Properties

Label 930.2.bg.i.691.2
Level $930$
Weight $2$
Character 930.691
Analytic conductor $7.426$
Analytic rank $0$
Dimension $24$
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] = [930,2,Mod(121,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([0, 0, 16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.121");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.bg (of order \(15\), degree \(8\), 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: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(3\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 691.2
Character \(\chi\) \(=\) 930.691
Dual form 930.2.bg.i.751.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.309017 + 0.951057i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.381451 + 0.169833i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})\) \(q+(-0.309017 + 0.951057i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.381451 + 0.169833i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +(-0.978148 + 0.207912i) q^{10} +(-0.275944 + 2.62543i) q^{11} +(0.669131 + 0.743145i) q^{12} +(-1.91862 + 2.13084i) q^{13} +(-0.0436459 - 0.415263i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.588175 - 5.59612i) q^{17} +(-0.669131 + 0.743145i) q^{18} +(1.98000 + 2.19901i) q^{19} +(0.104528 - 0.994522i) q^{20} +(0.408426 - 0.0868137i) q^{21} +(-2.41166 - 1.07374i) q^{22} +(2.85192 - 2.07204i) q^{23} +(-0.913545 + 0.406737i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.43367 - 2.48318i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.408426 + 0.0868137i) q^{28} +(-2.59211 + 7.97770i) q^{29} +1.00000 q^{30} +(-5.56703 - 0.0902791i) q^{31} -1.00000 q^{32} +(0.815772 - 2.51069i) q^{33} +(5.50398 + 1.16991i) q^{34} +(-0.337806 - 0.245430i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-3.43434 + 5.94846i) q^{37} +(-2.70324 + 1.20356i) q^{38} +(2.31972 - 1.68538i) q^{39} +(0.913545 + 0.406737i) q^{40} +(-10.6869 + 2.27157i) q^{41} +(-0.0436459 + 0.415263i) q^{42} +(6.56729 + 7.29372i) q^{43} +(1.76643 - 1.96182i) q^{44} +(0.104528 + 0.994522i) q^{45} +(1.08934 + 3.35263i) q^{46} +(-3.01457 - 9.27790i) q^{47} +(-0.104528 - 0.994522i) q^{48} +(-4.56725 + 5.07245i) q^{49} +(-0.669131 - 0.743145i) q^{50} +(-0.588175 + 5.59612i) q^{51} +(2.80467 - 0.596152i) q^{52} +(-3.06996 - 1.36683i) q^{53} +(0.809017 - 0.587785i) q^{54} +(-2.41166 + 1.07374i) q^{55} +(-0.208775 + 0.361609i) q^{56} +(-1.47953 - 2.56262i) q^{57} +(-6.78624 - 4.93049i) q^{58} +(-1.66800 - 0.354544i) q^{59} +(-0.309017 + 0.951057i) q^{60} -9.40663 q^{61} +(1.80617 - 5.26666i) q^{62} -0.417551 q^{63} +(0.309017 - 0.951057i) q^{64} +(-2.80467 - 0.596152i) q^{65} +(2.13572 + 1.55169i) q^{66} +(-0.288536 - 0.499759i) q^{67} +(-2.81347 + 4.87307i) q^{68} +(-3.22040 + 1.43381i) q^{69} +(0.337806 - 0.245430i) q^{70} +(-2.53210 - 1.12736i) q^{71} +(0.978148 - 0.207912i) q^{72} +(0.450994 - 4.29092i) q^{73} +(-4.59605 - 5.10443i) q^{74} +(0.669131 - 0.743145i) q^{75} +(-0.309306 - 2.94285i) q^{76} +(-0.340626 - 1.04834i) q^{77} +(0.886054 + 2.72699i) q^{78} +(-0.594502 - 5.65631i) q^{79} +(-0.669131 + 0.743145i) q^{80} +(0.669131 + 0.743145i) q^{81} +(1.14204 - 10.8658i) q^{82} +(-9.39662 + 1.99731i) q^{83} +(-0.381451 - 0.169833i) q^{84} +(4.55229 - 3.30743i) q^{85} +(-8.96614 + 3.99198i) q^{86} +(4.19413 - 7.26444i) q^{87} +(1.31995 + 2.28621i) q^{88} +(3.08580 + 2.24196i) q^{89} +(-0.978148 - 0.207912i) q^{90} +(0.369973 - 1.13866i) q^{91} -3.52517 q^{92} +(5.42661 + 1.24576i) q^{93} +9.75536 q^{94} +(-0.914400 + 2.81423i) q^{95} +(0.978148 + 0.207912i) q^{96} +(6.33471 + 4.60244i) q^{97} +(-3.41283 - 5.91119i) q^{98} +(-1.31995 + 2.28621i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 6 q^{2} + 3 q^{3} - 6 q^{4} + 12 q^{5} + 12 q^{6} - 7 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 6 q^{2} + 3 q^{3} - 6 q^{4} + 12 q^{5} + 12 q^{6} - 7 q^{7} + 6 q^{8} + 3 q^{9} + 3 q^{10} - 13 q^{11} + 3 q^{12} + 11 q^{13} - 8 q^{14} + 6 q^{15} - 6 q^{16} - 29 q^{17} - 3 q^{18} + 9 q^{19} - 3 q^{20} - 2 q^{21} - 17 q^{22} - 5 q^{23} - 3 q^{24} - 12 q^{25} + 9 q^{26} - 6 q^{27} - 2 q^{28} + 13 q^{29} + 24 q^{30} + 57 q^{31} - 24 q^{32} + 16 q^{33} + 29 q^{34} + q^{35} - 12 q^{36} - 24 q^{37} + 6 q^{38} - 17 q^{39} + 3 q^{40} + 32 q^{41} - 8 q^{42} + 49 q^{43} - 8 q^{44} - 3 q^{45} + 28 q^{47} + 3 q^{48} + 12 q^{49} - 3 q^{50} - 29 q^{51} - 19 q^{52} - 36 q^{53} + 6 q^{54} - 17 q^{55} - 3 q^{56} - 6 q^{57} + 2 q^{58} + 6 q^{60} + 33 q^{62} - 6 q^{63} - 6 q^{64} + 19 q^{65} + 4 q^{66} - 5 q^{67} + 11 q^{68} + 10 q^{69} - q^{70} - 11 q^{71} - 3 q^{72} - 13 q^{73} + 9 q^{74} + 3 q^{75} - 6 q^{76} + 4 q^{77} - 8 q^{78} - 68 q^{79} - 3 q^{80} + 3 q^{81} - 2 q^{82} + 10 q^{83} - 7 q^{84} + 2 q^{85} - 34 q^{86} + 11 q^{87} - 12 q^{88} + 55 q^{89} + 3 q^{90} + 38 q^{91} + 10 q^{92} + 19 q^{93} + 42 q^{94} + 18 q^{95} - 3 q^{96} - q^{97} + 63 q^{98} + 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{15}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.309017 + 0.951057i −0.218508 + 0.672499i
\(3\) −0.978148 0.207912i −0.564734 0.120038i
\(4\) −0.809017 0.587785i −0.404508 0.293893i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0.500000 0.866025i 0.204124 0.353553i
\(7\) −0.381451 + 0.169833i −0.144175 + 0.0641909i −0.477556 0.878601i \(-0.658477\pi\)
0.333381 + 0.942792i \(0.391811\pi\)
\(8\) 0.809017 0.587785i 0.286031 0.207813i
\(9\) 0.913545 + 0.406737i 0.304515 + 0.135579i
\(10\) −0.978148 + 0.207912i −0.309317 + 0.0657474i
\(11\) −0.275944 + 2.62543i −0.0832003 + 0.791598i 0.870769 + 0.491693i \(0.163622\pi\)
−0.953969 + 0.299905i \(0.903045\pi\)
\(12\) 0.669131 + 0.743145i 0.193161 + 0.214527i
\(13\) −1.91862 + 2.13084i −0.532129 + 0.590990i −0.947935 0.318464i \(-0.896833\pi\)
0.415806 + 0.909454i \(0.363500\pi\)
\(14\) −0.0436459 0.415263i −0.0116649 0.110984i
\(15\) −0.309017 0.951057i −0.0797878 0.245562i
\(16\) 0.309017 + 0.951057i 0.0772542 + 0.237764i
\(17\) −0.588175 5.59612i −0.142653 1.35726i −0.798332 0.602217i \(-0.794284\pi\)
0.655679 0.755040i \(-0.272383\pi\)
\(18\) −0.669131 + 0.743145i −0.157716 + 0.175161i
\(19\) 1.98000 + 2.19901i 0.454243 + 0.504487i 0.926147 0.377162i \(-0.123100\pi\)
−0.471905 + 0.881650i \(0.656433\pi\)
\(20\) 0.104528 0.994522i 0.0233733 0.222382i
\(21\) 0.408426 0.0868137i 0.0891259 0.0189443i
\(22\) −2.41166 1.07374i −0.514168 0.228922i
\(23\) 2.85192 2.07204i 0.594667 0.432051i −0.249315 0.968422i \(-0.580206\pi\)
0.843982 + 0.536372i \(0.180206\pi\)
\(24\) −0.913545 + 0.406737i −0.186477 + 0.0830248i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −1.43367 2.48318i −0.281165 0.486992i
\(27\) −0.809017 0.587785i −0.155695 0.113119i
\(28\) 0.408426 + 0.0868137i 0.0771853 + 0.0164062i
\(29\) −2.59211 + 7.97770i −0.481343 + 1.48142i 0.355864 + 0.934538i \(0.384186\pi\)
−0.837208 + 0.546885i \(0.815814\pi\)
\(30\) 1.00000 0.182574
\(31\) −5.56703 0.0902791i −0.999869 0.0162146i
\(32\) −1.00000 −0.176777
\(33\) 0.815772 2.51069i 0.142008 0.437055i
\(34\) 5.50398 + 1.16991i 0.943924 + 0.200637i
\(35\) −0.337806 0.245430i −0.0570996 0.0414853i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) −3.43434 + 5.94846i −0.564603 + 0.977921i 0.432484 + 0.901642i \(0.357637\pi\)
−0.997087 + 0.0762790i \(0.975696\pi\)
\(38\) −2.70324 + 1.20356i −0.438523 + 0.195243i
\(39\) 2.31972 1.68538i 0.371453 0.269876i
\(40\) 0.913545 + 0.406737i 0.144444 + 0.0643107i
\(41\) −10.6869 + 2.27157i −1.66902 + 0.354760i −0.942968 0.332884i \(-0.891978\pi\)
−0.726048 + 0.687645i \(0.758645\pi\)
\(42\) −0.0436459 + 0.415263i −0.00673471 + 0.0640765i
\(43\) 6.56729 + 7.29372i 1.00150 + 1.11228i 0.993673 + 0.112312i \(0.0358256\pi\)
0.00782959 + 0.999969i \(0.497508\pi\)
\(44\) 1.76643 1.96182i 0.266300 0.295756i
\(45\) 0.104528 + 0.994522i 0.0155822 + 0.148255i
\(46\) 1.08934 + 3.35263i 0.160614 + 0.494319i
\(47\) −3.01457 9.27790i −0.439720 1.35332i −0.888171 0.459513i \(-0.848024\pi\)
0.448451 0.893808i \(-0.351976\pi\)
\(48\) −0.104528 0.994522i −0.0150874 0.143547i
\(49\) −4.56725 + 5.07245i −0.652465 + 0.724635i
\(50\) −0.669131 0.743145i −0.0946294 0.105097i
\(51\) −0.588175 + 5.59612i −0.0823610 + 0.783613i
\(52\) 2.80467 0.596152i 0.388938 0.0826714i
\(53\) −3.06996 1.36683i −0.421692 0.187749i 0.184909 0.982756i \(-0.440801\pi\)
−0.606601 + 0.795006i \(0.707467\pi\)
\(54\) 0.809017 0.587785i 0.110093 0.0799874i
\(55\) −2.41166 + 1.07374i −0.325189 + 0.144783i
\(56\) −0.208775 + 0.361609i −0.0278988 + 0.0483221i
\(57\) −1.47953 2.56262i −0.195969 0.339427i
\(58\) −6.78624 4.93049i −0.891077 0.647405i
\(59\) −1.66800 0.354544i −0.217155 0.0461577i 0.0980493 0.995182i \(-0.468740\pi\)
−0.315204 + 0.949024i \(0.602073\pi\)
\(60\) −0.309017 + 0.951057i −0.0398939 + 0.122781i
\(61\) −9.40663 −1.20440 −0.602198 0.798347i \(-0.705708\pi\)
−0.602198 + 0.798347i \(0.705708\pi\)
\(62\) 1.80617 5.26666i 0.229384 0.668867i
\(63\) −0.417551 −0.0526064
\(64\) 0.309017 0.951057i 0.0386271 0.118882i
\(65\) −2.80467 0.596152i −0.347877 0.0739435i
\(66\) 2.13572 + 1.55169i 0.262889 + 0.191000i
\(67\) −0.288536 0.499759i −0.0352503 0.0610552i 0.847862 0.530217i \(-0.177889\pi\)
−0.883112 + 0.469162i \(0.844556\pi\)
\(68\) −2.81347 + 4.87307i −0.341183 + 0.590947i
\(69\) −3.22040 + 1.43381i −0.387691 + 0.172611i
\(70\) 0.337806 0.245430i 0.0403755 0.0293345i
\(71\) −2.53210 1.12736i −0.300505 0.133793i 0.250945 0.968001i \(-0.419259\pi\)
−0.551450 + 0.834208i \(0.685925\pi\)
\(72\) 0.978148 0.207912i 0.115276 0.0245026i
\(73\) 0.450994 4.29092i 0.0527848 0.502214i −0.935906 0.352249i \(-0.885417\pi\)
0.988691 0.149965i \(-0.0479162\pi\)
\(74\) −4.59605 5.10443i −0.534280 0.593378i
\(75\) 0.669131 0.743145i 0.0772645 0.0858110i
\(76\) −0.309306 2.94285i −0.0354798 0.337568i
\(77\) −0.340626 1.04834i −0.0388179 0.119469i
\(78\) 0.886054 + 2.72699i 0.100326 + 0.308771i
\(79\) −0.594502 5.65631i −0.0668868 0.636385i −0.975689 0.219158i \(-0.929669\pi\)
0.908803 0.417227i \(-0.136998\pi\)
\(80\) −0.669131 + 0.743145i −0.0748111 + 0.0830861i
\(81\) 0.669131 + 0.743145i 0.0743478 + 0.0825716i
\(82\) 1.14204 10.8658i 0.126118 1.19993i
\(83\) −9.39662 + 1.99731i −1.03141 + 0.219234i −0.692374 0.721539i \(-0.743435\pi\)
−0.339039 + 0.940772i \(0.610102\pi\)
\(84\) −0.381451 0.169833i −0.0416198 0.0185303i
\(85\) 4.55229 3.30743i 0.493765 0.358741i
\(86\) −8.96614 + 3.99198i −0.966844 + 0.430467i
\(87\) 4.19413 7.26444i 0.449658 0.778830i
\(88\) 1.31995 + 2.28621i 0.140707 + 0.243711i
\(89\) 3.08580 + 2.24196i 0.327094 + 0.237648i 0.739196 0.673490i \(-0.235205\pi\)
−0.412103 + 0.911137i \(0.635205\pi\)
\(90\) −0.978148 0.207912i −0.103106 0.0219158i
\(91\) 0.369973 1.13866i 0.0387837 0.119364i
\(92\) −3.52517 −0.367524
\(93\) 5.42661 + 1.24576i 0.562713 + 0.129179i
\(94\) 9.75536 1.00619
\(95\) −0.914400 + 2.81423i −0.0938154 + 0.288734i
\(96\) 0.978148 + 0.207912i 0.0998318 + 0.0212199i
\(97\) 6.33471 + 4.60244i 0.643192 + 0.467307i 0.860945 0.508697i \(-0.169873\pi\)
−0.217753 + 0.976004i \(0.569873\pi\)
\(98\) −3.41283 5.91119i −0.344747 0.597120i
\(99\) −1.31995 + 2.28621i −0.132660 + 0.229773i
\(100\) 0.913545 0.406737i 0.0913545 0.0406737i
\(101\) −6.49267 + 4.71720i −0.646044 + 0.469379i −0.861921 0.507042i \(-0.830739\pi\)
0.215877 + 0.976421i \(0.430739\pi\)
\(102\) −5.14047 2.28868i −0.508982 0.226613i
\(103\) 2.46255 0.523431i 0.242642 0.0515752i −0.0849852 0.996382i \(-0.527084\pi\)
0.327627 + 0.944807i \(0.393751\pi\)
\(104\) −0.299718 + 2.85162i −0.0293898 + 0.279625i
\(105\) 0.279396 + 0.310301i 0.0272662 + 0.0302822i
\(106\) 2.24861 2.49733i 0.218404 0.242562i
\(107\) −1.71876 16.3529i −0.166159 1.58089i −0.686624 0.727012i \(-0.740908\pi\)
0.520466 0.853883i \(-0.325758\pi\)
\(108\) 0.309017 + 0.951057i 0.0297352 + 0.0915155i
\(109\) 5.17771 + 15.9353i 0.495934 + 1.52633i 0.815496 + 0.578763i \(0.196464\pi\)
−0.319562 + 0.947566i \(0.603536\pi\)
\(110\) −0.275944 2.62543i −0.0263102 0.250325i
\(111\) 4.59605 5.10443i 0.436238 0.484491i
\(112\) −0.279396 0.310301i −0.0264004 0.0293206i
\(113\) −1.91170 + 18.1886i −0.179837 + 1.71104i 0.417191 + 0.908819i \(0.363015\pi\)
−0.597028 + 0.802220i \(0.703652\pi\)
\(114\) 2.89440 0.615223i 0.271085 0.0576209i
\(115\) 3.22040 + 1.43381i 0.300304 + 0.133704i
\(116\) 6.78624 4.93049i 0.630087 0.457785i
\(117\) −2.61944 + 1.16625i −0.242167 + 0.107820i
\(118\) 0.852632 1.47680i 0.0784911 0.135951i
\(119\) 1.17477 + 2.03475i 0.107691 + 0.186526i
\(120\) −0.809017 0.587785i −0.0738528 0.0536572i
\(121\) 3.94288 + 0.838084i 0.358443 + 0.0761895i
\(122\) 2.90681 8.94624i 0.263170 0.809954i
\(123\) 10.9257 0.985134
\(124\) 4.45076 + 3.34526i 0.399690 + 0.300413i
\(125\) −1.00000 −0.0894427
\(126\) 0.129030 0.397114i 0.0114949 0.0353777i
\(127\) −8.21881 1.74696i −0.729302 0.155018i −0.171727 0.985145i \(-0.554935\pi\)
−0.557575 + 0.830127i \(0.688268\pi\)
\(128\) 0.809017 + 0.587785i 0.0715077 + 0.0519534i
\(129\) −4.90733 8.49975i −0.432066 0.748361i
\(130\) 1.43367 2.48318i 0.125741 0.217790i
\(131\) 13.0360 5.80402i 1.13896 0.507099i 0.251445 0.967872i \(-0.419094\pi\)
0.887518 + 0.460772i \(0.152427\pi\)
\(132\) −2.13572 + 1.55169i −0.185890 + 0.135057i
\(133\) −1.12874 0.502546i −0.0978740 0.0435763i
\(134\) 0.564461 0.119980i 0.0487620 0.0103647i
\(135\) 0.104528 0.994522i 0.00899638 0.0855948i
\(136\) −3.76516 4.18163i −0.322860 0.358572i
\(137\) −11.6898 + 12.9828i −0.998724 + 1.10920i −0.00470494 + 0.999989i \(0.501498\pi\)
−0.994019 + 0.109206i \(0.965169\pi\)
\(138\) −0.368480 3.50586i −0.0313671 0.298438i
\(139\) 6.46929 + 19.9104i 0.548718 + 1.68878i 0.711981 + 0.702199i \(0.247798\pi\)
−0.163262 + 0.986583i \(0.552202\pi\)
\(140\) 0.129030 + 0.397114i 0.0109050 + 0.0335623i
\(141\) 1.01971 + 9.70192i 0.0858753 + 0.817049i
\(142\) 1.85465 2.05979i 0.155638 0.172854i
\(143\) −5.06495 5.62520i −0.423553 0.470403i
\(144\) −0.104528 + 0.994522i −0.00871071 + 0.0828768i
\(145\) −8.20495 + 1.74402i −0.681384 + 0.144833i
\(146\) 3.94154 + 1.75489i 0.326204 + 0.145236i
\(147\) 5.52207 4.01202i 0.455452 0.330906i
\(148\) 6.27486 2.79375i 0.515790 0.229645i
\(149\) 9.66371 16.7380i 0.791682 1.37123i −0.133242 0.991083i \(-0.542539\pi\)
0.924925 0.380150i \(-0.124128\pi\)
\(150\) 0.500000 + 0.866025i 0.0408248 + 0.0707107i
\(151\) 5.35760 + 3.89252i 0.435995 + 0.316769i 0.784042 0.620708i \(-0.213155\pi\)
−0.348047 + 0.937477i \(0.613155\pi\)
\(152\) 2.89440 + 0.615223i 0.234767 + 0.0499012i
\(153\) 1.73882 5.35154i 0.140575 0.432646i
\(154\) 1.10229 0.0888250
\(155\) −2.70533 4.86633i −0.217298 0.390873i
\(156\) −2.86733 −0.229570
\(157\) −2.30634 + 7.09818i −0.184066 + 0.566496i −0.999931 0.0117459i \(-0.996261\pi\)
0.815865 + 0.578242i \(0.196261\pi\)
\(158\) 5.56318 + 1.18249i 0.442583 + 0.0940740i
\(159\) 2.71869 + 1.97525i 0.215606 + 0.156647i
\(160\) −0.500000 0.866025i −0.0395285 0.0684653i
\(161\) −0.735968 + 1.27473i −0.0580024 + 0.100463i
\(162\) −0.913545 + 0.406737i −0.0717749 + 0.0319562i
\(163\) 13.4644 9.78247i 1.05461 0.766222i 0.0815296 0.996671i \(-0.474019\pi\)
0.973084 + 0.230449i \(0.0740195\pi\)
\(164\) 9.98109 + 4.44387i 0.779392 + 0.347008i
\(165\) 2.58221 0.548865i 0.201024 0.0427291i
\(166\) 1.00416 9.55392i 0.0779377 0.741528i
\(167\) −6.35543 7.05842i −0.491798 0.546197i 0.445246 0.895408i \(-0.353116\pi\)
−0.937044 + 0.349211i \(0.886450\pi\)
\(168\) 0.279396 0.310301i 0.0215559 0.0239402i
\(169\) 0.499479 + 4.75223i 0.0384215 + 0.365556i
\(170\) 1.73882 + 5.35154i 0.133361 + 0.410444i
\(171\) 0.914400 + 2.81423i 0.0699259 + 0.215210i
\(172\) −1.02591 9.76090i −0.0782250 0.744261i
\(173\) 13.6752 15.1879i 1.03971 1.15471i 0.0519593 0.998649i \(-0.483453\pi\)
0.987747 0.156062i \(-0.0498800\pi\)
\(174\) 5.61284 + 6.23369i 0.425508 + 0.472575i
\(175\) 0.0436459 0.415263i 0.00329932 0.0313910i
\(176\) −2.58221 + 0.548865i −0.194641 + 0.0413722i
\(177\) 1.55784 + 0.693593i 0.117094 + 0.0521336i
\(178\) −3.08580 + 2.24196i −0.231290 + 0.168042i
\(179\) −11.5859 + 5.15837i −0.865971 + 0.385555i −0.791135 0.611641i \(-0.790510\pi\)
−0.0748352 + 0.997196i \(0.523843\pi\)
\(180\) 0.500000 0.866025i 0.0372678 0.0645497i
\(181\) −0.162773 0.281931i −0.0120988 0.0209558i 0.859913 0.510441i \(-0.170518\pi\)
−0.872011 + 0.489486i \(0.837185\pi\)
\(182\) 0.968601 + 0.703730i 0.0717975 + 0.0521639i
\(183\) 9.20107 + 1.95575i 0.680163 + 0.144573i
\(184\) 1.08934 3.35263i 0.0803070 0.247159i
\(185\) −6.86869 −0.504996
\(186\) −2.86170 + 4.77605i −0.209830 + 0.350197i
\(187\) 14.8545 1.08627
\(188\) −3.01457 + 9.27790i −0.219860 + 0.676660i
\(189\) 0.408426 + 0.0868137i 0.0297086 + 0.00631476i
\(190\) −2.39393 1.73929i −0.173674 0.126181i
\(191\) 3.47170 + 6.01316i 0.251203 + 0.435097i 0.963857 0.266419i \(-0.0858403\pi\)
−0.712654 + 0.701516i \(0.752507\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) 9.88196 4.39973i 0.711319 0.316700i −0.0189871 0.999820i \(-0.506044\pi\)
0.730306 + 0.683120i \(0.239377\pi\)
\(194\) −6.33471 + 4.60244i −0.454806 + 0.330436i
\(195\) 2.61944 + 1.16625i 0.187582 + 0.0835168i
\(196\) 6.67649 1.41913i 0.476892 0.101367i
\(197\) 0.640962 6.09835i 0.0456667 0.434489i −0.947671 0.319249i \(-0.896569\pi\)
0.993338 0.115241i \(-0.0367639\pi\)
\(198\) −1.76643 1.96182i −0.125535 0.139421i
\(199\) 9.37105 10.4076i 0.664296 0.737776i −0.312977 0.949761i \(-0.601326\pi\)
0.977273 + 0.211985i \(0.0679929\pi\)
\(200\) 0.104528 + 0.994522i 0.00739128 + 0.0703233i
\(201\) 0.178325 + 0.548828i 0.0125781 + 0.0387113i
\(202\) −2.47998 7.63259i −0.174491 0.537027i
\(203\) −0.366113 3.48333i −0.0256961 0.244482i
\(204\) 3.76516 4.18163i 0.263614 0.292773i
\(205\) −7.31070 8.11935i −0.510601 0.567080i
\(206\) −0.263157 + 2.50377i −0.0183350 + 0.174446i
\(207\) 3.44813 0.732924i 0.239662 0.0509417i
\(208\) −2.61944 1.16625i −0.181625 0.0808648i
\(209\) −6.31972 + 4.59154i −0.437144 + 0.317604i
\(210\) −0.381451 + 0.169833i −0.0263227 + 0.0117196i
\(211\) −1.45776 + 2.52492i −0.100356 + 0.173822i −0.911832 0.410565i \(-0.865332\pi\)
0.811475 + 0.584387i \(0.198665\pi\)
\(212\) 1.68025 + 2.91027i 0.115400 + 0.199878i
\(213\) 2.24237 + 1.62918i 0.153645 + 0.111630i
\(214\) 16.0837 + 3.41869i 1.09946 + 0.233697i
\(215\) −3.03290 + 9.33430i −0.206842 + 0.636594i
\(216\) −1.00000 −0.0680414
\(217\) 2.13889 0.911030i 0.145197 0.0618447i
\(218\) −16.7554 −1.13482
\(219\) −1.33327 + 4.10339i −0.0900941 + 0.277281i
\(220\) 2.58221 + 0.548865i 0.174092 + 0.0370045i
\(221\) 13.0529 + 9.48351i 0.878035 + 0.637930i
\(222\) 3.43434 + 5.94846i 0.230498 + 0.399234i
\(223\) −9.36074 + 16.2133i −0.626842 + 1.08572i 0.361340 + 0.932434i \(0.382319\pi\)
−0.988182 + 0.153287i \(0.951014\pi\)
\(224\) 0.381451 0.169833i 0.0254868 0.0113475i
\(225\) −0.809017 + 0.587785i −0.0539345 + 0.0391857i
\(226\) −16.7076 7.43872i −1.11138 0.494816i
\(227\) 18.2933 3.88836i 1.21417 0.258080i 0.444064 0.895995i \(-0.353536\pi\)
0.770106 + 0.637916i \(0.220203\pi\)
\(228\) −0.309306 + 2.94285i −0.0204843 + 0.194895i
\(229\) 10.7374 + 11.9251i 0.709549 + 0.788034i 0.984866 0.173320i \(-0.0554493\pi\)
−0.275317 + 0.961354i \(0.588783\pi\)
\(230\) −2.35880 + 2.61971i −0.155534 + 0.172739i
\(231\) 0.115221 + 1.09625i 0.00758096 + 0.0721280i
\(232\) 2.59211 + 7.97770i 0.170181 + 0.523762i
\(233\) 1.65665 + 5.09864i 0.108531 + 0.334023i 0.990543 0.137204i \(-0.0438115\pi\)
−0.882012 + 0.471226i \(0.843811\pi\)
\(234\) −0.299718 2.85162i −0.0195932 0.186417i
\(235\) 6.52761 7.24964i 0.425814 0.472915i
\(236\) 1.14104 + 1.26726i 0.0742756 + 0.0824914i
\(237\) −0.594502 + 5.65631i −0.0386171 + 0.367417i
\(238\) −2.29819 + 0.488495i −0.148970 + 0.0316644i
\(239\) 9.90920 + 4.41186i 0.640973 + 0.285379i 0.701373 0.712795i \(-0.252571\pi\)
−0.0604000 + 0.998174i \(0.519238\pi\)
\(240\) 0.809017 0.587785i 0.0522218 0.0379414i
\(241\) −3.47642 + 1.54780i −0.223936 + 0.0997027i −0.515638 0.856806i \(-0.672445\pi\)
0.291702 + 0.956509i \(0.405778\pi\)
\(242\) −2.01548 + 3.49092i −0.129560 + 0.224405i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 7.61012 + 5.52908i 0.487188 + 0.353963i
\(245\) −6.67649 1.41913i −0.426546 0.0906651i
\(246\) −3.37622 + 10.3909i −0.215260 + 0.662501i
\(247\) −8.48461 −0.539863
\(248\) −4.55689 + 3.19918i −0.289363 + 0.203148i
\(249\) 9.60654 0.608790
\(250\) 0.309017 0.951057i 0.0195440 0.0601501i
\(251\) 20.2914 + 4.31307i 1.28078 + 0.272238i 0.797549 0.603254i \(-0.206129\pi\)
0.483232 + 0.875492i \(0.339463\pi\)
\(252\) 0.337806 + 0.245430i 0.0212797 + 0.0154606i
\(253\) 4.65303 + 8.05929i 0.292534 + 0.506683i
\(254\) 4.20121 7.27672i 0.263608 0.456582i
\(255\) −5.14047 + 2.28868i −0.321908 + 0.143323i
\(256\) −0.809017 + 0.587785i −0.0505636 + 0.0367366i
\(257\) −21.1822 9.43090i −1.32131 0.588284i −0.379735 0.925095i \(-0.623985\pi\)
−0.941572 + 0.336812i \(0.890651\pi\)
\(258\) 9.60019 2.04058i 0.597682 0.127041i
\(259\) 0.299790 2.85231i 0.0186281 0.177234i
\(260\) 1.91862 + 2.13084i 0.118988 + 0.132149i
\(261\) −5.61284 + 6.23369i −0.347426 + 0.385856i
\(262\) 1.49159 + 14.1915i 0.0921508 + 0.876757i
\(263\) 9.04765 + 27.8458i 0.557902 + 1.71704i 0.688155 + 0.725564i \(0.258421\pi\)
−0.130253 + 0.991481i \(0.541579\pi\)
\(264\) −0.815772 2.51069i −0.0502073 0.154522i
\(265\) −0.351267 3.34208i −0.0215782 0.205302i
\(266\) 0.826749 0.918198i 0.0506912 0.0562983i
\(267\) −2.55223 2.83454i −0.156194 0.173471i
\(268\) −0.0603204 + 0.573910i −0.00368466 + 0.0350572i
\(269\) −7.65658 + 1.62746i −0.466830 + 0.0992277i −0.435320 0.900276i \(-0.643365\pi\)
−0.0315096 + 0.999503i \(0.510031\pi\)
\(270\) 0.913545 + 0.406737i 0.0555966 + 0.0247532i
\(271\) −0.943076 + 0.685185i −0.0572878 + 0.0416220i −0.616061 0.787699i \(-0.711272\pi\)
0.558773 + 0.829321i \(0.311272\pi\)
\(272\) 5.14047 2.28868i 0.311687 0.138772i
\(273\) −0.598628 + 1.03685i −0.0362306 + 0.0627533i
\(274\) −8.73504 15.1295i −0.527703 0.914009i
\(275\) −2.13572 1.55169i −0.128789 0.0935705i
\(276\) 3.44813 + 0.732924i 0.207553 + 0.0441168i
\(277\) 9.06879 27.9109i 0.544891 1.67700i −0.176358 0.984326i \(-0.556432\pi\)
0.721249 0.692676i \(-0.243568\pi\)
\(278\) −20.9351 −1.25560
\(279\) −5.04902 2.34679i −0.302277 0.140499i
\(280\) −0.417551 −0.0249534
\(281\) 7.95532 24.4840i 0.474575 1.46059i −0.371956 0.928250i \(-0.621313\pi\)
0.846531 0.532340i \(-0.178687\pi\)
\(282\) −9.54218 2.02825i −0.568229 0.120781i
\(283\) −6.89405 5.00882i −0.409809 0.297744i 0.363715 0.931510i \(-0.381508\pi\)
−0.773524 + 0.633766i \(0.781508\pi\)
\(284\) 1.38586 + 2.40039i 0.0822358 + 0.142437i
\(285\) 1.47953 2.56262i 0.0876398 0.151797i
\(286\) 6.91504 3.07877i 0.408895 0.182052i
\(287\) 3.69075 2.68149i 0.217858 0.158283i
\(288\) −0.913545 0.406737i −0.0538312 0.0239672i
\(289\) −14.3420 + 3.04850i −0.843650 + 0.179323i
\(290\) 0.876811 8.34230i 0.0514881 0.489877i
\(291\) −5.23938 5.81892i −0.307138 0.341111i
\(292\) −2.88700 + 3.20634i −0.168949 + 0.187637i
\(293\) 0.745259 + 7.09067i 0.0435385 + 0.414241i 0.994484 + 0.104884i \(0.0334472\pi\)
−0.950946 + 0.309357i \(0.899886\pi\)
\(294\) 2.10924 + 6.49158i 0.123014 + 0.378597i
\(295\) −0.526955 1.62180i −0.0306805 0.0944250i
\(296\) 0.717974 + 6.83106i 0.0417314 + 0.397047i
\(297\) 1.76643 1.96182i 0.102499 0.113837i
\(298\) 12.9326 + 14.3631i 0.749164 + 0.832031i
\(299\) −1.05656 + 10.0525i −0.0611022 + 0.581348i
\(300\) −0.978148 + 0.207912i −0.0564734 + 0.0120038i
\(301\) −3.74382 1.66686i −0.215790 0.0960759i
\(302\) −5.35760 + 3.89252i −0.308295 + 0.223989i
\(303\) 7.33155 3.26421i 0.421186 0.187524i
\(304\) −1.47953 + 2.56262i −0.0848568 + 0.146976i
\(305\) −4.70332 8.14638i −0.269311 0.466460i
\(306\) 4.55229 + 3.30743i 0.260237 + 0.189073i
\(307\) −12.9299 2.74833i −0.737947 0.156855i −0.176421 0.984315i \(-0.556452\pi\)
−0.561526 + 0.827459i \(0.689785\pi\)
\(308\) −0.340626 + 1.04834i −0.0194090 + 0.0597347i
\(309\) −2.51756 −0.143219
\(310\) 5.46415 1.06914i 0.310343 0.0607233i
\(311\) 21.7385 1.23268 0.616338 0.787481i \(-0.288615\pi\)
0.616338 + 0.787481i \(0.288615\pi\)
\(312\) 0.886054 2.72699i 0.0501630 0.154386i
\(313\) 20.8167 + 4.42473i 1.17663 + 0.250101i 0.754417 0.656395i \(-0.227920\pi\)
0.422214 + 0.906496i \(0.361253\pi\)
\(314\) −6.03807 4.38691i −0.340748 0.247568i
\(315\) −0.208775 0.361609i −0.0117632 0.0203744i
\(316\) −2.84373 + 4.92549i −0.159973 + 0.277081i
\(317\) −19.7645 + 8.79971i −1.11008 + 0.494241i −0.878099 0.478479i \(-0.841188\pi\)
−0.231984 + 0.972720i \(0.574522\pi\)
\(318\) −2.71869 + 1.97525i −0.152457 + 0.110766i
\(319\) −20.2296 9.00682i −1.13264 0.504285i
\(320\) 0.978148 0.207912i 0.0546801 0.0116226i
\(321\) −1.71876 + 16.3529i −0.0959318 + 0.912730i
\(322\) −0.984917 1.09386i −0.0548873 0.0609585i
\(323\) 11.1413 12.3737i 0.619920 0.688491i
\(324\) −0.104528 0.994522i −0.00580714 0.0552512i
\(325\) −0.886054 2.72699i −0.0491495 0.151266i
\(326\) 5.14295 + 15.8284i 0.284841 + 0.876652i
\(327\) −1.75142 16.6636i −0.0968536 0.921500i
\(328\) −7.31070 + 8.11935i −0.403666 + 0.448316i
\(329\) 2.72561 + 3.02709i 0.150268 + 0.166889i
\(330\) −0.275944 + 2.62543i −0.0151902 + 0.144525i
\(331\) −17.3175 + 3.68095i −0.951856 + 0.202323i −0.657569 0.753394i \(-0.728415\pi\)
−0.294286 + 0.955717i \(0.595082\pi\)
\(332\) 8.77602 + 3.90733i 0.481646 + 0.214443i
\(333\) −5.55689 + 4.03731i −0.304516 + 0.221243i
\(334\) 8.67689 3.86320i 0.474779 0.211385i
\(335\) 0.288536 0.499759i 0.0157644 0.0273047i
\(336\) 0.208775 + 0.361609i 0.0113896 + 0.0197274i
\(337\) 13.2991 + 9.66235i 0.724447 + 0.526342i 0.887802 0.460226i \(-0.152231\pi\)
−0.163355 + 0.986567i \(0.552231\pi\)
\(338\) −4.67399 0.993487i −0.254231 0.0540385i
\(339\) 5.65154 17.3937i 0.306950 0.944694i
\(340\) −5.62694 −0.305164
\(341\) 1.77321 14.5910i 0.0960248 0.790144i
\(342\) −2.95906 −0.160008
\(343\) 1.78393 5.49036i 0.0963230 0.296452i
\(344\) 9.60019 + 2.04058i 0.517608 + 0.110021i
\(345\) −2.85192 2.07204i −0.153542 0.111555i
\(346\) 10.2186 + 17.6992i 0.549357 + 0.951515i
\(347\) 6.94012 12.0206i 0.372565 0.645302i −0.617394 0.786654i \(-0.711812\pi\)
0.989959 + 0.141352i \(0.0451449\pi\)
\(348\) −7.66305 + 3.41181i −0.410783 + 0.182892i
\(349\) −12.0855 + 8.78064i −0.646922 + 0.470017i −0.862221 0.506531i \(-0.830927\pi\)
0.215299 + 0.976548i \(0.430927\pi\)
\(350\) 0.381451 + 0.169833i 0.0203894 + 0.00907796i
\(351\) 2.80467 0.596152i 0.149702 0.0318202i
\(352\) 0.275944 2.62543i 0.0147079 0.139936i
\(353\) 10.9425 + 12.1529i 0.582412 + 0.646834i 0.960284 0.279023i \(-0.0900107\pi\)
−0.377872 + 0.925858i \(0.623344\pi\)
\(354\) −1.14104 + 1.26726i −0.0606458 + 0.0673540i
\(355\) −0.289724 2.75654i −0.0153770 0.146302i
\(356\) −1.17867 3.62757i −0.0624694 0.192261i
\(357\) −0.726045 2.23454i −0.0384264 0.118264i
\(358\) −1.32567 12.6129i −0.0700636 0.666611i
\(359\) 2.64376 2.93619i 0.139532 0.154966i −0.669328 0.742967i \(-0.733418\pi\)
0.808861 + 0.588001i \(0.200085\pi\)
\(360\) 0.669131 + 0.743145i 0.0352663 + 0.0391672i
\(361\) 1.07079 10.1878i 0.0563572 0.536203i
\(362\) 0.318432 0.0676848i 0.0167364 0.00355743i
\(363\) −3.68247 1.63954i −0.193279 0.0860535i
\(364\) −0.968601 + 0.703730i −0.0507685 + 0.0368855i
\(365\) 3.94154 1.75489i 0.206310 0.0918550i
\(366\) −4.70332 + 8.14638i −0.245846 + 0.425818i
\(367\) 10.3987 + 18.0111i 0.542808 + 0.940171i 0.998741 + 0.0501573i \(0.0159723\pi\)
−0.455933 + 0.890014i \(0.650694\pi\)
\(368\) 2.85192 + 2.07204i 0.148667 + 0.108013i
\(369\) −10.6869 2.27157i −0.556338 0.118253i
\(370\) 2.12254 6.53251i 0.110346 0.339609i
\(371\) 1.40318 0.0728492
\(372\) −3.65798 4.19752i −0.189657 0.217631i
\(373\) −38.4803 −1.99243 −0.996216 0.0869088i \(-0.972301\pi\)
−0.996216 + 0.0869088i \(0.972301\pi\)
\(374\) −4.59030 + 14.1275i −0.237359 + 0.730515i
\(375\) 0.978148 + 0.207912i 0.0505113 + 0.0107365i
\(376\) −7.89225 5.73406i −0.407012 0.295711i
\(377\) −12.0260 20.8296i −0.619368 1.07278i
\(378\) −0.208775 + 0.361609i −0.0107382 + 0.0185992i
\(379\) −13.9226 + 6.19874i −0.715156 + 0.318408i −0.731862 0.681453i \(-0.761349\pi\)
0.0167066 + 0.999860i \(0.494682\pi\)
\(380\) 2.39393 1.73929i 0.122806 0.0892238i
\(381\) 7.67600 + 3.41758i 0.393253 + 0.175088i
\(382\) −6.79167 + 1.44361i −0.347492 + 0.0738617i
\(383\) 2.96807 28.2393i 0.151661 1.44296i −0.608668 0.793425i \(-0.708296\pi\)
0.760329 0.649538i \(-0.225037\pi\)
\(384\) −0.669131 0.743145i −0.0341464 0.0379235i
\(385\) 0.737575 0.819161i 0.0375903 0.0417483i
\(386\) 1.13070 + 10.7579i 0.0575511 + 0.547562i
\(387\) 3.03290 + 9.33430i 0.154171 + 0.474489i
\(388\) −2.41964 7.44690i −0.122839 0.378059i
\(389\) −2.29186 21.8056i −0.116202 1.10559i −0.884837 0.465901i \(-0.845730\pi\)
0.768635 0.639688i \(-0.220936\pi\)
\(390\) −1.91862 + 2.13084i −0.0971531 + 0.107899i
\(391\) −13.2728 14.7410i −0.671235 0.745482i
\(392\) −0.713475 + 6.78826i −0.0360359 + 0.342859i
\(393\) −13.9579 + 2.96684i −0.704082 + 0.149657i
\(394\) 5.60181 + 2.49408i 0.282215 + 0.125650i
\(395\) 4.60126 3.34301i 0.231514 0.168205i
\(396\) 2.41166 1.07374i 0.121191 0.0539575i
\(397\) −3.44158 + 5.96100i −0.172728 + 0.299174i −0.939373 0.342898i \(-0.888592\pi\)
0.766645 + 0.642072i \(0.221925\pi\)
\(398\) 7.00241 + 12.1285i 0.350999 + 0.607948i
\(399\) 0.999587 + 0.726242i 0.0500419 + 0.0363576i
\(400\) −0.978148 0.207912i −0.0489074 0.0103956i
\(401\) −4.71125 + 14.4997i −0.235268 + 0.724082i 0.761817 + 0.647792i \(0.224307\pi\)
−0.997086 + 0.0762899i \(0.975693\pi\)
\(402\) −0.577072 −0.0287817
\(403\) 10.8734 11.6893i 0.541642 0.582284i
\(404\) 8.02538 0.399277
\(405\) −0.309017 + 0.951057i −0.0153552 + 0.0472584i
\(406\) 3.42598 + 0.728215i 0.170029 + 0.0361407i
\(407\) −14.6696 10.6581i −0.727145 0.528301i
\(408\) 2.81347 + 4.87307i 0.139288 + 0.241253i
\(409\) −5.28616 + 9.15590i −0.261384 + 0.452730i −0.966610 0.256252i \(-0.917512\pi\)
0.705226 + 0.708983i \(0.250846\pi\)
\(410\) 9.98109 4.44387i 0.492931 0.219467i
\(411\) 14.1336 10.2687i 0.697159 0.506515i
\(412\) −2.29991 1.02399i −0.113308 0.0504481i
\(413\) 0.696474 0.148040i 0.0342713 0.00728458i
\(414\) −0.368480 + 3.50586i −0.0181098 + 0.172303i
\(415\) −6.42803 7.13905i −0.315540 0.350442i
\(416\) 1.91862 2.13084i 0.0940681 0.104473i
\(417\) −2.18831 20.8204i −0.107162 1.01958i
\(418\) −2.41392 7.42928i −0.118069 0.363378i
\(419\) −1.53015 4.70931i −0.0747527 0.230065i 0.906698 0.421781i \(-0.138595\pi\)
−0.981450 + 0.191716i \(0.938595\pi\)
\(420\) −0.0436459 0.415263i −0.00212970 0.0202628i
\(421\) 24.2039 26.8812i 1.17963 1.31011i 0.238862 0.971053i \(-0.423226\pi\)
0.940766 0.339056i \(-0.110108\pi\)
\(422\) −1.95087 2.16666i −0.0949667 0.105471i
\(423\) 1.01971 9.70192i 0.0495801 0.471723i
\(424\) −3.28706 + 0.698685i −0.159634 + 0.0339312i
\(425\) 5.14047 + 2.28868i 0.249349 + 0.111017i
\(426\) −2.24237 + 1.62918i −0.108643 + 0.0789340i
\(427\) 3.58817 1.59756i 0.173644 0.0773112i
\(428\) −8.22149 + 14.2400i −0.397401 + 0.688318i
\(429\) 3.78473 + 6.55534i 0.182728 + 0.316495i
\(430\) −7.94023 5.76891i −0.382912 0.278202i
\(431\) 13.0555 + 2.77503i 0.628860 + 0.133668i 0.511307 0.859398i \(-0.329162\pi\)
0.117553 + 0.993067i \(0.462495\pi\)
\(432\) 0.309017 0.951057i 0.0148676 0.0457577i
\(433\) 1.63150 0.0784048 0.0392024 0.999231i \(-0.487518\pi\)
0.0392024 + 0.999231i \(0.487518\pi\)
\(434\) 0.205489 + 2.31572i 0.00986377 + 0.111158i
\(435\) 8.38826 0.402186
\(436\) 5.17771 15.9353i 0.247967 0.763164i
\(437\) 10.2032 + 2.16876i 0.488087 + 0.103746i
\(438\) −3.49055 2.53603i −0.166785 0.121176i
\(439\) 9.33346 + 16.1660i 0.445462 + 0.771562i 0.998084 0.0618693i \(-0.0197062\pi\)
−0.552623 + 0.833432i \(0.686373\pi\)
\(440\) −1.31995 + 2.28621i −0.0629260 + 0.108991i
\(441\) −6.23554 + 2.77624i −0.296931 + 0.132202i
\(442\) −13.0529 + 9.48351i −0.620864 + 0.451084i
\(443\) 10.4587 + 4.65649i 0.496905 + 0.221237i 0.639858 0.768493i \(-0.278993\pi\)
−0.142953 + 0.989730i \(0.545660\pi\)
\(444\) −6.71859 + 1.42808i −0.318850 + 0.0677737i
\(445\) −0.398698 + 3.79336i −0.0189001 + 0.179822i
\(446\) −12.5271 13.9128i −0.593176 0.658789i
\(447\) −12.9326 + 14.3631i −0.611690 + 0.679350i
\(448\) 0.0436459 + 0.415263i 0.00206208 + 0.0196193i
\(449\) 0.201086 + 0.618878i 0.00948981 + 0.0292066i 0.955689 0.294377i \(-0.0951122\pi\)
−0.946199 + 0.323584i \(0.895112\pi\)
\(450\) −0.309017 0.951057i −0.0145672 0.0448332i
\(451\) −3.01487 28.6846i −0.141965 1.35070i
\(452\) 12.2376 13.5912i 0.575607 0.639277i
\(453\) −4.43122 4.92137i −0.208197 0.231226i
\(454\) −1.95489 + 18.5995i −0.0917476 + 0.872920i
\(455\) 1.17109 0.248924i 0.0549017 0.0116697i
\(456\) −2.70324 1.20356i −0.126591 0.0563618i
\(457\) −13.2297 + 9.61192i −0.618858 + 0.449627i −0.852522 0.522691i \(-0.824928\pi\)
0.233664 + 0.972317i \(0.424928\pi\)
\(458\) −14.6595 + 6.52683i −0.684994 + 0.304979i
\(459\) −2.81347 + 4.87307i −0.131322 + 0.227456i
\(460\) −1.76258 3.05288i −0.0821809 0.142341i
\(461\) −17.6218 12.8030i −0.820730 0.596295i 0.0961918 0.995363i \(-0.469334\pi\)
−0.916921 + 0.399068i \(0.869334\pi\)
\(462\) −1.07820 0.229179i −0.0501625 0.0106624i
\(463\) −1.54391 + 4.75167i −0.0717516 + 0.220829i −0.980501 0.196513i \(-0.937038\pi\)
0.908750 + 0.417342i \(0.137038\pi\)
\(464\) −8.38826 −0.389415
\(465\) 1.63445 + 5.32246i 0.0757957 + 0.246823i
\(466\) −5.36102 −0.248345
\(467\) 1.68090 5.17327i 0.0777826 0.239390i −0.904603 0.426255i \(-0.859833\pi\)
0.982386 + 0.186865i \(0.0598326\pi\)
\(468\) 2.80467 + 0.596152i 0.129646 + 0.0275571i
\(469\) 0.194938 + 0.141631i 0.00900140 + 0.00653990i
\(470\) 4.87768 + 8.44839i 0.224991 + 0.389695i
\(471\) 3.73173 6.46355i 0.171949 0.297825i
\(472\) −1.55784 + 0.693593i −0.0717052 + 0.0319252i
\(473\) −20.9614 + 15.2293i −0.963804 + 0.700245i
\(474\) −5.19576 2.31330i −0.238649 0.106253i
\(475\) −2.89440 + 0.615223i −0.132804 + 0.0282284i
\(476\) 0.245593 2.33666i 0.0112567 0.107101i
\(477\) −2.24861 2.49733i −0.102957 0.114345i
\(478\) −7.25804 + 8.06087i −0.331975 + 0.368695i
\(479\) −2.80177 26.6570i −0.128016 1.21799i −0.850264 0.526357i \(-0.823558\pi\)
0.722248 0.691635i \(-0.243109\pi\)
\(480\) 0.309017 + 0.951057i 0.0141046 + 0.0434096i
\(481\) −6.08603 18.7309i −0.277499 0.854055i
\(482\) −0.397774 3.78457i −0.0181181 0.172383i
\(483\) 0.984917 1.09386i 0.0448153 0.0497724i
\(484\) −2.69724 2.99559i −0.122602 0.136163i
\(485\) −0.818472 + 7.78724i −0.0371649 + 0.353600i
\(486\) 0.978148 0.207912i 0.0443697 0.00943107i
\(487\) −28.8653 12.8517i −1.30801 0.582364i −0.370021 0.929023i \(-0.620649\pi\)
−0.937991 + 0.346659i \(0.887316\pi\)
\(488\) −7.61012 + 5.52908i −0.344494 + 0.250290i
\(489\) −15.2041 + 6.76929i −0.687552 + 0.306118i
\(490\) 3.41283 5.91119i 0.154176 0.267040i
\(491\) 14.6512 + 25.3767i 0.661200 + 1.14523i 0.980301 + 0.197512i \(0.0632861\pi\)
−0.319100 + 0.947721i \(0.603381\pi\)
\(492\) −8.83905 6.42194i −0.398495 0.289524i
\(493\) 46.1688 + 9.81348i 2.07934 + 0.441977i
\(494\) 2.62189 8.06934i 0.117964 0.363057i
\(495\) −2.63989 −0.118654
\(496\) −1.63445 5.32246i −0.0733888 0.238986i
\(497\) 1.15734 0.0519136
\(498\) −2.96859 + 9.13637i −0.133025 + 0.409410i
\(499\) −19.4516 4.13458i −0.870775 0.185089i −0.249208 0.968450i \(-0.580170\pi\)
−0.621567 + 0.783361i \(0.713504\pi\)
\(500\) 0.809017 + 0.587785i 0.0361803 + 0.0262866i
\(501\) 4.74902 + 8.22555i 0.212171 + 0.367490i
\(502\) −10.3724 + 17.9654i −0.462941 + 0.801837i
\(503\) 0.251834 0.112124i 0.0112287 0.00499936i −0.401115 0.916028i \(-0.631377\pi\)
0.412343 + 0.911029i \(0.364710\pi\)
\(504\) −0.337806 + 0.245430i −0.0150471 + 0.0109323i
\(505\) −7.33155 3.26421i −0.326249 0.145256i
\(506\) −9.10271 + 1.93484i −0.404665 + 0.0860141i
\(507\) 0.499479 4.75223i 0.0221827 0.211054i
\(508\) 5.62232 + 6.24422i 0.249450 + 0.277042i
\(509\) −3.12577 + 3.47152i −0.138547 + 0.153873i −0.808425 0.588599i \(-0.799680\pi\)
0.669878 + 0.742471i \(0.266346\pi\)
\(510\) −0.588175 5.59612i −0.0260448 0.247800i
\(511\) 0.556708 + 1.71337i 0.0246273 + 0.0757951i
\(512\) −0.309017 0.951057i −0.0136568 0.0420312i
\(513\) −0.309306 2.94285i −0.0136562 0.129930i
\(514\) 15.5150 17.2311i 0.684336 0.760032i
\(515\) 1.68458 + 1.87091i 0.0742314 + 0.0824423i
\(516\) −1.02591 + 9.76090i −0.0451632 + 0.429700i
\(517\) 25.1903 5.35437i 1.10787 0.235485i
\(518\) 2.62007 + 1.16653i 0.115119 + 0.0512544i
\(519\) −16.5341 + 12.0127i −0.725767 + 0.527300i
\(520\) −2.61944 + 1.16625i −0.114870 + 0.0511434i
\(521\) 8.80642 15.2532i 0.385816 0.668254i −0.606066 0.795415i \(-0.707253\pi\)
0.991882 + 0.127161i \(0.0405865\pi\)
\(522\) −4.19413 7.26444i −0.183572 0.317956i
\(523\) −11.1327 8.08838i −0.486799 0.353680i 0.317153 0.948374i \(-0.397273\pi\)
−0.803952 + 0.594694i \(0.797273\pi\)
\(524\) −13.9579 2.96684i −0.609753 0.129607i
\(525\) −0.129030 + 0.397114i −0.00563134 + 0.0173315i
\(526\) −29.2788 −1.27662
\(527\) 2.76918 + 31.2069i 0.120627 + 1.35939i
\(528\) 2.63989 0.114887
\(529\) −3.26730 + 10.0557i −0.142056 + 0.437205i
\(530\) 3.28706 + 0.698685i 0.142781 + 0.0303490i
\(531\) −1.37959 1.00233i −0.0598690 0.0434974i
\(532\) 0.617779 + 1.07002i 0.0267841 + 0.0463914i
\(533\) 15.6638 27.1304i 0.678472 1.17515i
\(534\) 3.48449 1.55140i 0.150789 0.0671355i
\(535\) 13.3027 9.66494i 0.575124 0.417852i
\(536\) −0.527181 0.234716i −0.0227708 0.0101382i
\(537\) 12.4052 2.63681i 0.535324 0.113787i
\(538\) 0.818210 7.78475i 0.0352755 0.335624i
\(539\) −12.0571 13.3907i −0.519334 0.576779i
\(540\) −0.669131 + 0.743145i −0.0287948 + 0.0319799i
\(541\) −2.30090 21.8916i −0.0989234 0.941193i −0.925597 0.378511i \(-0.876436\pi\)
0.826673 0.562682i \(-0.190230\pi\)
\(542\) −0.360223 1.10865i −0.0154729 0.0476207i
\(543\) 0.100599 + 0.309613i 0.00431713 + 0.0132867i
\(544\) 0.588175 + 5.59612i 0.0252178 + 0.239931i
\(545\) −11.2116 + 12.4517i −0.480250 + 0.533372i
\(546\) −0.801121 0.889735i −0.0342848 0.0380771i
\(547\) −4.69936 + 44.7114i −0.200930 + 1.91172i 0.174134 + 0.984722i \(0.444287\pi\)
−0.375064 + 0.926999i \(0.622379\pi\)
\(548\) 17.0883 3.63223i 0.729977 0.155161i
\(549\) −8.59338 3.82602i −0.366757 0.163291i
\(550\) 2.13572 1.55169i 0.0910674 0.0661643i
\(551\) −22.6754 + 10.0958i −0.966006 + 0.430093i
\(552\) −1.76258 + 3.05288i −0.0750205 + 0.129939i
\(553\) 1.18740 + 2.05664i 0.0504935 + 0.0874573i
\(554\) 23.7424 + 17.2499i 1.00872 + 0.732877i
\(555\) 6.71859 + 1.42808i 0.285188 + 0.0606187i
\(556\) 6.46929 19.9104i 0.274359 0.844391i
\(557\) −29.6915 −1.25807 −0.629035 0.777377i \(-0.716550\pi\)
−0.629035 + 0.777377i \(0.716550\pi\)
\(558\) 3.79216 4.07670i 0.160535 0.172581i
\(559\) −28.1419 −1.19028
\(560\) 0.129030 0.397114i 0.00545252 0.0167811i
\(561\) −14.5299 3.08843i −0.613454 0.130394i
\(562\) 20.8273 + 15.1319i 0.878547 + 0.638301i
\(563\) 8.64266 + 14.9695i 0.364245 + 0.630891i 0.988655 0.150206i \(-0.0479938\pi\)
−0.624410 + 0.781097i \(0.714660\pi\)
\(564\) 4.87768 8.44839i 0.205387 0.355741i
\(565\) −16.7076 + 7.43872i −0.702895 + 0.312949i
\(566\) 6.89405 5.00882i 0.289779 0.210537i
\(567\) −0.381451 0.169833i −0.0160195 0.00713232i
\(568\) −2.71116 + 0.576274i −0.113758 + 0.0241799i
\(569\) −4.10606 + 39.0666i −0.172135 + 1.63776i 0.478301 + 0.878196i \(0.341253\pi\)
−0.650436 + 0.759561i \(0.725414\pi\)
\(570\) 1.98000 + 2.19901i 0.0829330 + 0.0921064i
\(571\) −11.5636 + 12.8427i −0.483921 + 0.537448i −0.934818 0.355128i \(-0.884437\pi\)
0.450897 + 0.892576i \(0.351104\pi\)
\(572\) 0.791223 + 7.52799i 0.0330827 + 0.314761i
\(573\) −2.14563 6.60357i −0.0896349 0.275868i
\(574\) 1.40974 + 4.33874i 0.0588415 + 0.181095i
\(575\) 0.368480 + 3.50586i 0.0153667 + 0.146204i
\(576\) 0.669131 0.743145i 0.0278804 0.0309644i
\(577\) −13.4680 14.9577i −0.560680 0.622698i 0.394439 0.918922i \(-0.370939\pi\)
−0.955118 + 0.296224i \(0.904272\pi\)
\(578\) 1.53264 14.5821i 0.0637496 0.606537i
\(579\) −10.5808 + 2.24901i −0.439722 + 0.0934657i
\(580\) 7.66305 + 3.41181i 0.318191 + 0.141668i
\(581\) 3.24514 2.35774i 0.134631 0.0978153i
\(582\) 7.15318 3.18480i 0.296509 0.132014i
\(583\) 4.43567 7.68280i 0.183707 0.318189i
\(584\) −2.15728 3.73651i −0.0892688 0.154618i
\(585\) −2.31972 1.68538i −0.0959086 0.0696817i
\(586\) −6.97393 1.48235i −0.288090 0.0612355i
\(587\) −2.48478 + 7.64737i −0.102558 + 0.315641i −0.989150 0.146912i \(-0.953067\pi\)
0.886592 + 0.462553i \(0.153067\pi\)
\(588\) −6.82565 −0.281485
\(589\) −10.8242 12.4207i −0.446003 0.511786i
\(590\) 1.70526 0.0702046
\(591\) −1.89487 + 5.83182i −0.0779447 + 0.239889i
\(592\) −6.71859 1.42808i −0.276132 0.0586938i
\(593\) −6.50793 4.72829i −0.267249 0.194168i 0.446088 0.894989i \(-0.352817\pi\)
−0.713337 + 0.700822i \(0.752817\pi\)
\(594\) 1.31995 + 2.28621i 0.0541581 + 0.0938045i
\(595\) −1.17477 + 2.03475i −0.0481607 + 0.0834168i
\(596\) −17.6565 + 7.86117i −0.723238 + 0.322006i
\(597\) −11.3301 + 8.23182i −0.463711 + 0.336906i
\(598\) −9.23396 4.11122i −0.377605 0.168120i
\(599\) 10.8113 2.29801i 0.441738 0.0938943i 0.0183270 0.999832i \(-0.494166\pi\)
0.423411 + 0.905938i \(0.360833\pi\)
\(600\) 0.104528 0.994522i 0.00426736 0.0406012i
\(601\) −2.80988 3.12069i −0.114617 0.127295i 0.683106 0.730320i \(-0.260629\pi\)
−0.797723 + 0.603024i \(0.793962\pi\)
\(602\) 2.74218 3.04550i 0.111763 0.124125i
\(603\) −0.0603204 0.573910i −0.00245644 0.0233714i
\(604\) −2.04642 6.29823i −0.0832676 0.256271i
\(605\) 1.24564 + 3.83367i 0.0506423 + 0.155861i
\(606\) 0.838880 + 7.98141i 0.0340772 + 0.324223i
\(607\) 5.11712 5.68314i 0.207697 0.230671i −0.630292 0.776359i \(-0.717065\pi\)
0.837989 + 0.545687i \(0.183731\pi\)
\(608\) −1.98000 2.19901i −0.0802995 0.0891816i
\(609\) −0.366113 + 3.48333i −0.0148357 + 0.141152i
\(610\) 9.20107 1.95575i 0.372541 0.0791859i
\(611\) 25.5536 + 11.3772i 1.03379 + 0.460271i
\(612\) −4.55229 + 3.30743i −0.184015 + 0.133695i
\(613\) −29.1512 + 12.9790i −1.17741 + 0.524216i −0.899725 0.436457i \(-0.856233\pi\)
−0.277683 + 0.960673i \(0.589566\pi\)
\(614\) 6.60936 11.4478i 0.266732 0.461994i
\(615\) 5.46283 + 9.46190i 0.220283 + 0.381541i
\(616\) −0.891771 0.647909i −0.0359305 0.0261050i
\(617\) 38.6556 + 8.21650i 1.55622 + 0.330784i 0.904095 0.427332i \(-0.140546\pi\)
0.652120 + 0.758116i \(0.273880\pi\)
\(618\) 0.777970 2.39435i 0.0312945 0.0963147i
\(619\) 21.6246 0.869166 0.434583 0.900632i \(-0.356896\pi\)
0.434583 + 0.900632i \(0.356896\pi\)
\(620\) −0.671698 + 5.52710i −0.0269760 + 0.221974i
\(621\) −3.52517 −0.141460
\(622\) −6.71756 + 20.6745i −0.269350 + 0.828973i
\(623\) −1.55784 0.331129i −0.0624136 0.0132664i
\(624\) 2.31972 + 1.68538i 0.0928631 + 0.0674690i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −10.6409 + 18.4306i −0.425296 + 0.736634i
\(627\) 7.13625 3.17726i 0.284995 0.126888i
\(628\) 6.03807 4.38691i 0.240945 0.175057i
\(629\) 35.3083 + 15.7203i 1.40783 + 0.626807i
\(630\) 0.408426 0.0868137i 0.0162721 0.00345874i
\(631\) −0.586173 + 5.57706i −0.0233352 + 0.222019i 0.976639 + 0.214885i \(0.0689376\pi\)
−0.999975 + 0.00713436i \(0.997729\pi\)
\(632\) −3.80566 4.22661i −0.151381 0.168126i
\(633\) 1.95087 2.16666i 0.0775400 0.0861168i
\(634\) −2.26146 21.5164i −0.0898142 0.854525i
\(635\) −2.59649 7.99118i −0.103039 0.317120i
\(636\) −1.03845 3.19602i −0.0411772 0.126730i
\(637\) −2.04577 19.4642i −0.0810563 0.771200i
\(638\) 14.8173 16.4563i 0.586622 0.651510i
\(639\) −1.85465 2.05979i −0.0733687 0.0814842i
\(640\) −0.104528 + 0.994522i −0.00413185 + 0.0393119i
\(641\) −26.0886 + 5.54531i −1.03044 + 0.219027i −0.691951 0.721944i \(-0.743249\pi\)
−0.338488 + 0.940971i \(0.609915\pi\)
\(642\) −15.0214 6.68796i −0.592848 0.263953i
\(643\) −10.9623 + 7.96458i −0.432311 + 0.314092i −0.782572 0.622560i \(-0.786093\pi\)
0.350261 + 0.936652i \(0.386093\pi\)
\(644\) 1.34468 0.598690i 0.0529878 0.0235917i
\(645\) 4.90733 8.49975i 0.193226 0.334677i
\(646\) 8.32523 + 14.4197i 0.327552 + 0.567336i
\(647\) 11.8390 + 8.60153i 0.465439 + 0.338161i 0.795661 0.605742i \(-0.207124\pi\)
−0.330222 + 0.943903i \(0.607124\pi\)
\(648\) 0.978148 + 0.207912i 0.0384253 + 0.00816754i
\(649\) 1.39111 4.28138i 0.0546057 0.168059i
\(650\) 2.86733 0.112466
\(651\) −2.28156 + 0.446422i −0.0894213 + 0.0174967i
\(652\) −16.6429 −0.651787
\(653\) 1.79927 5.53757i 0.0704108 0.216702i −0.909659 0.415356i \(-0.863657\pi\)
0.980070 + 0.198654i \(0.0636570\pi\)
\(654\) 16.3893 + 3.48364i 0.640871 + 0.136221i
\(655\) 11.5444 + 8.38753i 0.451079 + 0.327728i
\(656\) −5.46283 9.46190i −0.213288 0.369425i
\(657\) 2.15728 3.73651i 0.0841634 0.145775i
\(658\) −3.72120 + 1.65678i −0.145067 + 0.0645881i
\(659\) 16.9680 12.3280i 0.660979 0.480229i −0.206014 0.978549i \(-0.566049\pi\)
0.866993 + 0.498320i \(0.166049\pi\)
\(660\) −2.41166 1.07374i −0.0938738 0.0417953i
\(661\) −26.1547 + 5.55936i −1.01730 + 0.216234i −0.686240 0.727375i \(-0.740740\pi\)
−0.331061 + 0.943609i \(0.607407\pi\)
\(662\) 1.85061 17.6074i 0.0719261 0.684331i
\(663\) −10.7960 11.9901i −0.419280 0.465658i
\(664\) −6.42803 + 7.13905i −0.249456 + 0.277049i
\(665\) −0.129151 1.22879i −0.00500826 0.0476504i
\(666\) −2.12254 6.53251i −0.0822468 0.253130i
\(667\) 9.13763 + 28.1227i 0.353811 + 1.08892i
\(668\) 0.992816 + 9.44601i 0.0384132 + 0.365477i
\(669\) 12.5271 13.9128i 0.484326 0.537899i
\(670\) 0.386136 + 0.428848i 0.0149177 + 0.0165678i
\(671\) 2.59570 24.6965i 0.100206 0.953397i
\(672\) −0.408426 + 0.0868137i −0.0157554 + 0.00334891i
\(673\) 32.8638 + 14.6319i 1.26681 + 0.564019i 0.926500 0.376295i \(-0.122802\pi\)
0.340308 + 0.940314i \(0.389469\pi\)
\(674\) −13.2991 + 9.66235i −0.512262 + 0.372180i
\(675\) 0.913545 0.406737i 0.0351624 0.0156553i
\(676\) 2.38920 4.13822i 0.0918924 0.159162i
\(677\) 7.30557 + 12.6536i 0.280776 + 0.486318i 0.971576 0.236727i \(-0.0760748\pi\)
−0.690800 + 0.723046i \(0.742742\pi\)
\(678\) 14.7959 + 10.7499i 0.568234 + 0.412846i
\(679\) −3.19803 0.679762i −0.122729 0.0260869i
\(680\) 1.73882 5.35154i 0.0666807 0.205222i
\(681\) −18.7020 −0.716662
\(682\) 13.3289 + 6.19528i 0.510389 + 0.237229i
\(683\) 16.3383 0.625169 0.312584 0.949890i \(-0.398805\pi\)
0.312584 + 0.949890i \(0.398805\pi\)
\(684\) 0.914400 2.81423i 0.0349629 0.107605i
\(685\) −17.0883 3.63223i −0.652911 0.138781i
\(686\) 4.67038 + 3.39323i 0.178316 + 0.129554i
\(687\) −8.02342 13.8970i −0.306112 0.530202i
\(688\) −4.90733 + 8.49975i −0.187090 + 0.324050i
\(689\) 8.80260 3.91917i 0.335352 0.149308i
\(690\) 2.85192 2.07204i 0.108571 0.0788813i
\(691\) 42.4354 + 18.8934i 1.61432 + 0.718740i 0.997652 0.0684850i \(-0.0218165\pi\)
0.616665 + 0.787225i \(0.288483\pi\)
\(692\) −19.9907 + 4.24915i −0.759931 + 0.161528i
\(693\) 0.115221 1.09625i 0.00437687 0.0416431i
\(694\) 9.28770 + 10.3150i 0.352556 + 0.391553i
\(695\) −14.0083 + 15.5578i −0.531365 + 0.590141i
\(696\) −0.876811 8.34230i −0.0332355 0.316214i
\(697\) 18.9978 + 58.4691i 0.719592 + 2.21468i
\(698\) −4.61625 14.2074i −0.174728 0.537757i
\(699\) −0.560380 5.33166i −0.0211955 0.201662i
\(700\) −0.279396 + 0.310301i −0.0105602 + 0.0117283i
\(701\) 32.5263 + 36.1241i 1.22850 + 1.36439i 0.908996 + 0.416804i \(0.136850\pi\)
0.319505 + 0.947585i \(0.396483\pi\)
\(702\) −0.299718 + 2.85162i −0.0113121 + 0.107628i
\(703\) −19.8807 + 4.22578i −0.749815 + 0.159378i
\(704\) 2.41166 + 1.07374i 0.0908930 + 0.0404682i
\(705\) −7.89225 + 5.73406i −0.297239 + 0.215957i
\(706\) −14.9395 + 6.65151i −0.562257 + 0.250333i
\(707\) 1.67550 2.90205i 0.0630137 0.109143i
\(708\) −0.852632 1.47680i −0.0320439 0.0555016i
\(709\) 15.4717 + 11.2408i 0.581050 + 0.422158i 0.839103 0.543973i \(-0.183081\pi\)
−0.258052 + 0.966131i \(0.583081\pi\)
\(710\) 2.71116 + 0.576274i 0.101748 + 0.0216272i
\(711\) 1.75752 5.40911i 0.0659123 0.202857i
\(712\) 3.81425 0.142945
\(713\) −16.0638 + 11.2777i −0.601594 + 0.422351i
\(714\) 2.34953 0.0879290
\(715\) 2.33909 7.19898i 0.0874770 0.269226i
\(716\) 12.4052 + 2.63681i 0.463604 + 0.0985421i
\(717\) −8.77538 6.37569i −0.327723 0.238104i
\(718\) 1.97552 + 3.42169i 0.0737256 + 0.127696i
\(719\) 1.02646 1.77787i 0.0382803 0.0663035i −0.846250 0.532785i \(-0.821145\pi\)
0.884531 + 0.466482i \(0.154479\pi\)
\(720\) −0.913545 + 0.406737i −0.0340458 + 0.0151582i
\(721\) −0.850447 + 0.617886i −0.0316723 + 0.0230113i
\(722\) 9.35833 + 4.16660i 0.348281 + 0.155065i
\(723\) 3.72226 0.791191i 0.138432 0.0294247i
\(724\) −0.0340288 + 0.323763i −0.00126467 + 0.0120325i
\(725\) −5.61284 6.23369i −0.208456 0.231513i
\(726\) 2.69724 2.99559i 0.100104 0.111177i
\(727\) 2.45815 + 23.3878i 0.0911679 + 0.867405i 0.940557 + 0.339637i \(0.110304\pi\)
−0.849389 + 0.527768i \(0.823029\pi\)
\(728\) −0.369973 1.13866i −0.0137121 0.0422015i
\(729\) 0.309017 + 0.951057i 0.0114451 + 0.0352243i
\(730\) 0.450994 + 4.29092i 0.0166920 + 0.158814i
\(731\) 36.9538 41.0413i 1.36678 1.51797i
\(732\) −6.29426 6.99049i −0.232643 0.258376i
\(733\) 0.463638 4.41122i 0.0171249 0.162932i −0.982617 0.185643i \(-0.940563\pi\)
0.999742 + 0.0227111i \(0.00722980\pi\)
\(734\) −20.3429 + 4.32403i −0.750872 + 0.159603i
\(735\) 6.23554 + 2.77624i 0.230001 + 0.102403i
\(736\) −2.85192 + 2.07204i −0.105123 + 0.0763765i
\(737\) 1.39170 0.619626i 0.0512640 0.0228242i
\(738\) 5.46283 9.46190i 0.201090 0.348297i
\(739\) −10.9005 18.8801i −0.400980 0.694517i 0.592865 0.805302i \(-0.297997\pi\)
−0.993844 + 0.110785i \(0.964664\pi\)
\(740\) 5.55689 + 4.03731i 0.204275 + 0.148415i
\(741\) 8.29920 + 1.76405i 0.304879 + 0.0648040i
\(742\) −0.433605 + 1.33450i −0.0159181 + 0.0489910i
\(743\) −36.9056 −1.35393 −0.676967 0.736013i \(-0.736706\pi\)
−0.676967 + 0.736013i \(0.736706\pi\)
\(744\) 5.12246 2.18184i 0.187798 0.0799902i
\(745\) 19.3274 0.708102
\(746\) 11.8911 36.5969i 0.435362 1.33991i
\(747\) −9.39662 1.99731i −0.343804 0.0730779i
\(748\) −12.0176 8.73127i −0.439406 0.319247i
\(749\) 3.43289 + 5.94594i 0.125435 + 0.217260i
\(750\) −0.500000 + 0.866025i −0.0182574 + 0.0316228i
\(751\) 37.8747 16.8629i 1.38207 0.615336i 0.424999 0.905194i \(-0.360275\pi\)
0.957070 + 0.289858i \(0.0936079\pi\)
\(752\) 7.89225 5.73406i 0.287801 0.209100i
\(753\) −18.9512 8.43763i −0.690622 0.307485i
\(754\) 23.5263 5.00067i 0.856778 0.182114i
\(755\) −0.692224 + 6.58607i −0.0251926 + 0.239692i
\(756\) −0.279396 0.310301i −0.0101615 0.0112855i
\(757\) −8.07898 + 8.97261i −0.293635 + 0.326115i −0.871853 0.489767i \(-0.837082\pi\)
0.578218 + 0.815882i \(0.303748\pi\)
\(758\) −1.59303 15.1567i −0.0578615 0.550516i
\(759\) −2.87573 8.85060i −0.104382 0.321256i
\(760\) 0.914400 + 2.81423i 0.0331688 + 0.102083i
\(761\) −3.83587 36.4959i −0.139050 1.32297i −0.812161 0.583433i \(-0.801709\pi\)
0.673111 0.739541i \(-0.264957\pi\)
\(762\) −5.62232 + 6.24422i −0.203675 + 0.226204i
\(763\) −4.68139 5.19921i −0.169478 0.188224i
\(764\) 0.725783 6.90536i 0.0262579 0.249827i
\(765\) 5.50398 1.16991i 0.198997 0.0422981i
\(766\) 25.9400 + 11.5492i 0.937251 + 0.417291i
\(767\) 3.95573 2.87401i 0.142833 0.103774i
\(768\) 0.913545 0.406737i 0.0329647 0.0146768i
\(769\) 5.31719 9.20965i 0.191743 0.332108i −0.754085 0.656777i \(-0.771919\pi\)
0.945828 + 0.324668i \(0.105253\pi\)
\(770\) 0.551145 + 0.954610i 0.0198619 + 0.0344018i
\(771\) 18.7585 + 13.6288i 0.675570 + 0.490831i
\(772\) −10.5808 2.24901i −0.380810 0.0809437i
\(773\) −5.87839 + 18.0918i −0.211431 + 0.650717i 0.787957 + 0.615730i \(0.211139\pi\)
−0.999388 + 0.0349870i \(0.988861\pi\)
\(774\) −9.81466 −0.352781
\(775\) 2.86170 4.77605i 0.102795 0.171561i
\(776\) 7.83013 0.281085
\(777\) −0.886269 + 2.72765i −0.0317947 + 0.0978541i
\(778\) 21.4466 + 4.55862i 0.768898 + 0.163434i
\(779\) −26.1553 19.0029i −0.937110 0.680850i
\(780\) −1.43367 2.48318i −0.0513335 0.0889122i
\(781\) 3.65853 6.33676i 0.130913 0.226747i
\(782\) 18.1210 8.06799i 0.648006 0.288511i
\(783\) 6.78624 4.93049i 0.242520 0.176201i
\(784\) −6.23554 2.77624i −0.222698 0.0991515i
\(785\) −7.30037 + 1.55174i −0.260561 + 0.0553840i
\(786\) 1.49159 14.1915i 0.0532033 0.506196i
\(787\) 16.4045 + 18.2191i 0.584759 + 0.649441i 0.960826 0.277152i \(-0.0893905\pi\)
−0.376067 + 0.926592i \(0.622724\pi\)
\(788\) −4.10307 + 4.55692i −0.146166 + 0.162334i
\(789\) −3.06047 29.1184i −0.108956 1.03664i
\(790\) 1.75752 + 5.40911i 0.0625299 + 0.192447i
\(791\) −2.35981 7.26274i −0.0839050 0.258233i
\(792\) 0.275944 + 2.62543i 0.00980524 + 0.0932907i
\(793\) 18.0477 20.0441i 0.640894 0.711785i
\(794\) −4.60574 5.11519i −0.163451 0.181531i
\(795\) −0.351267 + 3.34208i −0.0124582 + 0.118531i
\(796\) −13.6988 + 2.91176i −0.485540 + 0.103205i
\(797\) 31.1820 + 13.8831i 1.10452 + 0.491765i 0.876262 0.481836i \(-0.160030\pi\)
0.228260 + 0.973600i \(0.426696\pi\)
\(798\) −0.999587 + 0.726242i −0.0353850 + 0.0257087i
\(799\) −50.1471 + 22.3269i −1.77408 + 0.789870i
\(800\) 0.500000 0.866025i 0.0176777 0.0306186i
\(801\) 1.90713 + 3.30324i 0.0673850 + 0.116714i
\(802\) −12.3342 8.96133i −0.435536 0.316435i
\(803\) 11.1411 + 2.36811i 0.393160 + 0.0835687i
\(804\) 0.178325 0.548828i 0.00628904 0.0193557i
\(805\) −1.47194 −0.0518789
\(806\) 7.75709 + 13.9534i 0.273232 + 0.491487i
\(807\) 7.82763 0.275546
\(808\) −2.47998 + 7.63259i −0.0872453 + 0.268513i
\(809\) −4.07989 0.867208i −0.143441 0.0304894i 0.135631 0.990759i \(-0.456694\pi\)
−0.279073 + 0.960270i \(0.590027\pi\)
\(810\) −0.809017 0.587785i −0.0284260 0.0206527i
\(811\) −19.5935 33.9369i −0.688021 1.19169i −0.972477 0.232998i \(-0.925147\pi\)
0.284457 0.958689i \(-0.408187\pi\)
\(812\) −1.75126 + 3.03327i −0.0614572 + 0.106447i
\(813\) 1.06493 0.474135i 0.0373486 0.0166286i
\(814\) 14.6696 10.6581i 0.514169 0.373566i
\(815\) 15.2041 + 6.76929i 0.532575 + 0.237118i
\(816\) −5.50398 + 1.16991i −0.192678 + 0.0409549i
\(817\) −3.03573 + 28.8831i −0.106207 + 1.01049i
\(818\) −7.07427 7.85677i −0.247346 0.274705i
\(819\) 0.801121 0.889735i 0.0279934 0.0310899i
\(820\) 1.14204 + 10.8658i 0.0398819 + 0.379451i
\(821\) 8.95745 + 27.5682i 0.312617 + 0.962136i 0.976724 + 0.214499i \(0.0688118\pi\)
−0.664107 + 0.747637i \(0.731188\pi\)
\(822\) 5.39855 + 16.6150i 0.188296 + 0.579516i
\(823\) −3.02281 28.7601i −0.105368 1.00251i −0.911646 0.410977i \(-0.865188\pi\)
0.806277 0.591538i \(-0.201479\pi\)
\(824\) 1.68458 1.87091i 0.0586851 0.0651764i
\(825\) 1.76643 + 1.96182i 0.0614993 + 0.0683019i
\(826\) −0.0744278 + 0.708133i −0.00258967 + 0.0246391i
\(827\) −13.8398 + 2.94174i −0.481258 + 0.102294i −0.442151 0.896941i \(-0.645784\pi\)
−0.0391065 + 0.999235i \(0.512451\pi\)
\(828\) −3.22040 1.43381i −0.111917 0.0498285i
\(829\) 24.4738 17.7813i 0.850012 0.617570i −0.0751376 0.997173i \(-0.523940\pi\)
0.925149 + 0.379604i \(0.123940\pi\)
\(830\) 8.77602 3.90733i 0.304620 0.135626i
\(831\) −14.6736 + 25.4154i −0.509022 + 0.881652i
\(832\) 1.43367 + 2.48318i 0.0497034 + 0.0860889i
\(833\) 31.0723 + 22.5754i 1.07659 + 0.782191i
\(834\) 20.4776 + 4.35265i 0.709081 + 0.150720i
\(835\) 2.93506 9.03318i 0.101572 0.312606i
\(836\) 7.81160 0.270170
\(837\) 4.45076 + 3.34526i 0.153841 + 0.115629i
\(838\) 4.95167 0.171052
\(839\) −9.21911 + 28.3735i −0.318279 + 0.979562i 0.656105 + 0.754670i \(0.272203\pi\)
−0.974384 + 0.224892i \(0.927797\pi\)
\(840\) 0.408426 + 0.0868137i 0.0140920 + 0.00299536i
\(841\) −33.4632 24.3125i −1.15390 0.838361i
\(842\) 18.0861 + 31.3261i 0.623289 + 1.07957i
\(843\) −12.8720 + 22.2949i −0.443335 + 0.767878i
\(844\) 2.66346 1.18585i 0.0916802 0.0408186i
\(845\) −3.86581 + 2.80868i −0.132988 + 0.0966214i
\(846\) 8.91196 + 3.96786i 0.306400 + 0.136418i
\(847\) −1.64635 + 0.349943i −0.0565693 + 0.0120242i
\(848\) 0.351267 3.34208i 0.0120626 0.114768i
\(849\) 5.70201 + 6.33272i 0.195692 + 0.217339i
\(850\) −3.76516 + 4.18163i −0.129144 + 0.143429i
\(851\) 2.53098 + 24.0806i 0.0867608 + 0.825474i
\(852\) −0.856510 2.63607i −0.0293436 0.0903102i
\(853\) −4.50147 13.8541i −0.154128 0.474356i 0.843944 0.536431i \(-0.180228\pi\)
−0.998071 + 0.0620757i \(0.980228\pi\)
\(854\) 0.410561 + 3.90623i 0.0140491 + 0.133668i
\(855\) −1.98000 + 2.19901i −0.0677145 + 0.0752045i
\(856\) −11.0025 12.2195i −0.376058 0.417654i
\(857\) 1.53062 14.5629i 0.0522851 0.497460i −0.936773 0.349936i \(-0.886203\pi\)
0.989059 0.147523i \(-0.0471301\pi\)
\(858\) −7.40404 + 1.57378i −0.252770 + 0.0537279i
\(859\) −10.4234 4.64078i −0.355641 0.158342i 0.221137 0.975243i \(-0.429023\pi\)
−0.576777 + 0.816901i \(0.695690\pi\)
\(860\) 7.94023 5.76891i 0.270760 0.196718i
\(861\) −4.16761 + 1.85554i −0.142032 + 0.0632366i
\(862\) −6.67357 + 11.5590i −0.227303 + 0.393700i
\(863\) −12.4386 21.5443i −0.423415 0.733376i 0.572856 0.819656i \(-0.305835\pi\)
−0.996271 + 0.0862801i \(0.972502\pi\)
\(864\) 0.809017 + 0.587785i 0.0275233 + 0.0199969i
\(865\) 19.9907 + 4.24915i 0.679703 + 0.144475i
\(866\) −0.504161 + 1.55165i −0.0171321 + 0.0527271i
\(867\) 14.6625 0.497963
\(868\) −2.26588 0.520167i −0.0769091 0.0176556i
\(869\) 15.0143 0.509326
\(870\) −2.59211 + 7.97770i −0.0878809 + 0.270470i
\(871\) 1.61850 + 0.344022i 0.0548407 + 0.0116568i
\(872\) 13.5554 + 9.84858i 0.459044 + 0.333515i
\(873\) 3.91507 + 6.78109i 0.132505 + 0.229505i
\(874\) −5.21559 + 9.03367i −0.176420 + 0.305568i
\(875\) 0.381451 0.169833i 0.0128954 0.00574141i
\(876\) 3.49055 2.53603i 0.117935 0.0856846i
\(877\) 39.0656 + 17.3931i 1.31915 + 0.587324i 0.940996 0.338418i \(-0.109892\pi\)
0.378155 + 0.925742i \(0.376559\pi\)
\(878\) −18.2590 + 3.88107i −0.616212 + 0.130980i
\(879\) 0.745259 7.09067i 0.0251370 0.239162i
\(880\) −1.76643 1.96182i −0.0595465 0.0661330i
\(881\) −27.7294 + 30.7966i −0.934227 + 1.03756i 0.0649857 + 0.997886i \(0.479300\pi\)
−0.999213 + 0.0396778i \(0.987367\pi\)
\(882\) −0.713475 6.78826i −0.0240239 0.228573i
\(883\) 15.7017 + 48.3250i 0.528406 + 1.62627i 0.757481 + 0.652857i \(0.226430\pi\)
−0.229076 + 0.973409i \(0.573570\pi\)
\(884\) −4.98578 15.3446i −0.167690 0.516096i
\(885\) 0.178249 + 1.69592i 0.00599176 + 0.0570078i
\(886\) −7.66049 + 8.50783i −0.257359 + 0.285826i
\(887\) −34.5881 38.4140i −1.16136 1.28982i −0.949945 0.312418i \(-0.898861\pi\)
−0.211410 0.977397i \(-0.567806\pi\)
\(888\) 0.717974 6.83106i 0.0240936 0.229235i
\(889\) 3.43177 0.729445i 0.115098 0.0244648i
\(890\) −3.48449 1.55140i −0.116801 0.0520029i
\(891\) −2.13572 + 1.55169i −0.0715493 + 0.0519836i
\(892\) 17.1029 7.61471i 0.572648 0.254959i
\(893\) 14.4333 24.9993i 0.482993 0.836569i
\(894\) −9.66371 16.7380i −0.323203 0.559804i
\(895\) −10.2602 7.45449i −0.342962 0.249176i
\(896\) −0.408426 0.0868137i −0.0136446 0.00290024i
\(897\) 3.12349 9.61311i 0.104290 0.320973i
\(898\) −0.650726 −0.0217150
\(899\) 15.1506 44.1781i 0.505301 1.47342i
\(900\) 1.00000 0.0333333
\(901\) −5.84329 + 17.9838i −0.194668 + 0.599127i
\(902\) 28.2123 + 5.99671i 0.939367 + 0.199669i
\(903\) 3.31545 + 2.40881i 0.110331 + 0.0801603i
\(904\) 9.14439 + 15.8385i 0.304138 + 0.526782i
\(905\) 0.162773 0.281931i 0.00541076 0.00937170i
\(906\) 6.04982 2.69355i 0.200992 0.0894873i
\(907\) 1.52188 1.10571i 0.0505331 0.0367145i −0.562232 0.826980i \(-0.690057\pi\)
0.612765 + 0.790265i \(0.290057\pi\)
\(908\) −17.0851 7.60679i −0.566990 0.252440i
\(909\) −7.85000 + 1.66857i −0.260368 + 0.0553430i
\(910\) −0.125147 + 1.19070i −0.00414859 + 0.0394712i
\(911\) 16.1915 + 17.9825i 0.536449 + 0.595787i 0.949050 0.315125i \(-0.102046\pi\)
−0.412601 + 0.910912i \(0.635380\pi\)
\(912\) 1.98000 2.19901i 0.0655643 0.0728165i
\(913\) −2.65087 25.2213i −0.0877309 0.834704i
\(914\) −5.05329 15.5524i −0.167148 0.514428i
\(915\) 2.90681 + 8.94624i 0.0960961 + 0.295753i
\(916\) −1.67735 15.9589i −0.0554212 0.527298i
\(917\) −3.98690 + 4.42790i −0.131659 + 0.146222i
\(918\) −3.76516 4.18163i −0.124269 0.138014i
\(919\) −6.25103 + 59.4746i −0.206203 + 1.96189i 0.0606789 + 0.998157i \(0.480673\pi\)
−0.266882 + 0.963729i \(0.585993\pi\)
\(920\) 3.44813 0.732924i 0.113682 0.0241638i
\(921\) 12.0759 + 5.37654i 0.397915 + 0.177163i
\(922\) 17.6218 12.8030i 0.580343 0.421644i
\(923\) 7.26037 3.23252i 0.238978 0.106400i
\(924\) 0.551145 0.954610i 0.0181313 0.0314044i
\(925\) −3.43434 5.94846i −0.112921 0.195584i
\(926\) −4.04201 2.93669i −0.132829 0.0965057i
\(927\) 2.46255 + 0.523431i 0.0808807 + 0.0171917i
\(928\) 2.59211 7.97770i 0.0850903 0.261881i
\(929\) 14.7783 0.484860 0.242430 0.970169i \(-0.422055\pi\)
0.242430 + 0.970169i \(0.422055\pi\)
\(930\) −5.56703 0.0902791i −0.182550 0.00296037i
\(931\) −20.1975 −0.661947
\(932\) 1.65665 5.09864i 0.0542653 0.167011i
\(933\) −21.2635 4.51969i −0.696134 0.147968i
\(934\) 4.40065 + 3.19726i 0.143994 + 0.104617i
\(935\) 7.42726 + 12.8644i 0.242897 + 0.420711i
\(936\) −1.43367 + 2.48318i −0.0468608 + 0.0811654i
\(937\) 31.9108 14.2076i 1.04248 0.464142i 0.187208 0.982320i \(-0.440056\pi\)
0.855273 + 0.518178i \(0.173389\pi\)
\(938\) −0.194938 + 0.141631i −0.00636495 + 0.00462441i
\(939\) −19.4419 8.65609i −0.634462 0.282481i
\(940\) −9.54218 + 2.02825i −0.311232 + 0.0661543i
\(941\) −0.818109 + 7.78379i −0.0266696 + 0.253744i 0.973061 + 0.230546i \(0.0740514\pi\)
−0.999731 + 0.0231977i \(0.992615\pi\)
\(942\) 4.99403 + 5.54644i 0.162714 + 0.180713i
\(943\) −25.7714 + 28.6221i −0.839233 + 0.932063i
\(944\) −0.178249 1.69592i −0.00580150 0.0551976i
\(945\) 0.129030 + 0.397114i 0.00419735 + 0.0129181i
\(946\) −8.00653 24.6416i −0.260315 0.801166i
\(947\) −3.57272 33.9922i −0.116098 1.10460i −0.885116 0.465370i \(-0.845921\pi\)
0.769018 0.639227i \(-0.220746\pi\)
\(948\) 3.80566 4.22661i 0.123602 0.137274i
\(949\) 8.27799 + 9.19364i 0.268715 + 0.298438i
\(950\) 0.309306 2.94285i 0.0100352 0.0954786i
\(951\) 21.1621 4.49815i 0.686229 0.145862i
\(952\) 2.14640 + 0.955641i 0.0695654 + 0.0309725i
\(953\) 24.4019 17.7290i 0.790456 0.574300i −0.117643 0.993056i \(-0.537534\pi\)
0.908099 + 0.418756i \(0.137534\pi\)
\(954\) 3.06996 1.36683i 0.0993937 0.0442529i
\(955\) −3.47170 + 6.01316i −0.112342 + 0.194581i
\(956\) −5.42348 9.39375i −0.175408 0.303816i
\(957\) 17.9150 + 13.0160i 0.579108 + 0.420747i
\(958\) 26.2181 + 5.57284i 0.847070 + 0.180050i
\(959\) 2.25417 6.93762i 0.0727909 0.224027i
\(960\) −1.00000 −0.0322749
\(961\) 30.9837 + 1.00517i 0.999474 + 0.0324249i
\(962\) 19.6948 0.634986
\(963\) 5.08116 15.6382i 0.163738 0.503934i
\(964\) 3.72226 + 0.791191i 0.119886 + 0.0254825i
\(965\) 8.75126 + 6.35816i 0.281713 + 0.204676i
\(966\) 0.735968 + 1.27473i 0.0236794 + 0.0410139i
\(967\) 8.76554 15.1824i 0.281881 0.488232i −0.689967 0.723841i \(-0.742375\pi\)
0.971848 + 0.235609i \(0.0757084\pi\)
\(968\) 3.68247 1.63954i 0.118359 0.0526968i
\(969\) −13.4705 + 9.78689i −0.432735 + 0.314400i
\(970\) −7.15318 3.18480i −0.229675 0.102258i
\(971\) 18.5187 3.93627i 0.594293 0.126321i 0.0990603 0.995081i \(-0.468416\pi\)
0.495232 + 0.868761i \(0.335083\pi\)
\(972\) −0.104528 + 0.994522i −0.00335275 + 0.0318993i
\(973\) −5.84918 6.49617i −0.187516 0.208258i
\(974\) 21.1425 23.4812i 0.677450 0.752385i
\(975\) 0.299718 + 2.85162i 0.00959865 + 0.0913251i
\(976\) −2.90681 8.94624i −0.0930447 0.286362i
\(977\) −3.54087 10.8977i −0.113282 0.348647i 0.878303 0.478105i \(-0.158676\pi\)
−0.991585 + 0.129458i \(0.958676\pi\)
\(978\) −1.73966 16.5518i −0.0556282 0.529267i
\(979\) −6.73763 + 7.48289i −0.215336 + 0.239154i
\(980\) 4.56725 + 5.07245i 0.145896 + 0.162033i
\(981\) −1.75142 + 16.6636i −0.0559184 + 0.532028i
\(982\) −28.6621 + 6.09232i −0.914645 + 0.194414i
\(983\) 7.67318 + 3.41632i 0.244736 + 0.108964i 0.525439 0.850831i \(-0.323901\pi\)
−0.280703 + 0.959795i \(0.590568\pi\)
\(984\) 8.83905 6.42194i 0.281779 0.204724i
\(985\) 5.60181 2.49408i 0.178488 0.0794681i
\(986\) −23.6001 + 40.8766i −0.751580 + 1.30178i
\(987\) −2.03668 3.52763i −0.0648282 0.112286i
\(988\) 6.86419 + 4.98713i 0.218379 + 0.158662i
\(989\) 33.8423 + 7.19340i 1.07612 + 0.228737i
\(990\) 0.815772 2.51069i 0.0259269 0.0797949i
\(991\) 21.2059 0.673626 0.336813 0.941571i \(-0.390651\pi\)
0.336813 + 0.941571i \(0.390651\pi\)
\(992\) 5.56703 + 0.0902791i 0.176753 + 0.00286636i
\(993\) 17.7044 0.561831
\(994\) −0.357636 + 1.10069i −0.0113435 + 0.0349118i
\(995\) 13.6988 + 2.91176i 0.434280 + 0.0923091i
\(996\) −7.77186 5.64659i −0.246261 0.178919i
\(997\) 4.19882 + 7.27257i 0.132978 + 0.230325i 0.924823 0.380397i \(-0.124213\pi\)
−0.791845 + 0.610722i \(0.790879\pi\)
\(998\) 9.94310 17.2220i 0.314743 0.545152i
\(999\) 6.27486 2.79375i 0.198528 0.0883903i
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 930.2.bg.i.691.2 24
31.7 even 15 inner 930.2.bg.i.751.2 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.bg.i.691.2 24 1.1 even 1 trivial
930.2.bg.i.751.2 yes 24 31.7 even 15 inner