Properties

Label 405.2.r.a.8.9
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 8.9
Character \(\chi\) \(=\) 405.8
Dual form 405.2.r.a.152.9

$q$-expansion

\(f(q)\) \(=\) \(q+(0.377486 - 0.264318i) q^{2} +(-0.611409 + 1.67983i) q^{4} +(-0.538986 - 2.17014i) q^{5} +(-1.52168 + 3.26325i) q^{7} +(0.451753 + 1.68596i) q^{8} +O(q^{10})\) \(q+(0.377486 - 0.264318i) q^{2} +(-0.611409 + 1.67983i) q^{4} +(-0.538986 - 2.17014i) q^{5} +(-1.52168 + 3.26325i) q^{7} +(0.451753 + 1.68596i) q^{8} +(-0.777066 - 0.676732i) q^{10} +(-2.85486 + 3.40229i) q^{11} +(0.226257 - 0.323128i) q^{13} +(0.288125 + 1.63404i) q^{14} +(-2.12266 - 1.78113i) q^{16} +(-1.03506 + 3.86289i) q^{17} +(1.05819 + 0.610947i) q^{19} +(3.97501 + 0.421435i) q^{20} +(-0.178381 + 2.03891i) q^{22} +(3.57786 - 1.66839i) q^{23} +(-4.41899 + 2.33935i) q^{25} -0.181780i q^{26} +(-4.55135 - 4.55135i) q^{28} +(-0.885233 + 5.02040i) q^{29} +(9.19946 + 3.34833i) q^{31} +(-4.74965 - 0.415541i) q^{32} +(0.630312 + 1.73177i) q^{34} +(7.90187 + 1.54341i) q^{35} +(-10.6220 - 2.84615i) q^{37} +(0.560936 - 0.0490755i) q^{38} +(3.41529 - 1.88908i) q^{40} +(1.80826 - 0.318845i) q^{41} +(-0.218695 - 2.49969i) q^{43} +(-3.96979 - 6.87588i) q^{44} +(0.909608 - 1.57549i) q^{46} +(-1.19000 - 0.554905i) q^{47} +(-3.83380 - 4.56894i) q^{49} +(-1.04977 + 2.05109i) q^{50} +(0.404466 + 0.577637i) q^{52} +(3.53443 - 3.53443i) q^{53} +(8.92217 + 4.36165i) q^{55} +(-6.18915 - 1.09131i) q^{56} +(0.992822 + 2.12911i) q^{58} +(0.467138 - 0.391975i) q^{59} +(-1.87695 + 0.683152i) q^{61} +(4.35769 - 1.16764i) q^{62} +(2.89665 - 1.67238i) q^{64} +(-0.823182 - 0.316847i) q^{65} +(3.34241 + 2.34038i) q^{67} +(-5.85616 - 4.10053i) q^{68} +(3.39079 - 1.50600i) q^{70} +(10.9258 - 6.30801i) q^{71} +(4.00309 - 1.07262i) q^{73} +(-4.76194 + 1.73320i) q^{74} +(-1.67328 + 1.40404i) q^{76} +(-6.75835 - 14.4933i) q^{77} +(11.8688 + 2.09278i) q^{79} +(-2.72120 + 5.56647i) q^{80} +(0.598316 - 0.598316i) q^{82} +(-1.54510 - 2.20663i) q^{83} +(8.94087 + 0.164174i) q^{85} +(-0.743269 - 0.885794i) q^{86} +(-7.02584 - 3.27620i) q^{88} +(-1.23513 + 2.13931i) q^{89} +(0.710159 + 1.23003i) q^{91} +(0.615070 + 7.03028i) q^{92} +(-0.595878 + 0.105069i) q^{94} +(0.755488 - 2.62571i) q^{95} +(0.567380 - 0.0496393i) q^{97} +(-2.65486 - 0.711367i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.377486 0.264318i 0.266923 0.186901i −0.432451 0.901657i \(-0.642351\pi\)
0.699374 + 0.714756i \(0.253462\pi\)
\(3\) 0 0
\(4\) −0.611409 + 1.67983i −0.305705 + 0.839916i
\(5\) −0.538986 2.17014i −0.241042 0.970515i
\(6\) 0 0
\(7\) −1.52168 + 3.26325i −0.575141 + 1.23339i 0.376567 + 0.926389i \(0.377104\pi\)
−0.951708 + 0.307004i \(0.900673\pi\)
\(8\) 0.451753 + 1.68596i 0.159719 + 0.596078i
\(9\) 0 0
\(10\) −0.777066 0.676732i −0.245730 0.214001i
\(11\) −2.85486 + 3.40229i −0.860773 + 1.02583i 0.138597 + 0.990349i \(0.455741\pi\)
−0.999370 + 0.0354810i \(0.988704\pi\)
\(12\) 0 0
\(13\) 0.226257 0.323128i 0.0627524 0.0896196i −0.786549 0.617527i \(-0.788134\pi\)
0.849302 + 0.527908i \(0.177023\pi\)
\(14\) 0.288125 + 1.63404i 0.0770047 + 0.436715i
\(15\) 0 0
\(16\) −2.12266 1.78113i −0.530666 0.445281i
\(17\) −1.03506 + 3.86289i −0.251038 + 0.936888i 0.719213 + 0.694789i \(0.244502\pi\)
−0.970252 + 0.242098i \(0.922164\pi\)
\(18\) 0 0
\(19\) 1.05819 + 0.610947i 0.242766 + 0.140161i 0.616447 0.787396i \(-0.288571\pi\)
−0.373682 + 0.927557i \(0.621905\pi\)
\(20\) 3.97501 + 0.421435i 0.888839 + 0.0942357i
\(21\) 0 0
\(22\) −0.178381 + 2.03891i −0.0380310 + 0.434697i
\(23\) 3.57786 1.66839i 0.746036 0.347882i −0.0121450 0.999926i \(-0.503866\pi\)
0.758181 + 0.652044i \(0.226088\pi\)
\(24\) 0 0
\(25\) −4.41899 + 2.33935i −0.883798 + 0.467869i
\(26\) 0.181780i 0.0356500i
\(27\) 0 0
\(28\) −4.55135 4.55135i −0.860124 0.860124i
\(29\) −0.885233 + 5.02040i −0.164384 + 0.932266i 0.785314 + 0.619097i \(0.212501\pi\)
−0.949698 + 0.313168i \(0.898610\pi\)
\(30\) 0 0
\(31\) 9.19946 + 3.34833i 1.65227 + 0.601378i 0.989121 0.147107i \(-0.0469963\pi\)
0.663152 + 0.748485i \(0.269219\pi\)
\(32\) −4.74965 0.415541i −0.839628 0.0734579i
\(33\) 0 0
\(34\) 0.630312 + 1.73177i 0.108098 + 0.296996i
\(35\) 7.90187 + 1.54341i 1.33566 + 0.260883i
\(36\) 0 0
\(37\) −10.6220 2.84615i −1.74624 0.467905i −0.762426 0.647076i \(-0.775992\pi\)
−0.983818 + 0.179171i \(0.942658\pi\)
\(38\) 0.560936 0.0490755i 0.0909958 0.00796111i
\(39\) 0 0
\(40\) 3.41529 1.88908i 0.540004 0.298689i
\(41\) 1.80826 0.318845i 0.282403 0.0497952i −0.0306526 0.999530i \(-0.509759\pi\)
0.313055 + 0.949735i \(0.398647\pi\)
\(42\) 0 0
\(43\) −0.218695 2.49969i −0.0333507 0.381200i −0.994466 0.105054i \(-0.966498\pi\)
0.961116 0.276146i \(-0.0890572\pi\)
\(44\) −3.96979 6.87588i −0.598469 1.03658i
\(45\) 0 0
\(46\) 0.909608 1.57549i 0.134114 0.232293i
\(47\) −1.19000 0.554905i −0.173579 0.0809412i 0.333887 0.942613i \(-0.391640\pi\)
−0.507465 + 0.861672i \(0.669418\pi\)
\(48\) 0 0
\(49\) −3.83380 4.56894i −0.547685 0.652706i
\(50\) −1.04977 + 2.05109i −0.148460 + 0.290068i
\(51\) 0 0
\(52\) 0.404466 + 0.577637i 0.0560893 + 0.0801039i
\(53\) 3.53443 3.53443i 0.485491 0.485491i −0.421389 0.906880i \(-0.638457\pi\)
0.906880 + 0.421389i \(0.138457\pi\)
\(54\) 0 0
\(55\) 8.92217 + 4.36165i 1.20307 + 0.588125i
\(56\) −6.18915 1.09131i −0.827060 0.145833i
\(57\) 0 0
\(58\) 0.992822 + 2.12911i 0.130364 + 0.279566i
\(59\) 0.467138 0.391975i 0.0608162 0.0510308i −0.611873 0.790956i \(-0.709584\pi\)
0.672689 + 0.739925i \(0.265139\pi\)
\(60\) 0 0
\(61\) −1.87695 + 0.683152i −0.240318 + 0.0874687i −0.459372 0.888244i \(-0.651925\pi\)
0.219053 + 0.975713i \(0.429703\pi\)
\(62\) 4.35769 1.16764i 0.553427 0.148290i
\(63\) 0 0
\(64\) 2.89665 1.67238i 0.362081 0.209048i
\(65\) −0.823182 0.316847i −0.102103 0.0393000i
\(66\) 0 0
\(67\) 3.34241 + 2.34038i 0.408341 + 0.285923i 0.759645 0.650338i \(-0.225373\pi\)
−0.351304 + 0.936261i \(0.614262\pi\)
\(68\) −5.85616 4.10053i −0.710164 0.497262i
\(69\) 0 0
\(70\) 3.39079 1.50600i 0.405277 0.180001i
\(71\) 10.9258 6.30801i 1.29665 0.748623i 0.316829 0.948483i \(-0.397382\pi\)
0.979824 + 0.199860i \(0.0640487\pi\)
\(72\) 0 0
\(73\) 4.00309 1.07262i 0.468526 0.125541i −0.0168287 0.999858i \(-0.505357\pi\)
0.485355 + 0.874317i \(0.338690\pi\)
\(74\) −4.76194 + 1.73320i −0.553564 + 0.201481i
\(75\) 0 0
\(76\) −1.67328 + 1.40404i −0.191938 + 0.161055i
\(77\) −6.75835 14.4933i −0.770186 1.65167i
\(78\) 0 0
\(79\) 11.8688 + 2.09278i 1.33534 + 0.235457i 0.795317 0.606193i \(-0.207304\pi\)
0.540023 + 0.841650i \(0.318415\pi\)
\(80\) −2.72120 + 5.56647i −0.304239 + 0.622350i
\(81\) 0 0
\(82\) 0.598316 0.598316i 0.0660729 0.0660729i
\(83\) −1.54510 2.20663i −0.169597 0.242209i 0.725352 0.688378i \(-0.241677\pi\)
−0.894949 + 0.446169i \(0.852788\pi\)
\(84\) 0 0
\(85\) 8.94087 + 0.164174i 0.969774 + 0.0178072i
\(86\) −0.743269 0.885794i −0.0801488 0.0955176i
\(87\) 0 0
\(88\) −7.02584 3.27620i −0.748957 0.349244i
\(89\) −1.23513 + 2.13931i −0.130924 + 0.226766i −0.924033 0.382313i \(-0.875128\pi\)
0.793109 + 0.609079i \(0.208461\pi\)
\(90\) 0 0
\(91\) 0.710159 + 1.23003i 0.0744449 + 0.128942i
\(92\) 0.615070 + 7.03028i 0.0641254 + 0.732957i
\(93\) 0 0
\(94\) −0.595878 + 0.105069i −0.0614601 + 0.0108371i
\(95\) 0.755488 2.62571i 0.0775114 0.269392i
\(96\) 0 0
\(97\) 0.567380 0.0496393i 0.0576087 0.00504011i −0.0583150 0.998298i \(-0.518573\pi\)
0.115924 + 0.993258i \(0.463017\pi\)
\(98\) −2.65486 0.711367i −0.268181 0.0718589i
\(99\) 0 0
\(100\) −1.22790 8.85346i −0.122790 0.885346i
\(101\) 5.00202 + 13.7429i 0.497720 + 1.36747i 0.893473 + 0.449117i \(0.148261\pi\)
−0.395753 + 0.918357i \(0.629516\pi\)
\(102\) 0 0
\(103\) −17.1583 1.50115i −1.69066 0.147913i −0.799213 0.601048i \(-0.794750\pi\)
−0.891442 + 0.453135i \(0.850306\pi\)
\(104\) 0.646995 + 0.235487i 0.0634431 + 0.0230914i
\(105\) 0 0
\(106\) 0.399982 2.26841i 0.0388497 0.220328i
\(107\) −4.07639 4.07639i −0.394080 0.394080i 0.482059 0.876139i \(-0.339889\pi\)
−0.876139 + 0.482059i \(0.839889\pi\)
\(108\) 0 0
\(109\) 7.33084i 0.702167i −0.936344 0.351084i \(-0.885813\pi\)
0.936344 0.351084i \(-0.114187\pi\)
\(110\) 4.52086 0.711831i 0.431047 0.0678705i
\(111\) 0 0
\(112\) 9.04228 4.21648i 0.854415 0.398420i
\(113\) 0.638871 7.30233i 0.0600999 0.686945i −0.905060 0.425284i \(-0.860174\pi\)
0.965160 0.261661i \(-0.0842703\pi\)
\(114\) 0 0
\(115\) −5.54904 6.86522i −0.517451 0.640185i
\(116\) −7.89220 4.55656i −0.732772 0.423066i
\(117\) 0 0
\(118\) 0.0727316 0.271438i 0.00669549 0.0249879i
\(119\) −11.0305 9.25573i −1.01117 0.848471i
\(120\) 0 0
\(121\) −1.51523 8.59327i −0.137748 0.781206i
\(122\) −0.527950 + 0.753991i −0.0477984 + 0.0682632i
\(123\) 0 0
\(124\) −11.2493 + 13.4064i −1.01021 + 1.20393i
\(125\) 7.45848 + 8.32893i 0.667106 + 0.744962i
\(126\) 0 0
\(127\) 1.36574 + 5.09700i 0.121189 + 0.452285i 0.999675 0.0254832i \(-0.00811243\pi\)
−0.878486 + 0.477769i \(0.841446\pi\)
\(128\) 4.68132 10.0391i 0.413774 0.887341i
\(129\) 0 0
\(130\) −0.394488 + 0.0979769i −0.0345989 + 0.00859314i
\(131\) −0.242450 + 0.666126i −0.0211829 + 0.0581997i −0.949833 0.312756i \(-0.898748\pi\)
0.928650 + 0.370956i \(0.120970\pi\)
\(132\) 0 0
\(133\) −3.60390 + 2.52348i −0.312498 + 0.218813i
\(134\) 1.88032 0.162435
\(135\) 0 0
\(136\) −6.98028 −0.598554
\(137\) 0.834037 0.583999i 0.0712566 0.0498944i −0.537405 0.843324i \(-0.680595\pi\)
0.608662 + 0.793430i \(0.291707\pi\)
\(138\) 0 0
\(139\) −7.61336 + 20.9175i −0.645757 + 1.77420i −0.0129201 + 0.999917i \(0.504113\pi\)
−0.632837 + 0.774285i \(0.718110\pi\)
\(140\) −7.42394 + 12.3302i −0.627437 + 1.04209i
\(141\) 0 0
\(142\) 2.45701 5.26907i 0.206187 0.442170i
\(143\) 0.453445 + 1.69228i 0.0379189 + 0.141515i
\(144\) 0 0
\(145\) 11.3721 0.784852i 0.944401 0.0651784i
\(146\) 1.22759 1.46299i 0.101596 0.121078i
\(147\) 0 0
\(148\) 11.2754 16.1030i 0.926835 1.32366i
\(149\) 2.80203 + 15.8911i 0.229551 + 1.30185i 0.853791 + 0.520616i \(0.174298\pi\)
−0.624240 + 0.781233i \(0.714591\pi\)
\(150\) 0 0
\(151\) 6.91118 + 5.79917i 0.562424 + 0.471930i 0.879122 0.476597i \(-0.158130\pi\)
−0.316698 + 0.948526i \(0.602574\pi\)
\(152\) −0.551994 + 2.06007i −0.0447726 + 0.167094i
\(153\) 0 0
\(154\) −6.38204 3.68467i −0.514279 0.296919i
\(155\) 2.30795 21.7688i 0.185379 1.74851i
\(156\) 0 0
\(157\) −0.125040 + 1.42921i −0.00997924 + 0.114063i −0.999550 0.0299812i \(-0.990455\pi\)
0.989571 + 0.144044i \(0.0460108\pi\)
\(158\) 5.03345 2.34714i 0.400440 0.186728i
\(159\) 0 0
\(160\) 1.65822 + 10.5314i 0.131093 + 0.832578i
\(161\) 14.2142i 1.12024i
\(162\) 0 0
\(163\) 6.66882 + 6.66882i 0.522343 + 0.522343i 0.918278 0.395936i \(-0.129580\pi\)
−0.395936 + 0.918278i \(0.629580\pi\)
\(164\) −0.569980 + 3.23252i −0.0445080 + 0.252417i
\(165\) 0 0
\(166\) −1.16651 0.424573i −0.0905384 0.0329533i
\(167\) 16.7028 + 1.46130i 1.29250 + 0.113079i 0.712578 0.701593i \(-0.247528\pi\)
0.579922 + 0.814672i \(0.303083\pi\)
\(168\) 0 0
\(169\) 4.39304 + 12.0698i 0.337926 + 0.928445i
\(170\) 3.41845 2.30126i 0.262183 0.176499i
\(171\) 0 0
\(172\) 4.33278 + 1.16096i 0.330371 + 0.0885227i
\(173\) 7.61365 0.666108i 0.578855 0.0506432i 0.206031 0.978545i \(-0.433945\pi\)
0.372824 + 0.927902i \(0.378390\pi\)
\(174\) 0 0
\(175\) −0.909596 17.9800i −0.0687590 1.35916i
\(176\) 12.1198 2.13705i 0.913566 0.161086i
\(177\) 0 0
\(178\) 0.0992144 + 1.13403i 0.00743644 + 0.0849988i
\(179\) −2.10555 3.64692i −0.157376 0.272584i 0.776545 0.630061i \(-0.216970\pi\)
−0.933922 + 0.357477i \(0.883637\pi\)
\(180\) 0 0
\(181\) −2.97345 + 5.15017i −0.221015 + 0.382809i −0.955116 0.296231i \(-0.904270\pi\)
0.734102 + 0.679040i \(0.237604\pi\)
\(182\) 0.593194 + 0.276611i 0.0439705 + 0.0205038i
\(183\) 0 0
\(184\) 4.42915 + 5.27845i 0.326521 + 0.389133i
\(185\) −0.451438 + 24.5852i −0.0331904 + 1.80754i
\(186\) 0 0
\(187\) −10.1877 14.5496i −0.745000 1.06397i
\(188\) 1.65972 1.65972i 0.121048 0.121048i
\(189\) 0 0
\(190\) −0.408837 1.19086i −0.0296602 0.0863938i
\(191\) 10.6788 + 1.88297i 0.772694 + 0.136247i 0.546074 0.837737i \(-0.316122\pi\)
0.226619 + 0.973983i \(0.427233\pi\)
\(192\) 0 0
\(193\) 0.260068 + 0.557718i 0.0187201 + 0.0401454i 0.915446 0.402442i \(-0.131838\pi\)
−0.896725 + 0.442587i \(0.854061\pi\)
\(194\) 0.201057 0.168707i 0.0144351 0.0121124i
\(195\) 0 0
\(196\) 10.0191 3.64664i 0.715648 0.260475i
\(197\) −26.5467 + 7.11316i −1.89137 + 0.506791i −0.892980 + 0.450097i \(0.851389\pi\)
−0.998392 + 0.0566946i \(0.981944\pi\)
\(198\) 0 0
\(199\) 2.40020 1.38576i 0.170146 0.0982338i −0.412509 0.910954i \(-0.635347\pi\)
0.582655 + 0.812720i \(0.302014\pi\)
\(200\) −5.94035 6.39345i −0.420046 0.452085i
\(201\) 0 0
\(202\) 5.52070 + 3.86564i 0.388435 + 0.271985i
\(203\) −15.0358 10.5282i −1.05531 0.738934i
\(204\) 0 0
\(205\) −1.66656 3.75232i −0.116398 0.262073i
\(206\) −6.87379 + 3.96858i −0.478919 + 0.276504i
\(207\) 0 0
\(208\) −1.05580 + 0.282900i −0.0732065 + 0.0196156i
\(209\) −5.09961 + 1.85611i −0.352747 + 0.128389i
\(210\) 0 0
\(211\) −16.7925 + 14.0906i −1.15605 + 0.970038i −0.999844 0.0176876i \(-0.994370\pi\)
−0.156202 + 0.987725i \(0.549925\pi\)
\(212\) 3.77627 + 8.09823i 0.259355 + 0.556189i
\(213\) 0 0
\(214\) −2.61625 0.461315i −0.178843 0.0315348i
\(215\) −5.30681 + 1.82190i −0.361921 + 0.124252i
\(216\) 0 0
\(217\) −24.9251 + 24.9251i −1.69202 + 1.69202i
\(218\) −1.93768 2.76729i −0.131236 0.187424i
\(219\) 0 0
\(220\) −12.7819 + 12.3210i −0.861759 + 0.830682i
\(221\) 1.01402 + 1.20846i 0.0682103 + 0.0812899i
\(222\) 0 0
\(223\) 10.1077 + 4.71331i 0.676863 + 0.315627i 0.730479 0.682935i \(-0.239297\pi\)
−0.0536157 + 0.998562i \(0.517075\pi\)
\(224\) 8.58346 14.8670i 0.573507 0.993343i
\(225\) 0 0
\(226\) −1.68897 2.92539i −0.112349 0.194594i
\(227\) 1.11401 + 12.7332i 0.0739393 + 0.845130i 0.939102 + 0.343639i \(0.111660\pi\)
−0.865163 + 0.501492i \(0.832785\pi\)
\(228\) 0 0
\(229\) −14.6486 + 2.58295i −0.968008 + 0.170686i −0.635233 0.772320i \(-0.719096\pi\)
−0.332775 + 0.943006i \(0.607985\pi\)
\(230\) −3.90929 1.12481i −0.257771 0.0741676i
\(231\) 0 0
\(232\) −8.86413 + 0.775511i −0.581959 + 0.0509148i
\(233\) 4.81533 + 1.29026i 0.315463 + 0.0845279i 0.413076 0.910696i \(-0.364454\pi\)
−0.0976137 + 0.995224i \(0.531121\pi\)
\(234\) 0 0
\(235\) −0.562827 + 2.88154i −0.0367148 + 0.187971i
\(236\) 0.372840 + 1.02437i 0.0242698 + 0.0666808i
\(237\) 0 0
\(238\) −6.61033 0.578329i −0.428484 0.0374875i
\(239\) 6.83215 + 2.48670i 0.441935 + 0.160851i 0.553397 0.832918i \(-0.313331\pi\)
−0.111462 + 0.993769i \(0.535553\pi\)
\(240\) 0 0
\(241\) 3.42764 19.4391i 0.220794 1.25219i −0.649770 0.760131i \(-0.725135\pi\)
0.870564 0.492055i \(-0.163754\pi\)
\(242\) −2.84333 2.84333i −0.182776 0.182776i
\(243\) 0 0
\(244\) 3.57064i 0.228587i
\(245\) −7.84886 + 10.7825i −0.501445 + 0.688866i
\(246\) 0 0
\(247\) 0.436837 0.203700i 0.0277953 0.0129611i
\(248\) −1.48928 + 17.0226i −0.0945696 + 1.08094i
\(249\) 0 0
\(250\) 5.01696 + 1.17264i 0.317300 + 0.0741643i
\(251\) −14.7212 8.49927i −0.929191 0.536469i −0.0426356 0.999091i \(-0.513575\pi\)
−0.886556 + 0.462622i \(0.846909\pi\)
\(252\) 0 0
\(253\) −4.53797 + 16.9360i −0.285300 + 1.06475i
\(254\) 1.86278 + 1.56305i 0.116881 + 0.0980747i
\(255\) 0 0
\(256\) 0.275231 + 1.56091i 0.0172019 + 0.0975570i
\(257\) 8.87491 12.6747i 0.553601 0.790625i −0.440652 0.897678i \(-0.645253\pi\)
0.994253 + 0.107053i \(0.0341415\pi\)
\(258\) 0 0
\(259\) 25.4510 30.3313i 1.58145 1.88469i
\(260\) 1.03555 1.18908i 0.0642221 0.0737439i
\(261\) 0 0
\(262\) 0.0845478 + 0.315537i 0.00522338 + 0.0194939i
\(263\) −10.6896 + 22.9238i −0.659147 + 1.41355i 0.237759 + 0.971324i \(0.423587\pi\)
−0.896906 + 0.442221i \(0.854191\pi\)
\(264\) 0 0
\(265\) −9.57520 5.76519i −0.588200 0.354153i
\(266\) −0.693419 + 1.90515i −0.0425163 + 0.116812i
\(267\) 0 0
\(268\) −5.97503 + 4.18376i −0.364983 + 0.255564i
\(269\) 20.9181 1.27540 0.637698 0.770286i \(-0.279887\pi\)
0.637698 + 0.770286i \(0.279887\pi\)
\(270\) 0 0
\(271\) 6.02125 0.365765 0.182882 0.983135i \(-0.441457\pi\)
0.182882 + 0.983135i \(0.441457\pi\)
\(272\) 9.07736 6.35604i 0.550396 0.385391i
\(273\) 0 0
\(274\) 0.160475 0.440902i 0.00969467 0.0266359i
\(275\) 4.65646 21.7132i 0.280795 1.30936i
\(276\) 0 0
\(277\) 1.52924 3.27946i 0.0918830 0.197044i −0.854995 0.518636i \(-0.826440\pi\)
0.946878 + 0.321592i \(0.104218\pi\)
\(278\) 2.65495 + 9.90842i 0.159233 + 0.594267i
\(279\) 0 0
\(280\) 0.967565 + 14.0195i 0.0578230 + 0.837826i
\(281\) 15.0170 17.8966i 0.895839 1.06762i −0.101508 0.994835i \(-0.532367\pi\)
0.997348 0.0727851i \(-0.0231887\pi\)
\(282\) 0 0
\(283\) 10.0108 14.2969i 0.595080 0.849863i −0.402776 0.915298i \(-0.631955\pi\)
0.997857 + 0.0654355i \(0.0208437\pi\)
\(284\) 3.91627 + 22.2103i 0.232388 + 1.31794i
\(285\) 0 0
\(286\) 0.618469 + 0.518957i 0.0365708 + 0.0306866i
\(287\) −1.71112 + 6.38599i −0.101004 + 0.376953i
\(288\) 0 0
\(289\) 0.871882 + 0.503381i 0.0512872 + 0.0296107i
\(290\) 4.08535 3.30212i 0.239900 0.193907i
\(291\) 0 0
\(292\) −0.645696 + 7.38033i −0.0377865 + 0.431901i
\(293\) −14.9428 + 6.96793i −0.872966 + 0.407071i −0.806861 0.590742i \(-0.798835\pi\)
−0.0661055 + 0.997813i \(0.521057\pi\)
\(294\) 0 0
\(295\) −1.10242 0.802484i −0.0641854 0.0467224i
\(296\) 19.1940i 1.11563i
\(297\) 0 0
\(298\) 5.25803 + 5.25803i 0.304590 + 0.304590i
\(299\) 0.270414 1.53359i 0.0156384 0.0886899i
\(300\) 0 0
\(301\) 8.48992 + 3.09008i 0.489351 + 0.178109i
\(302\) 4.14170 + 0.362352i 0.238328 + 0.0208510i
\(303\) 0 0
\(304\) −1.15801 3.18160i −0.0664164 0.182477i
\(305\) 2.49418 + 3.70502i 0.142816 + 0.212149i
\(306\) 0 0
\(307\) 18.6145 + 4.98775i 1.06239 + 0.284666i 0.747362 0.664417i \(-0.231320\pi\)
0.315026 + 0.949083i \(0.397987\pi\)
\(308\) 28.4785 2.49155i 1.62271 0.141969i
\(309\) 0 0
\(310\) −4.88267 8.82744i −0.277317 0.501365i
\(311\) −4.11040 + 0.724775i −0.233079 + 0.0410982i −0.288968 0.957339i \(-0.593312\pi\)
0.0558883 + 0.998437i \(0.482201\pi\)
\(312\) 0 0
\(313\) −0.399794 4.56966i −0.0225977 0.258293i −0.999087 0.0427260i \(-0.986396\pi\)
0.976489 0.215567i \(-0.0691598\pi\)
\(314\) 0.330565 + 0.572556i 0.0186549 + 0.0323112i
\(315\) 0 0
\(316\) −10.7722 + 18.6580i −0.605983 + 1.04959i
\(317\) −21.0570 9.81902i −1.18268 0.551491i −0.271072 0.962559i \(-0.587378\pi\)
−0.911605 + 0.411068i \(0.865156\pi\)
\(318\) 0 0
\(319\) −14.5537 17.3444i −0.814849 0.971099i
\(320\) −5.19055 5.38473i −0.290160 0.301016i
\(321\) 0 0
\(322\) 3.75708 + 5.36567i 0.209374 + 0.299017i
\(323\) −3.45531 + 3.45531i −0.192258 + 0.192258i
\(324\) 0 0
\(325\) −0.243917 + 1.95719i −0.0135301 + 0.108566i
\(326\) 4.28008 + 0.754693i 0.237052 + 0.0417986i
\(327\) 0 0
\(328\) 1.35445 + 2.90462i 0.0747869 + 0.160381i
\(329\) 3.62159 3.03887i 0.199665 0.167539i
\(330\) 0 0
\(331\) 17.6555 6.42608i 0.970434 0.353209i 0.192320 0.981332i \(-0.438399\pi\)
0.778114 + 0.628123i \(0.216177\pi\)
\(332\) 4.65146 1.24635i 0.255282 0.0684026i
\(333\) 0 0
\(334\) 6.69131 3.86323i 0.366132 0.211386i
\(335\) 3.27744 8.51492i 0.179065 0.465220i
\(336\) 0 0
\(337\) −6.63124 4.64324i −0.361227 0.252934i 0.378847 0.925459i \(-0.376321\pi\)
−0.740074 + 0.672526i \(0.765209\pi\)
\(338\) 4.84857 + 3.39501i 0.263728 + 0.184664i
\(339\) 0 0
\(340\) −5.74232 + 14.9188i −0.311421 + 0.809085i
\(341\) −37.6552 + 21.7402i −2.03914 + 1.17730i
\(342\) 0 0
\(343\) −3.60198 + 0.965147i −0.194489 + 0.0521130i
\(344\) 4.11560 1.49796i 0.221898 0.0807644i
\(345\) 0 0
\(346\) 2.69798 2.26387i 0.145044 0.121707i
\(347\) −2.42251 5.19509i −0.130047 0.278887i 0.830493 0.557030i \(-0.188059\pi\)
−0.960540 + 0.278143i \(0.910281\pi\)
\(348\) 0 0
\(349\) 3.63192 + 0.640405i 0.194412 + 0.0342801i 0.270006 0.962859i \(-0.412974\pi\)
−0.0755941 + 0.997139i \(0.524085\pi\)
\(350\) −5.09580 6.54677i −0.272382 0.349940i
\(351\) 0 0
\(352\) 14.9734 14.9734i 0.798085 0.798085i
\(353\) −10.0809 14.3970i −0.536551 0.766275i 0.455752 0.890107i \(-0.349370\pi\)
−0.992303 + 0.123832i \(0.960482\pi\)
\(354\) 0 0
\(355\) −19.5781 20.3105i −1.03910 1.07797i
\(356\) −2.83851 3.38281i −0.150441 0.179288i
\(357\) 0 0
\(358\) −1.75876 0.820125i −0.0929535 0.0433449i
\(359\) 4.06033 7.03269i 0.214296 0.371171i −0.738759 0.673970i \(-0.764588\pi\)
0.953055 + 0.302799i \(0.0979210\pi\)
\(360\) 0 0
\(361\) −8.75349 15.1615i −0.460710 0.797973i
\(362\) 0.238849 + 2.73005i 0.0125536 + 0.143488i
\(363\) 0 0
\(364\) −2.50044 + 0.440896i −0.131059 + 0.0231092i
\(365\) −4.48535 8.10912i −0.234774 0.424451i
\(366\) 0 0
\(367\) 16.9819 1.48573i 0.886450 0.0775543i 0.365171 0.930940i \(-0.381011\pi\)
0.521279 + 0.853386i \(0.325455\pi\)
\(368\) −10.5662 2.83121i −0.550801 0.147587i
\(369\) 0 0
\(370\) 6.32791 + 9.39988i 0.328972 + 0.488677i
\(371\) 6.15547 + 16.9120i 0.319576 + 0.878028i
\(372\) 0 0
\(373\) 31.1095 + 2.72173i 1.61079 + 0.140926i 0.856688 0.515834i \(-0.172518\pi\)
0.754100 + 0.656760i \(0.228073\pi\)
\(374\) −7.69144 2.79945i −0.397715 0.144756i
\(375\) 0 0
\(376\) 0.397965 2.25697i 0.0205235 0.116394i
\(377\) 1.42194 + 1.42194i 0.0732339 + 0.0732339i
\(378\) 0 0
\(379\) 31.2281i 1.60408i −0.597269 0.802041i \(-0.703748\pi\)
0.597269 0.802041i \(-0.296252\pi\)
\(380\) 3.94884 + 2.87448i 0.202571 + 0.147458i
\(381\) 0 0
\(382\) 4.52881 2.11182i 0.231714 0.108050i
\(383\) −2.94643 + 33.6778i −0.150555 + 1.72086i 0.426786 + 0.904353i \(0.359646\pi\)
−0.577341 + 0.816503i \(0.695910\pi\)
\(384\) 0 0
\(385\) −27.8099 + 22.4783i −1.41732 + 1.14560i
\(386\) 0.245587 + 0.141790i 0.0125001 + 0.00721691i
\(387\) 0 0
\(388\) −0.263515 + 0.983453i −0.0133780 + 0.0499272i
\(389\) −20.9380 17.5690i −1.06160 0.890786i −0.0673324 0.997731i \(-0.521449\pi\)
−0.994265 + 0.106945i \(0.965893\pi\)
\(390\) 0 0
\(391\) 2.74149 + 15.5478i 0.138643 + 0.786284i
\(392\) 5.97114 8.52768i 0.301588 0.430713i
\(393\) 0 0
\(394\) −8.14085 + 9.70188i −0.410130 + 0.488774i
\(395\) −1.85547 26.8848i −0.0933589 1.35272i
\(396\) 0 0
\(397\) −3.30445 12.3324i −0.165846 0.618945i −0.997931 0.0642968i \(-0.979520\pi\)
0.832085 0.554648i \(-0.187147\pi\)
\(398\) 0.539761 1.15752i 0.0270558 0.0580213i
\(399\) 0 0
\(400\) 13.5467 + 2.90513i 0.677335 + 0.145256i
\(401\) 6.74752 18.5387i 0.336955 0.925776i −0.649298 0.760534i \(-0.724937\pi\)
0.986253 0.165242i \(-0.0528406\pi\)
\(402\) 0 0
\(403\) 3.16338 2.21502i 0.157579 0.110338i
\(404\) −26.1441 −1.30072
\(405\) 0 0
\(406\) −8.45859 −0.419793
\(407\) 40.0078 28.0137i 1.98311 1.38859i
\(408\) 0 0
\(409\) 0.987380 2.71280i 0.0488228 0.134139i −0.912885 0.408218i \(-0.866150\pi\)
0.961707 + 0.274078i \(0.0883727\pi\)
\(410\) −1.62091 0.975943i −0.0800511 0.0481984i
\(411\) 0 0
\(412\) 13.0124 27.9052i 0.641076 1.37479i
\(413\) 0.568280 + 2.12085i 0.0279632 + 0.104360i
\(414\) 0 0
\(415\) −3.95590 + 4.54242i −0.194188 + 0.222979i
\(416\) −1.20891 + 1.44073i −0.0592719 + 0.0706375i
\(417\) 0 0
\(418\) −1.43443 + 2.04857i −0.0701601 + 0.100199i
\(419\) −3.08760 17.5106i −0.150839 0.855451i −0.962492 0.271310i \(-0.912543\pi\)
0.811653 0.584140i \(-0.198568\pi\)
\(420\) 0 0
\(421\) 1.57150 + 1.31864i 0.0765901 + 0.0642667i 0.680279 0.732953i \(-0.261859\pi\)
−0.603689 + 0.797220i \(0.706303\pi\)
\(422\) −2.61453 + 9.75758i −0.127274 + 0.474991i
\(423\) 0 0
\(424\) 7.55561 + 4.36223i 0.366933 + 0.211849i
\(425\) −4.46273 19.4914i −0.216474 0.945472i
\(426\) 0 0
\(427\) 0.626811 7.16449i 0.0303335 0.346714i
\(428\) 9.34000 4.35531i 0.451466 0.210522i
\(429\) 0 0
\(430\) −1.52168 + 2.09043i −0.0733820 + 0.100809i
\(431\) 19.3828i 0.933636i −0.884353 0.466818i \(-0.845400\pi\)
0.884353 0.466818i \(-0.154600\pi\)
\(432\) 0 0
\(433\) −2.30954 2.30954i −0.110989 0.110989i 0.649431 0.760420i \(-0.275007\pi\)
−0.760420 + 0.649431i \(0.775007\pi\)
\(434\) −2.82071 + 15.9970i −0.135398 + 0.767881i
\(435\) 0 0
\(436\) 12.3146 + 4.48214i 0.589762 + 0.214656i
\(437\) 4.80536 + 0.420414i 0.229871 + 0.0201111i
\(438\) 0 0
\(439\) −1.67858 4.61187i −0.0801144 0.220112i 0.893168 0.449723i \(-0.148477\pi\)
−0.973283 + 0.229610i \(0.926255\pi\)
\(440\) −3.32298 + 17.0129i −0.158417 + 0.811056i
\(441\) 0 0
\(442\) 0.702196 + 0.188153i 0.0334000 + 0.00894952i
\(443\) −19.2540 + 1.68450i −0.914783 + 0.0800331i −0.534817 0.844968i \(-0.679620\pi\)
−0.379965 + 0.925001i \(0.624064\pi\)
\(444\) 0 0
\(445\) 5.30831 + 1.52734i 0.251638 + 0.0724031i
\(446\) 5.06133 0.892450i 0.239661 0.0422587i
\(447\) 0 0
\(448\) 1.04963 + 11.9973i 0.0495903 + 0.566820i
\(449\) 1.49368 + 2.58713i 0.0704911 + 0.122094i 0.899117 0.437709i \(-0.144210\pi\)
−0.828626 + 0.559803i \(0.810877\pi\)
\(450\) 0 0
\(451\) −4.07753 + 7.06249i −0.192003 + 0.332560i
\(452\) 11.8761 + 5.53791i 0.558604 + 0.260481i
\(453\) 0 0
\(454\) 3.78613 + 4.51214i 0.177692 + 0.211765i
\(455\) 2.28657 2.20411i 0.107196 0.103330i
\(456\) 0 0
\(457\) −3.78805 5.40989i −0.177197 0.253064i 0.720722 0.693224i \(-0.243811\pi\)
−0.897919 + 0.440160i \(0.854922\pi\)
\(458\) −4.84692 + 4.84692i −0.226482 + 0.226482i
\(459\) 0 0
\(460\) 14.9252 5.12401i 0.695889 0.238908i
\(461\) −41.0394 7.23636i −1.91140 0.337031i −0.913791 0.406185i \(-0.866859\pi\)
−0.997606 + 0.0691537i \(0.977970\pi\)
\(462\) 0 0
\(463\) 2.30650 + 4.94630i 0.107192 + 0.229874i 0.952586 0.304269i \(-0.0984122\pi\)
−0.845394 + 0.534143i \(0.820634\pi\)
\(464\) 10.8210 9.07991i 0.502353 0.421524i
\(465\) 0 0
\(466\) 2.15876 0.785723i 0.100002 0.0363979i
\(467\) 9.74812 2.61200i 0.451089 0.120869i −0.0261197 0.999659i \(-0.508315\pi\)
0.477209 + 0.878790i \(0.341648\pi\)
\(468\) 0 0
\(469\) −12.7233 + 7.34582i −0.587509 + 0.339199i
\(470\) 0.549185 + 1.23651i 0.0253320 + 0.0570358i
\(471\) 0 0
\(472\) 0.871887 + 0.610502i 0.0401319 + 0.0281006i
\(473\) 9.12904 + 6.39222i 0.419753 + 0.293915i
\(474\) 0 0
\(475\) −6.10535 0.224291i −0.280133 0.0102912i
\(476\) 22.2923 12.8704i 1.02176 0.589916i
\(477\) 0 0
\(478\) 3.23632 0.867168i 0.148026 0.0396634i
\(479\) −4.22629 + 1.53824i −0.193104 + 0.0702841i −0.436762 0.899577i \(-0.643875\pi\)
0.243658 + 0.969861i \(0.421653\pi\)
\(480\) 0 0
\(481\) −3.32297 + 2.78830i −0.151514 + 0.127136i
\(482\) −3.84423 8.24398i −0.175100 0.375503i
\(483\) 0 0
\(484\) 15.3617 + 2.70868i 0.698258 + 0.123122i
\(485\) −0.413534 1.20454i −0.0187776 0.0546952i
\(486\) 0 0
\(487\) −2.49814 + 2.49814i −0.113202 + 0.113202i −0.761439 0.648237i \(-0.775507\pi\)
0.648237 + 0.761439i \(0.275507\pi\)
\(488\) −1.99969 2.85585i −0.0905215 0.129278i
\(489\) 0 0
\(490\) −0.112832 + 6.14482i −0.00509725 + 0.277595i
\(491\) −9.95960 11.8694i −0.449471 0.535658i 0.492964 0.870050i \(-0.335914\pi\)
−0.942434 + 0.334392i \(0.891469\pi\)
\(492\) 0 0
\(493\) −18.4770 8.61596i −0.832162 0.388043i
\(494\) 0.111058 0.192358i 0.00499673 0.00865459i
\(495\) 0 0
\(496\) −13.5636 23.4928i −0.609022 1.05486i
\(497\) 3.95907 + 45.2524i 0.177589 + 2.02985i
\(498\) 0 0
\(499\) 16.9468 2.98818i 0.758644 0.133769i 0.219072 0.975709i \(-0.429697\pi\)
0.539572 + 0.841939i \(0.318586\pi\)
\(500\) −18.5514 + 7.43661i −0.829644 + 0.332575i
\(501\) 0 0
\(502\) −7.80354 + 0.682721i −0.348289 + 0.0304713i
\(503\) 38.6515 + 10.3567i 1.72339 + 0.461780i 0.978643 0.205569i \(-0.0659045\pi\)
0.744745 + 0.667349i \(0.232571\pi\)
\(504\) 0 0
\(505\) 27.1281 18.2623i 1.20718 0.812663i
\(506\) 2.76346 + 7.59255i 0.122851 + 0.337530i
\(507\) 0 0
\(508\) −9.39712 0.822142i −0.416930 0.0364766i
\(509\) 36.9106 + 13.4344i 1.63604 + 0.595468i 0.986339 0.164726i \(-0.0526738\pi\)
0.649696 + 0.760194i \(0.274896\pi\)
\(510\) 0 0
\(511\) −2.59118 + 14.6953i −0.114627 + 0.650081i
\(512\) 16.1816 + 16.1816i 0.715134 + 0.715134i
\(513\) 0 0
\(514\) 7.13031i 0.314504i
\(515\) 5.99036 + 38.0449i 0.263967 + 1.67646i
\(516\) 0 0
\(517\) 5.28523 2.46454i 0.232444 0.108390i
\(518\) 1.59026 18.1768i 0.0698721 0.798642i
\(519\) 0 0
\(520\) 0.162318 1.53099i 0.00711810 0.0671384i
\(521\) 26.5294 + 15.3168i 1.16227 + 0.671039i 0.951848 0.306571i \(-0.0991816\pi\)
0.210426 + 0.977610i \(0.432515\pi\)
\(522\) 0 0
\(523\) 1.16084 4.33233i 0.0507602 0.189439i −0.935890 0.352291i \(-0.885403\pi\)
0.986651 + 0.162852i \(0.0520693\pi\)
\(524\) −0.970744 0.814551i −0.0424071 0.0355838i
\(525\) 0 0
\(526\) 2.02403 + 11.4789i 0.0882521 + 0.500503i
\(527\) −22.4562 + 32.0708i −0.978207 + 1.39702i
\(528\) 0 0
\(529\) −4.76651 + 5.68051i −0.207240 + 0.246979i
\(530\) −5.13835 + 0.354626i −0.223195 + 0.0154040i
\(531\) 0 0
\(532\) −2.03556 7.59683i −0.0882529 0.329364i
\(533\) 0.306103 0.656441i 0.0132588 0.0284336i
\(534\) 0 0
\(535\) −6.64921 + 11.0435i −0.287471 + 0.477450i
\(536\) −2.43586 + 6.69246i −0.105213 + 0.289070i
\(537\) 0 0
\(538\) 7.89626 5.52902i 0.340432 0.238373i
\(539\) 26.4898 1.14100
\(540\) 0 0
\(541\) 4.96440 0.213436 0.106718 0.994289i \(-0.465966\pi\)
0.106718 + 0.994289i \(0.465966\pi\)
\(542\) 2.27293 1.59153i 0.0976309 0.0683619i
\(543\) 0 0
\(544\) 6.52135 17.9173i 0.279601 0.768196i
\(545\) −15.9089 + 3.95122i −0.681464 + 0.169252i
\(546\) 0 0
\(547\) −6.14812 + 13.1847i −0.262875 + 0.563737i −0.992799 0.119791i \(-0.961777\pi\)
0.729924 + 0.683528i \(0.239555\pi\)
\(548\) 0.471083 + 1.75810i 0.0201237 + 0.0751025i
\(549\) 0 0
\(550\) −3.98145 9.42721i −0.169770 0.401978i
\(551\) −4.00394 + 4.77171i −0.170574 + 0.203282i
\(552\) 0 0
\(553\) −24.8897 + 35.5462i −1.05842 + 1.51158i
\(554\) −0.289556 1.64216i −0.0123021 0.0697685i
\(555\) 0 0
\(556\) −30.4831 25.5783i −1.29277 1.08476i
\(557\) 7.79233 29.0814i 0.330171 1.23222i −0.578838 0.815442i \(-0.696494\pi\)
0.909010 0.416774i \(-0.136840\pi\)
\(558\) 0 0
\(559\) −0.857203 0.494906i −0.0362558 0.0209323i
\(560\) −14.0240 17.3504i −0.592622 0.733186i
\(561\) 0 0
\(562\) 0.938313 10.7250i 0.0395803 0.452405i
\(563\) −19.4537 + 9.07139i −0.819874 + 0.382314i −0.786852 0.617141i \(-0.788291\pi\)
−0.0330215 + 0.999455i \(0.510513\pi\)
\(564\) 0 0
\(565\) −16.1914 + 2.54942i −0.681177 + 0.107255i
\(566\) 8.04291i 0.338069i
\(567\) 0 0
\(568\) 15.5708 + 15.5708i 0.653338 + 0.653338i
\(569\) 2.94509 16.7024i 0.123465 0.700202i −0.858743 0.512406i \(-0.828754\pi\)
0.982208 0.187796i \(-0.0601345\pi\)
\(570\) 0 0
\(571\) −28.4369 10.3502i −1.19005 0.433142i −0.330307 0.943873i \(-0.607152\pi\)
−0.859740 + 0.510732i \(0.829375\pi\)
\(572\) −3.11998 0.272963i −0.130453 0.0114132i
\(573\) 0 0
\(574\) 1.04201 + 2.86290i 0.0434927 + 0.119495i
\(575\) −11.9076 + 15.7424i −0.496582 + 0.656505i
\(576\) 0 0
\(577\) −27.9807 7.49741i −1.16485 0.312121i −0.375950 0.926640i \(-0.622684\pi\)
−0.788903 + 0.614518i \(0.789350\pi\)
\(578\) 0.462176 0.0404352i 0.0192240 0.00168188i
\(579\) 0 0
\(580\) −5.63458 + 19.5831i −0.233963 + 0.813143i
\(581\) 9.55194 1.68426i 0.396281 0.0698751i
\(582\) 0 0
\(583\) 1.93485 + 22.1155i 0.0801334 + 0.915929i
\(584\) 3.61681 + 6.26451i 0.149665 + 0.259227i
\(585\) 0 0
\(586\) −3.79893 + 6.57994i −0.156932 + 0.271815i
\(587\) −5.92953 2.76499i −0.244738 0.114123i 0.296379 0.955070i \(-0.404221\pi\)
−0.541117 + 0.840947i \(0.681999\pi\)
\(588\) 0 0
\(589\) 7.68913 + 9.16355i 0.316825 + 0.377578i
\(590\) −0.628259 0.0115362i −0.0258650 0.000474939i
\(591\) 0 0
\(592\) 17.4775 + 24.9605i 0.718322 + 1.02587i
\(593\) −22.3175 + 22.3175i −0.916469 + 0.916469i −0.996771 0.0803015i \(-0.974412\pi\)
0.0803015 + 0.996771i \(0.474412\pi\)
\(594\) 0 0
\(595\) −14.1409 + 28.9265i −0.579720 + 1.18587i
\(596\) −28.4076 5.00902i −1.16362 0.205177i
\(597\) 0 0
\(598\) −0.303279 0.650384i −0.0124020 0.0265962i
\(599\) −8.78838 + 7.37433i −0.359083 + 0.301307i −0.804425 0.594054i \(-0.797527\pi\)
0.445342 + 0.895361i \(0.353082\pi\)
\(600\) 0 0
\(601\) −29.2326 + 10.6398i −1.19242 + 0.434007i −0.860574 0.509326i \(-0.829895\pi\)
−0.331850 + 0.943332i \(0.607673\pi\)
\(602\) 4.02159 1.07758i 0.163908 0.0439189i
\(603\) 0 0
\(604\) −13.9672 + 8.06397i −0.568317 + 0.328118i
\(605\) −17.8319 + 7.91990i −0.724969 + 0.321990i
\(606\) 0 0
\(607\) 12.0216 + 8.41759i 0.487940 + 0.341659i 0.791517 0.611148i \(-0.209292\pi\)
−0.303576 + 0.952807i \(0.598181\pi\)
\(608\) −4.77216 3.34151i −0.193537 0.135516i
\(609\) 0 0
\(610\) 1.92082 + 0.739334i 0.0777718 + 0.0299348i
\(611\) −0.448550 + 0.258971i −0.0181464 + 0.0104768i
\(612\) 0 0
\(613\) 19.4357 5.20779i 0.785002 0.210341i 0.156013 0.987755i \(-0.450136\pi\)
0.628989 + 0.777414i \(0.283469\pi\)
\(614\) 8.34507 3.03736i 0.336780 0.122578i
\(615\) 0 0
\(616\) 21.3821 17.9418i 0.861511 0.722894i
\(617\) −1.25995 2.70196i −0.0507236 0.108777i 0.879313 0.476245i \(-0.158002\pi\)
−0.930036 + 0.367468i \(0.880225\pi\)
\(618\) 0 0
\(619\) −13.1500 2.31870i −0.528542 0.0931962i −0.0969919 0.995285i \(-0.530922\pi\)
−0.431550 + 0.902089i \(0.642033\pi\)
\(620\) 35.1568 + 17.1866i 1.41193 + 0.690231i
\(621\) 0 0
\(622\) −1.36005 + 1.36005i −0.0545329 + 0.0545329i
\(623\) −5.10163 7.28589i −0.204393 0.291903i
\(624\) 0 0
\(625\) 14.0549 20.6751i 0.562196 0.827004i
\(626\) −1.35876 1.61931i −0.0543070 0.0647206i
\(627\) 0 0
\(628\) −2.32438 1.08388i −0.0927529 0.0432514i
\(629\) 21.9887 38.0856i 0.876748 1.51857i
\(630\) 0 0
\(631\) 0.693777 + 1.20166i 0.0276188 + 0.0478372i 0.879504 0.475891i \(-0.157874\pi\)
−0.851886 + 0.523728i \(0.824541\pi\)
\(632\) 1.83339 + 20.9557i 0.0729283 + 0.833575i
\(633\) 0 0
\(634\) −10.5440 + 1.85920i −0.418758 + 0.0738383i
\(635\) 10.3251 5.71104i 0.409738 0.226636i
\(636\) 0 0
\(637\) −2.34378 + 0.205054i −0.0928638 + 0.00812453i
\(638\) −10.0782 2.70046i −0.399001 0.106912i
\(639\) 0 0
\(640\) −24.3094 4.74815i −0.960914 0.187687i
\(641\) 6.63051 + 18.2172i 0.261890 + 0.719536i 0.999040 + 0.0438070i \(0.0139487\pi\)
−0.737150 + 0.675729i \(0.763829\pi\)
\(642\) 0 0
\(643\) 41.1928 + 3.60391i 1.62449 + 0.142124i 0.862705 0.505708i \(-0.168769\pi\)
0.761783 + 0.647833i \(0.224324\pi\)
\(644\) −23.8775 8.69071i −0.940906 0.342462i
\(645\) 0 0
\(646\) −0.391028 + 2.21763i −0.0153848 + 0.0872514i
\(647\) −12.4891 12.4891i −0.490997 0.490997i 0.417623 0.908620i \(-0.362863\pi\)
−0.908620 + 0.417623i \(0.862863\pi\)
\(648\) 0 0
\(649\) 2.70837i 0.106313i
\(650\) 0.425247 + 0.803284i 0.0166795 + 0.0315074i
\(651\) 0 0
\(652\) −15.2799 + 7.12513i −0.598407 + 0.279042i
\(653\) 1.28323 14.6673i 0.0502165 0.573977i −0.928853 0.370449i \(-0.879204\pi\)
0.979069 0.203528i \(-0.0652408\pi\)
\(654\) 0 0
\(655\) 1.57626 + 0.167117i 0.0615896 + 0.00652980i
\(656\) −4.40623 2.54394i −0.172034 0.0993241i
\(657\) 0 0
\(658\) 0.563868 2.10438i 0.0219819 0.0820374i
\(659\) 21.0565 + 17.6685i 0.820245 + 0.688268i 0.953030 0.302877i \(-0.0979473\pi\)
−0.132784 + 0.991145i \(0.542392\pi\)
\(660\) 0 0
\(661\) 1.73362 + 9.83186i 0.0674301 + 0.382415i 0.999782 + 0.0208639i \(0.00664165\pi\)
−0.932352 + 0.361551i \(0.882247\pi\)
\(662\) 4.96617 7.09243i 0.193016 0.275655i
\(663\) 0 0
\(664\) 3.02230 3.60183i 0.117288 0.139778i
\(665\) 7.41875 + 6.46084i 0.287687 + 0.250541i
\(666\) 0 0
\(667\) 5.20873 + 19.4392i 0.201683 + 0.752690i
\(668\) −12.6670 + 27.1644i −0.490100 + 1.05102i
\(669\) 0 0
\(670\) −1.01347 4.08055i −0.0391536 0.157645i
\(671\) 3.03414 8.33623i 0.117132 0.321816i
\(672\) 0 0
\(673\) −0.212002 + 0.148446i −0.00817209 + 0.00572216i −0.577655 0.816281i \(-0.696032\pi\)
0.569483 + 0.822003i \(0.307143\pi\)
\(674\) −3.73049 −0.143693
\(675\) 0 0
\(676\) −22.9612 −0.883122
\(677\) −20.1079 + 14.0797i −0.772810 + 0.541128i −0.892157 0.451725i \(-0.850809\pi\)
0.119347 + 0.992853i \(0.461920\pi\)
\(678\) 0 0
\(679\) −0.701384 + 1.92704i −0.0269167 + 0.0739529i
\(680\) 3.76227 + 15.1482i 0.144277 + 0.580906i
\(681\) 0 0
\(682\) −8.46795 + 18.1596i −0.324255 + 0.695366i
\(683\) −5.75081 21.4623i −0.220048 0.821232i −0.984328 0.176347i \(-0.943572\pi\)
0.764280 0.644885i \(-0.223095\pi\)
\(684\) 0 0
\(685\) −1.71689 1.49521i −0.0655991 0.0571289i
\(686\) −1.10459 + 1.31640i −0.0421734 + 0.0502603i
\(687\) 0 0
\(688\) −3.98805 + 5.69553i −0.152043 + 0.217140i
\(689\) −0.342385 1.94176i −0.0130438 0.0739753i
\(690\) 0 0
\(691\) −0.205042 0.172050i −0.00780016 0.00654511i 0.638879 0.769307i \(-0.279398\pi\)
−0.646679 + 0.762762i \(0.723843\pi\)
\(692\) −3.53610 + 13.1969i −0.134422 + 0.501672i
\(693\) 0 0
\(694\) −2.28762 1.32076i −0.0868369 0.0501353i
\(695\) 49.4974 + 5.24777i 1.87754 + 0.199059i
\(696\) 0 0
\(697\) −0.639991 + 7.31513i −0.0242414 + 0.277080i
\(698\) 1.54027 0.718239i 0.0583000 0.0271857i
\(699\) 0 0
\(700\) 30.7595 + 9.46517i 1.16260 + 0.357750i
\(701\) 38.5968i 1.45778i 0.684630 + 0.728891i \(0.259964\pi\)
−0.684630 + 0.728891i \(0.740036\pi\)
\(702\) 0 0
\(703\) −9.50124 9.50124i −0.358346 0.358346i
\(704\) −2.57960 + 14.6297i −0.0972225 + 0.551376i
\(705\) 0 0
\(706\) −7.61078 2.77010i −0.286435 0.104254i
\(707\) −52.4582 4.58950i −1.97289 0.172606i
\(708\) 0 0
\(709\) 16.0622 + 44.1305i 0.603228 + 1.65735i 0.744690 + 0.667410i \(0.232597\pi\)
−0.141463 + 0.989944i \(0.545181\pi\)
\(710\) −12.7589 2.49209i −0.478833 0.0935264i
\(711\) 0 0
\(712\) −4.16477 1.11595i −0.156081 0.0418219i
\(713\) 38.5007 3.36838i 1.44186 0.126147i
\(714\) 0 0
\(715\) 3.42808 1.89615i 0.128203 0.0709120i
\(716\) 7.41357 1.30721i 0.277058 0.0488528i
\(717\) 0 0
\(718\) −0.326154 3.72796i −0.0121720 0.139126i
\(719\) −0.577250 0.999826i −0.0215278 0.0372872i 0.855061 0.518528i \(-0.173520\pi\)
−0.876589 + 0.481241i \(0.840186\pi\)
\(720\) 0 0
\(721\) 31.0080 53.7075i 1.15480 2.00017i
\(722\) −7.31177 3.40954i −0.272116 0.126890i
\(723\) 0 0
\(724\) −6.83343 8.14376i −0.253962 0.302660i
\(725\) −7.83263 24.2560i −0.290897 0.900844i
\(726\) 0 0
\(727\) −22.7146 32.4399i −0.842439 1.20313i −0.977215 0.212252i \(-0.931920\pi\)
0.134776 0.990876i \(-0.456969\pi\)
\(728\) −1.75297 + 1.75297i −0.0649695 + 0.0649695i
\(729\) 0 0
\(730\) −3.83655 1.87552i −0.141997 0.0694160i
\(731\) 9.88240 + 1.74253i 0.365514 + 0.0644499i
\(732\) 0 0
\(733\) −2.90113 6.22149i −0.107156 0.229796i 0.845417 0.534106i \(-0.179352\pi\)
−0.952573 + 0.304310i \(0.901574\pi\)
\(734\) 6.01773 5.04948i 0.222119 0.186380i
\(735\) 0 0
\(736\) −17.6869 + 6.43750i −0.651948 + 0.237290i
\(737\) −17.5048 + 4.69039i −0.644797 + 0.172773i
\(738\) 0 0
\(739\) 28.7899 16.6218i 1.05905 0.611444i 0.133882 0.990997i \(-0.457256\pi\)
0.925170 + 0.379553i \(0.123922\pi\)
\(740\) −41.0230 15.7900i −1.50804 0.580450i
\(741\) 0 0
\(742\) 6.79375 + 4.75704i 0.249406 + 0.174636i
\(743\) 13.8249 + 9.68027i 0.507185 + 0.355135i 0.798991 0.601343i \(-0.205367\pi\)
−0.291806 + 0.956477i \(0.594256\pi\)
\(744\) 0 0
\(745\) 32.9756 14.6459i 1.20813 0.536583i
\(746\) 12.4628 7.19539i 0.456295 0.263442i
\(747\) 0 0
\(748\) 30.6697 8.21793i 1.12140 0.300477i
\(749\) 19.5053 7.09934i 0.712707 0.259404i
\(750\) 0 0
\(751\) 30.1032 25.2596i 1.09848 0.921734i 0.101158 0.994870i \(-0.467745\pi\)
0.997322 + 0.0731359i \(0.0233007\pi\)
\(752\) 1.53761 + 3.29741i 0.0560708 + 0.120244i
\(753\) 0 0
\(754\) 0.912609 + 0.160918i 0.0332353 + 0.00586028i
\(755\) 8.85996 18.1239i 0.322447 0.659596i
\(756\) 0 0
\(757\) 15.4181 15.4181i 0.560380 0.560380i −0.369036 0.929415i \(-0.620312\pi\)
0.929415 + 0.369036i \(0.120312\pi\)
\(758\) −8.25417 11.7882i −0.299805 0.428166i
\(759\) 0 0
\(760\) 4.76815 + 0.0875537i 0.172959 + 0.00317591i
\(761\) 14.9899 + 17.8642i 0.543382 + 0.647577i 0.965942 0.258757i \(-0.0833130\pi\)
−0.422560 + 0.906335i \(0.638869\pi\)
\(762\) 0 0
\(763\) 23.9224 + 11.1552i 0.866049 + 0.403845i
\(764\) −9.69221 + 16.7874i −0.350652 + 0.607347i
\(765\) 0 0
\(766\) 7.78943 + 13.4917i 0.281443 + 0.487474i
\(767\) −0.0209651 0.239632i −0.000757007 0.00865263i
\(768\) 0 0
\(769\) −40.5586 + 7.15158i −1.46258 + 0.257893i −0.847594 0.530645i \(-0.821950\pi\)
−0.614987 + 0.788537i \(0.710839\pi\)
\(770\) −4.55641 + 15.8359i −0.164202 + 0.570685i
\(771\) 0 0
\(772\) −1.09588 + 0.0958772i −0.0394416 + 0.00345069i
\(773\) 14.3875 + 3.85511i 0.517481 + 0.138659i 0.508101 0.861297i \(-0.330348\pi\)
0.00937966 + 0.999956i \(0.497014\pi\)
\(774\) 0 0
\(775\) −48.4852 + 6.72450i −1.74164 + 0.241551i
\(776\) 0.340005 + 0.934157i 0.0122055 + 0.0335343i
\(777\) 0 0
\(778\) −12.5476 1.09777i −0.449853 0.0393571i
\(779\) 2.10828 + 0.767352i 0.0755370 + 0.0274932i
\(780\) 0 0
\(781\) −9.72994 + 55.1812i −0.348165 + 1.97454i
\(782\) 5.14443 + 5.14443i 0.183964 + 0.183964i
\(783\) 0 0
\(784\) 16.5268i 0.590243i
\(785\) 3.16897 0.498971i 0.113105 0.0178090i
\(786\) 0 0
\(787\)