Properties

Label 91.2.f.c.29.3
Level $91$
Weight $2$
Character 91.29
Analytic conductor $0.727$
Analytic rank $0$
Dimension $8$
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] = [91,2,Mod(22,91)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(91, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("91.22");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.f (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.726638658394\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 7x^{6} + 38x^{4} - 16x^{3} + 15x^{2} + 3x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 29.3
Root \(0.355143 + 0.615126i\) of defining polynomial
Character \(\chi\) \(=\) 91.29
Dual form 91.2.f.c.22.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.355143 + 0.615126i) q^{2} +(-1.20394 - 2.08529i) q^{3} +(0.747746 - 1.29513i) q^{4} -1.28971 q^{5} +(0.855143 - 1.48115i) q^{6} +(0.500000 - 0.866025i) q^{7} +2.48280 q^{8} +(-1.39895 + 2.42305i) q^{9} +O(q^{10})\) \(q+(0.355143 + 0.615126i) q^{2} +(-1.20394 - 2.08529i) q^{3} +(0.747746 - 1.29513i) q^{4} -1.28971 q^{5} +(0.855143 - 1.48115i) q^{6} +(0.500000 - 0.866025i) q^{7} +2.48280 q^{8} +(-1.39895 + 2.42305i) q^{9} +(-0.458033 - 0.793337i) q^{10} +(1.20394 + 2.08529i) q^{11} -3.60097 q^{12} +(1.25409 + 3.38042i) q^{13} +0.710287 q^{14} +(1.55274 + 2.68942i) q^{15} +(-0.613742 - 1.06303i) q^{16} +(-1.95169 + 3.38042i) q^{17} -1.98731 q^{18} +(2.94534 - 5.10148i) q^{19} +(-0.964379 + 1.67035i) q^{20} -2.40788 q^{21} +(-0.855143 + 1.48115i) q^{22} +(3.16197 + 5.47670i) q^{23} +(-2.98915 - 5.17736i) q^{24} -3.33664 q^{25} +(-1.63400 + 1.97196i) q^{26} -0.486640 q^{27} +(-0.747746 - 1.29513i) q^{28} +(-2.80683 - 4.86157i) q^{29} +(-1.10289 + 1.91026i) q^{30} +2.20578 q^{31} +(2.91873 - 5.05540i) q^{32} +(2.89895 - 5.02113i) q^{33} -2.77252 q^{34} +(-0.644857 + 1.11692i) q^{35} +(2.09212 + 3.62365i) q^{36} +(2.55908 + 4.43246i) q^{37} +4.18407 q^{38} +(5.53930 - 6.68497i) q^{39} -3.20210 q^{40} +(3.89260 + 6.74219i) q^{41} +(-0.855143 - 1.48115i) q^{42} +(-0.144857 + 0.250899i) q^{43} +3.60097 q^{44} +(1.80424 - 3.12504i) q^{45} +(-2.24591 + 3.89003i) q^{46} +1.27702 q^{47} +(-1.47782 + 2.55966i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-1.18499 - 2.05245i) q^{50} +9.39887 q^{51} +(5.31585 + 0.903480i) q^{52} -13.6225 q^{53} +(-0.172827 - 0.299345i) q^{54} +(-1.55274 - 2.68942i) q^{55} +(1.24140 - 2.15017i) q^{56} -14.1841 q^{57} +(1.99365 - 3.45311i) q^{58} +(2.01528 - 3.49057i) q^{59} +4.64422 q^{60} +(2.30049 - 3.98456i) q^{61} +(0.783368 + 1.35683i) q^{62} +(1.39895 + 2.42305i) q^{63} +1.69131 q^{64} +(-1.61742 - 4.35978i) q^{65} +4.11817 q^{66} +(-3.78779 - 6.56065i) q^{67} +(2.91873 + 5.05540i) q^{68} +(7.61366 - 13.1872i) q^{69} -0.916066 q^{70} +(-3.61366 + 6.25905i) q^{71} +(-3.47331 + 6.01595i) q^{72} -15.0125 q^{73} +(-1.81768 + 3.14832i) q^{74} +(4.01712 + 6.95785i) q^{75} +(-4.40474 - 7.62923i) q^{76} +2.40788 q^{77} +(6.07935 + 1.03324i) q^{78} -9.30758 q^{79} +(0.791552 + 1.37101i) q^{80} +(4.78273 + 8.28393i) q^{81} +(-2.76486 + 4.78888i) q^{82} -1.36463 q^{83} +(-1.80049 + 3.11853i) q^{84} +(2.51712 - 4.35978i) q^{85} -0.205780 q^{86} +(-6.75852 + 11.7061i) q^{87} +(2.98915 + 5.17736i) q^{88} +(0.449849 + 0.779162i) q^{89} +2.56306 q^{90} +(3.55458 + 0.604136i) q^{91} +9.45742 q^{92} +(-2.65563 - 4.59968i) q^{93} +(0.453526 + 0.785530i) q^{94} +(-3.79865 + 6.57945i) q^{95} -14.0559 q^{96} +(-7.83288 + 13.5669i) q^{97} +(0.355143 - 0.615126i) q^{98} -6.73701 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + q^{2} - q^{3} - 5 q^{4} - 14 q^{5} + 5 q^{6} + 4 q^{7} - 12 q^{8} - 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + q^{2} - q^{3} - 5 q^{4} - 14 q^{5} + 5 q^{6} + 4 q^{7} - 12 q^{8} - 7 q^{9} + 11 q^{10} + q^{11} + 24 q^{12} + 4 q^{13} + 2 q^{14} - 3 q^{15} - 19 q^{16} + 4 q^{17} - 6 q^{18} - q^{19} + 2 q^{20} - 2 q^{21} - 5 q^{22} + 2 q^{23} + 3 q^{24} + 10 q^{25} + 12 q^{26} - 52 q^{27} + 5 q^{28} - q^{29} + 4 q^{30} - 8 q^{31} + 33 q^{32} + 19 q^{33} + 6 q^{34} - 7 q^{35} + 34 q^{36} + 10 q^{37} - 46 q^{38} + 20 q^{39} - 34 q^{40} + 22 q^{41} - 5 q^{42} - 3 q^{43} - 24 q^{44} + 11 q^{45} - 24 q^{46} + 4 q^{47} - 11 q^{48} - 4 q^{49} - 43 q^{50} + 14 q^{51} + 65 q^{52} + 4 q^{53} - 5 q^{54} + 3 q^{55} - 6 q^{56} - 34 q^{57} + 11 q^{58} + 8 q^{59} - 22 q^{60} - 8 q^{61} + 5 q^{62} + 7 q^{63} + 28 q^{64} + 7 q^{65} + 12 q^{66} + 6 q^{67} + 33 q^{68} + 18 q^{69} + 22 q^{70} + 14 q^{71} - 5 q^{72} - 16 q^{73} - 20 q^{74} + 7 q^{75} - 32 q^{76} + 2 q^{77} - q^{78} - 52 q^{79} - 7 q^{80} - 24 q^{81} + 14 q^{82} + 12 q^{84} - 5 q^{85} + 24 q^{86} - 13 q^{87} - 3 q^{88} + q^{89} + 52 q^{90} - 4 q^{91} + 24 q^{92} + 7 q^{93} - 33 q^{94} - 21 q^{95} - 116 q^{96} - 3 q^{97} + q^{98} + 46 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.355143 + 0.615126i 0.251124 + 0.434960i 0.963836 0.266497i \(-0.0858664\pi\)
−0.712711 + 0.701457i \(0.752533\pi\)
\(3\) −1.20394 2.08529i −0.695096 1.20394i −0.970148 0.242512i \(-0.922029\pi\)
0.275053 0.961429i \(-0.411305\pi\)
\(4\) 0.747746 1.29513i 0.373873 0.647567i
\(5\) −1.28971 −0.576777 −0.288389 0.957513i \(-0.593120\pi\)
−0.288389 + 0.957513i \(0.593120\pi\)
\(6\) 0.855143 1.48115i 0.349111 0.604678i
\(7\) 0.500000 0.866025i 0.188982 0.327327i
\(8\) 2.48280 0.877803
\(9\) −1.39895 + 2.42305i −0.466316 + 0.807683i
\(10\) −0.458033 0.793337i −0.144843 0.250875i
\(11\) 1.20394 + 2.08529i 0.363002 + 0.628738i 0.988453 0.151525i \(-0.0484185\pi\)
−0.625451 + 0.780263i \(0.715085\pi\)
\(12\) −3.60097 −1.03951
\(13\) 1.25409 + 3.38042i 0.347823 + 0.937560i
\(14\) 0.710287 0.189832
\(15\) 1.55274 + 2.68942i 0.400915 + 0.694406i
\(16\) −0.613742 1.06303i −0.153436 0.265758i
\(17\) −1.95169 + 3.38042i −0.473354 + 0.819873i −0.999535 0.0304998i \(-0.990290\pi\)
0.526181 + 0.850373i \(0.323623\pi\)
\(18\) −1.98731 −0.468413
\(19\) 2.94534 5.10148i 0.675708 1.17036i −0.300554 0.953765i \(-0.597171\pi\)
0.976261 0.216595i \(-0.0694952\pi\)
\(20\) −0.964379 + 1.67035i −0.215642 + 0.373502i
\(21\) −2.40788 −0.525443
\(22\) −0.855143 + 1.48115i −0.182317 + 0.315783i
\(23\) 3.16197 + 5.47670i 0.659317 + 1.14197i 0.980793 + 0.195053i \(0.0624879\pi\)
−0.321475 + 0.946918i \(0.604179\pi\)
\(24\) −2.98915 5.17736i −0.610157 1.05682i
\(25\) −3.33664 −0.667328
\(26\) −1.63400 + 1.97196i −0.320455 + 0.386733i
\(27\) −0.486640 −0.0936539
\(28\) −0.747746 1.29513i −0.141311 0.244757i
\(29\) −2.80683 4.86157i −0.521215 0.902772i −0.999696 0.0246732i \(-0.992145\pi\)
0.478480 0.878098i \(-0.341188\pi\)
\(30\) −1.10289 + 1.91026i −0.201359 + 0.348764i
\(31\) 2.20578 0.396170 0.198085 0.980185i \(-0.436528\pi\)
0.198085 + 0.980185i \(0.436528\pi\)
\(32\) 2.91873 5.05540i 0.515964 0.893676i
\(33\) 2.89895 5.02113i 0.504642 0.874066i
\(34\) −2.77252 −0.475482
\(35\) −0.644857 + 1.11692i −0.109001 + 0.188795i
\(36\) 2.09212 + 3.62365i 0.348686 + 0.603942i
\(37\) 2.55908 + 4.43246i 0.420711 + 0.728693i 0.996009 0.0892511i \(-0.0284473\pi\)
−0.575298 + 0.817944i \(0.695114\pi\)
\(38\) 4.18407 0.678746
\(39\) 5.53930 6.68497i 0.886998 1.07045i
\(40\) −3.20210 −0.506297
\(41\) 3.89260 + 6.74219i 0.607922 + 1.05295i 0.991582 + 0.129478i \(0.0413302\pi\)
−0.383660 + 0.923474i \(0.625336\pi\)
\(42\) −0.855143 1.48115i −0.131951 0.228547i
\(43\) −0.144857 + 0.250899i −0.0220904 + 0.0382618i −0.876859 0.480747i \(-0.840366\pi\)
0.854769 + 0.519009i \(0.173699\pi\)
\(44\) 3.60097 0.542867
\(45\) 1.80424 3.12504i 0.268961 0.465853i
\(46\) −2.24591 + 3.89003i −0.331141 + 0.573553i
\(47\) 1.27702 0.186273 0.0931364 0.995653i \(-0.470311\pi\)
0.0931364 + 0.995653i \(0.470311\pi\)
\(48\) −1.47782 + 2.55966i −0.213305 + 0.369455i
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) −1.18499 2.05245i −0.167582 0.290261i
\(51\) 9.39887 1.31610
\(52\) 5.31585 + 0.903480i 0.737175 + 0.125290i
\(53\) −13.6225 −1.87120 −0.935598 0.353067i \(-0.885139\pi\)
−0.935598 + 0.353067i \(0.885139\pi\)
\(54\) −0.172827 0.299345i −0.0235188 0.0407357i
\(55\) −1.55274 2.68942i −0.209371 0.362642i
\(56\) 1.24140 2.15017i 0.165889 0.287328i
\(57\) −14.1841 −1.87873
\(58\) 1.99365 3.45311i 0.261780 0.453416i
\(59\) 2.01528 3.49057i 0.262367 0.454433i −0.704503 0.709701i \(-0.748830\pi\)
0.966870 + 0.255268i \(0.0821636\pi\)
\(60\) 4.64422 0.599566
\(61\) 2.30049 3.98456i 0.294547 0.510170i −0.680332 0.732904i \(-0.738165\pi\)
0.974879 + 0.222733i \(0.0714979\pi\)
\(62\) 0.783368 + 1.35683i 0.0994878 + 0.172318i
\(63\) 1.39895 + 2.42305i 0.176251 + 0.305276i
\(64\) 1.69131 0.211413
\(65\) −1.61742 4.35978i −0.200616 0.540764i
\(66\) 4.11817 0.506912
\(67\) −3.78779 6.56065i −0.462753 0.801511i 0.536344 0.843999i \(-0.319805\pi\)
−0.999097 + 0.0424881i \(0.986472\pi\)
\(68\) 2.91873 + 5.05540i 0.353949 + 0.613057i
\(69\) 7.61366 13.1872i 0.916577 1.58756i
\(70\) −0.916066 −0.109491
\(71\) −3.61366 + 6.25905i −0.428863 + 0.742812i −0.996772 0.0802788i \(-0.974419\pi\)
0.567910 + 0.823091i \(0.307752\pi\)
\(72\) −3.47331 + 6.01595i −0.409334 + 0.708987i
\(73\) −15.0125 −1.75708 −0.878542 0.477665i \(-0.841483\pi\)
−0.878542 + 0.477665i \(0.841483\pi\)
\(74\) −1.81768 + 3.14832i −0.211301 + 0.365985i
\(75\) 4.01712 + 6.95785i 0.463857 + 0.803424i
\(76\) −4.40474 7.62923i −0.505258 0.875133i
\(77\) 2.40788 0.274404
\(78\) 6.07935 + 1.03324i 0.688350 + 0.116992i
\(79\) −9.30758 −1.04718 −0.523592 0.851969i \(-0.675408\pi\)
−0.523592 + 0.851969i \(0.675408\pi\)
\(80\) 0.791552 + 1.37101i 0.0884982 + 0.153283i
\(81\) 4.78273 + 8.28393i 0.531415 + 0.920437i
\(82\) −2.76486 + 4.78888i −0.305328 + 0.528844i
\(83\) −1.36463 −0.149788 −0.0748940 0.997192i \(-0.523862\pi\)
−0.0748940 + 0.997192i \(0.523862\pi\)
\(84\) −1.80049 + 3.11853i −0.196449 + 0.340260i
\(85\) 2.51712 4.35978i 0.273020 0.472884i
\(86\) −0.205780 −0.0221898
\(87\) −6.75852 + 11.7061i −0.724589 + 1.25503i
\(88\) 2.98915 + 5.17736i 0.318644 + 0.551908i
\(89\) 0.449849 + 0.779162i 0.0476839 + 0.0825910i 0.888882 0.458136i \(-0.151483\pi\)
−0.841198 + 0.540727i \(0.818149\pi\)
\(90\) 2.56306 0.270170
\(91\) 3.55458 + 0.604136i 0.372621 + 0.0633306i
\(92\) 9.45742 0.986004
\(93\) −2.65563 4.59968i −0.275376 0.476965i
\(94\) 0.453526 + 0.785530i 0.0467776 + 0.0810212i
\(95\) −3.79865 + 6.57945i −0.389733 + 0.675037i
\(96\) −14.0559 −1.43458
\(97\) −7.83288 + 13.5669i −0.795309 + 1.37752i 0.127334 + 0.991860i \(0.459358\pi\)
−0.922643 + 0.385655i \(0.873975\pi\)
\(98\) 0.355143 0.615126i 0.0358749 0.0621371i
\(99\) −6.73701 −0.677095
\(100\) −2.49496 + 4.32140i −0.249496 + 0.432140i
\(101\) −0.342452 0.593145i −0.0340753 0.0590201i 0.848485 0.529220i \(-0.177515\pi\)
−0.882560 + 0.470200i \(0.844182\pi\)
\(102\) 3.33795 + 5.78149i 0.330506 + 0.572453i
\(103\) 17.9249 1.76619 0.883097 0.469190i \(-0.155454\pi\)
0.883097 + 0.469190i \(0.155454\pi\)
\(104\) 3.11366 + 8.39292i 0.305320 + 0.822993i
\(105\) 3.10548 0.303064
\(106\) −4.83795 8.37957i −0.469903 0.813895i
\(107\) −4.24775 7.35731i −0.410645 0.711258i 0.584315 0.811527i \(-0.301363\pi\)
−0.994960 + 0.100268i \(0.968030\pi\)
\(108\) −0.363883 + 0.630264i −0.0350147 + 0.0606472i
\(109\) 12.0928 1.15828 0.579139 0.815228i \(-0.303389\pi\)
0.579139 + 0.815228i \(0.303389\pi\)
\(110\) 1.10289 1.91026i 0.105156 0.182136i
\(111\) 6.16197 10.6729i 0.584869 1.01302i
\(112\) −1.22748 −0.115986
\(113\) 7.12635 12.3432i 0.670391 1.16115i −0.307402 0.951580i \(-0.599460\pi\)
0.977793 0.209571i \(-0.0672069\pi\)
\(114\) −5.03738 8.72500i −0.471794 0.817171i
\(115\) −4.07804 7.06337i −0.380279 0.658663i
\(116\) −8.39519 −0.779474
\(117\) −9.94534 1.69031i −0.919447 0.156269i
\(118\) 2.86285 0.263547
\(119\) 1.95169 + 3.38042i 0.178911 + 0.309883i
\(120\) 3.85514 + 6.67730i 0.351925 + 0.609552i
\(121\) 2.60105 4.50515i 0.236459 0.409559i
\(122\) 3.26801 0.295872
\(123\) 9.37293 16.2344i 0.845129 1.46381i
\(124\) 1.64936 2.85678i 0.148117 0.256547i
\(125\) 10.7519 0.961677
\(126\) −0.993655 + 1.72106i −0.0885218 + 0.153324i
\(127\) 4.41231 + 7.64234i 0.391529 + 0.678148i 0.992651 0.121009i \(-0.0386129\pi\)
−0.601122 + 0.799157i \(0.705280\pi\)
\(128\) −5.23681 9.07043i −0.462873 0.801720i
\(129\) 0.697596 0.0614199
\(130\) 2.10740 2.54326i 0.184831 0.223059i
\(131\) −19.4294 −1.69756 −0.848778 0.528749i \(-0.822661\pi\)
−0.848778 + 0.528749i \(0.822661\pi\)
\(132\) −4.33536 7.50906i −0.377344 0.653580i
\(133\) −2.94534 5.10148i −0.255394 0.442355i
\(134\) 2.69042 4.65994i 0.232417 0.402558i
\(135\) 0.627626 0.0540174
\(136\) −4.84565 + 8.39292i −0.415511 + 0.719687i
\(137\) −5.11809 + 8.86479i −0.437268 + 0.757370i −0.997478 0.0709806i \(-0.977387\pi\)
0.560210 + 0.828351i \(0.310720\pi\)
\(138\) 10.8158 0.920699
\(139\) −4.07361 + 7.05571i −0.345519 + 0.598457i −0.985448 0.169977i \(-0.945631\pi\)
0.639929 + 0.768434i \(0.278964\pi\)
\(140\) 0.964379 + 1.67035i 0.0815049 + 0.141171i
\(141\) −1.53746 2.66296i −0.129477 0.224262i
\(142\) −5.13347 −0.430791
\(143\) −5.53930 + 6.68497i −0.463219 + 0.559025i
\(144\) 3.43438 0.286198
\(145\) 3.62001 + 6.27004i 0.300625 + 0.520698i
\(146\) −5.33160 9.23460i −0.441246 0.764261i
\(147\) −1.20394 + 2.08529i −0.0992994 + 0.171992i
\(148\) 7.65419 0.629170
\(149\) 4.89444 8.47742i 0.400968 0.694497i −0.592875 0.805295i \(-0.702007\pi\)
0.993843 + 0.110797i \(0.0353404\pi\)
\(150\) −2.85330 + 4.94207i −0.232971 + 0.403518i
\(151\) 14.7407 1.19958 0.599790 0.800158i \(-0.295251\pi\)
0.599790 + 0.800158i \(0.295251\pi\)
\(152\) 7.31270 12.6660i 0.593138 1.02735i
\(153\) −5.46062 9.45807i −0.441465 0.764640i
\(154\) 0.855143 + 1.48115i 0.0689094 + 0.119355i
\(155\) −2.84482 −0.228502
\(156\) −4.51595 12.1728i −0.361565 0.974604i
\(157\) 20.5844 1.64282 0.821409 0.570340i \(-0.193189\pi\)
0.821409 + 0.570340i \(0.193189\pi\)
\(158\) −3.30553 5.72534i −0.262973 0.455483i
\(159\) 16.4007 + 28.4069i 1.30066 + 2.25281i
\(160\) −3.76433 + 6.52001i −0.297597 + 0.515452i
\(161\) 6.32395 0.498397
\(162\) −3.39711 + 5.88397i −0.266902 + 0.462288i
\(163\) 1.99043 3.44753i 0.155902 0.270031i −0.777485 0.628902i \(-0.783505\pi\)
0.933387 + 0.358871i \(0.116838\pi\)
\(164\) 11.6427 0.909144
\(165\) −3.73881 + 6.47581i −0.291066 + 0.504141i
\(166\) −0.484640 0.839422i −0.0376154 0.0651518i
\(167\) −4.33923 7.51576i −0.335780 0.581587i 0.647855 0.761764i \(-0.275666\pi\)
−0.983634 + 0.180177i \(0.942333\pi\)
\(168\) −5.97829 −0.461235
\(169\) −9.85451 + 8.47872i −0.758039 + 0.652209i
\(170\) 3.57575 0.274248
\(171\) 8.24076 + 14.2734i 0.630187 + 1.09152i
\(172\) 0.216632 + 0.375218i 0.0165180 + 0.0286101i
\(173\) −0.466967 + 0.808810i −0.0355028 + 0.0614927i −0.883231 0.468938i \(-0.844637\pi\)
0.847728 + 0.530431i \(0.177970\pi\)
\(174\) −9.60097 −0.727848
\(175\) −1.66832 + 2.88961i −0.126113 + 0.218434i
\(176\) 1.47782 2.55966i 0.111395 0.192942i
\(177\) −9.70511 −0.729481
\(178\) −0.319522 + 0.553428i −0.0239492 + 0.0414812i
\(179\) −6.77305 11.7313i −0.506241 0.876836i −0.999974 0.00722197i \(-0.997701\pi\)
0.493733 0.869614i \(-0.335632\pi\)
\(180\) −2.69823 4.67348i −0.201114 0.348340i
\(181\) −8.86269 −0.658759 −0.329379 0.944198i \(-0.606839\pi\)
−0.329379 + 0.944198i \(0.606839\pi\)
\(182\) 0.890765 + 2.40107i 0.0660279 + 0.177979i
\(183\) −11.0786 −0.818953
\(184\) 7.85056 + 13.5976i 0.578751 + 1.00243i
\(185\) −3.30049 5.71661i −0.242657 0.420293i
\(186\) 1.88626 3.26709i 0.138307 0.239555i
\(187\) −9.39887 −0.687313
\(188\) 0.954889 1.65392i 0.0696424 0.120624i
\(189\) −0.243320 + 0.421442i −0.0176989 + 0.0306554i
\(190\) −5.39626 −0.391486
\(191\) 7.68674 13.3138i 0.556193 0.963355i −0.441616 0.897204i \(-0.645595\pi\)
0.997810 0.0661509i \(-0.0210719\pi\)
\(192\) −2.03623 3.52686i −0.146953 0.254529i
\(193\) 12.2477 + 21.2136i 0.881606 + 1.52699i 0.849555 + 0.527501i \(0.176871\pi\)
0.0320517 + 0.999486i \(0.489796\pi\)
\(194\) −11.1272 −0.798885
\(195\) −7.14411 + 8.62170i −0.511600 + 0.617413i
\(196\) −1.49549 −0.106821
\(197\) 3.35706 + 5.81460i 0.239181 + 0.414273i 0.960479 0.278351i \(-0.0897878\pi\)
−0.721299 + 0.692624i \(0.756454\pi\)
\(198\) −2.39260 4.14411i −0.170035 0.294509i
\(199\) 2.43641 4.21998i 0.172712 0.299147i −0.766655 0.642059i \(-0.778080\pi\)
0.939367 + 0.342913i \(0.111414\pi\)
\(200\) −8.28421 −0.585782
\(201\) −9.12056 + 15.7973i −0.643315 + 1.11425i
\(202\) 0.243239 0.421303i 0.0171143 0.0296428i
\(203\) −5.61366 −0.394002
\(204\) 7.02797 12.1728i 0.492056 0.852267i
\(205\) −5.02034 8.69549i −0.350636 0.607319i
\(206\) 6.36592 + 11.0261i 0.443534 + 0.768224i
\(207\) −17.6938 −1.22980
\(208\) 2.82381 3.40785i 0.195796 0.236292i
\(209\) 14.1841 0.981133
\(210\) 1.10289 + 1.91026i 0.0761066 + 0.131821i
\(211\) −1.84373 3.19344i −0.126928 0.219846i 0.795557 0.605879i \(-0.207178\pi\)
−0.922485 + 0.386033i \(0.873845\pi\)
\(212\) −10.1862 + 17.6430i −0.699590 + 1.21173i
\(213\) 17.4025 1.19240
\(214\) 3.01712 5.22580i 0.206246 0.357228i
\(215\) 0.186824 0.323588i 0.0127413 0.0220685i
\(216\) −1.20823 −0.0822096
\(217\) 1.10289 1.91026i 0.0748690 0.129677i
\(218\) 4.29467 + 7.43859i 0.290872 + 0.503805i
\(219\) 18.0742 + 31.3054i 1.22134 + 2.11543i
\(220\) −4.64422 −0.313113
\(221\) −13.8748 2.35817i −0.933323 0.158628i
\(222\) 8.75354 0.587499
\(223\) −4.40713 7.63338i −0.295123 0.511169i 0.679890 0.733314i \(-0.262027\pi\)
−0.975014 + 0.222145i \(0.928694\pi\)
\(224\) −2.91873 5.05540i −0.195016 0.337778i
\(225\) 4.66779 8.08484i 0.311186 0.538990i
\(226\) 10.1235 0.673406
\(227\) 6.72557 11.6490i 0.446391 0.773173i −0.551757 0.834005i \(-0.686042\pi\)
0.998148 + 0.0608325i \(0.0193756\pi\)
\(228\) −10.6061 + 18.3703i −0.702406 + 1.21660i
\(229\) 6.81576 0.450398 0.225199 0.974313i \(-0.427697\pi\)
0.225199 + 0.974313i \(0.427697\pi\)
\(230\) 2.89658 5.01702i 0.190995 0.330812i
\(231\) −2.89895 5.02113i −0.190737 0.330366i
\(232\) −6.96881 12.0703i −0.457524 0.792456i
\(233\) −25.0672 −1.64221 −0.821105 0.570777i \(-0.806642\pi\)
−0.821105 + 0.570777i \(0.806642\pi\)
\(234\) −2.49227 6.71794i −0.162925 0.439166i
\(235\) −1.64699 −0.107438
\(236\) −3.01384 5.22012i −0.196184 0.339801i
\(237\) 11.2058 + 19.4090i 0.727894 + 1.26075i
\(238\) −1.38626 + 2.40107i −0.0898577 + 0.155638i
\(239\) −2.78521 −0.180160 −0.0900800 0.995935i \(-0.528712\pi\)
−0.0900800 + 0.995935i \(0.528712\pi\)
\(240\) 1.90596 3.30123i 0.123029 0.213093i
\(241\) −3.48915 + 6.04338i −0.224756 + 0.389288i −0.956246 0.292563i \(-0.905492\pi\)
0.731490 + 0.681852i \(0.238825\pi\)
\(242\) 3.69498 0.237523
\(243\) 10.7863 18.6824i 0.691941 1.19848i
\(244\) −3.44036 5.95888i −0.220246 0.381478i
\(245\) 0.644857 + 1.11692i 0.0411984 + 0.0713577i
\(246\) 13.3149 0.848929
\(247\) 20.9389 + 3.55877i 1.33231 + 0.226439i
\(248\) 5.47651 0.347759
\(249\) 1.64294 + 2.84565i 0.104117 + 0.180336i
\(250\) 3.81846 + 6.61376i 0.241500 + 0.418291i
\(251\) 0.391515 0.678123i 0.0247122 0.0428028i −0.853405 0.521249i \(-0.825466\pi\)
0.878117 + 0.478446i \(0.158800\pi\)
\(252\) 4.18424 0.263582
\(253\) −7.61366 + 13.1872i −0.478667 + 0.829075i
\(254\) −3.13400 + 5.42825i −0.196645 + 0.340599i
\(255\) −12.1218 −0.759099
\(256\) 5.41095 9.37203i 0.338184 0.585752i
\(257\) −1.62902 2.82155i −0.101616 0.176003i 0.810735 0.585414i \(-0.199068\pi\)
−0.912350 + 0.409410i \(0.865734\pi\)
\(258\) 0.247746 + 0.429109i 0.0154240 + 0.0267152i
\(259\) 5.11817 0.318028
\(260\) −6.85592 1.16523i −0.425186 0.0722645i
\(261\) 15.7064 0.972205
\(262\) −6.90023 11.9516i −0.426298 0.738369i
\(263\) −14.7915 25.6196i −0.912081 1.57977i −0.811119 0.584881i \(-0.801141\pi\)
−0.100962 0.994890i \(-0.532192\pi\)
\(264\) 7.19752 12.4665i 0.442976 0.767258i
\(265\) 17.5691 1.07926
\(266\) 2.09204 3.62351i 0.128271 0.222172i
\(267\) 1.08318 1.87613i 0.0662898 0.114817i
\(268\) −11.3292 −0.692043
\(269\) −0.618249 + 1.07084i −0.0376953 + 0.0652902i −0.884258 0.467000i \(-0.845335\pi\)
0.846562 + 0.532290i \(0.178668\pi\)
\(270\) 0.222897 + 0.386069i 0.0135651 + 0.0234954i
\(271\) −12.6036 21.8300i −0.765612 1.32608i −0.939923 0.341388i \(-0.889103\pi\)
0.174311 0.984691i \(-0.444230\pi\)
\(272\) 4.79133 0.290517
\(273\) −3.01971 8.13966i −0.182761 0.492635i
\(274\) −7.27062 −0.439234
\(275\) −4.01712 6.95785i −0.242241 0.419574i
\(276\) −11.3862 19.7214i −0.685367 1.18709i
\(277\) −4.76801 + 8.25843i −0.286482 + 0.496201i −0.972967 0.230942i \(-0.925819\pi\)
0.686486 + 0.727143i \(0.259152\pi\)
\(278\) −5.78687 −0.347073
\(279\) −3.08577 + 5.34471i −0.184740 + 0.319980i
\(280\) −1.60105 + 2.77310i −0.0956811 + 0.165725i
\(281\) 9.56546 0.570628 0.285314 0.958434i \(-0.407902\pi\)
0.285314 + 0.958434i \(0.407902\pi\)
\(282\) 1.09204 1.89146i 0.0650299 0.112635i
\(283\) −5.71602 9.90044i −0.339782 0.588520i 0.644609 0.764512i \(-0.277020\pi\)
−0.984392 + 0.175992i \(0.943687\pi\)
\(284\) 5.40421 + 9.36036i 0.320681 + 0.555435i
\(285\) 18.2934 1.08361
\(286\) −6.07935 1.03324i −0.359479 0.0610971i
\(287\) 7.78521 0.459546
\(288\) 8.16632 + 14.1445i 0.481205 + 0.833472i
\(289\) 0.881831 + 1.52738i 0.0518724 + 0.0898457i
\(290\) −2.57124 + 4.45352i −0.150989 + 0.261520i
\(291\) 37.7213 2.21126
\(292\) −11.2256 + 19.4433i −0.656927 + 1.13783i
\(293\) 4.67781 8.10220i 0.273281 0.473336i −0.696419 0.717635i \(-0.745225\pi\)
0.969700 + 0.244299i \(0.0785579\pi\)
\(294\) −1.71029 −0.0997459
\(295\) −2.59913 + 4.50183i −0.151327 + 0.262107i
\(296\) 6.35370 + 11.0049i 0.369301 + 0.639649i
\(297\) −0.585886 1.01478i −0.0339965 0.0588837i
\(298\) 6.95291 0.402771
\(299\) −14.5482 + 17.5571i −0.841341 + 1.01535i
\(300\) 12.0151 0.693695
\(301\) 0.144857 + 0.250899i 0.00834940 + 0.0144616i
\(302\) 5.23506 + 9.06738i 0.301244 + 0.521769i
\(303\) −0.824585 + 1.42822i −0.0473712 + 0.0820493i
\(304\) −7.23072 −0.414711
\(305\) −2.96697 + 5.13894i −0.169888 + 0.294255i
\(306\) 3.87861 6.71794i 0.221725 0.384039i
\(307\) 8.11449 0.463119 0.231559 0.972821i \(-0.425617\pi\)
0.231559 + 0.972821i \(0.425617\pi\)
\(308\) 1.80049 3.11853i 0.102592 0.177695i
\(309\) −21.5805 37.3786i −1.22767 2.12639i
\(310\) −1.01032 1.74993i −0.0573823 0.0993891i
\(311\) −8.64016 −0.489938 −0.244969 0.969531i \(-0.578778\pi\)
−0.244969 + 0.969531i \(0.578778\pi\)
\(312\) 13.7530 16.5975i 0.778609 0.939646i
\(313\) −5.22732 −0.295466 −0.147733 0.989027i \(-0.547198\pi\)
−0.147733 + 0.989027i \(0.547198\pi\)
\(314\) 7.31043 + 12.6620i 0.412551 + 0.714560i
\(315\) −1.80424 3.12504i −0.101658 0.176076i
\(316\) −6.95971 + 12.0546i −0.391514 + 0.678123i
\(317\) 11.1929 0.628657 0.314329 0.949314i \(-0.398221\pi\)
0.314329 + 0.949314i \(0.398221\pi\)
\(318\) −11.6492 + 20.1770i −0.653255 + 1.13147i
\(319\) 6.75852 11.7061i 0.378404 0.655416i
\(320\) −2.18130 −0.121938
\(321\) −10.2281 + 17.7155i −0.570875 + 0.988785i
\(322\) 2.24591 + 3.89003i 0.125160 + 0.216783i
\(323\) 11.4968 + 19.9130i 0.639698 + 1.10799i
\(324\) 14.3051 0.794727
\(325\) −4.18445 11.2792i −0.232112 0.625660i
\(326\) 2.82755 0.156604
\(327\) −14.5590 25.2169i −0.805115 1.39450i
\(328\) 9.66456 + 16.7395i 0.533636 + 0.924285i
\(329\) 0.638511 1.10593i 0.0352023 0.0609721i
\(330\) −5.31126 −0.292375
\(331\) −10.0234 + 17.3610i −0.550935 + 0.954247i 0.447272 + 0.894398i \(0.352395\pi\)
−0.998207 + 0.0598495i \(0.980938\pi\)
\(332\) −1.02040 + 1.76738i −0.0560017 + 0.0969978i
\(333\) −14.3201 −0.784737
\(334\) 3.08210 5.33835i 0.168645 0.292101i
\(335\) 4.88517 + 8.46136i 0.266905 + 0.462294i
\(336\) 1.47782 + 2.55966i 0.0806217 + 0.139641i
\(337\) 18.5866 1.01248 0.506239 0.862393i \(-0.331035\pi\)
0.506239 + 0.862393i \(0.331035\pi\)
\(338\) −8.71525 3.05061i −0.474047 0.165931i
\(339\) −34.3188 −1.86394
\(340\) −3.76433 6.52001i −0.204150 0.353597i
\(341\) 2.65563 + 4.59968i 0.143810 + 0.249087i
\(342\) −5.85330 + 10.1382i −0.316510 + 0.548212i
\(343\) −1.00000 −0.0539949
\(344\) −0.359650 + 0.622933i −0.0193911 + 0.0335863i
\(345\) −9.81944 + 17.0078i −0.528661 + 0.915668i
\(346\) −0.663361 −0.0356625
\(347\) −11.1708 + 19.3484i −0.599681 + 1.03868i 0.393186 + 0.919459i \(0.371373\pi\)
−0.992868 + 0.119220i \(0.961961\pi\)
\(348\) 10.1073 + 17.5064i 0.541809 + 0.938441i
\(349\) −4.39316 7.60917i −0.235160 0.407310i 0.724159 0.689633i \(-0.242228\pi\)
−0.959319 + 0.282323i \(0.908895\pi\)
\(350\) −2.36997 −0.126680
\(351\) −0.610291 1.64505i −0.0325749 0.0878061i
\(352\) 14.0559 0.749184
\(353\) −3.85949 6.68483i −0.205420 0.355798i 0.744847 0.667236i \(-0.232523\pi\)
−0.950266 + 0.311438i \(0.899189\pi\)
\(354\) −3.44671 5.96987i −0.183190 0.317295i
\(355\) 4.66059 8.07238i 0.247358 0.428437i
\(356\) 1.34549 0.0713110
\(357\) 4.69943 8.13966i 0.248720 0.430796i
\(358\) 4.81081 8.33256i 0.254259 0.440389i
\(359\) −10.5956 −0.559216 −0.279608 0.960114i \(-0.590205\pi\)
−0.279608 + 0.960114i \(0.590205\pi\)
\(360\) 4.47958 7.75886i 0.236094 0.408928i
\(361\) −7.85008 13.5967i −0.413162 0.715618i
\(362\) −3.14753 5.45167i −0.165430 0.286534i
\(363\) −12.5261 −0.657447
\(364\) 3.44036 4.15192i 0.180324 0.217620i
\(365\) 19.3619 1.01345
\(366\) −3.93449 6.81474i −0.205659 0.356212i
\(367\) −2.91033 5.04085i −0.151918 0.263130i 0.780014 0.625762i \(-0.215212\pi\)
−0.931933 + 0.362632i \(0.881878\pi\)
\(368\) 3.88128 6.72257i 0.202325 0.350438i
\(369\) −21.7822 −1.13394
\(370\) 2.34429 4.06043i 0.121874 0.211092i
\(371\) −6.81126 + 11.7974i −0.353623 + 0.612493i
\(372\) −7.94295 −0.411823
\(373\) −13.0284 + 22.5659i −0.674587 + 1.16842i 0.302002 + 0.953307i \(0.402345\pi\)
−0.976589 + 0.215112i \(0.930988\pi\)
\(374\) −3.33795 5.78149i −0.172601 0.298954i
\(375\) −12.9446 22.4207i −0.668458 1.15780i
\(376\) 3.17059 0.163511
\(377\) 12.9141 15.5851i 0.665112 0.802675i
\(378\) −0.345654 −0.0177785
\(379\) −7.82662 13.5561i −0.402026 0.696330i 0.591944 0.805979i \(-0.298361\pi\)
−0.993970 + 0.109649i \(0.965027\pi\)
\(380\) 5.68085 + 9.83952i 0.291421 + 0.504757i
\(381\) 10.6243 18.4019i 0.544300 0.942756i
\(382\) 10.9196 0.558694
\(383\) 6.27939 10.8762i 0.320862 0.555749i −0.659804 0.751438i \(-0.729361\pi\)
0.980666 + 0.195688i \(0.0626941\pi\)
\(384\) −12.6096 + 21.8405i −0.643482 + 1.11454i
\(385\) −3.10548 −0.158270
\(386\) −8.69935 + 15.0677i −0.442785 + 0.766927i
\(387\) −0.405294 0.701990i −0.0206023 0.0356842i
\(388\) 11.7140 + 20.2893i 0.594689 + 1.03003i
\(389\) −0.503007 −0.0255035 −0.0127517 0.999919i \(-0.504059\pi\)
−0.0127517 + 0.999919i \(0.504059\pi\)
\(390\) −7.84061 1.33259i −0.397025 0.0674783i
\(391\) −24.6847 −1.24836
\(392\) −1.24140 2.15017i −0.0627002 0.108600i
\(393\) 23.3919 + 40.5159i 1.17996 + 2.04376i
\(394\) −2.38448 + 4.13003i −0.120128 + 0.208068i
\(395\) 12.0041 0.603992
\(396\) −5.03757 + 8.72533i −0.253148 + 0.438464i
\(397\) 1.17522 2.03554i 0.0589827 0.102161i −0.835026 0.550210i \(-0.814548\pi\)
0.894009 + 0.448049i \(0.147881\pi\)
\(398\) 3.46110 0.173489
\(399\) −7.09204 + 12.2838i −0.355046 + 0.614958i
\(400\) 2.04784 + 3.54696i 0.102392 + 0.177348i
\(401\) 17.3023 + 29.9685i 0.864037 + 1.49656i 0.868000 + 0.496564i \(0.165405\pi\)
−0.00396357 + 0.999992i \(0.501262\pi\)
\(402\) −12.9564 −0.646208
\(403\) 2.76625 + 7.45647i 0.137797 + 0.371433i
\(404\) −1.02427 −0.0509593
\(405\) −6.16835 10.6839i −0.306508 0.530887i
\(406\) −1.99365 3.45311i −0.0989434 0.171375i
\(407\) −6.16197 + 10.6729i −0.305438 + 0.529034i
\(408\) 23.3355 1.15528
\(409\) 4.01205 6.94908i 0.198383 0.343610i −0.749621 0.661867i \(-0.769764\pi\)
0.948004 + 0.318257i \(0.103098\pi\)
\(410\) 3.56588 6.17629i 0.176106 0.305025i
\(411\) 24.6475 1.21577
\(412\) 13.4033 23.2152i 0.660333 1.14373i
\(413\) −2.01528 3.49057i −0.0991654 0.171760i
\(414\) −6.28382 10.8839i −0.308833 0.534914i
\(415\) 1.75999 0.0863943
\(416\) 20.7497 + 3.52662i 1.01734 + 0.172907i
\(417\) 19.6176 0.960676
\(418\) 5.03738 + 8.72500i 0.246386 + 0.426754i
\(419\) 5.83472 + 10.1060i 0.285045 + 0.493712i 0.972620 0.232401i \(-0.0746582\pi\)
−0.687575 + 0.726113i \(0.741325\pi\)
\(420\) 2.32211 4.02201i 0.113307 0.196254i
\(421\) −18.3381 −0.893746 −0.446873 0.894597i \(-0.647462\pi\)
−0.446873 + 0.894597i \(0.647462\pi\)
\(422\) 1.30958 2.26826i 0.0637494 0.110417i
\(423\) −1.78649 + 3.09429i −0.0868621 + 0.150449i
\(424\) −33.8220 −1.64254
\(425\) 6.51208 11.2792i 0.315882 0.547124i
\(426\) 6.18040 + 10.7048i 0.299441 + 0.518647i
\(427\) −2.30049 3.98456i −0.111328 0.192826i
\(428\) −12.7049 −0.614117
\(429\) 20.6091 + 3.50272i 0.995015 + 0.169113i
\(430\) 0.265397 0.0127986
\(431\) 15.6218 + 27.0577i 0.752474 + 1.30332i 0.946620 + 0.322351i \(0.104473\pi\)
−0.194146 + 0.980973i \(0.562194\pi\)
\(432\) 0.298671 + 0.517314i 0.0143698 + 0.0248893i
\(433\) 15.2756 26.4582i 0.734100 1.27150i −0.221017 0.975270i \(-0.570938\pi\)
0.955117 0.296229i \(-0.0957291\pi\)
\(434\) 1.56674 0.0752057
\(435\) 8.71655 15.0975i 0.417927 0.723870i
\(436\) 9.04234 15.6618i 0.433049 0.750064i
\(437\) 37.2524 1.78202
\(438\) −12.8379 + 22.2358i −0.613417 + 1.06247i
\(439\) 6.07361 + 10.5198i 0.289878 + 0.502083i 0.973780 0.227490i \(-0.0730520\pi\)
−0.683903 + 0.729573i \(0.739719\pi\)
\(440\) −3.85514 6.67730i −0.183787 0.318328i
\(441\) 2.79790 0.133233
\(442\) −3.47699 9.37227i −0.165384 0.445794i
\(443\) −8.46532 −0.402200 −0.201100 0.979571i \(-0.564452\pi\)
−0.201100 + 0.979571i \(0.564452\pi\)
\(444\) −9.21519 15.9612i −0.437333 0.757484i
\(445\) −0.580177 1.00490i −0.0275030 0.0476366i
\(446\) 3.13033 5.42189i 0.148225 0.256734i
\(447\) −23.5705 −1.11485
\(448\) 0.845654 1.46472i 0.0399534 0.0692013i
\(449\) 11.6632 20.2013i 0.550420 0.953356i −0.447824 0.894122i \(-0.647801\pi\)
0.998244 0.0592342i \(-0.0188659\pi\)
\(450\) 6.63093 0.312585
\(451\) −9.37293 + 16.2344i −0.441354 + 0.764448i
\(452\) −10.6574 18.4592i −0.501282 0.868247i
\(453\) −17.7469 30.7386i −0.833823 1.44422i
\(454\) 9.55416 0.448399
\(455\) −4.58439 0.779162i −0.214919 0.0365277i
\(456\) −35.2162 −1.64915
\(457\) −7.74332 13.4118i −0.362217 0.627379i 0.626108 0.779736i \(-0.284647\pi\)
−0.988325 + 0.152358i \(0.951313\pi\)
\(458\) 2.42057 + 4.19256i 0.113106 + 0.195905i
\(459\) 0.949769 1.64505i 0.0443314 0.0767842i
\(460\) −12.1974 −0.568705
\(461\) 4.64102 8.03848i 0.216154 0.374389i −0.737475 0.675374i \(-0.763982\pi\)
0.953629 + 0.300985i \(0.0973154\pi\)
\(462\) 2.05908 3.56644i 0.0957973 0.165926i
\(463\) 28.8283 1.33976 0.669882 0.742467i \(-0.266345\pi\)
0.669882 + 0.742467i \(0.266345\pi\)
\(464\) −3.44534 + 5.96751i −0.159946 + 0.277035i
\(465\) 3.42500 + 5.93227i 0.158831 + 0.275103i
\(466\) −8.90246 15.4195i −0.412399 0.714295i
\(467\) −2.87393 −0.132990 −0.0664948 0.997787i \(-0.521182\pi\)
−0.0664948 + 0.997787i \(0.521182\pi\)
\(468\) −9.62577 + 11.6166i −0.444951 + 0.536979i
\(469\) −7.57559 −0.349808
\(470\) −0.584919 1.01311i −0.0269803 0.0467312i
\(471\) −24.7825 42.9245i −1.14192 1.97786i
\(472\) 5.00354 8.66638i 0.230307 0.398903i
\(473\) −0.697596 −0.0320755
\(474\) −7.95932 + 13.7859i −0.365583 + 0.633209i
\(475\) −9.82754 + 17.0218i −0.450919 + 0.781014i
\(476\) 5.83747 0.267560
\(477\) 19.0572 33.0080i 0.872569 1.51133i
\(478\) −0.989147 1.71325i −0.0452425 0.0783624i
\(479\) 11.3041 + 19.5792i 0.516497 + 0.894598i 0.999817 + 0.0191546i \(0.00609749\pi\)
−0.483320 + 0.875444i \(0.660569\pi\)
\(480\) 18.1281 0.827432
\(481\) −11.7743 + 14.2095i −0.536861 + 0.647898i
\(482\) −4.95659 −0.225766
\(483\) −7.61366 13.1872i −0.346434 0.600041i
\(484\) −3.88985 6.73742i −0.176812 0.306247i
\(485\) 10.1022 17.4975i 0.458716 0.794519i
\(486\) 15.3227 0.695053
\(487\) −1.43401 + 2.48379i −0.0649814 + 0.112551i −0.896686 0.442668i \(-0.854032\pi\)
0.831704 + 0.555219i \(0.187365\pi\)
\(488\) 5.71165 9.89287i 0.258554 0.447829i
\(489\) −9.58544 −0.433469
\(490\) −0.458033 + 0.793337i −0.0206918 + 0.0358393i
\(491\) 11.3600 + 19.6762i 0.512672 + 0.887973i 0.999892 + 0.0146943i \(0.00467751\pi\)
−0.487220 + 0.873279i \(0.661989\pi\)
\(492\) −14.0172 24.2784i −0.631942 1.09456i
\(493\) 21.9122 0.986877
\(494\) 5.24721 + 14.1439i 0.236083 + 0.636366i
\(495\) 8.68881 0.390533
\(496\) −1.35378 2.34482i −0.0607865 0.105285i
\(497\) 3.61366 + 6.25905i 0.162095 + 0.280757i
\(498\) −1.16696 + 2.02123i −0.0522926 + 0.0905734i
\(499\) −18.0151 −0.806466 −0.403233 0.915097i \(-0.632114\pi\)
−0.403233 + 0.915097i \(0.632114\pi\)
\(500\) 8.03968 13.9251i 0.359545 0.622751i
\(501\) −10.4483 + 18.0971i −0.466798 + 0.808518i
\(502\) 0.556175 0.0248233
\(503\) 15.5748 26.9764i 0.694447 1.20282i −0.275920 0.961181i \(-0.588983\pi\)
0.970367 0.241636i \(-0.0776841\pi\)
\(504\) 3.47331 + 6.01595i 0.154714 + 0.267972i
\(505\) 0.441665 + 0.764987i 0.0196539 + 0.0340415i
\(506\) −10.8158 −0.480819
\(507\) 29.5448 + 10.3416i 1.31213 + 0.459286i
\(508\) 13.1972 0.585529
\(509\) 19.7509 + 34.2096i 0.875444 + 1.51631i 0.856289 + 0.516497i \(0.172764\pi\)
0.0191556 + 0.999817i \(0.493902\pi\)
\(510\) −4.30499 7.45647i −0.190628 0.330178i
\(511\) −7.50626 + 13.0012i −0.332058 + 0.575141i
\(512\) −13.2606 −0.586042
\(513\) −1.43332 + 2.48258i −0.0632826 + 0.109609i
\(514\) 1.15707 2.00411i 0.0510363 0.0883974i
\(515\) −23.1180 −1.01870
\(516\) 0.521625 0.903480i 0.0229632 0.0397735i
\(517\) 1.53746 + 2.66296i 0.0676174 + 0.117117i
\(518\) 1.81768 + 3.14832i 0.0798644 + 0.138329i
\(519\) 2.24880 0.0987115
\(520\) −4.01573 10.8245i −0.176101 0.474684i
\(521\) −17.7672 −0.778394 −0.389197 0.921155i \(-0.627247\pi\)
−0.389197 + 0.921155i \(0.627247\pi\)
\(522\) 5.57804 + 9.66145i 0.244144 + 0.422870i
\(523\) 0.894522 + 1.54936i 0.0391147 + 0.0677487i 0.884920 0.465743i \(-0.154213\pi\)
−0.845805 + 0.533492i \(0.820880\pi\)
\(524\) −14.5283 + 25.1637i −0.634671 + 1.09928i
\(525\) 8.03424 0.350643
\(526\) 10.5062 18.1972i 0.458091 0.793438i
\(527\) −4.30499 + 7.45647i −0.187528 + 0.324809i
\(528\) −7.11683 −0.309720
\(529\) −8.49616 + 14.7158i −0.369398 + 0.639817i
\(530\) 6.23956 + 10.8072i 0.271029 + 0.469436i
\(531\) 5.63854 + 9.76624i 0.244692 + 0.423819i
\(532\) −8.80948 −0.381939
\(533\) −17.9098 + 21.6140i −0.775758 + 0.936205i
\(534\) 1.53874 0.0665879
\(535\) 5.47838 + 9.48882i 0.236851 + 0.410238i
\(536\) −9.40434 16.2888i −0.406206 0.703569i
\(537\) −16.3087 + 28.2475i −0.703772 + 1.21897i
\(538\) −0.878269 −0.0378649
\(539\) 1.20394 2.08529i 0.0518574 0.0898197i
\(540\) 0.469305 0.812860i 0.0201957 0.0349799i
\(541\) 15.4027 0.662214 0.331107 0.943593i \(-0.392578\pi\)
0.331107 + 0.943593i \(0.392578\pi\)
\(542\) 8.95214 15.5056i 0.384527 0.666021i
\(543\) 10.6702 + 18.4813i 0.457900 + 0.793107i
\(544\) 11.3929 + 19.7331i 0.488467 + 0.846050i
\(545\) −15.5962 −0.668069
\(546\) 3.93449 4.74825i 0.168381 0.203206i
\(547\) −3.96944 −0.169721 −0.0848605 0.996393i \(-0.527044\pi\)
−0.0848605 + 0.996393i \(0.527044\pi\)
\(548\) 7.65406 + 13.2572i 0.326965 + 0.566321i
\(549\) 6.43652 + 11.1484i 0.274704 + 0.475801i
\(550\) 2.85330 4.94207i 0.121665 0.210731i
\(551\) −33.0683 −1.40876
\(552\) 18.9032 32.7413i 0.804574 1.39356i
\(553\) −4.65379 + 8.06060i −0.197899 + 0.342772i
\(554\) −6.77331 −0.287770
\(555\) −7.94718 + 13.7649i −0.337339 + 0.584288i
\(556\) 6.09206 + 10.5518i 0.258361 + 0.447494i
\(557\) −9.34504 16.1861i −0.395962 0.685826i 0.597261 0.802047i \(-0.296255\pi\)
−0.993223 + 0.116220i \(0.962922\pi\)
\(558\) −4.38357 −0.185571
\(559\) −1.02981 0.175026i −0.0435563 0.00740282i
\(560\) 1.58310 0.0668983
\(561\) 11.3157 + 19.5993i 0.477749 + 0.827485i
\(562\) 3.39711 + 5.88397i 0.143298 + 0.248200i
\(563\) −18.1530 + 31.4418i −0.765056 + 1.32512i 0.175161 + 0.984540i \(0.443955\pi\)
−0.940217 + 0.340576i \(0.889378\pi\)
\(564\) −4.59852 −0.193633
\(565\) −9.19095 + 15.9192i −0.386666 + 0.669726i
\(566\) 4.06001 7.03215i 0.170655 0.295583i
\(567\) 9.56546 0.401712
\(568\) −8.97201 + 15.5400i −0.376457 + 0.652043i
\(569\) −5.48798 9.50546i −0.230068 0.398489i 0.727760 0.685832i \(-0.240562\pi\)
−0.957828 + 0.287343i \(0.907228\pi\)
\(570\) 6.49678 + 11.2527i 0.272120 + 0.471326i
\(571\) 31.3363 1.31138 0.655692 0.755028i \(-0.272377\pi\)
0.655692 + 0.755028i \(0.272377\pi\)
\(572\) 4.51595 + 12.1728i 0.188821 + 0.508970i
\(573\) −37.0175 −1.54643
\(574\) 2.76486 + 4.78888i 0.115403 + 0.199884i
\(575\) −10.5504 18.2738i −0.439981 0.762069i
\(576\) −2.36605 + 4.09812i −0.0985855 + 0.170755i
\(577\) −42.7876 −1.78127 −0.890636 0.454717i \(-0.849740\pi\)
−0.890636 + 0.454717i \(0.849740\pi\)
\(578\) −0.626353 + 1.08487i −0.0260528 + 0.0451248i
\(579\) 29.4909 51.0798i 1.22560 2.12280i
\(580\) 10.8274 0.449583
\(581\) −0.682316 + 1.18181i −0.0283073 + 0.0490296i
\(582\) 13.3965 + 23.2034i 0.555302 + 0.961811i
\(583\) −16.4007 28.4069i −0.679248 1.17649i
\(584\) −37.2731 −1.54237
\(585\) 12.8266 + 2.18001i 0.530316 + 0.0901325i
\(586\) 6.64517 0.274509
\(587\) 19.3943 + 33.5919i 0.800488 + 1.38649i 0.919296 + 0.393568i \(0.128759\pi\)
−0.118808 + 0.992917i \(0.537907\pi\)
\(588\) 1.80049 + 3.11853i 0.0742508 + 0.128606i
\(589\) 6.49678 11.2527i 0.267695 0.463661i
\(590\) −3.69226 −0.152008
\(591\) 8.08341 14.0009i 0.332507 0.575919i
\(592\) 3.14124 5.44078i 0.129104 0.223615i
\(593\) −29.9564 −1.23016 −0.615081 0.788464i \(-0.710877\pi\)
−0.615081 + 0.788464i \(0.710877\pi\)
\(594\) 0.416147 0.720787i 0.0170747 0.0295743i
\(595\) −2.51712 4.35978i −0.103192 0.178733i
\(596\) −7.31960 12.6779i −0.299823 0.519308i
\(597\) −11.7332 −0.480207
\(598\) −15.9665 2.71367i −0.652919 0.110970i
\(599\) 41.2539 1.68559 0.842794 0.538236i \(-0.180909\pi\)
0.842794 + 0.538236i \(0.180909\pi\)
\(600\) 9.97371 + 17.2750i 0.407175 + 0.705248i
\(601\) −3.30544 5.72520i −0.134832 0.233536i 0.790701 0.612202i \(-0.209716\pi\)
−0.925533 + 0.378666i \(0.876383\pi\)
\(602\) −0.102890 + 0.178210i −0.00419347 + 0.00726331i
\(603\) 21.1957 0.863156
\(604\) 11.0223 19.0912i 0.448491 0.776809i
\(605\) −3.35461 + 5.81036i −0.136384 + 0.236225i
\(606\) −1.17138 −0.0475842
\(607\) 10.4416 18.0854i 0.423811 0.734062i −0.572498 0.819906i \(-0.694025\pi\)
0.996309 + 0.0858444i \(0.0273588\pi\)
\(608\) −17.1933 29.7797i −0.697282 1.20773i
\(609\) 6.75852 + 11.7061i 0.273869 + 0.474355i
\(610\) −4.21479 −0.170652
\(611\) 1.60150 + 4.31687i 0.0647899 + 0.174642i
\(612\) −16.3326 −0.660208
\(613\) 2.14828 + 3.72092i 0.0867680 + 0.150287i 0.906143 0.422971i \(-0.139013\pi\)
−0.819375 + 0.573258i \(0.805679\pi\)
\(614\) 2.88181 + 4.99144i 0.116300 + 0.201438i
\(615\) −12.0884 + 20.9377i −0.487451 + 0.844290i
\(616\) 5.97829 0.240872
\(617\) 15.3690 26.6199i 0.618732 1.07167i −0.370986 0.928639i \(-0.620980\pi\)
0.989717 0.143036i \(-0.0456866\pi\)
\(618\) 15.3284 26.5495i 0.616598 1.06798i
\(619\) −20.6417 −0.829658 −0.414829 0.909899i \(-0.636159\pi\)
−0.414829 + 0.909899i \(0.636159\pi\)
\(620\) −2.12721 + 3.68443i −0.0854307 + 0.147970i
\(621\) −1.53874 2.66518i −0.0617476 0.106950i
\(622\) −3.06849 5.31479i −0.123035 0.213104i
\(623\) 0.899698 0.0360457
\(624\) −10.5060 1.78561i −0.420578 0.0714815i
\(625\) 2.81636 0.112654
\(626\) −1.85645 3.21546i −0.0741986 0.128516i
\(627\) −17.0768 29.5779i −0.681981 1.18123i
\(628\) 15.3919 26.6596i 0.614205 1.06383i
\(629\) −19.9781 −0.796580
\(630\) 1.28153 2.21967i 0.0510574 0.0884339i
\(631\) −14.6683 + 25.4063i −0.583937 + 1.01141i 0.411070 + 0.911604i \(0.365155\pi\)
−0.995007 + 0.0998043i \(0.968178\pi\)
\(632\) −23.1089 −0.919222
\(633\) −4.43950 + 7.68943i −0.176454 + 0.305628i
\(634\) 3.97509 + 6.88506i 0.157871 + 0.273441i
\(635\) −5.69061 9.85643i −0.225825 0.391141i
\(636\) 49.0543 1.94513
\(637\) 2.30049 2.77629i 0.0911486 0.110000i
\(638\) 9.60097 0.380106
\(639\) −10.1107 17.5122i −0.399971 0.692771i
\(640\) 6.75399 + 11.6983i 0.266975 + 0.462414i
\(641\) 2.00840 3.47865i 0.0793271 0.137399i −0.823633 0.567124i \(-0.808056\pi\)
0.902960 + 0.429725i \(0.141390\pi\)
\(642\) −14.5297 −0.573443
\(643\) 3.43641 5.95203i 0.135519 0.234725i −0.790277 0.612750i \(-0.790063\pi\)
0.925795 + 0.378025i \(0.123397\pi\)
\(644\) 4.72871 8.19037i 0.186337 0.322746i
\(645\) −0.899698 −0.0354256
\(646\) −8.16601 + 14.1439i −0.321287 + 0.556486i
\(647\) 16.8715 + 29.2224i 0.663289 + 1.14885i 0.979746 + 0.200243i \(0.0641732\pi\)
−0.316457 + 0.948607i \(0.602493\pi\)
\(648\) 11.8746 + 20.5674i 0.466477 + 0.807962i
\(649\) 9.70511 0.380959
\(650\) 5.45208 6.57972i 0.213848 0.258078i
\(651\) −5.31126 −0.208165
\(652\) −2.97667 5.15575i −0.116576 0.201915i
\(653\) −16.2001 28.0594i −0.633958 1.09805i −0.986735 0.162340i \(-0.948096\pi\)
0.352777 0.935708i \(-0.385238\pi\)
\(654\) 10.3411 17.9113i 0.404368 0.700385i
\(655\) 25.0584 0.979112
\(656\) 4.77811 8.27593i 0.186554 0.323121i
\(657\) 21.0018 36.3761i 0.819357 1.41917i
\(658\) 0.907052 0.0353606
\(659\) −2.00518 + 3.47307i −0.0781106 + 0.135291i −0.902435 0.430827i \(-0.858222\pi\)
0.824324 + 0.566118i \(0.191555\pi\)
\(660\) 5.59137 + 9.68453i 0.217644 + 0.376970i
\(661\) 0.908971 + 1.57438i 0.0353549 + 0.0612364i 0.883161 0.469069i \(-0.155411\pi\)
−0.847807 + 0.530306i \(0.822077\pi\)
\(662\) −14.2389 −0.553412
\(663\) 11.7870 + 31.7721i 0.457771 + 1.23393i
\(664\) −3.38811 −0.131484
\(665\) 3.79865 + 6.57945i 0.147305 + 0.255140i
\(666\) −5.08569 8.80868i −0.197067 0.341329i
\(667\) 17.7503 30.7443i 0.687293 1.19043i
\(668\) −12.9786 −0.502156
\(669\) −10.6119 + 18.3803i −0.410278 + 0.710622i
\(670\) −3.46987 + 6.00999i −0.134053 + 0.232186i
\(671\) 11.0786 0.427684
\(672\) −7.02797 + 12.1728i −0.271110 + 0.469576i
\(673\) 11.4871 + 19.8963i 0.442797 + 0.766947i 0.997896 0.0648375i \(-0.0206529\pi\)
−0.555099 + 0.831784i \(0.687320\pi\)
\(674\) 6.60091 + 11.4331i 0.254258 + 0.440387i
\(675\) 1.62374 0.0624978
\(676\) 3.61241 + 19.1028i 0.138939 + 0.734725i
\(677\) 38.0276 1.46152 0.730760 0.682634i \(-0.239166\pi\)
0.730760 + 0.682634i \(0.239166\pi\)
\(678\) −12.1881 21.1104i −0.468081 0.810741i
\(679\) 7.83288 + 13.5669i 0.300598 + 0.520652i
\(680\) 6.24950 10.8245i 0.239658 0.415099i
\(681\) −32.3887 −1.24114
\(682\) −1.88626 + 3.26709i −0.0722285 + 0.125103i
\(683\) 20.3893 35.3153i 0.780176 1.35130i −0.151663 0.988432i \(-0.548463\pi\)
0.931839 0.362872i \(-0.118204\pi\)
\(684\) 24.6480 0.942440
\(685\) 6.60087 11.4330i 0.252206 0.436834i
\(686\) −0.355143 0.615126i −0.0135594 0.0234856i
\(687\) −8.20578 14.2128i −0.313070 0.542253i
\(688\) 0.355619 0.0135578
\(689\) −17.0839 46.0499i −0.650844 1.75436i
\(690\) −13.9492 −0.531038
\(691\) 1.56434 + 2.70952i 0.0595104 + 0.103075i 0.894246 0.447576i \(-0.147713\pi\)
−0.834735 + 0.550651i \(0.814379\pi\)
\(692\) 0.698346 + 1.20957i 0.0265471 + 0.0459809i
\(693\) −3.36850 + 5.83442i −0.127959 + 0.221631i
\(694\) −15.8690 −0.602378
\(695\) 5.25379 9.09984i 0.199288 0.345177i
\(696\) −16.7801 + 29.0639i −0.636047 + 1.10167i
\(697\) −30.3886 −1.15105
\(698\) 3.12040 5.40470i 0.118109 0.204571i
\(699\) 30.1795 + 52.2724i 1.14149 + 1.97712i
\(700\) 2.49496 + 4.32140i 0.0943006 + 0.163333i
\(701\) 9.61382 0.363109 0.181555 0.983381i \(-0.441887\pi\)
0.181555 + 0.983381i \(0.441887\pi\)
\(702\) 0.795171 0.959634i 0.0300118 0.0362190i
\(703\) 30.1495 1.13711
\(704\) 2.03623 + 3.52686i 0.0767435 + 0.132924i
\(705\) 1.98288 + 3.43445i 0.0746797 + 0.129349i
\(706\) 2.74134 4.74815i 0.103172 0.178699i
\(707\) −0.684905 −0.0257585
\(708\) −7.25696 + 12.5694i −0.272733 + 0.472388i
\(709\) −14.0647 + 24.3608i −0.528211 + 0.914889i 0.471248 + 0.882001i \(0.343804\pi\)
−0.999459 + 0.0328880i \(0.989530\pi\)
\(710\) 6.62071 0.248471
\(711\) 13.0208 22.5527i 0.488319 0.845794i
\(712\) 1.11689 + 1.93450i 0.0418571 + 0.0724986i
\(713\) 6.97462 + 12.0804i 0.261201 + 0.452414i
\(714\) 6.67589 0.249839
\(715\) 7.14411 8.62170i 0.267174 0.322433i
\(716\) −20.2581 −0.757080
\(717\) 3.35322 + 5.80796i 0.125228 + 0.216902i
\(718\) −3.76297 6.51765i −0.140433 0.243237i
\(719\) −12.4522 + 21.5679i −0.464389 + 0.804346i −0.999174 0.0406425i \(-0.987060\pi\)
0.534784 + 0.844989i \(0.320393\pi\)
\(720\) −4.42936 −0.165073
\(721\) 8.96246 15.5234i 0.333779 0.578123i
\(722\) 5.57581 9.65758i 0.207510 0.359418i
\(723\) 16.8029 0.624907
\(724\) −6.62705 + 11.4784i −0.246292 + 0.426591i
\(725\) 9.36538 + 16.2213i 0.347822 + 0.602445i
\(726\) −4.44854 7.70510i −0.165101 0.285963i
\(727\) −24.2120 −0.897974 −0.448987 0.893538i \(-0.648215\pi\)
−0.448987 + 0.893538i \(0.648215\pi\)
\(728\) 8.82531 + 1.49995i 0.327088 + 0.0555918i
\(729\) −23.2479 −0.861032
\(730\) 6.87624 + 11.9100i 0.254501 + 0.440808i
\(731\) −0.565430 0.979353i −0.0209132 0.0362227i
\(732\) −8.28398 + 14.3483i −0.306185 + 0.530328i
\(733\) −12.3989 −0.457963 −0.228981 0.973431i \(-0.573539\pi\)
−0.228981 + 0.973431i \(0.573539\pi\)
\(734\) 2.06717 3.58045i 0.0763007 0.132157i
\(735\) 1.55274 2.68942i 0.0572736 0.0992009i
\(736\) 36.9159 1.36074
\(737\) 9.12056 15.7973i 0.335960 0.581900i
\(738\) −7.73581 13.3988i −0.284759 0.493217i
\(739\) 5.48019 + 9.49197i 0.201592 + 0.349168i 0.949042 0.315151i \(-0.102055\pi\)
−0.747450 + 0.664319i \(0.768722\pi\)
\(740\) −9.87170 −0.362891
\(741\) −17.7881 47.9482i −0.653463 1.76142i
\(742\) −9.67589 −0.355213
\(743\) −20.3462 35.2407i −0.746431 1.29286i −0.949523 0.313697i \(-0.898432\pi\)
0.203092 0.979160i \(-0.434901\pi\)
\(744\) −6.59340 11.4201i −0.241726 0.418681i
\(745\) −6.31243 + 10.9334i −0.231269 + 0.400570i
\(746\) −18.5079 −0.677621
\(747\) 1.90905 3.30657i 0.0698485 0.120981i
\(748\) −7.02797 + 12.1728i −0.256968 + 0.445082i
\(749\) −8.49549 −0.310419
\(750\) 9.19439 15.9252i 0.335732 0.581505i
\(751\) −4.70236 8.14473i −0.171592 0.297205i 0.767385 0.641187i \(-0.221558\pi\)
−0.938976 + 0.343981i \(0.888224\pi\)
\(752\) −0.783763 1.35752i −0.0285809 0.0495035i
\(753\) −1.88544 −0.0687093
\(754\) 14.1732 + 2.40888i 0.516157 + 0.0877261i
\(755\) −19.0113 −0.691890
\(756\) 0.363883 + 0.630264i 0.0132343 + 0.0229225i
\(757\) 14.7904 + 25.6177i 0.537566 + 0.931091i 0.999034 + 0.0439345i \(0.0139893\pi\)
−0.461469 + 0.887156i \(0.652677\pi\)
\(758\) 5.55914 9.62872i 0.201917 0.349731i
\(759\) 36.6656 1.33088
\(760\) −9.43129 + 16.3355i −0.342109 + 0.592550i
\(761\) −8.47086 + 14.6720i −0.307068 + 0.531858i −0.977720 0.209915i \(-0.932681\pi\)
0.670651 + 0.741773i \(0.266015\pi\)
\(762\) 15.0926 0.546748
\(763\) 6.04639 10.4727i 0.218894 0.379136i
\(764\) −11.4955 19.9107i −0.415891 0.720345i
\(765\) 7.04264 + 12.1982i 0.254627 + 0.441027i
\(766\) 8.92034 0.322305
\(767\) 14.3269 + 2.43500i 0.517316 + 0.0879229i
\(768\) −26.0578 −0.940281
\(769\) −3.68287 6.37892i −0.132808 0.230030i 0.791950 0.610586i \(-0.209066\pi\)
−0.924758 + 0.380556i \(0.875733\pi\)
\(770\) −1.10289 1.91026i −0.0397454 0.0688410i
\(771\) −3.92249 + 6.79396i −0.141265 + 0.244678i
\(772\) 36.6326 1.31844
\(773\) 22.3867 38.7749i 0.805194 1.39464i −0.110966 0.993824i \(-0.535394\pi\)
0.916160 0.400813i \(-0.131272\pi\)
\(774\) 0.287875 0.498614i 0.0103475 0.0179223i
\(775\) −7.35989 −0.264375
\(776\) −19.4475 + 33.6840i −0.698124 + 1.20919i
\(777\) −6.16197 10.6729i −0.221060 0.382886i
\(778\) −0.178640 0.309413i −0.00640454 0.0110930i
\(779\) 45.8602 1.64311
\(780\) 5.82428 + 15.6994i 0.208543 + 0.562130i
\(781\) −17.4025 −0.622712
\(782\) −8.76662 15.1842i −0.313494 0.542987i
\(783\) 1.36592 + 2.36583i 0.0488138 + 0.0845480i
\(784\) −0.613742 + 1.06303i −0.0219194 + 0.0379655i
\(785\) −26.5480 −0.947540
\(786\) −16.6149 + 28.7779i −0.592635 + 1.02647i
\(787\) 9.38412 16.2538i 0.334508 0.579385i −0.648882 0.760889i \(-0.724763\pi\)
0.983390 + 0.181504i \(0.0580966\pi\)
\(788\) 10.0409 0.357693
\(789\) −35.6161 + 61.6889i −1.26797 + 2.19618i
\(790\) 4.26318 + 7.38404i 0.151677 + 0.262713i
\(791\) −7.12635 12.3432i −0.253384 0.438874i
\(792\) −16.7267 −0.594356
\(793\) 16.3545 + 2.77961i 0.580766 + 0.0987069i
\(794\) 1.66949 0.0592479
\(795\) −21.1522 36.6367i −0.750192 1.29937i
\(796\) −3.64363 6.31095i −0.129145 0.223686i
\(797\) −3.60849 + 6.25008i −0.127819 + 0.221389i −0.922831 0.385204i \(-0.874131\pi\)
0.795012 + 0.606593i \(0.207464\pi\)
\(798\) −10.0748 −0.356643
\(799\) −2.49235 + 4.31687i −0.0881730 + 0.152720i
\(800\) −9.73877 + 16.8680i −0.344317 + 0.596375i
\(801\) −2.51726 −0.0889431
\(802\) −12.2896 + 21.2862i −0.433961 + 0.751643i
\(803\) −18.0742 31.3054i −0.637825 1.10474i
\(804\) 13.6397 + 23.6247i 0.481036 + 0.833180i
\(805\) −8.15608 −0.287464
\(806\) −3.60425 + 4.34971i −0.126954 + 0.153212i
\(807\) 2.97734 0.104807
\(808\) −0.850241 1.47266i −0.0299114 0.0518080i
\(809\) −7.41591 12.8447i −0.260729 0.451596i 0.705707 0.708504i \(-0.250630\pi\)
−0.966436 + 0.256908i \(0.917296\pi\)
\(810\) 4.38130 7.58863i 0.153943 0.266637i
\(811\) 18.5831 0.652541 0.326271 0.945276i \(-0.394208\pi\)
0.326271 + 0.945276i \(0.394208\pi\)
\(812\) −4.19760 + 7.27045i −0.147307 + 0.255143i
\(813\) −30.3479 + 52.5641i −1.06435 + 1.84350i
\(814\) −8.75354 −0.306811
\(815\) −2.56708 + 4.44632i −0.0899210 + 0.155748i
\(816\) −5.76848 9.99131i −0.201937 0.349766i
\(817\) 0.853305 + 1.47797i 0.0298534 + 0.0517075i
\(818\) 5.69942 0.199275
\(819\) −6.43652 + 7.76776i −0.224910 + 0.271428i
\(820\) −15.0158 −0.524374
\(821\) 13.3118 + 23.0567i 0.464585 + 0.804684i 0.999183 0.0404222i \(-0.0128703\pi\)
−0.534598 + 0.845106i \(0.679537\pi\)
\(822\) 8.75340 + 15.1613i 0.305310 + 0.528812i
\(823\) −3.37568 + 5.84685i −0.117669 + 0.203808i −0.918843 0.394622i \(-0.870875\pi\)
0.801175 + 0.598431i \(0.204209\pi\)
\(824\) 44.5040 1.55037
\(825\) −9.67275 + 16.7537i −0.336762 + 0.583289i
\(826\) 1.43143 2.47930i 0.0498057 0.0862660i
\(827\) −21.7430 −0.756079 −0.378039 0.925789i \(-0.623402\pi\)
−0.378039 + 0.925789i \(0.623402\pi\)
\(828\) −13.2304 + 22.9158i −0.459790 + 0.796379i
\(829\) 7.31078 + 12.6626i 0.253914 + 0.439792i 0.964600 0.263717i \(-0.0849487\pi\)
−0.710686 + 0.703509i \(0.751615\pi\)
\(830\) 0.625047 + 1.08261i 0.0216957 + 0.0375781i
\(831\) 22.9616 0.796529
\(832\) 2.12105 + 5.71733i 0.0735343 + 0.198213i
\(833\) 3.90338 0.135244
\(834\) 6.96705 + 12.0673i 0.241249 + 0.417856i
\(835\) 5.59636 + 9.69318i 0.193670 + 0.335446i
\(836\) 10.6061 18.3703i 0.366819 0.635350i
\(837\) −1.07342 −0.0371028
\(838\) −4.14432 + 7.17818i −0.143163 + 0.247966i
\(839\) 5.37343 9.30705i 0.185511 0.321315i −0.758237 0.651979i \(-0.773939\pi\)
0.943749 + 0.330663i \(0.107273\pi\)
\(840\) 7.71029 0.266030
\(841\) −1.25660 + 2.17649i −0.0433310 + 0.0750515i
\(842\) −6.51267 11.2803i −0.224441 0.388744i
\(843\) −11.5163 19.9467i −0.396641 0.687002i
\(844\) −5.51458 −0.189820
\(845\) 12.7095 10.9351i 0.437220 0.376180i
\(846\) −2.53784 −0.0872527
\(847\) −2.60105 4.50515i −0.0893732 0.154799i
\(848\) 8.36071 + 14.4812i 0.287108 + 0.497286i
\(849\) −13.7635 + 23.8391i −0.472362 + 0.818155i
\(850\) 9.25088 0.317303
\(851\) −16.1835 + 28.0307i −0.554764 + 0.960879i
\(852\) 13.0127 22.5386i 0.445807 0.772161i
\(853\) −31.7709 −1.08782 −0.543908 0.839145i \(-0.683056\pi\)
−0.543908 + 0.839145i \(0.683056\pi\)
\(854\) 1.63400 2.83018i 0.0559145 0.0968467i
\(855\) −10.6282 18.4086i −0.363478 0.629562i
\(856\) −10.5463 18.2667i −0.360466 0.624345i
\(857\) −0.648105 −0.0221388 −0.0110694 0.999939i \(-0.503524\pi\)
−0.0110694 + 0.999939i \(0.503524\pi\)
\(858\) 5.16456 + 13.9211i 0.176315 + 0.475260i
\(859\) −43.1902 −1.47363 −0.736815 0.676095i \(-0.763671\pi\)
−0.736815 + 0.676095i \(0.763671\pi\)
\(860\) −0.279393 0.483923i −0.00952723 0.0165017i
\(861\) −9.37293 16.2344i −0.319429 0.553267i
\(862\) −11.0959 + 19.2187i −0.377929 + 0.654592i
\(863\) 21.6094 0.735592 0.367796 0.929906i \(-0.380112\pi\)
0.367796 + 0.929906i \(0.380112\pi\)
\(864\) −1.42037 + 2.46016i −0.0483220 + 0.0836962i
\(865\) 0.602253 1.04313i 0.0204772 0.0354676i
\(866\) 21.7002 0.737401
\(867\) 2.12335 3.67774i 0.0721126 0.124903i
\(868\) −1.64936 2.85678i −0.0559831 0.0969655i
\(869\) −11.2058 19.4090i −0.380130 0.658405i
\(870\) 12.3825 0.419806
\(871\) 17.4275 21.0320i 0.590509 0.712642i
\(872\) 30.0240 1.01674
\(873\) −21.9156 37.9589i −0.741731 1.28472i
\(874\) 13.2299 + 22.9149i 0.447509 + 0.775109i
\(875\) 5.37594 9.31140i 0.181740 0.314783i
\(876\) 54.0597 1.82651
\(877\) 0.440383 0.762766i 0.0148707 0.0257568i −0.858494 0.512823i \(-0.828600\pi\)
0.873365 + 0.487066i \(0.161933\pi\)
\(878\) −4.31401 + 7.47208i −0.145591 + 0.252170i
\(879\) −22.5272 −0.759825
\(880\) −1.90596 + 3.30123i −0.0642500 + 0.111284i
\(881\) 0.0700176 + 0.121274i 0.00235895 + 0.00408583i 0.867202 0.497956i \(-0.165916\pi\)
−0.864844 + 0.502042i \(0.832582\pi\)
\(882\) 0.993655 + 1.72106i 0.0334581 + 0.0579511i
\(883\) −18.8253 −0.633522 −0.316761 0.948505i \(-0.602595\pi\)
−0.316761 + 0.948505i \(0.602595\pi\)
\(884\) −13.4290 + 16.2065i −0.451667 + 0.545083i
\(885\) 12.5168 0.420748
\(886\) −3.00640 5.20724i −0.101002 0.174941i
\(887\) 16.6505 + 28.8395i 0.559069 + 0.968337i 0.997574 + 0.0696078i \(0.0221748\pi\)
−0.438505 + 0.898729i \(0.644492\pi\)
\(888\) 15.2990 26.4986i 0.513400 0.889234i
\(889\) 8.82462 0.295968
\(890\) 0.412092 0.713764i 0.0138133 0.0239254i
\(891\) −11.5163 + 19.9467i −0.385809 + 0.668241i
\(892\) −13.1817 −0.441355
\(893\) 3.76127 6.51471i 0.125866 0.218006i
\(894\) −8.37090 14.4988i −0.279965 0.484913i
\(895\) 8.73529 + 15.1300i 0.291989 + 0.505739i
\(896\) −10.4736 −0.349899
\(897\) 54.1267 + 9.19937i 1.80724 + 0.307158i
\(898\) 16.5684 0.552896
\(899\) −6.19125 10.7236i −0.206490 0.357651i
\(900\) −6.98064 12.0908i −0.232688 0.403028i
\(901\) 26.5869 46.0499i 0.885738 1.53414i
\(902\) −13.3149 −0.443339
\(903\) 0.348798 0.604136i 0.0116073 0.0201044i
\(904\) 17.6933 30.6457i 0.588471 1.01926i
\(905\) 11.4303 0.379957
\(906\) 12.6054 21.8332i 0.418786 0.725359i
\(907\) −5.79350 10.0346i −0.192370 0.333195i 0.753665 0.657259i \(-0.228284\pi\)
−0.946035 + 0.324064i \(0.894951\pi\)
\(908\) −10.0580 17.4210i −0.333788 0.578137i
\(909\) 1.91629 0.0635594
\(910\) −1.14883 3.09669i −0.0380834 0.102654i
\(911\) 52.5489 1.74102 0.870512 0.492147i \(-0.163788\pi\)
0.870512 + 0.492147i \(0.163788\pi\)
\(912\) 8.70537 + 15.0781i 0.288264 + 0.499287i
\(913\) −1.64294 2.84565i −0.0543733 0.0941773i
\(914\) 5.49998 9.52624i 0.181923 0.315100i
\(915\) 14.2882 0.472354
\(916\) 5.09646 8.82733i 0.168392 0.291663i
\(917\) −9.71471 + 16.8264i −0.320808 + 0.555656i
\(918\) 1.34922 0.0445308
\(919\) 10.0267 17.3668i 0.330751 0.572878i −0.651908 0.758298i \(-0.726031\pi\)
0.982659 + 0.185420i \(0.0593646\pi\)
\(920\) −10.1250 17.5370i −0.333810 0.578176i
\(921\) −9.76937 16.9210i −0.321912 0.557567i
\(922\) 6.59291 0.217126
\(923\) −25.6901 4.36628i −0.845599 0.143718i
\(924\) −8.67071 −0.285246
\(925\) −8.53874 14.7895i −0.280752 0.486277i
\(926\) 10.2382 + 17.7330i 0.336447 + 0.582744i
\(927\) −25.0760 + 43.4330i −0.823605 + 1.42653i
\(928\) −32.7696 −1.07571
\(929\) 7.95425 13.7772i 0.260971 0.452014i −0.705530 0.708681i \(-0.749291\pi\)
0.966500 + 0.256666i \(0.0826241\pi\)
\(930\) −2.43273 + 4.21361i −0.0797724 + 0.138170i
\(931\) −5.89068 −0.193059
\(932\) −18.7439 + 32.4655i −0.613978 + 1.06344i
\(933\) 10.4022 + 18.0172i 0.340554 + 0.589857i
\(934\) −1.02066 1.76783i −0.0333969 0.0578451i
\(935\) 12.1218 0.396427
\(936\) −24.6923 4.19670i −0.807094 0.137174i
\(937\) 26.1978 0.855846 0.427923 0.903815i \(-0.359245\pi\)
0.427923 + 0.903815i \(0.359245\pi\)
\(938\) −2.69042 4.65994i −0.0878453 0.152153i
\(939\) 6.29339 + 10.9005i 0.205377 + 0.355723i
\(940\) −1.23153 + 2.13308i −0.0401682 + 0.0695733i
\(941\) −36.3059 −1.18354 −0.591769 0.806108i \(-0.701570\pi\)
−0.591769 + 0.806108i \(0.701570\pi\)
\(942\) 17.6026 30.4887i 0.573525 0.993375i
\(943\) −24.6166 + 42.6372i −0.801627 + 1.38846i
\(944\) −4.94745 −0.161026
\(945\) 0.313813 0.543540i 0.0102083 0.0176814i
\(946\) −0.247746 0.429109i −0.00805493 0.0139516i
\(947\) 0.459419 + 0.795738i 0.0149291 + 0.0258580i 0.873393 0.487015i \(-0.161914\pi\)
−0.858464 + 0.512873i \(0.828581\pi\)
\(948\) 33.5163 1.08856
\(949\) −18.8271 50.7487i −0.611153 1.64737i
\(950\) −13.9607 −0.452946
\(951\) −13.4756 23.3405i −0.436977 0.756867i
\(952\) 4.84565 + 8.39292i 0.157049 + 0.272016i
\(953\) 9.17943 15.8992i 0.297351 0.515027i −0.678178 0.734898i \(-0.737230\pi\)
0.975529 + 0.219871i \(0.0705635\pi\)
\(954\) 27.0721 0.876493
\(955\) −9.91370 + 17.1710i −0.320800 + 0.555641i
\(956\) −2.08263 + 3.60722i −0.0673570 + 0.116666i
\(957\) −32.5474 −1.05211
\(958\) −8.02914 + 13.9069i −0.259410 + 0.449311i
\(959\) 5.11809 + 8.86479i 0.165272 + 0.286259i
\(960\) 2.62616 + 4.54864i 0.0847589 + 0.146807i
\(961\) −26.1345 −0.843050
\(962\) −12.9222 2.19625i −0.416628 0.0708101i
\(963\) 23.7695 0.765962
\(964\) 5.21800 + 9.03783i 0.168060 + 0.291089i
\(965\) −15.7960 27.3594i −0.508491 0.880731i
\(966\) 5.40788 9.36673i 0.173996 0.301369i
\(967\) 12.5923 0.404940 0.202470 0.979288i \(-0.435103\pi\)
0.202470 + 0.979288i \(0.435103\pi\)
\(968\) 6.45790 11.1854i 0.207565 0.359512i
\(969\) 27.6829 47.9482i 0.889302 1.54032i
\(970\) 14.3509 0.460779
\(971\) 10.6654 18.4730i 0.342269 0.592827i −0.642585 0.766214i \(-0.722138\pi\)
0.984854 + 0.173388i \(0.0554713\pi\)
\(972\) −16.1308 27.9394i −0.517397 0.896157i
\(973\) 4.07361 + 7.05571i 0.130594 + 0.226196i
\(974\) −2.03712 −0.0652736
\(975\) −18.4826 + 22.3053i −0.591918 + 0.714343i
\(976\) −5.64762 −0.180776
\(977\) 21.2140 + 36.7437i 0.678695 + 1.17553i 0.975374 + 0.220557i \(0.0707874\pi\)
−0.296679 + 0.954977i \(0.595879\pi\)
\(978\) −3.40421 5.89626i −0.108854 0.188542i
\(979\) −1.08318 + 1.87613i −0.0346187 + 0.0599614i
\(980\) 1.92876 0.0616119
\(981\) −16.9172 + 29.3014i −0.540124 + 0.935523i
\(982\) −8.06889 + 13.9757i −0.257489 + 0.445983i
\(983\) 2.09758 0.0669023 0.0334511 0.999440i \(-0.489350\pi\)
0.0334511 + 0.999440i \(0.489350\pi\)
\(984\) 23.2711 40.3068i 0.741856 1.28493i
\(985\) −4.32965 7.49917i −0.137954 0.238943i
\(986\) 7.78198 + 13.4788i 0.247829 + 0.429252i
\(987\) −3.07492 −0.0978758
\(988\) 20.2661 24.4576i 0.644750 0.778101i
\(989\) −1.83213 −0.0582584
\(990\) 3.08577 + 5.34471i 0.0980723 + 0.169866i
\(991\) 13.8174 + 23.9325i 0.438926 + 0.760241i 0.997607 0.0691411i \(-0.0220259\pi\)
−0.558681 + 0.829382i \(0.688693\pi\)
\(992\) 6.43809 11.1511i 0.204409 0.354048i
\(993\) 48.2703 1.53181
\(994\) −2.56674 + 4.44572i −0.0814119 + 0.141010i
\(995\) −3.14227 + 5.44257i −0.0996166 + 0.172541i
\(996\) 4.91400 0.155706
\(997\) 1.01392 1.75615i 0.0321110 0.0556180i −0.849523 0.527551i \(-0.823110\pi\)
0.881634 + 0.471933i \(0.156444\pi\)
\(998\) −6.39794 11.0816i −0.202523 0.350781i
\(999\) −1.24535 2.15701i −0.0394012 0.0682449i
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 91.2.f.c.29.3 yes 8
3.2 odd 2 819.2.o.h.757.2 8
4.3 odd 2 1456.2.s.q.1121.4 8
7.2 even 3 637.2.g.k.263.3 8
7.3 odd 6 637.2.h.i.471.2 8
7.4 even 3 637.2.h.h.471.2 8
7.5 odd 6 637.2.g.j.263.3 8
7.6 odd 2 637.2.f.i.393.3 8
13.2 odd 12 1183.2.c.g.337.6 8
13.3 even 3 1183.2.a.k.1.2 4
13.9 even 3 inner 91.2.f.c.22.3 8
13.10 even 6 1183.2.a.l.1.3 4
13.11 odd 12 1183.2.c.g.337.3 8
39.35 odd 6 819.2.o.h.568.2 8
52.35 odd 6 1456.2.s.q.113.4 8
91.9 even 3 637.2.h.h.165.2 8
91.48 odd 6 637.2.f.i.295.3 8
91.55 odd 6 8281.2.a.bp.1.2 4
91.61 odd 6 637.2.h.i.165.2 8
91.62 odd 6 8281.2.a.bt.1.3 4
91.74 even 3 637.2.g.k.373.3 8
91.87 odd 6 637.2.g.j.373.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.f.c.22.3 8 13.9 even 3 inner
91.2.f.c.29.3 yes 8 1.1 even 1 trivial
637.2.f.i.295.3 8 91.48 odd 6
637.2.f.i.393.3 8 7.6 odd 2
637.2.g.j.263.3 8 7.5 odd 6
637.2.g.j.373.3 8 91.87 odd 6
637.2.g.k.263.3 8 7.2 even 3
637.2.g.k.373.3 8 91.74 even 3
637.2.h.h.165.2 8 91.9 even 3
637.2.h.h.471.2 8 7.4 even 3
637.2.h.i.165.2 8 91.61 odd 6
637.2.h.i.471.2 8 7.3 odd 6
819.2.o.h.568.2 8 39.35 odd 6
819.2.o.h.757.2 8 3.2 odd 2
1183.2.a.k.1.2 4 13.3 even 3
1183.2.a.l.1.3 4 13.10 even 6
1183.2.c.g.337.3 8 13.11 odd 12
1183.2.c.g.337.6 8 13.2 odd 12
1456.2.s.q.113.4 8 52.35 odd 6
1456.2.s.q.1121.4 8 4.3 odd 2
8281.2.a.bp.1.2 4 91.55 odd 6
8281.2.a.bt.1.3 4 91.62 odd 6