Properties

Label 819.2.fm.e.370.4
Level $819$
Weight $2$
Character 819.370
Analytic conductor $6.540$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.fm (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 370.4
Character \(\chi\) \(=\) 819.370
Dual form 819.2.fm.e.622.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.0473445 - 0.176692i) q^{2} +(1.70307 - 0.983269i) q^{4} +(-2.80040 - 2.80040i) q^{5} +(-0.467560 - 2.60411i) q^{7} +(-0.513062 - 0.513062i) q^{8} +O(q^{10})\) \(q+(-0.0473445 - 0.176692i) q^{2} +(1.70307 - 0.983269i) q^{4} +(-2.80040 - 2.80040i) q^{5} +(-0.467560 - 2.60411i) q^{7} +(-0.513062 - 0.513062i) q^{8} +(-0.362225 + 0.627392i) q^{10} +(2.53602 - 0.679524i) q^{11} +(1.37067 + 3.33485i) q^{13} +(-0.437989 + 0.205904i) q^{14} +(1.90018 - 3.29120i) q^{16} +(1.43204 + 2.48037i) q^{17} +(0.759707 - 2.83527i) q^{19} +(-7.52284 - 2.01574i) q^{20} +(-0.240133 - 0.415922i) q^{22} +(-7.27090 - 4.19786i) q^{23} +10.6845i q^{25} +(0.524348 - 0.400074i) q^{26} +(-3.35683 - 3.97525i) q^{28} +(-1.66138 + 2.87760i) q^{29} +(-6.75045 - 6.75045i) q^{31} +(-2.07320 - 0.555513i) q^{32} +(0.370463 - 0.370463i) q^{34} +(-5.98320 + 8.60192i) q^{35} +(-6.77592 + 1.81560i) q^{37} -0.536937 q^{38} +2.87356i q^{40} +(2.79099 - 0.747843i) q^{41} +(-2.43132 + 1.40372i) q^{43} +(3.65087 - 3.65087i) q^{44} +(-0.397491 + 1.48346i) q^{46} +(4.85765 - 4.85765i) q^{47} +(-6.56278 + 2.43516i) q^{49} +(1.88787 - 0.505853i) q^{50} +(5.61342 + 4.33176i) q^{52} +5.43259 q^{53} +(-9.00481 - 5.19893i) q^{55} +(-1.09618 + 1.57596i) q^{56} +(0.587105 + 0.157314i) q^{58} +(0.00666592 + 0.00178613i) q^{59} +(5.65469 - 3.26474i) q^{61} +(-0.873154 + 1.51235i) q^{62} -7.20808i q^{64} +(5.50050 - 13.1774i) q^{65} +(2.10207 + 7.84504i) q^{67} +(4.87775 + 2.81617i) q^{68} +(1.80316 + 0.649930i) q^{70} +(14.5933 + 3.91026i) q^{71} +(0.321617 - 0.321617i) q^{73} +(0.641604 + 1.11129i) q^{74} +(-1.49399 - 5.57566i) q^{76} +(-2.95530 - 6.28635i) q^{77} +0.280448 q^{79} +(-14.5379 + 3.89543i) q^{80} +(-0.264276 - 0.457739i) q^{82} +(2.42973 + 2.42973i) q^{83} +(2.93575 - 10.9564i) q^{85} +(0.363136 + 0.363136i) q^{86} +(-1.64977 - 0.952496i) q^{88} +(-0.0536096 - 0.200074i) q^{89} +(8.04346 - 5.12863i) q^{91} -16.5105 q^{92} +(-1.08829 - 0.628324i) q^{94} +(-10.0674 + 5.81240i) q^{95} +(0.197356 - 0.736543i) q^{97} +(0.740984 + 1.04430i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 2q^{2} + 6q^{4} - 2q^{5} + 2q^{7} - 2q^{8} + O(q^{10}) \) \( 32q + 2q^{2} + 6q^{4} - 2q^{5} + 2q^{7} - 2q^{8} + 2q^{10} + 4q^{11} + 6q^{13} - 34q^{14} + 14q^{16} + 8q^{17} + 2q^{19} - 44q^{20} - 4q^{22} + 18q^{23} + 28q^{26} - 32q^{28} + 18q^{29} - 14q^{31} + 8q^{32} - 66q^{34} - 22q^{35} - 24q^{37} - 24q^{38} - 6q^{43} + 20q^{44} - 58q^{46} + 28q^{47} + 8q^{49} - 70q^{50} + 28q^{52} + 80q^{53} + 60q^{55} + 54q^{56} - 4q^{58} + 42q^{59} + 36q^{61} - 52q^{62} - 14q^{65} + 26q^{67} + 72q^{68} - 116q^{70} + 4q^{71} + 12q^{73} + 18q^{74} - 48q^{76} - 28q^{77} - 4q^{79} + 98q^{80} + 20q^{82} + 36q^{83} - 10q^{85} + 40q^{86} + 96q^{88} + 54q^{89} + 148q^{91} + 4q^{92} - 60q^{95} - 40q^{97} - 36q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{12}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0473445 0.176692i −0.0334776 0.124940i 0.947165 0.320747i \(-0.103934\pi\)
−0.980642 + 0.195807i \(0.937267\pi\)
\(3\) 0 0
\(4\) 1.70307 0.983269i 0.851536 0.491635i
\(5\) −2.80040 2.80040i −1.25238 1.25238i −0.954651 0.297728i \(-0.903771\pi\)
−0.297728 0.954651i \(-0.596229\pi\)
\(6\) 0 0
\(7\) −0.467560 2.60411i −0.176721 0.984261i
\(8\) −0.513062 0.513062i −0.181395 0.181395i
\(9\) 0 0
\(10\) −0.362225 + 0.627392i −0.114546 + 0.198399i
\(11\) 2.53602 0.679524i 0.764638 0.204884i 0.144637 0.989485i \(-0.453799\pi\)
0.620001 + 0.784601i \(0.287132\pi\)
\(12\) 0 0
\(13\) 1.37067 + 3.33485i 0.380156 + 0.924922i
\(14\) −0.437989 + 0.205904i −0.117057 + 0.0550302i
\(15\) 0 0
\(16\) 1.90018 3.29120i 0.475044 0.822800i
\(17\) 1.43204 + 2.48037i 0.347322 + 0.601579i 0.985773 0.168083i \(-0.0537578\pi\)
−0.638451 + 0.769663i \(0.720424\pi\)
\(18\) 0 0
\(19\) 0.759707 2.83527i 0.174289 0.650455i −0.822383 0.568934i \(-0.807356\pi\)
0.996672 0.0815202i \(-0.0259775\pi\)
\(20\) −7.52284 2.01574i −1.68216 0.450733i
\(21\) 0 0
\(22\) −0.240133 0.415922i −0.0511965 0.0886749i
\(23\) −7.27090 4.19786i −1.51609 0.875314i −0.999822 0.0188857i \(-0.993988\pi\)
−0.516266 0.856428i \(-0.672679\pi\)
\(24\) 0 0
\(25\) 10.6845i 2.13690i
\(26\) 0.524348 0.400074i 0.102833 0.0784609i
\(27\) 0 0
\(28\) −3.35683 3.97525i −0.634381 0.751252i
\(29\) −1.66138 + 2.87760i −0.308511 + 0.534356i −0.978037 0.208432i \(-0.933164\pi\)
0.669526 + 0.742789i \(0.266497\pi\)
\(30\) 0 0
\(31\) −6.75045 6.75045i −1.21242 1.21242i −0.970229 0.242188i \(-0.922135\pi\)
−0.242188 0.970229i \(-0.577865\pi\)
\(32\) −2.07320 0.555513i −0.366494 0.0982017i
\(33\) 0 0
\(34\) 0.370463 0.370463i 0.0635339 0.0635339i
\(35\) −5.98320 + 8.60192i −1.01135 + 1.45399i
\(36\) 0 0
\(37\) −6.77592 + 1.81560i −1.11395 + 0.298483i −0.768434 0.639929i \(-0.778964\pi\)
−0.345519 + 0.938412i \(0.612297\pi\)
\(38\) −0.536937 −0.0871026
\(39\) 0 0
\(40\) 2.87356i 0.454350i
\(41\) 2.79099 0.747843i 0.435879 0.116793i −0.0342056 0.999415i \(-0.510890\pi\)
0.470085 + 0.882621i \(0.344223\pi\)
\(42\) 0 0
\(43\) −2.43132 + 1.40372i −0.370773 + 0.214066i −0.673796 0.738917i \(-0.735337\pi\)
0.303023 + 0.952983i \(0.402004\pi\)
\(44\) 3.65087 3.65087i 0.550389 0.550389i
\(45\) 0 0
\(46\) −0.397491 + 1.48346i −0.0586068 + 0.218724i
\(47\) 4.85765 4.85765i 0.708561 0.708561i −0.257672 0.966232i \(-0.582955\pi\)
0.966232 + 0.257672i \(0.0829554\pi\)
\(48\) 0 0
\(49\) −6.56278 + 2.43516i −0.937539 + 0.347879i
\(50\) 1.88787 0.505853i 0.266985 0.0715384i
\(51\) 0 0
\(52\) 5.61342 + 4.33176i 0.778441 + 0.600707i
\(53\) 5.43259 0.746224 0.373112 0.927786i \(-0.378291\pi\)
0.373112 + 0.927786i \(0.378291\pi\)
\(54\) 0 0
\(55\) −9.00481 5.19893i −1.21421 0.701024i
\(56\) −1.09618 + 1.57596i −0.146483 + 0.210596i
\(57\) 0 0
\(58\) 0.587105 + 0.157314i 0.0770907 + 0.0206564i
\(59\) 0.00666592 + 0.00178613i 0.000867829 + 0.000232534i 0.259253 0.965809i \(-0.416524\pi\)
−0.258385 + 0.966042i \(0.583190\pi\)
\(60\) 0 0
\(61\) 5.65469 3.26474i 0.724009 0.418007i −0.0922177 0.995739i \(-0.529396\pi\)
0.816226 + 0.577732i \(0.196062\pi\)
\(62\) −0.873154 + 1.51235i −0.110891 + 0.192068i
\(63\) 0 0
\(64\) 7.20808i 0.901010i
\(65\) 5.50050 13.1774i 0.682253 1.63445i
\(66\) 0 0
\(67\) 2.10207 + 7.84504i 0.256809 + 0.958424i 0.967075 + 0.254491i \(0.0819079\pi\)
−0.710266 + 0.703933i \(0.751425\pi\)
\(68\) 4.87775 + 2.81617i 0.591514 + 0.341511i
\(69\) 0 0
\(70\) 1.80316 + 0.649930i 0.215519 + 0.0776815i
\(71\) 14.5933 + 3.91026i 1.73191 + 0.464063i 0.980621 0.195914i \(-0.0627675\pi\)
0.751286 + 0.659977i \(0.229434\pi\)
\(72\) 0 0
\(73\) 0.321617 0.321617i 0.0376425 0.0376425i −0.688035 0.725677i \(-0.741526\pi\)
0.725677 + 0.688035i \(0.241526\pi\)
\(74\) 0.641604 + 1.11129i 0.0745850 + 0.129185i
\(75\) 0 0
\(76\) −1.49399 5.57566i −0.171373 0.639572i
\(77\) −2.95530 6.28635i −0.336787 0.716396i
\(78\) 0 0
\(79\) 0.280448 0.0315529 0.0157764 0.999876i \(-0.494978\pi\)
0.0157764 + 0.999876i \(0.494978\pi\)
\(80\) −14.5379 + 3.89543i −1.62539 + 0.435522i
\(81\) 0 0
\(82\) −0.264276 0.457739i −0.0291844 0.0505488i
\(83\) 2.42973 + 2.42973i 0.266698 + 0.266698i 0.827768 0.561070i \(-0.189610\pi\)
−0.561070 + 0.827768i \(0.689610\pi\)
\(84\) 0 0
\(85\) 2.93575 10.9564i 0.318426 1.18838i
\(86\) 0.363136 + 0.363136i 0.0391580 + 0.0391580i
\(87\) 0 0
\(88\) −1.64977 0.952496i −0.175866 0.101536i
\(89\) −0.0536096 0.200074i −0.00568261 0.0212078i 0.963026 0.269407i \(-0.0868278\pi\)
−0.968709 + 0.248200i \(0.920161\pi\)
\(90\) 0 0
\(91\) 8.04346 5.12863i 0.843183 0.537626i
\(92\) −16.5105 −1.72134
\(93\) 0 0
\(94\) −1.08829 0.628324i −0.112249 0.0648067i
\(95\) −10.0674 + 5.81240i −1.03289 + 0.596340i
\(96\) 0 0
\(97\) 0.197356 0.736543i 0.0200385 0.0747847i −0.955183 0.296017i \(-0.904341\pi\)
0.975221 + 0.221233i \(0.0710080\pi\)
\(98\) 0.740984 + 1.04430i 0.0748506 + 0.105490i
\(99\) 0 0
\(100\) 10.5058 + 18.1965i 1.05058 + 1.81965i
\(101\) −0.682084 + 1.18140i −0.0678699 + 0.117554i −0.897963 0.440070i \(-0.854954\pi\)
0.830094 + 0.557624i \(0.188287\pi\)
\(102\) 0 0
\(103\) −4.43543 −0.437036 −0.218518 0.975833i \(-0.570122\pi\)
−0.218518 + 0.975833i \(0.570122\pi\)
\(104\) 1.00775 2.41423i 0.0988177 0.236734i
\(105\) 0 0
\(106\) −0.257203 0.959895i −0.0249818 0.0932333i
\(107\) 1.81150 3.13761i 0.175124 0.303324i −0.765080 0.643935i \(-0.777301\pi\)
0.940204 + 0.340611i \(0.110634\pi\)
\(108\) 0 0
\(109\) 11.1249 11.1249i 1.06557 1.06557i 0.0678792 0.997694i \(-0.478377\pi\)
0.997694 0.0678792i \(-0.0216232\pi\)
\(110\) −0.492281 + 1.83722i −0.0469372 + 0.175172i
\(111\) 0 0
\(112\) −9.45909 3.40943i −0.893800 0.322161i
\(113\) 2.74763 + 4.75903i 0.258475 + 0.447692i 0.965834 0.259163i \(-0.0834466\pi\)
−0.707358 + 0.706855i \(0.750113\pi\)
\(114\) 0 0
\(115\) 8.60577 + 32.1172i 0.802492 + 2.99494i
\(116\) 6.53434i 0.606698i
\(117\) 0 0
\(118\) 0.00126238i 0.000116211i
\(119\) 5.78960 4.88893i 0.530732 0.448167i
\(120\) 0 0
\(121\) −3.55665 + 2.05343i −0.323331 + 0.186675i
\(122\) −0.844571 0.844571i −0.0764638 0.0764638i
\(123\) 0 0
\(124\) −18.1340 4.85900i −1.62848 0.436351i
\(125\) 15.9190 15.9190i 1.42383 1.42383i
\(126\) 0 0
\(127\) 8.80555 + 5.08389i 0.781367 + 0.451122i 0.836914 0.547334i \(-0.184357\pi\)
−0.0555478 + 0.998456i \(0.517691\pi\)
\(128\) −5.42001 + 1.45229i −0.479066 + 0.128365i
\(129\) 0 0
\(130\) −2.58875 0.348018i −0.227049 0.0305232i
\(131\) 19.5230i 1.70573i −0.522129 0.852867i \(-0.674862\pi\)
0.522129 0.852867i \(-0.325138\pi\)
\(132\) 0 0
\(133\) −7.73855 0.652704i −0.671018 0.0565966i
\(134\) 1.28663 0.742838i 0.111148 0.0641715i
\(135\) 0 0
\(136\) 0.537858 2.00731i 0.0461209 0.172126i
\(137\) 3.09421 11.5477i 0.264356 0.986590i −0.698287 0.715818i \(-0.746054\pi\)
0.962643 0.270773i \(-0.0872791\pi\)
\(138\) 0 0
\(139\) 14.4291 8.33062i 1.22386 0.706594i 0.258119 0.966113i \(-0.416897\pi\)
0.965738 + 0.259519i \(0.0835640\pi\)
\(140\) −1.73183 + 20.5328i −0.146366 + 1.73534i
\(141\) 0 0
\(142\) 2.76365i 0.231920i
\(143\) 5.74217 + 7.52585i 0.480184 + 0.629343i
\(144\) 0 0
\(145\) 12.7110 3.40589i 1.05559 0.282844i
\(146\) −0.0720540 0.0416004i −0.00596323 0.00344287i
\(147\) 0 0
\(148\) −9.75465 + 9.75465i −0.801827 + 0.801827i
\(149\) −14.7603 3.95502i −1.20921 0.324008i −0.402761 0.915305i \(-0.631949\pi\)
−0.806454 + 0.591297i \(0.798616\pi\)
\(150\) 0 0
\(151\) −7.50367 7.50367i −0.610640 0.610640i 0.332473 0.943113i \(-0.392117\pi\)
−0.943113 + 0.332473i \(0.892117\pi\)
\(152\) −1.84444 + 1.06489i −0.149604 + 0.0863740i
\(153\) 0 0
\(154\) −0.970831 + 0.819801i −0.0782318 + 0.0660614i
\(155\) 37.8080i 3.03681i
\(156\) 0 0
\(157\) 13.4871i 1.07639i −0.842820 0.538195i \(-0.819106\pi\)
0.842820 0.538195i \(-0.180894\pi\)
\(158\) −0.0132777 0.0495530i −0.00105632 0.00394222i
\(159\) 0 0
\(160\) 4.25014 + 7.36146i 0.336003 + 0.581975i
\(161\) −7.53210 + 20.8970i −0.593612 + 1.64691i
\(162\) 0 0
\(163\) −1.07320 + 4.00525i −0.0840598 + 0.313716i −0.995134 0.0985258i \(-0.968587\pi\)
0.911075 + 0.412241i \(0.135254\pi\)
\(164\) 4.01792 4.01792i 0.313747 0.313747i
\(165\) 0 0
\(166\) 0.314280 0.544349i 0.0243928 0.0422496i
\(167\) −3.62497 13.5286i −0.280508 1.04687i −0.952059 0.305913i \(-0.901038\pi\)
0.671551 0.740958i \(-0.265628\pi\)
\(168\) 0 0
\(169\) −9.24251 + 9.14199i −0.710962 + 0.703230i
\(170\) −2.07489 −0.159137
\(171\) 0 0
\(172\) −2.76048 + 4.78129i −0.210484 + 0.364570i
\(173\) 7.63123 + 13.2177i 0.580192 + 1.00492i 0.995456 + 0.0952206i \(0.0303556\pi\)
−0.415265 + 0.909701i \(0.636311\pi\)
\(174\) 0 0
\(175\) 27.8237 4.99566i 2.10327 0.377636i
\(176\) 2.58243 9.63776i 0.194658 0.726473i
\(177\) 0 0
\(178\) −0.0328133 + 0.0189448i −0.00245946 + 0.00141997i
\(179\) −6.94881 4.01190i −0.519379 0.299863i 0.217302 0.976104i \(-0.430274\pi\)
−0.736680 + 0.676241i \(0.763608\pi\)
\(180\) 0 0
\(181\) 9.08130 0.675008 0.337504 0.941324i \(-0.390417\pi\)
0.337504 + 0.941324i \(0.390417\pi\)
\(182\) −1.28700 1.17840i −0.0953988 0.0873489i
\(183\) 0 0
\(184\) 1.57666 + 5.88418i 0.116233 + 0.433788i
\(185\) 24.0597 + 13.8909i 1.76891 + 1.02128i
\(186\) 0 0
\(187\) 5.31717 + 5.31717i 0.388830 + 0.388830i
\(188\) 3.49655 13.0493i 0.255012 0.951718i
\(189\) 0 0
\(190\) 1.50364 + 1.50364i 0.109085 + 0.109085i
\(191\) 10.2571 + 17.7658i 0.742179 + 1.28549i 0.951501 + 0.307645i \(0.0995408\pi\)
−0.209323 + 0.977847i \(0.567126\pi\)
\(192\) 0 0
\(193\) 14.0081 3.75346i 1.00832 0.270180i 0.283396 0.959003i \(-0.408539\pi\)
0.724929 + 0.688823i \(0.241872\pi\)
\(194\) −0.139485 −0.0100144
\(195\) 0 0
\(196\) −8.78247 + 10.6002i −0.627319 + 0.757159i
\(197\) −4.65346 17.3669i −0.331545 1.23734i −0.907567 0.419908i \(-0.862062\pi\)
0.576022 0.817434i \(-0.304604\pi\)
\(198\) 0 0
\(199\) 1.63893 + 2.83871i 0.116181 + 0.201231i 0.918251 0.395999i \(-0.129601\pi\)
−0.802070 + 0.597230i \(0.796268\pi\)
\(200\) 5.48182 5.48182i 0.387623 0.387623i
\(201\) 0 0
\(202\) 0.241037 + 0.0645858i 0.0169593 + 0.00454424i
\(203\) 8.27037 + 2.98097i 0.580466 + 0.209223i
\(204\) 0 0
\(205\) −9.91015 5.72163i −0.692155 0.399616i
\(206\) 0.209993 + 0.783706i 0.0146309 + 0.0546034i
\(207\) 0 0
\(208\) 13.5802 + 1.82565i 0.941617 + 0.126586i
\(209\) 7.70652i 0.533071i
\(210\) 0 0
\(211\) 12.5254 21.6946i 0.862283 1.49352i −0.00743594 0.999972i \(-0.502367\pi\)
0.869719 0.493546i \(-0.164300\pi\)
\(212\) 9.25209 5.34170i 0.635436 0.366869i
\(213\) 0 0
\(214\) −0.640155 0.171529i −0.0437601 0.0117255i
\(215\) 10.7397 + 2.87769i 0.732440 + 0.196257i
\(216\) 0 0
\(217\) −14.4227 + 20.7352i −0.979075 + 1.40759i
\(218\) −2.49238 1.43898i −0.168806 0.0974599i
\(219\) 0 0
\(220\) −20.4478 −1.37859
\(221\) −6.30882 + 8.17544i −0.424377 + 0.549940i
\(222\) 0 0
\(223\) 9.63125 2.58069i 0.644956 0.172816i 0.0785089 0.996913i \(-0.474984\pi\)
0.566447 + 0.824098i \(0.308317\pi\)
\(224\) −0.477270 + 5.65858i −0.0318889 + 0.378080i
\(225\) 0 0
\(226\) 0.710798 0.710798i 0.0472816 0.0472816i
\(227\) −4.05289 + 15.1256i −0.269000 + 1.00392i 0.690757 + 0.723087i \(0.257278\pi\)
−0.959757 + 0.280833i \(0.909389\pi\)
\(228\) 0 0
\(229\) −1.59130 + 1.59130i −0.105156 + 0.105156i −0.757727 0.652571i \(-0.773690\pi\)
0.652571 + 0.757727i \(0.273690\pi\)
\(230\) 5.26741 3.04114i 0.347323 0.200527i
\(231\) 0 0
\(232\) 2.32878 0.623994i 0.152892 0.0409672i
\(233\) 8.49682i 0.556645i 0.960488 + 0.278323i \(0.0897784\pi\)
−0.960488 + 0.278323i \(0.910222\pi\)
\(234\) 0 0
\(235\) −27.2067 −1.77477
\(236\) 0.0131088 0.00351249i 0.000853310 0.000228644i
\(237\) 0 0
\(238\) −1.13794 0.791512i −0.0737617 0.0513061i
\(239\) 6.87958 6.87958i 0.445003 0.445003i −0.448686 0.893689i \(-0.648108\pi\)
0.893689 + 0.448686i \(0.148108\pi\)
\(240\) 0 0
\(241\) 19.8128 + 5.30883i 1.27626 + 0.341972i 0.832424 0.554139i \(-0.186952\pi\)
0.443831 + 0.896110i \(0.353619\pi\)
\(242\) 0.531212 + 0.531212i 0.0341476 + 0.0341476i
\(243\) 0 0
\(244\) 6.42023 11.1202i 0.411013 0.711895i
\(245\) 25.1978 + 11.5590i 1.60983 + 0.738477i
\(246\) 0 0
\(247\) 10.4965 1.35271i 0.667877 0.0860709i
\(248\) 6.92680i 0.439852i
\(249\) 0 0
\(250\) −3.56642 2.05908i −0.225561 0.130227i
\(251\) −4.35546 7.54388i −0.274914 0.476165i 0.695199 0.718817i \(-0.255316\pi\)
−0.970113 + 0.242652i \(0.921983\pi\)
\(252\) 0 0
\(253\) −21.2917 5.70509i −1.33860 0.358676i
\(254\) 0.481388 1.79656i 0.0302050 0.112726i
\(255\) 0 0
\(256\) −6.69487 11.5958i −0.418429 0.724741i
\(257\) −6.96099 + 12.0568i −0.434215 + 0.752082i −0.997231 0.0743637i \(-0.976307\pi\)
0.563016 + 0.826446i \(0.309641\pi\)
\(258\) 0 0
\(259\) 7.89617 + 16.7963i 0.490644 + 1.04367i
\(260\) −3.58916 27.8505i −0.222590 1.72721i
\(261\) 0 0
\(262\) −3.44956 + 0.924307i −0.213114 + 0.0571039i
\(263\) 5.34924 9.26516i 0.329848 0.571314i −0.652633 0.757674i \(-0.726336\pi\)
0.982482 + 0.186360i \(0.0596690\pi\)
\(264\) 0 0
\(265\) −15.2134 15.2134i −0.934555 0.934555i
\(266\) 0.251050 + 1.39824i 0.0153929 + 0.0857317i
\(267\) 0 0
\(268\) 11.2938 + 11.2938i 0.689877 + 0.689877i
\(269\) −7.98188 + 4.60834i −0.486664 + 0.280976i −0.723189 0.690650i \(-0.757325\pi\)
0.236526 + 0.971625i \(0.423991\pi\)
\(270\) 0 0
\(271\) −0.262832 0.980903i −0.0159659 0.0595856i 0.957483 0.288489i \(-0.0931528\pi\)
−0.973449 + 0.228903i \(0.926486\pi\)
\(272\) 10.8845 0.659972
\(273\) 0 0
\(274\) −2.18689 −0.132115
\(275\) 7.26039 + 27.0961i 0.437818 + 1.63396i
\(276\) 0 0
\(277\) 0.795438 0.459247i 0.0477933 0.0275935i −0.475913 0.879492i \(-0.657882\pi\)
0.523706 + 0.851899i \(0.324549\pi\)
\(278\) −2.15509 2.15509i −0.129254 0.129254i
\(279\) 0 0
\(280\) 7.48307 1.34356i 0.447199 0.0802932i
\(281\) −3.41893 3.41893i −0.203956 0.203956i 0.597737 0.801693i \(-0.296067\pi\)
−0.801693 + 0.597737i \(0.796067\pi\)
\(282\) 0 0
\(283\) 7.94500 13.7611i 0.472281 0.818015i −0.527216 0.849731i \(-0.676764\pi\)
0.999497 + 0.0317167i \(0.0100974\pi\)
\(284\) 28.6983 7.68968i 1.70293 0.456299i
\(285\) 0 0
\(286\) 1.05790 1.37090i 0.0625547 0.0810631i
\(287\) −3.25242 6.91838i −0.191984 0.408379i
\(288\) 0 0
\(289\) 4.39849 7.61842i 0.258735 0.448142i
\(290\) −1.20359 2.08468i −0.0706771 0.122416i
\(291\) 0 0
\(292\) 0.231501 0.863974i 0.0135476 0.0505603i
\(293\) 14.2807 + 3.82651i 0.834288 + 0.223547i 0.650584 0.759435i \(-0.274524\pi\)
0.183705 + 0.982981i \(0.441191\pi\)
\(294\) 0 0
\(295\) −0.0136654 0.0236692i −0.000795630 0.00137807i
\(296\) 4.40798 + 2.54495i 0.256209 + 0.147922i
\(297\) 0 0
\(298\) 2.79528i 0.161926i
\(299\) 4.03321 30.0013i 0.233247 1.73502i
\(300\) 0 0
\(301\) 4.79224 + 5.67510i 0.276220 + 0.327107i
\(302\) −0.970581 + 1.68110i −0.0558506 + 0.0967362i
\(303\) 0 0
\(304\) −7.88785 7.88785i −0.452399 0.452399i
\(305\) −24.9780 6.69283i −1.43024 0.383230i
\(306\) 0 0
\(307\) −11.9699 + 11.9699i −0.683157 + 0.683157i −0.960710 0.277553i \(-0.910477\pi\)
0.277553 + 0.960710i \(0.410477\pi\)
\(308\) −11.2143 7.80026i −0.638992 0.444461i
\(309\) 0 0
\(310\) 6.68037 1.79000i 0.379419 0.101665i
\(311\) −22.3022 −1.26464 −0.632322 0.774706i \(-0.717898\pi\)
−0.632322 + 0.774706i \(0.717898\pi\)
\(312\) 0 0
\(313\) 21.7630i 1.23012i 0.788481 + 0.615059i \(0.210868\pi\)
−0.788481 + 0.615059i \(0.789132\pi\)
\(314\) −2.38307 + 0.638541i −0.134484 + 0.0360349i
\(315\) 0 0
\(316\) 0.477624 0.275756i 0.0268684 0.0155125i
\(317\) −3.88719 + 3.88719i −0.218327 + 0.218327i −0.807793 0.589466i \(-0.799338\pi\)
0.589466 + 0.807793i \(0.299338\pi\)
\(318\) 0 0
\(319\) −2.25790 + 8.42659i −0.126418 + 0.471798i
\(320\) −20.1855 + 20.1855i −1.12841 + 1.12841i
\(321\) 0 0
\(322\) 4.04893 + 0.341505i 0.225638 + 0.0190313i
\(323\) 8.12046 2.17587i 0.451834 0.121069i
\(324\) 0 0
\(325\) −35.6313 + 14.6450i −1.97647 + 0.812358i
\(326\) 0.758506 0.0420098
\(327\) 0 0
\(328\) −1.81564 1.04826i −0.100252 0.0578804i
\(329\) −14.9211 10.3786i −0.822626 0.572191i
\(330\) 0 0
\(331\) −17.6440 4.72770i −0.969802 0.259858i −0.261058 0.965323i \(-0.584071\pi\)
−0.708744 + 0.705466i \(0.750738\pi\)
\(332\) 6.52709 + 1.74893i 0.358221 + 0.0959849i
\(333\) 0 0
\(334\) −2.21877 + 1.28101i −0.121406 + 0.0700935i
\(335\) 16.0826 27.8559i 0.878688 1.52193i
\(336\) 0 0
\(337\) 12.4905i 0.680402i 0.940353 + 0.340201i \(0.110495\pi\)
−0.940353 + 0.340201i \(0.889505\pi\)
\(338\) 2.05290 + 1.20025i 0.111663 + 0.0652852i
\(339\) 0 0
\(340\) −5.77326 21.5461i −0.313099 1.16850i
\(341\) −21.7064 12.5322i −1.17547 0.678655i
\(342\) 0 0
\(343\) 9.40990 + 15.9516i 0.508087 + 0.861306i
\(344\) 1.96762 + 0.527221i 0.106087 + 0.0284258i
\(345\) 0 0
\(346\) 1.97416 1.97416i 0.106132 0.106132i
\(347\) 2.70509 + 4.68534i 0.145217 + 0.251522i 0.929454 0.368939i \(-0.120279\pi\)
−0.784237 + 0.620461i \(0.786945\pi\)
\(348\) 0 0
\(349\) −1.60376 5.98531i −0.0858472 0.320386i 0.909626 0.415428i \(-0.136368\pi\)
−0.995473 + 0.0950418i \(0.969702\pi\)
\(350\) −2.19999 4.67970i −0.117594 0.250141i
\(351\) 0 0
\(352\) −5.63516 −0.300355
\(353\) −34.1022 + 9.13766i −1.81508 + 0.486348i −0.996159 0.0875628i \(-0.972092\pi\)
−0.818918 + 0.573911i \(0.805425\pi\)
\(354\) 0 0
\(355\) −29.9168 51.8175i −1.58782 2.75019i
\(356\) −0.288028 0.288028i −0.0152654 0.0152654i
\(357\) 0 0
\(358\) −0.379882 + 1.41774i −0.0200774 + 0.0749299i
\(359\) −7.81387 7.81387i −0.412400 0.412400i 0.470174 0.882574i \(-0.344191\pi\)
−0.882574 + 0.470174i \(0.844191\pi\)
\(360\) 0 0
\(361\) 8.99290 + 5.19206i 0.473311 + 0.273266i
\(362\) −0.429949 1.60459i −0.0225976 0.0843355i
\(363\) 0 0
\(364\) 8.65576 16.6433i 0.453685 0.872346i
\(365\) −1.80132 −0.0942852
\(366\) 0 0
\(367\) 19.4308 + 11.2184i 1.01428 + 0.585593i 0.912441 0.409208i \(-0.134195\pi\)
0.101836 + 0.994801i \(0.467528\pi\)
\(368\) −27.6320 + 15.9533i −1.44042 + 0.831625i
\(369\) 0 0
\(370\) 1.31531 4.90882i 0.0683799 0.255197i
\(371\) −2.54006 14.1471i −0.131873 0.734479i
\(372\) 0 0
\(373\) −3.45623 5.98637i −0.178957 0.309962i 0.762567 0.646910i \(-0.223939\pi\)
−0.941523 + 0.336947i \(0.890606\pi\)
\(374\) 0.687762 1.19124i 0.0355633 0.0615975i
\(375\) 0 0
\(376\) −4.98455 −0.257058
\(377\) −11.8736 1.59622i −0.611520 0.0822095i
\(378\) 0 0
\(379\) 2.16569 + 8.08246i 0.111244 + 0.415168i 0.998979 0.0451875i \(-0.0143885\pi\)
−0.887735 + 0.460356i \(0.847722\pi\)
\(380\) −11.4303 + 19.7979i −0.586363 + 1.01561i
\(381\) 0 0
\(382\) 2.65346 2.65346i 0.135763 0.135763i
\(383\) 0.572661 2.13720i 0.0292616 0.109206i −0.949750 0.313008i \(-0.898663\pi\)
0.979012 + 0.203802i \(0.0653300\pi\)
\(384\) 0 0
\(385\) −9.32830 + 25.8803i −0.475414 + 1.31898i
\(386\) −1.32641 2.29741i −0.0675126 0.116935i
\(387\) 0 0
\(388\) −0.388109 1.44844i −0.0197032 0.0735334i
\(389\) 24.7852i 1.25666i −0.777946 0.628331i \(-0.783738\pi\)
0.777946 0.628331i \(-0.216262\pi\)
\(390\) 0 0
\(391\) 24.0461i 1.21606i
\(392\) 4.61649 + 2.11772i 0.233168 + 0.106961i
\(393\) 0 0
\(394\) −2.84828 + 1.64446i −0.143494 + 0.0828465i
\(395\) −0.785368 0.785368i −0.0395162 0.0395162i
\(396\) 0 0
\(397\) 11.9456 + 3.20082i 0.599534 + 0.160645i 0.545807 0.837911i \(-0.316223\pi\)
0.0537271 + 0.998556i \(0.482890\pi\)
\(398\) 0.423983 0.423983i 0.0212524 0.0212524i
\(399\) 0 0
\(400\) 35.1649 + 20.3025i 1.75824 + 1.01512i
\(401\) 27.4395 7.35239i 1.37026 0.367161i 0.502688 0.864468i \(-0.332344\pi\)
0.867575 + 0.497307i \(0.165678\pi\)
\(402\) 0 0
\(403\) 13.2591 31.7644i 0.660484 1.58230i
\(404\) 2.68269i 0.133469i
\(405\) 0 0
\(406\) 0.135157 1.60244i 0.00670773 0.0795278i
\(407\) −15.9501 + 9.20880i −0.790617 + 0.456463i
\(408\) 0 0
\(409\) −8.06083 + 30.0834i −0.398583 + 1.48753i 0.417009 + 0.908902i \(0.363078\pi\)
−0.815592 + 0.578628i \(0.803588\pi\)
\(410\) −0.541775 + 2.02193i −0.0267564 + 0.0998561i
\(411\) 0 0
\(412\) −7.55386 + 4.36123i −0.372152 + 0.214862i
\(413\) 0.00153456 0.0181939i 7.55105e−5 0.000895264i
\(414\) 0 0
\(415\) 13.6085i 0.668013i
\(416\) −0.989128 7.67525i −0.0484960 0.376310i
\(417\) 0 0
\(418\) −1.36168 + 0.364861i −0.0666020 + 0.0178460i
\(419\) 15.4180 + 8.90159i 0.753219 + 0.434871i 0.826856 0.562414i \(-0.190127\pi\)
−0.0736368 + 0.997285i \(0.523461\pi\)
\(420\) 0 0
\(421\) −7.27536 + 7.27536i −0.354579 + 0.354579i −0.861810 0.507231i \(-0.830669\pi\)
0.507231 + 0.861810i \(0.330669\pi\)
\(422\) −4.42627 1.18602i −0.215468 0.0577344i
\(423\) 0 0
\(424\) −2.78725 2.78725i −0.135361 0.135361i
\(425\) −26.5016 + 15.3007i −1.28552 + 0.742194i
\(426\) 0 0
\(427\) −11.1456 13.1990i −0.539375 0.638743i
\(428\) 7.12477i 0.344389i
\(429\) 0 0
\(430\) 2.03386i 0.0980813i
\(431\) 5.92484 + 22.1118i 0.285389 + 1.06509i 0.948554 + 0.316615i \(0.102546\pi\)
−0.663165 + 0.748473i \(0.730787\pi\)
\(432\) 0 0
\(433\) 3.70820 + 6.42278i 0.178205 + 0.308659i 0.941266 0.337667i \(-0.109638\pi\)
−0.763061 + 0.646326i \(0.776304\pi\)
\(434\) 4.34657 + 1.56668i 0.208642 + 0.0752029i
\(435\) 0 0
\(436\) 8.00774 29.8853i 0.383501 1.43125i
\(437\) −17.4258 + 17.4258i −0.833589 + 0.833589i
\(438\) 0 0
\(439\) −18.4110 + 31.8888i −0.878709 + 1.52197i −0.0259510 + 0.999663i \(0.508261\pi\)
−0.852758 + 0.522306i \(0.825072\pi\)
\(440\) 1.95265 + 7.28740i 0.0930891 + 0.347413i
\(441\) 0 0
\(442\) 1.74322 + 0.727656i 0.0829167 + 0.0346111i
\(443\) −25.6906 −1.22060 −0.610298 0.792172i \(-0.708950\pi\)
−0.610298 + 0.792172i \(0.708950\pi\)
\(444\) 0 0
\(445\) −0.410159 + 0.710416i −0.0194434 + 0.0336770i
\(446\) −0.911973 1.57958i −0.0431832 0.0747955i
\(447\) 0 0
\(448\) −18.7706 + 3.37021i −0.886829 + 0.159228i
\(449\) 1.26128 4.70715i 0.0595234 0.222144i −0.929757 0.368174i \(-0.879983\pi\)
0.989280 + 0.146030i \(0.0466496\pi\)
\(450\) 0 0
\(451\) 6.56982 3.79308i 0.309361 0.178609i
\(452\) 9.35882 + 5.40332i 0.440202 + 0.254151i
\(453\) 0 0
\(454\) 2.86445 0.134435
\(455\) −36.8871 8.16269i −1.72930 0.382673i
\(456\) 0 0
\(457\) −1.32032 4.92751i −0.0617621 0.230499i 0.928145 0.372220i \(-0.121403\pi\)
−0.989907 + 0.141721i \(0.954737\pi\)
\(458\) 0.356509 + 0.205830i 0.0166586 + 0.00961783i
\(459\) 0 0
\(460\) 46.2361 + 46.2361i 2.15577 + 2.15577i
\(461\) 2.21189 8.25490i 0.103018 0.384469i −0.895095 0.445876i \(-0.852892\pi\)
0.998113 + 0.0614071i \(0.0195588\pi\)
\(462\) 0 0
\(463\) 0.176712 + 0.176712i 0.00821253 + 0.00821253i 0.711201 0.702989i \(-0.248152\pi\)
−0.702989 + 0.711201i \(0.748152\pi\)
\(464\) 6.31383 + 10.9359i 0.293112 + 0.507685i
\(465\) 0 0
\(466\) 1.50132 0.402277i 0.0695473 0.0186351i
\(467\) 23.3883 1.08228 0.541140 0.840932i \(-0.317993\pi\)
0.541140 + 0.840932i \(0.317993\pi\)
\(468\) 0 0
\(469\) 19.4465 9.14205i 0.897956 0.422141i
\(470\) 1.28809 + 4.80721i 0.0594151 + 0.221740i
\(471\) 0 0
\(472\) −0.00250364 0.00433642i −0.000115239 0.000199600i
\(473\) −5.21201 + 5.21201i −0.239648 + 0.239648i
\(474\) 0 0
\(475\) 30.2935 + 8.11711i 1.38996 + 0.372438i
\(476\) 5.05298 14.0189i 0.231603 0.642557i
\(477\) 0 0
\(478\) −1.54128 0.889857i −0.0704964 0.0407011i
\(479\) 8.63573 + 32.2290i 0.394577 + 1.47258i 0.822500 + 0.568765i \(0.192579\pi\)
−0.427924 + 0.903815i \(0.640755\pi\)
\(480\) 0 0
\(481\) −15.3423 20.1081i −0.699550 0.916851i
\(482\) 3.75211i 0.170904i
\(483\) 0 0
\(484\) −4.03815 + 6.99428i −0.183552 + 0.317922i
\(485\) −2.61530 + 1.50994i −0.118754 + 0.0685629i
\(486\) 0 0
\(487\) −14.6137 3.91573i −0.662211 0.177439i −0.0879671 0.996123i \(-0.528037\pi\)
−0.574243 + 0.818685i \(0.694704\pi\)
\(488\) −4.57622 1.22619i −0.207156 0.0555072i
\(489\) 0 0
\(490\) 0.849404 4.99951i 0.0383722 0.225855i
\(491\) 11.7579 + 6.78843i 0.530627 + 0.306357i 0.741272 0.671205i \(-0.234223\pi\)
−0.210645 + 0.977563i \(0.567556\pi\)
\(492\) 0 0
\(493\) −9.51669 −0.428610
\(494\) −0.735965 1.79061i −0.0331126 0.0805632i
\(495\) 0 0
\(496\) −35.0441 + 9.39005i −1.57353 + 0.421626i
\(497\) 3.35951 39.8308i 0.150695 1.78666i
\(498\) 0 0
\(499\) 9.45211 9.45211i 0.423135 0.423135i −0.463147 0.886282i \(-0.653280\pi\)
0.886282 + 0.463147i \(0.153280\pi\)
\(500\) 11.4585 42.7637i 0.512440 1.91245i
\(501\) 0 0
\(502\) −1.12674 + 1.12674i −0.0502887 + 0.0502887i
\(503\) −1.20476 + 0.695570i −0.0537177 + 0.0310140i −0.526618 0.850102i \(-0.676540\pi\)
0.472901 + 0.881116i \(0.343207\pi\)
\(504\) 0 0
\(505\) 5.21852 1.39830i 0.232221 0.0622234i
\(506\) 4.03217i 0.179252i
\(507\) 0 0
\(508\) 19.9953 0.887149
\(509\) 22.4834 6.02441i 0.996559 0.267027i 0.276556 0.960998i \(-0.410807\pi\)
0.720003 + 0.693971i \(0.244140\pi\)
\(510\) 0 0
\(511\) −0.987902 0.687152i −0.0437022 0.0303978i
\(512\) −9.66738 + 9.66738i −0.427242 + 0.427242i
\(513\) 0 0
\(514\) 2.45990 + 0.659129i 0.108502 + 0.0290729i
\(515\) 12.4210 + 12.4210i 0.547335 + 0.547335i
\(516\) 0 0
\(517\) 9.01819 15.6200i 0.396620 0.686965i
\(518\) 2.59394 2.19040i 0.113971 0.0962408i
\(519\) 0 0
\(520\) −9.58291 + 3.93871i −0.420238 + 0.172724i
\(521\) 6.02463i 0.263944i −0.991253 0.131972i \(-0.957869\pi\)
0.991253 0.131972i \(-0.0421309\pi\)
\(522\) 0 0
\(523\) 2.29311 + 1.32393i 0.100271 + 0.0578914i 0.549297 0.835627i \(-0.314896\pi\)
−0.449026 + 0.893519i \(0.648229\pi\)
\(524\) −19.1964 33.2491i −0.838598 1.45249i
\(525\) 0 0
\(526\) −1.89034 0.506514i −0.0824226 0.0220851i
\(527\) 7.07670 26.4106i 0.308266 1.15046i
\(528\) 0 0
\(529\) 23.7440 + 41.1258i 1.03235 + 1.78808i
\(530\) −1.96782 + 3.40837i −0.0854767 + 0.148050i
\(531\) 0 0
\(532\) −13.8211 + 6.49748i −0.599221 + 0.281701i
\(533\) 6.31948 + 8.28249i 0.273727 + 0.358754i
\(534\) 0 0
\(535\) −13.8595 + 3.71364i −0.599199 + 0.160555i
\(536\) 2.94650 5.10348i 0.127269 0.220437i
\(537\) 0 0
\(538\) 1.19215 + 1.19215i 0.0513974 + 0.0513974i
\(539\) −14.9886 + 10.6352i −0.645603 + 0.458089i
\(540\) 0 0
\(541\) −22.5427 22.5427i −0.969185 0.969185i 0.0303542 0.999539i \(-0.490336\pi\)
−0.999539 + 0.0303542i \(0.990336\pi\)
\(542\) −0.160874 + 0.0928807i −0.00691013 + 0.00398957i
\(543\) 0 0
\(544\) −1.59104 5.93784i −0.0682152 0.254583i
\(545\) −62.3085 −2.66900
\(546\) 0 0
\(547\) 24.3001 1.03900 0.519500 0.854471i \(-0.326118\pi\)
0.519500 + 0.854471i \(0.326118\pi\)
\(548\) −6.08488 22.7091i −0.259933 0.970084i
\(549\) 0 0
\(550\) 4.44393 2.56570i 0.189490 0.109402i
\(551\) 6.89659 + 6.89659i 0.293805 + 0.293805i
\(552\) 0 0
\(553\) −0.131126 0.730318i −0.00557606 0.0310563i
\(554\) −0.118805 0.118805i −0.00504753 0.00504753i
\(555\) 0 0
\(556\) 16.3825 28.3753i 0.694772 1.20338i
\(557\) 4.94226 1.32427i 0.209410 0.0561113i −0.152589 0.988290i \(-0.548761\pi\)
0.361999 + 0.932178i \(0.382094\pi\)
\(558\) 0 0
\(559\) −8.01376 6.18406i −0.338946 0.261558i
\(560\) 16.9415 + 36.0371i 0.715909 + 1.52284i
\(561\) 0 0
\(562\) −0.442230 + 0.765964i −0.0186543 + 0.0323102i
\(563\) 10.0206 + 17.3563i 0.422320 + 0.731480i 0.996166 0.0874837i \(-0.0278826\pi\)
−0.573846 + 0.818963i \(0.694549\pi\)
\(564\) 0 0
\(565\) 5.63274 21.0217i 0.236971 0.884389i
\(566\) −2.80763 0.752303i −0.118014 0.0316217i
\(567\) 0 0
\(568\) −5.48106 9.49347i −0.229980 0.398337i
\(569\) 29.3938 + 16.9705i 1.23225 + 0.711441i 0.967499 0.252875i \(-0.0813760\pi\)
0.264754 + 0.964316i \(0.414709\pi\)
\(570\) 0 0
\(571\) 19.5735i 0.819124i −0.912282 0.409562i \(-0.865681\pi\)
0.912282 0.409562i \(-0.134319\pi\)
\(572\) 17.1793 + 7.17096i 0.718301 + 0.299833i
\(573\) 0 0
\(574\) −1.06844 + 0.902223i −0.0445957 + 0.0376581i
\(575\) 44.8521 77.6861i 1.87046 3.23973i
\(576\) 0 0
\(577\) −32.3003 32.3003i −1.34468 1.34468i −0.891335 0.453345i \(-0.850231\pi\)
−0.453345 0.891335i \(-0.649769\pi\)
\(578\) −1.55436 0.416489i −0.0646527 0.0173237i
\(579\) 0 0
\(580\) 18.2988 18.2988i 0.759816 0.759816i
\(581\) 5.19124 7.46334i 0.215369 0.309631i
\(582\) 0 0
\(583\) 13.7771 3.69158i 0.570591 0.152889i
\(584\) −0.330019 −0.0136563
\(585\) 0 0
\(586\) 2.70445i 0.111720i
\(587\) 12.7987 3.42941i 0.528260 0.141547i 0.0151751 0.999885i \(-0.495169\pi\)
0.513084 + 0.858338i \(0.328503\pi\)
\(588\) 0 0
\(589\) −24.2677 + 14.0110i −0.999933 + 0.577312i
\(590\) −0.00353517 + 0.00353517i −0.000145541 + 0.000145541i
\(591\) 0 0
\(592\) −6.89992 + 25.7509i −0.283585 + 1.05835i
\(593\) −28.9194 + 28.9194i −1.18758 + 1.18758i −0.209843 + 0.977735i \(0.567295\pi\)
−0.977735 + 0.209843i \(0.932705\pi\)
\(594\) 0 0
\(595\) −29.9042 2.52225i −1.22595 0.103402i
\(596\) −29.0268 + 7.77770i −1.18898 + 0.318587i
\(597\) 0 0
\(598\) −5.49194 + 0.707759i −0.224582 + 0.0289424i
\(599\) −10.2540 −0.418967 −0.209484 0.977812i \(-0.567178\pi\)
−0.209484 + 0.977812i \(0.567178\pi\)
\(600\) 0 0
\(601\) 27.4693 + 15.8594i 1.12050 + 0.646919i 0.941528 0.336936i \(-0.109390\pi\)
0.178969 + 0.983855i \(0.442724\pi\)
\(602\) 0.775859 1.11544i 0.0316216 0.0454617i
\(603\) 0 0
\(604\) −20.1574 5.40116i −0.820194 0.219770i
\(605\) 15.7105 + 4.20961i 0.638722 + 0.171145i
\(606\) 0 0
\(607\) −23.1914 + 13.3895i −0.941309 + 0.543465i −0.890370 0.455237i \(-0.849555\pi\)
−0.0509383 + 0.998702i \(0.516221\pi\)
\(608\) −3.15005 + 5.45605i −0.127752 + 0.221272i
\(609\) 0 0
\(610\) 4.73028i 0.191523i
\(611\) 22.8578 + 9.54130i 0.924727 + 0.386000i
\(612\) 0 0
\(613\) 8.17678 + 30.5162i 0.330257 + 1.23254i 0.908920 + 0.416970i \(0.136908\pi\)
−0.578663 + 0.815567i \(0.696425\pi\)
\(614\) 2.68169 + 1.54827i 0.108224 + 0.0624833i
\(615\) 0 0
\(616\) −1.70904 + 4.74154i −0.0688591 + 0.191042i
\(617\) −35.9374 9.62939i −1.44678 0.387665i −0.551880 0.833923i \(-0.686089\pi\)
−0.894904 + 0.446259i \(0.852756\pi\)
\(618\) 0 0
\(619\) 13.9520 13.9520i 0.560777 0.560777i −0.368751 0.929528i \(-0.620215\pi\)
0.929528 + 0.368751i \(0.120215\pi\)
\(620\) 37.1754 + 64.3897i 1.49300 + 2.58595i
\(621\) 0 0
\(622\) 1.05589 + 3.94062i 0.0423372 + 0.158005i
\(623\) −0.495949 + 0.233152i −0.0198698 + 0.00934104i
\(624\) 0 0
\(625\) −35.7364 −1.42945
\(626\) 3.84535 1.03036i 0.153691 0.0411814i
\(627\) 0 0
\(628\) −13.2615 22.9695i −0.529190 0.916585i
\(629\) −14.2068 14.2068i −0.566462 0.566462i
\(630\) 0 0
\(631\) −2.16532 + 8.08109i −0.0862001 + 0.321703i −0.995539 0.0943536i \(-0.969922\pi\)
0.909339 + 0.416057i \(0.136588\pi\)
\(632\) −0.143887 0.143887i −0.00572353 0.00572353i
\(633\) 0 0
\(634\) 0.870873 + 0.502799i 0.0345868 + 0.0199687i
\(635\) −10.4222 38.8960i −0.413591 1.54354i
\(636\) 0 0
\(637\) −17.1163 18.5481i −0.678173 0.734902i
\(638\) 1.59581 0.0631787
\(639\) 0 0
\(640\) 19.2452 + 11.1112i 0.760734 + 0.439210i
\(641\) 19.7158 11.3829i 0.778726 0.449598i −0.0572524 0.998360i \(-0.518234\pi\)
0.835979 + 0.548762i \(0.184901\pi\)
\(642\) 0 0
\(643\) −3.68359 + 13.7474i −0.145267 + 0.542143i 0.854477 + 0.519490i \(0.173878\pi\)
−0.999743 + 0.0226531i \(0.992789\pi\)
\(644\) 7.71965 + 42.9951i 0.304197 + 1.69425i
\(645\) 0 0
\(646\) −0.768917 1.33180i −0.0302527 0.0523991i
\(647\) 22.6826 39.2874i 0.891744 1.54455i 0.0539612 0.998543i \(-0.482815\pi\)
0.837783 0.546003i \(-0.183851\pi\)
\(648\) 0 0
\(649\) 0.0181186 0.000711218
\(650\) 4.27460 + 5.60241i 0.167663 + 0.219745i
\(651\) 0 0
\(652\) 2.11050 + 7.87648i 0.0826534 + 0.308467i
\(653\) −5.43437 + 9.41260i −0.212663 + 0.368344i −0.952547 0.304391i \(-0.901547\pi\)
0.739884 + 0.672735i \(0.234880\pi\)
\(654\) 0 0
\(655\) −54.6723 + 54.6723i −2.13622 + 2.13622i
\(656\) 2.84206 10.6067i 0.110964 0.414123i
\(657\) 0 0
\(658\) −1.12738 + 3.12781i −0.0439500 + 0.121935i
\(659\) 4.13172 + 7.15635i 0.160949 + 0.278772i 0.935209 0.354096i \(-0.115211\pi\)
−0.774260 + 0.632867i \(0.781878\pi\)
\(660\) 0 0
\(661\) 0.844712 + 3.15251i 0.0328555 + 0.122618i 0.980406 0.196988i \(-0.0631160\pi\)
−0.947550 + 0.319606i \(0.896449\pi\)
\(662\) 3.34138i 0.129867i
\(663\) 0 0
\(664\) 2.49321i 0.0967552i
\(665\) 19.8432 + 23.4989i 0.769488 + 0.911248i
\(666\) 0 0
\(667\) 24.1595 13.9485i 0.935459 0.540088i
\(668\) −19.4758 19.4758i −0.753542 0.753542i
\(669\) 0 0
\(670\) −5.68334 1.52285i −0.219567 0.0588327i
\(671\) 12.1219 12.1219i 0.467962 0.467962i
\(672\) 0 0
\(673\) −29.2655 16.8964i −1.12810 0.651310i −0.184645 0.982805i \(-0.559114\pi\)
−0.943457 + 0.331495i \(0.892447\pi\)
\(674\) 2.20697 0.591357i 0.0850095 0.0227782i
\(675\) 0 0
\(676\) −6.75162 + 24.6573i −0.259678 + 0.948360i
\(677\) 26.7526i 1.02819i −0.857734 0.514093i \(-0.828129\pi\)
0.857734 0.514093i \(-0.171871\pi\)
\(678\) 0 0
\(679\) −2.01032 0.169559i −0.0771488 0.00650707i
\(680\) −7.12751 + 4.11507i −0.273327 + 0.157806i
\(681\) 0 0
\(682\) −1.18666 + 4.42867i −0.0454395 + 0.169583i
\(683\) 4.61892 17.2380i 0.176738 0.659595i −0.819511 0.573063i \(-0.805755\pi\)
0.996249 0.0865317i \(-0.0275784\pi\)
\(684\) 0 0
\(685\) −41.0034 + 23.6733i −1.56666 + 0.904511i
\(686\) 2.37301 2.41787i 0.0906021 0.0923149i
\(687\) 0 0
\(688\) 10.6693i 0.406763i
\(689\) 7.44631 + 18.1169i 0.283682 + 0.690199i
\(690\) 0 0
\(691\) 28.7650 7.70756i 1.09427 0.293209i 0.333842 0.942629i \(-0.391655\pi\)
0.760430 + 0.649420i \(0.224988\pi\)
\(692\) 25.9931 + 15.0071i 0.988108 + 0.570484i
\(693\) 0 0
\(694\) 0.699792 0.699792i 0.0265637 0.0265637i
\(695\) −63.7363 17.0781i −2.41766 0.647809i
\(696\) 0 0
\(697\) 5.85175 + 5.85175i 0.221651 + 0.221651i
\(698\) −0.981627 + 0.566743i −0.0371551 + 0.0214515i
\(699\) 0 0
\(700\) 42.4736 35.8661i 1.60535 1.35561i
\(701\) 23.3038i 0.880172i 0.897956 + 0.440086i \(0.145052\pi\)
−0.897956 + 0.440086i \(0.854948\pi\)
\(702\) 0 0
\(703\) 20.5909i 0.776599i
\(704\) −4.89806 18.2798i −0.184603 0.688947i
\(705\) 0 0
\(706\) 3.22910 + 5.59297i 0.121529 + 0.210494i
\(707\) 3.39542 + 1.22384i 0.127698 + 0.0460274i
\(708\) 0 0
\(709\) 2.40630 8.98045i 0.0903706 0.337268i −0.905906 0.423478i \(-0.860809\pi\)
0.996277 + 0.0862104i \(0.0274757\pi\)
\(710\) −7.73933 + 7.73933i −0.290452 + 0.290452i
\(711\) 0 0
\(712\) −0.0751452 + 0.130155i −0.00281619 + 0.00487778i
\(713\) 20.7444 + 77.4193i 0.776886 + 2.89938i
\(714\) 0 0
\(715\) 4.99502 37.1558i 0.186803 1.38955i
\(716\) −15.7791 −0.589693
\(717\) 0 0
\(718\) −1.01070 + 1.75059i −0.0377191 + 0.0653315i
\(719\) −7.87045 13.6320i −0.293518 0.508388i 0.681121 0.732171i \(-0.261493\pi\)
−0.974639 + 0.223783i \(0.928159\pi\)
\(720\) 0 0
\(721\) 2.07383 + 11.5504i 0.0772335 + 0.430158i
\(722\) 0.491630 1.83479i 0.0182966 0.0682838i
\(723\) 0 0
\(724\) 15.4661 8.92936i 0.574793 0.331857i
\(725\) −30.7457 17.7511i −1.14187 0.659258i
\(726\) 0 0
\(727\) 5.72068 0.212168 0.106084 0.994357i \(-0.466169\pi\)
0.106084 + 0.994357i \(0.466169\pi\)
\(728\) −6.75809 1.49549i −0.250472 0.0554264i
\(729\) 0 0
\(730\) 0.0852824 + 0.318278i 0.00315644 + 0.0117800i
\(731\) −6.96352 4.02039i −0.257555 0.148700i
\(732\) 0 0
\(733\) 12.5077 + 12.5077i 0.461982 + 0.461982i 0.899305 0.437322i \(-0.144073\pi\)
−0.437322 + 0.899305i \(0.644073\pi\)
\(734\) 1.06225 3.96439i 0.0392085 0.146328i
\(735\) 0 0
\(736\) 12.7421 + 12.7421i 0.469680 + 0.469680i
\(737\) 10.6618 + 18.4668i 0.392732 + 0.680232i
\(738\) 0 0
\(739\) 34.5884 9.26794i 1.27236 0.340927i 0.441423 0.897299i \(-0.354474\pi\)
0.830933 + 0.556372i \(0.187807\pi\)
\(740\) 54.6339 2.00838
\(741\) 0 0
\(742\) −2.37941 + 1.11859i −0.0873510 + 0.0410649i
\(743\) 1.35076 + 5.04112i 0.0495547 + 0.184941i 0.986267 0.165160i \(-0.0528140\pi\)
−0.936712 + 0.350101i \(0.886147\pi\)
\(744\) 0 0
\(745\) 30.2593 + 52.4106i 1.10861 + 1.92017i
\(746\) −0.894109 + 0.894109i −0.0327357 + 0.0327357i
\(747\) 0 0
\(748\) 14.2837 + 3.82731i 0.522265 + 0.139940i
\(749\) −9.01766 3.25032i −0.329498 0.118764i
\(750\) 0 0
\(751\) 24.9221 + 14.3888i 0.909421 + 0.525055i 0.880245 0.474520i \(-0.157378\pi\)
0.0291764 + 0.999574i \(0.490712\pi\)
\(752\) −6.75711 25.2179i −0.246406 0.919601i
\(753\) 0 0
\(754\) 0.280109 + 2.17354i 0.0102010 + 0.0791556i
\(755\) 42.0266i 1.52950i
\(756\) 0 0
\(757\) 8.90997 15.4325i 0.323838 0.560905i −0.657438 0.753508i \(-0.728360\pi\)
0.981277 + 0.192604i \(0.0616933\pi\)
\(758\) 1.32557 0.765320i 0.0481470 0.0277977i
\(759\) 0 0
\(760\) 8.14731 + 2.18306i 0.295534 + 0.0791881i
\(761\) 52.7426 + 14.1323i 1.91192 + 0.512296i 0.993044 + 0.117741i \(0.0375652\pi\)
0.918872 + 0.394556i \(0.129101\pi\)
\(762\) 0 0
\(763\) −34.1720 23.7689i −1.23711 0.860492i
\(764\) 34.9372 + 20.1710i 1.26398 + 0.729761i
\(765\) 0 0
\(766\) −0.404738 −0.0146238
\(767\) 0.00318032 + 0.0246781i 0.000114835 + 0.000891074i
\(768\) 0 0
\(769\) −23.1319 + 6.19819i −0.834159 + 0.223512i −0.650527 0.759483i \(-0.725452\pi\)
−0.183632 + 0.982995i \(0.558785\pi\)
\(770\) 5.01449 + 0.422944i 0.180710 + 0.0152419i
\(771\) 0 0
\(772\) 20.1661 20.1661i 0.725795 0.725795i
\(773\) −10.0708 + 37.5846i −0.362221 + 1.35183i 0.508929 + 0.860808i \(0.330042\pi\)
−0.871150 + 0.491017i \(0.836625\pi\)
\(774\) 0 0
\(775\) 72.1254 72.1254i 2.59082 2.59082i
\(776\) −0.479148 + 0.276636i −0.0172004 + 0.00993067i
\(777\) 0 0
\(778\) −4.37935 + 1.17344i −0.157007 + 0.0420700i
\(779\) 8.48133i 0.303875i
\(780\) 0 0
\(781\) 39.6660 1.41936
\(782\) −4.24875 + 1.13845i −0.151935 + 0.0407109i
\(783\) 0 0
\(784\) −4.45584 + 26.2266i −0.159137 + 0.936665i
\(785\) −37.7694 + 37.7694i −1.34805 + 1.34805i
\(786\) 0 0
\(787\) −17.8194 4.77470i −0.635194 0.170200i −0.0731686 0.997320i \(-0.523311\pi\)
−0.562026 + 0.827120i \(0.689978\pi\)
\(788\) −25.0015