Properties

Label 210.2.t.e.89.2
Level $210$
Weight $2$
Character 210.89
Analytic conductor $1.677$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [210,2,Mod(59,210)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(210, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("210.59");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 210.t (of order \(6\), degree \(2\), 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: \(1.67685844245\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.3317760000.3
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 89.2
Root \(-1.72286 - 0.178197i\) of defining polynomial
Character \(\chi\) \(=\) 210.89
Dual form 210.2.t.e.59.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-1.01575 + 1.40294i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.792893 + 2.09077i) q^{5} +(-0.707107 - 1.58114i) q^{6} +(1.41421 + 2.23607i) q^{7} +1.00000 q^{8} +(-0.936492 - 2.85008i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-1.01575 + 1.40294i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.792893 + 2.09077i) q^{5} +(-0.707107 - 1.58114i) q^{6} +(1.41421 + 2.23607i) q^{7} +1.00000 q^{8} +(-0.936492 - 2.85008i) q^{9} +(-2.20711 - 0.358719i) q^{10} +(-0.184829 + 0.106711i) q^{11} +(1.72286 + 0.178197i) q^{12} -6.70141 q^{13} +(-2.64360 + 0.106711i) q^{14} +(-3.73861 - 1.01132i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.73861 + 1.58114i) q^{17} +(2.93649 + 0.614017i) q^{18} +(4.23861 + 2.44716i) q^{19} +(1.41421 - 1.73205i) q^{20} +(-4.57357 - 0.287233i) q^{21} -0.213422i q^{22} +(3.23861 - 5.60944i) q^{23} +(-1.01575 + 1.40294i) q^{24} +(-3.74264 + 3.31552i) q^{25} +(3.35071 - 5.80359i) q^{26} +(4.94975 + 1.58114i) q^{27} +(1.22938 - 2.34278i) q^{28} +2.02265i q^{29} +(2.74514 - 2.73207i) q^{30} +(-0.261387 + 0.150912i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.0380311 - 0.367696i) q^{33} -3.16228i q^{34} +(-3.55378 + 4.72976i) q^{35} +(-2.00000 + 2.23607i) q^{36} +(6.17913 + 3.56752i) q^{37} +(-4.23861 + 2.44716i) q^{38} +(6.80698 - 9.40169i) q^{39} +(0.792893 + 2.09077i) q^{40} +6.70141 q^{41} +(2.53553 - 3.81721i) q^{42} +2.02265i q^{43} +(0.184829 + 0.106711i) q^{44} +(5.21633 - 4.21780i) q^{45} +(3.23861 + 5.60944i) q^{46} +(6.71584 + 3.87739i) q^{47} +(-0.707107 - 1.58114i) q^{48} +(-3.00000 + 6.32456i) q^{49} +(-1.00000 - 4.89898i) q^{50} +(0.563508 - 5.44816i) q^{51} +(3.35071 + 5.80359i) q^{52} +(-2.50000 - 4.33013i) q^{53} +(-3.84418 + 3.49604i) q^{54} +(-0.369657 - 0.301824i) q^{55} +(1.41421 + 2.23607i) q^{56} +(-7.73861 + 3.46081i) q^{57} +(-1.75166 - 1.01132i) q^{58} +(2.45877 + 4.25871i) q^{59} +(0.993475 + 3.74340i) q^{60} +(3.00000 + 1.73205i) q^{61} -0.301824i q^{62} +(5.04858 - 6.12469i) q^{63} +1.00000 q^{64} +(-5.31350 - 14.0111i) q^{65} +(0.299418 + 0.216784i) q^{66} +(4.61230 - 2.66291i) q^{67} +(2.73861 + 1.58114i) q^{68} +(4.58009 + 10.2414i) q^{69} +(-2.31920 - 5.44255i) q^{70} -2.02265i q^{71} +(-0.936492 - 2.85008i) q^{72} +(-5.99430 - 10.3824i) q^{73} +(-6.17913 + 3.56752i) q^{74} +(-0.849876 - 8.61845i) q^{75} -4.89433i q^{76} +(-0.500000 - 0.262377i) q^{77} +(4.73861 + 10.5959i) q^{78} +(-0.261387 + 0.452736i) q^{79} +(-2.20711 - 0.358719i) q^{80} +(-7.24597 + 5.33816i) q^{81} +(-3.35071 + 5.80359i) q^{82} +16.7169i q^{83} +(2.03803 + 4.10444i) q^{84} +(-5.47723 - 4.47214i) q^{85} +(-1.75166 - 1.01132i) q^{86} +(-2.83766 - 2.05451i) q^{87} +(-0.184829 + 0.106711i) q^{88} +(5.28720 - 9.15769i) q^{89} +(1.04456 + 6.62638i) q^{90} +(-9.47723 - 14.9848i) q^{91} -6.47723 q^{92} +(0.0537841 - 0.520000i) q^{93} +(-6.71584 + 3.87739i) q^{94} +(-1.75569 + 10.8023i) q^{95} +(1.72286 + 0.178197i) q^{96} +3.50333 q^{97} +(-3.97723 - 5.76035i) q^{98} +(0.477226 + 0.426844i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{2} - 4 q^{4} + 12 q^{5} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{2} - 4 q^{4} + 12 q^{5} + 8 q^{8} + 8 q^{9} - 12 q^{10} - 8 q^{15} - 4 q^{16} + 8 q^{18} + 12 q^{19} + 4 q^{21} + 4 q^{23} + 4 q^{25} + 4 q^{30} - 24 q^{31} - 4 q^{32} - 12 q^{33} - 8 q^{35} - 16 q^{36} - 12 q^{38} - 8 q^{39} + 12 q^{40} - 8 q^{42} + 24 q^{45} + 4 q^{46} - 12 q^{47} - 24 q^{49} - 8 q^{50} + 20 q^{51} - 20 q^{53} - 40 q^{57} + 4 q^{60} + 24 q^{61} + 20 q^{63} + 8 q^{64} + 16 q^{65} + 12 q^{66} - 8 q^{70} + 8 q^{72} - 24 q^{75} - 4 q^{77} + 16 q^{78} - 24 q^{79} - 12 q^{80} + 4 q^{81} + 4 q^{84} + 12 q^{87} - 32 q^{91} - 8 q^{92} - 20 q^{93} + 12 q^{94} + 12 q^{95} + 12 q^{98} - 40 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) −1.01575 + 1.40294i −0.586445 + 0.809989i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0.792893 + 2.09077i 0.354593 + 0.935021i
\(6\) −0.707107 1.58114i −0.288675 0.645497i
\(7\) 1.41421 + 2.23607i 0.534522 + 0.845154i
\(8\) 1.00000 0.353553
\(9\) −0.936492 2.85008i −0.312164 0.950028i
\(10\) −2.20711 0.358719i −0.697948 0.113437i
\(11\) −0.184829 + 0.106711i −0.0557279 + 0.0321745i −0.527605 0.849490i \(-0.676910\pi\)
0.471877 + 0.881664i \(0.343577\pi\)
\(12\) 1.72286 + 0.178197i 0.497347 + 0.0514410i
\(13\) −6.70141 −1.85864 −0.929318 0.369279i \(-0.879605\pi\)
−0.929318 + 0.369279i \(0.879605\pi\)
\(14\) −2.64360 + 0.106711i −0.706531 + 0.0285197i
\(15\) −3.73861 1.01132i −0.965306 0.261123i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.73861 + 1.58114i −0.664211 + 0.383482i −0.793880 0.608075i \(-0.791942\pi\)
0.129668 + 0.991557i \(0.458609\pi\)
\(18\) 2.93649 + 0.614017i 0.692138 + 0.144725i
\(19\) 4.23861 + 2.44716i 0.972404 + 0.561418i 0.899968 0.435955i \(-0.143589\pi\)
0.0724360 + 0.997373i \(0.476923\pi\)
\(20\) 1.41421 1.73205i 0.316228 0.387298i
\(21\) −4.57357 0.287233i −0.998034 0.0626795i
\(22\) 0.213422i 0.0455017i
\(23\) 3.23861 5.60944i 0.675297 1.16965i −0.301084 0.953597i \(-0.597349\pi\)
0.976382 0.216052i \(-0.0693181\pi\)
\(24\) −1.01575 + 1.40294i −0.207340 + 0.286374i
\(25\) −3.74264 + 3.31552i −0.748528 + 0.663103i
\(26\) 3.35071 5.80359i 0.657127 1.13818i
\(27\) 4.94975 + 1.58114i 0.952579 + 0.304290i
\(28\) 1.22938 2.34278i 0.232332 0.442744i
\(29\) 2.02265i 0.375596i 0.982208 + 0.187798i \(0.0601350\pi\)
−0.982208 + 0.187798i \(0.939865\pi\)
\(30\) 2.74514 2.73207i 0.501191 0.498806i
\(31\) −0.261387 + 0.150912i −0.0469465 + 0.0271046i −0.523290 0.852155i \(-0.675295\pi\)
0.476343 + 0.879260i \(0.341962\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0.0380311 0.367696i 0.00662037 0.0640076i
\(34\) 3.16228i 0.542326i
\(35\) −3.55378 + 4.72976i −0.600699 + 0.799475i
\(36\) −2.00000 + 2.23607i −0.333333 + 0.372678i
\(37\) 6.17913 + 3.56752i 1.01584 + 0.586497i 0.912897 0.408190i \(-0.133840\pi\)
0.102946 + 0.994687i \(0.467173\pi\)
\(38\) −4.23861 + 2.44716i −0.687594 + 0.396982i
\(39\) 6.80698 9.40169i 1.08999 1.50548i
\(40\) 0.792893 + 2.09077i 0.125367 + 0.330580i
\(41\) 6.70141 1.04658 0.523292 0.852153i \(-0.324704\pi\)
0.523292 + 0.852153i \(0.324704\pi\)
\(42\) 2.53553 3.81721i 0.391241 0.589008i
\(43\) 2.02265i 0.308451i 0.988036 + 0.154225i \(0.0492882\pi\)
−0.988036 + 0.154225i \(0.950712\pi\)
\(44\) 0.184829 + 0.106711i 0.0278640 + 0.0160873i
\(45\) 5.21633 4.21780i 0.777605 0.628753i
\(46\) 3.23861 + 5.60944i 0.477507 + 0.827067i
\(47\) 6.71584 + 3.87739i 0.979606 + 0.565576i 0.902151 0.431420i \(-0.141987\pi\)
0.0774546 + 0.996996i \(0.475321\pi\)
\(48\) −0.707107 1.58114i −0.102062 0.228218i
\(49\) −3.00000 + 6.32456i −0.428571 + 0.903508i
\(50\) −1.00000 4.89898i −0.141421 0.692820i
\(51\) 0.563508 5.44816i 0.0789069 0.762895i
\(52\) 3.35071 + 5.80359i 0.464659 + 0.804813i
\(53\) −2.50000 4.33013i −0.343401 0.594789i 0.641661 0.766989i \(-0.278246\pi\)
−0.985062 + 0.172200i \(0.944912\pi\)
\(54\) −3.84418 + 3.49604i −0.523127 + 0.475750i
\(55\) −0.369657 0.301824i −0.0498446 0.0406979i
\(56\) 1.41421 + 2.23607i 0.188982 + 0.298807i
\(57\) −7.73861 + 3.46081i −1.02500 + 0.458396i
\(58\) −1.75166 1.01132i −0.230005 0.132793i
\(59\) 2.45877 + 4.25871i 0.320105 + 0.554437i 0.980509 0.196472i \(-0.0629486\pi\)
−0.660405 + 0.750910i \(0.729615\pi\)
\(60\) 0.993475 + 3.74340i 0.128257 + 0.483270i
\(61\) 3.00000 + 1.73205i 0.384111 + 0.221766i 0.679605 0.733578i \(-0.262151\pi\)
−0.295495 + 0.955344i \(0.595484\pi\)
\(62\) 0.301824i 0.0383317i
\(63\) 5.04858 6.12469i 0.636062 0.771638i
\(64\) 1.00000 0.125000
\(65\) −5.31350 14.0111i −0.659059 1.73786i
\(66\) 0.299418 + 0.216784i 0.0368558 + 0.0266842i
\(67\) 4.61230 2.66291i 0.563482 0.325326i −0.191060 0.981578i \(-0.561192\pi\)
0.754542 + 0.656252i \(0.227859\pi\)
\(68\) 2.73861 + 1.58114i 0.332106 + 0.191741i
\(69\) 4.58009 + 10.2414i 0.551378 + 1.23292i
\(70\) −2.31920 5.44255i −0.277197 0.650509i
\(71\) 2.02265i 0.240044i −0.992771 0.120022i \(-0.961703\pi\)
0.992771 0.120022i \(-0.0382965\pi\)
\(72\) −0.936492 2.85008i −0.110367 0.335886i
\(73\) −5.99430 10.3824i −0.701580 1.21517i −0.967912 0.251291i \(-0.919145\pi\)
0.266331 0.963882i \(-0.414188\pi\)
\(74\) −6.17913 + 3.56752i −0.718310 + 0.414716i
\(75\) −0.849876 8.61845i −0.0981353 0.995173i
\(76\) 4.89433i 0.561418i
\(77\) −0.500000 0.262377i −0.0569803 0.0299007i
\(78\) 4.73861 + 10.5959i 0.536542 + 1.19974i
\(79\) −0.261387 + 0.452736i −0.0294084 + 0.0509368i −0.880355 0.474315i \(-0.842696\pi\)
0.850947 + 0.525252i \(0.176029\pi\)
\(80\) −2.20711 0.358719i −0.246762 0.0401061i
\(81\) −7.24597 + 5.33816i −0.805107 + 0.593129i
\(82\) −3.35071 + 5.80359i −0.370023 + 0.640899i
\(83\) 16.7169i 1.83491i 0.397835 + 0.917457i \(0.369762\pi\)
−0.397835 + 0.917457i \(0.630238\pi\)
\(84\) 2.03803 + 4.10444i 0.222367 + 0.447831i
\(85\) −5.47723 4.47214i −0.594089 0.485071i
\(86\) −1.75166 1.01132i −0.188887 0.109054i
\(87\) −2.83766 2.05451i −0.304229 0.220266i
\(88\) −0.184829 + 0.106711i −0.0197028 + 0.0113754i
\(89\) 5.28720 9.15769i 0.560442 0.970714i −0.437016 0.899454i \(-0.643965\pi\)
0.997458 0.0712599i \(-0.0227020\pi\)
\(90\) 1.04456 + 6.62638i 0.110106 + 0.698482i
\(91\) −9.47723 14.9848i −0.993483 1.57083i
\(92\) −6.47723 −0.675297
\(93\) 0.0537841 0.520000i 0.00557715 0.0539215i
\(94\) −6.71584 + 3.87739i −0.692686 + 0.399922i
\(95\) −1.75569 + 10.8023i −0.180130 + 1.10829i
\(96\) 1.72286 + 0.178197i 0.175839 + 0.0181872i
\(97\) 3.50333 0.355709 0.177854 0.984057i \(-0.443084\pi\)
0.177854 + 0.984057i \(0.443084\pi\)
\(98\) −3.97723 5.76035i −0.401760 0.581884i
\(99\) 0.477226 + 0.426844i 0.0479630 + 0.0428994i
\(100\) 4.74264 + 1.58346i 0.474264 + 0.158346i
\(101\) 5.65685 + 9.79796i 0.562878 + 0.974933i 0.997244 + 0.0741967i \(0.0236393\pi\)
−0.434366 + 0.900737i \(0.643027\pi\)
\(102\) 4.43649 + 3.21209i 0.439278 + 0.318045i
\(103\) 5.28720 9.15769i 0.520963 0.902334i −0.478740 0.877957i \(-0.658906\pi\)
0.999703 0.0243776i \(-0.00776038\pi\)
\(104\) −6.70141 −0.657127
\(105\) −3.02581 9.79002i −0.295289 0.955408i
\(106\) 5.00000 0.485643
\(107\) −2.73861 + 4.74342i −0.264752 + 0.458563i −0.967499 0.252877i \(-0.918623\pi\)
0.702747 + 0.711440i \(0.251957\pi\)
\(108\) −1.10557 5.07718i −0.106383 0.488552i
\(109\) −6.21584 10.7661i −0.595369 1.03121i −0.993495 0.113879i \(-0.963672\pi\)
0.398125 0.917331i \(-0.369661\pi\)
\(110\) 0.446216 0.169221i 0.0425450 0.0161346i
\(111\) −11.2815 + 5.04524i −1.07079 + 0.478873i
\(112\) −2.64360 + 0.106711i −0.249797 + 0.0100832i
\(113\) 6.52277 0.613611 0.306806 0.951772i \(-0.400740\pi\)
0.306806 + 0.951772i \(0.400740\pi\)
\(114\) 0.872155 8.43224i 0.0816848 0.789752i
\(115\) 14.2959 + 2.32351i 1.33310 + 0.216668i
\(116\) 1.75166 1.01132i 0.162638 0.0938990i
\(117\) 6.27582 + 19.0996i 0.580199 + 1.76576i
\(118\) −4.91754 −0.452696
\(119\) −7.40852 3.88766i −0.679138 0.356381i
\(120\) −3.73861 1.01132i −0.341287 0.0923207i
\(121\) −5.47723 + 9.48683i −0.497930 + 0.862439i
\(122\) −3.00000 + 1.73205i −0.271607 + 0.156813i
\(123\) −6.80698 + 9.40169i −0.613765 + 0.847722i
\(124\) 0.261387 + 0.150912i 0.0234733 + 0.0135523i
\(125\) −9.89949 5.19615i −0.885438 0.464758i
\(126\) 2.77984 + 7.43455i 0.247648 + 0.662322i
\(127\) 13.6298i 1.20945i −0.796434 0.604726i \(-0.793283\pi\)
0.796434 0.604726i \(-0.206717\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −2.83766 2.05451i −0.249842 0.180889i
\(130\) 14.7907 + 2.40393i 1.29723 + 0.210838i
\(131\) −3.01326 + 5.21911i −0.263269 + 0.455996i −0.967109 0.254363i \(-0.918134\pi\)
0.703839 + 0.710359i \(0.251467\pi\)
\(132\) −0.337449 + 0.150912i −0.0293712 + 0.0131352i
\(133\) 0.522278 + 12.9386i 0.0452873 + 1.12192i
\(134\) 5.32582i 0.460081i
\(135\) 0.618823 + 11.6025i 0.0532598 + 0.998581i
\(136\) −2.73861 + 1.58114i −0.234834 + 0.135582i
\(137\) −3.73861 6.47547i −0.319411 0.553237i 0.660954 0.750426i \(-0.270152\pi\)
−0.980365 + 0.197190i \(0.936818\pi\)
\(138\) −11.1594 1.15422i −0.949947 0.0982539i
\(139\) 7.53185i 0.638843i −0.947613 0.319422i \(-0.896511\pi\)
0.947613 0.319422i \(-0.103489\pi\)
\(140\) 5.87298 + 0.712788i 0.496358 + 0.0602416i
\(141\) −12.2614 + 5.48346i −1.03260 + 0.461791i
\(142\) 1.75166 + 1.01132i 0.146996 + 0.0848683i
\(143\) 1.23861 0.715113i 0.103578 0.0598008i
\(144\) 2.93649 + 0.614017i 0.244708 + 0.0511681i
\(145\) −4.22889 + 1.60374i −0.351190 + 0.133184i
\(146\) 11.9886 0.992184
\(147\) −5.82572 10.6330i −0.480498 0.876996i
\(148\) 7.13505i 0.586497i
\(149\) −2.12132 1.22474i −0.173785 0.100335i 0.410584 0.911823i \(-0.365325\pi\)
−0.584370 + 0.811488i \(0.698658\pi\)
\(150\) 7.88874 + 3.57321i 0.644113 + 0.291751i
\(151\) 1.00000 + 1.73205i 0.0813788 + 0.140952i 0.903842 0.427865i \(-0.140734\pi\)
−0.822464 + 0.568818i \(0.807401\pi\)
\(152\) 4.23861 + 2.44716i 0.343797 + 0.198491i
\(153\) 7.07107 + 6.32456i 0.571662 + 0.511310i
\(154\) 0.477226 0.301824i 0.0384559 0.0243217i
\(155\) −0.522774 0.426844i −0.0419903 0.0342849i
\(156\) −11.5456 1.19417i −0.924387 0.0956102i
\(157\) −4.39526 7.61282i −0.350780 0.607569i 0.635606 0.772013i \(-0.280750\pi\)
−0.986386 + 0.164445i \(0.947417\pi\)
\(158\) −0.261387 0.452736i −0.0207949 0.0360177i
\(159\) 8.61430 + 0.890985i 0.683158 + 0.0706597i
\(160\) 1.41421 1.73205i 0.111803 0.136931i
\(161\) 17.1232 0.691190i 1.34950 0.0544734i
\(162\) −1.00000 8.94427i −0.0785674 0.702728i
\(163\) 12.7279 + 7.34847i 0.996928 + 0.575577i 0.907338 0.420402i \(-0.138111\pi\)
0.0895899 + 0.995979i \(0.471444\pi\)
\(164\) −3.35071 5.80359i −0.261646 0.453184i
\(165\) 0.798922 0.212029i 0.0621960 0.0165064i
\(166\) −14.4772 8.35843i −1.12365 0.648740i
\(167\) 14.6830i 1.13620i −0.822958 0.568102i \(-0.807678\pi\)
0.822958 0.568102i \(-0.192322\pi\)
\(168\) −4.57357 0.287233i −0.352858 0.0221605i
\(169\) 31.9089 2.45453
\(170\) 6.61160 2.50735i 0.507086 0.192305i
\(171\) 3.00520 14.3722i 0.229813 1.09907i
\(172\) 1.75166 1.01132i 0.133563 0.0771127i
\(173\) −9.97723 5.76035i −0.758554 0.437952i 0.0702221 0.997531i \(-0.477629\pi\)
−0.828776 + 0.559580i \(0.810963\pi\)
\(174\) 3.19808 1.43023i 0.242446 0.108425i
\(175\) −12.7066 3.67995i −0.960529 0.278178i
\(176\) 0.213422i 0.0160873i
\(177\) −8.47223 0.876291i −0.636812 0.0658660i
\(178\) 5.28720 + 9.15769i 0.396292 + 0.686398i
\(179\) 12.9128 7.45518i 0.965144 0.557226i 0.0673918 0.997727i \(-0.478532\pi\)
0.897752 + 0.440500i \(0.145199\pi\)
\(180\) −6.26089 2.40858i −0.466659 0.179525i
\(181\) 3.16228i 0.235050i 0.993070 + 0.117525i \(0.0374961\pi\)
−0.993070 + 0.117525i \(0.962504\pi\)
\(182\) 17.7158 0.715113i 1.31319 0.0530077i
\(183\) −5.47723 + 2.44949i −0.404888 + 0.181071i
\(184\) 3.23861 5.60944i 0.238754 0.413534i
\(185\) −2.55948 + 15.7478i −0.188177 + 1.15780i
\(186\) 0.423441 + 0.306579i 0.0310482 + 0.0224794i
\(187\) 0.337449 0.584480i 0.0246767 0.0427414i
\(188\) 7.75478i 0.565576i
\(189\) 3.46447 + 13.3040i 0.252003 + 0.967726i
\(190\) −8.47723 6.92163i −0.615003 0.502148i
\(191\) 1.38201 + 0.797901i 0.0999984 + 0.0577341i 0.549165 0.835714i \(-0.314946\pi\)
−0.449167 + 0.893448i \(0.648279\pi\)
\(192\) −1.01575 + 1.40294i −0.0733057 + 0.101249i
\(193\) 6.36396 3.67423i 0.458088 0.264477i −0.253152 0.967427i \(-0.581467\pi\)
0.711240 + 0.702949i \(0.248134\pi\)
\(194\) −1.75166 + 3.03397i −0.125762 + 0.217826i
\(195\) 25.0540 + 6.77729i 1.79415 + 0.485332i
\(196\) 6.97723 0.564201i 0.498373 0.0403001i
\(197\) 9.00000 0.641223 0.320612 0.947211i \(-0.396112\pi\)
0.320612 + 0.947211i \(0.396112\pi\)
\(198\) −0.608270 + 0.199868i −0.0432279 + 0.0142040i
\(199\) −19.4317 + 11.2189i −1.37748 + 0.795286i −0.991855 0.127372i \(-0.959346\pi\)
−0.385620 + 0.922658i \(0.626012\pi\)
\(200\) −3.74264 + 3.31552i −0.264645 + 0.234442i
\(201\) −0.949046 + 9.17565i −0.0669405 + 0.647200i
\(202\) −11.3137 −0.796030
\(203\) −4.52277 + 2.86045i −0.317437 + 0.200764i
\(204\) −5.00000 + 2.23607i −0.350070 + 0.156556i
\(205\) 5.31350 + 14.0111i 0.371111 + 0.978578i
\(206\) 5.28720 + 9.15769i 0.368376 + 0.638047i
\(207\) −19.0203 3.97713i −1.32200 0.276429i
\(208\) 3.35071 5.80359i 0.232330 0.402407i
\(209\) −1.04456 −0.0722535
\(210\) 9.99131 + 2.27458i 0.689466 + 0.156961i
\(211\) 13.5228 0.930946 0.465473 0.885062i \(-0.345884\pi\)
0.465473 + 0.885062i \(0.345884\pi\)
\(212\) −2.50000 + 4.33013i −0.171701 + 0.297394i
\(213\) 2.83766 + 2.05451i 0.194433 + 0.140773i
\(214\) −2.73861 4.74342i −0.187208 0.324253i
\(215\) −4.22889 + 1.60374i −0.288408 + 0.109374i
\(216\) 4.94975 + 1.58114i 0.336788 + 0.107583i
\(217\) −0.707107 0.371058i −0.0480015 0.0251890i
\(218\) 12.4317 0.841979
\(219\) 20.6547 + 2.13633i 1.39571 + 0.144360i
\(220\) −0.0765585 + 0.471045i −0.00516158 + 0.0317578i
\(221\) 18.3526 10.5959i 1.23453 0.712755i
\(222\) 1.27144 12.2927i 0.0853337 0.825031i
\(223\) −6.39617 −0.428319 −0.214160 0.976799i \(-0.568701\pi\)
−0.214160 + 0.976799i \(0.568701\pi\)
\(224\) 1.22938 2.34278i 0.0821417 0.156533i
\(225\) 12.9545 + 7.56189i 0.863630 + 0.504126i
\(226\) −3.26139 + 5.64889i −0.216944 + 0.375758i
\(227\) 9.00000 5.19615i 0.597351 0.344881i −0.170648 0.985332i \(-0.554586\pi\)
0.767999 + 0.640451i \(0.221253\pi\)
\(228\) 6.86646 + 4.97143i 0.454742 + 0.329241i
\(229\) −6.26139 3.61501i −0.413764 0.238887i 0.278642 0.960395i \(-0.410116\pi\)
−0.692406 + 0.721508i \(0.743449\pi\)
\(230\) −9.16018 + 11.2189i −0.604004 + 0.739751i
\(231\) 0.875977 0.434960i 0.0576350 0.0286183i
\(232\) 2.02265i 0.132793i
\(233\) 2.00000 3.46410i 0.131024 0.226941i −0.793047 0.609160i \(-0.791507\pi\)
0.924072 + 0.382219i \(0.124840\pi\)
\(234\) −19.6786 4.11478i −1.28643 0.268992i
\(235\) −2.78179 + 17.1156i −0.181464 + 1.11650i
\(236\) 2.45877 4.25871i 0.160052 0.277219i
\(237\) −0.369657 0.826579i −0.0240118 0.0536921i
\(238\) 7.07107 4.47214i 0.458349 0.289886i
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 2.74514 2.73207i 0.177198 0.176354i
\(241\) 3.45445 1.99443i 0.222521 0.128472i −0.384596 0.923085i \(-0.625659\pi\)
0.607117 + 0.794613i \(0.292326\pi\)
\(242\) −5.47723 9.48683i −0.352089 0.609837i
\(243\) −0.129018 15.5879i −0.00827648 0.999966i
\(244\) 3.46410i 0.221766i
\(245\) −15.6019 1.25761i −0.996767 0.0803460i
\(246\) −4.73861 10.5959i −0.302123 0.675567i
\(247\) −28.4047 16.3995i −1.80735 1.04347i
\(248\) −0.261387 + 0.150912i −0.0165981 + 0.00958292i
\(249\) −23.4528 16.9802i −1.48626 1.07608i
\(250\) 9.44975 5.97514i 0.597655 0.377901i
\(251\) −16.6009 −1.04784 −0.523920 0.851768i \(-0.675531\pi\)
−0.523920 + 0.851768i \(0.675531\pi\)
\(252\) −7.82843 1.30986i −0.493145 0.0825133i
\(253\) 1.38238i 0.0869095i
\(254\) 11.8038 + 6.81491i 0.740635 + 0.427606i
\(255\) 11.8377 3.14164i 0.741303 0.196737i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −20.4772 11.8225i −1.27733 0.737469i −0.300977 0.953631i \(-0.597313\pi\)
−0.976357 + 0.216162i \(0.930646\pi\)
\(258\) 3.19808 1.43023i 0.199104 0.0890420i
\(259\) 0.761387 + 18.8622i 0.0473103 + 1.17204i
\(260\) −9.47723 + 11.6072i −0.587753 + 0.719847i
\(261\) 5.76471 1.89419i 0.356827 0.117248i
\(262\) −3.01326 5.21911i −0.186160 0.322438i
\(263\) 1.00000 + 1.73205i 0.0616626 + 0.106803i 0.895209 0.445647i \(-0.147026\pi\)
−0.833546 + 0.552450i \(0.813693\pi\)
\(264\) 0.0380311 0.367696i 0.00234065 0.0226301i
\(265\) 7.07107 8.66025i 0.434372 0.531995i
\(266\) −11.4663 6.01701i −0.703046 0.368927i
\(267\) 7.47723 + 16.7196i 0.457599 + 1.02322i
\(268\) −4.61230 2.66291i −0.281741 0.162663i
\(269\) −14.4474 25.0236i −0.880872 1.52572i −0.850373 0.526180i \(-0.823624\pi\)
−0.0304992 0.999535i \(-0.509710\pi\)
\(270\) −10.3574 5.26531i −0.630333 0.320437i
\(271\) 5.47723 + 3.16228i 0.332718 + 0.192095i 0.657047 0.753850i \(-0.271805\pi\)
−0.324329 + 0.945944i \(0.605139\pi\)
\(272\) 3.16228i 0.191741i
\(273\) 30.6493 + 1.92487i 1.85498 + 0.116498i
\(274\) 7.47723 0.451716
\(275\) 0.337946 1.01218i 0.0203789 0.0610369i
\(276\) 6.57926 9.08717i 0.396025 0.546983i
\(277\) −8.48528 + 4.89898i −0.509831 + 0.294351i −0.732764 0.680483i \(-0.761770\pi\)
0.222933 + 0.974834i \(0.428437\pi\)
\(278\) 6.52277 + 3.76593i 0.391210 + 0.225865i
\(279\) 0.674899 + 0.603648i 0.0404051 + 0.0361395i
\(280\) −3.55378 + 4.72976i −0.212379 + 0.282657i
\(281\) 11.6072i 0.692427i −0.938156 0.346213i \(-0.887467\pi\)
0.938156 0.346213i \(-0.112533\pi\)
\(282\) 1.38188 13.3604i 0.0822897 0.795600i
\(283\) 12.3583 + 21.4051i 0.734623 + 1.27240i 0.954889 + 0.296964i \(0.0959741\pi\)
−0.220266 + 0.975440i \(0.570693\pi\)
\(284\) −1.75166 + 1.01132i −0.103942 + 0.0600110i
\(285\) −13.3717 13.4356i −0.792069 0.795857i
\(286\) 1.43023i 0.0845711i
\(287\) 9.47723 + 14.9848i 0.559423 + 0.884525i
\(288\) −2.00000 + 2.23607i −0.117851 + 0.131762i
\(289\) −3.50000 + 6.06218i −0.205882 + 0.356599i
\(290\) 0.725563 4.46420i 0.0426065 0.262147i
\(291\) −3.55851 + 4.91496i −0.208604 + 0.288120i
\(292\) −5.99430 + 10.3824i −0.350790 + 0.607586i
\(293\) 4.59250i 0.268297i 0.990961 + 0.134148i \(0.0428299\pi\)
−0.990961 + 0.134148i \(0.957170\pi\)
\(294\) 12.1213 + 0.271281i 0.706930 + 0.0158214i
\(295\) −6.95445 + 8.51743i −0.404904 + 0.495904i
\(296\) 6.17913 + 3.56752i 0.359155 + 0.207358i
\(297\) −1.08358 + 0.235952i −0.0628757 + 0.0136913i
\(298\) 2.12132 1.22474i 0.122885 0.0709476i
\(299\) −21.7033 + 37.5912i −1.25513 + 2.17395i
\(300\) −7.03886 + 5.04524i −0.406389 + 0.291287i
\(301\) −4.52277 + 2.86045i −0.260688 + 0.164874i
\(302\) −2.00000 −0.115087
\(303\) −19.4919 2.01607i −1.11978 0.115820i
\(304\) −4.23861 + 2.44716i −0.243101 + 0.140354i
\(305\) −1.24264 + 7.64564i −0.0711534 + 0.437788i
\(306\) −9.01276 + 2.96145i −0.515225 + 0.169295i
\(307\) −3.50333 −0.199945 −0.0999727 0.994990i \(-0.531876\pi\)
−0.0999727 + 0.994990i \(0.531876\pi\)
\(308\) 0.0227744 + 0.564201i 0.00129769 + 0.0321484i
\(309\) 7.47723 + 16.7196i 0.425365 + 0.951144i
\(310\) 0.631045 0.239314i 0.0358409 0.0135921i
\(311\) −14.4474 25.0236i −0.819236 1.41896i −0.906246 0.422750i \(-0.861065\pi\)
0.0870106 0.996207i \(-0.472269\pi\)
\(312\) 6.80698 9.40169i 0.385369 0.532266i
\(313\) −11.6190 + 20.1246i −0.656742 + 1.13751i 0.324712 + 0.945813i \(0.394733\pi\)
−0.981454 + 0.191697i \(0.938601\pi\)
\(314\) 8.79052 0.496078
\(315\) 16.8083 + 5.69921i 0.947041 + 0.321114i
\(316\) 0.522774 0.0294084
\(317\) −16.9545 + 29.3660i −0.952257 + 1.64936i −0.211733 + 0.977328i \(0.567911\pi\)
−0.740524 + 0.672030i \(0.765423\pi\)
\(318\) −5.07877 + 7.01471i −0.284803 + 0.393365i
\(319\) −0.215838 0.373843i −0.0120846 0.0209312i
\(320\) 0.792893 + 2.09077i 0.0443241 + 0.116878i
\(321\) −3.87298 8.66025i −0.216169 0.483368i
\(322\) −7.96300 + 15.1747i −0.443761 + 0.845653i
\(323\) −15.4772 −0.861176
\(324\) 8.24597 + 3.60611i 0.458109 + 0.200339i
\(325\) 25.0810 22.2186i 1.39124 1.23247i
\(326\) −12.7279 + 7.34847i −0.704934 + 0.406994i
\(327\) 21.4180 + 2.21529i 1.18442 + 0.122506i
\(328\) 6.70141 0.370023
\(329\) 0.827520 + 20.5005i 0.0456226 + 1.13023i
\(330\) −0.215838 + 0.797901i −0.0118815 + 0.0439230i
\(331\) 5.71584 9.90012i 0.314171 0.544160i −0.665090 0.746763i \(-0.731607\pi\)
0.979261 + 0.202603i \(0.0649402\pi\)
\(332\) 14.4772 8.35843i 0.794541 0.458728i
\(333\) 4.38104 20.9520i 0.240079 1.14816i
\(334\) 12.7158 + 7.34149i 0.695780 + 0.401709i
\(335\) 9.22460 + 7.53185i 0.503994 + 0.411509i
\(336\) 2.53553 3.81721i 0.138325 0.208246i
\(337\) 17.1464i 0.934025i −0.884251 0.467013i \(-0.845330\pi\)
0.884251 0.467013i \(-0.154670\pi\)
\(338\) −15.9545 + 27.6339i −0.867808 + 1.50309i
\(339\) −6.62553 + 9.15107i −0.359849 + 0.497018i
\(340\) −1.13437 + 6.97948i −0.0615199 + 0.378516i
\(341\) 0.0322079 0.0557857i 0.00174416 0.00302097i
\(342\) 10.9441 + 9.78866i 0.591787 + 0.529310i
\(343\) −18.3848 + 2.23607i −0.992685 + 0.120736i
\(344\) 2.02265i 0.109054i
\(345\) −17.7809 + 17.6962i −0.957290 + 0.952734i
\(346\) 9.97723 5.76035i 0.536379 0.309679i
\(347\) 3.26139 + 5.64889i 0.175080 + 0.303248i 0.940189 0.340653i \(-0.110648\pi\)
−0.765109 + 0.643901i \(0.777315\pi\)
\(348\) −0.360429 + 3.48474i −0.0193210 + 0.186801i
\(349\) 32.5282i 1.74120i −0.491994 0.870599i \(-0.663732\pi\)
0.491994 0.870599i \(-0.336268\pi\)
\(350\) 9.54024 9.16427i 0.509947 0.489851i
\(351\) −33.1703 10.5959i −1.77050 0.565565i
\(352\) 0.184829 + 0.106711i 0.00985140 + 0.00568771i
\(353\) 11.4772 6.62638i 0.610871 0.352687i −0.162435 0.986719i \(-0.551935\pi\)
0.773306 + 0.634033i \(0.218602\pi\)
\(354\) 4.99501 6.89902i 0.265482 0.366679i
\(355\) 4.22889 1.60374i 0.224446 0.0851178i
\(356\) −10.5744 −0.560442
\(357\) 12.9794 6.44482i 0.686942 0.341096i
\(358\) 14.9104i 0.788037i
\(359\) −5.62465 3.24739i −0.296857 0.171391i 0.344173 0.938906i \(-0.388159\pi\)
−0.641030 + 0.767516i \(0.721493\pi\)
\(360\) 5.21633 4.21780i 0.274925 0.222298i
\(361\) 2.47723 + 4.29068i 0.130380 + 0.225825i
\(362\) −2.73861 1.58114i −0.143938 0.0831028i
\(363\) −7.74597 17.3205i −0.406558 0.909091i
\(364\) −8.23861 + 15.6999i −0.431821 + 0.822900i
\(365\) 16.9545 20.7649i 0.887437 1.08688i
\(366\) 0.617292 5.96816i 0.0322664 0.311961i
\(367\) 4.05781 + 7.02834i 0.211816 + 0.366876i 0.952283 0.305217i \(-0.0987289\pi\)
−0.740467 + 0.672093i \(0.765396\pi\)
\(368\) 3.23861 + 5.60944i 0.168824 + 0.292412i
\(369\) −6.27582 19.0996i −0.326706 0.994285i
\(370\) −12.3583 10.0905i −0.642476 0.524579i
\(371\) 6.14692 11.7139i 0.319132 0.608155i
\(372\) −0.477226 + 0.213422i −0.0247430 + 0.0110654i
\(373\) 3.13367 + 1.80922i 0.162255 + 0.0936781i 0.578929 0.815378i \(-0.303471\pi\)
−0.416674 + 0.909056i \(0.636804\pi\)
\(374\) 0.337449 + 0.584480i 0.0174491 + 0.0302227i
\(375\) 17.3453 8.61041i 0.895710 0.444640i
\(376\) 6.71584 + 3.87739i 0.346343 + 0.199961i
\(377\) 13.5546i 0.698097i
\(378\) −13.2539 3.65170i −0.681705 0.187823i
\(379\) −9.52277 −0.489152 −0.244576 0.969630i \(-0.578649\pi\)
−0.244576 + 0.969630i \(0.578649\pi\)
\(380\) 10.2329 3.88068i 0.524938 0.199075i
\(381\) 19.1219 + 13.8445i 0.979642 + 0.709277i
\(382\) −1.38201 + 0.797901i −0.0707096 + 0.0408242i
\(383\) −0.715838 0.413289i −0.0365776 0.0211181i 0.481600 0.876391i \(-0.340056\pi\)
−0.518177 + 0.855273i \(0.673389\pi\)
\(384\) −0.707107 1.58114i −0.0360844 0.0806872i
\(385\) 0.152124 1.25342i 0.00775298 0.0638803i
\(386\) 7.34847i 0.374027i
\(387\) 5.76471 1.89419i 0.293037 0.0962872i
\(388\) −1.75166 3.03397i −0.0889272 0.154026i
\(389\) 6.36396 3.67423i 0.322666 0.186291i −0.329914 0.944011i \(-0.607020\pi\)
0.652580 + 0.757720i \(0.273687\pi\)
\(390\) −18.3963 + 18.3087i −0.931533 + 0.927099i
\(391\) 20.4828i 1.03586i
\(392\) −3.00000 + 6.32456i −0.151523 + 0.319438i
\(393\) −4.26139 9.52875i −0.214959 0.480662i
\(394\) −4.50000 + 7.79423i −0.226707 + 0.392668i
\(395\) −1.15382 0.187529i −0.0580549 0.00943563i
\(396\) 0.131045 0.626711i 0.00658524 0.0314934i
\(397\) 15.1867 26.3041i 0.762198 1.32017i −0.179517 0.983755i \(-0.557453\pi\)
0.941715 0.336411i \(-0.109213\pi\)
\(398\) 22.4378i 1.12470i
\(399\) −18.6827 12.4097i −0.935303 0.621264i
\(400\) −1.00000 4.89898i −0.0500000 0.244949i
\(401\) 26.2834 + 15.1747i 1.31253 + 0.757789i 0.982514 0.186187i \(-0.0596131\pi\)
0.330014 + 0.943976i \(0.392946\pi\)
\(402\) −7.47182 5.40972i −0.372661 0.269812i
\(403\) 1.75166 1.01132i 0.0872565 0.0503776i
\(404\) 5.65685 9.79796i 0.281439 0.487467i
\(405\) −16.9061 10.9171i −0.840073 0.542473i
\(406\) −0.215838 5.34706i −0.0107119 0.265370i
\(407\) −1.52277 −0.0754811
\(408\) 0.563508 5.44816i 0.0278978 0.269724i
\(409\) −19.4317 + 11.2189i −0.960835 + 0.554738i −0.896430 0.443186i \(-0.853848\pi\)
−0.0644048 + 0.997924i \(0.520515\pi\)
\(410\) −14.7907 2.40393i −0.730462 0.118721i
\(411\) 12.8822 + 1.33242i 0.635433 + 0.0657234i
\(412\) −10.5744 −0.520963
\(413\) −6.04555 + 11.5207i −0.297482 + 0.566897i
\(414\) 12.9545 14.4835i 0.636677 0.711826i
\(415\) −34.9511 + 13.2547i −1.71568 + 0.650647i
\(416\) 3.35071 + 5.80359i 0.164282 + 0.284544i
\(417\) 10.5667 + 7.65050i 0.517456 + 0.374647i
\(418\) 0.522278 0.904612i 0.0255455 0.0442460i
\(419\) 16.6009 0.811007 0.405504 0.914093i \(-0.367096\pi\)
0.405504 + 0.914093i \(0.367096\pi\)
\(420\) −6.96550 + 7.51544i −0.339882 + 0.366716i
\(421\) −2.95445 −0.143991 −0.0719956 0.997405i \(-0.522937\pi\)
−0.0719956 + 0.997405i \(0.522937\pi\)
\(422\) −6.76139 + 11.7111i −0.329139 + 0.570086i
\(423\) 4.76157 22.7719i 0.231515 1.10721i
\(424\) −2.50000 4.33013i −0.121411 0.210290i
\(425\) 5.00735 14.9975i 0.242892 0.727488i
\(426\) −3.19808 + 1.43023i −0.154948 + 0.0692947i
\(427\) 0.369657 + 9.15769i 0.0178890 + 0.443172i
\(428\) 5.47723 0.264752
\(429\) −0.254862 + 2.46408i −0.0123049 + 0.118967i
\(430\) 0.725563 4.46420i 0.0349897 0.215283i
\(431\) −32.0928 + 18.5288i −1.54586 + 0.892501i −0.547406 + 0.836867i \(0.684385\pi\)
−0.998451 + 0.0556344i \(0.982282\pi\)
\(432\) −3.84418 + 3.49604i −0.184953 + 0.168203i
\(433\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) 0.674899 0.426844i 0.0323962 0.0204891i
\(435\) 2.04555 7.56189i 0.0980766 0.362565i
\(436\) −6.21584 + 10.7661i −0.297685 + 0.515605i
\(437\) 27.4545 15.8508i 1.31332 0.758248i
\(438\) −12.1775 + 16.8193i −0.581862 + 0.803658i
\(439\) 19.6931 + 11.3698i 0.939899 + 0.542651i 0.889929 0.456100i \(-0.150754\pi\)
0.0499701 + 0.998751i \(0.484087\pi\)
\(440\) −0.369657 0.301824i −0.0176227 0.0143889i
\(441\) 20.8350 + 2.62736i 0.992143 + 0.125112i
\(442\) 21.1917i 1.00799i
\(443\) 18.4772 32.0035i 0.877879 1.52053i 0.0242161 0.999707i \(-0.492291\pi\)
0.853663 0.520825i \(-0.174376\pi\)
\(444\) 10.0101 + 7.24745i 0.475056 + 0.343949i
\(445\) 23.3388 + 3.79324i 1.10637 + 0.179817i
\(446\) 3.19808 5.53924i 0.151434 0.262291i
\(447\) 3.87298 1.73205i 0.183186 0.0819232i
\(448\) 1.41421 + 2.23607i 0.0668153 + 0.105644i
\(449\) 3.51660i 0.165959i 0.996551 + 0.0829793i \(0.0264435\pi\)
−0.996551 + 0.0829793i \(0.973556\pi\)
\(450\) −13.0260 + 7.43794i −0.614052 + 0.350628i
\(451\) −1.23861 + 0.715113i −0.0583240 + 0.0336734i
\(452\) −3.26139 5.64889i −0.153403 0.265701i
\(453\) −3.44572 0.356394i −0.161894 0.0167448i
\(454\) 10.3923i 0.487735i
\(455\) 23.8154 31.6961i 1.11648 1.48593i
\(456\) −7.73861 + 3.46081i −0.362394 + 0.162067i
\(457\) 32.8322 + 18.9557i 1.53582 + 0.886708i 0.999077 + 0.0429646i \(0.0136803\pi\)
0.536747 + 0.843743i \(0.319653\pi\)
\(458\) 6.26139 3.61501i 0.292575 0.168918i
\(459\) −16.0554 + 3.49611i −0.749404 + 0.163184i
\(460\) −5.13575 13.5424i −0.239455 0.631417i
\(461\) 16.2957 0.758965 0.379482 0.925199i \(-0.376102\pi\)
0.379482 + 0.925199i \(0.376102\pi\)
\(462\) −0.0613019 + 0.976098i −0.00285202 + 0.0454122i
\(463\) 17.6751i 0.821433i −0.911763 0.410716i \(-0.865279\pi\)
0.911763 0.410716i \(-0.134721\pi\)
\(464\) −1.75166 1.01132i −0.0813189 0.0469495i
\(465\) 1.12985 0.299855i 0.0523954 0.0139054i
\(466\) 2.00000 + 3.46410i 0.0926482 + 0.160471i
\(467\) −29.7386 17.1696i −1.37614 0.794514i −0.384447 0.923147i \(-0.625608\pi\)
−0.991692 + 0.128633i \(0.958941\pi\)
\(468\) 13.4028 14.9848i 0.619546 0.692673i
\(469\) 12.4772 + 6.54749i 0.576145 + 0.302335i
\(470\) −13.4317 10.9669i −0.619557 0.505866i
\(471\) 15.1448 + 1.56644i 0.697837 + 0.0721780i
\(472\) 2.45877 + 4.25871i 0.113174 + 0.196023i
\(473\) −0.215838 0.373843i −0.00992426 0.0171893i
\(474\) 0.900667 + 0.0931568i 0.0413690 + 0.00427883i
\(475\) −23.9772 + 4.89433i −1.10015 + 0.224567i
\(476\) 0.337449 + 8.35979i 0.0154670 + 0.383170i
\(477\) −10.0000 + 11.1803i −0.457869 + 0.511913i
\(478\) 0 0
\(479\) −5.68906 9.85374i −0.259940 0.450229i 0.706286 0.707927i \(-0.250369\pi\)
−0.966226 + 0.257698i \(0.917036\pi\)
\(480\) 0.993475 + 3.74340i 0.0453457 + 0.170862i
\(481\) −41.4089 23.9074i −1.88808 1.09009i
\(482\) 3.98886i 0.181687i
\(483\) −16.4232 + 24.7249i −0.747283 + 1.12502i
\(484\) 10.9545 0.497930
\(485\) 2.77776 + 7.32465i 0.126132 + 0.332595i
\(486\) 13.5640 + 7.68223i 0.615278 + 0.348473i
\(487\) 31.7232 18.3154i 1.43751 0.829949i 0.439838 0.898077i \(-0.355036\pi\)
0.997677 + 0.0681277i \(0.0217025\pi\)
\(488\) 3.00000 + 1.73205i 0.135804 + 0.0784063i
\(489\) −23.2379 + 10.3923i −1.05085 + 0.469956i
\(490\) 8.89006 12.8828i 0.401612 0.581986i
\(491\) 4.04529i 0.182561i 0.995825 + 0.0912807i \(0.0290961\pi\)
−0.995825 + 0.0912807i \(0.970904\pi\)
\(492\) 11.5456 + 1.19417i 0.520515 + 0.0538374i
\(493\) −3.19808 5.53924i −0.144034 0.249475i
\(494\) 28.4047 16.3995i 1.27799 0.737846i
\(495\) −0.514043 + 1.33621i −0.0231045 + 0.0600582i
\(496\) 0.301824i 0.0135523i
\(497\) 4.52277 2.86045i 0.202874 0.128309i
\(498\) 26.4317 11.8206i 1.18443 0.529694i
\(499\) 20.9545 36.2942i 0.938050 1.62475i 0.168947 0.985625i \(-0.445963\pi\)
0.769103 0.639125i \(-0.220703\pi\)
\(500\) 0.449747 + 11.1713i 0.0201133 + 0.499595i
\(501\) 20.5994 + 14.9143i 0.920312 + 0.666321i
\(502\) 8.30045 14.3768i 0.370467 0.641668i
\(503\) 22.4378i 1.00045i 0.865895 + 0.500225i \(0.166749\pi\)
−0.865895 + 0.500225i \(0.833251\pi\)
\(504\) 5.04858 6.12469i 0.224882 0.272815i
\(505\) −16.0000 + 19.5959i −0.711991 + 0.872007i
\(506\) −1.19718 0.691190i −0.0532210 0.0307272i
\(507\) −32.4116 + 44.7663i −1.43945 + 1.98814i
\(508\) −11.8038 + 6.81491i −0.523708 + 0.302363i
\(509\) −4.61230 + 7.98873i −0.204437 + 0.354094i −0.949953 0.312393i \(-0.898870\pi\)
0.745517 + 0.666487i \(0.232203\pi\)
\(510\) −3.19808 + 11.8225i −0.141614 + 0.523511i
\(511\) 14.7386 28.0867i 0.651998 1.24248i
\(512\) 1.00000 0.0441942
\(513\) 17.1108 + 18.8147i 0.755458 + 0.830688i
\(514\) 20.4772 11.8225i 0.903212 0.521470i
\(515\) 23.3388 + 3.79324i 1.02843 + 0.167150i
\(516\) −0.360429 + 3.48474i −0.0158670 + 0.153407i
\(517\) −1.65504 −0.0727885
\(518\) −16.7158 8.77172i −0.734452 0.385407i
\(519\) 18.2158 8.14637i 0.799587 0.357586i
\(520\) −5.31350 14.0111i −0.233013 0.614428i
\(521\) 9.31280 + 16.1302i 0.408001 + 0.706679i 0.994666 0.103151i \(-0.0328926\pi\)
−0.586664 + 0.809830i \(0.699559\pi\)
\(522\) −1.24194 + 5.93948i −0.0543582 + 0.259964i
\(523\) 7.03886 12.1917i 0.307788 0.533104i −0.670090 0.742280i \(-0.733745\pi\)
0.977878 + 0.209175i \(0.0670780\pi\)
\(524\) 6.02651 0.263269
\(525\) 18.0695 14.0887i 0.788619 0.614882i
\(526\) −2.00000 −0.0872041
\(527\) 0.477226 0.826579i 0.0207883 0.0360063i
\(528\) 0.299418 + 0.216784i 0.0130305 + 0.00943430i
\(529\) −9.47723 16.4150i −0.412053 0.713697i
\(530\) 3.96447 + 10.4539i 0.172205 + 0.454086i
\(531\) 9.83508 10.9960i 0.426806 0.477184i
\(532\) 10.9441 6.92163i 0.474485 0.300091i
\(533\) −44.9089 −1.94522
\(534\) −18.2182 1.88433i −0.788379 0.0815427i
\(535\) −12.0888 1.96479i −0.522645 0.0849452i
\(536\) 4.61230 2.66291i 0.199221 0.115020i
\(537\) −2.65698 + 25.6885i −0.114657 + 1.10854i
\(538\) 28.8948 1.24574
\(539\) −0.120413 1.48909i −0.00518655 0.0641397i
\(540\) 9.73861 6.33715i 0.419083 0.272707i
\(541\) −9.73861 + 16.8678i −0.418696 + 0.725202i −0.995809 0.0914622i \(-0.970846\pi\)
0.577113 + 0.816664i \(0.304179\pi\)
\(542\) −5.47723 + 3.16228i −0.235267 + 0.135831i
\(543\) −4.43649 3.21209i −0.190388 0.137844i
\(544\) 2.73861 + 1.58114i 0.117417 + 0.0677908i
\(545\) 17.5810 21.5323i 0.753089 0.922342i
\(546\) −16.9917 + 25.5807i −0.727176 + 1.09475i
\(547\) 23.2144i 0.992575i 0.868158 + 0.496287i \(0.165304\pi\)
−0.868158 + 0.496287i \(0.834696\pi\)
\(548\) −3.73861 + 6.47547i −0.159706 + 0.276618i
\(549\) 2.12702 10.1723i 0.0907789 0.434143i
\(550\) 0.707603 + 0.798761i 0.0301723 + 0.0340593i
\(551\) −4.94975 + 8.57321i −0.210866 + 0.365231i
\(552\) 4.58009 + 10.2414i 0.194942 + 0.435903i
\(553\) −1.38201 + 0.0557857i −0.0587689 + 0.00237225i
\(554\) 9.79796i 0.416275i
\(555\) −19.4935 19.5867i −0.827451 0.831409i
\(556\) −6.52277 + 3.76593i −0.276627 + 0.159711i
\(557\) 18.9317 + 32.7906i 0.802161 + 1.38938i 0.918191 + 0.396138i \(0.129650\pi\)
−0.116030 + 0.993246i \(0.537017\pi\)
\(558\) −0.860224 + 0.282656i −0.0364162 + 0.0119658i
\(559\) 13.5546i 0.573298i
\(560\) −2.31920 5.44255i −0.0980041 0.229990i
\(561\) 0.477226 + 1.06711i 0.0201485 + 0.0450534i
\(562\) 10.0521 + 5.80359i 0.424023 + 0.244810i
\(563\) 9.00000 5.19615i 0.379305 0.218992i −0.298211 0.954500i \(-0.596390\pi\)
0.677516 + 0.735508i \(0.263057\pi\)
\(564\) 10.8795 + 7.87694i 0.458110 + 0.331679i
\(565\) 5.17186 + 13.6376i 0.217582 + 0.573739i
\(566\) −24.7165 −1.03891
\(567\) −22.1838 8.65317i −0.931634 0.363399i
\(568\) 2.02265i 0.0848683i
\(569\) −10.4218 6.01701i −0.436903 0.252246i 0.265380 0.964144i \(-0.414503\pi\)
−0.702283 + 0.711898i \(0.747836\pi\)
\(570\) 18.3214 4.86239i 0.767399 0.203663i
\(571\) 3.47723 + 6.02273i 0.145517 + 0.252043i 0.929566 0.368656i \(-0.120182\pi\)
−0.784048 + 0.620700i \(0.786849\pi\)
\(572\) −1.23861 0.715113i −0.0517890 0.0299004i
\(573\) −2.52319 + 1.12840i −0.105408 + 0.0471397i
\(574\) −17.7158 + 0.715113i −0.739445 + 0.0298483i
\(575\) 6.47723 + 31.7318i 0.270119 + 1.32331i
\(576\) −0.936492 2.85008i −0.0390205 0.118754i
\(577\) 7.40852 + 12.8319i 0.308421 + 0.534200i 0.978017 0.208525i \(-0.0668663\pi\)
−0.669596 + 0.742725i \(0.733533\pi\)
\(578\) −3.50000 6.06218i −0.145581 0.252153i
\(579\) −1.30948 + 12.6604i −0.0544199 + 0.526148i
\(580\) 3.50333 + 2.86045i 0.145468 + 0.118774i
\(581\) −37.3800 + 23.6412i −1.55079 + 0.980803i
\(582\) −2.47723 5.53924i −0.102684 0.229609i
\(583\) 0.924143 + 0.533554i 0.0382741 + 0.0220976i
\(584\) −5.99430 10.3824i −0.248046 0.429628i
\(585\) −34.9568 + 28.2652i −1.44529 + 1.16862i
\(586\) −3.97723 2.29625i −0.164298 0.0948573i
\(587\) 27.4110i 1.13137i 0.824621 + 0.565686i \(0.191389\pi\)
−0.824621 + 0.565686i \(0.808611\pi\)
\(588\) −6.29560 + 10.3617i −0.259626 + 0.427311i
\(589\) −1.47723 −0.0608680
\(590\) −3.89908 10.2814i −0.160523 0.423280i
\(591\) −9.14178 + 12.6265i −0.376042 + 0.519384i
\(592\) −6.17913 + 3.56752i −0.253961 + 0.146624i
\(593\) 31.4317 + 18.1471i 1.29074 + 0.745212i 0.978786 0.204884i \(-0.0656818\pi\)
0.311958 + 0.950096i \(0.399015\pi\)
\(594\) 0.337449 1.05638i 0.0138457 0.0433440i
\(595\) 2.25403 18.5720i 0.0924064 0.761378i
\(596\) 2.44949i 0.100335i
\(597\) 3.99834 38.6571i 0.163641 1.58213i
\(598\) −21.7033 37.5912i −0.887513 1.53722i
\(599\) −4.98196 + 2.87633i −0.203557 + 0.117524i −0.598314 0.801262i \(-0.704162\pi\)
0.394756 + 0.918786i \(0.370829\pi\)
\(600\) −0.849876 8.61845i −0.0346961 0.351847i
\(601\) 16.7169i 0.681895i 0.940082 + 0.340947i \(0.110748\pi\)
−0.940082 + 0.340947i \(0.889252\pi\)
\(602\) −0.215838 5.34706i −0.00879691 0.217930i
\(603\) −11.9089 10.6516i −0.484968 0.433769i
\(604\) 1.00000 1.73205i 0.0406894 0.0704761i
\(605\) −24.1776 3.92957i −0.982961 0.159760i
\(606\) 11.4919 15.8725i 0.466828 0.644775i
\(607\) −13.2180 + 22.8942i −0.536502 + 0.929248i 0.462587 + 0.886574i \(0.346921\pi\)
−0.999089 + 0.0426745i \(0.986412\pi\)
\(608\) 4.89433i 0.198491i
\(609\) 0.580971 9.25070i 0.0235422 0.374857i
\(610\) −6.00000 4.89898i −0.242933 0.198354i
\(611\) −45.0056 25.9840i −1.82073 1.05120i
\(612\) 1.94169 9.28600i 0.0784882 0.375364i
\(613\) −22.0407 + 12.7252i −0.890216 + 0.513967i −0.874013 0.485902i \(-0.838491\pi\)
−0.0162031 + 0.999869i \(0.505158\pi\)
\(614\) 1.75166 3.03397i 0.0706914 0.122441i
\(615\) −25.0540 6.77729i −1.01027 0.273287i
\(616\) −0.500000 0.262377i −0.0201456 0.0105715i
\(617\) 25.4772 1.02567 0.512837 0.858486i \(-0.328594\pi\)
0.512837 + 0.858486i \(0.328594\pi\)
\(618\) −18.2182 1.88433i −0.732843 0.0757987i
\(619\) −23.1475 + 13.3642i −0.930377 + 0.537154i −0.886931 0.461902i \(-0.847167\pi\)
−0.0434463 + 0.999056i \(0.513834\pi\)
\(620\) −0.108270 + 0.666158i −0.00434823 + 0.0267535i
\(621\) 24.8996 22.6446i 0.999187 0.908697i
\(622\) 28.8948 1.15857
\(623\) 27.9545 1.12840i 1.11997 0.0452085i
\(624\) 4.73861 + 10.5959i 0.189696 + 0.424174i
\(625\) 3.01472 24.8176i 0.120589 0.992703i
\(626\) −11.6190 20.1246i −0.464387 0.804341i
\(627\) 1.06101 1.46545i 0.0423727 0.0585245i
\(628\) −4.39526 + 7.61282i −0.175390 + 0.303784i
\(629\) −22.5630 −0.899646
\(630\) −13.3398 + 11.7068i −0.531471 + 0.466411i
\(631\) −7.47723 −0.297664 −0.148832 0.988863i \(-0.547551\pi\)
−0.148832 + 0.988863i \(0.547551\pi\)
\(632\) −0.261387 + 0.452736i −0.0103974 + 0.0180089i
\(633\) −13.7358 + 18.9717i −0.545949 + 0.754056i
\(634\) −16.9545 29.3660i −0.673347 1.16627i
\(635\) 28.4968 10.8070i 1.13086 0.428863i
\(636\) −3.53553 7.90569i −0.140193 0.313481i
\(637\) 20.1042 42.3834i 0.796559 1.67929i
\(638\) 0.431677 0.0170902
\(639\) −5.76471 + 1.89419i −0.228049 + 0.0749331i
\(640\) −2.20711 0.358719i −0.0872436 0.0141796i
\(641\) −5.43982 + 3.14068i −0.214860 + 0.124049i −0.603568 0.797312i \(-0.706255\pi\)
0.388708 + 0.921361i \(0.372921\pi\)
\(642\) 9.43649 + 0.976025i 0.372429 + 0.0385206i
\(643\) 20.4095 0.804871 0.402436 0.915448i \(-0.368164\pi\)
0.402436 + 0.915448i \(0.368164\pi\)
\(644\) −9.16018 14.4835i −0.360962 0.570731i
\(645\) 2.04555 7.56189i 0.0805434 0.297749i
\(646\) 7.73861 13.4037i 0.304472 0.527360i
\(647\) −20.6703 + 11.9340i −0.812633 + 0.469174i −0.847869 0.530205i \(-0.822115\pi\)
0.0352364 + 0.999379i \(0.488782\pi\)
\(648\) −7.24597 + 5.33816i −0.284648 + 0.209703i
\(649\) −0.908902 0.524755i −0.0356775 0.0205984i
\(650\) 6.70141 + 32.8301i 0.262851 + 1.28770i
\(651\) 1.23882 0.615127i 0.0485531 0.0241087i
\(652\) 14.6969i 0.575577i
\(653\) 12.9317 22.3983i 0.506056 0.876514i −0.493920 0.869507i \(-0.664436\pi\)
0.999975 0.00700659i \(-0.00223029\pi\)
\(654\) −12.6275 + 17.4409i −0.493775 + 0.681994i
\(655\) −13.3012 2.16183i −0.519719 0.0844696i
\(656\) −3.35071 + 5.80359i −0.130823 + 0.226592i
\(657\) −23.9772 + 26.8073i −0.935440 + 1.04585i
\(658\) −18.1677 9.53361i −0.708252 0.371659i
\(659\) 34.2929i 1.33586i 0.744224 + 0.667930i \(0.232819\pi\)
−0.744224 + 0.667930i \(0.767181\pi\)
\(660\) −0.583084 0.585872i −0.0226965 0.0228050i
\(661\) 11.4772 6.62638i 0.446412 0.257736i −0.259901 0.965635i \(-0.583690\pi\)
0.706314 + 0.707899i \(0.250357\pi\)
\(662\) 5.71584 + 9.90012i 0.222152 + 0.384779i
\(663\) −3.77630 + 36.5104i −0.146659 + 1.41795i
\(664\) 16.7169i 0.648740i
\(665\) −26.6376 + 11.3509i −1.03296 + 0.440170i
\(666\) 15.9545 + 14.2701i 0.618222 + 0.552955i
\(667\) 11.3459 + 6.55057i 0.439316 + 0.253639i
\(668\) −12.7158 + 7.34149i −0.491991 + 0.284051i
\(669\) 6.49693 8.97345i 0.251186 0.346934i
\(670\) −11.1351 + 4.22281i −0.430185 + 0.163141i
\(671\) −0.739315 −0.0285409
\(672\) 2.03803 + 4.10444i 0.0786188 + 0.158332i
\(673\) 48.4514i 1.86766i −0.357713 0.933832i \(-0.616443\pi\)
0.357713 0.933832i \(-0.383557\pi\)
\(674\) 14.8492 + 8.57321i 0.571971 + 0.330228i
\(675\) −23.7674 + 10.4933i −0.914808 + 0.403888i
\(676\) −15.9545 27.6339i −0.613633 1.06284i
\(677\) −28.5000 16.4545i −1.09534 0.632397i −0.160350 0.987060i \(-0.551262\pi\)
−0.934994 + 0.354663i \(0.884596\pi\)
\(678\) −4.61230 10.3134i −0.177134 0.396084i
\(679\) 4.95445 + 7.83368i 0.190134 + 0.300629i
\(680\) −5.47723 4.47214i −0.210042 0.171499i
\(681\) −1.85188 + 17.9045i −0.0709641 + 0.686101i
\(682\) 0.0322079 + 0.0557857i 0.00123330 + 0.00213615i
\(683\) −1.47723 2.55863i −0.0565245 0.0979032i 0.836379 0.548152i \(-0.184669\pi\)
−0.892903 + 0.450249i \(0.851335\pi\)
\(684\) −13.9493 + 4.58350i −0.533363 + 0.175254i
\(685\) 10.5744 12.9509i 0.404027 0.494830i
\(686\) 7.25590 17.0397i 0.277031 0.650579i
\(687\) 11.4317 5.11240i 0.436146 0.195050i
\(688\) −1.75166 1.01132i −0.0667815 0.0385563i
\(689\) 16.7535 + 29.0180i 0.638259 + 1.10550i
\(690\) −6.43496 24.2468i −0.244975 0.923060i
\(691\) 3.00000 + 1.73205i 0.114125 + 0.0658903i 0.555976 0.831198i \(-0.312345\pi\)
−0.441851 + 0.897089i \(0.645678\pi\)
\(692\) 11.5207i 0.437952i
\(693\) −0.279552 + 1.67076i −0.0106193 + 0.0634668i
\(694\) −6.52277 −0.247601
\(695\) 15.7474 5.97195i 0.597332 0.226529i
\(696\) −2.83766 2.05451i −0.107561 0.0778760i
\(697\) −18.3526 + 10.5959i −0.695153 + 0.401347i
\(698\) 28.1703 + 16.2641i 1.06626 + 0.615606i
\(699\) 2.82843 + 6.32456i 0.106981 + 0.239217i
\(700\) 3.16637 + 12.8442i 0.119678 + 0.485466i
\(701\) 7.03320i 0.265640i −0.991140 0.132820i \(-0.957597\pi\)
0.991140 0.132820i \(-0.0424033\pi\)
\(702\) 25.7614 23.4284i 0.972302 0.884247i
\(703\) 17.4606 + 30.2427i 0.658540 + 1.14063i
\(704\) −0.184829 + 0.106711i −0.00696599 + 0.00402182i
\(705\) −21.1866 21.2879i −0.797934 0.801750i
\(706\) 13.2528i 0.498774i
\(707\) −13.9089 + 26.5055i −0.523098 + 0.996843i
\(708\) 3.47723 + 7.77531i 0.130682 + 0.292214i
\(709\) −5.21584 + 9.03410i −0.195885 + 0.339283i −0.947190 0.320672i \(-0.896091\pi\)
0.751305 + 0.659955i \(0.229425\pi\)
\(710\) −0.725563 + 4.46420i −0.0272299 + 0.167538i
\(711\) 1.53512 + 0.320992i 0.0575716 + 0.0120382i
\(712\) 5.28720 9.15769i 0.198146 0.343199i
\(713\) 1.95498i 0.0732146i
\(714\) −0.908312 + 14.4629i −0.0339927 + 0.541260i
\(715\) 2.47723 + 2.02265i 0.0926430 + 0.0756427i
\(716\) −12.9128 7.45518i −0.482572 0.278613i
\(717\) 0 0
\(718\) 5.62465 3.24739i 0.209910 0.121192i
\(719\) 23.6398 40.9453i 0.881614 1.52700i 0.0320690 0.999486i \(-0.489790\pi\)
0.849545 0.527515i \(-0.176876\pi\)
\(720\) 1.04456 + 6.62638i 0.0389283 + 0.246951i
\(721\) 27.9545 1.12840i 1.04108 0.0420239i
\(722\) −4.95445 −0.184386
\(723\) −0.710802 + 6.87224i −0.0264350 + 0.255581i
\(724\) 2.73861 1.58114i 0.101780 0.0587626i
\(725\) −6.70611 7.57004i −0.249059 0.281144i
\(726\) 18.8730 + 1.95205i 0.700442 + 0.0724474i
\(727\) 23.6076 0.875556 0.437778 0.899083i \(-0.355766\pi\)
0.437778 + 0.899083i \(0.355766\pi\)
\(728\) −9.47723 14.9848i −0.351249 0.555374i
\(729\) 22.0000 + 15.6525i 0.814815 + 0.579721i
\(730\) 9.50569 + 25.0654i 0.351821 + 0.927713i
\(731\) −3.19808 5.53924i −0.118285 0.204876i
\(732\) 4.85993 + 3.51867i 0.179628 + 0.130054i
\(733\) −18.1677 + 31.4674i −0.671041 + 1.16228i 0.306569 + 0.951849i \(0.400819\pi\)
−0.977609 + 0.210428i \(0.932514\pi\)
\(734\) −8.11562 −0.299553
\(735\) 17.6120 20.6111i 0.649629 0.760252i
\(736\) −6.47723 −0.238754
\(737\) −0.568323 + 0.984365i −0.0209345 + 0.0362595i
\(738\) 19.6786 + 4.11478i 0.724381 + 0.151467i
\(739\) 2.23861 + 3.87739i 0.0823487 + 0.142632i 0.904258 0.426986i \(-0.140425\pi\)
−0.821910 + 0.569618i \(0.807091\pi\)
\(740\) 14.9177 5.65733i 0.548387 0.207968i
\(741\) 51.8596 23.1923i 1.90511 0.851991i
\(742\) 7.07107 + 11.1803i 0.259587 + 0.410443i
\(743\) −19.4317 −0.712879 −0.356440 0.934318i \(-0.616009\pi\)
−0.356440 + 0.934318i \(0.616009\pi\)
\(744\) 0.0537841 0.520000i 0.00197182 0.0190641i
\(745\) 0.878680 5.40629i 0.0321923 0.198071i
\(746\) −3.13367 + 1.80922i −0.114732 + 0.0662404i
\(747\) 47.6445 15.6552i 1.74322 0.572794i
\(748\) −0.674899 −0.0246767
\(749\) −14.4796 + 0.584480i −0.529073 + 0.0213564i
\(750\) −1.21584 + 19.3267i −0.0443961 + 0.705712i
\(751\) 16.0000 27.7128i 0.583848 1.01125i −0.411170 0.911559i \(-0.634880\pi\)
0.995018 0.0996961i \(-0.0317870\pi\)
\(752\) −6.71584 + 3.87739i −0.244901 + 0.141394i
\(753\) 16.8624 23.2901i 0.614501 0.848739i
\(754\) 11.7386 + 6.77729i 0.427495 + 0.246814i
\(755\) −2.82843 + 3.46410i −0.102937 + 0.126072i
\(756\) 9.78940 9.65234i 0.356037 0.351052i
\(757\) 30.2476i 1.09937i 0.835373 + 0.549683i \(0.185252\pi\)
−0.835373 + 0.549683i \(0.814748\pi\)
\(758\) 4.76139 8.24696i 0.172941 0.299543i
\(759\) −1.93940 1.40416i −0.0703958 0.0509677i
\(760\) −1.75569 + 10.8023i −0.0636856 + 0.391841i
\(761\) −4.76492 + 8.25308i −0.172728 + 0.299174i −0.939373 0.342898i \(-0.888592\pi\)
0.766645 + 0.642072i \(0.221925\pi\)
\(762\) −21.5507 + 9.63774i −0.780698 + 0.349139i
\(763\) 15.2833 29.1247i 0.553293 1.05438i
\(764\) 1.59580i 0.0577341i
\(765\) −7.61659 + 19.7987i −0.275378 + 0.715823i
\(766\) 0.715838 0.413289i 0.0258643 0.0149328i
\(767\) −16.4772 28.5394i −0.594958 1.03050i
\(768\) 1.72286 + 0.178197i 0.0621683 + 0.00643013i
\(769\) 28.8412i 1.04004i 0.854154 + 0.520020i \(0.174076\pi\)
−0.854154 + 0.520020i \(0.825924\pi\)
\(770\) 1.00943 + 0.758455i 0.0363775 + 0.0273328i
\(771\) 37.3861 16.7196i 1.34643 0.602141i
\(772\) −6.36396 3.67423i −0.229044 0.132239i
\(773\) −24.9772 + 14.4206i −0.898368 + 0.518673i −0.876670 0.481091i \(-0.840241\pi\)
−0.0216979 + 0.999765i \(0.506907\pi\)
\(774\) −1.24194 + 5.93948i −0.0446406 + 0.213490i
\(775\) 0.477927 1.43144i 0.0171677 0.0514189i
\(776\) 3.50333 0.125762
\(777\) −27.2360 18.0912i −0.977084 0.649017i
\(778\) 7.34847i 0.263455i
\(779\) 28.4047 + 16.3995i 1.01770 + 0.587571i
\(780\) −6.65768 25.0860i −0.238383 0.898224i
\(781\) 0.215838 + 0.373843i 0.00772330 + 0.0133772i
\(782\) −17.7386 10.2414i −0.634331 0.366231i
\(783\) −3.19808 + 10.0116i −0.114290 + 0.357785i
\(784\) −3.97723 5.76035i −0.142044 0.205727i
\(785\) 12.4317 15.2256i 0.443706 0.543426i
\(786\) 10.3828 + 1.07391i 0.370343 + 0.0383050i
\(787\) −17.3402 30.0341i −0.618112 1.07060i −0.989830 0.142256i \(-0.954564\pi\)
0.371718 0.928346i \(-0.378769\pi\)
\(788\) −4.50000 7.79423i −0.160306 0.277658i
\(789\) −3.44572 0.356394i −0.122671 0.0126880i
\(790\) 0.739315 0.905472i 0.0263036 0.0322152i
\(791\) 9.22460 + 14.5854i 0.327989 + 0.518596i
\(792\) 0.477226 + 0.426844i 0.0169575 + 0.0151672i
\(793\) −20.1042 11.6072i −0.713922 0.412183i
\(794\) 15.1867 + 26.3041i 0.538956 + 0.933498i
\(795\) 4.96737 + 18.7170i 0.176175 + 0.663823i
\(796\) 19.4317 + 11.2189i 0.688738 + 0.397643i
\(797\) 28.9201i 1.02440i −0.858865 0.512201i \(-0.828830\pi\)
0.858865 0.512201i \(-0.171170\pi\)
\(798\) 20.0885 9.97479i 0.711124 0.353104i
\(799\) −24.5228 −0.867553
\(800\) 4.74264 + 1.58346i 0.167678 + 0.0559839i
\(801\) −31.0516 6.49286i −1.09716 0.229414i
\(802\) −26.2834 + 15.1747i −0.928098 + 0.535838i
\(803\) 2.21584 + 1.27931i 0.0781952 + 0.0451460i
\(804\) 8.42087 3.76593i 0.296981 0.132814i
\(805\) 15.0220 + 35.2526i 0.529455 + 1.24249i
\(806\) 2.02265i 0.0712447i
\(807\) 49.7816 + 5.14896i 1.75240 + 0.181252i
\(808\) 5.65685 + 9.79796i 0.199007 + 0.344691i
\(809\) 34.7686 20.0737i 1.22240 0.705753i 0.256971 0.966419i \(-0.417275\pi\)
0.965429 + 0.260666i \(0.0839421\pi\)
\(810\) 17.9075 9.18262i 0.629206 0.322644i
\(811\) 6.70527i 0.235454i 0.993046 + 0.117727i \(0.0375608\pi\)
−0.993046 + 0.117727i \(0.962439\pi\)
\(812\) 4.73861 + 2.48661i 0.166293 + 0.0872629i
\(813\) −10.0000 + 4.47214i −0.350715 + 0.156845i
\(814\) 0.761387 1.31876i 0.0266866 0.0462226i
\(815\) −5.27208 + 32.4377i −0.184673 + 1.13624i
\(816\) 4.43649 + 3.21209i 0.155308 + 0.112446i
\(817\) −4.94975 + 8.57321i −0.173170 + 0.299939i
\(818\) 22.4378i 0.784518i
\(819\) −33.8326 + 41.0440i −1.18221 + 1.43420i
\(820\) 9.47723 11.6072i 0.330959 0.405340i
\(821\) −44.0814 25.4504i −1.53845 0.888226i −0.998930 0.0462557i \(-0.985271\pi\)
−0.539523 0.841971i \(-0.681396\pi\)
\(822\) −7.59501 + 10.4901i −0.264907 + 0.365885i
\(823\) 28.2199 16.2927i 0.983682 0.567929i 0.0803025 0.996771i \(-0.474411\pi\)
0.903380 + 0.428841i \(0.141078\pi\)
\(824\) 5.28720 9.15769i 0.184188 0.319023i
\(825\) 1.07676 + 1.50225i 0.0374881 + 0.0523015i
\(826\) −6.95445 10.9960i −0.241976 0.382598i
\(827\) 39.9089 1.38777 0.693884 0.720087i \(-0.255898\pi\)
0.693884 + 0.720087i \(0.255898\pi\)
\(828\) 6.06587 + 18.4606i 0.210803 + 0.641552i
\(829\) −16.3069 + 9.41481i −0.566363 + 0.326990i −0.755696 0.654923i \(-0.772701\pi\)
0.189332 + 0.981913i \(0.439368\pi\)
\(830\) 5.99666 36.8959i 0.208147 1.28068i
\(831\) 1.74597 16.8805i 0.0605669 0.585578i
\(832\) −6.70141 −0.232330
\(833\) −1.78416 22.0639i −0.0618175 0.764470i
\(834\) −11.9089 + 5.32582i −0.412372 + 0.184418i
\(835\) 30.6987 11.6420i 1.06237 0.402889i
\(836\) 0.522278 + 0.904612i 0.0180634 + 0.0312867i
\(837\) −1.53241 + 0.333687i −0.0529680 + 0.0115339i
\(838\) −8.30045 + 14.3768i −0.286734 + 0.496639i
\(839\) 37.3156 1.28828 0.644139 0.764908i \(-0.277216\pi\)
0.644139 + 0.764908i \(0.277216\pi\)
\(840\) −3.02581 9.79002i −0.104400 0.337788i
\(841\) 24.9089 0.858928
\(842\) 1.47723 2.55863i 0.0509086 0.0881762i
\(843\) 16.2842 + 11.7900i 0.560858 + 0.406070i
\(844\) −6.76139 11.7111i −0.232737 0.403112i
\(845\) 25.3004 + 66.7142i 0.870359 + 2.29504i
\(846\) 17.3402 + 15.5096i 0.596169 + 0.533230i
\(847\) −28.9592 + 1.16896i −0.995049 + 0.0401659i
\(848\) 5.00000 0.171701
\(849\) −42.5831 4.40441i −1.46145 0.151159i
\(850\) 10.4846 + 11.8353i 0.359618 + 0.405946i
\(851\) 40.0236 23.1077i 1.37199 0.792120i
\(852\) 0.360429 3.48474i 0.0123481 0.119385i
\(853\) −53.9165 −1.84607 −0.923033 0.384720i \(-0.874298\pi\)
−0.923033 + 0.384720i \(0.874298\pi\)
\(854\) −8.11562 4.25871i −0.277711 0.145730i
\(855\) 32.4317 5.11240i 1.10914 0.174840i
\(856\) −2.73861 + 4.74342i −0.0936039 + 0.162127i
\(857\) 34.9545 20.1810i 1.19402 0.689369i 0.234805 0.972042i \(-0.424555\pi\)
0.959216 + 0.282674i \(0.0912214\pi\)
\(858\) −2.00653 1.45276i −0.0685016 0.0495963i
\(859\) −15.5228 8.96208i −0.529630 0.305782i 0.211236 0.977435i \(-0.432251\pi\)
−0.740866 + 0.671653i \(0.765585\pi\)
\(860\) 3.50333 + 2.86045i 0.119462 + 0.0975407i
\(861\) −30.6493 1.92487i −1.04453 0.0655994i
\(862\) 37.0576i 1.26219i
\(863\) 7.76139 13.4431i 0.264201 0.457609i −0.703153 0.711038i \(-0.748225\pi\)
0.967354 + 0.253429i \(0.0815585\pi\)
\(864\) −1.10557 5.07718i −0.0376122 0.172729i
\(865\) 4.13270 25.4274i 0.140516 0.864559i
\(866\) 0 0
\(867\) −4.94975 11.0680i −0.168102 0.375888i
\(868\) 0.0322079 + 0.797901i 0.00109321 + 0.0270825i
\(869\) 0.111571i 0.00378480i
\(870\) 5.52602 + 5.55244i 0.187349 + 0.188245i
\(871\) −30.9089 + 17.8453i −1.04731 + 0.604664i
\(872\) −6.21584 10.7661i −0.210495 0.364588i
\(873\) −3.28084 9.98478i −0.111039 0.337933i
\(874\) 31.7017i 1.07232i
\(875\) −2.38105 29.4844i −0.0804942 0.996755i
\(876\) −8.47723 18.9557i −0.286419 0.640452i
\(877\) −36.6169 21.1408i −1.23647 0.713874i −0.268096 0.963392i \(-0.586394\pi\)
−0.968370 + 0.249518i \(0.919728\pi\)
\(878\) −19.6931 + 11.3698i −0.664609 + 0.383712i
\(879\) −6.44302 4.66485i −0.217318 0.157341i
\(880\) 0.446216 0.169221i 0.0150419 0.00570443i
\(881\) −26.5004 −0.892821 −0.446411 0.894828i \(-0.647298\pi\)
−0.446411 + 0.894828i \(0.647298\pi\)
\(882\) −12.6929 + 16.7300i −0.427391 + 0.563327i
\(883\) 29.2823i 0.985428i 0.870191 + 0.492714i \(0.163995\pi\)
−0.870191 + 0.492714i \(0.836005\pi\)
\(884\) −18.3526 10.5959i −0.617264 0.356377i
\(885\) −4.88545 18.4083i −0.164223 0.618788i
\(886\) 18.4772 + 32.0035i 0.620755 + 1.07518i
\(887\) 3.00000 + 1.73205i 0.100730 + 0.0581566i 0.549519 0.835481i \(-0.314811\pi\)
−0.448789 + 0.893638i \(0.648144\pi\)
\(888\) −11.2815 + 5.04524i −0.378582 + 0.169307i
\(889\) 30.4772 19.2755i 1.02217 0.646479i
\(890\) −14.9545 + 18.3154i −0.501274 + 0.613933i
\(891\) 0.769622 1.75987i 0.0257833 0.0589578i
\(892\) 3.19808 + 5.53924i 0.107080 + 0.185468i
\(893\) 18.9772 + 32.8695i 0.635049 + 1.09994i
\(894\) −0.436492 + 4.22013i −0.0145985 + 0.141142i
\(895\) 25.8255 + 21.0864i 0.863251 + 0.704842i
\(896\) −2.64360 + 0.106711i −0.0883164 + 0.00356496i
\(897\) −30.6931 68.6318i −1.02481 2.29155i
\(898\) −3.04546 1.75830i −0.101628 0.0586752i
\(899\) −0.305242 0.528694i −0.0101804 0.0176329i
\(900\) 0.0715641 14.9998i 0.00238547 0.499994i
\(901\) 13.6931 + 7.90569i 0.456182 + 0.263377i
\(902\) 1.43023i 0.0476213i
\(903\) 0.580971 9.25070i 0.0193335 0.307844i
\(904\) 6.52277 0.216944
\(905\) −6.61160 + 2.50735i −0.219777 + 0.0833471i
\(906\) 2.03151 2.80588i 0.0674923 0.0932192i
\(907\) −8.48528 + 4.89898i −0.281749 + 0.162668i −0.634215 0.773157i \(-0.718677\pi\)
0.352466 + 0.935825i \(0.385343\pi\)
\(908\) −9.00000 5.19615i −0.298675 0.172440i
\(909\) 22.6274 25.2982i 0.750504 0.839089i
\(910\) 15.5419 + 36.4727i 0.515209 + 1.20906i
\(911\) 15.1238i 0.501073i 0.968107 + 0.250537i \(0.0806071\pi\)
−0.968107 + 0.250537i \(0.919393\pi\)
\(912\) 0.872155 8.43224i 0.0288799 0.279219i
\(913\) −1.78387 3.08976i −0.0590375 0.102256i
\(914\) −32.8322 + 18.9557i −1.08599 + 0.626997i
\(915\) −9.46418 9.50944i −0.312876 0.314372i
\(916\) 7.23003i 0.238887i
\(917\) −15.9317 + 0.643094i −0.526110 + 0.0212368i
\(918\) 5.00000 15.6525i 0.165025 0.516609i
\(919\) 16.2158 28.0867i 0.534911 0.926493i −0.464256 0.885701i \(-0.653678\pi\)
0.999168 0.0407925i \(-0.0129883\pi\)
\(920\) 14.2959 + 2.32351i 0.471323 + 0.0766038i
\(921\) 3.55851 4.91496i 0.117257 0.161954i
\(922\) −8.14783 + 14.1125i −0.268335 + 0.464769i
\(923\) 13.5546i 0.446155i
\(924\) −0.814675 0.541138i −0.0268008 0.0178021i
\(925\) −34.9545 + 7.13505i −1.14930 + 0.234599i
\(926\) 15.3071 + 8.83756i 0.503023 + 0.290420i
\(927\) −31.0516 6.49286i −1.01987 0.213253i
\(928\) 1.75166 1.01132i 0.0575012 0.0331983i
\(929\) 11.8360 20.5005i 0.388326 0.672601i −0.603898 0.797061i \(-0.706387\pi\)
0.992225 + 0.124461i \(0.0397201\pi\)
\(930\) −0.305242 + 1.12840i −0.0100093 + 0.0370018i
\(931\) −28.1931 + 19.4658i −0.923990 + 0.637967i
\(932\) −4.00000 −0.131024
\(933\) 49.7816 + 5.14896i 1.62978 + 0.168569i
\(934\) 29.7386 17.1696i 0.973077 0.561806i
\(935\) 1.48957 + 0.242099i 0.0487143 + 0.00791750i
\(936\) 6.27582 + 19.0996i 0.205131 + 0.624290i
\(937\) −22.6918 −0.741310 −0.370655 0.928771i \(-0.620867\pi\)
−0.370655 + 0.928771i \(0.620867\pi\)
\(938\) −11.9089 + 7.53185i −0.388839 + 0.245924i
\(939\) −16.4317 36.7423i −0.536228 1.19904i
\(940\) 16.2135 6.14871i 0.528825 0.200549i
\(941\) −2.49098 4.31450i −0.0812036 0.140649i 0.822564 0.568673i \(-0.192543\pi\)
−0.903767 + 0.428024i \(0.859210\pi\)
\(942\) −8.92900 + 12.3326i −0.290923 + 0.401818i
\(943\) 21.7033 37.5912i 0.706756 1.22414i
\(944\) −4.91754 −0.160052
\(945\) −25.0687 + 17.7921i −0.815486 + 0.578777i
\(946\) 0.431677 0.0140350
\(947\) 16.4317 28.4605i 0.533958 0.924842i −0.465255 0.885177i \(-0.654037\pi\)
0.999213 0.0396654i \(-0.0126292\pi\)
\(948\) −0.531010 + 0.733422i −0.0172464 + 0.0238204i
\(949\) 40.1703 + 69.5770i 1.30398 + 2.25856i
\(950\) 7.74999 23.2120i 0.251443 0.753098i
\(951\) −23.9772 53.6147i −0.777514 1.73858i
\(952\) −7.40852 3.88766i −0.240111 0.126000i
\(953\) 25.0455 0.811305 0.405652 0.914027i \(-0.367044\pi\)
0.405652 + 0.914027i \(0.367044\pi\)
\(954\) −4.68246 14.2504i −0.151600 0.461375i
\(955\) −0.572445 + 3.52211i −0.0185239 + 0.113973i
\(956\) 0 0
\(957\) 0.743718 + 0.0769235i 0.0240410 + 0.00248658i
\(958\) 11.3781 0.367611
\(959\) 9.19239 17.5175i 0.296838 0.565669i
\(960\) −3.73861 1.01132i −0.120663 0.0326403i
\(961\) −15.4545 + 26.7679i −0.498531 + 0.863480i
\(962\) 41.4089 23.9074i 1.33508 0.770807i
\(963\) 16.0838 + 3.36311i 0.518294 + 0.108375i
\(964\) −3.45445 1.99443i −0.111260 0.0642362i
\(965\) 12.7279 + 10.3923i 0.409726 + 0.334540i
\(966\) −13.2008 26.5854i −0.424728 0.855371i
\(967\) 46.4287i 1.49305i 0.665359 + 0.746524i \(0.268279\pi\)
−0.665359 + 0.746524i \(0.731721\pi\)
\(968\) −5.47723 + 9.48683i −0.176045 + 0.304918i
\(969\) 15.7210 21.7136i 0.505033 0.697543i
\(970\) −7.73221 1.25671i −0.248266 0.0403506i
\(971\) 0.490070 0.848827i 0.0157271 0.0272401i −0.858055 0.513558i \(-0.828327\pi\)
0.873782 + 0.486318i \(0.161660\pi\)
\(972\) −13.4350 + 7.90569i −0.430929 + 0.253575i
\(973\) 16.8417 10.6516i 0.539921 0.341476i
\(974\) 36.6308i 1.17373i
\(975\) 5.69537 + 57.7558i 0.182398 + 1.84967i
\(976\) −3.00000 + 1.73205i −0.0960277 + 0.0554416i
\(977\) 19.9545 + 34.5621i 0.638399 + 1.10574i 0.985784 + 0.168018i \(0.0537365\pi\)
−0.347385 + 0.937723i \(0.612930\pi\)
\(978\) 2.61895 25.3208i 0.0837448 0.809669i
\(979\) 2.25681i 0.0721278i
\(980\) 6.71181 + 14.1404i 0.214401 + 0.451699i
\(981\) −24.8634 + 27.7981i −0.793826 + 0.887524i
\(982\) −3.50333 2.02265i −0.111796 0.0645452i
\(983\) −29.2842 + 16.9072i −0.934020 + 0.539257i −0.888081 0.459688i \(-0.847961\pi\)
−0.0459391 + 0.998944i \(0.514628\pi\)
\(984\) −6.80698 + 9.40169i −0.216999 + 0.299715i
\(985\) 7.13604 + 18.8169i 0.227373 + 0.599557i
\(986\) 6.39617 0.203696
\(987\) −29.6016 19.6625i −0.942230 0.625865i
\(988\) 32.7989i 1.04347i
\(989\) 11.3459 + 6.55057i 0.360779 + 0.208296i
\(990\) −0.900171 1.11328i −0.0286093 0.0353823i
\(991\) −10.7386 18.5998i −0.341123 0.590843i 0.643518 0.765431i \(-0.277474\pi\)
−0.984642 + 0.174588i \(0.944141\pi\)
\(992\) 0.261387 + 0.150912i 0.00829905 + 0.00479146i
\(993\) 8.08342 + 18.0751i 0.256519 + 0.573595i
\(994\) 0.215838 + 5.34706i 0.00684598 + 0.169599i
\(995\) −38.8634 31.7318i −1.23205 1.00597i
\(996\) −2.97889 + 28.8008i −0.0943899 + 0.912588i
\(997\) −7.74597 13.4164i −0.245317 0.424902i 0.716904 0.697172i \(-0.245559\pi\)
−0.962221 + 0.272270i \(0.912225\pi\)
\(998\) 20.9545 + 36.2942i 0.663302 + 1.14887i
\(999\) 24.9444 + 27.4284i 0.789206 + 0.867796i
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 210.2.t.e.89.2 yes 8
3.2 odd 2 210.2.t.f.89.4 yes 8
5.2 odd 4 1050.2.s.i.551.4 16
5.3 odd 4 1050.2.s.i.551.5 16
5.4 even 2 210.2.t.f.89.3 yes 8
7.2 even 3 1470.2.d.f.1469.1 8
7.3 odd 6 inner 210.2.t.e.59.1 8
7.5 odd 6 1470.2.d.f.1469.8 8
15.2 even 4 1050.2.s.i.551.6 16
15.8 even 4 1050.2.s.i.551.3 16
15.14 odd 2 inner 210.2.t.e.89.1 yes 8
21.2 odd 6 1470.2.d.e.1469.4 8
21.5 even 6 1470.2.d.e.1469.5 8
21.17 even 6 210.2.t.f.59.3 yes 8
35.3 even 12 1050.2.s.i.101.3 16
35.9 even 6 1470.2.d.e.1469.8 8
35.17 even 12 1050.2.s.i.101.6 16
35.19 odd 6 1470.2.d.e.1469.1 8
35.24 odd 6 210.2.t.f.59.4 yes 8
105.17 odd 12 1050.2.s.i.101.4 16
105.38 odd 12 1050.2.s.i.101.5 16
105.44 odd 6 1470.2.d.f.1469.5 8
105.59 even 6 inner 210.2.t.e.59.2 yes 8
105.89 even 6 1470.2.d.f.1469.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.t.e.59.1 8 7.3 odd 6 inner
210.2.t.e.59.2 yes 8 105.59 even 6 inner
210.2.t.e.89.1 yes 8 15.14 odd 2 inner
210.2.t.e.89.2 yes 8 1.1 even 1 trivial
210.2.t.f.59.3 yes 8 21.17 even 6
210.2.t.f.59.4 yes 8 35.24 odd 6
210.2.t.f.89.3 yes 8 5.4 even 2
210.2.t.f.89.4 yes 8 3.2 odd 2
1050.2.s.i.101.3 16 35.3 even 12
1050.2.s.i.101.4 16 105.17 odd 12
1050.2.s.i.101.5 16 105.38 odd 12
1050.2.s.i.101.6 16 35.17 even 12
1050.2.s.i.551.3 16 15.8 even 4
1050.2.s.i.551.4 16 5.2 odd 4
1050.2.s.i.551.5 16 5.3 odd 4
1050.2.s.i.551.6 16 15.2 even 4
1470.2.d.e.1469.1 8 35.19 odd 6
1470.2.d.e.1469.4 8 21.2 odd 6
1470.2.d.e.1469.5 8 21.5 even 6
1470.2.d.e.1469.8 8 35.9 even 6
1470.2.d.f.1469.1 8 7.2 even 3
1470.2.d.f.1469.4 8 105.89 even 6
1470.2.d.f.1469.5 8 105.44 odd 6
1470.2.d.f.1469.8 8 7.5 odd 6