Properties

Label 405.2.r.a.197.10
Level $405$
Weight $2$
Character 405.197
Analytic conductor $3.234$
Analytic rank $0$
Dimension $192$
CM no
Inner twists $4$

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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 197.10
Character \(\chi\) \(=\) 405.197
Dual form 405.2.r.a.368.10

$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.639298 0.0559313i 0.452052 0.0395494i 0.141143 0.989989i \(-0.454922\pi\)
0.310909 + 0.950440i \(0.399367\pi\)
\(3\) 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 0.333781 0.942651i \(-0.391675\pi\)
0.999962 + 0.00875387i \(0.00278648\pi\)
\(8\) −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 0.961217 0.275792i \(-0.0889401\pi\)
−0.913611 + 0.406590i \(0.866718\pi\)
\(12\) 0 0
\(13\) −0.462462 + 5.28596i −0.128264 + 1.46606i 0.610457 + 0.792050i \(0.290986\pi\)
−0.738720 + 0.674012i \(0.764570\pi\)
\(14\) 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 0.801191 0.598409i \(-0.204200\pi\)
0.394647 + 0.918833i \(0.370867\pi\)
\(18\) 0 0
\(19\) 1.03667 + 0.598524i 0.237829 + 0.137311i 0.614179 0.789167i \(-0.289487\pi\)
−0.376349 + 0.926478i \(0.622821\pi\)
\(20\) −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 −0.620195 0.784448i \(-0.712946\pi\)
0.949259 + 0.314496i \(0.101835\pi\)
\(24\) 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 0.643217 0.765684i \(-0.277599\pi\)
−0.642358 + 0.766404i \(0.722044\pi\)
\(30\) 0 0
\(31\) −0.387533 2.19781i −0.0696030 0.394738i −0.999629 0.0272441i \(-0.991327\pi\)
0.930026 0.367494i \(-0.119784\pi\)
\(32\) 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 0.600238 + 0.799822i \(0.295073\pi\)
−0.919732 + 0.392547i \(0.871594\pi\)
\(38\) 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 0.475855 0.879524i \(-0.342139\pi\)
−0.948793 + 0.315898i \(0.897694\pi\)
\(42\) 0 0
\(43\) 0.806157 1.72881i 0.122938 0.263641i −0.835201 0.549945i \(-0.814649\pi\)
0.958139 + 0.286304i \(0.0924266\pi\)
\(44\) −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 −0.937290 0.348549i \(-0.886674\pi\)
−0.00695690 0.999976i \(-0.502214\pi\)
\(48\) 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 0.382657 0.923890i \(-0.375009\pi\)
−0.923890 + 0.382657i \(0.875009\pi\)
\(54\) 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 0.367193 0.930145i \(-0.380319\pi\)
−0.316599 + 0.948559i \(0.602541\pi\)
\(60\) 0 0
\(61\) 0.399307 2.26458i 0.0511260 0.289950i −0.948515 0.316731i \(-0.897415\pi\)
0.999641 + 0.0267812i \(0.00852575\pi\)
\(62\) −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 −0.275750 0.961230i \(-0.588926\pi\)
−0.438476 + 0.898743i \(0.644482\pi\)
\(68\) −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 −0.537997 0.842947i \(-0.680819\pi\)
0.461015 + 0.887392i \(0.347485\pi\)
\(72\) 0 0
\(73\) −2.97508 11.1032i −0.348207 1.29953i −0.888821 0.458255i \(-0.848475\pi\)
0.540614 0.841271i \(-0.318192\pi\)
\(74\) −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 −0.819911 0.572491i \(-0.805977\pi\)
0.706170 + 0.708043i \(0.250422\pi\)
\(80\) 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 −0.858289 0.513167i \(-0.828472\pi\)
0.756139 0.654411i \(-0.227083\pi\)
\(84\) 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 0.302542 + 0.953136i \(0.402165\pi\)
−0.976711 + 0.214559i \(0.931168\pi\)
\(90\) 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 −0.0136208 0.999907i \(-0.504336\pi\)
−0.774729 + 0.632294i \(0.782114\pi\)
\(98\) 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 0.877569 0.479450i \(-0.159164\pi\)
0.660663 + 0.750682i \(0.270275\pi\)
\(102\) 0 0
\(103\) −12.6867 + 5.91592i −1.25006 + 0.582912i −0.931068 0.364845i \(-0.881122\pi\)
−0.318992 + 0.947758i \(0.603344\pi\)
\(104\) −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 −0.831887 0.554945i \(-0.812739\pi\)
0.554945 + 0.831887i \(0.312739\pi\)
\(108\) 0 0
\(109\) 6.64284i 0.636269i −0.948046 0.318134i \(-0.896944\pi\)
0.948046 0.318134i \(-0.103056\pi\)
\(110\) −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 0.995043 0.0994488i \(-0.0317080\pi\)
−0.715783 + 0.698322i \(0.753930\pi\)
\(114\) 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 0.119083 0.992884i \(-0.462005\pi\)
0.599571 + 0.800322i \(0.295338\pi\)
\(128\) −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 0.341682 0.939816i \(-0.389004\pi\)
0.642512 + 0.766276i \(0.277892\pi\)
\(132\) 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 −0.516961 0.856009i \(-0.672937\pi\)
−0.360463 + 0.932773i \(0.617381\pi\)
\(138\) 0 0
\(139\) −1.70385 + 0.300434i −0.144518 + 0.0254825i −0.245439 0.969412i \(-0.578932\pi\)
0.100921 + 0.994894i \(0.467821\pi\)
\(140\) −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 −0.487223 0.873277i \(-0.661990\pi\)
0.775405 + 0.631464i \(0.217546\pi\)
\(150\) 0 0
\(151\) −4.16351 + 1.51539i −0.338821 + 0.123321i −0.505827 0.862635i \(-0.668813\pi\)
0.167005 + 0.985956i \(0.446590\pi\)
\(152\) −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 0.919846 0.392281i \(-0.128314\pi\)
−0.891770 + 0.452489i \(0.850536\pi\)
\(158\) −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 −0.982394 0.186823i \(-0.940181\pi\)
0.186823 + 0.982394i \(0.440181\pi\)
\(164\) 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 0.577038 0.816718i \(-0.304209\pi\)
0.996555 + 0.0829395i \(0.0264308\pi\)
\(168\) 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 0.341413 0.939913i \(-0.389094\pi\)
−0.500559 + 0.865702i \(0.666872\pi\)
\(174\) 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 0.933936 + 0.357440i \(0.116350\pi\)
−0.157416 + 0.987532i \(0.550316\pi\)
\(180\) 0 0
\(181\) 1.61486 2.79701i 0.120031 0.207900i −0.799748 0.600335i \(-0.795034\pi\)
0.919780 + 0.392435i \(0.128367\pi\)
\(182\) 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 −0.776672 0.629905i \(-0.783094\pi\)
0.755203 + 0.655490i \(0.227538\pi\)
\(192\) 0 0
\(193\) −1.86360 1.30491i −0.134145 0.0939292i 0.504578 0.863366i \(-0.331648\pi\)
−0.638723 + 0.769437i \(0.720537\pi\)
\(194\) −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 −0.544153 0.838986i \(-0.683149\pi\)
0.0517571 0.998660i \(-0.483518\pi\)
\(198\) 0 0
\(199\) 20.6539 11.9246i 1.46412 0.845309i 0.464921 0.885352i \(-0.346083\pi\)
0.999198 + 0.0400428i \(0.0127494\pi\)
\(200\) 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 0.929209 0.369555i \(-0.120490\pi\)
0.474270 + 0.880379i \(0.342712\pi\)
\(212\) 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 0.550489 0.834842i \(-0.314441\pi\)
−0.972774 + 0.231757i \(0.925552\pi\)
\(224\) 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 −0.994831 0.101544i \(-0.967622\pi\)
0.717252 + 0.696814i \(0.245400\pi\)
\(228\) 0 0
\(229\) 6.25137 + 7.45009i 0.413102 + 0.492316i 0.931968 0.362540i \(-0.118090\pi\)
−0.518866 + 0.854855i \(0.673646\pi\)
\(230\) 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 −0.825563 0.564311i \(-0.809142\pi\)
0.997113 0.0759259i \(-0.0241913\pi\)
\(234\) 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 0.997478 0.0709702i \(-0.0226095\pi\)
−0.961596 + 0.274468i \(0.911498\pi\)
\(240\) 0 0
\(241\) −15.5334 13.0341i −1.00060 0.839600i −0.0135291 0.999908i \(-0.504307\pi\)
−0.987067 + 0.160309i \(0.948751\pi\)
\(242\) 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 0.0585840 0.998282i \(-0.481341\pi\)
−0.835246 + 0.549876i \(0.814675\pi\)
\(252\) 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 0.391701 + 0.920093i \(0.371887\pi\)
−0.545522 + 0.838096i \(0.683669\pi\)
\(258\) 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 −0.433444 0.901181i \(-0.642702\pi\)
0.698586 + 0.715526i \(0.253813\pi\)
\(264\) 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 −0.903026 0.429585i \(-0.858660\pi\)
0.0948247 + 0.995494i \(0.469771\pi\)
\(278\) −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 0.998369 0.0570865i \(-0.0181811\pi\)
−0.801490 + 0.598009i \(0.795959\pi\)
\(282\) 0 0
\(283\) −1.35265 + 15.4609i −0.0804068 + 0.919054i 0.843674 + 0.536856i \(0.180388\pi\)
−0.924080 + 0.382198i \(0.875167\pi\)
\(284\) 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 −0.947582 0.319512i \(-0.896481\pi\)
0.624335 + 0.781157i \(0.285370\pi\)
\(294\) 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 −0.990717 0.135940i \(-0.956595\pi\)
0.925956 + 0.377631i \(0.123261\pi\)
\(308\) −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 0.895694 0.444671i \(-0.146679\pi\)
−0.593451 + 0.804870i \(0.702235\pi\)
\(312\) 0 0
\(313\) 4.37462 9.38140i 0.247268 0.530268i −0.743025 0.669264i \(-0.766610\pi\)
0.990293 + 0.138996i \(0.0443874\pi\)
\(314\) 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 0.840433 0.541916i \(-0.182301\pi\)
−0.796679 + 0.604402i \(0.793412\pi\)
\(318\) 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 −0.931560 0.363588i \(-0.881552\pi\)
0.999734 0.0230485i \(-0.00733722\pi\)
\(332\) 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 0.834406 0.551151i \(-0.185811\pi\)
0.726023 + 0.687671i \(0.241367\pi\)
\(338\) −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 −0.297874 0.954605i \(-0.596277\pi\)
−0.998914 + 0.0465844i \(0.985166\pi\)
\(348\) 0 0
\(349\) −13.2402 + 15.7790i −0.708730 + 0.844632i −0.993484 0.113969i \(-0.963644\pi\)
0.284754 + 0.958601i \(0.408088\pi\)
\(350\) 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 0.991042 0.133552i \(-0.0426382\pi\)
−0.999177 + 0.0405701i \(0.987083\pi\)
\(354\) 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 −0.999994 0.00349274i \(-0.998888\pi\)
0.503022 + 0.864274i \(0.332222\pi\)
\(360\) 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 −0.334783 0.942295i \(-0.608663\pi\)
−0.937034 + 0.349237i \(0.886441\pi\)
\(368\) 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 −0.347120 0.937821i \(-0.612840\pi\)
0.495288 + 0.868729i \(0.335062\pi\)
\(374\) 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 \(-0.939982\pi\)
0.982277 0.187436i \(-0.0600179\pi\)
\(380\) −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 0.998617 + 0.0525799i \(0.0167444\pi\)
−0.601620 + 0.798783i \(0.705478\pi\)
\(384\) 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 −0.790093 0.612987i \(-0.789968\pi\)
−0.211226 + 0.977437i \(0.567746\pi\)
\(390\) 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 −0.958252 0.285926i \(-0.907699\pi\)
−0.686907 + 0.726745i \(0.741032\pi\)
\(398\) 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 0.541433 0.840744i \(-0.317882\pi\)
0.796332 + 0.604860i \(0.206771\pi\)
\(402\) 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 −0.494115 0.869396i \(-0.664508\pi\)
−0.166965 + 0.985963i \(0.553397\pi\)
\(410\) 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 −0.371613 0.928388i \(-0.621195\pi\)
0.849754 + 0.527180i \(0.176751\pi\)
\(420\) 0 0
\(421\) 16.9246 6.16004i 0.824853 0.300222i 0.105108 0.994461i \(-0.466481\pi\)
0.719745 + 0.694239i \(0.244259\pi\)
\(422\) 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 \(-0.963104\pi\)
0.993290 0.115654i \(-0.0368965\pi\)
\(432\) 0 0
\(433\) 23.6615 23.6615i 1.13710 1.13710i 0.148130 0.988968i \(-0.452675\pi\)
0.988968 0.148130i \(-0.0473253\pi\)
\(434\) −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 0.186321 0.982489i \(-0.440344\pi\)
−0.160947 + 0.986963i \(0.551455\pi\)
\(440\) 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 0.307393 0.951583i \(-0.400543\pi\)
−0.531366 + 0.847142i \(0.678321\pi\)
\(444\) 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 0.652300 0.757961i \(-0.273804\pi\)
−0.982564 + 0.185927i \(0.940471\pi\)
\(450\) 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 0.999997 + 0.00264047i \(0.000840488\pi\)
−0.984346 + 0.176248i \(0.943604\pi\)
\(458\) 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 −0.321276 0.946985i \(-0.604112\pi\)
0.988388 + 0.151953i \(0.0485563\pi\)
\(462\) 0 0
\(463\) −0.977400 0.684383i −0.0454236 0.0318060i 0.550644 0.834740i \(-0.314382\pi\)
−0.596068 + 0.802934i \(0.703271\pi\)
\(464\) 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 0.960324 0.278888i \(-0.0899659\pi\)
−0.971109 + 0.238638i \(0.923299\pi\)
\(468\) 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 −0.613001 0.790082i \(-0.710038\pi\)
0.846257 0.532775i \(-0.178851\pi\)
\(480\) 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 0.999702 + 0.0244298i \(0.00777702\pi\)
0.0244298 + 0.999702i \(0.492223\pi\)
\(488\) 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 −0.802320 0.596894i \(-0.796401\pi\)
0.998289 + 0.0584746i \(0.0186237\pi\)
\(492\) 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 0.563594 0.826052i \(-0.309418\pi\)
−0.911369 + 0.411589i \(0.864974\pi\)
\(500\) 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 0.717766 + 0.696285i \(0.245165\pi\)
−0.969746 + 0.244117i \(0.921502\pi\)
\(504\) 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 0.998487 0.0549834i \(-0.0175106\pi\)
−0.957077 + 0.289835i \(0.906399\pi\)
\(510\) 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 0.559005 0.829165i \(-0.311183\pi\)
−0.438575 + 0.898694i \(0.644517\pi\)
\(522\) 0 0
\(523\) −11.6055 3.10969i −0.507473 0.135977i −0.00400710 0.999992i \(-0.501276\pi\)
−0.503466 + 0.864015i \(0.667942\pi\)
\(524\) −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 −0.294887 0.955532i \(-0.595282\pi\)
0.797049 + 0.603914i \(0.206393\pi\)
\(548\) 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 0.459919 0.887961i \(-0.347878\pi\)
−0.0456789 + 0.998956i \(0.514545\pi\)
\(558\) 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 −0.319273 0.947663i \(-0.603439\pi\)
0.999710 0.0241016i \(-0.00767253\pi\)
\(564\) 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 0.789078 0.614292i \(-0.210558\pi\)
−0.467938 + 0.883761i \(0.655003\pi\)
\(570\) 0 0
\(571\) 4.25288 + 24.1193i 0.177978 + 1.00936i 0.934651 + 0.355568i \(0.115712\pi\)
−0.756673 + 0.653794i \(0.773176\pi\)
\(572\) 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 0.824655 + 0.565636i \(0.191369\pi\)
−0.996990 + 0.0775272i \(0.975298\pi\)
\(578\) 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 0.982316 0.187233i \(-0.0599518\pi\)
−0.511913 + 0.859037i \(0.671063\pi\)
\(588\) 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 0.999921 0.0125593i \(-0.00399784\pi\)
−0.0125593 + 0.999921i \(0.503998\pi\)
\(594\) 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 0.909901 0.414825i \(-0.136157\pi\)
0.430381 + 0.902647i \(0.358379\pi\)
\(600\) 0 0
\(601\) −4.52626 + 25.6697i −0.184630 + 1.04709i 0.741800 + 0.670621i \(0.233972\pi\)
−0.926430 + 0.376467i \(0.877139\pi\)
\(602\) −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 0.0145470 0.999894i \(-0.495369\pi\)
−0.159304 + 0.987230i \(0.550925\pi\)
\(608\) 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 0.993363 + 0.115019i \(0.0366928\pi\)
−0.802768 + 0.596291i \(0.796640\pi\)
\(614\) −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 0.521692 0.853134i \(-0.325301\pi\)
−0.623255 + 0.782019i \(0.714190\pi\)
\(618\) 0 0
\(619\) 22.9284 27.3250i 0.921572 1.09829i −0.0733171 0.997309i \(-0.523359\pi\)
0.994889 0.100978i \(-0.0321970\pi\)
\(620\) −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 0.875029 0.484071i \(-0.160842\pi\)
−0.856732 + 0.515761i \(0.827509\pi\)
\(632\) 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 −0.411875 0.911240i \(-0.635126\pi\)
−0.698699 + 0.715416i \(0.746237\pi\)
\(642\) 0 0
\(643\) 34.3252 16.0061i 1.35365 0.631220i 0.395764 0.918352i \(-0.370480\pi\)
0.957891 + 0.287133i \(0.0927020\pi\)
\(644\) 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 −0.211525 + 0.977373i \(0.567843\pi\)
−0.977373 + 0.211525i \(0.932157\pi\)
\(648\) 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 −0.935178 0.354178i \(-0.884761\pi\)
0.329804 0.944049i \(-0.393017\pi\)
\(654\) 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 0.303095 0.952960i \(-0.401980\pi\)
0.844735 + 0.535184i \(0.179758\pi\)
\(660\) 0 0
\(661\) 3.28171 2.75368i 0.127644 0.107106i −0.576731 0.816934i \(-0.695672\pi\)
0.704375 + 0.709828i \(0.251227\pi\)
\(662\) 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 0.474005 0.880522i \(-0.342808\pi\)
0.619705 + 0.784835i \(0.287252\pi\)
\(674\) 18.4533 0.710793
\(675\) 0 0
\(676\) 24.0691 0.925735
\(677\) −42.4749 + 3.71607i −1.63244 + 0.142820i −0.866189 0.499717i \(-0.833437\pi\)
−0.766255 + 0.642537i \(0.777882\pi\)
\(678\) 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 0.0716812 0.997428i \(-0.477164\pi\)
0.560792 + 0.827957i \(0.310497\pi\)
\(684\) 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 −0.824961 0.565190i \(-0.808803\pi\)
−0.268660 + 0.963235i \(0.586581\pi\)
\(692\) 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 \(0.214971\pi\)
−0.780488 + 0.625171i \(0.785029\pi\)
\(702\) 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 0.813182 0.582009i \(-0.197733\pi\)
0.565083 + 0.825034i \(0.308844\pi\)
\(710\) −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 −0.916502 0.400029i \(-0.869000\pi\)
0.111816 0.993729i \(-0.464333\pi\)
\(720\) 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 0.999248 + 0.0387690i \(0.0123436\pi\)
−0.977335 + 0.211698i \(0.932101\pi\)
\(728\) −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 0.122408 0.992480i \(-0.460938\pi\)
−0.890760 + 0.454474i \(0.849827\pi\)
\(734\) −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 −0.949245 0.314538i \(-0.898150\pi\)
−0.202224 + 0.979339i \(0.564817\pi\)
\(740\) 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 −0.590365 0.807136i \(-0.701016\pi\)
−0.721554 + 0.692358i \(0.756572\pi\)
\(744\) 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 0.689682 0.724113i \(-0.257750\pi\)
0.0628763 + 0.998021i \(0.479973\pi\)
\(752\) −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 0.243096 0.970002i \(-0.421837\pi\)
−0.970002 + 0.243096i \(0.921837\pi\)
\(758\) −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 −0.000683402 1.00000i \(0.500218\pi\)
−0.642264 + 0.766484i \(0.722005\pi\)
\(762\) 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 0.969350 + 0.245684i \(0.0790126\pi\)
0.0736257 + 0.997286i \(0.476543\pi\)
\(770\) 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 0.759342 + 0.650691i \(0.225521\pi\)
−0.982955 + 0.183844i \(0.941146\pi\)
\(774\) 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