Properties

Label 684.3.m.a.353.17
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 353.17
Character \(\chi\) \(=\) 684.353
Dual form 684.3.m.a.653.17

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.06149 + 2.80593i) q^{3} -1.84834i q^{5} +(2.46982 - 4.27785i) q^{7} +(-6.74649 - 5.95692i) q^{9} +O(q^{10})\) \(q+(-1.06149 + 2.80593i) q^{3} -1.84834i q^{5} +(2.46982 - 4.27785i) q^{7} +(-6.74649 - 5.95692i) q^{9} +(-10.4350 - 6.02464i) q^{11} +(-5.11176 + 8.85383i) q^{13} +(5.18632 + 1.96199i) q^{15} +(16.2730 + 9.39522i) q^{17} +(8.26716 + 17.1071i) q^{19} +(9.38166 + 11.4710i) q^{21} +(16.3016 + 9.41172i) q^{23} +21.5836 q^{25} +(23.8760 - 12.6070i) q^{27} -4.70293i q^{29} +(14.2830 + 24.7388i) q^{31} +(27.9813 - 22.8848i) q^{33} +(-7.90692 - 4.56506i) q^{35} -52.8630 q^{37} +(-19.4172 - 23.7415i) q^{39} +7.43066i q^{41} +(20.6996 + 35.8527i) q^{43} +(-11.0104 + 12.4698i) q^{45} +4.31930i q^{47} +(12.3000 + 21.3043i) q^{49} +(-43.6359 + 35.6880i) q^{51} +(41.4703 - 23.9429i) q^{53} +(-11.1356 + 19.2874i) q^{55} +(-56.7769 + 5.03809i) q^{57} +50.8643i q^{59} +23.0213 q^{61} +(-42.1454 + 14.1480i) q^{63} +(16.3649 + 9.44828i) q^{65} +(-19.3966 + 33.5959i) q^{67} +(-43.7125 + 35.7507i) q^{69} +(95.0990 + 54.9054i) q^{71} +(11.5505 - 20.0061i) q^{73} +(-22.9107 + 60.5622i) q^{75} +(-51.5450 + 29.7595i) q^{77} +(74.5143 + 129.062i) q^{79} +(10.0303 + 80.3766i) q^{81} +(-64.2549 - 37.0976i) q^{83} +(17.3656 - 30.0781i) q^{85} +(13.1961 + 4.99210i) q^{87} +(-9.22299 + 5.32490i) q^{89} +(25.2502 + 43.7346i) q^{91} +(-84.5765 + 13.8171i) q^{93} +(31.6198 - 15.2805i) q^{95} +(-50.3430 - 87.1966i) q^{97} +(34.5112 + 102.805i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + O(q^{10}) \) \( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99} + O(q^{100}) \)

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
\(3\) −1.06149 + 2.80593i −0.353829 + 0.935310i
\(4\) 0 0
\(5\) 1.84834i 0.369668i −0.982770 0.184834i \(-0.940825\pi\)
0.982770 0.184834i \(-0.0591748\pi\)
\(6\) 0 0
\(7\) 2.46982 4.27785i 0.352831 0.611121i −0.633913 0.773404i \(-0.718552\pi\)
0.986744 + 0.162283i \(0.0518858\pi\)
\(8\) 0 0
\(9\) −6.74649 5.95692i −0.749610 0.661880i
\(10\) 0 0
\(11\) −10.4350 6.02464i −0.948635 0.547694i −0.0559781 0.998432i \(-0.517828\pi\)
−0.892657 + 0.450738i \(0.851161\pi\)
\(12\) 0 0
\(13\) −5.11176 + 8.85383i −0.393212 + 0.681064i −0.992871 0.119192i \(-0.961970\pi\)
0.599659 + 0.800256i \(0.295303\pi\)
\(14\) 0 0
\(15\) 5.18632 + 1.96199i 0.345755 + 0.130799i
\(16\) 0 0
\(17\) 16.2730 + 9.39522i 0.957235 + 0.552660i 0.895321 0.445422i \(-0.146946\pi\)
0.0619139 + 0.998081i \(0.480280\pi\)
\(18\) 0 0
\(19\) 8.26716 + 17.1071i 0.435114 + 0.900375i
\(20\) 0 0
\(21\) 9.38166 + 11.4710i 0.446746 + 0.546239i
\(22\) 0 0
\(23\) 16.3016 + 9.41172i 0.708764 + 0.409205i 0.810603 0.585596i \(-0.199139\pi\)
−0.101839 + 0.994801i \(0.532473\pi\)
\(24\) 0 0
\(25\) 21.5836 0.863345
\(26\) 0 0
\(27\) 23.8760 12.6070i 0.884296 0.466926i
\(28\) 0 0
\(29\) 4.70293i 0.162170i −0.996707 0.0810850i \(-0.974161\pi\)
0.996707 0.0810850i \(-0.0258385\pi\)
\(30\) 0 0
\(31\) 14.2830 + 24.7388i 0.460740 + 0.798026i 0.998998 0.0447545i \(-0.0142506\pi\)
−0.538258 + 0.842780i \(0.680917\pi\)
\(32\) 0 0
\(33\) 27.9813 22.8848i 0.847919 0.693477i
\(34\) 0 0
\(35\) −7.90692 4.56506i −0.225912 0.130430i
\(36\) 0 0
\(37\) −52.8630 −1.42873 −0.714365 0.699773i \(-0.753285\pi\)
−0.714365 + 0.699773i \(0.753285\pi\)
\(38\) 0 0
\(39\) −19.4172 23.7415i −0.497876 0.608755i
\(40\) 0 0
\(41\) 7.43066i 0.181236i 0.995886 + 0.0906178i \(0.0288842\pi\)
−0.995886 + 0.0906178i \(0.971116\pi\)
\(42\) 0 0
\(43\) 20.6996 + 35.8527i 0.481385 + 0.833784i 0.999772 0.0213626i \(-0.00680046\pi\)
−0.518386 + 0.855146i \(0.673467\pi\)
\(44\) 0 0
\(45\) −11.0104 + 12.4698i −0.244676 + 0.277107i
\(46\) 0 0
\(47\) 4.31930i 0.0919000i 0.998944 + 0.0459500i \(0.0146315\pi\)
−0.998944 + 0.0459500i \(0.985369\pi\)
\(48\) 0 0
\(49\) 12.3000 + 21.3043i 0.251021 + 0.434781i
\(50\) 0 0
\(51\) −43.6359 + 35.6880i −0.855606 + 0.699764i
\(52\) 0 0
\(53\) 41.4703 23.9429i 0.782459 0.451753i −0.0548421 0.998495i \(-0.517466\pi\)
0.837301 + 0.546742i \(0.184132\pi\)
\(54\) 0 0
\(55\) −11.1356 + 19.2874i −0.202465 + 0.350680i
\(56\) 0 0
\(57\) −56.7769 + 5.03809i −0.996086 + 0.0883876i
\(58\) 0 0
\(59\) 50.8643i 0.862107i 0.902326 + 0.431053i \(0.141858\pi\)
−0.902326 + 0.431053i \(0.858142\pi\)
\(60\) 0 0
\(61\) 23.0213 0.377399 0.188699 0.982035i \(-0.439573\pi\)
0.188699 + 0.982035i \(0.439573\pi\)
\(62\) 0 0
\(63\) −42.1454 + 14.1480i −0.668974 + 0.224571i
\(64\) 0 0
\(65\) 16.3649 + 9.44828i 0.251768 + 0.145358i
\(66\) 0 0
\(67\) −19.3966 + 33.5959i −0.289502 + 0.501432i −0.973691 0.227873i \(-0.926823\pi\)
0.684189 + 0.729305i \(0.260156\pi\)
\(68\) 0 0
\(69\) −43.7125 + 35.7507i −0.633515 + 0.518126i
\(70\) 0 0
\(71\) 95.0990 + 54.9054i 1.33942 + 0.773316i 0.986722 0.162420i \(-0.0519301\pi\)
0.352701 + 0.935736i \(0.385263\pi\)
\(72\) 0 0
\(73\) 11.5505 20.0061i 0.158226 0.274056i −0.776003 0.630730i \(-0.782756\pi\)
0.934229 + 0.356673i \(0.116089\pi\)
\(74\) 0 0
\(75\) −22.9107 + 60.5622i −0.305477 + 0.807496i
\(76\) 0 0
\(77\) −51.5450 + 29.7595i −0.669415 + 0.386487i
\(78\) 0 0
\(79\) 74.5143 + 129.062i 0.943218 + 1.63370i 0.759280 + 0.650764i \(0.225551\pi\)
0.183939 + 0.982938i \(0.441115\pi\)
\(80\) 0 0
\(81\) 10.0303 + 80.3766i 0.123831 + 0.992303i
\(82\) 0 0
\(83\) −64.2549 37.0976i −0.774156 0.446959i 0.0601995 0.998186i \(-0.480826\pi\)
−0.834355 + 0.551227i \(0.814160\pi\)
\(84\) 0 0
\(85\) 17.3656 30.0781i 0.204301 0.353859i
\(86\) 0 0
\(87\) 13.1961 + 4.99210i 0.151679 + 0.0573805i
\(88\) 0 0
\(89\) −9.22299 + 5.32490i −0.103629 + 0.0598303i −0.550919 0.834559i \(-0.685723\pi\)
0.447290 + 0.894389i \(0.352389\pi\)
\(90\) 0 0
\(91\) 25.2502 + 43.7346i 0.277475 + 0.480601i
\(92\) 0 0
\(93\) −84.5765 + 13.8171i −0.909425 + 0.148571i
\(94\) 0 0
\(95\) 31.6198 15.2805i 0.332840 0.160848i
\(96\) 0 0
\(97\) −50.3430 87.1966i −0.519000 0.898934i −0.999756 0.0220799i \(-0.992971\pi\)
0.480756 0.876854i \(-0.340362\pi\)
\(98\) 0 0
\(99\) 34.5112 + 102.805i 0.348598 + 1.03844i
\(100\) 0 0
\(101\) 147.156i 1.45699i −0.685052 0.728495i \(-0.740220\pi\)
0.685052 0.728495i \(-0.259780\pi\)
\(102\) 0 0
\(103\) −28.4113 49.2098i −0.275838 0.477765i 0.694509 0.719484i \(-0.255622\pi\)
−0.970346 + 0.241720i \(0.922289\pi\)
\(104\) 0 0
\(105\) 21.2023 17.3405i 0.201927 0.165148i
\(106\) 0 0
\(107\) 62.5758i 0.584821i 0.956293 + 0.292410i \(0.0944573\pi\)
−0.956293 + 0.292410i \(0.905543\pi\)
\(108\) 0 0
\(109\) −32.2512 + 55.8606i −0.295882 + 0.512483i −0.975190 0.221371i \(-0.928947\pi\)
0.679308 + 0.733854i \(0.262280\pi\)
\(110\) 0 0
\(111\) 56.1134 148.330i 0.505526 1.33631i
\(112\) 0 0
\(113\) −110.388 + 63.7326i −0.976885 + 0.564005i −0.901328 0.433137i \(-0.857407\pi\)
−0.0755570 + 0.997141i \(0.524073\pi\)
\(114\) 0 0
\(115\) 17.3961 30.1309i 0.151270 0.262008i
\(116\) 0 0
\(117\) 87.2280 29.2819i 0.745538 0.250273i
\(118\) 0 0
\(119\) 80.3826 46.4089i 0.675484 0.389991i
\(120\) 0 0
\(121\) 12.0925 + 20.9449i 0.0999384 + 0.173098i
\(122\) 0 0
\(123\) −20.8499 7.88754i −0.169511 0.0641264i
\(124\) 0 0
\(125\) 86.1025i 0.688820i
\(126\) 0 0
\(127\) 118.378 + 205.036i 0.932109 + 1.61446i 0.779710 + 0.626141i \(0.215367\pi\)
0.152399 + 0.988319i \(0.451300\pi\)
\(128\) 0 0
\(129\) −122.573 + 20.0244i −0.950175 + 0.155228i
\(130\) 0 0
\(131\) 251.709i 1.92144i −0.277521 0.960720i \(-0.589513\pi\)
0.277521 0.960720i \(-0.410487\pi\)
\(132\) 0 0
\(133\) 93.6001 + 6.88581i 0.703760 + 0.0517730i
\(134\) 0 0
\(135\) −23.3020 44.1310i −0.172608 0.326896i
\(136\) 0 0
\(137\) 5.26681i 0.0384439i 0.999815 + 0.0192219i \(0.00611891\pi\)
−0.999815 + 0.0192219i \(0.993881\pi\)
\(138\) 0 0
\(139\) −81.3395 + 140.884i −0.585176 + 1.01355i 0.409677 + 0.912230i \(0.365641\pi\)
−0.994853 + 0.101324i \(0.967692\pi\)
\(140\) 0 0
\(141\) −12.1197 4.58488i −0.0859550 0.0325169i
\(142\) 0 0
\(143\) 106.682 61.5930i 0.746030 0.430720i
\(144\) 0 0
\(145\) −8.69263 −0.0599492
\(146\) 0 0
\(147\) −72.8346 + 11.8988i −0.495473 + 0.0809443i
\(148\) 0 0
\(149\) 71.4060i 0.479235i −0.970867 0.239617i \(-0.922978\pi\)
0.970867 0.239617i \(-0.0770220\pi\)
\(150\) 0 0
\(151\) 7.78566 13.4852i 0.0515607 0.0893057i −0.839093 0.543988i \(-0.816914\pi\)
0.890654 + 0.454682i \(0.150247\pi\)
\(152\) 0 0
\(153\) −53.8191 160.322i −0.351759 1.04785i
\(154\) 0 0
\(155\) 45.7258 26.3998i 0.295005 0.170321i
\(156\) 0 0
\(157\) −149.220 −0.950445 −0.475223 0.879866i \(-0.657633\pi\)
−0.475223 + 0.879866i \(0.657633\pi\)
\(158\) 0 0
\(159\) 23.1619 + 141.778i 0.145672 + 0.891685i
\(160\) 0 0
\(161\) 80.5238 46.4904i 0.500148 0.288760i
\(162\) 0 0
\(163\) 157.638 0.967101 0.483551 0.875316i \(-0.339347\pi\)
0.483551 + 0.875316i \(0.339347\pi\)
\(164\) 0 0
\(165\) −42.2989 51.7190i −0.256357 0.313449i
\(166\) 0 0
\(167\) 213.793 + 123.433i 1.28020 + 0.739123i 0.976884 0.213768i \(-0.0685738\pi\)
0.303313 + 0.952891i \(0.401907\pi\)
\(168\) 0 0
\(169\) 32.2398 + 55.8410i 0.190768 + 0.330420i
\(170\) 0 0
\(171\) 46.1314 164.660i 0.269774 0.962924i
\(172\) 0 0
\(173\) 90.5755 52.2938i 0.523558 0.302276i −0.214831 0.976651i \(-0.568920\pi\)
0.738389 + 0.674375i \(0.235587\pi\)
\(174\) 0 0
\(175\) 53.3076 92.3315i 0.304615 0.527608i
\(176\) 0 0
\(177\) −142.722 53.9918i −0.806337 0.305038i
\(178\) 0 0
\(179\) 238.780i 1.33397i −0.745072 0.666985i \(-0.767585\pi\)
0.745072 0.666985i \(-0.232415\pi\)
\(180\) 0 0
\(181\) 108.062 + 187.169i 0.597029 + 1.03408i 0.993257 + 0.115933i \(0.0369857\pi\)
−0.396228 + 0.918152i \(0.629681\pi\)
\(182\) 0 0
\(183\) −24.4368 + 64.5963i −0.133535 + 0.352985i
\(184\) 0 0
\(185\) 97.7090i 0.528157i
\(186\) 0 0
\(187\) −113.206 196.078i −0.605377 1.04854i
\(188\) 0 0
\(189\) 5.03853 133.275i 0.0266589 0.705158i
\(190\) 0 0
\(191\) 150.835 + 87.0849i 0.789714 + 0.455942i 0.839862 0.542800i \(-0.182636\pi\)
−0.0501477 + 0.998742i \(0.515969\pi\)
\(192\) 0 0
\(193\) −43.1000 −0.223316 −0.111658 0.993747i \(-0.535616\pi\)
−0.111658 + 0.993747i \(0.535616\pi\)
\(194\) 0 0
\(195\) −43.8823 + 35.8895i −0.225038 + 0.184049i
\(196\) 0 0
\(197\) 229.707i 1.16603i −0.812463 0.583013i \(-0.801874\pi\)
0.812463 0.583013i \(-0.198126\pi\)
\(198\) 0 0
\(199\) −32.8318 56.8663i −0.164984 0.285760i 0.771666 0.636028i \(-0.219424\pi\)
−0.936650 + 0.350268i \(0.886090\pi\)
\(200\) 0 0
\(201\) −73.6786 90.0872i −0.366560 0.448195i
\(202\) 0 0
\(203\) −20.1184 11.6154i −0.0991055 0.0572186i
\(204\) 0 0
\(205\) 13.7344 0.0669970
\(206\) 0 0
\(207\) −53.9136 160.603i −0.260452 0.775861i
\(208\) 0 0
\(209\) 16.7966 228.319i 0.0803666 1.09244i
\(210\) 0 0
\(211\) −154.549 −0.732460 −0.366230 0.930524i \(-0.619352\pi\)
−0.366230 + 0.930524i \(0.619352\pi\)
\(212\) 0 0
\(213\) −255.007 + 208.560i −1.19722 + 0.979154i
\(214\) 0 0
\(215\) 66.2681 38.2599i 0.308224 0.177953i
\(216\) 0 0
\(217\) 141.105 0.650254
\(218\) 0 0
\(219\) 43.8750 + 53.6462i 0.200342 + 0.244960i
\(220\) 0 0
\(221\) −166.367 + 96.0522i −0.752793 + 0.434625i
\(222\) 0 0
\(223\) −65.4369 113.340i −0.293439 0.508251i 0.681182 0.732115i \(-0.261466\pi\)
−0.974621 + 0.223863i \(0.928133\pi\)
\(224\) 0 0
\(225\) −145.614 128.572i −0.647172 0.571431i
\(226\) 0 0
\(227\) 140.131 + 80.9047i 0.617318 + 0.356409i 0.775824 0.630949i \(-0.217334\pi\)
−0.158506 + 0.987358i \(0.550668\pi\)
\(228\) 0 0
\(229\) 168.547 + 291.933i 0.736015 + 1.27482i 0.954277 + 0.298925i \(0.0966280\pi\)
−0.218262 + 0.975890i \(0.570039\pi\)
\(230\) 0 0
\(231\) −28.7888 176.221i −0.124627 0.762861i
\(232\) 0 0
\(233\) −7.44103 4.29608i −0.0319357 0.0184381i 0.483947 0.875097i \(-0.339203\pi\)
−0.515883 + 0.856659i \(0.672536\pi\)
\(234\) 0 0
\(235\) 7.98355 0.0339725
\(236\) 0 0
\(237\) −441.236 + 72.0837i −1.86176 + 0.304151i
\(238\) 0 0
\(239\) −216.237 + 124.844i −0.904756 + 0.522361i −0.878740 0.477300i \(-0.841615\pi\)
−0.0260161 + 0.999662i \(0.508282\pi\)
\(240\) 0 0
\(241\) 277.831 1.15283 0.576414 0.817158i \(-0.304452\pi\)
0.576414 + 0.817158i \(0.304452\pi\)
\(242\) 0 0
\(243\) −236.178 57.1743i −0.971926 0.235285i
\(244\) 0 0
\(245\) 39.3776 22.7346i 0.160725 0.0927945i
\(246\) 0 0
\(247\) −193.723 14.2515i −0.784305 0.0576984i
\(248\) 0 0
\(249\) 172.299 140.916i 0.691964 0.565929i
\(250\) 0 0
\(251\) 413.219 238.572i 1.64629 0.950486i 0.667761 0.744376i \(-0.267253\pi\)
0.978529 0.206110i \(-0.0660805\pi\)
\(252\) 0 0
\(253\) −113.404 196.422i −0.448239 0.776372i
\(254\) 0 0
\(255\) 65.9636 + 80.6540i 0.258681 + 0.316290i
\(256\) 0 0
\(257\) −152.662 88.1392i −0.594014 0.342954i 0.172669 0.984980i \(-0.444761\pi\)
−0.766683 + 0.642026i \(0.778094\pi\)
\(258\) 0 0
\(259\) −130.562 + 226.140i −0.504100 + 0.873127i
\(260\) 0 0
\(261\) −28.0150 + 31.7283i −0.107337 + 0.121564i
\(262\) 0 0
\(263\) 163.347 94.3087i 0.621093 0.358588i −0.156201 0.987725i \(-0.549925\pi\)
0.777294 + 0.629137i \(0.216592\pi\)
\(264\) 0 0
\(265\) −44.2547 76.6513i −0.166999 0.289250i
\(266\) 0 0
\(267\) −5.15121 31.5314i −0.0192929 0.118095i
\(268\) 0 0
\(269\) −356.589 205.877i −1.32561 0.765340i −0.340991 0.940067i \(-0.610763\pi\)
−0.984617 + 0.174726i \(0.944096\pi\)
\(270\) 0 0
\(271\) 24.3004 42.0896i 0.0896695 0.155312i −0.817702 0.575642i \(-0.804752\pi\)
0.907371 + 0.420330i \(0.138086\pi\)
\(272\) 0 0
\(273\) −149.519 + 24.4266i −0.547689 + 0.0894747i
\(274\) 0 0
\(275\) −225.225 130.034i −0.818999 0.472849i
\(276\) 0 0
\(277\) −76.9499 + 133.281i −0.277798 + 0.481159i −0.970837 0.239740i \(-0.922938\pi\)
0.693040 + 0.720900i \(0.256271\pi\)
\(278\) 0 0
\(279\) 51.0071 251.983i 0.182821 0.903163i
\(280\) 0 0
\(281\) 134.415i 0.478346i 0.970977 + 0.239173i \(0.0768763\pi\)
−0.970977 + 0.239173i \(0.923124\pi\)
\(282\) 0 0
\(283\) −63.6634 −0.224959 −0.112480 0.993654i \(-0.535879\pi\)
−0.112480 + 0.993654i \(0.535879\pi\)
\(284\) 0 0
\(285\) 9.31211 + 104.943i 0.0326741 + 0.368222i
\(286\) 0 0
\(287\) 31.7872 + 18.3524i 0.110757 + 0.0639455i
\(288\) 0 0
\(289\) 32.0401 + 55.4951i 0.110866 + 0.192025i
\(290\) 0 0
\(291\) 298.106 48.7009i 1.02442 0.167357i
\(292\) 0 0
\(293\) 186.208 107.507i 0.635523 0.366919i −0.147365 0.989082i \(-0.547079\pi\)
0.782888 + 0.622163i \(0.213746\pi\)
\(294\) 0 0
\(295\) 94.0146 0.318694
\(296\) 0 0
\(297\) −325.098 12.2905i −1.09461 0.0413822i
\(298\) 0 0
\(299\) −166.659 + 96.2209i −0.557390 + 0.321809i
\(300\) 0 0
\(301\) 204.496 0.679390
\(302\) 0 0
\(303\) 412.909 + 156.204i 1.36274 + 0.515525i
\(304\) 0 0
\(305\) 42.5513i 0.139512i
\(306\) 0 0
\(307\) −137.106 + 237.474i −0.446599 + 0.773532i −0.998162 0.0606011i \(-0.980698\pi\)
0.551563 + 0.834133i \(0.314032\pi\)
\(308\) 0 0
\(309\) 168.237 27.4845i 0.544457 0.0889467i
\(310\) 0 0
\(311\) −395.495 + 228.339i −1.27169 + 0.734209i −0.975305 0.220861i \(-0.929113\pi\)
−0.296382 + 0.955070i \(0.595780\pi\)
\(312\) 0 0
\(313\) 99.5291 0.317984 0.158992 0.987280i \(-0.449176\pi\)
0.158992 + 0.987280i \(0.449176\pi\)
\(314\) 0 0
\(315\) 26.1503 + 77.8990i 0.0830168 + 0.247299i
\(316\) 0 0
\(317\) 123.813i 0.390577i 0.980746 + 0.195289i \(0.0625644\pi\)
−0.980746 + 0.195289i \(0.937436\pi\)
\(318\) 0 0
\(319\) −28.3335 + 49.0750i −0.0888197 + 0.153840i
\(320\) 0 0
\(321\) −175.583 66.4234i −0.546989 0.206926i
\(322\) 0 0
\(323\) −26.1937 + 356.056i −0.0810951 + 1.10234i
\(324\) 0 0
\(325\) −110.330 + 191.098i −0.339478 + 0.587993i
\(326\) 0 0
\(327\) −122.507 149.790i −0.374639 0.458073i
\(328\) 0 0
\(329\) 18.4773 + 10.6679i 0.0561620 + 0.0324252i
\(330\) 0 0
\(331\) 284.794 493.278i 0.860406 1.49027i −0.0111320 0.999938i \(-0.503544\pi\)
0.871538 0.490328i \(-0.163123\pi\)
\(332\) 0 0
\(333\) 356.640 + 314.901i 1.07099 + 0.945648i
\(334\) 0 0
\(335\) 62.0968 + 35.8516i 0.185364 + 0.107020i
\(336\) 0 0
\(337\) −177.343 −0.526241 −0.263120 0.964763i \(-0.584752\pi\)
−0.263120 + 0.964763i \(0.584752\pi\)
\(338\) 0 0
\(339\) −61.6537 377.392i −0.181869 1.11325i
\(340\) 0 0
\(341\) 344.199i 1.00938i
\(342\) 0 0
\(343\) 363.557 1.05993
\(344\) 0 0
\(345\) 66.0795 + 80.7957i 0.191535 + 0.234190i
\(346\) 0 0
\(347\) 388.316i 1.11907i −0.828808 0.559533i \(-0.810980\pi\)
0.828808 0.559533i \(-0.189020\pi\)
\(348\) 0 0
\(349\) −165.385 + 286.456i −0.473884 + 0.820791i −0.999553 0.0298982i \(-0.990482\pi\)
0.525669 + 0.850689i \(0.323815\pi\)
\(350\) 0 0
\(351\) −10.4282 + 275.838i −0.0297100 + 0.785863i
\(352\) 0 0
\(353\) −152.631 88.1216i −0.432383 0.249636i 0.267979 0.963425i \(-0.413644\pi\)
−0.700361 + 0.713789i \(0.746978\pi\)
\(354\) 0 0
\(355\) 101.484 175.775i 0.285870 0.495142i
\(356\) 0 0
\(357\) 44.8951 + 274.810i 0.125757 + 0.769777i
\(358\) 0 0
\(359\) −208.764 120.530i −0.581515 0.335738i 0.180220 0.983626i \(-0.442319\pi\)
−0.761735 + 0.647888i \(0.775652\pi\)
\(360\) 0 0
\(361\) −224.308 + 282.855i −0.621352 + 0.783532i
\(362\) 0 0
\(363\) −71.6060 + 11.6981i −0.197262 + 0.0322262i
\(364\) 0 0
\(365\) −36.9781 21.3493i −0.101310 0.0584913i
\(366\) 0 0
\(367\) 190.391 0.518775 0.259388 0.965773i \(-0.416479\pi\)
0.259388 + 0.965773i \(0.416479\pi\)
\(368\) 0 0
\(369\) 44.2638 50.1309i 0.119956 0.135856i
\(370\) 0 0
\(371\) 236.538i 0.637569i
\(372\) 0 0
\(373\) 143.800 + 249.069i 0.385523 + 0.667745i 0.991842 0.127477i \(-0.0406878\pi\)
−0.606319 + 0.795222i \(0.707354\pi\)
\(374\) 0 0
\(375\) 241.598 + 91.3966i 0.644260 + 0.243724i
\(376\) 0 0
\(377\) 41.6390 + 24.0403i 0.110448 + 0.0637673i
\(378\) 0 0
\(379\) 127.708 0.336961 0.168481 0.985705i \(-0.446114\pi\)
0.168481 + 0.985705i \(0.446114\pi\)
\(380\) 0 0
\(381\) −700.975 + 114.517i −1.83983 + 0.300568i
\(382\) 0 0
\(383\) 387.164i 1.01087i 0.862864 + 0.505436i \(0.168668\pi\)
−0.862864 + 0.505436i \(0.831332\pi\)
\(384\) 0 0
\(385\) 55.0057 + 95.2727i 0.142872 + 0.247462i
\(386\) 0 0
\(387\) 73.9221 365.186i 0.191013 0.943632i
\(388\) 0 0
\(389\) 18.9972i 0.0488361i −0.999702 0.0244180i \(-0.992227\pi\)
0.999702 0.0244180i \(-0.00777327\pi\)
\(390\) 0 0
\(391\) 176.850 + 306.314i 0.452302 + 0.783411i
\(392\) 0 0
\(393\) 706.277 + 267.185i 1.79714 + 0.679861i
\(394\) 0 0
\(395\) 238.552 137.728i 0.603928 0.348678i
\(396\) 0 0
\(397\) 112.212 194.357i 0.282650 0.489564i −0.689387 0.724394i \(-0.742120\pi\)
0.972037 + 0.234829i \(0.0754531\pi\)
\(398\) 0 0
\(399\) −118.676 + 255.326i −0.297434 + 0.639915i
\(400\) 0 0
\(401\) 175.758i 0.438300i −0.975691 0.219150i \(-0.929672\pi\)
0.975691 0.219150i \(-0.0703284\pi\)
\(402\) 0 0
\(403\) −292.044 −0.724675
\(404\) 0 0
\(405\) 148.563 18.5394i 0.366823 0.0457764i
\(406\) 0 0
\(407\) 551.625 + 318.481i 1.35534 + 0.782508i
\(408\) 0 0
\(409\) 317.177 549.367i 0.775494 1.34320i −0.159022 0.987275i \(-0.550834\pi\)
0.934516 0.355921i \(-0.115833\pi\)
\(410\) 0 0
\(411\) −14.7783 5.59065i −0.0359569 0.0136026i
\(412\) 0 0
\(413\) 217.590 + 125.625i 0.526852 + 0.304178i
\(414\) 0 0
\(415\) −68.5690 + 118.765i −0.165227 + 0.286181i
\(416\) 0 0
\(417\) −308.970 377.779i −0.740936 0.905946i
\(418\) 0 0
\(419\) −329.899 + 190.467i −0.787348 + 0.454575i −0.839028 0.544088i \(-0.816876\pi\)
0.0516803 + 0.998664i \(0.483542\pi\)
\(420\) 0 0
\(421\) −134.754 233.400i −0.320080 0.554395i 0.660424 0.750893i \(-0.270377\pi\)
−0.980504 + 0.196498i \(0.937043\pi\)
\(422\) 0 0
\(423\) 25.7297 29.1401i 0.0608268 0.0688892i
\(424\) 0 0
\(425\) 351.230 + 202.783i 0.826424 + 0.477136i
\(426\) 0 0
\(427\) 56.8585 98.4817i 0.133158 0.230636i
\(428\) 0 0
\(429\) 59.5839 + 364.723i 0.138890 + 0.850170i
\(430\) 0 0
\(431\) 601.019 346.999i 1.39448 0.805101i 0.400669 0.916223i \(-0.368778\pi\)
0.993807 + 0.111122i \(0.0354443\pi\)
\(432\) 0 0
\(433\) −324.494 562.041i −0.749409 1.29802i −0.948106 0.317954i \(-0.897004\pi\)
0.198697 0.980061i \(-0.436329\pi\)
\(434\) 0 0
\(435\) 9.22711 24.3909i 0.0212117 0.0560711i
\(436\) 0 0
\(437\) −26.2397 + 356.681i −0.0600452 + 0.816205i
\(438\) 0 0
\(439\) −163.442 283.090i −0.372306 0.644852i 0.617614 0.786481i \(-0.288099\pi\)
−0.989920 + 0.141629i \(0.954766\pi\)
\(440\) 0 0
\(441\) 43.9257 216.999i 0.0996048 0.492062i
\(442\) 0 0
\(443\) 804.929i 1.81699i 0.417891 + 0.908497i \(0.362770\pi\)
−0.417891 + 0.908497i \(0.637230\pi\)
\(444\) 0 0
\(445\) 9.84223 + 17.0472i 0.0221174 + 0.0383084i
\(446\) 0 0
\(447\) 200.360 + 75.7965i 0.448233 + 0.169567i
\(448\) 0 0
\(449\) 201.130i 0.447951i 0.974595 + 0.223975i \(0.0719035\pi\)
−0.974595 + 0.223975i \(0.928096\pi\)
\(450\) 0 0
\(451\) 44.7670 77.5388i 0.0992617 0.171926i
\(452\) 0 0
\(453\) 29.5741 + 36.1604i 0.0652849 + 0.0798242i
\(454\) 0 0
\(455\) 80.8366 46.6710i 0.177663 0.102574i
\(456\) 0 0
\(457\) −211.138 + 365.702i −0.462010 + 0.800224i −0.999061 0.0433255i \(-0.986205\pi\)
0.537051 + 0.843549i \(0.319538\pi\)
\(458\) 0 0
\(459\) 506.979 + 19.1666i 1.10453 + 0.0417574i
\(460\) 0 0
\(461\) −315.862 + 182.363i −0.685167 + 0.395582i −0.801799 0.597594i \(-0.796124\pi\)
0.116632 + 0.993175i \(0.462790\pi\)
\(462\) 0 0
\(463\) 168.041 + 291.055i 0.362939 + 0.628629i 0.988443 0.151592i \(-0.0484400\pi\)
−0.625504 + 0.780221i \(0.715107\pi\)
\(464\) 0 0
\(465\) 25.5387 + 156.326i 0.0549219 + 0.336186i
\(466\) 0 0
\(467\) 33.3762i 0.0714693i 0.999361 + 0.0357347i \(0.0113771\pi\)
−0.999361 + 0.0357347i \(0.988623\pi\)
\(468\) 0 0
\(469\) 95.8122 + 165.952i 0.204290 + 0.353841i
\(470\) 0 0
\(471\) 158.395 418.701i 0.336295 0.888961i
\(472\) 0 0
\(473\) 498.830i 1.05461i
\(474\) 0 0
\(475\) 178.435 + 369.234i 0.375654 + 0.777335i
\(476\) 0 0
\(477\) −422.405 85.5046i −0.885545 0.179255i
\(478\) 0 0
\(479\) 481.973i 1.00621i 0.864226 + 0.503104i \(0.167809\pi\)
−0.864226 + 0.503104i \(0.832191\pi\)
\(480\) 0 0
\(481\) 270.223 468.040i 0.561795 0.973057i
\(482\) 0 0
\(483\) 44.9740 + 275.293i 0.0931138 + 0.569965i
\(484\) 0 0
\(485\) −161.169 + 93.0510i −0.332308 + 0.191858i
\(486\) 0 0
\(487\) −887.516 −1.82241 −0.911207 0.411948i \(-0.864849\pi\)
−0.911207 + 0.411948i \(0.864849\pi\)
\(488\) 0 0
\(489\) −167.330 + 442.320i −0.342188 + 0.904540i
\(490\) 0 0
\(491\) 930.811i 1.89575i 0.318649 + 0.947873i \(0.396771\pi\)
−0.318649 + 0.947873i \(0.603229\pi\)
\(492\) 0 0
\(493\) 44.1851 76.5308i 0.0896249 0.155235i
\(494\) 0 0
\(495\) 190.020 63.7886i 0.383878 0.128866i
\(496\) 0 0
\(497\) 469.754 271.213i 0.945179 0.545699i
\(498\) 0 0
\(499\) −652.342 −1.30730 −0.653649 0.756798i \(-0.726763\pi\)
−0.653649 + 0.756798i \(0.726763\pi\)
\(500\) 0 0
\(501\) −573.284 + 468.865i −1.14428 + 0.935859i
\(502\) 0 0
\(503\) −264.025 + 152.435i −0.524901 + 0.303052i −0.738937 0.673774i \(-0.764672\pi\)
0.214037 + 0.976826i \(0.431339\pi\)
\(504\) 0 0
\(505\) −271.994 −0.538603
\(506\) 0 0
\(507\) −190.908 + 31.1882i −0.376545 + 0.0615152i
\(508\) 0 0
\(509\) −44.7282 25.8238i −0.0878746 0.0507344i 0.455419 0.890277i \(-0.349490\pi\)
−0.543293 + 0.839543i \(0.682823\pi\)
\(510\) 0 0
\(511\) −57.0554 98.8228i −0.111654 0.193391i
\(512\) 0 0
\(513\) 413.056 + 304.226i 0.805178 + 0.593033i
\(514\) 0 0
\(515\) −90.9565 + 52.5137i −0.176614 + 0.101968i
\(516\) 0 0
\(517\) 26.0222 45.0718i 0.0503331 0.0871795i
\(518\) 0 0
\(519\) 50.5880 + 309.658i 0.0974722 + 0.596643i
\(520\) 0 0
\(521\) 733.507i 1.40788i −0.710258 0.703941i \(-0.751422\pi\)
0.710258 0.703941i \(-0.248578\pi\)
\(522\) 0 0
\(523\) 376.499 + 652.115i 0.719883 + 1.24687i 0.961046 + 0.276389i \(0.0891378\pi\)
−0.241163 + 0.970485i \(0.577529\pi\)
\(524\) 0 0
\(525\) 202.490 + 247.586i 0.385696 + 0.471592i
\(526\) 0 0
\(527\) 536.766i 1.01853i
\(528\) 0 0
\(529\) −87.3391 151.276i −0.165102 0.285965i
\(530\) 0 0
\(531\) 302.994 343.156i 0.570611 0.646244i
\(532\) 0 0
\(533\) −65.7897 37.9837i −0.123433 0.0712640i
\(534\) 0 0
\(535\) 115.661 0.216190
\(536\) 0 0
\(537\) 670.001 + 253.462i 1.24767 + 0.471997i
\(538\) 0 0
\(539\) 296.413i 0.549931i
\(540\) 0 0
\(541\) −161.332 279.436i −0.298211 0.516517i 0.677516 0.735508i \(-0.263057\pi\)
−0.975727 + 0.218992i \(0.929723\pi\)
\(542\) 0 0
\(543\) −639.891 + 104.537i −1.17844 + 0.192518i
\(544\) 0 0
\(545\) 103.250 + 59.6112i 0.189449 + 0.109378i
\(546\) 0 0
\(547\) 108.112 0.197645 0.0988223 0.995105i \(-0.468492\pi\)
0.0988223 + 0.995105i \(0.468492\pi\)
\(548\) 0 0
\(549\) −155.313 137.136i −0.282902 0.249793i
\(550\) 0 0
\(551\) 80.4537 38.8799i 0.146014 0.0705625i
\(552\) 0 0
\(553\) 736.146 1.33119
\(554\) 0 0
\(555\) −274.165 103.717i −0.493990 0.186877i
\(556\) 0 0
\(557\) −605.693 + 349.697i −1.08742 + 0.627822i −0.932888 0.360165i \(-0.882720\pi\)
−0.154532 + 0.987988i \(0.549387\pi\)
\(558\) 0 0
\(559\) −423.245 −0.757146
\(560\) 0 0
\(561\) 670.347 109.513i 1.19491 0.195210i
\(562\) 0 0
\(563\) −973.582 + 562.098i −1.72928 + 0.998398i −0.836348 + 0.548199i \(0.815314\pi\)
−0.892928 + 0.450199i \(0.851353\pi\)
\(564\) 0 0
\(565\) 117.800 + 204.035i 0.208495 + 0.361124i
\(566\) 0 0
\(567\) 368.612 + 155.607i 0.650109 + 0.274440i
\(568\) 0 0
\(569\) 76.7723 + 44.3245i 0.134925 + 0.0778989i 0.565943 0.824444i \(-0.308512\pi\)
−0.431018 + 0.902343i \(0.641846\pi\)
\(570\) 0 0
\(571\) −387.994 672.025i −0.679499 1.17693i −0.975132 0.221625i \(-0.928864\pi\)
0.295633 0.955302i \(-0.404469\pi\)
\(572\) 0 0
\(573\) −404.464 + 330.794i −0.705871 + 0.577302i
\(574\) 0 0
\(575\) 351.847 + 203.139i 0.611908 + 0.353285i
\(576\) 0 0
\(577\) 749.821 1.29952 0.649758 0.760141i \(-0.274870\pi\)
0.649758 + 0.760141i \(0.274870\pi\)
\(578\) 0 0
\(579\) 45.7500 120.935i 0.0790156 0.208870i
\(580\) 0 0
\(581\) −317.396 + 183.248i −0.546292 + 0.315402i
\(582\) 0 0
\(583\) −576.989 −0.989690
\(584\) 0 0
\(585\) −54.1231 161.227i −0.0925180 0.275602i
\(586\) 0 0
\(587\) −90.3895 + 52.1864i −0.153986 + 0.0889036i −0.575013 0.818144i \(-0.695003\pi\)
0.421027 + 0.907048i \(0.361670\pi\)
\(588\) 0 0
\(589\) −305.130 + 448.860i −0.518048 + 0.762072i
\(590\) 0 0
\(591\) 644.542 + 243.831i 1.09060 + 0.412574i
\(592\) 0 0
\(593\) −785.885 + 453.731i −1.32527 + 0.765145i −0.984564 0.175025i \(-0.944000\pi\)
−0.340706 + 0.940170i \(0.610666\pi\)
\(594\) 0 0
\(595\) −85.7795 148.574i −0.144167 0.249705i
\(596\) 0 0
\(597\) 194.413 31.7608i 0.325650 0.0532007i
\(598\) 0 0
\(599\) 84.5937 + 48.8402i 0.141225 + 0.0815362i 0.568948 0.822374i \(-0.307351\pi\)
−0.427723 + 0.903910i \(0.640684\pi\)
\(600\) 0 0
\(601\) −456.977 + 791.508i −0.760361 + 1.31698i 0.182303 + 0.983242i \(0.441645\pi\)
−0.942664 + 0.333742i \(0.891689\pi\)
\(602\) 0 0
\(603\) 330.987 111.111i 0.548901 0.184263i
\(604\) 0 0
\(605\) 38.7133 22.3512i 0.0639890 0.0369441i
\(606\) 0 0
\(607\) 107.749 + 186.627i 0.177511 + 0.307457i 0.941027 0.338331i \(-0.109862\pi\)
−0.763517 + 0.645788i \(0.776529\pi\)
\(608\) 0 0
\(609\) 53.9474 44.1213i 0.0885836 0.0724488i
\(610\) 0 0
\(611\) −38.2424 22.0792i −0.0625898 0.0361362i
\(612\) 0 0
\(613\) 401.592 695.578i 0.655126 1.13471i −0.326736 0.945116i \(-0.605949\pi\)
0.981862 0.189596i \(-0.0607178\pi\)
\(614\) 0 0
\(615\) −14.5789 + 38.5378i −0.0237055 + 0.0626630i
\(616\) 0 0
\(617\) −332.782 192.132i −0.539355 0.311397i 0.205462 0.978665i \(-0.434130\pi\)
−0.744818 + 0.667268i \(0.767464\pi\)
\(618\) 0 0
\(619\) −55.6379 + 96.3677i −0.0898835 + 0.155683i −0.907462 0.420135i \(-0.861983\pi\)
0.817578 + 0.575818i \(0.195316\pi\)
\(620\) 0 0
\(621\) 507.870 + 19.2003i 0.817826 + 0.0309184i
\(622\) 0 0
\(623\) 52.6061i 0.0844399i
\(624\) 0 0
\(625\) 380.444 0.608710
\(626\) 0 0
\(627\) 622.819 + 289.488i 0.993331 + 0.461703i
\(628\) 0 0
\(629\) −860.240 496.660i −1.36763 0.789602i
\(630\) 0 0
\(631\) −396.481 686.725i −0.628337 1.08831i −0.987885 0.155186i \(-0.950402\pi\)
0.359548 0.933127i \(-0.382931\pi\)
\(632\) 0 0
\(633\) 164.052 433.654i 0.259166 0.685078i
\(634\) 0 0
\(635\) 378.977 218.803i 0.596815 0.344571i
\(636\) 0 0
\(637\) −251.499 −0.394818
\(638\) 0 0
\(639\) −314.517 936.916i −0.492203 1.46622i
\(640\) 0 0
\(641\) 465.052 268.498i 0.725510 0.418873i −0.0912673 0.995826i \(-0.529092\pi\)
0.816777 + 0.576953i \(0.195758\pi\)
\(642\) 0 0
\(643\) −502.827 −0.782001 −0.391001 0.920390i \(-0.627871\pi\)
−0.391001 + 0.920390i \(0.627871\pi\)
\(644\) 0 0
\(645\) 37.0119 + 226.556i 0.0573828 + 0.351249i
\(646\) 0 0
\(647\) 42.7301i 0.0660435i −0.999455 0.0330217i \(-0.989487\pi\)
0.999455 0.0330217i \(-0.0105131\pi\)
\(648\) 0 0
\(649\) 306.439 530.768i 0.472171 0.817824i
\(650\) 0 0
\(651\) −149.781 + 395.931i −0.230079 + 0.608189i
\(652\) 0 0
\(653\) 539.034 311.211i 0.825473 0.476587i −0.0268270 0.999640i \(-0.508540\pi\)
0.852300 + 0.523053i \(0.175207\pi\)
\(654\) 0 0
\(655\) −465.243 −0.710295
\(656\) 0 0
\(657\) −197.100 + 66.1655i −0.300000 + 0.100708i
\(658\) 0 0
\(659\) 921.084i 1.39770i 0.715269 + 0.698850i \(0.246304\pi\)
−0.715269 + 0.698850i \(0.753696\pi\)
\(660\) 0 0
\(661\) 55.6683 96.4203i 0.0842183 0.145870i −0.820840 0.571159i \(-0.806494\pi\)
0.905058 + 0.425288i \(0.139827\pi\)
\(662\) 0 0
\(663\) −92.9191 568.773i −0.140149 0.857878i
\(664\) 0 0
\(665\) 12.7273 173.005i 0.0191389 0.260158i
\(666\) 0 0
\(667\) 44.2627 76.6652i 0.0663608 0.114940i
\(668\) 0 0
\(669\) 387.485 63.3024i 0.579200 0.0946225i
\(670\) 0 0
\(671\) −240.227 138.695i −0.358014 0.206699i
\(672\) 0 0
\(673\) 223.538 387.179i 0.332152 0.575304i −0.650782 0.759265i \(-0.725559\pi\)
0.982934 + 0.183961i \(0.0588921\pi\)
\(674\) 0 0
\(675\) 515.331 272.105i 0.763453 0.403118i
\(676\) 0 0
\(677\) 202.443 + 116.881i 0.299030 + 0.172645i 0.642007 0.766699i \(-0.278102\pi\)
−0.342977 + 0.939344i \(0.611435\pi\)
\(678\) 0 0
\(679\) −497.352 −0.732477
\(680\) 0 0
\(681\) −375.760 + 307.319i −0.551777 + 0.451276i
\(682\) 0 0
\(683\) 496.474i 0.726902i 0.931613 + 0.363451i \(0.118402\pi\)
−0.931613 + 0.363451i \(0.881598\pi\)
\(684\) 0 0
\(685\) 9.73487 0.0142115
\(686\) 0 0
\(687\) −998.054 + 163.050i −1.45277 + 0.237336i
\(688\) 0 0
\(689\) 489.561i 0.710539i
\(690\) 0 0
\(691\) 237.938 412.120i 0.344338 0.596411i −0.640895 0.767628i \(-0.721437\pi\)
0.985233 + 0.171217i \(0.0547701\pi\)
\(692\) 0 0
\(693\) 525.022 + 106.277i 0.757608 + 0.153358i
\(694\) 0 0
\(695\) 260.402 + 150.343i 0.374679 + 0.216321i
\(696\) 0 0
\(697\) −69.8126 + 120.919i −0.100162 + 0.173485i
\(698\) 0 0
\(699\) 19.9530 16.3188i 0.0285451 0.0233459i
\(700\) 0 0
\(701\) −484.715 279.850i −0.691462 0.399216i 0.112697 0.993629i \(-0.464051\pi\)
−0.804160 + 0.594413i \(0.797384\pi\)
\(702\) 0 0
\(703\) −437.027 904.335i −0.621661 1.28639i
\(704\) 0 0
\(705\) −8.47443 + 22.4013i −0.0120205 + 0.0317749i
\(706\) 0 0
\(707\) −629.510 363.448i −0.890397 0.514071i
\(708\) 0 0
\(709\) 690.685 0.974168 0.487084 0.873355i \(-0.338061\pi\)
0.487084 + 0.873355i \(0.338061\pi\)
\(710\) 0 0
\(711\) 266.105 1314.59i 0.374268 1.84894i
\(712\) 0 0
\(713\) 537.709i 0.754150i
\(714\) 0 0
\(715\) −113.845 197.185i −0.159224 0.275784i
\(716\) 0 0
\(717\) −120.772 739.266i −0.168441 1.03105i
\(718\) 0 0
\(719\) −673.685 388.952i −0.936975 0.540963i −0.0479641 0.998849i \(-0.515273\pi\)
−0.889011 + 0.457886i \(0.848607\pi\)
\(720\) 0 0
\(721\) −280.682 −0.389296
\(722\) 0 0
\(723\) −294.914 + 779.576i −0.407904 + 1.07825i
\(724\) 0 0
\(725\) 101.506i 0.140009i
\(726\) 0 0
\(727\) 210.717 + 364.972i 0.289844 + 0.502025i 0.973772 0.227525i \(-0.0730632\pi\)
−0.683928 + 0.729549i \(0.739730\pi\)
\(728\) 0 0
\(729\) 411.127 602.010i 0.563960 0.825802i
\(730\) 0 0
\(731\) 777.908i 1.06417i
\(732\) 0 0
\(733\) 216.673 + 375.289i 0.295598 + 0.511990i 0.975124 0.221661i \(-0.0711479\pi\)
−0.679526 + 0.733651i \(0.737815\pi\)
\(734\) 0 0
\(735\) 21.9931 + 134.623i 0.0299225 + 0.183161i
\(736\) 0 0
\(737\) 404.807 233.715i 0.549263 0.317117i
\(738\) 0 0
\(739\) 354.109 613.335i 0.479174 0.829953i −0.520541 0.853837i \(-0.674270\pi\)
0.999715 + 0.0238836i \(0.00760311\pi\)
\(740\) 0 0
\(741\) 245.624 528.446i 0.331476 0.713153i
\(742\) 0 0
\(743\) 815.843i 1.09804i −0.835810 0.549019i \(-0.815001\pi\)
0.835810 0.549019i \(-0.184999\pi\)
\(744\) 0 0
\(745\) −131.983 −0.177158
\(746\) 0 0
\(747\) 212.508 + 633.040i 0.284482 + 0.847443i
\(748\) 0 0
\(749\) 267.690 + 154.551i 0.357396 + 0.206343i
\(750\) 0 0
\(751\) 541.246 937.465i 0.720700 1.24829i −0.240019 0.970768i \(-0.577154\pi\)
0.960720 0.277521i \(-0.0895129\pi\)
\(752\) 0 0
\(753\) 230.790 + 1412.70i 0.306494 + 1.87610i
\(754\) 0 0
\(755\) −24.9252 14.3906i −0.0330135 0.0190604i
\(756\) 0 0
\(757\) 160.866 278.628i 0.212505 0.368069i −0.739993 0.672614i \(-0.765171\pi\)
0.952498 + 0.304546i \(0.0985046\pi\)
\(758\) 0 0
\(759\) 671.524 109.705i 0.884749 0.144539i
\(760\) 0 0
\(761\) 958.373 553.317i 1.25936 0.727092i 0.286410 0.958107i \(-0.407538\pi\)
0.972950 + 0.231015i \(0.0742048\pi\)
\(762\) 0 0
\(763\) 159.309 + 275.931i 0.208793 + 0.361640i
\(764\) 0 0
\(765\) −296.329 + 99.4761i −0.387358 + 0.130034i
\(766\) 0 0
\(767\) −450.344 260.006i −0.587150 0.338991i
\(768\) 0 0
\(769\) 420.271 727.930i 0.546516 0.946593i −0.451994 0.892021i \(-0.649287\pi\)
0.998510 0.0545721i \(-0.0173795\pi\)
\(770\) 0 0
\(771\) 409.361 334.799i 0.530948 0.434240i
\(772\) 0 0
\(773\) −676.445 + 390.545i −0.875090 + 0.505233i −0.869036 0.494748i \(-0.835260\pi\)
−0.00605359 + 0.999982i \(0.501927\pi\)
\(774\) 0 0
\(775\) 308.278 + 533.953i 0.397778 + 0.688972i
\(776\) 0 0
\(777\) −495.943 606.392i −0.638280 0.780428i
\(778\) 0 0
\(779\) −127.117 + 61.4304i −0.163180 + 0.0788581i
\(780\) 0 0
\(781\) −661.571 1145.87i −0.847081 1.46719i
\(782\) 0 0
\(783\) −59.2899 112.287i −0.0757214 0.143406i
\(784\) 0 0
\(785\) 275.809i 0.351350i
\(786\) 0 0
\(787\) −383.786 664.737i −0.487657 0.844647i 0.512242 0.858841i \(-0.328815\pi\)
−0.999899 + 0.0141942i \(0.995482\pi\)
\(788\) 0 0
\(789\) 91.2325 + 558.449i 0.115631 + 0.707794i
\(790\) 0 0
\(791\) 629.631i 0.795993i
\(792\) 0 0
\(793\) −117.680 + 203.827i −0.148398 + 0.257033i
\(794\) 0 0
\(795\) 262.054 42.8111i 0.329628 0.0538505i
\(796\) 0 0
\(797\) −796.725