Properties

Label 406.2.e.a.233.4
Level $406$
Weight $2$
Character 406.233
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 233.4
Root \(2.31940 - 0.319028i\) of defining polynomial
Character \(\chi\) \(=\) 406.233
Dual form 406.2.e.a.291.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.357289 + 0.618843i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.116584 + 0.201930i) q^{5} -0.714579 q^{6} +(2.36799 + 1.18009i) q^{7} +1.00000 q^{8} +(1.24469 - 2.15586i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.357289 + 0.618843i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.116584 + 0.201930i) q^{5} -0.714579 q^{6} +(2.36799 + 1.18009i) q^{7} +1.00000 q^{8} +(1.24469 - 2.15586i) q^{9} +(-0.116584 - 0.201930i) q^{10} +(-0.146694 - 0.254082i) q^{11} +(0.357289 - 0.618843i) q^{12} +4.15740 q^{13} +(-2.20598 + 1.46070i) q^{14} -0.166617 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.304717 - 0.527786i) q^{17} +(1.24469 + 2.15586i) q^{18} +(-3.33870 + 5.78280i) q^{19} +0.233169 q^{20} +(0.115767 + 1.88705i) q^{21} +0.293388 q^{22} +(0.743871 - 1.28842i) q^{23} +(0.357289 + 0.618843i) q^{24} +(2.47282 + 4.28304i) q^{25} +(-2.07870 + 3.60041i) q^{26} +3.92259 q^{27} +(-0.162007 - 2.64079i) q^{28} -1.00000 q^{29} +(0.0833087 - 0.144295i) q^{30} +(0.675875 + 1.17065i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.104824 - 0.181561i) q^{33} +0.609435 q^{34} +(-0.514366 + 0.340588i) q^{35} -2.48938 q^{36} +(-0.318586 + 0.551807i) q^{37} +(-3.33870 - 5.78280i) q^{38} +(1.48539 + 2.57278i) q^{39} +(-0.116584 + 0.201930i) q^{40} +3.31605 q^{41} +(-1.69212 - 0.843268i) q^{42} -3.29502 q^{43} +(-0.146694 + 0.254082i) q^{44} +(0.290222 + 0.502680i) q^{45} +(0.743871 + 1.28842i) q^{46} +(-1.09046 + 1.88873i) q^{47} -0.714579 q^{48} +(4.21477 + 5.58889i) q^{49} -4.94563 q^{50} +(0.217745 - 0.377145i) q^{51} +(-2.07870 - 3.60041i) q^{52} +(-5.99610 - 10.3855i) q^{53} +(-1.96130 + 3.39706i) q^{54} +0.0684089 q^{55} +(2.36799 + 1.18009i) q^{56} -4.77153 q^{57} +(0.500000 - 0.866025i) q^{58} +(-2.15057 - 3.72489i) q^{59} +(0.0833087 + 0.144295i) q^{60} +(-1.82401 + 3.15928i) q^{61} -1.35175 q^{62} +(5.49153 - 3.63622i) q^{63} +1.00000 q^{64} +(-0.484687 + 0.839503i) q^{65} +(0.104824 + 0.181561i) q^{66} +(-2.47824 - 4.29245i) q^{67} +(-0.304717 + 0.527786i) q^{68} +1.06311 q^{69} +(-0.0377749 - 0.615749i) q^{70} +4.21106 q^{71} +(1.24469 - 2.15586i) q^{72} +(-2.92149 - 5.06017i) q^{73} +(-0.318586 - 0.551807i) q^{74} +(-1.76702 + 3.06057i) q^{75} +6.67740 q^{76} +(-0.0475309 - 0.774776i) q^{77} -2.97079 q^{78} +(-1.05339 + 1.82452i) q^{79} +(-0.116584 - 0.201930i) q^{80} +(-2.33257 - 4.04012i) q^{81} +(-1.65802 + 2.87178i) q^{82} +6.73621 q^{83} +(1.57635 - 1.04378i) q^{84} +0.142101 q^{85} +(1.64751 - 2.85357i) q^{86} +(-0.357289 - 0.618843i) q^{87} +(-0.146694 - 0.254082i) q^{88} +(6.31233 - 10.9333i) q^{89} -0.580445 q^{90} +(9.84468 + 4.90611i) q^{91} -1.48774 q^{92} +(-0.482966 + 0.836522i) q^{93} +(-1.09046 - 1.88873i) q^{94} +(-0.778480 - 1.34837i) q^{95} +(0.357289 - 0.618843i) q^{96} +5.70498 q^{97} +(-6.94751 + 0.855651i) q^{98} -0.730354 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 \(\left(\mathbb{Z}/406\mathbb{Z}\right)^\times\).

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

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
\(3\) 0.357289 + 0.618843i 0.206281 + 0.357289i 0.950540 0.310602i \(-0.100531\pi\)
−0.744259 + 0.667891i \(0.767197\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −0.116584 + 0.201930i −0.0521381 + 0.0903058i −0.890917 0.454167i \(-0.849937\pi\)
0.838778 + 0.544473i \(0.183270\pi\)
\(6\) −0.714579 −0.291726
\(7\) 2.36799 + 1.18009i 0.895017 + 0.446033i
\(8\) 1.00000 0.353553
\(9\) 1.24469 2.15586i 0.414896 0.718621i
\(10\) −0.116584 0.201930i −0.0368672 0.0638559i
\(11\) −0.146694 0.254082i −0.0442299 0.0766085i 0.843063 0.537815i \(-0.180750\pi\)
−0.887293 + 0.461206i \(0.847417\pi\)
\(12\) 0.357289 0.618843i 0.103141 0.178645i
\(13\) 4.15740 1.15305 0.576527 0.817078i \(-0.304408\pi\)
0.576527 + 0.817078i \(0.304408\pi\)
\(14\) −2.20598 + 1.46070i −0.589574 + 0.390387i
\(15\) −0.166617 −0.0430204
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −0.304717 0.527786i −0.0739048 0.128007i 0.826705 0.562636i \(-0.190213\pi\)
−0.900610 + 0.434629i \(0.856879\pi\)
\(18\) 1.24469 + 2.15586i 0.293376 + 0.508142i
\(19\) −3.33870 + 5.78280i −0.765950 + 1.32666i 0.173793 + 0.984782i \(0.444398\pi\)
−0.939743 + 0.341882i \(0.888936\pi\)
\(20\) 0.233169 0.0521381
\(21\) 0.115767 + 1.88705i 0.0252624 + 0.411788i
\(22\) 0.293388 0.0625506
\(23\) 0.743871 1.28842i 0.155108 0.268655i −0.777990 0.628276i \(-0.783761\pi\)
0.933098 + 0.359621i \(0.117094\pi\)
\(24\) 0.357289 + 0.618843i 0.0729314 + 0.126321i
\(25\) 2.47282 + 4.28304i 0.494563 + 0.856609i
\(26\) −2.07870 + 3.60041i −0.407666 + 0.706099i
\(27\) 3.92259 0.754903
\(28\) −0.162007 2.64079i −0.0306164 0.499062i
\(29\) −1.00000 −0.185695
\(30\) 0.0833087 0.144295i 0.0152100 0.0263445i
\(31\) 0.675875 + 1.17065i 0.121391 + 0.210255i 0.920316 0.391175i \(-0.127931\pi\)
−0.798926 + 0.601430i \(0.794598\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0.104824 0.181561i 0.0182476 0.0316058i
\(34\) 0.609435 0.104517
\(35\) −0.514366 + 0.340588i −0.0869438 + 0.0575699i
\(36\) −2.48938 −0.414896
\(37\) −0.318586 + 0.551807i −0.0523752 + 0.0907164i −0.891024 0.453956i \(-0.850012\pi\)
0.838649 + 0.544672i \(0.183346\pi\)
\(38\) −3.33870 5.78280i −0.541609 0.938094i
\(39\) 1.48539 + 2.57278i 0.237853 + 0.411974i
\(40\) −0.116584 + 0.201930i −0.0184336 + 0.0319279i
\(41\) 3.31605 0.517880 0.258940 0.965893i \(-0.416627\pi\)
0.258940 + 0.965893i \(0.416627\pi\)
\(42\) −1.69212 0.843268i −0.261099 0.130119i
\(43\) −3.29502 −0.502486 −0.251243 0.967924i \(-0.580839\pi\)
−0.251243 + 0.967924i \(0.580839\pi\)
\(44\) −0.146694 + 0.254082i −0.0221150 + 0.0383042i
\(45\) 0.290222 + 0.502680i 0.0432638 + 0.0749351i
\(46\) 0.743871 + 1.28842i 0.109678 + 0.189967i
\(47\) −1.09046 + 1.88873i −0.159060 + 0.275499i −0.934530 0.355885i \(-0.884180\pi\)
0.775470 + 0.631384i \(0.217513\pi\)
\(48\) −0.714579 −0.103141
\(49\) 4.21477 + 5.58889i 0.602110 + 0.798413i
\(50\) −4.94563 −0.699418
\(51\) 0.217745 0.377145i 0.0304903 0.0528108i
\(52\) −2.07870 3.60041i −0.288264 0.499287i
\(53\) −5.99610 10.3855i −0.823627 1.42656i −0.902964 0.429716i \(-0.858614\pi\)
0.0793369 0.996848i \(-0.474720\pi\)
\(54\) −1.96130 + 3.39706i −0.266899 + 0.462282i
\(55\) 0.0684089 0.00922426
\(56\) 2.36799 + 1.18009i 0.316436 + 0.157696i
\(57\) −4.77153 −0.632004
\(58\) 0.500000 0.866025i 0.0656532 0.113715i
\(59\) −2.15057 3.72489i −0.279980 0.484939i 0.691400 0.722473i \(-0.256994\pi\)
−0.971379 + 0.237533i \(0.923661\pi\)
\(60\) 0.0833087 + 0.144295i 0.0107551 + 0.0186284i
\(61\) −1.82401 + 3.15928i −0.233541 + 0.404505i −0.958848 0.283921i \(-0.908365\pi\)
0.725307 + 0.688426i \(0.241698\pi\)
\(62\) −1.35175 −0.171672
\(63\) 5.49153 3.63622i 0.691868 0.458121i
\(64\) 1.00000 0.125000
\(65\) −0.484687 + 0.839503i −0.0601180 + 0.104128i
\(66\) 0.104824 + 0.181561i 0.0129030 + 0.0223487i
\(67\) −2.47824 4.29245i −0.302766 0.524406i 0.673996 0.738735i \(-0.264577\pi\)
−0.976761 + 0.214330i \(0.931243\pi\)
\(68\) −0.304717 + 0.527786i −0.0369524 + 0.0640035i
\(69\) 1.06311 0.127983
\(70\) −0.0377749 0.615749i −0.00451497 0.0735960i
\(71\) 4.21106 0.499761 0.249881 0.968277i \(-0.419609\pi\)
0.249881 + 0.968277i \(0.419609\pi\)
\(72\) 1.24469 2.15586i 0.146688 0.254071i
\(73\) −2.92149 5.06017i −0.341935 0.592248i 0.642857 0.765986i \(-0.277749\pi\)
−0.984792 + 0.173738i \(0.944416\pi\)
\(74\) −0.318586 0.551807i −0.0370348 0.0641462i
\(75\) −1.76702 + 3.06057i −0.204038 + 0.353404i
\(76\) 6.67740 0.765950
\(77\) −0.0475309 0.774776i −0.00541665 0.0882939i
\(78\) −2.97079 −0.336375
\(79\) −1.05339 + 1.82452i −0.118516 + 0.205275i −0.919180 0.393839i \(-0.871147\pi\)
0.800664 + 0.599114i \(0.204480\pi\)
\(80\) −0.116584 0.201930i −0.0130345 0.0225765i
\(81\) −2.33257 4.04012i −0.259174 0.448902i
\(82\) −1.65802 + 2.87178i −0.183098 + 0.317135i
\(83\) 6.73621 0.739395 0.369697 0.929152i \(-0.379461\pi\)
0.369697 + 0.929152i \(0.379461\pi\)
\(84\) 1.57635 1.04378i 0.171994 0.113886i
\(85\) 0.142101 0.0154130
\(86\) 1.64751 2.85357i 0.177656 0.307709i
\(87\) −0.357289 0.618843i −0.0383054 0.0663470i
\(88\) −0.146694 0.254082i −0.0156376 0.0270852i
\(89\) 6.31233 10.9333i 0.669106 1.15893i −0.309048 0.951046i \(-0.600011\pi\)
0.978154 0.207879i \(-0.0666561\pi\)
\(90\) −0.580445 −0.0611842
\(91\) 9.84468 + 4.90611i 1.03200 + 0.514300i
\(92\) −1.48774 −0.155108
\(93\) −0.482966 + 0.836522i −0.0500812 + 0.0867433i
\(94\) −1.09046 1.88873i −0.112472 0.194807i
\(95\) −0.778480 1.34837i −0.0798704 0.138340i
\(96\) 0.357289 0.618843i 0.0364657 0.0631604i
\(97\) 5.70498 0.579253 0.289626 0.957140i \(-0.406469\pi\)
0.289626 + 0.957140i \(0.406469\pi\)
\(98\) −6.94751 + 0.855651i −0.701804 + 0.0864338i
\(99\) −0.730354 −0.0734033
\(100\) 2.47282 4.28304i 0.247282 0.428304i
\(101\) −7.86693 13.6259i −0.782789 1.35583i −0.930311 0.366772i \(-0.880463\pi\)
0.147522 0.989059i \(-0.452870\pi\)
\(102\) 0.217745 + 0.377145i 0.0215599 + 0.0373429i
\(103\) 2.44775 4.23962i 0.241184 0.417742i −0.719868 0.694111i \(-0.755798\pi\)
0.961052 + 0.276369i \(0.0891310\pi\)
\(104\) 4.15740 0.407666
\(105\) −0.394549 0.196624i −0.0385040 0.0191885i
\(106\) 11.9922 1.16478
\(107\) −5.61573 + 9.72674i −0.542894 + 0.940319i 0.455843 + 0.890060i \(0.349338\pi\)
−0.998736 + 0.0502589i \(0.983995\pi\)
\(108\) −1.96130 3.39706i −0.188726 0.326883i
\(109\) −7.59327 13.1519i −0.727304 1.25973i −0.958019 0.286705i \(-0.907440\pi\)
0.230715 0.973021i \(-0.425893\pi\)
\(110\) −0.0342045 + 0.0592439i −0.00326127 + 0.00564868i
\(111\) −0.455309 −0.0432160
\(112\) −2.20598 + 1.46070i −0.208446 + 0.138023i
\(113\) −10.2976 −0.968717 −0.484359 0.874870i \(-0.660947\pi\)
−0.484359 + 0.874870i \(0.660947\pi\)
\(114\) 2.38576 4.13226i 0.223447 0.387022i
\(115\) 0.173447 + 0.300420i 0.0161741 + 0.0280143i
\(116\) 0.500000 + 0.866025i 0.0464238 + 0.0804084i
\(117\) 5.17466 8.96278i 0.478398 0.828609i
\(118\) 4.30113 0.395951
\(119\) −0.0987327 1.60939i −0.00905081 0.147532i
\(120\) −0.166617 −0.0152100
\(121\) 5.45696 9.45173i 0.496087 0.859249i
\(122\) −1.82401 3.15928i −0.165138 0.286028i
\(123\) 1.18479 + 2.05211i 0.106829 + 0.185033i
\(124\) 0.675875 1.17065i 0.0606954 0.105127i
\(125\) −2.31901 −0.207419
\(126\) 0.403296 + 6.57391i 0.0359285 + 0.585651i
\(127\) −15.3053 −1.35813 −0.679065 0.734078i \(-0.737615\pi\)
−0.679065 + 0.734078i \(0.737615\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −1.17728 2.03910i −0.103653 0.179533i
\(130\) −0.484687 0.839503i −0.0425099 0.0736293i
\(131\) −6.10878 + 10.5807i −0.533726 + 0.924441i 0.465498 + 0.885049i \(0.345875\pi\)
−0.999224 + 0.0393918i \(0.987458\pi\)
\(132\) −0.209649 −0.0182476
\(133\) −14.7302 + 9.75365i −1.27727 + 0.845748i
\(134\) 4.95649 0.428175
\(135\) −0.457313 + 0.792089i −0.0393592 + 0.0681722i
\(136\) −0.304717 0.527786i −0.0261293 0.0452573i
\(137\) −8.91455 15.4405i −0.761622 1.31917i −0.942014 0.335573i \(-0.891070\pi\)
0.180393 0.983595i \(-0.442263\pi\)
\(138\) −0.531554 + 0.920679i −0.0452489 + 0.0783734i
\(139\) 7.99852 0.678426 0.339213 0.940710i \(-0.389839\pi\)
0.339213 + 0.940710i \(0.389839\pi\)
\(140\) 0.552141 + 0.275160i 0.0466645 + 0.0232553i
\(141\) −1.55844 −0.131244
\(142\) −2.10553 + 3.64689i −0.176692 + 0.306040i
\(143\) −0.609865 1.05632i −0.0509995 0.0883338i
\(144\) 1.24469 + 2.15586i 0.103724 + 0.179655i
\(145\) 0.116584 0.201930i 0.00968180 0.0167694i
\(146\) 5.84298 0.483569
\(147\) −1.95276 + 4.60513i −0.161061 + 0.379825i
\(148\) 0.637171 0.0523752
\(149\) −3.90799 + 6.76883i −0.320155 + 0.554524i −0.980520 0.196421i \(-0.937068\pi\)
0.660365 + 0.750945i \(0.270402\pi\)
\(150\) −1.76702 3.06057i −0.144277 0.249895i
\(151\) 8.10878 + 14.0448i 0.659883 + 1.14295i 0.980646 + 0.195791i \(0.0627274\pi\)
−0.320763 + 0.947160i \(0.603939\pi\)
\(152\) −3.33870 + 5.78280i −0.270804 + 0.469047i
\(153\) −1.51711 −0.122651
\(154\) 0.694741 + 0.346225i 0.0559838 + 0.0278996i
\(155\) −0.315186 −0.0253163
\(156\) 1.48539 2.57278i 0.118927 0.205987i
\(157\) 11.8227 + 20.4776i 0.943556 + 1.63429i 0.758616 + 0.651538i \(0.225876\pi\)
0.184940 + 0.982750i \(0.440791\pi\)
\(158\) −1.05339 1.82452i −0.0838032 0.145151i
\(159\) 4.28468 7.42129i 0.339797 0.588546i
\(160\) 0.233169 0.0184336
\(161\) 3.28194 2.17314i 0.258653 0.171267i
\(162\) 4.66513 0.366527
\(163\) 6.80624 11.7888i 0.533106 0.923367i −0.466146 0.884708i \(-0.654358\pi\)
0.999252 0.0386591i \(-0.0123086\pi\)
\(164\) −1.65802 2.87178i −0.129470 0.224248i
\(165\) 0.0244418 + 0.0423344i 0.00190279 + 0.00329573i
\(166\) −3.36810 + 5.83373i −0.261415 + 0.452785i
\(167\) −3.59710 −0.278352 −0.139176 0.990268i \(-0.544445\pi\)
−0.139176 + 0.990268i \(0.544445\pi\)
\(168\) 0.115767 + 1.88705i 0.00893159 + 0.145589i
\(169\) 4.28394 0.329534
\(170\) −0.0710506 + 0.123063i −0.00544933 + 0.00943851i
\(171\) 8.31128 + 14.3956i 0.635580 + 1.10086i
\(172\) 1.64751 + 2.85357i 0.125622 + 0.217583i
\(173\) −6.19782 + 10.7349i −0.471212 + 0.816162i −0.999458 0.0329288i \(-0.989517\pi\)
0.528246 + 0.849091i \(0.322850\pi\)
\(174\) 0.714579 0.0541721
\(175\) 0.801226 + 13.0604i 0.0605670 + 0.987270i
\(176\) 0.293388 0.0221150
\(177\) 1.53675 2.66173i 0.115509 0.200068i
\(178\) 6.31233 + 10.9333i 0.473129 + 0.819484i
\(179\) −4.79172 8.29950i −0.358150 0.620334i 0.629502 0.776999i \(-0.283259\pi\)
−0.987652 + 0.156665i \(0.949926\pi\)
\(180\) 0.290222 0.502680i 0.0216319 0.0374675i
\(181\) 0.148655 0.0110495 0.00552473 0.999985i \(-0.498241\pi\)
0.00552473 + 0.999985i \(0.498241\pi\)
\(182\) −9.17115 + 6.07269i −0.679811 + 0.450138i
\(183\) −2.60680 −0.192700
\(184\) 0.743871 1.28842i 0.0548389 0.0949837i
\(185\) −0.0742842 0.128664i −0.00546148 0.00945956i
\(186\) −0.482966 0.836522i −0.0354128 0.0613367i
\(187\) −0.0894005 + 0.154846i −0.00653761 + 0.0113235i
\(188\) 2.18092 0.159060
\(189\) 9.28867 + 4.62902i 0.675651 + 0.336711i
\(190\) 1.55696 0.112954
\(191\) −5.14154 + 8.90541i −0.372029 + 0.644373i −0.989878 0.141924i \(-0.954671\pi\)
0.617849 + 0.786297i \(0.288004\pi\)
\(192\) 0.357289 + 0.618843i 0.0257851 + 0.0446612i
\(193\) −6.23407 10.7977i −0.448738 0.777237i 0.549566 0.835450i \(-0.314793\pi\)
−0.998304 + 0.0582133i \(0.981460\pi\)
\(194\) −2.85249 + 4.94065i −0.204797 + 0.354718i
\(195\) −0.692694 −0.0496049
\(196\) 2.73274 6.44454i 0.195196 0.460325i
\(197\) −19.0312 −1.35591 −0.677957 0.735101i \(-0.737135\pi\)
−0.677957 + 0.735101i \(0.737135\pi\)
\(198\) 0.365177 0.632505i 0.0259520 0.0449502i
\(199\) 5.30417 + 9.18709i 0.376003 + 0.651256i 0.990477 0.137681i \(-0.0439650\pi\)
−0.614474 + 0.788937i \(0.710632\pi\)
\(200\) 2.47282 + 4.28304i 0.174855 + 0.302857i
\(201\) 1.77090 3.06729i 0.124910 0.216350i
\(202\) 15.7339 1.10703
\(203\) −2.36799 1.18009i −0.166200 0.0828262i
\(204\) −0.435489 −0.0304903
\(205\) −0.386599 + 0.669609i −0.0270012 + 0.0467675i
\(206\) 2.44775 + 4.23962i 0.170543 + 0.295389i
\(207\) −1.85178 3.20737i −0.128707 0.222928i
\(208\) −2.07870 + 3.60041i −0.144132 + 0.249644i
\(209\) 1.95907 0.135512
\(210\) 0.367555 0.243377i 0.0253637 0.0167946i
\(211\) −8.69020 −0.598258 −0.299129 0.954213i \(-0.596696\pi\)
−0.299129 + 0.954213i \(0.596696\pi\)
\(212\) −5.99610 + 10.3855i −0.411814 + 0.713282i
\(213\) 1.50457 + 2.60599i 0.103091 + 0.178559i
\(214\) −5.61573 9.72674i −0.383884 0.664906i
\(215\) 0.384148 0.665364i 0.0261987 0.0453774i
\(216\) 3.92259 0.266899
\(217\) 0.218993 + 3.56968i 0.0148662 + 0.242326i
\(218\) 15.1865 1.02856
\(219\) 2.08764 3.61589i 0.141069 0.244339i
\(220\) −0.0342045 0.0592439i −0.00230606 0.00399422i
\(221\) −1.26683 2.19422i −0.0852163 0.147599i
\(222\) 0.227655 0.394309i 0.0152792 0.0264643i
\(223\) 9.99383 0.669236 0.334618 0.942354i \(-0.391393\pi\)
0.334618 + 0.942354i \(0.391393\pi\)
\(224\) −0.162007 2.64079i −0.0108245 0.176445i
\(225\) 12.3115 0.820770
\(226\) 5.14880 8.91799i 0.342493 0.593216i
\(227\) 12.6545 + 21.9183i 0.839910 + 1.45477i 0.889969 + 0.456020i \(0.150726\pi\)
−0.0500595 + 0.998746i \(0.515941\pi\)
\(228\) 2.38576 + 4.13226i 0.158001 + 0.273666i
\(229\) −9.23923 + 16.0028i −0.610545 + 1.05750i 0.380603 + 0.924738i \(0.375716\pi\)
−0.991149 + 0.132757i \(0.957617\pi\)
\(230\) −0.346895 −0.0228736
\(231\) 0.462482 0.306233i 0.0304291 0.0201487i
\(232\) −1.00000 −0.0656532
\(233\) 4.67954 8.10520i 0.306567 0.530989i −0.671042 0.741419i \(-0.734153\pi\)
0.977609 + 0.210430i \(0.0674864\pi\)
\(234\) 5.17466 + 8.96278i 0.338278 + 0.585915i
\(235\) −0.254261 0.440392i −0.0165861 0.0287280i
\(236\) −2.15057 + 3.72489i −0.139990 + 0.242470i
\(237\) −1.50546 −0.0977901
\(238\) 1.44314 + 0.719189i 0.0935447 + 0.0466181i
\(239\) −17.5424 −1.13473 −0.567363 0.823468i \(-0.692036\pi\)
−0.567363 + 0.823468i \(0.692036\pi\)
\(240\) 0.0833087 0.144295i 0.00537755 0.00931419i
\(241\) −1.52113 2.63467i −0.0979845 0.169714i 0.812866 0.582451i \(-0.197906\pi\)
−0.910850 + 0.412737i \(0.864573\pi\)
\(242\) 5.45696 + 9.45173i 0.350787 + 0.607581i
\(243\) 7.55069 13.0782i 0.484377 0.838966i
\(244\) 3.64803 0.233541
\(245\) −1.61994 + 0.199511i −0.103494 + 0.0127463i
\(246\) −2.36958 −0.151079
\(247\) −13.8803 + 24.0414i −0.883182 + 1.52972i
\(248\) 0.675875 + 1.17065i 0.0429181 + 0.0743363i
\(249\) 2.40677 + 4.16866i 0.152523 + 0.264178i
\(250\) 1.15950 2.00832i 0.0733335 0.127017i
\(251\) −17.2275 −1.08739 −0.543694 0.839283i \(-0.682975\pi\)
−0.543694 + 0.839283i \(0.682975\pi\)
\(252\) −5.89482 2.93769i −0.371339 0.185057i
\(253\) −0.436486 −0.0274416
\(254\) 7.65267 13.2548i 0.480172 0.831681i
\(255\) 0.0507712 + 0.0879383i 0.00317942 + 0.00550691i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −10.3227 + 17.8795i −0.643913 + 1.11529i 0.340638 + 0.940195i \(0.389357\pi\)
−0.984551 + 0.175096i \(0.943976\pi\)
\(258\) 2.35455 0.146588
\(259\) −1.40559 + 0.930713i −0.0873391 + 0.0578317i
\(260\) 0.969374 0.0601180
\(261\) −1.24469 + 2.15586i −0.0770443 + 0.133445i
\(262\) −6.10878 10.5807i −0.377401 0.653678i
\(263\) 8.28531 + 14.3506i 0.510894 + 0.884895i 0.999920 + 0.0126254i \(0.00401891\pi\)
−0.489026 + 0.872269i \(0.662648\pi\)
\(264\) 0.104824 0.181561i 0.00645150 0.0111743i
\(265\) 2.79620 0.171769
\(266\) −1.08178 17.6336i −0.0663285 1.08118i
\(267\) 9.02132 0.552096
\(268\) −2.47824 + 4.29245i −0.151383 + 0.262203i
\(269\) 1.31413 + 2.27614i 0.0801239 + 0.138779i 0.903303 0.429003i \(-0.141135\pi\)
−0.823179 + 0.567782i \(0.807802\pi\)
\(270\) −0.457313 0.792089i −0.0278312 0.0482050i
\(271\) 6.31120 10.9313i 0.383378 0.664030i −0.608165 0.793811i \(-0.708094\pi\)
0.991543 + 0.129781i \(0.0414274\pi\)
\(272\) 0.609435 0.0369524
\(273\) 0.481288 + 7.84522i 0.0291289 + 0.474814i
\(274\) 17.8291 1.07710
\(275\) 0.725495 1.25659i 0.0437490 0.0757755i
\(276\) −0.531554 0.920679i −0.0319958 0.0554184i
\(277\) −9.72977 16.8525i −0.584605 1.01257i −0.994924 0.100624i \(-0.967916\pi\)
0.410319 0.911942i \(-0.365417\pi\)
\(278\) −3.99926 + 6.92692i −0.239860 + 0.415449i
\(279\) 3.36502 0.201458
\(280\) −0.514366 + 0.340588i −0.0307393 + 0.0203540i
\(281\) 15.9906 0.953917 0.476958 0.878926i \(-0.341739\pi\)
0.476958 + 0.878926i \(0.341739\pi\)
\(282\) 0.779218 1.34965i 0.0464018 0.0803702i
\(283\) −13.9913 24.2337i −0.831699 1.44054i −0.896690 0.442659i \(-0.854035\pi\)
0.0649910 0.997886i \(-0.479298\pi\)
\(284\) −2.10553 3.64689i −0.124940 0.216403i
\(285\) 0.556285 0.963514i 0.0329515 0.0570737i
\(286\) 1.21973 0.0721242
\(287\) 7.85237 + 3.91324i 0.463511 + 0.230991i
\(288\) −2.48938 −0.146688
\(289\) 8.31429 14.4008i 0.489076 0.847105i
\(290\) 0.116584 + 0.201930i 0.00684607 + 0.0118577i
\(291\) 2.03833 + 3.53049i 0.119489 + 0.206961i
\(292\) −2.92149 + 5.06017i −0.170967 + 0.296124i
\(293\) 20.6845 1.20840 0.604202 0.796832i \(-0.293492\pi\)
0.604202 + 0.796832i \(0.293492\pi\)
\(294\) −3.01178 3.99370i −0.175651 0.232918i
\(295\) 1.00289 0.0583905
\(296\) −0.318586 + 0.551807i −0.0185174 + 0.0320731i
\(297\) −0.575421 0.996659i −0.0333893 0.0578320i
\(298\) −3.90799 6.76883i −0.226384 0.392108i
\(299\) 3.09257 5.35648i 0.178848 0.309773i
\(300\) 3.53404 0.204038
\(301\) −7.80259 3.88843i −0.449734 0.224125i
\(302\) −16.2176 −0.933215
\(303\) 5.62154 9.73680i 0.322949 0.559365i
\(304\) −3.33870 5.78280i −0.191488 0.331666i
\(305\) −0.425303 0.736646i −0.0243528 0.0421802i
\(306\) 0.758557 1.31386i 0.0433638 0.0751083i
\(307\) −28.6540 −1.63537 −0.817686 0.575664i \(-0.804744\pi\)
−0.817686 + 0.575664i \(0.804744\pi\)
\(308\) −0.647210 + 0.428551i −0.0368782 + 0.0244189i
\(309\) 3.49822 0.199007
\(310\) 0.157593 0.272959i 0.00895067 0.0155030i
\(311\) −5.23235 9.06270i −0.296699 0.513898i 0.678679 0.734435i \(-0.262553\pi\)
−0.975379 + 0.220536i \(0.929219\pi\)
\(312\) 1.48539 + 2.57278i 0.0840939 + 0.145655i
\(313\) 15.7086 27.2081i 0.887901 1.53789i 0.0455495 0.998962i \(-0.485496\pi\)
0.842352 0.538928i \(-0.181171\pi\)
\(314\) −23.6455 −1.33439
\(315\) 0.0940360 + 1.53283i 0.00529833 + 0.0863652i
\(316\) 2.10678 0.118516
\(317\) −6.37389 + 11.0399i −0.357993 + 0.620062i −0.987625 0.156831i \(-0.949872\pi\)
0.629632 + 0.776893i \(0.283206\pi\)
\(318\) 4.28468 + 7.42129i 0.240273 + 0.416165i
\(319\) 0.146694 + 0.254082i 0.00821329 + 0.0142258i
\(320\) −0.116584 + 0.201930i −0.00651726 + 0.0112882i
\(321\) −8.02577 −0.447955
\(322\) 0.241024 + 3.92881i 0.0134318 + 0.218944i
\(323\) 4.06944 0.226430
\(324\) −2.33257 + 4.04012i −0.129587 + 0.224451i
\(325\) 10.2805 + 17.8063i 0.570258 + 0.987716i
\(326\) 6.80624 + 11.7888i 0.376963 + 0.652919i
\(327\) 5.42599 9.39809i 0.300058 0.519716i
\(328\) 3.31605 0.183098
\(329\) −4.81107 + 3.18565i −0.265243 + 0.175631i
\(330\) −0.0488836 −0.00269095
\(331\) 5.13096 8.88709i 0.282023 0.488479i −0.689860 0.723943i \(-0.742328\pi\)
0.971883 + 0.235465i \(0.0756612\pi\)
\(332\) −3.36810 5.83373i −0.184849 0.320167i
\(333\) 0.793080 + 1.37365i 0.0434605 + 0.0752758i
\(334\) 1.79855 3.11518i 0.0984123 0.170455i
\(335\) 1.15570 0.0631425
\(336\) −1.69212 0.843268i −0.0923125 0.0460040i
\(337\) −26.9868 −1.47007 −0.735033 0.678031i \(-0.762833\pi\)
−0.735033 + 0.678031i \(0.762833\pi\)
\(338\) −2.14197 + 3.71001i −0.116508 + 0.201798i
\(339\) −3.67923 6.37260i −0.199828 0.346112i
\(340\) −0.0710506 0.123063i −0.00385326 0.00667404i
\(341\) 0.198294 0.343455i 0.0107382 0.0185991i
\(342\) −16.6226 −0.898845
\(343\) 3.38514 + 18.2083i 0.182780 + 0.983154i
\(344\) −3.29502 −0.177656
\(345\) −0.123942 + 0.214674i −0.00667280 + 0.0115576i
\(346\) −6.19782 10.7349i −0.333197 0.577114i
\(347\) −0.0149934 0.0259694i −0.000804890 0.00139411i 0.865623 0.500697i \(-0.166923\pi\)
−0.866428 + 0.499303i \(0.833590\pi\)
\(348\) −0.357289 + 0.618843i −0.0191527 + 0.0331735i
\(349\) 6.30027 0.337246 0.168623 0.985681i \(-0.446068\pi\)
0.168623 + 0.985681i \(0.446068\pi\)
\(350\) −11.7112 5.83630i −0.625991 0.311963i
\(351\) 16.3078 0.870444
\(352\) −0.146694 + 0.254082i −0.00781882 + 0.0135426i
\(353\) −13.8172 23.9321i −0.735415 1.27378i −0.954541 0.298079i \(-0.903654\pi\)
0.219126 0.975696i \(-0.429679\pi\)
\(354\) 1.53675 + 2.66173i 0.0816773 + 0.141469i
\(355\) −0.490944 + 0.850340i −0.0260566 + 0.0451313i
\(356\) −12.6247 −0.669106
\(357\) 0.960683 0.636117i 0.0508447 0.0336669i
\(358\) 9.58344 0.506501
\(359\) 9.23986 16.0039i 0.487661 0.844654i −0.512238 0.858843i \(-0.671184\pi\)
0.999899 + 0.0141898i \(0.00451691\pi\)
\(360\) 0.290222 + 0.502680i 0.0152961 + 0.0264936i
\(361\) −12.7938 22.1596i −0.673359 1.16629i
\(362\) −0.0743276 + 0.128739i −0.00390657 + 0.00676638i
\(363\) 7.79886 0.409334
\(364\) −0.673527 10.9788i −0.0353024 0.575445i
\(365\) 1.36240 0.0713113
\(366\) 1.30340 2.25756i 0.0681299 0.118004i
\(367\) 8.86676 + 15.3577i 0.462841 + 0.801665i 0.999101 0.0423883i \(-0.0134967\pi\)
−0.536260 + 0.844053i \(0.680163\pi\)
\(368\) 0.743871 + 1.28842i 0.0387770 + 0.0671637i
\(369\) 4.12745 7.14895i 0.214866 0.372159i
\(370\) 0.148568 0.00772370
\(371\) −1.94282 31.6688i −0.100866 1.64416i
\(372\) 0.965932 0.0500812
\(373\) −7.11961 + 12.3315i −0.368639 + 0.638502i −0.989353 0.145535i \(-0.953510\pi\)
0.620714 + 0.784037i \(0.286843\pi\)
\(374\) −0.0894005 0.154846i −0.00462279 0.00800691i
\(375\) −0.828558 1.43510i −0.0427865 0.0741084i
\(376\) −1.09046 + 1.88873i −0.0562361 + 0.0974037i
\(377\) −4.15740 −0.214117
\(378\) −8.65318 + 5.72971i −0.445072 + 0.294705i
\(379\) 33.9879 1.74584 0.872920 0.487863i \(-0.162224\pi\)
0.872920 + 0.487863i \(0.162224\pi\)
\(380\) −0.778480 + 1.34837i −0.0399352 + 0.0691698i
\(381\) −5.46844 9.47161i −0.280157 0.485246i
\(382\) −5.14154 8.90541i −0.263064 0.455641i
\(383\) 8.54059 14.7927i 0.436404 0.755873i −0.561005 0.827812i \(-0.689585\pi\)
0.997409 + 0.0719387i \(0.0229186\pi\)
\(384\) −0.714579 −0.0364657
\(385\) 0.161992 + 0.0807288i 0.00825586 + 0.00411432i
\(386\) 12.4681 0.634611
\(387\) −4.10128 + 7.10362i −0.208480 + 0.361097i
\(388\) −2.85249 4.94065i −0.144813 0.250824i
\(389\) 5.65882 + 9.80136i 0.286913 + 0.496949i 0.973071 0.230504i \(-0.0740375\pi\)
−0.686158 + 0.727453i \(0.740704\pi\)
\(390\) 0.346347 0.599891i 0.0175380 0.0303767i
\(391\) −0.906682 −0.0458529
\(392\) 4.21477 + 5.58889i 0.212878 + 0.282282i
\(393\) −8.73040 −0.440391
\(394\) 9.51558 16.4815i 0.479388 0.830325i
\(395\) −0.245617 0.425422i −0.0123584 0.0214053i
\(396\) 0.365177 + 0.632505i 0.0183508 + 0.0317846i
\(397\) −5.12573 + 8.87803i −0.257253 + 0.445575i −0.965505 0.260384i \(-0.916151\pi\)
0.708252 + 0.705960i \(0.249484\pi\)
\(398\) −10.6083 −0.531748
\(399\) −11.2989 5.63084i −0.565654 0.281894i
\(400\) −4.94563 −0.247282
\(401\) 8.80508 15.2509i 0.439705 0.761591i −0.557962 0.829867i \(-0.688416\pi\)
0.997667 + 0.0682755i \(0.0217497\pi\)
\(402\) 1.77090 + 3.06729i 0.0883245 + 0.152983i
\(403\) 2.80988 + 4.86686i 0.139970 + 0.242435i
\(404\) −7.86693 + 13.6259i −0.391395 + 0.677915i
\(405\) 1.08776 0.0540513
\(406\) 2.20598 1.46070i 0.109481 0.0724931i
\(407\) 0.186939 0.00926620
\(408\) 0.217745 0.377145i 0.0107800 0.0186714i
\(409\) 19.4479 + 33.6848i 0.961639 + 1.66561i 0.718386 + 0.695645i \(0.244881\pi\)
0.243254 + 0.969963i \(0.421785\pi\)
\(410\) −0.386599 0.669609i −0.0190928 0.0330696i
\(411\) 6.37015 11.0334i 0.314216 0.544239i
\(412\) −4.89549 −0.241184
\(413\) −0.696813 11.3584i −0.0342879 0.558909i
\(414\) 3.70355 0.182020
\(415\) −0.785336 + 1.36024i −0.0385506 + 0.0667716i
\(416\) −2.07870 3.60041i −0.101917 0.176525i
\(417\) 2.85779 + 4.94983i 0.139946 + 0.242394i
\(418\) −0.979535 + 1.69660i −0.0479106 + 0.0829836i
\(419\) −12.6437 −0.617683 −0.308842 0.951113i \(-0.599941\pi\)
−0.308842 + 0.951113i \(0.599941\pi\)
\(420\) 0.0269932 + 0.440001i 0.00131713 + 0.0214698i
\(421\) −10.7981 −0.526267 −0.263133 0.964759i \(-0.584756\pi\)
−0.263133 + 0.964759i \(0.584756\pi\)
\(422\) 4.34510 7.52593i 0.211516 0.366357i
\(423\) 2.71456 + 4.70176i 0.131986 + 0.228607i
\(424\) −5.99610 10.3855i −0.291196 0.504367i
\(425\) 1.50702 2.61024i 0.0731012 0.126615i
\(426\) −3.00914 −0.145793
\(427\) −8.04749 + 5.32866i −0.389445 + 0.257872i
\(428\) 11.2315 0.542894
\(429\) 0.435797 0.754822i 0.0210405 0.0364432i
\(430\) 0.384148 + 0.665364i 0.0185253 + 0.0320867i
\(431\) 18.0906 + 31.3339i 0.871394 + 1.50930i 0.860555 + 0.509358i \(0.170117\pi\)
0.0108397 + 0.999941i \(0.496550\pi\)
\(432\) −1.96130 + 3.39706i −0.0943629 + 0.163441i
\(433\) 10.6350 0.511084 0.255542 0.966798i \(-0.417746\pi\)
0.255542 + 0.966798i \(0.417746\pi\)
\(434\) −3.20093 1.59519i −0.153650 0.0765715i
\(435\) 0.166617 0.00798869
\(436\) −7.59327 + 13.1519i −0.363652 + 0.629863i
\(437\) 4.96712 + 8.60331i 0.237610 + 0.411552i
\(438\) 2.08764 + 3.61589i 0.0997511 + 0.172774i
\(439\) 1.48753 2.57648i 0.0709961 0.122969i −0.828342 0.560223i \(-0.810716\pi\)
0.899338 + 0.437254i \(0.144049\pi\)
\(440\) 0.0684089 0.00326127
\(441\) 17.2950 2.13004i 0.823570 0.101430i
\(442\) 2.53366 0.120514
\(443\) 13.9715 24.1993i 0.663804 1.14974i −0.315805 0.948824i \(-0.602274\pi\)
0.979608 0.200917i \(-0.0643923\pi\)
\(444\) 0.227655 + 0.394309i 0.0108040 + 0.0187131i
\(445\) 1.47184 + 2.54930i 0.0697718 + 0.120848i
\(446\) −4.99691 + 8.65491i −0.236611 + 0.409822i
\(447\) −5.58513 −0.264167
\(448\) 2.36799 + 1.18009i 0.111877 + 0.0557541i
\(449\) −0.604431 −0.0285248 −0.0142624 0.999898i \(-0.504540\pi\)
−0.0142624 + 0.999898i \(0.504540\pi\)
\(450\) −6.15577 + 10.6621i −0.290186 + 0.502617i
\(451\) −0.486444 0.842547i −0.0229058 0.0396740i
\(452\) 5.14880 + 8.91799i 0.242179 + 0.419467i
\(453\) −5.79436 + 10.0361i −0.272243 + 0.471538i
\(454\) −25.3090 −1.18781
\(455\) −2.13843 + 1.41596i −0.100251 + 0.0663813i
\(456\) −4.77153 −0.223447
\(457\) 3.55156 6.15148i 0.166135 0.287754i −0.770923 0.636929i \(-0.780205\pi\)
0.937058 + 0.349175i \(0.113538\pi\)
\(458\) −9.23923 16.0028i −0.431721 0.747762i
\(459\) −1.19528 2.07029i −0.0557910 0.0966329i
\(460\) 0.173447 0.300420i 0.00808703 0.0140071i
\(461\) 3.81028 0.177462 0.0887312 0.996056i \(-0.471719\pi\)
0.0887312 + 0.996056i \(0.471719\pi\)
\(462\) 0.0339646 + 0.553638i 0.00158018 + 0.0257576i
\(463\) −3.42327 −0.159093 −0.0795464 0.996831i \(-0.525347\pi\)
−0.0795464 + 0.996831i \(0.525347\pi\)
\(464\) 0.500000 0.866025i 0.0232119 0.0402042i
\(465\) −0.112613 0.195051i −0.00522228 0.00904525i
\(466\) 4.67954 + 8.10520i 0.216775 + 0.375466i
\(467\) −11.4351 + 19.8061i −0.529151 + 0.916517i 0.470271 + 0.882522i \(0.344156\pi\)
−0.999422 + 0.0339945i \(0.989177\pi\)
\(468\) −10.3493 −0.478398
\(469\) −0.802985 13.0890i −0.0370784 0.604395i
\(470\) 0.508521 0.0234563
\(471\) −8.44827 + 14.6328i −0.389276 + 0.674245i
\(472\) −2.15057 3.72489i −0.0989878 0.171452i
\(473\) 0.483360 + 0.837205i 0.0222249 + 0.0384947i
\(474\) 0.752730 1.30377i 0.0345740 0.0598840i
\(475\) −33.0240 −1.51524
\(476\) −1.34440 + 0.890199i −0.0616207 + 0.0408022i
\(477\) −29.8531 −1.36688
\(478\) 8.77121 15.1922i 0.401186 0.694874i
\(479\) 2.28610 + 3.95963i 0.104454 + 0.180920i 0.913515 0.406805i \(-0.133357\pi\)
−0.809061 + 0.587725i \(0.800024\pi\)
\(480\) 0.0833087 + 0.144295i 0.00380250 + 0.00658613i
\(481\) −1.32449 + 2.29408i −0.0603914 + 0.104601i
\(482\) 3.04226 0.138571
\(483\) 2.51743 + 1.25457i 0.114547 + 0.0570847i
\(484\) −10.9139 −0.496087
\(485\) −0.665111 + 1.15201i −0.0302011 + 0.0523099i
\(486\) 7.55069 + 13.0782i 0.342506 + 0.593238i
\(487\) −10.8284 18.7554i −0.490683 0.849889i 0.509259 0.860613i \(-0.329919\pi\)
−0.999942 + 0.0107247i \(0.996586\pi\)
\(488\) −1.82401 + 3.15928i −0.0825692 + 0.143014i
\(489\) 9.72719 0.439879
\(490\) 0.637189 1.50267i 0.0287853 0.0678835i
\(491\) 32.0537 1.44656 0.723281 0.690554i \(-0.242633\pi\)
0.723281 + 0.690554i \(0.242633\pi\)
\(492\) 1.18479 2.05211i 0.0534144 0.0925164i
\(493\) 0.304717 + 0.527786i 0.0137238 + 0.0237703i
\(494\) −13.8803 24.0414i −0.624504 1.08167i
\(495\) 0.0851478 0.147480i 0.00382711 0.00662875i
\(496\) −1.35175 −0.0606954
\(497\) 9.97176 + 4.96944i 0.447295 + 0.222910i
\(498\) −4.81355 −0.215700
\(499\) −12.3057 + 21.3140i −0.550877 + 0.954147i 0.447335 + 0.894367i \(0.352373\pi\)
−0.998212 + 0.0597801i \(0.980960\pi\)
\(500\) 1.15950 + 2.00832i 0.0518546 + 0.0898149i
\(501\) −1.28521 2.22604i −0.0574188 0.0994523i
\(502\) 8.61374 14.9194i 0.384450 0.665887i
\(503\) −35.0600 −1.56325 −0.781623 0.623751i \(-0.785608\pi\)
−0.781623 + 0.623751i \(0.785608\pi\)
\(504\) 5.49153 3.63622i 0.244612 0.161970i
\(505\) 3.66864 0.163253
\(506\) 0.218243 0.378008i 0.00970208 0.0168045i
\(507\) 1.53061 + 2.65109i 0.0679767 + 0.117739i
\(508\) 7.65267 + 13.2548i 0.339533 + 0.588088i
\(509\) 15.8796 27.5043i 0.703851 1.21910i −0.263254 0.964726i \(-0.584796\pi\)
0.967105 0.254378i \(-0.0818708\pi\)
\(510\) −0.101542 −0.00449638
\(511\) −0.946604 15.4301i −0.0418753 0.682586i
\(512\) 1.00000 0.0441942
\(513\) −13.0964 + 22.6836i −0.578218 + 1.00150i
\(514\) −10.3227 17.8795i −0.455315 0.788630i
\(515\) 0.570738 + 0.988547i 0.0251497 + 0.0435606i
\(516\) −1.17728 + 2.03910i −0.0518267 + 0.0897665i
\(517\) 0.639855 0.0281408
\(518\) −0.103226 1.68263i −0.00453550 0.0739307i
\(519\) −8.85766 −0.388808
\(520\) −0.484687 + 0.839503i −0.0212549 + 0.0368146i
\(521\) 7.08405 + 12.2699i 0.310358 + 0.537556i 0.978440 0.206532i \(-0.0662178\pi\)
−0.668082 + 0.744088i \(0.732884\pi\)
\(522\) −1.24469 2.15586i −0.0544785 0.0943596i
\(523\) 9.85144 17.0632i 0.430774 0.746122i −0.566167 0.824291i \(-0.691574\pi\)
0.996940 + 0.0781692i \(0.0249075\pi\)
\(524\) 12.2176 0.533726
\(525\) −7.79605 + 5.16216i −0.340247 + 0.225295i
\(526\) −16.5706 −0.722513
\(527\) 0.411902 0.713435i 0.0179427 0.0310777i
\(528\) 0.104824 + 0.181561i 0.00456190 + 0.00790144i
\(529\) 10.3933 + 18.0017i 0.451883 + 0.782685i
\(530\) −1.39810 + 2.42158i −0.0607296 + 0.105187i
\(531\) −10.7071 −0.464650
\(532\) 15.8120 + 7.87994i 0.685538 + 0.341639i
\(533\) 13.7861 0.597143
\(534\) −4.51066 + 7.81269i −0.195195 + 0.338088i
\(535\) −1.30941 2.26797i −0.0566109 0.0980529i
\(536\) −2.47824 4.29245i −0.107044 0.185405i
\(537\) 3.42406 5.93065i 0.147759 0.255926i
\(538\) −2.62826 −0.113312
\(539\) 0.801753 1.89075i 0.0345339 0.0814405i
\(540\) 0.914626 0.0393592
\(541\) 6.64270 11.5055i 0.285592 0.494660i −0.687161 0.726505i \(-0.741143\pi\)
0.972753 + 0.231846i \(0.0744765\pi\)
\(542\) 6.31120 + 10.9313i 0.271089 + 0.469540i
\(543\) 0.0531129 + 0.0919943i 0.00227929 + 0.00394785i
\(544\) −0.304717 + 0.527786i −0.0130647 + 0.0226286i
\(545\) 3.54103 0.151681
\(546\) −7.03480 3.50580i −0.301062 0.150034i
\(547\) −3.77149 −0.161257 −0.0806287 0.996744i \(-0.525693\pi\)
−0.0806287 + 0.996744i \(0.525693\pi\)
\(548\) −8.91455 + 15.4405i −0.380811 + 0.659584i
\(549\) 4.54066 + 7.86465i 0.193791 + 0.335655i
\(550\) 0.725495 + 1.25659i 0.0309352 + 0.0535814i
\(551\) 3.33870 5.78280i 0.142233 0.246355i
\(552\) 1.06311 0.0452489
\(553\) −4.64752 + 3.07736i −0.197633 + 0.130863i
\(554\) 19.4595 0.826757
\(555\) 0.0530819 0.0919405i 0.00225320 0.00390266i
\(556\) −3.99926 6.92692i −0.169606 0.293767i
\(557\) 20.6721 + 35.8052i 0.875907 + 1.51712i 0.855793 + 0.517318i \(0.173069\pi\)
0.0201136 + 0.999798i \(0.493597\pi\)
\(558\) −1.68251 + 2.91419i −0.0712262 + 0.123367i
\(559\) −13.6987 −0.579394
\(560\) −0.0377749 0.615749i −0.00159628 0.0260201i
\(561\) −0.127767 −0.00539434
\(562\) −7.99528 + 13.8482i −0.337260 + 0.584152i
\(563\) 3.31295 + 5.73821i 0.139624 + 0.241837i 0.927354 0.374184i \(-0.122077\pi\)
−0.787730 + 0.616021i \(0.788744\pi\)
\(564\) 0.779218 + 1.34965i 0.0328110 + 0.0568303i
\(565\) 1.20054 2.07939i 0.0505071 0.0874808i
\(566\) 27.9827 1.17620
\(567\) −0.755783 12.3196i −0.0317399 0.517375i
\(568\) 4.21106 0.176692
\(569\) 6.97747 12.0853i 0.292511 0.506644i −0.681892 0.731453i \(-0.738843\pi\)
0.974403 + 0.224809i \(0.0721759\pi\)
\(570\) 0.556285 + 0.963514i 0.0233002 + 0.0403572i
\(571\) 1.05581 + 1.82871i 0.0441841 + 0.0765291i 0.887272 0.461247i \(-0.152598\pi\)
−0.843088 + 0.537776i \(0.819265\pi\)
\(572\) −0.609865 + 1.05632i −0.0254998 + 0.0441669i
\(573\) −7.34807 −0.306970
\(574\) −7.31515 + 4.84373i −0.305328 + 0.202174i
\(575\) 7.35782 0.306842
\(576\) 1.24469 2.15586i 0.0518620 0.0898277i
\(577\) −1.39881 2.42281i −0.0582331 0.100863i 0.835439 0.549583i \(-0.185213\pi\)
−0.893672 + 0.448720i \(0.851880\pi\)
\(578\) 8.31429 + 14.4008i 0.345829 + 0.598994i
\(579\) 4.45473 7.71582i 0.185132 0.320659i
\(580\) −0.233169 −0.00968180
\(581\) 15.9513 + 7.94934i 0.661771 + 0.329794i
\(582\) −4.07666 −0.168983
\(583\) −1.75918 + 3.04700i −0.0728579 + 0.126194i
\(584\) −2.92149 5.06017i −0.120892 0.209391i
\(585\) 1.20657 + 2.08984i 0.0498855 + 0.0864042i
\(586\) −10.3423 + 17.9133i −0.427235 + 0.739993i
\(587\) 6.93586 0.286274 0.143137 0.989703i \(-0.454281\pi\)
0.143137 + 0.989703i \(0.454281\pi\)
\(588\) 4.96454 0.611430i 0.204734 0.0252150i
\(589\) −9.02617 −0.371917
\(590\) −0.501445 + 0.868528i −0.0206441 + 0.0357567i
\(591\) −6.79963 11.7773i −0.279700 0.484454i
\(592\) −0.318586 0.551807i −0.0130938 0.0226791i
\(593\) −1.69542 + 2.93655i −0.0696225 + 0.120590i −0.898735 0.438492i \(-0.855513\pi\)
0.829113 + 0.559082i \(0.188846\pi\)
\(594\) 1.15084 0.0472196
\(595\) 0.336494 + 0.167692i 0.0137949 + 0.00687471i
\(596\) 7.81597 0.320155
\(597\) −3.79025 + 6.56490i −0.155124 + 0.268684i
\(598\) 3.09257 + 5.35648i 0.126464 + 0.219043i
\(599\) 15.3624 + 26.6084i 0.627689 + 1.08719i 0.988014 + 0.154363i \(0.0493325\pi\)
−0.360325 + 0.932827i \(0.617334\pi\)
\(600\) −1.76702 + 3.06057i −0.0721384 + 0.124947i
\(601\) 32.5720 1.32864 0.664320 0.747448i \(-0.268721\pi\)
0.664320 + 0.747448i \(0.268721\pi\)
\(602\) 7.26877 4.81303i 0.296253 0.196164i
\(603\) −12.3386 −0.502465
\(604\) 8.10878 14.0448i 0.329941 0.571475i
\(605\) 1.27239 + 2.20385i 0.0517301 + 0.0895992i
\(606\) 5.62154 + 9.73680i 0.228360 + 0.395530i
\(607\) 0.960031 1.66282i 0.0389664 0.0674919i −0.845884 0.533366i \(-0.820927\pi\)
0.884851 + 0.465874i \(0.154260\pi\)
\(608\) 6.67740 0.270804
\(609\) −0.115767 1.88705i −0.00469110 0.0764671i
\(610\) 0.850606 0.0344400
\(611\) −4.53347 + 7.85219i −0.183404 + 0.317666i
\(612\) 0.758557 + 1.31386i 0.0306628 + 0.0531096i
\(613\) 14.4028 + 24.9463i 0.581722 + 1.00757i 0.995275 + 0.0970922i \(0.0309542\pi\)
−0.413553 + 0.910480i \(0.635713\pi\)
\(614\) 14.3270 24.8151i 0.578191 1.00146i
\(615\) −0.552511 −0.0222794
\(616\) −0.0475309 0.774776i −0.00191507 0.0312166i
\(617\) 41.9416 1.68850 0.844252 0.535946i \(-0.180045\pi\)
0.844252 + 0.535946i \(0.180045\pi\)
\(618\) −1.74911 + 3.02954i −0.0703595 + 0.121866i
\(619\) 0.376352 + 0.651862i 0.0151269 + 0.0262005i 0.873490 0.486843i \(-0.161851\pi\)
−0.858363 + 0.513043i \(0.828518\pi\)
\(620\) 0.157593 + 0.272959i 0.00632908 + 0.0109623i
\(621\) 2.91790 5.05396i 0.117091 0.202808i
\(622\) 10.4647 0.419596
\(623\) 27.8498 18.4408i 1.11578 0.738815i
\(624\) −2.97079 −0.118927
\(625\) −12.0937 + 20.9469i −0.483749 + 0.837878i
\(626\) 15.7086 + 27.2081i 0.627841 + 1.08745i
\(627\) 0.699955 + 1.21236i 0.0279535 + 0.0484169i
\(628\) 11.8227 20.4776i 0.471778 0.817144i
\(629\) 0.388314 0.0154831
\(630\) −1.37449 0.684978i −0.0547609 0.0272902i
\(631\) −36.3961 −1.44891 −0.724453 0.689325i \(-0.757907\pi\)
−0.724453 + 0.689325i \(0.757907\pi\)
\(632\) −1.05339 + 1.82452i −0.0419016 + 0.0725757i
\(633\) −3.10492 5.37787i −0.123409 0.213751i
\(634\) −6.37389 11.0399i −0.253139 0.438450i
\(635\) 1.78436 3.09061i 0.0708103 0.122647i
\(636\) −8.56937 −0.339797
\(637\) 17.5225 + 23.2352i 0.694265 + 0.920614i
\(638\) −0.293388 −0.0116153
\(639\) 5.24146 9.07848i 0.207349 0.359139i
\(640\) −0.116584 0.201930i −0.00460840 0.00798198i
\(641\) 10.2287 + 17.7167i 0.404010 + 0.699766i 0.994206 0.107494i \(-0.0342827\pi\)
−0.590195 + 0.807260i \(0.700949\pi\)
\(642\) 4.01289 6.95052i 0.158376 0.274315i
\(643\) −36.0350 −1.42108 −0.710541 0.703656i \(-0.751550\pi\)
−0.710541 + 0.703656i \(0.751550\pi\)
\(644\) −3.52296 1.75567i −0.138824 0.0691831i
\(645\) 0.549008 0.0216172
\(646\) −2.03472 + 3.52424i −0.0800550 + 0.138659i
\(647\) −21.3888 37.0464i −0.840879 1.45645i −0.889152 0.457611i \(-0.848705\pi\)
0.0482734 0.998834i \(-0.484628\pi\)
\(648\) −2.33257 4.04012i −0.0916318 0.158711i
\(649\) −0.630951 + 1.09284i −0.0247670 + 0.0428977i
\(650\) −20.5610 −0.806467
\(651\) −2.13083 + 1.41093i −0.0835139 + 0.0552988i
\(652\) −13.6125 −0.533106
\(653\) −14.0161 + 24.2766i −0.548493 + 0.950017i 0.449885 + 0.893086i \(0.351465\pi\)
−0.998378 + 0.0569310i \(0.981868\pi\)
\(654\) 5.42599 + 9.39809i 0.212173 + 0.367495i
\(655\) −1.42437 2.46709i −0.0556549 0.0963972i
\(656\) −1.65802 + 2.87178i −0.0647349 + 0.112124i
\(657\) −14.5454 −0.567470
\(658\) −0.353323 5.75933i −0.0137740 0.224522i
\(659\) 36.2772 1.41316 0.706579 0.707634i \(-0.250238\pi\)
0.706579 + 0.707634i \(0.250238\pi\)
\(660\) 0.0244418 0.0423344i 0.000951395 0.00164786i
\(661\) 3.01525 + 5.22256i 0.117279 + 0.203134i 0.918689 0.394983i \(-0.129249\pi\)
−0.801409 + 0.598116i \(0.795916\pi\)
\(662\) 5.13096 + 8.88709i 0.199421 + 0.345406i
\(663\) 0.905251 1.56794i 0.0351570 0.0608938i
\(664\) 6.73621 0.261415
\(665\) −0.252238 4.11160i −0.00978138 0.159441i
\(666\) −1.58616 −0.0614624
\(667\) −0.743871 + 1.28842i −0.0288028 + 0.0498879i
\(668\) 1.79855 + 3.11518i 0.0695880 + 0.120530i
\(669\) 3.57069 + 6.18461i 0.138051 + 0.239111i
\(670\) −0.577849 + 1.00086i −0.0223242 + 0.0386667i
\(671\) 1.07029 0.0413180
\(672\) 1.57635 1.04378i 0.0608090 0.0402648i
\(673\) 16.7412 0.645327 0.322663 0.946514i \(-0.395422\pi\)
0.322663 + 0.946514i \(0.395422\pi\)
\(674\) 13.4934 23.3713i 0.519747 0.900228i
\(675\) 9.69985 + 16.8006i 0.373347 + 0.646657i
\(676\) −2.14197 3.71001i −0.0823836 0.142693i
\(677\) −20.4963 + 35.5007i −0.787737 + 1.36440i 0.139613 + 0.990206i \(0.455414\pi\)
−0.927350 + 0.374195i \(0.877919\pi\)
\(678\) 7.35845 0.282600
\(679\) 13.5093 + 6.73239i 0.518441 + 0.258366i
\(680\) 0.142101 0.00544933
\(681\) −9.04265 + 15.6623i −0.346515 + 0.600182i
\(682\) 0.198294 + 0.343455i 0.00759306 + 0.0131516i
\(683\) 17.0734 + 29.5720i 0.653296 + 1.13154i 0.982318 + 0.187220i \(0.0599477\pi\)
−0.329022 + 0.944322i \(0.606719\pi\)
\(684\) 8.31128 14.3956i 0.317790 0.550428i
\(685\) 4.15719 0.158838
\(686\) −17.4614 6.17252i −0.666679 0.235668i
\(687\) −13.2043 −0.503776
\(688\) 1.64751 2.85357i 0.0628108 0.108791i
\(689\) −24.9281 43.1768i −0.949687 1.64491i
\(690\) −0.123942 0.214674i −0.00471838 0.00817248i
\(691\) 11.3172 19.6019i 0.430525 0.745692i −0.566393 0.824135i \(-0.691662\pi\)
0.996919 + 0.0784434i \(0.0249950\pi\)
\(692\) 12.3956 0.471212
\(693\) −1.72947 0.861884i −0.0656972 0.0327403i
\(694\) 0.0299869 0.00113829
\(695\) −0.932502 + 1.61514i −0.0353718 + 0.0612658i
\(696\) −0.357289 0.618843i −0.0135430 0.0234572i
\(697\) −1.01046 1.75016i −0.0382738 0.0662922i
\(698\) −3.15014 + 5.45620i −0.119234 + 0.206520i
\(699\) 6.68780 0.252956
\(700\) 10.9100 7.22406i 0.412359 0.273044i
\(701\) −15.1951 −0.573911 −0.286955 0.957944i \(-0.592643\pi\)
−0.286955 + 0.957944i \(0.592643\pi\)
\(702\) −8.15389 + 14.1229i −0.307749 + 0.533036i
\(703\) −2.12732 3.68463i −0.0802335 0.138969i
\(704\) −0.146694 0.254082i −0.00552874 0.00957606i
\(705\) 0.181689 0.314695i 0.00684281 0.0118521i
\(706\) 27.6344 1.04003
\(707\) −2.54899 41.5498i −0.0958648 1.56264i
\(708\) −3.07350 −0.115509
\(709\) −4.00781 + 6.94172i −0.150516 + 0.260702i −0.931417 0.363953i \(-0.881427\pi\)
0.780901 + 0.624655i \(0.214760\pi\)
\(710\) −0.490944 0.850340i −0.0184248 0.0319127i
\(711\) 2.62228 + 4.54193i 0.0983433 + 0.170336i
\(712\) 6.31233 10.9333i 0.236565 0.409742i
\(713\) 2.01106 0.0753146
\(714\) 0.0705523 + 1.15003i 0.00264035 + 0.0430390i
\(715\) 0.284403 0.0106361
\(716\) −4.79172 + 8.29950i −0.179075 + 0.310167i
\(717\) −6.26772 10.8560i −0.234072 0.405425i
\(718\) 9.23986 + 16.0039i 0.344828 + 0.597260i
\(719\) −1.08801 + 1.88448i −0.0405757 + 0.0702793i −0.885600 0.464449i \(-0.846253\pi\)
0.845024 + 0.534728i \(0.179586\pi\)
\(720\) −0.580445 −0.0216319
\(721\) 10.7994 7.15083i 0.402190 0.266311i
\(722\) 25.5877 0.952274
\(723\) 1.08697 1.88268i 0.0404247 0.0700177i
\(724\) −0.0743276 0.128739i −0.00276236 0.00478455i
\(725\) −2.47282 4.28304i −0.0918381 0.159068i
\(726\) −3.89943 + 6.75401i −0.144721 + 0.250665i
\(727\) −53.7791 −1.99456 −0.997278 0.0737366i \(-0.976508\pi\)
−0.997278 + 0.0737366i \(0.976508\pi\)
\(728\) 9.84468 + 4.90611i 0.364868 + 0.181832i
\(729\) −3.20426 −0.118676
\(730\) −0.681200 + 1.17987i −0.0252124 + 0.0436691i
\(731\) 1.00405 + 1.73907i 0.0371362 + 0.0643217i
\(732\) 1.30340 + 2.25756i 0.0481751 + 0.0834417i
\(733\) −13.3872 + 23.1874i −0.494469 + 0.856445i −0.999980 0.00637498i \(-0.997971\pi\)
0.505511 + 0.862820i \(0.331304\pi\)
\(734\) −17.7335 −0.654556
\(735\) −0.702254 0.931206i −0.0259030 0.0343481i
\(736\) −1.48774 −0.0548389
\(737\) −0.727088 + 1.25935i −0.0267826 + 0.0463889i
\(738\) 4.12745 + 7.14895i 0.151933 + 0.263156i
\(739\) −14.6468 25.3690i −0.538791 0.933213i −0.998969 0.0453869i \(-0.985548\pi\)
0.460179 0.887826i \(-0.347785\pi\)
\(740\) −0.0742842 + 0.128664i −0.00273074 + 0.00472978i
\(741\) −19.8371 −0.728735
\(742\) 28.3974 + 14.1519i 1.04250 + 0.519532i
\(743\) 6.53498 0.239745 0.119873 0.992789i \(-0.461751\pi\)
0.119873 + 0.992789i \(0.461751\pi\)
\(744\) −0.482966 + 0.836522i −0.0177064 + 0.0306684i
\(745\) −0.911220 1.57828i −0.0333845 0.0578237i
\(746\) −7.11961 12.3315i −0.260667 0.451489i
\(747\) 8.38448 14.5223i 0.306772 0.531345i
\(748\) 0.178801 0.00653761
\(749\) −24.7765 + 16.4058i −0.905312 + 0.599453i
\(750\) 1.65712 0.0605093
\(751\) −15.0999 + 26.1537i −0.551002 + 0.954363i 0.447201 + 0.894434i \(0.352421\pi\)
−0.998203 + 0.0599296i \(0.980912\pi\)
\(752\) −1.09046 1.88873i −0.0397649 0.0688748i
\(753\) −6.15519 10.6611i −0.224308 0.388512i
\(754\) 2.07870 3.60041i 0.0757017 0.131119i
\(755\) −3.78142 −0.137620
\(756\) −0.635487 10.3587i −0.0231124 0.376743i
\(757\) −26.5008 −0.963189 −0.481595 0.876394i \(-0.659942\pi\)
−0.481595 + 0.876394i \(0.659942\pi\)
\(758\) −16.9939 + 29.4344i −0.617248 + 1.06910i
\(759\) −0.155952 0.270116i −0.00566069 0.00980460i
\(760\) −0.778480 1.34837i −0.0282384 0.0489104i
\(761\) −2.18705 + 3.78808i −0.0792805 + 0.137318i −0.902940 0.429767i \(-0.858596\pi\)
0.823659 + 0.567085i \(0.191929\pi\)
\(762\) 10.9369 0.396201
\(763\) −2.46032 40.1044i −0.0890697 1.45188i
\(764\) 10.2831 0.372029
\(765\) 0.176872 0.306351i 0.00639481 0.0110761i
\(766\) 8.54059 + 14.7927i 0.308584 + 0.534483i
\(767\) −8.94076 15.4858i −0.322832 0.559161i
\(768\) 0.357289 0.618843i 0.0128926 0.0223306i
\(769\) 43.7523 1.57775 0.788874 0.614555i \(-0.210665\pi\)
0.788874 + 0.614555i \(0.210665\pi\)
\(770\) −0.150909 + 0.0999246i −0.00543838 + 0.00360103i
\(771\) −14.7528 −0.531309
\(772\) −6.23407 + 10.7977i −0.224369 + 0.388618i
\(773\) −7.17176 12.4219i −0.257950 0.446783i 0.707742 0.706471i \(-0.249714\pi\)
−0.965693 + 0.259687i \(0.916380\pi\)
\(774\) −4.10128 7.10362i −0.147417 0.255334i
\(775\) −3.34263 + 5.78960i −0.120071 + 0.207969i
\(776\) 5.70498 0.204797
\(777\) −1.07817 0.537306i −0.0386791 0.0192758i
\(778\) −11.3176 −0.405757
\(779\) −11.0713 + 19.1760i −0.396670 + 0.687052i
\(780\) 0.346347 + 0.599891i 0.0124012 + 0.0214795i
\(781\) −0.617738 1.06995i −0.0221044 0.0382859i
\(782\) 0.453341 0.785210i 0.0162114 0.0280790i
\(783\) −3.92259 −0.140182
\(784\) −6.94751 + 0.855651i −0.248125 + 0.0305590i
\(785\) −5.51338 −0.196781
\(786\) 4.36520 7.56075i 0.155702 0.269683i
\(787\) 15.8209 + 27.4025i 0.563953 + 0.976794i 0.997146 + 0.0754936i \(0.0240532\pi\)
−0.433194 + 0.901301i \(0.642613\pi\)
\(788\) 9.51558 + 16.4815i 0.338979 + 0.587128i
\(789\) −5.92051 + 10.2546i −0.210776 + 0.365074i
\(790\) 0.491235 0.0174773
\(791\) −24.3846 12.1521i −0.867018 0.432079i
\(792\) −0.730354 −0.0259520
\(793\) −7.58315 + 13.1344i −0.269285 + 0.466416i
\(794\) −5.12573 8.87803i −0.181905 0.315069i
\(795\) 0.999054 + 1.73041i 0.0354328 + 0.0613714i
\(796\) 5.30417 9.18709i 0.188001 0.325628i
\(797\) −12.6909 −0.449536 −0.224768 0.974412i \(-0.572162\pi\)
−0.224768 + 0.974412i \(0.572162\pi\)
\(798\) 10.5259 6.96975i 0.372613 0.246726i
\(799\) 1.32913 0.0470211
\(800\) 2.47282 4.28304i 0.0874273 0.151428i
\(801\) −15.7138 27.2171i −0.555219 0.961668i
\(802\) 8.80508 + 15.2509i 0.310918 + 0.538526i
\(803\) −0.857131 + 1.48460i −0.0302475 + 0.0523902i
\(804\) −3.54180 −0.124910
\(805\) 0.0561993 + 0.916075i 0.00198077 + 0.0322874i
\(806\) −5.61976 −0.197948
\(807\) −0.939049 + 1.62648i −0.0330561 + 0.0572548i
\(808\) −7.86693 13.6259i −0.276758 0.479359i
\(809\) −5.29226 9.16647i −0.186066 0.322276i 0.757869 0.652407i \(-0.226241\pi\)
−0.943935 + 0.330131i \(0.892907\pi\)
\(810\) −0.543881 + 0.942030i −0.0191100 + 0.0330995i
\(811\) −47.2614 −1.65957 −0.829786 0.558082i \(-0.811537\pi\)
−0.829786 + 0.558082i \(0.811537\pi\)
\(812\) 0.162007 + 2.64079i 0.00568533 + 0.0926734i
\(813\) 9.01969 0.316334
\(814\) −0.0934693 + 0.161894i −0.00327610 + 0.00567436i
\(815\) 1.58700 + 2.74877i 0.0555903 + 0.0962851i
\(816\) 0.217745 + 0.377145i 0.00762259 + 0.0132027i
\(817\) 11.0011 19.0545i 0.384880 0.666631i
\(818\) −38.8959 −1.35996
\(819\) 22.8305 15.1172i 0.797761 0.528238i
\(820\) 0.773198 0.0270012
\(821\) 0.410163 0.710423i 0.0143148 0.0247939i −0.858779 0.512346i \(-0.828777\pi\)
0.873094 + 0.487552i \(0.162110\pi\)
\(822\) 6.37015 + 11.0334i 0.222184 + 0.384835i
\(823\) −20.5851 35.6544i −0.717551 1.24283i −0.961967 0.273165i \(-0.911930\pi\)
0.244416 0.969670i \(-0.421404\pi\)
\(824\) 2.44775 4.23962i 0.0852713 0.147694i
\(825\) 1.03685 0.0360984
\(826\) 10.1850 + 5.07573i 0.354383 + 0.176607i
\(827\) −24.2372 −0.842810 −0.421405 0.906872i \(-0.638463\pi\)
−0.421405 + 0.906872i \(0.638463\pi\)
\(828\) −1.85178 + 3.20737i −0.0643536 + 0.111464i
\(829\) 14.8873 + 25.7855i 0.517057 + 0.895568i 0.999804 + 0.0198086i \(0.00630570\pi\)
−0.482747 + 0.875760i \(0.660361\pi\)
\(830\) −0.785336 1.36024i −0.0272594 0.0472147i
\(831\) 6.95269 12.0424i 0.241186 0.417747i
\(832\) 4.15740 0.144132
\(833\) 1.66543 3.92753i 0.0577036 0.136081i
\(834\) −5.71558 −0.197914
\(835\) 0.419366 0.726363i 0.0145127 0.0251368i
\(836\) −0.979535 1.69660i −0.0338779 0.0586783i
\(837\) 2.65118 + 4.59198i 0.0916383 + 0.158722i
\(838\) 6.32183 10.9497i 0.218384 0.378252i
\(839\) 14.8726 0.513459 0.256730 0.966483i \(-0.417355\pi\)
0.256730 + 0.966483i \(0.417355\pi\)
\(840\) −0.394549 0.196624i −0.0136132 0.00678416i
\(841\) 1.00000 0.0344828
\(842\) 5.39905 9.35143i 0.186063 0.322271i
\(843\) 5.71326 + 9.89565i 0.196775 + 0.340824i
\(844\) 4.34510 + 7.52593i 0.149564 + 0.259053i
\(845\) −0.499441 + 0.865057i −0.0171813 + 0.0297589i
\(846\) −5.42912 −0.186657
\(847\) 24.0759 15.9419i 0.827259 0.547771i
\(848\) 11.9922 0.411814
\(849\) 9.99792 17.3169i 0.343128 0.594314i
\(850\) 1.50702 + 2.61024i 0.0516904 + 0.0895304i
\(851\) 0.473973 + 0.820946i 0.0162476 + 0.0281417i
\(852\) 1.50457 2.60599i 0.0515456 0.0892797i
\(853\) 48.2468 1.65194 0.825970 0.563715i \(-0.190628\pi\)
0.825970 + 0.563715i \(0.190628\pi\)
\(854\) −0.591006 9.63366i −0.0202238 0.329657i
\(855\) −3.87586 −0.132552
\(856\) −5.61573 + 9.72674i −0.191942 + 0.332453i
\(857\) 11.1442 + 19.3023i 0.380677 + 0.659352i 0.991159 0.132678i \(-0.0423576\pi\)
−0.610482 + 0.792030i \(0.709024\pi\)
\(858\) 0.435797 + 0.754822i 0.0148779 + 0.0257692i
\(859\) −16.5053 + 28.5881i −0.563155 + 0.975413i 0.434063 + 0.900882i \(0.357079\pi\)
−0.997219 + 0.0745311i \(0.976254\pi\)
\(860\) −0.768296 −0.0261987
\(861\) 0.383888 + 6.25755i 0.0130829 + 0.213257i
\(862\) −36.1812 −1.23234
\(863\) −1.49100 + 2.58249i −0.0507543 + 0.0879090i −0.890286 0.455401i \(-0.849496\pi\)
0.839532 + 0.543310i \(0.182829\pi\)
\(864\) −1.96130 3.39706i −0.0667247 0.115570i
\(865\) −1.44514 2.50305i −0.0491361 0.0851063i
\(866\) −5.31749 + 9.21016i −0.180696 + 0.312974i
\(867\) 11.8824 0.403549
\(868\) 2.98194 1.97450i 0.101214 0.0670187i
\(869\) 0.618104 0.0209677
\(870\) −0.0833087 + 0.144295i −0.00282443 + 0.00489205i
\(871\) −10.3030 17.8454i −0.349105 0.604668i
\(872\) −7.59327 13.1519i −0.257141 0.445381i
\(873\) 7.10092 12.2992i 0.240330 0.416263i
\(874\) −9.93425 −0.336031
\(875\) −5.49140 2.73664i −0.185643 0.0925154i
\(876\) −4.17527 −0.141069
\(877\) 4.80059 8.31486i 0.162104 0.280773i −0.773519 0.633773i \(-0.781505\pi\)
0.935623 + 0.353000i \(0.114839\pi\)
\(878\) 1.48753 + 2.57648i 0.0502018 + 0.0869521i
\(879\) 7.39036 + 12.8005i 0.249271 + 0.431750i
\(880\) −0.0342045 + 0.0592439i −0.00115303 + 0.00199711i
\(881\) 11.0461 0.372153 0.186076 0.982535i \(-0.440423\pi\)
0.186076 + 0.982535i \(0.440423\pi\)
\(882\) −6.80282 + 16.0429i −0.229063 + 0.540193i
\(883\) −30.8011 −1.03654 −0.518269 0.855218i \(-0.673423\pi\)
−0.518269 + 0.855218i \(0.673423\pi\)
\(884\) −1.26683 + 2.19422i −0.0426081 + 0.0737995i
\(885\) 0.358322 + 0.620631i 0.0120449 + 0.0208623i
\(886\) 13.9715 + 24.1993i 0.469380 + 0.812990i
\(887\) 19.5367 33.8386i 0.655980 1.13619i −0.325667 0.945484i \(-0.605589\pi\)
0.981647 0.190706i \(-0.0610777\pi\)
\(888\) −0.455309 −0.0152792
\(889\) −36.2429 18.0617i −1.21555 0.605770i
\(890\) −2.94368 −0.0986723
\(891\) −0.684347 + 1.18532i −0.0229265 + 0.0397098i
\(892\) −4.99691 8.65491i −0.167309 0.289788i
\(893\) −7.28142 12.6118i −0.243664 0.422038i
\(894\) 2.79256 4.83686i 0.0933973 0.161769i
\(895\) 2.23456 0.0746930
\(896\) −2.20598 + 1.46070i −0.0736968 + 0.0487984i
\(897\) 4.41976 0.147572
\(898\) 0.302215 0.523452i 0.0100851 0.0174678i
\(899\) −0.675875 1.17065i −0.0225417 0.0390434i
\(900\) −6.15577 10.6621i −0.205192 0.355404i
\(901\) −3.65423 + 6.32931i −0.121740 + 0.210860i
\(902\) 0.972889 0.0323937
\(903\) −0.381454 6.21787i −0.0126940 0.206918i
\(904\) −10.2976 −0.342493
\(905\) −0.0173309 + 0.0300179i −0.000576097 + 0.000997830i
\(906\) −5.79436 10.0361i −0.192505 0.333428i
\(907\) 0.206207 + 0.357160i 0.00684697 + 0.0118593i 0.869429 0.494059i \(-0.164487\pi\)
−0.862582 + 0.505918i \(0.831154\pi\)
\(908\) 12.6545 21.9183i 0.419955 0.727383i
\(909\) −39.1675 −1.29911
\(910\) −0.157045 2.55991i −0.00520600 0.0848602i
\(911\) 31.6863 1.04981 0.524907 0.851160i \(-0.324100\pi\)
0.524907 + 0.851160i \(0.324100\pi\)
\(912\) 2.38576 4.13226i 0.0790005 0.136833i
\(913\) −0.988162 1.71155i −0.0327034 0.0566439i
\(914\) 3.55156 + 6.15148i 0.117475 + 0.203473i
\(915\) 0.303912 0.526392i 0.0100470 0.0174020i
\(916\) 18.4785 0.610545
\(917\) −26.9517 + 17.8461i −0.890025 + 0.589331i
\(918\) 2.39057 0.0789004
\(919\) 27.5749 47.7611i 0.909611 1.57549i 0.0950047 0.995477i \(-0.469713\pi\)
0.814606 0.580015i \(-0.196953\pi\)
\(920\) 0.173447 + 0.300420i 0.00571839 + 0.00990454i
\(921\) −10.2378 17.7324i −0.337346 0.584301i
\(922\) −1.90514 + 3.29980i −0.0627424 + 0.108673i
\(923\) 17.5071 0.576252
\(924\) −0.496447 0.247405i −0.0163319 0.00813902i
\(925\) −3.15122 −0.103611
\(926\) 1.71164 2.96464i 0.0562478 0.0974241i
\(927\) −6.09337 10.5540i −0.200132 0.346640i
\(928\) 0.500000 + 0.866025i 0.0164133 + 0.0284287i
\(929\) −19.8498 + 34.3809i −0.651251 + 1.12800i 0.331569 + 0.943431i \(0.392422\pi\)
−0.982820 + 0.184568i \(0.940911\pi\)
\(930\) 0.225225 0.00738542
\(931\) −46.3913 + 5.71352i −1.52041 + 0.187253i
\(932\) −9.35908 −0.306567
\(933\) 3.73893 6.47601i 0.122407 0.212015i
\(934\) −11.4351 19.8061i −0.374166 0.648075i
\(935\) −0.0208454 0.0361053i −0.000681717 0.00118077i
\(936\) 5.17466 8.96278i 0.169139 0.292958i
\(937\) 2.47672 0.0809108 0.0404554 0.999181i \(-0.487119\pi\)
0.0404554 + 0.999181i \(0.487119\pi\)
\(938\) 11.7369 + 5.84911i 0.383224 + 0.190980i
\(939\) 22.4500 0.732629
\(940\) −0.254261 + 0.440392i −0.00829307 + 0.0143640i
\(941\) −12.5890 21.8048i −0.410390 0.710817i 0.584542 0.811363i \(-0.301274\pi\)
−0.994932 + 0.100547i \(0.967941\pi\)
\(942\) −8.44827 14.6328i −0.275260 0.476764i
\(943\) 2.46671 4.27247i 0.0803272 0.139131i
\(944\) 4.30113 0.139990
\(945\) −2.01765 + 1.33599i −0.0656342 + 0.0434597i
\(946\) −0.966721 −0.0314308
\(947\) 19.0860 33.0579i 0.620212 1.07424i −0.369234 0.929336i \(-0.620380\pi\)
0.989446 0.144902i \(-0.0462867\pi\)
\(948\) 0.752730 + 1.30377i 0.0244475 + 0.0423444i
\(949\) −12.1458 21.0371i −0.394269 0.682895i
\(950\) 16.5120 28.5996i 0.535719 0.927893i
\(951\) −9.10929 −0.295389
\(952\) −0.0987327 1.60939i −0.00319994 0.0521606i
\(953\) 41.3605 1.33980 0.669900 0.742452i \(-0.266337\pi\)
0.669900 + 0.742452i \(0.266337\pi\)
\(954\) 14.9265 25.8535i 0.483265 0.837039i
\(955\) −1.19885 2.07646i −0.0387938 0.0671928i
\(956\) 8.77121 + 15.1922i 0.283681 + 0.491350i
\(957\) −0.104824 + 0.181561i −0.00338849 + 0.00586904i
\(958\) −4.57219 −0.147721
\(959\) −2.88844 47.0829i −0.0932725 1.52038i
\(960\) −0.166617 −0.00537755
\(961\) 14.5864 25.2644i 0.470529 0.814979i
\(962\) −1.32449 2.29408i −0.0427032 0.0739641i
\(963\) 13.9797 + 24.2135i 0.450489 + 0.780270i
\(964\) −1.52113 + 2.63467i −0.0489923 + 0.0848571i
\(965\) 2.90718 0.0935853
\(966\) −2.34520 + 1.55288i −0.0754556 + 0.0499630i
\(967\) 7.05786 0.226965 0.113483 0.993540i \(-0.463799\pi\)
0.113483 + 0.993540i \(0.463799\pi\)
\(968\) 5.45696 9.45173i 0.175393 0.303790i
\(969\) 1.45397 + 2.51835i 0.0467082 + 0.0809009i
\(970\) −0.665111 1.15201i −0.0213554 0.0369887i
\(971\) −17.7494 + 30.7428i −0.569605 + 0.986585i 0.427000 + 0.904252i \(0.359570\pi\)
−0.996605 + 0.0823332i \(0.973763\pi\)
\(972\) −15.1014 −0.484377
\(973\) 18.9404 + 9.43899i 0.607203 + 0.302600i
\(974\) 21.6569 0.693931
\(975\) −7.34621 + 12.7240i −0.235267 + 0.407494i
\(976\) −1.82401 3.15928i −0.0583853 0.101126i
\(977\) −7.43503 12.8778i −0.237868 0.411999i 0.722235 0.691648i \(-0.243115\pi\)
−0.960102 + 0.279649i \(0.909782\pi\)
\(978\) −4.86360 + 8.42400i −0.155521 + 0.269370i
\(979\) −3.70393 −0.118378
\(980\) 0.982752 + 1.30315i 0.0313929 + 0.0416277i
\(981\) −37.8050 −1.20702
\(982\) −16.0268 + 27.7593i −0.511437 + 0.885834i
\(983\) −18.3841 31.8422i −0.586362 1.01561i −0.994704 0.102779i \(-0.967226\pi\)
0.408343 0.912829i \(-0.366107\pi\)
\(984\) 1.18479 + 2.05211i 0.0377697 + 0.0654190i
\(985\) 2.21874 3.84296i 0.0706948 0.122447i
\(986\) −0.609435 −0.0194084
\(987\) −3.69036 1.83910i −0.117466 0.0585391i
\(988\) 27.7606 0.883182
\(989\) −2.45107 + 4.24538i −0.0779396 + 0.134995i
\(990\) 0.0851478 + 0.147480i 0.00270617 + 0.00468723i
\(991\) 13.4811 + 23.3500i 0.428242 + 0.741736i 0.996717 0.0809641i \(-0.0257999\pi\)
−0.568475 + 0.822700i \(0.692467\pi\)
\(992\) 0.675875 1.17065i 0.0214591 0.0371682i
\(993\) 7.33295 0.232704
\(994\) −9.28954 + 6.15108i −0.294646 + 0.195100i
\(995\) −2.47353 −0.0784162
\(996\) 2.40677 4.16866i 0.0762616 0.132089i
\(997\) −3.73465 6.46860i −0.118278 0.204863i 0.800808 0.598922i \(-0.204404\pi\)
−0.919085 + 0.394059i \(0.871071\pi\)
\(998\) −12.3057 21.3140i −0.389529 0.674684i
\(999\) −1.24968 + 2.16451i −0.0395382 + 0.0684821i
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.233.4 10
7.2 even 3 2842.2.a.z.1.2 5
7.4 even 3 inner 406.2.e.a.291.4 yes 10
7.5 odd 6 2842.2.a.x.1.4 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
406.2.e.a.233.4 10 1.1 even 1 trivial
406.2.e.a.291.4 yes 10 7.4 even 3 inner
2842.2.a.x.1.4 5 7.5 odd 6
2842.2.a.z.1.2 5 7.2 even 3