Properties

Label 735.2.q.e.79.5
Level $735$
Weight $2$
Character 735.79
Analytic conductor $5.869$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 735.q (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.86900454856\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.89539436150784.1
Defining polynomial: \( x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 79.5
Root \(-0.531325 - 1.98293i\) of defining polynomial
Character \(\chi\) \(=\) 735.79
Dual form 735.2.q.e.214.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.64823 + 0.951606i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.811108 + 1.40488i) q^{4} +(1.76210 + 1.37659i) q^{5} +1.90321 q^{6} -0.719004i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(1.64823 + 0.951606i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.811108 + 1.40488i) q^{4} +(1.76210 + 1.37659i) q^{5} +1.90321 q^{6} -0.719004i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.59438 + 3.94576i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(1.40488 + 0.811108i) q^{12} +6.42864i q^{13} +(2.21432 + 0.311108i) q^{15} +(2.30642 - 3.99484i) q^{16} +(3.83531 - 2.21432i) q^{17} +(1.64823 - 0.951606i) q^{18} +(-1.21432 + 2.10326i) q^{19} +(-0.504684 + 3.59210i) q^{20} -3.80642i q^{22} +(1.19320 + 0.688892i) q^{23} +(-0.359502 - 0.622675i) q^{24} +(1.21002 + 4.85138i) q^{25} +(-6.11753 + 10.5959i) q^{26} -1.00000i q^{27} -0.755569 q^{29} +(3.35366 + 2.61994i) q^{30} +(-2.59210 - 4.48966i) q^{31} +(6.35768 - 3.67061i) q^{32} +(-1.73205 - 1.00000i) q^{33} +8.42864 q^{34} +1.62222 q^{36} +(-6.59292 - 3.80642i) q^{37} +(-4.00296 + 2.31111i) q^{38} +(3.21432 + 5.56737i) q^{39} +(0.989771 - 1.26696i) q^{40} -8.23506 q^{41} -10.1017i q^{43} +(1.62222 - 2.80976i) q^{44} +(2.07321 - 0.837733i) q^{45} +(1.31111 + 2.27091i) q^{46} +(-2.38639 - 1.37778i) q^{47} -4.61285i q^{48} +(-2.62222 + 9.14764i) q^{50} +(2.21432 - 3.83531i) q^{51} +(-9.03147 + 5.21432i) q^{52} +(-7.95376 + 4.59210i) q^{53} +(0.951606 - 1.64823i) q^{54} +(0.622216 - 4.42864i) q^{55} +2.42864i q^{57} +(-1.24535 - 0.719004i) q^{58} +(7.05086 + 12.2124i) q^{59} +(1.35898 + 3.36320i) q^{60} +(-3.42864 + 5.93858i) q^{61} -9.86665i q^{62} +4.74620 q^{64} +(-8.84958 + 11.3279i) q^{65} +(-1.90321 - 3.29646i) q^{66} +(2.38639 - 1.37778i) q^{67} +(6.22171 + 3.59210i) q^{68} +1.37778 q^{69} +2.00000 q^{71} +(-0.622675 - 0.359502i) q^{72} +(1.36084 - 0.785680i) q^{73} +(-7.24443 - 12.5477i) q^{74} +(3.47359 + 3.59641i) q^{75} -3.93978 q^{76} +12.2351i q^{78} +(-2.42864 + 4.20653i) q^{79} +(9.56341 - 3.86433i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-13.5733 - 7.83654i) q^{82} -11.6128i q^{83} +(9.80642 + 1.37778i) q^{85} +(9.61285 - 16.6499i) q^{86} +(-0.654342 + 0.377784i) q^{87} +(-1.24535 + 0.719004i) q^{88} +(2.31111 - 4.00296i) q^{89} +(4.21432 + 0.592104i) q^{90} +2.23506i q^{92} +(-4.48966 - 2.59210i) q^{93} +(-2.62222 - 4.54181i) q^{94} +(-5.03508 + 2.03455i) q^{95} +(3.67061 - 6.35768i) q^{96} -11.9398i q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 10 q^{4} - 2 q^{5} - 4 q^{6} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 10 q^{4} - 2 q^{5} - 4 q^{6} + 6 q^{9} + 12 q^{10} - 12 q^{11} - 26 q^{16} + 12 q^{19} - 60 q^{20} - 18 q^{24} + 2 q^{25} - 20 q^{26} - 8 q^{29} + 10 q^{30} - 4 q^{31} + 48 q^{34} + 20 q^{36} + 12 q^{39} - 4 q^{40} + 8 q^{41} + 20 q^{44} + 2 q^{45} + 16 q^{46} - 32 q^{50} - 2 q^{54} + 8 q^{55} + 32 q^{59} + 8 q^{60} + 12 q^{61} - 52 q^{64} - 32 q^{65} + 4 q^{66} + 16 q^{69} + 24 q^{71} - 88 q^{74} - 8 q^{75} + 8 q^{76} + 24 q^{79} - 46 q^{80} - 6 q^{81} + 64 q^{85} + 8 q^{86} + 28 q^{89} + 24 q^{90} - 32 q^{94} - 4 q^{95} + 58 q^{96} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).

\(n\) \(346\) \(442\) \(491\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.64823 + 0.951606i 1.16547 + 0.672887i 0.952610 0.304195i \(-0.0983873\pi\)
0.212865 + 0.977082i \(0.431721\pi\)
\(3\) 0.866025 0.500000i 0.500000 0.288675i
\(4\) 0.811108 + 1.40488i 0.405554 + 0.702440i
\(5\) 1.76210 + 1.37659i 0.788037 + 0.615628i
\(6\) 1.90321 0.776983
\(7\) 0 0
\(8\) 0.719004i 0.254206i
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 1.59438 + 3.94576i 0.504188 + 1.24776i
\(11\) −1.00000 1.73205i −0.301511 0.522233i 0.674967 0.737848i \(-0.264158\pi\)
−0.976478 + 0.215615i \(0.930824\pi\)
\(12\) 1.40488 + 0.811108i 0.405554 + 0.234147i
\(13\) 6.42864i 1.78298i 0.453037 + 0.891492i \(0.350341\pi\)
−0.453037 + 0.891492i \(0.649659\pi\)
\(14\) 0 0
\(15\) 2.21432 + 0.311108i 0.571735 + 0.0803277i
\(16\) 2.30642 3.99484i 0.576606 0.998711i
\(17\) 3.83531 2.21432i 0.930200 0.537051i 0.0433254 0.999061i \(-0.486205\pi\)
0.886875 + 0.462010i \(0.152871\pi\)
\(18\) 1.64823 0.951606i 0.388492 0.224296i
\(19\) −1.21432 + 2.10326i −0.278584 + 0.482522i −0.971033 0.238945i \(-0.923198\pi\)
0.692449 + 0.721467i \(0.256532\pi\)
\(20\) −0.504684 + 3.59210i −0.112851 + 0.803219i
\(21\) 0 0
\(22\) 3.80642i 0.811532i
\(23\) 1.19320 + 0.688892i 0.248799 + 0.143644i 0.619214 0.785222i \(-0.287451\pi\)
−0.370415 + 0.928866i \(0.620785\pi\)
\(24\) −0.359502 0.622675i −0.0733830 0.127103i
\(25\) 1.21002 + 4.85138i 0.242003 + 0.970275i
\(26\) −6.11753 + 10.5959i −1.19975 + 2.07802i
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) −0.755569 −0.140306 −0.0701528 0.997536i \(-0.522349\pi\)
−0.0701528 + 0.997536i \(0.522349\pi\)
\(30\) 3.35366 + 2.61994i 0.612291 + 0.478333i
\(31\) −2.59210 4.48966i −0.465556 0.806366i 0.533671 0.845692i \(-0.320812\pi\)
−0.999226 + 0.0393263i \(0.987479\pi\)
\(32\) 6.35768 3.67061i 1.12389 0.648878i
\(33\) −1.73205 1.00000i −0.301511 0.174078i
\(34\) 8.42864 1.44550
\(35\) 0 0
\(36\) 1.62222 0.270369
\(37\) −6.59292 3.80642i −1.08387 0.625772i −0.151932 0.988391i \(-0.548549\pi\)
−0.931938 + 0.362619i \(0.881883\pi\)
\(38\) −4.00296 + 2.31111i −0.649365 + 0.374911i
\(39\) 3.21432 + 5.56737i 0.514703 + 0.891492i
\(40\) 0.989771 1.26696i 0.156497 0.200324i
\(41\) −8.23506 −1.28610 −0.643050 0.765824i \(-0.722331\pi\)
−0.643050 + 0.765824i \(0.722331\pi\)
\(42\) 0 0
\(43\) 10.1017i 1.54050i −0.637744 0.770248i \(-0.720132\pi\)
0.637744 0.770248i \(-0.279868\pi\)
\(44\) 1.62222 2.80976i 0.244558 0.423587i
\(45\) 2.07321 0.837733i 0.309056 0.124882i
\(46\) 1.31111 + 2.27091i 0.193312 + 0.334827i
\(47\) −2.38639 1.37778i −0.348091 0.200971i 0.315753 0.948841i \(-0.397743\pi\)
−0.663844 + 0.747871i \(0.731076\pi\)
\(48\) 4.61285i 0.665807i
\(49\) 0 0
\(50\) −2.62222 + 9.14764i −0.370837 + 1.29367i
\(51\) 2.21432 3.83531i 0.310067 0.537051i
\(52\) −9.03147 + 5.21432i −1.25244 + 0.723096i
\(53\) −7.95376 + 4.59210i −1.09253 + 0.630774i −0.934250 0.356620i \(-0.883929\pi\)
−0.158283 + 0.987394i \(0.550596\pi\)
\(54\) 0.951606 1.64823i 0.129497 0.224296i
\(55\) 0.622216 4.42864i 0.0838995 0.597158i
\(56\) 0 0
\(57\) 2.42864i 0.321681i
\(58\) −1.24535 0.719004i −0.163523 0.0944098i
\(59\) 7.05086 + 12.2124i 0.917943 + 1.58992i 0.802534 + 0.596606i \(0.203485\pi\)
0.115409 + 0.993318i \(0.463182\pi\)
\(60\) 1.35898 + 3.36320i 0.175444 + 0.434187i
\(61\) −3.42864 + 5.93858i −0.438992 + 0.760357i −0.997612 0.0690669i \(-0.977998\pi\)
0.558620 + 0.829424i \(0.311331\pi\)
\(62\) 9.86665i 1.25307i
\(63\) 0 0
\(64\) 4.74620 0.593275
\(65\) −8.84958 + 11.3279i −1.09766 + 1.40506i
\(66\) −1.90321 3.29646i −0.234269 0.405766i
\(67\) 2.38639 1.37778i 0.291544 0.168323i −0.347094 0.937830i \(-0.612831\pi\)
0.638638 + 0.769507i \(0.279498\pi\)
\(68\) 6.22171 + 3.59210i 0.754493 + 0.435607i
\(69\) 1.37778 0.165866
\(70\) 0 0
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) −0.622675 0.359502i −0.0733830 0.0423677i
\(73\) 1.36084 0.785680i 0.159274 0.0919569i −0.418244 0.908335i \(-0.637354\pi\)
0.577519 + 0.816378i \(0.304021\pi\)
\(74\) −7.24443 12.5477i −0.842148 1.45864i
\(75\) 3.47359 + 3.59641i 0.401096 + 0.415277i
\(76\) −3.93978 −0.451923
\(77\) 0 0
\(78\) 12.2351i 1.38535i
\(79\) −2.42864 + 4.20653i −0.273243 + 0.473271i −0.969690 0.244337i \(-0.921430\pi\)
0.696447 + 0.717608i \(0.254763\pi\)
\(80\) 9.56341 3.86433i 1.06922 0.432046i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −13.5733 7.83654i −1.49892 0.865401i
\(83\) 11.6128i 1.27468i −0.770585 0.637338i \(-0.780036\pi\)
0.770585 0.637338i \(-0.219964\pi\)
\(84\) 0 0
\(85\) 9.80642 + 1.37778i 1.06366 + 0.149442i
\(86\) 9.61285 16.6499i 1.03658 1.79541i
\(87\) −0.654342 + 0.377784i −0.0701528 + 0.0405027i
\(88\) −1.24535 + 0.719004i −0.132755 + 0.0766461i
\(89\) 2.31111 4.00296i 0.244977 0.424313i −0.717148 0.696921i \(-0.754553\pi\)
0.962125 + 0.272608i \(0.0878863\pi\)
\(90\) 4.21432 + 0.592104i 0.444228 + 0.0624133i
\(91\) 0 0
\(92\) 2.23506i 0.233021i
\(93\) −4.48966 2.59210i −0.465556 0.268789i
\(94\) −2.62222 4.54181i −0.270461 0.468452i
\(95\) −5.03508 + 2.03455i −0.516589 + 0.208740i
\(96\) 3.67061 6.35768i 0.374630 0.648878i
\(97\) 11.9398i 1.21230i −0.795350 0.606150i \(-0.792713\pi\)
0.795350 0.606150i \(-0.207287\pi\)
\(98\) 0 0
\(99\) −2.00000 −0.201008
\(100\) −5.83415 + 5.63492i −0.583415 + 0.563492i
\(101\) −0.739747 1.28128i −0.0736076 0.127492i 0.826872 0.562390i \(-0.190118\pi\)
−0.900480 + 0.434898i \(0.856785\pi\)
\(102\) 7.29942 4.21432i 0.722750 0.417280i
\(103\) −7.67063 4.42864i −0.755809 0.436367i 0.0719797 0.997406i \(-0.477068\pi\)
−0.827789 + 0.561039i \(0.810402\pi\)
\(104\) 4.62222 0.453246
\(105\) 0 0
\(106\) −17.4795 −1.69776
\(107\) −1.52848 0.882468i −0.147764 0.0853114i 0.424295 0.905524i \(-0.360522\pi\)
−0.572059 + 0.820212i \(0.693855\pi\)
\(108\) 1.40488 0.811108i 0.135185 0.0780489i
\(109\) 2.80642 + 4.86087i 0.268807 + 0.465587i 0.968554 0.248804i \(-0.0800374\pi\)
−0.699747 + 0.714390i \(0.746704\pi\)
\(110\) 5.23987 6.70731i 0.499602 0.639517i
\(111\) −7.61285 −0.722580
\(112\) 0 0
\(113\) 11.2859i 1.06169i 0.847469 + 0.530845i \(0.178125\pi\)
−0.847469 + 0.530845i \(0.821875\pi\)
\(114\) −2.31111 + 4.00296i −0.216455 + 0.374911i
\(115\) 1.15421 + 2.85644i 0.107631 + 0.266364i
\(116\) −0.612848 1.06148i −0.0569015 0.0985563i
\(117\) 5.56737 + 3.21432i 0.514703 + 0.297164i
\(118\) 26.8385i 2.47069i
\(119\) 0 0
\(120\) 0.223688 1.59210i 0.0204198 0.145339i
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) −11.3024 + 6.52543i −1.02327 + 0.590784i
\(123\) −7.13177 + 4.11753i −0.643050 + 0.371265i
\(124\) 4.20495 7.28319i 0.377616 0.654050i
\(125\) −4.54617 + 10.2143i −0.406622 + 0.913597i
\(126\) 0 0
\(127\) 12.8573i 1.14090i −0.821333 0.570450i \(-0.806769\pi\)
0.821333 0.570450i \(-0.193231\pi\)
\(128\) −4.89253 2.82471i −0.432443 0.249671i
\(129\) −5.05086 8.74834i −0.444703 0.770248i
\(130\) −25.3659 + 10.2497i −2.22473 + 0.898959i
\(131\) 1.05086 1.82013i 0.0918136 0.159026i −0.816461 0.577401i \(-0.804067\pi\)
0.908274 + 0.418375i \(0.137400\pi\)
\(132\) 3.24443i 0.282391i
\(133\) 0 0
\(134\) 5.24443 0.453050
\(135\) 1.37659 1.76210i 0.118478 0.151658i
\(136\) −1.59210 2.75761i −0.136522 0.236463i
\(137\) 13.8043 7.96989i 1.17938 0.680914i 0.223506 0.974702i \(-0.428250\pi\)
0.955870 + 0.293789i \(0.0949163\pi\)
\(138\) 2.27091 + 1.31111i 0.193312 + 0.111609i
\(139\) −11.6731 −0.990097 −0.495048 0.868865i \(-0.664850\pi\)
−0.495048 + 0.868865i \(0.664850\pi\)
\(140\) 0 0
\(141\) −2.75557 −0.232061
\(142\) 3.29646 + 1.90321i 0.276633 + 0.159714i
\(143\) 11.1347 6.42864i 0.931133 0.537590i
\(144\) −2.30642 3.99484i −0.192202 0.332904i
\(145\) −1.33139 1.04011i −0.110566 0.0863761i
\(146\) 2.99063 0.247506
\(147\) 0 0
\(148\) 12.3497i 1.01514i
\(149\) −10.6128 + 18.3820i −0.869438 + 1.50591i −0.00686675 + 0.999976i \(0.502186\pi\)
−0.862572 + 0.505935i \(0.831148\pi\)
\(150\) 2.30292 + 9.23320i 0.188032 + 0.753888i
\(151\) −8.42864 14.5988i −0.685913 1.18804i −0.973149 0.230176i \(-0.926070\pi\)
0.287236 0.957860i \(-0.407264\pi\)
\(152\) 1.51225 + 0.873100i 0.122660 + 0.0708178i
\(153\) 4.42864i 0.358034i
\(154\) 0 0
\(155\) 1.61285 11.4795i 0.129547 0.922055i
\(156\) −5.21432 + 9.03147i −0.417480 + 0.723096i
\(157\) −9.03147 + 5.21432i −0.720790 + 0.416148i −0.815043 0.579400i \(-0.803287\pi\)
0.0942537 + 0.995548i \(0.469954\pi\)
\(158\) −8.00591 + 4.62222i −0.636916 + 0.367724i
\(159\) −4.59210 + 7.95376i −0.364178 + 0.630774i
\(160\) 16.2558 + 2.28391i 1.28513 + 0.180559i
\(161\) 0 0
\(162\) 1.90321i 0.149530i
\(163\) 18.0629 + 10.4286i 1.41480 + 0.816834i 0.995835 0.0911693i \(-0.0290605\pi\)
0.418963 + 0.908003i \(0.362394\pi\)
\(164\) −6.67952 11.5693i −0.521583 0.903409i
\(165\) −1.67547 4.14642i −0.130435 0.322799i
\(166\) 11.0509 19.1406i 0.857713 1.48560i
\(167\) 15.3461i 1.18752i 0.804642 + 0.593760i \(0.202357\pi\)
−0.804642 + 0.593760i \(0.797643\pi\)
\(168\) 0 0
\(169\) −28.3274 −2.17903
\(170\) 14.8521 + 11.6028i 1.13911 + 0.889891i
\(171\) 1.21432 + 2.10326i 0.0928614 + 0.160841i
\(172\) 14.1917 8.19358i 1.08211 0.624754i
\(173\) 1.78421 + 1.03011i 0.135651 + 0.0783179i 0.566290 0.824206i \(-0.308378\pi\)
−0.430639 + 0.902524i \(0.641712\pi\)
\(174\) −1.43801 −0.109015
\(175\) 0 0
\(176\) −9.22570 −0.695413
\(177\) 12.2124 + 7.05086i 0.917943 + 0.529975i
\(178\) 7.61847 4.39853i 0.571029 0.329684i
\(179\) 5.00000 + 8.66025i 0.373718 + 0.647298i 0.990134 0.140122i \(-0.0447496\pi\)
−0.616417 + 0.787420i \(0.711416\pi\)
\(180\) 2.85851 + 2.23312i 0.213061 + 0.166447i
\(181\) −12.1017 −0.899513 −0.449757 0.893151i \(-0.648489\pi\)
−0.449757 + 0.893151i \(0.648489\pi\)
\(182\) 0 0
\(183\) 6.85728i 0.506905i
\(184\) 0.495316 0.857913i 0.0365152 0.0632462i
\(185\) −6.37753 15.7830i −0.468885 1.16039i
\(186\) −4.93332 8.54477i −0.361729 0.626533i
\(187\) −7.67063 4.42864i −0.560932 0.323854i
\(188\) 4.47013i 0.326017i
\(189\) 0 0
\(190\) −10.2351 1.43801i −0.742530 0.104324i
\(191\) −0.244431 + 0.423367i −0.0176864 + 0.0306338i −0.874733 0.484605i \(-0.838963\pi\)
0.857047 + 0.515239i \(0.172297\pi\)
\(192\) 4.11033 2.37310i 0.296638 0.171264i
\(193\) 19.8831 11.4795i 1.43121 0.826312i 0.434001 0.900912i \(-0.357101\pi\)
0.997214 + 0.0746003i \(0.0237681\pi\)
\(194\) 11.3620 19.6795i 0.815741 1.41291i
\(195\) −2.00000 + 14.2351i −0.143223 + 1.01939i
\(196\) 0 0
\(197\) 1.18421i 0.0843713i −0.999110 0.0421857i \(-0.986568\pi\)
0.999110 0.0421857i \(-0.0134321\pi\)
\(198\) −3.29646 1.90321i −0.234269 0.135255i
\(199\) 4.39853 + 7.61847i 0.311803 + 0.540059i 0.978753 0.205044i \(-0.0657336\pi\)
−0.666949 + 0.745103i \(0.732400\pi\)
\(200\) 3.48816 0.870006i 0.246650 0.0615187i
\(201\) 1.37778 2.38639i 0.0971814 0.168323i
\(202\) 2.81579i 0.198118i
\(203\) 0 0
\(204\) 7.18421 0.502995
\(205\) −14.5110 11.3363i −1.01349 0.791760i
\(206\) −8.42864 14.5988i −0.587251 1.01715i
\(207\) 1.19320 0.688892i 0.0829329 0.0478813i
\(208\) 25.6814 + 14.8272i 1.78069 + 1.02808i
\(209\) 4.85728 0.335985
\(210\) 0 0
\(211\) 23.2257 1.59892 0.799461 0.600717i \(-0.205118\pi\)
0.799461 + 0.600717i \(0.205118\pi\)
\(212\) −12.9027 7.44938i −0.886162 0.511626i
\(213\) 1.73205 1.00000i 0.118678 0.0685189i
\(214\) −1.67952 2.90902i −0.114810 0.198857i
\(215\) 13.9059 17.8003i 0.948373 1.21397i
\(216\) −0.719004 −0.0489220
\(217\) 0 0
\(218\) 10.6824i 0.723506i
\(219\) 0.785680 1.36084i 0.0530914 0.0919569i
\(220\) 6.72639 2.71797i 0.453493 0.183245i
\(221\) 14.2351 + 24.6559i 0.957554 + 1.65853i
\(222\) −12.5477 7.24443i −0.842148 0.486214i
\(223\) 15.2257i 1.01959i 0.860297 + 0.509794i \(0.170278\pi\)
−0.860297 + 0.509794i \(0.829722\pi\)
\(224\) 0 0
\(225\) 4.80642 + 1.37778i 0.320428 + 0.0918523i
\(226\) −10.7397 + 18.6018i −0.714397 + 1.23737i
\(227\) −12.4434 + 7.18421i −0.825898 + 0.476833i −0.852446 0.522815i \(-0.824882\pi\)
0.0265479 + 0.999648i \(0.491549\pi\)
\(228\) −3.41195 + 1.96989i −0.225962 + 0.130459i
\(229\) −2.80642 + 4.86087i −0.185454 + 0.321215i −0.943729 0.330719i \(-0.892709\pi\)
0.758276 + 0.651934i \(0.226042\pi\)
\(230\) −0.815792 + 5.80642i −0.0537917 + 0.382864i
\(231\) 0 0
\(232\) 0.543257i 0.0356666i
\(233\) 20.1662 + 11.6430i 1.32113 + 0.762756i 0.983909 0.178669i \(-0.0571793\pi\)
0.337222 + 0.941425i \(0.390513\pi\)
\(234\) 6.11753 + 10.5959i 0.399916 + 0.692674i
\(235\) −2.30843 5.71288i −0.150585 0.372667i
\(236\) −11.4380 + 19.8112i −0.744551 + 1.28960i
\(237\) 4.85728i 0.315514i
\(238\) 0 0
\(239\) 8.48886 0.549099 0.274549 0.961573i \(-0.411471\pi\)
0.274549 + 0.961573i \(0.411471\pi\)
\(240\) 6.34999 8.12831i 0.409890 0.524680i
\(241\) 3.62222 + 6.27386i 0.233327 + 0.404135i 0.958785 0.284132i \(-0.0917053\pi\)
−0.725458 + 0.688267i \(0.758372\pi\)
\(242\) 11.5376 6.66124i 0.741666 0.428201i
\(243\) −0.866025 0.500000i −0.0555556 0.0320750i
\(244\) −11.1240 −0.712140
\(245\) 0 0
\(246\) −15.6731 −0.999278
\(247\) −13.5211 7.80642i −0.860328 0.496711i
\(248\) −3.22808 + 1.86373i −0.204983 + 0.118347i
\(249\) −5.80642 10.0570i −0.367967 0.637338i
\(250\) −17.2131 + 12.5094i −1.08865 + 0.791163i
\(251\) 27.6128 1.74291 0.871454 0.490478i \(-0.163178\pi\)
0.871454 + 0.490478i \(0.163178\pi\)
\(252\) 0 0
\(253\) 2.75557i 0.173241i
\(254\) 12.2351 21.1918i 0.767696 1.32969i
\(255\) 9.18150 3.71002i 0.574968 0.232330i
\(256\) −10.1222 17.5322i −0.632638 1.09576i
\(257\) 0.371213 + 0.214320i 0.0231556 + 0.0133689i 0.511533 0.859264i \(-0.329078\pi\)
−0.488378 + 0.872632i \(0.662411\pi\)
\(258\) 19.2257i 1.19694i
\(259\) 0 0
\(260\) −23.0923 3.24443i −1.43213 0.201211i
\(261\) −0.377784 + 0.654342i −0.0233843 + 0.0405027i
\(262\) 3.46410 2.00000i 0.214013 0.123560i
\(263\) 8.12140 4.68889i 0.500787 0.289129i −0.228252 0.973602i \(-0.573301\pi\)
0.729038 + 0.684473i \(0.239968\pi\)
\(264\) −0.719004 + 1.24535i −0.0442516 + 0.0766461i
\(265\) −20.3368 2.85728i −1.24928 0.175521i
\(266\) 0 0
\(267\) 4.62222i 0.282875i
\(268\) 3.87124 + 2.23506i 0.236474 + 0.136528i
\(269\) 0.873100 + 1.51225i 0.0532339 + 0.0922038i 0.891414 0.453189i \(-0.149714\pi\)
−0.838181 + 0.545393i \(0.816380\pi\)
\(270\) 3.94576 1.59438i 0.240131 0.0970310i
\(271\) 1.34767 2.33424i 0.0818653 0.141795i −0.822186 0.569219i \(-0.807246\pi\)
0.904051 + 0.427424i \(0.140579\pi\)
\(272\) 20.4286i 1.23867i
\(273\) 0 0
\(274\) 30.3368 1.83271
\(275\) 7.19282 6.94719i 0.433743 0.418931i
\(276\) 1.11753 + 1.93562i 0.0672675 + 0.116511i
\(277\) −4.43750 + 2.56199i −0.266624 + 0.153935i −0.627352 0.778736i \(-0.715861\pi\)
0.360729 + 0.932671i \(0.382528\pi\)
\(278\) −19.2399 11.1082i −1.15393 0.666223i
\(279\) −5.18421 −0.310370
\(280\) 0 0
\(281\) 23.9813 1.43060 0.715301 0.698816i \(-0.246290\pi\)
0.715301 + 0.698816i \(0.246290\pi\)
\(282\) −4.54181 2.62222i −0.270461 0.156151i
\(283\) −2.05111 + 1.18421i −0.121926 + 0.0703939i −0.559723 0.828680i \(-0.689092\pi\)
0.437797 + 0.899074i \(0.355759\pi\)
\(284\) 1.62222 + 2.80976i 0.0962608 + 0.166729i
\(285\) −3.34323 + 4.27951i −0.198036 + 0.253497i
\(286\) 24.4701 1.44695
\(287\) 0 0
\(288\) 7.34122i 0.432585i
\(289\) 1.30642 2.26279i 0.0768485 0.133105i
\(290\) −1.20467 2.98129i −0.0707404 0.175068i
\(291\) −5.96989 10.3402i −0.349961 0.606150i
\(292\) 2.20757 + 1.27454i 0.129188 + 0.0745870i
\(293\) 8.42864i 0.492406i −0.969218 0.246203i \(-0.920817\pi\)
0.969218 0.246203i \(-0.0791831\pi\)
\(294\) 0 0
\(295\) −4.38715 + 31.2257i −0.255430 + 1.81803i
\(296\) −2.73683 + 4.74033i −0.159075 + 0.275526i
\(297\) −1.73205 + 1.00000i −0.100504 + 0.0580259i
\(298\) −34.9848 + 20.1985i −2.02662 + 1.17007i
\(299\) −4.42864 + 7.67063i −0.256115 + 0.443604i
\(300\) −2.23506 + 7.79706i −0.129041 + 0.450163i
\(301\) 0 0
\(302\) 32.0830i 1.84617i
\(303\) −1.28128 0.739747i −0.0736076 0.0424974i
\(304\) 5.60147 + 9.70203i 0.321266 + 0.556450i
\(305\) −14.2166 + 5.74457i −0.814039 + 0.328933i
\(306\) 4.21432 7.29942i 0.240917 0.417280i
\(307\) 22.5718i 1.28824i −0.764923 0.644121i \(-0.777223\pi\)
0.764923 0.644121i \(-0.222777\pi\)
\(308\) 0 0
\(309\) −8.85728 −0.503873
\(310\) 13.5823 17.3861i 0.771423 0.987461i
\(311\) 12.0415 + 20.8565i 0.682810 + 1.18266i 0.974120 + 0.226033i \(0.0725757\pi\)
−0.291310 + 0.956629i \(0.594091\pi\)
\(312\) 4.00296 2.31111i 0.226623 0.130841i
\(313\) 8.36090 + 4.82717i 0.472586 + 0.272848i 0.717322 0.696742i \(-0.245368\pi\)
−0.244736 + 0.969590i \(0.578701\pi\)
\(314\) −19.8479 −1.12008
\(315\) 0 0
\(316\) −7.87955 −0.443260
\(317\) 5.23208 + 3.02074i 0.293863 + 0.169662i 0.639683 0.768639i \(-0.279066\pi\)
−0.345820 + 0.938301i \(0.612399\pi\)
\(318\) −15.1377 + 8.73975i −0.848879 + 0.490101i
\(319\) 0.755569 + 1.30868i 0.0423037 + 0.0732722i
\(320\) 8.36330 + 6.53356i 0.467522 + 0.365237i
\(321\) −1.76494 −0.0985092
\(322\) 0 0
\(323\) 10.7556i 0.598456i
\(324\) 0.811108 1.40488i 0.0450615 0.0780489i
\(325\) −31.1878 + 7.77875i −1.72999 + 0.431488i
\(326\) 19.8479 + 34.3776i 1.09927 + 1.90400i
\(327\) 4.86087 + 2.80642i 0.268807 + 0.155196i
\(328\) 5.92104i 0.326935i
\(329\) 0 0
\(330\) 1.18421 8.42864i 0.0651885 0.463981i
\(331\) −6.75557 + 11.7010i −0.371320 + 0.643144i −0.989769 0.142680i \(-0.954428\pi\)
0.618449 + 0.785825i \(0.287761\pi\)
\(332\) 16.3147 9.41927i 0.895383 0.516950i
\(333\) −6.59292 + 3.80642i −0.361290 + 0.208591i
\(334\) −14.6035 + 25.2940i −0.799067 + 1.38402i
\(335\) 6.10171 + 0.857279i 0.333372 + 0.0468382i
\(336\) 0 0
\(337\) 10.4889i 0.571365i 0.958324 + 0.285682i \(0.0922202\pi\)
−0.958324 + 0.285682i \(0.907780\pi\)
\(338\) −46.6901 26.9565i −2.53961 1.46624i
\(339\) 5.64296 + 9.77389i 0.306483 + 0.530845i
\(340\) 6.01845 + 14.8944i 0.326396 + 0.807761i
\(341\) −5.18421 + 8.97931i −0.280741 + 0.486257i
\(342\) 4.62222i 0.249941i
\(343\) 0 0
\(344\) −7.26317 −0.391604
\(345\) 2.42780 + 1.89664i 0.130708 + 0.102112i
\(346\) 1.96052 + 3.39572i 0.105398 + 0.182555i
\(347\) −14.4833 + 8.36196i −0.777507 + 0.448894i −0.835546 0.549421i \(-0.814848\pi\)
0.0580392 + 0.998314i \(0.481515\pi\)
\(348\) −1.06148 0.612848i −0.0569015 0.0328521i
\(349\) 16.3684 0.876181 0.438091 0.898931i \(-0.355655\pi\)
0.438091 + 0.898931i \(0.355655\pi\)
\(350\) 0 0
\(351\) 6.42864 0.343135
\(352\) −12.7154 7.34122i −0.677731 0.391288i
\(353\) −0.475522 + 0.274543i −0.0253095 + 0.0146124i −0.512601 0.858627i \(-0.671318\pi\)
0.487292 + 0.873239i \(0.337985\pi\)
\(354\) 13.4193 + 23.2429i 0.713226 + 1.23534i
\(355\) 3.52421 + 2.75317i 0.187045 + 0.146123i
\(356\) 7.49823 0.397405
\(357\) 0 0
\(358\) 19.0321i 1.00588i
\(359\) −0.142721 + 0.247200i −0.00753253 + 0.0130467i −0.869767 0.493462i \(-0.835731\pi\)
0.862235 + 0.506509i \(0.169064\pi\)
\(360\) −0.602333 1.49065i −0.0317457 0.0785640i
\(361\) 6.55086 + 11.3464i 0.344782 + 0.597180i
\(362\) −19.9464 11.5161i −1.04836 0.605271i
\(363\) 7.00000i 0.367405i
\(364\) 0 0
\(365\) 3.47949 + 0.488863i 0.182125 + 0.0255882i
\(366\) −6.52543 + 11.3024i −0.341090 + 0.590784i
\(367\) 1.48485 0.857279i 0.0775086 0.0447496i −0.460745 0.887533i \(-0.652418\pi\)
0.538253 + 0.842783i \(0.319084\pi\)
\(368\) 5.50403 3.17775i 0.286918 0.165652i
\(369\) −4.11753 + 7.13177i −0.214350 + 0.371265i
\(370\) 4.50760 32.0830i 0.234339 1.66791i
\(371\) 0 0
\(372\) 8.40990i 0.436033i
\(373\) 13.8564 + 8.00000i 0.717458 + 0.414224i 0.813816 0.581122i \(-0.197386\pi\)
−0.0963587 + 0.995347i \(0.530720\pi\)
\(374\) −8.42864 14.5988i −0.435835 0.754888i
\(375\) 1.17006 + 11.1189i 0.0604216 + 0.574180i
\(376\) −0.990632 + 1.71583i −0.0510879 + 0.0884869i
\(377\) 4.85728i 0.250163i
\(378\) 0 0
\(379\) 4.85728 0.249502 0.124751 0.992188i \(-0.460187\pi\)
0.124751 + 0.992188i \(0.460187\pi\)
\(380\) −6.94229 5.42345i −0.356132 0.278217i
\(381\) −6.42864 11.1347i −0.329349 0.570450i
\(382\) −0.805758 + 0.465205i −0.0412262 + 0.0238019i
\(383\) −7.26349 4.19358i −0.371147 0.214282i 0.302813 0.953050i \(-0.402074\pi\)
−0.673959 + 0.738768i \(0.735408\pi\)
\(384\) −5.64941 −0.288295
\(385\) 0 0
\(386\) 43.6958 2.22406
\(387\) −8.74834 5.05086i −0.444703 0.256749i
\(388\) 16.7740 9.68445i 0.851568 0.491653i
\(389\) 4.47949 + 7.75871i 0.227119 + 0.393382i 0.956953 0.290242i \(-0.0937359\pi\)
−0.729834 + 0.683625i \(0.760403\pi\)
\(390\) −16.8426 + 21.5594i −0.852860 + 1.09170i
\(391\) 6.10171 0.308577
\(392\) 0 0
\(393\) 2.10171i 0.106017i
\(394\) 1.12690 1.95185i 0.0567724 0.0983326i
\(395\) −10.0702 + 4.06910i −0.506685 + 0.204739i
\(396\) −1.62222 2.80976i −0.0815194 0.141196i
\(397\) 2.20757 + 1.27454i 0.110795 + 0.0639675i 0.554373 0.832268i \(-0.312958\pi\)
−0.443579 + 0.896236i \(0.646291\pi\)
\(398\) 16.7427i 0.839234i
\(399\) 0 0
\(400\) 22.1713 + 6.35551i 1.10857 + 0.317775i
\(401\) −0.479495 + 0.830509i −0.0239448 + 0.0414736i −0.877750 0.479120i \(-0.840956\pi\)
0.853805 + 0.520593i \(0.174289\pi\)
\(402\) 4.54181 2.62222i 0.226525 0.130784i
\(403\) 28.8624 16.6637i 1.43774 0.830078i
\(404\) 1.20003 2.07851i 0.0597037 0.103410i
\(405\) 0.311108 2.21432i 0.0154591 0.110030i
\(406\) 0 0
\(407\) 15.2257i 0.754710i
\(408\) −2.75761 1.59210i −0.136522 0.0788209i
\(409\) −15.9906 27.6966i −0.790686 1.36951i −0.925543 0.378643i \(-0.876391\pi\)
0.134857 0.990865i \(-0.456943\pi\)
\(410\) −13.1298 32.4936i −0.648437 1.60474i
\(411\) 7.96989 13.8043i 0.393126 0.680914i
\(412\) 14.3684i 0.707881i
\(413\) 0 0
\(414\) 2.62222 0.128875
\(415\) 15.9861 20.4630i 0.784727 1.00449i
\(416\) 23.5970 + 40.8712i 1.15694 + 2.00388i
\(417\) −10.1092 + 5.83654i −0.495048 + 0.285816i
\(418\) 8.00591 + 4.62222i 0.391582 + 0.226080i
\(419\) 0.470127 0.0229672 0.0114836 0.999934i \(-0.496345\pi\)
0.0114836 + 0.999934i \(0.496345\pi\)
\(420\) 0 0
\(421\) −33.6128 −1.63819 −0.819095 0.573658i \(-0.805524\pi\)
−0.819095 + 0.573658i \(0.805524\pi\)
\(422\) 38.2813 + 22.1017i 1.86350 + 1.07589i
\(423\) −2.38639 + 1.37778i −0.116030 + 0.0669902i
\(424\) 3.30174 + 5.71878i 0.160347 + 0.277729i
\(425\) 15.3833 + 15.9272i 0.746199 + 0.772582i
\(426\) 3.80642 0.184422
\(427\) 0 0
\(428\) 2.86311i 0.138394i
\(429\) 6.42864 11.1347i 0.310378 0.537590i
\(430\) 39.8589 16.1060i 1.92217 0.776700i
\(431\) −5.85728 10.1451i −0.282135 0.488673i 0.689775 0.724024i \(-0.257709\pi\)
−0.971910 + 0.235351i \(0.924376\pi\)
\(432\) −3.99484 2.30642i −0.192202 0.110968i
\(433\) 0.0602231i 0.00289414i 0.999999 + 0.00144707i \(0.000460616\pi\)
−0.999999 + 0.00144707i \(0.999539\pi\)
\(434\) 0 0
\(435\) −1.67307 0.235063i −0.0802176 0.0112704i
\(436\) −4.55262 + 7.88538i −0.218031 + 0.377641i
\(437\) −2.89784 + 1.67307i −0.138623 + 0.0800338i
\(438\) 2.58996 1.49532i 0.123753 0.0714490i
\(439\) −11.2143 + 19.4238i −0.535230 + 0.927046i 0.463922 + 0.885876i \(0.346442\pi\)
−0.999152 + 0.0411699i \(0.986892\pi\)
\(440\) −3.18421 0.447375i −0.151801 0.0213278i
\(441\) 0 0
\(442\) 54.1847i 2.57730i
\(443\) −20.7410 11.9748i −0.985434 0.568940i −0.0815275 0.996671i \(-0.525980\pi\)
−0.903906 + 0.427731i \(0.859313\pi\)
\(444\) −6.17484 10.6951i −0.293045 0.507569i
\(445\) 9.58283 3.87218i 0.454270 0.183559i
\(446\) −14.4889 + 25.0954i −0.686068 + 1.18830i
\(447\) 21.2257i 1.00394i
\(448\) 0 0
\(449\) −29.4291 −1.38885 −0.694423 0.719567i \(-0.744340\pi\)
−0.694423 + 0.719567i \(0.744340\pi\)
\(450\) 6.61098 + 6.84473i 0.311645 + 0.322664i
\(451\) 8.23506 + 14.2635i 0.387774 + 0.671644i
\(452\) −15.8554 + 9.15410i −0.745773 + 0.430572i
\(453\) −14.5988 8.42864i −0.685913 0.396012i
\(454\) −27.3461 −1.28342
\(455\) 0 0
\(456\) 1.74620 0.0817733
\(457\) 2.72168 + 1.57136i 0.127315 + 0.0735051i 0.562305 0.826930i \(-0.309915\pi\)
−0.434990 + 0.900435i \(0.643248\pi\)
\(458\) −9.25126 + 5.34122i −0.432283 + 0.249579i
\(459\) −2.21432 3.83531i −0.103356 0.179017i
\(460\) −3.07676 + 3.93841i −0.143455 + 0.183629i
\(461\) −3.37778 −0.157319 −0.0786596 0.996902i \(-0.525064\pi\)
−0.0786596 + 0.996902i \(0.525064\pi\)
\(462\) 0 0
\(463\) 20.8573i 0.969320i −0.874703 0.484660i \(-0.838943\pi\)
0.874703 0.484660i \(-0.161057\pi\)
\(464\) −1.74266 + 3.01838i −0.0809010 + 0.140125i
\(465\) −4.34298 10.7480i −0.201401 0.498425i
\(466\) 22.1590 + 38.3805i 1.02650 + 1.77794i
\(467\) 12.4434 + 7.18421i 0.575813 + 0.332446i 0.759467 0.650545i \(-0.225460\pi\)
−0.183655 + 0.982991i \(0.558793\pi\)
\(468\) 10.4286i 0.482064i
\(469\) 0 0
\(470\) 1.63158 11.6128i 0.0752593 0.535661i
\(471\) −5.21432 + 9.03147i −0.240263 + 0.416148i
\(472\) 8.78079 5.06959i 0.404169 0.233347i
\(473\) −17.4967 + 10.1017i −0.804498 + 0.464477i
\(474\) −4.62222 + 8.00591i −0.212305 + 0.367724i
\(475\) −11.6731 3.34614i −0.535597 0.153532i
\(476\) 0 0
\(477\) 9.18421i 0.420516i
\(478\) 13.9916 + 8.07805i 0.639961 + 0.369482i
\(479\) 3.18421 + 5.51521i 0.145490 + 0.251996i 0.929556 0.368682i \(-0.120191\pi\)
−0.784066 + 0.620678i \(0.786857\pi\)
\(480\) 15.2199 6.14998i 0.694690 0.280707i
\(481\) 24.4701 42.3835i 1.11574 1.93252i
\(482\) 13.7877i 0.628012i
\(483\) 0 0
\(484\) 11.3555 0.516160
\(485\) 16.4361 21.0391i 0.746327 0.955337i
\(486\) −0.951606 1.64823i −0.0431657 0.0747652i
\(487\) 15.0060 8.66370i 0.679986 0.392590i −0.119864 0.992790i \(-0.538246\pi\)
0.799850 + 0.600200i \(0.204913\pi\)
\(488\) 4.26986 + 2.46520i 0.193287 + 0.111595i
\(489\) 20.8573 0.943199
\(490\) 0 0
\(491\) 2.00000 0.0902587 0.0451294 0.998981i \(-0.485630\pi\)
0.0451294 + 0.998981i \(0.485630\pi\)
\(492\) −11.5693 6.67952i −0.521583 0.301136i
\(493\) −2.89784 + 1.67307i −0.130512 + 0.0753513i
\(494\) −14.8573 25.7336i −0.668461 1.15781i
\(495\) −3.52421 2.75317i −0.158401 0.123746i
\(496\) −23.9140 −1.07377
\(497\) 0 0
\(498\) 22.1017i 0.990401i
\(499\) 11.6731 20.2184i 0.522558 0.905098i −0.477097 0.878851i \(-0.658311\pi\)
0.999655 0.0262471i \(-0.00835568\pi\)
\(500\) −18.0373 + 1.89809i −0.806654 + 0.0848852i
\(501\) 7.67307 + 13.2901i 0.342808 + 0.593760i
\(502\) 45.5123 + 26.2766i 2.03131 + 1.17278i
\(503\) 0.387152i 0.0172623i −0.999963 0.00863113i \(-0.997253\pi\)
0.999963 0.00863113i \(-0.00274741\pi\)
\(504\) 0 0
\(505\) 0.460282 3.27607i 0.0204823 0.145783i
\(506\) 2.62222 4.54181i 0.116572 0.201908i
\(507\) −24.5323 + 14.1637i −1.08952 + 0.629032i
\(508\) 18.0629 10.4286i 0.801413 0.462696i
\(509\) −14.9748 + 25.9371i −0.663747 + 1.14964i 0.315877 + 0.948800i \(0.397701\pi\)
−0.979623 + 0.200843i \(0.935632\pi\)
\(510\) 18.6637 + 2.62222i 0.826443 + 0.116114i
\(511\) 0 0
\(512\) 27.2306i 1.20343i
\(513\) 2.10326 + 1.21432i 0.0928614 + 0.0536135i
\(514\) 0.407896 + 0.706496i 0.0179915 + 0.0311622i
\(515\) −7.42003 18.3630i −0.326966 0.809171i
\(516\) 8.19358 14.1917i 0.360702 0.624754i
\(517\) 5.51114i 0.242380i
\(518\) 0 0
\(519\) 2.06022 0.0904338
\(520\) 8.14482 + 6.36288i 0.357174 + 0.279031i
\(521\) 9.26025 + 16.0392i 0.405699 + 0.702691i 0.994403 0.105658i \(-0.0336948\pi\)
−0.588704 + 0.808349i \(0.700361\pi\)
\(522\) −1.24535 + 0.719004i −0.0545075 + 0.0314699i
\(523\) −3.46410 2.00000i −0.151475 0.0874539i 0.422347 0.906434i \(-0.361206\pi\)
−0.573822 + 0.818980i \(0.694540\pi\)
\(524\) 3.40943 0.148942
\(525\) 0 0
\(526\) 17.8479 0.778206
\(527\) −19.8831 11.4795i −0.866120 0.500055i
\(528\) −7.98969 + 4.61285i −0.347706 + 0.200748i
\(529\) −10.5509 18.2746i −0.458733 0.794549i
\(530\) −30.8007 24.0620i −1.33790 1.04519i
\(531\) 14.1017 0.611962
\(532\) 0 0
\(533\) 52.9403i 2.29310i
\(534\) 4.39853 7.61847i 0.190343 0.329684i
\(535\) −1.47854 3.65909i −0.0639231 0.158196i
\(536\) −0.990632 1.71583i −0.0427888 0.0741124i
\(537\) 8.66025 + 5.00000i 0.373718 + 0.215766i
\(538\) 3.32339i 0.143282i
\(539\) 0 0
\(540\) 3.59210 + 0.504684i 0.154580 + 0.0217181i
\(541\) −7.29529 + 12.6358i −0.313649 + 0.543256i −0.979149 0.203142i \(-0.934885\pi\)
0.665501 + 0.746397i \(0.268218\pi\)
\(542\) 4.44255 2.56491i 0.190824 0.110172i
\(543\) −10.4804 + 6.05086i −0.449757 + 0.259667i
\(544\) 16.2558 28.1559i 0.696962 1.20717i
\(545\) −1.74620 + 12.4286i −0.0747990 + 0.532384i
\(546\) 0 0
\(547\) 18.7556i 0.801930i −0.916093 0.400965i \(-0.868675\pi\)
0.916093 0.400965i \(-0.131325\pi\)
\(548\) 22.3935 + 12.9289i 0.956602 + 0.552294i
\(549\) 3.42864 + 5.93858i 0.146331 + 0.253452i
\(550\) 18.4664 4.60583i 0.787410 0.196393i
\(551\) 0.917502 1.58916i 0.0390869 0.0677005i
\(552\) 0.990632i 0.0421641i
\(553\) 0 0
\(554\) −9.75203 −0.414324
\(555\) −13.4146 10.4797i −0.569419 0.444841i
\(556\) −9.46812 16.3993i −0.401538 0.695484i
\(557\) 27.6059 15.9382i 1.16970 0.675325i 0.216089 0.976374i \(-0.430670\pi\)
0.953609 + 0.301049i \(0.0973366\pi\)
\(558\) −8.54477 4.93332i −0.361729 0.208844i
\(559\) 64.9403 2.74668
\(560\) 0 0
\(561\) −8.85728 −0.373955
\(562\) 39.5266 + 22.8207i 1.66733 + 0.962634i
\(563\) 1.74828 1.00937i 0.0736811 0.0425398i −0.462707 0.886511i \(-0.653122\pi\)
0.536388 + 0.843972i \(0.319788\pi\)
\(564\) −2.23506 3.87124i −0.0941131 0.163009i
\(565\) −15.5361 + 19.8870i −0.653607 + 0.836650i
\(566\) −4.50760 −0.189468
\(567\) 0 0
\(568\) 1.43801i 0.0603375i
\(569\) −14.4795 + 25.0792i −0.607012 + 1.05138i 0.384718 + 0.923034i \(0.374299\pi\)
−0.991730 + 0.128341i \(0.959035\pi\)
\(570\) −9.58283 + 3.87218i −0.401381 + 0.162188i
\(571\) −4.48886 7.77494i −0.187853 0.325371i 0.756681 0.653784i \(-0.226820\pi\)
−0.944534 + 0.328413i \(0.893486\pi\)
\(572\) 18.0629 + 10.4286i 0.755249 + 0.436043i
\(573\) 0.488863i 0.0204225i
\(574\) 0 0
\(575\) −1.89829 + 6.62222i −0.0791642 + 0.276165i
\(576\) 2.37310 4.11033i 0.0988792 0.171264i
\(577\) 24.8347 14.3383i 1.03388 0.596911i 0.115787 0.993274i \(-0.463061\pi\)
0.918094 + 0.396363i \(0.129728\pi\)
\(578\) 4.30657 2.48640i 0.179130 0.103421i
\(579\) 11.4795 19.8831i 0.477072 0.826312i
\(580\) 0.381323 2.71408i 0.0158336 0.112696i
\(581\) 0 0
\(582\) 22.7239i 0.941937i
\(583\) 15.9075 + 9.18421i 0.658822 + 0.380371i
\(584\) −0.564907 0.978448i −0.0233760 0.0404885i
\(585\) 5.38548 + 13.3279i 0.222662 + 0.551042i
\(586\) 8.02074 13.8923i 0.331334 0.573887i
\(587\) 45.2070i 1.86589i 0.360018 + 0.932945i \(0.382771\pi\)
−0.360018 + 0.932945i \(0.617229\pi\)
\(588\) 0 0
\(589\) 12.5906 0.518786
\(590\) −36.9456 + 47.2923i −1.52103 + 1.94699i
\(591\) −0.592104 1.02555i −0.0243559 0.0421857i
\(592\) −30.4121 + 17.5585i −1.24993 + 0.721648i
\(593\) −15.8168 9.13182i −0.649517 0.374999i 0.138754 0.990327i \(-0.455690\pi\)
−0.788271 + 0.615328i \(0.789024\pi\)
\(594\) −3.80642 −0.156179
\(595\) 0 0
\(596\) −34.4327 −1.41042
\(597\) 7.61847 + 4.39853i 0.311803 + 0.180020i
\(598\) −14.5988 + 8.42864i −0.596991 + 0.344673i
\(599\) −11.3684 19.6907i −0.464501 0.804539i 0.534678 0.845056i \(-0.320433\pi\)
−0.999179 + 0.0405167i \(0.987100\pi\)
\(600\) 2.58583 2.49753i 0.105566 0.101961i
\(601\) 0.488863 0.0199411 0.00997056 0.999950i \(-0.496826\pi\)
0.00997056 + 0.999950i \(0.496826\pi\)
\(602\) 0 0
\(603\) 2.75557i 0.112215i
\(604\) 13.6731 23.6825i 0.556349 0.963625i
\(605\) 14.5125 5.86413i 0.590016 0.238411i
\(606\) −1.40790 2.43855i −0.0571919 0.0990592i
\(607\) −17.4967 10.1017i −0.710168 0.410016i 0.100955 0.994891i \(-0.467810\pi\)
−0.811123 + 0.584875i \(0.801143\pi\)
\(608\) 17.8292i 0.723069i
\(609\) 0 0
\(610\) −28.8988 4.06022i −1.17008 0.164394i
\(611\) 8.85728 15.3413i 0.358327 0.620641i
\(612\) 6.22171 3.59210i 0.251498 0.145202i
\(613\) 8.97931 5.18421i 0.362671 0.209388i −0.307581 0.951522i \(-0.599519\pi\)
0.670252 + 0.742134i \(0.266186\pi\)
\(614\) 21.4795 37.2036i 0.866842 1.50141i
\(615\) −18.2351 2.56199i −0.735309 0.103310i
\(616\) 0 0
\(617\) 39.2859i 1.58159i 0.612080 + 0.790796i \(0.290333\pi\)
−0.612080 + 0.790796i \(0.709667\pi\)
\(618\) −14.5988 8.42864i −0.587251 0.339050i
\(619\) 21.4494 + 37.1514i 0.862123 + 1.49324i 0.869875 + 0.493272i \(0.164199\pi\)
−0.00775178 + 0.999970i \(0.502467\pi\)
\(620\) 17.4355 7.04525i 0.700227 0.282944i
\(621\) 0.688892 1.19320i 0.0276443 0.0478813i
\(622\) 45.8350i 1.83782i
\(623\) 0 0
\(624\) 29.6543 1.18712
\(625\) −22.0717 + 11.7405i −0.882869 + 0.469619i
\(626\) 9.18712 + 15.9126i 0.367191 + 0.635994i
\(627\) 4.20653 2.42864i 0.167993 0.0969905i
\(628\) −14.6510 8.45875i −0.584638 0.337541i
\(629\) −33.7146 −1.34429
\(630\) 0 0
\(631\) 15.3461 0.610920 0.305460 0.952205i \(-0.401190\pi\)
0.305460 + 0.952205i \(0.401190\pi\)
\(632\) 3.02451 + 1.74620i 0.120308 + 0.0694601i
\(633\) 20.1140 11.6128i 0.799461 0.461569i
\(634\) 5.74912 + 9.95776i 0.228327 + 0.395473i
\(635\) 17.6992 22.6559i 0.702370 0.899070i
\(636\) −14.8988 −0.590775
\(637\) 0 0
\(638\) 2.87601i 0.113863i
\(639\) 1.00000 1.73205i 0.0395594 0.0685189i
\(640\) −4.73270 11.7124i −0.187076 0.462974i
\(641\) −15.3368 26.5641i −0.605766 1.04922i −0.991930 0.126787i \(-0.959533\pi\)
0.386164 0.922430i \(-0.373800\pi\)
\(642\) −2.90902 1.67952i −0.114810 0.0662855i
\(643\) 49.0607i 1.93477i −0.253320 0.967383i \(-0.581523\pi\)
0.253320 0.967383i \(-0.418477\pi\)
\(644\) 0 0
\(645\) 3.14272 22.3684i 0.123745 0.880756i
\(646\) −10.2351 + 17.7276i −0.402693 + 0.697485i
\(647\) 13.2901 7.67307i 0.522490 0.301660i −0.215463 0.976512i \(-0.569126\pi\)
0.737953 + 0.674852i \(0.235793\pi\)
\(648\) −0.622675 + 0.359502i −0.0244610 + 0.0141226i
\(649\) 14.1017 24.4249i 0.553541 0.958760i
\(650\) −58.8069 16.8573i −2.30660 0.661197i
\(651\) 0 0
\(652\) 33.8350i 1.32508i
\(653\) 16.8612 + 9.73483i 0.659830 + 0.380953i 0.792212 0.610246i \(-0.208929\pi\)
−0.132382 + 0.991199i \(0.542263\pi\)
\(654\) 5.34122 + 9.25126i 0.208858 + 0.361753i
\(655\) 4.35729 1.76067i 0.170253 0.0687951i
\(656\) −18.9935 + 32.8978i −0.741573 + 1.28444i
\(657\) 1.57136i 0.0613046i
\(658\) 0 0
\(659\) −30.9403 −1.20526 −0.602631 0.798020i \(-0.705881\pi\)
−0.602631 + 0.798020i \(0.705881\pi\)
\(660\) 4.46624 5.71702i 0.173848 0.222535i
\(661\) −23.8988 41.3939i −0.929554 1.61004i −0.784068 0.620675i \(-0.786859\pi\)
−0.145486 0.989360i \(-0.546475\pi\)
\(662\) −22.2695 + 12.8573i −0.865527 + 0.499712i
\(663\) 24.6559 + 14.2351i 0.957554 + 0.552844i
\(664\) −8.34968 −0.324030
\(665\) 0 0
\(666\) −14.4889 −0.561432
\(667\) −0.901542 0.520505i −0.0349078 0.0201540i
\(668\) −21.5595 + 12.4474i −0.834162 + 0.481603i
\(669\) 7.61285 + 13.1858i 0.294330 + 0.509794i
\(670\) 9.24123 + 7.21942i 0.357020 + 0.278910i
\(671\) 13.7146 0.529445
\(672\) 0 0
\(673\) 27.8163i 1.07224i 0.844142 + 0.536119i \(0.180110\pi\)
−0.844142 + 0.536119i \(0.819890\pi\)
\(674\) −9.98126 + 17.2881i −0.384464 + 0.665911i
\(675\) 4.85138 1.21002i 0.186730 0.0465735i
\(676\) −22.9766 39.7966i −0.883715 1.53064i
\(677\) −16.4549 9.50024i −0.632413 0.365124i 0.149273 0.988796i \(-0.452307\pi\)
−0.781686 + 0.623672i \(0.785640\pi\)
\(678\) 21.4795i 0.824915i
\(679\) 0 0
\(680\) 0.990632 7.05086i 0.0379890 0.270388i
\(681\) −7.18421 + 12.4434i −0.275299 + 0.476833i
\(682\) −17.0895 + 9.86665i −0.654392 + 0.377813i
\(683\) 3.91487 2.26025i 0.149798 0.0864862i −0.423227 0.906024i \(-0.639103\pi\)
0.573026 + 0.819537i \(0.305769\pi\)
\(684\) −1.96989 + 3.41195i −0.0753206 + 0.130459i
\(685\) 35.2958 + 4.95899i 1.34858 + 0.189473i
\(686\) 0 0
\(687\) 5.61285i 0.214143i
\(688\) −40.3547 23.2988i −1.53851 0.888259i
\(689\) −29.5210 51.1318i −1.12466 1.94797i
\(690\) 2.19672 + 5.43641i 0.0836275 + 0.206960i
\(691\) 0.592104 1.02555i 0.0225247 0.0390139i −0.854543 0.519380i \(-0.826163\pi\)
0.877068 + 0.480366i \(0.159496\pi\)
\(692\) 3.34213i 0.127049i
\(693\) 0 0
\(694\) −31.8292 −1.20822
\(695\) −20.5692 16.0690i −0.780233 0.609532i
\(696\) 0.271628 + 0.470474i 0.0102960 + 0.0178333i
\(697\) −31.5841 + 18.2351i −1.19633 + 0.690702i
\(698\) 26.9789 + 15.5763i 1.02117 + 0.589571i
\(699\) 23.2859 0.880754
\(700\) 0 0
\(701\) −26.6735 −1.00745 −0.503723 0.863865i \(-0.668037\pi\)
−0.503723 + 0.863865i \(0.668037\pi\)
\(702\) 10.5959 + 6.11753i 0.399916 + 0.230891i
\(703\) 16.0118 9.24443i 0.603897 0.348660i
\(704\) −4.74620 8.22066i −0.178879 0.309828i
\(705\) −4.85560 3.79328i −0.182872 0.142863i
\(706\) −1.04503 −0.0393301
\(707\) 0 0
\(708\) 22.8760i 0.859733i
\(709\) −9.10171 + 15.7646i −0.341822 + 0.592053i −0.984771 0.173856i \(-0.944377\pi\)
0.642949 + 0.765909i \(0.277711\pi\)
\(710\) 3.18877 + 7.89152i 0.119672 + 0.296163i
\(711\) 2.42864 + 4.20653i 0.0910811 + 0.157757i
\(712\) −2.87814 1.66170i −0.107863 0.0622747i
\(713\) 7.14272i 0.267497i
\(714\) 0 0
\(715\) 28.4701 + 4.00000i 1.06472 + 0.149592i
\(716\) −8.11108 + 14.0488i −0.303125 + 0.525028i
\(717\) 7.35157 4.24443i 0.274549 0.158511i
\(718\) −0.470474 + 0.271628i −0.0175579 + 0.0101371i
\(719\) 2.42864 4.20653i 0.0905730 0.156877i −0.817179 0.576383i \(-0.804463\pi\)
0.907752 + 0.419506i \(0.137797\pi\)
\(720\) 1.43509 10.2143i 0.0534828 0.380665i
\(721\) 0 0
\(722\) 24.9353i 0.927997i
\(723\) 6.27386 + 3.62222i 0.233327 + 0.134712i
\(724\) −9.81579 17.0015i −0.364801 0.631854i
\(725\) −0.914250 3.66555i −0.0339544 0.136135i
\(726\) 6.66124 11.5376i 0.247222 0.428201i
\(727\) 21.0607i 0.781098i −0.920582 0.390549i \(-0.872285\pi\)
0.920582 0.390549i \(-0.127715\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 5.26980 + 4.11687i 0.195044 + 0.152372i
\(731\) −22.3684 38.7432i −0.827326 1.43297i
\(732\) −9.63365 + 5.56199i −0.356070 + 0.205577i
\(733\) −8.18473 4.72546i −0.302310 0.174539i 0.341170 0.940002i \(-0.389177\pi\)
−0.643480 + 0.765463i \(0.722510\pi\)
\(734\) 3.26317 0.120446
\(735\) 0 0
\(736\) 10.1146 0.372830
\(737\) −4.77279 2.75557i −0.175808 0.101503i
\(738\) −13.5733 + 7.83654i −0.499639 + 0.288467i
\(739\) −4.10171 7.10437i −0.150884 0.261338i 0.780669 0.624945i \(-0.214879\pi\)
−0.931553 + 0.363607i \(0.881545\pi\)
\(740\) 17.0004 21.7614i 0.624948 0.799965i
\(741\) −15.6128 −0.573552
\(742\) 0 0
\(743\) 8.33677i 0.305847i 0.988238 + 0.152923i \(0.0488687\pi\)
−0.988238 + 0.152923i \(0.951131\pi\)
\(744\) −1.86373 + 3.22808i −0.0683277 + 0.118347i
\(745\) −44.0053 + 17.7815i −1.61223 + 0.651462i
\(746\) 15.2257 + 26.3717i 0.557452 + 0.965536i
\(747\) −10.0570 5.80642i −0.367967 0.212446i
\(748\) 14.3684i 0.525361i
\(749\) 0 0
\(750\) −8.65233 + 19.4400i −0.315938 + 0.709849i
\(751\) 12.9590 22.4456i 0.472880 0.819053i −0.526638 0.850090i \(-0.676548\pi\)
0.999518 + 0.0310371i \(0.00988099\pi\)
\(752\) −11.0081 + 6.35551i −0.401423 + 0.231762i
\(753\) 23.9134 13.8064i 0.871454 0.503134i
\(754\) 4.62222 8.00591i 0.168331 0.291558i
\(755\) 5.24443 37.3274i 0.190864 1.35848i
\(756\) 0 0
\(757\) 8.94025i 0.324939i −0.986714 0.162470i \(-0.948054\pi\)
0.986714 0.162470i \(-0.0519459\pi\)
\(758\) 8.00591 + 4.62222i 0.290788 + 0.167886i
\(759\) −1.37778 2.38639i −0.0500104 0.0866206i
\(760\) 1.46285 + 3.62024i 0.0530631 + 0.131320i
\(761\) 0.412818 0.715022i 0.0149646 0.0259195i −0.858446 0.512904i \(-0.828570\pi\)
0.873411 + 0.486984i \(0.161903\pi\)
\(762\) 24.4701i 0.886459i
\(763\) 0 0
\(764\) −0.793040 −0.0286912
\(765\) 6.09641 7.80372i 0.220416 0.282144i
\(766\) −7.98126 13.8240i −0.288375 0.499480i
\(767\) −78.5094 + 45.3274i −2.83481 + 1.63668i
\(768\) −17.5322 10.1222i −0.632638 0.365254i
\(769\) −21.2257 −0.765418 −0.382709 0.923869i \(-0.625009\pi\)
−0.382709 + 0.923869i \(0.625009\pi\)
\(770\) 0 0
\(771\) 0.428639 0.0154371
\(772\) 32.2546 + 18.6222i 1.16087 + 0.670228i
\(773\) 25.5385 14.7447i 0.918557 0.530329i 0.0353823 0.999374i \(-0.488735\pi\)
0.883174 + 0.469045i \(0.155402\pi\)
\(774\) −9.61285 16.6499i −0.345527 0.598470i
\(775\) 18.6445 18.0078i 0.669731 0.646860i
\(776\) −8.58474 −0.308174
\(777\) 0 0
\(778\) 17.0509i 0.611303i