Properties

Label 912.2.bo.f.769.1
Level $912$
Weight $2$
Character 912.769
Analytic conductor $7.282$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.bo (of order \(9\), degree \(6\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
Defining polynomial: \(x^{6} - x^{3} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 114)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 769.1
Root \(-0.766044 + 0.642788i\) of defining polynomial
Character \(\chi\) \(=\) 912.769
Dual form 912.2.bo.f.625.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.766044 - 0.642788i) q^{3} +(3.20574 + 1.16679i) q^{5} +(-1.43969 + 2.49362i) q^{7} +(0.173648 - 0.984808i) q^{9} +O(q^{10})\) \(q+(0.766044 - 0.642788i) q^{3} +(3.20574 + 1.16679i) q^{5} +(-1.43969 + 2.49362i) q^{7} +(0.173648 - 0.984808i) q^{9} +(-0.173648 - 0.300767i) q^{11} +(-1.26604 - 1.06234i) q^{13} +(3.20574 - 1.16679i) q^{15} +(1.20574 + 6.83807i) q^{17} +(2.82635 + 3.31839i) q^{19} +(0.500000 + 2.83564i) q^{21} +(6.39053 - 2.32596i) q^{23} +(5.08512 + 4.26692i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(1.10354 - 6.25849i) q^{29} +(0.798133 - 1.38241i) q^{31} +(-0.326352 - 0.118782i) q^{33} +(-7.52481 + 6.31407i) q^{35} -11.2121 q^{37} -1.65270 q^{39} +(-2.67365 + 2.24346i) q^{41} +(2.14543 + 0.780873i) q^{43} +(1.70574 - 2.95442i) q^{45} +(-0.971782 + 5.51125i) q^{47} +(-0.645430 - 1.11792i) q^{49} +(5.31908 + 4.46324i) q^{51} +(-1.86097 + 0.677337i) q^{53} +(-0.205737 - 1.16679i) q^{55} +(4.29813 + 0.725293i) q^{57} +(-0.0773815 - 0.438852i) q^{59} +(11.7763 - 4.28623i) q^{61} +(2.20574 + 1.85083i) q^{63} +(-2.81908 - 4.88279i) q^{65} +(0.187319 - 1.06234i) q^{67} +(3.40033 - 5.88954i) q^{69} +(-15.6211 - 5.68561i) q^{71} +(9.51367 - 7.98292i) q^{73} +6.63816 q^{75} +1.00000 q^{77} +(8.36824 - 7.02179i) q^{79} +(-0.939693 - 0.342020i) q^{81} +(5.85844 - 10.1471i) q^{83} +(-4.11334 + 23.3279i) q^{85} +(-3.17752 - 5.50362i) q^{87} +(1.37346 + 1.15247i) q^{89} +(4.47178 - 1.62760i) q^{91} +(-0.277189 - 1.57202i) q^{93} +(5.18866 + 13.9357i) q^{95} +(0.634285 + 3.59721i) q^{97} +(-0.326352 + 0.118782i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 9q^{5} - 3q^{7} + O(q^{10}) \) \( 6q + 9q^{5} - 3q^{7} - 3q^{13} + 9q^{15} - 3q^{17} + 18q^{19} + 3q^{21} + 21q^{23} + 9q^{25} - 3q^{27} - 3q^{29} - 9q^{31} - 3q^{33} - 18q^{35} - 18q^{37} - 12q^{39} - 15q^{41} - 3q^{43} + 9q^{47} + 12q^{49} + 15q^{51} + 12q^{53} + 9q^{55} + 12q^{57} - 27q^{59} + 3q^{61} + 3q^{63} - 21q^{67} + 6q^{69} - 39q^{71} + 36q^{73} + 6q^{75} + 6q^{77} + 45q^{79} + 27q^{83} - 18q^{85} + 6q^{87} - 30q^{89} + 12q^{91} + 9q^{93} - 6q^{97} - 3q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\) \(1\) \(1\) \(1\)

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
\(3\) 0.766044 0.642788i 0.442276 0.371114i
\(4\) 0 0
\(5\) 3.20574 + 1.16679i 1.43365 + 0.521806i 0.937975 0.346703i \(-0.112699\pi\)
0.495674 + 0.868509i \(0.334921\pi\)
\(6\) 0 0
\(7\) −1.43969 + 2.49362i −0.544153 + 0.942500i 0.454507 + 0.890743i \(0.349815\pi\)
−0.998660 + 0.0517569i \(0.983518\pi\)
\(8\) 0 0
\(9\) 0.173648 0.984808i 0.0578827 0.328269i
\(10\) 0 0
\(11\) −0.173648 0.300767i −0.0523569 0.0906848i 0.838659 0.544657i \(-0.183340\pi\)
−0.891016 + 0.453972i \(0.850007\pi\)
\(12\) 0 0
\(13\) −1.26604 1.06234i −0.351138 0.294639i 0.450109 0.892974i \(-0.351385\pi\)
−0.801247 + 0.598334i \(0.795830\pi\)
\(14\) 0 0
\(15\) 3.20574 1.16679i 0.827718 0.301265i
\(16\) 0 0
\(17\) 1.20574 + 6.83807i 0.292434 + 1.65848i 0.677452 + 0.735567i \(0.263084\pi\)
−0.385017 + 0.922909i \(0.625805\pi\)
\(18\) 0 0
\(19\) 2.82635 + 3.31839i 0.648410 + 0.761292i
\(20\) 0 0
\(21\) 0.500000 + 2.83564i 0.109109 + 0.618788i
\(22\) 0 0
\(23\) 6.39053 2.32596i 1.33252 0.484997i 0.425069 0.905161i \(-0.360250\pi\)
0.907448 + 0.420164i \(0.138027\pi\)
\(24\) 0 0
\(25\) 5.08512 + 4.26692i 1.01702 + 0.853385i
\(26\) 0 0
\(27\) −0.500000 0.866025i −0.0962250 0.166667i
\(28\) 0 0
\(29\) 1.10354 6.25849i 0.204922 1.16217i −0.692640 0.721284i \(-0.743552\pi\)
0.897562 0.440888i \(-0.145337\pi\)
\(30\) 0 0
\(31\) 0.798133 1.38241i 0.143349 0.248288i −0.785407 0.618980i \(-0.787546\pi\)
0.928756 + 0.370692i \(0.120880\pi\)
\(32\) 0 0
\(33\) −0.326352 0.118782i −0.0568106 0.0206774i
\(34\) 0 0
\(35\) −7.52481 + 6.31407i −1.27193 + 1.06727i
\(36\) 0 0
\(37\) −11.2121 −1.84326 −0.921632 0.388066i \(-0.873143\pi\)
−0.921632 + 0.388066i \(0.873143\pi\)
\(38\) 0 0
\(39\) −1.65270 −0.264644
\(40\) 0 0
\(41\) −2.67365 + 2.24346i −0.417554 + 0.350369i −0.827232 0.561861i \(-0.810086\pi\)
0.409678 + 0.912230i \(0.365641\pi\)
\(42\) 0 0
\(43\) 2.14543 + 0.780873i 0.327175 + 0.119082i 0.500385 0.865803i \(-0.333192\pi\)
−0.173210 + 0.984885i \(0.555414\pi\)
\(44\) 0 0
\(45\) 1.70574 2.95442i 0.254276 0.440419i
\(46\) 0 0
\(47\) −0.971782 + 5.51125i −0.141749 + 0.803898i 0.828171 + 0.560475i \(0.189381\pi\)
−0.969920 + 0.243423i \(0.921730\pi\)
\(48\) 0 0
\(49\) −0.645430 1.11792i −0.0922042 0.159702i
\(50\) 0 0
\(51\) 5.31908 + 4.46324i 0.744820 + 0.624978i
\(52\) 0 0
\(53\) −1.86097 + 0.677337i −0.255623 + 0.0930393i −0.466653 0.884440i \(-0.654540\pi\)
0.211030 + 0.977480i \(0.432318\pi\)
\(54\) 0 0
\(55\) −0.205737 1.16679i −0.0277416 0.157330i
\(56\) 0 0
\(57\) 4.29813 + 0.725293i 0.569302 + 0.0960674i
\(58\) 0 0
\(59\) −0.0773815 0.438852i −0.0100742 0.0571337i 0.979356 0.202142i \(-0.0647902\pi\)
−0.989430 + 0.145008i \(0.953679\pi\)
\(60\) 0 0
\(61\) 11.7763 4.28623i 1.50780 0.548795i 0.549735 0.835339i \(-0.314729\pi\)
0.958067 + 0.286544i \(0.0925064\pi\)
\(62\) 0 0
\(63\) 2.20574 + 1.85083i 0.277897 + 0.233183i
\(64\) 0 0
\(65\) −2.81908 4.88279i −0.349664 0.605635i
\(66\) 0 0
\(67\) 0.187319 1.06234i 0.0228846 0.129785i −0.971225 0.238163i \(-0.923455\pi\)
0.994110 + 0.108378i \(0.0345657\pi\)
\(68\) 0 0
\(69\) 3.40033 5.88954i 0.409352 0.709018i
\(70\) 0 0
\(71\) −15.6211 5.68561i −1.85388 0.674758i −0.983095 0.183096i \(-0.941388\pi\)
−0.870786 0.491662i \(-0.836390\pi\)
\(72\) 0 0
\(73\) 9.51367 7.98292i 1.11349 0.934330i 0.115233 0.993338i \(-0.463238\pi\)
0.998257 + 0.0590086i \(0.0187939\pi\)
\(74\) 0 0
\(75\) 6.63816 0.766508
\(76\) 0 0
\(77\) 1.00000 0.113961
\(78\) 0 0
\(79\) 8.36824 7.02179i 0.941501 0.790013i −0.0363452 0.999339i \(-0.511572\pi\)
0.977846 + 0.209326i \(0.0671271\pi\)
\(80\) 0 0
\(81\) −0.939693 0.342020i −0.104410 0.0380022i
\(82\) 0 0
\(83\) 5.85844 10.1471i 0.643047 1.11379i −0.341701 0.939809i \(-0.611003\pi\)
0.984749 0.173982i \(-0.0556635\pi\)
\(84\) 0 0
\(85\) −4.11334 + 23.3279i −0.446154 + 2.53027i
\(86\) 0 0
\(87\) −3.17752 5.50362i −0.340666 0.590050i
\(88\) 0 0
\(89\) 1.37346 + 1.15247i 0.145586 + 0.122161i 0.712672 0.701497i \(-0.247485\pi\)
−0.567086 + 0.823659i \(0.691929\pi\)
\(90\) 0 0
\(91\) 4.47178 1.62760i 0.468770 0.170618i
\(92\) 0 0
\(93\) −0.277189 1.57202i −0.0287431 0.163010i
\(94\) 0 0
\(95\) 5.18866 + 13.9357i 0.532346 + 1.42977i
\(96\) 0 0
\(97\) 0.634285 + 3.59721i 0.0644019 + 0.365241i 0.999928 + 0.0119843i \(0.00381481\pi\)
−0.935526 + 0.353257i \(0.885074\pi\)
\(98\) 0 0
\(99\) −0.326352 + 0.118782i −0.0327996 + 0.0119381i
\(100\) 0 0
\(101\) −7.58899 6.36792i −0.755133 0.633632i 0.181722 0.983350i \(-0.441833\pi\)
−0.936855 + 0.349718i \(0.886277\pi\)
\(102\) 0 0
\(103\) 3.92262 + 6.79417i 0.386507 + 0.669450i 0.991977 0.126418i \(-0.0403481\pi\)
−0.605470 + 0.795868i \(0.707015\pi\)
\(104\) 0 0
\(105\) −1.70574 + 9.67372i −0.166463 + 0.944058i
\(106\) 0 0
\(107\) −0.0136706 + 0.0236781i −0.00132158 + 0.00228905i −0.866685 0.498855i \(-0.833754\pi\)
0.865364 + 0.501144i \(0.167087\pi\)
\(108\) 0 0
\(109\) 10.1236 + 3.68469i 0.969666 + 0.352929i 0.777814 0.628494i \(-0.216329\pi\)
0.191852 + 0.981424i \(0.438551\pi\)
\(110\) 0 0
\(111\) −8.58899 + 7.20702i −0.815231 + 0.684060i
\(112\) 0 0
\(113\) −11.6604 −1.09692 −0.548461 0.836176i \(-0.684786\pi\)
−0.548461 + 0.836176i \(0.684786\pi\)
\(114\) 0 0
\(115\) 23.2003 2.16344
\(116\) 0 0
\(117\) −1.26604 + 1.06234i −0.117046 + 0.0982131i
\(118\) 0 0
\(119\) −18.7875 6.83807i −1.72224 0.626845i
\(120\) 0 0
\(121\) 5.43969 9.42182i 0.494518 0.856529i
\(122\) 0 0
\(123\) −0.606067 + 3.43718i −0.0546472 + 0.309920i
\(124\) 0 0
\(125\) 2.79426 + 4.83981i 0.249926 + 0.432885i
\(126\) 0 0
\(127\) −12.4192 10.4210i −1.10203 0.924711i −0.104467 0.994528i \(-0.533314\pi\)
−0.997560 + 0.0698178i \(0.977758\pi\)
\(128\) 0 0
\(129\) 2.14543 0.780873i 0.188895 0.0687520i
\(130\) 0 0
\(131\) 0.486329 + 2.75811i 0.0424908 + 0.240977i 0.998655 0.0518550i \(-0.0165134\pi\)
−0.956164 + 0.292832i \(0.905402\pi\)
\(132\) 0 0
\(133\) −12.3439 + 2.27038i −1.07035 + 0.196867i
\(134\) 0 0
\(135\) −0.592396 3.35965i −0.0509854 0.289152i
\(136\) 0 0
\(137\) −15.0680 + 5.48432i −1.28735 + 0.468557i −0.892856 0.450341i \(-0.851302\pi\)
−0.394494 + 0.918899i \(0.629080\pi\)
\(138\) 0 0
\(139\) 1.59240 + 1.33618i 0.135065 + 0.113333i 0.707818 0.706395i \(-0.249680\pi\)
−0.572752 + 0.819728i \(0.694124\pi\)
\(140\) 0 0
\(141\) 2.79813 + 4.84651i 0.235645 + 0.408150i
\(142\) 0 0
\(143\) −0.0996702 + 0.565258i −0.00833484 + 0.0472692i
\(144\) 0 0
\(145\) 10.8400 18.7755i 0.900215 1.55922i
\(146\) 0 0
\(147\) −1.21301 0.441500i −0.100047 0.0364143i
\(148\) 0 0
\(149\) −1.27719 + 1.07169i −0.104631 + 0.0877962i −0.693603 0.720358i \(-0.743978\pi\)
0.588971 + 0.808154i \(0.299533\pi\)
\(150\) 0 0
\(151\) −20.0523 −1.63183 −0.815917 0.578169i \(-0.803768\pi\)
−0.815917 + 0.578169i \(0.803768\pi\)
\(152\) 0 0
\(153\) 6.94356 0.561354
\(154\) 0 0
\(155\) 4.17159 3.50038i 0.335070 0.281157i
\(156\) 0 0
\(157\) 3.85117 + 1.40171i 0.307357 + 0.111869i 0.491094 0.871107i \(-0.336597\pi\)
−0.183737 + 0.982975i \(0.558820\pi\)
\(158\) 0 0
\(159\) −0.990200 + 1.71508i −0.0785280 + 0.136014i
\(160\) 0 0
\(161\) −3.40033 + 19.2842i −0.267984 + 1.51981i
\(162\) 0 0
\(163\) −4.06758 7.04526i −0.318598 0.551827i 0.661598 0.749859i \(-0.269879\pi\)
−0.980196 + 0.198031i \(0.936545\pi\)
\(164\) 0 0
\(165\) −0.907604 0.761570i −0.0706569 0.0592881i
\(166\) 0 0
\(167\) −12.5890 + 4.58202i −0.974166 + 0.354567i −0.779569 0.626316i \(-0.784562\pi\)
−0.194596 + 0.980883i \(0.562340\pi\)
\(168\) 0 0
\(169\) −1.78312 10.1126i −0.137163 0.777890i
\(170\) 0 0
\(171\) 3.75877 2.20718i 0.287440 0.168787i
\(172\) 0 0
\(173\) −0.177519 1.00676i −0.0134965 0.0765424i 0.977316 0.211788i \(-0.0679287\pi\)
−0.990812 + 0.135246i \(0.956818\pi\)
\(174\) 0 0
\(175\) −17.9611 + 6.53731i −1.35773 + 0.494174i
\(176\) 0 0
\(177\) −0.341367 0.286441i −0.0256587 0.0215302i
\(178\) 0 0
\(179\) 1.01754 + 1.76243i 0.0760546 + 0.131730i 0.901544 0.432687i \(-0.142434\pi\)
−0.825490 + 0.564417i \(0.809101\pi\)
\(180\) 0 0
\(181\) 3.87299 21.9648i 0.287877 1.63263i −0.406947 0.913452i \(-0.633407\pi\)
0.694824 0.719180i \(-0.255482\pi\)
\(182\) 0 0
\(183\) 6.26604 10.8531i 0.463199 0.802285i
\(184\) 0 0
\(185\) −35.9432 13.0822i −2.64259 0.961825i
\(186\) 0 0
\(187\) 1.84730 1.55007i 0.135088 0.113352i
\(188\) 0 0
\(189\) 2.87939 0.209444
\(190\) 0 0
\(191\) −10.7861 −0.780456 −0.390228 0.920718i \(-0.627604\pi\)
−0.390228 + 0.920718i \(0.627604\pi\)
\(192\) 0 0
\(193\) −2.19459 + 1.84148i −0.157970 + 0.132553i −0.718347 0.695685i \(-0.755101\pi\)
0.560377 + 0.828238i \(0.310656\pi\)
\(194\) 0 0
\(195\) −5.29813 1.92836i −0.379407 0.138093i
\(196\) 0 0
\(197\) 4.16772 7.21870i 0.296938 0.514311i −0.678496 0.734604i \(-0.737368\pi\)
0.975434 + 0.220293i \(0.0707013\pi\)
\(198\) 0 0
\(199\) 0.526874 2.98805i 0.0373491 0.211817i −0.960422 0.278550i \(-0.910146\pi\)
0.997771 + 0.0667324i \(0.0212574\pi\)
\(200\) 0 0
\(201\) −0.539363 0.934204i −0.0380437 0.0658937i
\(202\) 0 0
\(203\) 14.0175 + 11.7621i 0.983839 + 0.825539i
\(204\) 0 0
\(205\) −11.1887 + 4.07234i −0.781450 + 0.284425i
\(206\) 0 0
\(207\) −1.18092 6.69734i −0.0820798 0.465497i
\(208\) 0 0
\(209\) 0.507274 1.42631i 0.0350889 0.0986598i
\(210\) 0 0
\(211\) 2.88919 + 16.3854i 0.198900 + 1.12802i 0.906755 + 0.421659i \(0.138552\pi\)
−0.707855 + 0.706358i \(0.750337\pi\)
\(212\) 0 0
\(213\) −15.6211 + 5.68561i −1.07034 + 0.389571i
\(214\) 0 0
\(215\) 5.96657 + 5.00654i 0.406916 + 0.341443i
\(216\) 0 0
\(217\) 2.29813 + 3.98048i 0.156007 + 0.270213i
\(218\) 0 0
\(219\) 2.15657 12.2305i 0.145728 0.826463i
\(220\) 0 0
\(221\) 5.73783 9.93821i 0.385968 0.668516i
\(222\) 0 0
\(223\) −7.67752 2.79439i −0.514125 0.187126i 0.0719114 0.997411i \(-0.477090\pi\)
−0.586036 + 0.810285i \(0.699312\pi\)
\(224\) 0 0
\(225\) 5.08512 4.26692i 0.339008 0.284462i
\(226\) 0 0
\(227\) −1.80066 −0.119514 −0.0597570 0.998213i \(-0.519033\pi\)
−0.0597570 + 0.998213i \(0.519033\pi\)
\(228\) 0 0
\(229\) −18.7392 −1.23832 −0.619160 0.785265i \(-0.712527\pi\)
−0.619160 + 0.785265i \(0.712527\pi\)
\(230\) 0 0
\(231\) 0.766044 0.642788i 0.0504020 0.0422923i
\(232\) 0 0
\(233\) 3.85117 + 1.40171i 0.252298 + 0.0918291i 0.465073 0.885272i \(-0.346028\pi\)
−0.212775 + 0.977101i \(0.568250\pi\)
\(234\) 0 0
\(235\) −9.54576 + 16.5337i −0.622697 + 1.07854i
\(236\) 0 0
\(237\) 1.89693 10.7580i 0.123219 0.698807i
\(238\) 0 0
\(239\) −14.1138 24.4458i −0.912946 1.58127i −0.809881 0.586595i \(-0.800468\pi\)
−0.103066 0.994675i \(-0.532865\pi\)
\(240\) 0 0
\(241\) 5.02687 + 4.21805i 0.323809 + 0.271708i 0.790172 0.612885i \(-0.209991\pi\)
−0.466362 + 0.884594i \(0.654436\pi\)
\(242\) 0 0
\(243\) −0.939693 + 0.342020i −0.0602813 + 0.0219406i
\(244\) 0 0
\(245\) −0.764700 4.33683i −0.0488549 0.277070i
\(246\) 0 0
\(247\) −0.0530334 7.20377i −0.00337444 0.458365i
\(248\) 0 0
\(249\) −2.03462 11.5389i −0.128938 0.731247i
\(250\) 0 0
\(251\) 8.35756 3.04190i 0.527525 0.192003i −0.0645080 0.997917i \(-0.520548\pi\)
0.592033 + 0.805914i \(0.298326\pi\)
\(252\) 0 0
\(253\) −1.80928 1.51816i −0.113748 0.0954462i
\(254\) 0 0
\(255\) 11.8439 + 20.5142i 0.741693 + 1.28465i
\(256\) 0 0
\(257\) −2.33837 + 13.2616i −0.145864 + 0.827234i 0.820806 + 0.571207i \(0.193525\pi\)
−0.966670 + 0.256027i \(0.917586\pi\)
\(258\) 0 0
\(259\) 16.1420 27.9588i 1.00302 1.73728i
\(260\) 0 0
\(261\) −5.97178 2.17355i −0.369644 0.134539i
\(262\) 0 0
\(263\) 12.8327 10.7680i 0.791301 0.663981i −0.154766 0.987951i \(-0.549462\pi\)
0.946067 + 0.323971i \(0.105018\pi\)
\(264\) 0 0
\(265\) −6.75608 −0.415023
\(266\) 0 0
\(267\) 1.79292 0.109725
\(268\) 0 0
\(269\) 2.74969 2.30726i 0.167651 0.140676i −0.555102 0.831782i \(-0.687321\pi\)
0.722753 + 0.691106i \(0.242876\pi\)
\(270\) 0 0
\(271\) 22.5141 + 8.19448i 1.36764 + 0.497779i 0.918407 0.395637i \(-0.129476\pi\)
0.449230 + 0.893416i \(0.351699\pi\)
\(272\) 0 0
\(273\) 2.37939 4.12122i 0.144007 0.249427i
\(274\) 0 0
\(275\) 0.400330 2.27038i 0.0241408 0.136909i
\(276\) 0 0
\(277\) 9.36097 + 16.2137i 0.562446 + 0.974185i 0.997282 + 0.0736755i \(0.0234729\pi\)
−0.434836 + 0.900510i \(0.643194\pi\)
\(278\) 0 0
\(279\) −1.22281 1.02606i −0.0732078 0.0614286i
\(280\) 0 0
\(281\) 9.99660 3.63846i 0.596347 0.217053i −0.0261718 0.999657i \(-0.508332\pi\)
0.622519 + 0.782605i \(0.286109\pi\)
\(282\) 0 0
\(283\) 2.43330 + 13.7999i 0.144644 + 0.820319i 0.967652 + 0.252289i \(0.0811833\pi\)
−0.823008 + 0.568030i \(0.807706\pi\)
\(284\) 0 0
\(285\) 12.9324 + 7.34013i 0.766050 + 0.434792i
\(286\) 0 0
\(287\) −1.74510 9.89695i −0.103010 0.584199i
\(288\) 0 0
\(289\) −29.3307 + 10.6755i −1.72533 + 0.627970i
\(290\) 0 0
\(291\) 2.79813 + 2.34791i 0.164029 + 0.137637i
\(292\) 0 0
\(293\) 5.76011 + 9.97681i 0.336509 + 0.582852i 0.983774 0.179414i \(-0.0574202\pi\)
−0.647264 + 0.762266i \(0.724087\pi\)
\(294\) 0 0
\(295\) 0.263985 1.49713i 0.0153698 0.0871665i
\(296\) 0 0
\(297\) −0.173648 + 0.300767i −0.0100761 + 0.0174523i
\(298\) 0 0
\(299\) −10.5617 3.84413i −0.610796 0.222312i
\(300\) 0 0
\(301\) −5.03596 + 4.22567i −0.290268 + 0.243564i
\(302\) 0 0
\(303\) −9.90673 −0.569127
\(304\) 0 0
\(305\) 42.7529 2.44802
\(306\) 0 0
\(307\) −3.29220 + 2.76249i −0.187896 + 0.157663i −0.731883 0.681430i \(-0.761358\pi\)
0.543987 + 0.839093i \(0.316914\pi\)
\(308\) 0 0
\(309\) 7.37211 + 2.68323i 0.419385 + 0.152644i
\(310\) 0 0
\(311\) −11.4966 + 19.9127i −0.651912 + 1.12915i 0.330746 + 0.943720i \(0.392700\pi\)
−0.982658 + 0.185425i \(0.940634\pi\)
\(312\) 0 0
\(313\) −1.59926 + 9.06985i −0.0903955 + 0.512658i 0.905666 + 0.423992i \(0.139372\pi\)
−0.996061 + 0.0886663i \(0.971740\pi\)
\(314\) 0 0
\(315\) 4.91147 + 8.50692i 0.276730 + 0.479311i
\(316\) 0 0
\(317\) 2.57011 + 2.15658i 0.144352 + 0.121125i 0.712104 0.702074i \(-0.247742\pi\)
−0.567752 + 0.823199i \(0.692187\pi\)
\(318\) 0 0
\(319\) −2.07398 + 0.754866i −0.116120 + 0.0422644i
\(320\) 0 0
\(321\) 0.00474774 + 0.0269258i 0.000264993 + 0.00150285i
\(322\) 0 0
\(323\) −19.2836 + 23.3279i −1.07297 + 1.29800i
\(324\) 0 0
\(325\) −1.90508 10.8042i −0.105675 0.599311i
\(326\) 0 0
\(327\) 10.1236 3.68469i 0.559837 0.203764i
\(328\) 0 0
\(329\) −12.3439 10.3578i −0.680541 0.571042i
\(330\) 0 0
\(331\) −11.0371 19.1169i −0.606656 1.05076i −0.991787 0.127897i \(-0.959177\pi\)
0.385131 0.922862i \(-0.374156\pi\)
\(332\) 0 0
\(333\) −1.94697 + 11.0418i −0.106693 + 0.605087i
\(334\) 0 0
\(335\) 1.84002 3.18701i 0.100531 0.174125i
\(336\) 0 0
\(337\) 12.3255 + 4.48611i 0.671411 + 0.244374i 0.655155 0.755494i \(-0.272603\pi\)
0.0162559 + 0.999868i \(0.494825\pi\)
\(338\) 0 0
\(339\) −8.93242 + 7.49519i −0.485142 + 0.407083i
\(340\) 0 0
\(341\) −0.554378 −0.0300212
\(342\) 0 0
\(343\) −16.4388 −0.887613
\(344\) 0 0
\(345\) 17.7724 14.9128i 0.956836 0.802881i
\(346\) 0 0
\(347\) 8.23055 + 2.99568i 0.441839 + 0.160816i 0.553354 0.832947i \(-0.313348\pi\)
−0.111514 + 0.993763i \(0.535570\pi\)
\(348\) 0 0
\(349\) −1.63176 + 2.82629i −0.0873461 + 0.151288i −0.906389 0.422445i \(-0.861172\pi\)
0.819042 + 0.573733i \(0.194505\pi\)
\(350\) 0 0
\(351\) −0.286989 + 1.62760i −0.0153183 + 0.0868746i
\(352\) 0 0
\(353\) −14.5419 25.1873i −0.773987 1.34058i −0.935362 0.353691i \(-0.884926\pi\)
0.161376 0.986893i \(-0.448407\pi\)
\(354\) 0 0
\(355\) −43.4432 36.4531i −2.30572 1.93473i
\(356\) 0 0
\(357\) −18.7875 + 6.83807i −0.994338 + 0.361909i
\(358\) 0 0
\(359\) −1.14796 6.51038i −0.0605868 0.343605i −1.00000 0.000817017i \(-0.999740\pi\)
0.939413 0.342788i \(-0.111371\pi\)
\(360\) 0 0
\(361\) −3.02347 + 18.7579i −0.159130 + 0.987258i
\(362\) 0 0
\(363\) −1.88919 10.7141i −0.0991565 0.562345i
\(364\) 0 0
\(365\) 39.8127 14.4907i 2.08389 0.758475i
\(366\) 0 0
\(367\) 4.43969 + 3.72534i 0.231750 + 0.194461i 0.751266 0.659999i \(-0.229443\pi\)
−0.519516 + 0.854461i \(0.673888\pi\)
\(368\) 0 0
\(369\) 1.74510 + 3.02260i 0.0908463 + 0.157350i
\(370\) 0 0
\(371\) 0.990200 5.61570i 0.0514086 0.291553i
\(372\) 0 0
\(373\) 12.9449 22.4212i 0.670262 1.16093i −0.307568 0.951526i \(-0.599515\pi\)
0.977830 0.209401i \(-0.0671516\pi\)
\(374\) 0 0
\(375\) 5.25150 + 1.91139i 0.271186 + 0.0987037i
\(376\) 0 0
\(377\) −8.04576 + 6.75119i −0.414378 + 0.347704i
\(378\) 0 0
\(379\) 19.1557 0.983962 0.491981 0.870606i \(-0.336273\pi\)
0.491981 + 0.870606i \(0.336273\pi\)
\(380\) 0 0
\(381\) −16.2121 −0.830573
\(382\) 0 0
\(383\) 7.42649 6.23156i 0.379476 0.318418i −0.433021 0.901384i \(-0.642552\pi\)
0.812497 + 0.582966i \(0.198108\pi\)
\(384\) 0 0
\(385\) 3.20574 + 1.16679i 0.163379 + 0.0594653i
\(386\) 0 0
\(387\) 1.14156 1.97724i 0.0580287 0.100509i
\(388\) 0 0
\(389\) −0.142026 + 0.805470i −0.00720101 + 0.0408390i −0.988197 0.153191i \(-0.951045\pi\)
0.980996 + 0.194030i \(0.0621560\pi\)
\(390\) 0 0
\(391\) 23.6104 + 40.8944i 1.19403 + 2.06812i
\(392\) 0 0
\(393\) 2.14543 + 1.80023i 0.108223 + 0.0908096i
\(394\) 0 0
\(395\) 35.0194 12.7460i 1.76201 0.641321i
\(396\) 0 0
\(397\) −0.642026 3.64111i −0.0322224 0.182742i 0.964449 0.264270i \(-0.0851311\pi\)
−0.996671 + 0.0815281i \(0.974020\pi\)
\(398\) 0 0
\(399\) −7.99660 + 9.67372i −0.400331 + 0.484292i
\(400\) 0 0
\(401\) −3.77513 21.4098i −0.188521 1.06916i −0.921347 0.388740i \(-0.872910\pi\)
0.732827 0.680416i \(-0.238201\pi\)
\(402\) 0 0
\(403\) −2.47906 + 0.902302i −0.123491 + 0.0449469i
\(404\) 0 0
\(405\) −2.61334 2.19285i −0.129858 0.108964i
\(406\) 0 0
\(407\) 1.94697 + 3.37225i 0.0965076 + 0.167156i
\(408\) 0 0
\(409\) −0.704088 + 3.99308i −0.0348149 + 0.197445i −0.997254 0.0740509i \(-0.976407\pi\)
0.962440 + 0.271496i \(0.0875184\pi\)
\(410\) 0 0
\(411\) −8.01754 + 13.8868i −0.395476 + 0.684985i
\(412\) 0 0
\(413\) 1.20574 + 0.438852i 0.0593304 + 0.0215945i
\(414\) 0 0
\(415\) 30.6202 25.6934i 1.50309 1.26124i
\(416\) 0 0
\(417\) 2.07873 0.101796
\(418\) 0 0
\(419\) −23.4989 −1.14800 −0.573998 0.818857i \(-0.694608\pi\)
−0.573998 + 0.818857i \(0.694608\pi\)
\(420\) 0 0
\(421\) −17.6748 + 14.8309i −0.861419 + 0.722816i −0.962273 0.272085i \(-0.912287\pi\)
0.100855 + 0.994901i \(0.467842\pi\)
\(422\) 0 0
\(423\) 5.25877 + 1.91404i 0.255690 + 0.0930636i
\(424\) 0 0
\(425\) −23.0462 + 39.9172i −1.11791 + 1.93627i
\(426\) 0 0
\(427\) −6.26604 + 35.5365i −0.303235 + 1.71973i
\(428\) 0 0
\(429\) 0.286989 + 0.497079i 0.0138560 + 0.0239992i
\(430\) 0 0
\(431\) 2.69253 + 2.25930i 0.129695 + 0.108827i 0.705328 0.708881i \(-0.250800\pi\)
−0.575633 + 0.817708i \(0.695244\pi\)
\(432\) 0 0
\(433\) 32.0574 11.6679i 1.54058 0.560725i 0.574395 0.818578i \(-0.305237\pi\)
0.966184 + 0.257853i \(0.0830152\pi\)
\(434\) 0 0
\(435\) −3.76470 21.3507i −0.180504 1.02369i
\(436\) 0 0
\(437\) 25.7803 + 14.6323i 1.23324 + 0.699958i
\(438\) 0 0
\(439\) −1.68463 9.55401i −0.0804030 0.455988i −0.998254 0.0590636i \(-0.981189\pi\)
0.917851 0.396925i \(-0.129923\pi\)
\(440\) 0 0
\(441\) −1.21301 + 0.441500i −0.0577624 + 0.0210238i
\(442\) 0 0
\(443\) −11.6302 9.75887i −0.552566 0.463658i 0.323243 0.946316i \(-0.395227\pi\)
−0.875809 + 0.482658i \(0.839671\pi\)
\(444\) 0 0
\(445\) 3.05825 + 5.29704i 0.144975 + 0.251104i
\(446\) 0 0
\(447\) −0.289515 + 1.64192i −0.0136936 + 0.0776603i
\(448\) 0 0
\(449\) −17.4192 + 30.1710i −0.822064 + 1.42386i 0.0820794 + 0.996626i \(0.473844\pi\)
−0.904143 + 0.427230i \(0.859489\pi\)
\(450\) 0 0
\(451\) 1.13903 + 0.414574i 0.0536350 + 0.0195215i
\(452\) 0 0
\(453\) −15.3610 + 12.8894i −0.721721 + 0.605596i
\(454\) 0 0
\(455\) 16.2344 0.761081
\(456\) 0 0
\(457\) −31.8749 −1.49105 −0.745523 0.666479i \(-0.767800\pi\)
−0.745523 + 0.666479i \(0.767800\pi\)
\(458\) 0 0
\(459\) 5.31908 4.46324i 0.248273 0.208326i
\(460\) 0 0
\(461\) 10.0449 + 3.65604i 0.467837 + 0.170279i 0.565172 0.824973i \(-0.308810\pi\)
−0.0973354 + 0.995252i \(0.531032\pi\)
\(462\) 0 0
\(463\) 7.65910 13.2660i 0.355949 0.616521i −0.631331 0.775513i \(-0.717491\pi\)
0.987280 + 0.158992i \(0.0508245\pi\)
\(464\) 0 0
\(465\) 0.945622 5.36289i 0.0438522 0.248698i
\(466\) 0 0
\(467\) 14.2562 + 24.6925i 0.659700 + 1.14263i 0.980693 + 0.195553i \(0.0626501\pi\)
−0.320993 + 0.947082i \(0.604017\pi\)
\(468\) 0 0
\(469\) 2.37939 + 1.99654i 0.109870 + 0.0921917i
\(470\) 0 0
\(471\) 3.85117 1.40171i 0.177452 0.0645874i
\(472\) 0 0
\(473\) −0.137689 0.780873i −0.00633094 0.0359046i
\(474\) 0 0
\(475\) 0.213011 + 28.9343i 0.00977362 + 1.32760i
\(476\) 0 0
\(477\) 0.343893 + 1.95031i 0.0157458 + 0.0892987i
\(478\) 0 0
\(479\) 7.56583 2.75374i 0.345691 0.125821i −0.163339 0.986570i \(-0.552226\pi\)
0.509030 + 0.860749i \(0.330004\pi\)
\(480\) 0 0
\(481\) 14.1951 + 11.9111i 0.647239 + 0.543098i
\(482\) 0 0
\(483\) 9.79086 + 16.9583i 0.445500 + 0.771628i
\(484\) 0 0
\(485\) −2.16385 + 12.2718i −0.0982553 + 0.557233i
\(486\) 0 0
\(487\) 3.05778 5.29623i 0.138561 0.239995i −0.788391 0.615175i \(-0.789086\pi\)
0.926952 + 0.375179i \(0.122419\pi\)
\(488\) 0 0
\(489\) −7.64455 2.78239i −0.345699 0.125824i
\(490\) 0 0
\(491\) 17.3778 14.5817i 0.784249 0.658063i −0.160066 0.987106i \(-0.551171\pi\)
0.944315 + 0.329043i \(0.106726\pi\)
\(492\) 0 0
\(493\) 44.1266 1.98736
\(494\) 0 0
\(495\) −1.18479 −0.0532525
\(496\) 0 0
\(497\) 36.6673 30.7675i 1.64475 1.38011i
\(498\) 0 0
\(499\) 23.3567 + 8.50114i 1.04559 + 0.380563i 0.806996 0.590557i \(-0.201092\pi\)
0.238593 + 0.971120i \(0.423314\pi\)
\(500\) 0 0
\(501\) −6.69846 + 11.6021i −0.299265 + 0.518343i
\(502\) 0 0
\(503\) −4.34524 + 24.6431i −0.193745 + 1.09878i 0.720451 + 0.693506i \(0.243935\pi\)
−0.914195 + 0.405274i \(0.867176\pi\)
\(504\) 0 0
\(505\) −16.8983 29.2687i −0.751963 1.30244i
\(506\) 0 0
\(507\) −7.86618 6.60051i −0.349349 0.293139i
\(508\) 0 0
\(509\) −0.845075 + 0.307582i −0.0374573 + 0.0136333i −0.360681 0.932689i \(-0.617456\pi\)
0.323224 + 0.946323i \(0.395233\pi\)
\(510\) 0 0
\(511\) 6.20961 + 35.2164i 0.274697 + 1.55788i
\(512\) 0 0
\(513\) 1.46064 4.10689i 0.0644887 0.181324i
\(514\) 0 0
\(515\) 4.64749 + 26.3572i 0.204793 + 1.16144i
\(516\) 0 0
\(517\) 1.82635 0.664738i 0.0803229 0.0292351i
\(518\) 0 0
\(519\) −0.783119 0.657115i −0.0343751 0.0288441i
\(520\) 0 0
\(521\) 3.31773 + 5.74648i 0.145353 + 0.251758i 0.929504 0.368811i \(-0.120235\pi\)
−0.784152 + 0.620569i \(0.786902\pi\)
\(522\) 0 0
\(523\) −6.59034 + 37.3757i −0.288175 + 1.63432i 0.405542 + 0.914076i \(0.367083\pi\)
−0.693718 + 0.720247i \(0.744028\pi\)
\(524\) 0 0
\(525\) −9.55690 + 16.5530i −0.417097 + 0.722434i
\(526\) 0 0
\(527\) 10.4153 + 3.79088i 0.453700 + 0.165133i
\(528\) 0 0
\(529\) 17.8097 14.9442i 0.774337 0.649746i
\(530\) 0 0
\(531\) −0.445622 −0.0193384
\(532\) 0 0
\(533\) 5.76827 0.249851
\(534\) 0 0
\(535\) −0.0714517 + 0.0599551i −0.00308913 + 0.00259209i
\(536\) 0 0
\(537\) 1.91235 + 0.696039i 0.0825241 + 0.0300363i
\(538\) 0 0
\(539\) −0.224155 + 0.388249i −0.00965506 + 0.0167230i
\(540\) 0 0
\(541\) 2.62742 14.9009i 0.112962 0.640638i −0.874778 0.484525i \(-0.838993\pi\)
0.987739 0.156113i \(-0.0498963\pi\)
\(542\) 0 0
\(543\) −11.1518 19.3155i −0.478571 0.828909i
\(544\) 0 0
\(545\) 28.1544 + 23.6243i 1.20600 + 1.01195i
\(546\) 0 0
\(547\) 30.6215 11.1453i 1.30928 0.476540i 0.409274 0.912412i \(-0.365782\pi\)
0.900009 + 0.435872i \(0.143560\pi\)
\(548\) 0 0
\(549\) −2.17617 12.3417i −0.0928769 0.526731i
\(550\) 0 0
\(551\) 23.8871 14.0267i 1.01763 0.597558i
\(552\) 0 0
\(553\) 5.46198 + 30.9764i 0.232267 + 1.31725i
\(554\) 0 0
\(555\) −35.9432 + 13.0822i −1.52570 + 0.555310i
\(556\) 0 0
\(557\) −15.2777 12.8195i −0.647335 0.543179i 0.258926 0.965897i \(-0.416631\pi\)
−0.906261 + 0.422719i \(0.861076\pi\)
\(558\) 0 0
\(559\) −1.88666 3.26779i −0.0797972 0.138213i
\(560\) 0 0
\(561\) 0.418748 2.37484i 0.0176796 0.100266i
\(562\) 0 0
\(563\) 1.98411 3.43658i 0.0836202 0.144834i −0.821182 0.570666i \(-0.806685\pi\)
0.904802 + 0.425832i \(0.140018\pi\)
\(564\) 0 0
\(565\) −37.3803 13.6053i −1.57260 0.572380i
\(566\) 0 0
\(567\) 2.20574 1.85083i 0.0926322 0.0777277i
\(568\) 0 0
\(569\) 14.8135 0.621012 0.310506 0.950571i \(-0.399501\pi\)
0.310506 + 0.950571i \(0.399501\pi\)
\(570\) 0 0
\(571\) −21.0615 −0.881396 −0.440698 0.897655i \(-0.645269\pi\)
−0.440698 + 0.897655i \(0.645269\pi\)
\(572\) 0 0
\(573\) −8.26264 + 6.93318i −0.345177 + 0.289638i
\(574\) 0 0
\(575\) 42.4213 + 15.4401i 1.76909 + 0.643897i
\(576\) 0 0
\(577\) 22.1211 38.3148i 0.920913 1.59507i 0.122907 0.992418i \(-0.460778\pi\)
0.798006 0.602649i \(-0.205888\pi\)
\(578\) 0 0
\(579\) −0.497474 + 2.82131i −0.0206743 + 0.117250i
\(580\) 0 0
\(581\) 16.8687 + 29.2175i 0.699832 + 1.21214i
\(582\) 0 0
\(583\) 0.526874 + 0.442100i 0.0218209 + 0.0183099i
\(584\) 0 0
\(585\) −5.29813 + 1.92836i −0.219051 + 0.0797280i
\(586\) 0 0
\(587\) −1.73689 9.85041i −0.0716892 0.406570i −0.999443 0.0333765i \(-0.989374\pi\)
0.927754 0.373193i \(-0.121737\pi\)
\(588\) 0 0
\(589\) 6.84318 1.25865i 0.281968 0.0518617i
\(590\) 0 0
\(591\) −1.44743 8.20880i −0.0595395 0.337665i
\(592\) 0 0
\(593\) 10.7981 3.93020i 0.443426 0.161394i −0.110651 0.993859i \(-0.535294\pi\)
0.554077 + 0.832465i \(0.313071\pi\)
\(594\) 0 0
\(595\) −52.2490 43.8421i −2.14200 1.79735i
\(596\) 0 0
\(597\) −1.51707 2.62765i −0.0620897 0.107543i
\(598\) 0 0
\(599\) −1.11422 + 6.31905i −0.0455257 + 0.258189i −0.999073 0.0430552i \(-0.986291\pi\)
0.953547 + 0.301244i \(0.0974020\pi\)
\(600\) 0 0
\(601\) −15.7579 + 27.2935i −0.642778 + 1.11332i 0.342032 + 0.939688i \(0.388885\pi\)
−0.984810 + 0.173636i \(0.944448\pi\)
\(602\) 0 0
\(603\) −1.01367 0.368946i −0.0412799 0.0150246i
\(604\) 0 0
\(605\) 28.4315 23.8569i 1.15591 0.969921i
\(606\) 0 0
\(607\) −0.748341 −0.0303742 −0.0151871 0.999885i \(-0.504834\pi\)
−0.0151871 + 0.999885i \(0.504834\pi\)
\(608\) 0 0
\(609\) 18.2986 0.741497
\(610\) 0 0
\(611\) 7.08512 5.94512i 0.286633 0.240514i
\(612\) 0 0
\(613\) 28.8371 + 10.4958i 1.16472 + 0.423923i 0.850781 0.525520i \(-0.176129\pi\)
0.313938 + 0.949443i \(0.398352\pi\)
\(614\) 0 0
\(615\) −5.95336 + 10.3115i −0.240063 + 0.415801i
\(616\) 0 0
\(617\) −4.73917 + 26.8772i −0.190792 + 1.08203i 0.727493 + 0.686115i \(0.240685\pi\)
−0.918285 + 0.395919i \(0.870426\pi\)
\(618\) 0 0
\(619\) −6.61856 11.4637i −0.266022 0.460764i 0.701809 0.712365i \(-0.252376\pi\)
−0.967831 + 0.251601i \(0.919043\pi\)
\(620\) 0 0
\(621\) −5.20961 4.37138i −0.209054 0.175417i
\(622\) 0 0
\(623\) −4.85117 + 1.76568i −0.194358 + 0.0707405i
\(624\) 0 0
\(625\) −2.45290 13.9111i −0.0981159 0.556443i
\(626\) 0 0
\(627\) −0.528218 1.41868i −0.0210950 0.0566568i
\(628\) 0 0
\(629\) −13.5189 76.6694i −0.539033 3.05701i
\(630\) 0 0
\(631\) −11.5013 + 4.18615i −0.457861 + 0.166648i −0.560646 0.828056i \(-0.689447\pi\)
0.102784 + 0.994704i \(0.467225\pi\)
\(632\) 0 0
\(633\) 12.7456 + 10.6948i 0.506591 + 0.425080i
\(634\) 0 0
\(635\) −27.6536 47.8975i −1.09740 1.90075i
\(636\) 0 0
\(637\) −0.370462 + 2.10100i −0.0146783 + 0.0832445i
\(638\) 0 0
\(639\) −8.31180 + 14.3965i −0.328810 + 0.569515i
\(640\) 0 0
\(641\) −8.41370 3.06233i −0.332321 0.120955i 0.170470 0.985363i \(-0.445471\pi\)
−0.502791 + 0.864408i \(0.667694\pi\)
\(642\) 0 0
\(643\) 24.0305 20.1640i 0.947670 0.795190i −0.0312334 0.999512i \(-0.509944\pi\)
0.978904 + 0.204322i \(0.0654991\pi\)
\(644\) 0 0
\(645\) 7.78880 0.306684
\(646\) 0 0
\(647\) 5.54933 0.218166 0.109083 0.994033i \(-0.465208\pi\)
0.109083 + 0.994033i \(0.465208\pi\)
\(648\) 0 0
\(649\) −0.118555 + 0.0994798i −0.00465371 + 0.00390492i
\(650\) 0 0
\(651\) 4.31908 + 1.57202i 0.169278 + 0.0616122i
\(652\) 0 0
\(653\) −19.4552 + 33.6974i −0.761340 + 1.31868i 0.180820 + 0.983516i \(0.442125\pi\)
−0.942160 + 0.335163i \(0.891209\pi\)
\(654\) 0 0
\(655\) −1.65910 + 9.40923i −0.0648264 + 0.367649i
\(656\) 0 0
\(657\) −6.20961 10.7554i −0.242260 0.419606i
\(658\) 0 0
\(659\) 30.2708 + 25.4003i 1.17918 + 0.989454i 0.999984 + 0.00564104i \(0.00179561\pi\)
0.179201 + 0.983813i \(0.442649\pi\)
\(660\) 0 0
\(661\) 0.0859997 0.0313013i 0.00334500 0.00121748i −0.340347 0.940300i \(-0.610545\pi\)
0.343692 + 0.939082i \(0.388322\pi\)
\(662\) 0 0
\(663\) −1.99273 11.3013i −0.0773911 0.438907i
\(664\) 0 0
\(665\) −42.2203 7.12452i −1.63723 0.276277i
\(666\) 0 0
\(667\) −7.50480 42.5619i −0.290587 1.64800i
\(668\) 0 0
\(669\) −7.67752 + 2.79439i −0.296830 + 0.108037i
\(670\) 0 0
\(671\) −3.33409 2.79764i −0.128711 0.108002i
\(672\) 0 0
\(673\) 19.9281 + 34.5165i 0.768173 + 1.33052i 0.938552 + 0.345137i \(0.112167\pi\)
−0.170379 + 0.985379i \(0.554499\pi\)
\(674\) 0 0
\(675\) 1.15270 6.53731i 0.0443676 0.251621i
\(676\) 0 0
\(677\) −14.6912 + 25.4459i −0.564628 + 0.977965i 0.432456 + 0.901655i \(0.357647\pi\)
−0.997084 + 0.0763098i \(0.975686\pi\)
\(678\) 0 0
\(679\) −9.88326 3.59721i −0.379285 0.138048i
\(680\) 0 0
\(681\) −1.37939 + 1.15744i −0.0528582 + 0.0443533i
\(682\) 0 0
\(683\) 21.0933 0.807112 0.403556 0.914955i \(-0.367774\pi\)
0.403556 + 0.914955i \(0.367774\pi\)
\(684\) 0 0
\(685\) −54.7033 −2.09010
\(686\) 0 0
\(687\) −14.3550 + 12.0453i −0.547679 + 0.459557i
\(688\) 0 0
\(689\) 3.07563 + 1.11944i 0.117172 + 0.0426471i
\(690\) 0 0
\(691\) −8.08172 + 13.9979i −0.307443 + 0.532507i −0.977802 0.209530i \(-0.932807\pi\)
0.670359 + 0.742037i \(0.266140\pi\)
\(692\) 0 0
\(693\) 0.173648 0.984808i 0.00659635 0.0374098i
\(694\) 0 0
\(695\) 3.54576 + 6.14144i 0.134498 + 0.232958i
\(696\) 0 0
\(697\) −18.5646 15.5776i −0.703186 0.590043i
\(698\) 0 0
\(699\) 3.85117 1.40171i 0.145665 0.0530175i
\(700\) 0 0
\(701\) −3.48561 19.7679i −0.131650 0.746623i −0.977134 0.212623i \(-0.931799\pi\)
0.845484 0.534000i \(-0.179312\pi\)
\(702\) 0 0
\(703\) −31.6894 37.2063i −1.19519 1.40326i
\(704\) 0 0
\(705\) 3.31521 + 18.8015i 0.124858 + 0.708105i
\(706\) 0 0
\(707\) 26.8050 9.75622i 1.00811 0.366920i
\(708\) 0 0
\(709\) −29.7998 25.0050i −1.11915 0.939082i −0.120593 0.992702i \(-0.538480\pi\)
−0.998561 + 0.0536201i \(0.982924\pi\)
\(710\) 0 0
\(711\) −5.46198 9.46043i −0.204840 0.354794i
\(712\) 0 0
\(713\) 1.88507 10.6907i 0.0705963 0.400372i
\(714\) 0 0
\(715\) −0.979055 + 1.69577i −0.0366146 + 0.0634183i
\(716\) 0 0
\(717\) −26.5253 9.65441i −0.990605 0.360551i
\(718\) 0 0
\(719\) −2.34549 + 1.96810i −0.0874718 + 0.0733976i −0.685475 0.728096i \(-0.740405\pi\)
0.598003 + 0.801494i \(0.295961\pi\)
\(720\) 0 0
\(721\) −22.5895 −0.841275
\(722\) 0 0
\(723\) 6.56212 0.244048
\(724\) 0 0
\(725\) 32.3161 27.1165i 1.20019 1.00708i
\(726\) 0 0
\(727\) −16.4226 5.97734i −0.609081 0.221687i 0.0190200 0.999819i \(-0.493945\pi\)
−0.628101 + 0.778132i \(0.716168\pi\)
\(728\) 0 0
\(729\) −0.500000 + 0.866025i −0.0185185 + 0.0320750i
\(730\) 0 0
\(731\) −2.75284 + 15.6121i −0.101817 + 0.577436i
\(732\) 0 0
\(733\) 20.7087 + 35.8686i 0.764894 + 1.32484i 0.940302 + 0.340340i \(0.110542\pi\)
−0.175408 + 0.984496i \(0.556124\pi\)
\(734\) 0 0
\(735\) −3.37346 2.83067i −0.124432 0.104411i
\(736\) 0 0
\(737\) −0.352044 + 0.128134i −0.0129677 + 0.00471986i
\(738\) 0 0
\(739\) −4.59358 26.0515i −0.168978 0.958319i −0.944868 0.327451i \(-0.893810\pi\)
0.775890 0.630868i \(-0.217301\pi\)
\(740\) 0 0
\(741\) −4.67112 5.48432i −0.171598 0.201472i
\(742\) 0 0
\(743\) 2.61793 + 14.8470i 0.0960424 + 0.544684i 0.994423 + 0.105466i \(0.0336333\pi\)
−0.898381 + 0.439218i \(0.855256\pi\)
\(744\) 0 0
\(745\) −5.34477 + 1.94534i −0.195817 + 0.0712716i
\(746\) 0 0
\(747\) −8.97565 7.53147i −0.328402 0.275562i
\(748\) 0 0
\(749\) −0.0393628 0.0681784i −0.00143829 0.00249119i
\(750\) 0 0
\(751\) 0.921274 5.22481i 0.0336178 0.190656i −0.963374 0.268161i \(-0.913584\pi\)
0.996992 + 0.0775048i \(0.0246953\pi\)
\(752\) 0 0
\(753\) 4.44697 7.70237i 0.162056 0.280690i
\(754\) 0 0
\(755\) −64.2825 23.3969i −2.33948 0.851500i
\(756\) 0 0
\(757\) 6.23442 5.23130i 0.226594 0.190135i −0.522422 0.852687i \(-0.674971\pi\)
0.749016 + 0.662552i \(0.230527\pi\)
\(758\) 0 0
\(759\) −2.36184 −0.0857295
\(760\) 0 0
\(761\) −46.2113 −1.67516 −0.837579 0.546316i \(-0.816030\pi\)
−0.837579 + 0.546316i \(0.816030\pi\)
\(762\) 0 0
\(763\) −23.7631 + 19.9396i −0.860282 + 0.721863i
\(764\) 0 0
\(765\) 22.2592 + 8.10170i 0.804784 + 0.292918i
\(766\) 0 0
\(767\) −0.368241 + 0.637812i −0.0132964 + 0.0230301i
\(768\) 0 0
\(769\) −4.66132 + 26.4357i −0.168092 + 0.953295i 0.777728 + 0.628601i \(0.216372\pi\)
−0.945819 + 0.324693i \(0.894739\pi\)
\(770\) 0 0
\(771\) 6.73308 + 11.6620i 0.242486 + 0.419998i
\(772\) 0 0
\(773\) −16.1065 13.5150i −0.579312 0.486100i 0.305409 0.952221i \(-0.401207\pi\)
−0.884721 + 0.466121i \(0.845651\pi\)
\(774\) 0 0
\(775\) 9.95723 3.62414i 0.357674 0.130183i
\(776\) 0 0
\(777\) −5.60607 31.7936i −0.201117 1.14059i
\(778\) 0 0
\(779\) −15.0013 2.53142i −0.537479 0.0906974i
\(780\) 0 0
\(781\) 1.00253 + 5.68561i 0.0358732 + 0.203447i
\(782\) 0 0
\(783\) −5.97178 + 2.17355i −0.213414 + 0.0776764i
\(784\) 0 0
\(785\) 10.7103 + 8.98703i 0.382268 + 0.320761i
\(786\) 0 0
\(787\) 22.7656 + 39.4312i 0.811507 + 1.40557i 0.911809 + 0.410615i \(0.134686\pi\)
−0.100302 + 0.994957i \(0.531981\pi\)
\(788\) 0 0
\(789\) 2.90895 16.4975i 0.103561 0.587325i
\(790\) 0 0
\(791\) 16.7875 29.0767i 0.596893 1.03385i
\(792\) 0 0
\(793\) −19.4628 7.08386i −0.691143 0.251555i