Properties

Label 287.3.y.a.10.17
Level $287$
Weight $3$
Character 287.10
Analytic conductor $7.820$
Analytic rank $0$
Dimension $432$
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] = [287,3,Mod(10,287)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(287, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([5, 6]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("287.10");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 287 = 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 287.y (of order \(30\), degree \(8\), 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: \(7.82018358714\)
Analytic rank: \(0\)
Dimension: \(432\)
Relative dimension: \(54\) over \(\Q(\zeta_{30})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label 10.17
Character \(\chi\) \(=\) 287.10
Dual form 287.3.y.a.201.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.182448 + 1.73588i) q^{2} +(-4.79904 - 2.77073i) q^{3} +(0.932598 + 0.198230i) q^{4} +(-1.81832 - 1.63723i) q^{5} +(5.68522 - 7.82504i) q^{6} +(-1.44156 + 6.84996i) q^{7} +(-2.67174 + 8.22277i) q^{8} +(10.8538 + 18.7994i) q^{9} +O(q^{10})\) \(q+(-0.182448 + 1.73588i) q^{2} +(-4.79904 - 2.77073i) q^{3} +(0.932598 + 0.198230i) q^{4} +(-1.81832 - 1.63723i) q^{5} +(5.68522 - 7.82504i) q^{6} +(-1.44156 + 6.84996i) q^{7} +(-2.67174 + 8.22277i) q^{8} +(10.8538 + 18.7994i) q^{9} +(3.17378 - 2.85768i) q^{10} +(-8.44650 - 9.38078i) q^{11} +(-3.92633 - 3.53528i) q^{12} +(1.28784 - 1.77256i) q^{13} +(-11.6277 - 3.75214i) q^{14} +(4.18990 + 12.8952i) q^{15} +(-10.3023 - 4.58687i) q^{16} +(23.3855 - 21.0564i) q^{17} +(-34.6138 + 15.4110i) q^{18} +(3.29536 - 7.40149i) q^{19} +(-1.37122 - 1.88732i) q^{20} +(25.8975 - 28.8790i) q^{21} +(17.8250 - 12.9506i) q^{22} +(-1.77221 + 16.8614i) q^{23} +(35.6048 - 32.0587i) q^{24} +(-1.98742 - 18.9090i) q^{25} +(2.84199 + 2.55894i) q^{26} -70.4189i q^{27} +(-2.70226 + 6.10249i) q^{28} +(-13.7697 - 42.3787i) q^{29} +(-23.1489 + 4.92046i) q^{30} +(10.0181 - 9.02033i) q^{31} +(-7.44998 + 12.9037i) q^{32} +(14.5435 + 68.4217i) q^{33} +(32.2848 + 44.4362i) q^{34} +(13.8362 - 10.0953i) q^{35} +(6.39566 + 19.6838i) q^{36} +(29.6040 - 32.8786i) q^{37} +(12.2469 + 7.07074i) q^{38} +(-11.0917 + 4.93833i) q^{39} +(18.3206 - 10.5774i) q^{40} +(40.9437 + 2.14845i) q^{41} +(45.4056 + 50.2238i) q^{42} +(61.0025 + 44.3209i) q^{43} +(-6.01763 - 10.4228i) q^{44} +(11.0431 - 51.9536i) q^{45} +(-28.9461 - 6.15268i) q^{46} +(-51.3928 - 5.40160i) q^{47} +(36.7320 + 50.5573i) q^{48} +(-44.8438 - 19.7493i) q^{49} +33.1864 q^{50} +(-170.570 + 36.2557i) q^{51} +(1.55241 - 1.39780i) q^{52} +(8.48994 + 1.80459i) q^{53} +(122.239 + 12.8478i) q^{54} +30.8861i q^{55} +(-52.4741 - 30.1549i) q^{56} +(-36.3221 + 26.3895i) q^{57} +(76.0765 - 16.1706i) q^{58} +(-26.0155 - 58.4318i) q^{59} +(1.35128 + 12.8566i) q^{60} +(2.97531 - 6.68265i) q^{61} +(13.8304 + 19.0359i) q^{62} +(-144.422 + 47.2478i) q^{63} +(-57.5340 - 41.8009i) q^{64} +(-5.24379 + 1.11460i) q^{65} +(-121.425 + 12.7623i) q^{66} +(58.4822 + 12.4308i) q^{67} +(25.9833 - 15.0015i) q^{68} +(55.2233 - 76.0083i) q^{69} +(14.9998 + 25.8598i) q^{70} +(32.0396 - 98.6076i) q^{71} +(-183.582 + 39.0215i) q^{72} +(-28.6575 - 16.5454i) q^{73} +(51.6721 + 57.3877i) q^{74} +(-42.8540 + 96.2517i) q^{75} +(4.54044 - 6.24938i) q^{76} +(76.4341 - 44.3351i) q^{77} +(-6.54869 - 20.1548i) q^{78} +(56.6506 + 98.1217i) q^{79} +(11.2231 + 25.2076i) q^{80} +(-97.4270 + 168.749i) q^{81} +(-11.1996 + 70.6813i) q^{82} -13.0971i q^{83} +(29.8766 - 21.7989i) q^{84} -76.9966 q^{85} +(-88.0656 + 97.8067i) q^{86} +(-51.3385 + 241.529i) q^{87} +(99.7028 - 44.3906i) q^{88} +(41.8762 - 94.0556i) q^{89} +(88.1704 + 28.6483i) q^{90} +(10.2855 + 11.3769i) q^{91} +(-4.99519 + 15.3736i) q^{92} +(-73.0700 + 15.5315i) q^{93} +(18.7531 - 88.2263i) q^{94} +(-18.1100 + 8.06307i) q^{95} +(71.5054 - 41.2837i) q^{96} +(-56.6477 + 18.4059i) q^{97} +(42.4640 - 74.2402i) q^{98} +(84.6762 - 260.607i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 432 q - 3 q^{2} - 24 q^{3} + 101 q^{4} - 9 q^{5} - 6 q^{7} - 16 q^{8} + 576 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 432 q - 3 q^{2} - 24 q^{3} + 101 q^{4} - 9 q^{5} - 6 q^{7} - 16 q^{8} + 576 q^{9} + 72 q^{10} - 11 q^{11} - 33 q^{12} + 182 q^{14} - 54 q^{15} + 197 q^{16} - 63 q^{17} + 48 q^{18} + 63 q^{19} - 26 q^{21} - 52 q^{22} - 24 q^{23} - 510 q^{24} - 253 q^{25} - 159 q^{26} - 65 q^{28} + 152 q^{29} - 131 q^{30} - 45 q^{31} + 94 q^{32} + 36 q^{33} + 84 q^{35} + 474 q^{36} - 46 q^{37} - 6 q^{38} + 74 q^{39} + 258 q^{40} - 220 q^{42} - 88 q^{43} + 128 q^{44} - 156 q^{45} - 82 q^{46} - 309 q^{47} - 338 q^{49} + 704 q^{50} + 66 q^{51} + 291 q^{52} + 68 q^{53} + 483 q^{54} - 182 q^{56} + 114 q^{57} + 159 q^{58} - 207 q^{59} + 430 q^{60} + 423 q^{61} - 172 q^{63} - 896 q^{64} + 204 q^{65} - 1560 q^{66} + 33 q^{67} - 1242 q^{68} + 707 q^{70} - 162 q^{71} - 41 q^{72} - 78 q^{73} - 439 q^{74} - 1452 q^{75} + 164 q^{77} - 222 q^{78} - 138 q^{79} - 27 q^{80} - 928 q^{81} + 165 q^{82} - 543 q^{84} + 156 q^{85} + 609 q^{86} - 588 q^{87} + 394 q^{88} - 1161 q^{89} - 950 q^{91} + 482 q^{92} - 45 q^{93} + 1779 q^{94} - 475 q^{95} + 2412 q^{96} - 1100 q^{98} + 932 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).

\(n\) \(206\) \(211\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.182448 + 1.73588i −0.0912242 + 0.867940i 0.849231 + 0.528022i \(0.177066\pi\)
−0.940455 + 0.339918i \(0.889601\pi\)
\(3\) −4.79904 2.77073i −1.59968 0.923575i −0.991548 0.129738i \(-0.958586\pi\)
−0.608131 0.793837i \(-0.708080\pi\)
\(4\) 0.932598 + 0.198230i 0.233149 + 0.0495574i
\(5\) −1.81832 1.63723i −0.363665 0.327445i 0.466959 0.884279i \(-0.345349\pi\)
−0.830624 + 0.556834i \(0.812016\pi\)
\(6\) 5.68522 7.82504i 0.947537 1.30417i
\(7\) −1.44156 + 6.84996i −0.205937 + 0.978565i
\(8\) −2.67174 + 8.22277i −0.333967 + 1.02785i
\(9\) 10.8538 + 18.7994i 1.20598 + 2.08882i
\(10\) 3.17378 2.85768i 0.317378 0.285768i
\(11\) −8.44650 9.38078i −0.767863 0.852799i 0.224713 0.974425i \(-0.427856\pi\)
−0.992576 + 0.121626i \(0.961189\pi\)
\(12\) −3.92633 3.53528i −0.327194 0.294607i
\(13\) 1.28784 1.77256i 0.0990646 0.136351i −0.756607 0.653870i \(-0.773144\pi\)
0.855672 + 0.517519i \(0.173144\pi\)
\(14\) −11.6277 3.75214i −0.830549 0.268010i
\(15\) 4.18990 + 12.8952i 0.279327 + 0.859679i
\(16\) −10.3023 4.58687i −0.643892 0.286679i
\(17\) 23.3855 21.0564i 1.37562 1.23861i 0.434441 0.900700i \(-0.356946\pi\)
0.941177 0.337913i \(-0.109721\pi\)
\(18\) −34.6138 + 15.4110i −1.92299 + 0.856169i
\(19\) 3.29536 7.40149i 0.173440 0.389552i −0.805820 0.592161i \(-0.798275\pi\)
0.979260 + 0.202608i \(0.0649418\pi\)
\(20\) −1.37122 1.88732i −0.0685609 0.0943660i
\(21\) 25.8975 28.8790i 1.23321 1.37519i
\(22\) 17.8250 12.9506i 0.810226 0.588664i
\(23\) −1.77221 + 16.8614i −0.0770525 + 0.733105i 0.885981 + 0.463722i \(0.153486\pi\)
−0.963033 + 0.269383i \(0.913180\pi\)
\(24\) 35.6048 32.0587i 1.48353 1.33578i
\(25\) −1.98742 18.9090i −0.0794968 0.756361i
\(26\) 2.84199 + 2.55894i 0.109307 + 0.0984206i
\(27\) 70.4189i 2.60811i
\(28\) −2.70226 + 6.10249i −0.0965094 + 0.217946i
\(29\) −13.7697 42.3787i −0.474816 1.46133i −0.846206 0.532856i \(-0.821119\pi\)
0.371390 0.928477i \(-0.378881\pi\)
\(30\) −23.1489 + 4.92046i −0.771631 + 0.164015i
\(31\) 10.0181 9.02033i 0.323164 0.290978i −0.491540 0.870855i \(-0.663566\pi\)
0.814704 + 0.579877i \(0.196899\pi\)
\(32\) −7.44998 + 12.9037i −0.232812 + 0.403242i
\(33\) 14.5435 + 68.4217i 0.440711 + 2.07338i
\(34\) 32.2848 + 44.4362i 0.949552 + 1.30695i
\(35\) 13.8362 10.0953i 0.395319 0.288437i
\(36\) 6.39566 + 19.6838i 0.177657 + 0.546773i
\(37\) 29.6040 32.8786i 0.800109 0.888611i −0.195644 0.980675i \(-0.562680\pi\)
0.995753 + 0.0920637i \(0.0293463\pi\)
\(38\) 12.2469 + 7.07074i 0.322286 + 0.186072i
\(39\) −11.0917 + 4.93833i −0.284402 + 0.126624i
\(40\) 18.3206 10.5774i 0.458016 0.264435i
\(41\) 40.9437 + 2.14845i 0.998626 + 0.0524011i
\(42\) 45.4056 + 50.2238i 1.08109 + 1.19581i
\(43\) 61.0025 + 44.3209i 1.41866 + 1.03072i 0.991991 + 0.126312i \(0.0403140\pi\)
0.426672 + 0.904407i \(0.359686\pi\)
\(44\) −6.01763 10.4228i −0.136764 0.236883i
\(45\) 11.0431 51.9536i 0.245402 1.15452i
\(46\) −28.9461 6.15268i −0.629262 0.133754i
\(47\) −51.3928 5.40160i −1.09346 0.114928i −0.459416 0.888221i \(-0.651941\pi\)
−0.634048 + 0.773293i \(0.718608\pi\)
\(48\) 36.7320 + 50.5573i 0.765250 + 1.05328i
\(49\) −44.8438 19.7493i −0.915180 0.403046i
\(50\) 33.1864 0.663728
\(51\) −170.570 + 36.2557i −3.34450 + 0.710896i
\(52\) 1.55241 1.39780i 0.0298540 0.0268807i
\(53\) 8.48994 + 1.80459i 0.160188 + 0.0340489i 0.287307 0.957838i \(-0.407240\pi\)
−0.127120 + 0.991887i \(0.540573\pi\)
\(54\) 122.239 + 12.8478i 2.26368 + 0.237923i
\(55\) 30.8861i 0.561566i
\(56\) −52.4741 30.1549i −0.937038 0.538481i
\(57\) −36.3221 + 26.3895i −0.637229 + 0.462974i
\(58\) 76.0765 16.1706i 1.31166 0.278803i
\(59\) −26.0155 58.4318i −0.440941 0.990370i −0.988167 0.153385i \(-0.950983\pi\)
0.547226 0.836985i \(-0.315684\pi\)
\(60\) 1.35128 + 12.8566i 0.0225214 + 0.214276i
\(61\) 2.97531 6.68265i 0.0487755 0.109552i −0.887514 0.460781i \(-0.847569\pi\)
0.936290 + 0.351229i \(0.114236\pi\)
\(62\) 13.8304 + 19.0359i 0.223071 + 0.307031i
\(63\) −144.422 + 47.2478i −2.29241 + 0.749965i
\(64\) −57.5340 41.8009i −0.898969 0.653139i
\(65\) −5.24379 + 1.11460i −0.0806737 + 0.0171477i
\(66\) −121.425 + 12.7623i −1.83978 + 0.193368i
\(67\) 58.4822 + 12.4308i 0.872869 + 0.185534i 0.622503 0.782617i \(-0.286116\pi\)
0.250366 + 0.968151i \(0.419449\pi\)
\(68\) 25.9833 15.0015i 0.382107 0.220610i
\(69\) 55.2233 76.0083i 0.800337 1.10157i
\(70\) 14.9998 + 25.8598i 0.214283 + 0.369425i
\(71\) 32.0396 98.6076i 0.451261 1.38884i −0.424208 0.905565i \(-0.639447\pi\)
0.875469 0.483274i \(-0.160553\pi\)
\(72\) −183.582 + 39.0215i −2.54975 + 0.541965i
\(73\) −28.6575 16.5454i −0.392569 0.226650i 0.290704 0.956813i \(-0.406111\pi\)
−0.683273 + 0.730163i \(0.739444\pi\)
\(74\) 51.6721 + 57.3877i 0.698272 + 0.775510i
\(75\) −42.8540 + 96.2517i −0.571387 + 1.28336i
\(76\) 4.54044 6.24938i 0.0597426 0.0822287i
\(77\) 76.4341 44.3351i 0.992651 0.575781i
\(78\) −6.54869 20.1548i −0.0839575 0.258395i
\(79\) 56.6506 + 98.1217i 0.717096 + 1.24205i 0.962145 + 0.272537i \(0.0878626\pi\)
−0.245049 + 0.969511i \(0.578804\pi\)
\(80\) 11.2231 + 25.2076i 0.140289 + 0.315094i
\(81\) −97.4270 + 168.749i −1.20280 + 2.08332i
\(82\) −11.1996 + 70.6813i −0.136580 + 0.861967i
\(83\) 13.0971i 0.157796i −0.996883 0.0788980i \(-0.974860\pi\)
0.996883 0.0788980i \(-0.0251402\pi\)
\(84\) 29.8766 21.7989i 0.355674 0.259510i
\(85\) −76.9966 −0.905842
\(86\) −88.0656 + 97.8067i −1.02402 + 1.13729i
\(87\) −51.3385 + 241.529i −0.590098 + 2.77619i
\(88\) 99.7028 44.3906i 1.13299 0.504438i
\(89\) 41.8762 94.0556i 0.470520 1.05680i −0.509963 0.860197i \(-0.670341\pi\)
0.980482 0.196608i \(-0.0629926\pi\)
\(90\) 88.1704 + 28.6483i 0.979671 + 0.318315i
\(91\) 10.2855 + 11.3769i 0.113027 + 0.125021i
\(92\) −4.99519 + 15.3736i −0.0542956 + 0.167105i
\(93\) −73.0700 + 15.5315i −0.785699 + 0.167006i
\(94\) 18.7531 88.2263i 0.199501 0.938578i
\(95\) −18.1100 + 8.06307i −0.190631 + 0.0848744i
\(96\) 71.5054 41.2837i 0.744848 0.430038i
\(97\) −56.6477 + 18.4059i −0.583997 + 0.189752i −0.586090 0.810246i \(-0.699334\pi\)
0.00209360 + 0.999998i \(0.499334\pi\)
\(98\) 42.4640 74.2402i 0.433307 0.757553i
\(99\) 84.6762 260.607i 0.855315 2.63239i
\(100\) 1.89487 18.0285i 0.0189487 0.180285i
\(101\) 55.8505 5.87012i 0.552975 0.0581200i 0.176080 0.984376i \(-0.443658\pi\)
0.376895 + 0.926256i \(0.376992\pi\)
\(102\) −31.8154 302.703i −0.311915 2.96768i
\(103\) −59.1125 + 132.769i −0.573908 + 1.28902i 0.360482 + 0.932766i \(0.382612\pi\)
−0.934390 + 0.356252i \(0.884054\pi\)
\(104\) 11.1346 + 15.3254i 0.107063 + 0.147360i
\(105\) −94.3715 + 10.1114i −0.898776 + 0.0962993i
\(106\) −4.68153 + 14.4083i −0.0441654 + 0.135927i
\(107\) −0.300830 0.133938i −0.00281149 0.00125176i 0.405330 0.914170i \(-0.367156\pi\)
−0.408142 + 0.912918i \(0.633823\pi\)
\(108\) 13.9591 65.6726i 0.129251 0.608079i
\(109\) −31.6151 + 54.7590i −0.290047 + 0.502376i −0.973821 0.227318i \(-0.927004\pi\)
0.683774 + 0.729694i \(0.260338\pi\)
\(110\) −53.6146 5.63513i −0.487406 0.0512284i
\(111\) −233.169 + 75.7610i −2.10062 + 0.682532i
\(112\) 46.2712 63.9578i 0.413136 0.571052i
\(113\) 26.6378 81.9826i 0.235732 0.725510i −0.761291 0.648410i \(-0.775434\pi\)
0.997023 0.0770995i \(-0.0245659\pi\)
\(114\) −39.1821 67.8655i −0.343703 0.595311i
\(115\) 30.8284 27.7580i 0.268073 0.241374i
\(116\) −4.44084 42.2518i −0.0382831 0.364240i
\(117\) 47.3010 + 4.97154i 0.404282 + 0.0424918i
\(118\) 106.177 34.4990i 0.899806 0.292365i
\(119\) 110.524 + 190.544i 0.928772 + 1.60121i
\(120\) −117.228 −0.976904
\(121\) −4.00788 + 38.1324i −0.0331229 + 0.315144i
\(122\) 11.0574 + 6.38401i 0.0906347 + 0.0523280i
\(123\) −190.537 123.754i −1.54908 1.00613i
\(124\) 11.1309 6.42646i 0.0897657 0.0518263i
\(125\) −63.2994 + 87.1241i −0.506395 + 0.696993i
\(126\) −55.6671 259.319i −0.441802 2.05809i
\(127\) 12.6434 + 38.9125i 0.0995545 + 0.306397i 0.988414 0.151783i \(-0.0485014\pi\)
−0.888859 + 0.458180i \(0.848501\pi\)
\(128\) 43.1783 47.9543i 0.337330 0.374643i
\(129\) −169.952 381.719i −1.31746 2.95906i
\(130\) −0.978095 9.30595i −0.00752381 0.0715842i
\(131\) −32.5129 152.961i −0.248190 1.16764i −0.908904 0.417005i \(-0.863080\pi\)
0.660714 0.750638i \(-0.270254\pi\)
\(132\) 66.6928i 0.505249i
\(133\) 45.9495 + 33.2428i 0.345485 + 0.249946i
\(134\) −32.2483 + 99.2501i −0.240659 + 0.740672i
\(135\) −115.292 + 128.044i −0.854013 + 0.948478i
\(136\) 110.662 + 248.551i 0.813691 + 1.82758i
\(137\) −125.898 + 218.062i −0.918964 + 1.59169i −0.117973 + 0.993017i \(0.537640\pi\)
−0.800991 + 0.598676i \(0.795694\pi\)
\(138\) 121.866 + 109.729i 0.883086 + 0.795134i
\(139\) −75.8653 104.420i −0.545794 0.751221i 0.443640 0.896205i \(-0.353687\pi\)
−0.989434 + 0.144984i \(0.953687\pi\)
\(140\) 14.9048 6.67210i 0.106463 0.0476578i
\(141\) 231.670 + 168.318i 1.64305 + 1.19374i
\(142\) 165.325 + 73.6076i 1.16426 + 0.518363i
\(143\) −27.5057 + 2.89097i −0.192348 + 0.0202166i
\(144\) −25.5888 243.462i −0.177700 1.69070i
\(145\) −44.3458 + 99.6022i −0.305833 + 0.686912i
\(146\) 33.9494 46.7273i 0.232530 0.320050i
\(147\) 160.487 + 219.027i 1.09175 + 1.48998i
\(148\) 34.1262 24.7941i 0.230582 0.167528i
\(149\) 45.1516 50.1459i 0.303031 0.336550i −0.572327 0.820026i \(-0.693959\pi\)
0.875358 + 0.483476i \(0.160626\pi\)
\(150\) −159.263 91.9504i −1.06175 0.613003i
\(151\) −68.8744 + 30.6649i −0.456122 + 0.203079i −0.621919 0.783081i \(-0.713647\pi\)
0.165797 + 0.986160i \(0.446980\pi\)
\(152\) 52.0564 + 46.8718i 0.342477 + 0.308367i
\(153\) 649.671 + 211.091i 4.24621 + 1.37968i
\(154\) 63.0152 + 140.769i 0.409190 + 0.914087i
\(155\) −32.9845 −0.212803
\(156\) −11.3230 + 2.40677i −0.0725832 + 0.0154280i
\(157\) 114.587 12.0436i 0.729855 0.0767109i 0.267691 0.963505i \(-0.413740\pi\)
0.462165 + 0.886794i \(0.347073\pi\)
\(158\) −180.663 + 80.4365i −1.14344 + 0.509092i
\(159\) −35.7435 32.1836i −0.224802 0.202413i
\(160\) 34.6728 11.2659i 0.216705 0.0704118i
\(161\) −112.945 36.4463i −0.701523 0.226375i
\(162\) −275.152 199.910i −1.69847 1.23401i
\(163\) 10.0907 + 17.4776i 0.0619063 + 0.107225i 0.895317 0.445429i \(-0.146949\pi\)
−0.833411 + 0.552653i \(0.813615\pi\)
\(164\) 37.7581 + 10.1199i 0.230232 + 0.0617067i
\(165\) 85.5770 148.224i 0.518649 0.898326i
\(166\) 22.7350 + 2.38954i 0.136958 + 0.0143948i
\(167\) 251.555i 1.50632i −0.657838 0.753159i \(-0.728529\pi\)
0.657838 0.753159i \(-0.271471\pi\)
\(168\) 168.274 + 290.106i 1.00163 + 1.72682i
\(169\) 50.7404 + 156.163i 0.300239 + 0.924041i
\(170\) 14.0479 133.657i 0.0826347 0.786217i
\(171\) 174.911 18.3839i 1.02287 0.107508i
\(172\) 48.1051 + 53.4261i 0.279681 + 0.310617i
\(173\) 28.5116 16.4612i 0.164807 0.0951513i −0.415328 0.909672i \(-0.636333\pi\)
0.580135 + 0.814520i \(0.303000\pi\)
\(174\) −409.898 133.184i −2.35574 0.765425i
\(175\) 132.391 + 13.6448i 0.756520 + 0.0779703i
\(176\) 43.9897 + 135.386i 0.249941 + 0.769240i
\(177\) −37.0491 + 352.498i −0.209317 + 1.99152i
\(178\) 155.629 + 89.8524i 0.874320 + 0.504789i
\(179\) 85.5749 + 18.1895i 0.478072 + 0.101617i 0.440644 0.897682i \(-0.354750\pi\)
0.0374282 + 0.999299i \(0.488083\pi\)
\(180\) 20.5975 46.2627i 0.114431 0.257015i
\(181\) −18.8793 6.13427i −0.104306 0.0338910i 0.256399 0.966571i \(-0.417464\pi\)
−0.360705 + 0.932680i \(0.617464\pi\)
\(182\) −21.6255 + 15.7786i −0.118821 + 0.0866957i
\(183\) −32.7944 + 23.8265i −0.179204 + 0.130200i
\(184\) −133.913 59.6218i −0.727786 0.324031i
\(185\) −107.660 + 11.3155i −0.581943 + 0.0611647i
\(186\) −13.6293 129.675i −0.0732760 0.697175i
\(187\) −395.051 41.5216i −2.11257 0.222041i
\(188\) −46.8581 15.2251i −0.249245 0.0809847i
\(189\) 482.367 + 101.513i 2.55220 + 0.537107i
\(190\) −10.6924 32.9078i −0.0562758 0.173199i
\(191\) −112.698 195.198i −0.590040 1.02198i −0.994226 0.107303i \(-0.965778\pi\)
0.404186 0.914677i \(-0.367555\pi\)
\(192\) 160.289 + 360.015i 0.834839 + 1.87508i
\(193\) 230.133 + 48.9162i 1.19240 + 0.253452i 0.761025 0.648722i \(-0.224696\pi\)
0.431372 + 0.902174i \(0.358030\pi\)
\(194\) −21.6152 101.692i −0.111419 0.524184i
\(195\) 28.2534 + 9.18009i 0.144889 + 0.0470774i
\(196\) −37.9063 27.3075i −0.193400 0.139324i
\(197\) 55.4618 170.694i 0.281532 0.866466i −0.705885 0.708327i \(-0.749450\pi\)
0.987417 0.158139i \(-0.0505496\pi\)
\(198\) 436.933 + 194.535i 2.20673 + 0.982500i
\(199\) −82.0634 184.317i −0.412379 0.926219i −0.993651 0.112509i \(-0.964111\pi\)
0.581272 0.813710i \(-0.302555\pi\)
\(200\) 160.794 + 34.1779i 0.803972 + 0.170890i
\(201\) −246.216 221.694i −1.22495 1.10295i
\(202\) 98.0207i 0.485251i
\(203\) 310.142 33.2301i 1.52779 0.163695i
\(204\) −166.260 −0.814999
\(205\) −70.9314 70.9406i −0.346007 0.346052i
\(206\) −219.686 126.836i −1.06644 0.615707i
\(207\) −336.220 + 149.695i −1.62425 + 0.723163i
\(208\) −21.3982 + 12.3542i −0.102876 + 0.0593954i
\(209\) −97.2661 + 31.6037i −0.465388 + 0.151214i
\(210\) −0.334297 165.662i −0.00159189 0.788869i
\(211\) −36.5768 26.5746i −0.173350 0.125946i 0.497727 0.867334i \(-0.334168\pi\)
−0.671077 + 0.741388i \(0.734168\pi\)
\(212\) 7.55998 + 3.36592i 0.0356603 + 0.0158770i
\(213\) −426.974 + 384.449i −2.00457 + 1.80492i
\(214\) 0.287386 0.497768i 0.00134293 0.00232602i
\(215\) −38.3589 180.465i −0.178414 0.839370i
\(216\) 579.039 + 188.141i 2.68073 + 0.871023i
\(217\) 47.3472 + 81.6268i 0.218190 + 0.376161i
\(218\) −89.2869 64.8707i −0.409573 0.297572i
\(219\) 91.6856 + 158.804i 0.418656 + 0.725133i
\(220\) −6.12255 + 28.8043i −0.0278298 + 0.130929i
\(221\) −7.20695 68.5695i −0.0326106 0.310269i
\(222\) −88.9709 418.575i −0.400770 1.88547i
\(223\) −42.2126 + 58.1007i −0.189294 + 0.260541i −0.893107 0.449844i \(-0.851479\pi\)
0.703813 + 0.710386i \(0.251479\pi\)
\(224\) −77.6504 69.6336i −0.346654 0.310864i
\(225\) 333.907 242.598i 1.48403 1.07821i
\(226\) 137.452 + 61.1976i 0.608195 + 0.270786i
\(227\) −134.407 + 14.1268i −0.592103 + 0.0622325i −0.395841 0.918319i \(-0.629547\pi\)
−0.196262 + 0.980552i \(0.562880\pi\)
\(228\) −39.1051 + 17.4107i −0.171513 + 0.0763627i
\(229\) −38.7375 182.246i −0.169159 0.795832i −0.978132 0.207986i \(-0.933309\pi\)
0.808972 0.587847i \(-0.200024\pi\)
\(230\) 42.5600 + 58.5788i 0.185044 + 0.254691i
\(231\) −489.651 + 0.988087i −2.11970 + 0.00427743i
\(232\) 385.259 1.66060
\(233\) 37.0845 352.836i 0.159161 1.51432i −0.565234 0.824931i \(-0.691214\pi\)
0.724395 0.689385i \(-0.242119\pi\)
\(234\) −17.2600 + 81.2019i −0.0737607 + 0.347017i
\(235\) 84.6052 + 93.9636i 0.360022 + 0.399845i
\(236\) −12.6791 59.6504i −0.0537250 0.252756i
\(237\) 627.853i 2.64917i
\(238\) −350.926 + 157.092i −1.47448 + 0.660049i
\(239\) 20.6859 15.0292i 0.0865518 0.0628836i −0.543668 0.839300i \(-0.682965\pi\)
0.630220 + 0.776417i \(0.282965\pi\)
\(240\) 15.9830 152.068i 0.0665959 0.633617i
\(241\) 20.5636 96.7440i 0.0853260 0.401427i −0.914670 0.404201i \(-0.867550\pi\)
0.999996 + 0.00277372i \(0.000882904\pi\)
\(242\) −65.4620 13.9144i −0.270504 0.0574975i
\(243\) 386.250 223.002i 1.58951 0.917703i
\(244\) 4.09946 5.64243i 0.0168011 0.0231247i
\(245\) 49.2065 + 109.330i 0.200843 + 0.446245i
\(246\) 249.586 308.171i 1.01458 1.25273i
\(247\) −8.87570 15.3732i −0.0359340 0.0622395i
\(248\) 47.4063 + 106.476i 0.191155 + 0.429340i
\(249\) −36.2884 + 62.8533i −0.145737 + 0.252423i
\(250\) −139.688 125.776i −0.558753 0.503103i
\(251\) 27.8697 9.05540i 0.111034 0.0360773i −0.252973 0.967473i \(-0.581408\pi\)
0.364007 + 0.931396i \(0.381408\pi\)
\(252\) −144.053 + 15.4346i −0.571639 + 0.0612482i
\(253\) 173.142 125.795i 0.684357 0.497214i
\(254\) −69.8542 + 14.8480i −0.275016 + 0.0584565i
\(255\) 369.510 + 213.336i 1.44906 + 0.836613i
\(256\) −114.978 127.696i −0.449134 0.498814i
\(257\) −27.8787 131.159i −0.108477 0.510346i −0.998516 0.0544607i \(-0.982656\pi\)
0.890039 0.455885i \(-0.150677\pi\)
\(258\) 693.625 225.373i 2.68847 0.873537i
\(259\) 182.541 + 250.183i 0.704792 + 0.965957i
\(260\) −5.11130 −0.0196588
\(261\) 647.240 718.832i 2.47985 2.75415i
\(262\) 271.454 28.5310i 1.03608 0.108897i
\(263\) 174.350 + 193.635i 0.662928 + 0.736256i 0.977023 0.213136i \(-0.0683677\pi\)
−0.314095 + 0.949392i \(0.601701\pi\)
\(264\) −601.472 63.2172i −2.27830 0.239459i
\(265\) −12.4829 17.1813i −0.0471054 0.0648351i
\(266\) −66.0889 + 73.6977i −0.248454 + 0.277059i
\(267\) −461.568 + 335.349i −1.72872 + 1.25599i
\(268\) 52.0762 + 23.1858i 0.194314 + 0.0865143i
\(269\) 189.529 + 425.688i 0.704568 + 1.58248i 0.808903 + 0.587942i \(0.200062\pi\)
−0.104335 + 0.994542i \(0.533271\pi\)
\(270\) −201.235 223.494i −0.745315 0.827756i
\(271\) −10.5247 + 23.6389i −0.0388365 + 0.0872283i −0.931922 0.362659i \(-0.881869\pi\)
0.893085 + 0.449887i \(0.148536\pi\)
\(272\) −337.507 + 109.663i −1.24083 + 0.403171i
\(273\) −17.8380 83.0963i −0.0653407 0.304382i
\(274\) −355.560 258.329i −1.29766 0.942807i
\(275\) −160.595 + 178.359i −0.583981 + 0.648577i
\(276\) 66.5682 59.9383i 0.241189 0.217168i
\(277\) −166.553 184.976i −0.601274 0.667783i 0.363276 0.931682i \(-0.381658\pi\)
−0.964550 + 0.263899i \(0.914992\pi\)
\(278\) 195.102 112.642i 0.701804 0.405187i
\(279\) 278.311 + 90.4289i 0.997532 + 0.324118i
\(280\) 46.0445 + 140.743i 0.164445 + 0.502655i
\(281\) −42.6792 31.0082i −0.151883 0.110350i 0.509248 0.860620i \(-0.329923\pi\)
−0.661131 + 0.750270i \(0.729923\pi\)
\(282\) −334.448 + 371.442i −1.18598 + 1.31717i
\(283\) 33.6129 158.136i 0.118773 0.558785i −0.878010 0.478642i \(-0.841129\pi\)
0.996783 0.0801427i \(-0.0255376\pi\)
\(284\) 49.4270 85.6100i 0.174039 0.301444i
\(285\) 109.251 + 11.4827i 0.383336 + 0.0402903i
\(286\) 48.2741i 0.168791i
\(287\) −73.7396 + 277.365i −0.256932 + 0.966429i
\(288\) −323.443 −1.12307
\(289\) 73.3011 697.414i 0.253637 2.41320i
\(290\) −164.807 95.1512i −0.568299 0.328108i
\(291\) 322.852 + 68.6243i 1.10946 + 0.235822i
\(292\) −23.4461 21.1110i −0.0802950 0.0722979i
\(293\) −176.202 + 242.522i −0.601373 + 0.827720i −0.995833 0.0911937i \(-0.970932\pi\)
0.394460 + 0.918913i \(0.370932\pi\)
\(294\) −409.486 + 238.625i −1.39281 + 0.811651i
\(295\) −48.3615 + 148.841i −0.163937 + 0.504547i
\(296\) 191.259 + 331.270i 0.646145 + 1.11916i
\(297\) −660.585 + 594.793i −2.22419 + 2.00267i
\(298\) 78.8095 + 87.5268i 0.264461 + 0.293714i
\(299\) 27.6056 + 24.8561i 0.0923263 + 0.0831309i
\(300\) −59.0455 + 81.2692i −0.196818 + 0.270897i
\(301\) −391.535 + 353.973i −1.30078 + 1.17599i
\(302\) −40.6645 125.153i −0.134651 0.414412i
\(303\) −284.293 126.575i −0.938260 0.417740i
\(304\) −67.8993 + 61.1368i −0.223353 + 0.201108i
\(305\) −16.3511 + 7.27997i −0.0536101 + 0.0238688i
\(306\) −484.960 + 1089.24i −1.58484 + 3.55960i
\(307\) −171.914 236.620i −0.559981 0.770748i 0.431343 0.902188i \(-0.358040\pi\)
−0.991324 + 0.131440i \(0.958040\pi\)
\(308\) 80.0708 26.1953i 0.259970 0.0850498i
\(309\) 651.549 473.378i 2.10857 1.53197i
\(310\) 6.01796 57.2571i 0.0194128 0.184700i
\(311\) −350.319 + 315.428i −1.12643 + 1.01424i −0.126676 + 0.991944i \(0.540431\pi\)
−0.999751 + 0.0222953i \(0.992903\pi\)
\(312\) −10.9727 104.398i −0.0351689 0.334609i
\(313\) 222.962 + 200.756i 0.712340 + 0.641394i 0.943443 0.331536i \(-0.107567\pi\)
−0.231103 + 0.972929i \(0.574233\pi\)
\(314\) 201.107i 0.640469i
\(315\) 339.961 + 150.539i 1.07924 + 0.477901i
\(316\) 33.3816 + 102.738i 0.105638 + 0.325120i
\(317\) −310.513 + 66.0016i −0.979537 + 0.208207i −0.669740 0.742596i \(-0.733594\pi\)
−0.309797 + 0.950803i \(0.600261\pi\)
\(318\) 62.3882 56.1746i 0.196189 0.176650i
\(319\) −281.240 + 487.121i −0.881629 + 1.52703i
\(320\) 36.1779 + 170.204i 0.113056 + 0.531887i
\(321\) 1.07259 + 1.47629i 0.00334139 + 0.00459904i
\(322\) 83.8731 189.410i 0.260476 0.588229i
\(323\) −78.7853 242.476i −0.243917 0.750700i
\(324\) −124.311 + 138.062i −0.383677 + 0.426116i
\(325\) −36.0769 20.8290i −0.111006 0.0640892i
\(326\) −32.1801 + 14.3275i −0.0987121 + 0.0439494i
\(327\) 303.444 175.194i 0.927964 0.535760i
\(328\) −127.057 + 330.930i −0.387369 + 1.00893i
\(329\) 111.087 344.252i 0.337650 1.04636i
\(330\) 241.685 + 175.595i 0.732380 + 0.532105i
\(331\) −147.599 255.649i −0.445919 0.772355i 0.552197 0.833714i \(-0.313790\pi\)
−0.998116 + 0.0613592i \(0.980456\pi\)
\(332\) 2.59623 12.2143i 0.00781997 0.0367901i
\(333\) 939.416 + 199.679i 2.82107 + 0.599637i
\(334\) 436.670 + 45.8958i 1.30739 + 0.137413i
\(335\) −85.9876 118.352i −0.256679 0.353289i
\(336\) −399.267 + 178.731i −1.18829 + 0.531938i
\(337\) 51.3351 0.152330 0.0761649 0.997095i \(-0.475732\pi\)
0.0761649 + 0.997095i \(0.475732\pi\)
\(338\) −280.338 + 59.5876i −0.829402 + 0.176295i
\(339\) −354.987 + 319.632i −1.04716 + 0.942866i
\(340\) −71.8069 15.2630i −0.211197 0.0448912i
\(341\) −169.236 17.7874i −0.496292 0.0521624i
\(342\) 306.979i 0.897598i
\(343\) 199.927 278.708i 0.582877 0.812560i
\(344\) −527.423 + 383.195i −1.53321 + 1.11394i
\(345\) −224.857 + 47.7947i −0.651758 + 0.138535i
\(346\) 23.3727 + 52.4960i 0.0675512 + 0.151723i
\(347\) −49.4545 470.529i −0.142520 1.35599i −0.798857 0.601522i \(-0.794561\pi\)
0.656336 0.754469i \(-0.272105\pi\)
\(348\) −95.7564 + 215.072i −0.275162 + 0.618024i
\(349\) −101.836 140.165i −0.291794 0.401620i 0.637802 0.770200i \(-0.279844\pi\)
−0.929596 + 0.368581i \(0.879844\pi\)
\(350\) −47.8403 + 227.325i −0.136686 + 0.649501i
\(351\) −124.822 90.6883i −0.355618 0.258371i
\(352\) 183.973 39.1048i 0.522652 0.111093i
\(353\) 91.2002 9.58552i 0.258357 0.0271545i 0.0255358 0.999674i \(-0.491871\pi\)
0.232822 + 0.972519i \(0.425204\pi\)
\(354\) −605.135 128.625i −1.70942 0.363349i
\(355\) −219.701 + 126.845i −0.618877 + 0.357309i
\(356\) 57.6983 79.4149i 0.162074 0.223076i
\(357\) −2.46322 1220.66i −0.00689977 3.41921i
\(358\) −47.1878 + 145.229i −0.131810 + 0.405668i
\(359\) −428.672 + 91.1170i −1.19407 + 0.253808i −0.761726 0.647900i \(-0.775648\pi\)
−0.432347 + 0.901708i \(0.642314\pi\)
\(360\) 397.698 + 229.611i 1.10472 + 0.637809i
\(361\) 197.633 + 219.494i 0.547461 + 0.608017i
\(362\) 14.0929 31.6531i 0.0389306 0.0874395i
\(363\) 124.888 171.894i 0.344045 0.473537i
\(364\) 7.33695 + 12.6490i 0.0201565 + 0.0347499i
\(365\) 25.0200 + 77.0038i 0.0685481 + 0.210969i
\(366\) −35.3767 61.2742i −0.0966577 0.167416i
\(367\) 51.1326 + 114.846i 0.139326 + 0.312931i 0.969710 0.244261i \(-0.0785454\pi\)
−0.830384 + 0.557192i \(0.811879\pi\)
\(368\) 95.5988 165.582i 0.259779 0.449951i
\(369\) 404.006 + 793.035i 1.09487 + 2.14915i
\(370\) 188.948i 0.510672i
\(371\) −24.6002 + 55.5543i −0.0663077 + 0.149742i
\(372\) −71.2238 −0.191462
\(373\) 109.770 121.912i 0.294290 0.326842i −0.577809 0.816172i \(-0.696092\pi\)
0.872099 + 0.489330i \(0.162759\pi\)
\(374\) 144.153 678.186i 0.385436 1.81333i
\(375\) 545.173 242.727i 1.45379 0.647271i
\(376\) 181.724 408.160i 0.483310 1.08553i
\(377\) −92.8518 30.1694i −0.246291 0.0800249i
\(378\) −264.222 + 818.810i −0.699000 + 2.16616i
\(379\) 169.895 522.882i 0.448271 1.37964i −0.430586 0.902550i \(-0.641693\pi\)
0.878857 0.477086i \(-0.158307\pi\)
\(380\) −18.4876 + 3.92967i −0.0486517 + 0.0103412i
\(381\) 47.1395 221.774i 0.123726 0.582084i
\(382\) 359.402 160.016i 0.940843 0.418890i
\(383\) −150.009 + 86.6077i −0.391668 + 0.226130i −0.682883 0.730528i \(-0.739274\pi\)
0.291214 + 0.956658i \(0.405941\pi\)
\(384\) −340.083 + 110.500i −0.885632 + 0.287759i
\(385\) −211.569 44.5243i −0.549529 0.115647i
\(386\) −126.900 + 390.558i −0.328757 + 1.01181i
\(387\) −171.095 + 1627.86i −0.442106 + 4.20636i
\(388\) −56.4781 + 5.93609i −0.145562 + 0.0152992i
\(389\) 8.65164 + 82.3149i 0.0222407 + 0.211606i 0.999998 + 0.00186796i \(0.000594590\pi\)
−0.977758 + 0.209738i \(0.932739\pi\)
\(390\) −21.0903 + 47.3696i −0.0540777 + 0.121461i
\(391\) 313.597 + 431.629i 0.802039 + 1.10391i
\(392\) 282.205 315.975i 0.719910 0.806059i
\(393\) −267.783 + 824.151i −0.681381 + 2.09708i
\(394\) 286.185 + 127.418i 0.726358 + 0.323395i
\(395\) 57.6383 271.167i 0.145920 0.686499i
\(396\) 130.629 226.256i 0.329871 0.571353i
\(397\) −108.648 11.4193i −0.273672 0.0287641i −0.0333017 0.999445i \(-0.510602\pi\)
−0.240370 + 0.970681i \(0.577269\pi\)
\(398\) 334.925 108.824i 0.841521 0.273427i
\(399\) −128.407 286.847i −0.321821 0.718914i
\(400\) −66.2582 + 203.922i −0.165646 + 0.509805i
\(401\) 235.102 + 407.209i 0.586290 + 1.01548i 0.994713 + 0.102692i \(0.0327456\pi\)
−0.408423 + 0.912793i \(0.633921\pi\)
\(402\) 429.756 386.954i 1.06904 0.962571i
\(403\) −3.08737 29.3744i −0.00766098 0.0728893i
\(404\) 53.2497 + 5.59676i 0.131806 + 0.0138534i
\(405\) 453.434 147.330i 1.11959 0.363777i
\(406\) 1.09863 + 544.432i 0.00270599 + 1.34096i
\(407\) −558.478 −1.37218
\(408\) 157.595 1499.42i 0.386263 3.67505i
\(409\) 402.318 + 232.279i 0.983663 + 0.567918i 0.903374 0.428853i \(-0.141082\pi\)
0.0802891 + 0.996772i \(0.474416\pi\)
\(410\) 136.086 110.185i 0.331917 0.268745i
\(411\) 1208.38 697.658i 2.94010 1.69747i
\(412\) −81.4469 + 112.102i −0.197687 + 0.272092i
\(413\) 437.758 93.9721i 1.05995 0.227535i
\(414\) −198.509 610.949i −0.479491 1.47572i
\(415\) −21.4429 + 23.8147i −0.0516696 + 0.0573849i
\(416\) 13.2783 + 29.8235i 0.0319189 + 0.0716910i
\(417\) 74.7623 + 711.316i 0.179286 + 1.70579i
\(418\) −37.1141 174.608i −0.0887898 0.417723i
\(419\) 377.819i 0.901715i 0.892596 + 0.450858i \(0.148882\pi\)
−0.892596 + 0.450858i \(0.851118\pi\)
\(420\) −90.0150 9.27735i −0.214321 0.0220889i
\(421\) −23.9680 + 73.7659i −0.0569311 + 0.175216i −0.975478 0.220095i \(-0.929363\pi\)
0.918547 + 0.395311i \(0.129363\pi\)
\(422\) 52.8038 58.6445i 0.125127 0.138968i
\(423\) −456.263 1024.78i −1.07863 2.42265i
\(424\) −37.5217 + 64.9894i −0.0884945 + 0.153277i
\(425\) −444.633 400.350i −1.04620 0.941999i
\(426\) −589.456 811.317i −1.38370 1.90450i
\(427\) 41.4868 + 30.0142i 0.0971587 + 0.0702908i
\(428\) −0.254003 0.184544i −0.000593464 0.000431177i
\(429\) 140.011 + 62.3370i 0.326366 + 0.145308i
\(430\) 320.264 33.6611i 0.744799 0.0782815i
\(431\) 79.4331 + 755.755i 0.184300 + 1.75349i 0.561606 + 0.827405i \(0.310184\pi\)
−0.377307 + 0.926088i \(0.623150\pi\)
\(432\) −323.002 + 725.475i −0.747690 + 1.67934i
\(433\) −200.807 + 276.387i −0.463757 + 0.638307i −0.975283 0.220961i \(-0.929081\pi\)
0.511526 + 0.859268i \(0.329081\pi\)
\(434\) −150.333 + 67.2963i −0.346389 + 0.155061i
\(435\) 488.787 355.125i 1.12365 0.816379i
\(436\) −40.3391 + 44.8011i −0.0925208 + 0.102755i
\(437\) 118.960 + 68.6814i 0.272219 + 0.157166i
\(438\) −292.393 + 130.182i −0.667564 + 0.297219i
\(439\) 164.091 + 147.748i 0.373784 + 0.336556i 0.834517 0.550982i \(-0.185747\pi\)
−0.460733 + 0.887539i \(0.652414\pi\)
\(440\) −253.970 82.5197i −0.577203 0.187545i
\(441\) −115.453 1057.39i −0.261798 2.39771i
\(442\) 120.343 0.272270
\(443\) −454.969 + 96.7067i −1.02702 + 0.218300i −0.690466 0.723365i \(-0.742594\pi\)
−0.336553 + 0.941665i \(0.609261\pi\)
\(444\) −232.471 + 24.4336i −0.523582 + 0.0550307i
\(445\) −230.135 + 102.463i −0.517157 + 0.230253i
\(446\) −93.1543 83.8765i −0.208866 0.188064i
\(447\) −355.625 + 115.550i −0.795581 + 0.258500i
\(448\) 369.273 333.847i 0.824271 0.745194i
\(449\) 6.04321 + 4.39065i 0.0134593 + 0.00977872i 0.594495 0.804100i \(-0.297352\pi\)
−0.581035 + 0.813878i \(0.697352\pi\)
\(450\) 360.200 + 623.885i 0.800444 + 1.38641i
\(451\) −325.676 402.231i −0.722121 0.891864i
\(452\) 41.0937 71.1764i 0.0909153 0.157470i
\(453\) 415.495 + 43.6703i 0.917207 + 0.0964024i
\(454\) 235.893i 0.519587i
\(455\) −0.0757264 37.5265i −0.000166432 0.0824758i
\(456\) −119.952 369.174i −0.263052 0.809591i
\(457\) −1.91035 + 18.1758i −0.00418021 + 0.0397720i −0.996413 0.0846216i \(-0.973032\pi\)
0.992233 + 0.124394i \(0.0396985\pi\)
\(458\) 323.424 33.9933i 0.706166 0.0742211i
\(459\) −1482.77 1646.78i −3.23044 3.58776i
\(460\) 34.2530 19.7760i 0.0744630 0.0429912i
\(461\) −515.503 167.497i −1.11823 0.363335i −0.309137 0.951017i \(-0.600040\pi\)
−0.809091 + 0.587683i \(0.800040\pi\)
\(462\) 87.6208 850.155i 0.189655 1.84016i
\(463\) −241.046 741.864i −0.520619 1.60230i −0.772821 0.634624i \(-0.781155\pi\)
0.252202 0.967675i \(-0.418845\pi\)
\(464\) −52.5265 + 499.756i −0.113204 + 1.07706i
\(465\) 158.294 + 91.3909i 0.340416 + 0.196540i
\(466\) 605.714 + 128.749i 1.29982 + 0.276284i
\(467\) −90.8591 + 204.073i −0.194559 + 0.436987i −0.984312 0.176439i \(-0.943542\pi\)
0.789752 + 0.613426i \(0.210209\pi\)
\(468\) 43.1273 + 14.0129i 0.0921524 + 0.0299421i
\(469\) −169.456 + 382.681i −0.361313 + 0.815950i
\(470\) −178.546 + 129.721i −0.379884 + 0.276002i
\(471\) −583.278 259.692i −1.23838 0.551363i
\(472\) 549.978 57.8050i 1.16521 0.122468i
\(473\) −99.4924 946.607i −0.210343 2.00128i
\(474\) 1089.88 + 114.551i 2.29932 + 0.241668i
\(475\) −146.504 47.6021i −0.308430 0.100215i
\(476\) 65.3028 + 199.610i 0.137191 + 0.419349i
\(477\) 58.2232 + 179.193i 0.122061 + 0.375666i
\(478\) 22.3147 + 38.6503i 0.0466836 + 0.0808583i
\(479\) 260.753 + 585.660i 0.544369 + 1.22267i 0.951031 + 0.309094i \(0.100026\pi\)
−0.406662 + 0.913579i \(0.633307\pi\)
\(480\) −197.611 42.0035i −0.411689 0.0875072i
\(481\) −20.1540 94.8173i −0.0419003 0.197125i
\(482\) 164.184 + 53.3467i 0.340631 + 0.110678i
\(483\) 441.046 + 487.848i 0.913138 + 1.01004i
\(484\) −11.2967 + 34.7677i −0.0233403 + 0.0718341i
\(485\) 133.139 + 59.2771i 0.274512 + 0.122221i
\(486\) 316.634 + 711.171i 0.651510 + 1.46331i
\(487\) 549.752 + 116.853i 1.12885 + 0.239945i 0.734232 0.678898i \(-0.237542\pi\)
0.394622 + 0.918844i \(0.370876\pi\)
\(488\) 47.0006 + 42.3195i 0.0963127 + 0.0867204i
\(489\) 111.834i 0.228700i
\(490\) −198.762 + 65.4696i −0.405636 + 0.133611i
\(491\) −155.321 −0.316336 −0.158168 0.987412i \(-0.550559\pi\)
−0.158168 + 0.987412i \(0.550559\pi\)
\(492\) −153.163 153.183i −0.311307 0.311348i
\(493\) −1214.35 701.107i −2.46319 1.42212i
\(494\) 28.3053 12.6023i 0.0572982 0.0255108i
\(495\) −580.641 + 335.233i −1.17301 + 0.677239i
\(496\) −144.584 + 46.9782i −0.291500 + 0.0947141i
\(497\) 629.271 + 361.618i 1.26614 + 0.727603i
\(498\) −102.485 74.4598i −0.205793 0.149518i
\(499\) 415.812 + 185.131i 0.833291 + 0.371005i 0.778617 0.627499i \(-0.215922\pi\)
0.0546736 + 0.998504i \(0.482588\pi\)
\(500\) −76.3034 + 68.7039i −0.152607 + 0.137408i
\(501\) −696.990 + 1207.22i −1.39120 + 2.40963i
\(502\) 10.6343 + 50.0305i 0.0211839 + 0.0996624i
\(503\) 670.005 + 217.698i 1.33202 + 0.432799i 0.886606 0.462526i \(-0.153057\pi\)
0.445413 + 0.895325i \(0.353057\pi\)
\(504\) −2.65113 1313.78i −0.00526018 2.60670i
\(505\) −111.165 80.7661i −0.220129 0.159933i
\(506\) 186.776 + 323.505i 0.369122 + 0.639339i
\(507\) 189.180 890.020i 0.373135 1.75546i
\(508\) 4.07762 + 38.7960i 0.00802682 + 0.0763701i
\(509\) 197.930 + 931.187i 0.388861 + 1.82944i 0.540921 + 0.841074i \(0.318076\pi\)
−0.152060 + 0.988371i \(0.548591\pi\)
\(510\) −437.743 + 602.501i −0.858319 + 1.18138i
\(511\) 154.647 172.451i 0.302636 0.337478i
\(512\) 451.463 328.007i 0.881764 0.640639i
\(513\) −521.205 232.056i −1.01600 0.452350i
\(514\) 232.763 24.4643i 0.452846 0.0475960i
\(515\) 324.858 144.636i 0.630793 0.280847i
\(516\) −82.8290 389.680i −0.160521 0.755193i
\(517\) 383.418 + 527.730i 0.741621 + 1.02075i
\(518\) −467.592 + 271.224i −0.902687 + 0.523598i
\(519\) −182.438 −0.351517
\(520\) 4.84493 46.0964i 0.00931717 0.0886469i
\(521\) −94.6227 + 445.165i −0.181617 + 0.854443i 0.789109 + 0.614254i \(0.210543\pi\)
−0.970726 + 0.240189i \(0.922791\pi\)
\(522\) 1129.72 + 1254.68i 2.16421 + 2.40360i
\(523\) 127.263 + 598.724i 0.243332 + 1.14479i 0.914848 + 0.403798i \(0.132310\pi\)
−0.671516 + 0.740990i \(0.734357\pi\)
\(524\) 149.096i 0.284535i
\(525\) −597.543 432.301i −1.13818 0.823431i
\(526\) −367.938 + 267.322i −0.699501 + 0.508217i
\(527\) 44.3424 421.890i 0.0841413 0.800551i
\(528\) 164.010 771.607i 0.310625 1.46138i
\(529\) 236.273 + 50.2214i 0.446641 + 0.0949365i
\(530\) 32.1022 18.5342i 0.0605701 0.0349702i
\(531\) 816.115 1123.29i 1.53694 2.11542i
\(532\) 36.2627 + 40.1107i 0.0681629 + 0.0753960i
\(533\) 56.5371 69.8082i 0.106073 0.130972i
\(534\) −497.913 862.410i −0.932421 1.61500i
\(535\) 0.327719 + 0.736069i 0.000612559 + 0.00137583i
\(536\) −258.465 + 447.674i −0.482210 + 0.835212i
\(537\) −360.279 324.397i −0.670911 0.604091i
\(538\) −773.523 + 251.333i −1.43778 + 0.467162i
\(539\) 193.509 + 587.482i 0.359015 + 1.08995i
\(540\) −132.903 + 96.5598i −0.246117 + 0.178814i
\(541\) 119.788 25.4618i 0.221420 0.0470643i −0.0958655 0.995394i \(-0.530562\pi\)
0.317286 + 0.948330i \(0.397229\pi\)
\(542\) −39.1140 22.5825i −0.0721661 0.0416651i
\(543\) 73.6063 + 81.7480i 0.135555 + 0.150549i
\(544\) 97.4849 + 458.631i 0.179200 + 0.843071i
\(545\) 147.139 47.8085i 0.269981 0.0877220i
\(546\) 147.500 15.8038i 0.270146 0.0289448i
\(547\) 99.7916 0.182434 0.0912172 0.995831i \(-0.470924\pi\)
0.0912172 + 0.995831i \(0.470924\pi\)
\(548\) −160.639 + 178.407i −0.293136 + 0.325561i
\(549\) 157.923 16.5984i 0.287656 0.0302339i
\(550\) −280.309 311.315i −0.509653 0.566026i
\(551\) −359.041 37.7368i −0.651618 0.0684878i
\(552\) 477.456 + 657.162i 0.864957 + 1.19051i
\(553\) −753.795 + 246.606i −1.36310 + 0.445941i
\(554\) 351.483 255.368i 0.634446 0.460952i
\(555\) 548.014 + 243.992i 0.987413 + 0.439624i
\(556\) −50.0527 112.420i −0.0900229 0.202195i
\(557\) 179.805 + 199.693i 0.322809 + 0.358516i 0.882605 0.470115i \(-0.155787\pi\)
−0.559797 + 0.828630i \(0.689121\pi\)
\(558\) −207.751 + 466.617i −0.372314 + 0.836231i
\(559\) 157.123 51.0523i 0.281078 0.0913279i
\(560\) −188.849 + 40.5397i −0.337231 + 0.0723923i
\(561\) 1780.82 + 1293.84i 3.17437 + 2.30631i
\(562\) 61.6133 68.4285i 0.109632 0.121759i
\(563\) 783.864 705.795i 1.39230 1.25363i 0.461975 0.886893i \(-0.347141\pi\)
0.930324 0.366739i \(-0.119526\pi\)
\(564\) 182.689 + 202.897i 0.323917 + 0.359746i
\(565\) −182.660 + 105.459i −0.323293 + 0.186653i
\(566\) 268.373 + 87.1996i 0.474157 + 0.154063i
\(567\) −1015.47 910.632i −1.79096 1.60605i
\(568\) 725.226 + 526.908i 1.27681 + 0.927654i
\(569\) 516.719 573.875i 0.908119 1.00857i −0.0917997 0.995777i \(-0.529262\pi\)
0.999918 0.0127903i \(-0.00407139\pi\)
\(570\) −39.8653 + 187.551i −0.0699391 + 0.329038i
\(571\) 424.412 735.104i 0.743279 1.28740i −0.207715 0.978189i \(-0.566603\pi\)
0.950994 0.309208i \(-0.100064\pi\)
\(572\) −26.2249 2.75634i −0.0458477 0.00481878i
\(573\) 1249.02i 2.17979i
\(574\) −468.019 178.608i −0.815364 0.311164i
\(575\) 322.355 0.560618
\(576\) 161.367 1535.30i 0.280151 2.66546i
\(577\) 199.731 + 115.315i 0.346154 + 0.199852i 0.662990 0.748628i \(-0.269287\pi\)
−0.316836 + 0.948480i \(0.602621\pi\)
\(578\) 1197.25 + 254.484i 2.07137 + 0.440284i
\(579\) −968.882 872.385i −1.67337 1.50671i
\(580\) −61.1009 + 84.0982i −0.105346 + 0.144997i
\(581\) 89.7144 + 18.8802i 0.154414 + 0.0324961i
\(582\) −178.027 + 547.912i −0.305889 + 0.941430i
\(583\) −54.7818 94.8848i −0.0939653 0.162753i
\(584\) 212.615 191.439i 0.364066 0.327806i
\(585\) −77.8691 86.4824i −0.133110 0.147833i
\(586\) −388.841 350.114i −0.663551 0.597464i
\(587\) 282.219 388.441i 0.480781 0.661739i −0.497873 0.867250i \(-0.665886\pi\)
0.978655 + 0.205511i \(0.0658856\pi\)
\(588\) 106.252 + 236.078i 0.180701 + 0.401493i
\(589\) −33.7507 103.874i −0.0573017 0.176357i
\(590\) −249.547 111.106i −0.422961 0.188315i
\(591\) −739.109 + 665.496i −1.25061 + 1.12605i
\(592\) −455.799 + 202.935i −0.769930 + 0.342795i
\(593\) 187.589 421.333i 0.316340 0.710511i −0.683471 0.729978i \(-0.739530\pi\)
0.999810 + 0.0194673i \(0.00619703\pi\)
\(594\) −911.967 1255.22i −1.53530 2.11316i
\(595\) 110.995 527.423i 0.186547 0.886426i
\(596\) 52.0487 37.8156i 0.0873300 0.0634490i
\(597\) −116.868 + 1111.92i −0.195758 + 1.86252i
\(598\) −48.1839 + 43.3850i −0.0805751 + 0.0725501i
\(599\) 3.36369 + 32.0034i 0.00561551 + 0.0534280i 0.996971 0.0777767i \(-0.0247821\pi\)
−0.991355 + 0.131205i \(0.958115\pi\)
\(600\) −676.961 609.538i −1.12827 1.01590i
\(601\) 71.8420i 0.119537i −0.998212 0.0597687i \(-0.980964\pi\)
0.998212 0.0597687i \(-0.0190363\pi\)
\(602\) −543.020 744.240i −0.902026 1.23628i
\(603\) 401.065 + 1234.35i 0.665116 + 2.04702i
\(604\) −70.3108 + 14.9450i −0.116409 + 0.0247434i
\(605\) 69.7190 62.7753i 0.115238 0.103761i
\(606\) 271.588 470.405i 0.448166 0.776246i
\(607\) −87.4085 411.225i −0.144001 0.677471i −0.989623 0.143689i \(-0.954104\pi\)
0.845622 0.533782i \(-0.179230\pi\)
\(608\) 70.9566 + 97.6634i 0.116705 + 0.160631i
\(609\) −1580.45 699.845i −2.59516 1.14917i
\(610\) −9.65393 29.7117i −0.0158261 0.0487078i
\(611\) −75.7604 + 84.1404i −0.123994 + 0.137709i
\(612\) 564.037 + 325.647i 0.921629 + 0.532103i
\(613\) −701.065 + 312.134i −1.14366 + 0.509191i −0.889031 0.457847i \(-0.848621\pi\)
−0.254632 + 0.967038i \(0.581954\pi\)
\(614\) 442.109 255.252i 0.720047 0.415719i
\(615\) 143.845 + 536.978i 0.233895 + 0.873135i
\(616\) 160.346 + 746.952i 0.260301 + 1.21258i
\(617\) −73.1196 53.1245i −0.118508 0.0861013i 0.526952 0.849895i \(-0.323335\pi\)
−0.645461 + 0.763793i \(0.723335\pi\)
\(618\) 702.854 + 1217.38i 1.13730 + 1.96987i
\(619\) 137.353 646.197i 0.221896 1.04394i −0.716289 0.697803i \(-0.754161\pi\)
0.938185 0.346134i \(-0.112506\pi\)
\(620\) −30.7612 6.53850i −0.0496149 0.0105460i
\(621\) 1187.36 + 124.797i 1.91202 + 0.200961i
\(622\) −483.631 665.661i −0.777542 1.07019i
\(623\) 583.909 + 422.437i 0.937254 + 0.678070i
\(624\) 136.921 0.219424
\(625\) −207.202 + 44.0421i −0.331523 + 0.0704674i
\(626\) −389.168 + 350.408i −0.621674 + 0.559758i
\(627\) 554.348 + 117.830i 0.884128 + 0.187927i
\(628\) 109.251 + 11.4828i 0.173967 + 0.0182847i
\(629\) 1392.24i 2.21342i
\(630\) −323.343 + 562.665i −0.513243 + 0.893119i
\(631\) 776.099 563.869i 1.22995 0.893611i 0.233064 0.972461i \(-0.425125\pi\)
0.996886 + 0.0788504i \(0.0251249\pi\)
\(632\) −958.188 + 203.669i −1.51612 + 0.322261i
\(633\) 101.903 + 228.877i 0.160984 + 0.361575i
\(634\) −57.9183 551.056i −0.0913537 0.869173i
\(635\) 40.7187 91.4557i 0.0641239 0.144025i
\(636\) −26.9546 37.0998i −0.0423814 0.0583330i
\(637\) −92.7584 + 54.0544i −0.145618 + 0.0848578i
\(638\) −794.273 577.073i −1.24494 0.904503i
\(639\) 2201.52 467.947i 3.44525 0.732311i
\(640\) −157.024 + 16.5039i −0.245350 + 0.0257874i
\(641\) −663.417 141.014i −1.03497 0.219990i −0.341053 0.940044i \(-0.610784\pi\)
−0.693918 + 0.720054i \(0.744117\pi\)
\(642\) −2.75836 + 1.59254i −0.00429650 + 0.00248059i
\(643\) −574.765 + 791.096i −0.893880 + 1.23032i 0.0784992 + 0.996914i \(0.474987\pi\)
−0.972379 + 0.233406i \(0.925013\pi\)
\(644\) −98.1077 56.3789i −0.152341 0.0875448i
\(645\) −315.932 + 972.339i −0.489817 + 1.50750i
\(646\) 435.284 92.5225i 0.673814 0.143224i
\(647\) −436.779 252.175i −0.675084 0.389760i 0.122916 0.992417i \(-0.460775\pi\)
−0.798000 + 0.602657i \(0.794109\pi\)
\(648\) −1127.28 1251.97i −1.73963 1.93206i
\(649\) −328.396 + 737.590i −0.506004 + 1.13650i
\(650\) 42.7388 58.8249i 0.0657520 0.0904998i
\(651\) −1.05522 522.916i −0.00162091 0.803251i
\(652\) 5.94600 + 18.2999i 0.00911963 + 0.0280673i
\(653\) 396.032 + 685.948i 0.606481 + 1.05046i 0.991816 + 0.127679i \(0.0407528\pi\)
−0.385334 + 0.922777i \(0.625914\pi\)
\(654\) 248.752 + 558.707i 0.380355 + 0.854291i
\(655\) −191.313 + 331.364i −0.292081 + 0.505899i
\(656\) −411.958 209.937i −0.627985 0.320026i
\(657\) 718.325i 1.09334i
\(658\) 577.313 + 255.641i 0.877375 + 0.388513i
\(659\) 375.856 0.570343 0.285172 0.958476i \(-0.407949\pi\)
0.285172 + 0.958476i \(0.407949\pi\)
\(660\) 109.191 121.269i 0.165441 0.183741i
\(661\) 10.4337 49.0869i 0.0157848 0.0742616i −0.969550 0.244893i \(-0.921247\pi\)
0.985335 + 0.170631i \(0.0545806\pi\)
\(662\) 470.706 209.572i 0.711036 0.316574i
\(663\) −155.401 + 349.036i −0.234390 + 0.526450i
\(664\) 107.694 + 34.9920i 0.162190 + 0.0526987i
\(665\) −29.1251 135.676i −0.0437971 0.204024i
\(666\) −518.014 + 1594.28i −0.777798 + 2.39382i
\(667\) 738.967 157.072i 1.10790 0.235491i
\(668\) 49.8657 234.600i 0.0746493 0.351197i
\(669\) 363.561 161.868i 0.543440 0.241955i
\(670\) 221.133 127.671i 0.330049 0.190554i
\(671\) −87.8194 + 28.5343i −0.130878 + 0.0425250i
\(672\) 179.712 + 549.322i 0.267428 + 0.817444i
\(673\) −35.5708 + 109.476i −0.0528541 + 0.162668i −0.973999 0.226551i \(-0.927255\pi\)
0.921145 + 0.389219i \(0.127255\pi\)
\(674\) −9.36601 + 89.1117i −0.0138962 + 0.132213i
\(675\) −1331.55 + 139.952i −1.97267 + 0.207336i
\(676\) 16.3643 + 155.696i 0.0242075 + 0.230319i
\(677\) −248.631 + 558.434i −0.367254 + 0.824865i 0.631520 + 0.775359i \(0.282431\pi\)
−0.998774 + 0.0495058i \(0.984235\pi\)
\(678\) −490.076 674.531i −0.722825 0.994884i
\(679\) −44.4188 414.567i −0.0654179 0.610556i
\(680\) 205.715 633.125i 0.302522 0.931066i
\(681\) 684.168 + 304.611i 1.00465 + 0.447300i
\(682\) 61.7535 290.527i 0.0905476 0.425993i
\(683\) −101.998 + 176.666i −0.149339 + 0.258662i −0.930983 0.365062i \(-0.881048\pi\)
0.781644 + 0.623724i \(0.214381\pi\)
\(684\) 166.766 + 17.5278i 0.243810 + 0.0256254i
\(685\) 585.940 190.384i 0.855388 0.277932i
\(686\) 447.328 + 397.899i 0.652081 + 0.580027i
\(687\) −319.050 + 981.935i −0.464410 + 1.42931i
\(688\) −425.170 736.416i −0.617979 1.07037i
\(689\) 14.1324 12.7249i 0.0205115 0.0184686i
\(690\) −41.9412 399.044i −0.0607844 0.578325i
\(691\) −24.1524 2.53852i −0.0349529 0.00367369i 0.0870359 0.996205i \(-0.472261\pi\)
−0.121989 + 0.992531i \(0.538927\pi\)
\(692\) 29.8529 9.69981i 0.0431401 0.0140171i
\(693\) 1663.08 + 955.709i 2.39982 + 1.37909i
\(694\) 825.804 1.18992
\(695\) −33.0109 + 314.078i −0.0474977 + 0.451910i
\(696\) −1848.87 1067.45i −2.65642 1.53369i
\(697\) 1002.73 811.885i 1.43863 1.16483i
\(698\) 261.890 151.202i 0.375200 0.216622i
\(699\) −1155.58 + 1590.52i −1.65319 + 2.27542i
\(700\) 120.763 + 38.9690i 0.172518 + 0.0556699i
\(701\) 32.1645 + 98.9923i 0.0458838 + 0.141216i 0.971374 0.237556i \(-0.0763464\pi\)
−0.925490 + 0.378772i \(0.876346\pi\)
\(702\) 180.198 200.130i 0.256692 0.285085i
\(703\) −145.795 327.461i −0.207390 0.465805i
\(704\) 93.8355 + 892.785i 0.133289 + 1.26816i
\(705\) −145.676 685.353i −0.206633 0.972131i
\(706\) 160.061i 0.226716i
\(707\) −40.3018 + 391.035i −0.0570040 + 0.553091i
\(708\) −104.428 + 321.395i −0.147497 + 0.453948i
\(709\) −655.308 + 727.794i −0.924271 + 1.02651i 0.0752981 + 0.997161i \(0.476009\pi\)
−0.999569 + 0.0293461i \(0.990657\pi\)
\(710\) −180.103 404.518i −0.253666 0.569743i
\(711\) −1229.75 + 2129.99i −1.72961 + 2.99577i
\(712\) 661.515 + 595.631i 0.929094 + 0.836560i
\(713\) 134.341 + 184.905i 0.188417 + 0.259334i
\(714\) 2119.37 + 218.431i 2.96830 + 0.305926i
\(715\) 54.7475 + 39.7764i 0.0765699 + 0.0556313i
\(716\) 76.2013 + 33.9270i 0.106426 + 0.0473841i
\(717\) −140.914 + 14.8107i −0.196533 + 0.0206564i
\(718\) −79.9578 760.747i −0.111362 1.05954i
\(719\) 374.599 841.364i 0.521000 1.17019i −0.441092 0.897462i \(-0.645409\pi\)
0.962092 0.272724i \(-0.0879245\pi\)
\(720\) −352.073 + 484.587i −0.488990 + 0.673037i
\(721\) −824.247 596.313i −1.14320 0.827063i
\(722\) −417.073 + 303.022i −0.577664 + 0.419697i
\(723\) −366.736 + 407.302i −0.507243 + 0.563350i
\(724\) −16.3908 9.46325i −0.0226393 0.0130708i
\(725\) −773.973 + 344.595i −1.06755 + 0.475304i
\(726\) 275.602 + 248.153i 0.379617 + 0.341808i
\(727\) −1208.39 392.631i −1.66216 0.540070i −0.680840 0.732432i \(-0.738385\pi\)
−0.981324 + 0.192363i \(0.938385\pi\)
\(728\) −121.030 + 54.1788i −0.166249 + 0.0744214i
\(729\) −717.820 −0.984664
\(730\) −138.234 + 29.3826i −0.189362 + 0.0402501i
\(731\) 2359.81 248.026i 3.22820 0.339297i
\(732\) −35.3071 + 15.7197i −0.0482337 + 0.0214750i
\(733\) 292.927 + 263.752i 0.399627 + 0.359826i 0.844303 0.535866i \(-0.180015\pi\)
−0.444676 + 0.895691i \(0.646681\pi\)
\(734\) −208.687 + 67.8066i −0.284315 + 0.0923796i
\(735\) 66.7795 661.017i 0.0908565 0.899343i
\(736\) −204.372 148.485i −0.277680 0.201746i
\(737\) −377.359 653.605i −0.512021 0.886846i
\(738\) −1450.32 + 556.619i −1.96521 + 0.754226i
\(739\) −174.038 + 301.443i −0.235505 + 0.407906i −0.959419 0.281983i \(-0.909008\pi\)
0.723914 + 0.689890i \(0.242341\pi\)
\(740\) −102.646 10.7885i −0.138711 0.0145791i
\(741\) 98.3685i 0.132751i
\(742\) −91.9473 52.8387i −0.123918 0.0712112i
\(743\) −80.5552 247.923i −0.108419 0.333679i 0.882099 0.471064i \(-0.156130\pi\)
−0.990518 + 0.137386i \(0.956130\pi\)
\(744\) 67.5120 642.334i 0.0907420 0.863352i
\(745\) −164.201 + 17.2582i −0.220403 + 0.0231653i
\(746\) 191.597 + 212.790i 0.256833 + 0.285242i
\(747\) 246.217 142.154i 0.329608 0.190299i
\(748\) −360.193 117.034i −0.481542 0.156462i
\(749\) 1.35113 1.86759i 0.00180392 0.00249345i
\(750\) 321.878 + 990.640i 0.429171 + 1.32085i
\(751\) 69.8986 665.041i 0.0930741 0.885541i −0.843984 0.536368i \(-0.819796\pi\)
0.937058 0.349173i \(-0.113537\pi\)
\(752\) 504.686 + 291.381i 0.671125 + 0.387474i
\(753\) −158.838 33.7620i −0.210940 0.0448366i
\(754\) 69.3111 155.675i 0.0919245 0.206466i
\(755\) 175.441 + 57.0044i 0.232373 + 0.0755025i
\(756\) 429.731 + 190.291i 0.568427 + 0.251707i
\(757\) 94.3406 68.5424i 0.124624 0.0905448i −0.523727 0.851886i \(-0.675459\pi\)
0.648351 + 0.761341i \(0.275459\pi\)
\(758\) 876.663 + 390.316i 1.15655 + 0.514928i
\(759\) −1179.46 + 123.966i −1.55397 + 0.163328i
\(760\) −17.9157 170.456i −0.0235733 0.224285i
\(761\) 27.2338 + 2.86238i 0.0357868 + 0.00376135i 0.122405 0.992480i \(-0.460939\pi\)
−0.0866181 + 0.996242i \(0.527606\pi\)
\(762\) 376.372 + 122.291i 0.493927 + 0.160487i
\(763\) −329.522 295.501i −0.431876 0.387288i
\(764\) −66.4076 204.381i −0.0869209 0.267515i
\(765\) −835.709 1447.49i −1.09243 1.89214i
\(766\) −122.972 276.199i −0.160538 0.360573i
\(767\) −137.078 29.1368i −0.178719 0.0379880i
\(768\) 197.974 + 931.392i 0.257778 + 1.21275i
\(769\) −400.936 130.272i −0.521373 0.169405i 0.0364951 0.999334i \(-0.488381\pi\)
−0.557869 + 0.829929i \(0.688381\pi\)
\(770\) 115.889 359.135i 0.150505 0.466408i
\(771\) −229.615 + 706.681i −0.297814 + 0.916577i
\(772\) 204.925 + 91.2383i 0.265446 + 0.118184i
\(773\) 151.113 + 339.405i 0.195489 + 0.439075i 0.984519 0.175280i \(-0.0560831\pi\)
−0.789030 + 0.614355i \(0.789416\pi\)
\(774\) −2794.56 594.001i −3.61054 0.767444i
\(775\) −190.476 171.505i −0.245775 0.221297i
\(776\) 514.976i 0.663629i
\(777\) −182.833 1706.41i −0.235306 2.19615i
\(778\) −144.467 −0.185691
\(779\) 150.826 295.964i 0.193615 0.379929i
\(780\) 24.5293 + 14.1620i 0.0314478 + 0.0181564i
\(781\) −1195.64 + 532.333i −1.53091 + 0.681604i
\(782\) −806.472 + 465.617i −1.03129 + 0.595418i
\(783\) −2984.26 + 969.645i −3.81132 + 1.23837i
\(784\) 371.406 + 409.155i 0.473732 + 0.521881i
\(785\) −228.075 165.706i −0.290541 0.211091i
\(786\) −1381.77 615.204i −1.75798 0.782702i
\(787\) −169.900 + 152.979i −0.215883 + 0.194382i −0.769976 0.638073i \(-0.779732\pi\)
0.554093 + 0.832455i \(0.313065\pi\)
\(788\) 85.5601 148.194i 0.108579 0.188064i
\(789\) −300.202 1412.34i −0.380484 1.79004i
\(790\) 460.197 + 149.527i 0.582528 + 0.189275i
\(791\) 523.177 + 300.651i 0.661413 + 0.380089i
\(792\) 1916.67 + 1392.55i 2.42004 + 1.75826i
\(793\) −8.01367 13.8801i −0.0101055 0.0175033i
\(794\) 39.6452 186.516i 0.0499310 0.234907i
\(795\) 12.3014 + 117.040i 0.0154735 + 0.147221i
\(796\) −39.9950 188.161i −0.0502449 0.236384i
\(797\) −124.224 + 170.979i −0.155864 + 0.214528i −0.879807 0.475332i \(-0.842328\pi\)
0.723943 + 0.689860i \(0.242328\pi\)
\(798\) 521.359 170.564i 0.653332 0.213739i
\(799\) −1315.59 + 955.830i −1.64654 + 1.19628i
\(800\) 258.803 + 115.227i 0.323504 + 0.144033i
\(801\) 2222.71 233.616i 2.77491 0.291655i
\(802\) −749.761 + 333.815i −0.934864 + 0.416228i
\(803\) 86.8465 + 408.581i 0.108153 + 0.508818i
\(804\) −185.674 255.559i −0.230938 0.317859i
\(805\) 145.700 + 251.188i 0.180994 + 0.312035i
\(806\) 51.5537 0.0639624
\(807\) 269.910 2568.03i 0.334461 3.18219i
\(808\) −100.949 + 474.929i −0.124937 + 0.587783i
\(809\) 689.862 + 766.170i 0.852735 + 0.947058i 0.999110 0.0421712i \(-0.0134275\pi\)
−0.146376 + 0.989229i \(0.546761\pi\)
\(810\) 173.018 + 813.986i 0.213603 + 1.00492i
\(811\) 630.065i 0.776899i −0.921470 0.388450i \(-0.873011\pi\)
0.921470 0.388450i \(-0.126989\pi\)
\(812\) 295.825 + 30.4890i 0.364316 + 0.0375480i
\(813\) 116.005 84.2827i 0.142688 0.103669i
\(814\) 101.893 969.450i 0.125176 1.19097i
\(815\) 10.2667 48.3008i 0.0125971 0.0592648i
\(816\) 1923.55 + 408.864i 2.35730 + 0.501059i
\(817\) 529.066 305.456i 0.647571 0.373876i
\(818\) −476.610 + 655.997i −0.582653 + 0.801953i
\(819\) −102.242 + 316.843i −0.124838 + 0.386866i
\(820\) −52.0879 80.2198i −0.0635218 0.0978290i
\(821\) 609.033 + 1054.88i 0.741818 + 1.28487i 0.951667 + 0.307132i \(0.0993695\pi\)
−0.209849 + 0.977734i \(0.567297\pi\)
\(822\) 990.584 + 2224.89i 1.20509 + 2.70668i
\(823\) 549.069 951.015i 0.667155 1.15555i −0.311541 0.950233i \(-0.600845\pi\)
0.978696 0.205314i \(-0.0658216\pi\)
\(824\) −933.794 840.792i −1.13325 1.02038i
\(825\) 1264.88 410.985i 1.53319 0.498164i
\(826\) 83.2560 + 777.041i 0.100794 + 0.940728i
\(827\) −686.703 + 498.919i −0.830355 + 0.603288i −0.919660 0.392716i \(-0.871535\pi\)
0.0893051 + 0.996004i \(0.471535\pi\)
\(828\) −343.232 + 72.9562i −0.414531 + 0.0881113i
\(829\) −627.536 362.308i −0.756979 0.437042i 0.0712310 0.997460i \(-0.477307\pi\)
−0.828210 + 0.560418i \(0.810641\pi\)
\(830\) −37.4273 41.5672i −0.0450931 0.0500810i
\(831\) 286.777 + 1349.18i 0.345098 + 1.62356i
\(832\) −148.189 + 48.1496i −0.178112 + 0.0578721i
\(833\) −1464.54 + 482.403i −1.75816 + 0.579115i
\(834\) −1248.40 −1.49688
\(835\) −411.853 + 457.409i −0.493237 + 0.547795i
\(836\) −96.9749 + 10.1925i −0.115999 + 0.0121920i
\(837\) −635.202 705.463i −0.758903 0.842848i
\(838\) −655.848 68.9324i −0.782635 0.0822582i
\(839\) 363.468 + 500.271i 0.433216 + 0.596270i 0.968688 0.248283i \(-0.0798662\pi\)
−0.535472 + 0.844553i \(0.679866\pi\)
\(840\) 168.992 803.010i 0.201181 0.955964i
\(841\) −925.964 + 672.752i −1.10103 + 0.799943i
\(842\) −123.676 55.0641i −0.146884 0.0653968i
\(843\) 118.904 + 267.062i 0.141048 + 0.316799i
\(844\) −28.8436 32.0341i −0.0341749 0.0379550i
\(845\) 163.412 367.029i 0.193387 0.434353i
\(846\) 1862.14 605.047i 2.20112 0.715186i
\(847\) −255.428 82.4240i −0.301567 0.0973128i
\(848\) −79.1882 57.5336i −0.0933823 0.0678462i
\(849\) −599.461 + 665.769i −0.706079 + 0.784180i
\(850\) 776.081 698.787i 0.913037 0.822102i
\(851\) 501.916 + 557.434i 0.589795 + 0.655034i
\(852\) −474.404 + 273.897i −0.556812 + 0.321476i
\(853\) −1180.49 383.565i −1.38393 0.449665i −0.479969 0.877285i \(-0.659352\pi\)
−0.903959 + 0.427620i \(0.859352\pi\)
\(854\) −59.6702 + 66.5400i −0.0698714 + 0.0779157i
\(855\) −348.143 252.941i −0.407185 0.295837i
\(856\) 1.90508 2.11581i 0.00222556 0.00247174i
\(857\) 263.923 1241.66i 0.307961 1.44884i −0.503276 0.864126i \(-0.667872\pi\)
0.811237 0.584717i \(-0.198795\pi\)
\(858\) −133.754 + 231.669i −0.155891 + 0.270011i
\(859\) 1414.73 + 148.695i 1.64696 + 0.173102i 0.882088 0.471085i \(-0.156138\pi\)
0.764868 + 0.644187i \(0.222804\pi\)
\(860\) 175.905i 0.204540i
\(861\) 1122.38 1126.77i 1.30358 1.30868i
\(862\) −1326.39 −1.53874
\(863\) −143.762 + 1367.80i −0.166584 + 1.58494i 0.517594 + 0.855627i \(0.326828\pi\)
−0.684178 + 0.729315i \(0.739839\pi\)
\(864\) 908.668 + 524.620i 1.05170 + 0.607199i
\(865\) −78.7940 16.7482i −0.0910913 0.0193621i
\(866\) −443.137 399.003i −0.511706 0.460742i
\(867\) −2284.12 + 3143.82i −2.63451 + 3.62609i
\(868\) 27.9750 + 85.5106i 0.0322292 + 0.0985146i
\(869\) 441.960 1360.21i 0.508584 1.56526i
\(870\) 527.276 + 913.268i 0.606064 + 1.04973i
\(871\) 97.3500 87.6543i 0.111768 0.100636i
\(872\) −365.803 406.265i −0.419499 0.465901i
\(873\) −960.865 865.167i −1.10065 0.991027i
\(874\) −140.927 + 193.969i −0.161243 + 0.221932i
\(875\) −505.546 559.193i −0.577767 0.639077i
\(876\) 54.0261 + 166.275i 0.0616736 + 0.189812i
\(877\) 626.141 + 278.776i 0.713958 + 0.317875i 0.731377 0.681974i \(-0.238878\pi\)
−0.0174185 + 0.999848i \(0.505545\pi\)
\(878\) −286.411 + 257.886i −0.326209 + 0.293720i
\(879\) 1517.56 675.663i 1.72647 0.768672i
\(880\) 141.671 318.197i 0.160989 0.361588i
\(881\) −981.081 1350.34i −1.11360 1.53274i −0.816004 0.578046i \(-0.803815\pi\)
−0.297595 0.954692i \(-0.596185\pi\)
\(882\) 1856.57 7.49293i 2.10495 0.00849539i
\(883\) −357.385 + 259.655i −0.404739 + 0.294060i −0.771469 0.636267i \(-0.780477\pi\)
0.366729 + 0.930328i \(0.380477\pi\)
\(884\) 6.87134 65.3764i 0.00777301 0.0739552i
\(885\) 644.487 580.299i 0.728234 0.655705i
\(886\) −84.8628 807.416i −0.0957820 0.911305i
\(887\) −453.489 408.323i −0.511261 0.460342i 0.372666 0.927965i \(-0.378444\pi\)
−0.883928 + 0.467624i \(0.845110\pi\)
\(888\) 2119.70i 2.38705i
\(889\) −284.775 + 30.5122i −0.320332 + 0.0343219i
\(890\) −135.875 418.181i −0.152669 0.469866i
\(891\) 2405.91 511.392i 2.70024 0.573953i
\(892\) −50.8847 + 45.8168i −0.0570456 + 0.0513641i
\(893\) −209.338 + 362.584i −0.234421 + 0.406029i
\(894\) −135.697 638.404i −0.151786 0.714098i
\(895\) −125.823 173.180i −0.140584 0.193497i
\(896\) 266.241 + 364.899i 0.297144 + 0.407253i
\(897\) −63.6105 195.773i −0.0709147 0.218253i
\(898\) −8.72421 + 9.68922i −0.00971516 + 0.0107898i
\(899\) −520.215 300.346i −0.578660 0.334089i
\(900\) 359.491 160.056i 0.399435 0.177840i
\(901\) 236.540 136.566i 0.262530 0.151572i
\(902\) 757.643 491.949i 0.839959 0.545398i
\(903\) 2859.75 613.893i 3.16695 0.679838i
\(904\) 602.955 + 438.072i 0.666986 + 0.484593i
\(905\) 24.2856 + 42.0638i 0.0268349 + 0.0464794i
\(906\) −151.613 + 713.282i −0.167343 + 0.787287i
\(907\) −70.0808 14.8961i −0.0772665 0.0164235i 0.169116 0.985596i \(-0.445909\pi\)
−0.246383 + 0.969173i \(0.579242\pi\)
\(908\) −128.148 13.4689i −0.141133 0.0148336i
\(909\) 716.547 + 986.242i 0.788280 + 1.08497i
\(910\) 65.1553 + 6.71520i 0.0715993 + 0.00737934i
\(911\) 1674.88 1.83850 0.919251 0.393671i \(-0.128795\pi\)
0.919251 + 0.393671i \(0.128795\pi\)
\(912\) 495.245 105.268i 0.543031 0.115425i
\(913\) −122.861 + 110.624i −0.134568 + 0.121166i
\(914\) −31.2025 6.63229i −0.0341384 0.00725634i
\(915\) 98.6403 + 10.3675i 0.107804 + 0.0113306i
\(916\) 177.641i 0.193931i
\(917\) 1094.65 2.20893i 1.19373 0.00240887i
\(918\) 3129.15 2273.46i 3.40866 2.47654i
\(919\) 123.280 26.2040i 0.134146 0.0285136i −0.140349 0.990102i \(-0.544823\pi\)
0.274495 + 0.961588i \(0.411489\pi\)
\(920\) 145.882 + 327.657i 0.158568 + 0.356149i
\(921\) 169.415 + 1611.87i 0.183946 + 1.75013i
\(922\) 384.808 864.293i 0.417362 0.937411i
\(923\) −133.526 183.783i −0.144665 0.199115i
\(924\) −456.843 96.1419i −0.494419 0.104050i
\(925\) −680.538 494.440i −0.735717 0.534530i
\(926\) 1331.77 283.076i 1.43819 0.305697i
\(927\) −3137.57 + 329.772i −3.38465 + 0.355741i
\(928\) 649.427 + 138.040i 0.699813 + 0.148750i
\(929\) −268.973 + 155.291i −0.289529 + 0.167160i −0.637729 0.770260i \(-0.720126\pi\)
0.348200 + 0.937420i \(0.386793\pi\)
\(930\) −187.524 + 258.105i −0.201639 + 0.277532i
\(931\) −293.950 + 266.830i −0.315736 + 0.286606i
\(932\) 104.527 321.702i 0.112154 0.345174i
\(933\) 2555.16 543.116i 2.73865 0.582118i
\(934\) −337.669 194.953i −0.361530 0.208730i
\(935\) 650.351 + 722.289i 0.695563 + 0.772501i
\(936\) −167.256 + 375.663i −0.178692 + 0.401349i
\(937\) −65.7790 + 90.5370i −0.0702017 + 0.0966244i −0.842674 0.538424i \(-0.819020\pi\)
0.772472 + 0.635048i \(0.219020\pi\)
\(938\) −633.371 363.975i −0.675236 0.388033i
\(939\) −513.764 1581.20i −0.547140 1.68392i
\(940\) 60.2762 + 104.402i 0.0641237 + 0.111065i
\(941\) 297.410 + 667.994i 0.316057 + 0.709876i 0.999803 0.0198439i \(-0.00631694\pi\)
−0.683746 + 0.729720i \(0.739650\pi\)
\(942\) 557.213 965.121i 0.591521 1.02454i
\(943\) −108.787 + 686.561i −0.115362 + 0.728060i
\(944\) 721.310i 0.764099i
\(945\) −710.899 974.328i −0.752274 1.03103i
\(946\) 1661.35 1.75618
\(947\) −866.931 + 962.825i −0.915450 + 1.01671i 0.0843443 + 0.996437i \(0.473120\pi\)
−0.999794 + 0.0202738i \(0.993546\pi\)
\(948\) 124.459 585.534i 0.131286 0.617652i
\(949\) −66.2340 + 29.4893i −0.0697935 + 0.0310741i
\(950\) 109.361 245.629i 0.115117 0.258557i
\(951\) 1673.04 + 543.602i 1.75924 + 0.571611i
\(952\) −1862.09 + 399.728i −1.95598 + 0.419883i
\(953\) 227.691 700.760i 0.238920 0.735321i −0.757657 0.652653i \(-0.773656\pi\)
0.996577 0.0826677i \(-0.0263440\pi\)
\(954\) −321.679 + 68.3751i −0.337190 + 0.0716720i
\(955\) −114.663 + 539.445i −0.120066 + 0.564864i
\(956\) 22.2708 9.91562i 0.0232959 0.0103720i
\(957\) 2699.36 1558.48i 2.82065 1.62850i
\(958\) −1064.21 + 345.783i −1.11087 + 0.360942i
\(959\) −1312.22 1176.75i −1.36833 1.22706i
\(960\) 297.969 917.054i 0.310384 0.955264i
\(961\) −81.4561 + 775.003i −0.0847618 + 0.806454i
\(962\) 168.269 17.6857i 0.174915 0.0183843i
\(963\) −0.747203 7.10916i −0.000775912 0.00738231i
\(964\) 38.3551 86.1469i 0.0397874 0.0893640i
\(965\) −338.369 465.725i −0.350641 0.482616i
\(966\) −927.313 + 676.596i −0.959951 + 0.700409i
\(967\) −292.719 + 900.897i −0.302709 + 0.931641i 0.677814 + 0.735234i \(0.262928\pi\)
−0.980522 + 0.196408i \(0.937072\pi\)
\(968\) −302.846 134.836i −0.312857 0.139293i
\(969\) −293.741 + 1381.94i −0.303139 + 1.42616i
\(970\) −127.189 + 220.298i −0.131123 + 0.227111i
\(971\) 1781.74 + 187.269i 1.83495 + 0.192862i 0.957817 0.287378i \(-0.0927835\pi\)
0.877138 + 0.480239i \(0.159450\pi\)
\(972\) 404.422 131.405i 0.416072 0.135190i
\(973\) 824.635 369.147i 0.847518 0.379390i
\(974\) −303.145 + 932.983i −0.311237 + 0.957889i
\(975\) 115.423 + 199.918i 0.118382 + 0.205044i
\(976\) −61.3048 + 55.1991i −0.0628123 + 0.0565565i
\(977\) −147.205 1400.57i −0.150671 1.43354i −0.764767 0.644307i \(-0.777146\pi\)
0.614096 0.789231i \(-0.289521\pi\)
\(978\) 194.131 + 20.4040i 0.198498 + 0.0208630i
\(979\) −1236.02 + 401.608i −1.26254 + 0.410223i
\(980\) 24.2174 + 111.715i 0.0247117 + 0.113995i
\(981\) −1372.58 −1.39917
\(982\) 28.3381 269.619i 0.0288575 0.274561i
\(983\) −504.294 291.154i −0.513016 0.296190i 0.221057 0.975261i \(-0.429049\pi\)
−0.734072 + 0.679071i \(0.762383\pi\)
\(984\) 1526.67 1236.11i 1.55149 1.25621i
\(985\) −380.312 + 219.573i −0.386103 + 0.222917i
\(986\) 1438.60 1980.06i 1.45902 2.00817i
\(987\) −1486.94 + 1344.29i −1.50652 + 1.36199i
\(988\) −5.23004 16.0964i −0.00529356 0.0162919i
\(989\) −855.422 + 950.043i −0.864937 + 0.960609i
\(990\) −475.988 1069.09i −0.480796 1.07988i
\(991\) 131.406 + 1250.24i 0.132599 + 1.26160i 0.835174 + 0.549986i \(0.185367\pi\)
−0.702575 + 0.711610i \(0.747966\pi\)
\(992\) 41.7614 + 196.472i 0.0420982 + 0.198057i
\(993\) 1635.83i 1.64736i
\(994\) −742.536 + 1026.36i −0.747018 + 1.03256i
\(995\) −152.552 + 469.505i −0.153318 + 0.471865i
\(996\) −46.3019 + 51.4235i −0.0464878 + 0.0516300i
\(997\) 676.527 + 1519.50i 0.678563 + 1.52408i 0.843129 + 0.537711i \(0.180711\pi\)
−0.164567 + 0.986366i \(0.552623\pi\)
\(998\) −397.230 + 688.023i −0.398026 + 0.689402i
\(999\) −2315.28 2084.69i −2.31760 2.08677i
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 287.3.y.a.10.17 432
7.5 odd 6 inner 287.3.y.a.215.38 yes 432
41.37 even 5 inner 287.3.y.a.283.38 yes 432
287.201 odd 30 inner 287.3.y.a.201.17 yes 432
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
287.3.y.a.10.17 432 1.1 even 1 trivial
287.3.y.a.201.17 yes 432 287.201 odd 30 inner
287.3.y.a.215.38 yes 432 7.5 odd 6 inner
287.3.y.a.283.38 yes 432 41.37 even 5 inner