Properties

Label 684.3.m.a.353.2
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 353.2
Character \(\chi\) \(=\) 684.353
Dual form 684.3.m.a.653.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.99460 - 0.179992i) q^{3} -0.944063i q^{5} +(-5.01764 + 8.69081i) q^{7} +(8.93521 + 1.07801i) q^{9} +O(q^{10})\) \(q+(-2.99460 - 0.179992i) q^{3} -0.944063i q^{5} +(-5.01764 + 8.69081i) q^{7} +(8.93521 + 1.07801i) q^{9} +(2.50935 + 1.44878i) q^{11} +(3.63747 - 6.30028i) q^{13} +(-0.169924 + 2.82709i) q^{15} +(15.0969 + 8.71618i) q^{17} +(-18.3970 + 4.74856i) q^{19} +(16.5901 - 25.1223i) q^{21} +(-11.5334 - 6.65879i) q^{23} +24.1087 q^{25} +(-26.5633 - 4.83646i) q^{27} -16.6225i q^{29} +(4.71890 + 8.17338i) q^{31} +(-7.25373 - 4.79016i) q^{33} +(8.20467 + 4.73697i) q^{35} -63.1336 q^{37} +(-12.0267 + 18.2121i) q^{39} +34.1661i q^{41} +(-23.8541 - 41.3166i) q^{43} +(1.01771 - 8.43540i) q^{45} -42.6230i q^{47} +(-25.8534 - 44.7794i) q^{49} +(-43.6402 - 28.8188i) q^{51} +(-69.9633 + 40.3933i) q^{53} +(1.36774 - 2.36899i) q^{55} +(55.9464 - 10.9087i) q^{57} +92.1179i q^{59} -56.9441 q^{61} +(-54.2024 + 72.2451i) q^{63} +(-5.94786 - 3.43400i) q^{65} +(-39.6354 + 68.6505i) q^{67} +(33.3392 + 22.0163i) q^{69} +(-61.9380 - 35.7599i) q^{71} +(63.6907 - 110.316i) q^{73} +(-72.1959 - 4.33938i) q^{75} +(-25.1820 + 14.5389i) q^{77} +(-3.36504 - 5.82843i) q^{79} +(78.6758 + 19.2644i) q^{81} +(-101.821 - 58.7865i) q^{83} +(8.22863 - 14.2524i) q^{85} +(-2.99192 + 49.7777i) q^{87} +(-87.6080 + 50.5805i) q^{89} +(36.5030 + 63.2251i) q^{91} +(-12.6601 - 25.3253i) q^{93} +(4.48294 + 17.3680i) q^{95} +(-42.5419 - 73.6847i) q^{97} +(20.8598 + 15.6502i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + O(q^{10}) \) \( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99} + O(q^{100}) \)

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
\(3\) −2.99460 0.179992i −0.998199 0.0599974i
\(4\) 0 0
\(5\) 0.944063i 0.188813i −0.995534 0.0944063i \(-0.969905\pi\)
0.995534 0.0944063i \(-0.0300953\pi\)
\(6\) 0 0
\(7\) −5.01764 + 8.69081i −0.716806 + 1.24154i 0.245453 + 0.969408i \(0.421063\pi\)
−0.962259 + 0.272135i \(0.912270\pi\)
\(8\) 0 0
\(9\) 8.93521 + 1.07801i 0.992801 + 0.119779i
\(10\) 0 0
\(11\) 2.50935 + 1.44878i 0.228123 + 0.131707i 0.609706 0.792628i \(-0.291288\pi\)
−0.381583 + 0.924335i \(0.624621\pi\)
\(12\) 0 0
\(13\) 3.63747 6.30028i 0.279805 0.484637i −0.691531 0.722347i \(-0.743063\pi\)
0.971336 + 0.237710i \(0.0763967\pi\)
\(14\) 0 0
\(15\) −0.169924 + 2.82709i −0.0113283 + 0.188472i
\(16\) 0 0
\(17\) 15.0969 + 8.71618i 0.888051 + 0.512717i 0.873305 0.487175i \(-0.161972\pi\)
0.0147468 + 0.999891i \(0.495306\pi\)
\(18\) 0 0
\(19\) −18.3970 + 4.74856i −0.968265 + 0.249924i
\(20\) 0 0
\(21\) 16.5901 25.1223i 0.790004 1.19630i
\(22\) 0 0
\(23\) −11.5334 6.65879i −0.501450 0.289512i 0.227862 0.973693i \(-0.426826\pi\)
−0.729312 + 0.684181i \(0.760160\pi\)
\(24\) 0 0
\(25\) 24.1087 0.964350
\(26\) 0 0
\(27\) −26.5633 4.83646i −0.983826 0.179128i
\(28\) 0 0
\(29\) 16.6225i 0.573190i −0.958052 0.286595i \(-0.907477\pi\)
0.958052 0.286595i \(-0.0925234\pi\)
\(30\) 0 0
\(31\) 4.71890 + 8.17338i 0.152223 + 0.263657i 0.932044 0.362344i \(-0.118024\pi\)
−0.779822 + 0.626002i \(0.784690\pi\)
\(32\) 0 0
\(33\) −7.25373 4.79016i −0.219810 0.145156i
\(34\) 0 0
\(35\) 8.20467 + 4.73697i 0.234419 + 0.135342i
\(36\) 0 0
\(37\) −63.1336 −1.70631 −0.853156 0.521655i \(-0.825315\pi\)
−0.853156 + 0.521655i \(0.825315\pi\)
\(38\) 0 0
\(39\) −12.0267 + 18.2121i −0.308378 + 0.466976i
\(40\) 0 0
\(41\) 34.1661i 0.833319i 0.909063 + 0.416659i \(0.136799\pi\)
−0.909063 + 0.416659i \(0.863201\pi\)
\(42\) 0 0
\(43\) −23.8541 41.3166i −0.554747 0.960850i −0.997923 0.0644157i \(-0.979482\pi\)
0.443176 0.896435i \(-0.353852\pi\)
\(44\) 0 0
\(45\) 1.01771 8.43540i 0.0226157 0.187453i
\(46\) 0 0
\(47\) 42.6230i 0.906873i −0.891289 0.453437i \(-0.850198\pi\)
0.891289 0.453437i \(-0.149802\pi\)
\(48\) 0 0
\(49\) −25.8534 44.7794i −0.527620 0.913865i
\(50\) 0 0
\(51\) −43.6402 28.8188i −0.855690 0.565074i
\(52\) 0 0
\(53\) −69.9633 + 40.3933i −1.32006 + 0.762138i −0.983738 0.179609i \(-0.942517\pi\)
−0.336323 + 0.941747i \(0.609183\pi\)
\(54\) 0 0
\(55\) 1.36774 2.36899i 0.0248679 0.0430725i
\(56\) 0 0
\(57\) 55.9464 10.9087i 0.981516 0.191381i
\(58\) 0 0
\(59\) 92.1179i 1.56132i 0.624955 + 0.780661i \(0.285117\pi\)
−0.624955 + 0.780661i \(0.714883\pi\)
\(60\) 0 0
\(61\) −56.9441 −0.933509 −0.466755 0.884387i \(-0.654577\pi\)
−0.466755 + 0.884387i \(0.654577\pi\)
\(62\) 0 0
\(63\) −54.2024 + 72.2451i −0.860355 + 1.14675i
\(64\) 0 0
\(65\) −5.94786 3.43400i −0.0915056 0.0528308i
\(66\) 0 0
\(67\) −39.6354 + 68.6505i −0.591573 + 1.02463i 0.402448 + 0.915443i \(0.368160\pi\)
−0.994021 + 0.109192i \(0.965174\pi\)
\(68\) 0 0
\(69\) 33.3392 + 22.0163i 0.483177 + 0.319077i
\(70\) 0 0
\(71\) −61.9380 35.7599i −0.872366 0.503661i −0.00423248 0.999991i \(-0.501347\pi\)
−0.868134 + 0.496330i \(0.834681\pi\)
\(72\) 0 0
\(73\) 63.6907 110.316i 0.872475 1.51117i 0.0130472 0.999915i \(-0.495847\pi\)
0.859428 0.511257i \(-0.170820\pi\)
\(74\) 0 0
\(75\) −72.1959 4.33938i −0.962613 0.0578584i
\(76\) 0 0
\(77\) −25.1820 + 14.5389i −0.327040 + 0.188816i
\(78\) 0 0
\(79\) −3.36504 5.82843i −0.0425955 0.0737776i 0.843942 0.536435i \(-0.180229\pi\)
−0.886537 + 0.462657i \(0.846896\pi\)
\(80\) 0 0
\(81\) 78.6758 + 19.2644i 0.971306 + 0.237832i
\(82\) 0 0
\(83\) −101.821 58.7865i −1.22676 0.708271i −0.260410 0.965498i \(-0.583858\pi\)
−0.966351 + 0.257227i \(0.917191\pi\)
\(84\) 0 0
\(85\) 8.22863 14.2524i 0.0968074 0.167675i
\(86\) 0 0
\(87\) −2.99192 + 49.7777i −0.0343899 + 0.572157i
\(88\) 0 0
\(89\) −87.6080 + 50.5805i −0.984360 + 0.568320i −0.903584 0.428412i \(-0.859073\pi\)
−0.0807762 + 0.996732i \(0.525740\pi\)
\(90\) 0 0
\(91\) 36.5030 + 63.2251i 0.401132 + 0.694781i
\(92\) 0 0
\(93\) −12.6601 25.3253i −0.136130 0.272315i
\(94\) 0 0
\(95\) 4.48294 + 17.3680i 0.0471889 + 0.182821i
\(96\) 0 0
\(97\) −42.5419 73.6847i −0.438576 0.759637i 0.559004 0.829165i \(-0.311184\pi\)
−0.997580 + 0.0695287i \(0.977850\pi\)
\(98\) 0 0
\(99\) 20.8598 + 15.6502i 0.210705 + 0.158083i
\(100\) 0 0
\(101\) 196.653i 1.94706i −0.228552 0.973532i \(-0.573399\pi\)
0.228552 0.973532i \(-0.426601\pi\)
\(102\) 0 0
\(103\) −32.8937 56.9735i −0.319356 0.553141i 0.660998 0.750388i \(-0.270133\pi\)
−0.980354 + 0.197247i \(0.936800\pi\)
\(104\) 0 0
\(105\) −23.7170 15.6621i −0.225877 0.149163i
\(106\) 0 0
\(107\) 2.00186i 0.0187090i −0.999956 0.00935448i \(-0.997022\pi\)
0.999956 0.00935448i \(-0.00297767\pi\)
\(108\) 0 0
\(109\) 33.9399 58.7857i 0.311375 0.539318i −0.667285 0.744802i \(-0.732544\pi\)
0.978660 + 0.205485i \(0.0658770\pi\)
\(110\) 0 0
\(111\) 189.060 + 11.3635i 1.70324 + 0.102374i
\(112\) 0 0
\(113\) −92.2373 + 53.2532i −0.816260 + 0.471268i −0.849125 0.528192i \(-0.822870\pi\)
0.0328653 + 0.999460i \(0.489537\pi\)
\(114\) 0 0
\(115\) −6.28631 + 10.8882i −0.0546636 + 0.0946801i
\(116\) 0 0
\(117\) 39.2933 52.3731i 0.335840 0.447633i
\(118\) 0 0
\(119\) −151.501 + 87.4693i −1.27312 + 0.735036i
\(120\) 0 0
\(121\) −56.3021 97.5181i −0.465307 0.805935i
\(122\) 0 0
\(123\) 6.14962 102.314i 0.0499969 0.831818i
\(124\) 0 0
\(125\) 46.3617i 0.370894i
\(126\) 0 0
\(127\) −8.57128 14.8459i −0.0674904 0.116897i 0.830306 0.557308i \(-0.188166\pi\)
−0.897796 + 0.440412i \(0.854833\pi\)
\(128\) 0 0
\(129\) 63.9968 + 128.020i 0.496099 + 0.992403i
\(130\) 0 0
\(131\) 175.291i 1.33810i 0.743218 + 0.669049i \(0.233298\pi\)
−0.743218 + 0.669049i \(0.766702\pi\)
\(132\) 0 0
\(133\) 51.0409 183.712i 0.383766 1.38129i
\(134\) 0 0
\(135\) −4.56592 + 25.0774i −0.0338217 + 0.185759i
\(136\) 0 0
\(137\) 171.435i 1.25135i 0.780084 + 0.625675i \(0.215176\pi\)
−0.780084 + 0.625675i \(0.784824\pi\)
\(138\) 0 0
\(139\) 31.9396 55.3210i 0.229781 0.397993i −0.727962 0.685618i \(-0.759532\pi\)
0.957743 + 0.287625i \(0.0928655\pi\)
\(140\) 0 0
\(141\) −7.67181 + 127.639i −0.0544100 + 0.905240i
\(142\) 0 0
\(143\) 18.2554 10.5398i 0.127660 0.0737046i
\(144\) 0 0
\(145\) −15.6927 −0.108225
\(146\) 0 0
\(147\) 69.3605 + 138.750i 0.471840 + 0.943875i
\(148\) 0 0
\(149\) 161.148i 1.08153i 0.841173 + 0.540766i \(0.181866\pi\)
−0.841173 + 0.540766i \(0.818134\pi\)
\(150\) 0 0
\(151\) 97.2259 168.400i 0.643880 1.11523i −0.340679 0.940180i \(-0.610657\pi\)
0.984559 0.175053i \(-0.0560098\pi\)
\(152\) 0 0
\(153\) 125.498 + 94.1554i 0.820246 + 0.615395i
\(154\) 0 0
\(155\) 7.71618 4.45494i 0.0497818 0.0287415i
\(156\) 0 0
\(157\) −60.0978 −0.382789 −0.191394 0.981513i \(-0.561301\pi\)
−0.191394 + 0.981513i \(0.561301\pi\)
\(158\) 0 0
\(159\) 216.782 108.369i 1.36341 0.681565i
\(160\) 0 0
\(161\) 115.740 66.8228i 0.718885 0.415048i
\(162\) 0 0
\(163\) 37.0420 0.227252 0.113626 0.993524i \(-0.463753\pi\)
0.113626 + 0.993524i \(0.463753\pi\)
\(164\) 0 0
\(165\) −4.52221 + 6.84798i −0.0274073 + 0.0415029i
\(166\) 0 0
\(167\) 19.3428 + 11.1676i 0.115825 + 0.0668718i 0.556793 0.830651i \(-0.312031\pi\)
−0.440968 + 0.897523i \(0.645365\pi\)
\(168\) 0 0
\(169\) 58.0376 + 100.524i 0.343418 + 0.594817i
\(170\) 0 0
\(171\) −169.500 + 22.5972i −0.991230 + 0.132148i
\(172\) 0 0
\(173\) 189.603 109.467i 1.09597 0.632759i 0.160811 0.986985i \(-0.448589\pi\)
0.935160 + 0.354227i \(0.115256\pi\)
\(174\) 0 0
\(175\) −120.969 + 209.524i −0.691251 + 1.19728i
\(176\) 0 0
\(177\) 16.5805 275.856i 0.0936751 1.55851i
\(178\) 0 0
\(179\) 71.3531i 0.398621i 0.979936 + 0.199310i \(0.0638702\pi\)
−0.979936 + 0.199310i \(0.936130\pi\)
\(180\) 0 0
\(181\) 42.9974 + 74.4737i 0.237555 + 0.411457i 0.960012 0.279959i \(-0.0903207\pi\)
−0.722457 + 0.691416i \(0.756987\pi\)
\(182\) 0 0
\(183\) 170.524 + 10.2495i 0.931827 + 0.0560081i
\(184\) 0 0
\(185\) 59.6021i 0.322173i
\(186\) 0 0
\(187\) 25.2556 + 43.7440i 0.135057 + 0.233925i
\(188\) 0 0
\(189\) 175.318 206.589i 0.927607 1.09306i
\(190\) 0 0
\(191\) 276.487 + 159.630i 1.44757 + 0.835757i 0.998337 0.0576547i \(-0.0183623\pi\)
0.449238 + 0.893412i \(0.351696\pi\)
\(192\) 0 0
\(193\) 112.770 0.584300 0.292150 0.956372i \(-0.405629\pi\)
0.292150 + 0.956372i \(0.405629\pi\)
\(194\) 0 0
\(195\) 17.1933 + 11.3540i 0.0881710 + 0.0582257i
\(196\) 0 0
\(197\) 94.3781i 0.479077i 0.970887 + 0.239538i \(0.0769961\pi\)
−0.970887 + 0.239538i \(0.923004\pi\)
\(198\) 0 0
\(199\) 149.404 + 258.776i 0.750775 + 1.30038i 0.947447 + 0.319911i \(0.103653\pi\)
−0.196672 + 0.980469i \(0.563013\pi\)
\(200\) 0 0
\(201\) 131.049 198.446i 0.651983 0.987296i
\(202\) 0 0
\(203\) 144.463 + 83.4057i 0.711640 + 0.410866i
\(204\) 0 0
\(205\) 32.2549 0.157341
\(206\) 0 0
\(207\) −95.8747 71.9307i −0.463163 0.347491i
\(208\) 0 0
\(209\) −53.0443 14.7374i −0.253800 0.0705137i
\(210\) 0 0
\(211\) −32.9241 −0.156039 −0.0780193 0.996952i \(-0.524860\pi\)
−0.0780193 + 0.996952i \(0.524860\pi\)
\(212\) 0 0
\(213\) 179.043 + 118.235i 0.840577 + 0.555093i
\(214\) 0 0
\(215\) −39.0054 + 22.5198i −0.181421 + 0.104743i
\(216\) 0 0
\(217\) −94.7110 −0.436456
\(218\) 0 0
\(219\) −210.584 + 318.887i −0.961570 + 1.45610i
\(220\) 0 0
\(221\) 109.829 63.4097i 0.496963 0.286922i
\(222\) 0 0
\(223\) −122.138 211.549i −0.547704 0.948652i −0.998431 0.0559898i \(-0.982169\pi\)
0.450727 0.892662i \(-0.351165\pi\)
\(224\) 0 0
\(225\) 215.417 + 25.9894i 0.957407 + 0.115508i
\(226\) 0 0
\(227\) −376.013 217.091i −1.65644 0.956348i −0.974337 0.225095i \(-0.927731\pi\)
−0.682107 0.731253i \(-0.738936\pi\)
\(228\) 0 0
\(229\) −202.602 350.917i −0.884724 1.53239i −0.846030 0.533136i \(-0.821014\pi\)
−0.0386942 0.999251i \(-0.512320\pi\)
\(230\) 0 0
\(231\) 78.0269 39.0054i 0.337779 0.168855i
\(232\) 0 0
\(233\) 200.063 + 115.506i 0.858639 + 0.495735i 0.863556 0.504253i \(-0.168232\pi\)
−0.00491747 + 0.999988i \(0.501565\pi\)
\(234\) 0 0
\(235\) −40.2388 −0.171229
\(236\) 0 0
\(237\) 9.02788 + 18.0595i 0.0380923 + 0.0762003i
\(238\) 0 0
\(239\) −83.8959 + 48.4373i −0.351029 + 0.202667i −0.665138 0.746720i \(-0.731627\pi\)
0.314110 + 0.949387i \(0.398294\pi\)
\(240\) 0 0
\(241\) −298.299 −1.23775 −0.618877 0.785488i \(-0.712412\pi\)
−0.618877 + 0.785488i \(0.712412\pi\)
\(242\) 0 0
\(243\) −232.135 71.8502i −0.955287 0.295680i
\(244\) 0 0
\(245\) −42.2746 + 24.4072i −0.172549 + 0.0996214i
\(246\) 0 0
\(247\) −37.0014 + 133.179i −0.149803 + 0.539187i
\(248\) 0 0
\(249\) 294.332 + 194.369i 1.18206 + 0.780597i
\(250\) 0 0
\(251\) −2.82420 + 1.63055i −0.0112518 + 0.00649622i −0.505615 0.862759i \(-0.668734\pi\)
0.494364 + 0.869255i \(0.335401\pi\)
\(252\) 0 0
\(253\) −19.2942 33.4185i −0.0762615 0.132089i
\(254\) 0 0
\(255\) −27.2067 + 41.1991i −0.106693 + 0.161565i
\(256\) 0 0
\(257\) −75.6315 43.6659i −0.294286 0.169906i 0.345587 0.938387i \(-0.387680\pi\)
−0.639873 + 0.768481i \(0.721013\pi\)
\(258\) 0 0
\(259\) 316.781 548.682i 1.22309 2.11846i
\(260\) 0 0
\(261\) 17.9192 148.526i 0.0686559 0.569063i
\(262\) 0 0
\(263\) −146.393 + 84.5202i −0.556629 + 0.321370i −0.751791 0.659401i \(-0.770810\pi\)
0.195163 + 0.980771i \(0.437477\pi\)
\(264\) 0 0
\(265\) 38.1338 + 66.0497i 0.143901 + 0.249244i
\(266\) 0 0
\(267\) 271.455 135.699i 1.01668 0.508238i
\(268\) 0 0
\(269\) −28.8312 16.6457i −0.107179 0.0618798i 0.445452 0.895306i \(-0.353043\pi\)
−0.552631 + 0.833426i \(0.686376\pi\)
\(270\) 0 0
\(271\) 101.879 176.460i 0.375938 0.651144i −0.614529 0.788894i \(-0.710654\pi\)
0.990467 + 0.137750i \(0.0439871\pi\)
\(272\) 0 0
\(273\) −97.9317 195.904i −0.358724 0.717596i
\(274\) 0 0
\(275\) 60.4973 + 34.9282i 0.219990 + 0.127011i
\(276\) 0 0
\(277\) 69.4690 120.324i 0.250791 0.434382i −0.712953 0.701212i \(-0.752643\pi\)
0.963744 + 0.266830i \(0.0859761\pi\)
\(278\) 0 0
\(279\) 33.3534 + 78.1178i 0.119546 + 0.279992i
\(280\) 0 0
\(281\) 145.827i 0.518956i 0.965749 + 0.259478i \(0.0835505\pi\)
−0.965749 + 0.259478i \(0.916450\pi\)
\(282\) 0 0
\(283\) −333.171 −1.17728 −0.588641 0.808395i \(-0.700337\pi\)
−0.588641 + 0.808395i \(0.700337\pi\)
\(284\) 0 0
\(285\) −10.2985 52.8169i −0.0361351 0.185323i
\(286\) 0 0
\(287\) −296.931 171.433i −1.03460 0.597328i
\(288\) 0 0
\(289\) 7.44374 + 12.8929i 0.0257569 + 0.0446123i
\(290\) 0 0
\(291\) 114.133 + 228.313i 0.392210 + 0.784582i
\(292\) 0 0
\(293\) −163.865 + 94.6077i −0.559267 + 0.322893i −0.752851 0.658191i \(-0.771322\pi\)
0.193584 + 0.981084i \(0.437989\pi\)
\(294\) 0 0
\(295\) 86.9651 0.294797
\(296\) 0 0
\(297\) −59.6497 50.6206i −0.200841 0.170440i
\(298\) 0 0
\(299\) −83.9044 + 48.4423i −0.280617 + 0.162014i
\(300\) 0 0
\(301\) 478.766 1.59058
\(302\) 0 0
\(303\) −35.3960 + 588.897i −0.116819 + 1.94356i
\(304\) 0 0
\(305\) 53.7588i 0.176258i
\(306\) 0 0
\(307\) 42.5147 73.6377i 0.138484 0.239862i −0.788439 0.615113i \(-0.789110\pi\)
0.926923 + 0.375251i \(0.122444\pi\)
\(308\) 0 0
\(309\) 88.2485 + 176.533i 0.285594 + 0.571305i
\(310\) 0 0
\(311\) 119.243 68.8452i 0.383420 0.221367i −0.295885 0.955223i \(-0.595615\pi\)
0.679305 + 0.733856i \(0.262281\pi\)
\(312\) 0 0
\(313\) 38.4710 0.122910 0.0614552 0.998110i \(-0.480426\pi\)
0.0614552 + 0.998110i \(0.480426\pi\)
\(314\) 0 0
\(315\) 68.2039 + 51.1705i 0.216520 + 0.162446i
\(316\) 0 0
\(317\) 343.114i 1.08238i 0.840901 + 0.541189i \(0.182026\pi\)
−0.840901 + 0.541189i \(0.817974\pi\)
\(318\) 0 0
\(319\) 24.0823 41.7117i 0.0754930 0.130758i
\(320\) 0 0
\(321\) −0.360319 + 5.99476i −0.00112249 + 0.0186753i
\(322\) 0 0
\(323\) −319.127 88.6636i −0.988010 0.274500i
\(324\) 0 0
\(325\) 87.6948 151.892i 0.269830 0.467360i
\(326\) 0 0
\(327\) −112.217 + 169.930i −0.343172 + 0.519665i
\(328\) 0 0
\(329\) 370.429 + 213.867i 1.12592 + 0.650052i
\(330\) 0 0
\(331\) −59.9385 + 103.817i −0.181083 + 0.313645i −0.942250 0.334911i \(-0.891294\pi\)
0.761167 + 0.648556i \(0.224627\pi\)
\(332\) 0 0
\(333\) −564.111 68.0584i −1.69403 0.204380i
\(334\) 0 0
\(335\) 64.8104 + 37.4183i 0.193464 + 0.111696i
\(336\) 0 0
\(337\) −228.092 −0.676830 −0.338415 0.940997i \(-0.609891\pi\)
−0.338415 + 0.940997i \(0.609891\pi\)
\(338\) 0 0
\(339\) 285.799 142.870i 0.843064 0.421445i
\(340\) 0 0
\(341\) 27.3465i 0.0801951i
\(342\) 0 0
\(343\) 27.1635 0.0791938
\(344\) 0 0
\(345\) 20.7848 31.4743i 0.0602457 0.0912299i
\(346\) 0 0
\(347\) 153.282i 0.441734i −0.975304 0.220867i \(-0.929111\pi\)
0.975304 0.220867i \(-0.0708887\pi\)
\(348\) 0 0
\(349\) −166.507 + 288.398i −0.477097 + 0.826356i −0.999655 0.0262473i \(-0.991644\pi\)
0.522559 + 0.852603i \(0.324978\pi\)
\(350\) 0 0
\(351\) −127.094 + 149.764i −0.362092 + 0.426677i
\(352\) 0 0
\(353\) −158.739 91.6479i −0.449685 0.259626i 0.258012 0.966142i \(-0.416933\pi\)
−0.707697 + 0.706516i \(0.750266\pi\)
\(354\) 0 0
\(355\) −33.7596 + 58.4734i −0.0950975 + 0.164714i
\(356\) 0 0
\(357\) 469.429 234.666i 1.31493 0.657328i
\(358\) 0 0
\(359\) 420.734 + 242.911i 1.17196 + 0.676633i 0.954141 0.299356i \(-0.0967719\pi\)
0.217821 + 0.975989i \(0.430105\pi\)
\(360\) 0 0
\(361\) 315.902 174.719i 0.875076 0.483986i
\(362\) 0 0
\(363\) 151.050 + 302.161i 0.416114 + 0.832400i
\(364\) 0 0
\(365\) −104.145 60.1280i −0.285328 0.164734i
\(366\) 0 0
\(367\) −173.687 −0.473262 −0.236631 0.971600i \(-0.576043\pi\)
−0.236631 + 0.971600i \(0.576043\pi\)
\(368\) 0 0
\(369\) −36.8313 + 305.281i −0.0998137 + 0.827319i
\(370\) 0 0
\(371\) 810.716i 2.18522i
\(372\) 0 0
\(373\) 69.7815 + 120.865i 0.187082 + 0.324035i 0.944276 0.329155i \(-0.106764\pi\)
−0.757194 + 0.653190i \(0.773430\pi\)
\(374\) 0 0
\(375\) −8.34475 + 138.835i −0.0222527 + 0.370226i
\(376\) 0 0
\(377\) −104.726 60.4639i −0.277789 0.160382i
\(378\) 0 0
\(379\) 307.458 0.811234 0.405617 0.914043i \(-0.367057\pi\)
0.405617 + 0.914043i \(0.367057\pi\)
\(380\) 0 0
\(381\) 22.9954 + 46.0002i 0.0603553 + 0.120735i
\(382\) 0 0
\(383\) 187.428i 0.489369i 0.969603 + 0.244685i \(0.0786844\pi\)
−0.969603 + 0.244685i \(0.921316\pi\)
\(384\) 0 0
\(385\) 13.7256 + 23.7734i 0.0356509 + 0.0617492i
\(386\) 0 0
\(387\) −168.602 394.887i −0.435664 1.02038i
\(388\) 0 0
\(389\) 658.884i 1.69379i −0.531761 0.846895i \(-0.678469\pi\)
0.531761 0.846895i \(-0.321531\pi\)
\(390\) 0 0
\(391\) −116.078 201.054i −0.296876 0.514204i
\(392\) 0 0
\(393\) 31.5510 524.925i 0.0802824 1.33569i
\(394\) 0 0
\(395\) −5.50240 + 3.17681i −0.0139301 + 0.00804257i
\(396\) 0 0
\(397\) −357.219 + 618.721i −0.899796 + 1.55849i −0.0720408 + 0.997402i \(0.522951\pi\)
−0.827755 + 0.561090i \(0.810382\pi\)
\(398\) 0 0
\(399\) −185.913 + 540.955i −0.465948 + 1.35578i
\(400\) 0 0
\(401\) 712.138i 1.77590i 0.459936 + 0.887952i \(0.347872\pi\)
−0.459936 + 0.887952i \(0.652128\pi\)
\(402\) 0 0
\(403\) 68.6594 0.170371
\(404\) 0 0
\(405\) 18.1868 74.2749i 0.0449058 0.183395i
\(406\) 0 0
\(407\) −158.424 91.4664i −0.389249 0.224733i
\(408\) 0 0
\(409\) −35.7805 + 61.9736i −0.0874828 + 0.151525i −0.906446 0.422321i \(-0.861216\pi\)
0.818964 + 0.573845i \(0.194549\pi\)
\(410\) 0 0
\(411\) 30.8569 513.378i 0.0750777 1.24910i
\(412\) 0 0
\(413\) −800.579 462.215i −1.93845 1.11916i
\(414\) 0 0
\(415\) −55.4981 + 96.1256i −0.133730 + 0.231628i
\(416\) 0 0
\(417\) −105.604 + 159.915i −0.253246 + 0.383490i
\(418\) 0 0
\(419\) −339.757 + 196.159i −0.810875 + 0.468159i −0.847260 0.531179i \(-0.821749\pi\)
0.0363848 + 0.999338i \(0.488416\pi\)
\(420\) 0 0
\(421\) 100.615 + 174.271i 0.238991 + 0.413945i 0.960425 0.278538i \(-0.0898499\pi\)
−0.721434 + 0.692484i \(0.756517\pi\)
\(422\) 0 0
\(423\) 45.9479 380.846i 0.108624 0.900344i
\(424\) 0 0
\(425\) 363.967 + 210.136i 0.856392 + 0.494438i
\(426\) 0 0
\(427\) 285.725 494.890i 0.669144 1.15899i
\(428\) 0 0
\(429\) −56.5646 + 28.2765i −0.131852 + 0.0659125i
\(430\) 0 0
\(431\) −158.719 + 91.6364i −0.368257 + 0.212613i −0.672697 0.739918i \(-0.734864\pi\)
0.304440 + 0.952532i \(0.401531\pi\)
\(432\) 0 0
\(433\) −341.233 591.034i −0.788068 1.36497i −0.927149 0.374693i \(-0.877748\pi\)
0.139081 0.990281i \(-0.455585\pi\)
\(434\) 0 0
\(435\) 46.9933 + 2.82456i 0.108031 + 0.00649324i
\(436\) 0 0
\(437\) 243.799 + 67.7351i 0.557893 + 0.155000i
\(438\) 0 0
\(439\) 135.974 + 235.514i 0.309736 + 0.536478i 0.978304 0.207172i \(-0.0664261\pi\)
−0.668569 + 0.743650i \(0.733093\pi\)
\(440\) 0 0
\(441\) −182.733 427.983i −0.414360 0.970484i
\(442\) 0 0
\(443\) 139.879i 0.315754i −0.987459 0.157877i \(-0.949535\pi\)
0.987459 0.157877i \(-0.0504649\pi\)
\(444\) 0 0
\(445\) 47.7512 + 82.7075i 0.107306 + 0.185860i
\(446\) 0 0
\(447\) 29.0054 482.574i 0.0648890 1.07958i
\(448\) 0 0
\(449\) 290.887i 0.647855i −0.946082 0.323928i \(-0.894997\pi\)
0.946082 0.323928i \(-0.105003\pi\)
\(450\) 0 0
\(451\) −49.4990 + 85.7347i −0.109754 + 0.190099i
\(452\) 0 0
\(453\) −321.463 + 486.791i −0.709631 + 1.07459i
\(454\) 0 0
\(455\) 59.6884 34.4611i 0.131183 0.0757388i
\(456\) 0 0
\(457\) −256.031 + 443.459i −0.560244 + 0.970371i 0.437231 + 0.899349i \(0.355959\pi\)
−0.997475 + 0.0710214i \(0.977374\pi\)
\(458\) 0 0
\(459\) −358.867 304.546i −0.781846 0.663499i
\(460\) 0 0
\(461\) 655.852 378.657i 1.42267 0.821381i 0.426147 0.904654i \(-0.359871\pi\)
0.996527 + 0.0832733i \(0.0265375\pi\)
\(462\) 0 0
\(463\) 2.97566 + 5.15400i 0.00642692 + 0.0111318i 0.869221 0.494424i \(-0.164621\pi\)
−0.862794 + 0.505556i \(0.831288\pi\)
\(464\) 0 0
\(465\) −23.9087 + 11.9519i −0.0514166 + 0.0257030i
\(466\) 0 0
\(467\) 329.416i 0.705387i 0.935739 + 0.352693i \(0.114734\pi\)
−0.935739 + 0.352693i \(0.885266\pi\)
\(468\) 0 0
\(469\) −397.752 688.927i −0.848086 1.46893i
\(470\) 0 0
\(471\) 179.969 + 10.8171i 0.382099 + 0.0229663i
\(472\) 0 0
\(473\) 138.237i 0.292256i
\(474\) 0 0
\(475\) −443.530 + 114.482i −0.933747 + 0.241014i
\(476\) 0 0
\(477\) −668.680 + 285.502i −1.40185 + 0.598536i
\(478\) 0 0
\(479\) 63.0086i 0.131542i −0.997835 0.0657710i \(-0.979049\pi\)
0.997835 0.0657710i \(-0.0209507\pi\)
\(480\) 0 0
\(481\) −229.646 + 397.759i −0.477435 + 0.826942i
\(482\) 0 0
\(483\) −358.623 + 179.275i −0.742491 + 0.371169i
\(484\) 0 0
\(485\) −69.5630 + 40.1622i −0.143429 + 0.0828087i
\(486\) 0 0
\(487\) −83.6068 −0.171677 −0.0858386 0.996309i \(-0.527357\pi\)
−0.0858386 + 0.996309i \(0.527357\pi\)
\(488\) 0 0
\(489\) −110.926 6.66727i −0.226842 0.0136345i
\(490\) 0 0
\(491\) 15.2612i 0.0310819i −0.999879 0.0155409i \(-0.995053\pi\)
0.999879 0.0155409i \(-0.00494703\pi\)
\(492\) 0 0
\(493\) 144.885 250.948i 0.293884 0.509022i
\(494\) 0 0
\(495\) 14.7748 19.6930i 0.0298480 0.0397837i
\(496\) 0 0
\(497\) 621.565 358.861i 1.25063 0.722054i
\(498\) 0 0
\(499\) 38.5770 0.0773086 0.0386543 0.999253i \(-0.487693\pi\)
0.0386543 + 0.999253i \(0.487693\pi\)
\(500\) 0 0
\(501\) −55.9139 36.9240i −0.111605 0.0737005i
\(502\) 0 0
\(503\) −146.505 + 84.5850i −0.291263 + 0.168161i −0.638511 0.769612i \(-0.720449\pi\)
0.347248 + 0.937773i \(0.387116\pi\)
\(504\) 0 0
\(505\) −185.653 −0.367630
\(506\) 0 0
\(507\) −155.706 311.475i −0.307112 0.614350i
\(508\) 0 0
\(509\) −403.328 232.861i −0.792392 0.457488i 0.0484118 0.998827i \(-0.484584\pi\)
−0.840804 + 0.541340i \(0.817917\pi\)
\(510\) 0 0
\(511\) 639.154 + 1107.05i 1.25079 + 2.16643i
\(512\) 0 0
\(513\) 511.652 37.1609i 0.997373 0.0724384i
\(514\) 0 0
\(515\) −53.7866 + 31.0537i −0.104440 + 0.0602984i
\(516\) 0 0
\(517\) 61.7512 106.956i 0.119441 0.206879i
\(518\) 0 0
\(519\) −587.487 + 293.683i −1.13196 + 0.565863i
\(520\) 0 0
\(521\) 940.532i 1.80524i 0.430433 + 0.902622i \(0.358361\pi\)
−0.430433 + 0.902622i \(0.641639\pi\)
\(522\) 0 0
\(523\) 180.183 + 312.086i 0.344518 + 0.596723i 0.985266 0.171028i \(-0.0547090\pi\)
−0.640748 + 0.767751i \(0.721376\pi\)
\(524\) 0 0
\(525\) 399.966 605.667i 0.761840 1.15365i
\(526\) 0 0
\(527\) 164.523i 0.312188i
\(528\) 0 0
\(529\) −175.821 304.531i −0.332365 0.575673i
\(530\) 0 0
\(531\) −99.3038 + 823.093i −0.187013 + 1.55008i
\(532\) 0 0
\(533\) 215.256 + 124.278i 0.403857 + 0.233167i
\(534\) 0 0
\(535\) −1.88988 −0.00353249
\(536\) 0 0
\(537\) 12.8430 213.674i 0.0239162 0.397903i
\(538\) 0 0
\(539\) 149.823i 0.277965i
\(540\) 0 0
\(541\) 242.147 + 419.411i 0.447591 + 0.775251i 0.998229 0.0594939i \(-0.0189487\pi\)
−0.550638 + 0.834744i \(0.685615\pi\)
\(542\) 0 0
\(543\) −115.355 230.758i −0.212441 0.424969i
\(544\) 0 0
\(545\) −55.4974 32.0414i −0.101830 0.0587916i
\(546\) 0 0
\(547\) 31.1222 0.0568961 0.0284481 0.999595i \(-0.490943\pi\)
0.0284481 + 0.999595i \(0.490943\pi\)
\(548\) 0 0
\(549\) −508.807 61.3861i −0.926788 0.111814i
\(550\) 0 0
\(551\) 78.9330 + 305.805i 0.143254 + 0.555000i
\(552\) 0 0
\(553\) 67.5383 0.122131
\(554\) 0 0
\(555\) 10.7279 178.484i 0.0193295 0.321593i
\(556\) 0 0
\(557\) −267.742 + 154.581i −0.480685 + 0.277524i −0.720702 0.693245i \(-0.756180\pi\)
0.240017 + 0.970769i \(0.422847\pi\)
\(558\) 0 0
\(559\) −347.075 −0.620885
\(560\) 0 0
\(561\) −67.7567 135.541i −0.120778 0.241607i
\(562\) 0 0
\(563\) 694.453 400.943i 1.23349 0.712154i 0.265732 0.964047i \(-0.414386\pi\)
0.967755 + 0.251893i \(0.0810530\pi\)
\(564\) 0 0
\(565\) 50.2744 + 87.0778i 0.0889813 + 0.154120i
\(566\) 0 0
\(567\) −562.190 + 587.094i −0.991517 + 1.03544i
\(568\) 0 0
\(569\) 94.4488 + 54.5300i 0.165991 + 0.0958349i 0.580694 0.814122i \(-0.302781\pi\)
−0.414703 + 0.909957i \(0.636115\pi\)
\(570\) 0 0
\(571\) 240.420 + 416.419i 0.421050 + 0.729281i 0.996043 0.0888782i \(-0.0283282\pi\)
−0.574992 + 0.818159i \(0.694995\pi\)
\(572\) 0 0
\(573\) −799.234 527.792i −1.39482 0.921103i
\(574\) 0 0
\(575\) −278.055 160.535i −0.483573 0.279191i
\(576\) 0 0
\(577\) −1108.78 −1.92164 −0.960818 0.277179i \(-0.910601\pi\)
−0.960818 + 0.277179i \(0.910601\pi\)
\(578\) 0 0
\(579\) −337.700 20.2977i −0.583248 0.0350565i
\(580\) 0 0
\(581\) 1021.80 589.939i 1.75870 1.01538i
\(582\) 0 0
\(583\) −234.083 −0.401515
\(584\) 0 0
\(585\) −49.4435 37.0953i −0.0845188 0.0634108i
\(586\) 0 0
\(587\) 840.894 485.490i 1.43253 0.827070i 0.435215 0.900327i \(-0.356672\pi\)
0.997313 + 0.0732563i \(0.0233391\pi\)
\(588\) 0 0
\(589\) −125.626 127.958i −0.213286 0.217246i
\(590\) 0 0
\(591\) 16.9873 282.624i 0.0287433 0.478214i
\(592\) 0 0
\(593\) −399.441 + 230.618i −0.673594 + 0.388900i −0.797437 0.603402i \(-0.793811\pi\)
0.123843 + 0.992302i \(0.460478\pi\)
\(594\) 0 0
\(595\) 82.5765 + 143.027i 0.138784 + 0.240381i
\(596\) 0 0
\(597\) −400.828 801.820i −0.671403 1.34308i
\(598\) 0 0
\(599\) −930.550 537.253i −1.55351 0.896917i −0.997852 0.0655020i \(-0.979135\pi\)
−0.555653 0.831415i \(-0.687532\pi\)
\(600\) 0 0
\(601\) −352.905 + 611.249i −0.587196 + 1.01705i 0.407401 + 0.913249i \(0.366435\pi\)
−0.994598 + 0.103805i \(0.966898\pi\)
\(602\) 0 0
\(603\) −428.156 + 570.679i −0.710043 + 0.946400i
\(604\) 0 0
\(605\) −92.0632 + 53.1527i −0.152171 + 0.0878557i
\(606\) 0 0
\(607\) 499.764 + 865.617i 0.823335 + 1.42606i 0.903185 + 0.429251i \(0.141222\pi\)
−0.0798504 + 0.996807i \(0.525444\pi\)
\(608\) 0 0
\(609\) −417.596 275.769i −0.685707 0.452822i
\(610\) 0 0
\(611\) −268.537 155.040i −0.439504 0.253748i
\(612\) 0 0
\(613\) −26.0192 + 45.0666i −0.0424457 + 0.0735181i −0.886468 0.462790i \(-0.846848\pi\)
0.844022 + 0.536308i \(0.180182\pi\)
\(614\) 0 0
\(615\) −96.5904 5.80563i −0.157058 0.00944005i
\(616\) 0 0
\(617\) 1025.06 + 591.821i 1.66137 + 0.959191i 0.972063 + 0.234721i \(0.0754175\pi\)
0.689305 + 0.724471i \(0.257916\pi\)
\(618\) 0 0
\(619\) −94.2234 + 163.200i −0.152219 + 0.263650i −0.932043 0.362348i \(-0.881975\pi\)
0.779824 + 0.625999i \(0.215308\pi\)
\(620\) 0 0
\(621\) 274.159 + 232.660i 0.441480 + 0.374654i
\(622\) 0 0
\(623\) 1015.18i 1.62950i
\(624\) 0 0
\(625\) 558.950 0.894320
\(626\) 0 0
\(627\) 156.194 + 53.6800i 0.249112 + 0.0856140i
\(628\) 0 0
\(629\) −953.120 550.284i −1.51529 0.874855i
\(630\) 0 0
\(631\) 80.3672 + 139.200i 0.127365 + 0.220602i 0.922655 0.385627i \(-0.126015\pi\)
−0.795290 + 0.606229i \(0.792681\pi\)
\(632\) 0 0
\(633\) 98.5945 + 5.92608i 0.155757 + 0.00936190i
\(634\) 0 0
\(635\) −14.0155 + 8.09183i −0.0220716 + 0.0127430i
\(636\) 0 0
\(637\) −376.164 −0.590524
\(638\) 0 0
\(639\) −514.879 386.292i −0.805758 0.604526i
\(640\) 0 0
\(641\) −29.1362 + 16.8218i −0.0454543 + 0.0262430i −0.522555 0.852606i \(-0.675021\pi\)
0.477101 + 0.878849i \(0.341688\pi\)
\(642\) 0 0
\(643\) −681.548 −1.05995 −0.529975 0.848013i \(-0.677799\pi\)
−0.529975 + 0.848013i \(0.677799\pi\)
\(644\) 0 0
\(645\) 120.859 60.4170i 0.187378 0.0936698i
\(646\) 0 0
\(647\) 823.205i 1.27234i −0.771548 0.636171i \(-0.780517\pi\)
0.771548 0.636171i \(-0.219483\pi\)
\(648\) 0 0
\(649\) −133.458 + 231.156i −0.205637 + 0.356173i
\(650\) 0 0
\(651\) 283.621 + 17.0472i 0.435670 + 0.0261862i
\(652\) 0 0
\(653\) −252.547 + 145.808i −0.386750 + 0.223290i −0.680751 0.732515i \(-0.738346\pi\)
0.294001 + 0.955805i \(0.405013\pi\)
\(654\) 0 0
\(655\) 165.486 0.252650
\(656\) 0 0
\(657\) 688.010 917.033i 1.04720 1.39579i
\(658\) 0 0
\(659\) 578.433i 0.877743i −0.898550 0.438871i \(-0.855378\pi\)
0.898550 0.438871i \(-0.144622\pi\)
\(660\) 0 0
\(661\) 552.534 957.017i 0.835906 1.44783i −0.0573850 0.998352i \(-0.518276\pi\)
0.893291 0.449479i \(-0.148390\pi\)
\(662\) 0 0
\(663\) −340.306 + 170.118i −0.513282 + 0.256588i
\(664\) 0 0
\(665\) −173.435 48.1858i −0.260805 0.0724599i
\(666\) 0 0
\(667\) −110.686 + 191.713i −0.165946 + 0.287426i
\(668\) 0 0
\(669\) 327.677 + 655.488i 0.489801 + 0.979803i
\(670\) 0 0
\(671\) −142.893 82.4991i −0.212955 0.122950i
\(672\) 0 0
\(673\) −373.740 + 647.337i −0.555334 + 0.961867i 0.442543 + 0.896747i \(0.354076\pi\)
−0.997877 + 0.0651201i \(0.979257\pi\)
\(674\) 0 0
\(675\) −640.408 116.601i −0.948752 0.172742i
\(676\) 0 0
\(677\) 630.167 + 363.827i 0.930823 + 0.537411i 0.887072 0.461632i \(-0.152736\pi\)
0.0437512 + 0.999042i \(0.486069\pi\)
\(678\) 0 0
\(679\) 853.840 1.25750
\(680\) 0 0
\(681\) 1086.93 + 717.779i 1.59608 + 1.05401i
\(682\) 0 0
\(683\) 123.112i 0.180252i −0.995930 0.0901260i \(-0.971273\pi\)
0.995930 0.0901260i \(-0.0287270\pi\)
\(684\) 0 0
\(685\) 161.845 0.236271
\(686\) 0 0
\(687\) 543.548 + 1087.32i 0.791191 + 1.58271i
\(688\) 0 0
\(689\) 587.718i 0.853001i
\(690\) 0 0
\(691\) 471.063 815.905i 0.681712 1.18076i −0.292746 0.956190i \(-0.594569\pi\)
0.974458 0.224569i \(-0.0720975\pi\)
\(692\) 0 0
\(693\) −240.680 + 102.761i −0.347301 + 0.148285i
\(694\) 0 0
\(695\) −52.2265 30.1530i −0.0751461 0.0433856i
\(696\) 0 0
\(697\) −297.798 + 515.801i −0.427257 + 0.740030i
\(698\) 0 0
\(699\) −578.317 381.904i −0.827349 0.546358i
\(700\) 0 0
\(701\) 557.020 + 321.596i 0.794608 + 0.458767i 0.841582 0.540129i \(-0.181625\pi\)
−0.0469742 + 0.998896i \(0.514958\pi\)
\(702\) 0 0
\(703\) 1161.47 299.794i 1.65216 0.426449i
\(704\) 0 0
\(705\) 120.499 + 7.24267i 0.170921 + 0.0102733i
\(706\) 0 0
\(707\) 1709.08 + 986.736i 2.41736 + 1.39567i
\(708\) 0 0
\(709\) 508.567 0.717301 0.358651 0.933472i \(-0.383237\pi\)
0.358651 + 0.933472i \(0.383237\pi\)
\(710\) 0 0
\(711\) −23.7843 55.7057i −0.0334519 0.0783485i
\(712\) 0 0
\(713\) 125.689i 0.176281i
\(714\) 0 0
\(715\) −9.95019 17.2342i −0.0139163 0.0241038i
\(716\) 0 0
\(717\) 259.952 129.950i 0.362556 0.181241i
\(718\) 0 0
\(719\) −581.261 335.591i −0.808430 0.466747i 0.0379806 0.999278i \(-0.487907\pi\)
−0.846410 + 0.532531i \(0.821241\pi\)
\(720\) 0 0
\(721\) 660.194 0.915665
\(722\) 0 0
\(723\) 893.284 + 53.6914i 1.23552 + 0.0742620i
\(724\) 0 0
\(725\) 400.748i 0.552756i
\(726\) 0 0
\(727\) −243.419 421.613i −0.334826 0.579936i 0.648625 0.761108i \(-0.275344\pi\)
−0.983451 + 0.181172i \(0.942011\pi\)
\(728\) 0 0
\(729\) 682.217 + 256.945i 0.935826 + 0.352462i
\(730\) 0 0
\(731\) 831.668i 1.13771i
\(732\) 0 0
\(733\) 244.666 + 423.774i 0.333787 + 0.578136i 0.983251 0.182256i \(-0.0583400\pi\)
−0.649464 + 0.760392i \(0.725007\pi\)
\(734\) 0 0
\(735\) 130.988 65.4807i 0.178215 0.0890894i
\(736\) 0 0
\(737\) −198.918 + 114.846i −0.269903 + 0.155828i
\(738\) 0 0
\(739\) −313.307 + 542.664i −0.423961 + 0.734322i −0.996323 0.0856793i \(-0.972694\pi\)
0.572362 + 0.820001i \(0.306027\pi\)
\(740\) 0 0
\(741\) 134.775 392.158i 0.181883 0.529228i
\(742\) 0 0
\(743\) 1256.65i 1.69132i 0.533725 + 0.845658i \(0.320792\pi\)
−0.533725 + 0.845658i \(0.679208\pi\)
\(744\) 0 0
\(745\) 152.134 0.204207
\(746\) 0 0
\(747\) −846.421 635.033i −1.13309 0.850111i
\(748\) 0 0
\(749\) 17.3978 + 10.0446i 0.0232280 + 0.0134107i
\(750\) 0 0
\(751\) 396.432 686.641i 0.527873 0.914302i −0.471599 0.881813i \(-0.656323\pi\)
0.999472 0.0324894i \(-0.0103435\pi\)
\(752\) 0 0
\(753\) 8.75082 4.37451i 0.0116213 0.00580944i
\(754\) 0 0
\(755\) −158.980 91.7874i −0.210570 0.121573i
\(756\) 0 0
\(757\) 341.349 591.233i 0.450923 0.781021i −0.547521 0.836792i \(-0.684428\pi\)
0.998444 + 0.0557708i \(0.0177616\pi\)
\(758\) 0 0
\(759\) 51.7632 + 103.548i 0.0681992 + 0.136426i
\(760\) 0 0
\(761\) 931.990 538.085i 1.22469 0.707076i 0.258777 0.965937i \(-0.416681\pi\)
0.965915 + 0.258861i \(0.0833472\pi\)
\(762\) 0 0
\(763\) 340.596 + 589.930i 0.446391 + 0.773172i
\(764\) 0 0
\(765\) 88.8887 118.478i 0.116194 0.154873i
\(766\) 0 0
\(767\) 580.369 + 335.076i 0.756674 + 0.436866i
\(768\) 0 0
\(769\) 14.6952 25.4528i 0.0191095 0.0330986i −0.856313 0.516458i \(-0.827250\pi\)
0.875422 + 0.483359i \(0.160584\pi\)
\(770\) 0 0
\(771\) 218.626 + 144.375i 0.283562 + 0.187256i
\(772\) 0 0
\(773\) −587.271 + 339.061i −0.759729 + 0.438630i −0.829198 0.558954i \(-0.811203\pi\)
0.0694693 + 0.997584i \(0.477869\pi\)
\(774\) 0 0
\(775\) 113.767 + 197.050i 0.146796 + 0.254258i
\(776\) 0 0
\(777\) −1047.39 + 1586.06i −1.34799 + 2.04126i
\(778\) 0 0
\(779\) −162.240 628.555i −0.208267 0.806874i
\(780\) 0 0
\(781\) −103.616 179.469i −0.132671 0.229793i
\(782\) 0 0
\(783\) −80.3941 + 441.549i −0.102674 + 0.563919i
\(784\) 0 0
\(785\) 56.7361i 0.0722753i
\(786\) 0 0
\(787\) 472.469 + 818.341i 0.600342 + 1.03982i 0.992769 + 0.120040i \(0.0383022\pi\)
−0.392427 + 0.919783i \(0.628364\pi\)
\(788\) 0 0
\(789\) 453.602 226.754i 0.574907 0.287395i
\(790\) 0 0
\(791\) 1068.82i 1.35123i
\(792\) 0 0
\(793\) −207.132 + 358.764i −0.261201 + 0.452413i
\(794\) 0 0
\(795\) −102.307 204.656i −0.128688 0.257429i
\(796\) 0 0