Properties

Label 1380.2.p.a.91.16
Level $1380$
Weight $2$
Character 1380.91
Analytic conductor $11.019$
Analytic rank $0$
Dimension $48$
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] = [1380,2,Mod(91,1380)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1380, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1380.91");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1380.p (of order \(2\), degree \(1\), 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: \(11.0193554789\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 91.16
Character \(\chi\) \(=\) 1380.91
Dual form 1380.2.p.a.91.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.952347 + 1.04548i) q^{2} +1.00000i q^{3} +(-0.186069 - 1.99133i) q^{4} +1.00000i q^{5} +(-1.04548 - 0.952347i) q^{6} +3.49678 q^{7} +(2.25910 + 1.70190i) q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(-0.952347 + 1.04548i) q^{2} +1.00000i q^{3} +(-0.186069 - 1.99133i) q^{4} +1.00000i q^{5} +(-1.04548 - 0.952347i) q^{6} +3.49678 q^{7} +(2.25910 + 1.70190i) q^{8} -1.00000 q^{9} +(-1.04548 - 0.952347i) q^{10} +1.36625 q^{11} +(1.99133 - 0.186069i) q^{12} +3.35306 q^{13} +(-3.33015 + 3.65582i) q^{14} -1.00000 q^{15} +(-3.93076 + 0.741046i) q^{16} -0.0719348i q^{17} +(0.952347 - 1.04548i) q^{18} -5.04791 q^{19} +(1.99133 - 0.186069i) q^{20} +3.49678i q^{21} +(-1.30115 + 1.42839i) q^{22} +(4.76200 + 0.568640i) q^{23} +(-1.70190 + 2.25910i) q^{24} -1.00000 q^{25} +(-3.19327 + 3.50556i) q^{26} -1.00000i q^{27} +(-0.650640 - 6.96322i) q^{28} +9.80417 q^{29} +(0.952347 - 1.04548i) q^{30} -8.07183i q^{31} +(2.96870 - 4.81527i) q^{32} +1.36625i q^{33} +(0.0752066 + 0.0685069i) q^{34} +3.49678i q^{35} +(0.186069 + 1.99133i) q^{36} -3.32625i q^{37} +(4.80737 - 5.27750i) q^{38} +3.35306i q^{39} +(-1.70190 + 2.25910i) q^{40} +1.37906 q^{41} +(-3.65582 - 3.33015i) q^{42} +8.91103 q^{43} +(-0.254216 - 2.72065i) q^{44} -1.00000i q^{45} +(-5.12958 + 4.43705i) q^{46} +12.6923i q^{47} +(-0.741046 - 3.93076i) q^{48} +5.22746 q^{49} +(0.952347 - 1.04548i) q^{50} +0.0719348 q^{51} +(-0.623898 - 6.67703i) q^{52} -10.9669i q^{53} +(1.04548 + 0.952347i) q^{54} +1.36625i q^{55} +(7.89957 + 5.95118i) q^{56} -5.04791i q^{57} +(-9.33697 + 10.2501i) q^{58} +4.71711i q^{59} +(0.186069 + 1.99133i) q^{60} -6.38461i q^{61} +(8.43896 + 7.68719i) q^{62} -3.49678 q^{63} +(2.20705 + 7.68953i) q^{64} +3.35306i q^{65} +(-1.42839 - 1.30115i) q^{66} -15.2636 q^{67} +(-0.143246 + 0.0133848i) q^{68} +(-0.568640 + 4.76200i) q^{69} +(-3.65582 - 3.33015i) q^{70} +15.7028i q^{71} +(-2.25910 - 1.70190i) q^{72} +5.24792 q^{73} +(3.47754 + 3.16775i) q^{74} -1.00000i q^{75} +(0.939258 + 10.0520i) q^{76} +4.77748 q^{77} +(-3.50556 - 3.19327i) q^{78} +4.20591 q^{79} +(-0.741046 - 3.93076i) q^{80} +1.00000 q^{81} +(-1.31334 + 1.44178i) q^{82} -13.4916 q^{83} +(6.96322 - 0.650640i) q^{84} +0.0719348 q^{85} +(-8.48639 + 9.31632i) q^{86} +9.80417i q^{87} +(3.08650 + 2.32523i) q^{88} +11.5228i q^{89} +(1.04548 + 0.952347i) q^{90} +11.7249 q^{91} +(0.246289 - 9.58850i) q^{92} +8.07183 q^{93} +(-13.2696 - 12.0875i) q^{94} -5.04791i q^{95} +(4.81527 + 2.96870i) q^{96} -4.72490i q^{97} +(-4.97835 + 5.46522i) q^{98} -1.36625 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9} - 2 q^{10} + 20 q^{14} - 48 q^{15} - 6 q^{16} + 4 q^{18} + 16 q^{19} + 28 q^{22} + 4 q^{23} + 2 q^{24} - 48 q^{25} - 20 q^{26} + 32 q^{29} + 4 q^{30} + 16 q^{32} - 28 q^{34} + 2 q^{36} + 2 q^{40} - 8 q^{41} + 14 q^{46} + 16 q^{48} + 40 q^{49} + 4 q^{50} + 16 q^{51} - 16 q^{52} + 2 q^{54} + 40 q^{56} - 8 q^{58} + 2 q^{60} + 24 q^{62} - 26 q^{64} - 48 q^{67} - 44 q^{68} - 8 q^{69} + 4 q^{72} + 20 q^{74} - 64 q^{76} + 32 q^{77} - 64 q^{79} + 16 q^{80} + 48 q^{81} - 20 q^{82} + 16 q^{85} - 40 q^{86} + 2 q^{90} - 4 q^{92} - 32 q^{94} - 2 q^{96} + 24 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(691\) \(1201\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.952347 + 1.04548i −0.673411 + 0.739268i
\(3\) 1.00000i 0.577350i
\(4\) −0.186069 1.99133i −0.0930343 0.995663i
\(5\) 1.00000i 0.447214i
\(6\) −1.04548 0.952347i −0.426817 0.388794i
\(7\) 3.49678 1.32166 0.660829 0.750537i \(-0.270205\pi\)
0.660829 + 0.750537i \(0.270205\pi\)
\(8\) 2.25910 + 1.70190i 0.798712 + 0.601713i
\(9\) −1.00000 −0.333333
\(10\) −1.04548 0.952347i −0.330611 0.301159i
\(11\) 1.36625 0.411940 0.205970 0.978558i \(-0.433965\pi\)
0.205970 + 0.978558i \(0.433965\pi\)
\(12\) 1.99133 0.186069i 0.574846 0.0537134i
\(13\) 3.35306 0.929970 0.464985 0.885318i \(-0.346060\pi\)
0.464985 + 0.885318i \(0.346060\pi\)
\(14\) −3.33015 + 3.65582i −0.890019 + 0.977059i
\(15\) −1.00000 −0.258199
\(16\) −3.93076 + 0.741046i −0.982689 + 0.185262i
\(17\) 0.0719348i 0.0174468i −0.999962 0.00872338i \(-0.997223\pi\)
0.999962 0.00872338i \(-0.00277677\pi\)
\(18\) 0.952347 1.04548i 0.224470 0.246423i
\(19\) −5.04791 −1.15807 −0.579035 0.815303i \(-0.696571\pi\)
−0.579035 + 0.815303i \(0.696571\pi\)
\(20\) 1.99133 0.186069i 0.445274 0.0416062i
\(21\) 3.49678i 0.763060i
\(22\) −1.30115 + 1.42839i −0.277405 + 0.304534i
\(23\) 4.76200 + 0.568640i 0.992946 + 0.118570i
\(24\) −1.70190 + 2.25910i −0.347399 + 0.461137i
\(25\) −1.00000 −0.200000
\(26\) −3.19327 + 3.50556i −0.626253 + 0.687497i
\(27\) 1.00000i 0.192450i
\(28\) −0.650640 6.96322i −0.122959 1.31593i
\(29\) 9.80417 1.82059 0.910294 0.413962i \(-0.135855\pi\)
0.910294 + 0.413962i \(0.135855\pi\)
\(30\) 0.952347 1.04548i 0.173874 0.190878i
\(31\) 8.07183i 1.44974i −0.688884 0.724872i \(-0.741899\pi\)
0.688884 0.724872i \(-0.258101\pi\)
\(32\) 2.96870 4.81527i 0.524796 0.851228i
\(33\) 1.36625i 0.237834i
\(34\) 0.0752066 + 0.0685069i 0.0128978 + 0.0117488i
\(35\) 3.49678i 0.591063i
\(36\) 0.186069 + 1.99133i 0.0310114 + 0.331888i
\(37\) 3.32625i 0.546833i −0.961896 0.273416i \(-0.911846\pi\)
0.961896 0.273416i \(-0.0881537\pi\)
\(38\) 4.80737 5.27750i 0.779858 0.856124i
\(39\) 3.35306i 0.536919i
\(40\) −1.70190 + 2.25910i −0.269094 + 0.357195i
\(41\) 1.37906 0.215373 0.107686 0.994185i \(-0.465656\pi\)
0.107686 + 0.994185i \(0.465656\pi\)
\(42\) −3.65582 3.33015i −0.564105 0.513853i
\(43\) 8.91103 1.35892 0.679459 0.733713i \(-0.262214\pi\)
0.679459 + 0.733713i \(0.262214\pi\)
\(44\) −0.254216 2.72065i −0.0383246 0.410154i
\(45\) 1.00000i 0.149071i
\(46\) −5.12958 + 4.43705i −0.756316 + 0.654207i
\(47\) 12.6923i 1.85137i 0.378296 + 0.925684i \(0.376510\pi\)
−0.378296 + 0.925684i \(0.623490\pi\)
\(48\) −0.741046 3.93076i −0.106961 0.567356i
\(49\) 5.22746 0.746779
\(50\) 0.952347 1.04548i 0.134682 0.147854i
\(51\) 0.0719348 0.0100729
\(52\) −0.623898 6.67703i −0.0865191 0.925937i
\(53\) 10.9669i 1.50642i −0.657780 0.753210i \(-0.728504\pi\)
0.657780 0.753210i \(-0.271496\pi\)
\(54\) 1.04548 + 0.952347i 0.142272 + 0.129598i
\(55\) 1.36625i 0.184225i
\(56\) 7.89957 + 5.95118i 1.05562 + 0.795259i
\(57\) 5.04791i 0.668612i
\(58\) −9.33697 + 10.2501i −1.22600 + 1.34590i
\(59\) 4.71711i 0.614116i 0.951691 + 0.307058i \(0.0993445\pi\)
−0.951691 + 0.307058i \(0.900655\pi\)
\(60\) 0.186069 + 1.99133i 0.0240213 + 0.257079i
\(61\) 6.38461i 0.817465i −0.912654 0.408733i \(-0.865971\pi\)
0.912654 0.408733i \(-0.134029\pi\)
\(62\) 8.43896 + 7.68719i 1.07175 + 0.976274i
\(63\) −3.49678 −0.440553
\(64\) 2.20705 + 7.68953i 0.275882 + 0.961192i
\(65\) 3.35306i 0.415895i
\(66\) −1.42839 1.30115i −0.175823 0.160160i
\(67\) −15.2636 −1.86475 −0.932374 0.361496i \(-0.882266\pi\)
−0.932374 + 0.361496i \(0.882266\pi\)
\(68\) −0.143246 + 0.0133848i −0.0173711 + 0.00162315i
\(69\) −0.568640 + 4.76200i −0.0684562 + 0.573277i
\(70\) −3.65582 3.33015i −0.436954 0.398029i
\(71\) 15.7028i 1.86358i 0.362995 + 0.931791i \(0.381754\pi\)
−0.362995 + 0.931791i \(0.618246\pi\)
\(72\) −2.25910 1.70190i −0.266237 0.200571i
\(73\) 5.24792 0.614222 0.307111 0.951674i \(-0.400638\pi\)
0.307111 + 0.951674i \(0.400638\pi\)
\(74\) 3.47754 + 3.16775i 0.404256 + 0.368243i
\(75\) 1.00000i 0.115470i
\(76\) 0.939258 + 10.0520i 0.107740 + 1.15305i
\(77\) 4.77748 0.544444
\(78\) −3.50556 3.19327i −0.396927 0.361567i
\(79\) 4.20591 0.473202 0.236601 0.971607i \(-0.423967\pi\)
0.236601 + 0.971607i \(0.423967\pi\)
\(80\) −0.741046 3.93076i −0.0828515 0.439472i
\(81\) 1.00000 0.111111
\(82\) −1.31334 + 1.44178i −0.145034 + 0.159218i
\(83\) −13.4916 −1.48089 −0.740447 0.672115i \(-0.765386\pi\)
−0.740447 + 0.672115i \(0.765386\pi\)
\(84\) 6.96322 0.650640i 0.759750 0.0709907i
\(85\) 0.0719348 0.00780242
\(86\) −8.48639 + 9.31632i −0.915111 + 1.00461i
\(87\) 9.80417i 1.05112i
\(88\) 3.08650 + 2.32523i 0.329022 + 0.247870i
\(89\) 11.5228i 1.22141i 0.791857 + 0.610706i \(0.209114\pi\)
−0.791857 + 0.610706i \(0.790886\pi\)
\(90\) 1.04548 + 0.952347i 0.110204 + 0.100386i
\(91\) 11.7249 1.22910
\(92\) 0.246289 9.58850i 0.0256774 0.999670i
\(93\) 8.07183 0.837010
\(94\) −13.2696 12.0875i −1.36866 1.24673i
\(95\) 5.04791i 0.517905i
\(96\) 4.81527 + 2.96870i 0.491457 + 0.302991i
\(97\) 4.72490i 0.479741i −0.970805 0.239871i \(-0.922895\pi\)
0.970805 0.239871i \(-0.0771050\pi\)
\(98\) −4.97835 + 5.46522i −0.502890 + 0.552070i
\(99\) −1.36625 −0.137313
\(100\) 0.186069 + 1.99133i 0.0186069 + 0.199133i
\(101\) 10.7894 1.07358 0.536791 0.843715i \(-0.319636\pi\)
0.536791 + 0.843715i \(0.319636\pi\)
\(102\) −0.0685069 + 0.0752066i −0.00678320 + 0.00744656i
\(103\) 8.71856 0.859065 0.429533 0.903051i \(-0.358678\pi\)
0.429533 + 0.903051i \(0.358678\pi\)
\(104\) 7.57488 + 5.70657i 0.742779 + 0.559576i
\(105\) −3.49678 −0.341251
\(106\) 11.4657 + 10.4443i 1.11365 + 1.01444i
\(107\) −15.4237 −1.49106 −0.745530 0.666472i \(-0.767804\pi\)
−0.745530 + 0.666472i \(0.767804\pi\)
\(108\) −1.99133 + 0.186069i −0.191615 + 0.0179045i
\(109\) 2.16171i 0.207054i 0.994627 + 0.103527i \(0.0330129\pi\)
−0.994627 + 0.103527i \(0.966987\pi\)
\(110\) −1.42839 1.30115i −0.136192 0.124059i
\(111\) 3.32625 0.315714
\(112\) −13.7450 + 2.59127i −1.29878 + 0.244852i
\(113\) 8.97756i 0.844538i −0.906471 0.422269i \(-0.861234\pi\)
0.906471 0.422269i \(-0.138766\pi\)
\(114\) 5.27750 + 4.80737i 0.494284 + 0.450251i
\(115\) −0.568640 + 4.76200i −0.0530260 + 0.444059i
\(116\) −1.82425 19.5233i −0.169377 1.81269i
\(117\) −3.35306 −0.309990
\(118\) −4.93166 4.49233i −0.453996 0.413552i
\(119\) 0.251540i 0.0230586i
\(120\) −2.25910 1.70190i −0.206227 0.155362i
\(121\) −9.13336 −0.830305
\(122\) 6.67500 + 6.08036i 0.604326 + 0.550490i
\(123\) 1.37906i 0.124345i
\(124\) −16.0737 + 1.50191i −1.44346 + 0.134876i
\(125\) 1.00000i 0.0894427i
\(126\) 3.33015 3.65582i 0.296673 0.325686i
\(127\) 12.7171i 1.12846i 0.825618 + 0.564230i \(0.190827\pi\)
−0.825618 + 0.564230i \(0.809173\pi\)
\(128\) −10.1412 5.01567i −0.896360 0.443327i
\(129\) 8.91103i 0.784572i
\(130\) −3.50556 3.19327i −0.307458 0.280069i
\(131\) 21.4821i 1.87690i 0.345417 + 0.938449i \(0.387738\pi\)
−0.345417 + 0.938449i \(0.612262\pi\)
\(132\) 2.72065 0.254216i 0.236802 0.0221267i
\(133\) −17.6514 −1.53057
\(134\) 14.5363 15.9578i 1.25574 1.37855i
\(135\) 1.00000 0.0860663
\(136\) 0.122426 0.162508i 0.0104979 0.0139349i
\(137\) 8.83193i 0.754562i 0.926099 + 0.377281i \(0.123141\pi\)
−0.926099 + 0.377281i \(0.876859\pi\)
\(138\) −4.43705 5.12958i −0.377707 0.436659i
\(139\) 1.47914i 0.125459i −0.998031 0.0627295i \(-0.980019\pi\)
0.998031 0.0627295i \(-0.0199805\pi\)
\(140\) 6.96322 0.650640i 0.588500 0.0549892i
\(141\) −12.6923 −1.06889
\(142\) −16.4170 14.9545i −1.37769 1.25496i
\(143\) 4.58112 0.383092
\(144\) 3.93076 0.741046i 0.327563 0.0617539i
\(145\) 9.80417i 0.814192i
\(146\) −4.99784 + 5.48661i −0.413624 + 0.454075i
\(147\) 5.22746i 0.431153i
\(148\) −6.62366 + 0.618911i −0.544461 + 0.0508742i
\(149\) 12.9154i 1.05807i −0.848600 0.529034i \(-0.822554\pi\)
0.848600 0.529034i \(-0.177446\pi\)
\(150\) 1.04548 + 0.952347i 0.0853633 + 0.0777588i
\(151\) 1.48821i 0.121109i −0.998165 0.0605546i \(-0.980713\pi\)
0.998165 0.0605546i \(-0.0192869\pi\)
\(152\) −11.4037 8.59105i −0.924965 0.696827i
\(153\) 0.0719348i 0.00581558i
\(154\) −4.54982 + 4.99477i −0.366635 + 0.402490i
\(155\) 8.07183 0.648345
\(156\) 6.67703 0.623898i 0.534590 0.0499518i
\(157\) 0.789022i 0.0629708i 0.999504 + 0.0314854i \(0.0100238\pi\)
−0.999504 + 0.0314854i \(0.989976\pi\)
\(158\) −4.00549 + 4.39721i −0.318659 + 0.349823i
\(159\) 10.9669 0.869733
\(160\) 4.81527 + 2.96870i 0.380681 + 0.234696i
\(161\) 16.6517 + 1.98841i 1.31233 + 0.156708i
\(162\) −0.952347 + 1.04548i −0.0748235 + 0.0821409i
\(163\) 10.0679i 0.788576i 0.918987 + 0.394288i \(0.129009\pi\)
−0.918987 + 0.394288i \(0.870991\pi\)
\(164\) −0.256599 2.74615i −0.0200370 0.214439i
\(165\) −1.36625 −0.106363
\(166\) 12.8487 14.1052i 0.997251 1.09478i
\(167\) 12.3125i 0.952769i −0.879237 0.476384i \(-0.841947\pi\)
0.879237 0.476384i \(-0.158053\pi\)
\(168\) −5.95118 + 7.89957i −0.459143 + 0.609465i
\(169\) −1.75702 −0.135155
\(170\) −0.0685069 + 0.0752066i −0.00525424 + 0.00576808i
\(171\) 5.04791 0.386023
\(172\) −1.65806 17.7448i −0.126426 1.35303i
\(173\) 3.04079 0.231187 0.115593 0.993297i \(-0.463123\pi\)
0.115593 + 0.993297i \(0.463123\pi\)
\(174\) −10.2501 9.33697i −0.777057 0.707834i
\(175\) −3.49678 −0.264332
\(176\) −5.37040 + 1.01246i −0.404809 + 0.0763167i
\(177\) −4.71711 −0.354560
\(178\) −12.0469 10.9737i −0.902951 0.822513i
\(179\) 9.66616i 0.722483i −0.932472 0.361242i \(-0.882353\pi\)
0.932472 0.361242i \(-0.117647\pi\)
\(180\) −1.99133 + 0.186069i −0.148425 + 0.0138687i
\(181\) 26.0047i 1.93291i 0.256827 + 0.966457i \(0.417323\pi\)
−0.256827 + 0.966457i \(0.582677\pi\)
\(182\) −11.1662 + 12.2582i −0.827692 + 0.908636i
\(183\) 6.38461 0.471964
\(184\) 9.79006 + 9.38907i 0.721733 + 0.692172i
\(185\) 3.32625 0.244551
\(186\) −7.68719 + 8.43896i −0.563652 + 0.618775i
\(187\) 0.0982810i 0.00718702i
\(188\) 25.2746 2.36165i 1.84334 0.172241i
\(189\) 3.49678i 0.254353i
\(190\) 5.27750 + 4.80737i 0.382870 + 0.348763i
\(191\) 1.45243 0.105094 0.0525469 0.998618i \(-0.483266\pi\)
0.0525469 + 0.998618i \(0.483266\pi\)
\(192\) −7.68953 + 2.20705i −0.554944 + 0.159280i
\(193\) 12.6263 0.908861 0.454431 0.890782i \(-0.349843\pi\)
0.454431 + 0.890782i \(0.349843\pi\)
\(194\) 4.93981 + 4.49975i 0.354657 + 0.323063i
\(195\) −3.35306 −0.240117
\(196\) −0.972665 10.4096i −0.0694761 0.743541i
\(197\) −23.9878 −1.70906 −0.854530 0.519401i \(-0.826155\pi\)
−0.854530 + 0.519401i \(0.826155\pi\)
\(198\) 1.30115 1.42839i 0.0924684 0.101511i
\(199\) −16.8297 −1.19303 −0.596513 0.802603i \(-0.703448\pi\)
−0.596513 + 0.802603i \(0.703448\pi\)
\(200\) −2.25910 1.70190i −0.159742 0.120343i
\(201\) 15.2636i 1.07661i
\(202\) −10.2752 + 11.2801i −0.722962 + 0.793665i
\(203\) 34.2830 2.40619
\(204\) −0.0133848 0.143246i −0.000937124 0.0100292i
\(205\) 1.37906i 0.0963176i
\(206\) −8.30310 + 9.11510i −0.578504 + 0.635079i
\(207\) −4.76200 0.568640i −0.330982 0.0395232i
\(208\) −13.1800 + 2.48477i −0.913872 + 0.172288i
\(209\) −6.89672 −0.477056
\(210\) 3.33015 3.65582i 0.229802 0.252276i
\(211\) 20.6790i 1.42360i −0.702382 0.711800i \(-0.747880\pi\)
0.702382 0.711800i \(-0.252120\pi\)
\(212\) −21.8387 + 2.04060i −1.49989 + 0.140149i
\(213\) −15.7028 −1.07594
\(214\) 14.6887 16.1252i 1.00410 1.10229i
\(215\) 8.91103i 0.607727i
\(216\) 1.70190 2.25910i 0.115800 0.153712i
\(217\) 28.2254i 1.91607i
\(218\) −2.26003 2.05870i −0.153069 0.139433i
\(219\) 5.24792i 0.354621i
\(220\) 2.72065 0.254216i 0.183426 0.0171393i
\(221\) 0.241201i 0.0162250i
\(222\) −3.16775 + 3.47754i −0.212605 + 0.233397i
\(223\) 10.0263i 0.671409i −0.941967 0.335704i \(-0.891026\pi\)
0.941967 0.335704i \(-0.108974\pi\)
\(224\) 10.3809 16.8379i 0.693601 1.12503i
\(225\) 1.00000 0.0666667
\(226\) 9.38588 + 8.54976i 0.624340 + 0.568721i
\(227\) −5.76617 −0.382714 −0.191357 0.981520i \(-0.561289\pi\)
−0.191357 + 0.981520i \(0.561289\pi\)
\(228\) −10.0520 + 0.939258i −0.665712 + 0.0622039i
\(229\) 2.46613i 0.162966i 0.996675 + 0.0814831i \(0.0259657\pi\)
−0.996675 + 0.0814831i \(0.974034\pi\)
\(230\) −4.43705 5.12958i −0.292570 0.338235i
\(231\) 4.77748i 0.314335i
\(232\) 22.1486 + 16.6857i 1.45413 + 1.09547i
\(233\) 17.1486 1.12344 0.561722 0.827326i \(-0.310139\pi\)
0.561722 + 0.827326i \(0.310139\pi\)
\(234\) 3.19327 3.50556i 0.208751 0.229166i
\(235\) −12.6923 −0.827957
\(236\) 9.39331 0.877706i 0.611452 0.0571338i
\(237\) 4.20591i 0.273203i
\(238\) 0.262981 + 0.239554i 0.0170465 + 0.0155279i
\(239\) 7.88125i 0.509796i 0.966968 + 0.254898i \(0.0820419\pi\)
−0.966968 + 0.254898i \(0.917958\pi\)
\(240\) 3.93076 0.741046i 0.253729 0.0478343i
\(241\) 13.3123i 0.857523i 0.903418 + 0.428762i \(0.141050\pi\)
−0.903418 + 0.428762i \(0.858950\pi\)
\(242\) 8.69813 9.54877i 0.559137 0.613818i
\(243\) 1.00000i 0.0641500i
\(244\) −12.7138 + 1.18797i −0.813920 + 0.0760523i
\(245\) 5.22746i 0.333970i
\(246\) −1.44178 1.31334i −0.0919246 0.0837356i
\(247\) −16.9259 −1.07697
\(248\) 13.7375 18.2351i 0.872330 1.15793i
\(249\) 13.4916i 0.854994i
\(250\) 1.04548 + 0.952347i 0.0661221 + 0.0602317i
\(251\) −16.9160 −1.06773 −0.533865 0.845570i \(-0.679261\pi\)
−0.533865 + 0.845570i \(0.679261\pi\)
\(252\) 0.650640 + 6.96322i 0.0409865 + 0.438642i
\(253\) 6.50609 + 0.776905i 0.409034 + 0.0488436i
\(254\) −13.2955 12.1111i −0.834234 0.759918i
\(255\) 0.0719348i 0.00450473i
\(256\) 14.9017 5.82575i 0.931356 0.364109i
\(257\) 19.6697 1.22696 0.613482 0.789709i \(-0.289768\pi\)
0.613482 + 0.789709i \(0.289768\pi\)
\(258\) −9.31632 8.48639i −0.580009 0.528340i
\(259\) 11.6312i 0.722726i
\(260\) 6.67703 0.623898i 0.414092 0.0386925i
\(261\) −9.80417 −0.606863
\(262\) −22.4592 20.4584i −1.38753 1.26392i
\(263\) 3.46611 0.213730 0.106865 0.994274i \(-0.465919\pi\)
0.106865 + 0.994274i \(0.465919\pi\)
\(264\) −2.32523 + 3.08650i −0.143108 + 0.189961i
\(265\) 10.9669 0.673692
\(266\) 16.8103 18.4543i 1.03071 1.13150i
\(267\) −11.5228 −0.705183
\(268\) 2.84008 + 30.3948i 0.173485 + 1.85666i
\(269\) −0.230066 −0.0140274 −0.00701369 0.999975i \(-0.502233\pi\)
−0.00701369 + 0.999975i \(0.502233\pi\)
\(270\) −0.952347 + 1.04548i −0.0579580 + 0.0636261i
\(271\) 6.04603i 0.367270i −0.982994 0.183635i \(-0.941214\pi\)
0.982994 0.183635i \(-0.0587865\pi\)
\(272\) 0.0533070 + 0.282758i 0.00323221 + 0.0171447i
\(273\) 11.7249i 0.709623i
\(274\) −9.23363 8.41106i −0.557824 0.508131i
\(275\) −1.36625 −0.0823881
\(276\) 9.58850 + 0.246289i 0.577160 + 0.0148248i
\(277\) 14.3524 0.862355 0.431177 0.902267i \(-0.358098\pi\)
0.431177 + 0.902267i \(0.358098\pi\)
\(278\) 1.54642 + 1.40866i 0.0927479 + 0.0844855i
\(279\) 8.07183i 0.483248i
\(280\) −5.95118 + 7.89957i −0.355651 + 0.472089i
\(281\) 9.58403i 0.571735i −0.958269 0.285868i \(-0.907718\pi\)
0.958269 0.285868i \(-0.0922818\pi\)
\(282\) 12.0875 13.2696i 0.719802 0.790195i
\(283\) 29.7360 1.76762 0.883812 0.467842i \(-0.154969\pi\)
0.883812 + 0.467842i \(0.154969\pi\)
\(284\) 31.2694 2.92180i 1.85550 0.173377i
\(285\) 5.04791 0.299012
\(286\) −4.36282 + 4.78948i −0.257979 + 0.283208i
\(287\) 4.82226 0.284649
\(288\) −2.96870 + 4.81527i −0.174932 + 0.283743i
\(289\) 16.9948 0.999696
\(290\) −10.2501 9.33697i −0.601906 0.548286i
\(291\) 4.72490 0.276979
\(292\) −0.976473 10.4503i −0.0571437 0.611558i
\(293\) 19.4305i 1.13514i −0.823324 0.567572i \(-0.807883\pi\)
0.823324 0.567572i \(-0.192117\pi\)
\(294\) −5.46522 4.97835i −0.318738 0.290344i
\(295\) −4.71711 −0.274641
\(296\) 5.66096 7.51434i 0.329037 0.436762i
\(297\) 1.36625i 0.0792779i
\(298\) 13.5028 + 12.2999i 0.782196 + 0.712516i
\(299\) 15.9673 + 1.90668i 0.923410 + 0.110266i
\(300\) −1.99133 + 0.186069i −0.114969 + 0.0107427i
\(301\) 31.1599 1.79603
\(302\) 1.55590 + 1.41730i 0.0895321 + 0.0815562i
\(303\) 10.7894i 0.619833i
\(304\) 19.8421 3.74074i 1.13802 0.214546i
\(305\) 6.38461 0.365581
\(306\) −0.0752066 0.0685069i −0.00429928 0.00391628i
\(307\) 24.3915i 1.39209i −0.717996 0.696047i \(-0.754941\pi\)
0.717996 0.696047i \(-0.245059\pi\)
\(308\) −0.888938 9.51351i −0.0506520 0.542083i
\(309\) 8.71856i 0.495981i
\(310\) −7.68719 + 8.43896i −0.436603 + 0.479301i
\(311\) 3.30836i 0.187600i −0.995591 0.0937999i \(-0.970099\pi\)
0.995591 0.0937999i \(-0.0299014\pi\)
\(312\) −5.70657 + 7.57488i −0.323071 + 0.428843i
\(313\) 16.4380i 0.929130i 0.885539 + 0.464565i \(0.153789\pi\)
−0.885539 + 0.464565i \(0.846211\pi\)
\(314\) −0.824909 0.751424i −0.0465523 0.0424053i
\(315\) 3.49678i 0.197021i
\(316\) −0.782588 8.37534i −0.0440240 0.471149i
\(317\) −21.1799 −1.18958 −0.594791 0.803880i \(-0.702765\pi\)
−0.594791 + 0.803880i \(0.702765\pi\)
\(318\) −10.4443 + 11.4657i −0.585688 + 0.642965i
\(319\) 13.3950 0.749974
\(320\) −7.68953 + 2.20705i −0.429858 + 0.123378i
\(321\) 15.4237i 0.860864i
\(322\) −17.9370 + 15.5154i −0.999591 + 0.864638i
\(323\) 0.363121i 0.0202046i
\(324\) −0.186069 1.99133i −0.0103371 0.110629i
\(325\) −3.35306 −0.185994
\(326\) −10.5258 9.58810i −0.582969 0.531036i
\(327\) −2.16171 −0.119543
\(328\) 3.11543 + 2.34702i 0.172021 + 0.129593i
\(329\) 44.3823i 2.44688i
\(330\) 1.30115 1.42839i 0.0716257 0.0786304i
\(331\) 7.56275i 0.415687i 0.978162 + 0.207843i \(0.0666444\pi\)
−0.978162 + 0.207843i \(0.933356\pi\)
\(332\) 2.51036 + 26.8661i 0.137774 + 1.47447i
\(333\) 3.32625i 0.182278i
\(334\) 12.8725 + 11.7258i 0.704351 + 0.641605i
\(335\) 15.2636i 0.833940i
\(336\) −2.59127 13.7450i −0.141366 0.749850i
\(337\) 16.3852i 0.892556i −0.894894 0.446278i \(-0.852749\pi\)
0.894894 0.446278i \(-0.147251\pi\)
\(338\) 1.67329 1.83693i 0.0910150 0.0999159i
\(339\) 8.97756 0.487594
\(340\) −0.0133848 0.143246i −0.000725893 0.00776859i
\(341\) 11.0282i 0.597208i
\(342\) −4.80737 + 5.27750i −0.259953 + 0.285375i
\(343\) −6.19819 −0.334671
\(344\) 20.1309 + 15.1657i 1.08538 + 0.817680i
\(345\) −4.76200 0.568640i −0.256377 0.0306145i
\(346\) −2.89589 + 3.17909i −0.155684 + 0.170909i
\(347\) 10.3602i 0.556166i −0.960557 0.278083i \(-0.910301\pi\)
0.960557 0.278083i \(-0.0896991\pi\)
\(348\) 19.5233 1.82425i 1.04656 0.0977899i
\(349\) 0.414108 0.0221667 0.0110833 0.999939i \(-0.496472\pi\)
0.0110833 + 0.999939i \(0.496472\pi\)
\(350\) 3.33015 3.65582i 0.178004 0.195412i
\(351\) 3.35306i 0.178973i
\(352\) 4.05598 6.57887i 0.216185 0.350655i
\(353\) −33.5214 −1.78416 −0.892082 0.451874i \(-0.850756\pi\)
−0.892082 + 0.451874i \(0.850756\pi\)
\(354\) 4.49233 4.93166i 0.238765 0.262115i
\(355\) −15.7028 −0.833419
\(356\) 22.9456 2.14403i 1.21611 0.113633i
\(357\) 0.251540 0.0133129
\(358\) 10.1058 + 9.20555i 0.534109 + 0.486528i
\(359\) −15.7877 −0.833240 −0.416620 0.909081i \(-0.636786\pi\)
−0.416620 + 0.909081i \(0.636786\pi\)
\(360\) 1.70190 2.25910i 0.0896981 0.119065i
\(361\) 6.48141 0.341127
\(362\) −27.1875 24.7655i −1.42894 1.30165i
\(363\) 9.13336i 0.479377i
\(364\) −2.18163 23.3481i −0.114349 1.22377i
\(365\) 5.24792i 0.274689i
\(366\) −6.08036 + 6.67500i −0.317826 + 0.348908i
\(367\) −10.8732 −0.567578 −0.283789 0.958887i \(-0.591592\pi\)
−0.283789 + 0.958887i \(0.591592\pi\)
\(368\) −19.1397 + 1.29368i −0.997723 + 0.0674376i
\(369\) −1.37906 −0.0717909
\(370\) −3.16775 + 3.47754i −0.164683 + 0.180789i
\(371\) 38.3488i 1.99097i
\(372\) −1.50191 16.0737i −0.0778706 0.833380i
\(373\) 11.5032i 0.595614i −0.954626 0.297807i \(-0.903745\pi\)
0.954626 0.297807i \(-0.0962551\pi\)
\(374\) 0.102751 + 0.0935977i 0.00531313 + 0.00483982i
\(375\) 1.00000 0.0516398
\(376\) −21.6011 + 28.6733i −1.11399 + 1.47871i
\(377\) 32.8739 1.69309
\(378\) 3.65582 + 3.33015i 0.188035 + 0.171284i
\(379\) −22.3509 −1.14809 −0.574044 0.818825i \(-0.694626\pi\)
−0.574044 + 0.818825i \(0.694626\pi\)
\(380\) −10.0520 + 0.939258i −0.515659 + 0.0481829i
\(381\) −12.7171 −0.651517
\(382\) −1.38321 + 1.51849i −0.0707714 + 0.0776925i
\(383\) 11.2864 0.576709 0.288354 0.957524i \(-0.406892\pi\)
0.288354 + 0.957524i \(0.406892\pi\)
\(384\) 5.01567 10.1412i 0.255955 0.517514i
\(385\) 4.77748i 0.243483i
\(386\) −12.0246 + 13.2006i −0.612038 + 0.671892i
\(387\) −8.91103 −0.452973
\(388\) −9.40882 + 0.879156i −0.477661 + 0.0446324i
\(389\) 19.9787i 1.01296i −0.862252 0.506480i \(-0.830946\pi\)
0.862252 0.506480i \(-0.169054\pi\)
\(390\) 3.19327 3.50556i 0.161698 0.177511i
\(391\) 0.0409050 0.342554i 0.00206866 0.0173237i
\(392\) 11.8093 + 8.89662i 0.596462 + 0.449347i
\(393\) −21.4821 −1.08363
\(394\) 22.8447 25.0788i 1.15090 1.26345i
\(395\) 4.20591i 0.211622i
\(396\) 0.254216 + 2.72065i 0.0127749 + 0.136718i
\(397\) 17.1842 0.862452 0.431226 0.902244i \(-0.358081\pi\)
0.431226 + 0.902244i \(0.358081\pi\)
\(398\) 16.0277 17.5952i 0.803397 0.881966i
\(399\) 17.6514i 0.883677i
\(400\) 3.93076 0.741046i 0.196538 0.0370523i
\(401\) 21.5671i 1.07701i −0.842622 0.538505i \(-0.818989\pi\)
0.842622 0.538505i \(-0.181011\pi\)
\(402\) 15.9578 + 14.5363i 0.795905 + 0.725003i
\(403\) 27.0653i 1.34822i
\(404\) −2.00756 21.4851i −0.0998799 1.06893i
\(405\) 1.00000i 0.0496904i
\(406\) −32.6493 + 35.8423i −1.62036 + 1.77882i
\(407\) 4.54450i 0.225262i
\(408\) 0.162508 + 0.122426i 0.00804534 + 0.00606099i
\(409\) 20.5077 1.01404 0.507021 0.861934i \(-0.330747\pi\)
0.507021 + 0.861934i \(0.330747\pi\)
\(410\) −1.44178 1.31334i −0.0712045 0.0648613i
\(411\) −8.83193 −0.435647
\(412\) −1.62225 17.3615i −0.0799225 0.855339i
\(413\) 16.4947i 0.811651i
\(414\) 5.12958 4.43705i 0.252105 0.218069i
\(415\) 13.4916i 0.662276i
\(416\) 9.95420 16.1459i 0.488045 0.791617i
\(417\) 1.47914 0.0724338
\(418\) 6.56807 7.21040i 0.321255 0.352672i
\(419\) −6.48385 −0.316757 −0.158378 0.987378i \(-0.550627\pi\)
−0.158378 + 0.987378i \(0.550627\pi\)
\(420\) 0.650640 + 6.96322i 0.0317480 + 0.339771i
\(421\) 16.5039i 0.804351i −0.915563 0.402175i \(-0.868254\pi\)
0.915563 0.402175i \(-0.131746\pi\)
\(422\) 21.6195 + 19.6936i 1.05242 + 0.958668i
\(423\) 12.6923i 0.617123i
\(424\) 18.6646 24.7753i 0.906434 1.20320i
\(425\) 0.0719348i 0.00348935i
\(426\) 14.9545 16.4170i 0.724550 0.795408i
\(427\) 22.3256i 1.08041i
\(428\) 2.86986 + 30.7135i 0.138720 + 1.48459i
\(429\) 4.58112i 0.221178i
\(430\) −9.31632 8.48639i −0.449273 0.409250i
\(431\) 31.4733 1.51602 0.758009 0.652244i \(-0.226172\pi\)
0.758009 + 0.652244i \(0.226172\pi\)
\(432\) 0.741046 + 3.93076i 0.0356536 + 0.189119i
\(433\) 18.7432i 0.900741i −0.892842 0.450370i \(-0.851292\pi\)
0.892842 0.450370i \(-0.148708\pi\)
\(434\) 29.5092 + 26.8804i 1.41649 + 1.29030i
\(435\) −9.80417 −0.470074
\(436\) 4.30467 0.402227i 0.206156 0.0192632i
\(437\) −24.0382 2.87044i −1.14990 0.137312i
\(438\) −5.48661 4.99784i −0.262160 0.238806i
\(439\) 9.37553i 0.447470i −0.974650 0.223735i \(-0.928175\pi\)
0.974650 0.223735i \(-0.0718250\pi\)
\(440\) −2.32523 + 3.08650i −0.110851 + 0.147143i
\(441\) −5.22746 −0.248926
\(442\) 0.252172 + 0.229708i 0.0119946 + 0.0109261i
\(443\) 21.6166i 1.02704i −0.858079 0.513518i \(-0.828342\pi\)
0.858079 0.513518i \(-0.171658\pi\)
\(444\) −0.618911 6.62366i −0.0293722 0.314345i
\(445\) −11.5228 −0.546232
\(446\) 10.4823 + 9.54849i 0.496351 + 0.452134i
\(447\) 12.9154 0.610876
\(448\) 7.71758 + 26.8886i 0.364621 + 1.27037i
\(449\) −11.7632 −0.555141 −0.277571 0.960705i \(-0.589529\pi\)
−0.277571 + 0.960705i \(0.589529\pi\)
\(450\) −0.952347 + 1.04548i −0.0448941 + 0.0492845i
\(451\) 1.88414 0.0887207
\(452\) −17.8772 + 1.67044i −0.840875 + 0.0785710i
\(453\) 1.48821 0.0699224
\(454\) 5.49140 6.02843i 0.257724 0.282928i
\(455\) 11.7249i 0.549671i
\(456\) 8.59105 11.4037i 0.402313 0.534029i
\(457\) 35.4431i 1.65796i −0.559279 0.828980i \(-0.688922\pi\)
0.559279 0.828980i \(-0.311078\pi\)
\(458\) −2.57829 2.34861i −0.120476 0.109743i
\(459\) −0.0719348 −0.00335763
\(460\) 9.58850 + 0.246289i 0.447066 + 0.0114833i
\(461\) −14.2189 −0.662240 −0.331120 0.943589i \(-0.607427\pi\)
−0.331120 + 0.943589i \(0.607427\pi\)
\(462\) −4.99477 4.54982i −0.232378 0.211677i
\(463\) 1.35225i 0.0628444i 0.999506 + 0.0314222i \(0.0100036\pi\)
−0.999506 + 0.0314222i \(0.989996\pi\)
\(464\) −38.5378 + 7.26534i −1.78907 + 0.337285i
\(465\) 8.07183i 0.374322i
\(466\) −16.3314 + 17.9286i −0.756539 + 0.830525i
\(467\) −19.9740 −0.924289 −0.462144 0.886805i \(-0.652920\pi\)
−0.462144 + 0.886805i \(0.652920\pi\)
\(468\) 0.623898 + 6.67703i 0.0288397 + 0.308646i
\(469\) −53.3735 −2.46456
\(470\) 12.0875 13.2696i 0.557556 0.612082i
\(471\) −0.789022 −0.0363562
\(472\) −8.02807 + 10.6564i −0.369522 + 0.490502i
\(473\) 12.1747 0.559793
\(474\) −4.39721 4.00549i −0.201970 0.183978i
\(475\) 5.04791 0.231614
\(476\) −0.500898 + 0.0468037i −0.0229586 + 0.00214524i
\(477\) 10.9669i 0.502140i
\(478\) −8.23971 7.50569i −0.376876 0.343302i
\(479\) −27.9827 −1.27856 −0.639282 0.768972i \(-0.720768\pi\)
−0.639282 + 0.768972i \(0.720768\pi\)
\(480\) −2.96870 + 4.81527i −0.135502 + 0.219786i
\(481\) 11.1531i 0.508538i
\(482\) −13.9178 12.6780i −0.633939 0.577466i
\(483\) −1.98841 + 16.6517i −0.0904757 + 0.757677i
\(484\) 1.69943 + 18.1875i 0.0772468 + 0.826704i
\(485\) 4.72490 0.214547
\(486\) −1.04548 0.952347i −0.0474241 0.0431994i
\(487\) 30.1729i 1.36727i 0.729826 + 0.683633i \(0.239601\pi\)
−0.729826 + 0.683633i \(0.760399\pi\)
\(488\) 10.8660 14.4235i 0.491880 0.652919i
\(489\) −10.0679 −0.455284
\(490\) −5.46522 4.97835i −0.246893 0.224899i
\(491\) 7.08265i 0.319635i 0.987147 + 0.159818i \(0.0510906\pi\)
−0.987147 + 0.159818i \(0.948909\pi\)
\(492\) 2.74615 0.256599i 0.123806 0.0115684i
\(493\) 0.705261i 0.0317633i
\(494\) 16.1194 17.6958i 0.725245 0.796170i
\(495\) 1.36625i 0.0614084i
\(496\) 5.98160 + 31.7284i 0.268582 + 1.42465i
\(497\) 54.9093i 2.46302i
\(498\) 14.1052 + 12.8487i 0.632070 + 0.575763i
\(499\) 17.2498i 0.772207i 0.922455 + 0.386104i \(0.126179\pi\)
−0.922455 + 0.386104i \(0.873821\pi\)
\(500\) −1.99133 + 0.186069i −0.0890548 + 0.00832124i
\(501\) 12.3125 0.550081
\(502\) 16.1099 17.6854i 0.719022 0.789339i
\(503\) 34.6103 1.54320 0.771598 0.636111i \(-0.219458\pi\)
0.771598 + 0.636111i \(0.219458\pi\)
\(504\) −7.89957 5.95118i −0.351875 0.265086i
\(505\) 10.7894i 0.480120i
\(506\) −7.00830 + 6.06212i −0.311557 + 0.269494i
\(507\) 1.75702i 0.0780318i
\(508\) 25.3239 2.36625i 1.12357 0.104985i
\(509\) −15.0316 −0.666266 −0.333133 0.942880i \(-0.608106\pi\)
−0.333133 + 0.942880i \(0.608106\pi\)
\(510\) −0.0752066 0.0685069i −0.00333020 0.00303354i
\(511\) 18.3508 0.811792
\(512\) −8.10088 + 21.1276i −0.358012 + 0.933717i
\(513\) 5.04791i 0.222871i
\(514\) −18.7324 + 20.5644i −0.826251 + 0.907055i
\(515\) 8.71856i 0.384186i
\(516\) 17.7448 1.65806i 0.781169 0.0729921i
\(517\) 17.3409i 0.762653i
\(518\) 12.1602 + 11.0769i 0.534288 + 0.486692i
\(519\) 3.04079i 0.133476i
\(520\) −5.70657 + 7.57488i −0.250250 + 0.332181i
\(521\) 2.09374i 0.0917284i −0.998948 0.0458642i \(-0.985396\pi\)
0.998948 0.0458642i \(-0.0146041\pi\)
\(522\) 9.33697 10.2501i 0.408668 0.448634i
\(523\) −4.78053 −0.209038 −0.104519 0.994523i \(-0.533330\pi\)
−0.104519 + 0.994523i \(0.533330\pi\)
\(524\) 42.7778 3.99714i 1.86876 0.174616i
\(525\) 3.49678i 0.152612i
\(526\) −3.30094 + 3.62376i −0.143928 + 0.158003i
\(527\) −0.580646 −0.0252933
\(528\) −1.01246 5.37040i −0.0440615 0.233717i
\(529\) 22.3533 + 5.41573i 0.971882 + 0.235466i
\(530\) −10.4443 + 11.4657i −0.453672 + 0.498039i
\(531\) 4.71711i 0.204705i
\(532\) 3.28438 + 35.1497i 0.142396 + 1.52393i
\(533\) 4.62406 0.200290
\(534\) 10.9737 12.0469i 0.474878 0.521319i
\(535\) 15.4237i 0.666823i
\(536\) −34.4820 25.9772i −1.48940 1.12204i
\(537\) 9.66616 0.417126
\(538\) 0.219103 0.240530i 0.00944620 0.0103700i
\(539\) 7.14202 0.307629
\(540\) −0.186069 1.99133i −0.00800712 0.0856930i
\(541\) −32.7776 −1.40922 −0.704610 0.709594i \(-0.748878\pi\)
−0.704610 + 0.709594i \(0.748878\pi\)
\(542\) 6.32102 + 5.75792i 0.271511 + 0.247324i
\(543\) −26.0047 −1.11597
\(544\) −0.346386 0.213553i −0.0148512 0.00915599i
\(545\) −2.16171 −0.0925976
\(546\) −12.2582 11.1662i −0.524601 0.477868i
\(547\) 15.0838i 0.644936i −0.946580 0.322468i \(-0.895487\pi\)
0.946580 0.322468i \(-0.104513\pi\)
\(548\) 17.5872 1.64334i 0.751290 0.0702002i
\(549\) 6.38461i 0.272488i
\(550\) 1.30115 1.42839i 0.0554811 0.0609069i
\(551\) −49.4906 −2.10837
\(552\) −9.38907 + 9.79006i −0.399626 + 0.416693i
\(553\) 14.7071 0.625411
\(554\) −13.6685 + 15.0052i −0.580720 + 0.637511i
\(555\) 3.32625i 0.141192i
\(556\) −2.94545 + 0.275222i −0.124915 + 0.0116720i
\(557\) 18.7166i 0.793048i −0.918024 0.396524i \(-0.870216\pi\)
0.918024 0.396524i \(-0.129784\pi\)
\(558\) −8.43896 7.68719i −0.357250 0.325425i
\(559\) 29.8792 1.26375
\(560\) −2.59127 13.7450i −0.109501 0.580832i
\(561\) 0.0982810 0.00414943
\(562\) 10.0199 + 9.12733i 0.422666 + 0.385013i
\(563\) −1.60093 −0.0674712 −0.0337356 0.999431i \(-0.510740\pi\)
−0.0337356 + 0.999431i \(0.510740\pi\)
\(564\) 2.36165 + 25.2746i 0.0994433 + 1.06425i
\(565\) 8.97756 0.377689
\(566\) −28.3190 + 31.0885i −1.19034 + 1.30675i
\(567\) 3.49678 0.146851
\(568\) −26.7247 + 35.4742i −1.12134 + 1.48847i
\(569\) 25.5371i 1.07057i 0.844672 + 0.535285i \(0.179796\pi\)
−0.844672 + 0.535285i \(0.820204\pi\)
\(570\) −4.80737 + 5.27750i −0.201358 + 0.221050i
\(571\) 14.4267 0.603738 0.301869 0.953349i \(-0.402390\pi\)
0.301869 + 0.953349i \(0.402390\pi\)
\(572\) −0.852402 9.12250i −0.0356407 0.381431i
\(573\) 1.45243i 0.0606759i
\(574\) −4.59247 + 5.04159i −0.191686 + 0.210432i
\(575\) −4.76200 0.568640i −0.198589 0.0237139i
\(576\) −2.20705 7.68953i −0.0919606 0.320397i
\(577\) 2.17614 0.0905938 0.0452969 0.998974i \(-0.485577\pi\)
0.0452969 + 0.998974i \(0.485577\pi\)
\(578\) −16.1850 + 17.7678i −0.673206 + 0.739043i
\(579\) 12.6263i 0.524731i
\(580\) 19.5233 1.82425i 0.810660 0.0757477i
\(581\) −47.1771 −1.95723
\(582\) −4.49975 + 4.93981i −0.186521 + 0.204762i
\(583\) 14.9836i 0.620555i
\(584\) 11.8556 + 8.93145i 0.490587 + 0.369586i
\(585\) 3.35306i 0.138632i
\(586\) 20.3143 + 18.5046i 0.839176 + 0.764419i
\(587\) 30.9114i 1.27585i −0.770099 0.637925i \(-0.779793\pi\)
0.770099 0.637925i \(-0.220207\pi\)
\(588\) 10.4096 0.972665i 0.429283 0.0401120i
\(589\) 40.7459i 1.67891i
\(590\) 4.49233 4.93166i 0.184946 0.203033i
\(591\) 23.9878i 0.986727i
\(592\) 2.46491 + 13.0747i 0.101307 + 0.537367i
\(593\) −18.1730 −0.746276 −0.373138 0.927776i \(-0.621718\pi\)
−0.373138 + 0.927776i \(0.621718\pi\)
\(594\) 1.42839 + 1.30115i 0.0586076 + 0.0533867i
\(595\) 0.251540 0.0103121
\(596\) −25.7187 + 2.40315i −1.05348 + 0.0984367i
\(597\) 16.8297i 0.688794i
\(598\) −17.1998 + 14.8777i −0.703351 + 0.608393i
\(599\) 13.0346i 0.532581i 0.963893 + 0.266291i \(0.0857981\pi\)
−0.963893 + 0.266291i \(0.914202\pi\)
\(600\) 1.70190 2.25910i 0.0694799 0.0922273i
\(601\) −28.6319 −1.16792 −0.583959 0.811783i \(-0.698497\pi\)
−0.583959 + 0.811783i \(0.698497\pi\)
\(602\) −29.6750 + 32.5771i −1.20946 + 1.32774i
\(603\) 15.2636 0.621582
\(604\) −2.96352 + 0.276910i −0.120584 + 0.0112673i
\(605\) 9.13336i 0.371324i
\(606\) −11.2801 10.2752i −0.458222 0.417402i
\(607\) 8.85705i 0.359496i 0.983713 + 0.179748i \(0.0575283\pi\)
−0.983713 + 0.179748i \(0.942472\pi\)
\(608\) −14.9857 + 24.3071i −0.607751 + 0.985782i
\(609\) 34.2830i 1.38922i
\(610\) −6.08036 + 6.67500i −0.246187 + 0.270263i
\(611\) 42.5581i 1.72172i
\(612\) 0.143246 0.0133848i 0.00579036 0.000541049i
\(613\) 34.3412i 1.38703i 0.720443 + 0.693514i \(0.243939\pi\)
−0.720443 + 0.693514i \(0.756061\pi\)
\(614\) 25.5008 + 23.2291i 1.02913 + 0.937452i
\(615\) −1.37906 −0.0556090
\(616\) 10.7928 + 8.13080i 0.434854 + 0.327599i
\(617\) 7.75901i 0.312366i −0.987728 0.156183i \(-0.950081\pi\)
0.987728 0.156183i \(-0.0499190\pi\)
\(618\) −9.11510 8.30310i −0.366663 0.334000i
\(619\) −22.8208 −0.917244 −0.458622 0.888631i \(-0.651657\pi\)
−0.458622 + 0.888631i \(0.651657\pi\)
\(620\) −1.50191 16.0737i −0.0603183 0.645533i
\(621\) 0.568640 4.76200i 0.0228187 0.191092i
\(622\) 3.45883 + 3.15071i 0.138686 + 0.126332i
\(623\) 40.2926i 1.61429i
\(624\) −2.48477 13.1800i −0.0994704 0.527624i
\(625\) 1.00000 0.0400000
\(626\) −17.1856 15.6547i −0.686876 0.625687i
\(627\) 6.89672i 0.275428i
\(628\) 1.57120 0.146812i 0.0626977 0.00585845i
\(629\) −0.239273 −0.00954046
\(630\) 3.65582 + 3.33015i 0.145651 + 0.132676i
\(631\) 42.6051 1.69608 0.848041 0.529931i \(-0.177782\pi\)
0.848041 + 0.529931i \(0.177782\pi\)
\(632\) 9.50157 + 7.15805i 0.377952 + 0.284732i
\(633\) 20.6790 0.821916
\(634\) 20.1706 22.1432i 0.801078 0.879420i
\(635\) −12.7171 −0.504663
\(636\) −2.04060 21.8387i −0.0809149 0.865960i
\(637\) 17.5280 0.694483
\(638\) −12.7567 + 14.0042i −0.505041 + 0.554431i
\(639\) 15.7028i 0.621194i
\(640\) 5.01567 10.1412i 0.198262 0.400864i
\(641\) 34.2171i 1.35149i 0.737134 + 0.675746i \(0.236179\pi\)
−0.737134 + 0.675746i \(0.763821\pi\)
\(642\) 16.1252 + 14.6887i 0.636409 + 0.579716i
\(643\) 10.3253 0.407189 0.203595 0.979055i \(-0.434738\pi\)
0.203595 + 0.979055i \(0.434738\pi\)
\(644\) 0.861217 33.5289i 0.0339367 1.32122i
\(645\) −8.91103 −0.350871
\(646\) −0.379636 0.345817i −0.0149366 0.0136060i
\(647\) 4.42046i 0.173786i 0.996218 + 0.0868930i \(0.0276938\pi\)
−0.996218 + 0.0868930i \(0.972306\pi\)
\(648\) 2.25910 + 1.70190i 0.0887458 + 0.0668570i
\(649\) 6.44476i 0.252979i
\(650\) 3.19327 3.50556i 0.125251 0.137499i
\(651\) 28.2254 1.10624
\(652\) 20.0484 1.87331i 0.785155 0.0733646i
\(653\) −33.8914 −1.32627 −0.663137 0.748498i \(-0.730775\pi\)
−0.663137 + 0.748498i \(0.730775\pi\)
\(654\) 2.05870 2.26003i 0.0805016 0.0883743i
\(655\) −21.4821 −0.839375
\(656\) −5.42074 + 1.02195i −0.211644 + 0.0399003i
\(657\) −5.24792 −0.204741
\(658\) −46.4009 42.2674i −1.80890 1.64775i
\(659\) −35.4900 −1.38250 −0.691248 0.722618i \(-0.742939\pi\)
−0.691248 + 0.722618i \(0.742939\pi\)
\(660\) 0.254216 + 2.72065i 0.00989536 + 0.105901i
\(661\) 6.67221i 0.259519i −0.991546 0.129759i \(-0.958579\pi\)
0.991546 0.129759i \(-0.0414205\pi\)
\(662\) −7.90673 7.20237i −0.307304 0.279928i
\(663\) 0.241201 0.00936749
\(664\) −30.4788 22.9614i −1.18281 0.891074i
\(665\) 17.6514i 0.684493i
\(666\) −3.47754 3.16775i −0.134752 0.122748i
\(667\) 46.6874 + 5.57504i 1.80775 + 0.215866i
\(668\) −24.5182 + 2.29097i −0.948637 + 0.0886402i
\(669\) 10.0263 0.387638
\(670\) 15.9578 + 14.5363i 0.616505 + 0.561585i
\(671\) 8.72298i 0.336747i
\(672\) 16.8379 + 10.3809i 0.649538 + 0.400451i
\(673\) 19.0840 0.735634 0.367817 0.929898i \(-0.380105\pi\)
0.367817 + 0.929898i \(0.380105\pi\)
\(674\) 17.1304 + 15.6044i 0.659838 + 0.601058i
\(675\) 1.00000i 0.0384900i
\(676\) 0.326926 + 3.49879i 0.0125741 + 0.134569i
\(677\) 31.0941i 1.19505i 0.801852 + 0.597523i \(0.203848\pi\)
−0.801852 + 0.597523i \(0.796152\pi\)
\(678\) −8.54976 + 9.38588i −0.328351 + 0.360463i
\(679\) 16.5219i 0.634054i
\(680\) 0.162508 + 0.122426i 0.00623189 + 0.00469482i
\(681\) 5.76617i 0.220960i
\(682\) 11.5297 + 10.5026i 0.441497 + 0.402167i
\(683\) 0.183753i 0.00703110i −0.999994 0.00351555i \(-0.998881\pi\)
0.999994 0.00351555i \(-0.00111904\pi\)
\(684\) −0.939258 10.0520i −0.0359134 0.384349i
\(685\) −8.83193 −0.337451
\(686\) 5.90283 6.48010i 0.225371 0.247411i
\(687\) −2.46613 −0.0940886
\(688\) −35.0271 + 6.60348i −1.33539 + 0.251755i
\(689\) 36.7727i 1.40093i
\(690\) 5.12958 4.43705i 0.195280 0.168915i
\(691\) 19.4942i 0.741593i 0.928714 + 0.370796i \(0.120915\pi\)
−0.928714 + 0.370796i \(0.879085\pi\)
\(692\) −0.565795 6.05520i −0.0215083 0.230184i
\(693\) −4.77748 −0.181481
\(694\) 10.8314 + 9.86654i 0.411156 + 0.374529i
\(695\) 1.47914 0.0561070
\(696\) −16.6857 + 22.1486i −0.632471 + 0.839540i
\(697\) 0.0992022i 0.00375755i
\(698\) −0.394374 + 0.432942i −0.0149273 + 0.0163871i
\(699\) 17.1486i 0.648620i
\(700\) 0.650640 + 6.96322i 0.0245919 + 0.263185i
\(701\) 8.26187i 0.312047i 0.987753 + 0.156023i \(0.0498675\pi\)
−0.987753 + 0.156023i \(0.950132\pi\)
\(702\) 3.50556 + 3.19327i 0.132309 + 0.120522i
\(703\) 16.7906i 0.633271i
\(704\) 3.01539 + 10.5058i 0.113647 + 0.395954i
\(705\) 12.6923i 0.478021i
\(706\) 31.9240 35.0460i 1.20148 1.31898i
\(707\) 37.7280 1.41891
\(708\) 0.877706 + 9.39331i 0.0329862 + 0.353022i
\(709\) 18.7338i 0.703564i −0.936082 0.351782i \(-0.885576\pi\)
0.936082 0.351782i \(-0.114424\pi\)
\(710\) 14.9545 16.4170i 0.561234 0.616120i
\(711\) −4.20591 −0.157734
\(712\) −19.6106 + 26.0311i −0.734940 + 0.975556i
\(713\) 4.58997 38.4381i 0.171896 1.43952i
\(714\) −0.239554 + 0.262981i −0.00896507 + 0.00984181i
\(715\) 4.58112i 0.171324i
\(716\) −19.2485 + 1.79857i −0.719350 + 0.0672157i
\(717\) −7.88125 −0.294331
\(718\) 15.0353 16.5057i 0.561114 0.615988i
\(719\) 15.0358i 0.560741i 0.959892 + 0.280370i \(0.0904573\pi\)
−0.959892 + 0.280370i \(0.909543\pi\)
\(720\) 0.741046 + 3.93076i 0.0276172 + 0.146491i
\(721\) 30.4869 1.13539
\(722\) −6.17256 + 6.77621i −0.229719 + 0.252184i
\(723\) −13.3123 −0.495091
\(724\) 51.7838 4.83866i 1.92453 0.179827i
\(725\) −9.80417 −0.364118
\(726\) 9.54877 + 8.69813i 0.354388 + 0.322818i
\(727\) −35.8931 −1.33120 −0.665601 0.746308i \(-0.731825\pi\)
−0.665601 + 0.746308i \(0.731825\pi\)
\(728\) 26.4877 + 19.9546i 0.981699 + 0.739568i
\(729\) −1.00000 −0.0370370
\(730\) −5.48661 4.99784i −0.203068 0.184978i
\(731\) 0.641013i 0.0237087i
\(732\) −1.18797 12.7138i −0.0439088 0.469917i
\(733\) 31.3376i 1.15748i −0.815512 0.578740i \(-0.803545\pi\)
0.815512 0.578740i \(-0.196455\pi\)
\(734\) 10.3551 11.3678i 0.382213 0.419592i
\(735\) −5.22746 −0.192818
\(736\) 16.8751 21.2422i 0.622024 0.782998i
\(737\) −20.8539 −0.768165
\(738\) 1.31334 1.44178i 0.0483448 0.0530727i
\(739\) 18.0131i 0.662622i −0.943522 0.331311i \(-0.892509\pi\)
0.943522 0.331311i \(-0.107491\pi\)
\(740\) −0.618911 6.62366i −0.0227516 0.243490i
\(741\) 16.9259i 0.621790i
\(742\) 40.0931 + 36.5214i 1.47186 + 1.34074i
\(743\) 5.74188 0.210649 0.105325 0.994438i \(-0.466412\pi\)
0.105325 + 0.994438i \(0.466412\pi\)
\(744\) 18.2351 + 13.7375i 0.668530 + 0.503640i
\(745\) 12.9154 0.473183
\(746\) 12.0264 + 10.9551i 0.440318 + 0.401093i
\(747\) 13.4916 0.493631
\(748\) −0.195710 + 0.0182870i −0.00715585 + 0.000668639i
\(749\) −53.9331 −1.97067
\(750\) −0.952347 + 1.04548i −0.0347748 + 0.0381756i
\(751\) −47.7051 −1.74078 −0.870391 0.492361i \(-0.836134\pi\)
−0.870391 + 0.492361i \(0.836134\pi\)
\(752\) −9.40562 49.8905i −0.342988 1.81932i
\(753\) 16.9160i 0.616454i
\(754\) −31.3074 + 34.3691i −1.14015 + 1.25165i
\(755\) 1.48821 0.0541616
\(756\) −6.96322 + 0.650640i −0.253250 + 0.0236636i
\(757\) 33.3125i 1.21076i −0.795935 0.605382i \(-0.793020\pi\)
0.795935 0.605382i \(-0.206980\pi\)
\(758\) 21.2858 23.3675i 0.773135 0.848744i
\(759\) −0.776905 + 6.50609i −0.0281999 + 0.236156i
\(760\) 8.59105 11.4037i 0.311630 0.413657i
\(761\) −13.8151 −0.500797 −0.250399 0.968143i \(-0.580562\pi\)
−0.250399 + 0.968143i \(0.580562\pi\)
\(762\) 12.1111 13.2955i 0.438739 0.481646i
\(763\) 7.55903i 0.273655i
\(764\) −0.270251 2.89225i −0.00977733 0.104638i
\(765\) −0.0719348 −0.00260081
\(766\) −10.7486 + 11.7997i −0.388362 + 0.426342i
\(767\) 15.8167i 0.571109i
\(768\) 5.82575 + 14.9017i 0.210218 + 0.537719i
\(769\) 32.1778i 1.16036i −0.814487 0.580181i \(-0.802982\pi\)
0.814487 0.580181i \(-0.197018\pi\)
\(770\) −4.99477 4.54982i −0.179999 0.163964i
\(771\) 19.6697i 0.708388i
\(772\) −2.34936 25.1431i −0.0845553 0.904919i
\(773\) 9.57568i 0.344413i 0.985061 + 0.172207i \(0.0550897\pi\)
−0.985061 + 0.172207i \(0.944910\pi\)
\(774\) 8.48639 9.31632i 0.305037 0.334868i
\(775\) 8.07183i 0.289949i
\(776\) 8.04133 10.6740i 0.288667 0.383175i
\(777\) 11.6312 0.417266
\(778\) 20.8874 + 19.0267i 0.748849 + 0.682139i
\(779\) −6.96136 −0.249417
\(780\) 0.623898 + 6.67703i 0.0223391 + 0.239076i
\(781\) 21.4540i 0.767684i
\(782\) 0.319178 + 0.368996i 0.0114138 + 0.0131953i
\(783\) 9.80417i 0.350372i
\(784\) −20.5479 + 3.87379i −0.733852 + 0.138350i
\(785\) −0.789022 −0.0281614
\(786\) 20.4584 22.4592i 0.729727 0.801092i
\(787\) 48.0736 1.71364 0.856819 0.515617i \(-0.172437\pi\)
0.856819 + 0.515617i \(0.172437\pi\)
\(788\) 4.46338 + 47.7675i 0.159001 + 1.70165i
\(789\) 3.46611i 0.123397i
\(790\) −4.39721 4.00549i −0.156446 0.142509i
\(791\) 31.3925i 1.11619i
\(792\) −3.08650 2.32523i −0.109674 0.0826233i
\(793\) 21.4079i 0.760218i
\(794\) −16.3654 + 17.9658i −0.580785 + 0.637583i
\(795\) 10.9669i 0.388956i
\(796\) 3.13148 + 33.5134i 0.110992 + 1.18785i
\(797\) 47.3644i 1.67773i 0.544338 + 0.838866i \(0.316781\pi\)
−0.544338 + 0.838866i \(0.683219\pi\)
\(798\) 18.4543 + 16.8103i 0.653274 + 0.595078i
\(799\) 0.913021 0.0323004
\(800\) −2.96870 + 4.81527i −0.104959 + 0.170246i
\(801\) 11.5228i 0.407137i
\(802\) 22.5480 + 20.5394i 0.796199 + 0.725271i
\(803\) 7.16998 0.253023
\(804\) −30.3948 + 2.84008i −1.07194 + 0.100162i
\(805\) −1.98841 + 16.6517i −0.0700822 + 0.586894i
\(806\) 28.2963 + 25.7756i 0.996695 + 0.907906i
\(807\) 0.230066i 0.00809871i
\(808\) 24.3742 + 18.3624i 0.857483 + 0.645989i
\(809\) 32.6507 1.14794 0.573970 0.818877i \(-0.305403\pi\)
0.573970 + 0.818877i \(0.305403\pi\)
\(810\) −1.04548 0.952347i −0.0367345 0.0334621i
\(811\) 32.8029i 1.15187i 0.817497 + 0.575934i \(0.195361\pi\)
−0.817497 + 0.575934i \(0.804639\pi\)
\(812\) −6.37899 68.2686i −0.223859 2.39576i
\(813\) 6.04603 0.212044
\(814\) 4.75120 + 4.32794i 0.166529 + 0.151694i
\(815\) −10.0679 −0.352662
\(816\) −0.282758 + 0.0533070i −0.00989852 + 0.00186612i
\(817\) −44.9821 −1.57372
\(818\) −19.5305 + 21.4405i −0.682867 + 0.749648i
\(819\) −11.7249 −0.409701
\(820\) 2.74615 0.256599i 0.0958998 0.00896084i
\(821\) −12.6775 −0.442446 −0.221223 0.975223i \(-0.571005\pi\)
−0.221223 + 0.975223i \(0.571005\pi\)
\(822\) 8.41106 9.23363i 0.293369 0.322060i
\(823\) 34.7717i 1.21207i −0.795439 0.606033i \(-0.792760\pi\)
0.795439 0.606033i \(-0.207240\pi\)
\(824\) 19.6961 + 14.8381i 0.686146 + 0.516911i
\(825\) 1.36625i 0.0475668i
\(826\) −17.2449 15.7087i −0.600027 0.546575i
\(827\) 37.9777 1.32062 0.660308 0.750995i \(-0.270426\pi\)
0.660308 + 0.750995i \(0.270426\pi\)
\(828\) −0.246289 + 9.58850i −0.00855913 + 0.333223i
\(829\) 17.5863 0.610796 0.305398 0.952225i \(-0.401210\pi\)
0.305398 + 0.952225i \(0.401210\pi\)
\(830\) 14.1052 + 12.8487i 0.489599 + 0.445984i
\(831\) 14.3524i 0.497881i
\(832\) 7.40038 + 25.7834i 0.256562 + 0.893880i
\(833\) 0.376036i 0.0130289i
\(834\) −1.40866 + 1.54642i −0.0487778 + 0.0535480i
\(835\) 12.3125 0.426091
\(836\) 1.28326 + 13.7336i 0.0443825 + 0.474987i
\(837\) −8.07183 −0.279003
\(838\) 6.17488 6.77875i 0.213308 0.234168i
\(839\) −22.3742 −0.772444 −0.386222 0.922406i \(-0.626220\pi\)
−0.386222 + 0.922406i \(0.626220\pi\)
\(840\) −7.89957 5.95118i −0.272561 0.205335i
\(841\) 67.1217 2.31454
\(842\) 17.2545 + 15.7174i 0.594631 + 0.541659i
\(843\) 9.58403 0.330092
\(844\) −41.1786 + 3.84771i −1.41743 + 0.132444i
\(845\) 1.75702i 0.0604432i
\(846\) 13.2696 + 12.0875i 0.456219 + 0.415578i
\(847\) −31.9373 −1.09738
\(848\) 8.12699 + 43.1083i 0.279082 + 1.48034i
\(849\) 29.7360i 1.02054i
\(850\) −0.0752066 0.0685069i −0.00257957 0.00234977i
\(851\) 1.89144 15.8396i 0.0648378 0.542975i
\(852\) 2.92180 + 31.2694i 0.100099 + 1.07127i
\(853\) −42.0149 −1.43856 −0.719281 0.694719i \(-0.755529\pi\)
−0.719281 + 0.694719i \(0.755529\pi\)
\(854\) 23.3410 + 21.2617i 0.798712 + 0.727560i
\(855\) 5.04791i 0.172635i
\(856\) −34.8436 26.2496i −1.19093 0.897191i
\(857\) 6.03951 0.206306 0.103153 0.994666i \(-0.467107\pi\)
0.103153 + 0.994666i \(0.467107\pi\)
\(858\) −4.78948 4.36282i −0.163510 0.148944i
\(859\) 27.5246i 0.939128i 0.882899 + 0.469564i \(0.155589\pi\)
−0.882899 + 0.469564i \(0.844411\pi\)
\(860\) 17.7448 1.65806i 0.605091 0.0565394i
\(861\) 4.82226i 0.164342i
\(862\) −29.9736 + 32.9048i −1.02090 + 1.12074i
\(863\) 16.4378i 0.559551i −0.960066 0.279775i \(-0.909740\pi\)
0.960066 0.279775i \(-0.0902600\pi\)
\(864\) −4.81527 2.96870i −0.163819 0.100997i
\(865\) 3.04079i 0.103390i
\(866\) 19.5957 + 17.8500i 0.665889 + 0.606569i
\(867\) 16.9948i 0.577175i
\(868\) −56.2060 + 5.25186i −1.90776 + 0.178260i
\(869\) 5.74633 0.194931
\(870\) 9.33697 10.2501i 0.316553 0.347511i
\(871\) −51.1798 −1.73416
\(872\) −3.67902 + 4.88352i −0.124587 + 0.165377i
\(873\) 4.72490i 0.159914i
\(874\) 25.8937 22.3978i 0.875867 0.757618i
\(875\) 3.49678i 0.118213i
\(876\) 10.4503 0.976473i 0.353083 0.0329920i
\(877\) −22.5117 −0.760165 −0.380083 0.924953i \(-0.624104\pi\)
−0.380083 + 0.924953i \(0.624104\pi\)
\(878\) 9.80196 + 8.92877i 0.330800 + 0.301331i
\(879\) 19.4305 0.655376
\(880\) −1.01246 5.37040i −0.0341299 0.181036i
\(881\) 16.5757i 0.558448i −0.960226 0.279224i \(-0.909923\pi\)
0.960226 0.279224i \(-0.0900772\pi\)
\(882\) 4.97835 5.46522i 0.167630 0.184023i
\(883\) 23.5714i 0.793239i −0.917983 0.396620i \(-0.870183\pi\)
0.917983 0.396620i \(-0.129817\pi\)
\(884\) −0.480311 + 0.0448800i −0.0161546 + 0.00150948i
\(885\) 4.71711i 0.158564i
\(886\) 22.5998 + 20.5865i 0.759255 + 0.691618i
\(887\) 31.4813i 1.05704i 0.848921 + 0.528519i \(0.177253\pi\)
−0.848921 + 0.528519i \(0.822747\pi\)
\(888\) 7.51434 + 5.66096i 0.252165 + 0.189969i
\(889\) 44.4689i 1.49144i
\(890\) 10.9737 12.0469i 0.367839 0.403812i
\(891\) 1.36625 0.0457711
\(892\) −19.9656 + 1.86557i −0.668497 + 0.0624640i
\(893\) 64.0698i 2.14402i
\(894\) −12.2999 + 13.5028i −0.411371 + 0.451601i
\(895\) 9.66616 0.323104
\(896\) −35.4614 17.5387i −1.18468 0.585926i
\(897\) −1.90668 + 15.9673i −0.0636622 + 0.533131i
\(898\) 11.2027 12.2983i 0.373839 0.410398i
\(899\) 79.1376i 2.63939i
\(900\) −0.186069 1.99133i −0.00620229 0.0663775i
\(901\) −0.788903 −0.0262822
\(902\) −1.79436 + 1.96984i −0.0597455 + 0.0655883i
\(903\) 31.1599i 1.03694i
\(904\) 15.2789 20.2812i 0.508170 0.674542i
\(905\) −26.0047 −0.864426
\(906\) −1.41730 + 1.55590i −0.0470865 + 0.0516914i
\(907\) −3.62895 −0.120497 −0.0602486 0.998183i \(-0.519189\pi\)
−0.0602486 + 0.998183i \(0.519189\pi\)
\(908\) 1.07290 + 11.4823i 0.0356056 + 0.381054i
\(909\) −10.7894 −0.357861
\(910\) −12.2582 11.1662i −0.406354 0.370155i
\(911\) 37.6483 1.24735 0.623673 0.781686i \(-0.285640\pi\)
0.623673 + 0.781686i \(0.285640\pi\)
\(912\) 3.74074 + 19.8421i 0.123868 + 0.657038i
\(913\) −18.4329 −0.610040
\(914\) 37.0552 + 33.7542i 1.22568 + 1.11649i
\(915\) 6.38461i 0.211069i
\(916\) 4.91086 0.458868i 0.162259 0.0151614i
\(917\) 75.1181i 2.48062i
\(918\) 0.0685069 0.0752066i 0.00226107 0.00248219i
\(919\) 39.4637 1.30179 0.650893 0.759169i \(-0.274395\pi\)
0.650893 + 0.759169i \(0.274395\pi\)
\(920\) −9.38907 + 9.79006i −0.309549 + 0.322769i
\(921\) 24.3915 0.803726
\(922\) 13.5413 14.8656i 0.445960 0.489573i
\(923\) 52.6524i 1.73308i
\(924\) 9.51351 0.888938i 0.312972 0.0292439i
\(925\) 3.32625i 0.109367i
\(926\) −1.41375 1.28781i −0.0464588 0.0423201i
\(927\) −8.71856 −0.286355
\(928\) 29.1056 47.2097i 0.955438 1.54974i
\(929\) −18.7511 −0.615204 −0.307602 0.951515i \(-0.599527\pi\)
−0.307602 + 0.951515i \(0.599527\pi\)
\(930\) −8.43896 7.68719i −0.276724 0.252073i
\(931\) −26.3877 −0.864823
\(932\) −3.19082 34.1485i −0.104519 1.11857i
\(933\) 3.30836 0.108311
\(934\) 19.0222 20.8825i 0.622426 0.683297i
\(935\) 0.0982810 0.00321413
\(936\) −7.57488 5.70657i −0.247593 0.186525i
\(937\) 2.65735i 0.0868117i −0.999058 0.0434059i \(-0.986179\pi\)
0.999058 0.0434059i \(-0.0138209\pi\)
\(938\) 50.8301 55.8010i 1.65966 1.82197i
\(939\) −16.4380 −0.536434
\(940\) 2.36165 + 25.2746i 0.0770284 + 0.824366i
\(941\) 53.1284i 1.73194i −0.500100 0.865968i \(-0.666704\pi\)
0.500100 0.865968i \(-0.333296\pi\)
\(942\) 0.751424 0.824909i 0.0244827 0.0268770i
\(943\) 6.56707 + 0.784187i 0.213853 + 0.0255367i
\(944\) −3.49560 18.5418i −0.113772 0.603485i
\(945\) 3.49678 0.113750
\(946\) −11.5945 + 12.7284i −0.376971 + 0.413837i
\(947\) 22.2269i 0.722278i −0.932512 0.361139i \(-0.882388\pi\)
0.932512 0.361139i \(-0.117612\pi\)
\(948\) 8.37534 0.782588i 0.272018 0.0254173i
\(949\) 17.5966 0.571209
\(950\) −4.80737 + 5.27750i −0.155972 + 0.171225i
\(951\) 21.1799i 0.686806i
\(952\) 0.428097 0.568254i 0.0138747 0.0184172i
\(953\) 26.2415i 0.850046i −0.905183 0.425023i \(-0.860266\pi\)
0.905183 0.425023i \(-0.139734\pi\)
\(954\) −11.4657 10.4443i −0.371216 0.338147i
\(955\) 1.45243i 0.0469994i
\(956\) 15.6941 1.46645i 0.507585 0.0474285i
\(957\) 13.3950i 0.432997i
\(958\) 26.6493 29.2555i 0.860999 0.945201i
\(959\) 30.8833i 0.997273i
\(960\) −2.20705 7.68953i −0.0712324 0.248179i
\(961\) −34.1545 −1.10176
\(962\) 11.6604 + 10.6216i 0.375946 + 0.342456i
\(963\) 15.4237 0.497020
\(964\) 26.5092 2.47701i 0.853804 0.0797791i
\(965\) 12.6263i 0.406455i
\(966\) −15.5154 17.9370i −0.499199 0.577114i
\(967\) 7.54606i 0.242665i −0.992612 0.121333i \(-0.961283\pi\)
0.992612 0.121333i \(-0.0387167\pi\)
\(968\) −20.6332 15.5441i −0.663175 0.499606i
\(969\) −0.363121 −0.0116651
\(970\) −4.49975 + 4.93981i −0.144478 + 0.158608i
\(971\) 11.9488 0.383456 0.191728 0.981448i \(-0.438591\pi\)
0.191728 + 0.981448i \(0.438591\pi\)
\(972\) 1.99133 0.186069i 0.0638718 0.00596815i
\(973\) 5.17223i 0.165814i
\(974\) −31.5453 28.7351i −1.01078 0.920732i
\(975\) 3.35306i 0.107384i
\(976\) 4.73129 + 25.0963i 0.151445 + 0.803314i
\(977\) 19.3143i 0.617919i −0.951075 0.308960i \(-0.900019\pi\)
0.951075 0.308960i \(-0.0999808\pi\)
\(978\) 9.58810 10.5258i 0.306594 0.336577i
\(979\) 15.7430i 0.503149i
\(980\) 10.4096 0.972665i 0.332521 0.0310707i
\(981\) 2.16171i 0.0690181i
\(982\) −7.40479 6.74514i −0.236296 0.215246i
\(983\) 5.59462 0.178441 0.0892204 0.996012i \(-0.471562\pi\)
0.0892204 + 0.996012i \(0.471562\pi\)
\(984\) −2.34702 + 3.11543i −0.0748203 + 0.0993162i
\(985\) 23.9878i 0.764315i
\(986\) 0.737338 + 0.671653i 0.0234816 + 0.0213898i
\(987\) −44.3823 −1.41270
\(988\) 3.14938 + 33.7050i 0.100195 + 1.07230i
\(989\) 42.4343 + 5.06717i 1.34933 + 0.161126i
\(990\) 1.42839 + 1.30115i 0.0453973 + 0.0413531i
\(991\) 46.6872i 1.48307i −0.670916 0.741533i \(-0.734099\pi\)
0.670916 0.741533i \(-0.265901\pi\)
\(992\) −38.8681 23.9628i −1.23406 0.760820i
\(993\) −7.56275 −0.239997
\(994\) −57.4067 52.2927i −1.82083 1.65862i
\(995\) 16.8297i 0.533537i
\(996\) −26.8661 + 2.51036i −0.851286 + 0.0795438i
\(997\) −2.45370 −0.0777095 −0.0388547 0.999245i \(-0.512371\pi\)
−0.0388547 + 0.999245i \(0.512371\pi\)
\(998\) −18.0344 16.4278i −0.570868 0.520013i
\(999\) −3.32625 −0.105238
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 1380.2.p.a.91.16 yes 48
4.3 odd 2 1380.2.p.b.91.15 yes 48
23.22 odd 2 1380.2.p.b.91.16 yes 48
92.91 even 2 inner 1380.2.p.a.91.15 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1380.2.p.a.91.15 48 92.91 even 2 inner
1380.2.p.a.91.16 yes 48 1.1 even 1 trivial
1380.2.p.b.91.15 yes 48 4.3 odd 2
1380.2.p.b.91.16 yes 48 23.22 odd 2