Properties

Label 684.3.m.a.353.12
Level $684$
Weight $3$
Character 684.353
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.m (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 353.12
Character \(\chi\) \(=\) 684.353
Dual form 684.3.m.a.653.12

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.70356 - 2.46939i) q^{3} -9.28650i q^{5} +(-2.28067 + 3.95023i) q^{7} +(-3.19575 + 8.41351i) q^{9} +O(q^{10})\) \(q+(-1.70356 - 2.46939i) q^{3} -9.28650i q^{5} +(-2.28067 + 3.95023i) q^{7} +(-3.19575 + 8.41351i) q^{9} +(-1.10584 - 0.638454i) q^{11} +(-3.30958 + 5.73235i) q^{13} +(-22.9320 + 15.8201i) q^{15} +(-11.0966 - 6.40664i) q^{17} +(-18.7585 + 3.01961i) q^{19} +(13.6399 - 1.09762i) q^{21} +(16.3480 + 9.43853i) q^{23} -61.2390 q^{25} +(26.2204 - 6.44140i) q^{27} -7.10485i q^{29} +(7.90302 + 13.6884i) q^{31} +(0.307269 + 3.81838i) q^{33} +(36.6838 + 21.1794i) q^{35} -16.9760 q^{37} +(19.7935 - 1.59280i) q^{39} -17.6906i q^{41} +(20.8849 + 36.1738i) q^{43} +(78.1321 + 29.6773i) q^{45} -22.7792i q^{47} +(14.0971 + 24.4169i) q^{49} +(3.08332 + 38.3160i) q^{51} +(5.86723 - 3.38745i) q^{53} +(-5.92901 + 10.2693i) q^{55} +(39.4129 + 41.1779i) q^{57} +82.7526i q^{59} +47.4838 q^{61} +(-25.9469 - 31.8124i) q^{63} +(53.2335 + 30.7344i) q^{65} +(21.3601 - 36.9968i) q^{67} +(-4.54247 - 56.4487i) q^{69} +(-21.4678 - 12.3945i) q^{71} +(-39.6934 + 68.7509i) q^{73} +(104.325 + 151.223i) q^{75} +(5.04409 - 2.91221i) q^{77} +(-54.2353 - 93.9382i) q^{79} +(-60.5744 - 53.7749i) q^{81} +(34.7029 + 20.0357i) q^{83} +(-59.4952 + 103.049i) q^{85} +(-17.5446 + 12.1036i) q^{87} +(-49.2445 + 28.4313i) q^{89} +(-15.0961 - 26.1472i) q^{91} +(20.3387 - 42.8347i) q^{93} +(28.0416 + 174.201i) q^{95} +(-86.8612 - 150.448i) q^{97} +(8.90562 - 7.26362i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + O(q^{10}) \) \( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(325\) \(343\) \(533\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\)

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
\(3\) −1.70356 2.46939i −0.567854 0.823129i
\(4\) 0 0
\(5\) 9.28650i 1.85730i −0.370958 0.928650i \(-0.620971\pi\)
0.370958 0.928650i \(-0.379029\pi\)
\(6\) 0 0
\(7\) −2.28067 + 3.95023i −0.325810 + 0.564319i −0.981676 0.190558i \(-0.938970\pi\)
0.655866 + 0.754877i \(0.272304\pi\)
\(8\) 0 0
\(9\) −3.19575 + 8.41351i −0.355083 + 0.934835i
\(10\) 0 0
\(11\) −1.10584 0.638454i −0.100531 0.0580413i 0.448892 0.893586i \(-0.351819\pi\)
−0.549422 + 0.835545i \(0.685152\pi\)
\(12\) 0 0
\(13\) −3.30958 + 5.73235i −0.254583 + 0.440950i −0.964782 0.263050i \(-0.915271\pi\)
0.710199 + 0.704001i \(0.248605\pi\)
\(14\) 0 0
\(15\) −22.9320 + 15.8201i −1.52880 + 1.05468i
\(16\) 0 0
\(17\) −11.0966 6.40664i −0.652743 0.376861i 0.136764 0.990604i \(-0.456330\pi\)
−0.789506 + 0.613743i \(0.789663\pi\)
\(18\) 0 0
\(19\) −18.7585 + 3.01961i −0.987290 + 0.158927i
\(20\) 0 0
\(21\) 13.6399 1.09762i 0.649520 0.0522674i
\(22\) 0 0
\(23\) 16.3480 + 9.43853i 0.710783 + 0.410371i 0.811351 0.584559i \(-0.198733\pi\)
−0.100568 + 0.994930i \(0.532066\pi\)
\(24\) 0 0
\(25\) −61.2390 −2.44956
\(26\) 0 0
\(27\) 26.2204 6.44140i 0.971125 0.238570i
\(28\) 0 0
\(29\) 7.10485i 0.244995i −0.992469 0.122497i \(-0.960910\pi\)
0.992469 0.122497i \(-0.0390903\pi\)
\(30\) 0 0
\(31\) 7.90302 + 13.6884i 0.254936 + 0.441562i 0.964878 0.262698i \(-0.0846123\pi\)
−0.709942 + 0.704260i \(0.751279\pi\)
\(32\) 0 0
\(33\) 0.307269 + 3.81838i 0.00931117 + 0.115709i
\(34\) 0 0
\(35\) 36.6838 + 21.1794i 1.04811 + 0.605126i
\(36\) 0 0
\(37\) −16.9760 −0.458810 −0.229405 0.973331i \(-0.573678\pi\)
−0.229405 + 0.973331i \(0.573678\pi\)
\(38\) 0 0
\(39\) 19.7935 1.59280i 0.507525 0.0408410i
\(40\) 0 0
\(41\) 17.6906i 0.431477i −0.976451 0.215739i \(-0.930784\pi\)
0.976451 0.215739i \(-0.0692159\pi\)
\(42\) 0 0
\(43\) 20.8849 + 36.1738i 0.485696 + 0.841251i 0.999865 0.0164385i \(-0.00523277\pi\)
−0.514169 + 0.857689i \(0.671899\pi\)
\(44\) 0 0
\(45\) 78.1321 + 29.6773i 1.73627 + 0.659496i
\(46\) 0 0
\(47\) 22.7792i 0.484665i −0.970193 0.242332i \(-0.922088\pi\)
0.970193 0.242332i \(-0.0779124\pi\)
\(48\) 0 0
\(49\) 14.0971 + 24.4169i 0.287696 + 0.498304i
\(50\) 0 0
\(51\) 3.08332 + 38.3160i 0.0604572 + 0.751294i
\(52\) 0 0
\(53\) 5.86723 3.38745i 0.110702 0.0639141i −0.443626 0.896212i \(-0.646308\pi\)
0.554329 + 0.832298i \(0.312975\pi\)
\(54\) 0 0
\(55\) −5.92901 + 10.2693i −0.107800 + 0.186715i
\(56\) 0 0
\(57\) 39.4129 + 41.1779i 0.691454 + 0.722420i
\(58\) 0 0
\(59\) 82.7526i 1.40259i 0.712873 + 0.701293i \(0.247394\pi\)
−0.712873 + 0.701293i \(0.752606\pi\)
\(60\) 0 0
\(61\) 47.4838 0.778423 0.389211 0.921148i \(-0.372748\pi\)
0.389211 + 0.921148i \(0.372748\pi\)
\(62\) 0 0
\(63\) −25.9469 31.8124i −0.411855 0.504959i
\(64\) 0 0
\(65\) 53.2335 + 30.7344i 0.818977 + 0.472836i
\(66\) 0 0
\(67\) 21.3601 36.9968i 0.318807 0.552190i −0.661432 0.750005i \(-0.730051\pi\)
0.980239 + 0.197815i \(0.0633844\pi\)
\(68\) 0 0
\(69\) −4.54247 56.4487i −0.0658330 0.818097i
\(70\) 0 0
\(71\) −21.4678 12.3945i −0.302364 0.174570i 0.341140 0.940012i \(-0.389187\pi\)
−0.643504 + 0.765442i \(0.722520\pi\)
\(72\) 0 0
\(73\) −39.6934 + 68.7509i −0.543745 + 0.941793i 0.454940 + 0.890522i \(0.349661\pi\)
−0.998685 + 0.0512713i \(0.983673\pi\)
\(74\) 0 0
\(75\) 104.325 + 151.223i 1.39099 + 2.01631i
\(76\) 0 0
\(77\) 5.04409 2.91221i 0.0655076 0.0378209i
\(78\) 0 0
\(79\) −54.2353 93.9382i −0.686522 1.18909i −0.972956 0.230991i \(-0.925803\pi\)
0.286434 0.958100i \(-0.407530\pi\)
\(80\) 0 0
\(81\) −60.5744 53.7749i −0.747832 0.663888i
\(82\) 0 0
\(83\) 34.7029 + 20.0357i 0.418107 + 0.241394i 0.694267 0.719717i \(-0.255729\pi\)
−0.276160 + 0.961112i \(0.589062\pi\)
\(84\) 0 0
\(85\) −59.4952 + 103.049i −0.699944 + 1.21234i
\(86\) 0 0
\(87\) −17.5446 + 12.1036i −0.201662 + 0.139121i
\(88\) 0 0
\(89\) −49.2445 + 28.4313i −0.553309 + 0.319453i −0.750455 0.660921i \(-0.770166\pi\)
0.197147 + 0.980374i \(0.436832\pi\)
\(90\) 0 0
\(91\) −15.0961 26.1472i −0.165891 0.287332i
\(92\) 0 0
\(93\) 20.3387 42.8347i 0.218696 0.460588i
\(94\) 0 0
\(95\) 28.0416 + 174.201i 0.295175 + 1.83369i
\(96\) 0 0
\(97\) −86.8612 150.448i −0.895477 1.55101i −0.833214 0.552951i \(-0.813502\pi\)
−0.0622629 0.998060i \(-0.519832\pi\)
\(98\) 0 0
\(99\) 8.90562 7.26362i 0.0899557 0.0733699i
\(100\) 0 0
\(101\) 88.8592i 0.879794i 0.898048 + 0.439897i \(0.144985\pi\)
−0.898048 + 0.439897i \(0.855015\pi\)
\(102\) 0 0
\(103\) 43.5924 + 75.5043i 0.423227 + 0.733051i 0.996253 0.0864862i \(-0.0275639\pi\)
−0.573026 + 0.819537i \(0.694231\pi\)
\(104\) 0 0
\(105\) −10.1930 126.667i −0.0970763 1.20635i
\(106\) 0 0
\(107\) 85.1392i 0.795693i 0.917452 + 0.397847i \(0.130242\pi\)
−0.917452 + 0.397847i \(0.869758\pi\)
\(108\) 0 0
\(109\) −103.317 + 178.950i −0.947861 + 1.64174i −0.197941 + 0.980214i \(0.563426\pi\)
−0.749919 + 0.661529i \(0.769908\pi\)
\(110\) 0 0
\(111\) 28.9196 + 41.9203i 0.260537 + 0.377660i
\(112\) 0 0
\(113\) −180.905 + 104.445i −1.60093 + 0.924296i −0.609625 + 0.792690i \(0.708680\pi\)
−0.991302 + 0.131605i \(0.957987\pi\)
\(114\) 0 0
\(115\) 87.6509 151.816i 0.762181 1.32014i
\(116\) 0 0
\(117\) −37.6526 46.1643i −0.321817 0.394567i
\(118\) 0 0
\(119\) 50.6154 29.2228i 0.425340 0.245570i
\(120\) 0 0
\(121\) −59.6848 103.377i −0.493262 0.854356i
\(122\) 0 0
\(123\) −43.6849 + 30.1370i −0.355162 + 0.245016i
\(124\) 0 0
\(125\) 336.534i 2.69227i
\(126\) 0 0
\(127\) 56.4818 + 97.8294i 0.444739 + 0.770310i 0.998034 0.0626751i \(-0.0199632\pi\)
−0.553295 + 0.832985i \(0.686630\pi\)
\(128\) 0 0
\(129\) 53.7483 113.197i 0.416653 0.877499i
\(130\) 0 0
\(131\) 8.51243i 0.0649803i 0.999472 + 0.0324902i \(0.0103438\pi\)
−0.999472 + 0.0324902i \(0.989656\pi\)
\(132\) 0 0
\(133\) 30.8538 80.9873i 0.231983 0.608927i
\(134\) 0 0
\(135\) −59.8181 243.495i −0.443097 1.80367i
\(136\) 0 0
\(137\) 214.194i 1.56346i −0.623618 0.781729i \(-0.714338\pi\)
0.623618 0.781729i \(-0.285662\pi\)
\(138\) 0 0
\(139\) 25.7715 44.6376i 0.185407 0.321134i −0.758307 0.651898i \(-0.773973\pi\)
0.943713 + 0.330764i \(0.107306\pi\)
\(140\) 0 0
\(141\) −56.2508 + 38.8059i −0.398942 + 0.275219i
\(142\) 0 0
\(143\) 7.31969 4.22603i 0.0511867 0.0295526i
\(144\) 0 0
\(145\) −65.9792 −0.455029
\(146\) 0 0
\(147\) 36.2795 76.4069i 0.246799 0.519775i
\(148\) 0 0
\(149\) 143.809i 0.965164i −0.875851 0.482582i \(-0.839699\pi\)
0.875851 0.482582i \(-0.160301\pi\)
\(150\) 0 0
\(151\) 109.749 190.090i 0.726813 1.25888i −0.231411 0.972856i \(-0.574334\pi\)
0.958223 0.286021i \(-0.0923326\pi\)
\(152\) 0 0
\(153\) 89.3644 72.8876i 0.584081 0.476389i
\(154\) 0 0
\(155\) 127.118 73.3913i 0.820113 0.473493i
\(156\) 0 0
\(157\) −31.4750 −0.200477 −0.100239 0.994963i \(-0.531961\pi\)
−0.100239 + 0.994963i \(0.531961\pi\)
\(158\) 0 0
\(159\) −18.3601 8.71774i −0.115472 0.0548286i
\(160\) 0 0
\(161\) −74.5688 + 43.0523i −0.463160 + 0.267406i
\(162\) 0 0
\(163\) −27.3667 −0.167894 −0.0839469 0.996470i \(-0.526753\pi\)
−0.0839469 + 0.996470i \(0.526753\pi\)
\(164\) 0 0
\(165\) 35.4594 2.85345i 0.214906 0.0172936i
\(166\) 0 0
\(167\) 200.623 + 115.830i 1.20134 + 0.693592i 0.960852 0.277061i \(-0.0893603\pi\)
0.240485 + 0.970653i \(0.422694\pi\)
\(168\) 0 0
\(169\) 62.5934 + 108.415i 0.370375 + 0.641509i
\(170\) 0 0
\(171\) 34.5420 167.475i 0.202000 0.979386i
\(172\) 0 0
\(173\) −103.634 + 59.8331i −0.599041 + 0.345856i −0.768664 0.639653i \(-0.779078\pi\)
0.169623 + 0.985509i \(0.445745\pi\)
\(174\) 0 0
\(175\) 139.666 241.908i 0.798091 1.38233i
\(176\) 0 0
\(177\) 204.348 140.974i 1.15451 0.796465i
\(178\) 0 0
\(179\) 182.887i 1.02171i 0.859666 + 0.510856i \(0.170672\pi\)
−0.859666 + 0.510856i \(0.829328\pi\)
\(180\) 0 0
\(181\) 77.9550 + 135.022i 0.430691 + 0.745978i 0.996933 0.0782606i \(-0.0249366\pi\)
−0.566242 + 0.824239i \(0.691603\pi\)
\(182\) 0 0
\(183\) −80.8916 117.256i −0.442031 0.640743i
\(184\) 0 0
\(185\) 157.647i 0.852148i
\(186\) 0 0
\(187\) 8.18069 + 14.1694i 0.0437470 + 0.0757721i
\(188\) 0 0
\(189\) −34.3550 + 118.267i −0.181772 + 0.625753i
\(190\) 0 0
\(191\) −292.923 169.119i −1.53363 0.885440i −0.999190 0.0402304i \(-0.987191\pi\)
−0.534436 0.845209i \(-0.679476\pi\)
\(192\) 0 0
\(193\) −213.007 −1.10366 −0.551832 0.833955i \(-0.686071\pi\)
−0.551832 + 0.833955i \(0.686071\pi\)
\(194\) 0 0
\(195\) −14.7915 183.812i −0.0758539 0.942626i
\(196\) 0 0
\(197\) 7.74954i 0.0393378i 0.999807 + 0.0196689i \(0.00626120\pi\)
−0.999807 + 0.0196689i \(0.993739\pi\)
\(198\) 0 0
\(199\) −149.979 259.771i −0.753662 1.30538i −0.946037 0.324059i \(-0.894952\pi\)
0.192375 0.981321i \(-0.438381\pi\)
\(200\) 0 0
\(201\) −127.748 + 10.2800i −0.635560 + 0.0511441i
\(202\) 0 0
\(203\) 28.0658 + 16.2038i 0.138255 + 0.0798217i
\(204\) 0 0
\(205\) −164.283 −0.801383
\(206\) 0 0
\(207\) −131.655 + 107.381i −0.636016 + 0.518749i
\(208\) 0 0
\(209\) 22.6717 + 8.63726i 0.108477 + 0.0413266i
\(210\) 0 0
\(211\) −368.255 −1.74528 −0.872641 0.488362i \(-0.837595\pi\)
−0.872641 + 0.488362i \(0.837595\pi\)
\(212\) 0 0
\(213\) 5.96508 + 74.1272i 0.0280050 + 0.348015i
\(214\) 0 0
\(215\) 335.928 193.948i 1.56245 0.902083i
\(216\) 0 0
\(217\) −72.0966 −0.332243
\(218\) 0 0
\(219\) 237.393 19.1032i 1.08399 0.0872292i
\(220\) 0 0
\(221\) 73.4502 42.4065i 0.332354 0.191885i
\(222\) 0 0
\(223\) 76.6100 + 132.692i 0.343543 + 0.595033i 0.985088 0.172052i \(-0.0550397\pi\)
−0.641545 + 0.767085i \(0.721706\pi\)
\(224\) 0 0
\(225\) 195.705 515.235i 0.869798 2.28993i
\(226\) 0 0
\(227\) 119.451 + 68.9649i 0.526214 + 0.303810i 0.739474 0.673186i \(-0.235075\pi\)
−0.213259 + 0.976996i \(0.568408\pi\)
\(228\) 0 0
\(229\) −84.2944 146.002i −0.368098 0.637564i 0.621170 0.783676i \(-0.286657\pi\)
−0.989268 + 0.146112i \(0.953324\pi\)
\(230\) 0 0
\(231\) −15.7843 7.49468i −0.0683302 0.0324445i
\(232\) 0 0
\(233\) −257.617 148.735i −1.10565 0.638348i −0.167952 0.985795i \(-0.553715\pi\)
−0.937700 + 0.347447i \(0.887049\pi\)
\(234\) 0 0
\(235\) −211.539 −0.900167
\(236\) 0 0
\(237\) −139.577 + 293.957i −0.588931 + 1.24033i
\(238\) 0 0
\(239\) −277.929 + 160.462i −1.16288 + 0.671391i −0.951993 0.306119i \(-0.900969\pi\)
−0.210889 + 0.977510i \(0.567636\pi\)
\(240\) 0 0
\(241\) −393.874 −1.63433 −0.817167 0.576402i \(-0.804456\pi\)
−0.817167 + 0.576402i \(0.804456\pi\)
\(242\) 0 0
\(243\) −29.5990 + 241.191i −0.121806 + 0.992554i
\(244\) 0 0
\(245\) 226.747 130.913i 0.925500 0.534338i
\(246\) 0 0
\(247\) 44.7732 117.524i 0.181268 0.475806i
\(248\) 0 0
\(249\) −9.64259 119.827i −0.0387252 0.481233i
\(250\) 0 0
\(251\) 320.034 184.772i 1.27504 0.736142i 0.299104 0.954220i \(-0.403312\pi\)
0.975931 + 0.218078i \(0.0699788\pi\)
\(252\) 0 0
\(253\) −12.0521 20.8749i −0.0476369 0.0825096i
\(254\) 0 0
\(255\) 355.821 28.6332i 1.39538 0.112287i
\(256\) 0 0
\(257\) 159.326 + 91.9868i 0.619945 + 0.357925i 0.776847 0.629689i \(-0.216818\pi\)
−0.156903 + 0.987614i \(0.550151\pi\)
\(258\) 0 0
\(259\) 38.7166 67.0591i 0.149485 0.258915i
\(260\) 0 0
\(261\) 59.7767 + 22.7053i 0.229030 + 0.0869935i
\(262\) 0 0
\(263\) −146.456 + 84.5564i −0.556867 + 0.321507i −0.751887 0.659292i \(-0.770856\pi\)
0.195020 + 0.980799i \(0.437523\pi\)
\(264\) 0 0
\(265\) −31.4575 54.4860i −0.118708 0.205608i
\(266\) 0 0
\(267\) 154.099 + 73.1692i 0.577150 + 0.274042i
\(268\) 0 0
\(269\) 0.505277 + 0.291722i 0.00187835 + 0.00108447i 0.500939 0.865483i \(-0.332988\pi\)
−0.499061 + 0.866567i \(0.666321\pi\)
\(270\) 0 0
\(271\) −173.903 + 301.208i −0.641707 + 1.11147i 0.343344 + 0.939210i \(0.388440\pi\)
−0.985052 + 0.172260i \(0.944893\pi\)
\(272\) 0 0
\(273\) −38.8504 + 81.8215i −0.142309 + 0.299712i
\(274\) 0 0
\(275\) 67.7203 + 39.0983i 0.246256 + 0.142176i
\(276\) 0 0
\(277\) −115.851 + 200.660i −0.418235 + 0.724404i −0.995762 0.0919678i \(-0.970684\pi\)
0.577527 + 0.816371i \(0.304018\pi\)
\(278\) 0 0
\(279\) −140.424 + 22.7473i −0.503311 + 0.0815317i
\(280\) 0 0
\(281\) 501.455i 1.78454i −0.451505 0.892268i \(-0.649113\pi\)
0.451505 0.892268i \(-0.350887\pi\)
\(282\) 0 0
\(283\) −46.8874 −0.165680 −0.0828399 0.996563i \(-0.526399\pi\)
−0.0828399 + 0.996563i \(0.526399\pi\)
\(284\) 0 0
\(285\) 382.399 366.008i 1.34175 1.28424i
\(286\) 0 0
\(287\) 69.8819 + 40.3463i 0.243491 + 0.140580i
\(288\) 0 0
\(289\) −62.4099 108.097i −0.215951 0.374039i
\(290\) 0 0
\(291\) −223.541 + 470.792i −0.768182 + 1.61784i
\(292\) 0 0
\(293\) −67.5883 + 39.0221i −0.230677 + 0.133181i −0.610884 0.791720i \(-0.709186\pi\)
0.380207 + 0.924901i \(0.375853\pi\)
\(294\) 0 0
\(295\) 768.482 2.60502
\(296\) 0 0
\(297\) −33.1080 9.61739i −0.111475 0.0323818i
\(298\) 0 0
\(299\) −108.210 + 62.4750i −0.361906 + 0.208947i
\(300\) 0 0
\(301\) −190.526 −0.632978
\(302\) 0 0
\(303\) 219.428 151.377i 0.724184 0.499595i
\(304\) 0 0
\(305\) 440.958i 1.44576i
\(306\) 0 0
\(307\) −13.1550 + 22.7852i −0.0428503 + 0.0742188i −0.886655 0.462431i \(-0.846977\pi\)
0.843805 + 0.536650i \(0.180311\pi\)
\(308\) 0 0
\(309\) 112.187 236.273i 0.363064 0.764637i
\(310\) 0 0
\(311\) −339.125 + 195.794i −1.09043 + 0.629562i −0.933692 0.358078i \(-0.883432\pi\)
−0.156741 + 0.987640i \(0.550099\pi\)
\(312\) 0 0
\(313\) −93.3871 −0.298361 −0.149181 0.988810i \(-0.547664\pi\)
−0.149181 + 0.988810i \(0.547664\pi\)
\(314\) 0 0
\(315\) −295.426 + 240.956i −0.937859 + 0.764939i
\(316\) 0 0
\(317\) 57.0992i 0.180124i 0.995936 + 0.0900618i \(0.0287064\pi\)
−0.995936 + 0.0900618i \(0.971294\pi\)
\(318\) 0 0
\(319\) −4.53612 + 7.85679i −0.0142198 + 0.0246294i
\(320\) 0 0
\(321\) 210.242 145.040i 0.654958 0.451838i
\(322\) 0 0
\(323\) 227.502 + 86.6715i 0.704340 + 0.268333i
\(324\) 0 0
\(325\) 202.675 351.044i 0.623616 1.08013i
\(326\) 0 0
\(327\) 617.904 49.7232i 1.88961 0.152059i
\(328\) 0 0
\(329\) 89.9833 + 51.9519i 0.273505 + 0.157908i
\(330\) 0 0
\(331\) −5.97582 + 10.3504i −0.0180538 + 0.0312702i −0.874911 0.484283i \(-0.839080\pi\)
0.856857 + 0.515554i \(0.172414\pi\)
\(332\) 0 0
\(333\) 54.2510 142.828i 0.162916 0.428912i
\(334\) 0 0
\(335\) −343.570 198.360i −1.02558 0.592121i
\(336\) 0 0
\(337\) −100.450 −0.298071 −0.149035 0.988832i \(-0.547617\pi\)
−0.149035 + 0.988832i \(0.547617\pi\)
\(338\) 0 0
\(339\) 566.099 + 268.795i 1.66991 + 0.792905i
\(340\) 0 0
\(341\) 20.1829i 0.0591873i
\(342\) 0 0
\(343\) −352.109 −1.02656
\(344\) 0 0
\(345\) −524.211 + 42.1837i −1.51945 + 0.122272i
\(346\) 0 0
\(347\) 151.374i 0.436236i 0.975922 + 0.218118i \(0.0699917\pi\)
−0.975922 + 0.218118i \(0.930008\pi\)
\(348\) 0 0
\(349\) −219.737 + 380.596i −0.629619 + 1.09053i 0.358009 + 0.933718i \(0.383456\pi\)
−0.987628 + 0.156814i \(0.949878\pi\)
\(350\) 0 0
\(351\) −49.8539 + 171.623i −0.142034 + 0.488954i
\(352\) 0 0
\(353\) 524.353 + 302.736i 1.48542 + 0.857608i 0.999862 0.0165964i \(-0.00528304\pi\)
0.485558 + 0.874204i \(0.338616\pi\)
\(354\) 0 0
\(355\) −115.101 + 199.361i −0.324229 + 0.561580i
\(356\) 0 0
\(357\) −158.389 75.2062i −0.443667 0.210662i
\(358\) 0 0
\(359\) −84.9553 49.0490i −0.236644 0.136627i 0.376989 0.926218i \(-0.376959\pi\)
−0.613633 + 0.789591i \(0.710293\pi\)
\(360\) 0 0
\(361\) 342.764 113.287i 0.949484 0.313814i
\(362\) 0 0
\(363\) −153.601 + 323.494i −0.423144 + 0.891168i
\(364\) 0 0
\(365\) 638.455 + 368.612i 1.74919 + 1.00990i
\(366\) 0 0
\(367\) −324.259 −0.883539 −0.441769 0.897129i \(-0.645649\pi\)
−0.441769 + 0.897129i \(0.645649\pi\)
\(368\) 0 0
\(369\) 148.840 + 56.5346i 0.403360 + 0.153210i
\(370\) 0 0
\(371\) 30.9026i 0.0832954i
\(372\) 0 0
\(373\) −79.8812 138.358i −0.214159 0.370934i 0.738853 0.673866i \(-0.235368\pi\)
−0.953012 + 0.302933i \(0.902034\pi\)
\(374\) 0 0
\(375\) 831.032 573.306i 2.21609 1.52882i
\(376\) 0 0
\(377\) 40.7275 + 23.5140i 0.108030 + 0.0623714i
\(378\) 0 0
\(379\) 366.244 0.966343 0.483171 0.875526i \(-0.339485\pi\)
0.483171 + 0.875526i \(0.339485\pi\)
\(380\) 0 0
\(381\) 145.358 306.134i 0.381518 0.803501i
\(382\) 0 0
\(383\) 124.052i 0.323895i 0.986799 + 0.161948i \(0.0517775\pi\)
−0.986799 + 0.161948i \(0.948222\pi\)
\(384\) 0 0
\(385\) −27.0442 46.8419i −0.0702446 0.121667i
\(386\) 0 0
\(387\) −371.092 + 60.1134i −0.958893 + 0.155332i
\(388\) 0 0
\(389\) 415.200i 1.06735i −0.845689 0.533676i \(-0.820810\pi\)
0.845689 0.533676i \(-0.179190\pi\)
\(390\) 0 0
\(391\) −120.938 209.472i −0.309306 0.535733i
\(392\) 0 0
\(393\) 21.0205 14.5014i 0.0534872 0.0368994i
\(394\) 0 0
\(395\) −872.357 + 503.656i −2.20850 + 1.27508i
\(396\) 0 0
\(397\) 247.236 428.225i 0.622760 1.07865i −0.366209 0.930532i \(-0.619345\pi\)
0.988969 0.148120i \(-0.0473220\pi\)
\(398\) 0 0
\(399\) −252.550 + 61.7769i −0.632958 + 0.154829i
\(400\) 0 0
\(401\) 299.577i 0.747075i −0.927615 0.373538i \(-0.878145\pi\)
0.927615 0.373538i \(-0.121855\pi\)
\(402\) 0 0
\(403\) −104.623 −0.259609
\(404\) 0 0
\(405\) −499.381 + 562.524i −1.23304 + 1.38895i
\(406\) 0 0
\(407\) 18.7726 + 10.8384i 0.0461244 + 0.0266299i
\(408\) 0 0
\(409\) 80.2674 139.027i 0.196253 0.339920i −0.751058 0.660237i \(-0.770456\pi\)
0.947310 + 0.320317i \(0.103789\pi\)
\(410\) 0 0
\(411\) −528.928 + 364.893i −1.28693 + 0.887817i
\(412\) 0 0
\(413\) −326.892 188.731i −0.791506 0.456976i
\(414\) 0 0
\(415\) 186.062 322.268i 0.448342 0.776550i
\(416\) 0 0
\(417\) −154.131 + 12.4030i −0.369619 + 0.0297435i
\(418\) 0 0
\(419\) 442.295 255.359i 1.05560 0.609449i 0.131386 0.991331i \(-0.458057\pi\)
0.924211 + 0.381882i \(0.124724\pi\)
\(420\) 0 0
\(421\) −176.079 304.978i −0.418241 0.724414i 0.577522 0.816375i \(-0.304020\pi\)
−0.995763 + 0.0919610i \(0.970686\pi\)
\(422\) 0 0
\(423\) 191.653 + 72.7967i 0.453081 + 0.172096i
\(424\) 0 0
\(425\) 679.547 + 392.336i 1.59893 + 0.923144i
\(426\) 0 0
\(427\) −108.295 + 187.572i −0.253618 + 0.439279i
\(428\) 0 0
\(429\) −22.9052 10.8759i −0.0533922 0.0253516i
\(430\) 0 0
\(431\) −561.436 + 324.145i −1.30264 + 0.752077i −0.980855 0.194738i \(-0.937614\pi\)
−0.321780 + 0.946815i \(0.604281\pi\)
\(432\) 0 0
\(433\) 270.752 + 468.956i 0.625293 + 1.08304i 0.988484 + 0.151325i \(0.0483539\pi\)
−0.363191 + 0.931715i \(0.618313\pi\)
\(434\) 0 0
\(435\) 112.400 + 162.928i 0.258390 + 0.374547i
\(436\) 0 0
\(437\) −335.165 127.688i −0.766968 0.292192i
\(438\) 0 0
\(439\) 230.430 + 399.117i 0.524898 + 0.909151i 0.999580 + 0.0289930i \(0.00923004\pi\)
−0.474681 + 0.880158i \(0.657437\pi\)
\(440\) 0 0
\(441\) −250.483 + 40.5759i −0.567988 + 0.0920088i
\(442\) 0 0
\(443\) 798.745i 1.80304i −0.432740 0.901519i \(-0.642453\pi\)
0.432740 0.901519i \(-0.357547\pi\)
\(444\) 0 0
\(445\) 264.027 + 457.309i 0.593320 + 1.02766i
\(446\) 0 0
\(447\) −355.121 + 244.988i −0.794455 + 0.548072i
\(448\) 0 0
\(449\) 751.768i 1.67432i 0.546962 + 0.837158i \(0.315784\pi\)
−0.546962 + 0.837158i \(0.684216\pi\)
\(450\) 0 0
\(451\) −11.2946 + 19.5629i −0.0250435 + 0.0433766i
\(452\) 0 0
\(453\) −656.371 + 52.8187i −1.44894 + 0.116598i
\(454\) 0 0
\(455\) −242.816 + 140.190i −0.533661 + 0.308109i
\(456\) 0 0
\(457\) −341.536 + 591.557i −0.747343 + 1.29444i 0.201749 + 0.979437i \(0.435338\pi\)
−0.949092 + 0.314999i \(0.897996\pi\)
\(458\) 0 0
\(459\) −332.225 96.5067i −0.723803 0.210254i
\(460\) 0 0
\(461\) −495.618 + 286.145i −1.07509 + 0.620706i −0.929569 0.368649i \(-0.879820\pi\)
−0.145525 + 0.989355i \(0.546487\pi\)
\(462\) 0 0
\(463\) 221.398 + 383.473i 0.478182 + 0.828236i 0.999687 0.0250123i \(-0.00796250\pi\)
−0.521505 + 0.853248i \(0.674629\pi\)
\(464\) 0 0
\(465\) −397.784 188.876i −0.855450 0.406184i
\(466\) 0 0
\(467\) 246.829i 0.528542i 0.964449 + 0.264271i \(0.0851313\pi\)
−0.964449 + 0.264271i \(0.914869\pi\)
\(468\) 0 0
\(469\) 97.4306 + 168.755i 0.207741 + 0.359818i
\(470\) 0 0
\(471\) 53.6196 + 77.7239i 0.113842 + 0.165019i
\(472\) 0 0
\(473\) 53.3363i 0.112762i
\(474\) 0 0
\(475\) 1148.75 184.918i 2.41843 0.389301i
\(476\) 0 0
\(477\) 9.75013 + 60.1895i 0.0204405 + 0.126183i
\(478\) 0 0
\(479\) 208.455i 0.435188i 0.976039 + 0.217594i \(0.0698209\pi\)
−0.976039 + 0.217594i \(0.930179\pi\)
\(480\) 0 0
\(481\) 56.1833 97.3123i 0.116805 0.202312i
\(482\) 0 0
\(483\) 233.345 + 110.797i 0.483117 + 0.229393i
\(484\) 0 0
\(485\) −1397.14 + 806.637i −2.88069 + 1.66317i
\(486\) 0 0
\(487\) 467.236 0.959416 0.479708 0.877428i \(-0.340743\pi\)
0.479708 + 0.877428i \(0.340743\pi\)
\(488\) 0 0
\(489\) 46.6208 + 67.5789i 0.0953391 + 0.138198i
\(490\) 0 0
\(491\) 263.317i 0.536287i −0.963379 0.268143i \(-0.913590\pi\)
0.963379 0.268143i \(-0.0864101\pi\)
\(492\) 0 0
\(493\) −45.5182 + 78.8398i −0.0923290 + 0.159919i
\(494\) 0 0
\(495\) −67.4536 82.7020i −0.136270 0.167075i
\(496\) 0 0
\(497\) 97.9220 56.5353i 0.197026 0.113753i
\(498\) 0 0
\(499\) −891.558 −1.78669 −0.893345 0.449372i \(-0.851648\pi\)
−0.893345 + 0.449372i \(0.851648\pi\)
\(500\) 0 0
\(501\) −55.7454 692.740i −0.111268 1.38271i
\(502\) 0 0
\(503\) −383.876 + 221.631i −0.763174 + 0.440619i −0.830434 0.557117i \(-0.811908\pi\)
0.0672604 + 0.997735i \(0.478574\pi\)
\(504\) 0 0
\(505\) 825.191 1.63404
\(506\) 0 0
\(507\) 161.087 339.259i 0.317725 0.669150i
\(508\) 0 0
\(509\) 306.042 + 176.693i 0.601261 + 0.347138i 0.769538 0.638602i \(-0.220487\pi\)
−0.168276 + 0.985740i \(0.553820\pi\)
\(510\) 0 0
\(511\) −181.055 313.596i −0.354315 0.613691i
\(512\) 0 0
\(513\) −472.405 + 200.007i −0.920867 + 0.389876i
\(514\) 0 0
\(515\) 701.170 404.821i 1.36150 0.786060i
\(516\) 0 0
\(517\) −14.5435 + 25.1901i −0.0281306 + 0.0487236i
\(518\) 0 0
\(519\) 324.298 + 153.983i 0.624852 + 0.296692i
\(520\) 0 0
\(521\) 530.816i 1.01884i −0.860518 0.509420i \(-0.829860\pi\)
0.860518 0.509420i \(-0.170140\pi\)
\(522\) 0 0
\(523\) 518.783 + 898.559i 0.991938 + 1.71809i 0.605717 + 0.795680i \(0.292887\pi\)
0.386221 + 0.922406i \(0.373780\pi\)
\(524\) 0 0
\(525\) −835.295 + 67.2169i −1.59104 + 0.128032i
\(526\) 0 0
\(527\) 202.527i 0.384302i
\(528\) 0 0
\(529\) −86.3284 149.525i −0.163192 0.282656i
\(530\) 0 0
\(531\) −696.240 264.457i −1.31119 0.498035i
\(532\) 0 0
\(533\) 101.409 + 58.5483i 0.190260 + 0.109847i
\(534\) 0 0
\(535\) 790.645 1.47784
\(536\) 0 0
\(537\) 451.618 311.559i 0.841001 0.580184i
\(538\) 0 0
\(539\) 36.0014i 0.0667930i
\(540\) 0 0
\(541\) −427.224 739.974i −0.789693 1.36779i −0.926155 0.377143i \(-0.876906\pi\)
0.136462 0.990645i \(-0.456427\pi\)
\(542\) 0 0
\(543\) 200.621 422.520i 0.369467 0.778121i
\(544\) 0 0
\(545\) 1661.82 + 959.451i 3.04921 + 1.76046i
\(546\) 0 0
\(547\) −412.287 −0.753724 −0.376862 0.926269i \(-0.622997\pi\)
−0.376862 + 0.926269i \(0.622997\pi\)
\(548\) 0 0
\(549\) −151.746 + 399.506i −0.276405 + 0.727697i
\(550\) 0 0
\(551\) 21.4539 + 133.276i 0.0389363 + 0.241881i
\(552\) 0 0
\(553\) 494.770 0.894703
\(554\) 0 0
\(555\) 389.292 268.562i 0.701428 0.483896i
\(556\) 0 0
\(557\) 863.794 498.712i 1.55080 0.895353i 0.552720 0.833367i \(-0.313590\pi\)
0.998077 0.0619859i \(-0.0197434\pi\)
\(558\) 0 0
\(559\) −276.481 −0.494600
\(560\) 0 0
\(561\) 21.0534 44.3397i 0.0375283 0.0790369i
\(562\) 0 0
\(563\) −305.679 + 176.484i −0.542947 + 0.313470i −0.746272 0.665641i \(-0.768158\pi\)
0.203326 + 0.979111i \(0.434825\pi\)
\(564\) 0 0
\(565\) 969.932 + 1679.97i 1.71669 + 2.97340i
\(566\) 0 0
\(567\) 350.574 116.640i 0.618296 0.205714i
\(568\) 0 0
\(569\) 276.835 + 159.831i 0.486529 + 0.280897i 0.723133 0.690709i \(-0.242701\pi\)
−0.236605 + 0.971606i \(0.576035\pi\)
\(570\) 0 0
\(571\) 352.313 + 610.224i 0.617010 + 1.06869i 0.990028 + 0.140869i \(0.0449897\pi\)
−0.373018 + 0.927824i \(0.621677\pi\)
\(572\) 0 0
\(573\) 81.3918 + 1011.44i 0.142045 + 1.76517i
\(574\) 0 0
\(575\) −1001.14 578.006i −1.74111 1.00523i
\(576\) 0 0
\(577\) 322.338 0.558644 0.279322 0.960197i \(-0.409890\pi\)
0.279322 + 0.960197i \(0.409890\pi\)
\(578\) 0 0
\(579\) 362.871 + 525.997i 0.626720 + 0.908458i
\(580\) 0 0
\(581\) −158.292 + 91.3897i −0.272447 + 0.157297i
\(582\) 0 0
\(583\) −8.65093 −0.0148386
\(584\) 0 0
\(585\) −428.705 + 349.661i −0.732829 + 0.597711i
\(586\) 0 0
\(587\) 974.121 562.409i 1.65949 0.958107i 0.686541 0.727091i \(-0.259128\pi\)
0.972950 0.231016i \(-0.0742050\pi\)
\(588\) 0 0
\(589\) −189.583 232.911i −0.321872 0.395434i
\(590\) 0 0
\(591\) 19.1366 13.2018i 0.0323801 0.0223381i
\(592\) 0 0
\(593\) 686.343 396.261i 1.15741 0.668230i 0.206727 0.978399i \(-0.433719\pi\)
0.950682 + 0.310168i \(0.100385\pi\)
\(594\) 0 0
\(595\) −271.378 470.040i −0.456097 0.789983i
\(596\) 0 0
\(597\) −385.976 + 812.891i −0.646527 + 1.36163i
\(598\) 0 0
\(599\) −695.903 401.780i −1.16177 0.670750i −0.210045 0.977692i \(-0.567361\pi\)
−0.951728 + 0.306941i \(0.900695\pi\)
\(600\) 0 0
\(601\) 3.87039 6.70371i 0.00643992 0.0111543i −0.862787 0.505567i \(-0.831283\pi\)
0.869227 + 0.494412i \(0.164617\pi\)
\(602\) 0 0
\(603\) 243.011 + 297.946i 0.403004 + 0.494106i
\(604\) 0 0
\(605\) −960.010 + 554.262i −1.58679 + 0.916136i
\(606\) 0 0
\(607\) 111.655 + 193.392i 0.183945 + 0.318602i 0.943221 0.332167i \(-0.107780\pi\)
−0.759275 + 0.650769i \(0.774446\pi\)
\(608\) 0 0
\(609\) −7.79839 96.9095i −0.0128052 0.159129i
\(610\) 0 0
\(611\) 130.579 + 75.3896i 0.213713 + 0.123387i
\(612\) 0 0
\(613\) 188.469 326.438i 0.307454 0.532525i −0.670351 0.742044i \(-0.733856\pi\)
0.977805 + 0.209519i \(0.0671898\pi\)
\(614\) 0 0
\(615\) 279.867 + 405.679i 0.455068 + 0.659641i
\(616\) 0 0
\(617\) −404.809 233.717i −0.656093 0.378795i 0.134694 0.990887i \(-0.456995\pi\)
−0.790787 + 0.612092i \(0.790328\pi\)
\(618\) 0 0
\(619\) 481.347 833.718i 0.777621 1.34688i −0.155689 0.987806i \(-0.549760\pi\)
0.933310 0.359073i \(-0.116907\pi\)
\(620\) 0 0
\(621\) 489.448 + 142.178i 0.788162 + 0.228950i
\(622\) 0 0
\(623\) 259.370i 0.416324i
\(624\) 0 0
\(625\) 1594.24 2.55079
\(626\) 0 0
\(627\) −17.2939 70.6994i −0.0275820 0.112758i
\(628\) 0 0
\(629\) 188.376 + 108.759i 0.299485 + 0.172908i
\(630\) 0 0
\(631\) 132.578 + 229.632i 0.210108 + 0.363917i 0.951748 0.306880i \(-0.0992852\pi\)
−0.741640 + 0.670798i \(0.765952\pi\)
\(632\) 0 0
\(633\) 627.345 + 909.363i 0.991066 + 1.43659i
\(634\) 0 0
\(635\) 908.492 524.518i 1.43070 0.826013i
\(636\) 0 0
\(637\) −186.622 −0.292970
\(638\) 0 0
\(639\) 172.887 141.010i 0.270558 0.220673i
\(640\) 0 0
\(641\) −21.8673 + 12.6251i −0.0341143 + 0.0196959i −0.516960 0.856009i \(-0.672936\pi\)
0.482846 + 0.875705i \(0.339603\pi\)
\(642\) 0 0
\(643\) −335.777 −0.522204 −0.261102 0.965311i \(-0.584086\pi\)
−0.261102 + 0.965311i \(0.584086\pi\)
\(644\) 0 0
\(645\) −1051.21 499.133i −1.62978 0.773850i
\(646\) 0 0
\(647\) 905.889i 1.40014i −0.714075 0.700069i \(-0.753152\pi\)
0.714075 0.700069i \(-0.246848\pi\)
\(648\) 0 0
\(649\) 52.8338 91.5108i 0.0814080 0.141003i
\(650\) 0 0
\(651\) 122.821 + 178.035i 0.188665 + 0.273479i
\(652\) 0 0
\(653\) 929.143 536.441i 1.42288 0.821502i 0.426339 0.904564i \(-0.359803\pi\)
0.996544 + 0.0830615i \(0.0264698\pi\)
\(654\) 0 0
\(655\) 79.0506 0.120688
\(656\) 0 0
\(657\) −451.587 553.671i −0.687346 0.842726i
\(658\) 0 0
\(659\) 1036.04i 1.57214i −0.618135 0.786072i \(-0.712111\pi\)
0.618135 0.786072i \(-0.287889\pi\)
\(660\) 0 0
\(661\) 47.1772 81.7133i 0.0713725 0.123621i −0.828131 0.560535i \(-0.810595\pi\)
0.899503 + 0.436914i \(0.143929\pi\)
\(662\) 0 0
\(663\) −229.845 109.135i −0.346674 0.164608i
\(664\) 0 0
\(665\) −752.088 286.524i −1.13096 0.430862i
\(666\) 0 0
\(667\) 67.0593 116.150i 0.100539 0.174138i
\(668\) 0 0
\(669\) 197.159 415.230i 0.294707 0.620672i
\(670\) 0 0
\(671\) −52.5093 30.3162i −0.0782553 0.0451807i
\(672\) 0 0
\(673\) −156.533 + 271.123i −0.232590 + 0.402858i −0.958570 0.284858i \(-0.908053\pi\)
0.725979 + 0.687716i \(0.241387\pi\)
\(674\) 0 0
\(675\) −1605.71 + 394.465i −2.37883 + 0.584393i
\(676\) 0 0
\(677\) −523.760 302.393i −0.773649 0.446666i 0.0605259 0.998167i \(-0.480722\pi\)
−0.834175 + 0.551500i \(0.814056\pi\)
\(678\) 0 0
\(679\) 792.407 1.16702
\(680\) 0 0
\(681\) −33.1907 412.456i −0.0487382 0.605662i
\(682\) 0 0
\(683\) 27.4860i 0.0402430i −0.999798 0.0201215i \(-0.993595\pi\)
0.999798 0.0201215i \(-0.00640531\pi\)
\(684\) 0 0
\(685\) −1989.11 −2.90381
\(686\) 0 0
\(687\) −216.935 + 456.879i −0.315772 + 0.665035i
\(688\) 0 0
\(689\) 44.8441i 0.0650857i
\(690\) 0 0
\(691\) 2.35922 4.08630i 0.00341422 0.00591360i −0.864313 0.502954i \(-0.832247\pi\)
0.867727 + 0.497040i \(0.165580\pi\)
\(692\) 0 0
\(693\) 8.38224 + 51.7452i 0.0120956 + 0.0746684i
\(694\) 0 0
\(695\) −414.527 239.327i −0.596442 0.344356i
\(696\) 0 0
\(697\) −113.337 + 196.306i −0.162607 + 0.281644i
\(698\) 0 0
\(699\) 71.5817 + 889.536i 0.102406 + 1.27258i
\(700\) 0 0
\(701\) −81.6577 47.1451i −0.116487 0.0672541i 0.440624 0.897692i \(-0.354757\pi\)
−0.557112 + 0.830438i \(0.688090\pi\)
\(702\) 0 0
\(703\) 318.444 51.2609i 0.452979 0.0729173i
\(704\) 0 0
\(705\) 360.370 + 522.373i 0.511164 + 0.740954i
\(706\) 0 0
\(707\) −351.014 202.658i −0.496484 0.286645i
\(708\) 0 0
\(709\) −866.770 −1.22252 −0.611262 0.791428i \(-0.709338\pi\)
−0.611262 + 0.791428i \(0.709338\pi\)
\(710\) 0 0
\(711\) 963.673 156.106i 1.35538 0.219558i
\(712\) 0 0
\(713\) 298.371i 0.418473i
\(714\) 0 0
\(715\) −39.2450 67.9743i −0.0548881 0.0950689i
\(716\) 0 0
\(717\) 869.713 + 412.957i 1.21299 + 0.575951i
\(718\) 0 0
\(719\) −960.272 554.413i −1.33557 0.771089i −0.349419 0.936966i \(-0.613621\pi\)
−0.986146 + 0.165877i \(0.946954\pi\)
\(720\) 0 0
\(721\) −397.679 −0.551566
\(722\) 0 0
\(723\) 670.990 + 972.628i 0.928063 + 1.34527i
\(724\) 0 0
\(725\) 435.094i 0.600130i
\(726\) 0 0
\(727\) 202.057 + 349.973i 0.277933 + 0.481393i 0.970871 0.239604i \(-0.0770175\pi\)
−0.692938 + 0.720997i \(0.743684\pi\)
\(728\) 0 0
\(729\) 646.017 337.792i 0.886168 0.463363i
\(730\) 0 0
\(731\) 535.209i 0.732160i
\(732\) 0 0
\(733\) −564.680 978.054i −0.770368 1.33432i −0.937362 0.348358i \(-0.886739\pi\)
0.166994 0.985958i \(-0.446594\pi\)
\(734\) 0 0
\(735\) −709.553 336.909i −0.965378 0.458380i
\(736\) 0 0
\(737\) −47.2415 + 27.2749i −0.0640997 + 0.0370080i
\(738\) 0 0
\(739\) 321.557 556.953i 0.435124 0.753658i −0.562181 0.827014i \(-0.690038\pi\)
0.997306 + 0.0733563i \(0.0233710\pi\)
\(740\) 0 0
\(741\) −366.486 + 89.6471i −0.494584 + 0.120981i
\(742\) 0 0
\(743\) 1205.28i 1.62219i 0.584917 + 0.811093i \(0.301127\pi\)
−0.584917 + 0.811093i \(0.698873\pi\)
\(744\) 0 0
\(745\) −1335.49 −1.79260
\(746\) 0 0
\(747\) −279.473 + 227.944i −0.374127 + 0.305146i
\(748\) 0 0
\(749\) −336.320 194.174i −0.449025 0.259245i
\(750\) 0 0
\(751\) −123.979 + 214.738i −0.165086 + 0.285937i −0.936686 0.350171i \(-0.886123\pi\)
0.771600 + 0.636108i \(0.219457\pi\)
\(752\) 0 0
\(753\) −1001.47 475.518i −1.32997 0.631498i
\(754\) 0 0
\(755\) −1765.27 1019.18i −2.33811 1.34991i
\(756\) 0 0
\(757\) −313.951 + 543.779i −0.414731 + 0.718335i −0.995400 0.0958047i \(-0.969458\pi\)
0.580669 + 0.814139i \(0.302791\pi\)
\(758\) 0 0
\(759\) −31.0167 + 65.3231i −0.0408652 + 0.0860647i
\(760\) 0 0
\(761\) 856.714 494.624i 1.12577 0.649966i 0.182905 0.983131i \(-0.441450\pi\)
0.942869 + 0.333165i \(0.108117\pi\)
\(762\) 0 0
\(763\) −471.263 816.251i −0.617645 1.06979i
\(764\) 0 0
\(765\) −676.870 829.882i −0.884798 1.08481i
\(766\) 0 0
\(767\) −474.367 273.876i −0.618471 0.357074i
\(768\) 0 0
\(769\) −256.815 + 444.816i −0.333959 + 0.578434i −0.983284 0.182077i \(-0.941718\pi\)
0.649325 + 0.760511i \(0.275051\pi\)
\(770\) 0 0
\(771\) −44.2704 550.142i −0.0574195 0.713544i
\(772\) 0 0
\(773\) 464.596 268.235i 0.601030 0.347005i −0.168417 0.985716i \(-0.553865\pi\)
0.769447 + 0.638711i \(0.220532\pi\)
\(774\) 0 0
\(775\) −483.973 838.266i −0.624481 1.08163i
\(776\) 0 0
\(777\) −231.551 + 18.6331i −0.298006 + 0.0239808i
\(778\) 0 0
\(779\) 53.4187 + 331.849i 0.0685734 + 0.425993i
\(780\) 0 0
\(781\) 15.8266 + 27.4125i 0.0202645 + 0.0350992i
\(782\) 0 0
\(783\) −45.7652 186.292i −0.0584485 0.237921i
\(784\) 0 0
\(785\) 292.292i 0.372347i
\(786\) 0 0
\(787\) 60.3896 + 104.598i 0.0767339 + 0.132907i 0.901839 0.432072i \(-0.142217\pi\)
−0.825105 + 0.564979i \(0.808884\pi\)
\(788\) 0 0
\(789\) 458.300 + 217.610i 0.580861 + 0.275804i
\(790\) 0 0
\(791\) 952.821i 1.20458i
\(792\) 0 0
\(793\) −157.151 + 272.194i −0.198173 + 0.343246i
\(794\) 0 0
\(795\) −80.9573 + 170.501i −0.101833 + 0.214467i
\(796\) 0 0