Properties

Label 405.2.r.a.8.1
Level $405$
Weight $2$
Character 405.8
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 8.1
Character \(\chi\) \(=\) 405.8
Dual form 405.2.r.a.152.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.05499 + 1.43892i) q^{2} +(1.46845 - 4.03452i) q^{4} +(1.82626 + 1.29027i) q^{5} +(-1.14217 + 2.44940i) q^{7} +(1.48912 + 5.55747i) q^{8} +O(q^{10})\) \(q+(-2.05499 + 1.43892i) q^{2} +(1.46845 - 4.03452i) q^{4} +(1.82626 + 1.29027i) q^{5} +(-1.14217 + 2.44940i) q^{7} +(1.48912 + 5.55747i) q^{8} +(-5.60952 - 0.0236494i) q^{10} +(2.09979 - 2.50243i) q^{11} +(1.80484 - 2.57758i) q^{13} +(-1.17733 - 6.67697i) q^{14} +(-4.47891 - 3.75825i) q^{16} +(-1.57770 + 5.88806i) q^{17} +(2.91796 + 1.68469i) q^{19} +(7.88737 - 5.47338i) q^{20} +(-0.714248 + 8.16389i) q^{22} +(4.50352 - 2.10003i) q^{23} +(1.67042 + 4.71272i) q^{25} +7.89390i q^{26} +(8.20493 + 8.20493i) q^{28} +(-0.541940 + 3.07349i) q^{29} +(0.346096 + 0.125969i) q^{31} +(3.14866 + 0.275472i) q^{32} +(-5.23028 - 14.3701i) q^{34} +(-5.24628 + 2.99952i) q^{35} +(-4.28145 - 1.14721i) q^{37} +(-8.42050 + 0.736698i) q^{38} +(-4.45110 + 12.0707i) q^{40} +(-7.54663 + 1.33068i) q^{41} +(0.386956 + 4.42293i) q^{43} +(-7.01269 - 12.1463i) q^{44} +(-6.23291 + 10.7957i) q^{46} +(6.23750 + 2.90859i) q^{47} +(-0.195477 - 0.232960i) q^{49} +(-10.2139 - 7.28096i) q^{50} +(-7.74898 - 11.0667i) q^{52} +(-3.48010 + 3.48010i) q^{53} +(7.06356 - 1.86079i) q^{55} +(-15.3133 - 2.70014i) q^{56} +(-3.30882 - 7.09579i) q^{58} +(-5.87095 + 4.92631i) q^{59} +(-6.73344 + 2.45077i) q^{61} +(-0.892481 + 0.239140i) q^{62} +(3.26012 - 1.88223i) q^{64} +(6.62186 - 2.37859i) q^{65} +(-0.315748 - 0.221089i) q^{67} +(21.4388 + 15.0116i) q^{68} +(6.46497 - 13.7129i) q^{70} +(8.46099 - 4.88495i) q^{71} +(-0.0248963 + 0.00667095i) q^{73} +(10.4491 - 3.80315i) q^{74} +(11.0818 - 9.29871i) q^{76} +(3.73113 + 8.00143i) q^{77} +(10.9549 + 1.93165i) q^{79} +(-3.33049 - 12.6425i) q^{80} +(13.5935 - 13.5935i) q^{82} +(0.627725 + 0.896484i) q^{83} +(-10.4785 + 8.71746i) q^{85} +(-7.15941 - 8.53226i) q^{86} +(17.0340 + 7.94310i) q^{88} +(3.93198 - 6.81039i) q^{89} +(4.25207 + 7.36481i) q^{91} +(-1.85943 - 21.2533i) q^{92} +(-17.0032 + 2.99812i) q^{94} +(3.15525 + 6.84162i) q^{95} +(-5.10752 + 0.446850i) q^{97} +(0.736913 + 0.197455i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.05499 + 1.43892i −1.45309 + 1.01747i −0.461633 + 0.887071i \(0.652736\pi\)
−0.991462 + 0.130396i \(0.958375\pi\)
\(3\) 0 0
\(4\) 1.46845 4.03452i 0.734223 2.01726i
\(5\) 1.82626 + 1.29027i 0.816727 + 0.577025i
\(6\) 0 0
\(7\) −1.14217 + 2.44940i −0.431701 + 0.925785i 0.563331 + 0.826231i \(0.309519\pi\)
−0.995032 + 0.0995542i \(0.968258\pi\)
\(8\) 1.48912 + 5.55747i 0.526483 + 1.96486i
\(9\) 0 0
\(10\) −5.60952 0.0236494i −1.77389 0.00747861i
\(11\) 2.09979 2.50243i 0.633111 0.754512i −0.350155 0.936692i \(-0.613871\pi\)
0.983265 + 0.182180i \(0.0583154\pi\)
\(12\) 0 0
\(13\) 1.80484 2.57758i 0.500572 0.714891i −0.486764 0.873534i \(-0.661823\pi\)
0.987336 + 0.158642i \(0.0507117\pi\)
\(14\) −1.17733 6.67697i −0.314655 1.78450i
\(15\) 0 0
\(16\) −4.47891 3.75825i −1.11973 0.939563i
\(17\) −1.57770 + 5.88806i −0.382649 + 1.42807i 0.459191 + 0.888338i \(0.348139\pi\)
−0.841840 + 0.539728i \(0.818527\pi\)
\(18\) 0 0
\(19\) 2.91796 + 1.68469i 0.669427 + 0.386494i 0.795859 0.605481i \(-0.207019\pi\)
−0.126433 + 0.991975i \(0.540353\pi\)
\(20\) 7.88737 5.47338i 1.76367 1.22389i
\(21\) 0 0
\(22\) −0.714248 + 8.16389i −0.152278 + 1.74055i
\(23\) 4.50352 2.10003i 0.939049 0.437886i 0.108041 0.994146i \(-0.465542\pi\)
0.831008 + 0.556261i \(0.187764\pi\)
\(24\) 0 0
\(25\) 1.67042 + 4.71272i 0.334085 + 0.942543i
\(26\) 7.89390i 1.54812i
\(27\) 0 0
\(28\) 8.20493 + 8.20493i 1.55059 + 1.55059i
\(29\) −0.541940 + 3.07349i −0.100636 + 0.570733i 0.892238 + 0.451565i \(0.149134\pi\)
−0.992874 + 0.119169i \(0.961977\pi\)
\(30\) 0 0
\(31\) 0.346096 + 0.125969i 0.0621607 + 0.0226246i 0.372913 0.927866i \(-0.378359\pi\)
−0.310753 + 0.950491i \(0.600581\pi\)
\(32\) 3.14866 + 0.275472i 0.556610 + 0.0486971i
\(33\) 0 0
\(34\) −5.23028 14.3701i −0.896985 2.46445i
\(35\) −5.24628 + 2.99952i −0.886783 + 0.507011i
\(36\) 0 0
\(37\) −4.28145 1.14721i −0.703866 0.188600i −0.110904 0.993831i \(-0.535375\pi\)
−0.592962 + 0.805231i \(0.702041\pi\)
\(38\) −8.42050 + 0.736698i −1.36599 + 0.119508i
\(39\) 0 0
\(40\) −4.45110 + 12.0707i −0.703781 + 1.90855i
\(41\) −7.54663 + 1.33068i −1.17859 + 0.207817i −0.728422 0.685129i \(-0.759746\pi\)
−0.450164 + 0.892946i \(0.648635\pi\)
\(42\) 0 0
\(43\) 0.386956 + 4.42293i 0.0590102 + 0.674490i 0.966879 + 0.255236i \(0.0821530\pi\)
−0.907869 + 0.419255i \(0.862291\pi\)
\(44\) −7.01269 12.1463i −1.05720 1.83113i
\(45\) 0 0
\(46\) −6.23291 + 10.7957i −0.918992 + 1.59174i
\(47\) 6.23750 + 2.90859i 0.909832 + 0.424262i 0.820439 0.571735i \(-0.193729\pi\)
0.0893938 + 0.995996i \(0.471507\pi\)
\(48\) 0 0
\(49\) −0.195477 0.232960i −0.0279253 0.0332800i
\(50\) −10.2139 7.28096i −1.44446 1.02968i
\(51\) 0 0
\(52\) −7.74898 11.0667i −1.07459 1.53467i
\(53\) −3.48010 + 3.48010i −0.478029 + 0.478029i −0.904501 0.426472i \(-0.859756\pi\)
0.426472 + 0.904501i \(0.359756\pi\)
\(54\) 0 0
\(55\) 7.06356 1.86079i 0.952450 0.250909i
\(56\) −15.3133 2.70014i −2.04632 0.360822i
\(57\) 0 0
\(58\) −3.30882 7.09579i −0.434470 0.931723i
\(59\) −5.87095 + 4.92631i −0.764332 + 0.641351i −0.939251 0.343232i \(-0.888478\pi\)
0.174918 + 0.984583i \(0.444034\pi\)
\(60\) 0 0
\(61\) −6.73344 + 2.45077i −0.862128 + 0.313789i −0.734975 0.678094i \(-0.762806\pi\)
−0.127153 + 0.991883i \(0.540584\pi\)
\(62\) −0.892481 + 0.239140i −0.113345 + 0.0303708i
\(63\) 0 0
\(64\) 3.26012 1.88223i 0.407515 0.235279i
\(65\) 6.62186 2.37859i 0.821341 0.295028i
\(66\) 0 0
\(67\) −0.315748 0.221089i −0.0385747 0.0270103i 0.554130 0.832430i \(-0.313051\pi\)
−0.592705 + 0.805420i \(0.701940\pi\)
\(68\) 21.4388 + 15.0116i 2.59983 + 1.82042i
\(69\) 0 0
\(70\) 6.46497 13.7129i 0.772711 1.63901i
\(71\) 8.46099 4.88495i 1.00413 0.579737i 0.0946655 0.995509i \(-0.469822\pi\)
0.909469 + 0.415772i \(0.136489\pi\)
\(72\) 0 0
\(73\) −0.0248963 + 0.00667095i −0.00291389 + 0.000780776i −0.260276 0.965534i \(-0.583813\pi\)
0.257362 + 0.966315i \(0.417147\pi\)
\(74\) 10.4491 3.80315i 1.21468 0.442107i
\(75\) 0 0
\(76\) 11.0818 9.29871i 1.27117 1.06664i
\(77\) 3.73113 + 8.00143i 0.425202 + 0.911848i
\(78\) 0 0
\(79\) 10.9549 + 1.93165i 1.23253 + 0.217327i 0.751710 0.659494i \(-0.229230\pi\)
0.480816 + 0.876822i \(0.340341\pi\)
\(80\) −3.33049 12.6425i −0.372360 1.41348i
\(81\) 0 0
\(82\) 13.5935 13.5935i 1.50115 1.50115i
\(83\) 0.627725 + 0.896484i 0.0689018 + 0.0984019i 0.852124 0.523340i \(-0.175314\pi\)
−0.783222 + 0.621742i \(0.786425\pi\)
\(84\) 0 0
\(85\) −10.4785 + 8.71746i −1.13655 + 0.945541i
\(86\) −7.15941 8.53226i −0.772019 0.920057i
\(87\) 0 0
\(88\) 17.0340 + 7.94310i 1.81583 + 0.846737i
\(89\) 3.93198 6.81039i 0.416789 0.721900i −0.578825 0.815452i \(-0.696489\pi\)
0.995614 + 0.0935515i \(0.0298220\pi\)
\(90\) 0 0
\(91\) 4.25207 + 7.36481i 0.445738 + 0.772042i
\(92\) −1.85943 21.2533i −0.193858 2.21581i
\(93\) 0 0
\(94\) −17.0032 + 2.99812i −1.75375 + 0.309233i
\(95\) 3.15525 + 6.84162i 0.323722 + 0.701936i
\(96\) 0 0
\(97\) −5.10752 + 0.446850i −0.518590 + 0.0453707i −0.343447 0.939172i \(-0.611594\pi\)
−0.175143 + 0.984543i \(0.556039\pi\)
\(98\) 0.736913 + 0.197455i 0.0744394 + 0.0199460i
\(99\) 0 0
\(100\) 21.4665 + 0.181006i 2.14665 + 0.0181006i
\(101\) −0.406707 1.11742i −0.0404688 0.111187i 0.917812 0.397015i \(-0.129954\pi\)
−0.958281 + 0.285827i \(0.907732\pi\)
\(102\) 0 0
\(103\) 0.187413 + 0.0163965i 0.0184664 + 0.00161560i 0.0963852 0.995344i \(-0.469272\pi\)
−0.0779188 + 0.996960i \(0.524827\pi\)
\(104\) 17.0124 + 6.19202i 1.66821 + 0.607177i
\(105\) 0 0
\(106\) 2.14398 12.1591i 0.208242 1.18100i
\(107\) 1.76707 + 1.76707i 0.170829 + 0.170829i 0.787344 0.616515i \(-0.211456\pi\)
−0.616515 + 0.787344i \(0.711456\pi\)
\(108\) 0 0
\(109\) 7.80745i 0.747818i 0.927465 + 0.373909i \(0.121983\pi\)
−0.927465 + 0.373909i \(0.878017\pi\)
\(110\) −11.8380 + 13.9878i −1.12871 + 1.33368i
\(111\) 0 0
\(112\) 14.3211 6.67806i 1.35322 0.631017i
\(113\) 1.69916 19.4214i 0.159843 1.82701i −0.317455 0.948273i \(-0.602828\pi\)
0.477298 0.878741i \(-0.341616\pi\)
\(114\) 0 0
\(115\) 10.9342 + 1.97556i 1.01962 + 0.184222i
\(116\) 11.6043 + 6.69973i 1.07743 + 0.622054i
\(117\) 0 0
\(118\) 4.97617 18.5713i 0.458093 1.70963i
\(119\) −12.6202 10.5896i −1.15689 0.970748i
\(120\) 0 0
\(121\) 0.0570802 + 0.323718i 0.00518911 + 0.0294289i
\(122\) 10.3107 14.7252i 0.933484 1.33315i
\(123\) 0 0
\(124\) 1.01645 1.21135i 0.0912796 0.108783i
\(125\) −3.03004 + 10.7619i −0.271015 + 0.962575i
\(126\) 0 0
\(127\) −5.52679 20.6263i −0.490423 1.83028i −0.554286 0.832326i \(-0.687009\pi\)
0.0638628 0.997959i \(-0.479658\pi\)
\(128\) −6.66265 + 14.2881i −0.588901 + 1.26290i
\(129\) 0 0
\(130\) −10.1852 + 14.4163i −0.893304 + 1.26439i
\(131\) 5.67190 15.5834i 0.495556 1.36153i −0.399973 0.916527i \(-0.630980\pi\)
0.895529 0.445003i \(-0.146797\pi\)
\(132\) 0 0
\(133\) −7.45929 + 5.22305i −0.646802 + 0.452896i
\(134\) 0.966985 0.0835348
\(135\) 0 0
\(136\) −35.0721 −3.00741
\(137\) 16.4221 11.4989i 1.40304 0.982418i 0.405371 0.914152i \(-0.367142\pi\)
0.997667 0.0682654i \(-0.0217465\pi\)
\(138\) 0 0
\(139\) 6.07923 16.7026i 0.515634 1.41669i −0.359652 0.933087i \(-0.617105\pi\)
0.875286 0.483606i \(-0.160673\pi\)
\(140\) 4.39776 + 25.5708i 0.371678 + 2.16113i
\(141\) 0 0
\(142\) −10.3582 + 22.2132i −0.869238 + 1.86409i
\(143\) −2.66043 9.92886i −0.222476 0.830293i
\(144\) 0 0
\(145\) −4.95535 + 4.91374i −0.411519 + 0.408064i
\(146\) 0.0415627 0.0495324i 0.00343975 0.00409933i
\(147\) 0 0
\(148\) −10.9155 + 15.5890i −0.897250 + 1.28141i
\(149\) 0.147586 + 0.837002i 0.0120907 + 0.0685699i 0.990256 0.139258i \(-0.0444717\pi\)
−0.978165 + 0.207828i \(0.933361\pi\)
\(150\) 0 0
\(151\) 11.3395 + 9.51495i 0.922794 + 0.774316i 0.974510 0.224346i \(-0.0720246\pi\)
−0.0517160 + 0.998662i \(0.516469\pi\)
\(152\) −5.01740 + 18.7252i −0.406965 + 1.51881i
\(153\) 0 0
\(154\) −19.1808 11.0740i −1.54563 0.892372i
\(155\) 0.469527 + 0.676607i 0.0377133 + 0.0543464i
\(156\) 0 0
\(157\) 0.891290 10.1875i 0.0711327 0.813051i −0.873907 0.486094i \(-0.838421\pi\)
0.945039 0.326957i \(-0.106023\pi\)
\(158\) −25.2917 + 11.7937i −2.01210 + 0.938257i
\(159\) 0 0
\(160\) 5.39483 + 4.56570i 0.426499 + 0.360950i
\(161\) 13.4295i 1.05839i
\(162\) 0 0
\(163\) −9.20802 9.20802i −0.721228 0.721228i 0.247628 0.968855i \(-0.420349\pi\)
−0.968855 + 0.247628i \(0.920349\pi\)
\(164\) −5.71318 + 32.4011i −0.446125 + 2.53010i
\(165\) 0 0
\(166\) −2.57993 0.939019i −0.200242 0.0728820i
\(167\) −4.80307 0.420214i −0.371672 0.0325171i −0.100210 0.994966i \(-0.531952\pi\)
−0.271462 + 0.962449i \(0.587507\pi\)
\(168\) 0 0
\(169\) 1.05980 + 2.91178i 0.0815232 + 0.223983i
\(170\) 8.98940 32.9919i 0.689455 2.53036i
\(171\) 0 0
\(172\) 18.4126 + 4.93365i 1.40395 + 0.376187i
\(173\) −6.42280 + 0.561923i −0.488317 + 0.0427222i −0.328656 0.944450i \(-0.606596\pi\)
−0.159661 + 0.987172i \(0.551040\pi\)
\(174\) 0 0
\(175\) −13.4512 1.29120i −1.01682 0.0976058i
\(176\) −18.8095 + 3.31663i −1.41782 + 0.250000i
\(177\) 0 0
\(178\) 1.71942 + 19.6531i 0.128876 + 1.47306i
\(179\) −1.30891 2.26710i −0.0978327 0.169451i 0.812955 0.582327i \(-0.197858\pi\)
−0.910787 + 0.412876i \(0.864524\pi\)
\(180\) 0 0
\(181\) 8.91293 15.4376i 0.662493 1.14747i −0.317466 0.948270i \(-0.602832\pi\)
0.979959 0.199202i \(-0.0638348\pi\)
\(182\) −19.3353 9.01620i −1.43323 0.668325i
\(183\) 0 0
\(184\) 18.3771 + 21.9010i 1.35478 + 1.61456i
\(185\) −6.33881 7.61931i −0.466039 0.560183i
\(186\) 0 0
\(187\) 11.4216 + 16.3118i 0.835233 + 1.19284i
\(188\) 20.8942 20.8942i 1.52387 1.52387i
\(189\) 0 0
\(190\) −16.3285 9.51929i −1.18460 0.690602i
\(191\) 8.64200 + 1.52382i 0.625313 + 0.110260i 0.477321 0.878729i \(-0.341608\pi\)
0.147992 + 0.988989i \(0.452719\pi\)
\(192\) 0 0
\(193\) 0.517574 + 1.10994i 0.0372558 + 0.0798952i 0.924055 0.382260i \(-0.124854\pi\)
−0.886799 + 0.462155i \(0.847076\pi\)
\(194\) 9.85290 8.26756i 0.707397 0.593576i
\(195\) 0 0
\(196\) −1.22693 + 0.446566i −0.0876379 + 0.0318976i
\(197\) −13.5645 + 3.63461i −0.966434 + 0.258955i −0.707321 0.706892i \(-0.750097\pi\)
−0.259112 + 0.965847i \(0.583430\pi\)
\(198\) 0 0
\(199\) −11.1726 + 6.45050i −0.792004 + 0.457264i −0.840668 0.541552i \(-0.817837\pi\)
0.0486637 + 0.998815i \(0.484504\pi\)
\(200\) −23.7033 + 16.3011i −1.67608 + 1.15266i
\(201\) 0 0
\(202\) 2.44365 + 1.71106i 0.171934 + 0.120390i
\(203\) −6.90922 4.83789i −0.484932 0.339553i
\(204\) 0 0
\(205\) −15.4990 7.30702i −1.08250 0.510344i
\(206\) −0.408725 + 0.235978i −0.0284772 + 0.0164413i
\(207\) 0 0
\(208\) −17.7709 + 4.76170i −1.23219 + 0.330164i
\(209\) 10.3429 3.76452i 0.715435 0.260397i
\(210\) 0 0
\(211\) −0.0983096 + 0.0824916i −0.00676791 + 0.00567895i −0.646165 0.763197i \(-0.723628\pi\)
0.639397 + 0.768876i \(0.279184\pi\)
\(212\) 8.93021 + 19.1509i 0.613329 + 1.31529i
\(213\) 0 0
\(214\) −6.17397 1.08864i −0.422044 0.0744177i
\(215\) −5.00008 + 8.57668i −0.341002 + 0.584924i
\(216\) 0 0
\(217\) −0.703849 + 0.703849i −0.0477804 + 0.0477804i
\(218\) −11.2343 16.0442i −0.760881 1.08665i
\(219\) 0 0
\(220\) 2.86504 31.2306i 0.193161 2.10556i
\(221\) 12.3294 + 14.6937i 0.829368 + 0.988402i
\(222\) 0 0
\(223\) −7.59226 3.54033i −0.508415 0.237078i 0.151446 0.988466i \(-0.451607\pi\)
−0.659861 + 0.751388i \(0.729385\pi\)
\(224\) −4.27106 + 7.39769i −0.285372 + 0.494279i
\(225\) 0 0
\(226\) 24.4541 + 42.3557i 1.62666 + 2.81746i
\(227\) −0.314610 3.59601i −0.0208814 0.238675i −0.999462 0.0328096i \(-0.989555\pi\)
0.978580 0.205866i \(-0.0660010\pi\)
\(228\) 0 0
\(229\) −1.22130 + 0.215349i −0.0807059 + 0.0142306i −0.213855 0.976865i \(-0.568602\pi\)
0.133149 + 0.991096i \(0.457491\pi\)
\(230\) −25.3122 + 11.6736i −1.66904 + 0.769736i
\(231\) 0 0
\(232\) −17.8879 + 1.56498i −1.17440 + 0.102746i
\(233\) 20.0624 + 5.37571i 1.31433 + 0.352175i 0.846852 0.531828i \(-0.178495\pi\)
0.467481 + 0.884003i \(0.345161\pi\)
\(234\) 0 0
\(235\) 7.63841 + 13.3599i 0.498275 + 0.871502i
\(236\) 11.2541 + 30.9205i 0.732582 + 2.01275i
\(237\) 0 0
\(238\) 41.1719 + 3.60207i 2.66878 + 0.233488i
\(239\) 11.3730 + 4.13943i 0.735658 + 0.267758i 0.682558 0.730831i \(-0.260867\pi\)
0.0531004 + 0.998589i \(0.483090\pi\)
\(240\) 0 0
\(241\) −1.19187 + 6.75943i −0.0767751 + 0.435413i 0.922055 + 0.387059i \(0.126509\pi\)
−0.998830 + 0.0483548i \(0.984602\pi\)
\(242\) −0.583102 0.583102i −0.0374832 0.0374832i
\(243\) 0 0
\(244\) 30.7650i 1.96953i
\(245\) −0.0564100 0.677662i −0.00360390 0.0432943i
\(246\) 0 0
\(247\) 9.60887 4.48069i 0.611397 0.285099i
\(248\) −0.184689 + 2.11100i −0.0117277 + 0.134049i
\(249\) 0 0
\(250\) −9.25882 26.4756i −0.585579 1.67446i
\(251\) −8.53784 4.92932i −0.538904 0.311136i 0.205731 0.978609i \(-0.434043\pi\)
−0.744634 + 0.667472i \(0.767376\pi\)
\(252\) 0 0
\(253\) 4.20128 15.6794i 0.264132 0.985754i
\(254\) 41.0369 + 34.4341i 2.57489 + 2.16059i
\(255\) 0 0
\(256\) −5.56035 31.5343i −0.347522 1.97090i
\(257\) −6.45152 + 9.21372i −0.402435 + 0.574736i −0.968309 0.249755i \(-0.919650\pi\)
0.565874 + 0.824491i \(0.308539\pi\)
\(258\) 0 0
\(259\) 7.70013 9.17666i 0.478463 0.570210i
\(260\) 0.127359 30.2089i 0.00789847 1.87347i
\(261\) 0 0
\(262\) 10.7676 + 40.1851i 0.665222 + 2.48264i
\(263\) −3.48321 + 7.46977i −0.214784 + 0.460606i −0.983950 0.178443i \(-0.942894\pi\)
0.769166 + 0.639049i \(0.220672\pi\)
\(264\) 0 0
\(265\) −10.8458 + 1.86530i −0.666254 + 0.114584i
\(266\) 7.81320 21.4666i 0.479058 1.31620i
\(267\) 0 0
\(268\) −1.35565 + 0.949234i −0.0828093 + 0.0579837i
\(269\) −21.3745 −1.30322 −0.651612 0.758553i \(-0.725907\pi\)
−0.651612 + 0.758553i \(0.725907\pi\)
\(270\) 0 0
\(271\) −16.0063 −0.972313 −0.486157 0.873872i \(-0.661602\pi\)
−0.486157 + 0.873872i \(0.661602\pi\)
\(272\) 29.1952 20.4427i 1.77022 1.23952i
\(273\) 0 0
\(274\) −17.2013 + 47.2602i −1.03917 + 2.85509i
\(275\) 15.3008 + 5.71559i 0.922672 + 0.344663i
\(276\) 0 0
\(277\) 6.07443 13.0267i 0.364977 0.782696i −0.634971 0.772536i \(-0.718988\pi\)
0.999948 0.0101600i \(-0.00323409\pi\)
\(278\) 11.5408 + 43.0710i 0.692174 + 2.58323i
\(279\) 0 0
\(280\) −24.4821 24.6894i −1.46308 1.47547i
\(281\) 6.85563 8.17022i 0.408973 0.487395i −0.521761 0.853091i \(-0.674725\pi\)
0.930734 + 0.365697i \(0.119169\pi\)
\(282\) 0 0
\(283\) 14.1133 20.1559i 0.838951 1.19815i −0.139203 0.990264i \(-0.544454\pi\)
0.978154 0.207882i \(-0.0666570\pi\)
\(284\) −7.28395 41.3093i −0.432223 2.45126i
\(285\) 0 0
\(286\) 19.7539 + 16.5755i 1.16808 + 0.980132i
\(287\) 5.36021 20.0046i 0.316403 1.18083i
\(288\) 0 0
\(289\) −17.4577 10.0792i −1.02692 0.592895i
\(290\) 3.11271 17.2280i 0.182784 1.01166i
\(291\) 0 0
\(292\) −0.00964481 + 0.110241i −0.000564420 + 0.00645135i
\(293\) −21.7565 + 10.1452i −1.27103 + 0.592691i −0.936821 0.349809i \(-0.886247\pi\)
−0.334208 + 0.942499i \(0.608469\pi\)
\(294\) 0 0
\(295\) −17.0781 + 1.42162i −0.994326 + 0.0827697i
\(296\) 25.5023i 1.48229i
\(297\) 0 0
\(298\) −1.50766 1.50766i −0.0873366 0.0873366i
\(299\) 2.71515 15.3984i 0.157021 0.890512i
\(300\) 0 0
\(301\) −11.2755 4.10394i −0.649908 0.236547i
\(302\) −36.9937 3.23653i −2.12875 0.186241i
\(303\) 0 0
\(304\) −6.73782 18.5120i −0.386440 1.06174i
\(305\) −15.4591 4.21219i −0.885187 0.241190i
\(306\) 0 0
\(307\) −3.92820 1.05256i −0.224194 0.0600726i 0.144973 0.989436i \(-0.453690\pi\)
−0.369167 + 0.929363i \(0.620357\pi\)
\(308\) 37.7609 3.30365i 2.15163 0.188243i
\(309\) 0 0
\(310\) −1.93845 0.714808i −0.110097 0.0405984i
\(311\) 9.98381 1.76041i 0.566130 0.0998239i 0.116744 0.993162i \(-0.462754\pi\)
0.449385 + 0.893338i \(0.351643\pi\)
\(312\) 0 0
\(313\) −2.56936 29.3680i −0.145229 1.65998i −0.623545 0.781787i \(-0.714308\pi\)
0.478316 0.878188i \(-0.341247\pi\)
\(314\) 12.8274 + 22.2177i 0.723890 + 1.25381i
\(315\) 0 0
\(316\) 23.8800 41.3614i 1.34335 2.32676i
\(317\) −2.83348 1.32127i −0.159144 0.0742101i 0.341414 0.939913i \(-0.389094\pi\)
−0.500558 + 0.865703i \(0.666872\pi\)
\(318\) 0 0
\(319\) 6.55325 + 7.80986i 0.366912 + 0.437268i
\(320\) 8.38239 + 0.768988i 0.468590 + 0.0429877i
\(321\) 0 0
\(322\) −19.3239 27.5975i −1.07688 1.53795i
\(323\) −14.5232 + 14.5232i −0.808094 + 0.808094i
\(324\) 0 0
\(325\) 15.1622 + 4.20005i 0.841049 + 0.232977i
\(326\) 32.1719 + 5.67278i 1.78184 + 0.314186i
\(327\) 0 0
\(328\) −18.6330 39.9586i −1.02884 2.20635i
\(329\) −14.2486 + 11.9560i −0.785551 + 0.659155i
\(330\) 0 0
\(331\) 27.5786 10.0378i 1.51586 0.551727i 0.555747 0.831351i \(-0.312432\pi\)
0.960109 + 0.279624i \(0.0902099\pi\)
\(332\) 4.53867 1.21613i 0.249092 0.0667439i
\(333\) 0 0
\(334\) 10.4749 6.04768i 0.573160 0.330914i
\(335\) −0.291372 0.811164i −0.0159194 0.0443186i
\(336\) 0 0
\(337\) 13.1165 + 9.18427i 0.714501 + 0.500299i 0.873405 0.486995i \(-0.161907\pi\)
−0.158904 + 0.987294i \(0.550796\pi\)
\(338\) −6.36769 4.45870i −0.346356 0.242521i
\(339\) 0 0
\(340\) 19.7837 + 55.0767i 1.07292 + 2.98695i
\(341\) 1.04196 0.601574i 0.0564252 0.0325771i
\(342\) 0 0
\(343\) −17.4798 + 4.68369i −0.943819 + 0.252896i
\(344\) −24.0041 + 8.73676i −1.29421 + 0.471055i
\(345\) 0 0
\(346\) 12.3902 10.3966i 0.666102 0.558926i
\(347\) −0.872755 1.87163i −0.0468520 0.100474i 0.881488 0.472206i \(-0.156542\pi\)
−0.928340 + 0.371731i \(0.878764\pi\)
\(348\) 0 0
\(349\) 0.561803 + 0.0990609i 0.0300726 + 0.00530261i 0.188664 0.982042i \(-0.439584\pi\)
−0.158592 + 0.987344i \(0.550695\pi\)
\(350\) 29.5000 16.7018i 1.57684 0.892748i
\(351\) 0 0
\(352\) 7.30088 7.30088i 0.389138 0.389138i
\(353\) −4.33346 6.18882i −0.230647 0.329398i 0.687101 0.726562i \(-0.258883\pi\)
−0.917747 + 0.397165i \(0.869994\pi\)
\(354\) 0 0
\(355\) 21.7548 + 1.99575i 1.15463 + 0.105924i
\(356\) −21.7028 25.8644i −1.15024 1.37081i
\(357\) 0 0
\(358\) 5.95197 + 2.77545i 0.314571 + 0.146687i
\(359\) −7.12655 + 12.3435i −0.376125 + 0.651467i −0.990495 0.137551i \(-0.956077\pi\)
0.614370 + 0.789018i \(0.289410\pi\)
\(360\) 0 0
\(361\) −3.82366 6.62277i −0.201245 0.348567i
\(362\) 3.89754 + 44.5491i 0.204850 + 2.34145i
\(363\) 0 0
\(364\) 35.9574 6.34026i 1.88468 0.332320i
\(365\) −0.0540744 0.0199400i −0.00283038 0.00104371i
\(366\) 0 0
\(367\) −17.9778 + 1.57285i −0.938434 + 0.0821024i −0.546100 0.837720i \(-0.683888\pi\)
−0.392335 + 0.919823i \(0.628332\pi\)
\(368\) −28.0633 7.51954i −1.46290 0.391983i
\(369\) 0 0
\(370\) 23.9897 + 6.53655i 1.24717 + 0.339819i
\(371\) −4.54928 12.4990i −0.236187 0.648918i
\(372\) 0 0
\(373\) −5.43209 0.475246i −0.281263 0.0246073i −0.0543485 0.998522i \(-0.517308\pi\)
−0.226914 + 0.973915i \(0.572864\pi\)
\(374\) −46.9426 17.0857i −2.42735 0.883481i
\(375\) 0 0
\(376\) −6.87604 + 38.9959i −0.354604 + 2.01106i
\(377\) 6.94405 + 6.94405i 0.357637 + 0.357637i
\(378\) 0 0
\(379\) 4.04015i 0.207529i 0.994602 + 0.103764i \(0.0330888\pi\)
−0.994602 + 0.103764i \(0.966911\pi\)
\(380\) 32.2360 2.68339i 1.65367 0.137655i
\(381\) 0 0
\(382\) −19.9518 + 9.30369i −1.02082 + 0.476018i
\(383\) 2.67534 30.5793i 0.136704 1.56253i −0.549732 0.835341i \(-0.685270\pi\)
0.686436 0.727190i \(-0.259174\pi\)
\(384\) 0 0
\(385\) −3.50998 + 19.4268i −0.178885 + 0.990082i
\(386\) −2.66072 1.53617i −0.135427 0.0781888i
\(387\) 0 0
\(388\) −5.69729 + 21.2626i −0.289236 + 1.07944i
\(389\) 23.0823 + 19.3684i 1.17032 + 0.982014i 0.999994 0.00337359i \(-0.00107385\pi\)
0.170325 + 0.985388i \(0.445518\pi\)
\(390\) 0 0
\(391\) 5.25988 + 29.8302i 0.266003 + 1.50858i
\(392\) 1.00358 1.43326i 0.0506885 0.0723907i
\(393\) 0 0
\(394\) 22.6451 26.9873i 1.14084 1.35960i
\(395\) 17.5142 + 17.6625i 0.881233 + 0.888695i
\(396\) 0 0
\(397\) 7.37720 + 27.5321i 0.370251 + 1.38180i 0.860161 + 0.510023i \(0.170363\pi\)
−0.489910 + 0.871773i \(0.662970\pi\)
\(398\) 13.6778 29.3321i 0.685605 1.47029i
\(399\) 0 0
\(400\) 10.2299 27.3857i 0.511494 1.36928i
\(401\) −9.65646 + 26.5309i −0.482221 + 1.32489i 0.425364 + 0.905022i \(0.360146\pi\)
−0.907585 + 0.419868i \(0.862076\pi\)
\(402\) 0 0
\(403\) 0.949342 0.664736i 0.0472901 0.0331129i
\(404\) −5.10547 −0.254007
\(405\) 0 0
\(406\) 21.1597 1.05014
\(407\) −11.8610 + 8.30514i −0.587926 + 0.411670i
\(408\) 0 0
\(409\) 6.83310 18.7738i 0.337875 0.928304i −0.648121 0.761537i \(-0.724445\pi\)
0.985996 0.166767i \(-0.0533328\pi\)
\(410\) 42.3644 7.28597i 2.09223 0.359828i
\(411\) 0 0
\(412\) 0.341359 0.732046i 0.0168175 0.0360653i
\(413\) −5.36086 20.0070i −0.263790 0.984479i
\(414\) 0 0
\(415\) −0.0103170 + 2.44714i −0.000506443 + 0.120126i
\(416\) 6.39288 7.61873i 0.313437 0.373539i
\(417\) 0 0
\(418\) −15.8377 + 22.6186i −0.774649 + 1.10631i
\(419\) −1.26780 7.19003i −0.0619359 0.351256i −0.999989 0.00476336i \(-0.998484\pi\)
0.938053 0.346492i \(-0.112627\pi\)
\(420\) 0 0
\(421\) −22.3147 18.7243i −1.08755 0.912566i −0.0910275 0.995848i \(-0.529015\pi\)
−0.996526 + 0.0832827i \(0.973460\pi\)
\(422\) 0.0833264 0.310978i 0.00405627 0.0151382i
\(423\) 0 0
\(424\) −24.5229 14.1583i −1.19094 0.687587i
\(425\) −30.3842 + 2.40030i −1.47385 + 0.116432i
\(426\) 0 0
\(427\) 1.68784 19.2921i 0.0816802 0.933609i
\(428\) 9.72412 4.53443i 0.470033 0.219180i
\(429\) 0 0
\(430\) −2.06604 24.8196i −0.0996331 1.19691i
\(431\) 14.3391i 0.690690i −0.938476 0.345345i \(-0.887762\pi\)
0.938476 0.345345i \(-0.112238\pi\)
\(432\) 0 0
\(433\) 16.2907 + 16.2907i 0.782881 + 0.782881i 0.980316 0.197435i \(-0.0632612\pi\)
−0.197435 + 0.980316i \(0.563261\pi\)
\(434\) 0.433620 2.45918i 0.0208144 0.118044i
\(435\) 0 0
\(436\) 31.4993 + 11.4648i 1.50854 + 0.549065i
\(437\) 16.6790 + 1.45922i 0.797865 + 0.0698041i
\(438\) 0 0
\(439\) 6.36027 + 17.4747i 0.303559 + 0.834021i 0.993875 + 0.110513i \(0.0352494\pi\)
−0.690316 + 0.723508i \(0.742528\pi\)
\(440\) 20.8598 + 36.4846i 0.994451 + 1.73933i
\(441\) 0 0
\(442\) −46.4798 12.4542i −2.21082 0.592387i
\(443\) −27.1205 + 2.37273i −1.28853 + 0.112732i −0.710741 0.703453i \(-0.751640\pi\)
−0.577790 + 0.816185i \(0.696085\pi\)
\(444\) 0 0
\(445\) 15.9680 7.36422i 0.756957 0.349097i
\(446\) 20.6962 3.64930i 0.979994 0.172799i
\(447\) 0 0
\(448\) 0.886712 + 10.1352i 0.0418932 + 0.478841i
\(449\) −15.3860 26.6493i −0.726109 1.25766i −0.958516 0.285039i \(-0.907994\pi\)
0.232407 0.972619i \(-0.425340\pi\)
\(450\) 0 0
\(451\) −12.5164 + 21.6791i −0.589375 + 1.02083i
\(452\) −75.8611 35.3746i −3.56820 1.66388i
\(453\) 0 0
\(454\) 5.82087 + 6.93705i 0.273187 + 0.325572i
\(455\) −1.73719 + 18.9363i −0.0814407 + 0.887749i
\(456\) 0 0
\(457\) 13.4321 + 19.1830i 0.628327 + 0.897344i 0.999513 0.0312144i \(-0.00993748\pi\)
−0.371185 + 0.928559i \(0.621049\pi\)
\(458\) 2.19989 2.19989i 0.102794 0.102794i
\(459\) 0 0
\(460\) 24.0267 41.2132i 1.12025 1.92157i
\(461\) −31.1056 5.48476i −1.44873 0.255451i −0.606724 0.794913i \(-0.707517\pi\)
−0.842010 + 0.539462i \(0.818628\pi\)
\(462\) 0 0
\(463\) 12.3947 + 26.5805i 0.576030 + 1.23530i 0.951266 + 0.308371i \(0.0997839\pi\)
−0.375236 + 0.926929i \(0.622438\pi\)
\(464\) 13.9783 11.7292i 0.648924 0.544512i
\(465\) 0 0
\(466\) −48.9632 + 17.8212i −2.26818 + 0.825549i
\(467\) 20.0112 5.36199i 0.926008 0.248123i 0.235857 0.971788i \(-0.424210\pi\)
0.690152 + 0.723665i \(0.257544\pi\)
\(468\) 0 0
\(469\) 0.902173 0.520870i 0.0416585 0.0240515i
\(470\) −34.9206 16.4633i −1.61077 0.759396i
\(471\) 0 0
\(472\) −36.1204 25.2917i −1.66257 1.16415i
\(473\) 11.8806 + 8.31889i 0.546271 + 0.382503i
\(474\) 0 0
\(475\) −3.06521 + 16.5657i −0.140642 + 0.760085i
\(476\) −61.2561 + 35.3662i −2.80767 + 1.62101i
\(477\) 0 0
\(478\) −29.3277 + 7.85832i −1.34142 + 0.359431i
\(479\) −7.18880 + 2.61651i −0.328465 + 0.119551i −0.500988 0.865454i \(-0.667030\pi\)
0.172524 + 0.985005i \(0.444808\pi\)
\(480\) 0 0
\(481\) −10.6843 + 8.96523i −0.487164 + 0.408779i
\(482\) −7.27698 15.6055i −0.331458 0.710813i
\(483\) 0 0
\(484\) 1.38986 + 0.245071i 0.0631757 + 0.0111396i
\(485\) −9.90419 5.77400i −0.449726 0.262184i
\(486\) 0 0
\(487\) 8.90898 8.90898i 0.403704 0.403704i −0.475832 0.879536i \(-0.657853\pi\)
0.879536 + 0.475832i \(0.157853\pi\)
\(488\) −23.6470 33.7714i −1.07045 1.52876i
\(489\) 0 0
\(490\) 1.09102 + 1.31142i 0.0492873 + 0.0592438i
\(491\) −2.30460 2.74652i −0.104005 0.123949i 0.711531 0.702655i \(-0.248002\pi\)
−0.815536 + 0.578706i \(0.803558\pi\)
\(492\) 0 0
\(493\) −17.2419 8.04003i −0.776536 0.362105i
\(494\) −13.2987 + 23.0341i −0.598339 + 1.03635i
\(495\) 0 0
\(496\) −1.07671 1.86492i −0.0483458 0.0837373i
\(497\) 2.30128 + 26.3038i 0.103227 + 1.17989i
\(498\) 0 0
\(499\) −0.621729 + 0.109628i −0.0278324 + 0.00490760i −0.187547 0.982256i \(-0.560054\pi\)
0.159715 + 0.987163i \(0.448943\pi\)
\(500\) 38.9697 + 28.0280i 1.74278 + 1.25345i
\(501\) 0 0
\(502\) 24.6380 2.15555i 1.09965 0.0962068i
\(503\) 36.5596 + 9.79612i 1.63011 + 0.436788i 0.953950 0.299964i \(-0.0969748\pi\)
0.676163 + 0.736752i \(0.263641\pi\)
\(504\) 0 0
\(505\) 0.699016 2.56545i 0.0311058 0.114161i
\(506\) 13.9278 + 38.2662i 0.619164 + 1.70114i
\(507\) 0 0
\(508\) −91.3329 7.99059i −4.05224 0.354525i
\(509\) 27.9791 + 10.1836i 1.24015 + 0.451378i 0.877063 0.480376i \(-0.159500\pi\)
0.363089 + 0.931754i \(0.381722\pi\)
\(510\) 0 0
\(511\) 0.0120961 0.0686004i 0.000535100 0.00303470i
\(512\) 34.5064 + 34.5064i 1.52498 + 1.52498i
\(513\) 0 0
\(514\) 28.2173i 1.24461i
\(515\) 0.321109 + 0.271757i 0.0141497 + 0.0119751i
\(516\) 0 0
\(517\) 20.3760 9.50148i 0.896135 0.417875i
\(518\) −2.61921 + 29.9377i −0.115082 + 1.31539i
\(519\) 0 0
\(520\) 23.0797 + 33.2588i 1.01211 + 1.45849i
\(521\) −27.1230 15.6595i −1.18828 0.686054i −0.230365 0.973104i \(-0.573992\pi\)
−0.957915 + 0.287050i \(0.907325\pi\)
\(522\) 0 0
\(523\) 8.52925 31.8316i 0.372958 1.39190i −0.483347 0.875429i \(-0.660579\pi\)
0.856305 0.516470i \(-0.172754\pi\)
\(524\) −54.5428 45.7668i −2.38271 1.99933i
\(525\) 0 0
\(526\) −3.59043 20.3623i −0.156550 0.887840i
\(527\) −1.28775 + 1.83910i −0.0560952 + 0.0801122i
\(528\) 0 0
\(529\) 1.08748 1.29601i 0.0472817 0.0563482i
\(530\) 19.6040 19.4394i 0.851543 0.844394i
\(531\) 0 0
\(532\) 10.1189 + 37.7644i 0.438712 + 1.63730i
\(533\) −10.1905 + 21.8537i −0.441401 + 0.946588i
\(534\) 0 0
\(535\) 0.947130 + 5.50711i 0.0409480 + 0.238093i
\(536\) 0.758509 2.08399i 0.0327626 0.0900144i
\(537\) 0 0
\(538\) 43.9242 30.7561i 1.89371 1.32599i
\(539\) −0.993428 −0.0427900
\(540\) 0 0
\(541\) −19.8436 −0.853142 −0.426571 0.904454i \(-0.640279\pi\)
−0.426571 + 0.904454i \(0.640279\pi\)
\(542\) 32.8927 23.0317i 1.41286 0.989297i
\(543\) 0 0
\(544\) −6.58965 + 18.1049i −0.282529 + 0.776241i
\(545\) −10.0737 + 14.2584i −0.431510 + 0.610763i
\(546\) 0 0
\(547\) 7.36373 15.7916i 0.314851 0.675199i −0.683658 0.729803i \(-0.739612\pi\)
0.998508 + 0.0546038i \(0.0173896\pi\)
\(548\) −22.2776 83.1410i −0.951650 3.55161i
\(549\) 0 0
\(550\) −39.6672 + 10.2711i −1.69141 + 0.437961i
\(551\) −6.75924 + 8.05534i −0.287953 + 0.343169i
\(552\) 0 0
\(553\) −17.2438 + 24.6267i −0.733281 + 1.04723i
\(554\) 6.26140 + 35.5102i 0.266022 + 1.50868i
\(555\) 0 0
\(556\) −58.4598 49.0536i −2.47925 2.08034i
\(557\) 2.61924 9.77513i 0.110981 0.414185i −0.887974 0.459893i \(-0.847888\pi\)
0.998955 + 0.0457078i \(0.0145543\pi\)
\(558\) 0 0
\(559\) 12.0988 + 6.98526i 0.511726 + 0.295445i
\(560\) 34.7705 + 6.28225i 1.46932 + 0.265473i
\(561\) 0 0
\(562\) −2.33196 + 26.6544i −0.0983676 + 1.12435i
\(563\) 33.8599 15.7891i 1.42702 0.665432i 0.452923 0.891550i \(-0.350381\pi\)
0.974100 + 0.226118i \(0.0726034\pi\)
\(564\) 0 0
\(565\) 28.1619 33.2761i 1.18478 1.39994i
\(566\) 61.7281i 2.59462i
\(567\) 0 0
\(568\) 39.7474 + 39.7474i 1.66776 + 1.66776i
\(569\) −0.949414 + 5.38439i −0.0398015 + 0.225725i −0.998220 0.0596413i \(-0.981004\pi\)
0.958418 + 0.285367i \(0.0921154\pi\)
\(570\) 0 0
\(571\) −27.1899 9.89631i −1.13786 0.414148i −0.296721 0.954964i \(-0.595893\pi\)
−0.841141 + 0.540817i \(0.818115\pi\)
\(572\) −43.9649 3.84643i −1.83826 0.160827i
\(573\) 0 0
\(574\) 17.7698 + 48.8220i 0.741695 + 2.03779i
\(575\) 17.4196 + 17.7159i 0.726448 + 0.738803i
\(576\) 0 0
\(577\) −13.3085 3.56601i −0.554041 0.148455i −0.0290738 0.999577i \(-0.509256\pi\)
−0.524967 + 0.851122i \(0.675922\pi\)
\(578\) 50.3785 4.40755i 2.09547 0.183330i
\(579\) 0 0
\(580\) 12.5479 + 27.2080i 0.521024 + 1.12975i
\(581\) −2.91282 + 0.513608i −0.120844 + 0.0213081i
\(582\) 0 0
\(583\) 1.40124 + 16.0162i 0.0580333 + 0.663324i
\(584\) −0.0741472 0.128427i −0.00306823 0.00531433i
\(585\) 0 0
\(586\) 30.1112 52.1541i 1.24388 2.15447i
\(587\) 19.2878 + 8.99405i 0.796093 + 0.371224i 0.777723 0.628607i \(-0.216375\pi\)
0.0183698 + 0.999831i \(0.494152\pi\)
\(588\) 0 0
\(589\) 0.797678 + 0.950636i 0.0328678 + 0.0391703i
\(590\) 33.0497 27.4954i 1.36063 1.13197i
\(591\) 0 0
\(592\) 14.8647 + 21.2290i 0.610936 + 0.872507i
\(593\) 9.84862 9.84862i 0.404434 0.404434i −0.475358 0.879792i \(-0.657681\pi\)
0.879792 + 0.475358i \(0.157681\pi\)
\(594\) 0 0
\(595\) −9.38431 35.6228i −0.384719 1.46039i
\(596\) 3.59362 + 0.633653i 0.147201 + 0.0259554i
\(597\) 0 0
\(598\) 16.5774 + 35.5503i 0.677900 + 1.45376i
\(599\) −7.79546 + 6.54117i −0.318514 + 0.267265i −0.788000 0.615675i \(-0.788884\pi\)
0.469486 + 0.882940i \(0.344439\pi\)
\(600\) 0 0
\(601\) 29.1191 10.5985i 1.18779 0.432321i 0.328845 0.944384i \(-0.393341\pi\)
0.858948 + 0.512063i \(0.171119\pi\)
\(602\) 29.0762 7.79094i 1.18506 0.317535i
\(603\) 0 0
\(604\) 55.0397 31.7772i 2.23953 1.29299i
\(605\) −0.313439 + 0.664840i −0.0127431 + 0.0270296i
\(606\) 0 0
\(607\) −24.8874 17.4264i −1.01015 0.707315i −0.0535038 0.998568i \(-0.517039\pi\)
−0.956646 + 0.291253i \(0.905928\pi\)
\(608\) 8.72359 + 6.10833i 0.353788 + 0.247725i
\(609\) 0 0
\(610\) 37.8293 13.5884i 1.53166 0.550178i
\(611\) 18.7548 10.8281i 0.758738 0.438058i
\(612\) 0 0
\(613\) 3.57095 0.956834i 0.144229 0.0386462i −0.185982 0.982553i \(-0.559547\pi\)
0.330211 + 0.943907i \(0.392880\pi\)
\(614\) 9.58694 3.48936i 0.386897 0.140819i
\(615\) 0 0
\(616\) −38.9116 + 32.6507i −1.56779 + 1.31553i
\(617\) −6.83850 14.6652i −0.275308 0.590399i 0.719231 0.694771i \(-0.244494\pi\)
−0.994538 + 0.104372i \(0.966717\pi\)
\(618\) 0 0
\(619\) −20.5670 3.62651i −0.826656 0.145762i −0.255714 0.966752i \(-0.582311\pi\)
−0.570942 + 0.820991i \(0.693422\pi\)
\(620\) 3.41926 0.900756i 0.137321 0.0361752i
\(621\) 0 0
\(622\) −17.9835 + 17.9835i −0.721072 + 0.721072i
\(623\) 12.1904 + 17.4096i 0.488396 + 0.697502i
\(624\) 0 0
\(625\) −19.4194 + 15.7445i −0.776775 + 0.629778i
\(626\) 47.5380 + 56.6536i 1.90000 + 2.26433i
\(627\) 0 0
\(628\) −39.7929 18.5557i −1.58791 0.740454i
\(629\) 13.5097 23.3995i 0.538667 0.932999i
\(630\) 0 0
\(631\) 7.86152 + 13.6165i 0.312962 + 0.542066i 0.979002 0.203850i \(-0.0653454\pi\)
−0.666040 + 0.745916i \(0.732012\pi\)
\(632\) 5.57811 + 63.7581i 0.221885 + 2.53616i
\(633\) 0 0
\(634\) 7.72396 1.36194i 0.306758 0.0540897i
\(635\) 16.5200 44.7999i 0.655578 1.77783i
\(636\) 0 0
\(637\) −0.953277 + 0.0834010i −0.0377702 + 0.00330447i
\(638\) −24.7046 6.61957i −0.978063 0.262071i
\(639\) 0 0
\(640\) −30.6032 + 17.4971i −1.20970 + 0.691635i
\(641\) −13.8355 38.0128i −0.546471 1.50142i −0.838443 0.544990i \(-0.816533\pi\)
0.291971 0.956427i \(-0.405689\pi\)
\(642\) 0 0
\(643\) 25.8204 + 2.25900i 1.01826 + 0.0890861i 0.584043 0.811723i \(-0.301470\pi\)
0.434216 + 0.900809i \(0.357026\pi\)
\(644\) 54.1816 + 19.7205i 2.13506 + 0.777097i
\(645\) 0 0
\(646\) 8.94731 50.7427i 0.352027 1.99645i
\(647\) −23.1817 23.1817i −0.911366 0.911366i 0.0850141 0.996380i \(-0.472906\pi\)
−0.996380 + 0.0850141i \(0.972906\pi\)
\(648\) 0 0
\(649\) 25.0359i 0.982744i
\(650\) −37.2017 + 13.1862i −1.45917 + 0.517203i
\(651\) 0 0
\(652\) −50.6714 + 23.6285i −1.98445 + 0.925362i
\(653\) −2.87574 + 32.8699i −0.112537 + 1.28630i 0.704496 + 0.709708i \(0.251173\pi\)
−0.817033 + 0.576591i \(0.804383\pi\)
\(654\) 0 0
\(655\) 30.4651 21.1411i 1.19037 0.826049i
\(656\) 38.8017 + 22.4022i 1.51495 + 0.874658i
\(657\) 0 0
\(658\) 12.0770 45.0720i 0.470810 1.75709i
\(659\) −12.5302 10.5141i −0.488108 0.409571i 0.365240 0.930914i \(-0.380987\pi\)
−0.853348 + 0.521342i \(0.825432\pi\)
\(660\) 0 0
\(661\) 4.84704 + 27.4889i 0.188528 + 1.06920i 0.921338 + 0.388762i \(0.127097\pi\)
−0.732810 + 0.680433i \(0.761792\pi\)
\(662\) −42.2301 + 60.3108i −1.64132 + 2.34405i
\(663\) 0 0
\(664\) −4.04743 + 4.82353i −0.157071 + 0.187189i
\(665\) −20.3617 0.0858439i −0.789593 0.00332888i
\(666\) 0 0
\(667\) 4.01378 + 14.9796i 0.155414 + 0.580014i
\(668\) −8.74840 + 18.7610i −0.338486 + 0.725885i
\(669\) 0 0
\(670\) 1.76596 + 1.24767i 0.0682251 + 0.0482017i
\(671\) −8.00592 + 21.9961i −0.309065 + 0.849149i
\(672\) 0 0
\(673\) −29.0771 + 20.3600i −1.12084 + 0.784821i −0.978755 0.205034i \(-0.934270\pi\)
−0.142085 + 0.989854i \(0.545381\pi\)
\(674\) −40.1696 −1.54728
\(675\) 0 0
\(676\) 13.3039 0.511688
\(677\) 1.67557 1.17325i 0.0643975 0.0450916i −0.540934 0.841065i \(-0.681929\pi\)
0.605332 + 0.795973i \(0.293040\pi\)
\(678\) 0 0
\(679\) 4.73916 13.0207i 0.181872 0.499689i
\(680\) −64.0507 45.2524i −2.45623 1.73535i
\(681\) 0 0
\(682\) −1.27559 + 2.73552i −0.0488450 + 0.104748i
\(683\) −2.32207 8.66609i −0.0888516 0.331599i 0.907164 0.420777i \(-0.138243\pi\)
−0.996016 + 0.0891783i \(0.971576\pi\)
\(684\) 0 0
\(685\) 44.8277 + 0.188991i 1.71278 + 0.00722098i
\(686\) 29.1812 34.7769i 1.11415 1.32779i
\(687\) 0 0
\(688\) 14.8893 21.2642i 0.567650 0.810689i
\(689\) 2.68921 + 15.2513i 0.102451 + 0.581027i
\(690\) 0 0
\(691\) −22.2034 18.6309i −0.844657 0.708752i 0.113949 0.993487i \(-0.463650\pi\)
−0.958606 + 0.284735i \(0.908094\pi\)
\(692\) −7.16445 + 26.7381i −0.272352 + 1.01643i
\(693\) 0 0
\(694\) 4.48662 + 2.59035i 0.170310 + 0.0983284i
\(695\) 32.6530 22.6593i 1.23860 0.859517i
\(696\) 0 0
\(697\) 4.07124 46.5345i 0.154209 1.76262i
\(698\) −1.29704 + 0.604818i −0.0490936 + 0.0228927i
\(699\) 0 0
\(700\) −24.9618 + 52.3732i −0.943467 + 1.97952i
\(701\) 4.40189i 0.166257i −0.996539 0.0831285i \(-0.973509\pi\)
0.996539 0.0831285i \(-0.0264912\pi\)
\(702\) 0 0
\(703\) −10.5604 10.5604i −0.398294 0.398294i
\(704\) 2.13541 12.1105i 0.0804813 0.456432i
\(705\) 0 0
\(706\) 17.8104 + 6.48245i 0.670303 + 0.243970i
\(707\) 3.20153 + 0.280098i 0.120406 + 0.0105342i
\(708\) 0 0
\(709\) −8.05475 22.1303i −0.302503 0.831119i −0.994064 0.108801i \(-0.965299\pi\)
0.691561 0.722318i \(-0.256923\pi\)
\(710\) −47.5776 + 27.2021i −1.78555 + 1.02088i
\(711\) 0 0
\(712\) 43.7037 + 11.7104i 1.63787 + 0.438865i
\(713\) 1.82319 0.159508i 0.0682790 0.00597364i
\(714\) 0 0
\(715\) 7.95225 21.5653i 0.297397 0.806497i
\(716\) −11.0687 + 1.95172i −0.413658 + 0.0729391i
\(717\) 0 0
\(718\) −3.11637 35.6203i −0.116302 1.32934i
\(719\) 3.55440 + 6.15640i 0.132557 + 0.229595i 0.924661 0.380790i \(-0.124348\pi\)
−0.792105 + 0.610385i \(0.791015\pi\)
\(720\) 0 0
\(721\) −0.254220 + 0.440322i −0.00946765 + 0.0163985i
\(722\) 17.3872 + 8.10778i 0.647084 + 0.301740i
\(723\) 0 0
\(724\) −49.1954 58.6288i −1.82833 2.17892i
\(725\) −15.3898 + 2.58003i −0.571562 + 0.0958198i
\(726\) 0 0
\(727\) 11.1796 + 15.9661i 0.414627 + 0.592148i 0.971087 0.238726i \(-0.0767298\pi\)
−0.556460 + 0.830874i \(0.687841\pi\)
\(728\) −34.5978 + 34.5978i −1.28228 + 1.28228i
\(729\) 0 0
\(730\) 0.139814 0.0368320i 0.00517475 0.00136321i
\(731\) −26.6530 4.69964i −0.985796 0.173822i
\(732\) 0 0
\(733\) 15.4914 + 33.2213i 0.572186 + 1.22706i 0.953159 + 0.302471i \(0.0978116\pi\)
−0.380972 + 0.924587i \(0.624411\pi\)
\(734\) 34.6809 29.1008i 1.28010 1.07413i
\(735\) 0 0
\(736\) 14.7586 5.37168i 0.544008 0.198003i
\(737\) −1.21626 + 0.325897i −0.0448017 + 0.0120046i
\(738\) 0 0
\(739\) −39.9362 + 23.0572i −1.46908 + 0.848172i −0.999399 0.0346657i \(-0.988963\pi\)
−0.469678 + 0.882838i \(0.655630\pi\)
\(740\) −40.0485 + 14.3855i −1.47221 + 0.528823i
\(741\) 0 0
\(742\) 27.3338 + 19.1393i 1.00345 + 0.702626i
\(743\) −5.71577 4.00223i −0.209691 0.146828i 0.464013 0.885828i \(-0.346409\pi\)
−0.673705 + 0.739001i \(0.735298\pi\)
\(744\) 0 0
\(745\) −0.810426 + 1.71901i −0.0296917 + 0.0629795i
\(746\) 11.8467 6.83970i 0.433739 0.250419i
\(747\) 0 0
\(748\) 82.5823 22.1279i 3.01951 0.809075i
\(749\) −6.34655 + 2.30996i −0.231898 + 0.0844040i
\(750\) 0 0
\(751\) 14.9900 12.5781i 0.546995 0.458983i −0.326927 0.945050i \(-0.606013\pi\)
0.873922 + 0.486067i \(0.161569\pi\)
\(752\) −17.0060 36.4694i −0.620144 1.32990i
\(753\) 0 0
\(754\) −24.2618 4.27802i −0.883564 0.155796i
\(755\) 8.43197 + 32.0077i 0.306871 + 1.16488i
\(756\) 0 0
\(757\) −13.8377 + 13.8377i −0.502940 + 0.502940i −0.912350 0.409411i \(-0.865734\pi\)
0.409411 + 0.912350i \(0.365734\pi\)
\(758\) −5.81344 8.30245i −0.211154 0.301559i
\(759\) 0 0
\(760\) −33.3235 + 27.7232i −1.20877 + 1.00563i
\(761\) 4.04597 + 4.82180i 0.146666 + 0.174790i 0.834376 0.551196i \(-0.185828\pi\)
−0.687710 + 0.725986i \(0.741384\pi\)
\(762\) 0 0
\(763\) −19.1236 8.91746i −0.692319 0.322834i
\(764\) 18.8382 32.6287i 0.681542 1.18046i
\(765\) 0 0
\(766\) 38.5033 + 66.6897i 1.39118 + 2.40960i
\(767\) 2.10183 + 24.0240i 0.0758927 + 0.867457i
\(768\) 0 0
\(769\) −43.7099 + 7.70724i −1.57622 + 0.277930i −0.892237 0.451567i \(-0.850865\pi\)
−0.683983 + 0.729498i \(0.739754\pi\)
\(770\) −20.7406 44.9724i −0.747439 1.62069i
\(771\) 0 0
\(772\) 5.23811 0.458275i 0.188524 0.0164937i
\(773\) −17.1792 4.60315i −0.617893 0.165564i −0.0637231 0.997968i \(-0.520297\pi\)
−0.554170 + 0.832404i \(0.686964\pi\)
\(774\) 0 0
\(775\) −0.0155274 + 1.84147i −0.000557760 + 0.0661477i
\(776\) −10.0891 27.7195i −0.362176 0.995071i
\(777\) 0 0
\(778\) −75.3032 6.58818i −2.69975 0.236198i
\(779\) −24.2626 8.83085i −0.869297 0.316398i
\(780\) 0 0
\(781\) 5.54203 31.4304i 0.198310 1.12467i
\(782\) −53.7322 53.7322i −1.92146 1.92146i
\(783\) 0 0
\(784\) 1.77806i 0.0635021i
\(785\) 14.7723 17.4550i 0.527246 0.622995i
\(786\) 0 0
\(787\) −27.1112 + 12.6422i