Properties

Label 210.3.s.a.11.13
Level $210$
Weight $3$
Character 210.11
Analytic conductor $5.722$
Analytic rank $0$
Dimension $40$
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] = [210,3,Mod(11,210)]
 
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, 0, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("210.11");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.s (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: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 11.13
Character \(\chi\) \(=\) 210.11
Dual form 210.3.s.a.191.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.22474 - 0.707107i) q^{2} +(-2.41792 + 1.77586i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(-1.70561 + 3.88470i) q^{6} +(-5.45202 - 4.39039i) q^{7} -2.82843i q^{8} +(2.69265 - 8.58776i) q^{9} +O(q^{10})\) \(q+(1.22474 - 0.707107i) q^{2} +(-2.41792 + 1.77586i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(-1.70561 + 3.88470i) q^{6} +(-5.45202 - 4.39039i) q^{7} -2.82843i q^{8} +(2.69265 - 8.58776i) q^{9} +(-1.58114 + 2.73861i) q^{10} +(3.43624 + 1.98392i) q^{11} +(0.657959 + 5.96382i) q^{12} -22.5550 q^{13} +(-9.78180 - 1.52194i) q^{14} +(2.69681 - 6.14225i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(-13.7210 - 7.92182i) q^{17} +(-2.77465 - 12.4218i) q^{18} +(-14.1365 - 24.4851i) q^{19} +4.47214i q^{20} +(20.9792 + 0.933580i) q^{21} +5.61136 q^{22} +(8.65649 - 4.99782i) q^{23} +(5.02289 + 6.83890i) q^{24} +(2.50000 - 4.33013i) q^{25} +(-27.6241 + 15.9488i) q^{26} +(8.74003 + 25.5463i) q^{27} +(-13.0564 + 5.05279i) q^{28} +23.4934i q^{29} +(-1.04033 - 9.42962i) q^{30} +(2.22037 - 3.84579i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(-11.8317 + 1.30534i) q^{33} -22.4063 q^{34} +(15.4664 + 2.40640i) q^{35} +(-12.1818 - 13.2516i) q^{36} +(11.1661 + 19.3402i) q^{37} +(-34.6272 - 19.9920i) q^{38} +(54.5361 - 40.0544i) q^{39} +(3.16228 + 5.47723i) q^{40} +37.0140i q^{41} +(26.3544 - 13.6912i) q^{42} -33.1548 q^{43} +(6.87248 - 3.96783i) q^{44} +(4.38711 + 19.6406i) q^{45} +(7.06799 - 12.2421i) q^{46} +(64.3880 - 37.1744i) q^{47} +(10.9876 + 4.82420i) q^{48} +(10.4490 + 47.8729i) q^{49} -7.07107i q^{50} +(47.2442 - 5.21223i) q^{51} +(-22.5550 + 39.0664i) q^{52} +(-62.7080 - 36.2045i) q^{53} +(28.7682 + 25.1075i) q^{54} -8.87234 q^{55} +(-12.4179 + 15.4206i) q^{56} +(77.6631 + 34.0986i) q^{57} +(16.6123 + 28.7734i) q^{58} +(52.8665 + 30.5225i) q^{59} +(-7.94188 - 10.8133i) q^{60} +(15.5109 + 26.8657i) q^{61} -6.28015i q^{62} +(-52.3840 + 34.9988i) q^{63} -8.00000 q^{64} +(43.6775 - 25.2172i) q^{65} +(-13.5678 + 9.96498i) q^{66} +(0.891277 - 1.54374i) q^{67} +(-27.4420 + 15.8436i) q^{68} +(-12.0552 + 27.4570i) q^{69} +(20.6440 - 7.98916i) q^{70} -89.7060i q^{71} +(-24.2899 - 7.61597i) q^{72} +(-7.44284 + 12.8914i) q^{73} +(27.3512 + 15.7912i) q^{74} +(1.64490 + 14.9095i) q^{75} -56.5460 q^{76} +(-10.0243 - 25.9028i) q^{77} +(38.4700 - 87.6193i) q^{78} +(-44.9089 - 77.7844i) q^{79} +(7.74597 + 4.47214i) q^{80} +(-66.4992 - 46.2477i) q^{81} +(26.1729 + 45.3327i) q^{82} +42.3934i q^{83} +(22.5962 - 35.4035i) q^{84} +35.4274 q^{85} +(-40.6061 + 23.4440i) q^{86} +(-41.7209 - 56.8051i) q^{87} +(5.61136 - 9.71916i) q^{88} +(126.802 - 73.2090i) q^{89} +(19.2611 + 20.9526i) q^{90} +(122.970 + 99.0251i) q^{91} -19.9913i q^{92} +(1.46091 + 13.2419i) q^{93} +(52.5726 - 91.0584i) q^{94} +(54.7505 + 31.6102i) q^{95} +(16.8682 - 1.86099i) q^{96} -162.686 q^{97} +(46.6487 + 51.2436i) q^{98} +(26.2900 - 24.1676i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 40 q^{4} - 8 q^{6} + 20 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 40 q^{4} - 8 q^{6} + 20 q^{7} - 4 q^{9} + 136 q^{13} + 40 q^{15} - 80 q^{16} + 16 q^{18} - 140 q^{19} + 36 q^{21} - 8 q^{24} + 100 q^{25} - 120 q^{27} - 16 q^{28} - 20 q^{30} + 4 q^{31} + 232 q^{33} + 32 q^{34} - 16 q^{36} - 76 q^{37} - 4 q^{39} + 128 q^{42} - 104 q^{43} - 20 q^{45} - 56 q^{46} + 100 q^{49} + 168 q^{51} + 136 q^{52} + 40 q^{54} + 80 q^{55} + 200 q^{57} + 144 q^{58} + 40 q^{60} - 120 q^{61} - 324 q^{63} - 320 q^{64} - 288 q^{66} - 20 q^{67} - 416 q^{69} - 120 q^{70} - 32 q^{72} - 476 q^{73} - 560 q^{76} - 192 q^{78} - 508 q^{79} - 304 q^{81} + 224 q^{82} + 144 q^{84} - 240 q^{85} - 324 q^{87} + 468 q^{91} + 204 q^{93} + 400 q^{94} + 16 q^{96} - 512 q^{97} + 208 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22474 0.707107i 0.612372 0.353553i
\(3\) −2.41792 + 1.77586i −0.805973 + 0.591953i
\(4\) 1.00000 1.73205i 0.250000 0.433013i
\(5\) −1.93649 + 1.11803i −0.387298 + 0.223607i
\(6\) −1.70561 + 3.88470i −0.284268 + 0.647450i
\(7\) −5.45202 4.39039i −0.778860 0.627198i
\(8\) 2.82843i 0.353553i
\(9\) 2.69265 8.58776i 0.299184 0.954196i
\(10\) −1.58114 + 2.73861i −0.158114 + 0.273861i
\(11\) 3.43624 + 1.98392i 0.312386 + 0.180356i 0.647994 0.761646i \(-0.275608\pi\)
−0.335608 + 0.942002i \(0.608942\pi\)
\(12\) 0.657959 + 5.96382i 0.0548299 + 0.496985i
\(13\) −22.5550 −1.73500 −0.867499 0.497439i \(-0.834274\pi\)
−0.867499 + 0.497439i \(0.834274\pi\)
\(14\) −9.78180 1.52194i −0.698700 0.108710i
\(15\) 2.69681 6.14225i 0.179787 0.409483i
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) −13.7210 7.92182i −0.807117 0.465989i 0.0388368 0.999246i \(-0.487635\pi\)
−0.845954 + 0.533256i \(0.820968\pi\)
\(18\) −2.77465 12.4218i −0.154147 0.690100i
\(19\) −14.1365 24.4851i −0.744027 1.28869i −0.950648 0.310271i \(-0.899580\pi\)
0.206621 0.978421i \(-0.433753\pi\)
\(20\) 4.47214i 0.223607i
\(21\) 20.9792 + 0.933580i 0.999011 + 0.0444562i
\(22\) 5.61136 0.255062
\(23\) 8.65649 4.99782i 0.376369 0.217297i −0.299868 0.953981i \(-0.596943\pi\)
0.676237 + 0.736684i \(0.263609\pi\)
\(24\) 5.02289 + 6.83890i 0.209287 + 0.284954i
\(25\) 2.50000 4.33013i 0.100000 0.173205i
\(26\) −27.6241 + 15.9488i −1.06247 + 0.613414i
\(27\) 8.74003 + 25.5463i 0.323705 + 0.946158i
\(28\) −13.0564 + 5.05279i −0.466300 + 0.180457i
\(29\) 23.4934i 0.810117i 0.914291 + 0.405058i \(0.132749\pi\)
−0.914291 + 0.405058i \(0.867251\pi\)
\(30\) −1.04033 9.42962i −0.0346775 0.314321i
\(31\) 2.22037 3.84579i 0.0716248 0.124058i −0.827989 0.560745i \(-0.810515\pi\)
0.899614 + 0.436687i \(0.143848\pi\)
\(32\) −4.89898 2.82843i −0.153093 0.0883883i
\(33\) −11.8317 + 1.30534i −0.358536 + 0.0395556i
\(34\) −22.4063 −0.659008
\(35\) 15.4664 + 2.40640i 0.441897 + 0.0687544i
\(36\) −12.1818 13.2516i −0.338383 0.368099i
\(37\) 11.1661 + 19.3402i 0.301785 + 0.522708i 0.976540 0.215334i \(-0.0690840\pi\)
−0.674755 + 0.738042i \(0.735751\pi\)
\(38\) −34.6272 19.9920i −0.911243 0.526106i
\(39\) 54.5361 40.0544i 1.39836 1.02704i
\(40\) 3.16228 + 5.47723i 0.0790569 + 0.136931i
\(41\) 37.0140i 0.902781i 0.892327 + 0.451390i \(0.149072\pi\)
−0.892327 + 0.451390i \(0.850928\pi\)
\(42\) 26.3544 13.6912i 0.627485 0.325980i
\(43\) −33.1548 −0.771041 −0.385521 0.922699i \(-0.625978\pi\)
−0.385521 + 0.922699i \(0.625978\pi\)
\(44\) 6.87248 3.96783i 0.156193 0.0901780i
\(45\) 4.38711 + 19.6406i 0.0974913 + 0.436458i
\(46\) 7.06799 12.2421i 0.153652 0.266133i
\(47\) 64.3880 37.1744i 1.36996 0.790945i 0.379035 0.925382i \(-0.376256\pi\)
0.990922 + 0.134437i \(0.0429225\pi\)
\(48\) 10.9876 + 4.82420i 0.228908 + 0.100504i
\(49\) 10.4490 + 47.8729i 0.213245 + 0.976999i
\(50\) 7.07107i 0.141421i
\(51\) 47.2442 5.21223i 0.926358 0.102201i
\(52\) −22.5550 + 39.0664i −0.433750 + 0.751276i
\(53\) −62.7080 36.2045i −1.18317 0.683104i −0.226424 0.974029i \(-0.572704\pi\)
−0.956746 + 0.290925i \(0.906037\pi\)
\(54\) 28.7682 + 25.1075i 0.532745 + 0.464954i
\(55\) −8.87234 −0.161315
\(56\) −12.4179 + 15.4206i −0.221748 + 0.275369i
\(57\) 77.6631 + 34.0986i 1.36251 + 0.598222i
\(58\) 16.6123 + 28.7734i 0.286420 + 0.496093i
\(59\) 52.8665 + 30.5225i 0.896043 + 0.517330i 0.875914 0.482467i \(-0.160259\pi\)
0.0201284 + 0.999797i \(0.493593\pi\)
\(60\) −7.94188 10.8133i −0.132365 0.180221i
\(61\) 15.5109 + 26.8657i 0.254277 + 0.440421i 0.964699 0.263355i \(-0.0848290\pi\)
−0.710422 + 0.703776i \(0.751496\pi\)
\(62\) 6.28015i 0.101293i
\(63\) −52.3840 + 34.9988i −0.831492 + 0.555537i
\(64\) −8.00000 −0.125000
\(65\) 43.6775 25.2172i 0.671962 0.387957i
\(66\) −13.5678 + 9.96498i −0.205573 + 0.150985i
\(67\) 0.891277 1.54374i 0.0133026 0.0230408i −0.859297 0.511476i \(-0.829099\pi\)
0.872600 + 0.488435i \(0.162432\pi\)
\(68\) −27.4420 + 15.8436i −0.403558 + 0.232995i
\(69\) −12.0552 + 27.4570i −0.174714 + 0.397928i
\(70\) 20.6440 7.98916i 0.294914 0.114131i
\(71\) 89.7060i 1.26346i −0.775187 0.631732i \(-0.782344\pi\)
0.775187 0.631732i \(-0.217656\pi\)
\(72\) −24.2899 7.61597i −0.337359 0.105777i
\(73\) −7.44284 + 12.8914i −0.101957 + 0.176594i −0.912491 0.409097i \(-0.865844\pi\)
0.810534 + 0.585692i \(0.199177\pi\)
\(74\) 27.3512 + 15.7912i 0.369610 + 0.213395i
\(75\) 1.64490 + 14.9095i 0.0219320 + 0.198794i
\(76\) −56.5460 −0.744027
\(77\) −10.0243 25.9028i −0.130186 0.336400i
\(78\) 38.4700 87.6193i 0.493205 1.12332i
\(79\) −44.9089 77.7844i −0.568467 0.984613i −0.996718 0.0809535i \(-0.974203\pi\)
0.428251 0.903660i \(-0.359130\pi\)
\(80\) 7.74597 + 4.47214i 0.0968246 + 0.0559017i
\(81\) −66.4992 46.2477i −0.820978 0.570959i
\(82\) 26.1729 + 45.3327i 0.319181 + 0.552838i
\(83\) 42.3934i 0.510764i 0.966840 + 0.255382i \(0.0822013\pi\)
−0.966840 + 0.255382i \(0.917799\pi\)
\(84\) 22.5962 35.4035i 0.269003 0.421471i
\(85\) 35.4274 0.416793
\(86\) −40.6061 + 23.4440i −0.472165 + 0.272604i
\(87\) −41.7209 56.8051i −0.479551 0.652932i
\(88\) 5.61136 9.71916i 0.0637655 0.110445i
\(89\) 126.802 73.2090i 1.42474 0.822573i 0.428040 0.903760i \(-0.359204\pi\)
0.996699 + 0.0811863i \(0.0258709\pi\)
\(90\) 19.2611 + 20.9526i 0.214012 + 0.232806i
\(91\) 122.970 + 99.0251i 1.35132 + 1.08819i
\(92\) 19.9913i 0.217297i
\(93\) 1.46091 + 13.2419i 0.0157087 + 0.142386i
\(94\) 52.5726 91.0584i 0.559283 0.968706i
\(95\) 54.7505 + 31.6102i 0.576321 + 0.332739i
\(96\) 16.8682 1.86099i 0.175711 0.0193853i
\(97\) −162.686 −1.67718 −0.838590 0.544763i \(-0.816620\pi\)
−0.838590 + 0.544763i \(0.816620\pi\)
\(98\) 46.6487 + 51.2436i 0.476007 + 0.522894i
\(99\) 26.2900 24.1676i 0.265556 0.244117i
\(100\) −5.00000 8.66025i −0.0500000 0.0866025i
\(101\) −167.662 96.7995i −1.66002 0.958411i −0.972704 0.232049i \(-0.925457\pi\)
−0.687312 0.726362i \(-0.741210\pi\)
\(102\) 54.1765 39.7904i 0.531143 0.390102i
\(103\) −11.1583 19.3267i −0.108333 0.187638i 0.806762 0.590876i \(-0.201218\pi\)
−0.915095 + 0.403238i \(0.867885\pi\)
\(104\) 63.7951i 0.613414i
\(105\) −41.6699 + 21.6476i −0.396856 + 0.206168i
\(106\) −102.402 −0.966054
\(107\) −46.4988 + 26.8461i −0.434568 + 0.250898i −0.701291 0.712875i \(-0.747393\pi\)
0.266723 + 0.963773i \(0.414059\pi\)
\(108\) 52.9875 + 10.4081i 0.490625 + 0.0963712i
\(109\) −12.1187 + 20.9902i −0.111181 + 0.192570i −0.916247 0.400615i \(-0.868797\pi\)
0.805066 + 0.593185i \(0.202130\pi\)
\(110\) −10.8664 + 6.27369i −0.0987850 + 0.0570336i
\(111\) −61.3441 26.9336i −0.552649 0.242645i
\(112\) −4.30471 + 27.6671i −0.0384349 + 0.247028i
\(113\) 104.806i 0.927486i 0.885970 + 0.463743i \(0.153494\pi\)
−0.885970 + 0.463743i \(0.846506\pi\)
\(114\) 119.229 13.1539i 1.04587 0.115386i
\(115\) −11.1755 + 19.3565i −0.0971780 + 0.168317i
\(116\) 40.6917 + 23.4934i 0.350791 + 0.202529i
\(117\) −60.7327 + 193.697i −0.519083 + 1.65553i
\(118\) 86.3306 0.731616
\(119\) 40.0272 + 103.430i 0.336363 + 0.869162i
\(120\) −17.3729 7.62772i −0.144774 0.0635644i
\(121\) −52.6282 91.1546i −0.434943 0.753344i
\(122\) 37.9938 + 21.9358i 0.311425 + 0.179801i
\(123\) −65.7316 89.4968i −0.534403 0.727616i
\(124\) −4.44073 7.69158i −0.0358124 0.0620289i
\(125\) 11.1803i 0.0894427i
\(126\) −39.4091 + 79.9057i −0.312771 + 0.634172i
\(127\) −9.12083 −0.0718176 −0.0359088 0.999355i \(-0.511433\pi\)
−0.0359088 + 0.999355i \(0.511433\pi\)
\(128\) −9.79796 + 5.65685i −0.0765466 + 0.0441942i
\(129\) 80.1655 58.8782i 0.621438 0.456420i
\(130\) 35.6625 61.7693i 0.274327 0.475149i
\(131\) 196.552 113.479i 1.50040 0.866256i 0.500399 0.865795i \(-0.333187\pi\)
1.00000 0.000460802i \(-0.000146678\pi\)
\(132\) −9.57080 + 21.7984i −0.0725060 + 0.165140i
\(133\) −30.4268 + 195.558i −0.228773 + 1.47036i
\(134\) 2.52091i 0.0188128i
\(135\) −45.4866 39.6985i −0.336938 0.294063i
\(136\) −22.4063 + 38.8088i −0.164752 + 0.285359i
\(137\) 85.0732 + 49.1170i 0.620972 + 0.358518i 0.777247 0.629195i \(-0.216615\pi\)
−0.156275 + 0.987714i \(0.549949\pi\)
\(138\) 4.65045 + 42.1522i 0.0336989 + 0.305451i
\(139\) −116.853 −0.840669 −0.420335 0.907369i \(-0.638087\pi\)
−0.420335 + 0.907369i \(0.638087\pi\)
\(140\) 19.6344 24.3822i 0.140246 0.174158i
\(141\) −89.6684 + 204.229i −0.635946 + 1.44843i
\(142\) −63.4317 109.867i −0.446702 0.773711i
\(143\) −77.5044 44.7472i −0.541988 0.312917i
\(144\) −35.1342 + 7.84790i −0.243987 + 0.0544993i
\(145\) −26.2664 45.4948i −0.181148 0.313757i
\(146\) 21.0515i 0.144189i
\(147\) −110.280 97.1969i −0.750207 0.661203i
\(148\) 44.6642 0.301785
\(149\) −214.655 + 123.931i −1.44064 + 0.831754i −0.997892 0.0648923i \(-0.979330\pi\)
−0.442748 + 0.896646i \(0.645996\pi\)
\(150\) 12.5572 + 17.0973i 0.0837148 + 0.113982i
\(151\) 89.0829 154.296i 0.589953 1.02183i −0.404285 0.914633i \(-0.632480\pi\)
0.994238 0.107195i \(-0.0341870\pi\)
\(152\) −69.2545 + 39.9841i −0.455621 + 0.263053i
\(153\) −104.977 + 96.5018i −0.686121 + 0.630731i
\(154\) −30.5932 24.6360i −0.198657 0.159974i
\(155\) 9.92978i 0.0640631i
\(156\) −14.8403 134.514i −0.0951298 0.862267i
\(157\) 120.316 208.394i 0.766346 1.32735i −0.173187 0.984889i \(-0.555406\pi\)
0.939532 0.342461i \(-0.111260\pi\)
\(158\) −110.004 63.5107i −0.696227 0.401967i
\(159\) 215.917 23.8211i 1.35797 0.149818i
\(160\) 12.6491 0.0790569
\(161\) −69.1377 10.7571i −0.429427 0.0668142i
\(162\) −114.147 9.61959i −0.704609 0.0593802i
\(163\) −50.4545 87.3898i −0.309537 0.536134i 0.668724 0.743511i \(-0.266841\pi\)
−0.978261 + 0.207377i \(0.933507\pi\)
\(164\) 64.1101 + 37.0140i 0.390915 + 0.225695i
\(165\) 21.4526 15.7560i 0.130016 0.0954910i
\(166\) 29.9767 + 51.9211i 0.180582 + 0.312778i
\(167\) 250.792i 1.50175i −0.660447 0.750873i \(-0.729633\pi\)
0.660447 0.750873i \(-0.270367\pi\)
\(168\) 2.64056 59.3382i 0.0157176 0.353204i
\(169\) 339.727 2.01022
\(170\) 43.3896 25.0510i 0.255233 0.147359i
\(171\) −248.337 + 55.4709i −1.45226 + 0.324391i
\(172\) −33.1548 + 57.4258i −0.192760 + 0.333871i
\(173\) −133.220 + 76.9148i −0.770060 + 0.444594i −0.832896 0.553430i \(-0.813319\pi\)
0.0628361 + 0.998024i \(0.479985\pi\)
\(174\) −91.2648 40.0706i −0.524510 0.230291i
\(175\) −32.6410 + 12.6320i −0.186520 + 0.0721827i
\(176\) 15.8713i 0.0901780i
\(177\) −182.031 + 20.0826i −1.02842 + 0.113461i
\(178\) 103.533 179.325i 0.581647 1.00744i
\(179\) −60.3477 34.8418i −0.337138 0.194647i 0.321868 0.946785i \(-0.395689\pi\)
−0.659006 + 0.752138i \(0.729023\pi\)
\(180\) 38.4056 + 12.0419i 0.213365 + 0.0668995i
\(181\) 157.344 0.869306 0.434653 0.900598i \(-0.356871\pi\)
0.434653 + 0.900598i \(0.356871\pi\)
\(182\) 220.628 + 34.3274i 1.21224 + 0.188612i
\(183\) −85.2138 37.4139i −0.465649 0.204447i
\(184\) −14.1360 24.4842i −0.0768260 0.133067i
\(185\) −43.2460 24.9681i −0.233762 0.134963i
\(186\) 11.1527 + 15.1849i 0.0599605 + 0.0816391i
\(187\) −31.4324 54.4426i −0.168088 0.291137i
\(188\) 148.698i 0.790945i
\(189\) 64.5072 177.651i 0.341308 0.939952i
\(190\) 89.4071 0.470564
\(191\) −258.821 + 149.431i −1.35508 + 0.782359i −0.988957 0.148206i \(-0.952650\pi\)
−0.366128 + 0.930564i \(0.619317\pi\)
\(192\) 19.3433 14.2069i 0.100747 0.0739941i
\(193\) −51.1259 + 88.5526i −0.264901 + 0.458822i −0.967538 0.252727i \(-0.918673\pi\)
0.702637 + 0.711549i \(0.252006\pi\)
\(194\) −199.249 + 115.037i −1.02706 + 0.592973i
\(195\) −60.8264 + 138.538i −0.311930 + 0.710453i
\(196\) 93.3674 + 29.7747i 0.476364 + 0.151912i
\(197\) 204.233i 1.03671i −0.855164 0.518357i \(-0.826544\pi\)
0.855164 0.518357i \(-0.173456\pi\)
\(198\) 15.1094 48.1890i 0.0763103 0.243379i
\(199\) −106.371 + 184.240i −0.534529 + 0.925832i 0.464657 + 0.885491i \(0.346178\pi\)
−0.999186 + 0.0403408i \(0.987156\pi\)
\(200\) −12.2474 7.07107i −0.0612372 0.0353553i
\(201\) 0.586424 + 5.31541i 0.00291753 + 0.0264448i
\(202\) −273.790 −1.35540
\(203\) 103.145 128.086i 0.508104 0.630967i
\(204\) 38.2164 87.0417i 0.187335 0.426675i
\(205\) −41.3829 71.6773i −0.201868 0.349645i
\(206\) −27.3321 15.7802i −0.132680 0.0766030i
\(207\) −19.6112 87.7972i −0.0947401 0.424141i
\(208\) 45.1100 + 78.1327i 0.216875 + 0.375638i
\(209\) 112.183i 0.536759i
\(210\) −35.7278 + 55.9779i −0.170132 + 0.266561i
\(211\) 309.058 1.46473 0.732364 0.680913i \(-0.238417\pi\)
0.732364 + 0.680913i \(0.238417\pi\)
\(212\) −125.416 + 72.4090i −0.591585 + 0.341552i
\(213\) 159.305 + 216.902i 0.747911 + 1.01832i
\(214\) −37.9661 + 65.7592i −0.177412 + 0.307286i
\(215\) 64.2040 37.0682i 0.298623 0.172410i
\(216\) 72.2558 24.7205i 0.334517 0.114447i
\(217\) −28.9900 + 11.2190i −0.133594 + 0.0517007i
\(218\) 34.2768i 0.157233i
\(219\) −4.89709 44.3877i −0.0223611 0.202684i
\(220\) −8.87234 + 15.3673i −0.0403288 + 0.0698516i
\(221\) 309.477 + 178.676i 1.40035 + 0.808490i
\(222\) −94.1758 + 10.3900i −0.424215 + 0.0468016i
\(223\) −142.851 −0.640585 −0.320293 0.947319i \(-0.603781\pi\)
−0.320293 + 0.947319i \(0.603781\pi\)
\(224\) 14.2914 + 36.9291i 0.0638011 + 0.164862i
\(225\) −30.4545 33.1289i −0.135353 0.147240i
\(226\) 74.1090 + 128.361i 0.327916 + 0.567967i
\(227\) 251.985 + 145.484i 1.11007 + 0.640898i 0.938847 0.344335i \(-0.111896\pi\)
0.171221 + 0.985233i \(0.445229\pi\)
\(228\) 136.724 100.418i 0.599665 0.440429i
\(229\) 142.297 + 246.466i 0.621384 + 1.07627i 0.989228 + 0.146382i \(0.0467627\pi\)
−0.367844 + 0.929888i \(0.619904\pi\)
\(230\) 31.6090i 0.137431i
\(231\) 70.2376 + 44.8290i 0.304059 + 0.194065i
\(232\) 66.4493 0.286420
\(233\) 125.480 72.4457i 0.538539 0.310926i −0.205948 0.978563i \(-0.566028\pi\)
0.744487 + 0.667637i \(0.232694\pi\)
\(234\) 62.5822 + 280.174i 0.267445 + 1.19732i
\(235\) −83.1246 + 143.976i −0.353722 + 0.612664i
\(236\) 105.733 61.0450i 0.448021 0.258665i
\(237\) 246.720 + 108.325i 1.04101 + 0.457066i
\(238\) 122.159 + 98.3722i 0.513275 + 0.413329i
\(239\) 49.6402i 0.207700i 0.994593 + 0.103850i \(0.0331161\pi\)
−0.994593 + 0.103850i \(0.966884\pi\)
\(240\) −26.6710 + 2.94248i −0.111129 + 0.0122603i
\(241\) 59.3847 102.857i 0.246410 0.426794i −0.716117 0.697980i \(-0.754082\pi\)
0.962527 + 0.271186i \(0.0874158\pi\)
\(242\) −128.912 74.4275i −0.532695 0.307551i
\(243\) 242.919 6.27005i 0.999667 0.0258027i
\(244\) 62.0437 0.254277
\(245\) −73.7580 81.0232i −0.301053 0.330707i
\(246\) −143.788 63.1315i −0.584505 0.256632i
\(247\) 318.849 + 552.262i 1.29088 + 2.23588i
\(248\) −10.8775 6.28015i −0.0438610 0.0253232i
\(249\) −75.2847 102.504i −0.302348 0.411662i
\(250\) 7.90569 + 13.6931i 0.0316228 + 0.0547723i
\(251\) 29.8647i 0.118983i 0.998229 + 0.0594915i \(0.0189479\pi\)
−0.998229 + 0.0594915i \(0.981052\pi\)
\(252\) 8.23579 + 125.731i 0.0326817 + 0.498931i
\(253\) 39.6610 0.156763
\(254\) −11.1707 + 6.44940i −0.0439791 + 0.0253914i
\(255\) −85.6606 + 62.9141i −0.335924 + 0.246722i
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) 168.887 97.5067i 0.657146 0.379404i −0.134043 0.990976i \(-0.542796\pi\)
0.791189 + 0.611572i \(0.209463\pi\)
\(258\) 56.5492 128.796i 0.219183 0.499211i
\(259\) 24.0333 154.466i 0.0927927 0.596395i
\(260\) 100.869i 0.387957i
\(261\) 201.756 + 63.2596i 0.773010 + 0.242374i
\(262\) 160.484 277.967i 0.612535 1.06094i
\(263\) −111.411 64.3233i −0.423616 0.244575i 0.273007 0.962012i \(-0.411982\pi\)
−0.696623 + 0.717437i \(0.745315\pi\)
\(264\) 3.69205 + 33.4651i 0.0139850 + 0.126762i
\(265\) 161.911 0.610986
\(266\) 101.016 + 261.024i 0.379758 + 0.981293i
\(267\) −176.587 + 402.195i −0.661376 + 1.50635i
\(268\) −1.78255 3.08747i −0.00665132 0.0115204i
\(269\) −8.80833 5.08549i −0.0327447 0.0189052i 0.483538 0.875323i \(-0.339351\pi\)
−0.516283 + 0.856418i \(0.672685\pi\)
\(270\) −83.7805 16.4566i −0.310298 0.0609505i
\(271\) −183.165 317.251i −0.675886 1.17067i −0.976209 0.216832i \(-0.930428\pi\)
0.300323 0.953838i \(-0.402906\pi\)
\(272\) 63.3745i 0.232995i
\(273\) −473.186 21.0569i −1.73328 0.0771314i
\(274\) 138.924 0.507022
\(275\) 17.1812 9.91958i 0.0624771 0.0360712i
\(276\) 35.5017 + 48.3373i 0.128629 + 0.175135i
\(277\) 92.6418 160.460i 0.334447 0.579279i −0.648932 0.760847i \(-0.724784\pi\)
0.983378 + 0.181568i \(0.0581172\pi\)
\(278\) −143.115 + 82.6276i −0.514803 + 0.297221i
\(279\) −27.0480 29.4234i −0.0969464 0.105460i
\(280\) 6.80634 43.7456i 0.0243084 0.156234i
\(281\) 0.659344i 0.00234642i −0.999999 0.00117321i \(-0.999627\pi\)
0.999999 0.00117321i \(-0.000373444\pi\)
\(282\) 34.5906 + 313.533i 0.122662 + 1.11182i
\(283\) 168.327 291.550i 0.594794 1.03021i −0.398782 0.917046i \(-0.630567\pi\)
0.993576 0.113167i \(-0.0360996\pi\)
\(284\) −155.375 89.7060i −0.547096 0.315866i
\(285\) −188.517 + 20.7982i −0.661464 + 0.0729762i
\(286\) −126.564 −0.442532
\(287\) 162.506 201.801i 0.566222 0.703139i
\(288\) −37.4811 + 34.4553i −0.130143 + 0.119636i
\(289\) −18.9897 32.8911i −0.0657082 0.113810i
\(290\) −64.3393 37.1463i −0.221860 0.128091i
\(291\) 393.362 288.908i 1.35176 0.992811i
\(292\) 14.8857 + 25.7828i 0.0509784 + 0.0882971i
\(293\) 473.631i 1.61649i 0.588848 + 0.808244i \(0.299582\pi\)
−0.588848 + 0.808244i \(0.700418\pi\)
\(294\) −203.794 41.0613i −0.693177 0.139664i
\(295\) −136.501 −0.462714
\(296\) 54.7023 31.5824i 0.184805 0.106697i
\(297\) −20.6488 + 105.123i −0.0695245 + 0.353948i
\(298\) −175.265 + 303.569i −0.588139 + 1.01869i
\(299\) −195.247 + 112.726i −0.652999 + 0.377009i
\(300\) 27.4690 + 12.0605i 0.0915632 + 0.0402016i
\(301\) 180.760 + 145.562i 0.600533 + 0.483596i
\(302\) 251.964i 0.834319i
\(303\) 577.294 63.6901i 1.90526 0.210198i
\(304\) −56.5460 + 97.9406i −0.186007 + 0.322173i
\(305\) −60.0735 34.6835i −0.196962 0.113716i
\(306\) −60.3323 + 192.420i −0.197165 + 0.628823i
\(307\) 120.313 0.391900 0.195950 0.980614i \(-0.437221\pi\)
0.195950 + 0.980614i \(0.437221\pi\)
\(308\) −54.8892 8.54017i −0.178212 0.0277278i
\(309\) 61.3014 + 26.9149i 0.198386 + 0.0871033i
\(310\) 7.02142 + 12.1615i 0.0226497 + 0.0392305i
\(311\) −68.7978 39.7204i −0.221215 0.127718i 0.385298 0.922792i \(-0.374099\pi\)
−0.606513 + 0.795074i \(0.707432\pi\)
\(312\) −113.291 154.251i −0.363112 0.494395i
\(313\) −260.740 451.614i −0.833034 1.44286i −0.895621 0.444818i \(-0.853268\pi\)
0.0625867 0.998040i \(-0.480065\pi\)
\(314\) 340.306i 1.08378i
\(315\) 62.3112 126.342i 0.197813 0.401086i
\(316\) −179.635 −0.568467
\(317\) 39.2973 22.6883i 0.123966 0.0715719i −0.436735 0.899590i \(-0.643865\pi\)
0.560701 + 0.828018i \(0.310532\pi\)
\(318\) 247.599 181.851i 0.778613 0.571859i
\(319\) −46.6089 + 80.7290i −0.146109 + 0.253069i
\(320\) 15.4919 8.94427i 0.0484123 0.0279508i
\(321\) 64.7554 147.487i 0.201730 0.459461i
\(322\) −92.2825 + 35.7131i −0.286591 + 0.110910i
\(323\) 447.947i 1.38683i
\(324\) −146.603 + 68.9323i −0.452477 + 0.212754i
\(325\) −56.3874 + 97.6659i −0.173500 + 0.300510i
\(326\) −123.588 71.3535i −0.379104 0.218876i
\(327\) −7.97360 72.2736i −0.0243841 0.221020i
\(328\) 104.691 0.319181
\(329\) −514.255 80.0125i −1.56308 0.243199i
\(330\) 15.1328 34.4664i 0.0458568 0.104444i
\(331\) −96.5308 167.196i −0.291634 0.505125i 0.682562 0.730827i \(-0.260866\pi\)
−0.974196 + 0.225703i \(0.927532\pi\)
\(332\) 73.4276 + 42.3934i 0.221167 + 0.127691i
\(333\) 196.155 43.8150i 0.589055 0.131577i
\(334\) −177.336 307.156i −0.530947 0.919628i
\(335\) 3.98591i 0.0118982i
\(336\) −38.7245 74.5414i −0.115251 0.221849i
\(337\) 54.4172 0.161475 0.0807377 0.996735i \(-0.474272\pi\)
0.0807377 + 0.996735i \(0.474272\pi\)
\(338\) 416.079 240.223i 1.23100 0.710720i
\(339\) −186.121 253.412i −0.549028 0.747528i
\(340\) 35.4274 61.3621i 0.104198 0.180477i
\(341\) 15.2594 8.81004i 0.0447491 0.0258359i
\(342\) −264.926 + 243.539i −0.774637 + 0.712101i
\(343\) 153.212 306.879i 0.446684 0.894692i
\(344\) 93.7759i 0.272604i
\(345\) −7.35301 66.6485i −0.0213131 0.193184i
\(346\) −108.774 + 188.402i −0.314376 + 0.544515i
\(347\) 379.684 + 219.210i 1.09419 + 0.631730i 0.934689 0.355468i \(-0.115678\pi\)
0.159500 + 0.987198i \(0.449012\pi\)
\(348\) −140.110 + 15.4577i −0.402616 + 0.0444187i
\(349\) −645.311 −1.84903 −0.924514 0.381147i \(-0.875529\pi\)
−0.924514 + 0.381147i \(0.875529\pi\)
\(350\) −31.0447 + 38.5516i −0.0886992 + 0.110147i
\(351\) −197.131 576.195i −0.561627 1.64158i
\(352\) −11.2227 19.4383i −0.0318827 0.0552225i
\(353\) 309.702 + 178.806i 0.877342 + 0.506534i 0.869781 0.493438i \(-0.164260\pi\)
0.00756095 + 0.999971i \(0.497593\pi\)
\(354\) −208.740 + 153.311i −0.589662 + 0.433082i
\(355\) 100.294 + 173.715i 0.282519 + 0.489338i
\(356\) 292.836i 0.822573i
\(357\) −280.460 179.003i −0.785603 0.501410i
\(358\) −98.5474 −0.275272
\(359\) −529.863 + 305.917i −1.47594 + 0.852136i −0.999632 0.0271416i \(-0.991360\pi\)
−0.476311 + 0.879277i \(0.658026\pi\)
\(360\) 55.5520 12.4086i 0.154311 0.0344684i
\(361\) −219.182 + 379.634i −0.607152 + 1.05162i
\(362\) 192.707 111.259i 0.532339 0.307346i
\(363\) 289.128 + 126.944i 0.796497 + 0.349709i
\(364\) 294.487 113.965i 0.809029 0.313092i
\(365\) 33.2854i 0.0911929i
\(366\) −130.821 + 14.4328i −0.357434 + 0.0394340i
\(367\) −124.390 + 215.449i −0.338936 + 0.587055i −0.984233 0.176877i \(-0.943400\pi\)
0.645297 + 0.763932i \(0.276734\pi\)
\(368\) −34.6259 19.9913i −0.0940922 0.0543242i
\(369\) 317.867 + 99.6659i 0.861429 + 0.270097i
\(370\) −70.6204 −0.190866
\(371\) 182.934 + 472.700i 0.493082 + 1.27412i
\(372\) 24.3965 + 10.7115i 0.0655820 + 0.0287943i
\(373\) −87.3976 151.377i −0.234310 0.405837i 0.724762 0.688999i \(-0.241950\pi\)
−0.959072 + 0.283163i \(0.908616\pi\)
\(374\) −76.9934 44.4522i −0.205865 0.118856i
\(375\) −19.8547 27.0331i −0.0529459 0.0720884i
\(376\) −105.145 182.117i −0.279641 0.484353i
\(377\) 529.893i 1.40555i
\(378\) −46.6133 263.190i −0.123316 0.696271i
\(379\) 124.982 0.329768 0.164884 0.986313i \(-0.447275\pi\)
0.164884 + 0.986313i \(0.447275\pi\)
\(380\) 109.501 63.2204i 0.288160 0.166369i
\(381\) 22.0534 16.1973i 0.0578830 0.0425126i
\(382\) −211.327 + 366.028i −0.553211 + 0.958190i
\(383\) 248.710 143.593i 0.649374 0.374917i −0.138842 0.990315i \(-0.544338\pi\)
0.788217 + 0.615398i \(0.211005\pi\)
\(384\) 13.6449 31.0776i 0.0355336 0.0809312i
\(385\) 48.3722 + 38.9530i 0.125642 + 0.101177i
\(386\) 144.606i 0.374626i
\(387\) −89.2743 + 284.725i −0.230683 + 0.735724i
\(388\) −162.686 + 281.781i −0.419295 + 0.726240i
\(389\) −50.6506 29.2432i −0.130207 0.0751752i 0.433482 0.901162i \(-0.357285\pi\)
−0.563689 + 0.825987i \(0.690618\pi\)
\(390\) 23.4645 + 212.685i 0.0601654 + 0.545346i
\(391\) −158.367 −0.405032
\(392\) 135.405 29.5543i 0.345421 0.0753936i
\(393\) −273.724 + 623.433i −0.696498 + 1.58634i
\(394\) −144.414 250.133i −0.366534 0.634855i
\(395\) 173.931 + 100.419i 0.440332 + 0.254226i
\(396\) −15.5696 69.7032i −0.0393171 0.176018i
\(397\) −211.582 366.471i −0.532952 0.923100i −0.999259 0.0384774i \(-0.987749\pi\)
0.466307 0.884623i \(-0.345584\pi\)
\(398\) 300.863i 0.755938i
\(399\) −273.714 526.877i −0.686001 1.32049i
\(400\) −20.0000 −0.0500000
\(401\) 94.7200 54.6866i 0.236209 0.136376i −0.377224 0.926122i \(-0.623121\pi\)
0.613433 + 0.789747i \(0.289788\pi\)
\(402\) 4.47678 + 6.09536i 0.0111363 + 0.0151626i
\(403\) −50.0803 + 86.7417i −0.124269 + 0.215240i
\(404\) −335.323 + 193.599i −0.830008 + 0.479205i
\(405\) 180.482 + 15.2099i 0.445634 + 0.0375553i
\(406\) 35.7556 229.808i 0.0880680 0.566029i
\(407\) 88.6101i 0.217715i
\(408\) −14.7424 133.627i −0.0361334 0.327517i
\(409\) −371.048 + 642.674i −0.907209 + 1.57133i −0.0892836 + 0.996006i \(0.528458\pi\)
−0.817925 + 0.575325i \(0.804876\pi\)
\(410\) −101.367 58.5243i −0.247237 0.142742i
\(411\) −292.925 + 32.3170i −0.712713 + 0.0786302i
\(412\) −44.6332 −0.108333
\(413\) −154.224 398.514i −0.373423 0.964924i
\(414\) −86.1007 93.6620i −0.207973 0.226237i
\(415\) −47.3973 82.0945i −0.114210 0.197818i
\(416\) 110.496 + 63.7951i 0.265616 + 0.153354i
\(417\) 282.541 207.514i 0.677556 0.497636i
\(418\) −79.3250 137.395i −0.189773 0.328696i
\(419\) 539.509i 1.28761i 0.765189 + 0.643806i \(0.222645\pi\)
−0.765189 + 0.643806i \(0.777355\pi\)
\(420\) −4.17510 + 93.8220i −0.00994071 + 0.223386i
\(421\) −367.291 −0.872425 −0.436212 0.899844i \(-0.643680\pi\)
−0.436212 + 0.899844i \(0.643680\pi\)
\(422\) 378.517 218.537i 0.896959 0.517860i
\(423\) −145.871 653.047i −0.344848 1.54385i
\(424\) −102.402 + 177.365i −0.241514 + 0.418314i
\(425\) −68.6049 + 39.6091i −0.161423 + 0.0931978i
\(426\) 348.481 + 153.003i 0.818030 + 0.359163i
\(427\) 33.3850 214.571i 0.0781850 0.502509i
\(428\) 107.384i 0.250898i
\(429\) 266.864 29.4418i 0.622060 0.0686289i
\(430\) 52.4223 90.7981i 0.121912 0.211158i
\(431\) 8.82344 + 5.09421i 0.0204720 + 0.0118195i 0.510201 0.860055i \(-0.329571\pi\)
−0.489729 + 0.871875i \(0.662904\pi\)
\(432\) 71.0148 81.3689i 0.164386 0.188354i
\(433\) 709.612 1.63883 0.819413 0.573203i \(-0.194300\pi\)
0.819413 + 0.573203i \(0.194300\pi\)
\(434\) −27.5723 + 34.2395i −0.0635306 + 0.0788928i
\(435\) 144.302 + 63.3572i 0.331729 + 0.145649i
\(436\) 24.2374 + 41.9803i 0.0555903 + 0.0962852i
\(437\) −244.745 141.304i −0.560057 0.323349i
\(438\) −37.3846 50.9009i −0.0853529 0.116212i
\(439\) −167.463 290.054i −0.381464 0.660714i 0.609808 0.792549i \(-0.291247\pi\)
−0.991272 + 0.131835i \(0.957913\pi\)
\(440\) 25.0948i 0.0570336i
\(441\) 439.257 + 39.1716i 0.996047 + 0.0888245i
\(442\) 505.373 1.14338
\(443\) −74.5229 + 43.0258i −0.168223 + 0.0971237i −0.581748 0.813369i \(-0.697631\pi\)
0.413525 + 0.910493i \(0.364298\pi\)
\(444\) −107.994 + 79.3174i −0.243231 + 0.178643i
\(445\) −163.700 + 283.537i −0.367866 + 0.637163i
\(446\) −174.955 + 101.011i −0.392277 + 0.226481i
\(447\) 298.935 680.853i 0.668757 1.52316i
\(448\) 43.6161 + 35.1231i 0.0973575 + 0.0783998i
\(449\) 243.513i 0.542346i −0.962531 0.271173i \(-0.912588\pi\)
0.962531 0.271173i \(-0.0874116\pi\)
\(450\) −60.7246 19.0399i −0.134944 0.0423110i
\(451\) −73.4326 + 127.189i −0.162822 + 0.282016i
\(452\) 181.529 + 104.806i 0.401613 + 0.231872i
\(453\) 58.6129 + 531.274i 0.129388 + 1.17279i
\(454\) 411.490 0.906367
\(455\) −348.844 54.2764i −0.766690 0.119289i
\(456\) 96.4455 219.664i 0.211503 0.481720i
\(457\) −137.076 237.423i −0.299948 0.519525i 0.676176 0.736740i \(-0.263636\pi\)
−0.976124 + 0.217215i \(0.930303\pi\)
\(458\) 348.555 + 201.238i 0.761037 + 0.439385i
\(459\) 82.4510 419.757i 0.179632 0.914503i
\(460\) 22.3510 + 38.7130i 0.0485890 + 0.0841587i
\(461\) 462.678i 1.00364i −0.864972 0.501820i \(-0.832664\pi\)
0.864972 0.501820i \(-0.167336\pi\)
\(462\) 117.722 + 5.23865i 0.254810 + 0.0113391i
\(463\) −431.966 −0.932972 −0.466486 0.884529i \(-0.654480\pi\)
−0.466486 + 0.884529i \(0.654480\pi\)
\(464\) 81.3835 46.9868i 0.175395 0.101265i
\(465\) −17.6339 24.0094i −0.0379224 0.0516331i
\(466\) 102.454 177.455i 0.219858 0.380804i
\(467\) −220.608 + 127.368i −0.472394 + 0.272737i −0.717241 0.696825i \(-0.754596\pi\)
0.244847 + 0.969562i \(0.421262\pi\)
\(468\) 274.760 + 298.889i 0.587094 + 0.638651i
\(469\) −11.6369 + 4.50343i −0.0248121 + 0.00960220i
\(470\) 235.112i 0.500238i
\(471\) 79.1632 + 717.544i 0.168075 + 1.52345i
\(472\) 86.3306 149.529i 0.182904 0.316799i
\(473\) −113.928 65.7763i −0.240862 0.139062i
\(474\) 378.766 41.7875i 0.799085 0.0881592i
\(475\) −141.365 −0.297611
\(476\) 219.174 + 34.1011i 0.460449 + 0.0716410i
\(477\) −479.766 + 441.035i −1.00580 + 0.924602i
\(478\) 35.1009 + 60.7966i 0.0734329 + 0.127190i
\(479\) −396.255 228.778i −0.827254 0.477615i 0.0256574 0.999671i \(-0.491832\pi\)
−0.852912 + 0.522055i \(0.825165\pi\)
\(480\) −30.5845 + 22.4630i −0.0637177 + 0.0467980i
\(481\) −251.850 436.217i −0.523597 0.906897i
\(482\) 167.965i 0.348476i
\(483\) 186.272 96.7690i 0.385657 0.200350i
\(484\) −210.513 −0.434943
\(485\) 315.041 181.889i 0.649569 0.375029i
\(486\) 293.080 179.449i 0.603046 0.369237i
\(487\) −435.992 + 755.160i −0.895261 + 1.55064i −0.0617792 + 0.998090i \(0.519677\pi\)
−0.833482 + 0.552547i \(0.813656\pi\)
\(488\) 75.9877 43.8715i 0.155712 0.0899006i
\(489\) 277.187 + 121.701i 0.566844 + 0.248878i
\(490\) −147.627 47.0780i −0.301279 0.0960775i
\(491\) 43.6406i 0.0888810i 0.999012 + 0.0444405i \(0.0141505\pi\)
−0.999012 + 0.0444405i \(0.985849\pi\)
\(492\) −220.745 + 24.3537i −0.448668 + 0.0494994i
\(493\) 186.110 322.353i 0.377506 0.653859i
\(494\) 781.016 + 450.920i 1.58100 + 0.912793i
\(495\) −23.8901 + 76.1935i −0.0482629 + 0.153926i
\(496\) −17.7629 −0.0358124
\(497\) −393.844 + 489.079i −0.792442 + 0.984062i
\(498\) −164.686 72.3067i −0.330694 0.145194i
\(499\) 224.819 + 389.397i 0.450538 + 0.780355i 0.998419 0.0562011i \(-0.0178988\pi\)
−0.547881 + 0.836556i \(0.684565\pi\)
\(500\) 19.3649 + 11.1803i 0.0387298 + 0.0223607i
\(501\) 445.370 + 606.393i 0.888963 + 1.21037i
\(502\) 21.1176 + 36.5767i 0.0420668 + 0.0728619i
\(503\) 910.519i 1.81018i 0.425222 + 0.905089i \(0.360196\pi\)
−0.425222 + 0.905089i \(0.639804\pi\)
\(504\) 98.9917 + 148.164i 0.196412 + 0.293977i
\(505\) 432.901 0.857229
\(506\) 48.5747 28.0446i 0.0959973 0.0554241i
\(507\) −821.432 + 603.307i −1.62018 + 1.18995i
\(508\) −9.12083 + 15.7977i −0.0179544 + 0.0310979i
\(509\) −240.575 + 138.896i −0.472641 + 0.272880i −0.717345 0.696718i \(-0.754643\pi\)
0.244703 + 0.969598i \(0.421309\pi\)
\(510\) −60.4254 + 137.625i −0.118481 + 0.269853i
\(511\) 97.1767 37.6071i 0.190170 0.0735951i
\(512\) 22.6274i 0.0441942i
\(513\) 501.951 575.136i 0.978461 1.12112i
\(514\) 137.895 238.842i 0.268279 0.464673i
\(515\) 43.2159 + 24.9507i 0.0839144 + 0.0484480i
\(516\) −21.8145 197.729i −0.0422762 0.383196i
\(517\) 295.004 0.570607
\(518\) −79.7895 206.176i −0.154034 0.398023i
\(519\) 185.526 422.554i 0.357468 0.814170i
\(520\) −71.3251 123.539i −0.137164 0.237574i
\(521\) −765.920 442.204i −1.47010 0.848761i −0.470660 0.882315i \(-0.655984\pi\)
−0.999437 + 0.0335541i \(0.989317\pi\)
\(522\) 291.830 65.1859i 0.559062 0.124877i
\(523\) 238.156 + 412.499i 0.455366 + 0.788717i 0.998709 0.0507939i \(-0.0161752\pi\)
−0.543343 + 0.839511i \(0.682842\pi\)
\(524\) 453.918i 0.866256i
\(525\) 56.4906 88.5088i 0.107601 0.168588i
\(526\) −181.934 −0.345881
\(527\) −60.9313 + 35.1787i −0.115619 + 0.0667527i
\(528\) 28.1852 + 38.3756i 0.0533811 + 0.0726810i
\(529\) −214.543 + 371.600i −0.405564 + 0.702458i
\(530\) 198.300 114.489i 0.374151 0.216016i
\(531\) 404.471 371.818i 0.761716 0.700223i
\(532\) 308.290 + 248.259i 0.579493 + 0.466652i
\(533\) 834.850i 1.56632i
\(534\) 68.1206 + 617.453i 0.127567 + 1.15628i
\(535\) 60.0297 103.975i 0.112205 0.194345i
\(536\) −4.36635 2.52091i −0.00814617 0.00470319i
\(537\) 207.790 22.9245i 0.386946 0.0426899i
\(538\) −14.3839 −0.0267360
\(539\) −59.0705 + 185.233i −0.109593 + 0.343660i
\(540\) −114.246 + 39.0866i −0.211567 + 0.0723826i
\(541\) 232.979 + 403.531i 0.430645 + 0.745899i 0.996929 0.0783114i \(-0.0249528\pi\)
−0.566284 + 0.824210i \(0.691620\pi\)
\(542\) −448.661 259.035i −0.827788 0.477924i
\(543\) −380.446 + 279.421i −0.700637 + 0.514588i
\(544\) 44.8126 + 77.6176i 0.0823760 + 0.142679i
\(545\) 54.1964i 0.0994429i
\(546\) −594.422 + 308.804i −1.08868 + 0.565575i
\(547\) 168.476 0.308000 0.154000 0.988071i \(-0.450784\pi\)
0.154000 + 0.988071i \(0.450784\pi\)
\(548\) 170.146 98.2341i 0.310486 0.179259i
\(549\) 272.482 60.8640i 0.496324 0.110863i
\(550\) 14.0284 24.2979i 0.0255062 0.0441780i
\(551\) 575.239 332.114i 1.04399 0.602749i
\(552\) 77.6602 + 34.0974i 0.140689 + 0.0617706i
\(553\) −96.6598 + 621.250i −0.174792 + 1.12342i
\(554\) 262.030i 0.472979i
\(555\) 148.905 16.4280i 0.268297 0.0296000i
\(556\) −116.853 + 202.395i −0.210167 + 0.364020i
\(557\) −124.601 71.9384i −0.223700 0.129153i 0.383962 0.923349i \(-0.374559\pi\)
−0.607662 + 0.794195i \(0.707893\pi\)
\(558\) −53.9324 16.9103i −0.0966530 0.0303051i
\(559\) 747.805 1.33776
\(560\) −22.5967 58.3900i −0.0403513 0.104268i
\(561\) 172.683 + 75.8181i 0.307813 + 0.135148i
\(562\) −0.466226 0.807528i −0.000829584 0.00143688i
\(563\) 55.1604 + 31.8469i 0.0979758 + 0.0565664i 0.548187 0.836356i \(-0.315318\pi\)
−0.450212 + 0.892922i \(0.648651\pi\)
\(564\) 264.066 + 359.539i 0.468202 + 0.637480i
\(565\) −117.177 202.956i −0.207392 0.359214i
\(566\) 476.100i 0.841165i
\(567\) 159.510 + 544.101i 0.281322 + 0.959613i
\(568\) −253.727 −0.446702
\(569\) 697.403 402.646i 1.22566 0.707638i 0.259544 0.965731i \(-0.416428\pi\)
0.966120 + 0.258094i \(0.0830943\pi\)
\(570\) −216.179 + 158.774i −0.379262 + 0.278552i
\(571\) −330.642 + 572.690i −0.579059 + 1.00296i 0.416529 + 0.909122i \(0.363246\pi\)
−0.995588 + 0.0938366i \(0.970087\pi\)
\(572\) −155.009 + 89.4943i −0.270994 + 0.156459i
\(573\) 360.441 820.941i 0.629042 1.43271i
\(574\) 56.3332 362.064i 0.0981415 0.630773i
\(575\) 49.9782i 0.0869187i
\(576\) −21.5412 + 68.7021i −0.0373980 + 0.119274i
\(577\) 198.628 344.034i 0.344243 0.596247i −0.640973 0.767564i \(-0.721469\pi\)
0.985216 + 0.171317i \(0.0548022\pi\)
\(578\) −46.5150 26.8554i −0.0804758 0.0464627i
\(579\) −33.6387 304.905i −0.0580980 0.526607i
\(580\) −105.066 −0.181148
\(581\) 186.124 231.130i 0.320350 0.397814i
\(582\) 277.480 631.988i 0.476769 1.08589i
\(583\) −143.653 248.815i −0.246404 0.426783i
\(584\) 36.4623 + 21.0515i 0.0624355 + 0.0360472i
\(585\) −98.9511 442.993i −0.169147 0.757254i
\(586\) 334.907 + 580.077i 0.571514 + 0.989892i
\(587\) 251.560i 0.428552i 0.976773 + 0.214276i \(0.0687392\pi\)
−0.976773 + 0.214276i \(0.931261\pi\)
\(588\) −278.630 + 93.8144i −0.473861 + 0.159548i
\(589\) −125.553 −0.213163
\(590\) −167.179 + 96.5206i −0.283354 + 0.163594i
\(591\) 362.688 + 493.818i 0.613686 + 0.835563i
\(592\) 44.6642 77.3607i 0.0754464 0.130677i
\(593\) −90.1278 + 52.0353i −0.151986 + 0.0877493i −0.574064 0.818810i \(-0.694634\pi\)
0.422078 + 0.906559i \(0.361301\pi\)
\(594\) 49.0435 + 143.349i 0.0825648 + 0.241329i
\(595\) −193.151 155.540i −0.324624 0.261412i
\(596\) 495.725i 0.831754i
\(597\) −69.9880 634.379i −0.117233 1.06261i
\(598\) −159.418 + 276.121i −0.266586 + 0.461740i
\(599\) 272.192 + 157.150i 0.454411 + 0.262354i 0.709691 0.704513i \(-0.248834\pi\)
−0.255280 + 0.966867i \(0.582168\pi\)
\(600\) 42.1705 4.65247i 0.0702842 0.00775412i
\(601\) −504.012 −0.838622 −0.419311 0.907843i \(-0.637728\pi\)
−0.419311 + 0.907843i \(0.637728\pi\)
\(602\) 324.314 + 50.4597i 0.538727 + 0.0838201i
\(603\) −10.8573 11.8108i −0.0180055 0.0195868i
\(604\) −178.166 308.592i −0.294976 0.510914i
\(605\) 203.828 + 117.680i 0.336906 + 0.194513i
\(606\) 662.002 486.213i 1.09241 0.802331i
\(607\) −122.172 211.609i −0.201273 0.348614i 0.747666 0.664075i \(-0.231174\pi\)
−0.948939 + 0.315460i \(0.897841\pi\)
\(608\) 159.936i 0.263053i
\(609\) −21.9330 + 492.873i −0.0360147 + 0.809316i
\(610\) −98.0997 −0.160819
\(611\) −1452.27 + 838.468i −2.37687 + 1.37229i
\(612\) 62.1696 + 278.326i 0.101584 + 0.454782i
\(613\) −80.6234 + 139.644i −0.131523 + 0.227804i −0.924264 0.381755i \(-0.875320\pi\)
0.792741 + 0.609559i \(0.208653\pi\)
\(614\) 147.353 85.0743i 0.239989 0.138557i
\(615\) 227.349 + 99.8196i 0.369674 + 0.162308i
\(616\) −73.2641 + 28.3530i −0.118935 + 0.0460276i
\(617\) 115.268i 0.186820i −0.995628 0.0934102i \(-0.970223\pi\)
0.995628 0.0934102i \(-0.0297768\pi\)
\(618\) 94.1103 10.3827i 0.152282 0.0168005i
\(619\) 161.459 279.656i 0.260839 0.451786i −0.705626 0.708584i \(-0.749334\pi\)
0.966465 + 0.256798i \(0.0826675\pi\)
\(620\) 17.1989 + 9.92978i 0.0277401 + 0.0160158i
\(621\) 203.334 + 177.460i 0.327430 + 0.285765i
\(622\) −112.346 −0.180621
\(623\) −1012.74 157.572i −1.62559 0.252924i
\(624\) −247.825 108.810i −0.397155 0.174374i
\(625\) −12.5000 21.6506i −0.0200000 0.0346410i
\(626\) −638.679 368.742i −1.02025 0.589044i
\(627\) 199.220 + 271.248i 0.317736 + 0.432613i
\(628\) −240.633 416.788i −0.383173 0.663675i
\(629\) 353.822i 0.562515i
\(630\) −13.0219 198.797i −0.0206697 0.315552i
\(631\) 508.982 0.806628 0.403314 0.915062i \(-0.367858\pi\)
0.403314 + 0.915062i \(0.367858\pi\)
\(632\) −220.008 + 127.021i −0.348113 + 0.200983i
\(633\) −747.276 + 548.843i −1.18053 + 0.867050i
\(634\) 32.0861 55.5748i 0.0506090 0.0876574i
\(635\) 17.6624 10.1974i 0.0278148 0.0160589i
\(636\) 174.658 397.800i 0.274619 0.625472i
\(637\) −235.677 1079.77i −0.369980 1.69509i
\(638\) 131.830i 0.206630i
\(639\) −770.373 241.547i −1.20559 0.378008i
\(640\) 12.6491 21.9089i 0.0197642 0.0342327i
\(641\) 717.155 + 414.050i 1.11881 + 0.645943i 0.941096 0.338140i \(-0.109798\pi\)
0.177710 + 0.984083i \(0.443131\pi\)
\(642\) −24.9802 226.423i −0.0389099 0.352684i
\(643\) 676.813 1.05259 0.526293 0.850303i \(-0.323581\pi\)
0.526293 + 0.850303i \(0.323581\pi\)
\(644\) −87.7695 + 108.993i −0.136288 + 0.169244i
\(645\) −89.4121 + 203.645i −0.138623 + 0.315729i
\(646\) 316.747 + 548.621i 0.490320 + 0.849259i
\(647\) 262.244 + 151.407i 0.405323 + 0.234013i 0.688778 0.724972i \(-0.258147\pi\)
−0.283455 + 0.958985i \(0.591481\pi\)
\(648\) −130.808 + 188.088i −0.201865 + 0.290260i
\(649\) 121.108 + 209.765i 0.186607 + 0.323213i
\(650\) 159.488i 0.245366i
\(651\) 50.1720 78.6088i 0.0770691 0.120751i
\(652\) −201.818 −0.309537
\(653\) 525.385 303.331i 0.804572 0.464520i −0.0404956 0.999180i \(-0.512894\pi\)
0.845067 + 0.534660i \(0.179560\pi\)
\(654\) −60.8707 82.8785i −0.0930745 0.126726i
\(655\) −253.748 + 439.504i −0.387401 + 0.670999i
\(656\) 128.220 74.0280i 0.195458 0.112848i
\(657\) 90.6671 + 98.6294i 0.138002 + 0.150121i
\(658\) −686.408 + 265.638i −1.04317 + 0.403705i
\(659\) 48.8209i 0.0740833i 0.999314 + 0.0370416i \(0.0117934\pi\)
−0.999314 + 0.0370416i \(0.988207\pi\)
\(660\) −5.83764 52.9130i −0.00884491 0.0801712i
\(661\) 186.358 322.782i 0.281934 0.488324i −0.689927 0.723879i \(-0.742357\pi\)
0.971861 + 0.235555i \(0.0756908\pi\)
\(662\) −236.451 136.515i −0.357177 0.206216i
\(663\) −1065.59 + 117.562i −1.60723 + 0.177318i
\(664\) 119.907 0.180582
\(665\) −159.720 412.715i −0.240180 0.620624i
\(666\) 209.258 192.365i 0.314201 0.288836i
\(667\) 117.416 + 203.370i 0.176036 + 0.304903i
\(668\) −434.384 250.792i −0.650275 0.375436i
\(669\) 345.401 253.682i 0.516294 0.379196i
\(670\) 2.81846 + 4.88172i 0.00420666 + 0.00728616i
\(671\) 123.089i 0.183442i
\(672\) −100.136 63.9118i −0.149012 0.0951069i
\(673\) 600.023 0.891565 0.445782 0.895141i \(-0.352926\pi\)
0.445782 + 0.895141i \(0.352926\pi\)
\(674\) 66.6472 38.4788i 0.0988831 0.0570902i
\(675\) 132.469 + 26.0202i 0.196250 + 0.0385485i
\(676\) 339.727 588.424i 0.502555 0.870450i
\(677\) −49.4340 + 28.5407i −0.0730192 + 0.0421576i −0.536065 0.844177i \(-0.680090\pi\)
0.463046 + 0.886334i \(0.346757\pi\)
\(678\) −407.140 178.758i −0.600501 0.263655i
\(679\) 886.970 + 714.256i 1.30629 + 1.05192i
\(680\) 100.204i 0.147359i
\(681\) −867.639 + 95.7224i −1.27407 + 0.140562i
\(682\) 12.4593 21.5801i 0.0182687 0.0316424i
\(683\) −996.364 575.251i −1.45881 0.842241i −0.459852 0.887995i \(-0.652098\pi\)
−0.998953 + 0.0457539i \(0.985431\pi\)
\(684\) −152.259 + 485.604i −0.222601 + 0.709947i
\(685\) −219.658 −0.320669
\(686\) −29.3503 484.186i −0.0427847 0.705811i
\(687\) −781.751 343.234i −1.13792 0.499613i
\(688\) 66.3096 + 114.852i 0.0963802 + 0.166935i
\(689\) 1414.38 + 816.591i 2.05280 + 1.18518i
\(690\) −56.1331 76.4280i −0.0813524 0.110765i
\(691\) −677.214 1172.97i −0.980049 1.69749i −0.662152 0.749370i \(-0.730357\pi\)
−0.317897 0.948125i \(-0.602977\pi\)
\(692\) 307.659i 0.444594i
\(693\) −249.439 + 16.3391i −0.359940 + 0.0235774i
\(694\) 620.021 0.893401
\(695\) 226.285 130.646i 0.325590 0.187979i
\(696\) −160.669 + 118.005i −0.230846 + 0.169547i
\(697\) 293.218 507.869i 0.420686 0.728649i
\(698\) −790.341 + 456.304i −1.13229 + 0.653730i
\(699\) −174.746 + 398.002i −0.249994 + 0.569387i
\(700\) −10.7618 + 69.1678i −0.0153740 + 0.0988111i
\(701\) 224.033i 0.319590i 0.987150 + 0.159795i \(0.0510833\pi\)
−0.987150 + 0.159795i \(0.948917\pi\)
\(702\) −648.867 566.300i −0.924312 0.806695i
\(703\) 315.698 546.805i 0.449073 0.777817i
\(704\) −27.4899 15.8713i −0.0390482 0.0225445i
\(705\) −54.6926 495.740i −0.0775781 0.703177i
\(706\) 505.741 0.716347
\(707\) 489.107 + 1263.85i 0.691807 + 1.78763i
\(708\) −147.246 + 335.369i −0.207975 + 0.473685i
\(709\) −267.015 462.483i −0.376608 0.652304i 0.613958 0.789338i \(-0.289576\pi\)
−0.990566 + 0.137034i \(0.956243\pi\)
\(710\) 245.670 + 141.838i 0.346014 + 0.199771i
\(711\) −788.918 + 176.220i −1.10959 + 0.247848i
\(712\) −207.066 358.650i −0.290824 0.503721i
\(713\) 44.3880i 0.0622553i
\(714\) −470.067 20.9181i −0.658357 0.0292970i
\(715\) 200.115 0.279882
\(716\) −120.695 + 69.6836i −0.168569 + 0.0973234i
\(717\) −88.1540 120.026i −0.122948 0.167400i
\(718\) −432.632 + 749.340i −0.602551 + 1.04365i
\(719\) 451.069 260.425i 0.627356 0.362204i −0.152371 0.988323i \(-0.548691\pi\)
0.779727 + 0.626119i \(0.215358\pi\)
\(720\) 59.2628 54.4786i 0.0823095 0.0756647i
\(721\) −24.0166 + 154.359i −0.0333101 + 0.214090i
\(722\) 619.939i 0.858642i
\(723\) 39.0727 + 354.160i 0.0540425 + 0.489847i
\(724\) 157.344 272.528i 0.217327 0.376421i
\(725\) 101.729 + 58.7335i 0.140316 + 0.0810117i
\(726\) 443.872 48.9702i 0.611393 0.0674521i
\(727\) −283.691 −0.390221 −0.195111 0.980781i \(-0.562507\pi\)
−0.195111 + 0.980781i \(0.562507\pi\)
\(728\) 280.085 347.812i 0.384732 0.477764i
\(729\) −576.224 + 446.550i −0.790430 + 0.612552i
\(730\) −23.5363 40.7661i −0.0322416 0.0558440i
\(731\) 454.916 + 262.646i 0.622321 + 0.359297i
\(732\) −150.017 + 110.181i −0.204941 + 0.150520i
\(733\) 26.5529 + 45.9910i 0.0362250 + 0.0627435i 0.883569 0.468300i \(-0.155133\pi\)
−0.847344 + 0.531044i \(0.821800\pi\)
\(734\) 351.827i 0.479328i
\(735\) 322.227 + 64.9236i 0.438403 + 0.0883315i
\(736\) −56.5439 −0.0768260
\(737\) 6.12529 3.53644i 0.00831111 0.00479842i
\(738\) 459.781 102.701i 0.623009 0.139161i
\(739\) 350.373 606.864i 0.474118 0.821197i −0.525443 0.850829i \(-0.676100\pi\)
0.999561 + 0.0296323i \(0.00943363\pi\)
\(740\) −86.4919 + 49.9361i −0.116881 + 0.0674813i
\(741\) −1751.69 769.094i −2.36395 1.03791i
\(742\) 558.296 + 449.583i 0.752421 + 0.605907i
\(743\) 714.620i 0.961803i −0.876775 0.480902i \(-0.840309\pi\)
0.876775 0.480902i \(-0.159691\pi\)
\(744\) 37.4536 4.13208i 0.0503409 0.00555387i
\(745\) 277.119 479.984i 0.371972 0.644274i
\(746\) −214.079 123.599i −0.286970 0.165682i
\(747\) 364.065 + 114.151i 0.487369 + 0.152812i
\(748\) −125.730 −0.168088
\(749\) 371.377 + 57.7823i 0.495831 + 0.0771459i
\(750\) −43.4323 19.0693i −0.0579097 0.0254257i
\(751\) 206.062 + 356.909i 0.274383 + 0.475246i 0.969979 0.243187i \(-0.0781930\pi\)
−0.695596 + 0.718433i \(0.744860\pi\)
\(752\) −257.552 148.698i −0.342489 0.197736i
\(753\) −53.0355 72.2105i −0.0704323 0.0958970i
\(754\) −374.691 648.984i −0.496937 0.860721i
\(755\) 398.391i 0.527670i
\(756\) −243.193 289.381i −0.321684 0.382779i
\(757\) 85.9332 0.113518 0.0567590 0.998388i \(-0.481923\pi\)
0.0567590 + 0.998388i \(0.481923\pi\)
\(758\) 153.071 88.3758i 0.201941 0.116591i
\(759\) −95.8971 + 70.4324i −0.126347 + 0.0927963i
\(760\) 89.4071 154.858i 0.117641 0.203760i
\(761\) −466.638 + 269.414i −0.613191 + 0.354026i −0.774213 0.632925i \(-0.781854\pi\)
0.161022 + 0.986951i \(0.448521\pi\)
\(762\) 15.5566 35.4317i 0.0204155 0.0464983i
\(763\) 158.226 61.2331i 0.207374 0.0802531i
\(764\) 597.722i 0.782359i
\(765\) 95.3938 304.242i 0.124698 0.397702i
\(766\) 203.071 351.730i 0.265106 0.459177i
\(767\) −1192.40 688.434i −1.55463 0.897567i
\(768\) −5.26367 47.7105i −0.00685374 0.0621231i
\(769\) 284.283 0.369679 0.184840 0.982769i \(-0.440823\pi\)
0.184840 + 0.982769i \(0.440823\pi\)
\(770\) 86.7875 + 13.5032i 0.112711 + 0.0175366i
\(771\) −235.196 + 535.682i −0.305053 + 0.694788i
\(772\) 102.252 + 177.105i 0.132450 + 0.229411i
\(773\) 971.569 + 560.936i 1.25688 + 0.725661i 0.972467 0.233041i \(-0.0748676\pi\)
0.284414 + 0.958701i \(0.408201\pi\)
\(774\) 91.9929 + 411.842i 0.118854 + 0.532096i
\(775\) −11.1018 19.2289i −0.0143250 0.0248115i
\(776\) 460.147i 0.592973i
\(777\) 216.200 + 416.167i 0.278249 + 0.535607i
\(778\) −82.7121 −0.106314
\(779\) 906.293 523.249i 1.16341 0.671693i
\(780\) 179.129 + 243.893i 0.229652 + 0.312683i
\(781\) 177.969 308.251i 0.227873 0.394688i
\(782\) −193.960 + 111.983i −0.248030 + 0.143200i
\(783\) −600.168 + 205.333i −0.766499 + 0.262239i
\(784\) 144.939 131.942i 0.184871 0.168294i
\(785\) 538.071i 0.685440i
\(786\) 105.592 + 957.098i 0.134341 + 1.21768i
\(787\) −207.092 + 358.695i −0.263142 + 0.455775i −0.967075 0.254491i \(-0.918092\pi\)
0.703933 + 0.710266i \(0.251425\pi\)
\(788\) −353.742 204.233i −0.448911 0.259179i
\(789\) 383.612 42.3221i 0.486200 0.0536402i
\(790\) 284.029 0.359530
\(791\) 460.139 571.404i 0.581718 0.722382i
\(792\) −68.3564 74.3593i −0.0863085 0.0938881i
\(793\) −349.848 605.955i −0.441171 0.764130i
\(794\) −518.268 299.222i −0.652730 0.376854i
\(795\) −391.488 + 287.532i −0.492438 + 0.361675i
\(796\) 212.743 + 368.481i 0.267265 + 0.462916i
\(797\) 951.057i 1.19330i −0.802503 0.596648i \(-0.796499\pi\)
0.802503 0.596648i \(-0.203501\pi\)
\(798\) −707.789 451.745i −0.886953 0.566097i
\(799\) −1177.96 −1.47429
\(800\) −24.4949 + 14.1421i −0.0306186 + 0.0176777i
\(801\) −287.268 1286.07i −0.358637 1.60558i
\(802\) 77.3385 133.954i 0.0964321 0.167025i
\(803\) −51.1508 + 29.5319i −0.0636996 + 0.0367770i
\(804\) 9.79298 + 4.29969i 0.0121803 + 0.00534788i
\(805\) 145.911 56.4673i 0.181256 0.0701457i
\(806\) 141.649i 0.175743i
\(807\) 30.3289 3.34605i 0.0375823 0.00414628i
\(808\) −273.790 + 474.219i −0.338849 + 0.586904i
\(809\) 1065.12 + 614.948i 1.31659 + 0.760133i 0.983178 0.182649i \(-0.0584671\pi\)
0.333411 + 0.942782i \(0.391800\pi\)
\(810\) 231.799 108.992i 0.286172 0.134558i
\(811\) −1449.23 −1.78696 −0.893482 0.449098i \(-0.851745\pi\)
−0.893482 + 0.449098i \(0.851745\pi\)
\(812\) −118.707 306.739i −0.146191 0.377757i
\(813\) 1006.27 + 441.812i 1.23773 + 0.543435i
\(814\) 62.6568 + 108.525i 0.0769739 + 0.133323i
\(815\) 195.410 + 112.820i 0.239766 + 0.138429i
\(816\) −112.544 153.234i −0.137922 0.187787i
\(817\) 468.693 + 811.800i 0.573675 + 0.993635i
\(818\) 1049.48i 1.28299i
\(819\) 1181.52 789.398i 1.44264 0.963856i
\(820\) −165.532 −0.201868
\(821\) −393.845 + 227.387i −0.479714 + 0.276963i −0.720297 0.693665i \(-0.755995\pi\)
0.240583 + 0.970629i \(0.422661\pi\)
\(822\) −335.907 + 246.709i −0.408646 + 0.300133i
\(823\) 453.304 785.146i 0.550795 0.954005i −0.447422 0.894323i \(-0.647658\pi\)
0.998217 0.0596822i \(-0.0190087\pi\)
\(824\) −54.6643 + 31.5604i −0.0663401 + 0.0383015i
\(825\) −23.9270 + 54.4961i −0.0290024 + 0.0660559i
\(826\) −470.676 379.025i −0.569826 0.458868i
\(827\) 110.278i 0.133348i 0.997775 + 0.0666738i \(0.0212387\pi\)
−0.997775 + 0.0666738i \(0.978761\pi\)
\(828\) −171.680 53.8296i −0.207344 0.0650116i
\(829\) −559.990 + 969.931i −0.675501 + 1.17000i 0.300822 + 0.953680i \(0.402739\pi\)
−0.976322 + 0.216321i \(0.930594\pi\)
\(830\) −116.099 67.0299i −0.139879 0.0807589i
\(831\) 60.9545 + 552.498i 0.0733508 + 0.664860i
\(832\) 180.440 0.216875
\(833\) 235.870 739.639i 0.283157 0.887922i
\(834\) 199.306 453.939i 0.238976 0.544291i
\(835\) 280.393 + 485.656i 0.335801 + 0.581624i
\(836\) −194.306 112.183i −0.232423 0.134190i
\(837\) 117.652 + 23.1098i 0.140563 + 0.0276103i
\(838\) 381.491 + 660.761i 0.455239 + 0.788498i
\(839\) 824.753i 0.983019i −0.870872 0.491509i \(-0.836445\pi\)
0.870872 0.491509i \(-0.163555\pi\)
\(840\) 61.2287 + 117.860i 0.0728914 + 0.140310i
\(841\) 289.061 0.343711
\(842\) −449.838 + 259.714i −0.534249 + 0.308449i
\(843\) 1.17090 + 1.59424i 0.00138897 + 0.00189115i
\(844\) 309.058 535.304i 0.366182 0.634246i
\(845\) −657.878 + 379.826i −0.778554 + 0.449498i
\(846\) −640.428 696.669i −0.757007 0.823486i
\(847\) −113.274 + 728.035i −0.133736 + 0.859545i
\(848\) 289.636i 0.341552i
\(849\) 110.752 + 1003.87i 0.130450 + 1.18241i
\(850\) −56.0157 + 97.0220i −0.0659008 + 0.114144i
\(851\) 193.318 + 111.612i 0.227165 + 0.131154i
\(852\) 534.990 59.0229i 0.627922 0.0692757i
\(853\) −184.467 −0.216257 −0.108128 0.994137i \(-0.534486\pi\)
−0.108128 + 0.994137i \(0.534486\pi\)
\(854\) −110.837 286.402i −0.129785 0.335365i
\(855\) 418.885 385.069i 0.489924 0.450373i
\(856\) 75.9322 + 131.518i 0.0887059 + 0.153643i
\(857\) 157.934 + 91.1832i 0.184287 + 0.106398i 0.589305 0.807910i \(-0.299402\pi\)
−0.405018 + 0.914309i \(0.632735\pi\)
\(858\) 306.022 224.760i 0.356668 0.261958i
\(859\) 246.183 + 426.402i 0.286593 + 0.496393i 0.972994 0.230830i \(-0.0741441\pi\)
−0.686402 + 0.727223i \(0.740811\pi\)
\(860\) 148.273i 0.172410i
\(861\) −34.5555 + 776.526i −0.0401342 + 0.901888i
\(862\) 14.4086 0.0167153
\(863\) 1219.53 704.098i 1.41313 0.815872i 0.417450 0.908700i \(-0.362924\pi\)
0.995682 + 0.0928280i \(0.0295907\pi\)
\(864\) 29.4385 149.871i 0.0340724 0.173462i
\(865\) 171.987 297.890i 0.198829 0.344381i
\(866\) 869.093 501.771i 1.00357 0.579413i
\(867\) 104.325 + 45.8049i 0.120329 + 0.0528315i
\(868\) −9.55803 + 61.4312i −0.0110116 + 0.0707732i
\(869\) 356.382i 0.410105i
\(870\) 221.534 24.4408i 0.254636 0.0280928i
\(871\) −20.1027 + 34.8189i −0.0230801 + 0.0399758i
\(872\) 59.3692 + 34.2768i 0.0680839 + 0.0393083i
\(873\) −438.058 + 1397.11i −0.501785 + 1.60036i
\(874\) −399.667 −0.457285
\(875\) 49.0860 60.9554i 0.0560983 0.0696633i
\(876\) −81.7789 35.9057i −0.0933549 0.0409883i
\(877\) 373.148 + 646.311i 0.425482 + 0.736957i 0.996465 0.0840049i \(-0.0267711\pi\)
−0.570983 + 0.820962i \(0.693438\pi\)
\(878\) −410.198 236.828i −0.467196 0.269736i
\(879\) −841.101 1145.20i −0.956884 1.30284i
\(880\) 17.7447 + 30.7347i 0.0201644 + 0.0349258i
\(881\) 460.190i 0.522350i −0.965291 0.261175i \(-0.915890\pi\)
0.965291 0.261175i \(-0.0841100\pi\)
\(882\) 565.676 262.626i 0.641356 0.297762i
\(883\) 1254.38 1.42059 0.710295 0.703904i \(-0.248561\pi\)
0.710295 + 0.703904i \(0.248561\pi\)
\(884\) 618.953 357.353i 0.700173 0.404245i
\(885\) 330.048 242.406i 0.372935 0.273905i
\(886\) −60.8477 + 105.391i −0.0686768 + 0.118952i
\(887\) 1061.49 612.851i 1.19672 0.690926i 0.236896 0.971535i \(-0.423870\pi\)
0.959822 + 0.280609i \(0.0905365\pi\)
\(888\) −76.1798 + 173.507i −0.0857881 + 0.195391i
\(889\) 49.7270 + 40.0440i 0.0559358 + 0.0450439i
\(890\) 463.015i 0.520241i
\(891\) −136.756 290.847i −0.153486 0.326428i
\(892\) −142.851 + 247.424i −0.160146 + 0.277382i
\(893\) −1820.44 1051.03i −2.03857 1.17697i
\(894\) −115.317 1045.25i −0.128990 1.16918i
\(895\) 155.817 0.174097
\(896\) 78.2544 + 12.1756i 0.0873375 + 0.0135888i
\(897\) 271.906 619.292i 0.303128 0.690404i
\(898\) −172.190 298.242i −0.191748 0.332118i
\(899\) 90.3506 + 52.1640i 0.100501 + 0.0580244i
\(900\) −87.8354 + 19.6197i −0.0975949 + 0.0217997i
\(901\) 573.611 + 993.523i 0.636638 + 1.10269i
\(902\) 207.699i 0.230265i
\(903\) −695.562 30.9526i −0.770279 0.0342776i
\(904\) 296.436 0.327916
\(905\) −304.696 + 175.916i −0.336681 + 0.194383i
\(906\) 447.453 + 609.229i 0.493878 + 0.672439i
\(907\) 211.585 366.476i 0.233280 0.404052i −0.725492 0.688231i \(-0.758388\pi\)
0.958771 + 0.284179i \(0.0917209\pi\)
\(908\) 503.971 290.968i 0.555034 0.320449i
\(909\) −1282.75 + 1179.19i −1.41116 + 1.29724i
\(910\) −465.624 + 180.195i −0.511675 + 0.198017i
\(911\) 1111.02i 1.21956i −0.792569 0.609782i \(-0.791257\pi\)
0.792569 0.609782i \(-0.208743\pi\)
\(912\) −37.2050 337.230i −0.0407949 0.369770i
\(913\) −84.1050 + 145.674i −0.0921194 + 0.159555i
\(914\) −335.767 193.855i −0.367360 0.212095i
\(915\) 206.846 22.8203i 0.226061 0.0249402i
\(916\) 569.188 0.621384
\(917\) −1569.83 244.248i −1.71191 0.266356i
\(918\) −195.832 572.397i −0.213324 0.623526i
\(919\) −671.478 1163.03i −0.730661 1.26554i −0.956601 0.291401i \(-0.905879\pi\)
0.225940 0.974141i \(-0.427455\pi\)
\(920\) 54.7484 + 31.6090i 0.0595092 + 0.0343576i
\(921\) −290.907 + 213.659i −0.315860 + 0.231986i
\(922\) −327.163 566.662i −0.354840 0.614601i
\(923\) 2023.32i 2.19211i
\(924\) 147.884 76.8260i 0.160047 0.0831451i
\(925\) 111.661 0.120714
\(926\) −529.048 + 305.446i −0.571326 + 0.329855i
\(927\) −196.019 + 43.7846i −0.211455 + 0.0472325i
\(928\) 66.4493 115.094i 0.0716049 0.124023i
\(929\) −246.782 + 142.480i −0.265642 + 0.153369i −0.626906 0.779095i \(-0.715679\pi\)
0.361263 + 0.932464i \(0.382346\pi\)
\(930\) −38.5742 16.9363i −0.0414777 0.0182111i
\(931\) 1024.46 932.602i 1.10039 1.00172i
\(932\) 289.783i 0.310926i
\(933\) 236.885 26.1344i 0.253896 0.0280112i
\(934\) −180.126 + 311.987i −0.192854 + 0.334033i
\(935\) 121.737 + 70.2850i 0.130200 + 0.0751712i
\(936\) 547.857 + 171.778i 0.585317 + 0.183524i
\(937\) −930.931 −0.993523 −0.496761 0.867887i \(-0.665478\pi\)
−0.496761 + 0.867887i \(0.665478\pi\)
\(938\) −11.0678 + 13.7441i −0.0117993 + 0.0146525i
\(939\) 1432.45 + 628.930i 1.52551 + 0.669787i
\(940\) 166.249 + 287.952i 0.176861 + 0.306332i
\(941\) 1059.13 + 611.492i 1.12554 + 0.649832i 0.942810 0.333331i \(-0.108173\pi\)
0.182732 + 0.983163i \(0.441506\pi\)
\(942\) 604.335 + 822.831i 0.641545 + 0.873494i
\(943\) 184.989 + 320.411i 0.196171 + 0.339779i
\(944\) 244.180i 0.258665i
\(945\) 73.7021 + 416.141i 0.0779916 + 0.440360i
\(946\) −186.043 −0.196663
\(947\) 362.242 209.141i 0.382515 0.220845i −0.296397 0.955065i \(-0.595785\pi\)
0.678912 + 0.734220i \(0.262452\pi\)
\(948\) 434.344 319.007i 0.458169 0.336505i
\(949\) 167.873 290.765i 0.176895 0.306391i
\(950\) −173.136 + 99.9602i −0.182249 + 0.105221i
\(951\) −54.7264 + 124.645i −0.0575462 + 0.131067i
\(952\) 292.545 113.214i 0.307295 0.118922i
\(953\) 136.702i 0.143444i −0.997425 0.0717219i \(-0.977151\pi\)
0.997425 0.0717219i \(-0.0228494\pi\)
\(954\) −275.732 + 879.402i −0.289028 + 0.921805i
\(955\) 334.137 578.742i 0.349881 0.606012i
\(956\) 85.9794 + 49.6402i 0.0899366 + 0.0519249i
\(957\) −30.6668 277.967i −0.0320447 0.290456i
\(958\) −647.081 −0.675450
\(959\) −248.178 641.291i −0.258788 0.668708i
\(960\) −21.5745 + 49.1380i −0.0224734 + 0.0511854i
\(961\) 470.640 + 815.172i 0.489740 + 0.848254i
\(962\) −616.905 356.170i −0.641273 0.370239i
\(963\) 105.343 + 471.608i 0.109390 + 0.489728i
\(964\) −118.769 205.715i −0.123205 0.213397i
\(965\) 228.642i 0.236935i
\(966\) 159.710 250.232i 0.165331 0.259039i
\(967\) −1058.67 −1.09480 −0.547398 0.836873i \(-0.684382\pi\)
−0.547398 + 0.836873i \(0.684382\pi\)
\(968\) −257.824 + 148.855i −0.266347 + 0.153776i
\(969\) −795.491 1083.10i −0.820940 1.11775i
\(970\) 257.230 445.535i 0.265185 0.459315i
\(971\) −307.645 + 177.619i −0.316833 + 0.182924i −0.649980 0.759951i \(-0.725223\pi\)
0.333147 + 0.942875i \(0.391889\pi\)
\(972\) 232.059 427.018i 0.238744 0.439319i
\(973\) 637.085 + 513.030i 0.654763 + 0.527266i
\(974\) 1233.17i 1.26609i
\(975\) −37.1006 336.284i −0.0380519 0.344907i
\(976\) 62.0437 107.463i 0.0635694 0.110105i
\(977\) 1376.50 + 794.720i 1.40890 + 0.813429i 0.995282 0.0970221i \(-0.0309318\pi\)
0.413617 + 0.910451i \(0.364265\pi\)
\(978\) 425.539 46.9477i 0.435112 0.0480038i
\(979\) 580.962 0.593424
\(980\) −214.094 + 46.7294i −0.218464 + 0.0476831i
\(981\) 147.627 + 160.592i 0.150486 + 0.163702i
\(982\) 30.8586 + 53.4486i 0.0314242 + 0.0544283i
\(983\) 426.388 + 246.175i 0.433762 + 0.250433i 0.700948 0.713212i \(-0.252761\pi\)
−0.267186 + 0.963645i \(0.586094\pi\)
\(984\) −253.135 + 185.917i −0.257251 + 0.188940i
\(985\) 228.339 + 395.495i 0.231816 + 0.401518i
\(986\) 526.399i 0.533874i
\(987\) 1385.52 719.780i 1.40377 0.729260i
\(988\) 1275.39 1.29088
\(989\) −287.004 + 165.702i −0.290196 + 0.167545i
\(990\) 24.6176 + 110.210i 0.0248663 + 0.111324i
\(991\) −449.306 + 778.220i −0.453386 + 0.785288i −0.998594 0.0530133i \(-0.983117\pi\)
0.545208 + 0.838301i \(0.316451\pi\)
\(992\) −21.7551 + 12.5603i −0.0219305 + 0.0126616i
\(993\) 530.320 + 232.842i 0.534059 + 0.234483i
\(994\) −136.527 + 877.486i −0.137352 + 0.882783i
\(995\) 475.707i 0.478097i
\(996\) −252.827 + 27.8932i −0.253842 + 0.0280052i
\(997\) 333.890 578.314i 0.334894 0.580054i −0.648570 0.761155i \(-0.724633\pi\)
0.983465 + 0.181101i \(0.0579661\pi\)
\(998\) 550.691 + 317.941i 0.551794 + 0.318579i
\(999\) −396.478 + 454.285i −0.396875 + 0.454740i
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 210.3.s.a.11.13 yes 40
3.2 odd 2 inner 210.3.s.a.11.5 40
7.2 even 3 inner 210.3.s.a.191.5 yes 40
21.2 odd 6 inner 210.3.s.a.191.13 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.3.s.a.11.5 40 3.2 odd 2 inner
210.3.s.a.11.13 yes 40 1.1 even 1 trivial
210.3.s.a.191.5 yes 40 7.2 even 3 inner
210.3.s.a.191.13 yes 40 21.2 odd 6 inner