Properties

Label 405.2.r.a.152.9
Level $405$
Weight $2$
Character 405.152
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 152.9
Character \(\chi\) \(=\) 405.152
Dual form 405.2.r.a.8.9

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

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{17}{18}\right)\)

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 0.699374 0.714756i \(-0.253462\pi\)
−0.432451 + 0.901657i \(0.642351\pi\)
\(3\) 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 −0.951708 0.307004i \(-0.900673\pi\)
0.376567 0.926389i \(-0.377104\pi\)
\(8\) 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 −0.999370 0.0354810i \(-0.988704\pi\)
0.138597 0.990349i \(-0.455741\pi\)
\(12\) 0 0
\(13\) 0.226257 + 0.323128i 0.0627524 + 0.0896196i 0.849302 0.527908i \(-0.177023\pi\)
−0.786549 + 0.617527i \(0.788134\pi\)
\(14\) 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 −0.970252 0.242098i \(-0.922164\pi\)
0.719213 0.694789i \(-0.244502\pi\)
\(18\) 0 0
\(19\) 1.05819 0.610947i 0.242766 0.140161i −0.373682 0.927557i \(-0.621905\pi\)
0.616447 + 0.787396i \(0.288571\pi\)
\(20\) 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 0.758181 0.652044i \(-0.226088\pi\)
−0.0121450 + 0.999926i \(0.503866\pi\)
\(24\) 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 −0.949698 0.313168i \(-0.898610\pi\)
0.785314 0.619097i \(-0.212501\pi\)
\(30\) 0 0
\(31\) 9.19946 3.34833i 1.65227 0.601378i 0.663152 0.748485i \(-0.269219\pi\)
0.989121 + 0.147107i \(0.0469963\pi\)
\(32\) −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 −0.983818 0.179171i \(-0.942658\pi\)
−0.762426 + 0.647076i \(0.775992\pi\)
\(38\) 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 0.313055 0.949735i \(-0.398647\pi\)
−0.0306526 + 0.999530i \(0.509759\pi\)
\(42\) 0 0
\(43\) −0.218695 + 2.49969i −0.0333507 + 0.381200i 0.961116 + 0.276146i \(0.0890572\pi\)
−0.994466 + 0.105054i \(0.966498\pi\)
\(44\) −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 −0.507465 0.861672i \(-0.669418\pi\)
0.333887 + 0.942613i \(0.391640\pi\)
\(48\) 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 0.906880 0.421389i \(-0.138457\pi\)
−0.421389 + 0.906880i \(0.638457\pi\)
\(54\) 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 0.672689 0.739925i \(-0.265139\pi\)
−0.611873 + 0.790956i \(0.709584\pi\)
\(60\) 0 0
\(61\) −1.87695 0.683152i −0.240318 0.0874687i 0.219053 0.975713i \(-0.429703\pi\)
−0.459372 + 0.888244i \(0.651925\pi\)
\(62\) 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 −0.351304 0.936261i \(-0.614262\pi\)
0.759645 + 0.650338i \(0.225373\pi\)
\(68\) −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 0.979824 0.199860i \(-0.0640487\pi\)
0.316829 + 0.948483i \(0.397382\pi\)
\(72\) 0 0
\(73\) 4.00309 + 1.07262i 0.468526 + 0.125541i 0.485355 0.874317i \(-0.338690\pi\)
−0.0168287 + 0.999858i \(0.505357\pi\)
\(74\) −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 0.540023 0.841650i \(-0.318415\pi\)
0.795317 + 0.606193i \(0.207304\pi\)
\(80\) −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 −0.894949 0.446169i \(-0.852788\pi\)
0.725352 + 0.688378i \(0.241677\pi\)
\(84\) 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 0.793109 0.609079i \(-0.208461\pi\)
−0.924033 + 0.382313i \(0.875128\pi\)
\(90\) 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 0.115924 0.993258i \(-0.463017\pi\)
−0.0583150 + 0.998298i \(0.518573\pi\)
\(98\) −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 −0.395753 0.918357i \(-0.629516\pi\)
0.893473 0.449117i \(-0.148261\pi\)
\(102\) 0 0
\(103\) −17.1583 + 1.50115i −1.69066 + 0.147913i −0.891442 0.453135i \(-0.850306\pi\)
−0.799213 + 0.601048i \(0.794750\pi\)
\(104\) 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 −0.876139 0.482059i \(-0.839889\pi\)
0.482059 + 0.876139i \(0.339889\pi\)
\(108\) 0 0
\(109\) 7.33084i 0.702167i 0.936344 + 0.351084i \(0.114187\pi\)
−0.936344 + 0.351084i \(0.885813\pi\)
\(110\) 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 0.965160 + 0.261661i \(0.0842703\pi\)
−0.905060 + 0.425284i \(0.860174\pi\)
\(114\) 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 −0.878486 0.477769i \(-0.841446\pi\)
0.999675 + 0.0254832i \(0.00811243\pi\)
\(128\) 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 0.928650 0.370956i \(-0.120970\pi\)
−0.949833 + 0.312756i \(0.898748\pi\)
\(132\) 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 0.608662 0.793430i \(-0.291707\pi\)
−0.537405 + 0.843324i \(0.680595\pi\)
\(138\) 0 0
\(139\) −7.61336 20.9175i −0.645757 1.77420i −0.632837 0.774285i \(-0.718110\pi\)
−0.0129201 0.999917i \(-0.504113\pi\)
\(140\) −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 −0.624240 0.781233i \(-0.714591\pi\)
0.853791 0.520616i \(-0.174298\pi\)
\(150\) 0 0
\(151\) 6.91118 5.79917i 0.562424 0.471930i −0.316698 0.948526i \(-0.602574\pi\)
0.879122 + 0.476597i \(0.158130\pi\)
\(152\) −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 0.989571 0.144044i \(-0.0460108\pi\)
−0.999550 + 0.0299812i \(0.990455\pi\)
\(158\) 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 −0.395936 0.918278i \(-0.629580\pi\)
0.918278 + 0.395936i \(0.129580\pi\)
\(164\) −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 0.579922 0.814672i \(-0.303083\pi\)
0.712578 + 0.701593i \(0.247528\pi\)
\(168\) 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 0.372824 0.927902i \(-0.378390\pi\)
0.206031 + 0.978545i \(0.433945\pi\)
\(174\) 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 −0.933922 0.357477i \(-0.883637\pi\)
0.776545 + 0.630061i \(0.216970\pi\)
\(180\) 0 0
\(181\) −2.97345 5.15017i −0.221015 0.382809i 0.734102 0.679040i \(-0.237604\pi\)
−0.955116 + 0.296231i \(0.904270\pi\)
\(182\) 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 0.226619 0.973983i \(-0.427233\pi\)
0.546074 + 0.837737i \(0.316122\pi\)
\(192\) 0 0
\(193\) 0.260068 0.557718i 0.0187201 0.0401454i −0.896725 0.442587i \(-0.854061\pi\)
0.915446 + 0.402442i \(0.131838\pi\)
\(194\) 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 −0.998392 0.0566946i \(-0.981944\pi\)
−0.892980 0.450097i \(-0.851389\pi\)
\(198\) 0 0
\(199\) 2.40020 + 1.38576i 0.170146 + 0.0982338i 0.582655 0.812720i \(-0.302014\pi\)
−0.412509 + 0.910954i \(0.635347\pi\)
\(200\) −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 −0.156202 0.987725i \(-0.549925\pi\)
−0.999844 + 0.0176876i \(0.994370\pi\)
\(212\) 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 −0.0536157 0.998562i \(-0.517075\pi\)
0.730479 + 0.682935i \(0.239297\pi\)
\(224\) 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 −0.865163 0.501492i \(-0.832785\pi\)
0.939102 0.343639i \(-0.111660\pi\)
\(228\) 0 0
\(229\) −14.6486 2.58295i −0.968008 0.170686i −0.332775 0.943006i \(-0.607985\pi\)
−0.635233 + 0.772320i \(0.719096\pi\)
\(230\) −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 −0.0976137 0.995224i \(-0.531121\pi\)
0.413076 + 0.910696i \(0.364454\pi\)
\(234\) 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 −0.111462 0.993769i \(-0.535553\pi\)
0.553397 + 0.832918i \(0.313331\pi\)
\(240\) 0 0
\(241\) 3.42764 + 19.4391i 0.220794 + 1.25219i 0.870564 + 0.492055i \(0.163754\pi\)
−0.649770 + 0.760131i \(0.725135\pi\)
\(242\) −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 −0.886556 0.462622i \(-0.846909\pi\)
−0.0426356 + 0.999091i \(0.513575\pi\)
\(252\) 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 0.994253 0.107053i \(-0.0341415\pi\)
−0.440652 + 0.897678i \(0.645253\pi\)
\(258\) 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 −0.896906 0.442221i \(-0.854191\pi\)
0.237759 0.971324i \(-0.423587\pi\)
\(264\) 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 0.946878 0.321592i \(-0.104218\pi\)
−0.854995 + 0.518636i \(0.826440\pi\)
\(278\) 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 0.997348 + 0.0727851i \(0.0231887\pi\)
−0.101508 + 0.994835i \(0.532367\pi\)
\(282\) 0 0
\(283\) 10.0108 + 14.2969i 0.595080 + 0.849863i 0.997857 0.0654355i \(-0.0208437\pi\)
−0.402776 + 0.915298i \(0.631955\pi\)
\(284\) 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 −0.0661055 0.997813i \(-0.521057\pi\)
−0.806861 + 0.590742i \(0.798835\pi\)
\(294\) 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 0.315026 0.949083i \(-0.397987\pi\)
0.747362 + 0.664417i \(0.231320\pi\)
\(308\) 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 0.0558883 0.998437i \(-0.482201\pi\)
−0.288968 + 0.957339i \(0.593312\pi\)
\(312\) 0 0
\(313\) −0.399794 + 4.56966i −0.0225977 + 0.258293i 0.976489 + 0.215567i \(0.0691598\pi\)
−0.999087 + 0.0427260i \(0.986396\pi\)
\(314\) 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 −0.911605 0.411068i \(-0.865156\pi\)
−0.271072 + 0.962559i \(0.587378\pi\)
\(318\) 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 0.778114 0.628123i \(-0.216177\pi\)
0.192320 + 0.981332i \(0.438399\pi\)
\(332\) 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 −0.740074 0.672526i \(-0.765209\pi\)
0.378847 + 0.925459i \(0.376321\pi\)
\(338\) 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 −0.960540 0.278143i \(-0.910281\pi\)
0.830493 + 0.557030i \(0.188059\pi\)
\(348\) 0 0
\(349\) 3.63192 0.640405i 0.194412 0.0342801i −0.0755941 0.997139i \(-0.524085\pi\)
0.270006 + 0.962859i \(0.412974\pi\)
\(350\) −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 −0.992303 0.123832i \(-0.960482\pi\)
0.455752 + 0.890107i \(0.349370\pi\)
\(354\) 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 0.953055 0.302799i \(-0.0979210\pi\)
−0.738759 + 0.673970i \(0.764588\pi\)
\(360\) 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 0.521279 0.853386i \(-0.325455\pi\)
0.365171 + 0.930940i \(0.381011\pi\)
\(368\) −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 0.754100 0.656760i \(-0.228073\pi\)
0.856688 + 0.515834i \(0.172518\pi\)
\(374\) −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 \(0.296252\pi\)
−0.597269 + 0.802041i \(0.703748\pi\)
\(380\) 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 −0.577341 0.816503i \(-0.695910\pi\)
0.426786 0.904353i \(-0.359646\pi\)
\(384\) 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 −0.994265 0.106945i \(-0.965893\pi\)
−0.0673324 + 0.997731i \(0.521449\pi\)
\(390\) 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 0.832085 + 0.554648i \(0.187147\pi\)
−0.997931 + 0.0642968i \(0.979520\pi\)
\(398\) 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 0.986253 + 0.165242i \(0.0528406\pi\)
−0.649298 + 0.760534i \(0.724937\pi\)
\(402\) 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 0.961707 0.274078i \(-0.0883727\pi\)
−0.912885 + 0.408218i \(0.866150\pi\)
\(410\) −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 0.811653 + 0.584140i \(0.198568\pi\)
−0.962492 + 0.271310i \(0.912543\pi\)
\(420\) 0 0
\(421\) 1.57150 1.31864i 0.0765901 0.0642667i −0.603689 0.797220i \(-0.706303\pi\)
0.680279 + 0.732953i \(0.261859\pi\)
\(422\) −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 \(0.154600\pi\)
−0.884353 + 0.466818i \(0.845400\pi\)
\(432\) 0 0
\(433\) −2.30954 + 2.30954i −0.110989 + 0.110989i −0.760420 0.649431i \(-0.775007\pi\)
0.649431 + 0.760420i \(0.275007\pi\)
\(434\) −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 −0.973283 0.229610i \(-0.926255\pi\)
0.893168 + 0.449723i \(0.148477\pi\)
\(440\) −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 −0.379965 0.925001i \(-0.624064\pi\)
−0.534817 + 0.844968i \(0.679620\pi\)
\(444\) 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 −0.828626 0.559803i \(-0.810877\pi\)
0.899117 + 0.437709i \(0.144210\pi\)
\(450\) 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 −0.897919 0.440160i \(-0.854922\pi\)
0.720722 + 0.693224i \(0.243811\pi\)
\(458\) −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 −0.997606 0.0691537i \(-0.977970\pi\)
−0.913791 + 0.406185i \(0.866859\pi\)
\(462\) 0 0
\(463\) 2.30650 4.94630i 0.107192 0.229874i −0.845394 0.534143i \(-0.820634\pi\)
0.952586 + 0.304269i \(0.0984122\pi\)
\(464\) 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 0.477209 0.878790i \(-0.341648\pi\)
−0.0261197 + 0.999659i \(0.508315\pi\)
\(468\) 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 0.243658 0.969861i \(-0.421653\pi\)
−0.436762 + 0.899577i \(0.643875\pi\)
\(480\) 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 0.648237 0.761439i \(-0.275507\pi\)
−0.761439 + 0.648237i \(0.775507\pi\)
\(488\) −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 −0.942434 0.334392i \(-0.891469\pi\)
0.492964 + 0.870050i \(0.335914\pi\)
\(492\) 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 0.539572 0.841939i \(-0.318586\pi\)
0.219072 + 0.975709i \(0.429697\pi\)
\(500\) −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 0.744745 0.667349i \(-0.232571\pi\)
0.978643 + 0.205569i \(0.0659045\pi\)
\(504\) 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 0.649696 0.760194i \(-0.274896\pi\)
0.986339 + 0.164726i \(0.0526738\pi\)
\(510\) 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 0.210426 0.977610i \(-0.432515\pi\)
0.951848 + 0.306571i \(0.0991816\pi\)
\(522\) 0 0
\(523\) 1.16084 + 4.33233i 0.0507602 + 0.189439i 0.986651 0.162852i \(-0.0520693\pi\)
−0.935890 + 0.352291i \(0.885403\pi\)
\(524\) −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 0.729924 0.683528i \(-0.239555\pi\)
−0.992799 + 0.119791i \(0.961777\pi\)
\(548\) 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 0.909010 + 0.416774i \(0.136840\pi\)
−0.578838 + 0.815442i \(0.696494\pi\)
\(558\) 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 −0.0330215 0.999455i \(-0.510513\pi\)
−0.786852 + 0.617141i \(0.788291\pi\)
\(564\) 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 0.982208 + 0.187796i \(0.0601345\pi\)
−0.858743 + 0.512406i \(0.828754\pi\)
\(570\) 0 0
\(571\) −28.4369 + 10.3502i −1.19005 + 0.433142i −0.859740 0.510732i \(-0.829375\pi\)
−0.330307 + 0.943873i \(0.607152\pi\)
\(572\) −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 −0.788903 0.614518i \(-0.789350\pi\)
−0.375950 + 0.926640i \(0.622684\pi\)
\(578\) 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 −0.541117 0.840947i \(-0.681999\pi\)
0.296379 + 0.955070i \(0.404221\pi\)
\(588\) 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 0.0803015 0.996771i \(-0.474412\pi\)
−0.996771 + 0.0803015i \(0.974412\pi\)
\(594\) 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 0.445342 0.895361i \(-0.353082\pi\)
−0.804425 + 0.594054i \(0.797527\pi\)
\(600\) 0 0
\(601\) −29.2326 10.6398i −1.19242 0.434007i −0.331850 0.943332i \(-0.607673\pi\)
−0.860574 + 0.509326i \(0.829895\pi\)
\(602\) 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 −0.303576 0.952807i \(-0.598181\pi\)
0.791517 + 0.611148i \(0.209292\pi\)
\(608\) −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 0.628989 0.777414i \(-0.283469\pi\)
0.156013 + 0.987755i \(0.450136\pi\)
\(614\) 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 −0.930036 0.367468i \(-0.880225\pi\)
0.879313 + 0.476245i \(0.158002\pi\)
\(618\) 0 0
\(619\) −13.1500 + 2.31870i −0.528542 + 0.0931962i −0.431550 0.902089i \(-0.642033\pi\)
−0.0969919 + 0.995285i \(0.530922\pi\)
\(620\) 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 −0.851886 0.523728i \(-0.824541\pi\)
0.879504 + 0.475891i \(0.157874\pi\)
\(632\) 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 −0.737150 0.675729i \(-0.763829\pi\)
0.999040 0.0438070i \(-0.0139487\pi\)
\(642\) 0 0
\(643\) 41.1928 3.60391i 1.62449 0.142124i 0.761783 0.647833i \(-0.224324\pi\)
0.862705 + 0.505708i \(0.168769\pi\)
\(644\) −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 −0.908620 0.417623i \(-0.862863\pi\)
0.417623 + 0.908620i \(0.362863\pi\)
\(648\) 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 0.979069 + 0.203528i \(0.0652408\pi\)
−0.928853 + 0.370449i \(0.879204\pi\)
\(654\) 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 −0.132784 0.991145i \(-0.542392\pi\)
0.953030 + 0.302877i \(0.0979473\pi\)
\(660\) 0 0
\(661\) 1.73362 9.83186i 0.0674301 0.382415i −0.932352 0.361551i \(-0.882247\pi\)
0.999782 0.0208639i \(-0.00664165\pi\)
\(662\) 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 0.569483 0.822003i \(-0.307143\pi\)
−0.577655 + 0.816281i \(0.696032\pi\)
\(674\) −3.73049 −0.143693
\(675\) 0 0
\(676\) −22.9612 −0.883122
\(677\) −20.1079 14.0797i −0.772810 0.541128i 0.119347 0.992853i \(-0.461920\pi\)
−0.892157 + 0.451725i \(0.850809\pi\)
\(678\) 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 0.764280 + 0.644885i \(0.223095\pi\)
−0.984328 + 0.176347i \(0.943572\pi\)
\(684\) 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 −0.646679 0.762762i \(-0.723843\pi\)
0.638879 + 0.769307i \(0.279398\pi\)
\(692\) −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 \(-0.740036\pi\)
0.684630 0.728891i \(-0.259964\pi\)
\(702\) 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 −0.141463 0.989944i \(-0.545181\pi\)
0.744690 0.667410i \(-0.232597\pi\)
\(710\) −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 −0.876589 0.481241i \(-0.840186\pi\)
0.855061 + 0.518528i \(0.173520\pi\)
\(720\) 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 0.134776 + 0.990876i \(0.456969\pi\)
−0.977215 + 0.212252i \(0.931920\pi\)
\(728\) −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 −0.952573 0.304310i \(-0.901574\pi\)
0.845417 + 0.534106i \(0.179352\pi\)
\(734\) 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 0.925170 0.379553i \(-0.123922\pi\)
0.133882 + 0.990997i \(0.457256\pi\)
\(740\) −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 −0.291806 0.956477i \(-0.594256\pi\)
0.798991 + 0.601343i \(0.205367\pi\)
\(744\) 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 0.997322 0.0731359i \(-0.0233007\pi\)
0.101158 + 0.994870i \(0.467745\pi\)
\(752\) 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 0.929415 0.369036i \(-0.120312\pi\)
−0.369036 + 0.929415i \(0.620312\pi\)
\(758\) −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 −0.422560 0.906335i \(-0.638869\pi\)
0.965942 + 0.258757i \(0.0833130\pi\)
\(762\) 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 −0.614987 0.788537i \(-0.710839\pi\)
−0.847594 + 0.530645i \(0.821950\pi\)
\(770\) −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 0.00937966 0.999956i \(-0.497014\pi\)
0.508101 + 0.861297i \(0.330348\pi\)
\(774\) 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
\(787\) 14.0