Properties

Label 441.2.f.f.148.5
Level $441$
Weight $2$
Character 441.148
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 148.5
Root \(1.19343 + 2.06709i\) of defining polynomial
Character \(\chi\) \(=\) 441.148
Dual form 441.2.f.f.295.5

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

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

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 0.886585 + 0.462565i \(0.153071\pi\)
−0.0426999 + 0.999088i \(0.513596\pi\)
\(3\) −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 0.329235 + 0.944248i \(0.393209\pi\)
−0.982360 + 0.186998i \(0.940124\pi\)
\(6\) −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 0.949839 0.312738i \(-0.101246\pi\)
−0.745759 + 0.666216i \(0.767913\pi\)
\(12\) −0.987132 6.32710i −0.284960 1.82648i
\(13\) 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
\(17\) 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 −0.969887 0.243555i \(-0.921686\pi\)
0.695868 + 0.718169i \(0.255020\pi\)
\(24\) 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 0.910392 0.413747i \(-0.135780\pi\)
−0.813511 + 0.581549i \(0.802447\pi\)
\(30\) 9.40187 7.57758i 1.71654 1.38347i
\(31\) 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
\(33\) −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 −0.786732 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 \(0.940759\pi\)
\(44\) −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 0.973859 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
\(51\) −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 0.127735 + 0.991808i \(0.459229\pi\)
−0.922799 + 0.385283i \(0.874104\pi\)
\(60\) 17.4463 + 6.74331i 2.25231 + 0.870558i
\(61\) 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
\(66\) −0.862710 5.52960i −0.106192 0.680647i
\(67\) −6.40588 + 11.0953i −0.782603 + 1.35551i 0.147817 + 0.989015i \(0.452775\pi\)
−0.930420 + 0.366494i \(0.880558\pi\)
\(68\) −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 0.843625 0.536933i \(-0.180417\pi\)
−0.886810 + 0.462134i \(0.847084\pi\)
\(80\) 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 0.914950 0.403567i \(-0.132230\pi\)
−0.806974 + 0.590587i \(0.798896\pi\)
\(84\) 0 0
\(85\) −4.83443 + 8.37348i −0.524368 + 0.908232i
\(86\) 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 0.995988 0.0894847i \(-0.0285220\pi\)
−0.575490 + 0.817809i \(0.695189\pi\)
\(98\) 0 0
\(99\) 3.86814 1.23710i 0.388762 0.124333i
\(100\) 13.0563 1.30563
\(101\) −8.11331 14.0527i −0.807305 1.39829i −0.914724 0.404079i \(-0.867592\pi\)
0.107419 0.994214i \(-0.465741\pi\)
\(102\) −12.7649 4.93387i −1.26392 0.488526i
\(103\) −1.11342 + 1.92849i −0.109708 + 0.190020i −0.915652 0.401972i \(-0.868325\pi\)
0.805944 + 0.591992i \(0.201658\pi\)
\(104\) −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 −0.903012 0.429615i \(-0.858649\pi\)
0.823563 + 0.567224i \(0.191983\pi\)
\(114\) 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 −0.725844 0.687860i \(-0.758550\pi\)
0.958626 + 0.284669i \(0.0918837\pi\)
\(132\) 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 0.980527 0.196385i \(-0.0629202\pi\)
−0.660338 + 0.750969i \(0.729587\pi\)
\(138\) 8.46013 6.81856i 0.720174 0.580435i
\(139\) −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
\(143\) 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 −0.907209 0.420680i \(-0.861791\pi\)
0.817924 + 0.575326i \(0.195125\pi\)
\(150\) 2.25056 + 14.4252i 0.183758 + 1.17781i
\(151\) −7.01387 12.1484i −0.570781 0.988621i −0.996486 0.0837595i \(-0.973307\pi\)
0.425705 0.904862i \(-0.360026\pi\)
\(152\) 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 −0.800755 0.598993i \(-0.795568\pi\)
0.919120 + 0.393978i \(0.128901\pi\)
\(158\) 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 −0.971965 0.235124i \(-0.924450\pi\)
0.689606 + 0.724185i \(0.257784\pi\)
\(168\) 0 0
\(169\) 5.42542 + 9.39710i 0.417340 + 0.722854i
\(170\) −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 0.778598 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
\(177\) −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 0.676276 0.736648i \(-0.263593\pi\)
−0.976094 + 0.217348i \(0.930259\pi\)
\(192\) 14.7376 11.8780i 1.06359 0.857218i
\(193\) 9.39242 16.2682i 0.676082 1.17101i −0.300070 0.953917i \(-0.597010\pi\)
0.976152 0.217090i \(-0.0696566\pi\)
\(194\) −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 −0.999643 0.0267212i \(-0.991493\pi\)
0.522963 + 0.852356i \(0.324827\pi\)
\(212\) −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 0.777082 0.629399i \(-0.216699\pi\)
−0.933617 + 0.358273i \(0.883366\pi\)
\(224\) 0 0
\(225\) −10.0909 + 3.22724i −0.672725 + 0.215149i
\(226\) −4.03169 −0.268184
\(227\) 9.85631 + 17.0716i 0.654187 + 1.13308i 0.982097 + 0.188376i \(0.0603222\pi\)
−0.327910 + 0.944709i \(0.606344\pi\)
\(228\) 2.17819 + 13.9613i 0.144254 + 0.924609i
\(229\) 14.0364 24.3118i 0.927552 1.60657i 0.140148 0.990131i \(-0.455242\pi\)
0.787404 0.616437i \(-0.211425\pi\)
\(230\) 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 −0.629834 0.776730i \(-0.716877\pi\)
0.987585 + 0.157087i \(0.0502104\pi\)
\(240\) −8.95957 + 7.22110i −0.578338 + 0.466120i
\(241\) −11.5849 20.0656i −0.746247 1.29254i −0.949610 0.313435i \(-0.898520\pi\)
0.203362 0.979104i \(-0.434813\pi\)
\(242\) 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 −0.657614 0.753355i \(-0.728434\pi\)
0.981232 + 0.192833i \(0.0617676\pi\)
\(258\) 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 0.994245 + 0.107128i \(0.0341653\pi\)
−0.404347 + 0.914605i \(0.632501\pi\)
\(264\) 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 0.779101 0.626899i \(-0.215676\pi\)
−0.932460 + 0.361272i \(0.882343\pi\)
\(278\) −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 0.839455 0.543430i \(-0.182875\pi\)
−0.890351 + 0.455274i \(0.849541\pi\)
\(282\) −2.53587 16.2538i −0.151009 0.967903i
\(283\) −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
\(285\) 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 −0.779955 0.625835i \(-0.784758\pi\)
0.931967 + 0.362543i \(0.118091\pi\)
\(294\) 0 0
\(295\) −17.8377 30.8959i −1.03855 1.79883i
\(296\) 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 −0.116876 + 0.993146i \(0.537288\pi\)
−0.801652 + 0.597791i \(0.796045\pi\)
\(312\) −1.58559 10.1630i −0.0897663 0.575364i
\(313\) 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 \(0.626894\pi\)
\(318\) −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 −0.999149 0.0412580i \(-0.986863\pi\)
0.463844 0.885917i \(-0.346470\pi\)
\(332\) −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 −0.703260 0.710933i \(-0.748273\pi\)
0.967316 + 0.253575i \(0.0816063\pi\)
\(338\) −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 −0.891935 0.452164i \(-0.850652\pi\)
0.837553 + 0.546356i \(0.183985\pi\)
\(348\) 5.20245 4.19299i 0.278881 0.224768i
\(349\) −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
\(352\) −3.61792 −0.192836
\(353\) 8.53072 + 14.7756i 0.454045 + 0.786428i 0.998633 0.0522753i \(-0.0166473\pi\)
−0.544588 + 0.838704i \(0.683314\pi\)
\(354\) 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 0.702484 0.711700i \(-0.252074\pi\)
−0.967592 + 0.252519i \(0.918741\pi\)
\(368\) 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 −0.320904 0.947112i \(-0.603987\pi\)
0.980675 0.195645i \(-0.0626799\pi\)
\(374\) −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 0.271419 + 0.962461i \(0.412507\pi\)
−0.969225 + 0.246175i \(0.920826\pi\)
\(384\) 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 0.808099 0.589047i \(-0.200497\pi\)
−0.914179 + 0.405311i \(0.867163\pi\)
\(390\) −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 −0.767778 0.640716i \(-0.778638\pi\)
0.938765 + 0.344557i \(0.111971\pi\)
\(402\) 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 −0.998491 0.0549104i \(-0.982513\pi\)
0.546799 + 0.837264i \(0.315846\pi\)
\(410\) −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 0.449698 + 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 \(0.663819\pi\)
\(422\) −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 −0.884191 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 \(0.682523\pi\)
\(444\) 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 0.955912 0.293653i \(-0.0948711\pi\)
−0.732267 + 0.681017i \(0.761538\pi\)
\(458\) 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 −0.999951 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 \(-0.0412094\pi\)
\(464\) 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 −0.974662 0.223684i \(-0.928192\pi\)
0.293615 0.955924i \(-0.405142\pi\)
\(480\) 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 −0.134726 0.990883i \(-0.543016\pi\)
0.925493 0.378765i \(-0.123651\pi\)
\(492\) −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 −0.748530 0.663101i \(-0.769240\pi\)
0.948527 + 0.316696i \(0.102573\pi\)
\(500\) 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 0.365924 + 0.930645i \(0.380753\pi\)
−0.988924 + 0.148423i \(0.952580\pi\)
\(510\) 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 0.797709 0.603043i \(-0.206045\pi\)
−0.921105 + 0.389315i \(0.872712\pi\)
\(548\) −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 −0.842013 0.539457i \(-0.818630\pi\)
0.888190 + 0.459477i \(0.151963\pi\)
\(564\) 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 0.595507 0.803350i \(-0.296951\pi\)
−0.993475 + 0.114049i \(0.963618\pi\)
\(570\) −20.7460 + 16.7206i −0.868956 + 0.700348i
\(571\) 10.8690 18.8257i 0.454854 0.787831i −0.543825 0.839198i \(-0.683025\pi\)
0.998680 + 0.0513674i \(0.0163580\pi\)
\(572\) −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 0.990922 0.134436i \(-0.0429222\pi\)
−0.611886 + 0.790946i \(0.709589\pi\)
\(588\) 0 0
\(589\) −3.61282 + 6.25759i −0.148864 + 0.257840i
\(590\) 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 −0.870111 0.492856i \(-0.835953\pi\)
0.861881 + 0.507110i \(0.169286\pi\)
\(600\) −23.1114 8.93298i −0.943520 0.364687i
\(601\) −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
\(604\) 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 −0.511434 0.859323i \(-0.670885\pi\)
0.999912 + 0.0132531i \(0.00421872\pi\)
\(608\) 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 0.0449604 + 0.998989i \(0.485684\pi\)
−0.887630 + 0.460558i \(0.847650\pi\)
\(618\) 7.16786 5.77705i 0.288334 0.232387i
\(619\) 7.41095 + 12.8361i 0.297871 + 0.515928i 0.975649 0.219339i \(-0.0703900\pi\)
−0.677777 + 0.735267i \(0.737057\pi\)
\(620\) −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 0.723819 0.689990i \(-0.242385\pi\)
−0.959458 + 0.281850i \(0.909052\pi\)
\(642\) −67.5138 26.0953i −2.66456 1.02990i
\(643\) 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
\(647\) 0.988954 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 −0.998014 0.0630004i \(-0.979933\pi\)
0.553567 + 0.832805i \(0.313266\pi\)
\(654\) −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 −0.948922 0.315512i \(-0.897824\pi\)
0.201220 0.979546i \(-0.435509\pi\)
\(660\) 3.90314 + 25.0175i 0.151929 + 0.973804i
\(661\) 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
\(663\) 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 −0.989351 0.145549i \(-0.953505\pi\)
0.368626 0.929578i \(-0.379828\pi\)
\(674\) 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 −0.957043 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
\(681\) −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 0.890487 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
\(696\) 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 0.937278 + 0.348582i \(0.113337\pi\)
−0.166759 + 0.985998i \(0.553330\pi\)
\(710\) −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 0.840476 0.541849i \(-0.182276\pi\)
−0.889493 + 0.456949i \(0.848942\pi\)
\(728\) 0 0
\(729\) −16.1715 + 21.6213i −0.598945 + 0.800790i
\(730\) −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 −0.705287 0.708922i \(-0.749182\pi\)
0.966588 + 0.256335i \(0.0825151\pi\)
\(734\) 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 −0.605022 0.796208i \(-0.706836\pi\)
0.992048 + 0.125861i \(0.0401692\pi\)
\(744\) −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 −0.960101 0.279654i \(-0.909780\pi\)
0.722238 + 0.691644i \(0.243113\pi\)
\(752\) 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 −0.915563 0.402174i \(-0.868255\pi\)
0.806074 + 0.591814i \(0.201588\pi\)
\(762\) 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 −0.867968 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
\(773\) 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