Properties

Label 99.3.l.a.80.1
Level $99$
Weight $3$
Character 99.80
Analytic conductor $2.698$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 99.l (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.69755461717\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 80.1
Character \(\chi\) \(=\) 99.80
Dual form 99.3.l.a.26.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.91284 - 2.63279i) q^{2} +(-2.03659 + 6.26797i) q^{4} +(-0.936271 + 1.28867i) q^{5} +(-3.36204 + 10.3473i) q^{7} +(8.01778 - 2.60514i) q^{8} +O(q^{10})\) \(q+(-1.91284 - 2.63279i) q^{2} +(-2.03659 + 6.26797i) q^{4} +(-0.936271 + 1.28867i) q^{5} +(-3.36204 + 10.3473i) q^{7} +(8.01778 - 2.60514i) q^{8} +5.18373 q^{10} +(-5.25607 + 9.66301i) q^{11} +(7.47384 - 5.43007i) q^{13} +(33.6733 - 10.9411i) q^{14} +(-0.868063 - 0.630685i) q^{16} +(-2.83106 + 3.89662i) q^{17} +(-7.75281 - 23.8607i) q^{19} +(-6.17053 - 8.49300i) q^{20} +(35.4947 - 4.64560i) q^{22} +36.6892i q^{23} +(6.94137 + 21.3633i) q^{25} +(-28.5925 - 9.29026i) q^{26} +(-58.0094 - 42.1463i) q^{28} +(-23.2548 - 7.55594i) q^{29} +(-47.0703 + 34.1986i) q^{31} -30.2297i q^{32} +15.6743 q^{34} +(-10.1864 - 14.0204i) q^{35} +(3.95474 - 12.1714i) q^{37} +(-47.9904 + 66.0532i) q^{38} +(-4.14967 + 12.7714i) q^{40} +(-11.8089 + 3.83696i) q^{41} +19.6984 q^{43} +(-49.8630 - 52.6244i) q^{44} +(96.5949 - 70.1803i) q^{46} +(61.7676 - 20.0695i) q^{47} +(-56.1212 - 40.7744i) q^{49} +(42.9675 - 59.1397i) q^{50} +(18.8144 + 57.9046i) q^{52} +(29.0988 + 40.0511i) q^{53} +(-7.53129 - 15.8205i) q^{55} +91.7208i q^{56} +(24.5894 + 75.6782i) q^{58} +(22.9125 + 7.44473i) q^{59} +(-35.7910 - 26.0037i) q^{61} +(180.076 + 58.5101i) q^{62} +(-83.0609 + 60.3473i) q^{64} +14.7153i q^{65} +33.0898 q^{67} +(-18.6582 - 25.6808i) q^{68} +(-17.4279 + 53.6375i) q^{70} +(44.0480 - 60.6269i) q^{71} +(12.7859 - 39.3511i) q^{73} +(-39.6096 + 12.8700i) q^{74} +165.347 q^{76} +(-82.3148 - 86.8735i) q^{77} +(-51.7531 + 37.6008i) q^{79} +(1.62549 - 0.528152i) q^{80} +(32.6905 + 23.7510i) q^{82} +(-24.7962 + 34.1290i) q^{83} +(-2.37080 - 7.29658i) q^{85} +(-37.6797 - 51.8617i) q^{86} +(-16.9686 + 91.1687i) q^{88} -111.111i q^{89} +(31.0591 + 95.5901i) q^{91} +(-229.967 - 74.7207i) q^{92} +(-170.990 - 124.231i) q^{94} +(38.0072 + 12.3493i) q^{95} +(87.4573 - 63.5414i) q^{97} +225.750i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 16 q^{4} - 16 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 16 q^{4} - 16 q^{7} + 48 q^{10} + 8 q^{13} + 96 q^{16} - 40 q^{19} - 60 q^{22} - 188 q^{25} - 348 q^{28} - 164 q^{31} + 296 q^{34} - 36 q^{37} + 48 q^{40} + 544 q^{43} + 296 q^{46} + 196 q^{49} - 640 q^{52} - 440 q^{55} - 208 q^{58} - 432 q^{61} - 328 q^{64} + 48 q^{67} + 112 q^{70} + 712 q^{73} + 2104 q^{76} + 432 q^{79} + 676 q^{82} - 68 q^{85} - 176 q^{88} + 64 q^{91} - 1360 q^{94} + 132 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.91284 2.63279i −0.956418 1.31640i −0.948617 0.316426i \(-0.897517\pi\)
−0.00780058 0.999970i \(-0.502483\pi\)
\(3\) 0 0
\(4\) −2.03659 + 6.26797i −0.509147 + 1.56699i
\(5\) −0.936271 + 1.28867i −0.187254 + 0.257733i −0.892315 0.451414i \(-0.850920\pi\)
0.705060 + 0.709147i \(0.250920\pi\)
\(6\) 0 0
\(7\) −3.36204 + 10.3473i −0.480291 + 1.47818i 0.358396 + 0.933570i \(0.383324\pi\)
−0.838687 + 0.544614i \(0.816676\pi\)
\(8\) 8.01778 2.60514i 1.00222 0.325642i
\(9\) 0 0
\(10\) 5.18373 0.518373
\(11\) −5.25607 + 9.66301i −0.477825 + 0.878455i
\(12\) 0 0
\(13\) 7.47384 5.43007i 0.574911 0.417697i −0.261975 0.965075i \(-0.584374\pi\)
0.836886 + 0.547377i \(0.184374\pi\)
\(14\) 33.6733 10.9411i 2.40523 0.781508i
\(15\) 0 0
\(16\) −0.868063 0.630685i −0.0542540 0.0394178i
\(17\) −2.83106 + 3.89662i −0.166533 + 0.229213i −0.884125 0.467251i \(-0.845244\pi\)
0.717592 + 0.696464i \(0.245244\pi\)
\(18\) 0 0
\(19\) −7.75281 23.8607i −0.408043 1.25583i −0.918328 0.395821i \(-0.870460\pi\)
0.510285 0.860006i \(-0.329540\pi\)
\(20\) −6.17053 8.49300i −0.308526 0.424650i
\(21\) 0 0
\(22\) 35.4947 4.64560i 1.61339 0.211163i
\(23\) 36.6892i 1.59518i 0.603199 + 0.797590i \(0.293892\pi\)
−0.603199 + 0.797590i \(0.706108\pi\)
\(24\) 0 0
\(25\) 6.94137 + 21.3633i 0.277655 + 0.854533i
\(26\) −28.5925 9.29026i −1.09971 0.357318i
\(27\) 0 0
\(28\) −58.0094 42.1463i −2.07176 1.50522i
\(29\) −23.2548 7.55594i −0.801889 0.260549i −0.120730 0.992685i \(-0.538524\pi\)
−0.681159 + 0.732136i \(0.738524\pi\)
\(30\) 0 0
\(31\) −47.0703 + 34.1986i −1.51840 + 1.10318i −0.556123 + 0.831100i \(0.687712\pi\)
−0.962274 + 0.272081i \(0.912288\pi\)
\(32\) 30.2297i 0.944680i
\(33\) 0 0
\(34\) 15.6743 0.461009
\(35\) −10.1864 14.0204i −0.291041 0.400583i
\(36\) 0 0
\(37\) 3.95474 12.1714i 0.106885 0.328958i −0.883283 0.468840i \(-0.844672\pi\)
0.990168 + 0.139882i \(0.0446722\pi\)
\(38\) −47.9904 + 66.0532i −1.26291 + 1.73824i
\(39\) 0 0
\(40\) −4.14967 + 12.7714i −0.103742 + 0.319284i
\(41\) −11.8089 + 3.83696i −0.288023 + 0.0935843i −0.449465 0.893298i \(-0.648385\pi\)
0.161442 + 0.986882i \(0.448385\pi\)
\(42\) 0 0
\(43\) 19.6984 0.458102 0.229051 0.973414i \(-0.426438\pi\)
0.229051 + 0.973414i \(0.426438\pi\)
\(44\) −49.8630 52.6244i −1.13325 1.19601i
\(45\) 0 0
\(46\) 96.5949 70.1803i 2.09989 1.52566i
\(47\) 61.7676 20.0695i 1.31420 0.427011i 0.433703 0.901056i \(-0.357207\pi\)
0.880500 + 0.474045i \(0.157207\pi\)
\(48\) 0 0
\(49\) −56.1212 40.7744i −1.14533 0.832131i
\(50\) 42.9675 59.1397i 0.859350 1.18279i
\(51\) 0 0
\(52\) 18.8144 + 57.9046i 0.361814 + 1.11355i
\(53\) 29.0988 + 40.0511i 0.549034 + 0.755681i 0.989881 0.141901i \(-0.0453216\pi\)
−0.440846 + 0.897583i \(0.645322\pi\)
\(54\) 0 0
\(55\) −7.53129 15.8205i −0.136933 0.287646i
\(56\) 91.7208i 1.63787i
\(57\) 0 0
\(58\) 24.5894 + 75.6782i 0.423954 + 1.30480i
\(59\) 22.9125 + 7.44473i 0.388348 + 0.126182i 0.496682 0.867933i \(-0.334552\pi\)
−0.108334 + 0.994115i \(0.534552\pi\)
\(60\) 0 0
\(61\) −35.7910 26.0037i −0.586738 0.426290i 0.254409 0.967097i \(-0.418119\pi\)
−0.841147 + 0.540807i \(0.818119\pi\)
\(62\) 180.076 + 58.5101i 2.90444 + 0.943711i
\(63\) 0 0
\(64\) −83.0609 + 60.3473i −1.29783 + 0.942926i
\(65\) 14.7153i 0.226389i
\(66\) 0 0
\(67\) 33.0898 0.493878 0.246939 0.969031i \(-0.420575\pi\)
0.246939 + 0.969031i \(0.420575\pi\)
\(68\) −18.6582 25.6808i −0.274385 0.377658i
\(69\) 0 0
\(70\) −17.4279 + 53.6375i −0.248970 + 0.766250i
\(71\) 44.0480 60.6269i 0.620395 0.853900i −0.376987 0.926219i \(-0.623040\pi\)
0.997382 + 0.0723185i \(0.0230398\pi\)
\(72\) 0 0
\(73\) 12.7859 39.3511i 0.175150 0.539056i −0.824490 0.565876i \(-0.808538\pi\)
0.999640 + 0.0268199i \(0.00853807\pi\)
\(74\) −39.6096 + 12.8700i −0.535265 + 0.173918i
\(75\) 0 0
\(76\) 165.347 2.17562
\(77\) −82.3148 86.8735i −1.06902 1.12823i
\(78\) 0 0
\(79\) −51.7531 + 37.6008i −0.655102 + 0.475960i −0.865005 0.501763i \(-0.832685\pi\)
0.209903 + 0.977722i \(0.432685\pi\)
\(80\) 1.62549 0.528152i 0.0203186 0.00660190i
\(81\) 0 0
\(82\) 32.6905 + 23.7510i 0.398664 + 0.289647i
\(83\) −24.7962 + 34.1290i −0.298749 + 0.411193i −0.931831 0.362892i \(-0.881789\pi\)
0.633082 + 0.774085i \(0.281789\pi\)
\(84\) 0 0
\(85\) −2.37080 7.29658i −0.0278918 0.0858421i
\(86\) −37.6797 51.8617i −0.438137 0.603043i
\(87\) 0 0
\(88\) −16.9686 + 91.1687i −0.192825 + 1.03601i
\(89\) 111.111i 1.24844i −0.781249 0.624220i \(-0.785417\pi\)
0.781249 0.624220i \(-0.214583\pi\)
\(90\) 0 0
\(91\) 31.0591 + 95.5901i 0.341309 + 1.05044i
\(92\) −229.967 74.7207i −2.49964 0.812181i
\(93\) 0 0
\(94\) −170.990 124.231i −1.81904 1.32161i
\(95\) 38.0072 + 12.3493i 0.400076 + 0.129993i
\(96\) 0 0
\(97\) 87.4573 63.5414i 0.901622 0.655066i −0.0372604 0.999306i \(-0.511863\pi\)
0.938882 + 0.344239i \(0.111863\pi\)
\(98\) 225.750i 2.30357i
\(99\) 0 0
\(100\) −148.041 −1.48041
\(101\) 68.4285 + 94.1838i 0.677510 + 0.932513i 0.999901 0.0140942i \(-0.00448646\pi\)
−0.322391 + 0.946607i \(0.604486\pi\)
\(102\) 0 0
\(103\) −33.7693 + 103.931i −0.327857 + 1.00904i 0.642278 + 0.766472i \(0.277990\pi\)
−0.970134 + 0.242568i \(0.922010\pi\)
\(104\) 45.7776 63.0075i 0.440169 0.605841i
\(105\) 0 0
\(106\) 49.7849 153.222i 0.469669 1.44549i
\(107\) −41.0612 + 13.3416i −0.383750 + 0.124688i −0.494538 0.869156i \(-0.664663\pi\)
0.110788 + 0.993844i \(0.464663\pi\)
\(108\) 0 0
\(109\) 75.3063 0.690884 0.345442 0.938440i \(-0.387729\pi\)
0.345442 + 0.938440i \(0.387729\pi\)
\(110\) −27.2460 + 50.0904i −0.247691 + 0.455367i
\(111\) 0 0
\(112\) 9.44434 6.86171i 0.0843244 0.0612653i
\(113\) −3.34964 + 1.08836i −0.0296429 + 0.00963155i −0.323801 0.946125i \(-0.604961\pi\)
0.294158 + 0.955757i \(0.404961\pi\)
\(114\) 0 0
\(115\) −47.2801 34.3510i −0.411131 0.298704i
\(116\) 94.7207 130.372i 0.816558 1.12390i
\(117\) 0 0
\(118\) −24.2275 74.5644i −0.205317 0.631902i
\(119\) −30.8013 42.3943i −0.258834 0.356255i
\(120\) 0 0
\(121\) −65.7474 101.579i −0.543367 0.839495i
\(122\) 143.971i 1.18009i
\(123\) 0 0
\(124\) −118.493 364.684i −0.955588 2.94100i
\(125\) −71.9022 23.3624i −0.575218 0.186900i
\(126\) 0 0
\(127\) 192.213 + 139.651i 1.51349 + 1.09961i 0.964601 + 0.263713i \(0.0849472\pi\)
0.548884 + 0.835898i \(0.315053\pi\)
\(128\) 202.763 + 65.8816i 1.58408 + 0.514700i
\(129\) 0 0
\(130\) 38.7424 28.1480i 0.298018 0.216523i
\(131\) 64.9832i 0.496055i 0.968753 + 0.248027i \(0.0797823\pi\)
−0.968753 + 0.248027i \(0.920218\pi\)
\(132\) 0 0
\(133\) 272.959 2.05232
\(134\) −63.2954 87.1186i −0.472354 0.650139i
\(135\) 0 0
\(136\) −12.5476 + 38.6175i −0.0922616 + 0.283952i
\(137\) −73.7746 + 101.542i −0.538501 + 0.741183i −0.988396 0.151899i \(-0.951461\pi\)
0.449895 + 0.893081i \(0.351461\pi\)
\(138\) 0 0
\(139\) 25.9426 79.8431i 0.186637 0.574411i −0.813335 0.581795i \(-0.802351\pi\)
0.999973 + 0.00738425i \(0.00235050\pi\)
\(140\) 108.625 35.2944i 0.775893 0.252103i
\(141\) 0 0
\(142\) −243.875 −1.71743
\(143\) 13.1877 + 100.761i 0.0922217 + 0.704620i
\(144\) 0 0
\(145\) 31.5099 22.8933i 0.217309 0.157885i
\(146\) −128.061 + 41.6094i −0.877128 + 0.284996i
\(147\) 0 0
\(148\) 68.2360 + 49.5764i 0.461054 + 0.334976i
\(149\) 122.754 168.957i 0.823854 1.13394i −0.165182 0.986263i \(-0.552821\pi\)
0.989036 0.147675i \(-0.0471789\pi\)
\(150\) 0 0
\(151\) 19.1929 + 59.0698i 0.127106 + 0.391191i 0.994279 0.106816i \(-0.0340656\pi\)
−0.867173 + 0.498007i \(0.834066\pi\)
\(152\) −124.321 171.113i −0.817900 1.12574i
\(153\) 0 0
\(154\) −71.2651 + 382.892i −0.462761 + 2.48631i
\(155\) 92.6771i 0.597917i
\(156\) 0 0
\(157\) −33.1773 102.109i −0.211320 0.650377i −0.999394 0.0347966i \(-0.988922\pi\)
0.788074 0.615580i \(-0.211078\pi\)
\(158\) 197.990 + 64.3309i 1.25310 + 0.407158i
\(159\) 0 0
\(160\) 38.9561 + 28.3033i 0.243476 + 0.176895i
\(161\) −379.633 123.350i −2.35797 0.766151i
\(162\) 0 0
\(163\) −164.551 + 119.554i −1.00952 + 0.733457i −0.964108 0.265511i \(-0.914459\pi\)
−0.0454096 + 0.998968i \(0.514459\pi\)
\(164\) 81.8324i 0.498978i
\(165\) 0 0
\(166\) 137.286 0.827021
\(167\) 185.782 + 255.707i 1.11247 + 1.53118i 0.817732 + 0.575600i \(0.195231\pi\)
0.294735 + 0.955579i \(0.404769\pi\)
\(168\) 0 0
\(169\) −25.8511 + 79.5616i −0.152965 + 0.470779i
\(170\) −14.6754 + 20.1990i −0.0863260 + 0.118818i
\(171\) 0 0
\(172\) −40.1174 + 123.469i −0.233241 + 0.717842i
\(173\) −108.421 + 35.2281i −0.626711 + 0.203631i −0.605118 0.796136i \(-0.706874\pi\)
−0.0215935 + 0.999767i \(0.506874\pi\)
\(174\) 0 0
\(175\) −244.390 −1.39651
\(176\) 10.6569 5.07318i 0.0605507 0.0288249i
\(177\) 0 0
\(178\) −292.532 + 212.537i −1.64344 + 1.19403i
\(179\) 138.649 45.0498i 0.774575 0.251675i 0.105053 0.994467i \(-0.466499\pi\)
0.669522 + 0.742792i \(0.266499\pi\)
\(180\) 0 0
\(181\) 281.220 + 204.318i 1.55370 + 1.12883i 0.940944 + 0.338562i \(0.109940\pi\)
0.612759 + 0.790270i \(0.290060\pi\)
\(182\) 192.258 264.620i 1.05636 1.45396i
\(183\) 0 0
\(184\) 95.5802 + 294.166i 0.519458 + 1.59873i
\(185\) 11.9822 + 16.4921i 0.0647688 + 0.0891466i
\(186\) 0 0
\(187\) −22.7728 47.8374i −0.121780 0.255815i
\(188\) 428.030i 2.27676i
\(189\) 0 0
\(190\) −40.1885 123.687i −0.211518 0.650986i
\(191\) −71.2232 23.1418i −0.372896 0.121161i 0.116572 0.993182i \(-0.462809\pi\)
−0.489469 + 0.872021i \(0.662809\pi\)
\(192\) 0 0
\(193\) 25.7429 + 18.7033i 0.133383 + 0.0969085i 0.652476 0.757809i \(-0.273730\pi\)
−0.519093 + 0.854718i \(0.673730\pi\)
\(194\) −334.583 108.713i −1.72465 0.560374i
\(195\) 0 0
\(196\) 369.869 268.725i 1.88708 1.37105i
\(197\) 165.104i 0.838089i −0.907966 0.419045i \(-0.862365\pi\)
0.907966 0.419045i \(-0.137635\pi\)
\(198\) 0 0
\(199\) 195.093 0.980365 0.490182 0.871620i \(-0.336930\pi\)
0.490182 + 0.871620i \(0.336930\pi\)
\(200\) 111.309 + 153.203i 0.556544 + 0.766016i
\(201\) 0 0
\(202\) 117.074 360.316i 0.579573 1.78374i
\(203\) 156.367 215.220i 0.770280 1.06020i
\(204\) 0 0
\(205\) 6.11181 18.8102i 0.0298137 0.0917572i
\(206\) 338.224 109.896i 1.64186 0.533474i
\(207\) 0 0
\(208\) −9.91243 −0.0476559
\(209\) 271.316 + 50.4981i 1.29816 + 0.241618i
\(210\) 0 0
\(211\) −147.480 + 107.151i −0.698958 + 0.507823i −0.879593 0.475728i \(-0.842185\pi\)
0.180635 + 0.983550i \(0.442185\pi\)
\(212\) −310.301 + 100.823i −1.46369 + 0.475580i
\(213\) 0 0
\(214\) 113.669 + 82.5854i 0.531164 + 0.385913i
\(215\) −18.4430 + 25.3846i −0.0857815 + 0.118068i
\(216\) 0 0
\(217\) −195.610 602.027i −0.901431 2.77432i
\(218\) −144.049 198.266i −0.660773 0.909477i
\(219\) 0 0
\(220\) 114.501 14.9860i 0.520458 0.0681182i
\(221\) 44.4955i 0.201337i
\(222\) 0 0
\(223\) −35.4093 108.979i −0.158786 0.488693i 0.839739 0.542991i \(-0.182708\pi\)
−0.998525 + 0.0542974i \(0.982708\pi\)
\(224\) 312.796 + 101.634i 1.39641 + 0.453721i
\(225\) 0 0
\(226\) 9.27275 + 6.73705i 0.0410299 + 0.0298099i
\(227\) 222.208 + 72.1996i 0.978888 + 0.318060i 0.754399 0.656417i \(-0.227929\pi\)
0.224489 + 0.974477i \(0.427929\pi\)
\(228\) 0 0
\(229\) −112.679 + 81.8663i −0.492049 + 0.357495i −0.805972 0.591954i \(-0.798357\pi\)
0.313923 + 0.949449i \(0.398357\pi\)
\(230\) 190.187i 0.826898i
\(231\) 0 0
\(232\) −206.136 −0.888517
\(233\) 69.6784 + 95.9041i 0.299049 + 0.411606i 0.931927 0.362646i \(-0.118127\pi\)
−0.632878 + 0.774251i \(0.718127\pi\)
\(234\) 0 0
\(235\) −31.9683 + 98.3883i −0.136035 + 0.418674i
\(236\) −93.3267 + 128.453i −0.395452 + 0.544293i
\(237\) 0 0
\(238\) −52.6976 + 162.187i −0.221419 + 0.681457i
\(239\) −274.203 + 89.0941i −1.14729 + 0.372778i −0.820123 0.572187i \(-0.806095\pi\)
−0.327171 + 0.944965i \(0.606095\pi\)
\(240\) 0 0
\(241\) −115.517 −0.479324 −0.239662 0.970856i \(-0.577037\pi\)
−0.239662 + 0.970856i \(0.577037\pi\)
\(242\) −141.672 + 367.403i −0.585422 + 1.51819i
\(243\) 0 0
\(244\) 235.882 171.378i 0.966728 0.702369i
\(245\) 105.089 34.1456i 0.428936 0.139370i
\(246\) 0 0
\(247\) −187.509 136.233i −0.759144 0.551550i
\(248\) −288.308 + 396.821i −1.16253 + 1.60009i
\(249\) 0 0
\(250\) 76.0286 + 233.992i 0.304114 + 0.935968i
\(251\) 20.2429 + 27.8619i 0.0806489 + 0.111004i 0.847435 0.530899i \(-0.178145\pi\)
−0.766786 + 0.641902i \(0.778145\pi\)
\(252\) 0 0
\(253\) −354.528 192.841i −1.40130 0.762217i
\(254\) 773.185i 3.04403i
\(255\) 0 0
\(256\) −87.4935 269.277i −0.341771 1.05186i
\(257\) −198.210 64.4025i −0.771247 0.250593i −0.103148 0.994666i \(-0.532892\pi\)
−0.668099 + 0.744073i \(0.732892\pi\)
\(258\) 0 0
\(259\) 112.645 + 81.8417i 0.434924 + 0.315991i
\(260\) −92.2351 29.9690i −0.354750 0.115265i
\(261\) 0 0
\(262\) 171.087 124.302i 0.653005 0.474436i
\(263\) 230.901i 0.877952i −0.898499 0.438976i \(-0.855341\pi\)
0.898499 0.438976i \(-0.144659\pi\)
\(264\) 0 0
\(265\) −78.8569 −0.297573
\(266\) −522.125 718.644i −1.96288 2.70167i
\(267\) 0 0
\(268\) −67.3903 + 207.406i −0.251456 + 0.773903i
\(269\) −6.51517 + 8.96736i −0.0242200 + 0.0333359i −0.820955 0.570993i \(-0.806559\pi\)
0.796735 + 0.604328i \(0.206559\pi\)
\(270\) 0 0
\(271\) 31.1472 95.8612i 0.114934 0.353731i −0.876999 0.480492i \(-0.840458\pi\)
0.991933 + 0.126761i \(0.0404581\pi\)
\(272\) 4.91507 1.59700i 0.0180701 0.00587134i
\(273\) 0 0
\(274\) 408.458 1.49072
\(275\) −242.918 45.2127i −0.883339 0.164410i
\(276\) 0 0
\(277\) 43.2146 31.3972i 0.156009 0.113347i −0.507042 0.861921i \(-0.669261\pi\)
0.663051 + 0.748574i \(0.269261\pi\)
\(278\) −259.834 + 84.4253i −0.934656 + 0.303688i
\(279\) 0 0
\(280\) −118.198 85.8756i −0.422134 0.306699i
\(281\) −217.042 + 298.733i −0.772392 + 1.06311i 0.223689 + 0.974661i \(0.428190\pi\)
−0.996081 + 0.0884461i \(0.971810\pi\)
\(282\) 0 0
\(283\) 74.4927 + 229.265i 0.263225 + 0.810123i 0.992097 + 0.125473i \(0.0400450\pi\)
−0.728872 + 0.684650i \(0.759955\pi\)
\(284\) 290.300 + 399.564i 1.02218 + 1.40691i
\(285\) 0 0
\(286\) 240.056 227.459i 0.839356 0.795311i
\(287\) 135.090i 0.470699i
\(288\) 0 0
\(289\) 82.1372 + 252.792i 0.284212 + 0.874714i
\(290\) −120.546 39.1679i −0.415677 0.135062i
\(291\) 0 0
\(292\) 220.612 + 160.284i 0.755520 + 0.548917i
\(293\) 52.4316 + 17.0361i 0.178948 + 0.0581436i 0.397120 0.917767i \(-0.370010\pi\)
−0.218173 + 0.975910i \(0.570010\pi\)
\(294\) 0 0
\(295\) −31.0461 + 22.5563i −0.105241 + 0.0764621i
\(296\) 107.891i 0.364495i
\(297\) 0 0
\(298\) −679.637 −2.28066
\(299\) 199.225 + 274.209i 0.666303 + 0.917087i
\(300\) 0 0
\(301\) −66.2267 + 203.825i −0.220022 + 0.677158i
\(302\) 118.806 163.522i 0.393396 0.541463i
\(303\) 0 0
\(304\) −8.31866 + 25.6022i −0.0273640 + 0.0842177i
\(305\) 67.0202 21.7762i 0.219738 0.0713973i
\(306\) 0 0
\(307\) −12.5104 −0.0407504 −0.0203752 0.999792i \(-0.506486\pi\)
−0.0203752 + 0.999792i \(0.506486\pi\)
\(308\) 712.161 339.021i 2.31221 1.10072i
\(309\) 0 0
\(310\) −244.000 + 177.276i −0.787096 + 0.571858i
\(311\) 205.110 66.6443i 0.659518 0.214290i 0.0399116 0.999203i \(-0.487292\pi\)
0.619606 + 0.784913i \(0.287292\pi\)
\(312\) 0 0
\(313\) −352.445 256.066i −1.12602 0.818102i −0.140911 0.990022i \(-0.545003\pi\)
−0.985111 + 0.171920i \(0.945003\pi\)
\(314\) −205.370 + 282.667i −0.654043 + 0.900213i
\(315\) 0 0
\(316\) −130.281 400.964i −0.412282 1.26887i
\(317\) 184.456 + 253.883i 0.581882 + 0.800891i 0.993900 0.110284i \(-0.0351761\pi\)
−0.412018 + 0.911175i \(0.635176\pi\)
\(318\) 0 0
\(319\) 195.242 184.997i 0.612043 0.579926i
\(320\) 163.539i 0.511060i
\(321\) 0 0
\(322\) 401.420 + 1235.44i 1.24665 + 3.83678i
\(323\) 114.925 + 37.3413i 0.355804 + 0.115608i
\(324\) 0 0
\(325\) 167.883 + 121.974i 0.516563 + 0.375305i
\(326\) 629.519 + 204.543i 1.93104 + 0.627433i
\(327\) 0 0
\(328\) −84.6857 + 61.5278i −0.258188 + 0.187585i
\(329\) 706.601i 2.14772i
\(330\) 0 0
\(331\) 69.5045 0.209983 0.104992 0.994473i \(-0.466518\pi\)
0.104992 + 0.994473i \(0.466518\pi\)
\(332\) −163.420 224.928i −0.492229 0.677495i
\(333\) 0 0
\(334\) 317.853 978.250i 0.951655 2.92889i
\(335\) −30.9811 + 42.6418i −0.0924808 + 0.127289i
\(336\) 0 0
\(337\) −33.6193 + 103.469i −0.0997604 + 0.307031i −0.988465 0.151449i \(-0.951606\pi\)
0.888705 + 0.458480i \(0.151606\pi\)
\(338\) 258.918 84.1276i 0.766030 0.248898i
\(339\) 0 0
\(340\) 50.5631 0.148715
\(341\) −83.0562 634.591i −0.243567 1.86097i
\(342\) 0 0
\(343\) 179.292 130.263i 0.522717 0.379776i
\(344\) 157.937 51.3169i 0.459120 0.149177i
\(345\) 0 0
\(346\) 300.140 + 218.064i 0.867456 + 0.630244i
\(347\) −225.036 + 309.735i −0.648518 + 0.892608i −0.999034 0.0439485i \(-0.986006\pi\)
0.350516 + 0.936557i \(0.386006\pi\)
\(348\) 0 0
\(349\) 136.469 + 420.008i 0.391029 + 1.20346i 0.932012 + 0.362429i \(0.118052\pi\)
−0.540983 + 0.841034i \(0.681948\pi\)
\(350\) 467.477 + 643.427i 1.33565 + 1.83836i
\(351\) 0 0
\(352\) 292.110 + 158.890i 0.829859 + 0.451391i
\(353\) 237.587i 0.673051i −0.941674 0.336525i \(-0.890748\pi\)
0.941674 0.336525i \(-0.109252\pi\)
\(354\) 0 0
\(355\) 36.8870 + 113.526i 0.103907 + 0.319793i
\(356\) 696.441 + 226.287i 1.95630 + 0.635639i
\(357\) 0 0
\(358\) −383.819 278.861i −1.07212 0.778941i
\(359\) −366.865 119.202i −1.02191 0.332038i −0.250321 0.968163i \(-0.580536\pi\)
−0.771586 + 0.636125i \(0.780536\pi\)
\(360\) 0 0
\(361\) −217.172 + 157.785i −0.601585 + 0.437077i
\(362\) 1131.22i 3.12492i
\(363\) 0 0
\(364\) −662.410 −1.81981
\(365\) 38.7393 + 53.3201i 0.106135 + 0.146083i
\(366\) 0 0
\(367\) 47.6728 146.722i 0.129899 0.399787i −0.864863 0.502008i \(-0.832595\pi\)
0.994762 + 0.102221i \(0.0325949\pi\)
\(368\) 23.1393 31.8485i 0.0628785 0.0865449i
\(369\) 0 0
\(370\) 20.5003 63.0934i 0.0554062 0.170523i
\(371\) −512.251 + 166.441i −1.38073 + 0.448627i
\(372\) 0 0
\(373\) 440.608 1.18125 0.590627 0.806944i \(-0.298880\pi\)
0.590627 + 0.806944i \(0.298880\pi\)
\(374\) −82.3854 + 151.461i −0.220282 + 0.404976i
\(375\) 0 0
\(376\) 442.955 321.826i 1.17807 0.855919i
\(377\) −214.832 + 69.8031i −0.569846 + 0.185154i
\(378\) 0 0
\(379\) −450.261 327.134i −1.18802 0.863149i −0.194969 0.980809i \(-0.562461\pi\)
−0.993054 + 0.117660i \(0.962461\pi\)
\(380\) −154.810 + 213.078i −0.407395 + 0.560731i
\(381\) 0 0
\(382\) 75.3106 + 231.782i 0.197148 + 0.606760i
\(383\) −73.8657 101.667i −0.192861 0.265450i 0.701625 0.712546i \(-0.252458\pi\)
−0.894486 + 0.447096i \(0.852458\pi\)
\(384\) 0 0
\(385\) 189.020 24.7392i 0.490961 0.0642577i
\(386\) 103.552i 0.268270i
\(387\) 0 0
\(388\) 220.161 + 677.587i 0.567426 + 1.74636i
\(389\) 63.8640 + 20.7507i 0.164175 + 0.0533437i 0.389951 0.920835i \(-0.372492\pi\)
−0.225776 + 0.974179i \(0.572492\pi\)
\(390\) 0 0
\(391\) −142.964 103.869i −0.365636 0.265650i
\(392\) −556.190 180.717i −1.41885 0.461013i
\(393\) 0 0
\(394\) −434.683 + 315.816i −1.10326 + 0.801563i
\(395\) 101.897i 0.257967i
\(396\) 0 0
\(397\) 342.588 0.862942 0.431471 0.902127i \(-0.357995\pi\)
0.431471 + 0.902127i \(0.357995\pi\)
\(398\) −373.180 513.638i −0.937638 1.29055i
\(399\) 0 0
\(400\) 7.44798 22.9225i 0.0186200 0.0573063i
\(401\) 217.794 299.767i 0.543126 0.747549i −0.445933 0.895066i \(-0.647128\pi\)
0.989060 + 0.147517i \(0.0471281\pi\)
\(402\) 0 0
\(403\) −166.096 + 511.190i −0.412148 + 1.26846i
\(404\) −729.701 + 237.094i −1.80619 + 0.586867i
\(405\) 0 0
\(406\) −865.735 −2.13235
\(407\) 96.8263 + 102.189i 0.237902 + 0.251078i
\(408\) 0 0
\(409\) 259.018 188.188i 0.633296 0.460116i −0.224245 0.974533i \(-0.571991\pi\)
0.857540 + 0.514417i \(0.171991\pi\)
\(410\) −61.2143 + 19.8897i −0.149303 + 0.0485115i
\(411\) 0 0
\(412\) −582.663 423.329i −1.41423 1.02750i
\(413\) −154.065 + 212.053i −0.373040 + 0.513445i
\(414\) 0 0
\(415\) −20.7650 63.9080i −0.0500361 0.153995i
\(416\) −164.150 225.932i −0.394590 0.543107i
\(417\) 0 0
\(418\) −386.031 810.912i −0.923519 1.93998i
\(419\) 574.973i 1.37225i 0.727483 + 0.686126i \(0.240690\pi\)
−0.727483 + 0.686126i \(0.759310\pi\)
\(420\) 0 0
\(421\) 43.7992 + 134.800i 0.104036 + 0.320190i 0.989503 0.144512i \(-0.0461613\pi\)
−0.885467 + 0.464702i \(0.846161\pi\)
\(422\) 564.210 + 183.323i 1.33699 + 0.434415i
\(423\) 0 0
\(424\) 337.647 + 245.315i 0.796336 + 0.578572i
\(425\) −102.896 33.4330i −0.242108 0.0786658i
\(426\) 0 0
\(427\) 389.398 282.914i 0.911940 0.662563i
\(428\) 284.542i 0.664817i
\(429\) 0 0
\(430\) 102.111 0.237467
\(431\) −230.211 316.859i −0.534133 0.735171i 0.453620 0.891195i \(-0.350132\pi\)
−0.987753 + 0.156024i \(0.950132\pi\)
\(432\) 0 0
\(433\) −106.300 + 327.159i −0.245497 + 0.755564i 0.750057 + 0.661373i \(0.230026\pi\)
−0.995554 + 0.0941901i \(0.969974\pi\)
\(434\) −1210.84 + 1666.58i −2.78996 + 3.84005i
\(435\) 0 0
\(436\) −153.368 + 472.018i −0.351761 + 1.08261i
\(437\) 875.429 284.444i 2.00327 0.650902i
\(438\) 0 0
\(439\) 36.1143 0.0822650 0.0411325 0.999154i \(-0.486903\pi\)
0.0411325 + 0.999154i \(0.486903\pi\)
\(440\) −101.599 107.225i −0.230906 0.243694i
\(441\) 0 0
\(442\) 117.147 85.1126i 0.265039 0.192562i
\(443\) 363.367 118.065i 0.820241 0.266512i 0.131312 0.991341i \(-0.458081\pi\)
0.688929 + 0.724829i \(0.258081\pi\)
\(444\) 0 0
\(445\) 143.185 + 104.030i 0.321765 + 0.233776i
\(446\) −219.186 + 301.683i −0.491448 + 0.676420i
\(447\) 0 0
\(448\) −345.177 1062.34i −0.770484 2.37130i
\(449\) −18.0511 24.8453i −0.0402030 0.0553347i 0.788442 0.615109i \(-0.210888\pi\)
−0.828645 + 0.559774i \(0.810888\pi\)
\(450\) 0 0
\(451\) 24.9921 134.277i 0.0554149 0.297732i
\(452\) 23.2120i 0.0513540i
\(453\) 0 0
\(454\) −234.960 723.132i −0.517533 1.59280i
\(455\) −152.264 49.4734i −0.334645 0.108733i
\(456\) 0 0
\(457\) −333.880 242.578i −0.730592 0.530806i 0.159159 0.987253i \(-0.449122\pi\)
−0.889751 + 0.456447i \(0.849122\pi\)
\(458\) 431.074 + 140.064i 0.941209 + 0.305817i
\(459\) 0 0
\(460\) 311.601 226.391i 0.677394 0.492155i
\(461\) 765.072i 1.65959i −0.558066 0.829797i \(-0.688456\pi\)
0.558066 0.829797i \(-0.311544\pi\)
\(462\) 0 0
\(463\) 113.587 0.245328 0.122664 0.992448i \(-0.460856\pi\)
0.122664 + 0.992448i \(0.460856\pi\)
\(464\) 15.4212 + 21.2255i 0.0332354 + 0.0457445i
\(465\) 0 0
\(466\) 119.212 366.897i 0.255820 0.787334i
\(467\) 444.846 612.278i 0.952561 1.31109i 0.00218113 0.999998i \(-0.499306\pi\)
0.950380 0.311091i \(-0.100694\pi\)
\(468\) 0 0
\(469\) −111.249 + 342.390i −0.237205 + 0.730042i
\(470\) 320.186 104.035i 0.681247 0.221351i
\(471\) 0 0
\(472\) 203.102 0.430301
\(473\) −103.536 + 190.346i −0.218892 + 0.402422i
\(474\) 0 0
\(475\) 455.929 331.252i 0.959851 0.697372i
\(476\) 328.456 106.722i 0.690033 0.224205i
\(477\) 0 0
\(478\) 759.072 + 551.498i 1.58802 + 1.15376i
\(479\) 214.285 294.937i 0.447358 0.615736i −0.524469 0.851429i \(-0.675736\pi\)
0.971827 + 0.235694i \(0.0757362\pi\)
\(480\) 0 0
\(481\) −36.5346 112.442i −0.0759555 0.233767i
\(482\) 220.965 + 304.133i 0.458434 + 0.630981i
\(483\) 0 0
\(484\) 770.594 205.228i 1.59214 0.424026i
\(485\) 172.195i 0.355042i
\(486\) 0 0
\(487\) −74.1795 228.301i −0.152319 0.468790i 0.845560 0.533880i \(-0.179267\pi\)
−0.997879 + 0.0650898i \(0.979267\pi\)
\(488\) −354.708 115.251i −0.726860 0.236171i
\(489\) 0 0
\(490\) −290.917 211.363i −0.593708 0.431354i
\(491\) −796.791 258.893i −1.62279 0.527277i −0.650194 0.759768i \(-0.725312\pi\)
−0.972599 + 0.232491i \(0.925312\pi\)
\(492\) 0 0
\(493\) 95.2782 69.2236i 0.193262 0.140413i
\(494\) 754.262i 1.52685i
\(495\) 0 0
\(496\) 62.4286 0.125864
\(497\) 479.233 + 659.607i 0.964251 + 1.32718i
\(498\) 0 0
\(499\) 199.212 613.111i 0.399222 1.22868i −0.526403 0.850235i \(-0.676460\pi\)
0.925624 0.378443i \(-0.123540\pi\)
\(500\) 292.870 403.101i 0.585740 0.806202i
\(501\) 0 0
\(502\) 34.6334 106.591i 0.0689907 0.212332i
\(503\) −9.99329 + 3.24702i −0.0198674 + 0.00645530i −0.318934 0.947777i \(-0.603325\pi\)
0.299066 + 0.954232i \(0.403325\pi\)
\(504\) 0 0
\(505\) −185.439 −0.367206
\(506\) 170.443 + 1302.27i 0.336844 + 2.57366i
\(507\) 0 0
\(508\) −1266.78 + 920.372i −2.49367 + 1.81176i
\(509\) 870.887 282.968i 1.71098 0.555930i 0.720481 0.693475i \(-0.243921\pi\)
0.990496 + 0.137545i \(0.0439211\pi\)
\(510\) 0 0
\(511\) 364.190 + 264.600i 0.712701 + 0.517808i
\(512\) −40.3331 + 55.5138i −0.0787757 + 0.108425i
\(513\) 0 0
\(514\) 209.586 + 645.038i 0.407754 + 1.25494i
\(515\) −102.315 140.825i −0.198671 0.273447i
\(516\) 0 0
\(517\) −130.723 + 702.347i −0.252849 + 1.35851i
\(518\) 453.121i 0.874752i
\(519\) 0 0
\(520\) 38.3354 + 117.984i 0.0737219 + 0.226893i
\(521\) −224.438 72.9245i −0.430784 0.139970i 0.0855957 0.996330i \(-0.472721\pi\)
−0.516380 + 0.856360i \(0.672721\pi\)
\(522\) 0 0
\(523\) 122.429 + 88.9499i 0.234090 + 0.170076i 0.698646 0.715467i \(-0.253786\pi\)
−0.464556 + 0.885544i \(0.653786\pi\)
\(524\) −407.313 132.344i −0.777314 0.252565i
\(525\) 0 0
\(526\) −607.916 + 441.677i −1.15573 + 0.839689i
\(527\) 280.233i 0.531752i
\(528\) 0 0
\(529\) −817.095 −1.54460
\(530\) 150.840 + 207.614i 0.284604 + 0.391724i
\(531\) 0 0
\(532\) −555.904 + 1710.90i −1.04493 + 3.21597i
\(533\) −67.4233 + 92.8002i −0.126498 + 0.174109i
\(534\) 0 0
\(535\) 21.2516 65.4056i 0.0397226 0.122253i
\(536\) 265.307 86.2035i 0.494976 0.160827i
\(537\) 0 0
\(538\) 36.0716 0.0670477
\(539\) 688.981 327.986i 1.27826 0.608509i
\(540\) 0 0
\(541\) −243.056 + 176.591i −0.449272 + 0.326415i −0.789308 0.613997i \(-0.789561\pi\)
0.340036 + 0.940412i \(0.389561\pi\)
\(542\) −311.962 + 101.363i −0.575576 + 0.187016i
\(543\) 0 0
\(544\) 117.794 + 85.5821i 0.216533 + 0.157320i
\(545\) −70.5072 + 97.0448i −0.129371 + 0.178064i
\(546\) 0 0
\(547\) −100.418 309.055i −0.183580 0.565001i 0.816341 0.577570i \(-0.195999\pi\)
−0.999921 + 0.0125693i \(0.995999\pi\)
\(548\) −486.214 669.216i −0.887252 1.22120i
\(549\) 0 0
\(550\) 345.627 + 726.038i 0.628413 + 1.32007i
\(551\) 613.455i 1.11335i
\(552\) 0 0
\(553\) −215.071 661.919i −0.388916 1.19696i
\(554\) −165.325 53.7173i −0.298420 0.0969626i
\(555\) 0 0
\(556\) 447.620 + 325.215i 0.805072 + 0.584919i
\(557\) −43.0763 13.9963i −0.0773363 0.0251281i 0.270093 0.962834i \(-0.412945\pi\)
−0.347430 + 0.937706i \(0.612945\pi\)
\(558\) 0 0
\(559\) 147.223 106.963i 0.263368 0.191348i
\(560\) 18.5950i 0.0332054i
\(561\) 0 0
\(562\) 1201.67 2.13820
\(563\) −428.403 589.646i −0.760928 1.04733i −0.997136 0.0756257i \(-0.975905\pi\)
0.236208 0.971703i \(-0.424095\pi\)
\(564\) 0 0
\(565\) 1.73363 5.33558i 0.00306838 0.00944350i
\(566\) 461.115 634.670i 0.814690 1.12132i
\(567\) 0 0
\(568\) 195.226 600.844i 0.343708 1.05782i
\(569\) 138.993 45.1615i 0.244276 0.0793700i −0.184320 0.982866i \(-0.559008\pi\)
0.428596 + 0.903496i \(0.359008\pi\)
\(570\) 0 0
\(571\) 398.941 0.698672 0.349336 0.936998i \(-0.386407\pi\)
0.349336 + 0.936998i \(0.386407\pi\)
\(572\) −658.422 122.548i −1.15109 0.214244i
\(573\) 0 0
\(574\) −355.665 + 258.406i −0.619626 + 0.450184i
\(575\) −783.803 + 254.673i −1.36314 + 0.442909i
\(576\) 0 0
\(577\) −204.268 148.409i −0.354017 0.257209i 0.396535 0.918020i \(-0.370212\pi\)
−0.750552 + 0.660811i \(0.770212\pi\)
\(578\) 508.435 699.800i 0.879644 1.21073i
\(579\) 0 0
\(580\) 79.3217 + 244.127i 0.136761 + 0.420909i
\(581\) −269.777 371.316i −0.464332 0.639098i
\(582\) 0 0
\(583\) −539.960 + 70.6707i −0.926174 + 0.121219i
\(584\) 348.818i 0.597290i
\(585\) 0 0
\(586\) −55.4407 170.629i −0.0946086 0.291175i
\(587\) −937.333 304.558i −1.59682 0.518838i −0.630501 0.776188i \(-0.717151\pi\)
−0.966318 + 0.257350i \(0.917151\pi\)
\(588\) 0 0
\(589\) 1180.93 + 857.996i 2.00498 + 1.45670i
\(590\) 118.772 + 38.5914i 0.201309 + 0.0654092i
\(591\) 0 0
\(592\) −11.1093 + 8.07139i −0.0187657 + 0.0136341i
\(593\) 795.418i 1.34135i 0.741753 + 0.670673i \(0.233995\pi\)
−0.741753 + 0.670673i \(0.766005\pi\)
\(594\) 0 0
\(595\) 83.4705 0.140287
\(596\) 809.016 + 1113.51i 1.35741 + 1.86831i
\(597\) 0 0
\(598\) 340.852 1049.03i 0.569986 1.75424i
\(599\) 67.5385 92.9587i 0.112752 0.155190i −0.748911 0.662670i \(-0.769423\pi\)
0.861663 + 0.507480i \(0.169423\pi\)
\(600\) 0 0
\(601\) −91.0388 + 280.189i −0.151479 + 0.466204i −0.997787 0.0664894i \(-0.978820\pi\)
0.846308 + 0.532694i \(0.178820\pi\)
\(602\) 663.309 215.522i 1.10184 0.358010i
\(603\) 0 0
\(604\) −409.336 −0.677708
\(605\) 192.459 + 10.3789i 0.318114 + 0.0171553i
\(606\) 0 0
\(607\) 352.020 255.758i 0.579934 0.421347i −0.258766 0.965940i \(-0.583316\pi\)
0.838700 + 0.544593i \(0.183316\pi\)
\(608\) −721.303 + 234.366i −1.18635 + 0.385470i
\(609\) 0 0
\(610\) −185.531 134.796i −0.304149 0.220977i
\(611\) 352.662 485.398i 0.577189 0.794432i
\(612\) 0 0
\(613\) 194.113 + 597.417i 0.316660 + 0.974579i 0.975066 + 0.221916i \(0.0712310\pi\)
−0.658406 + 0.752663i \(0.728769\pi\)
\(614\) 23.9303 + 32.9372i 0.0389744 + 0.0536436i
\(615\) 0 0
\(616\) −886.299 482.091i −1.43880 0.782616i
\(617\) 215.080i 0.348590i 0.984694 + 0.174295i \(0.0557646\pi\)
−0.984694 + 0.174295i \(0.944235\pi\)
\(618\) 0 0
\(619\) −295.694 910.053i −0.477697 1.47020i −0.842286 0.539031i \(-0.818791\pi\)
0.364589 0.931168i \(-0.381209\pi\)
\(620\) 580.897 + 188.745i 0.936931 + 0.304427i
\(621\) 0 0
\(622\) −567.802 412.532i −0.912865 0.663235i
\(623\) 1149.70 + 373.560i 1.84542 + 0.599614i
\(624\) 0 0
\(625\) −356.892 + 259.297i −0.571027 + 0.414875i
\(626\) 1417.73i 2.26474i
\(627\) 0 0
\(628\) 707.585 1.12673
\(629\) 36.2313 + 49.8681i 0.0576015 + 0.0792816i
\(630\) 0 0
\(631\) −197.152 + 606.771i −0.312443 + 0.961602i 0.664351 + 0.747421i \(0.268708\pi\)
−0.976794 + 0.214181i \(0.931292\pi\)
\(632\) −316.990 + 436.299i −0.501566 + 0.690346i
\(633\) 0 0
\(634\) 315.585 971.271i 0.497768 1.53197i
\(635\) −359.926 + 116.947i −0.566813 + 0.184169i
\(636\) 0 0
\(637\) −640.849 −1.00604
\(638\) −860.523 160.163i −1.34878 0.251040i
\(639\) 0 0
\(640\) −274.741 + 199.611i −0.429282 + 0.311892i
\(641\) −911.311 + 296.103i −1.42170 + 0.461939i −0.916143 0.400853i \(-0.868714\pi\)
−0.505560 + 0.862792i \(0.668714\pi\)
\(642\) 0 0
\(643\) 238.550 + 173.317i 0.370995 + 0.269544i 0.757623 0.652692i \(-0.226360\pi\)
−0.386628 + 0.922236i \(0.626360\pi\)
\(644\) 1546.31 2128.32i 2.40111 3.30484i
\(645\) 0 0
\(646\) −121.520 374.000i −0.188112 0.578948i
\(647\) 590.791 + 813.155i 0.913124 + 1.25681i 0.966088 + 0.258211i \(0.0831331\pi\)
−0.0529642 + 0.998596i \(0.516867\pi\)
\(648\) 0 0
\(649\) −192.368 + 182.274i −0.296407 + 0.280853i
\(650\) 675.317i 1.03895i
\(651\) 0 0
\(652\) −414.235 1274.88i −0.635329 1.95534i
\(653\) 984.939 + 320.026i 1.50833 + 0.490086i 0.942434 0.334392i \(-0.108531\pi\)
0.565895 + 0.824477i \(0.308531\pi\)
\(654\) 0 0
\(655\) −83.7417 60.8419i −0.127850 0.0928884i
\(656\) 12.6708 + 4.11700i 0.0193153 + 0.00627591i
\(657\) 0 0
\(658\) 1860.33 1351.61i 2.82725 2.05412i
\(659\) 572.524i 0.868777i 0.900726 + 0.434388i \(0.143035\pi\)
−0.900726 + 0.434388i \(0.856965\pi\)
\(660\) 0 0
\(661\) −717.443 −1.08539 −0.542695 0.839930i \(-0.682596\pi\)
−0.542695 + 0.839930i \(0.682596\pi\)
\(662\) −132.951 182.991i −0.200832 0.276421i
\(663\) 0 0
\(664\) −109.900 + 338.236i −0.165511 + 0.509392i
\(665\) −255.564 + 351.753i −0.384306 + 0.528952i
\(666\) 0 0
\(667\) 277.221 853.198i 0.415624 1.27916i
\(668\) −1981.12 + 643.706i −2.96575 + 0.963632i
\(669\) 0 0
\(670\) 171.529 0.256013
\(671\) 439.394 209.171i 0.654834 0.311731i
\(672\) 0 0
\(673\) 705.491 512.569i 1.04828 0.761619i 0.0763941 0.997078i \(-0.475659\pi\)
0.971884 + 0.235459i \(0.0756593\pi\)
\(674\) 336.722 109.408i 0.499587 0.162326i
\(675\) 0 0
\(676\) −446.042 324.068i −0.659825 0.479391i
\(677\) −750.046 + 1032.35i −1.10790 + 1.52489i −0.283418 + 0.958997i \(0.591468\pi\)
−0.824479 + 0.565893i \(0.808532\pi\)
\(678\) 0 0
\(679\) 363.447 + 1118.57i 0.535268 + 1.64738i
\(680\) −38.0171 52.3261i −0.0559076 0.0769502i
\(681\) 0 0
\(682\) −1511.87 + 1432.54i −2.21682 + 2.10050i
\(683\) 411.727i 0.602822i 0.953494 + 0.301411i \(0.0974575\pi\)
−0.953494 + 0.301411i \(0.902542\pi\)
\(684\) 0 0
\(685\) −61.7808 190.142i −0.0901910 0.277579i
\(686\) −685.911 222.866i −0.999871 0.324878i
\(687\) 0 0
\(688\) −17.0994 12.4235i −0.0248538 0.0180574i
\(689\) 434.960 + 141.327i 0.631292 + 0.205119i
\(690\) 0 0
\(691\) 673.521 489.342i 0.974705 0.708165i 0.0181860 0.999835i \(-0.494211\pi\)
0.956519 + 0.291670i \(0.0942109\pi\)
\(692\) 751.325i 1.08573i
\(693\) 0 0
\(694\) 1245.92 1.79528
\(695\) 78.6019 + 108.186i 0.113096 + 0.155664i
\(696\) 0 0
\(697\) 18.4806 56.8775i 0.0265145 0.0816034i
\(698\) 844.752 1162.70i 1.21025 1.66576i
\(699\) 0 0
\(700\) 497.721 1531.83i 0.711029 2.18832i
\(701\) −86.3690 + 28.0630i −0.123208 + 0.0400328i −0.369972 0.929043i \(-0.620633\pi\)
0.246764 + 0.969076i \(0.420633\pi\)
\(702\) 0 0
\(703\) −321.080 −0.456728
\(704\) −146.562 1119.81i −0.208185 1.59064i
\(705\) 0 0
\(706\) −625.517 + 454.465i −0.886001 + 0.643718i
\(707\) −1204.61 + 391.400i −1.70383 + 0.553607i
\(708\) 0 0
\(709\) 553.750 + 402.323i 0.781030 + 0.567451i 0.905288 0.424799i \(-0.139655\pi\)
−0.124258 + 0.992250i \(0.539655\pi\)
\(710\) 228.333 314.273i 0.321596 0.442638i
\(711\) 0 0
\(712\) −289.459 890.865i −0.406544 1.25121i
\(713\) −1254.72 1726.97i −1.75977 2.42212i
\(714\) 0 0
\(715\) −142.194 77.3447i −0.198873 0.108174i
\(716\) 960.795i 1.34189i
\(717\) 0 0
\(718\) 387.919 + 1193.89i 0.540277 + 1.66280i
\(719\) −1185.83 385.298i −1.64927 0.535880i −0.670689 0.741739i \(-0.734001\pi\)
−0.978582 + 0.205859i \(0.934001\pi\)
\(720\) 0 0
\(721\) −961.871 698.840i −1.33408 0.969266i
\(722\) 830.829 + 269.953i 1.15073 + 0.373896i
\(723\) 0 0
\(724\) −1853.39 + 1346.57i −2.55993 + 1.85990i
\(725\) 549.248i 0.757583i
\(726\) 0 0
\(727\) −837.811 −1.15242 −0.576211 0.817301i \(-0.695469\pi\)
−0.576211 + 0.817301i \(0.695469\pi\)
\(728\) 498.050 + 685.507i 0.684135 + 0.941631i
\(729\) 0 0
\(730\) 66.2788 203.985i 0.0907929 0.279432i
\(731\) −55.7672 + 76.7570i −0.0762889 + 0.105003i
\(732\) 0 0
\(733\) −19.4439 + 59.8422i −0.0265265 + 0.0816401i −0.963443 0.267912i \(-0.913666\pi\)
0.936917 + 0.349552i \(0.113666\pi\)
\(734\) −477.478 + 155.142i −0.650515 + 0.211365i
\(735\) 0 0
\(736\) 1109.10 1.50694
\(737\) −173.922 + 319.747i −0.235987 + 0.433850i
\(738\) 0 0
\(739\) −954.793 + 693.698i −1.29201 + 0.938698i −0.999844 0.0176705i \(-0.994375\pi\)
−0.292163 + 0.956369i \(0.594375\pi\)
\(740\) −127.775 + 41.5166i −0.172669 + 0.0561035i
\(741\) 0 0
\(742\) 1418.06 + 1030.28i 1.91113 + 1.38852i
\(743\) −291.584 + 401.331i −0.392441 + 0.540149i −0.958827 0.283991i \(-0.908341\pi\)
0.566386 + 0.824140i \(0.308341\pi\)
\(744\) 0 0
\(745\) 102.798 + 316.379i 0.137983 + 0.424669i
\(746\) −842.811 1160.03i −1.12977 1.55500i
\(747\) 0 0
\(748\) 346.222 45.3141i 0.462864 0.0605803i
\(749\) 469.727i 0.627139i
\(750\) 0 0
\(751\) 126.227 + 388.487i 0.168079 + 0.517293i 0.999250 0.0387234i \(-0.0123291\pi\)
−0.831171 + 0.556017i \(0.812329\pi\)
\(752\) −66.2757 21.5343i −0.0881326 0.0286360i
\(753\) 0 0
\(754\) 594.715 + 432.086i 0.788747 + 0.573058i
\(755\) −94.0911 30.5720i −0.124624 0.0404928i
\(756\) 0 0
\(757\) 613.228 445.536i 0.810077 0.588555i −0.103776 0.994601i \(-0.533093\pi\)
0.913853 + 0.406045i \(0.133093\pi\)
\(758\) 1811.20i 2.38944i
\(759\) 0 0
\(760\) 336.905 0.443297
\(761\) 795.597 + 1095.05i 1.04546 + 1.43896i 0.892677 + 0.450697i \(0.148825\pi\)
0.152786 + 0.988259i \(0.451175\pi\)
\(762\) 0 0
\(763\) −253.183 + 779.216i −0.331825 + 1.02125i
\(764\) 290.104 399.294i 0.379718 0.522637i
\(765\) 0 0
\(766\) −126.376 + 388.946i −0.164982 + 0.507763i
\(767\) 211.670 68.7757i 0.275971 0.0896685i
\(768\) 0 0
\(769\) 550.877 0.716355 0.358178 0.933654i \(-0.383398\pi\)
0.358178 + 0.933654i \(0.383398\pi\)
\(770\) −426.697 450.328i −0.554152 0.584842i
\(771\) 0 0
\(772\) −169.660 + 123.265i −0.219766 + 0.159670i
\(773\) 841.817 273.523i 1.08903 0.353846i 0.291156 0.956676i \(-0.405960\pi\)
0.797870 + 0.602830i \(0.205960\pi\)
\(774\) 0 0
\(775\) −1057.33 768.194i −1.36429 0.991218i
\(776\) 535.679 737.299i 0.690309 0.950128i
\(777\) 0 0
\(778\) −67.5292 207.833i −0.0867984 0.267138i
\(779\) 183.105 + 252.023i 0.235051 + 0.323521i
\(780\) 0 0
\(781\) 354.319 + 744.296i 0.453673 + 0.953004i
\(782\) 575.078i 0.735394i
\(783\) 0 0
\(784\) 23.0009 + 70.7896i 0.0293379 + 0.0902928i
\(785\) 162.648 + 52.8474i 0.207194 + 0.0673216i
\(786\) 0 0
\(787\) −1198.79 870.971i −1.52324