Properties

Label 231.2.n.a.89.12
Level $231$
Weight $2$
Character 231.89
Analytic conductor $1.845$
Analytic rank $0$
Dimension $52$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [231,2,Mod(89,231)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(231, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("231.89");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 231 = 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 231.n (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.84454428669\)
Analytic rank: \(0\)
Dimension: \(52\)
Relative dimension: \(26\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 89.12
Character \(\chi\) \(=\) 231.89
Dual form 231.2.n.a.122.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.408229 - 0.235691i) q^{2} +(-1.32879 - 1.11100i) q^{3} +(-0.888900 - 1.53962i) q^{4} +(1.95312 - 3.38291i) q^{5} +(0.280598 + 0.766725i) q^{6} +(-2.47945 + 0.923218i) q^{7} +1.78079i q^{8} +(0.531368 + 2.95257i) q^{9} +O(q^{10})\) \(q+(-0.408229 - 0.235691i) q^{2} +(-1.32879 - 1.11100i) q^{3} +(-0.888900 - 1.53962i) q^{4} +(1.95312 - 3.38291i) q^{5} +(0.280598 + 0.766725i) q^{6} +(-2.47945 + 0.923218i) q^{7} +1.78079i q^{8} +(0.531368 + 2.95257i) q^{9} +(-1.59464 + 0.920666i) q^{10} +(-0.866025 + 0.500000i) q^{11} +(-0.529352 + 3.03340i) q^{12} -1.06912i q^{13} +(1.22978 + 0.207500i) q^{14} +(-6.35369 + 2.32526i) q^{15} +(-1.35808 + 2.35227i) q^{16} +(-2.07932 - 3.60148i) q^{17} +(0.478973 - 1.33056i) q^{18} +(5.11329 + 2.95216i) q^{19} -6.94452 q^{20} +(4.32036 + 1.52790i) q^{21} +0.471382 q^{22} +(-4.27331 - 2.46720i) q^{23} +(1.97845 - 2.36629i) q^{24} +(-5.12937 - 8.88432i) q^{25} +(-0.251982 + 0.436445i) q^{26} +(2.57422 - 4.51369i) q^{27} +(3.62539 + 2.99676i) q^{28} -4.40659i q^{29} +(3.14180 + 0.548269i) q^{30} +(-4.27970 + 2.47089i) q^{31} +(4.19323 - 2.42096i) q^{32} +(1.70627 + 0.297757i) q^{33} +1.96030i q^{34} +(-1.71951 + 10.1909i) q^{35} +(4.07349 - 3.44264i) q^{36} +(0.718698 - 1.24482i) q^{37} +(-1.39159 - 2.41031i) q^{38} +(-1.18779 + 1.42063i) q^{39} +(6.02423 + 3.47809i) q^{40} +2.23267 q^{41} +(-1.40358 - 1.64200i) q^{42} +5.91566 q^{43} +(1.53962 + 0.888900i) q^{44} +(11.0261 + 3.96915i) q^{45} +(1.16299 + 2.01436i) q^{46} +(1.55717 - 2.69711i) q^{47} +(4.41798 - 1.61685i) q^{48} +(5.29534 - 4.57814i) q^{49} +4.83578i q^{50} +(-1.23826 + 7.09573i) q^{51} +(-1.64604 + 0.950339i) q^{52} +(-5.23203 + 3.02072i) q^{53} +(-2.11471 + 1.23590i) q^{54} +3.90624i q^{55} +(-1.64405 - 4.41537i) q^{56} +(-3.51465 - 9.60366i) q^{57} +(-1.03859 + 1.79890i) q^{58} +(-0.240199 - 0.416038i) q^{59} +(9.22781 + 7.71534i) q^{60} +(-2.78463 - 1.60771i) q^{61} +2.32946 q^{62} +(-4.04336 - 6.83017i) q^{63} +3.14994 q^{64} +(-3.61673 - 2.08812i) q^{65} +(-0.626368 - 0.523704i) q^{66} +(-7.40799 - 12.8310i) q^{67} +(-3.69661 + 6.40271i) q^{68} +(2.93729 + 8.02603i) q^{69} +(3.10385 - 3.75494i) q^{70} -10.0055i q^{71} +(-5.25789 + 0.946253i) q^{72} +(10.7524 - 6.20787i) q^{73} +(-0.586787 + 0.338781i) q^{74} +(-3.05461 + 17.5041i) q^{75} -10.4967i q^{76} +(1.68566 - 2.03925i) q^{77} +(0.819720 - 0.299993i) q^{78} +(-2.94229 + 5.09619i) q^{79} +(5.30501 + 9.18854i) q^{80} +(-8.43530 + 3.13780i) q^{81} +(-0.911441 - 0.526220i) q^{82} +7.65786 q^{83} +(-1.48799 - 8.00986i) q^{84} -16.2446 q^{85} +(-2.41494 - 1.39427i) q^{86} +(-4.89571 + 5.85544i) q^{87} +(-0.890393 - 1.54221i) q^{88} +(0.824642 - 1.42832i) q^{89} +(-3.56567 - 4.21907i) q^{90} +(0.987030 + 2.65083i) q^{91} +8.77237i q^{92} +(8.43198 + 1.47145i) q^{93} +(-1.27137 + 0.734024i) q^{94} +(19.9738 - 11.5319i) q^{95} +(-8.26161 - 1.44172i) q^{96} -5.22606i q^{97} +(-3.24074 + 0.620867i) q^{98} +(-1.93646 - 2.29131i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52 q + 24 q^{4} - 6 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 52 q + 24 q^{4} - 6 q^{7} - 4 q^{9} - 30 q^{12} - 4 q^{15} - 20 q^{16} - 18 q^{18} + 6 q^{19} - 2 q^{21} + 36 q^{24} - 22 q^{25} - 40 q^{28} - 20 q^{30} - 54 q^{31} + 36 q^{36} + 2 q^{37} + 20 q^{39} + 60 q^{40} - 36 q^{42} + 36 q^{43} - 54 q^{45} + 4 q^{46} + 22 q^{49} - 16 q^{51} + 12 q^{52} + 66 q^{54} - 44 q^{57} - 16 q^{58} + 20 q^{60} - 36 q^{61} - 24 q^{63} - 48 q^{64} - 30 q^{66} - 6 q^{67} - 116 q^{70} + 36 q^{72} - 6 q^{73} + 72 q^{75} + 112 q^{78} + 14 q^{79} + 52 q^{81} - 84 q^{82} + 8 q^{84} + 8 q^{85} + 18 q^{87} - 12 q^{88} + 46 q^{91} + 6 q^{93} + 48 q^{94} - 18 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/231\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.408229 0.235691i −0.288661 0.166659i 0.348677 0.937243i \(-0.386631\pi\)
−0.637338 + 0.770584i \(0.719964\pi\)
\(3\) −1.32879 1.11100i −0.767178 0.641435i
\(4\) −0.888900 1.53962i −0.444450 0.769810i
\(5\) 1.95312 3.38291i 0.873462 1.51288i 0.0150708 0.999886i \(-0.495203\pi\)
0.858392 0.512995i \(-0.171464\pi\)
\(6\) 0.280598 + 0.766725i 0.114554 + 0.313014i
\(7\) −2.47945 + 0.923218i −0.937144 + 0.348944i
\(8\) 1.78079i 0.629603i
\(9\) 0.531368 + 2.95257i 0.177123 + 0.984189i
\(10\) −1.59464 + 0.920666i −0.504269 + 0.291140i
\(11\) −0.866025 + 0.500000i −0.261116 + 0.150756i
\(12\) −0.529352 + 3.03340i −0.152811 + 0.875666i
\(13\) 1.06912i 0.296520i −0.988948 0.148260i \(-0.952633\pi\)
0.988948 0.148260i \(-0.0473673\pi\)
\(14\) 1.22978 + 0.207500i 0.328672 + 0.0554566i
\(15\) −6.35369 + 2.32526i −1.64052 + 0.600379i
\(16\) −1.35808 + 2.35227i −0.339521 + 0.588068i
\(17\) −2.07932 3.60148i −0.504309 0.873488i −0.999988 0.00498221i \(-0.998414\pi\)
0.495679 0.868506i \(-0.334919\pi\)
\(18\) 0.478973 1.33056i 0.112895 0.313616i
\(19\) 5.11329 + 2.95216i 1.17307 + 0.677272i 0.954401 0.298527i \(-0.0964953\pi\)
0.218669 + 0.975799i \(0.429829\pi\)
\(20\) −6.94452 −1.55284
\(21\) 4.32036 + 1.52790i 0.942780 + 0.333415i
\(22\) 0.471382 0.100499
\(23\) −4.27331 2.46720i −0.891047 0.514446i −0.0167624 0.999860i \(-0.505336\pi\)
−0.874285 + 0.485413i \(0.838669\pi\)
\(24\) 1.97845 2.36629i 0.403849 0.483017i
\(25\) −5.12937 8.88432i −1.02587 1.77686i
\(26\) −0.251982 + 0.436445i −0.0494176 + 0.0855939i
\(27\) 2.57422 4.51369i 0.495408 0.868660i
\(28\) 3.62539 + 2.99676i 0.685134 + 0.566334i
\(29\) 4.40659i 0.818283i −0.912471 0.409142i \(-0.865828\pi\)
0.912471 0.409142i \(-0.134172\pi\)
\(30\) 3.14180 + 0.548269i 0.573612 + 0.100100i
\(31\) −4.27970 + 2.47089i −0.768657 + 0.443784i −0.832395 0.554182i \(-0.813031\pi\)
0.0637383 + 0.997967i \(0.479698\pi\)
\(32\) 4.19323 2.42096i 0.741265 0.427970i
\(33\) 1.70627 + 0.297757i 0.297023 + 0.0518328i
\(34\) 1.96030i 0.336189i
\(35\) −1.71951 + 10.1909i −0.290649 + 1.72258i
\(36\) 4.07349 3.44264i 0.678916 0.573773i
\(37\) 0.718698 1.24482i 0.118153 0.204648i −0.800883 0.598821i \(-0.795636\pi\)
0.919036 + 0.394174i \(0.128969\pi\)
\(38\) −1.39159 2.41031i −0.225746 0.391004i
\(39\) −1.18779 + 1.42063i −0.190198 + 0.227484i
\(40\) 6.02423 + 3.47809i 0.952514 + 0.549934i
\(41\) 2.23267 0.348685 0.174342 0.984685i \(-0.444220\pi\)
0.174342 + 0.984685i \(0.444220\pi\)
\(42\) −1.40358 1.64200i −0.216578 0.253366i
\(43\) 5.91566 0.902129 0.451065 0.892491i \(-0.351044\pi\)
0.451065 + 0.892491i \(0.351044\pi\)
\(44\) 1.53962 + 0.888900i 0.232106 + 0.134007i
\(45\) 11.0261 + 3.96915i 1.64367 + 0.591686i
\(46\) 1.16299 + 2.01436i 0.171474 + 0.297001i
\(47\) 1.55717 2.69711i 0.227137 0.393413i −0.729821 0.683638i \(-0.760397\pi\)
0.956959 + 0.290225i \(0.0937301\pi\)
\(48\) 4.41798 1.61685i 0.637680 0.233372i
\(49\) 5.29534 4.57814i 0.756477 0.654021i
\(50\) 4.83578i 0.683883i
\(51\) −1.23826 + 7.09573i −0.173391 + 0.993601i
\(52\) −1.64604 + 0.950339i −0.228264 + 0.131788i
\(53\) −5.23203 + 3.02072i −0.718675 + 0.414927i −0.814265 0.580494i \(-0.802860\pi\)
0.0955899 + 0.995421i \(0.469526\pi\)
\(54\) −2.11471 + 1.23590i −0.287775 + 0.168184i
\(55\) 3.90624i 0.526718i
\(56\) −1.64405 4.41537i −0.219696 0.590028i
\(57\) −3.51465 9.60366i −0.465527 1.27204i
\(58\) −1.03859 + 1.79890i −0.136374 + 0.236207i
\(59\) −0.240199 0.416038i −0.0312713 0.0541635i 0.849966 0.526837i \(-0.176622\pi\)
−0.881238 + 0.472674i \(0.843289\pi\)
\(60\) 9.22781 + 7.71534i 1.19130 + 0.996046i
\(61\) −2.78463 1.60771i −0.356536 0.205846i 0.311024 0.950402i \(-0.399328\pi\)
−0.667560 + 0.744556i \(0.732661\pi\)
\(62\) 2.32946 0.295842
\(63\) −4.04336 6.83017i −0.509416 0.860520i
\(64\) 3.14994 0.393743
\(65\) −3.61673 2.08812i −0.448600 0.258999i
\(66\) −0.626368 0.523704i −0.0771005 0.0644635i
\(67\) −7.40799 12.8310i −0.905031 1.56756i −0.820876 0.571106i \(-0.806514\pi\)
−0.0841542 0.996453i \(-0.526819\pi\)
\(68\) −3.69661 + 6.40271i −0.448280 + 0.776443i
\(69\) 2.93729 + 8.02603i 0.353608 + 0.966221i
\(70\) 3.10385 3.75494i 0.370981 0.448802i
\(71\) 10.0055i 1.18743i −0.804674 0.593717i \(-0.797660\pi\)
0.804674 0.593717i \(-0.202340\pi\)
\(72\) −5.25789 + 0.946253i −0.619648 + 0.111517i
\(73\) 10.7524 6.20787i 1.25847 0.726577i 0.285691 0.958322i \(-0.407777\pi\)
0.972777 + 0.231745i \(0.0744435\pi\)
\(74\) −0.586787 + 0.338781i −0.0682126 + 0.0393825i
\(75\) −3.05461 + 17.5041i −0.352716 + 2.02120i
\(76\) 10.4967i 1.20405i
\(77\) 1.68566 2.03925i 0.192098 0.232395i
\(78\) 0.819720 0.299993i 0.0928150 0.0339675i
\(79\) −2.94229 + 5.09619i −0.331033 + 0.573367i −0.982715 0.185126i \(-0.940731\pi\)
0.651681 + 0.758493i \(0.274064\pi\)
\(80\) 5.30501 + 9.18854i 0.593118 + 1.02731i
\(81\) −8.43530 + 3.13780i −0.937255 + 0.348644i
\(82\) −0.911441 0.526220i −0.100652 0.0581113i
\(83\) 7.65786 0.840559 0.420280 0.907395i \(-0.361932\pi\)
0.420280 + 0.907395i \(0.361932\pi\)
\(84\) −1.48799 8.00986i −0.162352 0.873947i
\(85\) −16.2446 −1.76198
\(86\) −2.41494 1.39427i −0.260410 0.150348i
\(87\) −4.89571 + 5.85544i −0.524875 + 0.627769i
\(88\) −0.890393 1.54221i −0.0949162 0.164400i
\(89\) 0.824642 1.42832i 0.0874119 0.151402i −0.819005 0.573787i \(-0.805474\pi\)
0.906416 + 0.422385i \(0.138807\pi\)
\(90\) −3.56567 4.21907i −0.375854 0.444729i
\(91\) 0.987030 + 2.65083i 0.103469 + 0.277882i
\(92\) 8.77237i 0.914582i
\(93\) 8.43198 + 1.47145i 0.874355 + 0.152582i
\(94\) −1.27137 + 0.734024i −0.131131 + 0.0757088i
\(95\) 19.9738 11.5319i 2.04926 1.18314i
\(96\) −8.26161 1.44172i −0.843197 0.147145i
\(97\) 5.22606i 0.530626i −0.964162 0.265313i \(-0.914525\pi\)
0.964162 0.265313i \(-0.0854753\pi\)
\(98\) −3.24074 + 0.620867i −0.327364 + 0.0627171i
\(99\) −1.93646 2.29131i −0.194622 0.230286i
\(100\) −9.11898 + 15.7945i −0.911898 + 1.57945i
\(101\) 1.34223 + 2.32480i 0.133557 + 0.231327i 0.925045 0.379857i \(-0.124027\pi\)
−0.791489 + 0.611184i \(0.790694\pi\)
\(102\) 2.17789 2.60483i 0.215644 0.257917i
\(103\) 10.9732 + 6.33537i 1.08122 + 0.624242i 0.931225 0.364445i \(-0.118741\pi\)
0.149994 + 0.988687i \(0.452075\pi\)
\(104\) 1.90387 0.186690
\(105\) 13.6069 11.6312i 1.32790 1.13509i
\(106\) 2.84782 0.276605
\(107\) −8.45146 4.87945i −0.817034 0.471715i 0.0323588 0.999476i \(-0.489698\pi\)
−0.849392 + 0.527762i \(0.823031\pi\)
\(108\) −9.23759 + 0.0489034i −0.888887 + 0.00470573i
\(109\) 4.39285 + 7.60864i 0.420759 + 0.728776i 0.996014 0.0891983i \(-0.0284305\pi\)
−0.575255 + 0.817974i \(0.695097\pi\)
\(110\) 0.920666 1.59464i 0.0877820 0.152043i
\(111\) −2.33799 + 0.855636i −0.221913 + 0.0812133i
\(112\) 1.19564 7.08614i 0.112978 0.669578i
\(113\) 7.33403i 0.689927i 0.938616 + 0.344964i \(0.112109\pi\)
−0.938616 + 0.344964i \(0.887891\pi\)
\(114\) −0.828714 + 4.74886i −0.0776162 + 0.444771i
\(115\) −16.6926 + 9.63748i −1.55659 + 0.898699i
\(116\) −6.78447 + 3.91702i −0.629922 + 0.363686i
\(117\) 3.15664 0.568096i 0.291832 0.0525205i
\(118\) 0.226451i 0.0208465i
\(119\) 8.48052 + 7.01003i 0.777408 + 0.642608i
\(120\) −4.14079 11.3146i −0.378001 1.03287i
\(121\) 0.500000 0.866025i 0.0454545 0.0787296i
\(122\) 0.757845 + 1.31263i 0.0686121 + 0.118840i
\(123\) −2.96675 2.48049i −0.267503 0.223659i
\(124\) 7.60845 + 4.39274i 0.683259 + 0.394480i
\(125\) −20.5419 −1.83732
\(126\) 0.0408078 + 3.74125i 0.00363545 + 0.333297i
\(127\) −14.2480 −1.26430 −0.632152 0.774844i \(-0.717828\pi\)
−0.632152 + 0.774844i \(0.717828\pi\)
\(128\) −9.67235 5.58434i −0.854923 0.493590i
\(129\) −7.86067 6.57228i −0.692093 0.578657i
\(130\) 0.984301 + 1.70486i 0.0863289 + 0.149526i
\(131\) 10.7855 18.6811i 0.942338 1.63218i 0.181342 0.983420i \(-0.441956\pi\)
0.760996 0.648757i \(-0.224711\pi\)
\(132\) −1.05827 2.89167i −0.0921102 0.251688i
\(133\) −15.4036 2.59905i −1.33566 0.225366i
\(134\) 6.98399i 0.603325i
\(135\) −10.2416 17.5241i −0.881459 1.50824i
\(136\) 6.41347 3.70282i 0.549951 0.317514i
\(137\) 2.39232 1.38121i 0.204390 0.118005i −0.394312 0.918977i \(-0.629017\pi\)
0.598701 + 0.800972i \(0.295684\pi\)
\(138\) 0.692578 3.96875i 0.0589562 0.337842i
\(139\) 20.6106i 1.74817i 0.485776 + 0.874083i \(0.338537\pi\)
−0.485776 + 0.874083i \(0.661463\pi\)
\(140\) 17.2186 6.41130i 1.45523 0.541854i
\(141\) −5.06564 + 1.85387i −0.426604 + 0.156124i
\(142\) −2.35820 + 4.08453i −0.197896 + 0.342766i
\(143\) 0.534559 + 0.925884i 0.0447021 + 0.0774263i
\(144\) −7.66688 2.75991i −0.638907 0.229993i
\(145\) −14.9071 8.60661i −1.23797 0.714740i
\(146\) −5.85256 −0.484361
\(147\) −12.1227 + 0.200289i −0.999864 + 0.0165195i
\(148\) −2.55540 −0.210053
\(149\) 13.8040 + 7.96975i 1.13087 + 0.652907i 0.944153 0.329507i \(-0.106883\pi\)
0.186715 + 0.982414i \(0.440216\pi\)
\(150\) 5.37254 6.42574i 0.438666 0.524659i
\(151\) 8.92946 + 15.4663i 0.726669 + 1.25863i 0.958283 + 0.285820i \(0.0922661\pi\)
−0.231614 + 0.972808i \(0.574401\pi\)
\(152\) −5.25717 + 9.10568i −0.426412 + 0.738568i
\(153\) 9.52873 8.05304i 0.770353 0.651049i
\(154\) −1.16877 + 0.435188i −0.0941819 + 0.0350685i
\(155\) 19.3038i 1.55052i
\(156\) 3.24306 + 0.565940i 0.259653 + 0.0453115i
\(157\) 2.79410 1.61317i 0.222994 0.128745i −0.384342 0.923191i \(-0.625572\pi\)
0.607336 + 0.794445i \(0.292238\pi\)
\(158\) 2.40225 1.38694i 0.191113 0.110339i
\(159\) 10.3083 + 1.79888i 0.817500 + 0.142660i
\(160\) 18.9137i 1.49526i
\(161\) 12.8732 + 2.17209i 1.01455 + 0.171185i
\(162\) 4.18308 + 0.707183i 0.328654 + 0.0555615i
\(163\) 8.37708 14.5095i 0.656143 1.13647i −0.325463 0.945555i \(-0.605520\pi\)
0.981606 0.190919i \(-0.0611466\pi\)
\(164\) −1.98462 3.43746i −0.154973 0.268421i
\(165\) 4.33983 5.19058i 0.337855 0.404086i
\(166\) −3.12616 1.80489i −0.242637 0.140086i
\(167\) −10.6160 −0.821488 −0.410744 0.911751i \(-0.634731\pi\)
−0.410744 + 0.911751i \(0.634731\pi\)
\(168\) −2.72086 + 7.69364i −0.209919 + 0.593577i
\(169\) 11.8570 0.912076
\(170\) 6.63153 + 3.82871i 0.508615 + 0.293649i
\(171\) −5.99941 + 16.6660i −0.458786 + 1.27448i
\(172\) −5.25842 9.10786i −0.400951 0.694468i
\(173\) −7.00634 + 12.1353i −0.532682 + 0.922632i 0.466590 + 0.884474i \(0.345482\pi\)
−0.999272 + 0.0381583i \(0.987851\pi\)
\(174\) 3.37864 1.23648i 0.256134 0.0937374i
\(175\) 20.9202 + 17.2927i 1.58142 + 1.30721i
\(176\) 2.71617i 0.204739i
\(177\) −0.143042 + 0.819688i −0.0107517 + 0.0616115i
\(178\) −0.673285 + 0.388721i −0.0504649 + 0.0291359i
\(179\) −3.44243 + 1.98749i −0.257299 + 0.148552i −0.623102 0.782141i \(-0.714128\pi\)
0.365803 + 0.930692i \(0.380794\pi\)
\(180\) −3.69009 20.5041i −0.275043 1.52829i
\(181\) 4.57190i 0.339827i −0.985459 0.169913i \(-0.945651\pi\)
0.985459 0.169913i \(-0.0543488\pi\)
\(182\) 0.221842 1.31478i 0.0164440 0.0974577i
\(183\) 1.91403 + 5.23003i 0.141489 + 0.386615i
\(184\) 4.39355 7.60986i 0.323897 0.561006i
\(185\) −2.80741 4.86258i −0.206405 0.357504i
\(186\) −3.09537 2.58803i −0.226963 0.189763i
\(187\) 3.60148 + 2.07932i 0.263367 + 0.152055i
\(188\) −5.53669 −0.403804
\(189\) −2.21552 + 13.5680i −0.161155 + 0.986929i
\(190\) −10.8718 −0.788724
\(191\) 9.48395 + 5.47556i 0.686234 + 0.396198i 0.802200 0.597056i \(-0.203663\pi\)
−0.115965 + 0.993253i \(0.536996\pi\)
\(192\) −4.18561 3.49958i −0.302071 0.252560i
\(193\) 4.74840 + 8.22447i 0.341797 + 0.592010i 0.984767 0.173882i \(-0.0556310\pi\)
−0.642969 + 0.765892i \(0.722298\pi\)
\(194\) −1.23174 + 2.13343i −0.0884334 + 0.153171i
\(195\) 2.48598 + 6.79285i 0.178025 + 0.486446i
\(196\) −11.7556 4.08329i −0.839687 0.291664i
\(197\) 12.4496i 0.886997i 0.896275 + 0.443498i \(0.146263\pi\)
−0.896275 + 0.443498i \(0.853737\pi\)
\(198\) 0.250477 + 1.39179i 0.0178006 + 0.0989099i
\(199\) 19.4647 11.2380i 1.37982 0.796638i 0.387680 0.921794i \(-0.373277\pi\)
0.992137 + 0.125156i \(0.0399433\pi\)
\(200\) 15.8211 9.13430i 1.11872 0.645893i
\(201\) −4.41156 + 25.2800i −0.311168 + 1.78311i
\(202\) 1.26540i 0.0890334i
\(203\) 4.06824 + 10.9259i 0.285535 + 0.766849i
\(204\) 12.0254 4.40094i 0.841948 0.308128i
\(205\) 4.36068 7.55292i 0.304563 0.527519i
\(206\) −2.98638 5.17256i −0.208071 0.360389i
\(207\) 5.01386 13.9282i 0.348488 0.968079i
\(208\) 2.51486 + 1.45195i 0.174374 + 0.100675i
\(209\) −5.90432 −0.408410
\(210\) −8.29611 + 1.54116i −0.572486 + 0.106350i
\(211\) 2.77052 0.190731 0.0953654 0.995442i \(-0.469598\pi\)
0.0953654 + 0.995442i \(0.469598\pi\)
\(212\) 9.30150 + 5.37022i 0.638830 + 0.368829i
\(213\) −11.1161 + 13.2952i −0.761662 + 0.910973i
\(214\) 2.30009 + 3.98387i 0.157231 + 0.272331i
\(215\) 11.5540 20.0121i 0.787976 1.36481i
\(216\) 8.03792 + 4.58413i 0.546911 + 0.311911i
\(217\) 8.33013 10.0775i 0.565486 0.684108i
\(218\) 4.14142i 0.280492i
\(219\) −21.1846 3.69688i −1.43152 0.249812i
\(220\) 6.01413 3.47226i 0.405472 0.234100i
\(221\) −3.85041 + 2.22304i −0.259007 + 0.149538i
\(222\) 1.15610 + 0.201749i 0.0775925 + 0.0135405i
\(223\) 10.9682i 0.734484i 0.930125 + 0.367242i \(0.119698\pi\)
−0.930125 + 0.367242i \(0.880302\pi\)
\(224\) −8.16182 + 9.87392i −0.545335 + 0.659729i
\(225\) 23.5060 19.8656i 1.56706 1.32438i
\(226\) 1.72856 2.99396i 0.114982 0.199155i
\(227\) −6.32034 10.9472i −0.419496 0.726588i 0.576393 0.817173i \(-0.304460\pi\)
−0.995889 + 0.0905845i \(0.971126\pi\)
\(228\) −11.6618 + 13.9479i −0.772322 + 0.923723i
\(229\) −0.565883 0.326713i −0.0373946 0.0215898i 0.481186 0.876618i \(-0.340206\pi\)
−0.518581 + 0.855029i \(0.673539\pi\)
\(230\) 9.08586 0.599104
\(231\) −4.50549 + 0.836982i −0.296440 + 0.0550693i
\(232\) 7.84719 0.515194
\(233\) −20.3793 11.7660i −1.33509 0.770815i −0.349016 0.937117i \(-0.613484\pi\)
−0.986075 + 0.166302i \(0.946817\pi\)
\(234\) −1.42253 0.512079i −0.0929935 0.0334757i
\(235\) −6.08270 10.5355i −0.396792 0.687263i
\(236\) −0.427026 + 0.739631i −0.0277970 + 0.0481459i
\(237\) 9.57154 3.50290i 0.621739 0.227538i
\(238\) −1.80979 4.86048i −0.117311 0.315058i
\(239\) 12.8951i 0.834118i 0.908879 + 0.417059i \(0.136939\pi\)
−0.908879 + 0.417059i \(0.863061\pi\)
\(240\) 3.15921 18.1035i 0.203926 1.16858i
\(241\) 18.6347 10.7588i 1.20037 0.693034i 0.239732 0.970839i \(-0.422940\pi\)
0.960637 + 0.277806i \(0.0896071\pi\)
\(242\) −0.408229 + 0.235691i −0.0262419 + 0.0151508i
\(243\) 14.6948 + 5.20212i 0.942674 + 0.333716i
\(244\) 5.71637i 0.365953i
\(245\) −5.14500 26.8553i −0.328702 1.71572i
\(246\) 0.626484 + 1.71184i 0.0399431 + 0.109143i
\(247\) 3.15621 5.46672i 0.200825 0.347839i
\(248\) −4.40012 7.62123i −0.279408 0.483949i
\(249\) −10.1757 8.50786i −0.644858 0.539164i
\(250\) 8.38579 + 4.84154i 0.530364 + 0.306206i
\(251\) 2.36882 0.149519 0.0747594 0.997202i \(-0.476181\pi\)
0.0747594 + 0.997202i \(0.476181\pi\)
\(252\) −6.92172 + 12.2966i −0.436027 + 0.774611i
\(253\) 4.93440 0.310223
\(254\) 5.81644 + 3.35812i 0.364956 + 0.210707i
\(255\) 21.5857 + 18.0478i 1.35175 + 1.13019i
\(256\) −0.517587 0.896487i −0.0323492 0.0560304i
\(257\) 1.14080 1.97593i 0.0711612 0.123255i −0.828249 0.560360i \(-0.810663\pi\)
0.899410 + 0.437105i \(0.143996\pi\)
\(258\) 1.65992 + 4.53568i 0.103342 + 0.282379i
\(259\) −0.632734 + 3.74999i −0.0393162 + 0.233013i
\(260\) 7.42451i 0.460449i
\(261\) 13.0108 2.34152i 0.805345 0.144937i
\(262\) −8.80594 + 5.08411i −0.544033 + 0.314097i
\(263\) −10.5208 + 6.07421i −0.648742 + 0.374552i −0.787974 0.615708i \(-0.788870\pi\)
0.139232 + 0.990260i \(0.455537\pi\)
\(264\) −0.530241 + 3.03849i −0.0326341 + 0.187006i
\(265\) 23.5993i 1.44969i
\(266\) 5.67563 + 4.69150i 0.347995 + 0.287654i
\(267\) −2.68264 + 0.981765i −0.164175 + 0.0600831i
\(268\) −13.1699 + 22.8110i −0.804481 + 1.39340i
\(269\) 1.12011 + 1.94008i 0.0682941 + 0.118289i 0.898151 0.439688i \(-0.144911\pi\)
−0.829856 + 0.557977i \(0.811578\pi\)
\(270\) 0.0506510 + 9.56771i 0.00308252 + 0.582272i
\(271\) −15.4313 8.90928i −0.937387 0.541200i −0.0482464 0.998835i \(-0.515363\pi\)
−0.889140 + 0.457635i \(0.848697\pi\)
\(272\) 11.2956 0.684893
\(273\) 1.63351 4.61898i 0.0988642 0.279553i
\(274\) −1.30215 −0.0786659
\(275\) 8.88432 + 5.12937i 0.535745 + 0.309312i
\(276\) 9.74608 11.6566i 0.586645 0.701647i
\(277\) 3.19654 + 5.53657i 0.192062 + 0.332660i 0.945933 0.324361i \(-0.105149\pi\)
−0.753872 + 0.657022i \(0.771816\pi\)
\(278\) 4.85773 8.41383i 0.291347 0.504628i
\(279\) −9.56955 11.3232i −0.572914 0.677899i
\(280\) −18.1478 3.06207i −1.08454 0.182994i
\(281\) 6.57145i 0.392020i 0.980602 + 0.196010i \(0.0627985\pi\)
−0.980602 + 0.196010i \(0.937202\pi\)
\(282\) 2.50488 + 0.437121i 0.149163 + 0.0260302i
\(283\) 2.21575 1.27926i 0.131713 0.0760444i −0.432696 0.901540i \(-0.642438\pi\)
0.564409 + 0.825496i \(0.309104\pi\)
\(284\) −15.4047 + 8.89388i −0.914098 + 0.527755i
\(285\) −39.3528 6.86738i −2.33106 0.406789i
\(286\) 0.503963i 0.0298000i
\(287\) −5.53580 + 2.06124i −0.326768 + 0.121671i
\(288\) 9.37620 + 11.0944i 0.552498 + 0.653742i
\(289\) −0.147121 + 0.254821i −0.00865416 + 0.0149895i
\(290\) 4.05700 + 7.02693i 0.238235 + 0.412635i
\(291\) −5.80614 + 6.94434i −0.340362 + 0.407084i
\(292\) −19.1155 11.0364i −1.11865 0.645854i
\(293\) 26.2396 1.53293 0.766467 0.642284i \(-0.222013\pi\)
0.766467 + 0.642284i \(0.222013\pi\)
\(294\) 4.99604 + 2.77545i 0.291375 + 0.161867i
\(295\) −1.87655 −0.109257
\(296\) 2.21676 + 1.27985i 0.128847 + 0.0743897i
\(297\) 0.0275078 + 5.19608i 0.00159617 + 0.301507i
\(298\) −3.75679 6.50696i −0.217625 0.376938i
\(299\) −2.63773 + 4.56868i −0.152544 + 0.264213i
\(300\) 29.6649 10.8565i 1.71270 0.626798i
\(301\) −14.6676 + 5.46144i −0.845425 + 0.314792i
\(302\) 8.41837i 0.484423i
\(303\) 0.799314 4.58039i 0.0459194 0.263136i
\(304\) −13.8886 + 8.01857i −0.796564 + 0.459896i
\(305\) −10.8775 + 6.28010i −0.622841 + 0.359598i
\(306\) −5.78793 + 1.04164i −0.330874 + 0.0595468i
\(307\) 0.463588i 0.0264584i 0.999912 + 0.0132292i \(0.00421111\pi\)
−0.999912 + 0.0132292i \(0.995789\pi\)
\(308\) −4.63806 0.782577i −0.264278 0.0445915i
\(309\) −7.54247 20.6095i −0.429076 1.17244i
\(310\) 4.54972 7.88035i 0.258407 0.447574i
\(311\) −14.0883 24.4017i −0.798876 1.38369i −0.920349 0.391099i \(-0.872095\pi\)
0.121473 0.992595i \(-0.461238\pi\)
\(312\) −2.52985 2.11520i −0.143224 0.119749i
\(313\) 1.05728 + 0.610419i 0.0597609 + 0.0345029i 0.529583 0.848258i \(-0.322349\pi\)
−0.469822 + 0.882761i \(0.655682\pi\)
\(314\) −1.52084 −0.0858261
\(315\) −31.0030 + 0.338166i −1.74682 + 0.0190535i
\(316\) 10.4616 0.588511
\(317\) 29.0062 + 16.7467i 1.62915 + 0.940591i 0.984347 + 0.176243i \(0.0563944\pi\)
0.644804 + 0.764348i \(0.276939\pi\)
\(318\) −3.78416 3.16392i −0.212205 0.177424i
\(319\) 2.20330 + 3.81622i 0.123361 + 0.213667i
\(320\) 6.15222 10.6560i 0.343919 0.595686i
\(321\) 5.80916 + 15.8733i 0.324236 + 0.885963i
\(322\) −4.74328 3.92081i −0.264332 0.218498i
\(323\) 24.5539i 1.36622i
\(324\) 12.3291 + 10.1980i 0.684953 + 0.566553i
\(325\) −9.49839 + 5.48390i −0.526876 + 0.304192i
\(326\) −6.83952 + 3.94880i −0.378806 + 0.218704i
\(327\) 2.61600 14.9907i 0.144665 0.828990i
\(328\) 3.97591i 0.219533i
\(329\) −1.37092 + 8.12495i −0.0755812 + 0.447943i
\(330\) −2.99501 + 1.09608i −0.164870 + 0.0603375i
\(331\) 2.16592 3.75149i 0.119050 0.206200i −0.800342 0.599544i \(-0.795348\pi\)
0.919391 + 0.393344i \(0.128682\pi\)
\(332\) −6.80707 11.7902i −0.373586 0.647070i
\(333\) 4.05731 + 1.46055i 0.222339 + 0.0800374i
\(334\) 4.33374 + 2.50209i 0.237132 + 0.136908i
\(335\) −57.8748 −3.16204
\(336\) −9.46145 + 8.08765i −0.516164 + 0.441217i
\(337\) 2.61781 0.142601 0.0713006 0.997455i \(-0.477285\pi\)
0.0713006 + 0.997455i \(0.477285\pi\)
\(338\) −4.84036 2.79458i −0.263281 0.152005i
\(339\) 8.14809 9.74538i 0.442543 0.529297i
\(340\) 14.4399 + 25.0106i 0.783111 + 1.35639i
\(341\) 2.47089 4.27970i 0.133806 0.231759i
\(342\) 6.37716 5.38954i 0.344837 0.291433i
\(343\) −8.90289 + 16.2400i −0.480711 + 0.876879i
\(344\) 10.5345i 0.567983i
\(345\) 32.8882 + 5.73925i 1.77064 + 0.308991i
\(346\) 5.72037 3.30266i 0.307529 0.177552i
\(347\) −13.7933 + 7.96356i −0.740463 + 0.427506i −0.822238 0.569144i \(-0.807275\pi\)
0.0817747 + 0.996651i \(0.473941\pi\)
\(348\) 13.3669 + 2.33264i 0.716543 + 0.125043i
\(349\) 5.93887i 0.317901i −0.987287 0.158950i \(-0.949189\pi\)
0.987287 0.158950i \(-0.0508110\pi\)
\(350\) −4.46448 11.9901i −0.238636 0.640896i
\(351\) −4.82567 2.75214i −0.257575 0.146899i
\(352\) −2.42096 + 4.19323i −0.129038 + 0.223500i
\(353\) 8.63189 + 14.9509i 0.459429 + 0.795754i 0.998931 0.0462300i \(-0.0147207\pi\)
−0.539502 + 0.841984i \(0.681387\pi\)
\(354\) 0.251587 0.300906i 0.0133717 0.0159930i
\(355\) −33.8477 19.5420i −1.79645 1.03718i
\(356\) −2.93210 −0.155401
\(357\) −3.48070 18.7367i −0.184218 0.991651i
\(358\) 1.87373 0.0990297
\(359\) −27.2535 15.7348i −1.43838 0.830451i −0.440645 0.897681i \(-0.645250\pi\)
−0.997737 + 0.0672305i \(0.978584\pi\)
\(360\) −7.06821 + 19.6351i −0.372527 + 1.03486i
\(361\) 7.93050 + 13.7360i 0.417395 + 0.722949i
\(362\) −1.07756 + 1.86638i −0.0566351 + 0.0980948i
\(363\) −1.62655 + 0.595267i −0.0853716 + 0.0312434i
\(364\) 3.20389 3.87597i 0.167930 0.203156i
\(365\) 48.4989i 2.53855i
\(366\) 0.451307 2.58617i 0.0235902 0.135181i
\(367\) 3.35150 1.93499i 0.174947 0.101006i −0.409970 0.912099i \(-0.634461\pi\)
0.584916 + 0.811094i \(0.301127\pi\)
\(368\) 11.6070 6.70133i 0.605059 0.349331i
\(369\) 1.18637 + 6.59211i 0.0617600 + 0.343172i
\(370\) 2.64672i 0.137597i
\(371\) 10.1838 12.3200i 0.528715 0.639623i
\(372\) −5.22971 14.2900i −0.271148 0.740902i
\(373\) 1.49777 2.59421i 0.0775514 0.134323i −0.824642 0.565656i \(-0.808623\pi\)
0.902193 + 0.431333i \(0.141956\pi\)
\(374\) −0.980152 1.69767i −0.0506825 0.0877846i
\(375\) 27.2959 + 22.8220i 1.40955 + 1.17852i
\(376\) 4.80297 + 2.77299i 0.247694 + 0.143006i
\(377\) −4.71117 −0.242637
\(378\) 4.10230 5.01668i 0.211000 0.258030i
\(379\) −30.0561 −1.54388 −0.771938 0.635697i \(-0.780713\pi\)
−0.771938 + 0.635697i \(0.780713\pi\)
\(380\) −35.5093 20.5013i −1.82159 1.05170i
\(381\) 18.9326 + 15.8295i 0.969946 + 0.810969i
\(382\) −2.58108 4.47056i −0.132060 0.228734i
\(383\) 10.2996 17.8395i 0.526286 0.911554i −0.473245 0.880931i \(-0.656917\pi\)
0.999531 0.0306231i \(-0.00974917\pi\)
\(384\) 6.64835 + 18.1664i 0.339272 + 0.927049i
\(385\) −3.60631 9.68533i −0.183795 0.493610i
\(386\) 4.47662i 0.227854i
\(387\) 3.14339 + 17.4664i 0.159788 + 0.887865i
\(388\) −8.04614 + 4.64544i −0.408481 + 0.235837i
\(389\) 8.68694 5.01541i 0.440445 0.254291i −0.263341 0.964703i \(-0.584824\pi\)
0.703787 + 0.710412i \(0.251491\pi\)
\(390\) 0.586165 3.35896i 0.0296816 0.170087i
\(391\) 20.5204i 1.03776i
\(392\) 8.15270 + 9.42986i 0.411773 + 0.476280i
\(393\) −35.0864 + 12.8406i −1.76988 + 0.647721i
\(394\) 2.93426 5.08228i 0.147826 0.256042i
\(395\) 11.4933 + 19.9070i 0.578290 + 1.00163i
\(396\) −1.80643 + 5.01816i −0.0907765 + 0.252172i
\(397\) −29.6673 17.1284i −1.48896 0.859650i −0.489037 0.872263i \(-0.662652\pi\)
−0.999920 + 0.0126130i \(0.995985\pi\)
\(398\) −10.5947 −0.531066
\(399\) 17.5807 + 20.5670i 0.880134 + 1.02964i
\(400\) 27.8644 1.39322
\(401\) 23.6000 + 13.6255i 1.17853 + 0.680423i 0.955673 0.294429i \(-0.0951293\pi\)
0.222854 + 0.974852i \(0.428463\pi\)
\(402\) 7.75919 9.28026i 0.386993 0.462857i
\(403\) 2.64167 + 4.57551i 0.131591 + 0.227922i
\(404\) 2.38621 4.13303i 0.118718 0.205626i
\(405\) −5.86028 + 34.6643i −0.291199 + 1.72248i
\(406\) 0.914366 5.41912i 0.0453792 0.268946i
\(407\) 1.43740i 0.0712491i
\(408\) −12.6360 2.20508i −0.625574 0.109168i
\(409\) 10.1269 5.84676i 0.500742 0.289104i −0.228278 0.973596i \(-0.573309\pi\)
0.729020 + 0.684492i \(0.239976\pi\)
\(410\) −3.56031 + 2.05554i −0.175831 + 0.101516i
\(411\) −4.71341 0.822528i −0.232495 0.0405723i
\(412\) 22.5260i 1.10978i
\(413\) 0.979656 + 0.809788i 0.0482057 + 0.0398470i
\(414\) −5.32956 + 4.50418i −0.261934 + 0.221368i
\(415\) 14.9567 25.9058i 0.734197 1.27167i
\(416\) −2.58830 4.48306i −0.126902 0.219800i
\(417\) 22.8983 27.3871i 1.12134 1.34115i
\(418\) 2.41031 + 1.39159i 0.117892 + 0.0680651i
\(419\) 8.63636 0.421914 0.210957 0.977495i \(-0.432342\pi\)
0.210957 + 0.977495i \(0.432342\pi\)
\(420\) −30.0028 10.6105i −1.46399 0.517740i
\(421\) 23.5610 1.14829 0.574146 0.818753i \(-0.305334\pi\)
0.574146 + 0.818753i \(0.305334\pi\)
\(422\) −1.13101 0.652988i −0.0550566 0.0317869i
\(423\) 8.79082 + 3.16450i 0.427424 + 0.153863i
\(424\) −5.37925 9.31713i −0.261239 0.452480i
\(425\) −21.3312 + 36.9467i −1.03471 + 1.79218i
\(426\) 7.67146 2.80753i 0.371684 0.136025i
\(427\) 8.38863 + 1.41541i 0.405954 + 0.0684964i
\(428\) 17.3494i 0.838614i
\(429\) 0.318338 1.82420i 0.0153695 0.0880732i
\(430\) −9.43334 + 5.44634i −0.454916 + 0.262646i
\(431\) 7.17728 4.14380i 0.345717 0.199600i −0.317080 0.948399i \(-0.602702\pi\)
0.662797 + 0.748799i \(0.269369\pi\)
\(432\) 7.12142 + 12.1852i 0.342629 + 0.586262i
\(433\) 8.45254i 0.406203i 0.979158 + 0.203101i \(0.0651021\pi\)
−0.979158 + 0.203101i \(0.934898\pi\)
\(434\) −5.77578 + 2.15060i −0.277246 + 0.103232i
\(435\) 10.2465 + 27.9981i 0.491280 + 1.34241i
\(436\) 7.80961 13.5266i 0.374012 0.647809i
\(437\) −14.5671 25.2310i −0.696840 1.20696i
\(438\) 7.77682 + 6.50218i 0.371591 + 0.310686i
\(439\) −9.30550 5.37254i −0.444127 0.256417i 0.261219 0.965279i \(-0.415875\pi\)
−0.705347 + 0.708862i \(0.749209\pi\)
\(440\) −6.95618 −0.331623
\(441\) 16.3311 + 13.2022i 0.777669 + 0.628674i
\(442\) 2.09580 0.0996870
\(443\) 11.8729 + 6.85484i 0.564100 + 0.325684i 0.754790 0.655967i \(-0.227739\pi\)
−0.190689 + 0.981650i \(0.561072\pi\)
\(444\) 3.39560 + 2.83905i 0.161148 + 0.134735i
\(445\) −3.22125 5.57937i −0.152702 0.264488i
\(446\) 2.58510 4.47753i 0.122408 0.212017i
\(447\) −9.48826 25.9263i −0.448779 1.22627i
\(448\) −7.81012 + 2.90808i −0.368994 + 0.137394i
\(449\) 16.9934i 0.801968i 0.916085 + 0.400984i \(0.131332\pi\)
−0.916085 + 0.400984i \(0.868668\pi\)
\(450\) −14.2780 + 2.56958i −0.673070 + 0.121131i
\(451\) −1.93355 + 1.11634i −0.0910473 + 0.0525662i
\(452\) 11.2916 6.51921i 0.531112 0.306638i
\(453\) 5.31762 30.4721i 0.249844 1.43170i
\(454\) 5.95859i 0.279650i
\(455\) 10.8953 + 1.83836i 0.510779 + 0.0861834i
\(456\) 17.1021 6.25884i 0.800877 0.293097i
\(457\) −6.03723 + 10.4568i −0.282410 + 0.489148i −0.971978 0.235073i \(-0.924467\pi\)
0.689568 + 0.724221i \(0.257800\pi\)
\(458\) 0.154006 + 0.266747i 0.00719624 + 0.0124643i
\(459\) −21.6086 + 0.114395i −1.00860 + 0.00533950i
\(460\) 29.6761 + 17.1335i 1.38365 + 0.798853i
\(461\) −36.9486 −1.72087 −0.860434 0.509563i \(-0.829807\pi\)
−0.860434 + 0.509563i \(0.829807\pi\)
\(462\) 2.03654 + 0.720224i 0.0947484 + 0.0335078i
\(463\) −8.35061 −0.388086 −0.194043 0.980993i \(-0.562160\pi\)
−0.194043 + 0.980993i \(0.562160\pi\)
\(464\) 10.3655 + 5.98452i 0.481206 + 0.277824i
\(465\) 21.4464 25.6507i 0.994555 1.18952i
\(466\) 5.54627 + 9.60642i 0.256926 + 0.445009i
\(467\) −5.02423 + 8.70222i −0.232494 + 0.402691i −0.958541 0.284954i \(-0.908022\pi\)
0.726048 + 0.687644i \(0.241355\pi\)
\(468\) −3.68059 4.35505i −0.170135 0.201312i
\(469\) 30.2136 + 24.9747i 1.39513 + 1.15322i
\(470\) 5.73455i 0.264515i
\(471\) −5.50501 0.960668i −0.253657 0.0442653i
\(472\) 0.740874 0.427744i 0.0341015 0.0196885i
\(473\) −5.12311 + 2.95783i −0.235561 + 0.136001i
\(474\) −4.73298 0.825943i −0.217393 0.0379368i
\(475\) 60.5709i 2.77918i
\(476\) 3.25445 19.2880i 0.149168 0.884063i
\(477\) −11.6990 13.8428i −0.535660 0.633819i
\(478\) 3.03927 5.26417i 0.139013 0.240777i
\(479\) 1.11912 + 1.93837i 0.0511337 + 0.0885662i 0.890459 0.455063i \(-0.150383\pi\)
−0.839326 + 0.543629i \(0.817050\pi\)
\(480\) −21.0131 + 25.1324i −0.959113 + 1.14713i
\(481\) −1.33086 0.768374i −0.0606821 0.0350348i
\(482\) −10.1430 −0.462000
\(483\) −14.6926 17.1884i −0.668538 0.782098i
\(484\) −1.77780 −0.0808091
\(485\) −17.6793 10.2071i −0.802774 0.463482i
\(486\) −4.77276 5.58709i −0.216497 0.253436i
\(487\) 1.46555 + 2.53840i 0.0664103 + 0.115026i 0.897319 0.441383i \(-0.145512\pi\)
−0.830908 + 0.556409i \(0.812179\pi\)
\(488\) 2.86299 4.95884i 0.129601 0.224476i
\(489\) −27.2514 + 9.97320i −1.23235 + 0.451004i
\(490\) −4.22921 + 12.1757i −0.191056 + 0.550043i
\(491\) 22.0744i 0.996206i 0.867118 + 0.498103i \(0.165970\pi\)
−0.867118 + 0.498103i \(0.834030\pi\)
\(492\) −1.18187 + 6.77258i −0.0532828 + 0.305331i
\(493\) −15.8703 + 9.16270i −0.714761 + 0.412667i
\(494\) −2.57691 + 1.48778i −0.115941 + 0.0669384i
\(495\) −11.5334 + 2.07565i −0.518390 + 0.0932937i
\(496\) 13.4227i 0.602697i
\(497\) 9.23726 + 24.8081i 0.414348 + 1.11280i
\(498\) 2.14878 + 5.87147i 0.0962892 + 0.263107i
\(499\) 20.8831 36.1706i 0.934855 1.61922i 0.159964 0.987123i \(-0.448862\pi\)
0.774891 0.632094i \(-0.217805\pi\)
\(500\) 18.2597 + 31.6267i 0.816597 + 1.41439i
\(501\) 14.1064 + 11.7943i 0.630227 + 0.526931i
\(502\) −0.967021 0.558310i −0.0431603 0.0249186i
\(503\) 23.4080 1.04371 0.521855 0.853034i \(-0.325240\pi\)
0.521855 + 0.853034i \(0.325240\pi\)
\(504\) 12.1631 7.20036i 0.541786 0.320730i
\(505\) 10.4861 0.466626
\(506\) −2.01436 1.16299i −0.0895493 0.0517013i
\(507\) −15.7554 13.1731i −0.699724 0.585037i
\(508\) 12.6650 + 21.9365i 0.561920 + 0.973274i
\(509\) 7.33533 12.7052i 0.325133 0.563147i −0.656406 0.754407i \(-0.727924\pi\)
0.981539 + 0.191261i \(0.0612577\pi\)
\(510\) −4.55822 12.4552i −0.201841 0.551524i
\(511\) −20.9287 + 25.3189i −0.925831 + 1.12004i
\(512\) 22.8253i 1.00875i
\(513\) 26.4879 15.4803i 1.16947 0.683473i
\(514\) −0.931415 + 0.537753i −0.0410830 + 0.0237193i
\(515\) 42.8639 24.7475i 1.88881 1.09050i
\(516\) −3.13147 + 17.9445i −0.137855 + 0.789964i
\(517\) 3.11435i 0.136969i
\(518\) 1.14214 1.38172i 0.0501827 0.0607094i
\(519\) 22.7923 8.34129i 1.00047 0.366142i
\(520\) 3.71849 6.44062i 0.163067 0.282440i
\(521\) −4.63455 8.02728i −0.203044 0.351682i 0.746464 0.665426i \(-0.231750\pi\)
−0.949508 + 0.313744i \(0.898417\pi\)
\(522\) −5.86324 2.11064i −0.256627 0.0923802i
\(523\) 36.0039 + 20.7868i 1.57434 + 0.908945i 0.995627 + 0.0934133i \(0.0297778\pi\)
0.578712 + 0.815532i \(0.303556\pi\)
\(524\) −38.3491 −1.67529
\(525\) −8.58637 46.2206i −0.374740 2.01723i
\(526\) 5.72654 0.249689
\(527\) 17.7977 + 10.2755i 0.775281 + 0.447608i
\(528\) −3.01766 + 3.60922i −0.131327 + 0.157071i
\(529\) 0.674136 + 1.16764i 0.0293103 + 0.0507669i
\(530\) 5.56214 9.63391i 0.241604 0.418470i
\(531\) 1.10074 0.930274i 0.0477682 0.0403704i
\(532\) 9.69074 + 26.0260i 0.420147 + 1.12837i
\(533\) 2.38699i 0.103392i
\(534\) 1.32652 + 0.231489i 0.0574043 + 0.0100175i
\(535\) −33.0135 + 19.0603i −1.42730 + 0.824050i
\(536\) 22.8493 13.1921i 0.986940 0.569810i
\(537\) 6.78236 + 1.18358i 0.292680 + 0.0510751i
\(538\) 1.05600i 0.0455272i
\(539\) −2.29682 + 6.61246i −0.0989312 + 0.284819i
\(540\) −17.8767 + 31.3454i −0.769290 + 1.34889i
\(541\) −18.1823 + 31.4927i −0.781719 + 1.35398i 0.149220 + 0.988804i \(0.452324\pi\)
−0.930939 + 0.365173i \(0.881010\pi\)
\(542\) 4.19967 + 7.27405i 0.180391 + 0.312447i
\(543\) −5.07937 + 6.07510i −0.217977 + 0.260707i
\(544\) −17.4381 10.0679i −0.747653 0.431657i
\(545\) 34.3191 1.47007
\(546\) −1.75549 + 1.50060i −0.0751282 + 0.0642196i
\(547\) 0.291428 0.0124606 0.00623028 0.999981i \(-0.498017\pi\)
0.00623028 + 0.999981i \(0.498017\pi\)
\(548\) −4.25307 2.45551i −0.181682 0.104894i
\(549\) 3.26720 9.07610i 0.139441 0.387359i
\(550\) −2.41789 4.18791i −0.103099 0.178573i
\(551\) 13.0090 22.5322i 0.554200 0.959903i
\(552\) −14.2926 + 5.23068i −0.608335 + 0.222632i
\(553\) 2.59036 15.3521i 0.110153 0.652839i
\(554\) 3.01358i 0.128035i
\(555\) −1.67185 + 9.58037i −0.0709662 + 0.406664i
\(556\) 31.7325 18.3207i 1.34576 0.776972i
\(557\) −29.6985 + 17.1464i −1.25836 + 0.726517i −0.972756 0.231830i \(-0.925529\pi\)
−0.285608 + 0.958347i \(0.592195\pi\)
\(558\) 1.23780 + 6.87789i 0.0524003 + 0.291164i
\(559\) 6.32454i 0.267499i
\(560\) −21.6365 17.8848i −0.914310 0.755773i
\(561\) −2.47550 6.76422i −0.104516 0.285585i
\(562\) 1.54883 2.68265i 0.0653335 0.113161i
\(563\) 11.4094 + 19.7616i 0.480848 + 0.832854i 0.999759 0.0219750i \(-0.00699543\pi\)
−0.518910 + 0.854829i \(0.673662\pi\)
\(564\) 7.35710 + 6.15125i 0.309790 + 0.259014i
\(565\) 24.8103 + 14.3242i 1.04378 + 0.602625i
\(566\) −1.20604 −0.0506938
\(567\) 18.0180 15.5676i 0.756685 0.653779i
\(568\) 17.8176 0.747612
\(569\) −14.7142 8.49522i −0.616850 0.356138i 0.158792 0.987312i \(-0.449240\pi\)
−0.775641 + 0.631174i \(0.782573\pi\)
\(570\) 14.4464 + 12.0786i 0.605092 + 0.505915i
\(571\) −8.93189 15.4705i −0.373788 0.647420i 0.616357 0.787467i \(-0.288608\pi\)
−0.990145 + 0.140047i \(0.955275\pi\)
\(572\) 0.950339 1.64604i 0.0397357 0.0688242i
\(573\) −6.51885 17.8125i −0.272329 0.744129i
\(574\) 2.74569 + 0.463278i 0.114603 + 0.0193369i
\(575\) 50.6207i 2.11103i
\(576\) 1.67378 + 9.30041i 0.0697408 + 0.387517i
\(577\) 8.92725 5.15415i 0.371646 0.214570i −0.302531 0.953139i \(-0.597832\pi\)
0.674177 + 0.738569i \(0.264498\pi\)
\(578\) 0.120118 0.0693501i 0.00499624 0.00288458i
\(579\) 2.82774 16.2041i 0.117517 0.673418i
\(580\) 30.6016i 1.27066i
\(581\) −18.9873 + 7.06987i −0.787725 + 0.293308i
\(582\) 4.00695 1.46642i 0.166093 0.0607852i
\(583\) 3.02072 5.23203i 0.125105 0.216689i
\(584\) 11.0549 + 19.1476i 0.457455 + 0.792335i
\(585\) 4.24349 11.7882i 0.175447 0.487382i
\(586\) −10.7118 6.18444i −0.442499 0.255477i
\(587\) 38.7455 1.59920 0.799599 0.600535i \(-0.205046\pi\)
0.799599 + 0.600535i \(0.205046\pi\)
\(588\) 11.0842 + 18.4863i 0.457106 + 0.762362i
\(589\) −29.1778 −1.20225
\(590\) 0.766063 + 0.442287i 0.0315383 + 0.0182087i
\(591\) 13.8315 16.5429i 0.568951 0.680484i
\(592\) 1.95211 + 3.38115i 0.0802311 + 0.138964i
\(593\) 16.4622 28.5133i 0.676020 1.17090i −0.300150 0.953892i \(-0.597037\pi\)
0.976170 0.217009i \(-0.0696299\pi\)
\(594\) 1.21344 2.12767i 0.0497880 0.0872994i
\(595\) 40.2778 14.9973i 1.65123 0.614831i
\(596\) 28.3372i 1.16074i
\(597\) −38.3499 6.69236i −1.56956 0.273900i
\(598\) 2.15359 1.24338i 0.0880669 0.0508455i
\(599\) 16.2703 9.39369i 0.664788 0.383816i −0.129311 0.991604i \(-0.541276\pi\)
0.794099 + 0.607788i \(0.207943\pi\)
\(600\) −31.1711 5.43961i −1.27255 0.222071i
\(601\) 14.9145i 0.608377i −0.952612 0.304188i \(-0.901615\pi\)
0.952612 0.304188i \(-0.0983852\pi\)
\(602\) 7.27493 + 1.22750i 0.296504 + 0.0500290i
\(603\) 33.9481 28.6906i 1.38247 1.16837i
\(604\) 15.8748 27.4959i 0.645936 1.11879i
\(605\) −1.95312 3.38291i −0.0794057 0.137535i
\(606\) −1.40586 + 1.68145i −0.0571091 + 0.0683044i
\(607\) 10.3735 + 5.98914i 0.421047 + 0.243092i 0.695525 0.718502i \(-0.255172\pi\)
−0.274478 + 0.961593i \(0.588505\pi\)
\(608\) 28.5883 1.15941
\(609\) 6.73282 19.0381i 0.272828 0.771461i
\(610\) 5.92065 0.239720
\(611\) −2.88353 1.66480i −0.116655 0.0673508i
\(612\) −20.8687 7.51228i −0.843567 0.303666i
\(613\) 1.23060 + 2.13146i 0.0497035 + 0.0860890i 0.889807 0.456338i \(-0.150839\pi\)
−0.840103 + 0.542427i \(0.817506\pi\)
\(614\) 0.109264 0.189250i 0.00440952 0.00763751i
\(615\) −14.1857 + 5.19154i −0.572023 + 0.209343i
\(616\) 3.63148 + 3.00179i 0.146316 + 0.120946i
\(617\) 17.5483i 0.706468i −0.935535 0.353234i \(-0.885082\pi\)
0.935535 0.353234i \(-0.114918\pi\)
\(618\) −1.77843 + 10.1911i −0.0715389 + 0.409946i
\(619\) −32.9669 + 19.0334i −1.32505 + 0.765019i −0.984530 0.175218i \(-0.943937\pi\)
−0.340522 + 0.940237i \(0.610604\pi\)
\(620\) 29.7205 17.1591i 1.19360 0.689126i
\(621\) −22.1366 + 12.9373i −0.888311 + 0.519156i
\(622\) 13.2820i 0.532558i
\(623\) −0.726005 + 4.30278i −0.0290868 + 0.172387i
\(624\) −1.72860 4.72334i −0.0691994 0.189085i
\(625\) −14.4740 + 25.0696i −0.578959 + 1.00279i
\(626\) −0.287741 0.498381i −0.0115004 0.0199193i
\(627\) 7.84561 + 6.55969i 0.313323 + 0.261969i
\(628\) −4.96735 2.86790i −0.198219 0.114442i
\(629\) −5.97761 −0.238343
\(630\) 12.7360 + 7.16908i 0.507415 + 0.285623i
\(631\) 1.25547 0.0499794 0.0249897 0.999688i \(-0.492045\pi\)
0.0249897 + 0.999688i \(0.492045\pi\)
\(632\) −9.07523 5.23959i −0.360993 0.208420i
\(633\) −3.68145 3.07805i −0.146324 0.122341i
\(634\) −7.89411 13.6730i −0.313515 0.543024i
\(635\) −27.8280 + 48.1996i −1.10432 + 1.91274i
\(636\) −6.39344 17.4699i −0.253516 0.692725i
\(637\) −4.89458 5.66134i −0.193930 0.224311i
\(638\) 2.07719i 0.0822366i
\(639\) 29.5419 5.31660i 1.16866 0.210322i
\(640\) −37.7826 + 21.8138i −1.49349 + 0.862265i
\(641\) −35.6839 + 20.6021i −1.40943 + 0.813735i −0.995333 0.0964984i \(-0.969236\pi\)
−0.414097 + 0.910233i \(0.635902\pi\)
\(642\) 1.36973 7.84911i 0.0540591 0.309780i
\(643\) 17.3235i 0.683174i −0.939850 0.341587i \(-0.889036\pi\)
0.939850 0.341587i \(-0.110964\pi\)
\(644\) −8.09881 21.7506i −0.319138 0.857095i
\(645\) −37.5862 + 13.7554i −1.47996 + 0.541620i
\(646\) −5.78713 + 10.0236i −0.227692 + 0.394374i
\(647\) −10.0149 17.3464i −0.393728 0.681957i 0.599210 0.800592i \(-0.295482\pi\)
−0.992938 + 0.118635i \(0.962148\pi\)
\(648\) −5.58775 15.0215i −0.219508 0.590098i
\(649\) 0.416038 + 0.240199i 0.0163309 + 0.00942865i
\(650\) 5.17002 0.202785
\(651\) −22.2651 + 4.13617i −0.872639 + 0.162109i
\(652\) −29.7855 −1.16649
\(653\) −38.2992 22.1121i −1.49876 0.865312i −0.498765 0.866737i \(-0.666213\pi\)
−0.999999 + 0.00142529i \(0.999546\pi\)
\(654\) −4.60111 + 5.50308i −0.179918 + 0.215187i
\(655\) −42.1310 72.9730i −1.64619 2.85129i
\(656\) −3.03216 + 5.25185i −0.118386 + 0.205050i
\(657\) 24.0426 + 28.4484i 0.937992 + 1.10988i
\(658\) 2.47462 2.99372i 0.0964709 0.116707i
\(659\) 34.0478i 1.32631i −0.748480 0.663157i \(-0.769216\pi\)
0.748480 0.663157i \(-0.230784\pi\)
\(660\) −11.8492 2.06778i −0.461229 0.0804881i
\(661\) −27.2842 + 15.7526i −1.06123 + 0.612704i −0.925773 0.378079i \(-0.876585\pi\)
−0.135461 + 0.990783i \(0.543251\pi\)
\(662\) −1.76838 + 1.02098i −0.0687302 + 0.0396814i
\(663\) 7.58618 + 1.32385i 0.294623 + 0.0514141i
\(664\) 13.6370i 0.529218i
\(665\) −38.8775 + 47.0328i −1.50760 + 1.82385i
\(666\) −1.31207 1.55251i −0.0508418 0.0601585i
\(667\) −10.8719 + 18.8307i −0.420963 + 0.729129i
\(668\) 9.43652 + 16.3445i 0.365110 + 0.632389i
\(669\) 12.1856 14.5744i 0.471124 0.563480i
\(670\) 23.6262 + 13.6406i 0.912759 + 0.526981i
\(671\) 3.21542 0.124130
\(672\) 21.8153 4.05260i 0.841542 0.156332i
\(673\) 24.6061 0.948496 0.474248 0.880391i \(-0.342720\pi\)
0.474248 + 0.880391i \(0.342720\pi\)
\(674\) −1.06867 0.616994i −0.0411635 0.0237657i
\(675\) −53.3052 + 0.282195i −2.05172 + 0.0108617i
\(676\) −10.5397 18.2552i −0.405372 0.702125i
\(677\) −19.9027 + 34.4725i −0.764924 + 1.32489i 0.175363 + 0.984504i \(0.443890\pi\)
−0.940287 + 0.340384i \(0.889443\pi\)
\(678\) −5.62318 + 2.05791i −0.215957 + 0.0790337i
\(679\) 4.82479 + 12.9578i 0.185159 + 0.497273i
\(680\) 28.9282i 1.10935i
\(681\) −3.76385 + 21.5684i −0.144231 + 0.826502i
\(682\) −2.01737 + 1.16473i −0.0772492 + 0.0445999i
\(683\) −25.8221 + 14.9084i −0.988055 + 0.570454i −0.904692 0.426066i \(-0.859899\pi\)
−0.0833625 + 0.996519i \(0.526566\pi\)
\(684\) 30.9922 5.57761i 1.18502 0.213265i
\(685\) 10.7907i 0.412290i
\(686\) 7.46204 4.53131i 0.284902 0.173006i
\(687\) 0.388963 + 1.06283i 0.0148399 + 0.0405494i
\(688\) −8.03396 + 13.9152i −0.306292 + 0.530513i
\(689\) 3.22950 + 5.59366i 0.123034 + 0.213102i
\(690\) −12.0732 10.0944i −0.459619 0.384286i
\(691\) −20.7657 11.9891i −0.789965 0.456086i 0.0499853 0.998750i \(-0.484083\pi\)
−0.839950 + 0.542663i \(0.817416\pi\)
\(692\) 24.9117 0.947001
\(693\) 6.91674 + 3.89342i 0.262745 + 0.147899i
\(694\) 7.50776 0.284991
\(695\) 69.7237 + 40.2550i 2.64477 + 1.52696i
\(696\) −10.4273 8.71821i −0.395245 0.330463i
\(697\) −4.64243 8.04093i −0.175845 0.304572i
\(698\) −1.39974 + 2.42442i −0.0529809 + 0.0917656i
\(699\) 14.0078 + 38.2758i 0.529824 + 1.44773i
\(700\) 8.02825 47.5806i 0.303439 1.79838i
\(701\) 1.73905i 0.0656829i −0.999461 0.0328414i \(-0.989544\pi\)
0.999461 0.0328414i \(-0.0104556\pi\)
\(702\) 1.32132 + 2.26087i 0.0498701 + 0.0853311i
\(703\) 7.34983 4.24343i 0.277204 0.160044i
\(704\) −2.72793 + 1.57497i −0.102813 + 0.0593589i
\(705\) −3.62233 + 20.7574i −0.136425 + 0.781769i
\(706\) 8.13783i 0.306271i
\(707\) −5.47428 4.52507i −0.205882 0.170183i
\(708\) 1.38916 0.508390i 0.0522077 0.0191065i
\(709\) −16.6746 + 28.8813i −0.626228 + 1.08466i 0.362074 + 0.932149i \(0.382069\pi\)
−0.988302 + 0.152509i \(0.951265\pi\)
\(710\) 9.21172 + 15.9552i 0.345710 + 0.598787i
\(711\) −16.6103 5.97935i −0.622934 0.224243i
\(712\) 2.54354 + 1.46851i 0.0953230 + 0.0550348i
\(713\) 24.3847 0.913213
\(714\) −2.99515 + 8.46923i −0.112091 + 0.316953i
\(715\) 4.17624 0.156182
\(716\) 6.11995 + 3.53335i 0.228713 + 0.132048i
\(717\) 14.3265 17.1349i 0.535032 0.639916i
\(718\) 7.41710 + 12.8468i 0.276804 + 0.479438i
\(719\) −8.19635 + 14.1965i −0.305672 + 0.529440i −0.977411 0.211348i \(-0.932215\pi\)
0.671738 + 0.740788i \(0.265548\pi\)
\(720\) −24.3109 + 20.5459i −0.906012 + 0.765700i
\(721\) −33.0564 5.57758i −1.23108 0.207720i
\(722\) 7.47659i 0.278250i
\(723\) −36.7146 6.40700i −1.36543 0.238279i
\(724\) −7.03899 + 4.06396i −0.261602 + 0.151036i
\(725\) −39.1496 + 22.6030i −1.45398 + 0.839455i
\(726\) 0.804302 + 0.140357i 0.0298505 + 0.00520915i
\(727\) 13.3976i 0.496890i 0.968646 + 0.248445i \(0.0799195\pi\)
−0.968646 + 0.248445i \(0.920081\pi\)
\(728\) −4.72055 + 1.75769i −0.174955 + 0.0651443i
\(729\) −13.7468 23.2384i −0.509141 0.860683i
\(730\) −11.4308 + 19.7987i −0.423071 + 0.732781i
\(731\) −12.3005 21.3051i −0.454951 0.787999i
\(732\) 6.35087 7.59586i 0.234735 0.280751i
\(733\) −15.8778 9.16703i −0.586458 0.338592i 0.177237 0.984168i \(-0.443284\pi\)
−0.763696 + 0.645576i \(0.776617\pi\)
\(734\) −1.82424 −0.0673338
\(735\) −22.9995 + 41.4011i −0.848351 + 1.52710i
\(736\) −23.8920 −0.880670
\(737\) 12.8310 + 7.40799i 0.472637 + 0.272877i
\(738\) 1.06939 2.97071i 0.0393648 0.109353i
\(739\) 3.86930 + 6.70183i 0.142335 + 0.246531i 0.928375 0.371644i \(-0.121206\pi\)
−0.786041 + 0.618175i \(0.787872\pi\)
\(740\) −4.99101 + 8.64469i −0.183473 + 0.317785i
\(741\) −10.2674 + 3.75758i −0.377184 + 0.138038i
\(742\) −7.06103 + 2.62916i −0.259218 + 0.0965195i
\(743\) 18.1032i 0.664144i 0.943254 + 0.332072i \(0.107748\pi\)
−0.943254 + 0.332072i \(0.892252\pi\)
\(744\) −2.62033 + 15.0155i −0.0960661 + 0.550497i
\(745\) 53.9218 31.1318i 1.97554 1.14058i
\(746\) −1.22286 + 0.706020i −0.0447722 + 0.0258492i
\(747\) 4.06914 + 22.6103i 0.148882 + 0.827269i
\(748\) 7.39322i 0.270323i
\(749\) 25.4598 + 4.29582i 0.930280 + 0.156966i
\(750\) −5.76402 15.7500i −0.210472 0.575108i
\(751\) 7.09821 12.2945i 0.259017 0.448631i −0.706962 0.707252i \(-0.749935\pi\)
0.965979 + 0.258621i \(0.0832680\pi\)
\(752\) 4.22955 + 7.32579i 0.154236 + 0.267144i
\(753\) −3.14767 2.63176i −0.114707 0.0959065i
\(754\) 1.92323 + 1.11038i 0.0700400 + 0.0404376i
\(755\) 69.7613 2.53887
\(756\) 22.8590 8.64956i 0.831373 0.314581i
\(757\) −20.4284 −0.742484 −0.371242 0.928536i \(-0.621068\pi\)
−0.371242 + 0.928536i \(0.621068\pi\)
\(758\) 12.2697 + 7.08394i 0.445657 + 0.257300i
\(759\) −6.55678 5.48210i −0.237996 0.198988i
\(760\) 20.5358 + 35.5690i 0.744911 + 1.29022i
\(761\) 2.30246 3.98799i 0.0834643 0.144564i −0.821272 0.570538i \(-0.806735\pi\)
0.904736 + 0.425973i \(0.140068\pi\)
\(762\) −3.99796 10.9243i −0.144831 0.395745i
\(763\) −17.9163 14.8097i −0.648613 0.536147i
\(764\) 19.4689i 0.704360i
\(765\) −8.63188 47.9634i −0.312086 1.73412i
\(766\) −8.40920 + 4.85505i −0.303837 + 0.175420i
\(767\) −0.444794 + 0.256802i −0.0160606 + 0.00927257i
\(768\) −0.308230 + 1.76628i −0.0111223 + 0.0637352i
\(769\) 9.58284i 0.345566i 0.984960 + 0.172783i \(0.0552759\pi\)
−0.984960 + 0.172783i \(0.944724\pi\)
\(770\) −0.810544 + 4.80380i −0.0292100 + 0.173117i
\(771\) −3.71113 + 1.35816i −0.133653 + 0.0489131i
\(772\) 8.44170 14.6215i 0.303824 0.526238i
\(773\) 4.15980 + 7.20498i 0.149617 + 0.259145i 0.931086 0.364799i \(-0.118862\pi\)
−0.781469 + 0.623944i \(0.785529\pi\)
\(774\) 2.83344 7.87114i 0.101846 0.282922i
\(775\) 43.9043 + 25.3482i 1.57709 + 0.910533i
\(776\) 9.30650 0.334084
\(777\) 5.00700 4.27998i 0.179625 0.153544i
\(778\) −4.72834 −0.169519
\(779\) 11.4163 + 6.59121i 0.409031 + 0.236154i
\(780\) 8.24861 9.86562i 0.295348 0.353246i
\(781\) 5.00275 + 8.66502i 0.179012 + 0.310059i
\(782\) 4.83646 8.37700i 0.172951 0.299561i
\(783\) −19.8900 11.3435i −0.710810 0.405384i
\(784\) 3.57752 + 18.6736i 0.127769 + 0.666913i
\(785\) 12.6029i 0.449817i
\(786\) 17.3497 + 3.02766i 0.618843 + 0.107993i
\(787\) 47.0972 27.1916i 1.67883 0.969274i 0.716425 0.697664i \(-0.245777\pi\)
0.962407 0.271610i \(-0.0875562\pi\)
\(788\) 19.1676 11.0664i 0.682819 0.394226i
\(789\) 20.7284 + 3.61728i 0.737951 + 0.128778i
\(790\) 10.8355i 0.385508i
\(791\) −6.77091 18.1843i −0.240746 0.646561i
\(792\) 4.08034 3.44842i 0.144989 0.122534i
\(793\) −1.71883 + 2.97710i −0.0610375 + 0.105720i
\(794\) 8.07402 + 13.9846i 0.286536 + 0.496295i
\(795\) 26.2188 31.3585i 0.929884 1.11217i
\(796\) −34.6043 19.9788i −1.22652 0.708131i
\(797\) −18.5539 −0.657212 −0.328606 0.944467i \(-0.606579\pi\)
−0.328606 + 0.944467i \(0.606579\pi\)
\(798\) −2.32948 12.5396i −0.0824626 0.443898i
\(799\) −12.9514 −0.458189
\(800\) −43.0172 24.8360i −1.52089 0.878085i
\(801\) 4.65540 + 1.67585i 0.164491 + 0.0592131i
\(802\) −6.42280 11.1246i −0.226797 0.392824i
\(803\) −6.20787 + 10.7524i −0.219071 + 0.379442i
\(804\) 42.8430 15.6793i 1.51096 0.552965i
\(805\) 32.4910 39.3065i 1.14516 1.38537i
\(806\) 2.49047i 0.0877231i
\(807\) 0.667040 3.82240i 0.0234809 0.134555i
\(808\) −4.13998 + 2.39022i −0.145644 + 0.0840876i
\(809\) 12.5255 7.23159i 0.440373 0.254249i −0.263383 0.964691i \(-0.584838\pi\)
0.703756 + 0.710442i \(0.251505\pi\)
\(810\) 10.5624 12.7698i 0.371125 0.448683i
\(811\) 27.1561i 0.953578i 0.879018 + 0.476789i \(0.158199\pi\)
−0.879018 + 0.476789i \(0.841801\pi\)
\(812\) 13.2055 15.9756i 0.463422 0.560633i
\(813\) 10.6068 + 28.9827i 0.371997 + 1.01647i
\(814\) 0.338781 0.586787i 0.0118743 0.0205669i
\(815\) −32.7229 56.6777i −1.14623 1.98533i
\(816\) −15.0094 12.5493i −0.525435 0.439314i
\(817\) 30.2485 + 17.4640i 1.05826 + 0.610987i
\(818\) −5.51211 −0.192726
\(819\) −7.30226 + 4.32283i −0.255162 + 0.151052i
\(820\) −15.5048 −0.541452
\(821\) −33.6203 19.4107i −1.17336 0.677438i −0.218889 0.975750i \(-0.570243\pi\)
−0.954469 + 0.298311i \(0.903577\pi\)
\(822\) 1.73029 + 1.44669i 0.0603507 + 0.0504590i
\(823\) −4.75046 8.22804i −0.165591 0.286811i 0.771274 0.636503i \(-0.219620\pi\)
−0.936865 + 0.349692i \(0.886286\pi\)
\(824\) −11.2819 + 19.5409i −0.393025 + 0.680739i
\(825\) −6.10669 16.6863i −0.212608 0.580943i
\(826\) −0.209064 0.561474i −0.00727426 0.0195362i
\(827\) 2.24422i 0.0780391i 0.999238 + 0.0390195i \(0.0124235\pi\)
−0.999238 + 0.0390195i \(0.987577\pi\)
\(828\) −25.9010 + 4.66136i −0.900122 + 0.161993i
\(829\) 11.3765 6.56822i 0.395122 0.228124i −0.289255 0.957252i \(-0.593408\pi\)
0.684377 + 0.729128i \(0.260074\pi\)
\(830\) −12.2115 + 7.05033i −0.423868 + 0.244720i
\(831\) 1.90359 10.9083i 0.0660347 0.378405i
\(832\) 3.36766i 0.116753i
\(833\) −27.4988 9.55165i −0.952777 0.330945i
\(834\) −15.8026 + 5.78329i −0.547201 + 0.200259i
\(835\) −20.7343 + 35.9128i −0.717539 + 1.24281i
\(836\) 5.24835 + 9.09041i 0.181518 + 0.314398i
\(837\) 0.135937 + 25.6778i 0.00469868 + 0.887556i
\(838\) −3.52561 2.03551i −0.121790 0.0703156i
\(839\) 5.42803 0.187396 0.0936982 0.995601i \(-0.470131\pi\)
0.0936982 + 0.995601i \(0.470131\pi\)
\(840\) 20.7127 + 24.2310i 0.714655 + 0.836050i
\(841\) 9.58196 0.330412
\(842\) −9.61827 5.55311i −0.331468 0.191373i
\(843\) 7.30086 8.73208i 0.251455 0.300749i
\(844\) −2.46272 4.26555i −0.0847703 0.146826i
\(845\) 23.1581 40.1111i 0.796664 1.37986i
\(846\) −2.84282 3.36376i −0.0977381 0.115648i
\(847\) −0.440194 + 2.60888i −0.0151253 + 0.0896420i
\(848\) 16.4095i 0.563506i
\(849\) −4.36553 0.761820i −0.149825 0.0261456i
\(850\) 17.4160 10.0551i 0.597363 0.344888i
\(851\) −6.14245 + 3.54634i −0.210560 + 0.121567i
\(852\) 30.3506 + 5.29643i 1.03980 + 0.181453i
\(853\) 6.40649i 0.219354i −0.993967 0.109677i \(-0.965018\pi\)
0.993967 0.109677i \(-0.0349817\pi\)
\(854\) −3.09088 2.55493i −0.105768 0.0874280i
\(855\) 44.6620 + 52.8462i 1.52741 + 1.80730i
\(856\) 8.68926 15.0502i 0.296993 0.514407i
\(857\) 14.4948 + 25.1058i 0.495134 + 0.857596i 0.999984 0.00561020i \(-0.00178579\pi\)
−0.504851 + 0.863207i \(0.668452\pi\)
\(858\) −0.559902 + 0.669661i −0.0191147 + 0.0228619i
\(859\) 19.0459 + 10.9962i 0.649839 + 0.375184i 0.788394 0.615170i \(-0.210913\pi\)
−0.138556 + 0.990355i \(0.544246\pi\)
\(860\) −41.0814 −1.40086
\(861\) 9.64595 + 3.41130i 0.328733 + 0.116257i
\(862\) −3.90663 −0.133060
\(863\) 11.3830 + 6.57195i 0.387480 + 0.223712i 0.681068 0.732220i \(-0.261516\pi\)
−0.293588 + 0.955932i \(0.594849\pi\)
\(864\) −0.133191 25.1590i −0.00453124 0.855927i
\(865\) 27.3685 + 47.4035i 0.930555 + 1.61177i
\(866\) 1.99219 3.45057i 0.0676972 0.117255i
\(867\) 0.478598 0.175152i 0.0162540 0.00594849i
\(868\) −22.9202 3.86732i −0.777963 0.131265i
\(869\) 5.88458i 0.199621i
\(870\) 2.41600 13.8446i 0.0819100 0.469377i
\(871\) −13.7179 + 7.92002i −0.464813 + 0.268360i
\(872\) −13.5494 + 7.82273i −0.458839 + 0.264911i
\(873\) 15.4303 2.77696i 0.522236 0.0939860i
\(874\) 13.7334i 0.464538i
\(875\) 50.9326 18.9646i 1.72183 0.641122i
\(876\) 13.1392 + 35.9023i 0.443931 + 1.21303i
\(877\) −21.8068 + 37.7706i −0.736365 + 1.27542i 0.217757 + 0.976003i \(0.430126\pi\)
−0.954122 + 0.299418i \(0.903207\pi\)
\(878\) 2.53252 + 4.38645i 0.0854683 + 0.148035i
\(879\) −34.8669 29.1521i −1.17603 0.983277i
\(880\) −9.18854 5.30501i −0.309746 0.178832i
\(881\) 35.2188 1.18655 0.593276 0.804999i \(-0.297834\pi\)
0.593276 + 0.804999i \(0.297834\pi\)
\(882\) −3.55518 9.23858i −0.119709 0.311079i
\(883\) −0.651143 −0.0219127 −0.0109564 0.999940i \(-0.503488\pi\)
−0.0109564 + 0.999940i \(0.503488\pi\)
\(884\) 6.84526 + 3.95211i 0.230231 + 0.132924i
\(885\) 2.49355 + 2.08485i 0.0838197 + 0.0700814i
\(886\) −3.23125 5.59669i −0.108556 0.188024i
\(887\) −0.626447 + 1.08504i −0.0210340 + 0.0364320i −0.876351 0.481673i \(-0.840029\pi\)
0.855317 + 0.518105i \(0.173363\pi\)
\(888\) −1.52370 4.16347i −0.0511322 0.139717i
\(889\) 35.3272 13.1540i 1.18483 0.441171i
\(890\) 3.03688i 0.101796i
\(891\) 5.73628 6.93506i 0.192173 0.232333i
\(892\) 16.8868 9.74961i 0.565413 0.326441i
\(893\) 15.9246 9.19406i 0.532896 0.307667i
\(894\) −2.23722 + 12.8202i −0.0748239 + 0.428771i
\(895\) 15.5272i 0.519017i
\(896\) 29.1377 + 4.91639i 0.973421 + 0.164245i
\(897\) 8.58078 3.14031i 0.286504 0.104852i
\(898\) 4.00519 6.93719i 0.133655 0.231497i
\(899\) 10.8882 + 18.8589i 0.363141 + 0.628979i
\(900\) −51.4800 18.5317i −1.71600 0.617723i
\(901\) 21.7581 + 12.5621i 0.724868 + 0.418503i
\(902\) 1.05244 0.0350424
\(903\) 25.5578 + 9.03853i 0.850510 + 0.300783i
\(904\) −13.0603 −0.434380
\(905\) −15.4663 8.92948i −0.514118 0.296826i
\(906\) −9.35279 + 11.1863i −0.310726 + 0.371638i
\(907\) 6.45593 + 11.1820i 0.214366 + 0.371292i 0.953076 0.302731i \(-0.0978982\pi\)
−0.738710 + 0.674023i \(0.764565\pi\)
\(908\) −11.2363 + 19.4618i −0.372890 + 0.645864i
\(909\) −6.15092 + 5.19834i −0.204013 + 0.172418i
\(910\) −4.01448 3.31839i −0.133079 0.110003i
\(911\) 12.4393i 0.412134i 0.978538 + 0.206067i \(0.0660664\pi\)
−0.978538 + 0.206067i \(0.933934\pi\)
\(912\) 27.3636 + 4.77517i 0.906099 + 0.158122i
\(913\) −6.63190 + 3.82893i −0.219484 + 0.126719i
\(914\) 4.92914 2.84584i 0.163042 0.0941321i
\(915\) 21.4310 + 3.73989i 0.708488 + 0.123637i
\(916\) 1.16166i 0.0383823i
\(917\) −9.49547 + 56.2763i −0.313568 + 1.85841i
\(918\) 8.84821 + 5.04625i 0.292034 + 0.166551i
\(919\) 5.32262 9.21905i 0.175577 0.304109i −0.764784 0.644287i \(-0.777154\pi\)
0.940361 + 0.340179i \(0.110488\pi\)
\(920\) −17.1623 29.7259i −0.565824 0.980035i
\(921\) 0.515046 0.616012i 0.0169713 0.0202983i
\(922\) 15.0835 + 8.70845i 0.496748 + 0.286797i
\(923\) −10.6971 −0.352098
\(924\) 5.29356 + 6.19275i 0.174145 + 0.203727i
\(925\) −14.7459 −0.484841
\(926\) 3.40896 + 1.96816i 0.112025 + 0.0646778i
\(927\) −12.8748 + 35.7654i −0.422864 + 1.17469i
\(928\) −10.6682 18.4778i −0.350200 0.606565i
\(929\) 12.4288 21.5273i 0.407775 0.706287i −0.586865 0.809685i \(-0.699638\pi\)
0.994640 + 0.103398i \(0.0329715\pi\)
\(930\) −14.8007 + 5.41660i −0.485333 + 0.177617i
\(931\) 40.5920 7.77671i 1.33035 0.254871i
\(932\) 41.8351i 1.37035i
\(933\) −8.38980 + 48.0768i −0.274670 + 1.57397i
\(934\) 4.10207 2.36833i 0.134224 0.0774941i
\(935\) 14.0683 8.12232i 0.460082 0.265628i
\(936\) 1.01166 + 5.62131i 0.0330670 + 0.183738i
\(937\) 15.1506i 0.494950i 0.968894 + 0.247475i \(0.0796008\pi\)
−0.968894 + 0.247475i \(0.920399\pi\)
\(938\) −6.44774 17.3164i −0.210526 0.565402i
\(939\) −0.726726 1.98575i −0.0237158 0.0648026i
\(940\) −10.8138 + 18.7301i −0.352708 + 0.610908i
\(941\) −3.89566 6.74748i −0.126995 0.219962i 0.795516 0.605933i \(-0.207200\pi\)
−0.922511 + 0.385971i \(0.873867\pi\)
\(942\) 2.02088 + 1.68965i 0.0658439 + 0.0550519i
\(943\) −9.54091 5.50844i −0.310695 0.179380i
\(944\) 1.30484 0.0424691
\(945\) 41.5722 + 33.9949i 1.35234 + 1.10585i
\(946\) 2.78853 0.0906630
\(947\) −16.0640 9.27454i −0.522009 0.301382i 0.215747 0.976449i \(-0.430781\pi\)
−0.737756 + 0.675067i \(0.764115\pi\)
\(948\) −13.9013 11.6228i −0.451492 0.377491i
\(949\) −6.63695 11.4955i −0.215445 0.373161i
\(950\) −14.2760 + 24.7268i −0.463175 + 0.802242i
\(951\) −19.9376 54.4787i −0.646520 1.76659i
\(952\) −12.4834 + 15.1020i −0.404588 + 0.489458i
\(953\) 17.3867i 0.563211i 0.959530 + 0.281606i \(0.0908670\pi\)
−0.959530 + 0.281606i \(0.909133\pi\)
\(954\) 1.51324 + 8.40838i 0.0489930 + 0.272231i
\(955\) 37.0466 21.3889i 1.19880 0.692128i
\(956\) 19.8536 11.4625i 0.642112 0.370723i
\(957\) 1.31209 7.51881i 0.0424139 0.243049i
\(958\) 1.05506i 0.0340875i
\(959\) −4.65648 + 5.63327i −0.150366 + 0.181908i
\(960\) −20.0138 + 7.32443i −0.645941 + 0.236395i
\(961\) −3.28944 + 5.69747i −0.106111 + 0.183789i
\(962\) 0.362197 + 0.627344i 0.0116777 + 0.0202264i
\(963\) 9.91607 27.5463i 0.319541 0.887667i
\(964\) −33.1288 19.1269i −1.06701 0.616037i
\(965\) 37.0968 1.19419
\(966\) 1.94681 + 10.4797i 0.0626375 + 0.337179i
\(967\) 14.3108 0.460205 0.230103 0.973166i \(-0.426094\pi\)
0.230103 + 0.973166i \(0.426094\pi\)
\(968\) 1.54221 + 0.890393i 0.0495684 + 0.0286183i
\(969\) −27.2793 + 32.6270i −0.876339 + 1.04813i
\(970\) 4.81146 + 8.33369i 0.154487 + 0.267579i
\(971\) −3.47472 + 6.01839i −0.111509 + 0.193139i −0.916379 0.400312i \(-0.868902\pi\)
0.804870 + 0.593451i \(0.202235\pi\)
\(972\) −5.05295 27.2486i −0.162073 0.873999i
\(973\) −19.0281 51.1029i −0.610012 1.63828i
\(974\) 1.38167i 0.0442714i
\(975\) 18.7140 + 3.26574i 0.599327 + 0.104587i
\(976\) 7.56354 4.36681i 0.242103 0.139778i
\(977\) −40.2337 + 23.2289i −1.28719 + 0.743160i −0.978152 0.207890i \(-0.933340\pi\)
−0.309038 + 0.951050i \(0.600007\pi\)
\(978\) 13.4754 + 2.35157i 0.430896 + 0.0751948i
\(979\) 1.64928i 0.0527114i
\(980\) −36.7735 + 31.7930i −1.17469 + 1.01559i
\(981\) −20.1308 + 17.0132i −0.642727 + 0.543189i
\(982\) 5.20274 9.01142i 0.166026 0.287566i
\(983\) −3.37017 5.83731i −0.107492 0.186181i 0.807262 0.590194i \(-0.200949\pi\)
−0.914754 + 0.404012i \(0.867615\pi\)
\(984\) 4.41723 5.28315i 0.140816 0.168421i
\(985\) 42.1158 + 24.3156i 1.34192 + 0.774758i
\(986\) 8.63826 0.275098
\(987\) 10.8485 9.27327i 0.345310 0.295171i
\(988\) −11.2222 −0.357026
\(989\) −25.2795 14.5951i −0.803840 0.464097i
\(990\) 5.19749 + 1.87099i 0.165187 + 0.0594638i
\(991\) −4.43379 7.67955i −0.140844 0.243949i 0.786971 0.616990i \(-0.211648\pi\)
−0.927815 + 0.373041i \(0.878315\pi\)
\(992\) −11.9638 + 20.7220i −0.379852 + 0.657924i
\(993\) −7.04595 + 2.57861i −0.223596 + 0.0818296i
\(994\) 2.07614 12.3045i 0.0658510 0.390276i
\(995\) 87.7964i 2.78333i
\(996\) −4.05370 + 23.2293i −0.128446 + 0.736049i
\(997\) 8.35506 4.82380i 0.264608 0.152771i −0.361827 0.932245i \(-0.617847\pi\)
0.626435 + 0.779474i \(0.284514\pi\)
\(998\) −17.0502 + 9.84391i −0.539713 + 0.311603i
\(999\) −3.76866 6.44843i −0.119235 0.204019i
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 231.2.n.a.89.12 52
3.2 odd 2 inner 231.2.n.a.89.15 yes 52
7.3 odd 6 inner 231.2.n.a.122.15 yes 52
21.17 even 6 inner 231.2.n.a.122.12 yes 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
231.2.n.a.89.12 52 1.1 even 1 trivial
231.2.n.a.89.15 yes 52 3.2 odd 2 inner
231.2.n.a.122.12 yes 52 21.17 even 6 inner
231.2.n.a.122.15 yes 52 7.3 odd 6 inner