0.952741i \(0.598250\pi\)
\(618\) −19.7494 34.2070i −0.794438 1.37601i
\(619\) 22.2955 38.6170i 0.896133 1.55215i 0.0637362 0.997967i \(-0.479698\pi\)
0.832396 0.554181i \(-0.186968\pi\)
\(620\) 2.00760 3.47727i 0.0806272 0.139650i
\(621\) 0.0914163 + 0.158338i 0.00366841 + 0.00635387i
\(622\) 24.4252 0.979360
\(623\) 32.3787 13.5483i 1.29723 0.542803i
\(624\) 4.66657 0.186812
\(625\) −31.1133 53.8899i −1.24453 2.15560i
\(626\) 9.13225 15.8175i 0.364998 0.632195i
\(627\) −23.2253 + 40.2274i −0.927529 + 1.60653i
\(628\) −8.91431 15.4400i −0.355720 0.616125i
\(629\) −4.07712 −0.162565
\(630\) −4.12746 + 32.2470i −0.164442 + 1.28475i
\(631\) −14.3265 −0.570328 −0.285164 0.958479i \(-0.592048\pi\)
−0.285164 + 0.958479i \(0.592048\pi\)
\(632\) 2.23146 + 3.86501i 0.0887629 + 0.153742i
\(633\) 10.5715 18.3103i 0.420178 0.727770i
\(634\) 5.21086 9.02547i 0.206950 0.358447i
\(635\) −11.3196 19.6061i −0.449203 0.778043i
\(636\) 6.79201 0.269321
\(637\) 12.9431 + 3.36850i 0.512826 + 0.133465i
\(638\) 4.70697 0.186351
\(639\) 9.26219 + 16.0426i 0.366407 + 0.634635i
\(640\) −2.07173 + 3.58835i −0.0818925 + 0.141842i
\(641\) 8.71772 15.0995i 0.344329 0.596395i −0.640903 0.767622i \(-0.721440\pi\)
0.985232 + 0.171227i \(0.0547731\pi\)
\(642\) 12.9750 + 22.4733i 0.512082 + 0.886952i
\(643\) −6.99067 −0.275685 −0.137843 0.990454i \(-0.544017\pi\)
−0.137843 + 0.990454i \(0.544017\pi\)
\(644\) 0.729811 5.70187i 0.0287586 0.224685i
\(645\) −79.3950 −3.12618
\(646\) −5.59019 9.68249i −0.219943 0.380952i
\(647\) 8.11703 14.0591i 0.319113 0.552721i −0.661190 0.750219i \(-0.729948\pi\)
0.980303 + 0.197498i \(0.0632816\pi\)
\(648\) 4.55109 7.88271i 0.178784 0.309662i
\(649\) 8.04122 + 13.9278i 0.315646 + 0.546714i
\(650\) −23.2490 −0.911899
\(651\) 5.77674 2.41718i 0.226408 0.0947369i
\(652\) −10.8789 −0.426051
\(653\) −11.2601 19.5030i −0.440641 0.763212i 0.557097 0.830448i \(-0.311915\pi\)
−0.997737 + 0.0672359i \(0.978582\pi\)
\(654\) 7.44804 12.9004i 0.291241 0.504445i
\(655\) 27.7989 48.1491i 1.08619 1.88134i
\(656\) −5.23706 9.07085i −0.204473 0.354157i
\(657\) −40.1030 −1.56457
\(658\) −24.6880 18.8030i −0.962437 0.733019i
\(659\) −6.71682 −0.261650 −0.130825 0.991405i \(-0.541763\pi\)
−0.130825 + 0.991405i \(0.541763\pi\)
\(660\) −23.8178 41.2536i −0.927105 1.60579i
\(661\) 17.6804 30.6234i 0.687689 1.19111i −0.284895 0.958559i \(-0.591959\pi\)
0.972584 0.232553i \(-0.0747079\pi\)
\(662\) −2.34176 + 4.05604i −0.0910149 + 0.157643i
\(663\) −6.45653 11.1830i −0.250751 0.434313i
\(664\) −6.06003 −0.235175
\(665\) −35.2370 26.8375i −1.36643 1.04071i
\(666\) −4.36944 −0.169313
\(667\) −1.08634 1.88160i −0.0420633 0.0728559i
\(668\) −8.01628 + 13.8846i −0.310159 + 0.537211i
\(669\) −13.3346 + 23.0962i −0.515546 + 0.892951i
\(670\) 4.71475 + 8.16619i 0.182147 + 0.315487i
\(671\) −53.7498 −2.07499
\(672\) −5.96128 + 2.49440i −0.229961 + 0.0962235i
\(673\) −23.1388 −0.891935 −0.445967 0.895049i \(-0.647140\pi\)
−0.445967 + 0.895049i \(0.647140\pi\)
\(674\) 12.6860 + 21.9727i 0.488645 + 0.846358i
\(675\) −0.511986 + 0.886786i −0.0197064 + 0.0341324i
\(676\) 4.67478 8.09696i 0.179799 0.311421i
\(677\) −11.3672 19.6886i −0.436878 0.756694i 0.560569 0.828108i \(-0.310582\pi\)
−0.997447 + 0.0714135i \(0.977249\pi\)
\(678\) −35.6292 −1.36833
\(679\) −5.65835 + 44.2076i −0.217148 + 1.69653i
\(680\) 11.4656 0.439685
\(681\) −12.8168 22.1994i −0.491142 0.850684i
\(682\) −2.28063 + 3.95017i −0.0873299 + 0.151260i
\(683\) −10.1464 + 17.5741i −0.388242 + 0.672454i −0.992213 0.124552i \(-0.960251\pi\)
0.603972 + 0.797006i \(0.293584\pi\)
\(684\) −5.99100 10.3767i −0.229072 0.396764i
\(685\) 70.8667 2.70768
\(686\) −18.3347 + 2.61536i −0.700021 + 0.0998550i
\(687\) 18.3556 0.700310
\(688\) −3.92260 6.79415i −0.149548 0.259024i
\(689\) −2.65654 + 4.60125i −0.101206 + 0.175294i
\(690\) −10.9940 + 19.0422i −0.418535 + 0.724923i
\(691\) −1.00590 1.74227i −0.0382662 0.0662790i 0.846258 0.532773i \(-0.178850\pi\)
−0.884524 + 0.466494i \(0.845517\pi\)
\(692\) −6.18878 −0.235262
\(693\) 4.68878 36.6325i 0.178112 1.39155i
\(694\) −1.93057 −0.0732836
\(695\) 8.09450 + 14.0201i 0.307042 + 0.531812i
\(696\) −1.22122 + 2.11522i −0.0462904 + 0.0801772i
\(697\) −14.4917 + 25.1003i −0.548912 + 0.950743i
\(698\) −0.978909 1.69552i −0.0370523 0.0641764i
\(699\) −12.5606 −0.475084
\(700\) 29.6992 12.4272i 1.12253 0.469702i
\(701\) −3.02432 −0.114227 −0.0571136 0.998368i \(-0.518190\pi\)
−0.0571136 + 0.998368i \(0.518190\pi\)
\(702\) 0.0803895 + 0.139239i 0.00303411 + 0.00525523i
\(703\) 2.97657 5.15557i 0.112263 0.194446i
\(704\) 2.35349 4.07636i 0.0887003 0.153633i
\(705\) 59.3519 + 102.800i 2.23532 + 3.87169i
\(706\) −16.3330 −0.614700
\(707\) 26.1543 + 19.9199i 0.983634 + 0.749163i
\(708\) −8.34518 −0.313631
\(709\) 22.7334 + 39.3755i 0.853772 + 1.47878i 0.877779 + 0.479065i \(0.159024\pi\)
−0.0240072 + 0.999712i \(0.507642\pi\)
\(710\) 12.9412 22.4147i 0.485673 0.841210i
\(711\) 6.61751 11.4619i 0.248176 0.429853i
\(712\) −6.63308 11.4888i −0.248585 0.430562i
\(713\) 2.10543 0.0788489
\(714\) 14.2255 + 10.8345i 0.532375 + 0.405472i
\(715\) 37.2630 1.39356
\(716\) −0.602699 1.04391i −0.0225239 0.0390126i
\(717\) 0.915519 1.58572i 0.0341907 0.0592200i
\(718\) 5.89004 10.2019i 0.219814 0.380730i
\(719\) −15.0720 26.1055i −0.562092 0.973572i −0.997314 0.0732489i \(-0.976663\pi\)
0.435221 0.900323i \(-0.356670\pi\)
\(720\) 12.2876 0.457934
\(721\) −39.4706 + 16.5158i −1.46996 + 0.615081i
\(722\) −2.67514 −0.0995585
\(723\) −11.0149 19.0784i −0.409650 0.709534i
\(724\) −3.47553 + 6.01979i −0.129167 + 0.223724i
\(725\) 6.08417 10.5381i 0.225960 0.391375i
\(726\) 13.6235 + 23.5965i 0.505614 + 0.875749i
\(727\) 45.6599 1.69343 0.846717 0.532044i \(-0.178576\pi\)
0.846717 + 0.532044i \(0.178576\pi\)
\(728\) 0.641780 5.01410i 0.0237860 0.185835i
\(729\) −26.3763 −0.976901
\(730\) 28.0160 + 48.5251i 1.03692 + 1.79599i
\(731\) −10.8544 + 18.8004i −0.401465 + 0.695357i
\(732\) 13.9454 24.1541i 0.515436 0.892761i
\(733\) 13.6729 + 23.6822i 0.505020 + 0.874721i 0.999983 + 0.00580686i \(0.00184839\pi\)
−0.494963 + 0.868914i \(0.664818\pi\)
\(734\) 35.6438 1.31564
\(735\) 68.5577 + 17.8424i 2.52879 + 0.658127i
\(736\) −2.17268 −0.0800862
\(737\) −5.35595 9.27677i −0.197289 0.341714i
\(738\) −15.5307 + 26.9000i −0.571694 + 0.990204i
\(739\) −24.9583 + 43.2291i −0.918106 + 1.59021i −0.115817 + 0.993271i \(0.536949\pi\)
−0.802289 + 0.596936i \(0.796385\pi\)
\(740\) 3.05250 + 5.28708i 0.112212 + 0.194357i
\(741\) 18.8548 0.692649
\(742\) 0.934086 7.29783i 0.0342914 0.267912i
\(743\) 28.6655 1.05164 0.525818 0.850597i \(-0.323759\pi\)
0.525818 + 0.850597i \(0.323759\pi\)
\(744\) −1.18342 2.04974i −0.0433863 0.0751472i
\(745\) 15.5344 26.9064i 0.569137 0.985774i
\(746\) −8.87414 + 15.3705i −0.324905 + 0.562753i
\(747\) 8.98565 + 15.5636i 0.328768 + 0.569443i
\(748\) −13.0249 −0.476236
\(749\) 25.9314 10.8506i 0.947512 0.396471i
\(750\) −72.5450 −2.64897
\(751\) 9.51580 + 16.4818i 0.347236 + 0.601431i 0.985757 0.168173i \(-0.0537868\pi\)
−0.638521 + 0.769604i \(0.720453\pi\)
\(752\) −5.86469 + 10.1579i −0.213863 + 0.370422i
\(753\) −35.5582 + 61.5887i −1.29581 + 2.24442i
\(754\) −0.955306 1.65464i −0.0347902 0.0602584i
\(755\) 39.0239 1.42023
\(756\) −0.177120 0.134899i −0.00644178 0.00490624i
\(757\) −9.39694 −0.341538 −0.170769 0.985311i \(-0.554625\pi\)
−0.170769 + 0.985311i \(0.554625\pi\)
\(758\) 7.61317 + 13.1864i 0.276523 + 0.478951i
\(759\) 12.4892 21.6319i 0.453328 0.785187i
\(760\) −8.37064 + 14.4984i −0.303635 + 0.525911i
\(761\) 5.37464 + 9.30916i 0.194831 + 0.337457i 0.946845 0.321690i \(-0.104251\pi\)
−0.752014 + 0.659147i \(0.770918\pi\)
\(762\) −13.3451 −0.483441
\(763\) −12.8368 9.77687i −0.464723 0.353946i
\(764\) −6.80847 −0.246322
\(765\) −17.0008 29.4463i −0.614667 1.06463i
\(766\) 7.90588 13.6934i 0.285651 0.494762i
\(767\) 3.26402 5.65345i 0.117857 0.204134i
\(768\) 1.22122 + 2.11522i 0.0440671 + 0.0763265i
\(769\) 39.3774 1.41998 0.709992 0.704209i \(-0.248698\pi\)
0.709992 + 0.704209i \(0.248698\pi\)
\(770\) −47.6014 + 19.9180i −1.71544 + 0.717796i
\(771\) 56.7321 2.04316
\(772\) 1.94832 + 3.37459i 0.0701216 + 0.121454i
\(773\) 9.52357 16.4953i 0.342539 0.593295i −0.642365 0.766399i \(-0.722046\pi\)
0.984903 + 0.173104i \(0.0553798\pi\)
\(774\) −11.6327 + 20.1484i −0.418127 + 0.724218i
\(775\) 5.89583 + 10.2119i 0.211784 + 0.366821i
\(776\) 16.8452 0.604708
\(777\) −1.20882 + 9.44424i −0.0433660 + 0.338810i
\(778\) −21.7172 −0.778598
\(779\) −21.1598 36.6499i −0.758129 1.31312i
\(780\) −9.66789 + 16.7453i −0.346166 + 0.599577i
\(781\) −14.7011 + 25.4631i −0.526048 + 0.911142i
\(782\) 3.00607 + 5.20666i 0.107497 + 0.186190i
\(783\) −0.0841506 −0.00300730
\(784\) 1.86032 + 6.74827i 0.0664402 + 0.241010i
\(785\) 73.8723 2.63662
\(786\) −16.3866 28.3824i −0.584490 1.01237i
\(787\) −13.2223 + 22.9017i −0.471325 + 0.816358i −0.999462 0.0328007i \(-0.989557\pi\)
0.528137 + 0.849159i \(0.322891\pi\)
\(788\) −7.78118 + 13.4774i −0.277193 + 0.480112i
\(789\) −25.0391 43.3691i −0.891417 1.54398i
\(790\) −18.4920 −0.657916
\(791\) −4.89999 + 38.2826i −0.174224 + 1.36117i
\(792\) −13.9587 −0.496002
\(793\) 10.9088 + 18.8946i 0.387383 + 0.670968i
\(794\) −0.630167 + 1.09148i −0.0223638 + 0.0387352i
\(795\) −14.0712 + 24.3721i −0.499055 + 0.864389i
\(796\) −12.2868 21.2813i −0.435493 0.754296i
\(797\) −42.8772 −1.51879 −0.759395 0.650630i \(-0.774505\pi\)
−0.759395 + 0.650630i \(0.774505\pi\)
\(798\) −24.0860 + 10.0784i −0.852634 + 0.356771i
\(799\) 32.4569 1.14824
\(800\) −6.08417 10.5381i −0.215108 0.372578i
\(801\) −19.6707 + 34.0707i −0.695030 + 1.20383i
\(802\) 0.955905 1.65568i 0.0337542 0.0584640i
\(803\) −31.8261 55.1244i −1.12312 1.94530i
\(804\) 5.55840 0.196030
\(805\) 18.9483 + 14.4316i 0.667840 + 0.508646i
\(806\) 1.85147 0.0652152
\(807\) −13.9161 24.1034i −0.489869 0.848479i
\(808\) 6.21303 10.7613i 0.218574 0.378580i
\(809\) 0.861958 1.49295i 0.0303048 0.0524895i −0.850475 0.526015i \(-0.823686\pi\)
0.880780 + 0.473526i \(0.157019\pi\)
\(810\) 18.8573 + 32.6618i 0.662577 + 1.14762i
\(811\) 7.23311 0.253989 0.126995 0.991903i \(-0.459467\pi\)
0.126995 + 0.991903i \(0.459467\pi\)
\(812\) 2.10480 + 1.60307i 0.0738638 + 0.0562568i
\(813\) −43.9031 −1.53975
\(814\) −3.46763 6.00611i −0.121540 0.210514i
\(815\) 22.5382 39.0373i 0.789479 1.36742i
\(816\) 3.37930 5.85312i 0.118299 0.204900i
\(817\) −15.8489 27.4511i −0.554482 0.960392i
\(818\) −3.01815 −0.105527
\(819\) −13.8290 + 5.78653i −0.483225 + 0.202198i
\(820\) 43.3992 1.51556
\(821\) −15.3520 26.5905i −0.535789 0.928014i −0.999125 0.0418313i \(-0.986681\pi\)
0.463335 0.886183i \(-0.346653\pi\)
\(822\) 20.8869 36.1771i 0.728513 1.26182i
\(823\) 4.79289 8.30153i 0.167070 0.289373i −0.770319 0.637659i \(-0.779903\pi\)
0.937388 + 0.348286i \(0.113236\pi\)
\(824\) 8.08592 + 14.0052i 0.281686 + 0.487895i
\(825\) 139.894 4.87047
\(826\) −1.14769 + 8.96666i −0.0399332 + 0.311990i
\(827\) −6.26986 −0.218025 −0.109012 0.994040i \(-0.534769\pi\)
−0.109012 + 0.994040i \(0.534769\pi\)
\(828\) 3.22160 + 5.57997i 0.111958 + 0.193917i
\(829\) −5.64488 + 9.77723i −0.196055 + 0.339577i −0.947246 0.320508i \(-0.896146\pi\)
0.751191 + 0.660085i \(0.229480\pi\)
\(830\) 12.5548 21.7455i 0.435783 0.754798i
\(831\) −2.54053 4.40034i −0.0881302 0.152646i
\(832\) −1.91061 −0.0662386
\(833\) 13.5978 13.7948i 0.471135 0.477963i
\(834\) 9.54292 0.330444
\(835\) −33.2152 57.5304i −1.14946 1.99092i
\(836\) 9.50903 16.4701i 0.328877 0.569631i
\(837\) 0.0407728 0.0706206i 0.00140931 0.00244100i
\(838\) −2.32252 4.02272i −0.0802302 0.138963i
\(839\) −44.0101 −1.51940 −0.759698 0.650276i \(-0.774653\pi\)
−0.759698 + 0.650276i \(0.774653\pi\)
\(840\) 3.39941 26.5589i 0.117291 0.916368i
\(841\) 1.00000 0.0344828
\(842\) 13.3101 + 23.0538i 0.458697 + 0.794486i
\(843\) 8.98504 15.5625i 0.309461 0.536003i
\(844\) −4.32823 + 7.49671i −0.148984 + 0.258048i
\(845\) 19.3698 + 33.5495i 0.666342 + 1.15414i
\(846\) 34.7840 1.19590
\(847\) 27.2274 11.3929i 0.935545 0.391463i
\(848\) −2.78082 −0.0954938
\(849\) −7.42569 12.8617i −0.254849 0.441411i
\(850\) −16.8358 + 29.1604i −0.577462 + 1.00019i
\(851\) −1.60062 + 2.77235i −0.0548685 + 0.0950351i
\(852\) −7.62841 13.2128i −0.261345 0.452663i
\(853\) 10.9272 0.374141 0.187070 0.982347i \(-0.440101\pi\)
0.187070 + 0.982347i \(0.440101\pi\)
\(854\) −24.0350 18.3058i −0.822462 0.626410i
\(855\) 49.6471 1.69789
\(856\) −5.31229 9.20116i −0.181570 0.314489i
\(857\) −14.6377 + 25.3533i −0.500015 + 0.866052i 0.499985 + 0.866034i \(0.333339\pi\)
−1.00000 1.75014e-5i \(0.999994\pi\)
\(858\) 10.9827 19.0226i 0.374943 0.649421i
\(859\) 21.6611 + 37.5181i 0.739067 + 1.28010i 0.952916 + 0.303235i \(0.0980666\pi\)
−0.213849 + 0.976867i \(0.568600\pi\)
\(860\) 32.5064 1.10846
\(861\) 53.8459 + 41.0105i 1.83506 + 1.39763i
\(862\) −9.63869 −0.328295
\(863\) 21.9190 + 37.9649i 0.746133 + 1.29234i 0.949664 + 0.313271i \(0.101425\pi\)
−0.203531 + 0.979069i \(0.565242\pi\)
\(864\) −0.0420753 + 0.0728765i −0.00143143 + 0.00247931i
\(865\) 12.8215 22.2075i 0.435944 0.755077i
\(866\) 1.58233 + 2.74068i 0.0537698 + 0.0931320i
\(867\) 22.8196 0.774994
\(868\) −2.36514 + 0.989656i −0.0802782 + 0.0335911i
\(869\) 21.0069 0.712609
\(870\) −5.06010 8.76435i −0.171553 0.297139i
\(871\) −2.17404 + 3.76555i −0.0736645 + 0.127591i
\(872\) −3.04942 + 5.28175i −0.103266 + 0.178862i
\(873\) −24.9776 43.2625i −0.845364 1.46421i
\(874\) −8.77852 −0.296938
\(875\) −9.97691 + 77.9476i −0.337281 + 2.63511i
\(876\) 33.0291 1.11595
\(877\) −14.7536 25.5540i −0.498194 0.862898i 0.501804 0.864982i \(-0.332670\pi\)
−0.999998 + 0.00208396i \(0.999337\pi\)
\(878\) −6.94499 + 12.0291i −0.234382 + 0.405962i
\(879\) 16.7502 29.0122i 0.564969 0.978556i
\(880\) 9.75159 + 16.8903i 0.328726 + 0.569370i
\(881\) −13.1060 −0.441554 −0.220777 0.975324i \(-0.570859\pi\)
−0.220777 + 0.975324i \(0.570859\pi\)
\(882\) 14.5727 14.7839i 0.490690 0.497800i
\(883\) −7.44435 −0.250522 −0.125261 0.992124i \(-0.539977\pi\)
−0.125261 + 0.992124i \(0.539977\pi\)
\(884\) 2.64347 + 4.57862i 0.0889095 + 0.153996i
\(885\) 17.2890 29.9454i 0.581163 1.00660i
\(886\) −10.1854 + 17.6416i −0.342185 + 0.592682i
\(887\) −19.3417 33.5008i −0.649430 1.12485i −0.983259 0.182212i \(-0.941674\pi\)
0.333830 0.942633i \(-0.391659\pi\)
\(888\) 3.59871 0.120765
\(889\) −1.83531 + 14.3389i −0.0615544 + 0.480912i
\(890\) 54.9679 1.84253
\(891\) −21.4218 37.1037i −0.717658 1.24302i
\(892\) 5.45953 9.45618i 0.182798 0.316616i
\(893\) −23.6957 + 41.0422i −0.792947 + 1.37342i
\(894\) −9.15706 15.8605i −0.306258 0.530454i
\(895\) 4.99453 0.166949
\(896\) 2.44070 1.02127i 0.0815380 0.0341182i
\(897\) −10.1390 −0.338531
\(898\) −16.5721 28.7037i −0.553018 0.957856i
\(899\) −0.484522 + 0.839217i −0.0161597 + 0.0279895i
\(900\) −18.0429 + 31.2512i −0.601429 + 1.04171i
\(901\) 3.84747 + 6.66401i 0.128178 + 0.222010i
\(902\) −49.3014 −1.64156
\(903\) 40.3310 + 30.7172i 1.34213 + 1.02221i
\(904\) 14.5875 0.485173
\(905\) −14.4007 24.9428i −0.478697 0.829127i
\(906\) 11.5017 19.9215i 0.382118 0.661848i
\(907\) −1.21313 + 2.10120i −0.0402812 + 0.0697691i −0.885463 0.464710i \(-0.846159\pi\)
0.845182 + 0.534479i \(0.179492\pi\)
\(908\) 5.24754 + 9.08901i 0.174146 + 0.301629i
\(909\) −36.8500 −1.22224
\(910\) 16.6627 + 12.6908i 0.552364 + 0.420696i
\(911\) −1.86661 −0.0618435 −0.0309218 0.999522i \(-0.509844\pi\)
−0.0309218 + 0.999522i \(0.509844\pi\)
\(912\) 4.93423 + 8.54635i 0.163389 + 0.282998i
\(913\) −14.2622 + 24.7028i −0.472010 + 0.817545i
\(914\) 9.10435 15.7692i 0.301145 0.521599i
\(915\) 57.7822 + 100.082i 1.91022 + 3.30860i
\(916\) −7.51525 −0.248311
\(917\) −32.7497 + 13.7036i −1.08149 + 0.452532i
\(918\) 0.232857 0.00768542
\(919\) −13.7029 23.7340i −0.452015 0.782914i 0.546496 0.837462i \(-0.315961\pi\)
−0.998511 + 0.0545482i \(0.982628\pi\)
\(920\) 4.50123 7.79635i 0.148401 0.257038i
\(921\) 9.33618 16.1707i 0.307638 0.532844i
\(922\) 1.76242 + 3.05260i 0.0580422 + 0.100532i
\(923\) 11.9347 0.392836
\(924\) −3.86172 + 30.1708i −0.127041 + 0.992547i
\(925\) −17.9289 −0.589497
\(926\) −5.38263 9.32299i −0.176884 0.306372i
\(927\) 23.9792 41.5331i 0.787579 1.36413i
\(928\) 0.500000 0.866025i 0.0164133 0.0284287i
\(929\) −21.9798 38.0701i −0.721133 1.24904i −0.960546 0.278121i \(-0.910288\pi\)
0.239413 0.970918i \(-0.423045\pi\)
\(930\) 9.80692 0.321582
\(931\) 7.51646 + 27.2657i 0.246342 + 0.893599i
\(932\) 5.14262 0.168452
\(933\) 29.8286 + 51.6646i 0.976544 + 1.69142i
\(934\) −6.00994 + 10.4095i −0.196651 + 0.340610i
\(935\) 26.9841 46.7378i 0.882473 1.52849i
\(936\) 2.83300 + 4.90691i 0.0925997 + 0.160387i
\(937\) −29.9446 −0.978246 −0.489123 0.872215i \(-0.662683\pi\)
−0.489123 + 0.872215i \(0.662683\pi\)
\(938\) 0.764431 5.97235i 0.0249596 0.195004i
\(939\) 44.6101 1.45579
\(940\) −24.3002 42.0891i −0.792584 1.37280i
\(941\) −10.7861 + 18.6821i −0.351618 + 0.609020i −0.986533 0.163562i \(-0.947702\pi\)
0.634915 + 0.772582i \(0.281035\pi\)
\(942\) 21.7727 37.7115i 0.709394 1.22871i
\(943\) 11.3785 + 19.7081i 0.370534 + 0.641784i
\(944\) 3.41673 0.111205
\(945\) 0.851011 0.356092i 0.0276834 0.0115837i
\(946\) −36.9271 −1.20061
\(947\) −2.19606 3.80369i −0.0713624 0.123603i 0.828136 0.560527i \(-0.189401\pi\)
−0.899499 + 0.436924i \(0.856068\pi\)
\(948\) −5.45023 + 9.44008i −0.177015 + 0.306600i
\(949\) −12.9186 + 22.3756i −0.419354 + 0.726343i
\(950\) −24.5825 42.5781i −0.797561 1.38142i
\(951\) 25.4545 0.825418
\(952\) −5.82427 4.43593i −0.188766 0.143769i
\(953\) 32.9052 1.06591 0.532953 0.846145i \(-0.321082\pi\)
0.532953 + 0.846145i \(0.321082\pi\)
\(954\) 4.12333 + 7.14181i 0.133498 + 0.231225i
\(955\) 14.1053 24.4312i 0.456438 0.790574i
\(956\) −0.374837 + 0.649236i −0.0121231 + 0.0209978i
\(957\) 5.74826 + 9.95629i 0.185815 + 0.321841i
\(958\) 8.29202 0.267903
\(959\) −35.9988 27.4177i −1.16246 0.885363i
\(960\) −10.1202 −0.326628
\(961\) 15.0305 + 26.0335i 0.484854 + 0.839792i
\(962\) −1.40755 + 2.43795i −0.0453812 + 0.0786026i
\(963\) −15.7538 + 27.2865i −0.507660 + 0.879294i
\(964\) 4.50979 + 7.81119i 0.145251 + 0.251582i
\(965\) −16.1456 −0.519745
\(966\) 12.9520 5.41954i 0.416723 0.174371i
\(967\) 4.50365 0.144827 0.0724137 0.997375i \(-0.476930\pi\)
0.0724137 + 0.997375i \(0.476930\pi\)
\(968\) −5.57779 9.66102i −0.179277 0.310517i
\(969\) 13.6537 23.6490i 0.438621 0.759714i
\(970\) −34.8988 + 60.4465i −1.12053 + 1.94082i
\(971\) −15.2094 26.3435i −0.488094 0.845403i 0.511813 0.859097i \(-0.328974\pi\)
−0.999906 + 0.0136941i \(0.995641\pi\)
\(972\) 21.9791 0.704981
\(973\) 1.31241 10.2536i 0.0420740 0.328715i
\(974\) 7.89345 0.252923
\(975\) −28.3922 49.1767i −0.909278 1.57491i
\(976\) −5.70959 + 9.88930i −0.182760 + 0.316549i
\(977\) −18.7601 + 32.4935i −0.600189 + 1.03956i 0.392603 + 0.919708i \(0.371575\pi\)
−0.992792 + 0.119850i \(0.961759\pi\)
\(978\) −13.2856 23.0113i −0.424826 0.735820i
\(979\) −62.4434 −1.99570
\(980\) −28.0693 7.30513i −0.896640 0.233354i
\(981\) 18.0864 0.577454
\(982\) 18.8625 + 32.6708i 0.601926 + 1.04257i
\(983\) −21.7439 + 37.6615i −0.693523 + 1.20122i 0.277153 + 0.960826i \(0.410609\pi\)
−0.970676 + 0.240391i \(0.922724\pi\)
\(984\) 12.7912 22.1551i 0.407770 0.706278i
\(985\) −32.2411 55.8432i −1.02729 1.77931i
\(986\) −2.76714 −0.0881238
\(987\) 9.62308 75.1832i 0.306306 2.39311i
\(988\) −7.71964 −0.245595
\(989\) 8.52258 + 14.7615i 0.271002 + 0.469390i
\(990\) 28.9188 50.0888i 0.919100 1.59193i
\(991\) 27.7099 47.9949i 0.880233 1.52461i 0.0291517 0.999575i \(-0.490719\pi\)
0.851081 0.525034i \(-0.175947\pi\)
\(992\) 0.484522 + 0.839217i 0.0153836 + 0.0266452i
\(993\) −11.4392 −0.363013
\(994\) −15.2459 + 6.37940i −0.483571 + 0.202342i
\(995\) 101.820 3.22790
\(996\) −7.40065 12.8183i −0.234499 0.406164i
\(997\) 11.9445 20.6884i 0.378285 0.655209i −0.612528 0.790449i \(-0.709847\pi\)
0.990813 + 0.135240i \(0.0431805\pi\)
\(998\) 4.23971 7.34340i 0.134206 0.232451i
\(999\) 0.0619938 + 0.107376i 0.00196140 + 0.00339724i
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 406.2.e.a.291.5 yes 10
7.2 even 3 inner 406.2.e.a.233.5 10
7.3 odd 6 2842.2.a.x.1.5 5
7.4 even 3 2842.2.a.z.1.1 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
406.2.e.a.233.5 10 7.2 even 3 inner
406.2.e.a.291.5 yes 10 1.1 even 1 trivial
2842.2.a.x.1.5 5 7.3 odd 6
2842.2.a.z.1.1 5 7.4 even 3