Properties

Label 441.2.f.c.148.3
Level $441$
Weight $2$
Character 441.148
Analytic conductor $3.521$
Analytic rank $0$
Dimension $6$
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: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{18})\)
Defining polynomial: \(x^{6} - x^{3} + 1\)
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 148.3
Root \(0.939693 - 0.342020i\) of defining polynomial
Character \(\chi\) \(=\) 441.148
Dual form 441.2.f.c.295.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.439693 + 0.761570i) q^{2} +(0.592396 - 1.62760i) q^{3} +(0.613341 - 1.06234i) q^{4} +(0.673648 - 1.16679i) q^{5} +(1.50000 - 0.264490i) q^{6} +2.83750 q^{8} +(-2.29813 - 1.92836i) q^{9} +O(q^{10})\) \(q+(0.439693 + 0.761570i) q^{2} +(0.592396 - 1.62760i) q^{3} +(0.613341 - 1.06234i) q^{4} +(0.673648 - 1.16679i) q^{5} +(1.50000 - 0.264490i) q^{6} +2.83750 q^{8} +(-2.29813 - 1.92836i) q^{9} +1.18479 q^{10} +(-0.826352 - 1.43128i) q^{11} +(-1.36571 - 1.62760i) q^{12} +(-1.68479 + 2.91815i) q^{13} +(-1.50000 - 1.78763i) q^{15} +(0.0209445 + 0.0362770i) q^{16} -0.467911 q^{17} +(0.458111 - 2.59808i) q^{18} +3.22668 q^{19} +(-0.826352 - 1.43128i) q^{20} +(0.726682 - 1.25865i) q^{22} +(-4.47178 + 7.74535i) q^{23} +(1.68092 - 4.61830i) q^{24} +(1.59240 + 2.75811i) q^{25} -2.96316 q^{26} +(-4.50000 + 2.59808i) q^{27} +(-3.13429 - 5.42874i) q^{29} +(0.701867 - 1.92836i) q^{30} +(4.61721 - 7.99724i) q^{31} +(2.81908 - 4.88279i) q^{32} +(-2.81908 + 0.497079i) q^{33} +(-0.205737 - 0.356347i) q^{34} +(-3.45811 + 1.25865i) q^{36} +9.23442 q^{37} +(1.41875 + 2.45734i) q^{38} +(3.75150 + 4.47086i) q^{39} +(1.91147 - 3.31077i) q^{40} +(1.70574 - 2.95442i) q^{41} +(2.20574 + 3.82045i) q^{43} -2.02734 q^{44} +(-3.79813 + 1.38241i) q^{45} -7.86484 q^{46} +(4.67752 + 8.10170i) q^{47} +(0.0714517 - 0.0125989i) q^{48} +(-1.40033 + 2.42544i) q^{50} +(-0.277189 + 0.761570i) q^{51} +(2.06670 + 3.57964i) q^{52} -0.573978 q^{53} +(-3.95723 - 2.28471i) q^{54} -2.22668 q^{55} +(1.91147 - 5.25173i) q^{57} +(2.75624 - 4.77396i) q^{58} +(-5.19846 + 9.00400i) q^{59} +(-2.81908 + 0.497079i) q^{60} +(3.81908 + 6.61484i) q^{61} +8.12061 q^{62} +5.04189 q^{64} +(2.26991 + 3.93161i) q^{65} +(-1.61809 - 1.92836i) q^{66} +(-0.298133 + 0.516382i) q^{67} +(-0.286989 + 0.497079i) q^{68} +(9.95723 + 11.8666i) q^{69} -0.554378 q^{71} +(-6.52094 - 5.47172i) q^{72} -2.04963 q^{73} +(4.06031 + 7.03266i) q^{74} +(5.43242 - 0.957882i) q^{75} +(1.97906 - 3.42782i) q^{76} +(-1.75537 + 4.82283i) q^{78} +(1.20187 + 2.08169i) q^{79} +0.0564370 q^{80} +(1.56283 + 8.86327i) q^{81} +3.00000 q^{82} +(-7.52481 - 13.0334i) q^{83} +(-0.315207 + 0.545955i) q^{85} +(-1.93969 + 3.35965i) q^{86} +(-10.6925 + 1.88538i) q^{87} +(-2.34477 - 4.06126i) q^{88} -9.08647 q^{89} +(-2.72281 - 2.28471i) q^{90} +(5.48545 + 9.50108i) q^{92} +(-10.2811 - 12.2525i) q^{93} +(-4.11334 + 7.12452i) q^{94} +(2.17365 - 3.76487i) q^{95} +(-6.27719 - 7.48086i) q^{96} +(-0.949493 - 1.64457i) q^{97} +(-0.860967 + 4.88279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 3q^{2} - 3q^{4} + 3q^{5} + 9q^{6} + 12q^{8} + O(q^{10}) \) \( 6q - 3q^{2} - 3q^{4} + 3q^{5} + 9q^{6} + 12q^{8} - 6q^{11} - 18q^{12} - 3q^{13} - 9q^{15} - 3q^{16} - 12q^{17} + 9q^{18} + 6q^{19} - 6q^{20} - 9q^{22} - 12q^{23} + 27q^{24} + 6q^{25} + 6q^{26} - 27q^{27} - 9q^{29} + 18q^{30} - 3q^{31} + 9q^{34} - 27q^{36} - 6q^{37} + 6q^{38} - 18q^{39} - 9q^{40} + 3q^{43} + 30q^{44} - 9q^{45} + 3q^{47} + 6q^{50} + 9q^{51} - 21q^{52} + 12q^{53} + 27q^{54} - 9q^{57} + 9q^{58} - 3q^{59} + 6q^{61} + 60q^{62} + 24q^{64} - 15q^{65} - 36q^{66} + 12q^{67} + 6q^{68} + 9q^{69} + 18q^{71} - 36q^{72} + 42q^{73} + 30q^{74} + 9q^{75} + 15q^{76} + 54q^{78} + 21q^{79} + 30q^{80} + 18q^{82} - 18q^{83} - 9q^{85} - 6q^{86} - 9q^{87} - 27q^{88} - 24q^{89} - 27q^{90} - 3q^{92} - 27q^{93} - 18q^{94} + 12q^{95} - 27q^{96} - 3q^{97} + 18q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.439693 + 0.761570i 0.310910 + 0.538511i 0.978560 0.205964i \(-0.0660330\pi\)
−0.667650 + 0.744475i \(0.732700\pi\)
\(3\) 0.592396 1.62760i 0.342020 0.939693i
\(4\) 0.613341 1.06234i 0.306670 0.531169i
\(5\) 0.673648 1.16679i 0.301265 0.521806i −0.675158 0.737673i \(-0.735925\pi\)
0.976423 + 0.215867i \(0.0692579\pi\)
\(6\) 1.50000 0.264490i 0.612372 0.107978i
\(7\) 0 0
\(8\) 2.83750 1.00321
\(9\) −2.29813 1.92836i −0.766044 0.642788i
\(10\) 1.18479 0.374664
\(11\) −0.826352 1.43128i −0.249154 0.431548i 0.714137 0.700006i \(-0.246819\pi\)
−0.963291 + 0.268458i \(0.913486\pi\)
\(12\) −1.36571 1.62760i −0.394248 0.469846i
\(13\) −1.68479 + 2.91815i −0.467277 + 0.809348i −0.999301 0.0373813i \(-0.988098\pi\)
0.532024 + 0.846729i \(0.321432\pi\)
\(14\) 0 0
\(15\) −1.50000 1.78763i −0.387298 0.461564i
\(16\) 0.0209445 + 0.0362770i 0.00523613 + 0.00906925i
\(17\) −0.467911 −0.113485 −0.0567426 0.998389i \(-0.518071\pi\)
−0.0567426 + 0.998389i \(0.518071\pi\)
\(18\) 0.458111 2.59808i 0.107978 0.612372i
\(19\) 3.22668 0.740252 0.370126 0.928982i \(-0.379315\pi\)
0.370126 + 0.928982i \(0.379315\pi\)
\(20\) −0.826352 1.43128i −0.184778 0.320045i
\(21\) 0 0
\(22\) 0.726682 1.25865i 0.154929 0.268345i
\(23\) −4.47178 + 7.74535i −0.932431 + 1.61502i −0.153279 + 0.988183i \(0.548983\pi\)
−0.779152 + 0.626835i \(0.784350\pi\)
\(24\) 1.68092 4.61830i 0.343117 0.942706i
\(25\) 1.59240 + 2.75811i 0.318479 + 0.551622i
\(26\) −2.96316 −0.581124
\(27\) −4.50000 + 2.59808i −0.866025 + 0.500000i
\(28\) 0 0
\(29\) −3.13429 5.42874i −0.582022 1.00809i −0.995239 0.0974595i \(-0.968928\pi\)
0.413217 0.910632i \(-0.364405\pi\)
\(30\) 0.701867 1.92836i 0.128143 0.352069i
\(31\) 4.61721 7.99724i 0.829276 1.43635i −0.0693317 0.997594i \(-0.522087\pi\)
0.898607 0.438754i \(-0.144580\pi\)
\(32\) 2.81908 4.88279i 0.498347 0.863163i
\(33\) −2.81908 + 0.497079i −0.490738 + 0.0865304i
\(34\) −0.205737 0.356347i −0.0352836 0.0611130i
\(35\) 0 0
\(36\) −3.45811 + 1.25865i −0.576352 + 0.209775i
\(37\) 9.23442 1.51813 0.759065 0.651015i \(-0.225657\pi\)
0.759065 + 0.651015i \(0.225657\pi\)
\(38\) 1.41875 + 2.45734i 0.230151 + 0.398634i
\(39\) 3.75150 + 4.47086i 0.600720 + 0.715910i
\(40\) 1.91147 3.31077i 0.302231 0.523479i
\(41\) 1.70574 2.95442i 0.266391 0.461403i −0.701536 0.712634i \(-0.747502\pi\)
0.967927 + 0.251231i \(0.0808353\pi\)
\(42\) 0 0
\(43\) 2.20574 + 3.82045i 0.336372 + 0.582613i 0.983747 0.179558i \(-0.0574668\pi\)
−0.647376 + 0.762171i \(0.724133\pi\)
\(44\) −2.02734 −0.305633
\(45\) −3.79813 + 1.38241i −0.566192 + 0.206077i
\(46\) −7.86484 −1.15961
\(47\) 4.67752 + 8.10170i 0.682286 + 1.18175i 0.974281 + 0.225335i \(0.0723475\pi\)
−0.291995 + 0.956420i \(0.594319\pi\)
\(48\) 0.0714517 0.0125989i 0.0103132 0.00181849i
\(49\) 0 0
\(50\) −1.40033 + 2.42544i −0.198037 + 0.343009i
\(51\) −0.277189 + 0.761570i −0.0388142 + 0.106641i
\(52\) 2.06670 + 3.57964i 0.286600 + 0.496406i
\(53\) −0.573978 −0.0788419 −0.0394210 0.999223i \(-0.512551\pi\)
−0.0394210 + 0.999223i \(0.512551\pi\)
\(54\) −3.95723 2.28471i −0.538511 0.310910i
\(55\) −2.22668 −0.300246
\(56\) 0 0
\(57\) 1.91147 5.25173i 0.253181 0.695609i
\(58\) 2.75624 4.77396i 0.361913 0.626851i
\(59\) −5.19846 + 9.00400i −0.676782 + 1.17222i 0.299162 + 0.954202i \(0.403293\pi\)
−0.975945 + 0.218019i \(0.930041\pi\)
\(60\) −2.81908 + 0.497079i −0.363941 + 0.0641727i
\(61\) 3.81908 + 6.61484i 0.488983 + 0.846943i 0.999920 0.0126752i \(-0.00403474\pi\)
−0.510937 + 0.859618i \(0.670701\pi\)
\(62\) 8.12061 1.03132
\(63\) 0 0
\(64\) 5.04189 0.630236
\(65\) 2.26991 + 3.93161i 0.281548 + 0.487656i
\(66\) −1.61809 1.92836i −0.199173 0.237365i
\(67\) −0.298133 + 0.516382i −0.0364228 + 0.0630861i −0.883662 0.468125i \(-0.844930\pi\)
0.847239 + 0.531211i \(0.178263\pi\)
\(68\) −0.286989 + 0.497079i −0.0348025 + 0.0602797i
\(69\) 9.95723 + 11.8666i 1.19871 + 1.42857i
\(70\) 0 0
\(71\) −0.554378 −0.0657925 −0.0328963 0.999459i \(-0.510473\pi\)
−0.0328963 + 0.999459i \(0.510473\pi\)
\(72\) −6.52094 5.47172i −0.768501 0.644849i
\(73\) −2.04963 −0.239891 −0.119946 0.992780i \(-0.538272\pi\)
−0.119946 + 0.992780i \(0.538272\pi\)
\(74\) 4.06031 + 7.03266i 0.472001 + 0.817530i
\(75\) 5.43242 0.957882i 0.627282 0.110607i
\(76\) 1.97906 3.42782i 0.227013 0.393198i
\(77\) 0 0
\(78\) −1.75537 + 4.82283i −0.198756 + 0.546078i
\(79\) 1.20187 + 2.08169i 0.135221 + 0.234209i 0.925682 0.378303i \(-0.123492\pi\)
−0.790461 + 0.612512i \(0.790159\pi\)
\(80\) 0.0564370 0.00630985
\(81\) 1.56283 + 8.86327i 0.173648 + 0.984808i
\(82\) 3.00000 0.331295
\(83\) −7.52481 13.0334i −0.825956 1.43060i −0.901187 0.433431i \(-0.857303\pi\)
0.0752309 0.997166i \(-0.476031\pi\)
\(84\) 0 0
\(85\) −0.315207 + 0.545955i −0.0341891 + 0.0592172i
\(86\) −1.93969 + 3.35965i −0.209162 + 0.362280i
\(87\) −10.6925 + 1.88538i −1.14636 + 0.202134i
\(88\) −2.34477 4.06126i −0.249953 0.432932i
\(89\) −9.08647 −0.963164 −0.481582 0.876401i \(-0.659938\pi\)
−0.481582 + 0.876401i \(0.659938\pi\)
\(90\) −2.72281 2.28471i −0.287010 0.240830i
\(91\) 0 0
\(92\) 5.48545 + 9.50108i 0.571898 + 0.990556i
\(93\) −10.2811 12.2525i −1.06610 1.27052i
\(94\) −4.11334 + 7.12452i −0.424259 + 0.734838i
\(95\) 2.17365 3.76487i 0.223012 0.386267i
\(96\) −6.27719 7.48086i −0.640663 0.763512i
\(97\) −0.949493 1.64457i −0.0964064 0.166981i 0.813788 0.581161i \(-0.197402\pi\)
−0.910195 + 0.414181i \(0.864068\pi\)
\(98\) 0 0
\(99\) −0.860967 + 4.88279i −0.0865304 + 0.490738i
\(100\) 3.90673 0.390673
\(101\) −0.854570 1.48016i −0.0850329 0.147281i 0.820372 0.571830i \(-0.193766\pi\)
−0.905405 + 0.424548i \(0.860433\pi\)
\(102\) −0.701867 + 0.123758i −0.0694952 + 0.0122539i
\(103\) −1.81908 + 3.15074i −0.179239 + 0.310451i −0.941620 0.336677i \(-0.890697\pi\)
0.762381 + 0.647128i \(0.224030\pi\)
\(104\) −4.78059 + 8.28023i −0.468776 + 0.811943i
\(105\) 0 0
\(106\) −0.252374 0.437124i −0.0245127 0.0424573i
\(107\) 7.12836 0.689124 0.344562 0.938764i \(-0.388027\pi\)
0.344562 + 0.938764i \(0.388027\pi\)
\(108\) 6.37402i 0.613341i
\(109\) 0.403733 0.0386706 0.0193353 0.999813i \(-0.493845\pi\)
0.0193353 + 0.999813i \(0.493845\pi\)
\(110\) −0.979055 1.69577i −0.0933493 0.161686i
\(111\) 5.47044 15.0299i 0.519231 1.42658i
\(112\) 0 0
\(113\) −7.18479 + 12.4444i −0.675888 + 1.17067i 0.300320 + 0.953839i \(0.402907\pi\)
−0.976208 + 0.216835i \(0.930427\pi\)
\(114\) 4.84002 0.853427i 0.453310 0.0799307i
\(115\) 6.02481 + 10.4353i 0.561817 + 0.973095i
\(116\) −7.68954 −0.713956
\(117\) 9.49912 3.45740i 0.878194 0.319637i
\(118\) −9.14290 −0.841672
\(119\) 0 0
\(120\) −4.25624 5.07239i −0.388540 0.463044i
\(121\) 4.13429 7.16079i 0.375844 0.650981i
\(122\) −3.35844 + 5.81699i −0.304059 + 0.526646i
\(123\) −3.79813 4.52644i −0.342466 0.408135i
\(124\) −5.66385 9.81007i −0.508629 0.880971i
\(125\) 11.0273 0.986315
\(126\) 0 0
\(127\) −20.7716 −1.84318 −0.921589 0.388167i \(-0.873108\pi\)
−0.921589 + 0.388167i \(0.873108\pi\)
\(128\) −3.42127 5.92582i −0.302401 0.523774i
\(129\) 7.52481 1.32683i 0.662523 0.116821i
\(130\) −1.99613 + 3.45740i −0.175072 + 0.303234i
\(131\) −3.58260 + 6.20524i −0.313013 + 0.542154i −0.979013 0.203797i \(-0.934672\pi\)
0.666000 + 0.745952i \(0.268005\pi\)
\(132\) −1.20099 + 3.29969i −0.104533 + 0.287201i
\(133\) 0 0
\(134\) −0.524348 −0.0452968
\(135\) 7.00076i 0.602529i
\(136\) −1.32770 −0.113849
\(137\) −1.28446 2.22475i −0.109739 0.190074i 0.805925 0.592017i \(-0.201668\pi\)
−0.915665 + 0.401943i \(0.868335\pi\)
\(138\) −4.65910 + 12.8008i −0.396609 + 1.08967i
\(139\) −3.06670 + 5.31169i −0.260114 + 0.450531i −0.966272 0.257523i \(-0.917094\pi\)
0.706158 + 0.708055i \(0.250427\pi\)
\(140\) 0 0
\(141\) 15.9572 2.81369i 1.34384 0.236956i
\(142\) −0.243756 0.422197i −0.0204555 0.0354300i
\(143\) 5.56893 0.465697
\(144\) 0.0218219 0.123758i 0.00181849 0.0103132i
\(145\) −8.44562 −0.701371
\(146\) −0.901207 1.56094i −0.0745844 0.129184i
\(147\) 0 0
\(148\) 5.66385 9.81007i 0.465565 0.806383i
\(149\) −0.215537 + 0.373321i −0.0176575 + 0.0305837i −0.874719 0.484630i \(-0.838954\pi\)
0.857062 + 0.515214i \(0.172288\pi\)
\(150\) 3.11809 + 3.71599i 0.254591 + 0.303410i
\(151\) 1.23530 + 2.13960i 0.100527 + 0.174118i 0.911902 0.410408i \(-0.134614\pi\)
−0.811375 + 0.584526i \(0.801280\pi\)
\(152\) 9.15570 0.742625
\(153\) 1.07532 + 0.902302i 0.0869346 + 0.0729468i
\(154\) 0 0
\(155\) −6.22075 10.7747i −0.499663 0.865441i
\(156\) 7.05051 1.24319i 0.564492 0.0995352i
\(157\) 5.06670 8.77579i 0.404367 0.700384i −0.589881 0.807491i \(-0.700825\pi\)
0.994248 + 0.107106i \(0.0341585\pi\)
\(158\) −1.05690 + 1.83061i −0.0840828 + 0.145636i
\(159\) −0.340022 + 0.934204i −0.0269655 + 0.0740872i
\(160\) −3.79813 6.57856i −0.300269 0.520081i
\(161\) 0 0
\(162\) −6.06283 + 5.08732i −0.476341 + 0.399698i
\(163\) −2.59627 −0.203355 −0.101678 0.994817i \(-0.532421\pi\)
−0.101678 + 0.994817i \(0.532421\pi\)
\(164\) −2.09240 3.62414i −0.163389 0.282998i
\(165\) −1.31908 + 3.62414i −0.102690 + 0.282139i
\(166\) 6.61721 11.4613i 0.513595 0.889573i
\(167\) −11.5915 + 20.0771i −0.896979 + 1.55361i −0.0656422 + 0.997843i \(0.520910\pi\)
−0.831337 + 0.555769i \(0.812424\pi\)
\(168\) 0 0
\(169\) 0.822948 + 1.42539i 0.0633037 + 0.109645i
\(170\) −0.554378 −0.0425188
\(171\) −7.41534 6.22221i −0.567066 0.475825i
\(172\) 5.41147 0.412621
\(173\) −2.37598 4.11532i −0.180643 0.312882i 0.761457 0.648215i \(-0.224484\pi\)
−0.942100 + 0.335333i \(0.891151\pi\)
\(174\) −6.13728 7.31412i −0.465266 0.554482i
\(175\) 0 0
\(176\) 0.0346151 0.0599551i 0.00260921 0.00451929i
\(177\) 11.5753 + 13.7949i 0.870054 + 1.03689i
\(178\) −3.99525 6.91998i −0.299457 0.518674i
\(179\) −8.53209 −0.637718 −0.318859 0.947802i \(-0.603300\pi\)
−0.318859 + 0.947802i \(0.603300\pi\)
\(180\) −0.860967 + 4.88279i −0.0641727 + 0.363941i
\(181\) 17.2344 1.28102 0.640512 0.767948i \(-0.278722\pi\)
0.640512 + 0.767948i \(0.278722\pi\)
\(182\) 0 0
\(183\) 13.0287 2.29731i 0.963108 0.169822i
\(184\) −12.6887 + 21.9774i −0.935421 + 1.62020i
\(185\) 6.22075 10.7747i 0.457359 0.792169i
\(186\) 4.81062 13.2171i 0.352732 0.969123i
\(187\) 0.386659 + 0.669713i 0.0282753 + 0.0489743i
\(188\) 11.4757 0.836948
\(189\) 0 0
\(190\) 3.82295 0.277346
\(191\) −6.45471 11.1799i −0.467046 0.808948i 0.532245 0.846590i \(-0.321349\pi\)
−0.999291 + 0.0376425i \(0.988015\pi\)
\(192\) 2.98680 8.20616i 0.215553 0.592228i
\(193\) 0.319078 0.552659i 0.0229677 0.0397813i −0.854313 0.519759i \(-0.826022\pi\)
0.877281 + 0.479977i \(0.159355\pi\)
\(194\) 0.834970 1.44621i 0.0599473 0.103832i
\(195\) 7.74376 1.36543i 0.554542 0.0977807i
\(196\) 0 0
\(197\) 11.4456 0.815467 0.407733 0.913101i \(-0.366319\pi\)
0.407733 + 0.913101i \(0.366319\pi\)
\(198\) −4.09714 + 1.49124i −0.291171 + 0.105978i
\(199\) 3.63816 0.257902 0.128951 0.991651i \(-0.458839\pi\)
0.128951 + 0.991651i \(0.458839\pi\)
\(200\) 4.51842 + 7.82613i 0.319500 + 0.553391i
\(201\) 0.663848 + 0.791143i 0.0468242 + 0.0558029i
\(202\) 0.751497 1.30163i 0.0528751 0.0915824i
\(203\) 0 0
\(204\) 0.639033 + 0.761570i 0.0447413 + 0.0533206i
\(205\) −2.29813 3.98048i −0.160509 0.278009i
\(206\) −3.19934 −0.222909
\(207\) 25.2126 9.17664i 1.75240 0.637820i
\(208\) −0.141149 −0.00978691
\(209\) −2.66637 4.61830i −0.184437 0.319454i
\(210\) 0 0
\(211\) −2.91147 + 5.04282i −0.200434 + 0.347162i −0.948668 0.316273i \(-0.897569\pi\)
0.748234 + 0.663435i \(0.230902\pi\)
\(212\) −0.352044 + 0.609758i −0.0241785 + 0.0418784i
\(213\) −0.328411 + 0.902302i −0.0225024 + 0.0618247i
\(214\) 3.13429 + 5.42874i 0.214255 + 0.371101i
\(215\) 5.94356 0.405348
\(216\) −12.7687 + 7.37203i −0.868802 + 0.501603i
\(217\) 0 0
\(218\) 0.177519 + 0.307471i 0.0120231 + 0.0208246i
\(219\) −1.21419 + 3.33597i −0.0820476 + 0.225424i
\(220\) −1.36571 + 2.36549i −0.0920765 + 0.159481i
\(221\) 0.788333 1.36543i 0.0530290 0.0918490i
\(222\) 13.8516 2.44242i 0.929661 0.163924i
\(223\) 3.54189 + 6.13473i 0.237182 + 0.410812i 0.959905 0.280327i \(-0.0904428\pi\)
−0.722722 + 0.691139i \(0.757109\pi\)
\(224\) 0 0
\(225\) 1.65910 9.40923i 0.110607 0.627282i
\(226\) −12.6364 −0.840561
\(227\) −5.97178 10.3434i −0.396361 0.686517i 0.596913 0.802306i \(-0.296394\pi\)
−0.993274 + 0.115789i \(0.963060\pi\)
\(228\) −4.40673 5.25173i −0.291843 0.347804i
\(229\) −8.77631 + 15.2010i −0.579955 + 1.00451i 0.415529 + 0.909580i \(0.363597\pi\)
−0.995484 + 0.0949315i \(0.969737\pi\)
\(230\) −5.29813 + 9.17664i −0.349349 + 0.605089i
\(231\) 0 0
\(232\) −8.89352 15.4040i −0.583888 1.01132i
\(233\) 16.2540 1.06484 0.532418 0.846481i \(-0.321283\pi\)
0.532418 + 0.846481i \(0.321283\pi\)
\(234\) 6.80974 + 5.71405i 0.445167 + 0.373539i
\(235\) 12.6040 0.822195
\(236\) 6.37686 + 11.0450i 0.415098 + 0.718971i
\(237\) 4.10014 0.722965i 0.266333 0.0469616i
\(238\) 0 0
\(239\) 7.54963 13.0763i 0.488345 0.845838i −0.511565 0.859244i \(-0.670934\pi\)
0.999910 + 0.0134062i \(0.00426745\pi\)
\(240\) 0.0334331 0.0918566i 0.00215809 0.00592932i
\(241\) −7.81908 13.5430i −0.503671 0.872384i −0.999991 0.00424420i \(-0.998649\pi\)
0.496320 0.868140i \(-0.334684\pi\)
\(242\) 7.27126 0.467414
\(243\) 15.3516 + 2.70691i 0.984808 + 0.173648i
\(244\) 9.36959 0.599826
\(245\) 0 0
\(246\) 1.77719 4.88279i 0.113309 0.311315i
\(247\) −5.43629 + 9.41593i −0.345903 + 0.599121i
\(248\) 13.1013 22.6922i 0.831935 1.44095i
\(249\) −25.6707 + 4.52644i −1.62682 + 0.286851i
\(250\) 4.84864 + 8.39809i 0.306655 + 0.531142i
\(251\) −19.0651 −1.20338 −0.601690 0.798730i \(-0.705506\pi\)
−0.601690 + 0.798730i \(0.705506\pi\)
\(252\) 0 0
\(253\) 14.7811 0.929277
\(254\) −9.13310 15.8190i −0.573062 0.992572i
\(255\) 0.701867 + 0.836452i 0.0439526 + 0.0523807i
\(256\) 8.05051 13.9439i 0.503157 0.871493i
\(257\) 13.2909 23.0204i 0.829061 1.43598i −0.0697146 0.997567i \(-0.522209\pi\)
0.898776 0.438409i \(-0.144458\pi\)
\(258\) 4.31908 + 5.14728i 0.268894 + 0.320455i
\(259\) 0 0
\(260\) 5.56893 0.345370
\(261\) −3.26558 + 18.5200i −0.202134 + 1.14636i
\(262\) −6.30096 −0.389275
\(263\) 0.367059 + 0.635765i 0.0226338 + 0.0392029i 0.877120 0.480270i \(-0.159461\pi\)
−0.854487 + 0.519473i \(0.826128\pi\)
\(264\) −7.99912 + 1.41046i −0.492312 + 0.0868079i
\(265\) −0.386659 + 0.669713i −0.0237523 + 0.0411402i
\(266\) 0 0
\(267\) −5.38279 + 14.7891i −0.329421 + 0.905078i
\(268\) 0.365715 + 0.633436i 0.0223396 + 0.0386933i
\(269\) 20.8503 1.27126 0.635632 0.771992i \(-0.280739\pi\)
0.635632 + 0.771992i \(0.280739\pi\)
\(270\) −5.33157 + 3.07818i −0.324469 + 0.187332i
\(271\) −6.95811 −0.422675 −0.211338 0.977413i \(-0.567782\pi\)
−0.211338 + 0.977413i \(0.567782\pi\)
\(272\) −0.00980018 0.0169744i −0.000594223 0.00102922i
\(273\) 0 0
\(274\) 1.12954 1.95642i 0.0682379 0.118191i
\(275\) 2.63176 4.55834i 0.158701 0.274878i
\(276\) 18.7135 3.29969i 1.12642 0.198618i
\(277\) −8.93629 15.4781i −0.536930 0.929989i −0.999067 0.0431811i \(-0.986251\pi\)
0.462138 0.886808i \(-0.347083\pi\)
\(278\) −5.39363 −0.323488
\(279\) −26.0326 + 9.47508i −1.55853 + 0.567258i
\(280\) 0 0
\(281\) −11.1552 19.3214i −0.665465 1.15262i −0.979159 0.203095i \(-0.934900\pi\)
0.313694 0.949524i \(-0.398433\pi\)
\(282\) 9.15910 + 10.9154i 0.545416 + 0.650002i
\(283\) −9.29726 + 16.1033i −0.552665 + 0.957243i 0.445417 + 0.895323i \(0.353056\pi\)
−0.998081 + 0.0619196i \(0.980278\pi\)
\(284\) −0.340022 + 0.588936i −0.0201766 + 0.0349469i
\(285\) −4.84002 5.76811i −0.286698 0.341674i
\(286\) 2.44862 + 4.24113i 0.144790 + 0.250783i
\(287\) 0 0
\(288\) −15.8944 + 5.78509i −0.936587 + 0.340890i
\(289\) −16.7811 −0.987121
\(290\) −3.71348 6.43193i −0.218063 0.377696i
\(291\) −3.23917 + 0.571153i −0.189884 + 0.0334816i
\(292\) −1.25712 + 2.17740i −0.0735675 + 0.127423i
\(293\) 6.54576 11.3376i 0.382407 0.662349i −0.608998 0.793171i \(-0.708428\pi\)
0.991406 + 0.130822i \(0.0417618\pi\)
\(294\) 0 0
\(295\) 7.00387 + 12.1311i 0.407781 + 0.706298i
\(296\) 26.2026 1.52300
\(297\) 7.43717 + 4.29385i 0.431548 + 0.249154i
\(298\) −0.379081 −0.0219595
\(299\) −15.0680 26.0986i −0.871408 1.50932i
\(300\) 2.31433 6.35857i 0.133618 0.367112i
\(301\) 0 0
\(302\) −1.08630 + 1.88153i −0.0625098 + 0.108270i
\(303\) −2.91534 + 0.514054i −0.167482 + 0.0295316i
\(304\) 0.0675813 + 0.117054i 0.00387606 + 0.00671353i
\(305\) 10.2909 0.589253
\(306\) −0.214355 + 1.21567i −0.0122539 + 0.0694952i
\(307\) −6.31046 −0.360157 −0.180078 0.983652i \(-0.557635\pi\)
−0.180078 + 0.983652i \(0.557635\pi\)
\(308\) 0 0
\(309\) 4.05051 + 4.82721i 0.230425 + 0.274610i
\(310\) 5.47044 9.47508i 0.310700 0.538148i
\(311\) −4.76217 + 8.24833i −0.270038 + 0.467720i −0.968871 0.247565i \(-0.920370\pi\)
0.698833 + 0.715285i \(0.253703\pi\)
\(312\) 10.6449 + 12.6860i 0.602646 + 0.718206i
\(313\) −8.81433 15.2669i −0.498215 0.862934i 0.501782 0.864994i \(-0.332678\pi\)
−0.999998 + 0.00205946i \(0.999344\pi\)
\(314\) 8.91117 0.502886
\(315\) 0 0
\(316\) 2.94862 0.165873
\(317\) −4.03849 6.99486i −0.226824 0.392871i 0.730041 0.683403i \(-0.239501\pi\)
−0.956865 + 0.290533i \(0.906168\pi\)
\(318\) −0.860967 + 0.151812i −0.0482806 + 0.00851318i
\(319\) −5.18004 + 8.97210i −0.290027 + 0.502341i
\(320\) 3.39646 5.88284i 0.189868 0.328861i
\(321\) 4.22281 11.6021i 0.235694 0.647565i
\(322\) 0 0
\(323\) −1.50980 −0.0840075
\(324\) 10.3743 + 3.77595i 0.576352 + 0.209775i
\(325\) −10.7314 −0.595273
\(326\) −1.14156 1.97724i −0.0632251 0.109509i
\(327\) 0.239170 0.657115i 0.0132261 0.0363385i
\(328\) 4.84002 8.38316i 0.267246 0.462883i
\(329\) 0 0
\(330\) −3.34002 + 0.588936i −0.183862 + 0.0324199i
\(331\) −11.5248 19.9616i −0.633461 1.09719i −0.986839 0.161706i \(-0.948300\pi\)
0.353378 0.935481i \(-0.385033\pi\)
\(332\) −18.4611 −1.01318
\(333\) −21.2219 17.8073i −1.16295 0.975835i
\(334\) −20.3868 −1.11552
\(335\) 0.401674 + 0.695720i 0.0219458 + 0.0380112i
\(336\) 0 0
\(337\) −14.5116 + 25.1348i −0.790498 + 1.36918i 0.135161 + 0.990824i \(0.456845\pi\)
−0.925659 + 0.378359i \(0.876489\pi\)
\(338\) −0.723689 + 1.25347i −0.0393635 + 0.0681795i
\(339\) 15.9982 + 19.0660i 0.868905 + 1.03552i
\(340\) 0.386659 + 0.669713i 0.0209695 + 0.0363203i
\(341\) −15.2618 −0.826471
\(342\) 1.47818 8.38316i 0.0799307 0.453310i
\(343\) 0 0
\(344\) 6.25877 + 10.8405i 0.337450 + 0.584481i
\(345\) 20.5535 3.62414i 1.10656 0.195117i
\(346\) 2.08940 3.61895i 0.112327 0.194556i
\(347\) −6.47313 + 11.2118i −0.347496 + 0.601880i −0.985804 0.167901i \(-0.946301\pi\)
0.638308 + 0.769781i \(0.279635\pi\)
\(348\) −4.55525 + 12.5155i −0.244187 + 0.670899i
\(349\) 0.731429 + 1.26687i 0.0391525 + 0.0678141i 0.884938 0.465710i \(-0.154201\pi\)
−0.845785 + 0.533524i \(0.820868\pi\)
\(350\) 0 0
\(351\) 17.5089i 0.934555i
\(352\) −9.31820 −0.496662
\(353\) 7.16637 + 12.4125i 0.381428 + 0.660652i 0.991267 0.131873i \(-0.0420992\pi\)
−0.609839 + 0.792525i \(0.708766\pi\)
\(354\) −5.41622 + 14.8809i −0.287869 + 0.790913i
\(355\) −0.373455 + 0.646844i −0.0198210 + 0.0343309i
\(356\) −5.57310 + 9.65289i −0.295374 + 0.511602i
\(357\) 0 0
\(358\) −3.75150 6.49778i −0.198273 0.343418i
\(359\) −20.9368 −1.10500 −0.552500 0.833513i \(-0.686326\pi\)
−0.552500 + 0.833513i \(0.686326\pi\)
\(360\) −10.7772 + 3.92258i −0.568008 + 0.206738i
\(361\) −8.58853 −0.452028
\(362\) 7.57785 + 13.1252i 0.398283 + 0.689846i
\(363\) −9.20574 10.9710i −0.483176 0.575827i
\(364\) 0 0
\(365\) −1.38073 + 2.39149i −0.0722707 + 0.125176i
\(366\) 7.47818 + 8.91215i 0.390891 + 0.465845i
\(367\) −6.02869 10.4420i −0.314695 0.545067i 0.664678 0.747130i \(-0.268569\pi\)
−0.979373 + 0.202063i \(0.935236\pi\)
\(368\) −0.374638 −0.0195293
\(369\) −9.61721 + 3.50038i −0.500652 + 0.182222i
\(370\) 10.9409 0.568789
\(371\) 0 0
\(372\) −19.3221 + 3.40700i −1.00180 + 0.176645i
\(373\) 0.390530 0.676417i 0.0202209 0.0350235i −0.855738 0.517410i \(-0.826896\pi\)
0.875959 + 0.482386i \(0.160230\pi\)
\(374\) −0.340022 + 0.588936i −0.0175821 + 0.0304532i
\(375\) 6.53256 17.9480i 0.337340 0.926833i
\(376\) 13.2724 + 22.9885i 0.684474 + 1.18554i
\(377\) 21.1225 1.08786
\(378\) 0 0
\(379\) −6.92396 −0.355660 −0.177830 0.984061i \(-0.556908\pi\)
−0.177830 + 0.984061i \(0.556908\pi\)
\(380\) −2.66637 4.61830i −0.136782 0.236914i
\(381\) −12.3050 + 33.8077i −0.630404 + 1.73202i
\(382\) 5.67617 9.83142i 0.290418 0.503019i
\(383\) 3.86618 6.69642i 0.197553 0.342171i −0.750182 0.661232i \(-0.770034\pi\)
0.947734 + 0.319061i \(0.103367\pi\)
\(384\) −11.6716 + 2.05802i −0.595613 + 0.105023i
\(385\) 0 0
\(386\) 0.561185 0.0285636
\(387\) 2.29813 13.0334i 0.116821 0.662523i
\(388\) −2.32945 −0.118260
\(389\) −2.69981 4.67620i −0.136886 0.237093i 0.789431 0.613840i \(-0.210376\pi\)
−0.926316 + 0.376747i \(0.877043\pi\)
\(390\) 4.44475 + 5.29704i 0.225068 + 0.268226i
\(391\) 2.09240 3.62414i 0.105817 0.183280i
\(392\) 0 0
\(393\) 7.97730 + 9.50698i 0.402402 + 0.479564i
\(394\) 5.03256 + 8.71664i 0.253536 + 0.439138i
\(395\) 3.23854 0.162949
\(396\) 4.65910 + 3.90945i 0.234129 + 0.196457i
\(397\) 29.2344 1.46723 0.733617 0.679563i \(-0.237831\pi\)
0.733617 + 0.679563i \(0.237831\pi\)
\(398\) 1.59967 + 2.77071i 0.0801842 + 0.138883i
\(399\) 0 0
\(400\) −0.0667040 + 0.115535i −0.00333520 + 0.00577674i
\(401\) 13.6989 23.7272i 0.684092 1.18488i −0.289629 0.957139i \(-0.593532\pi\)
0.973721 0.227743i \(-0.0731346\pi\)
\(402\) −0.310622 + 0.853427i −0.0154924 + 0.0425650i
\(403\) 15.5581 + 26.9474i 0.775003 + 1.34235i
\(404\) −2.09657 −0.104308
\(405\) 11.3944 + 4.14722i 0.566192 + 0.206077i
\(406\) 0 0
\(407\) −7.63088 13.2171i −0.378249 0.655146i
\(408\) −0.786522 + 2.16095i −0.0389386 + 0.106983i
\(409\) −4.51249 + 7.81586i −0.223128 + 0.386469i −0.955756 0.294160i \(-0.904960\pi\)
0.732628 + 0.680629i \(0.238294\pi\)
\(410\) 2.02094 3.50038i 0.0998073 0.172871i
\(411\) −4.38191 + 0.772649i −0.216144 + 0.0381120i
\(412\) 2.23143 + 3.86495i 0.109935 + 0.190412i
\(413\) 0 0
\(414\) 18.0744 + 15.1663i 0.888310 + 0.745381i
\(415\) −20.2763 −0.995325
\(416\) 9.49912 + 16.4530i 0.465733 + 0.806673i
\(417\) 6.82857 + 8.13798i 0.334397 + 0.398518i
\(418\) 2.34477 4.06126i 0.114686 0.198643i
\(419\) 0.0876485 0.151812i 0.00428191 0.00741649i −0.863877 0.503704i \(-0.831970\pi\)
0.868158 + 0.496287i \(0.165304\pi\)
\(420\) 0 0
\(421\) 12.3525 + 21.3952i 0.602025 + 1.04274i 0.992514 + 0.122130i \(0.0389724\pi\)
−0.390490 + 0.920607i \(0.627694\pi\)
\(422\) −5.12061 −0.249268
\(423\) 4.87346 27.6387i 0.236956 1.34384i
\(424\) −1.62866 −0.0790947
\(425\) −0.745100 1.29055i −0.0361427 0.0626009i
\(426\) −0.831566 + 0.146628i −0.0402895 + 0.00710413i
\(427\) 0 0
\(428\) 4.37211 7.57272i 0.211334 0.366041i
\(429\) 3.29901 9.06396i 0.159278 0.437612i
\(430\) 2.61334 + 4.52644i 0.126026 + 0.218284i
\(431\) −29.3191 −1.41225 −0.706126 0.708086i \(-0.749559\pi\)
−0.706126 + 0.708086i \(0.749559\pi\)
\(432\) −0.188501 0.108831i −0.00906925 0.00523613i
\(433\) −19.6554 −0.944578 −0.472289 0.881444i \(-0.656572\pi\)
−0.472289 + 0.881444i \(0.656572\pi\)
\(434\) 0 0
\(435\) −5.00316 + 13.7461i −0.239883 + 0.659073i
\(436\) 0.247626 0.428901i 0.0118591 0.0205406i
\(437\) −14.4290 + 24.9918i −0.690233 + 1.19552i
\(438\) −3.07444 + 0.542108i −0.146903 + 0.0259029i
\(439\) −10.9650 18.9919i −0.523330 0.906434i −0.999631 0.0271516i \(-0.991356\pi\)
0.476302 0.879282i \(-0.341977\pi\)
\(440\) −6.31820 −0.301208
\(441\) 0 0
\(442\) 1.38650 0.0659489
\(443\) 9.35504 + 16.2034i 0.444471 + 0.769847i 0.998015 0.0629732i \(-0.0200583\pi\)
−0.553544 + 0.832820i \(0.686725\pi\)
\(444\) −12.6116 15.0299i −0.598519 0.713288i
\(445\) −6.12108 + 10.6020i −0.290167 + 0.502584i
\(446\) −3.11468 + 5.39479i −0.147485 + 0.255451i
\(447\) 0.479933 + 0.571962i 0.0227000 + 0.0270529i
\(448\) 0 0
\(449\) 6.68004 0.315251 0.157625 0.987499i \(-0.449616\pi\)
0.157625 + 0.987499i \(0.449616\pi\)
\(450\) 7.89528 2.87365i 0.372187 0.135465i
\(451\) −5.63816 −0.265490
\(452\) 8.81345 + 15.2653i 0.414550 + 0.718022i
\(453\) 4.21419 0.743076i 0.198000 0.0349128i
\(454\) 5.25150 9.09586i 0.246465 0.426890i
\(455\) 0 0
\(456\) 5.42380 14.9018i 0.253993 0.697839i
\(457\) 9.71436 + 16.8258i 0.454418 + 0.787076i 0.998655 0.0518563i \(-0.0165138\pi\)
−0.544236 + 0.838932i \(0.683180\pi\)
\(458\) −15.4355 −0.721254
\(459\) 2.10560 1.21567i 0.0982810 0.0567426i
\(460\) 14.7811 0.689170
\(461\) −0.482926 0.836452i −0.0224921 0.0389575i 0.854560 0.519352i \(-0.173827\pi\)
−0.877052 + 0.480395i \(0.840493\pi\)
\(462\) 0 0
\(463\) 0.222811 0.385920i 0.0103549 0.0179352i −0.860802 0.508941i \(-0.830037\pi\)
0.871156 + 0.491006i \(0.163371\pi\)
\(464\) 0.131292 0.227405i 0.00609509 0.0105570i
\(465\) −21.2219 + 3.74200i −0.984144 + 0.173531i
\(466\) 7.14677 + 12.3786i 0.331068 + 0.573426i
\(467\) 34.2148 1.58327 0.791637 0.610992i \(-0.209229\pi\)
0.791637 + 0.610992i \(0.209229\pi\)
\(468\) 2.15328 12.2118i 0.0995352 0.564492i
\(469\) 0 0
\(470\) 5.54189 + 9.59883i 0.255628 + 0.442761i
\(471\) −11.2819 13.4453i −0.519844 0.619526i
\(472\) −14.7506 + 25.5488i −0.678952 + 1.17598i
\(473\) 3.64543 6.31407i 0.167617 0.290321i
\(474\) 2.35339 + 2.80466i 0.108095 + 0.128822i
\(475\) 5.13816 + 8.89955i 0.235755 + 0.408339i
\(476\) 0 0
\(477\) 1.31908 + 1.10684i 0.0603964 + 0.0506786i
\(478\) 13.2781 0.607325
\(479\) −10.8965 18.8732i −0.497872 0.862339i 0.502125 0.864795i \(-0.332552\pi\)
−0.999997 + 0.00245553i \(0.999218\pi\)
\(480\) −12.9572 + 2.28471i −0.591414 + 0.104282i
\(481\) −15.5581 + 26.9474i −0.709388 + 1.22870i
\(482\) 6.87598 11.9095i 0.313192 0.542465i
\(483\) 0 0
\(484\) −5.07145 8.78401i −0.230521 0.399273i
\(485\) −2.55850 −0.116175
\(486\) 4.68850 + 12.8816i 0.212675 + 0.584319i
\(487\) 19.3928 0.878772 0.439386 0.898298i \(-0.355196\pi\)
0.439386 + 0.898298i \(0.355196\pi\)
\(488\) 10.8366 + 18.7696i 0.490551 + 0.849659i
\(489\) −1.53802 + 4.22567i −0.0695516 + 0.191091i
\(490\) 0 0
\(491\) −13.0783 + 22.6523i −0.590216 + 1.02228i 0.403987 + 0.914765i \(0.367624\pi\)
−0.994203 + 0.107519i \(0.965709\pi\)
\(492\) −7.13816 + 1.25865i −0.321813 + 0.0567443i
\(493\) 1.46657 + 2.54017i 0.0660509 + 0.114403i
\(494\) −9.56118 −0.430178
\(495\) 5.11721 + 4.29385i 0.230002 + 0.192994i
\(496\) 0.386821 0.0173688
\(497\) 0 0
\(498\) −14.7344 17.5598i −0.660265 0.786873i
\(499\) 7.15064 12.3853i 0.320107 0.554441i −0.660403 0.750911i \(-0.729615\pi\)
0.980510 + 0.196470i \(0.0629479\pi\)
\(500\) 6.76352 11.7148i 0.302474 0.523900i
\(501\) 25.8106 + 30.7599i 1.15313 + 1.37425i
\(502\) −8.38279 14.5194i −0.374142 0.648033i
\(503\) −18.7033 −0.833937 −0.416969 0.908921i \(-0.636908\pi\)
−0.416969 + 0.908921i \(0.636908\pi\)
\(504\) 0 0
\(505\) −2.30272 −0.102470
\(506\) 6.49912 + 11.2568i 0.288921 + 0.500426i
\(507\) 2.80747 0.495032i 0.124684 0.0219851i
\(508\) −12.7400 + 22.0664i −0.565248 + 0.979039i
\(509\) −12.8045 + 22.1781i −0.567551 + 0.983027i 0.429257 + 0.903183i \(0.358776\pi\)
−0.996807 + 0.0798442i \(0.974558\pi\)
\(510\) −0.328411 + 0.902302i −0.0145423 + 0.0399546i
\(511\) 0 0
\(512\) 0.473897 0.0209435
\(513\) −14.5201 + 8.38316i −0.641077 + 0.370126i
\(514\) 23.3756 1.03105
\(515\) 2.45084 + 4.24497i 0.107997 + 0.187056i
\(516\) 3.20574 8.80769i 0.141125 0.387737i
\(517\) 7.73055 13.3897i 0.339989 0.588879i
\(518\) 0 0
\(519\) −8.10560 + 1.42924i −0.355796 + 0.0627365i
\(520\) 6.44087 + 11.1559i 0.282451 + 0.489220i
\(521\) 21.2121 0.929320 0.464660 0.885489i \(-0.346176\pi\)
0.464660 + 0.885489i \(0.346176\pi\)
\(522\) −15.5401 + 5.65615i −0.680173 + 0.247563i
\(523\) −20.8057 −0.909770 −0.454885 0.890550i \(-0.650320\pi\)
−0.454885 + 0.890550i \(0.650320\pi\)
\(524\) 4.39470 + 7.61185i 0.191984 + 0.332525i
\(525\) 0 0
\(526\) −0.322786 + 0.559082i −0.0140741 + 0.0243771i
\(527\) −2.16044 + 3.74200i −0.0941104 + 0.163004i
\(528\) −0.0770768 0.0918566i −0.00335434 0.00399754i
\(529\) −28.4937 49.3525i −1.23885 2.14576i
\(530\) −0.680045 −0.0295393
\(531\) 29.3097 10.6679i 1.27193 0.462946i
\(532\) 0 0
\(533\) 5.74763 + 9.95518i 0.248957 + 0.431207i
\(534\) −13.6297 + 2.40328i −0.589815 + 0.104000i
\(535\) 4.80200 8.31731i 0.207609 0.359589i
\(536\) −0.845952 + 1.46523i −0.0365396 + 0.0632884i
\(537\) −5.05438 + 13.8868i −0.218112 + 0.599259i
\(538\) 9.16772 + 15.8790i 0.395248 + 0.684590i
\(539\) 0 0
\(540\) 7.43717 + 4.29385i 0.320045 + 0.184778i
\(541\) 26.7297 1.14920 0.574599 0.818435i \(-0.305158\pi\)
0.574599 + 0.818435i \(0.305158\pi\)
\(542\) −3.05943 5.29909i −0.131414 0.227615i
\(543\) 10.2096 28.0507i 0.438136 1.20377i
\(544\) −1.31908 + 2.28471i −0.0565550 + 0.0979561i
\(545\) 0.271974 0.471073i 0.0116501 0.0201786i
\(546\) 0 0
\(547\) −18.3812 31.8372i −0.785923 1.36126i −0.928446 0.371467i \(-0.878855\pi\)
0.142523 0.989792i \(-0.454479\pi\)
\(548\) −3.15125 −0.134615
\(549\) 3.97906 22.5663i 0.169822 0.963108i
\(550\) 4.62866 0.197367
\(551\) −10.1133 17.5168i −0.430843 0.746242i
\(552\) 28.2536 + 33.6713i 1.20255 + 1.43315i
\(553\) 0 0
\(554\) 7.85844 13.6112i 0.333873 0.578285i
\(555\) −13.8516 16.5077i −0.587969 0.700714i
\(556\) 3.76187 + 6.51575i 0.159539 + 0.276329i
\(557\) 32.3387 1.37024 0.685118 0.728432i \(-0.259751\pi\)
0.685118 + 0.728432i \(0.259751\pi\)
\(558\) −18.6623 15.6595i −0.790036 0.662919i
\(559\) −14.8648 −0.628716
\(560\) 0 0
\(561\) 1.31908 0.232589i 0.0556915 0.00981992i
\(562\) 9.80974 16.9910i 0.413799 0.716721i
\(563\) −8.87093 + 15.3649i −0.373865 + 0.647553i −0.990156 0.139965i \(-0.955301\pi\)
0.616291 + 0.787518i \(0.288634\pi\)
\(564\) 6.79813 18.6777i 0.286253 0.786474i
\(565\) 9.68004 + 16.7663i 0.407243 + 0.705365i
\(566\) −16.3517 −0.687315
\(567\) 0 0
\(568\) −1.57304 −0.0660035
\(569\) 13.3007 + 23.0374i 0.557593 + 0.965779i 0.997697 + 0.0678320i \(0.0216082\pi\)
−0.440104 + 0.897947i \(0.645058\pi\)
\(570\) 2.26470 6.22221i 0.0948579 0.260620i
\(571\) 5.00862 8.67518i 0.209604 0.363045i −0.741986 0.670416i \(-0.766116\pi\)
0.951590 + 0.307371i \(0.0994491\pi\)
\(572\) 3.41565 5.91608i 0.142815 0.247364i
\(573\) −22.0201 + 3.88273i −0.919902 + 0.162203i
\(574\) 0 0
\(575\) −28.4834 −1.18784
\(576\) −11.5869 9.72259i −0.482789 0.405108i
\(577\) 32.9145 1.37025 0.685124 0.728427i \(-0.259748\pi\)
0.685124 + 0.728427i \(0.259748\pi\)
\(578\) −7.37851 12.7800i −0.306905 0.531576i
\(579\) −0.710485 0.846723i −0.0295267 0.0351886i
\(580\) −5.18004 + 8.97210i −0.215090 + 0.372546i
\(581\) 0 0
\(582\) −1.85921 2.21572i −0.0770668 0.0918447i
\(583\) 0.474308 + 0.821525i 0.0196438 + 0.0340241i
\(584\) −5.81582 −0.240660
\(585\) 2.36500 13.4126i 0.0977807 0.554542i
\(586\) 11.5125 0.475577
\(587\) −7.53643 13.0535i −0.311062 0.538774i 0.667531 0.744582i \(-0.267351\pi\)
−0.978592 + 0.205808i \(0.934018\pi\)
\(588\) 0 0
\(589\) 14.8983 25.8046i 0.613873 1.06326i
\(590\) −6.15910 + 10.6679i −0.253566 + 0.439189i
\(591\) 6.78034 18.6288i 0.278906 0.766288i
\(592\) 0.193411 + 0.334997i 0.00794913 + 0.0137683i
\(593\) −41.0009 −1.68371 −0.841853 0.539706i \(-0.818535\pi\)
−0.841853 + 0.539706i \(0.818535\pi\)
\(594\) 7.55190i 0.309858i
\(595\) 0 0
\(596\) 0.264396 + 0.457947i 0.0108301 + 0.0187582i
\(597\) 2.15523 5.92145i 0.0882077 0.242349i
\(598\) 13.2506 22.9507i 0.541858 0.938526i
\(599\) −3.03684 + 5.25996i −0.124082 + 0.214916i −0.921374 0.388678i \(-0.872932\pi\)
0.797292 + 0.603594i \(0.206265\pi\)
\(600\) 15.4145 2.71799i 0.629293 0.110961i
\(601\) −7.06758 12.2414i −0.288293 0.499338i 0.685110 0.728440i \(-0.259754\pi\)
−0.973402 + 0.229102i \(0.926421\pi\)
\(602\) 0 0
\(603\) 1.68092 0.611806i 0.0684524 0.0249147i
\(604\) 3.03064 0.123315
\(605\) −5.57011 9.64771i −0.226457 0.392235i
\(606\) −1.67334 1.99421i −0.0679749 0.0810094i
\(607\) 23.0449 39.9149i 0.935363 1.62010i 0.161377 0.986893i \(-0.448406\pi\)
0.773986 0.633203i \(-0.218260\pi\)
\(608\) 9.09627 15.7552i 0.368902 0.638958i
\(609\) 0 0
\(610\) 4.52481 + 7.83721i 0.183204 + 0.317319i
\(611\) −31.5226 −1.27527
\(612\) 1.61809 0.588936i 0.0654074 0.0238063i
\(613\) −26.4938 −1.07008 −0.535038 0.844828i \(-0.679703\pi\)
−0.535038 + 0.844828i \(0.679703\pi\)
\(614\) −2.77466 4.80586i −0.111976 0.193949i
\(615\) −7.84002 + 1.38241i −0.316140 + 0.0557440i
\(616\) 0 0
\(617\) 1.12495 1.94847i 0.0452889 0.0784426i −0.842492 0.538708i \(-0.818913\pi\)
0.887781 + 0.460266i \(0.152246\pi\)
\(618\) −1.89528 + 5.20723i −0.0762392 + 0.209466i
\(619\) 3.09539 + 5.36137i 0.124414 + 0.215492i 0.921504 0.388369i \(-0.126962\pi\)
−0.797090 + 0.603861i \(0.793628\pi\)
\(620\) −15.2618 −0.612927
\(621\) 46.4721i 1.86486i
\(622\) −8.37557 −0.335830
\(623\) 0 0
\(624\) −0.0836160 + 0.229733i −0.00334732 + 0.00919668i
\(625\) −0.533433 + 0.923933i −0.0213373 + 0.0369573i
\(626\) 7.75119 13.4255i 0.309800 0.536589i
\(627\) −9.09627 + 1.60392i −0.363270 + 0.0640543i
\(628\) −6.21523 10.7651i −0.248015 0.429574i
\(629\) −4.32089 −0.172285
\(630\) 0 0
\(631\) 26.1661 1.04166 0.520829 0.853661i \(-0.325623\pi\)
0.520829 + 0.853661i \(0.325623\pi\)
\(632\) 3.41029 + 5.90680i 0.135654 + 0.234960i
\(633\) 6.48293 + 7.72605i 0.257673 + 0.307083i
\(634\) 3.55138 6.15118i 0.141043 0.244295i
\(635\) −13.9927 + 24.2361i −0.555284 + 0.961781i
\(636\) 0.783890 + 0.934204i 0.0310833 + 0.0370436i
\(637\) 0 0
\(638\) −9.11051 −0.360689
\(639\) 1.27403 + 1.06904i 0.0504000 + 0.0422906i
\(640\) −9.21894 −0.364411
\(641\) −2.44444 4.23389i −0.0965496 0.167229i 0.813705 0.581278i \(-0.197447\pi\)
−0.910254 + 0.414050i \(0.864114\pi\)
\(642\) 10.6925 1.88538i 0.422001 0.0744101i
\(643\) −20.1839 + 34.9596i −0.795976 + 1.37867i 0.126242 + 0.992000i \(0.459709\pi\)
−0.922218 + 0.386671i \(0.873625\pi\)
\(644\) 0 0
\(645\) 3.52094 9.67372i 0.138637 0.380902i
\(646\) −0.663848 1.14982i −0.0261188 0.0452390i
\(647\) 2.28075 0.0896657 0.0448329 0.998995i \(-0.485724\pi\)
0.0448329 + 0.998995i \(0.485724\pi\)
\(648\) 4.43453 + 25.1495i 0.174205 + 0.987965i
\(649\) 17.1830 0.674493
\(650\) −4.71853 8.17273i −0.185076 0.320561i
\(651\) 0 0
\(652\) −1.59240 + 2.75811i −0.0623631 + 0.108016i
\(653\) −11.7396 + 20.3336i −0.459407 + 0.795717i −0.998930 0.0462542i \(-0.985272\pi\)
0.539522 + 0.841971i \(0.318605\pi\)
\(654\) 0.605600 0.106784i 0.0236808 0.00417557i
\(655\) 4.82682 + 8.36030i 0.188599 + 0.326664i
\(656\) 0.142903 0.00557944
\(657\) 4.71032 + 3.95243i 0.183767 + 0.154199i
\(658\) 0 0
\(659\) 23.9812 + 41.5366i 0.934174 + 1.61804i 0.776101 + 0.630609i \(0.217195\pi\)
0.158073 + 0.987427i \(0.449472\pi\)
\(660\) 3.04101 + 3.62414i 0.118371 + 0.141069i
\(661\) 14.6545 25.3824i 0.569995 0.987260i −0.426571 0.904454i \(-0.640279\pi\)
0.996566 0.0828055i \(-0.0263880\pi\)
\(662\) 10.1348 17.5539i 0.393898 0.682252i
\(663\) −1.75537 2.09196i −0.0681728 0.0812452i
\(664\) −21.3516 36.9821i −0.828604 1.43518i
\(665\) 0 0
\(666\) 4.23039 23.9917i 0.163924 0.929661i
\(667\) 56.0634 2.17078
\(668\) 14.2191 + 24.6282i 0.550154 + 0.952894i
\(669\) 12.0831 2.13057i 0.467158 0.0823726i
\(670\) −0.353226 + 0.611806i −0.0136463 + 0.0236361i
\(671\) 6.31180 10.9324i 0.243664 0.422039i
\(672\) 0 0
\(673\) −13.1591 22.7922i −0.507246 0.878576i −0.999965 0.00838731i \(-0.997330\pi\)
0.492719 0.870189i \(-0.336003\pi\)
\(674\) −25.5226 −0.983094
\(675\) −14.3316 8.27433i −0.551622 0.318479i
\(676\) 2.01899 0.0776535
\(677\) 17.9454 + 31.0823i 0.689697 + 1.19459i 0.971936 + 0.235246i \(0.0755895\pi\)
−0.282239 + 0.959344i \(0.591077\pi\)
\(678\) −7.48576 + 20.5669i −0.287489 + 0.789869i
\(679\) 0 0
\(680\) −0.894400 + 1.54915i −0.0342987 + 0.0594070i
\(681\) −20.3726 + 3.59224i −0.780679 + 0.137655i
\(682\) −6.71048 11.6229i −0.256958 0.445064i
\(683\) 35.0642 1.34169 0.670847 0.741596i \(-0.265931\pi\)
0.670847 + 0.741596i \(0.265931\pi\)
\(684\) −11.1582 + 4.06126i −0.426645 + 0.155286i
\(685\) −3.46110 −0.132242
\(686\) 0 0
\(687\) 19.5421 + 23.2893i 0.745576 + 0.888543i
\(688\) −0.0923963 + 0.160035i −0.00352257 + 0.00610128i
\(689\) 0.967034 1.67495i 0.0368411 0.0638106i
\(690\) 11.7973 + 14.0594i 0.449114 + 0.535233i
\(691\) 1.03343 + 1.78996i 0.0393136 + 0.0680932i 0.885013 0.465567i \(-0.154150\pi\)
−0.845699 + 0.533660i \(0.820816\pi\)
\(692\) −5.82915 −0.221591
\(693\) 0 0
\(694\) −11.3847 −0.432159
\(695\) 4.13176 + 7.15642i 0.156727 + 0.271458i
\(696\) −30.3400 + 5.34976i −1.15004 + 0.202782i
\(697\) −0.798133 + 1.38241i −0.0302315 + 0.0523624i
\(698\) −0.643208 + 1.11407i −0.0243458 + 0.0421681i
\(699\) 9.62882 26.4550i 0.364196 1.00062i
\(700\) 0 0
\(701\) −7.36009 −0.277987 −0.138993 0.990293i \(-0.544387\pi\)
−0.138993 + 0.990293i \(0.544387\pi\)
\(702\) 13.3342 7.69852i 0.503268 0.290562i
\(703\) 29.7965 1.12380
\(704\) −4.16637 7.21637i −0.157026 0.271977i
\(705\) 7.46657 20.5142i 0.281207 0.772610i
\(706\) −6.30200 + 10.9154i −0.237179 + 0.410806i
\(707\) 0 0
\(708\) 21.7545 3.83590i 0.817584 0.144162i
\(709\) −4.55438 7.88841i −0.171043 0.296256i 0.767742 0.640760i \(-0.221380\pi\)
−0.938785 + 0.344504i \(0.888047\pi\)
\(710\) −0.656822 −0.0246501
\(711\) 1.25221 7.10165i 0.0469616 0.266333i
\(712\) −25.7828 −0.966252
\(713\) 41.2943 + 71.5239i 1.54648 + 2.67859i
\(714\) 0 0
\(715\) 3.75150 6.49778i 0.140298 0.243003i
\(716\) −5.23308 + 9.06396i −0.195569 + 0.338736i
\(717\) −16.8106 20.0341i −0.627804 0.748188i
\(718\) −9.20574 15.9448i −0.343555 0.595055i
\(719\) 25.9537 0.967908 0.483954 0.875093i \(-0.339200\pi\)
0.483954 + 0.875093i \(0.339200\pi\)
\(720\) −0.129700 0.108831i −0.00483362 0.00405589i
\(721\) 0 0
\(722\) −3.77631 6.54076i −0.140540 0.243422i
\(723\) −26.6746 + 4.70345i −0.992038 + 0.174923i
\(724\) 10.5706 18.3088i 0.392852 0.680440i
\(725\) 9.98205 17.2894i 0.370724 0.642113i
\(726\) 4.30747 11.8347i 0.159865 0.439226i
\(727\) −5.08007 8.79894i −0.188409 0.326335i 0.756311 0.654213i \(-0.227000\pi\)
−0.944720 + 0.327878i \(0.893667\pi\)
\(728\) 0 0
\(729\) 13.5000 23.3827i 0.500000 0.866025i
\(730\) −2.42839 −0.0898786
\(731\) −1.03209 1.78763i −0.0381732 0.0661179i
\(732\) 5.55051 15.2499i 0.205153 0.563652i
\(733\) 20.3307 35.2138i 0.750931 1.30065i −0.196441 0.980516i \(-0.562938\pi\)
0.947372 0.320135i \(-0.103728\pi\)
\(734\) 5.30154 9.18253i 0.195683 0.338933i
\(735\) 0 0
\(736\) 25.2126 + 43.6695i 0.929349 + 1.60968i
\(737\) 0.985452 0.0362996
\(738\) −6.89440 5.78509i −0.253786 0.212952i
\(739\) −25.3618 −0.932951 −0.466475 0.884534i \(-0.654476\pi\)
−0.466475 + 0.884534i \(0.654476\pi\)
\(740\) −7.63088 13.2171i −0.280517 0.485869i
\(741\) 12.1049 + 14.4260i 0.444684 + 0.529954i
\(742\) 0 0
\(743\) 11.2221 19.4372i 0.411699 0.713083i −0.583377 0.812202i \(-0.698269\pi\)
0.995076 + 0.0991184i \(0.0316023\pi\)
\(744\) −29.1725 34.7664i −1.06951 1.27460i
\(745\) 0.290393 + 0.502975i 0.0106392 + 0.0184276i
\(746\) 0.686852 0.0251474
\(747\) −7.84002 + 44.4630i −0.286851 + 1.62682i
\(748\) 0.948615 0.0346848
\(749\) 0 0
\(750\) 16.5410 2.91663i 0.603992 0.106500i
\(751\) −12.1086 + 20.9727i −0.441849 + 0.765305i −0.997827 0.0658924i \(-0.979011\pi\)
0.555978 + 0.831197i \(0.312344\pi\)
\(752\) −0.195937 + 0.339373i −0.00714508 + 0.0123756i
\(753\) −11.2941 + 31.0303i −0.411580 + 1.13081i
\(754\) 9.28740 + 16.0862i 0.338227 + 0.585827i
\(755\) 3.32863 0.121141
\(756\) 0 0
\(757\) 9.11793 0.331397 0.165698 0.986176i \(-0.447012\pi\)
0.165698 + 0.986176i \(0.447012\pi\)
\(758\) −3.04442 5.27308i −0.110578 0.191527i
\(759\) 8.75624 24.0576i 0.317832 0.873235i
\(760\) 6.16772 10.6828i 0.223727 0.387506i
\(761\) −9.13610 + 15.8242i −0.331183 + 0.573626i −0.982744 0.184970i \(-0.940781\pi\)
0.651561 + 0.758596i \(0.274114\pi\)
\(762\) −31.1573 + 5.49388i −1.12871 + 0.199022i
\(763\) 0 0
\(764\) −15.8357 −0.572917
\(765\) 1.77719 0.646844i 0.0642544 0.0233867i
\(766\) 6.79973 0.245684
\(767\) −17.5167 30.3398i −0.632490 1.09550i
\(768\) −17.9259 21.3633i −0.646846 0.770881i
\(769\) 9.26470 16.0469i 0.334094 0.578667i −0.649217 0.760604i \(-0.724903\pi\)
0.983310 + 0.181936i \(0.0582365\pi\)
\(770\) 0 0
\(771\) −29.5945 35.2694i −1.06582 1.27020i
\(772\) −0.391407 0.677937i −0.0140870 0.0243995i
\(773\) 2.96080 0.106493 0.0532463 0.998581i \(-0.483043\pi\)
0.0532463 + 0.998581i \(0.483043\pi\)
\(774\) 10.9363 3.98048i 0.393097 0.143076i
\(775\) 29.4097 1.05643
\(776\) −2.69418 4.66646i −0.0967155 0.167516i
\(777\) 0 0
\(778\) 2.37417 4.11218i 0.0851181 0.147429i
\(779\) 5.50387 9.53298i 0.197197 0.341555i
\(780\) 3.29901 9.06396i 0.118124 0.324542i