Properties

Label 60.3.l.a.23.4
Level $60$
Weight $3$
Character 60.23
Analytic conductor $1.635$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [60,3,Mod(23,60)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(60, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 2, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("60.23");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 60.l (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.63488158616\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 23.4
Character \(\chi\) \(=\) 60.23
Dual form 60.3.l.a.47.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.75394 - 0.961083i) q^{2} +(0.903948 - 2.86057i) q^{3} +(2.15264 + 3.37137i) q^{4} +(4.95584 - 0.663068i) q^{5} +(-4.33472 + 4.14852i) q^{6} +(-7.30016 - 7.30016i) q^{7} +(-0.535443 - 7.98206i) q^{8} +(-7.36576 - 5.17162i) q^{9} +O(q^{10})\) \(q+(-1.75394 - 0.961083i) q^{2} +(0.903948 - 2.86057i) q^{3} +(2.15264 + 3.37137i) q^{4} +(4.95584 - 0.663068i) q^{5} +(-4.33472 + 4.14852i) q^{6} +(-7.30016 - 7.30016i) q^{7} +(-0.535443 - 7.98206i) q^{8} +(-7.36576 - 5.17162i) q^{9} +(-9.32953 - 3.59999i) q^{10} +4.41713 q^{11} +(11.5899 - 3.11024i) q^{12} +(7.53253 + 7.53253i) q^{13} +(5.78801 + 19.8201i) q^{14} +(2.58307 - 14.7759i) q^{15} +(-6.73229 + 14.5147i) q^{16} +(-0.350578 - 0.350578i) q^{17} +(7.94877 + 16.1498i) q^{18} +9.24359 q^{19} +(12.9036 + 15.2806i) q^{20} +(-27.4816 + 14.2837i) q^{21} +(-7.74740 - 4.24523i) q^{22} +(17.9810 + 17.9810i) q^{23} +(-23.3173 - 5.68370i) q^{24} +(24.1207 - 6.57212i) q^{25} +(-5.97225 - 20.4510i) q^{26} +(-21.4521 + 16.3954i) q^{27} +(8.89693 - 40.3261i) q^{28} +5.52099 q^{29} +(-18.7314 + 23.4336i) q^{30} +48.1716i q^{31} +(25.7579 - 18.9877i) q^{32} +(3.99285 - 12.6355i) q^{33} +(0.277960 + 0.951830i) q^{34} +(-41.0189 - 31.3379i) q^{35} +(1.57963 - 35.9653i) q^{36} +(3.39462 - 3.39462i) q^{37} +(-16.2127 - 8.88386i) q^{38} +(28.3564 - 14.7383i) q^{39} +(-7.94622 - 39.2028i) q^{40} -33.0983i q^{41} +(61.9290 + 1.35933i) q^{42} +(1.45103 - 1.45103i) q^{43} +(9.50848 + 14.8918i) q^{44} +(-39.9326 - 20.7457i) q^{45} +(-14.2565 - 48.8190i) q^{46} +(-27.8943 + 27.8943i) q^{47} +(35.4347 + 32.3787i) q^{48} +57.5846i q^{49} +(-48.6227 - 11.6548i) q^{50} +(-1.31976 + 0.685951i) q^{51} +(-9.18014 + 41.6098i) q^{52} +(-52.6835 + 52.6835i) q^{53} +(53.3830 - 8.13943i) q^{54} +(21.8906 - 2.92886i) q^{55} +(-54.3615 + 62.1791i) q^{56} +(8.35573 - 26.4420i) q^{57} +(-9.68351 - 5.30613i) q^{58} -24.6578i q^{59} +(55.3755 - 23.0988i) q^{60} +46.1739 q^{61} +(46.2969 - 84.4904i) q^{62} +(16.0176 + 91.5248i) q^{63} +(-63.4266 + 8.54787i) q^{64} +(42.3246 + 32.3354i) q^{65} +(-19.1470 + 18.3245i) q^{66} +(-32.1110 - 32.1110i) q^{67} +(0.427261 - 1.93660i) q^{68} +(67.6900 - 35.1822i) q^{69} +(41.8265 + 94.3875i) q^{70} +116.455 q^{71} +(-37.3362 + 61.5630i) q^{72} +(-72.2123 - 72.2123i) q^{73} +(-9.21650 + 2.69147i) q^{74} +(3.00382 - 74.9398i) q^{75} +(19.8981 + 31.1636i) q^{76} +(-32.2457 - 32.2457i) q^{77} +(-63.9003 - 1.40260i) q^{78} -55.9466 q^{79} +(-23.7399 + 76.3964i) q^{80} +(27.5087 + 76.1858i) q^{81} +(-31.8102 + 58.0526i) q^{82} +(-46.5302 - 46.5302i) q^{83} +(-107.314 - 61.9031i) q^{84} +(-1.96987 - 1.50495i) q^{85} +(-3.93959 + 1.15047i) q^{86} +(4.99069 - 15.7932i) q^{87} +(-2.36512 - 35.2578i) q^{88} -33.2025 q^{89} +(50.1013 + 74.7654i) q^{90} -109.977i q^{91} +(-21.9141 + 99.3275i) q^{92} +(137.798 + 43.5447i) q^{93} +(75.7338 - 22.1163i) q^{94} +(45.8098 - 6.12913i) q^{95} +(-31.0319 - 90.8462i) q^{96} +(-24.6341 + 24.6341i) q^{97} +(55.3436 - 101.000i) q^{98} +(-32.5355 - 22.8437i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 4 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 4 q^{6} - 12 q^{10} - 20 q^{12} - 8 q^{13} - 36 q^{16} - 24 q^{18} - 24 q^{21} - 76 q^{22} - 8 q^{25} - 84 q^{28} + 68 q^{30} - 40 q^{33} + 172 q^{36} - 40 q^{37} + 104 q^{40} + 236 q^{42} - 104 q^{45} + 240 q^{46} + 196 q^{48} + 304 q^{52} - 72 q^{57} + 180 q^{58} - 284 q^{60} + 48 q^{61} - 552 q^{66} - 372 q^{70} - 600 q^{72} + 104 q^{73} - 736 q^{76} - 408 q^{78} + 72 q^{81} - 720 q^{82} + 216 q^{85} - 580 q^{88} + 528 q^{90} + 368 q^{93} + 884 q^{96} + 72 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(37\) \(41\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.75394 0.961083i −0.876972 0.480541i
\(3\) 0.903948 2.86057i 0.301316 0.953524i
\(4\) 2.15264 + 3.37137i 0.538160 + 0.842843i
\(5\) 4.95584 0.663068i 0.991168 0.132614i
\(6\) −4.33472 + 4.14852i −0.722454 + 0.691419i
\(7\) −7.30016 7.30016i −1.04288 1.04288i −0.999039 0.0438411i \(-0.986040\pi\)
−0.0438411 0.999039i \(-0.513960\pi\)
\(8\) −0.535443 7.98206i −0.0669303 0.997758i
\(9\) −7.36576 5.17162i −0.818417 0.574624i
\(10\) −9.32953 3.59999i −0.932953 0.359999i
\(11\) 4.41713 0.401557 0.200779 0.979637i \(-0.435653\pi\)
0.200779 + 0.979637i \(0.435653\pi\)
\(12\) 11.5899 3.11024i 0.965827 0.259187i
\(13\) 7.53253 + 7.53253i 0.579426 + 0.579426i 0.934745 0.355319i \(-0.115628\pi\)
−0.355319 + 0.934745i \(0.615628\pi\)
\(14\) 5.78801 + 19.8201i 0.413429 + 1.41572i
\(15\) 2.58307 14.7759i 0.172204 0.985061i
\(16\) −6.73229 + 14.5147i −0.420768 + 0.907168i
\(17\) −0.350578 0.350578i −0.0206223 0.0206223i 0.696720 0.717343i \(-0.254642\pi\)
−0.717343 + 0.696720i \(0.754642\pi\)
\(18\) 7.94877 + 16.1498i 0.441598 + 0.897213i
\(19\) 9.24359 0.486505 0.243252 0.969963i \(-0.421786\pi\)
0.243252 + 0.969963i \(0.421786\pi\)
\(20\) 12.9036 + 15.2806i 0.645179 + 0.764031i
\(21\) −27.4816 + 14.2837i −1.30865 + 0.680175i
\(22\) −7.74740 4.24523i −0.352154 0.192965i
\(23\) 17.9810 + 17.9810i 0.781785 + 0.781785i 0.980132 0.198347i \(-0.0635573\pi\)
−0.198347 + 0.980132i \(0.563557\pi\)
\(24\) −23.3173 5.68370i −0.971553 0.236821i
\(25\) 24.1207 6.57212i 0.964827 0.262885i
\(26\) −5.97225 20.4510i −0.229702 0.786578i
\(27\) −21.4521 + 16.3954i −0.794520 + 0.607237i
\(28\) 8.89693 40.3261i 0.317748 1.44022i
\(29\) 5.52099 0.190379 0.0951895 0.995459i \(-0.469654\pi\)
0.0951895 + 0.995459i \(0.469654\pi\)
\(30\) −18.7314 + 23.4336i −0.624381 + 0.781120i
\(31\) 48.1716i 1.55392i 0.629548 + 0.776962i \(0.283240\pi\)
−0.629548 + 0.776962i \(0.716760\pi\)
\(32\) 25.7579 18.9877i 0.804934 0.593365i
\(33\) 3.99285 12.6355i 0.120996 0.382894i
\(34\) 0.277960 + 0.951830i 0.00817530 + 0.0279950i
\(35\) −41.0189 31.3379i −1.17197 0.895369i
\(36\) 1.57963 35.9653i 0.0438785 0.999037i
\(37\) 3.39462 3.39462i 0.0917466 0.0917466i −0.659744 0.751491i \(-0.729335\pi\)
0.751491 + 0.659744i \(0.229335\pi\)
\(38\) −16.2127 8.88386i −0.426651 0.233786i
\(39\) 28.3564 14.7383i 0.727087 0.377906i
\(40\) −7.94622 39.2028i −0.198655 0.980069i
\(41\) 33.0983i 0.807276i −0.914919 0.403638i \(-0.867746\pi\)
0.914919 0.403638i \(-0.132254\pi\)
\(42\) 61.9290 + 1.35933i 1.47450 + 0.0323650i
\(43\) 1.45103 1.45103i 0.0337449 0.0337449i −0.690033 0.723778i \(-0.742404\pi\)
0.723778 + 0.690033i \(0.242404\pi\)
\(44\) 9.50848 + 14.8918i 0.216102 + 0.338449i
\(45\) −39.9326 20.7457i −0.887392 0.461016i
\(46\) −14.2565 48.8190i −0.309923 1.06128i
\(47\) −27.8943 + 27.8943i −0.593496 + 0.593496i −0.938574 0.345078i \(-0.887853\pi\)
0.345078 + 0.938574i \(0.387853\pi\)
\(48\) 35.4347 + 32.3787i 0.738223 + 0.674557i
\(49\) 57.5846i 1.17520i
\(50\) −48.6227 11.6548i −0.972453 0.233097i
\(51\) −1.31976 + 0.685951i −0.0258776 + 0.0134500i
\(52\) −9.18014 + 41.6098i −0.176541 + 0.800188i
\(53\) −52.6835 + 52.6835i −0.994028 + 0.994028i −0.999982 0.00595455i \(-0.998105\pi\)
0.00595455 + 0.999982i \(0.498105\pi\)
\(54\) 53.3830 8.13943i 0.988575 0.150730i
\(55\) 21.8906 2.92886i 0.398010 0.0532519i
\(56\) −54.3615 + 62.1791i −0.970741 + 1.11034i
\(57\) 8.35573 26.4420i 0.146592 0.463894i
\(58\) −9.68351 5.30613i −0.166957 0.0914850i
\(59\) 24.6578i 0.417929i −0.977923 0.208964i \(-0.932991\pi\)
0.977923 0.208964i \(-0.0670093\pi\)
\(60\) 55.3755 23.0988i 0.922925 0.384979i
\(61\) 46.1739 0.756950 0.378475 0.925612i \(-0.376449\pi\)
0.378475 + 0.925612i \(0.376449\pi\)
\(62\) 46.2969 84.4904i 0.746725 1.36275i
\(63\) 16.0176 + 91.5248i 0.254247 + 1.45277i
\(64\) −63.4266 + 8.54787i −0.991041 + 0.133560i
\(65\) 42.3246 + 32.3354i 0.651148 + 0.497468i
\(66\) −19.1470 + 18.3245i −0.290106 + 0.277644i
\(67\) −32.1110 32.1110i −0.479269 0.479269i 0.425629 0.904898i \(-0.360053\pi\)
−0.904898 + 0.425629i \(0.860053\pi\)
\(68\) 0.427261 1.93660i 0.00628325 0.0284794i
\(69\) 67.6900 35.1822i 0.981015 0.509887i
\(70\) 41.8265 + 94.3875i 0.597522 + 1.34839i
\(71\) 116.455 1.64021 0.820103 0.572216i \(-0.193916\pi\)
0.820103 + 0.572216i \(0.193916\pi\)
\(72\) −37.3362 + 61.5630i −0.518559 + 0.855042i
\(73\) −72.2123 72.2123i −0.989210 0.989210i 0.0107324 0.999942i \(-0.496584\pi\)
−0.999942 + 0.0107324i \(0.996584\pi\)
\(74\) −9.21650 + 2.69147i −0.124547 + 0.0363712i
\(75\) 3.00382 74.9398i 0.0400510 0.999198i
\(76\) 19.8981 + 31.1636i 0.261817 + 0.410047i
\(77\) −32.2457 32.2457i −0.418776 0.418776i
\(78\) −63.9003 1.40260i −0.819234 0.0179821i
\(79\) −55.9466 −0.708185 −0.354092 0.935210i \(-0.615210\pi\)
−0.354092 + 0.935210i \(0.615210\pi\)
\(80\) −23.7399 + 76.3964i −0.296749 + 0.954956i
\(81\) 27.5087 + 76.1858i 0.339614 + 0.940565i
\(82\) −31.8102 + 58.0526i −0.387929 + 0.707958i
\(83\) −46.5302 46.5302i −0.560605 0.560605i 0.368874 0.929479i \(-0.379743\pi\)
−0.929479 + 0.368874i \(0.879743\pi\)
\(84\) −107.314 61.9031i −1.27754 0.736941i
\(85\) −1.96987 1.50495i −0.0231749 0.0177053i
\(86\) −3.93959 + 1.15047i −0.0458092 + 0.0133775i
\(87\) 4.99069 15.7932i 0.0573642 0.181531i
\(88\) −2.36512 35.2578i −0.0268763 0.400657i
\(89\) −33.2025 −0.373062 −0.186531 0.982449i \(-0.559724\pi\)
−0.186531 + 0.982449i \(0.559724\pi\)
\(90\) 50.1013 + 74.7654i 0.556681 + 0.830727i
\(91\) 109.977i 1.20854i
\(92\) −21.9141 + 99.3275i −0.238196 + 1.07965i
\(93\) 137.798 + 43.5447i 1.48170 + 0.468222i
\(94\) 75.7338 22.1163i 0.805679 0.235280i
\(95\) 45.8098 6.12913i 0.482208 0.0645172i
\(96\) −31.0319 90.8462i −0.323248 0.946314i
\(97\) −24.6341 + 24.6341i −0.253959 + 0.253959i −0.822592 0.568632i \(-0.807473\pi\)
0.568632 + 0.822592i \(0.307473\pi\)
\(98\) 55.3436 101.000i 0.564730 1.03061i
\(99\) −32.5355 22.8437i −0.328641 0.230744i
\(100\) 74.0802 + 67.1724i 0.740802 + 0.671724i
\(101\) 12.2683i 0.121468i −0.998154 0.0607342i \(-0.980656\pi\)
0.998154 0.0607342i \(-0.0193442\pi\)
\(102\) 2.97404 + 0.0652797i 0.0291573 + 0.000639997i
\(103\) 21.2333 21.2333i 0.206149 0.206149i −0.596479 0.802628i \(-0.703434\pi\)
0.802628 + 0.596479i \(0.203434\pi\)
\(104\) 56.0919 64.1584i 0.539345 0.616907i
\(105\) −126.723 + 89.0097i −1.20689 + 0.847712i
\(106\) 143.037 41.7707i 1.34941 0.394063i
\(107\) −77.4288 + 77.4288i −0.723634 + 0.723634i −0.969343 0.245710i \(-0.920979\pi\)
0.245710 + 0.969343i \(0.420979\pi\)
\(108\) −101.454 37.0294i −0.939385 0.342865i
\(109\) 62.5243i 0.573618i −0.957988 0.286809i \(-0.907406\pi\)
0.957988 0.286809i \(-0.0925945\pi\)
\(110\) −41.2097 15.9016i −0.374634 0.144560i
\(111\) −6.64201 12.7791i −0.0598379 0.115127i
\(112\) 155.106 56.8128i 1.38488 0.507257i
\(113\) 64.0685 64.0685i 0.566977 0.566977i −0.364303 0.931280i \(-0.618693\pi\)
0.931280 + 0.364303i \(0.118693\pi\)
\(114\) −40.0684 + 38.3472i −0.351477 + 0.336379i
\(115\) 101.034 + 77.1885i 0.878555 + 0.671205i
\(116\) 11.8847 + 18.6133i 0.102454 + 0.160460i
\(117\) −16.5274 94.4382i −0.141260 0.807164i
\(118\) −23.6982 + 43.2484i −0.200832 + 0.366512i
\(119\) 5.11856i 0.0430131i
\(120\) −119.325 12.7065i −0.994378 0.105888i
\(121\) −101.489 −0.838752
\(122\) −80.9865 44.3770i −0.663824 0.363746i
\(123\) −94.6801 29.9191i −0.769757 0.243245i
\(124\) −162.404 + 103.696i −1.30971 + 0.836259i
\(125\) 115.180 48.5640i 0.921444 0.388512i
\(126\) 59.8690 175.924i 0.475151 1.39622i
\(127\) 36.2102 + 36.2102i 0.285120 + 0.285120i 0.835147 0.550027i \(-0.185383\pi\)
−0.550027 + 0.835147i \(0.685383\pi\)
\(128\) 119.462 + 45.9657i 0.933296 + 0.359107i
\(129\) −2.83912 5.46244i −0.0220087 0.0423445i
\(130\) −43.1580 97.3920i −0.331984 0.749169i
\(131\) −78.8270 −0.601733 −0.300866 0.953666i \(-0.597276\pi\)
−0.300866 + 0.953666i \(0.597276\pi\)
\(132\) 51.1942 13.7383i 0.387835 0.104078i
\(133\) −67.4797 67.4797i −0.507366 0.507366i
\(134\) 25.4596 + 87.1822i 0.189997 + 0.650614i
\(135\) −95.4416 + 95.4772i −0.706975 + 0.707238i
\(136\) −2.61062 + 2.98605i −0.0191958 + 0.0219563i
\(137\) 178.746 + 178.746i 1.30472 + 1.30472i 0.925174 + 0.379544i \(0.123919\pi\)
0.379544 + 0.925174i \(0.376081\pi\)
\(138\) −152.538 3.34817i −1.10534 0.0242621i
\(139\) 15.4896 0.111436 0.0557180 0.998447i \(-0.482255\pi\)
0.0557180 + 0.998447i \(0.482255\pi\)
\(140\) 17.3528 205.749i 0.123948 1.46964i
\(141\) 54.5787 + 105.009i 0.387083 + 0.744743i
\(142\) −204.255 111.922i −1.43841 0.788187i
\(143\) 33.2722 + 33.2722i 0.232672 + 0.232672i
\(144\) 124.653 72.0949i 0.865645 0.500659i
\(145\) 27.3611 3.66079i 0.188698 0.0252468i
\(146\) 57.2544 + 196.058i 0.392153 + 1.34287i
\(147\) 164.725 + 52.0535i 1.12058 + 0.354105i
\(148\) 18.7519 + 4.13714i 0.126702 + 0.0279536i
\(149\) −209.818 −1.40817 −0.704086 0.710115i \(-0.748643\pi\)
−0.704086 + 0.710115i \(0.748643\pi\)
\(150\) −77.2919 + 128.553i −0.515279 + 0.857022i
\(151\) 144.169i 0.954759i 0.878697 + 0.477380i \(0.158413\pi\)
−0.878697 + 0.477380i \(0.841587\pi\)
\(152\) −4.94941 73.7829i −0.0325619 0.485414i
\(153\) 0.769217 + 4.39533i 0.00502756 + 0.0287277i
\(154\) 25.5664 + 87.5480i 0.166016 + 0.568494i
\(155\) 31.9411 + 238.731i 0.206071 + 1.54020i
\(156\) 110.729 + 63.8735i 0.709804 + 0.409446i
\(157\) −161.893 + 161.893i −1.03117 + 1.03117i −0.0316669 + 0.999498i \(0.510082\pi\)
−0.999498 + 0.0316669i \(0.989918\pi\)
\(158\) 98.1272 + 53.7693i 0.621058 + 0.340312i
\(159\) 103.082 + 198.328i 0.648313 + 1.24735i
\(160\) 115.062 111.179i 0.719136 0.694869i
\(161\) 262.529i 1.63061i
\(162\) 24.9721 160.064i 0.154149 0.988048i
\(163\) −19.4060 + 19.4060i −0.119055 + 0.119055i −0.764124 0.645069i \(-0.776829\pi\)
0.645069 + 0.764124i \(0.276829\pi\)
\(164\) 111.587 71.2487i 0.680406 0.434443i
\(165\) 11.4097 65.2671i 0.0691499 0.395558i
\(166\) 36.8920 + 126.331i 0.222241 + 0.761029i
\(167\) 183.816 183.816i 1.10069 1.10069i 0.106366 0.994327i \(-0.466078\pi\)
0.994327 0.106366i \(-0.0339216\pi\)
\(168\) 128.728 + 211.712i 0.766238 + 1.26019i
\(169\) 55.5219i 0.328532i
\(170\) 2.00865 + 4.53281i 0.0118156 + 0.0266636i
\(171\) −68.0861 47.8043i −0.398164 0.279558i
\(172\) 8.01551 + 1.76842i 0.0466018 + 0.0102815i
\(173\) −198.939 + 198.939i −1.14993 + 1.14993i −0.163370 + 0.986565i \(0.552236\pi\)
−0.986565 + 0.163370i \(0.947764\pi\)
\(174\) −23.9320 + 22.9039i −0.137540 + 0.131632i
\(175\) −224.062 128.107i −1.28036 0.732042i
\(176\) −29.7374 + 64.1133i −0.168962 + 0.364280i
\(177\) −70.5354 22.2894i −0.398505 0.125929i
\(178\) 58.2353 + 31.9103i 0.327165 + 0.179272i
\(179\) 167.155i 0.933828i −0.884303 0.466914i \(-0.845366\pi\)
0.884303 0.466914i \(-0.154634\pi\)
\(180\) −16.0191 179.286i −0.0889949 0.996032i
\(181\) 46.3698 0.256187 0.128093 0.991762i \(-0.459114\pi\)
0.128093 + 0.991762i \(0.459114\pi\)
\(182\) −105.697 + 192.894i −0.580755 + 1.05986i
\(183\) 41.7388 132.084i 0.228081 0.721770i
\(184\) 133.898 153.154i 0.727707 0.832357i
\(185\) 14.5723 19.0741i 0.0787694 0.103103i
\(186\) −199.841 208.811i −1.07441 1.12264i
\(187\) −1.54855 1.54855i −0.00828102 0.00828102i
\(188\) −154.089 33.9957i −0.819620 0.180828i
\(189\) 276.292 + 36.9143i 1.46186 + 0.195314i
\(190\) −86.2384 33.2768i −0.453886 0.175141i
\(191\) −299.293 −1.56698 −0.783490 0.621405i \(-0.786562\pi\)
−0.783490 + 0.621405i \(0.786562\pi\)
\(192\) −32.8825 + 189.163i −0.171263 + 0.985225i
\(193\) 207.042 + 207.042i 1.07276 + 1.07276i 0.997137 + 0.0756225i \(0.0240944\pi\)
0.0756225 + 0.997137i \(0.475906\pi\)
\(194\) 66.8821 19.5314i 0.344753 0.100677i
\(195\) 130.757 91.8431i 0.670549 0.470990i
\(196\) −194.139 + 123.959i −0.990505 + 0.632443i
\(197\) −5.31992 5.31992i −0.0270047 0.0270047i 0.693476 0.720480i \(-0.256079\pi\)
−0.720480 + 0.693476i \(0.756079\pi\)
\(198\) 35.1107 + 71.3359i 0.177327 + 0.360282i
\(199\) 61.5955 0.309525 0.154762 0.987952i \(-0.450539\pi\)
0.154762 + 0.987952i \(0.450539\pi\)
\(200\) −65.3743 189.014i −0.326871 0.945069i
\(201\) −120.883 + 62.8292i −0.601406 + 0.312583i
\(202\) −11.7909 + 21.5179i −0.0583706 + 0.106524i
\(203\) −40.3041 40.3041i −0.198542 0.198542i
\(204\) −5.15356 2.97280i −0.0252626 0.0145725i
\(205\) −21.9464 164.030i −0.107056 0.800146i
\(206\) −57.6491 + 16.8351i −0.279850 + 0.0817237i
\(207\) −39.4529 225.435i −0.190594 1.08906i
\(208\) −160.044 + 58.6212i −0.769440 + 0.281833i
\(209\) 40.8301 0.195360
\(210\) 307.811 34.3265i 1.46577 0.163460i
\(211\) 184.930i 0.876444i −0.898867 0.438222i \(-0.855608\pi\)
0.898867 0.438222i \(-0.144392\pi\)
\(212\) −291.024 64.2070i −1.37275 0.302863i
\(213\) 105.269 333.127i 0.494220 1.56398i
\(214\) 210.221 61.3903i 0.982343 0.286871i
\(215\) 6.22894 8.15321i 0.0289718 0.0379219i
\(216\) 142.356 + 162.453i 0.659053 + 0.752096i
\(217\) 351.661 351.661i 1.62056 1.62056i
\(218\) −60.0911 + 109.664i −0.275647 + 0.503047i
\(219\) −271.845 + 141.292i −1.24130 + 0.645171i
\(220\) 56.9968 + 67.4965i 0.259076 + 0.306802i
\(221\) 5.28149i 0.0238981i
\(222\) −0.632098 + 28.7974i −0.00284729 + 0.129718i
\(223\) 206.560 206.560i 0.926280 0.926280i −0.0711833 0.997463i \(-0.522678\pi\)
0.997463 + 0.0711833i \(0.0226775\pi\)
\(224\) −326.650 49.4235i −1.45826 0.220641i
\(225\) −211.656 76.3344i −0.940691 0.339264i
\(226\) −173.948 + 50.7974i −0.769680 + 0.224767i
\(227\) 174.751 174.751i 0.769827 0.769827i −0.208249 0.978076i \(-0.566776\pi\)
0.978076 + 0.208249i \(0.0667763\pi\)
\(228\) 107.133 28.7498i 0.469880 0.126096i
\(229\) 287.354i 1.25482i 0.778689 + 0.627410i \(0.215885\pi\)
−0.778689 + 0.627410i \(0.784115\pi\)
\(230\) −103.023 232.486i −0.447927 1.01081i
\(231\) −121.390 + 63.0928i −0.525497 + 0.273129i
\(232\) −2.95617 44.0689i −0.0127421 0.189952i
\(233\) −1.51498 + 1.51498i −0.00650206 + 0.00650206i −0.710350 0.703848i \(-0.751463\pi\)
0.703848 + 0.710350i \(0.251463\pi\)
\(234\) −61.7748 + 181.524i −0.263995 + 0.775742i
\(235\) −119.744 + 156.736i −0.509549 + 0.666960i
\(236\) 83.1306 53.0794i 0.352248 0.224913i
\(237\) −50.5728 + 160.039i −0.213387 + 0.675271i
\(238\) 4.91936 8.97766i 0.0206696 0.0377213i
\(239\) 271.429i 1.13569i 0.823137 + 0.567843i \(0.192222\pi\)
−0.823137 + 0.567843i \(0.807778\pi\)
\(240\) 197.078 + 136.968i 0.821158 + 0.570701i
\(241\) 122.522 0.508390 0.254195 0.967153i \(-0.418190\pi\)
0.254195 + 0.967153i \(0.418190\pi\)
\(242\) 178.006 + 97.5393i 0.735562 + 0.403055i
\(243\) 242.801 9.82275i 0.999183 0.0404229i
\(244\) 99.3959 + 155.669i 0.407360 + 0.637990i
\(245\) 38.1825 + 285.380i 0.155847 + 1.16482i
\(246\) 137.309 + 143.472i 0.558166 + 0.583219i
\(247\) 69.6277 + 69.6277i 0.281893 + 0.281893i
\(248\) 384.509 25.7931i 1.55044 0.104005i
\(249\) −175.164 + 91.0422i −0.703470 + 0.365631i
\(250\) −248.694 25.5194i −0.994776 0.102078i
\(251\) 335.099 1.33506 0.667529 0.744584i \(-0.267352\pi\)
0.667529 + 0.744584i \(0.267352\pi\)
\(252\) −274.084 + 251.021i −1.08764 + 0.996115i
\(253\) 79.4246 + 79.4246i 0.313931 + 0.313931i
\(254\) −28.7097 98.3118i −0.113030 0.387054i
\(255\) −6.08569 + 4.27455i −0.0238654 + 0.0167629i
\(256\) −165.353 195.434i −0.645909 0.763415i
\(257\) 11.3695 + 11.3695i 0.0442393 + 0.0442393i 0.728880 0.684641i \(-0.240041\pi\)
−0.684641 + 0.728880i \(0.740041\pi\)
\(258\) −0.270190 + 12.3094i −0.00104725 + 0.0477110i
\(259\) −49.5626 −0.191361
\(260\) −17.9052 + 212.298i −0.0688660 + 0.816533i
\(261\) −40.6663 28.5525i −0.155809 0.109396i
\(262\) 138.258 + 75.7593i 0.527703 + 0.289158i
\(263\) −211.355 211.355i −0.803631 0.803631i 0.180030 0.983661i \(-0.442380\pi\)
−0.983661 + 0.180030i \(0.942380\pi\)
\(264\) −102.995 25.1056i −0.390134 0.0950970i
\(265\) −226.158 + 296.024i −0.853427 + 1.11707i
\(266\) 53.5020 + 183.209i 0.201135 + 0.688756i
\(267\) −30.0133 + 94.9781i −0.112409 + 0.355723i
\(268\) 39.1347 177.382i 0.146025 0.661871i
\(269\) −174.453 −0.648523 −0.324261 0.945968i \(-0.605116\pi\)
−0.324261 + 0.945968i \(0.605116\pi\)
\(270\) 259.161 75.7343i 0.959855 0.280497i
\(271\) 189.665i 0.699869i 0.936774 + 0.349935i \(0.113796\pi\)
−0.936774 + 0.349935i \(0.886204\pi\)
\(272\) 7.44873 2.72834i 0.0273850 0.0100307i
\(273\) −314.598 99.4138i −1.15237 0.364153i
\(274\) −141.721 485.301i −0.517230 1.77117i
\(275\) 106.544 29.0299i 0.387433 0.105563i
\(276\) 264.324 + 152.474i 0.957697 + 0.552441i
\(277\) 46.8665 46.8665i 0.169193 0.169193i −0.617431 0.786625i \(-0.711827\pi\)
0.786625 + 0.617431i \(0.211827\pi\)
\(278\) −27.1679 14.8868i −0.0977263 0.0535496i
\(279\) 249.125 354.821i 0.892922 1.27176i
\(280\) −228.178 + 344.195i −0.814921 + 1.22927i
\(281\) 266.157i 0.947179i −0.880746 0.473590i \(-0.842958\pi\)
0.880746 0.473590i \(-0.157042\pi\)
\(282\) 5.19408 236.634i 0.0184187 0.839128i
\(283\) −370.389 + 370.389i −1.30880 + 1.30880i −0.386512 + 0.922285i \(0.626320\pi\)
−0.922285 + 0.386512i \(0.873680\pi\)
\(284\) 250.685 + 392.612i 0.882693 + 1.38244i
\(285\) 23.8768 136.583i 0.0837783 0.479237i
\(286\) −26.3802 90.3348i −0.0922385 0.315856i
\(287\) −241.623 + 241.623i −0.841891 + 0.841891i
\(288\) −287.923 + 6.64869i −0.999733 + 0.0230857i
\(289\) 288.754i 0.999149i
\(290\) −51.5082 19.8755i −0.177615 0.0685362i
\(291\) 48.1996 + 92.7354i 0.165634 + 0.318678i
\(292\) 88.0074 398.902i 0.301395 1.36610i
\(293\) 50.2973 50.2973i 0.171663 0.171663i −0.616047 0.787710i \(-0.711267\pi\)
0.787710 + 0.616047i \(0.211267\pi\)
\(294\) −238.891 249.613i −0.812553 0.849025i
\(295\) −16.3498 122.200i −0.0554230 0.414238i
\(296\) −28.9137 25.2785i −0.0976815 0.0854003i
\(297\) −94.7565 + 72.4206i −0.319045 + 0.243840i
\(298\) 368.008 + 201.652i 1.23493 + 0.676685i
\(299\) 270.886i 0.905972i
\(300\) 259.116 151.191i 0.863720 0.503971i
\(301\) −21.1855 −0.0703838
\(302\) 138.558 252.864i 0.458801 0.837297i
\(303\) −35.0944 11.0899i −0.115823 0.0366004i
\(304\) −62.2305 + 134.168i −0.204706 + 0.441342i
\(305\) 228.831 30.6165i 0.750264 0.100382i
\(306\) 2.87512 8.44845i 0.00939580 0.0276093i
\(307\) 295.562 + 295.562i 0.962741 + 0.962741i 0.999330 0.0365891i \(-0.0116493\pi\)
−0.0365891 + 0.999330i \(0.511649\pi\)
\(308\) 39.2989 178.126i 0.127594 0.578330i
\(309\) −41.5457 79.9333i −0.134452 0.258684i
\(310\) 173.417 449.419i 0.559411 1.44974i
\(311\) −168.540 −0.541930 −0.270965 0.962589i \(-0.587343\pi\)
−0.270965 + 0.962589i \(0.587343\pi\)
\(312\) −132.826 218.451i −0.425723 0.700163i
\(313\) 139.822 + 139.822i 0.446717 + 0.446717i 0.894262 0.447545i \(-0.147701\pi\)
−0.447545 + 0.894262i \(0.647701\pi\)
\(314\) 439.544 128.359i 1.39982 0.408786i
\(315\) 140.068 + 442.962i 0.444659 + 1.40623i
\(316\) −120.433 188.617i −0.381117 0.596888i
\(317\) −168.037 168.037i −0.530086 0.530086i 0.390512 0.920598i \(-0.372298\pi\)
−0.920598 + 0.390512i \(0.872298\pi\)
\(318\) 9.80996 446.926i 0.0308489 1.40543i
\(319\) 24.3869 0.0764480
\(320\) −308.664 + 84.4180i −0.964576 + 0.263806i
\(321\) 151.499 + 291.482i 0.471960 + 0.908045i
\(322\) −252.312 + 460.461i −0.783578 + 1.43000i
\(323\) −3.24061 3.24061i −0.0100328 0.0100328i
\(324\) −197.634 + 256.743i −0.609982 + 0.792415i
\(325\) 231.195 + 132.185i 0.711368 + 0.406724i
\(326\) 52.6878 15.3863i 0.161619 0.0471971i
\(327\) −178.855 56.5187i −0.546958 0.172840i
\(328\) −264.193 + 17.7222i −0.805465 + 0.0540312i
\(329\) 407.266 1.23789
\(330\) −82.7391 + 103.509i −0.250725 + 0.313664i
\(331\) 278.549i 0.841538i −0.907168 0.420769i \(-0.861760\pi\)
0.907168 0.420769i \(-0.138240\pi\)
\(332\) 56.7079 257.034i 0.170807 0.774197i
\(333\) −42.5597 + 7.44827i −0.127807 + 0.0223672i
\(334\) −499.065 + 145.740i −1.49421 + 0.436349i
\(335\) −180.429 137.845i −0.538593 0.411478i
\(336\) −22.3091 495.049i −0.0663963 1.47336i
\(337\) −371.125 + 371.125i −1.10126 + 1.10126i −0.107001 + 0.994259i \(0.534125\pi\)
−0.994259 + 0.107001i \(0.965875\pi\)
\(338\) −53.3611 + 97.3823i −0.157873 + 0.288113i
\(339\) −125.358 241.187i −0.369787 0.711466i
\(340\) 0.833340 9.88078i 0.00245100 0.0290611i
\(341\) 212.780i 0.623989i
\(342\) 73.4752 + 149.282i 0.214840 + 0.436498i
\(343\) 62.6689 62.6689i 0.182708 0.182708i
\(344\) −12.3592 10.8053i −0.0359278 0.0314107i
\(345\) 312.133 219.240i 0.904733 0.635479i
\(346\) 540.124 157.731i 1.56105 0.455869i
\(347\) −160.180 + 160.180i −0.461613 + 0.461613i −0.899184 0.437571i \(-0.855839\pi\)
0.437571 + 0.899184i \(0.355839\pi\)
\(348\) 63.9879 17.1716i 0.183873 0.0493437i
\(349\) 395.209i 1.13240i −0.824266 0.566202i \(-0.808412\pi\)
0.824266 0.566202i \(-0.191588\pi\)
\(350\) 269.871 + 440.035i 0.771060 + 1.25724i
\(351\) −285.087 38.0893i −0.812214 0.108517i
\(352\) 113.776 83.8710i 0.323227 0.238270i
\(353\) 143.113 143.113i 0.405418 0.405418i −0.474719 0.880137i \(-0.657450\pi\)
0.880137 + 0.474719i \(0.157450\pi\)
\(354\) 102.293 + 106.885i 0.288964 + 0.301934i
\(355\) 577.130 77.2173i 1.62572 0.217514i
\(356\) −71.4730 111.938i −0.200767 0.314432i
\(357\) 14.6420 + 4.62691i 0.0410140 + 0.0129605i
\(358\) −160.650 + 293.181i −0.448743 + 0.818941i
\(359\) 388.897i 1.08328i −0.840611 0.541639i \(-0.817804\pi\)
0.840611 0.541639i \(-0.182196\pi\)
\(360\) −144.212 + 329.853i −0.400589 + 0.916258i
\(361\) −275.556 −0.763313
\(362\) −81.3301 44.5652i −0.224669 0.123108i
\(363\) −91.7408 + 290.317i −0.252729 + 0.799770i
\(364\) 370.774 236.742i 1.01861 0.650389i
\(365\) −405.754 309.991i −1.11166 0.849290i
\(366\) −200.151 + 191.553i −0.546861 + 0.523370i
\(367\) −361.520 361.520i −0.985069 0.985069i 0.0148215 0.999890i \(-0.495282\pi\)
−0.999890 + 0.0148215i \(0.995282\pi\)
\(368\) −382.043 + 139.936i −1.03816 + 0.380260i
\(369\) −171.172 + 243.794i −0.463880 + 0.660688i
\(370\) −43.8909 + 19.4496i −0.118624 + 0.0525666i
\(371\) 769.195 2.07330
\(372\) 149.825 + 558.306i 0.402756 + 1.50082i
\(373\) −104.714 104.714i −0.280735 0.280735i 0.552667 0.833402i \(-0.313610\pi\)
−0.833402 + 0.552667i \(0.813610\pi\)
\(374\) 1.22779 + 4.20435i 0.00328285 + 0.0112416i
\(375\) −34.8037 373.381i −0.0928100 0.995684i
\(376\) 237.590 + 207.718i 0.631888 + 0.552442i
\(377\) 41.5870 + 41.5870i 0.110310 + 0.110310i
\(378\) −449.124 330.286i −1.18816 0.873771i
\(379\) −40.1346 −0.105896 −0.0529480 0.998597i \(-0.516862\pi\)
−0.0529480 + 0.998597i \(0.516862\pi\)
\(380\) 119.275 + 141.248i 0.313883 + 0.371705i
\(381\) 136.314 70.8499i 0.357780 0.185958i
\(382\) 524.943 + 287.645i 1.37420 + 0.752998i
\(383\) 340.574 + 340.574i 0.889226 + 0.889226i 0.994449 0.105223i \(-0.0335556\pi\)
−0.105223 + 0.994449i \(0.533556\pi\)
\(384\) 239.476 300.179i 0.623635 0.781716i
\(385\) −181.186 138.424i −0.470612 0.359542i
\(386\) −164.156 562.126i −0.425275 1.45628i
\(387\) −18.1921 + 3.18376i −0.0470081 + 0.00822678i
\(388\) −136.079 30.0223i −0.350719 0.0773771i
\(389\) 98.4019 0.252961 0.126481 0.991969i \(-0.459632\pi\)
0.126481 + 0.991969i \(0.459632\pi\)
\(390\) −317.609 + 35.4192i −0.814383 + 0.0908184i
\(391\) 12.6075i 0.0322443i
\(392\) 459.644 30.8332i 1.17256 0.0786562i
\(393\) −71.2555 + 225.490i −0.181312 + 0.573767i
\(394\) 4.21796 + 14.4437i 0.0107055 + 0.0366592i
\(395\) −277.262 + 37.0964i −0.701930 + 0.0939149i
\(396\) 6.97741 158.863i 0.0176197 0.401170i
\(397\) 323.459 323.459i 0.814758 0.814758i −0.170585 0.985343i \(-0.554566\pi\)
0.985343 + 0.170585i \(0.0545658\pi\)
\(398\) −108.035 59.1983i −0.271445 0.148740i
\(399\) −254.029 + 132.032i −0.636663 + 0.330908i
\(400\) −66.9951 + 394.350i −0.167488 + 0.985874i
\(401\) 648.291i 1.61669i 0.588712 + 0.808343i \(0.299635\pi\)
−0.588712 + 0.808343i \(0.700365\pi\)
\(402\) 272.405 + 5.97925i 0.677625 + 0.0148738i
\(403\) −362.854 + 362.854i −0.900383 + 0.900383i
\(404\) 41.3610 26.4092i 0.102379 0.0653694i
\(405\) 186.845 + 359.324i 0.461346 + 0.887220i
\(406\) 31.9556 + 109.427i 0.0787083 + 0.269524i
\(407\) 14.9945 14.9945i 0.0368415 0.0368415i
\(408\) 6.18196 + 10.1671i 0.0151519 + 0.0249194i
\(409\) 13.9598i 0.0341315i 0.999854 + 0.0170658i \(0.00543247\pi\)
−0.999854 + 0.0170658i \(0.994568\pi\)
\(410\) −119.153 + 308.791i −0.290618 + 0.753150i
\(411\) 672.894 349.740i 1.63721 0.850948i
\(412\) 117.293 + 25.8777i 0.284692 + 0.0628100i
\(413\) −180.006 + 180.006i −0.435849 + 0.435849i
\(414\) −147.464 + 433.318i −0.356192 + 1.04666i
\(415\) −261.449 199.744i −0.629998 0.481310i
\(416\) 337.047 + 50.9968i 0.810210 + 0.122588i
\(417\) 14.0018 44.3092i 0.0335775 0.106257i
\(418\) −71.6138 39.2411i −0.171325 0.0938783i
\(419\) 317.783i 0.758433i −0.925308 0.379216i \(-0.876194\pi\)
0.925308 0.379216i \(-0.123806\pi\)
\(420\) −572.875 235.625i −1.36399 0.561013i
\(421\) −56.9987 −0.135389 −0.0676944 0.997706i \(-0.521564\pi\)
−0.0676944 + 0.997706i \(0.521564\pi\)
\(422\) −177.733 + 324.356i −0.421168 + 0.768617i
\(423\) 349.722 61.2040i 0.826765 0.144690i
\(424\) 448.732 + 392.314i 1.05833 + 0.925268i
\(425\) −10.7602 6.15215i −0.0253182 0.0144756i
\(426\) −504.798 + 483.114i −1.18497 + 1.13407i
\(427\) −337.077 337.077i −0.789408 0.789408i
\(428\) −427.718 94.3649i −0.999340 0.220479i
\(429\) 125.254 65.1011i 0.291967 0.151751i
\(430\) −18.7611 + 8.31374i −0.0436305 + 0.0193343i
\(431\) −146.371 −0.339607 −0.169803 0.985478i \(-0.554313\pi\)
−0.169803 + 0.985478i \(0.554313\pi\)
\(432\) −93.5530 421.749i −0.216558 0.976270i
\(433\) −425.454 425.454i −0.982572 0.982572i 0.0172788 0.999851i \(-0.494500\pi\)
−0.999851 + 0.0172788i \(0.994500\pi\)
\(434\) −954.768 + 278.818i −2.19993 + 0.642438i
\(435\) 14.2611 81.5777i 0.0327841 0.187535i
\(436\) 210.793 134.592i 0.483470 0.308698i
\(437\) 166.210 + 166.210i 0.380342 + 0.380342i
\(438\) 612.594 + 13.4463i 1.39862 + 0.0306994i
\(439\) 679.724 1.54835 0.774173 0.632974i \(-0.218166\pi\)
0.774173 + 0.632974i \(0.218166\pi\)
\(440\) −35.0995 173.164i −0.0797715 0.393554i
\(441\) 297.806 424.154i 0.675296 0.961801i
\(442\) −5.07595 + 9.26343i −0.0114840 + 0.0209580i
\(443\) 192.731 + 192.731i 0.435059 + 0.435059i 0.890345 0.455286i \(-0.150463\pi\)
−0.455286 + 0.890345i \(0.650463\pi\)
\(444\) 28.7854 49.9015i 0.0648319 0.112391i
\(445\) −164.546 + 22.0155i −0.369767 + 0.0494730i
\(446\) −560.817 + 163.774i −1.25744 + 0.367206i
\(447\) −189.664 + 600.199i −0.424305 + 1.34273i
\(448\) 525.425 + 400.623i 1.17282 + 0.894249i
\(449\) −167.799 −0.373717 −0.186859 0.982387i \(-0.559831\pi\)
−0.186859 + 0.982387i \(0.559831\pi\)
\(450\) 297.868 + 337.305i 0.661930 + 0.749566i
\(451\) 146.199i 0.324167i
\(452\) 353.915 + 78.0822i 0.782997 + 0.172748i
\(453\) 412.405 + 130.321i 0.910386 + 0.287684i
\(454\) −474.453 + 138.553i −1.04505 + 0.305183i
\(455\) −72.9225 545.030i −0.160269 1.19787i
\(456\) −215.535 52.5378i −0.472666 0.115214i
\(457\) −124.480 + 124.480i −0.272385 + 0.272385i −0.830060 0.557674i \(-0.811694\pi\)
0.557674 + 0.830060i \(0.311694\pi\)
\(458\) 276.171 504.002i 0.602993 1.10044i
\(459\) 13.2685 + 1.77275i 0.0289074 + 0.00386220i
\(460\) −42.7417 + 506.782i −0.0929168 + 1.10170i
\(461\) 355.022i 0.770114i −0.922893 0.385057i \(-0.874182\pi\)
0.922893 0.385057i \(-0.125818\pi\)
\(462\) 273.548 + 6.00434i 0.592096 + 0.0129964i
\(463\) 244.127 244.127i 0.527272 0.527272i −0.392486 0.919758i \(-0.628385\pi\)
0.919758 + 0.392486i \(0.128385\pi\)
\(464\) −37.1689 + 80.1355i −0.0801054 + 0.172706i
\(465\) 711.780 + 124.431i 1.53071 + 0.267593i
\(466\) 4.11321 1.20117i 0.00882663 0.00257762i
\(467\) −184.217 + 184.217i −0.394468 + 0.394468i −0.876277 0.481808i \(-0.839980\pi\)
0.481808 + 0.876277i \(0.339980\pi\)
\(468\) 282.809 259.011i 0.604292 0.553443i
\(469\) 468.831i 0.999639i
\(470\) 360.660 159.822i 0.767362 0.340046i
\(471\) 316.764 + 609.449i 0.672535 + 1.29395i
\(472\) −196.820 + 13.2028i −0.416992 + 0.0279721i
\(473\) 6.40939 6.40939i 0.0135505 0.0135505i
\(474\) 242.513 232.095i 0.511631 0.489653i
\(475\) 222.962 60.7500i 0.469393 0.127895i
\(476\) −17.2566 + 11.0184i −0.0362533 + 0.0231479i
\(477\) 660.512 115.595i 1.38472 0.242337i
\(478\) 260.866 476.071i 0.545744 0.995965i
\(479\) 178.759i 0.373192i −0.982437 0.186596i \(-0.940254\pi\)
0.982437 0.186596i \(-0.0597455\pi\)
\(480\) −214.026 429.643i −0.445888 0.895089i
\(481\) 51.1402 0.106321
\(482\) −214.897 117.754i −0.445844 0.244302i
\(483\) −750.983 237.313i −1.55483 0.491330i
\(484\) −218.469 342.157i −0.451383 0.706936i
\(485\) −105.748 + 138.416i −0.218038 + 0.285395i
\(486\) −435.301 216.124i −0.895680 0.444699i
\(487\) −11.7814 11.7814i −0.0241918 0.0241918i 0.694907 0.719099i \(-0.255445\pi\)
−0.719099 + 0.694907i \(0.755445\pi\)
\(488\) −24.7235 368.563i −0.0506629 0.755253i
\(489\) 37.9703 + 73.0543i 0.0776488 + 0.149395i
\(490\) 207.304 537.237i 0.423069 1.09640i
\(491\) −741.254 −1.50968 −0.754842 0.655907i \(-0.772286\pi\)
−0.754842 + 0.655907i \(0.772286\pi\)
\(492\) −102.944 383.607i −0.209235 0.779689i
\(493\) −1.93554 1.93554i −0.00392605 0.00392605i
\(494\) −55.2051 189.041i −0.111751 0.382674i
\(495\) −176.388 91.6365i −0.356339 0.185124i
\(496\) −699.197 324.305i −1.40967 0.653841i
\(497\) −850.137 850.137i −1.71054 1.71054i
\(498\) 394.727 + 8.66419i 0.792625 + 0.0173980i
\(499\) −659.372 −1.32139 −0.660693 0.750656i \(-0.729738\pi\)
−0.660693 + 0.750656i \(0.729738\pi\)
\(500\) 411.669 + 283.775i 0.823339 + 0.567551i
\(501\) −359.659 691.978i −0.717881 1.38119i
\(502\) −587.746 322.058i −1.17081 0.641550i
\(503\) 138.296 + 138.296i 0.274942 + 0.274942i 0.831086 0.556144i \(-0.187720\pi\)
−0.556144 + 0.831086i \(0.687720\pi\)
\(504\) 721.980 176.859i 1.43250 0.350911i
\(505\) −8.13472 60.7998i −0.0161084 0.120396i
\(506\) −62.9727 215.640i −0.124452 0.426166i
\(507\) −158.824 50.1889i −0.313263 0.0989919i
\(508\) −44.1306 + 200.026i −0.0868712 + 0.393751i
\(509\) 0.354751 0.000696957 0.000348478 1.00000i \(-0.499889\pi\)
0.000348478 1.00000i \(0.499889\pi\)
\(510\) 14.7822 1.64848i 0.0289846 0.00323230i
\(511\) 1054.32i 2.06325i
\(512\) 102.191 + 501.698i 0.199592 + 0.979879i
\(513\) −198.294 + 151.553i −0.386538 + 0.295424i
\(514\) −9.01444 30.8685i −0.0175378 0.0600555i
\(515\) 91.1499 119.308i 0.176990 0.231666i
\(516\) 12.3043 21.3304i 0.0238455 0.0413380i
\(517\) −123.213 + 123.213i −0.238323 + 0.238323i
\(518\) 86.9300 + 47.6338i 0.167819 + 0.0919571i
\(519\) 389.249 + 748.909i 0.749997 + 1.44298i
\(520\) 235.441 355.151i 0.452771 0.682983i
\(521\) 594.299i 1.14069i 0.821406 + 0.570345i \(0.193190\pi\)
−0.821406 + 0.570345i \(0.806810\pi\)
\(522\) 43.8851 + 89.1631i 0.0840711 + 0.170810i
\(523\) 543.498 543.498i 1.03919 1.03919i 0.0399922 0.999200i \(-0.487267\pi\)
0.999200 0.0399922i \(-0.0127333\pi\)
\(524\) −169.686 265.755i −0.323829 0.507166i
\(525\) −569.001 + 525.144i −1.08381 + 1.00027i
\(526\) 167.575 + 573.834i 0.318584 + 1.09094i
\(527\) 16.8879 16.8879i 0.0320454 0.0320454i
\(528\) 156.520 + 143.021i 0.296439 + 0.270873i
\(529\) 117.636i 0.222375i
\(530\) 681.172 301.852i 1.28523 0.569532i
\(531\) −127.521 + 181.623i −0.240152 + 0.342040i
\(532\) 82.2396 372.759i 0.154586 0.700674i
\(533\) 249.314 249.314i 0.467756 0.467756i
\(534\) 143.924 137.741i 0.269520 0.257942i
\(535\) −332.384 + 435.065i −0.621279 + 0.813206i
\(536\) −239.118 + 273.506i −0.446116 + 0.510272i
\(537\) −478.160 151.100i −0.890428 0.281377i
\(538\) 305.980 + 167.663i 0.568736 + 0.311642i
\(539\) 254.359i 0.471908i
\(540\) −527.340 116.241i −0.976556 0.215262i
\(541\) −446.978 −0.826206 −0.413103 0.910684i \(-0.635555\pi\)
−0.413103 + 0.910684i \(0.635555\pi\)
\(542\) 182.283 332.661i 0.336316 0.613766i
\(543\) 41.9159 132.644i 0.0771932 0.244280i
\(544\) −15.6868 2.37349i −0.0288361 0.00436303i
\(545\) −41.4579 309.861i −0.0760695 0.568551i
\(546\) 456.243 + 476.721i 0.835610 + 0.873116i
\(547\) 492.299 + 492.299i 0.899998 + 0.899998i 0.995435 0.0954376i \(-0.0304250\pi\)
−0.0954376 + 0.995435i \(0.530425\pi\)
\(548\) −217.844 + 987.397i −0.397525 + 1.80182i
\(549\) −340.106 238.794i −0.619501 0.434962i
\(550\) −214.773 51.4810i −0.390496 0.0936017i
\(551\) 51.0338 0.0926203
\(552\) −317.070 521.468i −0.574403 0.944688i
\(553\) 408.419 + 408.419i 0.738552 + 0.738552i
\(554\) −127.244 + 37.1587i −0.229682 + 0.0670734i
\(555\) −41.3902 58.9272i −0.0745769 0.106175i
\(556\) 33.3436 + 52.2212i 0.0599704 + 0.0939231i
\(557\) 367.436 + 367.436i 0.659670 + 0.659670i 0.955302 0.295632i \(-0.0955301\pi\)
−0.295632 + 0.955302i \(0.595530\pi\)
\(558\) −777.964 + 382.905i −1.39420 + 0.686210i
\(559\) 21.8599 0.0391053
\(560\) 731.011 384.401i 1.30538 0.686431i
\(561\) −5.82955 + 3.02993i −0.0103914 + 0.00540095i
\(562\) −255.799 + 466.825i −0.455159 + 0.830650i
\(563\) −129.412 129.412i −0.229861 0.229861i 0.582773 0.812635i \(-0.301968\pi\)
−0.812635 + 0.582773i \(0.801968\pi\)
\(564\) −236.535 + 410.051i −0.419389 + 0.727041i
\(565\) 275.031 359.995i 0.486781 0.637159i
\(566\) 1005.62 293.667i 1.77671 0.518847i
\(567\) 355.350 756.986i 0.626720 1.33507i
\(568\) −62.3547 929.548i −0.109779 1.63653i
\(569\) 658.832 1.15788 0.578939 0.815371i \(-0.303467\pi\)
0.578939 + 0.815371i \(0.303467\pi\)
\(570\) −173.146 + 216.611i −0.303765 + 0.380019i
\(571\) 153.311i 0.268496i 0.990948 + 0.134248i \(0.0428618\pi\)
−0.990948 + 0.134248i \(0.957138\pi\)
\(572\) −40.5498 + 183.796i −0.0708913 + 0.321321i
\(573\) −270.545 + 856.149i −0.472156 + 1.49415i
\(574\) 656.012 191.573i 1.14288 0.333751i
\(575\) 551.889 + 315.542i 0.959806 + 0.548768i
\(576\) 511.391 + 265.057i 0.887832 + 0.460168i
\(577\) 379.812 379.812i 0.658252 0.658252i −0.296714 0.954966i \(-0.595891\pi\)
0.954966 + 0.296714i \(0.0958909\pi\)
\(578\) −277.517 + 506.459i −0.480133 + 0.876226i
\(579\) 779.416 405.105i 1.34614 0.699662i
\(580\) 71.2406 + 84.3642i 0.122829 + 0.145456i
\(581\) 679.356i 1.16929i
\(582\) 4.58700 208.977i 0.00788144 0.359066i
\(583\) −232.710 + 232.710i −0.399159 + 0.399159i
\(584\) −537.738 + 615.069i −0.920784 + 1.05320i
\(585\) −144.526 457.062i −0.247053 0.781302i
\(586\) −136.559 + 39.8788i −0.233035 + 0.0680525i
\(587\) −80.3753 + 80.3753i −0.136925 + 0.136925i −0.772247 0.635322i \(-0.780867\pi\)
0.635322 + 0.772247i \(0.280867\pi\)
\(588\) 179.102 + 667.401i 0.304595 + 1.13504i
\(589\) 445.279i 0.755992i
\(590\) −88.7678 + 230.046i −0.150454 + 0.389908i
\(591\) −20.0270 + 10.4091i −0.0338866 + 0.0176127i
\(592\) 26.4184 + 72.1255i 0.0446256 + 0.121834i
\(593\) 417.804 417.804i 0.704559 0.704559i −0.260826 0.965386i \(-0.583995\pi\)
0.965386 + 0.260826i \(0.0839950\pi\)
\(594\) 235.800 35.9529i 0.396969 0.0605268i
\(595\) 3.39395 + 25.3667i 0.00570412 + 0.0426332i
\(596\) −451.662 707.373i −0.757822 1.18687i
\(597\) 55.6791 176.198i 0.0932648 0.295140i
\(598\) 260.344 475.118i 0.435357 0.794512i
\(599\) 806.349i 1.34616i 0.739570 + 0.673080i \(0.235029\pi\)
−0.739570 + 0.673080i \(0.764971\pi\)
\(600\) −599.783 + 16.1493i −0.999638 + 0.0269154i
\(601\) 687.797 1.14442 0.572211 0.820107i \(-0.306086\pi\)
0.572211 + 0.820107i \(0.306086\pi\)
\(602\) 37.1582 + 20.3610i 0.0617246 + 0.0338223i
\(603\) 70.4560 + 402.588i 0.116842 + 0.667641i
\(604\) −486.046 + 310.343i −0.804712 + 0.513813i
\(605\) −502.963 + 67.2941i −0.831344 + 0.111230i
\(606\) 50.8953 + 53.1797i 0.0839856 + 0.0877553i
\(607\) −232.895 232.895i −0.383682 0.383682i 0.488745 0.872427i \(-0.337455\pi\)
−0.872427 + 0.488745i \(0.837455\pi\)
\(608\) 238.095 175.514i 0.391604 0.288675i
\(609\) −151.726 + 78.8600i −0.249139 + 0.129491i
\(610\) −430.781 166.226i −0.706199 0.272501i
\(611\) −420.230 −0.687774
\(612\) −13.1625 + 12.0549i −0.0215073 + 0.0196975i
\(613\) −575.631 575.631i −0.939038 0.939038i 0.0592074 0.998246i \(-0.481143\pi\)
−0.998246 + 0.0592074i \(0.981143\pi\)
\(614\) −234.339 802.458i −0.381660 1.30693i
\(615\) −489.058 85.4951i −0.795216 0.139016i
\(616\) −240.122 + 274.653i −0.389808 + 0.445865i
\(617\) 475.711 + 475.711i 0.771007 + 0.771007i 0.978283 0.207275i \(-0.0664596\pi\)
−0.207275 + 0.978283i \(0.566460\pi\)
\(618\) −3.95377 + 180.127i −0.00639768 + 0.291468i
\(619\) −215.170 −0.347610 −0.173805 0.984780i \(-0.555606\pi\)
−0.173805 + 0.984780i \(0.555606\pi\)
\(620\) −736.093 + 621.587i −1.18725 + 1.00256i
\(621\) −680.537 90.9238i −1.09587 0.146415i
\(622\) 295.610 + 161.981i 0.475258 + 0.260420i
\(623\) 242.383 + 242.383i 0.389058 + 0.389058i
\(624\) 23.0193 + 510.807i 0.0368899 + 0.818601i
\(625\) 538.615 317.048i 0.861783 0.507277i
\(626\) −110.860 379.622i −0.177092 0.606424i
\(627\) 36.9083 116.798i 0.0588649 0.186280i
\(628\) −894.298 197.304i −1.42404 0.314178i
\(629\) −2.38016 −0.00378405
\(630\) 180.052 911.546i 0.285797 1.44690i
\(631\) 710.672i 1.12626i −0.826367 0.563132i \(-0.809596\pi\)
0.826367 0.563132i \(-0.190404\pi\)
\(632\) 29.9562 + 446.569i 0.0473990 + 0.706597i
\(633\) −529.005 167.167i −0.835711 0.264087i
\(634\) 133.230 + 456.225i 0.210142 + 0.719598i
\(635\) 203.462 + 155.442i 0.320413 + 0.244791i
\(636\) −446.739 + 774.456i −0.702420 + 1.21770i
\(637\) −433.758 + 433.758i −0.680939 + 0.680939i
\(638\) −42.7733 23.4379i −0.0670428 0.0367364i
\(639\) −857.776 602.259i −1.34237 0.942502i
\(640\) 622.512 + 148.587i 0.972676 + 0.232168i
\(641\) 445.381i 0.694822i −0.937713 0.347411i \(-0.887061\pi\)
0.937713 0.347411i \(-0.112939\pi\)
\(642\) 14.4177 656.847i 0.0224574 1.02313i
\(643\) 310.249 310.249i 0.482502 0.482502i −0.423428 0.905930i \(-0.639173\pi\)
0.905930 + 0.423428i \(0.139173\pi\)
\(644\) 885.083 565.130i 1.37435 0.877531i
\(645\) −17.6922 25.1884i −0.0274298 0.0390518i
\(646\) 2.56935 + 8.79833i 0.00397732 + 0.0136197i
\(647\) 797.318 797.318i 1.23233 1.23233i 0.269265 0.963066i \(-0.413219\pi\)
0.963066 0.269265i \(-0.0867806\pi\)
\(648\) 593.390 260.369i 0.915725 0.401805i
\(649\) 108.917i 0.167822i
\(650\) −278.461 454.042i −0.428402 0.698527i
\(651\) −688.068 1323.83i −1.05694 2.03354i
\(652\) −107.199 23.6507i −0.164416 0.0362741i
\(653\) 686.842 686.842i 1.05183 1.05183i 0.0532438 0.998582i \(-0.483044\pi\)
0.998582 0.0532438i \(-0.0169560\pi\)
\(654\) 259.383 + 271.026i 0.396610 + 0.414412i
\(655\) −390.654 + 52.2677i −0.596418 + 0.0797980i
\(656\) 480.412 + 222.827i 0.732335 + 0.339676i
\(657\) 158.444 + 905.353i 0.241163 + 1.37801i
\(658\) −714.322 391.416i −1.08560 0.594858i
\(659\) 633.604i 0.961463i −0.876868 0.480732i \(-0.840371\pi\)
0.876868 0.480732i \(-0.159629\pi\)
\(660\) 244.601 102.030i 0.370607 0.154591i
\(661\) 893.706 1.35205 0.676026 0.736878i \(-0.263701\pi\)
0.676026 + 0.736878i \(0.263701\pi\)
\(662\) −267.709 + 488.560i −0.404394 + 0.738006i
\(663\) −15.1081 4.77419i −0.0227875 0.00720089i
\(664\) −346.493 + 396.322i −0.521827 + 0.596870i
\(665\) −379.162 289.675i −0.570169 0.435601i
\(666\) 81.8057 + 27.8395i 0.122831 + 0.0418011i
\(667\) 99.2732 + 99.2732i 0.148835 + 0.148835i
\(668\) 1015.40 + 224.022i 1.52006 + 0.335362i
\(669\) −404.161 777.601i −0.604128 1.16233i
\(670\) 183.981 + 415.180i 0.274599 + 0.619671i
\(671\) 203.956 0.303959
\(672\) −436.654 + 889.729i −0.649782 + 1.32400i
\(673\) 656.768 + 656.768i 0.975881 + 0.975881i 0.999716 0.0238351i \(-0.00758766\pi\)
−0.0238351 + 0.999716i \(0.507588\pi\)
\(674\) 1007.61 294.250i 1.49498 0.436573i
\(675\) −409.686 + 536.454i −0.606942 + 0.794746i
\(676\) 187.185 119.519i 0.276901 0.176803i
\(677\) −119.083 119.083i −0.175898 0.175898i 0.613667 0.789565i \(-0.289694\pi\)
−0.789565 + 0.613667i \(0.789694\pi\)
\(678\) −11.9299 + 543.508i −0.0175957 + 0.801634i
\(679\) 359.665 0.529698
\(680\) −10.9579 + 16.5294i −0.0161145 + 0.0243080i
\(681\) −341.922 657.853i −0.502088 0.966010i
\(682\) 204.499 373.205i 0.299853 0.547221i
\(683\) −894.185 894.185i −1.30920 1.30920i −0.921991 0.387211i \(-0.873439\pi\)
−0.387211 0.921991i \(-0.626561\pi\)
\(684\) 14.6014 332.449i 0.0213471 0.486036i
\(685\) 1004.36 + 767.317i 1.46622 + 1.12017i
\(686\) −170.148 + 49.6878i −0.248029 + 0.0724312i
\(687\) 821.996 + 259.753i 1.19650 + 0.378097i
\(688\) 11.2925 + 30.8300i 0.0164135 + 0.0448111i
\(689\) −793.680 −1.15193
\(690\) −758.171 + 84.5497i −1.09880 + 0.122536i
\(691\) 957.776i 1.38607i −0.720903 0.693036i \(-0.756272\pi\)
0.720903 0.693036i \(-0.243728\pi\)
\(692\) −1098.94 242.453i −1.58806 0.350365i
\(693\) 70.7516 + 404.277i 0.102095 + 0.583372i
\(694\) 434.892 127.000i 0.626646 0.182998i
\(695\) 76.7640 10.2707i 0.110452 0.0147779i
\(696\) −128.734 31.3796i −0.184963 0.0450857i
\(697\) −11.6036 + 11.6036i −0.0166478 + 0.0166478i
\(698\) −379.829 + 693.175i −0.544167 + 0.993087i
\(699\) 2.96425 + 5.70317i 0.00424070 + 0.00815905i
\(700\) −50.4281 1031.17i −0.0720401 1.47309i
\(701\) 236.408i 0.337244i −0.985681 0.168622i \(-0.946068\pi\)
0.985681 0.168622i \(-0.0539317\pi\)
\(702\) 463.420 + 340.799i 0.660143 + 0.485469i
\(703\) 31.3785 31.3785i 0.0446352 0.0446352i
\(704\) −280.163 + 37.7570i −0.397959 + 0.0536322i
\(705\) 340.111 + 484.217i 0.482427 + 0.686833i
\(706\) −388.555 + 113.469i −0.550361 + 0.160720i
\(707\) −89.5606 + 89.5606i −0.126677 + 0.126677i
\(708\) −76.6916 285.782i −0.108322 0.403647i
\(709\) 3.07348i 0.00433495i −0.999998 0.00216747i \(-0.999310\pi\)
0.999998 0.00216747i \(-0.000689929\pi\)
\(710\) −1086.47 419.235i −1.53023 0.590472i
\(711\) 412.089 + 289.334i 0.579591 + 0.406940i
\(712\) 17.7780 + 265.024i 0.0249691 + 0.372225i
\(713\) −866.177 + 866.177i −1.21483 + 1.21483i
\(714\) −21.2344 22.1875i −0.0297401 0.0310750i
\(715\) 186.953 + 142.830i 0.261473 + 0.199762i
\(716\) 563.542 359.825i 0.787070 0.502549i
\(717\) 776.442 + 245.358i 1.08290 + 0.342200i
\(718\) −373.762 + 682.103i −0.520560 + 0.950004i
\(719\) 893.990i 1.24338i 0.783264 + 0.621690i \(0.213553\pi\)
−0.783264 + 0.621690i \(0.786447\pi\)
\(720\) 569.956 439.944i 0.791605 0.611033i
\(721\) −310.013 −0.429977
\(722\) 483.310 + 264.832i 0.669404 + 0.366803i
\(723\) 110.753 350.483i 0.153186 0.484762i
\(724\) 99.8175 + 156.330i 0.137869 + 0.215925i
\(725\) 133.170 36.2846i 0.183683 0.0500477i
\(726\) 439.926 421.029i 0.605959 0.579929i
\(727\) −319.871 319.871i −0.439988 0.439988i 0.452020 0.892008i \(-0.350704\pi\)
−0.892008 + 0.452020i \(0.850704\pi\)
\(728\) −877.846 + 58.8866i −1.20583 + 0.0808881i
\(729\) 191.381 703.430i 0.262526 0.964925i
\(730\) 413.743 + 933.670i 0.566772 + 1.27900i
\(731\) −1.01740 −0.00139179
\(732\) 535.153 143.612i 0.731083 0.196191i
\(733\) −577.382 577.382i −0.787698 0.787698i 0.193419 0.981116i \(-0.438042\pi\)
−0.981116 + 0.193419i \(0.938042\pi\)
\(734\) 286.635 + 981.537i 0.390511 + 1.33724i
\(735\) 850.865 + 148.745i 1.15764 + 0.202374i
\(736\) 804.572 + 121.735i 1.09317 + 0.165401i
\(737\) −141.838 141.838i −0.192454 0.192454i
\(738\) 534.532 263.091i 0.724298 0.356492i
\(739\) −1125.12 −1.52248 −0.761242 0.648468i \(-0.775410\pi\)
−0.761242 + 0.648468i \(0.775410\pi\)
\(740\) 95.6748 + 8.06917i 0.129290 + 0.0109043i
\(741\) 262.115 136.235i 0.353731 0.183853i
\(742\) −1349.13 739.260i −1.81823 0.996308i
\(743\) 63.1774 + 63.1774i 0.0850302 + 0.0850302i 0.748343 0.663312i \(-0.230850\pi\)
−0.663312 + 0.748343i \(0.730850\pi\)
\(744\) 273.793 1123.23i 0.368001 1.50972i
\(745\) −1039.82 + 139.123i −1.39573 + 0.186743i
\(746\) 83.0237 + 284.302i 0.111292 + 0.381101i
\(747\) 102.094 + 583.367i 0.136672 + 0.780947i
\(748\) 1.88727 8.55421i 0.00252308 0.0114361i
\(749\) 1130.49 1.50933
\(750\) −297.807 + 688.339i −0.397076 + 0.917786i
\(751\) 705.259i 0.939093i 0.882908 + 0.469547i \(0.155583\pi\)
−0.882908 + 0.469547i \(0.844417\pi\)
\(752\) −217.085 592.670i −0.288677 0.788125i
\(753\) 302.912 958.576i 0.402274 1.27301i
\(754\) −32.9728 112.910i −0.0437304 0.149748i
\(755\) 95.5936 + 714.477i 0.126614 + 0.946327i
\(756\) 470.306 + 1010.95i 0.622098 + 1.33723i
\(757\) −555.302 + 555.302i −0.733556 + 0.733556i −0.971322 0.237766i \(-0.923585\pi\)
0.237766 + 0.971322i \(0.423585\pi\)
\(758\) 70.3938 + 38.5727i 0.0928679 + 0.0508874i
\(759\) 298.996 155.404i 0.393934 0.204749i
\(760\) −73.4516 362.375i −0.0966468 0.476809i
\(761\) 1189.64i 1.56326i 0.623745 + 0.781628i \(0.285610\pi\)
−0.623745 + 0.781628i \(0.714390\pi\)
\(762\) −307.180 6.74255i −0.403123 0.00884849i
\(763\) −456.438 + 456.438i −0.598214 + 0.598214i
\(764\) −644.270 1009.03i −0.843285 1.32072i
\(765\) 6.72652 + 21.2725i 0.00879284 + 0.0278072i
\(766\) −270.028 924.666i −0.352516 1.20714i
\(767\) 185.736 185.736i 0.242159 0.242159i
\(768\) −708.524 + 296.341i −0.922557 + 0.385861i
\(769\) 900.882i 1.17150i −0.810492 0.585749i \(-0.800800\pi\)
0.810492 0.585749i \(-0.199200\pi\)
\(770\) 184.753 + 416.922i 0.239939 + 0.541457i
\(771\) 42.8007 22.2459i 0.0555133 0.0288533i
\(772\) −252.329 + 1143.70i −0.326851 + 1.48148i
\(773\) 464.010 464.010i 0.600272 0.600272i −0.340113 0.940385i \(-0.610465\pi\)
0.940385 + 0.340113i \(0.110465\pi\)
\(774\) 34.9678 + 11.9000i 0.0451781 + 0.0153747i
\(775\) 316.590 + 1161.93i 0.408503 + 1.49927i
\(776\) 209.821 + 183.440i 0.270387 + 0.236392i
\(777\) −44.8020 + 141.777i −0.0576602 + 0.182468i
\(778\) −172.591 94.5724i −0.221840 0.121558i
\(779\) 305.947i 0.392744i
\(780\) 591.110 + 243.126i 0.757833 + 0.311700i
\(781\) 514.395 0.658636
\(782\) −12.1169 + 22.1129i −0.0154947 + 0.0282774i
\(783\) −118.437 + 90.5189i −0.151260 + 0.115605i
\(784\) −835.823 387.676i −1.06610 0.494485i
\(785\) −694.969 + 909.662i −0.885311 + 1.15880i
\(786\) 341.693 327.015i 0.434724 0.416050i
\(787\) 511.685 + 511.685i 0.650172 + 0.650172i 0.953034 0.302862i \(-0.0979422\pi\)
−0.302862 + 0.953034i \(0.597942\pi\)
\(788\) 6.48355 29.3873i 0.00822786 0.0372935i
\(789\) −795.650 + 413.542i −1.00843 + 0.524135i
\(790\) 521.955 + 201.407i 0.660703 + 0.254946i
\(791\) −935.420 −1.18258
\(792\) −164.919 + 271.932i −0.208231 + 0.343348i
\(793\) 347.807 + 347.807i 0.438596 + 0.438596i
\(794\) −878.200 + 256.458i −1.10604 + 0.322995i
\(795\) 642.362 + 914.532i 0.808002 + 1.15035i
\(796\) 132.593 + 207.661i 0.166574 + 0.260881i
\(797\) −606.760 606.760i −0.761305 0.761305i 0.215253 0.976558i \(-0.430942\pi\)
−0.976558 + 0.215253i \(0.930942\pi\)
\(798\) 572.446 + 12.5651i 0.717351 + 0.0157457i
\(799\) 19.5583 0.0244785
\(800\) 496.508 627.279i 0.620635 0.784099i
\(801\) 244.561 + 171.711i 0.305320 + 0.214370i
\(802\) 623.062 1137.07i 0.776885 1.41779i
\(803\) −318.971 318.971i −0.397224 0.397224i
\(804\) −472.037 272.291i −0.587111 0.338671i
\(805\) −174.075 1301.05i −0.216242 1.61621i
\(806\) 985.160 287.693i 1.22228 0.356939i
\(807\) −157.696 + 499.034i −0.195410 + 0.618382i
\(808\) −97.9264 + 6.56897i −0.121196 + 0.00812992i
\(809\) −9.70812 −0.0120001 −0.00600007 0.999982i \(-0.501910\pi\)
−0.00600007 + 0.999982i \(0.501910\pi\)
\(810\) 17.6244 809.808i 0.0217585 0.999763i
\(811\) 109.279i 0.134747i 0.997728 + 0.0673733i \(0.0214618\pi\)
−0.997728 + 0.0673733i \(0.978538\pi\)
\(812\) 49.1199 222.640i 0.0604925 0.274188i
\(813\) 542.549 + 171.447i 0.667342 + 0.210882i
\(814\) −40.7104 + 11.8886i −0.0500128 + 0.0146051i
\(815\) −83.3055 + 109.040i −0.102215 + 0.133792i
\(816\) −1.07136 23.7739i −0.00131294 0.0291347i
\(817\) 13.4127 13.4127i 0.0164171 0.0164171i
\(818\) 13.4165 24.4847i 0.0164016 0.0299324i
\(819\) −568.761 + 810.066i −0.694458 + 0.989092i
\(820\) 505.763 427.087i 0.616784 0.520837i
\(821\) 219.704i 0.267606i 0.991008 + 0.133803i \(0.0427189\pi\)
−0.991008 + 0.133803i \(0.957281\pi\)
\(822\) −1516.35 33.2836i −1.84471 0.0404910i
\(823\) −1.99663 + 1.99663i −0.00242604 + 0.00242604i −0.708319 0.705893i \(-0.750546\pi\)
0.705893 + 0.708319i \(0.250546\pi\)
\(824\) −180.855 158.117i −0.219484 0.191889i
\(825\) 13.2683 331.019i 0.0160828 0.401235i
\(826\) 488.721 142.720i 0.591672 0.172784i
\(827\) 917.802 917.802i 1.10980 1.10980i 0.116620 0.993177i \(-0.462794\pi\)
0.993177 0.116620i \(-0.0372061\pi\)
\(828\) 675.098 618.291i 0.815335 0.746728i
\(829\) 1134.07i 1.36800i 0.729482 + 0.684000i \(0.239761\pi\)
−0.729482 + 0.684000i \(0.760239\pi\)
\(830\) 266.597 + 601.613i 0.321201 + 0.724836i
\(831\) −91.7003 176.430i −0.110349 0.212311i
\(832\) −542.150 413.376i −0.651623 0.496846i
\(833\) 20.1879 20.1879i 0.0242352 0.0242352i
\(834\) −67.1432 + 64.2589i −0.0805074 + 0.0770491i
\(835\) 789.079 1032.84i 0.945005 1.23694i
\(836\) 87.8926 + 137.654i 0.105135 + 0.164657i
\(837\) −789.794 1033.38i −0.943601 1.23462i
\(838\) −305.416 + 557.374i −0.364458 + 0.665124i
\(839\) 624.895i 0.744809i 0.928070 + 0.372405i \(0.121467\pi\)
−0.928070 + 0.372405i \(0.878533\pi\)
\(840\) 778.334 + 963.854i 0.926588 + 1.14744i
\(841\) −810.519 −0.963756
\(842\) 99.9726 + 54.7805i 0.118732 + 0.0650600i
\(843\) −761.362 240.592i −0.903158 0.285400i
\(844\) 623.467 398.087i 0.738705 0.471667i
\(845\) −36.8148 275.158i −0.0435678 0.325630i
\(846\) −672.214 228.763i −0.794579 0.270405i
\(847\) 740.886 + 740.886i 0.874717 + 0.874717i
\(848\) −410.004 1119.36i −0.483496 1.32001i
\(849\) 724.713 + 1394.34i 0.853608 + 1.64233i
\(850\) 12.9601 + 21.1320i 0.0152472 + 0.0248612i
\(851\) 122.078 0.143452
\(852\) 1349.70 362.202i 1.58415 0.425119i
\(853\) −462.091 462.091i −0.541724 0.541724i 0.382310 0.924034i \(-0.375129\pi\)
−0.924034 + 0.382310i \(0.875129\pi\)
\(854\) 267.255 + 915.173i 0.312945 + 1.07163i
\(855\) −369.121 191.765i −0.431721 0.224286i
\(856\) 659.500 + 576.583i 0.770444 + 0.673578i
\(857\) −343.527 343.527i −0.400848 0.400848i 0.477684 0.878532i \(-0.341476\pi\)
−0.878532 + 0.477684i \(0.841476\pi\)
\(858\) −282.256 6.19546i −0.328969 0.00722082i
\(859\) 1108.16 1.29006 0.645028 0.764159i \(-0.276846\pi\)
0.645028 + 0.764159i \(0.276846\pi\)
\(860\) 40.8962 + 3.44916i 0.0475537 + 0.00401065i
\(861\) 472.765 + 909.594i 0.549089 + 1.05644i
\(862\) 256.726 + 140.674i 0.297826 + 0.163195i
\(863\) −247.757 247.757i −0.287089 0.287089i 0.548839 0.835928i \(-0.315070\pi\)
−0.835928 + 0.548839i \(0.815070\pi\)
\(864\) −241.249 + 829.636i −0.279223 + 0.960226i
\(865\) −853.998 + 1117.82i −0.987281 + 1.29228i
\(866\) 337.326 + 1155.12i 0.389522 + 1.33385i
\(867\) −826.002 261.019i −0.952713 0.301060i
\(868\) 1942.58 + 428.580i 2.23799 + 0.493756i
\(869\) −247.123 −0.284377
\(870\) −103.416 + 129.377i −0.118869 + 0.148709i
\(871\) 483.754i 0.555401i
\(872\) −499.073 + 33.4782i −0.572332 + 0.0383924i
\(873\) 308.846 54.0505i 0.353776 0.0619135i
\(874\) −131.781 451.263i −0.150779 0.516320i
\(875\) −1195.36 486.311i −1.36613 0.555784i
\(876\) −1061.53 612.338i −1.21180 0.699016i
\(877\) 477.322 477.322i 0.544266 0.544266i −0.380510 0.924777i \(-0.624252\pi\)
0.924777 + 0.380510i \(0.124252\pi\)
\(878\) −1192.20 653.271i −1.35786 0.744044i
\(879\) −98.4130 189.345i −0.111960 0.215410i
\(880\) −104.862 + 337.453i −0.119162 + 0.383469i
\(881\) 907.230i 1.02977i −0.857259 0.514886i \(-0.827834\pi\)
0.857259 0.514886i \(-0.172166\pi\)
\(882\) −929.982 + 457.727i −1.05440 + 0.518965i
\(883\) 55.2196 55.2196i 0.0625364 0.0625364i −0.675147 0.737683i \(-0.735920\pi\)
0.737683 + 0.675147i \(0.235920\pi\)
\(884\) 17.8059 11.3691i 0.0201424 0.0128610i
\(885\) −364.342 63.6927i −0.411685 0.0719692i
\(886\) −152.809 523.270i −0.172471 0.590599i
\(887\) −587.061 + 587.061i −0.661850 + 0.661850i −0.955816 0.293966i \(-0.905025\pi\)
0.293966 + 0.955816i \(0.405025\pi\)
\(888\) −98.4474 + 59.8594i −0.110864 + 0.0674092i
\(889\) 528.681i 0.594692i
\(890\) 309.764 + 119.529i 0.348049 + 0.134302i
\(891\) 121.510 + 336.522i 0.136374 + 0.377691i
\(892\) 1141.04 + 251.742i 1.27920 + 0.282222i
\(893\) −257.844 + 257.844i −0.288739 + 0.288739i
\(894\) 909.501 870.432i 1.01734 0.973637i
\(895\) −110.835 828.394i −0.123838 0.925580i
\(896\) −536.534 1207.65i −0.598810 1.34782i
\(897\) 774.888 + 244.867i 0.863867 + 0.272984i
\(898\) 294.310 + 161.269i 0.327740 + 0.179587i
\(899\) 265.955i 0.295834i
\(900\) −198.267 877.890i −0.220296 0.975433i
\(901\) 36.9394 0.0409982
\(902\) −140.510 + 256.426i −0.155776 + 0.284286i
\(903\) −19.1506 + 60.6027i −0.0212078 + 0.0671126i
\(904\) −545.703 477.093i −0.603654 0.527758i
\(905\) 229.801 30.7463i 0.253924 0.0339739i
\(906\) −598.086 624.931i −0.660139 0.689769i
\(907\) −570.349 570.349i −0.628831 0.628831i 0.318943 0.947774i \(-0.396672\pi\)
−0.947774 + 0.318943i \(0.896672\pi\)
\(908\) 965.325 + 212.974i 1.06313 + 0.234553i
\(909\) −63.4470 + 90.3654i −0.0697987 + 0.0994118i
\(910\) −395.917 + 1026.04i −0.435074 + 1.12751i
\(911\) 809.153 0.888203 0.444102 0.895976i \(-0.353523\pi\)
0.444102 + 0.895976i \(0.353523\pi\)
\(912\) 327.544 + 299.296i 0.359149 + 0.328175i
\(913\) −205.530 205.530i −0.225115 0.225115i
\(914\) 337.967 98.6954i 0.369767 0.107982i
\(915\) 119.270 682.262i 0.130350 0.745642i
\(916\) −968.776 + 618.569i −1.05762 + 0.675293i
\(917\) 575.450 + 575.450i 0.627535 + 0.627535i
\(918\) −21.5685 15.8614i −0.0234951 0.0172783i
\(919\) −683.390 −0.743623 −0.371812 0.928308i \(-0.621263\pi\)
−0.371812 + 0.928308i \(0.621263\pi\)
\(920\) 562.026 847.788i 0.610898 0.921509i
\(921\) 1112.65 578.303i 1.20809 0.627908i
\(922\) −341.206 + 622.689i −0.370071 + 0.675368i
\(923\) 877.198 + 877.198i 0.950377 + 0.950377i
\(924\) −474.018 273.434i −0.513006 0.295924i
\(925\) 59.5708 104.191i 0.0644009 0.112638i
\(926\) −662.811 + 193.559i −0.715778 + 0.209027i
\(927\) −266.210 + 46.5889i −0.287174 + 0.0502577i
\(928\) 142.209 104.831i 0.153242 0.112964i
\(929\) 533.625 0.574408 0.287204 0.957869i \(-0.407274\pi\)
0.287204 + 0.957869i \(0.407274\pi\)
\(930\) −1128.83 902.324i −1.21380 0.970241i
\(931\) 532.289i 0.571739i
\(932\) −8.36876 1.84635i −0.00897936 0.00198107i
\(933\) −152.352 + 482.122i −0.163292 + 0.516744i
\(934\) 500.153 146.058i 0.535496 0.156379i
\(935\) −8.70116 6.64757i −0.00930605 0.00710970i
\(936\) −744.962 + 182.489i −0.795899 + 0.194967i
\(937\) 757.665 757.665i 0.808607 0.808607i −0.175816 0.984423i \(-0.556256\pi\)
0.984423 + 0.175816i \(0.0562564\pi\)
\(938\) 450.585 822.303i 0.480368 0.876656i
\(939\) 526.364 273.580i 0.560558 0.291352i
\(940\) −786.179 66.3060i −0.836361 0.0705383i
\(941\) 1555.04i 1.65254i −0.563277 0.826268i \(-0.690460\pi\)
0.563277 0.826268i \(-0.309540\pi\)
\(942\) 30.1454 1373.38i 0.0320015 1.45794i
\(943\) 595.142 595.142i 0.631116 0.631116i
\(944\) 357.900 + 166.003i 0.379132 + 0.175851i
\(945\) 1393.74 0.259361i 1.47485 0.000274456i
\(946\) −17.4017 + 5.08176i −0.0183950 + 0.00537184i
\(947\) −385.141 + 385.141i −0.406696 + 0.406696i −0.880585 0.473889i \(-0.842850\pi\)
0.473889 + 0.880585i \(0.342850\pi\)
\(948\) −648.417 + 174.007i −0.683984 + 0.183552i
\(949\) 1087.88i 1.14635i
\(950\) −449.448 107.733i −0.473103 0.113403i
\(951\) −632.579 + 328.786i −0.665173 + 0.345726i
\(952\) 40.8566 2.74069i 0.0429166 0.00287888i
\(953\) −450.513 + 450.513i −0.472731 + 0.472731i −0.902797 0.430066i \(-0.858490\pi\)
0.430066 + 0.902797i \(0.358490\pi\)
\(954\) −1269.60 432.060i −1.33082 0.452893i
\(955\) −1483.25 + 198.452i −1.55314 + 0.207803i
\(956\) −915.088 + 584.289i −0.957205 + 0.611181i
\(957\) 22.0445 69.7606i 0.0230350 0.0728951i
\(958\) −171.802 + 313.533i −0.179334 + 0.327279i
\(959\) 2609.75i 2.72133i
\(960\) −37.5325 + 959.266i −0.0390963 + 0.999235i
\(961\) −1359.51 −1.41468
\(962\) −89.6971 49.1500i −0.0932403 0.0510915i
\(963\) 970.754 169.889i 1.00805 0.176417i
\(964\) 263.746 + 413.067i 0.273595 + 0.428493i
\(965\) 1163.35 + 888.786i 1.20555 + 0.921022i
\(966\) 1089.11 + 1137.99i 1.12744 + 1.17804i
\(967\) −577.404 577.404i −0.597108 0.597108i 0.342434 0.939542i \(-0.388749\pi\)
−0.939542 + 0.342434i \(0.888749\pi\)
\(968\) 54.3415 + 810.091i 0.0561379 + 0.836871i
\(969\) −12.1993 + 6.34065i −0.0125896 + 0.00654350i
\(970\) 318.506 141.142i 0.328357 0.145507i
\(971\) 983.651 1.01303 0.506514 0.862231i \(-0.330934\pi\)
0.506514 + 0.862231i \(0.330934\pi\)
\(972\) 555.780 + 797.429i 0.571790 + 0.820400i
\(973\) −113.077 113.077i −0.116214 0.116214i
\(974\) 9.34100 + 31.9868i 0.00959035 + 0.0328406i
\(975\) 587.113 541.860i 0.602167 0.555754i
\(976\) −310.856 + 670.201i −0.318500 + 0.686681i
\(977\) 734.412 + 734.412i 0.751702 + 0.751702i 0.974797 0.223095i \(-0.0716160\pi\)
−0.223095 + 0.974797i \(0.571616\pi\)
\(978\) 3.61351 164.626i 0.00369479 0.168329i
\(979\) −146.660 −0.149806
\(980\) −879.929 + 743.048i −0.897886 + 0.758212i
\(981\) −323.352 + 460.539i −0.329615 + 0.469459i
\(982\) 1300.12 + 712.407i 1.32395 + 0.725465i
\(983\) 421.808 + 421.808i 0.429103 + 0.429103i 0.888323 0.459220i \(-0.151871\pi\)
−0.459220 + 0.888323i \(0.651871\pi\)
\(984\) −188.121 + 771.762i −0.191180 + 0.784311i
\(985\) −29.8921 22.8372i −0.0303473 0.0231850i
\(986\) 1.53462 + 5.25504i 0.00155640 + 0.00532966i
\(987\) 368.147 1165.01i 0.372996 1.18036i
\(988\) −84.8574 + 384.624i −0.0858881 + 0.389296i
\(989\) 52.1821 0.0527625
\(990\) 221.304 + 330.248i 0.223539 + 0.333584i
\(991\) 1077.21i 1.08699i −0.839411 0.543496i \(-0.817100\pi\)
0.839411 0.543496i \(-0.182900\pi\)
\(992\) 914.667 + 1240.80i 0.922044 + 1.25081i
\(993\) −796.810 251.794i −0.802427 0.253569i
\(994\) 674.040 + 2308.14i 0.678109 + 2.32208i
\(995\) 305.257 40.8420i 0.306791 0.0410472i
\(996\) −684.002 394.562i −0.686749 0.396147i
\(997\) −999.351 + 999.351i −1.00236 + 1.00236i −0.00236078 + 0.999997i \(0.500751\pi\)
−0.999997 + 0.00236078i \(0.999249\pi\)
\(998\) 1156.50 + 633.711i 1.15882 + 0.634981i
\(999\) −17.1654 + 128.478i −0.0171826 + 0.128607i
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 60.3.l.a.23.4 40
3.2 odd 2 inner 60.3.l.a.23.17 yes 40
4.3 odd 2 inner 60.3.l.a.23.7 yes 40
5.2 odd 4 inner 60.3.l.a.47.14 yes 40
5.3 odd 4 300.3.l.g.107.7 40
5.4 even 2 300.3.l.g.143.17 40
12.11 even 2 inner 60.3.l.a.23.14 yes 40
15.2 even 4 inner 60.3.l.a.47.7 yes 40
15.8 even 4 300.3.l.g.107.14 40
15.14 odd 2 300.3.l.g.143.4 40
20.3 even 4 300.3.l.g.107.4 40
20.7 even 4 inner 60.3.l.a.47.17 yes 40
20.19 odd 2 300.3.l.g.143.14 40
60.23 odd 4 300.3.l.g.107.17 40
60.47 odd 4 inner 60.3.l.a.47.4 yes 40
60.59 even 2 300.3.l.g.143.7 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
60.3.l.a.23.4 40 1.1 even 1 trivial
60.3.l.a.23.7 yes 40 4.3 odd 2 inner
60.3.l.a.23.14 yes 40 12.11 even 2 inner
60.3.l.a.23.17 yes 40 3.2 odd 2 inner
60.3.l.a.47.4 yes 40 60.47 odd 4 inner
60.3.l.a.47.7 yes 40 15.2 even 4 inner
60.3.l.a.47.14 yes 40 5.2 odd 4 inner
60.3.l.a.47.17 yes 40 20.7 even 4 inner
300.3.l.g.107.4 40 20.3 even 4
300.3.l.g.107.7 40 5.3 odd 4
300.3.l.g.107.14 40 15.8 even 4
300.3.l.g.107.17 40 60.23 odd 4
300.3.l.g.143.4 40 15.14 odd 2
300.3.l.g.143.7 40 60.59 even 2
300.3.l.g.143.14 40 20.19 odd 2
300.3.l.g.143.17 40 5.4 even 2