Properties

Label 672.2.bs.a.155.6
Level $672$
Weight $2$
Character 672.155
Analytic conductor $5.366$
Analytic rank $0$
Dimension $192$
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] = [672,2,Mod(155,672)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(672, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([4, 1, 4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("672.155");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 672.bs (of order \(8\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.36594701583\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(48\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 155.6
Character \(\chi\) \(=\) 672.155
Dual form 672.2.bs.a.659.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.28283 - 0.595271i) q^{2} +(-1.60604 + 0.648559i) q^{3} +(1.29131 + 1.52726i) q^{4} +(-0.327082 + 0.789647i) q^{5} +(2.44635 + 0.124039i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.747392 - 2.72789i) q^{8} +(2.15874 - 2.08323i) q^{9} +O(q^{10})\) \(q+(-1.28283 - 0.595271i) q^{2} +(-1.60604 + 0.648559i) q^{3} +(1.29131 + 1.52726i) q^{4} +(-0.327082 + 0.789647i) q^{5} +(2.44635 + 0.124039i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.747392 - 2.72789i) q^{8} +(2.15874 - 2.08323i) q^{9} +(0.889645 - 0.818280i) q^{10} +(1.57113 - 3.79305i) q^{11} +(-3.06441 - 1.61536i) q^{12} +(-4.34408 + 1.79938i) q^{13} +(1.32802 - 0.486178i) q^{14} +(0.0131756 - 1.48034i) q^{15} +(-0.665059 + 3.94432i) q^{16} -4.61062 q^{17} +(-4.00938 + 1.38739i) q^{18} +(0.545588 + 1.31717i) q^{19} +(-1.62836 + 0.520135i) q^{20} +(0.677043 - 1.59424i) q^{21} +(-4.27338 + 3.93058i) q^{22} +(4.33234 - 4.33234i) q^{23} +(2.96954 + 3.89639i) q^{24} +(3.01897 + 3.01897i) q^{25} +(6.64383 + 0.277609i) q^{26} +(-2.11594 + 4.74582i) q^{27} +(-1.99303 - 0.166846i) q^{28} +(2.52053 - 1.04404i) q^{29} +(-0.898104 + 1.89118i) q^{30} -8.96065i q^{31} +(3.20110 - 4.66401i) q^{32} +(-0.0632888 + 7.11076i) q^{33} +(5.91464 + 2.74457i) q^{34} +(-0.327082 - 0.789647i) q^{35} +(5.96923 + 0.606884i) q^{36} +(2.36682 + 0.980368i) q^{37} +(0.0841736 - 2.01447i) q^{38} +(5.80977 - 5.70727i) q^{39} +(2.39853 + 0.302071i) q^{40} +(7.23773 + 7.23773i) q^{41} +(-1.81754 + 1.64212i) q^{42} +(2.03307 + 0.842127i) q^{43} +(7.82179 - 2.49845i) q^{44} +(0.938926 + 2.38603i) q^{45} +(-8.13658 + 2.97874i) q^{46} -12.4290i q^{47} +(-1.49001 - 6.76608i) q^{48} -1.00000i q^{49} +(-2.07572 - 5.66994i) q^{50} +(7.40485 - 2.99026i) q^{51} +(-8.35766 - 4.31100i) q^{52} +(-3.19259 - 1.32241i) q^{53} +(5.53943 - 4.82853i) q^{54} +(2.48128 + 2.48128i) q^{55} +(2.45740 + 1.40043i) q^{56} +(-1.73050 - 1.76158i) q^{57} +(-3.85490 - 0.161075i) q^{58} +(-1.18761 - 0.491922i) q^{59} +(2.27788 - 1.89145i) q^{60} +(-0.703592 - 1.69862i) q^{61} +(-5.33401 + 11.4950i) q^{62} +(-0.0533983 + 2.99952i) q^{63} +(-6.88281 + 4.07761i) q^{64} -4.01883i q^{65} +(4.31402 - 9.08423i) q^{66} +(8.83223 - 3.65843i) q^{67} +(-5.95372 - 7.04162i) q^{68} +(-4.14815 + 9.76771i) q^{69} +(-0.0504624 + 1.20769i) q^{70} +(0.710165 + 0.710165i) q^{71} +(-7.29625 - 4.33184i) q^{72} +(10.2721 - 10.2721i) q^{73} +(-2.45264 - 2.66654i) q^{74} +(-6.80658 - 2.89062i) q^{75} +(-1.30714 + 2.53412i) q^{76} +(1.57113 + 3.79305i) q^{77} +(-10.8503 + 3.86307i) q^{78} +15.4424 q^{79} +(-2.89709 - 1.81528i) q^{80} +(0.320339 - 8.99430i) q^{81} +(-4.97637 - 13.5932i) q^{82} +(2.74127 - 1.13547i) q^{83} +(3.30910 - 1.02463i) q^{84} +(1.50805 - 3.64076i) q^{85} +(-2.10680 - 2.29054i) q^{86} +(-3.37096 + 3.31148i) q^{87} +(-11.5213 - 1.45099i) q^{88} +(3.60370 - 3.60370i) q^{89} +(0.215852 - 3.61979i) q^{90} +(1.79938 - 4.34408i) q^{91} +(12.2110 + 1.02224i) q^{92} +(5.81151 + 14.3912i) q^{93} +(-7.39863 + 15.9443i) q^{94} -1.21855 q^{95} +(-2.11621 + 9.56669i) q^{96} +14.5603 q^{97} +(-0.595271 + 1.28283i) q^{98} +(-4.51010 - 11.4612i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q - 16 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 192 q - 16 q^{4} + 8 q^{10} + 16 q^{16} + 16 q^{22} + 24 q^{27} - 84 q^{30} + 40 q^{36} + 32 q^{37} + 24 q^{39} - 96 q^{46} - 72 q^{48} + 16 q^{52} - 32 q^{55} - 72 q^{58} - 28 q^{60} - 16 q^{61} - 64 q^{64} - 12 q^{66} - 32 q^{67} + 56 q^{69} - 24 q^{70} + 60 q^{72} + 80 q^{75} - 56 q^{76} + 100 q^{78} - 32 q^{79} - 120 q^{82} - 56 q^{87} + 40 q^{88} + 60 q^{90} - 80 q^{93} + 216 q^{94} + 96 q^{96} - 64 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(421\) \(449\) \(577\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{8}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.28283 0.595271i −0.907098 0.420920i
\(3\) −1.60604 + 0.648559i −0.927249 + 0.374446i
\(4\) 1.29131 + 1.52726i 0.645653 + 0.763631i
\(5\) −0.327082 + 0.789647i −0.146276 + 0.353141i −0.979987 0.199059i \(-0.936211\pi\)
0.833712 + 0.552200i \(0.186211\pi\)
\(6\) 2.44635 + 0.124039i 0.998717 + 0.0506386i
\(7\) −0.707107 + 0.707107i −0.267261 + 0.267261i
\(8\) −0.747392 2.72789i −0.264243 0.964456i
\(9\) 2.15874 2.08323i 0.719581 0.694409i
\(10\) 0.889645 0.818280i 0.281330 0.258763i
\(11\) 1.57113 3.79305i 0.473714 1.14365i −0.488796 0.872398i \(-0.662564\pi\)
0.962509 0.271248i \(-0.0874364\pi\)
\(12\) −3.06441 1.61536i −0.884619 0.466314i
\(13\) −4.34408 + 1.79938i −1.20483 + 0.499057i −0.892557 0.450935i \(-0.851091\pi\)
−0.312274 + 0.949992i \(0.601091\pi\)
\(14\) 1.32802 0.486178i 0.354928 0.129937i
\(15\) 0.0131756 1.48034i 0.00340194 0.382222i
\(16\) −0.665059 + 3.94432i −0.166265 + 0.986081i
\(17\) −4.61062 −1.11824 −0.559120 0.829087i \(-0.688861\pi\)
−0.559120 + 0.829087i \(0.688861\pi\)
\(18\) −4.00938 + 1.38739i −0.945021 + 0.327011i
\(19\) 0.545588 + 1.31717i 0.125167 + 0.302179i 0.974025 0.226442i \(-0.0727094\pi\)
−0.848858 + 0.528621i \(0.822709\pi\)
\(20\) −1.62836 + 0.520135i −0.364113 + 0.116306i
\(21\) 0.677043 1.59424i 0.147743 0.347892i
\(22\) −4.27338 + 3.93058i −0.911088 + 0.838004i
\(23\) 4.33234 4.33234i 0.903356 0.903356i −0.0923686 0.995725i \(-0.529444\pi\)
0.995725 + 0.0923686i \(0.0294438\pi\)
\(24\) 2.96954 + 3.89639i 0.606155 + 0.795346i
\(25\) 3.01897 + 3.01897i 0.603795 + 0.603795i
\(26\) 6.64383 + 0.277609i 1.30296 + 0.0544435i
\(27\) −2.11594 + 4.74582i −0.407212 + 0.913334i
\(28\) −1.99303 0.166846i −0.376647 0.0315310i
\(29\) 2.52053 1.04404i 0.468051 0.193873i −0.136177 0.990685i \(-0.543482\pi\)
0.604228 + 0.796811i \(0.293482\pi\)
\(30\) −0.898104 + 1.89118i −0.163971 + 0.345280i
\(31\) 8.96065i 1.60938i −0.593695 0.804690i \(-0.702332\pi\)
0.593695 0.804690i \(-0.297668\pi\)
\(32\) 3.20110 4.66401i 0.565880 0.824488i
\(33\) −0.0632888 + 7.11076i −0.0110172 + 1.23782i
\(34\) 5.91464 + 2.74457i 1.01435 + 0.470689i
\(35\) −0.327082 0.789647i −0.0552870 0.133475i
\(36\) 5.96923 + 0.606884i 0.994871 + 0.101147i
\(37\) 2.36682 + 0.980368i 0.389103 + 0.161172i 0.568654 0.822577i \(-0.307464\pi\)
−0.179551 + 0.983749i \(0.557464\pi\)
\(38\) 0.0841736 2.01447i 0.0136548 0.326791i
\(39\) 5.80977 5.70727i 0.930308 0.913894i
\(40\) 2.39853 + 0.302071i 0.379241 + 0.0477616i
\(41\) 7.23773 + 7.23773i 1.13034 + 1.13034i 0.990120 + 0.140223i \(0.0447820\pi\)
0.140223 + 0.990120i \(0.455218\pi\)
\(42\) −1.81754 + 1.64212i −0.280452 + 0.253385i
\(43\) 2.03307 + 0.842127i 0.310041 + 0.128423i 0.532278 0.846569i \(-0.321336\pi\)
−0.222237 + 0.974993i \(0.571336\pi\)
\(44\) 7.82179 2.49845i 1.17918 0.376656i
\(45\) 0.938926 + 2.38603i 0.139967 + 0.355688i
\(46\) −8.13658 + 2.97874i −1.19967 + 0.439192i
\(47\) 12.4290i 1.81296i −0.422249 0.906480i \(-0.638759\pi\)
0.422249 0.906480i \(-0.361241\pi\)
\(48\) −1.49001 6.76608i −0.215065 0.976600i
\(49\) 1.00000i 0.142857i
\(50\) −2.07572 5.66994i −0.293552 0.801850i
\(51\) 7.40485 2.99026i 1.03689 0.418720i
\(52\) −8.35766 4.31100i −1.15900 0.597829i
\(53\) −3.19259 1.32241i −0.438535 0.181647i 0.152482 0.988306i \(-0.451273\pi\)
−0.591017 + 0.806659i \(0.701273\pi\)
\(54\) 5.53943 4.82853i 0.753822 0.657079i
\(55\) 2.48128 + 2.48128i 0.334575 + 0.334575i
\(56\) 2.45740 + 1.40043i 0.328384 + 0.187140i
\(57\) −1.73050 1.76158i −0.229210 0.233327i
\(58\) −3.85490 0.161075i −0.506173 0.0211501i
\(59\) −1.18761 0.491922i −0.154613 0.0640428i 0.304035 0.952661i \(-0.401666\pi\)
−0.458648 + 0.888618i \(0.651666\pi\)
\(60\) 2.27788 1.89145i 0.294073 0.244185i
\(61\) −0.703592 1.69862i −0.0900857 0.217486i 0.872415 0.488766i \(-0.162553\pi\)
−0.962500 + 0.271280i \(0.912553\pi\)
\(62\) −5.33401 + 11.4950i −0.677420 + 1.45987i
\(63\) −0.0533983 + 2.99952i −0.00672756 + 0.377905i
\(64\) −6.88281 + 4.07761i −0.860351 + 0.509701i
\(65\) 4.01883i 0.498475i
\(66\) 4.31402 9.08423i 0.531019 1.11819i
\(67\) 8.83223 3.65843i 1.07903 0.446948i 0.228860 0.973459i \(-0.426500\pi\)
0.850168 + 0.526511i \(0.176500\pi\)
\(68\) −5.95372 7.04162i −0.721995 0.853922i
\(69\) −4.14815 + 9.76771i −0.499378 + 1.17589i
\(70\) −0.0504624 + 1.20769i −0.00603141 + 0.144346i
\(71\) 0.710165 + 0.710165i 0.0842811 + 0.0842811i 0.747991 0.663709i \(-0.231019\pi\)
−0.663709 + 0.747991i \(0.731019\pi\)
\(72\) −7.29625 4.33184i −0.859871 0.510512i
\(73\) 10.2721 10.2721i 1.20226 1.20226i 0.228787 0.973476i \(-0.426524\pi\)
0.973476 0.228787i \(-0.0734760\pi\)
\(74\) −2.45264 2.66654i −0.285114 0.309979i
\(75\) −6.80658 2.89062i −0.785957 0.333780i
\(76\) −1.30714 + 2.53412i −0.149939 + 0.290684i
\(77\) 1.57113 + 3.79305i 0.179047 + 0.432258i
\(78\) −10.8503 + 3.86307i −1.22856 + 0.437406i
\(79\) 15.4424 1.73741 0.868703 0.495333i \(-0.164954\pi\)
0.868703 + 0.495333i \(0.164954\pi\)
\(80\) −2.89709 1.81528i −0.323905 0.202955i
\(81\) 0.320339 8.99430i 0.0355932 0.999366i
\(82\) −4.97637 13.5932i −0.549548 1.50112i
\(83\) 2.74127 1.13547i 0.300893 0.124634i −0.227129 0.973865i \(-0.572934\pi\)
0.528022 + 0.849231i \(0.322934\pi\)
\(84\) 3.30910 1.02463i 0.361052 0.111797i
\(85\) 1.50805 3.64076i 0.163571 0.394896i
\(86\) −2.10680 2.29054i −0.227182 0.246995i
\(87\) −3.37096 + 3.31148i −0.361405 + 0.355028i
\(88\) −11.5213 1.45099i −1.22817 0.154676i
\(89\) 3.60370 3.60370i 0.381991 0.381991i −0.489828 0.871819i \(-0.662940\pi\)
0.871819 + 0.489828i \(0.162940\pi\)
\(90\) 0.215852 3.61979i 0.0227528 0.381559i
\(91\) 1.79938 4.34408i 0.188626 0.455383i
\(92\) 12.2110 + 1.02224i 1.27309 + 0.106576i
\(93\) 5.81151 + 14.3912i 0.602625 + 1.49230i
\(94\) −7.39863 + 15.9443i −0.763111 + 1.64453i
\(95\) −1.21855 −0.125020
\(96\) −2.11621 + 9.56669i −0.215985 + 0.976397i
\(97\) 14.5603 1.47837 0.739185 0.673502i \(-0.235211\pi\)
0.739185 + 0.673502i \(0.235211\pi\)
\(98\) −0.595271 + 1.28283i −0.0601314 + 0.129585i
\(99\) −4.51010 11.4612i −0.453283 1.15190i
\(100\) −0.712346 + 8.50919i −0.0712346 + 0.850919i
\(101\) 2.04890 4.94648i 0.203873 0.492193i −0.788563 0.614953i \(-0.789175\pi\)
0.992436 + 0.122761i \(0.0391748\pi\)
\(102\) −11.2792 0.571896i −1.11680 0.0566261i
\(103\) −0.886730 + 0.886730i −0.0873721 + 0.0873721i −0.749442 0.662070i \(-0.769678\pi\)
0.662070 + 0.749442i \(0.269678\pi\)
\(104\) 8.15524 + 10.5054i 0.799687 + 1.03013i
\(105\) 1.03744 + 1.05607i 0.101244 + 0.103062i
\(106\) 3.30835 + 3.59688i 0.321335 + 0.349360i
\(107\) −7.52882 + 18.1762i −0.727839 + 1.75716i −0.0781710 + 0.996940i \(0.524908\pi\)
−0.649668 + 0.760218i \(0.725092\pi\)
\(108\) −9.98043 + 2.89672i −0.960368 + 0.278737i
\(109\) −0.783062 + 0.324355i −0.0750038 + 0.0310676i −0.419870 0.907584i \(-0.637924\pi\)
0.344866 + 0.938652i \(0.387924\pi\)
\(110\) −1.70603 4.66009i −0.162663 0.444322i
\(111\) −4.43704 0.0394915i −0.421145 0.00374837i
\(112\) −2.31879 3.25933i −0.219105 0.307977i
\(113\) −10.1322 −0.953158 −0.476579 0.879132i \(-0.658123\pi\)
−0.476579 + 0.879132i \(0.658123\pi\)
\(114\) 1.17132 + 3.28992i 0.109704 + 0.308129i
\(115\) 2.00399 + 4.83805i 0.186873 + 0.451151i
\(116\) 4.84930 + 2.50134i 0.450246 + 0.232244i
\(117\) −5.62924 + 12.9341i −0.520424 + 1.19576i
\(118\) 1.23067 + 1.33800i 0.113292 + 0.123173i
\(119\) 3.26020 3.26020i 0.298862 0.298862i
\(120\) −4.04805 + 1.07045i −0.369535 + 0.0977183i
\(121\) −4.14057 4.14057i −0.376415 0.376415i
\(122\) −0.108550 + 2.59787i −0.00982770 + 0.235200i
\(123\) −16.3182 6.93000i −1.47136 0.624857i
\(124\) 13.6853 11.5709i 1.22897 1.03910i
\(125\) −7.31961 + 3.03188i −0.654686 + 0.271180i
\(126\) 1.85403 3.81609i 0.165170 0.339965i
\(127\) 0.439748i 0.0390213i 0.999810 + 0.0195107i \(0.00621083\pi\)
−0.999810 + 0.0195107i \(0.993789\pi\)
\(128\) 11.2568 1.13374i 0.994966 0.100210i
\(129\) −3.81137 0.0339228i −0.335573 0.00298674i
\(130\) −2.39229 + 5.15548i −0.209818 + 0.452166i
\(131\) −5.92811 14.3117i −0.517941 1.25042i −0.939166 0.343465i \(-0.888399\pi\)
0.421224 0.906957i \(-0.361601\pi\)
\(132\) −10.9417 + 9.08551i −0.952355 + 0.790792i
\(133\) −1.31717 0.545588i −0.114213 0.0473085i
\(134\) −13.5080 0.564424i −1.16691 0.0487588i
\(135\) −3.05544 3.22312i −0.262970 0.277402i
\(136\) 3.44594 + 12.5773i 0.295487 + 1.07849i
\(137\) 5.20385 + 5.20385i 0.444595 + 0.444595i 0.893553 0.448958i \(-0.148205\pi\)
−0.448958 + 0.893553i \(0.648205\pi\)
\(138\) 11.1358 10.0610i 0.947942 0.856453i
\(139\) 7.30702 + 3.02667i 0.619773 + 0.256719i 0.670401 0.741999i \(-0.266122\pi\)
−0.0506276 + 0.998718i \(0.516122\pi\)
\(140\) 0.783634 1.51922i 0.0662292 0.128397i
\(141\) 8.06096 + 19.9615i 0.678855 + 1.68106i
\(142\) −0.488281 1.33376i −0.0409756 0.111927i
\(143\) 19.3044i 1.61431i
\(144\) 6.78123 + 9.90025i 0.565102 + 0.825021i
\(145\) 2.33182i 0.193647i
\(146\) −19.2921 + 7.06271i −1.59663 + 0.584514i
\(147\) 0.648559 + 1.60604i 0.0534922 + 0.132464i
\(148\) 1.55901 + 4.88071i 0.128150 + 0.401192i
\(149\) −18.8727 7.81735i −1.54612 0.640422i −0.563507 0.826111i \(-0.690548\pi\)
−0.982608 + 0.185690i \(0.940548\pi\)
\(150\) 7.01099 + 7.75993i 0.572445 + 0.633596i
\(151\) −13.8539 13.8539i −1.12742 1.12742i −0.990596 0.136822i \(-0.956311\pi\)
−0.136822 0.990596i \(-0.543689\pi\)
\(152\) 3.18532 2.47275i 0.258364 0.200566i
\(153\) −9.95314 + 9.60496i −0.804664 + 0.776515i
\(154\) 0.242395 5.80108i 0.0195327 0.467464i
\(155\) 7.07575 + 2.93087i 0.568338 + 0.235413i
\(156\) 16.2187 + 1.50322i 1.29853 + 0.120354i
\(157\) −1.97051 4.75724i −0.157264 0.379669i 0.825534 0.564352i \(-0.190874\pi\)
−0.982798 + 0.184683i \(0.940874\pi\)
\(158\) −19.8100 9.19241i −1.57600 0.731309i
\(159\) 5.98509 + 0.0532698i 0.474648 + 0.00422457i
\(160\) 2.63590 + 4.05325i 0.208386 + 0.320438i
\(161\) 6.12686i 0.482864i
\(162\) −5.76498 + 11.3475i −0.452940 + 0.891541i
\(163\) −11.3771 + 4.71255i −0.891124 + 0.369115i −0.780801 0.624780i \(-0.785189\pi\)
−0.110323 + 0.993896i \(0.535189\pi\)
\(164\) −1.70779 + 20.4000i −0.133356 + 1.59297i
\(165\) −5.59429 2.37578i −0.435515 0.184954i
\(166\) −4.19249 0.175181i −0.325400 0.0135967i
\(167\) −1.97579 1.97579i −0.152891 0.152891i 0.626517 0.779408i \(-0.284480\pi\)
−0.779408 + 0.626517i \(0.784480\pi\)
\(168\) −4.85494 0.655377i −0.374567 0.0505634i
\(169\) 6.44089 6.44089i 0.495453 0.495453i
\(170\) −4.10181 + 3.77278i −0.314595 + 0.289359i
\(171\) 3.92174 + 1.70684i 0.299903 + 0.130525i
\(172\) 1.33917 + 4.19248i 0.102111 + 0.319674i
\(173\) 5.32667 + 12.8597i 0.404980 + 0.977707i 0.986438 + 0.164131i \(0.0524821\pi\)
−0.581459 + 0.813576i \(0.697518\pi\)
\(174\) 6.29560 2.24144i 0.477268 0.169923i
\(175\) −4.26948 −0.322742
\(176\) 13.9161 + 8.71965i 1.04897 + 0.657268i
\(177\) 2.22639 + 0.0198158i 0.167345 + 0.00148945i
\(178\) −6.76811 + 2.47776i −0.507291 + 0.185716i
\(179\) 21.6597 8.97176i 1.61893 0.670581i 0.624999 0.780626i \(-0.285099\pi\)
0.993927 + 0.110045i \(0.0350995\pi\)
\(180\) −2.43165 + 4.51508i −0.181245 + 0.336534i
\(181\) −6.73608 + 16.2623i −0.500689 + 1.20877i 0.448420 + 0.893823i \(0.351987\pi\)
−0.949109 + 0.314947i \(0.898013\pi\)
\(182\) −4.89420 + 4.50160i −0.362782 + 0.333681i
\(183\) 2.23165 + 2.27174i 0.164969 + 0.167932i
\(184\) −15.0561 8.58022i −1.10995 0.632542i
\(185\) −1.54829 + 1.54829i −0.113832 + 0.113832i
\(186\) 1.11147 21.9209i 0.0814968 1.60732i
\(187\) −7.24389 + 17.4883i −0.529726 + 1.27887i
\(188\) 18.9824 16.0497i 1.38443 1.17054i
\(189\) −1.85961 4.85200i −0.135267 0.352931i
\(190\) 1.56319 + 0.725366i 0.113406 + 0.0526236i
\(191\) −2.41495 −0.174740 −0.0873698 0.996176i \(-0.527846\pi\)
−0.0873698 + 0.996176i \(0.527846\pi\)
\(192\) 8.40952 11.0127i 0.606905 0.794775i
\(193\) 4.24466 0.305538 0.152769 0.988262i \(-0.451181\pi\)
0.152769 + 0.988262i \(0.451181\pi\)
\(194\) −18.6783 8.66730i −1.34103 0.622276i
\(195\) 2.60645 + 6.45442i 0.186652 + 0.462210i
\(196\) 1.52726 1.29131i 0.109090 0.0922361i
\(197\) 3.13406 7.56629i 0.223292 0.539076i −0.772041 0.635573i \(-0.780764\pi\)
0.995333 + 0.0964973i \(0.0307639\pi\)
\(198\) −1.03684 + 17.3875i −0.0736848 + 1.23568i
\(199\) 7.39141 7.39141i 0.523963 0.523963i −0.394803 0.918766i \(-0.629187\pi\)
0.918766 + 0.394803i \(0.129187\pi\)
\(200\) 5.97909 10.4918i 0.422785 0.741882i
\(201\) −11.8122 + 11.6038i −0.833170 + 0.818470i
\(202\) −5.57288 + 5.12584i −0.392106 + 0.360653i
\(203\) −1.04404 + 2.52053i −0.0732771 + 0.176907i
\(204\) 14.1288 + 7.44781i 0.989216 + 0.521451i
\(205\) −8.08258 + 3.34791i −0.564512 + 0.233828i
\(206\) 1.66537 0.609679i 0.116032 0.0424784i
\(207\) 0.327164 18.3777i 0.0227395 1.27734i
\(208\) −4.20826 18.3312i −0.291790 1.27104i
\(209\) 5.85326 0.404879
\(210\) −0.702210 1.97232i −0.0484571 0.136103i
\(211\) −5.12945 12.3836i −0.353126 0.852522i −0.996231 0.0867433i \(-0.972354\pi\)
0.643105 0.765778i \(-0.277646\pi\)
\(212\) −2.10293 6.58355i −0.144430 0.452160i
\(213\) −1.60114 0.679971i −0.109708 0.0465909i
\(214\) 20.4779 18.8353i 1.39984 1.28755i
\(215\) −1.32997 + 1.32997i −0.0907029 + 0.0907029i
\(216\) 14.5275 + 2.22507i 0.988473 + 0.151397i
\(217\) 6.33614 + 6.33614i 0.430125 + 0.430125i
\(218\) 1.19761 + 0.0500416i 0.0811127 + 0.00338925i
\(219\) −9.83541 + 23.1596i −0.664615 + 1.56498i
\(220\) −0.585473 + 6.99365i −0.0394726 + 0.471512i
\(221\) 20.0289 8.29624i 1.34729 0.558066i
\(222\) 5.66846 + 2.69190i 0.380442 + 0.180668i
\(223\) 7.77810i 0.520860i −0.965493 0.260430i \(-0.916136\pi\)
0.965493 0.260430i \(-0.0838643\pi\)
\(224\) 1.03443 + 5.56147i 0.0691160 + 0.371591i
\(225\) 12.8064 + 0.227983i 0.853760 + 0.0151989i
\(226\) 12.9979 + 6.03141i 0.864608 + 0.401203i
\(227\) 2.09978 + 5.06933i 0.139368 + 0.336463i 0.978117 0.208054i \(-0.0667129\pi\)
−0.838750 + 0.544517i \(0.816713\pi\)
\(228\) 0.455791 4.91766i 0.0301855 0.325680i
\(229\) −15.1333 6.26843i −1.00004 0.414230i −0.178227 0.983989i \(-0.557036\pi\)
−0.821811 + 0.569760i \(0.807036\pi\)
\(230\) 0.309176 7.39932i 0.0203865 0.487897i
\(231\) −4.98332 5.07282i −0.327878 0.333767i
\(232\) −4.73185 6.09544i −0.310661 0.400185i
\(233\) −9.76684 9.76684i −0.639847 0.639847i 0.310671 0.950518i \(-0.399446\pi\)
−0.950518 + 0.310671i \(0.899446\pi\)
\(234\) 14.9206 13.2413i 0.975393 0.865612i
\(235\) 9.81454 + 4.06532i 0.640230 + 0.265192i
\(236\) −0.782268 2.44901i −0.0509213 0.159417i
\(237\) −24.8012 + 10.0153i −1.61101 + 0.650564i
\(238\) −6.12298 + 2.24158i −0.396894 + 0.145300i
\(239\) 19.5456i 1.26430i 0.774846 + 0.632150i \(0.217827\pi\)
−0.774846 + 0.632150i \(0.782173\pi\)
\(240\) 5.83017 + 1.03648i 0.376336 + 0.0669046i
\(241\) 4.39112i 0.282857i −0.989948 0.141428i \(-0.954830\pi\)
0.989948 0.141428i \(-0.0451695\pi\)
\(242\) 2.84689 + 7.77641i 0.183005 + 0.499886i
\(243\) 5.31885 + 14.6530i 0.341205 + 0.939989i
\(244\) 1.68569 3.26801i 0.107915 0.209213i
\(245\) 0.789647 + 0.327082i 0.0504487 + 0.0208965i
\(246\) 16.8082 + 18.6038i 1.07165 + 1.18613i
\(247\) −4.74016 4.74016i −0.301609 0.301609i
\(248\) −24.4437 + 6.69711i −1.55218 + 0.425267i
\(249\) −3.66617 + 3.60149i −0.232334 + 0.228235i
\(250\) 11.1946 + 0.467760i 0.708009 + 0.0295837i
\(251\) −2.48710 1.03019i −0.156984 0.0650251i 0.302808 0.953052i \(-0.402076\pi\)
−0.459792 + 0.888027i \(0.652076\pi\)
\(252\) −4.65001 + 3.79175i −0.292923 + 0.238858i
\(253\) −9.62610 23.2395i −0.605188 1.46105i
\(254\) 0.261769 0.564122i 0.0164248 0.0353961i
\(255\) −0.0607479 + 6.82528i −0.00380418 + 0.427415i
\(256\) −15.1154 5.24642i −0.944712 0.327901i
\(257\) 19.7184i 1.23000i −0.788526 0.615001i \(-0.789155\pi\)
0.788526 0.615001i \(-0.210845\pi\)
\(258\) 4.86915 + 2.31232i 0.303140 + 0.143958i
\(259\) −2.36682 + 0.980368i −0.147067 + 0.0609171i
\(260\) 6.13781 5.18954i 0.380651 0.321842i
\(261\) 3.26621 7.50465i 0.202173 0.464526i
\(262\) −0.914591 + 21.8883i −0.0565036 + 1.35227i
\(263\) −18.5553 18.5553i −1.14417 1.14417i −0.987679 0.156493i \(-0.949981\pi\)
−0.156493 0.987679i \(-0.550019\pi\)
\(264\) 19.4447 5.14188i 1.19674 0.316461i
\(265\) 2.08848 2.08848i 0.128294 0.128294i
\(266\) 1.36493 + 1.48397i 0.0836891 + 0.0909879i
\(267\) −3.45048 + 8.12491i −0.211166 + 0.497236i
\(268\) 16.9925 + 8.76498i 1.03798 + 0.535406i
\(269\) 2.61089 + 6.30325i 0.159189 + 0.384316i 0.983270 0.182156i \(-0.0583077\pi\)
−0.824081 + 0.566473i \(0.808308\pi\)
\(270\) 2.00098 + 5.95352i 0.121776 + 0.362320i
\(271\) −23.3120 −1.41610 −0.708052 0.706160i \(-0.750426\pi\)
−0.708052 + 0.706160i \(0.750426\pi\)
\(272\) 3.06633 18.1858i 0.185924 1.10267i
\(273\) −0.0724831 + 8.14378i −0.00438688 + 0.492884i
\(274\) −3.57795 9.77335i −0.216152 0.590430i
\(275\) 16.1943 6.70791i 0.976554 0.404502i
\(276\) −20.2744 + 6.27779i −1.22037 + 0.377879i
\(277\) −3.09577 + 7.47384i −0.186007 + 0.449059i −0.989184 0.146680i \(-0.953141\pi\)
0.803177 + 0.595740i \(0.203141\pi\)
\(278\) −7.57198 8.23235i −0.454137 0.493744i
\(279\) −18.6671 19.3437i −1.11757 1.15808i
\(280\) −1.90961 + 1.48242i −0.114121 + 0.0885916i
\(281\) −5.79112 + 5.79112i −0.345469 + 0.345469i −0.858419 0.512950i \(-0.828553\pi\)
0.512950 + 0.858419i \(0.328553\pi\)
\(282\) 1.54168 30.4057i 0.0918058 1.81063i
\(283\) 8.52482 20.5807i 0.506748 1.22340i −0.438998 0.898488i \(-0.644666\pi\)
0.945745 0.324909i \(-0.105334\pi\)
\(284\) −0.167568 + 2.00165i −0.00994333 + 0.118776i
\(285\) 1.95704 0.790300i 0.115925 0.0468134i
\(286\) 11.4913 24.7642i 0.679496 1.46434i
\(287\) −10.2357 −0.604194
\(288\) −2.80584 16.7370i −0.165335 0.986237i
\(289\) 4.25782 0.250460
\(290\) 1.38806 2.99132i 0.0815098 0.175657i
\(291\) −23.3844 + 9.44319i −1.37082 + 0.553570i
\(292\) 28.9527 + 2.42378i 1.69433 + 0.141841i
\(293\) 6.10740 14.7446i 0.356798 0.861388i −0.638948 0.769250i \(-0.720630\pi\)
0.995746 0.0921375i \(-0.0293699\pi\)
\(294\) 0.124039 2.44635i 0.00723409 0.142674i
\(295\) 0.776890 0.776890i 0.0452323 0.0452323i
\(296\) 0.905401 7.18915i 0.0526254 0.417861i
\(297\) 14.6767 + 15.4822i 0.851629 + 0.898366i
\(298\) 19.5571 + 21.2627i 1.13291 + 1.23172i
\(299\) −11.0245 + 26.6156i −0.637565 + 1.53922i
\(300\) −4.37465 14.1281i −0.252571 0.815687i
\(301\) −2.03307 + 0.842127i −0.117184 + 0.0485394i
\(302\) 9.52540 + 26.0191i 0.548125 + 1.49723i
\(303\) −0.0825343 + 9.27308i −0.00474147 + 0.532724i
\(304\) −5.55818 + 1.27598i −0.318783 + 0.0731827i
\(305\) 1.57144 0.0899806
\(306\) 18.4857 6.39672i 1.05676 0.365676i
\(307\) 7.66784 + 18.5118i 0.437627 + 1.05652i 0.976766 + 0.214308i \(0.0687496\pi\)
−0.539139 + 0.842217i \(0.681250\pi\)
\(308\) −3.76416 + 7.29751i −0.214483 + 0.415814i
\(309\) 0.849029 1.99922i 0.0482996 0.113732i
\(310\) −7.33232 7.97179i −0.416448 0.452767i
\(311\) 8.60776 8.60776i 0.488101 0.488101i −0.419605 0.907707i \(-0.637832\pi\)
0.907707 + 0.419605i \(0.137832\pi\)
\(312\) −19.9110 11.5829i −1.12724 0.655752i
\(313\) 3.37970 + 3.37970i 0.191032 + 0.191032i 0.796142 0.605110i \(-0.206871\pi\)
−0.605110 + 0.796142i \(0.706871\pi\)
\(314\) −0.304011 + 7.27572i −0.0171564 + 0.410592i
\(315\) −2.35110 1.02326i −0.132469 0.0576540i
\(316\) 19.9409 + 23.5846i 1.12176 + 1.32674i
\(317\) 15.4190 6.38676i 0.866018 0.358716i 0.0949595 0.995481i \(-0.469728\pi\)
0.771058 + 0.636765i \(0.219728\pi\)
\(318\) −7.64614 3.63108i −0.428774 0.203621i
\(319\) 11.2008i 0.627125i
\(320\) −0.968625 6.76870i −0.0541478 0.378382i
\(321\) 0.303278 34.0746i 0.0169274 1.90186i
\(322\) 3.64714 7.85972i 0.203247 0.438005i
\(323\) −2.51550 6.07295i −0.139966 0.337908i
\(324\) 14.1503 11.1251i 0.786128 0.618064i
\(325\) −18.5469 7.68240i −1.02880 0.426143i
\(326\) 17.4001 + 0.727054i 0.963704 + 0.0402678i
\(327\) 1.04727 1.02879i 0.0579140 0.0568922i
\(328\) 14.3343 25.1532i 0.791481 1.38885i
\(329\) 8.78865 + 8.78865i 0.484534 + 0.484534i
\(330\) 5.76229 + 6.37784i 0.317204 + 0.351088i
\(331\) −0.928123 0.384441i −0.0510142 0.0211308i 0.357030 0.934093i \(-0.383789\pi\)
−0.408045 + 0.912962i \(0.633789\pi\)
\(332\) 5.27397 + 2.72039i 0.289447 + 0.149301i
\(333\) 7.15168 2.81426i 0.391910 0.154220i
\(334\) 1.35848 + 3.71074i 0.0743324 + 0.203043i
\(335\) 8.17095i 0.446427i
\(336\) 5.83794 + 3.73074i 0.318486 + 0.203529i
\(337\) 8.96457i 0.488331i 0.969734 + 0.244166i \(0.0785141\pi\)
−0.969734 + 0.244166i \(0.921486\pi\)
\(338\) −12.0966 + 4.42850i −0.657971 + 0.240878i
\(339\) 16.2728 6.57134i 0.883815 0.356906i
\(340\) 7.50775 2.39814i 0.407165 0.130058i
\(341\) −33.9882 14.0784i −1.84056 0.762386i
\(342\) −4.01489 4.52408i −0.217101 0.244634i
\(343\) 0.707107 + 0.707107i 0.0381802 + 0.0381802i
\(344\) 0.777731 6.17541i 0.0419324 0.332956i
\(345\) −6.35625 6.47042i −0.342209 0.348355i
\(346\) 0.821802 19.6677i 0.0441803 1.05734i
\(347\) −16.0478 6.64723i −0.861493 0.356842i −0.0922017 0.995740i \(-0.529390\pi\)
−0.769291 + 0.638898i \(0.779390\pi\)
\(348\) −9.41044 0.872202i −0.504453 0.0467549i
\(349\) 3.78792 + 9.14486i 0.202763 + 0.489513i 0.992250 0.124254i \(-0.0396536\pi\)
−0.789488 + 0.613766i \(0.789654\pi\)
\(350\) 5.47701 + 2.54149i 0.292759 + 0.135849i
\(351\) 0.652279 24.4236i 0.0348161 1.30364i
\(352\) −12.6615 19.4697i −0.674858 1.03774i
\(353\) 17.1513i 0.912870i −0.889757 0.456435i \(-0.849126\pi\)
0.889757 0.456435i \(-0.150874\pi\)
\(354\) −2.84428 1.35072i −0.151172 0.0717901i
\(355\) −0.793062 + 0.328497i −0.0420914 + 0.0174348i
\(356\) 10.1573 + 0.850316i 0.538334 + 0.0450666i
\(357\) −3.12159 + 7.35045i −0.165212 + 0.389027i
\(358\) −33.1264 1.38417i −1.75078 0.0731555i
\(359\) 25.3034 + 25.3034i 1.33546 + 1.33546i 0.900399 + 0.435066i \(0.143275\pi\)
0.435066 + 0.900399i \(0.356725\pi\)
\(360\) 5.80709 4.34459i 0.306061 0.228980i
\(361\) 11.9978 11.9978i 0.631461 0.631461i
\(362\) 18.3217 16.8520i 0.962969 0.885723i
\(363\) 9.33533 + 3.96453i 0.489978 + 0.208084i
\(364\) 8.95810 2.86142i 0.469532 0.149979i
\(365\) 4.75153 + 11.4712i 0.248706 + 0.600430i
\(366\) −1.51054 4.24269i −0.0789570 0.221769i
\(367\) −28.5539 −1.49050 −0.745250 0.666785i \(-0.767670\pi\)
−0.745250 + 0.666785i \(0.767670\pi\)
\(368\) 14.2069 + 19.9694i 0.740586 + 1.04098i
\(369\) 30.7022 + 0.546569i 1.59829 + 0.0284532i
\(370\) 2.90784 1.06454i 0.151172 0.0553428i
\(371\) 3.19259 1.32241i 0.165751 0.0686562i
\(372\) −14.4747 + 27.4591i −0.750477 + 1.42369i
\(373\) 12.4715 30.1090i 0.645752 1.55898i −0.173054 0.984912i \(-0.555364\pi\)
0.818806 0.574070i \(-0.194636\pi\)
\(374\) 19.7029 18.1224i 1.01881 0.937089i
\(375\) 9.78925 9.61653i 0.505515 0.496595i
\(376\) −33.9051 + 9.28935i −1.74852 + 0.479062i
\(377\) −9.07077 + 9.07077i −0.467169 + 0.467169i
\(378\) −0.502688 + 7.33126i −0.0258555 + 0.377079i
\(379\) 5.85723 14.1406i 0.300866 0.726354i −0.699071 0.715053i \(-0.746403\pi\)
0.999936 0.0113011i \(-0.00359733\pi\)
\(380\) −1.57352 1.86104i −0.0807198 0.0954695i
\(381\) −0.285202 0.706254i −0.0146114 0.0361825i
\(382\) 3.09797 + 1.43755i 0.158506 + 0.0735513i
\(383\) −2.54545 −0.130067 −0.0650333 0.997883i \(-0.520715\pi\)
−0.0650333 + 0.997883i \(0.520715\pi\)
\(384\) −17.3435 + 9.12151i −0.885058 + 0.465480i
\(385\) −3.50906 −0.178838
\(386\) −5.44518 2.52672i −0.277153 0.128607i
\(387\) 6.14323 2.41742i 0.312278 0.122884i
\(388\) 18.8018 + 22.2373i 0.954514 + 1.12893i
\(389\) −10.0399 + 24.2384i −0.509042 + 1.22894i 0.435393 + 0.900240i \(0.356609\pi\)
−0.944435 + 0.328697i \(0.893391\pi\)
\(390\) 0.498491 9.83146i 0.0252421 0.497835i
\(391\) −19.9748 + 19.9748i −1.01017 + 1.01017i
\(392\) −2.72789 + 0.747392i −0.137779 + 0.0377490i
\(393\) 18.8028 + 19.1405i 0.948475 + 0.965511i
\(394\) −8.52446 + 7.84065i −0.429456 + 0.395006i
\(395\) −5.05094 + 12.1940i −0.254140 + 0.613549i
\(396\) 11.6804 21.6881i 0.586961 1.08987i
\(397\) 12.7125 5.26571i 0.638024 0.264278i −0.0401340 0.999194i \(-0.512778\pi\)
0.678158 + 0.734916i \(0.262778\pi\)
\(398\) −13.8818 + 5.08203i −0.695832 + 0.254739i
\(399\) 2.46927 + 0.0219776i 0.123618 + 0.00110025i
\(400\) −13.9156 + 9.90002i −0.695781 + 0.495001i
\(401\) −32.5152 −1.62373 −0.811867 0.583842i \(-0.801549\pi\)
−0.811867 + 0.583842i \(0.801549\pi\)
\(402\) 22.0605 7.85425i 1.10028 0.391734i
\(403\) 16.1236 + 38.9258i 0.803173 + 1.93903i
\(404\) 10.2003 3.25821i 0.507485 0.162102i
\(405\) 6.99754 + 3.19483i 0.347711 + 0.158752i
\(406\) 2.83972 2.61193i 0.140933 0.129628i
\(407\) 7.43716 7.43716i 0.368647 0.368647i
\(408\) −13.6914 17.9648i −0.677827 0.889388i
\(409\) 22.1803 + 22.1803i 1.09674 + 1.09674i 0.994789 + 0.101954i \(0.0325094\pi\)
0.101954 + 0.994789i \(0.467491\pi\)
\(410\) 12.3615 + 0.516518i 0.610491 + 0.0255090i
\(411\) −11.7326 4.98260i −0.578727 0.245773i
\(412\) −2.49931 0.209229i −0.123132 0.0103080i
\(413\) 1.18761 0.491922i 0.0584383 0.0242059i
\(414\) −11.3594 + 23.3807i −0.558283 + 1.14910i
\(415\) 2.53602i 0.124489i
\(416\) −5.51352 + 26.0208i −0.270323 + 1.27578i
\(417\) −13.6984 0.121921i −0.670811 0.00597051i
\(418\) −7.50874 3.48428i −0.367265 0.170421i
\(419\) 0.0924059 + 0.223088i 0.00451432 + 0.0108985i 0.926121 0.377228i \(-0.123123\pi\)
−0.921606 + 0.388126i \(0.873123\pi\)
\(420\) −0.273248 + 2.94816i −0.0133332 + 0.143855i
\(421\) 1.80380 + 0.747158i 0.0879118 + 0.0364143i 0.426206 0.904626i \(-0.359850\pi\)
−0.338294 + 0.941040i \(0.609850\pi\)
\(422\) −0.791374 + 18.9395i −0.0385235 + 0.921958i
\(423\) −25.8925 26.8311i −1.25893 1.30457i
\(424\) −1.22129 + 9.69739i −0.0593110 + 0.470947i
\(425\) −13.9193 13.9193i −0.675187 0.675187i
\(426\) 1.64922 + 1.82540i 0.0799051 + 0.0884409i
\(427\) 1.69862 + 0.703592i 0.0822021 + 0.0340492i
\(428\) −37.4818 + 11.9725i −1.81175 + 0.578714i
\(429\) −12.5200 31.0036i −0.604472 1.49687i
\(430\) 2.49781 0.914430i 0.120455 0.0440977i
\(431\) 10.6345i 0.512248i 0.966644 + 0.256124i \(0.0824455\pi\)
−0.966644 + 0.256124i \(0.917555\pi\)
\(432\) −17.3118 11.5022i −0.832916 0.553399i
\(433\) 24.3357i 1.16950i 0.811213 + 0.584751i \(0.198808\pi\)
−0.811213 + 0.584751i \(0.801192\pi\)
\(434\) −4.35647 11.8999i −0.209117 0.571213i
\(435\) −1.51232 3.74499i −0.0725102 0.179559i
\(436\) −1.50655 0.777100i −0.0721506 0.0372163i
\(437\) 8.07009 + 3.34274i 0.386045 + 0.159905i
\(438\) 26.4034 23.8551i 1.26160 1.13984i
\(439\) 14.8534 + 14.8534i 0.708915 + 0.708915i 0.966307 0.257392i \(-0.0828633\pi\)
−0.257392 + 0.966307i \(0.582863\pi\)
\(440\) 4.91418 8.62315i 0.234274 0.411092i
\(441\) −2.08323 2.15874i −0.0992012 0.102797i
\(442\) −30.6322 1.27995i −1.45702 0.0608809i
\(443\) 14.2315 + 5.89490i 0.676161 + 0.280075i 0.694221 0.719762i \(-0.255749\pi\)
−0.0180602 + 0.999837i \(0.505749\pi\)
\(444\) −5.66926 6.82751i −0.269051 0.324019i
\(445\) 1.66694 + 4.02436i 0.0790207 + 0.190773i
\(446\) −4.63007 + 9.97798i −0.219240 + 0.472471i
\(447\) 35.3804 + 0.314901i 1.67344 + 0.0148943i
\(448\) 1.98358 7.75019i 0.0937152 0.366162i
\(449\) 12.4804i 0.588986i −0.955654 0.294493i \(-0.904849\pi\)
0.955654 0.294493i \(-0.0951508\pi\)
\(450\) −16.2927 7.91573i −0.768046 0.373151i
\(451\) 38.8245 16.0816i 1.82817 0.757254i
\(452\) −13.0838 15.4745i −0.615409 0.727861i
\(453\) 31.2351 + 13.2649i 1.46755 + 0.623240i
\(454\) 0.323956 7.75303i 0.0152040 0.363868i
\(455\) 2.84174 + 2.84174i 0.133223 + 0.133223i
\(456\) −3.51204 + 6.03720i −0.164466 + 0.282718i
\(457\) −20.9844 + 20.9844i −0.981611 + 0.981611i −0.999834 0.0182230i \(-0.994199\pi\)
0.0182230 + 0.999834i \(0.494199\pi\)
\(458\) 15.6821 + 17.0498i 0.732775 + 0.796683i
\(459\) 9.75578 21.8812i 0.455361 1.02133i
\(460\) −4.80122 + 9.30802i −0.223858 + 0.433989i
\(461\) −0.727642 1.75668i −0.0338897 0.0818169i 0.906029 0.423217i \(-0.139099\pi\)
−0.939918 + 0.341400i \(0.889099\pi\)
\(462\) 3.37305 + 9.47399i 0.156928 + 0.440770i
\(463\) 11.5625 0.537357 0.268678 0.963230i \(-0.413413\pi\)
0.268678 + 0.963230i \(0.413413\pi\)
\(464\) 2.44172 + 10.6361i 0.113354 + 0.493771i
\(465\) −13.2648 0.118062i −0.615140 0.00547501i
\(466\) 6.71528 + 18.3431i 0.311079 + 0.849728i
\(467\) 18.5993 7.70408i 0.860673 0.356502i 0.0917022 0.995786i \(-0.470769\pi\)
0.768971 + 0.639284i \(0.220769\pi\)
\(468\) −27.0228 + 8.10454i −1.24913 + 0.374633i
\(469\) −3.65843 + 8.83223i −0.168931 + 0.407835i
\(470\) −10.1704 11.0574i −0.469127 0.510041i
\(471\) 6.25007 + 6.36233i 0.287988 + 0.293161i
\(472\) −0.454306 + 3.60732i −0.0209111 + 0.166040i
\(473\) 6.38845 6.38845i 0.293741 0.293741i
\(474\) 37.7775 + 1.91546i 1.73518 + 0.0879799i
\(475\) −2.32938 + 5.62361i −0.106879 + 0.258029i
\(476\) 9.18910 + 0.769265i 0.421182 + 0.0352592i
\(477\) −9.64685 + 3.79613i −0.441699 + 0.173813i
\(478\) 11.6349 25.0737i 0.532169 1.14684i
\(479\) 8.30224 0.379339 0.189670 0.981848i \(-0.439258\pi\)
0.189670 + 0.981848i \(0.439258\pi\)
\(480\) −6.86213 4.80016i −0.313212 0.219096i
\(481\) −12.0457 −0.549237
\(482\) −2.61390 + 5.63306i −0.119060 + 0.256579i
\(483\) −3.97363 9.84000i −0.180806 0.447735i
\(484\) 0.976994 11.6705i 0.0444088 0.530476i
\(485\) −4.76241 + 11.4975i −0.216250 + 0.522073i
\(486\) 1.89930 21.9634i 0.0861541 0.996282i
\(487\) 0.907128 0.907128i 0.0411059 0.0411059i −0.686255 0.727361i \(-0.740747\pi\)
0.727361 + 0.686255i \(0.240747\pi\)
\(488\) −4.10780 + 3.18886i −0.185951 + 0.144353i
\(489\) 15.2157 14.9473i 0.688080 0.675939i
\(490\) −0.818280 0.889645i −0.0369661 0.0401900i
\(491\) 5.93382 14.3255i 0.267789 0.646501i −0.731589 0.681746i \(-0.761221\pi\)
0.999379 + 0.0352448i \(0.0112211\pi\)
\(492\) −10.4878 33.8709i −0.472828 1.52702i
\(493\) −11.6212 + 4.81366i −0.523393 + 0.216797i
\(494\) 3.25914 + 8.90249i 0.146636 + 0.400542i
\(495\) 10.5255 + 0.187378i 0.473086 + 0.00842200i
\(496\) 35.3437 + 5.95936i 1.58698 + 0.267583i
\(497\) −1.00433 −0.0450501
\(498\) 6.84693 2.43773i 0.306818 0.109237i
\(499\) −13.2334 31.9483i −0.592409 1.43020i −0.881169 0.472801i \(-0.843243\pi\)
0.288760 0.957402i \(-0.406757\pi\)
\(500\) −14.0823 7.26388i −0.629781 0.324850i
\(501\) 4.45463 + 1.89179i 0.199018 + 0.0845189i
\(502\) 2.57729 + 2.80206i 0.115030 + 0.125062i
\(503\) −7.92582 + 7.92582i −0.353395 + 0.353395i −0.861371 0.507976i \(-0.830394\pi\)
0.507976 + 0.861371i \(0.330394\pi\)
\(504\) 8.22230 2.09615i 0.366250 0.0933701i
\(505\) 3.23581 + 3.23581i 0.143992 + 0.143992i
\(506\) −1.48512 + 35.5424i −0.0660216 + 1.58005i
\(507\) −6.16705 + 14.5216i −0.273888 + 0.644929i
\(508\) −0.671610 + 0.567849i −0.0297979 + 0.0251942i
\(509\) 37.0692 15.3546i 1.64307 0.680580i 0.646463 0.762945i \(-0.276247\pi\)
0.996602 + 0.0823650i \(0.0262473\pi\)
\(510\) 4.14082 8.71951i 0.183358 0.386106i
\(511\) 14.5270i 0.642637i
\(512\) 16.2674 + 15.7280i 0.718926 + 0.695086i
\(513\) −7.40546 0.197777i −0.326959 0.00873207i
\(514\) −11.7378 + 25.2954i −0.517733 + 1.11573i
\(515\) −0.410170 0.990237i −0.0180742 0.0436350i
\(516\) −4.86984 5.86477i −0.214383 0.258182i
\(517\) −47.1439 19.5276i −2.07338 0.858824i
\(518\) 3.61981 + 0.151252i 0.159045 + 0.00664562i
\(519\) −16.8952 17.1986i −0.741615 0.754935i
\(520\) −10.9630 + 3.00364i −0.480757 + 0.131718i
\(521\) 10.9267 + 10.9267i 0.478706 + 0.478706i 0.904718 0.426012i \(-0.140082\pi\)
−0.426012 + 0.904718i \(0.640082\pi\)
\(522\) −8.65729 + 7.68291i −0.378919 + 0.336272i
\(523\) 3.80919 + 1.57782i 0.166564 + 0.0689931i 0.464408 0.885622i \(-0.346267\pi\)
−0.297843 + 0.954615i \(0.596267\pi\)
\(524\) 14.2028 27.5346i 0.620450 1.20285i
\(525\) 6.85696 2.76901i 0.299262 0.120849i
\(526\) 12.7579 + 34.8488i 0.556271 + 1.51948i
\(527\) 41.3141i 1.79967i
\(528\) −28.0051 4.97871i −1.21876 0.216670i
\(529\) 14.5384i 0.632105i
\(530\) −3.92237 + 1.43595i −0.170377 + 0.0623738i
\(531\) −3.58852 + 1.41212i −0.155729 + 0.0612807i
\(532\) −0.867608 2.71618i −0.0376156 0.117761i
\(533\) −44.4647 18.4179i −1.92598 0.797767i
\(534\) 9.26290 8.36890i 0.400845 0.362158i
\(535\) −11.8902 11.8902i −0.514059 0.514059i
\(536\) −16.5809 21.3591i −0.716188 0.922573i
\(537\) −28.9677 + 28.4566i −1.25005 + 1.22799i
\(538\) 0.402810 9.64019i 0.0173664 0.415618i
\(539\) −3.79305 1.57113i −0.163378 0.0676734i
\(540\) 0.977042 8.82848i 0.0420452 0.379917i
\(541\) −1.50349 3.62973i −0.0646399 0.156054i 0.888259 0.459343i \(-0.151915\pi\)
−0.952899 + 0.303289i \(0.901915\pi\)
\(542\) 29.9054 + 13.8770i 1.28455 + 0.596066i
\(543\) 0.271345 30.4867i 0.0116445 1.30831i
\(544\) −14.7590 + 21.5040i −0.632789 + 0.921975i
\(545\) 0.724433i 0.0310313i
\(546\) 4.94074 10.4039i 0.211444 0.445247i
\(547\) 18.0556 7.47886i 0.772000 0.319773i 0.0383179 0.999266i \(-0.487800\pi\)
0.733682 + 0.679493i \(0.237800\pi\)
\(548\) −1.22788 + 14.6674i −0.0524525 + 0.626560i
\(549\) −5.05749 2.20115i −0.215848 0.0939426i
\(550\) −24.7676 1.03490i −1.05609 0.0441282i
\(551\) 2.75034 + 2.75034i 0.117169 + 0.117169i
\(552\) 29.7456 + 4.01540i 1.26606 + 0.170907i
\(553\) −10.9194 + 10.9194i −0.464341 + 0.464341i
\(554\) 8.42030 7.74485i 0.357744 0.329047i
\(555\) 1.48246 3.49077i 0.0629270 0.148175i
\(556\) 4.81308 + 15.0681i 0.204120 + 0.639029i
\(557\) −3.89866 9.41220i −0.165191 0.398808i 0.819508 0.573067i \(-0.194247\pi\)
−0.984700 + 0.174260i \(0.944247\pi\)
\(558\) 12.4319 + 35.9267i 0.526284 + 1.52090i
\(559\) −10.3471 −0.437638
\(560\) 3.33215 0.764957i 0.140809 0.0323254i
\(561\) 0.291801 32.7850i 0.0123198 1.38418i
\(562\) 10.8763 3.98174i 0.458789 0.167959i
\(563\) −32.4168 + 13.4275i −1.36621 + 0.565901i −0.940757 0.339082i \(-0.889884\pi\)
−0.425449 + 0.904983i \(0.639884\pi\)
\(564\) −20.0773 + 38.0876i −0.845409 + 1.60378i
\(565\) 3.31407 8.00087i 0.139424 0.336599i
\(566\) −23.1870 + 21.3270i −0.974622 + 0.896441i
\(567\) 6.13341 + 6.58644i 0.257579 + 0.276605i
\(568\) 1.40648 2.46803i 0.0590148 0.103556i
\(569\) 19.2523 19.2523i 0.807097 0.807097i −0.177096 0.984194i \(-0.556670\pi\)
0.984194 + 0.177096i \(0.0566704\pi\)
\(570\) −2.98099 0.151147i −0.124860 0.00633086i
\(571\) −9.88196 + 23.8572i −0.413547 + 0.998391i 0.570631 + 0.821207i \(0.306699\pi\)
−0.984178 + 0.177184i \(0.943301\pi\)
\(572\) −29.4828 + 24.9278i −1.23274 + 1.04228i
\(573\) 3.87851 1.56624i 0.162027 0.0654305i
\(574\) 13.1307 + 6.09301i 0.548063 + 0.254317i
\(575\) 26.1585 1.09088
\(576\) −6.36364 + 23.1410i −0.265152 + 0.964207i
\(577\) 22.2764 0.927380 0.463690 0.885998i \(-0.346525\pi\)
0.463690 + 0.885998i \(0.346525\pi\)
\(578\) −5.46205 2.53455i −0.227191 0.105423i
\(579\) −6.81711 + 2.75292i −0.283309 + 0.114407i
\(580\) −3.56129 + 3.01109i −0.147875 + 0.125029i
\(581\) −1.13547 + 2.74127i −0.0471072 + 0.113727i
\(582\) 35.6195 + 1.80604i 1.47647 + 0.0748627i
\(583\) −10.0319 + 10.0319i −0.415480 + 0.415480i
\(584\) −35.6986 20.3440i −1.47722 0.841841i
\(585\) −8.37214 8.67563i −0.346145 0.358693i
\(586\) −16.6118 + 15.2792i −0.686226 + 0.631179i
\(587\) −13.1122 + 31.6557i −0.541199 + 1.30657i 0.382679 + 0.923881i \(0.375002\pi\)
−0.923878 + 0.382688i \(0.874998\pi\)
\(588\) −1.61536 + 3.06441i −0.0666163 + 0.126374i
\(589\) 11.8027 4.88882i 0.486320 0.201440i
\(590\) −1.45908 + 0.534158i −0.0600693 + 0.0219909i
\(591\) −0.126247 + 14.1844i −0.00519312 + 0.583468i
\(592\) −5.44097 + 8.68350i −0.223622 + 0.356890i
\(593\) 35.0902 1.44098 0.720492 0.693464i \(-0.243916\pi\)
0.720492 + 0.693464i \(0.243916\pi\)
\(594\) −9.61164 28.5976i −0.394370 1.17337i
\(595\) 1.50805 + 3.64076i 0.0618241 + 0.149257i
\(596\) −12.4313 38.9182i −0.509208 1.59415i
\(597\) −7.07715 + 16.6647i −0.289648 + 0.682040i
\(598\) 29.9861 27.5807i 1.22622 1.12786i
\(599\) −17.2410 + 17.2410i −0.704446 + 0.704446i −0.965362 0.260915i \(-0.915976\pi\)
0.260915 + 0.965362i \(0.415976\pi\)
\(600\) −2.79812 + 20.7281i −0.114233 + 0.846220i
\(601\) 15.9790 + 15.9790i 0.651796 + 0.651796i 0.953425 0.301630i \(-0.0975306\pi\)
−0.301630 + 0.953425i \(0.597531\pi\)
\(602\) 3.10938 + 0.129924i 0.126729 + 0.00529529i
\(603\) 11.4452 26.2971i 0.466084 1.07090i
\(604\) 3.26892 39.0483i 0.133011 1.58885i
\(605\) 4.62389 1.91528i 0.187988 0.0778672i
\(606\) 5.62587 11.8467i 0.228535 0.481237i
\(607\) 10.0664i 0.408582i 0.978910 + 0.204291i \(0.0654889\pi\)
−0.978910 + 0.204291i \(0.934511\pi\)
\(608\) 7.88976 + 1.67175i 0.319972 + 0.0677985i
\(609\) 0.0420563 4.72520i 0.00170421 0.191475i
\(610\) −2.01590 0.935434i −0.0816212 0.0378746i
\(611\) 22.3645 + 53.9927i 0.904771 + 2.18431i
\(612\) −27.5218 2.79811i −1.11250 0.113107i
\(613\) 28.3770 + 11.7541i 1.14614 + 0.474746i 0.873237 0.487297i \(-0.162017\pi\)
0.272901 + 0.962042i \(0.412017\pi\)
\(614\) 1.18300 28.3119i 0.0477419 1.14258i
\(615\) 10.8096 10.6189i 0.435887 0.428196i
\(616\) 9.17278 7.12077i 0.369582 0.286904i
\(617\) −2.05184 2.05184i −0.0826041 0.0826041i 0.664597 0.747202i \(-0.268603\pi\)
−0.747202 + 0.664597i \(0.768603\pi\)
\(618\) −2.27924 + 2.05926i −0.0916844 + 0.0828356i
\(619\) 5.60091 + 2.31997i 0.225120 + 0.0932476i 0.492392 0.870373i \(-0.336123\pi\)
−0.267273 + 0.963621i \(0.586123\pi\)
\(620\) 4.66075 + 14.5912i 0.187180 + 0.585995i
\(621\) 11.3936 + 29.7275i 0.457208 + 1.19292i
\(622\) −16.1662 + 5.91835i −0.648207 + 0.237304i
\(623\) 5.09640i 0.204183i
\(624\) 18.6475 + 26.7113i 0.746496 + 1.06931i
\(625\) 14.5758i 0.583032i
\(626\) −2.32374 6.34741i −0.0928754 0.253694i
\(627\) −9.40059 + 3.79619i −0.375423 + 0.151605i
\(628\) 4.72101 9.15254i 0.188389 0.365226i
\(629\) −10.9125 4.52011i −0.435110 0.180228i
\(630\) 2.40695 + 2.71221i 0.0958950 + 0.108057i
\(631\) −9.05228 9.05228i −0.360366 0.360366i 0.503582 0.863948i \(-0.332015\pi\)
−0.863948 + 0.503582i \(0.832015\pi\)
\(632\) −11.5415 42.1253i −0.459097 1.67565i
\(633\) 16.2696 + 16.5618i 0.646659 + 0.658273i
\(634\) −23.5818 0.985352i −0.936553 0.0391333i
\(635\) −0.347245 0.143834i −0.0137800 0.00570787i
\(636\) 7.64722 + 9.20959i 0.303232 + 0.365184i
\(637\) 1.79938 + 4.34408i 0.0712939 + 0.172119i
\(638\) −6.66752 + 14.3687i −0.263969 + 0.568864i
\(639\) 3.01250 + 0.0536293i 0.119173 + 0.00212154i
\(640\) −2.78663 + 9.25969i −0.110151 + 0.366021i
\(641\) 16.6514i 0.657689i 0.944384 + 0.328845i \(0.106659\pi\)
−0.944384 + 0.328845i \(0.893341\pi\)
\(642\) −20.6727 + 43.5314i −0.815885 + 1.71805i
\(643\) 21.1378 8.75558i 0.833595 0.345286i 0.0752701 0.997163i \(-0.476018\pi\)
0.758325 + 0.651877i \(0.226018\pi\)
\(644\) −9.35732 + 7.91165i −0.368730 + 0.311763i
\(645\) 1.27342 2.99854i 0.0501409 0.118067i
\(646\) −0.388092 + 9.28797i −0.0152693 + 0.365430i
\(647\) −3.61890 3.61890i −0.142274 0.142274i 0.632383 0.774656i \(-0.282077\pi\)
−0.774656 + 0.632383i \(0.782077\pi\)
\(648\) −24.7749 + 5.84841i −0.973250 + 0.229747i
\(649\) −3.73177 + 3.73177i −0.146485 + 0.146485i
\(650\) 19.2195 + 20.8957i 0.753850 + 0.819595i
\(651\) −14.2855 6.06674i −0.559891 0.237774i
\(652\) −21.8886 11.2905i −0.857225 0.442169i
\(653\) −12.4735 30.1138i −0.488127 1.17844i −0.955661 0.294468i \(-0.904857\pi\)
0.467534 0.883975i \(-0.345143\pi\)
\(654\) −1.95587 + 0.696355i −0.0764807 + 0.0272296i
\(655\) 13.2402 0.517337
\(656\) −33.3615 + 23.7344i −1.30255 + 0.926674i
\(657\) 0.775718 43.5741i 0.0302636 1.69999i
\(658\) −6.04272 16.5060i −0.235570 0.643470i
\(659\) −29.1373 + 12.0691i −1.13503 + 0.470144i −0.869487 0.493956i \(-0.835550\pi\)
−0.265540 + 0.964100i \(0.585550\pi\)
\(660\) −3.59550 11.6118i −0.139955 0.451989i
\(661\) 2.59423 6.26302i 0.100904 0.243603i −0.865363 0.501145i \(-0.832912\pi\)
0.966267 + 0.257541i \(0.0829124\pi\)
\(662\) 0.961777 + 1.04566i 0.0373805 + 0.0406406i
\(663\) −26.7867 + 26.3140i −1.04031 + 1.02195i
\(664\) −5.14624 6.62924i −0.199713 0.257265i
\(665\) 0.861644 0.861644i 0.0334131 0.0334131i
\(666\) −10.8496 0.646975i −0.420415 0.0250698i
\(667\) 6.39668 15.4429i 0.247680 0.597953i
\(668\) 0.466201 5.56891i 0.0180379 0.215467i
\(669\) 5.04456 + 12.4920i 0.195034 + 0.482967i
\(670\) 4.86393 10.4819i 0.187910 0.404953i
\(671\) −7.54839 −0.291402
\(672\) −5.26828 8.26106i −0.203228 0.318677i
\(673\) −0.323919 −0.0124862 −0.00624309 0.999981i \(-0.501987\pi\)
−0.00624309 + 0.999981i \(0.501987\pi\)
\(674\) 5.33635 11.5000i 0.205548 0.442964i
\(675\) −20.7155 + 7.93955i −0.797339 + 0.305594i
\(676\) 18.1541 + 1.51977i 0.698234 + 0.0584527i
\(677\) −1.57541 + 3.80337i −0.0605478 + 0.146175i −0.951258 0.308396i \(-0.900208\pi\)
0.890710 + 0.454572i \(0.150208\pi\)
\(678\) −24.7869 1.25679i −0.951936 0.0482666i
\(679\) −10.2957 + 10.2957i −0.395111 + 0.395111i
\(680\) −11.0587 1.39273i −0.424082 0.0534089i
\(681\) −6.66010 6.77972i −0.255216 0.259800i
\(682\) 35.2206 + 38.2923i 1.34867 + 1.46629i
\(683\) −19.7967 + 47.7935i −0.757501 + 1.82877i −0.246633 + 0.969109i \(0.579324\pi\)
−0.510868 + 0.859659i \(0.670676\pi\)
\(684\) 2.45737 + 8.19358i 0.0939600 + 0.313289i
\(685\) −5.81129 + 2.40711i −0.222038 + 0.0919711i
\(686\) −0.486178 1.32802i −0.0185624 0.0507040i
\(687\) 28.3702 + 0.252507i 1.08239 + 0.00963374i
\(688\) −4.67374 + 7.45904i −0.178185 + 0.284373i
\(689\) 16.2484 0.619013
\(690\) 4.30234 + 12.0841i 0.163787 + 0.460035i
\(691\) −4.03747 9.74731i −0.153593 0.370805i 0.828289 0.560301i \(-0.189315\pi\)
−0.981882 + 0.189496i \(0.939315\pi\)
\(692\) −12.7618 + 24.7411i −0.485131 + 0.940514i
\(693\) 11.2934 + 4.91519i 0.429002 + 0.186713i
\(694\) 16.6297 + 18.0801i 0.631256 + 0.686310i
\(695\) −4.77999 + 4.77999i −0.181316 + 0.181316i
\(696\) 11.5528 + 6.72065i 0.437908 + 0.254745i
\(697\) −33.3704 33.3704i −1.26399 1.26399i
\(698\) 0.584402 13.9861i 0.0221200 0.529383i
\(699\) 22.0203 + 9.35158i 0.832885 + 0.353709i
\(700\) −5.51320 6.52061i −0.208379 0.246456i
\(701\) −9.75134 + 4.03914i −0.368303 + 0.152556i −0.559156 0.829063i \(-0.688875\pi\)
0.190853 + 0.981619i \(0.438875\pi\)
\(702\) −15.3754 + 30.9430i −0.580308 + 1.16787i
\(703\) 3.65237i 0.137752i
\(704\) 4.65276 + 32.5133i 0.175358 + 1.22539i
\(705\) −18.3992 0.163760i −0.692952 0.00616757i
\(706\) −10.2096 + 22.0022i −0.384245 + 0.828062i
\(707\) 2.04890 + 4.94648i 0.0770567 + 0.186031i
\(708\) 2.84468 + 3.42586i 0.106910 + 0.128752i
\(709\) 7.64758 + 3.16773i 0.287211 + 0.118967i 0.521638 0.853167i \(-0.325321\pi\)
−0.234427 + 0.972134i \(0.575321\pi\)
\(710\) 1.21291 + 0.0506807i 0.0455197 + 0.00190201i
\(711\) 33.3362 32.1700i 1.25020 1.20647i
\(712\) −12.5239 7.13714i −0.469352 0.267476i
\(713\) −38.8206 38.8206i −1.45384 1.45384i
\(714\) 8.37997 7.57119i 0.313613 0.283345i
\(715\) −15.2436 6.31411i −0.570079 0.236134i
\(716\) 41.6716 + 21.4948i 1.55734 + 0.803299i
\(717\) −12.6765 31.3911i −0.473412 1.17232i
\(718\) −17.3976 47.5224i −0.649273 1.77352i
\(719\) 18.0723i 0.673984i −0.941508 0.336992i \(-0.890590\pi\)
0.941508 0.336992i \(-0.109410\pi\)
\(720\) −10.0357 + 2.11658i −0.374009 + 0.0788802i
\(721\) 1.25403i 0.0467023i
\(722\) −22.5330 + 8.24918i −0.838592 + 0.307003i
\(723\) 2.84790 + 7.05232i 0.105915 + 0.262279i
\(724\) −33.5352 + 10.7119i −1.24633 + 0.398104i
\(725\) 10.7613 + 4.45750i 0.399666 + 0.165547i
\(726\) −9.61568 10.6429i −0.356871 0.394994i
\(727\) −2.47204 2.47204i −0.0916827 0.0916827i 0.659778 0.751461i \(-0.270650\pi\)
−0.751461 + 0.659778i \(0.770650\pi\)
\(728\) −13.1950 1.66178i −0.489040 0.0615897i
\(729\) −18.0456 20.0837i −0.668356 0.743841i
\(730\) 0.733068 17.5440i 0.0271321 0.649334i
\(731\) −9.37373 3.88273i −0.346700 0.143608i
\(732\) −0.587789 + 6.34183i −0.0217253 + 0.234401i
\(733\) 8.48130 + 20.4757i 0.313264 + 0.756286i 0.999580 + 0.0289824i \(0.00922668\pi\)
−0.686316 + 0.727303i \(0.740773\pi\)
\(734\) 36.6298 + 16.9973i 1.35203 + 0.627381i
\(735\) −1.48034 0.0131756i −0.0546031 0.000485991i
\(736\) −6.33783 34.0743i −0.233615 1.25600i
\(737\) 39.2489i 1.44575i
\(738\) −39.0604 18.9773i −1.43783 0.698563i
\(739\) −24.4495 + 10.1273i −0.899390 + 0.372540i −0.783986 0.620779i \(-0.786816\pi\)
−0.115405 + 0.993319i \(0.536816\pi\)
\(740\) −4.36396 0.365329i −0.160422 0.0134297i
\(741\) 10.6872 + 4.53862i 0.392603 + 0.166730i
\(742\) −4.88274 0.204022i −0.179251 0.00748989i
\(743\) −27.9409 27.9409i −1.02505 1.02505i −0.999678 0.0253737i \(-0.991922\pi\)
−0.0253737 0.999678i \(-0.508078\pi\)
\(744\) 34.9141 26.6090i 1.28001 0.975534i
\(745\) 12.3459 12.3459i 0.452318 0.452318i
\(746\) −33.9218 + 31.2007i −1.24197 + 1.14234i
\(747\) 3.55225 8.16187i 0.129970 0.298627i
\(748\) −36.0633 + 11.5194i −1.31860 + 0.421192i
\(749\) −7.52882 18.1762i −0.275097 0.664143i
\(750\) −18.2824 + 6.50912i −0.667578 + 0.237679i
\(751\) −34.7248 −1.26713 −0.633563 0.773691i \(-0.718408\pi\)
−0.633563 + 0.773691i \(0.718408\pi\)
\(752\) 49.0241 + 8.26603i 1.78773 + 0.301431i
\(753\) 4.66253 + 0.0414985i 0.169912 + 0.00151229i
\(754\) 17.0358 6.23670i 0.620408 0.227127i
\(755\) 15.4711 6.40834i 0.563051 0.233223i
\(756\) 5.00894 9.10552i 0.182174 0.331165i
\(757\) 16.8506 40.6809i 0.612444 1.47857i −0.247863 0.968795i \(-0.579728\pi\)
0.860307 0.509776i \(-0.170272\pi\)
\(758\) −15.9313 + 14.6534i −0.578651 + 0.532234i
\(759\) 30.5321 + 31.0805i 1.10824 + 1.12815i
\(760\) 0.910733 + 3.32407i 0.0330357 + 0.120577i
\(761\) −29.8147 + 29.8147i −1.08078 + 1.08078i −0.0843469 + 0.996436i \(0.526880\pi\)
−0.996436 + 0.0843469i \(0.973120\pi\)
\(762\) −0.0545458 + 1.07578i −0.00197599 + 0.0389712i
\(763\) 0.324355 0.783062i 0.0117424 0.0283488i
\(764\) −3.11844 3.68826i −0.112821 0.133437i
\(765\) −4.32903 11.0011i −0.156516 0.397745i
\(766\) 3.26538 + 1.51523i 0.117983 + 0.0547476i
\(767\) 6.04421 0.218244
\(768\) 27.6786 1.37726i 0.998764 0.0496975i
\(769\) 52.1985 1.88233 0.941163 0.337953i \(-0.109734\pi\)
0.941163 + 0.337953i \(0.109734\pi\)
\(770\) 4.50152 + 2.08884i 0.162224 + 0.0752765i
\(771\) 12.7886 + 31.6686i 0.460569 + 1.14052i
\(772\) 5.48116 + 6.48272i 0.197271 + 0.233318i
\(773\) −2.37779 + 5.74048i −0.0855230 + 0.206471i −0.960855 0.277051i \(-0.910643\pi\)
0.875332 + 0.483522i \(0.160643\pi\)
\(774\) −9.31973 0.555745i −0.334991 0.0199758i
\(775\) 27.0520 27.0520i 0.971736 0.971736i
\(776\) −10.8822 39.7189i −0.390649 1.42582i
\(777\) 3.16538 3.10953i 0.113558 0.111554i
\(778\) 27.3079 25.1173i 0.979035 0.900500i
\(779\) −5.58447 + 13.4821i −0.200084 + 0.483047i
\(780\) −6.49186 + 12.3154i −0.232446 + 0.440961i
\(781\) 3.80945 1.57793i 0.136313 0.0564627i
\(782\) 37.5147 13.7339i 1.34152 0.491122i
\(783\) −0.378467 + 14.1711i −0.0135253 + 0.506434i
\(784\) 3.94432 + 0.665059i 0.140869 + 0.0237521i
\(785\) 4.40106 0.157080
\(786\) −12.7270 35.7468i −0.453957 1.27504i
\(787\) −9.07471 21.9083i −0.323478 0.780946i −0.999047 0.0436486i \(-0.986102\pi\)
0.675569 0.737297i \(-0.263898\pi\)
\(788\) 15.6027 4.98386i 0.555824 0.177543i
\(789\) 41.8349 + 17.7664i 1.48936 + 0.632502i
\(790\) 13.7383 12.6362i 0.488785 0.449576i
\(791\) 7.16456 7.16456i 0.254742 0.254742i
\(792\) −27.8942 + 20.8691i −0.991178 + 0.741552i
\(793\) 6.11292 + 6.11292i 0.217076 + 0.217076i
\(794\) −19.4425 0.812395i −0.689990 0.0288308i
\(795\) −1.99968 + 4.70868i −0.0709214 + 0.167000i
\(796\) 20.8332 + 1.74405i 0.738413 + 0.0618162i
\(797\) 15.9558 6.60911i 0.565183 0.234107i −0.0817504 0.996653i \(-0.526051\pi\)
0.646934 + 0.762546i \(0.276051\pi\)
\(798\) −3.15457 1.49808i −0.111671 0.0530314i
\(799\) 57.3055i 2.02732i
\(800\) 23.7446 4.41649i 0.839497 0.156146i
\(801\) 0.272139 15.2868i 0.00961557 0.540132i
\(802\) 41.7115 + 19.3554i 1.47289 + 0.683462i
\(803\) −22.8238 55.1016i −0.805436 1.94449i
\(804\) −32.9753 3.05629i −1.16295 0.107787i
\(805\) −4.83805 2.00399i −0.170519 0.0706313i
\(806\) 2.48755 59.5331i 0.0876203 2.09696i
\(807\) −8.28124 8.42997i −0.291513 0.296749i
\(808\) −15.0248 1.89222i −0.528570 0.0665681i
\(809\) 30.4647 + 30.4647i 1.07108 + 1.07108i 0.997272 + 0.0738079i \(0.0235152\pi\)
0.0738079 + 0.997272i \(0.476485\pi\)
\(810\) −7.07487 8.26385i −0.248585 0.290362i
\(811\) 7.17939 + 2.97380i 0.252103 + 0.104424i 0.505156 0.863028i \(-0.331435\pi\)
−0.253054 + 0.967452i \(0.581435\pi\)
\(812\) −5.19769 + 1.66026i −0.182403 + 0.0582636i
\(813\) 37.4401 15.1192i 1.31308 0.530254i
\(814\) −13.9677 + 5.11349i −0.489569 + 0.179228i
\(815\) 10.5253i 0.368685i
\(816\) 6.86989 + 31.1958i 0.240494 + 1.09207i
\(817\) 3.13735i 0.109762i
\(818\) −15.2502 41.6567i −0.533212 1.45649i
\(819\) −5.16531 13.1263i −0.180491 0.458669i
\(820\) −15.5502 8.02104i −0.543037 0.280107i
\(821\) −39.7843 16.4792i −1.38848 0.575128i −0.441747 0.897140i \(-0.645641\pi\)
−0.946736 + 0.322011i \(0.895641\pi\)
\(822\) 12.0849 + 13.3759i 0.421511 + 0.466538i
\(823\) 13.7823 + 13.7823i 0.480422 + 0.480422i 0.905266 0.424844i \(-0.139671\pi\)
−0.424844 + 0.905266i \(0.639671\pi\)
\(824\) 3.08164 + 1.75617i 0.107354 + 0.0611791i
\(825\) −21.6583 + 21.2761i −0.754045 + 0.740740i
\(826\) −1.81632 0.0758940i −0.0631980 0.00264069i
\(827\) 34.7083 + 14.3766i 1.20693 + 0.499925i 0.893230 0.449599i \(-0.148433\pi\)
0.313695 + 0.949524i \(0.398433\pi\)
\(828\) 28.4900 23.2315i 0.990095 0.807351i
\(829\) −14.1867 34.2496i −0.492723 1.18954i −0.953329 0.301934i \(-0.902368\pi\)
0.460606 0.887605i \(-0.347632\pi\)
\(830\) 1.50962 3.25329i 0.0523997 0.112923i
\(831\) 0.124705 14.0111i 0.00432596 0.486039i
\(832\) 22.5623 30.0982i 0.782208 1.04347i
\(833\) 4.61062i 0.159749i
\(834\) 17.5001 + 8.31063i 0.605978 + 0.287774i
\(835\) 2.20643 0.913931i 0.0763565 0.0316279i
\(836\) 7.55835 + 8.93947i 0.261411 + 0.309178i
\(837\) 42.5256 + 18.9602i 1.46990 + 0.655359i
\(838\) 0.0142564 0.341190i 0.000492480 0.0117862i
\(839\) 2.18797 + 2.18797i 0.0755371 + 0.0755371i 0.743866 0.668329i \(-0.232990\pi\)
−0.668329 + 0.743866i \(0.732990\pi\)
\(840\) 2.10548 3.61933i 0.0726461 0.124879i
\(841\) −15.2430 + 15.2430i −0.525622 + 0.525622i
\(842\) −1.86921 2.03223i −0.0644171 0.0700351i
\(843\) 5.54490 13.0567i 0.190976 0.449695i
\(844\) 12.2893 23.8250i 0.423015 0.820091i
\(845\) 2.97933 + 7.19273i 0.102492 + 0.247437i
\(846\) 17.2439 + 49.8327i 0.592857 + 1.71328i
\(847\) 5.85565 0.201203
\(848\) 7.33928 11.7131i 0.252032 0.402230i
\(849\) −0.343399 + 38.5824i −0.0117854 + 1.32414i
\(850\) 9.57038 + 26.1419i 0.328261 + 0.896661i
\(851\) 14.5012 6.00658i 0.497094 0.205903i
\(852\) −1.02907 3.32341i −0.0352552 0.113858i
\(853\) −3.86556 + 9.33229i −0.132354 + 0.319532i −0.976138 0.217152i \(-0.930323\pi\)
0.843783 + 0.536684i \(0.180323\pi\)
\(854\) −1.76022 1.91373i −0.0602333 0.0654864i
\(855\) −2.63053 + 2.53851i −0.0899623 + 0.0868153i
\(856\) 55.2097 + 6.95310i 1.88703 + 0.237652i
\(857\) 9.61025 9.61025i 0.328280 0.328280i −0.523652 0.851932i \(-0.675431\pi\)
0.851932 + 0.523652i \(0.175431\pi\)
\(858\) −2.39449 + 47.2252i −0.0817465 + 1.61224i
\(859\) 15.5404 37.5179i 0.530232 1.28009i −0.401137 0.916018i \(-0.631385\pi\)
0.931369 0.364076i \(-0.118615\pi\)
\(860\) −3.74860 0.313814i −0.127826 0.0107010i
\(861\) 16.4390 6.63845i 0.560238 0.226238i
\(862\) 6.33043 13.6423i 0.215615 0.464659i
\(863\) 37.5202 1.27720 0.638602 0.769537i \(-0.279513\pi\)
0.638602 + 0.769537i \(0.279513\pi\)
\(864\) 15.3612 + 25.0606i 0.522599 + 0.852578i
\(865\) −11.8969 −0.404507
\(866\) 14.4864 31.2186i 0.492266 1.06085i
\(867\) −6.83823 + 2.76144i −0.232238 + 0.0937836i
\(868\) −1.49505 + 17.8588i −0.0507453 + 0.606168i
\(869\) 24.2620 58.5738i 0.823034 1.98698i
\(870\) −0.289236 + 5.70443i −0.00980601 + 0.193398i
\(871\) −31.7850 + 31.7850i −1.07699 + 1.07699i
\(872\) 1.47006 + 1.89369i 0.0497825 + 0.0641285i
\(873\) 31.4319 30.3323i 1.06381 1.02659i
\(874\) −8.36272 9.09206i −0.282873 0.307544i
\(875\) 3.03188 7.31961i 0.102496 0.247448i
\(876\) −48.0713 + 14.8849i −1.62418 + 0.502913i
\(877\) 0.133993 0.0555018i 0.00452463 0.00187416i −0.380420 0.924814i \(-0.624221\pi\)
0.384945 + 0.922940i \(0.374221\pi\)
\(878\) −10.2126 27.8962i −0.344659 0.941451i
\(879\) −0.246020 + 27.6414i −0.00829806 + 0.932322i
\(880\) −11.4372 + 8.13677i −0.385546 + 0.274290i
\(881\) 22.4256 0.755536 0.377768 0.925900i \(-0.376692\pi\)
0.377768 + 0.925900i \(0.376692\pi\)
\(882\) 1.38739 + 4.00938i 0.0467158 + 0.135003i
\(883\) −7.27614 17.5661i −0.244861 0.591148i 0.752892 0.658144i \(-0.228658\pi\)
−0.997753 + 0.0669965i \(0.978658\pi\)
\(884\) 38.5340 + 19.8764i 1.29604 + 0.668516i
\(885\) −0.743859 + 1.75158i −0.0250045 + 0.0588786i
\(886\) −14.7476 16.0338i −0.495455 0.538665i
\(887\) −10.8685 + 10.8685i −0.364927 + 0.364927i −0.865623 0.500696i \(-0.833078\pi\)
0.500696 + 0.865623i \(0.333078\pi\)
\(888\) 3.20848 + 12.1333i 0.107669 + 0.407166i
\(889\) −0.310949 0.310949i −0.0104289 0.0104289i
\(890\) 0.257177 6.15485i 0.00862058 0.206311i
\(891\) −33.6125 15.3463i −1.12606 0.514120i
\(892\) 11.8792 10.0439i 0.397745 0.336295i
\(893\) 16.3711 6.78113i 0.547838 0.226922i
\(894\) −45.1996 21.4649i −1.51170 0.717893i
\(895\) 20.0381i 0.669798i
\(896\) −7.15805 + 8.76141i −0.239134 + 0.292698i
\(897\) 0.444094 49.8958i 0.0148279 1.66597i
\(898\) −7.42921 + 16.0102i −0.247916 + 0.534268i
\(899\) −9.35526 22.5856i −0.312015 0.753272i
\(900\) 16.1888 + 19.8531i 0.539626 + 0.661771i
\(901\) 14.7198 + 6.09714i 0.490387 + 0.203125i
\(902\) −59.3781 2.48108i −1.97707 0.0826109i
\(903\) 2.71903 2.67106i 0.0904838 0.0888873i
\(904\) 7.57273 + 27.6396i 0.251865 + 0.919280i
\(905\) −10.6382 10.6382i −0.353627 0.353627i
\(906\) −32.1731 35.6100i −1.06888 1.18306i
\(907\) −27.7384 11.4896i −0.921037 0.381506i −0.128766 0.991675i \(-0.541101\pi\)
−0.792271 + 0.610169i \(0.791101\pi\)
\(908\) −5.03073 + 9.75298i −0.166951 + 0.323664i
\(909\) −5.88158 14.9465i −0.195080 0.495744i
\(910\) −1.95387 5.33708i −0.0647701 0.176923i
\(911\) 19.5290i 0.647024i 0.946224 + 0.323512i \(0.104864\pi\)
−0.946224 + 0.323512i \(0.895136\pi\)
\(912\) 8.09912 5.65409i 0.268189 0.187226i
\(913\) 12.1817i 0.403156i
\(914\) 39.4109 14.4281i 1.30360 0.477238i
\(915\) −2.52380 + 1.01917i −0.0834344 + 0.0336928i
\(916\) −9.96822 31.2070i −0.329359 1.03111i
\(917\) 14.3117 + 5.92811i 0.472615 + 0.195763i
\(918\) −25.5402 + 22.2625i −0.842953 + 0.734772i
\(919\) 24.4689 + 24.4689i 0.807153 + 0.807153i 0.984202 0.177049i \(-0.0566550\pi\)
−0.177049 + 0.984202i \(0.556655\pi\)
\(920\) 11.6999 9.08259i 0.385736 0.299444i
\(921\) −24.3209 24.7577i −0.801400 0.815794i
\(922\) −0.112261 + 2.68667i −0.00369712 + 0.0884808i
\(923\) −4.36287 1.80716i −0.143606 0.0594834i
\(924\) 1.31254 14.1614i 0.0431794 0.465876i
\(925\) 4.18566 + 10.1051i 0.137624 + 0.332253i
\(926\) −14.8328 6.88284i −0.487435 0.226184i
\(927\) −0.0669628 + 3.76148i −0.00219935 + 0.123543i
\(928\) 3.19907 15.0978i 0.105014 0.495611i
\(929\) 0.278857i 0.00914899i 0.999990 + 0.00457449i \(0.00145611\pi\)
−0.999990 + 0.00457449i \(0.998544\pi\)
\(930\) 16.9462 + 8.04759i 0.555687 + 0.263891i
\(931\) 1.31717 0.545588i 0.0431684 0.0178809i
\(932\) 2.30455 27.5285i 0.0754880 0.901726i
\(933\) −8.24179 + 19.4071i −0.269824 + 0.635359i
\(934\) −28.4457 1.18859i −0.930773 0.0388918i
\(935\) −11.4402 11.4402i −0.374135 0.374135i
\(936\) 39.4901 + 5.68915i 1.29077 + 0.185956i
\(937\) −5.03953 + 5.03953i −0.164634 + 0.164634i −0.784616 0.619982i \(-0.787140\pi\)
0.619982 + 0.784616i \(0.287140\pi\)
\(938\) 9.95071 9.15250i 0.324902 0.298840i
\(939\) −7.61987 3.23600i −0.248665 0.105603i
\(940\) 6.46477 + 20.2389i 0.210858 + 0.660121i
\(941\) 22.1398 + 53.4502i 0.721736 + 1.74243i 0.668345 + 0.743852i \(0.267003\pi\)
0.0533915 + 0.998574i \(0.482997\pi\)
\(942\) −4.23047 11.8823i −0.137836 0.387145i
\(943\) 62.7127 2.04221
\(944\) 2.73013 4.35715i 0.0888582 0.141813i
\(945\) 4.43961 + 0.118568i 0.144420 + 0.00385702i
\(946\) −11.9982 + 4.39244i −0.390094 + 0.142811i
\(947\) 38.2455 15.8418i 1.24281 0.514789i 0.338218 0.941068i \(-0.390176\pi\)
0.904592 + 0.426279i \(0.140176\pi\)
\(948\) −47.3219 24.9450i −1.53694 0.810177i
\(949\) −26.1396 + 63.1065i −0.848526 + 2.04852i
\(950\) 6.33576 5.82753i 0.205559 0.189070i
\(951\) −20.6214 + 20.2575i −0.668694 + 0.656896i
\(952\) −11.3301 6.45684i −0.367212 0.209267i
\(953\) 15.2723 15.2723i 0.494718 0.494718i −0.415071 0.909789i \(-0.636243\pi\)
0.909789 + 0.415071i \(0.136243\pi\)
\(954\) 14.6350 + 0.872700i 0.473825 + 0.0282547i
\(955\) 0.789887 1.90696i 0.0255601 0.0617076i
\(956\) −29.8513 + 25.2394i −0.965459 + 0.816299i
\(957\) 7.26439 + 17.9890i 0.234824 + 0.581501i
\(958\) −10.6504 4.94208i −0.344098 0.159671i
\(959\) −7.35935 −0.237646
\(960\) 5.94556 + 10.2426i 0.191892 + 0.330579i
\(961\) −49.2932 −1.59010
\(962\) 15.4526 + 7.17045i 0.498212 + 0.231185i
\(963\) 21.6123 + 54.9219i 0.696447 + 1.76983i
\(964\) 6.70639 5.67028i 0.215998 0.182627i
\(965\) −1.38835 + 3.35179i −0.0446927 + 0.107898i
\(966\) −0.759969 + 14.9884i −0.0244516 + 0.482245i
\(967\) 13.8644 13.8644i 0.445850 0.445850i −0.448122 0.893972i \(-0.647907\pi\)
0.893972 + 0.448122i \(0.147907\pi\)
\(968\) −8.20041 + 14.3897i −0.263571 + 0.462501i
\(969\) 7.97867 + 8.12197i 0.256312 + 0.260915i
\(970\) 12.9535 11.9144i 0.415911 0.382547i
\(971\) 2.44546 5.90386i 0.0784785 0.189464i −0.879771 0.475398i \(-0.842304\pi\)
0.958249 + 0.285934i \(0.0923040\pi\)
\(972\) −15.5107 + 27.0448i −0.497505 + 0.867461i
\(973\) −7.30702 + 3.02667i −0.234252 + 0.0970305i
\(974\) −1.70368 + 0.623704i −0.0545893 + 0.0199848i
\(975\) 34.7697 + 0.309465i 1.11352 + 0.00991080i
\(976\) 7.16785 1.64551i 0.229437 0.0526716i
\(977\) −28.6329 −0.916048 −0.458024 0.888940i \(-0.651443\pi\)
−0.458024 + 0.888940i \(0.651443\pi\)
\(978\) −28.4169 + 10.1173i −0.908672 + 0.323517i
\(979\) −8.00711 19.3309i −0.255908 0.617818i
\(980\) 0.520135 + 1.62836i 0.0166151 + 0.0520161i
\(981\) −1.01473 + 2.33149i −0.0323977 + 0.0744389i
\(982\) −16.1396 + 14.8450i −0.515036 + 0.473722i
\(983\) 25.3238 25.3238i 0.807704 0.807704i −0.176582 0.984286i \(-0.556504\pi\)
0.984286 + 0.176582i \(0.0565041\pi\)
\(984\) −6.70824 + 49.6937i −0.213851 + 1.58418i
\(985\) 4.94960 + 4.94960i 0.157707 + 0.157707i
\(986\) 17.7735 + 0.742654i 0.566023 + 0.0236509i
\(987\) −19.8149 8.41498i −0.630715 0.267852i
\(988\) 1.11847 13.3605i 0.0355833 0.425053i
\(989\) 12.4564 5.15959i 0.396089 0.164066i
\(990\) −13.3909 6.50589i −0.425590 0.206771i
\(991\) 21.0760i 0.669503i −0.942307 0.334751i \(-0.891348\pi\)
0.942307 0.334751i \(-0.108652\pi\)
\(992\) −41.7925 28.6839i −1.32691 0.910715i
\(993\) 1.73994 + 0.0154862i 0.0552152 + 0.000491439i
\(994\) 1.28838 + 0.597845i 0.0408649 + 0.0189625i
\(995\) 3.41900 + 8.25420i 0.108390 + 0.261676i
\(996\) −10.2346 0.948585i −0.324294 0.0300571i
\(997\) −12.8035 5.30339i −0.405491 0.167960i 0.170609 0.985339i \(-0.445426\pi\)
−0.576101 + 0.817379i \(0.695426\pi\)
\(998\) −2.04166 + 48.8617i −0.0646276 + 1.54669i
\(999\) −9.66069 + 9.15810i −0.305651 + 0.289749i
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 672.2.bs.a.155.6 192
3.2 odd 2 inner 672.2.bs.a.155.43 yes 192
32.19 odd 8 inner 672.2.bs.a.659.43 yes 192
96.83 even 8 inner 672.2.bs.a.659.6 yes 192
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
672.2.bs.a.155.6 192 1.1 even 1 trivial
672.2.bs.a.155.43 yes 192 3.2 odd 2 inner
672.2.bs.a.659.6 yes 192 96.83 even 8 inner
672.2.bs.a.659.43 yes 192 32.19 odd 8 inner