Properties

Label 1152.2.p.e.959.5
Level $1152$
Weight $2$
Character 1152.959
Analytic conductor $9.199$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.p (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.19876631285\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: 16.0.9349208943630483456.9
Defining polynomial: \(x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + 9297 x^{8} - 11276 x^{7} + 11224 x^{6} - 9024 x^{5} + 5736 x^{4} - 2780 x^{3} + 972 x^{2} - 220 x + 25\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 959.5
Root \(0.500000 + 2.00333i\) of defining polynomial
Character \(\chi\) \(=\) 1152.959
Dual form 1152.2.p.e.191.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.524648 + 1.65068i) q^{3} +(-0.158919 + 0.275255i) q^{5} +(-2.93038 + 1.69185i) q^{7} +(-2.44949 + 1.73205i) q^{9} +O(q^{10})\) \(q+(0.524648 + 1.65068i) q^{3} +(-0.158919 + 0.275255i) q^{5} +(-2.93038 + 1.69185i) q^{7} +(-2.44949 + 1.73205i) q^{9} +(-0.642559 + 0.370982i) q^{11} +(-2.59808 - 1.50000i) q^{13} +(-0.537734 - 0.117912i) q^{15} -4.24264i q^{17} +2.57024 q^{19} +(-4.33013 - 3.94949i) q^{21} +(-2.02166 + 3.50162i) q^{23} +(2.44949 + 4.24264i) q^{25} +(-4.14418 - 3.13461i) q^{27} +(-4.01229 - 6.94949i) q^{29} +(-4.24755 - 2.45233i) q^{31} +(-0.949490 - 0.866025i) q^{33} -1.07547i q^{35} -7.34847i q^{37} +(1.11295 - 5.07556i) q^{39} +(-0.825765 - 0.476756i) q^{41} +(-3.50162 - 6.06499i) q^{43} +(-0.0874863 - 0.949490i) q^{45} +(5.15627 + 8.93092i) q^{47} +(2.22474 - 3.85337i) q^{49} +(7.00324 - 2.22589i) q^{51} -5.51399 q^{53} -0.235824i q^{55} +(1.34847 + 4.24264i) q^{57} +(3.50162 + 2.02166i) q^{59} +(-7.79423 + 4.50000i) q^{61} +(4.24755 - 9.21975i) q^{63} +(0.825765 - 0.476756i) q^{65} +(-6.36068 + 11.0170i) q^{67} +(-6.84072 - 1.50000i) q^{69} +13.5389 q^{71} -6.44949 q^{73} +(-5.71812 + 6.26922i) q^{75} +(1.25529 - 2.17423i) q^{77} +(-8.29088 + 4.78674i) q^{79} +(3.00000 - 8.48528i) q^{81} +(2.21650 - 1.27970i) q^{83} +(1.16781 + 0.674235i) q^{85} +(9.36635 - 10.2690i) q^{87} +14.6349i q^{89} +10.1511 q^{91} +(1.81954 - 8.29796i) q^{93} +(-0.408459 + 0.707471i) q^{95} +(-5.62372 - 9.74058i) q^{97} +(0.931383 - 2.02166i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + O(q^{10}) \) \( 16 q + 24 q^{33} - 72 q^{41} + 16 q^{49} - 96 q^{57} + 72 q^{65} - 64 q^{73} + 48 q^{81} + 8 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(641\) \(901\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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 0
\(3\) 0.524648 + 1.65068i 0.302905 + 0.953021i
\(4\) 0 0
\(5\) −0.158919 + 0.275255i −0.0710706 + 0.123098i −0.899371 0.437187i \(-0.855975\pi\)
0.828300 + 0.560285i \(0.189308\pi\)
\(6\) 0 0
\(7\) −2.93038 + 1.69185i −1.10758 + 0.639461i −0.938201 0.346090i \(-0.887509\pi\)
−0.169378 + 0.985551i \(0.554176\pi\)
\(8\) 0 0
\(9\) −2.44949 + 1.73205i −0.816497 + 0.577350i
\(10\) 0 0
\(11\) −0.642559 + 0.370982i −0.193739 + 0.111855i −0.593732 0.804663i \(-0.702346\pi\)
0.399993 + 0.916518i \(0.369013\pi\)
\(12\) 0 0
\(13\) −2.59808 1.50000i −0.720577 0.416025i 0.0943882 0.995535i \(-0.469911\pi\)
−0.814965 + 0.579510i \(0.803244\pi\)
\(14\) 0 0
\(15\) −0.537734 0.117912i −0.138842 0.0304447i
\(16\) 0 0
\(17\) 4.24264i 1.02899i −0.857493 0.514496i \(-0.827979\pi\)
0.857493 0.514496i \(-0.172021\pi\)
\(18\) 0 0
\(19\) 2.57024 0.589653 0.294827 0.955551i \(-0.404738\pi\)
0.294827 + 0.955551i \(0.404738\pi\)
\(20\) 0 0
\(21\) −4.33013 3.94949i −0.944911 0.861849i
\(22\) 0 0
\(23\) −2.02166 + 3.50162i −0.421546 + 0.730139i −0.996091 0.0883343i \(-0.971846\pi\)
0.574545 + 0.818473i \(0.305179\pi\)
\(24\) 0 0
\(25\) 2.44949 + 4.24264i 0.489898 + 0.848528i
\(26\) 0 0
\(27\) −4.14418 3.13461i −0.797548 0.603256i
\(28\) 0 0
\(29\) −4.01229 6.94949i −0.745064 1.29049i −0.950165 0.311747i \(-0.899086\pi\)
0.205102 0.978741i \(-0.434248\pi\)
\(30\) 0 0
\(31\) −4.24755 2.45233i −0.762883 0.440451i 0.0674468 0.997723i \(-0.478515\pi\)
−0.830330 + 0.557272i \(0.811848\pi\)
\(32\) 0 0
\(33\) −0.949490 0.866025i −0.165285 0.150756i
\(34\) 0 0
\(35\) 1.07547i 0.181787i
\(36\) 0 0
\(37\) 7.34847i 1.20808i −0.796954 0.604040i \(-0.793557\pi\)
0.796954 0.604040i \(-0.206443\pi\)
\(38\) 0 0
\(39\) 1.11295 5.07556i 0.178214 0.812741i
\(40\) 0 0
\(41\) −0.825765 0.476756i −0.128963 0.0744568i 0.434131 0.900850i \(-0.357056\pi\)
−0.563094 + 0.826393i \(0.690389\pi\)
\(42\) 0 0
\(43\) −3.50162 6.06499i −0.533992 0.924902i −0.999211 0.0397062i \(-0.987358\pi\)
0.465219 0.885196i \(-0.345976\pi\)
\(44\) 0 0
\(45\) −0.0874863 0.949490i −0.0130417 0.141542i
\(46\) 0 0
\(47\) 5.15627 + 8.93092i 0.752119 + 1.30271i 0.946794 + 0.321841i \(0.104302\pi\)
−0.194675 + 0.980868i \(0.562365\pi\)
\(48\) 0 0
\(49\) 2.22474 3.85337i 0.317821 0.550482i
\(50\) 0 0
\(51\) 7.00324 2.22589i 0.980650 0.311687i
\(52\) 0 0
\(53\) −5.51399 −0.757405 −0.378702 0.925519i \(-0.623630\pi\)
−0.378702 + 0.925519i \(0.623630\pi\)
\(54\) 0 0
\(55\) 0.235824i 0.0317985i
\(56\) 0 0
\(57\) 1.34847 + 4.24264i 0.178609 + 0.561951i
\(58\) 0 0
\(59\) 3.50162 + 2.02166i 0.455872 + 0.263198i 0.710307 0.703892i \(-0.248556\pi\)
−0.254435 + 0.967090i \(0.581889\pi\)
\(60\) 0 0
\(61\) −7.79423 + 4.50000i −0.997949 + 0.576166i −0.907641 0.419748i \(-0.862118\pi\)
−0.0903080 + 0.995914i \(0.528785\pi\)
\(62\) 0 0
\(63\) 4.24755 9.21975i 0.535141 1.16158i
\(64\) 0 0
\(65\) 0.825765 0.476756i 0.102424 0.0591343i
\(66\) 0 0
\(67\) −6.36068 + 11.0170i −0.777081 + 1.34594i 0.156536 + 0.987672i \(0.449967\pi\)
−0.933617 + 0.358272i \(0.883366\pi\)
\(68\) 0 0
\(69\) −6.84072 1.50000i −0.823526 0.180579i
\(70\) 0 0
\(71\) 13.5389 1.60678 0.803389 0.595455i \(-0.203028\pi\)
0.803389 + 0.595455i \(0.203028\pi\)
\(72\) 0 0
\(73\) −6.44949 −0.754856 −0.377428 0.926039i \(-0.623191\pi\)
−0.377428 + 0.926039i \(0.623191\pi\)
\(74\) 0 0
\(75\) −5.71812 + 6.26922i −0.660272 + 0.723907i
\(76\) 0 0
\(77\) 1.25529 2.17423i 0.143054 0.247777i
\(78\) 0 0
\(79\) −8.29088 + 4.78674i −0.932797 + 0.538550i −0.887695 0.460432i \(-0.847694\pi\)
−0.0451016 + 0.998982i \(0.514361\pi\)
\(80\) 0 0
\(81\) 3.00000 8.48528i 0.333333 0.942809i
\(82\) 0 0
\(83\) 2.21650 1.27970i 0.243293 0.140465i −0.373396 0.927672i \(-0.621807\pi\)
0.616689 + 0.787207i \(0.288474\pi\)
\(84\) 0 0
\(85\) 1.16781 + 0.674235i 0.126667 + 0.0731310i
\(86\) 0 0
\(87\) 9.36635 10.2690i 1.00418 1.10096i
\(88\) 0 0
\(89\) 14.6349i 1.55130i 0.631163 + 0.775651i \(0.282578\pi\)
−0.631163 + 0.775651i \(0.717422\pi\)
\(90\) 0 0
\(91\) 10.1511 1.06413
\(92\) 0 0
\(93\) 1.81954 8.29796i 0.188677 0.860458i
\(94\) 0 0
\(95\) −0.408459 + 0.707471i −0.0419070 + 0.0725850i
\(96\) 0 0
\(97\) −5.62372 9.74058i −0.571003 0.989006i −0.996463 0.0840287i \(-0.973221\pi\)
0.425461 0.904977i \(-0.360112\pi\)
\(98\) 0 0
\(99\) 0.931383 2.02166i 0.0936076 0.203185i
\(100\) 0 0
\(101\) 0.158919 + 0.275255i 0.0158130 + 0.0273889i 0.873824 0.486243i \(-0.161633\pi\)
−0.858011 + 0.513632i \(0.828300\pi\)
\(102\) 0 0
\(103\) −13.2429 7.64580i −1.30486 0.753363i −0.323629 0.946184i \(-0.604903\pi\)
−0.981234 + 0.192821i \(0.938236\pi\)
\(104\) 0 0
\(105\) 1.77526 0.564242i 0.173247 0.0550644i
\(106\) 0 0
\(107\) 8.75366i 0.846248i 0.906072 + 0.423124i \(0.139067\pi\)
−0.906072 + 0.423124i \(0.860933\pi\)
\(108\) 0 0
\(109\) 13.3485i 1.27855i −0.768978 0.639276i \(-0.779234\pi\)
0.768978 0.639276i \(-0.220766\pi\)
\(110\) 0 0
\(111\) 12.1300 3.85536i 1.15133 0.365934i
\(112\) 0 0
\(113\) 4.50000 + 2.59808i 0.423324 + 0.244406i 0.696499 0.717558i \(-0.254740\pi\)
−0.273174 + 0.961965i \(0.588074\pi\)
\(114\) 0 0
\(115\) −0.642559 1.11295i −0.0599190 0.103783i
\(116\) 0 0
\(117\) 8.96204 0.825765i 0.828541 0.0763420i
\(118\) 0 0
\(119\) 7.17793 + 12.4325i 0.658000 + 1.13969i
\(120\) 0 0
\(121\) −5.22474 + 9.04952i −0.474977 + 0.822684i
\(122\) 0 0
\(123\) 0.353736 1.61320i 0.0318953 0.145458i
\(124\) 0 0
\(125\) −3.14626 −0.281410
\(126\) 0 0
\(127\) 1.62694i 0.144368i 0.997391 + 0.0721839i \(0.0229969\pi\)
−0.997391 + 0.0721839i \(0.977003\pi\)
\(128\) 0 0
\(129\) 8.17423 8.96204i 0.719701 0.789063i
\(130\) 0 0
\(131\) −16.2230 9.36635i −1.41741 0.818341i −0.421338 0.906904i \(-0.638440\pi\)
−0.996071 + 0.0885620i \(0.971773\pi\)
\(132\) 0 0
\(133\) −7.53177 + 4.34847i −0.653087 + 0.377060i
\(134\) 0 0
\(135\) 1.52140 0.642559i 0.130942 0.0553027i
\(136\) 0 0
\(137\) −6.52270 + 3.76588i −0.557272 + 0.321741i −0.752050 0.659106i \(-0.770935\pi\)
0.194778 + 0.980847i \(0.437601\pi\)
\(138\) 0 0
\(139\) 6.64951 11.5173i 0.564004 0.976883i −0.433138 0.901328i \(-0.642594\pi\)
0.997142 0.0755556i \(-0.0240730\pi\)
\(140\) 0 0
\(141\) −12.0369 + 13.1969i −1.01369 + 1.11138i
\(142\) 0 0
\(143\) 2.22589 0.186138
\(144\) 0 0
\(145\) 2.55051 0.211808
\(146\) 0 0
\(147\) 7.52789 + 1.65068i 0.620890 + 0.136146i
\(148\) 0 0
\(149\) 2.91591 5.05051i 0.238881 0.413754i −0.721513 0.692401i \(-0.756553\pi\)
0.960393 + 0.278647i \(0.0898861\pi\)
\(150\) 0 0
\(151\) −14.1516 + 8.17045i −1.15164 + 0.664902i −0.949287 0.314410i \(-0.898193\pi\)
−0.202356 + 0.979312i \(0.564860\pi\)
\(152\) 0 0
\(153\) 7.34847 + 10.3923i 0.594089 + 0.840168i
\(154\) 0 0
\(155\) 1.35003 0.779441i 0.108437 0.0626062i
\(156\) 0 0
\(157\) 19.3543 + 11.1742i 1.54464 + 0.891801i 0.998536 + 0.0540865i \(0.0172247\pi\)
0.546108 + 0.837715i \(0.316109\pi\)
\(158\) 0 0
\(159\) −2.89290 9.10183i −0.229422 0.721822i
\(160\) 0 0
\(161\) 13.6814i 1.07825i
\(162\) 0 0
\(163\) −11.4362 −0.895756 −0.447878 0.894095i \(-0.647820\pi\)
−0.447878 + 0.894095i \(0.647820\pi\)
\(164\) 0 0
\(165\) 0.389270 0.123724i 0.0303046 0.00963193i
\(166\) 0 0
\(167\) −9.19959 + 15.9342i −0.711886 + 1.23302i 0.252262 + 0.967659i \(0.418825\pi\)
−0.964148 + 0.265364i \(0.914508\pi\)
\(168\) 0 0
\(169\) −2.00000 3.46410i −0.153846 0.266469i
\(170\) 0 0
\(171\) −6.29577 + 4.45178i −0.481450 + 0.340436i
\(172\) 0 0
\(173\) 9.59771 + 16.6237i 0.729701 + 1.26388i 0.957010 + 0.290056i \(0.0936738\pi\)
−0.227309 + 0.973823i \(0.572993\pi\)
\(174\) 0 0
\(175\) −14.3559 8.28836i −1.08520 0.626541i
\(176\) 0 0
\(177\) −1.50000 + 6.84072i −0.112747 + 0.514180i
\(178\) 0 0
\(179\) 22.7760i 1.70236i −0.524874 0.851180i \(-0.675888\pi\)
0.524874 0.851180i \(-0.324112\pi\)
\(180\) 0 0
\(181\) 4.65153i 0.345746i 0.984944 + 0.172873i \(0.0553049\pi\)
−0.984944 + 0.172873i \(0.944695\pi\)
\(182\) 0 0
\(183\) −11.5173 10.5049i −0.851382 0.776542i
\(184\) 0 0
\(185\) 2.02270 + 1.16781i 0.148712 + 0.0858590i
\(186\) 0 0
\(187\) 1.57394 + 2.72615i 0.115098 + 0.199356i
\(188\) 0 0
\(189\) 17.4473 + 2.17423i 1.26911 + 0.158152i
\(190\) 0 0
\(191\) 12.8345 + 22.2299i 0.928669 + 1.60850i 0.785552 + 0.618796i \(0.212379\pi\)
0.143117 + 0.989706i \(0.454287\pi\)
\(192\) 0 0
\(193\) 1.27526 2.20881i 0.0917949 0.158993i −0.816472 0.577386i \(-0.804073\pi\)
0.908266 + 0.418392i \(0.137406\pi\)
\(194\) 0 0
\(195\) 1.22021 + 1.11295i 0.0873809 + 0.0796997i
\(196\) 0 0
\(197\) 11.0280 0.785711 0.392855 0.919600i \(-0.371487\pi\)
0.392855 + 0.919600i \(0.371487\pi\)
\(198\) 0 0
\(199\) 5.24648i 0.371913i 0.982558 + 0.185956i \(0.0595383\pi\)
−0.982558 + 0.185956i \(0.940462\pi\)
\(200\) 0 0
\(201\) −21.5227 4.71940i −1.51809 0.332881i
\(202\) 0 0
\(203\) 23.5151 + 13.5764i 1.65043 + 0.952878i
\(204\) 0 0
\(205\) 0.262459 0.151531i 0.0183309 0.0105834i
\(206\) 0 0
\(207\) −1.11295 12.0788i −0.0773551 0.839535i
\(208\) 0 0
\(209\) −1.65153 + 0.953512i −0.114239 + 0.0659558i
\(210\) 0 0
\(211\) −5.07556 + 8.79114i −0.349416 + 0.605207i −0.986146 0.165880i \(-0.946953\pi\)
0.636730 + 0.771087i \(0.280287\pi\)
\(212\) 0 0
\(213\) 7.10318 + 22.3485i 0.486702 + 1.53129i
\(214\) 0 0
\(215\) 2.22589 0.151805
\(216\) 0 0
\(217\) 16.5959 1.12660
\(218\) 0 0
\(219\) −3.38371 10.6460i −0.228650 0.719393i
\(220\) 0 0
\(221\) −6.36396 + 11.0227i −0.428086 + 0.741467i
\(222\) 0 0
\(223\) −16.4693 + 9.50857i −1.10287 + 0.636741i −0.936973 0.349403i \(-0.886385\pi\)
−0.165895 + 0.986143i \(0.553051\pi\)
\(224\) 0 0
\(225\) −13.3485 6.14966i −0.889898 0.409978i
\(226\) 0 0
\(227\) −12.7863 + 7.38216i −0.848655 + 0.489971i −0.860197 0.509962i \(-0.829659\pi\)
0.0115418 + 0.999933i \(0.496326\pi\)
\(228\) 0 0
\(229\) 16.4938 + 9.52270i 1.08994 + 0.629278i 0.933561 0.358419i \(-0.116684\pi\)
0.156381 + 0.987697i \(0.450017\pi\)
\(230\) 0 0
\(231\) 4.24755 + 0.931383i 0.279468 + 0.0612805i
\(232\) 0 0
\(233\) 8.48528i 0.555889i −0.960597 0.277945i \(-0.910347\pi\)
0.960597 0.277945i \(-0.0896532\pi\)
\(234\) 0 0
\(235\) −3.27771 −0.213814
\(236\) 0 0
\(237\) −12.2512 11.1742i −0.795799 0.725845i
\(238\) 0 0
\(239\) −2.02166 + 3.50162i −0.130770 + 0.226501i −0.923974 0.382456i \(-0.875078\pi\)
0.793203 + 0.608957i \(0.208412\pi\)
\(240\) 0 0
\(241\) 7.84847 + 13.5939i 0.505564 + 0.875663i 0.999979 + 0.00643712i \(0.00204901\pi\)
−0.494415 + 0.869226i \(0.664618\pi\)
\(242\) 0 0
\(243\) 15.5804 + 0.500258i 0.999485 + 0.0320915i
\(244\) 0 0
\(245\) 0.707107 + 1.22474i 0.0451754 + 0.0782461i
\(246\) 0 0
\(247\) −6.67767 3.85536i −0.424890 0.245310i
\(248\) 0 0
\(249\) 3.27526 + 2.98735i 0.207561 + 0.189315i
\(250\) 0 0
\(251\) 24.2599i 1.53127i 0.643273 + 0.765637i \(0.277576\pi\)
−0.643273 + 0.765637i \(0.722424\pi\)
\(252\) 0 0
\(253\) 3.00000i 0.188608i
\(254\) 0 0
\(255\) −0.500258 + 2.28141i −0.0313274 + 0.142868i
\(256\) 0 0
\(257\) −2.84847 1.64456i −0.177683 0.102585i 0.408521 0.912749i \(-0.366045\pi\)
−0.586203 + 0.810164i \(0.699378\pi\)
\(258\) 0 0
\(259\) 12.4325 + 21.5338i 0.772521 + 1.33804i
\(260\) 0 0
\(261\) 21.8649 + 10.0732i 1.35341 + 0.623516i
\(262\) 0 0
\(263\) −1.61320 2.79415i −0.0994744 0.172295i 0.811993 0.583667i \(-0.198383\pi\)
−0.911467 + 0.411373i \(0.865049\pi\)
\(264\) 0 0
\(265\) 0.876276 1.51775i 0.0538292 0.0932349i
\(266\) 0 0
\(267\) −24.1576 + 7.67819i −1.47842 + 0.469898i
\(268\) 0 0
\(269\) 17.4634 1.06476 0.532380 0.846505i \(-0.321298\pi\)
0.532380 + 0.846505i \(0.321298\pi\)
\(270\) 0 0
\(271\) 4.19718i 0.254961i −0.991841 0.127480i \(-0.959311\pi\)
0.991841 0.127480i \(-0.0406890\pi\)
\(272\) 0 0
\(273\) 5.32577 + 16.7563i 0.322330 + 1.01414i
\(274\) 0 0
\(275\) −3.14789 1.81743i −0.189825 0.109595i
\(276\) 0 0
\(277\) −16.4938 + 9.52270i −0.991017 + 0.572164i −0.905578 0.424180i \(-0.860563\pi\)
−0.0854387 + 0.996343i \(0.527229\pi\)
\(278\) 0 0
\(279\) 14.6519 1.35003i 0.877186 0.0808242i
\(280\) 0 0
\(281\) 22.8712 13.2047i 1.36438 0.787725i 0.374176 0.927358i \(-0.377925\pi\)
0.990203 + 0.139633i \(0.0445921\pi\)
\(282\) 0 0
\(283\) 11.7900 20.4208i 0.700842 1.21389i −0.267330 0.963605i \(-0.586141\pi\)
0.968171 0.250288i \(-0.0805254\pi\)
\(284\) 0 0
\(285\) −1.38211 0.303062i −0.0818689 0.0179518i
\(286\) 0 0
\(287\) 3.22641 0.190449
\(288\) 0 0
\(289\) −1.00000 −0.0588235
\(290\) 0 0
\(291\) 13.1281 14.3933i 0.769583 0.843753i
\(292\) 0 0
\(293\) −3.30518 + 5.72474i −0.193091 + 0.334443i −0.946273 0.323369i \(-0.895185\pi\)
0.753182 + 0.657812i \(0.228518\pi\)
\(294\) 0 0
\(295\) −1.11295 + 0.642559i −0.0647982 + 0.0374113i
\(296\) 0 0
\(297\) 3.82577 + 0.476756i 0.221993 + 0.0276642i
\(298\) 0 0
\(299\) 10.5049 6.06499i 0.607512 0.350747i
\(300\) 0 0
\(301\) 20.5222 + 11.8485i 1.18288 + 0.682934i
\(302\) 0 0
\(303\) −0.370982 + 0.406736i −0.0213124 + 0.0233664i
\(304\) 0 0
\(305\) 2.86054i 0.163794i
\(306\) 0 0
\(307\) −17.7320 −1.01202 −0.506010 0.862528i \(-0.668880\pi\)
−0.506010 + 0.862528i \(0.668880\pi\)
\(308\) 0 0
\(309\) 5.67291 25.8712i 0.322720 1.47176i
\(310\) 0 0
\(311\) 5.65653 9.79739i 0.320752 0.555559i −0.659891 0.751361i \(-0.729398\pi\)
0.980643 + 0.195802i \(0.0627310\pi\)
\(312\) 0 0
\(313\) 4.05051 + 7.01569i 0.228948 + 0.396550i 0.957497 0.288444i \(-0.0931380\pi\)
−0.728548 + 0.684994i \(0.759805\pi\)
\(314\) 0 0
\(315\) 1.86277 + 2.63435i 0.104955 + 0.148429i
\(316\) 0 0
\(317\) 1.96240 + 3.39898i 0.110219 + 0.190906i 0.915859 0.401501i \(-0.131511\pi\)
−0.805639 + 0.592406i \(0.798178\pi\)
\(318\) 0 0
\(319\) 5.15627 + 2.97697i 0.288696 + 0.166679i
\(320\) 0 0
\(321\) −14.4495 + 4.59259i −0.806492 + 0.256333i
\(322\) 0 0
\(323\) 10.9046i 0.606748i
\(324\) 0 0
\(325\) 14.6969i 0.815239i
\(326\) 0 0
\(327\) 22.0341 7.00324i 1.21849 0.387280i
\(328\) 0 0
\(329\) −30.2196 17.4473i −1.66606 0.961902i
\(330\) 0 0
\(331\) −9.50857 16.4693i −0.522638 0.905236i −0.999653 0.0263407i \(-0.991615\pi\)
0.477015 0.878895i \(-0.341719\pi\)
\(332\) 0 0
\(333\) 12.7279 + 18.0000i 0.697486 + 0.986394i
\(334\) 0 0
\(335\) −2.02166 3.50162i −0.110455 0.191314i
\(336\) 0 0
\(337\) 0.848469 1.46959i 0.0462191 0.0800538i −0.841990 0.539493i \(-0.818616\pi\)
0.888209 + 0.459439i \(0.151949\pi\)
\(338\) 0 0
\(339\) −1.92768 + 8.79114i −0.104697 + 0.477469i
\(340\) 0 0
\(341\) 3.63907 0.197067
\(342\) 0 0
\(343\) 8.63019i 0.465986i
\(344\) 0 0
\(345\) 1.50000 1.64456i 0.0807573 0.0885404i
\(346\) 0 0
\(347\) −14.6490 8.45763i −0.786402 0.454029i 0.0522924 0.998632i \(-0.483347\pi\)
−0.838694 + 0.544602i \(0.816681\pi\)
\(348\) 0 0
\(349\) −14.1582 + 8.17423i −0.757871 + 0.437557i −0.828531 0.559944i \(-0.810823\pi\)
0.0706601 + 0.997500i \(0.477489\pi\)
\(350\) 0 0
\(351\) 6.06499 + 14.3602i 0.323725 + 0.766492i
\(352\) 0 0
\(353\) −17.1742 + 9.91555i −0.914092 + 0.527751i −0.881746 0.471725i \(-0.843631\pi\)
−0.0323467 + 0.999477i \(0.510298\pi\)
\(354\) 0 0
\(355\) −2.15159 + 3.72666i −0.114195 + 0.197791i
\(356\) 0 0
\(357\) −16.7563 + 18.3712i −0.886836 + 0.972306i
\(358\) 0 0
\(359\) 8.08665 0.426797 0.213398 0.976965i \(-0.431547\pi\)
0.213398 + 0.976965i \(0.431547\pi\)
\(360\) 0 0
\(361\) −12.3939 −0.652309
\(362\) 0 0
\(363\) −17.6790 3.87657i −0.927908 0.203467i
\(364\) 0 0
\(365\) 1.02494 1.77526i 0.0536480 0.0929211i
\(366\) 0 0
\(367\) 11.9257 6.88533i 0.622519 0.359411i −0.155330 0.987863i \(-0.549644\pi\)
0.777849 + 0.628451i \(0.216311\pi\)
\(368\) 0 0
\(369\) 2.84847 0.262459i 0.148285 0.0136631i
\(370\) 0 0
\(371\) 16.1581 9.32887i 0.838886 0.484331i
\(372\) 0 0
\(373\) 25.7183 + 14.8485i 1.33164 + 0.768825i 0.985551 0.169376i \(-0.0541752\pi\)
0.346092 + 0.938201i \(0.387509\pi\)
\(374\) 0 0
\(375\) −1.65068 5.19348i −0.0852408 0.268190i
\(376\) 0 0
\(377\) 24.0737i 1.23986i
\(378\) 0 0
\(379\) 8.28836 0.425745 0.212872 0.977080i \(-0.431718\pi\)
0.212872 + 0.977080i \(0.431718\pi\)
\(380\) 0 0
\(381\) −2.68556 + 0.853572i −0.137586 + 0.0437298i
\(382\) 0 0
\(383\) 5.15627 8.93092i 0.263473 0.456349i −0.703689 0.710508i \(-0.748465\pi\)
0.967162 + 0.254159i \(0.0817987\pi\)
\(384\) 0 0
\(385\) 0.398979 + 0.691053i 0.0203339 + 0.0352193i
\(386\) 0 0
\(387\) 19.0820 + 8.79114i 0.969995 + 0.446879i
\(388\) 0 0
\(389\) −1.11243 1.92679i −0.0564025 0.0976919i 0.836446 0.548050i \(-0.184630\pi\)
−0.892848 + 0.450358i \(0.851296\pi\)
\(390\) 0 0
\(391\) 14.8561 + 8.57719i 0.751306 + 0.433767i
\(392\) 0 0
\(393\) 6.94949 31.6930i 0.350555 1.59870i
\(394\) 0 0
\(395\) 3.04281i 0.153100i
\(396\) 0 0
\(397\) 16.0454i 0.805296i −0.915355 0.402648i \(-0.868090\pi\)
0.915355 0.402648i \(-0.131910\pi\)
\(398\) 0 0
\(399\) −11.1295 10.1511i −0.557170 0.508192i
\(400\) 0 0
\(401\) 33.5227 + 19.3543i 1.67404 + 0.966510i 0.965337 + 0.261007i \(0.0840545\pi\)
0.708707 + 0.705503i \(0.249279\pi\)
\(402\) 0 0
\(403\) 7.35698 + 12.7427i 0.366477 + 0.634757i
\(404\) 0 0
\(405\) 1.85886 + 2.17423i 0.0923676 + 0.108039i
\(406\) 0 0
\(407\) 2.72615 + 4.72183i 0.135130 + 0.234052i
\(408\) 0 0
\(409\) 6.29796 10.9084i 0.311414 0.539385i −0.667255 0.744830i \(-0.732531\pi\)
0.978669 + 0.205445i \(0.0658641\pi\)
\(410\) 0 0
\(411\) −9.63839 8.79114i −0.475427 0.433635i
\(412\) 0 0
\(413\) −13.6814 −0.673219
\(414\) 0 0
\(415\) 0.813472i 0.0399317i
\(416\) 0 0
\(417\) 22.5000 + 4.93369i 1.10183 + 0.241604i
\(418\) 0 0
\(419\) −8.22345 4.74781i −0.401742 0.231946i 0.285493 0.958381i \(-0.407843\pi\)
−0.687235 + 0.726435i \(0.741176\pi\)
\(420\) 0 0
\(421\) −10.1298 + 5.84847i −0.493698 + 0.285037i −0.726108 0.687581i \(-0.758673\pi\)
0.232409 + 0.972618i \(0.425339\pi\)
\(422\) 0 0
\(423\) −28.0990 12.9453i −1.36622 0.629421i
\(424\) 0 0
\(425\) 18.0000 10.3923i 0.873128 0.504101i
\(426\) 0 0
\(427\) 15.2267 26.3734i 0.736871 1.27630i
\(428\) 0 0
\(429\) 1.16781 + 3.67423i 0.0563823 + 0.177394i
\(430\) 0 0
\(431\) 8.08665 0.389520 0.194760 0.980851i \(-0.437607\pi\)
0.194760 + 0.980851i \(0.437607\pi\)
\(432\) 0 0
\(433\) −17.5505 −0.843424 −0.421712 0.906730i \(-0.638571\pi\)
−0.421712 + 0.906730i \(0.638571\pi\)
\(434\) 0 0
\(435\) 1.33812 + 4.21008i 0.0641579 + 0.201858i
\(436\) 0 0
\(437\) −5.19615 + 9.00000i −0.248566 + 0.430528i
\(438\) 0 0
\(439\) 15.5606 8.98392i 0.742667 0.428779i −0.0803710 0.996765i \(-0.525611\pi\)
0.823038 + 0.567986i \(0.192277\pi\)
\(440\) 0 0
\(441\) 1.22474 + 13.2922i 0.0583212 + 0.632960i
\(442\) 0 0
\(443\) −31.5146 + 18.1950i −1.49730 + 0.864469i −0.999995 0.00310536i \(-0.999012\pi\)
−0.497308 + 0.867574i \(0.665678\pi\)
\(444\) 0 0
\(445\) −4.02834 2.32577i −0.190962 0.110252i
\(446\) 0 0
\(447\) 9.86660 + 2.16350i 0.466674 + 0.102330i
\(448\) 0 0
\(449\) 10.8209i 0.510670i 0.966853 + 0.255335i \(0.0821857\pi\)
−0.966853 + 0.255335i \(0.917814\pi\)
\(450\) 0 0
\(451\) 0.707471 0.0333135
\(452\) 0 0
\(453\) −20.9114 19.0732i −0.982504 0.896138i
\(454\) 0 0
\(455\) −1.61320 + 2.79415i −0.0756281 + 0.130992i
\(456\) 0 0
\(457\) −18.0732 31.3037i −0.845429 1.46433i −0.885248 0.465120i \(-0.846011\pi\)
0.0398186 0.999207i \(-0.487322\pi\)
\(458\) 0 0
\(459\) −13.2990 + 17.5823i −0.620745 + 0.820670i
\(460\) 0 0
\(461\) −10.4477 18.0959i −0.486597 0.842811i 0.513284 0.858219i \(-0.328429\pi\)
−0.999881 + 0.0154078i \(0.995095\pi\)
\(462\) 0 0
\(463\) 8.69934 + 5.02256i 0.404292 + 0.233418i 0.688334 0.725393i \(-0.258342\pi\)
−0.284042 + 0.958812i \(0.591676\pi\)
\(464\) 0 0
\(465\) 1.99490 + 1.81954i 0.0925112 + 0.0843790i
\(466\) 0 0
\(467\) 15.5063i 0.717545i 0.933425 + 0.358773i \(0.116805\pi\)
−0.933425 + 0.358773i \(0.883195\pi\)
\(468\) 0 0
\(469\) 43.0454i 1.98765i
\(470\) 0 0
\(471\) −8.29088 + 37.8104i −0.382023 + 1.74221i
\(472\) 0 0
\(473\) 4.50000 + 2.59808i 0.206910 + 0.119460i
\(474\) 0 0
\(475\) 6.29577 + 10.9046i 0.288870 + 0.500337i
\(476\) 0 0
\(477\) 13.5065 9.55051i 0.618418 0.437288i
\(478\) 0 0
\(479\) −15.9691 27.6592i −0.729645 1.26378i −0.957033 0.289978i \(-0.906352\pi\)
0.227388 0.973804i \(-0.426981\pi\)
\(480\) 0 0
\(481\) −11.0227 + 19.0919i −0.502592 + 0.870515i
\(482\) 0 0
\(483\) 22.5837 7.17793i 1.02759 0.326607i
\(484\) 0 0
\(485\) 3.57486 0.162326
\(486\) 0 0
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) −6.00000 18.8776i −0.271329 0.853674i
\(490\) 0 0
\(491\) 32.0922 + 18.5285i 1.44830 + 0.836178i 0.998380 0.0568900i \(-0.0181184\pi\)
0.449922 + 0.893068i \(0.351452\pi\)
\(492\) 0 0
\(493\) −29.4842 + 17.0227i −1.32790 + 0.766664i
\(494\) 0 0
\(495\) 0.408459 + 0.577648i 0.0183589 + 0.0259633i
\(496\) 0 0
\(497\) −39.6742 + 22.9059i −1.77963 + 1.02747i
\(498\) 0 0
\(499\) −6.07186 + 10.5168i −0.271814 + 0.470795i −0.969326 0.245777i \(-0.920957\pi\)
0.697513 + 0.716573i \(0.254290\pi\)
\(500\) 0 0
\(501\) −31.1288 6.82577i −1.39073 0.304953i
\(502\) 0 0
\(503\) −33.3471 −1.48687 −0.743437 0.668806i \(-0.766806\pi\)
−0.743437 + 0.668806i \(0.766806\pi\)
\(504\) 0 0
\(505\) −0.101021 −0.00449535
\(506\) 0 0
\(507\) 4.66883 5.11879i 0.207350 0.227334i
\(508\) 0 0
\(509\) 19.8865 34.4444i 0.881453 1.52672i 0.0317262 0.999497i \(-0.489900\pi\)
0.849726 0.527224i \(-0.176767\pi\)
\(510\) 0 0
\(511\) 18.8994 10.9116i 0.836062 0.482701i
\(512\) 0 0
\(513\) −10.6515 8.05669i −0.470277 0.355711i
\(514\) 0 0
\(515\) 4.20909 2.43012i 0.185475 0.107084i
\(516\) 0 0
\(517\) −6.62642 3.82577i −0.291430 0.168257i
\(518\) 0 0
\(519\) −22.4050 + 24.5643i −0.983472 + 1.07826i
\(520\) 0 0
\(521\) 1.90702i 0.0835482i −0.999127 0.0417741i \(-0.986699\pi\)
0.999127 0.0417741i \(-0.0133010\pi\)
\(522\) 0 0
\(523\) −13.4288 −0.587202 −0.293601 0.955928i \(-0.594854\pi\)
−0.293601 + 0.955928i \(0.594854\pi\)
\(524\) 0 0
\(525\) 6.14966 28.0454i 0.268393 1.22400i
\(526\) 0 0
\(527\) −10.4043 + 18.0208i −0.453220 + 0.785000i
\(528\) 0 0
\(529\) 3.32577 + 5.76039i 0.144598 + 0.250452i
\(530\) 0 0
\(531\) −12.0788 + 1.11295i −0.524176 + 0.0482977i
\(532\) 0 0
\(533\) 1.43027 + 2.47730i 0.0619518 + 0.107304i
\(534\) 0 0
\(535\) −2.40949 1.39112i −0.104171 0.0601433i
\(536\) 0 0
\(537\) 37.5959 11.9494i 1.62238 0.515654i
\(538\) 0 0
\(539\) 3.30136i 0.142200i
\(540\) 0 0
\(541\) 20.6969i 0.889831i −0.895573 0.444915i \(-0.853234\pi\)
0.895573 0.444915i \(-0.146766\pi\)
\(542\) 0 0
\(543\) −7.67819 + 2.44041i −0.329503 + 0.104728i
\(544\) 0 0
\(545\) 3.67423 + 2.12132i 0.157387 + 0.0908674i
\(546\) 0 0
\(547\) 3.79045 + 6.56524i 0.162068 + 0.280710i 0.935610 0.353035i \(-0.114850\pi\)
−0.773542 + 0.633745i \(0.781517\pi\)
\(548\) 0 0
\(549\) 11.2977 24.5227i 0.482172 1.04660i
\(550\) 0 0
\(551\) −10.3125 17.8618i −0.439329 0.760940i
\(552\) 0 0
\(553\) 16.1969 28.0539i 0.688764 1.19297i
\(554\) 0 0
\(555\) −0.866472 + 3.95153i −0.0367797 + 0.167733i
\(556\) 0 0
\(557\) −34.7839 −1.47384 −0.736920 0.675980i \(-0.763721\pi\)
−0.736920 + 0.675980i \(0.763721\pi\)
\(558\) 0 0
\(559\) 21.0097i 0.888617i
\(560\) 0 0
\(561\) −3.67423 + 4.02834i −0.155126 + 0.170077i
\(562\) 0 0
\(563\) −17.9268 10.3500i −0.755523 0.436201i 0.0721633 0.997393i \(-0.477010\pi\)
−0.827686 + 0.561192i \(0.810343\pi\)
\(564\) 0 0
\(565\) −1.43027 + 0.825765i −0.0601718 + 0.0347402i
\(566\) 0 0
\(567\) 5.56473 + 29.9406i 0.233697 + 1.25739i
\(568\) 0 0
\(569\) 13.5000 7.79423i 0.565949 0.326751i −0.189580 0.981865i \(-0.560713\pi\)
0.755530 + 0.655114i \(0.227379\pi\)
\(570\) 0 0
\(571\) −14.6490 + 25.3729i −0.613043 + 1.06182i 0.377681 + 0.925936i \(0.376722\pi\)
−0.990724 + 0.135887i \(0.956612\pi\)
\(572\) 0 0
\(573\) −29.9609 + 32.8485i −1.25164 + 1.37226i
\(574\) 0 0
\(575\) −19.8082 −0.826057
\(576\) 0 0
\(577\) −5.34847 −0.222660 −0.111330 0.993784i \(-0.535511\pi\)
−0.111330 + 0.993784i \(0.535511\pi\)
\(578\) 0 0
\(579\) 4.31509 + 0.946193i 0.179329 + 0.0393224i
\(580\) 0 0
\(581\) −4.33013 + 7.50000i −0.179644 + 0.311152i
\(582\) 0 0
\(583\) 3.54307 2.04559i 0.146739 0.0847197i
\(584\) 0 0
\(585\) −1.19694 + 2.59808i −0.0494873 + 0.107417i
\(586\) 0 0
\(587\) 39.8030 22.9802i 1.64284 0.948496i 0.663028 0.748595i \(-0.269271\pi\)
0.979816 0.199901i \(-0.0640622\pi\)
\(588\) 0 0
\(589\) −10.9172 6.30306i −0.449836 0.259713i
\(590\) 0 0
\(591\) 5.78580 + 18.2037i 0.237996 + 0.748799i
\(592\) 0 0
\(593\) 16.5420i 0.679297i −0.940552 0.339649i \(-0.889692\pi\)
0.940552 0.339649i \(-0.110308\pi\)
\(594\) 0 0
\(595\) −4.56283 −0.187058
\(596\) 0 0
\(597\) −8.66025 + 2.75255i −0.354441 + 0.112654i
\(598\) 0 0
\(599\) 19.5121 33.7960i 0.797244 1.38087i −0.124160 0.992262i \(-0.539624\pi\)
0.921404 0.388605i \(-0.127043\pi\)
\(600\) 0 0
\(601\) 11.6237 + 20.1329i 0.474142 + 0.821237i 0.999562 0.0296056i \(-0.00942514\pi\)
−0.525420 + 0.850843i \(0.676092\pi\)
\(602\) 0 0
\(603\) −3.50162 38.0031i −0.142597 1.54761i
\(604\) 0 0
\(605\) −1.66062 2.87628i −0.0675137 0.116937i
\(606\) 0 0
\(607\) 3.33884 + 1.92768i 0.135519 + 0.0782421i 0.566227 0.824249i \(-0.308403\pi\)
−0.430708 + 0.902492i \(0.641736\pi\)
\(608\) 0 0
\(609\) −10.0732 + 45.9387i −0.408187 + 1.86153i
\(610\) 0 0
\(611\) 30.9376i 1.25160i
\(612\) 0 0
\(613\) 4.04541i 0.163392i −0.996657 0.0816962i \(-0.973966\pi\)
0.996657 0.0816962i \(-0.0260337\pi\)
\(614\) 0 0
\(615\) 0.387827 + 0.353736i 0.0156387 + 0.0142640i
\(616\) 0 0
\(617\) −22.8712 13.2047i −0.920759 0.531600i −0.0368817 0.999320i \(-0.511742\pi\)
−0.883877 + 0.467719i \(0.845076\pi\)
\(618\) 0 0
\(619\) −19.0820 33.0511i −0.766972 1.32844i −0.939197 0.343377i \(-0.888429\pi\)
0.172225 0.985058i \(-0.444904\pi\)
\(620\) 0 0
\(621\) 19.3543 8.17423i 0.776663 0.328021i
\(622\) 0 0
\(623\) −24.7602 42.8859i −0.991997 1.71819i
\(624\) 0 0
\(625\) −11.7474 + 20.3472i −0.469898 + 0.813887i
\(626\) 0 0
\(627\) −2.44041 2.22589i −0.0974608 0.0888935i
\(628\) 0 0
\(629\) −31.1769 −1.24310
\(630\) 0 0
\(631\) 9.33766i 0.371726i 0.982576 + 0.185863i \(0.0595081\pi\)
−0.982576 + 0.185863i \(0.940492\pi\)
\(632\) 0 0
\(633\) −17.1742 3.76588i −0.682615 0.149680i
\(634\) 0 0
\(635\) −0.447824 0.258552i −0.0177714 0.0102603i
\(636\) 0 0
\(637\) −11.5601 + 6.67423i −0.458028 + 0.264443i
\(638\) 0 0
\(639\) −33.1635 + 23.4501i −1.31193 + 0.927673i
\(640\) 0 0
\(641\) 10.1969 5.88721i 0.402755 0.232531i −0.284917 0.958552i \(-0.591966\pi\)
0.687672 + 0.726022i \(0.258633\pi\)
\(642\) 0 0
\(643\) −6.36068 + 11.0170i −0.250841 + 0.434469i −0.963758 0.266780i \(-0.914040\pi\)
0.712917 + 0.701249i \(0.247374\pi\)
\(644\) 0 0
\(645\) 1.16781 + 3.67423i 0.0459824 + 0.144673i
\(646\) 0 0
\(647\) −20.6251 −0.810856 −0.405428 0.914127i \(-0.632877\pi\)
−0.405428 + 0.914127i \(0.632877\pi\)
\(648\) 0 0
\(649\) −3.00000 −0.117760
\(650\) 0 0
\(651\) 8.70701 + 27.3946i 0.341255 + 1.07368i
\(652\) 0 0
\(653\) −3.13021 + 5.42168i −0.122495 + 0.212167i −0.920751 0.390151i \(-0.872423\pi\)
0.798256 + 0.602318i \(0.205756\pi\)
\(654\) 0 0
\(655\) 5.15627 2.97697i 0.201472 0.116320i
\(656\) 0 0
\(657\) 15.7980 11.1708i 0.616337 0.435816i
\(658\) 0 0
\(659\) −24.8002 + 14.3184i −0.966078 + 0.557765i −0.898038 0.439917i \(-0.855008\pi\)
−0.0680394 + 0.997683i \(0.521674\pi\)
\(660\) 0 0
\(661\) −3.76588 2.17423i −0.146476 0.0845679i 0.424971 0.905207i \(-0.360284\pi\)
−0.571447 + 0.820639i \(0.693618\pi\)
\(662\) 0 0
\(663\) −21.5338 4.72183i −0.836303 0.183381i
\(664\) 0 0
\(665\) 2.76421i 0.107192i
\(666\) 0 0
\(667\) 32.4460 1.25631
\(668\) 0 0
\(669\) −24.3362 22.1969i −0.940892 0.858183i
\(670\) 0 0
\(671\) 3.33884 5.78304i 0.128894 0.223252i
\(672\) 0 0
\(673\) 2.62372 + 4.54442i 0.101137 + 0.175175i 0.912153 0.409849i \(-0.134419\pi\)
−0.811016 + 0.585024i \(0.801085\pi\)
\(674\) 0 0
\(675\) 3.14789 25.2605i 0.121162 0.972276i
\(676\) 0 0
\(677\) −10.3763 17.9722i −0.398792 0.690728i 0.594785 0.803885i \(-0.297237\pi\)
−0.993577 + 0.113157i \(0.963904\pi\)
\(678\) 0 0
\(679\) 32.9593 + 19.0290i 1.26486 + 0.730268i
\(680\) 0 0
\(681\) −18.8939 17.2330i −0.724015 0.660371i
\(682\) 0 0
\(683\) 18.9912i 0.726680i 0.931657 + 0.363340i \(0.118364\pi\)
−0.931657 + 0.363340i \(0.881636\pi\)
\(684\) 0 0
\(685\) 2.39388i 0.0914653i
\(686\) 0 0
\(687\) −7.06550 + 32.2221i −0.269566 + 1.22935i
\(688\) 0 0
\(689\) 14.3258 + 8.27098i 0.545768 + 0.315099i
\(690\) 0 0
\(691\) −23.2262 40.2290i −0.883567 1.53038i −0.847347 0.531040i \(-0.821801\pi\)
−0.0362206 0.999344i \(-0.511532\pi\)
\(692\) 0 0
\(693\) 0.691053 + 7.50000i 0.0262509 + 0.284901i
\(694\) 0 0
\(695\) 2.11346 + 3.66062i 0.0801681 + 0.138855i
\(696\) 0 0
\(697\) −2.02270 + 3.50343i −0.0766154 + 0.132702i
\(698\) 0 0
\(699\) 14.0065 4.45178i 0.529774 0.168382i
\(700\) 0 0
\(701\) 32.8769 1.24174 0.620871 0.783913i \(-0.286779\pi\)
0.620871 + 0.783913i \(0.286779\pi\)
\(702\) 0 0
\(703\) 18.8873i 0.712349i
\(704\) 0 0
\(705\) −1.71964 5.41045i −0.0647655 0.203769i
\(706\) 0 0
\(707\) −0.931383 0.537734i −0.0350283 0.0202236i
\(708\) 0 0
\(709\) 3.76588 2.17423i 0.141431 0.0816551i −0.427615 0.903961i \(-0.640646\pi\)
0.569046 + 0.822306i \(0.307313\pi\)
\(710\) 0 0
\(711\) 12.0175 26.0853i 0.450693 0.978275i
\(712\) 0 0
\(713\) 17.1742 9.91555i 0.643180 0.371340i
\(714\) 0 0
\(715\) −0.353736 + 0.612688i −0.0132290 + 0.0229132i
\(716\) 0 0
\(717\) −6.84072 1.50000i −0.255471 0.0560185i
\(718\) 0 0
\(719\) 8.90357 0.332047 0.166023 0.986122i \(-0.446907\pi\)
0.166023 + 0.986122i \(0.446907\pi\)
\(720\) 0 0
\(721\) 51.7423 1.92699
\(722\) 0 0
\(723\) −18.3216 + 20.0873i −0.681387 + 0.747056i
\(724\) 0 0
\(725\) 19.6561 34.0454i 0.730010 1.26441i
\(726\) 0 0
\(727\) 23.0552 13.3109i 0.855070 0.493675i −0.00728826 0.999973i \(-0.502320\pi\)
0.862358 + 0.506299i \(0.168987\pi\)
\(728\) 0 0
\(729\) 7.34847 + 25.9808i 0.272166 + 0.962250i
\(730\) 0 0
\(731\) −25.7316 + 14.8561i −0.951716 + 0.549473i
\(732\) 0 0
\(733\) 12.9904 + 7.50000i 0.479811 + 0.277019i 0.720338 0.693624i \(-0.243987\pi\)
−0.240527 + 0.970642i \(0.577320\pi\)
\(734\) 0 0
\(735\) −1.65068 + 1.80977i −0.0608863 + 0.0667542i
\(736\) 0 0
\(737\) 9.43879i 0.347682i
\(738\) 0 0
\(739\) 31.1609 1.14627 0.573135 0.819461i \(-0.305727\pi\)
0.573135 + 0.819461i \(0.305727\pi\)
\(740\) 0 0
\(741\) 2.86054 13.0454i 0.105084 0.479235i
\(742\) 0 0
\(743\) 9.60805 16.6416i 0.352485 0.610522i −0.634199 0.773170i \(-0.718670\pi\)
0.986684 + 0.162647i \(0.0520033\pi\)
\(744\) 0 0
\(745\) 0.926786 + 1.60524i 0.0339548 + 0.0588115i
\(746\) 0 0
\(747\) −3.21280 + 6.97370i −0.117550 + 0.255154i
\(748\) 0 0
\(749\) −14.8099 25.6515i −0.541143 0.937287i
\(750\) 0 0
\(751\) 42.5467 + 24.5643i 1.55255 + 0.896366i 0.997933 + 0.0642608i \(0.0204689\pi\)
0.554618 + 0.832105i \(0.312864\pi\)
\(752\) 0 0
\(753\) −40.0454 + 12.7279i −1.45934 + 0.463831i
\(754\) 0 0
\(755\) 5.19375i 0.189020i
\(756\) 0 0
\(757\) 12.0000i 0.436147i −0.975932 0.218074i \(-0.930023\pi\)
0.975932 0.218074i \(-0.0699773\pi\)
\(758\) 0 0
\(759\) 4.95204 1.57394i 0.179748 0.0571305i
\(760\) 0 0
\(761\) −20.4773 11.8226i −0.742301 0.428568i 0.0806041 0.996746i \(-0.474315\pi\)
−0.822905 + 0.568178i \(0.807648\pi\)
\(762\) 0 0
\(763\) 22.5837 + 39.1161i 0.817584 + 1.41610i
\(764\) 0 0
\(765\) −4.02834 + 0.371173i −0.145645 + 0.0134198i
\(766\) 0 0
\(767\) −6.06499 10.5049i −0.218994 0.379309i
\(768\) 0 0
\(769\) 6.29796 10.9084i 0.227110 0.393366i −0.729840 0.683618i \(-0.760406\pi\)
0.956950 + 0.290251i \(0.0937389\pi\)
\(770\) 0 0
\(771\) 1.22021 5.56473i 0.0439447 0.200409i
\(772\) 0 0
\(773\) −22.1346 −0.796126 −0.398063 0.917358i \(-0.630318\pi\)
−0.398063 + 0.917358i \(0.630318\pi\)
\(774\) 0 0
\(775\) 24.0278i 0.863104i
\(776\) 0 0
\(777\) −29.0227 + 31.8198i −1.04118 + 1.14153i
\(778\) 0 0
\(779\) −2.12241 1.22538i −0.0760434 0.0439037i
\(780\) 0 0
\(781\) −8.69958 + 5.02270i −0.311295 + 0.179726i
\(782\) 0 0
\(783\) −5.15627 + 41.3769i −0.184270 + 1.47869i
\(784\) 0 0
\(785\) −6.15153 + 3.55159i −0.219558 + 0.126762i
\(786\) 0 0
\(787\) −2.92397 + 5.06447i −0.104228 + 0.180529i −0.913423 0.407012i \(-0.866571\pi\)
0.809194 + 0.587541i \(0.199904\pi\)
\(788\) 0 0
\(789\) 3.76588 4.12883i 0.134069 0.146990i
\(790\) 0 0
\(791\) −17.5823 −0.625154
\(792\) 0 0
\(793\) 27.0000 0.958798
\(794\) 0 0
\(795\) 2.96506 + 0.650165i 0.105160 + 0.0230590i
\(796\) 0 0
\(797\)