Properties

Label 441.2.bg.a.17.4
Level $441$
Weight $2$
Character 441.17
Analytic conductor $3.521$
Analytic rank $0$
Dimension $216$
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] = [441,2,Mod(17,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([21, 25]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.bg (of order \(42\), degree \(12\), 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: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(216\)
Relative dimension: \(18\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label 17.4
Character \(\chi\) \(=\) 441.17
Dual form 441.2.bg.a.26.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.57786 + 0.118244i) q^{2} +(0.497985 - 0.0750592i) q^{4} +(-2.70933 + 2.51389i) q^{5} +(1.38562 - 2.25390i) q^{7} +(2.30834 - 0.526865i) q^{8} +O(q^{10})\) \(q+(-1.57786 + 0.118244i) q^{2} +(0.497985 - 0.0750592i) q^{4} +(-2.70933 + 2.51389i) q^{5} +(1.38562 - 2.25390i) q^{7} +(2.30834 - 0.526865i) q^{8} +(3.97769 - 4.28693i) q^{10} +(2.08781 + 3.06225i) q^{11} +(-1.81859 + 3.77635i) q^{13} +(-1.91979 + 3.72017i) q^{14} +(-4.54241 + 1.40115i) q^{16} +(-0.686097 - 1.74815i) q^{17} +(-0.369695 + 0.213443i) q^{19} +(-1.16052 + 1.45524i) q^{20} +(-3.65635 - 4.58492i) q^{22} +(-8.16396 - 3.20412i) q^{23} +(0.647174 - 8.63594i) q^{25} +(2.42295 - 6.17357i) q^{26} +(0.520840 - 1.22641i) q^{28} +(-7.23589 - 5.77043i) q^{29} +(1.63700 + 0.945120i) q^{31} +(2.59351 - 1.01788i) q^{32} +(1.28927 + 2.67720i) q^{34} +(1.91197 + 9.58986i) q^{35} +(-5.99050 - 0.902922i) q^{37} +(0.558086 - 0.380497i) q^{38} +(-4.92959 + 7.23039i) q^{40} +(-0.210940 - 0.924187i) q^{41} +(-0.484253 + 2.12165i) q^{43} +(1.26955 + 1.36825i) q^{44} +(13.2604 + 4.09030i) q^{46} +(-0.0205569 - 0.274312i) q^{47} +(-3.16014 - 6.24608i) q^{49} +13.7028i q^{50} +(-0.622183 + 2.01707i) q^{52} +(-1.01410 - 6.72809i) q^{53} +(-13.3548 - 3.04814i) q^{55} +(2.01098 - 5.93281i) q^{56} +(12.0995 + 8.24930i) q^{58} +(3.04988 + 2.82987i) q^{59} +(-2.00731 + 13.3177i) q^{61} +(-2.69470 - 1.29770i) q^{62} +(4.59385 - 2.21228i) q^{64} +(-4.56617 - 14.8031i) q^{65} +(-0.116151 + 0.201179i) q^{67} +(-0.472881 - 0.819053i) q^{68} +(-4.15076 - 14.9053i) q^{70} +(-9.97267 + 7.95294i) q^{71} +(-16.4185 - 1.23040i) q^{73} +(9.55891 + 0.716341i) q^{74} +(-0.168082 + 0.134041i) q^{76} +(9.79492 - 0.462609i) q^{77} +(-3.31826 - 5.74740i) q^{79} +(8.78456 - 15.2153i) q^{80} +(0.442112 + 1.43329i) q^{82} +(11.8980 - 5.72975i) q^{83} +(6.25352 + 3.01154i) q^{85} +(0.513209 - 3.40492i) q^{86} +(6.43278 + 5.96874i) q^{88} +(10.1016 + 6.88713i) q^{89} +(5.99165 + 9.33150i) q^{91} +(-4.30603 - 0.982823i) q^{92} +(0.0648716 + 0.430395i) q^{94} +(0.465052 - 1.50766i) q^{95} -2.46635i q^{97} +(5.72480 + 9.48175i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 216 q - 16 q^{4} + 2 q^{7} + 12 q^{10} + 12 q^{16} - 6 q^{19} + 44 q^{22} + 26 q^{25} + 84 q^{28} - 6 q^{31} - 112 q^{34} + 60 q^{37} - 304 q^{40} + 20 q^{43} - 20 q^{46} - 86 q^{49} - 168 q^{52} - 84 q^{55} - 120 q^{58} - 2 q^{61} + 32 q^{64} + 22 q^{67} - 136 q^{70} - 6 q^{73} + 84 q^{76} + 2 q^{79} - 104 q^{82} + 96 q^{85} - 12 q^{88} + 58 q^{91} + 52 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{25}{42}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.57786 + 0.118244i −1.11571 + 0.0836111i −0.619799 0.784761i \(-0.712786\pi\)
−0.495914 + 0.868372i \(0.665167\pi\)
\(3\) 0 0
\(4\) 0.497985 0.0750592i 0.248993 0.0375296i
\(5\) −2.70933 + 2.51389i −1.21165 + 1.12425i −0.222874 + 0.974847i \(0.571544\pi\)
−0.988777 + 0.149401i \(0.952266\pi\)
\(6\) 0 0
\(7\) 1.38562 2.25390i 0.523713 0.851894i
\(8\) 2.30834 0.526865i 0.816123 0.186275i
\(9\) 0 0
\(10\) 3.97769 4.28693i 1.25785 1.35564i
\(11\) 2.08781 + 3.06225i 0.629498 + 0.923304i 0.999985 0.00553360i \(-0.00176141\pi\)
−0.370487 + 0.928838i \(0.620809\pi\)
\(12\) 0 0
\(13\) −1.81859 + 3.77635i −0.504387 + 1.04737i 0.480949 + 0.876748i \(0.340292\pi\)
−0.985336 + 0.170622i \(0.945422\pi\)
\(14\) −1.91979 + 3.72017i −0.513086 + 0.994258i
\(15\) 0 0
\(16\) −4.54241 + 1.40115i −1.13560 + 0.350287i
\(17\) −0.686097 1.74815i −0.166403 0.423988i 0.823212 0.567735i \(-0.192180\pi\)
−0.989614 + 0.143747i \(0.954085\pi\)
\(18\) 0 0
\(19\) −0.369695 + 0.213443i −0.0848137 + 0.0489672i −0.541807 0.840503i \(-0.682260\pi\)
0.456993 + 0.889470i \(0.348926\pi\)
\(20\) −1.16052 + 1.45524i −0.259500 + 0.325402i
\(21\) 0 0
\(22\) −3.65635 4.58492i −0.779537 0.977509i
\(23\) −8.16396 3.20412i −1.70230 0.668105i −0.703222 0.710970i \(-0.748256\pi\)
−0.999081 + 0.0428658i \(0.986351\pi\)
\(24\) 0 0
\(25\) 0.647174 8.63594i 0.129435 1.72719i
\(26\) 2.42295 6.17357i 0.475179 1.21074i
\(27\) 0 0
\(28\) 0.520840 1.22641i 0.0984295 0.231770i
\(29\) −7.23589 5.77043i −1.34367 1.07154i −0.990723 0.135899i \(-0.956608\pi\)
−0.352948 0.935643i \(-0.614821\pi\)
\(30\) 0 0
\(31\) 1.63700 + 0.945120i 0.294013 + 0.169749i 0.639750 0.768583i \(-0.279038\pi\)
−0.345737 + 0.938331i \(0.612371\pi\)
\(32\) 2.59351 1.01788i 0.458473 0.179937i
\(33\) 0 0
\(34\) 1.28927 + 2.67720i 0.221108 + 0.459135i
\(35\) 1.91197 + 9.58986i 0.323183 + 1.62098i
\(36\) 0 0
\(37\) −5.99050 0.902922i −0.984832 0.148440i −0.363168 0.931724i \(-0.618305\pi\)
−0.621664 + 0.783284i \(0.713543\pi\)
\(38\) 0.558086 0.380497i 0.0905335 0.0617247i
\(39\) 0 0
\(40\) −4.92959 + 7.23039i −0.779437 + 1.14322i
\(41\) −0.210940 0.924187i −0.0329433 0.144334i 0.955782 0.294077i \(-0.0950123\pi\)
−0.988725 + 0.149744i \(0.952155\pi\)
\(42\) 0 0
\(43\) −0.484253 + 2.12165i −0.0738479 + 0.323549i −0.998336 0.0576617i \(-0.981636\pi\)
0.924488 + 0.381210i \(0.124493\pi\)
\(44\) 1.26955 + 1.36825i 0.191392 + 0.206271i
\(45\) 0 0
\(46\) 13.2604 + 4.09030i 1.95514 + 0.603081i
\(47\) −0.0205569 0.274312i −0.00299853 0.0400126i 0.995504 0.0947213i \(-0.0301960\pi\)
−0.998502 + 0.0547088i \(0.982577\pi\)
\(48\) 0 0
\(49\) −3.16014 6.24608i −0.451448 0.892297i
\(50\) 13.7028i 1.93787i
\(51\) 0 0
\(52\) −0.622183 + 2.01707i −0.0862813 + 0.279717i
\(53\) −1.01410 6.72809i −0.139297 0.924174i −0.943869 0.330319i \(-0.892844\pi\)
0.804572 0.593854i \(-0.202395\pi\)
\(54\) 0 0
\(55\) −13.3548 3.04814i −1.80075 0.411011i
\(56\) 2.01098 5.93281i 0.268728 0.792805i
\(57\) 0 0
\(58\) 12.0995 + 8.24930i 1.58874 + 1.08319i
\(59\) 3.04988 + 2.82987i 0.397060 + 0.368418i 0.853284 0.521447i \(-0.174608\pi\)
−0.456223 + 0.889865i \(0.650798\pi\)
\(60\) 0 0
\(61\) −2.00731 + 13.3177i −0.257010 + 1.70515i 0.372395 + 0.928074i \(0.378537\pi\)
−0.629405 + 0.777077i \(0.716701\pi\)
\(62\) −2.69470 1.29770i −0.342227 0.164808i
\(63\) 0 0
\(64\) 4.59385 2.21228i 0.574232 0.276535i
\(65\) −4.56617 14.8031i −0.566363 1.83610i
\(66\) 0 0
\(67\) −0.116151 + 0.201179i −0.0141900 + 0.0245779i −0.873033 0.487661i \(-0.837850\pi\)
0.858843 + 0.512239i \(0.171184\pi\)
\(68\) −0.472881 0.819053i −0.0573452 0.0993248i
\(69\) 0 0
\(70\) −4.15076 14.9053i −0.496111 1.78153i
\(71\) −9.97267 + 7.95294i −1.18354 + 0.943840i −0.999238 0.0390297i \(-0.987573\pi\)
−0.184300 + 0.982870i \(0.559002\pi\)
\(72\) 0 0
\(73\) −16.4185 1.23040i −1.92164 0.144007i −0.940819 0.338909i \(-0.889942\pi\)
−0.980823 + 0.194901i \(0.937561\pi\)
\(74\) 9.55891 + 0.716341i 1.11120 + 0.0832730i
\(75\) 0 0
\(76\) −0.168082 + 0.134041i −0.0192803 + 0.0153755i
\(77\) 9.79492 0.462609i 1.11623 0.0527192i
\(78\) 0 0
\(79\) −3.31826 5.74740i −0.373334 0.646633i 0.616743 0.787165i \(-0.288452\pi\)
−0.990076 + 0.140532i \(0.955119\pi\)
\(80\) 8.78456 15.2153i 0.982144 1.70112i
\(81\) 0 0
\(82\) 0.442112 + 1.43329i 0.0488231 + 0.158281i
\(83\) 11.8980 5.72975i 1.30597 0.628922i 0.354038 0.935231i \(-0.384808\pi\)
0.951932 + 0.306309i \(0.0990941\pi\)
\(84\) 0 0
\(85\) 6.25352 + 3.01154i 0.678290 + 0.326647i
\(86\) 0.513209 3.40492i 0.0553407 0.367162i
\(87\) 0 0
\(88\) 6.43278 + 5.96874i 0.685736 + 0.636270i
\(89\) 10.1016 + 6.88713i 1.07076 + 0.730034i 0.964441 0.264298i \(-0.0851402\pi\)
0.106322 + 0.994332i \(0.466093\pi\)
\(90\) 0 0
\(91\) 5.99165 + 9.33150i 0.628095 + 0.978207i
\(92\) −4.30603 0.982823i −0.448935 0.102466i
\(93\) 0 0
\(94\) 0.0648716 + 0.430395i 0.00669099 + 0.0443918i
\(95\) 0.465052 1.50766i 0.0477133 0.154683i
\(96\) 0 0
\(97\) 2.46635i 0.250420i −0.992130 0.125210i \(-0.960040\pi\)
0.992130 0.125210i \(-0.0399604\pi\)
\(98\) 5.72480 + 9.48175i 0.578293 + 0.957801i
\(99\) 0 0
\(100\) −0.325924 4.34915i −0.0325924 0.434915i
\(101\) −3.51151 1.08316i −0.349408 0.107778i 0.115083 0.993356i \(-0.463287\pi\)
−0.464491 + 0.885578i \(0.653763\pi\)
\(102\) 0 0
\(103\) 3.75257 + 4.04431i 0.369752 + 0.398498i 0.890330 0.455316i \(-0.150474\pi\)
−0.520578 + 0.853814i \(0.674283\pi\)
\(104\) −2.20832 + 9.67527i −0.216543 + 0.948738i
\(105\) 0 0
\(106\) 2.39565 + 10.4960i 0.232686 + 1.01947i
\(107\) −4.30053 + 6.30771i −0.415748 + 0.609790i −0.975799 0.218668i \(-0.929829\pi\)
0.560052 + 0.828458i \(0.310781\pi\)
\(108\) 0 0
\(109\) −0.0919472 + 0.0626885i −0.00880694 + 0.00600447i −0.567716 0.823225i \(-0.692173\pi\)
0.558909 + 0.829229i \(0.311220\pi\)
\(110\) 21.4323 + 3.23040i 2.04349 + 0.308007i
\(111\) 0 0
\(112\) −3.13598 + 12.1796i −0.296323 + 1.15086i
\(113\) 3.22553 + 6.69787i 0.303432 + 0.630083i 0.995809 0.0914525i \(-0.0291510\pi\)
−0.692378 + 0.721535i \(0.743437\pi\)
\(114\) 0 0
\(115\) 30.1737 11.8423i 2.81371 1.10430i
\(116\) −4.03649 2.33047i −0.374779 0.216379i
\(117\) 0 0
\(118\) −5.14688 4.10450i −0.473809 0.377850i
\(119\) −4.89082 0.875864i −0.448340 0.0802904i
\(120\) 0 0
\(121\) −0.999699 + 2.54719i −0.0908817 + 0.231563i
\(122\) 1.59252 21.2507i 0.144180 1.92395i
\(123\) 0 0
\(124\) 0.886140 + 0.347784i 0.0795777 + 0.0312320i
\(125\) 8.43445 + 10.5765i 0.754400 + 0.945988i
\(126\) 0 0
\(127\) 9.27637 11.6322i 0.823145 1.03219i −0.175714 0.984441i \(-0.556224\pi\)
0.998859 0.0477498i \(-0.0152050\pi\)
\(128\) −11.8125 + 6.81997i −1.04409 + 0.602806i
\(129\) 0 0
\(130\) 8.95513 + 22.8173i 0.785417 + 2.00121i
\(131\) −17.6370 + 5.44031i −1.54096 + 0.475322i −0.944828 0.327567i \(-0.893771\pi\)
−0.596128 + 0.802889i \(0.703295\pi\)
\(132\) 0 0
\(133\) −0.0311746 + 1.12901i −0.00270318 + 0.0978972i
\(134\) 0.159481 0.331165i 0.0137770 0.0286083i
\(135\) 0 0
\(136\) −2.50478 3.67384i −0.214783 0.315030i
\(137\) 3.45520 3.72382i 0.295198 0.318148i −0.567985 0.823039i \(-0.692277\pi\)
0.863183 + 0.504891i \(0.168467\pi\)
\(138\) 0 0
\(139\) −13.9111 + 3.17511i −1.17992 + 0.269310i −0.767116 0.641509i \(-0.778309\pi\)
−0.412807 + 0.910818i \(0.635452\pi\)
\(140\) 1.67194 + 4.63210i 0.141305 + 0.391484i
\(141\) 0 0
\(142\) 14.7950 13.7278i 1.24157 1.15201i
\(143\) −15.3610 + 2.31530i −1.28455 + 0.193615i
\(144\) 0 0
\(145\) 34.1107 2.55624i 2.83274 0.212284i
\(146\) 26.0515 2.15604
\(147\) 0 0
\(148\) −3.05095 −0.250787
\(149\) 15.7536 1.18057i 1.29059 0.0967161i 0.588319 0.808629i \(-0.299790\pi\)
0.702268 + 0.711913i \(0.252171\pi\)
\(150\) 0 0
\(151\) −13.9058 + 2.09596i −1.13164 + 0.170567i −0.688049 0.725664i \(-0.741533\pi\)
−0.443588 + 0.896231i \(0.646294\pi\)
\(152\) −0.740927 + 0.687479i −0.0600971 + 0.0557619i
\(153\) 0 0
\(154\) −15.4003 + 1.88812i −1.24099 + 0.152149i
\(155\) −6.81110 + 1.55459i −0.547081 + 0.124868i
\(156\) 0 0
\(157\) 0.807372 0.870140i 0.0644353 0.0694448i −0.700011 0.714132i \(-0.746822\pi\)
0.764447 + 0.644687i \(0.223012\pi\)
\(158\) 5.91533 + 8.67620i 0.470599 + 0.690241i
\(159\) 0 0
\(160\) −4.46785 + 9.27759i −0.353215 + 0.733458i
\(161\) −18.5339 + 13.9611i −1.46067 + 1.10029i
\(162\) 0 0
\(163\) 8.50588 2.62372i 0.666232 0.205505i 0.0568506 0.998383i \(-0.481894\pi\)
0.609381 + 0.792877i \(0.291418\pi\)
\(164\) −0.174414 0.444399i −0.0136194 0.0347017i
\(165\) 0 0
\(166\) −18.0957 + 10.4476i −1.40450 + 0.810890i
\(167\) 6.78697 8.51059i 0.525191 0.658569i −0.446511 0.894778i \(-0.647334\pi\)
0.971702 + 0.236209i \(0.0759051\pi\)
\(168\) 0 0
\(169\) −2.84816 3.57148i −0.219090 0.274730i
\(170\) −10.2233 4.01233i −0.784088 0.307732i
\(171\) 0 0
\(172\) −0.0819014 + 1.09290i −0.00624492 + 0.0833327i
\(173\) 2.15991 5.50336i 0.164215 0.418412i −0.824953 0.565201i \(-0.808799\pi\)
0.989168 + 0.146789i \(0.0468938\pi\)
\(174\) 0 0
\(175\) −18.5678 13.4248i −1.40360 1.01482i
\(176\) −13.7744 10.9847i −1.03828 0.828001i
\(177\) 0 0
\(178\) −16.7532 9.67244i −1.25570 0.724980i
\(179\) −4.34885 + 1.70680i −0.325049 + 0.127572i −0.522254 0.852790i \(-0.674909\pi\)
0.197205 + 0.980362i \(0.436813\pi\)
\(180\) 0 0
\(181\) −2.59066 5.37956i −0.192562 0.399859i 0.782225 0.622996i \(-0.214085\pi\)
−0.974787 + 0.223137i \(0.928370\pi\)
\(182\) −10.5573 14.0153i −0.782562 1.03888i
\(183\) 0 0
\(184\) −20.5334 3.09491i −1.51374 0.228160i
\(185\) 18.5001 12.6132i 1.36016 0.927338i
\(186\) 0 0
\(187\) 3.92083 5.75080i 0.286719 0.420540i
\(188\) −0.0308267 0.135061i −0.00224827 0.00985030i
\(189\) 0 0
\(190\) −0.555513 + 2.43386i −0.0403012 + 0.176571i
\(191\) −1.13621 1.22454i −0.0822133 0.0886049i 0.690605 0.723232i \(-0.257344\pi\)
−0.772819 + 0.634627i \(0.781154\pi\)
\(192\) 0 0
\(193\) −3.68813 1.13764i −0.265477 0.0818889i 0.159159 0.987253i \(-0.449122\pi\)
−0.424636 + 0.905364i \(0.639598\pi\)
\(194\) 0.291631 + 3.89154i 0.0209379 + 0.279396i
\(195\) 0 0
\(196\) −2.04253 2.87326i −0.145895 0.205233i
\(197\) 3.58713i 0.255572i 0.991802 + 0.127786i \(0.0407871\pi\)
−0.991802 + 0.127786i \(0.959213\pi\)
\(198\) 0 0
\(199\) 0.179176 0.580875i 0.0127015 0.0411771i −0.949000 0.315275i \(-0.897903\pi\)
0.961702 + 0.274098i \(0.0883793\pi\)
\(200\) −3.05607 20.2757i −0.216097 1.43371i
\(201\) 0 0
\(202\) 5.66873 + 1.29385i 0.398850 + 0.0910350i
\(203\) −23.0321 + 8.31338i −1.61654 + 0.583485i
\(204\) 0 0
\(205\) 2.89482 + 1.97365i 0.202183 + 0.137846i
\(206\) −6.39923 5.93762i −0.445856 0.413694i
\(207\) 0 0
\(208\) 2.96957 19.7018i 0.205903 1.36608i
\(209\) −1.42547 0.686470i −0.0986018 0.0474841i
\(210\) 0 0
\(211\) −7.38006 + 3.55405i −0.508064 + 0.244671i −0.670312 0.742079i \(-0.733840\pi\)
0.162248 + 0.986750i \(0.448126\pi\)
\(212\) −1.01001 3.27437i −0.0693677 0.224885i
\(213\) 0 0
\(214\) 6.03976 10.4612i 0.412870 0.715111i
\(215\) −4.02160 6.96562i −0.274271 0.475051i
\(216\) 0 0
\(217\) 4.39846 2.38005i 0.298587 0.161569i
\(218\) 0.137667 0.109786i 0.00932397 0.00743562i
\(219\) 0 0
\(220\) −6.87926 0.515529i −0.463800 0.0347570i
\(221\) 7.84934 + 0.588227i 0.528004 + 0.0395684i
\(222\) 0 0
\(223\) −0.481571 + 0.384040i −0.0322484 + 0.0257172i −0.639481 0.768807i \(-0.720851\pi\)
0.607233 + 0.794524i \(0.292279\pi\)
\(224\) 1.29941 7.25591i 0.0868208 0.484806i
\(225\) 0 0
\(226\) −5.88140 10.1869i −0.391225 0.677621i
\(227\) −5.95885 + 10.3210i −0.395503 + 0.685031i −0.993165 0.116717i \(-0.962763\pi\)
0.597662 + 0.801748i \(0.296096\pi\)
\(228\) 0 0
\(229\) 8.24281 + 26.7225i 0.544700 + 1.76587i 0.637783 + 0.770216i \(0.279852\pi\)
−0.0930829 + 0.995658i \(0.529672\pi\)
\(230\) −46.2095 + 22.2533i −3.04696 + 1.46734i
\(231\) 0 0
\(232\) −19.7432 9.50780i −1.29620 0.624218i
\(233\) 0.695670 4.61547i 0.0455749 0.302370i −0.954418 0.298475i \(-0.903522\pi\)
0.999992 0.00389485i \(-0.00123977\pi\)
\(234\) 0 0
\(235\) 0.745288 + 0.691526i 0.0486172 + 0.0451102i
\(236\) 1.73120 + 1.18031i 0.112692 + 0.0768319i
\(237\) 0 0
\(238\) 7.82057 + 0.803678i 0.506932 + 0.0520947i
\(239\) −8.96689 2.04663i −0.580020 0.132386i −0.0775621 0.996988i \(-0.524714\pi\)
−0.502458 + 0.864602i \(0.667571\pi\)
\(240\) 0 0
\(241\) 4.51065 + 29.9262i 0.290557 + 1.92772i 0.366102 + 0.930575i \(0.380692\pi\)
−0.0755452 + 0.997142i \(0.524070\pi\)
\(242\) 1.27619 4.13731i 0.0820367 0.265956i
\(243\) 0 0
\(244\) 6.78267i 0.434216i
\(245\) 24.2639 + 8.97846i 1.55016 + 0.573613i
\(246\) 0 0
\(247\) −0.133712 1.78426i −0.00850789 0.113530i
\(248\) 4.27670 + 1.31919i 0.271571 + 0.0837685i
\(249\) 0 0
\(250\) −14.5590 15.6908i −0.920789 0.992374i
\(251\) −3.19381 + 13.9930i −0.201591 + 0.883229i 0.768377 + 0.639997i \(0.221065\pi\)
−0.969968 + 0.243231i \(0.921793\pi\)
\(252\) 0 0
\(253\) −7.23297 31.6897i −0.454733 1.99231i
\(254\) −13.2613 + 19.4508i −0.832090 + 1.22045i
\(255\) 0 0
\(256\) 9.40640 6.41318i 0.587900 0.400824i
\(257\) 4.77127 + 0.719153i 0.297624 + 0.0448595i 0.296157 0.955139i \(-0.404295\pi\)
0.00146698 + 0.999999i \(0.499533\pi\)
\(258\) 0 0
\(259\) −10.3356 + 12.2509i −0.642224 + 0.761233i
\(260\) −3.38500 7.02902i −0.209929 0.435921i
\(261\) 0 0
\(262\) 27.1854 10.6695i 1.67952 0.659164i
\(263\) 20.2728 + 11.7045i 1.25008 + 0.721732i 0.971124 0.238573i \(-0.0766797\pi\)
0.278952 + 0.960305i \(0.410013\pi\)
\(264\) 0 0
\(265\) 19.6612 + 15.6793i 1.20778 + 0.963172i
\(266\) −0.0843090 1.78509i −0.00516932 0.109451i
\(267\) 0 0
\(268\) −0.0427410 + 0.108902i −0.00261082 + 0.00665226i
\(269\) −0.822144 + 10.9708i −0.0501270 + 0.668899i 0.914383 + 0.404851i \(0.132677\pi\)
−0.964510 + 0.264048i \(0.914942\pi\)
\(270\) 0 0
\(271\) −25.6381 10.0622i −1.55741 0.611237i −0.578524 0.815665i \(-0.696371\pi\)
−0.978881 + 0.204429i \(0.934466\pi\)
\(272\) 5.56594 + 6.97947i 0.337485 + 0.423193i
\(273\) 0 0
\(274\) −5.01149 + 6.28421i −0.302755 + 0.379643i
\(275\) 27.7966 16.0484i 1.67620 0.967754i
\(276\) 0 0
\(277\) 2.17380 + 5.53876i 0.130611 + 0.332792i 0.981187 0.193061i \(-0.0618415\pi\)
−0.850576 + 0.525853i \(0.823746\pi\)
\(278\) 21.5742 6.65477i 1.29394 0.399127i
\(279\) 0 0
\(280\) 9.46605 + 21.1294i 0.565705 + 1.26272i
\(281\) −9.10986 + 18.9168i −0.543449 + 1.12848i 0.430683 + 0.902503i \(0.358273\pi\)
−0.974132 + 0.225980i \(0.927442\pi\)
\(282\) 0 0
\(283\) 9.58714 + 14.0617i 0.569896 + 0.835884i 0.997686 0.0679943i \(-0.0216600\pi\)
−0.427790 + 0.903878i \(0.640708\pi\)
\(284\) −4.36930 + 4.70899i −0.259270 + 0.279427i
\(285\) 0 0
\(286\) 23.9637 5.46956i 1.41700 0.323422i
\(287\) −2.37531 0.805131i −0.140210 0.0475254i
\(288\) 0 0
\(289\) 9.87659 9.16414i 0.580976 0.539067i
\(290\) −53.5195 + 8.06676i −3.14277 + 0.473697i
\(291\) 0 0
\(292\) −8.26853 + 0.619641i −0.483879 + 0.0362617i
\(293\) −15.9997 −0.934711 −0.467356 0.884069i \(-0.654793\pi\)
−0.467356 + 0.884069i \(0.654793\pi\)
\(294\) 0 0
\(295\) −15.3771 −0.895292
\(296\) −14.3039 + 1.07193i −0.831394 + 0.0623044i
\(297\) 0 0
\(298\) −24.7173 + 3.72554i −1.43184 + 0.215815i
\(299\) 26.9468 25.0030i 1.55837 1.44596i
\(300\) 0 0
\(301\) 4.11100 + 4.03125i 0.236954 + 0.232357i
\(302\) 21.6935 4.95140i 1.24832 0.284921i
\(303\) 0 0
\(304\) 1.38024 1.48754i 0.0791621 0.0853164i
\(305\) −28.0407 41.1282i −1.60561 2.35499i
\(306\) 0 0
\(307\) 8.92187 18.5265i 0.509198 1.05736i −0.474950 0.880013i \(-0.657534\pi\)
0.984148 0.177348i \(-0.0567519\pi\)
\(308\) 4.84300 0.965571i 0.275956 0.0550185i
\(309\) 0 0
\(310\) 10.5631 3.25829i 0.599945 0.185058i
\(311\) 6.50779 + 16.5816i 0.369023 + 0.940255i 0.987945 + 0.154803i \(0.0494742\pi\)
−0.618923 + 0.785452i \(0.712431\pi\)
\(312\) 0 0
\(313\) −11.6742 + 6.74008i −0.659863 + 0.380972i −0.792225 0.610229i \(-0.791077\pi\)
0.132362 + 0.991201i \(0.457744\pi\)
\(314\) −1.17103 + 1.46842i −0.0660849 + 0.0828679i
\(315\) 0 0
\(316\) −2.08384 2.61305i −0.117225 0.146996i
\(317\) −16.5602 6.49940i −0.930114 0.365043i −0.148576 0.988901i \(-0.547469\pi\)
−0.781538 + 0.623858i \(0.785564\pi\)
\(318\) 0 0
\(319\) 2.56336 34.2057i 0.143521 1.91515i
\(320\) −6.88484 + 17.5423i −0.384874 + 0.980643i
\(321\) 0 0
\(322\) 27.5930 24.2201i 1.53770 1.34973i
\(323\) 0.626776 + 0.499837i 0.0348748 + 0.0278117i
\(324\) 0 0
\(325\) 31.4354 + 18.1492i 1.74372 + 1.00674i
\(326\) −13.1108 + 5.14561i −0.726140 + 0.284989i
\(327\) 0 0
\(328\) −0.973843 2.02221i −0.0537715 0.111658i
\(329\) −0.646757 0.333758i −0.0356569 0.0184007i
\(330\) 0 0
\(331\) 19.3216 + 2.91227i 1.06201 + 0.160073i 0.656735 0.754121i \(-0.271937\pi\)
0.405277 + 0.914194i \(0.367175\pi\)
\(332\) 5.49493 3.74638i 0.301574 0.205609i
\(333\) 0 0
\(334\) −9.70253 + 14.2310i −0.530899 + 0.778685i
\(335\) −0.191051 0.837050i −0.0104382 0.0457330i
\(336\) 0 0
\(337\) 2.93386 12.8541i 0.159817 0.700206i −0.829988 0.557781i \(-0.811653\pi\)
0.989806 0.142425i \(-0.0454899\pi\)
\(338\) 4.91630 + 5.29851i 0.267411 + 0.288201i
\(339\) 0 0
\(340\) 3.34021 + 1.03032i 0.181148 + 0.0558768i
\(341\) 0.523538 + 6.98613i 0.0283512 + 0.378320i
\(342\) 0 0
\(343\) −18.4568 1.53203i −0.996573 0.0827216i
\(344\) 5.15264i 0.277811i
\(345\) 0 0
\(346\) −2.75729 + 8.93890i −0.148233 + 0.480558i
\(347\) −2.43939 16.1843i −0.130953 0.868819i −0.953776 0.300520i \(-0.902840\pi\)
0.822822 0.568299i \(-0.192398\pi\)
\(348\) 0 0
\(349\) 12.7346 + 2.90660i 0.681669 + 0.155587i 0.549314 0.835616i \(-0.314889\pi\)
0.132355 + 0.991202i \(0.457746\pi\)
\(350\) 30.8847 + 18.9868i 1.65086 + 1.01489i
\(351\) 0 0
\(352\) 8.53177 + 5.81686i 0.454745 + 0.310040i
\(353\) 9.44447 + 8.76319i 0.502679 + 0.466418i 0.890283 0.455408i \(-0.150507\pi\)
−0.387604 + 0.921826i \(0.626697\pi\)
\(354\) 0 0
\(355\) 7.02644 46.6174i 0.372925 2.47420i
\(356\) 5.54737 + 2.67147i 0.294010 + 0.141588i
\(357\) 0 0
\(358\) 6.66005 3.20731i 0.351994 0.169512i
\(359\) 4.74043 + 15.3681i 0.250190 + 0.811097i 0.990341 + 0.138655i \(0.0442780\pi\)
−0.740151 + 0.672441i \(0.765246\pi\)
\(360\) 0 0
\(361\) −9.40888 + 16.2967i −0.495204 + 0.857719i
\(362\) 4.72378 + 8.18184i 0.248277 + 0.430028i
\(363\) 0 0
\(364\) 3.68417 + 4.19722i 0.193103 + 0.219994i
\(365\) 47.5763 37.9409i 2.49026 1.98592i
\(366\) 0 0
\(367\) −24.3415 1.82414i −1.27061 0.0952194i −0.577706 0.816245i \(-0.696052\pi\)
−0.692909 + 0.721025i \(0.743671\pi\)
\(368\) 41.5735 + 3.11550i 2.16717 + 0.162407i
\(369\) 0 0
\(370\) −27.6991 + 22.0893i −1.44001 + 1.14837i
\(371\) −16.5696 7.03687i −0.860250 0.365336i
\(372\) 0 0
\(373\) 3.52813 + 6.11090i 0.182680 + 0.316411i 0.942792 0.333381i \(-0.108190\pi\)
−0.760112 + 0.649792i \(0.774856\pi\)
\(374\) −5.50650 + 9.53755i −0.284735 + 0.493175i
\(375\) 0 0
\(376\) −0.191978 0.622377i −0.00990050 0.0320966i
\(377\) 34.9503 16.8312i 1.80003 0.866850i
\(378\) 0 0
\(379\) −12.8626 6.19432i −0.660709 0.318181i 0.0733102 0.997309i \(-0.476644\pi\)
−0.734020 + 0.679128i \(0.762358\pi\)
\(380\) 0.118425 0.785700i 0.00607509 0.0403056i
\(381\) 0 0
\(382\) 1.93757 + 1.79780i 0.0991348 + 0.0919836i
\(383\) −17.5153 11.9417i −0.894991 0.610194i 0.0260499 0.999661i \(-0.491707\pi\)
−0.921041 + 0.389466i \(0.872660\pi\)
\(384\) 0 0
\(385\) −25.3748 + 25.8768i −1.29322 + 1.31880i
\(386\) 5.95385 + 1.35893i 0.303043 + 0.0691676i
\(387\) 0 0
\(388\) −0.185122 1.22820i −0.00939815 0.0623526i
\(389\) −7.88011 + 25.5467i −0.399537 + 1.29527i 0.502862 + 0.864367i \(0.332280\pi\)
−0.902399 + 0.430901i \(0.858196\pi\)
\(390\) 0 0
\(391\) 16.4701i 0.832930i
\(392\) −10.5855 12.7531i −0.534650 0.644131i
\(393\) 0 0
\(394\) −0.424156 5.65997i −0.0213687 0.285145i
\(395\) 23.4386 + 7.22986i 1.17933 + 0.363774i
\(396\) 0 0
\(397\) 10.3190 + 11.1212i 0.517894 + 0.558157i 0.936797 0.349874i \(-0.113776\pi\)
−0.418903 + 0.908031i \(0.637585\pi\)
\(398\) −0.214029 + 0.937723i −0.0107283 + 0.0470038i
\(399\) 0 0
\(400\) 9.16050 + 40.1348i 0.458025 + 2.00674i
\(401\) 5.57969 8.18391i 0.278637 0.408685i −0.661253 0.750163i \(-0.729975\pi\)
0.939890 + 0.341478i \(0.110927\pi\)
\(402\) 0 0
\(403\) −6.54614 + 4.46308i −0.326086 + 0.222322i
\(404\) −1.82998 0.275825i −0.0910449 0.0137228i
\(405\) 0 0
\(406\) 35.3584 15.8407i 1.75481 0.786162i
\(407\) −9.74204 20.2296i −0.482895 1.00274i
\(408\) 0 0
\(409\) −7.75843 + 3.04496i −0.383630 + 0.150564i −0.549316 0.835615i \(-0.685112\pi\)
0.165686 + 0.986179i \(0.447016\pi\)
\(410\) −4.80097 2.77184i −0.237103 0.136892i
\(411\) 0 0
\(412\) 2.17229 + 1.73234i 0.107021 + 0.0853464i
\(413\) 10.6042 2.95301i 0.521799 0.145308i
\(414\) 0 0
\(415\) −17.8315 + 45.4340i −0.875316 + 2.23027i
\(416\) −0.872681 + 11.6451i −0.0427867 + 0.570949i
\(417\) 0 0
\(418\) 2.33036 + 0.914597i 0.113981 + 0.0447344i
\(419\) 13.3451 + 16.7342i 0.651948 + 0.817517i 0.992440 0.122730i \(-0.0391650\pi\)
−0.340492 + 0.940248i \(0.610594\pi\)
\(420\) 0 0
\(421\) 18.2516 22.8867i 0.889527 1.11543i −0.103154 0.994665i \(-0.532893\pi\)
0.992681 0.120766i \(-0.0385351\pi\)
\(422\) 11.2244 6.48043i 0.546396 0.315462i
\(423\) 0 0
\(424\) −5.88567 14.9964i −0.285834 0.728292i
\(425\) −15.5409 + 4.79374i −0.753845 + 0.232530i
\(426\) 0 0
\(427\) 27.2353 + 22.9774i 1.31801 + 1.11196i
\(428\) −1.66815 + 3.46394i −0.0806329 + 0.167436i
\(429\) 0 0
\(430\) 7.16915 + 10.5152i 0.345727 + 0.507089i
\(431\) −2.98851 + 3.22084i −0.143951 + 0.155143i −0.800912 0.598783i \(-0.795651\pi\)
0.656960 + 0.753925i \(0.271842\pi\)
\(432\) 0 0
\(433\) 24.5036 5.59278i 1.17757 0.268772i 0.411425 0.911444i \(-0.365031\pi\)
0.766141 + 0.642672i \(0.222174\pi\)
\(434\) −6.65870 + 4.27547i −0.319628 + 0.205229i
\(435\) 0 0
\(436\) −0.0410830 + 0.0381194i −0.00196752 + 0.00182559i
\(437\) 3.70207 0.557997i 0.177094 0.0266926i
\(438\) 0 0
\(439\) −6.75124 + 0.505936i −0.322219 + 0.0241470i −0.234858 0.972030i \(-0.575463\pi\)
−0.0873613 + 0.996177i \(0.527843\pi\)
\(440\) −32.4333 −1.54620
\(441\) 0 0
\(442\) −12.4547 −0.592409
\(443\) −16.6583 + 1.24837i −0.791461 + 0.0593118i −0.464324 0.885665i \(-0.653703\pi\)
−0.327137 + 0.944977i \(0.606084\pi\)
\(444\) 0 0
\(445\) −44.6820 + 6.73473i −2.11813 + 0.319257i
\(446\) 0.714440 0.662903i 0.0338297 0.0313894i
\(447\) 0 0
\(448\) 1.37905 13.4195i 0.0651539 0.634010i
\(449\) 32.3488 7.38340i 1.52663 0.348444i 0.624890 0.780713i \(-0.285144\pi\)
0.901745 + 0.432269i \(0.142287\pi\)
\(450\) 0 0
\(451\) 2.38969 2.57548i 0.112526 0.121275i
\(452\) 2.10900 + 3.09334i 0.0991991 + 0.145498i
\(453\) 0 0
\(454\) 8.18181 16.9897i 0.383991 0.797366i
\(455\) −39.6918 10.2198i −1.86078 0.479111i
\(456\) 0 0
\(457\) −21.8928 + 6.75304i −1.02410 + 0.315894i −0.760916 0.648851i \(-0.775250\pi\)
−0.263187 + 0.964745i \(0.584774\pi\)
\(458\) −16.1657 41.1896i −0.755375 1.92467i
\(459\) 0 0
\(460\) 14.1372 8.16211i 0.659150 0.380560i
\(461\) 12.1939 15.2907i 0.567928 0.712159i −0.412073 0.911151i \(-0.635195\pi\)
0.980001 + 0.198992i \(0.0637667\pi\)
\(462\) 0 0
\(463\) 21.3266 + 26.7427i 0.991132 + 1.24284i 0.970010 + 0.243064i \(0.0781524\pi\)
0.0211221 + 0.999777i \(0.493276\pi\)
\(464\) 40.9536 + 16.0731i 1.90122 + 0.746175i
\(465\) 0 0
\(466\) −0.551916 + 7.36481i −0.0255670 + 0.341168i
\(467\) 12.4824 31.8045i 0.577615 1.47174i −0.281300 0.959620i \(-0.590766\pi\)
0.858915 0.512119i \(-0.171139\pi\)
\(468\) 0 0
\(469\) 0.292497 + 0.540548i 0.0135062 + 0.0249602i
\(470\) −1.25773 1.00300i −0.0580146 0.0462651i
\(471\) 0 0
\(472\) 8.53113 + 4.92545i 0.392677 + 0.226712i
\(473\) −7.50806 + 2.94670i −0.345221 + 0.135489i
\(474\) 0 0
\(475\) 1.60403 + 3.33080i 0.0735978 + 0.152827i
\(476\) −2.50130 0.0690669i −0.114647 0.00316567i
\(477\) 0 0
\(478\) 14.3905 + 2.16901i 0.658204 + 0.0992083i
\(479\) 0.503579 0.343335i 0.0230091 0.0156874i −0.551761 0.834002i \(-0.686044\pi\)
0.574770 + 0.818315i \(0.305092\pi\)
\(480\) 0 0
\(481\) 14.3040 20.9802i 0.652208 0.956613i
\(482\) −10.6558 46.6859i −0.485356 2.12648i
\(483\) 0 0
\(484\) −0.306645 + 1.34350i −0.0139384 + 0.0610682i
\(485\) 6.20014 + 6.68216i 0.281534 + 0.303421i
\(486\) 0 0
\(487\) −10.1670 3.13609i −0.460709 0.142110i 0.0557079 0.998447i \(-0.482258\pi\)
−0.516417 + 0.856337i \(0.672735\pi\)
\(488\) 2.38303 + 31.7993i 0.107875 + 1.43949i
\(489\) 0 0
\(490\) −39.3465 11.2977i −1.77749 0.510376i
\(491\) 17.6897i 0.798323i −0.916881 0.399162i \(-0.869301\pi\)
0.916881 0.399162i \(-0.130699\pi\)
\(492\) 0 0
\(493\) −5.12303 + 16.6085i −0.230730 + 0.748008i
\(494\) 0.421956 + 2.79950i 0.0189847 + 0.125955i
\(495\) 0 0
\(496\) −8.76016 1.99945i −0.393343 0.0897779i
\(497\) 4.10685 + 33.4971i 0.184217 + 1.50255i
\(498\) 0 0
\(499\) −24.2187 16.5120i −1.08418 0.739180i −0.116963 0.993136i \(-0.537316\pi\)
−0.967216 + 0.253956i \(0.918268\pi\)
\(500\) 4.99409 + 4.63384i 0.223343 + 0.207232i
\(501\) 0 0
\(502\) 3.38478 22.4565i 0.151070 1.00228i
\(503\) 14.5378 + 7.00104i 0.648209 + 0.312161i 0.728943 0.684575i \(-0.240012\pi\)
−0.0807339 + 0.996736i \(0.525726\pi\)
\(504\) 0 0
\(505\) 12.2368 5.89292i 0.544530 0.262232i
\(506\) 15.1597 + 49.1465i 0.673930 + 2.18483i
\(507\) 0 0
\(508\) 3.74639 6.48894i 0.166219 0.287900i
\(509\) −7.20106 12.4726i −0.319181 0.552838i 0.661136 0.750266i \(-0.270075\pi\)
−0.980317 + 0.197428i \(0.936741\pi\)
\(510\) 0 0
\(511\) −25.5229 + 35.3009i −1.12907 + 1.56162i
\(512\) 7.24463 5.77740i 0.320170 0.255327i
\(513\) 0 0
\(514\) −7.61341 0.570546i −0.335813 0.0251657i
\(515\) −20.3339 1.52382i −0.896021 0.0671475i
\(516\) 0 0
\(517\) 0.797095 0.635662i 0.0350562 0.0279564i
\(518\) 14.8595 20.5523i 0.652890 0.903014i
\(519\) 0 0
\(520\) −18.3395 31.7650i −0.804242 1.39299i
\(521\) 8.06844 13.9749i 0.353485 0.612254i −0.633373 0.773847i \(-0.718330\pi\)
0.986857 + 0.161593i \(0.0516633\pi\)
\(522\) 0 0
\(523\) 8.46609 + 27.4464i 0.370196 + 1.20015i 0.928759 + 0.370685i \(0.120877\pi\)
−0.558563 + 0.829462i \(0.688647\pi\)
\(524\) −8.37465 + 4.03302i −0.365848 + 0.176183i
\(525\) 0 0
\(526\) −33.3716 16.0709i −1.45507 0.700725i
\(527\) 0.529071 3.51015i 0.0230467 0.152905i
\(528\) 0 0
\(529\) 39.5236 + 36.6726i 1.71842 + 1.59446i
\(530\) −32.8766 22.4149i −1.42807 0.973639i
\(531\) 0 0
\(532\) 0.0692177 + 0.564568i 0.00300097 + 0.0244771i
\(533\) 3.87367 + 0.884140i 0.167787 + 0.0382963i
\(534\) 0 0
\(535\) −4.20537 27.9008i −0.181814 1.20626i
\(536\) −0.162122 + 0.525585i −0.00700259 + 0.0227018i
\(537\) 0 0
\(538\) 17.4075i 0.750490i
\(539\) 12.5293 22.7178i 0.539676 0.978524i
\(540\) 0 0
\(541\) 1.08248 + 14.4447i 0.0465395 + 0.621027i 0.970897 + 0.239499i \(0.0769830\pi\)
−0.924357 + 0.381528i \(0.875398\pi\)
\(542\) 41.6431 + 12.8452i 1.78872 + 0.551748i
\(543\) 0 0
\(544\) −3.55880 3.83548i −0.152582 0.164445i
\(545\) 0.0915233 0.400990i 0.00392043 0.0171765i
\(546\) 0 0
\(547\) 5.09694 + 22.3311i 0.217929 + 0.954810i 0.959005 + 0.283389i \(0.0914588\pi\)
−0.741076 + 0.671421i \(0.765684\pi\)
\(548\) 1.44113 2.11375i 0.0615621 0.0902951i
\(549\) 0 0
\(550\) −41.9614 + 28.6088i −1.78924 + 1.21988i
\(551\) 3.90673 + 0.588844i 0.166432 + 0.0250856i
\(552\) 0 0
\(553\) −17.5519 0.484651i −0.746383 0.0206094i
\(554\) −4.08487 8.48232i −0.173550 0.360379i
\(555\) 0 0
\(556\) −6.68919 + 2.62532i −0.283685 + 0.111338i
\(557\) −11.6819 6.74456i −0.494979 0.285776i 0.231659 0.972797i \(-0.425585\pi\)
−0.726638 + 0.687021i \(0.758918\pi\)
\(558\) 0 0
\(559\) −7.13143 5.68713i −0.301628 0.240540i
\(560\) −22.1218 40.8821i −0.934816 1.72758i
\(561\) 0 0
\(562\) 12.1373 30.9252i 0.511979 1.30450i
\(563\) −3.05208 + 40.7272i −0.128630 + 1.71645i 0.443493 + 0.896278i \(0.353739\pi\)
−0.572123 + 0.820168i \(0.693880\pi\)
\(564\) 0 0
\(565\) −25.5768 10.0381i −1.07602 0.422308i
\(566\) −16.7898 21.0538i −0.705729 0.884957i
\(567\) 0 0
\(568\) −18.8302 + 23.6124i −0.790099 + 0.990753i
\(569\) −0.886893 + 0.512048i −0.0371805 + 0.0214662i −0.518475 0.855093i \(-0.673500\pi\)
0.481295 + 0.876559i \(0.340167\pi\)
\(570\) 0 0
\(571\) 0.297902 + 0.759041i 0.0124668 + 0.0317649i 0.936972 0.349405i \(-0.113616\pi\)
−0.924505 + 0.381170i \(0.875521\pi\)
\(572\) −7.47578 + 2.30597i −0.312578 + 0.0964175i
\(573\) 0 0
\(574\) 3.84310 + 0.989515i 0.160408 + 0.0413016i
\(575\) −32.9541 + 68.4298i −1.37428 + 2.85372i
\(576\) 0 0
\(577\) −25.9073 37.9990i −1.07853 1.58192i −0.778127 0.628107i \(-0.783830\pi\)
−0.300407 0.953811i \(-0.597123\pi\)
\(578\) −14.5002 + 15.6275i −0.603130 + 0.650020i
\(579\) 0 0
\(580\) 16.7948 3.83329i 0.697364 0.159169i
\(581\) 3.57169 34.7560i 0.148179 1.44192i
\(582\) 0 0
\(583\) 18.4859 17.1524i 0.765607 0.710379i
\(584\) −38.5478 + 5.81015i −1.59512 + 0.240426i
\(585\) 0 0
\(586\) 25.2452 1.89186i 1.04287 0.0781522i
\(587\) 16.9176 0.698266 0.349133 0.937073i \(-0.386476\pi\)
0.349133 + 0.937073i \(0.386476\pi\)
\(588\) 0 0
\(589\) −0.806918 −0.0332485
\(590\) 24.2629 1.81825i 0.998889 0.0748564i
\(591\) 0 0
\(592\) 28.4764 4.29213i 1.17037 0.176405i
\(593\) −19.1336 + 17.7534i −0.785722 + 0.729044i −0.967107 0.254368i \(-0.918132\pi\)
0.181385 + 0.983412i \(0.441942\pi\)
\(594\) 0 0
\(595\) 15.4527 9.92199i 0.633498 0.406762i
\(596\) 7.75646 1.77036i 0.317717 0.0725168i
\(597\) 0 0
\(598\) −39.5617 + 42.6374i −1.61780 + 1.74357i
\(599\) 14.6447 + 21.4799i 0.598368 + 0.877644i 0.999259 0.0384812i \(-0.0122520\pi\)
−0.400892 + 0.916126i \(0.631300\pi\)
\(600\) 0 0
\(601\) 9.05090 18.7944i 0.369194 0.766639i −0.630763 0.775976i \(-0.717258\pi\)
0.999956 + 0.00933691i \(0.00297207\pi\)
\(602\) −6.96324 5.87463i −0.283800 0.239432i
\(603\) 0 0
\(604\) −6.76755 + 2.08751i −0.275368 + 0.0849397i
\(605\) −3.69485 9.41433i −0.150217 0.382747i
\(606\) 0 0
\(607\) 27.8025 16.0518i 1.12847 0.651521i 0.184919 0.982754i \(-0.440798\pi\)
0.943549 + 0.331232i \(0.107464\pi\)
\(608\) −0.741548 + 0.929872i −0.0300738 + 0.0377113i
\(609\) 0 0
\(610\) 49.1073 + 61.5787i 1.98830 + 2.49325i
\(611\) 1.07328 + 0.421233i 0.0434204 + 0.0170413i
\(612\) 0 0
\(613\) 3.24518 43.3039i 0.131072 1.74903i −0.413673 0.910426i \(-0.635754\pi\)
0.544744 0.838602i \(-0.316627\pi\)
\(614\) −11.8868 + 30.2870i −0.479712 + 1.22229i
\(615\) 0 0
\(616\) 22.3663 6.22846i 0.901164 0.250952i
\(617\) −16.7016 13.3191i −0.672382 0.536207i 0.226712 0.973962i \(-0.427202\pi\)
−0.899094 + 0.437755i \(0.855774\pi\)
\(618\) 0 0
\(619\) −30.9448 17.8660i −1.24378 0.718095i −0.273916 0.961754i \(-0.588319\pi\)
−0.969861 + 0.243658i \(0.921652\pi\)
\(620\) −3.27514 + 1.28540i −0.131533 + 0.0516229i
\(621\) 0 0
\(622\) −12.2290 25.3938i −0.490339 1.01820i
\(623\) 29.5198 13.2250i 1.18268 0.529849i
\(624\) 0 0
\(625\) −6.62272 0.998215i −0.264909 0.0399286i
\(626\) 17.6232 12.0153i 0.704364 0.480227i
\(627\) 0 0
\(628\) 0.336747 0.493918i 0.0134377 0.0197095i
\(629\) 2.53162 + 11.0918i 0.100942 + 0.442257i
\(630\) 0 0
\(631\) 0.787058 3.44833i 0.0313323 0.137276i −0.956843 0.290607i \(-0.906143\pi\)
0.988175 + 0.153331i \(0.0490000\pi\)
\(632\) −10.6878 11.5187i −0.425137 0.458189i
\(633\) 0 0
\(634\) 26.8981 + 8.29698i 1.06826 + 0.329515i
\(635\) 4.10934 + 54.8353i 0.163074 + 2.17607i
\(636\) 0 0
\(637\) 29.3344 0.574705i 1.16227 0.0227706i
\(638\) 54.2747i 2.14876i
\(639\) 0 0
\(640\) 14.8594 48.1730i 0.587370 1.90421i
\(641\) 2.62231 + 17.3979i 0.103575 + 0.687176i 0.979006 + 0.203833i \(0.0653398\pi\)
−0.875431 + 0.483344i \(0.839422\pi\)
\(642\) 0 0
\(643\) −3.49763 0.798310i −0.137933 0.0314823i 0.152997 0.988227i \(-0.451108\pi\)
−0.290930 + 0.956744i \(0.593965\pi\)
\(644\) −8.18169 + 8.34355i −0.322404 + 0.328782i
\(645\) 0 0
\(646\) −1.04807 0.714559i −0.0412356 0.0281139i
\(647\) −9.27890 8.60956i −0.364791 0.338477i 0.476386 0.879236i \(-0.341946\pi\)
−0.841177 + 0.540760i \(0.818137\pi\)
\(648\) 0 0
\(649\) −2.29823 + 15.2477i −0.0902133 + 0.598526i
\(650\) −51.7465 24.9198i −2.02967 0.977436i
\(651\) 0 0
\(652\) 4.03887 1.94502i 0.158174 0.0761727i
\(653\) −5.99595 19.4384i −0.234640 0.760684i −0.993938 0.109941i \(-0.964934\pi\)
0.759298 0.650743i \(-0.225542\pi\)
\(654\) 0 0
\(655\) 34.1083 59.0773i 1.33272 2.30834i
\(656\) 2.25310 + 3.90248i 0.0879687 + 0.152366i
\(657\) 0 0
\(658\) 1.05995 + 0.450147i 0.0413213 + 0.0175486i
\(659\) −3.85986 + 3.07813i −0.150359 + 0.119907i −0.695780 0.718255i \(-0.744941\pi\)
0.545421 + 0.838162i \(0.316370\pi\)
\(660\) 0 0
\(661\) −28.9885 2.17239i −1.12752 0.0844961i −0.502119 0.864798i \(-0.667446\pi\)
−0.625402 + 0.780302i \(0.715065\pi\)
\(662\) −30.8311 2.31047i −1.19828 0.0897990i
\(663\) 0 0
\(664\) 24.4458 19.4948i 0.948680 0.756547i
\(665\) −2.75374 3.13722i −0.106785 0.121656i
\(666\) 0 0
\(667\) 40.5844 + 70.2942i 1.57143 + 2.72180i
\(668\) 2.74101 4.74757i 0.106053 0.183689i
\(669\) 0 0
\(670\) 0.400428 + 1.29815i 0.0154699 + 0.0501521i
\(671\) −44.9729 + 21.6578i −1.73616 + 0.836091i
\(672\) 0 0
\(673\) 35.4825 + 17.0875i 1.36775 + 0.658673i 0.966350 0.257230i \(-0.0828099\pi\)
0.401399 + 0.915903i \(0.368524\pi\)
\(674\) −3.10929 + 20.6288i −0.119765 + 0.794591i
\(675\) 0 0
\(676\) −1.68642 1.56477i −0.0648622 0.0601833i
\(677\) −12.9080 8.80049i −0.496093 0.338230i 0.289289 0.957242i \(-0.406581\pi\)
−0.785382 + 0.619011i \(0.787533\pi\)
\(678\) 0 0
\(679\) −5.55890 3.41741i −0.213331 0.131148i
\(680\) 16.0220 + 3.65691i 0.614414 + 0.140236i
\(681\) 0 0
\(682\) −1.65213 10.9612i −0.0632635 0.419726i
\(683\) −5.65164 + 18.3222i −0.216254 + 0.701078i 0.780828 + 0.624746i \(0.214797\pi\)
−0.997082 + 0.0763327i \(0.975679\pi\)
\(684\) 0 0
\(685\) 18.7751i 0.717359i
\(686\) 29.3033 + 0.234913i 1.11881 + 0.00896901i
\(687\) 0 0
\(688\) −0.773071 10.3159i −0.0294730 0.393290i
\(689\) 27.2518 + 8.40608i 1.03821 + 0.320246i
\(690\) 0 0
\(691\) 5.36039 + 5.77713i 0.203919 + 0.219772i 0.826728 0.562601i \(-0.190199\pi\)
−0.622810 + 0.782373i \(0.714009\pi\)
\(692\) 0.662525 2.90271i 0.0251854 0.110345i
\(693\) 0 0
\(694\) 5.76270 + 25.2480i 0.218749 + 0.958403i
\(695\) 29.7079 43.5734i 1.12688 1.65283i
\(696\) 0 0
\(697\) −1.47089 + 1.00284i −0.0557139 + 0.0379851i
\(698\) −20.4371 3.08040i −0.773556 0.116595i
\(699\) 0 0
\(700\) −10.2542 5.29165i −0.387571 0.200005i
\(701\) −13.8180 28.6935i −0.521900 1.08374i −0.980758 0.195227i \(-0.937456\pi\)
0.458858 0.888510i \(-0.348259\pi\)
\(702\) 0 0
\(703\) 2.40738 0.944826i 0.0907959 0.0356348i
\(704\) 16.3657 + 9.44872i 0.616804 + 0.356112i
\(705\) 0 0
\(706\) −15.9382 12.7103i −0.599842 0.478358i
\(707\) −7.30692 + 6.41375i −0.274805 + 0.241214i
\(708\) 0 0
\(709\) 5.01627 12.7813i 0.188390 0.480010i −0.805207 0.592994i \(-0.797946\pi\)
0.993597 + 0.112984i \(0.0360409\pi\)
\(710\) −5.57449 + 74.3864i −0.209207 + 2.79167i
\(711\) 0 0
\(712\) 26.9465 + 10.5757i 1.00986 + 0.396341i
\(713\) −10.3361 12.9611i −0.387090 0.485395i
\(714\) 0 0
\(715\) 35.7977 44.8889i 1.33876 1.67875i
\(716\) −2.03755 + 1.17638i −0.0761470 + 0.0439635i
\(717\) 0 0
\(718\) −9.29689 23.6881i −0.346957 0.884032i
\(719\) −42.4928 + 13.1073i −1.58472 + 0.488820i −0.957113 0.289714i \(-0.906440\pi\)
−0.627602 + 0.778534i \(0.715963\pi\)
\(720\) 0 0
\(721\) 14.3151 2.85407i 0.533122 0.106291i
\(722\) 12.9189 26.8263i 0.480791 0.998373i
\(723\) 0 0
\(724\) −1.69389 2.48449i −0.0629531 0.0923353i
\(725\) −54.5160 + 58.7542i −2.02467 + 2.18208i
\(726\) 0 0
\(727\) −31.7733 + 7.25205i −1.17841 + 0.268964i −0.766489 0.642257i \(-0.777998\pi\)
−0.411918 + 0.911221i \(0.635141\pi\)
\(728\) 18.7472 + 18.3835i 0.694818 + 0.681339i
\(729\) 0 0
\(730\) −70.5823 + 65.4908i −2.61237 + 2.42392i
\(731\) 4.04120 0.609113i 0.149469 0.0225289i
\(732\) 0 0
\(733\) −16.3986 + 1.22891i −0.605697 + 0.0453907i −0.374049 0.927409i \(-0.622031\pi\)
−0.231648 + 0.972800i \(0.574412\pi\)
\(734\) 38.6230 1.42560
\(735\) 0 0
\(736\) −24.4347 −0.900676
\(737\) −0.858560 + 0.0643402i −0.0316255 + 0.00237000i
\(738\) 0 0
\(739\) −20.1029 + 3.03003i −0.739498 + 0.111461i −0.507980 0.861369i \(-0.669608\pi\)
−0.231519 + 0.972830i \(0.574369\pi\)
\(740\) 8.26605 7.66977i 0.303866 0.281946i
\(741\) 0 0
\(742\) 26.9765 + 9.14391i 0.990338 + 0.335684i
\(743\) 0.819561 0.187060i 0.0300668 0.00686255i −0.207461 0.978243i \(-0.566520\pi\)
0.237528 + 0.971381i \(0.423663\pi\)
\(744\) 0 0
\(745\) −39.7140 + 42.8015i −1.45501 + 1.56813i
\(746\) −6.28946 9.22494i −0.230273 0.337749i
\(747\) 0 0
\(748\) 1.52086 3.15811i 0.0556083 0.115472i
\(749\) 8.25809 + 18.4330i 0.301744 + 0.673528i
\(750\) 0 0
\(751\) 31.6040 9.74854i 1.15325 0.355729i 0.341581 0.939852i \(-0.389038\pi\)
0.811665 + 0.584123i \(0.198561\pi\)
\(752\) 0.477730 + 1.21724i 0.0174210 + 0.0443880i
\(753\) 0 0
\(754\) −53.1563 + 30.6898i −1.93584 + 1.11766i
\(755\) 32.4064 40.6363i 1.17939 1.47891i
\(756\) 0 0
\(757\) −19.0169 23.8464i −0.691180 0.866712i 0.305150 0.952304i \(-0.401293\pi\)
−0.996330 + 0.0855920i \(0.972722\pi\)
\(758\) 21.0278 + 8.25281i 0.763765 + 0.299756i
\(759\) 0 0
\(760\) 0.279167 3.72522i 0.0101264 0.135128i
\(761\) 13.0112 33.1520i 0.471656 1.20176i −0.475136 0.879912i \(-0.657601\pi\)
0.946792 0.321847i \(-0.104304\pi\)
\(762\) 0 0
\(763\) 0.0138903 + 0.294102i 0.000502862 + 0.0106472i
\(764\) −0.657730 0.524522i −0.0237958 0.0189765i
\(765\) 0 0
\(766\) 29.0487 + 16.7713i 1.04957 + 0.605970i
\(767\) −16.2331 + 6.37102i −0.586143 + 0.230044i
\(768\) 0 0
\(769\) −13.2443 27.5020i −0.477601 0.991749i −0.991033 0.133619i \(-0.957340\pi\)
0.513432 0.858131i \(-0.328374\pi\)
\(770\) 36.9779 43.8302i 1.33259 1.57953i
\(771\) 0 0
\(772\) −1.92202 0.289698i −0.0691751 0.0104265i
\(773\) 6.52978 4.45193i 0.234860 0.160125i −0.440172 0.897914i \(-0.645082\pi\)
0.675032 + 0.737789i \(0.264130\pi\)
\(774\) 0 0
\(775\) 9.22143 13.5253i 0.331243 0.485845i
\(776\) −1.29943 5.69318i −0.0466469 0.204373i
\(777\) 0 0
\(778\) 9.41293 41.2408i 0.337470 1.47855i
\(779\) 0.275245 + 0.296643i 0.00986167 + 0.0106284i
\(780\) 0 0
\(781\) −45.1750 13.9346i −1.61649 0.498620i
\(782\) −1.94749 25.9875i −0.0696422 0.929311i
\(783\) 0 0
\(784\) 23.1063 + 23.9444i 0.825226 + 0.855158i
\(785\) 4.38715i 0.156584i
\(786\) 0 0
\(787\) 9.67101 31.3526i 0.344734 1.11760i −0.602785 0.797903i \(-0.705942\pi\)
0.947520 0.319698i \(-0.103581\pi\)
\(788\) 0.269247 + 1.78634i 0.00959153 + 0.0636356i
\(789\) 0 0
\(790\) −37.8377 8.63620i −1.34620 0.307262i
\(791\) 19.5657 + 2.01066i 0.695676 + 0.0714909i
\(792\) 0 0
\(793\) −46.6416 31.7997i −1.65629 1.12924i
\(794\) −17.5968 16.3275i −0.624488 0.579441i
\(795\) 0 0
\(796\) 0.0456271 0.302716i 0.00161721 0.0107295i
\(797\) −35.9376 17.3066i −1.27297 0.613032i −0.329399 0.944191i \(-0.606846\pi\)
−0.943575 + 0.331159i \(0.892560\pi\)
\(798\) 0 0
\(799\) −0.465434 + 0.224141i −0.0164659 + 0.00792955i
\(800\) −7.11189 23.0562i −0.251443 0.815159i
\(801\) 0 0
\(802\) −7.83625 + 13.5728i −0.276708 + 0.479272i
\(803\) −30.5109 52.8465i −1.07671 1.86491i
\(804\) 0 0
\(805\) 15.1178 84.4174i 0.532831 2.97532i
\(806\) 9.80113 7.81614i 0.345230 0.275312i
\(807\) 0 0
\(808\) −8.67644 0.650209i −0.305236 0.0228743i
\(809\) 5.36904 + 0.402354i 0.188765 + 0.0141460i 0.168777 0.985654i \(-0.446018\pi\)
0.0199880 + 0.999800i \(0.493637\pi\)
\(810\) 0 0
\(811\) −12.0024 + 9.57160i −0.421462 + 0.336104i −0.811146 0.584844i \(-0.801156\pi\)
0.389684 + 0.920949i \(0.372584\pi\)
\(812\) −10.8457 + 5.86872i −0.380608 + 0.205952i
\(813\) 0 0
\(814\) 17.7636 + 30.7674i 0.622612 + 1.07840i
\(815\) −16.4495 + 28.4914i −0.576201 + 0.998010i
\(816\) 0 0
\(817\) −0.273826 0.887723i −0.00957997 0.0310575i
\(818\) 11.8816 5.72190i 0.415432 0.200061i
\(819\) 0 0
\(820\) 1.58972 + 0.765567i 0.0555153 + 0.0267348i
\(821\) −0.838008 + 5.55982i −0.0292467 + 0.194039i −0.998683 0.0513036i \(-0.983662\pi\)
0.969436 + 0.245343i \(0.0789005\pi\)
\(822\) 0 0
\(823\) 10.6016 + 9.83684i 0.369548 + 0.342891i 0.842985 0.537937i \(-0.180796\pi\)
−0.473437 + 0.880828i \(0.656987\pi\)
\(824\) 10.7930 + 7.35857i 0.375993 + 0.256348i
\(825\) 0 0
\(826\) −16.3827 + 5.91330i −0.570029 + 0.205750i
\(827\) −16.7531 3.82379i −0.582562 0.132966i −0.0789240 0.996881i \(-0.525148\pi\)
−0.503638 + 0.863915i \(0.668006\pi\)
\(828\) 0 0
\(829\) −4.15913 27.5940i −0.144453 0.958380i −0.937191 0.348818i \(-0.886583\pi\)
0.792738 0.609563i \(-0.208655\pi\)
\(830\) 22.7633 73.7968i 0.790125 2.56152i
\(831\) 0 0
\(832\) 21.3712i 0.740915i
\(833\) −8.75090 + 9.80980i −0.303201 + 0.339890i
\(834\) 0 0
\(835\) 3.00656 + 40.1197i 0.104046 + 1.38840i
\(836\) −0.761388 0.234857i −0.0263332 0.00812271i
\(837\) 0 0
\(838\) −23.0353 24.8261i −0.795740 0.857604i
\(839\) −5.12198 + 22.4409i −0.176830 + 0.774745i 0.806251 + 0.591574i \(0.201493\pi\)
−0.983081 + 0.183171i \(0.941364\pi\)
\(840\) 0 0
\(841\) 12.6071 + 55.2355i 0.434729 + 1.90467i
\(842\) −26.0921 + 38.2701i −0.899194 + 1.31888i
\(843\) 0 0
\(844\) −3.40840 + 2.32381i −0.117322 + 0.0799887i
\(845\) 16.6950 + 2.51636i 0.574324 + 0.0865654i
\(846\) 0 0
\(847\) 4.35592 + 5.78265i 0.149671 + 0.198694i
\(848\) 14.0335 + 29.1408i 0.481912 + 1.00070i
\(849\) 0 0
\(850\) 23.9545 9.40144i 0.821632 0.322467i
\(851\) 46.0131 + 26.5657i 1.57731 + 0.910660i
\(852\) 0 0
\(853\) 45.2780 + 36.1080i 1.55029 + 1.23631i 0.856519 + 0.516115i \(0.172622\pi\)
0.693768 + 0.720198i \(0.255949\pi\)
\(854\) −45.6903 33.0347i −1.56349 1.13042i
\(855\) 0 0
\(856\) −6.60379 + 16.8262i −0.225713 + 0.575107i
\(857\) 1.05092 14.0236i 0.0358988 0.479036i −0.950062 0.312061i \(-0.898981\pi\)
0.985961 0.166976i \(-0.0534001\pi\)
\(858\) 0 0
\(859\) −23.1206 9.07416i −0.788864 0.309606i −0.0635090 0.997981i \(-0.520229\pi\)
−0.725355 + 0.688375i \(0.758324\pi\)
\(860\) −2.52553 3.16692i −0.0861200 0.107991i
\(861\) 0 0
\(862\) 4.33459 5.43540i 0.147637 0.185130i
\(863\) −35.8904 + 20.7213i −1.22172 + 0.705363i −0.965285 0.261198i \(-0.915882\pi\)
−0.256438 + 0.966561i \(0.582549\pi\)
\(864\) 0 0
\(865\) 7.98295 + 20.3402i 0.271428 + 0.691588i
\(866\) −38.0018 + 11.7220i −1.29135 + 0.398330i
\(867\) 0 0
\(868\) 2.01172 1.51538i 0.0682823 0.0514352i
\(869\) 10.6721 22.1608i 0.362026 0.751755i
\(870\) 0 0
\(871\) −0.548490 0.804487i −0.0185849 0.0272590i
\(872\) −0.179217 + 0.193150i −0.00606907 + 0.00654090i
\(873\) 0 0
\(874\) −5.77535 + 1.31819i −0.195354 + 0.0445883i
\(875\) 35.5252 4.35550i 1.20097 0.147243i
\(876\) 0 0
\(877\) −32.9057 + 30.5320i −1.11115 + 1.03099i −0.111840 + 0.993726i \(0.535674\pi\)
−0.999305 + 0.0372659i \(0.988135\pi\)
\(878\) 10.5927 1.59659i 0.357485 0.0538822i
\(879\) 0 0
\(880\) 64.9336 4.86610i 2.18891 0.164036i
\(881\) 41.6366 1.40277 0.701387 0.712781i \(-0.252564\pi\)
0.701387 + 0.712781i \(0.252564\pi\)
\(882\) 0 0
\(883\) −28.6568 −0.964379 −0.482190 0.876067i \(-0.660158\pi\)
−0.482190 + 0.876067i \(0.660158\pi\)
\(884\) 3.95301 0.296237i 0.132954 0.00996353i
\(885\) 0 0
\(886\) 26.1368 3.93949i 0.878084 0.132350i
\(887\) −15.9961 + 14.8422i −0.537095 + 0.498352i −0.901435 0.432914i \(-0.857485\pi\)
0.364340 + 0.931266i \(0.381295\pi\)
\(888\) 0 0
\(889\) −13.3643 37.0258i −0.448226 1.24180i
\(890\) 69.7054 15.9098i 2.33653 0.533298i
\(891\) 0 0
\(892\) −0.210990 + 0.227393i −0.00706446 + 0.00761367i
\(893\) 0.0661499 + 0.0970241i 0.00221362 + 0.00324679i
\(894\) 0 0
\(895\) 7.49178 15.5568i 0.250423 0.520008i
\(896\) −0.996094 + 36.0741i −0.0332772 + 1.20515i
\(897\) 0 0
\(898\) −50.1687 + 15.4750i −1.67415 + 0.516407i
\(899\) −6.39137 16.2850i −0.213164 0.543134i
\(900\) 0 0
\(901\) −11.0659 + 6.38891i −0.368659 + 0.212845i
\(902\) −3.46606 + 4.34630i −0.115407 + 0.144716i
\(903\) 0 0
\(904\) 10.9745 + 13.7616i 0.365006 + 0.457703i
\(905\) 20.5426 + 8.06238i 0.682859 + 0.268002i
\(906\) 0 0
\(907\) −3.16496 + 42.2334i −0.105091 + 1.40234i 0.656522 + 0.754307i \(0.272027\pi\)
−0.761613 + 0.648032i \(0.775592\pi\)
\(908\) −2.19273 + 5.58699i −0.0727683 + 0.185411i
\(909\) 0 0
\(910\) 63.8363 + 11.4320i 2.11615 + 0.378968i
\(911\) 17.7832 + 14.1816i 0.589184 + 0.469859i 0.872128 0.489278i \(-0.162740\pi\)
−0.282944 + 0.959136i \(0.591311\pi\)
\(912\) 0 0
\(913\) 42.3866 + 24.4719i 1.40279 + 0.809902i
\(914\) 33.7452 13.2440i 1.11619 0.438073i
\(915\) 0 0
\(916\) 6.11057 + 12.6887i 0.201899 + 0.419247i
\(917\) −12.1763 + 47.2903i −0.402095 + 1.56166i
\(918\) 0 0
\(919\) 16.3160 + 2.45924i 0.538215 + 0.0811229i 0.412524 0.910947i \(-0.364647\pi\)
0.125691 + 0.992069i \(0.459885\pi\)
\(920\) 63.4120 43.2336i 2.09063 1.42537i
\(921\) 0 0
\(922\) −17.4322 + 25.5684i −0.574100 + 0.842050i
\(923\) −11.8968 52.1235i −0.391589 1.71566i
\(924\) 0 0
\(925\) −11.6745 + 51.1492i −0.383855 + 1.68178i
\(926\) −36.8125 39.6744i −1.20973 1.30378i
\(927\) 0 0
\(928\) −24.6400 7.60043i −0.808847 0.249496i
\(929\) −3.24578 43.3120i −0.106491 1.42102i −0.752953 0.658074i \(-0.771371\pi\)
0.646463 0.762946i \(-0.276248\pi\)
\(930\) 0 0
\(931\) 2.50147 + 1.63463i 0.0819824 + 0.0535729i
\(932\) 2.35065i 0.0769982i
\(933\) 0 0
\(934\) −15.9347 + 51.6589i −0.521398 + 1.69033i
\(935\) 3.83407 + 25.4374i 0.125387 + 0.831891i
\(936\) 0 0
\(937\) −21.1113 4.81853i −0.689677 0.157414i −0.136702 0.990612i \(-0.543650\pi\)
−0.552975 + 0.833198i \(0.686508\pi\)
\(938\) −0.525434 0.818321i −0.0171560 0.0267191i
\(939\) 0 0
\(940\) 0.423048 + 0.288429i 0.0137983 + 0.00940752i
\(941\) 22.4245 + 20.8069i 0.731019 + 0.678286i 0.955100 0.296284i \(-0.0957476\pi\)
−0.224081 + 0.974571i \(0.571938\pi\)
\(942\) 0 0
\(943\) −1.23910 + 8.22090i −0.0403507 + 0.267709i
\(944\) −17.8189 8.58111i −0.579955 0.279291i
\(945\) 0 0
\(946\) 11.4982 5.53724i 0.373839 0.180031i
\(947\) −1.34716 4.36738i −0.0437768 0.141921i 0.931046 0.364902i \(-0.118897\pi\)
−0.974823 + 0.222981i \(0.928421\pi\)
\(948\) 0 0
\(949\) 34.5050 59.7645i 1.12008 1.94004i
\(950\) −2.92477 5.06585i −0.0948920 0.164358i
\(951\) 0 0
\(952\) −11.7511 + 0.555001i −0.380857 + 0.0179877i
\(953\) −27.4267 + 21.8721i −0.888439 + 0.708506i −0.957293 0.289120i \(-0.906637\pi\)
0.0688538 + 0.997627i \(0.478066\pi\)
\(954\) 0 0
\(955\) 6.15675 + 0.461385i 0.199228 + 0.0149301i
\(956\) −4.61900 0.346146i −0.149389 0.0111952i
\(957\) 0 0
\(958\) −0.753978 + 0.601278i −0.0243599 + 0.0194264i
\(959\) −3.60554 12.9475i −0.116429 0.418096i
\(960\) 0 0
\(961\) −13.7135 23.7525i −0.442371 0.766209i
\(962\) −20.0889 + 34.7950i −0.647693 + 1.12184i
\(963\) 0 0
\(964\) 4.49248 + 14.5643i 0.144693 + 0.469083i
\(965\) 12.8523 6.18933i 0.413729 0.199241i
\(966\) 0 0
\(967\) −8.17747 3.93806i −0.262970 0.126640i 0.297754 0.954643i \(-0.403763\pi\)
−0.560723 + 0.828003i \(0.689477\pi\)
\(968\) −0.965625 + 6.40650i −0.0310364 + 0.205913i
\(969\) 0 0
\(970\) −10.5730 9.81035i −0.339480 0.314991i
\(971\) 10.2557 + 6.99225i 0.329123 + 0.224392i 0.716595 0.697489i \(-0.245699\pi\)
−0.387473 + 0.921881i \(0.626652\pi\)
\(972\) 0 0
\(973\) −12.1190 + 35.7537i −0.388518 + 1.14621i
\(974\) 16.4128 + 3.74612i 0.525901 + 0.120033i
\(975\) 0 0
\(976\) −9.54196 63.3068i −0.305431 2.02640i
\(977\) −9.66937 + 31.3473i −0.309350 + 1.00289i 0.658757 + 0.752355i \(0.271082\pi\)
−0.968108 + 0.250534i \(0.919394\pi\)
\(978\) 0 0
\(979\) 45.3125i 1.44819i
\(980\) 12.7570 + 2.64992i 0.407506 + 0.0846485i
\(981\) 0 0
\(982\) 2.09169 + 27.9117i 0.0667487 + 0.890699i
\(983\) 5.95985 + 1.83837i 0.190090 + 0.0586349i 0.388338 0.921517i \(-0.373049\pi\)
−0.198249 + 0.980152i \(0.563525\pi\)
\(984\) 0 0
\(985\) −9.01766 9.71873i −0.287327 0.309665i
\(986\) 6.11956 26.8115i 0.194886 0.853853i
\(987\) 0 0
\(988\) −0.200512 0.878500i −0.00637913 0.0279488i
\(989\) 10.7514 15.7695i 0.341876 0.501440i
\(990\) 0 0
\(991\) −1.72667 + 1.17722i −0.0548493 + 0.0373956i −0.590434 0.807086i \(-0.701044\pi\)
0.535585 + 0.844481i \(0.320091\pi\)
\(992\) 5.20759 + 0.784918i 0.165341 + 0.0249212i
\(993\) 0 0
\(994\) −10.4408 52.3680i −0.331164 1.66101i
\(995\) 0.974810 + 2.02421i 0.0309036 + 0.0641719i
\(996\) 0 0
\(997\) 27.1794 10.6671i 0.860779 0.337831i 0.106443 0.994319i \(-0.466054\pi\)
0.754337 + 0.656488i \(0.227959\pi\)
\(998\) 40.1661 + 23.1899i 1.27143 + 0.734063i
\(999\) 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 441.2.bg.a.17.4 216
3.2 odd 2 inner 441.2.bg.a.17.15 yes 216
49.26 odd 42 inner 441.2.bg.a.26.15 yes 216
147.26 even 42 inner 441.2.bg.a.26.4 yes 216
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.bg.a.17.4 216 1.1 even 1 trivial
441.2.bg.a.17.15 yes 216 3.2 odd 2 inner
441.2.bg.a.26.4 yes 216 147.26 even 42 inner
441.2.bg.a.26.15 yes 216 49.26 odd 42 inner