Properties

Label 462.2.i.f.67.3
Level $462$
Weight $2$
Character 462.67
Analytic conductor $3.689$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.1156923.1
Defining polynomial: \(x^{6} - 3 x^{5} + 12 x^{4} - 19 x^{3} + 27 x^{2} - 18 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.3
Root \(0.500000 - 2.43956i\) of defining polynomial
Character \(\chi\) \(=\) 462.67
Dual form 462.2.i.f.331.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.60074 + 2.77256i) q^{5} +1.00000 q^{6} +(1.60074 + 2.10657i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.60074 + 2.77256i) q^{5} +1.00000 q^{6} +(1.60074 + 2.10657i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.60074 - 2.77256i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.500000 - 0.866025i) q^{12} -6.40294 q^{13} +(1.02398 - 2.43956i) q^{14} -3.20147 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-0.576760 - 0.998977i) q^{19} -3.20147 q^{20} +(-2.62471 + 0.332992i) q^{21} +1.00000 q^{22} +(-0.976024 - 1.69052i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-2.62471 + 4.54614i) q^{25} +(3.20147 + 5.54511i) q^{26} +1.00000 q^{27} +(-2.62471 + 0.332992i) q^{28} +7.24943 q^{29} +(1.60074 + 2.77256i) q^{30} +(-5.24943 + 9.09227i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.500000 - 0.866025i) q^{33} +1.00000 q^{34} +(-3.27823 + 7.81020i) q^{35} +1.00000 q^{36} +(-2.57676 - 4.46308i) q^{37} +(-0.576760 + 0.998977i) q^{38} +(3.20147 - 5.54511i) q^{39} +(1.60074 + 2.77256i) q^{40} +8.24943 q^{41} +(1.60074 + 2.10657i) q^{42} +5.15352 q^{43} +(-0.500000 - 0.866025i) q^{44} +(1.60074 - 2.77256i) q^{45} +(-0.976024 + 1.69052i) q^{46} +(3.02398 + 5.23768i) q^{47} +1.00000 q^{48} +(-1.87529 + 6.74413i) q^{49} +5.24943 q^{50} +(-0.500000 - 0.866025i) q^{51} +(3.20147 - 5.54511i) q^{52} +(3.20147 - 5.54511i) q^{53} +(-0.500000 - 0.866025i) q^{54} -3.20147 q^{55} +(1.60074 + 2.10657i) q^{56} +1.15352 q^{57} +(-3.62471 - 6.27819i) q^{58} +(-5.77823 + 10.0082i) q^{59} +(1.60074 - 2.77256i) q^{60} +(-4.85016 - 8.40073i) q^{61} +10.4989 q^{62} +(1.02398 - 2.43956i) q^{63} +1.00000 q^{64} +(-10.2494 - 17.7525i) q^{65} +(-0.500000 + 0.866025i) q^{66} +(-3.12471 + 5.41216i) q^{67} +(-0.500000 - 0.866025i) q^{68} +1.95205 q^{69} +(8.40294 - 1.06607i) q^{70} +5.24943 q^{71} +(-0.500000 - 0.866025i) q^{72} +(1.04795 - 1.81511i) q^{73} +(-2.57676 + 4.46308i) q^{74} +(-2.62471 - 4.54614i) q^{75} +1.15352 q^{76} +(-2.62471 + 0.332992i) q^{77} -6.40294 q^{78} +(2.80221 + 4.85357i) q^{79} +(1.60074 - 2.77256i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.12471 - 7.14421i) q^{82} +6.55646 q^{83} +(1.02398 - 2.43956i) q^{84} -3.20147 q^{85} +(-2.57676 - 4.46308i) q^{86} +(-3.62471 + 6.27819i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(9.20147 + 15.9374i) q^{89} -3.20147 q^{90} +(-10.2494 - 13.4883i) q^{91} +1.95205 q^{92} +(-5.24943 - 9.09227i) q^{93} +(3.02398 - 5.23768i) q^{94} +(1.84648 - 3.19820i) q^{95} +(-0.500000 - 0.866025i) q^{96} -5.49885 q^{97} +(6.77823 - 1.74802i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 3q^{2} - 3q^{3} - 3q^{4} + 6q^{6} + 6q^{8} - 3q^{9} + O(q^{10}) \) \( 6q - 3q^{2} - 3q^{3} - 3q^{4} + 6q^{6} + 6q^{8} - 3q^{9} - 3q^{11} - 3q^{12} + 3q^{14} - 3q^{16} - 3q^{17} - 3q^{18} + 3q^{19} - 3q^{21} + 6q^{22} - 9q^{23} - 3q^{24} - 3q^{25} + 6q^{27} - 3q^{28} + 18q^{29} - 6q^{31} - 3q^{32} - 3q^{33} + 6q^{34} + 6q^{35} + 6q^{36} - 9q^{37} + 3q^{38} + 24q^{41} + 18q^{43} - 3q^{44} - 9q^{46} + 15q^{47} + 6q^{48} - 24q^{49} + 6q^{50} - 3q^{51} - 3q^{54} - 6q^{57} - 9q^{58} - 9q^{59} + 6q^{61} + 12q^{62} + 3q^{63} + 6q^{64} - 36q^{65} - 3q^{66} - 6q^{67} - 3q^{68} + 18q^{69} + 12q^{70} + 6q^{71} - 3q^{72} - 9q^{74} - 3q^{75} - 6q^{76} - 3q^{77} - 12q^{79} - 3q^{81} - 12q^{82} - 12q^{83} + 3q^{84} - 9q^{86} - 9q^{87} - 3q^{88} + 36q^{89} - 36q^{91} + 18q^{92} - 6q^{93} + 15q^{94} + 24q^{95} - 3q^{96} + 18q^{97} + 15q^{98} + 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 1.60074 + 2.77256i 0.715871 + 1.23992i 0.962623 + 0.270846i \(0.0873035\pi\)
−0.246752 + 0.969079i \(0.579363\pi\)
\(6\) 1.00000 0.408248
\(7\) 1.60074 + 2.10657i 0.605021 + 0.796209i
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 1.60074 2.77256i 0.506197 0.876759i
\(11\) −0.500000 + 0.866025i −0.150756 + 0.261116i
\(12\) −0.500000 0.866025i −0.144338 0.250000i
\(13\) −6.40294 −1.77586 −0.887929 0.459981i \(-0.847856\pi\)
−0.887929 + 0.459981i \(0.847856\pi\)
\(14\) 1.02398 2.43956i 0.273669 0.652001i
\(15\) −3.20147 −0.826617
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −0.500000 + 0.866025i −0.121268 + 0.210042i −0.920268 0.391289i \(-0.872029\pi\)
0.799000 + 0.601331i \(0.205363\pi\)
\(18\) −0.500000 + 0.866025i −0.117851 + 0.204124i
\(19\) −0.576760 0.998977i −0.132318 0.229181i 0.792252 0.610194i \(-0.208909\pi\)
−0.924570 + 0.381013i \(0.875575\pi\)
\(20\) −3.20147 −0.715871
\(21\) −2.62471 + 0.332992i −0.572759 + 0.0726649i
\(22\) 1.00000 0.213201
\(23\) −0.976024 1.69052i −0.203515 0.352498i 0.746144 0.665785i \(-0.231903\pi\)
−0.949659 + 0.313287i \(0.898570\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) −2.62471 + 4.54614i −0.524943 + 0.909227i
\(26\) 3.20147 + 5.54511i 0.627860 + 1.08749i
\(27\) 1.00000 0.192450
\(28\) −2.62471 + 0.332992i −0.496024 + 0.0629297i
\(29\) 7.24943 1.34618 0.673092 0.739559i \(-0.264966\pi\)
0.673092 + 0.739559i \(0.264966\pi\)
\(30\) 1.60074 + 2.77256i 0.292253 + 0.506197i
\(31\) −5.24943 + 9.09227i −0.942825 + 1.63302i −0.182775 + 0.983155i \(0.558508\pi\)
−0.760049 + 0.649865i \(0.774825\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −0.500000 0.866025i −0.0870388 0.150756i
\(34\) 1.00000 0.171499
\(35\) −3.27823 + 7.81020i −0.554122 + 1.32016i
\(36\) 1.00000 0.166667
\(37\) −2.57676 4.46308i −0.423617 0.733726i 0.572673 0.819784i \(-0.305906\pi\)
−0.996290 + 0.0860579i \(0.972573\pi\)
\(38\) −0.576760 + 0.998977i −0.0935628 + 0.162056i
\(39\) 3.20147 5.54511i 0.512646 0.887929i
\(40\) 1.60074 + 2.77256i 0.253099 + 0.438380i
\(41\) 8.24943 1.28834 0.644172 0.764881i \(-0.277202\pi\)
0.644172 + 0.764881i \(0.277202\pi\)
\(42\) 1.60074 + 2.10657i 0.246999 + 0.325051i
\(43\) 5.15352 0.785904 0.392952 0.919559i \(-0.371454\pi\)
0.392952 + 0.919559i \(0.371454\pi\)
\(44\) −0.500000 0.866025i −0.0753778 0.130558i
\(45\) 1.60074 2.77256i 0.238624 0.413308i
\(46\) −0.976024 + 1.69052i −0.143907 + 0.249254i
\(47\) 3.02398 + 5.23768i 0.441092 + 0.763994i 0.997771 0.0667337i \(-0.0212578\pi\)
−0.556679 + 0.830728i \(0.687924\pi\)
\(48\) 1.00000 0.144338
\(49\) −1.87529 + 6.74413i −0.267898 + 0.963447i
\(50\) 5.24943 0.742381
\(51\) −0.500000 0.866025i −0.0700140 0.121268i
\(52\) 3.20147 5.54511i 0.443964 0.768969i
\(53\) 3.20147 5.54511i 0.439756 0.761680i −0.557914 0.829899i \(-0.688398\pi\)
0.997670 + 0.0682187i \(0.0217316\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) −3.20147 −0.431686
\(56\) 1.60074 + 2.10657i 0.213907 + 0.281502i
\(57\) 1.15352 0.152787
\(58\) −3.62471 6.27819i −0.475948 0.824366i
\(59\) −5.77823 + 10.0082i −0.752262 + 1.30296i 0.194462 + 0.980910i \(0.437704\pi\)
−0.946724 + 0.322046i \(0.895630\pi\)
\(60\) 1.60074 2.77256i 0.206654 0.357935i
\(61\) −4.85016 8.40073i −0.621000 1.07560i −0.989300 0.145896i \(-0.953394\pi\)
0.368300 0.929707i \(-0.379940\pi\)
\(62\) 10.4989 1.33336
\(63\) 1.02398 2.43956i 0.129009 0.307356i
\(64\) 1.00000 0.125000
\(65\) −10.2494 17.7525i −1.27128 2.20193i
\(66\) −0.500000 + 0.866025i −0.0615457 + 0.106600i
\(67\) −3.12471 + 5.41216i −0.381744 + 0.661201i −0.991312 0.131534i \(-0.958010\pi\)
0.609567 + 0.792734i \(0.291343\pi\)
\(68\) −0.500000 0.866025i −0.0606339 0.105021i
\(69\) 1.95205 0.234999
\(70\) 8.40294 1.06607i 1.00434 0.127419i
\(71\) 5.24943 0.622992 0.311496 0.950247i \(-0.399170\pi\)
0.311496 + 0.950247i \(0.399170\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) 1.04795 1.81511i 0.122654 0.212442i −0.798160 0.602446i \(-0.794193\pi\)
0.920813 + 0.390004i \(0.127526\pi\)
\(74\) −2.57676 + 4.46308i −0.299542 + 0.518822i
\(75\) −2.62471 4.54614i −0.303076 0.524943i
\(76\) 1.15352 0.132318
\(77\) −2.62471 + 0.332992i −0.299114 + 0.0379480i
\(78\) −6.40294 −0.724991
\(79\) 2.80221 + 4.85357i 0.315273 + 0.546069i 0.979496 0.201466i \(-0.0645706\pi\)
−0.664222 + 0.747535i \(0.731237\pi\)
\(80\) 1.60074 2.77256i 0.178968 0.309981i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −4.12471 7.14421i −0.455498 0.788946i
\(83\) 6.55646 0.719665 0.359833 0.933017i \(-0.382834\pi\)
0.359833 + 0.933017i \(0.382834\pi\)
\(84\) 1.02398 2.43956i 0.111725 0.266178i
\(85\) −3.20147 −0.347248
\(86\) −2.57676 4.46308i −0.277859 0.481266i
\(87\) −3.62471 + 6.27819i −0.388610 + 0.673092i
\(88\) −0.500000 + 0.866025i −0.0533002 + 0.0923186i
\(89\) 9.20147 + 15.9374i 0.975354 + 1.68936i 0.678761 + 0.734359i \(0.262517\pi\)
0.296593 + 0.955004i \(0.404150\pi\)
\(90\) −3.20147 −0.337465
\(91\) −10.2494 13.4883i −1.07443 1.41395i
\(92\) 1.95205 0.203515
\(93\) −5.24943 9.09227i −0.544340 0.942825i
\(94\) 3.02398 5.23768i 0.311899 0.540226i
\(95\) 1.84648 3.19820i 0.189445 0.328128i
\(96\) −0.500000 0.866025i −0.0510310 0.0883883i
\(97\) −5.49885 −0.558324 −0.279162 0.960244i \(-0.590057\pi\)
−0.279162 + 0.960244i \(0.590057\pi\)
\(98\) 6.77823 1.74802i 0.684705 0.176577i
\(99\) 1.00000 0.100504
\(100\) −2.62471 4.54614i −0.262471 0.454614i
\(101\) 9.97970 17.2854i 0.993018 1.71996i 0.394348 0.918961i \(-0.370971\pi\)
0.598670 0.800996i \(-0.295696\pi\)
\(102\) −0.500000 + 0.866025i −0.0495074 + 0.0857493i
\(103\) −0.153520 0.265904i −0.0151267 0.0262003i 0.858363 0.513043i \(-0.171482\pi\)
−0.873490 + 0.486843i \(0.838149\pi\)
\(104\) −6.40294 −0.627860
\(105\) −5.12471 6.74413i −0.500121 0.658160i
\(106\) −6.40294 −0.621909
\(107\) 4.52766 + 7.84213i 0.437705 + 0.758128i 0.997512 0.0704955i \(-0.0224580\pi\)
−0.559807 + 0.828623i \(0.689125\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) 4.85016 8.40073i 0.464561 0.804644i −0.534620 0.845092i \(-0.679545\pi\)
0.999182 + 0.0404487i \(0.0128787\pi\)
\(110\) 1.60074 + 2.77256i 0.152624 + 0.264353i
\(111\) 5.15352 0.489150
\(112\) 1.02398 2.43956i 0.0967567 0.230517i
\(113\) −12.4989 −1.17579 −0.587896 0.808936i \(-0.700044\pi\)
−0.587896 + 0.808936i \(0.700044\pi\)
\(114\) −0.576760 0.998977i −0.0540185 0.0935628i
\(115\) 3.12471 5.41216i 0.291381 0.504687i
\(116\) −3.62471 + 6.27819i −0.336546 + 0.582915i
\(117\) 3.20147 + 5.54511i 0.295976 + 0.512646i
\(118\) 11.5565 1.06386
\(119\) −2.62471 + 0.332992i −0.240607 + 0.0305254i
\(120\) −3.20147 −0.292253
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) −4.85016 + 8.40073i −0.439113 + 0.760566i
\(123\) −4.12471 + 7.14421i −0.371913 + 0.644172i
\(124\) −5.24943 9.09227i −0.471412 0.816510i
\(125\) −0.798528 −0.0714225
\(126\) −2.62471 + 0.332992i −0.233828 + 0.0296653i
\(127\) 8.35499 0.741386 0.370693 0.928756i \(-0.379120\pi\)
0.370693 + 0.928756i \(0.379120\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) −2.57676 + 4.46308i −0.226871 + 0.392952i
\(130\) −10.2494 + 17.7525i −0.898934 + 1.55700i
\(131\) −7.65237 13.2543i −0.668591 1.15803i −0.978298 0.207201i \(-0.933565\pi\)
0.309708 0.950832i \(-0.399769\pi\)
\(132\) 1.00000 0.0870388
\(133\) 1.18118 2.81408i 0.102421 0.244012i
\(134\) 6.24943 0.539868
\(135\) 1.60074 + 2.77256i 0.137769 + 0.238624i
\(136\) −0.500000 + 0.866025i −0.0428746 + 0.0742611i
\(137\) 3.20147 5.54511i 0.273520 0.473751i −0.696240 0.717809i \(-0.745145\pi\)
0.969761 + 0.244058i \(0.0784786\pi\)
\(138\) −0.976024 1.69052i −0.0830846 0.143907i
\(139\) 21.7483 1.84466 0.922332 0.386398i \(-0.126281\pi\)
0.922332 + 0.386398i \(0.126281\pi\)
\(140\) −5.12471 6.74413i −0.433117 0.569983i
\(141\) −6.04795 −0.509330
\(142\) −2.62471 4.54614i −0.220261 0.381503i
\(143\) 3.20147 5.54511i 0.267721 0.463706i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) 11.6044 + 20.0994i 0.963694 + 1.66917i
\(146\) −2.09591 −0.173458
\(147\) −4.90294 4.99611i −0.404388 0.412072i
\(148\) 5.15352 0.423617
\(149\) −3.42324 5.92923i −0.280443 0.485741i 0.691051 0.722806i \(-0.257148\pi\)
−0.971494 + 0.237065i \(0.923815\pi\)
\(150\) −2.62471 + 4.54614i −0.214307 + 0.371190i
\(151\) −7.42692 + 12.8638i −0.604394 + 1.04684i 0.387753 + 0.921763i \(0.373251\pi\)
−0.992147 + 0.125078i \(0.960082\pi\)
\(152\) −0.576760 0.998977i −0.0467814 0.0810278i
\(153\) 1.00000 0.0808452
\(154\) 1.60074 + 2.10657i 0.128991 + 0.169752i
\(155\) −33.6118 −2.69976
\(156\) 3.20147 + 5.54511i 0.256323 + 0.443964i
\(157\) 4.73028 8.19308i 0.377517 0.653879i −0.613183 0.789941i \(-0.710111\pi\)
0.990700 + 0.136062i \(0.0434445\pi\)
\(158\) 2.80221 4.85357i 0.222932 0.386129i
\(159\) 3.20147 + 5.54511i 0.253893 + 0.439756i
\(160\) −3.20147 −0.253099
\(161\) 1.99885 4.76214i 0.157531 0.375310i
\(162\) 1.00000 0.0785674
\(163\) −6.52766 11.3062i −0.511286 0.885573i −0.999914 0.0130809i \(-0.995836\pi\)
0.488629 0.872492i \(-0.337497\pi\)
\(164\) −4.12471 + 7.14421i −0.322086 + 0.557869i
\(165\) 1.60074 2.77256i 0.124617 0.215843i
\(166\) −3.27823 5.67806i −0.254440 0.440703i
\(167\) −6.70998 −0.519234 −0.259617 0.965712i \(-0.583596\pi\)
−0.259617 + 0.965712i \(0.583596\pi\)
\(168\) −2.62471 + 0.332992i −0.202501 + 0.0256909i
\(169\) 27.9977 2.15367
\(170\) 1.60074 + 2.77256i 0.122771 + 0.212645i
\(171\) −0.576760 + 0.998977i −0.0441059 + 0.0763937i
\(172\) −2.57676 + 4.46308i −0.196476 + 0.340307i
\(173\) 2.75057 + 4.76414i 0.209122 + 0.362211i 0.951438 0.307839i \(-0.0996060\pi\)
−0.742316 + 0.670050i \(0.766273\pi\)
\(174\) 7.24943 0.549578
\(175\) −13.7782 + 1.74802i −1.04154 + 0.132138i
\(176\) 1.00000 0.0753778
\(177\) −5.77823 10.0082i −0.434319 0.752262i
\(178\) 9.20147 15.9374i 0.689680 1.19456i
\(179\) −0.826185 + 1.43099i −0.0617520 + 0.106958i −0.895249 0.445567i \(-0.853002\pi\)
0.833497 + 0.552525i \(0.186335\pi\)
\(180\) 1.60074 + 2.77256i 0.119312 + 0.206654i
\(181\) 24.9018 1.85094 0.925468 0.378826i \(-0.123672\pi\)
0.925468 + 0.378826i \(0.123672\pi\)
\(182\) −6.55646 + 15.6204i −0.485997 + 1.15786i
\(183\) 9.70032 0.717068
\(184\) −0.976024 1.69052i −0.0719534 0.124627i
\(185\) 8.24943 14.2884i 0.606510 1.05051i
\(186\) −5.24943 + 9.09227i −0.384907 + 0.666678i
\(187\) −0.500000 0.866025i −0.0365636 0.0633300i
\(188\) −6.04795 −0.441092
\(189\) 1.60074 + 2.10657i 0.116436 + 0.153231i
\(190\) −3.69296 −0.267916
\(191\) 2.40294 + 4.16202i 0.173871 + 0.301153i 0.939770 0.341808i \(-0.111039\pi\)
−0.765899 + 0.642961i \(0.777706\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −4.35499 + 7.54307i −0.313479 + 0.542962i −0.979113 0.203317i \(-0.934828\pi\)
0.665634 + 0.746278i \(0.268161\pi\)
\(194\) 2.74943 + 4.76214i 0.197397 + 0.341902i
\(195\) 20.4989 1.46795
\(196\) −4.90294 4.99611i −0.350210 0.356865i
\(197\) 0.654669 0.0466433 0.0233216 0.999728i \(-0.492576\pi\)
0.0233216 + 0.999728i \(0.492576\pi\)
\(198\) −0.500000 0.866025i −0.0355335 0.0615457i
\(199\) 3.84648 6.66230i 0.272670 0.472278i −0.696875 0.717193i \(-0.745427\pi\)
0.969545 + 0.244915i \(0.0787600\pi\)
\(200\) −2.62471 + 4.54614i −0.185595 + 0.321460i
\(201\) −3.12471 5.41216i −0.220400 0.381744i
\(202\) −19.9594 −1.40434
\(203\) 11.6044 + 15.2714i 0.814470 + 1.07184i
\(204\) 1.00000 0.0700140
\(205\) 13.2052 + 22.8720i 0.922288 + 1.59745i
\(206\) −0.153520 + 0.265904i −0.0106962 + 0.0185264i
\(207\) −0.976024 + 1.69052i −0.0678383 + 0.117499i
\(208\) 3.20147 + 5.54511i 0.221982 + 0.384484i
\(209\) 1.15352 0.0797906
\(210\) −3.27823 + 7.81020i −0.226220 + 0.538955i
\(211\) 14.5948 1.00474 0.502372 0.864651i \(-0.332461\pi\)
0.502372 + 0.864651i \(0.332461\pi\)
\(212\) 3.20147 + 5.54511i 0.219878 + 0.380840i
\(213\) −2.62471 + 4.54614i −0.179842 + 0.311496i
\(214\) 4.52766 7.84213i 0.309504 0.536077i
\(215\) 8.24943 + 14.2884i 0.562606 + 0.974462i
\(216\) 1.00000 0.0680414
\(217\) −27.5565 + 3.49604i −1.87065 + 0.237326i
\(218\) −9.70032 −0.656989
\(219\) 1.04795 + 1.81511i 0.0708141 + 0.122654i
\(220\) 1.60074 2.77256i 0.107922 0.186926i
\(221\) 3.20147 5.54511i 0.215354 0.373005i
\(222\) −2.57676 4.46308i −0.172941 0.299542i
\(223\) −14.9018 −0.997898 −0.498949 0.866631i \(-0.666281\pi\)
−0.498949 + 0.866631i \(0.666281\pi\)
\(224\) −2.62471 + 0.332992i −0.175371 + 0.0222490i
\(225\) 5.24943 0.349962
\(226\) 6.24943 + 10.8243i 0.415706 + 0.720023i
\(227\) 0.124713 0.216009i 0.00827746 0.0143370i −0.861857 0.507151i \(-0.830699\pi\)
0.870134 + 0.492814i \(0.164032\pi\)
\(228\) −0.576760 + 0.998977i −0.0381968 + 0.0661589i
\(229\) 2.04795 + 3.54716i 0.135333 + 0.234403i 0.925724 0.378199i \(-0.123456\pi\)
−0.790392 + 0.612602i \(0.790123\pi\)
\(230\) −6.24943 −0.412075
\(231\) 1.02398 2.43956i 0.0673727 0.160512i
\(232\) 7.24943 0.475948
\(233\) −5.65352 9.79218i −0.370374 0.641507i 0.619249 0.785195i \(-0.287437\pi\)
−0.989623 + 0.143688i \(0.954104\pi\)
\(234\) 3.20147 5.54511i 0.209287 0.362495i
\(235\) −9.68118 + 16.7683i −0.631530 + 1.09384i
\(236\) −5.77823 10.0082i −0.376131 0.651478i
\(237\) −5.60442 −0.364046
\(238\) 1.60074 + 2.10657i 0.103760 + 0.136549i
\(239\) 6.59476 0.426579 0.213290 0.976989i \(-0.431582\pi\)
0.213290 + 0.976989i \(0.431582\pi\)
\(240\) 1.60074 + 2.77256i 0.103327 + 0.178968i
\(241\) −8.55646 + 14.8202i −0.551170 + 0.954655i 0.447020 + 0.894524i \(0.352485\pi\)
−0.998190 + 0.0601311i \(0.980848\pi\)
\(242\) −0.500000 + 0.866025i −0.0321412 + 0.0556702i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 9.70032 0.621000
\(245\) −21.7003 + 5.59623i −1.38638 + 0.357530i
\(246\) 8.24943 0.525964
\(247\) 3.69296 + 6.39640i 0.234977 + 0.406993i
\(248\) −5.24943 + 9.09227i −0.333339 + 0.577360i
\(249\) −3.27823 + 5.67806i −0.207750 + 0.359833i
\(250\) 0.399264 + 0.691545i 0.0252517 + 0.0437372i
\(251\) 7.95941 0.502393 0.251197 0.967936i \(-0.419176\pi\)
0.251197 + 0.967936i \(0.419176\pi\)
\(252\) 1.60074 + 2.10657i 0.100837 + 0.132702i
\(253\) 1.95205 0.122724
\(254\) −4.17750 7.23564i −0.262119 0.454004i
\(255\) 1.60074 2.77256i 0.100242 0.173624i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 11.2015 + 19.4015i 0.698729 + 1.21023i 0.968907 + 0.247423i \(0.0795838\pi\)
−0.270179 + 0.962810i \(0.587083\pi\)
\(258\) 5.15352 0.320844
\(259\) 5.27708 12.5723i 0.327902 0.781207i
\(260\) 20.4989 1.27128
\(261\) −3.62471 6.27819i −0.224364 0.388610i
\(262\) −7.65237 + 13.2543i −0.472765 + 0.818853i
\(263\) 12.5085 21.6654i 0.771308 1.33594i −0.165539 0.986203i \(-0.552936\pi\)
0.936846 0.349741i \(-0.113730\pi\)
\(264\) −0.500000 0.866025i −0.0307729 0.0533002i
\(265\) 20.4989 1.25923
\(266\) −3.02766 + 0.384113i −0.185638 + 0.0235515i
\(267\) −18.4029 −1.12624
\(268\) −3.12471 5.41216i −0.190872 0.330600i
\(269\) −4.05163 + 7.01764i −0.247032 + 0.427873i −0.962701 0.270567i \(-0.912789\pi\)
0.715669 + 0.698440i \(0.246122\pi\)
\(270\) 1.60074 2.77256i 0.0974177 0.168732i
\(271\) 2.40294 + 4.16202i 0.145968 + 0.252825i 0.929734 0.368232i \(-0.120037\pi\)
−0.783765 + 0.621057i \(0.786704\pi\)
\(272\) 1.00000 0.0606339
\(273\) 16.8059 2.13213i 1.01714 0.129042i
\(274\) −6.40294 −0.386816
\(275\) −2.62471 4.54614i −0.158276 0.274142i
\(276\) −0.976024 + 1.69052i −0.0587497 + 0.101757i
\(277\) 5.60442 9.70714i 0.336737 0.583245i −0.647080 0.762422i \(-0.724010\pi\)
0.983817 + 0.179177i \(0.0573434\pi\)
\(278\) −10.8741 18.8346i −0.652187 1.12962i
\(279\) 10.4989 0.628550
\(280\) −3.27823 + 7.81020i −0.195912 + 0.466749i
\(281\) −17.4989 −1.04389 −0.521947 0.852978i \(-0.674794\pi\)
−0.521947 + 0.852978i \(0.674794\pi\)
\(282\) 3.02398 + 5.23768i 0.180075 + 0.311899i
\(283\) −13.7003 + 23.7297i −0.814400 + 1.41058i 0.0953585 + 0.995443i \(0.469600\pi\)
−0.909758 + 0.415139i \(0.863733\pi\)
\(284\) −2.62471 + 4.54614i −0.155748 + 0.269764i
\(285\) 1.84648 + 3.19820i 0.109376 + 0.189445i
\(286\) −6.40294 −0.378614
\(287\) 13.2052 + 17.3780i 0.779476 + 1.02579i
\(288\) 1.00000 0.0589256
\(289\) 8.00000 + 13.8564i 0.470588 + 0.815083i
\(290\) 11.6044 20.0994i 0.681435 1.18028i
\(291\) 2.74943 4.76214i 0.161174 0.279162i
\(292\) 1.04795 + 1.81511i 0.0613268 + 0.106221i
\(293\) −19.7483 −1.15371 −0.576853 0.816848i \(-0.695720\pi\)
−0.576853 + 0.816848i \(0.695720\pi\)
\(294\) −1.87529 + 6.74413i −0.109369 + 0.393326i
\(295\) −36.9977 −2.15409
\(296\) −2.57676 4.46308i −0.149771 0.259411i
\(297\) −0.500000 + 0.866025i −0.0290129 + 0.0502519i
\(298\) −3.42324 + 5.92923i −0.198303 + 0.343471i
\(299\) 6.24943 + 10.8243i 0.361414 + 0.625987i
\(300\) 5.24943 0.303076
\(301\) 8.24943 + 10.8563i 0.475489 + 0.625744i
\(302\) 14.8538 0.854743
\(303\) 9.97970 + 17.2854i 0.573319 + 0.993018i
\(304\) −0.576760 + 0.998977i −0.0330794 + 0.0572953i
\(305\) 15.5277 26.8947i 0.889111 1.53999i
\(306\) −0.500000 0.866025i −0.0285831 0.0495074i
\(307\) 4.30704 0.245816 0.122908 0.992418i \(-0.460778\pi\)
0.122908 + 0.992418i \(0.460778\pi\)
\(308\) 1.02398 2.43956i 0.0583465 0.139007i
\(309\) 0.307039 0.0174668
\(310\) 16.8059 + 29.1087i 0.954510 + 1.65326i
\(311\) 7.37897 12.7807i 0.418423 0.724730i −0.577358 0.816491i \(-0.695916\pi\)
0.995781 + 0.0917613i \(0.0292497\pi\)
\(312\) 3.20147 5.54511i 0.181248 0.313930i
\(313\) −10.3753 17.9705i −0.586446 1.01575i −0.994693 0.102883i \(-0.967193\pi\)
0.408248 0.912871i \(-0.366140\pi\)
\(314\) −9.46056 −0.533890
\(315\) 8.40294 1.06607i 0.473452 0.0600660i
\(316\) −5.60442 −0.315273
\(317\) −8.09959 14.0289i −0.454918 0.787941i 0.543765 0.839237i \(-0.316998\pi\)
−0.998683 + 0.0512960i \(0.983665\pi\)
\(318\) 3.20147 5.54511i 0.179530 0.310954i
\(319\) −3.62471 + 6.27819i −0.202945 + 0.351511i
\(320\) 1.60074 + 2.77256i 0.0894839 + 0.154991i
\(321\) −9.05531 −0.505418
\(322\) −5.12356 + 0.650017i −0.285525 + 0.0362240i
\(323\) 1.15352 0.0641835
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) 16.8059 29.1087i 0.932223 1.61466i
\(326\) −6.52766 + 11.3062i −0.361533 + 0.626194i
\(327\) 4.85016 + 8.40073i 0.268215 + 0.464561i
\(328\) 8.24943 0.455498
\(329\) −6.19296 + 14.7544i −0.341429 + 0.813435i
\(330\) −3.20147 −0.176235
\(331\) −10.6236 18.4006i −0.583924 1.01139i −0.995009 0.0997886i \(-0.968183\pi\)
0.411085 0.911597i \(-0.365150\pi\)
\(332\) −3.27823 + 5.67806i −0.179916 + 0.311624i
\(333\) −2.57676 + 4.46308i −0.141206 + 0.244575i
\(334\) 3.35499 + 5.81102i 0.183577 + 0.317965i
\(335\) −20.0074 −1.09312
\(336\) 1.60074 + 2.10657i 0.0873273 + 0.114923i
\(337\) −25.5159 −1.38994 −0.694969 0.719040i \(-0.744582\pi\)
−0.694969 + 0.719040i \(0.744582\pi\)
\(338\) −13.9989 24.2467i −0.761437 1.31885i
\(339\) 6.24943 10.8243i 0.339422 0.587896i
\(340\) 1.60074 2.77256i 0.0868121 0.150363i
\(341\) −5.24943 9.09227i −0.284272 0.492374i
\(342\) 1.15352 0.0623752
\(343\) −17.2088 + 6.84515i −0.929190 + 0.369603i
\(344\) 5.15352 0.277859
\(345\) 3.12471 + 5.41216i 0.168229 + 0.291381i
\(346\) 2.75057 4.76414i 0.147872 0.256122i
\(347\) −1.52766 + 2.64598i −0.0820089 + 0.142044i −0.904113 0.427294i \(-0.859467\pi\)
0.822104 + 0.569338i \(0.192800\pi\)
\(348\) −3.62471 6.27819i −0.194305 0.336546i
\(349\) −4.00736 −0.214509 −0.107255 0.994232i \(-0.534206\pi\)
−0.107255 + 0.994232i \(0.534206\pi\)
\(350\) 8.40294 + 11.0583i 0.449156 + 0.591090i
\(351\) −6.40294 −0.341764
\(352\) −0.500000 0.866025i −0.0266501 0.0461593i
\(353\) 0.549103 0.951073i 0.0292258 0.0506205i −0.851043 0.525097i \(-0.824029\pi\)
0.880268 + 0.474476i \(0.157362\pi\)
\(354\) −5.77823 + 10.0082i −0.307110 + 0.531929i
\(355\) 8.40294 + 14.5543i 0.445982 + 0.772463i
\(356\) −18.4029 −0.975354
\(357\) 1.02398 2.43956i 0.0541946 0.129115i
\(358\) 1.65237 0.0873305
\(359\) −7.80589 13.5202i −0.411979 0.713569i 0.583127 0.812381i \(-0.301829\pi\)
−0.995106 + 0.0988123i \(0.968496\pi\)
\(360\) 1.60074 2.77256i 0.0843662 0.146127i
\(361\) 8.83470 15.3021i 0.464984 0.805376i
\(362\) −12.4509 21.5656i −0.654405 1.13346i
\(363\) 1.00000 0.0524864
\(364\) 16.8059 2.13213i 0.880868 0.111754i
\(365\) 6.70998 0.351217
\(366\) −4.85016 8.40073i −0.253522 0.439113i
\(367\) −0.395583 + 0.685170i −0.0206493 + 0.0357656i −0.876165 0.482011i \(-0.839907\pi\)
0.855516 + 0.517776i \(0.173240\pi\)
\(368\) −0.976024 + 1.69052i −0.0508787 + 0.0881246i
\(369\) −4.12471 7.14421i −0.214724 0.371913i
\(370\) −16.4989 −0.857734
\(371\) 16.8059 2.13213i 0.872518 0.110695i
\(372\) 10.4989 0.544340
\(373\) −7.95573 13.7797i −0.411932 0.713487i 0.583169 0.812351i \(-0.301813\pi\)
−0.995101 + 0.0988637i \(0.968479\pi\)
\(374\) −0.500000 + 0.866025i −0.0258544 + 0.0447811i
\(375\) 0.399264 0.691545i 0.0206179 0.0357112i
\(376\) 3.02398 + 5.23768i 0.155950 + 0.270113i
\(377\) −46.4177 −2.39063
\(378\) 1.02398 2.43956i 0.0526677 0.125478i
\(379\) −17.0553 −0.876073 −0.438036 0.898957i \(-0.644326\pi\)
−0.438036 + 0.898957i \(0.644326\pi\)
\(380\) 1.84648 + 3.19820i 0.0947224 + 0.164064i
\(381\) −4.17750 + 7.23564i −0.214020 + 0.370693i
\(382\) 2.40294 4.16202i 0.122945 0.212948i
\(383\) −6.72062 11.6405i −0.343408 0.594799i 0.641656 0.766993i \(-0.278248\pi\)
−0.985063 + 0.172194i \(0.944915\pi\)
\(384\) 1.00000 0.0510310
\(385\) −5.12471 6.74413i −0.261180 0.343713i
\(386\) 8.70998 0.443327
\(387\) −2.57676 4.46308i −0.130984 0.226871i
\(388\) 2.74943 4.76214i 0.139581 0.241761i
\(389\) 3.60074 6.23666i 0.182565 0.316211i −0.760189 0.649702i \(-0.774893\pi\)
0.942753 + 0.333491i \(0.108227\pi\)
\(390\) −10.2494 17.7525i −0.519000 0.898934i
\(391\) 1.95205 0.0987193
\(392\) −1.87529 + 6.74413i −0.0947163 + 0.340630i
\(393\) 15.3047 0.772022
\(394\) −0.327335 0.566960i −0.0164909 0.0285630i
\(395\) −8.97119 + 15.5386i −0.451390 + 0.781830i
\(396\) −0.500000 + 0.866025i −0.0251259 + 0.0435194i
\(397\) −6.47119 11.2084i −0.324780 0.562535i 0.656688 0.754162i \(-0.271957\pi\)
−0.981468 + 0.191627i \(0.938624\pi\)
\(398\) −7.69296 −0.385613
\(399\) 1.84648 + 2.42997i 0.0924396 + 0.121651i
\(400\) 5.24943 0.262471
\(401\) 8.45090 + 14.6374i 0.422018 + 0.730956i 0.996137 0.0878158i \(-0.0279887\pi\)
−0.574119 + 0.818772i \(0.694655\pi\)
\(402\) −3.12471 + 5.41216i −0.155846 + 0.269934i
\(403\) 33.6118 58.2173i 1.67432 2.90001i
\(404\) 9.97970 + 17.2854i 0.496509 + 0.859979i
\(405\) −3.20147 −0.159082
\(406\) 7.42324 17.6854i 0.368409 0.877713i
\(407\) 5.15352 0.255450
\(408\) −0.500000 0.866025i −0.0247537 0.0428746i
\(409\) 18.5468 32.1240i 0.917080 1.58843i 0.113254 0.993566i \(-0.463873\pi\)
0.803827 0.594864i \(-0.202794\pi\)
\(410\) 13.2052 22.8720i 0.652156 1.12957i
\(411\) 3.20147 + 5.54511i 0.157917 + 0.273520i
\(412\) 0.307039 0.0151267
\(413\) −30.3324 + 3.84821i −1.49256 + 0.189358i
\(414\) 1.95205 0.0959379
\(415\) 10.4952 + 18.1782i 0.515188 + 0.892331i
\(416\) 3.20147 5.54511i 0.156965 0.271872i
\(417\) −10.8741 + 18.8346i −0.532509 + 0.922332i
\(418\) −0.576760 0.998977i −0.0282102 0.0488616i
\(419\) 22.4583 1.09716 0.548579 0.836099i \(-0.315169\pi\)
0.548579 + 0.836099i \(0.315169\pi\)
\(420\) 8.40294 1.06607i 0.410022 0.0520187i
\(421\) −23.3453 −1.13778 −0.568891 0.822413i \(-0.692627\pi\)
−0.568891 + 0.822413i \(0.692627\pi\)
\(422\) −7.29738 12.6394i −0.355231 0.615278i
\(423\) 3.02398 5.23768i 0.147031 0.254665i
\(424\) 3.20147 5.54511i 0.155477 0.269294i
\(425\) −2.62471 4.54614i −0.127317 0.220520i
\(426\) 5.24943 0.254335
\(427\) 9.93290 23.6646i 0.480687 1.14521i
\(428\) −9.05531 −0.437705
\(429\) 3.20147 + 5.54511i 0.154569 + 0.267721i
\(430\) 8.24943 14.2884i 0.397823 0.689049i
\(431\) −15.9115 + 27.5595i −0.766428 + 1.32749i 0.173060 + 0.984911i \(0.444634\pi\)
−0.939488 + 0.342581i \(0.888699\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) 30.3047 1.45635 0.728176 0.685390i \(-0.240368\pi\)
0.728176 + 0.685390i \(0.240368\pi\)
\(434\) 16.8059 + 22.1166i 0.806709 + 1.06163i
\(435\) −23.2088 −1.11278
\(436\) 4.85016 + 8.40073i 0.232281 + 0.402322i
\(437\) −1.12586 + 1.95005i −0.0538573 + 0.0932836i
\(438\) 1.04795 1.81511i 0.0500731 0.0867292i
\(439\) 5.33102 + 9.23359i 0.254435 + 0.440695i 0.964742 0.263197i \(-0.0847770\pi\)
−0.710307 + 0.703892i \(0.751444\pi\)
\(440\) −3.20147 −0.152624
\(441\) 6.77823 1.74802i 0.322773 0.0832390i
\(442\) −6.40294 −0.304557
\(443\) 18.0277 + 31.2248i 0.856520 + 1.48354i 0.875228 + 0.483711i \(0.160711\pi\)
−0.0187080 + 0.999825i \(0.505955\pi\)
\(444\) −2.57676 + 4.46308i −0.122288 + 0.211808i
\(445\) −29.4583 + 51.0232i −1.39646 + 2.41873i
\(446\) 7.45090 + 12.9053i 0.352810 + 0.611085i
\(447\) 6.84648 0.323827
\(448\) 1.60074 + 2.10657i 0.0756277 + 0.0995262i
\(449\) 23.4006 1.10434 0.552172 0.833730i \(-0.313799\pi\)
0.552172 + 0.833730i \(0.313799\pi\)
\(450\) −2.62471 4.54614i −0.123730 0.214307i
\(451\) −4.12471 + 7.14421i −0.194225 + 0.336408i
\(452\) 6.24943 10.8243i 0.293948 0.509133i
\(453\) −7.42692 12.8638i −0.348947 0.604394i
\(454\) −0.249425 −0.0117061
\(455\) 20.9903 50.0083i 0.984042 2.34442i
\(456\) 1.15352 0.0540185
\(457\) 9.30704 + 16.1203i 0.435365 + 0.754074i 0.997325 0.0730899i \(-0.0232860\pi\)
−0.561960 + 0.827164i \(0.689953\pi\)
\(458\) 2.04795 3.54716i 0.0956945 0.165748i
\(459\) −0.500000 + 0.866025i −0.0233380 + 0.0404226i
\(460\) 3.12471 + 5.41216i 0.145690 + 0.252343i
\(461\) −31.4412 −1.46436 −0.732182 0.681109i \(-0.761498\pi\)
−0.732182 + 0.681109i \(0.761498\pi\)
\(462\) −2.62471 + 0.332992i −0.122113 + 0.0154922i
\(463\) −22.0959 −1.02688 −0.513442 0.858124i \(-0.671630\pi\)
−0.513442 + 0.858124i \(0.671630\pi\)
\(464\) −3.62471 6.27819i −0.168273 0.291457i
\(465\) 16.8059 29.1087i 0.779354 1.34988i
\(466\) −5.65352 + 9.79218i −0.261894 + 0.453614i
\(467\) −10.5288 18.2364i −0.487215 0.843881i 0.512677 0.858582i \(-0.328654\pi\)
−0.999892 + 0.0147004i \(0.995321\pi\)
\(468\) −6.40294 −0.295976
\(469\) −16.4029 + 2.08101i −0.757418 + 0.0960922i
\(470\) 19.3624 0.893119
\(471\) 4.73028 + 8.19308i 0.217960 + 0.377517i
\(472\) −5.77823 + 10.0082i −0.265965 + 0.460664i
\(473\) −2.57676 + 4.46308i −0.118480 + 0.205213i
\(474\) 2.80221 + 4.85357i 0.128710 + 0.222932i
\(475\) 6.05531 0.277837
\(476\) 1.02398 2.43956i 0.0469339 0.111817i
\(477\) −6.40294 −0.293171
\(478\) −3.29738 5.71123i −0.150819 0.261225i
\(479\) 10.6044 18.3674i 0.484528 0.839227i −0.515314 0.857002i \(-0.672325\pi\)
0.999842 + 0.0177741i \(0.00565797\pi\)
\(480\) 1.60074 2.77256i 0.0730633 0.126549i
\(481\) 16.4989 + 28.5768i 0.752283 + 1.30299i
\(482\) 17.1129 0.779473
\(483\) 3.12471 + 4.11213i 0.142179 + 0.187108i
\(484\) 1.00000 0.0454545
\(485\) −8.80221 15.2459i −0.399688 0.692279i
\(486\) −0.500000 + 0.866025i −0.0226805 + 0.0392837i
\(487\) 19.3550 33.5238i 0.877058 1.51911i 0.0225047 0.999747i \(-0.492836\pi\)
0.854554 0.519363i \(-0.173831\pi\)
\(488\) −4.85016 8.40073i −0.219556 0.380283i
\(489\) 13.0553 0.590382
\(490\) 15.6966 + 15.9949i 0.709102 + 0.722577i
\(491\) 19.1705 0.865154 0.432577 0.901597i \(-0.357604\pi\)
0.432577 + 0.901597i \(0.357604\pi\)
\(492\) −4.12471 7.14421i −0.185956 0.322086i
\(493\) −3.62471 + 6.27819i −0.163249 + 0.282755i
\(494\) 3.69296 6.39640i 0.166154 0.287787i
\(495\) 1.60074 + 2.77256i 0.0719477 + 0.124617i
\(496\) 10.4989 0.471412
\(497\) 8.40294 + 11.0583i 0.376924 + 0.496032i
\(498\) 6.55646 0.293802
\(499\) 13.9594 + 24.1784i 0.624909 + 1.08237i 0.988558 + 0.150838i \(0.0481973\pi\)
−0.363649 + 0.931536i \(0.618469\pi\)
\(500\) 0.399264 0.691545i 0.0178556 0.0309268i
\(501\) 3.35499 5.81102i 0.149890 0.259617i
\(502\) −3.97970 6.89305i −0.177623 0.307652i
\(503\) −8.70998 −0.388359 −0.194179 0.980966i \(-0.562204\pi\)
−0.194179 + 0.980966i \(0.562204\pi\)
\(504\) 1.02398 2.43956i 0.0456115 0.108667i
\(505\) 63.8995 2.84349
\(506\) −0.976024 1.69052i −0.0433895 0.0751529i
\(507\) −13.9989 + 24.2467i −0.621711 + 1.07683i
\(508\) −4.17750 + 7.23564i −0.185346 + 0.321029i
\(509\) 0.894433 + 1.54920i 0.0396451 + 0.0686673i 0.885167 0.465273i \(-0.154044\pi\)
−0.845522 + 0.533941i \(0.820711\pi\)
\(510\) −3.20147 −0.141764
\(511\) 5.50115 0.697921i 0.243357 0.0308742i
\(512\) 1.00000 0.0441942
\(513\) −0.576760 0.998977i −0.0254646 0.0441059i
\(514\) 11.2015 19.4015i 0.494076 0.855764i
\(515\) 0.491489 0.851283i 0.0216576 0.0375120i
\(516\) −2.57676 4.46308i −0.113436 0.196476i
\(517\) −6.04795 −0.265989
\(518\) −13.5265 + 1.71608i −0.594321 + 0.0754004i
\(519\) −5.50115 −0.241474
\(520\) −10.2494 17.7525i −0.449467 0.778500i
\(521\) −11.8059 + 20.4484i −0.517225 + 0.895861i 0.482574 + 0.875855i \(0.339702\pi\)
−0.999800 + 0.0200057i \(0.993632\pi\)
\(522\) −3.62471 + 6.27819i −0.158649 + 0.274789i
\(523\) −21.7003 37.5861i −0.948889 1.64352i −0.747771 0.663957i \(-0.768876\pi\)
−0.201118 0.979567i \(-0.564457\pi\)
\(524\) 15.3047 0.668591
\(525\) 5.37529 12.8063i 0.234597 0.558913i
\(526\) −25.0170 −1.09079
\(527\) −5.24943 9.09227i −0.228669 0.396066i
\(528\) −0.500000 + 0.866025i −0.0217597 + 0.0376889i
\(529\) 9.59476 16.6186i 0.417163 0.722548i
\(530\) −10.2494 17.7525i −0.445207 0.771120i
\(531\) 11.5565 0.501508
\(532\) 1.84648 + 2.42997i 0.0800551 + 0.105353i
\(533\) −52.8206 −2.28791
\(534\) 9.20147 + 15.9374i 0.398187 + 0.689680i
\(535\) −14.4952 + 25.1064i −0.626681 + 1.08544i
\(536\) −3.12471 + 5.41216i −0.134967 + 0.233770i
\(537\) −0.826185 1.43099i −0.0356525 0.0617520i
\(538\) 8.10327 0.349357
\(539\) −4.90294 4.99611i −0.211185 0.215198i
\(540\) −3.20147 −0.137769
\(541\) −8.49517 14.7141i −0.365236 0.632607i 0.623578 0.781761i \(-0.285678\pi\)
−0.988814 + 0.149154i \(0.952345\pi\)
\(542\) 2.40294 4.16202i 0.103215 0.178774i
\(543\) −12.4509 + 21.5656i −0.534319 + 0.925468i
\(544\) −0.500000 0.866025i −0.0214373 0.0371305i
\(545\) 31.0553 1.33026
\(546\) −10.2494 13.4883i −0.438635 0.577244i
\(547\) −1.34533 −0.0575222 −0.0287611 0.999586i \(-0.509156\pi\)
−0.0287611 + 0.999586i \(0.509156\pi\)
\(548\) 3.20147 + 5.54511i 0.136760 + 0.236875i
\(549\) −4.85016 + 8.40073i −0.207000 + 0.358534i
\(550\) −2.62471 + 4.54614i −0.111918 + 0.193848i
\(551\) −4.18118 7.24201i −0.178124 0.308520i
\(552\) 1.95205 0.0830846
\(553\) −5.73879 + 13.6723i −0.244038 + 0.581407i
\(554\) −11.2088 −0.476218
\(555\) 8.24943 + 14.2884i 0.350169 + 0.606510i
\(556\) −10.8741 + 18.8346i −0.461166 + 0.798763i
\(557\) 8.32733 14.4234i 0.352840 0.611138i −0.633905 0.773411i \(-0.718549\pi\)
0.986746 + 0.162273i \(0.0518825\pi\)
\(558\) −5.24943 9.09227i −0.222226 0.384907i
\(559\) −32.9977 −1.39565
\(560\) 8.40294 1.06607i 0.355089 0.0450495i
\(561\) 1.00000 0.0422200
\(562\) 8.74943 + 15.1544i 0.369072 + 0.639252i
\(563\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(564\) 3.02398 5.23768i 0.127332 0.220546i
\(565\) −20.0074 34.6538i −0.841716 1.45789i
\(566\) 27.4006 1.15174
\(567\) −2.62471 + 0.332992i −0.110228 + 0.0139844i
\(568\) 5.24943 0.220261
\(569\) 5.27708 + 9.14017i 0.221227 + 0.383176i 0.955181 0.296023i \(-0.0956606\pi\)
−0.733954 + 0.679199i \(0.762327\pi\)
\(570\) 1.84648 3.19820i 0.0773406 0.133958i
\(571\) −2.37529 + 4.11412i −0.0994027 + 0.172171i −0.911438 0.411438i \(-0.865027\pi\)
0.812035 + 0.583609i \(0.198360\pi\)
\(572\) 3.20147 + 5.54511i 0.133860 + 0.231853i
\(573\) −4.80589 −0.200769
\(574\) 8.44722 20.1250i 0.352580 0.840001i
\(575\) 10.2471 0.427335
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −18.7771 + 32.5229i −0.781700 + 1.35394i 0.149250 + 0.988799i \(0.452314\pi\)
−0.930951 + 0.365145i \(0.881019\pi\)
\(578\) 8.00000 13.8564i 0.332756 0.576351i
\(579\) −4.35499 7.54307i −0.180987 0.313479i
\(580\) −23.2088 −0.963694
\(581\) 10.4952 + 13.8117i 0.435413 + 0.573004i
\(582\) −5.49885 −0.227935
\(583\) 3.20147 + 5.54511i 0.132591 + 0.229655i
\(584\) 1.04795 1.81511i 0.0433646 0.0751097i
\(585\) −10.2494 + 17.7525i −0.423762 + 0.733977i
\(586\) 9.87414 + 17.1025i 0.407897 + 0.706498i
\(587\) −17.0982 −0.705718 −0.352859 0.935676i \(-0.614791\pi\)
−0.352859 + 0.935676i \(0.614791\pi\)
\(588\) 6.77823 1.74802i 0.279530 0.0720871i
\(589\) 12.1106 0.499010
\(590\) 18.4989 + 32.0409i 0.761586 + 1.31910i
\(591\) −0.327335 + 0.566960i −0.0134647 + 0.0233216i
\(592\) −2.57676 + 4.46308i −0.105904 + 0.183431i
\(593\) 16.1236 + 27.9268i 0.662115 + 1.14682i 0.980059 + 0.198708i \(0.0636745\pi\)
−0.317943 + 0.948110i \(0.602992\pi\)
\(594\) 1.00000 0.0410305
\(595\) −5.12471 6.74413i −0.210093 0.276482i
\(596\) 6.84648 0.280443
\(597\) 3.84648 + 6.66230i 0.157426 + 0.272670i
\(598\) 6.24943 10.8243i 0.255558 0.442639i
\(599\) −1.69664 + 2.93867i −0.0693229 + 0.120071i −0.898603 0.438762i \(-0.855417\pi\)
0.829281 + 0.558833i \(0.188751\pi\)
\(600\) −2.62471 4.54614i −0.107153 0.185595i
\(601\) 30.4989 1.24407 0.622037 0.782988i \(-0.286305\pi\)
0.622037 + 0.782988i \(0.286305\pi\)
\(602\) 5.27708 12.5723i 0.215078 0.512410i
\(603\) 6.24943 0.254496
\(604\) −7.42692 12.8638i −0.302197 0.523421i
\(605\) 1.60074 2.77256i 0.0650792 0.112720i
\(606\) 9.97970 17.2854i 0.405398 0.702170i
\(607\) −6.49517 11.2500i −0.263631 0.456622i 0.703573 0.710623i \(-0.251587\pi\)
−0.967204 + 0.254001i \(0.918253\pi\)
\(608\) 1.15352 0.0467814
\(609\) −19.0277 + 2.41400i −0.771040 + 0.0978204i
\(610\) −31.0553 −1.25739
\(611\) −19.3624 33.5366i −0.783317 1.35674i
\(612\) −0.500000 + 0.866025i −0.0202113 + 0.0350070i
\(613\) −10.0996 + 17.4930i −0.407918 + 0.706535i −0.994656 0.103241i \(-0.967079\pi\)
0.586738 + 0.809777i \(0.300412\pi\)
\(614\) −2.15352 3.73001i −0.0869090 0.150531i
\(615\) −26.4103 −1.06497
\(616\) −2.62471 + 0.332992i −0.105753 + 0.0134166i
\(617\) 17.0936 0.688163 0.344081 0.938940i \(-0.388190\pi\)
0.344081 + 0.938940i \(0.388190\pi\)
\(618\) −0.153520 0.265904i −0.00617546 0.0106962i
\(619\) −20.8347 + 36.0868i −0.837417 + 1.45045i 0.0546300 + 0.998507i \(0.482602\pi\)
−0.892047 + 0.451942i \(0.850731\pi\)
\(620\) 16.8059 29.1087i 0.674941 1.16903i
\(621\) −0.976024 1.69052i −0.0391665 0.0678383i
\(622\) −14.7579 −0.591739
\(623\) −18.8442 + 44.8952i −0.754976 + 1.79869i
\(624\) −6.40294 −0.256323
\(625\) 11.8453 + 20.5167i 0.473813 + 0.820669i
\(626\) −10.3753 + 17.9705i −0.414680 + 0.718247i
\(627\) −0.576760 + 0.998977i −0.0230336 + 0.0398953i
\(628\) 4.73028 + 8.19308i 0.188759 + 0.326940i
\(629\) 5.15352 0.205484
\(630\) −5.12471 6.74413i −0.204173 0.268693i
\(631\) −23.8995 −0.951424 −0.475712 0.879601i \(-0.657810\pi\)
−0.475712 + 0.879601i \(0.657810\pi\)
\(632\) 2.80221 + 4.85357i 0.111466 + 0.193065i
\(633\) −7.29738 + 12.6394i −0.290045 + 0.502372i
\(634\) −8.09959 + 14.0289i −0.321676 + 0.557159i
\(635\) 13.3741 + 23.1647i 0.530736 + 0.919263i
\(636\) −6.40294 −0.253893
\(637\) 12.0074 43.1823i 0.475749 1.71094i
\(638\) 7.24943 0.287007
\(639\) −2.62471 4.54614i −0.103832 0.179842i
\(640\) 1.60074 2.77256i 0.0632747 0.109595i
\(641\) 7.15352 12.3903i 0.282547 0.489386i −0.689464 0.724320i \(-0.742154\pi\)
0.972011 + 0.234934i \(0.0754873\pi\)
\(642\) 4.52766 + 7.84213i 0.178692 + 0.309504i
\(643\) −35.4966 −1.39985 −0.699924 0.714218i \(-0.746783\pi\)
−0.699924 + 0.714218i \(0.746783\pi\)
\(644\) 3.12471 + 4.11213i 0.123131 + 0.162041i
\(645\) −16.4989 −0.649642
\(646\) −0.576760 0.998977i −0.0226923 0.0393042i
\(647\) −11.9078 + 20.6249i −0.468143 + 0.810847i −0.999337 0.0364027i \(-0.988410\pi\)
0.531194 + 0.847250i \(0.321743\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) −5.77823 10.0082i −0.226815 0.392856i
\(650\) −33.6118 −1.31836
\(651\) 10.7506 25.6126i 0.421348 1.00384i
\(652\) 13.0553 0.511286
\(653\) 6.89811 + 11.9479i 0.269944 + 0.467557i 0.968847 0.247660i \(-0.0796615\pi\)
−0.698903 + 0.715216i \(0.746328\pi\)
\(654\) 4.85016 8.40073i 0.189656 0.328494i
\(655\) 24.4989 42.4333i 0.957249 1.65800i
\(656\) −4.12471 7.14421i −0.161043 0.278935i
\(657\) −2.09591 −0.0817691
\(658\) 15.8741 2.01392i 0.618838 0.0785109i
\(659\) 18.9447 0.737980 0.368990 0.929433i \(-0.379704\pi\)
0.368990 + 0.929433i \(0.379704\pi\)
\(660\) 1.60074 + 2.77256i 0.0623086 + 0.107922i
\(661\) −1.97970 + 3.42895i −0.0770016 + 0.133371i −0.901955 0.431830i \(-0.857868\pi\)
0.824953 + 0.565201i \(0.191201\pi\)
\(662\) −10.6236 + 18.4006i −0.412896 + 0.715158i
\(663\) 3.20147 + 5.54511i 0.124335 + 0.215354i
\(664\) 6.55646 0.254440
\(665\) 9.69296 1.22973i 0.375877 0.0476868i
\(666\) 5.15352 0.199695
\(667\) −7.07561 12.2553i −0.273969 0.474528i
\(668\) 3.35499 5.81102i 0.129809 0.224835i
\(669\) 7.45090 12.9053i 0.288068 0.498949i
\(670\) 10.0037 + 17.3269i 0.386476 + 0.669396i
\(671\) 9.70032 0.374477
\(672\) 1.02398 2.43956i 0.0395007 0.0941082i
\(673\) −8.69066 −0.335000 −0.167500 0.985872i \(-0.553569\pi\)
−0.167500 + 0.985872i \(0.553569\pi\)
\(674\) 12.7579 + 22.0974i 0.491417 + 0.851160i
\(675\) −2.62471 + 4.54614i −0.101025 + 0.174981i
\(676\) −13.9989 + 24.2467i −0.538417 + 0.932566i
\(677\) 15.7303 + 27.2456i 0.604564 + 1.04714i 0.992120 + 0.125289i \(0.0399859\pi\)
−0.387557 + 0.921846i \(0.626681\pi\)
\(678\) −12.4989 −0.480015
\(679\) −8.80221 11.5837i −0.337798 0.444542i
\(680\) −3.20147 −0.122771
\(681\) 0.124713 + 0.216009i 0.00477900 + 0.00827746i
\(682\) −5.24943 + 9.09227i −0.201011 + 0.348161i
\(683\) −12.3730 + 21.4306i −0.473439 + 0.820021i −0.999538 0.0304028i \(-0.990321\pi\)
0.526098 + 0.850424i \(0.323654\pi\)
\(684\) −0.576760 0.998977i −0.0220530 0.0381968i
\(685\) 20.4989 0.783221
\(686\) 14.5325 + 11.4807i 0.554853 + 0.438336i
\(687\) −4.09591 −0.156269
\(688\) −2.57676 4.46308i −0.0982380 0.170153i
\(689\) −20.4989 + 35.5051i −0.780944 + 1.35263i
\(690\) 3.12471 5.41216i 0.118956 0.206037i
\(691\) −12.7771 22.1306i −0.486063 0.841886i 0.513809 0.857905i \(-0.328234\pi\)
−0.999872 + 0.0160188i \(0.994901\pi\)
\(692\) −5.50115 −0.209122
\(693\) 1.60074 + 2.10657i 0.0608069 + 0.0800220i
\(694\) 3.05531 0.115978
\(695\) 34.8133 + 60.2983i 1.32054 + 2.28725i
\(696\) −3.62471 + 6.27819i −0.137394 + 0.237974i
\(697\) −4.12471 + 7.14421i −0.156235 + 0.270606i
\(698\) 2.00368 + 3.47048i 0.0758404 + 0.131359i
\(699\) 11.3070 0.427671
\(700\) 5.37529 12.8063i 0.203167 0.484033i
\(701\) −14.1512 −0.534484 −0.267242 0.963629i \(-0.586112\pi\)
−0.267242 + 0.963629i \(0.586112\pi\)
\(702\) 3.20147 + 5.54511i 0.120832 + 0.209287i
\(703\) −2.97234 + 5.14825i −0.112104 + 0.194170i
\(704\) −0.500000 + 0.866025i −0.0188445 + 0.0326396i
\(705\) −9.68118 16.7683i −0.364614 0.631530i
\(706\) −1.09821 −0.0413315
\(707\) 52.3877 6.64633i 1.97024 0.249961i
\(708\) 11.5565 0.434319
\(709\) 5.37529 + 9.31027i 0.201873 + 0.349655i 0.949132 0.314879i \(-0.101964\pi\)
−0.747259 + 0.664533i \(0.768630\pi\)
\(710\) 8.40294 14.5543i 0.315357 0.546214i
\(711\) 2.80221 4.85357i 0.105091 0.182023i
\(712\) 9.20147 + 15.9374i 0.344840 + 0.597280i
\(713\) 20.4943 0.767516
\(714\) −2.62471 + 0.332992i −0.0982274 + 0.0124619i
\(715\) 20.4989 0.766614
\(716\) −0.826185 1.43099i −0.0308760 0.0534788i
\(717\) −3.29738 + 5.71123i −0.123143 + 0.213290i
\(718\) −7.80589 + 13.5202i −0.291313 + 0.504569i
\(719\) −1.37897 2.38844i −0.0514268 0.0890739i 0.839166 0.543875i \(-0.183044\pi\)
−0.890593 + 0.454801i \(0.849710\pi\)
\(720\) −3.20147 −0.119312
\(721\) 0.314401 0.749041i 0.0117089 0.0278958i
\(722\) −17.6694 −0.657587
\(723\) −8.55646 14.8202i −0.318218 0.551170i
\(724\) −12.4509 + 21.5656i −0.462734 + 0.801479i
\(725\) −19.0277 + 32.9569i −0.706669 + 1.22399i
\(726\) −0.500000 0.866025i −0.0185567 0.0321412i
\(727\) 14.6141 0.542006 0.271003 0.962578i \(-0.412645\pi\)
0.271003 + 0.962578i \(0.412645\pi\)
\(728\) −10.2494 13.4883i −0.379869 0.499908i
\(729\) 1.00000 0.0370370
\(730\) −3.35499 5.81102i −0.124174 0.215075i
\(731\) −2.57676 + 4.46308i −0.0953049 + 0.165073i
\(732\) −4.85016 + 8.40073i −0.179267 + 0.310500i
\(733\) −3.55278 6.15360i −0.131225 0.227288i 0.792924 0.609321i \(-0.208558\pi\)
−0.924149 + 0.382032i \(0.875224\pi\)
\(734\) 0.791166 0.0292025
\(735\) 6.00368 21.5911i 0.221449 0.796401i
\(736\) 1.95205 0.0719534
\(737\) −3.12471 5.41216i −0.115100 0.199360i
\(738\) −4.12471 + 7.14421i −0.151833 + 0.262982i
\(739\) 20.7483 35.9371i 0.763238 1.32197i −0.177936 0.984042i \(-0.556942\pi\)
0.941173 0.337924i \(-0.109725\pi\)
\(740\) 8.24943 + 14.2884i 0.303255 + 0.525253i
\(741\) −7.38592 −0.271329
\(742\) −10.2494 13.4883i −0.376268 0.495170i
\(743\) −31.9041 −1.17045 −0.585224 0.810872i \(-0.698993\pi\)
−0.585224 + 0.810872i \(0.698993\pi\)
\(744\) −5.24943 9.09227i −0.192453 0.333339i
\(745\) 10.9594 18.9823i 0.401522 0.695456i
\(746\) −7.95573 + 13.7797i −0.291280 + 0.504512i
\(747\) −3.27823 5.67806i −0.119944 0.207750i
\(748\) 1.00000 0.0365636
\(749\) −9.27243 + 22.0910i −0.338807 + 0.807188i
\(750\) −0.798528 −0.0291581
\(751\) −6.75794 11.7051i −0.246601 0.427125i 0.715980 0.698121i \(-0.245980\pi\)
−0.962580 + 0.270996i \(0.912647\pi\)
\(752\) 3.02398 5.23768i 0.110273 0.190999i
\(753\) −3.97970 + 6.89305i −0.145028 + 0.251197i
\(754\) 23.2088 + 40.1989i 0.845216 + 1.46396i
\(755\) −47.5542 −1.73067
\(756\) −2.62471 + 0.332992i −0.0954599 + 0.0121108i
\(757\) −18.5542 −0.674363 −0.337181 0.941440i \(-0.609474\pi\)
−0.337181 + 0.941440i \(0.609474\pi\)
\(758\) 8.52766 + 14.7703i 0.309738 + 0.536483i
\(759\) −0.976024 + 1.69052i −0.0354274 + 0.0613621i
\(760\) 1.84648 3.19820i 0.0669789 0.116011i
\(761\) −7.87529 13.6404i −0.285479 0.494464i 0.687246 0.726425i \(-0.258819\pi\)
−0.972725 + 0.231960i \(0.925486\pi\)
\(762\) 8.35499 0.302669
\(763\) 25.4606 3.23013i 0.921734 0.116939i
\(764\) −4.80589 −0.173871
\(765\) 1.60074 + 2.77256i 0.0578747 + 0.100242i
\(766\) −6.72062 + 11.6405i −0.242826 + 0.420587i
\(767\) 36.9977 64.0819i 1.33591 2.31386i
\(768\) −0.500000 0.866025i −0.0180422 0.0312500i
\(769\) 41.2854 1.48879 0.744395 0.667739i \(-0.232738\pi\)
0.744395 + 0.667739i \(0.232738\pi\)
\(770\) −3.27823 + 7.81020i −0.118139 + 0.281460i
\(771\) −22.4029 −0.806822
\(772\) −4.35499 7.54307i −0.156740 0.271481i
\(773\) −2.45458 + 4.25145i −0.0882850 + 0.152914i −0.906786 0.421591i \(-0.861472\pi\)
0.818501 + 0.574505i \(0.194805\pi\)
\(774\) −2.57676 + 4.46308i −0.0926197 + 0.160422i
\(775\) −27.5565 47.7292i −0.989857 1.71448i
\(776\) −5.49885 −0.197397
\(777\) 8.24943 + 10.8563i 0.295946 + 0.389466i