Properties

Label 405.2.r.a.197.14
Level $405$
Weight $2$
Character 405.197
Analytic conductor $3.234$
Analytic rank $0$
Dimension $192$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.r (of order \(36\), degree \(12\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.23394128186\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(16\) over \(\Q(\zeta_{36})\)
Twist minimal: no (minimal twist has level 135)
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 197.14
Character \(\chi\) \(=\) 405.197
Dual form 405.2.r.a.368.14

$q$-expansion

\(f(q)\) \(=\) \(q+(2.19031 - 0.191628i) q^{2} +(2.79113 - 0.492152i) q^{4} +(2.15257 + 0.605349i) q^{5} +(0.000530458 - 0.000371431i) q^{7} +(1.77162 - 0.474704i) q^{8} +O(q^{10})\) \(q+(2.19031 - 0.191628i) q^{2} +(2.79113 - 0.492152i) q^{4} +(2.15257 + 0.605349i) q^{5} +(0.000530458 - 0.000371431i) q^{7} +(1.77162 - 0.474704i) q^{8} +(4.83080 + 0.913412i) q^{10} +(-0.925209 - 2.54199i) q^{11} +(-0.277011 + 3.16625i) q^{13} +(0.00109069 - 0.000915200i) q^{14} +(-1.53710 + 0.559459i) q^{16} +(-6.58840 - 1.76536i) q^{17} +(1.52337 + 0.879517i) q^{19} +(6.30603 + 0.630218i) q^{20} +(-2.51361 - 5.39046i) q^{22} +(2.93096 - 4.18584i) q^{23} +(4.26710 + 2.60611i) q^{25} +6.98815i q^{26} +(0.00129778 - 0.00129778i) q^{28} +(4.37718 + 3.67289i) q^{29} +(-0.944975 - 5.35922i) q^{31} +(-6.58407 + 3.07020i) q^{32} +(-14.7689 - 2.60416i) q^{34} +(0.00136669 - 0.000478418i) q^{35} +(-0.0678960 + 0.253391i) q^{37} +(3.50519 + 1.63450i) q^{38} +(4.10090 + 0.0506152i) q^{40} +(-7.56097 - 9.01082i) q^{41} +(-3.67622 + 7.88368i) q^{43} +(-3.83342 - 6.63969i) q^{44} +(5.61759 - 9.72995i) q^{46} +(0.403711 + 0.576559i) q^{47} +(-2.39414 + 6.57785i) q^{49} +(9.84570 + 4.89050i) q^{50} +(0.785101 + 8.97374i) q^{52} +(-5.73786 - 5.73786i) q^{53} +(-0.452784 - 6.03188i) q^{55} +(0.000763450 - 0.000909845i) q^{56} +(10.2912 + 7.20599i) q^{58} +(2.11198 + 0.768697i) q^{59} +(-1.14333 + 6.48417i) q^{61} +(-3.09676 - 11.5573i) q^{62} +(-10.9996 + 6.35064i) q^{64} +(-2.51297 + 6.64787i) q^{65} +(2.47165 + 0.216242i) q^{67} +(-19.2579 - 1.68485i) q^{68} +(0.00290181 - 0.00130978i) q^{70} +(10.4316 - 6.02267i) q^{71} +(-0.375408 - 1.40104i) q^{73} +(-0.100157 + 0.568017i) q^{74} +(4.68478 + 1.70512i) q^{76} +(-0.00143496 - 0.00100477i) q^{77} +(3.36157 - 4.00616i) q^{79} +(-3.64738 + 0.273791i) q^{80} +(-18.2876 - 18.2876i) q^{82} +(1.39592 + 15.9554i) q^{83} +(-13.1133 - 7.78833i) q^{85} +(-6.54134 + 17.9722i) q^{86} +(-2.84581 - 4.06424i) q^{88} +(-2.99426 + 5.18621i) q^{89} +(0.00102910 + 0.00178245i) q^{91} +(6.12062 - 13.1257i) q^{92} +(0.994737 + 1.18548i) q^{94} +(2.74674 + 2.81539i) q^{95} +(7.62753 + 3.55678i) q^{97} +(-3.98342 + 14.8663i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{13}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.19031 0.191628i 1.54878 0.135501i 0.719566 0.694425i \(-0.244341\pi\)
0.829219 + 0.558923i \(0.188785\pi\)
\(3\) 0 0
\(4\) 2.79113 0.492152i 1.39557 0.246076i
\(5\) 2.15257 + 0.605349i 0.962658 + 0.270720i
\(6\) 0 0
\(7\) 0.000530458 0 0.000371431i 0.000200494 0 0.000140388i −0.573476 0.819222i \(-0.694405\pi\)
0.573677 + 0.819082i \(0.305517\pi\)
\(8\) 1.77162 0.474704i 0.626362 0.167833i
\(9\) 0 0
\(10\) 4.83080 + 0.913412i 1.52763 + 0.288846i
\(11\) −0.925209 2.54199i −0.278961 0.766439i −0.997481 0.0709326i \(-0.977402\pi\)
0.718520 0.695506i \(-0.244820\pi\)
\(12\) 0 0
\(13\) −0.277011 + 3.16625i −0.0768289 + 0.878159i 0.855797 + 0.517313i \(0.173068\pi\)
−0.932625 + 0.360846i \(0.882488\pi\)
\(14\) 0.00109069 0.000915200i 0.000291500 0.000244597i
\(15\) 0 0
\(16\) −1.53710 + 0.559459i −0.384275 + 0.139865i
\(17\) −6.58840 1.76536i −1.59792 0.428162i −0.653507 0.756921i \(-0.726703\pi\)
−0.944414 + 0.328759i \(0.893370\pi\)
\(18\) 0 0
\(19\) 1.52337 + 0.879517i 0.349485 + 0.201775i 0.664458 0.747325i \(-0.268662\pi\)
−0.314974 + 0.949100i \(0.601996\pi\)
\(20\) 6.30603 + 0.630218i 1.41007 + 0.140921i
\(21\) 0 0
\(22\) −2.51361 5.39046i −0.535904 1.14925i
\(23\) 2.93096 4.18584i 0.611147 0.872808i −0.387652 0.921806i \(-0.626714\pi\)
0.998799 + 0.0489979i \(0.0156028\pi\)
\(24\) 0 0
\(25\) 4.26710 + 2.60611i 0.853421 + 0.521222i
\(26\) 6.98815i 1.37049i
\(27\) 0 0
\(28\) 0.00129778 0.00129778i 0.000245257 0.000245257i
\(29\) 4.37718 + 3.67289i 0.812822 + 0.682038i 0.951279 0.308330i \(-0.0997701\pi\)
−0.138458 + 0.990368i \(0.544215\pi\)
\(30\) 0 0
\(31\) −0.944975 5.35922i −0.169723 0.962544i −0.944061 0.329772i \(-0.893028\pi\)
0.774338 0.632772i \(-0.218083\pi\)
\(32\) −6.58407 + 3.07020i −1.16391 + 0.542740i
\(33\) 0 0
\(34\) −14.7689 2.60416i −2.53285 0.446610i
\(35\) 0.00136669 0.000478418i 0.000231013 8.08674e-5i
\(36\) 0 0
\(37\) −0.0678960 + 0.253391i −0.0111620 + 0.0416573i −0.971282 0.237930i \(-0.923531\pi\)
0.960120 + 0.279587i \(0.0901977\pi\)
\(38\) 3.50519 + 1.63450i 0.568617 + 0.265151i
\(39\) 0 0
\(40\) 4.10090 + 0.0506152i 0.648408 + 0.00800297i
\(41\) −7.56097 9.01082i −1.18083 1.40725i −0.893289 0.449483i \(-0.851608\pi\)
−0.287537 0.957770i \(-0.592836\pi\)
\(42\) 0 0
\(43\) −3.67622 + 7.88368i −0.560618 + 1.20225i 0.397955 + 0.917405i \(0.369720\pi\)
−0.958574 + 0.284845i \(0.908058\pi\)
\(44\) −3.83342 6.63969i −0.577910 1.00097i
\(45\) 0 0
\(46\) 5.61759 9.72995i 0.828268 1.43460i
\(47\) 0.403711 + 0.576559i 0.0588873 + 0.0840997i 0.847516 0.530770i \(-0.178097\pi\)
−0.788628 + 0.614870i \(0.789208\pi\)
\(48\) 0 0
\(49\) −2.39414 + 6.57785i −0.342020 + 0.939693i
\(50\) 9.84570 + 4.89050i 1.39239 + 0.691622i
\(51\) 0 0
\(52\) 0.785101 + 8.97374i 0.108874 + 1.24443i
\(53\) −5.73786 5.73786i −0.788156 0.788156i 0.193036 0.981192i \(-0.438167\pi\)
−0.981192 + 0.193036i \(0.938167\pi\)
\(54\) 0 0
\(55\) −0.452784 6.03188i −0.0610534 0.813339i
\(56\) 0.000763450 0 0.000909845i 0.000102020 0 0.000121583i
\(57\) 0 0
\(58\) 10.2912 + 7.20599i 1.35130 + 0.946193i
\(59\) 2.11198 + 0.768697i 0.274956 + 0.100076i 0.475818 0.879544i \(-0.342152\pi\)
−0.200862 + 0.979620i \(0.564374\pi\)
\(60\) 0 0
\(61\) −1.14333 + 6.48417i −0.146389 + 0.830213i 0.819852 + 0.572575i \(0.194055\pi\)
−0.966241 + 0.257638i \(0.917056\pi\)
\(62\) −3.09676 11.5573i −0.393290 1.46778i
\(63\) 0 0
\(64\) −10.9996 + 6.35064i −1.37495 + 0.793830i
\(65\) −2.51297 + 6.64787i −0.311695 + 0.824567i
\(66\) 0 0
\(67\) 2.47165 + 0.216242i 0.301960 + 0.0264181i 0.237129 0.971478i \(-0.423794\pi\)
0.0648313 + 0.997896i \(0.479349\pi\)
\(68\) −19.2579 1.68485i −2.33536 0.204318i
\(69\) 0 0
\(70\) 0.00290181 0.00130978i 0.000346832 0.000156549i
\(71\) 10.4316 6.02267i 1.23800 0.714759i 0.269314 0.963052i \(-0.413203\pi\)
0.968685 + 0.248294i \(0.0798698\pi\)
\(72\) 0 0
\(73\) −0.375408 1.40104i −0.0439381 0.163979i 0.940471 0.339875i \(-0.110385\pi\)
−0.984409 + 0.175895i \(0.943718\pi\)
\(74\) −0.100157 + 0.568017i −0.0116430 + 0.0660306i
\(75\) 0 0
\(76\) 4.68478 + 1.70512i 0.537381 + 0.195591i
\(77\) −0.00143496 0.00100477i −0.000163529 0.000114504i
\(78\) 0 0
\(79\) 3.36157 4.00616i 0.378206 0.450729i −0.543041 0.839706i \(-0.682727\pi\)
0.921247 + 0.388978i \(0.127172\pi\)
\(80\) −3.64738 + 0.273791i −0.407790 + 0.0306108i
\(81\) 0 0
\(82\) −18.2876 18.2876i −2.01953 2.01953i
\(83\) 1.39592 + 15.9554i 0.153222 + 1.75134i 0.551594 + 0.834113i \(0.314020\pi\)
−0.398372 + 0.917224i \(0.630425\pi\)
\(84\) 0 0
\(85\) −13.1133 7.78833i −1.42234 0.844763i
\(86\) −6.54134 + 17.9722i −0.705371 + 1.93799i
\(87\) 0 0
\(88\) −2.84581 4.06424i −0.303364 0.433249i
\(89\) −2.99426 + 5.18621i −0.317391 + 0.549737i −0.979943 0.199279i \(-0.936140\pi\)
0.662552 + 0.749016i \(0.269473\pi\)
\(90\) 0 0
\(91\) 0.00102910 + 0.00178245i 0.000107879 + 0.000186852i
\(92\) 6.12062 13.1257i 0.638118 1.36845i
\(93\) 0 0
\(94\) 0.994737 + 1.18548i 0.102599 + 0.122273i
\(95\) 2.74674 + 2.81539i 0.281810 + 0.288853i
\(96\) 0 0
\(97\) 7.62753 + 3.55678i 0.774459 + 0.361136i 0.769331 0.638851i \(-0.220590\pi\)
0.00512815 + 0.999987i \(0.498368\pi\)
\(98\) −3.98342 + 14.8663i −0.402386 + 1.50173i
\(99\) 0 0
\(100\) 13.1927 + 5.17394i 1.31927 + 0.517394i
\(101\) −11.3335 1.99841i −1.12773 0.198849i −0.421496 0.906830i \(-0.638495\pi\)
−0.706231 + 0.707981i \(0.749606\pi\)
\(102\) 0 0
\(103\) 6.21507 2.89813i 0.612389 0.285562i −0.0915740 0.995798i \(-0.529190\pi\)
0.703963 + 0.710237i \(0.251412\pi\)
\(104\) 1.01227 + 5.74088i 0.0992615 + 0.562940i
\(105\) 0 0
\(106\) −13.6672 11.4682i −1.32748 1.11389i
\(107\) 9.67551 9.67551i 0.935367 0.935367i −0.0626673 0.998034i \(-0.519961\pi\)
0.998034 + 0.0626673i \(0.0199607\pi\)
\(108\) 0 0
\(109\) 3.73835i 0.358069i −0.983843 0.179034i \(-0.942703\pi\)
0.983843 0.179034i \(-0.0572974\pi\)
\(110\) −2.14761 13.1249i −0.204767 1.25141i
\(111\) 0 0
\(112\) −0.000607567 0 0.000867696i −5.74097e−5 0 8.19895e-5i
\(113\) 0.472320 + 1.01289i 0.0444322 + 0.0952851i 0.927271 0.374391i \(-0.122148\pi\)
−0.882839 + 0.469676i \(0.844371\pi\)
\(114\) 0 0
\(115\) 8.84298 7.23605i 0.824612 0.674766i
\(116\) 14.0249 + 8.09728i 1.30218 + 0.751814i
\(117\) 0 0
\(118\) 4.77320 + 1.27897i 0.439408 + 0.117739i
\(119\) −0.00415058 + 0.00151069i −0.000380483 + 0.000138484i
\(120\) 0 0
\(121\) 2.82079 2.36692i 0.256435 0.215175i
\(122\) −1.26171 + 14.4215i −0.114230 + 1.30566i
\(123\) 0 0
\(124\) −5.27510 14.4932i −0.473718 1.30153i
\(125\) 7.60763 + 8.19292i 0.680447 + 0.732797i
\(126\) 0 0
\(127\) −10.0914 + 2.70398i −0.895467 + 0.239940i −0.677068 0.735920i \(-0.736750\pi\)
−0.218398 + 0.975860i \(0.570083\pi\)
\(128\) −10.9739 + 7.68398i −0.969962 + 0.679175i
\(129\) 0 0
\(130\) −4.23027 + 15.0425i −0.371019 + 1.31931i
\(131\) 14.3376 2.52811i 1.25269 0.220882i 0.492341 0.870402i \(-0.336141\pi\)
0.760345 + 0.649520i \(0.225030\pi\)
\(132\) 0 0
\(133\) 0.00113476 9.92788e-5i 9.83964e−5 8.60857e-6i
\(134\) 5.45513 0.471251
\(135\) 0 0
\(136\) −12.5102 −1.07274
\(137\) 7.28394 0.637262i 0.622309 0.0544450i 0.228359 0.973577i \(-0.426664\pi\)
0.393950 + 0.919132i \(0.371108\pi\)
\(138\) 0 0
\(139\) 3.00586 0.530014i 0.254953 0.0449552i −0.0447106 0.999000i \(-0.514237\pi\)
0.299664 + 0.954045i \(0.403125\pi\)
\(140\) 0.00357917 0.00200795i 0.000302495 0.000169703i
\(141\) 0 0
\(142\) 21.6943 15.1905i 1.82054 1.27476i
\(143\) 8.30486 2.22528i 0.694487 0.186087i
\(144\) 0 0
\(145\) 7.19880 + 10.5559i 0.597828 + 0.876617i
\(146\) −1.09074 2.99678i −0.0902701 0.248015i
\(147\) 0 0
\(148\) −0.0647997 + 0.740664i −0.00532650 + 0.0608822i
\(149\) 7.76525 6.51582i 0.636154 0.533797i −0.266680 0.963785i \(-0.585927\pi\)
0.902834 + 0.429988i \(0.141482\pi\)
\(150\) 0 0
\(151\) 17.4779 6.36142i 1.42233 0.517685i 0.487605 0.873064i \(-0.337870\pi\)
0.934722 + 0.355379i \(0.115648\pi\)
\(152\) 3.11634 + 0.835020i 0.252768 + 0.0677291i
\(153\) 0 0
\(154\) −0.00333555 0.00192578i −0.000268786 0.000155184i
\(155\) 1.21008 12.1081i 0.0971956 0.972548i
\(156\) 0 0
\(157\) −0.136723 0.293204i −0.0109117 0.0234002i 0.900776 0.434283i \(-0.142998\pi\)
−0.911688 + 0.410883i \(0.865220\pi\)
\(158\) 6.59520 9.41892i 0.524686 0.749329i
\(159\) 0 0
\(160\) −16.0312 + 2.62316i −1.26738 + 0.207379i
\(161\) 0.00330906i 0.000260790i
\(162\) 0 0
\(163\) −3.86594 + 3.86594i −0.302804 + 0.302804i −0.842110 0.539306i \(-0.818687\pi\)
0.539306 + 0.842110i \(0.318687\pi\)
\(164\) −25.5384 21.4292i −1.99421 1.67334i
\(165\) 0 0
\(166\) 6.11500 + 34.6799i 0.474616 + 2.69168i
\(167\) −16.6893 + 7.78235i −1.29146 + 0.602217i −0.942276 0.334838i \(-0.891318\pi\)
−0.349182 + 0.937055i \(0.613541\pi\)
\(168\) 0 0
\(169\) 2.85412 + 0.503259i 0.219548 + 0.0387122i
\(170\) −30.2147 14.5460i −2.31736 1.11563i
\(171\) 0 0
\(172\) −6.38085 + 23.8136i −0.486535 + 1.81577i
\(173\) 2.69896 + 1.25855i 0.205198 + 0.0956855i 0.522501 0.852639i \(-0.324999\pi\)
−0.317302 + 0.948324i \(0.602777\pi\)
\(174\) 0 0
\(175\) 0.00323151 0.000202501i 0.000244279 1.53077e-5i
\(176\) 2.84428 + 3.38968i 0.214395 + 0.255506i
\(177\) 0 0
\(178\) −5.56454 + 11.9332i −0.417080 + 0.894431i
\(179\) −8.26245 14.3110i −0.617564 1.06965i −0.989929 0.141566i \(-0.954786\pi\)
0.372365 0.928087i \(-0.378547\pi\)
\(180\) 0 0
\(181\) 4.81540 8.34051i 0.357926 0.619945i −0.629688 0.776848i \(-0.716817\pi\)
0.987614 + 0.156902i \(0.0501508\pi\)
\(182\) 0.00259561 + 0.00370692i 0.000192400 + 0.000274775i
\(183\) 0 0
\(184\) 3.20550 8.80705i 0.236313 0.649264i
\(185\) −0.299541 + 0.504341i −0.0220227 + 0.0370799i
\(186\) 0 0
\(187\) 1.60813 + 18.3810i 0.117598 + 1.34415i
\(188\) 1.41056 + 1.41056i 0.102876 + 0.102876i
\(189\) 0 0
\(190\) 6.55572 + 5.64023i 0.475602 + 0.409185i
\(191\) −0.797244 + 0.950119i −0.0576866 + 0.0687482i −0.794116 0.607766i \(-0.792066\pi\)
0.736430 + 0.676514i \(0.236510\pi\)
\(192\) 0 0
\(193\) −14.5052 10.1567i −1.04411 0.731093i −0.0800524 0.996791i \(-0.525509\pi\)
−0.964056 + 0.265698i \(0.914398\pi\)
\(194\) 17.3883 + 6.32881i 1.24840 + 0.454382i
\(195\) 0 0
\(196\) −3.44506 + 19.5379i −0.246076 + 1.39557i
\(197\) 4.39615 + 16.4067i 0.313213 + 1.16893i 0.925642 + 0.378401i \(0.123526\pi\)
−0.612429 + 0.790526i \(0.709807\pi\)
\(198\) 0 0
\(199\) 9.13371 5.27335i 0.647472 0.373818i −0.140015 0.990149i \(-0.544715\pi\)
0.787487 + 0.616331i \(0.211382\pi\)
\(200\) 8.79682 + 2.59143i 0.622029 + 0.183241i
\(201\) 0 0
\(202\) −25.2069 2.20532i −1.77355 0.155166i
\(203\) 0.00368613 0.000322495i 0.000258716 2.26347e-5i
\(204\) 0 0
\(205\) −10.8208 23.9734i −0.755759 1.67438i
\(206\) 13.0576 7.53880i 0.909765 0.525253i
\(207\) 0 0
\(208\) −1.34559 5.02181i −0.0932999 0.348200i
\(209\) 0.826290 4.68612i 0.0571557 0.324146i
\(210\) 0 0
\(211\) 0.169003 + 0.0615119i 0.0116346 + 0.00423465i 0.347831 0.937557i \(-0.386918\pi\)
−0.336196 + 0.941792i \(0.609141\pi\)
\(212\) −18.8390 13.1912i −1.29387 0.905978i
\(213\) 0 0
\(214\) 19.3383 23.0465i 1.32194 1.57543i
\(215\) −12.6857 + 14.7448i −0.865157 + 1.00558i
\(216\) 0 0
\(217\) −0.00249185 0.00249185i −0.000169158 0.000169158i
\(218\) −0.716371 8.18815i −0.0485187 0.554572i
\(219\) 0 0
\(220\) −4.23238 16.6129i −0.285347 1.12004i
\(221\) 7.41460 20.3715i 0.498760 1.37033i
\(222\) 0 0
\(223\) 10.5728 + 15.0996i 0.708010 + 1.01114i 0.998526 + 0.0542728i \(0.0172841\pi\)
−0.290516 + 0.956870i \(0.593827\pi\)
\(224\) −0.00235221 + 0.00407414i −0.000157163 + 0.000272215i
\(225\) 0 0
\(226\) 1.22863 + 2.12804i 0.0817271 + 0.141555i
\(227\) −6.61613 + 14.1883i −0.439128 + 0.941713i 0.554831 + 0.831963i \(0.312783\pi\)
−0.993959 + 0.109750i \(0.964995\pi\)
\(228\) 0 0
\(229\) 4.54463 + 5.41608i 0.300318 + 0.357904i 0.895008 0.446050i \(-0.147170\pi\)
−0.594690 + 0.803955i \(0.702725\pi\)
\(230\) 17.9823 17.5438i 1.18571 1.15680i
\(231\) 0 0
\(232\) 9.49823 + 4.42910i 0.623590 + 0.290785i
\(233\) −0.591957 + 2.20921i −0.0387804 + 0.144730i −0.982601 0.185726i \(-0.940536\pi\)
0.943821 + 0.330457i \(0.107203\pi\)
\(234\) 0 0
\(235\) 0.519996 + 1.48547i 0.0339208 + 0.0969013i
\(236\) 6.27313 + 1.10612i 0.408346 + 0.0720024i
\(237\) 0 0
\(238\) −0.00880157 + 0.00410424i −0.000570521 + 0.000266038i
\(239\) −1.33675 7.58107i −0.0864670 0.490379i −0.997030 0.0770092i \(-0.975463\pi\)
0.910563 0.413369i \(-0.135648\pi\)
\(240\) 0 0
\(241\) −7.35154 6.16868i −0.473555 0.397359i 0.374535 0.927213i \(-0.377802\pi\)
−0.848089 + 0.529853i \(0.822247\pi\)
\(242\) 5.72484 5.72484i 0.368007 0.368007i
\(243\) 0 0
\(244\) 18.6609i 1.19464i
\(245\) −9.13545 + 12.7100i −0.583642 + 0.812011i
\(246\) 0 0
\(247\) −3.20676 + 4.57972i −0.204041 + 0.291401i
\(248\) −4.21818 9.04592i −0.267855 0.574416i
\(249\) 0 0
\(250\) 18.2331 + 16.4872i 1.15316 + 1.04274i
\(251\) 4.10987 + 2.37283i 0.259413 + 0.149772i 0.624067 0.781371i \(-0.285479\pi\)
−0.364654 + 0.931143i \(0.618813\pi\)
\(252\) 0 0
\(253\) −13.3521 3.57769i −0.839440 0.224927i
\(254\) −21.5852 + 7.85635i −1.35437 + 0.492951i
\(255\) 0 0
\(256\) −3.10423 + 2.60476i −0.194015 + 0.162798i
\(257\) −1.05277 + 12.0332i −0.0656701 + 0.750612i 0.889959 + 0.456040i \(0.150733\pi\)
−0.955629 + 0.294572i \(0.904823\pi\)
\(258\) 0 0
\(259\) 5.81013e−5 0 0.000159632i 3.61024e−6 0 9.91906e-6i
\(260\) −3.74226 + 19.7919i −0.232085 + 1.22744i
\(261\) 0 0
\(262\) 30.9195 8.28485i 1.91021 0.511840i
\(263\) 7.01542 4.91225i 0.432589 0.302902i −0.336926 0.941531i \(-0.609387\pi\)
0.769515 + 0.638629i \(0.220498\pi\)
\(264\) 0 0
\(265\) −8.87774 15.8246i −0.545355 0.972095i
\(266\) 0.00246646 0.000434903i 0.000151228 2.66656e-5i
\(267\) 0 0
\(268\) 7.00513 0.612870i 0.427907 0.0374370i
\(269\) 17.3406 1.05728 0.528638 0.848847i \(-0.322703\pi\)
0.528638 + 0.848847i \(0.322703\pi\)
\(270\) 0 0
\(271\) −11.8573 −0.720278 −0.360139 0.932899i \(-0.617271\pi\)
−0.360139 + 0.932899i \(0.617271\pi\)
\(272\) 11.1147 0.972407i 0.673926 0.0589609i
\(273\) 0 0
\(274\) 15.8320 2.79161i 0.956446 0.168647i
\(275\) 2.67675 13.2581i 0.161414 0.799495i
\(276\) 0 0
\(277\) −16.3872 + 11.4745i −0.984613 + 0.689433i −0.950739 0.309993i \(-0.899673\pi\)
−0.0338740 + 0.999426i \(0.510784\pi\)
\(278\) 6.48220 1.73690i 0.388776 0.104172i
\(279\) 0 0
\(280\) 0.00219415 0.00149635i 0.000131126 8.94240e-5i
\(281\) 2.66069 + 7.31019i 0.158724 + 0.436089i 0.993407 0.114641i \(-0.0365716\pi\)
−0.834683 + 0.550730i \(0.814349\pi\)
\(282\) 0 0
\(283\) 1.30970 14.9700i 0.0778538 0.889873i −0.852384 0.522916i \(-0.824844\pi\)
0.930238 0.366957i \(-0.119600\pi\)
\(284\) 26.1518 21.9440i 1.55182 1.30213i
\(285\) 0 0
\(286\) 17.7638 6.46550i 1.05040 0.382313i
\(287\) −0.00735767 0.00197148i −0.000434310 0.000116373i
\(288\) 0 0
\(289\) 25.5680 + 14.7617i 1.50400 + 0.868336i
\(290\) 17.7904 + 21.7412i 1.04469 + 1.27669i
\(291\) 0 0
\(292\) −1.73734 3.72573i −0.101670 0.218032i
\(293\) −12.9347 + 18.4726i −0.755651 + 1.07918i 0.238495 + 0.971144i \(0.423346\pi\)
−0.994147 + 0.108038i \(0.965543\pi\)
\(294\) 0 0
\(295\) 4.08085 + 2.93316i 0.237596 + 0.170775i
\(296\) 0.481143i 0.0279659i
\(297\) 0 0
\(298\) 15.7597 15.7597i 0.912936 0.912936i
\(299\) 12.4415 + 10.4396i 0.719510 + 0.603740i
\(300\) 0 0
\(301\) 0.000978160 0.00554742i 5.63802e−5 0.000319748i
\(302\) 37.0629 17.2827i 2.13273 0.994510i
\(303\) 0 0
\(304\) −2.83362 0.499644i −0.162519 0.0286566i
\(305\) −6.38629 + 13.2655i −0.365678 + 0.759581i
\(306\) 0 0
\(307\) −1.30818 + 4.88220i −0.0746619 + 0.278642i −0.993156 0.116792i \(-0.962739\pi\)
0.918495 + 0.395434i \(0.129406\pi\)
\(308\) −0.00449965 0.00209822i −0.000256392 0.000119557i
\(309\) 0 0
\(310\) 0.330192 26.7525i 0.0187536 1.51944i
\(311\) −12.6744 15.1048i −0.718699 0.856512i 0.275805 0.961214i \(-0.411056\pi\)
−0.994504 + 0.104702i \(0.966611\pi\)
\(312\) 0 0
\(313\) −11.4671 + 24.5912i −0.648157 + 1.38998i 0.257629 + 0.966244i \(0.417059\pi\)
−0.905787 + 0.423734i \(0.860719\pi\)
\(314\) −0.355652 0.616007i −0.0200706 0.0347633i
\(315\) 0 0
\(316\) 7.41094 12.8361i 0.416898 0.722089i
\(317\) −0.143177 0.204479i −0.00804165 0.0114847i 0.815111 0.579305i \(-0.196676\pi\)
−0.823153 + 0.567820i \(0.807787\pi\)
\(318\) 0 0
\(319\) 5.28664 14.5249i 0.295995 0.813240i
\(320\) −27.5218 + 7.01157i −1.53852 + 0.391959i
\(321\) 0 0
\(322\) −0.000634107 0.00724787i −3.53374e−5 0.000403908i
\(323\) −8.48389 8.48389i −0.472056 0.472056i
\(324\) 0 0
\(325\) −9.43362 + 12.7888i −0.523283 + 0.709394i
\(326\) −7.72680 + 9.20844i −0.427948 + 0.510009i
\(327\) 0 0
\(328\) −17.6726 12.3745i −0.975808 0.683268i
\(329\) 0.000428303 0 0.000155890i 2.36131e−5 0 8.59448e-6i
\(330\) 0 0
\(331\) 0.820786 4.65491i 0.0451145 0.255857i −0.953906 0.300105i \(-0.902978\pi\)
0.999021 + 0.0442484i \(0.0140893\pi\)
\(332\) 11.7487 + 43.8467i 0.644794 + 2.40640i
\(333\) 0 0
\(334\) −35.0635 + 20.2439i −1.91859 + 1.10770i
\(335\) 5.18950 + 1.96169i 0.283533 + 0.107178i
\(336\) 0 0
\(337\) 10.7791 + 0.943046i 0.587173 + 0.0513710i 0.376872 0.926266i \(-0.377000\pi\)
0.210302 + 0.977637i \(0.432555\pi\)
\(338\) 6.34786 + 0.555366i 0.345278 + 0.0302079i
\(339\) 0 0
\(340\) −40.4340 15.2845i −2.19284 0.828919i
\(341\) −12.7488 + 7.36051i −0.690385 + 0.398594i
\(342\) 0 0
\(343\) 0.00234645 + 0.00875706i 0.000126696 + 0.000472837i
\(344\) −2.77045 + 15.7120i −0.149373 + 0.847134i
\(345\) 0 0
\(346\) 6.15274 + 2.23942i 0.330774 + 0.120392i
\(347\) −19.7058 13.7981i −1.05786 0.740723i −0.0909561 0.995855i \(-0.528992\pi\)
−0.966906 + 0.255132i \(0.917881\pi\)
\(348\) 0 0
\(349\) 0.752338 0.896601i 0.0402717 0.0479940i −0.745533 0.666469i \(-0.767805\pi\)
0.785804 + 0.618475i \(0.212249\pi\)
\(350\) 0.00703921 0.00106279i 0.000376262 5.68084e-5i
\(351\) 0 0
\(352\) 13.8961 + 13.8961i 0.740662 + 0.740662i
\(353\) −1.76656 20.1919i −0.0940245 1.07470i −0.885855 0.463963i \(-0.846427\pi\)
0.791830 0.610741i \(-0.209129\pi\)
\(354\) 0 0
\(355\) 26.1005 6.64946i 1.38527 0.352917i
\(356\) −5.80497 + 15.9490i −0.307663 + 0.845296i
\(357\) 0 0
\(358\) −20.8397 29.7622i −1.10141 1.57298i
\(359\) 13.1082 22.7040i 0.691823 1.19827i −0.279418 0.960170i \(-0.590141\pi\)
0.971240 0.238102i \(-0.0765253\pi\)
\(360\) 0 0
\(361\) −7.95290 13.7748i −0.418574 0.724991i
\(362\) 8.94895 19.1911i 0.470347 1.00866i
\(363\) 0 0
\(364\) 0.00374959 + 0.00446858i 0.000196532 + 0.000234217i
\(365\) 0.0400278 3.24309i 0.00209515 0.169751i
\(366\) 0 0
\(367\) −19.0178 8.86817i −0.992723 0.462914i −0.142761 0.989757i \(-0.545598\pi\)
−0.849963 + 0.526843i \(0.823376\pi\)
\(368\) −2.16337 + 8.07380i −0.112773 + 0.420876i
\(369\) 0 0
\(370\) −0.559443 + 1.16207i −0.0290840 + 0.0604129i
\(371\) −0.00517492 0.000912477i −0.000268668 4.73735e-5i
\(372\) 0 0
\(373\) −1.52296 + 0.710169i −0.0788560 + 0.0367712i −0.461646 0.887064i \(-0.652741\pi\)
0.382790 + 0.923835i \(0.374963\pi\)
\(374\) 7.04459 + 39.9519i 0.364267 + 2.06586i
\(375\) 0 0
\(376\) 0.988917 + 0.829800i 0.0509995 + 0.0427937i
\(377\) −12.8418 + 12.8418i −0.661386 + 0.661386i
\(378\) 0 0
\(379\) 11.6637i 0.599126i −0.954077 0.299563i \(-0.903159\pi\)
0.954077 0.299563i \(-0.0968408\pi\)
\(380\) 9.05211 + 6.50631i 0.464364 + 0.333767i
\(381\) 0 0
\(382\) −1.56415 + 2.23383i −0.0800286 + 0.114293i
\(383\) 4.44907 + 9.54105i 0.227337 + 0.487525i 0.986579 0.163283i \(-0.0522082\pi\)
−0.759243 + 0.650808i \(0.774430\pi\)
\(384\) 0 0
\(385\) −0.00248061 0.00303148i −0.000126424 0.000154499i
\(386\) −33.7173 19.4667i −1.71616 0.990828i
\(387\) 0 0
\(388\) 23.0399 + 6.17353i 1.16968 + 0.313414i
\(389\) −36.8621 + 13.4167i −1.86898 + 0.680254i −0.898557 + 0.438858i \(0.855383\pi\)
−0.970427 + 0.241396i \(0.922395\pi\)
\(390\) 0 0
\(391\) −26.6998 + 22.4038i −1.35027 + 1.13301i
\(392\) −1.11898 + 12.7900i −0.0565168 + 0.645990i
\(393\) 0 0
\(394\) 12.7729 + 35.0933i 0.643491 + 1.76798i
\(395\) 9.66114 6.58862i 0.486105 0.331509i
\(396\) 0 0
\(397\) −10.0653 + 2.69699i −0.505162 + 0.135358i −0.502395 0.864638i \(-0.667548\pi\)
−0.00276748 + 0.999996i \(0.500881\pi\)
\(398\) 18.9952 13.3006i 0.952141 0.666697i
\(399\) 0 0
\(400\) −8.01698 1.61858i −0.400849 0.0809292i
\(401\) −26.3401 + 4.64448i −1.31536 + 0.231934i −0.786931 0.617041i \(-0.788331\pi\)
−0.528433 + 0.848975i \(0.677220\pi\)
\(402\) 0 0
\(403\) 17.2304 1.50746i 0.858306 0.0750921i
\(404\) −32.6169 −1.62275
\(405\) 0 0
\(406\) 0.00813559 0.000403762
\(407\) 0.706936 0.0618489i 0.0350415 0.00306574i
\(408\) 0 0
\(409\) −33.6400 + 5.93165i −1.66339 + 0.293301i −0.924687 0.380727i \(-0.875674\pi\)
−0.738705 + 0.674028i \(0.764562\pi\)
\(410\) −28.2950 50.4357i −1.39739 2.49084i
\(411\) 0 0
\(412\) 15.9208 11.1478i 0.784359 0.549214i
\(413\) 0.00140583 0.000376692i 6.91766e−5 1.85358e-5i
\(414\) 0 0
\(415\) −6.65380 + 35.1902i −0.326622 + 1.72742i
\(416\) −7.89716 21.6973i −0.387190 1.06380i
\(417\) 0 0
\(418\) 0.911843 10.4224i 0.0445997 0.509777i
\(419\) −12.2431 + 10.2731i −0.598112 + 0.501876i −0.890838 0.454321i \(-0.849882\pi\)
0.292726 + 0.956196i \(0.405438\pi\)
\(420\) 0 0
\(421\) 29.9345 10.8953i 1.45892 0.531002i 0.513850 0.857880i \(-0.328219\pi\)
0.945067 + 0.326878i \(0.105997\pi\)
\(422\) 0.381956 + 0.102345i 0.0185933 + 0.00498206i
\(423\) 0 0
\(424\) −12.8891 7.44152i −0.625950 0.361392i
\(425\) −23.5127 24.7030i −1.14053 1.19827i
\(426\) 0 0
\(427\) 0.00180193 + 0.00386425i 8.72015e−5 + 0.000187004i
\(428\) 22.2438 31.7675i 1.07520 1.53554i
\(429\) 0 0
\(430\) −24.9601 + 34.7266i −1.20368 + 1.67466i
\(431\) 5.93676i 0.285963i 0.989725 + 0.142982i \(0.0456690\pi\)
−0.989725 + 0.142982i \(0.954331\pi\)
\(432\) 0 0
\(433\) −7.73933 + 7.73933i −0.371929 + 0.371929i −0.868179 0.496251i \(-0.834710\pi\)
0.496251 + 0.868179i \(0.334710\pi\)
\(434\) −0.00593543 0.00498042i −0.000284910 0.000239068i
\(435\) 0 0
\(436\) −1.83984 10.4342i −0.0881122 0.499709i
\(437\) 8.14644 3.79875i 0.389697 0.181719i
\(438\) 0 0
\(439\) −28.6483 5.05146i −1.36731 0.241093i −0.558665 0.829394i \(-0.688686\pi\)
−0.808642 + 0.588300i \(0.799797\pi\)
\(440\) −3.66552 10.4713i −0.174747 0.499198i
\(441\) 0 0
\(442\) 12.3366 46.0407i 0.586791 2.18993i
\(443\) −24.6030 11.4725i −1.16892 0.545077i −0.261461 0.965214i \(-0.584204\pi\)
−0.907461 + 0.420137i \(0.861982\pi\)
\(444\) 0 0
\(445\) −9.58481 + 9.35110i −0.454364 + 0.443284i
\(446\) 26.0513 + 31.0468i 1.23357 + 1.47011i
\(447\) 0 0
\(448\) −0.00347602 + 0.00745435i −0.000164227 + 0.000352185i
\(449\) 1.73698 + 3.00854i 0.0819733 + 0.141982i 0.904097 0.427326i \(-0.140544\pi\)
−0.822124 + 0.569308i \(0.807211\pi\)
\(450\) 0 0
\(451\) −15.9099 + 27.5568i −0.749169 + 1.29760i
\(452\) 1.81681 + 2.59467i 0.0854554 + 0.122043i
\(453\) 0 0
\(454\) −11.7725 + 32.3447i −0.552511 + 1.51801i
\(455\) 0.00113620 + 0.00445981i 5.32659e−5 + 0.000209079i
\(456\) 0 0
\(457\) −2.05624 23.5029i −0.0961868 1.09942i −0.878890 0.477025i \(-0.841715\pi\)
0.782703 0.622395i \(-0.213840\pi\)
\(458\) 10.9920 + 10.9920i 0.513624 + 0.513624i
\(459\) 0 0
\(460\) 21.1207 24.5489i 0.984757 1.14460i
\(461\) −5.14645 + 6.13330i −0.239694 + 0.285656i −0.872459 0.488688i \(-0.837476\pi\)
0.632765 + 0.774344i \(0.281920\pi\)
\(462\) 0 0
\(463\) 1.93475 + 1.35473i 0.0899154 + 0.0629594i 0.617670 0.786438i \(-0.288077\pi\)
−0.527754 + 0.849397i \(0.676966\pi\)
\(464\) −8.78299 3.19675i −0.407740 0.148405i
\(465\) 0 0
\(466\) −0.873225 + 4.95230i −0.0404514 + 0.229411i
\(467\) −5.32380 19.8687i −0.246356 0.919414i −0.972697 0.232079i \(-0.925447\pi\)
0.726341 0.687335i \(-0.241220\pi\)
\(468\) 0 0
\(469\) 0.00139143 0.000803341i 6.42501e−5 3.70948e-5i
\(470\) 1.42361 + 3.15399i 0.0656662 + 0.145483i
\(471\) 0 0
\(472\) 4.10653 + 0.359274i 0.189018 + 0.0165369i
\(473\) 23.4415 + 2.05087i 1.07784 + 0.0942989i
\(474\) 0 0
\(475\) 4.20825 + 7.72306i 0.193088 + 0.354358i
\(476\) −0.0108413 + 0.00625924i −0.000496911 + 0.000286892i
\(477\) 0 0
\(478\) −4.38064 16.3488i −0.200366 0.747775i
\(479\) −3.74161 + 21.2197i −0.170958 + 0.969553i 0.771748 + 0.635929i \(0.219383\pi\)
−0.942706 + 0.333624i \(0.891728\pi\)
\(480\) 0 0
\(481\) −0.783491 0.285167i −0.0357241 0.0130025i
\(482\) −17.2843 12.1026i −0.787277 0.551257i
\(483\) 0 0
\(484\) 6.70831 7.99465i 0.304923 0.363393i
\(485\) 14.2657 + 12.2735i 0.647772 + 0.557312i
\(486\) 0 0
\(487\) 2.20133 + 2.20133i 0.0997518 + 0.0997518i 0.755221 0.655470i \(-0.227529\pi\)
−0.655470 + 0.755221i \(0.727529\pi\)
\(488\) 1.05251 + 12.0302i 0.0476449 + 0.544583i
\(489\) 0 0
\(490\) −17.5739 + 29.5894i −0.793908 + 1.33671i
\(491\) 2.81965 7.74693i 0.127249 0.349614i −0.859666 0.510857i \(-0.829328\pi\)
0.986915 + 0.161243i \(0.0515503\pi\)
\(492\) 0 0
\(493\) −22.3546 31.9257i −1.00680 1.43786i
\(494\) −6.14620 + 10.6455i −0.276530 + 0.478965i
\(495\) 0 0
\(496\) 4.45078 + 7.70898i 0.199846 + 0.346144i
\(497\) 0.00329650 0.00706937i 0.000147868 0.000317105i
\(498\) 0 0
\(499\) 16.9583 + 20.2101i 0.759156 + 0.904727i 0.997794 0.0663815i \(-0.0211454\pi\)
−0.238638 + 0.971109i \(0.576701\pi\)
\(500\) 25.2661 + 19.1234i 1.12993 + 0.855225i
\(501\) 0 0
\(502\) 9.45659 + 4.40968i 0.422068 + 0.196814i
\(503\) −2.01259 + 7.51109i −0.0897370 + 0.334903i −0.996169 0.0874487i \(-0.972129\pi\)
0.906432 + 0.422352i \(0.138795\pi\)
\(504\) 0 0
\(505\) −23.1865 11.1624i −1.03178 0.496722i
\(506\) −29.9309 5.27762i −1.33059 0.234619i
\(507\) 0 0
\(508\) −26.8357 + 12.5137i −1.19064 + 0.555204i
\(509\) 5.25087 + 29.7791i 0.232741 + 1.31994i 0.847320 + 0.531082i \(0.178215\pi\)
−0.614580 + 0.788855i \(0.710674\pi\)
\(510\) 0 0
\(511\) −0.000719528 0 0.000603755i −3.18300e−5 0 2.67086e-5i
\(512\) 12.6456 12.6456i 0.558861 0.558861i
\(513\) 0 0
\(514\) 26.5583i 1.17144i
\(515\) 15.1327 2.47615i 0.666829 0.109112i
\(516\) 0 0
\(517\) 1.09209 1.55967i 0.0480300 0.0685940i
\(518\) 0.000157850 0 0.000338510i 6.93553e−6 0 1.48733e-5i
\(519\) 0 0
\(520\) −1.29625 + 12.9704i −0.0568444 + 0.568791i
\(521\) −2.44020 1.40885i −0.106907 0.0617227i 0.445593 0.895236i \(-0.352993\pi\)
−0.552500 + 0.833513i \(0.686326\pi\)
\(522\) 0 0
\(523\) 12.7481 + 3.41584i 0.557436 + 0.149364i 0.526528 0.850158i \(-0.323494\pi\)
0.0309077 + 0.999522i \(0.490160\pi\)
\(524\) 38.7741 14.1126i 1.69385 0.616512i
\(525\) 0 0
\(526\) 14.4246 12.1037i 0.628944 0.527747i
\(527\) −3.23506 + 36.9769i −0.140921 + 1.61074i
\(528\) 0 0
\(529\) −1.06428 2.92409i −0.0462731 0.127134i
\(530\) −22.4774 32.9595i −0.976357 1.43167i
\(531\) 0 0
\(532\) 0.00311841 0.000835576i 0.000135200 3.62268e-5i
\(533\) 30.6249 21.4438i 1.32651 0.928834i
\(534\) 0 0
\(535\) 26.6843 14.9701i 1.15366 0.647216i
\(536\) 4.48148 0.790206i 0.193570 0.0341317i
\(537\) 0 0
\(538\) 37.9814 3.32294i 1.63749 0.143262i
\(539\) 18.9359 0.815627
\(540\) 0 0
\(541\) −11.4416 −0.491911 −0.245956 0.969281i \(-0.579102\pi\)
−0.245956 + 0.969281i \(0.579102\pi\)
\(542\) −25.9711 + 2.27218i −1.11556 + 0.0975985i
\(543\) 0 0
\(544\) 48.7984 8.60448i 2.09222 0.368914i
\(545\) 2.26301 8.04706i 0.0969366 0.344698i
\(546\) 0 0
\(547\) 26.2542 18.3834i 1.12255 0.786018i 0.143503 0.989650i \(-0.454163\pi\)
0.979048 + 0.203632i \(0.0652745\pi\)
\(548\) 20.0168 5.36349i 0.855076 0.229117i
\(549\) 0 0
\(550\) 3.32229 29.5524i 0.141663 1.26012i
\(551\) 3.43769 + 9.44496i 0.146450 + 0.402369i
\(552\) 0 0
\(553\) 0.000295160 0.00337369i 1.25515e−5 0.000143464i
\(554\) −33.6943 + 28.2729i −1.43153 + 1.20120i
\(555\) 0 0
\(556\) 8.12889 2.95868i 0.344742 0.125476i
\(557\) 28.6955 + 7.68893i 1.21587 + 0.325791i 0.809061 0.587724i \(-0.199976\pi\)
0.406806 + 0.913515i \(0.366643\pi\)
\(558\) 0 0
\(559\) −23.9433 13.8237i −1.01269 0.584679i
\(560\) −0.00183309 + 0.00149998i −7.74621e−5 + 6.33859e-5i
\(561\) 0 0
\(562\) 7.22858 + 15.5017i 0.304919 + 0.653902i
\(563\) −3.43987 + 4.91264i −0.144973 + 0.207043i −0.885071 0.465456i \(-0.845890\pi\)
0.740098 + 0.672499i \(0.234779\pi\)
\(564\) 0 0
\(565\) 0.403547 + 2.46624i 0.0169774 + 0.103756i
\(566\) 33.0399i 1.38877i
\(567\) 0 0
\(568\) 15.6218 15.6218i 0.655475 0.655475i
\(569\) 8.00903 + 6.72037i 0.335756 + 0.281733i 0.795040 0.606557i \(-0.207450\pi\)
−0.459284 + 0.888289i \(0.651894\pi\)
\(570\) 0 0
\(571\) −1.98699 11.2688i −0.0831531 0.471584i −0.997740 0.0671948i \(-0.978595\pi\)
0.914587 0.404390i \(-0.132516\pi\)
\(572\) 22.0848 10.2983i 0.923411 0.430594i
\(573\) 0 0
\(574\) −0.0164934 0.00290823i −0.000688421 0.000121387i
\(575\) 23.4155 10.2230i 0.976492 0.426329i
\(576\) 0 0
\(577\) 11.8211 44.1170i 0.492120 1.83662i −0.0534774 0.998569i \(-0.517031\pi\)
0.545597 0.838047i \(-0.316303\pi\)
\(578\) 58.8308 + 27.4332i 2.44704 + 1.14107i
\(579\) 0 0
\(580\) 25.2879 + 25.9199i 1.05002 + 1.07627i
\(581\) 0.00666682 + 0.00794521i 0.000276586 + 0.000329623i
\(582\) 0 0
\(583\) −9.27687 + 19.8943i −0.384209 + 0.823938i
\(584\) −1.33016 2.30390i −0.0550424 0.0953362i
\(585\) 0 0
\(586\) −24.7911 + 42.9394i −1.02411 + 1.77381i
\(587\) −15.9259 22.7446i −0.657334 0.938770i 0.342666 0.939457i \(-0.388670\pi\)
−1.00000 0.000687603i \(0.999781\pi\)
\(588\) 0 0
\(589\) 3.27398 8.99519i 0.134902 0.370640i
\(590\) 9.50041 + 5.64253i 0.391126 + 0.232299i
\(591\) 0 0
\(592\) −0.0373990 0.427473i −0.00153709 0.0175690i
\(593\) −12.5526 12.5526i −0.515474 0.515474i 0.400725 0.916199i \(-0.368758\pi\)
−0.916199 + 0.400725i \(0.868758\pi\)
\(594\) 0 0
\(595\) −0.00984889 0.000739308i −0.000403765 3.03087e-5i
\(596\) 18.4671 22.0082i 0.756441 0.901491i
\(597\) 0 0
\(598\) 29.2513 + 20.4820i 1.19617 + 0.837570i
\(599\) −9.47392 3.44823i −0.387094 0.140891i 0.141140 0.989990i \(-0.454923\pi\)
−0.528234 + 0.849099i \(0.677146\pi\)
\(600\) 0 0
\(601\) −0.977209 + 5.54203i −0.0398612 + 0.226064i −0.998230 0.0594686i \(-0.981059\pi\)
0.958369 + 0.285533i \(0.0921705\pi\)
\(602\) 0.00320552 + 0.0119631i 0.000130647 + 0.000487581i
\(603\) 0 0
\(604\) 45.6522 26.3573i 1.85756 1.07246i
\(605\) 7.50476 3.38740i 0.305112 0.137717i
\(606\) 0 0
\(607\) 12.1412 + 1.06222i 0.492796 + 0.0431140i 0.330846 0.943685i \(-0.392666\pi\)
0.161950 + 0.986799i \(0.448222\pi\)
\(608\) −12.7303 1.11375i −0.516280 0.0451686i
\(609\) 0 0
\(610\) −11.4459 + 30.2794i −0.463433 + 1.22598i
\(611\) −1.93736 + 1.11853i −0.0783771 + 0.0452511i
\(612\) 0 0
\(613\) 5.69311 + 21.2470i 0.229942 + 0.858157i 0.980364 + 0.197197i \(0.0631839\pi\)
−0.750422 + 0.660960i \(0.770149\pi\)
\(614\) −1.92976 + 10.9442i −0.0778789 + 0.441673i
\(615\) 0 0
\(616\) −0.00301917 0.00109889i −0.000121646 4.42754e-5i
\(617\) 5.87642 + 4.11472i 0.236576 + 0.165652i 0.685853 0.727740i \(-0.259429\pi\)
−0.449277 + 0.893393i \(0.648318\pi\)
\(618\) 0 0
\(619\) −0.611202 + 0.728403i −0.0245663 + 0.0292770i −0.778188 0.628032i \(-0.783861\pi\)
0.753621 + 0.657309i \(0.228305\pi\)
\(620\) −2.58156 34.3909i −0.103678 1.38117i
\(621\) 0 0
\(622\) −30.6554 30.6554i −1.22917 1.22917i
\(623\) 0.000337988 0.00386323i 1.35412e−5 0.000154777i
\(624\) 0 0
\(625\) 11.4164 + 22.2411i 0.456655 + 0.889644i
\(626\) −20.4041 + 56.0599i −0.815513 + 2.24060i
\(627\) 0 0
\(628\) −0.525913 0.751081i −0.0209862 0.0299714i
\(629\) 0.894651 1.54958i 0.0356721 0.0617859i
\(630\) 0 0
\(631\) −19.0880 33.0615i −0.759883 1.31616i −0.942910 0.333048i \(-0.891923\pi\)
0.183027 0.983108i \(-0.441411\pi\)
\(632\) 4.05368 8.69315i 0.161247 0.345795i
\(633\) 0 0
\(634\) −0.352787 0.420435i −0.0140110 0.0166976i
\(635\) −23.3593 0.288311i −0.926985 0.0114413i
\(636\) 0 0
\(637\) −20.1639 9.40257i −0.798922 0.372543i
\(638\) 8.79602 32.8272i 0.348238 1.29964i
\(639\) 0 0
\(640\) −28.2735 + 9.89728i −1.11761 + 0.391224i
\(641\) 24.5606 + 4.33069i 0.970084 + 0.171052i 0.636168 0.771551i \(-0.280519\pi\)
0.333916 + 0.942603i \(0.391630\pi\)
\(642\) 0 0
\(643\) 40.2010 18.7461i 1.58537 0.739272i 0.587808 0.809000i \(-0.299991\pi\)
0.997566 + 0.0697279i \(0.0222131\pi\)
\(644\) −0.00162856 0.00923602i −6.41742e−5 0.000363950i
\(645\) 0 0
\(646\) −20.2081 16.9566i −0.795078 0.667149i
\(647\) −4.55768 + 4.55768i −0.179181 + 0.179181i −0.790999 0.611818i \(-0.790439\pi\)
0.611818 + 0.790999i \(0.290439\pi\)
\(648\) 0 0
\(649\) 6.07983i 0.238654i
\(650\) −18.2119 + 29.8192i −0.714329 + 1.16960i
\(651\) 0 0
\(652\) −8.88773 + 12.6930i −0.348070 + 0.497096i
\(653\) 2.85735 + 6.12762i 0.111817 + 0.239792i 0.954251 0.299008i \(-0.0966557\pi\)
−0.842434 + 0.538800i \(0.818878\pi\)
\(654\) 0 0
\(655\) 32.3932 + 3.23734i 1.26571 + 0.126493i
\(656\) 16.6632 + 9.62047i 0.650587 + 0.375616i
\(657\) 0 0
\(658\) 0.000967991 0 0.000259372i 3.77362e−5 0 1.01114e-5i
\(659\) 29.5176 10.7435i 1.14984 0.418508i 0.304383 0.952550i \(-0.401550\pi\)
0.845458 + 0.534042i \(0.179327\pi\)
\(660\) 0 0
\(661\) −12.6918 + 10.6497i −0.493654 + 0.414225i −0.855334 0.518078i \(-0.826648\pi\)
0.361680 + 0.932302i \(0.382203\pi\)
\(662\) 0.905769 10.3530i 0.0352037 0.402380i
\(663\) 0 0
\(664\) 10.0472 + 27.6043i 0.389905 + 1.07126i
\(665\) 0.00250275 0.000473223i 9.70526e−5 1.83508e-5i
\(666\) 0 0
\(667\) 28.2034 7.55709i 1.09204 0.292612i
\(668\) −42.7520 + 29.9353i −1.65412 + 1.15823i
\(669\) 0 0
\(670\) 11.7425 + 3.30226i 0.453654 + 0.127577i
\(671\) 17.5405 3.09287i 0.677144 0.119399i
\(672\) 0 0
\(673\) 7.80022 0.682431i 0.300676 0.0263058i 0.0641806 0.997938i \(-0.479557\pi\)
0.236496 + 0.971633i \(0.424001\pi\)
\(674\) 23.7902 0.916366
\(675\) 0 0
\(676\) 8.21392 0.315920
\(677\) −30.1802 + 2.64043i −1.15992 + 0.101480i −0.650823 0.759229i \(-0.725576\pi\)
−0.509097 + 0.860709i \(0.670021\pi\)
\(678\) 0 0
\(679\) 0.00536718 0.000946379i 0.000205974 3.63187e-5i
\(680\) −26.9290 7.57301i −1.03268 0.290412i
\(681\) 0 0
\(682\) −26.5133 + 18.5648i −1.01525 + 0.710885i
\(683\) −30.0707 + 8.05741i −1.15062 + 0.308308i −0.783214 0.621752i \(-0.786421\pi\)
−0.367408 + 0.930060i \(0.619755\pi\)
\(684\) 0 0
\(685\) 16.0650 + 3.03758i 0.613810 + 0.116060i
\(686\) 0.00681755 + 0.0187311i 0.000260295 + 0.000715155i
\(687\) 0 0
\(688\) 1.24013 14.1747i 0.0472793 0.540405i
\(689\) 19.7569 16.5780i 0.752679 0.631573i
\(690\) 0 0
\(691\) 6.70424 2.44014i 0.255041 0.0928274i −0.211336 0.977414i \(-0.567781\pi\)
0.466377 + 0.884586i \(0.345559\pi\)
\(692\) 8.15256 + 2.18447i 0.309914 + 0.0830411i
\(693\) 0 0
\(694\) −45.8059 26.4461i −1.73877 1.00388i
\(695\) 6.79115 + 0.678702i 0.257603 + 0.0257446i
\(696\) 0 0
\(697\) 33.9074 + 72.7146i 1.28433 + 2.75426i
\(698\) 1.47604 2.10801i 0.0558690 0.0797892i
\(699\) 0 0
\(700\) 0.00891991 0.00215560i 0.000337141 8.14741e-5i
\(701\) 18.1226i 0.684482i 0.939612 + 0.342241i \(0.111186\pi\)
−0.939612 + 0.342241i \(0.888814\pi\)
\(702\) 0 0
\(703\) −0.326292 + 0.326292i −0.0123064 + 0.0123064i
\(704\) 26.3202 + 22.0853i 0.991981 + 0.832371i
\(705\) 0 0
\(706\) −7.73863 43.8880i −0.291247 1.65175i
\(707\) −0.00675423 + 0.00314955i −0.000254019 + 0.000118451i
\(708\) 0 0
\(709\) −20.6080 3.63375i −0.773951 0.136469i −0.227296 0.973826i \(-0.572988\pi\)
−0.546656 + 0.837357i \(0.684099\pi\)
\(710\) 55.8940 19.5660i 2.09766 0.734298i
\(711\) 0 0
\(712\) −2.84277 + 10.6094i −0.106537 + 0.397603i
\(713\) −25.2025 11.7521i −0.943842 0.440121i
\(714\) 0 0
\(715\) 19.2238 + 0.237270i 0.718931 + 0.00887339i
\(716\) −30.1048 35.8774i −1.12507 1.34080i
\(717\) 0 0
\(718\) 24.3603 52.2408i 0.909117 1.94961i
\(719\) −4.36807 7.56572i −0.162902 0.282154i 0.773007 0.634398i \(-0.218752\pi\)
−0.935908 + 0.352244i \(0.885419\pi\)
\(720\) 0 0
\(721\) 0.00222038 0.00384581i 8.26912e−5 0.000143225i
\(722\) −20.0590 28.6472i −0.746518 1.06614i
\(723\) 0 0
\(724\) 9.33561 25.6494i 0.346955 0.953252i
\(725\) 9.10592 + 27.0800i 0.338186 + 1.00573i
\(726\) 0 0
\(727\) 3.90529 + 44.6377i 0.144839 + 1.65552i 0.626690 + 0.779268i \(0.284409\pi\)
−0.481851 + 0.876253i \(0.660035\pi\)
\(728\) 0.00266931 + 0.00266931i 9.89311e−5 + 9.89311e-5i
\(729\) 0 0
\(730\) −0.533792 7.11105i −0.0197565 0.263192i
\(731\) 38.1379 45.4510i 1.41058 1.68106i
\(732\) 0 0
\(733\) −18.4458 12.9159i −0.681312 0.477060i 0.180970 0.983489i \(-0.442076\pi\)
−0.862282 + 0.506429i \(0.830965\pi\)
\(734\) −43.3544 15.7797i −1.60024 0.582440i
\(735\) 0 0
\(736\) −6.44625 + 36.5585i −0.237612 + 1.34756i
\(737\) −1.73711 6.48298i −0.0639873 0.238804i
\(738\) 0 0
\(739\) −29.3820 + 16.9637i −1.08084 + 0.624020i −0.931122 0.364709i \(-0.881168\pi\)
−0.149714 + 0.988729i \(0.547835\pi\)
\(740\) −0.587846 + 1.55510i −0.0216096 + 0.0571667i
\(741\) 0 0
\(742\) −0.0115095 0.00100695i −0.000422528 3.69664e-5i
\(743\) −25.4881 2.22992i −0.935068 0.0818078i −0.390573 0.920572i \(-0.627723\pi\)
−0.544495 + 0.838764i \(0.683279\pi\)
\(744\) 0 0
\(745\) 20.6596 9.32506i 0.756908 0.341644i
\(746\) −3.19968 + 1.84733i −0.117148 + 0.0676357i
\(747\) 0 0
\(748\) 13.5347 + 50.5122i 0.494878 + 1.84691i
\(749\) 0.00153867 0.00872624i 5.62218e−5 0.000318850i
\(750\) 0 0
\(751\) −18.3171 6.66687i −0.668400 0.243278i −0.0145411 0.999894i \(-0.504629\pi\)
−0.653859 + 0.756617i \(0.726851\pi\)
\(752\) −0.943105 0.660369i −0.0343915 0.0240812i
\(753\) 0 0
\(754\) −25.6667 + 30.5884i −0.934726 + 1.11396i
\(755\) 41.4732 3.11319i 1.50936 0.113301i
\(756\) 0 0
\(757\) 37.3446 + 37.3446i 1.35731 + 1.35731i 0.877215 + 0.480097i \(0.159399\pi\)
0.480097 + 0.877215i \(0.340601\pi\)
\(758\) −2.23509 25.5472i −0.0811822 0.927917i
\(759\) 0 0
\(760\) 6.20265 + 3.68391i 0.224994 + 0.133630i
\(761\) −13.8978 + 38.1838i −0.503793 + 1.38416i 0.383750 + 0.923437i \(0.374632\pi\)
−0.887543 + 0.460724i \(0.847590\pi\)
\(762\) 0 0
\(763\) −0.00138854 0.00198304i −5.02685e−5 7.17908e-5i
\(764\) −1.75761 + 3.04427i −0.0635881 + 0.110138i
\(765\) 0 0
\(766\) 11.5732 + 20.0453i 0.418156 + 0.724267i
\(767\) −3.01892 + 6.47410i −0.109007 + 0.233766i
\(768\) 0 0
\(769\) 1.03060 + 1.22823i 0.0371646 + 0.0442910i 0.784307 0.620373i \(-0.213019\pi\)
−0.747142 + 0.664664i \(0.768575\pi\)
\(770\) −0.00601423 0.00616454i −0.000216738 0.000222155i
\(771\) 0 0
\(772\) −45.4846 21.2098i −1.63703 0.763358i
\(773\) 8.72934 32.5784i 0.313973 1.17176i −0.610970 0.791654i \(-0.709220\pi\)
0.924942 0.380108i \(-0.124113\pi\)
\(774\) 0 0
\(775\) 9.93442 25.3311i 0.356855 0.909919i
\(776\) 15.2015 + 2.68044i 0.545702 + 0.0962220i
\(777\) 0 0
\(778\) −78.1685 + 36.4506i −2.80248 + 1.30682i
\(779\) −3.59298 20.3768i −0.128732 0.730074i
\(780\) 0 0
\(781\) −24.9609 20.9447i −0.893172 0.749460i
\(782\) −54.1877 + 54.1877i −1.93775 + 1.93775i
\(783\) 0 0
\(784\) 11.4502i 0.408937i
\(785\) −0.116815 0.713906i −0.00416932 0.0254804i
\(786\) 0 0