Properties

Label 429.2.bd.a.76.5
Level $429$
Weight $2$
Character 429.76
Analytic conductor $3.426$
Analytic rank $0$
Dimension $56$
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] = [429,2,Mod(76,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 6, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.76");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.bd (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 76.5
Character \(\chi\) \(=\) 429.76
Dual form 429.2.bd.a.175.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.42470 - 0.381747i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.151984 + 0.0877479i) q^{4} +(-0.971227 - 0.971227i) q^{5} +(0.381747 + 1.42470i) q^{6} +(4.17142 - 1.11773i) q^{7} +(1.90287 + 1.90287i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-1.42470 - 0.381747i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.151984 + 0.0877479i) q^{4} +(-0.971227 - 0.971227i) q^{5} +(0.381747 + 1.42470i) q^{6} +(4.17142 - 1.11773i) q^{7} +(1.90287 + 1.90287i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.01294 + 1.75447i) q^{10} +(1.01743 + 3.15671i) q^{11} -0.175496i q^{12} +(3.58322 + 0.400646i) q^{13} -6.36970 q^{14} +(-0.355494 + 1.32672i) q^{15} +(-2.16010 - 3.74140i) q^{16} +(-0.301427 + 0.522088i) q^{17} +(1.04295 - 1.04295i) q^{18} +(-0.159121 - 0.593849i) q^{19} +(-0.0623876 - 0.232834i) q^{20} +(-3.05369 - 3.05369i) q^{21} +(-0.244469 - 4.88576i) q^{22} +(1.91532 - 1.10581i) q^{23} +(0.696499 - 2.59937i) q^{24} -3.11344i q^{25} +(-4.95207 - 1.93868i) q^{26} +1.00000 q^{27} +(0.732066 + 0.196156i) q^{28} +(4.74047 - 2.73691i) q^{29} +(1.01294 - 1.75447i) q^{30} +(-3.56405 - 3.56405i) q^{31} +(0.256222 + 0.956235i) q^{32} +(2.22508 - 2.45948i) q^{33} +(0.628748 - 0.628748i) q^{34} +(-5.13696 - 2.96583i) q^{35} +(-0.151984 + 0.0877479i) q^{36} +(10.4857 + 2.80963i) q^{37} +0.906800i q^{38} +(-1.44464 - 3.30348i) q^{39} -3.69624i q^{40} +(-4.48549 - 1.20188i) q^{41} +(3.18485 + 5.51632i) q^{42} +(-2.00257 + 3.46855i) q^{43} +(-0.122362 + 0.569046i) q^{44} +(1.32672 - 0.355494i) q^{45} +(-3.15090 + 0.844280i) q^{46} +(-1.15089 + 1.15089i) q^{47} +(-2.16010 + 3.74140i) q^{48} +(10.0892 - 5.82501i) q^{49} +(-1.18854 + 4.43571i) q^{50} +0.602855 q^{51} +(0.509436 + 0.375312i) q^{52} -12.3364 q^{53} +(-1.42470 - 0.381747i) q^{54} +(2.07773 - 4.05404i) q^{55} +(10.0646 + 5.81077i) q^{56} +(-0.434728 + 0.434728i) q^{57} +(-7.79855 + 2.08962i) q^{58} +(-2.37217 - 8.85304i) q^{59} +(-0.170446 + 0.170446i) q^{60} +(5.89575 + 3.40391i) q^{61} +(3.71713 + 6.43826i) q^{62} +(-1.11773 + 4.17142i) q^{63} +7.18023i q^{64} +(-3.09101 - 3.86924i) q^{65} +(-4.10896 + 2.65460i) q^{66} +(2.37464 - 8.86227i) q^{67} +(-0.0916241 + 0.0528992i) q^{68} +(-1.91532 - 1.10581i) q^{69} +(6.18642 + 6.18642i) q^{70} +(7.44392 - 1.99459i) q^{71} +(-2.59937 + 0.696499i) q^{72} +(-8.48375 - 8.48375i) q^{73} +(-13.8663 - 8.00574i) q^{74} +(-2.69631 + 1.55672i) q^{75} +(0.0279251 - 0.104218i) q^{76} +(7.77248 + 12.0307i) q^{77} +(0.797085 + 5.25796i) q^{78} +13.7568i q^{79} +(-1.53580 + 5.73169i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.93165 + 3.42464i) q^{82} +(5.50139 - 5.50139i) q^{83} +(-0.196156 - 0.732066i) q^{84} +(0.799820 - 0.214311i) q^{85} +(4.17717 - 4.17717i) q^{86} +(-4.74047 - 2.73691i) q^{87} +(-4.07077 + 7.94285i) q^{88} +(7.03147 + 1.88408i) q^{89} -2.02589 q^{90} +(15.3949 - 2.33381i) q^{91} +0.388131 q^{92} +(-1.30453 + 4.86858i) q^{93} +(2.07902 - 1.20032i) q^{94} +(-0.422219 + 0.731306i) q^{95} +(0.700012 - 0.700012i) q^{96} +(-12.9643 + 3.47376i) q^{97} +(-16.5978 + 4.44736i) q^{98} +(-3.24251 - 0.697234i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q - 28 q^{3} + 4 q^{5} - 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 56 q - 28 q^{3} + 4 q^{5} - 28 q^{9} - 12 q^{11} + 24 q^{14} - 8 q^{15} + 68 q^{16} - 8 q^{20} - 10 q^{22} - 12 q^{23} - 48 q^{26} + 56 q^{27} + 4 q^{31} + 12 q^{33} + 32 q^{34} + 36 q^{37} - 12 q^{42} + 24 q^{44} + 4 q^{45} - 8 q^{47} + 68 q^{48} - 24 q^{49} - 56 q^{53} - 2 q^{55} + 72 q^{56} - 88 q^{58} + 56 q^{59} - 44 q^{60} + 20 q^{66} + 92 q^{67} + 12 q^{69} - 216 q^{70} + 72 q^{71} - 12 q^{75} - 12 q^{78} + 44 q^{80} - 28 q^{81} - 156 q^{82} - 120 q^{86} - 6 q^{88} - 56 q^{89} + 92 q^{91} + 32 q^{92} - 20 q^{93} - 44 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(e\left(\frac{7}{12}\right)\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.42470 0.381747i −1.00741 0.269936i −0.282865 0.959160i \(-0.591285\pi\)
−0.724548 + 0.689224i \(0.757952\pi\)
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 0.151984 + 0.0877479i 0.0759919 + 0.0438739i
\(5\) −0.971227 0.971227i −0.434346 0.434346i 0.455758 0.890104i \(-0.349368\pi\)
−0.890104 + 0.455758i \(0.849368\pi\)
\(6\) 0.381747 + 1.42470i 0.155847 + 0.581631i
\(7\) 4.17142 1.11773i 1.57665 0.422461i 0.638761 0.769405i \(-0.279447\pi\)
0.937886 + 0.346944i \(0.112781\pi\)
\(8\) 1.90287 + 1.90287i 0.672766 + 0.672766i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 1.01294 + 1.75447i 0.320321 + 0.554812i
\(11\) 1.01743 + 3.15671i 0.306767 + 0.951785i
\(12\) 0.175496i 0.0506612i
\(13\) 3.58322 + 0.400646i 0.993807 + 0.111119i
\(14\) −6.36970 −1.70237
\(15\) −0.355494 + 1.32672i −0.0917881 + 0.342558i
\(16\) −2.16010 3.74140i −0.540024 0.935349i
\(17\) −0.301427 + 0.522088i −0.0731069 + 0.126625i −0.900261 0.435350i \(-0.856625\pi\)
0.827155 + 0.561974i \(0.189958\pi\)
\(18\) 1.04295 1.04295i 0.245826 0.245826i
\(19\) −0.159121 0.593849i −0.0365050 0.136238i 0.945268 0.326294i \(-0.105800\pi\)
−0.981773 + 0.190055i \(0.939133\pi\)
\(20\) −0.0623876 0.232834i −0.0139503 0.0520632i
\(21\) −3.05369 3.05369i −0.666369 0.666369i
\(22\) −0.244469 4.88576i −0.0521210 1.04165i
\(23\) 1.91532 1.10581i 0.399372 0.230578i −0.286841 0.957978i \(-0.592605\pi\)
0.686213 + 0.727401i \(0.259272\pi\)
\(24\) 0.696499 2.59937i 0.142172 0.530594i
\(25\) 3.11344i 0.622687i
\(26\) −4.95207 1.93868i −0.971180 0.380207i
\(27\) 1.00000 0.192450
\(28\) 0.732066 + 0.196156i 0.138347 + 0.0370701i
\(29\) 4.74047 2.73691i 0.880284 0.508232i 0.00953186 0.999955i \(-0.496966\pi\)
0.870752 + 0.491722i \(0.163633\pi\)
\(30\) 1.01294 1.75447i 0.184937 0.320321i
\(31\) −3.56405 3.56405i −0.640122 0.640122i 0.310464 0.950585i \(-0.399516\pi\)
−0.950585 + 0.310464i \(0.899516\pi\)
\(32\) 0.256222 + 0.956235i 0.0452941 + 0.169040i
\(33\) 2.22508 2.45948i 0.387336 0.428140i
\(34\) 0.628748 0.628748i 0.107829 0.107829i
\(35\) −5.13696 2.96583i −0.868305 0.501316i
\(36\) −0.151984 + 0.0877479i −0.0253306 + 0.0146246i
\(37\) 10.4857 + 2.80963i 1.72383 + 0.461900i 0.978748 0.205069i \(-0.0657418\pi\)
0.745086 + 0.666969i \(0.232408\pi\)
\(38\) 0.906800i 0.147102i
\(39\) −1.44464 3.30348i −0.231328 0.528981i
\(40\) 3.69624i 0.584426i
\(41\) −4.48549 1.20188i −0.700516 0.187703i −0.109054 0.994036i \(-0.534782\pi\)
−0.591462 + 0.806333i \(0.701449\pi\)
\(42\) 3.18485 + 5.51632i 0.491433 + 0.851187i
\(43\) −2.00257 + 3.46855i −0.305389 + 0.528949i −0.977348 0.211639i \(-0.932120\pi\)
0.671959 + 0.740588i \(0.265453\pi\)
\(44\) −0.122362 + 0.569046i −0.0184467 + 0.0857870i
\(45\) 1.32672 0.355494i 0.197776 0.0529939i
\(46\) −3.15090 + 0.844280i −0.464574 + 0.124482i
\(47\) −1.15089 + 1.15089i −0.167875 + 0.167875i −0.786045 0.618170i \(-0.787874\pi\)
0.618170 + 0.786045i \(0.287874\pi\)
\(48\) −2.16010 + 3.74140i −0.311783 + 0.540024i
\(49\) 10.0892 5.82501i 1.44132 0.832145i
\(50\) −1.18854 + 4.43571i −0.168085 + 0.627304i
\(51\) 0.602855 0.0844166
\(52\) 0.509436 + 0.375312i 0.0706460 + 0.0520464i
\(53\) −12.3364 −1.69453 −0.847266 0.531169i \(-0.821753\pi\)
−0.847266 + 0.531169i \(0.821753\pi\)
\(54\) −1.42470 0.381747i −0.193877 0.0519492i
\(55\) 2.07773 4.05404i 0.280161 0.546647i
\(56\) 10.0646 + 5.81077i 1.34493 + 0.776497i
\(57\) −0.434728 + 0.434728i −0.0575811 + 0.0575811i
\(58\) −7.79855 + 2.08962i −1.02400 + 0.274380i
\(59\) −2.37217 8.85304i −0.308830 1.15257i −0.929598 0.368574i \(-0.879846\pi\)
0.620769 0.783994i \(-0.286821\pi\)
\(60\) −0.170446 + 0.170446i −0.0220045 + 0.0220045i
\(61\) 5.89575 + 3.40391i 0.754873 + 0.435826i 0.827452 0.561536i \(-0.189790\pi\)
−0.0725787 + 0.997363i \(0.523123\pi\)
\(62\) 3.71713 + 6.43826i 0.472076 + 0.817659i
\(63\) −1.11773 + 4.17142i −0.140820 + 0.525549i
\(64\) 7.18023i 0.897528i
\(65\) −3.09101 3.86924i −0.383392 0.479920i
\(66\) −4.10896 + 2.65460i −0.505778 + 0.326758i
\(67\) 2.37464 8.86227i 0.290108 1.08270i −0.654917 0.755701i \(-0.727296\pi\)
0.945025 0.326998i \(-0.106037\pi\)
\(68\) −0.0916241 + 0.0528992i −0.0111111 + 0.00641497i
\(69\) −1.91532 1.10581i −0.230578 0.133124i
\(70\) 6.18642 + 6.18642i 0.739419 + 0.739419i
\(71\) 7.44392 1.99459i 0.883431 0.236715i 0.211544 0.977368i \(-0.432151\pi\)
0.671887 + 0.740654i \(0.265484\pi\)
\(72\) −2.59937 + 0.696499i −0.306338 + 0.0820831i
\(73\) −8.48375 8.48375i −0.992947 0.992947i 0.00702788 0.999975i \(-0.497763\pi\)
−0.999975 + 0.00702788i \(0.997763\pi\)
\(74\) −13.8663 8.00574i −1.61193 0.930648i
\(75\) −2.69631 + 1.55672i −0.311344 + 0.179754i
\(76\) 0.0279251 0.104218i 0.00320323 0.0119546i
\(77\) 7.77248 + 12.0307i 0.885756 + 1.37103i
\(78\) 0.797085 + 5.25796i 0.0902521 + 0.595346i
\(79\) 13.7568i 1.54776i 0.633335 + 0.773878i \(0.281686\pi\)
−0.633335 + 0.773878i \(0.718314\pi\)
\(80\) −1.53580 + 5.73169i −0.171708 + 0.640822i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 5.93165 + 3.42464i 0.655042 + 0.378188i
\(83\) 5.50139 5.50139i 0.603855 0.603855i −0.337478 0.941333i \(-0.609574\pi\)
0.941333 + 0.337478i \(0.109574\pi\)
\(84\) −0.196156 0.732066i −0.0214024 0.0798749i
\(85\) 0.799820 0.214311i 0.0867527 0.0232453i
\(86\) 4.17717 4.17717i 0.450435 0.450435i
\(87\) −4.74047 2.73691i −0.508232 0.293428i
\(88\) −4.07077 + 7.94285i −0.433946 + 0.846711i
\(89\) 7.03147 + 1.88408i 0.745334 + 0.199712i 0.611447 0.791285i \(-0.290588\pi\)
0.133886 + 0.990997i \(0.457254\pi\)
\(90\) −2.02589 −0.213547
\(91\) 15.3949 2.33381i 1.61383 0.244649i
\(92\) 0.388131 0.0404654
\(93\) −1.30453 + 4.86858i −0.135274 + 0.504848i
\(94\) 2.07902 1.20032i 0.214435 0.123804i
\(95\) −0.422219 + 0.731306i −0.0433188 + 0.0750304i
\(96\) 0.700012 0.700012i 0.0714447 0.0714447i
\(97\) −12.9643 + 3.47376i −1.31632 + 0.352707i −0.847598 0.530639i \(-0.821952\pi\)
−0.468722 + 0.883346i \(0.655285\pi\)
\(98\) −16.5978 + 4.44736i −1.67663 + 0.449251i
\(99\) −3.24251 0.697234i −0.325884 0.0700747i
\(100\) 0.273197 0.473192i 0.0273197 0.0473192i
\(101\) 1.88356 + 3.26242i 0.187421 + 0.324623i 0.944390 0.328828i \(-0.106654\pi\)
−0.756969 + 0.653451i \(0.773320\pi\)
\(102\) −0.858886 0.230138i −0.0850424 0.0227870i
\(103\) 3.80982i 0.375392i 0.982227 + 0.187696i \(0.0601020\pi\)
−0.982227 + 0.187696i \(0.939898\pi\)
\(104\) 6.05603 + 7.58078i 0.593842 + 0.743357i
\(105\) 5.93165i 0.578870i
\(106\) 17.5756 + 4.70937i 1.70709 + 0.457415i
\(107\) 11.2041 6.46866i 1.08314 0.625349i 0.151396 0.988473i \(-0.451623\pi\)
0.931741 + 0.363124i \(0.118290\pi\)
\(108\) 0.151984 + 0.0877479i 0.0146246 + 0.00844354i
\(109\) −0.843461 + 0.843461i −0.0807889 + 0.0807889i −0.746346 0.665558i \(-0.768194\pi\)
0.665558 + 0.746346i \(0.268194\pi\)
\(110\) −4.50775 + 4.98262i −0.429797 + 0.475074i
\(111\) −2.80963 10.4857i −0.266678 0.995256i
\(112\) −13.1925 13.1925i −1.24658 1.24658i
\(113\) −2.95576 + 5.11953i −0.278055 + 0.481605i −0.970901 0.239480i \(-0.923023\pi\)
0.692847 + 0.721085i \(0.256356\pi\)
\(114\) 0.785312 0.453400i 0.0735512 0.0424648i
\(115\) −2.93421 0.786219i −0.273616 0.0733153i
\(116\) 0.960633 0.0891926
\(117\) −2.13858 + 2.90284i −0.197712 + 0.268368i
\(118\) 13.5185i 1.24448i
\(119\) −0.673828 + 2.51476i −0.0617697 + 0.230528i
\(120\) −3.20104 + 1.84812i −0.292213 + 0.168709i
\(121\) −8.92966 + 6.42348i −0.811788 + 0.583953i
\(122\) −7.10023 7.10023i −0.642825 0.642825i
\(123\) 1.20188 + 4.48549i 0.108370 + 0.404443i
\(124\) −0.228940 0.854415i −0.0205594 0.0767287i
\(125\) −7.87999 + 7.87999i −0.704808 + 0.704808i
\(126\) 3.18485 5.51632i 0.283729 0.491433i
\(127\) 4.85479 + 8.40874i 0.430793 + 0.746155i 0.996942 0.0781481i \(-0.0249007\pi\)
−0.566149 + 0.824303i \(0.691567\pi\)
\(128\) 3.25347 12.1421i 0.287569 1.07322i
\(129\) 4.00514 0.352633
\(130\) 2.92668 + 6.69248i 0.256687 + 0.586970i
\(131\) 7.68938i 0.671824i 0.941893 + 0.335912i \(0.109044\pi\)
−0.941893 + 0.335912i \(0.890956\pi\)
\(132\) 0.553989 0.178555i 0.0482186 0.0155412i
\(133\) −1.32752 2.29934i −0.115111 0.199378i
\(134\) −6.76629 + 11.7196i −0.584518 + 1.01242i
\(135\) −0.971227 0.971227i −0.0835899 0.0835899i
\(136\) −1.56704 + 0.419888i −0.134373 + 0.0360051i
\(137\) 1.18418 + 4.41942i 0.101171 + 0.377576i 0.997883 0.0650393i \(-0.0207173\pi\)
−0.896711 + 0.442616i \(0.854051\pi\)
\(138\) 2.30662 + 2.30662i 0.196352 + 0.196352i
\(139\) 11.0038 + 6.35304i 0.933330 + 0.538858i 0.887863 0.460108i \(-0.152189\pi\)
0.0454665 + 0.998966i \(0.485523\pi\)
\(140\) −0.520490 0.901514i −0.0439894 0.0761919i
\(141\) 1.57215 + 0.421256i 0.132399 + 0.0354761i
\(142\) −11.3668 −0.953878
\(143\) 2.38096 + 11.7188i 0.199106 + 0.979978i
\(144\) 4.32019 0.360016
\(145\) −7.26224 1.94591i −0.603096 0.161599i
\(146\) 8.84814 + 15.3254i 0.732277 + 1.26834i
\(147\) −10.0892 5.82501i −0.832145 0.480439i
\(148\) 1.34711 + 1.34711i 0.110732 + 0.110732i
\(149\) −3.48349 13.0006i −0.285379 1.06505i −0.948562 0.316591i \(-0.897462\pi\)
0.663183 0.748457i \(-0.269205\pi\)
\(150\) 4.43571 1.18854i 0.362174 0.0970442i
\(151\) −0.616275 0.616275i −0.0501517 0.0501517i 0.681586 0.731738i \(-0.261290\pi\)
−0.731738 + 0.681586i \(0.761290\pi\)
\(152\) 0.827230 1.43280i 0.0670972 0.116216i
\(153\) −0.301427 0.522088i −0.0243690 0.0422083i
\(154\) −6.48074 20.1073i −0.522233 1.62029i
\(155\) 6.92300i 0.556069i
\(156\) 0.0703116 0.628840i 0.00562943 0.0503475i
\(157\) 4.87547 0.389105 0.194552 0.980892i \(-0.437675\pi\)
0.194552 + 0.980892i \(0.437675\pi\)
\(158\) 5.25160 19.5992i 0.417795 1.55923i
\(159\) 6.16819 + 10.6836i 0.489169 + 0.847266i
\(160\) 0.679871 1.17757i 0.0537485 0.0930952i
\(161\) 6.75361 6.75361i 0.532259 0.532259i
\(162\) 0.381747 + 1.42470i 0.0299929 + 0.111935i
\(163\) −4.83304 18.0371i −0.378553 1.41278i −0.848084 0.529862i \(-0.822244\pi\)
0.469531 0.882916i \(-0.344423\pi\)
\(164\) −0.576259 0.576259i −0.0449982 0.0449982i
\(165\) −4.54977 + 0.227657i −0.354199 + 0.0177231i
\(166\) −9.93795 + 5.73768i −0.771334 + 0.445330i
\(167\) 2.91807 10.8904i 0.225807 0.842722i −0.756273 0.654256i \(-0.772982\pi\)
0.982080 0.188466i \(-0.0603515\pi\)
\(168\) 11.6215i 0.896621i
\(169\) 12.6790 + 2.87120i 0.975305 + 0.220862i
\(170\) −1.22132 −0.0936706
\(171\) 0.593849 + 0.159121i 0.0454128 + 0.0121683i
\(172\) −0.608716 + 0.351442i −0.0464142 + 0.0267972i
\(173\) −0.996067 + 1.72524i −0.0757296 + 0.131167i −0.901403 0.432980i \(-0.857462\pi\)
0.825674 + 0.564148i \(0.190795\pi\)
\(174\) 5.70894 + 5.70894i 0.432793 + 0.432793i
\(175\) −3.47997 12.9874i −0.263061 0.981758i
\(176\) 9.61276 10.6254i 0.724589 0.800921i
\(177\) −6.48088 + 6.48088i −0.487133 + 0.487133i
\(178\) −9.29848 5.36848i −0.696950 0.402384i
\(179\) 18.3369 10.5868i 1.37056 0.791296i 0.379566 0.925165i \(-0.376073\pi\)
0.990999 + 0.133869i \(0.0427401\pi\)
\(180\) 0.232834 + 0.0623876i 0.0173544 + 0.00465010i
\(181\) 15.3435i 1.14047i −0.821481 0.570237i \(-0.806852\pi\)
0.821481 0.570237i \(-0.193148\pi\)
\(182\) −22.8240 2.55199i −1.69183 0.189166i
\(183\) 6.80782i 0.503249i
\(184\) 5.74883 + 1.54039i 0.423809 + 0.113559i
\(185\) −7.45518 12.9128i −0.548116 0.949364i
\(186\) 3.71713 6.43826i 0.272553 0.472076i
\(187\) −1.95476 0.420331i −0.142946 0.0307376i
\(188\) −0.275905 + 0.0739286i −0.0201225 + 0.00539180i
\(189\) 4.17142 1.11773i 0.303426 0.0813027i
\(190\) 0.880709 0.880709i 0.0638933 0.0638933i
\(191\) 7.36438 12.7555i 0.532868 0.922954i −0.466395 0.884576i \(-0.654448\pi\)
0.999263 0.0383778i \(-0.0122190\pi\)
\(192\) 6.21826 3.59011i 0.448764 0.259094i
\(193\) −2.91553 + 10.8809i −0.209864 + 0.783225i 0.778047 + 0.628206i \(0.216210\pi\)
−0.987912 + 0.155019i \(0.950456\pi\)
\(194\) 19.7962 1.42129
\(195\) −1.80536 + 4.61151i −0.129284 + 0.330237i
\(196\) 2.04453 0.146038
\(197\) 9.41073 + 2.52160i 0.670487 + 0.179656i 0.577974 0.816055i \(-0.303843\pi\)
0.0925127 + 0.995712i \(0.470510\pi\)
\(198\) 4.35343 + 2.23117i 0.309385 + 0.158562i
\(199\) −9.96615 5.75396i −0.706481 0.407887i 0.103275 0.994653i \(-0.467068\pi\)
−0.809757 + 0.586766i \(0.800401\pi\)
\(200\) 5.92446 5.92446i 0.418923 0.418923i
\(201\) −8.86227 + 2.37464i −0.625096 + 0.167494i
\(202\) −1.43808 5.36701i −0.101183 0.377621i
\(203\) 16.7154 16.7154i 1.17319 1.17319i
\(204\) 0.0916241 + 0.0528992i 0.00641497 + 0.00370369i
\(205\) 3.18913 + 5.52373i 0.222738 + 0.385794i
\(206\) 1.45438 5.42784i 0.101332 0.378175i
\(207\) 2.21162i 0.153719i
\(208\) −6.24113 14.2717i −0.432745 0.989564i
\(209\) 1.71272 1.10650i 0.118471 0.0765383i
\(210\) 2.26439 8.45081i 0.156258 0.583161i
\(211\) −11.5406 + 6.66295i −0.794485 + 0.458696i −0.841539 0.540196i \(-0.818350\pi\)
0.0470539 + 0.998892i \(0.485017\pi\)
\(212\) −1.87493 1.08249i −0.128771 0.0743458i
\(213\) −5.44933 5.44933i −0.373382 0.373382i
\(214\) −18.4318 + 4.93878i −1.25997 + 0.337608i
\(215\) 5.31370 1.42380i 0.362391 0.0971025i
\(216\) 1.90287 + 1.90287i 0.129474 + 0.129474i
\(217\) −18.8508 10.8835i −1.27967 0.738819i
\(218\) 1.52367 0.879689i 0.103196 0.0595800i
\(219\) −3.10527 + 11.5890i −0.209834 + 0.783113i
\(220\) 0.671514 0.433832i 0.0452735 0.0292490i
\(221\) −1.28925 + 1.74999i −0.0867246 + 0.117717i
\(222\) 16.0115i 1.07462i
\(223\) −5.95008 + 22.2060i −0.398447 + 1.48702i 0.417382 + 0.908731i \(0.362948\pi\)
−0.815829 + 0.578293i \(0.803719\pi\)
\(224\) 2.13762 + 3.70247i 0.142826 + 0.247381i
\(225\) 2.69631 + 1.55672i 0.179754 + 0.103781i
\(226\) 6.16543 6.16543i 0.410118 0.410118i
\(227\) 6.20018 + 23.1394i 0.411520 + 1.53581i 0.791705 + 0.610904i \(0.209194\pi\)
−0.380185 + 0.924911i \(0.624140\pi\)
\(228\) −0.104218 + 0.0279251i −0.00690200 + 0.00184939i
\(229\) −9.65421 + 9.65421i −0.637968 + 0.637968i −0.950054 0.312086i \(-0.898972\pi\)
0.312086 + 0.950054i \(0.398972\pi\)
\(230\) 3.88022 + 2.24025i 0.255854 + 0.147718i
\(231\) 6.53269 12.7465i 0.429820 0.838661i
\(232\) 14.2285 + 3.81251i 0.934146 + 0.250304i
\(233\) −26.9246 −1.76389 −0.881944 0.471354i \(-0.843766\pi\)
−0.881944 + 0.471354i \(0.843766\pi\)
\(234\) 4.15498 3.31927i 0.271620 0.216988i
\(235\) 2.23556 0.145832
\(236\) 0.416305 1.55367i 0.0270991 0.101135i
\(237\) 11.9137 6.87838i 0.773878 0.446799i
\(238\) 1.92000 3.32554i 0.124455 0.215563i
\(239\) 8.79544 8.79544i 0.568930 0.568930i −0.362899 0.931829i \(-0.618213\pi\)
0.931829 + 0.362899i \(0.118213\pi\)
\(240\) 5.73169 1.53580i 0.369979 0.0991356i
\(241\) −20.6313 + 5.52814i −1.32898 + 0.356099i −0.852334 0.522998i \(-0.824814\pi\)
−0.476644 + 0.879096i \(0.658147\pi\)
\(242\) 15.1742 5.74265i 0.975436 0.369152i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 0.597372 + 1.03468i 0.0382428 + 0.0662385i
\(245\) −15.4563 4.14151i −0.987469 0.264592i
\(246\) 6.84928i 0.436694i
\(247\) −0.332244 2.19165i −0.0211402 0.139451i
\(248\) 13.5638i 0.861304i
\(249\) −7.51503 2.01365i −0.476246 0.127610i
\(250\) 14.2348 8.21845i 0.900286 0.519780i
\(251\) 10.2387 + 5.91130i 0.646259 + 0.373118i 0.787021 0.616926i \(-0.211622\pi\)
−0.140763 + 0.990043i \(0.544955\pi\)
\(252\) −0.535909 + 0.535909i −0.0337591 + 0.0337591i
\(253\) 5.43944 + 4.92103i 0.341975 + 0.309383i
\(254\) −3.70660 13.8332i −0.232573 0.867973i
\(255\) −0.585509 0.585509i −0.0366660 0.0366660i
\(256\) −2.09021 + 3.62035i −0.130638 + 0.226272i
\(257\) −23.4522 + 13.5402i −1.46291 + 0.844612i −0.999145 0.0413458i \(-0.986835\pi\)
−0.463766 + 0.885958i \(0.653502\pi\)
\(258\) −5.70611 1.52895i −0.355247 0.0951882i
\(259\) 46.8805 2.91301
\(260\) −0.130265 0.859291i −0.00807869 0.0532910i
\(261\) 5.47383i 0.338821i
\(262\) 2.93539 10.9550i 0.181349 0.676805i
\(263\) −19.0763 + 11.0137i −1.17630 + 0.679135i −0.955155 0.296106i \(-0.904312\pi\)
−0.221142 + 0.975242i \(0.570978\pi\)
\(264\) 8.91410 0.446035i 0.548625 0.0274516i
\(265\) 11.9814 + 11.9814i 0.736013 + 0.736013i
\(266\) 1.01356 + 3.78264i 0.0621451 + 0.231929i
\(267\) −1.88408 7.03147i −0.115304 0.430319i
\(268\) 1.13855 1.13855i 0.0695481 0.0695481i
\(269\) 1.09246 1.89220i 0.0666086 0.115369i −0.830798 0.556574i \(-0.812115\pi\)
0.897406 + 0.441205i \(0.145449\pi\)
\(270\) 1.01294 + 1.75447i 0.0616457 + 0.106774i
\(271\) 0.465197 1.73614i 0.0282587 0.105463i −0.950356 0.311165i \(-0.899281\pi\)
0.978615 + 0.205702i \(0.0659476\pi\)
\(272\) 2.60445 0.157918
\(273\) −9.71860 12.1655i −0.588196 0.736289i
\(274\) 6.74840i 0.407685i
\(275\) 9.82822 3.16771i 0.592664 0.191020i
\(276\) −0.194065 0.336131i −0.0116814 0.0202327i
\(277\) −5.90148 + 10.2217i −0.354585 + 0.614160i −0.987047 0.160432i \(-0.948711\pi\)
0.632461 + 0.774592i \(0.282045\pi\)
\(278\) −13.2518 13.2518i −0.794792 0.794792i
\(279\) 4.86858 1.30453i 0.291474 0.0781003i
\(280\) −4.13139 15.4185i −0.246898 0.921434i
\(281\) 7.24760 + 7.24760i 0.432356 + 0.432356i 0.889429 0.457073i \(-0.151102\pi\)
−0.457073 + 0.889429i \(0.651102\pi\)
\(282\) −2.07902 1.20032i −0.123804 0.0714783i
\(283\) −1.44242 2.49835i −0.0857431 0.148511i 0.819965 0.572414i \(-0.193993\pi\)
−0.905708 + 0.423903i \(0.860660\pi\)
\(284\) 1.30638 + 0.350042i 0.0775191 + 0.0207712i
\(285\) 0.844439 0.0500202
\(286\) 1.08147 17.6047i 0.0639488 1.04099i
\(287\) −20.0542 −1.18376
\(288\) −0.956235 0.256222i −0.0563467 0.0150980i
\(289\) 8.31828 + 14.4077i 0.489311 + 0.847511i
\(290\) 9.60366 + 5.54467i 0.563946 + 0.325595i
\(291\) 9.49049 + 9.49049i 0.556342 + 0.556342i
\(292\) −0.544961 2.03382i −0.0318914 0.119020i
\(293\) −22.2475 + 5.96119i −1.29971 + 0.348257i −0.841341 0.540505i \(-0.818233\pi\)
−0.458370 + 0.888761i \(0.651567\pi\)
\(294\) 12.1504 + 12.1504i 0.708626 + 0.708626i
\(295\) −6.29440 + 10.9022i −0.366474 + 0.634752i
\(296\) 14.6065 + 25.2992i 0.848986 + 1.47049i
\(297\) 1.01743 + 3.15671i 0.0590374 + 0.183171i
\(298\) 19.8517i 1.14998i
\(299\) 7.30607 3.19501i 0.422521 0.184772i
\(300\) −0.546395 −0.0315461
\(301\) −4.47665 + 16.7071i −0.258030 + 0.962981i
\(302\) 0.642745 + 1.11327i 0.0369858 + 0.0640613i
\(303\) 1.88356 3.26242i 0.108208 0.187421i
\(304\) −1.87811 + 1.87811i −0.107717 + 0.107717i
\(305\) −2.42014 9.03208i −0.138577 0.517176i
\(306\) 0.230138 + 0.858886i 0.0131561 + 0.0490993i
\(307\) −17.9596 17.9596i −1.02501 1.02501i −0.999679 0.0253307i \(-0.991936\pi\)
−0.0253307 0.999679i \(-0.508064\pi\)
\(308\) 0.125618 + 2.51050i 0.00715774 + 0.143049i
\(309\) 3.29940 1.90491i 0.187696 0.108366i
\(310\) 2.64283 9.86318i 0.150103 0.560191i
\(311\) 17.6408i 1.00032i −0.865933 0.500160i \(-0.833275\pi\)
0.865933 0.500160i \(-0.166725\pi\)
\(312\) 3.53713 9.03507i 0.200251 0.511510i
\(313\) −29.9083 −1.69052 −0.845259 0.534356i \(-0.820554\pi\)
−0.845259 + 0.534356i \(0.820554\pi\)
\(314\) −6.94607 1.86119i −0.391990 0.105033i
\(315\) 5.13696 2.96583i 0.289435 0.167105i
\(316\) −1.20713 + 2.09080i −0.0679061 + 0.117617i
\(317\) 6.22820 + 6.22820i 0.349810 + 0.349810i 0.860039 0.510229i \(-0.170439\pi\)
−0.510229 + 0.860039i \(0.670439\pi\)
\(318\) −4.70937 17.5756i −0.264088 0.985592i
\(319\) 13.4628 + 12.1797i 0.753770 + 0.681932i
\(320\) 6.97363 6.97363i 0.389838 0.389838i
\(321\) −11.2041 6.46866i −0.625349 0.361045i
\(322\) −12.2000 + 7.04369i −0.679881 + 0.392529i
\(323\) 0.358005 + 0.0959271i 0.0199199 + 0.00533753i
\(324\) 0.175496i 0.00974976i
\(325\) 1.24738 11.1561i 0.0691924 0.618831i
\(326\) 27.5425i 1.52544i
\(327\) 1.15219 + 0.308728i 0.0637162 + 0.0170727i
\(328\) −6.24827 10.8223i −0.345003 0.597563i
\(329\) −3.51447 + 6.08723i −0.193759 + 0.335600i
\(330\) 6.56895 + 1.41252i 0.361609 + 0.0777565i
\(331\) 18.1172 4.85449i 0.995811 0.266827i 0.276121 0.961123i \(-0.410951\pi\)
0.719690 + 0.694296i \(0.244284\pi\)
\(332\) 1.31886 0.353386i 0.0723816 0.0193946i
\(333\) −7.67604 + 7.67604i −0.420645 + 0.420645i
\(334\) −8.31473 + 14.4015i −0.454962 + 0.788016i
\(335\) −10.9136 + 6.30097i −0.596273 + 0.344259i
\(336\) −4.82880 + 18.0213i −0.263433 + 0.983144i
\(337\) 3.65081 0.198872 0.0994362 0.995044i \(-0.468296\pi\)
0.0994362 + 0.995044i \(0.468296\pi\)
\(338\) −16.9676 8.93075i −0.922917 0.485769i
\(339\) 5.91152 0.321070
\(340\) 0.140365 + 0.0376107i 0.00761236 + 0.00203973i
\(341\) 7.62449 14.8768i 0.412890 0.805626i
\(342\) −0.785312 0.453400i −0.0424648 0.0245171i
\(343\) 14.1997 14.1997i 0.766714 0.766714i
\(344\) −10.4108 + 2.78957i −0.561314 + 0.150404i
\(345\) 0.786219 + 2.93421i 0.0423286 + 0.157972i
\(346\) 2.07770 2.07770i 0.111698 0.111698i
\(347\) 28.5017 + 16.4555i 1.53005 + 0.883376i 0.999359 + 0.0358122i \(0.0114018\pi\)
0.530694 + 0.847564i \(0.321932\pi\)
\(348\) −0.480317 0.831933i −0.0257477 0.0445963i
\(349\) −2.76148 + 10.3060i −0.147818 + 0.551666i 0.851795 + 0.523875i \(0.175514\pi\)
−0.999614 + 0.0277913i \(0.991153\pi\)
\(350\) 19.8316i 1.06005i
\(351\) 3.58322 + 0.400646i 0.191258 + 0.0213849i
\(352\) −2.75787 + 1.78172i −0.146995 + 0.0949662i
\(353\) −2.63681 + 9.84070i −0.140343 + 0.523768i 0.859575 + 0.511009i \(0.170728\pi\)
−0.999919 + 0.0127589i \(0.995939\pi\)
\(354\) 11.7073 6.75924i 0.622239 0.359250i
\(355\) −9.16694 5.29253i −0.486531 0.280899i
\(356\) 0.903345 + 0.903345i 0.0478772 + 0.0478772i
\(357\) 2.51476 0.673828i 0.133095 0.0356627i
\(358\) −30.1660 + 8.08297i −1.59432 + 0.427198i
\(359\) −10.0933 10.0933i −0.532703 0.532703i 0.388673 0.921376i \(-0.372934\pi\)
−0.921376 + 0.388673i \(0.872934\pi\)
\(360\) 3.20104 + 1.84812i 0.168709 + 0.0974044i
\(361\) 16.1271 9.31101i 0.848797 0.490053i
\(362\) −5.85733 + 21.8599i −0.307854 + 1.14893i
\(363\) 10.0277 + 4.52158i 0.526319 + 0.237321i
\(364\) 2.54456 + 0.996171i 0.133371 + 0.0522135i
\(365\) 16.4793i 0.862566i
\(366\) −2.59887 + 9.69910i −0.135845 + 0.506980i
\(367\) 1.94841 + 3.37474i 0.101706 + 0.176160i 0.912388 0.409327i \(-0.134237\pi\)
−0.810682 + 0.585487i \(0.800903\pi\)
\(368\) −8.27456 4.77732i −0.431341 0.249035i
\(369\) 3.28361 3.28361i 0.170938 0.170938i
\(370\) 5.69198 + 21.2428i 0.295912 + 1.10436i
\(371\) −51.4602 + 13.7887i −2.67168 + 0.715874i
\(372\) −0.625475 + 0.625475i −0.0324294 + 0.0324294i
\(373\) 3.80079 + 2.19439i 0.196798 + 0.113621i 0.595161 0.803607i \(-0.297088\pi\)
−0.398363 + 0.917228i \(0.630422\pi\)
\(374\) 2.62449 + 1.34507i 0.135709 + 0.0695519i
\(375\) 10.7643 + 2.88428i 0.555864 + 0.148943i
\(376\) −4.37999 −0.225881
\(377\) 18.0827 7.90772i 0.931307 0.407268i
\(378\) −6.36970 −0.327622
\(379\) −6.95472 + 25.9554i −0.357240 + 1.33324i 0.520402 + 0.853922i \(0.325782\pi\)
−0.877642 + 0.479317i \(0.840884\pi\)
\(380\) −0.128341 + 0.0740977i −0.00658375 + 0.00380113i
\(381\) 4.85479 8.40874i 0.248718 0.430793i
\(382\) −15.3614 + 15.3614i −0.785957 + 0.785957i
\(383\) −3.13216 + 0.839259i −0.160046 + 0.0428841i −0.337952 0.941163i \(-0.609734\pi\)
0.177906 + 0.984047i \(0.443068\pi\)
\(384\) −12.1421 + 3.25347i −0.619625 + 0.166028i
\(385\) 4.13575 19.2334i 0.210777 0.980226i
\(386\) 8.30750 14.3890i 0.422841 0.732381i
\(387\) −2.00257 3.46855i −0.101796 0.176316i
\(388\) −2.27517 0.609630i −0.115504 0.0309493i
\(389\) 32.0226i 1.62361i 0.583927 + 0.811806i \(0.301515\pi\)
−0.583927 + 0.811806i \(0.698485\pi\)
\(390\) 4.33252 5.88082i 0.219386 0.297787i
\(391\) 1.33329i 0.0674273i
\(392\) 30.2827 + 8.11423i 1.52951 + 0.409830i
\(393\) 6.65920 3.84469i 0.335912 0.193939i
\(394\) −12.4448 7.18503i −0.626962 0.361977i
\(395\) 13.3609 13.3609i 0.672262 0.672262i
\(396\) −0.431628 0.390491i −0.0216901 0.0196229i
\(397\) 0.267945 + 0.999985i 0.0134478 + 0.0501878i 0.972324 0.233638i \(-0.0750630\pi\)
−0.958876 + 0.283826i \(0.908396\pi\)
\(398\) 12.0022 + 12.0022i 0.601616 + 0.601616i
\(399\) −1.32752 + 2.29934i −0.0664593 + 0.115111i
\(400\) −11.6486 + 6.72532i −0.582430 + 0.336266i
\(401\) −14.3052 3.83308i −0.714370 0.191415i −0.116712 0.993166i \(-0.537235\pi\)
−0.597658 + 0.801751i \(0.703902\pi\)
\(402\) 13.5326 0.674943
\(403\) −11.3429 14.1987i −0.565028 0.707287i
\(404\) 0.661113i 0.0328916i
\(405\) −0.355494 + 1.32672i −0.0176646 + 0.0659253i
\(406\) −30.1954 + 17.4333i −1.49857 + 0.865201i
\(407\) 1.79927 + 35.9588i 0.0891867 + 1.78241i
\(408\) 1.14715 + 1.14715i 0.0567926 + 0.0567926i
\(409\) −1.14958 4.29030i −0.0568431 0.212141i 0.931663 0.363325i \(-0.118358\pi\)
−0.988506 + 0.151183i \(0.951692\pi\)
\(410\) −2.43488 9.08709i −0.120250 0.448779i
\(411\) 3.23524 3.23524i 0.159583 0.159583i
\(412\) −0.334303 + 0.579030i −0.0164699 + 0.0285268i
\(413\) −19.7906 34.2783i −0.973831 1.68672i
\(414\) 0.844280 3.15090i 0.0414941 0.154858i
\(415\) −10.6862 −0.524564
\(416\) 0.534990 + 3.52906i 0.0262301 + 0.173026i
\(417\) 12.7061i 0.622220i
\(418\) −2.86251 + 0.922607i −0.140010 + 0.0451262i
\(419\) 4.20883 + 7.28991i 0.205615 + 0.356135i 0.950328 0.311249i \(-0.100747\pi\)
−0.744714 + 0.667384i \(0.767414\pi\)
\(420\) −0.520490 + 0.901514i −0.0253973 + 0.0439894i
\(421\) 22.2254 + 22.2254i 1.08320 + 1.08320i 0.996209 + 0.0869907i \(0.0277250\pi\)
0.0869907 + 0.996209i \(0.472275\pi\)
\(422\) 18.9854 5.08712i 0.924194 0.247637i
\(423\) −0.421256 1.57215i −0.0204822 0.0764404i
\(424\) −23.4745 23.4745i −1.14002 1.14002i
\(425\) 1.62549 + 0.938475i 0.0788477 + 0.0455227i
\(426\) 5.68338 + 9.84391i 0.275361 + 0.476939i
\(427\) 28.3983 + 7.60929i 1.37429 + 0.368240i
\(428\) 2.27044 0.109746
\(429\) 8.95832 7.92139i 0.432512 0.382448i
\(430\) −8.11395 −0.391290
\(431\) −32.6412 8.74620i −1.57227 0.421289i −0.635750 0.771895i \(-0.719309\pi\)
−0.936523 + 0.350605i \(0.885976\pi\)
\(432\) −2.16010 3.74140i −0.103928 0.180008i
\(433\) 15.1842 + 8.76658i 0.729704 + 0.421295i 0.818314 0.574771i \(-0.194909\pi\)
−0.0886097 + 0.996066i \(0.528242\pi\)
\(434\) 22.7019 + 22.7019i 1.08973 + 1.08973i
\(435\) 1.94591 + 7.26224i 0.0932993 + 0.348198i
\(436\) −0.202204 + 0.0541805i −0.00968383 + 0.00259477i
\(437\) −0.961454 0.961454i −0.0459926 0.0459926i
\(438\) 8.84814 15.3254i 0.422780 0.732277i
\(439\) 17.7664 + 30.7724i 0.847946 + 1.46869i 0.883038 + 0.469301i \(0.155494\pi\)
−0.0350923 + 0.999384i \(0.511173\pi\)
\(440\) 11.6680 3.76067i 0.556248 0.179283i
\(441\) 11.6500i 0.554763i
\(442\) 2.50485 2.00104i 0.119144 0.0951798i
\(443\) −15.6020 −0.741276 −0.370638 0.928777i \(-0.620861\pi\)
−0.370638 + 0.928777i \(0.620861\pi\)
\(444\) 0.493077 1.84019i 0.0234004 0.0873315i
\(445\) −4.99929 8.65902i −0.236989 0.410477i
\(446\) 16.9541 29.3654i 0.802802 1.39049i
\(447\) −9.51708 + 9.51708i −0.450142 + 0.450142i
\(448\) 8.02554 + 29.9517i 0.379171 + 1.41509i
\(449\) 6.82810 + 25.4828i 0.322238 + 1.20261i 0.917059 + 0.398751i \(0.130556\pi\)
−0.594821 + 0.803858i \(0.702777\pi\)
\(450\) −3.24716 3.24716i −0.153073 0.153073i
\(451\) −0.769681 15.3822i −0.0362429 0.724321i
\(452\) −0.898455 + 0.518723i −0.0422598 + 0.0243987i
\(453\) −0.225572 + 0.841847i −0.0105983 + 0.0395534i
\(454\) 35.3335i 1.65828i
\(455\) −17.2186 12.6853i −0.807222 0.594697i
\(456\) −1.65446 −0.0774772
\(457\) −2.81822 0.755141i −0.131831 0.0353240i 0.192300 0.981336i \(-0.438405\pi\)
−0.324131 + 0.946012i \(0.605072\pi\)
\(458\) 17.4398 10.0689i 0.814909 0.470488i
\(459\) −0.301427 + 0.522088i −0.0140694 + 0.0243690i
\(460\) −0.376963 0.376963i −0.0175760 0.0175760i
\(461\) −6.90925 25.7857i −0.321796 1.20096i −0.917494 0.397750i \(-0.869791\pi\)
0.595698 0.803209i \(-0.296876\pi\)
\(462\) −14.1731 + 15.6661i −0.659391 + 0.728854i
\(463\) 13.0023 13.0023i 0.604267 0.604267i −0.337175 0.941442i \(-0.609471\pi\)
0.941442 + 0.337175i \(0.109471\pi\)
\(464\) −20.4798 11.8240i −0.950749 0.548915i
\(465\) 5.99549 3.46150i 0.278034 0.160523i
\(466\) 38.3594 + 10.2784i 1.77697 + 0.476137i
\(467\) 37.2648i 1.72441i 0.506561 + 0.862204i \(0.330916\pi\)
−0.506561 + 0.862204i \(0.669084\pi\)
\(468\) −0.579747 + 0.253528i −0.0267988 + 0.0117194i
\(469\) 39.6224i 1.82959i
\(470\) −3.18499 0.853416i −0.146913 0.0393651i
\(471\) −2.43773 4.22228i −0.112325 0.194552i
\(472\) 12.3323 21.3601i 0.567638 0.983179i
\(473\) −12.9867 2.79252i −0.597129 0.128400i
\(474\) −19.5992 + 5.25160i −0.900222 + 0.241214i
\(475\) −1.84891 + 0.495414i −0.0848339 + 0.0227312i
\(476\) −0.323076 + 0.323076i −0.0148081 + 0.0148081i
\(477\) 6.16819 10.6836i 0.282422 0.489169i
\(478\) −15.8885 + 9.17322i −0.726722 + 0.419573i
\(479\) −1.63954 + 6.11884i −0.0749124 + 0.279577i −0.993213 0.116306i \(-0.962895\pi\)
0.918301 + 0.395883i \(0.129561\pi\)
\(480\) −1.35974 −0.0620635
\(481\) 36.4468 + 14.2686i 1.66183 + 0.650590i
\(482\) 31.5037 1.43495
\(483\) −9.22560 2.47199i −0.419780 0.112480i
\(484\) −1.92081 + 0.192706i −0.0873096 + 0.00875936i
\(485\) 15.9650 + 9.21742i 0.724935 + 0.418542i
\(486\) 1.04295 1.04295i 0.0473092 0.0473092i
\(487\) 22.9832 6.15833i 1.04147 0.279060i 0.302746 0.953071i \(-0.402097\pi\)
0.738721 + 0.674011i \(0.235430\pi\)
\(488\) 4.74164 + 17.6960i 0.214644 + 0.801062i
\(489\) −13.2041 + 13.2041i −0.597110 + 0.597110i
\(490\) 20.4396 + 11.8008i 0.923367 + 0.533106i
\(491\) 2.38360 + 4.12852i 0.107570 + 0.186317i 0.914785 0.403940i \(-0.132360\pi\)
−0.807215 + 0.590257i \(0.799026\pi\)
\(492\) −0.210925 + 0.787184i −0.00950925 + 0.0354890i
\(493\) 3.29992i 0.148621i
\(494\) −0.363305 + 3.24927i −0.0163459 + 0.146191i
\(495\) 2.47204 + 3.82639i 0.111110 + 0.171983i
\(496\) −5.63583 + 21.0332i −0.253056 + 0.944419i
\(497\) 28.8223 16.6405i 1.29286 0.746430i
\(498\) 9.93795 + 5.73768i 0.445330 + 0.257111i
\(499\) −30.3234 30.3234i −1.35746 1.35746i −0.877034 0.480429i \(-0.840481\pi\)
−0.480429 0.877034i \(-0.659519\pi\)
\(500\) −1.88908 + 0.506178i −0.0844823 + 0.0226370i
\(501\) −10.8904 + 2.91807i −0.486546 + 0.130370i
\(502\) −12.3304 12.3304i −0.550332 0.550332i
\(503\) −20.7982 12.0078i −0.927346 0.535404i −0.0413749 0.999144i \(-0.513174\pi\)
−0.885971 + 0.463740i \(0.846507\pi\)
\(504\) −10.0646 + 5.81077i −0.448311 + 0.258832i
\(505\) 1.33919 4.99791i 0.0595930 0.222404i
\(506\) −5.87097 9.08748i −0.260997 0.403988i
\(507\) −3.85295 12.4159i −0.171115 0.551410i
\(508\) 1.70399i 0.0756023i
\(509\) 9.59521 35.8098i 0.425300 1.58724i −0.337967 0.941158i \(-0.609739\pi\)
0.763267 0.646083i \(-0.223594\pi\)
\(510\) 0.610658 + 1.05769i 0.0270404 + 0.0468353i
\(511\) −44.8718 25.9067i −1.98501 1.14605i
\(512\) −13.4173 + 13.4173i −0.592968 + 0.592968i
\(513\) −0.159121 0.593849i −0.00702538 0.0262191i
\(514\) 38.5813 10.3378i 1.70175 0.455982i
\(515\) 3.70020 3.70020i 0.163050 0.163050i
\(516\) 0.608716 + 0.351442i 0.0267972 + 0.0154714i
\(517\) −4.80399 2.46208i −0.211279 0.108282i
\(518\) −66.7905 17.8965i −2.93461 0.786326i
\(519\) 1.99213 0.0874450
\(520\) 1.48088 13.2444i 0.0649409 0.580807i
\(521\) −24.7847 −1.08584 −0.542918 0.839785i \(-0.682681\pi\)
−0.542918 + 0.839785i \(0.682681\pi\)
\(522\) 2.08962 7.79855i 0.0914600 0.341333i
\(523\) −20.1497 + 11.6334i −0.881084 + 0.508694i −0.871016 0.491255i \(-0.836538\pi\)
−0.0100682 + 0.999949i \(0.503205\pi\)
\(524\) −0.674726 + 1.16866i −0.0294756 + 0.0510532i
\(525\) −9.50746 + 9.50746i −0.414940 + 0.414940i
\(526\) 31.3825 8.40891i 1.36834 0.366646i
\(527\) 2.93505 0.786443i 0.127853 0.0342580i
\(528\) −14.0083 3.01219i −0.609631 0.131089i
\(529\) −9.05436 + 15.6826i −0.393668 + 0.681853i
\(530\) −12.4960 21.6438i −0.542794 0.940146i
\(531\) 8.85304 + 2.37217i 0.384189 + 0.102943i
\(532\) 0.465949i 0.0202015i
\(533\) −15.5910 6.10371i −0.675320 0.264381i
\(534\) 10.7370i 0.464634i
\(535\) −17.1642 4.59914i −0.742074 0.198838i
\(536\) 21.3824 12.3451i 0.923578 0.533228i
\(537\) −18.3369 10.5868i −0.791296 0.456855i
\(538\) −2.27877 + 2.27877i −0.0982447 + 0.0982447i
\(539\) 28.6530 + 25.9222i 1.23417 + 1.11655i
\(540\) −0.0623876 0.232834i −0.00268474 0.0100196i
\(541\) 22.1057 + 22.1057i 0.950397 + 0.950397i 0.998827 0.0484299i \(-0.0154218\pi\)
−0.0484299 + 0.998827i \(0.515422\pi\)
\(542\) −1.32553 + 2.29589i −0.0569365 + 0.0986168i
\(543\) −13.2879 + 7.67175i −0.570237 + 0.329226i
\(544\) −0.576471 0.154465i −0.0247160 0.00662263i
\(545\) 1.63838 0.0701807
\(546\) 9.20193 + 21.0422i 0.393806 + 0.900523i
\(547\) 1.64115i 0.0701703i 0.999384 + 0.0350852i \(0.0111702\pi\)
−0.999384 + 0.0350852i \(0.988830\pi\)
\(548\) −0.207818 + 0.775589i −0.00887756 + 0.0331315i
\(549\) −5.89575 + 3.40391i −0.251624 + 0.145275i
\(550\) −15.2115 + 0.761139i −0.648621 + 0.0324551i
\(551\) −2.37962 2.37962i −0.101375 0.101375i
\(552\) −1.54039 5.74883i −0.0655635 0.244686i
\(553\) 15.3763 + 57.3851i 0.653867 + 2.44026i
\(554\) 12.3099 12.3099i 0.522998 0.522998i
\(555\) −7.45518 + 12.9128i −0.316455 + 0.548116i
\(556\) 1.11493 + 1.93112i 0.0472836 + 0.0818977i
\(557\) −2.40873 + 8.98949i −0.102061 + 0.380897i −0.997995 0.0632899i \(-0.979841\pi\)
0.895934 + 0.444187i \(0.146507\pi\)
\(558\) −7.43426 −0.314717
\(559\) −8.56531 + 11.6263i −0.362274 + 0.491739i
\(560\) 25.6259i 1.08289i
\(561\) 0.613364 + 1.90304i 0.0258962 + 0.0803464i
\(562\) −7.55890 13.0924i −0.318853 0.552270i
\(563\) 3.93627 6.81783i 0.165894 0.287337i −0.771078 0.636740i \(-0.780282\pi\)
0.936972 + 0.349403i \(0.113616\pi\)
\(564\) 0.201977 + 0.201977i 0.00850475 + 0.00850475i
\(565\) 7.84294 2.10151i 0.329955 0.0884112i
\(566\) 1.10128 + 4.11003i 0.0462902 + 0.172757i
\(567\) −3.05369 3.05369i −0.128243 0.128243i
\(568\) 17.9603 + 10.3694i 0.753595 + 0.435089i
\(569\) −13.1458 22.7693i −0.551102 0.954537i −0.998195 0.0600498i \(-0.980874\pi\)
0.447093 0.894487i \(-0.352459\pi\)
\(570\) −1.20307 0.322362i −0.0503911 0.0135023i
\(571\) −27.8935 −1.16731 −0.583653 0.812003i \(-0.698377\pi\)
−0.583653 + 0.812003i \(0.698377\pi\)
\(572\) −0.666435 + 1.99000i −0.0278650 + 0.0832059i
\(573\) −14.7288 −0.615303
\(574\) 28.5712 + 7.65563i 1.19254 + 0.319540i
\(575\) −3.44287 5.96323i −0.143578 0.248684i
\(576\) −6.21826 3.59011i −0.259094 0.149588i
\(577\) −12.3051 12.3051i −0.512267 0.512267i 0.402954 0.915220i \(-0.367984\pi\)
−0.915220 + 0.402954i \(0.867984\pi\)
\(578\) −6.35095 23.7021i −0.264165 0.985877i
\(579\) 10.8809 2.91553i 0.452195 0.121165i
\(580\) −0.932993 0.932993i −0.0387404 0.0387404i
\(581\) 16.7995 29.0976i 0.696961 1.20717i
\(582\) −9.89812 17.1441i −0.410290 0.710644i
\(583\) −12.5514 38.9424i −0.519827 1.61283i
\(584\) 32.2869i 1.33604i
\(585\) 4.89636 0.742269i 0.202440 0.0306890i
\(586\) 33.9716 1.40335
\(587\) 8.41376 31.4006i 0.347273 1.29604i −0.542662 0.839951i \(-0.682583\pi\)
0.889934 0.456088i \(-0.150750\pi\)
\(588\) −1.02226 1.77061i −0.0421575 0.0730189i
\(589\) −1.54939 + 2.68362i −0.0638415 + 0.110577i
\(590\) 13.1295 13.1295i 0.540534 0.540534i
\(591\) −2.52160 9.41073i −0.103725 0.387106i
\(592\) −12.1381 45.3001i −0.498874 1.86182i
\(593\) 16.5134 + 16.5134i 0.678124 + 0.678124i 0.959576 0.281451i \(-0.0908158\pi\)
−0.281451 + 0.959576i \(0.590816\pi\)
\(594\) −0.244469 4.88576i −0.0100307 0.200465i
\(595\) 3.09684 1.78796i 0.126958 0.0732993i
\(596\) 0.611338 2.28154i 0.0250414 0.0934557i
\(597\) 11.5079i 0.470988i
\(598\) −11.6286 + 1.76285i −0.475530 + 0.0720884i
\(599\) 16.6193 0.679046 0.339523 0.940598i \(-0.389734\pi\)
0.339523 + 0.940598i \(0.389734\pi\)
\(600\) −8.09296 2.16850i −0.330394 0.0885288i
\(601\) −13.7223 + 7.92259i −0.559746 + 0.323169i −0.753043 0.657971i \(-0.771415\pi\)
0.193298 + 0.981140i \(0.438082\pi\)
\(602\) 12.7558 22.0936i 0.519886 0.900469i
\(603\) 6.48763 + 6.48763i 0.264197 + 0.264197i
\(604\) −0.0395870 0.147741i −0.00161077 0.00601148i
\(605\) 14.9114 + 2.43407i 0.606234 + 0.0989591i
\(606\) −3.92892 + 3.92892i −0.159601 + 0.159601i
\(607\) 27.4007 + 15.8198i 1.11216 + 0.642106i 0.939388 0.342856i \(-0.111394\pi\)
0.172772 + 0.984962i \(0.444728\pi\)
\(608\) 0.527089 0.304315i 0.0213763 0.0123416i
\(609\) −22.8336 6.11825i −0.925265 0.247924i
\(610\) 13.7919i 0.558417i
\(611\) −4.58500 + 3.66280i −0.185489 + 0.148181i
\(612\) 0.105798i 0.00427665i
\(613\) 15.8562 + 4.24865i 0.640426 + 0.171602i 0.564396 0.825504i \(-0.309109\pi\)
0.0760294 + 0.997106i \(0.475776\pi\)
\(614\) 18.7310 + 32.4431i 0.755922 + 1.30930i
\(615\) 3.18913 5.52373i 0.128598 0.222738i
\(616\) −8.10293 + 37.6830i −0.326477 + 1.51829i
\(617\) −28.8494 + 7.73016i −1.16143 + 0.311205i −0.787537 0.616267i \(-0.788644\pi\)
−0.373894 + 0.927471i \(0.621978\pi\)
\(618\) −5.42784 + 1.45438i −0.218340 + 0.0585039i
\(619\) 28.9839 28.9839i 1.16496 1.16496i 0.181588 0.983375i \(-0.441876\pi\)
0.983375 0.181588i \(-0.0581237\pi\)
\(620\) −0.607478 + 1.05218i −0.0243969 + 0.0422567i
\(621\) 1.91532 1.10581i 0.0768593 0.0443747i
\(622\) −6.73433 + 25.1329i −0.270022 + 1.00774i
\(623\) 31.4371 1.25950
\(624\) −9.23908 + 12.5408i −0.369859 + 0.502035i
\(625\) −0.260657 −0.0104263
\(626\) 42.6103 + 11.4174i 1.70305 + 0.456331i
\(627\) −1.81462 0.930005i −0.0724688 0.0371408i
\(628\) 0.740992 + 0.427812i 0.0295688 + 0.0170716i
\(629\) −4.62754 + 4.62754i −0.184512 + 0.184512i
\(630\) −8.45081 + 2.26439i −0.336688 + 0.0902154i
\(631\) −4.02573 15.0242i −0.160262 0.598105i −0.998597 0.0529502i \(-0.983138\pi\)
0.838335 0.545155i \(-0.183529\pi\)
\(632\) −26.1773 + 26.1773i −1.04128 + 1.04128i
\(633\) 11.5406 + 6.66295i 0.458696 + 0.264828i
\(634\) −6.49571 11.2509i −0.257977 0.446830i
\(635\) 3.45169 12.8819i 0.136976 0.511202i
\(636\) 2.16498i 0.0858471i
\(637\) 38.4857 16.8301i 1.52486 0.666834i
\(638\) −14.5308 22.4917i −0.575280 0.890457i
\(639\) −1.99459 + 7.44392i −0.0789048 + 0.294477i
\(640\) −14.9526 + 8.63290i −0.591054 + 0.341245i
\(641\) 17.3216 + 10.0006i 0.684163 + 0.395002i 0.801422 0.598100i \(-0.204077\pi\)
−0.117259 + 0.993101i \(0.537411\pi\)
\(642\) 13.4930 + 13.4930i 0.532526 + 0.532526i
\(643\) 25.8913 6.93755i 1.02105 0.273590i 0.290812 0.956780i \(-0.406075\pi\)
0.730241 + 0.683190i \(0.239408\pi\)
\(644\) 1.61905 0.433824i 0.0637997 0.0170951i
\(645\) −3.88990 3.88990i −0.153165 0.153165i
\(646\) −0.473429 0.273334i −0.0186268 0.0107542i
\(647\) −14.2389 + 8.22086i −0.559790 + 0.323195i −0.753061 0.657950i \(-0.771424\pi\)
0.193271 + 0.981145i \(0.438090\pi\)
\(648\) 0.696499 2.59937i 0.0273610 0.102113i
\(649\) 25.5330 16.4956i 1.00226 0.647510i
\(650\) −6.03596 + 15.4179i −0.236750 + 0.604741i
\(651\) 21.7670i 0.853115i
\(652\) 0.848177 3.16544i 0.0332172 0.123968i
\(653\) −4.68516 8.11494i −0.183345 0.317562i 0.759673 0.650305i \(-0.225359\pi\)
−0.943017 + 0.332743i \(0.892026\pi\)
\(654\) −1.52367 0.879689i −0.0595800 0.0343986i
\(655\) 7.46813 7.46813i 0.291804 0.291804i
\(656\) 5.19237 + 19.3782i 0.202728 + 0.756591i
\(657\) 11.5890 3.10527i 0.452130 0.121148i
\(658\) 7.33083 7.33083i 0.285786 0.285786i
\(659\) 26.6796 + 15.4035i 1.03929 + 0.600033i 0.919632 0.392782i \(-0.128487\pi\)
0.119657 + 0.992815i \(0.461821\pi\)
\(660\) −0.711467 0.364632i −0.0276938 0.0141933i
\(661\) −26.7782 7.17520i −1.04155 0.279083i −0.302796 0.953055i \(-0.597920\pi\)
−0.738757 + 0.673972i \(0.764587\pi\)
\(662\) −27.6647 −1.07522
\(663\) 2.16016 + 0.241531i 0.0838938 + 0.00938029i
\(664\) 20.9368 0.812507
\(665\) −0.943853 + 3.52251i −0.0366010 + 0.136597i
\(666\) 13.8663 8.00574i 0.537310 0.310216i
\(667\) 6.05302 10.4841i 0.234374 0.405948i
\(668\) 1.39910 1.39910i 0.0541330 0.0541330i
\(669\) 22.2060 5.95008i 0.858534 0.230043i
\(670\) 17.9539 4.81075i 0.693622 0.185855i
\(671\) −4.74665 + 22.0744i −0.183242 + 0.852174i
\(672\) 2.13762 3.70247i 0.0824605 0.142826i
\(673\) 13.5885 + 23.5359i 0.523796 + 0.907242i 0.999616 + 0.0276993i \(0.00881808\pi\)
−0.475820 + 0.879543i \(0.657849\pi\)
\(674\) −5.20131 1.39369i −0.200347 0.0536828i
\(675\) 3.11344i 0.119836i
\(676\) 1.67505 + 1.54893i 0.0644252 + 0.0595742i
\(677\) 8.32855i 0.320092i −0.987110 0.160046i \(-0.948836\pi\)
0.987110 0.160046i \(-0.0511643\pi\)
\(678\) −8.42214 2.25670i −0.323450 0.0866682i
\(679\) −50.1966 + 28.9810i −1.92637 + 1.11219i
\(680\) 1.92976 + 1.11415i 0.0740029 + 0.0427256i
\(681\) 16.9392 16.9392i 0.649111 0.649111i
\(682\) −16.5418 + 18.2844i −0.633418 + 0.700146i
\(683\) 12.9730 + 48.4160i 0.496399 + 1.85259i 0.522051 + 0.852914i \(0.325167\pi\)
−0.0256521 + 0.999671i \(0.508166\pi\)
\(684\) 0.0762929 + 0.0762929i 0.00291713 + 0.00291713i
\(685\) 3.14215 5.44237i 0.120055 0.207942i
\(686\) −25.6510 + 14.8096i −0.979361 + 0.565434i
\(687\) 13.1879 + 3.53369i 0.503150 + 0.134819i
\(688\) 17.3030 0.659670
\(689\) −44.2040 4.94251i −1.68404 0.188295i
\(690\) 4.48050i 0.170570i
\(691\) 3.30613 12.3387i 0.125771 0.469385i −0.874095 0.485755i \(-0.838545\pi\)
0.999866 + 0.0163709i \(0.00521124\pi\)
\(692\) −0.302772 + 0.174805i −0.0115097 + 0.00664511i
\(693\) −14.3052 + 0.715789i −0.543409 + 0.0271906i
\(694\) −34.3245 34.3245i −1.30294 1.30294i
\(695\) −4.51694 16.8574i −0.171337 0.639439i
\(696\) −3.81251 14.2285i −0.144513 0.539330i
\(697\) 1.97954 1.97954i 0.0749803 0.0749803i
\(698\) 7.86854 13.6287i 0.297829 0.515855i
\(699\) 13.4623 + 23.3174i 0.509191 + 0.881944i
\(700\) 0.610720 2.27924i 0.0230831 0.0861471i
\(701\) −16.6520 −0.628937 −0.314469 0.949268i \(-0.601826\pi\)
−0.314469 + 0.949268i \(0.601826\pi\)
\(702\) −4.95207 1.93868i −0.186904 0.0731709i
\(703\) 6.67398i 0.251714i
\(704\) −22.6659 + 7.30539i −0.854254 + 0.275332i
\(705\) −1.11778 1.93605i −0.0420979 0.0729158i
\(706\) 7.51331 13.0134i 0.282767 0.489767i
\(707\) 11.5036 + 11.5036i 0.432638 + 0.432638i
\(708\) −1.55367 + 0.416305i −0.0583905 + 0.0156457i
\(709\) −7.79400 29.0876i −0.292710 1.09241i −0.943019 0.332738i \(-0.892027\pi\)
0.650309 0.759670i \(-0.274639\pi\)
\(710\) 11.0397 + 11.0397i 0.414313 + 0.414313i
\(711\) −11.9137 6.87838i −0.446799 0.257959i
\(712\) 9.79481 + 16.9651i 0.367076 + 0.635794i
\(713\) −10.7675 2.88513i −0.403245 0.108049i
\(714\) −3.84000 −0.143709
\(715\) 9.06919 13.6941i 0.339169 0.512130i
\(716\) 3.71588 0.138869
\(717\) −12.0148 3.21935i −0.448701 0.120229i
\(718\) 10.5268 + 18.2330i 0.392857 + 0.680448i
\(719\) −14.3703 8.29672i −0.535923 0.309415i 0.207502 0.978235i \(-0.433467\pi\)
−0.743425 + 0.668819i \(0.766800\pi\)
\(720\) −4.19589 4.19589i −0.156372 0.156372i
\(721\) 4.25834 + 15.8923i 0.158589 + 0.591861i
\(722\) −26.5308 + 7.10890i −0.987373 + 0.264566i
\(723\) 15.1032 + 15.1032i 0.561692 + 0.561692i
\(724\) 1.34636 2.33196i 0.0500370 0.0866667i
\(725\) −8.52120 14.7592i −0.316470 0.548141i
\(726\) −12.5604 10.2699i −0.466160 0.381153i
\(727\) 21.4839i 0.796794i −0.917213 0.398397i \(-0.869567\pi\)
0.917213 0.398397i \(-0.130433\pi\)
\(728\) 33.7355 + 24.8536i 1.25032 + 0.921136i
\(729\) 1.00000 0.0370370
\(730\) 6.29092 23.4780i 0.232837 0.868960i
\(731\) −1.20726 2.09103i −0.0446521 0.0773397i
\(732\) 0.597372 1.03468i 0.0220795 0.0382428i
\(733\) −33.0243 + 33.0243i −1.21978 + 1.21978i −0.252071 + 0.967709i \(0.581112\pi\)
−0.967709 + 0.252071i \(0.918888\pi\)
\(734\) −1.48760 5.55179i −0.0549082 0.204920i
\(735\) 4.14151 + 15.4563i 0.152762 + 0.570116i
\(736\) 1.54816 + 1.54816i 0.0570661 + 0.0570661i
\(737\) 30.3917 1.52071i 1.11949 0.0560161i
\(738\) −5.93165 + 3.42464i −0.218347 + 0.126063i
\(739\) 3.84705 14.3574i 0.141516 0.528145i −0.858370 0.513031i \(-0.828522\pi\)
0.999886 0.0151134i \(-0.00481091\pi\)
\(740\) 2.61670i 0.0961920i
\(741\) −1.73190 + 1.38355i −0.0636229 + 0.0508262i
\(742\) 78.5790 2.88473
\(743\) −11.6396 3.11883i −0.427017 0.114419i 0.0389088 0.999243i \(-0.487612\pi\)
−0.465925 + 0.884824i \(0.654278\pi\)
\(744\) −11.7466 + 6.78192i −0.430652 + 0.248637i
\(745\) −9.24324 + 16.0098i −0.338646 + 0.586552i
\(746\) −4.57728 4.57728i −0.167586 0.167586i
\(747\) 2.01365 + 7.51503i 0.0736755 + 0.274961i
\(748\) −0.260209 0.235410i −0.00951418 0.00860743i
\(749\) 39.5066 39.5066i 1.44354 1.44354i
\(750\) −14.2348 8.21845i −0.519780 0.300095i
\(751\) −30.7140 + 17.7328i −1.12077 + 0.647078i −0.941598 0.336740i \(-0.890676\pi\)
−0.179173 + 0.983817i \(0.557342\pi\)
\(752\) 6.79198 + 1.81991i 0.247678 + 0.0663651i
\(753\) 11.8226i 0.430839i
\(754\) −28.7811 + 4.36310i −1.04815 + 0.158895i
\(755\) 1.19709i 0.0435664i
\(756\) 0.732066 + 0.196156i 0.0266250 + 0.00713414i
\(757\) −19.0339 32.9677i −0.691800 1.19823i −0.971247 0.238072i \(-0.923485\pi\)
0.279447 0.960161i \(-0.409849\pi\)
\(758\) 19.8168 34.3237i 0.719777 1.24669i
\(759\) 1.54202 7.17121i 0.0559718 0.260298i
\(760\) −2.19501 + 0.588151i −0.0796213 + 0.0213345i
\(761\) 37.4519 10.0352i 1.35763 0.363776i 0.494684 0.869073i \(-0.335284\pi\)
0.862946 + 0.505297i \(0.168617\pi\)
\(762\) −10.1266 + 10.1266i −0.366848 + 0.366848i
\(763\) −2.57567 + 4.46119i −0.0932454 + 0.161506i
\(764\) 2.23853 1.29242i 0.0809872 0.0467580i
\(765\) −0.214311 + 0.799820i −0.00774844 + 0.0289176i
\(766\) 4.78277 0.172808
\(767\) −4.95307 32.6728i −0.178845 1.17975i
\(768\) 4.18042 0.150848
\(769\) −2.21715 0.594083i −0.0799524 0.0214232i 0.218621 0.975810i \(-0.429844\pi\)
−0.298574 + 0.954387i \(0.596511\pi\)
\(770\) −13.2345 + 25.8230i −0.476938 + 0.930597i
\(771\) 23.4522 + 13.5402i 0.844612 + 0.487637i
\(772\) −1.39789 + 1.39789i −0.0503111 + 0.0503111i
\(773\) −18.3647 + 4.92081i −0.660533 + 0.176989i −0.573487 0.819215i \(-0.694410\pi\)
−0.0870466 + 0.996204i \(0.527743\pi\)
\(774\) 1.52895 + 5.70611i 0.0549569 + 0.205102i
\(775\) −11.0964 + 11.0964i −0.398596 + 0.398596i
\(776\) −31.2794 18.0592i −1.12286 0.648286i
\(777\) −23.4402 40.5997i −0.840914 1.45651i
\(778\) 12.2245 45.6226i 0.438271 1.63565i
\(779\) 2.85495i 0.102289i
\(780\) −0.679035 + 0.542458i −0.0243134 + 0.0194231i
\(781\) 13.8700 + 21.4689i 0.496309 + 0.768219i
\(782\) 0.508979 1.89953i 0.0182010 0.0679272i
\(783\) 4.74047 2.73691i 0.169411 0.0978093i
\(784\) −43.5874 25.1652i −1.55669 0.898756i
\(785\) −4.73519 4.73519i −0.169006 0.169006i
\(786\) −10.9550 + 2.93539i −0.390753 + 0.104702i
\(787\) 3.56021 0.953956i 0.126908 0.0340049i −0.194806 0.980842i \(-0.562408\pi\)
0.321714 + 0.946837i \(0.395741\pi\)
\(788\) 1.20901 + 1.20901i 0.0430693 + 0.0430693i
\(789\) 19.0763 + 11.0137i 0.679135 + 0.392099i
\(790\) −24.1358 + 13.9348i −0.858713 + 0.495778i
\(791\) −6.60747 + 24.6594i −0.234935 + 0.876788i
\(792\) −4.84333 7.49682i −0.172100 0.266388i
\(793\) 19.7620 + 14.5591i 0.701770 + 0.517008i
\(794\) 1.52696i 0.0541899i
\(795\) 4.38551 16.3669i 0.155538 0.580475i
\(796\) −1.00979 1.74902i −0.0357912 0.0619922i
\(797\) −16.5030 9.52803i −0.584567 0.337500i 0.178379 0.983962i \(-0.442915\pi\)
−0.762946 + 0.646462i \(0.776248\pi\)
\(798\) 2.76908 2.76908i 0.0980245 0.0980245i
\(799\) −0.253956 0.947777i −0.00898432 0.0335299i
\(800\) 2.97718 0.797732i 0.105259 0.0282041i
\(801\) −5.14739 + 5.14739i −0.181874 + 0.181874i
\(802\) 18.9174 + 10.9220i 0.667996 + 0.385668i
\(803\) 18.1491 35.4124i 0.640468 1.24968i
\(804\) −1.55529 0.416739i −0.0548509 0.0146972i
\(805\) −13.1186 −0.462369
\(806\) 10.7398 + 24.5590i 0.378295 + 0.865052i
\(807\) −2.18492 −0.0769130
\(808\) −2.62379 + 9.79212i −0.0923047 + 0.344486i
\(809\) −2.52321 + 1.45678i −0.0887115 + 0.0512176i −0.543699 0.839280i \(-0.682977\pi\)
0.454988 + 0.890498i \(0.349644\pi\)
\(810\) 1.01294 1.75447i 0.0355912 0.0616457i
\(811\) 34.9996 34.9996i 1.22900 1.22900i 0.264660 0.964342i \(-0.414740\pi\)
0.964342 0.264660i \(-0.0852596\pi\)
\(812\) 4.00720 1.07373i 0.140625 0.0376804i
\(813\) −1.73614 + 0.465197i −0.0608891 + 0.0163152i
\(814\) 11.1637 51.9174i 0.391289 1.81970i
\(815\) −12.8242 + 22.2121i −0.449212 + 0.778057i
\(816\) −1.30222 2.25552i −0.0455870 0.0789590i
\(817\) 2.37845 + 0.637303i 0.0832114 + 0.0222964i
\(818\) 6.55122i 0.229058i
\(819\) −5.67633 + 14.4993i −0.198347 + 0.506647i
\(820\) 1.11936i 0.0390896i
\(821\) −13.3514 3.57751i −0.465968 0.124856i 0.0181932 0.999834i \(-0.494209\pi\)
−0.484161 + 0.874979i \(0.660875\pi\)
\(822\) −5.84428 + 3.37420i −0.203843 + 0.117689i
\(823\) −4.05633 2.34192i −0.141395 0.0816343i 0.427634 0.903952i \(-0.359347\pi\)
−0.569029 + 0.822318i \(0.692681\pi\)
\(824\) −7.24958 + 7.24958i −0.252551 + 0.252551i
\(825\) −7.65743 6.92763i −0.266597 0.241189i
\(826\) 15.1100 + 56.3912i 0.525743 + 1.96210i
\(827\) 29.6021 + 29.6021i 1.02937 + 1.02937i 0.999556 + 0.0298111i \(0.00949057\pi\)
0.0298111 + 0.999556i \(0.490509\pi\)
\(828\) −0.194065 + 0.336131i −0.00674423 + 0.0116814i
\(829\) 7.28722 4.20728i 0.253095 0.146125i −0.368085 0.929792i \(-0.619987\pi\)
0.621181 + 0.783667i \(0.286653\pi\)
\(830\) 15.2246 + 4.07942i 0.528453 + 0.141599i
\(831\) 11.8030 0.409440
\(832\) −2.87673 + 25.7284i −0.0997325 + 0.891970i
\(833\) 7.02328i 0.243342i
\(834\) −4.85051 + 18.1023i −0.167959 + 0.626833i
\(835\) −13.4111 + 7.74292i −0.464111 + 0.267955i
\(836\) 0.357398 0.0178831i 0.0123609 0.000618501i
\(837\) −3.56405 3.56405i −0.123191 0.123191i
\(838\) −3.21341 11.9926i −0.111006 0.414278i
\(839\) −2.38103 8.88613i −0.0822023 0.306783i 0.912567 0.408926i \(-0.134097\pi\)
−0.994770 + 0.102143i \(0.967430\pi\)
\(840\) −11.2872 + 11.2872i −0.389444 + 0.389444i
\(841\) 0.481394 0.833798i 0.0165998 0.0287517i
\(842\) −23.1800 40.1490i −0.798836 1.38362i
\(843\) 2.65281 9.90041i 0.0913675 0.340988i
\(844\) −2.33864 −0.0804992
\(845\) −9.52557 15.1027i −0.327689 0.519550i
\(846\) 2.40065i 0.0825360i
\(847\) −30.0696 + 36.7759i −1.03321 + 1.26364i
\(848\) 26.6478 + 46.1553i 0.915088 + 1.58498i
\(849\) −1.44242 + 2.49835i −0.0495038 + 0.0857431i
\(850\) −1.95757 1.95757i −0.0671440 0.0671440i
\(851\) 23.1904 6.21384i 0.794955 0.213008i
\(852\) −0.350042 1.30638i −0.0119923 0.0447557i
\(853\) 6.31748 + 6.31748i 0.216306 + 0.216306i 0.806940 0.590634i \(-0.201122\pi\)
−0.590634 + 0.806940i \(0.701122\pi\)
\(854\) −37.5541 21.6819i −1.28508 0.741939i
\(855\) −0.422219 0.731306i −0.0144396 0.0250101i
\(856\) 33.6289 + 9.01083i 1.14941 + 0.307984i
\(857\) 11.5493 0.394516 0.197258 0.980352i \(-0.436796\pi\)
0.197258 + 0.980352i \(0.436796\pi\)
\(858\) −15.7869 + 7.86578i −0.538955 + 0.268533i
\(859\) −20.0351 −0.683589 −0.341795 0.939775i \(-0.611035\pi\)
−0.341795 + 0.939775i \(0.611035\pi\)
\(860\) 0.932532 + 0.249871i 0.0317991 + 0.00852054i
\(861\) 10.0271 + 17.3675i 0.341723 + 0.591882i
\(862\) 43.1651 + 24.9214i 1.47021 + 0.848826i
\(863\) 3.11411 + 3.11411i 0.106005 + 0.106005i 0.758120 0.652115i \(-0.226118\pi\)
−0.652115 + 0.758120i \(0.726118\pi\)
\(864\) 0.256222 + 0.956235i 0.00871686 + 0.0325318i
\(865\) 2.64301 0.708191i 0.0898649 0.0240792i
\(866\) −18.2862 18.2862i −0.621392 0.621392i
\(867\) 8.31828 14.4077i 0.282504 0.489311i
\(868\) −1.91001 3.30823i −0.0648298 0.112289i
\(869\) −43.4261 + 13.9966i −1.47313 + 0.474801i
\(870\) 11.0893i 0.375964i
\(871\) 12.0595 30.8041i 0.408620 1.04376i
\(872\) −3.20999 −0.108704
\(873\) 3.47376 12.9643i 0.117569 0.438773i
\(874\) 1.00275 + 1.73681i 0.0339185 + 0.0587486i
\(875\) −24.0630 + 41.6784i −0.813479 + 1.40899i
\(876\) −1.48886 + 1.48886i −0.0503040 + 0.0503040i
\(877\) −0.305217 1.13909i −0.0103065 0.0384642i 0.960581 0.278000i \(-0.0896715\pi\)
−0.970888 + 0.239536i \(0.923005\pi\)
\(878\) −13.5646 50.6236i −0.457782 1.70846i
\(879\) 16.2863 + 16.2863i 0.549323 + 0.549323i
\(880\) −19.6559 + 0.983522i −0.662599 + 0.0331545i
\(881\) 19.5851 11.3075i 0.659840 0.380959i −0.132376 0.991200i \(-0.542261\pi\)
0.792216 + 0.610241i \(0.208927\pi\)
\(882\) 4.44736 16.5978i 0.149750 0.558876i
\(883\) 1.17978i 0.0397027i 0.999803 + 0.0198514i \(0.00631930\pi\)
−0.999803 + 0.0198514i \(0.993681\pi\)
\(884\) −0.349504 + 0.152841i −0.0117551 + 0.00514060i
\(885\) 12.5888 0.423168
\(886\) 22.2282 + 5.95603i 0.746771 + 0.200097i
\(887\) 32.5378 18.7857i 1.09251 0.630762i 0.158268 0.987396i \(-0.449409\pi\)
0.934244 + 0.356634i \(0.116076\pi\)
\(888\) 14.6065 25.2992i 0.490162 0.848986i
\(889\) 29.6500 + 29.6500i 0.994429 + 0.994429i
\(890\) 3.81692 + 14.2449i 0.127944 + 0.477492i
\(891\) 2.22508 2.45948i 0.0745429 0.0823956i
\(892\) −2.85284 + 2.85284i −0.0955203 + 0.0955203i
\(893\) 0.866588 + 0.500325i 0.0289993 + 0.0167427i
\(894\) 17.1921 9.92585i 0.574989 0.331970i
\(895\) −28.0915 7.52710i −0.938996 0.251603i
\(896\) 54.2864i 1.81358i
\(897\) −6.41999 4.72974i −0.214357 0.157921i
\(898\) 38.9119i 1.29851i
\(899\) −26.6498 7.14078i −0.888819 0.238158i
\(900\) 0.273197 + 0.473192i 0.00910658 + 0.0157731i
\(901\) 3.71852 6.44067i 0.123882 0.214570i
\(902\) −4.77555 + 22.2089i −0.159009 + 0.739474i
\(903\) 16.7071 4.47665i 0.555977 0.148974i
\(904\) −15.3662 + 4.11737i −0.511073 + 0.136942i
\(905\) −14.9020 + 14.9020i −0.495360 + 0.495360i
\(906\) 0.642745 1.11327i 0.0213538 0.0369858i
\(907\) 6.15366 3.55282i 0.204329 0.117969i −0.394344 0.918963i \(-0.629028\pi\)
0.598673 + 0.800994i \(0.295695\pi\)
\(908\) −1.08810 + 4.06086i −0.0361100 + 0.134764i
\(909\) −3.76712 −0.124947
\(910\) 19.6888 + 24.6459i 0.652676 + 0.817004i
\(911\) −12.7493 −0.422402 −0.211201 0.977443i \(-0.567737\pi\)
−0.211201 + 0.977443i \(0.567737\pi\)
\(912\) 2.56554 + 0.687435i 0.0849536 + 0.0227633i
\(913\) 22.9636 + 11.7690i 0.759983 + 0.389497i
\(914\) 3.72685 + 2.15170i 0.123273 + 0.0711718i
\(915\) −6.61194 + 6.61194i −0.218584 + 0.218584i
\(916\) −2.31442 + 0.620147i −0.0764706 + 0.0204902i
\(917\) 8.59463 + 32.0756i 0.283820 + 1.05923i
\(918\) 0.628748 0.628748i 0.0207518 0.0207518i
\(919\) −7.72958 4.46267i −0.254975 0.147210i 0.367065 0.930195i \(-0.380363\pi\)
−0.622040 + 0.782985i \(0.713696\pi\)
\(920\) −4.08734 7.07949i −0.134756 0.233404i
\(921\) −6.57368 + 24.5333i −0.216610 + 0.808400i
\(922\) 39.3744i 1.29673i
\(923\) 27.4723 4.16469i 0.904263 0.137083i
\(924\) 2.11134 1.36404i 0.0694581 0.0448735i
\(925\) 8.74759 32.6465i 0.287619 1.07341i
\(926\) −23.4879 + 13.5607i −0.771860 + 0.445633i
\(927\) −3.29940 1.90491i −0.108366 0.0625654i
\(928\) 3.83175 + 3.83175i 0.125783 + 0.125783i
\(929\) 8.33769 2.23408i 0.273551 0.0732977i −0.119436 0.992842i \(-0.538109\pi\)
0.392986 + 0.919544i \(0.371442\pi\)
\(930\) −9.86318 + 2.64283i −0.323427 + 0.0866619i
\(931\) −5.06459 5.06459i −0.165985 0.165985i
\(932\) −4.09210 2.36258i −0.134041 0.0773887i
\(933\) −15.2774 + 8.82041i −0.500160 + 0.288767i
\(934\) 14.2257 53.0911i 0.465479 1.73719i
\(935\) 1.49028 + 2.30676i 0.0487374 + 0.0754390i
\(936\) −9.59316 + 1.45428i −0.313562 + 0.0475348i
\(937\) 29.3584i 0.959098i 0.877515 + 0.479549i \(0.159200\pi\)
−0.877515 + 0.479549i \(0.840800\pi\)
\(938\) −15.1257 + 56.4500i −0.493873 + 1.84316i
\(939\) 14.9542 + 25.9014i 0.488011 + 0.845259i
\(940\) 0.339768 + 0.196165i 0.0110820 + 0.00639820i
\(941\) −35.6549 + 35.6549i −1.16232 + 1.16232i −0.178349 + 0.983967i \(0.557076\pi\)
−0.983967 + 0.178349i \(0.942924\pi\)
\(942\) 1.86119 + 6.94607i 0.0606410 + 0.226315i
\(943\) −9.92022 + 2.65811i −0.323047 + 0.0865601i
\(944\) −27.9986 + 27.9986i −0.911278 + 0.911278i
\(945\) −5.13696 2.96583i −0.167105 0.0964783i
\(946\) 17.4361 + 8.93613i 0.566896 + 0.290539i
\(947\) 0.222822 + 0.0597050i 0.00724074 + 0.00194015i 0.262438 0.964949i \(-0.415474\pi\)
−0.255197 + 0.966889i \(0.582140\pi\)
\(948\) 2.41425 0.0784112
\(949\) −27.0002 33.7981i −0.876463 1.09713i
\(950\) 2.82326 0.0915988
\(951\) 2.27968 8.50787i 0.0739236 0.275887i
\(952\) −6.06746 + 3.50305i −0.196648 + 0.113535i
\(953\) −25.0444 + 43.3781i −0.811266 + 1.40515i 0.100712 + 0.994916i \(0.467888\pi\)
−0.911978 + 0.410239i \(0.865445\pi\)
\(954\) −12.8662 + 12.8662i −0.416560 + 0.416560i
\(955\) −19.5410 + 5.23598i −0.632330 + 0.169432i
\(956\) 2.10854 0.564983i 0.0681952 0.0182729i
\(957\) 3.81654 17.7489i 0.123371 0.573742i
\(958\) 4.67169 8.09161i 0.150936 0.261428i
\(959\) 9.87941 + 17.1116i 0.319023 + 0.552564i
\(960\) −9.52616 2.55253i −0.307455 0.0823824i
\(961\) 5.59514i 0.180488i
\(962\) −46.4787 34.2418i −1.49854 1.10400i
\(963\) 12.9373i 0.416899i
\(964\) −3.62070 0.970164i −0.116615 0.0312469i
\(965\) 13.3995 7.73619i 0.431344 0.249037i
\(966\) 12.2000 + 7.04369i 0.392529 + 0.226627i
\(967\) 10.6077 10.6077i 0.341121 0.341121i −0.515667 0.856789i \(-0.672456\pi\)
0.856789 + 0.515667i \(0.172456\pi\)
\(968\) −29.2150 4.76894i −0.939007 0.153280i
\(969\) −0.0959271 0.358005i −0.00308162 0.0115008i
\(970\) −19.2267 19.2267i −0.617331 0.617331i
\(971\) −20.4936 + 35.4960i −0.657671 + 1.13912i 0.323546 + 0.946213i \(0.395125\pi\)
−0.981217 + 0.192908i \(0.938208\pi\)
\(972\) −0.151984 + 0.0877479i −0.00487488 + 0.00281451i
\(973\) 53.0024 + 14.2019i 1.69918 + 0.455293i
\(974\) −35.0950 −1.12452
\(975\) −10.2852 + 4.49780i −0.329390 + 0.144045i
\(976\) 29.4111i 0.941427i
\(977\) 11.0371 41.1909i 0.353107 1.31781i −0.529743 0.848158i \(-0.677712\pi\)
0.882850 0.469655i \(-0.155622\pi\)
\(978\) 23.8525 13.7712i 0.762719 0.440356i
\(979\) 1.20655 + 24.1132i 0.0385617 + 0.770662i
\(980\) −1.98570 1.98570i −0.0634310 0.0634310i
\(981\) −0.308728 1.15219i −0.00985693 0.0367866i
\(982\) −1.81986 6.79182i −0.0580742 0.216736i
\(983\) 9.76556 9.76556i 0.311473 0.311473i −0.534007 0.845480i \(-0.679314\pi\)
0.845480 + 0.534007i \(0.179314\pi\)
\(984\) −6.24827 + 10.8223i −0.199188 + 0.345003i
\(985\) −6.69091 11.5890i −0.213190 0.369256i
\(986\) 1.25974 4.70140i 0.0401181 0.149723i
\(987\) 7.02893 0.223733
\(988\) 0.141816 0.362248i 0.00451178 0.0115246i
\(989\) 8.85786i 0.281664i
\(990\) −2.06120 6.39514i −0.0655093 0.203251i
\(991\) 3.52517 + 6.10578i 0.111981 + 0.193956i 0.916569 0.399877i \(-0.130947\pi\)
−0.804588 + 0.593833i \(0.797614\pi\)
\(992\) 2.49488 4.32125i 0.0792124 0.137200i
\(993\) −13.2627 13.2627i −0.420879 0.420879i
\(994\) −47.4155 + 12.7049i −1.50393 + 0.402976i
\(995\) 4.09099 + 15.2678i 0.129693 + 0.484022i
\(996\) −0.965469 0.965469i −0.0305921 0.0305921i
\(997\) 4.82924 + 2.78816i 0.152943 + 0.0883020i 0.574519 0.818492i \(-0.305189\pi\)
−0.421575 + 0.906793i \(0.638523\pi\)
\(998\) 31.6259 + 54.7776i 1.00110 + 1.73395i
\(999\) 10.4857 + 2.80963i 0.331752 + 0.0888927i
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 429.2.bd.a.76.5 56
11.10 odd 2 inner 429.2.bd.a.76.10 yes 56
13.6 odd 12 inner 429.2.bd.a.175.10 yes 56
143.32 even 12 inner 429.2.bd.a.175.5 yes 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.bd.a.76.5 56 1.1 even 1 trivial
429.2.bd.a.76.10 yes 56 11.10 odd 2 inner
429.2.bd.a.175.5 yes 56 143.32 even 12 inner
429.2.bd.a.175.10 yes 56 13.6 odd 12 inner