Properties

Label 405.2.r.a.8.3
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 8.3
Character \(\chi\) \(=\) 405.8
Dual form 405.2.r.a.152.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.65044 + 1.15565i) q^{2} +(0.704386 - 1.93528i) q^{4} +(0.268922 + 2.21984i) q^{5} +(0.618828 - 1.32708i) q^{7} +(0.0310202 + 0.115769i) q^{8} +O(q^{10})\) \(q+(-1.65044 + 1.15565i) q^{2} +(0.704386 - 1.93528i) q^{4} +(0.268922 + 2.21984i) q^{5} +(0.618828 - 1.32708i) q^{7} +(0.0310202 + 0.115769i) q^{8} +(-3.00920 - 3.35293i) q^{10} +(-1.86051 + 2.21727i) q^{11} +(-3.51558 + 5.02076i) q^{13} +(0.512304 + 2.90542i) q^{14} +(2.97033 + 2.49240i) q^{16} +(0.833002 - 3.10881i) q^{17} +(3.51741 + 2.03078i) q^{19} +(4.48544 + 1.04318i) q^{20} +(0.508272 - 5.80958i) q^{22} +(-4.58997 + 2.14034i) q^{23} +(-4.85536 + 1.19393i) q^{25} -12.3493i q^{26} +(-2.13239 - 2.13239i) q^{28} +(-0.368261 + 2.08851i) q^{29} +(-3.20394 - 1.16614i) q^{31} +(-8.02150 - 0.701790i) q^{32} +(2.21787 + 6.09356i) q^{34} +(3.11232 + 1.01682i) q^{35} +(-11.3656 - 3.04540i) q^{37} +(-8.15214 + 0.713220i) q^{38} +(-0.248646 + 0.0999926i) q^{40} +(-0.839107 + 0.147957i) q^{41} +(-0.0641287 - 0.732994i) q^{43} +(2.98053 + 5.16243i) q^{44} +(5.10199 - 8.83690i) q^{46} +(-2.61254 - 1.21825i) q^{47} +(3.12132 + 3.71984i) q^{49} +(6.63372 - 7.58161i) q^{50} +(7.24028 + 10.3402i) q^{52} +(0.0757900 - 0.0757900i) q^{53} +(-5.42232 - 3.53376i) q^{55} +(0.172831 + 0.0304748i) q^{56} +(-1.80580 - 3.87255i) q^{58} +(2.89613 - 2.43014i) q^{59} +(-4.21993 + 1.53593i) q^{61} +(6.63556 - 1.77799i) q^{62} +(7.33402 - 4.23430i) q^{64} +(-12.0907 - 6.45381i) q^{65} +(3.65313 + 2.55795i) q^{67} +(-5.42967 - 3.80189i) q^{68} +(-6.31179 + 1.91856i) q^{70} +(7.84988 - 4.53213i) q^{71} +(-8.04880 + 2.15667i) q^{73} +(22.2777 - 8.10840i) q^{74} +(6.40774 - 5.37673i) q^{76} +(1.79116 + 3.84116i) q^{77} +(1.44073 + 0.254040i) q^{79} +(-4.73394 + 7.26391i) q^{80} +(1.21391 - 1.21391i) q^{82} +(9.69375 + 13.8441i) q^{83} +(7.12506 + 1.01310i) q^{85} +(0.952926 + 1.13565i) q^{86} +(-0.314404 - 0.146609i) q^{88} +(-3.05075 + 5.28406i) q^{89} +(4.48742 + 7.77244i) q^{91} +(0.909052 + 10.3905i) q^{92} +(5.71971 - 1.00854i) q^{94} +(-3.56209 + 8.35420i) q^{95} +(16.1512 - 1.41304i) q^{97} +(-9.45039 - 2.53222i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.65044 + 1.15565i −1.16704 + 0.817169i −0.986072 0.166320i \(-0.946811\pi\)
−0.180966 + 0.983489i \(0.557923\pi\)
\(3\) 0 0
\(4\) 0.704386 1.93528i 0.352193 0.967642i
\(5\) 0.268922 + 2.21984i 0.120266 + 0.992742i
\(6\) 0 0
\(7\) 0.618828 1.32708i 0.233895 0.501590i −0.753969 0.656910i \(-0.771863\pi\)
0.987864 + 0.155320i \(0.0496410\pi\)
\(8\) 0.0310202 + 0.115769i 0.0109673 + 0.0409305i
\(9\) 0 0
\(10\) −3.00920 3.35293i −0.951592 1.06029i
\(11\) −1.86051 + 2.21727i −0.560965 + 0.668532i −0.969751 0.244098i \(-0.921508\pi\)
0.408785 + 0.912631i \(0.365953\pi\)
\(12\) 0 0
\(13\) −3.51558 + 5.02076i −0.975045 + 1.39251i −0.0559675 + 0.998433i \(0.517824\pi\)
−0.919078 + 0.394076i \(0.871065\pi\)
\(14\) 0.512304 + 2.90542i 0.136919 + 0.776506i
\(15\) 0 0
\(16\) 2.97033 + 2.49240i 0.742582 + 0.623101i
\(17\) 0.833002 3.10881i 0.202033 0.753996i −0.788301 0.615290i \(-0.789039\pi\)
0.990334 0.138706i \(-0.0442944\pi\)
\(18\) 0 0
\(19\) 3.51741 + 2.03078i 0.806949 + 0.465892i 0.845895 0.533349i \(-0.179067\pi\)
−0.0389464 + 0.999241i \(0.512400\pi\)
\(20\) 4.48544 + 1.04318i 1.00298 + 0.233262i
\(21\) 0 0
\(22\) 0.508272 5.80958i 0.108364 1.23861i
\(23\) −4.58997 + 2.14034i −0.957074 + 0.446291i −0.837441 0.546527i \(-0.815949\pi\)
−0.119633 + 0.992818i \(0.538172\pi\)
\(24\) 0 0
\(25\) −4.85536 + 1.19393i −0.971072 + 0.238785i
\(26\) 12.3493i 2.42189i
\(27\) 0 0
\(28\) −2.13239 2.13239i −0.402983 0.402983i
\(29\) −0.368261 + 2.08851i −0.0683844 + 0.387827i 0.931336 + 0.364162i \(0.118645\pi\)
−0.999720 + 0.0236650i \(0.992466\pi\)
\(30\) 0 0
\(31\) −3.20394 1.16614i −0.575445 0.209445i 0.0378710 0.999283i \(-0.487942\pi\)
−0.613316 + 0.789838i \(0.710165\pi\)
\(32\) −8.02150 0.701790i −1.41801 0.124060i
\(33\) 0 0
\(34\) 2.21787 + 6.09356i 0.380362 + 1.04504i
\(35\) 3.11232 + 1.01682i 0.526079 + 0.171873i
\(36\) 0 0
\(37\) −11.3656 3.04540i −1.86849 0.500661i −0.999988 0.00497757i \(-0.998416\pi\)
−0.868503 0.495683i \(-0.834918\pi\)
\(38\) −8.15214 + 0.713220i −1.32245 + 0.115700i
\(39\) 0 0
\(40\) −0.248646 + 0.0999926i −0.0393144 + 0.0158102i
\(41\) −0.839107 + 0.147957i −0.131046 + 0.0231070i −0.238787 0.971072i \(-0.576750\pi\)
0.107740 + 0.994179i \(0.465639\pi\)
\(42\) 0 0
\(43\) −0.0641287 0.732994i −0.00977953 0.111781i 0.989736 0.142909i \(-0.0456455\pi\)
−0.999515 + 0.0311282i \(0.990090\pi\)
\(44\) 2.98053 + 5.16243i 0.449332 + 0.778266i
\(45\) 0 0
\(46\) 5.10199 8.83690i 0.752247 1.30293i
\(47\) −2.61254 1.21825i −0.381078 0.177700i 0.222634 0.974902i \(-0.428535\pi\)
−0.603712 + 0.797203i \(0.706312\pi\)
\(48\) 0 0
\(49\) 3.12132 + 3.71984i 0.445902 + 0.531406i
\(50\) 6.63372 7.58161i 0.938150 1.07220i
\(51\) 0 0
\(52\) 7.24028 + 10.3402i 1.00405 + 1.43393i
\(53\) 0.0757900 0.0757900i 0.0104106 0.0104106i −0.701882 0.712293i \(-0.747657\pi\)
0.712293 + 0.701882i \(0.247657\pi\)
\(54\) 0 0
\(55\) −5.42232 3.53376i −0.731145 0.476492i
\(56\) 0.172831 + 0.0304748i 0.0230955 + 0.00407236i
\(57\) 0 0
\(58\) −1.80580 3.87255i −0.237113 0.508491i
\(59\) 2.89613 2.43014i 0.377044 0.316377i −0.434497 0.900673i \(-0.643074\pi\)
0.811540 + 0.584296i \(0.198629\pi\)
\(60\) 0 0
\(61\) −4.21993 + 1.53593i −0.540306 + 0.196655i −0.597734 0.801694i \(-0.703932\pi\)
0.0574282 + 0.998350i \(0.481710\pi\)
\(62\) 6.63556 1.77799i 0.842717 0.225805i
\(63\) 0 0
\(64\) 7.33402 4.23430i 0.916753 0.529287i
\(65\) −12.0907 6.45381i −1.49967 0.800497i
\(66\) 0 0
\(67\) 3.65313 + 2.55795i 0.446301 + 0.312504i 0.775034 0.631919i \(-0.217733\pi\)
−0.328733 + 0.944423i \(0.606622\pi\)
\(68\) −5.42967 3.80189i −0.658444 0.461047i
\(69\) 0 0
\(70\) −6.31179 + 1.91856i −0.754403 + 0.229312i
\(71\) 7.84988 4.53213i 0.931609 0.537865i 0.0442890 0.999019i \(-0.485898\pi\)
0.887320 + 0.461154i \(0.152564\pi\)
\(72\) 0 0
\(73\) −8.04880 + 2.15667i −0.942041 + 0.252419i −0.696982 0.717089i \(-0.745474\pi\)
−0.245059 + 0.969508i \(0.578807\pi\)
\(74\) 22.2777 8.10840i 2.58972 0.942583i
\(75\) 0 0
\(76\) 6.40774 5.37673i 0.735018 0.616754i
\(77\) 1.79116 + 3.84116i 0.204122 + 0.437741i
\(78\) 0 0
\(79\) 1.44073 + 0.254040i 0.162095 + 0.0285818i 0.254107 0.967176i \(-0.418219\pi\)
−0.0920115 + 0.995758i \(0.529330\pi\)
\(80\) −4.73394 + 7.26391i −0.529271 + 0.812130i
\(81\) 0 0
\(82\) 1.21391 1.21391i 0.134054 0.134054i
\(83\) 9.69375 + 13.8441i 1.06403 + 1.51959i 0.838155 + 0.545431i \(0.183634\pi\)
0.225872 + 0.974157i \(0.427477\pi\)
\(84\) 0 0
\(85\) 7.12506 + 1.01310i 0.772821 + 0.109886i
\(86\) 0.952926 + 1.13565i 0.102757 + 0.122461i
\(87\) 0 0
\(88\) −0.314404 0.146609i −0.0335156 0.0156286i
\(89\) −3.05075 + 5.28406i −0.323379 + 0.560109i −0.981183 0.193080i \(-0.938152\pi\)
0.657804 + 0.753189i \(0.271486\pi\)
\(90\) 0 0
\(91\) 4.48742 + 7.77244i 0.470410 + 0.814774i
\(92\) 0.909052 + 10.3905i 0.0947752 + 1.08329i
\(93\) 0 0
\(94\) 5.71971 1.00854i 0.589943 0.104023i
\(95\) −3.56209 + 8.35420i −0.365462 + 0.857123i
\(96\) 0 0
\(97\) 16.1512 1.41304i 1.63990 0.143473i 0.770453 0.637496i \(-0.220030\pi\)
0.869449 + 0.494023i \(0.164474\pi\)
\(98\) −9.45039 2.53222i −0.954633 0.255793i
\(99\) 0 0
\(100\) −1.10946 + 10.2375i −0.110946 + 1.02375i
\(101\) 1.88053 + 5.16673i 0.187120 + 0.514108i 0.997410 0.0719204i \(-0.0229128\pi\)
−0.810290 + 0.586029i \(0.800691\pi\)
\(102\) 0 0
\(103\) 3.90922 + 0.342012i 0.385186 + 0.0336994i 0.278105 0.960551i \(-0.410294\pi\)
0.107082 + 0.994250i \(0.465849\pi\)
\(104\) −0.690302 0.251249i −0.0676897 0.0246370i
\(105\) 0 0
\(106\) −0.0375001 + 0.212674i −0.00364233 + 0.0206567i
\(107\) 10.5329 + 10.5329i 1.01825 + 1.01825i 0.999830 + 0.0184189i \(0.00586325\pi\)
0.0184189 + 0.999830i \(0.494137\pi\)
\(108\) 0 0
\(109\) 9.91447i 0.949634i 0.880085 + 0.474817i \(0.157486\pi\)
−0.880085 + 0.474817i \(0.842514\pi\)
\(110\) 13.0330 0.434043i 1.24265 0.0413843i
\(111\) 0 0
\(112\) 5.14574 2.39950i 0.486227 0.226731i
\(113\) 1.32748 15.1732i 0.124879 1.42737i −0.632583 0.774492i \(-0.718005\pi\)
0.757462 0.652879i \(-0.226439\pi\)
\(114\) 0 0
\(115\) −5.98554 9.61340i −0.558155 0.896454i
\(116\) 3.78247 + 2.18381i 0.351193 + 0.202762i
\(117\) 0 0
\(118\) −1.97149 + 7.35771i −0.181491 + 0.677332i
\(119\) −3.61015 3.02928i −0.330942 0.277693i
\(120\) 0 0
\(121\) 0.455341 + 2.58237i 0.0413946 + 0.234761i
\(122\) 5.18974 7.41172i 0.469857 0.671026i
\(123\) 0 0
\(124\) −4.51362 + 5.37912i −0.405335 + 0.483059i
\(125\) −3.95604 10.4570i −0.353839 0.935306i
\(126\) 0 0
\(127\) 2.58018 + 9.62937i 0.228954 + 0.854468i 0.980782 + 0.195109i \(0.0625059\pi\)
−0.751828 + 0.659360i \(0.770827\pi\)
\(128\) −0.405037 + 0.868604i −0.0358005 + 0.0767745i
\(129\) 0 0
\(130\) 27.4133 3.32099i 2.40431 0.291270i
\(131\) −3.84111 + 10.5534i −0.335599 + 0.922051i 0.651028 + 0.759054i \(0.274338\pi\)
−0.986627 + 0.162997i \(0.947884\pi\)
\(132\) 0 0
\(133\) 4.87168 3.41119i 0.422428 0.295787i
\(134\) −8.98538 −0.776219
\(135\) 0 0
\(136\) 0.385743 0.0330772
\(137\) −16.1027 + 11.2752i −1.37574 + 0.963306i −0.376424 + 0.926448i \(0.622846\pi\)
−0.999320 + 0.0368588i \(0.988265\pi\)
\(138\) 0 0
\(139\) 0.508611 1.39740i 0.0431398 0.118526i −0.916252 0.400602i \(-0.868801\pi\)
0.959392 + 0.282076i \(0.0910232\pi\)
\(140\) 4.16010 5.30700i 0.351593 0.448523i
\(141\) 0 0
\(142\) −7.71820 + 16.5517i −0.647697 + 1.38899i
\(143\) −4.59162 17.1362i −0.383971 1.43300i
\(144\) 0 0
\(145\) −4.73520 0.255833i −0.393237 0.0212458i
\(146\) 10.7917 12.8611i 0.893129 1.06439i
\(147\) 0 0
\(148\) −13.8995 + 19.8505i −1.14253 + 1.63170i
\(149\) −0.861743 4.88719i −0.0705968 0.400374i −0.999545 0.0301644i \(-0.990397\pi\)
0.928948 0.370210i \(-0.120714\pi\)
\(150\) 0 0
\(151\) −15.8833 13.3277i −1.29257 1.08459i −0.991379 0.131025i \(-0.958173\pi\)
−0.301186 0.953565i \(-0.597383\pi\)
\(152\) −0.125990 + 0.470202i −0.0102191 + 0.0381384i
\(153\) 0 0
\(154\) −7.39525 4.26965i −0.595926 0.344058i
\(155\) 1.72703 7.42583i 0.138718 0.596457i
\(156\) 0 0
\(157\) 0.591932 6.76582i 0.0472413 0.539971i −0.935291 0.353879i \(-0.884862\pi\)
0.982532 0.186092i \(-0.0595821\pi\)
\(158\) −2.67143 + 1.24571i −0.212528 + 0.0991032i
\(159\) 0 0
\(160\) −0.599298 17.9951i −0.0473787 1.42264i
\(161\) 7.41576i 0.584444i
\(162\) 0 0
\(163\) 14.3864 + 14.3864i 1.12683 + 1.12683i 0.990689 + 0.136142i \(0.0434702\pi\)
0.136142 + 0.990689i \(0.456530\pi\)
\(164\) −0.304716 + 1.72813i −0.0237943 + 0.134944i
\(165\) 0 0
\(166\) −31.9979 11.6463i −2.48352 0.903928i
\(167\) 0.469806 + 0.0411027i 0.0363547 + 0.00318063i 0.105319 0.994439i \(-0.466414\pi\)
−0.0689639 + 0.997619i \(0.521969\pi\)
\(168\) 0 0
\(169\) −8.40252 23.0857i −0.646348 1.77583i
\(170\) −12.9303 + 6.56202i −0.991707 + 0.503284i
\(171\) 0 0
\(172\) −1.46372 0.392203i −0.111608 0.0299052i
\(173\) 18.3690 1.60708i 1.39657 0.122184i 0.636125 0.771586i \(-0.280536\pi\)
0.760446 + 0.649402i \(0.224981\pi\)
\(174\) 0 0
\(175\) −1.42020 + 7.18230i −0.107357 + 0.542931i
\(176\) −11.0527 + 1.94888i −0.833126 + 0.146903i
\(177\) 0 0
\(178\) −1.07144 12.2466i −0.0803080 0.917925i
\(179\) 3.95796 + 6.85540i 0.295832 + 0.512396i 0.975178 0.221422i \(-0.0710697\pi\)
−0.679346 + 0.733818i \(0.737736\pi\)
\(180\) 0 0
\(181\) 9.86110 17.0799i 0.732970 1.26954i −0.222638 0.974901i \(-0.571467\pi\)
0.955608 0.294640i \(-0.0951998\pi\)
\(182\) −16.3885 7.64207i −1.21479 0.566468i
\(183\) 0 0
\(184\) −0.390166 0.464982i −0.0287634 0.0342789i
\(185\) 3.70384 26.0487i 0.272311 1.91514i
\(186\) 0 0
\(187\) 5.34326 + 7.63096i 0.390738 + 0.558031i
\(188\) −4.19789 + 4.19789i −0.306162 + 0.306162i
\(189\) 0 0
\(190\) −3.77553 17.9046i −0.273905 1.29894i
\(191\) 8.60644 + 1.51755i 0.622740 + 0.109806i 0.476110 0.879386i \(-0.342046\pi\)
0.146630 + 0.989191i \(0.453157\pi\)
\(192\) 0 0
\(193\) −3.65180 7.83132i −0.262863 0.563711i 0.729935 0.683517i \(-0.239550\pi\)
−0.992797 + 0.119806i \(0.961773\pi\)
\(194\) −25.0236 + 20.9973i −1.79659 + 1.50752i
\(195\) 0 0
\(196\) 9.39756 3.42043i 0.671254 0.244316i
\(197\) −1.93720 + 0.519071i −0.138020 + 0.0369822i −0.327167 0.944966i \(-0.606094\pi\)
0.189148 + 0.981949i \(0.439427\pi\)
\(198\) 0 0
\(199\) 15.5130 8.95641i 1.09968 0.634903i 0.163546 0.986536i \(-0.447707\pi\)
0.936138 + 0.351633i \(0.114373\pi\)
\(200\) −0.288834 0.525064i −0.0204236 0.0371276i
\(201\) 0 0
\(202\) −9.07464 6.35413i −0.638490 0.447075i
\(203\) 2.54374 + 1.78114i 0.178535 + 0.125012i
\(204\) 0 0
\(205\) −0.554096 1.82289i −0.0386997 0.127316i
\(206\) −6.84718 + 3.95322i −0.477065 + 0.275434i
\(207\) 0 0
\(208\) −22.9562 + 6.15109i −1.59172 + 0.426501i
\(209\) −11.0470 + 4.02077i −0.764134 + 0.278122i
\(210\) 0 0
\(211\) −8.17709 + 6.86139i −0.562934 + 0.472358i −0.879293 0.476282i \(-0.841984\pi\)
0.316359 + 0.948640i \(0.397540\pi\)
\(212\) −0.0932898 0.200061i −0.00640717 0.0137402i
\(213\) 0 0
\(214\) −29.5562 5.21155i −2.02042 0.356254i
\(215\) 1.60988 0.339474i 0.109793 0.0231519i
\(216\) 0 0
\(217\) −3.53025 + 3.53025i −0.239649 + 0.239649i
\(218\) −11.4577 16.3632i −0.776011 1.10826i
\(219\) 0 0
\(220\) −10.6582 + 8.00459i −0.718578 + 0.539669i
\(221\) 12.6801 + 15.1115i 0.852955 + 1.01651i
\(222\) 0 0
\(223\) 10.8301 + 5.05016i 0.725238 + 0.338184i 0.749936 0.661511i \(-0.230084\pi\)
−0.0246975 + 0.999695i \(0.507862\pi\)
\(224\) −5.89526 + 10.2109i −0.393894 + 0.682244i
\(225\) 0 0
\(226\) 15.3440 + 26.5765i 1.02067 + 1.76784i
\(227\) −0.100851 1.15273i −0.00669369 0.0765092i 0.992113 0.125346i \(-0.0400041\pi\)
−0.998807 + 0.0488368i \(0.984449\pi\)
\(228\) 0 0
\(229\) −8.62548 + 1.52090i −0.569988 + 0.100504i −0.451212 0.892417i \(-0.649008\pi\)
−0.118776 + 0.992921i \(0.537897\pi\)
\(230\) 20.9885 + 8.94914i 1.38394 + 0.590089i
\(231\) 0 0
\(232\) −0.253208 + 0.0221529i −0.0166240 + 0.00145441i
\(233\) 15.8052 + 4.23498i 1.03543 + 0.277443i 0.736219 0.676743i \(-0.236609\pi\)
0.299213 + 0.954186i \(0.403276\pi\)
\(234\) 0 0
\(235\) 2.00174 6.12703i 0.130579 0.399683i
\(236\) −2.66302 7.31658i −0.173348 0.476269i
\(237\) 0 0
\(238\) 9.45913 + 0.827567i 0.613145 + 0.0536432i
\(239\) 8.07123 + 2.93769i 0.522085 + 0.190023i 0.589601 0.807695i \(-0.299285\pi\)
−0.0675160 + 0.997718i \(0.521507\pi\)
\(240\) 0 0
\(241\) 0.358872 2.03527i 0.0231170 0.131103i −0.971065 0.238815i \(-0.923241\pi\)
0.994182 + 0.107712i \(0.0343523\pi\)
\(242\) −3.73583 3.73583i −0.240148 0.240148i
\(243\) 0 0
\(244\) 9.24864i 0.592083i
\(245\) −7.41805 + 7.92916i −0.473922 + 0.506576i
\(246\) 0 0
\(247\) −22.5618 + 10.5207i −1.43557 + 0.669417i
\(248\) 0.0356158 0.407090i 0.00226161 0.0258503i
\(249\) 0 0
\(250\) 18.6139 + 12.6869i 1.17725 + 0.802392i
\(251\) −9.55376 5.51587i −0.603028 0.348158i 0.167204 0.985922i \(-0.446526\pi\)
−0.770232 + 0.637764i \(0.779860\pi\)
\(252\) 0 0
\(253\) 3.79398 14.1593i 0.238525 0.890189i
\(254\) −15.3866 12.9109i −0.965443 0.810103i
\(255\) 0 0
\(256\) 2.60580 + 14.7782i 0.162862 + 0.923639i
\(257\) 3.31253 4.73079i 0.206630 0.295098i −0.702439 0.711744i \(-0.747906\pi\)
0.909069 + 0.416646i \(0.136794\pi\)
\(258\) 0 0
\(259\) −11.0748 + 13.1985i −0.688157 + 0.820114i
\(260\) −21.0065 + 18.8529i −1.30277 + 1.16921i
\(261\) 0 0
\(262\) −5.85647 21.8567i −0.361814 1.35031i
\(263\) −7.79728 + 16.7213i −0.480801 + 1.03108i 0.504993 + 0.863123i \(0.331495\pi\)
−0.985794 + 0.167958i \(0.946283\pi\)
\(264\) 0 0
\(265\) 0.188623 + 0.147860i 0.0115870 + 0.00908296i
\(266\) −4.09828 + 11.2599i −0.251281 + 0.690390i
\(267\) 0 0
\(268\) 7.52358 5.26807i 0.459576 0.321798i
\(269\) 15.7262 0.958842 0.479421 0.877585i \(-0.340847\pi\)
0.479421 + 0.877585i \(0.340847\pi\)
\(270\) 0 0
\(271\) −17.4326 −1.05895 −0.529477 0.848324i \(-0.677612\pi\)
−0.529477 + 0.848324i \(0.677612\pi\)
\(272\) 10.2227 7.15800i 0.619841 0.434018i
\(273\) 0 0
\(274\) 13.5463 37.2181i 0.818362 2.24843i
\(275\) 6.38620 12.9870i 0.385102 0.783144i
\(276\) 0 0
\(277\) 6.49002 13.9179i 0.389947 0.836245i −0.609120 0.793078i \(-0.708477\pi\)
0.999068 0.0431672i \(-0.0137448\pi\)
\(278\) 0.775471 + 2.89410i 0.0465097 + 0.173576i
\(279\) 0 0
\(280\) −0.0211709 + 0.391852i −0.00126521 + 0.0234176i
\(281\) −4.76302 + 5.67634i −0.284138 + 0.338622i −0.889168 0.457580i \(-0.848716\pi\)
0.605031 + 0.796202i \(0.293161\pi\)
\(282\) 0 0
\(283\) 8.24647 11.7772i 0.490202 0.700081i −0.495495 0.868611i \(-0.665013\pi\)
0.985696 + 0.168530i \(0.0539021\pi\)
\(284\) −3.24161 18.3841i −0.192354 1.09090i
\(285\) 0 0
\(286\) 27.3816 + 22.9759i 1.61911 + 1.35859i
\(287\) −0.322912 + 1.20512i −0.0190609 + 0.0711362i
\(288\) 0 0
\(289\) 5.75165 + 3.32072i 0.338332 + 0.195336i
\(290\) 8.11081 5.05000i 0.476283 0.296546i
\(291\) 0 0
\(292\) −1.49569 + 17.0958i −0.0875288 + 1.00046i
\(293\) −18.2561 + 8.51297i −1.06653 + 0.497333i −0.874985 0.484150i \(-0.839129\pi\)
−0.191549 + 0.981483i \(0.561351\pi\)
\(294\) 0 0
\(295\) 6.17335 + 5.77541i 0.359426 + 0.336258i
\(296\) 1.41025i 0.0819691i
\(297\) 0 0
\(298\) 7.07014 + 7.07014i 0.409562 + 0.409562i
\(299\) 5.39025 30.5696i 0.311726 1.76789i
\(300\) 0 0
\(301\) −1.01243 0.368493i −0.0583553 0.0212396i
\(302\) 41.6166 + 3.64098i 2.39477 + 0.209515i
\(303\) 0 0
\(304\) 5.38635 + 14.7989i 0.308928 + 0.848774i
\(305\) −4.54434 8.95451i −0.260208 0.512733i
\(306\) 0 0
\(307\) 11.5423 + 3.09276i 0.658756 + 0.176513i 0.572684 0.819776i \(-0.305902\pi\)
0.0860714 + 0.996289i \(0.472569\pi\)
\(308\) 8.69540 0.760749i 0.495467 0.0433477i
\(309\) 0 0
\(310\) 5.73131 + 14.2517i 0.325516 + 0.809444i
\(311\) −2.38442 + 0.420438i −0.135208 + 0.0238408i −0.240843 0.970564i \(-0.577424\pi\)
0.105634 + 0.994405i \(0.466313\pi\)
\(312\) 0 0
\(313\) 1.06842 + 12.2121i 0.0603905 + 0.690267i 0.964693 + 0.263375i \(0.0848358\pi\)
−0.904303 + 0.426891i \(0.859609\pi\)
\(314\) 6.84198 + 11.8506i 0.386115 + 0.668771i
\(315\) 0 0
\(316\) 1.50647 2.60929i 0.0847457 0.146784i
\(317\) −20.5585 9.58656i −1.15468 0.538435i −0.251566 0.967840i \(-0.580945\pi\)
−0.903112 + 0.429405i \(0.858723\pi\)
\(318\) 0 0
\(319\) −3.94565 4.70224i −0.220914 0.263275i
\(320\) 11.3717 + 15.1416i 0.635700 + 0.846444i
\(321\) 0 0
\(322\) −8.57003 12.2393i −0.477589 0.682068i
\(323\) 9.24330 9.24330i 0.514311 0.514311i
\(324\) 0 0
\(325\) 11.0750 28.5750i 0.614329 1.58505i
\(326\) −40.3696 7.11825i −2.23587 0.394243i
\(327\) 0 0
\(328\) −0.0431581 0.0925528i −0.00238301 0.00511038i
\(329\) −3.23343 + 2.71317i −0.178265 + 0.149582i
\(330\) 0 0
\(331\) 15.3336 5.58098i 0.842812 0.306758i 0.115706 0.993284i \(-0.463087\pi\)
0.727106 + 0.686525i \(0.240865\pi\)
\(332\) 33.6204 9.00856i 1.84516 0.494409i
\(333\) 0 0
\(334\) −0.822888 + 0.475095i −0.0450264 + 0.0259960i
\(335\) −4.69583 + 8.79726i −0.256561 + 0.480646i
\(336\) 0 0
\(337\) −3.28511 2.30026i −0.178951 0.125303i 0.480669 0.876902i \(-0.340394\pi\)
−0.659620 + 0.751599i \(0.729283\pi\)
\(338\) 40.5469 + 28.3913i 2.20546 + 1.54428i
\(339\) 0 0
\(340\) 6.97943 13.0754i 0.378513 0.709113i
\(341\) 8.54661 4.93439i 0.462825 0.267212i
\(342\) 0 0
\(343\) 16.7687 4.49317i 0.905427 0.242608i
\(344\) 0.0828686 0.0301617i 0.00446798 0.00162621i
\(345\) 0 0
\(346\) −28.4598 + 23.8806i −1.53001 + 1.28383i
\(347\) 5.24496 + 11.2479i 0.281564 + 0.603816i 0.995326 0.0965722i \(-0.0307879\pi\)
−0.713762 + 0.700389i \(0.753010\pi\)
\(348\) 0 0
\(349\) −7.52479 1.32682i −0.402793 0.0710232i −0.0314181 0.999506i \(-0.510002\pi\)
−0.371375 + 0.928483i \(0.621113\pi\)
\(350\) −5.95628 13.4952i −0.318377 0.721349i
\(351\) 0 0
\(352\) 16.4801 16.4801i 0.878395 0.878395i
\(353\) −10.2693 14.6661i −0.546579 0.780595i 0.446904 0.894582i \(-0.352527\pi\)
−0.993482 + 0.113987i \(0.963638\pi\)
\(354\) 0 0
\(355\) 12.1716 + 16.2067i 0.646001 + 0.860161i
\(356\) 8.07725 + 9.62609i 0.428093 + 0.510182i
\(357\) 0 0
\(358\) −14.4548 6.74040i −0.763962 0.356241i
\(359\) −6.26521 + 10.8517i −0.330665 + 0.572729i −0.982642 0.185510i \(-0.940606\pi\)
0.651977 + 0.758239i \(0.273940\pi\)
\(360\) 0 0
\(361\) −1.25189 2.16834i −0.0658891 0.114123i
\(362\) 3.46328 + 39.5854i 0.182026 + 2.08056i
\(363\) 0 0
\(364\) 18.2028 3.20964i 0.954084 0.168231i
\(365\) −6.95196 17.2871i −0.363882 0.904846i
\(366\) 0 0
\(367\) −13.6352 + 1.19292i −0.711750 + 0.0622701i −0.437280 0.899325i \(-0.644058\pi\)
−0.274470 + 0.961596i \(0.588503\pi\)
\(368\) −18.9683 5.08254i −0.988790 0.264946i
\(369\) 0 0
\(370\) 23.9903 + 47.2723i 1.24720 + 2.45757i
\(371\) −0.0536785 0.147481i −0.00278685 0.00765681i
\(372\) 0 0
\(373\) −12.0608 1.05518i −0.624485 0.0546353i −0.229478 0.973314i \(-0.573702\pi\)
−0.395006 + 0.918678i \(0.629258\pi\)
\(374\) −17.6375 6.41951i −0.912011 0.331945i
\(375\) 0 0
\(376\) 0.0599937 0.340241i 0.00309394 0.0175466i
\(377\) −9.19128 9.19128i −0.473375 0.473375i
\(378\) 0 0
\(379\) 22.5213i 1.15684i 0.815738 + 0.578421i \(0.196331\pi\)
−0.815738 + 0.578421i \(0.803669\pi\)
\(380\) 13.6587 + 12.7782i 0.700674 + 0.655509i
\(381\) 0 0
\(382\) −15.9582 + 7.44142i −0.816491 + 0.380736i
\(383\) −1.26087 + 14.4118i −0.0644275 + 0.736410i 0.893437 + 0.449189i \(0.148287\pi\)
−0.957864 + 0.287221i \(0.907269\pi\)
\(384\) 0 0
\(385\) −8.04507 + 5.00906i −0.410015 + 0.255286i
\(386\) 15.0774 + 8.70492i 0.767417 + 0.443069i
\(387\) 0 0
\(388\) 8.64201 32.2524i 0.438731 1.63737i
\(389\) 9.68308 + 8.12507i 0.490951 + 0.411957i 0.854367 0.519670i \(-0.173945\pi\)
−0.363416 + 0.931627i \(0.618390\pi\)
\(390\) 0 0
\(391\) 2.83044 + 16.0522i 0.143141 + 0.811795i
\(392\) −0.333818 + 0.476742i −0.0168604 + 0.0240791i
\(393\) 0 0
\(394\) 2.59737 3.09542i 0.130853 0.155945i
\(395\) −0.176483 + 3.26651i −0.00887982 + 0.164356i
\(396\) 0 0
\(397\) 3.89075 + 14.5205i 0.195271 + 0.728761i 0.992197 + 0.124684i \(0.0397916\pi\)
−0.796926 + 0.604077i \(0.793542\pi\)
\(398\) −15.2527 + 32.7096i −0.764550 + 1.63958i
\(399\) 0 0
\(400\) −17.3978 8.55516i −0.869889 0.427758i
\(401\) 8.96818 24.6399i 0.447849 1.23046i −0.486369 0.873754i \(-0.661679\pi\)
0.934218 0.356703i \(-0.116099\pi\)
\(402\) 0 0
\(403\) 17.1186 11.9866i 0.852738 0.597094i
\(404\) 11.3237 0.563375
\(405\) 0 0
\(406\) −6.25667 −0.310513
\(407\) 27.8983 19.5346i 1.38287 0.968294i
\(408\) 0 0
\(409\) −2.57831 + 7.08384i −0.127489 + 0.350273i −0.986972 0.160891i \(-0.948563\pi\)
0.859483 + 0.511164i \(0.170786\pi\)
\(410\) 3.02113 + 2.36824i 0.149203 + 0.116959i
\(411\) 0 0
\(412\) 3.41549 7.32453i 0.168269 0.360854i
\(413\) −1.43279 5.34723i −0.0705028 0.263120i
\(414\) 0 0
\(415\) −28.1248 + 25.2415i −1.38059 + 1.23906i
\(416\) 31.7237 37.8068i 1.55538 1.85363i
\(417\) 0 0
\(418\) 13.5858 19.4025i 0.664501 0.949006i
\(419\) −3.59622 20.3952i −0.175687 0.996370i −0.937348 0.348394i \(-0.886727\pi\)
0.761661 0.647975i \(-0.224384\pi\)
\(420\) 0 0
\(421\) −5.26964 4.42176i −0.256827 0.215503i 0.505279 0.862956i \(-0.331390\pi\)
−0.762105 + 0.647453i \(0.775834\pi\)
\(422\) 5.56643 20.7742i 0.270969 1.01127i
\(423\) 0 0
\(424\) 0.0111251 + 0.00642311i 0.000540285 + 0.000311934i
\(425\) −0.332837 + 16.0889i −0.0161450 + 0.780427i
\(426\) 0 0
\(427\) −0.573108 + 6.55066i −0.0277347 + 0.317009i
\(428\) 27.8032 12.9649i 1.34392 0.626680i
\(429\) 0 0
\(430\) −2.26470 + 2.42074i −0.109214 + 0.116739i
\(431\) 2.91928i 0.140617i −0.997525 0.0703084i \(-0.977602\pi\)
0.997525 0.0703084i \(-0.0223983\pi\)
\(432\) 0 0
\(433\) 3.01763 + 3.01763i 0.145018 + 0.145018i 0.775888 0.630870i \(-0.217302\pi\)
−0.630870 + 0.775888i \(0.717302\pi\)
\(434\) 1.74673 9.90621i 0.0838458 0.475513i
\(435\) 0 0
\(436\) 19.1873 + 6.98361i 0.918905 + 0.334454i
\(437\) −20.4913 1.79276i −0.980233 0.0857593i
\(438\) 0 0
\(439\) −1.28129 3.52030i −0.0611524 0.168015i 0.905354 0.424658i \(-0.139606\pi\)
−0.966506 + 0.256643i \(0.917383\pi\)
\(440\) 0.240898 0.737353i 0.0114844 0.0351519i
\(441\) 0 0
\(442\) −38.3914 10.2870i −1.82609 0.489300i
\(443\) 27.8809 2.43927i 1.32466 0.115893i 0.597229 0.802070i \(-0.296268\pi\)
0.727434 + 0.686177i \(0.240713\pi\)
\(444\) 0 0
\(445\) −12.5502 5.35118i −0.594935 0.253670i
\(446\) −23.7107 + 4.18083i −1.12273 + 0.197968i
\(447\) 0 0
\(448\) −1.08076 12.3531i −0.0510611 0.583631i
\(449\) −4.77256 8.26631i −0.225231 0.390111i 0.731158 0.682208i \(-0.238980\pi\)
−0.956389 + 0.292097i \(0.905647\pi\)
\(450\) 0 0
\(451\) 1.23311 2.13580i 0.0580647 0.100571i
\(452\) −28.4293 13.2568i −1.33720 0.623548i
\(453\) 0 0
\(454\) 1.49860 + 1.78596i 0.0703328 + 0.0838193i
\(455\) −16.0468 + 12.0515i −0.752286 + 0.564985i
\(456\) 0 0
\(457\) 20.3246 + 29.0265i 0.950745 + 1.35780i 0.933741 + 0.357949i \(0.116524\pi\)
0.0170039 + 0.999855i \(0.494587\pi\)
\(458\) 12.4782 12.4782i 0.583068 0.583068i
\(459\) 0 0
\(460\) −22.8208 + 4.81219i −1.06402 + 0.224369i
\(461\) −24.4088 4.30393i −1.13683 0.200454i −0.426612 0.904435i \(-0.640293\pi\)
−0.710219 + 0.703981i \(0.751404\pi\)
\(462\) 0 0
\(463\) −2.28775 4.90609i −0.106321 0.228005i 0.845949 0.533264i \(-0.179035\pi\)
−0.952269 + 0.305259i \(0.901257\pi\)
\(464\) −6.29927 + 5.28572i −0.292436 + 0.245383i
\(465\) 0 0
\(466\) −30.9797 + 11.2757i −1.43511 + 0.522336i
\(467\) −39.5591 + 10.5998i −1.83058 + 0.490502i −0.997989 0.0633888i \(-0.979809\pi\)
−0.832589 + 0.553891i \(0.813143\pi\)
\(468\) 0 0
\(469\) 5.65527 3.26507i 0.261136 0.150767i
\(470\) 3.77695 + 12.4256i 0.174218 + 0.573151i
\(471\) 0 0
\(472\) 0.371173 + 0.259898i 0.0170846 + 0.0119628i
\(473\) 1.74456 + 1.22155i 0.0802149 + 0.0561671i
\(474\) 0 0
\(475\) −19.5029 5.66062i −0.894854 0.259727i
\(476\) −8.40545 + 4.85289i −0.385263 + 0.222432i
\(477\) 0 0
\(478\) −16.7160 + 4.47905i −0.764574 + 0.204867i
\(479\) 25.9636 9.44996i 1.18631 0.431780i 0.327880 0.944719i \(-0.393666\pi\)
0.858425 + 0.512940i \(0.171444\pi\)
\(480\) 0 0
\(481\) 55.2468 46.3576i 2.51904 2.11372i
\(482\) 1.75976 + 3.77382i 0.0801549 + 0.171893i
\(483\) 0 0
\(484\) 5.31835 + 0.937769i 0.241743 + 0.0426258i
\(485\) 7.48013 + 35.4730i 0.339655 + 1.61074i
\(486\) 0 0
\(487\) 28.3122 28.3122i 1.28295 1.28295i 0.343969 0.938981i \(-0.388228\pi\)
0.938981 0.343969i \(-0.111772\pi\)
\(488\) −0.308715 0.440891i −0.0139749 0.0199582i
\(489\) 0 0
\(490\) 3.07971 21.6593i 0.139127 0.978467i
\(491\) −15.4259 18.3839i −0.696161 0.829652i 0.295925 0.955211i \(-0.404372\pi\)
−0.992086 + 0.125559i \(0.959928\pi\)
\(492\) 0 0
\(493\) 6.18602 + 2.88459i 0.278604 + 0.129915i
\(494\) 25.0786 43.4374i 1.12834 1.95434i
\(495\) 0 0
\(496\) −6.61027 11.4493i −0.296810 0.514090i
\(497\) −1.15678 13.2220i −0.0518886 0.593089i
\(498\) 0 0
\(499\) −31.1017 + 5.48406i −1.39230 + 0.245500i −0.818976 0.573828i \(-0.805458\pi\)
−0.573325 + 0.819328i \(0.694347\pi\)
\(500\) −23.0239 + 0.290269i −1.02966 + 0.0129812i
\(501\) 0 0
\(502\) 22.1423 1.93720i 0.988261 0.0864616i
\(503\) 2.72503 + 0.730168i 0.121503 + 0.0325566i 0.319058 0.947735i \(-0.396634\pi\)
−0.197555 + 0.980292i \(0.563300\pi\)
\(504\) 0 0
\(505\) −10.9636 + 5.56393i −0.487873 + 0.247592i
\(506\) 10.1015 + 27.7536i 0.449066 + 1.23380i
\(507\) 0 0
\(508\) 20.4530 + 1.78941i 0.907455 + 0.0793920i
\(509\) −20.7599 7.55598i −0.920166 0.334913i −0.161861 0.986814i \(-0.551750\pi\)
−0.758304 + 0.651901i \(0.773972\pi\)
\(510\) 0 0
\(511\) −2.11875 + 12.0160i −0.0937279 + 0.531557i
\(512\) −22.7346 22.7346i −1.00474 1.00474i
\(513\) 0 0
\(514\) 11.6360i 0.513243i
\(515\) 0.292064 + 8.76980i 0.0128699 + 0.386444i
\(516\) 0 0
\(517\) 7.56184 3.52615i 0.332569 0.155080i
\(518\) 3.02553 34.5820i 0.132934 1.51944i
\(519\) 0 0
\(520\) 0.372095 1.59992i 0.0163175 0.0701614i
\(521\) 7.62484 + 4.40220i 0.334050 + 0.192864i 0.657638 0.753334i \(-0.271556\pi\)
−0.323588 + 0.946198i \(0.604889\pi\)
\(522\) 0 0
\(523\) −0.332937 + 1.24254i −0.0145583 + 0.0543324i −0.972823 0.231550i \(-0.925620\pi\)
0.958265 + 0.285883i \(0.0922868\pi\)
\(524\) 17.7181 + 14.8673i 0.774019 + 0.649479i
\(525\) 0 0
\(526\) −6.45507 36.6085i −0.281454 1.59621i
\(527\) −6.29419 + 8.98903i −0.274179 + 0.391568i
\(528\) 0 0
\(529\) 1.70263 2.02911i 0.0740274 0.0882224i
\(530\) −0.482186 0.0260515i −0.0209448 0.00113161i
\(531\) 0 0
\(532\) −3.17007 11.8309i −0.137440 0.512933i
\(533\) 2.20709 4.73311i 0.0955995 0.205014i
\(534\) 0 0
\(535\) −20.5487 + 26.2137i −0.888398 + 1.13332i
\(536\) −0.182810 + 0.502268i −0.00789621 + 0.0216947i
\(537\) 0 0
\(538\) −25.9551 + 18.1740i −1.11900 + 0.783535i
\(539\) −14.0551 −0.605398
\(540\) 0 0
\(541\) −9.16794 −0.394160 −0.197080 0.980387i \(-0.563146\pi\)
−0.197080 + 0.980387i \(0.563146\pi\)
\(542\) 28.7714 20.1460i 1.23584 0.865344i
\(543\) 0 0
\(544\) −8.86365 + 24.3527i −0.380026 + 1.04411i
\(545\) −22.0085 + 2.66622i −0.942741 + 0.114208i
\(546\) 0 0
\(547\) 1.95267 4.18752i 0.0834904 0.179046i −0.860130 0.510074i \(-0.829618\pi\)
0.943621 + 0.331029i \(0.107396\pi\)
\(548\) 10.4782 + 39.1053i 0.447608 + 1.67050i
\(549\) 0 0
\(550\) 4.46837 + 28.8144i 0.190532 + 1.22865i
\(551\) −5.53663 + 6.59830i −0.235868 + 0.281097i
\(552\) 0 0
\(553\) 1.22870 1.75476i 0.0522496 0.0746202i
\(554\) 5.37283 + 30.4709i 0.228270 + 1.29458i
\(555\) 0 0
\(556\) −2.34610 1.96861i −0.0994968 0.0834878i
\(557\) −2.60809 + 9.73354i −0.110509 + 0.412423i −0.998912 0.0466405i \(-0.985148\pi\)
0.888403 + 0.459064i \(0.151815\pi\)
\(558\) 0 0
\(559\) 3.90564 + 2.25492i 0.165191 + 0.0953730i
\(560\) 6.71031 + 10.7774i 0.283562 + 0.455430i
\(561\) 0 0
\(562\) 1.30121 14.8729i 0.0548881 0.627373i
\(563\) 15.0076 6.99817i 0.632496 0.294938i −0.0798064 0.996810i \(-0.525430\pi\)
0.712302 + 0.701873i \(0.247652\pi\)
\(564\) 0 0
\(565\) 34.0390 1.13361i 1.43203 0.0476914i
\(566\) 28.9676i 1.21760i
\(567\) 0 0
\(568\) 0.768184 + 0.768184i 0.0322323 + 0.0322323i
\(569\) −1.89828 + 10.7657i −0.0795799 + 0.451320i 0.918815 + 0.394688i \(0.129147\pi\)
−0.998395 + 0.0566320i \(0.981964\pi\)
\(570\) 0 0
\(571\) 15.2515 + 5.55110i 0.638256 + 0.232306i 0.640821 0.767691i \(-0.278594\pi\)
−0.00256475 + 0.999997i \(0.500816\pi\)
\(572\) −36.3976 3.18438i −1.52186 0.133146i
\(573\) 0 0
\(574\) −0.859755 2.36216i −0.0358855 0.0985946i
\(575\) 19.7305 15.8722i 0.822820 0.661916i
\(576\) 0 0
\(577\) 17.0234 + 4.56140i 0.708693 + 0.189894i 0.595121 0.803636i \(-0.297104\pi\)
0.113572 + 0.993530i \(0.463771\pi\)
\(578\) −13.3304 + 1.16625i −0.554469 + 0.0485098i
\(579\) 0 0
\(580\) −3.83051 + 8.98374i −0.159053 + 0.373030i
\(581\) 24.3710 4.29727i 1.01108 0.178281i
\(582\) 0 0
\(583\) 0.0270388 + 0.309055i 0.00111983 + 0.0127998i
\(584\) −0.499351 0.864901i −0.0206633 0.0357898i
\(585\) 0 0
\(586\) 20.2926 35.1479i 0.838280 1.45194i
\(587\) 7.40736 + 3.45411i 0.305734 + 0.142566i 0.569430 0.822040i \(-0.307164\pi\)
−0.263696 + 0.964606i \(0.584942\pi\)
\(588\) 0 0
\(589\) −8.90140 10.6083i −0.366776 0.437106i
\(590\) −16.8631 2.39774i −0.694243 0.0987135i
\(591\) 0 0
\(592\) −26.1692 37.3735i −1.07555 1.53604i
\(593\) −28.1239 + 28.1239i −1.15491 + 1.15491i −0.169357 + 0.985555i \(0.554169\pi\)
−0.985555 + 0.169357i \(0.945831\pi\)
\(594\) 0 0
\(595\) 5.75366 8.82860i 0.235877 0.361937i
\(596\) −10.0651 1.77475i −0.412282 0.0726965i
\(597\) 0 0
\(598\) 26.4315 + 56.6826i 1.08087 + 2.31793i
\(599\) 27.5968 23.1564i 1.12757 0.946147i 0.128612 0.991695i \(-0.458948\pi\)
0.998962 + 0.0455483i \(0.0145035\pi\)
\(600\) 0 0
\(601\) −21.4617 + 7.81141i −0.875440 + 0.318634i −0.740368 0.672202i \(-0.765349\pi\)
−0.135072 + 0.990836i \(0.543126\pi\)
\(602\) 2.09680 0.561836i 0.0854593 0.0228987i
\(603\) 0 0
\(604\) −36.9808 + 21.3509i −1.50473 + 0.868755i
\(605\) −5.60999 + 1.70524i −0.228078 + 0.0693279i
\(606\) 0 0
\(607\) −7.00562 4.90539i −0.284349 0.199104i 0.422696 0.906271i \(-0.361084\pi\)
−0.707046 + 0.707168i \(0.749973\pi\)
\(608\) −26.7897 18.7583i −1.08647 0.760751i
\(609\) 0 0
\(610\) 17.8485 + 9.52721i 0.722663 + 0.385745i
\(611\) 15.3011 8.83410i 0.619017 0.357389i
\(612\) 0 0
\(613\) −35.7827 + 9.58796i −1.44525 + 0.387254i −0.894369 0.447329i \(-0.852375\pi\)
−0.550882 + 0.834583i \(0.685709\pi\)
\(614\) −22.6241 + 8.23450i −0.913034 + 0.332317i
\(615\) 0 0
\(616\) −0.389125 + 0.326514i −0.0156783 + 0.0131556i
\(617\) 5.17963 + 11.1077i 0.208524 + 0.447181i 0.982556 0.185965i \(-0.0595411\pi\)
−0.774032 + 0.633146i \(0.781763\pi\)
\(618\) 0 0
\(619\) 8.63834 + 1.52317i 0.347204 + 0.0612215i 0.344531 0.938775i \(-0.388038\pi\)
0.00267331 + 0.999996i \(0.499149\pi\)
\(620\) −13.1546 8.57294i −0.528301 0.344297i
\(621\) 0 0
\(622\) 3.44947 3.44947i 0.138311 0.138311i
\(623\) 5.12449 + 7.31853i 0.205308 + 0.293211i
\(624\) 0 0
\(625\) 22.1491 11.5939i 0.885963 0.463756i
\(626\) −15.8763 18.9206i −0.634543 0.756218i
\(627\) 0 0
\(628\) −12.6768 5.91130i −0.505860 0.235887i
\(629\) −18.9351 + 32.7966i −0.754992 + 1.30769i
\(630\) 0 0
\(631\) 16.1540 + 27.9796i 0.643083 + 1.11385i 0.984741 + 0.174027i \(0.0556781\pi\)
−0.341658 + 0.939824i \(0.610989\pi\)
\(632\) 0.0152819 + 0.174673i 0.000607880 + 0.00694810i
\(633\) 0 0
\(634\) 45.0092 7.93634i 1.78755 0.315192i
\(635\) −20.6818 + 8.31714i −0.820731 + 0.330056i
\(636\) 0 0
\(637\) −29.6497 + 2.59401i −1.17476 + 0.102778i
\(638\) 11.9462 + 3.20098i 0.472955 + 0.126728i
\(639\) 0 0
\(640\) −2.03708 0.665529i −0.0805228 0.0263073i
\(641\) 3.35944 + 9.23000i 0.132690 + 0.364563i 0.988189 0.153242i \(-0.0489715\pi\)
−0.855499 + 0.517805i \(0.826749\pi\)
\(642\) 0 0
\(643\) 18.5293 + 1.62110i 0.730723 + 0.0639299i 0.446444 0.894812i \(-0.352690\pi\)
0.284279 + 0.958742i \(0.408246\pi\)
\(644\) 14.3516 + 5.22355i 0.565532 + 0.205837i
\(645\) 0 0
\(646\) −4.57349 + 25.9375i −0.179942 + 1.02050i
\(647\) 14.2018 + 14.2018i 0.558331 + 0.558331i 0.928832 0.370501i \(-0.120814\pi\)
−0.370501 + 0.928832i \(0.620814\pi\)
\(648\) 0 0
\(649\) 10.9428i 0.429542i
\(650\) 14.7441 + 59.9601i 0.578312 + 2.35183i
\(651\) 0 0
\(652\) 37.9754 17.7082i 1.48723 0.693507i
\(653\) −1.73834 + 19.8693i −0.0680265 + 0.777546i 0.883189 + 0.469018i \(0.155392\pi\)
−0.951215 + 0.308528i \(0.900164\pi\)
\(654\) 0 0
\(655\) −24.4597 5.68860i −0.955719 0.222272i
\(656\) −2.86119 1.65191i −0.111711 0.0644963i
\(657\) 0 0
\(658\) 2.20110 8.21463i 0.0858080 0.320240i
\(659\) −0.815140 0.683983i −0.0317533 0.0266442i 0.626773 0.779202i \(-0.284375\pi\)
−0.658526 + 0.752558i \(0.728820\pi\)
\(660\) 0 0
\(661\) −5.78183 32.7904i −0.224887 1.27540i −0.862901 0.505373i \(-0.831355\pi\)
0.638014 0.770025i \(-0.279756\pi\)
\(662\) −18.8576 + 26.9314i −0.732920 + 1.04672i
\(663\) 0 0
\(664\) −1.30202 + 1.55168i −0.0505280 + 0.0602169i
\(665\) 8.88238 + 9.89699i 0.344444 + 0.383789i
\(666\) 0 0
\(667\) −2.77981 10.3744i −0.107635 0.401699i
\(668\) 0.410470 0.880256i 0.0158816 0.0340581i
\(669\) 0 0
\(670\) −2.41637 19.9461i −0.0933525 0.770585i
\(671\) 4.44565 12.2143i 0.171622 0.471529i
\(672\) 0 0
\(673\) −20.0466 + 14.0367i −0.772738 + 0.541077i −0.892135 0.451770i \(-0.850793\pi\)
0.119397 + 0.992847i \(0.461904\pi\)
\(674\) 8.08017 0.311236
\(675\) 0 0
\(676\) −50.5961 −1.94600
\(677\) 16.7682 11.7412i 0.644455 0.451252i −0.205108 0.978739i \(-0.565755\pi\)
0.849563 + 0.527487i \(0.176866\pi\)
\(678\) 0 0
\(679\) 8.11957 22.3083i 0.311601 0.856115i
\(680\) 0.103735 + 0.856287i 0.00397805 + 0.0328371i
\(681\) 0 0
\(682\) −8.40325 + 18.0208i −0.321777 + 0.690053i
\(683\) 5.71751 + 21.3380i 0.218774 + 0.816477i 0.984804 + 0.173671i \(0.0555630\pi\)
−0.766029 + 0.642806i \(0.777770\pi\)
\(684\) 0 0
\(685\) −29.3595 32.7132i −1.12177 1.24991i
\(686\) −22.4833 + 26.7945i −0.858416 + 1.02302i
\(687\) 0 0
\(688\) 1.63643 2.33707i 0.0623884 0.0890999i
\(689\) 0.114078 + 0.646969i 0.00434603 + 0.0246476i
\(690\) 0 0
\(691\) 13.7398 + 11.5291i 0.522688 + 0.438587i 0.865568 0.500792i \(-0.166958\pi\)
−0.342880 + 0.939379i \(0.611402\pi\)
\(692\) 9.82872 36.6813i 0.373632 1.39441i
\(693\) 0 0
\(694\) −21.6551 12.5026i −0.822016 0.474591i
\(695\) 3.23877 + 0.753243i 0.122854 + 0.0285721i
\(696\) 0 0
\(697\) −0.239008 + 2.73187i −0.00905306 + 0.103477i
\(698\) 13.9526 6.50619i 0.528112 0.246263i
\(699\) 0 0
\(700\) 12.8994 + 7.80759i 0.487552 + 0.295099i
\(701\) 11.4005i 0.430590i −0.976549 0.215295i \(-0.930929\pi\)
0.976549 0.215295i \(-0.0690713\pi\)
\(702\) 0 0
\(703\) −33.7929 33.7929i −1.27452 1.27452i
\(704\) −4.25644 + 24.1395i −0.160421 + 0.909791i
\(705\) 0 0
\(706\) 33.8977 + 12.3377i 1.27576 + 0.464337i
\(707\) 8.02039 + 0.701693i 0.301638 + 0.0263899i
\(708\) 0 0
\(709\) 5.28444 + 14.5189i 0.198461 + 0.545268i 0.998504 0.0546749i \(-0.0174122\pi\)
−0.800043 + 0.599943i \(0.795190\pi\)
\(710\) −38.8178 12.6820i −1.45680 0.475948i
\(711\) 0 0
\(712\) −0.706365 0.189270i −0.0264722 0.00709319i
\(713\) 17.2019 1.50497i 0.644216 0.0563616i
\(714\) 0 0
\(715\) 36.8047 14.8010i 1.37642 0.553524i
\(716\) 16.0551 2.83094i 0.600006 0.105797i
\(717\) 0 0
\(718\) −2.20038 25.1504i −0.0821174 0.938606i
\(719\) −4.71157 8.16068i −0.175712 0.304342i 0.764695 0.644392i \(-0.222889\pi\)
−0.940407 + 0.340050i \(0.889556\pi\)
\(720\) 0 0
\(721\) 2.87301 4.97620i 0.106997 0.185323i
\(722\) 4.57202 + 2.13197i 0.170153 + 0.0793437i
\(723\) 0 0
\(724\) −26.1085 31.1149i −0.970315 1.15638i
\(725\) −0.705492 10.5802i −0.0262013 0.392938i
\(726\) 0 0
\(727\) −24.6272 35.1712i −0.913371 1.30443i −0.952293 0.305186i \(-0.901281\pi\)
0.0389219 0.999242i \(-0.487608\pi\)
\(728\) −0.760607 + 0.760607i −0.0281900 + 0.0281900i
\(729\) 0 0
\(730\) 31.4516 + 20.4972i 1.16408 + 0.758636i
\(731\) −2.33216 0.411222i −0.0862579 0.0152096i
\(732\) 0 0
\(733\) 0.264636 + 0.567513i 0.00977454 + 0.0209616i 0.911134 0.412109i \(-0.135208\pi\)
−0.901360 + 0.433071i \(0.857430\pi\)
\(734\) 21.1255 17.7264i 0.779755 0.654292i
\(735\) 0 0
\(736\) 38.3205 13.9475i 1.41251 0.514112i
\(737\) −12.4684 + 3.34089i −0.459278 + 0.123063i
\(738\) 0 0
\(739\) 23.6846 13.6743i 0.871251 0.503017i 0.00348723 0.999994i \(-0.498890\pi\)
0.867764 + 0.496977i \(0.165557\pi\)
\(740\) −47.8028 25.5163i −1.75726 0.937999i
\(741\) 0 0
\(742\) 0.259029 + 0.181374i 0.00950927 + 0.00665846i
\(743\) −29.3796 20.5718i −1.07783 0.754706i −0.106950 0.994264i \(-0.534109\pi\)
−0.970882 + 0.239558i \(0.922997\pi\)
\(744\) 0 0
\(745\) 10.6170 3.22720i 0.388978 0.118236i
\(746\) 21.1251 12.1966i 0.773444 0.446548i
\(747\) 0 0
\(748\) 18.5318 4.96558i 0.677589 0.181559i
\(749\) 20.4960 7.45993i 0.748907 0.272580i
\(750\) 0 0
\(751\) −27.0935 + 22.7342i −0.988657 + 0.829582i −0.985373 0.170413i \(-0.945490\pi\)
−0.00328459 + 0.999995i \(0.501046\pi\)
\(752\) −4.72374 10.1301i −0.172257 0.369407i
\(753\) 0 0
\(754\) 25.7916 + 4.54775i 0.939274 + 0.165619i
\(755\) 25.3139 38.8425i 0.921267 1.41362i
\(756\) 0 0
\(757\) −26.1262 + 26.1262i −0.949573 + 0.949573i −0.998788 0.0492153i \(-0.984328\pi\)
0.0492153 + 0.998788i \(0.484328\pi\)
\(758\) −26.0268 37.1701i −0.945336 1.35008i
\(759\) 0 0
\(760\) −1.07765 0.153230i −0.0390906 0.00555824i
\(761\) −5.19201 6.18759i −0.188210 0.224300i 0.663685 0.748012i \(-0.268991\pi\)
−0.851896 + 0.523712i \(0.824547\pi\)
\(762\) 0 0
\(763\) 13.1573 + 6.13535i 0.476326 + 0.222115i
\(764\) 8.99914 15.5870i 0.325577 0.563917i
\(765\) 0 0
\(766\) −14.5740 25.2430i −0.526582 0.912066i
\(767\) 2.01960 + 23.0841i 0.0729234 + 0.833519i
\(768\) 0 0
\(769\) −16.0619 + 2.83215i −0.579208 + 0.102130i −0.455574 0.890198i \(-0.650566\pi\)
−0.123634 + 0.992328i \(0.539455\pi\)
\(770\) 7.48918 17.5645i 0.269891 0.632979i
\(771\) 0 0
\(772\) −17.7281 + 1.55101i −0.638048 + 0.0558220i
\(773\) −11.4302 3.06271i −0.411116 0.110158i 0.0473325 0.998879i \(-0.484928\pi\)
−0.458448 + 0.888721i \(0.651595\pi\)
\(774\) 0 0
\(775\) 16.9486 + 1.83675i 0.608811 + 0.0659781i
\(776\) 0.664599 + 1.82597i 0.0238577 + 0.0655485i
\(777\) 0 0
\(778\) −25.3711 2.21968i −0.909598 0.0795795i
\(779\) −3.25195 1.18361i −0.116513 0.0424073i
\(780\) 0 0
\(781\) −4.55583 + 25.8374i −0.163020 + 0.924534i
\(782\) −23.2222 23.2222i −0.830425 0.830425i
\(783\) 0 0
\(784\) 18.8287i 0.672455i
\(785\) 15.1782 0.505485i 0.541733 0.0180415i
\(786\) 0 0
\(787\) −43.1572