Properties

Label 273.2.cg.a.124.7
Level $273$
Weight $2$
Character 273.124
Analytic conductor $2.180$
Analytic rank $0$
Dimension $36$
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] = [273,2,Mod(19,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 10, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.cg (of order \(12\), degree \(4\), 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: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(9\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 124.7
Character \(\chi\) \(=\) 273.124
Dual form 273.2.cg.a.262.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.255728 - 0.954388i) q^{2} +1.00000i q^{3} +(0.886590 + 0.511873i) q^{4} +(-0.244406 - 0.912136i) q^{5} +(0.954388 + 0.255728i) q^{6} +(2.46785 + 0.953787i) q^{7} +(2.11257 - 2.11257i) q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(0.255728 - 0.954388i) q^{2} +1.00000i q^{3} +(0.886590 + 0.511873i) q^{4} +(-0.244406 - 0.912136i) q^{5} +(0.954388 + 0.255728i) q^{6} +(2.46785 + 0.953787i) q^{7} +(2.11257 - 2.11257i) q^{8} -1.00000 q^{9} -0.933034 q^{10} +(-4.64956 + 4.64956i) q^{11} +(-0.511873 + 0.886590i) q^{12} +(3.43957 - 1.08136i) q^{13} +(1.54138 - 2.11138i) q^{14} +(0.912136 - 0.244406i) q^{15} +(-0.452226 - 0.783279i) q^{16} +(1.86677 - 3.23334i) q^{17} +(-0.255728 + 0.954388i) q^{18} +(0.889632 - 0.889632i) q^{19} +(0.250210 - 0.933796i) q^{20} +(-0.953787 + 2.46785i) q^{21} +(3.24847 + 5.62651i) q^{22} +(0.202140 - 0.116706i) q^{23} +(2.11257 + 2.11257i) q^{24} +(3.55787 - 2.05414i) q^{25} +(-0.152440 - 3.55922i) q^{26} -1.00000i q^{27} +(1.69975 + 2.10884i) q^{28} +(-2.32457 + 4.02628i) q^{29} -0.933034i q^{30} +(-7.35090 - 1.96967i) q^{31} +(4.90846 - 1.31522i) q^{32} +(-4.64956 - 4.64956i) q^{33} +(-2.60848 - 2.60848i) q^{34} +(0.266825 - 2.48413i) q^{35} +(-0.886590 - 0.511873i) q^{36} +(-4.85874 - 1.30189i) q^{37} +(-0.621551 - 1.07656i) q^{38} +(1.08136 + 3.43957i) q^{39} +(-2.44328 - 1.41063i) q^{40} +(-2.49056 - 9.29490i) q^{41} +(2.11138 + 1.54138i) q^{42} +(-10.4062 + 6.00801i) q^{43} +(-6.50224 + 1.74227i) q^{44} +(0.244406 + 0.912136i) q^{45} +(-0.0596897 - 0.222765i) q^{46} +(-2.10393 + 0.563747i) q^{47} +(0.783279 - 0.452226i) q^{48} +(5.18058 + 4.70761i) q^{49} +(-1.05060 - 3.92089i) q^{50} +(3.23334 + 1.86677i) q^{51} +(3.60301 + 0.801905i) q^{52} +(2.04084 + 3.53484i) q^{53} +(-0.954388 - 0.255728i) q^{54} +(5.37742 + 3.10465i) q^{55} +(7.22846 - 3.19857i) q^{56} +(0.889632 + 0.889632i) q^{57} +(3.24817 + 3.24817i) q^{58} +(-7.20872 + 1.93157i) q^{59} +(0.933796 + 0.250210i) q^{60} -2.45527i q^{61} +(-3.75966 + 6.51191i) q^{62} +(-2.46785 - 0.953787i) q^{63} -6.82982i q^{64} +(-1.82700 - 2.87307i) q^{65} +(-5.62651 + 3.24847i) q^{66} +(-7.19137 - 7.19137i) q^{67} +(3.31012 - 1.91110i) q^{68} +(0.116706 + 0.202140i) q^{69} +(-2.30259 - 0.889915i) q^{70} +(0.433350 - 1.61728i) q^{71} +(-2.11257 + 2.11257i) q^{72} +(-2.10388 + 7.85180i) q^{73} +(-2.48503 + 4.30419i) q^{74} +(2.05414 + 3.55787i) q^{75} +(1.24412 - 0.333360i) q^{76} +(-15.9091 + 7.03974i) q^{77} +(3.55922 - 0.152440i) q^{78} +(-0.942160 + 1.63187i) q^{79} +(-0.603930 + 0.603930i) q^{80} +1.00000 q^{81} -9.50785 q^{82} +(9.95023 - 9.95023i) q^{83} +(-2.10884 + 1.69975i) q^{84} +(-3.40550 - 0.912500i) q^{85} +(3.07283 + 11.4680i) q^{86} +(-4.02628 - 2.32457i) q^{87} +19.6451i q^{88} +(1.05604 - 3.94121i) q^{89} +0.933034 q^{90} +(9.51974 + 0.611992i) q^{91} +0.238954 q^{92} +(1.96967 - 7.35090i) q^{93} +2.15213i q^{94} +(-1.02890 - 0.594034i) q^{95} +(1.31522 + 4.90846i) q^{96} +(-2.41702 - 0.647638i) q^{97} +(5.81770 - 3.74042i) q^{98} +(4.64956 - 4.64956i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 4 q^{7} - 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 4 q^{7} - 36 q^{9} + 4 q^{11} + 16 q^{12} + 42 q^{14} + 12 q^{16} - 4 q^{17} - 24 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} - 24 q^{25} - 28 q^{26} - 12 q^{28} + 8 q^{29} - 6 q^{31} + 46 q^{32} + 4 q^{33} + 24 q^{34} - 10 q^{35} - 20 q^{37} + 8 q^{38} - 2 q^{39} - 30 q^{40} - 34 q^{41} + 24 q^{42} + 30 q^{43} - 32 q^{44} - 26 q^{46} + 4 q^{47} - 24 q^{48} - 20 q^{50} + 24 q^{51} + 98 q^{52} - 8 q^{53} + 30 q^{55} - 10 q^{56} - 24 q^{57} - 96 q^{58} - 14 q^{59} - 46 q^{60} + 48 q^{62} - 4 q^{63} + 28 q^{65} + 18 q^{66} + 62 q^{67} - 54 q^{68} - 4 q^{69} - 148 q^{70} + 42 q^{71} - 52 q^{73} - 20 q^{74} - 10 q^{75} - 12 q^{76} - 24 q^{77} - 16 q^{78} + 76 q^{80} + 36 q^{81} + 48 q^{82} + 60 q^{83} + 50 q^{84} + 2 q^{85} + 12 q^{86} + 18 q^{87} + 50 q^{89} + 40 q^{91} - 100 q^{92} - 6 q^{93} + 24 q^{95} - 4 q^{96} - 36 q^{97} + 16 q^{98} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.255728 0.954388i 0.180827 0.674855i −0.814659 0.579941i \(-0.803076\pi\)
0.995485 0.0949139i \(-0.0302576\pi\)
\(3\) 1.00000i 0.577350i
\(4\) 0.886590 + 0.511873i 0.443295 + 0.255936i
\(5\) −0.244406 0.912136i −0.109302 0.407920i 0.889496 0.456943i \(-0.151056\pi\)
−0.998798 + 0.0490235i \(0.984389\pi\)
\(6\) 0.954388 + 0.255728i 0.389627 + 0.104400i
\(7\) 2.46785 + 0.953787i 0.932760 + 0.360497i
\(8\) 2.11257 2.11257i 0.746907 0.746907i
\(9\) −1.00000 −0.333333
\(10\) −0.933034 −0.295051
\(11\) −4.64956 + 4.64956i −1.40190 + 1.40190i −0.607824 + 0.794071i \(0.707958\pi\)
−0.794071 + 0.607824i \(0.792042\pi\)
\(12\) −0.511873 + 0.886590i −0.147765 + 0.255936i
\(13\) 3.43957 1.08136i 0.953966 0.299914i
\(14\) 1.54138 2.11138i 0.411951 0.564290i
\(15\) 0.912136 0.244406i 0.235513 0.0631054i
\(16\) −0.452226 0.783279i −0.113057 0.195820i
\(17\) 1.86677 3.23334i 0.452758 0.784200i −0.545798 0.837917i \(-0.683773\pi\)
0.998556 + 0.0537166i \(0.0171068\pi\)
\(18\) −0.255728 + 0.954388i −0.0602756 + 0.224952i
\(19\) 0.889632 0.889632i 0.204095 0.204095i −0.597657 0.801752i \(-0.703901\pi\)
0.801752 + 0.597657i \(0.203901\pi\)
\(20\) 0.250210 0.933796i 0.0559486 0.208803i
\(21\) −0.953787 + 2.46785i −0.208133 + 0.538529i
\(22\) 3.24847 + 5.62651i 0.692576 + 1.19958i
\(23\) 0.202140 0.116706i 0.0421491 0.0243348i −0.478777 0.877936i \(-0.658920\pi\)
0.520927 + 0.853602i \(0.325587\pi\)
\(24\) 2.11257 + 2.11257i 0.431227 + 0.431227i
\(25\) 3.55787 2.05414i 0.711574 0.410827i
\(26\) −0.152440 3.55922i −0.0298960 0.698021i
\(27\) 1.00000i 0.192450i
\(28\) 1.69975 + 2.10884i 0.321223 + 0.398534i
\(29\) −2.32457 + 4.02628i −0.431662 + 0.747661i −0.997017 0.0771873i \(-0.975406\pi\)
0.565354 + 0.824848i \(0.308739\pi\)
\(30\) 0.933034i 0.170348i
\(31\) −7.35090 1.96967i −1.32026 0.353763i −0.471185 0.882034i \(-0.656174\pi\)
−0.849075 + 0.528272i \(0.822840\pi\)
\(32\) 4.90846 1.31522i 0.867701 0.232500i
\(33\) −4.64956 4.64956i −0.809385 0.809385i
\(34\) −2.60848 2.60848i −0.447350 0.447350i
\(35\) 0.266825 2.48413i 0.0451017 0.419894i
\(36\) −0.886590 0.511873i −0.147765 0.0853122i
\(37\) −4.85874 1.30189i −0.798771 0.214030i −0.163727 0.986506i \(-0.552352\pi\)
−0.635045 + 0.772476i \(0.719018\pi\)
\(38\) −0.621551 1.07656i −0.100829 0.174641i
\(39\) 1.08136 + 3.43957i 0.173156 + 0.550773i
\(40\) −2.44328 1.41063i −0.386317 0.223040i
\(41\) −2.49056 9.29490i −0.388960 1.45162i −0.831828 0.555033i \(-0.812706\pi\)
0.442868 0.896587i \(-0.353961\pi\)
\(42\) 2.11138 + 1.54138i 0.325793 + 0.237840i
\(43\) −10.4062 + 6.00801i −1.58693 + 0.916213i −0.593119 + 0.805115i \(0.702104\pi\)
−0.993809 + 0.111099i \(0.964563\pi\)
\(44\) −6.50224 + 1.74227i −0.980250 + 0.262657i
\(45\) 0.244406 + 0.912136i 0.0364339 + 0.135973i
\(46\) −0.0596897 0.222765i −0.00880077 0.0328449i
\(47\) −2.10393 + 0.563747i −0.306890 + 0.0822309i −0.408977 0.912545i \(-0.634115\pi\)
0.102087 + 0.994775i \(0.467448\pi\)
\(48\) 0.783279 0.452226i 0.113057 0.0652732i
\(49\) 5.18058 + 4.70761i 0.740083 + 0.672515i
\(50\) −1.05060 3.92089i −0.148577 0.554497i
\(51\) 3.23334 + 1.86677i 0.452758 + 0.261400i
\(52\) 3.60301 + 0.801905i 0.499647 + 0.111204i
\(53\) 2.04084 + 3.53484i 0.280331 + 0.485548i 0.971466 0.237178i \(-0.0762224\pi\)
−0.691135 + 0.722726i \(0.742889\pi\)
\(54\) −0.954388 0.255728i −0.129876 0.0348001i
\(55\) 5.37742 + 3.10465i 0.725091 + 0.418631i
\(56\) 7.22846 3.19857i 0.965944 0.427427i
\(57\) 0.889632 + 0.889632i 0.117835 + 0.117835i
\(58\) 3.24817 + 3.24817i 0.426506 + 0.426506i
\(59\) −7.20872 + 1.93157i −0.938495 + 0.251469i −0.695473 0.718552i \(-0.744805\pi\)
−0.243022 + 0.970021i \(0.578139\pi\)
\(60\) 0.933796 + 0.250210i 0.120553 + 0.0323020i
\(61\) 2.45527i 0.314365i −0.987570 0.157183i \(-0.949759\pi\)
0.987570 0.157183i \(-0.0502412\pi\)
\(62\) −3.75966 + 6.51191i −0.477477 + 0.827014i
\(63\) −2.46785 0.953787i −0.310920 0.120166i
\(64\) 6.82982i 0.853727i
\(65\) −1.82700 2.87307i −0.226611 0.356361i
\(66\) −5.62651 + 3.24847i −0.692576 + 0.399859i
\(67\) −7.19137 7.19137i −0.878566 0.878566i 0.114820 0.993386i \(-0.463371\pi\)
−0.993386 + 0.114820i \(0.963371\pi\)
\(68\) 3.31012 1.91110i 0.401411 0.231755i
\(69\) 0.116706 + 0.202140i 0.0140497 + 0.0243348i
\(70\) −2.30259 0.889915i −0.275212 0.106365i
\(71\) 0.433350 1.61728i 0.0514292 0.191936i −0.935432 0.353507i \(-0.884989\pi\)
0.986861 + 0.161570i \(0.0516559\pi\)
\(72\) −2.11257 + 2.11257i −0.248969 + 0.248969i
\(73\) −2.10388 + 7.85180i −0.246241 + 0.918984i 0.726515 + 0.687151i \(0.241139\pi\)
−0.972756 + 0.231833i \(0.925528\pi\)
\(74\) −2.48503 + 4.30419i −0.288878 + 0.500352i
\(75\) 2.05414 + 3.55787i 0.237191 + 0.410827i
\(76\) 1.24412 0.333360i 0.142710 0.0382390i
\(77\) −15.9091 + 7.03974i −1.81301 + 0.802253i
\(78\) 3.55922 0.152440i 0.403003 0.0172605i
\(79\) −0.942160 + 1.63187i −0.106001 + 0.183600i −0.914147 0.405383i \(-0.867138\pi\)
0.808146 + 0.588983i \(0.200471\pi\)
\(80\) −0.603930 + 0.603930i −0.0675214 + 0.0675214i
\(81\) 1.00000 0.111111
\(82\) −9.50785 −1.04997
\(83\) 9.95023 9.95023i 1.09218 1.09218i 0.0968835 0.995296i \(-0.469113\pi\)
0.995296 0.0968835i \(-0.0308874\pi\)
\(84\) −2.10884 + 1.69975i −0.230094 + 0.185458i
\(85\) −3.40550 0.912500i −0.369378 0.0989745i
\(86\) 3.07283 + 11.4680i 0.331352 + 1.23662i
\(87\) −4.02628 2.32457i −0.431662 0.249220i
\(88\) 19.6451i 2.09417i
\(89\) 1.05604 3.94121i 0.111940 0.417767i −0.887099 0.461578i \(-0.847283\pi\)
0.999040 + 0.0438111i \(0.0139500\pi\)
\(90\) 0.933034 0.0983504
\(91\) 9.51974 + 0.611992i 0.997940 + 0.0641542i
\(92\) 0.238954 0.0249127
\(93\) 1.96967 7.35090i 0.204245 0.762253i
\(94\) 2.15213i 0.221976i
\(95\) −1.02890 0.594034i −0.105563 0.0609466i
\(96\) 1.31522 + 4.90846i 0.134234 + 0.500967i
\(97\) −2.41702 0.647638i −0.245411 0.0657576i 0.134017 0.990979i \(-0.457212\pi\)
−0.379428 + 0.925221i \(0.623879\pi\)
\(98\) 5.81770 3.74042i 0.587677 0.377840i
\(99\) 4.64956 4.64956i 0.467299 0.467299i
\(100\) 4.20583 0.420583
\(101\) 2.40441 0.239248 0.119624 0.992819i \(-0.461831\pi\)
0.119624 + 0.992819i \(0.461831\pi\)
\(102\) 2.60848 2.60848i 0.258278 0.258278i
\(103\) −1.45067 + 2.51263i −0.142938 + 0.247577i −0.928602 0.371077i \(-0.878988\pi\)
0.785663 + 0.618654i \(0.212322\pi\)
\(104\) 4.98191 9.55080i 0.488516 0.936533i
\(105\) 2.48413 + 0.266825i 0.242426 + 0.0260395i
\(106\) 3.89551 1.04380i 0.378366 0.101383i
\(107\) 5.54205 + 9.59911i 0.535770 + 0.927981i 0.999126 + 0.0418082i \(0.0133119\pi\)
−0.463356 + 0.886172i \(0.653355\pi\)
\(108\) 0.511873 0.886590i 0.0492550 0.0853122i
\(109\) −1.87996 + 7.01612i −0.180068 + 0.672023i 0.815565 + 0.578666i \(0.196426\pi\)
−0.995633 + 0.0933569i \(0.970240\pi\)
\(110\) 4.33820 4.33820i 0.413631 0.413631i
\(111\) 1.30189 4.85874i 0.123570 0.461171i
\(112\) −0.368946 2.36434i −0.0348621 0.223409i
\(113\) −0.604359 1.04678i −0.0568533 0.0984728i 0.836198 0.548428i \(-0.184773\pi\)
−0.893051 + 0.449955i \(0.851440\pi\)
\(114\) 1.07656 0.621551i 0.100829 0.0582136i
\(115\) −0.155856 0.155856i −0.0145336 0.0145336i
\(116\) −4.12188 + 2.37977i −0.382707 + 0.220956i
\(117\) −3.43957 + 1.08136i −0.317989 + 0.0999715i
\(118\) 7.37387i 0.678820i
\(119\) 7.69083 6.19890i 0.705017 0.568253i
\(120\) 1.41063 2.44328i 0.128772 0.223040i
\(121\) 32.2369i 2.93062i
\(122\) −2.34328 0.627881i −0.212151 0.0568457i
\(123\) 9.29490 2.49056i 0.838093 0.224566i
\(124\) −5.50901 5.50901i −0.494724 0.494724i
\(125\) −6.08187 6.08187i −0.543979 0.543979i
\(126\) −1.54138 + 2.11138i −0.137317 + 0.188097i
\(127\) −8.44594 4.87627i −0.749456 0.432699i 0.0760413 0.997105i \(-0.475772\pi\)
−0.825497 + 0.564406i \(0.809105\pi\)
\(128\) 3.29862 + 0.883862i 0.291559 + 0.0781231i
\(129\) −6.00801 10.4062i −0.528976 0.916213i
\(130\) −3.20924 + 1.00894i −0.281469 + 0.0884901i
\(131\) 14.7264 + 8.50232i 1.28666 + 0.742851i 0.978056 0.208341i \(-0.0668065\pi\)
0.308599 + 0.951192i \(0.400140\pi\)
\(132\) −1.74227 6.50224i −0.151645 0.565947i
\(133\) 3.04400 1.34696i 0.263948 0.116796i
\(134\) −8.70239 + 5.02433i −0.751772 + 0.434036i
\(135\) −0.912136 + 0.244406i −0.0785042 + 0.0210351i
\(136\) −2.88698 10.7744i −0.247556 0.923893i
\(137\) −1.24138 4.63290i −0.106058 0.395816i 0.892405 0.451236i \(-0.149017\pi\)
−0.998463 + 0.0554205i \(0.982350\pi\)
\(138\) 0.222765 0.0596897i 0.0189630 0.00508113i
\(139\) 6.97771 4.02859i 0.591842 0.341700i −0.173984 0.984749i \(-0.555664\pi\)
0.765826 + 0.643048i \(0.222331\pi\)
\(140\) 1.50812 2.06582i 0.127460 0.174594i
\(141\) −0.563747 2.10393i −0.0474760 0.177183i
\(142\) −1.43270 0.827168i −0.120229 0.0694144i
\(143\) −10.9647 + 21.0203i −0.916912 + 1.75781i
\(144\) 0.452226 + 0.783279i 0.0376855 + 0.0652732i
\(145\) 4.24065 + 1.13628i 0.352167 + 0.0943629i
\(146\) 6.95565 + 4.01584i 0.575653 + 0.332354i
\(147\) −4.70761 + 5.18058i −0.388277 + 0.427287i
\(148\) −3.64130 3.64130i −0.299313 0.299313i
\(149\) 10.8793 + 10.8793i 0.891265 + 0.891265i 0.994642 0.103378i \(-0.0329650\pi\)
−0.103378 + 0.994642i \(0.532965\pi\)
\(150\) 3.92089 1.05060i 0.320139 0.0857810i
\(151\) 23.6057 + 6.32512i 1.92100 + 0.514731i 0.987892 + 0.155142i \(0.0495836\pi\)
0.933111 + 0.359589i \(0.117083\pi\)
\(152\) 3.75882i 0.304881i
\(153\) −1.86677 + 3.23334i −0.150919 + 0.261400i
\(154\) 2.65024 + 16.9837i 0.213563 + 1.36859i
\(155\) 7.18642i 0.577227i
\(156\) −0.801905 + 3.60301i −0.0642038 + 0.288472i
\(157\) 8.18219 4.72399i 0.653010 0.377015i −0.136599 0.990626i \(-0.543617\pi\)
0.789608 + 0.613611i \(0.210284\pi\)
\(158\) 1.31650 + 1.31650i 0.104735 + 0.104735i
\(159\) −3.53484 + 2.04084i −0.280331 + 0.161849i
\(160\) −2.39932 4.15574i −0.189683 0.328540i
\(161\) 0.610164 0.0952137i 0.0480877 0.00750389i
\(162\) 0.255728 0.954388i 0.0200919 0.0749838i
\(163\) 13.3170 13.3170i 1.04306 1.04306i 0.0440343 0.999030i \(-0.485979\pi\)
0.999030 0.0440343i \(-0.0140211\pi\)
\(164\) 2.54970 9.51562i 0.199098 0.743045i
\(165\) −3.10465 + 5.37742i −0.241697 + 0.418631i
\(166\) −6.95183 12.0409i −0.539567 0.934557i
\(167\) −22.1608 + 5.93797i −1.71486 + 0.459494i −0.976606 0.215034i \(-0.931014\pi\)
−0.738249 + 0.674528i \(0.764347\pi\)
\(168\) 3.19857 + 7.22846i 0.246775 + 0.557688i
\(169\) 10.6613 7.43881i 0.820103 0.572216i
\(170\) −1.74176 + 3.01682i −0.133587 + 0.231379i
\(171\) −0.889632 + 0.889632i −0.0680318 + 0.0680318i
\(172\) −12.3014 −0.937970
\(173\) 8.58805 0.652937 0.326469 0.945208i \(-0.394141\pi\)
0.326469 + 0.945208i \(0.394141\pi\)
\(174\) −3.24817 + 3.24817i −0.246243 + 0.246243i
\(175\) 10.7395 1.67586i 0.811830 0.126683i
\(176\) 5.74456 + 1.53925i 0.433012 + 0.116025i
\(177\) −1.93157 7.20872i −0.145186 0.541840i
\(178\) −3.49138 2.01575i −0.261690 0.151087i
\(179\) 13.6367i 1.01926i 0.860394 + 0.509629i \(0.170217\pi\)
−0.860394 + 0.509629i \(0.829783\pi\)
\(180\) −0.250210 + 0.933796i −0.0186495 + 0.0696010i
\(181\) −11.2556 −0.836622 −0.418311 0.908304i \(-0.637378\pi\)
−0.418311 + 0.908304i \(0.637378\pi\)
\(182\) 3.01854 8.92903i 0.223749 0.661864i
\(183\) 2.45527 0.181499
\(184\) 0.180487 0.673585i 0.0133057 0.0496574i
\(185\) 4.75002i 0.349229i
\(186\) −6.51191 3.75966i −0.477477 0.275671i
\(187\) 6.35395 + 23.7133i 0.464647 + 1.73409i
\(188\) −2.15389 0.577134i −0.157089 0.0420918i
\(189\) 0.953787 2.46785i 0.0693778 0.179510i
\(190\) −0.830056 + 0.830056i −0.0602186 + 0.0602186i
\(191\) 11.3967 0.824637 0.412319 0.911040i \(-0.364719\pi\)
0.412319 + 0.911040i \(0.364719\pi\)
\(192\) 6.82982 0.492900
\(193\) −1.75587 + 1.75587i −0.126390 + 0.126390i −0.767472 0.641082i \(-0.778486\pi\)
0.641082 + 0.767472i \(0.278486\pi\)
\(194\) −1.23620 + 2.14115i −0.0887537 + 0.153726i
\(195\) 2.87307 1.82700i 0.205745 0.130834i
\(196\) 2.18336 + 6.82552i 0.155954 + 0.487537i
\(197\) −14.0826 + 3.77342i −1.00334 + 0.268845i −0.722846 0.691009i \(-0.757166\pi\)
−0.280498 + 0.959854i \(0.590500\pi\)
\(198\) −3.24847 5.62651i −0.230859 0.399859i
\(199\) 2.61480 4.52897i 0.185358 0.321050i −0.758339 0.651860i \(-0.773989\pi\)
0.943697 + 0.330811i \(0.107322\pi\)
\(200\) 3.17674 11.8558i 0.224630 0.838330i
\(201\) 7.19137 7.19137i 0.507240 0.507240i
\(202\) 0.614874 2.29474i 0.0432624 0.161457i
\(203\) −9.57691 + 7.71911i −0.672167 + 0.541775i
\(204\) 1.91110 + 3.31012i 0.133804 + 0.231755i
\(205\) −7.86951 + 4.54346i −0.549630 + 0.317329i
\(206\) 2.02705 + 2.02705i 0.141231 + 0.141231i
\(207\) −0.202140 + 0.116706i −0.0140497 + 0.00811161i
\(208\) −2.40247 2.20513i −0.166581 0.152898i
\(209\) 8.27280i 0.572241i
\(210\) 0.889915 2.30259i 0.0614100 0.158894i
\(211\) 5.55565 9.62266i 0.382466 0.662451i −0.608948 0.793210i \(-0.708408\pi\)
0.991414 + 0.130759i \(0.0417414\pi\)
\(212\) 4.17861i 0.286988i
\(213\) 1.61728 + 0.433350i 0.110814 + 0.0296926i
\(214\) 10.5785 2.83451i 0.723133 0.193763i
\(215\) 8.02346 + 8.02346i 0.547196 + 0.547196i
\(216\) −2.11257 2.11257i −0.143742 0.143742i
\(217\) −16.2623 11.8720i −1.10396 0.805926i
\(218\) 6.21535 + 3.58843i 0.420956 + 0.243039i
\(219\) −7.85180 2.10388i −0.530576 0.142167i
\(220\) 3.17838 + 5.50511i 0.214286 + 0.371154i
\(221\) 2.92450 13.1400i 0.196723 0.883889i
\(222\) −4.30419 2.48503i −0.288878 0.166784i
\(223\) 7.12168 + 26.5785i 0.476903 + 1.77983i 0.614040 + 0.789275i \(0.289543\pi\)
−0.137137 + 0.990552i \(0.543790\pi\)
\(224\) 13.3678 + 1.43586i 0.893173 + 0.0959374i
\(225\) −3.55787 + 2.05414i −0.237191 + 0.136942i
\(226\) −1.15359 + 0.309102i −0.0767354 + 0.0205612i
\(227\) 3.03858 + 11.3401i 0.201677 + 0.752670i 0.990437 + 0.137968i \(0.0440571\pi\)
−0.788759 + 0.614702i \(0.789276\pi\)
\(228\) 0.333360 + 1.24412i 0.0220773 + 0.0823937i
\(229\) −13.5399 + 3.62802i −0.894745 + 0.239746i −0.676758 0.736206i \(-0.736616\pi\)
−0.217987 + 0.975952i \(0.569949\pi\)
\(230\) −0.188604 + 0.108890i −0.0124362 + 0.00718002i
\(231\) −7.03974 15.9091i −0.463181 1.04674i
\(232\) 3.59498 + 13.4166i 0.236022 + 0.880845i
\(233\) 5.26788 + 3.04141i 0.345110 + 0.199249i 0.662529 0.749036i \(-0.269483\pi\)
−0.317419 + 0.948285i \(0.602816\pi\)
\(234\) 0.152440 + 3.55922i 0.00996534 + 0.232674i
\(235\) 1.02843 + 1.78129i 0.0670872 + 0.116199i
\(236\) −7.37989 1.97744i −0.480390 0.128720i
\(237\) −1.63187 0.942160i −0.106001 0.0611999i
\(238\) −3.94940 8.92527i −0.256002 0.578539i
\(239\) −3.72605 3.72605i −0.241018 0.241018i 0.576253 0.817271i \(-0.304514\pi\)
−0.817271 + 0.576253i \(0.804514\pi\)
\(240\) −0.603930 0.603930i −0.0389835 0.0389835i
\(241\) −25.9354 + 6.94938i −1.67065 + 0.447649i −0.965285 0.261197i \(-0.915883\pi\)
−0.705363 + 0.708846i \(0.749216\pi\)
\(242\) −30.7665 8.24386i −1.97775 0.529935i
\(243\) 1.00000i 0.0641500i
\(244\) 1.25679 2.17682i 0.0804576 0.139357i
\(245\) 3.02781 5.87597i 0.193440 0.375402i
\(246\) 9.50785i 0.606198i
\(247\) 2.09794 4.02196i 0.133489 0.255911i
\(248\) −19.6904 + 11.3682i −1.25034 + 0.721884i
\(249\) 9.95023 + 9.95023i 0.630570 + 0.630570i
\(250\) −7.35977 + 4.24916i −0.465473 + 0.268741i
\(251\) 6.48321 + 11.2292i 0.409217 + 0.708784i 0.994802 0.101827i \(-0.0324687\pi\)
−0.585586 + 0.810611i \(0.699135\pi\)
\(252\) −1.69975 2.10884i −0.107074 0.132845i
\(253\) −0.397233 + 1.48249i −0.0249738 + 0.0932036i
\(254\) −6.81371 + 6.81371i −0.427530 + 0.427530i
\(255\) 0.912500 3.40550i 0.0571430 0.213261i
\(256\) 8.51691 14.7517i 0.532307 0.921983i
\(257\) 9.28663 + 16.0849i 0.579284 + 1.00335i 0.995562 + 0.0941119i \(0.0300011\pi\)
−0.416278 + 0.909238i \(0.636666\pi\)
\(258\) −11.4680 + 3.07283i −0.713964 + 0.191306i
\(259\) −10.7489 7.84708i −0.667905 0.487594i
\(260\) −0.149151 3.48243i −0.00924996 0.215971i
\(261\) 2.32457 4.02628i 0.143887 0.249220i
\(262\) 11.8805 11.8805i 0.733978 0.733978i
\(263\) −8.66221 −0.534135 −0.267067 0.963678i \(-0.586055\pi\)
−0.267067 + 0.963678i \(0.586055\pi\)
\(264\) −19.6451 −1.20907
\(265\) 2.72546 2.72546i 0.167424 0.167424i
\(266\) −0.507089 3.24961i −0.0310916 0.199246i
\(267\) 3.94121 + 1.05604i 0.241198 + 0.0646288i
\(268\) −2.69473 10.0569i −0.164607 0.614321i
\(269\) −6.31308 3.64486i −0.384915 0.222231i 0.295039 0.955485i \(-0.404667\pi\)
−0.679955 + 0.733254i \(0.738001\pi\)
\(270\) 0.933034i 0.0567826i
\(271\) 6.08174 22.6974i 0.369440 1.37877i −0.491862 0.870673i \(-0.663683\pi\)
0.861301 0.508094i \(-0.169650\pi\)
\(272\) −3.37681 −0.204749
\(273\) −0.611992 + 9.51974i −0.0370394 + 0.576161i
\(274\) −4.73904 −0.286296
\(275\) −6.99170 + 26.0934i −0.421615 + 1.57349i
\(276\) 0.238954i 0.0143833i
\(277\) −2.12311 1.22578i −0.127565 0.0736499i 0.434859 0.900498i \(-0.356798\pi\)
−0.562425 + 0.826848i \(0.690131\pi\)
\(278\) −2.06044 7.68967i −0.123577 0.461196i
\(279\) 7.35090 + 1.96967i 0.440087 + 0.117921i
\(280\) −4.68422 5.81159i −0.279935 0.347309i
\(281\) −9.26224 + 9.26224i −0.552539 + 0.552539i −0.927173 0.374634i \(-0.877768\pi\)
0.374634 + 0.927173i \(0.377768\pi\)
\(282\) −2.15213 −0.128158
\(283\) 0.575760 0.0342254 0.0171127 0.999854i \(-0.494553\pi\)
0.0171127 + 0.999854i \(0.494553\pi\)
\(284\) 1.21205 1.21205i 0.0719218 0.0719218i
\(285\) 0.594034 1.02890i 0.0351875 0.0609466i
\(286\) 17.2576 + 15.8400i 1.02046 + 0.936642i
\(287\) 2.71902 25.3139i 0.160498 1.49423i
\(288\) −4.90846 + 1.31522i −0.289234 + 0.0774999i
\(289\) 1.53034 + 2.65063i 0.0900201 + 0.155919i
\(290\) 2.16890 3.75665i 0.127362 0.220598i
\(291\) 0.647638 2.41702i 0.0379652 0.141688i
\(292\) −5.88441 + 5.88441i −0.344359 + 0.344359i
\(293\) 4.53613 16.9291i 0.265004 0.989007i −0.697245 0.716833i \(-0.745591\pi\)
0.962248 0.272174i \(-0.0877425\pi\)
\(294\) 3.74042 + 5.81770i 0.218146 + 0.339295i
\(295\) 3.52371 + 6.10324i 0.205158 + 0.355345i
\(296\) −13.0148 + 7.51409i −0.756469 + 0.436748i
\(297\) 4.64956 + 4.64956i 0.269795 + 0.269795i
\(298\) 13.1652 7.60092i 0.762638 0.440310i
\(299\) 0.569076 0.620004i 0.0329105 0.0358557i
\(300\) 4.20583i 0.242824i
\(301\) −31.4113 + 4.90161i −1.81052 + 0.282524i
\(302\) 12.0732 20.9115i 0.694737 1.20332i
\(303\) 2.40441i 0.138130i
\(304\) −1.09914 0.294515i −0.0630402 0.0168916i
\(305\) −2.23954 + 0.600084i −0.128236 + 0.0343607i
\(306\) 2.60848 + 2.60848i 0.149117 + 0.149117i
\(307\) 10.3888 + 10.3888i 0.592923 + 0.592923i 0.938420 0.345497i \(-0.112290\pi\)
−0.345497 + 0.938420i \(0.612290\pi\)
\(308\) −17.7083 1.90209i −1.00903 0.108381i
\(309\) −2.51263 1.45067i −0.142938 0.0825256i
\(310\) 6.85864 + 1.83777i 0.389544 + 0.104378i
\(311\) −6.38744 11.0634i −0.362199 0.627346i 0.626124 0.779724i \(-0.284640\pi\)
−0.988322 + 0.152377i \(0.951307\pi\)
\(312\) 9.55080 + 4.98191i 0.540707 + 0.282045i
\(313\) 12.3070 + 7.10546i 0.695633 + 0.401624i 0.805719 0.592298i \(-0.201779\pi\)
−0.110086 + 0.993922i \(0.535112\pi\)
\(314\) −2.41611 9.01704i −0.136349 0.508861i
\(315\) −0.266825 + 2.48413i −0.0150339 + 0.139965i
\(316\) −1.67062 + 0.964532i −0.0939797 + 0.0542592i
\(317\) 18.0701 4.84186i 1.01492 0.271946i 0.287234 0.957860i \(-0.407264\pi\)
0.727682 + 0.685914i \(0.240598\pi\)
\(318\) 1.04380 + 3.89551i 0.0585333 + 0.218449i
\(319\) −7.91218 29.5287i −0.442997 1.65329i
\(320\) −6.22973 + 1.66925i −0.348252 + 0.0933139i
\(321\) −9.59911 + 5.54205i −0.535770 + 0.309327i
\(322\) 0.0651650 0.606683i 0.00363150 0.0338091i
\(323\) −1.21574 4.53722i −0.0676458 0.252458i
\(324\) 0.886590 + 0.511873i 0.0492550 + 0.0284374i
\(325\) 10.0163 10.9127i 0.555604 0.605326i
\(326\) −9.30403 16.1151i −0.515303 0.892531i
\(327\) −7.01612 1.87996i −0.387992 0.103962i
\(328\) −24.8976 14.3747i −1.37474 0.793708i
\(329\) −5.72989 0.615458i −0.315899 0.0339313i
\(330\) 4.33820 + 4.33820i 0.238810 + 0.238810i
\(331\) −2.79186 2.79186i −0.153454 0.153454i 0.626204 0.779659i \(-0.284608\pi\)
−0.779659 + 0.626204i \(0.784608\pi\)
\(332\) 13.9150 3.72852i 0.763686 0.204629i
\(333\) 4.85874 + 1.30189i 0.266257 + 0.0713434i
\(334\) 22.6685i 1.24037i
\(335\) −4.80190 + 8.31713i −0.262356 + 0.454413i
\(336\) 2.36434 0.368946i 0.128985 0.0201277i
\(337\) 15.1443i 0.824962i 0.910966 + 0.412481i \(0.135338\pi\)
−0.910966 + 0.412481i \(0.864662\pi\)
\(338\) −4.37312 12.0774i −0.237866 0.656922i
\(339\) 1.04678 0.604359i 0.0568533 0.0328243i
\(340\) −2.55220 2.55220i −0.138412 0.138412i
\(341\) 43.3366 25.0204i 2.34681 1.35493i
\(342\) 0.621551 + 1.07656i 0.0336096 + 0.0582136i
\(343\) 8.29486 + 16.5588i 0.447880 + 0.894094i
\(344\) −9.29146 + 34.6762i −0.500962 + 1.86961i
\(345\) 0.155856 0.155856i 0.00839100 0.00839100i
\(346\) 2.19620 8.19633i 0.118069 0.440638i
\(347\) −3.39724 + 5.88420i −0.182374 + 0.315880i −0.942688 0.333675i \(-0.891711\pi\)
0.760315 + 0.649555i \(0.225045\pi\)
\(348\) −2.37977 4.12188i −0.127569 0.220956i
\(349\) −0.378000 + 0.101285i −0.0202339 + 0.00542165i −0.268922 0.963162i \(-0.586667\pi\)
0.248688 + 0.968584i \(0.420001\pi\)
\(350\) 1.14697 10.6782i 0.0613081 0.570775i
\(351\) −1.08136 3.43957i −0.0577185 0.183591i
\(352\) −16.7070 + 28.9374i −0.890486 + 1.54237i
\(353\) 14.1200 14.1200i 0.751534 0.751534i −0.223232 0.974765i \(-0.571661\pi\)
0.974765 + 0.223232i \(0.0716606\pi\)
\(354\) −7.37387 −0.391917
\(355\) −1.58110 −0.0839159
\(356\) 2.95368 2.95368i 0.156545 0.156545i
\(357\) 6.19890 + 7.69083i 0.328081 + 0.407042i
\(358\) 13.0147 + 3.48729i 0.687851 + 0.184309i
\(359\) −7.17397 26.7736i −0.378628 1.41306i −0.847971 0.530042i \(-0.822176\pi\)
0.469344 0.883016i \(-0.344491\pi\)
\(360\) 2.44328 + 1.41063i 0.128772 + 0.0743467i
\(361\) 17.4171i 0.916690i
\(362\) −2.87837 + 10.7422i −0.151284 + 0.564598i
\(363\) 32.2369 1.69200
\(364\) 8.12685 + 5.41548i 0.425962 + 0.283848i
\(365\) 7.67612 0.401786
\(366\) 0.627881 2.34328i 0.0328199 0.122485i
\(367\) 6.67905i 0.348644i 0.984689 + 0.174322i \(0.0557733\pi\)
−0.984689 + 0.174322i \(0.944227\pi\)
\(368\) −0.182826 0.105555i −0.00953047 0.00550242i
\(369\) 2.49056 + 9.29490i 0.129653 + 0.483873i
\(370\) 4.53337 + 1.21471i 0.235678 + 0.0631499i
\(371\) 1.66501 + 10.6700i 0.0864430 + 0.553958i
\(372\) 5.50901 5.50901i 0.285629 0.285629i
\(373\) 1.00610 0.0520939 0.0260469 0.999661i \(-0.491708\pi\)
0.0260469 + 0.999661i \(0.491708\pi\)
\(374\) 24.2566 1.25428
\(375\) 6.08187 6.08187i 0.314066 0.314066i
\(376\) −3.25375 + 5.63567i −0.167800 + 0.290637i
\(377\) −3.64170 + 16.3624i −0.187557 + 0.842705i
\(378\) −2.11138 1.54138i −0.108598 0.0792801i
\(379\) −20.6414 + 5.53086i −1.06028 + 0.284101i −0.746493 0.665393i \(-0.768264\pi\)
−0.313786 + 0.949494i \(0.601597\pi\)
\(380\) −0.608140 1.05333i −0.0311969 0.0540346i
\(381\) 4.87627 8.44594i 0.249819 0.432699i
\(382\) 2.91445 10.8769i 0.149116 0.556510i
\(383\) 16.1566 16.1566i 0.825562 0.825562i −0.161338 0.986899i \(-0.551581\pi\)
0.986899 + 0.161338i \(0.0515808\pi\)
\(384\) −0.883862 + 3.29862i −0.0451044 + 0.168332i
\(385\) 10.3095 + 12.7907i 0.525420 + 0.651876i
\(386\) 1.22676 + 2.12480i 0.0624402 + 0.108150i
\(387\) 10.4062 6.00801i 0.528976 0.305404i
\(388\) −1.81139 1.81139i −0.0919596 0.0919596i
\(389\) −17.3058 + 9.99148i −0.877437 + 0.506588i −0.869812 0.493383i \(-0.835760\pi\)
−0.00762436 + 0.999971i \(0.502427\pi\)
\(390\) −1.00894 3.20924i −0.0510898 0.162506i
\(391\) 0.871451i 0.0440712i
\(392\) 20.8895 0.999194i 1.05508 0.0504669i
\(393\) −8.50232 + 14.7264i −0.428885 + 0.742851i
\(394\) 14.4052i 0.725726i
\(395\) 1.71876 + 0.460539i 0.0864800 + 0.0231723i
\(396\) 6.50224 1.74227i 0.326750 0.0875524i
\(397\) 17.6864 + 17.6864i 0.887654 + 0.887654i 0.994297 0.106643i \(-0.0340103\pi\)
−0.106643 + 0.994297i \(0.534010\pi\)
\(398\) −3.65372 3.65372i −0.183144 0.183144i
\(399\) 1.34696 + 3.04400i 0.0674323 + 0.152390i
\(400\) −3.21792 1.85787i −0.160896 0.0928934i
\(401\) −1.35838 0.363977i −0.0678343 0.0181761i 0.224742 0.974418i \(-0.427846\pi\)
−0.292577 + 0.956242i \(0.594513\pi\)
\(402\) −5.02433 8.70239i −0.250591 0.434036i
\(403\) −27.4139 + 1.17413i −1.36558 + 0.0584874i
\(404\) 2.13173 + 1.23075i 0.106057 + 0.0612322i
\(405\) −0.244406 0.912136i −0.0121446 0.0453244i
\(406\) 4.91795 + 11.1141i 0.244074 + 0.551582i
\(407\) 28.6442 16.5378i 1.41984 0.819746i
\(408\) 10.7744 2.88698i 0.533410 0.142927i
\(409\) −0.717754 2.67870i −0.0354907 0.132453i 0.945907 0.324436i \(-0.105175\pi\)
−0.981398 + 0.191984i \(0.938508\pi\)
\(410\) 2.32378 + 8.67246i 0.114763 + 0.428302i
\(411\) 4.63290 1.24138i 0.228524 0.0612329i
\(412\) −2.57229 + 1.48511i −0.126728 + 0.0731663i
\(413\) −19.6323 2.10875i −0.966044 0.103765i
\(414\) 0.0596897 + 0.222765i 0.00293359 + 0.0109483i
\(415\) −11.5079 6.64407i −0.564899 0.326144i
\(416\) 15.4608 9.83158i 0.758027 0.482033i
\(417\) 4.02859 + 6.97771i 0.197281 + 0.341700i
\(418\) 7.89546 + 2.11558i 0.386180 + 0.103477i
\(419\) −16.7456 9.66807i −0.818075 0.472316i 0.0316770 0.999498i \(-0.489915\pi\)
−0.849752 + 0.527182i \(0.823249\pi\)
\(420\) 2.06582 + 1.50812i 0.100802 + 0.0735889i
\(421\) 2.40433 + 2.40433i 0.117180 + 0.117180i 0.763265 0.646085i \(-0.223595\pi\)
−0.646085 + 0.763265i \(0.723595\pi\)
\(422\) −7.76303 7.76303i −0.377898 0.377898i
\(423\) 2.10393 0.563747i 0.102297 0.0274103i
\(424\) 11.7790 + 3.15618i 0.572041 + 0.153278i
\(425\) 15.3384i 0.744022i
\(426\) 0.827168 1.43270i 0.0400764 0.0694144i
\(427\) 2.34181 6.05925i 0.113328 0.293228i
\(428\) 11.3473i 0.548492i
\(429\) −21.0203 10.9647i −1.01487 0.529380i
\(430\) 9.70932 5.60568i 0.468225 0.270330i
\(431\) −0.490482 0.490482i −0.0236257 0.0236257i 0.695195 0.718821i \(-0.255318\pi\)
−0.718821 + 0.695195i \(0.755318\pi\)
\(432\) −0.783279 + 0.452226i −0.0376855 + 0.0217577i
\(433\) −10.5144 18.2115i −0.505290 0.875188i −0.999981 0.00611893i \(-0.998052\pi\)
0.494691 0.869069i \(-0.335281\pi\)
\(434\) −15.4892 + 12.4845i −0.743508 + 0.599277i
\(435\) −1.13628 + 4.24065i −0.0544804 + 0.203324i
\(436\) −5.25812 + 5.25812i −0.251818 + 0.251818i
\(437\) 0.0760052 0.283655i 0.00363582 0.0135691i
\(438\) −4.01584 + 6.95565i −0.191884 + 0.332354i
\(439\) −11.4119 19.7659i −0.544659 0.943376i −0.998628 0.0523593i \(-0.983326\pi\)
0.453970 0.891017i \(-0.350007\pi\)
\(440\) 17.9190 4.80138i 0.854255 0.228897i
\(441\) −5.18058 4.70761i −0.246694 0.224172i
\(442\) −11.7927 6.15136i −0.560924 0.292590i
\(443\) −8.38733 + 14.5273i −0.398494 + 0.690212i −0.993540 0.113480i \(-0.963800\pi\)
0.595046 + 0.803691i \(0.297134\pi\)
\(444\) 3.64130 3.64130i 0.172809 0.172809i
\(445\) −3.85302 −0.182651
\(446\) 27.1874 1.28736
\(447\) −10.8793 + 10.8793i −0.514572 + 0.514572i
\(448\) 6.51419 16.8550i 0.307766 0.796323i
\(449\) 14.8030 + 3.96646i 0.698599 + 0.187189i 0.590603 0.806962i \(-0.298890\pi\)
0.107996 + 0.994151i \(0.465557\pi\)
\(450\) 1.05060 + 3.92089i 0.0495257 + 0.184832i
\(451\) 54.7972 + 31.6372i 2.58030 + 1.48974i
\(452\) 1.23742i 0.0582033i
\(453\) −6.32512 + 23.6057i −0.297180 + 1.10909i
\(454\) 11.5999 0.544412
\(455\) −1.76846 8.83288i −0.0829069 0.414092i
\(456\) 3.75882 0.176023
\(457\) −3.60447 + 13.4521i −0.168610 + 0.629261i 0.828942 + 0.559334i \(0.188943\pi\)
−0.997552 + 0.0699267i \(0.977723\pi\)
\(458\) 13.8501i 0.647175i
\(459\) −3.23334 1.86677i −0.150919 0.0871333i
\(460\) −0.0584018 0.217959i −0.00272300 0.0101624i
\(461\) −15.2937 4.09793i −0.712298 0.190860i −0.115565 0.993300i \(-0.536868\pi\)
−0.596733 + 0.802440i \(0.703535\pi\)
\(462\) −16.9837 + 2.65024i −0.790155 + 0.123301i
\(463\) 26.2699 26.2699i 1.22086 1.22086i 0.253538 0.967325i \(-0.418406\pi\)
0.967325 0.253538i \(-0.0815943\pi\)
\(464\) 4.20493 0.195209
\(465\) −7.18642 −0.333262
\(466\) 4.24983 4.24983i 0.196869 0.196869i
\(467\) −16.6813 + 28.8928i −0.771917 + 1.33700i 0.164595 + 0.986361i \(0.447368\pi\)
−0.936511 + 0.350637i \(0.885965\pi\)
\(468\) −3.60301 0.801905i −0.166549 0.0370681i
\(469\) −10.8882 24.6063i −0.502771 1.13621i
\(470\) 1.96304 0.525995i 0.0905483 0.0242623i
\(471\) 4.72399 + 8.18219i 0.217670 + 0.377015i
\(472\) −11.1484 + 19.3095i −0.513145 + 0.888793i
\(473\) 20.4496 76.3188i 0.940272 3.50914i
\(474\) −1.31650 + 1.31650i −0.0604689 + 0.0604689i
\(475\) 1.33777 4.99262i 0.0613810 0.229077i
\(476\) 9.99166 1.55916i 0.457967 0.0714639i
\(477\) −2.04084 3.53484i −0.0934437 0.161849i
\(478\) −4.50896 + 2.60325i −0.206235 + 0.119070i
\(479\) 3.75854 + 3.75854i 0.171732 + 0.171732i 0.787740 0.616008i \(-0.211251\pi\)
−0.616008 + 0.787740i \(0.711251\pi\)
\(480\) 4.15574 2.39932i 0.189683 0.109513i
\(481\) −18.1198 + 0.776065i −0.826192 + 0.0353855i
\(482\) 26.5296i 1.20839i
\(483\) 0.0952137 + 0.610164i 0.00433237 + 0.0277634i
\(484\) 16.5012 28.5809i 0.750054 1.29913i
\(485\) 2.36294i 0.107295i
\(486\) 0.954388 + 0.255728i 0.0432919 + 0.0116000i
\(487\) −13.4339 + 3.59961i −0.608749 + 0.163114i −0.550008 0.835160i \(-0.685375\pi\)
−0.0587410 + 0.998273i \(0.518709\pi\)
\(488\) −5.18694 5.18694i −0.234802 0.234802i
\(489\) 13.3170 + 13.3170i 0.602213 + 0.602213i
\(490\) −4.83366 4.39236i −0.218362 0.198426i
\(491\) −6.73956 3.89109i −0.304152 0.175602i 0.340155 0.940370i \(-0.389521\pi\)
−0.644307 + 0.764767i \(0.722854\pi\)
\(492\) 9.51562 + 2.54970i 0.428997 + 0.114949i
\(493\) 8.67888 + 15.0323i 0.390877 + 0.677019i
\(494\) −3.30201 3.03078i −0.148565 0.136361i
\(495\) −5.37742 3.10465i −0.241697 0.139544i
\(496\) 1.78147 + 6.64854i 0.0799904 + 0.298528i
\(497\) 2.61199 3.57789i 0.117164 0.160490i
\(498\) 12.0409 6.95183i 0.539567 0.311519i
\(499\) 12.4657 3.34017i 0.558041 0.149527i 0.0312347 0.999512i \(-0.490056\pi\)
0.526806 + 0.849985i \(0.323389\pi\)
\(500\) −2.27898 8.50527i −0.101919 0.380367i
\(501\) −5.93797 22.1608i −0.265289 0.990072i
\(502\) 12.3750 3.31587i 0.552323 0.147995i
\(503\) 0.631010 0.364314i 0.0281354 0.0162440i −0.485866 0.874033i \(-0.661496\pi\)
0.514002 + 0.857789i \(0.328162\pi\)
\(504\) −7.22846 + 3.19857i −0.321981 + 0.142476i
\(505\) −0.587653 2.19315i −0.0261502 0.0975939i
\(506\) 1.31329 + 0.758229i 0.0583829 + 0.0337074i
\(507\) 7.43881 + 10.6613i 0.330369 + 0.473487i
\(508\) −4.99206 8.64650i −0.221487 0.383626i
\(509\) −14.4291 3.86626i −0.639557 0.171369i −0.0755542 0.997142i \(-0.524073\pi\)
−0.564003 + 0.825773i \(0.690739\pi\)
\(510\) −3.01682 1.74176i −0.133587 0.0771264i
\(511\) −12.6810 + 17.3704i −0.560975 + 0.768422i
\(512\) −7.07136 7.07136i −0.312513 0.312513i
\(513\) −0.889632 0.889632i −0.0392782 0.0392782i
\(514\) 17.7261 4.74970i 0.781865 0.209500i
\(515\) 2.64641 + 0.709104i 0.116615 + 0.0312469i
\(516\) 12.3014i 0.541537i
\(517\) 7.16119 12.4035i 0.314949 0.545507i
\(518\) −10.2380 + 8.25192i −0.449830 + 0.362569i
\(519\) 8.58805i 0.376973i
\(520\) −9.92924 2.20990i −0.435426 0.0969107i
\(521\) 26.7816 15.4624i 1.17332 0.677419i 0.218864 0.975755i \(-0.429765\pi\)
0.954461 + 0.298336i \(0.0964317\pi\)
\(522\) −3.24817 3.24817i −0.142169 0.142169i
\(523\) −17.2017 + 9.93138i −0.752176 + 0.434269i −0.826479 0.562967i \(-0.809660\pi\)
0.0743038 + 0.997236i \(0.476327\pi\)
\(524\) 8.70421 + 15.0761i 0.380245 + 0.658604i
\(525\) 1.67586 + 10.7395i 0.0731404 + 0.468710i
\(526\) −2.21517 + 8.26711i −0.0965858 + 0.360463i
\(527\) −20.0910 + 20.0910i −0.875179 + 0.875179i
\(528\) −1.53925 + 5.74456i −0.0669872 + 0.250000i
\(529\) −11.4728 + 19.8714i −0.498816 + 0.863974i
\(530\) −1.90417 3.29813i −0.0827120 0.143261i
\(531\) 7.20872 1.93157i 0.312832 0.0838230i
\(532\) 3.38825 + 0.363939i 0.146899 + 0.0157787i
\(533\) −18.6176 29.2773i −0.806417 1.26814i
\(534\) 2.01575 3.49138i 0.0872301 0.151087i
\(535\) 7.40118 7.40118i 0.319981 0.319981i
\(536\) −30.3846 −1.31241
\(537\) −13.6367 −0.588469
\(538\) −5.09304 + 5.09304i −0.219577 + 0.219577i
\(539\) −45.9758 + 2.19913i −1.98032 + 0.0947231i
\(540\) −0.933796 0.250210i −0.0401842 0.0107673i
\(541\) −2.57018 9.59205i −0.110501 0.412395i 0.888410 0.459050i \(-0.151810\pi\)
−0.998911 + 0.0466559i \(0.985144\pi\)
\(542\) −20.1068 11.6087i −0.863663 0.498636i
\(543\) 11.2556i 0.483024i
\(544\) 4.91042 18.3259i 0.210532 0.785717i
\(545\) 6.85914 0.293813
\(546\) 8.92903 + 3.01854i 0.382127 + 0.129182i
\(547\) −5.37266 −0.229718 −0.114859 0.993382i \(-0.536642\pi\)
−0.114859 + 0.993382i \(0.536642\pi\)
\(548\) 1.27086 4.74291i 0.0542885 0.202607i
\(549\) 2.45527i 0.104788i
\(550\) 23.1152 + 13.3456i 0.985637 + 0.569058i
\(551\) 1.51389 + 5.64992i 0.0644939 + 0.240694i
\(552\) 0.673585 + 0.180487i 0.0286697 + 0.00768202i
\(553\) −3.88157 + 3.12859i −0.165061 + 0.133041i
\(554\) −1.71281 + 1.71281i −0.0727702 + 0.0727702i
\(555\) −4.75002 −0.201627
\(556\) 8.24850 0.349814
\(557\) 9.08545 9.08545i 0.384963 0.384963i −0.487923 0.872886i \(-0.662245\pi\)
0.872886 + 0.487923i \(0.162245\pi\)
\(558\) 3.75966 6.51191i 0.159159 0.275671i
\(559\) −29.2960 + 31.9178i −1.23909 + 1.34998i
\(560\) −2.06643 + 0.914389i −0.0873226 + 0.0386400i
\(561\) −23.7133 + 6.35395i −1.00118 + 0.268264i
\(562\) 6.47117 + 11.2084i 0.272970 + 0.472797i
\(563\) 3.15942 5.47228i 0.133154 0.230629i −0.791737 0.610862i \(-0.790823\pi\)
0.924891 + 0.380233i \(0.124156\pi\)
\(564\) 0.577134 2.15389i 0.0243017 0.0906952i
\(565\) −0.807097 + 0.807097i −0.0339548 + 0.0339548i
\(566\) 0.147238 0.549498i 0.00618886 0.0230971i
\(567\) 2.46785 + 0.953787i 0.103640 + 0.0400553i
\(568\) −2.50115 4.33211i −0.104946 0.181771i
\(569\) 4.42917 2.55718i 0.185680 0.107203i −0.404278 0.914636i \(-0.632477\pi\)
0.589959 + 0.807433i \(0.299144\pi\)
\(570\) −0.830056 0.830056i −0.0347672 0.0347672i
\(571\) 24.2776 14.0167i 1.01599 0.586580i 0.103047 0.994676i \(-0.467141\pi\)
0.912939 + 0.408097i \(0.133807\pi\)
\(572\) −20.4809 + 13.0239i −0.856350 + 0.544557i
\(573\) 11.3967i 0.476105i
\(574\) −23.4640 9.06846i −0.979367 0.378510i
\(575\) 0.479459 0.830447i 0.0199948 0.0346320i
\(576\) 6.82982i 0.284576i
\(577\) −19.3359 5.18104i −0.804964 0.215689i −0.167202 0.985923i \(-0.553473\pi\)
−0.637762 + 0.770233i \(0.720140\pi\)
\(578\) 2.92108 0.782701i 0.121501 0.0325561i
\(579\) −1.75587 1.75587i −0.0729713 0.0729713i
\(580\) 3.17809 + 3.17809i 0.131963 + 0.131963i
\(581\) 34.0461 15.0653i 1.41247 0.625014i
\(582\) −2.14115 1.23620i −0.0887537 0.0512420i
\(583\) −25.9245 6.94644i −1.07368 0.287692i
\(584\) 12.1429 + 21.0321i 0.502477 + 0.870315i
\(585\) 1.82700 + 2.87307i 0.0755371 + 0.118787i
\(586\) −14.9969 8.65846i −0.619516 0.357678i
\(587\) −1.06109 3.96003i −0.0437957 0.163448i 0.940565 0.339615i \(-0.110297\pi\)
−0.984360 + 0.176167i \(0.943630\pi\)
\(588\) −6.82552 + 2.18336i −0.281480 + 0.0900401i
\(589\) −8.29187 + 4.78731i −0.341661 + 0.197258i
\(590\) 6.72598 1.80222i 0.276904 0.0741962i
\(591\) −3.77342 14.0826i −0.155218 0.579281i
\(592\) 1.17750 + 4.39450i 0.0483950 + 0.180613i
\(593\) −16.7775 + 4.49553i −0.688971 + 0.184609i −0.586285 0.810105i \(-0.699410\pi\)
−0.102686 + 0.994714i \(0.532744\pi\)
\(594\) 5.62651 3.24847i 0.230859 0.133286i
\(595\) −7.53393 5.50003i −0.308861 0.225479i
\(596\) 4.07665 + 15.2143i 0.166986 + 0.623200i
\(597\) 4.52897 + 2.61480i 0.185358 + 0.107017i
\(598\) −0.446196 0.701671i −0.0182463 0.0286935i
\(599\) −7.18140 12.4386i −0.293424 0.508226i 0.681193 0.732104i \(-0.261461\pi\)
−0.974617 + 0.223878i \(0.928128\pi\)
\(600\) 11.8558 + 3.17674i 0.484010 + 0.129690i
\(601\) −7.65598 4.42018i −0.312294 0.180303i 0.335659 0.941984i \(-0.391041\pi\)
−0.647952 + 0.761681i \(0.724374\pi\)
\(602\) −3.35470 + 31.2320i −0.136727 + 1.27292i
\(603\) 7.19137 + 7.19137i 0.292855 + 0.292855i
\(604\) 17.6909 + 17.6909i 0.719833 + 0.719833i
\(605\) −29.4044 + 7.87889i −1.19546 + 0.320322i
\(606\) 2.29474 + 0.614874i 0.0932175 + 0.0249776i
\(607\) 27.1962i 1.10386i −0.833890 0.551930i \(-0.813891\pi\)
0.833890 0.551930i \(-0.186109\pi\)
\(608\) 3.19666 5.53678i 0.129642 0.224546i
\(609\) −7.71911 9.57691i −0.312794 0.388076i
\(610\) 2.29085i 0.0927539i
\(611\) −6.62702 + 4.21415i −0.268100 + 0.170486i
\(612\) −3.31012 + 1.91110i −0.133804 + 0.0772516i
\(613\) 31.3428 + 31.3428i 1.26593 + 1.26593i 0.948174 + 0.317751i \(0.102928\pi\)
0.317751 + 0.948174i \(0.397072\pi\)
\(614\) 12.5717 7.25828i 0.507353 0.292920i
\(615\) −4.54346 7.86951i −0.183210 0.317329i
\(616\) −18.7372 + 48.4811i −0.754944 + 1.95336i
\(617\) −7.15534 + 26.7041i −0.288063 + 1.07507i 0.658509 + 0.752573i \(0.271188\pi\)
−0.946572 + 0.322493i \(0.895479\pi\)
\(618\) −2.02705 + 2.02705i −0.0815398 + 0.0815398i
\(619\) −10.1905 + 38.0315i −0.409591 + 1.52861i 0.385838 + 0.922567i \(0.373912\pi\)
−0.795429 + 0.606047i \(0.792754\pi\)
\(620\) −3.67853 + 6.37141i −0.147734 + 0.255882i
\(621\) −0.116706 0.202140i −0.00468324 0.00811161i
\(622\) −12.1922 + 3.26689i −0.488863 + 0.130990i
\(623\) 6.36523 8.71908i 0.255018 0.349322i
\(624\) 2.20513 2.40247i 0.0882757 0.0961757i
\(625\) 6.20963 10.7554i 0.248385 0.430216i
\(626\) 9.92861 9.92861i 0.396827 0.396827i
\(627\) −8.27280 −0.330384
\(628\) 9.67233 0.385968
\(629\) −13.2796 + 13.2796i −0.529493 + 0.529493i
\(630\) 2.30259 + 0.889915i 0.0917373 + 0.0354551i
\(631\) 7.08811 + 1.89925i 0.282173 + 0.0756081i 0.397130 0.917762i \(-0.370006\pi\)
−0.114957 + 0.993371i \(0.536673\pi\)
\(632\) 1.45706 + 5.43782i 0.0579588 + 0.216305i
\(633\) 9.62266 + 5.55565i 0.382466 + 0.220817i
\(634\) 18.4841i 0.734096i
\(635\) −2.38358 + 8.89564i −0.0945895 + 0.353013i
\(636\) −4.17861 −0.165693
\(637\) 22.9096 + 10.5901i 0.907711 + 0.419595i
\(638\) −30.2052 −1.19583
\(639\) −0.433350 + 1.61728i −0.0171431 + 0.0639787i
\(640\) 3.22481i 0.127472i
\(641\) 29.1101 + 16.8067i 1.14978 + 0.663826i 0.948834 0.315777i \(-0.102265\pi\)
0.200946 + 0.979602i \(0.435598\pi\)
\(642\) 2.83451 + 10.5785i 0.111869 + 0.417501i
\(643\) −22.8004 6.10935i −0.899160 0.240929i −0.220504 0.975386i \(-0.570770\pi\)
−0.678655 + 0.734457i \(0.737437\pi\)
\(644\) 0.589703 + 0.227911i 0.0232376 + 0.00898096i
\(645\) −8.02346 + 8.02346i −0.315924 + 0.315924i
\(646\) −4.64117 −0.182604
\(647\) 1.02762 0.0403998 0.0201999 0.999796i \(-0.493570\pi\)
0.0201999 + 0.999796i \(0.493570\pi\)
\(648\) 2.11257 2.11257i 0.0829897 0.0829897i
\(649\) 24.5364 42.4983i 0.963139 1.66821i
\(650\) −7.85349 12.3501i −0.308039 0.484411i
\(651\) 11.8720 16.2623i 0.465302 0.637369i
\(652\) 18.6233 4.99009i 0.729343 0.195427i
\(653\) −11.2342 19.4582i −0.439628 0.761458i 0.558033 0.829819i \(-0.311556\pi\)
−0.997661 + 0.0683609i \(0.978223\pi\)
\(654\) −3.58843 + 6.21535i −0.140319 + 0.243039i
\(655\) 4.15604 15.5105i 0.162390 0.606047i
\(656\) −6.15420 + 6.15420i −0.240281 + 0.240281i
\(657\) 2.10388 7.85180i 0.0820803 0.306328i
\(658\) −2.05268 + 5.31115i −0.0800217 + 0.207050i
\(659\) −15.3326 26.5569i −0.597275 1.03451i −0.993222 0.116237i \(-0.962917\pi\)
0.395947 0.918273i \(-0.370416\pi\)
\(660\) −5.50511 + 3.17838i −0.214286 + 0.123718i
\(661\) −24.4206 24.4206i −0.949852 0.949852i 0.0489491 0.998801i \(-0.484413\pi\)
−0.998801 + 0.0489491i \(0.984413\pi\)
\(662\) −3.37847 + 1.95056i −0.131308 + 0.0758107i
\(663\) 13.1400 + 2.92450i 0.510314 + 0.113578i
\(664\) 42.0412i 1.63151i
\(665\) −1.97258 2.44734i −0.0764935 0.0949036i
\(666\) 2.48503 4.30419i 0.0962928 0.166784i
\(667\) 1.08516i 0.0420177i
\(668\) −22.6870 6.07898i −0.877788 0.235203i
\(669\) −26.5785 + 7.12168i −1.02758 + 0.275340i
\(670\) 6.70979 + 6.70979i 0.259222 + 0.259222i
\(671\) 11.4159 + 11.4159i 0.440708 + 0.440708i
\(672\) −1.43586 + 13.3678i −0.0553895 + 0.515673i
\(673\) 27.9964 + 16.1637i 1.07918 + 0.623066i 0.930675 0.365846i \(-0.119220\pi\)
0.148506 + 0.988912i \(0.452554\pi\)
\(674\) 14.4535 + 3.87281i 0.556729 + 0.149175i
\(675\) −2.05414 3.55787i −0.0790637 0.136942i
\(676\) 13.2600 1.13793i 0.509998 0.0437664i
\(677\) −25.7232 14.8513i −0.988623 0.570782i −0.0837606 0.996486i \(-0.526693\pi\)
−0.904862 + 0.425704i \(0.860026\pi\)
\(678\) −0.309102 1.15359i −0.0118710 0.0443032i
\(679\) −5.34713 3.90359i −0.205204 0.149806i
\(680\) −9.12208 + 5.26664i −0.349816 + 0.201966i
\(681\) −11.3401 + 3.03858i −0.434554 + 0.116439i
\(682\) −12.7968 47.7583i −0.490015 1.82876i
\(683\) 4.83332 + 18.0382i 0.184942 + 0.690213i 0.994643 + 0.103370i \(0.0329626\pi\)
−0.809701 + 0.586843i \(0.800371\pi\)
\(684\) −1.24412 + 0.333360i −0.0475700 + 0.0127463i
\(685\) −3.92244 + 2.26462i −0.149869 + 0.0865267i
\(686\) 17.9248 3.68196i 0.684372 0.140578i
\(687\) −3.62802 13.5399i −0.138417 0.516581i
\(688\) 9.41190 + 5.43396i 0.358825 + 0.207168i
\(689\) 10.8420 + 9.95147i 0.413049 + 0.379121i
\(690\) −0.108890 0.188604i −0.00414539 0.00718002i
\(691\) 10.7277 + 2.87447i 0.408100 + 0.109350i 0.457028 0.889452i \(-0.348914\pi\)
−0.0489282 + 0.998802i \(0.515581\pi\)
\(692\) 7.61408 + 4.39599i 0.289444 + 0.167110i
\(693\) 15.9091 7.03974i 0.604338 0.267418i
\(694\) 4.74704 + 4.74704i 0.180195 + 0.180195i
\(695\) −5.38002 5.38002i −0.204076 0.204076i
\(696\) −13.4166 + 3.59498i −0.508556 + 0.136267i
\(697\) −34.7029 9.29861i −1.31447 0.352210i
\(698\) 0.386660i 0.0146353i
\(699\) −3.04141 + 5.26788i −0.115037 + 0.199249i
\(700\) 10.3794 + 4.01146i 0.392303 + 0.151619i
\(701\) 9.68156i 0.365668i 0.983144 + 0.182834i \(0.0585270\pi\)
−0.983144 + 0.182834i \(0.941473\pi\)
\(702\) −3.55922 + 0.152440i −0.134334 + 0.00575349i
\(703\) −5.48069 + 3.16428i −0.206708 + 0.119343i
\(704\) 31.7557 + 31.7557i 1.19684 + 1.19684i
\(705\) −1.78129 + 1.02843i −0.0670872 + 0.0387328i
\(706\) −9.86512 17.0869i −0.371279 0.643074i
\(707\) 5.93373 + 2.29329i 0.223161 + 0.0862482i
\(708\) 1.97744 7.37989i 0.0743166 0.277353i
\(709\) −1.06906 + 1.06906i −0.0401494 + 0.0401494i −0.726896 0.686747i \(-0.759038\pi\)
0.686747 + 0.726896i \(0.259038\pi\)
\(710\) −0.404330 + 1.50898i −0.0151742 + 0.0566310i
\(711\) 0.942160 1.63187i 0.0353338 0.0611999i
\(712\) −6.09512 10.5571i −0.228424 0.395643i
\(713\) −1.71578 + 0.459743i −0.0642566 + 0.0172175i
\(714\) 8.92527 3.94940i 0.334020 0.147803i
\(715\) 21.8533 + 4.86378i 0.817266 + 0.181895i
\(716\) −6.98028 + 12.0902i −0.260865 + 0.451832i
\(717\) 3.72605 3.72605i 0.139152 0.139152i
\(718\) −27.3870 −1.02207
\(719\) 27.7174 1.03368 0.516842 0.856081i \(-0.327108\pi\)
0.516842 + 0.856081i \(0.327108\pi\)
\(720\) 0.603930 0.603930i 0.0225071 0.0225071i
\(721\) −5.97654 + 4.81717i −0.222578 + 0.179401i
\(722\) 16.6227 + 4.45404i 0.618632 + 0.165762i
\(723\) −6.94938 25.9354i −0.258450 0.964549i
\(724\) −9.97910 5.76143i −0.370870 0.214122i
\(725\) 19.0999i 0.709354i
\(726\) 8.24386 30.7665i 0.305958 1.14185i
\(727\) 29.0510 1.07744 0.538721 0.842484i \(-0.318908\pi\)
0.538721 + 0.842484i \(0.318908\pi\)
\(728\) 21.4040 18.8183i 0.793286 0.697452i
\(729\) −1.00000 −0.0370370
\(730\) 1.96299 7.32600i 0.0726537 0.271147i
\(731\) 44.8623i 1.65929i
\(732\) 2.17682 + 1.25679i 0.0804576 + 0.0464522i
\(733\) 8.78993 + 32.8045i 0.324663 + 1.21166i 0.914650 + 0.404247i \(0.132466\pi\)
−0.589986 + 0.807413i \(0.700867\pi\)
\(734\) 6.37441 + 1.70802i 0.235284 + 0.0630441i
\(735\) 5.87597 + 3.02781i 0.216738 + 0.111683i
\(736\) 0.838703 0.838703i 0.0309150 0.0309150i
\(737\) 66.8735 2.46332
\(738\) 9.50785 0.349989
\(739\) 9.73435 9.73435i 0.358084 0.358084i −0.505022 0.863106i \(-0.668516\pi\)
0.863106 + 0.505022i \(0.168516\pi\)
\(740\) −2.43141 + 4.21132i −0.0893803 + 0.154811i
\(741\) 4.02196 + 2.09794i 0.147750 + 0.0770699i
\(742\) 10.6091 + 1.13955i 0.389472 + 0.0418340i
\(743\) −30.3940 + 8.14404i −1.11505 + 0.298776i −0.768878 0.639396i \(-0.779184\pi\)
−0.346169 + 0.938172i \(0.612518\pi\)
\(744\) −11.3682 19.6904i −0.416780 0.721884i
\(745\) 7.26442 12.5823i 0.266148 0.460981i
\(746\) 0.257288 0.960210i 0.00941997 0.0351558i
\(747\) −9.95023 + 9.95023i −0.364060 + 0.364060i
\(748\) −6.50483 + 24.2764i −0.237840 + 0.887632i
\(749\) 4.52145 + 28.9751i 0.165210 + 1.05873i
\(750\) −4.24916 7.35977i −0.155158 0.268741i
\(751\) 22.9765 13.2655i 0.838423 0.484064i −0.0183050 0.999832i \(-0.505827\pi\)
0.856728 + 0.515769i \(0.172494\pi\)
\(752\) 1.39302 + 1.39302i 0.0507983 + 0.0507983i
\(753\) −11.2292 + 6.48321i −0.409217 + 0.236261i
\(754\) 14.6848 + 7.65990i 0.534788 + 0.278957i
\(755\) 23.0775i 0.839876i
\(756\) 2.10884 1.69975i 0.0766979 0.0618195i
\(757\) 7.38184 12.7857i 0.268298 0.464705i −0.700125 0.714021i \(-0.746872\pi\)
0.968422 + 0.249315i \(0.0802056\pi\)
\(758\) 21.1143i 0.766908i
\(759\) −1.48249 0.397233i −0.0538111 0.0144186i
\(760\) −3.42856 + 0.918680i −0.124367 + 0.0333240i
\(761\) 23.1965 + 23.1965i 0.840873 + 0.840873i 0.988972 0.148100i \(-0.0473156\pi\)
−0.148100 + 0.988972i \(0.547316\pi\)
\(762\) −6.81371 6.81371i −0.246835 0.246835i
\(763\) −11.3314 + 15.5217i −0.410223 + 0.561922i
\(764\) 10.1042 + 5.83367i 0.365558 + 0.211055i
\(765\) 3.40550 + 0.912500i 0.123126 + 0.0329915i
\(766\) −11.2880 19.5513i −0.407850 0.706418i
\(767\) −22.7062 + 14.4390i −0.819873 + 0.521361i
\(768\) 14.7517 + 8.51691i 0.532307 + 0.307328i
\(769\) 1.79577 + 6.70191i 0.0647572 + 0.241677i 0.990716 0.135947i \(-0.0434078\pi\)
−0.925959 + 0.377624i \(0.876741\pi\)
\(770\) 14.8437 6.56832i 0.534932 0.236706i
\(771\) −16.0849 + 9.28663i −0.579284 + 0.334450i
\(772\) −2.45551 + 0.657953i −0.0883759 + 0.0236802i
\(773\) −0.260414 0.971880i −0.00936645 0.0349561i 0.961084 0.276255i \(-0.0890933\pi\)
−0.970451 + 0.241299i \(0.922427\pi\)
\(774\) −3.07283 11.4680i −0.110451 0.412207i
\(775\) −30.1995 + 8.09193i −1.08480 + 0.290671i
\(776\) −6.47431 + 3.73794i −0.232414 + 0.134184i
\(777\) 7.84708 10.7489i 0.281512 0.385615i
\(778\) 5.11020 + 19.0715i 0.183209 + 0.683747i
\(779\) −10.4847 6.05336i −0.375654 0.216884i
\(780\) 3.48243 0.149151i 0.124691 0.00534047i
\(781\) 5.50477 + 9.53455i 0.196976 + 0.341173i
\(782\) −0.831702 0.222854i −0.0297416 0.00796924i
\(783\) 4.02628 + 2.32457i 0.143887 + 0.0830734i
\(784\) 1.34457 6.18674i 0.0480205 0.220955i
\(785\) −6.30870 6.30870i −0.225167 0.225167i
\(786\) 11.8805 + 11.8805i 0.423762 + 0.423762i
\(787\) −38.2900 + 10.2598i −1.36489 + 0.365721i −0.865610 0.500719i \(-0.833069\pi\)
−0.499281 + 0.866440i \(0.666402\pi\)
\(788\) −14.4170 3.86303i −0.513585 0.137615i
\(789\) 8.66221i 0.308383i
\(790\) 0.879067 1.52259i 0.0312758 0.0541713i
\(791\) −0.493063 3.15973i −0.0175313 0.112347i
\(792\) 19.6451i 0.698058i
\(793\) −2.65502 8.44509i −0.0942827 0.299894i
\(794\) 21.4026 12.3568i 0.759549 0.438526i
\(795\) 2.72546 + 2.72546i 0.0966622 + 0.0966622i
\(796\) 4.63651 2.67689i 0.164337 0.0948799i
\(797\) 18.4889 + 32.0238i 0.654912 + 1.13434i 0.981916 + 0.189318i \(0.0606276\pi\)
−0.327004 + 0.945023i \(0.606039\pi\)
\(798\) 3.24961 0.507089i 0.115035 0.0179508i
\(799\) −2.10477 + 7.85511i −0.0744614 + 0.277894i
\(800\) 14.7620 14.7620i 0.521916 0.521916i
\(801\) −1.05604 + 3.94121i −0.0373135 + 0.139256i
\(802\) −0.694751 + 1.20334i −0.0245325 + 0.0424915i
\(803\) −26.7253 46.2896i −0.943115 1.63352i
\(804\) 10.0569 2.69473i 0.354678 0.0950358i
\(805\) −0.235976 0.533282i −0.00831706 0.0187957i
\(806\) −5.88991 + 26.4637i −0.207463 + 0.932145i
\(807\) 3.64486 6.31308i 0.128305 0.222231i
\(808\) 5.07949 5.07949i 0.178696 0.178696i
\(809\) 19.6908 0.692293 0.346146 0.938181i \(-0.387490\pi\)
0.346146 + 0.938181i \(0.387490\pi\)
\(810\) −0.933034 −0.0327835
\(811\) 25.0100 25.0100i 0.878220 0.878220i −0.115131 0.993350i \(-0.536729\pi\)
0.993350 + 0.115131i \(0.0367287\pi\)
\(812\) −12.4420 + 1.94152i −0.436628 + 0.0681341i
\(813\) 22.6974 + 6.08174i 0.796032 + 0.213296i
\(814\) −8.45832 31.5669i −0.296464 1.10642i
\(815\) −15.4016 8.89213i −0.539495 0.311478i
\(816\) 3.37681i 0.118212i
\(817\) −3.91275 + 14.6026i −0.136890 + 0.510880i
\(818\) −2.74007 −0.0958042
\(819\) −9.51974 0.611992i −0.332647 0.0213847i
\(820\) −9.30270 −0.324865
\(821\) −1.60713 + 5.99790i −0.0560893 + 0.209328i −0.988283 0.152631i \(-0.951225\pi\)
0.932194 + 0.361959i \(0.117892\pi\)
\(822\) 4.73904i 0.165293i
\(823\) −2.18495 1.26148i −0.0761627 0.0439726i 0.461435 0.887174i \(-0.347335\pi\)
−0.537598 + 0.843201i \(0.680668\pi\)
\(824\) 2.24347 + 8.37275i 0.0781550 + 0.291679i
\(825\) −26.0934 6.99170i −0.908454 0.243420i
\(826\) −7.03310 + 18.1976i −0.244713 + 0.633176i
\(827\) 36.7114 36.7114i 1.27658 1.27658i 0.334011 0.942569i \(-0.391598\pi\)
0.942569 0.334011i \(-0.108402\pi\)
\(828\) −0.238954 −0.00830422
\(829\) 26.2330 0.911111 0.455555 0.890207i \(-0.349441\pi\)
0.455555 + 0.890207i \(0.349441\pi\)
\(830\) −9.28390 + 9.28390i −0.322249 + 0.322249i
\(831\) 1.22578 2.12311i 0.0425218 0.0736499i
\(832\) −7.38547 23.4917i −0.256045 0.814427i
\(833\) 24.8922 7.96257i 0.862465 0.275887i
\(834\) 7.68967 2.06044i 0.266272 0.0713472i
\(835\) 10.8325 + 18.7624i 0.374873 + 0.649300i
\(836\) −4.23462 + 7.33458i −0.146457 + 0.253672i
\(837\) −1.96967 + 7.35090i −0.0680817 + 0.254084i
\(838\) −13.5094 + 13.5094i −0.466674 + 0.466674i
\(839\) −9.29570 + 34.6920i −0.320923 + 1.19770i 0.597424 + 0.801926i \(0.296191\pi\)
−0.918347 + 0.395776i \(0.870476\pi\)
\(840\) 5.81159 4.68422i 0.200519 0.161621i
\(841\) 3.69273 + 6.39600i 0.127336 + 0.220552i
\(842\) 2.90951 1.67981i 0.100268 0.0578900i
\(843\) −9.26224 9.26224i −0.319009 0.319009i
\(844\) 9.85116 5.68757i 0.339091 0.195774i
\(845\) −9.39091 7.90650i −0.323057 0.271992i
\(846\) 2.15213i 0.0739919i
\(847\) 30.7471 79.5558i 1.05648 2.73357i
\(848\) 1.84584 3.19709i 0.0633865 0.109789i
\(849\) 0.575760i 0.0197600i
\(850\) −14.6388 3.92245i −0.502106 0.134539i
\(851\) −1.13408 + 0.303877i −0.0388759 + 0.0104168i
\(852\) 1.21205 + 1.21205i 0.0415241 + 0.0415241i
\(853\) −0.749751 0.749751i −0.0256710 0.0256710i 0.694155 0.719826i \(-0.255778\pi\)
−0.719826 + 0.694155i \(0.755778\pi\)
\(854\) −5.18401 3.78451i −0.177393 0.129503i
\(855\) 1.02890 + 0.594034i 0.0351875 + 0.0203155i
\(856\) 31.9868 + 8.57083i 1.09329 + 0.292945i
\(857\) 1.48116 + 2.56544i 0.0505953 + 0.0876336i 0.890214 0.455543i \(-0.150555\pi\)
−0.839619 + 0.543176i \(0.817221\pi\)
\(858\) −15.8400 + 17.2576i −0.540770 + 0.589165i
\(859\) 20.5020 + 11.8368i 0.699518 + 0.403867i 0.807168 0.590322i \(-0.200999\pi\)
−0.107650 + 0.994189i \(0.534333\pi\)
\(860\) 3.00653 + 11.2205i 0.102522 + 0.382616i
\(861\) 25.3139 + 2.71902i 0.862695 + 0.0926638i
\(862\) −0.593540 + 0.342681i −0.0202161 + 0.0116717i
\(863\) −18.8188 + 5.04247i −0.640598 + 0.171648i −0.564474 0.825451i \(-0.690921\pi\)
−0.0761238 + 0.997098i \(0.524254\pi\)
\(864\) −1.31522 4.90846i −0.0447446 0.166989i
\(865\) −2.09897 7.83347i −0.0713672 0.266346i
\(866\) −20.0696 + 5.37764i −0.681994 + 0.182740i
\(867\) −2.65063 + 1.53034i −0.0900201 + 0.0519731i
\(868\) −8.34100 18.8498i −0.283112 0.639806i
\(869\) −3.20684 11.9681i −0.108785 0.405990i
\(870\) 3.75665 + 2.16890i 0.127362 + 0.0735327i
\(871\) −32.5117 16.9588i −1.10162 0.574628i
\(872\) 10.8505 + 18.7936i 0.367445 + 0.636433i
\(873\) 2.41702 + 0.647638i 0.0818036 + 0.0219192i
\(874\) −0.251281 0.145077i −0.00849970 0.00490730i
\(875\) −9.20834 20.8100i −0.311299 0.703505i
\(876\) −5.88441 5.88441i −0.198816 0.198816i
\(877\) 24.3318 + 24.3318i 0.821626 + 0.821626i 0.986341 0.164715i \(-0.0526704\pi\)
−0.164715 + 0.986341i \(0.552670\pi\)
\(878\) −21.7827 + 5.83666i −0.735131 + 0.196978i
\(879\) 16.9291 + 4.53613i 0.571003 + 0.153000i
\(880\) 5.61602i 0.189316i
\(881\) 16.0850 27.8600i 0.541918 0.938629i −0.456876 0.889530i \(-0.651032\pi\)
0.998794 0.0490986i \(-0.0156348\pi\)
\(882\) −5.81770 + 3.74042i −0.195892 + 0.125947i
\(883\) 24.5604i 0.826522i −0.910613 0.413261i \(-0.864390\pi\)
0.910613 0.413261i \(-0.135610\pi\)
\(884\) 9.31882 10.1528i 0.313426 0.341475i
\(885\) −6.10324 + 3.52371i −0.205158 + 0.118448i
\(886\) 11.7198 + 11.7198i 0.393734 + 0.393734i
\(887\) −18.9519 + 10.9419i −0.636343 + 0.367393i −0.783204 0.621764i \(-0.786416\pi\)
0.146861 + 0.989157i \(0.453083\pi\)
\(888\) −7.51409 13.0148i −0.252156 0.436748i
\(889\) −16.1924 20.0895i −0.543076 0.673781i
\(890\) −0.985325 + 3.67728i −0.0330282 + 0.123263i
\(891\) −4.64956 + 4.64956i −0.155766 + 0.155766i
\(892\) −7.29080 + 27.2096i −0.244114 + 0.911045i
\(893\) −1.37020 + 2.37325i −0.0458519 + 0.0794178i
\(894\) 7.60092 + 13.1652i 0.254213 + 0.440310i
\(895\) 12.4386 3.33290i 0.415775 0.111407i
\(896\) 7.29748 + 5.32742i 0.243792 + 0.177976i
\(897\) 0.620004 + 0.569076i 0.0207013 + 0.0190009i
\(898\) 7.57109 13.1135i 0.252651 0.437604i
\(899\) 25.0181 25.0181i 0.834401 0.834401i
\(900\) −4.20583 −0.140194
\(901\) 15.2391 0.507689
\(902\) 44.2074 44.2074i 1.47194 1.47194i
\(903\) −4.90161 31.4113i −0.163115 1.04530i
\(904\) −3.48815 0.934647i −0.116014 0.0310859i
\(905\) 2.75094 + 10.2666i 0.0914442 + 0.341275i
\(906\) 20.9115 + 12.0732i 0.694737 + 0.401107i
\(907\) 1.56364i 0.0519198i −0.999663 0.0259599i \(-0.991736\pi\)
0.999663 0.0259599i \(-0.00826422\pi\)
\(908\) −3.11073 + 11.6094i −0.103233 + 0.385272i
\(909\) −2.40441 −0.0797493
\(910\) −8.88224 0.571009i −0.294443 0.0189288i
\(911\) 27.1812 0.900555 0.450277 0.892889i \(-0.351325\pi\)
0.450277 + 0.892889i \(0.351325\pi\)
\(912\) 0.294515 1.09914i 0.00975236 0.0363963i
\(913\) 92.5284i 3.06224i
\(914\) 11.9167 + 6.88013i 0.394171 + 0.227574i
\(915\) −0.600084 2.23954i −0.0198382 0.0740370i
\(916\) −13.8615 3.71417i −0.457996 0.122720i
\(917\) 28.2333 + 35.0283i 0.932345 + 1.15674i
\(918\) −2.60848 + 2.60848i −0.0860926 + 0.0860926i
\(919\) −52.1835 −1.72137 −0.860687 0.509134i \(-0.829966\pi\)
−0.860687 + 0.509134i \(0.829966\pi\)
\(920\) −0.658514 −0.0217106
\(921\) −10.3888 + 10.3888i −0.342324 + 0.342324i
\(922\) −7.82204 + 13.5482i −0.257605 + 0.446185i
\(923\) −0.258322 6.03137i −0.00850276 0.198525i
\(924\) 1.90209 17.7083i 0.0625740 0.582561i
\(925\) −19.9610 + 5.34854i −0.656314 + 0.175859i
\(926\) −18.3537 31.7896i −0.603141 1.04467i
\(927\) 1.45067 2.51263i 0.0476461 0.0825256i
\(928\) −6.11463 + 22.8201i −0.200723 + 0.749107i
\(929\) 19.3280 19.3280i 0.634133 0.634133i −0.314969 0.949102i \(-0.601994\pi\)
0.949102 + 0.314969i \(0.101994\pi\)
\(930\) −1.83777 + 6.85864i −0.0602627 + 0.224904i
\(931\) 8.79685 0.420773i 0.288305 0.0137903i
\(932\) 3.11363 + 5.39297i 0.101990 + 0.176653i
\(933\) 11.0634 6.38744i 0.362199 0.209115i
\(934\) 23.3091 + 23.3091i 0.762697 + 0.762697i
\(935\) 20.0768 11.5913i 0.656582 0.379078i
\(936\) −4.98191 + 9.55080i −0.162839 + 0.312178i
\(937\) 33.8356i 1.10536i −0.833393 0.552680i \(-0.813605\pi\)
0.833393 0.552680i \(-0.186395\pi\)
\(938\) −26.2684 + 4.09907i −0.857692 + 0.133839i
\(939\) −7.10546 + 12.3070i −0.231878 + 0.401624i
\(940\) 2.10570i 0.0686803i
\(941\) −50.0997 13.4242i −1.63320 0.437615i −0.678360 0.734729i \(-0.737309\pi\)
−0.954842 + 0.297114i \(0.903976\pi\)
\(942\) 9.01704 2.41611i 0.293791 0.0787211i
\(943\) −1.58821 1.58821i −0.0517192 0.0517192i
\(944\) 4.77293 + 4.77293i 0.155346 + 0.155346i
\(945\) −2.48413 0.266825i −0.0808087 0.00867983i
\(946\) −67.6083 39.0337i −2.19814 1.26909i
\(947\) 31.3506 + 8.40036i 1.01876 + 0.272975i 0.729284 0.684211i \(-0.239853\pi\)
0.289473 + 0.957186i \(0.406520\pi\)
\(948\) −0.964532 1.67062i −0.0313266 0.0542592i
\(949\) 1.25413 + 29.2819i 0.0407109 + 0.950531i
\(950\) −4.42279 2.55350i −0.143494 0.0828465i
\(951\) 4.84186 + 18.0701i 0.157008 + 0.585962i
\(952\) 3.15180 29.3431i 0.102150 0.951014i
\(953\) −4.71317 + 2.72115i −0.152675 + 0.0881468i −0.574391 0.818581i \(-0.694761\pi\)
0.421716 + 0.906728i \(0.361428\pi\)
\(954\) −3.89551 + 1.04380i −0.126122 + 0.0337942i
\(955\) −2.78543 10.3954i −0.0901343 0.336386i
\(956\) −1.39622 5.21075i −0.0451569 0.168528i
\(957\) 29.5287 7.91218i 0.954526 0.255765i
\(958\) 4.54827 2.62595i 0.146948 0.0848405i
\(959\) 1.35525 12.6173i 0.0437634 0.407435i
\(960\) −1.66925 6.22973i −0.0538748 0.201064i
\(961\) 23.3093 + 13.4576i 0.751914 + 0.434118i
\(962\) −3.89307 + 17.4918i −0.125517 + 0.563958i
\(963\) −5.54205 9.59911i −0.178590 0.309327i
\(964\) −26.5513 7.11440i −0.855160 0.229139i
\(965\) 2.03073 + 1.17245i 0.0653717 + 0.0377423i
\(966\) 0.606683 + 0.0651650i 0.0195197 + 0.00209665i
\(967\) 17.2286 + 17.2286i 0.554035 + 0.554035i 0.927603 0.373568i \(-0.121866\pi\)
−0.373568 + 0.927603i \(0.621866\pi\)
\(968\) −68.1027 68.1027i −2.18890 2.18890i
\(969\) 4.53722 1.21574i 0.145756 0.0390553i
\(970\) 2.25516 + 0.604268i 0.0724088 + 0.0194019i
\(971\) 37.8393i 1.21432i 0.794580 + 0.607160i \(0.207691\pi\)
−0.794580 + 0.607160i \(0.792309\pi\)
\(972\) −0.511873 + 0.886590i −0.0164183 + 0.0284374i
\(973\) 21.0624 3.28670i 0.675229 0.105367i
\(974\) 13.7417i 0.440312i
\(975\) 10.9127 + 10.0163i 0.349485 + 0.320778i
\(976\) −1.92316 + 1.11034i −0.0615589 + 0.0355411i
\(977\) 42.0348 + 42.0348i 1.34481 + 1.34481i 0.891197 + 0.453616i \(0.149866\pi\)
0.453616 + 0.891197i \(0.350134\pi\)
\(978\) 16.1151 9.30403i 0.515303 0.297510i
\(979\) 13.4148 + 23.2350i 0.428737 + 0.742595i
\(980\) 5.69218 3.65972i 0.181830 0.116905i
\(981\) 1.87996 7.01612i 0.0600226 0.224008i
\(982\) −5.43710 + 5.43710i −0.173505 + 0.173505i
\(983\) 2.63615 9.83824i 0.0840800 0.313791i −0.911058 0.412277i \(-0.864733\pi\)
0.995138 + 0.0984864i \(0.0314001\pi\)
\(984\) 14.3747 24.8976i 0.458248 0.793708i
\(985\) 6.88375 + 11.9230i 0.219335 + 0.379899i
\(986\) 16.5660 4.43886i 0.527570 0.141362i
\(987\) 0.615458 5.72989i 0.0195903 0.182384i
\(988\) 3.91875 2.49195i 0.124672 0.0792795i
\(989\) −1.40234 + 2.42892i −0.0445918 + 0.0772352i
\(990\) −4.33820 + 4.33820i −0.137877 + 0.137877i
\(991\) −51.8338 −1.64655 −0.823277 0.567640i \(-0.807857\pi\)
−0.823277 + 0.567640i \(0.807857\pi\)
\(992\) −38.6721 −1.22784
\(993\) 2.79186 2.79186i 0.0885969 0.0885969i
\(994\) −2.74674 3.40782i −0.0871214 0.108089i
\(995\) −4.77011 1.27815i −0.151223 0.0405200i
\(996\) 3.72852 + 13.9150i 0.118143 + 0.440914i
\(997\) −38.0778 21.9842i −1.20593 0.696247i −0.244066 0.969759i \(-0.578481\pi\)
−0.961869 + 0.273512i \(0.911815\pi\)
\(998\) 12.7513i 0.403635i
\(999\) −1.30189 + 4.85874i −0.0411901 + 0.153724i
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 273.2.cg.a.124.7 yes 36
3.2 odd 2 819.2.gh.c.397.3 36
7.3 odd 6 273.2.bt.a.241.7 yes 36
13.2 odd 12 273.2.bt.a.145.7 36
21.17 even 6 819.2.et.c.514.3 36
39.2 even 12 819.2.et.c.145.3 36
91.80 even 12 inner 273.2.cg.a.262.7 yes 36
273.80 odd 12 819.2.gh.c.262.3 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.bt.a.145.7 36 13.2 odd 12
273.2.bt.a.241.7 yes 36 7.3 odd 6
273.2.cg.a.124.7 yes 36 1.1 even 1 trivial
273.2.cg.a.262.7 yes 36 91.80 even 12 inner
819.2.et.c.145.3 36 39.2 even 12
819.2.et.c.514.3 36 21.17 even 6
819.2.gh.c.262.3 36 273.80 odd 12
819.2.gh.c.397.3 36 3.2 odd 2