Properties

Label 729.2.i.a.685.17
Level $729$
Weight $2$
Character 729.685
Analytic conductor $5.821$
Analytic rank $0$
Dimension $1404$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.i (of order \(81\), degree \(54\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(1404\)
Relative dimension: \(26\) over \(\Q(\zeta_{81})\)
Twist minimal: no (minimal twist has level 243)
Sato-Tate group: $\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label 685.17
Character \(\chi\) \(=\) 729.685
Dual form 729.2.i.a.613.17

$q$-expansion

\(f(q)\) \(=\) \(q+(1.04528 + 0.290973i) q^{2} +(-0.704391 - 0.425102i) q^{4} +(2.06977 - 0.0803163i) q^{5} +(-4.16283 - 0.651054i) q^{7} +(-2.10177 - 2.22774i) q^{8} +O(q^{10})\) \(q+(1.04528 + 0.290973i) q^{2} +(-0.704391 - 0.425102i) q^{4} +(2.06977 - 0.0803163i) q^{5} +(-4.16283 - 0.651054i) q^{7} +(-2.10177 - 2.22774i) q^{8} +(2.18685 + 0.518294i) q^{10} +(-0.767098 - 5.61615i) q^{11} +(-3.39021 + 4.94305i) q^{13} +(-4.16188 - 1.89181i) q^{14} +(-0.781868 - 1.48434i) q^{16} +(-1.18240 + 0.593821i) q^{17} +(-0.383327 - 6.58146i) q^{19} +(-1.49207 - 0.823287i) q^{20} +(0.832318 - 6.09365i) q^{22} +(0.756746 - 1.96002i) q^{23} +(-0.707484 + 0.0549900i) q^{25} +(-4.98201 + 4.18040i) q^{26} +(2.65549 + 2.22822i) q^{28} +(3.30770 + 2.36420i) q^{29} +(0.0367254 - 0.0420827i) q^{31} +(0.911413 + 4.20755i) q^{32} +(-1.40872 + 0.276663i) q^{34} +(-8.66837 - 1.01319i) q^{35} +(-2.13975 - 2.87418i) q^{37} +(1.51435 - 6.99101i) q^{38} +(-4.52909 - 4.44210i) q^{40} +(0.587714 - 2.28165i) q^{41} +(2.40574 + 2.18309i) q^{43} +(-1.84710 + 4.28206i) q^{44} +(1.36132 - 1.82858i) q^{46} +(-0.143743 - 0.164711i) q^{47} +(10.2395 + 3.28317i) q^{49} +(-0.755519 - 0.148379i) q^{50} +(4.48933 - 2.04065i) q^{52} +(1.06035 - 6.01354i) q^{53} +(-2.03878 - 11.5625i) q^{55} +(7.29891 + 10.6421i) q^{56} +(2.76955 + 3.43370i) q^{58} +(-0.683778 + 0.279354i) q^{59} +(11.3205 - 6.83197i) q^{61} +(0.0506333 - 0.0333020i) q^{62} +(-0.466700 + 8.01293i) q^{64} +(-6.61994 + 10.5032i) q^{65} +(-4.99078 + 3.56720i) q^{67} +(1.08530 + 0.0843564i) q^{68} +(-8.76606 - 3.58133i) q^{70} +(-3.11481 - 10.4042i) q^{71} +(-1.60703 + 0.380872i) q^{73} +(-1.40032 - 3.62693i) q^{74} +(-2.52778 + 4.79887i) q^{76} +(-0.463123 + 23.8785i) q^{77} +(-0.413794 + 0.405846i) q^{79} +(-1.73750 - 3.00944i) q^{80} +(1.27822 - 2.21395i) q^{82} +(0.994054 + 3.85915i) q^{83} +(-2.39959 + 1.32404i) q^{85} +(1.87945 + 2.98195i) q^{86} +(-10.8991 + 13.5127i) q^{88} +(2.78199 - 9.29248i) q^{89} +(17.3311 - 18.3698i) q^{91} +(-1.36625 + 1.05893i) q^{92} +(-0.102325 - 0.213994i) q^{94} +(-1.32200 - 13.5913i) q^{95} +(-6.85532 - 0.266018i) q^{97} +(9.74785 + 6.41126i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{81}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.04528 + 0.290973i 0.739124 + 0.205749i 0.617218 0.786792i \(-0.288260\pi\)
0.121906 + 0.992542i \(0.461099\pi\)
\(3\) 0 0
\(4\) −0.704391 0.425102i −0.352195 0.212551i
\(5\) 2.06977 0.0803163i 0.925627 0.0359186i 0.428448 0.903566i \(-0.359060\pi\)
0.497179 + 0.867648i \(0.334369\pi\)
\(6\) 0 0
\(7\) −4.16283 0.651054i −1.57340 0.246075i −0.693224 0.720722i \(-0.743810\pi\)
−0.880177 + 0.474646i \(0.842576\pi\)
\(8\) −2.10177 2.22774i −0.743087 0.787626i
\(9\) 0 0
\(10\) 2.18685 + 0.518294i 0.691544 + 0.163899i
\(11\) −0.767098 5.61615i −0.231289 1.69333i −0.630272 0.776374i \(-0.717057\pi\)
0.398983 0.916958i \(-0.369363\pi\)
\(12\) 0 0
\(13\) −3.39021 + 4.94305i −0.940275 + 1.37095i −0.0116516 + 0.999932i \(0.503709\pi\)
−0.928624 + 0.371023i \(0.879007\pi\)
\(14\) −4.16188 1.89181i −1.11231 0.505606i
\(15\) 0 0
\(16\) −0.781868 1.48434i −0.195467 0.371085i
\(17\) −1.18240 + 0.593821i −0.286773 + 0.144023i −0.586371 0.810043i \(-0.699444\pi\)
0.299598 + 0.954066i \(0.403148\pi\)
\(18\) 0 0
\(19\) −0.383327 6.58146i −0.0879412 1.50989i −0.697175 0.716901i \(-0.745560\pi\)
0.609234 0.792991i \(-0.291477\pi\)
\(20\) −1.49207 0.823287i −0.333636 0.184093i
\(21\) 0 0
\(22\) 0.832318 6.09365i 0.177451 1.29917i
\(23\) 0.756746 1.96002i 0.157792 0.408692i −0.831332 0.555777i \(-0.812421\pi\)
0.989124 + 0.147084i \(0.0469889\pi\)
\(24\) 0 0
\(25\) −0.707484 + 0.0549900i −0.141497 + 0.0109980i
\(26\) −4.98201 + 4.18040i −0.977053 + 0.819845i
\(27\) 0 0
\(28\) 2.65549 + 2.22822i 0.501841 + 0.421094i
\(29\) 3.30770 + 2.36420i 0.614224 + 0.439021i 0.845580 0.533848i \(-0.179255\pi\)
−0.231356 + 0.972869i \(0.574316\pi\)
\(30\) 0 0
\(31\) 0.0367254 0.0420827i 0.00659609 0.00755828i −0.750128 0.661292i \(-0.770008\pi\)
0.756724 + 0.653734i \(0.226798\pi\)
\(32\) 0.911413 + 4.20755i 0.161117 + 0.743797i
\(33\) 0 0
\(34\) −1.40872 + 0.276663i −0.241593 + 0.0474474i
\(35\) −8.66837 1.01319i −1.46522 0.171260i
\(36\) 0 0
\(37\) −2.13975 2.87418i −0.351772 0.472512i 0.590655 0.806924i \(-0.298870\pi\)
−0.942427 + 0.334413i \(0.891462\pi\)
\(38\) 1.51435 6.99101i 0.245660 1.13409i
\(39\) 0 0
\(40\) −4.52909 4.44210i −0.716112 0.702358i
\(41\) 0.587714 2.28165i 0.0917856 0.356333i −0.905966 0.423350i \(-0.860854\pi\)
0.997752 + 0.0670163i \(0.0213480\pi\)
\(42\) 0 0
\(43\) 2.40574 + 2.18309i 0.366872 + 0.332919i 0.834501 0.551006i \(-0.185756\pi\)
−0.467629 + 0.883925i \(0.654892\pi\)
\(44\) −1.84710 + 4.28206i −0.278461 + 0.645544i
\(45\) 0 0
\(46\) 1.36132 1.82858i 0.200716 0.269609i
\(47\) −0.143743 0.164711i −0.0209670 0.0240255i 0.742857 0.669451i \(-0.233470\pi\)
−0.763824 + 0.645425i \(0.776680\pi\)
\(48\) 0 0
\(49\) 10.2395 + 3.28317i 1.46279 + 0.469025i
\(50\) −0.755519 0.148379i −0.106847 0.0209840i
\(51\) 0 0
\(52\) 4.48933 2.04065i 0.622558 0.282987i
\(53\) 1.06035 6.01354i 0.145650 0.826024i −0.821193 0.570651i \(-0.806691\pi\)
0.966843 0.255372i \(-0.0821981\pi\)
\(54\) 0 0
\(55\) −2.03878 11.5625i −0.274909 1.55909i
\(56\) 7.29891 + 10.6421i 0.975358 + 1.42211i
\(57\) 0 0
\(58\) 2.76955 + 3.43370i 0.363660 + 0.450867i
\(59\) −0.683778 + 0.279354i −0.0890204 + 0.0363688i −0.422273 0.906469i \(-0.638768\pi\)
0.333252 + 0.942838i \(0.391854\pi\)
\(60\) 0 0
\(61\) 11.3205 6.83197i 1.44944 0.874745i 0.449616 0.893222i \(-0.351561\pi\)
0.999829 + 0.0184776i \(0.00588194\pi\)
\(62\) 0.0506333 0.0333020i 0.00643043 0.00422936i
\(63\) 0 0
\(64\) −0.466700 + 8.01293i −0.0583375 + 1.00162i
\(65\) −6.61994 + 10.5032i −0.821102 + 1.30277i
\(66\) 0 0
\(67\) −4.99078 + 3.56720i −0.609721 + 0.435802i −0.843982 0.536371i \(-0.819795\pi\)
0.234261 + 0.972174i \(0.424733\pi\)
\(68\) 1.08530 + 0.0843564i 0.131612 + 0.0102297i
\(69\) 0 0
\(70\) −8.76606 3.58133i −1.04774 0.428051i
\(71\) −3.11481 10.4042i −0.369660 1.23475i −0.917355 0.398071i \(-0.869680\pi\)
0.547695 0.836678i \(-0.315505\pi\)
\(72\) 0 0
\(73\) −1.60703 + 0.380872i −0.188088 + 0.0445777i −0.323580 0.946201i \(-0.604887\pi\)
0.135492 + 0.990778i \(0.456738\pi\)
\(74\) −1.40032 3.62693i −0.162784 0.421622i
\(75\) 0 0
\(76\) −2.52778 + 4.79887i −0.289956 + 0.550469i
\(77\) −0.463123 + 23.8785i −0.0527777 + 2.72121i
\(78\) 0 0
\(79\) −0.413794 + 0.405846i −0.0465555 + 0.0456613i −0.723123 0.690720i \(-0.757294\pi\)
0.676567 + 0.736381i \(0.263467\pi\)
\(80\) −1.73750 3.00944i −0.194258 0.336465i
\(81\) 0 0
\(82\) 1.27822 2.21395i 0.141156 0.244490i
\(83\) 0.994054 + 3.85915i 0.109112 + 0.423597i 0.999500 0.0316034i \(-0.0100614\pi\)
−0.890389 + 0.455201i \(0.849568\pi\)
\(84\) 0 0
\(85\) −2.39959 + 1.32404i −0.260272 + 0.143612i
\(86\) 1.87945 + 2.98195i 0.202666 + 0.321552i
\(87\) 0 0
\(88\) −10.8991 + 13.5127i −1.16185 + 1.44046i
\(89\) 2.78199 9.29248i 0.294890 0.985001i −0.674253 0.738501i \(-0.735534\pi\)
0.969143 0.246500i \(-0.0792806\pi\)
\(90\) 0 0
\(91\) 17.3311 18.3698i 1.81679 1.92568i
\(92\) −1.36625 + 1.05893i −0.142442 + 0.110401i
\(93\) 0 0
\(94\) −0.102325 0.213994i −0.0105540 0.0220718i
\(95\) −1.32200 13.5913i −0.135634 1.39444i
\(96\) 0 0
\(97\) −6.85532 0.266018i −0.696052 0.0270100i −0.311678 0.950188i \(-0.600891\pi\)
−0.384374 + 0.923178i \(0.625583\pi\)
\(98\) 9.74785 + 6.41126i 0.984681 + 0.647635i
\(99\) 0 0
\(100\) 0.521721 + 0.262018i 0.0521721 + 0.0262018i
\(101\) −0.0139667 0.720121i −0.00138974 0.0716547i −0.999865 0.0164485i \(-0.994764\pi\)
0.998475 0.0552062i \(-0.0175816\pi\)
\(102\) 0 0
\(103\) 9.02470 + 6.99467i 0.889231 + 0.689206i 0.951102 0.308878i \(-0.0999536\pi\)
−0.0618710 + 0.998084i \(0.519707\pi\)
\(104\) 18.1373 2.83662i 1.77851 0.278153i
\(105\) 0 0
\(106\) 2.85814 5.97730i 0.277607 0.580567i
\(107\) −5.54390 2.01781i −0.535949 0.195069i 0.0598438 0.998208i \(-0.480940\pi\)
−0.595793 + 0.803138i \(0.703162\pi\)
\(108\) 0 0
\(109\) 1.37106 0.499023i 0.131323 0.0477978i −0.275523 0.961295i \(-0.588851\pi\)
0.406846 + 0.913497i \(0.366629\pi\)
\(110\) 1.23328 12.6793i 0.117589 1.20892i
\(111\) 0 0
\(112\) 2.28839 + 6.68809i 0.216233 + 0.631965i
\(113\) −9.69927 + 8.80161i −0.912430 + 0.827986i −0.985558 0.169336i \(-0.945838\pi\)
0.0731282 + 0.997323i \(0.476702\pi\)
\(114\) 0 0
\(115\) 1.40886 4.11756i 0.131377 0.383965i
\(116\) −1.32489 3.07143i −0.123012 0.285175i
\(117\) 0 0
\(118\) −0.796024 + 0.0930419i −0.0732799 + 0.00856520i
\(119\) 5.30872 1.70217i 0.486649 0.156038i
\(120\) 0 0
\(121\) −20.3556 + 5.66637i −1.85051 + 0.515125i
\(122\) 13.8210 3.84735i 1.25130 0.348323i
\(123\) 0 0
\(124\) −0.0437585 + 0.0140306i −0.00392963 + 0.00125998i
\(125\) −11.7465 + 1.37297i −1.05064 + 0.122802i
\(126\) 0 0
\(127\) 7.70782 + 17.8687i 0.683958 + 1.58559i 0.805222 + 0.592973i \(0.202046\pi\)
−0.121264 + 0.992620i \(0.538695\pi\)
\(128\) −0.0319456 + 0.0933645i −0.00282362 + 0.00825234i
\(129\) 0 0
\(130\) −9.97585 + 9.05260i −0.874940 + 0.793965i
\(131\) −1.13479 3.31655i −0.0991470 0.289768i 0.885416 0.464800i \(-0.153874\pi\)
−0.984563 + 0.175032i \(0.943997\pi\)
\(132\) 0 0
\(133\) −2.68917 + 27.6471i −0.233180 + 2.39730i
\(134\) −6.25472 + 2.27653i −0.540325 + 0.196662i
\(135\) 0 0
\(136\) 3.80800 + 1.38600i 0.326533 + 0.118848i
\(137\) 10.0360 20.9886i 0.857437 1.79318i 0.328549 0.944487i \(-0.393440\pi\)
0.528888 0.848691i \(-0.322609\pi\)
\(138\) 0 0
\(139\) 19.9394 3.11847i 1.69124 0.264505i 0.765711 0.643185i \(-0.222387\pi\)
0.925528 + 0.378680i \(0.123622\pi\)
\(140\) 5.67521 + 4.39862i 0.479643 + 0.371751i
\(141\) 0 0
\(142\) −0.228504 11.7816i −0.0191756 0.988690i
\(143\) 30.3615 + 15.2481i 2.53896 + 1.27511i
\(144\) 0 0
\(145\) 7.03604 + 4.62768i 0.584312 + 0.384308i
\(146\) −1.79061 0.0694840i −0.148192 0.00575054i
\(147\) 0 0
\(148\) 0.285399 + 2.93415i 0.0234596 + 0.241186i
\(149\) 8.61731 + 18.0216i 0.705957 + 1.47638i 0.871610 + 0.490200i \(0.163076\pi\)
−0.165653 + 0.986184i \(0.552973\pi\)
\(150\) 0 0
\(151\) −1.59151 + 1.23351i −0.129515 + 0.100382i −0.675299 0.737544i \(-0.735985\pi\)
0.545783 + 0.837926i \(0.316232\pi\)
\(152\) −13.8561 + 14.6867i −1.12388 + 1.19125i
\(153\) 0 0
\(154\) −7.43209 + 24.8249i −0.598895 + 2.00045i
\(155\) 0.0726332 0.0900510i 0.00583404 0.00723307i
\(156\) 0 0
\(157\) −3.43534 5.45054i −0.274170 0.435000i 0.680464 0.732781i \(-0.261778\pi\)
−0.954634 + 0.297781i \(0.903753\pi\)
\(158\) −0.550621 + 0.303820i −0.0438050 + 0.0241706i
\(159\) 0 0
\(160\) 2.22435 + 8.63545i 0.175850 + 0.682692i
\(161\) −4.42628 + 7.66654i −0.348840 + 0.604208i
\(162\) 0 0
\(163\) −1.47948 2.56253i −0.115882 0.200713i 0.802250 0.596988i \(-0.203636\pi\)
−0.918132 + 0.396275i \(0.870303\pi\)
\(164\) −1.38391 + 1.35733i −0.108065 + 0.105990i
\(165\) 0 0
\(166\) −0.0838472 + 4.32314i −0.00650780 + 0.335541i
\(167\) 2.71931 5.16249i 0.210427 0.399485i −0.756707 0.653755i \(-0.773193\pi\)
0.967134 + 0.254269i \(0.0818349\pi\)
\(168\) 0 0
\(169\) −8.25789 21.3885i −0.635222 1.64527i
\(170\) −2.89350 + 0.685772i −0.221921 + 0.0525963i
\(171\) 0 0
\(172\) −0.766544 2.56044i −0.0584484 0.195231i
\(173\) 7.73215 + 3.15893i 0.587865 + 0.240169i 0.652561 0.757736i \(-0.273694\pi\)
−0.0646967 + 0.997905i \(0.520608\pi\)
\(174\) 0 0
\(175\) 2.98094 + 0.231697i 0.225338 + 0.0175146i
\(176\) −7.73650 + 5.52972i −0.583161 + 0.416818i
\(177\) 0 0
\(178\) 5.61182 8.90375i 0.420623 0.667364i
\(179\) −0.253842 + 4.35830i −0.0189730 + 0.325755i 0.975445 + 0.220243i \(0.0706850\pi\)
−0.994418 + 0.105512i \(0.966352\pi\)
\(180\) 0 0
\(181\) −11.1262 + 7.31784i −0.827006 + 0.543930i −0.890991 0.454020i \(-0.849989\pi\)
0.0639852 + 0.997951i \(0.479619\pi\)
\(182\) 23.4609 14.1587i 1.73904 1.04952i
\(183\) 0 0
\(184\) −5.95692 + 2.43367i −0.439150 + 0.179413i
\(185\) −4.65962 5.77702i −0.342582 0.424735i
\(186\) 0 0
\(187\) 4.24200 + 6.18499i 0.310206 + 0.452291i
\(188\) 0.0312321 + 0.177126i 0.00227783 + 0.0129182i
\(189\) 0 0
\(190\) 2.57285 14.5914i 0.186654 1.05857i
\(191\) −0.339837 + 0.154475i −0.0245898 + 0.0111774i −0.426068 0.904691i \(-0.640102\pi\)
0.401478 + 0.915869i \(0.368497\pi\)
\(192\) 0 0
\(193\) −19.8836 3.90502i −1.43125 0.281089i −0.583774 0.811916i \(-0.698425\pi\)
−0.847480 + 0.530827i \(0.821881\pi\)
\(194\) −7.08832 2.27278i −0.508911 0.163176i
\(195\) 0 0
\(196\) −5.81694 6.66548i −0.415496 0.476105i
\(197\) 7.82208 10.5069i 0.557300 0.748584i −0.430791 0.902452i \(-0.641766\pi\)
0.988091 + 0.153868i \(0.0491730\pi\)
\(198\) 0 0
\(199\) 4.41653 10.2387i 0.313080 0.725800i −0.686920 0.726733i \(-0.741038\pi\)
1.00000 0.000933098i \(0.000297014\pi\)
\(200\) 1.60947 + 1.46052i 0.113807 + 0.103274i
\(201\) 0 0
\(202\) 0.194937 0.756791i 0.0137157 0.0532476i
\(203\) −12.2302 11.9952i −0.858388 0.841901i
\(204\) 0 0
\(205\) 1.03318 4.76968i 0.0721603 0.333129i
\(206\) 7.39807 + 9.93734i 0.515448 + 0.692367i
\(207\) 0 0
\(208\) 9.98786 + 1.16741i 0.692533 + 0.0809455i
\(209\) −36.6684 + 7.20145i −2.53641 + 0.498134i
\(210\) 0 0
\(211\) −3.03033 13.9896i −0.208617 0.963082i −0.954779 0.297318i \(-0.903908\pi\)
0.746162 0.665765i \(-0.231895\pi\)
\(212\) −3.30327 + 3.78513i −0.226869 + 0.259964i
\(213\) 0 0
\(214\) −5.20779 3.72231i −0.355997 0.254452i
\(215\) 5.15466 + 4.32527i 0.351545 + 0.294981i
\(216\) 0 0
\(217\) −0.180280 + 0.151273i −0.0122382 + 0.0102691i
\(218\) 1.57834 0.122678i 0.106899 0.00830881i
\(219\) 0 0
\(220\) −3.47914 + 9.01121i −0.234564 + 0.607536i
\(221\) 1.07328 7.85782i 0.0721968 0.528574i
\(222\) 0 0
\(223\) −2.77245 1.52977i −0.185657 0.102441i 0.387561 0.921844i \(-0.373318\pi\)
−0.573218 + 0.819403i \(0.694305\pi\)
\(224\) −1.05471 18.1087i −0.0704708 1.20994i
\(225\) 0 0
\(226\) −12.6995 + 6.37792i −0.844757 + 0.424253i
\(227\) −9.57731 18.1821i −0.635668 1.20679i −0.964920 0.262544i \(-0.915439\pi\)
0.329252 0.944242i \(-0.393203\pi\)
\(228\) 0 0
\(229\) 20.5994 + 9.36356i 1.36124 + 0.618761i 0.955436 0.295197i \(-0.0953853\pi\)
0.405808 + 0.913958i \(0.366990\pi\)
\(230\) 2.67076 3.89406i 0.176105 0.256767i
\(231\) 0 0
\(232\) −1.68518 12.3377i −0.110637 0.810010i
\(233\) 0.992700 + 0.235274i 0.0650339 + 0.0154133i 0.263004 0.964795i \(-0.415287\pi\)
−0.197970 + 0.980208i \(0.563435\pi\)
\(234\) 0 0
\(235\) −0.310742 0.329368i −0.0202706 0.0214856i
\(236\) 0.600401 + 0.0939010i 0.0390828 + 0.00611243i
\(237\) 0 0
\(238\) 6.04438 0.234549i 0.391799 0.0152036i
\(239\) −5.61958 3.39143i −0.363501 0.219374i 0.323173 0.946340i \(-0.395251\pi\)
−0.686673 + 0.726966i \(0.740930\pi\)
\(240\) 0 0
\(241\) −12.4054 3.45327i −0.799101 0.222445i −0.155530 0.987831i \(-0.549708\pi\)
−0.643571 + 0.765386i \(0.722548\pi\)
\(242\) −22.9261 −1.47374
\(243\) 0 0
\(244\) −10.8784 −0.696415
\(245\) 21.4571 + 5.97300i 1.37084 + 0.381601i
\(246\) 0 0
\(247\) 33.8321 + 20.4177i 2.15268 + 1.29915i
\(248\) −0.170938 + 0.00663316i −0.0108546 + 0.000421206i
\(249\) 0 0
\(250\) −12.6779 1.98278i −0.801819 0.125402i
\(251\) −9.51765 10.0881i −0.600749 0.636757i 0.353619 0.935389i \(-0.384951\pi\)
−0.954368 + 0.298633i \(0.903469\pi\)
\(252\) 0 0
\(253\) −11.5883 2.74647i −0.728548 0.172669i
\(254\) 2.85750 + 20.9206i 0.179295 + 1.31267i
\(255\) 0 0
\(256\) 9.01914 13.1502i 0.563696 0.821889i
\(257\) 7.86924 + 3.57701i 0.490870 + 0.223128i 0.643923 0.765090i \(-0.277306\pi\)
−0.153053 + 0.988218i \(0.548911\pi\)
\(258\) 0 0
\(259\) 7.03615 + 13.3578i 0.437205 + 0.830013i
\(260\) 9.12797 4.58424i 0.566093 0.284302i
\(261\) 0 0
\(262\) −0.221145 3.79691i −0.0136624 0.234574i
\(263\) −18.7578 10.3501i −1.15665 0.638214i −0.215603 0.976481i \(-0.569172\pi\)
−0.941050 + 0.338267i \(0.890159\pi\)
\(264\) 0 0
\(265\) 1.71169 12.5318i 0.105148 0.769822i
\(266\) −10.8555 + 28.1164i −0.665593 + 1.72393i
\(267\) 0 0
\(268\) 5.03188 0.391109i 0.307371 0.0238908i
\(269\) 19.5545 16.4082i 1.19226 1.00042i 0.192442 0.981308i \(-0.438359\pi\)
0.999817 0.0191163i \(-0.00608526\pi\)
\(270\) 0 0
\(271\) −10.0479 8.43121i −0.610368 0.512160i 0.284391 0.958708i \(-0.408209\pi\)
−0.894759 + 0.446549i \(0.852653\pi\)
\(272\) 1.80591 + 1.29079i 0.109499 + 0.0782654i
\(273\) 0 0
\(274\) 16.5976 19.0187i 1.00270 1.14896i
\(275\) 0.851542 + 3.93115i 0.0513499 + 0.237057i
\(276\) 0 0
\(277\) −22.4112 + 4.40141i −1.34656 + 0.264455i −0.813471 0.581606i \(-0.802425\pi\)
−0.533086 + 0.846061i \(0.678968\pi\)
\(278\) 21.7496 + 2.54217i 1.30446 + 0.152469i
\(279\) 0 0
\(280\) 15.9618 + 21.4404i 0.953898 + 1.28131i
\(281\) −4.89552 + 22.6002i −0.292042 + 1.34822i 0.561623 + 0.827393i \(0.310177\pi\)
−0.853665 + 0.520823i \(0.825625\pi\)
\(282\) 0 0
\(283\) 3.92356 + 3.84820i 0.233231 + 0.228752i 0.807429 0.589965i \(-0.200859\pi\)
−0.574197 + 0.818717i \(0.694686\pi\)
\(284\) −2.22880 + 8.65272i −0.132255 + 0.513444i
\(285\) 0 0
\(286\) 27.2995 + 24.7729i 1.61425 + 1.46485i
\(287\) −3.93203 + 9.11547i −0.232100 + 0.538069i
\(288\) 0 0
\(289\) −9.10626 + 12.2318i −0.535662 + 0.719520i
\(290\) 6.00810 + 6.88452i 0.352808 + 0.404273i
\(291\) 0 0
\(292\) 1.29388 + 0.414867i 0.0757188 + 0.0242783i
\(293\) 7.07478 + 1.38944i 0.413313 + 0.0811720i 0.395047 0.918661i \(-0.370728\pi\)
0.0182666 + 0.999833i \(0.494185\pi\)
\(294\) 0 0
\(295\) −1.39282 + 0.633116i −0.0810934 + 0.0368615i
\(296\) −1.90568 + 10.8077i −0.110765 + 0.628182i
\(297\) 0 0
\(298\) 3.76370 + 21.3450i 0.218025 + 1.23648i
\(299\) 7.12295 + 10.3855i 0.411931 + 0.600610i
\(300\) 0 0
\(301\) −8.59337 10.6541i −0.495314 0.614093i
\(302\) −2.02249 + 0.826278i −0.116381 + 0.0475470i
\(303\) 0 0
\(304\) −9.46941 + 5.71482i −0.543108 + 0.327767i
\(305\) 22.8821 15.0498i 1.31023 0.861750i
\(306\) 0 0
\(307\) 0.144842 2.48685i 0.00826659 0.141932i −0.991649 0.128964i \(-0.958835\pi\)
0.999916 0.0129682i \(-0.00412803\pi\)
\(308\) 10.4770 16.6229i 0.596983 0.947178i
\(309\) 0 0
\(310\) 0.102124 0.0729941i 0.00580027 0.00414579i
\(311\) −21.2432 1.65115i −1.20459 0.0936282i −0.540542 0.841317i \(-0.681781\pi\)
−0.664049 + 0.747689i \(0.731163\pi\)
\(312\) 0 0
\(313\) 11.5247 + 4.70836i 0.651415 + 0.266132i 0.679725 0.733467i \(-0.262099\pi\)
−0.0283100 + 0.999599i \(0.509013\pi\)
\(314\) −2.00493 6.69693i −0.113145 0.377930i
\(315\) 0 0
\(316\) 0.463999 0.109970i 0.0261020 0.00618628i
\(317\) −7.79162 20.1808i −0.437621 1.13347i −0.959813 0.280639i \(-0.909454\pi\)
0.522193 0.852828i \(-0.325114\pi\)
\(318\) 0 0
\(319\) 10.7404 20.3901i 0.601345 1.14163i
\(320\) −0.322391 + 16.6224i −0.0180222 + 0.929219i
\(321\) 0 0
\(322\) −6.85746 + 6.72575i −0.382151 + 0.374811i
\(323\) 4.36146 + 7.55426i 0.242678 + 0.420331i
\(324\) 0 0
\(325\) 2.12670 3.68356i 0.117968 0.204327i
\(326\) −0.800839 3.10905i −0.0443544 0.172194i
\(327\) 0 0
\(328\) −6.31816 + 3.48621i −0.348862 + 0.192494i
\(329\) 0.491140 + 0.779247i 0.0270774 + 0.0429613i
\(330\) 0 0
\(331\) 21.5273 26.6897i 1.18325 1.46700i 0.331183 0.943566i \(-0.392552\pi\)
0.852067 0.523433i \(-0.175349\pi\)
\(332\) 0.940332 3.14093i 0.0516074 0.172381i
\(333\) 0 0
\(334\) 4.34459 4.60500i 0.237725 0.251974i
\(335\) −10.0432 + 7.78410i −0.548721 + 0.425291i
\(336\) 0 0
\(337\) −6.61256 13.8290i −0.360209 0.753313i 0.639673 0.768647i \(-0.279070\pi\)
−0.999882 + 0.0153334i \(0.995119\pi\)
\(338\) −2.40832 24.7597i −0.130996 1.34675i
\(339\) 0 0
\(340\) 2.25310 + 0.0874304i 0.122191 + 0.00474158i
\(341\) −0.264515 0.173974i −0.0143243 0.00942122i
\(342\) 0 0
\(343\) −14.1310 7.09687i −0.763004 0.383195i
\(344\) −0.192936 9.94773i −0.0104024 0.536345i
\(345\) 0 0
\(346\) 7.16310 + 5.55182i 0.385090 + 0.298468i
\(347\) 3.84583 0.601476i 0.206455 0.0322889i −0.0504457 0.998727i \(-0.516064\pi\)
0.256900 + 0.966438i \(0.417299\pi\)
\(348\) 0 0
\(349\) 8.63417 18.0568i 0.462176 0.966560i −0.530716 0.847549i \(-0.678077\pi\)
0.992893 0.119011i \(-0.0379723\pi\)
\(350\) 3.04849 + 1.10956i 0.162949 + 0.0593085i
\(351\) 0 0
\(352\) 22.9311 8.34623i 1.22223 0.444856i
\(353\) 1.45659 14.9750i 0.0775263 0.797040i −0.873273 0.487232i \(-0.838007\pi\)
0.950799 0.309809i \(-0.100265\pi\)
\(354\) 0 0
\(355\) −7.28255 21.2840i −0.386517 1.12964i
\(356\) −5.90985 + 5.36291i −0.313222 + 0.284233i
\(357\) 0 0
\(358\) −1.53348 + 4.48178i −0.0810472 + 0.236869i
\(359\) 5.07641 + 11.7684i 0.267922 + 0.621114i 0.998065 0.0621809i \(-0.0198056\pi\)
−0.730142 + 0.683295i \(0.760546\pi\)
\(360\) 0 0
\(361\) −24.2972 + 2.83994i −1.27880 + 0.149470i
\(362\) −13.7593 + 4.41175i −0.723173 + 0.231876i
\(363\) 0 0
\(364\) −20.0169 + 5.57208i −1.04917 + 0.292056i
\(365\) −3.29558 + 0.917387i −0.172498 + 0.0480182i
\(366\) 0 0
\(367\) 3.32897 1.06739i 0.173771 0.0557174i −0.217167 0.976134i \(-0.569682\pi\)
0.390938 + 0.920417i \(0.372151\pi\)
\(368\) −3.50101 + 0.409209i −0.182503 + 0.0213315i
\(369\) 0 0
\(370\) −3.18964 7.39442i −0.165822 0.384418i
\(371\) −8.32920 + 24.3430i −0.432430 + 1.26383i
\(372\) 0 0
\(373\) 17.4903 15.8716i 0.905614 0.821801i −0.0789405 0.996879i \(-0.525154\pi\)
0.984554 + 0.175078i \(0.0560179\pi\)
\(374\) 2.63441 + 7.69935i 0.136222 + 0.398124i
\(375\) 0 0
\(376\) −0.0648197 + 0.666405i −0.00334282 + 0.0343672i
\(377\) −22.9001 + 8.33497i −1.17942 + 0.429273i
\(378\) 0 0
\(379\) −7.89684 2.87422i −0.405634 0.147639i 0.131142 0.991364i \(-0.458136\pi\)
−0.536776 + 0.843725i \(0.680358\pi\)
\(380\) −4.84649 + 10.1356i −0.248620 + 0.519944i
\(381\) 0 0
\(382\) −0.400173 + 0.0625859i −0.0204746 + 0.00320217i
\(383\) −25.2875 19.5993i −1.29213 1.00148i −0.998968 0.0454146i \(-0.985539\pi\)
−0.293163 0.956063i \(-0.594708\pi\)
\(384\) 0 0
\(385\) 0.959277 + 49.4601i 0.0488893 + 2.52072i
\(386\) −19.6477 9.86744i −1.00004 0.502239i
\(387\) 0 0
\(388\) 4.71574 + 3.10159i 0.239405 + 0.157459i
\(389\) 1.16611 + 0.0452504i 0.0591241 + 0.00229428i 0.0683204 0.997663i \(-0.478236\pi\)
−0.00919635 + 0.999958i \(0.502927\pi\)
\(390\) 0 0
\(391\) 0.269129 + 2.76689i 0.0136104 + 0.139928i
\(392\) −14.2070 29.7115i −0.717564 1.50066i
\(393\) 0 0
\(394\) 11.2335 8.70660i 0.565934 0.438632i
\(395\) −0.823861 + 0.873241i −0.0414529 + 0.0439375i
\(396\) 0 0
\(397\) 3.72068 12.4279i 0.186736 0.623740i −0.812436 0.583050i \(-0.801859\pi\)
0.999172 0.0406903i \(-0.0129557\pi\)
\(398\) 7.59569 9.41717i 0.380737 0.472040i
\(399\) 0 0
\(400\) 0.634783 + 1.00715i 0.0317391 + 0.0503576i
\(401\) 29.1695 16.0950i 1.45666 0.803748i 0.460195 0.887818i \(-0.347779\pi\)
0.996460 + 0.0840692i \(0.0267917\pi\)
\(402\) 0 0
\(403\) 0.0835098 + 0.324205i 0.00415992 + 0.0161498i
\(404\) −0.296287 + 0.513183i −0.0147408 + 0.0255318i
\(405\) 0 0
\(406\) −9.29363 16.0970i −0.461235 0.798882i
\(407\) −14.5004 + 14.2219i −0.718759 + 0.704954i
\(408\) 0 0
\(409\) −0.477971 + 24.6441i −0.0236342 + 1.21857i 0.780897 + 0.624660i \(0.214763\pi\)
−0.804531 + 0.593911i \(0.797583\pi\)
\(410\) 2.46781 4.68502i 0.121876 0.231377i
\(411\) 0 0
\(412\) −3.38347 8.76340i −0.166691 0.431742i
\(413\) 3.02833 0.717726i 0.149014 0.0353170i
\(414\) 0 0
\(415\) 2.36741 + 7.90771i 0.116212 + 0.388174i
\(416\) −23.8880 9.75933i −1.17121 0.478490i
\(417\) 0 0
\(418\) −40.4242 3.14202i −1.97721 0.153681i
\(419\) 10.4789 7.48988i 0.511929 0.365905i −0.295997 0.955189i \(-0.595652\pi\)
0.807926 + 0.589284i \(0.200590\pi\)
\(420\) 0 0
\(421\) 10.3082 16.3551i 0.502390 0.797096i −0.495030 0.868876i \(-0.664843\pi\)
0.997421 + 0.0717793i \(0.0228677\pi\)
\(422\) 0.903050 15.5048i 0.0439598 0.754760i
\(423\) 0 0
\(424\) −15.6252 + 10.2769i −0.758829 + 0.499089i
\(425\) 0.803872 0.485139i 0.0389935 0.0235327i
\(426\) 0 0
\(427\) −51.5734 + 21.0700i −2.49581 + 1.01965i
\(428\) 3.04729 + 3.77805i 0.147296 + 0.182619i
\(429\) 0 0
\(430\) 4.12952 + 6.02099i 0.199143 + 0.290358i
\(431\) −1.76488 10.0091i −0.0850111 0.482122i −0.997354 0.0726954i \(-0.976840\pi\)
0.912343 0.409427i \(-0.134271\pi\)
\(432\) 0 0
\(433\) 2.65017 15.0299i 0.127359 0.722290i −0.852519 0.522696i \(-0.824926\pi\)
0.979879 0.199594i \(-0.0639624\pi\)
\(434\) −0.232459 + 0.105666i −0.0111584 + 0.00507211i
\(435\) 0 0
\(436\) −1.17789 0.231331i −0.0564109 0.0110787i
\(437\) −13.1899 4.22917i −0.630958 0.202308i
\(438\) 0 0
\(439\) 12.4563 + 14.2733i 0.594506 + 0.681228i 0.969300 0.245880i \(-0.0790769\pi\)
−0.374795 + 0.927108i \(0.622287\pi\)
\(440\) −21.4732 + 28.8436i −1.02370 + 1.37506i
\(441\) 0 0
\(442\) 3.40829 7.90132i 0.162116 0.375827i
\(443\) 17.9719 + 16.3086i 0.853870 + 0.774846i 0.976023 0.217665i \(-0.0698441\pi\)
−0.122153 + 0.992511i \(0.538980\pi\)
\(444\) 0 0
\(445\) 5.01172 19.4567i 0.237578 0.922336i
\(446\) −2.45286 2.40575i −0.116146 0.113915i
\(447\) 0 0
\(448\) 7.15964 33.0526i 0.338261 1.56159i
\(449\) 5.12488 + 6.88390i 0.241858 + 0.324871i 0.906433 0.422350i \(-0.138795\pi\)
−0.664575 + 0.747222i \(0.731387\pi\)
\(450\) 0 0
\(451\) −13.2649 1.55045i −0.624620 0.0730076i
\(452\) 10.5737 2.07660i 0.497343 0.0976749i
\(453\) 0 0
\(454\) −4.72046 21.7921i −0.221542 1.02275i
\(455\) 34.3958 39.4132i 1.61250 1.84772i
\(456\) 0 0
\(457\) 7.74455 + 5.53547i 0.362275 + 0.258938i 0.748033 0.663661i \(-0.230998\pi\)
−0.385758 + 0.922600i \(0.626060\pi\)
\(458\) 18.8075 + 15.7814i 0.878819 + 0.737416i
\(459\) 0 0
\(460\) −2.74277 + 2.30146i −0.127883 + 0.107306i
\(461\) −9.89019 + 0.768726i −0.460632 + 0.0358032i −0.305712 0.952124i \(-0.598895\pi\)
−0.154920 + 0.987927i \(0.549512\pi\)
\(462\) 0 0
\(463\) 2.55690 6.62255i 0.118829 0.307776i −0.860689 0.509131i \(-0.829967\pi\)
0.979518 + 0.201355i \(0.0645346\pi\)
\(464\) 0.923093 6.75824i 0.0428535 0.313743i
\(465\) 0 0
\(466\) 0.969190 + 0.534776i 0.0448969 + 0.0247730i
\(467\) −0.0967509 1.66115i −0.00447710 0.0768688i 0.995329 0.0965361i \(-0.0307763\pi\)
−0.999807 + 0.0196673i \(0.993739\pi\)
\(468\) 0 0
\(469\) 23.0982 11.6003i 1.06658 0.535654i
\(470\) −0.228975 0.434699i −0.0105618 0.0200512i
\(471\) 0 0
\(472\) 2.05947 + 0.936145i 0.0947949 + 0.0430896i
\(473\) 10.4151 15.1856i 0.478889 0.698237i
\(474\) 0 0
\(475\) 0.633112 + 4.63520i 0.0290492 + 0.212678i
\(476\) −4.46301 1.05775i −0.204562 0.0484820i
\(477\) 0 0
\(478\) −4.88721 5.18015i −0.223536 0.236934i
\(479\) −14.1069 2.20627i −0.644559 0.100807i −0.176212 0.984352i \(-0.556385\pi\)
−0.468346 + 0.883545i \(0.655150\pi\)
\(480\) 0 0
\(481\) 21.4614 0.832800i 0.978555 0.0379724i
\(482\) −11.9623 7.21927i −0.544867 0.328829i
\(483\) 0 0
\(484\) 16.7471 + 4.66187i 0.761231 + 0.211903i
\(485\) −14.2103 −0.645255
\(486\) 0 0
\(487\) −16.7491 −0.758976 −0.379488 0.925197i \(-0.623900\pi\)
−0.379488 + 0.925197i \(0.623900\pi\)
\(488\) −39.0130 10.8600i −1.76604 0.491609i
\(489\) 0 0
\(490\) 20.6907 + 12.4869i 0.934710 + 0.564100i
\(491\) −12.5492 + 0.486965i −0.566336 + 0.0219764i −0.320354 0.947298i \(-0.603802\pi\)
−0.245982 + 0.969274i \(0.579111\pi\)
\(492\) 0 0
\(493\) −5.31492 0.831238i −0.239372 0.0374371i
\(494\) 29.4229 + 31.1865i 1.32380 + 1.40315i
\(495\) 0 0
\(496\) −0.0911794 0.0216099i −0.00409408 0.000970314i
\(497\) 6.19272 + 45.3387i 0.277781 + 2.03372i
\(498\) 0 0
\(499\) −18.2355 + 26.5880i −0.816334 + 1.19024i 0.162726 + 0.986671i \(0.447971\pi\)
−0.979060 + 0.203572i \(0.934745\pi\)
\(500\) 8.85778 + 4.02635i 0.396132 + 0.180064i
\(501\) 0 0
\(502\) −7.01323 13.3143i −0.313016 0.594246i
\(503\) 36.7503 18.4567i 1.63861 0.822942i 0.640107 0.768285i \(-0.278890\pi\)
0.998505 0.0546568i \(-0.0174065\pi\)
\(504\) 0 0
\(505\) −0.0867453 1.48936i −0.00386012 0.0662756i
\(506\) −11.3138 6.24270i −0.502961 0.277522i
\(507\) 0 0
\(508\) 2.16672 15.8632i 0.0961325 0.703814i
\(509\) −5.36061 + 13.8843i −0.237605 + 0.615412i −0.999478 0.0323146i \(-0.989712\pi\)
0.761873 + 0.647727i \(0.224280\pi\)
\(510\) 0 0
\(511\) 6.93774 0.539244i 0.306908 0.0238547i
\(512\) 13.4051 11.2482i 0.592426 0.497104i
\(513\) 0 0
\(514\) 7.18474 + 6.02872i 0.316905 + 0.265915i
\(515\) 19.2408 + 13.7525i 0.847852 + 0.606008i
\(516\) 0 0
\(517\) −0.814775 + 0.933629i −0.0358338 + 0.0410610i
\(518\) 3.46798 + 16.0100i 0.152374 + 0.703437i
\(519\) 0 0
\(520\) 37.3121 7.32785i 1.63624 0.321348i
\(521\) −33.9224 3.96497i −1.48617 0.173708i −0.666053 0.745905i \(-0.732017\pi\)
−0.820117 + 0.572196i \(0.806092\pi\)
\(522\) 0 0
\(523\) 13.1600 + 17.6769i 0.575446 + 0.772958i 0.990600 0.136793i \(-0.0436796\pi\)
−0.415154 + 0.909751i \(0.636272\pi\)
\(524\) −0.610536 + 2.81855i −0.0266714 + 0.123129i
\(525\) 0 0
\(526\) −16.5955 16.2767i −0.723598 0.709700i
\(527\) −0.0184344 + 0.0715667i −0.000803015 + 0.00311750i
\(528\) 0 0
\(529\) 13.7635 + 12.4897i 0.598413 + 0.543031i
\(530\) 5.43561 12.6012i 0.236108 0.547360i
\(531\) 0 0
\(532\) 13.6470 18.3312i 0.591674 0.794757i
\(533\) 9.28582 + 10.6404i 0.402213 + 0.460885i
\(534\) 0 0
\(535\) −11.6366 3.73114i −0.503096 0.161311i
\(536\) 18.4363 + 3.62076i 0.796325 + 0.156393i
\(537\) 0 0
\(538\) 25.2143 11.4613i 1.08706 0.494131i
\(539\) 10.5841 60.0252i 0.455888 2.58547i
\(540\) 0 0
\(541\) 2.13348 + 12.0996i 0.0917254 + 0.520200i 0.995702 + 0.0926180i \(0.0295235\pi\)
−0.903976 + 0.427582i \(0.859365\pi\)
\(542\) −8.04963 11.7367i −0.345761 0.504132i
\(543\) 0 0
\(544\) −3.57618 4.43377i −0.153328 0.190096i
\(545\) 2.79768 1.14298i 0.119840 0.0489599i
\(546\) 0 0
\(547\) −25.8445 + 15.5972i −1.10503 + 0.666890i −0.947222 0.320580i \(-0.896122\pi\)
−0.157810 + 0.987470i \(0.550443\pi\)
\(548\) −15.9916 + 10.5178i −0.683127 + 0.449300i
\(549\) 0 0
\(550\) −0.253762 + 4.35693i −0.0108205 + 0.185780i
\(551\) 14.2920 22.6758i 0.608858 0.966020i
\(552\) 0 0
\(553\) 1.98678 1.42007i 0.0844865 0.0603873i
\(554\) −24.7066 1.92035i −1.04968 0.0815879i
\(555\) 0 0
\(556\) −15.3708 6.27966i −0.651867 0.266317i
\(557\) 11.1259 + 37.1631i 0.471420 + 1.57465i 0.781477 + 0.623934i \(0.214467\pi\)
−0.310057 + 0.950718i \(0.600348\pi\)
\(558\) 0 0
\(559\) −18.9471 + 4.49055i −0.801377 + 0.189930i
\(560\) 5.27360 + 13.6590i 0.222850 + 0.577197i
\(561\) 0 0
\(562\) −11.6932 + 22.1991i −0.493250 + 0.936411i
\(563\) −0.657827 + 33.9174i −0.0277241 + 1.42945i 0.685276 + 0.728283i \(0.259682\pi\)
−0.713000 + 0.701164i \(0.752664\pi\)
\(564\) 0 0
\(565\) −19.3683 + 18.9963i −0.814830 + 0.799180i
\(566\) 2.98149 + 5.16409i 0.125321 + 0.217063i
\(567\) 0 0
\(568\) −16.6312 + 28.8062i −0.697831 + 1.20868i
\(569\) 8.09955 + 31.4444i 0.339551 + 1.31822i 0.879251 + 0.476359i \(0.158044\pi\)
−0.539700 + 0.841857i \(0.681462\pi\)
\(570\) 0 0
\(571\) 3.13375 1.72913i 0.131143 0.0723617i −0.416184 0.909280i \(-0.636633\pi\)
0.547327 + 0.836919i \(0.315645\pi\)
\(572\) −14.9044 23.6474i −0.623183 0.988746i
\(573\) 0 0
\(574\) −6.76243 + 8.38410i −0.282258 + 0.349945i
\(575\) −0.427604 + 1.42830i −0.0178323 + 0.0595641i
\(576\) 0 0
\(577\) −13.8841 + 14.7163i −0.578002 + 0.612646i −0.948727 0.316096i \(-0.897628\pi\)
0.370725 + 0.928743i \(0.379109\pi\)
\(578\) −13.0777 + 10.1360i −0.543962 + 0.421602i
\(579\) 0 0
\(580\) −2.98889 6.25073i −0.124107 0.259547i
\(581\) −1.62556 16.7122i −0.0674394 0.693338i
\(582\) 0 0
\(583\) −34.5863 1.34211i −1.43242 0.0555844i
\(584\) 4.22608 + 2.77954i 0.174876 + 0.115018i
\(585\) 0 0
\(586\) 6.99083 + 3.51093i 0.288789 + 0.145035i
\(587\) −0.0773927 3.99035i −0.00319434 0.164699i −0.998012 0.0630241i \(-0.979925\pi\)
0.994818 0.101675i \(-0.0324202\pi\)
\(588\) 0 0
\(589\) −0.291044 0.225576i −0.0119922 0.00929469i
\(590\) −1.64011 + 0.256509i −0.0675223 + 0.0105603i
\(591\) 0 0
\(592\) −2.59326 + 5.42333i −0.106582 + 0.222898i
\(593\) 1.42711 + 0.519426i 0.0586044 + 0.0213303i 0.371156 0.928571i \(-0.378962\pi\)
−0.312552 + 0.949901i \(0.601184\pi\)
\(594\) 0 0
\(595\) 10.8511 3.94947i 0.444851 0.161913i
\(596\) 1.59105 16.3575i 0.0651721 0.670027i
\(597\) 0 0
\(598\) 4.42356 + 12.9283i 0.180893 + 0.528679i
\(599\) −21.9036 + 19.8764i −0.894955 + 0.812129i −0.982927 0.183994i \(-0.941097\pi\)
0.0879721 + 0.996123i \(0.471961\pi\)
\(600\) 0 0
\(601\) 3.63929 10.6362i 0.148450 0.433861i −0.846719 0.532041i \(-0.821425\pi\)
0.995169 + 0.0981794i \(0.0313019\pi\)
\(602\) −5.88241 13.6370i −0.239749 0.555801i
\(603\) 0 0
\(604\) 1.64541 0.192321i 0.0669509 0.00782543i
\(605\) −41.6762 + 13.3630i −1.69438 + 0.543281i
\(606\) 0 0
\(607\) 16.0875 4.47826i 0.652971 0.181767i 0.0741827 0.997245i \(-0.476365\pi\)
0.578788 + 0.815478i \(0.303526\pi\)
\(608\) 27.3425 7.61130i 1.10888 0.308679i
\(609\) 0 0
\(610\) 28.2973 9.07316i 1.14572 0.367362i
\(611\) 1.30149 0.152122i 0.0526527 0.00615422i
\(612\) 0 0
\(613\) 15.3124 + 35.4980i 0.618460 + 1.43375i 0.882998 + 0.469377i \(0.155522\pi\)
−0.264537 + 0.964375i \(0.585219\pi\)
\(614\) 0.875007 2.55731i 0.0353124 0.103204i
\(615\) 0 0
\(616\) 54.1685 49.1553i 2.18251 1.98052i
\(617\) −11.6928 34.1735i −0.470735 1.37577i −0.884989 0.465613i \(-0.845834\pi\)
0.414254 0.910161i \(-0.364043\pi\)
\(618\) 0 0
\(619\) −1.86745 + 19.1991i −0.0750593 + 0.771677i 0.879943 + 0.475079i \(0.157581\pi\)
−0.955002 + 0.296598i \(0.904148\pi\)
\(620\) −0.0894430 + 0.0325546i −0.00359212 + 0.00130742i
\(621\) 0 0
\(622\) −21.7246 7.90712i −0.871078 0.317047i
\(623\) −17.6308 + 36.8718i −0.706364 + 1.47724i
\(624\) 0 0
\(625\) −20.6968 + 3.23691i −0.827870 + 0.129477i
\(626\) 10.6765 + 8.27494i 0.426720 + 0.330733i
\(627\) 0 0
\(628\) 0.102787 + 5.29968i 0.00410165 + 0.211480i
\(629\) 4.23677 + 2.12779i 0.168931 + 0.0848404i
\(630\) 0 0
\(631\) 13.4371 + 8.83774i 0.534924 + 0.351825i 0.788053 0.615608i \(-0.211089\pi\)
−0.253129 + 0.967433i \(0.581460\pi\)
\(632\) 1.77382 + 0.0688323i 0.0705588 + 0.00273800i
\(633\) 0 0
\(634\) −2.27234 23.3617i −0.0902462 0.927813i
\(635\) 17.3885 + 36.3650i 0.690043 + 1.44310i
\(636\) 0 0
\(637\) −50.9430 + 39.4838i −2.01844 + 1.56441i
\(638\) 17.1597 18.1882i 0.679358 0.720077i
\(639\) 0 0
\(640\) −0.0586212 + 0.195808i −0.00231721 + 0.00774001i
\(641\) 10.0323 12.4382i 0.396254 0.491278i −0.540462 0.841369i \(-0.681750\pi\)
0.936716 + 0.350091i \(0.113849\pi\)
\(642\) 0 0
\(643\) −14.8800 23.6088i −0.586812 0.931040i −0.999794 0.0203010i \(-0.993538\pi\)
0.412982 0.910739i \(-0.364487\pi\)
\(644\) 6.37689 3.51862i 0.251285 0.138653i
\(645\) 0 0
\(646\) 2.36085 + 9.16538i 0.0928864 + 0.360607i
\(647\) 0.401769 0.695885i 0.0157952 0.0273581i −0.858020 0.513617i \(-0.828305\pi\)
0.873815 + 0.486259i \(0.161639\pi\)
\(648\) 0 0
\(649\) 2.09342 + 3.62591i 0.0821739 + 0.142329i
\(650\) 3.29481 3.23153i 0.129233 0.126751i
\(651\) 0 0
\(652\) −0.0472064 + 2.43395i −0.00184875 + 0.0953208i
\(653\) −6.20800 + 11.7856i −0.242938 + 0.461206i −0.975650 0.219332i \(-0.929612\pi\)
0.732712 + 0.680539i \(0.238254\pi\)
\(654\) 0 0
\(655\) −2.61512 6.77334i −0.102181 0.264656i
\(656\) −3.84625 + 0.911579i −0.150171 + 0.0355912i
\(657\) 0 0
\(658\) 0.286638 + 0.957439i 0.0111743 + 0.0373249i
\(659\) 21.5026 + 8.78478i 0.837623 + 0.342207i 0.756093 0.654464i \(-0.227106\pi\)
0.0815298 + 0.996671i \(0.474019\pi\)
\(660\) 0 0
\(661\) −8.29399 0.644660i −0.322599 0.0250744i −0.0848279 0.996396i \(-0.527034\pi\)
−0.237771 + 0.971321i \(0.576417\pi\)
\(662\) 30.2681 21.6343i 1.17640 0.840842i
\(663\) 0 0
\(664\) 6.50793 10.3255i 0.252557 0.400709i
\(665\) −3.34544 + 57.4389i −0.129730 + 2.22739i
\(666\) 0 0
\(667\) 7.13697 4.69406i 0.276344 0.181755i
\(668\) −4.11004 + 2.48042i −0.159022 + 0.0959705i
\(669\) 0 0
\(670\) −12.7630 + 5.21424i −0.493076 + 0.201444i
\(671\) −47.0533 58.3370i −1.81647 2.25207i
\(672\) 0 0
\(673\) 5.55884 + 8.10498i 0.214277 + 0.312424i 0.916884 0.399155i \(-0.130696\pi\)
−0.702606 + 0.711579i \(0.747980\pi\)
\(674\) −2.88810 16.3792i −0.111246 0.630905i
\(675\) 0 0
\(676\) −3.27550 + 18.5763i −0.125981 + 0.714472i
\(677\) 43.0634 19.5747i 1.65506 0.752318i 0.655067 0.755571i \(-0.272640\pi\)
0.999995 + 0.00325290i \(0.00103543\pi\)
\(678\) 0 0
\(679\) 28.3643 + 5.57057i 1.08852 + 0.213779i
\(680\) 7.99299 + 2.56285i 0.306517 + 0.0982808i
\(681\) 0 0
\(682\) −0.225870 0.258818i −0.00864901 0.00991066i
\(683\) 0.281656 0.378329i 0.0107773 0.0144764i −0.796702 0.604372i \(-0.793424\pi\)
0.807479 + 0.589896i \(0.200831\pi\)
\(684\) 0 0
\(685\) 19.0865 44.2476i 0.729259 1.69061i
\(686\) −12.7059 11.5300i −0.485113 0.440216i
\(687\) 0 0
\(688\) 1.35948 5.27783i 0.0518297 0.201215i
\(689\) 26.1304 + 25.6285i 0.995490 + 0.976370i
\(690\) 0 0
\(691\) 4.95733 22.8856i 0.188586 0.870608i −0.780745 0.624849i \(-0.785160\pi\)
0.969331 0.245759i \(-0.0790371\pi\)
\(692\) −4.10359 5.51208i −0.155995 0.209538i
\(693\) 0 0
\(694\) 4.19498 + 0.490322i 0.159239 + 0.0186124i
\(695\) 41.0194 8.05596i 1.55596 0.305580i
\(696\) 0 0
\(697\) 0.659980 + 3.04681i 0.0249985 + 0.115406i
\(698\) 14.2792 16.3621i 0.540475 0.619315i
\(699\) 0 0
\(700\) −2.00125 1.43041i −0.0756401 0.0540643i
\(701\) 23.2425 + 19.5028i 0.877859 + 0.736611i 0.965738 0.259520i \(-0.0835644\pi\)
−0.0878790 + 0.996131i \(0.528009\pi\)
\(702\) 0 0
\(703\) −18.0961 + 15.1844i −0.682506 + 0.572691i
\(704\) 45.3598 3.52564i 1.70956 0.132878i
\(705\) 0 0
\(706\) 5.87988 15.2293i 0.221292 0.573161i
\(707\) −0.410697 + 3.00683i −0.0154458 + 0.113084i
\(708\) 0 0
\(709\) 38.8710 + 21.4481i 1.45983 + 0.805501i 0.996730 0.0808040i \(-0.0257488\pi\)
0.463102 + 0.886305i \(0.346736\pi\)
\(710\) −1.41920 24.3668i −0.0532618 0.914470i
\(711\) 0 0
\(712\) −26.5483 + 13.3331i −0.994941 + 0.499678i
\(713\) −0.0546911 0.103829i −0.00204820 0.00388841i
\(714\) 0 0
\(715\) 64.0659 + 29.1215i 2.39593 + 1.08908i
\(716\) 2.03153 2.96204i 0.0759217 0.110696i
\(717\) 0 0
\(718\) 1.88196 + 13.7784i 0.0702342 + 0.514205i
\(719\) 20.0540 + 4.75288i 0.747887 + 0.177252i 0.586850 0.809696i \(-0.300368\pi\)
0.161037 + 0.986948i \(0.448516\pi\)
\(720\) 0 0
\(721\) −33.0144 34.9932i −1.22952 1.30321i
\(722\) −26.2237 4.10131i −0.975945 0.152635i
\(723\) 0 0
\(724\) 10.9480 0.424834i 0.406881 0.0157888i
\(725\) −2.47015 1.49074i −0.0917391 0.0553648i
\(726\) 0 0
\(727\) 26.5964 + 7.40362i 0.986407 + 0.274585i 0.723567 0.690254i \(-0.242501\pi\)
0.262840 + 0.964839i \(0.415341\pi\)
\(728\) −77.3491 −2.86675
\(729\) 0 0
\(730\) −3.71173 −0.137377
\(731\) −4.14090 1.15270i −0.153157 0.0426341i
\(732\) 0 0
\(733\) −35.2240 21.2578i −1.30103 0.785174i −0.314577 0.949232i \(-0.601863\pi\)
−0.986451 + 0.164058i \(0.947542\pi\)
\(734\) 3.79029 0.147080i 0.139902 0.00542884i
\(735\) 0 0
\(736\) 8.93659 + 1.39766i 0.329407 + 0.0515183i
\(737\) 23.8623 + 25.2926i 0.878980 + 0.931664i
\(738\) 0 0
\(739\) −12.0514 2.85623i −0.443318 0.105068i 0.00289380 0.999996i \(-0.499079\pi\)
−0.446211 + 0.894928i \(0.647227\pi\)
\(740\) 0.826369 + 6.05009i 0.0303779 + 0.222406i
\(741\) 0 0
\(742\) −15.7895 + 23.0217i −0.579651 + 0.845152i
\(743\) 0.790351 + 0.359258i 0.0289952 + 0.0131799i 0.428256 0.903658i \(-0.359128\pi\)
−0.399261 + 0.916837i \(0.630733\pi\)
\(744\) 0 0
\(745\) 19.2832 + 36.6083i 0.706483 + 1.34123i
\(746\) 22.9005 11.5011i 0.838446 0.421083i
\(747\) 0 0
\(748\) −0.358775 6.15993i −0.0131181 0.225229i
\(749\) 21.7646 + 12.0092i 0.795261 + 0.438806i
\(750\) 0 0
\(751\) −4.73604 + 34.6739i −0.172821 + 1.26527i 0.676124 + 0.736788i \(0.263658\pi\)
−0.848944 + 0.528482i \(0.822761\pi\)
\(752\) −0.132099 + 0.342145i −0.00481715 + 0.0124767i
\(753\) 0 0
\(754\) −26.3623 + 2.04904i −0.960059 + 0.0746217i
\(755\) −3.19498 + 2.68091i −0.116277 + 0.0975681i
\(756\) 0 0
\(757\) −12.3117 10.3308i −0.447477 0.375478i 0.391021 0.920382i \(-0.372122\pi\)
−0.838499 + 0.544904i \(0.816566\pi\)
\(758\) −7.41809 5.30213i −0.269437 0.192582i
\(759\) 0 0
\(760\) −27.4994 + 31.5108i −0.997508 + 1.14302i
\(761\) 2.69287 + 12.4317i 0.0976163 + 0.450647i 0.999813 + 0.0193228i \(0.00615102\pi\)
−0.902197 + 0.431324i \(0.858047\pi\)
\(762\) 0 0
\(763\) −6.03236 + 1.18472i −0.218386 + 0.0428896i
\(764\) 0.305046 + 0.0356548i 0.0110362 + 0.00128994i
\(765\) 0 0
\(766\) −20.7296 27.8447i −0.748992 1.00607i
\(767\) 0.937291 4.32702i 0.0338436 0.156240i
\(768\) 0 0
\(769\) 37.3292 + 36.6122i 1.34612 + 1.32027i 0.906571 + 0.422053i \(0.138690\pi\)
0.439553 + 0.898217i \(0.355137\pi\)
\(770\) −13.3888 + 51.9787i −0.482501 + 1.87318i
\(771\) 0 0
\(772\) 12.3458 + 11.2032i 0.444335 + 0.403213i
\(773\) −9.20251 + 21.3338i −0.330991 + 0.767324i 0.668725 + 0.743510i \(0.266840\pi\)
−0.999716 + 0.0238141i \(0.992419\pi\)
\(774\) 0 0
\(775\) −0.0236685 + 0.0317924i −0.000850199 + 0.00114202i
\(776\) 13.8157 + 15.8310i 0.495953 + 0.568299i
\(777\) 0 0
\(778\) 1.20574 + 0.386606i 0.0432280 + 0.0138605i
\(779\) −15.2419 2.99341i −0.546097 0.107250i
\(780\) 0 0
\(781\) −56.0421 + 25.4742i −2.00534 + 0.911540i
\(782\) −0.523776 + 2.97048i −0.0187302 + 0.106224i
\(783\) 0 0
\(784\) −3.13261 17.7659i −0.111879 0.634498i
\(785\) −7.54812 11.0054i −0.269404 0.392801i
\(786\) 0 0