Properties

Label 300.2.x.a.233.6
Level $300$
Weight $2$
Character 300.233
Analytic conductor $2.396$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.x (of order \(20\), degree \(8\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(10\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 233.6
Character \(\chi\) \(=\) 300.233
Dual form 300.2.x.a.197.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.0384027 - 1.73163i) q^{3} +(-2.22910 - 0.176414i) q^{5} +(3.29686 - 3.29686i) q^{7} +(-2.99705 + 0.132998i) q^{9} +O(q^{10})\) \(q+(-0.0384027 - 1.73163i) q^{3} +(-2.22910 - 0.176414i) q^{5} +(3.29686 - 3.29686i) q^{7} +(-2.99705 + 0.132998i) q^{9} +(-2.51720 + 0.817889i) q^{11} +(-2.61460 + 1.33221i) q^{13} +(-0.219879 + 3.86674i) q^{15} +(-1.07325 - 6.77623i) q^{17} +(0.761063 - 1.04751i) q^{19} +(-5.83553 - 5.58232i) q^{21} +(0.460230 + 0.234499i) q^{23} +(4.93776 + 0.786487i) q^{25} +(0.345398 + 5.18466i) q^{27} +(3.38873 - 2.46206i) q^{29} +(-6.95448 - 5.05272i) q^{31} +(1.51294 + 4.32744i) q^{33} +(-7.93063 + 6.76741i) q^{35} +(0.868677 + 1.70487i) q^{37} +(2.40729 + 4.47635i) q^{39} +(6.79828 + 2.20889i) q^{41} +(6.48953 + 6.48953i) q^{43} +(6.70418 + 0.232255i) q^{45} +(9.43571 + 1.49447i) q^{47} -14.7386i q^{49} +(-11.6927 + 2.11869i) q^{51} +(0.368009 - 2.32352i) q^{53} +(5.75538 - 1.37909i) q^{55} +(-1.84313 - 1.27765i) q^{57} +(0.216043 - 0.664912i) q^{59} +(-1.56100 - 4.80426i) q^{61} +(-9.44238 + 10.3193i) q^{63} +(6.06323 - 2.50837i) q^{65} +(11.0275 - 1.74659i) q^{67} +(0.388390 - 0.805952i) q^{69} +(3.02291 + 4.16068i) q^{71} +(-1.39613 + 2.74005i) q^{73} +(1.17228 - 8.58055i) q^{75} +(-5.60240 + 10.9953i) q^{77} +(1.41634 + 1.94942i) q^{79} +(8.96462 - 0.797205i) q^{81} +(0.525550 - 0.0832390i) q^{83} +(1.19696 + 15.2942i) q^{85} +(-4.39350 - 5.77346i) q^{87} +(1.78061 + 5.48014i) q^{89} +(-4.22788 + 13.0121i) q^{91} +(-8.48235 + 12.2366i) q^{93} +(-1.88128 + 2.20075i) q^{95} +(1.58455 - 10.0045i) q^{97} +(7.43541 - 2.78604i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 2q^{3} + 4q^{7} + O(q^{10}) \) \( 80q - 2q^{3} + 4q^{7} + 12q^{13} + 10q^{15} + 20q^{19} + 40q^{25} - 14q^{27} - 20q^{33} + 12q^{37} - 40q^{39} + 12q^{43} - 60q^{45} - 76q^{57} - 98q^{63} - 36q^{67} - 70q^{69} - 44q^{73} - 90q^{75} - 40q^{79} + 20q^{81} - 100q^{85} - 70q^{87} - 18q^{93} - 56q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{3}{20}\right)\)

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
\(3\) −0.0384027 1.73163i −0.0221718 0.999754i
\(4\) 0 0
\(5\) −2.22910 0.176414i −0.996883 0.0788946i
\(6\) 0 0
\(7\) 3.29686 3.29686i 1.24610 1.24610i 0.288666 0.957430i \(-0.406788\pi\)
0.957430 0.288666i \(-0.0932116\pi\)
\(8\) 0 0
\(9\) −2.99705 + 0.132998i −0.999017 + 0.0443328i
\(10\) 0 0
\(11\) −2.51720 + 0.817889i −0.758965 + 0.246603i −0.662834 0.748766i \(-0.730647\pi\)
−0.0961308 + 0.995369i \(0.530647\pi\)
\(12\) 0 0
\(13\) −2.61460 + 1.33221i −0.725160 + 0.369488i −0.777281 0.629153i \(-0.783402\pi\)
0.0521211 + 0.998641i \(0.483402\pi\)
\(14\) 0 0
\(15\) −0.219879 + 3.86674i −0.0567725 + 0.998387i
\(16\) 0 0
\(17\) −1.07325 6.77623i −0.260301 1.64348i −0.678123 0.734949i \(-0.737206\pi\)
0.417821 0.908529i \(-0.362794\pi\)
\(18\) 0 0
\(19\) 0.761063 1.04751i 0.174600 0.240316i −0.712744 0.701424i \(-0.752548\pi\)
0.887344 + 0.461108i \(0.152548\pi\)
\(20\) 0 0
\(21\) −5.83553 5.58232i −1.27342 1.21816i
\(22\) 0 0
\(23\) 0.460230 + 0.234499i 0.0959646 + 0.0488964i 0.501314 0.865265i \(-0.332850\pi\)
−0.405349 + 0.914162i \(0.632850\pi\)
\(24\) 0 0
\(25\) 4.93776 + 0.786487i 0.987551 + 0.157297i
\(26\) 0 0
\(27\) 0.345398 + 5.18466i 0.0664719 + 0.997788i
\(28\) 0 0
\(29\) 3.38873 2.46206i 0.629272 0.457193i −0.226876 0.973924i \(-0.572851\pi\)
0.856148 + 0.516731i \(0.172851\pi\)
\(30\) 0 0
\(31\) −6.95448 5.05272i −1.24906 0.907496i −0.250894 0.968015i \(-0.580725\pi\)
−0.998167 + 0.0605186i \(0.980725\pi\)
\(32\) 0 0
\(33\) 1.51294 + 4.32744i 0.263370 + 0.753311i
\(34\) 0 0
\(35\) −7.93063 + 6.76741i −1.34052 + 1.14390i
\(36\) 0 0
\(37\) 0.868677 + 1.70487i 0.142810 + 0.280280i 0.951322 0.308200i \(-0.0997267\pi\)
−0.808512 + 0.588480i \(0.799727\pi\)
\(38\) 0 0
\(39\) 2.40729 + 4.47635i 0.385475 + 0.716790i
\(40\) 0 0
\(41\) 6.79828 + 2.20889i 1.06171 + 0.344971i 0.787255 0.616628i \(-0.211502\pi\)
0.274458 + 0.961599i \(0.411502\pi\)
\(42\) 0 0
\(43\) 6.48953 + 6.48953i 0.989644 + 0.989644i 0.999947 0.0103030i \(-0.00327959\pi\)
−0.0103030 + 0.999947i \(0.503280\pi\)
\(44\) 0 0
\(45\) 6.70418 + 0.232255i 0.999400 + 0.0346225i
\(46\) 0 0
\(47\) 9.43571 + 1.49447i 1.37634 + 0.217991i 0.800383 0.599489i \(-0.204630\pi\)
0.575957 + 0.817480i \(0.304630\pi\)
\(48\) 0 0
\(49\) 14.7386i 2.10551i
\(50\) 0 0
\(51\) −11.6927 + 2.11869i −1.63730 + 0.296676i
\(52\) 0 0
\(53\) 0.368009 2.32352i 0.0505499 0.319159i −0.949437 0.313959i \(-0.898345\pi\)
0.999986 0.00520061i \(-0.00165541\pi\)
\(54\) 0 0
\(55\) 5.75538 1.37909i 0.776055 0.185956i
\(56\) 0 0
\(57\) −1.84313 1.27765i −0.244128 0.169229i
\(58\) 0 0
\(59\) 0.216043 0.664912i 0.0281264 0.0865641i −0.936008 0.351979i \(-0.885509\pi\)
0.964134 + 0.265415i \(0.0855089\pi\)
\(60\) 0 0
\(61\) −1.56100 4.80426i −0.199865 0.615122i −0.999885 0.0151489i \(-0.995178\pi\)
0.800020 0.599974i \(-0.204822\pi\)
\(62\) 0 0
\(63\) −9.44238 + 10.3193i −1.18963 + 1.30011i
\(64\) 0 0
\(65\) 6.06323 2.50837i 0.752051 0.311125i
\(66\) 0 0
\(67\) 11.0275 1.74659i 1.34723 0.213380i 0.559205 0.829029i \(-0.311106\pi\)
0.788020 + 0.615650i \(0.211106\pi\)
\(68\) 0 0
\(69\) 0.388390 0.805952i 0.0467567 0.0970252i
\(70\) 0 0
\(71\) 3.02291 + 4.16068i 0.358753 + 0.493782i 0.949801 0.312855i \(-0.101285\pi\)
−0.591048 + 0.806637i \(0.701285\pi\)
\(72\) 0 0
\(73\) −1.39613 + 2.74005i −0.163404 + 0.320699i −0.958161 0.286229i \(-0.907598\pi\)
0.794757 + 0.606928i \(0.207598\pi\)
\(74\) 0 0
\(75\) 1.17228 8.58055i 0.135363 0.990796i
\(76\) 0 0
\(77\) −5.60240 + 10.9953i −0.638453 + 1.25303i
\(78\) 0 0
\(79\) 1.41634 + 1.94942i 0.159350 + 0.219327i 0.881225 0.472697i \(-0.156719\pi\)
−0.721875 + 0.692024i \(0.756719\pi\)
\(80\) 0 0
\(81\) 8.96462 0.797205i 0.996069 0.0885784i
\(82\) 0 0
\(83\) 0.525550 0.0832390i 0.0576866 0.00913666i −0.127524 0.991835i \(-0.540703\pi\)
0.185211 + 0.982699i \(0.440703\pi\)
\(84\) 0 0
\(85\) 1.19696 + 15.2942i 0.129828 + 1.65889i
\(86\) 0 0
\(87\) −4.39350 5.77346i −0.471032 0.618980i
\(88\) 0 0
\(89\) 1.78061 + 5.48014i 0.188744 + 0.580894i 0.999993 0.00380724i \(-0.00121189\pi\)
−0.811249 + 0.584701i \(0.801212\pi\)
\(90\) 0 0
\(91\) −4.22788 + 13.0121i −0.443202 + 1.36404i
\(92\) 0 0
\(93\) −8.48235 + 12.2366i −0.879579 + 1.26887i
\(94\) 0 0
\(95\) −1.88128 + 2.20075i −0.193015 + 0.225792i
\(96\) 0 0
\(97\) 1.58455 10.0045i 0.160887 1.01580i −0.766649 0.642066i \(-0.778077\pi\)
0.927536 0.373733i \(-0.121923\pi\)
\(98\) 0 0
\(99\) 7.43541 2.78604i 0.747287 0.280007i
\(100\) 0 0
\(101\) 2.41412i 0.240214i 0.992761 + 0.120107i \(0.0383238\pi\)
−0.992761 + 0.120107i \(0.961676\pi\)
\(102\) 0 0
\(103\) −13.7381 2.17590i −1.35366 0.214398i −0.562897 0.826527i \(-0.690313\pi\)
−0.790758 + 0.612129i \(0.790313\pi\)
\(104\) 0 0
\(105\) 12.0232 + 13.4730i 1.17334 + 1.31483i
\(106\) 0 0
\(107\) 11.6789 + 11.6789i 1.12905 + 1.12905i 0.990333 + 0.138713i \(0.0442964\pi\)
0.138713 + 0.990333i \(0.455704\pi\)
\(108\) 0 0
\(109\) −10.3444 3.36109i −0.990810 0.321934i −0.231623 0.972806i \(-0.574403\pi\)
−0.759187 + 0.650872i \(0.774403\pi\)
\(110\) 0 0
\(111\) 2.91884 1.56969i 0.277044 0.148989i
\(112\) 0 0
\(113\) −8.87975 17.4275i −0.835336 1.63944i −0.766884 0.641785i \(-0.778194\pi\)
−0.0684521 0.997654i \(-0.521806\pi\)
\(114\) 0 0
\(115\) −0.984529 0.603912i −0.0918078 0.0563151i
\(116\) 0 0
\(117\) 7.65891 4.34043i 0.708067 0.401273i
\(118\) 0 0
\(119\) −25.8786 18.8019i −2.37229 1.72357i
\(120\) 0 0
\(121\) −3.23182 + 2.34805i −0.293802 + 0.213459i
\(122\) 0 0
\(123\) 3.56390 11.8569i 0.321346 1.06910i
\(124\) 0 0
\(125\) −10.8680 2.62425i −0.972063 0.234720i
\(126\) 0 0
\(127\) −2.04315 1.04104i −0.181300 0.0923770i 0.360985 0.932572i \(-0.382441\pi\)
−0.542285 + 0.840195i \(0.682441\pi\)
\(128\) 0 0
\(129\) 10.9882 11.4866i 0.967458 1.01134i
\(130\) 0 0
\(131\) −0.615704 + 0.847443i −0.0537943 + 0.0740415i −0.835067 0.550149i \(-0.814571\pi\)
0.781272 + 0.624190i \(0.214571\pi\)
\(132\) 0 0
\(133\) −0.944386 5.96262i −0.0818887 0.517025i
\(134\) 0 0
\(135\) 0.144719 11.6180i 0.0124554 0.999922i
\(136\) 0 0
\(137\) 13.3366 6.79532i 1.13942 0.580564i 0.220649 0.975353i \(-0.429183\pi\)
0.918771 + 0.394790i \(0.129183\pi\)
\(138\) 0 0
\(139\) 7.95528 2.58483i 0.674758 0.219242i 0.0484593 0.998825i \(-0.484569\pi\)
0.626299 + 0.779583i \(0.284569\pi\)
\(140\) 0 0
\(141\) 2.22550 16.3965i 0.187421 1.38083i
\(142\) 0 0
\(143\) 5.49189 5.49189i 0.459255 0.459255i
\(144\) 0 0
\(145\) −7.98815 + 4.89035i −0.663380 + 0.406121i
\(146\) 0 0
\(147\) −25.5217 + 0.566001i −2.10499 + 0.0466830i
\(148\) 0 0
\(149\) −16.5905 −1.35914 −0.679572 0.733609i \(-0.737834\pi\)
−0.679572 + 0.733609i \(0.737834\pi\)
\(150\) 0 0
\(151\) 6.48124 0.527436 0.263718 0.964600i \(-0.415051\pi\)
0.263718 + 0.964600i \(0.415051\pi\)
\(152\) 0 0
\(153\) 4.11781 + 20.1660i 0.332905 + 1.63032i
\(154\) 0 0
\(155\) 14.6108 + 12.4899i 1.17357 + 1.00321i
\(156\) 0 0
\(157\) −2.84503 + 2.84503i −0.227058 + 0.227058i −0.811462 0.584405i \(-0.801328\pi\)
0.584405 + 0.811462i \(0.301328\pi\)
\(158\) 0 0
\(159\) −4.03759 0.548024i −0.320202 0.0434611i
\(160\) 0 0
\(161\) 2.29042 0.744204i 0.180511 0.0586515i
\(162\) 0 0
\(163\) −4.72683 + 2.40844i −0.370234 + 0.188644i −0.629201 0.777243i \(-0.716618\pi\)
0.258967 + 0.965886i \(0.416618\pi\)
\(164\) 0 0
\(165\) −2.60908 9.91320i −0.203117 0.771741i
\(166\) 0 0
\(167\) 0.192101 + 1.21288i 0.0148653 + 0.0938555i 0.994006 0.109330i \(-0.0348705\pi\)
−0.979140 + 0.203186i \(0.934871\pi\)
\(168\) 0 0
\(169\) −2.57984 + 3.55084i −0.198449 + 0.273142i
\(170\) 0 0
\(171\) −2.14163 + 3.24067i −0.163774 + 0.247820i
\(172\) 0 0
\(173\) 4.94847 + 2.52137i 0.376225 + 0.191696i 0.631870 0.775075i \(-0.282288\pi\)
−0.255645 + 0.966771i \(0.582288\pi\)
\(174\) 0 0
\(175\) 18.8720 13.6861i 1.42659 1.03458i
\(176\) 0 0
\(177\) −1.15967 0.348571i −0.0871665 0.0262002i
\(178\) 0 0
\(179\) 8.40448 6.10621i 0.628180 0.456400i −0.227589 0.973757i \(-0.573084\pi\)
0.855769 + 0.517358i \(0.173084\pi\)
\(180\) 0 0
\(181\) −10.6877 7.76504i −0.794408 0.577171i 0.114861 0.993382i \(-0.463358\pi\)
−0.909268 + 0.416211i \(0.863358\pi\)
\(182\) 0 0
\(183\) −8.25923 + 2.88756i −0.610540 + 0.213455i
\(184\) 0 0
\(185\) −1.63560 3.95358i −0.120252 0.290673i
\(186\) 0 0
\(187\) 8.24379 + 16.1794i 0.602846 + 1.18315i
\(188\) 0 0
\(189\) 18.2318 + 15.9544i 1.32617 + 1.16051i
\(190\) 0 0
\(191\) −17.2545 5.60632i −1.24849 0.405659i −0.391111 0.920344i \(-0.627909\pi\)
−0.857380 + 0.514684i \(0.827909\pi\)
\(192\) 0 0
\(193\) 16.4813 + 16.4813i 1.18635 + 1.18635i 0.978068 + 0.208285i \(0.0667882\pi\)
0.208285 + 0.978068i \(0.433212\pi\)
\(194\) 0 0
\(195\) −4.57640 10.4029i −0.327723 0.744967i
\(196\) 0 0
\(197\) −19.3571 3.06586i −1.37914 0.218434i −0.577570 0.816341i \(-0.695999\pi\)
−0.801565 + 0.597907i \(0.795999\pi\)
\(198\) 0 0
\(199\) 17.0715i 1.21017i 0.796161 + 0.605085i \(0.206861\pi\)
−0.796161 + 0.605085i \(0.793139\pi\)
\(200\) 0 0
\(201\) −3.44792 19.0284i −0.243198 1.34216i
\(202\) 0 0
\(203\) 3.05511 19.2892i 0.214427 1.35384i
\(204\) 0 0
\(205\) −14.7643 6.12315i −1.03119 0.427659i
\(206\) 0 0
\(207\) −1.41052 0.641596i −0.0980380 0.0445940i
\(208\) 0 0
\(209\) −1.05900 + 3.25927i −0.0732526 + 0.225448i
\(210\) 0 0
\(211\) 2.31272 + 7.11781i 0.159214 + 0.490010i 0.998563 0.0535819i \(-0.0170638\pi\)
−0.839349 + 0.543592i \(0.817064\pi\)
\(212\) 0 0
\(213\) 7.08865 5.39433i 0.485706 0.369613i
\(214\) 0 0
\(215\) −13.3210 15.6106i −0.908482 1.06464i
\(216\) 0 0
\(217\) −39.5860 + 6.26981i −2.68728 + 0.425623i
\(218\) 0 0
\(219\) 4.79836 + 2.31234i 0.324243 + 0.156254i
\(220\) 0 0
\(221\) 11.8335 + 16.2874i 0.796005 + 1.09561i
\(222\) 0 0
\(223\) 0.771097 1.51336i 0.0516365 0.101342i −0.863746 0.503927i \(-0.831888\pi\)
0.915383 + 0.402585i \(0.131888\pi\)
\(224\) 0 0
\(225\) −14.9033 1.70043i −0.993554 0.113362i
\(226\) 0 0
\(227\) 9.28911 18.2309i 0.616540 1.21003i −0.345834 0.938296i \(-0.612404\pi\)
0.962373 0.271731i \(-0.0875962\pi\)
\(228\) 0 0
\(229\) 6.08934 + 8.38126i 0.402395 + 0.553849i 0.961343 0.275353i \(-0.0887948\pi\)
−0.558948 + 0.829203i \(0.688795\pi\)
\(230\) 0 0
\(231\) 19.2549 + 9.27900i 1.26688 + 0.610514i
\(232\) 0 0
\(233\) 10.4859 1.66080i 0.686955 0.108803i 0.196807 0.980442i \(-0.436943\pi\)
0.490148 + 0.871639i \(0.336943\pi\)
\(234\) 0 0
\(235\) −20.7695 4.99591i −1.35485 0.325897i
\(236\) 0 0
\(237\) 3.32128 2.52743i 0.215740 0.164174i
\(238\) 0 0
\(239\) 6.75814 + 20.7994i 0.437148 + 1.34540i 0.890870 + 0.454259i \(0.150096\pi\)
−0.453722 + 0.891143i \(0.649904\pi\)
\(240\) 0 0
\(241\) 3.43227 10.5634i 0.221092 0.680451i −0.777573 0.628793i \(-0.783549\pi\)
0.998665 0.0516582i \(-0.0164506\pi\)
\(242\) 0 0
\(243\) −1.72473 15.4928i −0.110641 0.993860i
\(244\) 0 0
\(245\) −2.60008 + 32.8537i −0.166113 + 2.09895i
\(246\) 0 0
\(247\) −0.594373 + 3.75272i −0.0378191 + 0.238780i
\(248\) 0 0
\(249\) −0.164321 0.906859i −0.0104134 0.0574699i
\(250\) 0 0
\(251\) 10.0302i 0.633100i 0.948576 + 0.316550i \(0.102524\pi\)
−0.948576 + 0.316550i \(0.897476\pi\)
\(252\) 0 0
\(253\) −1.35029 0.213864i −0.0848918 0.0134455i
\(254\) 0 0
\(255\) 26.4379 2.66002i 1.65561 0.166577i
\(256\) 0 0
\(257\) 14.2299 + 14.2299i 0.887636 + 0.887636i 0.994296 0.106659i \(-0.0340154\pi\)
−0.106659 + 0.994296i \(0.534015\pi\)
\(258\) 0 0
\(259\) 8.48463 + 2.75682i 0.527209 + 0.171301i
\(260\) 0 0
\(261\) −9.82875 + 7.82960i −0.608384 + 0.484640i
\(262\) 0 0
\(263\) 9.27721 + 18.2076i 0.572057 + 1.12273i 0.977957 + 0.208808i \(0.0669583\pi\)
−0.405899 + 0.913918i \(0.633042\pi\)
\(264\) 0 0
\(265\) −1.23023 + 5.11442i −0.0755723 + 0.314177i
\(266\) 0 0
\(267\) 9.42117 3.29379i 0.576566 0.201577i
\(268\) 0 0
\(269\) −9.47744 6.88577i −0.577850 0.419833i 0.260098 0.965582i \(-0.416245\pi\)
−0.837948 + 0.545750i \(0.816245\pi\)
\(270\) 0 0
\(271\) −1.24045 + 0.901239i −0.0753519 + 0.0547463i −0.624823 0.780766i \(-0.714829\pi\)
0.549472 + 0.835512i \(0.314829\pi\)
\(272\) 0 0
\(273\) 22.6944 + 6.82140i 1.37353 + 0.412850i
\(274\) 0 0
\(275\) −13.0726 + 2.05879i −0.788307 + 0.124150i
\(276\) 0 0
\(277\) −7.36701 3.75368i −0.442641 0.225537i 0.218442 0.975850i \(-0.429903\pi\)
−0.661082 + 0.750313i \(0.729903\pi\)
\(278\) 0 0
\(279\) 21.5149 + 14.2183i 1.28806 + 0.851229i
\(280\) 0 0
\(281\) −16.4737 + 22.6741i −0.982737 + 1.35262i −0.0473952 + 0.998876i \(0.515092\pi\)
−0.935342 + 0.353745i \(0.884908\pi\)
\(282\) 0 0
\(283\) −2.95822 18.6774i −0.175848 1.11026i −0.904845 0.425742i \(-0.860013\pi\)
0.728997 0.684517i \(-0.239987\pi\)
\(284\) 0 0
\(285\) 3.88312 + 3.17316i 0.230016 + 0.187962i
\(286\) 0 0
\(287\) 29.6954 15.1305i 1.75286 0.893128i
\(288\) 0 0
\(289\) −28.5975 + 9.29189i −1.68221 + 0.546582i
\(290\) 0 0
\(291\) −17.3848 2.35965i −1.01912 0.138325i
\(292\) 0 0
\(293\) 2.21527 2.21527i 0.129417 0.129417i −0.639431 0.768848i \(-0.720830\pi\)
0.768848 + 0.639431i \(0.220830\pi\)
\(294\) 0 0
\(295\) −0.598880 + 1.44404i −0.0348682 + 0.0840753i
\(296\) 0 0
\(297\) −5.10991 12.7683i −0.296507 0.740895i
\(298\) 0 0
\(299\) −1.51572 −0.0876564
\(300\) 0 0
\(301\) 42.7901 2.46638
\(302\) 0 0
\(303\) 4.18035 0.0927089i 0.240155 0.00532599i
\(304\) 0 0
\(305\) 2.63208 + 10.9845i 0.150713 + 0.628973i
\(306\) 0 0
\(307\) 5.97093 5.97093i 0.340779 0.340779i −0.515881 0.856660i \(-0.672535\pi\)
0.856660 + 0.515881i \(0.172535\pi\)
\(308\) 0 0
\(309\) −3.24026 + 23.8728i −0.184332 + 1.35808i
\(310\) 0 0
\(311\) 24.1306 7.84050i 1.36832 0.444594i 0.469508 0.882928i \(-0.344431\pi\)
0.898812 + 0.438334i \(0.144431\pi\)
\(312\) 0 0
\(313\) 18.5441 9.44868i 1.04817 0.534071i 0.156936 0.987609i \(-0.449838\pi\)
0.891237 + 0.453538i \(0.149838\pi\)
\(314\) 0 0
\(315\) 22.8685 21.3370i 1.28849 1.20221i
\(316\) 0 0
\(317\) −1.87932 11.8655i −0.105553 0.666435i −0.982558 0.185955i \(-0.940462\pi\)
0.877005 0.480481i \(-0.159538\pi\)
\(318\) 0 0
\(319\) −6.51643 + 8.96910i −0.364850 + 0.502173i
\(320\) 0 0
\(321\) 19.7750 20.6720i 1.10373 1.15380i
\(322\) 0 0
\(323\) −7.91500 4.03290i −0.440403 0.224396i
\(324\) 0 0
\(325\) −13.9580 + 4.52176i −0.774252 + 0.250822i
\(326\) 0 0
\(327\) −5.42289 + 18.0416i −0.299886 + 0.997704i
\(328\) 0 0
\(329\) 36.0353 26.1811i 1.98669 1.44341i
\(330\) 0 0
\(331\) 8.81611 + 6.40528i 0.484577 + 0.352066i 0.803095 0.595851i \(-0.203185\pi\)
−0.318518 + 0.947917i \(0.603185\pi\)
\(332\) 0 0
\(333\) −2.83021 4.99406i −0.155095 0.273673i
\(334\) 0 0
\(335\) −24.8895 + 1.94791i −1.35986 + 0.106426i
\(336\) 0 0
\(337\) 3.69026 + 7.24255i 0.201021 + 0.394527i 0.969406 0.245461i \(-0.0789393\pi\)
−0.768385 + 0.639988i \(0.778939\pi\)
\(338\) 0 0
\(339\) −29.8369 + 16.0457i −1.62052 + 0.871480i
\(340\) 0 0
\(341\) 21.6384 + 7.03074i 1.17178 + 0.380736i
\(342\) 0 0
\(343\) −25.5129 25.5129i −1.37757 1.37757i
\(344\) 0 0
\(345\) −1.00794 + 1.72803i −0.0542657 + 0.0930339i
\(346\) 0 0
\(347\) −23.9622 3.79524i −1.28636 0.203739i −0.524460 0.851435i \(-0.675733\pi\)
−0.761899 + 0.647696i \(0.775733\pi\)
\(348\) 0 0
\(349\) 0.686028i 0.0367222i 0.999831 + 0.0183611i \(0.00584486\pi\)
−0.999831 + 0.0183611i \(0.994155\pi\)
\(350\) 0 0
\(351\) −7.81012 13.0957i −0.416873 0.698996i
\(352\) 0 0
\(353\) −0.458795 + 2.89672i −0.0244192 + 0.154177i −0.996885 0.0788690i \(-0.974869\pi\)
0.972466 + 0.233046i \(0.0748691\pi\)
\(354\) 0 0
\(355\) −6.00436 9.80784i −0.318678 0.520546i
\(356\) 0 0
\(357\) −31.5641 + 45.5341i −1.67055 + 2.40992i
\(358\) 0 0
\(359\) −7.07630 + 21.7786i −0.373473 + 1.14943i 0.571031 + 0.820929i \(0.306544\pi\)
−0.944503 + 0.328502i \(0.893456\pi\)
\(360\) 0 0
\(361\) 5.35326 + 16.4756i 0.281750 + 0.867138i
\(362\) 0 0
\(363\) 4.19006 + 5.50612i 0.219921 + 0.288997i
\(364\) 0 0
\(365\) 3.59548 5.86155i 0.188196 0.306807i
\(366\) 0 0
\(367\) 7.75783 1.22872i 0.404955 0.0641386i 0.0493656 0.998781i \(-0.484280\pi\)
0.355590 + 0.934642i \(0.384280\pi\)
\(368\) 0 0
\(369\) −20.6686 5.71601i −1.07596 0.297563i
\(370\) 0 0
\(371\) −6.44703 8.87358i −0.334713 0.460693i
\(372\) 0 0
\(373\) 8.90498 17.4770i 0.461082 0.904925i −0.537033 0.843561i \(-0.680455\pi\)
0.998115 0.0613640i \(-0.0195451\pi\)
\(374\) 0 0
\(375\) −4.12685 + 18.9201i −0.213110 + 0.977028i
\(376\) 0 0
\(377\) −5.58022 + 10.9518i −0.287396 + 0.564046i
\(378\) 0 0
\(379\) 10.7496 + 14.7956i 0.552172 + 0.760000i 0.990305 0.138910i \(-0.0443600\pi\)
−0.438133 + 0.898910i \(0.644360\pi\)
\(380\) 0 0
\(381\) −1.72422 + 3.57794i −0.0883345 + 0.183304i
\(382\) 0 0
\(383\) 4.77981 0.757047i 0.244237 0.0386833i −0.0331158 0.999452i \(-0.510543\pi\)
0.277353 + 0.960768i \(0.410543\pi\)
\(384\) 0 0
\(385\) 14.4280 23.5213i 0.735320 1.19876i
\(386\) 0 0
\(387\) −20.3125 18.5864i −1.03254 0.944797i
\(388\) 0 0
\(389\) −4.33329 13.3365i −0.219707 0.676188i −0.998786 0.0492621i \(-0.984313\pi\)
0.779079 0.626926i \(-0.215687\pi\)
\(390\) 0 0
\(391\) 1.09508 3.37030i 0.0553805 0.170444i
\(392\) 0 0
\(393\) 1.49110 + 1.03362i 0.0752160 + 0.0521394i
\(394\) 0 0
\(395\) −2.81325 4.59531i −0.141550 0.231215i
\(396\) 0 0
\(397\) −2.55903 + 16.1570i −0.128434 + 0.810899i 0.836416 + 0.548096i \(0.184647\pi\)
−0.964849 + 0.262803i \(0.915353\pi\)
\(398\) 0 0
\(399\) −10.2888 + 1.86430i −0.515082 + 0.0933319i
\(400\) 0 0
\(401\) 21.7930i 1.08829i 0.838991 + 0.544145i \(0.183146\pi\)
−0.838991 + 0.544145i \(0.816854\pi\)
\(402\) 0 0
\(403\) 24.9145 + 3.94606i 1.24108 + 0.196567i
\(404\) 0 0
\(405\) −20.1237 + 0.195566i −0.999953 + 0.00971774i
\(406\) 0 0
\(407\) −3.58103 3.58103i −0.177505 0.177505i
\(408\) 0 0
\(409\) 12.1283 + 3.94072i 0.599705 + 0.194856i 0.593109 0.805122i \(-0.297900\pi\)
0.00659637 + 0.999978i \(0.497900\pi\)
\(410\) 0 0
\(411\) −12.2791 22.8330i −0.605684 1.12627i
\(412\) 0 0
\(413\) −1.47986 2.90438i −0.0728190 0.142915i
\(414\) 0 0
\(415\) −1.18619 + 0.0928335i −0.0582276 + 0.00455702i
\(416\) 0 0
\(417\) −4.78146 13.6763i −0.234149 0.669731i
\(418\) 0 0
\(419\) −22.6925 16.4871i −1.10860 0.805447i −0.126160 0.992010i \(-0.540265\pi\)
−0.982443 + 0.186563i \(0.940265\pi\)
\(420\) 0 0
\(421\) 4.60347 3.34462i 0.224360 0.163007i −0.469927 0.882705i \(-0.655720\pi\)
0.694287 + 0.719698i \(0.255720\pi\)
\(422\) 0 0
\(423\) −28.4781 3.22407i −1.38465 0.156760i
\(424\) 0 0
\(425\) 0.0299739 34.3035i 0.00145395 1.66396i
\(426\) 0 0
\(427\) −20.9854 10.6926i −1.01555 0.517450i
\(428\) 0 0
\(429\) −9.72080 9.29899i −0.469324 0.448959i
\(430\) 0 0
\(431\) 12.4959 17.1991i 0.601904 0.828450i −0.393977 0.919120i \(-0.628901\pi\)
0.995881 + 0.0906706i \(0.0289010\pi\)
\(432\) 0 0
\(433\) 3.63581 + 22.9556i 0.174726 + 1.10318i 0.906679 + 0.421821i \(0.138609\pi\)
−0.731953 + 0.681355i \(0.761391\pi\)
\(434\) 0 0
\(435\) 8.77502 + 13.6447i 0.420730 + 0.654213i
\(436\) 0 0
\(437\) 0.595905 0.303629i 0.0285060 0.0145245i
\(438\) 0 0
\(439\) 24.5061 7.96251i 1.16961 0.380030i 0.341114 0.940022i \(-0.389196\pi\)
0.828498 + 0.559992i \(0.189196\pi\)
\(440\) 0 0
\(441\) 1.96020 + 44.1722i 0.0933430 + 2.10344i
\(442\) 0 0
\(443\) −9.30295 + 9.30295i −0.441997 + 0.441997i −0.892683 0.450686i \(-0.851179\pi\)
0.450686 + 0.892683i \(0.351179\pi\)
\(444\) 0 0
\(445\) −3.00237 12.5299i −0.142326 0.593974i
\(446\) 0 0
\(447\) 0.637119 + 28.7285i 0.0301347 + 1.35881i
\(448\) 0 0
\(449\) −22.1737 −1.04644 −0.523221 0.852197i \(-0.675270\pi\)
−0.523221 + 0.852197i \(0.675270\pi\)
\(450\) 0 0
\(451\) −18.9193 −0.890874
\(452\) 0 0
\(453\) −0.248898 11.2231i −0.0116942 0.527306i
\(454\) 0 0
\(455\) 11.7199 28.2593i 0.549436 1.32482i
\(456\) 0 0
\(457\) 10.0840 10.0840i 0.471711 0.471711i −0.430757 0.902468i \(-0.641753\pi\)
0.902468 + 0.430757i \(0.141753\pi\)
\(458\) 0 0
\(459\) 34.7618 7.90493i 1.62254 0.368971i
\(460\) 0 0
\(461\) −24.5459 + 7.97544i −1.14322 + 0.371453i −0.818584 0.574387i \(-0.805240\pi\)
−0.324632 + 0.945841i \(0.605240\pi\)
\(462\) 0 0
\(463\) 20.3415 10.3645i 0.945350 0.481680i 0.0878325 0.996135i \(-0.472006\pi\)
0.857517 + 0.514456i \(0.172006\pi\)
\(464\) 0 0
\(465\) 21.0667 25.7801i 0.976945 1.19553i
\(466\) 0 0
\(467\) −2.18498 13.7954i −0.101109 0.638376i −0.985245 0.171148i \(-0.945252\pi\)
0.884136 0.467229i \(-0.154748\pi\)
\(468\) 0 0
\(469\) 30.5979 42.1144i 1.41288 1.94466i
\(470\) 0 0
\(471\) 5.03578 + 4.81726i 0.232036 + 0.221968i
\(472\) 0 0
\(473\) −21.6432 11.0277i −0.995154 0.507056i
\(474\) 0 0
\(475\) 4.58180 4.57380i 0.210227 0.209860i
\(476\) 0 0
\(477\) −0.793917 + 7.01264i −0.0363510 + 0.321087i
\(478\) 0 0
\(479\) −2.14256 + 1.55666i −0.0978960 + 0.0711256i −0.635656 0.771972i \(-0.719270\pi\)
0.537760 + 0.843098i \(0.319270\pi\)
\(480\) 0 0
\(481\) −4.54249 3.30031i −0.207120 0.150481i
\(482\) 0 0
\(483\) −1.37664 3.93758i −0.0626393 0.179166i
\(484\) 0 0
\(485\) −5.29705 + 22.0214i −0.240526 + 0.999940i
\(486\) 0 0
\(487\) 2.86281 + 5.61858i 0.129726 + 0.254602i 0.946729 0.322032i \(-0.104366\pi\)
−0.817002 + 0.576634i \(0.804366\pi\)
\(488\) 0 0
\(489\) 4.35204 + 8.09261i 0.196806 + 0.365960i
\(490\) 0 0
\(491\) 17.2145 + 5.59334i 0.776881 + 0.252424i 0.670508 0.741902i \(-0.266076\pi\)
0.106373 + 0.994326i \(0.466076\pi\)
\(492\) 0 0
\(493\) −20.3204 20.3204i −0.915186 0.915186i
\(494\) 0 0
\(495\) −17.0657 + 4.89864i −0.767048 + 0.220178i
\(496\) 0 0
\(497\) 23.6833 + 3.75106i 1.06234 + 0.168258i
\(498\) 0 0
\(499\) 25.8514i 1.15727i 0.815587 + 0.578634i \(0.196414\pi\)
−0.815587 + 0.578634i \(0.803586\pi\)
\(500\) 0 0
\(501\) 2.09288 0.379225i 0.0935028 0.0169425i
\(502\) 0 0
\(503\) −2.21885 + 14.0093i −0.0989337 + 0.624643i 0.887541 + 0.460729i \(0.152412\pi\)
−0.986475 + 0.163914i \(0.947588\pi\)
\(504\) 0 0
\(505\) 0.425884 5.38131i 0.0189516 0.239465i
\(506\) 0 0
\(507\) 6.24780 + 4.33095i 0.277474 + 0.192344i
\(508\) 0 0
\(509\) 7.07081 21.7617i 0.313408 0.964571i −0.662997 0.748622i \(-0.730716\pi\)
0.976405 0.215949i \(-0.0692844\pi\)
\(510\) 0 0
\(511\) 4.43073 + 13.6364i 0.196004 + 0.603239i
\(512\) 0 0
\(513\) 5.69387 + 3.58404i 0.251390 + 0.158239i
\(514\) 0 0
\(515\) 30.2397 + 7.27389i 1.33252 + 0.320526i
\(516\) 0 0
\(517\) −24.9739 + 3.95548i −1.09835 + 0.173962i
\(518\) 0 0
\(519\) 4.17603 8.66572i 0.183308 0.380383i
\(520\) 0 0
\(521\) −21.3145 29.3369i −0.933805 1.28527i −0.958357 0.285574i \(-0.907816\pi\)
0.0245518 0.999699i \(-0.492184\pi\)
\(522\) 0 0
\(523\) −8.90012 + 17.4675i −0.389175 + 0.763799i −0.999600 0.0282747i \(-0.990999\pi\)
0.610425 + 0.792074i \(0.290999\pi\)
\(524\) 0 0
\(525\) −24.4240 32.1537i −1.06595 1.40330i
\(526\) 0 0
\(527\) −26.7745 + 52.5480i −1.16632 + 2.28903i
\(528\) 0 0
\(529\) −13.3622 18.3915i −0.580967 0.799632i
\(530\) 0 0
\(531\) −0.559059 + 2.02151i −0.0242611 + 0.0877259i
\(532\) 0 0
\(533\) −20.7175 + 3.28133i −0.897374 + 0.142130i
\(534\) 0 0
\(535\) −23.9732 28.0938i −1.03645 1.21460i
\(536\) 0 0
\(537\) −10.8964 14.3189i −0.470215 0.617907i
\(538\) 0 0
\(539\) 12.0545 + 37.0999i 0.519224 + 1.59801i
\(540\) 0 0
\(541\) 13.0093 40.0384i 0.559312 1.72138i −0.124964 0.992161i \(-0.539881\pi\)
0.684275 0.729224i \(-0.260119\pi\)
\(542\) 0 0
\(543\) −13.0357 + 18.8052i −0.559416 + 0.807009i
\(544\) 0 0
\(545\) 22.4657 + 9.31708i 0.962323 + 0.399100i
\(546\) 0 0
\(547\) 3.47779 21.9579i 0.148699 0.938851i −0.794654 0.607062i \(-0.792348\pi\)
0.943354 0.331789i \(-0.107652\pi\)
\(548\) 0 0
\(549\) 5.31735 + 14.1910i 0.226939 + 0.605657i
\(550\) 0 0
\(551\) 5.42352i 0.231050i
\(552\) 0 0
\(553\) 11.0964 + 1.75750i 0.471868 + 0.0747366i
\(554\) 0 0
\(555\) −6.78330 + 2.98408i −0.287935 + 0.126667i
\(556\) 0 0
\(557\) 0.749164 + 0.749164i 0.0317431 + 0.0317431i 0.722800 0.691057i \(-0.242855\pi\)
−0.691057 + 0.722800i \(0.742855\pi\)
\(558\) 0 0
\(559\) −25.6129 8.32215i −1.08331 0.351989i
\(560\) 0 0
\(561\) 27.7000 14.8965i 1.16949 0.628930i
\(562\) 0 0
\(563\) −0.652641 1.28088i −0.0275055 0.0539827i 0.876845 0.480773i \(-0.159644\pi\)
−0.904350 + 0.426791i \(0.859644\pi\)
\(564\) 0 0
\(565\) 16.7194 + 40.4141i 0.703390 + 1.70023i
\(566\) 0 0
\(567\) 26.9268 32.1834i 1.13082 1.35157i
\(568\) 0 0
\(569\) −6.70335 4.87027i −0.281019 0.204172i 0.438343 0.898808i \(-0.355566\pi\)
−0.719362 + 0.694636i \(0.755566\pi\)
\(570\) 0 0
\(571\) −5.69591 + 4.13832i −0.238366 + 0.173183i −0.700555 0.713598i \(-0.747064\pi\)
0.462189 + 0.886781i \(0.347064\pi\)
\(572\) 0 0
\(573\) −9.04543 + 30.0936i −0.377878 + 1.25718i
\(574\) 0 0
\(575\) 2.08807 + 1.51986i 0.0870787 + 0.0633827i
\(576\) 0 0
\(577\) 18.4348 + 9.39300i 0.767451 + 0.391036i 0.793457 0.608626i \(-0.208279\pi\)
−0.0260065 + 0.999662i \(0.508279\pi\)
\(578\) 0 0
\(579\) 27.9066 29.1724i 1.15976 1.21237i
\(580\) 0 0
\(581\) 1.45824 2.00709i 0.0604979 0.0832682i
\(582\) 0 0
\(583\) 0.974025 + 6.14975i 0.0403400 + 0.254697i
\(584\) 0 0
\(585\) −17.8382 + 8.32410i −0.737518 + 0.344159i
\(586\) 0 0
\(587\) −0.296037 + 0.150838i −0.0122187 + 0.00622576i −0.460089 0.887873i \(-0.652183\pi\)
0.447870 + 0.894098i \(0.352183\pi\)
\(588\) 0 0
\(589\) −10.5856 + 3.43947i −0.436172 + 0.141721i
\(590\) 0 0
\(591\) −4.56556 + 33.6370i −0.187802 + 1.38364i
\(592\) 0 0
\(593\) 27.1484 27.1484i 1.11485 1.11485i 0.122365 0.992485i \(-0.460952\pi\)
0.992485 0.122365i \(-0.0390480\pi\)
\(594\) 0 0
\(595\) 54.3691 + 46.4767i 2.22892 + 1.90536i
\(596\) 0 0
\(597\) 29.5615 0.655594i 1.20987 0.0268317i
\(598\) 0 0
\(599\) −15.8427 −0.647315 −0.323657 0.946174i \(-0.604913\pi\)
−0.323657 + 0.946174i \(0.604913\pi\)
\(600\) 0 0
\(601\) −10.1851 −0.415459 −0.207729 0.978186i \(-0.566607\pi\)
−0.207729 + 0.978186i \(0.566607\pi\)
\(602\) 0 0
\(603\) −32.8177 + 6.70125i −1.33644 + 0.272896i
\(604\) 0 0
\(605\) 7.61827 4.66390i 0.309727 0.189615i
\(606\) 0 0
\(607\) 15.8821 15.8821i 0.644635 0.644635i −0.307056 0.951691i \(-0.599344\pi\)
0.951691 + 0.307056i \(0.0993441\pi\)
\(608\) 0 0
\(609\) −33.5190 4.54955i −1.35826 0.184357i
\(610\) 0 0
\(611\) −26.6616 + 8.66287i −1.07861 + 0.350462i
\(612\) 0 0
\(613\) −14.2208 + 7.24586i −0.574373 + 0.292658i −0.716948 0.697126i \(-0.754462\pi\)
0.142576 + 0.989784i \(0.454462\pi\)
\(614\) 0 0
\(615\) −10.0360 + 25.8015i −0.404691 + 1.04041i
\(616\) 0 0
\(617\) −1.40300 8.85819i −0.0564826 0.356617i −0.999701 0.0244446i \(-0.992218\pi\)
0.943219 0.332173i \(-0.107782\pi\)
\(618\) 0 0
\(619\) −8.67904 + 11.9457i −0.348840 + 0.480137i −0.946997 0.321242i \(-0.895900\pi\)
0.598157 + 0.801379i \(0.295900\pi\)
\(620\) 0 0
\(621\) −1.05683 + 2.46713i −0.0424093 + 0.0990026i
\(622\) 0 0
\(623\) 23.9377 + 12.1968i 0.959042 + 0.488656i
\(624\) 0 0
\(625\) 23.7629 + 7.76696i 0.950515 + 0.310679i
\(626\) 0 0
\(627\) 5.68450 + 1.70863i 0.227017 + 0.0682360i
\(628\) 0 0
\(629\) 10.6203 7.71611i 0.423460 0.307661i
\(630\) 0 0
\(631\) 5.22678 + 3.79747i 0.208075 + 0.151175i 0.686942 0.726712i \(-0.258953\pi\)
−0.478868 + 0.877887i \(0.658953\pi\)
\(632\) 0 0
\(633\) 12.2366 4.27810i 0.486360 0.170039i
\(634\) 0 0
\(635\) 4.37072 + 2.68101i 0.173447 + 0.106393i
\(636\) 0 0
\(637\) 19.6348 + 38.5355i 0.777959 + 1.52683i
\(638\) 0 0
\(639\) −9.61317 12.0677i −0.380291 0.477392i
\(640\) 0 0
\(641\) 10.6889 + 3.47304i 0.422187 + 0.137177i 0.512402 0.858745i \(-0.328756\pi\)
−0.0902157 + 0.995922i \(0.528756\pi\)
\(642\) 0 0
\(643\) −8.44140 8.44140i −0.332896 0.332896i 0.520789 0.853685i \(-0.325638\pi\)
−0.853685 + 0.520789i \(0.825638\pi\)
\(644\) 0 0
\(645\) −26.5202 + 23.6664i −1.04423 + 0.931863i
\(646\) 0 0
\(647\) 12.8707 + 2.03852i 0.506001 + 0.0801427i 0.404216 0.914664i \(-0.367545\pi\)
0.101785 + 0.994806i \(0.467545\pi\)
\(648\) 0 0
\(649\) 1.85042i 0.0726352i
\(650\) 0 0
\(651\) 12.3772 + 68.3074i 0.485100 + 2.67718i
\(652\) 0 0
\(653\) −1.55677 + 9.82909i −0.0609213 + 0.384642i 0.938323 + 0.345761i \(0.112379\pi\)
−0.999244 + 0.0388808i \(0.987621\pi\)
\(654\) 0 0
\(655\) 1.52196 1.78042i 0.0594681 0.0695666i
\(656\) 0 0
\(657\) 3.81984 8.39775i 0.149026 0.327628i
\(658\) 0 0
\(659\) −12.8415 + 39.5220i −0.500232 + 1.53956i 0.308408 + 0.951254i \(0.400204\pi\)
−0.808641 + 0.588303i \(0.799796\pi\)
\(660\) 0 0
\(661\) −0.168013 0.517089i −0.00653493 0.0201124i 0.947736 0.319056i \(-0.103366\pi\)
−0.954271 + 0.298943i \(0.903366\pi\)
\(662\) 0 0
\(663\) 27.7492 21.1166i 1.07769 0.820101i
\(664\) 0 0
\(665\) 1.05324 + 13.4579i 0.0408429 + 0.521874i
\(666\) 0 0
\(667\) 2.13695 0.338459i 0.0827429 0.0131052i
\(668\) 0 0
\(669\) −2.65019 1.27713i −0.102462 0.0493768i
\(670\) 0 0
\(671\) 7.85870 + 10.8166i 0.303382 + 0.417569i
\(672\) 0 0
\(673\) −8.48836 + 16.6593i −0.327202 + 0.642170i −0.994743 0.102403i \(-0.967347\pi\)
0.667541 + 0.744573i \(0.267347\pi\)
\(674\) 0 0
\(675\) −2.37218 + 25.8722i −0.0913051 + 0.995823i
\(676\) 0 0
\(677\) −2.20359 + 4.32479i −0.0846909 + 0.166215i −0.929468 0.368904i \(-0.879733\pi\)
0.844777 + 0.535119i \(0.179733\pi\)
\(678\) 0 0
\(679\) −27.7593 38.2074i −1.06530 1.46626i
\(680\) 0 0
\(681\) −31.9258 15.3851i −1.22340 0.589560i
\(682\) 0 0
\(683\) 37.0496 5.86808i 1.41766 0.224536i 0.599893 0.800080i \(-0.295210\pi\)
0.817770 + 0.575545i \(0.195210\pi\)
\(684\) 0 0
\(685\) −30.9273 + 12.7947i −1.18167 + 0.488860i
\(686\) 0 0
\(687\) 14.2794 10.8663i 0.544791 0.414576i
\(688\) 0 0
\(689\) 2.13321 + 6.56534i 0.0812687 + 0.250119i
\(690\) 0 0
\(691\) 10.4266 32.0898i 0.396647 1.22075i −0.531025 0.847356i \(-0.678193\pi\)
0.927672 0.373397i \(-0.121807\pi\)
\(692\) 0 0
\(693\) 15.3283 33.6987i 0.582274 1.28011i
\(694\) 0 0
\(695\) −18.1891 + 4.35841i −0.689952 + 0.165324i
\(696\) 0 0
\(697\) 7.67173 48.4374i 0.290587 1.83470i
\(698\) 0 0
\(699\) −3.27858 18.0939i −0.124007 0.684373i
\(700\) 0 0
\(701\) 50.3263i 1.90080i −0.311032 0.950399i \(-0.600675\pi\)
0.311032 0.950399i \(-0.399325\pi\)
\(702\) 0 0
\(703\) 2.44700 + 0.387566i 0.0922902 + 0.0146173i
\(704\) 0 0
\(705\) −7.85343 + 36.1568i −0.295777 + 1.36174i
\(706\) 0 0
\(707\) 7.95902 + 7.95902i 0.299330 + 0.299330i
\(708\) 0 0
\(709\) 36.5771 + 11.8846i 1.37368 + 0.446337i 0.900588 0.434675i \(-0.143137\pi\)
0.473095 + 0.881011i \(0.343137\pi\)
\(710\) 0 0
\(711\) −4.50411 5.65415i −0.168917 0.212047i
\(712\) 0 0
\(713\) −2.01580 3.95623i −0.0754924 0.148162i
\(714\) 0 0
\(715\) −13.2108 + 11.2731i −0.494056 + 0.421591i
\(716\) 0 0
\(717\) 35.7573 12.5013i 1.33538 0.466870i
\(718\) 0 0
\(719\) 41.8068 + 30.3745i 1.55913 + 1.13278i 0.936716 + 0.350089i \(0.113849\pi\)
0.622416 + 0.782687i \(0.286151\pi\)
\(720\) 0 0
\(721\) −52.4662 + 38.1189i −1.95394 + 1.41962i
\(722\) 0 0
\(723\) −18.4237 5.53774i −0.685186 0.205951i
\(724\) 0 0
\(725\) 18.6691 9.49184i 0.693353 0.352518i
\(726\) 0 0
\(727\) −28.7844 14.6664i −1.06755 0.543946i −0.170269 0.985398i \(-0.554464\pi\)
−0.897285 + 0.441452i \(0.854464\pi\)
\(728\) 0 0
\(729\) −26.7614 + 3.58154i −0.991163 + 0.132650i
\(730\) 0 0
\(731\) 37.0097 50.9394i 1.36885 1.88406i
\(732\) 0 0
\(733\) 5.26046 + 33.2132i 0.194300 + 1.22676i 0.871291 + 0.490768i \(0.163284\pi\)
−0.676991 + 0.735991i \(0.736716\pi\)
\(734\) 0 0
\(735\) 56.9901 + 3.24070i 2.10211 + 0.119535i
\(736\) 0 0
\(737\) −26.3300 + 13.4158i −0.969877 + 0.494177i
\(738\) 0 0
\(739\) −22.5536 + 7.32812i −0.829649 + 0.269569i −0.692897 0.721036i \(-0.743666\pi\)
−0.136751 + 0.990605i \(0.543666\pi\)
\(740\) 0 0
\(741\) 6.52114 + 0.885116i 0.239560 + 0.0325156i
\(742\) 0 0
\(743\) −16.0850 + 16.0850i −0.590100 + 0.590100i −0.937658 0.347559i \(-0.887011\pi\)
0.347559 + 0.937658i \(0.387011\pi\)
\(744\) 0 0
\(745\) 36.9818 + 2.92679i 1.35491 + 0.107229i
\(746\) 0 0
\(747\) −1.56403 + 0.319369i −0.0572249 + 0.0116851i
\(748\) 0 0
\(749\) 77.0076 2.81380
\(750\) 0 0
\(751\) −36.4969 −1.33179 −0.665896 0.746045i \(-0.731951\pi\)
−0.665896 + 0.746045i \(0.731951\pi\)
\(752\) 0 0
\(753\) 17.3685 0.385187i 0.632944 0.0140370i
\(754\) 0 0
\(755\) −14.4473 1.14338i −0.525792 0.0416119i
\(756\) 0 0
\(757\) 30.7730 30.7730i 1.11846 1.11846i 0.126497 0.991967i \(-0.459626\pi\)
0.991967 0.126497i \(-0.0403735\pi\)
\(758\) 0 0
\(759\) −0.318478 + 2.34640i −0.0115600 + 0.0851691i
\(760\) 0 0
\(761\) −26.0146 + 8.45266i −0.943029 + 0.306409i −0.739880 0.672739i \(-0.765118\pi\)
−0.203149 + 0.979148i \(0.565118\pi\)
\(762\) 0 0
\(763\) −45.1849 + 23.0229i −1.63580 + 0.833484i
\(764\) 0 0
\(765\) −5.62145 45.6784i −0.203244 1.65150i
\(766\) 0 0
\(767\) 0.320933 + 2.02629i 0.0115882 + 0.0731652i
\(768\) 0 0
\(769\) −1.09156 + 1.50240i −0.0393625 + 0.0541779i −0.828245 0.560367i \(-0.810660\pi\)
0.788882 + 0.614545i \(0.210660\pi\)
\(770\) 0 0
\(771\) 24.0944 25.1873i 0.867738 0.907099i
\(772\) 0 0
\(773\) 13.8988 + 7.08181i 0.499906 + 0.254715i 0.685714 0.727871i \(-0.259490\pi\)
−0.185808 + 0.982586i \(0.559490\pi\)
\(774\) 0 0
\(775\) −30.3656 30.4187i −1.09077 1.09267i
\(776\) 0 0
\(777\) 4.44795 14.7981i 0.159569 0.530878i
\(778\) 0 0
\(779\) 7.48776 5.44018i 0.268277 0.194915i
\(780\) 0 0
\(781\) −11.0122 8.00087i −0.394049 0.286294i
\(782\) 0 0
\(783\) 13.9354 + 16.7190i 0.498010 + 0.597489i
\(784\) 0 0
\(785\) 6.84375 5.83994i 0.244264 0.208437i
\(786\) 0 0
\(787\) 20.3851 + 40.0079i 0.726649 + 1.42613i 0.897583 + 0.440846i \(0.145321\pi\)
−0.170934 + 0.985282i \(0.554679\pi\)
\(788\) 0 0
\(789\) 31.1724 16.7639i 1.10977 0.596810i
\(790\) 0 0
\(791\) −86.7312 28.1807i −3.08381 1.00199i
\(792\) 0 0
\(793\) 10.4817 + 10.4817i 0.372215 + 0.372215i
\(794\) 0 0
\(795\) 8.90351 + 1.93389i 0.315775 + 0.0685879i
\(796\) 0 0