Properties

Label 441.2.f.f.295.5
Level $441$
Weight $2$
Character 441.295
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.f (of order \(3\), degree \(2\), 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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 295.5
Root \(1.19343 - 2.06709i\) of defining polynomial
Character \(\chi\) \(=\) 441.295
Dual form 441.2.f.f.148.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.19343 - 2.06709i) q^{2} +(-1.34857 - 1.08690i) q^{3} +(-1.84857 - 3.20182i) q^{4} +(-1.46043 - 2.52954i) q^{5} +(-3.85615 + 1.49047i) q^{6} -4.05086 q^{8} +(0.637290 + 2.93153i) q^{9} +O(q^{10})\) \(q+(1.19343 - 2.06709i) q^{2} +(-1.34857 - 1.08690i) q^{3} +(-1.84857 - 3.20182i) q^{4} +(-1.46043 - 2.52954i) q^{5} +(-3.85615 + 1.49047i) q^{6} -4.05086 q^{8} +(0.637290 + 2.93153i) q^{9} -6.97172 q^{10} +(0.676857 - 1.17235i) q^{11} +(-0.987132 + 6.32710i) q^{12} +(0.733001 + 1.26960i) q^{13} +(-0.779867 + 4.99862i) q^{15} +(-1.13729 + 1.96984i) q^{16} +3.31027 q^{17} +(6.82030 + 2.18125i) q^{18} -2.20659 q^{19} +(-5.39943 + 9.35209i) q^{20} +(-1.61557 - 2.79825i) q^{22} +(-1.31415 - 2.27617i) q^{23} +(5.46287 + 4.40288i) q^{24} +(-1.76573 + 3.05833i) q^{25} +3.49916 q^{26} +(2.32685 - 4.64605i) q^{27} +(0.521720 - 0.903646i) q^{29} +(9.40187 + 7.57758i) q^{30} +(1.63729 + 2.83587i) q^{31} +(-1.33629 - 2.31453i) q^{32} +(-2.18702 + 0.845323i) q^{33} +(3.95060 - 6.84263i) q^{34} +(8.20815 - 7.45963i) q^{36} -10.8755 q^{37} +(-2.63342 + 4.56121i) q^{38} +(0.391421 - 2.50884i) q^{39} +(5.91601 + 10.2468i) q^{40} +(0.904289 + 1.56627i) q^{41} +(-2.17129 + 3.76078i) q^{43} -5.00488 q^{44} +(6.48471 - 5.89336i) q^{45} -6.27340 q^{46} +(1.98957 - 3.44604i) q^{47} +(3.67474 - 1.42035i) q^{48} +(4.21456 + 7.29984i) q^{50} +(-4.46414 - 3.59794i) q^{51} +(2.71001 - 4.69388i) q^{52} +6.45486 q^{53} +(-6.82685 - 10.3546i) q^{54} -3.95402 q^{55} +(2.97574 + 2.39834i) q^{57} +(-1.24528 - 2.15688i) q^{58} +(-6.10700 - 10.5776i) q^{59} +(17.4463 - 6.74331i) q^{60} +(0.279867 - 0.484744i) q^{61} +7.81600 q^{62} -10.9283 q^{64} +(2.14100 - 3.70832i) q^{65} +(-0.862710 + 5.52960i) q^{66} +(-6.40588 - 11.0953i) q^{67} +(-6.11928 - 10.5989i) q^{68} +(-0.701751 + 4.49793i) q^{69} +12.9177 q^{71} +(-2.58157 - 11.8752i) q^{72} +10.4554 q^{73} +(-12.9791 + 22.4805i) q^{74} +(5.70532 - 2.20521i) q^{75} +(4.07903 + 7.06509i) q^{76} +(-4.71886 - 3.80324i) q^{78} +(-0.383838 + 0.664827i) q^{79} +6.64375 q^{80} +(-8.18772 + 3.73647i) q^{81} +4.31684 q^{82} +(0.983707 - 1.70383i) q^{83} +(-4.83443 - 8.37348i) q^{85} +(5.18258 + 8.97649i) q^{86} +(-1.68575 + 0.651573i) q^{87} +(-2.74185 + 4.74903i) q^{88} +6.40711 q^{89} +(-4.44301 - 20.4378i) q^{90} +(-4.85859 + 8.41533i) q^{92} +(0.874308 - 5.60395i) q^{93} +(-4.74884 - 8.22524i) q^{94} +(3.22257 + 5.58166i) q^{95} +(-0.713577 + 4.57373i) q^{96} +(4.14143 - 7.17316i) q^{97} +(3.86814 + 1.23710i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{2} + q^{3} - 4q^{4} - 4q^{5} + 2q^{6} - 6q^{8} - 7q^{9} + O(q^{10}) \) \( 10q + 2q^{2} + q^{3} - 4q^{4} - 4q^{5} + 2q^{6} - 6q^{8} - 7q^{9} - 14q^{10} + 4q^{11} + 2q^{12} + 8q^{13} - 19q^{15} + 2q^{16} + 24q^{17} - 2q^{18} + 2q^{19} - 5q^{20} - q^{22} + 3q^{23} + 9q^{24} - q^{25} + 22q^{26} + 7q^{27} + 7q^{29} + 10q^{30} + 3q^{31} - 2q^{32} + 13q^{33} - 3q^{34} + 34q^{36} - 20q^{38} - 22q^{39} + 3q^{40} - 5q^{41} - 7q^{43} + 20q^{44} - 17q^{45} - 6q^{46} - 27q^{47} + 5q^{48} + 19q^{50} - 15q^{51} + 10q^{52} + 42q^{53} - 52q^{54} - 4q^{55} - 4q^{57} - 10q^{58} - 30q^{59} + 31q^{60} + 14q^{61} + 12q^{62} - 50q^{64} - 11q^{65} - 22q^{66} - 2q^{67} - 27q^{68} - 15q^{69} - 6q^{71} - 12q^{72} + 30q^{73} - 36q^{74} + 17q^{75} - 5q^{76} - 20q^{78} - 4q^{79} + 40q^{80} - 31q^{81} - 10q^{82} - 9q^{83} - 6q^{85} - 8q^{86} + 34q^{87} - 18q^{88} + 56q^{89} - 28q^{90} + 27q^{92} + 18q^{93} + 3q^{94} - 14q^{95} + 58q^{96} + 12q^{97} + 35q^{99} + O(q^{100}) \)

Character values

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

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

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 −0.0426999 0.999088i \(-0.513596\pi\)
0.886585 0.462565i \(-0.153071\pi\)
\(3\) −1.34857 1.08690i −0.778598 0.627523i
\(4\) −1.84857 3.20182i −0.924286 1.60091i
\(5\) −1.46043 2.52954i −0.653125 1.13125i −0.982360 0.186998i \(-0.940124\pi\)
0.329235 0.944248i \(-0.393209\pi\)
\(6\) −3.85615 + 1.49047i −1.57427 + 0.608483i
\(7\) 0 0
\(8\) −4.05086 −1.43219
\(9\) 0.637290 + 2.93153i 0.212430 + 0.977176i
\(10\) −6.97172 −2.20465
\(11\) 0.676857 1.17235i 0.204080 0.353477i −0.745759 0.666216i \(-0.767913\pi\)
0.949839 + 0.312738i \(0.101246\pi\)
\(12\) −0.987132 + 6.32710i −0.284960 + 1.82648i
\(13\) 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
\(17\) 3.31027 0.802859 0.401430 0.915890i \(-0.368513\pi\)
0.401430 + 0.915890i \(0.368513\pi\)
\(18\) 6.82030 + 2.18125i 1.60756 + 0.514126i
\(19\) −2.20659 −0.506226 −0.253113 0.967437i \(-0.581454\pi\)
−0.253113 + 0.967437i \(0.581454\pi\)
\(20\) −5.39943 + 9.35209i −1.20735 + 2.09119i
\(21\) 0 0
\(22\) −1.61557 2.79825i −0.344441 0.596589i
\(23\) −1.31415 2.27617i −0.274019 0.474614i 0.695868 0.718169i \(-0.255020\pi\)
−0.969887 + 0.243555i \(0.921686\pi\)
\(24\) 5.46287 + 4.40288i 1.11510 + 0.898735i
\(25\) −1.76573 + 3.05833i −0.353146 + 0.611666i
\(26\) 3.49916 0.686241
\(27\) 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 \(0.135780\pi\)
\(30\) 9.40187 + 7.57758i 1.71654 + 1.38347i
\(31\) 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
\(33\) −2.18702 + 0.845323i −0.380712 + 0.147152i
\(34\) 3.95060 6.84263i 0.677521 1.17350i
\(35\) 0 0
\(36\) 8.20815 7.45963i 1.36803 1.24327i
\(37\) −10.8755 −1.78791 −0.893957 0.448153i \(-0.852082\pi\)
−0.893957 + 0.448153i \(0.852082\pi\)
\(38\) −2.63342 + 4.56121i −0.427197 + 0.739926i
\(39\) 0.391421 2.50884i 0.0626775 0.401736i
\(40\) 5.91601 + 10.2468i 0.935403 + 1.62017i
\(41\) 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 \(0.274093\pi\)
\(44\) −5.00488 −0.754514
\(45\) 6.48471 5.89336i 0.966684 0.878530i
\(46\) −6.27340 −0.924962
\(47\) 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
\(51\) −4.46414 3.59794i −0.625105 0.503813i
\(52\) 2.71001 4.69388i 0.375811 0.650924i
\(53\) 6.45486 0.886644 0.443322 0.896363i \(-0.353800\pi\)
0.443322 + 0.896363i \(0.353800\pi\)
\(54\) −6.82685 10.3546i −0.929017 1.40908i
\(55\) −3.95402 −0.533160
\(56\) 0 0
\(57\) 2.97574 + 2.39834i 0.394146 + 0.317668i
\(58\) −1.24528 2.15688i −0.163513 0.283213i
\(59\) −6.10700 10.5776i −0.795064 1.37709i −0.922799 0.385283i \(-0.874104\pi\)
0.127735 0.991808i \(-0.459229\pi\)
\(60\) 17.4463 6.74331i 2.25231 0.870558i
\(61\) 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
\(66\) −0.862710 + 5.52960i −0.106192 + 0.680647i
\(67\) −6.40588 11.0953i −0.782603 1.35551i −0.930420 0.366494i \(-0.880558\pi\)
0.147817 0.989015i \(-0.452775\pi\)
\(68\) −6.11928 10.5989i −0.742072 1.28531i
\(69\) −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 \(0.221984\pi\)
\(72\) −2.58157 11.8752i −0.304241 1.39951i
\(73\) 10.4554 1.22372 0.611858 0.790968i \(-0.290422\pi\)
0.611858 + 0.790968i \(0.290422\pi\)
\(74\) −12.9791 + 22.4805i −1.50879 + 2.61331i
\(75\) 5.70532 2.20521i 0.658793 0.254635i
\(76\) 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 \(0.180417\pi\)
\(80\) 6.64375 0.742793
\(81\) −8.18772 + 3.73647i −0.909747 + 0.415163i
\(82\) 4.31684 0.476715
\(83\) 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
\(86\) 5.18258 + 8.97649i 0.558852 + 0.967960i
\(87\) −1.68575 + 0.651573i −0.180732 + 0.0698559i
\(88\) −2.74185 + 4.74903i −0.292283 + 0.506248i
\(89\) 6.40711 0.679153 0.339576 0.940579i \(-0.389716\pi\)
0.339576 + 0.940579i \(0.389716\pi\)
\(90\) −4.44301 20.4378i −0.468335 2.15433i
\(91\) 0 0
\(92\) −4.85859 + 8.41533i −0.506543 + 0.877359i
\(93\) 0.874308 5.60395i 0.0906615 0.581102i
\(94\) −4.74884 8.22524i −0.489806 0.848369i
\(95\) 3.22257 + 5.58166i 0.330629 + 0.572666i
\(96\) −0.713577 + 4.57373i −0.0728292 + 0.466804i
\(97\) 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
\(100\) 13.0563 1.30563
\(101\) −8.11331 + 14.0527i −0.807305 + 1.39829i 0.107419 + 0.994214i \(0.465741\pi\)
−0.914724 + 0.404079i \(0.867592\pi\)
\(102\) −12.7649 + 4.93387i −1.26392 + 0.488526i
\(103\) −1.11342 1.92849i −0.109708 0.190020i 0.805944 0.591992i \(-0.201658\pi\)
−0.915652 + 0.401972i \(0.868325\pi\)
\(104\) −2.96929 5.14295i −0.291162 0.504308i
\(105\) 0 0
\(106\) 7.70346 13.3428i 0.748226 1.29597i
\(107\) 17.5081 1.69257 0.846284 0.532732i \(-0.178835\pi\)
0.846284 + 0.532732i \(0.178835\pi\)
\(108\) −19.1772 + 1.13839i −1.84532 + 0.109542i
\(109\) 15.5983 1.49405 0.747025 0.664796i \(-0.231482\pi\)
0.747025 + 0.664796i \(0.231482\pi\)
\(110\) −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 \(0.858649\pi\)
\(114\) 8.50894 3.28886i 0.796935 0.308030i
\(115\) −3.83845 + 6.64839i −0.357937 + 0.619966i
\(116\) −3.85775 −0.358183
\(117\) −3.25472 + 2.95792i −0.300899 + 0.273459i
\(118\) −29.1532 −2.68377
\(119\) 0 0
\(120\) 3.15913 20.2487i 0.288388 1.84844i
\(121\) 4.58373 + 7.93925i 0.416703 + 0.721750i
\(122\) −0.668005 1.15702i −0.0604784 0.104752i
\(123\) 0.482888 3.09511i 0.0435405 0.279076i
\(124\) 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
\(129\) 7.01573 2.71171i 0.617701 0.238752i
\(130\) −5.11028 8.85127i −0.448202 0.776308i
\(131\) 2.66432 + 4.61473i 0.232782 + 0.403191i 0.958626 0.284669i \(-0.0918837\pi\)
−0.725844 + 0.687860i \(0.758550\pi\)
\(132\) 6.74944 + 5.43981i 0.587463 + 0.473475i
\(133\) 0 0
\(134\) −30.5800 −2.64171
\(135\) −15.1506 + 0.899369i −1.30396 + 0.0774054i
\(136\) −13.4095 −1.14985
\(137\) 3.74772 6.49124i 0.320189 0.554584i −0.660338 0.750969i \(-0.729587\pi\)
0.980527 + 0.196385i \(0.0629202\pi\)
\(138\) 8.46013 + 6.81856i 0.720174 + 0.580435i
\(139\) −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
\(143\) 1.98455 0.165956
\(144\) −6.49944 2.07864i −0.541620 0.173220i
\(145\) −3.04775 −0.253102
\(146\) 12.4779 21.6123i 1.03268 1.78865i
\(147\) 0 0
\(148\) 20.1041 + 34.8212i 1.65254 + 2.86229i
\(149\) −1.08986 1.88769i −0.0892846 0.154645i 0.817924 0.575326i \(-0.195125\pi\)
−0.907209 + 0.420680i \(0.861791\pi\)
\(150\) 2.25056 14.4252i 0.183758 1.17781i
\(151\) −7.01387 + 12.1484i −0.570781 + 0.988621i 0.425705 + 0.904862i \(0.360026\pi\)
−0.996486 + 0.0837595i \(0.973307\pi\)
\(152\) 8.93857 0.725014
\(153\) 2.10961 + 9.70416i 0.170552 + 0.784535i
\(154\) 0 0
\(155\) 4.78231 8.28320i 0.384124 0.665322i
\(156\) −8.75643 + 3.38451i −0.701075 + 0.270978i
\(157\) 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
\(159\) −8.70484 7.01580i −0.690339 0.556389i
\(160\) −3.90314 + 6.76043i −0.308570 + 0.534459i
\(161\) 0 0
\(162\) −2.04789 + 21.3840i −0.160898 + 1.68008i
\(163\) 0.388555 0.0304340 0.0152170 0.999884i \(-0.495156\pi\)
0.0152170 + 0.999884i \(0.495156\pi\)
\(164\) 3.34329 5.79074i 0.261067 0.452181i
\(165\) 5.33228 + 4.29763i 0.415117 + 0.334570i
\(166\) −2.34798 4.06682i −0.182239 0.315646i
\(167\) −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
\(170\) −23.0783 −1.77003
\(171\) −1.40624 6.46867i −0.107538 0.494672i
\(172\) 16.0551 1.22419
\(173\) −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
\(177\) −3.26112 + 20.9024i −0.245121 + 1.57112i
\(178\) 7.64647 13.2441i 0.573127 0.992685i
\(179\) −10.5849 −0.791149 −0.395575 0.918434i \(-0.629455\pi\)
−0.395575 + 0.918434i \(0.629455\pi\)
\(180\) −30.8569 9.86859i −2.29994 0.735561i
\(181\) 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
\(184\) 5.32343 + 9.22045i 0.392448 + 0.679740i
\(185\) 15.8829 + 27.5099i 1.16773 + 2.02257i
\(186\) −10.5404 8.49522i −0.772862 0.622899i
\(187\) 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 \(0.263593\pi\)
\(192\) 14.7376 + 11.8780i 1.06359 + 0.857218i
\(193\) 9.39242 + 16.2682i 0.676082 + 1.17101i 0.976152 + 0.217090i \(0.0696566\pi\)
−0.300070 + 0.953917i \(0.597010\pi\)
\(194\) −9.88504 17.1214i −0.709705 1.22924i
\(195\) −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 \(0.431478\pi\)
\(198\) 7.17356 6.51939i 0.509803 0.463313i
\(199\) 14.4087 1.02140 0.510702 0.859758i \(-0.329385\pi\)
0.510702 + 0.859758i \(0.329385\pi\)
\(200\) 7.15272 12.3889i 0.505773 0.876025i
\(201\) −3.42072 + 21.9254i −0.241279 + 1.54650i
\(202\) 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
\(206\) −5.31515 −0.370324
\(207\) 5.83517 5.30304i 0.405572 0.368587i
\(208\) −3.33454 −0.231209
\(209\) −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 \(0.991493\pi\)
\(212\) −11.9323 20.6673i −0.819512 1.41944i
\(213\) −17.4205 14.0403i −1.19363 0.962024i
\(214\) 20.8947 36.1907i 1.42833 2.47395i
\(215\) 12.6841 0.865047
\(216\) −9.42574 + 18.8205i −0.641341 + 1.28057i
\(217\) 0 0
\(218\) 18.6156 32.2431i 1.26081 2.18378i
\(219\) −14.0999 11.3640i −0.952783 0.767910i
\(220\) 7.30929 + 12.6601i 0.492792 + 0.853541i
\(221\) 2.42644 + 4.20271i 0.163220 + 0.282705i
\(222\) 41.9374 16.2096i 2.81466 1.08791i
\(223\) −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
\(226\) −4.03169 −0.268184
\(227\) 9.85631 17.0716i 0.654187 1.13308i −0.327910 0.944709i \(-0.606344\pi\)
0.982097 0.188376i \(-0.0603222\pi\)
\(228\) 2.17819 13.9613i 0.144254 0.924609i
\(229\) 14.0364 + 24.3118i 0.927552 + 1.60657i 0.787404 + 0.616437i \(0.211425\pi\)
0.140148 + 0.990131i \(0.455242\pi\)
\(230\) 9.16188 + 15.8688i 0.604116 + 1.04636i
\(231\) 0 0
\(232\) −2.11342 + 3.66054i −0.138753 + 0.240326i
\(233\) 13.8023 0.904216 0.452108 0.891963i \(-0.350672\pi\)
0.452108 + 0.891963i \(0.350672\pi\)
\(234\) 2.22998 + 10.2579i 0.145778 + 0.670579i
\(235\) −11.6225 −0.758171
\(236\) −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 \(0.716877\pi\)
\(240\) −8.95957 7.22110i −0.578338 0.466120i
\(241\) −11.5849 + 20.0656i −0.746247 + 1.29254i 0.203362 + 0.979104i \(0.434813\pi\)
−0.949610 + 0.313435i \(0.898520\pi\)
\(242\) 21.8815 1.40660
\(243\) 15.1029 + 3.86035i 0.968852 + 0.247642i
\(244\) −2.06942 −0.132481
\(245\) 0 0
\(246\) −5.82157 4.69198i −0.371169 0.299150i
\(247\) −1.61743 2.80147i −0.102915 0.178253i
\(248\) −6.63243 11.4877i −0.421160 0.729470i
\(249\) −3.17850 + 1.22854i −0.201429 + 0.0778559i
\(250\) −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
\(255\) −2.58157 + 16.5468i −0.161664 + 1.03620i
\(256\) 13.8226 + 23.9414i 0.863912 + 1.49634i
\(257\) 5.18798 + 8.98585i 0.323618 + 0.560522i 0.981232 0.192833i \(-0.0617676\pi\)
−0.657614 + 0.753355i \(0.728434\pi\)
\(258\) 2.76748 17.7384i 0.172296 1.10434i
\(259\) 0 0
\(260\) −15.8312 −0.981807
\(261\) 2.98155 + 0.953553i 0.184553 + 0.0590235i
\(262\) 12.7187 0.785767
\(263\) 9.56654 16.5697i 0.589898 1.02173i −0.404347 0.914605i \(-0.632501\pi\)
0.994245 0.107128i \(-0.0341653\pi\)
\(264\) 8.85931 3.42428i 0.545253 0.210750i
\(265\) −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
\(269\) −8.83681 −0.538790 −0.269395 0.963030i \(-0.586824\pi\)
−0.269395 + 0.963030i \(0.586824\pi\)
\(270\) −16.2222 + 32.3910i −0.987249 + 1.97125i
\(271\) −18.3391 −1.11402 −0.557010 0.830506i \(-0.688052\pi\)
−0.557010 + 0.830506i \(0.688052\pi\)
\(272\) −3.76474 + 6.52073i −0.228271 + 0.395377i
\(273\) 0 0
\(274\) −8.94531 15.4937i −0.540406 0.936010i
\(275\) 2.39029 + 4.14011i 0.144140 + 0.249658i
\(276\) 15.6988 6.06786i 0.944956 0.365242i
\(277\) −2.55241 + 4.42091i −0.153360 + 0.265627i −0.932460 0.361272i \(-0.882343\pi\)
0.779101 + 0.626899i \(0.215676\pi\)
\(278\) −33.5730 −2.01357
\(279\) −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 \(0.182875\pi\)
\(282\) −2.53587 + 16.2538i −0.151009 + 0.967903i
\(283\) −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
\(285\) 1.72084 11.0299i 0.101934 0.653354i
\(286\) 2.36843 4.10224i 0.140048 0.242571i
\(287\) 0 0
\(288\) 5.93351 5.39242i 0.349635 0.317751i
\(289\) −6.04208 −0.355417
\(290\) −3.63729 + 6.29997i −0.213589 + 0.369947i
\(291\) −13.3815 + 5.17220i −0.784439 + 0.303200i
\(292\) −19.3276 33.4764i −1.13106 1.95906i
\(293\) 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
\(296\) 44.0549 2.56064
\(297\) −3.87186 5.87260i −0.224668 0.340763i
\(298\) −5.20269 −0.301384
\(299\) 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
\(303\) 26.2153 10.1327i 1.50603 0.582106i
\(304\) 2.50953 4.34663i 0.143931 0.249297i
\(305\) −1.63491 −0.0936145
\(306\) 22.5770 + 7.22054i 1.29064 + 0.412771i
\(307\) −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
\(310\) −11.4147 19.7709i −0.648313 1.12291i
\(311\) −16.1984 28.0565i −0.918528 1.59094i −0.801652 0.597791i \(-0.796045\pi\)
−0.116876 0.993146i \(-0.537288\pi\)
\(312\) −1.58559 + 10.1630i −0.0897663 + 0.575364i
\(313\) 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 \(-0.0397723\pi\)
\(318\) −24.8909 + 9.62079i −1.39581 + 0.539507i
\(319\) −0.706261 1.22328i −0.0395430 0.0684905i
\(320\) 15.9600 + 27.6436i 0.892193 + 1.54532i
\(321\) −23.6109 19.0295i −1.31783 1.06213i
\(322\) 0 0
\(323\) −7.30441 −0.406428
\(324\) 27.0991 + 19.3085i 1.50551 + 1.07269i
\(325\) −5.17713 −0.287175
\(326\) 0.463715 0.803178i 0.0256828 0.0444839i
\(327\) −21.0355 16.9539i −1.16326 0.937550i
\(328\) −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 \(0.986863\pi\)
\(332\) −7.27381 −0.399202
\(333\) −6.93082 31.8817i −0.379807 1.74711i
\(334\) −17.4188 −0.953116
\(335\) −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 \(0.748273\pi\)
\(338\) −12.9498 22.4296i −0.704374 1.22001i
\(339\) −0.450990 + 2.89066i −0.0244944 + 0.156999i
\(340\) −17.8736 + 30.9580i −0.969332 + 1.67893i
\(341\) 4.43285 0.240052
\(342\) −15.0496 4.81312i −0.813788 0.260264i
\(343\) 0 0
\(344\) 8.79558 15.2344i 0.474226 0.821383i
\(345\) 12.4026 4.79381i 0.667732 0.258090i
\(346\) 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 \(0.850652\pi\)
\(348\) 5.20245 + 4.19299i 0.278881 + 0.224768i
\(349\) −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
\(352\) −3.61792 −0.192836
\(353\) 8.53072 14.7756i 0.454045 0.786428i −0.544588 0.838704i \(-0.683314\pi\)
0.998633 + 0.0522753i \(0.0166473\pi\)
\(354\) 39.3152 + 31.6867i 2.08958 + 1.68413i
\(355\) −18.8655 32.6759i −1.00127 1.73426i
\(356\) −11.8440 20.5144i −0.627731 1.08726i
\(357\) 0 0
\(358\) −12.6323 + 21.8798i −0.667639 + 1.15639i
\(359\) −2.96726 −0.156606 −0.0783030 0.996930i \(-0.524950\pi\)
−0.0783030 + 0.996930i \(0.524950\pi\)
\(360\) −26.2686 + 23.8731i −1.38448 + 1.25823i
\(361\) −14.1310 −0.743736
\(362\) 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
\(366\) −0.356713 + 2.28638i −0.0186457 + 0.119511i
\(367\) −5.07874 + 8.79664i −0.265108 + 0.459181i −0.967592 0.252519i \(-0.918741\pi\)
0.702484 + 0.711700i \(0.252074\pi\)
\(368\) 5.97827 0.311639
\(369\) −4.01528 + 3.64912i −0.209027 + 0.189966i
\(370\) 75.8207 3.94173
\(371\) 0 0
\(372\) −19.5591 + 7.55992i −1.01409 + 0.391964i
\(373\) 12.7423 + 22.0703i 0.659771 + 1.14276i 0.980675 + 0.195645i \(0.0626799\pi\)
−0.320904 + 0.947112i \(0.603987\pi\)
\(374\) −5.34798 9.26297i −0.276537 0.478977i
\(375\) 5.78458 + 4.66217i 0.298715 + 0.240754i
\(376\) −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
\(381\) 5.35273 + 4.31411i 0.274229 + 0.221019i
\(382\) 9.89016 + 17.1303i 0.506025 + 0.876460i
\(383\) −13.6563 23.6535i −0.697806 1.20864i −0.969225 0.246175i \(-0.920826\pi\)
0.271419 0.962461i \(-0.412507\pi\)
\(384\) 33.5056 12.9505i 1.70983 0.660878i
\(385\) 0 0
\(386\) 44.8370 2.28214
\(387\) −12.4086 3.96848i −0.630763 0.201729i
\(388\) −30.6229 −1.55464
\(389\) −2.09223 + 3.62385i −0.106080 + 0.183736i −0.914179 0.405311i \(-0.867163\pi\)
0.808099 + 0.589047i \(0.200497\pi\)
\(390\) −2.72888 + 17.4909i −0.138182 + 0.885689i
\(391\) −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
\(395\) 2.24228 0.112821
\(396\) −3.18956 14.6719i −0.160281 0.737293i
\(397\) 30.6709 1.53933 0.769664 0.638450i \(-0.220424\pi\)
0.769664 + 0.638450i \(0.220424\pi\)
\(398\) 17.1958 29.7840i 0.861948 1.49294i
\(399\) 0 0
\(400\) −4.01629 6.95642i −0.200815 0.347821i
\(401\) 3.42402 + 5.93057i 0.170987 + 0.296158i 0.938765 0.344557i \(-0.111971\pi\)
−0.767778 + 0.640716i \(0.778638\pi\)
\(402\) 41.2393 + 33.2375i 2.05683 + 1.65773i
\(403\) −2.40027 + 4.15739i −0.119566 + 0.207095i
\(404\) 59.9922 2.98472
\(405\) 21.4092 + 15.2543i 1.06383 + 0.757994i
\(406\) 0 0
\(407\) −7.36113 + 12.7499i −0.364878 + 0.631987i
\(408\) 18.0836 + 14.5748i 0.895272 + 0.721558i
\(409\) −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
\(411\) −12.1094 + 4.68050i −0.597313 + 0.230872i
\(412\) −4.11646 + 7.12991i −0.202803 + 0.351265i
\(413\) 0 0
\(414\) −3.99798 18.3906i −0.196490 0.903851i
\(415\) −5.74655 −0.282087
\(416\) 1.95901 3.39311i 0.0960485 0.166361i
\(417\) −3.75552 + 24.0713i −0.183909 + 1.17878i
\(418\) 3.56490 + 6.17458i 0.174365 + 0.302009i
\(419\) −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 \(-0.00284791\pi\)
\(422\) −33.0542 −1.60905
\(423\) 11.3701 + 3.63636i 0.552833 + 0.176806i
\(424\) −26.1477 −1.26985
\(425\) −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
\(429\) −2.67631 2.15701i −0.129213 0.104141i
\(430\) 15.1376 26.2191i 0.730001 1.26440i
\(431\) 20.2427 0.975055 0.487527 0.873108i \(-0.337899\pi\)
0.487527 + 0.873108i \(0.337899\pi\)
\(432\) 6.50569 + 9.86744i 0.313005 + 0.474748i
\(433\) 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
\(436\) −28.8346 49.9431i −1.38093 2.39184i
\(437\) 2.89978 + 5.02257i 0.138715 + 0.240262i
\(438\) −40.3178 + 15.5835i −1.92646 + 0.744610i
\(439\) −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 \(0.0158559\pi\)
\(444\) 10.7355 68.8101i 0.509485 3.26558i
\(445\) −9.35716 16.2071i −0.443572 0.768289i
\(446\) 5.57946 + 9.66391i 0.264195 + 0.457599i
\(447\) −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 \(0.746215\pi\)
\(450\) −18.7138 + 17.0072i −0.882176 + 0.801728i
\(451\) 2.44830 0.115286
\(452\) −3.12244 + 5.40823i −0.146867 + 0.254382i
\(453\) 22.6628 8.75958i 1.06479 0.411561i
\(454\) −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 \(0.0948711\pi\)
\(458\) 67.0062 3.13099
\(459\) 7.70252 15.3797i 0.359523 0.717863i
\(460\) 28.3826 1.32335
\(461\) −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 \(0.625457\pi\)
\(464\) 1.18670 + 2.05542i 0.0550909 + 0.0954203i
\(465\) −15.4523 + 5.97259i −0.716583 + 0.276972i
\(466\) 16.4721 28.5305i 0.763054 1.32165i
\(467\) −34.9527 −1.61742 −0.808709 0.588209i \(-0.799833\pi\)
−0.808709 + 0.588209i \(0.799833\pi\)
\(468\) 15.4873 + 4.95311i 0.715901 + 0.228958i
\(469\) 0 0
\(470\) −13.8707 + 24.0248i −0.639809 + 1.10818i
\(471\) 0.791979 5.07625i 0.0364925 0.233901i
\(472\) 24.7386 + 42.8485i 1.13869 + 1.97226i
\(473\) 2.93930 + 5.09102i 0.135149 + 0.234086i
\(474\) 0.489233 3.13578i 0.0224712 0.144031i
\(475\) 3.89623 6.74848i 0.178771 0.309641i
\(476\) 0 0
\(477\) 4.11362 + 18.9226i 0.188350 + 0.866407i
\(478\) 26.4021 1.20760
\(479\) −14.9054 + 25.8170i −0.681047 + 1.17961i 0.293615 + 0.955924i \(0.405142\pi\)
−0.974662 + 0.223684i \(0.928192\pi\)
\(480\) 12.6116 4.87460i 0.575638 0.222494i
\(481\) −7.97172 13.8074i −0.363479 0.629565i
\(482\) 27.6516 + 47.8939i 1.25949 + 2.18151i
\(483\) 0 0
\(484\) 16.9467 29.3525i 0.770304 1.33421i
\(485\) −24.1931 −1.09855
\(486\) 26.0040 26.6120i 1.17957 1.20714i
\(487\) 22.4506 1.01733 0.508667 0.860964i \(-0.330139\pi\)
0.508667 + 0.860964i \(0.330139\pi\)
\(488\) −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 \(0.543016\pi\)
\(492\) −10.8026 + 4.17541i −0.487020 + 0.188242i
\(493\) 1.72704 2.99132i 0.0777819 0.134722i
\(494\) −7.72119 −0.347393
\(495\) −2.51986 11.5913i −0.113259 0.520991i
\(496\) −7.44830 −0.334438
\(497\) 0 0
\(498\) −1.25381 + 8.03642i −0.0561848 + 0.360121i
\(499\) 4.46760 + 7.73811i 0.199997 + 0.346405i 0.948527 0.316696i \(-0.102573\pi\)
−0.748530 + 0.663101i \(0.769240\pi\)
\(500\) 7.92929 + 13.7339i 0.354609 + 0.614200i
\(501\) −1.94850 + 12.4890i −0.0870524 + 0.557969i
\(502\) 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
\(507\) −17.5303 + 6.77577i −0.778547 + 0.300922i
\(508\) 7.33732 + 12.7086i 0.325541 + 0.563854i
\(509\) −14.0555 24.3449i −0.623000 1.07907i −0.988924 0.148423i \(-0.952580\pi\)
0.365924 0.930645i \(-0.380753\pi\)
\(510\) 31.1228 + 25.0839i 1.37814 + 1.11073i
\(511\) 0 0
\(512\) 24.5070 1.08307
\(513\) −5.13440 + 10.2519i −0.226689 + 0.452633i
\(514\) 24.7661 1.09238
\(515\) −3.25214 + 5.63287i −0.143306 + 0.248214i
\(516\) −21.6515 17.4503i −0.953153 0.768208i
\(517\) −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
\(521\) 8.47536 0.371312 0.185656 0.982615i \(-0.440559\pi\)
0.185656 + 0.982615i \(0.440559\pi\)
\(522\) 5.52937 5.02513i 0.242014 0.219944i
\(523\) 33.4473 1.46255 0.731273 0.682085i \(-0.238926\pi\)
0.731273 + 0.682085i \(0.238926\pi\)
\(524\) 9.85035 17.0613i 0.430315 0.745327i
\(525\) 0 0
\(526\) −22.8341 39.5498i −0.995613 1.72445i
\(527\) 5.41988 + 9.38751i 0.236094 + 0.408926i
\(528\) 0.822124 5.26947i 0.0357784 0.229324i
\(529\) 8.04603 13.9361i 0.349827 0.605919i
\(530\) −45.0015 −1.95474
\(531\) 27.1167 24.6439i 1.17677 1.06945i
\(532\) 0 0
\(533\) −1.32569 + 2.29616i −0.0574220 + 0.0994579i
\(534\) −24.7068 + 9.54962i −1.06917 + 0.413253i
\(535\) −25.5693 44.2874i −1.10546 1.91471i
\(536\) 25.9493 + 44.9456i 1.12084 + 1.94135i
\(537\) 14.2744 + 11.5047i 0.615987 + 0.496464i
\(538\) −10.5461 + 18.2665i −0.454677 + 0.787523i
\(539\) 0 0
\(540\) 30.8866 + 46.8469i 1.32915 + 2.01597i
\(541\) 18.2586 0.784998 0.392499 0.919752i \(-0.371611\pi\)
0.392499 + 0.919752i \(0.371611\pi\)
\(542\) −21.8865 + 37.9085i −0.940106 + 1.62831i
\(543\) −26.4740 21.3371i −1.13611 0.915664i
\(544\) −4.42350 7.66173i −0.189656 0.328494i
\(545\) −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 \(0.206045\pi\)
\(548\) −27.7117 −1.18378
\(549\) 1.59940 + 0.511515i 0.0682606 + 0.0218309i
\(550\) 11.4106 0.486551
\(551\) −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
\(555\) 8.48141 54.3622i 0.360016 2.30755i
\(556\) −26.0014 + 45.0358i −1.10271 + 1.90994i
\(557\) −33.3821 −1.41445 −0.707223 0.706991i \(-0.750052\pi\)
−0.707223 + 0.706991i \(0.750052\pi\)
\(558\) 4.98106 + 22.9128i 0.210865 + 0.969977i
\(559\) −6.36623 −0.269263
\(560\) 0 0
\(561\) −7.23964 + 2.79825i −0.305658 + 0.118142i
\(562\) 2.03643 + 3.52720i 0.0859015 + 0.148786i
\(563\) 1.09566 + 1.89773i 0.0461764 + 0.0799799i 0.888190 0.459477i \(-0.151963\pi\)
−0.842013 + 0.539457i \(0.818630\pi\)
\(564\) 19.8394 + 15.9899i 0.835392 + 0.673296i
\(565\) −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 \(0.296951\pi\)
\(570\) −20.7460 16.7206i −0.868956 0.700348i
\(571\) 10.8690 + 18.8257i 0.454854 + 0.787831i 0.998680 0.0513674i \(-0.0163580\pi\)
−0.543825 + 0.839198i \(0.683025\pi\)
\(572\) −3.66858 6.35417i −0.153391 0.265681i
\(573\) 13.3885 5.17488i 0.559311 0.216184i
\(574\) 0 0
\(575\) 9.28172 0.387074
\(576\) −6.96449 32.0366i −0.290187 1.33486i
\(577\) −30.9032 −1.28652 −0.643258 0.765649i \(-0.722418\pi\)
−0.643258 + 0.765649i \(0.722418\pi\)
\(578\) −7.21083 + 12.4895i −0.299931 + 0.519496i
\(579\) 5.01553 32.1474i 0.208438 1.33600i
\(580\) 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
\(584\) −42.3535 −1.75260
\(585\) 12.2355 + 3.91312i 0.505875 + 0.161788i
\(586\) 12.4214 0.513122
\(587\) 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
\(590\) 42.5763 + 73.7444i 1.75284 + 3.03601i
\(591\) −8.08650 6.51743i −0.332634 0.268091i
\(592\) 12.3685 21.4230i 0.508344 0.880478i
\(593\) 27.7550 1.13976 0.569880 0.821728i \(-0.306990\pi\)
0.569880 + 0.821728i \(0.306990\pi\)
\(594\) −16.7600 + 0.994906i −0.687671 + 0.0408215i
\(595\) 0 0
\(596\) −4.02936 + 6.97905i −0.165049 + 0.285873i
\(597\) −19.4311 15.6608i −0.795264 0.640955i
\(598\) −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 \(0.835953\pi\)
\(600\) −23.1114 + 8.93298i −0.943520 + 0.364687i
\(601\) −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
\(604\) 51.8626 2.11026
\(605\) 13.3885 23.1895i 0.544318 0.942787i
\(606\) 10.3411 66.2819i 0.420077 2.69252i
\(607\) 12.0348 + 20.8449i 0.488479 + 0.846070i 0.999912 0.0132531i \(-0.00421872\pi\)
−0.511434 + 0.859323i \(0.670885\pi\)
\(608\) 2.94865 + 5.10721i 0.119584 + 0.207125i
\(609\) 0 0
\(610\) −1.95115 + 3.37950i −0.0789999 + 0.136832i
\(611\) 5.83343 0.235995
\(612\) 27.1712 24.6934i 1.09833 0.998172i
\(613\) −20.3815 −0.823200 −0.411600 0.911365i \(-0.635030\pi\)
−0.411600 + 0.911365i \(0.635030\pi\)
\(614\) −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 \(-0.485684\pi\)
\(618\) 7.16786 + 5.77705i 0.288334 + 0.232387i
\(619\) 7.41095 12.8361i 0.297871 0.515928i −0.677777 0.735267i \(-0.737057\pi\)
0.975649 + 0.219339i \(0.0703900\pi\)
\(620\) −35.3617 −1.42016
\(621\) −13.6330 + 0.809283i −0.547075 + 0.0324754i
\(622\) −77.3270 −3.10053
\(623\) 0 0
\(624\) 4.49687 + 3.62432i 0.180019 + 0.145089i
\(625\) 15.0930 + 26.1419i 0.603722 + 1.04568i
\(626\) −1.81291 3.14005i −0.0724585 0.125502i
\(627\) 4.82585 1.86528i 0.192726 0.0744920i
\(628\) 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
\(633\) −3.69749 + 23.6994i −0.146962 + 0.941965i
\(634\) −25.6694 44.4607i −1.01946 1.76576i
\(635\) 5.79673 + 10.0402i 0.230036 + 0.398434i
\(636\) −6.37180 + 40.8406i −0.252658 + 1.61943i
\(637\) 0 0
\(638\) −3.37150 −0.133479
\(639\) 8.23233 + 37.8686i 0.325666 + 1.49806i
\(640\) 60.5764 2.39449
\(641\) −5.96592 + 10.3333i −0.235640 + 0.408140i −0.959458 0.281850i \(-0.909052\pi\)
0.723819 + 0.689990i \(0.242385\pi\)
\(642\) −67.5138 + 26.0953i −2.66456 + 1.02990i
\(643\) 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
\(647\) 0.988954 0.0388798 0.0194399 0.999811i \(-0.493812\pi\)
0.0194399 + 0.999811i \(0.493812\pi\)
\(648\) 33.1673 15.1359i 1.30293 0.594595i
\(649\) −16.5343 −0.649027
\(650\) −6.17856 + 10.7016i −0.242343 + 0.419751i
\(651\) 0 0
\(652\) −0.718272 1.24408i −0.0281297 0.0487221i
\(653\) −11.3573 19.6715i −0.444447 0.769804i 0.553567 0.832805i \(-0.313266\pi\)
−0.998014 + 0.0630004i \(0.979933\pi\)
\(654\) −60.1496 + 23.2489i −2.35203 + 0.909103i
\(655\) 7.78211 13.4790i 0.304072 0.526668i
\(656\) −4.11376 −0.160615
\(657\) 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 \(0.897824\pi\)
\(660\) 3.90314 25.0175i 0.151929 0.973804i
\(661\) 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
\(663\) 1.29571 8.30495i 0.0503212 0.322538i
\(664\) −3.98486 + 6.90198i −0.154642 + 0.267849i
\(665\) 0 0
\(666\) −74.1738 23.7221i −2.87418 0.919213i
\(667\) −2.74247 −0.106189
\(668\) −13.4905 + 23.3662i −0.521962 + 0.904064i
\(669\) 7.55300 2.91937i 0.292016 0.112869i
\(670\) 44.6601 + 77.3535i 1.72537 + 2.98843i
\(671\) −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 \(0.953505\pi\)
\(674\) 23.1403 0.891332
\(675\) 10.1006 + 15.3199i 0.388771 + 0.589665i
\(676\) −40.1171 −1.54297
\(677\) −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
\(681\) −31.8471 + 12.3095i −1.22038 + 0.471700i
\(682\) 5.29031 9.16309i 0.202577 0.350873i
\(683\) −15.1871 −0.581120 −0.290560 0.956857i \(-0.593842\pi\)
−0.290560 + 0.956857i \(0.593842\pi\)
\(684\) −18.1120 + 16.4603i −0.692529 + 0.629376i
\(685\) −21.8932 −0.836495
\(686\) 0 0
\(687\) 7.49540 48.0424i 0.285967 1.83293i
\(688\) −4.93877 8.55420i −0.188289 0.326126i
\(689\) 4.73142 + 8.19507i 0.180253 + 0.312207i
\(690\) 4.89241 31.3583i 0.186251 1.19379i
\(691\) 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
\(696\) 6.82874 2.63943i 0.258843 0.100047i
\(697\) 2.99344 + 5.18480i 0.113385 + 0.196388i
\(698\) 19.4429 + 33.6761i 0.735924 + 1.27466i
\(699\) −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 \(0.571850\pi\)
\(702\) 8.14202 16.2573i 0.307301 0.613590i
\(703\) 23.9976 0.905088
\(704\) −7.39689 + 12.8118i −0.278781 + 0.482862i
\(705\) 15.6738 + 12.6326i 0.590310 + 0.475769i
\(706\) −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 \(-0.113337\pi\)
\(710\) −90.0587 −3.37984
\(711\) −2.19358 0.701545i −0.0822656 0.0263100i
\(712\) −25.9543 −0.972679
\(713\) 4.30328 7.45351i 0.161159 0.279136i
\(714\) 0 0
\(715\) −2.89830 5.02001i −0.108390 0.187738i
\(716\) 19.5669 + 33.8908i 0.731248 + 1.26656i
\(717\) 2.95337 18.9299i 0.110296 0.706949i
\(718\) −3.54123 + 6.13359i −0.132158 + 0.228904i
\(719\) 20.9109 0.779845 0.389923 0.920848i \(-0.372502\pi\)
0.389923 + 0.920848i \(0.372502\pi\)
\(720\) 4.23400 + 19.4763i 0.157792 + 0.725840i
\(721\) 0 0
\(722\) −16.8644 + 29.2100i −0.627628 + 1.08708i
\(723\) 37.4323 14.4683i 1.39212 0.538081i
\(724\) −36.2896 62.8554i −1.34869 2.33600i
\(725\) 1.84243 + 3.19119i 0.0684263 + 0.118518i
\(726\) −29.5088 23.7831i −1.09517 0.882672i
\(727\) −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
\(730\) −72.8924 −2.69787
\(731\) −7.18756 + 12.4492i −0.265841 + 0.460451i
\(732\) 2.79075 + 2.24925i 0.103149 + 0.0831347i
\(733\) 7.07446 + 12.2533i 0.261301 + 0.452587i 0.966588 0.256335i \(-0.0825151\pi\)
−0.705287 + 0.708922i \(0.749182\pi\)
\(734\) 12.1223 + 20.9964i 0.447442 + 0.774992i
\(735\) 0 0
\(736\) −3.51218 + 6.08327i −0.129461 + 0.224232i
\(737\) −17.3435 −0.638855
\(738\) 2.75108 + 12.6549i 0.101269 + 0.465835i
\(739\) 15.7181 0.578200 0.289100 0.957299i \(-0.406644\pi\)
0.289100 + 0.957299i \(0.406644\pi\)
\(740\) 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 \(0.706836\pi\)
\(744\) −3.54170 + 22.7008i −0.129845 + 0.832252i
\(745\) −3.18333 + 5.51368i −0.116628 + 0.202006i
\(746\) 60.8283 2.22708
\(747\) 5.62174 + 1.79793i 0.205689 + 0.0657828i
\(748\) −16.5675 −0.605768
\(749\) 0 0
\(750\) 16.5406 6.39325i 0.603979 0.233449i
\(751\) −6.51848 11.2903i −0.237863 0.411990i 0.722238 0.691644i \(-0.243113\pi\)
−0.960101 + 0.279654i \(0.909780\pi\)
\(752\) 4.52544 + 7.83829i 0.165026 + 0.285833i
\(753\) −10.4973 8.46047i −0.382543 0.308317i
\(754\) 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
\(759\) 4.79817 + 3.86716i 0.174162 + 0.140369i
\(760\) −13.0542 22.6105i −0.473525 0.820169i
\(761\) −3.02038 5.23146i −0.109489 0.189640i 0.806074 0.591814i \(-0.201588\pi\)
−0.915563 + 0.402174i \(0.868255\pi\)
\(762\) 15.3058 5.91596i 0.554470 0.214313i
\(763\) 0 0
\(764\) 30.6388 1.10847
\(765\) 21.4662 19.5086i 0.776111 0.705336i
\(766\) −65.1918 −2.35547
\(767\) 8.95288 15.5068i 0.323270 0.559920i
\(768\) 7.38122 47.3105i 0.266347 1.70717i
\(769\) −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
\(773\) 37.6264 1.35333 0.676663 0.736293i \(-0.263425\pi\)
0.676663 + 0.736293i \(0.263425\pi\)
\(774\) −23.0120 + 20.9135i −0.827150 + 0.751721i
\(775\) −11.5640 −0.415393
\(776\) −16.7763 + 29.0575i −0.602235 + 1.04310i
\(777\) 0 0
\(778\) 4.99388 + 8.64965i 0.179039 + 0.310105i
\(779\) −1.99539 3.45612i −0.0714923 0.123828i
\(780\) 21.3495 + 17.2069i 0.764433 + 0.616106i
\(781\) 8.74345 15.1441i 0.312865 0.541898i