Properties

Label 912.2.cc.d.401.1
Level $912$
Weight $2$
Character 912.401
Analytic conductor $7.282$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [912,2,Mod(257,912)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(912, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 0, 9, 17]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("912.257");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.cc (of order \(18\), degree \(6\), not 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: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(3\) over \(\Q(\zeta_{18})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} - x^{15} - 18 x^{14} + 36 x^{13} + 10 x^{12} + 18 x^{11} + 90 x^{10} - 567 x^{9} + 270 x^{8} + 162 x^{7} + 270 x^{6} + 2916 x^{5} - 4374 x^{4} - 729 x^{3} + 19683 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 114)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 401.1
Root \(0.0786547 + 1.73026i\) of defining polynomial
Character \(\chi\) \(=\) 912.401
Dual form 912.2.cc.d.257.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.53778 + 0.797015i) q^{3} +(0.258510 + 0.710252i) q^{5} +(-0.777943 - 1.34744i) q^{7} +(1.72953 - 2.45127i) q^{9} +O(q^{10})\) \(q+(-1.53778 + 0.797015i) q^{3} +(0.258510 + 0.710252i) q^{5} +(-0.777943 - 1.34744i) q^{7} +(1.72953 - 2.45127i) q^{9} +(0.832399 + 0.480586i) q^{11} +(0.416982 + 0.496940i) q^{13} +(-0.963613 - 0.886174i) q^{15} +(-6.73013 - 1.18670i) q^{17} +(4.14364 - 1.35288i) q^{19} +(2.27023 + 1.45203i) q^{21} +(0.400647 - 1.10077i) q^{23} +(3.39259 - 2.84672i) q^{25} +(-0.705946 + 5.14797i) q^{27} +(-1.39666 - 7.92086i) q^{29} +(2.63927 - 1.52379i) q^{31} +(-1.66308 - 0.0756007i) q^{33} +(0.755913 - 0.900862i) q^{35} +4.12648i q^{37} +(-1.03729 - 0.431843i) q^{39} +(4.09755 + 3.43825i) q^{41} +(7.34330 - 2.67274i) q^{43} +(2.18812 + 0.594726i) q^{45} +(-3.11004 + 0.548383i) q^{47} +(2.28961 - 3.96572i) q^{49} +(11.2953 - 3.53912i) q^{51} +(13.6276 + 4.96002i) q^{53} +(-0.126153 + 0.715449i) q^{55} +(-5.29374 + 5.38297i) q^{57} +(2.02192 - 11.4669i) q^{59} +(10.1813 + 3.70568i) q^{61} +(-4.64841 - 0.423492i) q^{63} +(-0.245158 + 0.424626i) q^{65} +(9.19012 - 1.62047i) q^{67} +(0.261222 + 2.01206i) q^{69} +(0.0322101 - 0.0117235i) q^{71} +(-3.04446 - 2.55461i) q^{73} +(-2.94818 + 7.08158i) q^{75} -1.49547i q^{77} +(0.893115 - 1.06437i) q^{79} +(-3.01742 - 8.47910i) q^{81} +(-10.4856 + 6.05389i) q^{83} +(-0.896950 - 5.08686i) q^{85} +(8.46081 + 11.0674i) q^{87} +(-4.68075 + 3.92762i) q^{89} +(0.345207 - 0.948448i) q^{91} +(-2.84414 + 4.44679i) q^{93} +(2.03206 + 2.59329i) q^{95} +(9.54804 + 1.68358i) q^{97} +(2.61771 - 1.20924i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q+O(q^{10}) \) Copy content Toggle raw display \( 18 q - 12 q^{13} + 24 q^{15} - 6 q^{17} + 6 q^{19} - 18 q^{25} + 3 q^{27} + 6 q^{29} - 27 q^{33} - 24 q^{35} - 6 q^{39} - 3 q^{41} + 6 q^{43} + 54 q^{45} + 30 q^{47} + 21 q^{49} + 33 q^{51} + 60 q^{53} - 30 q^{55} + 12 q^{57} + 3 q^{59} + 54 q^{61} - 84 q^{63} - 24 q^{65} + 15 q^{67} + 24 q^{69} + 36 q^{71} - 42 q^{73} + 6 q^{79} + 36 q^{83} + 54 q^{87} + 60 q^{89} + 18 q^{91} - 84 q^{93} + 6 q^{95} + 9 q^{97} + 30 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{1}{18}\right)\) \(1\) \(-1\) \(1\)

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 0
\(3\) −1.53778 + 0.797015i −0.887838 + 0.460157i
\(4\) 0 0
\(5\) 0.258510 + 0.710252i 0.115609 + 0.317634i 0.983979 0.178283i \(-0.0570542\pi\)
−0.868370 + 0.495917i \(0.834832\pi\)
\(6\) 0 0
\(7\) −0.777943 1.34744i −0.294035 0.509283i 0.680725 0.732539i \(-0.261665\pi\)
−0.974760 + 0.223256i \(0.928331\pi\)
\(8\) 0 0
\(9\) 1.72953 2.45127i 0.576511 0.817089i
\(10\) 0 0
\(11\) 0.832399 + 0.480586i 0.250978 + 0.144902i 0.620212 0.784434i \(-0.287047\pi\)
−0.369234 + 0.929336i \(0.620380\pi\)
\(12\) 0 0
\(13\) 0.416982 + 0.496940i 0.115650 + 0.137826i 0.820763 0.571268i \(-0.193548\pi\)
−0.705113 + 0.709095i \(0.749104\pi\)
\(14\) 0 0
\(15\) −0.963613 0.886174i −0.248804 0.228809i
\(16\) 0 0
\(17\) −6.73013 1.18670i −1.63230 0.287818i −0.718968 0.695043i \(-0.755385\pi\)
−0.913328 + 0.407226i \(0.866496\pi\)
\(18\) 0 0
\(19\) 4.14364 1.35288i 0.950615 0.310371i
\(20\) 0 0
\(21\) 2.27023 + 1.45203i 0.495405 + 0.316859i
\(22\) 0 0
\(23\) 0.400647 1.10077i 0.0835407 0.229526i −0.890888 0.454223i \(-0.849917\pi\)
0.974429 + 0.224697i \(0.0721392\pi\)
\(24\) 0 0
\(25\) 3.39259 2.84672i 0.678519 0.569345i
\(26\) 0 0
\(27\) −0.705946 + 5.14797i −0.135859 + 0.990728i
\(28\) 0 0
\(29\) −1.39666 7.92086i −0.259354 1.47087i −0.784645 0.619945i \(-0.787155\pi\)
0.525292 0.850922i \(-0.323956\pi\)
\(30\) 0 0
\(31\) 2.63927 1.52379i 0.474028 0.273680i −0.243897 0.969801i \(-0.578426\pi\)
0.717924 + 0.696121i \(0.245092\pi\)
\(32\) 0 0
\(33\) −1.66308 0.0756007i −0.289505 0.0131604i
\(34\) 0 0
\(35\) 0.755913 0.900862i 0.127773 0.152273i
\(36\) 0 0
\(37\) 4.12648i 0.678389i 0.940716 + 0.339195i \(0.110154\pi\)
−0.940716 + 0.339195i \(0.889846\pi\)
\(38\) 0 0
\(39\) −1.03729 0.431843i −0.166100 0.0691502i
\(40\) 0 0
\(41\) 4.09755 + 3.43825i 0.639929 + 0.536964i 0.903996 0.427540i \(-0.140620\pi\)
−0.264067 + 0.964504i \(0.585064\pi\)
\(42\) 0 0
\(43\) 7.34330 2.67274i 1.11984 0.407589i 0.285248 0.958454i \(-0.407924\pi\)
0.834595 + 0.550865i \(0.185702\pi\)
\(44\) 0 0
\(45\) 2.18812 + 0.594726i 0.326186 + 0.0886566i
\(46\) 0 0
\(47\) −3.11004 + 0.548383i −0.453646 + 0.0799899i −0.395802 0.918336i \(-0.629533\pi\)
−0.0578432 + 0.998326i \(0.518422\pi\)
\(48\) 0 0
\(49\) 2.28961 3.96572i 0.327087 0.566531i
\(50\) 0 0
\(51\) 11.2953 3.53912i 1.58165 0.495576i
\(52\) 0 0
\(53\) 13.6276 + 4.96002i 1.87189 + 0.681312i 0.966462 + 0.256809i \(0.0826711\pi\)
0.905427 + 0.424503i \(0.139551\pi\)
\(54\) 0 0
\(55\) −0.126153 + 0.715449i −0.0170105 + 0.0964711i
\(56\) 0 0
\(57\) −5.29374 + 5.38297i −0.701173 + 0.712991i
\(58\) 0 0
\(59\) 2.02192 11.4669i 0.263231 1.49286i −0.510793 0.859704i \(-0.670648\pi\)
0.774024 0.633156i \(-0.218241\pi\)
\(60\) 0 0
\(61\) 10.1813 + 3.70568i 1.30358 + 0.474464i 0.898161 0.439667i \(-0.144903\pi\)
0.405419 + 0.914131i \(0.367126\pi\)
\(62\) 0 0
\(63\) −4.64841 0.423492i −0.585644 0.0533549i
\(64\) 0 0
\(65\) −0.245158 + 0.424626i −0.0304081 + 0.0526684i
\(66\) 0 0
\(67\) 9.19012 1.62047i 1.12275 0.197972i 0.418703 0.908123i \(-0.362485\pi\)
0.704049 + 0.710151i \(0.251374\pi\)
\(68\) 0 0
\(69\) 0.261222 + 2.01206i 0.0314475 + 0.242224i
\(70\) 0 0
\(71\) 0.0322101 0.0117235i 0.00382263 0.00139132i −0.340108 0.940386i \(-0.610464\pi\)
0.343931 + 0.938995i \(0.388241\pi\)
\(72\) 0 0
\(73\) −3.04446 2.55461i −0.356327 0.298994i 0.446998 0.894535i \(-0.352493\pi\)
−0.803325 + 0.595541i \(0.796938\pi\)
\(74\) 0 0
\(75\) −2.94818 + 7.08158i −0.340426 + 0.817711i
\(76\) 0 0
\(77\) 1.49547i 0.170425i
\(78\) 0 0
\(79\) 0.893115 1.06437i 0.100483 0.119751i −0.713459 0.700697i \(-0.752873\pi\)
0.813943 + 0.580945i \(0.197317\pi\)
\(80\) 0 0
\(81\) −3.01742 8.47910i −0.335269 0.942122i
\(82\) 0 0
\(83\) −10.4856 + 6.05389i −1.15095 + 0.664500i −0.949118 0.314920i \(-0.898022\pi\)
−0.201830 + 0.979421i \(0.564689\pi\)
\(84\) 0 0
\(85\) −0.896950 5.08686i −0.0972879 0.551747i
\(86\) 0 0
\(87\) 8.46081 + 11.0674i 0.907094 + 1.18655i
\(88\) 0 0
\(89\) −4.68075 + 3.92762i −0.496159 + 0.416327i −0.856227 0.516599i \(-0.827198\pi\)
0.360069 + 0.932926i \(0.382753\pi\)
\(90\) 0 0
\(91\) 0.345207 0.948448i 0.0361875 0.0994243i
\(92\) 0 0
\(93\) −2.84414 + 4.44679i −0.294924 + 0.461110i
\(94\) 0 0
\(95\) 2.03206 + 2.59329i 0.208485 + 0.266066i
\(96\) 0 0
\(97\) 9.54804 + 1.68358i 0.969457 + 0.170941i 0.635885 0.771784i \(-0.280635\pi\)
0.333571 + 0.942725i \(0.391746\pi\)
\(98\) 0 0
\(99\) 2.61771 1.20924i 0.263089 0.121533i
\(100\) 0 0
\(101\) −12.0945 14.4137i −1.20345 1.43422i −0.871130 0.491053i \(-0.836612\pi\)
−0.332323 0.943166i \(-0.607832\pi\)
\(102\) 0 0
\(103\) −9.92876 5.73237i −0.978310 0.564828i −0.0765505 0.997066i \(-0.524391\pi\)
−0.901759 + 0.432238i \(0.857724\pi\)
\(104\) 0 0
\(105\) −0.444427 + 1.98780i −0.0433716 + 0.193990i
\(106\) 0 0
\(107\) −1.17826 2.04080i −0.113906 0.197292i 0.803436 0.595392i \(-0.203003\pi\)
−0.917342 + 0.398100i \(0.869670\pi\)
\(108\) 0 0
\(109\) −2.21678 6.09056i −0.212329 0.583370i 0.787111 0.616811i \(-0.211576\pi\)
−0.999441 + 0.0334410i \(0.989353\pi\)
\(110\) 0 0
\(111\) −3.28887 6.34562i −0.312165 0.602299i
\(112\) 0 0
\(113\) 10.0387 0.944358 0.472179 0.881503i \(-0.343468\pi\)
0.472179 + 0.881503i \(0.343468\pi\)
\(114\) 0 0
\(115\) 0.885394 0.0825635
\(116\) 0 0
\(117\) 1.93932 0.162660i 0.179290 0.0150379i
\(118\) 0 0
\(119\) 3.63665 + 9.99161i 0.333371 + 0.915929i
\(120\) 0 0
\(121\) −5.03807 8.72620i −0.458007 0.793291i
\(122\) 0 0
\(123\) −9.04146 2.02147i −0.815241 0.182269i
\(124\) 0 0
\(125\) 6.17177 + 3.56327i 0.552020 + 0.318709i
\(126\) 0 0
\(127\) −8.95146 10.6679i −0.794313 0.946626i 0.205171 0.978726i \(-0.434225\pi\)
−0.999485 + 0.0321003i \(0.989780\pi\)
\(128\) 0 0
\(129\) −9.16216 + 9.96280i −0.806683 + 0.877176i
\(130\) 0 0
\(131\) 10.9610 + 1.93273i 0.957671 + 0.168863i 0.630575 0.776128i \(-0.282819\pi\)
0.327096 + 0.944991i \(0.393930\pi\)
\(132\) 0 0
\(133\) −5.04643 4.53083i −0.437581 0.392873i
\(134\) 0 0
\(135\) −3.83885 + 0.829406i −0.330396 + 0.0713839i
\(136\) 0 0
\(137\) 1.69757 4.66403i 0.145033 0.398475i −0.845812 0.533482i \(-0.820883\pi\)
0.990845 + 0.135007i \(0.0431056\pi\)
\(138\) 0 0
\(139\) 2.76202 2.31761i 0.234272 0.196577i −0.518093 0.855325i \(-0.673358\pi\)
0.752364 + 0.658747i \(0.228913\pi\)
\(140\) 0 0
\(141\) 4.34548 3.32204i 0.365956 0.279766i
\(142\) 0 0
\(143\) 0.108273 + 0.614047i 0.00905425 + 0.0513492i
\(144\) 0 0
\(145\) 5.26475 3.03961i 0.437214 0.252426i
\(146\) 0 0
\(147\) −0.360177 + 7.92326i −0.0297069 + 0.653499i
\(148\) 0 0
\(149\) −12.3170 + 14.6788i −1.00904 + 1.20253i −0.0298610 + 0.999554i \(0.509506\pi\)
−0.979183 + 0.202978i \(0.934938\pi\)
\(150\) 0 0
\(151\) 19.2624i 1.56755i 0.621042 + 0.783777i \(0.286710\pi\)
−0.621042 + 0.783777i \(0.713290\pi\)
\(152\) 0 0
\(153\) −14.5489 + 14.4449i −1.17621 + 1.16780i
\(154\) 0 0
\(155\) 1.76455 + 1.48063i 0.141732 + 0.118927i
\(156\) 0 0
\(157\) −0.200940 + 0.0731363i −0.0160368 + 0.00583691i −0.350026 0.936740i \(-0.613827\pi\)
0.333989 + 0.942577i \(0.391605\pi\)
\(158\) 0 0
\(159\) −24.9094 + 3.23394i −1.97544 + 0.256468i
\(160\) 0 0
\(161\) −1.79490 + 0.316489i −0.141458 + 0.0249428i
\(162\) 0 0
\(163\) −7.51668 + 13.0193i −0.588752 + 1.01975i 0.405645 + 0.914031i \(0.367047\pi\)
−0.994396 + 0.105717i \(0.966286\pi\)
\(164\) 0 0
\(165\) −0.376228 1.20075i −0.0292893 0.0934782i
\(166\) 0 0
\(167\) −8.87982 3.23199i −0.687141 0.250099i −0.0252305 0.999682i \(-0.508032\pi\)
−0.661911 + 0.749583i \(0.730254\pi\)
\(168\) 0 0
\(169\) 2.18435 12.3881i 0.168027 0.952929i
\(170\) 0 0
\(171\) 3.85030 12.4970i 0.294440 0.955670i
\(172\) 0 0
\(173\) −2.33529 + 13.2441i −0.177549 + 1.00693i 0.757612 + 0.652705i \(0.226366\pi\)
−0.935161 + 0.354224i \(0.884745\pi\)
\(174\) 0 0
\(175\) −6.47502 2.35672i −0.489466 0.178151i
\(176\) 0 0
\(177\) 6.03000 + 19.2450i 0.453243 + 1.44655i
\(178\) 0 0
\(179\) 8.34644 14.4565i 0.623842 1.08053i −0.364921 0.931038i \(-0.618904\pi\)
0.988764 0.149488i \(-0.0477625\pi\)
\(180\) 0 0
\(181\) −10.0398 + 1.77029i −0.746251 + 0.131584i −0.533828 0.845593i \(-0.679247\pi\)
−0.212424 + 0.977178i \(0.568136\pi\)
\(182\) 0 0
\(183\) −18.6101 + 2.41611i −1.37570 + 0.178604i
\(184\) 0 0
\(185\) −2.93084 + 1.06674i −0.215480 + 0.0784281i
\(186\) 0 0
\(187\) −5.03184 4.22221i −0.367964 0.308759i
\(188\) 0 0
\(189\) 7.48576 3.05361i 0.544509 0.222118i
\(190\) 0 0
\(191\) 12.0667i 0.873115i 0.899676 + 0.436558i \(0.143802\pi\)
−0.899676 + 0.436558i \(0.856198\pi\)
\(192\) 0 0
\(193\) −2.14990 + 2.56215i −0.154753 + 0.184427i −0.837850 0.545900i \(-0.816188\pi\)
0.683098 + 0.730327i \(0.260632\pi\)
\(194\) 0 0
\(195\) 0.0385657 0.848376i 0.00276175 0.0607535i
\(196\) 0 0
\(197\) −5.15098 + 2.97392i −0.366992 + 0.211883i −0.672144 0.740421i \(-0.734626\pi\)
0.305151 + 0.952304i \(0.401293\pi\)
\(198\) 0 0
\(199\) −1.94088 11.0073i −0.137585 0.780286i −0.973024 0.230703i \(-0.925898\pi\)
0.835439 0.549583i \(-0.185214\pi\)
\(200\) 0 0
\(201\) −12.8409 + 9.81659i −0.905724 + 0.692409i
\(202\) 0 0
\(203\) −9.58634 + 8.04389i −0.672829 + 0.564571i
\(204\) 0 0
\(205\) −1.38276 + 3.79911i −0.0965764 + 0.265342i
\(206\) 0 0
\(207\) −2.00535 2.88591i −0.139381 0.200585i
\(208\) 0 0
\(209\) 4.09933 + 0.865240i 0.283557 + 0.0598499i
\(210\) 0 0
\(211\) 20.9377 + 3.69188i 1.44141 + 0.254159i 0.839045 0.544063i \(-0.183115\pi\)
0.602364 + 0.798222i \(0.294226\pi\)
\(212\) 0 0
\(213\) −0.0401882 + 0.0437001i −0.00275365 + 0.00299428i
\(214\) 0 0
\(215\) 3.79664 + 4.52466i 0.258928 + 0.308579i
\(216\) 0 0
\(217\) −4.10641 2.37084i −0.278761 0.160943i
\(218\) 0 0
\(219\) 6.71777 + 1.50194i 0.453945 + 0.101492i
\(220\) 0 0
\(221\) −2.21662 3.83930i −0.149106 0.258259i
\(222\) 0 0
\(223\) −4.71184 12.9457i −0.315528 0.866907i −0.991515 0.129993i \(-0.958505\pi\)
0.675987 0.736914i \(-0.263718\pi\)
\(224\) 0 0
\(225\) −1.11047 13.2397i −0.0740316 0.882644i
\(226\) 0 0
\(227\) 16.1886 1.07448 0.537238 0.843430i \(-0.319468\pi\)
0.537238 + 0.843430i \(0.319468\pi\)
\(228\) 0 0
\(229\) −25.6462 −1.69475 −0.847374 0.530997i \(-0.821817\pi\)
−0.847374 + 0.530997i \(0.821817\pi\)
\(230\) 0 0
\(231\) 1.19191 + 2.29971i 0.0784222 + 0.151310i
\(232\) 0 0
\(233\) −3.98107 10.9379i −0.260808 0.716565i −0.999113 0.0420981i \(-0.986596\pi\)
0.738305 0.674467i \(-0.235626\pi\)
\(234\) 0 0
\(235\) −1.19347 2.06715i −0.0778532 0.134846i
\(236\) 0 0
\(237\) −0.525093 + 2.34860i −0.0341085 + 0.152558i
\(238\) 0 0
\(239\) −13.1831 7.61128i −0.852746 0.492333i 0.00883069 0.999961i \(-0.497189\pi\)
−0.861576 + 0.507628i \(0.830522\pi\)
\(240\) 0 0
\(241\) 9.76016 + 11.6317i 0.628707 + 0.749264i 0.982541 0.186044i \(-0.0595666\pi\)
−0.353834 + 0.935308i \(0.615122\pi\)
\(242\) 0 0
\(243\) 11.3981 + 10.6341i 0.731189 + 0.682175i
\(244\) 0 0
\(245\) 3.40855 + 0.601019i 0.217764 + 0.0383977i
\(246\) 0 0
\(247\) 2.40012 + 1.49501i 0.152716 + 0.0951254i
\(248\) 0 0
\(249\) 11.2996 17.6668i 0.716081 1.11958i
\(250\) 0 0
\(251\) −3.71032 + 10.1940i −0.234193 + 0.643441i 0.765807 + 0.643071i \(0.222340\pi\)
−1.00000 0.000369965i \(0.999882\pi\)
\(252\) 0 0
\(253\) 0.862512 0.723733i 0.0542257 0.0455007i
\(254\) 0 0
\(255\) 5.43361 + 7.10759i 0.340266 + 0.445094i
\(256\) 0 0
\(257\) 0.00786014 + 0.0445771i 0.000490302 + 0.00278064i 0.985052 0.172258i \(-0.0551062\pi\)
−0.984562 + 0.175038i \(0.943995\pi\)
\(258\) 0 0
\(259\) 5.56017 3.21017i 0.345492 0.199470i
\(260\) 0 0
\(261\) −21.8317 10.2758i −1.35135 0.636057i
\(262\) 0 0
\(263\) −3.52577 + 4.20185i −0.217408 + 0.259097i −0.863715 0.503981i \(-0.831868\pi\)
0.646307 + 0.763078i \(0.276313\pi\)
\(264\) 0 0
\(265\) 10.9612i 0.673342i
\(266\) 0 0
\(267\) 4.06760 9.77044i 0.248933 0.597941i
\(268\) 0 0
\(269\) −1.50432 1.26228i −0.0917202 0.0769623i 0.595775 0.803152i \(-0.296845\pi\)
−0.687495 + 0.726189i \(0.741290\pi\)
\(270\) 0 0
\(271\) −19.8494 + 7.22458i −1.20576 + 0.438862i −0.865232 0.501371i \(-0.832829\pi\)
−0.340531 + 0.940233i \(0.610607\pi\)
\(272\) 0 0
\(273\) 0.225075 + 1.73364i 0.0136222 + 0.104925i
\(274\) 0 0
\(275\) 4.19208 0.739177i 0.252792 0.0445741i
\(276\) 0 0
\(277\) −3.91899 + 6.78789i −0.235469 + 0.407845i −0.959409 0.282018i \(-0.908996\pi\)
0.723940 + 0.689863i \(0.242329\pi\)
\(278\) 0 0
\(279\) 0.829509 9.10501i 0.0496614 0.545102i
\(280\) 0 0
\(281\) 11.0064 + 4.00600i 0.656587 + 0.238978i 0.648762 0.760991i \(-0.275287\pi\)
0.00782495 + 0.999969i \(0.497509\pi\)
\(282\) 0 0
\(283\) −1.21905 + 6.91356i −0.0724648 + 0.410968i 0.926899 + 0.375310i \(0.122464\pi\)
−0.999364 + 0.0356581i \(0.988647\pi\)
\(284\) 0 0
\(285\) −5.19175 2.36833i −0.307533 0.140288i
\(286\) 0 0
\(287\) 1.44517 8.19595i 0.0853055 0.483791i
\(288\) 0 0
\(289\) 27.9116 + 10.1590i 1.64186 + 0.597587i
\(290\) 0 0
\(291\) −16.0246 + 5.02096i −0.939380 + 0.294334i
\(292\) 0 0
\(293\) 1.29095 2.23599i 0.0754180 0.130628i −0.825850 0.563890i \(-0.809304\pi\)
0.901268 + 0.433262i \(0.142638\pi\)
\(294\) 0 0
\(295\) 8.66705 1.52824i 0.504615 0.0889773i
\(296\) 0 0
\(297\) −3.06167 + 3.94590i −0.177656 + 0.228964i
\(298\) 0 0
\(299\) 0.714078 0.259903i 0.0412962 0.0150306i
\(300\) 0 0
\(301\) −9.31401 7.81539i −0.536851 0.450471i
\(302\) 0 0
\(303\) 30.0867 + 12.5256i 1.72844 + 0.719577i
\(304\) 0 0
\(305\) 8.18923i 0.468914i
\(306\) 0 0
\(307\) 1.26629 1.50910i 0.0722709 0.0861290i −0.728698 0.684836i \(-0.759874\pi\)
0.800968 + 0.598707i \(0.204318\pi\)
\(308\) 0 0
\(309\) 19.8370 + 0.901757i 1.12849 + 0.0512991i
\(310\) 0 0
\(311\) 22.4909 12.9851i 1.27534 0.736320i 0.299355 0.954142i \(-0.403229\pi\)
0.975989 + 0.217822i \(0.0698952\pi\)
\(312\) 0 0
\(313\) −2.32842 13.2051i −0.131610 0.746398i −0.977161 0.212502i \(-0.931839\pi\)
0.845551 0.533895i \(-0.179272\pi\)
\(314\) 0 0
\(315\) −0.900876 3.41102i −0.0507586 0.192189i
\(316\) 0 0
\(317\) 23.3056 19.5557i 1.30897 1.09836i 0.320454 0.947264i \(-0.396165\pi\)
0.988519 0.151095i \(-0.0482799\pi\)
\(318\) 0 0
\(319\) 2.64407 7.26453i 0.148040 0.406736i
\(320\) 0 0
\(321\) 3.43845 + 2.19922i 0.191916 + 0.122748i
\(322\) 0 0
\(323\) −29.4927 + 4.18776i −1.64102 + 0.233013i
\(324\) 0 0
\(325\) 2.82930 + 0.498882i 0.156941 + 0.0276730i
\(326\) 0 0
\(327\) 8.26319 + 7.59913i 0.456956 + 0.420233i
\(328\) 0 0
\(329\) 3.15834 + 3.76397i 0.174125 + 0.207514i
\(330\) 0 0
\(331\) 9.22014 + 5.32325i 0.506785 + 0.292592i 0.731511 0.681830i \(-0.238815\pi\)
−0.224726 + 0.974422i \(0.572149\pi\)
\(332\) 0 0
\(333\) 10.1151 + 7.13689i 0.554304 + 0.391099i
\(334\) 0 0
\(335\) 3.52668 + 6.10839i 0.192683 + 0.333737i
\(336\) 0 0
\(337\) −2.38138 6.54278i −0.129722 0.356408i 0.857780 0.514018i \(-0.171843\pi\)
−0.987501 + 0.157610i \(0.949621\pi\)
\(338\) 0 0
\(339\) −15.4373 + 8.00096i −0.838436 + 0.434553i
\(340\) 0 0
\(341\) 2.92924 0.158627
\(342\) 0 0
\(343\) −18.0159 −0.972770
\(344\) 0 0
\(345\) −1.36154 + 0.705673i −0.0733029 + 0.0379921i
\(346\) 0 0
\(347\) −9.63081 26.4604i −0.517009 1.42047i −0.873799 0.486287i \(-0.838351\pi\)
0.356790 0.934185i \(-0.383871\pi\)
\(348\) 0 0
\(349\) 9.79155 + 16.9595i 0.524130 + 0.907819i 0.999605 + 0.0280904i \(0.00894261\pi\)
−0.475476 + 0.879729i \(0.657724\pi\)
\(350\) 0 0
\(351\) −2.85260 + 1.79580i −0.152261 + 0.0958527i
\(352\) 0 0
\(353\) 3.55050 + 2.04988i 0.188974 + 0.109104i 0.591502 0.806303i \(-0.298535\pi\)
−0.402528 + 0.915408i \(0.631868\pi\)
\(354\) 0 0
\(355\) 0.0166533 + 0.0198466i 0.000883864 + 0.00105335i
\(356\) 0 0
\(357\) −13.5558 12.4664i −0.717450 0.659793i
\(358\) 0 0
\(359\) −5.52450 0.974118i −0.291572 0.0514120i 0.0259490 0.999663i \(-0.491739\pi\)
−0.317521 + 0.948251i \(0.602850\pi\)
\(360\) 0 0
\(361\) 15.3395 11.2117i 0.807340 0.590087i
\(362\) 0 0
\(363\) 14.7024 + 9.40356i 0.771674 + 0.493559i
\(364\) 0 0
\(365\) 1.02739 2.82273i 0.0537760 0.147748i
\(366\) 0 0
\(367\) 2.28539 1.91767i 0.119296 0.100101i −0.581188 0.813769i \(-0.697412\pi\)
0.700484 + 0.713668i \(0.252967\pi\)
\(368\) 0 0
\(369\) 15.5149 4.09761i 0.807674 0.213313i
\(370\) 0 0
\(371\) −3.91814 22.2209i −0.203420 1.15365i
\(372\) 0 0
\(373\) −18.2415 + 10.5317i −0.944510 + 0.545313i −0.891371 0.453274i \(-0.850256\pi\)
−0.0531391 + 0.998587i \(0.516923\pi\)
\(374\) 0 0
\(375\) −12.3308 0.560536i −0.636760 0.0289460i
\(376\) 0 0
\(377\) 3.35381 3.99691i 0.172730 0.205852i
\(378\) 0 0
\(379\) 9.54057i 0.490066i 0.969515 + 0.245033i \(0.0787988\pi\)
−0.969515 + 0.245033i \(0.921201\pi\)
\(380\) 0 0
\(381\) 22.2679 + 9.27048i 1.14082 + 0.474941i
\(382\) 0 0
\(383\) 5.96084 + 5.00173i 0.304584 + 0.255577i 0.782249 0.622965i \(-0.214072\pi\)
−0.477665 + 0.878542i \(0.658517\pi\)
\(384\) 0 0
\(385\) 1.06216 0.386595i 0.0541328 0.0197027i
\(386\) 0 0
\(387\) 6.14888 22.6230i 0.312565 1.14999i
\(388\) 0 0
\(389\) −9.63724 + 1.69931i −0.488627 + 0.0861582i −0.412533 0.910942i \(-0.635356\pi\)
−0.0760939 + 0.997101i \(0.524245\pi\)
\(390\) 0 0
\(391\) −4.00269 + 6.93287i −0.202425 + 0.350610i
\(392\) 0 0
\(393\) −18.3961 + 5.76401i −0.927960 + 0.290756i
\(394\) 0 0
\(395\) 0.986853 + 0.359185i 0.0496539 + 0.0180726i
\(396\) 0 0
\(397\) −2.05329 + 11.6448i −0.103052 + 0.584435i 0.888929 + 0.458045i \(0.151450\pi\)
−0.991981 + 0.126390i \(0.959661\pi\)
\(398\) 0 0
\(399\) 11.3714 + 2.94534i 0.569284 + 0.147451i
\(400\) 0 0
\(401\) 3.59086 20.3648i 0.179319 1.01697i −0.753720 0.657195i \(-0.771743\pi\)
0.933039 0.359774i \(-0.117146\pi\)
\(402\) 0 0
\(403\) 1.85776 + 0.676169i 0.0925416 + 0.0336824i
\(404\) 0 0
\(405\) 5.24226 4.33507i 0.260490 0.215411i
\(406\) 0 0
\(407\) −1.98313 + 3.43488i −0.0982999 + 0.170260i
\(408\) 0 0
\(409\) 3.39761 0.599090i 0.168001 0.0296231i −0.0890148 0.996030i \(-0.528372\pi\)
0.257016 + 0.966407i \(0.417261\pi\)
\(410\) 0 0
\(411\) 1.10682 + 8.52524i 0.0545952 + 0.420519i
\(412\) 0 0
\(413\) −17.0238 + 6.19617i −0.837688 + 0.304893i
\(414\) 0 0
\(415\) −7.01043 5.88245i −0.344128 0.288758i
\(416\) 0 0
\(417\) −2.40021 + 5.76535i −0.117539 + 0.282331i
\(418\) 0 0
\(419\) 25.3156i 1.23675i 0.785884 + 0.618374i \(0.212208\pi\)
−0.785884 + 0.618374i \(0.787792\pi\)
\(420\) 0 0
\(421\) 20.4536 24.3756i 0.996845 1.18799i 0.0146955 0.999892i \(-0.495322\pi\)
0.982150 0.188102i \(-0.0602334\pi\)
\(422\) 0 0
\(423\) −4.03468 + 8.57198i −0.196173 + 0.416784i
\(424\) 0 0
\(425\) −26.2108 + 15.1328i −1.27141 + 0.734049i
\(426\) 0 0
\(427\) −2.92728 16.6014i −0.141661 0.803400i
\(428\) 0 0
\(429\) −0.655905 0.857975i −0.0316674 0.0414234i
\(430\) 0 0
\(431\) −25.2345 + 21.1742i −1.21550 + 1.01993i −0.216455 + 0.976293i \(0.569449\pi\)
−0.999048 + 0.0436350i \(0.986106\pi\)
\(432\) 0 0
\(433\) −5.46188 + 15.0064i −0.262481 + 0.721161i 0.736517 + 0.676419i \(0.236469\pi\)
−0.998999 + 0.0447423i \(0.985753\pi\)
\(434\) 0 0
\(435\) −5.67342 + 8.87034i −0.272020 + 0.425300i
\(436\) 0 0
\(437\) 0.170932 5.10321i 0.00817679 0.244120i
\(438\) 0 0
\(439\) 30.5401 + 5.38505i 1.45760 + 0.257014i 0.845589 0.533835i \(-0.179250\pi\)
0.612011 + 0.790849i \(0.290361\pi\)
\(440\) 0 0
\(441\) −5.76108 12.4713i −0.274337 0.593871i
\(442\) 0 0
\(443\) 12.5287 + 14.9311i 0.595257 + 0.709400i 0.976607 0.215031i \(-0.0689852\pi\)
−0.381350 + 0.924431i \(0.624541\pi\)
\(444\) 0 0
\(445\) −3.99962 2.30918i −0.189600 0.109466i
\(446\) 0 0
\(447\) 7.24156 32.3895i 0.342514 1.53197i
\(448\) 0 0
\(449\) −6.61607 11.4594i −0.312232 0.540801i 0.666613 0.745404i \(-0.267743\pi\)
−0.978845 + 0.204602i \(0.934410\pi\)
\(450\) 0 0
\(451\) 1.75842 + 4.83122i 0.0828007 + 0.227493i
\(452\) 0 0
\(453\) −15.3524 29.6214i −0.721321 1.39173i
\(454\) 0 0
\(455\) 0.762876 0.0357642
\(456\) 0 0
\(457\) −15.4038 −0.720559 −0.360279 0.932844i \(-0.617319\pi\)
−0.360279 + 0.932844i \(0.617319\pi\)
\(458\) 0 0
\(459\) 10.8602 33.8088i 0.506912 1.57806i
\(460\) 0 0
\(461\) 5.65076 + 15.5253i 0.263182 + 0.723087i 0.998948 + 0.0458511i \(0.0146000\pi\)
−0.735766 + 0.677236i \(0.763178\pi\)
\(462\) 0 0
\(463\) 4.69170 + 8.12625i 0.218042 + 0.377659i 0.954209 0.299140i \(-0.0966998\pi\)
−0.736168 + 0.676799i \(0.763366\pi\)
\(464\) 0 0
\(465\) −3.89358 0.870516i −0.180560 0.0403692i
\(466\) 0 0
\(467\) 18.5458 + 10.7074i 0.858196 + 0.495480i 0.863408 0.504507i \(-0.168326\pi\)
−0.00521153 + 0.999986i \(0.501659\pi\)
\(468\) 0 0
\(469\) −9.33287 11.1225i −0.430952 0.513588i
\(470\) 0 0
\(471\) 0.250711 0.272620i 0.0115522 0.0125617i
\(472\) 0 0
\(473\) 7.39703 + 1.30430i 0.340116 + 0.0599716i
\(474\) 0 0
\(475\) 10.2064 16.3855i 0.468302 0.751820i
\(476\) 0 0
\(477\) 35.7277 24.8262i 1.63586 1.13672i
\(478\) 0 0
\(479\) 11.4165 31.3665i 0.521632 1.43317i −0.347071 0.937839i \(-0.612824\pi\)
0.868703 0.495333i \(-0.164954\pi\)
\(480\) 0 0
\(481\) −2.05061 + 1.72067i −0.0934998 + 0.0784557i
\(482\) 0 0
\(483\) 2.50791 1.91725i 0.114114 0.0872379i
\(484\) 0 0
\(485\) 1.27250 + 7.21673i 0.0577815 + 0.327695i
\(486\) 0 0
\(487\) 28.9750 16.7288i 1.31298 0.758052i 0.330395 0.943843i \(-0.392818\pi\)
0.982589 + 0.185791i \(0.0594846\pi\)
\(488\) 0 0
\(489\) 1.18244 26.0117i 0.0534720 1.17629i
\(490\) 0 0
\(491\) 0.635055 0.756829i 0.0286596 0.0341552i −0.751524 0.659705i \(-0.770681\pi\)
0.780184 + 0.625550i \(0.215125\pi\)
\(492\) 0 0
\(493\) 54.9658i 2.47554i
\(494\) 0 0
\(495\) 1.53557 + 1.54663i 0.0690188 + 0.0695158i
\(496\) 0 0
\(497\) −0.0408543 0.0342808i −0.00183256 0.00153770i
\(498\) 0 0
\(499\) 4.11402 1.49738i 0.184169 0.0670319i −0.248290 0.968686i \(-0.579868\pi\)
0.432458 + 0.901654i \(0.357646\pi\)
\(500\) 0 0
\(501\) 16.2312 2.10726i 0.725155 0.0941454i
\(502\) 0 0
\(503\) 31.7905 5.60552i 1.41747 0.249938i 0.588167 0.808740i \(-0.299850\pi\)
0.829301 + 0.558802i \(0.188739\pi\)
\(504\) 0 0
\(505\) 7.11080 12.3163i 0.316426 0.548067i
\(506\) 0 0
\(507\) 6.51443 + 20.7911i 0.289316 + 0.923365i
\(508\) 0 0
\(509\) −21.2608 7.73831i −0.942370 0.342994i −0.175268 0.984521i \(-0.556079\pi\)
−0.767101 + 0.641526i \(0.778302\pi\)
\(510\) 0 0
\(511\) −1.07375 + 6.08956i −0.0475000 + 0.269386i
\(512\) 0 0
\(513\) 4.03939 + 22.2864i 0.178343 + 0.983968i
\(514\) 0 0
\(515\) 1.50474 8.53380i 0.0663067 0.376044i
\(516\) 0 0
\(517\) −2.85234 1.03817i −0.125446 0.0456585i
\(518\) 0 0
\(519\) −6.96458 22.2278i −0.305711 0.975690i
\(520\) 0 0
\(521\) −4.86213 + 8.42145i −0.213014 + 0.368950i −0.952656 0.304049i \(-0.901661\pi\)
0.739643 + 0.673000i \(0.234995\pi\)
\(522\) 0 0
\(523\) −33.5671 + 5.91879i −1.46779 + 0.258810i −0.849686 0.527288i \(-0.823209\pi\)
−0.618101 + 0.786099i \(0.712098\pi\)
\(524\) 0 0
\(525\) 11.8355 1.53658i 0.516544 0.0670619i
\(526\) 0 0
\(527\) −19.5709 + 7.12324i −0.852523 + 0.310293i
\(528\) 0 0
\(529\) 16.5678 + 13.9021i 0.720341 + 0.604438i
\(530\) 0 0
\(531\) −24.6114 24.7886i −1.06804 1.07573i
\(532\) 0 0
\(533\) 3.46992i 0.150299i
\(534\) 0 0
\(535\) 1.14489 1.36443i 0.0494980 0.0589894i
\(536\) 0 0
\(537\) −1.31297 + 28.8831i −0.0566590 + 1.24640i
\(538\) 0 0
\(539\) 3.81174 2.20071i 0.164183 0.0947911i
\(540\) 0 0
\(541\) 0.180608 + 1.02428i 0.00776495 + 0.0440372i 0.988444 0.151586i \(-0.0484381\pi\)
−0.980679 + 0.195623i \(0.937327\pi\)
\(542\) 0 0
\(543\) 14.0280 10.7242i 0.602001 0.460218i
\(544\) 0 0
\(545\) 3.75277 3.14895i 0.160751 0.134886i
\(546\) 0 0
\(547\) −8.86889 + 24.3671i −0.379207 + 1.04186i 0.592480 + 0.805586i \(0.298149\pi\)
−0.971686 + 0.236276i \(0.924073\pi\)
\(548\) 0 0
\(549\) 26.6925 18.5479i 1.13921 0.791607i
\(550\) 0 0
\(551\) −16.5032 30.9317i −0.703060 1.31773i
\(552\) 0 0
\(553\) −2.12897 0.375395i −0.0905330 0.0159634i
\(554\) 0 0
\(555\) 3.65678 3.97633i 0.155222 0.168786i
\(556\) 0 0
\(557\) 2.42914 + 2.89494i 0.102926 + 0.122662i 0.815048 0.579393i \(-0.196710\pi\)
−0.712122 + 0.702055i \(0.752266\pi\)
\(558\) 0 0
\(559\) 4.39021 + 2.53469i 0.185686 + 0.107206i
\(560\) 0 0
\(561\) 11.1030 + 2.48238i 0.468770 + 0.104806i
\(562\) 0 0
\(563\) 5.99208 + 10.3786i 0.252536 + 0.437406i 0.964223 0.265091i \(-0.0854020\pi\)
−0.711687 + 0.702496i \(0.752069\pi\)
\(564\) 0 0
\(565\) 2.59510 + 7.12998i 0.109177 + 0.299960i
\(566\) 0 0
\(567\) −9.07767 + 10.6620i −0.381226 + 0.447764i
\(568\) 0 0
\(569\) −11.2148 −0.470147 −0.235074 0.971978i \(-0.575533\pi\)
−0.235074 + 0.971978i \(0.575533\pi\)
\(570\) 0 0
\(571\) −16.2525 −0.680144 −0.340072 0.940399i \(-0.610452\pi\)
−0.340072 + 0.940399i \(0.610452\pi\)
\(572\) 0 0
\(573\) −9.61733 18.5559i −0.401770 0.775185i
\(574\) 0 0
\(575\) −1.77435 4.87499i −0.0739956 0.203301i
\(576\) 0 0
\(577\) −4.02000 6.96284i −0.167355 0.289867i 0.770134 0.637882i \(-0.220189\pi\)
−0.937489 + 0.348015i \(0.886856\pi\)
\(578\) 0 0
\(579\) 1.26400 5.65351i 0.0525299 0.234952i
\(580\) 0 0
\(581\) 16.3145 + 9.41916i 0.676838 + 0.390772i
\(582\) 0 0
\(583\) 8.95984 + 10.6779i 0.371079 + 0.442234i
\(584\) 0 0
\(585\) 0.616863 + 1.33535i 0.0255041 + 0.0552101i
\(586\) 0 0
\(587\) −19.5628 3.44945i −0.807444 0.142374i −0.245336 0.969438i \(-0.578898\pi\)
−0.562108 + 0.827064i \(0.690009\pi\)
\(588\) 0 0
\(589\) 8.87470 9.88463i 0.365676 0.407289i
\(590\) 0 0
\(591\) 5.55081 8.67864i 0.228330 0.356992i
\(592\) 0 0
\(593\) 7.64203 20.9963i 0.313821 0.862215i −0.678056 0.735010i \(-0.737177\pi\)
0.991876 0.127205i \(-0.0406006\pi\)
\(594\) 0 0
\(595\) −6.15644 + 5.16587i −0.252390 + 0.211780i
\(596\) 0 0
\(597\) 11.7576 + 15.3799i 0.481208 + 0.629456i
\(598\) 0 0
\(599\) 2.89198 + 16.4012i 0.118163 + 0.670136i 0.985135 + 0.171780i \(0.0549517\pi\)
−0.866972 + 0.498356i \(0.833937\pi\)
\(600\) 0 0
\(601\) 17.9204 10.3464i 0.730990 0.422037i −0.0877940 0.996139i \(-0.527982\pi\)
0.818784 + 0.574101i \(0.194648\pi\)
\(602\) 0 0
\(603\) 11.9224 25.3301i 0.485519 1.03152i
\(604\) 0 0
\(605\) 4.89540 5.83411i 0.199026 0.237191i
\(606\) 0 0
\(607\) 39.3916i 1.59886i 0.600761 + 0.799428i \(0.294864\pi\)
−0.600761 + 0.799428i \(0.705136\pi\)
\(608\) 0 0
\(609\) 8.33058 20.0102i 0.337572 0.810854i
\(610\) 0 0
\(611\) −1.56934 1.31683i −0.0634888 0.0532734i
\(612\) 0 0
\(613\) −26.4005 + 9.60900i −1.06631 + 0.388104i −0.814794 0.579750i \(-0.803150\pi\)
−0.251512 + 0.967854i \(0.580928\pi\)
\(614\) 0 0
\(615\) −0.901563 6.94428i −0.0363545 0.280020i
\(616\) 0 0
\(617\) −20.3648 + 3.59086i −0.819854 + 0.144562i −0.567817 0.823155i \(-0.692212\pi\)
−0.252038 + 0.967717i \(0.581101\pi\)
\(618\) 0 0
\(619\) −16.8830 + 29.2423i −0.678586 + 1.17535i 0.296821 + 0.954933i \(0.404074\pi\)
−0.975407 + 0.220412i \(0.929260\pi\)
\(620\) 0 0
\(621\) 5.38390 + 2.83960i 0.216048 + 0.113949i
\(622\) 0 0
\(623\) 8.93358 + 3.25156i 0.357916 + 0.130271i
\(624\) 0 0
\(625\) 2.90984 16.5025i 0.116394 0.660101i
\(626\) 0 0
\(627\) −6.99348 + 1.93668i −0.279293 + 0.0773435i
\(628\) 0 0
\(629\) 4.89690 27.7717i 0.195252 1.10733i
\(630\) 0 0
\(631\) 35.0060 + 12.7411i 1.39357 + 0.507217i 0.926262 0.376880i \(-0.123003\pi\)
0.467304 + 0.884096i \(0.345225\pi\)
\(632\) 0 0
\(633\) −35.1400 + 11.0103i −1.39669 + 0.437622i
\(634\) 0 0
\(635\) 5.26287 9.11556i 0.208851 0.361740i
\(636\) 0 0
\(637\) 2.92545 0.515836i 0.115911 0.0204382i
\(638\) 0 0
\(639\) 0.0269710 0.0992317i 0.00106695 0.00392554i
\(640\) 0 0
\(641\) 7.37099 2.68282i 0.291137 0.105965i −0.192323 0.981332i \(-0.561602\pi\)
0.483460 + 0.875367i \(0.339380\pi\)
\(642\) 0 0
\(643\) −29.9819 25.1578i −1.18237 0.992126i −0.999960 0.00890393i \(-0.997166\pi\)
−0.182410 0.983223i \(-0.558390\pi\)
\(644\) 0 0
\(645\) −9.44461 3.93195i −0.371881 0.154820i
\(646\) 0 0
\(647\) 6.21339i 0.244274i −0.992513 0.122137i \(-0.961025\pi\)
0.992513 0.122137i \(-0.0389747\pi\)
\(648\) 0 0
\(649\) 7.19386 8.57331i 0.282384 0.336532i
\(650\) 0 0
\(651\) 8.20435 + 0.372955i 0.321554 + 0.0146173i
\(652\) 0 0
\(653\) 23.3831 13.5002i 0.915050 0.528304i 0.0329976 0.999455i \(-0.489495\pi\)
0.882053 + 0.471151i \(0.156161\pi\)
\(654\) 0 0
\(655\) 1.46082 + 8.28473i 0.0570790 + 0.323711i
\(656\) 0 0
\(657\) −11.5275 + 3.04451i −0.449731 + 0.118778i
\(658\) 0 0
\(659\) 23.3482 19.5915i 0.909517 0.763176i −0.0625097 0.998044i \(-0.519910\pi\)
0.972027 + 0.234869i \(0.0754660\pi\)
\(660\) 0 0
\(661\) −11.2133 + 30.8082i −0.436146 + 1.19830i 0.505834 + 0.862631i \(0.331185\pi\)
−0.941980 + 0.335670i \(0.891037\pi\)
\(662\) 0 0
\(663\) 6.46866 + 4.13732i 0.251222 + 0.160680i
\(664\) 0 0
\(665\) 1.91347 4.75550i 0.0742013 0.184410i
\(666\) 0 0
\(667\) −9.27861 1.63607i −0.359269 0.0633489i
\(668\) 0 0
\(669\) 17.5637 + 16.1522i 0.679051 + 0.624480i
\(670\) 0 0
\(671\) 6.69399 + 7.97759i 0.258419 + 0.307971i
\(672\) 0 0
\(673\) 26.7750 + 15.4586i 1.03210 + 0.595884i 0.917586 0.397537i \(-0.130135\pi\)
0.114516 + 0.993421i \(0.463468\pi\)
\(674\) 0 0
\(675\) 12.2599 + 19.4746i 0.471883 + 0.749578i
\(676\) 0 0
\(677\) 19.6720 + 34.0729i 0.756057 + 1.30953i 0.944847 + 0.327511i \(0.106210\pi\)
−0.188791 + 0.982017i \(0.560457\pi\)
\(678\) 0 0
\(679\) −5.15932 14.1751i −0.197996 0.543991i
\(680\) 0 0
\(681\) −24.8945 + 12.9026i −0.953961 + 0.494428i
\(682\) 0 0
\(683\) 12.0176 0.459840 0.229920 0.973210i \(-0.426154\pi\)
0.229920 + 0.973210i \(0.426154\pi\)
\(684\) 0 0
\(685\) 3.75147 0.143336
\(686\) 0 0
\(687\) 39.4382 20.4404i 1.50466 0.779849i
\(688\) 0 0
\(689\) 3.21761 + 8.84031i 0.122581 + 0.336789i
\(690\) 0 0
\(691\) 17.5214 + 30.3479i 0.666544 + 1.15449i 0.978864 + 0.204512i \(0.0655606\pi\)
−0.312320 + 0.949977i \(0.601106\pi\)
\(692\) 0 0
\(693\) −3.66580 2.58647i −0.139252 0.0982519i
\(694\) 0 0
\(695\) 2.36010 + 1.36260i 0.0895237 + 0.0516865i
\(696\) 0 0
\(697\) −23.4968 28.0024i −0.890006 1.06067i
\(698\) 0 0
\(699\) 14.8397 + 13.6471i 0.561288 + 0.516181i
\(700\) 0 0
\(701\) 2.95841 + 0.521647i 0.111738 + 0.0197023i 0.229237 0.973371i \(-0.426377\pi\)
−0.117500 + 0.993073i \(0.537488\pi\)
\(702\) 0 0
\(703\) 5.58262 + 17.0986i 0.210552 + 0.644887i
\(704\) 0 0
\(705\) 3.48284 + 2.22760i 0.131171 + 0.0838964i
\(706\) 0 0
\(707\) −10.0127 + 27.5097i −0.376567 + 1.03461i
\(708\) 0 0
\(709\) 2.36012 1.98037i 0.0886360 0.0743744i −0.597393 0.801949i \(-0.703797\pi\)
0.686029 + 0.727574i \(0.259352\pi\)
\(710\) 0 0
\(711\) −1.06439 4.03013i −0.0399178 0.151142i
\(712\) 0 0
\(713\) −0.619918 3.51573i −0.0232161 0.131665i
\(714\) 0 0
\(715\) −0.408138 + 0.235639i −0.0152635 + 0.00881239i
\(716\) 0 0
\(717\) 26.3391 + 1.19733i 0.983650 + 0.0447150i
\(718\) 0 0
\(719\) 7.13781 8.50651i 0.266195 0.317239i −0.616345 0.787476i \(-0.711387\pi\)
0.882540 + 0.470237i \(0.155832\pi\)
\(720\) 0 0
\(721\) 17.8378i 0.664316i
\(722\) 0 0
\(723\) −24.2796 10.1080i −0.902969 0.375921i
\(724\) 0 0
\(725\) −27.2868 22.8964i −1.01341 0.850349i
\(726\) 0 0
\(727\) −13.8709 + 5.04860i −0.514444 + 0.187242i −0.586179 0.810182i \(-0.699368\pi\)
0.0717355 + 0.997424i \(0.477146\pi\)
\(728\) 0 0
\(729\) −26.0033 7.26839i −0.963084 0.269199i
\(730\) 0 0
\(731\) −52.5931 + 9.27357i −1.94522 + 0.342996i
\(732\) 0 0
\(733\) −18.1447 + 31.4276i −0.670191 + 1.16080i 0.307659 + 0.951497i \(0.400454\pi\)
−0.977850 + 0.209308i \(0.932879\pi\)
\(734\) 0 0
\(735\) −5.72062 + 1.79243i −0.211008 + 0.0661147i
\(736\) 0 0
\(737\) 8.42862 + 3.06777i 0.310472 + 0.113003i
\(738\) 0 0
\(739\) 2.94942 16.7270i 0.108496 0.615312i −0.881270 0.472613i \(-0.843311\pi\)
0.989766 0.142699i \(-0.0455780\pi\)
\(740\) 0 0
\(741\) −4.88240 0.386069i −0.179360 0.0141826i
\(742\) 0 0
\(743\) −4.59818 + 26.0776i −0.168691 + 0.956693i 0.776486 + 0.630134i \(0.217000\pi\)
−0.945177 + 0.326559i \(0.894111\pi\)
\(744\) 0 0
\(745\) −13.6097 4.95352i −0.498620 0.181483i
\(746\) 0 0
\(747\) −3.29558 + 36.1735i −0.120579 + 1.32352i
\(748\) 0 0
\(749\) −1.83324 + 3.17526i −0.0669850 + 0.116021i
\(750\) 0 0
\(751\) −46.8929 + 8.26849i −1.71115 + 0.301722i −0.941566 0.336827i \(-0.890646\pi\)
−0.769581 + 0.638549i \(0.779535\pi\)
\(752\) 0 0
\(753\) −2.41913 18.6333i −0.0881581 0.679037i
\(754\) 0 0
\(755\) −13.6812 + 4.97954i −0.497909 + 0.181224i
\(756\) 0 0
\(757\) −12.6519 10.6162i −0.459843 0.385854i 0.383230 0.923653i \(-0.374812\pi\)
−0.843073 + 0.537799i \(0.819256\pi\)
\(758\) 0 0
\(759\) −0.749527 + 1.80038i −0.0272061 + 0.0653496i
\(760\) 0 0
\(761\) 19.1974i 0.695906i −0.937512 0.347953i \(-0.886877\pi\)
0.937512 0.347953i \(-0.113123\pi\)
\(762\) 0 0
\(763\) −6.48211 + 7.72508i −0.234668 + 0.279667i
\(764\) 0 0
\(765\) −14.0206 6.59923i −0.506914 0.238596i
\(766\) 0 0
\(767\) 6.54145 3.77671i 0.236198 0.136369i
\(768\) 0 0
\(769\) −5.25863 29.8231i −0.189631 1.07545i −0.919860 0.392248i \(-0.871698\pi\)
0.730229 0.683203i \(-0.239413\pi\)
\(770\) 0 0
\(771\) −0.0476157 0.0622851i −0.00171484 0.00224314i
\(772\) 0 0
\(773\) −21.9958 + 18.4567i −0.791134 + 0.663840i −0.946026 0.324091i \(-0.894942\pi\)
0.154892 + 0.987931i \(0.450497\pi\)
\(774\) 0 0
\(775\) 4.61619 12.6829i 0.165818 0.455582i
\(776\) 0 0
\(777\) −5.99177 + 9.36807i −0.214953 + 0.336078i
\(778\) 0 0
\(779\) 21.6303 + 8.70339i 0.774985 + 0.311831i
\(780\) 0 0
\(781\) 0.0324458 + 0.00572106i 0.00116100 + 0.000204716i
\(782\) 0 0
\(783\) 41.7624 1.59828i 1.49247 0.0571177i
\(784\) 0 0
\(785\) −0.103890 0.123812i −0.00370800 0.00441903i
\(786\) 0 0
\(787\) −22.1812 12.8063i −0.790673 0.456495i 0.0495262 0.998773i \(-0.484229\pi\)
−0.840200 + 0.542277i \(0.817562\pi\)
\(788\) 0 0
\(789\) 2.07292 9.27161i 0.0737980 0.330078i
\(790\) 0 0
\(791\) −7.80951 13.5265i −0.277674 0.480946i
\(792\) 0 0
\(793\) 2.40391 + 6.60469i 0.0853653 + 0.234539i
\(794\) 0 0
\(795\) −8.73625 16.8559i −0.309843 0.597818i
\(796\) 0 0
\(797\) 32.4074 1.14793 0.573965 0.818880i \(-0.305405\pi\)
0.573965 + 0.818880i \(0.305405\pi\)
\(798\) 0 0
\(799\) 21.5817 0.763506
\(800\) 0 0
\(801\) 1.53212 + 18.2667i 0.0541348 + 0.645423i
\(802\) 0 0
\(803\) −1.30650 3.58957i −0.0461053 0.126673i
\(804\) 0 0
\(805\) −0.688786 1.19301i −0.0242765 0.0420482i
\(806\) 0 0
\(807\) 3.31937 + 0.742136i 0.116847 + 0.0261244i
\(808\) 0 0
\(809\) 30.3938 + 17.5479i 1.06859 + 0.616950i 0.927796 0.373089i \(-0.121701\pi\)
0.140793 + 0.990039i \(0.455035\pi\)
\(810\) 0 0
\(811\) −14.0733 16.7719i −0.494181 0.588942i 0.460095 0.887870i \(-0.347815\pi\)
−0.954276 + 0.298928i \(0.903371\pi\)
\(812\) 0 0
\(813\) 24.7659 26.9301i 0.868577 0.944479i
\(814\) 0 0
\(815\) −11.1901 1.97312i −0.391972 0.0691152i
\(816\) 0 0
\(817\) 26.8121 21.0094i 0.938035 0.735027i
\(818\) 0 0
\(819\) −1.72785 2.48657i −0.0603760 0.0868877i
\(820\) 0 0
\(821\) −4.83332 + 13.2794i −0.168684 + 0.463455i −0.995015 0.0997301i \(-0.968202\pi\)
0.826331 + 0.563185i \(0.190424\pi\)
\(822\) 0 0
\(823\) −11.4669 + 9.62189i −0.399712 + 0.335398i −0.820382 0.571815i \(-0.806239\pi\)
0.420670 + 0.907214i \(0.361795\pi\)
\(824\) 0 0
\(825\) −5.85737 + 4.47785i −0.203927 + 0.155899i
\(826\) 0 0
\(827\) 3.63051 + 20.5896i 0.126245 + 0.715972i 0.980561 + 0.196217i \(0.0628657\pi\)
−0.854315 + 0.519755i \(0.826023\pi\)
\(828\) 0 0
\(829\) −12.1611 + 7.02120i −0.422371 + 0.243856i −0.696091 0.717953i \(-0.745079\pi\)
0.273720 + 0.961809i \(0.411746\pi\)
\(830\) 0 0
\(831\) 0.616494 13.5618i 0.0213859 0.470453i
\(832\) 0 0
\(833\) −20.1155 + 23.9727i −0.696960 + 0.830605i
\(834\) 0 0
\(835\) 7.14241i 0.247173i
\(836\) 0 0
\(837\) 5.98122 + 14.6626i 0.206741 + 0.506815i
\(838\) 0 0
\(839\) −42.8654 35.9683i −1.47988 1.24176i −0.906315 0.422603i \(-0.861116\pi\)
−0.573563 0.819162i \(-0.694439\pi\)
\(840\) 0 0
\(841\) −33.5383 + 12.2070i −1.15649 + 0.420929i
\(842\) 0 0
\(843\) −20.1183 + 2.61192i −0.692910 + 0.0899592i
\(844\) 0 0
\(845\) 9.36332 1.65101i 0.322108 0.0567964i
\(846\) 0 0
\(847\) −7.83867 + 13.5770i −0.269340 + 0.466510i
\(848\) 0 0
\(849\) −3.63558 11.6031i −0.124773 0.398218i
\(850\) 0 0
\(851\) 4.54230 + 1.65326i 0.155708 + 0.0566731i
\(852\) 0 0
\(853\) −7.55129 + 42.8255i −0.258551 + 1.46632i 0.528239 + 0.849096i \(0.322853\pi\)
−0.786790 + 0.617221i \(0.788259\pi\)
\(854\) 0 0
\(855\) 9.87136 0.495925i 0.337593 0.0169603i
\(856\) 0 0
\(857\) −8.77792 + 49.7820i −0.299848 + 1.70052i 0.346969 + 0.937877i \(0.387211\pi\)
−0.646817 + 0.762645i \(0.723900\pi\)
\(858\) 0 0
\(859\) −23.3783 8.50899i −0.797656 0.290323i −0.0891412 0.996019i \(-0.528412\pi\)
−0.708515 + 0.705696i \(0.750634\pi\)
\(860\) 0 0
\(861\) 4.30994 + 13.7554i 0.146883 + 0.468782i
\(862\) 0 0
\(863\) −16.9638 + 29.3822i −0.577455 + 1.00018i 0.418315 + 0.908302i \(0.362621\pi\)
−0.995770 + 0.0918798i \(0.970712\pi\)
\(864\) 0 0
\(865\) −10.0103 + 1.76509i −0.340362 + 0.0600149i
\(866\) 0 0
\(867\) −51.0187 + 6.62366i −1.73269 + 0.224951i
\(868\) 0 0
\(869\) 1.25495 0.456765i 0.0425713 0.0154947i
\(870\) 0 0
\(871\) 4.63739 + 3.89123i 0.157132 + 0.131849i
\(872\) 0 0
\(873\) 20.6406 20.4930i 0.698577 0.693583i
\(874\) 0 0
\(875\) 11.0881i 0.374846i
\(876\) 0 0
\(877\) 19.1891 22.8687i 0.647971 0.772222i −0.337636 0.941277i \(-0.609627\pi\)
0.985607 + 0.169055i \(0.0540717\pi\)
\(878\) 0 0
\(879\) −0.203078 + 4.46736i −0.00684966 + 0.150680i
\(880\) 0 0
\(881\) 9.59448 5.53938i 0.323246 0.186626i −0.329592 0.944123i \(-0.606911\pi\)
0.652839 + 0.757497i \(0.273578\pi\)
\(882\) 0 0
\(883\) −9.62988 54.6138i −0.324071 1.83790i −0.516122 0.856515i \(-0.672625\pi\)
0.192051 0.981385i \(-0.438486\pi\)
\(884\) 0 0
\(885\) −12.1100 + 9.25786i −0.407073 + 0.311200i
\(886\) 0 0
\(887\) 19.9548 16.7441i 0.670017 0.562211i −0.243054 0.970013i \(-0.578149\pi\)
0.913070 + 0.407802i \(0.133705\pi\)
\(888\) 0 0
\(889\) −7.41064 + 20.3606i −0.248545 + 0.682871i
\(890\) 0 0
\(891\) 1.56324 8.50812i 0.0523703 0.285033i
\(892\) 0 0
\(893\) −12.1450 + 6.47980i −0.406416 + 0.216838i
\(894\) 0 0
\(895\) 12.4254 + 2.19093i 0.415334 + 0.0732346i
\(896\) 0 0
\(897\) −0.890949 + 0.968805i −0.0297479 + 0.0323475i
\(898\) 0 0
\(899\) −15.7559 18.7771i −0.525488 0.626252i
\(900\) 0 0
\(901\) −85.8291 49.5535i −2.85938 1.65086i
\(902\) 0 0
\(903\) 20.5519 + 4.59493i 0.683924 + 0.152910i
\(904\) 0 0
\(905\) −3.85274 6.67314i −0.128069 0.221823i
\(906\) 0 0
\(907\) −5.92780 16.2865i −0.196830 0.540785i 0.801535 0.597947i \(-0.204017\pi\)
−0.998365 + 0.0571627i \(0.981795\pi\)
\(908\) 0 0
\(909\) −56.2498 + 4.71795i −1.86569 + 0.156484i
\(910\) 0 0
\(911\) 35.0957 1.16277 0.581386 0.813628i \(-0.302511\pi\)
0.581386 + 0.813628i \(0.302511\pi\)
\(912\) 0 0
\(913\) −11.6376 −0.385150
\(914\) 0 0
\(915\) −6.52694 12.5932i −0.215774 0.416320i
\(916\) 0 0
\(917\) −5.92284 16.2729i −0.195589 0.537377i
\(918\) 0 0
\(919\) 15.0221 + 26.0190i 0.495533 + 0.858288i 0.999987 0.00515052i \(-0.00163947\pi\)
−0.504454 + 0.863439i \(0.668306\pi\)
\(920\) 0 0
\(921\) −0.744494 + 3.32992i −0.0245319 + 0.109725i
\(922\) 0 0
\(923\) 0.0192569 + 0.0111180i 0.000633848 + 0.000365952i
\(924\) 0 0
\(925\) 11.7469 + 13.9995i 0.386237 + 0.460300i
\(926\) 0 0
\(927\) −31.2237 + 14.4237i −1.02552 + 0.473737i
\(928\) 0 0
\(929\) −32.1458 5.66817i −1.05467 0.185967i −0.380680 0.924707i \(-0.624310\pi\)
−0.673990 + 0.738740i \(0.735421\pi\)
\(930\) 0 0
\(931\) 4.12218 19.5301i 0.135099 0.640072i
\(932\) 0 0
\(933\) −24.2367 + 37.8939i −0.793475 + 1.24059i
\(934\) 0 0
\(935\) 1.69805 4.66536i 0.0555322 0.152573i
\(936\) 0 0
\(937\) −24.8914 + 20.8863i −0.813165 + 0.682327i −0.951361 0.308078i \(-0.900314\pi\)
0.138196 + 0.990405i \(0.455870\pi\)
\(938\) 0 0
\(939\) 14.1053 + 18.4508i 0.460308 + 0.602119i
\(940\) 0 0
\(941\) −2.50659 14.2156i −0.0817126 0.463415i −0.998018 0.0629344i \(-0.979954\pi\)
0.916305 0.400481i \(-0.131157\pi\)
\(942\) 0 0
\(943\) 5.42639 3.13293i 0.176708 0.102022i
\(944\) 0 0
\(945\) 4.10398 + 4.52738i 0.133502 + 0.147276i
\(946\) 0 0
\(947\) −28.2988 + 33.7252i −0.919588 + 1.09592i 0.0755210 + 0.997144i \(0.475938\pi\)
−0.995109 + 0.0987786i \(0.968506\pi\)
\(948\) 0 0
\(949\) 2.57814i 0.0836899i
\(950\) 0 0
\(951\) −20.2527 + 48.6473i −0.656738 + 1.57750i
\(952\) 0 0
\(953\) −15.8037 13.2609i −0.511932 0.429562i 0.349877 0.936796i \(-0.386223\pi\)
−0.861808 + 0.507234i \(0.830668\pi\)
\(954\) 0 0
\(955\) −8.57039 + 3.11937i −0.277331 + 0.100940i
\(956\) 0 0
\(957\) 1.72394 + 13.2786i 0.0557270 + 0.429237i
\(958\) 0 0
\(959\) −7.60509 + 1.34098i −0.245581 + 0.0433026i
\(960\) 0 0
\(961\) −10.8562 + 18.8034i −0.350199 + 0.606562i
\(962\) 0 0
\(963\) −7.04039 0.641413i −0.226873 0.0206692i
\(964\) 0 0
\(965\) −2.37554 0.864625i −0.0764713 0.0278333i
\(966\) 0 0
\(967\) 7.05922 40.0348i 0.227009 1.28743i −0.631798 0.775133i \(-0.717683\pi\)
0.858807 0.512300i \(-0.171206\pi\)
\(968\) 0 0
\(969\) 42.0155 29.9459i 1.34973 0.962003i
\(970\) 0 0
\(971\) 0.764165 4.33380i 0.0245232 0.139078i −0.970088 0.242754i \(-0.921949\pi\)
0.994611 + 0.103676i \(0.0330604\pi\)
\(972\) 0 0
\(973\) −5.27154 1.91868i −0.168998 0.0615101i
\(974\) 0 0
\(975\) −4.74846 + 1.48782i −0.152072 + 0.0476485i
\(976\) 0 0
\(977\) −0.538610 + 0.932899i −0.0172317 + 0.0298461i −0.874513 0.485003i \(-0.838819\pi\)
0.857281 + 0.514849i \(0.172152\pi\)
\(978\) 0 0
\(979\) −5.78381 + 1.01984i −0.184851 + 0.0325943i
\(980\) 0 0
\(981\) −18.7636 5.09990i −0.599075 0.162827i
\(982\) 0 0
\(983\) 4.78675 1.74223i 0.152674 0.0555687i −0.264553 0.964371i \(-0.585224\pi\)
0.417227 + 0.908803i \(0.363002\pi\)
\(984\) 0 0
\(985\) −3.44381 2.88970i −0.109729 0.0920736i
\(986\) 0 0
\(987\) −7.85678 3.27091i −0.250084 0.104114i
\(988\) 0 0
\(989\) 9.15410i 0.291083i
\(990\) 0 0
\(991\) 7.72397 9.20507i 0.245360 0.292409i −0.629283 0.777176i \(-0.716651\pi\)
0.874643 + 0.484768i \(0.161096\pi\)
\(992\) 0 0
\(993\) −18.4213 0.837398i −0.584581 0.0265740i
\(994\) 0 0
\(995\) 7.31621 4.22401i 0.231939 0.133910i
\(996\) 0 0
\(997\) −6.23994 35.3885i −0.197621 1.12076i −0.908637 0.417588i \(-0.862876\pi\)
0.711016 0.703176i \(-0.248235\pi\)
\(998\) 0 0
\(999\) −21.2430 2.91307i −0.672099 0.0921655i
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 912.2.cc.d.401.1 18
3.2 odd 2 912.2.cc.c.401.2 18
4.3 odd 2 114.2.l.a.59.3 yes 18
12.11 even 2 114.2.l.b.59.2 yes 18
19.10 odd 18 912.2.cc.c.257.2 18
57.29 even 18 inner 912.2.cc.d.257.1 18
76.67 even 18 114.2.l.b.29.2 yes 18
228.143 odd 18 114.2.l.a.29.3 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
114.2.l.a.29.3 18 228.143 odd 18
114.2.l.a.59.3 yes 18 4.3 odd 2
114.2.l.b.29.2 yes 18 76.67 even 18
114.2.l.b.59.2 yes 18 12.11 even 2
912.2.cc.c.257.2 18 19.10 odd 18
912.2.cc.c.401.2 18 3.2 odd 2
912.2.cc.d.257.1 18 57.29 even 18 inner
912.2.cc.d.401.1 18 1.1 even 1 trivial