Properties

Label 74.2.c.c.63.1
Level $74$
Weight $2$
Character 74.63
Analytic conductor $0.591$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 74.c (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.590892974957\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.4406832.1
Defining polynomial: \( x^{6} - x^{5} + 6x^{4} + 7x^{3} + 24x^{2} + 5x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 63.1
Root \(-0.105378 + 0.182520i\) of defining polynomial
Character \(\chi\) \(=\) 74.63
Dual form 74.2.c.c.47.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.26704 + 2.19457i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.97779 + 3.42563i) q^{5} +2.53407 q^{6} +(1.26704 - 2.19457i) q^{7} +1.00000 q^{8} +(-1.71076 - 2.96312i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.26704 + 2.19457i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.97779 + 3.42563i) q^{5} +2.53407 q^{6} +(1.26704 - 2.19457i) q^{7} +1.00000 q^{8} +(-1.71076 - 2.96312i) q^{9} +3.95558 q^{10} +2.42151 q^{11} +(-1.26704 - 2.19457i) q^{12} +(-1.00000 + 1.73205i) q^{13} -2.53407 q^{14} +(-5.01186 - 8.68080i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.03407 + 5.25516i) q^{17} +(-1.71076 + 2.96312i) q^{18} +(1.74483 - 3.02213i) q^{19} +(-1.97779 - 3.42563i) q^{20} +(3.21076 + 5.56119i) q^{21} +(-1.21076 - 2.09709i) q^{22} -0.955582 q^{23} +(-1.26704 + 2.19457i) q^{24} +(-5.32331 - 9.22025i) q^{25} +2.00000 q^{26} +1.06814 q^{27} +(1.26704 + 2.19457i) q^{28} +1.53407 q^{29} +(-5.01186 + 8.68080i) q^{30} +7.48965 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.06814 + 5.31418i) q^{33} +(3.03407 - 5.25516i) q^{34} +(5.01186 + 8.68080i) q^{35} +3.42151 q^{36} +(-0.0222090 + 6.08272i) q^{37} -3.48965 q^{38} +(-2.53407 - 4.38914i) q^{39} +(-1.97779 + 3.42563i) q^{40} +(4.24483 - 7.35225i) q^{41} +(3.21076 - 5.56119i) q^{42} +4.11256 q^{43} +(-1.21076 + 2.09709i) q^{44} +13.5341 q^{45} +(0.477791 + 0.827558i) q^{46} -11.4897 q^{47} +2.53407 q^{48} +(0.289244 + 0.500986i) q^{49} +(-5.32331 + 9.22025i) q^{50} -15.3771 q^{51} +(-1.00000 - 1.73205i) q^{52} +(-4.21076 - 7.29324i) q^{53} +(-0.534070 - 0.925037i) q^{54} +(-4.78924 + 8.29521i) q^{55} +(1.26704 - 2.19457i) q^{56} +(4.42151 + 7.65828i) q^{57} +(-0.767035 - 1.32854i) q^{58} +(-2.11256 - 3.65906i) q^{59} +10.0237 q^{60} +(-0.232965 + 0.403507i) q^{61} +(-3.74483 - 6.48623i) q^{62} -8.67035 q^{63} +1.00000 q^{64} +(-3.95558 - 6.85127i) q^{65} +6.13628 q^{66} +(3.21076 - 5.56119i) q^{67} -6.06814 q^{68} +(1.21076 - 2.09709i) q^{69} +(5.01186 - 8.68080i) q^{70} +(0.732965 - 1.26953i) q^{71} +(-1.71076 - 2.96312i) q^{72} -0.421512 q^{73} +(5.27890 - 3.02213i) q^{74} +26.9793 q^{75} +(1.74483 + 3.02213i) q^{76} +(3.06814 - 5.31418i) q^{77} +(-2.53407 + 4.38914i) q^{78} +(-1.32331 + 2.29205i) q^{79} +3.95558 q^{80} +(3.77890 - 6.54524i) q^{81} -8.48965 q^{82} +(1.68855 + 2.92465i) q^{83} -6.42151 q^{84} -24.0030 q^{85} +(-2.05628 - 3.56158i) q^{86} +(-1.94372 + 3.36662i) q^{87} +2.42151 q^{88} +(5.20041 + 9.00737i) q^{89} +(-6.76704 - 11.7208i) q^{90} +(2.53407 + 4.38914i) q^{91} +(0.477791 - 0.827558i) q^{92} +(-9.48965 + 16.4366i) q^{93} +(5.74483 + 9.95033i) q^{94} +(6.90180 + 11.9543i) q^{95} +(-1.26704 - 2.19457i) q^{96} +10.4897 q^{97} +(0.289244 - 0.500986i) q^{98} +(-4.14262 - 7.17522i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 3 q^{2} - 3 q^{4} - q^{5} + 6 q^{8} - 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 3 q^{2} - 3 q^{4} - q^{5} + 6 q^{8} - 7 q^{9} + 2 q^{10} + 8 q^{11} - 6 q^{13} - 4 q^{15} - 3 q^{16} + 3 q^{17} - 7 q^{18} - 8 q^{19} - q^{20} + 16 q^{21} - 4 q^{22} + 16 q^{23} - 20 q^{25} + 12 q^{26} - 24 q^{27} - 6 q^{29} - 4 q^{30} + 8 q^{31} - 3 q^{32} + 12 q^{33} + 3 q^{34} + 4 q^{35} + 14 q^{36} - 11 q^{37} + 16 q^{38} - q^{40} + 7 q^{41} + 16 q^{42} + 16 q^{43} - 4 q^{44} + 66 q^{45} - 8 q^{46} - 32 q^{47} + 5 q^{49} - 20 q^{50} - 64 q^{51} - 6 q^{52} - 22 q^{53} + 12 q^{54} - 32 q^{55} + 20 q^{57} + 3 q^{58} - 4 q^{59} + 8 q^{60} - 9 q^{61} - 4 q^{62} + 24 q^{63} + 6 q^{64} - 2 q^{65} - 24 q^{66} + 16 q^{67} - 6 q^{68} + 4 q^{69} + 4 q^{70} + 12 q^{71} - 7 q^{72} + 4 q^{73} - 2 q^{74} + 88 q^{75} - 8 q^{76} - 12 q^{77} + 4 q^{79} + 2 q^{80} - 11 q^{81} - 14 q^{82} - 4 q^{83} - 32 q^{84} - 18 q^{85} - 8 q^{86} - 16 q^{87} + 8 q^{88} - 9 q^{89} - 33 q^{90} - 8 q^{92} - 20 q^{93} + 16 q^{94} + 36 q^{95} + 26 q^{97} + 5 q^{98} - 52 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) −1.26704 + 2.19457i −0.731523 + 1.26704i 0.224709 + 0.974426i \(0.427857\pi\)
−0.956232 + 0.292609i \(0.905477\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −1.97779 + 3.42563i −0.884495 + 1.53199i −0.0382037 + 0.999270i \(0.512164\pi\)
−0.846291 + 0.532720i \(0.821170\pi\)
\(6\) 2.53407 1.03453
\(7\) 1.26704 2.19457i 0.478894 0.829469i −0.520813 0.853671i \(-0.674371\pi\)
0.999707 + 0.0242017i \(0.00770440\pi\)
\(8\) 1.00000 0.353553
\(9\) −1.71076 2.96312i −0.570252 0.987705i
\(10\) 3.95558 1.25086
\(11\) 2.42151 0.730113 0.365057 0.930985i \(-0.381050\pi\)
0.365057 + 0.930985i \(0.381050\pi\)
\(12\) −1.26704 2.19457i −0.365762 0.633518i
\(13\) −1.00000 + 1.73205i −0.277350 + 0.480384i −0.970725 0.240192i \(-0.922790\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) −2.53407 −0.677259
\(15\) −5.01186 8.68080i −1.29406 2.24137i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 3.03407 + 5.25516i 0.735870 + 1.27456i 0.954341 + 0.298721i \(0.0965599\pi\)
−0.218470 + 0.975844i \(0.570107\pi\)
\(18\) −1.71076 + 2.96312i −0.403229 + 0.698413i
\(19\) 1.74483 3.02213i 0.400291 0.693324i −0.593470 0.804856i \(-0.702243\pi\)
0.993761 + 0.111532i \(0.0355759\pi\)
\(20\) −1.97779 3.42563i −0.442248 0.765995i
\(21\) 3.21076 + 5.56119i 0.700644 + 1.21355i
\(22\) −1.21076 2.09709i −0.258134 0.447101i
\(23\) −0.955582 −0.199253 −0.0996263 0.995025i \(-0.531765\pi\)
−0.0996263 + 0.995025i \(0.531765\pi\)
\(24\) −1.26704 + 2.19457i −0.258632 + 0.447965i
\(25\) −5.32331 9.22025i −1.06466 1.84405i
\(26\) 2.00000 0.392232
\(27\) 1.06814 0.205564
\(28\) 1.26704 + 2.19457i 0.239447 + 0.414735i
\(29\) 1.53407 0.284870 0.142435 0.989804i \(-0.454507\pi\)
0.142435 + 0.989804i \(0.454507\pi\)
\(30\) −5.01186 + 8.68080i −0.915036 + 1.58489i
\(31\) 7.48965 1.34518 0.672591 0.740015i \(-0.265182\pi\)
0.672591 + 0.740015i \(0.265182\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −3.06814 + 5.31418i −0.534095 + 0.925079i
\(34\) 3.03407 5.25516i 0.520339 0.901253i
\(35\) 5.01186 + 8.68080i 0.847159 + 1.46732i
\(36\) 3.42151 0.570252
\(37\) −0.0222090 + 6.08272i −0.00365114 + 0.999993i
\(38\) −3.48965 −0.566096
\(39\) −2.53407 4.38914i −0.405776 0.702825i
\(40\) −1.97779 + 3.42563i −0.312716 + 0.541640i
\(41\) 4.24483 7.35225i 0.662930 1.14823i −0.316912 0.948455i \(-0.602646\pi\)
0.979842 0.199774i \(-0.0640208\pi\)
\(42\) 3.21076 5.56119i 0.495430 0.858111i
\(43\) 4.11256 0.627159 0.313580 0.949562i \(-0.398472\pi\)
0.313580 + 0.949562i \(0.398472\pi\)
\(44\) −1.21076 + 2.09709i −0.182528 + 0.316148i
\(45\) 13.5341 2.01754
\(46\) 0.477791 + 0.827558i 0.0704464 + 0.122017i
\(47\) −11.4897 −1.67594 −0.837969 0.545718i \(-0.816257\pi\)
−0.837969 + 0.545718i \(0.816257\pi\)
\(48\) 2.53407 0.365762
\(49\) 0.289244 + 0.500986i 0.0413206 + 0.0715694i
\(50\) −5.32331 + 9.22025i −0.752830 + 1.30394i
\(51\) −15.3771 −2.15322
\(52\) −1.00000 1.73205i −0.138675 0.240192i
\(53\) −4.21076 7.29324i −0.578392 1.00180i −0.995664 0.0930224i \(-0.970347\pi\)
0.417272 0.908782i \(-0.362986\pi\)
\(54\) −0.534070 0.925037i −0.0726777 0.125882i
\(55\) −4.78924 + 8.29521i −0.645782 + 1.11853i
\(56\) 1.26704 2.19457i 0.169315 0.293262i
\(57\) 4.42151 + 7.65828i 0.585644 + 1.01436i
\(58\) −0.767035 1.32854i −0.100717 0.174446i
\(59\) −2.11256 3.65906i −0.275032 0.476369i 0.695111 0.718902i \(-0.255355\pi\)
−0.970143 + 0.242533i \(0.922022\pi\)
\(60\) 10.0237 1.29406
\(61\) −0.232965 + 0.403507i −0.0298281 + 0.0516638i −0.880554 0.473946i \(-0.842829\pi\)
0.850726 + 0.525609i \(0.176163\pi\)
\(62\) −3.74483 6.48623i −0.475593 0.823752i
\(63\) −8.67035 −1.09236
\(64\) 1.00000 0.125000
\(65\) −3.95558 6.85127i −0.490630 0.849795i
\(66\) 6.13628 0.755324
\(67\) 3.21076 5.56119i 0.392256 0.679408i −0.600491 0.799632i \(-0.705028\pi\)
0.992747 + 0.120224i \(0.0383613\pi\)
\(68\) −6.06814 −0.735870
\(69\) 1.21076 2.09709i 0.145758 0.252460i
\(70\) 5.01186 8.68080i 0.599032 1.03755i
\(71\) 0.732965 1.26953i 0.0869869 0.150666i −0.819249 0.573438i \(-0.805609\pi\)
0.906236 + 0.422772i \(0.138943\pi\)
\(72\) −1.71076 2.96312i −0.201615 0.349207i
\(73\) −0.421512 −0.0493342 −0.0246671 0.999696i \(-0.507853\pi\)
−0.0246671 + 0.999696i \(0.507853\pi\)
\(74\) 5.27890 3.02213i 0.613659 0.351315i
\(75\) 26.9793 3.11530
\(76\) 1.74483 + 3.02213i 0.200145 + 0.346662i
\(77\) 3.06814 5.31418i 0.349647 0.605606i
\(78\) −2.53407 + 4.38914i −0.286927 + 0.496972i
\(79\) −1.32331 + 2.29205i −0.148884 + 0.257876i −0.930815 0.365490i \(-0.880902\pi\)
0.781931 + 0.623365i \(0.214235\pi\)
\(80\) 3.95558 0.442248
\(81\) 3.77890 6.54524i 0.419877 0.727249i
\(82\) −8.48965 −0.937525
\(83\) 1.68855 + 2.92465i 0.185342 + 0.321022i 0.943692 0.330826i \(-0.107327\pi\)
−0.758350 + 0.651848i \(0.773994\pi\)
\(84\) −6.42151 −0.700644
\(85\) −24.0030 −2.60349
\(86\) −2.05628 3.56158i −0.221734 0.384055i
\(87\) −1.94372 + 3.36662i −0.208389 + 0.360940i
\(88\) 2.42151 0.258134
\(89\) 5.20041 + 9.00737i 0.551242 + 0.954779i 0.998185 + 0.0602171i \(0.0191793\pi\)
−0.446943 + 0.894562i \(0.647487\pi\)
\(90\) −6.76704 11.7208i −0.713308 1.23549i
\(91\) 2.53407 + 4.38914i 0.265643 + 0.460107i
\(92\) 0.477791 0.827558i 0.0498132 0.0862789i
\(93\) −9.48965 + 16.4366i −0.984031 + 1.70439i
\(94\) 5.74483 + 9.95033i 0.592534 + 1.02630i
\(95\) 6.90180 + 11.9543i 0.708110 + 1.22648i
\(96\) −1.26704 2.19457i −0.129316 0.223982i
\(97\) 10.4897 1.06506 0.532531 0.846410i \(-0.321241\pi\)
0.532531 + 0.846410i \(0.321241\pi\)
\(98\) 0.289244 0.500986i 0.0292181 0.0506072i
\(99\) −4.14262 7.17522i −0.416349 0.721137i
\(100\) 10.6466 1.06466
\(101\) −5.11256 −0.508719 −0.254359 0.967110i \(-0.581865\pi\)
−0.254359 + 0.967110i \(0.581865\pi\)
\(102\) 7.68855 + 13.3170i 0.761280 + 1.31857i
\(103\) 0.397789 0.0391954 0.0195977 0.999808i \(-0.493761\pi\)
0.0195977 + 0.999808i \(0.493761\pi\)
\(104\) −1.00000 + 1.73205i −0.0980581 + 0.169842i
\(105\) −25.4008 −2.47887
\(106\) −4.21076 + 7.29324i −0.408985 + 0.708382i
\(107\) 4.05628 7.02568i 0.392135 0.679198i −0.600596 0.799553i \(-0.705070\pi\)
0.992731 + 0.120355i \(0.0384032\pi\)
\(108\) −0.534070 + 0.925037i −0.0513909 + 0.0890117i
\(109\) −5.72262 9.91186i −0.548127 0.949384i −0.998403 0.0564947i \(-0.982008\pi\)
0.450276 0.892890i \(-0.351326\pi\)
\(110\) 9.57849 0.913273
\(111\) −13.3208 7.75576i −1.26436 0.736144i
\(112\) −2.53407 −0.239447
\(113\) 1.78924 + 3.09906i 0.168318 + 0.291535i 0.937829 0.347099i \(-0.112833\pi\)
−0.769511 + 0.638634i \(0.779500\pi\)
\(114\) 4.42151 7.65828i 0.414113 0.717264i
\(115\) 1.88994 3.27347i 0.176238 0.305253i
\(116\) −0.767035 + 1.32854i −0.0712174 + 0.123352i
\(117\) 6.84302 0.632638
\(118\) −2.11256 + 3.65906i −0.194477 + 0.336844i
\(119\) 15.3771 1.40962
\(120\) −5.01186 8.68080i −0.457518 0.792445i
\(121\) −5.13628 −0.466935
\(122\) 0.465930 0.0421833
\(123\) 10.7567 + 18.6311i 0.969898 + 1.67991i
\(124\) −3.74483 + 6.48623i −0.336295 + 0.582481i
\(125\) 22.3357 1.99777
\(126\) 4.33518 + 7.50874i 0.386208 + 0.668932i
\(127\) 0.365233 + 0.632601i 0.0324091 + 0.0561343i 0.881775 0.471670i \(-0.156349\pi\)
−0.849366 + 0.527804i \(0.823015\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) −5.21076 + 9.02529i −0.458781 + 0.794633i
\(130\) −3.95558 + 6.85127i −0.346927 + 0.600896i
\(131\) −8.64413 14.9721i −0.755241 1.30812i −0.945254 0.326334i \(-0.894186\pi\)
0.190013 0.981782i \(-0.439147\pi\)
\(132\) −3.06814 5.31418i −0.267047 0.462540i
\(133\) −4.42151 7.65828i −0.383394 0.664057i
\(134\) −6.42151 −0.554734
\(135\) −2.11256 + 3.65906i −0.181820 + 0.314922i
\(136\) 3.03407 + 5.25516i 0.260169 + 0.450627i
\(137\) 11.0474 0.943847 0.471923 0.881640i \(-0.343560\pi\)
0.471923 + 0.881640i \(0.343560\pi\)
\(138\) −2.42151 −0.206133
\(139\) 6.11006 + 10.5829i 0.518248 + 0.897633i 0.999775 + 0.0212012i \(0.00674906\pi\)
−0.481527 + 0.876431i \(0.659918\pi\)
\(140\) −10.0237 −0.847159
\(141\) 14.5578 25.2148i 1.22599 2.12347i
\(142\) −1.46593 −0.123018
\(143\) −2.42151 + 4.19418i −0.202497 + 0.350735i
\(144\) −1.71076 + 2.96312i −0.142563 + 0.246926i
\(145\) −3.03407 + 5.25516i −0.251966 + 0.436418i
\(146\) 0.210756 + 0.365040i 0.0174423 + 0.0302109i
\(147\) −1.46593 −0.120908
\(148\) −5.25669 3.06059i −0.432097 0.251579i
\(149\) 2.55477 0.209295 0.104647 0.994509i \(-0.466629\pi\)
0.104647 + 0.994509i \(0.466629\pi\)
\(150\) −13.4897 23.3648i −1.10143 1.90772i
\(151\) 3.43337 5.94678i 0.279404 0.483942i −0.691833 0.722058i \(-0.743196\pi\)
0.971237 + 0.238116i \(0.0765298\pi\)
\(152\) 1.74483 3.02213i 0.141524 0.245127i
\(153\) 10.3811 17.9806i 0.839263 1.45365i
\(154\) −6.13628 −0.494476
\(155\) −14.8130 + 25.6568i −1.18981 + 2.06080i
\(156\) 5.06814 0.405776
\(157\) 1.87959 + 3.25555i 0.150008 + 0.259821i 0.931230 0.364432i \(-0.118737\pi\)
−0.781222 + 0.624253i \(0.785403\pi\)
\(158\) 2.64663 0.210554
\(159\) 21.3407 1.69243
\(160\) −1.97779 3.42563i −0.156358 0.270820i
\(161\) −1.21076 + 2.09709i −0.0954209 + 0.165274i
\(162\) −7.55779 −0.593796
\(163\) −3.01186 5.21670i −0.235907 0.408603i 0.723629 0.690189i \(-0.242473\pi\)
−0.959536 + 0.281586i \(0.909139\pi\)
\(164\) 4.24483 + 7.35225i 0.331465 + 0.574115i
\(165\) −12.1363 21.0207i −0.944808 1.63646i
\(166\) 1.68855 2.92465i 0.131057 0.226997i
\(167\) 6.00000 10.3923i 0.464294 0.804181i −0.534875 0.844931i \(-0.679641\pi\)
0.999169 + 0.0407502i \(0.0129748\pi\)
\(168\) 3.21076 + 5.56119i 0.247715 + 0.429055i
\(169\) 4.50000 + 7.79423i 0.346154 + 0.599556i
\(170\) 12.0015 + 20.7872i 0.920474 + 1.59431i
\(171\) −11.9399 −0.913066
\(172\) −2.05628 + 3.56158i −0.156790 + 0.271568i
\(173\) −7.72262 13.3760i −0.587140 1.01696i −0.994605 0.103735i \(-0.966921\pi\)
0.407465 0.913221i \(-0.366413\pi\)
\(174\) 3.88744 0.294706
\(175\) −26.9793 −2.03944
\(176\) −1.21076 2.09709i −0.0912642 0.158074i
\(177\) 10.7067 0.804768
\(178\) 5.20041 9.00737i 0.389787 0.675131i
\(179\) −2.93186 −0.219137 −0.109569 0.993979i \(-0.534947\pi\)
−0.109569 + 0.993979i \(0.534947\pi\)
\(180\) −6.76704 + 11.7208i −0.504385 + 0.873620i
\(181\) 3.09035 5.35264i 0.229704 0.397859i −0.728016 0.685560i \(-0.759558\pi\)
0.957720 + 0.287701i \(0.0928909\pi\)
\(182\) 2.53407 4.38914i 0.187838 0.325345i
\(183\) −0.590349 1.02252i −0.0436399 0.0755865i
\(184\) −0.955582 −0.0704464
\(185\) −20.7933 12.1064i −1.52875 0.890083i
\(186\) 18.9793 1.39163
\(187\) 7.34704 + 12.7254i 0.537269 + 0.930576i
\(188\) 5.74483 9.95033i 0.418985 0.725702i
\(189\) 1.35337 2.34411i 0.0984433 0.170509i
\(190\) 6.90180 11.9543i 0.500709 0.867254i
\(191\) −21.0030 −1.51973 −0.759863 0.650083i \(-0.774734\pi\)
−0.759863 + 0.650083i \(0.774734\pi\)
\(192\) −1.26704 + 2.19457i −0.0914404 + 0.158379i
\(193\) −2.91116 −0.209550 −0.104775 0.994496i \(-0.533412\pi\)
−0.104775 + 0.994496i \(0.533412\pi\)
\(194\) −5.24483 9.08431i −0.376557 0.652215i
\(195\) 20.0474 1.43563
\(196\) −0.578488 −0.0413206
\(197\) 3.76704 + 6.52470i 0.268390 + 0.464865i 0.968446 0.249222i \(-0.0801750\pi\)
−0.700056 + 0.714088i \(0.746842\pi\)
\(198\) −4.14262 + 7.17522i −0.294403 + 0.509921i
\(199\) −18.3564 −1.30125 −0.650625 0.759399i \(-0.725493\pi\)
−0.650625 + 0.759399i \(0.725493\pi\)
\(200\) −5.32331 9.22025i −0.376415 0.651970i
\(201\) 8.13628 + 14.0925i 0.573889 + 0.994005i
\(202\) 2.55628 + 4.42761i 0.179859 + 0.311525i
\(203\) 1.94372 3.36662i 0.136422 0.236291i
\(204\) 7.68855 13.3170i 0.538306 0.932373i
\(205\) 16.7908 + 29.0824i 1.17272 + 2.03121i
\(206\) −0.198895 0.344496i −0.0138577 0.0240022i
\(207\) 1.63477 + 2.83150i 0.113624 + 0.196803i
\(208\) 2.00000 0.138675
\(209\) 4.22512 7.31812i 0.292257 0.506205i
\(210\) 12.7004 + 21.9978i 0.876411 + 1.51799i
\(211\) 8.33768 0.573989 0.286995 0.957932i \(-0.407344\pi\)
0.286995 + 0.957932i \(0.407344\pi\)
\(212\) 8.42151 0.578392
\(213\) 1.85738 + 3.21708i 0.127266 + 0.220431i
\(214\) −8.11256 −0.554563
\(215\) −8.13378 + 14.0881i −0.554719 + 0.960802i
\(216\) 1.06814 0.0726777
\(217\) 9.48965 16.4366i 0.644200 1.11579i
\(218\) −5.72262 + 9.91186i −0.387585 + 0.671316i
\(219\) 0.534070 0.925037i 0.0360891 0.0625082i
\(220\) −4.78924 8.29521i −0.322891 0.559263i
\(221\) −12.1363 −0.816375
\(222\) −0.0562792 + 15.4140i −0.00377721 + 1.03452i
\(223\) −23.0919 −1.54635 −0.773173 0.634195i \(-0.781331\pi\)
−0.773173 + 0.634195i \(0.781331\pi\)
\(224\) 1.26704 + 2.19457i 0.0846573 + 0.146631i
\(225\) −18.2138 + 31.5472i −1.21425 + 2.10315i
\(226\) 1.78924 3.09906i 0.119019 0.206147i
\(227\) −9.32331 + 16.1485i −0.618810 + 1.07181i 0.370893 + 0.928676i \(0.379052\pi\)
−0.989703 + 0.143135i \(0.954282\pi\)
\(228\) −8.84302 −0.585644
\(229\) −10.2567 + 17.7651i −0.677781 + 1.17395i 0.297867 + 0.954607i \(0.403725\pi\)
−0.975648 + 0.219344i \(0.929608\pi\)
\(230\) −3.77988 −0.249238
\(231\) 7.77488 + 13.4665i 0.511550 + 0.886030i
\(232\) 1.53407 0.100717
\(233\) 18.8223 1.23309 0.616546 0.787319i \(-0.288531\pi\)
0.616546 + 0.787319i \(0.288531\pi\)
\(234\) −3.42151 5.92623i −0.223671 0.387410i
\(235\) 22.7241 39.3593i 1.48236 2.56752i
\(236\) 4.22512 0.275032
\(237\) −3.35337 5.80821i −0.217825 0.377284i
\(238\) −7.68855 13.3170i −0.498374 0.863210i
\(239\) 10.7567 + 18.6311i 0.695792 + 1.20515i 0.969913 + 0.243452i \(0.0782799\pi\)
−0.274121 + 0.961695i \(0.588387\pi\)
\(240\) −5.01186 + 8.68080i −0.323514 + 0.560343i
\(241\) −8.85738 + 15.3414i −0.570554 + 0.988229i 0.425955 + 0.904744i \(0.359938\pi\)
−0.996509 + 0.0834846i \(0.973395\pi\)
\(242\) 2.56814 + 4.44815i 0.165086 + 0.285938i
\(243\) 11.1782 + 19.3612i 0.717082 + 1.24202i
\(244\) −0.232965 0.403507i −0.0149140 0.0258319i
\(245\) −2.28826 −0.146191
\(246\) 10.7567 18.6311i 0.685821 1.18788i
\(247\) 3.48965 + 6.04425i 0.222041 + 0.384587i
\(248\) 7.48965 0.475593
\(249\) −8.55779 −0.542328
\(250\) −11.1679 19.3433i −0.706317 1.22338i
\(251\) −5.79861 −0.366005 −0.183002 0.983112i \(-0.558582\pi\)
−0.183002 + 0.983112i \(0.558582\pi\)
\(252\) 4.33518 7.50874i 0.273090 0.473006i
\(253\) −2.31395 −0.145477
\(254\) 0.365233 0.632601i 0.0229167 0.0396929i
\(255\) 30.4127 52.6763i 1.90452 3.29872i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −14.8470 25.7158i −0.926133 1.60411i −0.789729 0.613456i \(-0.789779\pi\)
−0.136403 0.990653i \(-0.543554\pi\)
\(258\) 10.4215 0.648815
\(259\) 13.3208 + 7.75576i 0.827715 + 0.481920i
\(260\) 7.91116 0.490630
\(261\) −2.62442 4.54563i −0.162447 0.281367i
\(262\) −8.64413 + 14.9721i −0.534036 + 0.924978i
\(263\) 9.37709 16.2416i 0.578216 1.00150i −0.417468 0.908692i \(-0.637082\pi\)
0.995684 0.0928083i \(-0.0295844\pi\)
\(264\) −3.06814 + 5.31418i −0.188831 + 0.327065i
\(265\) 33.3120 2.04634
\(266\) −4.42151 + 7.65828i −0.271100 + 0.469559i
\(267\) −26.3564 −1.61299
\(268\) 3.21076 + 5.56119i 0.196128 + 0.339704i
\(269\) 23.1156 1.40938 0.704691 0.709514i \(-0.251086\pi\)
0.704691 + 0.709514i \(0.251086\pi\)
\(270\) 4.22512 0.257132
\(271\) −11.3470 19.6536i −0.689283 1.19387i −0.972070 0.234691i \(-0.924592\pi\)
0.282787 0.959183i \(-0.408741\pi\)
\(272\) 3.03407 5.25516i 0.183968 0.318641i
\(273\) −12.8430 −0.777295
\(274\) −5.52372 9.56737i −0.333700 0.577986i
\(275\) −12.8905 22.3269i −0.777324 1.34637i
\(276\) 1.21076 + 2.09709i 0.0728789 + 0.126230i
\(277\) −9.35488 + 16.2031i −0.562081 + 0.973552i 0.435234 + 0.900317i \(0.356666\pi\)
−0.997315 + 0.0732348i \(0.976668\pi\)
\(278\) 6.11006 10.5829i 0.366457 0.634722i
\(279\) −12.8130 22.1927i −0.767092 1.32864i
\(280\) 5.01186 + 8.68080i 0.299516 + 0.518777i
\(281\) 13.5681 + 23.5007i 0.809407 + 1.40193i 0.913275 + 0.407344i \(0.133545\pi\)
−0.103868 + 0.994591i \(0.533122\pi\)
\(282\) −29.1156 −1.73381
\(283\) −0.454069 + 0.786470i −0.0269916 + 0.0467508i −0.879206 0.476442i \(-0.841926\pi\)
0.852214 + 0.523193i \(0.175259\pi\)
\(284\) 0.732965 + 1.26953i 0.0434935 + 0.0753329i
\(285\) −34.9793 −2.07200
\(286\) 4.84302 0.286374
\(287\) −10.7567 18.6311i −0.634947 1.09976i
\(288\) 3.42151 0.201615
\(289\) −9.91116 + 17.1666i −0.583010 + 1.00980i
\(290\) 6.06814 0.356333
\(291\) −13.2908 + 23.0203i −0.779118 + 1.34947i
\(292\) 0.210756 0.365040i 0.0123336 0.0213623i
\(293\) −8.23296 + 14.2599i −0.480975 + 0.833073i −0.999762 0.0218306i \(-0.993051\pi\)
0.518787 + 0.854904i \(0.326384\pi\)
\(294\) 0.732965 + 1.26953i 0.0427474 + 0.0740406i
\(295\) 16.7128 0.973057
\(296\) −0.0222090 + 6.08272i −0.00129087 + 0.353551i
\(297\) 2.58651 0.150085
\(298\) −1.27738 2.21249i −0.0739968 0.128166i
\(299\) 0.955582 1.65512i 0.0552627 0.0957179i
\(300\) −13.4897 + 23.3648i −0.778825 + 1.34897i
\(301\) 5.21076 9.02529i 0.300343 0.520209i
\(302\) −6.86675 −0.395137
\(303\) 6.47779 11.2199i 0.372139 0.644564i
\(304\) −3.48965 −0.200145
\(305\) −0.921512 1.59611i −0.0527656 0.0913927i
\(306\) −20.7622 −1.18690
\(307\) −3.04442 −0.173754 −0.0868771 0.996219i \(-0.527689\pi\)
−0.0868771 + 0.996219i \(0.527689\pi\)
\(308\) 3.06814 + 5.31418i 0.174824 + 0.302803i
\(309\) −0.504013 + 0.872976i −0.0286723 + 0.0496619i
\(310\) 29.6259 1.68264
\(311\) −0.222617 0.385584i −0.0126235 0.0218645i 0.859645 0.510892i \(-0.170685\pi\)
−0.872268 + 0.489028i \(0.837352\pi\)
\(312\) −2.53407 4.38914i −0.143463 0.248486i
\(313\) −13.6663 23.6708i −0.772467 1.33795i −0.936207 0.351449i \(-0.885689\pi\)
0.163740 0.986504i \(-0.447644\pi\)
\(314\) 1.87959 3.25555i 0.106072 0.183721i
\(315\) 17.1481 29.7015i 0.966188 1.67349i
\(316\) −1.32331 2.29205i −0.0744422 0.128938i
\(317\) −10.7370 18.5970i −0.603049 1.04451i −0.992357 0.123403i \(-0.960619\pi\)
0.389308 0.921108i \(-0.372714\pi\)
\(318\) −10.6704 18.4816i −0.598364 1.03640i
\(319\) 3.71477 0.207987
\(320\) −1.97779 + 3.42563i −0.110562 + 0.191499i
\(321\) 10.2789 + 17.8036i 0.573712 + 0.993698i
\(322\) 2.42151 0.134946
\(323\) 21.1757 1.17825
\(324\) 3.77890 + 6.54524i 0.209939 + 0.363624i
\(325\) 21.2933 1.18114
\(326\) −3.01186 + 5.21670i −0.166812 + 0.288926i
\(327\) 29.0030 1.60387
\(328\) 4.24483 7.35225i 0.234381 0.405960i
\(329\) −14.5578 + 25.2148i −0.802597 + 1.39014i
\(330\) −12.1363 + 21.0207i −0.668080 + 1.15715i
\(331\) 4.55779 + 7.89433i 0.250519 + 0.433912i 0.963669 0.267100i \(-0.0860654\pi\)
−0.713150 + 0.701012i \(0.752732\pi\)
\(332\) −3.37709 −0.185342
\(333\) 18.0618 10.3402i 0.989781 0.566642i
\(334\) −12.0000 −0.656611
\(335\) 12.7004 + 21.9978i 0.693897 + 1.20187i
\(336\) 3.21076 5.56119i 0.175161 0.303388i
\(337\) 13.2004 22.8638i 0.719072 1.24547i −0.242296 0.970202i \(-0.577900\pi\)
0.961368 0.275267i \(-0.0887662\pi\)
\(338\) 4.50000 7.79423i 0.244768 0.423950i
\(339\) −9.06814 −0.492514
\(340\) 12.0015 20.7872i 0.650873 1.12735i
\(341\) 18.1363 0.982135
\(342\) 5.96994 + 10.3402i 0.322818 + 0.559136i
\(343\) 19.2044 1.03694
\(344\) 4.11256 0.221734
\(345\) 4.78924 + 8.29521i 0.257844 + 0.446599i
\(346\) −7.72262 + 13.3760i −0.415170 + 0.719096i
\(347\) −31.8748 −1.71113 −0.855564 0.517698i \(-0.826789\pi\)
−0.855564 + 0.517698i \(0.826789\pi\)
\(348\) −1.94372 3.36662i −0.104194 0.180470i
\(349\) 11.8208 + 20.4743i 0.632754 + 1.09596i 0.986986 + 0.160804i \(0.0514088\pi\)
−0.354233 + 0.935157i \(0.615258\pi\)
\(350\) 13.4897 + 23.3648i 0.721052 + 1.24890i
\(351\) −1.06814 + 1.85007i −0.0570131 + 0.0987496i
\(352\) −1.21076 + 2.09709i −0.0645335 + 0.111775i
\(353\) −11.7789 20.4016i −0.626927 1.08587i −0.988165 0.153396i \(-0.950979\pi\)
0.361237 0.932474i \(-0.382354\pi\)
\(354\) −5.35337 9.27231i −0.284528 0.492818i
\(355\) 2.89930 + 5.02174i 0.153879 + 0.266526i
\(356\) −10.4008 −0.551242
\(357\) −19.4833 + 33.7461i −1.03117 + 1.78603i
\(358\) 1.46593 + 2.53906i 0.0774768 + 0.134194i
\(359\) −5.86372 −0.309475 −0.154738 0.987956i \(-0.549453\pi\)
−0.154738 + 0.987956i \(0.549453\pi\)
\(360\) 13.5341 0.713308
\(361\) 3.41116 + 5.90831i 0.179535 + 0.310964i
\(362\) −6.18070 −0.324850
\(363\) 6.50785 11.2719i 0.341573 0.591623i
\(364\) −5.06814 −0.265643
\(365\) 0.833662 1.44395i 0.0436359 0.0755795i
\(366\) −0.590349 + 1.02252i −0.0308581 + 0.0534477i
\(367\) 2.00000 3.46410i 0.104399 0.180825i −0.809093 0.587680i \(-0.800041\pi\)
0.913493 + 0.406855i \(0.133375\pi\)
\(368\) 0.477791 + 0.827558i 0.0249066 + 0.0431395i
\(369\) −29.0474 −1.51215
\(370\) −0.0878496 + 24.0607i −0.00456708 + 1.25086i
\(371\) −21.3407 −1.10795
\(372\) −9.48965 16.4366i −0.492016 0.852196i
\(373\) 16.1822 28.0284i 0.837883 1.45126i −0.0537780 0.998553i \(-0.517126\pi\)
0.891661 0.452703i \(-0.149540\pi\)
\(374\) 7.34704 12.7254i 0.379906 0.658017i
\(375\) −28.3001 + 49.0172i −1.46141 + 2.53124i
\(376\) −11.4897 −0.592534
\(377\) −1.53407 + 2.65709i −0.0790086 + 0.136847i
\(378\) −2.70674 −0.139220
\(379\) −15.4571 26.7725i −0.793978 1.37521i −0.923486 0.383631i \(-0.874673\pi\)
0.129509 0.991578i \(-0.458660\pi\)
\(380\) −13.8036 −0.708110
\(381\) −1.85105 −0.0948322
\(382\) 10.5015 + 18.1892i 0.537304 + 0.930638i
\(383\) −15.5997 + 27.0195i −0.797108 + 1.38063i 0.124384 + 0.992234i \(0.460305\pi\)
−0.921492 + 0.388397i \(0.873029\pi\)
\(384\) 2.53407 0.129316
\(385\) 12.1363 + 21.0207i 0.618522 + 1.07131i
\(386\) 1.45558 + 2.52114i 0.0740872 + 0.128323i
\(387\) −7.03558 12.1860i −0.357639 0.619449i
\(388\) −5.24483 + 9.08431i −0.266266 + 0.461186i
\(389\) −2.62442 + 4.54563i −0.133063 + 0.230472i −0.924856 0.380318i \(-0.875815\pi\)
0.791793 + 0.610790i \(0.209148\pi\)
\(390\) −10.0237 17.3616i −0.507571 0.879139i
\(391\) −2.89930 5.02174i −0.146624 0.253960i
\(392\) 0.289244 + 0.500986i 0.0146090 + 0.0253036i
\(393\) 43.8097 2.20990
\(394\) 3.76704 6.52470i 0.189780 0.328709i
\(395\) −5.23448 9.06638i −0.263375 0.456179i
\(396\) 8.28523 0.416349
\(397\) 17.4740 0.876993 0.438496 0.898733i \(-0.355511\pi\)
0.438496 + 0.898733i \(0.355511\pi\)
\(398\) 9.17820 + 15.8971i 0.460062 + 0.796850i
\(399\) 22.4088 1.12185
\(400\) −5.32331 + 9.22025i −0.266166 + 0.461013i
\(401\) 2.28523 0.114119 0.0570595 0.998371i \(-0.481828\pi\)
0.0570595 + 0.998371i \(0.481828\pi\)
\(402\) 8.13628 14.0925i 0.405801 0.702868i
\(403\) −7.48965 + 12.9725i −0.373086 + 0.646204i
\(404\) 2.55628 4.42761i 0.127180 0.220282i
\(405\) 14.9477 + 25.8902i 0.742759 + 1.28650i
\(406\) −3.88744 −0.192930
\(407\) −0.0537794 + 14.7294i −0.00266575 + 0.730108i
\(408\) −15.3771 −0.761280
\(409\) −13.1560 22.7868i −0.650522 1.12674i −0.982996 0.183625i \(-0.941217\pi\)
0.332475 0.943112i \(-0.392116\pi\)
\(410\) 16.7908 29.0824i 0.829236 1.43628i
\(411\) −13.9975 + 24.2444i −0.690446 + 1.19589i
\(412\) −0.198895 + 0.344496i −0.00979884 + 0.0169721i
\(413\) −10.7067 −0.526844
\(414\) 1.63477 2.83150i 0.0803444 0.139161i
\(415\) −13.3584 −0.655737
\(416\) −1.00000 1.73205i −0.0490290 0.0849208i
\(417\) −30.9666 −1.51644
\(418\) −8.45023 −0.413314
\(419\) −13.1244 22.7322i −0.641170 1.11054i −0.985172 0.171570i \(-0.945116\pi\)
0.344002 0.938969i \(-0.388217\pi\)
\(420\) 12.7004 21.9978i 0.619716 1.07338i
\(421\) 12.9763 0.632425 0.316213 0.948688i \(-0.397589\pi\)
0.316213 + 0.948688i \(0.397589\pi\)
\(422\) −4.16884 7.22064i −0.202936 0.351495i
\(423\) 19.6560 + 34.0452i 0.955707 + 1.65533i
\(424\) −4.21076 7.29324i −0.204492 0.354191i
\(425\) 32.3026 55.9498i 1.56691 2.71396i
\(426\) 1.85738 3.21708i 0.0899906 0.155868i
\(427\) 0.590349 + 1.02252i 0.0285690 + 0.0494830i
\(428\) 4.05628 + 7.02568i 0.196068 + 0.339599i
\(429\) −6.13628 10.6284i −0.296262 0.513142i
\(430\) 16.2676 0.784491
\(431\) 6.25517 10.8343i 0.301301 0.521869i −0.675130 0.737699i \(-0.735912\pi\)
0.976431 + 0.215830i \(0.0692457\pi\)
\(432\) −0.534070 0.925037i −0.0256955 0.0445058i
\(433\) 2.03942 0.0980082 0.0490041 0.998799i \(-0.484395\pi\)
0.0490041 + 0.998799i \(0.484395\pi\)
\(434\) −18.9793 −0.911036
\(435\) −7.68855 13.3170i −0.368638 0.638499i
\(436\) 11.4452 0.548127
\(437\) −1.66732 + 2.88789i −0.0797589 + 0.138147i
\(438\) −1.06814 −0.0510377
\(439\) 14.4452 25.0199i 0.689433 1.19413i −0.282588 0.959241i \(-0.591193\pi\)
0.972021 0.234892i \(-0.0754737\pi\)
\(440\) −4.78924 + 8.29521i −0.228318 + 0.395459i
\(441\) 0.989652 1.71413i 0.0471263 0.0816251i
\(442\) 6.06814 + 10.5103i 0.288632 + 0.499925i
\(443\) −2.52907 −0.120160 −0.0600799 0.998194i \(-0.519136\pi\)
−0.0600799 + 0.998194i \(0.519136\pi\)
\(444\) 13.3771 7.65828i 0.634849 0.363446i
\(445\) −41.1413 −1.95028
\(446\) 11.5459 + 19.9981i 0.546716 + 0.946939i
\(447\) −3.23698 + 5.60661i −0.153104 + 0.265184i
\(448\) 1.26704 2.19457i 0.0598618 0.103684i
\(449\) −2.43587 + 4.21906i −0.114956 + 0.199110i −0.917762 0.397131i \(-0.870006\pi\)
0.802806 + 0.596240i \(0.203339\pi\)
\(450\) 36.4276 1.71721
\(451\) 10.2789 17.8036i 0.484014 0.838337i
\(452\) −3.57849 −0.168318
\(453\) 8.70041 + 15.0695i 0.408781 + 0.708029i
\(454\) 18.6466 0.875130
\(455\) −20.0474 −0.939839
\(456\) 4.42151 + 7.65828i 0.207056 + 0.358632i
\(457\) −3.52372 + 6.10327i −0.164833 + 0.285499i −0.936596 0.350411i \(-0.886042\pi\)
0.771763 + 0.635910i \(0.219375\pi\)
\(458\) 20.5134 0.958527
\(459\) 3.24081 + 5.61325i 0.151268 + 0.262004i
\(460\) 1.88994 + 3.27347i 0.0881190 + 0.152627i
\(461\) 0.0681404 + 0.118023i 0.00317361 + 0.00549686i 0.867608 0.497249i \(-0.165656\pi\)
−0.864434 + 0.502746i \(0.832323\pi\)
\(462\) 7.77488 13.4665i 0.361720 0.626518i
\(463\) −8.11006 + 14.0470i −0.376906 + 0.652821i −0.990610 0.136715i \(-0.956345\pi\)
0.613704 + 0.789536i \(0.289679\pi\)
\(464\) −0.767035 1.32854i −0.0356087 0.0616761i
\(465\) −37.5371 65.0162i −1.74074 3.01505i
\(466\) −9.41116 16.3006i −0.435964 0.755111i
\(467\) 38.1837 1.76693 0.883466 0.468495i \(-0.155204\pi\)
0.883466 + 0.468495i \(0.155204\pi\)
\(468\) −3.42151 + 5.92623i −0.158159 + 0.273940i
\(469\) −8.13628 14.0925i −0.375699 0.650729i
\(470\) −45.4483 −2.09637
\(471\) −9.52604 −0.438937
\(472\) −2.11256 3.65906i −0.0972384 0.168422i
\(473\) 9.95861 0.457897
\(474\) −3.35337 + 5.80821i −0.154025 + 0.266780i
\(475\) −37.1530 −1.70470
\(476\) −7.68855 + 13.3170i −0.352404 + 0.610382i
\(477\) −14.4072 + 24.9539i −0.659658 + 1.14256i
\(478\) 10.7567 18.6311i 0.491999 0.852168i
\(479\) 14.2488 + 24.6797i 0.651046 + 1.12764i 0.982869 + 0.184303i \(0.0590029\pi\)
−0.331823 + 0.943342i \(0.607664\pi\)
\(480\) 10.0237 0.457518
\(481\) −10.5134 6.12119i −0.479369 0.279102i
\(482\) 17.7148 0.806886
\(483\) −3.06814 5.31418i −0.139605 0.241803i
\(484\) 2.56814 4.44815i 0.116734 0.202189i
\(485\) −20.7463 + 35.9337i −0.942043 + 1.63167i
\(486\) 11.1782 19.3612i 0.507053 0.878242i
\(487\) 28.1126 1.27390 0.636951 0.770904i \(-0.280195\pi\)
0.636951 + 0.770904i \(0.280195\pi\)
\(488\) −0.232965 + 0.403507i −0.0105458 + 0.0182659i
\(489\) 15.2645 0.690286
\(490\) 1.14413 + 1.98169i 0.0516865 + 0.0895236i
\(491\) −2.42151 −0.109281 −0.0546406 0.998506i \(-0.517401\pi\)
−0.0546406 + 0.998506i \(0.517401\pi\)
\(492\) −21.5134 −0.969898
\(493\) 4.65448 + 8.06179i 0.209627 + 0.363085i
\(494\) 3.48965 6.04425i 0.157007 0.271944i
\(495\) 32.7729 1.47303
\(496\) −3.74483 6.48623i −0.168148 0.291240i
\(497\) −1.85738 3.21708i −0.0833151 0.144306i
\(498\) 4.27890 + 7.41127i 0.191742 + 0.332107i
\(499\) 1.23448 2.13818i 0.0552628 0.0957180i −0.837071 0.547095i \(-0.815734\pi\)
0.892333 + 0.451377i \(0.149067\pi\)
\(500\) −11.1679 + 19.3433i −0.499441 + 0.865058i
\(501\) 15.2044 + 26.3348i 0.679283 + 1.17655i
\(502\) 2.89930 + 5.02174i 0.129402 + 0.224131i
\(503\) −18.7004 32.3901i −0.833810 1.44420i −0.894996 0.446075i \(-0.852822\pi\)
0.0611857 0.998126i \(-0.480512\pi\)
\(504\) −8.67035 −0.386208
\(505\) 10.1116 17.5138i 0.449959 0.779352i
\(506\) 1.15698 + 2.00394i 0.0514339 + 0.0890861i
\(507\) −22.8066 −1.01288
\(508\) −0.730465 −0.0324091
\(509\) 4.97779 + 8.62179i 0.220637 + 0.382154i 0.955001 0.296601i \(-0.0958532\pi\)
−0.734365 + 0.678755i \(0.762520\pi\)
\(510\) −60.8254 −2.69339
\(511\) −0.534070 + 0.925037i −0.0236259 + 0.0409212i
\(512\) 1.00000 0.0441942
\(513\) 1.86372 3.22806i 0.0822852 0.142522i
\(514\) −14.8470 + 25.7158i −0.654875 + 1.13428i
\(515\) −0.786744 + 1.36268i −0.0346681 + 0.0600469i
\(516\) −5.21076 9.02529i −0.229391 0.397316i
\(517\) −27.8223 −1.22362
\(518\) 0.0562792 15.4140i 0.00247277 0.677254i
\(519\) 39.1393 1.71802
\(520\) −3.95558 6.85127i −0.173464 0.300448i
\(521\) −5.36773 + 9.29719i −0.235165 + 0.407317i −0.959321 0.282319i \(-0.908896\pi\)
0.724156 + 0.689636i \(0.242230\pi\)
\(522\) −2.62442 + 4.54563i −0.114868 + 0.198957i
\(523\) −9.60471 + 16.6358i −0.419985 + 0.727435i −0.995937 0.0900482i \(-0.971298\pi\)
0.575953 + 0.817483i \(0.304631\pi\)
\(524\) 17.2883 0.755241
\(525\) 34.1837 59.2079i 1.49190 2.58405i
\(526\) −18.7542 −0.817721
\(527\) 22.7241 + 39.3593i 0.989879 + 1.71452i
\(528\) 6.13628 0.267047
\(529\) −22.0869 −0.960298
\(530\) −16.6560 28.8490i −0.723490 1.25312i
\(531\) −7.22814 + 12.5195i −0.313675 + 0.543301i
\(532\) 8.84302 0.383394
\(533\) 8.48965 + 14.7045i 0.367728 + 0.636923i
\(534\) 13.1782 + 22.8253i 0.570276 + 0.987748i
\(535\) 16.0449 + 27.7907i 0.693683 + 1.20149i
\(536\) 3.21076 5.56119i 0.138684 0.240207i
\(537\) 3.71477 6.43417i 0.160304 0.277655i
\(538\) −11.5578 20.0187i −0.498292 0.863067i
\(539\) 0.700408 + 1.21314i 0.0301687 + 0.0522537i
\(540\) −2.11256 3.65906i −0.0909100 0.157461i
\(541\) −29.6704 −1.27563 −0.637814 0.770190i \(-0.720161\pi\)
−0.637814 + 0.770190i \(0.720161\pi\)
\(542\) −11.3470 + 19.6536i −0.487397 + 0.844196i
\(543\) 7.83116 + 13.5640i 0.336067 + 0.582086i
\(544\) −6.06814 −0.260169
\(545\) 45.2726 1.93926
\(546\) 6.42151 + 11.1224i 0.274815 + 0.475994i
\(547\) −4.78291 −0.204502 −0.102251 0.994759i \(-0.532605\pi\)
−0.102251 + 0.994759i \(0.532605\pi\)
\(548\) −5.52372 + 9.56737i −0.235962 + 0.408698i
\(549\) 1.59418 0.0680381
\(550\) −12.8905 + 22.3269i −0.549651 + 0.952024i
\(551\) 2.67669 4.63616i 0.114031 0.197507i
\(552\) 1.21076 2.09709i 0.0515332 0.0892581i
\(553\) 3.35337 + 5.80821i 0.142600 + 0.246990i
\(554\) 18.7098 0.794902
\(555\) 52.9142 30.2930i 2.24608 1.28586i
\(556\) −12.2201 −0.518248
\(557\) 10.0222 + 17.3590i 0.424655 + 0.735523i 0.996388 0.0849160i \(-0.0270622\pi\)
−0.571733 + 0.820439i \(0.693729\pi\)
\(558\) −12.8130 + 22.1927i −0.542416 + 0.939492i
\(559\) −4.11256 + 7.12316i −0.173943 + 0.301278i
\(560\) 5.01186 8.68080i 0.211790 0.366831i
\(561\) −37.2358 −1.57210
\(562\) 13.5681 23.5007i 0.572337 0.991318i
\(563\) −24.4452 −1.03024 −0.515122 0.857117i \(-0.672253\pi\)
−0.515122 + 0.857117i \(0.672253\pi\)
\(564\) 14.5578 + 25.2148i 0.612994 + 1.06174i
\(565\) −14.1550 −0.595505
\(566\) 0.908137 0.0381719
\(567\) −9.57599 16.5861i −0.402154 0.696551i
\(568\) 0.732965 1.26953i 0.0307545 0.0532684i
\(569\) 6.09686 0.255594 0.127797 0.991800i \(-0.459209\pi\)
0.127797 + 0.991800i \(0.459209\pi\)
\(570\) 17.4897 + 30.2930i 0.732561 + 1.26883i
\(571\) 5.49215 + 9.51269i 0.229839 + 0.398094i 0.957760 0.287568i \(-0.0928466\pi\)
−0.727921 + 0.685661i \(0.759513\pi\)
\(572\) −2.42151 4.19418i −0.101248 0.175368i
\(573\) 26.6116 46.0926i 1.11171 1.92555i
\(574\) −10.7567 + 18.6311i −0.448975 + 0.777648i
\(575\) 5.08686 + 8.81071i 0.212137 + 0.367432i
\(576\) −1.71076 2.96312i −0.0712815 0.123463i
\(577\) 20.9586 + 36.3014i 0.872518 + 1.51125i 0.859383 + 0.511332i \(0.170848\pi\)
0.0131352 + 0.999914i \(0.495819\pi\)
\(578\) 19.8223 0.824500
\(579\) 3.68855 6.38875i 0.153291 0.265507i
\(580\) −3.03407 5.25516i −0.125983 0.218209i
\(581\) 8.55779 0.355037
\(582\) 26.5815 1.10184
\(583\) −10.1964 17.6607i −0.422292 0.731430i
\(584\) −0.421512 −0.0174423
\(585\) −13.5341 + 23.4417i −0.559565 + 0.969195i
\(586\) 16.4659 0.680201
\(587\) 10.8930 18.8672i 0.449601 0.778732i −0.548759 0.835981i \(-0.684900\pi\)
0.998360 + 0.0572490i \(0.0182329\pi\)
\(588\) 0.732965 1.26953i 0.0302270 0.0523546i
\(589\) 13.0681 22.6347i 0.538463 0.932646i
\(590\) −8.35640 14.4737i −0.344027 0.595873i
\(591\) −19.0919 −0.785334
\(592\) 5.27890 3.02213i 0.216961 0.124209i
\(593\) −1.73546 −0.0712670 −0.0356335 0.999365i \(-0.511345\pi\)
−0.0356335 + 0.999365i \(0.511345\pi\)
\(594\) −1.29326 2.23999i −0.0530630 0.0919078i
\(595\) −30.4127 + 52.6763i −1.24680 + 2.15952i
\(596\) −1.27738 + 2.21249i −0.0523236 + 0.0906272i
\(597\) 23.2582 40.2844i 0.951895 1.64873i
\(598\) −1.91116 −0.0781533
\(599\) 4.14262 7.17522i 0.169263 0.293172i −0.768898 0.639371i \(-0.779195\pi\)
0.938161 + 0.346200i \(0.112528\pi\)
\(600\) 26.9793 1.10143
\(601\) −18.1466 31.4309i −0.740216 1.28209i −0.952397 0.304862i \(-0.901390\pi\)
0.212180 0.977231i \(-0.431944\pi\)
\(602\) −10.4215 −0.424749
\(603\) −21.9713 −0.894740
\(604\) 3.43337 + 5.94678i 0.139702 + 0.241971i
\(605\) 10.1585 17.5950i 0.413001 0.715339i
\(606\) −12.9556 −0.526285
\(607\) 14.0538 + 24.3419i 0.570425 + 0.988006i 0.996522 + 0.0833281i \(0.0265549\pi\)
−0.426097 + 0.904678i \(0.640112\pi\)
\(608\) 1.74483 + 3.02213i 0.0707620 + 0.122563i
\(609\) 4.92552 + 8.53126i 0.199592 + 0.345704i
\(610\) −0.921512 + 1.59611i −0.0373109 + 0.0646244i
\(611\) 11.4897 19.9007i 0.464822 0.805095i
\(612\) 10.3811 + 17.9806i 0.419631 + 0.726823i
\(613\) 3.73698 + 6.47264i 0.150935 + 0.261427i 0.931571 0.363558i \(-0.118438\pi\)
−0.780636 + 0.624985i \(0.785105\pi\)
\(614\) 1.52221 + 2.63654i 0.0614314 + 0.106402i
\(615\) −85.0979 −3.43148
\(616\) 3.06814 5.31418i 0.123619 0.214114i
\(617\) −10.3470 17.9216i −0.416556 0.721496i 0.579034 0.815303i \(-0.303430\pi\)
−0.995590 + 0.0938069i \(0.970096\pi\)
\(618\) 1.00803 0.0405488
\(619\) −5.63093 −0.226326 −0.113163 0.993576i \(-0.536098\pi\)
−0.113163 + 0.993576i \(0.536098\pi\)
\(620\) −14.8130 25.6568i −0.594903 1.03040i
\(621\) −1.02070 −0.0409591
\(622\) −0.222617 + 0.385584i −0.00892613 + 0.0154605i
\(623\) 26.3564 1.05595
\(624\) −2.53407 + 4.38914i −0.101444 + 0.175706i
\(625\) −17.5588 + 30.4127i −0.702351 + 1.21651i
\(626\) −13.6663 + 23.6708i −0.546217 + 0.946075i
\(627\) 10.7067 + 18.5446i 0.427586 + 0.740601i
\(628\) −3.75919 −0.150008
\(629\) −32.0331 + 18.3387i −1.27724 + 0.731212i
\(630\) −34.2963 −1.36640
\(631\) −7.99117 13.8411i −0.318123 0.551006i 0.661973 0.749528i \(-0.269719\pi\)
−0.980096 + 0.198522i \(0.936386\pi\)
\(632\) −1.32331 + 2.29205i −0.0526386 + 0.0911728i
\(633\) −10.5641 + 18.2976i −0.419886 + 0.727265i
\(634\) −10.7370 + 18.5970i −0.426420 + 0.738581i
\(635\) −2.88941 −0.114663
\(636\) −10.6704 + 18.4816i −0.423107 + 0.732843i
\(637\) −1.15698 −0.0458411
\(638\) −1.85738 3.21708i −0.0735346 0.127366i
\(639\) −5.01570 −0.198418
\(640\) 3.95558 0.156358
\(641\) −1.89145 3.27610i −0.0747080 0.129398i 0.826251 0.563302i \(-0.190469\pi\)
−0.900959 + 0.433904i \(0.857136\pi\)
\(642\) 10.2789 17.8036i 0.405676 0.702651i
\(643\) 15.6673 0.617859 0.308929 0.951085i \(-0.400029\pi\)
0.308929 + 0.951085i \(0.400029\pi\)
\(644\) −1.21076 2.09709i −0.0477105 0.0826370i
\(645\) −20.6116 35.7003i −0.811580 1.40570i
\(646\) −10.5878 18.3387i −0.416573 0.721526i
\(647\) 4.82180 8.35160i 0.189565 0.328335i −0.755541 0.655102i \(-0.772626\pi\)
0.945105 + 0.326766i \(0.105959\pi\)
\(648\) 3.77890 6.54524i 0.148449 0.257121i
\(649\) −5.11559 8.86045i −0.200804 0.347803i
\(650\) −10.6466 18.4405i −0.417595 0.723296i
\(651\) 24.0474 + 41.6514i 0.942494 + 1.63245i
\(652\) 6.02372 0.235907
\(653\) 4.97779 8.62179i 0.194796 0.337397i −0.752038 0.659120i \(-0.770929\pi\)
0.946834 + 0.321724i \(0.104262\pi\)
\(654\) −14.5015 25.1174i −0.567054 0.982166i
\(655\) 68.3851 2.67203
\(656\) −8.48965 −0.331465
\(657\) 0.721104 + 1.24899i 0.0281329 + 0.0487277i
\(658\) 29.1156 1.13504
\(659\) 18.8905 32.7193i 0.735868 1.27456i −0.218473 0.975843i \(-0.570108\pi\)
0.954341 0.298718i \(-0.0965590\pi\)
\(660\) 24.2726 0.944808
\(661\) 15.3993 26.6724i 0.598963 1.03744i −0.394011 0.919106i \(-0.628913\pi\)
0.992974 0.118329i \(-0.0377539\pi\)
\(662\) 4.55779 7.89433i 0.177144 0.306822i
\(663\) 15.3771 26.6339i 0.597197 1.03438i
\(664\) 1.68855 + 2.92465i 0.0655283 + 0.113498i
\(665\) 34.9793 1.35644
\(666\) −17.9858 10.4719i −0.696936 0.405776i
\(667\) −1.46593 −0.0567610
\(668\) 6.00000 + 10.3923i 0.232147 + 0.402090i
\(669\) 29.2582 50.6767i 1.13119 1.95927i
\(670\) 12.7004 21.9978i 0.490660 0.849847i
\(671\) −0.564127 + 0.977097i −0.0217779 + 0.0377204i
\(672\) −6.42151 −0.247715
\(673\) −21.7479 + 37.6684i −0.838318 + 1.45201i 0.0529819 + 0.998595i \(0.483127\pi\)
−0.891300 + 0.453414i \(0.850206\pi\)
\(674\) −26.4008 −1.01692
\(675\) −5.68605 9.84852i −0.218856 0.379070i
\(676\) −9.00000 −0.346154
\(677\) −11.7592 −0.451942 −0.225971 0.974134i \(-0.572556\pi\)
−0.225971 + 0.974134i \(0.572556\pi\)
\(678\) 4.53407 + 7.85324i 0.174130 + 0.301602i
\(679\) 13.2908 23.0203i 0.510052 0.883437i
\(680\) −24.0030 −0.920474
\(681\) −23.6259 40.9213i −0.905348 1.56811i
\(682\) −9.06814 15.7065i −0.347237 0.601432i
\(683\) −10.9467 18.9603i −0.418866 0.725497i 0.576960 0.816772i \(-0.304239\pi\)
−0.995826 + 0.0912758i \(0.970906\pi\)
\(684\) 5.96994 10.3402i 0.228266 0.395369i
\(685\) −21.8495 + 37.8445i −0.834828 + 1.44596i
\(686\) −9.60221 16.6315i −0.366614 0.634994i
\(687\) −25.9912 45.0180i −0.991625 1.71754i
\(688\) −2.05628 3.56158i −0.0783949 0.135784i
\(689\) 16.8430 0.641668
\(690\) 4.78924 8.29521i 0.182323 0.315793i
\(691\) 10.8130 + 18.7286i 0.411345 + 0.712470i 0.995037 0.0995050i \(-0.0317259\pi\)
−0.583692 + 0.811975i \(0.698393\pi\)
\(692\) 15.4452 0.587140
\(693\) −20.9954 −0.797548
\(694\) 15.9374 + 27.6044i 0.604975 + 1.04785i
\(695\) −48.3377 −1.83355
\(696\) −1.94372 + 3.36662i −0.0736765 + 0.127612i
\(697\) 51.5164 1.95132
\(698\) 11.8208 20.4743i 0.447424 0.774962i
\(699\) −23.8485 + 41.3069i −0.902035 + 1.56237i
\(700\) 13.4897 23.3648i 0.509861 0.883105i
\(701\) 7.46896 + 12.9366i 0.282099 + 0.488609i 0.971901 0.235388i \(-0.0756361\pi\)
−0.689803 + 0.723997i \(0.742303\pi\)
\(702\) 2.13628 0.0806287
\(703\) 18.3440 + 10.6804i 0.691857 + 0.402819i
\(704\) 2.42151 0.0912642
\(705\) 57.5845 + 99.7394i 2.16876 + 3.75640i
\(706\) −11.7789 + 20.4016i −0.443305 + 0.767826i
\(707\) −6.47779 + 11.2199i −0.243622 + 0.421966i
\(708\) −5.35337 + 9.27231i −0.201192 + 0.348475i
\(709\) −21.2519 −0.798131 −0.399065 0.916923i \(-0.630665\pi\)
−0.399065 + 0.916923i \(0.630665\pi\)
\(710\) 2.89930 5.02174i 0.108809 0.188463i
\(711\) 9.05547 0.339607
\(712\) 5.20041 + 9.00737i 0.194894 + 0.337565i
\(713\) −7.15698 −0.268031
\(714\) 38.9666 1.45829
\(715\) −9.57849 16.5904i −0.358215 0.620447i
\(716\) 1.46593 2.53906i 0.0547844 0.0948893i
\(717\) −54.5164 −2.03595
\(718\) 2.93186 + 5.07813i 0.109416 + 0.189514i
\(719\) 21.9912 + 38.0898i 0.820132 + 1.42051i 0.905583 + 0.424168i \(0.139433\pi\)
−0.0854514 + 0.996342i \(0.527233\pi\)
\(720\) −6.76704 11.7208i −0.252193 0.436810i
\(721\) 0.504013 0.872976i 0.0187704 0.0325113i
\(722\) 3.41116 5.90831i 0.126950 0.219885i
\(723\) −22.4452 38.8763i −0.834747 1.44582i
\(724\) 3.09035 + 5.35264i 0.114852 + 0.198929i
\(725\) −8.16634 14.1445i −0.303290 0.525314i
\(726\) −13.0157 −0.483058
\(727\) −26.1313 + 45.2607i −0.969156 + 1.67863i −0.271146 + 0.962538i \(0.587403\pi\)
−0.698010 + 0.716088i \(0.745931\pi\)
\(728\) 2.53407 + 4.38914i 0.0939189 + 0.162672i
\(729\) −33.9793 −1.25849
\(730\) −1.66732 −0.0617104
\(731\) 12.4778 + 21.6122i 0.461508 + 0.799355i
\(732\) 1.18070 0.0436399
\(733\) −5.33268 + 9.23647i −0.196967 + 0.341157i −0.947544 0.319627i \(-0.896442\pi\)
0.750577 + 0.660783i \(0.229776\pi\)
\(734\) −4.00000 −0.147643
\(735\) 2.89930 5.02174i 0.106942 0.185230i
\(736\) 0.477791 0.827558i 0.0176116 0.0305042i
\(737\) 7.77488 13.4665i 0.286392 0.496045i
\(738\) 14.5237 + 25.1558i 0.534626 + 0.925999i
\(739\) −36.4927 −1.34240 −0.671202 0.741274i \(-0.734222\pi\)
−0.671202 + 0.741274i \(0.734222\pi\)
\(740\) 20.8811 11.9543i 0.767605 0.439448i
\(741\) −17.6860 −0.649713
\(742\) 10.6704 + 18.4816i 0.391721 + 0.678481i
\(743\) −10.0775 + 17.4547i −0.369708 + 0.640352i −0.989520 0.144398i \(-0.953876\pi\)
0.619812 + 0.784750i \(0.287209\pi\)
\(744\) −9.48965 + 16.4366i −0.347908 + 0.602594i
\(745\) −5.05279 + 8.75169i −0.185120 + 0.320637i
\(746\) −32.3644 −1.18495
\(747\) 5.77738 10.0067i 0.211383 0.366127i
\(748\) −14.6941 −0.537269
\(749\) −10.2789 17.8036i −0.375583 0.650528i
\(750\) 56.6002 2.06675
\(751\) 51.4720 1.87824 0.939120 0.343590i \(-0.111643\pi\)
0.939120 + 0.343590i \(0.111643\pi\)
\(752\) 5.74483 + 9.95033i 0.209492 + 0.362851i
\(753\) 7.34704 12.7254i 0.267741 0.463741i
\(754\) 3.06814 0.111735
\(755\) 13.5810 + 23.5230i 0.494263 + 0.856088i
\(756\) 1.35337 + 2.34411i 0.0492216 + 0.0852544i
\(757\) −1.38994 2.40745i −0.0505183 0.0875002i 0.839660 0.543112i \(-0.182754\pi\)
−0.890179 + 0.455611i \(0.849421\pi\)
\(758\) −15.4571 + 26.7725i −0.561427 + 0.972420i
\(759\) 2.93186 5.07813i 0.106420 0.184324i
\(760\) 6.90180 + 11.9543i 0.250355 + 0.433627i
\(761\) 22.5712 + 39.0944i 0.818204 + 1.41717i 0.907004 + 0.421122i \(0.138363\pi\)
−0.0888000 + 0.996049i \(0.528303\pi\)
\(762\) 0.925525 + 1.60306i 0.0335282 + 0.0580726i
\(763\) −29.0030 −1.04998
\(764\) 10.5015 18.1892i 0.379931 0.658061i
\(765\) 41.0633 + 71.1238i 1.48465 + 2.57148i
\(766\) 31.1994 1.12728
\(767\) 8.45023 0.305120
\(768\) −1.26704 2.19457i −0.0457202 0.0791897i
\(769\) −27.2231 −0.981692 −0.490846 0.871246i \(-0.663312\pi\)
−0.490846 + 0.871246i \(0.663312\pi\)
\(770\) 12.1363 21.0207i 0.437361 0.757532i
\(771\) 75.2469 2.70995
\(772\) 1.45558 2.52114i 0.0523875 0.0907379i
\(773\) 18.7701 32.5107i 0.675112 1.16933i −0.301324 0.953522i \(-0.597429\pi\)
0.976436 0.215807i \(-0.0692381\pi\)
\(774\) −7.03558 + 12.1860i −0.252889 + 0.438016i
\(775\) −39.8698 69.0565i −1.43216 2.48058i
\(776\) 10.4897