Properties

Label 855.2.da.b.199.3
Level $855$
Weight $2$
Character 855.199
Analytic conductor $6.827$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [855,2,Mod(199,855)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(855, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 9, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("855.199");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.da (of order \(18\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.82720937282\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(8\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 199.3
Character \(\chi\) \(=\) 855.199
Dual form 855.2.da.b.739.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.20303 + 0.212126i) q^{2} +(-0.477108 + 0.173653i) q^{4} +(-2.06524 - 0.857189i) q^{5} +(-3.28379 - 1.89590i) q^{7} +(2.65299 - 1.53170i) q^{8} +O(q^{10})\) \(q+(-1.20303 + 0.212126i) q^{2} +(-0.477108 + 0.173653i) q^{4} +(-2.06524 - 0.857189i) q^{5} +(-3.28379 - 1.89590i) q^{7} +(2.65299 - 1.53170i) q^{8} +(2.66638 + 0.593130i) q^{10} +(-0.618663 - 1.07156i) q^{11} +(2.22146 - 2.64744i) q^{13} +(4.35266 + 1.58424i) q^{14} +(-2.08882 + 1.75273i) q^{16} +(2.96127 - 0.522152i) q^{17} +(-4.28612 + 0.793231i) q^{19} +(1.13420 + 0.0503361i) q^{20} +(0.971573 + 1.15788i) q^{22} +(-2.10267 - 5.77705i) q^{23} +(3.53045 + 3.54061i) q^{25} +(-2.11089 + 3.65617i) q^{26} +(1.89595 + 0.334308i) q^{28} +(-0.744476 + 4.22213i) q^{29} +(-2.55067 + 4.41789i) q^{31} +(-1.79713 + 2.14174i) q^{32} +(-3.45173 + 1.25633i) q^{34} +(5.15669 + 6.73032i) q^{35} +9.13084i q^{37} +(4.98805 - 1.86348i) q^{38} +(-6.79202 + 0.889225i) q^{40} +(-4.08318 + 3.42620i) q^{41} +(3.12092 - 8.57465i) q^{43} +(0.481248 + 0.403815i) q^{44} +(3.75504 + 6.50391i) q^{46} +(-7.19237 - 1.26821i) q^{47} +(3.68887 + 6.38931i) q^{49} +(-4.99829 - 3.51055i) q^{50} +(-0.600142 + 1.64888i) q^{52} +(1.13973 + 3.13139i) q^{53} +(0.359163 + 2.74333i) q^{55} -11.6158 q^{56} -5.23727i q^{58} +(-0.141926 - 0.804901i) q^{59} +(-6.01592 + 2.18962i) q^{61} +(2.13137 - 5.85590i) q^{62} +(4.43444 - 7.68067i) q^{64} +(-6.85722 + 3.56338i) q^{65} +(-0.995566 - 0.175545i) q^{67} +(-1.32217 + 0.763357i) q^{68} +(-7.63131 - 7.00290i) q^{70} +(12.8546 + 4.67867i) q^{71} +(7.11096 + 8.47451i) q^{73} +(-1.93689 - 10.9846i) q^{74} +(1.90719 - 1.12275i) q^{76} +4.69169i q^{77} +(1.06036 - 0.889746i) q^{79} +(5.81633 - 1.82929i) q^{80} +(4.18539 - 4.98796i) q^{82} +(2.18283 + 1.26026i) q^{83} +(-6.56333 - 1.46000i) q^{85} +(-1.93564 + 10.9776i) q^{86} +(-3.28261 - 1.89521i) q^{88} +(2.06711 + 1.73451i) q^{89} +(-12.3141 + 4.48197i) q^{91} +(2.00640 + 2.39114i) q^{92} +8.92164 q^{94} +(9.53182 + 2.03580i) q^{95} +(-3.01600 + 0.531802i) q^{97} +(-5.79315 - 6.90401i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 18 q^{4} + 6 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 18 q^{4} + 6 q^{5} - 15 q^{10} + 12 q^{11} - 6 q^{14} - 42 q^{16} + 12 q^{19} - 42 q^{20} + 12 q^{25} - 12 q^{26} - 42 q^{31} - 36 q^{34} - 6 q^{35} + 66 q^{40} - 6 q^{41} + 6 q^{44} - 6 q^{46} + 12 q^{49} + 18 q^{50} - 36 q^{56} + 36 q^{59} + 48 q^{61} + 18 q^{65} - 123 q^{70} + 24 q^{71} - 84 q^{74} + 66 q^{76} + 48 q^{79} + 39 q^{80} - 84 q^{85} + 42 q^{86} + 12 q^{89} - 30 q^{91} - 72 q^{94} + 63 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).

\(n\) \(172\) \(191\) \(496\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{4}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.20303 + 0.212126i −0.850669 + 0.149996i −0.581952 0.813223i \(-0.697711\pi\)
−0.268717 + 0.963219i \(0.586600\pi\)
\(3\) 0 0
\(4\) −0.477108 + 0.173653i −0.238554 + 0.0868266i
\(5\) −2.06524 0.857189i −0.923605 0.383347i
\(6\) 0 0
\(7\) −3.28379 1.89590i −1.24116 0.716583i −0.271828 0.962346i \(-0.587628\pi\)
−0.969330 + 0.245763i \(0.920961\pi\)
\(8\) 2.65299 1.53170i 0.937972 0.541539i
\(9\) 0 0
\(10\) 2.66638 + 0.593130i 0.843182 + 0.187564i
\(11\) −0.618663 1.07156i −0.186534 0.323086i 0.757558 0.652767i \(-0.226392\pi\)
−0.944092 + 0.329681i \(0.893059\pi\)
\(12\) 0 0
\(13\) 2.22146 2.64744i 0.616123 0.734267i −0.364275 0.931291i \(-0.618683\pi\)
0.980399 + 0.197024i \(0.0631278\pi\)
\(14\) 4.35266 + 1.58424i 1.16330 + 0.423406i
\(15\) 0 0
\(16\) −2.08882 + 1.75273i −0.522204 + 0.438181i
\(17\) 2.96127 0.522152i 0.718214 0.126640i 0.197415 0.980320i \(-0.436745\pi\)
0.520799 + 0.853680i \(0.325634\pi\)
\(18\) 0 0
\(19\) −4.28612 + 0.793231i −0.983302 + 0.181980i
\(20\) 1.13420 + 0.0503361i 0.253614 + 0.0112555i
\(21\) 0 0
\(22\) 0.971573 + 1.15788i 0.207140 + 0.246860i
\(23\) −2.10267 5.77705i −0.438438 1.20460i −0.940508 0.339771i \(-0.889650\pi\)
0.502071 0.864827i \(-0.332572\pi\)
\(24\) 0 0
\(25\) 3.53045 + 3.54061i 0.706091 + 0.708122i
\(26\) −2.11089 + 3.65617i −0.413980 + 0.717034i
\(27\) 0 0
\(28\) 1.89595 + 0.334308i 0.358302 + 0.0631782i
\(29\) −0.744476 + 4.22213i −0.138246 + 0.784031i 0.834299 + 0.551313i \(0.185873\pi\)
−0.972544 + 0.232718i \(0.925238\pi\)
\(30\) 0 0
\(31\) −2.55067 + 4.41789i −0.458114 + 0.793476i −0.998861 0.0477088i \(-0.984808\pi\)
0.540748 + 0.841185i \(0.318141\pi\)
\(32\) −1.79713 + 2.14174i −0.317691 + 0.378610i
\(33\) 0 0
\(34\) −3.45173 + 1.25633i −0.591966 + 0.215458i
\(35\) 5.15669 + 6.73032i 0.871639 + 1.13763i
\(36\) 0 0
\(37\) 9.13084i 1.50110i 0.660813 + 0.750550i \(0.270211\pi\)
−0.660813 + 0.750550i \(0.729789\pi\)
\(38\) 4.98805 1.86348i 0.809168 0.302296i
\(39\) 0 0
\(40\) −6.79202 + 0.889225i −1.07391 + 0.140599i
\(41\) −4.08318 + 3.42620i −0.637686 + 0.535082i −0.903307 0.428996i \(-0.858868\pi\)
0.265621 + 0.964078i \(0.414423\pi\)
\(42\) 0 0
\(43\) 3.12092 8.57465i 0.475935 1.30762i −0.436979 0.899471i \(-0.643952\pi\)
0.912915 0.408150i \(-0.133826\pi\)
\(44\) 0.481248 + 0.403815i 0.0725509 + 0.0608774i
\(45\) 0 0
\(46\) 3.75504 + 6.50391i 0.553650 + 0.958950i
\(47\) −7.19237 1.26821i −1.04912 0.184987i −0.377593 0.925972i \(-0.623248\pi\)
−0.671522 + 0.740984i \(0.734359\pi\)
\(48\) 0 0
\(49\) 3.68887 + 6.38931i 0.526981 + 0.912758i
\(50\) −4.99829 3.51055i −0.706864 0.496466i
\(51\) 0 0
\(52\) −0.600142 + 1.64888i −0.0832248 + 0.228658i
\(53\) 1.13973 + 3.13139i 0.156554 + 0.430129i 0.993028 0.117877i \(-0.0376090\pi\)
−0.836474 + 0.548007i \(0.815387\pi\)
\(54\) 0 0
\(55\) 0.359163 + 2.74333i 0.0484295 + 0.369911i
\(56\) −11.6158 −1.55223
\(57\) 0 0
\(58\) 5.23727i 0.687687i
\(59\) −0.141926 0.804901i −0.0184772 0.104789i 0.974174 0.225797i \(-0.0724986\pi\)
−0.992652 + 0.121008i \(0.961387\pi\)
\(60\) 0 0
\(61\) −6.01592 + 2.18962i −0.770260 + 0.280352i −0.697105 0.716969i \(-0.745529\pi\)
−0.0731548 + 0.997321i \(0.523307\pi\)
\(62\) 2.13137 5.85590i 0.270685 0.743700i
\(63\) 0 0
\(64\) 4.43444 7.68067i 0.554305 0.960084i
\(65\) −6.85722 + 3.56338i −0.850533 + 0.441983i
\(66\) 0 0
\(67\) −0.995566 0.175545i −0.121628 0.0214463i 0.112503 0.993651i \(-0.464113\pi\)
−0.234131 + 0.972205i \(0.575224\pi\)
\(68\) −1.32217 + 0.763357i −0.160337 + 0.0925706i
\(69\) 0 0
\(70\) −7.63131 7.00290i −0.912116 0.837006i
\(71\) 12.8546 + 4.67867i 1.52555 + 0.555257i 0.962528 0.271182i \(-0.0874146\pi\)
0.563027 + 0.826439i \(0.309637\pi\)
\(72\) 0 0
\(73\) 7.11096 + 8.47451i 0.832275 + 0.991867i 0.999982 + 0.00602966i \(0.00191931\pi\)
−0.167707 + 0.985837i \(0.553636\pi\)
\(74\) −1.93689 10.9846i −0.225159 1.27694i
\(75\) 0 0
\(76\) 1.90719 1.12275i 0.218770 0.128789i
\(77\) 4.69169i 0.534668i
\(78\) 0 0
\(79\) 1.06036 0.889746i 0.119300 0.100104i −0.581186 0.813771i \(-0.697411\pi\)
0.700486 + 0.713666i \(0.252967\pi\)
\(80\) 5.81633 1.82929i 0.650286 0.204521i
\(81\) 0 0
\(82\) 4.18539 4.98796i 0.462199 0.550828i
\(83\) 2.18283 + 1.26026i 0.239597 + 0.138332i 0.614992 0.788534i \(-0.289159\pi\)
−0.375394 + 0.926865i \(0.622493\pi\)
\(84\) 0 0
\(85\) −6.56333 1.46000i −0.711893 0.158359i
\(86\) −1.93564 + 10.9776i −0.208726 + 1.18374i
\(87\) 0 0
\(88\) −3.28261 1.89521i −0.349927 0.202031i
\(89\) 2.06711 + 1.73451i 0.219113 + 0.183858i 0.745736 0.666241i \(-0.232098\pi\)
−0.526624 + 0.850099i \(0.676542\pi\)
\(90\) 0 0
\(91\) −12.3141 + 4.48197i −1.29087 + 0.469838i
\(92\) 2.00640 + 2.39114i 0.209182 + 0.249294i
\(93\) 0 0
\(94\) 8.92164 0.920197
\(95\) 9.53182 + 2.03580i 0.977944 + 0.208869i
\(96\) 0 0
\(97\) −3.01600 + 0.531802i −0.306228 + 0.0539963i −0.324651 0.945834i \(-0.605247\pi\)
0.0184223 + 0.999830i \(0.494136\pi\)
\(98\) −5.79315 6.90401i −0.585196 0.697410i
\(99\) 0 0
\(100\) −2.29925 1.07618i −0.229925 0.107618i
\(101\) −2.85509 2.39570i −0.284092 0.238381i 0.489594 0.871950i \(-0.337145\pi\)
−0.773686 + 0.633569i \(0.781589\pi\)
\(102\) 0 0
\(103\) −11.4390 + 6.60432i −1.12712 + 0.650743i −0.943209 0.332200i \(-0.892209\pi\)
−0.183911 + 0.982943i \(0.558876\pi\)
\(104\) 1.83843 10.4262i 0.180273 1.02238i
\(105\) 0 0
\(106\) −2.03538 3.52538i −0.197693 0.342415i
\(107\) 4.44535 + 2.56652i 0.429748 + 0.248115i 0.699239 0.714888i \(-0.253522\pi\)
−0.269491 + 0.963003i \(0.586855\pi\)
\(108\) 0 0
\(109\) −1.49202 0.543049i −0.142909 0.0520147i 0.269575 0.962979i \(-0.413117\pi\)
−0.412485 + 0.910965i \(0.635339\pi\)
\(110\) −1.01402 3.22412i −0.0966826 0.307407i
\(111\) 0 0
\(112\) 10.1822 1.79540i 0.962131 0.169650i
\(113\) 20.0832i 1.88927i 0.328126 + 0.944634i \(0.393583\pi\)
−0.328126 + 0.944634i \(0.606417\pi\)
\(114\) 0 0
\(115\) −0.609493 + 13.7334i −0.0568355 + 1.28065i
\(116\) −0.377991 2.14369i −0.0350956 0.199037i
\(117\) 0 0
\(118\) 0.341481 + 0.938212i 0.0314359 + 0.0863694i
\(119\) −10.7142 3.89963i −0.982165 0.357479i
\(120\) 0 0
\(121\) 4.73451 8.20042i 0.430410 0.745492i
\(122\) 6.77284 3.91030i 0.613184 0.354022i
\(123\) 0 0
\(124\) 0.449765 2.55074i 0.0403901 0.229063i
\(125\) −4.25627 10.3385i −0.380692 0.924702i
\(126\) 0 0
\(127\) −2.21957 + 2.64518i −0.196955 + 0.234722i −0.855479 0.517838i \(-0.826737\pi\)
0.658523 + 0.752560i \(0.271181\pi\)
\(128\) −1.79301 + 4.92625i −0.158481 + 0.435423i
\(129\) 0 0
\(130\) 7.49353 5.74144i 0.657226 0.503558i
\(131\) 1.31755 + 7.47219i 0.115115 + 0.652848i 0.986693 + 0.162592i \(0.0519856\pi\)
−0.871579 + 0.490256i \(0.836903\pi\)
\(132\) 0 0
\(133\) 15.5786 + 5.52124i 1.35084 + 0.478752i
\(134\) 1.23493 0.106682
\(135\) 0 0
\(136\) 7.05643 5.92105i 0.605084 0.507726i
\(137\) −1.26080 3.46401i −0.107717 0.295951i 0.874110 0.485728i \(-0.161446\pi\)
−0.981827 + 0.189778i \(0.939223\pi\)
\(138\) 0 0
\(139\) 14.2693 + 11.9734i 1.21031 + 1.01557i 0.999274 + 0.0380898i \(0.0121273\pi\)
0.211033 + 0.977479i \(0.432317\pi\)
\(140\) −3.62904 2.31562i −0.306710 0.195705i
\(141\) 0 0
\(142\) −16.4568 2.90179i −1.38103 0.243512i
\(143\) −4.21121 0.742550i −0.352159 0.0620952i
\(144\) 0 0
\(145\) 5.15669 8.08157i 0.428240 0.671138i
\(146\) −10.3523 8.68665i −0.856766 0.718912i
\(147\) 0 0
\(148\) −1.58560 4.35640i −0.130335 0.358094i
\(149\) 1.29297 1.08493i 0.105924 0.0888807i −0.588288 0.808652i \(-0.700198\pi\)
0.694212 + 0.719771i \(0.255753\pi\)
\(150\) 0 0
\(151\) 1.33890 0.108958 0.0544791 0.998515i \(-0.482650\pi\)
0.0544791 + 0.998515i \(0.482650\pi\)
\(152\) −10.1560 + 8.66948i −0.823761 + 0.703188i
\(153\) 0 0
\(154\) −0.995230 5.64423i −0.0801979 0.454825i
\(155\) 9.05472 6.93760i 0.727292 0.557242i
\(156\) 0 0
\(157\) 2.06672 5.67825i 0.164942 0.453174i −0.829494 0.558515i \(-0.811371\pi\)
0.994436 + 0.105341i \(0.0335935\pi\)
\(158\) −1.08690 + 1.29532i −0.0864692 + 0.103050i
\(159\) 0 0
\(160\) 5.54739 2.88273i 0.438560 0.227900i
\(161\) −4.04795 + 22.9571i −0.319023 + 1.80927i
\(162\) 0 0
\(163\) 8.48469 4.89864i 0.664572 0.383691i −0.129445 0.991587i \(-0.541319\pi\)
0.794017 + 0.607896i \(0.207986\pi\)
\(164\) 1.35315 2.34372i 0.105663 0.183014i
\(165\) 0 0
\(166\) −2.89334 1.05309i −0.224567 0.0817357i
\(167\) 1.32578 + 3.64255i 0.102592 + 0.281869i 0.980360 0.197217i \(-0.0631904\pi\)
−0.877768 + 0.479086i \(0.840968\pi\)
\(168\) 0 0
\(169\) 0.183403 + 1.04013i 0.0141079 + 0.0800101i
\(170\) 8.20556 + 0.364166i 0.629338 + 0.0279303i
\(171\) 0 0
\(172\) 4.63299i 0.353262i
\(173\) 4.66030 0.821737i 0.354316 0.0624755i 0.00634275 0.999980i \(-0.497981\pi\)
0.347973 + 0.937504i \(0.386870\pi\)
\(174\) 0 0
\(175\) −4.88064 18.3200i −0.368942 1.38486i
\(176\) 3.17042 + 1.15394i 0.238979 + 0.0869813i
\(177\) 0 0
\(178\) −2.85472 1.64817i −0.213970 0.123536i
\(179\) 4.68907 + 8.12172i 0.350478 + 0.607045i 0.986333 0.164763i \(-0.0526859\pi\)
−0.635855 + 0.771808i \(0.719353\pi\)
\(180\) 0 0
\(181\) −3.38627 + 19.2045i −0.251700 + 1.42746i 0.552704 + 0.833377i \(0.313596\pi\)
−0.804404 + 0.594083i \(0.797515\pi\)
\(182\) 13.8635 8.00407i 1.02763 0.593301i
\(183\) 0 0
\(184\) −14.4271 12.1058i −1.06358 0.892448i
\(185\) 7.82686 18.8574i 0.575442 1.38642i
\(186\) 0 0
\(187\) −2.39154 2.85013i −0.174887 0.208422i
\(188\) 3.65177 0.643905i 0.266332 0.0469616i
\(189\) 0 0
\(190\) −11.8989 0.427174i −0.863236 0.0309904i
\(191\) −15.5024 −1.12171 −0.560857 0.827913i \(-0.689528\pi\)
−0.560857 + 0.827913i \(0.689528\pi\)
\(192\) 0 0
\(193\) −12.7550 15.2008i −0.918122 1.09417i −0.995269 0.0971550i \(-0.969026\pi\)
0.0771477 0.997020i \(-0.475419\pi\)
\(194\) 3.51552 1.27955i 0.252400 0.0918660i
\(195\) 0 0
\(196\) −2.86951 2.40781i −0.204965 0.171986i
\(197\) −22.4913 12.9854i −1.60244 0.925170i −0.990997 0.133882i \(-0.957256\pi\)
−0.611444 0.791288i \(-0.709411\pi\)
\(198\) 0 0
\(199\) 0.940467 5.33365i 0.0666680 0.378093i −0.933159 0.359465i \(-0.882959\pi\)
0.999826 0.0186277i \(-0.00592971\pi\)
\(200\) 14.7894 + 3.98558i 1.04577 + 0.281823i
\(201\) 0 0
\(202\) 3.94294 + 2.27646i 0.277424 + 0.160171i
\(203\) 10.4494 12.4532i 0.733407 0.874041i
\(204\) 0 0
\(205\) 11.3697 3.57587i 0.794091 0.249749i
\(206\) 12.3605 10.3717i 0.861197 0.722630i
\(207\) 0 0
\(208\) 9.42363i 0.653411i
\(209\) 3.50165 + 4.10207i 0.242214 + 0.283746i
\(210\) 0 0
\(211\) −3.49375 19.8141i −0.240520 1.36406i −0.830671 0.556764i \(-0.812043\pi\)
0.590151 0.807293i \(-0.299068\pi\)
\(212\) −1.08755 1.29609i −0.0746933 0.0890160i
\(213\) 0 0
\(214\) −5.89230 2.14462i −0.402790 0.146603i
\(215\) −13.7955 + 15.0335i −0.940848 + 1.02528i
\(216\) 0 0
\(217\) 16.7517 9.67162i 1.13718 0.656553i
\(218\) 1.91013 + 0.336808i 0.129370 + 0.0228115i
\(219\) 0 0
\(220\) −0.647748 1.24650i −0.0436711 0.0840388i
\(221\) 5.19599 8.99972i 0.349520 0.605387i
\(222\) 0 0
\(223\) 3.71080 10.1953i 0.248493 0.682730i −0.751249 0.660019i \(-0.770548\pi\)
0.999742 0.0227106i \(-0.00722963\pi\)
\(224\) 9.96194 3.62585i 0.665610 0.242262i
\(225\) 0 0
\(226\) −4.26017 24.1606i −0.283382 1.60714i
\(227\) 8.78226i 0.582899i −0.956586 0.291449i \(-0.905862\pi\)
0.956586 0.291449i \(-0.0941375\pi\)
\(228\) 0 0
\(229\) −18.0824 −1.19492 −0.597459 0.801899i \(-0.703823\pi\)
−0.597459 + 0.801899i \(0.703823\pi\)
\(230\) −2.17997 16.6509i −0.143743 1.09793i
\(231\) 0 0
\(232\) 4.49197 + 12.3416i 0.294912 + 0.810264i
\(233\) 9.01763 24.7757i 0.590765 1.62311i −0.178325 0.983972i \(-0.557068\pi\)
0.769090 0.639141i \(-0.220710\pi\)
\(234\) 0 0
\(235\) 13.7669 + 8.78438i 0.898053 + 0.573030i
\(236\) 0.207488 + 0.359379i 0.0135063 + 0.0233936i
\(237\) 0 0
\(238\) 13.7166 + 2.41861i 0.889117 + 0.156775i
\(239\) 4.58448 + 7.94056i 0.296546 + 0.513632i 0.975343 0.220693i \(-0.0708320\pi\)
−0.678798 + 0.734325i \(0.737499\pi\)
\(240\) 0 0
\(241\) 20.3130 + 17.0446i 1.30847 + 1.09794i 0.988614 + 0.150474i \(0.0480800\pi\)
0.319859 + 0.947465i \(0.396364\pi\)
\(242\) −3.95623 + 10.8696i −0.254316 + 0.698727i
\(243\) 0 0
\(244\) 2.49001 2.08937i 0.159407 0.133758i
\(245\) −2.14156 16.3575i −0.136819 1.04504i
\(246\) 0 0
\(247\) −7.42142 + 13.1094i −0.472214 + 0.834128i
\(248\) 15.6275i 0.992345i
\(249\) 0 0
\(250\) 7.31347 + 11.5346i 0.462545 + 0.729513i
\(251\) −14.0457 + 5.11220i −0.886554 + 0.322679i −0.744852 0.667230i \(-0.767480\pi\)
−0.141703 + 0.989909i \(0.545258\pi\)
\(252\) 0 0
\(253\) −4.88958 + 5.82717i −0.307405 + 0.366351i
\(254\) 2.10909 3.65306i 0.132336 0.229213i
\(255\) 0 0
\(256\) −1.96808 + 11.1615i −0.123005 + 0.697595i
\(257\) 10.6347 + 1.87519i 0.663376 + 0.116971i 0.495191 0.868784i \(-0.335098\pi\)
0.168185 + 0.985755i \(0.446209\pi\)
\(258\) 0 0
\(259\) 17.3111 29.9838i 1.07566 1.86310i
\(260\) 2.65284 2.89090i 0.164522 0.179286i
\(261\) 0 0
\(262\) −3.17009 8.70976i −0.195849 0.538091i
\(263\) −0.352998 0.420687i −0.0217668 0.0259407i 0.755051 0.655666i \(-0.227612\pi\)
−0.776818 + 0.629725i \(0.783168\pi\)
\(264\) 0 0
\(265\) 0.330370 7.44404i 0.0202944 0.457284i
\(266\) −19.9127 3.33757i −1.22093 0.204639i
\(267\) 0 0
\(268\) 0.505477 0.0891292i 0.0308769 0.00544443i
\(269\) 16.7970 14.0944i 1.02413 0.859350i 0.0339919 0.999422i \(-0.489178\pi\)
0.990141 + 0.140072i \(0.0447335\pi\)
\(270\) 0 0
\(271\) 4.96664 + 1.80771i 0.301702 + 0.109810i 0.488435 0.872600i \(-0.337568\pi\)
−0.186734 + 0.982411i \(0.559790\pi\)
\(272\) −5.27036 + 6.28098i −0.319563 + 0.380840i
\(273\) 0 0
\(274\) 2.25158 + 3.89985i 0.136023 + 0.235599i
\(275\) 1.60980 5.97352i 0.0970744 0.360217i
\(276\) 0 0
\(277\) −15.1027 + 8.71954i −0.907433 + 0.523906i −0.879604 0.475706i \(-0.842193\pi\)
−0.0278284 + 0.999613i \(0.508859\pi\)
\(278\) −19.7062 11.3774i −1.18190 0.682371i
\(279\) 0 0
\(280\) 23.9895 + 9.95695i 1.43365 + 0.595042i
\(281\) −21.7859 + 7.92943i −1.29964 + 0.473030i −0.896879 0.442275i \(-0.854171\pi\)
−0.402760 + 0.915305i \(0.631949\pi\)
\(282\) 0 0
\(283\) −4.52409 + 0.797719i −0.268929 + 0.0474195i −0.306487 0.951875i \(-0.599153\pi\)
0.0375573 + 0.999294i \(0.488042\pi\)
\(284\) −6.94548 −0.412138
\(285\) 0 0
\(286\) 5.22372 0.308885
\(287\) 19.9040 3.50962i 1.17490 0.207166i
\(288\) 0 0
\(289\) −7.47829 + 2.72188i −0.439899 + 0.160110i
\(290\) −4.48933 + 10.8162i −0.263622 + 0.635150i
\(291\) 0 0
\(292\) −4.86432 2.80842i −0.284663 0.164350i
\(293\) 15.7033 9.06630i 0.917396 0.529659i 0.0345929 0.999401i \(-0.488987\pi\)
0.882804 + 0.469742i \(0.155653\pi\)
\(294\) 0 0
\(295\) −0.396842 + 1.78397i −0.0231050 + 0.103867i
\(296\) 13.9857 + 24.2240i 0.812904 + 1.40799i
\(297\) 0 0
\(298\) −1.32533 + 1.57947i −0.0767744 + 0.0914962i
\(299\) −19.9654 7.26680i −1.15463 0.420250i
\(300\) 0 0
\(301\) −26.5051 + 22.2404i −1.52773 + 1.28192i
\(302\) −1.61073 + 0.284016i −0.0926873 + 0.0163433i
\(303\) 0 0
\(304\) 7.56259 9.16930i 0.433745 0.525895i
\(305\) 14.3013 + 0.634695i 0.818887 + 0.0363425i
\(306\) 0 0
\(307\) −2.83731 3.38137i −0.161934 0.192985i 0.678976 0.734160i \(-0.262424\pi\)
−0.840910 + 0.541175i \(0.817980\pi\)
\(308\) −0.814726 2.23844i −0.0464234 0.127547i
\(309\) 0 0
\(310\) −9.42142 + 10.2669i −0.535101 + 0.583119i
\(311\) 7.51688 13.0196i 0.426243 0.738275i −0.570292 0.821442i \(-0.693170\pi\)
0.996536 + 0.0831667i \(0.0265034\pi\)
\(312\) 0 0
\(313\) 7.68691 + 1.35541i 0.434490 + 0.0766123i 0.386615 0.922241i \(-0.373644\pi\)
0.0478746 + 0.998853i \(0.484755\pi\)
\(314\) −1.28181 + 7.26950i −0.0723367 + 0.410242i
\(315\) 0 0
\(316\) −0.351398 + 0.608639i −0.0197677 + 0.0342386i
\(317\) −17.5037 + 20.8601i −0.983107 + 1.17162i 0.00205551 + 0.999998i \(0.499346\pi\)
−0.985163 + 0.171624i \(0.945099\pi\)
\(318\) 0 0
\(319\) 4.98483 1.81433i 0.279097 0.101583i
\(320\) −15.7420 + 12.0613i −0.880003 + 0.674247i
\(321\) 0 0
\(322\) 28.4767i 1.58694i
\(323\) −12.2782 + 4.58697i −0.683175 + 0.255226i
\(324\) 0 0
\(325\) 17.2163 1.48132i 0.954989 0.0821689i
\(326\) −9.16818 + 7.69302i −0.507779 + 0.426077i
\(327\) 0 0
\(328\) −5.58471 + 15.3439i −0.308364 + 0.847224i
\(329\) 21.2139 + 17.8005i 1.16956 + 0.981376i
\(330\) 0 0
\(331\) 5.98999 + 10.3750i 0.329240 + 0.570260i 0.982361 0.186993i \(-0.0598742\pi\)
−0.653121 + 0.757253i \(0.726541\pi\)
\(332\) −1.26030 0.222224i −0.0691677 0.0121961i
\(333\) 0 0
\(334\) −2.36763 4.10085i −0.129551 0.224389i
\(335\) 1.90561 + 1.21593i 0.104115 + 0.0664335i
\(336\) 0 0
\(337\) −1.41714 + 3.89355i −0.0771963 + 0.212095i −0.972288 0.233788i \(-0.924888\pi\)
0.895091 + 0.445883i \(0.147110\pi\)
\(338\) −0.441278 1.21240i −0.0240024 0.0659460i
\(339\) 0 0
\(340\) 3.38495 0.443165i 0.183575 0.0240340i
\(341\) 6.31201 0.341815
\(342\) 0 0
\(343\) 1.43230i 0.0773370i
\(344\) −4.85406 27.5287i −0.261713 1.48425i
\(345\) 0 0
\(346\) −5.43216 + 1.97714i −0.292035 + 0.106292i
\(347\) −3.13610 + 8.61637i −0.168355 + 0.462551i −0.994965 0.100224i \(-0.968044\pi\)
0.826610 + 0.562775i \(0.190266\pi\)
\(348\) 0 0
\(349\) −16.3441 + 28.3089i −0.874881 + 1.51534i −0.0179923 + 0.999838i \(0.505727\pi\)
−0.856889 + 0.515501i \(0.827606\pi\)
\(350\) 9.75770 + 21.0042i 0.521571 + 1.12272i
\(351\) 0 0
\(352\) 3.40681 + 0.600713i 0.181584 + 0.0320181i
\(353\) −22.9238 + 13.2351i −1.22011 + 0.704431i −0.964941 0.262466i \(-0.915464\pi\)
−0.255169 + 0.966897i \(0.582131\pi\)
\(354\) 0 0
\(355\) −22.5373 20.6814i −1.19615 1.09765i
\(356\) −1.28744 0.468589i −0.0682340 0.0248351i
\(357\) 0 0
\(358\) −7.36391 8.77597i −0.389195 0.463824i
\(359\) 2.15533 + 12.2235i 0.113754 + 0.645131i 0.987360 + 0.158496i \(0.0506646\pi\)
−0.873606 + 0.486635i \(0.838224\pi\)
\(360\) 0 0
\(361\) 17.7416 6.79976i 0.933767 0.357882i
\(362\) 23.8219i 1.25205i
\(363\) 0 0
\(364\) 5.09685 4.27677i 0.267148 0.224163i
\(365\) −7.42159 23.5974i −0.388464 1.23514i
\(366\) 0 0
\(367\) −3.42041 + 4.07628i −0.178544 + 0.212780i −0.847892 0.530168i \(-0.822129\pi\)
0.669349 + 0.742948i \(0.266573\pi\)
\(368\) 14.5177 + 8.38178i 0.756786 + 0.436931i
\(369\) 0 0
\(370\) −5.41578 + 24.3462i −0.281553 + 1.26570i
\(371\) 2.19415 12.4437i 0.113915 0.646042i
\(372\) 0 0
\(373\) −16.7186 9.65250i −0.865657 0.499788i 0.000245325 1.00000i \(-0.499922\pi\)
−0.865903 + 0.500212i \(0.833255\pi\)
\(374\) 3.48168 + 2.92147i 0.180033 + 0.151066i
\(375\) 0 0
\(376\) −21.0238 + 7.65203i −1.08422 + 0.394623i
\(377\) 9.52401 + 11.3503i 0.490511 + 0.584569i
\(378\) 0 0
\(379\) −20.5109 −1.05357 −0.526787 0.849997i \(-0.676603\pi\)
−0.526787 + 0.849997i \(0.676603\pi\)
\(380\) −4.90123 + 0.683934i −0.251428 + 0.0350851i
\(381\) 0 0
\(382\) 18.6498 3.28846i 0.954207 0.168252i
\(383\) −14.6076 17.4086i −0.746411 0.889538i 0.250497 0.968117i \(-0.419406\pi\)
−0.996908 + 0.0785793i \(0.974962\pi\)
\(384\) 0 0
\(385\) 4.02167 9.68947i 0.204963 0.493821i
\(386\) 18.5690 + 15.5813i 0.945139 + 0.793066i
\(387\) 0 0
\(388\) 1.34661 0.777465i 0.0683637 0.0394698i
\(389\) 0.876043 4.96829i 0.0444172 0.251902i −0.954512 0.298173i \(-0.903623\pi\)
0.998929 + 0.0462710i \(0.0147338\pi\)
\(390\) 0 0
\(391\) −9.24308 16.0095i −0.467443 0.809635i
\(392\) 19.5730 + 11.3005i 0.988588 + 0.570761i
\(393\) 0 0
\(394\) 29.8122 + 10.8508i 1.50192 + 0.546654i
\(395\) −2.95258 + 0.928613i −0.148560 + 0.0467236i
\(396\) 0 0
\(397\) −22.5943 + 3.98399i −1.13398 + 0.199951i −0.708970 0.705239i \(-0.750840\pi\)
−0.425008 + 0.905190i \(0.639729\pi\)
\(398\) 6.61603i 0.331632i
\(399\) 0 0
\(400\) −13.5802 1.20777i −0.679009 0.0603883i
\(401\) 3.95308 + 22.4191i 0.197408 + 1.11955i 0.908948 + 0.416909i \(0.136887\pi\)
−0.711540 + 0.702645i \(0.752002\pi\)
\(402\) 0 0
\(403\) 6.02986 + 16.5669i 0.300369 + 0.825257i
\(404\) 1.77821 + 0.647214i 0.0884691 + 0.0322001i
\(405\) 0 0
\(406\) −9.92933 + 17.1981i −0.492784 + 0.853527i
\(407\) 9.78420 5.64891i 0.484985 0.280006i
\(408\) 0 0
\(409\) −4.13331 + 23.4412i −0.204379 + 1.15909i 0.694035 + 0.719941i \(0.255831\pi\)
−0.898414 + 0.439150i \(0.855280\pi\)
\(410\) −12.9195 + 6.71367i −0.638047 + 0.331564i
\(411\) 0 0
\(412\) 4.31079 5.13740i 0.212377 0.253101i
\(413\) −1.05996 + 2.91221i −0.0521571 + 0.143300i
\(414\) 0 0
\(415\) −3.42780 4.47385i −0.168264 0.219612i
\(416\) 1.67786 + 9.51559i 0.0822636 + 0.466540i
\(417\) 0 0
\(418\) −5.08274 4.19211i −0.248605 0.205043i
\(419\) −15.9374 −0.778593 −0.389296 0.921113i \(-0.627282\pi\)
−0.389296 + 0.921113i \(0.627282\pi\)
\(420\) 0 0
\(421\) −2.03273 + 1.70566i −0.0990692 + 0.0831290i −0.690977 0.722877i \(-0.742819\pi\)
0.591908 + 0.806006i \(0.298375\pi\)
\(422\) 8.40616 + 23.0957i 0.409206 + 1.12428i
\(423\) 0 0
\(424\) 7.82005 + 6.56180i 0.379775 + 0.318669i
\(425\) 12.3034 + 8.64127i 0.596801 + 0.419163i
\(426\) 0 0
\(427\) 23.9063 + 4.21533i 1.15691 + 0.203994i
\(428\) −2.56660 0.452560i −0.124061 0.0218753i
\(429\) 0 0
\(430\) 13.4074 21.0121i 0.646563 1.01329i
\(431\) −25.5262 21.4191i −1.22956 1.03172i −0.998268 0.0588349i \(-0.981261\pi\)
−0.231288 0.972885i \(-0.574294\pi\)
\(432\) 0 0
\(433\) 7.65442 + 21.0303i 0.367848 + 1.01065i 0.976178 + 0.216970i \(0.0696173\pi\)
−0.608330 + 0.793684i \(0.708160\pi\)
\(434\) −18.1012 + 15.1887i −0.868885 + 0.729081i
\(435\) 0 0
\(436\) 0.806155 0.0386078
\(437\) 13.5948 + 23.0932i 0.650329 + 1.10470i
\(438\) 0 0
\(439\) 3.03121 + 17.1909i 0.144672 + 0.820475i 0.967630 + 0.252373i \(0.0812110\pi\)
−0.822958 + 0.568102i \(0.807678\pi\)
\(440\) 5.15482 + 6.72789i 0.245747 + 0.320740i
\(441\) 0 0
\(442\) −4.34184 + 11.9291i −0.206520 + 0.567410i
\(443\) −0.963275 + 1.14799i −0.0457666 + 0.0545425i −0.788442 0.615109i \(-0.789112\pi\)
0.742676 + 0.669651i \(0.233556\pi\)
\(444\) 0 0
\(445\) −2.78228 5.35408i −0.131892 0.253808i
\(446\) −2.30149 + 13.0524i −0.108979 + 0.618050i
\(447\) 0 0
\(448\) −29.1236 + 16.8145i −1.37596 + 0.794410i
\(449\) −5.99556 + 10.3846i −0.282948 + 0.490081i −0.972110 0.234527i \(-0.924646\pi\)
0.689161 + 0.724608i \(0.257979\pi\)
\(450\) 0 0
\(451\) 6.19747 + 2.25569i 0.291827 + 0.106217i
\(452\) −3.48751 9.58185i −0.164039 0.450693i
\(453\) 0 0
\(454\) 1.86295 + 10.5653i 0.0874324 + 0.495854i
\(455\) 29.2735 + 1.29917i 1.37236 + 0.0609060i
\(456\) 0 0
\(457\) 12.9472i 0.605646i −0.953047 0.302823i \(-0.902071\pi\)
0.953047 0.302823i \(-0.0979291\pi\)
\(458\) 21.7536 3.83575i 1.01648 0.179233i
\(459\) 0 0
\(460\) −2.09405 6.65815i −0.0976357 0.310438i
\(461\) 13.0317 + 4.74315i 0.606946 + 0.220910i 0.627166 0.778885i \(-0.284215\pi\)
−0.0202204 + 0.999796i \(0.506437\pi\)
\(462\) 0 0
\(463\) −3.62408 2.09237i −0.168425 0.0972405i 0.413418 0.910541i \(-0.364335\pi\)
−0.581843 + 0.813301i \(0.697668\pi\)
\(464\) −5.84517 10.1241i −0.271355 0.470001i
\(465\) 0 0
\(466\) −5.59287 + 31.7188i −0.259085 + 1.46934i
\(467\) −20.1800 + 11.6509i −0.933820 + 0.539141i −0.888018 0.459810i \(-0.847918\pi\)
−0.0458021 + 0.998951i \(0.514584\pi\)
\(468\) 0 0
\(469\) 2.93642 + 2.46395i 0.135591 + 0.113775i
\(470\) −18.4253 7.64753i −0.849898 0.352754i
\(471\) 0 0
\(472\) −1.60940 1.91800i −0.0740785 0.0882833i
\(473\) −11.1190 + 1.96058i −0.511252 + 0.0901476i
\(474\) 0 0
\(475\) −17.9404 12.3750i −0.823164 0.567803i
\(476\) 5.78899 0.265338
\(477\) 0 0
\(478\) −7.19966 8.58022i −0.329305 0.392450i
\(479\) −32.9992 + 12.0107i −1.50777 + 0.548784i −0.958059 0.286570i \(-0.907485\pi\)
−0.549712 + 0.835354i \(0.685263\pi\)
\(480\) 0 0
\(481\) 24.1733 + 20.2838i 1.10221 + 0.924863i
\(482\) −28.0527 16.1962i −1.27776 0.737717i
\(483\) 0 0
\(484\) −0.834846 + 4.73465i −0.0379476 + 0.215211i
\(485\) 6.68463 + 1.48698i 0.303533 + 0.0675204i
\(486\) 0 0
\(487\) 28.9434 + 16.7105i 1.31155 + 0.757223i 0.982353 0.187038i \(-0.0598889\pi\)
0.329196 + 0.944262i \(0.393222\pi\)
\(488\) −12.6063 + 15.0236i −0.570661 + 0.680088i
\(489\) 0 0
\(490\) 6.04622 + 19.2243i 0.273140 + 0.868464i
\(491\) 13.4354 11.2737i 0.606332 0.508773i −0.287142 0.957888i \(-0.592705\pi\)
0.893474 + 0.449115i \(0.148261\pi\)
\(492\) 0 0
\(493\) 12.8916i 0.580609i
\(494\) 6.14733 17.3452i 0.276582 0.780397i
\(495\) 0 0
\(496\) −2.41546 13.6988i −0.108458 0.615093i
\(497\) −33.3414 39.7347i −1.49557 1.78235i
\(498\) 0 0
\(499\) 30.7119 + 11.1782i 1.37486 + 0.500407i 0.920615 0.390472i \(-0.127688\pi\)
0.454241 + 0.890879i \(0.349910\pi\)
\(500\) 3.82601 + 4.19346i 0.171104 + 0.187537i
\(501\) 0 0
\(502\) 15.8129 9.12957i 0.705764 0.407473i
\(503\) 17.2581 + 3.04306i 0.769499 + 0.135684i 0.544597 0.838698i \(-0.316683\pi\)
0.224902 + 0.974381i \(0.427794\pi\)
\(504\) 0 0
\(505\) 3.84288 + 7.39506i 0.171006 + 0.329076i
\(506\) 4.64620 8.04746i 0.206549 0.357753i
\(507\) 0 0
\(508\) 0.599632 1.64748i 0.0266044 0.0730949i
\(509\) −28.1903 + 10.2604i −1.24951 + 0.454786i −0.880237 0.474534i \(-0.842617\pi\)
−0.369276 + 0.929320i \(0.620394\pi\)
\(510\) 0 0
\(511\) −7.28411 41.3102i −0.322230 1.82746i
\(512\) 24.3299i 1.07524i
\(513\) 0 0
\(514\) −13.1916 −0.581858
\(515\) 29.2855 3.83412i 1.29047 0.168951i
\(516\) 0 0
\(517\) 3.09070 + 8.49162i 0.135929 + 0.373461i
\(518\) −14.4654 + 39.7435i −0.635575 + 1.74623i
\(519\) 0 0
\(520\) −12.7341 + 19.9568i −0.558425 + 0.875165i
\(521\) −5.24373 9.08241i −0.229732 0.397907i 0.727997 0.685581i \(-0.240452\pi\)
−0.957729 + 0.287673i \(0.907118\pi\)
\(522\) 0 0
\(523\) −32.2610 5.68848i −1.41067 0.248740i −0.584152 0.811644i \(-0.698573\pi\)
−0.826522 + 0.562905i \(0.809684\pi\)
\(524\) −1.92618 3.33625i −0.0841457 0.145745i
\(525\) 0 0
\(526\) 0.513906 + 0.431218i 0.0224073 + 0.0188020i
\(527\) −5.24641 + 14.4144i −0.228537 + 0.627901i
\(528\) 0 0
\(529\) −11.3340 + 9.51037i −0.492783 + 0.413494i
\(530\) 1.18163 + 9.02547i 0.0513269 + 0.392041i
\(531\) 0 0
\(532\) −8.39146 + 0.0710470i −0.363816 + 0.00308028i
\(533\) 18.4211i 0.797908i
\(534\) 0 0
\(535\) −6.98073 9.11100i −0.301803 0.393903i
\(536\) −2.91011 + 1.05919i −0.125697 + 0.0457501i
\(537\) 0 0
\(538\) −17.2175 + 20.5190i −0.742299 + 0.884638i
\(539\) 4.56433 7.90565i 0.196600 0.340521i
\(540\) 0 0
\(541\) 2.56927 14.5710i 0.110461 0.626458i −0.878436 0.477860i \(-0.841413\pi\)
0.988898 0.148598i \(-0.0474761\pi\)
\(542\) −6.35846 1.12117i −0.273119 0.0481583i
\(543\) 0 0
\(544\) −4.20348 + 7.28065i −0.180223 + 0.312155i
\(545\) 2.61588 + 2.40047i 0.112052 + 0.102825i
\(546\) 0 0
\(547\) 0.550656 + 1.51291i 0.0235443 + 0.0646875i 0.950908 0.309474i \(-0.100153\pi\)
−0.927364 + 0.374161i \(0.877931\pi\)
\(548\) 1.20307 + 1.43377i 0.0513927 + 0.0612475i
\(549\) 0 0
\(550\) −0.669491 + 7.52778i −0.0285472 + 0.320986i
\(551\) −0.158216 18.6871i −0.00674022 0.796097i
\(552\) 0 0
\(553\) −5.16886 + 0.911410i −0.219802 + 0.0387571i
\(554\) 16.3193 13.6935i 0.693341 0.581782i
\(555\) 0 0
\(556\) −8.88722 3.23468i −0.376902 0.137181i
\(557\) 14.3448 17.0954i 0.607808 0.724357i −0.371115 0.928587i \(-0.621025\pi\)
0.978923 + 0.204230i \(0.0654690\pi\)
\(558\) 0 0
\(559\) −15.7678 27.3107i −0.666909 1.15512i
\(560\) −22.5678 5.02016i −0.953663 0.212141i
\(561\) 0 0
\(562\) 24.5270 14.1607i 1.03461 0.597333i
\(563\) −2.09682 1.21060i −0.0883706 0.0510208i 0.455163 0.890408i \(-0.349581\pi\)
−0.543534 + 0.839387i \(0.682914\pi\)
\(564\) 0 0
\(565\) 17.2151 41.4767i 0.724245 1.74494i
\(566\) 5.27339 1.91936i 0.221657 0.0806766i
\(567\) 0 0
\(568\) 41.2693 7.27689i 1.73162 0.305332i
\(569\) 25.3556 1.06296 0.531481 0.847070i \(-0.321636\pi\)
0.531481 + 0.847070i \(0.321636\pi\)
\(570\) 0 0
\(571\) 3.79252 0.158712 0.0793561 0.996846i \(-0.474714\pi\)
0.0793561 + 0.996846i \(0.474714\pi\)
\(572\) 2.13815 0.377013i 0.0894005 0.0157637i
\(573\) 0 0
\(574\) −23.2006 + 8.44434i −0.968376 + 0.352460i
\(575\) 13.0309 27.8403i 0.543425 1.16102i
\(576\) 0 0
\(577\) −31.8817 18.4069i −1.32725 0.766289i −0.342378 0.939562i \(-0.611232\pi\)
−0.984874 + 0.173274i \(0.944566\pi\)
\(578\) 8.41921 4.86083i 0.350193 0.202184i
\(579\) 0 0
\(580\) −1.05691 + 4.75126i −0.0438858 + 0.197285i
\(581\) −4.77865 8.27687i −0.198252 0.343382i
\(582\) 0 0
\(583\) 2.65035 3.15856i 0.109766 0.130814i
\(584\) 31.8457 + 11.5909i 1.31778 + 0.479634i
\(585\) 0 0
\(586\) −16.9683 + 14.2381i −0.700954 + 0.588170i
\(587\) 27.1575 4.78860i 1.12091 0.197647i 0.417669 0.908599i \(-0.362847\pi\)
0.703240 + 0.710953i \(0.251736\pi\)
\(588\) 0 0
\(589\) 7.42806 20.9588i 0.306068 0.863594i
\(590\) 0.0989838 2.23035i 0.00407510 0.0918220i
\(591\) 0 0
\(592\) −16.0039 19.0726i −0.657754 0.783881i
\(593\) 2.54255 + 6.98559i 0.104410 + 0.286864i 0.980887 0.194580i \(-0.0623345\pi\)
−0.876477 + 0.481444i \(0.840112\pi\)
\(594\) 0 0
\(595\) 18.7846 + 17.2377i 0.770093 + 0.706679i
\(596\) −0.428484 + 0.742155i −0.0175514 + 0.0303999i
\(597\) 0 0
\(598\) 25.5604 + 4.50698i 1.04524 + 0.184304i
\(599\) 1.30033 7.37456i 0.0531302 0.301316i −0.946650 0.322262i \(-0.895557\pi\)
0.999781 + 0.0209459i \(0.00666778\pi\)
\(600\) 0 0
\(601\) 12.4586 21.5790i 0.508199 0.880226i −0.491756 0.870733i \(-0.663645\pi\)
0.999955 0.00949287i \(-0.00302172\pi\)
\(602\) 27.1686 32.3783i 1.10731 1.31964i
\(603\) 0 0
\(604\) −0.638800 + 0.232504i −0.0259924 + 0.00946046i
\(605\) −16.8072 + 12.8775i −0.683311 + 0.523544i
\(606\) 0 0
\(607\) 13.5201i 0.548764i −0.961621 0.274382i \(-0.911527\pi\)
0.961621 0.274382i \(-0.0884733\pi\)
\(608\) 6.00383 10.6053i 0.243487 0.430101i
\(609\) 0 0
\(610\) −17.3394 + 2.27011i −0.702053 + 0.0919143i
\(611\) −19.3351 + 16.2241i −0.782214 + 0.656356i
\(612\) 0 0
\(613\) 1.93380 5.31308i 0.0781055 0.214593i −0.894494 0.447080i \(-0.852464\pi\)
0.972600 + 0.232487i \(0.0746862\pi\)
\(614\) 4.13064 + 3.46602i 0.166699 + 0.139877i
\(615\) 0 0
\(616\) 7.18627 + 12.4470i 0.289543 + 0.501503i
\(617\) 18.1567 + 3.20152i 0.730963 + 0.128888i 0.526729 0.850034i \(-0.323418\pi\)
0.204234 + 0.978922i \(0.434530\pi\)
\(618\) 0 0
\(619\) −3.49951 6.06133i −0.140657 0.243625i 0.787087 0.616842i \(-0.211588\pi\)
−0.927744 + 0.373216i \(0.878255\pi\)
\(620\) −3.11534 + 4.88237i −0.125115 + 0.196081i
\(621\) 0 0
\(622\) −6.28121 + 17.2575i −0.251854 + 0.691962i
\(623\) −3.49950 9.61480i −0.140205 0.385209i
\(624\) 0 0
\(625\) −0.0718048 + 24.9999i −0.00287219 + 0.999996i
\(626\) −9.53508 −0.381099
\(627\) 0 0
\(628\) 3.06803i 0.122428i
\(629\) 4.76768 + 27.0389i 0.190100 + 1.07811i
\(630\) 0 0
\(631\) −26.3690 + 9.59752i −1.04973 + 0.382071i −0.808562 0.588412i \(-0.799753\pi\)
−0.241170 + 0.970483i \(0.577531\pi\)
\(632\) 1.45029 3.98464i 0.0576894 0.158500i
\(633\) 0 0
\(634\) 16.6325 28.8083i 0.660560 1.14412i
\(635\) 6.85138 3.56035i 0.271889 0.141288i
\(636\) 0 0
\(637\) 25.1100 + 4.42757i 0.994893 + 0.175427i
\(638\) −5.61202 + 3.24010i −0.222182 + 0.128277i
\(639\) 0 0
\(640\) 7.92573 8.63696i 0.313292 0.341406i
\(641\) 25.2148 + 9.17744i 0.995925 + 0.362487i 0.788012 0.615660i \(-0.211111\pi\)
0.207913 + 0.978147i \(0.433333\pi\)
\(642\) 0 0
\(643\) 17.2770 + 20.5900i 0.681339 + 0.811989i 0.990279 0.139093i \(-0.0444187\pi\)
−0.308940 + 0.951082i \(0.599974\pi\)
\(644\) −2.05526 11.6560i −0.0809885 0.459309i
\(645\) 0 0
\(646\) 13.7979 8.12278i 0.542873 0.319586i
\(647\) 8.88424i 0.349275i 0.984633 + 0.174638i \(0.0558754\pi\)
−0.984633 + 0.174638i \(0.944125\pi\)
\(648\) 0 0
\(649\) −0.774692 + 0.650044i −0.0304093 + 0.0255164i
\(650\) −20.3975 + 5.43410i −0.800054 + 0.213143i
\(651\) 0 0
\(652\) −3.19745 + 3.81057i −0.125222 + 0.149234i
\(653\) −34.1303 19.7051i −1.33562 0.771121i −0.349465 0.936949i \(-0.613637\pi\)
−0.986155 + 0.165829i \(0.946970\pi\)
\(654\) 0 0
\(655\) 3.68402 16.5613i 0.143947 0.647103i
\(656\) 2.52384 14.3134i 0.0985393 0.558844i
\(657\) 0 0
\(658\) −29.2968 16.9145i −1.14211 0.659397i
\(659\) 13.2617 + 11.1279i 0.516603 + 0.433481i 0.863446 0.504442i \(-0.168302\pi\)
−0.346843 + 0.937923i \(0.612746\pi\)
\(660\) 0 0
\(661\) −13.3832 + 4.87107i −0.520544 + 0.189463i −0.588911 0.808198i \(-0.700443\pi\)
0.0683671 + 0.997660i \(0.478221\pi\)
\(662\) −9.40693 11.2107i −0.365611 0.435718i
\(663\) 0 0
\(664\) 7.72138 0.299647
\(665\) −27.4409 24.7565i −1.06411 0.960016i
\(666\) 0 0
\(667\) 25.9569 4.57689i 1.00505 0.177218i
\(668\) −1.26508 1.50766i −0.0489474 0.0583332i
\(669\) 0 0
\(670\) −2.55043 1.05857i −0.0985318 0.0408961i
\(671\) 6.06812 + 5.09176i 0.234257 + 0.196565i
\(672\) 0 0
\(673\) −3.34892 + 1.93350i −0.129091 + 0.0745310i −0.563155 0.826351i \(-0.690413\pi\)
0.434064 + 0.900882i \(0.357079\pi\)
\(674\) 0.878929 4.98466i 0.0338551 0.192002i
\(675\) 0 0
\(676\) −0.268125 0.464407i −0.0103125 0.0178618i
\(677\) 13.6054 + 7.85508i 0.522898 + 0.301895i 0.738119 0.674670i \(-0.235714\pi\)
−0.215222 + 0.976565i \(0.569047\pi\)
\(678\) 0 0
\(679\) 10.9122 + 3.97170i 0.418771 + 0.152420i
\(680\) −19.6487 + 6.17970i −0.753493 + 0.236981i
\(681\) 0 0
\(682\) −7.59353 + 1.33894i −0.290771 + 0.0512708i
\(683\) 11.3613i 0.434727i 0.976091 + 0.217364i \(0.0697458\pi\)
−0.976091 + 0.217364i \(0.930254\pi\)
\(684\) 0 0
\(685\) −0.365462 + 8.23477i −0.0139636 + 0.314634i
\(686\) 0.303829 + 1.72310i 0.0116002 + 0.0657882i
\(687\) 0 0
\(688\) 8.50998 + 23.3810i 0.324440 + 0.891392i
\(689\) 10.8220 + 3.93890i 0.412287 + 0.150060i
\(690\) 0 0
\(691\) 1.00544 1.74147i 0.0382487 0.0662487i −0.846267 0.532758i \(-0.821155\pi\)
0.884516 + 0.466510i \(0.154489\pi\)
\(692\) −2.08077 + 1.20133i −0.0790990 + 0.0456679i
\(693\) 0 0
\(694\) 1.94506 11.0310i 0.0738334 0.418730i
\(695\) −19.2061 36.9594i −0.728531 1.40195i
\(696\) 0 0
\(697\) −10.3024 + 12.2779i −0.390232 + 0.465060i
\(698\) 13.6574 37.5234i 0.516940 1.42028i
\(699\) 0 0
\(700\) 5.50992 + 7.89309i 0.208255 + 0.298331i
\(701\) −2.16414 12.2735i −0.0817385 0.463562i −0.998013 0.0630107i \(-0.979930\pi\)
0.916274 0.400551i \(-0.131181\pi\)
\(702\) 0 0
\(703\) −7.24286 39.1358i −0.273170 1.47604i
\(704\) −10.9737 −0.413586
\(705\) 0 0
\(706\) 24.7704 20.7849i 0.932248 0.782249i
\(707\) 4.83351 + 13.2800i 0.181783 + 0.499444i
\(708\) 0 0
\(709\) 2.69839 + 2.26422i 0.101340 + 0.0850346i 0.692050 0.721849i \(-0.256708\pi\)
−0.590710 + 0.806884i \(0.701152\pi\)
\(710\) 31.5000 + 20.0995i 1.18217 + 0.754322i
\(711\) 0 0
\(712\) 8.14076 + 1.43544i 0.305088 + 0.0537952i
\(713\) 30.8856 + 5.44596i 1.15667 + 0.203953i
\(714\) 0 0
\(715\) 8.06067 + 5.14335i 0.301452 + 0.192350i
\(716\) −3.64756 3.06066i −0.136316 0.114382i
\(717\) 0 0
\(718\) −5.18584 14.2480i −0.193534 0.531730i
\(719\) −18.3135 + 15.3668i −0.682977 + 0.573086i −0.916874 0.399176i \(-0.869296\pi\)
0.233898 + 0.972261i \(0.424852\pi\)
\(720\) 0 0
\(721\) 50.0845 1.86524
\(722\) −19.9012 + 11.9437i −0.740645 + 0.444500i
\(723\) 0 0
\(724\) −1.71931 9.75067i −0.0638975 0.362381i
\(725\) −17.5773 + 12.2701i −0.652803 + 0.455702i
\(726\) 0 0
\(727\) −1.87402 + 5.14882i −0.0695034 + 0.190959i −0.969581 0.244770i \(-0.921287\pi\)
0.900078 + 0.435730i \(0.143510\pi\)
\(728\) −25.8041 + 30.7521i −0.956364 + 1.13975i
\(729\) 0 0
\(730\) 13.9340 + 26.8140i 0.515720 + 0.992429i
\(731\) 4.76461 27.0215i 0.176226 0.999424i
\(732\) 0 0
\(733\) −16.3586 + 9.44464i −0.604218 + 0.348846i −0.770699 0.637199i \(-0.780093\pi\)
0.166481 + 0.986045i \(0.446760\pi\)
\(734\) 3.25016 5.62944i 0.119965 0.207786i
\(735\) 0 0
\(736\) 16.1517 + 5.87874i 0.595360 + 0.216693i
\(737\) 0.427813 + 1.17541i 0.0157587 + 0.0432967i
\(738\) 0 0
\(739\) −6.07048 34.4274i −0.223306 1.26643i −0.865897 0.500223i \(-0.833251\pi\)
0.642590 0.766210i \(-0.277860\pi\)
\(740\) −0.459611 + 10.3562i −0.0168956 + 0.380700i
\(741\) 0 0
\(742\) 15.4355i 0.566655i
\(743\) −27.2185 + 4.79935i −0.998549 + 0.176071i −0.648952 0.760829i \(-0.724792\pi\)
−0.349597 + 0.936900i \(0.613681\pi\)
\(744\) 0 0
\(745\) −3.60028 + 1.13232i −0.131904 + 0.0414851i
\(746\) 22.1605 + 8.06576i 0.811354 + 0.295309i
\(747\) 0 0
\(748\) 1.63596 + 0.944521i 0.0598166 + 0.0345351i
\(749\) −9.73174 16.8559i −0.355590 0.615900i
\(750\) 0 0
\(751\) 9.32641 52.8927i 0.340326 1.93008i −0.0261566 0.999658i \(-0.508327\pi\)
0.366482 0.930425i \(-0.380562\pi\)
\(752\) 17.2464 9.95720i 0.628910 0.363102i
\(753\) 0 0
\(754\) −13.8653 11.6344i −0.504946 0.423700i
\(755\) −2.76515 1.14769i −0.100634 0.0417687i
\(756\) 0 0
\(757\) −15.7996 18.8292i −0.574246 0.684360i 0.398251 0.917277i \(-0.369617\pi\)
−0.972497 + 0.232917i \(0.925173\pi\)
\(758\) 24.6752 4.35090i 0.896242 0.158032i
\(759\) 0 0
\(760\) 28.4060 9.19896i 1.03039 0.333681i
\(761\) 0.906887 0.0328746 0.0164373 0.999865i \(-0.494768\pi\)
0.0164373 + 0.999865i \(0.494768\pi\)
\(762\) 0 0
\(763\) 3.86991 + 4.61197i 0.140100 + 0.166965i
\(764\) 7.39632 2.69204i 0.267589 0.0973945i
\(765\) 0 0
\(766\) 21.2661 + 17.8444i 0.768376 + 0.644744i
\(767\) −2.44621 1.41232i −0.0883275 0.0509959i
\(768\) 0 0
\(769\) −3.70205 + 20.9954i −0.133499 + 0.757113i 0.842393 + 0.538863i \(0.181146\pi\)
−0.975893 + 0.218250i \(0.929965\pi\)
\(770\) −2.78278 + 12.5098i −0.100285 + 0.450822i
\(771\) 0 0
\(772\) 8.72515 + 5.03747i 0.314025 + 0.181302i
\(773\) 10.6726 12.7191i 0.383868 0.457476i −0.539163 0.842201i \(-0.681259\pi\)
0.923031 + 0.384725i \(0.125704\pi\)
\(774\) 0 0
\(775\) −24.6470 + 6.56623i −0.885347 + 0.235866i
\(776\) −7.18685 + 6.03048i −0.257993 + 0.216482i
\(777\) 0 0
\(778\) 6.16282i 0.220948i
\(779\) 14.7832 17.9240i 0.529664 0.642193i
\(780\) 0 0
\(781\) −2.93917 16.6689i −0.105172 0.596460i
\(782\) 14.5157 + 17.2992i 0.519081 + 0.618616i
\(783\) 0 0
\(784\) −18.9041 6.88052i −0.675145 0.245733i
\(785\) −9.13561 + 9.95541i −0.326064 + 0.355324i
\(786\) 0 0
\(787\) −35.8079 + 20.6737i −1.27641 + 0.736938i −0.976187 0.216929i \(-0.930396\pi\)
−0.300228 + 0.953868i \(0.597063\pi\)
\(788\) 12.9858 + 2.28974i 0.462598 + 0.0815685i
\(789\) 0 0
\(790\) 3.35505 1.74347i 0.119367 0.0620297i
\(791\) 38.0757 65.9491i 1.35382 2.34488i
\(792\) 0 0
\(793\) −7.56728 + 20.7909i −0.268722 + 0.738308i
\(794\) 26.3365 9.58570i 0.934647 0.340184i
\(795\) 0 0
\(796\) 0.477501 + 2.70804i 0.0169246 + 0.0959841i
\(797\) 22.7002i 0.804083i 0.915621 + 0.402042i \(0.131699\pi\)
−0.915621 + 0.402042i \(0.868301\pi\)
\(798\) 0 0
\(799\) −21.9608 −0.776916
\(800\) −13.9278 + 1.19837i −0.492420 + 0.0423687i
\(801\) 0 0
\(802\) −9.51134 26.1322i −0.335857 0.922760i
\(803\) 4.68162 12.8626i 0.165211 0.453913i
\(804\) 0 0
\(805\) 28.0386 43.9421i 0.988230 1.54876i
\(806\) −10.7684 18.6514i −0.379299 0.656966i
\(807\) 0 0
\(808\) −11.2440 1.98262i −0.395563 0.0697484i
\(809\) 13.5754 + 23.5133i 0.477285 + 0.826683i 0.999661 0.0260328i \(-0.00828745\pi\)
−0.522376 + 0.852715i \(0.674954\pi\)
\(810\) 0 0
\(811\) −34.6710 29.0925i −1.21746 1.02157i −0.998953 0.0457400i \(-0.985435\pi\)
−0.218512 0.975834i \(-0.570120\pi\)
\(812\) −2.82298 + 7.75609i −0.0990673 + 0.272185i
\(813\) 0 0
\(814\) −10.5724 + 8.87127i −0.370561 + 0.310938i
\(815\) −21.7220 + 2.84389i −0.760889 + 0.0996171i
\(816\) 0 0
\(817\) −6.57493 + 39.2275i −0.230028 + 1.37240i
\(818\) 29.0771i 1.01666i
\(819\) 0 0
\(820\) −4.80360 + 3.68045i −0.167749 + 0.128527i
\(821\) 13.8883 5.05494i 0.484706 0.176419i −0.0880966 0.996112i \(-0.528078\pi\)
0.572802 + 0.819693i \(0.305856\pi\)
\(822\) 0 0
\(823\) 24.5396 29.2452i 0.855398 1.01942i −0.144156 0.989555i \(-0.546047\pi\)
0.999554 0.0298685i \(-0.00950886\pi\)
\(824\) −20.2317 + 35.0424i −0.704805 + 1.22076i
\(825\) 0 0
\(826\) 0.657401 3.72831i 0.0228739 0.129724i
\(827\) −44.6391 7.87107i −1.55225 0.273704i −0.669237 0.743049i \(-0.733379\pi\)
−0.883015 + 0.469345i \(0.844490\pi\)
\(828\) 0 0
\(829\) 18.9638 32.8463i 0.658640 1.14080i −0.322328 0.946628i \(-0.604465\pi\)
0.980968 0.194170i \(-0.0622013\pi\)
\(830\) 5.07276 + 4.65503i 0.176078 + 0.161579i
\(831\) 0 0
\(832\) −10.4832 28.8022i −0.363438 0.998537i
\(833\) 14.2599 + 16.9943i 0.494077 + 0.588818i
\(834\) 0 0
\(835\) 0.384298 8.65919i 0.0132992 0.299664i
\(836\) −2.38300 1.34906i −0.0824179 0.0466581i
\(837\) 0 0
\(838\) 19.1731 3.38074i 0.662324 0.116786i
\(839\) −5.47159 + 4.59121i −0.188900 + 0.158506i −0.732333 0.680946i \(-0.761569\pi\)
0.543433 + 0.839453i \(0.317124\pi\)
\(840\) 0 0
\(841\) 9.97892 + 3.63203i 0.344101 + 0.125242i
\(842\) 2.08361 2.48316i 0.0718061 0.0855752i
\(843\) 0 0
\(844\) 5.10767 + 8.84675i 0.175813 + 0.304518i
\(845\) 0.512817 2.30533i 0.0176415 0.0793059i
\(846\) 0 0
\(847\) −31.0943 + 17.9523i −1.06841 + 0.616849i
\(848\) −7.86916 4.54326i −0.270228 0.156016i
\(849\) 0 0
\(850\) −16.6343 7.78581i −0.570552 0.267051i
\(851\) 52.7493 19.1992i 1.80822 0.658139i
\(852\) 0 0
\(853\) 50.2637 8.86285i 1.72100 0.303458i 0.776047 0.630675i \(-0.217222\pi\)
0.944949 + 0.327217i \(0.106111\pi\)
\(854\) −29.6542 −1.01474
\(855\) 0 0
\(856\) 15.7246 0.537456
\(857\) −13.3975 + 2.36234i −0.457650 + 0.0806961i −0.397721 0.917507i \(-0.630199\pi\)
−0.0599294 + 0.998203i \(0.519088\pi\)
\(858\) 0 0
\(859\) −36.1194 + 13.1464i −1.23238 + 0.448549i −0.874411 0.485185i \(-0.838752\pi\)
−0.357967 + 0.933734i \(0.616530\pi\)
\(860\) 3.97135 9.56825i 0.135422 0.326275i
\(861\) 0 0
\(862\) 35.2523 + 20.3529i 1.20070 + 0.693224i
\(863\) −47.0645 + 27.1727i −1.60210 + 0.924970i −0.611028 + 0.791609i \(0.709244\pi\)
−0.991067 + 0.133362i \(0.957423\pi\)
\(864\) 0 0
\(865\) −10.3290 2.29768i −0.351198 0.0781233i
\(866\) −13.6696 23.6764i −0.464511 0.804556i
\(867\) 0 0
\(868\) −6.31288 + 7.52340i −0.214273 + 0.255361i
\(869\) −1.60942 0.585779i −0.0545957 0.0198712i
\(870\) 0 0
\(871\) −2.67636 + 2.24573i −0.0906850 + 0.0760937i
\(872\) −4.79009 + 0.844622i −0.162213 + 0.0286025i
\(873\) 0 0
\(874\) −21.2536 24.8979i −0.718914 0.842184i
\(875\) −5.62400 + 42.0189i −0.190126 + 1.42050i
\(876\) 0 0
\(877\) 8.69855 + 10.3665i 0.293729 + 0.350053i 0.892646 0.450759i \(-0.148846\pi\)
−0.598917 + 0.800811i \(0.704402\pi\)
\(878\) −7.29327 20.0381i −0.246136 0.676253i
\(879\) 0 0
\(880\) −5.55853 5.10081i −0.187378 0.171948i
\(881\) −13.9789 + 24.2121i −0.470960 + 0.815726i −0.999448 0.0332142i \(-0.989426\pi\)
0.528488 + 0.848940i \(0.322759\pi\)
\(882\) 0 0
\(883\) −53.7200 9.47229i −1.80782 0.318768i −0.834987 0.550269i \(-0.814525\pi\)
−0.972835 + 0.231501i \(0.925636\pi\)
\(884\) −0.916220 + 5.19614i −0.0308158 + 0.174765i
\(885\) 0 0
\(886\) 0.915328 1.58539i 0.0307510 0.0532624i
\(887\) −23.1261 + 27.5606i −0.776497 + 0.925393i −0.998770 0.0495912i \(-0.984208\pi\)
0.222272 + 0.974985i \(0.428653\pi\)
\(888\) 0 0
\(889\) 12.3036 4.47815i 0.412650 0.150192i
\(890\) 4.48289 + 5.85092i 0.150267 + 0.196123i
\(891\) 0 0
\(892\) 5.50867i 0.184444i
\(893\) 31.8333 0.269519i 1.06526 0.00901912i
\(894\) 0 0
\(895\) −2.72223 20.7927i −0.0909940 0.695024i
\(896\) 15.2276 12.7774i 0.508717 0.426864i
\(897\) 0 0
\(898\) 5.00998 13.7648i 0.167185 0.459337i
\(899\) −16.7540 14.0583i −0.558777 0.468870i
\(900\) 0 0
\(901\) 5.01012 + 8.67778i 0.166911 + 0.289099i
\(902\) −7.93422 1.39902i −0.264181 0.0465822i
\(903\) 0 0
\(904\) 30.7615 + 53.2804i 1.02311 + 1.77208i
\(905\) 23.4554 36.7593i 0.779683 1.22192i
\(906\) 0 0
\(907\) −1.50616 + 4.13814i −0.0500112 + 0.137405i −0.962183 0.272403i \(-0.912182\pi\)
0.912172 + 0.409807i \(0.134404\pi\)
\(908\) 1.52507 + 4.19009i 0.0506111 + 0.139053i
\(909\) 0 0
\(910\) −35.4924 + 4.64674i −1.17656 + 0.154038i
\(911\) 14.2563 0.472333 0.236166 0.971713i \(-0.424109\pi\)
0.236166 + 0.971713i \(0.424109\pi\)
\(912\) 0 0
\(913\) 3.11870i 0.103214i
\(914\) 2.74645 + 15.5759i 0.0908444 + 0.515204i
\(915\) 0 0
\(916\) 8.62726 3.14006i 0.285053 0.103751i
\(917\) 9.83996 27.0351i 0.324944 0.892777i
\(918\) 0 0
\(919\) −14.3638 + 24.8789i −0.473819 + 0.820678i −0.999551 0.0299723i \(-0.990458\pi\)
0.525732 + 0.850650i \(0.323791\pi\)
\(920\) 19.4185 + 37.3681i 0.640209 + 1.23199i
\(921\) 0 0
\(922\) −16.6836 2.94177i −0.549446 0.0968821i
\(923\) 40.9424 23.6381i 1.34764 0.778058i
\(924\) 0 0
\(925\) −32.3287 + 32.2360i −1.06296 + 1.05991i
\(926\) 4.80372 + 1.74841i 0.157860 + 0.0574563i
\(927\) 0 0
\(928\) −7.70479 9.18221i −0.252922 0.301421i
\(929\) −5.32975 30.2265i −0.174864 0.991700i −0.938301 0.345819i \(-0.887601\pi\)
0.763438 0.645881i \(-0.223510\pi\)
\(930\) 0 0
\(931\) −20.8791 24.4592i −0.684285 0.801617i
\(932\) 13.3866i 0.438494i
\(933\) 0 0
\(934\) 21.8056 18.2971i 0.713502 0.598699i
\(935\) 2.49601 + 7.93621i 0.0816284 + 0.259542i
\(936\) 0 0
\(937\) 32.4167 38.6327i 1.05901 1.26208i 0.0952059 0.995458i \(-0.469649\pi\)
0.963802 0.266619i \(-0.0859065\pi\)
\(938\) −4.05526 2.34131i −0.132409 0.0764463i
\(939\) 0 0
\(940\) −8.09373 1.80044i −0.263988 0.0587237i
\(941\) −1.48399 + 8.41611i −0.0483766 + 0.274357i −0.999395 0.0347766i \(-0.988928\pi\)
0.951019 + 0.309134i \(0.100039\pi\)
\(942\) 0 0
\(943\) 28.3789 + 16.3846i 0.924144 + 0.533555i
\(944\) 1.70723 + 1.43253i 0.0555655 + 0.0466250i
\(945\) 0 0
\(946\) 12.9606 4.71726i 0.421385 0.153371i
\(947\) −13.2302 15.7671i −0.429923 0.512362i 0.506977 0.861959i \(-0.330763\pi\)
−0.936900 + 0.349597i \(0.886318\pi\)
\(948\) 0 0
\(949\) 38.2325 1.24108
\(950\) 24.2079 + 11.0818i 0.785408 + 0.359541i
\(951\) 0 0
\(952\) −34.3976 + 6.06522i −1.11483 + 0.196575i
\(953\) 38.0480 + 45.3438i 1.23249 + 1.46883i 0.834098 + 0.551617i \(0.185989\pi\)
0.398397 + 0.917213i \(0.369567\pi\)
\(954\) 0 0
\(955\) 32.0162 + 13.2885i 1.03602 + 0.430005i
\(956\) −3.56620 2.99239i −0.115339 0.0967810i
\(957\) 0 0
\(958\) 37.1511 21.4492i 1.20030 0.692993i
\(959\) −2.42722 + 13.7654i −0.0783790 + 0.444510i
\(960\) 0 0
\(961\) 2.48818 + 4.30965i 0.0802638 + 0.139021i
\(962\) −33.3839 19.2742i −1.07634 0.621425i
\(963\) 0 0
\(964\) −12.6513 4.60471i −0.407472 0.148308i
\(965\) 13.3121 + 42.3267i 0.428533 + 1.36254i
\(966\) 0 0
\(967\) −10.8299 + 1.90960i −0.348266 + 0.0614087i −0.345045 0.938586i \(-0.612136\pi\)
−0.00322103 + 0.999995i \(0.501025\pi\)
\(968\) 29.0075i 0.932335i
\(969\) 0 0
\(970\) −8.35722 0.370897i −0.268334 0.0119088i
\(971\) −5.62086 31.8775i −0.180382 1.02300i −0.931746 0.363109i \(-0.881715\pi\)
0.751365 0.659887i \(-0.229396\pi\)
\(972\) 0 0
\(973\) −24.1572 66.3713i −0.774444 2.12777i
\(974\) −38.3644 13.9635i −1.22927 0.447419i
\(975\) 0 0
\(976\) 8.72836 15.1180i 0.279388 0.483914i
\(977\) 9.61615 5.55189i 0.307648 0.177621i −0.338226 0.941065i \(-0.609827\pi\)
0.645873 + 0.763445i \(0.276493\pi\)
\(978\) 0 0
\(979\) 0.579780 3.28810i 0.0185298 0.105088i
\(980\) 3.86229 + 7.43242i 0.123376 + 0.237420i
\(981\) 0 0
\(982\) −13.7718 + 16.4125i −0.439474 + 0.523745i
\(983\) 4.28627 11.7764i 0.136711 0.375610i −0.852379 0.522925i \(-0.824841\pi\)
0.989090 + 0.147315i \(0.0470630\pi\)
\(984\) 0 0
\(985\) 35.3191 + 46.0973i 1.12536 + 1.46878i
\(986\) −2.73465 15.5090i −0.0870889 0.493906i
\(987\) 0 0
\(988\) 1.26434 7.54333i 0.0402240 0.239985i
\(989\) −56.0984 −1.78383
\(990\) 0 0
\(991\) 28.1596 23.6287i 0.894519 0.750591i −0.0745922 0.997214i \(-0.523766\pi\)
0.969111 + 0.246623i \(0.0793211\pi\)
\(992\) −4.87807 13.4024i −0.154879 0.425527i
\(993\) 0 0
\(994\) 48.5394 + 40.7294i 1.53958 + 1.29186i
\(995\) −6.51424 + 10.2091i −0.206515 + 0.323651i
\(996\) 0 0
\(997\) 24.1082 + 4.25092i 0.763513 + 0.134628i 0.541827 0.840490i \(-0.317733\pi\)
0.221686 + 0.975118i \(0.428844\pi\)
\(998\) −39.3185 6.93291i −1.24461 0.219458i
\(999\) 0 0
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 855.2.da.b.199.3 48
3.2 odd 2 95.2.p.a.9.6 yes 48
5.4 even 2 inner 855.2.da.b.199.6 48
15.2 even 4 475.2.l.f.351.6 48
15.8 even 4 475.2.l.f.351.3 48
15.14 odd 2 95.2.p.a.9.3 48
19.17 even 9 inner 855.2.da.b.739.6 48
57.17 odd 18 95.2.p.a.74.3 yes 48
57.32 even 18 1805.2.b.l.1084.17 24
57.44 odd 18 1805.2.b.k.1084.8 24
95.74 even 18 inner 855.2.da.b.739.3 48
285.17 even 36 475.2.l.f.226.6 48
285.32 odd 36 9025.2.a.ct.1.8 24
285.44 odd 18 1805.2.b.k.1084.17 24
285.74 odd 18 95.2.p.a.74.6 yes 48
285.89 even 18 1805.2.b.l.1084.8 24
285.158 even 36 9025.2.a.cu.1.8 24
285.188 even 36 475.2.l.f.226.3 48
285.203 odd 36 9025.2.a.ct.1.17 24
285.272 even 36 9025.2.a.cu.1.17 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.p.a.9.3 48 15.14 odd 2
95.2.p.a.9.6 yes 48 3.2 odd 2
95.2.p.a.74.3 yes 48 57.17 odd 18
95.2.p.a.74.6 yes 48 285.74 odd 18
475.2.l.f.226.3 48 285.188 even 36
475.2.l.f.226.6 48 285.17 even 36
475.2.l.f.351.3 48 15.8 even 4
475.2.l.f.351.6 48 15.2 even 4
855.2.da.b.199.3 48 1.1 even 1 trivial
855.2.da.b.199.6 48 5.4 even 2 inner
855.2.da.b.739.3 48 95.74 even 18 inner
855.2.da.b.739.6 48 19.17 even 9 inner
1805.2.b.k.1084.8 24 57.44 odd 18
1805.2.b.k.1084.17 24 285.44 odd 18
1805.2.b.l.1084.8 24 285.89 even 18
1805.2.b.l.1084.17 24 57.32 even 18
9025.2.a.ct.1.8 24 285.32 odd 36
9025.2.a.ct.1.17 24 285.203 odd 36
9025.2.a.cu.1.8 24 285.158 even 36
9025.2.a.cu.1.17 24 285.272 even 36