Properties

Label 684.3.s.a.445.11
Level $684$
Weight $3$
Character 684.445
Analytic conductor $18.638$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 684.s (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.6376500822\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(40\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 445.11
Character \(\chi\) \(=\) 684.445
Dual form 684.3.s.a.601.11

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.18497 - 2.05570i) q^{3} +(3.46044 + 5.99365i) q^{5} +(-3.78976 - 6.56406i) q^{7} +(0.548164 + 8.98329i) q^{9} +O(q^{10})\) \(q+(-2.18497 - 2.05570i) q^{3} +(3.46044 + 5.99365i) q^{5} +(-3.78976 - 6.56406i) q^{7} +(0.548164 + 8.98329i) q^{9} +(1.11214 + 1.92629i) q^{11} -11.6560i q^{13} +(4.76023 - 20.2096i) q^{15} +(-11.1844 + 19.3719i) q^{17} +(-18.9863 + 0.721079i) q^{19} +(-5.21326 + 22.1329i) q^{21} +33.5116 q^{23} +(-11.4492 + 19.8307i) q^{25} +(17.2693 - 20.7551i) q^{27} +(-11.2228 - 6.47950i) q^{29} +(-37.6445 - 21.7341i) q^{31} +(1.52988 - 6.49511i) q^{33} +(26.2285 - 45.4290i) q^{35} -65.7083i q^{37} +(-23.9612 + 25.4679i) q^{39} +(-55.5146 + 32.0514i) q^{41} -4.06038 q^{43} +(-51.9458 + 34.3716i) q^{45} +(7.65503 - 13.2589i) q^{47} +(-4.22462 + 7.31726i) q^{49} +(64.2603 - 19.3352i) q^{51} +(-72.0176 + 41.5794i) q^{53} +(-7.69699 + 13.3316i) q^{55} +(42.9668 + 37.4547i) q^{57} +(-83.7382 + 48.3463i) q^{59} +(-45.6758 + 79.1128i) q^{61} +(56.8895 - 37.6427i) q^{63} +(69.8618 - 40.3347i) q^{65} +37.2589i q^{67} +(-73.2217 - 68.8899i) q^{69} +(-69.8995 - 40.3565i) q^{71} +(-43.7295 + 75.7417i) q^{73} +(65.7822 - 19.7931i) q^{75} +(8.42951 - 14.6003i) q^{77} -96.2184i q^{79} +(-80.3990 + 9.84863i) q^{81} +(24.8505 + 43.0423i) q^{83} -154.811 q^{85} +(11.2016 + 37.2283i) q^{87} +(18.8082 - 10.8589i) q^{89} +(-76.5105 + 44.1733i) q^{91} +(37.5732 + 124.874i) q^{93} +(-70.0228 - 111.302i) q^{95} +154.384i q^{97} +(-16.6948 + 11.0466i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - q^{7} + 4 q^{9} + O(q^{10}) \) \( 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(343\) \(533\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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 0
\(3\) −2.18497 2.05570i −0.728322 0.685235i
\(4\) 0 0
\(5\) 3.46044 + 5.99365i 0.692087 + 1.19873i 0.971153 + 0.238458i \(0.0766420\pi\)
−0.279065 + 0.960272i \(0.590025\pi\)
\(6\) 0 0
\(7\) −3.78976 6.56406i −0.541395 0.937723i −0.998824 0.0484775i \(-0.984563\pi\)
0.457429 0.889246i \(-0.348770\pi\)
\(8\) 0 0
\(9\) 0.548164 + 8.98329i 0.0609071 + 0.998143i
\(10\) 0 0
\(11\) 1.11214 + 1.92629i 0.101104 + 0.175117i 0.912140 0.409879i \(-0.134429\pi\)
−0.811036 + 0.584996i \(0.801096\pi\)
\(12\) 0 0
\(13\) 11.6560i 0.896612i −0.893880 0.448306i \(-0.852027\pi\)
0.893880 0.448306i \(-0.147973\pi\)
\(14\) 0 0
\(15\) 4.76023 20.2096i 0.317349 1.34730i
\(16\) 0 0
\(17\) −11.1844 + 19.3719i −0.657904 + 1.13952i 0.323253 + 0.946312i \(0.395223\pi\)
−0.981157 + 0.193210i \(0.938110\pi\)
\(18\) 0 0
\(19\) −18.9863 + 0.721079i −0.999280 + 0.0379515i
\(20\) 0 0
\(21\) −5.21326 + 22.1329i −0.248251 + 1.05395i
\(22\) 0 0
\(23\) 33.5116 1.45703 0.728513 0.685032i \(-0.240212\pi\)
0.728513 + 0.685032i \(0.240212\pi\)
\(24\) 0 0
\(25\) −11.4492 + 19.8307i −0.457970 + 0.793227i
\(26\) 0 0
\(27\) 17.2693 20.7551i 0.639602 0.768706i
\(28\) 0 0
\(29\) −11.2228 6.47950i −0.386994 0.223431i 0.293863 0.955848i \(-0.405059\pi\)
−0.680857 + 0.732417i \(0.738392\pi\)
\(30\) 0 0
\(31\) −37.6445 21.7341i −1.21434 0.701099i −0.250637 0.968081i \(-0.580640\pi\)
−0.963701 + 0.266983i \(0.913973\pi\)
\(32\) 0 0
\(33\) 1.52988 6.49511i 0.0463600 0.196821i
\(34\) 0 0
\(35\) 26.2285 45.4290i 0.749385 1.29797i
\(36\) 0 0
\(37\) 65.7083i 1.77590i −0.459940 0.887950i \(-0.652129\pi\)
0.459940 0.887950i \(-0.347871\pi\)
\(38\) 0 0
\(39\) −23.9612 + 25.4679i −0.614390 + 0.653023i
\(40\) 0 0
\(41\) −55.5146 + 32.0514i −1.35401 + 0.781741i −0.988809 0.149186i \(-0.952335\pi\)
−0.365206 + 0.930927i \(0.619001\pi\)
\(42\) 0 0
\(43\) −4.06038 −0.0944275 −0.0472138 0.998885i \(-0.515034\pi\)
−0.0472138 + 0.998885i \(0.515034\pi\)
\(44\) 0 0
\(45\) −51.9458 + 34.3716i −1.15435 + 0.763814i
\(46\) 0 0
\(47\) 7.65503 13.2589i 0.162873 0.282104i −0.773025 0.634376i \(-0.781257\pi\)
0.935898 + 0.352271i \(0.114591\pi\)
\(48\) 0 0
\(49\) −4.22462 + 7.31726i −0.0862168 + 0.149332i
\(50\) 0 0
\(51\) 64.2603 19.3352i 1.26001 0.379122i
\(52\) 0 0
\(53\) −72.0176 + 41.5794i −1.35882 + 0.784517i −0.989465 0.144771i \(-0.953756\pi\)
−0.369358 + 0.929287i \(0.620422\pi\)
\(54\) 0 0
\(55\) −7.69699 + 13.3316i −0.139945 + 0.242392i
\(56\) 0 0
\(57\) 42.9668 + 37.4547i 0.753803 + 0.657100i
\(58\) 0 0
\(59\) −83.7382 + 48.3463i −1.41929 + 0.819428i −0.996237 0.0866761i \(-0.972375\pi\)
−0.423055 + 0.906104i \(0.639042\pi\)
\(60\) 0 0
\(61\) −45.6758 + 79.1128i −0.748783 + 1.29693i 0.199623 + 0.979873i \(0.436028\pi\)
−0.948406 + 0.317058i \(0.897305\pi\)
\(62\) 0 0
\(63\) 56.8895 37.6427i 0.903008 0.597504i
\(64\) 0 0
\(65\) 69.8618 40.3347i 1.07480 0.620534i
\(66\) 0 0
\(67\) 37.2589i 0.556103i 0.960566 + 0.278052i \(0.0896887\pi\)
−0.960566 + 0.278052i \(0.910311\pi\)
\(68\) 0 0
\(69\) −73.2217 68.8899i −1.06118 0.998405i
\(70\) 0 0
\(71\) −69.8995 40.3565i −0.984500 0.568401i −0.0808744 0.996724i \(-0.525771\pi\)
−0.903626 + 0.428323i \(0.859105\pi\)
\(72\) 0 0
\(73\) −43.7295 + 75.7417i −0.599034 + 1.03756i 0.393930 + 0.919140i \(0.371115\pi\)
−0.992964 + 0.118417i \(0.962218\pi\)
\(74\) 0 0
\(75\) 65.7822 19.7931i 0.877096 0.263908i
\(76\) 0 0
\(77\) 8.42951 14.6003i 0.109474 0.189615i
\(78\) 0 0
\(79\) 96.2184i 1.21795i −0.793188 0.608977i \(-0.791580\pi\)
0.793188 0.608977i \(-0.208420\pi\)
\(80\) 0 0
\(81\) −80.3990 + 9.84863i −0.992581 + 0.121588i
\(82\) 0 0
\(83\) 24.8505 + 43.0423i 0.299404 + 0.518582i 0.976000 0.217772i \(-0.0698790\pi\)
−0.676596 + 0.736354i \(0.736546\pi\)
\(84\) 0 0
\(85\) −154.811 −1.82131
\(86\) 0 0
\(87\) 11.2016 + 37.2283i 0.128754 + 0.427911i
\(88\) 0 0
\(89\) 18.8082 10.8589i 0.211328 0.122011i −0.390600 0.920560i \(-0.627732\pi\)
0.601929 + 0.798550i \(0.294399\pi\)
\(90\) 0 0
\(91\) −76.5105 + 44.1733i −0.840774 + 0.485421i
\(92\) 0 0
\(93\) 37.5732 + 124.874i 0.404013 + 1.34273i
\(94\) 0 0
\(95\) −70.0228 111.302i −0.737082 1.17160i
\(96\) 0 0
\(97\) 154.384i 1.59158i 0.605570 + 0.795792i \(0.292945\pi\)
−0.605570 + 0.795792i \(0.707055\pi\)
\(98\) 0 0
\(99\) −16.6948 + 11.0466i −0.168634 + 0.111582i
\(100\) 0 0
\(101\) 41.8141 72.4242i 0.414001 0.717071i −0.581322 0.813674i \(-0.697464\pi\)
0.995323 + 0.0966026i \(0.0307976\pi\)
\(102\) 0 0
\(103\) −118.486 68.4077i −1.15035 0.664153i −0.201375 0.979514i \(-0.564541\pi\)
−0.948972 + 0.315362i \(0.897874\pi\)
\(104\) 0 0
\(105\) −150.697 + 45.3430i −1.43521 + 0.431838i
\(106\) 0 0
\(107\) 37.1337i 0.347044i −0.984830 0.173522i \(-0.944485\pi\)
0.984830 0.173522i \(-0.0555148\pi\)
\(108\) 0 0
\(109\) 63.7561 + 36.8096i 0.584918 + 0.337703i 0.763085 0.646298i \(-0.223684\pi\)
−0.178167 + 0.984000i \(0.557017\pi\)
\(110\) 0 0
\(111\) −135.077 + 143.570i −1.21691 + 1.29343i
\(112\) 0 0
\(113\) −140.095 80.8841i −1.23978 0.715788i −0.270732 0.962655i \(-0.587266\pi\)
−0.969050 + 0.246866i \(0.920599\pi\)
\(114\) 0 0
\(115\) 115.965 + 200.857i 1.00839 + 1.74658i
\(116\) 0 0
\(117\) 104.709 6.38938i 0.894948 0.0546101i
\(118\) 0 0
\(119\) 169.544 1.42474
\(120\) 0 0
\(121\) 58.0263 100.504i 0.479556 0.830615i
\(122\) 0 0
\(123\) 187.186 + 44.0904i 1.52184 + 0.358458i
\(124\) 0 0
\(125\) 14.5443 0.116355
\(126\) 0 0
\(127\) −116.814 + 67.4425i −0.919794 + 0.531043i −0.883569 0.468300i \(-0.844867\pi\)
−0.0362248 + 0.999344i \(0.511533\pi\)
\(128\) 0 0
\(129\) 8.87181 + 8.34695i 0.0687737 + 0.0647050i
\(130\) 0 0
\(131\) 25.5748 + 44.2969i 0.195228 + 0.338144i 0.946975 0.321307i \(-0.104122\pi\)
−0.751748 + 0.659451i \(0.770789\pi\)
\(132\) 0 0
\(133\) 76.6869 + 121.895i 0.576593 + 0.916501i
\(134\) 0 0
\(135\) 184.158 + 31.6844i 1.36413 + 0.234699i
\(136\) 0 0
\(137\) 68.9943 119.502i 0.503608 0.872275i −0.496383 0.868104i \(-0.665339\pi\)
0.999991 0.00417145i \(-0.00132782\pi\)
\(138\) 0 0
\(139\) 68.8165 0.495083 0.247541 0.968877i \(-0.420377\pi\)
0.247541 + 0.968877i \(0.420377\pi\)
\(140\) 0 0
\(141\) −43.9823 + 13.2338i −0.311932 + 0.0938566i
\(142\) 0 0
\(143\) 22.4527 12.9631i 0.157012 0.0906510i
\(144\) 0 0
\(145\) 89.6876i 0.618535i
\(146\) 0 0
\(147\) 24.2728 7.30340i 0.165121 0.0496830i
\(148\) 0 0
\(149\) −105.104 182.045i −0.705395 1.22178i −0.966549 0.256482i \(-0.917436\pi\)
0.261154 0.965297i \(-0.415897\pi\)
\(150\) 0 0
\(151\) 94.5876 54.6102i 0.626408 0.361657i −0.152952 0.988234i \(-0.548878\pi\)
0.779360 + 0.626577i \(0.215545\pi\)
\(152\) 0 0
\(153\) −180.154 89.8534i −1.17748 0.587277i
\(154\) 0 0
\(155\) 300.837i 1.94089i
\(156\) 0 0
\(157\) −77.4998 134.234i −0.493629 0.854991i 0.506344 0.862332i \(-0.330997\pi\)
−0.999973 + 0.00734074i \(0.997663\pi\)
\(158\) 0 0
\(159\) 242.831 + 57.1973i 1.52724 + 0.359731i
\(160\) 0 0
\(161\) −127.001 219.972i −0.788826 1.36629i
\(162\) 0 0
\(163\) −185.560 −1.13841 −0.569204 0.822196i \(-0.692748\pi\)
−0.569204 + 0.822196i \(0.692748\pi\)
\(164\) 0 0
\(165\) 44.2235 13.3063i 0.268021 0.0806445i
\(166\) 0 0
\(167\) 77.8292i 0.466043i −0.972472 0.233021i \(-0.925139\pi\)
0.972472 0.233021i \(-0.0748612\pi\)
\(168\) 0 0
\(169\) 33.1385 0.196086
\(170\) 0 0
\(171\) −16.8853 170.164i −0.0987443 0.995113i
\(172\) 0 0
\(173\) 139.414i 0.805864i 0.915230 + 0.402932i \(0.132009\pi\)
−0.915230 + 0.402932i \(0.867991\pi\)
\(174\) 0 0
\(175\) 173.560 0.991770
\(176\) 0 0
\(177\) 282.351 + 66.5059i 1.59520 + 0.375740i
\(178\) 0 0
\(179\) 79.8752i 0.446230i 0.974792 + 0.223115i \(0.0716225\pi\)
−0.974792 + 0.223115i \(0.928377\pi\)
\(180\) 0 0
\(181\) 277.769 160.370i 1.53464 0.886022i 0.535496 0.844537i \(-0.320125\pi\)
0.999139 0.0414848i \(-0.0132088\pi\)
\(182\) 0 0
\(183\) 262.433 78.9629i 1.43406 0.431492i
\(184\) 0 0
\(185\) 393.833 227.379i 2.12882 1.22908i
\(186\) 0 0
\(187\) −49.7544 −0.266066
\(188\) 0 0
\(189\) −201.684 34.6998i −1.06711 0.183597i
\(190\) 0 0
\(191\) 11.9414 + 20.6831i 0.0625204 + 0.108289i 0.895591 0.444878i \(-0.146753\pi\)
−0.833071 + 0.553166i \(0.813419\pi\)
\(192\) 0 0
\(193\) 40.9187 23.6244i 0.212014 0.122406i −0.390233 0.920716i \(-0.627606\pi\)
0.602247 + 0.798310i \(0.294272\pi\)
\(194\) 0 0
\(195\) −235.562 55.4851i −1.20801 0.284539i
\(196\) 0 0
\(197\) 323.931 1.64432 0.822160 0.569256i \(-0.192769\pi\)
0.822160 + 0.569256i \(0.192769\pi\)
\(198\) 0 0
\(199\) −22.5516 39.0605i −0.113324 0.196284i 0.803784 0.594921i \(-0.202817\pi\)
−0.917109 + 0.398637i \(0.869483\pi\)
\(200\) 0 0
\(201\) 76.5933 81.4095i 0.381061 0.405023i
\(202\) 0 0
\(203\) 98.2231i 0.483858i
\(204\) 0 0
\(205\) −384.210 221.824i −1.87419 1.08207i
\(206\) 0 0
\(207\) 18.3698 + 301.044i 0.0887432 + 1.45432i
\(208\) 0 0
\(209\) −22.5045 35.7711i −0.107677 0.171154i
\(210\) 0 0
\(211\) −32.8915 + 18.9899i −0.155884 + 0.0899996i −0.575913 0.817511i \(-0.695353\pi\)
0.420029 + 0.907511i \(0.362020\pi\)
\(212\) 0 0
\(213\) 69.7671 + 231.870i 0.327545 + 1.08859i
\(214\) 0 0
\(215\) −14.0507 24.3365i −0.0653521 0.113193i
\(216\) 0 0
\(217\) 329.468i 1.51828i
\(218\) 0 0
\(219\) 251.250 75.5982i 1.14726 0.345197i
\(220\) 0 0
\(221\) 225.798 + 130.365i 1.02171 + 0.589885i
\(222\) 0 0
\(223\) 129.266i 0.579666i 0.957077 + 0.289833i \(0.0935998\pi\)
−0.957077 + 0.289833i \(0.906400\pi\)
\(224\) 0 0
\(225\) −184.421 91.9814i −0.819648 0.408806i
\(226\) 0 0
\(227\) 262.063 151.302i 1.15446 0.666529i 0.204491 0.978868i \(-0.434446\pi\)
0.949971 + 0.312340i \(0.101113\pi\)
\(228\) 0 0
\(229\) −86.1574 + 149.229i −0.376233 + 0.651655i −0.990511 0.137435i \(-0.956114\pi\)
0.614278 + 0.789090i \(0.289447\pi\)
\(230\) 0 0
\(231\) −48.4322 + 14.5727i −0.209663 + 0.0630852i
\(232\) 0 0
\(233\) −222.274 + 384.990i −0.953965 + 1.65232i −0.217246 + 0.976117i \(0.569707\pi\)
−0.736719 + 0.676199i \(0.763626\pi\)
\(234\) 0 0
\(235\) 105.959 0.450889
\(236\) 0 0
\(237\) −197.797 + 210.234i −0.834585 + 0.887064i
\(238\) 0 0
\(239\) −131.653 + 228.030i −0.550850 + 0.954100i 0.447364 + 0.894352i \(0.352363\pi\)
−0.998214 + 0.0597478i \(0.980970\pi\)
\(240\) 0 0
\(241\) 10.4042 + 6.00684i 0.0431707 + 0.0249246i 0.521430 0.853294i \(-0.325399\pi\)
−0.478259 + 0.878219i \(0.658732\pi\)
\(242\) 0 0
\(243\) 195.915 + 143.758i 0.806235 + 0.591595i
\(244\) 0 0
\(245\) −58.4761 −0.238678
\(246\) 0 0
\(247\) 8.40487 + 221.304i 0.0340278 + 0.895967i
\(248\) 0 0
\(249\) 34.1848 145.131i 0.137288 0.582857i
\(250\) 0 0
\(251\) −101.728 176.197i −0.405289 0.701981i 0.589066 0.808085i \(-0.299496\pi\)
−0.994355 + 0.106104i \(0.966162\pi\)
\(252\) 0 0
\(253\) 37.2697 + 64.5529i 0.147311 + 0.255150i
\(254\) 0 0
\(255\) 338.257 + 318.246i 1.32650 + 1.24802i
\(256\) 0 0
\(257\) 152.109i 0.591863i 0.955209 + 0.295932i \(0.0956301\pi\)
−0.955209 + 0.295932i \(0.904370\pi\)
\(258\) 0 0
\(259\) −431.313 + 249.019i −1.66530 + 0.961463i
\(260\) 0 0
\(261\) 52.0553 104.370i 0.199446 0.399884i
\(262\) 0 0
\(263\) 96.2390 0.365928 0.182964 0.983120i \(-0.441431\pi\)
0.182964 + 0.983120i \(0.441431\pi\)
\(264\) 0 0
\(265\) −498.425 287.766i −1.88085 1.08591i
\(266\) 0 0
\(267\) −63.4181 14.9377i −0.237521 0.0559466i
\(268\) 0 0
\(269\) −209.351 120.869i −0.778255 0.449326i 0.0575566 0.998342i \(-0.481669\pi\)
−0.835811 + 0.549017i \(0.815002\pi\)
\(270\) 0 0
\(271\) 87.1064 150.873i 0.321426 0.556726i −0.659357 0.751830i \(-0.729171\pi\)
0.980783 + 0.195104i \(0.0625045\pi\)
\(272\) 0 0
\(273\) 257.980 + 60.7656i 0.944982 + 0.222585i
\(274\) 0 0
\(275\) −50.9327 −0.185210
\(276\) 0 0
\(277\) 190.066 + 329.203i 0.686157 + 1.18846i 0.973072 + 0.230503i \(0.0740371\pi\)
−0.286914 + 0.957956i \(0.592630\pi\)
\(278\) 0 0
\(279\) 174.608 350.085i 0.625835 1.25479i
\(280\) 0 0
\(281\) 113.389 + 65.4652i 0.403520 + 0.232972i 0.688002 0.725709i \(-0.258488\pi\)
−0.284482 + 0.958681i \(0.591822\pi\)
\(282\) 0 0
\(283\) −53.3848 92.4652i −0.188639 0.326732i 0.756158 0.654389i \(-0.227074\pi\)
−0.944797 + 0.327657i \(0.893741\pi\)
\(284\) 0 0
\(285\) −75.8066 + 387.138i −0.265988 + 1.35838i
\(286\) 0 0
\(287\) 420.775 + 242.934i 1.46611 + 0.846461i
\(288\) 0 0
\(289\) −105.680 183.043i −0.365675 0.633368i
\(290\) 0 0
\(291\) 317.367 337.323i 1.09061 1.15919i
\(292\) 0 0
\(293\) 80.0984 + 46.2449i 0.273374 + 0.157832i 0.630420 0.776254i \(-0.282883\pi\)
−0.357046 + 0.934087i \(0.616216\pi\)
\(294\) 0 0
\(295\) −579.541 334.598i −1.96455 1.13423i
\(296\) 0 0
\(297\) 59.1861 + 10.1830i 0.199280 + 0.0342861i
\(298\) 0 0
\(299\) 390.610i 1.30639i
\(300\) 0 0
\(301\) 15.3879 + 26.6526i 0.0511226 + 0.0885469i
\(302\) 0 0
\(303\) −240.245 + 72.2870i −0.792888 + 0.238571i
\(304\) 0 0
\(305\) −632.233 −2.07289
\(306\) 0 0
\(307\) 336.092 + 194.043i 1.09476 + 0.632062i 0.934841 0.355067i \(-0.115542\pi\)
0.159923 + 0.987130i \(0.448875\pi\)
\(308\) 0 0
\(309\) 118.261 + 393.040i 0.382722 + 1.27197i
\(310\) 0 0
\(311\) 3.84097 6.65275i 0.0123504 0.0213915i −0.859784 0.510658i \(-0.829402\pi\)
0.872135 + 0.489266i \(0.162735\pi\)
\(312\) 0 0
\(313\) 174.620 302.450i 0.557891 0.966295i −0.439782 0.898105i \(-0.644944\pi\)
0.997672 0.0681904i \(-0.0217225\pi\)
\(314\) 0 0
\(315\) 422.480 + 210.715i 1.34121 + 0.668938i
\(316\) 0 0
\(317\) 47.7851 + 27.5888i 0.150742 + 0.0870308i 0.573474 0.819224i \(-0.305595\pi\)
−0.422732 + 0.906255i \(0.638929\pi\)
\(318\) 0 0
\(319\) 28.8245i 0.0903589i
\(320\) 0 0
\(321\) −76.3359 + 81.1359i −0.237807 + 0.252760i
\(322\) 0 0
\(323\) 198.381 375.866i 0.614183 1.16367i
\(324\) 0 0
\(325\) 231.145 + 133.452i 0.711217 + 0.410621i
\(326\) 0 0
\(327\) −63.6353 211.491i −0.194603 0.646763i
\(328\) 0 0
\(329\) −116.043 −0.352714
\(330\) 0 0
\(331\) 318.401 183.829i 0.961936 0.555374i 0.0651679 0.997874i \(-0.479242\pi\)
0.896768 + 0.442500i \(0.145908\pi\)
\(332\) 0 0
\(333\) 590.277 36.0189i 1.77260 0.108165i
\(334\) 0 0
\(335\) −223.317 + 128.932i −0.666618 + 0.384872i
\(336\) 0 0
\(337\) −154.839 + 89.3966i −0.459464 + 0.265272i −0.711819 0.702363i \(-0.752128\pi\)
0.252355 + 0.967635i \(0.418795\pi\)
\(338\) 0 0
\(339\) 139.830 + 464.724i 0.412478 + 1.37087i
\(340\) 0 0
\(341\) 96.6854i 0.283535i
\(342\) 0 0
\(343\) −307.356 −0.896080
\(344\) 0 0
\(345\) 159.523 677.255i 0.462385 1.96306i
\(346\) 0 0
\(347\) −146.595 253.910i −0.422464 0.731729i 0.573716 0.819054i \(-0.305501\pi\)
−0.996180 + 0.0873254i \(0.972168\pi\)
\(348\) 0 0
\(349\) −141.578 245.220i −0.405667 0.702637i 0.588731 0.808329i \(-0.299628\pi\)
−0.994399 + 0.105692i \(0.966294\pi\)
\(350\) 0 0
\(351\) −241.920 201.290i −0.689231 0.573476i
\(352\) 0 0
\(353\) −163.732 283.592i −0.463829 0.803376i 0.535319 0.844650i \(-0.320192\pi\)
−0.999148 + 0.0412744i \(0.986858\pi\)
\(354\) 0 0
\(355\) 558.604i 1.57353i
\(356\) 0 0
\(357\) −370.449 348.533i −1.03767 0.976283i
\(358\) 0 0
\(359\) −158.090 + 273.821i −0.440363 + 0.762732i −0.997716 0.0675439i \(-0.978484\pi\)
0.557353 + 0.830276i \(0.311817\pi\)
\(360\) 0 0
\(361\) 359.960 27.3813i 0.997119 0.0758484i
\(362\) 0 0
\(363\) −333.393 + 100.314i −0.918438 + 0.276347i
\(364\) 0 0
\(365\) −605.292 −1.65833
\(366\) 0 0
\(367\) −186.657 + 323.299i −0.508602 + 0.880924i 0.491349 + 0.870963i \(0.336504\pi\)
−0.999950 + 0.00996107i \(0.996829\pi\)
\(368\) 0 0
\(369\) −318.358 481.135i −0.862759 1.30389i
\(370\) 0 0
\(371\) 545.860 + 315.152i 1.47132 + 0.849467i
\(372\) 0 0
\(373\) 352.184 + 203.333i 0.944192 + 0.545130i 0.891272 0.453469i \(-0.149814\pi\)
0.0529201 + 0.998599i \(0.483147\pi\)
\(374\) 0 0
\(375\) −31.7789 29.8989i −0.0847438 0.0797303i
\(376\) 0 0
\(377\) −75.5248 + 130.813i −0.200331 + 0.346984i
\(378\) 0 0
\(379\) 468.372i 1.23581i −0.786253 0.617905i \(-0.787982\pi\)
0.786253 0.617905i \(-0.212018\pi\)
\(380\) 0 0
\(381\) 393.876 + 92.7750i 1.03380 + 0.243504i
\(382\) 0 0
\(383\) 200.495 115.756i 0.523485 0.302234i −0.214874 0.976642i \(-0.568934\pi\)
0.738359 + 0.674408i \(0.235601\pi\)
\(384\) 0 0
\(385\) 116.679 0.303063
\(386\) 0 0
\(387\) −2.22576 36.4756i −0.00575131 0.0942522i
\(388\) 0 0
\(389\) −13.6263 + 23.6015i −0.0350291 + 0.0606721i −0.883008 0.469357i \(-0.844486\pi\)
0.847979 + 0.530029i \(0.177819\pi\)
\(390\) 0 0
\(391\) −374.806 + 649.183i −0.958583 + 1.66031i
\(392\) 0 0
\(393\) 35.1811 149.361i 0.0895194 0.380055i
\(394\) 0 0
\(395\) 576.700 332.958i 1.46000 0.842931i
\(396\) 0 0
\(397\) −65.6998 + 113.795i −0.165491 + 0.286638i −0.936829 0.349787i \(-0.886254\pi\)
0.771339 + 0.636425i \(0.219587\pi\)
\(398\) 0 0
\(399\) 83.0210 423.981i 0.208073 1.06261i
\(400\) 0 0
\(401\) −16.9256 + 9.77199i −0.0422084 + 0.0243690i −0.520956 0.853584i \(-0.674424\pi\)
0.478747 + 0.877953i \(0.341091\pi\)
\(402\) 0 0
\(403\) −253.331 + 438.783i −0.628614 + 1.08879i
\(404\) 0 0
\(405\) −337.245 447.803i −0.832704 1.10569i
\(406\) 0 0
\(407\) 126.573 73.0770i 0.310990 0.179550i
\(408\) 0 0
\(409\) 676.132i 1.65313i 0.562838 + 0.826567i \(0.309709\pi\)
−0.562838 + 0.826567i \(0.690291\pi\)
\(410\) 0 0
\(411\) −396.410 + 119.275i −0.964502 + 0.290208i
\(412\) 0 0
\(413\) 634.696 + 366.442i 1.53679 + 0.887268i
\(414\) 0 0
\(415\) −171.987 + 297.890i −0.414427 + 0.717808i
\(416\) 0 0
\(417\) −150.362 141.466i −0.360580 0.339248i
\(418\) 0 0
\(419\) −13.4954 + 23.3748i −0.0322087 + 0.0557871i −0.881680 0.471847i \(-0.843587\pi\)
0.849472 + 0.527634i \(0.176921\pi\)
\(420\) 0 0
\(421\) 17.8620i 0.0424274i −0.999775 0.0212137i \(-0.993247\pi\)
0.999775 0.0212137i \(-0.00675304\pi\)
\(422\) 0 0
\(423\) 123.305 + 61.4993i 0.291501 + 0.145388i
\(424\) 0 0
\(425\) −256.105 443.587i −0.602600 1.04373i
\(426\) 0 0
\(427\) 692.402 1.62155
\(428\) 0 0
\(429\) −75.7067 17.8322i −0.176473 0.0415670i
\(430\) 0 0
\(431\) −409.592 + 236.478i −0.950330 + 0.548673i −0.893183 0.449693i \(-0.851534\pi\)
−0.0571465 + 0.998366i \(0.518200\pi\)
\(432\) 0 0
\(433\) −301.419 + 174.024i −0.696117 + 0.401903i −0.805900 0.592052i \(-0.798318\pi\)
0.109782 + 0.993956i \(0.464985\pi\)
\(434\) 0 0
\(435\) −184.371 + 195.964i −0.423842 + 0.450493i
\(436\) 0 0
\(437\) −636.262 + 24.1645i −1.45598 + 0.0552964i
\(438\) 0 0
\(439\) 223.938i 0.510109i 0.966927 + 0.255055i \(0.0820934\pi\)
−0.966927 + 0.255055i \(0.917907\pi\)
\(440\) 0 0
\(441\) −68.0488 33.9399i −0.154306 0.0769613i
\(442\) 0 0
\(443\) 12.6061 21.8343i 0.0284561 0.0492874i −0.851447 0.524441i \(-0.824274\pi\)
0.879903 + 0.475154i \(0.157608\pi\)
\(444\) 0 0
\(445\) 130.169 + 75.1533i 0.292515 + 0.168884i
\(446\) 0 0
\(447\) −144.582 + 613.825i −0.323451 + 1.37321i
\(448\) 0 0
\(449\) 364.578i 0.811977i 0.913878 + 0.405989i \(0.133073\pi\)
−0.913878 + 0.405989i \(0.866927\pi\)
\(450\) 0 0
\(451\) −123.480 71.2914i −0.273792 0.158074i
\(452\) 0 0
\(453\) −318.933 75.1227i −0.704047 0.165834i
\(454\) 0 0
\(455\) −529.519 305.718i −1.16378 0.671908i
\(456\) 0 0
\(457\) −181.131 313.729i −0.396349 0.686496i 0.596924 0.802298i \(-0.296390\pi\)
−0.993272 + 0.115802i \(0.963056\pi\)
\(458\) 0 0
\(459\) 208.919 + 566.670i 0.455161 + 1.23458i
\(460\) 0 0
\(461\) 739.769 1.60471 0.802353 0.596850i \(-0.203581\pi\)
0.802353 + 0.596850i \(0.203581\pi\)
\(462\) 0 0
\(463\) 224.968 389.656i 0.485893 0.841591i −0.513976 0.857805i \(-0.671828\pi\)
0.999869 + 0.0162140i \(0.00516130\pi\)
\(464\) 0 0
\(465\) −618.432 + 657.320i −1.32996 + 1.41359i
\(466\) 0 0
\(467\) −6.47232 −0.0138593 −0.00692967 0.999976i \(-0.502206\pi\)
−0.00692967 + 0.999976i \(0.502206\pi\)
\(468\) 0 0
\(469\) 244.570 141.203i 0.521471 0.301071i
\(470\) 0 0
\(471\) −106.610 + 452.613i −0.226348 + 0.960961i
\(472\) 0 0
\(473\) −4.51572 7.82146i −0.00954699 0.0165359i
\(474\) 0 0
\(475\) 203.079 384.767i 0.427536 0.810036i
\(476\) 0 0
\(477\) −412.997 624.163i −0.865822 1.30852i
\(478\) 0 0
\(479\) −405.295 + 701.991i −0.846126 + 1.46553i 0.0385129 + 0.999258i \(0.487738\pi\)
−0.884639 + 0.466276i \(0.845595\pi\)
\(480\) 0 0
\(481\) −765.893 −1.59229
\(482\) 0 0
\(483\) −174.705 + 741.709i −0.361707 + 1.53563i
\(484\) 0 0
\(485\) −925.322 + 534.235i −1.90788 + 1.10152i
\(486\) 0 0
\(487\) 877.229i 1.80129i −0.434553 0.900646i \(-0.643094\pi\)
0.434553 0.900646i \(-0.356906\pi\)
\(488\) 0 0
\(489\) 405.443 + 381.457i 0.829128 + 0.780076i
\(490\) 0 0
\(491\) −442.507 766.445i −0.901237 1.56099i −0.825890 0.563831i \(-0.809327\pi\)
−0.0753463 0.997157i \(-0.524006\pi\)
\(492\) 0 0
\(493\) 251.040 144.938i 0.509210 0.293992i
\(494\) 0 0
\(495\) −123.981 61.8364i −0.250466 0.124922i
\(496\) 0 0
\(497\) 611.766i 1.23092i
\(498\) 0 0
\(499\) 319.587 + 553.540i 0.640454 + 1.10930i 0.985331 + 0.170651i \(0.0545872\pi\)
−0.344877 + 0.938648i \(0.612079\pi\)
\(500\) 0 0
\(501\) −159.994 + 170.054i −0.319349 + 0.339429i
\(502\) 0 0
\(503\) −24.2858 42.0642i −0.0482818 0.0836266i 0.840874 0.541230i \(-0.182041\pi\)
−0.889156 + 0.457604i \(0.848708\pi\)
\(504\) 0 0
\(505\) 578.781 1.14610
\(506\) 0 0
\(507\) −72.4066 68.1230i −0.142814 0.134365i
\(508\) 0 0
\(509\) 292.865i 0.575373i −0.957725 0.287687i \(-0.907114\pi\)
0.957725 0.287687i \(-0.0928861\pi\)
\(510\) 0 0
\(511\) 662.897 1.29726
\(512\) 0 0
\(513\) −312.914 + 406.515i −0.609968 + 0.792426i
\(514\) 0 0
\(515\) 946.882i 1.83861i
\(516\) 0 0
\(517\) 34.0539 0.0658683
\(518\) 0 0
\(519\) 286.595 304.616i 0.552206 0.586928i
\(520\) 0 0
\(521\) 228.496i 0.438572i −0.975661 0.219286i \(-0.929627\pi\)
0.975661 0.219286i \(-0.0703728\pi\)
\(522\) 0 0
\(523\) −353.160 + 203.897i −0.675258 + 0.389860i −0.798066 0.602570i \(-0.794143\pi\)
0.122808 + 0.992430i \(0.460810\pi\)
\(524\) 0 0
\(525\) −379.222 356.787i −0.722328 0.679595i
\(526\) 0 0
\(527\) 842.059 486.163i 1.59784 0.922511i
\(528\) 0 0
\(529\) 594.027 1.12292
\(530\) 0 0
\(531\) −480.211 725.743i −0.904352 1.36675i
\(532\) 0 0
\(533\) 373.590 + 647.076i 0.700919 + 1.21403i
\(534\) 0 0
\(535\) 222.566 128.499i 0.416012 0.240185i
\(536\) 0 0
\(537\) 164.200 174.525i 0.305772 0.324999i
\(538\) 0 0
\(539\) −18.7935 −0.0348674
\(540\) 0 0
\(541\) −485.750 841.344i −0.897875 1.55516i −0.830206 0.557457i \(-0.811777\pi\)
−0.0676689 0.997708i \(-0.521556\pi\)
\(542\) 0 0
\(543\) −936.590 220.608i −1.72484 0.406276i
\(544\) 0 0
\(545\) 509.509i 0.934879i
\(546\) 0 0
\(547\) 138.605 + 80.0238i 0.253392 + 0.146296i 0.621316 0.783560i \(-0.286598\pi\)
−0.367925 + 0.929856i \(0.619932\pi\)
\(548\) 0 0
\(549\) −735.731 366.952i −1.34013 0.668401i
\(550\) 0 0
\(551\) 217.752 + 114.929i 0.395195 + 0.208583i
\(552\) 0 0
\(553\) −631.584 + 364.645i −1.14210 + 0.659394i
\(554\) 0 0
\(555\) −1327.94 312.787i −2.39268 0.563580i
\(556\) 0 0
\(557\) 389.437 + 674.525i 0.699169 + 1.21100i 0.968755 + 0.248020i \(0.0797799\pi\)
−0.269586 + 0.962976i \(0.586887\pi\)
\(558\) 0 0
\(559\) 47.3277i 0.0846649i
\(560\) 0 0
\(561\) 108.712 + 102.280i 0.193782 + 0.182318i
\(562\) 0 0
\(563\) −127.949 73.8716i −0.227263 0.131211i 0.382046 0.924143i \(-0.375220\pi\)
−0.609309 + 0.792933i \(0.708553\pi\)
\(564\) 0 0
\(565\) 1119.58i 1.98155i
\(566\) 0 0
\(567\) 369.340 + 490.420i 0.651394 + 0.864939i
\(568\) 0 0
\(569\) −312.172 + 180.232i −0.548632 + 0.316753i −0.748570 0.663056i \(-0.769259\pi\)
0.199938 + 0.979809i \(0.435926\pi\)
\(570\) 0 0
\(571\) 80.4968 139.425i 0.140975 0.244176i −0.786889 0.617095i \(-0.788310\pi\)
0.927864 + 0.372919i \(0.121643\pi\)
\(572\) 0 0
\(573\) 16.4268 69.7399i 0.0286680 0.121710i
\(574\) 0 0
\(575\) −383.682 + 664.557i −0.667274 + 1.15575i
\(576\) 0 0
\(577\) −622.152 −1.07825 −0.539126 0.842225i \(-0.681245\pi\)
−0.539126 + 0.842225i \(0.681245\pi\)
\(578\) 0 0
\(579\) −137.971 32.4981i −0.238291 0.0561280i
\(580\) 0 0
\(581\) 188.355 326.241i 0.324191 0.561516i
\(582\) 0 0
\(583\) −160.188 92.4844i −0.274764 0.158635i
\(584\) 0 0
\(585\) 400.634 + 605.479i 0.684845 + 1.03501i
\(586\) 0 0
\(587\) 649.470 1.10642 0.553211 0.833041i \(-0.313402\pi\)
0.553211 + 0.833041i \(0.313402\pi\)
\(588\) 0 0
\(589\) 730.402 + 385.505i 1.24007 + 0.654507i
\(590\) 0 0
\(591\) −707.779 665.906i −1.19760 1.12675i
\(592\) 0 0
\(593\) 249.951 + 432.928i 0.421503 + 0.730065i 0.996087 0.0883811i \(-0.0281693\pi\)
−0.574584 + 0.818446i \(0.694836\pi\)
\(594\) 0 0
\(595\) 586.698 + 1016.19i 0.986046 + 1.70788i
\(596\) 0 0
\(597\) −31.0223 + 131.705i −0.0519636 + 0.220612i
\(598\) 0 0
\(599\) 285.505i 0.476635i 0.971187 + 0.238318i \(0.0765959\pi\)
−0.971187 + 0.238318i \(0.923404\pi\)
\(600\) 0 0
\(601\) 429.579 248.017i 0.714773 0.412675i −0.0980525 0.995181i \(-0.531261\pi\)
0.812826 + 0.582507i \(0.197928\pi\)
\(602\) 0 0
\(603\) −334.708 + 20.4240i −0.555071 + 0.0338706i
\(604\) 0 0
\(605\) 803.185 1.32758
\(606\) 0 0
\(607\) −751.147 433.675i −1.23747 0.714456i −0.268897 0.963169i \(-0.586659\pi\)
−0.968577 + 0.248713i \(0.919992\pi\)
\(608\) 0 0
\(609\) 201.918 214.614i 0.331556 0.352404i
\(610\) 0 0
\(611\) −154.545 89.2267i −0.252938 0.146034i
\(612\) 0 0
\(613\) 329.632 570.939i 0.537736 0.931386i −0.461290 0.887249i \(-0.652613\pi\)
0.999026 0.0441360i \(-0.0140535\pi\)
\(614\) 0 0
\(615\) 383.482 + 1274.50i 0.623548 + 2.07235i
\(616\) 0 0
\(617\) −1212.73 −1.96552 −0.982761 0.184883i \(-0.940809\pi\)
−0.982761 + 0.184883i \(0.940809\pi\)
\(618\) 0 0
\(619\) 199.245 + 345.102i 0.321882 + 0.557516i 0.980876 0.194632i \(-0.0623513\pi\)
−0.658994 + 0.752148i \(0.729018\pi\)
\(620\) 0 0
\(621\) 578.721 695.535i 0.931917 1.12002i
\(622\) 0 0
\(623\) −142.558 82.3056i −0.228824 0.132112i
\(624\) 0 0
\(625\) 336.561 + 582.940i 0.538497 + 0.932705i
\(626\) 0 0
\(627\) −24.3633 + 124.421i −0.0388569 + 0.198439i
\(628\) 0 0
\(629\) 1272.89 + 734.906i 2.02368 + 1.16837i
\(630\) 0 0
\(631\) −185.584 321.441i −0.294111 0.509415i 0.680667 0.732593i \(-0.261690\pi\)
−0.974778 + 0.223178i \(0.928357\pi\)
\(632\) 0 0
\(633\) 110.905 + 26.1228i 0.175205 + 0.0412683i
\(634\) 0 0
\(635\) −808.454 466.761i −1.27316 0.735057i
\(636\) 0 0
\(637\) 85.2897 + 49.2420i 0.133893 + 0.0773030i
\(638\) 0 0
\(639\) 324.218 650.050i 0.507383 1.01729i
\(640\) 0 0
\(641\) 523.079i 0.816037i 0.912974 + 0.408018i \(0.133780\pi\)
−0.912974 + 0.408018i \(0.866220\pi\)
\(642\) 0 0
\(643\) 452.340 + 783.477i 0.703484 + 1.21847i 0.967236 + 0.253880i \(0.0817068\pi\)
−0.263751 + 0.964591i \(0.584960\pi\)
\(644\) 0 0
\(645\) −19.3284 + 82.0586i −0.0299665 + 0.127223i
\(646\) 0 0
\(647\) −33.5058 −0.0517863 −0.0258932 0.999665i \(-0.508243\pi\)
−0.0258932 + 0.999665i \(0.508243\pi\)
\(648\) 0 0
\(649\) −186.258 107.536i −0.286992 0.165695i
\(650\) 0 0
\(651\) 677.288 719.876i 1.04038 1.10580i
\(652\) 0 0
\(653\) −210.443 + 364.498i −0.322271 + 0.558190i −0.980956 0.194229i \(-0.937780\pi\)
0.658685 + 0.752419i \(0.271113\pi\)
\(654\) 0 0
\(655\) −177.000 + 306.573i −0.270229 + 0.468051i
\(656\) 0 0
\(657\) −704.380 351.316i −1.07212 0.534727i
\(658\) 0 0
\(659\) −901.500 520.481i −1.36798 0.789804i −0.377311 0.926087i \(-0.623151\pi\)
−0.990670 + 0.136282i \(0.956485\pi\)
\(660\) 0 0
\(661\) 315.285i 0.476982i −0.971145 0.238491i \(-0.923347\pi\)
0.971145 0.238491i \(-0.0766527\pi\)
\(662\) 0 0
\(663\) −225.370 749.016i −0.339925 1.12974i
\(664\) 0 0
\(665\) −465.224 + 881.443i −0.699585 + 1.32548i
\(666\) 0 0
\(667\) −376.095 217.138i −0.563860 0.325545i
\(668\) 0 0
\(669\) 265.732 282.441i 0.397207 0.422184i
\(670\) 0 0
\(671\) −203.192 −0.302819
\(672\) 0 0
\(673\) −162.025 + 93.5454i −0.240751 + 0.138998i −0.615522 0.788120i \(-0.711055\pi\)
0.374771 + 0.927117i \(0.377721\pi\)
\(674\) 0 0
\(675\) 213.867 + 580.091i 0.316840 + 0.859394i
\(676\) 0 0
\(677\) 638.183 368.455i 0.942663 0.544247i 0.0518690 0.998654i \(-0.483482\pi\)
0.890794 + 0.454407i \(0.150149\pi\)
\(678\) 0 0
\(679\) 1013.38 585.078i 1.49247 0.861675i
\(680\) 0 0
\(681\) −883.631 208.134i −1.29755 0.305629i
\(682\) 0 0
\(683\) 887.445i 1.29933i 0.760219 + 0.649667i \(0.225092\pi\)
−0.760219 + 0.649667i \(0.774908\pi\)
\(684\) 0 0
\(685\) 955.002 1.39416
\(686\) 0 0
\(687\) 495.022 148.946i 0.720555 0.216807i
\(688\) 0 0
\(689\) 484.648 + 839.435i 0.703408 + 1.21834i
\(690\) 0 0
\(691\) −604.385 1046.83i −0.874652 1.51494i −0.857133 0.515096i \(-0.827756\pi\)
−0.0175197 0.999847i \(-0.505577\pi\)
\(692\) 0 0
\(693\) 135.780 + 67.7214i 0.195931 + 0.0977221i
\(694\) 0 0
\(695\) 238.135 + 412.462i 0.342641 + 0.593471i
\(696\) 0 0
\(697\) 1433.90i 2.05724i
\(698\) 0 0
\(699\) 1277.09 384.260i 1.82702 0.549729i
\(700\) 0 0
\(701\) −217.885 + 377.388i −0.310821 + 0.538357i −0.978540 0.206056i \(-0.933937\pi\)
0.667720 + 0.744413i \(0.267270\pi\)
\(702\) 0 0
\(703\) 47.3809 + 1247.56i 0.0673981 + 1.77462i
\(704\) 0 0
\(705\) −231.517 217.820i −0.328393 0.308965i
\(706\) 0 0
\(707\) −633.863 −0.896553
\(708\) 0 0
\(709\) −554.474 + 960.378i −0.782051 + 1.35455i 0.148693 + 0.988883i \(0.452493\pi\)
−0.930745 + 0.365670i \(0.880840\pi\)
\(710\) 0 0
\(711\) 864.358 52.7435i 1.21569 0.0741821i
\(712\) 0 0
\(713\) −1261.53 728.343i −1.76932 1.02152i
\(714\) 0 0
\(715\) 155.392 + 89.7159i 0.217332 + 0.125477i
\(716\) 0 0
\(717\) 756.420 227.598i 1.05498 0.317431i
\(718\) 0 0
\(719\) 108.126 187.279i 0.150384 0.260472i −0.780985 0.624550i \(-0.785282\pi\)
0.931369 + 0.364078i \(0.118616\pi\)
\(720\) 0 0
\(721\) 1037.00i 1.43828i
\(722\) 0 0
\(723\) −10.3844 34.5126i −0.0143630 0.0477353i
\(724\) 0 0
\(725\) 256.986 148.371i 0.354463 0.204649i
\(726\) 0 0
\(727\) −852.055 −1.17201 −0.586007 0.810306i \(-0.699301\pi\)
−0.586007 + 0.810306i \(0.699301\pi\)
\(728\) 0 0
\(729\) −132.545 716.849i −0.181817 0.983332i
\(730\) 0 0
\(731\) 45.4128 78.6573i 0.0621242 0.107602i
\(732\) 0 0
\(733\) 125.080 216.645i 0.170641 0.295559i −0.768003 0.640446i \(-0.778749\pi\)
0.938644 + 0.344887i \(0.112083\pi\)
\(734\) 0 0
\(735\) 127.768 + 120.210i 0.173835 + 0.163550i
\(736\) 0 0
\(737\) −71.7714 + 41.4372i −0.0973831 + 0.0562242i
\(738\) 0 0
\(739\) −618.939 + 1072.03i −0.837536 + 1.45065i 0.0544130 + 0.998519i \(0.482671\pi\)
−0.891949 + 0.452136i \(0.850662\pi\)
\(740\) 0 0
\(741\) 436.571 500.819i 0.589164 0.675870i
\(742\) 0 0
\(743\) 795.437 459.246i 1.07057 0.618096i 0.142236 0.989833i \(-0.454571\pi\)
0.928338 + 0.371736i \(0.121237\pi\)
\(744\) 0 0
\(745\) 727.410 1259.91i 0.976389 1.69116i
\(746\) 0 0
\(747\) −373.040 + 246.834i −0.499384 + 0.330433i
\(748\) 0 0
\(749\) −243.748 + 140.728i −0.325431 + 0.187888i
\(750\) 0 0
\(751\) 91.6457i 0.122032i −0.998137 0.0610158i \(-0.980566\pi\)
0.998137 0.0610158i \(-0.0194340\pi\)
\(752\) 0 0
\(753\) −139.938 + 594.107i −0.185841 + 0.788987i
\(754\) 0 0
\(755\) 654.629 + 377.950i 0.867058 + 0.500596i
\(756\) 0 0
\(757\) 337.641 584.812i 0.446026 0.772539i −0.552097 0.833780i \(-0.686172\pi\)
0.998123 + 0.0612407i \(0.0195057\pi\)
\(758\) 0 0
\(759\) 51.2687 217.661i 0.0675478 0.286774i
\(760\) 0 0
\(761\) −446.414 + 773.212i −0.586615 + 1.01605i 0.408056 + 0.912957i \(0.366207\pi\)
−0.994672 + 0.103091i \(0.967127\pi\)
\(762\) 0 0
\(763\) 557.999i 0.731322i
\(764\) 0 0
\(765\) −84.8619 1390.71i −0.110931 1.81793i
\(766\) 0 0
\(767\) 563.522 + 976.049i 0.734709 + 1.27255i
\(768\) 0 0
\(769\) 453.086 0.589188 0.294594 0.955622i \(-0.404816\pi\)
0.294594 + 0.955622i \(0.404816\pi\)
\(770\) 0 0
\(771\) 312.691 332.353i 0.405565 0.431067i
\(772\) 0 0
\(773\) 47.5624 27.4601i 0.0615296 0.0355241i −0.468920 0.883241i \(-0.655357\pi\)
0.530449 + 0.847717i \(0.322023\pi\)
\(774\) 0 0
\(775\) 862.002 497.677i 1.11226 0.642164i
\(776\) 0 0
\(777\) 1454.31 + 342.554i 1.87170 + 0.440868i
\(778\) 0 0
\(779\) 1030.91 648.568i 1.32337 0.832565i
\(780\) 0 0
\(781\) 179.529i 0.229870i
\(782\) 0 0
\(783\) −328.292 + 121.034i −0.419275 + 0.154577i
\(784\) 0 0
\(785\) 536.366 929.014i 0.683269 1.18346i
\(786\) 0 0
\(787\) 190.023 + 109.710i 0.241452 + 0.139402i 0.615844 0.787868i \(-0.288815\pi\)
−0.374392 + 0.927271i \(0.622149\pi\)
\(788\) 0 0
\(789\) −210.279 197.839i −0.266513 0.250746i
\(790\) 0 0
\(791\) 1226.13i 1.55010i
\(792\) 0 0
\(793\) 922.136 + 532.395i 1.16284 + 0.671369i
\(794\) 0 0
\(795\) 497.481 + 1653.37i 0.625762 + 2.07971i
\(796\) 0 0
\(797\) 907.132 + 523.733i 1.13818