Properties

Label 441.2.g.f.67.5
Level $441$
Weight $2$
Character 441.67
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 67.5
Root \(1.19343 - 2.06709i\) of defining polynomial
Character \(\chi\) \(=\) 441.67
Dual form 441.2.g.f.79.5

$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.19343 2.06709i 0.843886 1.46165i −0.0426999 0.999088i \(-0.513596\pi\)
0.886585 0.462565i \(-0.153071\pi\)
\(3\) −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 −0.746291 0.665620i \(-0.768167\pi\)
0.949589 + 0.313497i \(0.101501\pi\)
\(14\) 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 −0.993899 0.110297i \(-0.964820\pi\)
0.592469 + 0.805593i \(0.298153\pi\)
\(18\) −1.52113 + 6.99717i −0.358533 + 1.64925i
\(19\) 1.10329 + 1.91096i 0.253113 + 0.438404i 0.964381 0.264516i \(-0.0852123\pi\)
−0.711268 + 0.702921i \(0.751879\pi\)
\(20\) −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 0.910392 0.413747i \(-0.135780\pi\)
−0.813511 + 0.581549i \(0.802447\pi\)
\(30\) −11.2633 4.35347i −2.05639 0.794831i
\(31\) 1.63729 + 2.83587i 0.294066 + 0.509337i 0.974767 0.223224i \(-0.0716581\pi\)
−0.680701 + 0.732561i \(0.738325\pi\)
\(32\) −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 0.835090 + 0.550113i \(0.185415\pi\)
0.0588664 + 0.998266i \(0.481251\pi\)
\(38\) 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 −0.786732 0.617294i \(-0.788229\pi\)
0.927959 + 0.372683i \(0.121562\pi\)
\(42\) 0 0
\(43\) −2.17129 3.76078i −0.331118 0.573514i 0.651613 0.758551i \(-0.274093\pi\)
−0.982731 + 0.185038i \(0.940759\pi\)
\(44\) 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 −0.683650 0.729810i \(-0.739609\pi\)
0.973859 + 0.227154i \(0.0729419\pi\)
\(48\) 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 −0.997934 0.0642533i \(-0.979533\pi\)
0.554612 + 0.832109i \(0.312867\pi\)
\(54\) 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 −0.922799 0.385283i \(-0.874104\pi\)
0.127735 0.991808i \(-0.459229\pi\)
\(60\) −14.5630 + 11.7373i −1.88008 + 1.51528i
\(61\) 0.279867 0.484744i 0.0358333 0.0620651i −0.847553 0.530711i \(-0.821925\pi\)
0.883386 + 0.468646i \(0.155258\pi\)
\(62\) 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 −0.930420 0.366494i \(-0.880558\pi\)
0.147817 0.989015i \(-0.452775\pi\)
\(68\) 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 0.379069 + 0.925368i \(0.376244\pi\)
−0.990927 + 0.134401i \(0.957089\pi\)
\(74\) 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 −0.886810 0.462134i \(-0.847084\pi\)
0.843625 + 0.536933i \(0.180417\pi\)
\(80\) −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 0.914950 0.403567i \(-0.132230\pi\)
−0.806974 + 0.590587i \(0.798896\pi\)
\(84\) 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 0.644777 0.764371i \(-0.276950\pi\)
−0.984353 + 0.176208i \(0.943617\pi\)
\(90\) −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 0.995988 0.0894847i \(-0.0285220\pi\)
−0.575490 + 0.817809i \(0.695189\pi\)
\(98\) 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 −0.884501 0.466537i \(-0.845501\pi\)
0.0382175 0.999269i \(-0.487832\pi\)
\(108\) 10.5745 16.0387i 1.01753 1.54333i
\(109\) −7.79917 + 13.5086i −0.747025 + 1.29388i 0.202218 + 0.979341i \(0.435185\pi\)
−0.949243 + 0.314544i \(0.898148\pi\)
\(110\) −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 −0.903012 0.429615i \(-0.858649\pi\)
0.823563 + 0.567224i \(0.191983\pi\)
\(114\) −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 0.396812 + 0.917900i \(0.370116\pi\)
−0.993331 + 0.115300i \(0.963217\pi\)
\(140\) 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 0.919120 0.393978i \(-0.128901\pi\)
−0.800755 + 0.598993i \(0.795568\pi\)
\(158\) 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 0.858317 0.513120i \(-0.171511\pi\)
−0.873534 + 0.486764i \(0.838177\pi\)
\(164\) −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 −0.971965 0.235124i \(-0.924450\pi\)
0.689606 + 0.724185i \(0.257784\pi\)
\(168\) 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 −0.932750 0.360525i \(-0.882598\pi\)
0.778598 + 0.627522i \(0.215931\pi\)
\(174\) −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 −0.597600 0.801795i \(-0.703879\pi\)
0.993174 + 0.116639i \(0.0372121\pi\)
\(180\) 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 −0.976094 0.217348i \(-0.930259\pi\)
0.676276 + 0.736648i \(0.263593\pi\)
\(192\) 2.91784 + 18.7021i 0.210577 + 1.34971i
\(193\) 9.39242 + 16.2682i 0.676082 + 1.17101i 0.976152 + 0.217090i \(0.0696566\pi\)
−0.300070 + 0.953917i \(0.597010\pi\)
\(194\) 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 0.489221 + 0.872160i \(0.337281\pi\)
−0.999923 + 0.0124022i \(0.996052\pi\)
\(200\) −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 −0.999643 0.0267212i \(-0.991493\pi\)
0.522963 + 0.852356i \(0.324827\pi\)
\(212\) 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 0.777082 0.629399i \(-0.216699\pi\)
−0.933617 + 0.358273i \(0.883366\pi\)
\(224\) 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 0.546409 0.837518i \(-0.315994\pi\)
−0.998517 + 0.0544448i \(0.982661\pi\)
\(234\) 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 −0.629834 0.776730i \(-0.716877\pi\)
0.987585 + 0.157087i \(0.0502104\pi\)
\(240\) 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 −0.699311 0.714818i \(-0.746510\pi\)
0.968706 + 0.248212i \(0.0798430\pi\)
\(270\) 36.1625 + 2.14668i 2.20078 + 0.130643i
\(271\) 9.16955 + 15.8821i 0.557010 + 0.964770i 0.997744 + 0.0671321i \(0.0213849\pi\)
−0.440734 + 0.897638i \(0.645282\pi\)
\(272\) −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 0.839455 0.543430i \(-0.182875\pi\)
−0.890351 + 0.455274i \(0.849541\pi\)
\(282\) −12.8083 + 10.3231i −0.762724 + 0.614729i
\(283\) −6.24415 10.8152i −0.371176 0.642896i 0.618571 0.785729i \(-0.287712\pi\)
−0.989747 + 0.142833i \(0.954379\pi\)
\(284\) −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 −0.779955 0.625835i \(-0.784758\pi\)
0.931967 + 0.362543i \(0.118091\pi\)
\(294\) 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 −0.801652 0.597791i \(-0.796045\pi\)
−0.116876 0.993146i \(-0.537288\pi\)
\(312\) 9.59418 + 3.70832i 0.543163 + 0.209942i
\(313\) 0.759535 1.31555i 0.0429315 0.0743595i −0.843761 0.536719i \(-0.819664\pi\)
0.886693 + 0.462359i \(0.152997\pi\)
\(314\) 7.08000 0.399548
\(315\) 0 0
\(316\) 2.83821 0.159662
\(317\) 10.7544 18.6272i 0.604029 1.04621i −0.388175 0.921586i \(-0.626894\pi\)
0.992204 0.124623i \(-0.0397723\pi\)
\(318\) 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 0.463844 + 0.885917i \(0.346470\pi\)
−0.999149 + 0.0412580i \(0.986863\pi\)
\(332\) 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 −0.703260 0.710933i \(-0.748273\pi\)
0.967316 + 0.253575i \(0.0816063\pi\)
\(338\) 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 0.837553 0.546356i \(-0.183985\pi\)
−0.891935 + 0.452164i \(0.850652\pi\)
\(348\) −6.23246 2.40896i −0.334095 0.129134i
\(349\) −8.14577 14.1089i −0.436033 0.755231i 0.561346 0.827581i \(-0.310284\pi\)
−0.997379 + 0.0723497i \(0.976950\pi\)
\(350\) 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 0.902518 0.430652i \(-0.141717\pi\)
−0.824215 + 0.566277i \(0.808383\pi\)
\(360\) 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 −0.937745 0.347323i \(-0.887091\pi\)
0.168082 0.985773i \(-0.446243\pi\)
\(398\) 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 0.546799 0.837264i \(-0.315846\pi\)
−0.998491 + 0.0549104i \(0.982513\pi\)
\(410\) −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 0.449698 + 0.893181i \(0.351532\pi\)
−0.998366 + 0.0571410i \(0.981802\pi\)
\(420\) 0 0
\(421\) 10.4177 + 18.0440i 0.507728 + 0.879411i 0.999960 + 0.00894684i \(0.00284791\pi\)
−0.492232 + 0.870464i \(0.663819\pi\)
\(422\) 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 −0.999897 0.0143427i \(-0.995434\pi\)
0.512370 + 0.858765i \(0.328768\pi\)
\(432\) −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 0.0375520 + 0.999295i \(0.488044\pi\)
−0.884191 + 0.467126i \(0.845289\pi\)
\(440\) 16.0172 0.763589
\(441\) 0 0
\(442\) 11.5832 0.550955
\(443\) 9.60313 16.6331i 0.456258 0.790263i −0.542501 0.840055i \(-0.682523\pi\)
0.998760 + 0.0497923i \(0.0158559\pi\)
\(444\) −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 −0.732267 0.681017i \(-0.761538\pi\)
0.955912 + 0.293653i \(0.0948711\pi\)
\(458\) −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 −0.999951 0.00988416i \(-0.996854\pi\)
0.491416 0.870925i \(-0.336480\pi\)
\(462\) 0 0
\(463\) 13.0744 22.6456i 0.607621 1.05243i −0.384010 0.923329i \(-0.625457\pi\)
0.991631 0.129102i \(-0.0412094\pi\)
\(464\) −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 0.913758 + 0.406258i \(0.133167\pi\)
−0.105049 + 0.994467i \(0.533500\pi\)
\(468\) 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 0.491283 + 0.871000i \(0.336528\pi\)
−0.999950 + 0.0100365i \(0.996805\pi\)
\(488\) −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 −0.134726 0.990883i \(-0.543016\pi\)
0.925493 0.378765i \(-0.123651\pi\)
\(492\) 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 −0.943797 0.330524i \(-0.892774\pi\)
0.758141 + 0.652090i \(0.226108\pi\)
\(522\) −7.11657 + 2.27601i −0.311484 + 0.0996181i
\(523\) −16.7236 28.9662i −0.731273 1.26660i −0.956339 0.292259i \(-0.905593\pi\)
0.225066 0.974344i \(-0.427740\pi\)
\(524\) 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 0.600280 0.799790i \(-0.295056\pi\)
−0.992778 + 0.119962i \(0.961723\pi\)
\(542\) 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 0.797709 0.603043i \(-0.206045\pi\)
−0.921105 + 0.389315i \(0.872712\pi\)
\(548\) 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 −0.258661 0.965968i \(-0.583281\pi\)
0.965883 0.258977i \(-0.0833855\pi\)
\(558\) −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 0.888190 0.459477i \(-0.151963\pi\)
−0.842013 + 0.539457i \(0.818630\pi\)
\(564\) 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 −0.993475 0.114049i \(-0.963618\pi\)
0.595507 + 0.803350i \(0.296951\pi\)
\(570\) −4.10743 26.3269i −0.172041 1.10271i
\(571\) 10.8690 + 18.8257i 0.454854 + 0.787831i 0.998680 0.0513674i \(-0.0163580\pi\)
−0.543825 + 0.839198i \(0.683025\pi\)
\(572\) 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 −0.341443 0.939903i \(-0.610916\pi\)
0.984701 0.174253i \(-0.0557511\pi\)
\(578\) 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 0.990922 0.134436i \(-0.0429222\pi\)
−0.611886 + 0.790946i \(0.709589\pi\)
\(588\) 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 −0.996577 0.0826662i \(-0.973656\pi\)
0.426698 0.904394i \(-0.359677\pi\)
\(594\) −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 0.861881 0.507110i \(-0.169286\pi\)
−0.870111 + 0.492856i \(0.835953\pi\)
\(600\) 3.81953 + 24.4816i 0.155932 + 0.999456i
\(601\) −12.3733 21.4312i −0.504717 0.874196i −0.999985 0.00545577i \(-0.998263\pi\)
0.495268 0.868740i \(-0.335070\pi\)
\(602\) 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 −0.583465 0.812138i \(-0.698303\pi\)
0.995065 + 0.0992261i \(0.0316367\pi\)
\(614\) −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 0.0449604 + 0.998989i \(0.485684\pi\)
−0.887630 + 0.460558i \(0.847650\pi\)
\(618\) −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 −0.140072 0.990141i \(-0.544733\pi\)
0.927524 0.373765i \(-0.121933\pi\)
\(644\) 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 −0.875582 0.483070i \(-0.839522\pi\)
0.856142 + 0.516741i \(0.172855\pi\)
\(648\) −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 −0.948922 0.315512i \(-0.897824\pi\)
0.201220 0.979546i \(-0.435509\pi\)
\(660\) 19.7142 15.8890i 0.767374 0.618477i
\(661\) 16.9629 + 29.3806i 0.659780 + 1.14277i 0.980672 + 0.195657i \(0.0626839\pi\)
−0.320892 + 0.947116i \(0.603983\pi\)
\(662\) 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 −0.989351 0.145549i \(-0.953505\pi\)
0.368626 0.929578i \(-0.379828\pi\)
\(674\) −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 0.227421 + 0.973797i \(0.426971\pi\)
−0.957043 + 0.289946i \(0.906363\pi\)
\(678\) 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 −0.683382 0.730061i \(-0.739492\pi\)
0.973942 + 0.226796i \(0.0728251\pi\)
\(684\) −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 −0.839293 0.543680i \(-0.817031\pi\)
0.890487 + 0.455009i \(0.150364\pi\)
\(692\) 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 −0.166759 0.985998i \(-0.553330\pi\)
0.937278 0.348582i \(-0.113337\pi\)
\(710\) 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 0.602516 0.798107i \(-0.294165\pi\)
−0.992439 + 0.122741i \(0.960832\pi\)
\(720\) 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 0.840476 0.541849i \(-0.182276\pi\)
−0.889493 + 0.456949i \(0.848942\pi\)
\(728\) 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 −0.973595 0.228282i \(-0.926689\pi\)
0.684495 + 0.729017i \(0.260023\pi\)
\(740\) 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 −0.605022 0.796208i \(-0.706836\pi\)
0.992048 + 0.125861i \(0.0401692\pi\)
\(744\) −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 −0.867968 0.496619i \(-0.834575\pi\)
0.864069 + 0.503373i \(0.167908\pi\)
\(770\) 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 0.299316 + 0.954154i \(0.403241\pi\)
−0.975980 + 0.217861i \(0.930092\pi\)
\(774\) 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