Properties

Label 950.2.h.d.381.5
Level $950$
Weight $2$
Character 950.381
Analytic conductor $7.586$
Analytic rank $0$
Dimension $44$
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] = [950,2,Mod(191,950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(950, base_ring=CyclotomicField(10))
 
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("950.191");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.h (of order \(5\), degree \(4\), 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: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(11\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 381.5
Character \(\chi\) \(=\) 950.381
Dual form 950.2.h.d.571.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.309017 - 0.951057i) q^{2} +(-0.628367 + 0.456535i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.766450 + 2.10061i) q^{5} +(0.628367 + 0.456535i) q^{6} -4.62972 q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.740631 + 2.27943i) q^{9} +O(q^{10})\) \(q+(-0.309017 - 0.951057i) q^{2} +(-0.628367 + 0.456535i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.766450 + 2.10061i) q^{5} +(0.628367 + 0.456535i) q^{6} -4.62972 q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.740631 + 2.27943i) q^{9} +(2.23464 + 0.0798131i) q^{10} +(0.182320 + 0.561123i) q^{11} +(0.240015 - 0.738689i) q^{12} +(1.06588 - 3.28045i) q^{13} +(1.43066 + 4.40312i) q^{14} +(-0.477390 - 1.66986i) q^{15} +(0.309017 - 0.951057i) q^{16} +(6.08749 + 4.42282i) q^{17} +2.39673 q^{18} +(0.809017 + 0.587785i) q^{19} +(-0.614636 - 2.14994i) q^{20} +(2.90916 - 2.11363i) q^{21} +(0.477319 - 0.346793i) q^{22} +(-2.36429 - 7.27655i) q^{23} -0.776704 q^{24} +(-3.82511 - 3.22002i) q^{25} -3.44927 q^{26} +(-1.29529 - 3.98651i) q^{27} +(3.74552 - 2.72128i) q^{28} +(-7.65136 + 5.55904i) q^{29} +(-1.44061 + 0.970041i) q^{30} +(-7.03302 - 5.10979i) q^{31} -1.00000 q^{32} +(-0.370736 - 0.269355i) q^{33} +(2.32521 - 7.15627i) q^{34} +(3.54844 - 9.72522i) q^{35} +(-0.740631 - 2.27943i) q^{36} +(1.23211 - 3.79205i) q^{37} +(0.309017 - 0.951057i) q^{38} +(0.827875 + 2.54794i) q^{39} +(-1.85478 + 1.24892i) q^{40} +(-0.136679 + 0.420654i) q^{41} +(-2.90916 - 2.11363i) q^{42} +7.68977 q^{43} +(-0.477319 - 0.346793i) q^{44} +(-4.22053 - 3.30284i) q^{45} +(-6.18980 + 4.49715i) q^{46} +(7.46499 - 5.42364i) q^{47} +(0.240015 + 0.738689i) q^{48} +14.4343 q^{49} +(-1.88040 + 4.63294i) q^{50} -5.84434 q^{51} +(1.06588 + 3.28045i) q^{52} +(-2.55770 + 1.85827i) q^{53} +(-3.39113 + 2.46380i) q^{54} +(-1.31844 - 0.0470897i) q^{55} +(-3.74552 - 2.72128i) q^{56} -0.776704 q^{57} +(7.65136 + 5.55904i) q^{58} +(2.02419 - 6.22981i) q^{59} +(1.36774 + 1.07034i) q^{60} +(-2.74269 - 8.44112i) q^{61} +(-2.68638 + 8.26782i) q^{62} +(3.42891 - 10.5531i) q^{63} +(0.309017 + 0.951057i) q^{64} +(6.07399 + 4.75330i) q^{65} +(-0.141609 + 0.435826i) q^{66} +(-0.436653 - 0.317247i) q^{67} -7.52455 q^{68} +(4.80764 + 3.49296i) q^{69} +(-10.3458 - 0.369512i) q^{70} +(-4.90045 + 3.56039i) q^{71} +(-1.93900 + 1.40876i) q^{72} +(-4.05208 - 12.4710i) q^{73} -3.98720 q^{74} +(3.87362 + 0.277056i) q^{75} -1.00000 q^{76} +(-0.844089 - 2.59784i) q^{77} +(2.16740 - 1.57471i) q^{78} +(4.34677 - 3.15811i) q^{79} +(1.76095 + 1.37806i) q^{80} +(-3.18309 - 2.31265i) q^{81} +0.442302 q^{82} +(0.322084 + 0.234008i) q^{83} +(-1.11120 + 3.41992i) q^{84} +(-13.9564 + 9.39756i) q^{85} +(-2.37627 - 7.31341i) q^{86} +(2.26996 - 6.98623i) q^{87} +(-0.182320 + 0.561123i) q^{88} +(2.28048 + 7.01860i) q^{89} +(-1.83697 + 5.03459i) q^{90} +(-4.93473 + 15.1876i) q^{91} +(6.18980 + 4.49715i) q^{92} +6.75212 q^{93} +(-7.46499 - 5.42364i) q^{94} +(-1.85478 + 1.24892i) q^{95} +(0.628367 - 0.456535i) q^{96} +(-8.76998 + 6.37177i) q^{97} +(-4.46044 - 13.7278i) q^{98} -1.41407 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 11 q^{5} + q^{6} - 10 q^{7} + 11 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 11 q^{5} + q^{6} - 10 q^{7} + 11 q^{8} - 4 q^{10} + 7 q^{11} + 4 q^{12} + 10 q^{13} - 5 q^{14} - 20 q^{15} - 11 q^{16} + 11 q^{17} - 50 q^{18} + 11 q^{19} + 4 q^{20} + 9 q^{21} + 8 q^{22} - 7 q^{23} + 6 q^{24} - 3 q^{25} + 10 q^{26} + 5 q^{27} - 20 q^{29} - 10 q^{30} - 11 q^{31} - 44 q^{32} - 2 q^{33} - q^{34} + 5 q^{35} + 43 q^{37} - 11 q^{38} - 33 q^{39} - 4 q^{40} - 32 q^{41} - 9 q^{42} - 74 q^{43} - 8 q^{44} + 10 q^{45} - 8 q^{46} - 19 q^{47} + 4 q^{48} + 54 q^{49} + 18 q^{50} + 34 q^{51} + 10 q^{52} + 23 q^{53} - 40 q^{54} + 2 q^{55} + 6 q^{57} + 20 q^{58} + 24 q^{59} - 35 q^{60} - 12 q^{61} + q^{62} - 44 q^{63} - 11 q^{64} + 43 q^{65} - 8 q^{66} + 35 q^{67} - 24 q^{68} + 29 q^{69} - 5 q^{70} - 2 q^{71} + 25 q^{72} + 22 q^{73} + 72 q^{74} + 7 q^{75} - 44 q^{76} - 3 q^{77} - 22 q^{78} - 19 q^{79} - q^{80} - 26 q^{81} - 58 q^{82} - 24 q^{83} - 21 q^{84} - 18 q^{85} - 6 q^{86} + 83 q^{87} - 7 q^{88} - 8 q^{89} + 60 q^{90} - 30 q^{91} + 8 q^{92} - 72 q^{93} + 19 q^{94} - 4 q^{95} + q^{96} - 16 q^{97} + q^{98} + 84 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.309017 0.951057i −0.218508 0.672499i
\(3\) −0.628367 + 0.456535i −0.362788 + 0.263581i −0.754214 0.656629i \(-0.771982\pi\)
0.391426 + 0.920209i \(0.371982\pi\)
\(4\) −0.809017 + 0.587785i −0.404508 + 0.293893i
\(5\) −0.766450 + 2.10061i −0.342767 + 0.939421i
\(6\) 0.628367 + 0.456535i 0.256530 + 0.186380i
\(7\) −4.62972 −1.74987 −0.874934 0.484241i \(-0.839096\pi\)
−0.874934 + 0.484241i \(0.839096\pi\)
\(8\) 0.809017 + 0.587785i 0.286031 + 0.207813i
\(9\) −0.740631 + 2.27943i −0.246877 + 0.759809i
\(10\) 2.23464 + 0.0798131i 0.706656 + 0.0252391i
\(11\) 0.182320 + 0.561123i 0.0549715 + 0.169185i 0.974773 0.223200i \(-0.0716502\pi\)
−0.919801 + 0.392385i \(0.871650\pi\)
\(12\) 0.240015 0.738689i 0.0692863 0.213241i
\(13\) 1.06588 3.28045i 0.295623 0.909833i −0.687389 0.726289i \(-0.741243\pi\)
0.983012 0.183543i \(-0.0587568\pi\)
\(14\) 1.43066 + 4.40312i 0.382360 + 1.17678i
\(15\) −0.477390 1.66986i −0.123262 0.431157i
\(16\) 0.309017 0.951057i 0.0772542 0.237764i
\(17\) 6.08749 + 4.42282i 1.47643 + 1.07269i 0.978685 + 0.205369i \(0.0658394\pi\)
0.497748 + 0.867322i \(0.334161\pi\)
\(18\) 2.39673 0.564915
\(19\) 0.809017 + 0.587785i 0.185601 + 0.134847i
\(20\) −0.614636 2.14994i −0.137437 0.480740i
\(21\) 2.90916 2.11363i 0.634831 0.461232i
\(22\) 0.477319 0.346793i 0.101765 0.0739365i
\(23\) −2.36429 7.27655i −0.492989 1.51727i −0.820067 0.572268i \(-0.806064\pi\)
0.327078 0.944998i \(-0.393936\pi\)
\(24\) −0.776704 −0.158544
\(25\) −3.82511 3.22002i −0.765022 0.644004i
\(26\) −3.44927 −0.676457
\(27\) −1.29529 3.98651i −0.249280 0.767204i
\(28\) 3.74552 2.72128i 0.707837 0.514274i
\(29\) −7.65136 + 5.55904i −1.42082 + 1.03229i −0.429188 + 0.903215i \(0.641200\pi\)
−0.991635 + 0.129073i \(0.958800\pi\)
\(30\) −1.44061 + 0.970041i −0.263019 + 0.177104i
\(31\) −7.03302 5.10979i −1.26317 0.917746i −0.264260 0.964452i \(-0.585128\pi\)
−0.998909 + 0.0467060i \(0.985128\pi\)
\(32\) −1.00000 −0.176777
\(33\) −0.370736 0.269355i −0.0645368 0.0468888i
\(34\) 2.32521 7.15627i 0.398771 1.22729i
\(35\) 3.54844 9.72522i 0.599797 1.64386i
\(36\) −0.740631 2.27943i −0.123438 0.379904i
\(37\) 1.23211 3.79205i 0.202558 0.623409i −0.797247 0.603653i \(-0.793711\pi\)
0.999805 0.0197560i \(-0.00628893\pi\)
\(38\) 0.309017 0.951057i 0.0501292 0.154282i
\(39\) 0.827875 + 2.54794i 0.132566 + 0.407996i
\(40\) −1.85478 + 1.24892i −0.293266 + 0.197472i
\(41\) −0.136679 + 0.420654i −0.0213456 + 0.0656951i −0.961162 0.275985i \(-0.910996\pi\)
0.939816 + 0.341680i \(0.110996\pi\)
\(42\) −2.90916 2.11363i −0.448893 0.326140i
\(43\) 7.68977 1.17268 0.586340 0.810065i \(-0.300568\pi\)
0.586340 + 0.810065i \(0.300568\pi\)
\(44\) −0.477319 0.346793i −0.0719586 0.0522810i
\(45\) −4.22053 3.30284i −0.629159 0.492358i
\(46\) −6.18980 + 4.49715i −0.912636 + 0.663069i
\(47\) 7.46499 5.42364i 1.08888 0.791119i 0.109671 0.993968i \(-0.465020\pi\)
0.979210 + 0.202849i \(0.0650202\pi\)
\(48\) 0.240015 + 0.738689i 0.0346431 + 0.106621i
\(49\) 14.4343 2.06204
\(50\) −1.88040 + 4.63294i −0.265928 + 0.655196i
\(51\) −5.84434 −0.818372
\(52\) 1.06588 + 3.28045i 0.147811 + 0.454916i
\(53\) −2.55770 + 1.85827i −0.351326 + 0.255254i −0.749425 0.662089i \(-0.769670\pi\)
0.398099 + 0.917343i \(0.369670\pi\)
\(54\) −3.39113 + 2.46380i −0.461474 + 0.335280i
\(55\) −1.31844 0.0470897i −0.177778 0.00634957i
\(56\) −3.74552 2.72128i −0.500516 0.363646i
\(57\) −0.776704 −0.102877
\(58\) 7.65136 + 5.55904i 1.00467 + 0.729938i
\(59\) 2.02419 6.22981i 0.263527 0.811053i −0.728502 0.685044i \(-0.759783\pi\)
0.992029 0.126009i \(-0.0402168\pi\)
\(60\) 1.36774 + 1.07034i 0.176574 + 0.138181i
\(61\) −2.74269 8.44112i −0.351165 1.08077i −0.958200 0.286100i \(-0.907641\pi\)
0.607035 0.794675i \(-0.292359\pi\)
\(62\) −2.68638 + 8.26782i −0.341170 + 1.05001i
\(63\) 3.42891 10.5531i 0.432002 1.32957i
\(64\) 0.309017 + 0.951057i 0.0386271 + 0.118882i
\(65\) 6.07399 + 4.75330i 0.753386 + 0.589574i
\(66\) −0.141609 + 0.435826i −0.0174308 + 0.0536465i
\(67\) −0.436653 0.317247i −0.0533457 0.0387579i 0.560793 0.827956i \(-0.310496\pi\)
−0.614139 + 0.789198i \(0.710496\pi\)
\(68\) −7.52455 −0.912485
\(69\) 4.80764 + 3.49296i 0.578772 + 0.420503i
\(70\) −10.3458 0.369512i −1.23656 0.0441652i
\(71\) −4.90045 + 3.56039i −0.581577 + 0.422540i −0.839292 0.543681i \(-0.817030\pi\)
0.257716 + 0.966221i \(0.417030\pi\)
\(72\) −1.93900 + 1.40876i −0.228513 + 0.166024i
\(73\) −4.05208 12.4710i −0.474260 1.45962i −0.846953 0.531667i \(-0.821566\pi\)
0.372694 0.927954i \(-0.378434\pi\)
\(74\) −3.98720 −0.463502
\(75\) 3.87362 + 0.277056i 0.447288 + 0.0319917i
\(76\) −1.00000 −0.114708
\(77\) −0.844089 2.59784i −0.0961929 0.296051i
\(78\) 2.16740 1.57471i 0.245410 0.178301i
\(79\) 4.34677 3.15811i 0.489050 0.355316i −0.315769 0.948836i \(-0.602262\pi\)
0.804819 + 0.593521i \(0.202262\pi\)
\(80\) 1.76095 + 1.37806i 0.196880 + 0.154072i
\(81\) −3.18309 2.31265i −0.353676 0.256961i
\(82\) 0.442302 0.0488440
\(83\) 0.322084 + 0.234008i 0.0353533 + 0.0256857i 0.605322 0.795981i \(-0.293045\pi\)
−0.569968 + 0.821667i \(0.693045\pi\)
\(84\) −1.11120 + 3.41992i −0.121242 + 0.373144i
\(85\) −13.9564 + 9.39756i −1.51378 + 1.01931i
\(86\) −2.37627 7.31341i −0.256240 0.788625i
\(87\) 2.26996 6.98623i 0.243366 0.749003i
\(88\) −0.182320 + 0.561123i −0.0194354 + 0.0598159i
\(89\) 2.28048 + 7.01860i 0.241731 + 0.743970i 0.996157 + 0.0875856i \(0.0279151\pi\)
−0.754426 + 0.656385i \(0.772085\pi\)
\(90\) −1.83697 + 5.03459i −0.193634 + 0.530693i
\(91\) −4.93473 + 15.1876i −0.517301 + 1.59209i
\(92\) 6.18980 + 4.49715i 0.645331 + 0.468861i
\(93\) 6.75212 0.700162
\(94\) −7.46499 5.42364i −0.769955 0.559405i
\(95\) −1.85478 + 1.24892i −0.190296 + 0.128136i
\(96\) 0.628367 0.456535i 0.0641324 0.0465949i
\(97\) −8.76998 + 6.37177i −0.890457 + 0.646955i −0.935997 0.352008i \(-0.885499\pi\)
0.0455403 + 0.998963i \(0.485499\pi\)
\(98\) −4.46044 13.7278i −0.450572 1.38672i
\(99\) −1.41407 −0.142119
\(100\) 4.98726 + 0.356708i 0.498726 + 0.0356708i
\(101\) 3.69002 0.367171 0.183586 0.983004i \(-0.441230\pi\)
0.183586 + 0.983004i \(0.441230\pi\)
\(102\) 1.80600 + 5.55830i 0.178821 + 0.550354i
\(103\) −12.8695 + 9.35024i −1.26807 + 0.921306i −0.999124 0.0418491i \(-0.986675\pi\)
−0.268945 + 0.963155i \(0.586675\pi\)
\(104\) 2.79052 2.02743i 0.273633 0.198806i
\(105\) 2.21018 + 7.73100i 0.215692 + 0.754468i
\(106\) 2.55770 + 1.85827i 0.248425 + 0.180492i
\(107\) 2.46664 0.238459 0.119229 0.992867i \(-0.461958\pi\)
0.119229 + 0.992867i \(0.461958\pi\)
\(108\) 3.39113 + 2.46380i 0.326311 + 0.237079i
\(109\) −2.97219 + 9.14746i −0.284684 + 0.876168i 0.701809 + 0.712365i \(0.252376\pi\)
−0.986493 + 0.163803i \(0.947624\pi\)
\(110\) 0.362635 + 1.26846i 0.0345759 + 0.120943i
\(111\) 0.956986 + 2.94530i 0.0908331 + 0.279556i
\(112\) −1.43066 + 4.40312i −0.135185 + 0.416056i
\(113\) 3.51641 10.8224i 0.330796 1.01809i −0.637959 0.770070i \(-0.720221\pi\)
0.968756 0.248017i \(-0.0797787\pi\)
\(114\) 0.240015 + 0.738689i 0.0224794 + 0.0691846i
\(115\) 17.0973 + 0.610652i 1.59433 + 0.0569436i
\(116\) 2.92256 8.99472i 0.271353 0.835139i
\(117\) 6.68812 + 4.85920i 0.618317 + 0.449233i
\(118\) −6.55041 −0.603014
\(119\) −28.1833 20.4764i −2.58356 1.87707i
\(120\) 0.595304 1.63155i 0.0543436 0.148940i
\(121\) 8.61757 6.26103i 0.783415 0.569185i
\(122\) −7.18045 + 5.21690i −0.650087 + 0.472316i
\(123\) −0.106159 0.326723i −0.00957202 0.0294597i
\(124\) 8.69330 0.780681
\(125\) 9.69576 5.56708i 0.867215 0.497934i
\(126\) −11.0962 −0.988527
\(127\) 3.93123 + 12.0991i 0.348840 + 1.07362i 0.959496 + 0.281724i \(0.0909062\pi\)
−0.610655 + 0.791897i \(0.709094\pi\)
\(128\) 0.809017 0.587785i 0.0715077 0.0519534i
\(129\) −4.83200 + 3.51065i −0.425434 + 0.309096i
\(130\) 2.64369 7.24556i 0.231867 0.635478i
\(131\) 3.22073 + 2.34000i 0.281396 + 0.204446i 0.719526 0.694465i \(-0.244359\pi\)
−0.438130 + 0.898912i \(0.644359\pi\)
\(132\) 0.458255 0.0398860
\(133\) −3.74552 2.72128i −0.324778 0.235965i
\(134\) −0.166787 + 0.513317i −0.0144082 + 0.0443438i
\(135\) 9.36687 + 0.334550i 0.806172 + 0.0287935i
\(136\) 2.32521 + 7.15627i 0.199385 + 0.613645i
\(137\) 3.45205 10.6243i 0.294929 0.907697i −0.688317 0.725410i \(-0.741650\pi\)
0.983245 0.182287i \(-0.0583500\pi\)
\(138\) 1.83636 5.65172i 0.156321 0.481107i
\(139\) −0.117690 0.362214i −0.00998237 0.0307226i 0.945941 0.324338i \(-0.105142\pi\)
−0.955924 + 0.293615i \(0.905142\pi\)
\(140\) 2.84559 + 9.95359i 0.240496 + 0.841232i
\(141\) −2.21467 + 6.81606i −0.186509 + 0.574016i
\(142\) 4.90045 + 3.56039i 0.411237 + 0.298781i
\(143\) 2.03507 0.170181
\(144\) 1.93900 + 1.40876i 0.161583 + 0.117397i
\(145\) −5.81298 20.3332i −0.482742 1.68858i
\(146\) −10.6085 + 7.70751i −0.877964 + 0.637878i
\(147\) −9.07002 + 6.58976i −0.748083 + 0.543514i
\(148\) 1.23211 + 3.79205i 0.101279 + 0.311705i
\(149\) 4.34739 0.356152 0.178076 0.984017i \(-0.443013\pi\)
0.178076 + 0.984017i \(0.443013\pi\)
\(150\) −0.933519 3.76965i −0.0762215 0.307791i
\(151\) −17.9720 −1.46254 −0.731268 0.682090i \(-0.761071\pi\)
−0.731268 + 0.682090i \(0.761071\pi\)
\(152\) 0.309017 + 0.951057i 0.0250646 + 0.0771409i
\(153\) −14.5901 + 10.6003i −1.17954 + 0.856984i
\(154\) −2.20985 + 1.60555i −0.178075 + 0.129379i
\(155\) 16.1241 10.8572i 1.29512 0.872074i
\(156\) −2.16740 1.57471i −0.173531 0.126078i
\(157\) −5.03405 −0.401761 −0.200880 0.979616i \(-0.564380\pi\)
−0.200880 + 0.979616i \(0.564380\pi\)
\(158\) −4.34677 3.15811i −0.345811 0.251246i
\(159\) 0.758803 2.33536i 0.0601770 0.185206i
\(160\) 0.766450 2.10061i 0.0605932 0.166068i
\(161\) 10.9460 + 33.6884i 0.862667 + 2.65501i
\(162\) −1.21583 + 3.74194i −0.0955247 + 0.293995i
\(163\) −1.17814 + 3.62594i −0.0922789 + 0.284005i −0.986535 0.163550i \(-0.947705\pi\)
0.894256 + 0.447556i \(0.147705\pi\)
\(164\) −0.136679 0.420654i −0.0106728 0.0328475i
\(165\) 0.849961 0.572324i 0.0661693 0.0445553i
\(166\) 0.123025 0.378632i 0.00954860 0.0293876i
\(167\) −11.0834 8.05257i −0.857660 0.623126i 0.0695874 0.997576i \(-0.477832\pi\)
−0.927247 + 0.374449i \(0.877832\pi\)
\(168\) 3.59592 0.277431
\(169\) 0.891982 + 0.648063i 0.0686140 + 0.0498510i
\(170\) 13.2504 + 10.3693i 1.01626 + 0.795287i
\(171\) −1.93900 + 1.40876i −0.148279 + 0.107731i
\(172\) −6.22116 + 4.51994i −0.474359 + 0.344642i
\(173\) −3.15320 9.70455i −0.239733 0.737823i −0.996458 0.0840897i \(-0.973202\pi\)
0.756725 0.653733i \(-0.226798\pi\)
\(174\) −7.34576 −0.556881
\(175\) 17.7092 + 14.9078i 1.33869 + 1.12692i
\(176\) 0.589999 0.0444729
\(177\) 1.57220 + 4.83872i 0.118173 + 0.363700i
\(178\) 5.97038 4.33773i 0.447499 0.325127i
\(179\) −7.17617 + 5.21379i −0.536372 + 0.389697i −0.822736 0.568424i \(-0.807553\pi\)
0.286364 + 0.958121i \(0.407553\pi\)
\(180\) 5.35584 + 0.191291i 0.399201 + 0.0142580i
\(181\) 9.77114 + 7.09915i 0.726283 + 0.527675i 0.888385 0.459099i \(-0.151828\pi\)
−0.162102 + 0.986774i \(0.551828\pi\)
\(182\) 15.9691 1.18371
\(183\) 5.57708 + 4.05199i 0.412270 + 0.299531i
\(184\) 2.36429 7.27655i 0.174298 0.536434i
\(185\) 7.02126 + 5.49460i 0.516214 + 0.403971i
\(186\) −2.08652 6.42164i −0.152991 0.470858i
\(187\) −1.37187 + 4.22219i −0.100321 + 0.308757i
\(188\) −2.85137 + 8.77563i −0.207958 + 0.640028i
\(189\) 5.99685 + 18.4564i 0.436207 + 1.34251i
\(190\) 1.76095 + 1.37806i 0.127753 + 0.0999750i
\(191\) 6.72052 20.6836i 0.486280 1.49662i −0.343839 0.939029i \(-0.611727\pi\)
0.830119 0.557587i \(-0.188273\pi\)
\(192\) −0.628367 0.456535i −0.0453485 0.0329476i
\(193\) −9.29404 −0.668999 −0.334500 0.942396i \(-0.608567\pi\)
−0.334500 + 0.942396i \(0.608567\pi\)
\(194\) 8.76998 + 6.37177i 0.629648 + 0.457466i
\(195\) −5.98674 0.213824i −0.428720 0.0153123i
\(196\) −11.6776 + 8.48426i −0.834113 + 0.606019i
\(197\) −4.35403 + 3.16339i −0.310212 + 0.225382i −0.731987 0.681318i \(-0.761407\pi\)
0.421776 + 0.906700i \(0.361407\pi\)
\(198\) 0.436972 + 1.34486i 0.0310542 + 0.0955751i
\(199\) −1.32008 −0.0935782 −0.0467891 0.998905i \(-0.514899\pi\)
−0.0467891 + 0.998905i \(0.514899\pi\)
\(200\) −1.20190 4.85339i −0.0849871 0.343187i
\(201\) 0.419213 0.0295690
\(202\) −1.14028 3.50942i −0.0802298 0.246922i
\(203\) 35.4237 25.7368i 2.48625 1.80637i
\(204\) 4.72817 3.43522i 0.331038 0.240513i
\(205\) −0.778872 0.609518i −0.0543987 0.0425706i
\(206\) 12.8695 + 9.35024i 0.896660 + 0.651462i
\(207\) 18.3374 1.27454
\(208\) −2.79052 2.02743i −0.193487 0.140577i
\(209\) −0.182320 + 0.561123i −0.0126113 + 0.0388137i
\(210\) 6.66963 4.49102i 0.460248 0.309910i
\(211\) −5.80510 17.8663i −0.399639 1.22996i −0.925289 0.379263i \(-0.876178\pi\)
0.525650 0.850701i \(-0.323822\pi\)
\(212\) 0.976953 3.00675i 0.0670974 0.206504i
\(213\) 1.45384 4.47446i 0.0996154 0.306585i
\(214\) −0.762233 2.34591i −0.0521052 0.160363i
\(215\) −5.89382 + 16.1532i −0.401955 + 1.10164i
\(216\) 1.29529 3.98651i 0.0881336 0.271247i
\(217\) 32.5609 + 23.6569i 2.21038 + 1.60593i
\(218\) 9.61821 0.651427
\(219\) 8.23964 + 5.98645i 0.556784 + 0.404527i
\(220\) 1.09432 0.736862i 0.0737789 0.0496792i
\(221\) 20.9974 15.2555i 1.41244 1.02619i
\(222\) 2.50542 1.82030i 0.168153 0.122170i
\(223\) 0.566208 + 1.74261i 0.0379161 + 0.116694i 0.968223 0.250088i \(-0.0804596\pi\)
−0.930307 + 0.366782i \(0.880460\pi\)
\(224\) 4.62972 0.309336
\(225\) 10.1728 6.33421i 0.678186 0.422281i
\(226\) −11.3794 −0.756943
\(227\) −6.82456 21.0038i −0.452962 1.39407i −0.873512 0.486803i \(-0.838163\pi\)
0.420550 0.907269i \(-0.361837\pi\)
\(228\) 0.628367 0.456535i 0.0416146 0.0302348i
\(229\) −17.5605 + 12.7584i −1.16043 + 0.843100i −0.989832 0.142241i \(-0.954569\pi\)
−0.170596 + 0.985341i \(0.554569\pi\)
\(230\) −4.70259 16.4492i −0.310080 1.08463i
\(231\) 1.71640 + 1.24704i 0.112931 + 0.0820492i
\(232\) −9.45761 −0.620922
\(233\) −6.11438 4.44236i −0.400567 0.291029i 0.369205 0.929348i \(-0.379630\pi\)
−0.769772 + 0.638319i \(0.779630\pi\)
\(234\) 2.55463 7.86235i 0.167002 0.513978i
\(235\) 5.67139 + 19.8380i 0.369961 + 1.29409i
\(236\) 2.02419 + 6.22981i 0.131763 + 0.405526i
\(237\) −1.28958 + 3.96891i −0.0837670 + 0.257808i
\(238\) −10.7651 + 33.1315i −0.697796 + 2.14760i
\(239\) 4.26291 + 13.1199i 0.275744 + 0.848654i 0.989021 + 0.147772i \(0.0472102\pi\)
−0.713277 + 0.700882i \(0.752790\pi\)
\(240\) −1.73566 0.0619912i −0.112036 0.00400151i
\(241\) −3.37943 + 10.4008i −0.217688 + 0.669975i 0.781264 + 0.624201i \(0.214575\pi\)
−0.998952 + 0.0457740i \(0.985425\pi\)
\(242\) −8.61757 6.26103i −0.553958 0.402474i
\(243\) 15.6309 1.00273
\(244\) 7.18045 + 5.21690i 0.459681 + 0.333978i
\(245\) −11.0632 + 30.3208i −0.706799 + 1.93712i
\(246\) −0.277928 + 0.201926i −0.0177200 + 0.0128743i
\(247\) 2.79052 2.02743i 0.177556 0.129002i
\(248\) −2.68638 8.26782i −0.170585 0.525007i
\(249\) −0.309220 −0.0195960
\(250\) −8.29076 7.50089i −0.524353 0.474398i
\(251\) −2.32925 −0.147021 −0.0735106 0.997294i \(-0.523420\pi\)
−0.0735106 + 0.997294i \(0.523420\pi\)
\(252\) 3.42891 + 10.5531i 0.216001 + 0.664783i
\(253\) 3.65198 2.65332i 0.229598 0.166813i
\(254\) 10.2921 7.47765i 0.645784 0.469189i
\(255\) 4.47939 12.2767i 0.280511 0.768795i
\(256\) −0.809017 0.587785i −0.0505636 0.0367366i
\(257\) −18.3886 −1.14705 −0.573524 0.819189i \(-0.694424\pi\)
−0.573524 + 0.819189i \(0.694424\pi\)
\(258\) 4.83200 + 3.51065i 0.300827 + 0.218564i
\(259\) −5.70433 + 17.5561i −0.354450 + 1.09088i
\(260\) −7.70788 0.275297i −0.478023 0.0170732i
\(261\) −7.00459 21.5579i −0.433573 1.33440i
\(262\) 1.23021 3.78619i 0.0760026 0.233912i
\(263\) 1.63282 5.02529i 0.100684 0.309873i −0.888009 0.459825i \(-0.847912\pi\)
0.988693 + 0.149952i \(0.0479121\pi\)
\(264\) −0.141609 0.435826i −0.00871540 0.0268232i
\(265\) −1.94316 6.79699i −0.119368 0.417536i
\(266\) −1.43066 + 4.40312i −0.0877195 + 0.269973i
\(267\) −4.63722 3.36913i −0.283793 0.206188i
\(268\) 0.539733 0.0329695
\(269\) −7.02714 5.10551i −0.428452 0.311289i 0.352578 0.935783i \(-0.385305\pi\)
−0.781030 + 0.624494i \(0.785305\pi\)
\(270\) −2.57635 9.01180i −0.156791 0.548441i
\(271\) 5.61387 4.07871i 0.341018 0.247764i −0.404073 0.914727i \(-0.632406\pi\)
0.745091 + 0.666962i \(0.232406\pi\)
\(272\) 6.08749 4.42282i 0.369108 0.268173i
\(273\) −3.83283 11.7962i −0.231973 0.713940i
\(274\) −11.1711 −0.674869
\(275\) 1.10943 2.73343i 0.0669013 0.164832i
\(276\) −5.94257 −0.357701
\(277\) −7.52693 23.1655i −0.452249 1.39188i −0.874334 0.485324i \(-0.838702\pi\)
0.422085 0.906556i \(-0.361298\pi\)
\(278\) −0.308117 + 0.223860i −0.0184796 + 0.0134263i
\(279\) 16.8563 12.2468i 1.00916 0.733196i
\(280\) 8.58709 5.78215i 0.513177 0.345549i
\(281\) −14.8864 10.8156i −0.888049 0.645206i 0.0473193 0.998880i \(-0.484932\pi\)
−0.935369 + 0.353674i \(0.884932\pi\)
\(282\) 7.16683 0.426779
\(283\) −10.0470 7.29954i −0.597230 0.433913i 0.247665 0.968846i \(-0.420337\pi\)
−0.844894 + 0.534933i \(0.820337\pi\)
\(284\) 1.87181 5.76083i 0.111071 0.341842i
\(285\) 0.595304 1.63155i 0.0352628 0.0966447i
\(286\) −0.628870 1.93546i −0.0371859 0.114446i
\(287\) 0.632784 1.94751i 0.0373520 0.114958i
\(288\) 0.740631 2.27943i 0.0436421 0.134317i
\(289\) 12.2429 + 37.6797i 0.720170 + 2.21645i
\(290\) −17.5418 + 11.8118i −1.03009 + 0.693612i
\(291\) 2.60183 8.00761i 0.152522 0.469414i
\(292\) 10.6085 + 7.70751i 0.620814 + 0.451048i
\(293\) 4.20129 0.245442 0.122721 0.992441i \(-0.460838\pi\)
0.122721 + 0.992441i \(0.460838\pi\)
\(294\) 9.07002 + 6.58976i 0.528975 + 0.384322i
\(295\) 11.5350 + 9.02686i 0.671591 + 0.525564i
\(296\) 3.22571 2.34362i 0.187491 0.136220i
\(297\) 2.00076 1.45364i 0.116096 0.0843487i
\(298\) −1.34342 4.13461i −0.0778221 0.239512i
\(299\) −26.3904 −1.52620
\(300\) −3.29668 + 2.05272i −0.190334 + 0.118514i
\(301\) −35.6015 −2.05204
\(302\) 5.55364 + 17.0923i 0.319576 + 0.983554i
\(303\) −2.31869 + 1.68463i −0.133205 + 0.0967792i
\(304\) 0.809017 0.587785i 0.0464003 0.0337118i
\(305\) 19.8336 + 0.708383i 1.13567 + 0.0405619i
\(306\) 14.5901 + 10.6003i 0.834059 + 0.605979i
\(307\) −3.38024 −0.192921 −0.0964603 0.995337i \(-0.530752\pi\)
−0.0964603 + 0.995337i \(0.530752\pi\)
\(308\) 2.20985 + 1.60555i 0.125918 + 0.0914849i
\(309\) 3.81805 11.7508i 0.217201 0.668477i
\(310\) −15.3085 11.9799i −0.869463 0.680412i
\(311\) 5.39224 + 16.5956i 0.305766 + 0.941051i 0.979390 + 0.201977i \(0.0647366\pi\)
−0.673624 + 0.739074i \(0.735263\pi\)
\(312\) −0.827875 + 2.54794i −0.0468692 + 0.144249i
\(313\) 2.81691 8.66957i 0.159221 0.490033i −0.839343 0.543602i \(-0.817060\pi\)
0.998564 + 0.0535697i \(0.0170599\pi\)
\(314\) 1.55561 + 4.78766i 0.0877879 + 0.270183i
\(315\) 19.5398 + 15.2912i 1.10095 + 0.861563i
\(316\) −1.66032 + 5.10994i −0.0934002 + 0.287456i
\(317\) −3.49485 2.53916i −0.196290 0.142613i 0.485299 0.874348i \(-0.338711\pi\)
−0.681589 + 0.731735i \(0.738711\pi\)
\(318\) −2.45554 −0.137700
\(319\) −4.51430 3.27983i −0.252752 0.183635i
\(320\) −2.23464 0.0798131i −0.124920 0.00446169i
\(321\) −1.54995 + 1.12611i −0.0865099 + 0.0628531i
\(322\) 28.6570 20.8206i 1.59699 1.16028i
\(323\) 2.32521 + 7.15627i 0.129378 + 0.398185i
\(324\) 3.93451 0.218584
\(325\) −14.6402 + 9.11592i −0.812094 + 0.505660i
\(326\) 3.81254 0.211157
\(327\) −2.30851 7.10487i −0.127661 0.392900i
\(328\) −0.357829 + 0.259978i −0.0197578 + 0.0143549i
\(329\) −34.5608 + 25.1099i −1.90540 + 1.38435i
\(330\) −0.806964 0.631503i −0.0444219 0.0347631i
\(331\) −23.1621 16.8282i −1.27310 0.924963i −0.273780 0.961792i \(-0.588274\pi\)
−0.999322 + 0.0368297i \(0.988274\pi\)
\(332\) −0.398118 −0.0218495
\(333\) 7.73116 + 5.61702i 0.423665 + 0.307811i
\(334\) −4.23349 + 13.0293i −0.231646 + 0.712933i
\(335\) 1.00109 0.674084i 0.0546951 0.0368291i
\(336\) −1.11120 3.41992i −0.0606209 0.186572i
\(337\) −7.47054 + 22.9920i −0.406946 + 1.25245i 0.512313 + 0.858799i \(0.328789\pi\)
−0.919259 + 0.393653i \(0.871211\pi\)
\(338\) 0.340707 1.04859i 0.0185320 0.0570357i
\(339\) 2.73121 + 8.40581i 0.148339 + 0.456541i
\(340\) 5.76718 15.8061i 0.312770 0.857207i
\(341\) 1.58496 4.87801i 0.0858304 0.264159i
\(342\) 1.93900 + 1.40876i 0.104849 + 0.0761772i
\(343\) −34.4186 −1.85843
\(344\) 6.22116 + 4.51994i 0.335422 + 0.243699i
\(345\) −11.0222 + 7.42180i −0.593413 + 0.399576i
\(346\) −8.25518 + 5.99774i −0.443801 + 0.322440i
\(347\) 16.3956 11.9121i 0.880164 0.639476i −0.0531312 0.998588i \(-0.516920\pi\)
0.933295 + 0.359111i \(0.116920\pi\)
\(348\) 2.26996 + 6.98623i 0.121683 + 0.374501i
\(349\) −14.7736 −0.790815 −0.395407 0.918506i \(-0.629397\pi\)
−0.395407 + 0.918506i \(0.629397\pi\)
\(350\) 8.70571 21.4492i 0.465340 1.14651i
\(351\) −14.4582 −0.771720
\(352\) −0.182320 0.561123i −0.00971768 0.0299079i
\(353\) 14.7349 10.7055i 0.784261 0.569799i −0.121994 0.992531i \(-0.538929\pi\)
0.906255 + 0.422732i \(0.138929\pi\)
\(354\) 4.11606 2.99049i 0.218766 0.158943i
\(355\) −3.72303 13.0228i −0.197598 0.691178i
\(356\) −5.97038 4.33773i −0.316429 0.229899i
\(357\) 27.0577 1.43204
\(358\) 7.17617 + 5.21379i 0.379272 + 0.275557i
\(359\) −0.738951 + 2.27426i −0.0390004 + 0.120031i −0.968661 0.248386i \(-0.920100\pi\)
0.929661 + 0.368417i \(0.120100\pi\)
\(360\) −1.47312 5.15282i −0.0776401 0.271577i
\(361\) 0.309017 + 0.951057i 0.0162641 + 0.0500556i
\(362\) 3.73224 11.4867i 0.196162 0.603725i
\(363\) −2.55661 + 7.86845i −0.134187 + 0.412986i
\(364\) −4.93473 15.1876i −0.258650 0.796044i
\(365\) 29.3024 + 1.04657i 1.53376 + 0.0547802i
\(366\) 2.13026 6.55625i 0.111350 0.342701i
\(367\) 6.48781 + 4.71367i 0.338661 + 0.246052i 0.744097 0.668072i \(-0.232880\pi\)
−0.405436 + 0.914124i \(0.632880\pi\)
\(368\) −7.65102 −0.398837
\(369\) −0.857621 0.623098i −0.0446460 0.0324372i
\(370\) 3.05599 8.37554i 0.158873 0.435424i
\(371\) 11.8414 8.60329i 0.614775 0.446660i
\(372\) −5.46258 + 3.96879i −0.283221 + 0.205772i
\(373\) 3.99780 + 12.3040i 0.206998 + 0.637076i 0.999625 + 0.0273688i \(0.00871285\pi\)
−0.792627 + 0.609707i \(0.791287\pi\)
\(374\) 4.43948 0.229560
\(375\) −3.55092 + 7.92462i −0.183369 + 0.409225i
\(376\) 9.22724 0.475859
\(377\) 10.0807 + 31.0252i 0.519182 + 1.59788i
\(378\) 15.7000 11.4067i 0.807519 0.586697i
\(379\) −12.9467 + 9.40631i −0.665026 + 0.483170i −0.868357 0.495940i \(-0.834823\pi\)
0.203330 + 0.979110i \(0.434823\pi\)
\(380\) 0.766450 2.10061i 0.0393180 0.107759i
\(381\) −7.99391 5.80792i −0.409541 0.297549i
\(382\) −21.7481 −1.11273
\(383\) −4.26975 3.10216i −0.218174 0.158513i 0.473330 0.880885i \(-0.343052\pi\)
−0.691504 + 0.722372i \(0.743052\pi\)
\(384\) −0.240015 + 0.738689i −0.0122482 + 0.0376961i
\(385\) 6.10400 + 0.218012i 0.311088 + 0.0111109i
\(386\) 2.87201 + 8.83915i 0.146182 + 0.449901i
\(387\) −5.69528 + 17.5283i −0.289507 + 0.891012i
\(388\) 3.34984 10.3097i 0.170062 0.523397i
\(389\) −8.72252 26.8452i −0.442250 1.36110i −0.885472 0.464693i \(-0.846165\pi\)
0.443223 0.896412i \(-0.353835\pi\)
\(390\) 1.64665 + 5.75981i 0.0833812 + 0.291659i
\(391\) 17.7902 54.7527i 0.899691 2.76896i
\(392\) 11.6776 + 8.48426i 0.589807 + 0.428520i
\(393\) −3.09209 −0.155975
\(394\) 4.35403 + 3.16339i 0.219353 + 0.159369i
\(395\) 3.30238 + 11.5514i 0.166161 + 0.581214i
\(396\) 1.14401 0.831169i 0.0574885 0.0417678i
\(397\) 5.79692 4.21171i 0.290939 0.211379i −0.432736 0.901521i \(-0.642452\pi\)
0.723675 + 0.690141i \(0.242452\pi\)
\(398\) 0.407928 + 1.25547i 0.0204476 + 0.0629312i
\(399\) 3.59592 0.180021
\(400\) −4.24445 + 2.64286i −0.212222 + 0.132143i
\(401\) −8.92851 −0.445868 −0.222934 0.974833i \(-0.571564\pi\)
−0.222934 + 0.974833i \(0.571564\pi\)
\(402\) −0.129544 0.398695i −0.00646107 0.0198851i
\(403\) −24.2588 + 17.6250i −1.20842 + 0.877966i
\(404\) −2.98529 + 2.16894i −0.148524 + 0.107909i
\(405\) 7.29765 4.91389i 0.362623 0.244173i
\(406\) −35.4237 25.7368i −1.75805 1.27730i
\(407\) 2.35244 0.116606
\(408\) −4.72817 3.43522i −0.234079 0.170069i
\(409\) −8.38799 + 25.8156i −0.414759 + 1.27650i 0.497707 + 0.867345i \(0.334176\pi\)
−0.912466 + 0.409152i \(0.865824\pi\)
\(410\) −0.339002 + 0.929102i −0.0167421 + 0.0458851i
\(411\) 2.68122 + 8.25195i 0.132255 + 0.407039i
\(412\) 4.91571 15.1290i 0.242180 0.745352i
\(413\) −9.37142 + 28.8423i −0.461138 + 1.41924i
\(414\) −5.66658 17.4399i −0.278497 0.857126i
\(415\) −0.738420 + 0.497217i −0.0362476 + 0.0244074i
\(416\) −1.06588 + 3.28045i −0.0522592 + 0.160837i
\(417\) 0.239316 + 0.173873i 0.0117194 + 0.00851461i
\(418\) 0.589999 0.0288578
\(419\) 9.30697 + 6.76191i 0.454675 + 0.330341i 0.791439 0.611248i \(-0.209332\pi\)
−0.336764 + 0.941589i \(0.609332\pi\)
\(420\) −6.33224 4.95539i −0.308982 0.241799i
\(421\) 28.7516 20.8892i 1.40127 1.01808i 0.406745 0.913542i \(-0.366664\pi\)
0.994521 0.104537i \(-0.0333362\pi\)
\(422\) −15.1979 + 11.0420i −0.739824 + 0.537514i
\(423\) 6.83398 + 21.0328i 0.332279 + 1.02265i
\(424\) −3.16148 −0.153535
\(425\) −9.04374 36.5196i −0.438686 1.77146i
\(426\) −4.70472 −0.227945
\(427\) 12.6979 + 39.0800i 0.614493 + 1.89121i
\(428\) −1.99555 + 1.44985i −0.0964586 + 0.0700813i
\(429\) −1.27877 + 0.929079i −0.0617395 + 0.0448564i
\(430\) 17.1839 + 0.613745i 0.828681 + 0.0295974i
\(431\) 8.49838 + 6.17443i 0.409352 + 0.297412i 0.773340 0.633992i \(-0.218585\pi\)
−0.363987 + 0.931404i \(0.618585\pi\)
\(432\) −4.19166 −0.201671
\(433\) 27.6183 + 20.0659i 1.32725 + 0.964305i 0.999811 + 0.0194340i \(0.00618642\pi\)
0.327441 + 0.944871i \(0.393814\pi\)
\(434\) 12.4372 38.2777i 0.597003 1.83739i
\(435\) 12.9355 + 10.1229i 0.620211 + 0.485356i
\(436\) −2.97219 9.14746i −0.142342 0.438084i
\(437\) 2.36429 7.27655i 0.113100 0.348085i
\(438\) 3.14726 9.68628i 0.150382 0.462829i
\(439\) −6.43752 19.8126i −0.307246 0.945606i −0.978830 0.204677i \(-0.934386\pi\)
0.671584 0.740929i \(-0.265614\pi\)
\(440\) −1.03896 0.813055i −0.0495305 0.0387609i
\(441\) −10.6905 + 32.9019i −0.509070 + 1.56676i
\(442\) −20.9974 15.2555i −0.998743 0.725629i
\(443\) −25.3990 −1.20674 −0.603372 0.797460i \(-0.706176\pi\)
−0.603372 + 0.797460i \(0.706176\pi\)
\(444\) −2.50542 1.82030i −0.118902 0.0863874i
\(445\) −16.4912 0.589005i −0.781758 0.0279215i
\(446\) 1.48235 1.07699i 0.0701914 0.0509971i
\(447\) −2.73176 + 1.98474i −0.129208 + 0.0938748i
\(448\) −1.43066 4.40312i −0.0675924 0.208028i
\(449\) −11.9617 −0.564509 −0.282255 0.959340i \(-0.591082\pi\)
−0.282255 + 0.959340i \(0.591082\pi\)
\(450\) −9.16776 7.71752i −0.432172 0.363808i
\(451\) −0.260958 −0.0122880
\(452\) 3.51641 + 10.8224i 0.165398 + 0.509043i
\(453\) 11.2930 8.20483i 0.530590 0.385496i
\(454\) −17.8669 + 12.9811i −0.838536 + 0.609232i
\(455\) −28.1209 22.0064i −1.31833 1.03168i
\(456\) −0.628367 0.456535i −0.0294260 0.0213792i
\(457\) −33.0112 −1.54420 −0.772099 0.635502i \(-0.780793\pi\)
−0.772099 + 0.635502i \(0.780793\pi\)
\(458\) 17.5605 + 12.7584i 0.820547 + 0.596162i
\(459\) 9.74651 29.9967i 0.454928 1.40012i
\(460\) −14.1909 + 9.55551i −0.661656 + 0.445528i
\(461\) 8.41344 + 25.8939i 0.391853 + 1.20600i 0.931386 + 0.364034i \(0.118601\pi\)
−0.539533 + 0.841965i \(0.681399\pi\)
\(462\) 0.655607 2.01775i 0.0305016 0.0938743i
\(463\) 6.48247 19.9510i 0.301266 0.927201i −0.679779 0.733417i \(-0.737924\pi\)
0.981044 0.193783i \(-0.0620758\pi\)
\(464\) 2.92256 + 8.99472i 0.135676 + 0.417569i
\(465\) −5.17516 + 14.1836i −0.239992 + 0.657746i
\(466\) −2.33549 + 7.18789i −0.108189 + 0.332973i
\(467\) −24.4871 17.7909i −1.13313 0.823267i −0.146982 0.989139i \(-0.546956\pi\)
−0.986147 + 0.165873i \(0.946956\pi\)
\(468\) −8.26697 −0.382141
\(469\) 2.02158 + 1.46877i 0.0933480 + 0.0678213i
\(470\) 17.1145 11.5241i 0.789432 0.531566i
\(471\) 3.16323 2.29822i 0.145754 0.105896i
\(472\) 5.29940 3.85024i 0.243924 0.177221i
\(473\) 1.40200 + 4.31491i 0.0644639 + 0.198400i
\(474\) 4.17316 0.191679
\(475\) −1.20190 4.85339i −0.0551469 0.222689i
\(476\) 34.8365 1.59673
\(477\) −2.34149 7.20637i −0.107210 0.329957i
\(478\) 11.1604 8.10853i 0.510466 0.370875i
\(479\) −12.6534 + 9.19325i −0.578150 + 0.420050i −0.838057 0.545583i \(-0.816308\pi\)
0.259907 + 0.965634i \(0.416308\pi\)
\(480\) 0.477390 + 1.66986i 0.0217898 + 0.0762185i
\(481\) −11.1263 8.08376i −0.507318 0.368588i
\(482\) 10.9361 0.498124
\(483\) −22.2580 16.1714i −1.01278 0.735824i
\(484\) −3.29162 + 10.1306i −0.149619 + 0.460480i
\(485\) −6.66283 23.3059i −0.302544 1.05827i
\(486\) −4.83023 14.8659i −0.219103 0.674331i
\(487\) 0.751774 2.31372i 0.0340661 0.104845i −0.932578 0.360970i \(-0.882446\pi\)
0.966644 + 0.256125i \(0.0824458\pi\)
\(488\) 2.74269 8.44112i 0.124156 0.382112i
\(489\) −0.915065 2.81628i −0.0413807 0.127357i
\(490\) 32.2555 + 1.15205i 1.45715 + 0.0520441i
\(491\) 2.57170 7.91487i 0.116059 0.357193i −0.876107 0.482116i \(-0.839868\pi\)
0.992166 + 0.124923i \(0.0398684\pi\)
\(492\) 0.277928 + 0.201926i 0.0125299 + 0.00910354i
\(493\) −71.1642 −3.20507
\(494\) −2.79052 2.02743i −0.125551 0.0912183i
\(495\) 1.08381 2.97041i 0.0487138 0.133510i
\(496\) −7.03302 + 5.10979i −0.315792 + 0.229436i
\(497\) 22.6877 16.4836i 1.01768 0.739390i
\(498\) 0.0955541 + 0.294085i 0.00428188 + 0.0131783i
\(499\) −18.1475 −0.812396 −0.406198 0.913785i \(-0.633146\pi\)
−0.406198 + 0.913785i \(0.633146\pi\)
\(500\) −4.57179 + 10.2029i −0.204456 + 0.456287i
\(501\) 10.6407 0.475393
\(502\) 0.719779 + 2.21525i 0.0321253 + 0.0988716i
\(503\) −16.3283 + 11.8632i −0.728044 + 0.528955i −0.888944 0.458016i \(-0.848560\pi\)
0.160900 + 0.986971i \(0.448560\pi\)
\(504\) 8.97700 6.52218i 0.399868 0.290521i
\(505\) −2.82822 + 7.75130i −0.125854 + 0.344928i
\(506\) −3.65198 2.65332i −0.162350 0.117954i
\(507\) −0.856356 −0.0380321
\(508\) −10.2921 7.47765i −0.456638 0.331767i
\(509\) 5.02190 15.4558i 0.222592 0.685067i −0.775935 0.630812i \(-0.782722\pi\)
0.998527 0.0542547i \(-0.0172783\pi\)
\(510\) −13.0600 0.466455i −0.578308 0.0206550i
\(511\) 18.7600 + 57.7373i 0.829892 + 2.55415i
\(512\) −0.309017 + 0.951057i −0.0136568 + 0.0420312i
\(513\) 1.29529 3.98651i 0.0571887 0.176009i
\(514\) 5.68238 + 17.4886i 0.250639 + 0.771388i
\(515\) −9.77737 34.2003i −0.430842 1.50704i
\(516\) 1.84566 5.68035i 0.0812506 0.250064i
\(517\) 4.40434 + 3.19994i 0.193703 + 0.140733i
\(518\) 18.4596 0.811068
\(519\) 6.41183 + 4.65847i 0.281448 + 0.204484i
\(520\) 2.12004 + 7.41570i 0.0929701 + 0.325200i
\(521\) 6.13968 4.46074i 0.268984 0.195429i −0.445114 0.895474i \(-0.646837\pi\)
0.714098 + 0.700045i \(0.246837\pi\)
\(522\) −18.3383 + 13.3235i −0.802644 + 0.583155i
\(523\) −5.14567 15.8367i −0.225004 0.692492i −0.998291 0.0584358i \(-0.981389\pi\)
0.773287 0.634056i \(-0.218611\pi\)
\(524\) −3.98104 −0.173913
\(525\) −17.9338 1.28269i −0.782695 0.0559813i
\(526\) −5.28390 −0.230389
\(527\) −20.2138 62.2116i −0.880525 2.70998i
\(528\) −0.370736 + 0.269355i −0.0161342 + 0.0117222i
\(529\) −28.7509 + 20.8887i −1.25004 + 0.908206i
\(530\) −5.86385 + 3.94844i −0.254709 + 0.171509i
\(531\) 12.7012 + 9.22798i 0.551186 + 0.400460i
\(532\) 4.62972 0.200724
\(533\) 1.23425 + 0.896735i 0.0534613 + 0.0388419i
\(534\) −1.77126 + 5.45137i −0.0766499 + 0.235904i
\(535\) −1.89055 + 5.18144i −0.0817357 + 0.224013i
\(536\) −0.166787 0.513317i −0.00720409 0.0221719i
\(537\) 2.12899 6.55235i 0.0918725 0.282755i
\(538\) −2.68413 + 8.26089i −0.115721 + 0.356152i
\(539\) 2.63166 + 8.09941i 0.113353 + 0.348866i
\(540\) −7.77460 + 5.23505i −0.334565 + 0.225281i
\(541\) 7.48796 23.0456i 0.321933 0.990807i −0.650873 0.759186i \(-0.725597\pi\)
0.972806 0.231621i \(-0.0744028\pi\)
\(542\) −5.61387 4.07871i −0.241136 0.175196i
\(543\) −9.38087 −0.402572
\(544\) −6.08749 4.42282i −0.260999 0.189627i
\(545\) −16.9372 13.2545i −0.725510 0.567759i
\(546\) −10.0345 + 7.29047i −0.429436 + 0.312003i
\(547\) −24.2723 + 17.6349i −1.03781 + 0.754013i −0.969857 0.243675i \(-0.921647\pi\)
−0.0679536 + 0.997688i \(0.521647\pi\)
\(548\) 3.45205 + 10.6243i 0.147464 + 0.453849i
\(549\) 21.2722 0.907877
\(550\) −2.94248 0.210457i −0.125468 0.00897393i
\(551\) −9.45761 −0.402908
\(552\) 1.83636 + 5.65172i 0.0781605 + 0.240553i
\(553\) −20.1243 + 14.6212i −0.855773 + 0.621756i
\(554\) −19.7058 + 14.3171i −0.837217 + 0.608274i
\(555\) −6.92041 0.247171i −0.293755 0.0104918i
\(556\) 0.308117 + 0.223860i 0.0130671 + 0.00949379i
\(557\) 6.37166 0.269976 0.134988 0.990847i \(-0.456900\pi\)
0.134988 + 0.990847i \(0.456900\pi\)
\(558\) −16.8563 12.2468i −0.713583 0.518448i
\(559\) 8.19639 25.2259i 0.346671 1.06694i
\(560\) −8.15271 6.38003i −0.344515 0.269606i
\(561\) −1.06554 3.27939i −0.0449871 0.138456i
\(562\) −5.68611 + 17.5000i −0.239854 + 0.738195i
\(563\) 13.4071 41.2628i 0.565041 1.73902i −0.102787 0.994703i \(-0.532776\pi\)
0.667828 0.744315i \(-0.267224\pi\)
\(564\) −2.21467 6.81606i −0.0932546 0.287008i
\(565\) 20.0385 + 15.6814i 0.843026 + 0.659723i
\(566\) −3.83760 + 11.8109i −0.161306 + 0.496449i
\(567\) 14.7368 + 10.7069i 0.618887 + 0.449648i
\(568\) −6.05729 −0.254158
\(569\) 12.6369 + 9.18122i 0.529765 + 0.384897i 0.820270 0.571977i \(-0.193823\pi\)
−0.290505 + 0.956873i \(0.593823\pi\)
\(570\) −1.73566 0.0619912i −0.0726986 0.00259652i
\(571\) 25.6662 18.6476i 1.07410 0.780377i 0.0974529 0.995240i \(-0.468930\pi\)
0.976644 + 0.214863i \(0.0689305\pi\)
\(572\) −1.64640 + 1.19618i −0.0688396 + 0.0500149i
\(573\) 5.21985 + 16.0651i 0.218063 + 0.671128i
\(574\) −2.04773 −0.0854707
\(575\) −14.3869 + 35.4467i −0.599977 + 1.47823i
\(576\) −2.39673 −0.0998638
\(577\) −10.0163 30.8270i −0.416983 1.28334i −0.910465 0.413587i \(-0.864276\pi\)
0.493481 0.869756i \(-0.335724\pi\)
\(578\) 32.0523 23.2873i 1.33320 0.968626i
\(579\) 5.84006 4.24305i 0.242705 0.176335i
\(580\) 16.6544 + 13.0332i 0.691536 + 0.541172i
\(581\) −1.49116 1.08339i −0.0618637 0.0449466i
\(582\) −8.41970 −0.349008
\(583\) −1.50904 1.09638i −0.0624980 0.0454074i
\(584\) 4.05208 12.4710i 0.167676 0.516054i
\(585\) −15.3334 + 10.3248i −0.633957 + 0.426877i
\(586\) −1.29827 3.99566i −0.0536310 0.165059i
\(587\) −5.94601 + 18.2999i −0.245418 + 0.755319i 0.750149 + 0.661268i \(0.229982\pi\)
−0.995567 + 0.0940505i \(0.970018\pi\)
\(588\) 3.46444 10.6625i 0.142871 0.439712i
\(589\) −2.68638 8.26782i −0.110690 0.340669i
\(590\) 5.02056 13.7599i 0.206693 0.566484i
\(591\) 1.29173 3.97553i 0.0531346 0.163532i
\(592\) −3.22571 2.34362i −0.132576 0.0963221i
\(593\) −33.2301 −1.36460 −0.682298 0.731074i \(-0.739020\pi\)
−0.682298 + 0.731074i \(0.739020\pi\)
\(594\) −2.00076 1.45364i −0.0820923 0.0596435i
\(595\) 64.6140 43.5080i 2.64892 1.78366i
\(596\) −3.51711 + 2.55533i −0.144067 + 0.104670i
\(597\) 0.829496 0.602664i 0.0339490 0.0246654i
\(598\) 8.15508 + 25.0988i 0.333486 + 1.02636i
\(599\) −4.57928 −0.187104 −0.0935521 0.995614i \(-0.529822\pi\)
−0.0935521 + 0.995614i \(0.529822\pi\)
\(600\) 2.97098 + 2.50100i 0.121290 + 0.102103i
\(601\) 41.8432 1.70682 0.853410 0.521241i \(-0.174531\pi\)
0.853410 + 0.521241i \(0.174531\pi\)
\(602\) 11.0015 + 33.8590i 0.448386 + 1.37999i
\(603\) 1.04654 0.760357i 0.0426184 0.0309641i
\(604\) 14.5396 10.5636i 0.591609 0.429829i
\(605\) 6.54704 + 22.9009i 0.266175 + 0.931054i
\(606\) 2.31869 + 1.68463i 0.0941903 + 0.0684332i
\(607\) −30.0669 −1.22038 −0.610188 0.792256i \(-0.708906\pi\)
−0.610188 + 0.792256i \(0.708906\pi\)
\(608\) −0.809017 0.587785i −0.0328100 0.0238378i
\(609\) −10.5093 + 32.3443i −0.425858 + 1.31066i
\(610\) −5.45521 19.0818i −0.220875 0.772599i
\(611\) −9.83515 30.2695i −0.397888 1.22457i
\(612\) 5.57291 17.1517i 0.225272 0.693314i
\(613\) 4.26416 13.1237i 0.172228 0.530063i −0.827268 0.561807i \(-0.810106\pi\)
0.999496 + 0.0317443i \(0.0101062\pi\)
\(614\) 1.04455 + 3.21480i 0.0421547 + 0.129739i
\(615\) 0.767683 + 0.0274188i 0.0309560 + 0.00110563i
\(616\) 0.844089 2.59784i 0.0340093 0.104670i
\(617\) 6.59478 + 4.79138i 0.265496 + 0.192894i 0.712566 0.701605i \(-0.247533\pi\)
−0.447071 + 0.894499i \(0.647533\pi\)
\(618\) −12.3555 −0.497010
\(619\) −17.5341 12.7393i −0.704754 0.512034i 0.176723 0.984261i \(-0.443450\pi\)
−0.881477 + 0.472227i \(0.843450\pi\)
\(620\) −6.66297 + 18.2612i −0.267591 + 0.733388i
\(621\) −25.9456 + 18.8506i −1.04116 + 0.756447i
\(622\) 14.1171 10.2567i 0.566043 0.411254i
\(623\) −10.5580 32.4941i −0.422997 1.30185i
\(624\) 2.67906 0.107248
\(625\) 4.26294 + 24.6339i 0.170518 + 0.985355i
\(626\) −9.11572 −0.364337
\(627\) −0.141609 0.435826i −0.00565530 0.0174052i
\(628\) 4.07263 2.95894i 0.162516 0.118075i
\(629\) 24.2720 17.6347i 0.967789 0.703140i
\(630\) 8.50467 23.3087i 0.338834 0.928643i
\(631\) 33.8255 + 24.5757i 1.34657 + 0.978343i 0.999174 + 0.0406253i \(0.0129350\pi\)
0.347399 + 0.937717i \(0.387065\pi\)
\(632\) 5.37291 0.213723
\(633\) 11.8043 + 8.57633i 0.469179 + 0.340878i
\(634\) −1.33491 + 4.10844i −0.0530162 + 0.163167i
\(635\) −28.4285 1.01536i −1.12815 0.0402934i
\(636\) 0.758803 + 2.33536i 0.0300885 + 0.0926029i
\(637\) 15.3853 47.3509i 0.609586 1.87611i
\(638\) −1.72431 + 5.30688i −0.0682660 + 0.210101i
\(639\) −4.48622 13.8072i −0.177472 0.546202i
\(640\) 0.614636 + 2.14994i 0.0242956 + 0.0849837i
\(641\) −0.118600 + 0.365014i −0.00468443 + 0.0144172i −0.953371 0.301800i \(-0.902413\pi\)
0.948687 + 0.316217i \(0.102413\pi\)
\(642\) 1.54995 + 1.12611i 0.0611717 + 0.0444439i
\(643\) −27.9446 −1.10203 −0.551014 0.834496i \(-0.685759\pi\)
−0.551014 + 0.834496i \(0.685759\pi\)
\(644\) −28.6570 20.8206i −1.12925 0.820445i
\(645\) −3.67102 12.8409i −0.144546 0.505609i
\(646\) 6.08749 4.42282i 0.239509 0.174013i
\(647\) −1.32908 + 0.965632i −0.0522514 + 0.0379629i −0.613604 0.789614i \(-0.710281\pi\)
0.561353 + 0.827576i \(0.310281\pi\)
\(648\) −1.21583 3.74194i −0.0477624 0.146997i
\(649\) 3.86474 0.151704
\(650\) 13.1938 + 11.1067i 0.517505 + 0.435641i
\(651\) −31.2604 −1.22519
\(652\) −1.17814 3.62594i −0.0461395 0.142003i
\(653\) 32.3330 23.4913i 1.26529 0.919285i 0.266283 0.963895i \(-0.414204\pi\)
0.999005 + 0.0446094i \(0.0142043\pi\)
\(654\) −6.04376 + 4.39105i −0.236330 + 0.171704i
\(655\) −7.38394 + 4.97200i −0.288514 + 0.194272i
\(656\) 0.357829 + 0.259978i 0.0139709 + 0.0101504i
\(657\) 31.4278 1.22612
\(658\) 34.5608 + 25.1099i 1.34732 + 0.978886i
\(659\) 0.443764 1.36576i 0.0172866 0.0532026i −0.942041 0.335497i \(-0.891096\pi\)
0.959328 + 0.282295i \(0.0910956\pi\)
\(660\) −0.351229 + 0.962614i −0.0136716 + 0.0374697i
\(661\) 13.2175 + 40.6792i 0.514100 + 1.58224i 0.784914 + 0.619605i \(0.212707\pi\)
−0.270814 + 0.962632i \(0.587293\pi\)
\(662\) −8.84712 + 27.2286i −0.343853 + 1.05827i
\(663\) −6.22938 + 19.1721i −0.241929 + 0.744582i
\(664\) 0.123025 + 0.378632i 0.00477430 + 0.0146938i
\(665\) 8.58709 5.78215i 0.332993 0.224222i
\(666\) 2.95304 9.08853i 0.114428 0.352173i
\(667\) 58.5407 + 42.5323i 2.26671 + 1.64686i
\(668\) 13.6998 0.530063
\(669\) −1.15135 0.836504i −0.0445137 0.0323411i
\(670\) −0.950444 0.743785i −0.0367189 0.0287349i
\(671\) 4.23646 3.07797i 0.163547 0.118824i
\(672\) −2.90916 + 2.11363i −0.112223 + 0.0815350i
\(673\) 8.83160 + 27.1809i 0.340433 + 1.04775i 0.963983 + 0.265962i \(0.0856896\pi\)
−0.623550 + 0.781783i \(0.714310\pi\)
\(674\) 24.1752 0.931193
\(675\) −7.88199 + 19.4197i −0.303378 + 0.747465i
\(676\) −1.10255 −0.0424058
\(677\) 8.65070 + 26.6241i 0.332473 + 1.02325i 0.967953 + 0.251130i \(0.0808023\pi\)
−0.635480 + 0.772117i \(0.719198\pi\)
\(678\) 7.15041 5.19507i 0.274610 0.199516i
\(679\) 40.6025 29.4995i 1.55818 1.13209i
\(680\) −16.8147 0.600558i −0.644813 0.0230303i
\(681\) 13.8773 + 10.0825i 0.531780 + 0.386360i
\(682\) −5.12904 −0.196401
\(683\) −17.2242 12.5141i −0.659067 0.478840i 0.207281 0.978282i \(-0.433539\pi\)
−0.866348 + 0.499441i \(0.833539\pi\)
\(684\) 0.740631 2.27943i 0.0283187 0.0871561i
\(685\) 19.6717 + 15.3944i 0.751618 + 0.588190i
\(686\) 10.6359 + 32.7341i 0.406082 + 1.24979i
\(687\) 5.20974 16.0339i 0.198764 0.611733i
\(688\) 2.37627 7.31341i 0.0905945 0.278821i
\(689\) 3.36977 + 10.3711i 0.128378 + 0.395107i
\(690\) 10.4646 + 8.18923i 0.398380 + 0.311758i
\(691\) −10.8318 + 33.3370i −0.412062 + 1.26820i 0.502790 + 0.864409i \(0.332307\pi\)
−0.914852 + 0.403789i \(0.867693\pi\)
\(692\) 8.25518 + 5.99774i 0.313815 + 0.228000i
\(693\) 6.54674 0.248690
\(694\) −16.3956 11.9121i −0.622370 0.452178i
\(695\) 0.851073 + 0.0303972i 0.0322830 + 0.00115303i
\(696\) 5.94284 4.31773i 0.225263 0.163663i
\(697\) −2.69250 + 1.95622i −0.101986 + 0.0740971i
\(698\) 4.56530 + 14.0506i 0.172799 + 0.531822i
\(699\) 5.87017 0.222030
\(700\) −23.0896 1.65146i −0.872705 0.0624192i
\(701\) −0.445917 −0.0168420 −0.00842102 0.999965i \(-0.502681\pi\)
−0.00842102 + 0.999965i \(0.502681\pi\)
\(702\) 4.46782 + 13.7505i 0.168627 + 0.518980i
\(703\) 3.22571 2.34362i 0.121660 0.0883912i
\(704\) −0.477319 + 0.346793i −0.0179897 + 0.0130702i
\(705\) −12.6204 9.87633i −0.475313 0.371964i
\(706\) −14.7349 10.7055i −0.554556 0.402909i
\(707\) −17.0838 −0.642501
\(708\) −4.11606 2.99049i −0.154691 0.112390i
\(709\) 12.0629 37.1257i 0.453031 1.39429i −0.420400 0.907339i \(-0.638110\pi\)
0.873431 0.486947i \(-0.161890\pi\)
\(710\) −11.2349 + 7.56507i −0.421639 + 0.283912i
\(711\) 3.97934 + 12.2471i 0.149237 + 0.459304i
\(712\) −2.28048 + 7.01860i −0.0854647 + 0.263033i
\(713\) −20.5535 + 63.2572i −0.769735 + 2.36900i
\(714\) −8.36128 25.7334i −0.312913 0.963047i
\(715\) −1.55978 + 4.27488i −0.0583323 + 0.159871i
\(716\) 2.74105 8.43609i 0.102438 0.315272i
\(717\) −8.66835 6.29793i −0.323726 0.235200i
\(718\) 2.39130 0.0892424
\(719\) −11.4476 8.31713i −0.426922 0.310177i 0.353495 0.935436i \(-0.384993\pi\)
−0.780417 + 0.625260i \(0.784993\pi\)
\(720\) −4.44540 + 2.99333i −0.165670 + 0.111555i
\(721\) 59.5821 43.2890i 2.21895 1.61217i
\(722\) 0.809017 0.587785i 0.0301085 0.0218751i
\(723\) −2.62482 8.07835i −0.0976179 0.300437i
\(724\) −12.0778 −0.448868
\(725\) 47.1675 + 3.37360i 1.75176 + 0.125292i
\(726\) 8.27337 0.307054
\(727\) 6.51829 + 20.0612i 0.241750 + 0.744030i 0.996154 + 0.0876195i \(0.0279260\pi\)
−0.754404 + 0.656410i \(0.772074\pi\)
\(728\) −12.9193 + 9.38642i −0.478821 + 0.347884i
\(729\) −0.272697 + 0.198126i −0.0100999 + 0.00733799i
\(730\) −8.05960 28.1917i −0.298299 1.04342i
\(731\) 46.8114 + 34.0105i 1.73138 + 1.25792i
\(732\) −6.89365 −0.254797
\(733\) −12.6139 9.16452i −0.465904 0.338499i 0.329939 0.944002i \(-0.392972\pi\)
−0.795843 + 0.605503i \(0.792972\pi\)
\(734\) 2.47812 7.62688i 0.0914692 0.281513i
\(735\) −6.89078 24.1033i −0.254170 0.889063i
\(736\) 2.36429 + 7.27655i 0.0871490 + 0.268217i
\(737\) 0.0984041 0.302857i 0.00362476 0.0111559i
\(738\) −0.327582 + 1.00819i −0.0120585 + 0.0371121i
\(739\) −10.5190 32.3742i −0.386949 1.19091i −0.935057 0.354498i \(-0.884652\pi\)
0.548108 0.836407i \(-0.315348\pi\)
\(740\) −8.90997 0.318231i −0.327537 0.0116984i
\(741\) −0.827875 + 2.54794i −0.0304127 + 0.0936008i
\(742\) −11.8414 8.60329i −0.434712 0.315837i
\(743\) −13.1498 −0.482419 −0.241210 0.970473i \(-0.577544\pi\)
−0.241210 + 0.970473i \(0.577544\pi\)
\(744\) 5.46258 + 3.96879i 0.200268 + 0.145503i
\(745\) −3.33206 + 9.13216i −0.122077 + 0.334577i
\(746\) 10.4664 7.60428i 0.383202 0.278412i
\(747\) −0.771949 + 0.560854i −0.0282441 + 0.0205206i
\(748\) −1.37187 4.22219i −0.0501607 0.154379i
\(749\) −11.4198 −0.417272
\(750\) 8.63405 + 0.928288i 0.315271 + 0.0338963i
\(751\) −22.6095 −0.825031 −0.412516 0.910951i \(-0.635350\pi\)
−0.412516 + 0.910951i \(0.635350\pi\)
\(752\) −2.85137 8.77563i −0.103979 0.320014i
\(753\) 1.46363 1.06339i 0.0533375 0.0387520i
\(754\) 26.3916 19.1746i 0.961126 0.698299i
\(755\) 13.7746 37.7520i 0.501309 1.37394i
\(756\) −15.7000 11.4067i −0.571002 0.414857i
\(757\) −43.7541 −1.59027 −0.795135 0.606432i \(-0.792600\pi\)
−0.795135 + 0.606432i \(0.792600\pi\)
\(758\) 12.9467 + 9.40631i 0.470244 + 0.341653i
\(759\) −1.08345 + 3.33451i −0.0393267 + 0.121035i
\(760\) −2.23464 0.0798131i −0.0810590 0.00289513i
\(761\) −10.0720 30.9983i −0.365108 1.12369i −0.949913 0.312514i \(-0.898829\pi\)
0.584805 0.811174i \(-0.301171\pi\)
\(762\) −3.05340 + 9.39741i −0.110613 + 0.340432i
\(763\) 13.7604 42.3502i 0.498160 1.53318i
\(764\) 6.72052 + 20.6836i 0.243140 + 0.748308i
\(765\) −11.0845 38.7726i −0.400762 1.40183i
\(766\) −1.63090 + 5.01939i −0.0589268 + 0.181358i
\(767\) −18.2790 13.2805i −0.660018 0.479531i
\(768\) 0.776704 0.0280269
\(769\) 38.0673 + 27.6575i 1.37274 + 0.997355i 0.997517 + 0.0704215i \(0.0224344\pi\)
0.375225 + 0.926934i \(0.377566\pi\)
\(770\) −1.67890 5.87261i −0.0605032 0.211634i
\(771\) 11.5548 8.39503i 0.416135 0.302340i
\(772\) 7.51903 5.46290i 0.270616 0.196614i
\(773\) 5.41713 + 16.6722i 0.194841 + 0.599658i 0.999978 + 0.00656985i \(0.00209126\pi\)
−0.805138 + 0.593088i \(0.797909\pi\)
\(774\) 18.4303 0.662464
\(775\) 10.4485 + 42.1920i 0.375320 + 1.51558i
\(776\) −10.8403 −0.389144
\(777\) −4.43058 13.6359i −0.158946 0.489186i
\(778\) −22.8359 + 16.5912i −0.818705 + 0.594824i
\(779\) −0.357829 + 0.259978i −0.0128206 + 0.00931469i
\(780\) 4.96906 3.34593i 0.177921 0.119804i
\(781\) −2.89126 2.10063i −0.103458 0.0751663i
\(782\) −57.5704 −2.05871
\(783\) 32.0719 + 23.3016i 1.14616 + 0.832732i
\(784\) 4.46044 13.7278i 0.159301 0.490279i
\(785\) 3.85834 10.5746i 0.137710 0.377422i
\(786\) 0.955508 + 2.94075i 0.0340818 + 0.104893i
\(787\) 11.6341 35.8062i 0.414712 1.27635i −0.497796 0.867294i \(-0.665857\pi\)
0.912508 0.409058i \(-0.134143\pi\)
\(788\) 1.66309 5.11847i 0.0592451 0.182338i
\(789\) 1.26821 + 3.90316i 0.0451496 + 0.138956i
\(790\) 9.96554 6.71033i 0.354558 0.238743i
\(791\) −16.2800 + 50.1047i −0.578850 + 1.78152i
\(792\) −1.14401 0.831169i −0.0406505 0.0295343i
\(793\) −30.6140 −1.08714
\(794\) −5.79692 4.21171i −0.205725 0.149468i
\(795\) 4.32408 + 3.38388i 0.153359 + 0.120014i
\(796\) 1.06797 0.775925i 0.0378532 0.0275019i
\(797\) 6.20757 4.51007i 0.219884 0.159755i −0.472391 0.881389i \(-0.656609\pi\)
0.692274 + 0.721635i \(0.256609\pi\)
\(798\) −1.11120 3.41992i −0.0393361 0.121064i
\(799\) 69.4308 2.45628
\(800\) 3.82511 + 3.22002i 0.135238 + 0.113845i
\(801\) −17.6874 −0.624953
\(802\) 2.75906 + 8.49152i 0.0974258 + 0.299846i
\(803\) 6.25899 4.54743i 0.220875 0.160475i
\(804\) −0.339150 + 0.246407i −0.0119609 + 0.00869011i
\(805\) −79.1556 2.82714i −2.78987 0.0996437i
\(806\) 24.2588 + 17.6250i 0.854479 + 0.620815i
\(807\) 6.74646 0.237487
\(808\) 2.98529 + 2.16894i 0.105022 + 0.0763031i
\(809\) −3.84924 + 11.8467i −0.135332 + 0.416509i −0.995642 0.0932629i \(-0.970270\pi\)
0.860309 + 0.509772i \(0.170270\pi\)
\(810\) −6.92849 5.42200i −0.243442 0.190510i
\(811\) −9.27900 28.5578i −0.325830 1.00280i −0.971065 0.238817i \(-0.923241\pi\)
0.645235 0.763984i \(-0.276759\pi\)
\(812\) −13.5306 + 41.6430i −0.474832 + 1.46138i
\(813\) −1.66549 + 5.12586i −0.0584113 + 0.179772i
\(814\) −0.726945 2.23731i −0.0254794 0.0784176i
\(815\) −6.71369 5.25390i −0.235170 0.184036i
\(816\) −1.80600 + 5.55830i −0.0632227 + 0.194579i
\(817\) 6.22116 + 4.51994i 0.217651 + 0.158133i
\(818\) 27.1441 0.949071
\(819\) −30.9641 22.4967i −1.08197 0.786099i
\(820\) 0.988386 + 0.0353015i 0.0345159 + 0.00123278i
\(821\) 29.2794 21.2727i 1.02186 0.742423i 0.0551946 0.998476i \(-0.482422\pi\)
0.966663 + 0.256053i \(0.0824221\pi\)
\(822\) 7.01953 5.09999i 0.244834 0.177882i
\(823\) 5.29451 + 16.2948i 0.184555 + 0.568001i 0.999940 0.0109168i \(-0.00347501\pi\)
−0.815386 + 0.578918i \(0.803475\pi\)
\(824\) −15.9076 −0.554167
\(825\) 0.550776 + 2.22409i 0.0191756 + 0.0774329i
\(826\) 30.3266 1.05520
\(827\) 15.6821 + 48.2646i 0.545321 + 1.67833i 0.720225 + 0.693740i \(0.244038\pi\)
−0.174904 + 0.984585i \(0.555962\pi\)
\(828\) −14.8353 + 10.7785i −0.515562 + 0.374578i
\(829\) 3.57482 2.59726i 0.124159 0.0902066i −0.523973 0.851735i \(-0.675551\pi\)
0.648132 + 0.761528i \(0.275551\pi\)
\(830\) 0.701066 + 0.548630i 0.0243344 + 0.0190432i
\(831\) 15.3055 + 11.1201i 0.530943 + 0.385753i
\(832\) 3.44927 0.119582
\(833\) 87.8685 + 63.8402i 3.04446 + 2.21193i
\(834\) 0.0914106 0.281333i 0.00316529 0.00974176i
\(835\) 25.4102 17.1100i 0.879355 0.592116i
\(836\) −0.182320 0.561123i −0.00630566 0.0194068i
\(837\) −11.2604 + 34.6559i −0.389216 + 1.19788i
\(838\) 3.55495 10.9410i 0.122804 0.377951i
\(839\) 1.85974 + 5.72369i 0.0642054 + 0.197604i 0.978013 0.208543i \(-0.0668721\pi\)
−0.913808 + 0.406147i \(0.866872\pi\)
\(840\) −2.75609 + 7.55362i −0.0950942 + 0.260625i
\(841\) 18.6789 57.4879i 0.644101 1.98234i
\(842\) −28.7516 20.8892i −0.990845 0.719891i
\(843\) 14.2918 0.492237
\(844\) 15.1979 + 11.0420i 0.523135 + 0.380080i
\(845\) −2.04499 + 1.37700i −0.0703497 + 0.0473702i
\(846\) 17.8916 12.9990i 0.615125 0.446915i
\(847\) −39.8969 + 28.9868i −1.37087 + 0.995998i
\(848\) 0.976953 + 3.00675i 0.0335487 + 0.103252i
\(849\) 9.64567 0.331039
\(850\) −31.9375 + 19.8863i −1.09545 + 0.682094i
\(851\) −30.5061 −1.04574
\(852\) 1.45384 + 4.47446i 0.0498077 + 0.153292i
\(853\) 4.68655 3.40498i 0.160464 0.116584i −0.504655 0.863321i \(-0.668380\pi\)
0.665120 + 0.746737i \(0.268380\pi\)
\(854\) 33.2434 24.1528i 1.13757 0.826491i
\(855\) −1.47312 5.15282i −0.0503795 0.176223i
\(856\) 1.99555 + 1.44985i 0.0682065 + 0.0495549i
\(857\) 33.5669 1.14662 0.573312 0.819337i \(-0.305658\pi\)
0.573312 + 0.819337i \(0.305658\pi\)
\(858\) 1.27877 + 0.929079i 0.0436564 + 0.0317182i
\(859\) −17.5196 + 53.9199i −0.597762 + 1.83972i −0.0572967 + 0.998357i \(0.518248\pi\)
−0.540466 + 0.841366i \(0.681752\pi\)
\(860\) −4.72641 16.5325i −0.161169 0.563754i
\(861\) 0.491486 + 1.51264i 0.0167498 + 0.0515505i
\(862\) 3.24609 9.99044i 0.110562 0.340276i
\(863\) −15.3186 + 47.1459i −0.521453 + 1.60487i 0.249773 + 0.968304i \(0.419644\pi\)
−0.771226 + 0.636562i \(0.780356\pi\)
\(864\) 1.29529 + 3.98651i 0.0440668 + 0.135624i
\(865\) 22.8022 + 0.814410i 0.775299 + 0.0276908i
\(866\) 10.5493 32.4673i 0.358479 1.10328i
\(867\) −24.8951 18.0874i −0.845483 0.614279i
\(868\) −40.2475 −1.36609
\(869\) 2.56459 + 1.86329i 0.0869978 + 0.0632076i
\(870\) 5.63015 15.4306i 0.190880 0.523145i
\(871\) −1.50613 + 1.09427i −0.0510334 + 0.0370780i
\(872\) −7.78130 + 5.65344i −0.263508 + 0.191450i
\(873\) −8.02865 24.7097i −0.271729 0.836295i
\(874\) −7.65102 −0.258799
\(875\) −44.8886 + 25.7740i −1.51751 + 0.871320i
\(876\) −10.1848 −0.344111
\(877\) −13.2156 40.6735i −0.446260 1.37345i −0.881096 0.472937i \(-0.843194\pi\)
0.434836 0.900510i \(-0.356806\pi\)
\(878\) −16.8536 + 12.2449i −0.568783 + 0.413245i
\(879\) −2.63995 + 1.91803i −0.0890433 + 0.0646937i
\(880\) −0.452205 + 1.23936i −0.0152438 + 0.0417787i
\(881\) 27.5993 + 20.0521i 0.929844 + 0.675571i 0.945955 0.324299i \(-0.105128\pi\)
−0.0161106 + 0.999870i \(0.505128\pi\)
\(882\) 34.5951 1.16488
\(883\) −21.7925 15.8332i −0.733376 0.532829i 0.157253 0.987558i \(-0.449736\pi\)
−0.890630 + 0.454729i \(0.849736\pi\)
\(884\) −8.02028 + 24.6839i −0.269751 + 0.830209i
\(885\) −11.3693 0.406068i −0.382174 0.0136498i
\(886\) 7.84873 + 24.1559i 0.263683 + 0.811533i
\(887\) −9.09338 + 27.9865i −0.305326 + 0.939696i 0.674230 + 0.738522i \(0.264476\pi\)
−0.979555 + 0.201174i \(0.935524\pi\)
\(888\) −0.956986 + 2.94530i −0.0321144 + 0.0988378i
\(889\) −18.2005 56.0154i −0.610425 1.87869i
\(890\) 4.53589 + 15.8661i 0.152043 + 0.531832i
\(891\) 0.717340 2.20774i 0.0240318 0.0739622i
\(892\) −1.48235 1.07699i −0.0496328 0.0360604i
\(893\) 9.22724 0.308778
\(894\) 2.73176 + 1.98474i 0.0913636 + 0.0663795i
\(895\) −5.45196 19.0704i −0.182239 0.637454i
\(896\) −3.74552 + 2.72128i −0.125129 + 0.0909116i
\(897\) 16.5828 12.0481i 0.553685 0.402276i
\(898\) 3.69638 + 11.3763i 0.123350 + 0.379632i
\(899\) 82.2178 2.74212
\(900\) −4.50681 + 11.1039i −0.150227 + 0.370130i
\(901\) −23.7887 −0.792518
\(902\) 0.0806403 + 0.248185i 0.00268503 + 0.00826367i
\(903\) 22.3708 16.2533i 0.744453 0.540877i
\(904\) 9.20609 6.68862i 0.306190 0.222460i
\(905\) −22.4016 + 15.0842i −0.744655 + 0.501416i
\(906\) −11.2930 8.20483i −0.375184 0.272587i
\(907\) 29.0178 0.963520 0.481760 0.876303i \(-0.339998\pi\)
0.481760 + 0.876303i \(0.339998\pi\)
\(908\) 17.8669 + 12.9811i 0.592935 + 0.430792i
\(909\) −2.73294 + 8.41114i −0.0906461 + 0.278980i
\(910\) −12.2395 + 33.5449i −0.405737 + 1.11200i
\(911\) 13.3344 + 41.0392i 0.441790 + 1.35969i 0.885966 + 0.463750i \(0.153496\pi\)
−0.444176 + 0.895939i \(0.646504\pi\)
\(912\) −0.240015 + 0.738689i −0.00794768 + 0.0244604i
\(913\) −0.0725848 + 0.223393i −0.00240220 + 0.00739323i
\(914\) 10.2010 + 31.3955i 0.337420 + 1.03847i
\(915\) −12.7862 + 8.60962i −0.422698 + 0.284625i
\(916\) 6.70750 20.6436i 0.221622 0.682083i
\(917\) −14.9111 10.8335i −0.492407 0.357754i
\(918\) −31.5404 −1.04099
\(919\) 28.0349 + 20.3685i 0.924785 + 0.671896i 0.944710 0.327906i \(-0.106343\pi\)
−0.0199253 + 0.999801i \(0.506343\pi\)
\(920\) 13.4731 + 10.5436i 0.444194 + 0.347611i
\(921\) 2.12403 1.54320i 0.0699892 0.0508502i
\(922\) 22.0267 16.0033i 0.725409 0.527041i
\(923\) 6.45636 + 19.8706i 0.212514 + 0.654050i
\(924\) −2.12159 −0.0697952
\(925\) −16.9234 + 10.5376i −0.556440 + 0.346474i
\(926\) −20.9777 −0.689370
\(927\) −11.7816 36.2602i −0.386960 1.19094i
\(928\) 7.65136 5.55904i 0.251168 0.182484i
\(929\) −5.68195 + 4.12818i −0.186419 + 0.135441i −0.677080 0.735909i \(-0.736755\pi\)
0.490662 + 0.871350i \(0.336755\pi\)
\(930\) 15.0886 + 0.538908i 0.494774 + 0.0176715i
\(931\) 11.6776 + 8.48426i 0.382717 + 0.278060i
\(932\) 7.55780 0.247564
\(933\) −10.9648 7.96638i −0.358971 0.260808i
\(934\) −9.35325 + 28.7863i −0.306048 + 0.941918i
\(935\) −7.81770 6.11787i −0.255666 0.200076i
\(936\) 2.55463 + 7.86235i 0.0835008 + 0.256989i
\(937\) 1.05953 3.26090i 0.0346134 0.106529i −0.932257 0.361796i \(-0.882164\pi\)
0.966870 + 0.255267i \(0.0821635\pi\)
\(938\) 0.772176 2.37651i 0.0252124 0.0775959i
\(939\) 2.18791 + 6.73368i 0.0713996 + 0.219746i
\(940\) −16.2487 12.7157i −0.529975 0.414740i
\(941\) −8.85301 + 27.2468i −0.288600 + 0.888219i 0.696697 + 0.717366i \(0.254652\pi\)
−0.985297 + 0.170853i \(0.945348\pi\)
\(942\) −3.16323 2.29822i −0.103064 0.0748800i
\(943\) 3.38406 0.110200
\(944\) −5.29940 3.85024i −0.172481 0.125315i
\(945\) −43.3660 1.54887i −1.41069 0.0503848i
\(946\) 3.67048 2.66676i 0.119338 0.0867038i
\(947\) −4.65018 + 3.37855i −0.151110 + 0.109788i −0.660772 0.750587i \(-0.729771\pi\)
0.509661 + 0.860375i \(0.329771\pi\)
\(948\) −1.28958 3.96891i −0.0418835 0.128904i
\(949\) −45.2296 −1.46821
\(950\) −4.24445 + 2.64286i −0.137708 + 0.0857455i
\(951\) 3.35526 0.108802
\(952\) −10.7651 33.1315i −0.348898 1.07380i
\(953\) 36.7650 26.7114i 1.19094 0.865266i 0.197573 0.980288i \(-0.436694\pi\)
0.993363 + 0.115022i \(0.0366940\pi\)
\(954\) −6.13011 + 4.45378i −0.198470 + 0.144197i
\(955\) 38.2973 + 29.9701i 1.23927 + 0.969811i
\(956\) −11.1604 8.10853i −0.360954 0.262249i
\(957\) 4.33399 0.140098
\(958\) 12.6534 + 9.19325i 0.408814 + 0.297021i
\(959\) −15.9820 + 49.1876i −0.516087 + 1.58835i
\(960\) 1.44061 0.970041i 0.0464956 0.0313079i
\(961\) 13.7739 + 42.3918i 0.444320 + 1.36748i
\(962\) −4.24989 + 13.0798i −0.137022 + 0.421710i
\(963\) −1.82687 + 5.62252i −0.0588700 + 0.181183i
\(964\) −3.37943 10.4008i −0.108844 0.334988i
\(965\) 7.12341 19.5231i 0.229311 0.628472i
\(966\) −8.50181 + 26.1659i −0.273541 + 0.841873i
\(967\) 4.12233 + 2.99505i 0.132565 + 0.0963142i 0.652092 0.758140i \(-0.273892\pi\)
−0.519527 + 0.854454i \(0.673892\pi\)
\(968\) 10.6519 0.342365
\(969\) −4.72817 3.43522i −0.151891 0.110355i
\(970\) −20.1063 + 13.5387i −0.645575 + 0.434700i
\(971\) −39.6978 + 28.8422i −1.27396 + 0.925589i −0.999353 0.0359669i \(-0.988549\pi\)
−0.274611 + 0.961556i \(0.588549\pi\)
\(972\) −12.6457 + 9.18763i −0.405611 + 0.294694i
\(973\) 0.544873 + 1.67695i 0.0174678 + 0.0537604i
\(974\) −2.43279 −0.0779517
\(975\) 5.03770 12.4119i 0.161335 0.397499i
\(976\) −8.87552 −0.284098
\(977\) −11.6569 35.8761i −0.372936 1.14778i −0.944861 0.327472i \(-0.893803\pi\)
0.571925 0.820306i \(-0.306197\pi\)
\(978\) −2.39567 + 1.74056i −0.0766051 + 0.0556569i
\(979\) −3.52252 + 2.55926i −0.112580 + 0.0817943i
\(980\) −8.87183 31.0328i −0.283400 0.991306i
\(981\) −18.6497 13.5498i −0.595438 0.432611i
\(982\) −8.32219 −0.265572
\(983\) 33.6915 + 24.4783i 1.07459 + 0.780737i 0.976732 0.214463i \(-0.0688001\pi\)
0.0978605 + 0.995200i \(0.468800\pi\)
\(984\) 0.106159 0.326723i 0.00338422 0.0104156i
\(985\) −3.30789 11.5707i −0.105398 0.368673i
\(986\) 21.9909 + 67.6812i 0.700334 + 2.15541i
\(987\) 10.2533 31.5564i 0.326367 1.00445i
\(988\) −1.06588 + 3.28045i −0.0339102 + 0.104365i
\(989\) −18.1809 55.9550i −0.578118 1.77927i
\(990\) −3.15994 0.112861i −0.100430 0.00358697i
\(991\) −3.31895 + 10.2147i −0.105430 + 0.324480i −0.989831 0.142248i \(-0.954567\pi\)
0.884401 + 0.466727i \(0.154567\pi\)
\(992\) 7.03302 + 5.10979i 0.223299 + 0.162236i
\(993\) 22.2369 0.705668
\(994\) −22.6877 16.4836i −0.719610 0.522828i
\(995\) 1.01178 2.77298i 0.0320755 0.0879093i
\(996\) 0.250164 0.181755i 0.00792675 0.00575912i
\(997\) −27.4052 + 19.9111i −0.867933 + 0.630590i −0.930031 0.367480i \(-0.880221\pi\)
0.0620987 + 0.998070i \(0.480221\pi\)
\(998\) 5.60790 + 17.2593i 0.177515 + 0.546335i
\(999\) −16.7130 −0.528776
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 950.2.h.d.381.5 44
25.21 even 5 inner 950.2.h.d.571.5 yes 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
950.2.h.d.381.5 44 1.1 even 1 trivial
950.2.h.d.571.5 yes 44 25.21 even 5 inner