Properties

Label 210.3.w.a.173.16
Level $210$
Weight $3$
Character 210.173
Analytic conductor $5.722$
Analytic rank $0$
Dimension $64$
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(17,210)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(210, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 3, 2]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("210.17");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.w (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 173.16
Character \(\chi\) \(=\) 210.173
Dual form 210.3.w.a.17.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.36603 + 0.366025i) q^{2} +(2.97842 - 0.359186i) q^{3} +(1.73205 - 1.00000i) q^{4} +(2.39011 + 4.39174i) q^{5} +(-3.93713 + 1.58084i) q^{6} +(6.65191 - 2.17994i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(8.74197 - 2.13962i) q^{9} +O(q^{10})\) \(q+(-1.36603 + 0.366025i) q^{2} +(2.97842 - 0.359186i) q^{3} +(1.73205 - 1.00000i) q^{4} +(2.39011 + 4.39174i) q^{5} +(-3.93713 + 1.58084i) q^{6} +(6.65191 - 2.17994i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(8.74197 - 2.13962i) q^{9} +(-4.87243 - 5.12439i) q^{10} +(-5.82368 + 3.36230i) q^{11} +(4.79959 - 3.60055i) q^{12} +(-3.78650 + 3.78650i) q^{13} +(-8.28876 + 5.41262i) q^{14} +(8.69619 + 12.2220i) q^{15} +(2.00000 - 3.46410i) q^{16} +(3.69500 + 0.990073i) q^{17} +(-11.1586 + 6.12255i) q^{18} +(2.17576 - 3.76853i) q^{19} +(8.53153 + 5.21661i) q^{20} +(19.0292 - 8.88204i) q^{21} +(6.72461 - 6.72461i) q^{22} +(-3.48168 - 12.9938i) q^{23} +(-5.23847 + 6.67521i) q^{24} +(-13.5748 + 20.9935i) q^{25} +(3.78650 - 6.55841i) q^{26} +(25.2687 - 9.51267i) q^{27} +(9.34151 - 10.4277i) q^{28} +19.0062 q^{29} +(-16.3528 - 13.5125i) q^{30} +(0.140971 - 0.0813895i) q^{31} +(-1.46410 + 5.46410i) q^{32} +(-16.1377 + 12.1061i) q^{33} -5.40986 q^{34} +(25.4725 + 24.0032i) q^{35} +(13.0019 - 12.4479i) q^{36} +(13.9748 + 52.1548i) q^{37} +(-1.59277 + 5.94429i) q^{38} +(-9.91773 + 12.6378i) q^{39} +(-13.5637 - 4.00327i) q^{40} +64.3886 q^{41} +(-22.7433 + 19.0983i) q^{42} +(-49.3467 - 49.3467i) q^{43} +(-6.72461 + 11.6474i) q^{44} +(30.2909 + 33.2786i) q^{45} +(9.51213 + 16.4755i) q^{46} +(8.05536 + 30.0630i) q^{47} +(4.71258 - 11.0359i) q^{48} +(39.4958 - 29.0015i) q^{49} +(10.8594 - 33.6463i) q^{50} +(11.3609 + 1.62166i) q^{51} +(-2.77191 + 10.3449i) q^{52} +(-79.5945 - 21.3273i) q^{53} +(-31.0359 + 22.2436i) q^{54} +(-28.6856 - 17.5398i) q^{55} +(-8.94394 + 17.6637i) q^{56} +(5.12672 - 12.0058i) q^{57} +(-25.9629 + 6.95675i) q^{58} +(-1.10247 + 0.636510i) q^{59} +(27.2842 + 12.4729i) q^{60} +(-88.4000 - 51.0378i) q^{61} +(-0.162779 + 0.162779i) q^{62} +(53.4866 - 33.2895i) q^{63} -8.00000i q^{64} +(-25.6795 - 7.57919i) q^{65} +(17.6133 - 22.4441i) q^{66} +(-98.3650 - 26.3568i) q^{67} +(7.39001 - 1.98015i) q^{68} +(-15.0371 - 37.4504i) q^{69} +(-43.5818 - 23.4654i) q^{70} -119.115i q^{71} +(-13.2047 + 21.7632i) q^{72} +(-68.2204 - 18.2796i) q^{73} +(-38.1800 - 66.1296i) q^{74} +(-32.8908 + 67.4032i) q^{75} -8.70304i q^{76} +(-31.4090 + 35.0610i) q^{77} +(8.92209 - 20.8938i) q^{78} +(89.1596 + 51.4763i) q^{79} +(19.9937 + 0.503911i) q^{80} +(71.8441 - 37.4089i) q^{81} +(-87.9564 + 23.5678i) q^{82} +(-21.3161 - 21.3161i) q^{83} +(24.0775 - 34.4133i) q^{84} +(4.48331 + 18.5939i) q^{85} +(85.4709 + 49.3467i) q^{86} +(56.6084 - 6.82676i) q^{87} +(4.92275 - 18.3720i) q^{88} +(-83.4011 - 48.1516i) q^{89} +(-53.5589 - 34.3721i) q^{90} +(-16.9331 + 33.4418i) q^{91} +(-19.0243 - 19.0243i) q^{92} +(0.390636 - 0.293047i) q^{93} +(-22.0076 - 38.1184i) q^{94} +(21.7507 + 0.548195i) q^{95} +(-2.39808 + 16.8003i) q^{96} +(-37.6895 - 37.6895i) q^{97} +(-43.3369 + 54.0732i) q^{98} +(-43.7164 + 41.8536i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 32 q^{2} - 6 q^{3} - 12 q^{5} + 4 q^{7} - 128 q^{8} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 32 q^{2} - 6 q^{3} - 12 q^{5} + 4 q^{7} - 128 q^{8} - 16 q^{9} + 24 q^{10} + 12 q^{12} - 16 q^{14} - 44 q^{15} + 128 q^{16} - 20 q^{18} + 36 q^{21} + 16 q^{22} - 12 q^{23} - 16 q^{25} + 8 q^{28} - 112 q^{29} + 26 q^{30} + 128 q^{32} + 30 q^{33} + 16 q^{36} - 32 q^{37} + 24 q^{38} + 64 q^{39} - 136 q^{42} + 32 q^{43} - 16 q^{44} - 114 q^{45} - 24 q^{46} - 96 q^{47} + 40 q^{50} - 84 q^{51} + 56 q^{53} - 72 q^{54} - 316 q^{57} + 56 q^{58} + 672 q^{59} + 8 q^{60} + 600 q^{61} - 210 q^{63} + 28 q^{65} + 16 q^{67} + 24 q^{72} - 624 q^{73} - 64 q^{74} + 48 q^{75} + 208 q^{77} - 8 q^{78} - 48 q^{80} - 64 q^{81} - 192 q^{82} + 160 q^{84} - 152 q^{85} + 60 q^{87} - 16 q^{88} + 144 q^{89} - 232 q^{91} + 48 q^{92} - 170 q^{93} + 136 q^{95} - 48 q^{96} + 128 q^{98} + 160 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36603 + 0.366025i −0.683013 + 0.183013i
\(3\) 2.97842 0.359186i 0.992807 0.119729i
\(4\) 1.73205 1.00000i 0.433013 0.250000i
\(5\) 2.39011 + 4.39174i 0.478021 + 0.878348i
\(6\) −3.93713 + 1.58084i −0.656188 + 0.263473i
\(7\) 6.65191 2.17994i 0.950273 0.311419i
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) 8.74197 2.13962i 0.971330 0.237735i
\(10\) −4.87243 5.12439i −0.487243 0.512439i
\(11\) −5.82368 + 3.36230i −0.529425 + 0.305664i −0.740782 0.671745i \(-0.765545\pi\)
0.211357 + 0.977409i \(0.432212\pi\)
\(12\) 4.79959 3.60055i 0.399966 0.300046i
\(13\) −3.78650 + 3.78650i −0.291269 + 0.291269i −0.837582 0.546312i \(-0.816031\pi\)
0.546312 + 0.837582i \(0.316031\pi\)
\(14\) −8.28876 + 5.41262i −0.592055 + 0.386615i
\(15\) 8.69619 + 12.2220i 0.579746 + 0.814797i
\(16\) 2.00000 3.46410i 0.125000 0.216506i
\(17\) 3.69500 + 0.990073i 0.217353 + 0.0582396i 0.365852 0.930673i \(-0.380778\pi\)
−0.148499 + 0.988913i \(0.547444\pi\)
\(18\) −11.1586 + 6.12255i −0.619922 + 0.340142i
\(19\) 2.17576 3.76853i 0.114514 0.198344i −0.803072 0.595883i \(-0.796802\pi\)
0.917585 + 0.397539i \(0.130136\pi\)
\(20\) 8.53153 + 5.21661i 0.426576 + 0.260831i
\(21\) 19.0292 8.88204i 0.906151 0.422954i
\(22\) 6.72461 6.72461i 0.305664 0.305664i
\(23\) −3.48168 12.9938i −0.151377 0.564948i −0.999388 0.0349695i \(-0.988867\pi\)
0.848011 0.529979i \(-0.177800\pi\)
\(24\) −5.23847 + 6.67521i −0.218269 + 0.278134i
\(25\) −13.5748 + 20.9935i −0.542991 + 0.839738i
\(26\) 3.78650 6.55841i 0.145635 0.252247i
\(27\) 25.2687 9.51267i 0.935879 0.352321i
\(28\) 9.34151 10.4277i 0.333625 0.372417i
\(29\) 19.0062 0.655386 0.327693 0.944784i \(-0.393729\pi\)
0.327693 + 0.944784i \(0.393729\pi\)
\(30\) −16.3528 13.5125i −0.545092 0.450416i
\(31\) 0.140971 0.0813895i 0.00454744 0.00262547i −0.497725 0.867335i \(-0.665831\pi\)
0.502272 + 0.864710i \(0.332498\pi\)
\(32\) −1.46410 + 5.46410i −0.0457532 + 0.170753i
\(33\) −16.1377 + 12.1061i −0.489020 + 0.366853i
\(34\) −5.40986 −0.159114
\(35\) 25.4725 + 24.0032i 0.727785 + 0.685805i
\(36\) 13.0019 12.4479i 0.361164 0.345775i
\(37\) 13.9748 + 52.1548i 0.377698 + 1.40959i 0.849362 + 0.527811i \(0.176987\pi\)
−0.471664 + 0.881779i \(0.656346\pi\)
\(38\) −1.59277 + 5.94429i −0.0419149 + 0.156429i
\(39\) −9.91773 + 12.6378i −0.254301 + 0.324047i
\(40\) −13.5637 4.00327i −0.339092 0.100082i
\(41\) 64.3886 1.57045 0.785226 0.619209i \(-0.212547\pi\)
0.785226 + 0.619209i \(0.212547\pi\)
\(42\) −22.7433 + 19.0983i −0.541507 + 0.454720i
\(43\) −49.3467 49.3467i −1.14760 1.14760i −0.987024 0.160573i \(-0.948666\pi\)
−0.160573 0.987024i \(-0.551334\pi\)
\(44\) −6.72461 + 11.6474i −0.152832 + 0.264713i
\(45\) 30.2909 + 33.2786i 0.673131 + 0.739524i
\(46\) 9.51213 + 16.4755i 0.206785 + 0.358163i
\(47\) 8.05536 + 30.0630i 0.171391 + 0.639638i 0.997138 + 0.0755987i \(0.0240868\pi\)
−0.825748 + 0.564040i \(0.809247\pi\)
\(48\) 4.71258 11.0359i 0.0981788 0.229915i
\(49\) 39.4958 29.0015i 0.806036 0.591867i
\(50\) 10.8594 33.6463i 0.217187 0.672926i
\(51\) 11.3609 + 1.62166i 0.222763 + 0.0317972i
\(52\) −2.77191 + 10.3449i −0.0533060 + 0.198941i
\(53\) −79.5945 21.3273i −1.50178 0.402402i −0.588086 0.808798i \(-0.700118\pi\)
−0.913697 + 0.406397i \(0.866785\pi\)
\(54\) −31.0359 + 22.2436i −0.574738 + 0.411918i
\(55\) −28.6856 17.5398i −0.521556 0.318906i
\(56\) −8.94394 + 17.6637i −0.159713 + 0.315423i
\(57\) 5.12672 12.0058i 0.0899425 0.210627i
\(58\) −25.9629 + 6.95675i −0.447637 + 0.119944i
\(59\) −1.10247 + 0.636510i −0.0186859 + 0.0107883i −0.509314 0.860581i \(-0.670101\pi\)
0.490628 + 0.871369i \(0.336767\pi\)
\(60\) 27.2842 + 12.4729i 0.454737 + 0.207881i
\(61\) −88.4000 51.0378i −1.44918 0.836685i −0.450748 0.892651i \(-0.648843\pi\)
−0.998433 + 0.0559667i \(0.982176\pi\)
\(62\) −0.162779 + 0.162779i −0.00262547 + 0.00262547i
\(63\) 53.4866 33.2895i 0.848993 0.528404i
\(64\) 8.00000i 0.125000i
\(65\) −25.6795 7.57919i −0.395069 0.116603i
\(66\) 17.6133 22.4441i 0.266868 0.340062i
\(67\) −98.3650 26.3568i −1.46813 0.393386i −0.565844 0.824513i \(-0.691449\pi\)
−0.902291 + 0.431127i \(0.858116\pi\)
\(68\) 7.39001 1.98015i 0.108677 0.0291198i
\(69\) −15.0371 37.4504i −0.217929 0.542760i
\(70\) −43.5818 23.4654i −0.622598 0.335220i
\(71\) 119.115i 1.67768i −0.544376 0.838841i \(-0.683233\pi\)
0.544376 0.838841i \(-0.316767\pi\)
\(72\) −13.2047 + 21.7632i −0.183399 + 0.302266i
\(73\) −68.2204 18.2796i −0.934526 0.250405i −0.240742 0.970589i \(-0.577391\pi\)
−0.693783 + 0.720184i \(0.744058\pi\)
\(74\) −38.1800 66.1296i −0.515945 0.893644i
\(75\) −32.8908 + 67.4032i −0.438544 + 0.898709i
\(76\) 8.70304i 0.114514i
\(77\) −31.4090 + 35.0610i −0.407909 + 0.455337i
\(78\) 8.92209 20.8938i 0.114386 0.267869i
\(79\) 89.1596 + 51.4763i 1.12860 + 0.651599i 0.943583 0.331136i \(-0.107432\pi\)
0.185020 + 0.982735i \(0.440765\pi\)
\(80\) 19.9937 + 0.503911i 0.249921 + 0.00629889i
\(81\) 71.8441 37.4089i 0.886964 0.461839i
\(82\) −87.9564 + 23.5678i −1.07264 + 0.287413i
\(83\) −21.3161 21.3161i −0.256821 0.256821i 0.566939 0.823760i \(-0.308127\pi\)
−0.823760 + 0.566939i \(0.808127\pi\)
\(84\) 24.0775 34.4133i 0.286636 0.409682i
\(85\) 4.48331 + 18.5939i 0.0527448 + 0.218752i
\(86\) 85.4709 + 49.3467i 0.993848 + 0.573799i
\(87\) 56.6084 6.82676i 0.650671 0.0784685i
\(88\) 4.92275 18.3720i 0.0559404 0.208772i
\(89\) −83.4011 48.1516i −0.937091 0.541030i −0.0480436 0.998845i \(-0.515299\pi\)
−0.889047 + 0.457816i \(0.848632\pi\)
\(90\) −53.5589 34.3721i −0.595099 0.381913i
\(91\) −16.9331 + 33.4418i −0.186078 + 0.367492i
\(92\) −19.0243 19.0243i −0.206785 0.206785i
\(93\) 0.390636 0.293047i 0.00420039 0.00315104i
\(94\) −22.0076 38.1184i −0.234124 0.405514i
\(95\) 21.7507 + 0.548195i 0.228955 + 0.00577047i
\(96\) −2.39808 + 16.8003i −0.0249800 + 0.175003i
\(97\) −37.6895 37.6895i −0.388552 0.388552i 0.485619 0.874171i \(-0.338594\pi\)
−0.874171 + 0.485619i \(0.838594\pi\)
\(98\) −43.3369 + 54.0732i −0.442214 + 0.551767i
\(99\) −43.7164 + 41.8536i −0.441580 + 0.422764i
\(100\) −2.51876 + 49.9365i −0.0251876 + 0.499365i
\(101\) 11.4760 + 19.8770i 0.113624 + 0.196802i 0.917229 0.398361i \(-0.130421\pi\)
−0.803605 + 0.595163i \(0.797087\pi\)
\(102\) −16.1128 + 1.94315i −0.157969 + 0.0190505i
\(103\) 21.7638 + 81.2236i 0.211299 + 0.788578i 0.987437 + 0.158015i \(0.0505094\pi\)
−0.776138 + 0.630563i \(0.782824\pi\)
\(104\) 15.1460i 0.145635i
\(105\) 84.4894 + 62.3422i 0.804661 + 0.593735i
\(106\) 116.534 1.09938
\(107\) −106.956 + 28.6588i −0.999591 + 0.267840i −0.721274 0.692650i \(-0.756443\pi\)
−0.278317 + 0.960489i \(0.589776\pi\)
\(108\) 34.2541 41.7452i 0.317167 0.386529i
\(109\) 76.8368 44.3618i 0.704925 0.406989i −0.104254 0.994551i \(-0.533245\pi\)
0.809179 + 0.587562i \(0.199912\pi\)
\(110\) 45.6053 + 13.4602i 0.414593 + 0.122366i
\(111\) 60.3562 + 150.319i 0.543750 + 1.35423i
\(112\) 5.75230 27.4028i 0.0513598 0.244667i
\(113\) −96.4512 + 96.4512i −0.853551 + 0.853551i −0.990569 0.137018i \(-0.956248\pi\)
0.137018 + 0.990569i \(0.456248\pi\)
\(114\) −2.60882 + 18.2767i −0.0228844 + 0.160322i
\(115\) 48.7439 46.3472i 0.423860 0.403019i
\(116\) 32.9197 19.0062i 0.283790 0.163846i
\(117\) −24.9998 + 41.2031i −0.213674 + 0.352163i
\(118\) 1.27302 1.27302i 0.0107883 0.0107883i
\(119\) 26.7371 1.46899i 0.224682 0.0123445i
\(120\) −41.8363 7.05152i −0.348636 0.0587627i
\(121\) −37.8898 + 65.6271i −0.313139 + 0.542373i
\(122\) 139.438 + 37.3622i 1.14293 + 0.306248i
\(123\) 191.776 23.1275i 1.55916 0.188028i
\(124\) 0.162779 0.281942i 0.00131273 0.00227372i
\(125\) −124.643 9.44033i −0.997144 0.0755227i
\(126\) −60.8792 + 65.0517i −0.483168 + 0.516283i
\(127\) 150.961 150.961i 1.18867 1.18867i 0.211232 0.977436i \(-0.432252\pi\)
0.977436 0.211232i \(-0.0677477\pi\)
\(128\) 2.92820 + 10.9282i 0.0228766 + 0.0853766i
\(129\) −164.700 129.250i −1.27674 1.00194i
\(130\) 37.8530 + 0.954029i 0.291177 + 0.00733869i
\(131\) 81.2787 140.779i 0.620448 1.07465i −0.368954 0.929448i \(-0.620284\pi\)
0.989402 0.145200i \(-0.0463825\pi\)
\(132\) −15.8451 + 37.1061i −0.120039 + 0.281107i
\(133\) 6.25781 29.8109i 0.0470512 0.224142i
\(134\) 144.016 1.07475
\(135\) 102.172 + 88.2375i 0.756831 + 0.653611i
\(136\) −9.37015 + 5.40986i −0.0688982 + 0.0397784i
\(137\) −49.3770 + 184.278i −0.360416 + 1.34509i 0.513113 + 0.858321i \(0.328492\pi\)
−0.873529 + 0.486771i \(0.838175\pi\)
\(138\) 34.2489 + 45.6543i 0.248180 + 0.330828i
\(139\) −66.3531 −0.477360 −0.238680 0.971098i \(-0.576715\pi\)
−0.238680 + 0.971098i \(0.576715\pi\)
\(140\) 68.1228 + 16.1022i 0.486592 + 0.115016i
\(141\) 34.7905 + 86.6468i 0.246741 + 0.614517i
\(142\) 43.5993 + 162.715i 0.307037 + 1.14588i
\(143\) 9.32000 34.7827i 0.0651748 0.243236i
\(144\) 10.0721 34.5623i 0.0699451 0.240016i
\(145\) 45.4268 + 83.4702i 0.313288 + 0.575657i
\(146\) 99.8816 0.684120
\(147\) 107.218 100.565i 0.729374 0.684115i
\(148\) 76.3599 + 76.3599i 0.515945 + 0.515945i
\(149\) 23.3448 40.4345i 0.156677 0.271372i −0.776992 0.629511i \(-0.783255\pi\)
0.933668 + 0.358139i \(0.116589\pi\)
\(150\) 20.2584 104.113i 0.135056 0.694089i
\(151\) 95.0699 + 164.666i 0.629602 + 1.09050i 0.987632 + 0.156793i \(0.0501154\pi\)
−0.358029 + 0.933710i \(0.616551\pi\)
\(152\) 3.18553 + 11.8886i 0.0209575 + 0.0782143i
\(153\) 34.4200 + 0.749301i 0.224967 + 0.00489739i
\(154\) 30.0722 59.3907i 0.195274 0.385654i
\(155\) 0.694377 + 0.424578i 0.00447985 + 0.00273921i
\(156\) −4.54016 + 31.8071i −0.0291036 + 0.203892i
\(157\) 58.8702 219.707i 0.374969 1.39940i −0.478420 0.878131i \(-0.658790\pi\)
0.853390 0.521274i \(-0.174543\pi\)
\(158\) −140.636 37.6833i −0.890101 0.238502i
\(159\) −244.726 34.9323i −1.53916 0.219700i
\(160\) −27.4963 + 6.62983i −0.171852 + 0.0414364i
\(161\) −51.4855 78.8438i −0.319786 0.489713i
\(162\) −84.4482 + 77.3983i −0.521285 + 0.477767i
\(163\) 113.940 30.5302i 0.699021 0.187302i 0.108229 0.994126i \(-0.465482\pi\)
0.590792 + 0.806824i \(0.298815\pi\)
\(164\) 111.524 64.3886i 0.680026 0.392613i
\(165\) −91.7378 41.9375i −0.555986 0.254167i
\(166\) 36.9206 + 21.3161i 0.222413 + 0.128410i
\(167\) 56.9075 56.9075i 0.340764 0.340764i −0.515891 0.856654i \(-0.672539\pi\)
0.856654 + 0.515891i \(0.172539\pi\)
\(168\) −20.2943 + 55.8224i −0.120799 + 0.332276i
\(169\) 140.325i 0.830324i
\(170\) −12.9301 23.7587i −0.0760597 0.139757i
\(171\) 10.9572 37.5997i 0.0640774 0.219881i
\(172\) −134.818 36.1243i −0.783823 0.210025i
\(173\) −264.119 + 70.7704i −1.52670 + 0.409078i −0.921940 0.387332i \(-0.873397\pi\)
−0.604758 + 0.796409i \(0.706730\pi\)
\(174\) −74.8297 + 30.0456i −0.430056 + 0.172676i
\(175\) −44.5338 + 169.239i −0.254479 + 0.967078i
\(176\) 26.8984i 0.152832i
\(177\) −3.05498 + 2.29178i −0.0172598 + 0.0129479i
\(178\) 131.553 + 35.2494i 0.739060 + 0.198031i
\(179\) 83.4294 + 144.504i 0.466086 + 0.807285i 0.999250 0.0387273i \(-0.0123304\pi\)
−0.533164 + 0.846012i \(0.678997\pi\)
\(180\) 85.7439 + 27.3493i 0.476355 + 0.151940i
\(181\) 214.129i 1.18303i −0.806293 0.591516i \(-0.798530\pi\)
0.806293 0.591516i \(-0.201470\pi\)
\(182\) 10.8905 51.8803i 0.0598381 0.285056i
\(183\) −281.624 120.260i −1.53893 0.657157i
\(184\) 32.9510 + 19.0243i 0.179081 + 0.103393i
\(185\) −195.649 + 186.029i −1.05756 + 1.00556i
\(186\) −0.426356 + 0.543292i −0.00229224 + 0.00292093i
\(187\) −24.8474 + 6.65785i −0.132874 + 0.0356035i
\(188\) 44.0153 + 44.0153i 0.234124 + 0.234124i
\(189\) 147.348 118.362i 0.779621 0.626252i
\(190\) −29.9127 + 7.21246i −0.157435 + 0.0379603i
\(191\) −81.4585 47.0301i −0.426484 0.246231i 0.271363 0.962477i \(-0.412525\pi\)
−0.697848 + 0.716246i \(0.745859\pi\)
\(192\) −2.87349 23.8274i −0.0149661 0.124101i
\(193\) −8.62307 + 32.1818i −0.0446791 + 0.166745i −0.984661 0.174481i \(-0.944175\pi\)
0.939981 + 0.341226i \(0.110842\pi\)
\(194\) 65.2801 + 37.6895i 0.336496 + 0.194276i
\(195\) −79.2066 13.3503i −0.406188 0.0684630i
\(196\) 39.4072 89.7278i 0.201057 0.457795i
\(197\) 15.6791 + 15.6791i 0.0795891 + 0.0795891i 0.745781 0.666192i \(-0.232077\pi\)
−0.666192 + 0.745781i \(0.732077\pi\)
\(198\) 44.3982 73.1744i 0.224233 0.369568i
\(199\) −34.1697 59.1837i −0.171707 0.297405i 0.767310 0.641277i \(-0.221595\pi\)
−0.939017 + 0.343871i \(0.888262\pi\)
\(200\) −14.8374 69.1365i −0.0741868 0.345682i
\(201\) −302.439 43.1703i −1.50467 0.214778i
\(202\) −22.9520 22.9520i −0.113624 0.113624i
\(203\) 126.427 41.4323i 0.622795 0.204100i
\(204\) 21.2993 8.55210i 0.104408 0.0419221i
\(205\) 153.896 + 282.778i 0.750710 + 1.37940i
\(206\) −59.4598 102.987i −0.288640 0.499939i
\(207\) −58.2385 106.142i −0.281345 0.512763i
\(208\) 5.54382 + 20.6898i 0.0266530 + 0.0994703i
\(209\) 29.2623i 0.140011i
\(210\) −138.233 54.2357i −0.658254 0.258265i
\(211\) 96.2506 0.456164 0.228082 0.973642i \(-0.426755\pi\)
0.228082 + 0.973642i \(0.426755\pi\)
\(212\) −159.189 + 42.6546i −0.750891 + 0.201201i
\(213\) −42.7847 354.776i −0.200867 1.66561i
\(214\) 135.615 78.2974i 0.633715 0.365876i
\(215\) 98.7740 334.662i 0.459414 1.55657i
\(216\) −31.5121 + 69.5628i −0.145889 + 0.322050i
\(217\) 0.760301 0.848703i 0.00350369 0.00391107i
\(218\) −88.7235 + 88.7235i −0.406989 + 0.406989i
\(219\) −209.755 29.9405i −0.957784 0.136714i
\(220\) −67.2247 1.69430i −0.305567 0.00770137i
\(221\) −17.7400 + 10.2422i −0.0802717 + 0.0463449i
\(222\) −137.469 183.248i −0.619229 0.825442i
\(223\) 112.186 112.186i 0.503075 0.503075i −0.409317 0.912392i \(-0.634233\pi\)
0.912392 + 0.409317i \(0.134233\pi\)
\(224\) 2.17232 + 39.5383i 0.00969787 + 0.176510i
\(225\) −73.7524 + 212.569i −0.327788 + 0.944751i
\(226\) 96.4512 167.058i 0.426775 0.739197i
\(227\) 225.570 + 60.4414i 0.993702 + 0.266262i 0.718805 0.695212i \(-0.244689\pi\)
0.274897 + 0.961474i \(0.411356\pi\)
\(228\) −3.12602 25.9213i −0.0137106 0.113690i
\(229\) −90.9875 + 157.595i −0.397326 + 0.688188i −0.993395 0.114745i \(-0.963395\pi\)
0.596069 + 0.802933i \(0.296728\pi\)
\(230\) −49.6211 + 81.1530i −0.215744 + 0.352839i
\(231\) −80.9557 + 115.708i −0.350458 + 0.500900i
\(232\) −38.0124 + 38.0124i −0.163846 + 0.163846i
\(233\) −3.87883 14.4760i −0.0166473 0.0621286i 0.957103 0.289749i \(-0.0935720\pi\)
−0.973750 + 0.227621i \(0.926905\pi\)
\(234\) 19.0690 65.4351i 0.0814914 0.279637i
\(235\) −112.776 + 107.231i −0.479897 + 0.456301i
\(236\) −1.27302 + 2.20493i −0.00539415 + 0.00934294i
\(237\) 284.044 + 121.293i 1.19850 + 0.511786i
\(238\) −35.9859 + 11.7932i −0.151201 + 0.0495511i
\(239\) 373.492 1.56273 0.781365 0.624075i \(-0.214524\pi\)
0.781365 + 0.624075i \(0.214524\pi\)
\(240\) 59.7305 5.68059i 0.248877 0.0236691i
\(241\) −91.8906 + 53.0531i −0.381289 + 0.220137i −0.678379 0.734712i \(-0.737317\pi\)
0.297090 + 0.954849i \(0.403984\pi\)
\(242\) 27.7373 103.517i 0.114617 0.427756i
\(243\) 200.545 137.225i 0.825288 0.564712i
\(244\) −204.151 −0.836685
\(245\) 221.766 + 104.139i 0.905167 + 0.425055i
\(246\) −253.506 + 101.788i −1.03051 + 0.413771i
\(247\) 6.03101 + 22.5080i 0.0244171 + 0.0911257i
\(248\) −0.119163 + 0.444721i −0.000480494 + 0.00179323i
\(249\) −71.1448 55.8319i −0.285722 0.224224i
\(250\) 173.721 32.7268i 0.694884 0.130907i
\(251\) −171.959 −0.685097 −0.342548 0.939500i \(-0.611290\pi\)
−0.342548 + 0.939500i \(0.611290\pi\)
\(252\) 59.3520 111.146i 0.235524 0.441054i
\(253\) 63.9653 + 63.9653i 0.252827 + 0.252827i
\(254\) −150.961 + 261.472i −0.594334 + 1.02942i
\(255\) 20.0318 + 53.7700i 0.0785562 + 0.210863i
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) 25.0505 + 93.4896i 0.0974726 + 0.363773i 0.997383 0.0723027i \(-0.0230348\pi\)
−0.899910 + 0.436075i \(0.856368\pi\)
\(258\) 272.293 + 116.275i 1.05540 + 0.450679i
\(259\) 206.653 + 316.465i 0.797890 + 1.22187i
\(260\) −52.0573 + 12.5519i −0.200220 + 0.0482766i
\(261\) 166.151 40.6659i 0.636596 0.155808i
\(262\) −59.5001 + 222.057i −0.227100 + 0.847548i
\(263\) 370.341 + 99.2327i 1.40814 + 0.377311i 0.881262 0.472629i \(-0.156695\pi\)
0.526881 + 0.849939i \(0.323362\pi\)
\(264\) 8.06307 56.4876i 0.0305419 0.213968i
\(265\) −96.5754 400.533i −0.364436 1.51144i
\(266\) 2.36323 + 43.0130i 0.00888431 + 0.161703i
\(267\) −265.699 113.459i −0.995127 0.424941i
\(268\) −196.730 + 52.7137i −0.734067 + 0.196693i
\(269\) −359.720 + 207.684i −1.33725 + 0.772061i −0.986399 0.164370i \(-0.947441\pi\)
−0.350850 + 0.936432i \(0.614107\pi\)
\(270\) −171.867 83.1370i −0.636544 0.307915i
\(271\) −148.971 86.0086i −0.549710 0.317375i 0.199295 0.979940i \(-0.436135\pi\)
−0.749005 + 0.662564i \(0.769468\pi\)
\(272\) 10.8197 10.8197i 0.0397784 0.0397784i
\(273\) −38.4221 + 105.686i −0.140740 + 0.387127i
\(274\) 269.801i 0.984676i
\(275\) 8.46882 167.902i 0.0307957 0.610552i
\(276\) −63.4955 49.8290i −0.230056 0.180540i
\(277\) 212.684 + 56.9885i 0.767812 + 0.205735i 0.621405 0.783490i \(-0.286562\pi\)
0.146407 + 0.989224i \(0.453229\pi\)
\(278\) 90.6400 24.2869i 0.326043 0.0873630i
\(279\) 1.05822 1.01313i 0.00379290 0.00363128i
\(280\) −98.9513 + 2.93860i −0.353398 + 0.0104950i
\(281\) 151.432i 0.538902i 0.963014 + 0.269451i \(0.0868423\pi\)
−0.963014 + 0.269451i \(0.913158\pi\)
\(282\) −79.2396 105.628i −0.280991 0.374566i
\(283\) −25.9365 6.94966i −0.0916484 0.0245571i 0.212703 0.977117i \(-0.431773\pi\)
−0.304352 + 0.952560i \(0.598440\pi\)
\(284\) −119.115 206.314i −0.419421 0.726458i
\(285\) 64.9796 6.17980i 0.227999 0.0216835i
\(286\) 50.9254i 0.178061i
\(287\) 428.307 140.363i 1.49236 0.489069i
\(288\) −1.10805 + 50.8996i −0.00384741 + 0.176735i
\(289\) −237.609 137.183i −0.822175 0.474683i
\(290\) −92.6064 97.3951i −0.319332 0.335845i
\(291\) −125.793 98.7176i −0.432277 0.339236i
\(292\) −136.441 + 36.5592i −0.467263 + 0.125203i
\(293\) −272.300 272.300i −0.929353 0.929353i 0.0683113 0.997664i \(-0.478239\pi\)
−0.997664 + 0.0683113i \(0.978239\pi\)
\(294\) −109.653 + 176.619i −0.372970 + 0.600744i
\(295\) −5.43040 3.32042i −0.0184081 0.0112557i
\(296\) −132.259 76.3599i −0.446822 0.257973i
\(297\) −115.173 + 140.360i −0.387786 + 0.472592i
\(298\) −17.0896 + 63.7793i −0.0573477 + 0.214024i
\(299\) 62.3844 + 36.0177i 0.208644 + 0.120460i
\(300\) 10.4346 + 149.637i 0.0347820 + 0.498789i
\(301\) −435.822 220.677i −1.44791 0.733146i
\(302\) −190.140 190.140i −0.629602 0.629602i
\(303\) 41.3199 + 55.0801i 0.136369 + 0.181783i
\(304\) −8.70304 15.0741i −0.0286284 0.0495859i
\(305\) 12.8592 510.216i 0.0421615 1.67284i
\(306\) −47.2928 + 11.5750i −0.154552 + 0.0378269i
\(307\) −138.707 138.707i −0.451814 0.451814i 0.444142 0.895956i \(-0.353509\pi\)
−0.895956 + 0.444142i \(0.853509\pi\)
\(308\) −19.3410 + 92.1364i −0.0627953 + 0.299144i
\(309\) 93.9961 + 234.101i 0.304194 + 0.757607i
\(310\) −1.10394 0.325824i −0.00356110 0.00105105i
\(311\) 106.582 + 184.606i 0.342708 + 0.593587i 0.984935 0.172927i \(-0.0553226\pi\)
−0.642227 + 0.766515i \(0.721989\pi\)
\(312\) −5.44024 45.1111i −0.0174367 0.144587i
\(313\) 57.9840 + 216.399i 0.185252 + 0.691371i 0.994576 + 0.104009i \(0.0331670\pi\)
−0.809324 + 0.587362i \(0.800166\pi\)
\(314\) 321.673i 1.02444i
\(315\) 274.037 + 155.334i 0.869960 + 0.493123i
\(316\) 205.905 0.651599
\(317\) 373.738 100.143i 1.17899 0.315908i 0.384462 0.923141i \(-0.374387\pi\)
0.794524 + 0.607233i \(0.207720\pi\)
\(318\) 347.088 41.8576i 1.09147 0.131628i
\(319\) −110.686 + 63.9045i −0.346978 + 0.200328i
\(320\) 35.1339 19.1209i 0.109794 0.0597527i
\(321\) −308.267 + 123.775i −0.960332 + 0.385593i
\(322\) 99.1893 + 88.8576i 0.308041 + 0.275955i
\(323\) 11.7706 11.7706i 0.0364414 0.0364414i
\(324\) 87.0287 136.638i 0.268607 0.421723i
\(325\) −28.0908 130.893i −0.0864333 0.402747i
\(326\) −144.471 + 83.4102i −0.443161 + 0.255859i
\(327\) 212.918 159.727i 0.651126 0.488461i
\(328\) −128.777 + 128.777i −0.392613 + 0.392613i
\(329\) 119.119 + 182.416i 0.362063 + 0.554456i
\(330\) 140.666 + 23.7094i 0.426262 + 0.0718465i
\(331\) −135.009 + 233.842i −0.407881 + 0.706471i −0.994652 0.103282i \(-0.967065\pi\)
0.586771 + 0.809753i \(0.300399\pi\)
\(332\) −58.2367 15.6045i −0.175412 0.0470014i
\(333\) 233.759 + 426.035i 0.701979 + 1.27938i
\(334\) −56.9075 + 98.5667i −0.170382 + 0.295110i
\(335\) −119.351 494.989i −0.356270 1.47758i
\(336\) 7.29006 83.6831i 0.0216966 0.249057i
\(337\) 384.011 384.011i 1.13950 1.13950i 0.150959 0.988540i \(-0.451764\pi\)
0.988540 0.150959i \(-0.0482361\pi\)
\(338\) −51.3625 191.687i −0.151960 0.567122i
\(339\) −252.628 + 321.916i −0.745216 + 0.949606i
\(340\) 26.3592 + 27.7222i 0.0775270 + 0.0815360i
\(341\) −0.547312 + 0.947973i −0.00160502 + 0.00277998i
\(342\) −1.20543 + 55.3727i −0.00352465 + 0.161908i
\(343\) 199.501 279.013i 0.581635 0.813450i
\(344\) 197.387 0.573799
\(345\) 128.532 155.550i 0.372558 0.450869i
\(346\) 334.889 193.348i 0.967888 0.558810i
\(347\) −172.277 + 642.948i −0.496477 + 1.85288i 0.0251213 + 0.999684i \(0.492003\pi\)
−0.521598 + 0.853191i \(0.674664\pi\)
\(348\) 91.2218 68.4327i 0.262132 0.196646i
\(349\) 427.589 1.22518 0.612592 0.790399i \(-0.290127\pi\)
0.612592 + 0.790399i \(0.290127\pi\)
\(350\) −1.11135 247.485i −0.00317528 0.707100i
\(351\) −59.6603 + 131.700i −0.169972 + 0.375213i
\(352\) −9.84551 36.7439i −0.0279702 0.104386i
\(353\) −61.2407 + 228.554i −0.173487 + 0.647460i 0.823318 + 0.567580i \(0.192120\pi\)
−0.996804 + 0.0798800i \(0.974546\pi\)
\(354\) 3.33434 4.24884i 0.00941903 0.0120024i
\(355\) 523.124 284.699i 1.47359 0.801968i
\(356\) −192.607 −0.541030
\(357\) 79.1067 13.9789i 0.221587 0.0391566i
\(358\) −166.859 166.859i −0.466086 0.466086i
\(359\) 195.109 337.939i 0.543480 0.941335i −0.455221 0.890378i \(-0.650440\pi\)
0.998701 0.0509562i \(-0.0162269\pi\)
\(360\) −127.139 5.97536i −0.353164 0.0165982i
\(361\) 171.032 + 296.236i 0.473773 + 0.820599i
\(362\) 78.3766 + 292.505i 0.216510 + 0.808026i
\(363\) −89.2795 + 209.075i −0.245949 + 0.575963i
\(364\) 4.11275 + 74.8560i 0.0112988 + 0.205648i
\(365\) −82.7747 343.296i −0.226780 0.940538i
\(366\) 428.724 + 61.1963i 1.17138 + 0.167203i
\(367\) −183.972 + 686.592i −0.501285 + 1.87082i −0.00977244 + 0.999952i \(0.503111\pi\)
−0.491513 + 0.870870i \(0.663556\pi\)
\(368\) −51.9752 13.9267i −0.141237 0.0378444i
\(369\) 562.883 137.767i 1.52543 0.373352i
\(370\) 199.170 325.733i 0.538298 0.880361i
\(371\) −575.947 + 31.6438i −1.55242 + 0.0852932i
\(372\) 0.383555 0.898208i 0.00103106 0.00241454i
\(373\) −497.049 + 133.184i −1.33257 + 0.357062i −0.853674 0.520809i \(-0.825631\pi\)
−0.478899 + 0.877870i \(0.658964\pi\)
\(374\) 31.5053 18.1896i 0.0842388 0.0486353i
\(375\) −374.630 + 16.6528i −0.999014 + 0.0444075i
\(376\) −76.2367 44.0153i −0.202757 0.117062i
\(377\) −71.9669 + 71.9669i −0.190894 + 0.190894i
\(378\) −157.958 + 215.618i −0.417879 + 0.570419i
\(379\) 19.8509i 0.0523770i −0.999657 0.0261885i \(-0.991663\pi\)
0.999657 0.0261885i \(-0.00833701\pi\)
\(380\) 38.2215 20.8012i 0.100583 0.0547400i
\(381\) 395.402 503.848i 1.03780 1.32244i
\(382\) 128.489 + 34.4284i 0.336358 + 0.0901268i
\(383\) −378.907 + 101.528i −0.989312 + 0.265085i −0.716962 0.697113i \(-0.754468\pi\)
−0.272351 + 0.962198i \(0.587801\pi\)
\(384\) 12.6467 + 31.4970i 0.0329341 + 0.0820235i
\(385\) −229.050 54.1406i −0.594934 0.140625i
\(386\) 47.1174i 0.122066i
\(387\) −536.970 325.804i −1.38752 0.841871i
\(388\) −102.970 27.5906i −0.265386 0.0711099i
\(389\) −27.1111 46.9578i −0.0696943 0.120714i 0.829072 0.559141i \(-0.188869\pi\)
−0.898767 + 0.438427i \(0.855536\pi\)
\(390\) 113.085 10.7548i 0.289961 0.0275763i
\(391\) 51.4593i 0.131609i
\(392\) −20.9886 + 136.994i −0.0535423 + 0.349476i
\(393\) 191.516 448.493i 0.487319 1.14120i
\(394\) −27.1569 15.6791i −0.0689262 0.0397946i
\(395\) −12.9697 + 514.600i −0.0328348 + 1.30278i
\(396\) −33.8654 + 116.209i −0.0855188 + 0.293457i
\(397\) 594.125 159.195i 1.49654 0.400996i 0.584598 0.811323i \(-0.301252\pi\)
0.911939 + 0.410327i \(0.134585\pi\)
\(398\) 68.3394 + 68.3394i 0.171707 + 0.171707i
\(399\) 7.93071 91.0372i 0.0198765 0.228163i
\(400\) 45.5739 + 89.0113i 0.113935 + 0.222528i
\(401\) 391.648 + 226.118i 0.976679 + 0.563886i 0.901266 0.433266i \(-0.142639\pi\)
0.0754133 + 0.997152i \(0.475972\pi\)
\(402\) 428.941 51.7287i 1.06702 0.128678i
\(403\) −0.225604 + 0.841967i −0.000559812 + 0.00208925i
\(404\) 39.7541 + 22.9520i 0.0984012 + 0.0568119i
\(405\) 336.005 + 226.109i 0.829643 + 0.558295i
\(406\) −157.538 + 102.873i −0.388024 + 0.253382i
\(407\) −256.745 256.745i −0.630824 0.630824i
\(408\) −25.9651 + 19.4785i −0.0636400 + 0.0477413i
\(409\) 160.349 + 277.733i 0.392052 + 0.679054i 0.992720 0.120445i \(-0.0384321\pi\)
−0.600668 + 0.799498i \(0.705099\pi\)
\(410\) −313.729 329.952i −0.765193 0.804761i
\(411\) −80.8755 + 566.592i −0.196777 + 1.37857i
\(412\) 118.920 + 118.920i 0.288640 + 0.288640i
\(413\) −5.94596 + 6.63731i −0.0143970 + 0.0160710i
\(414\) 118.406 + 123.676i 0.286005 + 0.298734i
\(415\) 42.6671 144.563i 0.102812 0.348344i
\(416\) −15.1460 26.2336i −0.0364087 0.0630616i
\(417\) −197.627 + 23.8331i −0.473926 + 0.0571538i
\(418\) −10.7107 39.9730i −0.0256238 0.0956292i
\(419\) 416.098i 0.993073i 0.868016 + 0.496537i \(0.165395\pi\)
−0.868016 + 0.496537i \(0.834605\pi\)
\(420\) 208.682 + 23.4905i 0.496862 + 0.0559297i
\(421\) 86.6033 0.205708 0.102854 0.994696i \(-0.467202\pi\)
0.102854 + 0.994696i \(0.467202\pi\)
\(422\) −131.481 + 35.2302i −0.311566 + 0.0834838i
\(423\) 134.743 + 245.574i 0.318541 + 0.580554i
\(424\) 201.844 116.534i 0.476046 0.274845i
\(425\) −70.9439 + 64.1309i −0.166927 + 0.150896i
\(426\) 188.302 + 468.973i 0.442023 + 1.10087i
\(427\) −699.288 146.792i −1.63768 0.343776i
\(428\) −156.595 + 156.595i −0.365876 + 0.365876i
\(429\) 15.2654 106.945i 0.0355837 0.249289i
\(430\) −12.4332 + 493.310i −0.0289143 + 1.14723i
\(431\) 306.389 176.894i 0.710880 0.410427i −0.100507 0.994936i \(-0.532046\pi\)
0.811387 + 0.584510i \(0.198713\pi\)
\(432\) 17.5846 106.559i 0.0407051 0.246664i
\(433\) −184.106 + 184.106i −0.425186 + 0.425186i −0.886985 0.461799i \(-0.847204\pi\)
0.461799 + 0.886985i \(0.347204\pi\)
\(434\) −0.727943 + 1.43764i −0.00167729 + 0.00331253i
\(435\) 165.281 + 232.293i 0.379957 + 0.534006i
\(436\) 88.7235 153.674i 0.203494 0.352463i
\(437\) −56.5428 15.1506i −0.129389 0.0346696i
\(438\) 297.489 35.8761i 0.679199 0.0819089i
\(439\) 151.405 262.241i 0.344887 0.597361i −0.640447 0.768003i \(-0.721251\pi\)
0.985333 + 0.170642i \(0.0545841\pi\)
\(440\) 92.4508 22.2915i 0.210116 0.0506625i
\(441\) 283.219 338.036i 0.642219 0.766521i
\(442\) 20.4844 20.4844i 0.0463449 0.0463449i
\(443\) 89.7849 + 335.082i 0.202675 + 0.756392i 0.990146 + 0.140041i \(0.0447233\pi\)
−0.787471 + 0.616352i \(0.788610\pi\)
\(444\) 254.859 + 200.004i 0.574008 + 0.450461i
\(445\) 12.1321 481.364i 0.0272631 1.08172i
\(446\) −112.186 + 194.311i −0.251538 + 0.435676i
\(447\) 55.0072 128.816i 0.123059 0.288179i
\(448\) −17.4395 53.2153i −0.0389274 0.118784i
\(449\) 119.472 0.266084 0.133042 0.991110i \(-0.457525\pi\)
0.133042 + 0.991110i \(0.457525\pi\)
\(450\) 22.9420 317.370i 0.0509822 0.705266i
\(451\) −374.978 + 216.494i −0.831438 + 0.480031i
\(452\) −70.6072 + 263.510i −0.156211 + 0.582986i
\(453\) 342.304 + 456.296i 0.755638 + 1.00728i
\(454\) −330.258 −0.727440
\(455\) −187.340 + 5.56351i −0.411735 + 0.0122275i
\(456\) 13.7581 + 34.2650i 0.0301712 + 0.0751425i
\(457\) 92.1811 + 344.025i 0.201709 + 0.752789i 0.990427 + 0.138034i \(0.0440784\pi\)
−0.788718 + 0.614755i \(0.789255\pi\)
\(458\) 66.6075 248.583i 0.145431 0.542757i
\(459\) 102.786 10.1315i 0.223935 0.0220729i
\(460\) 38.0796 129.020i 0.0827818 0.280477i
\(461\) 621.253 1.34762 0.673810 0.738905i \(-0.264657\pi\)
0.673810 + 0.738905i \(0.264657\pi\)
\(462\) 68.2355 187.692i 0.147696 0.406260i
\(463\) 26.5760 + 26.5760i 0.0573995 + 0.0573995i 0.735224 0.677824i \(-0.237077\pi\)
−0.677824 + 0.735224i \(0.737077\pi\)
\(464\) 38.0124 65.8393i 0.0819232 0.141895i
\(465\) 2.22065 + 1.01516i 0.00477559 + 0.00218314i
\(466\) 10.5971 + 18.3548i 0.0227407 + 0.0393880i
\(467\) −124.540 464.791i −0.266682 0.995269i −0.961213 0.275807i \(-0.911055\pi\)
0.694531 0.719462i \(-0.255612\pi\)
\(468\) −2.09782 + 96.3657i −0.00448252 + 0.205910i
\(469\) −711.771 + 39.1062i −1.51764 + 0.0833822i
\(470\) 114.805 187.759i 0.244267 0.399487i
\(471\) 96.4245 675.524i 0.204723 1.43423i
\(472\) 0.931915 3.47795i 0.00197440 0.00736855i
\(473\) 453.298 + 121.461i 0.958346 + 0.256788i
\(474\) −432.408 61.7221i −0.912254 0.130215i
\(475\) 49.5790 + 96.8337i 0.104377 + 0.203860i
\(476\) 44.8411 29.2815i 0.0942039 0.0615157i
\(477\) −741.445 16.1408i −1.55439 0.0338381i
\(478\) −510.200 + 136.708i −1.06736 + 0.285999i
\(479\) 361.804 208.888i 0.755331 0.436091i −0.0722856 0.997384i \(-0.523029\pi\)
0.827617 + 0.561293i \(0.189696\pi\)
\(480\) −79.5141 + 29.6227i −0.165654 + 0.0617140i
\(481\) −250.400 144.568i −0.520582 0.300558i
\(482\) 106.106 106.106i 0.220137 0.220137i
\(483\) −181.665 216.337i −0.376118 0.447903i
\(484\) 151.559i 0.313139i
\(485\) 75.4406 255.604i 0.155548 0.527020i
\(486\) −223.722 + 260.857i −0.460333 + 0.536743i
\(487\) −387.966 103.955i −0.796645 0.213460i −0.162534 0.986703i \(-0.551967\pi\)
−0.634110 + 0.773243i \(0.718633\pi\)
\(488\) 278.876 74.7245i 0.571466 0.153124i
\(489\) 328.396 131.858i 0.671567 0.269648i
\(490\) −341.055 61.0839i −0.696031 0.124661i
\(491\) 451.546i 0.919646i 0.888011 + 0.459823i \(0.152087\pi\)
−0.888011 + 0.459823i \(0.847913\pi\)
\(492\) 309.039 231.834i 0.628127 0.471208i
\(493\) 70.2279 + 18.8175i 0.142450 + 0.0381694i
\(494\) −16.4770 28.5391i −0.0333543 0.0577714i
\(495\) −288.297 91.9566i −0.582418 0.185771i
\(496\) 0.651116i 0.00131273i
\(497\) −259.664 792.345i −0.522463 1.59426i
\(498\) 117.621 + 50.2270i 0.236188 + 0.100857i
\(499\) −731.784 422.496i −1.46650 0.846685i −0.467204 0.884150i \(-0.654739\pi\)
−0.999298 + 0.0374644i \(0.988072\pi\)
\(500\) −225.328 + 108.292i −0.450657 + 0.216584i
\(501\) 149.054 189.935i 0.297513 0.379111i
\(502\) 234.901 62.9415i 0.467930 0.125381i
\(503\) 140.492 + 140.492i 0.279308 + 0.279308i 0.832833 0.553525i \(-0.186718\pi\)
−0.553525 + 0.832833i \(0.686718\pi\)
\(504\) −40.3942 + 173.552i −0.0801472 + 0.344349i
\(505\) −59.8659 + 97.9079i −0.118546 + 0.193877i
\(506\) −110.791 63.9653i −0.218955 0.126414i
\(507\) 50.4028 + 417.946i 0.0994138 + 0.824352i
\(508\) 110.511 412.433i 0.217541 0.811876i
\(509\) 378.654 + 218.616i 0.743918 + 0.429501i 0.823492 0.567328i \(-0.192023\pi\)
−0.0795742 + 0.996829i \(0.525356\pi\)
\(510\) −47.0452 66.1191i −0.0922455 0.129645i
\(511\) −493.644 + 27.1219i −0.966035 + 0.0530761i
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) 19.1300 115.923i 0.0372904 0.225971i
\(514\) −68.4391 118.540i −0.133150 0.230623i
\(515\) −304.695 + 289.714i −0.591641 + 0.562551i
\(516\) −414.519 59.1686i −0.803331 0.114668i
\(517\) −147.993 147.993i −0.286253 0.286253i
\(518\) −398.128 356.658i −0.768587 0.688530i
\(519\) −761.237 + 305.652i −1.46674 + 0.588925i
\(520\) 66.5173 36.2005i 0.127918 0.0696164i
\(521\) −490.536 849.633i −0.941527 1.63077i −0.762559 0.646918i \(-0.776058\pi\)
−0.178968 0.983855i \(-0.557276\pi\)
\(522\) −212.082 + 116.366i −0.406288 + 0.222924i
\(523\) −83.0151 309.817i −0.158729 0.592384i −0.998757 0.0498414i \(-0.984128\pi\)
0.840028 0.542542i \(-0.182538\pi\)
\(524\) 325.115i 0.620448i
\(525\) −71.8521 + 520.060i −0.136861 + 0.990590i
\(526\) −542.217 −1.03083
\(527\) 0.601469 0.161163i 0.00114131 0.000305812i
\(528\) 9.66155 + 80.1148i 0.0182984 + 0.151733i
\(529\) 301.410 174.019i 0.569774 0.328959i
\(530\) 278.530 + 511.789i 0.525528 + 0.965640i
\(531\) −8.27585 + 7.92321i −0.0155854 + 0.0149213i
\(532\) −18.9721 57.8918i −0.0356618 0.108819i
\(533\) −243.807 + 243.807i −0.457425 + 0.457425i
\(534\) 404.480 + 57.7357i 0.757454 + 0.108119i
\(535\) −381.499 401.226i −0.713082 0.749956i
\(536\) 249.444 144.016i 0.465380 0.268687i
\(537\) 300.392 + 400.427i 0.559389 + 0.745674i
\(538\) 415.369 415.369i 0.772061 0.772061i
\(539\) −132.499 + 301.692i −0.245824 + 0.559725i
\(540\) 265.205 + 50.6596i 0.491120 + 0.0938141i
\(541\) −34.9843 + 60.5947i −0.0646661 + 0.112005i −0.896546 0.442951i \(-0.853932\pi\)
0.831880 + 0.554956i \(0.187265\pi\)
\(542\) 234.980 + 62.9627i 0.433542 + 0.116167i
\(543\) −76.9122 637.766i −0.141643 1.17452i
\(544\) −10.8197 + 18.7403i −0.0198892 + 0.0344491i
\(545\) 378.474 + 231.418i 0.694447 + 0.424621i
\(546\) 13.8019 158.433i 0.0252782 0.290170i
\(547\) 159.245 159.245i 0.291124 0.291124i −0.546400 0.837524i \(-0.684002\pi\)
0.837524 + 0.546400i \(0.184002\pi\)
\(548\) 98.7541 + 368.555i 0.180208 + 0.672546i
\(549\) −881.991 257.029i −1.60654 0.468176i
\(550\) 49.8877 + 232.458i 0.0907049 + 0.422651i
\(551\) 41.3529 71.6253i 0.0750506 0.129992i
\(552\) 104.975 + 44.8267i 0.190172 + 0.0812078i
\(553\) 705.297 + 148.054i 1.27540 + 0.267728i
\(554\) −311.391 −0.562077
\(555\) −515.906 + 624.348i −0.929560 + 1.12495i
\(556\) −114.927 + 66.3531i −0.206703 + 0.119340i
\(557\) −223.552 + 834.309i −0.401351 + 1.49786i 0.409337 + 0.912383i \(0.365760\pi\)
−0.810688 + 0.585479i \(0.800907\pi\)
\(558\) −1.07472 + 1.77129i −0.00192603 + 0.00317436i
\(559\) 373.702 0.668519
\(560\) 134.094 40.2329i 0.239454 0.0718445i
\(561\) −71.6147 + 28.7547i −0.127655 + 0.0512562i
\(562\) −55.4278 206.859i −0.0986260 0.368077i
\(563\) 167.352 624.566i 0.297251 1.10935i −0.642163 0.766568i \(-0.721963\pi\)
0.939414 0.342786i \(-0.111371\pi\)
\(564\) 146.906 + 115.286i 0.260471 + 0.204408i
\(565\) −654.118 193.060i −1.15773 0.341699i
\(566\) 37.9737 0.0670913
\(567\) 396.351 405.456i 0.699032 0.715090i
\(568\) 238.231 + 238.231i 0.419421 + 0.419421i
\(569\) 172.352 298.522i 0.302903 0.524644i −0.673889 0.738833i \(-0.735377\pi\)
0.976792 + 0.214189i \(0.0687108\pi\)
\(570\) −86.5019 + 32.2260i −0.151758 + 0.0565368i
\(571\) 106.891 + 185.140i 0.187199 + 0.324239i 0.944315 0.329042i \(-0.106726\pi\)
−0.757116 + 0.653280i \(0.773392\pi\)
\(572\) −18.6400 69.5654i −0.0325874 0.121618i
\(573\) −259.510 110.817i −0.452898 0.193397i
\(574\) −533.702 + 348.510i −0.929794 + 0.607161i
\(575\) 320.048 + 103.296i 0.556605 + 0.179645i
\(576\) −17.1169 69.9358i −0.0297169 0.121416i
\(577\) −199.206 + 743.448i −0.345245 + 1.28847i 0.547081 + 0.837080i \(0.315739\pi\)
−0.892326 + 0.451392i \(0.850928\pi\)
\(578\) 374.792 + 100.425i 0.648429 + 0.173746i
\(579\) −14.1239 + 98.9481i −0.0243936 + 0.170895i
\(580\) 162.152 + 99.1479i 0.279572 + 0.170945i
\(581\) −188.261 95.3250i −0.324028 0.164071i
\(582\) 207.969 + 88.8074i 0.357335 + 0.152590i
\(583\) 535.242 143.418i 0.918082 0.245999i
\(584\) 173.000 99.8816i 0.296233 0.171030i
\(585\) −240.706 11.3129i −0.411463 0.0193382i
\(586\) 471.638 + 272.300i 0.804843 + 0.464676i
\(587\) −34.1370 + 34.1370i −0.0581550 + 0.0581550i −0.735586 0.677431i \(-0.763093\pi\)
0.677431 + 0.735586i \(0.263093\pi\)
\(588\) 85.1422 281.402i 0.144800 0.478574i
\(589\) 0.708336i 0.00120261i
\(590\) 8.63342 + 2.54812i 0.0146329 + 0.00431885i
\(591\) 52.3305 + 41.0671i 0.0885457 + 0.0694875i
\(592\) 208.619 + 55.8994i 0.352397 + 0.0944246i
\(593\) −839.420 + 224.922i −1.41555 + 0.379295i −0.883902 0.467671i \(-0.845093\pi\)
−0.531646 + 0.846967i \(0.678426\pi\)
\(594\) 105.953 233.891i 0.178373 0.393756i
\(595\) 70.3560 + 113.911i 0.118245 + 0.191448i
\(596\) 93.3794i 0.156677i
\(597\) −123.030 164.001i −0.206080 0.274708i
\(598\) −98.4021 26.3668i −0.164552 0.0440916i
\(599\) −183.387 317.635i −0.306155 0.530276i 0.671363 0.741129i \(-0.265709\pi\)
−0.977518 + 0.210853i \(0.932376\pi\)
\(600\) −69.0247 200.588i −0.115041 0.334313i
\(601\) 107.243i 0.178440i 0.996012 + 0.0892202i \(0.0284375\pi\)
−0.996012 + 0.0892202i \(0.971563\pi\)
\(602\) 676.117 + 141.928i 1.12312 + 0.235761i
\(603\) −916.298 19.9472i −1.51956 0.0330800i
\(604\) 329.332 + 190.140i 0.545251 + 0.314801i
\(605\) −378.778 9.54655i −0.626079 0.0157794i
\(606\) −76.6048 60.1167i −0.126411 0.0992025i
\(607\) 61.6948 16.5311i 0.101639 0.0272340i −0.207641 0.978205i \(-0.566579\pi\)
0.309280 + 0.950971i \(0.399912\pi\)
\(608\) 17.4061 + 17.4061i 0.0286284 + 0.0286284i
\(609\) 361.672 168.814i 0.593878 0.277198i
\(610\) 169.186 + 701.674i 0.277354 + 1.15029i
\(611\) −144.335 83.3319i −0.236228 0.136386i
\(612\) 60.3665 33.1222i 0.0986380 0.0541212i
\(613\) 20.7243 77.3443i 0.0338081 0.126173i −0.946959 0.321353i \(-0.895862\pi\)
0.980767 + 0.195180i \(0.0625290\pi\)
\(614\) 240.247 + 138.707i 0.391283 + 0.225907i
\(615\) 559.935 + 786.954i 0.910464 + 1.27960i
\(616\) −7.30400 132.940i −0.0118571 0.215812i
\(617\) −443.200 443.200i −0.718314 0.718314i 0.249946 0.968260i \(-0.419587\pi\)
−0.968260 + 0.249946i \(0.919587\pi\)
\(618\) −214.088 285.382i −0.346420 0.461784i
\(619\) 31.3094 + 54.2294i 0.0505806 + 0.0876081i 0.890207 0.455556i \(-0.150560\pi\)
−0.839627 + 0.543164i \(0.817226\pi\)
\(620\) 1.62727 + 0.0410131i 0.00262463 + 6.61501e-5i
\(621\) −211.584 295.217i −0.340714 0.475390i
\(622\) −213.164 213.164i −0.342708 0.342708i
\(623\) −659.744 138.491i −1.05898 0.222297i
\(624\) 23.9433 + 59.6317i 0.0383707 + 0.0955636i
\(625\) −256.451 569.963i −0.410321 0.911941i
\(626\) −158.415 274.383i −0.253059 0.438312i
\(627\) 10.5106 + 87.1553i 0.0167633 + 0.139004i
\(628\) −117.740 439.413i −0.187485 0.699702i
\(629\) 206.548i 0.328376i
\(630\) −431.198 111.885i −0.684441 0.177596i
\(631\) 518.483 0.821684 0.410842 0.911707i \(-0.365235\pi\)
0.410842 + 0.911707i \(0.365235\pi\)
\(632\) −281.272 + 75.3666i −0.445050 + 0.119251i
\(633\) 286.675 34.5719i 0.452883 0.0546160i
\(634\) −473.881 + 273.596i −0.747447 + 0.431539i
\(635\) 1023.79 + 302.169i 1.61227 + 0.475856i
\(636\) −458.811 + 184.222i −0.721400 + 0.289657i
\(637\) −39.7366 + 259.365i −0.0623809 + 0.407166i
\(638\) 127.809 127.809i 0.200328 0.200328i
\(639\) −254.861 1041.30i −0.398844 1.62958i
\(640\) −40.9951 + 38.9795i −0.0640549 + 0.0609054i
\(641\) 282.179 162.916i 0.440217 0.254159i −0.263473 0.964667i \(-0.584868\pi\)
0.703690 + 0.710507i \(0.251535\pi\)
\(642\) 375.795 281.914i 0.585351 0.439118i
\(643\) 238.396 238.396i 0.370756 0.370756i −0.496996 0.867753i \(-0.665564\pi\)
0.867753 + 0.496996i \(0.165564\pi\)
\(644\) −168.019 85.0759i −0.260899 0.132106i
\(645\) 173.985 1032.24i 0.269744 1.60037i
\(646\) −11.7706 + 20.3872i −0.0182207 + 0.0315592i
\(647\) 677.491 + 181.533i 1.04713 + 0.280577i 0.741064 0.671435i \(-0.234322\pi\)
0.306062 + 0.952011i \(0.400988\pi\)
\(648\) −68.8703 + 218.506i −0.106281 + 0.337201i
\(649\) 4.28028 7.41366i 0.00659519 0.0114232i
\(650\) 86.2828 + 168.521i 0.132743 + 0.259263i
\(651\) 1.95965 2.80088i 0.00301022 0.00430243i
\(652\) 166.820 166.820i 0.255859 0.255859i
\(653\) 202.218 + 754.689i 0.309676 + 1.15573i 0.928845 + 0.370468i \(0.120803\pi\)
−0.619170 + 0.785257i \(0.712531\pi\)
\(654\) −232.388 + 296.124i −0.355333 + 0.452789i
\(655\) 812.529 + 20.4786i 1.24050 + 0.0312651i
\(656\) 128.777 223.049i 0.196307 0.340013i
\(657\) −635.492 13.8343i −0.967263 0.0210567i
\(658\) −229.488 205.585i −0.348766 0.312438i
\(659\) −296.676 −0.450191 −0.225096 0.974337i \(-0.572269\pi\)
−0.225096 + 0.974337i \(0.572269\pi\)
\(660\) −200.832 + 19.0999i −0.304291 + 0.0289392i
\(661\) 502.629 290.193i 0.760407 0.439021i −0.0690350 0.997614i \(-0.521992\pi\)
0.829442 + 0.558593i \(0.188659\pi\)
\(662\) 98.8331 368.850i 0.149295 0.557176i
\(663\) −49.1584 + 36.8776i −0.0741454 + 0.0556223i
\(664\) 85.2644 0.128410
\(665\) 145.879 43.7686i 0.219366 0.0658174i
\(666\) −475.260 496.413i −0.713604 0.745365i
\(667\) −66.1735 246.963i −0.0992106 0.370259i
\(668\) 41.6592 155.474i 0.0623641 0.232746i
\(669\) 293.841 374.432i 0.439224 0.559689i
\(670\) 344.215 + 632.483i 0.513753 + 0.944004i
\(671\) 686.418 1.02298
\(672\) 20.6717 + 116.982i 0.0307615 + 0.174080i
\(673\) 578.339 + 578.339i 0.859345 + 0.859345i 0.991261 0.131916i \(-0.0421130\pi\)
−0.131916 + 0.991261i \(0.542113\pi\)
\(674\) −384.011 + 665.127i −0.569749 + 0.986835i
\(675\) −143.314 + 659.611i −0.212317 + 0.977201i
\(676\) 140.325 + 243.050i 0.207581 + 0.359541i
\(677\) 34.6936 + 129.478i 0.0512461 + 0.191253i 0.986804 0.161921i \(-0.0517690\pi\)
−0.935558 + 0.353174i \(0.885102\pi\)
\(678\) 227.267 532.214i 0.335202 0.784977i
\(679\) −332.868 168.546i −0.490232 0.248227i
\(680\) −46.1544 28.2211i −0.0678741 0.0415017i
\(681\) 693.553 + 98.9980i 1.01843 + 0.145372i
\(682\) 0.400660 1.49529i 0.000587479 0.00219250i
\(683\) −263.899 70.7116i −0.386382 0.103531i 0.0603983 0.998174i \(-0.480763\pi\)
−0.446781 + 0.894644i \(0.647430\pi\)
\(684\) −18.6212 76.0817i −0.0272239 0.111231i
\(685\) −927.316 + 223.592i −1.35375 + 0.326412i
\(686\) −170.397 + 454.162i −0.248392 + 0.662043i
\(687\) −214.393 + 502.066i −0.312071 + 0.730809i
\(688\) −269.635 + 72.2485i −0.391912 + 0.105012i
\(689\) 382.140 220.629i 0.554630 0.320216i
\(690\) −118.643 + 259.531i −0.171947 + 0.376132i
\(691\) 954.298 + 550.964i 1.38104 + 0.797343i 0.992283 0.123997i \(-0.0395714\pi\)
0.388757 + 0.921341i \(0.372905\pi\)
\(692\) −386.697 + 386.697i −0.558810 + 0.558810i
\(693\) −199.559 + 373.705i −0.287964 + 0.539257i
\(694\) 941.341i 1.35640i
\(695\) −158.591 291.405i −0.228188 0.419288i
\(696\) −99.5633 + 126.870i −0.143051 + 0.182285i
\(697\) 237.916 + 63.7494i 0.341343 + 0.0914625i
\(698\) −584.097 + 156.508i −0.836816 + 0.224224i
\(699\) −16.7523 41.7223i −0.0239662 0.0596886i
\(700\) 92.1039 + 337.664i 0.131577 + 0.482377i
\(701\) 1133.69i 1.61725i 0.588327 + 0.808623i \(0.299787\pi\)
−0.588327 + 0.808623i \(0.700213\pi\)
\(702\) 33.2921 201.742i 0.0474246 0.287382i
\(703\) 226.953 + 60.8118i 0.322835 + 0.0865033i
\(704\) 26.8984 + 46.5894i 0.0382080 + 0.0661782i
\(705\) −297.378 + 359.886i −0.421812 + 0.510476i
\(706\) 334.626i 0.473974i
\(707\) 119.668 + 107.203i 0.169262 + 0.151631i
\(708\) −2.99960 + 7.02447i −0.00423673 + 0.00992157i
\(709\) 892.396 + 515.225i 1.25867 + 0.726693i 0.972816 0.231581i \(-0.0743897\pi\)
0.285853 + 0.958273i \(0.407723\pi\)
\(710\) −610.394 + 580.382i −0.859710 + 0.817440i
\(711\) 889.570 + 259.237i 1.25115 + 0.364609i
\(712\) 263.105 70.4989i 0.369530 0.0990153i
\(713\) −1.54837 1.54837i −0.00217163 0.00217163i
\(714\) −102.945 + 48.0506i −0.144181 + 0.0672978i
\(715\) 175.033 42.2034i 0.244801 0.0590257i
\(716\) 289.008 + 166.859i 0.403642 + 0.233043i
\(717\) 1112.42 134.153i 1.55149 0.187104i
\(718\) −142.830 + 533.048i −0.198927 + 0.742407i
\(719\) −946.111 546.238i −1.31587 0.759718i −0.332809 0.942994i \(-0.607997\pi\)
−0.983062 + 0.183276i \(0.941330\pi\)
\(720\) 175.862 38.3736i 0.244253 0.0532966i
\(721\) 321.833 + 492.848i 0.446370 + 0.683562i
\(722\) −342.064 342.064i −0.473773 0.473773i
\(723\) −254.633 + 191.020i −0.352189 + 0.264205i
\(724\) −214.129 370.882i −0.295758 0.512268i
\(725\) −258.005 + 399.005i −0.355869 + 0.550352i
\(726\) 45.4314 318.280i 0.0625777 0.438402i
\(727\) 195.469 + 195.469i 0.268870 + 0.268870i 0.828645 0.559775i \(-0.189112\pi\)
−0.559775 + 0.828645i \(0.689112\pi\)
\(728\) −33.0173 100.750i −0.0453534 0.138393i
\(729\) 548.018 480.746i 0.751740 0.659460i
\(730\) 238.728 + 438.654i 0.327024 + 0.600896i
\(731\) −133.479 231.193i −0.182598 0.316269i
\(732\) −608.048 + 73.3283i −0.830666 + 0.100175i
\(733\) 41.8982 + 156.366i 0.0571599 + 0.213324i 0.988599 0.150574i \(-0.0481123\pi\)
−0.931439 + 0.363898i \(0.881446\pi\)
\(734\) 1005.24i 1.36954i
\(735\) 697.917 + 230.513i 0.949548 + 0.313623i
\(736\) 76.0970 0.103393
\(737\) 661.466 177.239i 0.897512 0.240488i
\(738\) −718.486 + 394.222i −0.973558 + 0.534177i
\(739\) −442.881 + 255.698i −0.599298 + 0.346005i −0.768765 0.639531i \(-0.779129\pi\)
0.169467 + 0.985536i \(0.445795\pi\)
\(740\) −152.845 + 517.861i −0.206547 + 0.699813i
\(741\) 26.0475 + 64.8722i 0.0351518 + 0.0875468i
\(742\) 775.176 254.038i 1.04471 0.342369i
\(743\) 366.443 366.443i 0.493194 0.493194i −0.416117 0.909311i \(-0.636609\pi\)
0.909311 + 0.416117i \(0.136609\pi\)
\(744\) −0.195178 + 1.36737i −0.000262337 + 0.00183786i
\(745\) 233.374 + 5.88186i 0.313254 + 0.00789512i
\(746\) 630.233 363.865i 0.844817 0.487755i
\(747\) −231.953 140.737i −0.310513 0.188402i
\(748\) −36.3792 + 36.3792i −0.0486353 + 0.0486353i
\(749\) −648.988 + 423.794i −0.866473 + 0.565813i
\(750\) 505.659 159.872i 0.674212 0.213163i
\(751\) −258.355 + 447.484i −0.344015 + 0.595851i −0.985174 0.171557i \(-0.945120\pi\)
0.641160 + 0.767408i \(0.278454\pi\)
\(752\) 120.252 + 32.2214i 0.159910 + 0.0428476i
\(753\) −512.167 + 61.7654i −0.680169 + 0.0820258i
\(754\) 71.9669 124.650i 0.0954468 0.165319i
\(755\) −495.943 + 811.092i −0.656878 + 1.07429i
\(756\) 136.853 352.357i 0.181023 0.466080i
\(757\) 211.287 211.287i 0.279111 0.279111i −0.553643 0.832754i \(-0.686763\pi\)
0.832754 + 0.553643i \(0.186763\pi\)
\(758\) 7.26593 + 27.1168i 0.00958565 + 0.0357741i
\(759\) 213.491 + 167.540i 0.281279 + 0.220738i
\(760\) −44.5978 + 42.4050i −0.0586813 + 0.0557961i
\(761\) 327.295 566.892i 0.430086 0.744930i −0.566795 0.823859i \(-0.691817\pi\)
0.996880 + 0.0789291i \(0.0251501\pi\)
\(762\) −355.708 + 832.996i −0.466808 + 1.09317i
\(763\) 414.406 462.590i 0.543127 0.606278i
\(764\) −188.120 −0.246231
\(765\) 78.9767 + 152.955i 0.103238 + 0.199941i
\(766\) 480.434 277.379i 0.627199 0.362113i
\(767\) 1.76435 6.58464i 0.00230032 0.00858492i
\(768\) −28.8044 38.3967i −0.0375057 0.0499957i
\(769\) 378.964 0.492801 0.246401 0.969168i \(-0.420752\pi\)
0.246401 + 0.969168i \(0.420752\pi\)
\(770\) 332.704 9.88048i 0.432084 0.0128318i
\(771\) 108.191 + 269.453i 0.140326 + 0.349486i
\(772\) 17.2461 + 64.3635i 0.0223396 + 0.0833724i
\(773\) 374.638 1398.17i 0.484654 1.80875i −0.0969586 0.995288i \(-0.530911\pi\)
0.581613 0.813466i \(-0.302422\pi\)
\(774\) 852.767 + 248.512i 1.10177 + 0.321075i
\(775\) −0.205000 + 4.06431i −0.000264516 + 0.00524427i
\(776\) 150.758 0.194276
\(777\) 729.171 + 868.338i 0.938444 + 1.11755i
\(778\) 54.2222 + 54.2222i 0.0696943 + 0.0696943i
\(779\) 140.094 242.650i 0.179838 0.311489i
\(780\) −150.540 + 56.0832i −0.193000 + 0.0719015i
\(781\) 400.502 + 693.690i 0.512807 + 0.888208i
\(782\) 18.8354 + 70.2947i 0.0240862 + 0.0898909i
\(783\) 480.262 180.800i 0.613362 0.230906i
\(784\) −21.4725 194.820i −0.0273884 0.248495i
\(785\) 1105.60 266.579i 1.40841 0.339592i
\(786\) −97.4563 + 682.752i −0.123990 + 0.868641i
\(787\) 47.3821 176.832i 0.0602060 0.224692i −0.929267 0.369408i \(-0.879560\pi\)
0.989473 + 0.144717i \(0.0462270\pi\)
\(788\) 42.8360 + 11.4779i 0.0543604 + 0.0145658i
\(789\) 1138.68 + 162.535i 1.44319 + 0.206001i
\(790\) −170.640 707.704i −0.216000 0.895827i
\(791\) −431.327 + 851.842i −0.545294 + 1.07692i
\(792\) 3.72561 171.140i 0.00470405 0.216086i
\(793\) 527.981 141.472i 0.665802 0.178401i
\(794\) −753.321 + 434.930i −0.948766 + 0.547771i
\(795\) −431.508 1158.27i −0.542777 1.45694i
\(796\) −118.367 68.3394i −0.148703 0.0858536i
\(797\) −971.725 + 971.725i −1.21923 + 1.21923i −0.251326 + 0.967902i \(0.580867\pi\)
−0.967902 + 0.251326i \(0.919133\pi\)
\(798\) 22.4884 + 127.262i 0.0281809 + 0.159476i
\(799\) 119.058i 0.149009i
\(800\) −94.8355 104.911i −0.118544 0.131138i
\(801\) −832.116 242.494i −1.03885 0.302739i
\(802\) −617.767 165.530i −0.770283 0.206397i
\(803\) 458.755 122.923i 0.571302 0.153080i
\(804\) −567.011 + 227.666i −0.705237 + 0.283167i
\(805\) 223.206 414.556i 0.277274 0.514976i
\(806\) 1.23273i 0.00152944i
\(807\) −996.800 + 747.778i −1.23519 + 0.926615i
\(808\) −62.7061 16.8020i −0.0776066 0.0207946i
\(809\) −475.295 823.235i −0.587509 1.01760i −0.994557 0.104190i \(-0.966775\pi\)
0.407048 0.913407i \(-0.366558\pi\)
\(810\) −541.754 185.885i −0.668832 0.229487i
\(811\) 916.050i 1.12953i −0.825251 0.564765i \(-0.808967\pi\)
0.825251 0.564765i \(-0.191033\pi\)
\(812\) 177.546 198.190i 0.218653 0.244077i
\(813\) −474.592 202.661i −0.583754 0.249276i
\(814\) 444.696 + 256.745i 0.546309 + 0.315412i
\(815\) 406.411 + 427.426i 0.498663 + 0.524449i
\(816\) 28.3394 36.1120i 0.0347296 0.0442549i
\(817\) −293.331 + 78.5978i −0.359034 + 0.0962029i
\(818\) −320.698 320.698i −0.392052 0.392052i
\(819\) −76.4763 + 328.577i −0.0933776 + 0.401193i
\(820\) 549.333 + 335.890i 0.669918 + 0.409622i
\(821\) −231.737 133.794i −0.282262 0.162964i 0.352185 0.935931i \(-0.385439\pi\)
−0.634447 + 0.772966i \(0.718772\pi\)
\(822\) −96.9089 803.581i −0.117894 0.977593i
\(823\) −171.635 + 640.549i −0.208548 + 0.778310i 0.779791 + 0.626040i \(0.215325\pi\)
−0.988339 + 0.152271i \(0.951341\pi\)
\(824\) −205.975 118.920i −0.249969 0.144320i
\(825\) −35.0843 503.124i −0.0425264 0.609847i
\(826\) 5.69291 11.2431i 0.00689214 0.0136115i
\(827\) 658.320 + 658.320i 0.796034 + 0.796034i 0.982468 0.186434i \(-0.0596930\pi\)
−0.186434 + 0.982468i \(0.559693\pi\)
\(828\) −207.014 125.605i −0.250017 0.151697i
\(829\) 191.308 + 331.355i 0.230769 + 0.399704i 0.958035 0.286652i \(-0.0925424\pi\)
−0.727265 + 0.686356i \(0.759209\pi\)
\(830\) −5.37071 + 213.093i −0.00647074 + 0.256739i
\(831\) 653.931 + 93.3424i 0.786921 + 0.112325i
\(832\) 30.2920 + 30.2920i 0.0364087 + 0.0364087i
\(833\) 174.651 68.0568i 0.209665 0.0817009i
\(834\) 261.240 104.893i 0.313238 0.125771i
\(835\) 385.938 + 113.908i 0.462201 + 0.136417i
\(836\) 29.2623 + 50.6837i 0.0350027 + 0.0606265i
\(837\) 2.78792 3.39762i 0.00333085 0.00405928i
\(838\) −152.302 568.400i −0.181745 0.678281i
\(839\) 1402.36i 1.67146i −0.549138 0.835732i \(-0.685044\pi\)
0.549138 0.835732i \(-0.314956\pi\)
\(840\) −293.663 + 44.2944i −0.349599 + 0.0527314i
\(841\) −479.765 −0.570470
\(842\) −118.302 + 31.6990i −0.140502 + 0.0376473i
\(843\) 54.3922 + 451.027i 0.0645221 + 0.535026i
\(844\) 166.711 96.2506i 0.197525 0.114041i
\(845\) −616.270 + 335.391i −0.729314 + 0.396913i
\(846\) −273.949 286.142i −0.323817 0.338229i
\(847\) −108.977 + 519.143i −0.128662 + 0.612920i
\(848\) −233.069 + 233.069i −0.274845 + 0.274845i
\(849\) −79.7460 11.3830i −0.0939293 0.0134075i
\(850\) 73.4377 113.572i 0.0863973 0.133614i
\(851\) 629.034 363.173i 0.739170 0.426760i
\(852\) −428.881 571.705i −0.503382 0.671016i
\(853\) −1004.58 + 1004.58i −1.17770 + 1.17770i −0.197375 + 0.980328i \(0.563242\pi\)
−0.980328 + 0.197375i \(0.936758\pi\)
\(854\) 1008.97 55.4352i 1.18147 0.0649124i
\(855\) 191.317 41.7458i 0.223762 0.0488256i
\(856\) 156.595 271.230i 0.182938 0.316858i
\(857\) −551.603 147.802i −0.643644 0.172464i −0.0777906 0.996970i \(-0.524787\pi\)
−0.565853 + 0.824506i \(0.691453\pi\)
\(858\) 18.2917 + 151.677i 0.0213190 + 0.176780i
\(859\) −748.085 + 1295.72i −0.870879 + 1.50841i −0.00979076 + 0.999952i \(0.503117\pi\)
−0.861089 + 0.508455i \(0.830217\pi\)
\(860\) −163.580 678.425i −0.190209 0.788866i
\(861\) 1225.26 571.902i 1.42307 0.664230i
\(862\) −353.788 + 353.788i −0.410427 + 0.410427i
\(863\) −98.5642 367.847i −0.114211 0.426242i 0.885016 0.465562i \(-0.154148\pi\)
−0.999227 + 0.0393196i \(0.987481\pi\)
\(864\) 14.9822 + 151.998i 0.0173405 + 0.175924i
\(865\) −942.077 990.793i −1.08911 1.14543i
\(866\) 184.106 318.880i 0.212593 0.368222i
\(867\) −756.972 323.244i −0.873094 0.372830i
\(868\) 0.468177 2.23030i 0.000539374 0.00256947i
\(869\) −692.316 −0.796681
\(870\) −310.804 256.821i −0.357246 0.295196i
\(871\) 472.259 272.659i 0.542204 0.313041i
\(872\) −64.9501 + 242.397i −0.0744841 + 0.277978i
\(873\) −410.122 248.839i −0.469784 0.285039i
\(874\) 82.7845 0.0947191
\(875\) −849.693 + 208.918i −0.971078 + 0.238763i
\(876\) −393.246 + 157.896i −0.448911 + 0.180247i
\(877\) −1.60946 6.00658i −0.00183519 0.00684901i 0.965002 0.262242i \(-0.0844618\pi\)
−0.966837 + 0.255393i \(0.917795\pi\)
\(878\) −110.836 + 413.647i −0.126237 + 0.471124i
\(879\) −908.831 713.218i −1.03394 0.811397i
\(880\) −118.131 + 64.2901i −0.134240 + 0.0730569i
\(881\) −667.037 −0.757136 −0.378568 0.925574i \(-0.623583\pi\)
−0.378568 + 0.925574i \(0.623583\pi\)
\(882\) −263.154 + 565.431i −0.298361 + 0.641078i
\(883\) −241.670 241.670i −0.273693 0.273693i 0.556892 0.830585i \(-0.311994\pi\)
−0.830585 + 0.556892i \(0.811994\pi\)
\(884\) −20.4844 + 35.4801i −0.0231724 + 0.0401358i
\(885\) −17.3667 7.93909i −0.0196233 0.00897073i
\(886\) −245.297 424.867i −0.276859 0.479533i
\(887\) −313.746 1170.92i −0.353716 1.32009i −0.882093 0.471076i \(-0.843866\pi\)
0.528377 0.849010i \(-0.322801\pi\)
\(888\) −421.351 179.926i −0.474495 0.202620i
\(889\) 675.093 1333.26i 0.759384 1.49973i
\(890\) 159.619 + 661.995i 0.179347 + 0.743815i
\(891\) −292.617 + 459.419i −0.328414 + 0.515622i
\(892\) 82.1257 306.497i 0.0920692 0.343607i
\(893\) 130.820 + 35.0531i 0.146495 + 0.0392531i
\(894\) −27.9914 + 196.100i −0.0313103 + 0.219351i
\(895\) −435.219 + 711.780i −0.486278 + 0.795285i
\(896\) 43.3009 + 66.3101i 0.0483269 + 0.0740068i
\(897\) 198.744 + 84.8681i 0.221565 + 0.0946133i
\(898\) −163.201 + 43.7297i −0.181739 + 0.0486968i
\(899\) 2.67932 1.54690i 0.00298033 0.00172069i
\(900\) 84.8261 + 441.933i 0.0942512 + 0.491036i
\(901\) −272.986 157.609i −0.302982 0.174926i
\(902\) 432.988 432.988i 0.480031 0.480031i
\(903\) −1377.33 500.727i −1.52528 0.554515i
\(904\) 385.805i 0.426775i
\(905\) 940.398 511.791i 1.03911 0.565515i
\(906\) −634.612 498.021i −0.700455 0.549692i
\(907\) −1226.59 328.664i −1.35236 0.362364i −0.491355 0.870960i \(-0.663498\pi\)
−0.861005 + 0.508596i \(0.830165\pi\)
\(908\) 451.141 120.883i 0.496851 0.133131i
\(909\) 142.852 + 149.210i 0.157153 + 0.164148i
\(910\) 253.874 76.1709i 0.278983 0.0837043i
\(911\) 865.824i 0.950411i 0.879875 + 0.475205i \(0.157626\pi\)
−0.879875 + 0.475205i \(0.842374\pi\)
\(912\) −31.3357 41.7710i −0.0343594 0.0458016i
\(913\) 195.809 + 52.4670i 0.214468 + 0.0574666i
\(914\) −251.844 436.206i −0.275540 0.477249i
\(915\) −144.962 1524.26i −0.158429 1.66585i
\(916\) 363.950i 0.397326i
\(917\) 233.770 1113.63i 0.254929 1.21443i
\(918\) −136.700 + 51.4622i −0.148911 + 0.0560591i
\(919\) 533.082 + 307.775i 0.580067 + 0.334902i 0.761160 0.648564i \(-0.224630\pi\)
−0.181093 + 0.983466i \(0.557964\pi\)
\(920\) −4.79327 + 190.182i −0.00521007 + 0.206720i
\(921\) −462.949 363.306i −0.502659 0.394469i
\(922\) −848.647 + 227.394i −0.920442 + 0.246632i
\(923\) 451.031 + 451.031i 0.488657 + 0.488657i
\(924\) −24.5114 + 281.368i −0.0265275 + 0.304511i
\(925\) −1284.62 414.610i −1.38877 0.448227i
\(926\) −46.0309 26.5760i −0.0497094 0.0286997i
\(927\) 364.046 + 663.488i 0.392714 + 0.715737i
\(928\) −27.8270 + 103.852i −0.0299860 + 0.111909i
\(929\) −380.587 219.732i −0.409674 0.236526i 0.280975 0.959715i \(-0.409342\pi\)
−0.690650 + 0.723189i \(0.742675\pi\)
\(930\) −3.40504 0.573920i −0.00366133 0.000617118i
\(931\) −23.3595 211.941i −0.0250908 0.227649i
\(932\) −21.1943 21.1943i −0.0227407 0.0227407i
\(933\) 383.754 + 511.550i 0.411312 + 0.548286i
\(934\) 340.250 + 589.331i 0.364294 + 0.630976i
\(935\) −88.6276 93.2106i −0.0947889 0.0996904i
\(936\) −32.4066 132.406i −0.0346225 0.141459i
\(937\) −592.606 592.606i −0.632450 0.632450i 0.316232 0.948682i \(-0.397582\pi\)
−0.948682 + 0.316232i \(0.897582\pi\)
\(938\) 957.984 313.947i 1.02130 0.334698i
\(939\) 250.428 + 623.700i 0.266697 + 0.664218i
\(940\) −88.1025 + 298.505i −0.0937261 + 0.317558i
\(941\) −70.6791 122.420i −0.0751106 0.130095i 0.826024 0.563635i \(-0.190598\pi\)
−0.901134 + 0.433540i \(0.857264\pi\)
\(942\) 115.540 + 958.076i 0.122654 + 1.01707i
\(943\) −224.180 836.653i −0.237731 0.887224i
\(944\) 5.09208i 0.00539415i
\(945\) 871.992 + 364.219i 0.922743 + 0.385417i
\(946\) −663.674 −0.701558
\(947\) −1746.87 + 468.071i −1.84463 + 0.494267i −0.999207 0.0398282i \(-0.987319\pi\)
−0.845424 + 0.534096i \(0.820652\pi\)
\(948\) 613.272 73.9584i 0.646912 0.0780152i
\(949\) 327.532 189.101i 0.345134 0.199263i
\(950\) −103.170 114.130i −0.108600 0.120137i
\(951\) 1077.18 432.509i 1.13268 0.454794i
\(952\) −50.5363 + 56.4122i −0.0530843 + 0.0592565i
\(953\) −100.695 + 100.695i −0.105661 + 0.105661i −0.757961 0.652300i \(-0.773804\pi\)
0.652300 + 0.757961i \(0.273804\pi\)
\(954\) 1018.74 249.339i 1.06786 0.261362i
\(955\) 11.8495 470.152i 0.0124078 0.492305i
\(956\) 646.908 373.492i 0.676682 0.390682i
\(957\) −306.715 + 230.091i −0.320497 + 0.240430i
\(958\) −417.775 + 417.775i −0.436091 + 0.436091i
\(959\) 73.2619 + 1333.44i 0.0763940 + 1.39045i
\(960\) 97.7756 69.5696i 0.101850 0.0724683i
\(961\) −480.487 + 832.227i −0.499986 + 0.866002i
\(962\) 394.968 + 105.831i 0.410570 + 0.110012i
\(963\) −873.689 + 479.380i −0.907258 + 0.497798i
\(964\) −106.106 + 183.781i −0.110069 + 0.190644i
\(965\) −161.944 + 39.0475i −0.167818 + 0.0404637i
\(966\) 327.344 + 229.028i 0.338865 + 0.237089i
\(967\) 259.912 259.912i 0.268782 0.268782i −0.559827 0.828609i \(-0.689133\pi\)
0.828609 + 0.559827i \(0.189133\pi\)
\(968\) −55.4746 207.034i −0.0573084 0.213878i
\(969\) 30.8299 39.2855i 0.0318162 0.0405423i
\(970\) −9.49608 + 376.775i −0.00978977 + 0.388428i
\(971\) 588.918 1020.04i 0.606506 1.05050i −0.385305 0.922789i \(-0.625904\pi\)
0.991811 0.127711i \(-0.0407629\pi\)
\(972\) 210.129 438.226i 0.216182 0.450849i
\(973\) −441.374 + 144.645i −0.453622 + 0.148659i
\(974\) 568.022 0.583184
\(975\) −130.681 379.763i −0.134032 0.389501i
\(976\) −353.600 + 204.151i −0.362295 + 0.209171i
\(977\) −46.8824 + 174.967i −0.0479861 + 0.179086i −0.985759 0.168161i \(-0.946217\pi\)
0.937773 + 0.347248i \(0.112884\pi\)
\(978\) −400.334 + 300.322i −0.409340 + 0.307078i
\(979\) 647.602 0.661493
\(980\) 488.249 41.3927i 0.498213 0.0422375i
\(981\) 576.788 552.211i 0.587959 0.562906i
\(982\) −165.277 616.823i −0.168307 0.628130i
\(983\) 144.233 538.283i 0.146727 0.547592i −0.852946 0.522000i \(-0.825186\pi\)
0.999672 0.0255925i \(-0.00814723\pi\)
\(984\) −337.297 + 429.807i −0.342782 + 0.436796i
\(985\) −31.3838 + 106.333i −0.0318617 + 0.107952i
\(986\) −102.821 −0.104281
\(987\) 420.307 + 500.526i 0.425843 + 0.507118i
\(988\) 32.9541 + 32.9541i 0.0333543 + 0.0333543i
\(989\) −469.392 + 813.011i −0.474613 + 0.822053i
\(990\) 427.479 + 20.0910i 0.431797 + 0.0202939i
\(991\) −191.237 331.232i −0.192974 0.334240i 0.753261 0.657722i \(-0.228480\pi\)
−0.946234 + 0.323482i \(0.895146\pi\)
\(992\) 0.238325 + 0.889441i 0.000240247 + 0.000896614i
\(993\) −318.119 + 744.972i −0.320362 + 0.750224i
\(994\) 644.726 + 987.320i 0.648618 + 0.993280i
\(995\) 178.250 291.520i 0.179146 0.292985i
\(996\) −179.058 25.5588i −0.179777 0.0256615i
\(997\) 233.051 869.759i 0.233752 0.872376i −0.744955 0.667115i \(-0.767529\pi\)
0.978707 0.205261i \(-0.0658043\pi\)
\(998\) 1154.28 + 309.288i 1.15659 + 0.309908i
\(999\) 849.258 + 1184.95i 0.850108 + 1.18613i
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.w.a.173.16 yes 64
3.2 odd 2 210.3.w.b.173.14 yes 64
5.2 odd 4 210.3.w.b.47.7 yes 64
7.3 odd 6 inner 210.3.w.a.143.12 yes 64
15.2 even 4 inner 210.3.w.a.47.12 yes 64
21.17 even 6 210.3.w.b.143.7 yes 64
35.17 even 12 210.3.w.b.17.14 yes 64
105.17 odd 12 inner 210.3.w.a.17.16 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.3.w.a.17.16 64 105.17 odd 12 inner
210.3.w.a.47.12 yes 64 15.2 even 4 inner
210.3.w.a.143.12 yes 64 7.3 odd 6 inner
210.3.w.a.173.16 yes 64 1.1 even 1 trivial
210.3.w.b.17.14 yes 64 35.17 even 12
210.3.w.b.47.7 yes 64 5.2 odd 4
210.3.w.b.143.7 yes 64 21.17 even 6
210.3.w.b.173.14 yes 64 3.2 odd 2