Properties

Label 405.2.r.a.368.10
Level $405$
Weight $2$
Character 405.368
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 368.10
Character \(\chi\) \(=\) 405.368
Dual form 405.2.r.a.197.10

$q$-expansion

\(f(q)\) \(=\) \(q+(0.639298 + 0.0559313i) q^{2} +(-1.56404 - 0.275783i) q^{4} +(1.26232 - 1.84568i) q^{5} +(3.52875 + 2.47086i) q^{7} +(-2.22421 - 0.595975i) q^{8} +O(q^{10})\) \(q+(0.639298 + 0.0559313i) q^{2} +(-1.56404 - 0.275783i) q^{4} +(1.26232 - 1.84568i) q^{5} +(3.52875 + 2.47086i) q^{7} +(-2.22421 - 0.595975i) q^{8} +(0.910229 - 1.10934i) q^{10} +(0.157893 - 0.433806i) q^{11} +(-0.462462 - 5.28596i) q^{13} +(2.11772 + 1.77698i) q^{14} +(1.59619 + 0.580964i) q^{16} +(4.93057 - 1.32114i) q^{17} +(1.03667 - 0.598524i) q^{19} +(-2.48333 + 2.53860i) q^{20} +(0.125204 - 0.268500i) q^{22} +(1.57814 + 2.25381i) q^{23} +(-1.81310 - 4.65968i) q^{25} -3.40517i q^{26} +(-4.83770 - 4.83770i) q^{28} +(0.00462297 - 0.00387914i) q^{29} +(-0.387533 + 2.19781i) q^{31} +(5.16180 + 2.40699i) q^{32} +(3.22599 - 0.568830i) q^{34} +(9.01483 - 3.39395i) q^{35} +(-1.94341 - 7.25290i) q^{37} +(0.696220 - 0.324653i) q^{38} +(-3.90764 + 3.35288i) q^{40} +(-3.02828 + 3.60897i) q^{41} +(0.806157 + 1.72881i) q^{43} +(-0.366587 + 0.634947i) q^{44} +(0.882840 + 1.52912i) q^{46} +(-6.47343 + 9.24502i) q^{47} +(3.95281 + 10.8602i) q^{49} +(-0.898490 - 3.08033i) q^{50} +(-0.734468 + 8.39501i) q^{52} +(-3.94023 + 3.94023i) q^{53} +(-0.601359 - 0.839022i) q^{55} +(-6.37611 - 7.59875i) q^{56} +(0.00317242 - 0.00222135i) q^{58} +(0.388624 - 0.141448i) q^{59} +(0.399307 + 2.26458i) q^{61} +(-0.370675 + 1.38338i) q^{62} +(0.223194 + 0.128861i) q^{64} +(-10.3400 - 5.81901i) q^{65} +(-5.84619 + 0.511475i) q^{67} +(-8.07597 + 0.706556i) q^{68} +(5.95299 - 1.66553i) q^{70} +(-0.648656 - 0.374502i) q^{71} +(-2.97508 + 11.1032i) q^{73} +(-0.836752 - 4.74546i) q^{74} +(-1.78647 + 0.650220i) q^{76} +(1.62904 - 1.14066i) q^{77} +(-1.01095 - 1.20481i) q^{79} +(3.08717 - 2.21269i) q^{80} +(-2.13783 + 2.13783i) q^{82} +(-0.930629 + 10.6371i) q^{83} +(3.78554 - 10.7680i) q^{85} +(0.418680 + 1.15031i) q^{86} +(-0.609724 + 0.870776i) q^{88} +(-6.36010 - 11.0160i) q^{89} +(11.4289 - 19.7955i) q^{91} +(-1.84671 - 3.96028i) q^{92} +(-4.65554 + 5.54825i) q^{94} +(0.203927 - 2.66890i) q^{95} +(-7.76434 + 3.62057i) q^{97} +(1.91959 + 7.16401i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{5}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.639298 + 0.0559313i 0.452052 + 0.0395494i 0.310909 0.950440i \(-0.399367\pi\)
0.141143 + 0.989989i \(0.454922\pi\)
\(3\) 0 0
\(4\) −1.56404 0.275783i −0.782021 0.137891i
\(5\) 1.26232 1.84568i 0.564526 0.825415i
\(6\) 0 0
\(7\) 3.52875 + 2.47086i 1.33374 + 0.933897i 0.999962 0.00875387i \(-0.00278648\pi\)
0.333781 + 0.942651i \(0.391675\pi\)
\(8\) −2.22421 0.595975i −0.786377 0.210709i
\(9\) 0 0
\(10\) 0.910229 1.10934i 0.287840 0.350804i
\(11\) 0.157893 0.433806i 0.0476064 0.130798i −0.913611 0.406590i \(-0.866718\pi\)
0.961217 + 0.275792i \(0.0889401\pi\)
\(12\) 0 0
\(13\) −0.462462 5.28596i −0.128264 1.46606i −0.738720 0.674012i \(-0.764570\pi\)
0.610457 0.792050i \(-0.290986\pi\)
\(14\) 2.11772 + 1.77698i 0.565986 + 0.474918i
\(15\) 0 0
\(16\) 1.59619 + 0.580964i 0.399047 + 0.145241i
\(17\) 4.93057 1.32114i 1.19584 0.320424i 0.394647 0.918833i \(-0.370867\pi\)
0.801191 + 0.598409i \(0.204200\pi\)
\(18\) 0 0
\(19\) 1.03667 0.598524i 0.237829 0.137311i −0.376349 0.926478i \(-0.622821\pi\)
0.614179 + 0.789167i \(0.289487\pi\)
\(20\) −2.48333 + 2.53860i −0.555289 + 0.567649i
\(21\) 0 0
\(22\) 0.125204 0.268500i 0.0266935 0.0572444i
\(23\) 1.57814 + 2.25381i 0.329064 + 0.469952i 0.949259 0.314496i \(-0.101835\pi\)
−0.620195 + 0.784448i \(0.712946\pi\)
\(24\) 0 0
\(25\) −1.81310 4.65968i −0.362621 0.931937i
\(26\) 3.40517i 0.667808i
\(27\) 0 0
\(28\) −4.83770 4.83770i −0.914239 0.914239i
\(29\) 0.00462297 0.00387914i 0.000858465 0.000720337i −0.642358 0.766404i \(-0.722044\pi\)
0.643217 + 0.765684i \(0.277599\pi\)
\(30\) 0 0
\(31\) −0.387533 + 2.19781i −0.0696030 + 0.394738i 0.930026 + 0.367494i \(0.119784\pi\)
−0.999629 + 0.0272441i \(0.991327\pi\)
\(32\) 5.16180 + 2.40699i 0.912486 + 0.425499i
\(33\) 0 0
\(34\) 3.22599 0.568830i 0.553253 0.0975535i
\(35\) 9.01483 3.39395i 1.52379 0.573683i
\(36\) 0 0
\(37\) −1.94341 7.25290i −0.319494 1.19237i −0.919732 0.392547i \(-0.871594\pi\)
0.600238 0.799822i \(-0.295073\pi\)
\(38\) 0.696220 0.324653i 0.112942 0.0526656i
\(39\) 0 0
\(40\) −3.90764 + 3.35288i −0.617853 + 0.530137i
\(41\) −3.02828 + 3.60897i −0.472939 + 0.563626i −0.948793 0.315898i \(-0.897694\pi\)
0.475855 + 0.879524i \(0.342139\pi\)
\(42\) 0 0
\(43\) 0.806157 + 1.72881i 0.122938 + 0.263641i 0.958139 0.286304i \(-0.0924266\pi\)
−0.835201 + 0.549945i \(0.814649\pi\)
\(44\) −0.366587 + 0.634947i −0.0552651 + 0.0957219i
\(45\) 0 0
\(46\) 0.882840 + 1.52912i 0.130168 + 0.225457i
\(47\) −6.47343 + 9.24502i −0.944247 + 1.34853i −0.00695690 + 0.999976i \(0.502214\pi\)
−0.937290 + 0.348549i \(0.886674\pi\)
\(48\) 0 0
\(49\) 3.95281 + 10.8602i 0.564687 + 1.55146i
\(50\) −0.898490 3.08033i −0.127066 0.435625i
\(51\) 0 0
\(52\) −0.734468 + 8.39501i −0.101852 + 1.16418i
\(53\) −3.94023 + 3.94023i −0.541233 + 0.541233i −0.923890 0.382657i \(-0.875009\pi\)
0.382657 + 0.923890i \(0.375009\pi\)
\(54\) 0 0
\(55\) −0.601359 0.839022i −0.0810872 0.113134i
\(56\) −6.37611 7.59875i −0.852044 1.01543i
\(57\) 0 0
\(58\) 0.00317242 0.00222135i 0.000416559 0.000291678i
\(59\) 0.388624 0.141448i 0.0505945 0.0184149i −0.316599 0.948559i \(-0.602541\pi\)
0.367193 + 0.930145i \(0.380319\pi\)
\(60\) 0 0
\(61\) 0.399307 + 2.26458i 0.0511260 + 0.289950i 0.999641 0.0267812i \(-0.00852575\pi\)
−0.948515 + 0.316731i \(0.897415\pi\)
\(62\) −0.370675 + 1.38338i −0.0470758 + 0.175689i
\(63\) 0 0
\(64\) 0.223194 + 0.128861i 0.0278993 + 0.0161077i
\(65\) −10.3400 5.81901i −1.28252 0.721759i
\(66\) 0 0
\(67\) −5.84619 + 0.511475i −0.714226 + 0.0624866i −0.438476 0.898743i \(-0.644482\pi\)
−0.275750 + 0.961230i \(0.588926\pi\)
\(68\) −8.07597 + 0.706556i −0.979355 + 0.0856824i
\(69\) 0 0
\(70\) 5.95299 1.66553i 0.711518 0.199069i
\(71\) −0.648656 0.374502i −0.0769813 0.0444452i 0.461015 0.887392i \(-0.347485\pi\)
−0.537997 + 0.842947i \(0.680819\pi\)
\(72\) 0 0
\(73\) −2.97508 + 11.1032i −0.348207 + 1.29953i 0.540614 + 0.841271i \(0.318192\pi\)
−0.888821 + 0.458255i \(0.848475\pi\)
\(74\) −0.836752 4.74546i −0.0972705 0.551648i
\(75\) 0 0
\(76\) −1.78647 + 0.650220i −0.204922 + 0.0745854i
\(77\) 1.62904 1.14066i 0.185646 0.129991i
\(78\) 0 0
\(79\) −1.01095 1.20481i −0.113741 0.135551i 0.706170 0.708043i \(-0.250422\pi\)
−0.819911 + 0.572491i \(0.805977\pi\)
\(80\) 3.08717 2.21269i 0.345156 0.247387i
\(81\) 0 0
\(82\) −2.13783 + 2.13783i −0.236084 + 0.236084i
\(83\) −0.930629 + 10.6371i −0.102150 + 1.16758i 0.756139 + 0.654411i \(0.227083\pi\)
−0.858289 + 0.513167i \(0.828472\pi\)
\(84\) 0 0
\(85\) 3.78554 10.7680i 0.410599 1.16795i
\(86\) 0.418680 + 1.15031i 0.0451474 + 0.124041i
\(87\) 0 0
\(88\) −0.609724 + 0.870776i −0.0649968 + 0.0928250i
\(89\) −6.36010 11.0160i −0.674169 1.16770i −0.976711 0.214559i \(-0.931168\pi\)
0.302542 0.953136i \(-0.402165\pi\)
\(90\) 0 0
\(91\) 11.4289 19.7955i 1.19808 2.07513i
\(92\) −1.84671 3.96028i −0.192533 0.412888i
\(93\) 0 0
\(94\) −4.65554 + 5.54825i −0.480182 + 0.572259i
\(95\) 0.203927 2.66890i 0.0209224 0.273824i
\(96\) 0 0
\(97\) −7.76434 + 3.62057i −0.788349 + 0.367613i −0.774729 0.632294i \(-0.782114\pi\)
−0.0136208 + 0.999907i \(0.504336\pi\)
\(98\) 1.91959 + 7.16401i 0.193908 + 0.723675i
\(99\) 0 0
\(100\) 1.55071 + 7.78797i 0.155071 + 0.778797i
\(101\) 15.4590 2.72585i 1.53823 0.271232i 0.660663 0.750682i \(-0.270275\pi\)
0.877569 + 0.479450i \(0.159164\pi\)
\(102\) 0 0
\(103\) −12.6867 5.91592i −1.25006 0.582912i −0.318992 0.947758i \(-0.603344\pi\)
−0.931068 + 0.364845i \(0.881122\pi\)
\(104\) −2.12169 + 12.0327i −0.208049 + 1.17990i
\(105\) 0 0
\(106\) −2.73936 + 2.29860i −0.266071 + 0.223260i
\(107\) −2.86472 2.86472i −0.276943 0.276943i 0.554945 0.831887i \(-0.312739\pi\)
−0.831887 + 0.554945i \(0.812739\pi\)
\(108\) 0 0
\(109\) 6.64284i 0.636269i 0.948046 + 0.318134i \(0.103056\pi\)
−0.948046 + 0.318134i \(0.896944\pi\)
\(110\) −0.337520 0.570019i −0.0321812 0.0543492i
\(111\) 0 0
\(112\) 4.19706 + 5.99403i 0.396585 + 0.566382i
\(113\) 2.96857 6.36611i 0.279259 0.598874i −0.715783 0.698322i \(-0.753930\pi\)
0.995043 + 0.0994488i \(0.0317080\pi\)
\(114\) 0 0
\(115\) 6.15193 0.0677124i 0.573671 0.00631422i
\(116\) −0.00830033 + 0.00479220i −0.000770666 + 0.000444944i
\(117\) 0 0
\(118\) 0.256358 0.0686908i 0.0235996 0.00632350i
\(119\) 20.6631 + 7.52076i 1.89418 + 0.689427i
\(120\) 0 0
\(121\) 8.26323 + 6.93367i 0.751203 + 0.630334i
\(122\) 0.128615 + 1.47008i 0.0116443 + 0.133094i
\(123\) 0 0
\(124\) 1.21224 3.33059i 0.108862 0.299096i
\(125\) −10.8890 2.53559i −0.973944 0.226790i
\(126\) 0 0
\(127\) 8.09882 + 2.17007i 0.718654 + 0.192563i 0.599571 0.800322i \(-0.295338\pi\)
0.119083 + 0.992884i \(0.462005\pi\)
\(128\) −9.19534 6.43865i −0.812761 0.569102i
\(129\) 0 0
\(130\) −6.28487 4.29841i −0.551219 0.376995i
\(131\) 11.2646 + 1.98625i 0.984193 + 0.173540i 0.642512 0.766276i \(-0.277892\pi\)
0.341682 + 0.939816i \(0.389004\pi\)
\(132\) 0 0
\(133\) 5.13704 + 0.449432i 0.445437 + 0.0389707i
\(134\) −3.76606 −0.325338
\(135\) 0 0
\(136\) −11.7540 −1.00790
\(137\) −10.2700 0.898508i −0.877424 0.0767647i −0.360463 0.932773i \(-0.617381\pi\)
−0.516961 + 0.856009i \(0.672937\pi\)
\(138\) 0 0
\(139\) −1.70385 0.300434i −0.144518 0.0254825i 0.100921 0.994894i \(-0.467821\pi\)
−0.245439 + 0.969412i \(0.578932\pi\)
\(140\) −15.0356 + 2.82215i −1.27074 + 0.238515i
\(141\) 0 0
\(142\) −0.393738 0.275698i −0.0330417 0.0231361i
\(143\) −2.36610 0.633995i −0.197863 0.0530173i
\(144\) 0 0
\(145\) −0.00132399 0.0134293i −0.000109952 0.00111524i
\(146\) −2.52298 + 6.93182i −0.208803 + 0.573681i
\(147\) 0 0
\(148\) 1.03935 + 11.8798i 0.0854339 + 0.976513i
\(149\) 3.51771 + 2.95171i 0.288182 + 0.241813i 0.775405 0.631464i \(-0.217546\pi\)
−0.487223 + 0.873277i \(0.661990\pi\)
\(150\) 0 0
\(151\) −4.16351 1.51539i −0.338821 0.123321i 0.167005 0.985956i \(-0.446590\pi\)
−0.505827 + 0.862635i \(0.668813\pi\)
\(152\) −2.66249 + 0.713411i −0.215956 + 0.0578653i
\(153\) 0 0
\(154\) 1.10524 0.638110i 0.0890627 0.0514204i
\(155\) 3.56727 + 3.48960i 0.286530 + 0.280291i
\(156\) 0 0
\(157\) 0.351788 0.754412i 0.0280757 0.0602086i −0.891770 0.452489i \(-0.850536\pi\)
0.919846 + 0.392281i \(0.128314\pi\)
\(158\) −0.578913 0.826774i −0.0460559 0.0657746i
\(159\) 0 0
\(160\) 10.9584 6.48867i 0.866336 0.512974i
\(161\) 11.8525i 0.934107i
\(162\) 0 0
\(163\) −10.1572 10.1572i −0.795571 0.795571i 0.186823 0.982394i \(-0.440181\pi\)
−0.982394 + 0.186823i \(0.940181\pi\)
\(164\) 5.73166 4.80943i 0.447567 0.375554i
\(165\) 0 0
\(166\) −1.18990 + 6.74824i −0.0923540 + 0.523765i
\(167\) 20.3353 + 9.48250i 1.57359 + 0.733778i 0.996555 0.0829395i \(-0.0264308\pi\)
0.577038 + 0.816718i \(0.304209\pi\)
\(168\) 0 0
\(169\) −14.9250 + 2.63168i −1.14808 + 0.202437i
\(170\) 3.02235 6.67221i 0.231804 0.511735i
\(171\) 0 0
\(172\) −0.784088 2.92626i −0.0597861 0.223125i
\(173\) −2.09324 + 0.976093i −0.159146 + 0.0742110i −0.500559 0.865702i \(-0.666872\pi\)
0.341413 + 0.939913i \(0.389094\pi\)
\(174\) 0 0
\(175\) 5.11543 20.9228i 0.386690 1.58161i
\(176\) 0.504052 0.600706i 0.0379943 0.0452799i
\(177\) 0 0
\(178\) −3.44986 7.39824i −0.258578 0.554522i
\(179\) 10.3891 17.9945i 0.776520 1.34497i −0.157416 0.987532i \(-0.550316\pi\)
0.933936 0.357440i \(-0.116350\pi\)
\(180\) 0 0
\(181\) 1.61486 + 2.79701i 0.120031 + 0.207900i 0.919780 0.392435i \(-0.128367\pi\)
−0.799748 + 0.600335i \(0.795034\pi\)
\(182\) 8.41369 12.0160i 0.623664 0.890685i
\(183\) 0 0
\(184\) −2.16689 5.95348i −0.159745 0.438896i
\(185\) −15.8398 5.56855i −1.16456 0.409408i
\(186\) 0 0
\(187\) 0.205381 2.34751i 0.0150189 0.171667i
\(188\) 12.6743 12.6743i 0.924372 0.924372i
\(189\) 0 0
\(190\) 0.279645 1.69482i 0.0202876 0.122955i
\(191\) −0.296698 0.353591i −0.0214683 0.0255850i 0.755203 0.655490i \(-0.227538\pi\)
−0.776672 + 0.629905i \(0.783094\pi\)
\(192\) 0 0
\(193\) −1.86360 + 1.30491i −0.134145 + 0.0939292i −0.638723 0.769437i \(-0.720537\pi\)
0.504578 + 0.863366i \(0.331648\pi\)
\(194\) −5.16623 + 1.88035i −0.370914 + 0.135001i
\(195\) 0 0
\(196\) −3.18729 18.0760i −0.227663 1.29114i
\(197\) −6.91110 + 25.7926i −0.492396 + 1.83765i 0.0517571 + 0.998660i \(0.483518\pi\)
−0.544153 + 0.838986i \(0.683149\pi\)
\(198\) 0 0
\(199\) 20.6539 + 11.9246i 1.46412 + 0.845309i 0.999198 0.0400428i \(-0.0127494\pi\)
0.464921 + 0.885352i \(0.346083\pi\)
\(200\) 1.25566 + 11.4447i 0.0887889 + 0.809261i
\(201\) 0 0
\(202\) 10.0354 0.877983i 0.706088 0.0617747i
\(203\) 0.0258981 0.00226579i 0.00181769 0.000159027i
\(204\) 0 0
\(205\) 2.83836 + 10.1449i 0.198240 + 0.708552i
\(206\) −7.77970 4.49161i −0.542038 0.312946i
\(207\) 0 0
\(208\) 2.33278 8.70605i 0.161749 0.603656i
\(209\) −0.0959604 0.544219i −0.00663772 0.0376444i
\(210\) 0 0
\(211\) 20.3867 7.42015i 1.40348 0.510825i 0.474270 0.880379i \(-0.342712\pi\)
0.929209 + 0.369555i \(0.120490\pi\)
\(212\) 7.24934 5.07605i 0.497887 0.348624i
\(213\) 0 0
\(214\) −1.67118 1.99163i −0.114239 0.136145i
\(215\) 4.20846 + 0.694397i 0.287015 + 0.0473575i
\(216\) 0 0
\(217\) −6.79799 + 6.79799i −0.461477 + 0.461477i
\(218\) −0.371543 + 4.24675i −0.0251640 + 0.287626i
\(219\) 0 0
\(220\) 0.709163 + 1.47811i 0.0478118 + 0.0996542i
\(221\) −9.26370 25.4518i −0.623144 1.71207i
\(222\) 0 0
\(223\) −6.30605 + 9.00598i −0.422285 + 0.603085i −0.972774 0.231757i \(-0.925552\pi\)
0.550489 + 0.834842i \(0.314441\pi\)
\(224\) 12.2674 + 21.2477i 0.819649 + 1.41967i
\(225\) 0 0
\(226\) 2.25386 3.90381i 0.149925 0.259677i
\(227\) −4.18215 8.96865i −0.277579 0.595270i 0.717252 0.696814i \(-0.245400\pi\)
−0.994831 + 0.101544i \(0.967622\pi\)
\(228\) 0 0
\(229\) 6.25137 7.45009i 0.413102 0.492316i −0.518866 0.854855i \(-0.673646\pi\)
0.931968 + 0.362540i \(0.118090\pi\)
\(230\) 3.93670 + 0.300797i 0.259579 + 0.0198340i
\(231\) 0 0
\(232\) −0.0125943 + 0.00587283i −0.000826858 + 0.000385570i
\(233\) 2.61861 + 9.77279i 0.171551 + 0.640236i 0.997113 + 0.0759259i \(0.0241913\pi\)
−0.825563 + 0.564311i \(0.809142\pi\)
\(234\) 0 0
\(235\) 8.89186 + 23.6181i 0.580041 + 1.54067i
\(236\) −0.646833 + 0.114054i −0.0421053 + 0.00742429i
\(237\) 0 0
\(238\) 12.7892 + 5.96371i 0.829002 + 0.386570i
\(239\) 0.554723 3.14599i 0.0358821 0.203497i −0.961596 0.274468i \(-0.911498\pi\)
0.997478 + 0.0709702i \(0.0226095\pi\)
\(240\) 0 0
\(241\) −15.5334 + 13.0341i −1.00060 + 0.839600i −0.987067 0.160309i \(-0.948751\pi\)
−0.0135291 + 0.999908i \(0.504307\pi\)
\(242\) 4.89485 + 4.89485i 0.314653 + 0.314653i
\(243\) 0 0
\(244\) 3.65203i 0.233797i
\(245\) 25.0343 + 6.41346i 1.59938 + 0.409741i
\(246\) 0 0
\(247\) −3.64320 5.20303i −0.231811 0.331061i
\(248\) 2.17179 4.65743i 0.137909 0.295747i
\(249\) 0 0
\(250\) −6.81951 2.23003i −0.431303 0.141040i
\(251\) −12.3046 + 7.10409i −0.776662 + 0.448406i −0.835246 0.549876i \(-0.814675\pi\)
0.0585840 + 0.998282i \(0.481341\pi\)
\(252\) 0 0
\(253\) 1.22689 0.328745i 0.0771341 0.0206680i
\(254\) 5.05618 + 1.84030i 0.317253 + 0.115471i
\(255\) 0 0
\(256\) −5.91329 4.96184i −0.369581 0.310115i
\(257\) −2.46595 28.1859i −0.153822 1.75819i −0.545522 0.838096i \(-0.683669\pi\)
0.391701 0.920093i \(-0.371887\pi\)
\(258\) 0 0
\(259\) 11.0631 30.3956i 0.687426 1.88869i
\(260\) 14.5674 + 11.9528i 0.903432 + 0.741279i
\(261\) 0 0
\(262\) 7.09034 + 1.89985i 0.438043 + 0.117373i
\(263\) 4.29988 + 3.01081i 0.265142 + 0.185655i 0.698586 0.715526i \(-0.253813\pi\)
−0.433444 + 0.901181i \(0.642702\pi\)
\(264\) 0 0
\(265\) 2.29860 + 12.2463i 0.141202 + 0.752282i
\(266\) 3.25896 + 0.574642i 0.199819 + 0.0352336i
\(267\) 0 0
\(268\) 9.28474 + 0.812310i 0.567156 + 0.0496197i
\(269\) −11.2342 −0.684961 −0.342480 0.939525i \(-0.611267\pi\)
−0.342480 + 0.939525i \(0.611267\pi\)
\(270\) 0 0
\(271\) −15.3871 −0.934699 −0.467349 0.884073i \(-0.654791\pi\)
−0.467349 + 0.884073i \(0.654791\pi\)
\(272\) 8.63764 + 0.755696i 0.523734 + 0.0458208i
\(273\) 0 0
\(274\) −6.51532 1.14883i −0.393605 0.0694032i
\(275\) −2.30768 + 0.0508059i −0.139158 + 0.00306371i
\(276\) 0 0
\(277\) −13.4512 9.41860i −0.808202 0.565909i 0.0948247 0.995494i \(-0.469771\pi\)
−0.903026 + 0.429585i \(0.858660\pi\)
\(278\) −1.07246 0.287365i −0.0643219 0.0172350i
\(279\) 0 0
\(280\) −22.0736 + 2.17624i −1.31915 + 0.130055i
\(281\) 3.30030 9.06751i 0.196880 0.540922i −0.801490 0.598009i \(-0.795959\pi\)
0.998369 + 0.0570865i \(0.0181811\pi\)
\(282\) 0 0
\(283\) −1.35265 15.4609i −0.0804068 0.919054i −0.924080 0.382198i \(-0.875167\pi\)
0.843674 0.536856i \(-0.180388\pi\)
\(284\) 0.911245 + 0.764625i 0.0540724 + 0.0453721i
\(285\) 0 0
\(286\) −1.47718 0.537651i −0.0873477 0.0317920i
\(287\) −19.6033 + 5.25269i −1.15715 + 0.310057i
\(288\) 0 0
\(289\) 7.84266 4.52796i 0.461333 0.266351i
\(290\) −9.53107e−5 0.00865934i −5.59684e−6 0.000508494i
\(291\) 0 0
\(292\) 7.71521 16.5453i 0.451499 0.968242i
\(293\) −5.53310 7.90208i −0.323247 0.461645i 0.624335 0.781157i \(-0.285370\pi\)
−0.947582 + 0.319512i \(0.896481\pi\)
\(294\) 0 0
\(295\) 0.229500 0.895829i 0.0133620 0.0521572i
\(296\) 17.2902i 1.00497i
\(297\) 0 0
\(298\) 2.08377 + 2.08377i 0.120709 + 0.120709i
\(299\) 11.1837 9.38426i 0.646772 0.542706i
\(300\) 0 0
\(301\) −1.42692 + 8.09244i −0.0822460 + 0.466440i
\(302\) −2.57696 1.20166i −0.148288 0.0691476i
\(303\) 0 0
\(304\) 2.00245 0.353085i 0.114848 0.0202508i
\(305\) 4.68376 + 2.12163i 0.268191 + 0.121484i
\(306\) 0 0
\(307\) −1.13471 4.23478i −0.0647610 0.241692i 0.925956 0.377631i \(-0.123261\pi\)
−0.990717 + 0.135940i \(0.956595\pi\)
\(308\) −2.86246 + 1.33479i −0.163104 + 0.0760566i
\(309\) 0 0
\(310\) 2.08537 + 2.43042i 0.118441 + 0.138038i
\(311\) 5.33012 6.35219i 0.302243 0.360199i −0.593451 0.804870i \(-0.702235\pi\)
0.895694 + 0.444671i \(0.146679\pi\)
\(312\) 0 0
\(313\) 4.37462 + 9.38140i 0.247268 + 0.530268i 0.990293 0.138996i \(-0.0443874\pi\)
−0.743025 + 0.669264i \(0.766610\pi\)
\(314\) 0.267093 0.462618i 0.0150729 0.0261070i
\(315\) 0 0
\(316\) 1.24891 + 2.16317i 0.0702566 + 0.121688i
\(317\) 0.779004 1.11253i 0.0437532 0.0624861i −0.796679 0.604402i \(-0.793412\pi\)
0.840433 + 0.541916i \(0.182301\pi\)
\(318\) 0 0
\(319\) −0.000952860 0.00261796i −5.33499e−5 0.000146578i
\(320\) 0.519580 0.249282i 0.0290454 0.0139353i
\(321\) 0 0
\(322\) −0.662925 + 7.57727i −0.0369434 + 0.422265i
\(323\) 4.32066 4.32066i 0.240408 0.240408i
\(324\) 0 0
\(325\) −23.7924 + 11.7389i −1.31977 + 0.651158i
\(326\) −5.92535 7.06156i −0.328175 0.391104i
\(327\) 0 0
\(328\) 8.88639 6.22232i 0.490669 0.343570i
\(329\) −45.6863 + 16.6284i −2.51877 + 0.916756i
\(330\) 0 0
\(331\) 1.24032 + 7.03423i 0.0681744 + 0.386636i 0.999734 + 0.0230485i \(0.00733722\pi\)
−0.931560 + 0.363588i \(0.881552\pi\)
\(332\) 4.38908 16.3803i 0.240882 0.898985i
\(333\) 0 0
\(334\) 12.4699 + 7.19952i 0.682324 + 0.393940i
\(335\) −6.43573 + 11.4359i −0.351622 + 0.624808i
\(336\) 0 0
\(337\) 28.6457 2.50617i 1.56043 0.136520i 0.726023 0.687671i \(-0.241367\pi\)
0.834406 + 0.551151i \(0.185811\pi\)
\(338\) −9.68871 + 0.847653i −0.526997 + 0.0461062i
\(339\) 0 0
\(340\) −8.89037 + 15.7976i −0.482148 + 0.856744i
\(341\) 0.892235 + 0.515132i 0.0483172 + 0.0278960i
\(342\) 0 0
\(343\) −5.08105 + 18.9628i −0.274351 + 1.02389i
\(344\) −0.762735 4.32568i −0.0411239 0.233225i
\(345\) 0 0
\(346\) −1.39280 + 0.506936i −0.0748772 + 0.0272531i
\(347\) −24.1565 + 16.9146i −1.29679 + 0.908021i −0.998914 0.0465844i \(-0.985166\pi\)
−0.297874 + 0.954605i \(0.596277\pi\)
\(348\) 0 0
\(349\) −13.2402 15.7790i −0.708730 0.844632i 0.284754 0.958601i \(-0.408088\pi\)
−0.993484 + 0.113969i \(0.963644\pi\)
\(350\) 4.44052 13.0898i 0.237356 0.699678i
\(351\) 0 0
\(352\) 1.85918 1.85918i 0.0990944 0.0990944i
\(353\) −0.152839 + 1.74696i −0.00813482 + 0.0929814i −0.999177 0.0405701i \(-0.987083\pi\)
0.991042 + 0.133552i \(0.0426382\pi\)
\(354\) 0 0
\(355\) −1.51002 + 0.724474i −0.0801437 + 0.0384511i
\(356\) 6.90944 + 18.9835i 0.366199 + 1.00612i
\(357\) 0 0
\(358\) 7.64820 10.9228i 0.404220 0.577286i
\(359\) −9.41628 16.3095i −0.496972 0.860781i 0.503022 0.864274i \(-0.332222\pi\)
−0.999994 + 0.00349274i \(0.998888\pi\)
\(360\) 0 0
\(361\) −8.78354 + 15.2135i −0.462291 + 0.800712i
\(362\) 0.875933 + 1.87844i 0.0460380 + 0.0987288i
\(363\) 0 0
\(364\) −23.3346 + 27.8091i −1.22307 + 1.45759i
\(365\) 16.7374 + 19.5068i 0.876076 + 1.02103i
\(366\) 0 0
\(367\) −24.3645 + 11.3614i −1.27182 + 0.593058i −0.937034 0.349237i \(-0.886441\pi\)
−0.334783 + 0.942295i \(0.608663\pi\)
\(368\) 1.20961 + 4.51434i 0.0630555 + 0.235326i
\(369\) 0 0
\(370\) −9.81486 4.44590i −0.510251 0.231131i
\(371\) −23.6399 + 4.16835i −1.22732 + 0.216410i
\(372\) 0 0
\(373\) 2.86161 + 1.33439i 0.148169 + 0.0690922i 0.495288 0.868729i \(-0.335062\pi\)
−0.347120 + 0.937821i \(0.612840\pi\)
\(374\) 0.262599 1.48927i 0.0135786 0.0770083i
\(375\) 0 0
\(376\) 19.9081 16.7049i 1.02668 0.861487i
\(377\) −0.0226429 0.0226429i −0.00116617 0.00116617i
\(378\) 0 0
\(379\) 7.29800i 0.374873i 0.982277 + 0.187436i \(0.0600179\pi\)
−0.982277 + 0.187436i \(0.939982\pi\)
\(380\) −1.05499 + 4.11804i −0.0541197 + 0.211251i
\(381\) 0 0
\(382\) −0.169902 0.242645i −0.00869293 0.0124148i
\(383\) 7.76938 16.6615i 0.396997 0.851362i −0.601620 0.798783i \(-0.705478\pi\)
0.998617 0.0525799i \(-0.0167444\pi\)
\(384\) 0 0
\(385\) −0.0489420 4.44657i −0.00249432 0.226618i
\(386\) −1.26438 + 0.729990i −0.0643552 + 0.0371555i
\(387\) 0 0
\(388\) 13.1423 3.52146i 0.667197 0.178775i
\(389\) −19.7491 7.18808i −1.00132 0.364450i −0.211226 0.977437i \(-0.567746\pi\)
−0.790093 + 0.612987i \(0.789968\pi\)
\(390\) 0 0
\(391\) 10.7587 + 9.02763i 0.544091 + 0.456547i
\(392\) −2.31943 26.5112i −0.117149 1.33902i
\(393\) 0 0
\(394\) −5.86086 + 16.1026i −0.295266 + 0.811237i
\(395\) −3.49984 + 0.345050i −0.176096 + 0.0173614i
\(396\) 0 0
\(397\) −32.7796 8.78326i −1.64516 0.440819i −0.686907 0.726745i \(-0.741032\pi\)
−0.958252 + 0.285926i \(0.907699\pi\)
\(398\) 12.5371 + 8.77854i 0.628426 + 0.440029i
\(399\) 0 0
\(400\) −0.186940 8.49107i −0.00934699 0.424554i
\(401\) 26.7887 + 4.72357i 1.33776 + 0.235884i 0.796332 0.604860i \(-0.206771\pi\)
0.541433 + 0.840744i \(0.317882\pi\)
\(402\) 0 0
\(403\) 11.7968 + 1.03208i 0.587638 + 0.0514117i
\(404\) −24.9303 −1.24033
\(405\) 0 0
\(406\) 0.0166833 0.000827980
\(407\) −3.45320 0.302116i −0.171169 0.0149753i
\(408\) 0 0
\(409\) −13.3695 2.35741i −0.661081 0.116566i −0.166965 0.985963i \(-0.553397\pi\)
−0.494115 + 0.869396i \(0.664508\pi\)
\(410\) 1.24714 + 6.64438i 0.0615917 + 0.328143i
\(411\) 0 0
\(412\) 18.2111 + 12.7515i 0.897195 + 0.628222i
\(413\) 1.72085 + 0.461102i 0.0846777 + 0.0226893i
\(414\) 0 0
\(415\) 18.4580 + 15.1451i 0.906070 + 0.743444i
\(416\) 10.3361 28.3982i 0.506769 1.39234i
\(417\) 0 0
\(418\) −0.0309084 0.353285i −0.00151178 0.0172797i
\(419\) 9.78730 + 8.21252i 0.478141 + 0.401208i 0.849754 0.527180i \(-0.176751\pi\)
−0.371613 + 0.928388i \(0.621195\pi\)
\(420\) 0 0
\(421\) 16.9246 + 6.16004i 0.824853 + 0.300222i 0.719745 0.694239i \(-0.244259\pi\)
0.105108 + 0.994461i \(0.466481\pi\)
\(422\) 13.4482 3.60343i 0.654648 0.175412i
\(423\) 0 0
\(424\) 11.1122 6.41562i 0.539656 0.311570i
\(425\) −15.0957 20.5795i −0.732251 0.998254i
\(426\) 0 0
\(427\) −4.18641 + 8.97778i −0.202595 + 0.434465i
\(428\) 3.69050 + 5.27058i 0.178387 + 0.254763i
\(429\) 0 0
\(430\) 2.65162 + 0.679311i 0.127873 + 0.0327593i
\(431\) 4.80209i 0.231309i 0.993290 + 0.115654i \(0.0368965\pi\)
−0.993290 + 0.115654i \(0.963104\pi\)
\(432\) 0 0
\(433\) 23.6615 + 23.6615i 1.13710 + 1.13710i 0.988968 + 0.148130i \(0.0473253\pi\)
0.148130 + 0.988968i \(0.452675\pi\)
\(434\) −4.72616 + 3.96572i −0.226863 + 0.190360i
\(435\) 0 0
\(436\) 1.83198 10.3897i 0.0877360 0.497576i
\(437\) 2.98497 + 1.39192i 0.142791 + 0.0665844i
\(438\) 0 0
\(439\) 0.531654 0.0937450i 0.0253745 0.00447420i −0.160947 0.986963i \(-0.551455\pi\)
0.186321 + 0.982489i \(0.440344\pi\)
\(440\) 0.837512 + 2.22455i 0.0399268 + 0.106051i
\(441\) 0 0
\(442\) −4.49871 16.7894i −0.213982 0.798591i
\(443\) −4.71408 + 2.19821i −0.223973 + 0.104440i −0.531366 0.847142i \(-0.678321\pi\)
0.307393 + 0.951583i \(0.400543\pi\)
\(444\) 0 0
\(445\) −28.3606 2.16699i −1.34442 0.102725i
\(446\) −4.53516 + 5.40479i −0.214746 + 0.255924i
\(447\) 0 0
\(448\) 0.469199 + 1.00620i 0.0221676 + 0.0475385i
\(449\) −6.99817 + 12.1212i −0.330264 + 0.572034i −0.982564 0.185927i \(-0.940471\pi\)
0.652300 + 0.757961i \(0.273804\pi\)
\(450\) 0 0
\(451\) 1.08745 + 1.88352i 0.0512060 + 0.0886914i
\(452\) −6.39863 + 9.13819i −0.300966 + 0.429824i
\(453\) 0 0
\(454\) −2.17201 5.96755i −0.101937 0.280071i
\(455\) −22.1093 46.0825i −1.03650 2.16038i
\(456\) 0 0
\(457\) 0.334574 3.82420i 0.0156507 0.178888i −0.984346 0.176248i \(-0.943604\pi\)
0.999997 0.00264047i \(-0.000840488\pi\)
\(458\) 4.41318 4.41318i 0.206214 0.206214i
\(459\) 0 0
\(460\) −9.64056 1.59069i −0.449493 0.0741664i
\(461\) 14.3235 + 17.0701i 0.667111 + 0.795032i 0.988388 0.151953i \(-0.0485563\pi\)
−0.321276 + 0.946985i \(0.604112\pi\)
\(462\) 0 0
\(463\) −0.977400 + 0.684383i −0.0454236 + 0.0318060i −0.596068 0.802934i \(-0.703271\pi\)
0.550644 + 0.834740i \(0.314382\pi\)
\(464\) 0.00963277 0.00350604i 0.000447190 0.000162764i
\(465\) 0 0
\(466\) 1.12747 + 6.39418i 0.0522289 + 0.296205i
\(467\) −0.233069 + 0.869824i −0.0107851 + 0.0402506i −0.971109 0.238638i \(-0.923299\pi\)
0.960324 + 0.278888i \(0.0899659\pi\)
\(468\) 0 0
\(469\) −21.8935 12.6402i −1.01095 0.583672i
\(470\) 4.36355 + 15.5963i 0.201276 + 0.719404i
\(471\) 0 0
\(472\) −0.948680 + 0.0829988i −0.0436665 + 0.00382033i
\(473\) 0.877255 0.0767499i 0.0403362 0.00352896i
\(474\) 0 0
\(475\) −4.66853 3.74539i −0.214207 0.171850i
\(476\) −30.2439 17.4613i −1.38623 0.800338i
\(477\) 0 0
\(478\) 0.530593 1.98020i 0.0242687 0.0905722i
\(479\) 5.10504 + 28.9521i 0.233255 + 1.32286i 0.846257 + 0.532775i \(0.178851\pi\)
−0.613001 + 0.790082i \(0.710038\pi\)
\(480\) 0 0
\(481\) −37.4398 + 13.6270i −1.70711 + 0.621336i
\(482\) −10.6595 + 7.46386i −0.485527 + 0.339969i
\(483\) 0 0
\(484\) −11.0119 13.1234i −0.500539 0.596519i
\(485\) −3.11864 + 18.9008i −0.141610 + 0.858243i
\(486\) 0 0
\(487\) 22.6006 22.6006i 1.02413 1.02413i 0.0244298 0.999702i \(-0.492223\pi\)
0.999702 0.0244298i \(-0.00777702\pi\)
\(488\) 0.461492 5.27488i 0.0208908 0.238783i
\(489\) 0 0
\(490\) 15.6456 + 5.50031i 0.706798 + 0.248479i
\(491\) 4.34237 + 11.9306i 0.195968 + 0.538419i 0.998289 0.0584746i \(-0.0186237\pi\)
−0.802320 + 0.596894i \(0.796401\pi\)
\(492\) 0 0
\(493\) 0.0176690 0.0252339i 0.000795772 0.00113648i
\(494\) −2.03808 3.53005i −0.0916974 0.158824i
\(495\) 0 0
\(496\) −1.89542 + 3.28297i −0.0851071 + 0.147410i
\(497\) −1.36361 2.92426i −0.0611661 0.131171i
\(498\) 0 0
\(499\) −7.76871 + 9.25839i −0.347775 + 0.414463i −0.911369 0.411589i \(-0.864974\pi\)
0.563594 + 0.826052i \(0.309418\pi\)
\(500\) 16.3316 + 6.96878i 0.730372 + 0.311653i
\(501\) 0 0
\(502\) −8.26367 + 3.85341i −0.368825 + 0.171986i
\(503\) −5.65132 21.0910i −0.251980 0.940402i −0.969746 0.244117i \(-0.921502\pi\)
0.717766 0.696285i \(-0.245165\pi\)
\(504\) 0 0
\(505\) 14.4832 31.9734i 0.644493 1.42280i
\(506\) 0.802737 0.141544i 0.0356860 0.00629241i
\(507\) 0 0
\(508\) −12.0684 5.62760i −0.535450 0.249684i
\(509\) 0.934268 5.29850i 0.0414107 0.234852i −0.957077 0.289835i \(-0.906399\pi\)
0.998487 + 0.0549834i \(0.0175106\pi\)
\(510\) 0 0
\(511\) −37.9326 + 31.8293i −1.67804 + 1.40804i
\(512\) 12.3723 + 12.3723i 0.546785 + 0.546785i
\(513\) 0 0
\(514\) 18.1571i 0.800876i
\(515\) −26.9336 + 15.9479i −1.18684 + 0.702749i
\(516\) 0 0
\(517\) 2.98844 + 4.26794i 0.131432 + 0.187704i
\(518\) 8.77266 18.8130i 0.385449 0.826597i
\(519\) 0 0
\(520\) 19.5303 + 19.1051i 0.856461 + 0.837813i
\(521\) 2.74885 1.58705i 0.120429 0.0695300i −0.438575 0.898694i \(-0.644517\pi\)
0.559005 + 0.829165i \(0.311183\pi\)
\(522\) 0 0
\(523\) −11.6055 + 3.10969i −0.507473 + 0.135977i −0.503466 0.864015i \(-0.667942\pi\)
−0.00400710 + 0.999992i \(0.501276\pi\)
\(524\) −17.0706 6.21317i −0.745731 0.271424i
\(525\) 0 0
\(526\) 2.58051 + 2.16530i 0.112515 + 0.0944116i
\(527\) 0.992860 + 11.3484i 0.0432496 + 0.494346i
\(528\) 0 0
\(529\) 5.27731 14.4993i 0.229448 0.630404i
\(530\) 0.784539 + 7.95757i 0.0340782 + 0.345655i
\(531\) 0 0
\(532\) −7.91060 2.11964i −0.342968 0.0918980i
\(533\) 20.4773 + 14.3384i 0.886972 + 0.621064i
\(534\) 0 0
\(535\) −8.90355 + 1.67118i −0.384934 + 0.0722513i
\(536\) 13.3080 + 2.34655i 0.574817 + 0.101356i
\(537\) 0 0
\(538\) −7.18199 0.628343i −0.309638 0.0270898i
\(539\) 5.33536 0.229810
\(540\) 0 0
\(541\) 33.7781 1.45223 0.726116 0.687572i \(-0.241324\pi\)
0.726116 + 0.687572i \(0.241324\pi\)
\(542\) −9.83692 0.860619i −0.422532 0.0369668i
\(543\) 0 0
\(544\) 28.6306 + 5.04834i 1.22753 + 0.216446i
\(545\) 12.2606 + 8.38538i 0.525186 + 0.359190i
\(546\) 0 0
\(547\) 11.7446 + 8.22365i 0.502162 + 0.351618i 0.797049 0.603914i \(-0.206393\pi\)
−0.294887 + 0.955532i \(0.595282\pi\)
\(548\) 15.8149 + 4.23759i 0.675579 + 0.181021i
\(549\) 0 0
\(550\) −1.47813 0.0965912i −0.0630278 0.00411866i
\(551\) 0.00247076 0.00678836i 0.000105258 0.000289194i
\(552\) 0 0
\(553\) −0.590495 6.74939i −0.0251104 0.287013i
\(554\) −8.07250 6.77363i −0.342968 0.287784i
\(555\) 0 0
\(556\) 2.58203 + 0.939783i 0.109503 + 0.0398557i
\(557\) 9.77642 2.61958i 0.414240 0.110995i −0.0456789 0.998956i \(-0.514545\pi\)
0.459919 + 0.887961i \(0.347878\pi\)
\(558\) 0 0
\(559\) 8.76560 5.06082i 0.370745 0.214050i
\(560\) 16.3611 0.180082i 0.691383 0.00760984i
\(561\) 0 0
\(562\) 2.61703 5.61224i 0.110393 0.236738i
\(563\) 16.1451 + 23.0577i 0.680437 + 0.971765i 0.999710 + 0.0241016i \(0.00767253\pi\)
−0.319273 + 0.947663i \(0.603439\pi\)
\(564\) 0 0
\(565\) −8.00256 13.5151i −0.336670 0.568585i
\(566\) 9.95976i 0.418640i
\(567\) 0 0
\(568\) 1.21955 + 1.21955i 0.0511713 + 0.0511713i
\(569\) 7.66040 6.42784i 0.321141 0.269469i −0.467938 0.883761i \(-0.655003\pi\)
0.789078 + 0.614292i \(0.210558\pi\)
\(570\) 0 0
\(571\) 4.25288 24.1193i 0.177978 1.00936i −0.756673 0.653794i \(-0.773176\pi\)
0.934651 0.355568i \(-0.115712\pi\)
\(572\) 3.52584 + 1.64413i 0.147423 + 0.0687444i
\(573\) 0 0
\(574\) −12.8261 + 2.26159i −0.535353 + 0.0943971i
\(575\) 7.64073 11.4400i 0.318640 0.477081i
\(576\) 0 0
\(577\) −4.13963 15.4493i −0.172335 0.643163i −0.996990 0.0775272i \(-0.975298\pi\)
0.824655 0.565636i \(-0.191369\pi\)
\(578\) 5.26705 2.45606i 0.219080 0.102159i
\(579\) 0 0
\(580\) −0.00163278 + 0.0213691i −6.77973e−5 + 0.000887302i
\(581\) −29.5668 + 35.2364i −1.22664 + 1.46185i
\(582\) 0 0
\(583\) 1.08716 + 2.33143i 0.0450258 + 0.0965581i
\(584\) 13.2344 22.9227i 0.547643 0.948546i
\(585\) 0 0
\(586\) −3.09532 5.36125i −0.127867 0.221471i
\(587\) 11.3970 16.2765i 0.470403 0.671805i −0.511913 0.859037i \(-0.671063\pi\)
0.982316 + 0.187233i \(0.0599518\pi\)
\(588\) 0 0
\(589\) 0.913697 + 2.51036i 0.0376482 + 0.103438i
\(590\) 0.196823 0.559865i 0.00810309 0.0230493i
\(591\) 0 0
\(592\) 1.11163 12.7060i 0.0456878 0.522214i
\(593\) 24.0438 24.0438i 0.987362 0.987362i −0.0125593 0.999921i \(-0.503998\pi\)
0.999921 + 0.0125593i \(0.00399784\pi\)
\(594\) 0 0
\(595\) 39.9644 28.6440i 1.63838 1.17429i
\(596\) −4.68781 5.58672i −0.192020 0.228841i
\(597\) 0 0
\(598\) 7.67460 5.37382i 0.313838 0.219752i
\(599\) 32.8027 11.9392i 1.34028 0.487823i 0.430381 0.902647i \(-0.358379\pi\)
0.909901 + 0.414825i \(0.136157\pi\)
\(600\) 0 0
\(601\) −4.52626 25.6697i −0.184630 1.04709i −0.926430 0.376467i \(-0.877139\pi\)
0.741800 0.670621i \(-0.233972\pi\)
\(602\) −1.36484 + 5.09367i −0.0556269 + 0.207602i
\(603\) 0 0
\(604\) 6.09398 + 3.51836i 0.247961 + 0.143160i
\(605\) 23.2282 6.49881i 0.944361 0.264214i
\(606\) 0 0
\(607\) −3.56643 + 0.312022i −0.144757 + 0.0126646i −0.159304 0.987230i \(-0.550925\pi\)
0.0145470 + 0.999894i \(0.495369\pi\)
\(608\) 6.79175 0.594201i 0.275442 0.0240980i
\(609\) 0 0
\(610\) 2.87565 + 1.61832i 0.116432 + 0.0655239i
\(611\) 51.8625 + 29.9428i 2.09813 + 1.21136i
\(612\) 0 0
\(613\) 4.71891 17.6112i 0.190595 0.711310i −0.802768 0.596291i \(-0.796640\pi\)
0.993363 0.115019i \(-0.0366928\pi\)
\(614\) −0.488558 2.77075i −0.0197166 0.111818i
\(615\) 0 0
\(616\) −4.30313 + 1.56621i −0.173378 + 0.0631044i
\(617\) −2.52278 + 1.76647i −0.101563 + 0.0711153i −0.623255 0.782019i \(-0.714190\pi\)
0.521692 + 0.853134i \(0.325301\pi\)
\(618\) 0 0
\(619\) 22.9284 + 27.3250i 0.921572 + 1.09829i 0.994889 + 0.100978i \(0.0321970\pi\)
−0.0733171 + 0.997309i \(0.523359\pi\)
\(620\) −4.61699 6.44168i −0.185423 0.258704i
\(621\) 0 0
\(622\) 3.76282 3.76282i 0.150875 0.150875i
\(623\) 4.77580 54.5877i 0.191339 2.18701i
\(624\) 0 0
\(625\) −18.4253 + 16.8970i −0.737013 + 0.675879i
\(626\) 2.27197 + 6.24218i 0.0908062 + 0.249488i
\(627\) 0 0
\(628\) −0.758266 + 1.08292i −0.0302581 + 0.0432130i
\(629\) −19.1642 33.1934i −0.764127 1.32351i
\(630\) 0 0
\(631\) 0.459598 0.796047i 0.0182963 0.0316901i −0.856732 0.515761i \(-0.827509\pi\)
0.875029 + 0.484071i \(0.160842\pi\)
\(632\) 1.53054 + 3.28225i 0.0608815 + 0.130561i
\(633\) 0 0
\(634\) 0.560241 0.667669i 0.0222500 0.0265165i
\(635\) 14.2286 12.2085i 0.564643 0.484481i
\(636\) 0 0
\(637\) 55.5788 25.9168i 2.20211 1.02686i
\(638\) −0.000462735 0.00172695i −1.83199e−5 6.83707e-5i
\(639\) 0 0
\(640\) −23.4912 + 8.84408i −0.928570 + 0.349593i
\(641\) −28.1175 + 4.95787i −1.11057 + 0.195824i −0.698699 0.715416i \(-0.746237\pi\)
−0.411875 + 0.911240i \(0.635126\pi\)
\(642\) 0 0
\(643\) 34.3252 + 16.0061i 1.35365 + 0.631220i 0.957891 0.287133i \(-0.0927020\pi\)
0.395764 + 0.918352i \(0.370480\pi\)
\(644\) 3.26871 18.5378i 0.128805 0.730492i
\(645\) 0 0
\(646\) 3.00385 2.52053i 0.118185 0.0991688i
\(647\) −30.2410 30.2410i −1.18890 1.18890i −0.977373 0.211525i \(-0.932157\pi\)
−0.211525 0.977373i \(-0.567843\pi\)
\(648\) 0 0
\(649\) 0.190921i 0.00749431i
\(650\) −15.8670 + 6.17392i −0.622355 + 0.242161i
\(651\) 0 0
\(652\) 13.0851 + 18.6874i 0.512451 + 0.731856i
\(653\) −15.4696 + 33.1747i −0.605374 + 1.29823i 0.329804 + 0.944049i \(0.393017\pi\)
−0.935178 + 0.354178i \(0.884761\pi\)
\(654\) 0 0
\(655\) 17.8855 18.2836i 0.698845 0.714400i
\(656\) −6.93039 + 4.00126i −0.270586 + 0.156223i
\(657\) 0 0
\(658\) −30.1372 + 8.07523i −1.17487 + 0.314805i
\(659\) 29.4659 + 10.7247i 1.14783 + 0.417776i 0.844735 0.535184i \(-0.179758\pi\)
0.303095 + 0.952960i \(0.401980\pi\)
\(660\) 0 0
\(661\) 3.28171 + 2.75368i 0.127644 + 0.107106i 0.704375 0.709828i \(-0.251227\pi\)
−0.576731 + 0.816934i \(0.695672\pi\)
\(662\) 0.399503 + 4.56634i 0.0155271 + 0.177476i
\(663\) 0 0
\(664\) 8.40938 23.1046i 0.326347 0.896632i
\(665\) 7.31409 8.91402i 0.283628 0.345671i
\(666\) 0 0
\(667\) 0.0160385 + 0.00429751i 0.000621014 + 0.000166400i
\(668\) −29.1901 20.4392i −1.12940 0.790815i
\(669\) 0 0
\(670\) −4.75397 + 6.95096i −0.183662 + 0.268539i
\(671\) 1.04544 + 0.184339i 0.0403587 + 0.00711633i
\(672\) 0 0
\(673\) 28.3733 + 2.48234i 1.09371 + 0.0956872i 0.619705 0.784835i \(-0.287252\pi\)
0.474005 + 0.880522i \(0.342808\pi\)
\(674\) 18.4533 0.710793
\(675\) 0 0
\(676\) 24.0691 0.925735
\(677\) −42.4749 3.71607i −1.63244 0.142820i −0.766255 0.642537i \(-0.777882\pi\)
−0.866189 + 0.499717i \(0.833437\pi\)
\(678\) 0 0
\(679\) −36.3444 6.40849i −1.39477 0.245935i
\(680\) −14.8373 + 21.6941i −0.568983 + 0.831933i
\(681\) 0 0
\(682\) 0.541592 + 0.379227i 0.0207386 + 0.0145213i
\(683\) 16.5292 + 4.42899i 0.632473 + 0.169471i 0.560792 0.827957i \(-0.310497\pi\)
0.0716812 + 0.997428i \(0.477164\pi\)
\(684\) 0 0
\(685\) −14.6224 + 17.8210i −0.558692 + 0.680904i
\(686\) −4.30892 + 11.8386i −0.164515 + 0.452002i
\(687\) 0 0
\(688\) 0.282400 + 3.22785i 0.0107664 + 0.123061i
\(689\) 22.6501 + 19.0057i 0.862901 + 0.724060i
\(690\) 0 0
\(691\) −28.7479 10.4634i −1.09362 0.398045i −0.268660 0.963235i \(-0.586581\pi\)
−0.824961 + 0.565190i \(0.808803\pi\)
\(692\) 3.54310 0.949372i 0.134689 0.0360897i
\(693\) 0 0
\(694\) −16.3892 + 9.46233i −0.622127 + 0.359185i
\(695\) −2.70530 + 2.76552i −0.102618 + 0.104902i
\(696\) 0 0
\(697\) −10.1632 + 21.7951i −0.384959 + 0.825547i
\(698\) −7.58187 10.8280i −0.286978 0.409847i
\(699\) 0 0
\(700\) −13.7709 + 31.3134i −0.520491 + 1.18353i
\(701\) 33.1045i 1.25034i −0.780488 0.625171i \(-0.785029\pi\)
0.780488 0.625171i \(-0.214971\pi\)
\(702\) 0 0
\(703\) −6.35572 6.35572i −0.239710 0.239710i
\(704\) 0.0911416 0.0764768i 0.00343503 0.00288233i
\(705\) 0 0
\(706\) −0.195420 + 1.10828i −0.00735472 + 0.0417107i
\(707\) 61.2863 + 28.5783i 2.30491 + 1.07480i
\(708\) 0 0
\(709\) 36.6991 6.47105i 1.37827 0.243025i 0.565083 0.825034i \(-0.308844\pi\)
0.813182 + 0.582009i \(0.197733\pi\)
\(710\) −1.00587 + 0.378697i −0.0377498 + 0.0142122i
\(711\) 0 0
\(712\) 7.58092 + 28.2924i 0.284107 + 1.06030i
\(713\) −5.56503 + 2.59502i −0.208412 + 0.0971841i
\(714\) 0 0
\(715\) −4.15693 + 3.56677i −0.155460 + 0.133390i
\(716\) −21.2116 + 25.2790i −0.792716 + 0.944722i
\(717\) 0 0
\(718\) −5.10759 10.9533i −0.190614 0.408772i
\(719\) −21.5770 + 37.3725i −0.804687 + 1.39376i 0.111816 + 0.993729i \(0.464333\pi\)
−0.916502 + 0.400029i \(0.869000\pi\)
\(720\) 0 0
\(721\) −30.1509 52.2229i −1.12288 1.94488i
\(722\) −6.46621 + 9.23470i −0.240647 + 0.343680i
\(723\) 0 0
\(724\) −1.75433 4.82000i −0.0651993 0.179134i
\(725\) −0.0264575 0.0145083i −0.000982606 0.000538826i
\(726\) 0 0
\(727\) 0.590839 6.75332i 0.0219130 0.250467i −0.977335 0.211698i \(-0.932101\pi\)
0.999248 0.0387690i \(-0.0123436\pi\)
\(728\) −37.2180 + 37.2180i −1.37939 + 1.37939i
\(729\) 0 0
\(730\) 9.60915 + 13.4068i 0.355651 + 0.496207i
\(731\) 6.25882 + 7.45897i 0.231491 + 0.275880i
\(732\) 0 0
\(733\) −20.8024 + 14.5660i −0.768353 + 0.538006i −0.890760 0.454474i \(-0.849827\pi\)
0.122408 + 0.992480i \(0.460938\pi\)
\(734\) −16.2116 + 5.90055i −0.598382 + 0.217793i
\(735\) 0 0
\(736\) 2.72113 + 15.4323i 0.100302 + 0.568841i
\(737\) −0.701189 + 2.61687i −0.0258286 + 0.0963937i
\(738\) 0 0
\(739\) −31.3022 18.0723i −1.15147 0.664801i −0.202224 0.979339i \(-0.564817\pi\)
−0.949245 + 0.314538i \(0.898150\pi\)
\(740\) 23.2384 + 13.0778i 0.854259 + 0.480749i
\(741\) 0 0
\(742\) −15.3461 + 1.34261i −0.563371 + 0.0492886i
\(743\) −35.7603 + 3.12862i −1.31192 + 0.114778i −0.721554 0.692358i \(-0.756572\pi\)
−0.590365 + 0.807136i \(0.701016\pi\)
\(744\) 0 0
\(745\) 9.88838 2.76658i 0.362282 0.101360i
\(746\) 1.75479 + 1.01313i 0.0642473 + 0.0370932i
\(747\) 0 0
\(748\) −0.968627 + 3.61497i −0.0354165 + 0.132176i
\(749\) −3.03056 17.1872i −0.110734 0.628006i
\(750\) 0 0
\(751\) 20.6234 7.50630i 0.752558 0.273909i 0.0628763 0.998021i \(-0.479973\pi\)
0.689682 + 0.724113i \(0.257750\pi\)
\(752\) −15.7038 + 10.9959i −0.572660 + 0.400981i
\(753\) 0 0
\(754\) −0.0132091 0.0157420i −0.000481047 0.000573290i
\(755\) −8.05261 + 5.77161i −0.293065 + 0.210051i
\(756\) 0 0
\(757\) −19.9998 + 19.9998i −0.726906 + 0.726906i −0.970002 0.243096i \(-0.921837\pi\)
0.243096 + 0.970002i \(0.421837\pi\)
\(758\) −0.408186 + 4.66559i −0.0148260 + 0.169462i
\(759\) 0 0
\(760\) −2.04417 + 5.81466i −0.0741500 + 0.210920i
\(761\) −17.7365 48.7306i −0.642947 1.76648i −0.642264 0.766484i \(-0.722005\pi\)
−0.000683402 1.00000i \(-0.500218\pi\)
\(762\) 0 0
\(763\) −16.4135 + 23.4409i −0.594209 + 0.848619i
\(764\) 0.366534 + 0.634856i 0.0132607 + 0.0229683i
\(765\) 0 0
\(766\) 5.89884 10.2171i 0.213134 0.369159i
\(767\) −0.927410 1.98884i −0.0334868 0.0718127i
\(768\) 0 0
\(769\) 28.9226 34.4686i 1.04298 1.24297i 0.0736257 0.997286i \(-0.476543\pi\)
0.969350 0.245684i \(-0.0790126\pi\)
\(770\) 0.217414 2.84542i 0.00783506 0.102542i
\(771\) 0 0
\(772\) 3.27462 1.52698i 0.117856 0.0549572i
\(773\) −6.21709 23.2025i −0.223613 0.834536i −0.982955 0.183844i \(-0.941146\pi\)
0.759342 0.650691i \(-0.225521\pi\)
\(774\) 0 0
\(775\) 10.9437 2.17907i 0.393111 0.0782746i
\(776\) 19.4273 3.42556i 0.697399 0.122970i
\(777\) 0 0
\(778\) −12.2235 5.69992i −0.438234 0.204352i
\(779\) −0.979290 + 5.55383i −0.0350867 + 0.198987i
\(780\) 0 0
\(781\) −0.264879 + 0.222260i −0.00947813 + 0.00795309i
\(782\) 6.37309 + 6.37309i 0.227901 + 0.227901i
\(783\) 0 0
\(784\) 19.6314i 0.701122i
\(785\) −0.948338 1.60160i −0.0338476 0.0571635i
\(786\) 0 0