Properties

Label 441.2.g.f.79.5
Level $441$
Weight $2$
Character 441.79
Analytic conductor $3.521$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.991381711347.1
Defining polynomial: \(x^{10} - 2 x^{9} + 9 x^{8} - 8 x^{7} + 40 x^{6} - 36 x^{5} + 90 x^{4} - 3 x^{3} + 36 x^{2} - 9 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.5
Root \(1.19343 + 2.06709i\) of defining polynomial
Character \(\chi\) \(=\) 441.79
Dual form 441.2.g.f.67.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.19343 + 2.06709i) q^{2} +(-0.266999 + 1.71135i) q^{3} +(-1.84857 + 3.20182i) q^{4} +2.92087 q^{5} +(-3.85615 + 1.49047i) q^{6} -4.05086 q^{8} +(-2.85742 - 0.913855i) q^{9} +O(q^{10})\) \(q+(1.19343 + 2.06709i) q^{2} +(-0.266999 + 1.71135i) q^{3} +(-1.84857 + 3.20182i) q^{4} +2.92087 q^{5} +(-3.85615 + 1.49047i) q^{6} -4.05086 q^{8} +(-2.85742 - 0.913855i) q^{9} +(3.48586 + 6.03769i) q^{10} -1.35371 q^{11} +(-4.98586 - 4.01843i) q^{12} +(0.733001 + 1.26960i) q^{13} +(-0.779867 + 4.99862i) q^{15} +(-1.13729 - 1.96984i) q^{16} +(-1.65514 - 2.86678i) q^{17} +(-1.52113 - 6.99717i) q^{18} +(1.10329 - 1.91096i) q^{19} +(-5.39943 + 9.35209i) q^{20} +(-1.61557 - 2.79825i) q^{22} +2.62830 q^{23} +(1.08157 - 6.93243i) q^{24} +3.53146 q^{25} +(-1.74958 + 3.03036i) q^{26} +(2.32685 - 4.64605i) q^{27} +(0.521720 - 0.903646i) q^{29} +(-11.2633 + 4.35347i) q^{30} +(1.63729 - 2.83587i) q^{31} +(-1.33629 + 2.31453i) q^{32} +(0.361440 - 2.31668i) q^{33} +(3.95060 - 6.84263i) q^{34} +(8.20815 - 7.45963i) q^{36} +(5.43773 - 9.41842i) q^{37} +5.26683 q^{38} +(-2.36843 + 0.915440i) q^{39} -11.8320 q^{40} +(0.904289 + 1.56627i) q^{41} +(-2.17129 + 3.76078i) q^{43} +(2.50244 - 4.33435i) q^{44} +(-8.34615 - 2.66925i) q^{45} +(3.13670 + 5.43292i) q^{46} +(1.98957 + 3.44604i) q^{47} +(3.67474 - 1.42035i) q^{48} +(4.21456 + 7.29984i) q^{50} +(5.34798 - 2.06709i) q^{51} -5.42002 q^{52} +(-3.22743 - 5.59008i) q^{53} +(12.3807 - 0.734945i) q^{54} -3.95402 q^{55} +(2.97574 + 2.39834i) q^{57} +2.49056 q^{58} +(-6.10700 + 10.5776i) q^{59} +(-14.5630 - 11.7373i) q^{60} +(0.279867 + 0.484744i) q^{61} +7.81600 q^{62} -10.9283 q^{64} +(2.14100 + 3.70832i) q^{65} +(5.22013 - 2.01767i) q^{66} +(-6.40588 + 11.0953i) q^{67} +12.2386 q^{68} +(-0.701751 + 4.49793i) q^{69} +12.9177 q^{71} +(11.5750 + 3.70190i) q^{72} +(-5.22772 - 9.05467i) q^{73} +25.9583 q^{74} +(-0.942894 + 6.04355i) q^{75} +(4.07903 + 7.06509i) q^{76} +(-4.71886 - 3.80324i) q^{78} +(-0.383838 - 0.664827i) q^{79} +(-3.32187 - 5.75365i) q^{80} +(7.32974 + 5.22254i) q^{81} +(-2.15842 + 3.73849i) q^{82} +(0.983707 - 1.70383i) q^{83} +(-4.83443 - 8.37348i) q^{85} -10.3652 q^{86} +(1.40715 + 1.13412i) q^{87} +5.48371 q^{88} +(-3.20356 + 5.54872i) q^{89} +(-4.44301 - 20.4378i) q^{90} +(-4.85859 + 8.41533i) q^{92} +(4.41601 + 3.55915i) q^{93} +(-4.74884 + 8.22524i) q^{94} +(3.22257 - 5.58166i) q^{95} +(-3.60418 - 2.90484i) q^{96} +(4.14143 - 7.17316i) q^{97} +(3.86814 + 1.23710i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{2} - 2q^{3} - 4q^{4} + 8q^{5} + 2q^{6} - 6q^{8} - 4q^{9} + O(q^{10}) \) \( 10q + 2q^{2} - 2q^{3} - 4q^{4} + 8q^{5} + 2q^{6} - 6q^{8} - 4q^{9} + 7q^{10} - 8q^{11} - 22q^{12} + 8q^{13} - 19q^{15} + 2q^{16} - 12q^{17} - 2q^{18} - q^{19} - 5q^{20} - q^{22} - 6q^{23} - 3q^{24} + 2q^{25} - 11q^{26} + 7q^{27} + 7q^{29} - 26q^{30} + 3q^{31} - 2q^{32} + q^{33} - 3q^{34} + 34q^{36} + 40q^{38} + 20q^{39} - 6q^{40} - 5q^{41} - 7q^{43} - 10q^{44} + q^{45} + 3q^{46} - 27q^{47} + 5q^{48} + 19q^{50} + 24q^{51} - 20q^{52} - 21q^{53} + 53q^{54} - 4q^{55} - 4q^{57} + 20q^{58} - 30q^{59} - 41q^{60} + 14q^{61} + 12q^{62} - 50q^{64} - 11q^{65} + 41q^{66} - 2q^{67} + 54q^{68} - 15q^{69} - 6q^{71} + 48q^{72} - 15q^{73} + 72q^{74} - 31q^{75} - 5q^{76} - 20q^{78} - 4q^{79} - 20q^{80} + 8q^{81} + 5q^{82} - 9q^{83} - 6q^{85} + 16q^{86} - 32q^{87} + 36q^{88} - 28q^{89} - 28q^{90} + 27q^{92} - 12q^{93} + 3q^{94} - 14q^{95} + q^{96} + 12q^{97} + 35q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.19343 + 2.06709i 0.843886 + 1.46165i 0.886585 + 0.462565i \(0.153071\pi\)
−0.0426999 + 0.999088i \(0.513596\pi\)
\(3\) −0.266999 + 1.71135i −0.154152 + 0.988047i
\(4\) −1.84857 + 3.20182i −0.924286 + 1.60091i
\(5\) 2.92087 1.30625 0.653125 0.757250i \(-0.273457\pi\)
0.653125 + 0.757250i \(0.273457\pi\)
\(6\) −3.85615 + 1.49047i −1.57427 + 0.608483i
\(7\) 0 0
\(8\) −4.05086 −1.43219
\(9\) −2.85742 0.913855i −0.952475 0.304618i
\(10\) 3.48586 + 6.03769i 1.10233 + 1.90929i
\(11\) −1.35371 −0.408160 −0.204080 0.978954i \(-0.565420\pi\)
−0.204080 + 0.978954i \(0.565420\pi\)
\(12\) −4.98586 4.01843i −1.43929 1.16002i
\(13\) 0.733001 + 1.26960i 0.203298 + 0.352123i 0.949589 0.313497i \(-0.101501\pi\)
−0.746291 + 0.665620i \(0.768167\pi\)
\(14\) 0 0
\(15\) −0.779867 + 4.99862i −0.201361 + 1.29064i
\(16\) −1.13729 1.96984i −0.284323 0.492461i
\(17\) −1.65514 2.86678i −0.401430 0.695297i 0.592469 0.805593i \(-0.298153\pi\)
−0.993899 + 0.110297i \(0.964820\pi\)
\(18\) −1.52113 6.99717i −0.358533 1.64925i
\(19\) 1.10329 1.91096i 0.253113 0.438404i −0.711268 0.702921i \(-0.751879\pi\)
0.964381 + 0.264516i \(0.0852123\pi\)
\(20\) −5.39943 + 9.35209i −1.20735 + 2.09119i
\(21\) 0 0
\(22\) −1.61557 2.79825i −0.344441 0.596589i
\(23\) 2.62830 0.548038 0.274019 0.961724i \(-0.411647\pi\)
0.274019 + 0.961724i \(0.411647\pi\)
\(24\) 1.08157 6.93243i 0.220775 1.41508i
\(25\) 3.53146 0.706292
\(26\) −1.74958 + 3.03036i −0.343121 + 0.594302i
\(27\) 2.32685 4.64605i 0.447803 0.894132i
\(28\) 0 0
\(29\) 0.521720 0.903646i 0.0968810 0.167803i −0.813511 0.581549i \(-0.802447\pi\)
0.910392 + 0.413747i \(0.135780\pi\)
\(30\) −11.2633 + 4.35347i −2.05639 + 0.794831i
\(31\) 1.63729 2.83587i 0.294066 0.509337i −0.680701 0.732561i \(-0.738325\pi\)
0.974767 + 0.223224i \(0.0716581\pi\)
\(32\) −1.33629 + 2.31453i −0.236226 + 0.409155i
\(33\) 0.361440 2.31668i 0.0629186 0.403282i
\(34\) 3.95060 6.84263i 0.677521 1.17350i
\(35\) 0 0
\(36\) 8.20815 7.45963i 1.36803 1.24327i
\(37\) 5.43773 9.41842i 0.893957 1.54838i 0.0588664 0.998266i \(-0.481251\pi\)
0.835090 0.550113i \(-0.185415\pi\)
\(38\) 5.26683 0.854393
\(39\) −2.36843 + 0.915440i −0.379252 + 0.146588i
\(40\) −11.8320 −1.87081
\(41\) 0.904289 + 1.56627i 0.141226 + 0.244611i 0.927959 0.372683i \(-0.121562\pi\)
−0.786732 + 0.617294i \(0.788229\pi\)
\(42\) 0 0
\(43\) −2.17129 + 3.76078i −0.331118 + 0.573514i −0.982731 0.185038i \(-0.940759\pi\)
0.651613 + 0.758551i \(0.274093\pi\)
\(44\) 2.50244 4.33435i 0.377257 0.653428i
\(45\) −8.34615 2.66925i −1.24417 0.397908i
\(46\) 3.13670 + 5.43292i 0.462481 + 0.801041i
\(47\) 1.98957 + 3.44604i 0.290209 + 0.502656i 0.973859 0.227154i \(-0.0729419\pi\)
−0.683650 + 0.729810i \(0.739609\pi\)
\(48\) 3.67474 1.42035i 0.530404 0.205010i
\(49\) 0 0
\(50\) 4.21456 + 7.29984i 0.596029 + 1.03235i
\(51\) 5.34798 2.06709i 0.748867 0.289450i
\(52\) −5.42002 −0.751622
\(53\) −3.22743 5.59008i −0.443322 0.767856i 0.554612 0.832109i \(-0.312867\pi\)
−0.997934 + 0.0642533i \(0.979533\pi\)
\(54\) 12.3807 0.734945i 1.68481 0.100013i
\(55\) −3.95402 −0.533160
\(56\) 0 0
\(57\) 2.97574 + 2.39834i 0.394146 + 0.317668i
\(58\) 2.49056 0.327026
\(59\) −6.10700 + 10.5776i −0.795064 + 1.37709i 0.127735 + 0.991808i \(0.459229\pi\)
−0.922799 + 0.385283i \(0.874104\pi\)
\(60\) −14.5630 11.7373i −1.88008 1.51528i
\(61\) 0.279867 + 0.484744i 0.0358333 + 0.0620651i 0.883386 0.468646i \(-0.155258\pi\)
−0.847553 + 0.530711i \(0.821925\pi\)
\(62\) 7.81600 0.992632
\(63\) 0 0
\(64\) −10.9283 −1.36604
\(65\) 2.14100 + 3.70832i 0.265558 + 0.459960i
\(66\) 5.22013 2.01767i 0.642554 0.248359i
\(67\) −6.40588 + 11.0953i −0.782603 + 1.35551i 0.147817 + 0.989015i \(0.452775\pi\)
−0.930420 + 0.366494i \(0.880558\pi\)
\(68\) 12.2386 1.48414
\(69\) −0.701751 + 4.49793i −0.0844809 + 0.541487i
\(70\) 0 0
\(71\) 12.9177 1.53305 0.766525 0.642214i \(-0.221984\pi\)
0.766525 + 0.642214i \(0.221984\pi\)
\(72\) 11.5750 + 3.70190i 1.36413 + 0.436273i
\(73\) −5.22772 9.05467i −0.611858 1.05977i −0.990927 0.134401i \(-0.957089\pi\)
0.379069 0.925368i \(-0.376244\pi\)
\(74\) 25.9583 3.01759
\(75\) −0.942894 + 6.04355i −0.108876 + 0.697849i
\(76\) 4.07903 + 7.06509i 0.467897 + 0.810422i
\(77\) 0 0
\(78\) −4.71886 3.80324i −0.534306 0.430632i
\(79\) −0.383838 0.664827i −0.0431852 0.0747989i 0.843625 0.536933i \(-0.180417\pi\)
−0.886810 + 0.462134i \(0.847084\pi\)
\(80\) −3.32187 5.75365i −0.371397 0.643278i
\(81\) 7.32974 + 5.22254i 0.814415 + 0.580282i
\(82\) −2.15842 + 3.73849i −0.238358 + 0.412847i
\(83\) 0.983707 1.70383i 0.107976 0.187020i −0.806974 0.590587i \(-0.798896\pi\)
0.914950 + 0.403567i \(0.132230\pi\)
\(84\) 0 0
\(85\) −4.83443 8.37348i −0.524368 0.908232i
\(86\) −10.3652 −1.11770
\(87\) 1.40715 + 1.13412i 0.150863 + 0.121590i
\(88\) 5.48371 0.584565
\(89\) −3.20356 + 5.54872i −0.339576 + 0.588163i −0.984353 0.176208i \(-0.943617\pi\)
0.644777 + 0.764371i \(0.276950\pi\)
\(90\) −4.44301 20.4378i −0.468335 2.15433i
\(91\) 0 0
\(92\) −4.85859 + 8.41533i −0.506543 + 0.877359i
\(93\) 4.41601 + 3.55915i 0.457919 + 0.369066i
\(94\) −4.74884 + 8.22524i −0.489806 + 0.848369i
\(95\) 3.22257 5.58166i 0.330629 0.572666i
\(96\) −3.60418 2.90484i −0.367850 0.296474i
\(97\) 4.14143 7.17316i 0.420498 0.728324i −0.575490 0.817809i \(-0.695189\pi\)
0.995988 + 0.0894847i \(0.0285220\pi\)
\(98\) 0 0
\(99\) 3.86814 + 1.23710i 0.388762 + 0.124333i
\(100\) −6.52815 + 11.3071i −0.652815 + 1.13071i
\(101\) 16.2266 1.61461 0.807305 0.590134i \(-0.200925\pi\)
0.807305 + 0.590134i \(0.200925\pi\)
\(102\) 10.6553 + 8.58782i 1.05503 + 0.850320i
\(103\) 2.22683 0.219416 0.109708 0.993964i \(-0.465008\pi\)
0.109708 + 0.993964i \(0.465008\pi\)
\(104\) −2.96929 5.14295i −0.291162 0.504308i
\(105\) 0 0
\(106\) 7.70346 13.3428i 0.748226 1.29597i
\(107\) −8.75403 + 15.1624i −0.846284 + 1.46581i 0.0382175 + 0.999269i \(0.487832\pi\)
−0.884501 + 0.466537i \(0.845501\pi\)
\(108\) 10.5745 + 16.0387i 1.01753 + 1.54333i
\(109\) −7.79917 13.5086i −0.747025 1.29388i −0.949243 0.314544i \(-0.898148\pi\)
0.202218 0.979341i \(-0.435185\pi\)
\(110\) −4.71886 8.17331i −0.449926 0.779295i
\(111\) 14.6663 + 11.8205i 1.39207 + 1.12196i
\(112\) 0 0
\(113\) −0.844555 1.46281i −0.0794491 0.137610i 0.823563 0.567224i \(-0.191983\pi\)
−0.903012 + 0.429615i \(0.858649\pi\)
\(114\) −1.40624 + 9.01338i −0.131706 + 0.844181i
\(115\) 7.67690 0.715875
\(116\) 1.92887 + 3.34091i 0.179092 + 0.310196i
\(117\) −0.934270 4.29763i −0.0863733 0.397316i
\(118\) −29.1532 −2.68377
\(119\) 0 0
\(120\) 3.15913 20.2487i 0.288388 1.84844i
\(121\) −9.16746 −0.833405
\(122\) −0.668005 + 1.15702i −0.0604784 + 0.104752i
\(123\) −2.92188 + 1.12936i −0.263457 + 0.101831i
\(124\) 6.05330 + 10.4846i 0.543602 + 0.941546i
\(125\) −4.28942 −0.383657
\(126\) 0 0
\(127\) −3.96918 −0.352208 −0.176104 0.984372i \(-0.556350\pi\)
−0.176104 + 0.984372i \(0.556350\pi\)
\(128\) −10.3696 17.9607i −0.916552 1.58751i
\(129\) −5.85627 4.71995i −0.515616 0.415569i
\(130\) −5.11028 + 8.85127i −0.448202 + 0.776308i
\(131\) −5.32863 −0.465565 −0.232782 0.972529i \(-0.574783\pi\)
−0.232782 + 0.972529i \(0.574783\pi\)
\(132\) 6.74944 + 5.43981i 0.587463 + 0.473475i
\(133\) 0 0
\(134\) −30.5800 −2.64171
\(135\) 6.79642 13.5705i 0.584943 1.16796i
\(136\) 6.70473 + 11.6129i 0.574925 + 0.995800i
\(137\) −7.49543 −0.640378 −0.320189 0.947354i \(-0.603746\pi\)
−0.320189 + 0.947354i \(0.603746\pi\)
\(138\) −10.1351 + 3.91740i −0.862758 + 0.333471i
\(139\) −7.03285 12.1812i −0.596518 1.03320i −0.993331 0.115300i \(-0.963217\pi\)
0.396812 0.917900i \(-0.370116\pi\)
\(140\) 0 0
\(141\) −6.42858 + 2.48476i −0.541384 + 0.209255i
\(142\) 15.4164 + 26.7021i 1.29372 + 2.24079i
\(143\) −0.992275 1.71867i −0.0829782 0.143722i
\(144\) 1.44957 + 6.66800i 0.120797 + 0.555667i
\(145\) 1.52388 2.63943i 0.126551 0.219193i
\(146\) 12.4779 21.6123i 1.03268 1.78865i
\(147\) 0 0
\(148\) 20.1041 + 34.8212i 1.65254 + 2.86229i
\(149\) 2.17971 0.178569 0.0892846 0.996006i \(-0.471542\pi\)
0.0892846 + 0.996006i \(0.471542\pi\)
\(150\) −13.6178 + 5.26354i −1.11189 + 0.429766i
\(151\) 14.0277 1.14156 0.570781 0.821102i \(-0.306641\pi\)
0.570781 + 0.821102i \(0.306641\pi\)
\(152\) −4.46929 + 7.74103i −0.362507 + 0.627880i
\(153\) 2.10961 + 9.70416i 0.170552 + 0.784535i
\(154\) 0 0
\(155\) 4.78231 8.28320i 0.384124 0.665322i
\(156\) 1.44714 9.27554i 0.115864 0.742638i
\(157\) 1.48312 2.56883i 0.118365 0.205015i −0.800755 0.598993i \(-0.795568\pi\)
0.919120 + 0.393978i \(0.128901\pi\)
\(158\) 0.916172 1.58686i 0.0728867 0.126243i
\(159\) 10.4283 4.03072i 0.827017 0.319657i
\(160\) −3.90314 + 6.76043i −0.308570 + 0.534459i
\(161\) 0 0
\(162\) −2.04789 + 21.3840i −0.160898 + 1.68008i
\(163\) −0.194278 + 0.336499i −0.0152170 + 0.0263566i −0.873534 0.486764i \(-0.838177\pi\)
0.858317 + 0.513120i \(0.171511\pi\)
\(164\) −6.68657 −0.522133
\(165\) 1.05572 6.76670i 0.0821875 0.526787i
\(166\) 4.69596 0.364477
\(167\) −3.64889 6.32006i −0.282360 0.489061i 0.689606 0.724185i \(-0.257784\pi\)
−0.971965 + 0.235124i \(0.924450\pi\)
\(168\) 0 0
\(169\) 5.42542 9.39710i 0.417340 0.722854i
\(170\) 11.5392 19.9864i 0.885013 1.53289i
\(171\) −4.89892 + 4.45217i −0.374630 + 0.340466i
\(172\) −8.02756 13.9041i −0.612096 1.06018i
\(173\) −2.02754 3.51181i −0.154151 0.266998i 0.778598 0.627522i \(-0.215931\pi\)
−0.932750 + 0.360525i \(0.882598\pi\)
\(174\) −0.664975 + 4.26221i −0.0504116 + 0.323117i
\(175\) 0 0
\(176\) 1.53957 + 2.66661i 0.116049 + 0.201003i
\(177\) −16.4715 13.2754i −1.23807 0.997842i
\(178\) −15.2929 −1.14625
\(179\) 5.29243 + 9.16675i 0.395575 + 0.685155i 0.993174 0.116639i \(-0.0372121\pi\)
−0.597600 + 0.801795i \(0.703879\pi\)
\(180\) 23.9749 21.7886i 1.78698 1.62402i
\(181\) 19.6312 1.45917 0.729586 0.683889i \(-0.239713\pi\)
0.729586 + 0.683889i \(0.239713\pi\)
\(182\) 0 0
\(183\) −0.904289 + 0.349524i −0.0668470 + 0.0258375i
\(184\) −10.6469 −0.784896
\(185\) 15.8829 27.5099i 1.16773 2.02257i
\(186\) −2.08686 + 13.3759i −0.153016 + 0.980768i
\(187\) 2.24058 + 3.88081i 0.163848 + 0.283793i
\(188\) −14.7115 −1.07294
\(189\) 0 0
\(190\) 15.3837 1.11605
\(191\) −4.14357 7.17688i −0.299818 0.519301i 0.676276 0.736648i \(-0.263593\pi\)
−0.976094 + 0.217348i \(0.930259\pi\)
\(192\) 2.91784 18.7021i 0.210577 1.34971i
\(193\) 9.39242 16.2682i 0.676082 1.17101i −0.300070 0.953917i \(-0.597010\pi\)
0.976152 0.217090i \(-0.0696566\pi\)
\(194\) 19.7701 1.41941
\(195\) −6.91787 + 2.67388i −0.495399 + 0.191480i
\(196\) 0 0
\(197\) 5.99634 0.427222 0.213611 0.976919i \(-0.431478\pi\)
0.213611 + 0.976919i \(0.431478\pi\)
\(198\) 2.05917 + 9.47218i 0.146339 + 0.673159i
\(199\) −7.20434 12.4783i −0.510702 0.884562i −0.999923 0.0124022i \(-0.996052\pi\)
0.489221 0.872160i \(-0.337281\pi\)
\(200\) −14.3054 −1.01155
\(201\) −17.2776 13.9251i −1.21867 0.982203i
\(202\) 19.3654 + 33.5419i 1.36255 + 2.36000i
\(203\) 0 0
\(204\) −3.26768 + 20.9444i −0.228783 + 1.46640i
\(205\) 2.64131 + 4.57488i 0.184477 + 0.319523i
\(206\) 2.65758 + 4.60306i 0.185162 + 0.320710i
\(207\) −7.51015 2.40188i −0.521992 0.166942i
\(208\) 1.66727 2.88780i 0.115604 0.200233i
\(209\) −1.49354 + 2.58690i −0.103311 + 0.178939i
\(210\) 0 0
\(211\) −6.92418 11.9930i −0.476680 0.825634i 0.522963 0.852356i \(-0.324827\pi\)
−0.999643 + 0.0267212i \(0.991493\pi\)
\(212\) 23.8646 1.63902
\(213\) −3.44901 + 22.1067i −0.236322 + 1.51473i
\(214\) −41.7894 −2.85667
\(215\) −6.34204 + 10.9847i −0.432523 + 0.749153i
\(216\) −9.42574 + 18.8205i −0.641341 + 1.28057i
\(217\) 0 0
\(218\) 18.6156 32.2431i 1.26081 2.18378i
\(219\) 16.8915 6.52886i 1.14142 0.441179i
\(220\) 7.30929 12.6601i 0.492792 0.853541i
\(221\) 2.42644 4.20271i 0.163220 0.282705i
\(222\) −6.93082 + 44.4237i −0.465166 + 2.98152i
\(223\) −2.33756 + 4.04878i −0.156535 + 0.271126i −0.933617 0.358273i \(-0.883366\pi\)
0.777082 + 0.629399i \(0.216699\pi\)
\(224\) 0 0
\(225\) −10.0909 3.22724i −0.672725 0.215149i
\(226\) 2.01584 3.49154i 0.134092 0.232254i
\(227\) −19.7126 −1.30837 −0.654187 0.756333i \(-0.726989\pi\)
−0.654187 + 0.756333i \(0.726989\pi\)
\(228\) −13.1799 + 5.09428i −0.872862 + 0.337377i
\(229\) −28.0728 −1.85510 −0.927552 0.373694i \(-0.878091\pi\)
−0.927552 + 0.373694i \(0.878091\pi\)
\(230\) 9.16188 + 15.8688i 0.604116 + 1.04636i
\(231\) 0 0
\(232\) −2.11342 + 3.66054i −0.138753 + 0.240326i
\(233\) −6.90113 + 11.9531i −0.452108 + 0.783074i −0.998517 0.0544448i \(-0.982661\pi\)
0.546409 + 0.837518i \(0.315994\pi\)
\(234\) 7.76859 7.06016i 0.507849 0.461537i
\(235\) 5.81127 + 10.0654i 0.379085 + 0.656595i
\(236\) −22.5785 39.1070i −1.46973 2.54565i
\(237\) 1.24024 0.479373i 0.0805619 0.0311386i
\(238\) 0 0
\(239\) 5.53069 + 9.57944i 0.357751 + 0.619642i 0.987585 0.157087i \(-0.0502104\pi\)
−0.629834 + 0.776730i \(0.716877\pi\)
\(240\) 10.7334 4.14866i 0.692840 0.267795i
\(241\) 23.1697 1.49249 0.746247 0.665669i \(-0.231854\pi\)
0.746247 + 0.665669i \(0.231854\pi\)
\(242\) −10.9408 18.9499i −0.703299 1.21815i
\(243\) −10.8946 + 11.1493i −0.698890 + 0.715229i
\(244\) −2.06942 −0.132481
\(245\) 0 0
\(246\) −5.82157 4.69198i −0.371169 0.299150i
\(247\) 3.23486 0.205829
\(248\) −6.63243 + 11.4877i −0.421160 + 0.729470i
\(249\) 2.65320 + 2.13839i 0.168140 + 0.135515i
\(250\) −5.11914 8.86660i −0.323763 0.560773i
\(251\) 7.78402 0.491323 0.245662 0.969356i \(-0.420995\pi\)
0.245662 + 0.969356i \(0.420995\pi\)
\(252\) 0 0
\(253\) −3.55796 −0.223687
\(254\) −4.73696 8.20466i −0.297223 0.514806i
\(255\) 15.6207 6.03769i 0.978208 0.378095i
\(256\) 13.8226 23.9414i 0.863912 1.49634i
\(257\) −10.3760 −0.647235 −0.323618 0.946188i \(-0.604899\pi\)
−0.323618 + 0.946188i \(0.604899\pi\)
\(258\) 2.76748 17.7384i 0.172296 1.10434i
\(259\) 0 0
\(260\) −15.8312 −0.981807
\(261\) −2.31658 + 2.10532i −0.143393 + 0.130316i
\(262\) −6.35937 11.0148i −0.392883 0.680494i
\(263\) −19.1331 −1.17980 −0.589898 0.807478i \(-0.700832\pi\)
−0.589898 + 0.807478i \(0.700832\pi\)
\(264\) −1.46414 + 9.38453i −0.0901117 + 0.577578i
\(265\) −9.42689 16.3279i −0.579090 1.00301i
\(266\) 0 0
\(267\) −8.64045 6.96390i −0.528787 0.426184i
\(268\) −23.6835 41.0210i −1.44670 2.50576i
\(269\) 4.41840 + 7.65290i 0.269395 + 0.466605i 0.968706 0.248212i \(-0.0798430\pi\)
−0.699311 + 0.714818i \(0.746510\pi\)
\(270\) 36.1625 2.14668i 2.20078 0.130643i
\(271\) 9.16955 15.8821i 0.557010 0.964770i −0.440734 0.897638i \(-0.645282\pi\)
0.997744 0.0671321i \(-0.0213849\pi\)
\(272\) −3.76474 + 6.52073i −0.228271 + 0.395377i
\(273\) 0 0
\(274\) −8.94531 15.4937i −0.540406 0.936010i
\(275\) −4.78059 −0.288280
\(276\) −13.1043 10.5616i −0.788787 0.635735i
\(277\) 5.10482 0.306719 0.153360 0.988170i \(-0.450991\pi\)
0.153360 + 0.988170i \(0.450991\pi\)
\(278\) 16.7865 29.0750i 1.00679 1.74381i
\(279\) −7.27001 + 6.60704i −0.435244 + 0.395553i
\(280\) 0 0
\(281\) −0.853180 + 1.47775i −0.0508964 + 0.0881552i −0.890351 0.455274i \(-0.849541\pi\)
0.839455 + 0.543430i \(0.182875\pi\)
\(282\) −12.8083 10.3231i −0.762724 0.614729i
\(283\) −6.24415 + 10.8152i −0.371176 + 0.642896i −0.989747 0.142833i \(-0.954379\pi\)
0.618571 + 0.785729i \(0.287712\pi\)
\(284\) −23.8793 + 41.3602i −1.41698 + 2.45428i
\(285\) 8.69174 + 7.00524i 0.514854 + 0.414954i
\(286\) 2.36843 4.10224i 0.140048 0.242571i
\(287\) 0 0
\(288\) 5.93351 5.39242i 0.349635 0.317751i
\(289\) 3.02104 5.23260i 0.177708 0.307800i
\(290\) 7.27458 0.427178
\(291\) 11.1700 + 9.00264i 0.654798 + 0.527744i
\(292\) 38.6552 2.26213
\(293\) 2.60202 + 4.50684i 0.152012 + 0.263292i 0.931967 0.362543i \(-0.118091\pi\)
−0.779955 + 0.625835i \(0.784758\pi\)
\(294\) 0 0
\(295\) −17.8377 + 30.8959i −1.03855 + 1.79883i
\(296\) −22.0275 + 38.1527i −1.28032 + 2.21758i
\(297\) −3.14989 + 6.28942i −0.182775 + 0.364949i
\(298\) 2.60135 + 4.50566i 0.150692 + 0.261006i
\(299\) 1.92654 + 3.33687i 0.111415 + 0.192976i
\(300\) −17.6074 14.1909i −1.01656 0.819313i
\(301\) 0 0
\(302\) 16.7412 + 28.9966i 0.963347 + 1.66857i
\(303\) −4.33249 + 27.7694i −0.248895 + 1.59531i
\(304\) −5.01906 −0.287863
\(305\) 0.817453 + 1.41587i 0.0468072 + 0.0810725i
\(306\) −17.5417 + 15.9420i −1.00279 + 0.911345i
\(307\) −5.00136 −0.285442 −0.142721 0.989763i \(-0.545585\pi\)
−0.142721 + 0.989763i \(0.545585\pi\)
\(308\) 0 0
\(309\) −0.594560 + 3.81088i −0.0338234 + 0.216793i
\(310\) 22.8295 1.29663
\(311\) −16.1984 + 28.0565i −0.918528 + 1.59094i −0.116876 + 0.993146i \(0.537288\pi\)
−0.801652 + 0.597791i \(0.796045\pi\)
\(312\) 9.59418 3.70832i 0.543163 0.209942i
\(313\) 0.759535 + 1.31555i 0.0429315 + 0.0743595i 0.886693 0.462359i \(-0.152997\pi\)
−0.843761 + 0.536719i \(0.819664\pi\)
\(314\) 7.08000 0.399548
\(315\) 0 0
\(316\) 2.83821 0.159662
\(317\) 10.7544 + 18.6272i 0.604029 + 1.04621i 0.992204 + 0.124623i \(0.0397723\pi\)
−0.388175 + 0.921586i \(0.626894\pi\)
\(318\) 20.7773 + 16.7458i 1.16513 + 0.939058i
\(319\) −0.706261 + 1.22328i −0.0395430 + 0.0684905i
\(320\) −31.9200 −1.78439
\(321\) −23.6109 19.0295i −1.31783 1.06213i
\(322\) 0 0
\(323\) −7.30441 −0.406428
\(324\) −30.2712 + 13.8143i −1.68173 + 0.767459i
\(325\) 2.58856 + 4.48352i 0.143588 + 0.248701i
\(326\) −0.927430 −0.0513656
\(327\) 25.2002 9.74032i 1.39357 0.538641i
\(328\) −3.66315 6.34476i −0.202263 0.350330i
\(329\) 0 0
\(330\) 15.2473 5.89336i 0.839337 0.324419i
\(331\) −9.73902 16.8685i −0.535305 0.927175i −0.999149 0.0412580i \(-0.986863\pi\)
0.463844 0.885917i \(-0.346470\pi\)
\(332\) 3.63691 + 6.29931i 0.199601 + 0.345719i
\(333\) −24.1450 + 21.9431i −1.32314 + 1.20248i
\(334\) 8.70942 15.0852i 0.476558 0.825423i
\(335\) −18.7107 + 32.4079i −1.02228 + 1.77063i
\(336\) 0 0
\(337\) 4.84742 + 8.39598i 0.264056 + 0.457358i 0.967316 0.253575i \(-0.0816063\pi\)
−0.703260 + 0.710933i \(0.748273\pi\)
\(338\) 25.8995 1.40875
\(339\) 2.72888 1.05476i 0.148212 0.0572867i
\(340\) 35.7472 1.93866
\(341\) −2.21642 + 3.83896i −0.120026 + 0.207891i
\(342\) −15.0496 4.81312i −0.813788 0.260264i
\(343\) 0 0
\(344\) 8.79558 15.2344i 0.474226 0.821383i
\(345\) −2.04972 + 13.1378i −0.110353 + 0.707318i
\(346\) 4.83948 8.38222i 0.260172 0.450631i
\(347\) −1.01302 + 1.75460i −0.0543817 + 0.0941919i −0.891935 0.452164i \(-0.850652\pi\)
0.837553 + 0.546356i \(0.183985\pi\)
\(348\) −6.23246 + 2.40896i −0.334095 + 0.129134i
\(349\) −8.14577 + 14.1089i −0.436033 + 0.755231i −0.997379 0.0723497i \(-0.976950\pi\)
0.561346 + 0.827581i \(0.310284\pi\)
\(350\) 0 0
\(351\) 7.60419 0.451400i 0.405882 0.0240939i
\(352\) 1.80896 3.13321i 0.0964180 0.167001i
\(353\) −17.0614 −0.908089 −0.454045 0.890979i \(-0.650019\pi\)
−0.454045 + 0.890979i \(0.650019\pi\)
\(354\) 7.78387 49.8913i 0.413708 2.65169i
\(355\) 37.7309 2.00255
\(356\) −11.8440 20.5144i −0.627731 1.08726i
\(357\) 0 0
\(358\) −12.6323 + 21.8798i −0.667639 + 1.15639i
\(359\) 1.48363 2.56972i 0.0783030 0.135625i −0.824215 0.566277i \(-0.808383\pi\)
0.902518 + 0.430652i \(0.141717\pi\)
\(360\) 33.8091 + 10.8127i 1.78189 + 0.569881i
\(361\) 7.06549 + 12.2378i 0.371868 + 0.644094i
\(362\) 23.4285 + 40.5794i 1.23137 + 2.13280i
\(363\) 2.44770 15.6887i 0.128471 0.823444i
\(364\) 0 0
\(365\) −15.2695 26.4475i −0.799240 1.38432i
\(366\) −1.80171 1.45211i −0.0941767 0.0759031i
\(367\) 10.1575 0.530216 0.265108 0.964219i \(-0.414592\pi\)
0.265108 + 0.964219i \(0.414592\pi\)
\(368\) −2.98914 5.17733i −0.155819 0.269887i
\(369\) −1.15259 5.30190i −0.0600014 0.276006i
\(370\) 75.8207 3.94173
\(371\) 0 0
\(372\) −19.5591 + 7.55992i −1.01409 + 0.391964i
\(373\) −25.4846 −1.31954 −0.659771 0.751467i \(-0.729347\pi\)
−0.659771 + 0.751467i \(0.729347\pi\)
\(374\) −5.34798 + 9.26297i −0.276537 + 0.478977i
\(375\) 1.14527 7.34068i 0.0591414 0.379071i
\(376\) −8.05947 13.9594i −0.415635 0.719902i
\(377\) 1.52969 0.0787829
\(378\) 0 0
\(379\) 9.85497 0.506216 0.253108 0.967438i \(-0.418547\pi\)
0.253108 + 0.967438i \(0.418547\pi\)
\(380\) 11.9143 + 20.6362i 0.611191 + 1.05861i
\(381\) 1.05977 6.79266i 0.0542935 0.347998i
\(382\) 9.89016 17.1303i 0.506025 0.876460i
\(383\) 27.3127 1.39561 0.697806 0.716286i \(-0.254160\pi\)
0.697806 + 0.716286i \(0.254160\pi\)
\(384\) 33.5056 12.9505i 1.70983 0.660878i
\(385\) 0 0
\(386\) 44.8370 2.28214
\(387\) 9.64109 8.76190i 0.490084 0.445392i
\(388\) 15.3114 + 26.5202i 0.777321 + 1.34636i
\(389\) 4.18446 0.212161 0.106080 0.994358i \(-0.466170\pi\)
0.106080 + 0.994358i \(0.466170\pi\)
\(390\) −13.7832 11.1088i −0.697938 0.562513i
\(391\) −4.35019 7.53475i −0.219999 0.381049i
\(392\) 0 0
\(393\) 1.42274 9.11914i 0.0717676 0.460000i
\(394\) 7.15624 + 12.3950i 0.360526 + 0.624450i
\(395\) −1.12114 1.94187i −0.0564107 0.0977062i
\(396\) −11.1115 + 10.0982i −0.558374 + 0.507454i
\(397\) −15.3354 + 26.5618i −0.769664 + 1.33310i 0.168082 + 0.985773i \(0.446243\pi\)
−0.937745 + 0.347323i \(0.887091\pi\)
\(398\) 17.1958 29.7840i 0.861948 1.49294i
\(399\) 0 0
\(400\) −4.01629 6.95642i −0.200815 0.347821i
\(401\) −6.84803 −0.341974 −0.170987 0.985273i \(-0.554696\pi\)
−0.170987 + 0.985273i \(0.554696\pi\)
\(402\) 8.16482 52.3330i 0.407224 2.61014i
\(403\) 4.80055 0.239132
\(404\) −29.9961 + 51.9547i −1.49236 + 2.58485i
\(405\) 21.4092 + 15.2543i 1.06383 + 0.757994i
\(406\) 0 0
\(407\) −7.36113 + 12.7499i −0.364878 + 0.631987i
\(408\) −21.6639 + 8.37348i −1.07252 + 0.414549i
\(409\) −9.13490 + 15.8221i −0.451692 + 0.782353i −0.998491 0.0549104i \(-0.982513\pi\)
0.546799 + 0.837264i \(0.315846\pi\)
\(410\) −6.30445 + 10.9196i −0.311355 + 0.539282i
\(411\) 2.00127 12.8273i 0.0987154 0.632724i
\(412\) −4.11646 + 7.12991i −0.202803 + 0.351265i
\(413\) 0 0
\(414\) −3.99798 18.3906i −0.196490 0.903851i
\(415\) 2.87328 4.97666i 0.141044 0.244295i
\(416\) −3.91802 −0.192097
\(417\) 22.7241 8.78327i 1.11280 0.430119i
\(418\) −7.12979 −0.348729
\(419\) −11.2310 19.4526i −0.548669 0.950322i −0.998366 0.0571410i \(-0.981802\pi\)
0.449698 0.893181i \(-0.351532\pi\)
\(420\) 0 0
\(421\) 10.4177 18.0440i 0.507728 0.879411i −0.492232 0.870464i \(-0.663819\pi\)
0.999960 0.00894684i \(-0.00284791\pi\)
\(422\) 16.5271 28.6258i 0.804527 1.39348i
\(423\) −2.53587 11.6650i −0.123298 0.567170i
\(424\) 13.0739 + 22.6446i 0.634923 + 1.09972i
\(425\) −5.84505 10.1239i −0.283526 0.491082i
\(426\) −49.8127 + 19.2535i −2.41343 + 0.932834i
\(427\) 0 0
\(428\) −32.3649 56.0577i −1.56442 2.70965i
\(429\) 3.20618 1.23925i 0.154796 0.0598313i
\(430\) −30.2752 −1.46000
\(431\) −10.1213 17.5307i −0.487527 0.844422i 0.512370 0.858765i \(-0.328768\pi\)
−0.999897 + 0.0143427i \(0.995434\pi\)
\(432\) −11.7983 + 0.700370i −0.567646 + 0.0336966i
\(433\) 21.6764 1.04170 0.520851 0.853648i \(-0.325615\pi\)
0.520851 + 0.853648i \(0.325615\pi\)
\(434\) 0 0
\(435\) 4.11011 + 3.31260i 0.197065 + 0.158827i
\(436\) 57.6693 2.76186
\(437\) 2.89978 5.02257i 0.138715 0.240262i
\(438\) 33.6546 + 27.1244i 1.60808 + 1.29606i
\(439\) −17.7390 30.7249i −0.846639 1.46642i −0.884191 0.467126i \(-0.845289\pi\)
0.0375520 0.999295i \(-0.488044\pi\)
\(440\) 16.0172 0.763589
\(441\) 0 0
\(442\) 11.5832 0.550955
\(443\) 9.60313 + 16.6331i 0.456258 + 0.790263i 0.998760 0.0497923i \(-0.0158559\pi\)
−0.542501 + 0.840055i \(0.682523\pi\)
\(444\) −64.9590 + 25.1078i −3.08282 + 1.19156i
\(445\) −9.35716 + 16.2071i −0.443572 + 0.768289i
\(446\) −11.1589 −0.528390
\(447\) −0.581980 + 3.73025i −0.0275267 + 0.176435i
\(448\) 0 0
\(449\) −29.6082 −1.39730 −0.698648 0.715465i \(-0.746215\pi\)
−0.698648 + 0.715465i \(0.746215\pi\)
\(450\) −5.37180 24.7102i −0.253229 1.16485i
\(451\) −1.22415 2.12029i −0.0576429 0.0998405i
\(452\) 6.24488 0.293735
\(453\) −3.74539 + 24.0064i −0.175974 + 1.12792i
\(454\) −23.5257 40.7478i −1.10412 1.91239i
\(455\) 0 0
\(456\) −12.0543 9.71534i −0.564494 0.454963i
\(457\) 4.78098 + 8.28090i 0.223645 + 0.387364i 0.955912 0.293653i \(-0.0948711\pi\)
−0.732267 + 0.681017i \(0.761538\pi\)
\(458\) −33.5031 58.0290i −1.56550 2.71152i
\(459\) −17.1705 + 1.01927i −0.801449 + 0.0475756i
\(460\) −14.1913 + 24.5800i −0.661673 + 1.14605i
\(461\) −10.9187 + 18.9118i −0.508536 + 0.880809i 0.491416 + 0.870925i \(0.336480\pi\)
−0.999951 + 0.00988416i \(0.996854\pi\)
\(462\) 0 0
\(463\) 13.0744 + 22.6456i 0.607621 + 1.05243i 0.991631 + 0.129102i \(0.0412094\pi\)
−0.384010 + 0.923329i \(0.625457\pi\)
\(464\) −2.37339 −0.110182
\(465\) 12.8986 + 10.3958i 0.598157 + 0.482093i
\(466\) −32.9442 −1.52611
\(467\) 17.4764 30.2699i 0.808709 1.40073i −0.105049 0.994467i \(-0.533500\pi\)
0.913758 0.406258i \(-0.133167\pi\)
\(468\) 15.4873 + 4.95311i 0.715901 + 0.228958i
\(469\) 0 0
\(470\) −13.8707 + 24.0248i −0.639809 + 1.10818i
\(471\) 4.00017 + 3.22400i 0.184318 + 0.148554i
\(472\) 24.7386 42.8485i 1.13869 1.97226i
\(473\) 2.93930 5.09102i 0.135149 0.234086i
\(474\) 2.47105 + 1.99158i 0.113499 + 0.0914761i
\(475\) 3.89623 6.74848i 0.178771 0.309641i
\(476\) 0 0
\(477\) 4.11362 + 18.9226i 0.188350 + 0.866407i
\(478\) −13.2010 + 22.8649i −0.603801 + 1.04581i
\(479\) 29.8109 1.36209 0.681047 0.732240i \(-0.261525\pi\)
0.681047 + 0.732240i \(0.261525\pi\)
\(480\) −10.5273 8.48465i −0.480504 0.387270i
\(481\) 15.9434 0.726959
\(482\) 27.6516 + 47.8939i 1.25949 + 2.18151i
\(483\) 0 0
\(484\) 16.9467 29.3525i 0.770304 1.33421i
\(485\) 12.0965 20.9518i 0.549276 0.951374i
\(486\) −36.0487 9.21415i −1.63520 0.417962i
\(487\) −11.2253 19.4428i −0.508667 0.881037i −0.999950 0.0100365i \(-0.996805\pi\)
0.491283 0.871000i \(-0.336528\pi\)
\(488\) −1.13370 1.96363i −0.0513202 0.0888892i
\(489\) −0.523994 0.422321i −0.0236958 0.0190980i
\(490\) 0 0
\(491\) 17.5222 + 30.3494i 0.790767 + 1.36965i 0.925493 + 0.378765i \(0.123651\pi\)
−0.134726 + 0.990883i \(0.543016\pi\)
\(492\) 1.78530 11.4430i 0.0804877 0.515893i
\(493\) −3.45407 −0.155564
\(494\) 3.86060 + 6.68675i 0.173696 + 0.300851i
\(495\) 11.2983 + 3.61340i 0.507821 + 0.162410i
\(496\) −7.44830 −0.334438
\(497\) 0 0
\(498\) −1.25381 + 8.03642i −0.0561848 + 0.360121i
\(499\) −8.93520 −0.399994 −0.199997 0.979796i \(-0.564093\pi\)
−0.199997 + 0.979796i \(0.564093\pi\)
\(500\) 7.92929 13.7339i 0.354609 0.614200i
\(501\) 11.7901 4.55707i 0.526742 0.203595i
\(502\) 9.28972 + 16.0903i 0.414621 + 0.718144i
\(503\) 12.6403 0.563603 0.281802 0.959473i \(-0.409068\pi\)
0.281802 + 0.959473i \(0.409068\pi\)
\(504\) 0 0
\(505\) 47.3958 2.10909
\(506\) −4.24620 7.35463i −0.188766 0.326953i
\(507\) 14.6331 + 11.7938i 0.649880 + 0.523781i
\(508\) 7.33732 12.7086i 0.325541 0.563854i
\(509\) 28.1110 1.24600 0.623000 0.782222i \(-0.285914\pi\)
0.623000 + 0.782222i \(0.285914\pi\)
\(510\) 31.1228 + 25.0839i 1.37814 + 1.11073i
\(511\) 0 0
\(512\) 24.5070 1.08307
\(513\) −6.31121 9.57247i −0.278647 0.422635i
\(514\) −12.3830 21.4480i −0.546192 0.946033i
\(515\) 6.50427 0.286613
\(516\) 25.9382 10.0256i 1.14186 0.441351i
\(517\) −2.69331 4.66495i −0.118452 0.205164i
\(518\) 0 0
\(519\) 6.55127 2.53218i 0.287569 0.111150i
\(520\) −8.67288 15.0219i −0.380331 0.658753i
\(521\) −4.23768 7.33988i −0.185656 0.321566i 0.758141 0.652090i \(-0.226108\pi\)
−0.943797 + 0.330524i \(0.892774\pi\)
\(522\) −7.11657 2.27601i −0.311484 0.0996181i
\(523\) −16.7236 + 28.9662i −0.731273 + 1.26660i 0.225066 + 0.974344i \(0.427740\pi\)
−0.956339 + 0.292259i \(0.905593\pi\)
\(524\) 9.85035 17.0613i 0.430315 0.745327i
\(525\) 0 0
\(526\) −22.8341 39.5498i −0.995613 1.72445i
\(527\) −10.8398 −0.472187
\(528\) −4.97456 + 1.92275i −0.216490 + 0.0836771i
\(529\) −16.0921 −0.699655
\(530\) 22.5008 38.9725i 0.977371 1.69286i
\(531\) 27.1167 24.6439i 1.17677 1.06945i
\(532\) 0 0
\(533\) −1.32569 + 2.29616i −0.0574220 + 0.0994579i
\(534\) 4.08319 26.1715i 0.176697 1.13255i
\(535\) −25.5693 + 44.2874i −1.10546 + 1.91471i
\(536\) 25.9493 44.9456i 1.12084 1.94135i
\(537\) −17.1006 + 6.60968i −0.737944 + 0.285229i
\(538\) −10.5461 + 18.2665i −0.454677 + 0.787523i
\(539\) 0 0
\(540\) 30.8866 + 46.8469i 1.32915 + 2.01597i
\(541\) −9.12929 + 15.8124i −0.392499 + 0.679828i −0.992778 0.119962i \(-0.961723\pi\)
0.600280 + 0.799790i \(0.295056\pi\)
\(542\) 43.7730 1.88021
\(543\) −5.24149 + 33.5957i −0.224934 + 1.44173i
\(544\) 8.84701 0.379312
\(545\) −22.7803 39.4567i −0.975802 1.69014i
\(546\) 0 0
\(547\) −2.88599 + 4.99869i −0.123396 + 0.213728i −0.921105 0.389315i \(-0.872712\pi\)
0.797709 + 0.603043i \(0.206045\pi\)
\(548\) 13.8558 23.9990i 0.591892 1.02519i
\(549\) −0.356713 1.64088i −0.0152241 0.0700309i
\(550\) −5.70532 9.88190i −0.243276 0.421366i
\(551\) −1.15122 1.99397i −0.0490437 0.0849461i
\(552\) 2.84269 18.2205i 0.120993 0.775515i
\(553\) 0 0
\(554\) 6.09227 + 10.5521i 0.258836 + 0.448317i
\(555\) 42.8384 + 34.5262i 1.81839 + 1.46556i
\(556\) 52.0029 2.20541
\(557\) 16.6911 + 28.9098i 0.707223 + 1.22495i 0.965883 + 0.258977i \(0.0833855\pi\)
−0.258661 + 0.965968i \(0.583281\pi\)
\(558\) −22.3336 7.14268i −0.945457 0.302374i
\(559\) −6.36623 −0.269263
\(560\) 0 0
\(561\) −7.23964 + 2.79825i −0.305658 + 0.118142i
\(562\) −4.07286 −0.171803
\(563\) 1.09566 1.89773i 0.0461764 0.0799799i −0.842013 0.539457i \(-0.818630\pi\)
0.888190 + 0.459477i \(0.151963\pi\)
\(564\) 3.92794 25.1764i 0.165396 1.06012i
\(565\) −2.46683 4.27268i −0.103780 0.179753i
\(566\) −29.8079 −1.25292
\(567\) 0 0
\(568\) −52.3278 −2.19563
\(569\) −9.49302 16.4424i −0.397968 0.689301i 0.595507 0.803350i \(-0.296951\pi\)
−0.993475 + 0.114049i \(0.963618\pi\)
\(570\) −4.10743 + 26.3269i −0.172041 + 1.10271i
\(571\) 10.8690 18.8257i 0.454854 0.787831i −0.543825 0.839198i \(-0.683025\pi\)
0.998680 + 0.0513674i \(0.0163580\pi\)
\(572\) 7.33717 0.306782
\(573\) 13.3885 5.17488i 0.559311 0.216184i
\(574\) 0 0
\(575\) 9.28172 0.387074
\(576\) 31.2267 + 9.98686i 1.30111 + 0.416119i
\(577\) 15.4516 + 26.7629i 0.643258 + 1.11416i 0.984701 + 0.174253i \(0.0557511\pi\)
−0.341443 + 0.939903i \(0.610916\pi\)
\(578\) 14.4217 0.599862
\(579\) 25.3327 + 20.4173i 1.05279 + 0.848513i
\(580\) 5.63398 + 9.75835i 0.233938 + 0.405193i
\(581\) 0 0
\(582\) −5.27858 + 33.8335i −0.218804 + 1.40244i
\(583\) 4.36902 + 7.56737i 0.180946 + 0.313408i
\(584\) 21.1767 + 36.6792i 0.876299 + 1.51780i
\(585\) −2.72888 12.5528i −0.112825 0.518994i
\(586\) −6.21069 + 10.7572i −0.256561 + 0.444377i
\(587\) 9.18332 15.9060i 0.379036 0.656510i −0.611886 0.790946i \(-0.709589\pi\)
0.990922 + 0.134436i \(0.0429222\pi\)
\(588\) 0 0
\(589\) −3.61282 6.25759i −0.148864 0.257840i
\(590\) −85.1527 −3.50568
\(591\) −1.60101 + 10.2618i −0.0658569 + 0.422115i
\(592\) −24.7371 −1.01669
\(593\) −13.8775 + 24.0365i −0.569880 + 0.987061i 0.426698 + 0.904394i \(0.359677\pi\)
−0.996577 + 0.0826662i \(0.973656\pi\)
\(594\) −16.7600 + 0.994906i −0.687671 + 0.0408215i
\(595\) 0 0
\(596\) −4.02936 + 6.97905i −0.165049 + 0.285873i
\(597\) 23.2782 8.99745i 0.952715 0.368241i
\(598\) −4.59841 + 7.96468i −0.188043 + 0.325700i
\(599\) −0.201412 + 0.348855i −0.00822945 + 0.0142538i −0.870111 0.492856i \(-0.835953\pi\)
0.861881 + 0.507110i \(0.169286\pi\)
\(600\) 3.81953 24.4816i 0.155932 0.999456i
\(601\) −12.3733 + 21.4312i −0.504717 + 0.874196i 0.495268 + 0.868740i \(0.335070\pi\)
−0.999985 + 0.00545577i \(0.998263\pi\)
\(602\) 0 0
\(603\) 28.4438 25.8500i 1.15832 1.05269i
\(604\) −25.9313 + 44.9143i −1.05513 + 1.82754i
\(605\) −26.7769 −1.08864
\(606\) −62.5724 + 24.1853i −2.54183 + 0.982462i
\(607\) −24.0697 −0.976957 −0.488479 0.872576i \(-0.662448\pi\)
−0.488479 + 0.872576i \(0.662448\pi\)
\(608\) 2.94865 + 5.10721i 0.119584 + 0.207125i
\(609\) 0 0
\(610\) −1.95115 + 3.37950i −0.0789999 + 0.136832i
\(611\) −2.91672 + 5.05190i −0.117998 + 0.204378i
\(612\) −34.9707 11.1843i −1.41361 0.452097i
\(613\) 10.1907 + 17.6509i 0.411600 + 0.712912i 0.995065 0.0992261i \(-0.0316367\pi\)
−0.583465 + 0.812138i \(0.698303\pi\)
\(614\) −5.96879 10.3382i −0.240881 0.417218i
\(615\) −8.53443 + 3.29871i −0.344142 + 0.133017i
\(616\) 0 0
\(617\) −20.9315 36.2544i −0.842669 1.45955i −0.887630 0.460558i \(-0.847650\pi\)
0.0449604 0.998989i \(-0.485684\pi\)
\(618\) −8.58700 + 3.31903i −0.345420 + 0.133511i
\(619\) −14.8219 −0.595743 −0.297871 0.954606i \(-0.596277\pi\)
−0.297871 + 0.954606i \(0.596277\pi\)
\(620\) 17.6809 + 30.6242i 0.710081 + 1.22990i
\(621\) 6.11565 12.2112i 0.245413 0.490018i
\(622\) −77.3270 −3.10053
\(623\) 0 0
\(624\) 4.49687 + 3.62432i 0.180019 + 0.145089i
\(625\) −30.1861 −1.20744
\(626\) −1.81291 + 3.14005i −0.0724585 + 0.125502i
\(627\) −4.02830 3.24667i −0.160875 0.129660i
\(628\) 5.48329 + 9.49734i 0.218807 + 0.378985i
\(629\) −36.0007 −1.43544
\(630\) 0 0
\(631\) −21.0294 −0.837169 −0.418585 0.908178i \(-0.637474\pi\)
−0.418585 + 0.908178i \(0.637474\pi\)
\(632\) 1.55487 + 2.69312i 0.0618496 + 0.107127i
\(633\) 22.3730 8.64756i 0.889247 0.343710i
\(634\) −25.6694 + 44.4607i −1.01946 + 1.76576i
\(635\) −11.5935 −0.460072
\(636\) −6.37180 + 40.8406i −0.252658 + 1.61943i
\(637\) 0 0
\(638\) −3.37150 −0.133479
\(639\) −36.9114 11.8049i −1.46019 0.466995i
\(640\) −30.2882 52.4607i −1.19725 2.07369i
\(641\) 11.9318 0.471279 0.235640 0.971840i \(-0.424281\pi\)
0.235640 + 0.971840i \(0.424281\pi\)
\(642\) 11.1577 71.5163i 0.440360 2.82252i
\(643\) 19.9678 + 34.5852i 0.787452 + 1.36391i 0.927524 + 0.373765i \(0.121933\pi\)
−0.140072 + 0.990141i \(0.544733\pi\)
\(644\) 0 0
\(645\) −17.1054 13.7863i −0.673524 0.542837i
\(646\) −8.71733 15.0989i −0.342979 0.594057i
\(647\) −0.494477 0.856459i −0.0194399 0.0336709i 0.856142 0.516741i \(-0.172855\pi\)
−0.875582 + 0.483070i \(0.839522\pi\)
\(648\) −29.6917 21.1558i −1.16640 0.831077i
\(649\) 8.26714 14.3191i 0.324514 0.562074i
\(650\) −6.17856 + 10.7016i −0.242343 + 0.419751i
\(651\) 0 0
\(652\) −0.718272 1.24408i −0.0281297 0.0487221i
\(653\) 22.7147 0.888894 0.444447 0.895805i \(-0.353400\pi\)
0.444447 + 0.895805i \(0.353400\pi\)
\(654\) 50.2089 + 40.4666i 1.96332 + 1.58237i
\(655\) −15.5642 −0.608144
\(656\) 2.05688 3.56262i 0.0803076 0.139097i
\(657\) 6.66315 + 30.6504i 0.259954 + 1.19579i
\(658\) 0 0
\(659\) −19.1943 + 33.2454i −0.747702 + 1.29506i 0.201220 + 0.979546i \(0.435509\pi\)
−0.948922 + 0.315512i \(0.897824\pi\)
\(660\) 19.7142 + 15.8890i 0.767374 + 0.618477i
\(661\) 16.9629 29.3806i 0.659780 1.14277i −0.320892 0.947116i \(-0.603983\pi\)
0.980672 0.195657i \(-0.0626839\pi\)
\(662\) 23.2458 40.2628i 0.903472 1.56486i
\(663\) 6.54444 + 5.27459i 0.254165 + 0.204848i
\(664\) −3.98486 + 6.90198i −0.154642 + 0.267849i
\(665\) 0 0
\(666\) −74.1738 23.7221i −2.87418 0.919213i
\(667\) 1.37124 2.37505i 0.0530944 0.0919623i
\(668\) 26.9809 1.04392
\(669\) −6.30475 5.08140i −0.243756 0.196458i
\(670\) −89.3201 −3.45074
\(671\) −0.378860 0.656205i −0.0146257 0.0253325i
\(672\) 0 0
\(673\) −16.1030 + 27.8912i −0.620725 + 1.07513i 0.368626 + 0.929578i \(0.379828\pi\)
−0.989351 + 0.145549i \(0.953505\pi\)
\(674\) −11.5702 + 20.0401i −0.445666 + 0.771916i
\(675\) 8.21718 16.4073i 0.316279 0.631518i
\(676\) 20.0585 + 34.7424i 0.771483 + 1.33625i
\(677\) −18.9842 32.8816i −0.729622 1.26374i −0.957043 0.289946i \(-0.906363\pi\)
0.227421 0.973797i \(-0.426971\pi\)
\(678\) 5.43702 + 4.38204i 0.208807 + 0.168291i
\(679\) 0 0
\(680\) 19.5836 + 33.9198i 0.750997 + 1.30076i
\(681\) 5.26324 33.7352i 0.201688 1.29273i
\(682\) −10.5806 −0.405153
\(683\) 7.59357 + 13.1525i 0.290560 + 0.503265i 0.973942 0.226796i \(-0.0728251\pi\)
−0.683382 + 0.730061i \(0.739492\pi\)
\(684\) −5.19906 23.9156i −0.198791 0.914436i
\(685\) −21.8932 −0.836495
\(686\) 0 0
\(687\) 7.49540 48.0424i 0.285967 1.83293i
\(688\) 9.87754 0.376578
\(689\) 4.73142 8.19507i 0.180253 0.312207i
\(690\) −29.6033 + 11.4422i −1.12698 + 0.435597i
\(691\) 1.34574 + 2.33089i 0.0511943 + 0.0886711i 0.890487 0.455009i \(-0.150364\pi\)
−0.839293 + 0.543680i \(0.817031\pi\)
\(692\) 14.9922 0.569919
\(693\) 0 0
\(694\) −4.83589 −0.183568
\(695\) −20.5420 35.5798i −0.779203 1.34962i
\(696\) −5.70018 4.59415i −0.216065 0.174141i
\(697\) 2.99344 5.18480i 0.113385 0.196388i
\(698\) −38.8858 −1.47185
\(699\) −18.6133 15.0017i −0.704021 0.567416i
\(700\) 0 0
\(701\) −11.8515 −0.447625 −0.223813 0.974632i \(-0.571850\pi\)
−0.223813 + 0.974632i \(0.571850\pi\)
\(702\) 10.0082 + 15.1798i 0.377735 + 0.572925i
\(703\) −11.9988 20.7826i −0.452544 0.783829i
\(704\) 14.7938 0.557562
\(705\) −18.7770 + 7.25765i −0.707184 + 0.273339i
\(706\) −20.3617 35.2675i −0.766323 1.32731i
\(707\) 0 0
\(708\) 72.9542 28.1981i 2.74179 1.05975i
\(709\) 20.5167 + 35.5359i 0.770520 + 1.33458i 0.937278 + 0.348582i \(0.113337\pi\)
−0.166759 + 0.985998i \(0.553330\pi\)
\(710\) 45.0294 + 77.9931i 1.68992 + 2.92703i
\(711\) 0.489233 + 2.25047i 0.0183477 + 0.0843991i
\(712\) 12.9772 22.4771i 0.486339 0.842364i
\(713\) 4.30328 7.45351i 0.161159 0.279136i
\(714\) 0 0
\(715\) −2.89830 5.02001i −0.108390 0.187738i
\(716\) −39.1337 −1.46250
\(717\) −17.8704 + 6.90724i −0.667384 + 0.257956i
\(718\) 7.08246 0.264315
\(719\) −10.4555 + 18.1094i −0.389923 + 0.675366i −0.992439 0.122741i \(-0.960832\pi\)
0.602516 + 0.798107i \(0.294165\pi\)
\(720\) 4.23400 + 19.4763i 0.157792 + 0.725840i
\(721\) 0 0
\(722\) −16.8644 + 29.2100i −0.627628 + 1.08708i
\(723\) −6.18629 + 39.6515i −0.230071 + 1.47466i
\(724\) −36.2896 + 62.8554i −1.34869 + 2.33600i
\(725\) 1.84243 3.19119i 0.0684263 0.118518i
\(726\) 35.3511 13.6638i 1.31200 0.507112i
\(727\) −1.32165 + 2.28917i −0.0490173 + 0.0849005i −0.889493 0.456949i \(-0.848942\pi\)
0.840476 + 0.541849i \(0.182276\pi\)
\(728\) 0 0
\(729\) −16.1715 21.6213i −0.598945 0.800790i
\(730\) 36.4462 63.1267i 1.34893 2.33642i
\(731\) 14.3751 0.531683
\(732\) 0.552531 3.54149i 0.0204221 0.130897i
\(733\) −14.1489 −0.522602 −0.261301 0.965257i \(-0.584152\pi\)
−0.261301 + 0.965257i \(0.584152\pi\)
\(734\) 12.1223 + 20.9964i 0.447442 + 0.774992i
\(735\) 0 0
\(736\) −3.51218 + 6.08327i −0.129461 + 0.224232i
\(737\) 8.67174 15.0199i 0.319428 0.553265i
\(738\) 9.58396 8.70997i 0.352790 0.320619i
\(739\) −7.85905 13.6123i −0.289100 0.500736i 0.684495 0.729017i \(-0.260023\pi\)
−0.973595 + 0.228282i \(0.926689\pi\)
\(740\) 58.7212 + 101.708i 2.15864 + 3.73887i
\(741\) −0.863704 + 5.53598i −0.0317289 + 0.203369i
\(742\) 0 0
\(743\) 10.5496 + 18.2724i 0.387026 + 0.670348i 0.992048 0.125861i \(-0.0401692\pi\)
−0.605022 + 0.796208i \(0.706836\pi\)
\(744\) −17.8886 14.4176i −0.655828 0.528575i
\(745\) 6.36665 0.233256
\(746\) −30.4142 52.6789i −1.11354 1.92871i
\(747\) −4.36792 + 3.96960i −0.159814 + 0.145240i
\(748\) −16.5675 −0.605768
\(749\) 0 0
\(750\) 16.5406 6.39325i 0.603979 0.233449i
\(751\) 13.0370 0.475725 0.237863 0.971299i \(-0.423553\pi\)
0.237863 + 0.971299i \(0.423553\pi\)
\(752\) 4.52544 7.83829i 0.165026 0.285833i
\(753\) −2.07832 + 13.3212i −0.0757383 + 0.485451i
\(754\) 1.82558 + 3.16200i 0.0664838 + 0.115153i
\(755\) 40.9732 1.49117
\(756\) 0 0
\(757\) −12.6856 −0.461065 −0.230532 0.973065i \(-0.574047\pi\)
−0.230532 + 0.973065i \(0.574047\pi\)
\(758\) 11.7613 + 20.3711i 0.427188 + 0.739912i
\(759\) 0.949971 6.08891i 0.0344818 0.221014i
\(760\) −13.0542 + 22.6105i −0.473525 + 0.820169i
\(761\) 6.04077 0.218978 0.109489 0.993988i \(-0.465079\pi\)
0.109489 + 0.993988i \(0.465079\pi\)
\(762\) 15.3058 5.91596i 0.554470 0.214313i
\(763\) 0 0
\(764\) 30.6388 1.10847
\(765\) 6.16188 + 28.3446i 0.222783 + 1.02480i
\(766\) 32.5959 + 56.4577i 1.17774 + 2.03990i
\(767\) −17.9058 −0.646540
\(768\) 37.2815 + 30.0476i 1.34528 + 1.08425i
\(769\) −0.108129 0.187285i −0.00389924 0.00675368i 0.864069 0.503373i \(-0.167908\pi\)
−0.867968 + 0.496619i \(0.834575\pi\)
\(770\) 0 0
\(771\) 2.77037 17.7569i 0.0997724 0.639499i
\(772\) 34.7251 + 60.1457i 1.24979 + 2.16469i
\(773\) −18.8132 32.5854i −0.676663 1.17202i −0.975980 0.217861i \(-0.930092\pi\)
0.299316 0.954154i \(-0.403241\pi\)
\(774\) 29.6176 + 9.47225i 1.06458 + 0.340473i
\(775\) 5.78202 10.0148i 0.207696 0.359741i
\(776\) −16.7763 + 29.0575i −0.602235 + 1.04310i
\(777\) 0 0
\(778\) 4.99388 + 8.64965i 0.179039 + 0.310105i
\(779\) 3.99078 0.142985
\(780\) 4.22690 27.0926i 0.151347 0.970072i
\(781\) −17.4869 −0.625730