Properties

Label 684.3.s.a.445.8
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 445.8
Character \(\chi\) \(=\) 684.445
Dual form 684.3.s.a.601.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.56169 - 1.56133i) q^{3} +(-1.88587 - 3.26643i) q^{5} +(-0.501515 - 0.868649i) q^{7} +(4.12453 + 7.99927i) q^{9} +O(q^{10})\) \(q+(-2.56169 - 1.56133i) q^{3} +(-1.88587 - 3.26643i) q^{5} +(-0.501515 - 0.868649i) q^{7} +(4.12453 + 7.99927i) q^{9} +(3.99634 + 6.92187i) q^{11} -2.03077i q^{13} +(-0.268931 + 11.3120i) q^{15} +(-9.87125 + 17.0975i) q^{17} +(13.5594 + 13.3095i) q^{19} +(-0.0715175 + 3.00824i) q^{21} +10.1092 q^{23} +(5.38697 - 9.33051i) q^{25} +(1.92369 - 26.9314i) q^{27} +(8.88104 + 5.12747i) q^{29} +(-34.4152 - 19.8696i) q^{31} +(0.569890 - 23.9713i) q^{33} +(-1.89159 + 3.27632i) q^{35} +34.3129i q^{37} +(-3.17069 + 5.20221i) q^{39} +(60.5759 - 34.9735i) q^{41} +12.8877 q^{43} +(18.3507 - 28.5581i) q^{45} +(-17.4941 + 30.3007i) q^{47} +(23.9970 - 41.5640i) q^{49} +(51.9819 - 28.3863i) q^{51} +(77.7697 - 44.9004i) q^{53} +(15.0732 - 26.1075i) q^{55} +(-13.9546 - 55.2654i) q^{57} +(-50.2397 + 29.0059i) q^{59} +(14.6592 - 25.3904i) q^{61} +(4.88005 - 7.59452i) q^{63} +(-6.63336 + 3.82977i) q^{65} -95.7549i q^{67} +(-25.8966 - 15.7837i) q^{69} +(89.8877 + 51.8967i) q^{71} +(28.1575 - 48.7702i) q^{73} +(-28.3677 + 15.4911i) q^{75} +(4.00845 - 6.94284i) q^{77} +35.8073i q^{79} +(-46.9765 + 65.9864i) q^{81} +(40.7844 + 70.6407i) q^{83} +74.4637 q^{85} +(-14.7448 - 27.0012i) q^{87} +(84.1236 - 48.5688i) q^{89} +(-1.76403 + 1.01846i) q^{91} +(57.1382 + 104.633i) q^{93} +(17.9031 - 69.3908i) q^{95} -170.003i q^{97} +(-38.8869 + 60.5173i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - q^{7} + 4 q^{9} + O(q^{10}) \) \( 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99} + O(q^{100}) \)

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
\(3\) −2.56169 1.56133i −0.853897 0.520442i
\(4\) 0 0
\(5\) −1.88587 3.26643i −0.377174 0.653285i 0.613476 0.789714i \(-0.289771\pi\)
−0.990650 + 0.136429i \(0.956438\pi\)
\(6\) 0 0
\(7\) −0.501515 0.868649i −0.0716450 0.124093i 0.827977 0.560761i \(-0.189492\pi\)
−0.899622 + 0.436669i \(0.856158\pi\)
\(8\) 0 0
\(9\) 4.12453 + 7.99927i 0.458281 + 0.888807i
\(10\) 0 0
\(11\) 3.99634 + 6.92187i 0.363304 + 0.629261i 0.988502 0.151205i \(-0.0483153\pi\)
−0.625199 + 0.780466i \(0.714982\pi\)
\(12\) 0 0
\(13\) 2.03077i 0.156213i −0.996945 0.0781066i \(-0.975113\pi\)
0.996945 0.0781066i \(-0.0248874\pi\)
\(14\) 0 0
\(15\) −0.268931 + 11.3120i −0.0179287 + 0.754136i
\(16\) 0 0
\(17\) −9.87125 + 17.0975i −0.580662 + 1.00574i 0.414739 + 0.909940i \(0.363873\pi\)
−0.995401 + 0.0957957i \(0.969460\pi\)
\(18\) 0 0
\(19\) 13.5594 + 13.3095i 0.713654 + 0.700499i
\(20\) 0 0
\(21\) −0.0715175 + 3.00824i −0.00340559 + 0.143250i
\(22\) 0 0
\(23\) 10.1092 0.439529 0.219764 0.975553i \(-0.429471\pi\)
0.219764 + 0.975553i \(0.429471\pi\)
\(24\) 0 0
\(25\) 5.38697 9.33051i 0.215479 0.373220i
\(26\) 0 0
\(27\) 1.92369 26.9314i 0.0712477 0.997459i
\(28\) 0 0
\(29\) 8.88104 + 5.12747i 0.306243 + 0.176809i 0.645244 0.763977i \(-0.276756\pi\)
−0.339001 + 0.940786i \(0.610089\pi\)
\(30\) 0 0
\(31\) −34.4152 19.8696i −1.11017 0.640955i −0.171294 0.985220i \(-0.554795\pi\)
−0.938873 + 0.344265i \(0.888128\pi\)
\(32\) 0 0
\(33\) 0.569890 23.9713i 0.0172694 0.726403i
\(34\) 0 0
\(35\) −1.89159 + 3.27632i −0.0540453 + 0.0936092i
\(36\) 0 0
\(37\) 34.3129i 0.927376i 0.885999 + 0.463688i \(0.153474\pi\)
−0.885999 + 0.463688i \(0.846526\pi\)
\(38\) 0 0
\(39\) −3.17069 + 5.20221i −0.0812999 + 0.133390i
\(40\) 0 0
\(41\) 60.5759 34.9735i 1.47746 0.853013i 0.477785 0.878477i \(-0.341440\pi\)
0.999676 + 0.0254640i \(0.00810631\pi\)
\(42\) 0 0
\(43\) 12.8877 0.299715 0.149857 0.988708i \(-0.452119\pi\)
0.149857 + 0.988708i \(0.452119\pi\)
\(44\) 0 0
\(45\) 18.3507 28.5581i 0.407793 0.634624i
\(46\) 0 0
\(47\) −17.4941 + 30.3007i −0.372216 + 0.644696i −0.989906 0.141725i \(-0.954735\pi\)
0.617690 + 0.786421i \(0.288068\pi\)
\(48\) 0 0
\(49\) 23.9970 41.5640i 0.489734 0.848244i
\(50\) 0 0
\(51\) 51.9819 28.3863i 1.01925 0.556595i
\(52\) 0 0
\(53\) 77.7697 44.9004i 1.46735 0.847177i 0.468021 0.883717i \(-0.344967\pi\)
0.999332 + 0.0365408i \(0.0116339\pi\)
\(54\) 0 0
\(55\) 15.0732 26.1075i 0.274058 0.474682i
\(56\) 0 0
\(57\) −13.9546 55.2654i −0.244818 0.969569i
\(58\) 0 0
\(59\) −50.2397 + 29.0059i −0.851521 + 0.491626i −0.861164 0.508328i \(-0.830264\pi\)
0.00964297 + 0.999954i \(0.496930\pi\)
\(60\) 0 0
\(61\) 14.6592 25.3904i 0.240314 0.416236i −0.720490 0.693466i \(-0.756083\pi\)
0.960804 + 0.277230i \(0.0894163\pi\)
\(62\) 0 0
\(63\) 4.88005 7.59452i 0.0774611 0.120548i
\(64\) 0 0
\(65\) −6.63336 + 3.82977i −0.102052 + 0.0589196i
\(66\) 0 0
\(67\) 95.7549i 1.42918i −0.699545 0.714589i \(-0.746614\pi\)
0.699545 0.714589i \(-0.253386\pi\)
\(68\) 0 0
\(69\) −25.8966 15.7837i −0.375312 0.228749i
\(70\) 0 0
\(71\) 89.8877 + 51.8967i 1.26602 + 0.730940i 0.974233 0.225542i \(-0.0724154\pi\)
0.291791 + 0.956482i \(0.405749\pi\)
\(72\) 0 0
\(73\) 28.1575 48.7702i 0.385719 0.668085i −0.606149 0.795351i \(-0.707287\pi\)
0.991869 + 0.127265i \(0.0406200\pi\)
\(74\) 0 0
\(75\) −28.3677 + 15.4911i −0.378236 + 0.206548i
\(76\) 0 0
\(77\) 4.00845 6.94284i 0.0520578 0.0901668i
\(78\) 0 0
\(79\) 35.8073i 0.453257i 0.973981 + 0.226628i \(0.0727703\pi\)
−0.973981 + 0.226628i \(0.927230\pi\)
\(80\) 0 0
\(81\) −46.9765 + 65.9864i −0.579957 + 0.814647i
\(82\) 0 0
\(83\) 40.7844 + 70.6407i 0.491379 + 0.851093i 0.999951 0.00992637i \(-0.00315971\pi\)
−0.508572 + 0.861020i \(0.669826\pi\)
\(84\) 0 0
\(85\) 74.4637 0.876043
\(86\) 0 0
\(87\) −14.7448 27.0012i −0.169481 0.310358i
\(88\) 0 0
\(89\) 84.1236 48.5688i 0.945209 0.545717i 0.0536194 0.998561i \(-0.482924\pi\)
0.891589 + 0.452845i \(0.149591\pi\)
\(90\) 0 0
\(91\) −1.76403 + 1.01846i −0.0193849 + 0.0111919i
\(92\) 0 0
\(93\) 57.1382 + 104.633i 0.614389 + 1.12509i
\(94\) 0 0
\(95\) 17.9031 69.3908i 0.188454 0.730430i
\(96\) 0 0
\(97\) 170.003i 1.75261i −0.481760 0.876303i \(-0.660002\pi\)
0.481760 0.876303i \(-0.339998\pi\)
\(98\) 0 0
\(99\) −38.8869 + 60.5173i −0.392796 + 0.611285i
\(100\) 0 0
\(101\) −61.4065 + 106.359i −0.607986 + 1.05306i 0.383586 + 0.923505i \(0.374689\pi\)
−0.991572 + 0.129557i \(0.958645\pi\)
\(102\) 0 0
\(103\) 2.99449 + 1.72887i 0.0290728 + 0.0167852i 0.514466 0.857511i \(-0.327990\pi\)
−0.485393 + 0.874296i \(0.661324\pi\)
\(104\) 0 0
\(105\) 9.96107 5.43955i 0.0948673 0.0518052i
\(106\) 0 0
\(107\) 0.821328i 0.00767596i −0.999993 0.00383798i \(-0.998778\pi\)
0.999993 0.00383798i \(-0.00122167\pi\)
\(108\) 0 0
\(109\) 182.562 + 105.402i 1.67488 + 0.966993i 0.964842 + 0.262832i \(0.0846564\pi\)
0.710040 + 0.704162i \(0.248677\pi\)
\(110\) 0 0
\(111\) 53.5736 87.8991i 0.482645 0.791883i
\(112\) 0 0
\(113\) −45.7178 26.3952i −0.404582 0.233586i 0.283877 0.958861i \(-0.408379\pi\)
−0.688459 + 0.725275i \(0.741713\pi\)
\(114\) 0 0
\(115\) −19.0646 33.0208i −0.165779 0.287138i
\(116\) 0 0
\(117\) 16.2447 8.37597i 0.138843 0.0715895i
\(118\) 0 0
\(119\) 19.8023 0.166406
\(120\) 0 0
\(121\) 28.5585 49.4647i 0.236021 0.408800i
\(122\) 0 0
\(123\) −209.782 4.98732i −1.70554 0.0405473i
\(124\) 0 0
\(125\) −134.930 −1.07944
\(126\) 0 0
\(127\) −107.781 + 62.2275i −0.848671 + 0.489981i −0.860202 0.509953i \(-0.829663\pi\)
0.0115310 + 0.999934i \(0.496329\pi\)
\(128\) 0 0
\(129\) −33.0144 20.1220i −0.255926 0.155984i
\(130\) 0 0
\(131\) 29.4340 + 50.9812i 0.224687 + 0.389169i 0.956225 0.292631i \(-0.0945307\pi\)
−0.731539 + 0.681800i \(0.761197\pi\)
\(132\) 0 0
\(133\) 4.76102 18.4533i 0.0357971 0.138746i
\(134\) 0 0
\(135\) −91.5972 + 44.5056i −0.678498 + 0.329671i
\(136\) 0 0
\(137\) 38.6832 67.0014i 0.282359 0.489061i −0.689606 0.724185i \(-0.742216\pi\)
0.971965 + 0.235124i \(0.0755496\pi\)
\(138\) 0 0
\(139\) 196.034 1.41032 0.705158 0.709050i \(-0.250876\pi\)
0.705158 + 0.709050i \(0.250876\pi\)
\(140\) 0 0
\(141\) 92.1239 50.3071i 0.653361 0.356788i
\(142\) 0 0
\(143\) 14.0567 8.11566i 0.0982988 0.0567529i
\(144\) 0 0
\(145\) 38.6790i 0.266752i
\(146\) 0 0
\(147\) −126.368 + 69.0070i −0.859644 + 0.469435i
\(148\) 0 0
\(149\) 0.381960 + 0.661575i 0.00256349 + 0.00444010i 0.867304 0.497778i \(-0.165851\pi\)
−0.864741 + 0.502218i \(0.832517\pi\)
\(150\) 0 0
\(151\) 62.9575 36.3485i 0.416937 0.240719i −0.276829 0.960919i \(-0.589284\pi\)
0.693766 + 0.720200i \(0.255950\pi\)
\(152\) 0 0
\(153\) −177.482 8.44363i −1.16001 0.0551871i
\(154\) 0 0
\(155\) 149.886i 0.967008i
\(156\) 0 0
\(157\) 5.63241 + 9.75561i 0.0358752 + 0.0621377i 0.883406 0.468609i \(-0.155245\pi\)
−0.847530 + 0.530747i \(0.821911\pi\)
\(158\) 0 0
\(159\) −269.326 6.40292i −1.69387 0.0402699i
\(160\) 0 0
\(161\) −5.06990 8.78132i −0.0314900 0.0545424i
\(162\) 0 0
\(163\) −186.996 −1.14721 −0.573606 0.819131i \(-0.694456\pi\)
−0.573606 + 0.819131i \(0.694456\pi\)
\(164\) 0 0
\(165\) −79.3752 + 43.3453i −0.481062 + 0.262699i
\(166\) 0 0
\(167\) 197.860i 1.18479i 0.805648 + 0.592394i \(0.201817\pi\)
−0.805648 + 0.592394i \(0.798183\pi\)
\(168\) 0 0
\(169\) 164.876 0.975597
\(170\) 0 0
\(171\) −50.5399 + 163.361i −0.295555 + 0.955326i
\(172\) 0 0
\(173\) 78.1322i 0.451631i 0.974170 + 0.225816i \(0.0725047\pi\)
−0.974170 + 0.225816i \(0.927495\pi\)
\(174\) 0 0
\(175\) −10.8066 −0.0617520
\(176\) 0 0
\(177\) 173.986 + 4.13633i 0.982974 + 0.0233691i
\(178\) 0 0
\(179\) 4.88651i 0.0272989i 0.999907 + 0.0136495i \(0.00434490\pi\)
−0.999907 + 0.0136495i \(0.995655\pi\)
\(180\) 0 0
\(181\) −116.553 + 67.2919i −0.643940 + 0.371779i −0.786130 0.618061i \(-0.787919\pi\)
0.142191 + 0.989839i \(0.454585\pi\)
\(182\) 0 0
\(183\) −77.1949 + 42.1547i −0.421830 + 0.230353i
\(184\) 0 0
\(185\) 112.081 64.7097i 0.605841 0.349782i
\(186\) 0 0
\(187\) −157.796 −0.843827
\(188\) 0 0
\(189\) −24.3587 + 11.8355i −0.128882 + 0.0626216i
\(190\) 0 0
\(191\) 154.154 + 267.003i 0.807091 + 1.39792i 0.914871 + 0.403747i \(0.132292\pi\)
−0.107780 + 0.994175i \(0.534374\pi\)
\(192\) 0 0
\(193\) 208.666 120.473i 1.08117 0.624215i 0.149960 0.988692i \(-0.452086\pi\)
0.931212 + 0.364477i \(0.118752\pi\)
\(194\) 0 0
\(195\) 22.9722 + 0.546137i 0.117806 + 0.00280070i
\(196\) 0 0
\(197\) −66.8721 −0.339452 −0.169726 0.985491i \(-0.554288\pi\)
−0.169726 + 0.985491i \(0.554288\pi\)
\(198\) 0 0
\(199\) −96.3760 166.928i −0.484302 0.838835i 0.515536 0.856868i \(-0.327593\pi\)
−0.999837 + 0.0180331i \(0.994260\pi\)
\(200\) 0 0
\(201\) −149.505 + 245.294i −0.743804 + 1.22037i
\(202\) 0 0
\(203\) 10.2860i 0.0506700i
\(204\) 0 0
\(205\) −228.477 131.911i −1.11452 0.643469i
\(206\) 0 0
\(207\) 41.6955 + 80.8659i 0.201428 + 0.390657i
\(208\) 0 0
\(209\) −37.9384 + 147.046i −0.181523 + 0.703568i
\(210\) 0 0
\(211\) 24.2380 13.9938i 0.114872 0.0663215i −0.441463 0.897279i \(-0.645540\pi\)
0.556335 + 0.830958i \(0.312207\pi\)
\(212\) 0 0
\(213\) −149.237 273.287i −0.700643 1.28304i
\(214\) 0 0
\(215\) −24.3046 42.0969i −0.113045 0.195799i
\(216\) 0 0
\(217\) 39.8596i 0.183685i
\(218\) 0 0
\(219\) −148.277 + 80.9713i −0.677064 + 0.369732i
\(220\) 0 0
\(221\) 34.7211 + 20.0463i 0.157109 + 0.0907071i
\(222\) 0 0
\(223\) 184.895i 0.829125i −0.910021 0.414562i \(-0.863935\pi\)
0.910021 0.414562i \(-0.136065\pi\)
\(224\) 0 0
\(225\) 96.8560 + 4.60788i 0.430471 + 0.0204795i
\(226\) 0 0
\(227\) −335.661 + 193.794i −1.47868 + 0.853718i −0.999709 0.0241103i \(-0.992325\pi\)
−0.478975 + 0.877829i \(0.658991\pi\)
\(228\) 0 0
\(229\) −96.1432 + 166.525i −0.419839 + 0.727183i −0.995923 0.0902078i \(-0.971247\pi\)
0.576084 + 0.817391i \(0.304580\pi\)
\(230\) 0 0
\(231\) −21.1085 + 11.5269i −0.0913786 + 0.0499001i
\(232\) 0 0
\(233\) 46.2780 80.1558i 0.198618 0.344017i −0.749463 0.662047i \(-0.769688\pi\)
0.948081 + 0.318030i \(0.103021\pi\)
\(234\) 0 0
\(235\) 131.967 0.561561
\(236\) 0 0
\(237\) 55.9068 91.7272i 0.235894 0.387035i
\(238\) 0 0
\(239\) −126.585 + 219.252i −0.529646 + 0.917374i 0.469756 + 0.882796i \(0.344342\pi\)
−0.999402 + 0.0345778i \(0.988991\pi\)
\(240\) 0 0
\(241\) 144.462 + 83.4051i 0.599427 + 0.346079i 0.768816 0.639470i \(-0.220846\pi\)
−0.169389 + 0.985549i \(0.554179\pi\)
\(242\) 0 0
\(243\) 223.366 95.6911i 0.919200 0.393791i
\(244\) 0 0
\(245\) −181.021 −0.738860
\(246\) 0 0
\(247\) 27.0285 27.5361i 0.109427 0.111482i
\(248\) 0 0
\(249\) 5.81598 244.638i 0.0233573 0.982480i
\(250\) 0 0
\(251\) 61.6172 + 106.724i 0.245487 + 0.425196i 0.962268 0.272102i \(-0.0877188\pi\)
−0.716781 + 0.697298i \(0.754385\pi\)
\(252\) 0 0
\(253\) 40.3997 + 69.9743i 0.159683 + 0.276578i
\(254\) 0 0
\(255\) −190.753 116.262i −0.748051 0.455930i
\(256\) 0 0
\(257\) 80.9176i 0.314854i −0.987531 0.157427i \(-0.949680\pi\)
0.987531 0.157427i \(-0.0503200\pi\)
\(258\) 0 0
\(259\) 29.8059 17.2084i 0.115081 0.0664418i
\(260\) 0 0
\(261\) −4.38591 + 92.1902i −0.0168043 + 0.353219i
\(262\) 0 0
\(263\) 155.651 0.591828 0.295914 0.955215i \(-0.404376\pi\)
0.295914 + 0.955215i \(0.404376\pi\)
\(264\) 0 0
\(265\) −293.327 169.353i −1.10690 0.639067i
\(266\) 0 0
\(267\) −291.330 6.92604i −1.09112 0.0259402i
\(268\) 0 0
\(269\) 181.987 + 105.070i 0.676530 + 0.390595i 0.798546 0.601933i \(-0.205603\pi\)
−0.122016 + 0.992528i \(0.538936\pi\)
\(270\) 0 0
\(271\) −25.3355 + 43.8825i −0.0934891 + 0.161928i −0.908977 0.416846i \(-0.863135\pi\)
0.815488 + 0.578774i \(0.196469\pi\)
\(272\) 0 0
\(273\) 6.10905 + 0.145236i 0.0223775 + 0.000531999i
\(274\) 0 0
\(275\) 86.1128 0.313137
\(276\) 0 0
\(277\) −105.030 181.917i −0.379169 0.656739i 0.611773 0.791033i \(-0.290457\pi\)
−0.990942 + 0.134294i \(0.957123\pi\)
\(278\) 0 0
\(279\) 16.9960 357.249i 0.0609175 1.28046i
\(280\) 0 0
\(281\) 172.080 + 99.3502i 0.612383 + 0.353560i 0.773898 0.633311i \(-0.218304\pi\)
−0.161514 + 0.986870i \(0.551638\pi\)
\(282\) 0 0
\(283\) −29.3373 50.8136i −0.103665 0.179553i 0.809527 0.587083i \(-0.199724\pi\)
−0.913192 + 0.407529i \(0.866390\pi\)
\(284\) 0 0
\(285\) −154.204 + 149.805i −0.541066 + 0.525633i
\(286\) 0 0
\(287\) −60.7595 35.0795i −0.211705 0.122228i
\(288\) 0 0
\(289\) −50.3833 87.2665i −0.174337 0.301960i
\(290\) 0 0
\(291\) −265.430 + 435.495i −0.912130 + 1.49655i
\(292\) 0 0
\(293\) 262.055 + 151.298i 0.894387 + 0.516374i 0.875375 0.483445i \(-0.160615\pi\)
0.0190118 + 0.999819i \(0.493948\pi\)
\(294\) 0 0
\(295\) 189.491 + 109.403i 0.642344 + 0.370857i
\(296\) 0 0
\(297\) 194.103 94.3115i 0.653546 0.317547i
\(298\) 0 0
\(299\) 20.5294i 0.0686602i
\(300\) 0 0
\(301\) −6.46340 11.1949i −0.0214731 0.0371925i
\(302\) 0 0
\(303\) 323.366 176.584i 1.06721 0.582786i
\(304\) 0 0
\(305\) −110.581 −0.362561
\(306\) 0 0
\(307\) 183.372 + 105.870i 0.597302 + 0.344853i 0.767980 0.640474i \(-0.221262\pi\)
−0.170677 + 0.985327i \(0.554596\pi\)
\(308\) 0 0
\(309\) −4.97164 9.10422i −0.0160895 0.0294635i
\(310\) 0 0
\(311\) 252.534 437.401i 0.812005 1.40643i −0.0994537 0.995042i \(-0.531710\pi\)
0.911459 0.411392i \(-0.134957\pi\)
\(312\) 0 0
\(313\) −146.971 + 254.562i −0.469558 + 0.813297i −0.999394 0.0348022i \(-0.988920\pi\)
0.529837 + 0.848100i \(0.322253\pi\)
\(314\) 0 0
\(315\) −34.0101 1.61802i −0.107969 0.00513656i
\(316\) 0 0
\(317\) 351.760 + 203.089i 1.10965 + 0.640658i 0.938739 0.344628i \(-0.111995\pi\)
0.170913 + 0.985286i \(0.445328\pi\)
\(318\) 0 0
\(319\) 81.9645i 0.256942i
\(320\) 0 0
\(321\) −1.28236 + 2.10399i −0.00399489 + 0.00655448i
\(322\) 0 0
\(323\) −361.407 + 100.451i −1.11891 + 0.310994i
\(324\) 0 0
\(325\) −18.9481 10.9397i −0.0583020 0.0336607i
\(326\) 0 0
\(327\) −303.101 555.047i −0.926913 1.69739i
\(328\) 0 0
\(329\) 35.0943 0.106670
\(330\) 0 0
\(331\) −131.702 + 76.0384i −0.397892 + 0.229723i −0.685574 0.728003i \(-0.740449\pi\)
0.287682 + 0.957726i \(0.407115\pi\)
\(332\) 0 0
\(333\) −274.478 + 141.524i −0.824258 + 0.424998i
\(334\) 0 0
\(335\) −312.776 + 180.581i −0.933660 + 0.539049i
\(336\) 0 0
\(337\) 282.157 162.903i 0.837260 0.483393i −0.0190716 0.999818i \(-0.506071\pi\)
0.856332 + 0.516426i \(0.172738\pi\)
\(338\) 0 0
\(339\) 75.9034 + 138.997i 0.223904 + 0.410019i
\(340\) 0 0
\(341\) 317.623i 0.931446i
\(342\) 0 0
\(343\) −97.2878 −0.283638
\(344\) 0 0
\(345\) −2.71866 + 114.355i −0.00788019 + 0.331464i
\(346\) 0 0
\(347\) 126.002 + 218.241i 0.363117 + 0.628938i 0.988472 0.151403i \(-0.0483791\pi\)
−0.625355 + 0.780341i \(0.715046\pi\)
\(348\) 0 0
\(349\) −233.068 403.685i −0.667815 1.15669i −0.978514 0.206182i \(-0.933896\pi\)
0.310698 0.950509i \(-0.399437\pi\)
\(350\) 0 0
\(351\) −54.6915 3.90657i −0.155816 0.0111298i
\(352\) 0 0
\(353\) −95.5556 165.507i −0.270696 0.468859i 0.698345 0.715762i \(-0.253920\pi\)
−0.969040 + 0.246903i \(0.920587\pi\)
\(354\) 0 0
\(355\) 391.482i 1.10277i
\(356\) 0 0
\(357\) −50.7275 30.9179i −0.142094 0.0866047i
\(358\) 0 0
\(359\) 10.0336 17.3787i 0.0279487 0.0484086i −0.851713 0.524009i \(-0.824436\pi\)
0.879661 + 0.475600i \(0.157769\pi\)
\(360\) 0 0
\(361\) 6.71567 + 360.938i 0.0186030 + 0.999827i
\(362\) 0 0
\(363\) −150.389 + 82.1243i −0.414294 + 0.226238i
\(364\) 0 0
\(365\) −212.406 −0.581934
\(366\) 0 0
\(367\) 91.6576 158.756i 0.249748 0.432577i −0.713708 0.700444i \(-0.752985\pi\)
0.963456 + 0.267867i \(0.0863188\pi\)
\(368\) 0 0
\(369\) 529.610 + 340.314i 1.43526 + 0.922259i
\(370\) 0 0
\(371\) −78.0053 45.0364i −0.210257 0.121392i
\(372\) 0 0
\(373\) 461.366 + 266.370i 1.23691 + 0.714128i 0.968461 0.249167i \(-0.0801567\pi\)
0.268446 + 0.963295i \(0.413490\pi\)
\(374\) 0 0
\(375\) 345.649 + 210.670i 0.921732 + 0.561786i
\(376\) 0 0
\(377\) 10.4127 18.0354i 0.0276199 0.0478391i
\(378\) 0 0
\(379\) 741.313i 1.95597i −0.208676 0.977985i \(-0.566915\pi\)
0.208676 0.977985i \(-0.433085\pi\)
\(380\) 0 0
\(381\) 373.260 + 8.87382i 0.979684 + 0.0232909i
\(382\) 0 0
\(383\) 266.510 153.870i 0.695849 0.401749i −0.109950 0.993937i \(-0.535069\pi\)
0.805800 + 0.592188i \(0.201736\pi\)
\(384\) 0 0
\(385\) −30.2377 −0.0785395
\(386\) 0 0
\(387\) 53.1559 + 103.092i 0.137354 + 0.266389i
\(388\) 0 0
\(389\) 12.8970 22.3383i 0.0331543 0.0574249i −0.848972 0.528438i \(-0.822778\pi\)
0.882126 + 0.471013i \(0.156111\pi\)
\(390\) 0 0
\(391\) −99.7901 + 172.842i −0.255218 + 0.442050i
\(392\) 0 0
\(393\) 4.19737 176.554i 0.0106803 0.449247i
\(394\) 0 0
\(395\) 116.962 67.5279i 0.296106 0.170957i
\(396\) 0 0
\(397\) −19.9789 + 34.6045i −0.0503247 + 0.0871649i −0.890090 0.455784i \(-0.849359\pi\)
0.839766 + 0.542949i \(0.182692\pi\)
\(398\) 0 0
\(399\) −41.0078 + 39.8381i −0.102777 + 0.0998449i
\(400\) 0 0
\(401\) −180.581 + 104.259i −0.450327 + 0.259997i −0.707968 0.706244i \(-0.750388\pi\)
0.257641 + 0.966241i \(0.417055\pi\)
\(402\) 0 0
\(403\) −40.3506 + 69.8894i −0.100126 + 0.173423i
\(404\) 0 0
\(405\) 304.131 + 29.0035i 0.750942 + 0.0716136i
\(406\) 0 0
\(407\) −237.509 + 137.126i −0.583561 + 0.336919i
\(408\) 0 0
\(409\) 577.273i 1.41143i 0.708498 + 0.705713i \(0.249373\pi\)
−0.708498 + 0.705713i \(0.750627\pi\)
\(410\) 0 0
\(411\) −203.705 + 111.240i −0.495634 + 0.270656i
\(412\) 0 0
\(413\) 50.3919 + 29.0938i 0.122014 + 0.0704450i
\(414\) 0 0
\(415\) 153.828 266.439i 0.370671 0.642021i
\(416\) 0 0
\(417\) −502.178 306.073i −1.20426 0.733987i
\(418\) 0 0
\(419\) 186.079 322.299i 0.444103 0.769210i −0.553886 0.832593i \(-0.686856\pi\)
0.997989 + 0.0633830i \(0.0201890\pi\)
\(420\) 0 0
\(421\) 635.854i 1.51034i 0.655528 + 0.755171i \(0.272446\pi\)
−0.655528 + 0.755171i \(0.727554\pi\)
\(422\) 0 0
\(423\) −314.539 14.9641i −0.743590 0.0353760i
\(424\) 0 0
\(425\) 106.352 + 184.208i 0.250241 + 0.433430i
\(426\) 0 0
\(427\) −29.4071 −0.0688692
\(428\) 0 0
\(429\) −48.6802 1.15732i −0.113474 0.00269771i
\(430\) 0 0
\(431\) 303.633 175.302i 0.704484 0.406734i −0.104531 0.994522i \(-0.533334\pi\)
0.809015 + 0.587788i \(0.200001\pi\)
\(432\) 0 0
\(433\) 194.800 112.468i 0.449886 0.259742i −0.257896 0.966173i \(-0.583029\pi\)
0.707782 + 0.706431i \(0.249696\pi\)
\(434\) 0 0
\(435\) −60.3905 + 99.0837i −0.138829 + 0.227779i
\(436\) 0 0
\(437\) 137.074 + 134.548i 0.313671 + 0.307889i
\(438\) 0 0
\(439\) 340.680i 0.776036i −0.921652 0.388018i \(-0.873160\pi\)
0.921652 0.388018i \(-0.126840\pi\)
\(440\) 0 0
\(441\) 431.457 + 20.5264i 0.978361 + 0.0465452i
\(442\) 0 0
\(443\) 79.8755 138.348i 0.180306 0.312299i −0.761679 0.647955i \(-0.775625\pi\)
0.941985 + 0.335656i \(0.108958\pi\)
\(444\) 0 0
\(445\) −317.293 183.189i −0.713017 0.411661i
\(446\) 0 0
\(447\) 0.0544686 2.29112i 0.000121854 0.00512554i
\(448\) 0 0
\(449\) 743.382i 1.65564i −0.560994 0.827820i \(-0.689581\pi\)
0.560994 0.827820i \(-0.310419\pi\)
\(450\) 0 0
\(451\) 484.164 + 279.532i 1.07353 + 0.619806i
\(452\) 0 0
\(453\) −218.030 5.18340i −0.481302 0.0114424i
\(454\) 0 0
\(455\) 6.65346 + 3.84138i 0.0146230 + 0.00844259i
\(456\) 0 0
\(457\) 13.4752 + 23.3398i 0.0294863 + 0.0510718i 0.880392 0.474247i \(-0.157280\pi\)
−0.850906 + 0.525318i \(0.823946\pi\)
\(458\) 0 0
\(459\) 441.470 + 298.737i 0.961809 + 0.650843i
\(460\) 0 0
\(461\) −266.300 −0.577657 −0.288829 0.957381i \(-0.593266\pi\)
−0.288829 + 0.957381i \(0.593266\pi\)
\(462\) 0 0
\(463\) −82.8037 + 143.420i −0.178842 + 0.309763i −0.941484 0.337057i \(-0.890568\pi\)
0.762642 + 0.646820i \(0.223902\pi\)
\(464\) 0 0
\(465\) 234.021 383.962i 0.503271 0.825725i
\(466\) 0 0
\(467\) −256.078 −0.548346 −0.274173 0.961680i \(-0.588404\pi\)
−0.274173 + 0.961680i \(0.588404\pi\)
\(468\) 0 0
\(469\) −83.1774 + 48.0225i −0.177351 + 0.102393i
\(470\) 0 0
\(471\) 0.803197 33.7849i 0.00170530 0.0717301i
\(472\) 0 0
\(473\) 51.5038 + 89.2073i 0.108888 + 0.188599i
\(474\) 0 0
\(475\) 197.228 54.8185i 0.415218 0.115407i
\(476\) 0 0
\(477\) 679.933 + 436.908i 1.42544 + 0.915949i
\(478\) 0 0
\(479\) −249.469 + 432.093i −0.520812 + 0.902073i 0.478895 + 0.877872i \(0.341038\pi\)
−0.999707 + 0.0242012i \(0.992296\pi\)
\(480\) 0 0
\(481\) 69.6816 0.144868
\(482\) 0 0
\(483\) −0.722982 + 30.4108i −0.00149686 + 0.0629623i
\(484\) 0 0
\(485\) −555.302 + 320.604i −1.14495 + 0.661038i
\(486\) 0 0
\(487\) 236.165i 0.484938i −0.970159 0.242469i \(-0.922043\pi\)
0.970159 0.242469i \(-0.0779572\pi\)
\(488\) 0 0
\(489\) 479.025 + 291.961i 0.979602 + 0.597057i
\(490\) 0 0
\(491\) 210.641 + 364.841i 0.429004 + 0.743057i 0.996785 0.0801228i \(-0.0255312\pi\)
−0.567781 + 0.823180i \(0.692198\pi\)
\(492\) 0 0
\(493\) −175.334 + 101.229i −0.355647 + 0.205333i
\(494\) 0 0
\(495\) 271.011 + 12.8932i 0.547497 + 0.0260469i
\(496\) 0 0
\(497\) 104.108i 0.209473i
\(498\) 0 0
\(499\) 311.249 + 539.099i 0.623745 + 1.08036i 0.988782 + 0.149366i \(0.0477231\pi\)
−0.365037 + 0.930993i \(0.618944\pi\)
\(500\) 0 0
\(501\) 308.923 506.856i 0.616614 1.01169i
\(502\) 0 0
\(503\) −202.986 351.581i −0.403550 0.698969i 0.590602 0.806963i \(-0.298891\pi\)
−0.994152 + 0.107994i \(0.965557\pi\)
\(504\) 0 0
\(505\) 463.219 0.917266
\(506\) 0 0
\(507\) −422.361 257.425i −0.833060 0.507742i
\(508\) 0 0
\(509\) 816.478i 1.60408i −0.597269 0.802041i \(-0.703747\pi\)
0.597269 0.802041i \(-0.296253\pi\)
\(510\) 0 0
\(511\) −56.4856 −0.110539
\(512\) 0 0
\(513\) 384.527 339.571i 0.749565 0.661931i
\(514\) 0 0
\(515\) 13.0417i 0.0253237i
\(516\) 0 0
\(517\) −279.650 −0.540910
\(518\) 0 0
\(519\) 121.990 200.151i 0.235048 0.385646i
\(520\) 0 0
\(521\) 112.777i 0.216463i −0.994126 0.108231i \(-0.965481\pi\)
0.994126 0.108231i \(-0.0345187\pi\)
\(522\) 0 0
\(523\) −320.482 + 185.031i −0.612777 + 0.353787i −0.774051 0.633123i \(-0.781773\pi\)
0.161275 + 0.986910i \(0.448440\pi\)
\(524\) 0 0
\(525\) 27.6832 + 16.8726i 0.0527298 + 0.0321383i
\(526\) 0 0
\(527\) 679.442 392.276i 1.28926 0.744357i
\(528\) 0 0
\(529\) −426.805 −0.806814
\(530\) 0 0
\(531\) −439.241 282.245i −0.827196 0.531535i
\(532\) 0 0
\(533\) −71.0232 123.016i −0.133252 0.230799i
\(534\) 0 0
\(535\) −2.68281 + 1.54892i −0.00501459 + 0.00289518i
\(536\) 0 0
\(537\) 7.62943 12.5177i 0.0142075 0.0233105i
\(538\) 0 0
\(539\) 383.600 0.711689
\(540\) 0 0
\(541\) 145.381 + 251.807i 0.268726 + 0.465447i 0.968533 0.248885i \(-0.0800640\pi\)
−0.699807 + 0.714332i \(0.746731\pi\)
\(542\) 0 0
\(543\) 403.638 + 9.59602i 0.743347 + 0.0176722i
\(544\) 0 0
\(545\) 795.101i 1.45890i
\(546\) 0 0
\(547\) 608.607 + 351.380i 1.11263 + 0.642376i 0.939509 0.342525i \(-0.111282\pi\)
0.173119 + 0.984901i \(0.444616\pi\)
\(548\) 0 0
\(549\) 263.567 + 12.5391i 0.480085 + 0.0228398i
\(550\) 0 0
\(551\) 52.1778 + 187.727i 0.0946965 + 0.340703i
\(552\) 0 0
\(553\) 31.1040 17.9579i 0.0562459 0.0324736i
\(554\) 0 0
\(555\) −388.149 9.22779i −0.699367 0.0166266i
\(556\) 0 0
\(557\) −389.549 674.718i −0.699369 1.21134i −0.968685 0.248291i \(-0.920131\pi\)
0.269316 0.963052i \(-0.413202\pi\)
\(558\) 0 0
\(559\) 26.1721i 0.0468194i
\(560\) 0 0
\(561\) 404.224 + 246.370i 0.720542 + 0.439163i
\(562\) 0 0
\(563\) 246.738 + 142.454i 0.438256 + 0.253028i 0.702858 0.711330i \(-0.251907\pi\)
−0.264601 + 0.964358i \(0.585240\pi\)
\(564\) 0 0
\(565\) 199.112i 0.352410i
\(566\) 0 0
\(567\) 80.8785 + 7.71298i 0.142643 + 0.0136031i
\(568\) 0 0
\(569\) 589.255 340.206i 1.03560 0.597902i 0.117014 0.993130i \(-0.462668\pi\)
0.918583 + 0.395228i \(0.129334\pi\)
\(570\) 0 0
\(571\) −82.1934 + 142.363i −0.143946 + 0.249323i −0.928979 0.370131i \(-0.879313\pi\)
0.785033 + 0.619454i \(0.212646\pi\)
\(572\) 0 0
\(573\) 21.9828 924.665i 0.0383645 1.61373i
\(574\) 0 0
\(575\) 54.4578 94.3237i 0.0947092 0.164041i
\(576\) 0 0
\(577\) 203.019 0.351852 0.175926 0.984403i \(-0.443708\pi\)
0.175926 + 0.984403i \(0.443708\pi\)
\(578\) 0 0
\(579\) −722.637 17.1799i −1.24808 0.0296716i
\(580\) 0 0
\(581\) 40.9080 70.8548i 0.0704097 0.121953i
\(582\) 0 0
\(583\) 621.589 + 358.875i 1.06619 + 0.615565i
\(584\) 0 0
\(585\) −57.9949 37.2660i −0.0991366 0.0637026i
\(586\) 0 0
\(587\) −145.425 −0.247742 −0.123871 0.992298i \(-0.539531\pi\)
−0.123871 + 0.992298i \(0.539531\pi\)
\(588\) 0 0
\(589\) −202.196 727.468i −0.343286 1.23509i
\(590\) 0 0
\(591\) 171.306 + 104.409i 0.289857 + 0.176665i
\(592\) 0 0
\(593\) −496.970 860.778i −0.838061 1.45156i −0.891513 0.452994i \(-0.850356\pi\)
0.0534521 0.998570i \(-0.482978\pi\)
\(594\) 0 0
\(595\) −37.3447 64.6828i −0.0627641 0.108711i
\(596\) 0 0
\(597\) −13.7435 + 578.093i −0.0230209 + 0.968329i
\(598\) 0 0
\(599\) 479.940i 0.801235i 0.916245 + 0.400617i \(0.131204\pi\)
−0.916245 + 0.400617i \(0.868796\pi\)
\(600\) 0 0
\(601\) −712.751 + 411.507i −1.18594 + 0.684704i −0.957382 0.288826i \(-0.906735\pi\)
−0.228560 + 0.973530i \(0.573402\pi\)
\(602\) 0 0
\(603\) 765.969 394.944i 1.27026 0.654965i
\(604\) 0 0
\(605\) −215.431 −0.356084
\(606\) 0 0
\(607\) −371.185 214.304i −0.611508 0.353054i 0.162048 0.986783i \(-0.448190\pi\)
−0.773555 + 0.633729i \(0.781524\pi\)
\(608\) 0 0
\(609\) −16.0598 + 26.3496i −0.0263708 + 0.0432670i
\(610\) 0 0
\(611\) 61.5339 + 35.5266i 0.100710 + 0.0581450i
\(612\) 0 0
\(613\) 40.2965 69.7956i 0.0657365 0.113859i −0.831284 0.555848i \(-0.812394\pi\)
0.897020 + 0.441989i \(0.145727\pi\)
\(614\) 0 0
\(615\) 379.331 + 694.642i 0.616798 + 1.12950i
\(616\) 0 0
\(617\) 154.136 0.249815 0.124907 0.992168i \(-0.460137\pi\)
0.124907 + 0.992168i \(0.460137\pi\)
\(618\) 0 0
\(619\) 115.167 + 199.476i 0.186054 + 0.322255i 0.943931 0.330143i \(-0.107097\pi\)
−0.757877 + 0.652397i \(0.773763\pi\)
\(620\) 0 0
\(621\) 19.4469 272.254i 0.0313154 0.438412i
\(622\) 0 0
\(623\) −84.3785 48.7159i −0.135439 0.0781957i
\(624\) 0 0
\(625\) 119.787 + 207.477i 0.191659 + 0.331963i
\(626\) 0 0
\(627\) 326.773 317.452i 0.521168 0.506303i
\(628\) 0 0
\(629\) −586.665 338.711i −0.932695 0.538492i
\(630\) 0 0
\(631\) −504.397 873.641i −0.799362 1.38453i −0.920032 0.391842i \(-0.871838\pi\)
0.120671 0.992693i \(-0.461495\pi\)
\(632\) 0 0
\(633\) −83.9393 1.99556i −0.132606 0.00315255i
\(634\) 0 0
\(635\) 406.523 + 234.706i 0.640194 + 0.369616i
\(636\) 0 0
\(637\) −84.4069 48.7324i −0.132507 0.0765029i
\(638\) 0 0
\(639\) −44.3912 + 933.086i −0.0694697 + 1.46023i
\(640\) 0 0
\(641\) 554.858i 0.865613i 0.901487 + 0.432806i \(0.142477\pi\)
−0.901487 + 0.432806i \(0.857523\pi\)
\(642\) 0 0
\(643\) −303.297 525.326i −0.471691 0.816993i 0.527785 0.849378i \(-0.323023\pi\)
−0.999475 + 0.0323857i \(0.989690\pi\)
\(644\) 0 0
\(645\) −3.46591 + 145.787i −0.00537350 + 0.226026i
\(646\) 0 0
\(647\) −955.421 −1.47669 −0.738347 0.674421i \(-0.764393\pi\)
−0.738347 + 0.674421i \(0.764393\pi\)
\(648\) 0 0
\(649\) −401.550 231.835i −0.618722 0.357219i
\(650\) 0 0
\(651\) 62.2339 102.108i 0.0955973 0.156848i
\(652\) 0 0
\(653\) 111.484 193.096i 0.170726 0.295706i −0.767948 0.640512i \(-0.778722\pi\)
0.938674 + 0.344806i \(0.112055\pi\)
\(654\) 0 0
\(655\) 111.017 192.288i 0.169492 0.293569i
\(656\) 0 0
\(657\) 506.262 + 24.0852i 0.770567 + 0.0366594i
\(658\) 0 0
\(659\) −733.409 423.434i −1.11291 0.642540i −0.173330 0.984864i \(-0.555453\pi\)
−0.939582 + 0.342323i \(0.888786\pi\)
\(660\) 0 0
\(661\) 664.232i 1.00489i −0.864609 0.502445i \(-0.832434\pi\)
0.864609 0.502445i \(-0.167566\pi\)
\(662\) 0 0
\(663\) −57.6461 105.563i −0.0869474 0.159221i
\(664\) 0 0
\(665\) −69.2550 + 19.2490i −0.104143 + 0.0289459i
\(666\) 0 0
\(667\) 89.7799 + 51.8344i 0.134602 + 0.0777128i
\(668\) 0 0
\(669\) −288.681 + 473.644i −0.431511 + 0.707987i
\(670\) 0 0
\(671\) 234.332 0.349228
\(672\) 0 0
\(673\) 669.446 386.505i 0.994719 0.574301i 0.0880375 0.996117i \(-0.471940\pi\)
0.906681 + 0.421816i \(0.138607\pi\)
\(674\) 0 0
\(675\) −240.921 163.028i −0.356920 0.241522i
\(676\) 0 0
\(677\) 367.895 212.404i 0.543419 0.313743i −0.203044 0.979170i \(-0.565084\pi\)
0.746464 + 0.665426i \(0.231750\pi\)
\(678\) 0 0
\(679\) −147.673 + 85.2590i −0.217486 + 0.125565i
\(680\) 0 0
\(681\) 1162.44 + 27.6356i 1.70695 + 0.0405809i
\(682\) 0 0
\(683\) 516.511i 0.756239i −0.925757 0.378119i \(-0.876571\pi\)
0.925757 0.378119i \(-0.123429\pi\)
\(684\) 0 0
\(685\) −291.807 −0.425995
\(686\) 0 0
\(687\) 506.289 276.475i 0.736956 0.402438i
\(688\) 0 0
\(689\) −91.1824 157.932i −0.132340 0.229220i
\(690\) 0 0
\(691\) 586.356 + 1015.60i 0.848561 + 1.46975i 0.882492 + 0.470327i \(0.155864\pi\)
−0.0339306 + 0.999424i \(0.510803\pi\)
\(692\) 0 0
\(693\) 72.0706 + 3.42873i 0.103998 + 0.00494766i
\(694\) 0 0
\(695\) −369.695 640.330i −0.531935 0.921338i
\(696\) 0 0
\(697\) 1380.93i 1.98125i
\(698\) 0 0
\(699\) −243.699 + 133.080i −0.348640 + 0.190386i
\(700\) 0 0
\(701\) −638.858 + 1106.53i −0.911352 + 1.57851i −0.0991952 + 0.995068i \(0.531627\pi\)
−0.812157 + 0.583440i \(0.801706\pi\)
\(702\) 0 0
\(703\) −456.687 + 465.263i −0.649625 + 0.661825i
\(704\) 0 0
\(705\) −338.058 206.043i −0.479515 0.292260i
\(706\) 0 0
\(707\) 123.185 0.174236
\(708\) 0 0
\(709\) −487.184 + 843.828i −0.687143 + 1.19017i 0.285615 + 0.958344i \(0.407802\pi\)
−0.972758 + 0.231822i \(0.925531\pi\)
\(710\) 0 0
\(711\) −286.432 + 147.688i −0.402858 + 0.207719i
\(712\) 0 0
\(713\) −347.909 200.865i −0.487951 0.281718i
\(714\) 0 0
\(715\) −53.0184 30.6102i −0.0741516 0.0428115i
\(716\) 0 0
\(717\) 666.597 364.016i 0.929703 0.507693i
\(718\) 0 0
\(719\) −627.049 + 1086.08i −0.872113 + 1.51054i −0.0123064 + 0.999924i \(0.503917\pi\)
−0.859807 + 0.510620i \(0.829416\pi\)
\(720\) 0 0
\(721\) 3.46822i 0.00481029i
\(722\) 0 0
\(723\) −239.844 439.210i −0.331735 0.607483i
\(724\) 0 0
\(725\) 95.6838 55.2431i 0.131978 0.0761974i
\(726\) 0 0
\(727\) −107.976 −0.148522 −0.0742611 0.997239i \(-0.523660\pi\)
−0.0742611 + 0.997239i \(0.523660\pi\)
\(728\) 0 0
\(729\) −721.599 103.615i −0.989848 0.142133i
\(730\) 0 0
\(731\) −127.218 + 220.348i −0.174033 + 0.301434i
\(732\) 0 0
\(733\) −579.104 + 1003.04i −0.790046 + 1.36840i 0.135892 + 0.990724i \(0.456610\pi\)
−0.925938 + 0.377676i \(0.876723\pi\)
\(734\) 0 0
\(735\) 463.720 + 282.632i 0.630911 + 0.384534i
\(736\) 0 0
\(737\) 662.803 382.669i 0.899325 0.519226i
\(738\) 0 0
\(739\) −380.668 + 659.336i −0.515112 + 0.892201i 0.484734 + 0.874662i \(0.338916\pi\)
−0.999846 + 0.0175390i \(0.994417\pi\)
\(740\) 0 0
\(741\) −112.231 + 28.3387i −0.151459 + 0.0382438i
\(742\) 0 0
\(743\) 211.718 122.235i 0.284950 0.164516i −0.350712 0.936483i \(-0.614060\pi\)
0.635662 + 0.771967i \(0.280727\pi\)
\(744\) 0 0
\(745\) 1.44066 2.49529i 0.00193377 0.00334938i
\(746\) 0 0
\(747\) −396.858 + 617.605i −0.531268 + 0.826781i
\(748\) 0 0
\(749\) −0.713446 + 0.411908i −0.000952531 + 0.000549944i
\(750\) 0 0
\(751\) 1293.40i 1.72224i 0.508403 + 0.861119i \(0.330236\pi\)
−0.508403 + 0.861119i \(0.669764\pi\)
\(752\) 0 0
\(753\) 8.78679 369.599i 0.0116690 0.490835i
\(754\) 0 0
\(755\) −237.460 137.097i −0.314516 0.181586i
\(756\) 0 0
\(757\) −744.651 + 1289.77i −0.983687 + 1.70380i −0.336053 + 0.941843i \(0.609092\pi\)
−0.647633 + 0.761952i \(0.724241\pi\)
\(758\) 0 0
\(759\) 5.76111 242.330i 0.00759040 0.319275i
\(760\) 0 0
\(761\) −668.295 + 1157.52i −0.878181 + 1.52105i −0.0248450 + 0.999691i \(0.507909\pi\)
−0.853336 + 0.521362i \(0.825424\pi\)
\(762\) 0 0
\(763\) 211.443i 0.277121i
\(764\) 0 0
\(765\) 307.128 + 595.655i 0.401474 + 0.778634i
\(766\) 0 0
\(767\) 58.9044 + 102.025i 0.0767984 + 0.133019i
\(768\) 0 0
\(769\) −1380.60 −1.79532 −0.897659 0.440690i \(-0.854734\pi\)
−0.897659 + 0.440690i \(0.854734\pi\)
\(770\) 0 0
\(771\) −126.339 + 207.286i −0.163863 + 0.268853i
\(772\) 0 0
\(773\) −0.163790 + 0.0945641i −0.000211889 + 0.000122334i −0.500106 0.865964i \(-0.666706\pi\)
0.499894 + 0.866087i \(0.333372\pi\)
\(774\) 0 0
\(775\) −370.787 + 214.074i −0.478435 + 0.276225i
\(776\) 0 0
\(777\) −103.221 2.45397i −0.132846 0.00315826i
\(778\) 0 0
\(779\) 1286.85 + 332.013i 1.65193 + 0.426204i
\(780\) 0 0
\(781\) 829.588i 1.06221i
\(782\) 0 0
\(783\) 155.174 229.315i 0.198179 0.292867i
\(784\) 0 0
\(785\) 21.2440 36.7957i 0.0270624 0.0468735i
\(786\) 0 0
\(787\) −936.257 540.548i −1.18965 0.686847i −0.231426 0.972853i \(-0.574339\pi\)
−0.958228 + 0.286006i \(0.907672\pi\)
\(788\) 0 0
\(789\) −398.729 243.021i −0.505360 0.308012i
\(790\) 0 0
\(791\) 52.9503i 0.0669409i
\(792\) 0 0
\(793\) −51.5621 29.7694i −0.0650216 0.0375402i
\(794\) 0 0
\(795\) 487.000 + 891.809i 0.612578 + 1.12177i
\(796\) 0 0
\(797\) −858.884 495.877i