Properties

Label 336.2.bu.a.11.5
Level $336$
Weight $2$
Character 336.11
Analytic conductor $2.683$
Analytic rank $0$
Dimension $240$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [336,2,Mod(11,336)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(336, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 3, 6, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("336.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 336.bu (of order \(12\), 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: \(2.68297350792\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(60\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 11.5
Character \(\chi\) \(=\) 336.11
Dual form 336.2.bu.a.275.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.37118 + 0.346233i) q^{2} +(1.54917 - 0.774639i) q^{3} +(1.76025 - 0.949493i) q^{4} +(2.52702 + 0.677113i) q^{5} +(-1.85598 + 1.59854i) q^{6} +(0.885088 - 2.49331i) q^{7} +(-2.08486 + 1.91138i) q^{8} +(1.79987 - 2.40010i) q^{9} +O(q^{10})\) \(q+(-1.37118 + 0.346233i) q^{2} +(1.54917 - 0.774639i) q^{3} +(1.76025 - 0.949493i) q^{4} +(2.52702 + 0.677113i) q^{5} +(-1.85598 + 1.59854i) q^{6} +(0.885088 - 2.49331i) q^{7} +(-2.08486 + 1.91138i) q^{8} +(1.79987 - 2.40010i) q^{9} +(-3.69943 - 0.0535028i) q^{10} +(3.26252 - 0.874188i) q^{11} +(1.99141 - 2.83448i) q^{12} +(-3.62728 + 3.62728i) q^{13} +(-0.350343 + 3.72522i) q^{14} +(4.43931 - 0.908564i) q^{15} +(2.19693 - 3.34268i) q^{16} +(-6.30359 - 3.63938i) q^{17} +(-1.63694 + 3.91413i) q^{18} +(-1.51093 + 5.63886i) q^{19} +(5.09109 - 1.20750i) q^{20} +(-0.560266 - 4.54820i) q^{21} +(-4.17081 + 2.32826i) q^{22} +(-0.902810 + 0.521238i) q^{23} +(-1.74918 + 4.57607i) q^{24} +(1.59722 + 0.922157i) q^{25} +(3.71775 - 6.22952i) q^{26} +(0.929096 - 5.11241i) q^{27} +(-0.809413 - 5.22923i) q^{28} +(-0.164130 - 0.164130i) q^{29} +(-5.77250 + 2.78284i) q^{30} +(2.66713 + 1.53987i) q^{31} +(-1.85503 + 5.34405i) q^{32} +(4.37702 - 3.88154i) q^{33} +(9.90341 + 2.80772i) q^{34} +(3.92489 - 5.70135i) q^{35} +(0.889334 - 5.93372i) q^{36} +(-0.790868 + 2.95156i) q^{37} +(0.119388 - 8.25501i) q^{38} +(-2.80945 + 8.42911i) q^{39} +(-6.56270 + 3.41840i) q^{40} +9.40208 q^{41} +(2.34296 + 6.04240i) q^{42} +(1.63803 - 1.63803i) q^{43} +(4.91279 - 4.63652i) q^{44} +(6.17344 - 4.84638i) q^{45} +(1.05744 - 1.02729i) q^{46} +(2.82149 + 4.88697i) q^{47} +(0.814046 - 6.88021i) q^{48} +(-5.43324 - 4.41361i) q^{49} +(-2.50935 - 0.711428i) q^{50} +(-12.5846 - 0.755018i) q^{51} +(-2.94082 + 9.82897i) q^{52} +(1.43905 + 5.37060i) q^{53} +(0.496133 + 7.33170i) q^{54} +8.83637 q^{55} +(2.92038 + 6.88995i) q^{56} +(2.02740 + 9.90600i) q^{57} +(0.281877 + 0.168223i) q^{58} +(-3.61727 + 0.969245i) q^{59} +(6.95159 - 5.81439i) q^{60} +(-5.10170 - 1.36700i) q^{61} +(-4.19026 - 1.18798i) q^{62} +(-4.39116 - 6.61194i) q^{63} +(0.693278 - 7.96990i) q^{64} +(-11.6223 + 6.71013i) q^{65} +(-4.65774 + 6.83774i) q^{66} +(7.62060 - 2.04193i) q^{67} +(-14.5514 - 0.420987i) q^{68} +(-0.994837 + 1.50684i) q^{69} +(-3.40772 + 9.17648i) q^{70} +2.28487i q^{71} +(0.835019 + 8.44410i) q^{72} +(-9.32837 - 5.38574i) q^{73} +(0.0624912 - 4.32093i) q^{74} +(3.18871 + 0.191309i) q^{75} +(2.69446 + 11.3604i) q^{76} +(0.707986 - 8.90821i) q^{77} +(0.933808 - 12.5305i) q^{78} +(-6.93760 + 4.00542i) q^{79} +(7.81505 - 6.95945i) q^{80} +(-2.52095 - 8.63972i) q^{81} +(-12.8919 + 3.25531i) q^{82} +(-4.18395 + 4.18395i) q^{83} +(-5.30469 - 7.47398i) q^{84} +(-13.4650 - 13.4650i) q^{85} +(-1.67889 + 2.81317i) q^{86} +(-0.381406 - 0.127124i) q^{87} +(-5.13098 + 8.05846i) q^{88} +(-3.04256 - 5.26988i) q^{89} +(-6.78690 + 8.78269i) q^{90} +(5.83349 + 12.2544i) q^{91} +(-1.09426 + 1.77472i) q^{92} +(5.32469 + 0.319458i) q^{93} +(-5.56080 - 5.72400i) q^{94} +(-7.63630 + 13.2265i) q^{95} +(1.26596 + 9.71583i) q^{96} -10.8329 q^{97} +(8.97806 + 4.17066i) q^{98} +(3.77396 - 9.40378i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 16 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 240 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 16 q^{7} - 4 q^{10} - 2 q^{12} - 16 q^{13} - 20 q^{16} + 16 q^{18} - 4 q^{19} + 2 q^{21} - 40 q^{22} - 22 q^{24} - 8 q^{27} - 4 q^{28} - 26 q^{30} - 4 q^{33} + 16 q^{36} - 4 q^{37} - 4 q^{39} + 8 q^{40} - 18 q^{42} - 16 q^{43} + 18 q^{45} - 20 q^{46} - 88 q^{48} - 16 q^{49} + 6 q^{51} + 8 q^{52} + 14 q^{54} - 32 q^{55} - 36 q^{58} - 42 q^{60} - 4 q^{61} - 64 q^{64} - 30 q^{66} - 36 q^{67} - 20 q^{69} + 116 q^{70} - 46 q^{72} - 24 q^{75} - 112 q^{76} - 92 q^{78} - 4 q^{81} - 32 q^{82} + 44 q^{84} - 56 q^{85} - 4 q^{87} - 20 q^{88} + 28 q^{90} - 40 q^{91} - 14 q^{93} + 72 q^{94} + 36 q^{96} - 32 q^{97} + 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(-1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.37118 + 0.346233i −0.969568 + 0.244824i
\(3\) 1.54917 0.774639i 0.894415 0.447238i
\(4\) 1.76025 0.949493i 0.880123 0.474746i
\(5\) 2.52702 + 0.677113i 1.13012 + 0.302814i 0.774971 0.631996i \(-0.217764\pi\)
0.355147 + 0.934811i \(0.384431\pi\)
\(6\) −1.85598 + 1.59854i −0.757701 + 0.652602i
\(7\) 0.885088 2.49331i 0.334532 0.942384i
\(8\) −2.08486 + 1.91138i −0.737109 + 0.675774i
\(9\) 1.79987 2.40010i 0.599956 0.800033i
\(10\) −3.69943 0.0535028i −1.16986 0.0169191i
\(11\) 3.26252 0.874188i 0.983686 0.263578i 0.269090 0.963115i \(-0.413277\pi\)
0.714596 + 0.699537i \(0.246611\pi\)
\(12\) 1.99141 2.83448i 0.574870 0.818245i
\(13\) −3.62728 + 3.62728i −1.00603 + 1.00603i −0.00604406 + 0.999982i \(0.501924\pi\)
−0.999982 + 0.00604406i \(0.998076\pi\)
\(14\) −0.350343 + 3.72522i −0.0936330 + 0.995607i
\(15\) 4.43931 0.908564i 1.14622 0.234590i
\(16\) 2.19693 3.34268i 0.549232 0.835670i
\(17\) −6.30359 3.63938i −1.52885 0.882680i −0.999411 0.0343291i \(-0.989071\pi\)
−0.529435 0.848350i \(-0.677596\pi\)
\(18\) −1.63694 + 3.91413i −0.385831 + 0.922569i
\(19\) −1.51093 + 5.63886i −0.346631 + 1.29364i 0.544064 + 0.839043i \(0.316885\pi\)
−0.890695 + 0.454601i \(0.849782\pi\)
\(20\) 5.09109 1.20750i 1.13840 0.270006i
\(21\) −0.560266 4.54820i −0.122260 0.992498i
\(22\) −4.17081 + 2.32826i −0.889219 + 0.496386i
\(23\) −0.902810 + 0.521238i −0.188249 + 0.108686i −0.591163 0.806552i \(-0.701331\pi\)
0.402914 + 0.915238i \(0.367998\pi\)
\(24\) −1.74918 + 4.57607i −0.357050 + 0.934085i
\(25\) 1.59722 + 0.922157i 0.319444 + 0.184431i
\(26\) 3.71775 6.22952i 0.729111 1.22171i
\(27\) 0.929096 5.11241i 0.178805 0.983885i
\(28\) −0.809413 5.22923i −0.152965 0.988232i
\(29\) −0.164130 0.164130i −0.0304781 0.0304781i 0.691704 0.722182i \(-0.256861\pi\)
−0.722182 + 0.691704i \(0.756861\pi\)
\(30\) −5.77250 + 2.78284i −1.05391 + 0.508074i
\(31\) 2.66713 + 1.53987i 0.479031 + 0.276569i 0.720012 0.693961i \(-0.244136\pi\)
−0.240982 + 0.970530i \(0.577469\pi\)
\(32\) −1.85503 + 5.34405i −0.327925 + 0.944704i
\(33\) 4.37702 3.88154i 0.761941 0.675689i
\(34\) 9.90341 + 2.80772i 1.69842 + 0.481520i
\(35\) 3.92489 5.70135i 0.663428 0.963705i
\(36\) 0.889334 5.93372i 0.148222 0.988954i
\(37\) −0.790868 + 2.95156i −0.130018 + 0.485233i −0.999969 0.00790499i \(-0.997484\pi\)
0.869951 + 0.493138i \(0.164150\pi\)
\(38\) 0.119388 8.25501i 0.0193672 1.33914i
\(39\) −2.80945 + 8.42911i −0.449871 + 1.34974i
\(40\) −6.56270 + 3.41840i −1.03765 + 0.540497i
\(41\) 9.40208 1.46836 0.734179 0.678956i \(-0.237567\pi\)
0.734179 + 0.678956i \(0.237567\pi\)
\(42\) 2.34296 + 6.04240i 0.361526 + 0.932362i
\(43\) 1.63803 1.63803i 0.249798 0.249798i −0.571090 0.820888i \(-0.693479\pi\)
0.820888 + 0.571090i \(0.193479\pi\)
\(44\) 4.91279 4.63652i 0.740631 0.698982i
\(45\) 6.17344 4.84638i 0.920282 0.722456i
\(46\) 1.05744 1.02729i 0.155911 0.151466i
\(47\) 2.82149 + 4.88697i 0.411557 + 0.712838i 0.995060 0.0992728i \(-0.0316517\pi\)
−0.583503 + 0.812111i \(0.698318\pi\)
\(48\) 0.814046 6.88021i 0.117497 0.993073i
\(49\) −5.43324 4.41361i −0.776177 0.630515i
\(50\) −2.50935 0.711428i −0.354876 0.100611i
\(51\) −12.5846 0.755018i −1.76219 0.105724i
\(52\) −2.94082 + 9.82897i −0.407819 + 1.36303i
\(53\) 1.43905 + 5.37060i 0.197668 + 0.737708i 0.991560 + 0.129649i \(0.0413851\pi\)
−0.793892 + 0.608059i \(0.791948\pi\)
\(54\) 0.496133 + 7.33170i 0.0675152 + 0.997718i
\(55\) 8.83637 1.19150
\(56\) 2.92038 + 6.88995i 0.390252 + 0.920708i
\(57\) 2.02740 + 9.90600i 0.268535 + 1.31208i
\(58\) 0.281877 + 0.168223i 0.0370123 + 0.0220888i
\(59\) −3.61727 + 0.969245i −0.470929 + 0.126185i −0.486475 0.873694i \(-0.661718\pi\)
0.0155470 + 0.999879i \(0.495051\pi\)
\(60\) 6.95159 5.81439i 0.897447 0.750634i
\(61\) −5.10170 1.36700i −0.653206 0.175026i −0.0830278 0.996547i \(-0.526459\pi\)
−0.570178 + 0.821521i \(0.693126\pi\)
\(62\) −4.19026 1.18798i −0.532163 0.150874i
\(63\) −4.39116 6.61194i −0.553234 0.833026i
\(64\) 0.693278 7.96990i 0.0866598 0.996238i
\(65\) −11.6223 + 6.71013i −1.44157 + 0.832289i
\(66\) −4.65774 + 6.83774i −0.573328 + 0.841668i
\(67\) 7.62060 2.04193i 0.931005 0.249462i 0.238722 0.971088i \(-0.423272\pi\)
0.692283 + 0.721626i \(0.256605\pi\)
\(68\) −14.5514 0.420987i −1.76462 0.0510521i
\(69\) −0.994837 + 1.50684i −0.119764 + 0.181402i
\(70\) −3.40772 + 9.17648i −0.407300 + 1.09680i
\(71\) 2.28487i 0.271165i 0.990766 + 0.135582i \(0.0432905\pi\)
−0.990766 + 0.135582i \(0.956709\pi\)
\(72\) 0.835019 + 8.44410i 0.0984080 + 0.995146i
\(73\) −9.32837 5.38574i −1.09180 0.630353i −0.157747 0.987480i \(-0.550423\pi\)
−0.934056 + 0.357127i \(0.883756\pi\)
\(74\) 0.0624912 4.32093i 0.00726446 0.502298i
\(75\) 3.18871 + 0.191309i 0.368201 + 0.0220904i
\(76\) 2.69446 + 11.3604i 0.309075 + 1.30313i
\(77\) 0.707986 8.90821i 0.0806825 1.01519i
\(78\) 0.933808 12.5305i 0.105733 1.41880i
\(79\) −6.93760 + 4.00542i −0.780541 + 0.450645i −0.836622 0.547781i \(-0.815473\pi\)
0.0560811 + 0.998426i \(0.482139\pi\)
\(80\) 7.81505 6.95945i 0.873749 0.778091i
\(81\) −2.52095 8.63972i −0.280105 0.959969i
\(82\) −12.8919 + 3.25531i −1.42367 + 0.359489i
\(83\) −4.18395 + 4.18395i −0.459248 + 0.459248i −0.898409 0.439161i \(-0.855276\pi\)
0.439161 + 0.898409i \(0.355276\pi\)
\(84\) −5.30469 7.47398i −0.578789 0.815478i
\(85\) −13.4650 13.4650i −1.46049 1.46049i
\(86\) −1.67889 + 2.81317i −0.181039 + 0.303352i
\(87\) −0.381406 0.127124i −0.0408910 0.0136291i
\(88\) −5.13098 + 8.05846i −0.546965 + 0.859034i
\(89\) −3.04256 5.26988i −0.322511 0.558606i 0.658494 0.752586i \(-0.271194\pi\)
−0.981006 + 0.193980i \(0.937860\pi\)
\(90\) −6.78690 + 8.78269i −0.715402 + 0.925777i
\(91\) 5.83349 + 12.2544i 0.611515 + 1.28461i
\(92\) −1.09426 + 1.77472i −0.114084 + 0.185027i
\(93\) 5.32469 + 0.319458i 0.552144 + 0.0331262i
\(94\) −5.56080 5.72400i −0.573552 0.590386i
\(95\) −7.63630 + 13.2265i −0.783467 + 1.35701i
\(96\) 1.26596 + 9.71583i 0.129206 + 0.991618i
\(97\) −10.8329 −1.09991 −0.549956 0.835193i \(-0.685356\pi\)
−0.549956 + 0.835193i \(0.685356\pi\)
\(98\) 8.97806 + 4.17066i 0.906921 + 0.421300i
\(99\) 3.77396 9.40378i 0.379297 0.945116i
\(100\) 3.68708 + 0.106671i 0.368708 + 0.0106671i
\(101\) 3.88246 + 14.4895i 0.386319 + 1.44176i 0.836077 + 0.548612i \(0.184844\pi\)
−0.449758 + 0.893151i \(0.648490\pi\)
\(102\) 17.5170 3.32193i 1.73445 0.328920i
\(103\) 7.78320 + 13.4809i 0.766901 + 1.32831i 0.939236 + 0.343273i \(0.111536\pi\)
−0.172334 + 0.985039i \(0.555131\pi\)
\(104\) 0.629270 14.4955i 0.0617050 1.42140i
\(105\) 1.66384 11.8728i 0.162374 1.15866i
\(106\) −3.83267 6.86579i −0.372261 0.666864i
\(107\) 2.62276 9.78826i 0.253551 0.946266i −0.715339 0.698777i \(-0.753728\pi\)
0.968891 0.247489i \(-0.0796055\pi\)
\(108\) −3.21876 9.88127i −0.309726 0.950826i
\(109\) 0.136530 + 0.509537i 0.0130772 + 0.0488048i 0.972156 0.234334i \(-0.0752910\pi\)
−0.959079 + 0.283139i \(0.908624\pi\)
\(110\) −12.1162 + 3.05944i −1.15524 + 0.291706i
\(111\) 1.06120 + 5.18511i 0.100725 + 0.492149i
\(112\) −6.38988 8.43620i −0.603787 0.797146i
\(113\) 6.87732i 0.646963i −0.946234 0.323482i \(-0.895147\pi\)
0.946234 0.323482i \(-0.104853\pi\)
\(114\) −6.20970 12.8809i −0.581592 1.20641i
\(115\) −2.63436 + 0.705874i −0.245655 + 0.0658231i
\(116\) −0.444748 0.133068i −0.0412938 0.0123551i
\(117\) 2.17720 + 15.2344i 0.201282 + 1.40843i
\(118\) 4.62433 2.58142i 0.425704 0.237639i
\(119\) −14.6534 + 12.4957i −1.34327 + 1.14548i
\(120\) −7.51872 + 10.3794i −0.686362 + 0.947507i
\(121\) 0.353524 0.204107i 0.0321385 0.0185552i
\(122\) 7.46863 + 0.108015i 0.676178 + 0.00977918i
\(123\) 14.5654 7.28322i 1.31332 0.656706i
\(124\) 6.15690 + 0.178125i 0.552906 + 0.0159961i
\(125\) −5.83773 5.83773i −0.522142 0.522142i
\(126\) 8.31032 + 7.54576i 0.740342 + 0.672230i
\(127\) 4.45854i 0.395631i 0.980239 + 0.197816i \(0.0633848\pi\)
−0.980239 + 0.197816i \(0.936615\pi\)
\(128\) 1.80884 + 11.1682i 0.159880 + 0.987136i
\(129\) 1.26871 3.80648i 0.111704 0.335142i
\(130\) 13.6129 13.2248i 1.19393 1.15989i
\(131\) 4.27640 + 1.14586i 0.373631 + 0.100114i 0.440748 0.897631i \(-0.354713\pi\)
−0.0671169 + 0.997745i \(0.521380\pi\)
\(132\) 4.01913 10.9884i 0.349820 0.956418i
\(133\) 12.7222 + 8.75811i 1.10315 + 0.759425i
\(134\) −9.74220 + 5.43836i −0.841598 + 0.469802i
\(135\) 5.80953 12.2901i 0.500004 1.05776i
\(136\) 20.0983 4.46094i 1.72342 0.382523i
\(137\) −11.1596 + 19.3289i −0.953425 + 1.65138i −0.215494 + 0.976505i \(0.569136\pi\)
−0.737931 + 0.674876i \(0.764197\pi\)
\(138\) 0.842379 2.41059i 0.0717081 0.205203i
\(139\) 9.56395 9.56395i 0.811204 0.811204i −0.173611 0.984814i \(-0.555543\pi\)
0.984814 + 0.173611i \(0.0555434\pi\)
\(140\) 1.49538 13.7624i 0.126382 1.16314i
\(141\) 8.15662 + 5.38512i 0.686911 + 0.453509i
\(142\) −0.791099 3.13296i −0.0663876 0.262913i
\(143\) −8.66313 + 15.0050i −0.724447 + 1.25478i
\(144\) −4.06858 11.2892i −0.339049 0.940769i
\(145\) −0.303624 0.525893i −0.0252146 0.0436730i
\(146\) 14.6556 + 4.15500i 1.21290 + 0.343870i
\(147\) −11.8360 2.62864i −0.976215 0.216806i
\(148\) 1.41036 + 5.94639i 0.115931 + 0.488790i
\(149\) 4.35004 + 1.16559i 0.356369 + 0.0954888i 0.432562 0.901604i \(-0.357610\pi\)
−0.0761927 + 0.997093i \(0.524276\pi\)
\(150\) −4.43852 + 0.841720i −0.362404 + 0.0687261i
\(151\) 4.83337 8.37165i 0.393334 0.681275i −0.599553 0.800335i \(-0.704655\pi\)
0.992887 + 0.119060i \(0.0379881\pi\)
\(152\) −7.62792 14.6442i −0.618706 1.18780i
\(153\) −20.0805 + 8.57884i −1.62341 + 0.693558i
\(154\) 2.11355 + 12.4599i 0.170314 + 1.00404i
\(155\) 5.69723 + 5.69723i 0.457612 + 0.457612i
\(156\) 3.05806 + 17.5048i 0.244841 + 1.40151i
\(157\) 1.13751 + 4.24524i 0.0907831 + 0.338807i 0.996346 0.0854039i \(-0.0272181\pi\)
−0.905563 + 0.424211i \(0.860551\pi\)
\(158\) 8.12586 7.89417i 0.646458 0.628026i
\(159\) 6.38961 + 7.20524i 0.506729 + 0.571413i
\(160\) −8.30621 + 12.2485i −0.656664 + 0.968326i
\(161\) 0.500543 + 2.71233i 0.0394484 + 0.213762i
\(162\) 6.44802 + 10.9737i 0.506604 + 0.862179i
\(163\) 3.88416 14.4959i 0.304231 1.13541i −0.629374 0.777102i \(-0.716689\pi\)
0.933605 0.358303i \(-0.116645\pi\)
\(164\) 16.5500 8.92721i 1.29234 0.697098i
\(165\) 13.6891 6.84500i 1.06569 0.532882i
\(166\) 4.28830 7.18555i 0.332837 0.557707i
\(167\) 10.6269i 0.822332i −0.911561 0.411166i \(-0.865122\pi\)
0.911561 0.411166i \(-0.134878\pi\)
\(168\) 9.86139 + 8.41147i 0.760823 + 0.648959i
\(169\) 13.3143i 1.02418i
\(170\) 23.1250 + 13.8009i 1.77360 + 1.05848i
\(171\) 10.8144 + 13.7756i 0.826994 + 1.05345i
\(172\) 1.32804 4.43864i 0.101262 0.338443i
\(173\) −0.338854 + 1.26462i −0.0257626 + 0.0961474i −0.977610 0.210425i \(-0.932515\pi\)
0.951847 + 0.306572i \(0.0991820\pi\)
\(174\) 0.566989 + 0.0422536i 0.0429833 + 0.00320323i
\(175\) 3.71291 3.16619i 0.280670 0.239341i
\(176\) 4.24537 12.8261i 0.320007 0.966802i
\(177\) −4.85296 + 4.30361i −0.364771 + 0.323479i
\(178\) 5.99650 + 6.17249i 0.449456 + 0.462648i
\(179\) −2.81479 10.5050i −0.210388 0.785177i −0.987739 0.156111i \(-0.950104\pi\)
0.777352 0.629066i \(-0.216562\pi\)
\(180\) 6.26517 14.3925i 0.466978 1.07275i
\(181\) −5.73837 5.73837i −0.426530 0.426530i 0.460915 0.887444i \(-0.347521\pi\)
−0.887444 + 0.460915i \(0.847521\pi\)
\(182\) −12.2416 14.7832i −0.907409 1.09580i
\(183\) −8.96234 + 1.83426i −0.662515 + 0.135593i
\(184\) 0.885951 2.81232i 0.0653132 0.207327i
\(185\) −3.99708 + 6.92314i −0.293871 + 0.509000i
\(186\) −7.41169 + 1.40555i −0.543451 + 0.103060i
\(187\) −23.7471 6.36301i −1.73656 0.465309i
\(188\) 9.60667 + 5.92328i 0.700638 + 0.432000i
\(189\) −11.9245 6.84147i −0.867382 0.497643i
\(190\) 5.89127 20.7797i 0.427397 1.50752i
\(191\) −6.72903 11.6550i −0.486896 0.843328i 0.512991 0.858394i \(-0.328537\pi\)
−0.999886 + 0.0150661i \(0.995204\pi\)
\(192\) −5.09979 12.8838i −0.368046 0.929808i
\(193\) 6.12985 10.6172i 0.441236 0.764243i −0.556546 0.830817i \(-0.687874\pi\)
0.997781 + 0.0665740i \(0.0212068\pi\)
\(194\) 14.8538 3.75070i 1.06644 0.269285i
\(195\) −12.8070 + 19.3982i −0.917127 + 1.38914i
\(196\) −13.7545 2.61021i −0.982466 0.186443i
\(197\) 7.79286 7.79286i 0.555219 0.555219i −0.372724 0.927942i \(-0.621576\pi\)
0.927942 + 0.372724i \(0.121576\pi\)
\(198\) −1.91886 + 14.2009i −0.136368 + 1.00921i
\(199\) 1.47583 2.55620i 0.104618 0.181204i −0.808964 0.587858i \(-0.799971\pi\)
0.913582 + 0.406654i \(0.133305\pi\)
\(200\) −5.09257 + 1.13033i −0.360099 + 0.0799261i
\(201\) 10.2239 9.06653i 0.721136 0.639503i
\(202\) −10.3403 18.5235i −0.727540 1.30331i
\(203\) −0.554496 + 0.263958i −0.0389180 + 0.0185262i
\(204\) −22.8688 + 10.6199i −1.60114 + 0.743544i
\(205\) 23.7593 + 6.36627i 1.65942 + 0.444640i
\(206\) −15.3397 15.7899i −1.06876 1.10013i
\(207\) −0.373918 + 3.10499i −0.0259891 + 0.215812i
\(208\) 4.15597 + 20.0937i 0.288165 + 1.39325i
\(209\) 19.7177i 1.36390i
\(210\) 1.82932 + 16.8557i 0.126235 + 1.16315i
\(211\) 11.9004 + 11.9004i 0.819254 + 0.819254i 0.986000 0.166745i \(-0.0533258\pi\)
−0.166745 + 0.986000i \(0.553326\pi\)
\(212\) 7.63242 + 8.08720i 0.524197 + 0.555431i
\(213\) 1.76995 + 3.53966i 0.121275 + 0.242534i
\(214\) −0.207240 + 14.3295i −0.0141666 + 0.979545i
\(215\) 5.24847 3.03021i 0.357943 0.206658i
\(216\) 7.83471 + 12.4345i 0.533085 + 0.846062i
\(217\) 6.20002 5.28708i 0.420885 0.358910i
\(218\) −0.363625 0.651393i −0.0246278 0.0441179i
\(219\) −18.6233 1.11731i −1.25844 0.0755010i
\(220\) 15.5542 8.39007i 1.04866 0.565658i
\(221\) 36.0659 9.66384i 2.42606 0.650060i
\(222\) −3.25035 6.74228i −0.218149 0.452512i
\(223\) 7.42867i 0.497461i −0.968573 0.248730i \(-0.919987\pi\)
0.968573 0.248730i \(-0.0800133\pi\)
\(224\) 11.6825 + 9.35512i 0.780573 + 0.625065i
\(225\) 5.08806 2.17373i 0.339204 0.144915i
\(226\) 2.38115 + 9.43001i 0.158392 + 0.627275i
\(227\) 1.46401 + 5.46376i 0.0971698 + 0.362642i 0.997339 0.0728968i \(-0.0232244\pi\)
−0.900170 + 0.435539i \(0.856558\pi\)
\(228\) 12.9744 + 15.5120i 0.859250 + 1.02731i
\(229\) −0.484703 + 1.80894i −0.0320301 + 0.119538i −0.980090 0.198554i \(-0.936375\pi\)
0.948060 + 0.318092i \(0.103042\pi\)
\(230\) 3.36777 1.87998i 0.222064 0.123962i
\(231\) −5.80386 14.3488i −0.381866 0.944081i
\(232\) 0.655900 + 0.0284736i 0.0430620 + 0.00186939i
\(233\) −2.84179 4.92212i −0.186172 0.322459i 0.757799 0.652488i \(-0.226275\pi\)
−0.943971 + 0.330029i \(0.892941\pi\)
\(234\) −8.25999 20.1353i −0.539973 1.31628i
\(235\) 3.82094 + 14.2599i 0.249251 + 0.930217i
\(236\) −5.44699 + 5.14068i −0.354569 + 0.334630i
\(237\) −7.64478 + 11.5792i −0.496582 + 0.752152i
\(238\) 15.7659 22.2072i 1.02195 1.43948i
\(239\) −14.1287 −0.913909 −0.456954 0.889490i \(-0.651060\pi\)
−0.456954 + 0.889490i \(0.651060\pi\)
\(240\) 6.71579 16.8352i 0.433503 1.08671i
\(241\) −10.5955 + 18.3519i −0.682513 + 1.18215i 0.291698 + 0.956510i \(0.405780\pi\)
−0.974211 + 0.225637i \(0.927554\pi\)
\(242\) −0.414075 + 0.402268i −0.0266177 + 0.0258588i
\(243\) −10.5980 11.4316i −0.679865 0.733337i
\(244\) −10.2782 + 2.43778i −0.657994 + 0.156063i
\(245\) −10.7414 14.8322i −0.686243 0.947594i
\(246\) −17.4501 + 15.0296i −1.11258 + 0.958253i
\(247\) −14.9732 25.9343i −0.952720 1.65016i
\(248\) −8.50386 + 1.88748i −0.539996 + 0.119855i
\(249\) −3.24060 + 9.72270i −0.205365 + 0.616151i
\(250\) 10.0258 + 5.98334i 0.634085 + 0.378419i
\(251\) 10.6988 + 10.6988i 0.675301 + 0.675301i 0.958933 0.283632i \(-0.0915393\pi\)
−0.283632 + 0.958933i \(0.591539\pi\)
\(252\) −14.0075 7.46926i −0.882390 0.470519i
\(253\) −2.48977 + 2.48977i −0.156531 + 0.156531i
\(254\) −1.54369 6.11344i −0.0968600 0.383591i
\(255\) −31.2902 10.4291i −1.95947 0.653096i
\(256\) −6.34703 14.6872i −0.396689 0.917953i
\(257\) −14.9863 + 8.65236i −0.934821 + 0.539719i −0.888333 0.459200i \(-0.848136\pi\)
−0.0464880 + 0.998919i \(0.514803\pi\)
\(258\) −0.421696 + 5.65862i −0.0262536 + 0.352290i
\(259\) 6.65918 + 4.58427i 0.413781 + 0.284853i
\(260\) −14.0868 + 22.8467i −0.873629 + 1.41689i
\(261\) −0.689339 + 0.0985155i −0.0426690 + 0.00609795i
\(262\) −6.26043 0.0905411i −0.386771 0.00559365i
\(263\) −14.9718 8.64397i −0.923201 0.533010i −0.0385461 0.999257i \(-0.512273\pi\)
−0.884655 + 0.466246i \(0.845606\pi\)
\(264\) −1.70638 + 16.4586i −0.105020 + 1.01296i
\(265\) 14.5460i 0.893554i
\(266\) −20.4767 7.60408i −1.25550 0.466236i
\(267\) −8.79571 5.80706i −0.538289 0.355386i
\(268\) 11.4753 10.8300i 0.700967 0.661548i
\(269\) −21.7841 + 5.83702i −1.32820 + 0.355889i −0.852043 0.523472i \(-0.824636\pi\)
−0.476155 + 0.879362i \(0.657970\pi\)
\(270\) −3.71065 + 18.8633i −0.225823 + 1.14798i
\(271\) 0.996893 0.575557i 0.0605570 0.0349626i −0.469416 0.882977i \(-0.655535\pi\)
0.529973 + 0.848015i \(0.322202\pi\)
\(272\) −26.0138 + 13.0754i −1.57732 + 0.792815i
\(273\) 18.5298 + 14.4653i 1.12148 + 0.875482i
\(274\) 8.60940 30.3672i 0.520113 1.83455i
\(275\) 6.01710 + 1.61228i 0.362845 + 0.0972240i
\(276\) −0.320425 + 3.59700i −0.0192873 + 0.216514i
\(277\) −13.4467 + 3.60302i −0.807932 + 0.216485i −0.639063 0.769154i \(-0.720678\pi\)
−0.168868 + 0.985639i \(0.554011\pi\)
\(278\) −9.80250 + 16.4252i −0.587915 + 0.985119i
\(279\) 8.49632 3.62982i 0.508661 0.217311i
\(280\) 2.71459 + 19.3885i 0.162228 + 1.15868i
\(281\) 30.9858 1.84846 0.924229 0.381839i \(-0.124709\pi\)
0.924229 + 0.381839i \(0.124709\pi\)
\(282\) −13.0487 4.55985i −0.777037 0.271535i
\(283\) −2.35985 8.80706i −0.140278 0.523526i −0.999920 0.0126287i \(-0.995980\pi\)
0.859642 0.510897i \(-0.170687\pi\)
\(284\) 2.16947 + 4.02194i 0.128734 + 0.238658i
\(285\) −1.58421 + 26.4054i −0.0938405 + 1.56412i
\(286\) 6.68345 23.5739i 0.395201 1.39395i
\(287\) 8.32167 23.4424i 0.491213 1.38376i
\(288\) 9.48745 + 14.0708i 0.559053 + 0.829132i
\(289\) 17.9902 + 31.1599i 1.05825 + 1.83294i
\(290\) 0.598404 + 0.615967i 0.0351395 + 0.0361708i
\(291\) −16.7820 + 8.39157i −0.983778 + 0.491923i
\(292\) −21.5339 0.622997i −1.26018 0.0364581i
\(293\) 0.312653 0.312653i 0.0182654 0.0182654i −0.697915 0.716180i \(-0.745889\pi\)
0.716180 + 0.697915i \(0.245889\pi\)
\(294\) 17.1393 0.493685i 0.999585 0.0287923i
\(295\) −9.79720 −0.570415
\(296\) −3.99269 7.66523i −0.232071 0.445533i
\(297\) −1.43802 17.4915i −0.0834426 1.01496i
\(298\) −6.36823 0.0921002i −0.368902 0.00533522i
\(299\) 1.38407 5.16542i 0.0800428 0.298724i
\(300\) 5.79456 2.69091i 0.334549 0.155360i
\(301\) −2.63433 5.53393i −0.151840 0.318971i
\(302\) −3.72886 + 13.1525i −0.214572 + 0.756840i
\(303\) 17.2388 + 19.4393i 0.990341 + 1.11676i
\(304\) 15.5295 + 17.4387i 0.890679 + 1.00018i
\(305\) −11.9665 6.90885i −0.685199 0.395600i
\(306\) 24.5636 18.7156i 1.40421 1.06990i
\(307\) −5.18531 5.18531i −0.295941 0.295941i 0.543480 0.839422i \(-0.317106\pi\)
−0.839422 + 0.543480i \(0.817106\pi\)
\(308\) −7.21206 16.3529i −0.410945 0.931791i
\(309\) 22.5003 + 14.8551i 1.28000 + 0.845075i
\(310\) −9.78447 5.83933i −0.555721 0.331652i
\(311\) 23.6785 + 13.6708i 1.34268 + 0.775198i 0.987200 0.159485i \(-0.0509834\pi\)
0.355482 + 0.934683i \(0.384317\pi\)
\(312\) −10.2539 22.9434i −0.580513 1.29892i
\(313\) 5.63063 3.25085i 0.318262 0.183749i −0.332356 0.943154i \(-0.607843\pi\)
0.650618 + 0.759405i \(0.274510\pi\)
\(314\) −3.02957 5.42713i −0.170968 0.306271i
\(315\) −6.61952 19.6818i −0.372968 1.10894i
\(316\) −8.40875 + 13.6377i −0.473029 + 0.767182i
\(317\) 6.82939 25.4876i 0.383577 1.43153i −0.456822 0.889558i \(-0.651012\pi\)
0.840399 0.541969i \(-0.182321\pi\)
\(318\) −11.2560 7.66735i −0.631203 0.429964i
\(319\) −0.678955 0.391995i −0.0380142 0.0219475i
\(320\) 7.14845 19.6707i 0.399611 1.09962i
\(321\) −3.51927 17.1954i −0.196426 0.959753i
\(322\) −1.62543 3.54578i −0.0905818 0.197599i
\(323\) 30.0463 30.0463i 1.67182 1.67182i
\(324\) −12.6408 12.8144i −0.702269 0.711912i
\(325\) −9.13849 + 2.44865i −0.506912 + 0.135827i
\(326\) −0.306911 + 21.2212i −0.0169982 + 1.17534i
\(327\) 0.606215 + 0.683599i 0.0335238 + 0.0378031i
\(328\) −19.6020 + 17.9709i −1.08234 + 0.992278i
\(329\) 14.6820 2.70948i 0.809447 0.149378i
\(330\) −16.4001 + 14.1253i −0.902798 + 0.777572i
\(331\) −8.74625 2.34355i −0.480737 0.128813i 0.0103085 0.999947i \(-0.496719\pi\)
−0.491046 + 0.871134i \(0.663385\pi\)
\(332\) −3.39214 + 11.3374i −0.186168 + 0.622221i
\(333\) 5.66058 + 7.21058i 0.310198 + 0.395137i
\(334\) 3.67937 + 14.5713i 0.201326 + 0.797306i
\(335\) 20.6400 1.12769
\(336\) −16.4340 8.11927i −0.896550 0.442942i
\(337\) 12.1331 0.660930 0.330465 0.943818i \(-0.392794\pi\)
0.330465 + 0.943818i \(0.392794\pi\)
\(338\) 4.60985 + 18.2562i 0.250743 + 0.993008i
\(339\) −5.32744 10.6541i −0.289347 0.578654i
\(340\) −36.4867 10.9168i −1.97877 0.592047i
\(341\) 10.0477 + 2.69227i 0.544113 + 0.145795i
\(342\) −19.5979 15.1445i −1.05974 0.818919i
\(343\) −15.8134 + 9.64035i −0.853844 + 0.520530i
\(344\) −0.284170 + 6.54596i −0.0153214 + 0.352935i
\(345\) −3.53427 + 3.13420i −0.190279 + 0.168739i
\(346\) 0.0267749 1.85134i 0.00143943 0.0995287i
\(347\) −1.90188 + 0.509606i −0.102098 + 0.0273571i −0.309506 0.950897i \(-0.600164\pi\)
0.207408 + 0.978254i \(0.433497\pi\)
\(348\) −0.792071 + 0.138373i −0.0424595 + 0.00741759i
\(349\) 17.8288 17.8288i 0.954351 0.954351i −0.0446512 0.999003i \(-0.514218\pi\)
0.999003 + 0.0446512i \(0.0142176\pi\)
\(350\) −3.99481 + 5.62693i −0.213532 + 0.300772i
\(351\) 15.1741 + 21.9142i 0.809931 + 1.16970i
\(352\) −1.38034 + 19.0567i −0.0735725 + 1.01573i
\(353\) 18.7066 + 10.8003i 0.995654 + 0.574841i 0.906960 0.421218i \(-0.138397\pi\)
0.0886947 + 0.996059i \(0.471730\pi\)
\(354\) 5.16421 7.58126i 0.274475 0.402939i
\(355\) −1.54712 + 5.77392i −0.0821125 + 0.306448i
\(356\) −10.3594 6.38738i −0.549046 0.338531i
\(357\) −13.0209 + 30.7090i −0.689141 + 1.62529i
\(358\) 7.49674 + 13.4296i 0.396215 + 0.709774i
\(359\) −1.46649 + 0.846678i −0.0773983 + 0.0446859i −0.538200 0.842817i \(-0.680895\pi\)
0.460801 + 0.887503i \(0.347562\pi\)
\(360\) −3.60750 + 21.9038i −0.190132 + 1.15443i
\(361\) −13.0594 7.53985i −0.687337 0.396834i
\(362\) 9.85513 + 5.88150i 0.517974 + 0.309125i
\(363\) 0.389560 0.590051i 0.0204466 0.0309696i
\(364\) 21.9038 + 16.0319i 1.14807 + 0.840300i
\(365\) −19.9262 19.9262i −1.04299 1.04299i
\(366\) 11.6539 5.61816i 0.609157 0.293666i
\(367\) 25.2699 + 14.5896i 1.31908 + 0.761570i 0.983580 0.180471i \(-0.0577622\pi\)
0.335498 + 0.942041i \(0.391096\pi\)
\(368\) −0.241077 + 4.16293i −0.0125670 + 0.217008i
\(369\) 16.9225 22.5659i 0.880951 1.17474i
\(370\) 3.08368 10.8768i 0.160313 0.565456i
\(371\) 14.6643 + 1.16545i 0.761331 + 0.0605073i
\(372\) 9.67608 4.49343i 0.501681 0.232973i
\(373\) −2.67337 + 9.97716i −0.138422 + 0.516598i 0.861538 + 0.507692i \(0.169501\pi\)
−0.999960 + 0.00890526i \(0.997165\pi\)
\(374\) 34.7645 + 0.502780i 1.79763 + 0.0259981i
\(375\) −13.5658 4.52151i −0.700534 0.233490i
\(376\) −15.2233 4.79571i −0.785080 0.247320i
\(377\) 1.19069 0.0613235
\(378\) 18.7194 + 5.25218i 0.962820 + 0.270143i
\(379\) 15.1494 15.1494i 0.778170 0.778170i −0.201349 0.979520i \(-0.564533\pi\)
0.979520 + 0.201349i \(0.0645326\pi\)
\(380\) −0.883331 + 30.5324i −0.0453139 + 1.56628i
\(381\) 3.45376 + 6.90705i 0.176941 + 0.353859i
\(382\) 13.2620 + 13.6513i 0.678545 + 0.698460i
\(383\) −17.5315 30.3655i −0.895820 1.55161i −0.832786 0.553594i \(-0.813256\pi\)
−0.0630335 0.998011i \(-0.520078\pi\)
\(384\) 11.4535 + 15.9002i 0.584484 + 0.811405i
\(385\) 7.82096 22.0318i 0.398593 1.12285i
\(386\) −4.72907 + 16.6804i −0.240703 + 0.849010i
\(387\) −0.983196 6.87968i −0.0499787 0.349714i
\(388\) −19.0685 + 10.2857i −0.968058 + 0.522180i
\(389\) −5.43803 20.2950i −0.275719 1.02900i −0.955358 0.295451i \(-0.904530\pi\)
0.679639 0.733547i \(-0.262136\pi\)
\(390\) 10.8443 31.0326i 0.549124 1.57139i
\(391\) 7.58793 0.383738
\(392\) 19.7636 1.18322i 0.998213 0.0597615i
\(393\) 7.51250 1.53753i 0.378956 0.0775584i
\(394\) −7.98724 + 13.3835i −0.402391 + 0.674253i
\(395\) −20.2436 + 5.42425i −1.01856 + 0.272924i
\(396\) −2.28573 20.1363i −0.114862 1.01189i
\(397\) −24.4308 6.54620i −1.22614 0.328545i −0.413068 0.910700i \(-0.635543\pi\)
−0.813077 + 0.582156i \(0.802209\pi\)
\(398\) −1.13857 + 4.01598i −0.0570715 + 0.201303i
\(399\) 26.4932 + 3.71274i 1.32632 + 0.185870i
\(400\) 6.59146 3.31309i 0.329573 0.165655i
\(401\) 1.87721 1.08381i 0.0937434 0.0541228i −0.452395 0.891817i \(-0.649430\pi\)
0.546139 + 0.837695i \(0.316097\pi\)
\(402\) −10.8796 + 15.9716i −0.542624 + 0.796593i
\(403\) −15.2600 + 4.08889i −0.760152 + 0.203682i
\(404\) 20.5918 + 21.8188i 1.02448 + 1.08552i
\(405\) −0.520413 23.5397i −0.0258595 1.16970i
\(406\) 0.668920 0.553917i 0.0331979 0.0274904i
\(407\) 10.3209i 0.511587i
\(408\) 27.6802 22.4797i 1.37037 1.11291i
\(409\) 20.0783 + 11.5922i 0.992809 + 0.573199i 0.906113 0.423036i \(-0.139036\pi\)
0.0866966 + 0.996235i \(0.472369\pi\)
\(410\) −34.7823 0.503037i −1.71778 0.0248432i
\(411\) −2.31514 + 38.5885i −0.114197 + 1.90343i
\(412\) 26.5003 + 16.3396i 1.30558 + 0.804994i
\(413\) −0.784970 + 9.87686i −0.0386259 + 0.486009i
\(414\) −0.562344 4.38695i −0.0276377 0.215607i
\(415\) −13.4059 + 7.73991i −0.658071 + 0.379937i
\(416\) −12.6557 26.1130i −0.620495 1.28030i
\(417\) 7.40760 22.2248i 0.362751 1.08835i
\(418\) −6.82693 27.0365i −0.333916 1.32240i
\(419\) −8.05061 + 8.05061i −0.393298 + 0.393298i −0.875861 0.482563i \(-0.839706\pi\)
0.482563 + 0.875861i \(0.339706\pi\)
\(420\) −8.34432 22.4788i −0.407161 1.09685i
\(421\) 0.873466 + 0.873466i 0.0425701 + 0.0425701i 0.728071 0.685501i \(-0.240417\pi\)
−0.685501 + 0.728071i \(0.740417\pi\)
\(422\) −20.4378 12.1972i −0.994896 0.593750i
\(423\) 16.8075 + 2.02404i 0.817210 + 0.0984123i
\(424\) −13.2654 8.44638i −0.644227 0.410192i
\(425\) −6.71216 11.6258i −0.325588 0.563934i
\(426\) −3.65247 4.24069i −0.176963 0.205462i
\(427\) −7.92380 + 11.5102i −0.383460 + 0.557019i
\(428\) −4.67719 19.7200i −0.226080 0.953203i
\(429\) −1.79723 + 29.9561i −0.0867713 + 1.44629i
\(430\) −6.14742 + 5.97214i −0.296455 + 0.288002i
\(431\) 10.4850 18.1606i 0.505047 0.874766i −0.494936 0.868929i \(-0.664809\pi\)
0.999983 0.00583707i \(-0.00185801\pi\)
\(432\) −15.0480 14.3373i −0.723998 0.689802i
\(433\) −16.4987 −0.792877 −0.396438 0.918061i \(-0.629754\pi\)
−0.396438 + 0.918061i \(0.629754\pi\)
\(434\) −6.67076 + 9.39616i −0.320207 + 0.451030i
\(435\) −0.877744 0.579499i −0.0420846 0.0277849i
\(436\) 0.724128 + 0.767275i 0.0346794 + 0.0367458i
\(437\) −1.57511 5.87838i −0.0753476 0.281201i
\(438\) 25.9226 4.91595i 1.23863 0.234893i
\(439\) −2.57666 4.46290i −0.122977 0.213003i 0.797963 0.602706i \(-0.205911\pi\)
−0.920940 + 0.389703i \(0.872578\pi\)
\(440\) −18.4226 + 16.8896i −0.878262 + 0.805181i
\(441\) −20.3722 + 5.09640i −0.970105 + 0.242686i
\(442\) −46.1068 + 25.7380i −2.19308 + 1.22423i
\(443\) 2.48294 9.26646i 0.117968 0.440263i −0.881524 0.472140i \(-0.843482\pi\)
0.999492 + 0.0318768i \(0.0101484\pi\)
\(444\) 6.79120 + 8.11946i 0.322296 + 0.385333i
\(445\) −4.12032 15.3772i −0.195322 0.728951i
\(446\) 2.57205 + 10.1860i 0.121790 + 0.482322i
\(447\) 7.64187 1.56401i 0.361448 0.0739752i
\(448\) −19.2579 8.78263i −0.909849 0.414940i
\(449\) 0.701207i 0.0330920i −0.999863 0.0165460i \(-0.994733\pi\)
0.999863 0.0165460i \(-0.00526699\pi\)
\(450\) −6.22400 + 4.74222i −0.293402 + 0.223550i
\(451\) 30.6744 8.21919i 1.44440 0.387027i
\(452\) −6.52996 12.1058i −0.307144 0.569407i
\(453\) 1.00272 16.7132i 0.0471120 0.785257i
\(454\) −3.89915 6.98489i −0.182996 0.327817i
\(455\) 6.44372 + 34.9171i 0.302086 + 1.63694i
\(456\) −23.1609 16.7775i −1.08461 0.785678i
\(457\) 0.359990 0.207840i 0.0168396 0.00972235i −0.491557 0.870846i \(-0.663572\pi\)
0.508396 + 0.861123i \(0.330239\pi\)
\(458\) 0.0382993 2.64819i 0.00178961 0.123742i
\(459\) −24.4627 + 28.8452i −1.14182 + 1.34638i
\(460\) −3.96689 + 3.74381i −0.184957 + 0.174556i
\(461\) −13.2059 13.2059i −0.615061 0.615061i 0.329200 0.944260i \(-0.393221\pi\)
−0.944260 + 0.329200i \(0.893221\pi\)
\(462\) 12.9261 + 17.6652i 0.601378 + 0.821860i
\(463\) 24.2762i 1.12821i −0.825704 0.564104i \(-0.809222\pi\)
0.825704 0.564104i \(-0.190778\pi\)
\(464\) −0.909213 + 0.188052i −0.0422092 + 0.00873010i
\(465\) 13.2393 + 4.41269i 0.613957 + 0.204634i
\(466\) 5.60079 + 5.76517i 0.259452 + 0.267066i
\(467\) 15.7069 + 4.20865i 0.726829 + 0.194753i 0.603217 0.797577i \(-0.293885\pi\)
0.123612 + 0.992331i \(0.460552\pi\)
\(468\) 18.2974 + 24.7491i 0.845798 + 1.14403i
\(469\) 1.65372 20.8079i 0.0763616 0.960818i
\(470\) −10.1764 18.2300i −0.469405 0.840885i
\(471\) 5.05073 + 5.69545i 0.232725 + 0.262433i
\(472\) 5.68891 8.93471i 0.261853 0.411253i
\(473\) 3.91216 6.77606i 0.179881 0.311563i
\(474\) 6.47322 18.5240i 0.297325 0.850837i
\(475\) −7.61321 + 7.61321i −0.349318 + 0.349318i
\(476\) −13.9290 + 35.9087i −0.638432 + 1.64587i
\(477\) 15.4801 + 6.21251i 0.708783 + 0.284451i
\(478\) 19.3729 4.89182i 0.886096 0.223747i
\(479\) 2.20778 3.82399i 0.100876 0.174723i −0.811170 0.584811i \(-0.801169\pi\)
0.912046 + 0.410088i \(0.134502\pi\)
\(480\) −3.37962 + 25.4093i −0.154258 + 1.15977i
\(481\) −7.83743 13.5748i −0.357356 0.618959i
\(482\) 8.17421 28.8321i 0.372325 1.31327i
\(483\) 2.87651 + 3.81413i 0.130886 + 0.173549i
\(484\) 0.428491 0.694947i 0.0194768 0.0315885i
\(485\) −27.3749 7.33509i −1.24303 0.333069i
\(486\) 18.4898 + 12.0053i 0.838714 + 0.544573i
\(487\) −20.3373 + 35.2252i −0.921569 + 1.59620i −0.124580 + 0.992210i \(0.539758\pi\)
−0.796989 + 0.603994i \(0.793575\pi\)
\(488\) 13.2492 6.90127i 0.599762 0.312406i
\(489\) −5.21185 25.4654i −0.235688 1.15159i
\(490\) 19.8637 + 16.6185i 0.897352 + 0.750748i
\(491\) −9.25599 9.25599i −0.417717 0.417717i 0.466699 0.884416i \(-0.345443\pi\)
−0.884416 + 0.466699i \(0.845443\pi\)
\(492\) 18.7234 26.6500i 0.844116 1.20148i
\(493\) 0.437276 + 1.63194i 0.0196939 + 0.0734987i
\(494\) 29.5101 + 30.3763i 1.32772 + 1.36669i
\(495\) 15.9043 21.2082i 0.714845 0.953236i
\(496\) 11.0068 5.53239i 0.494219 0.248412i
\(497\) 5.69691 + 2.02232i 0.255541 + 0.0907132i
\(498\) 1.07712 14.4535i 0.0482668 0.647678i
\(499\) 6.57495 24.5381i 0.294335 1.09847i −0.647408 0.762143i \(-0.724147\pi\)
0.941744 0.336331i \(-0.109186\pi\)
\(500\) −15.8187 4.73295i −0.707434 0.211664i
\(501\) −8.23199 16.4628i −0.367778 0.735506i
\(502\) −18.3742 10.9656i −0.820080 0.489421i
\(503\) 5.54151i 0.247084i −0.992339 0.123542i \(-0.960575\pi\)
0.992339 0.123542i \(-0.0394253\pi\)
\(504\) 21.7929 + 5.39180i 0.970731 + 0.240170i
\(505\) 39.2442i 1.74634i
\(506\) 2.55187 4.27596i 0.113445 0.190090i
\(507\) −10.3138 20.6261i −0.458050 0.916038i
\(508\) 4.23335 + 7.84812i 0.187825 + 0.348204i
\(509\) −10.3227 + 38.5250i −0.457548 + 1.70759i 0.222940 + 0.974832i \(0.428435\pi\)
−0.680488 + 0.732759i \(0.738232\pi\)
\(510\) 46.5153 + 3.46644i 2.05973 + 0.153497i
\(511\) −21.6848 + 18.4917i −0.959278 + 0.818025i
\(512\) 13.7881 + 17.9412i 0.609354 + 0.792899i
\(513\) 27.4244 + 12.9635i 1.21082 + 0.572354i
\(514\) 17.5531 17.0527i 0.774236 0.752161i
\(515\) 10.5402 + 39.3366i 0.464457 + 1.73338i
\(516\) −1.38098 7.90497i −0.0607944 0.347997i
\(517\) 13.4773 + 13.4773i 0.592731 + 0.592731i
\(518\) −10.7181 3.98021i −0.470928 0.174881i
\(519\) 0.454681 + 2.22161i 0.0199583 + 0.0975177i
\(520\) 11.4052 36.2042i 0.500153 1.58766i
\(521\) −3.33292 + 5.77279i −0.146018 + 0.252910i −0.929752 0.368186i \(-0.879979\pi\)
0.783734 + 0.621096i \(0.213312\pi\)
\(522\) 0.911095 0.373754i 0.0398775 0.0163588i
\(523\) 30.8400 + 8.26355i 1.34854 + 0.361340i 0.859595 0.510976i \(-0.170716\pi\)
0.488943 + 0.872316i \(0.337383\pi\)
\(524\) 8.61549 2.04342i 0.376370 0.0892672i
\(525\) 3.29928 7.78114i 0.143992 0.339597i
\(526\) 23.5218 + 6.66867i 1.02560 + 0.290768i
\(527\) −11.2083 19.4134i −0.488243 0.845661i
\(528\) −3.35876 23.1584i −0.146171 1.00784i
\(529\) −10.9566 + 18.9774i −0.476375 + 0.825106i
\(530\) −5.03631 19.9451i −0.218763 0.866361i
\(531\) −4.18433 + 10.4263i −0.181584 + 0.452464i
\(532\) 30.7099 + 3.33683i 1.33144 + 0.144670i
\(533\) −34.1040 + 34.1040i −1.47721 + 1.47721i
\(534\) 14.0711 + 4.91713i 0.608914 + 0.212785i
\(535\) 13.2555 22.9592i 0.573086 0.992614i
\(536\) −11.9850 + 18.8230i −0.517672 + 0.813029i
\(537\) −12.4981 14.0935i −0.539335 0.608181i
\(538\) 27.8488 15.5459i 1.20065 0.670233i
\(539\) −21.5844 9.64978i −0.929704 0.415646i
\(540\) −1.44314 27.1496i −0.0621030 1.16833i
\(541\) 2.64502 + 0.708732i 0.113718 + 0.0304708i 0.315229 0.949015i \(-0.397919\pi\)
−0.201511 + 0.979486i \(0.564585\pi\)
\(542\) −1.16764 + 1.13435i −0.0501544 + 0.0487244i
\(543\) −13.3349 4.44456i −0.572255 0.190734i
\(544\) 31.1424 26.9356i 1.33522 1.15485i
\(545\) 1.38006i 0.0591151i
\(546\) −30.4160 13.4189i −1.30169 0.574275i
\(547\) 9.50732 + 9.50732i 0.406504 + 0.406504i 0.880517 0.474014i \(-0.157195\pi\)
−0.474014 + 0.880517i \(0.657195\pi\)
\(548\) −1.29089 + 44.6196i −0.0551439 + 1.90605i
\(549\) −12.4633 + 9.78417i −0.531921 + 0.417578i
\(550\) −8.80873 0.127396i −0.375605 0.00543217i
\(551\) 1.17349 0.677516i 0.0499924 0.0288631i
\(552\) −0.806041 5.04306i −0.0343074 0.214647i
\(553\) 3.84640 + 20.8428i 0.163566 + 0.886325i
\(554\) 17.1902 9.59606i 0.730344 0.407697i
\(555\) −0.829226 + 13.8214i −0.0351987 + 0.586687i
\(556\) 7.75400 25.9158i 0.328843 1.09907i
\(557\) 30.8981 8.27911i 1.30919 0.350797i 0.464274 0.885691i \(-0.346315\pi\)
0.844919 + 0.534894i \(0.179649\pi\)
\(558\) −10.3932 + 7.91882i −0.439979 + 0.335230i
\(559\) 11.8832i 0.502606i
\(560\) −10.4351 25.6451i −0.440964 1.08370i
\(561\) −41.7173 + 8.53802i −1.76131 + 0.360475i
\(562\) −42.4870 + 10.7283i −1.79220 + 0.452546i
\(563\) 1.04342 + 3.89411i 0.0439750 + 0.164117i 0.984421 0.175825i \(-0.0562593\pi\)
−0.940446 + 0.339942i \(0.889593\pi\)
\(564\) 19.4708 + 1.73448i 0.819868 + 0.0730348i
\(565\) 4.65672 17.3791i 0.195910 0.731145i
\(566\) 6.28506 + 11.2590i 0.264181 + 0.473250i
\(567\) −23.7728 1.36140i −0.998364 0.0571735i
\(568\) −4.36726 4.76364i −0.183246 0.199878i
\(569\) −2.48807 4.30946i −0.104305 0.180662i 0.809149 0.587604i \(-0.199929\pi\)
−0.913454 + 0.406942i \(0.866595\pi\)
\(570\) −6.97020 36.7550i −0.291950 1.53950i
\(571\) −7.85817 29.3271i −0.328854 1.22730i −0.910380 0.413773i \(-0.864211\pi\)
0.581526 0.813528i \(-0.302456\pi\)
\(572\) −1.00211 + 34.6380i −0.0419003 + 1.44829i
\(573\) −19.4529 12.8431i −0.812655 0.536527i
\(574\) −3.29395 + 35.0248i −0.137487 + 1.46191i
\(575\) −1.92265 −0.0801801
\(576\) −17.8807 16.0087i −0.745031 0.667030i
\(577\) 0.860428 1.49031i 0.0358201 0.0620422i −0.847560 0.530700i \(-0.821929\pi\)
0.883380 + 0.468658i \(0.155262\pi\)
\(578\) −35.4563 36.4969i −1.47479 1.51807i
\(579\) 1.27168 21.1963i 0.0528494 0.880888i
\(580\) −1.03378 0.637411i −0.0429256 0.0264671i
\(581\) 6.72874 + 14.1351i 0.279155 + 0.586421i
\(582\) 20.1056 17.3168i 0.833405 0.717805i
\(583\) 9.38983 + 16.2637i 0.388887 + 0.673572i
\(584\) 29.7425 6.60152i 1.23075 0.273173i
\(585\) −4.81361 + 39.9720i −0.199018 + 1.65264i
\(586\) −0.320451 + 0.536952i −0.0132377 + 0.0221813i
\(587\) 15.5903 + 15.5903i 0.643480 + 0.643480i 0.951409 0.307930i \(-0.0996361\pi\)
−0.307930 + 0.951409i \(0.599636\pi\)
\(588\) −23.3301 + 6.61113i −0.962117 + 0.272638i
\(589\) −12.7130 + 12.7130i −0.523828 + 0.523828i
\(590\) 13.4337 3.39212i 0.553056 0.139651i
\(591\) 6.03583 18.1091i 0.248281 0.744911i
\(592\) 8.12864 + 9.12798i 0.334085 + 0.375158i
\(593\) 24.8897 14.3701i 1.02210 0.590109i 0.107387 0.994217i \(-0.465752\pi\)
0.914711 + 0.404109i \(0.132418\pi\)
\(594\) 8.02793 + 23.4861i 0.329390 + 0.963645i
\(595\) −45.4903 + 21.6548i −1.86492 + 0.887762i
\(596\) 8.76385 2.07861i 0.358981 0.0851431i
\(597\) 0.306172 5.10323i 0.0125308 0.208861i
\(598\) −0.109364 + 7.56191i −0.00447221 + 0.309229i
\(599\) −25.1110 14.4978i −1.02601 0.592365i −0.110169 0.993913i \(-0.535139\pi\)
−0.915838 + 0.401547i \(0.868472\pi\)
\(600\) −7.01368 + 5.69598i −0.286332 + 0.232537i
\(601\) 25.2326i 1.02926i −0.857413 0.514629i \(-0.827930\pi\)
0.857413 0.514629i \(-0.172070\pi\)
\(602\) 5.52816 + 6.67590i 0.225311 + 0.272089i
\(603\) 8.81524 21.9654i 0.358984 0.894501i
\(604\) 0.559102 19.3254i 0.0227496 0.786340i
\(605\) 1.03157 0.276407i 0.0419391 0.0112376i
\(606\) −30.3679 20.6860i −1.23361 0.840313i
\(607\) −3.05575 + 1.76424i −0.124029 + 0.0716083i −0.560731 0.827998i \(-0.689480\pi\)
0.436702 + 0.899606i \(0.356146\pi\)
\(608\) −27.3316 18.5347i −1.10844 0.751682i
\(609\) −0.654537 + 0.838450i −0.0265232 + 0.0339757i
\(610\) 18.8002 + 5.33006i 0.761199 + 0.215808i
\(611\) −27.9608 7.49206i −1.13117 0.303096i
\(612\) −27.2011 + 34.1672i −1.09954 + 1.38113i
\(613\) 8.53316 2.28645i 0.344651 0.0923489i −0.0823414 0.996604i \(-0.526240\pi\)
0.426992 + 0.904255i \(0.359573\pi\)
\(614\) 8.90530 + 5.31465i 0.359389 + 0.214482i
\(615\) 41.7387 8.54239i 1.68307 0.344463i
\(616\) 15.5509 + 19.9256i 0.626564 + 0.802825i
\(617\) −0.165107 −0.00664695 −0.00332347 0.999994i \(-0.501058\pi\)
−0.00332347 + 0.999994i \(0.501058\pi\)
\(618\) −35.9952 12.5785i −1.44794 0.505983i
\(619\) −4.36898 16.3052i −0.175604 0.655363i −0.996448 0.0842106i \(-0.973163\pi\)
0.820844 0.571152i \(-0.193504\pi\)
\(620\) 15.4380 + 4.61904i 0.620005 + 0.185505i
\(621\) 1.82599 + 5.09982i 0.0732743 + 0.204649i
\(622\) −37.2006 10.5468i −1.49161 0.422886i
\(623\) −15.8324 + 2.92177i −0.634312 + 0.117058i
\(624\) 22.0037 + 27.9092i 0.880852 + 1.11726i
\(625\) −15.4100 26.6910i −0.616402 1.06764i
\(626\) −6.59504 + 6.40699i −0.263591 + 0.256075i
\(627\) 15.2741 + 30.5461i 0.609989 + 1.21990i
\(628\) 6.03312 + 6.39261i 0.240748 + 0.255093i
\(629\) 15.7272 15.7272i 0.627083 0.627083i
\(630\) 15.8910 + 24.6953i 0.633113 + 0.983885i
\(631\) 46.9954 1.87086 0.935428 0.353517i \(-0.115014\pi\)
0.935428 + 0.353517i \(0.115014\pi\)
\(632\) 6.80804 21.6111i 0.270809 0.859644i
\(633\) 27.6542 + 9.21722i 1.09916 + 0.366352i
\(634\) −0.539631 + 37.3126i −0.0214315 + 1.48187i
\(635\) −3.01894 + 11.2668i −0.119803 + 0.447110i
\(636\) 18.0886 + 6.61610i 0.717260 + 0.262345i
\(637\) 35.7172 3.69849i 1.41517 0.146540i
\(638\) 1.06669 + 0.302417i 0.0422306 + 0.0119728i
\(639\) 5.48392 + 4.11247i 0.216941 + 0.162687i
\(640\) −2.99114 + 29.4470i −0.118235 + 1.16399i
\(641\) 31.0249 + 17.9123i 1.22541 + 0.707491i 0.966067 0.258293i \(-0.0831601\pi\)
0.259345 + 0.965785i \(0.416493\pi\)
\(642\) 10.7791 + 22.3594i 0.425419 + 0.882455i
\(643\) −7.82538 7.82538i −0.308603 0.308603i 0.535765 0.844367i \(-0.320023\pi\)
−0.844367 + 0.535765i \(0.820023\pi\)
\(644\) 3.45642 + 4.29911i 0.136202 + 0.169409i
\(645\) 5.78347 8.75999i 0.227724 0.344924i
\(646\) −30.7957 + 51.6017i −1.21164 + 2.03024i
\(647\) −21.1311 12.2001i −0.830751 0.479634i 0.0233589 0.999727i \(-0.492564\pi\)
−0.854110 + 0.520093i \(0.825897\pi\)
\(648\) 21.7696 + 13.1941i 0.855190 + 0.518314i
\(649\) −10.9541 + 6.32435i −0.429986 + 0.248253i
\(650\) 11.6827 6.52158i 0.458232 0.255797i
\(651\) 5.50932 12.9934i 0.215927 0.509250i
\(652\) −6.92667 29.2043i −0.271269 1.14373i
\(653\) −3.16947 + 11.8286i −0.124031 + 0.462890i −0.999803 0.0198345i \(-0.993686\pi\)
0.875772 + 0.482724i \(0.160353\pi\)
\(654\) −1.06791 0.727442i −0.0417587 0.0284452i
\(655\) 10.0307 + 5.79121i 0.391931 + 0.226281i
\(656\) 20.6557 31.4282i 0.806469 1.22706i
\(657\) −29.7161 + 12.6954i −1.15934 + 0.495294i
\(658\) −19.1935 + 8.79857i −0.748242 + 0.343004i
\(659\) −13.5753 + 13.5753i −0.528820 + 0.528820i −0.920220 0.391400i \(-0.871991\pi\)
0.391400 + 0.920220i \(0.371991\pi\)
\(660\) 17.5968 25.0465i 0.684955 0.974935i
\(661\) 21.2416 5.69167i 0.826203 0.221380i 0.179146 0.983822i \(-0.442666\pi\)
0.647057 + 0.762442i \(0.276000\pi\)
\(662\) 12.8041 + 0.185178i 0.497644 + 0.00719715i
\(663\) 48.3863 42.9090i 1.87917 1.66645i
\(664\) 0.725843 16.7200i 0.0281682 0.648863i
\(665\) 26.2189 + 30.7463i 1.01673 + 1.19229i
\(666\) −10.2582 7.92709i −0.397497 0.307169i
\(667\) 0.233728 + 0.0626273i 0.00905000 + 0.00242494i
\(668\) −10.0901 18.7059i −0.390399 0.723753i
\(669\) −5.75454 11.5083i −0.222483 0.444936i
\(670\) −28.3011 + 7.14627i −1.09337 + 0.276084i
\(671\) −17.8394 −0.688682
\(672\) 25.3451 + 5.44293i 0.977709 + 0.209966i
\(673\) −4.23796 −0.163361 −0.0816806 0.996659i \(-0.526029\pi\)
−0.0816806 + 0.996659i \(0.526029\pi\)
\(674\) −16.6366 + 4.20087i −0.640817 + 0.161811i
\(675\) 6.19842 7.30889i 0.238577 0.281319i
\(676\) −12.6418 23.4364i −0.486224 0.901400i
\(677\) 28.7855 + 7.71305i 1.10632 + 0.296436i 0.765334 0.643633i \(-0.222574\pi\)
0.340982 + 0.940070i \(0.389241\pi\)
\(678\) 10.9937 + 12.7642i 0.422209 + 0.490205i
\(679\) −9.58805 + 27.0098i −0.367956 + 1.03654i
\(680\) 53.8095 + 2.33595i 2.06350 + 0.0895797i
\(681\) 6.50045 + 7.33022i 0.249098 + 0.280895i
\(682\) −14.7093 0.212732i −0.563248 0.00814595i
\(683\) 37.1934 9.96595i 1.42317 0.381336i 0.536561 0.843862i \(-0.319723\pi\)
0.886606 + 0.462525i \(0.153057\pi\)
\(684\) 32.1157 + 13.9803i 1.22798 + 0.534549i
\(685\) −41.2883 + 41.2883i −1.57754 + 1.57754i
\(686\) 18.3451 18.6937i 0.700421 0.713730i
\(687\) 0.650384 + 3.17782i 0.0248137 + 0.121242i
\(688\) −1.87678 9.07406i −0.0715516 0.345945i
\(689\) −24.7005 14.2608i −0.941013 0.543294i
\(690\) 3.76095 5.52122i 0.143177 0.210189i
\(691\) −11.2585 + 42.0172i −0.428293 + 1.59841i 0.328333 + 0.944562i \(0.393513\pi\)
−0.756625 + 0.653849i \(0.773153\pi\)
\(692\) 0.604282 + 2.54778i 0.0229714 + 0.0968522i
\(693\) −20.1063 17.7328i −0.763775 0.673615i
\(694\) 2.43136 1.35725i 0.0922933 0.0515206i
\(695\) 30.6442 17.6924i 1.16240 0.671112i
\(696\) 1.03816 0.463975i 0.0393513 0.0175869i
\(697\) −59.2669 34.2178i −2.24489 1.29609i
\(698\) −18.2735 + 30.6193i −0.691660 + 1.15896i
\(699\) −8.21528 5.42385i −0.310731 0.205149i
\(700\) 3.52936 9.09865i 0.133397 0.343897i
\(701\) −32.7611 32.7611i −1.23737 1.23737i −0.961073 0.276295i \(-0.910893\pi\)
−0.276295 0.961073i \(-0.589107\pi\)
\(702\) −28.3937 24.7945i −1.07165 0.935808i
\(703\) −15.4485 8.91920i −0.582651 0.336394i
\(704\) −4.70537 26.6080i −0.177340 1.00283i
\(705\) 16.9656 + 19.1313i 0.638962 + 0.720525i
\(706\) −29.3895 8.33223i −1.10609 0.313588i
\(707\) 39.5633 + 3.14432i 1.48793 + 0.118254i
\(708\) −4.45616 + 12.1833i −0.167473 + 0.457875i
\(709\) −4.06017 + 15.1528i −0.152483 + 0.569074i 0.846825 + 0.531872i \(0.178511\pi\)
−0.999308 + 0.0372022i \(0.988155\pi\)
\(710\) 0.122247 8.45273i 0.00458785 0.317225i
\(711\) −2.87335 + 23.8602i −0.107759 + 0.894826i
\(712\) 16.4160 + 5.17147i 0.615217 + 0.193809i
\(713\) −3.21055 −0.120236
\(714\) 7.22152 46.6157i 0.270258 1.74455i
\(715\) −32.0520 + 32.0520i −1.19868 + 1.19868i
\(716\) −14.9291 15.8187i −0.557927 0.591171i
\(717\) −21.8878 + 10.9446i −0.817414 + 0.408735i
\(718\) 1.71767 1.66869i 0.0641027 0.0622750i
\(719\) 10.0861 + 17.4697i 0.376149 + 0.651508i 0.990498 0.137525i \(-0.0439149\pi\)
−0.614350 + 0.789034i \(0.710582\pi\)
\(720\) −2.63731 31.2830i −0.0982868 1.16585i
\(721\) 40.5009 7.47419i 1.50833 0.278353i
\(722\) 20.5173 + 5.81686i 0.763574 + 0.216481i
\(723\) −2.19811 + 36.6379i −0.0817486 + 1.36258i
\(724\) −15.5495 4.65240i −0.577892 0.172905i
\(725\) −0.110798 0.413504i −0.00411494 0.0153572i
\(726\) −0.329860 + 0.943942i −0.0122423 + 0.0350330i
\(727\) −17.7130 −0.656938 −0.328469 0.944515i \(-0.606533\pi\)
−0.328469 + 0.944515i \(0.606533\pi\)
\(728\) −35.5848 14.3987i −1.31886 0.533652i
\(729\) −25.2736 9.49985i −0.936058 0.351846i
\(730\) 34.2215 + 20.4232i 1.26659 + 0.755898i
\(731\) −16.2869 + 4.36406i −0.602393 + 0.161411i
\(732\) −14.0343 + 11.7384i −0.518722 + 0.433865i
\(733\) −16.7903 4.49895i −0.620164 0.166173i −0.0649619 0.997888i \(-0.520693\pi\)
−0.555203 + 0.831715i \(0.687359\pi\)
\(734\) −39.7009 11.2556i −1.46539 0.415452i
\(735\) −28.1299 14.6569i −1.03759 0.540628i
\(736\) −1.11079 5.79157i −0.0409441 0.213480i
\(737\) 23.0773 13.3237i 0.850063 0.490784i
\(738\) −15.3907 + 36.8010i −0.566538 + 1.35466i
\(739\) −5.06287 + 1.35659i −0.186241 + 0.0499031i −0.350734 0.936475i \(-0.614068\pi\)
0.164493 + 0.986378i \(0.447401\pi\)
\(740\) −0.462364 + 15.9816i −0.0169968 + 0.587496i
\(741\) −43.2857 28.5779i −1.59014 1.04983i
\(742\) −20.5108 + 3.47922i −0.752976 + 0.127726i
\(743\) 47.2591i 1.73377i 0.498511 + 0.866883i \(0.333880\pi\)
−0.498511 + 0.866883i \(0.666120\pi\)
\(744\) −11.7118 + 9.51146i −0.429376 + 0.348707i
\(745\) 10.2034 + 5.89094i 0.373824 + 0.215827i
\(746\) 0.211239 14.6060i 0.00773401 0.534765i
\(747\) 2.51133 + 17.5724i 0.0918848 + 0.642942i
\(748\) −47.8423 + 11.3472i −1.74929 + 0.414895i
\(749\) −22.0838 15.2028i −0.806926 0.555499i
\(750\) 20.1666 + 1.50287i 0.736379 + 0.0548769i
\(751\) 36.2802 20.9464i 1.32388 0.764343i 0.339536 0.940593i \(-0.389730\pi\)
0.984346 + 0.176250i \(0.0563966\pi\)
\(752\) 22.5342 + 1.30496i 0.821738 + 0.0475871i
\(753\) 24.8620 + 8.28656i 0.906020 + 0.301979i
\(754\) −1.63264 + 0.412255i −0.0594573 + 0.0150134i
\(755\) 17.8826 17.8826i 0.650814 0.650814i
\(756\) −27.4860 0.720403i −0.999657 0.0262008i
\(757\) −14.1962 14.1962i −0.515968 0.515968i 0.400381 0.916349i \(-0.368878\pi\)
−0.916349 + 0.400381i \(0.868878\pi\)
\(758\) −15.5272 + 26.0176i −0.563974 + 0.945003i
\(759\) −1.92841 + 5.78576i −0.0699969 + 0.210010i
\(760\) −9.36013 42.1711i −0.339528 1.52971i
\(761\) −22.1520 38.3684i −0.803009 1.39085i −0.917627 0.397442i \(-0.869898\pi\)
0.114619 0.993410i \(-0.463435\pi\)
\(762\) −7.12716 8.27497i −0.258190 0.299770i
\(763\) 1.39128 + 0.110573i 0.0503676 + 0.00400300i
\(764\) −22.9111 14.1265i −0.828895 0.511080i
\(765\) −56.5527 + 8.08212i −2.04467 + 0.292210i
\(766\) 34.5524 + 35.5665i 1.24843 + 1.28507i
\(767\) 9.60512 16.6366i 0.346821 0.600712i
\(768\) −21.2100 17.8364i −0.765348 0.643616i
\(769\) 1.96166 0.0707392 0.0353696 0.999374i \(-0.488739\pi\)
0.0353696 + 0.999374i \(0.488739\pi\)
\(770\) −3.09576 + 32.9174i −0.111563 + 1.18626i
\(771\) −16.5139 + 25.0130i −0.594735 + 0.900820i
\(772\) 0.709072 24.5091i 0.0255201 0.882103i
\(773\) −13.4150 50.0655i −0.482505 1.80073i −0.591043 0.806640i \(-0.701284\pi\)
0.108538 0.994092i \(-0.465383\pi\)
\(774\) 3.73011 + 9.09284i 0.134076 + 0.326835i
\(775\) 2.84000 + 4.91902i 0.102016 + 0.176697i
\(776\) 22.5850 20.7057i 0.810756 0.743292i
\(777\) 13.8674 + 1.94337i 0.497489 + 0.0697179i
\(778\) 14.4833 + 25.9452i 0.519251 + 0.930180i
\(779\) −14.2059 + 53.0171i −0.508978 + 1.89953i
\(780\) −4.12497 + 46.3058i −0.147698 + 1.65801i
\(781\) 1.99741 + 7.45444i 0.0714730 + 0.266741i
\(782\) −10.4044 + 2.62719i −0.372060 + 0.0939482i
\(783\) −0.991590 + 0.686606i −0.0354365 + 0.0245373i
\(784\) −26.6897 + 8.46521i −0.953204 + 0.302329i
\(785\) 11.4980i 0.410383i
\(786\) −9.76862 + 4.70931i −0.348435 + 0.167975i
\(787\) −39.3287 + 10.5381i −1.40192 + 0.375642i −0.879033 0.476762i \(-0.841810\pi\)
−0.522884 + 0.852404i \(0.675144\pi\)
\(788\) 6.31808 21.1166i 0.225072 0.752249i
\(789\) −29.8899 1.79326i −1.06411 0.0638418i
\(790\) 25.8794 14.4466i 0.920749 0.513987i
\(791\) −17.1473 6.08703i −0.609688 0.216430i
\(792\) 10.1060 + 26.8190i 0.359101 + 0.952973i
\(793\) 23.4638 13.5468i 0.833222 0.481061i
\(794\) 35.7654 + 0.517255i 1.26927 + 0.0183567i
\(795\) 11.2679 + 22.5343i 0.399631 + 0.799208i
\(796\) 0.170717 5.90083i 0.00605089 0.209149i
\(797\) 36.7521 + 36.7521i 1.30183 + 1.30183i 0.927160 + 0.374666i \(0.122242\pi\)
0.374666 + 0.927160i \(0.377758\pi\)
\(798\) −37.6123 + 4.08200i −1.33146 + 0.144501i
\(799\) 41.0740i 1.45309i
\(800\) −7.89094 + 6.82501i −0.278987 + 0.241301i
\(801\) −18.1244 2.18263i −0.640396 0.0771194i
\(802\) −2.19874 + 2.13604i −0.0776400 + 0.0754263i
\(803\) −35.1421 9.41630i −1.24014 0.332294i
\(804\) 9.38791 25.6668i 0.331086 0.905198i
\(805\) −0.571672 + 7.19304i −0.0201488 + 0.253521i
\(806\) 19.5084 10.8901i 0.687153 0.383587i
\(807\) −29.2257 + 25.9173i −1.02879 + 0.912333i
\(808\) −35.7893 22.7878i −1.25906 0.801672i
\(809\) −15.1841 + 26.2996i −0.533843 + 0.924643i 0.465375 + 0.885113i \(0.345919\pi\)
−0.999218 + 0.0395298i \(0.987414\pi\)
\(810\) 8.86381 + 32.0969i 0.311442 + 1.12777i
\(811\) 14.9312 14.9312i 0.524304 0.524304i −0.394564 0.918868i \(-0.629104\pi\)
0.918868 + 0.394564i \(0.129104\pi\)
\(812\) −0.725422 + 0.991120i −0.0254573 + 0.0347815i
\(813\) 1.09851 1.66387i 0.0385264 0.0583544i
\(814\) −3.57343 14.1517i −0.125249 0.496018i
\(815\) 19.6307 34.0014i 0.687634 1.19102i
\(816\) −30.1711 + 40.4074i −1.05620 + 1.41454i
\(817\) 6.76169 + 11.7116i 0.236562 + 0.409737i
\(818\) −31.5445 8.94320i −1.10293 0.312692i
\(819\) 39.9113 + 8.05538i 1.39461 + 0.281478i
\(820\) 47.8668 11.3530i 1.67158 0.396465i
\(821\) −7.78694 2.08650i −0.271766 0.0728195i 0.120362 0.992730i \(-0.461594\pi\)
−0.392128 + 0.919911i \(0.628261\pi\)
\(822\) −10.1861 53.7131i −0.355282 1.87346i
\(823\) 23.1086 40.0253i 0.805515 1.39519i −0.110428 0.993884i \(-0.535222\pi\)
0.915943 0.401309i \(-0.131445\pi\)
\(824\) −41.9939 13.2291i −1.46293 0.460859i
\(825\) 10.5705 2.16339i 0.368016 0.0753195i
\(826\) −2.34336 13.8147i −0.0815361 0.480675i
\(827\) −2.26431 2.26431i −0.0787379 0.0787379i 0.666641 0.745379i \(-0.267731\pi\)
−0.745379 + 0.666641i \(0.767731\pi\)
\(828\) 2.28998 + 5.82058i 0.0795824 + 0.202279i
\(829\) 1.68025 + 6.27079i 0.0583576 + 0.217794i 0.988947 0.148272i \(-0.0473712\pi\)
−0.930589 + 0.366066i \(0.880704\pi\)
\(830\) 15.7021 15.2544i 0.545026 0.529486i
\(831\) −18.0402 + 15.9980i −0.625806 + 0.554965i
\(832\) 26.3943 + 31.4238i 0.915059 + 1.08942i
\(833\) 18.1861 + 47.5952i 0.630112 + 1.64908i
\(834\) −2.46215 + 33.0389i −0.0852572 + 1.14404i
\(835\) 7.19559 26.8543i 0.249014 0.929332i
\(836\) 18.7218 + 34.7080i 0.647508 + 1.20040i
\(837\) 10.3505 12.2048i 0.357764 0.421859i
\(838\) 8.25141 13.8262i 0.285040 0.477618i
\(839\) 5.18575i 0.179032i 0.995985 + 0.0895160i \(0.0285320\pi\)
−0.995985 + 0.0895160i \(0.971468\pi\)
\(840\) 19.2244 + 27.9332i 0.663306 + 0.963789i
\(841\) 28.9461i 0.998142i
\(842\) −1.50010 0.895253i −0.0516968 0.0308524i
\(843\) 48.0023 24.0028i 1.65329 0.826701i
\(844\) 32.2469 + 9.64824i 1.10998 + 0.332106i
\(845\) 9.01528 33.6455i 0.310135 1.15744i
\(846\) −23.7469 + 3.04401i −0.816434 + 0.104655i
\(847\) −0.196004 1.06210i −0.00673476 0.0364942i
\(848\) 21.1137 + 6.98853i 0.725047 + 0.239987i
\(849\) −10.4781 11.8156i −0.359608 0.405511i
\(850\) 13.2288 + 13.6170i 0.453744 + 0.467061i
\(851\) −0.824461 3.07693i −0.0282621 0.105476i
\(852\) 6.47644 + 4.55012i 0.221879 + 0.155885i
\(853\) 40.1345 + 40.1345i 1.37418 + 1.37418i 0.854147 + 0.520032i \(0.174080\pi\)
0.520032 + 0.854147i \(0.325920\pi\)
\(854\) 6.87970 18.5260i 0.235419 0.633948i
\(855\) 18.0005 + 42.1337i 0.615603 + 1.44094i
\(856\) 13.2410 + 25.4202i 0.452567 + 0.868845i
\(857\) −11.6264 + 20.1374i −0.397149 + 0.687882i −0.993373 0.114936i \(-0.963334\pi\)
0.596224 + 0.802818i \(0.296667\pi\)
\(858\) −7.90747 41.6973i −0.269956 1.42352i
\(859\) 29.1525 + 7.81139i 0.994671 + 0.266521i 0.719211 0.694791i \(-0.244503\pi\)
0.275459 + 0.961313i \(0.411170\pi\)
\(860\) 6.36144 10.3173i 0.216923 0.351817i
\(861\) −5.26766 42.7625i −0.179522 1.45734i
\(862\) −8.08902 + 28.5317i −0.275513 + 0.971792i
\(863\) 7.03655 + 12.1877i 0.239527 + 0.414873i 0.960579 0.278009i \(-0.0896743\pi\)
−0.721052 + 0.692881i \(0.756341\pi\)
\(864\) 25.5975 + 14.4488i 0.870845 + 0.491558i
\(865\) −1.71258 + 2.96628i −0.0582296 + 0.100857i
\(866\) 22.6226 5.71239i 0.768748 0.194115i
\(867\) 52.0076 + 34.3362i 1.76627 + 1.16612i
\(868\) 5.89352 15.1934i 0.200039 0.515699i
\(869\) −19.1325 + 19.1325i −0.649027 + 0.649027i
\(870\) 1.40418 + 0.490691i 0.0476062 + 0.0166360i
\(871\) −20.2354 + 35.0487i −0.685650 + 1.18758i
\(872\) −1.25856 0.801352i −0.0426203 0.0271372i
\(873\) −19.4978 + 26.0000i −0.659899 + 0.879966i
\(874\) 4.19504 + 7.51493i 0.141899 + 0.254196i
\(875\) −19.7222 + 9.38839i −0.666732 + 0.317386i
\(876\) −33.8424 + 15.7159i −1.14343 + 0.530991i
\(877\) −12.8938 3.45489i −0.435393 0.116663i 0.0344635 0.999406i \(-0.489028\pi\)
−0.469857 + 0.882743i \(0.655694\pi\)
\(878\) 5.07825 + 5.22730i 0.171383 + 0.176413i
\(879\) 0.242160 0.726546i 0.00816785 0.0245058i
\(880\) 19.4129 29.5372i 0.654407 0.995697i
\(881\) 8.31543i 0.280154i −0.990141 0.140077i \(-0.955265\pi\)
0.990141 0.140077i \(-0.0447350\pi\)
\(882\) 26.1693 14.0416i 0.881167 0.472805i
\(883\) −15.0386 15.0386i −0.506088 0.506088i 0.407235 0.913323i \(-0.366493\pi\)
−0.913323 + 0.407235i \(0.866493\pi\)
\(884\) 54.3091 51.2551i 1.82661 1.72389i
\(885\) −15.1776 + 7.58930i −0.510188 + 0.255111i
\(886\) −0.196192 + 13.5656i −0.00659120 + 0.455746i
\(887\) 3.51087 2.02700i 0.117884 0.0680601i −0.439899 0.898047i \(-0.644986\pi\)
0.557782 + 0.829987i \(0.311652\pi\)
\(888\) −12.1232 8.78187i −0.406827 0.294700i
\(889\) 11.1165 + 3.94620i 0.372837 + 0.132351i
\(890\) 10.9738 + 19.6583i 0.367842 + 0.658948i
\(891\) −15.7774 25.9835i −0.528562 0.870478i
\(892\) −7.05347 13.0763i −0.236168 0.437827i
\(893\) −31.8201 + 8.52616i −1.06482 + 0.285317i
\(894\) −9.93683 + 4.79040i −0.332337 + 0.160215i
\(895\) 28.4522i 0.951051i
\(896\) 29.4468 + 5.37481i 0.983747 + 0.179560i
\(897\) −1.85717 9.07428i −0.0620092 0.302981i
\(898\) 0.242781 + 0.961478i 0.00810171 + 0.0320849i
\(899\) −0.185017 0.690493i −0.00617066 0.0230292i
\(900\) 6.89229 8.65737i 0.229743 0.288579i
\(901\) 10.4745 39.0913i 0.348956 1.30232i
\(902\) −39.2143 + 21.8905i −1.30569 + 0.728873i
\(903\) −8.36783 6.53236i −0.278464 0.217383i
\(904\) 13.1451 + 14.3382i 0.437201 + 0.476883i
\(905\) −10.6155 18.3865i −0.352870 0.611188i
\(906\) 4.41177 + 23.2640i 0.146571 + 0.772894i
\(907\) 13.1137 + 48.9410i 0.435433 + 1.62506i 0.740027 + 0.672577i \(0.234813\pi\)
−0.304594 + 0.952482i \(0.598521\pi\)
\(908\) 7.76482 + 8.22749i 0.257685 + 0.273039i
\(909\) 41.7642 + 16.7610i 1.38523 + 0.555927i
\(910\) −20.9249 45.6464i −0.693654 1.51316i
\(911\) −45.2661 −1.49973 −0.749866 0.661590i \(-0.769882\pi\)
−0.749866 + 0.661590i \(0.769882\pi\)
\(912\) 37.5666 + 14.9858i 1.24395 + 0.496230i
\(913\) −9.99263 + 17.3077i −0.330708 + 0.572803i
\(914\) −0.421648 + 0.409626i −0.0139469 + 0.0135492i
\(915\) −23.8900 1.43330i −0.789780 0.0473833i
\(916\) 0.864376 + 3.64439i 0.0285598 + 0.120414i
\(917\) 6.64197 9.64822i 0.219337 0.318612i
\(918\) 23.5554 48.0217i 0.777445 1.58495i
\(919\) −24.2461 41.9954i −0.799804 1.38530i −0.919744 0.392519i \(-0.871604\pi\)
0.119940 0.992781i \(-0.461730\pi\)
\(920\) 4.14307 6.50690i 0.136593 0.214526i
\(921\) −12.0497 4.01620i −0.397051 0.132338i
\(922\) 22.6800 + 13.5353i 0.746924 + 0.445761i
\(923\) −8.28788 8.28788i −0.272799 0.272799i
\(924\) −23.8403 19.7467i −0.784288 0.649618i
\(925\) −3.98499 + 3.98499i −0.131026 + 0.131026i
\(926\) 8.40521 + 33.2869i 0.276212 + 1.09387i
\(927\) 46.3642 + 5.58340i 1.52280 + 0.183383i
\(928\) 1.18158 0.572652i 0.0387873 0.0187982i
\(929\) −27.0597 + 15.6230i −0.887801 + 0.512572i −0.873223 0.487321i \(-0.837974\pi\)
−0.0145787 + 0.999894i \(0.504641\pi\)
\(930\) −19.6812 1.46670i −0.645372 0.0480949i
\(931\) 33.0970 23.9686i 1.08471 0.785541i
\(932\) −9.67576 5.96588i −0.316940 0.195419i
\(933\) 47.2719 + 2.83611i 1.54761 + 0.0928500i
\(934\) −22.9941 0.332551i −0.752390 0.0108814i
\(935\) −55.7009 32.1589i −1.82161 1.05171i
\(936\) −33.6579 27.6002i −1.10014 0.902142i
\(937\) 27.8911i 0.911163i 0.890194 + 0.455581i \(0.150569\pi\)
−0.890194 + 0.455581i \(0.849431\pi\)
\(938\) 4.93683 + 29.1038i 0.161193 + 0.950273i
\(939\) 6.20459 9.39783i 0.202479 0.306687i
\(940\) 20.2655 + 21.4731i 0.660988 + 0.700374i
\(941\) −18.9423 + 5.07558i −0.617503 + 0.165459i −0.553992 0.832522i \(-0.686896\pi\)
−0.0635104 + 0.997981i \(0.520230\pi\)
\(942\) −8.89739 6.06074i −0.289893 0.197469i
\(943\) −8.48830 + 4.90072i −0.276417 + 0.159589i
\(944\) −4.70700 + 14.2207i −0.153200 + 0.462846i
\(945\) −25.5011 25.3628i −0.829550 0.825051i
\(946\) −3.01816 + 10.6457i −0.0981288 + 0.346121i
\(947\) 39.2403 + 10.5144i 1.27514 + 0.341672i 0.831997 0.554780i \(-0.187198\pi\)
0.443140 + 0.896452i \(0.353864\pi\)
\(948\) −2.46229 + 27.6409i −0.0799714 + 0.897736i
\(949\) 53.3721 14.3010i 1.73253 0.464231i
\(950\) 7.80310 13.0750i 0.253166 0.424209i
\(951\) −9.16381 44.7750i −0.297157 1.45193i
\(952\) 6.66626 54.0598i 0.216055 1.75209i
\(953\) 22.3127 0.722778 0.361389 0.932415i \(-0.382303\pi\)
0.361389 + 0.932415i \(0.382303\pi\)
\(954\) −23.3769 3.15874i −0.756854 0.102268i
\(955\) −9.11263 34.0088i −0.294878 1.10050i
\(956\) −24.8700 + 13.4151i −0.804352 + 0.433875i
\(957\) −1.35547 0.0813224i −0.0438162 0.00262878i
\(958\) −1.70327 + 6.00777i −0.0550300 + 0.194102i
\(959\) 38.3159 + 44.9321i 1.23728 + 1.45093i
\(960\) −4.16349 36.0107i −0.134376 1.16224i
\(961\) −10.7576 18.6327i −0.347020 0.601056i
\(962\) 15.4465 + 15.8999i 0.498017 + 0.512633i
\(963\) −18.7722 23.9124i −0.604925 0.770568i
\(964\) −1.22563 + 42.3641i −0.0394750 + 1.36446i
\(965\) 22.6793 22.6793i 0.730072 0.730072i
\(966\) −5.26477 4.23390i −0.169391 0.136223i
\(967\) 0.0670260 0.00215541 0.00107771 0.999999i \(-0.499657\pi\)
0.00107771 + 0.999999i \(0.499657\pi\)
\(968\) −0.346922 + 1.10125i −0.0111505 + 0.0353956i
\(969\) 23.2718 69.8218i 0.747598 2.24300i
\(970\) 40.0755 + 0.579589i 1.28675 + 0.0186095i
\(971\) −3.09803 + 11.5620i −0.0994206 + 0.371043i −0.997653 0.0684790i \(-0.978185\pi\)
0.898232 + 0.439522i \(0.144852\pi\)
\(972\) −29.5094 10.0596i −0.946514 0.322663i
\(973\) −15.3810 32.3109i −0.493092 1.03584i
\(974\) 15.6898 55.3413i 0.502735 1.77325i
\(975\) −12.2603 + 10.8724i −0.392643 + 0.348196i
\(976\) −15.7775 + 14.0502i −0.505025 + 0.449735i
\(977\) −25.5256 14.7372i −0.816637 0.471485i 0.0326185 0.999468i \(-0.489615\pi\)
−0.849255 + 0.527982i \(0.822949\pi\)
\(978\) 15.9633 + 33.1131i 0.510451 + 1.05884i
\(979\) −14.5333 14.5333i −0.464486 0.464486i
\(980\) −32.9905 15.9094i −1.05384 0.508207i
\(981\) 1.46867 + 0.589414i 0.0468912 + 0.0188185i
\(982\) 15.8963 + 9.48685i 0.507272 + 0.302738i
\(983\) 17.5590 + 10.1377i 0.560045 + 0.323342i 0.753164 0.657833i \(-0.228527\pi\)
−0.193119 + 0.981175i \(0.561860\pi\)
\(984\) −16.4459 + 43.0245i −0.524277 + 1.37157i
\(985\) 24.9694 14.4161i 0.795591 0.459334i
\(986\) −1.16461 2.08627i −0.0370888 0.0664404i
\(987\) 20.6461 15.5707i 0.657174 0.495621i
\(988\) −50.9809 31.4338i −1.62192 1.00004i
\(989\) −0.625028 + 2.33264i −0.0198747 + 0.0741735i
\(990\) −14.4646 + 34.5867i −0.459716 + 1.09924i
\(991\) 22.1478 + 12.7871i 0.703549 + 0.406194i 0.808668 0.588265i \(-0.200189\pi\)
−0.105119 + 0.994460i \(0.533522\pi\)
\(992\) −13.1767 + 11.3968i −0.418362 + 0.361848i
\(993\) −15.3649 + 3.14462i −0.487589 + 0.0997916i
\(994\) −8.51166 0.800489i −0.269973 0.0253900i
\(995\) 5.46028 5.46028i 0.173102 0.173102i
\(996\) 3.52738 + 20.1913i 0.111769 + 0.639785i
\(997\) −7.32386 + 1.96242i −0.231949 + 0.0621506i −0.372921 0.927863i \(-0.621644\pi\)
0.140972 + 0.990014i \(0.454977\pi\)
\(998\) −0.519527 + 35.9225i −0.0164453 + 1.13711i
\(999\) 14.3548 + 6.78553i 0.454166 + 0.214685i
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 336.2.bu.a.11.5 240
3.2 odd 2 inner 336.2.bu.a.11.56 yes 240
7.2 even 3 inner 336.2.bu.a.107.46 yes 240
16.3 odd 4 inner 336.2.bu.a.179.15 yes 240
21.2 odd 6 inner 336.2.bu.a.107.15 yes 240
48.35 even 4 inner 336.2.bu.a.179.46 yes 240
112.51 odd 12 inner 336.2.bu.a.275.56 yes 240
336.275 even 12 inner 336.2.bu.a.275.5 yes 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
336.2.bu.a.11.5 240 1.1 even 1 trivial
336.2.bu.a.11.56 yes 240 3.2 odd 2 inner
336.2.bu.a.107.15 yes 240 21.2 odd 6 inner
336.2.bu.a.107.46 yes 240 7.2 even 3 inner
336.2.bu.a.179.15 yes 240 16.3 odd 4 inner
336.2.bu.a.179.46 yes 240 48.35 even 4 inner
336.2.bu.a.275.5 yes 240 336.275 even 12 inner
336.2.bu.a.275.56 yes 240 112.51 odd 12 inner