Properties

Label 35.3.l.a.2.6
Level $35$
Weight $3$
Character 35.2
Analytic conductor $0.954$
Analytic rank $0$
Dimension $24$
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] = [35,3,Mod(2,35)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(35, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("35.2");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 35.l (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: \(0.953680925261\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 2.6
Character \(\chi\) \(=\) 35.2
Dual form 35.3.l.a.18.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.95850 - 0.792728i) q^{2} +(-2.36445 - 0.633552i) q^{3} +(4.66022 - 2.69058i) q^{4} +(-4.16825 + 2.76146i) q^{5} -7.49746 q^{6} +(5.78419 + 3.94249i) q^{7} +(2.99127 - 2.99127i) q^{8} +(-2.60501 - 1.50400i) q^{9} +O(q^{10})\) \(q+(2.95850 - 0.792728i) q^{2} +(-2.36445 - 0.633552i) q^{3} +(4.66022 - 2.69058i) q^{4} +(-4.16825 + 2.76146i) q^{5} -7.49746 q^{6} +(5.78419 + 3.94249i) q^{7} +(2.99127 - 2.99127i) q^{8} +(-2.60501 - 1.50400i) q^{9} +(-10.1427 + 11.4741i) q^{10} +(-3.12159 - 5.40675i) q^{11} +(-12.7235 + 3.40924i) q^{12} +(11.7345 - 11.7345i) q^{13} +(20.2378 + 7.07857i) q^{14} +(11.6051 - 3.88853i) q^{15} +(-4.28389 + 7.41992i) q^{16} +(1.22400 - 4.56805i) q^{17} +(-8.89918 - 2.38453i) q^{18} +(-11.4064 - 6.58549i) q^{19} +(-11.9950 + 24.0840i) q^{20} +(-11.1786 - 12.9864i) q^{21} +(-13.5213 - 13.5213i) q^{22} +(9.33654 + 34.8444i) q^{23} +(-8.96783 + 5.17758i) q^{24} +(9.74863 - 23.0210i) q^{25} +(25.4144 - 44.0190i) q^{26} +(20.7846 + 20.7846i) q^{27} +(37.5631 + 2.81005i) q^{28} -28.5683i q^{29} +(31.2513 - 20.7040i) q^{30} +(10.1948 + 17.6579i) q^{31} +(-11.1715 + 41.6924i) q^{32} +(3.95538 + 14.7617i) q^{33} -14.4849i q^{34} +(-34.9970 - 0.460456i) q^{35} -16.1865 q^{36} +(22.6479 - 6.06849i) q^{37} +(-38.9664 - 10.4410i) q^{38} +(-35.1801 + 20.3113i) q^{39} +(-4.20808 + 20.7287i) q^{40} -45.1077 q^{41} +(-43.3667 - 29.5586i) q^{42} +(-21.9185 + 21.9185i) q^{43} +(-29.0946 - 16.7978i) q^{44} +(15.0116 - 0.924577i) q^{45} +(55.2443 + 95.6860i) q^{46} +(-10.4426 + 2.79810i) q^{47} +(14.8299 - 14.8299i) q^{48} +(17.9136 + 45.6081i) q^{49} +(10.5920 - 75.8356i) q^{50} +(-5.78819 + 10.0254i) q^{51} +(23.1128 - 86.2582i) q^{52} +(-71.6904 - 19.2094i) q^{53} +(77.9678 + 45.0147i) q^{54} +(27.9421 + 13.9165i) q^{55} +(29.0951 - 5.50902i) q^{56} +(22.7976 + 22.7976i) q^{57} +(-22.6469 - 84.5194i) q^{58} +(-14.6115 + 8.43595i) q^{59} +(43.6201 - 49.3459i) q^{60} +(16.7743 - 29.0540i) q^{61} +(44.1593 + 44.1593i) q^{62} +(-9.13833 - 18.9696i) q^{63} +97.9319i q^{64} +(-16.5080 + 81.3170i) q^{65} +(23.4040 + 40.5369i) q^{66} +(25.6891 - 95.8731i) q^{67} +(-6.58656 - 24.5814i) q^{68} -88.3030i q^{69} +(-103.904 + 26.3808i) q^{70} +66.2415 q^{71} +(-12.2912 + 3.29341i) q^{72} +(99.8826 + 26.7635i) q^{73} +(62.1933 - 35.9073i) q^{74} +(-37.6351 + 48.2556i) q^{75} -70.8751 q^{76} +(3.26020 - 43.5805i) q^{77} +(-87.9792 + 87.9792i) q^{78} +(-36.1253 - 20.8569i) q^{79} +(-2.63350 - 42.7579i) q^{80} +(-22.4400 - 38.8671i) q^{81} +(-133.451 + 35.7582i) q^{82} +(7.39450 - 7.39450i) q^{83} +(-87.0357 - 30.4424i) q^{84} +(7.51254 + 22.4208i) q^{85} +(-47.4706 + 82.2215i) q^{86} +(-18.0995 + 67.5483i) q^{87} +(-25.5106 - 6.83554i) q^{88} +(-19.2257 - 11.0999i) q^{89} +(43.6788 - 14.6355i) q^{90} +(114.138 - 21.6115i) q^{91} +(137.262 + 137.262i) q^{92} +(-12.9179 - 48.2102i) q^{93} +(-28.6764 + 16.5563i) q^{94} +(65.7303 - 4.04840i) q^{95} +(52.8286 - 91.5018i) q^{96} +(-73.6717 - 73.6717i) q^{97} +(89.1523 + 120.731i) q^{98} +18.7795i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 2 q^{2} - 2 q^{3} - 4 q^{5} - 6 q^{7} - 36 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 2 q^{2} - 2 q^{3} - 4 q^{5} - 6 q^{7} - 36 q^{8} + 14 q^{10} - 24 q^{11} - 46 q^{12} - 8 q^{13} + 52 q^{15} + 20 q^{16} - 48 q^{17} - 4 q^{18} - 72 q^{20} + 56 q^{21} + 104 q^{22} - 86 q^{23} - 16 q^{25} + 140 q^{26} + 76 q^{27} + 186 q^{28} + 64 q^{30} + 120 q^{31} + 130 q^{32} + 116 q^{33} - 240 q^{35} - 496 q^{36} + 44 q^{37} + 16 q^{38} - 158 q^{40} + 16 q^{41} - 370 q^{42} - 196 q^{43} - 104 q^{45} - 148 q^{46} - 208 q^{47} - 52 q^{48} + 580 q^{50} - 160 q^{51} - 288 q^{52} - 72 q^{53} + 208 q^{55} + 420 q^{56} + 656 q^{57} - 2 q^{58} + 262 q^{60} + 308 q^{61} + 176 q^{62} + 212 q^{63} + 132 q^{65} + 316 q^{66} + 198 q^{67} + 332 q^{68} - 200 q^{70} - 792 q^{71} + 308 q^{72} + 380 q^{73} - 450 q^{75} - 400 q^{76} - 472 q^{77} - 720 q^{78} - 324 q^{80} - 352 q^{81} - 818 q^{82} - 460 q^{83} + 144 q^{85} - 336 q^{86} - 214 q^{87} - 288 q^{88} + 120 q^{90} + 984 q^{91} + 1372 q^{92} - 68 q^{93} - 88 q^{95} + 816 q^{96} - 72 q^{97} + 482 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.95850 0.792728i 1.47925 0.396364i 0.573159 0.819444i \(-0.305718\pi\)
0.906092 + 0.423080i \(0.139051\pi\)
\(3\) −2.36445 0.633552i −0.788149 0.211184i −0.157775 0.987475i \(-0.550432\pi\)
−0.630374 + 0.776291i \(0.717099\pi\)
\(4\) 4.66022 2.69058i 1.16505 0.672645i
\(5\) −4.16825 + 2.76146i −0.833650 + 0.552293i
\(6\) −7.49746 −1.24958
\(7\) 5.78419 + 3.94249i 0.826312 + 0.563212i
\(8\) 2.99127 2.99127i 0.373909 0.373909i
\(9\) −2.60501 1.50400i −0.289445 0.167111i
\(10\) −10.1427 + 11.4741i −1.01427 + 1.14741i
\(11\) −3.12159 5.40675i −0.283781 0.491523i 0.688532 0.725206i \(-0.258256\pi\)
−0.972313 + 0.233683i \(0.924922\pi\)
\(12\) −12.7235 + 3.40924i −1.06029 + 0.284103i
\(13\) 11.7345 11.7345i 0.902657 0.902657i −0.0930085 0.995665i \(-0.529648\pi\)
0.995665 + 0.0930085i \(0.0296484\pi\)
\(14\) 20.2378 + 7.07857i 1.44556 + 0.505612i
\(15\) 11.6051 3.88853i 0.773676 0.259236i
\(16\) −4.28389 + 7.41992i −0.267743 + 0.463745i
\(17\) 1.22400 4.56805i 0.0720003 0.268709i −0.920536 0.390657i \(-0.872248\pi\)
0.992536 + 0.121949i \(0.0389144\pi\)
\(18\) −8.89918 2.38453i −0.494399 0.132474i
\(19\) −11.4064 6.58549i −0.600337 0.346605i 0.168837 0.985644i \(-0.445999\pi\)
−0.769174 + 0.639039i \(0.779332\pi\)
\(20\) −11.9950 + 24.0840i −0.599751 + 1.20420i
\(21\) −11.1786 12.9864i −0.532316 0.618399i
\(22\) −13.5213 13.5213i −0.614606 0.614606i
\(23\) 9.33654 + 34.8444i 0.405936 + 1.51498i 0.802322 + 0.596891i \(0.203598\pi\)
−0.396386 + 0.918084i \(0.629736\pi\)
\(24\) −8.96783 + 5.17758i −0.373660 + 0.215732i
\(25\) 9.74863 23.0210i 0.389945 0.920838i
\(26\) 25.4144 44.0190i 0.977475 1.69304i
\(27\) 20.7846 + 20.7846i 0.769800 + 0.769800i
\(28\) 37.5631 + 2.81005i 1.34154 + 0.100359i
\(29\) 28.5683i 0.985114i −0.870280 0.492557i \(-0.836062\pi\)
0.870280 0.492557i \(-0.163938\pi\)
\(30\) 31.2513 20.7040i 1.04171 0.690132i
\(31\) 10.1948 + 17.6579i 0.328865 + 0.569611i 0.982287 0.187383i \(-0.0600006\pi\)
−0.653422 + 0.756994i \(0.726667\pi\)
\(32\) −11.1715 + 41.6924i −0.349108 + 1.30289i
\(33\) 3.95538 + 14.7617i 0.119860 + 0.447323i
\(34\) 14.4849i 0.426026i
\(35\) −34.9970 0.460456i −0.999913 0.0131559i
\(36\) −16.1865 −0.449626
\(37\) 22.6479 6.06849i 0.612106 0.164013i 0.0605694 0.998164i \(-0.480708\pi\)
0.551537 + 0.834151i \(0.314042\pi\)
\(38\) −38.9664 10.4410i −1.02543 0.274763i
\(39\) −35.1801 + 20.3113i −0.902055 + 0.520802i
\(40\) −4.20808 + 20.7287i −0.105202 + 0.518217i
\(41\) −45.1077 −1.10019 −0.550094 0.835103i \(-0.685408\pi\)
−0.550094 + 0.835103i \(0.685408\pi\)
\(42\) −43.3667 29.5586i −1.03254 0.703777i
\(43\) −21.9185 + 21.9185i −0.509733 + 0.509733i −0.914445 0.404711i \(-0.867372\pi\)
0.404711 + 0.914445i \(0.367372\pi\)
\(44\) −29.0946 16.7978i −0.661241 0.381767i
\(45\) 15.0116 0.924577i 0.333590 0.0205461i
\(46\) 55.2443 + 95.6860i 1.20096 + 2.08013i
\(47\) −10.4426 + 2.79810i −0.222184 + 0.0595339i −0.368193 0.929749i \(-0.620024\pi\)
0.146010 + 0.989283i \(0.453357\pi\)
\(48\) 14.8299 14.8299i 0.308957 0.308957i
\(49\) 17.9136 + 45.6081i 0.365584 + 0.930779i
\(50\) 10.5920 75.8356i 0.211840 1.51671i
\(51\) −5.78819 + 10.0254i −0.113494 + 0.196577i
\(52\) 23.1128 86.2582i 0.444477 1.65881i
\(53\) −71.6904 19.2094i −1.35265 0.362441i −0.491537 0.870856i \(-0.663565\pi\)
−0.861112 + 0.508415i \(0.830232\pi\)
\(54\) 77.9678 + 45.0147i 1.44385 + 0.833606i
\(55\) 27.9421 + 13.9165i 0.508039 + 0.253028i
\(56\) 29.0951 5.50902i 0.519556 0.0983754i
\(57\) 22.7976 + 22.7976i 0.399958 + 0.399958i
\(58\) −22.6469 84.5194i −0.390464 1.45723i
\(59\) −14.6115 + 8.43595i −0.247652 + 0.142982i −0.618689 0.785636i \(-0.712336\pi\)
0.371036 + 0.928618i \(0.379002\pi\)
\(60\) 43.6201 49.3459i 0.727001 0.822432i
\(61\) 16.7743 29.0540i 0.274989 0.476295i −0.695143 0.718871i \(-0.744659\pi\)
0.970132 + 0.242576i \(0.0779924\pi\)
\(62\) 44.1593 + 44.1593i 0.712247 + 0.712247i
\(63\) −9.13833 18.9696i −0.145053 0.301105i
\(64\) 97.9319i 1.53019i
\(65\) −16.5080 + 81.3170i −0.253969 + 1.25103i
\(66\) 23.4040 + 40.5369i 0.354606 + 0.614196i
\(67\) 25.6891 95.8731i 0.383420 1.43094i −0.457223 0.889352i \(-0.651156\pi\)
0.840643 0.541590i \(-0.182177\pi\)
\(68\) −6.58656 24.5814i −0.0968612 0.361491i
\(69\) 88.3030i 1.27975i
\(70\) −103.904 + 26.3808i −1.48434 + 0.376869i
\(71\) 66.2415 0.932979 0.466489 0.884527i \(-0.345519\pi\)
0.466489 + 0.884527i \(0.345519\pi\)
\(72\) −12.2912 + 3.29341i −0.170711 + 0.0457417i
\(73\) 99.8826 + 26.7635i 1.36825 + 0.366623i 0.866841 0.498585i \(-0.166147\pi\)
0.501414 + 0.865208i \(0.332813\pi\)
\(74\) 62.1933 35.9073i 0.840450 0.485234i
\(75\) −37.6351 + 48.2556i −0.501801 + 0.643407i
\(76\) −70.8751 −0.932567
\(77\) 3.26020 43.5805i 0.0423402 0.565980i
\(78\) −87.9792 + 87.9792i −1.12794 + 1.12794i
\(79\) −36.1253 20.8569i −0.457282 0.264012i 0.253619 0.967304i \(-0.418379\pi\)
−0.710901 + 0.703292i \(0.751712\pi\)
\(80\) −2.63350 42.7579i −0.0329188 0.534474i
\(81\) −22.4400 38.8671i −0.277036 0.479841i
\(82\) −133.451 + 35.7582i −1.62745 + 0.436075i
\(83\) 7.39450 7.39450i 0.0890904 0.0890904i −0.661157 0.750247i \(-0.729934\pi\)
0.750247 + 0.661157i \(0.229934\pi\)
\(84\) −87.0357 30.4424i −1.03614 0.362409i
\(85\) 7.51254 + 22.4208i 0.0883828 + 0.263774i
\(86\) −47.4706 + 82.2215i −0.551984 + 0.956064i
\(87\) −18.0995 + 67.5483i −0.208040 + 0.776417i
\(88\) −25.5106 6.83554i −0.289893 0.0776766i
\(89\) −19.2257 11.0999i −0.216019 0.124718i 0.388087 0.921623i \(-0.373136\pi\)
−0.604105 + 0.796904i \(0.706469\pi\)
\(90\) 43.6788 14.6355i 0.485320 0.162616i
\(91\) 114.138 21.6115i 1.25426 0.237489i
\(92\) 137.262 + 137.262i 1.49198 + 1.49198i
\(93\) −12.9179 48.2102i −0.138902 0.518389i
\(94\) −28.6764 + 16.5563i −0.305068 + 0.176131i
\(95\) 65.7303 4.04840i 0.691898 0.0426147i
\(96\) 52.8286 91.5018i 0.550298 0.953144i
\(97\) −73.6717 73.6717i −0.759502 0.759502i 0.216730 0.976232i \(-0.430461\pi\)
−0.976232 + 0.216730i \(0.930461\pi\)
\(98\) 89.1523 + 120.731i 0.909717 + 1.23195i
\(99\) 18.7795i 0.189692i
\(100\) −16.5089 133.512i −0.165089 1.33512i
\(101\) −0.211559 0.366431i −0.00209464 0.00362803i 0.864976 0.501813i \(-0.167333\pi\)
−0.867071 + 0.498185i \(0.834000\pi\)
\(102\) −9.17692 + 34.2488i −0.0899699 + 0.335772i
\(103\) 8.74233 + 32.6268i 0.0848770 + 0.316765i 0.995291 0.0969334i \(-0.0309034\pi\)
−0.910414 + 0.413699i \(0.864237\pi\)
\(104\) 70.2024i 0.675023i
\(105\) 82.4568 + 23.2611i 0.785303 + 0.221534i
\(106\) −227.324 −2.14457
\(107\) 19.7531 5.29283i 0.184609 0.0494657i −0.165330 0.986238i \(-0.552869\pi\)
0.349939 + 0.936773i \(0.386202\pi\)
\(108\) 152.783 + 40.9382i 1.41466 + 0.379057i
\(109\) −63.2172 + 36.4985i −0.579974 + 0.334848i −0.761123 0.648607i \(-0.775352\pi\)
0.181149 + 0.983456i \(0.442018\pi\)
\(110\) 93.6989 + 19.0216i 0.851808 + 0.172924i
\(111\) −57.3945 −0.517068
\(112\) −54.0318 + 26.0290i −0.482426 + 0.232402i
\(113\) 37.4431 37.4431i 0.331355 0.331355i −0.521746 0.853101i \(-0.674719\pi\)
0.853101 + 0.521746i \(0.174719\pi\)
\(114\) 85.5190 + 49.3744i 0.750167 + 0.433109i
\(115\) −135.139 119.458i −1.17512 1.03876i
\(116\) −76.8653 133.135i −0.662632 1.14771i
\(117\) −48.2173 + 12.9198i −0.412114 + 0.110426i
\(118\) −36.5407 + 36.5407i −0.309667 + 0.309667i
\(119\) 25.0893 21.5968i 0.210835 0.181486i
\(120\) 23.0825 46.3458i 0.192354 0.386215i
\(121\) 41.0113 71.0337i 0.338937 0.587056i
\(122\) 26.5950 99.2538i 0.217992 0.813556i
\(123\) 106.655 + 28.5781i 0.867112 + 0.232342i
\(124\) 95.0201 + 54.8599i 0.766291 + 0.442418i
\(125\) 22.9368 + 122.878i 0.183494 + 0.983021i
\(126\) −42.0735 48.8775i −0.333917 0.387916i
\(127\) 14.8254 + 14.8254i 0.116736 + 0.116736i 0.763061 0.646326i \(-0.223695\pi\)
−0.646326 + 0.763061i \(0.723695\pi\)
\(128\) 32.9476 + 122.962i 0.257403 + 0.960642i
\(129\) 65.7117 37.9387i 0.509393 0.294098i
\(130\) 15.6233 + 253.663i 0.120180 + 1.95125i
\(131\) −22.2565 + 38.5494i −0.169897 + 0.294270i −0.938383 0.345596i \(-0.887677\pi\)
0.768487 + 0.639866i \(0.221010\pi\)
\(132\) 58.1504 + 58.1504i 0.440533 + 0.440533i
\(133\) −40.0135 83.0613i −0.300854 0.624521i
\(134\) 304.005i 2.26870i
\(135\) −144.031 29.2395i −1.06690 0.216589i
\(136\) −10.0029 17.3256i −0.0735511 0.127394i
\(137\) −37.2653 + 139.076i −0.272009 + 1.01515i 0.685810 + 0.727781i \(0.259448\pi\)
−0.957819 + 0.287372i \(0.907218\pi\)
\(138\) −70.0003 261.245i −0.507249 1.89308i
\(139\) 191.287i 1.37616i 0.725634 + 0.688081i \(0.241547\pi\)
−0.725634 + 0.688081i \(0.758453\pi\)
\(140\) −164.332 + 92.0163i −1.17380 + 0.657259i
\(141\) 26.4638 0.187686
\(142\) 195.976 52.5115i 1.38011 0.369799i
\(143\) −100.076 26.8153i −0.699834 0.187520i
\(144\) 22.3191 12.8860i 0.154994 0.0894858i
\(145\) 78.8904 + 119.080i 0.544072 + 0.821241i
\(146\) 316.719 2.16931
\(147\) −13.4606 119.187i −0.0915689 0.810798i
\(148\) 89.2165 89.2165i 0.602814 0.602814i
\(149\) −29.0196 16.7545i −0.194762 0.112446i 0.399448 0.916756i \(-0.369202\pi\)
−0.594210 + 0.804310i \(0.702535\pi\)
\(150\) −73.0900 + 172.599i −0.487266 + 1.15066i
\(151\) −21.4781 37.2012i −0.142239 0.246365i 0.786100 0.618099i \(-0.212097\pi\)
−0.928339 + 0.371734i \(0.878764\pi\)
\(152\) −53.8187 + 14.4207i −0.354070 + 0.0948728i
\(153\) −10.0589 + 10.0589i −0.0657444 + 0.0657444i
\(154\) −24.9022 131.517i −0.161703 0.854010i
\(155\) −91.2563 45.4501i −0.588750 0.293226i
\(156\) −109.298 + 189.310i −0.700629 + 1.21352i
\(157\) −19.3536 + 72.2287i −0.123271 + 0.460055i −0.999772 0.0213453i \(-0.993205\pi\)
0.876501 + 0.481400i \(0.159872\pi\)
\(158\) −123.411 33.0678i −0.781080 0.209290i
\(159\) 157.338 + 90.8392i 0.989548 + 0.571316i
\(160\) −68.5667 204.634i −0.428542 1.27896i
\(161\) −83.3694 + 238.356i −0.517823 + 1.48047i
\(162\) −97.1998 97.1998i −0.599998 0.599998i
\(163\) 31.7047 + 118.324i 0.194507 + 0.725912i 0.992394 + 0.123104i \(0.0392848\pi\)
−0.797886 + 0.602808i \(0.794049\pi\)
\(164\) −210.212 + 121.366i −1.28178 + 0.740035i
\(165\) −57.2508 50.6077i −0.346975 0.306713i
\(166\) 16.0148 27.7385i 0.0964748 0.167099i
\(167\) −102.412 102.412i −0.613244 0.613244i 0.330546 0.943790i \(-0.392767\pi\)
−0.943790 + 0.330546i \(0.892767\pi\)
\(168\) −72.2841 5.40747i −0.430263 0.0321874i
\(169\) 106.399i 0.629579i
\(170\) 39.9995 + 60.3766i 0.235291 + 0.355157i
\(171\) 19.8092 + 34.3105i 0.115843 + 0.200646i
\(172\) −43.1716 + 161.119i −0.250998 + 0.936736i
\(173\) −37.4559 139.787i −0.216508 0.808020i −0.985630 0.168918i \(-0.945973\pi\)
0.769122 0.639102i \(-0.220694\pi\)
\(174\) 214.190i 1.23098i
\(175\) 147.148 94.7236i 0.840844 0.541278i
\(176\) 53.4902 0.303922
\(177\) 39.8927 10.6892i 0.225382 0.0603911i
\(178\) −65.6784 17.5985i −0.368980 0.0988679i
\(179\) 53.2683 30.7544i 0.297588 0.171813i −0.343771 0.939054i \(-0.611704\pi\)
0.641359 + 0.767241i \(0.278371\pi\)
\(180\) 67.4695 44.6985i 0.374831 0.248325i
\(181\) −96.6453 −0.533952 −0.266976 0.963703i \(-0.586024\pi\)
−0.266976 + 0.963703i \(0.586024\pi\)
\(182\) 320.546 154.418i 1.76124 0.848451i
\(183\) −58.0692 + 58.0692i −0.317318 + 0.317318i
\(184\) 132.157 + 76.3011i 0.718246 + 0.414680i
\(185\) −77.6443 + 87.8364i −0.419699 + 0.474791i
\(186\) −76.4352 132.390i −0.410942 0.711772i
\(187\) −28.5192 + 7.64169i −0.152509 + 0.0408646i
\(188\) −41.1365 + 41.1365i −0.218811 + 0.218811i
\(189\) 38.2790 + 202.165i 0.202534 + 1.06966i
\(190\) 191.254 64.0835i 1.00660 0.337282i
\(191\) 168.824 292.411i 0.883893 1.53095i 0.0369153 0.999318i \(-0.488247\pi\)
0.846977 0.531629i \(-0.178420\pi\)
\(192\) 62.0450 231.555i 0.323151 1.20602i
\(193\) 165.599 + 44.3720i 0.858024 + 0.229907i 0.660902 0.750472i \(-0.270174\pi\)
0.197122 + 0.980379i \(0.436840\pi\)
\(194\) −276.360 159.556i −1.42453 0.822455i
\(195\) 90.5508 181.811i 0.464363 0.932365i
\(196\) 206.194 + 164.346i 1.05201 + 0.838500i
\(197\) 133.522 + 133.522i 0.677777 + 0.677777i 0.959497 0.281720i \(-0.0909049\pi\)
−0.281720 + 0.959497i \(0.590905\pi\)
\(198\) 14.8870 + 55.5592i 0.0751871 + 0.280602i
\(199\) 179.523 103.648i 0.902127 0.520843i 0.0242371 0.999706i \(-0.492284\pi\)
0.877890 + 0.478863i \(0.158951\pi\)
\(200\) −39.7011 98.0227i −0.198506 0.490114i
\(201\) −121.481 + 210.411i −0.604384 + 1.04682i
\(202\) −0.916378 0.916378i −0.00453653 0.00453653i
\(203\) 112.630 165.244i 0.554829 0.814012i
\(204\) 62.2943i 0.305364i
\(205\) 188.020 124.563i 0.917172 0.607626i
\(206\) 51.7284 + 89.5962i 0.251109 + 0.434933i
\(207\) 28.0843 104.812i 0.135673 0.506339i
\(208\) 36.7998 + 137.339i 0.176922 + 0.660283i
\(209\) 82.2288i 0.393439i
\(210\) 262.388 + 3.45225i 1.24947 + 0.0164393i
\(211\) −143.499 −0.680092 −0.340046 0.940409i \(-0.610443\pi\)
−0.340046 + 0.940409i \(0.610443\pi\)
\(212\) −385.777 + 103.369i −1.81970 + 0.487588i
\(213\) −156.624 41.9674i −0.735326 0.197030i
\(214\) 54.2439 31.3177i 0.253476 0.146344i
\(215\) 30.8347 151.889i 0.143417 0.706461i
\(216\) 124.345 0.575670
\(217\) −10.6475 + 142.330i −0.0490667 + 0.655897i
\(218\) −158.095 + 158.095i −0.725206 + 0.725206i
\(219\) −219.211 126.562i −1.00096 0.577907i
\(220\) 167.660 10.3263i 0.762091 0.0469379i
\(221\) −39.2408 67.9671i −0.177560 0.307543i
\(222\) −169.802 + 45.4983i −0.764873 + 0.204947i
\(223\) −294.434 + 294.434i −1.32033 + 1.32033i −0.406822 + 0.913507i \(0.633363\pi\)
−0.913507 + 0.406822i \(0.866637\pi\)
\(224\) −228.990 + 197.113i −1.02227 + 0.879971i
\(225\) −60.0188 + 45.3078i −0.266750 + 0.201368i
\(226\) 81.0932 140.458i 0.358820 0.621494i
\(227\) −39.0177 + 145.616i −0.171884 + 0.641481i 0.825177 + 0.564874i \(0.191075\pi\)
−0.997061 + 0.0766067i \(0.975591\pi\)
\(228\) 167.580 + 44.9030i 0.735002 + 0.196943i
\(229\) −371.780 214.647i −1.62349 0.937324i −0.985976 0.166888i \(-0.946628\pi\)
−0.637517 0.770436i \(-0.720038\pi\)
\(230\) −494.506 246.288i −2.15002 1.07082i
\(231\) −35.3191 + 100.978i −0.152896 + 0.437135i
\(232\) −85.4556 85.4556i −0.368343 0.368343i
\(233\) 80.0187 + 298.634i 0.343428 + 1.28169i 0.894438 + 0.447192i \(0.147576\pi\)
−0.551010 + 0.834499i \(0.685757\pi\)
\(234\) −132.409 + 76.4464i −0.565851 + 0.326694i
\(235\) 35.8007 40.5001i 0.152343 0.172341i
\(236\) −45.3951 + 78.6267i −0.192352 + 0.333164i
\(237\) 72.2024 + 72.2024i 0.304651 + 0.304651i
\(238\) 57.1065 83.7833i 0.239943 0.352031i
\(239\) 8.06350i 0.0337385i 0.999858 + 0.0168692i \(0.00536990\pi\)
−0.999858 + 0.0168692i \(0.994630\pi\)
\(240\) −20.8626 + 102.767i −0.0869274 + 0.428197i
\(241\) 80.5302 + 139.482i 0.334150 + 0.578765i 0.983321 0.181877i \(-0.0582173\pi\)
−0.649171 + 0.760643i \(0.724884\pi\)
\(242\) 65.0217 242.664i 0.268685 1.00275i
\(243\) −40.0355 149.414i −0.164755 0.614874i
\(244\) 180.531i 0.739880i
\(245\) −200.614 140.638i −0.818831 0.574035i
\(246\) 338.193 1.37477
\(247\) −211.127 + 56.5712i −0.854763 + 0.229033i
\(248\) 83.3151 + 22.3242i 0.335948 + 0.0900170i
\(249\) −22.1687 + 12.7991i −0.0890310 + 0.0514020i
\(250\) 165.267 + 345.351i 0.661068 + 1.38140i
\(251\) 353.645 1.40894 0.704472 0.709732i \(-0.251184\pi\)
0.704472 + 0.709732i \(0.251184\pi\)
\(252\) −93.6259 63.8152i −0.371531 0.253235i
\(253\) 159.250 159.250i 0.629448 0.629448i
\(254\) 55.6136 + 32.1085i 0.218951 + 0.126411i
\(255\) −3.55826 57.7724i −0.0139540 0.226559i
\(256\) −0.912626 1.58071i −0.00356495 0.00617467i
\(257\) 410.808 110.076i 1.59848 0.428310i 0.653894 0.756586i \(-0.273134\pi\)
0.944582 + 0.328276i \(0.106468\pi\)
\(258\) 164.333 164.333i 0.636951 0.636951i
\(259\) 154.925 + 54.1878i 0.598165 + 0.209219i
\(260\) 141.859 + 423.371i 0.545611 + 1.62835i
\(261\) −42.9668 + 74.4206i −0.164624 + 0.285137i
\(262\) −35.2867 + 131.692i −0.134682 + 0.502640i
\(263\) 54.3856 + 14.5726i 0.206789 + 0.0554090i 0.360727 0.932672i \(-0.382529\pi\)
−0.153937 + 0.988081i \(0.549195\pi\)
\(264\) 55.9878 + 32.3246i 0.212075 + 0.122442i
\(265\) 351.870 117.901i 1.32781 0.444909i
\(266\) −184.225 214.017i −0.692576 0.804576i
\(267\) 38.4257 + 38.4257i 0.143916 + 0.143916i
\(268\) −138.237 515.908i −0.515810 1.92503i
\(269\) 383.575 221.457i 1.42593 0.823261i 0.429133 0.903241i \(-0.358819\pi\)
0.996796 + 0.0799807i \(0.0254859\pi\)
\(270\) −449.296 + 27.6726i −1.66406 + 0.102491i
\(271\) 36.5421 63.2927i 0.134842 0.233552i −0.790695 0.612210i \(-0.790281\pi\)
0.925537 + 0.378657i \(0.123614\pi\)
\(272\) 28.6510 + 28.6510i 0.105335 + 0.105335i
\(273\) −283.565 21.2131i −1.03870 0.0777037i
\(274\) 440.998i 1.60948i
\(275\) −154.900 + 19.1535i −0.563272 + 0.0696492i
\(276\) −237.586 411.511i −0.860819 1.49098i
\(277\) −48.1733 + 179.785i −0.173911 + 0.649043i 0.822824 + 0.568296i \(0.192397\pi\)
−0.996735 + 0.0807471i \(0.974269\pi\)
\(278\) 151.638 + 565.922i 0.545461 + 2.03569i
\(279\) 61.3320i 0.219828i
\(280\) −106.063 + 103.308i −0.378796 + 0.368958i
\(281\) −466.249 −1.65925 −0.829624 0.558322i \(-0.811445\pi\)
−0.829624 + 0.558322i \(0.811445\pi\)
\(282\) 78.2932 20.9786i 0.277635 0.0743922i
\(283\) −227.191 60.8755i −0.802793 0.215108i −0.165983 0.986129i \(-0.553080\pi\)
−0.636810 + 0.771021i \(0.719746\pi\)
\(284\) 308.700 178.228i 1.08697 0.627563i
\(285\) −157.981 32.0714i −0.554319 0.112531i
\(286\) −317.333 −1.10956
\(287\) −260.911 177.837i −0.909099 0.619639i
\(288\) 91.8071 91.8071i 0.318775 0.318775i
\(289\) 230.912 + 133.317i 0.799005 + 0.461306i
\(290\) 327.795 + 289.760i 1.13033 + 0.999171i
\(291\) 127.518 + 220.868i 0.438206 + 0.758995i
\(292\) 537.484 144.018i 1.84070 0.493214i
\(293\) 269.768 269.768i 0.920711 0.920711i −0.0763691 0.997080i \(-0.524333\pi\)
0.997080 + 0.0763691i \(0.0243327\pi\)
\(294\) −134.306 341.945i −0.456825 1.16308i
\(295\) 37.6088 75.5122i 0.127487 0.255974i
\(296\) 49.5936 85.8986i 0.167546 0.290198i
\(297\) 47.4962 177.258i 0.159920 0.596829i
\(298\) −99.1362 26.5635i −0.332672 0.0891392i
\(299\) 518.443 + 299.323i 1.73392 + 1.00108i
\(300\) −45.5524 + 326.142i −0.151841 + 1.08714i
\(301\) −213.194 + 40.3673i −0.708287 + 0.134111i
\(302\) −93.0334 93.0334i −0.308058 0.308058i
\(303\) 0.268067 + 1.00044i 0.000884710 + 0.00330178i
\(304\) 97.7276 56.4231i 0.321472 0.185602i
\(305\) 10.3119 + 167.426i 0.0338096 + 0.548938i
\(306\) −21.7853 + 37.7332i −0.0711937 + 0.123311i
\(307\) −93.9665 93.9665i −0.306080 0.306080i 0.537307 0.843387i \(-0.319442\pi\)
−0.843387 + 0.537307i \(0.819442\pi\)
\(308\) −102.064 211.866i −0.331375 0.687878i
\(309\) 82.6831i 0.267583i
\(310\) −306.012 62.1228i −0.987134 0.200396i
\(311\) −10.2138 17.6908i −0.0328418 0.0568837i 0.849137 0.528172i \(-0.177122\pi\)
−0.881979 + 0.471288i \(0.843789\pi\)
\(312\) −44.4768 + 165.990i −0.142554 + 0.532019i
\(313\) −61.0200 227.730i −0.194952 0.727571i −0.992279 0.124024i \(-0.960420\pi\)
0.797327 0.603547i \(-0.206247\pi\)
\(314\) 229.031i 0.729398i
\(315\) 90.4748 + 53.8350i 0.287222 + 0.170905i
\(316\) −224.469 −0.710345
\(317\) 192.112 51.4761i 0.606030 0.162385i 0.0572611 0.998359i \(-0.481763\pi\)
0.548769 + 0.835974i \(0.315097\pi\)
\(318\) 537.496 + 144.022i 1.69024 + 0.452898i
\(319\) −154.462 + 89.1786i −0.484207 + 0.279557i
\(320\) −270.436 408.205i −0.845111 1.27564i
\(321\) −50.0585 −0.155945
\(322\) −57.6973 + 771.266i −0.179184 + 2.39523i
\(323\) −44.0443 + 44.0443i −0.136360 + 0.136360i
\(324\) −209.150 120.753i −0.645525 0.372694i
\(325\) −155.745 384.536i −0.479214 1.18319i
\(326\) 187.597 + 324.927i 0.575451 + 0.996710i
\(327\) 172.597 46.2473i 0.527821 0.141429i
\(328\) −134.929 + 134.929i −0.411370 + 0.411370i
\(329\) −71.4336 24.9852i −0.217123 0.0759430i
\(330\) −209.495 104.339i −0.634833 0.316178i
\(331\) −14.1019 + 24.4253i −0.0426041 + 0.0737924i −0.886541 0.462650i \(-0.846899\pi\)
0.843937 + 0.536442i \(0.180232\pi\)
\(332\) 14.5645 54.3555i 0.0438690 0.163721i
\(333\) −68.1250 18.2540i −0.204580 0.0548169i
\(334\) −384.170 221.801i −1.15021 0.664074i
\(335\) 157.671 + 470.563i 0.470661 + 1.40466i
\(336\) 144.246 27.3123i 0.429303 0.0812865i
\(337\) −143.639 143.639i −0.426230 0.426230i 0.461112 0.887342i \(-0.347451\pi\)
−0.887342 + 0.461112i \(0.847451\pi\)
\(338\) −84.3453 314.781i −0.249542 0.931305i
\(339\) −112.254 + 64.8100i −0.331134 + 0.191180i
\(340\) 95.3350 + 84.2728i 0.280397 + 0.247861i
\(341\) 63.6481 110.242i 0.186651 0.323289i
\(342\) 85.8044 + 85.8044i 0.250890 + 0.250890i
\(343\) −76.1940 + 334.430i −0.222140 + 0.975015i
\(344\) 131.129i 0.381188i
\(345\) 243.846 + 368.069i 0.706799 + 1.06687i
\(346\) −221.627 383.869i −0.640540 1.10945i
\(347\) −120.779 + 450.752i −0.348066 + 1.29900i 0.540924 + 0.841071i \(0.318075\pi\)
−0.888990 + 0.457927i \(0.848592\pi\)
\(348\) 97.3963 + 363.488i 0.279874 + 1.04451i
\(349\) 585.176i 1.67672i −0.545115 0.838361i \(-0.683514\pi\)
0.545115 0.838361i \(-0.316486\pi\)
\(350\) 360.247 396.888i 1.02928 1.13397i
\(351\) 487.795 1.38973
\(352\) 260.293 69.7454i 0.739470 0.198140i
\(353\) 435.638 + 116.729i 1.23410 + 0.330676i 0.816175 0.577805i \(-0.196091\pi\)
0.417926 + 0.908481i \(0.362757\pi\)
\(354\) 109.549 63.2482i 0.309460 0.178667i
\(355\) −276.111 + 182.923i −0.777778 + 0.515277i
\(356\) −119.461 −0.335565
\(357\) −73.0051 + 35.1691i −0.204496 + 0.0985130i
\(358\) 133.214 133.214i 0.372107 0.372107i
\(359\) −391.709 226.154i −1.09111 0.629954i −0.157240 0.987560i \(-0.550260\pi\)
−0.933872 + 0.357606i \(0.883593\pi\)
\(360\) 42.1380 47.6693i 0.117050 0.132415i
\(361\) −93.7626 162.402i −0.259730 0.449866i
\(362\) −285.925 + 76.6134i −0.789849 + 0.211639i
\(363\) −141.973 + 141.973i −0.391109 + 0.391109i
\(364\) 473.761 407.811i 1.30154 1.12036i
\(365\) −490.242 + 164.265i −1.34313 + 0.450042i
\(366\) −125.765 + 217.831i −0.343620 + 0.595167i
\(367\) −127.353 + 475.287i −0.347010 + 1.29506i 0.543236 + 0.839580i \(0.317199\pi\)
−0.890246 + 0.455480i \(0.849468\pi\)
\(368\) −298.540 79.9934i −0.811249 0.217373i
\(369\) 117.506 + 67.8420i 0.318444 + 0.183854i
\(370\) −160.080 + 321.415i −0.432650 + 0.868690i
\(371\) −338.938 393.749i −0.913579 1.06132i
\(372\) −189.913 189.913i −0.510520 0.510520i
\(373\) 58.9285 + 219.924i 0.157985 + 0.589609i 0.998831 + 0.0483344i \(0.0153913\pi\)
−0.840846 + 0.541274i \(0.817942\pi\)
\(374\) −78.3162 + 45.2159i −0.209402 + 0.120898i
\(375\) 23.6165 305.069i 0.0629774 0.813518i
\(376\) −22.8669 + 39.6066i −0.0608162 + 0.105337i
\(377\) −335.236 335.236i −0.889220 0.889220i
\(378\) 273.510 + 567.761i 0.723572 + 1.50201i
\(379\) 568.936i 1.50115i 0.660784 + 0.750576i \(0.270224\pi\)
−0.660784 + 0.750576i \(0.729776\pi\)
\(380\) 295.425 195.719i 0.777435 0.515050i
\(381\) −25.6613 44.4466i −0.0673524 0.116658i
\(382\) 267.662 998.930i 0.700687 2.61500i
\(383\) −5.88759 21.9728i −0.0153723 0.0573702i 0.957814 0.287390i \(-0.0927876\pi\)
−0.973186 + 0.230020i \(0.926121\pi\)
\(384\) 311.612i 0.811489i
\(385\) 106.757 + 190.657i 0.277290 + 0.495214i
\(386\) 525.099 1.36036
\(387\) 90.0634 24.1324i 0.232722 0.0623577i
\(388\) −541.546 145.107i −1.39574 0.373986i
\(389\) −427.548 + 246.845i −1.09909 + 0.634562i −0.935983 0.352045i \(-0.885486\pi\)
−0.163111 + 0.986608i \(0.552153\pi\)
\(390\) 123.768 609.671i 0.317354 1.56326i
\(391\) 170.599 0.436315
\(392\) 190.011 + 82.8419i 0.484721 + 0.211331i
\(393\) 77.0473 77.0473i 0.196049 0.196049i
\(394\) 500.872 + 289.179i 1.27125 + 0.733956i
\(395\) 208.175 12.8217i 0.527025 0.0324600i
\(396\) 50.5277 + 87.5166i 0.127595 + 0.221001i
\(397\) −97.1023 + 26.0185i −0.244590 + 0.0655377i −0.379031 0.925384i \(-0.623743\pi\)
0.134441 + 0.990922i \(0.457076\pi\)
\(398\) 448.955 448.955i 1.12803 1.12803i
\(399\) 41.9863 + 221.745i 0.105229 + 0.555751i
\(400\) 129.051 + 170.953i 0.322629 + 0.427383i
\(401\) −115.076 + 199.317i −0.286972 + 0.497050i −0.973086 0.230444i \(-0.925982\pi\)
0.686113 + 0.727495i \(0.259315\pi\)
\(402\) −192.603 + 718.804i −0.479112 + 1.78807i
\(403\) 326.839 + 87.5763i 0.811015 + 0.217311i
\(404\) −1.97182 1.13843i −0.00488075 0.00281790i
\(405\) 200.866 + 100.041i 0.495964 + 0.247015i
\(406\) 202.223 578.161i 0.498086 1.42404i
\(407\) −103.508 103.508i −0.254320 0.254320i
\(408\) 12.6748 + 47.3029i 0.0310656 + 0.115938i
\(409\) −628.868 + 363.077i −1.53758 + 0.887720i −0.538596 + 0.842564i \(0.681045\pi\)
−0.998980 + 0.0451555i \(0.985622\pi\)
\(410\) 457.513 517.570i 1.11589 1.26237i
\(411\) 176.224 305.228i 0.428768 0.742648i
\(412\) 128.526 + 128.526i 0.311957 + 0.311957i
\(413\) −117.774 8.81052i −0.285167 0.0213330i
\(414\) 332.350i 0.802778i
\(415\) −10.4025 + 51.2418i −0.0250662 + 0.123474i
\(416\) 358.150 + 620.333i 0.860936 + 1.49119i
\(417\) 121.190 452.287i 0.290623 1.08462i
\(418\) 65.1851 + 243.274i 0.155945 + 0.581996i
\(419\) 168.701i 0.402628i 0.979527 + 0.201314i \(0.0645211\pi\)
−0.979527 + 0.201314i \(0.935479\pi\)
\(420\) 446.852 113.455i 1.06393 0.270130i
\(421\) 584.470 1.38829 0.694145 0.719836i \(-0.255783\pi\)
0.694145 + 0.719836i \(0.255783\pi\)
\(422\) −424.544 + 113.756i −1.00603 + 0.269564i
\(423\) 31.4115 + 8.41668i 0.0742588 + 0.0198976i
\(424\) −271.906 + 156.985i −0.641288 + 0.370248i
\(425\) −93.2284 72.7100i −0.219361 0.171082i
\(426\) −496.643 −1.16583
\(427\) 211.571 101.921i 0.495482 0.238691i
\(428\) 77.8131 77.8131i 0.181806 0.181806i
\(429\) 219.636 + 126.807i 0.511972 + 0.295587i
\(430\) −29.1823 473.808i −0.0678658 1.10188i
\(431\) 64.6697 + 112.011i 0.150046 + 0.259887i 0.931244 0.364396i \(-0.118725\pi\)
−0.781198 + 0.624283i \(0.785391\pi\)
\(432\) −243.259 + 65.1810i −0.563099 + 0.150882i
\(433\) 80.7522 80.7522i 0.186495 0.186495i −0.607684 0.794179i \(-0.707901\pi\)
0.794179 + 0.607684i \(0.207901\pi\)
\(434\) 81.3282 + 429.523i 0.187392 + 0.989685i
\(435\) −111.089 331.539i −0.255377 0.762159i
\(436\) −196.404 + 340.182i −0.450468 + 0.780233i
\(437\) 122.971 458.935i 0.281399 1.05020i
\(438\) −748.865 200.658i −1.70974 0.458123i
\(439\) −473.216 273.211i −1.07794 0.622349i −0.147601 0.989047i \(-0.547155\pi\)
−0.930340 + 0.366698i \(0.880488\pi\)
\(440\) 125.211 41.9543i 0.284570 0.0953508i
\(441\) 21.9297 145.752i 0.0497271 0.330502i
\(442\) −169.973 169.973i −0.384555 0.384555i
\(443\) −125.794 469.471i −0.283960 1.05975i −0.949596 0.313477i \(-0.898506\pi\)
0.665635 0.746277i \(-0.268161\pi\)
\(444\) −267.471 + 154.424i −0.602412 + 0.347803i
\(445\) 110.790 6.82363i 0.248965 0.0153340i
\(446\) −637.676 + 1104.49i −1.42977 + 2.47643i
\(447\) 58.0004 + 58.0004i 0.129755 + 0.129755i
\(448\) −386.095 + 566.456i −0.861820 + 1.26441i
\(449\) 403.465i 0.898586i −0.893385 0.449293i \(-0.851676\pi\)
0.893385 0.449293i \(-0.148324\pi\)
\(450\) −141.649 + 181.622i −0.314775 + 0.403604i
\(451\) 140.808 + 243.886i 0.312212 + 0.540768i
\(452\) 73.7494 275.236i 0.163162 0.608930i
\(453\) 27.2150 + 101.568i 0.0600772 + 0.224211i
\(454\) 461.736i 1.01704i
\(455\) −416.077 + 405.270i −0.914454 + 0.890703i
\(456\) 136.388 0.299096
\(457\) −109.577 + 29.3611i −0.239775 + 0.0642474i −0.376705 0.926333i \(-0.622943\pi\)
0.136930 + 0.990581i \(0.456276\pi\)
\(458\) −1270.07 340.314i −2.77308 0.743043i
\(459\) 120.385 69.5046i 0.262278 0.151426i
\(460\) −951.186 193.098i −2.06780 0.419779i
\(461\) −268.155 −0.581681 −0.290841 0.956772i \(-0.593935\pi\)
−0.290841 + 0.956772i \(0.593935\pi\)
\(462\) −24.4432 + 326.743i −0.0529073 + 0.707236i
\(463\) 191.993 191.993i 0.414671 0.414671i −0.468691 0.883362i \(-0.655274\pi\)
0.883362 + 0.468691i \(0.155274\pi\)
\(464\) 211.975 + 122.384i 0.456842 + 0.263758i
\(465\) 186.976 + 165.280i 0.402098 + 0.355441i
\(466\) 473.471 + 820.076i 1.01603 + 1.75982i
\(467\) 54.1285 14.5037i 0.115907 0.0310572i −0.200399 0.979714i \(-0.564224\pi\)
0.316306 + 0.948657i \(0.397557\pi\)
\(468\) −189.941 + 189.941i −0.405858 + 0.405858i
\(469\) 526.569 453.269i 1.12275 0.966458i
\(470\) 73.8108 148.200i 0.157044 0.315319i
\(471\) 91.5212 158.519i 0.194312 0.336559i
\(472\) −18.4727 + 68.9411i −0.0391371 + 0.146062i
\(473\) 186.929 + 50.0874i 0.395198 + 0.105893i
\(474\) 270.848 + 156.374i 0.571409 + 0.329903i
\(475\) −262.801 + 198.387i −0.553265 + 0.417656i
\(476\) 58.8139 168.151i 0.123559 0.353258i
\(477\) 157.863 + 157.863i 0.330950 + 0.330950i
\(478\) 6.39217 + 23.8559i 0.0133727 + 0.0499077i
\(479\) 285.149 164.631i 0.595301 0.343697i −0.171890 0.985116i \(-0.554987\pi\)
0.767191 + 0.641419i \(0.221654\pi\)
\(480\) 32.4761 + 527.287i 0.0676586 + 1.09851i
\(481\) 194.552 336.974i 0.404474 0.700569i
\(482\) 348.821 + 348.821i 0.723694 + 0.723694i
\(483\) 348.133 510.761i 0.720773 1.05748i
\(484\) 441.377i 0.911936i
\(485\) 510.524 + 103.640i 1.05263 + 0.213691i
\(486\) −236.890 410.306i −0.487428 0.844250i
\(487\) 87.3154 325.866i 0.179292 0.669128i −0.816488 0.577362i \(-0.804082\pi\)
0.995781 0.0917662i \(-0.0292513\pi\)
\(488\) −36.7318 137.085i −0.0752701 0.280912i
\(489\) 299.856i 0.613203i
\(490\) −705.004 257.047i −1.43878 0.524586i
\(491\) −387.132 −0.788456 −0.394228 0.919013i \(-0.628988\pi\)
−0.394228 + 0.919013i \(0.628988\pi\)
\(492\) 573.926 153.783i 1.16652 0.312567i
\(493\) −130.501 34.9678i −0.264709 0.0709285i
\(494\) −579.773 + 334.732i −1.17363 + 0.677595i
\(495\) −51.8589 78.2777i −0.104765 0.158137i
\(496\) −174.694 −0.352205
\(497\) 383.153 + 261.156i 0.770932 + 0.525465i
\(498\) −55.4400 + 55.4400i −0.111325 + 0.111325i
\(499\) −535.365 309.093i −1.07288 0.619425i −0.143910 0.989591i \(-0.545968\pi\)
−0.928966 + 0.370166i \(0.879301\pi\)
\(500\) 437.502 + 510.923i 0.875004 + 1.02185i
\(501\) 177.264 + 307.030i 0.353821 + 0.612835i
\(502\) 1046.26 280.344i 2.08418 0.558455i
\(503\) −64.4794 + 64.4794i −0.128190 + 0.128190i −0.768291 0.640101i \(-0.778892\pi\)
0.640101 + 0.768291i \(0.278892\pi\)
\(504\) −84.0785 29.4081i −0.166822 0.0583493i
\(505\) 1.89372 + 0.943164i 0.00374993 + 0.00186765i
\(506\) 344.900 597.385i 0.681621 1.18060i
\(507\) −67.4091 + 251.574i −0.132957 + 0.496202i
\(508\) 108.979 + 29.2007i 0.214525 + 0.0574818i
\(509\) 465.249 + 268.611i 0.914044 + 0.527724i 0.881730 0.471754i \(-0.156379\pi\)
0.0323142 + 0.999478i \(0.489712\pi\)
\(510\) −56.3250 168.099i −0.110441 0.329606i
\(511\) 472.225 + 548.591i 0.924119 + 1.07356i
\(512\) −364.011 364.011i −0.710960 0.710960i
\(513\) −100.201 373.954i −0.195323 0.728956i
\(514\) 1128.12 651.319i 2.19478 1.26716i
\(515\) −126.538 111.855i −0.245705 0.217194i
\(516\) 204.154 353.605i 0.395647 0.685281i
\(517\) 47.7262 + 47.7262i 0.0923138 + 0.0923138i
\(518\) 501.301 + 37.5017i 0.967763 + 0.0723970i
\(519\) 354.250i 0.682563i
\(520\) 193.861 + 292.621i 0.372810 + 0.562733i
\(521\) −333.155 577.042i −0.639453 1.10757i −0.985553 0.169368i \(-0.945827\pi\)
0.346099 0.938198i \(-0.387506\pi\)
\(522\) −68.1220 + 254.235i −0.130502 + 0.487040i
\(523\) 121.685 + 454.136i 0.232668 + 0.868329i 0.979186 + 0.202964i \(0.0650574\pi\)
−0.746518 + 0.665365i \(0.768276\pi\)
\(524\) 239.531i 0.457121i
\(525\) −407.935 + 130.743i −0.777019 + 0.249035i
\(526\) 172.452 0.327856
\(527\) 93.1408 24.9570i 0.176738 0.0473567i
\(528\) −126.475 33.8888i −0.239536 0.0641834i
\(529\) −668.836 + 386.153i −1.26434 + 0.729967i
\(530\) 947.544 627.747i 1.78782 1.18443i
\(531\) 50.7507 0.0955757
\(532\) −409.955 279.424i −0.770592 0.525233i
\(533\) −529.318 + 529.318i −0.993092 + 0.993092i
\(534\) 144.144 + 83.2214i 0.269932 + 0.155845i
\(535\) −67.7200 + 76.6094i −0.126579 + 0.143195i
\(536\) −209.939 363.626i −0.391678 0.678406i
\(537\) −145.435 + 38.9691i −0.270828 + 0.0725681i
\(538\) 959.252 959.252i 1.78300 1.78300i
\(539\) 190.673 239.224i 0.353753 0.443830i
\(540\) −749.889 + 251.265i −1.38868 + 0.465306i
\(541\) −16.6073 + 28.7646i −0.0306973 + 0.0531693i −0.880966 0.473180i \(-0.843106\pi\)
0.850269 + 0.526349i \(0.176439\pi\)
\(542\) 57.9359 216.220i 0.106893 0.398929i
\(543\) 228.513 + 61.2298i 0.420834 + 0.112762i
\(544\) 176.779 + 102.063i 0.324962 + 0.187617i
\(545\) 162.716 326.707i 0.298561 0.599462i
\(546\) −855.745 + 162.031i −1.56730 + 0.296760i
\(547\) −495.595 495.595i −0.906024 0.906024i 0.0899243 0.995949i \(-0.471337\pi\)
−0.995949 + 0.0899243i \(0.971337\pi\)
\(548\) 200.530 + 748.389i 0.365931 + 1.36567i
\(549\) −87.3945 + 50.4572i −0.159188 + 0.0919075i
\(550\) −443.088 + 179.459i −0.805615 + 0.326290i
\(551\) −188.136 + 325.862i −0.341445 + 0.591401i
\(552\) −264.138 264.138i −0.478511 0.478511i
\(553\) −126.727 263.064i −0.229163 0.475703i
\(554\) 570.083i 1.02903i
\(555\) 239.235 158.493i 0.431054 0.285573i
\(556\) 514.671 + 891.437i 0.925668 + 1.60330i
\(557\) −189.223 + 706.189i −0.339718 + 1.26784i 0.558946 + 0.829204i \(0.311206\pi\)
−0.898663 + 0.438639i \(0.855461\pi\)
\(558\) −48.6196 181.451i −0.0871320 0.325181i
\(559\) 514.408i 0.920228i
\(560\) 153.340 257.702i 0.273821 0.460182i
\(561\) 72.2734 0.128830
\(562\) −1379.40 + 369.609i −2.45445 + 0.657667i
\(563\) −175.573 47.0445i −0.311852 0.0835604i 0.0994987 0.995038i \(-0.468276\pi\)
−0.411350 + 0.911477i \(0.634943\pi\)
\(564\) 123.327 71.2029i 0.218665 0.126246i
\(565\) −52.6744 + 259.470i −0.0932291 + 0.459239i
\(566\) −720.401 −1.27279
\(567\) 23.4363 313.284i 0.0413339 0.552529i
\(568\) 198.146 198.146i 0.348849 0.348849i
\(569\) −161.027 92.9689i −0.283000 0.163390i 0.351781 0.936082i \(-0.385576\pi\)
−0.634781 + 0.772692i \(0.718910\pi\)
\(570\) −492.811 + 30.3527i −0.864580 + 0.0532503i
\(571\) −459.608 796.064i −0.804917 1.39416i −0.916347 0.400385i \(-0.868876\pi\)
0.111430 0.993772i \(-0.464457\pi\)
\(572\) −538.526 + 144.298i −0.941478 + 0.252268i
\(573\) −584.432 + 584.432i −1.01995 + 1.01995i
\(574\) −912.883 319.298i −1.59039 0.556268i
\(575\) 893.170 + 124.750i 1.55334 + 0.216956i
\(576\) 147.290 255.113i 0.255711 0.442905i
\(577\) 29.5595 110.318i 0.0512297 0.191192i −0.935569 0.353144i \(-0.885112\pi\)
0.986799 + 0.161952i \(0.0517791\pi\)
\(578\) 788.840 + 211.369i 1.36477 + 0.365690i
\(579\) −363.437 209.831i −0.627698 0.362402i
\(580\) 688.040 + 342.678i 1.18628 + 0.590824i
\(581\) 71.9239 13.6184i 0.123793 0.0234397i
\(582\) 552.350 + 552.350i 0.949056 + 0.949056i
\(583\) 119.928 + 447.576i 0.205708 + 0.767712i
\(584\) 378.833 218.719i 0.648686 0.374519i
\(585\) 165.304 187.003i 0.282571 0.319664i
\(586\) 584.257 1011.96i 0.997026 1.72690i
\(587\) 425.502 + 425.502i 0.724875 + 0.724875i 0.969594 0.244719i \(-0.0786956\pi\)
−0.244719 + 0.969594i \(0.578696\pi\)
\(588\) −383.412 519.222i −0.652061 0.883030i
\(589\) 268.551i 0.455945i
\(590\) 51.4050 253.217i 0.0871271 0.429181i
\(591\) −231.113 400.299i −0.391054 0.677325i
\(592\) −51.9935 + 194.043i −0.0878269 + 0.327775i
\(593\) 2.24058 + 8.36195i 0.00377838 + 0.0141011i 0.967789 0.251762i \(-0.0810099\pi\)
−0.964011 + 0.265863i \(0.914343\pi\)
\(594\) 562.070i 0.946247i
\(595\) −44.9398 + 159.304i −0.0755292 + 0.267738i
\(596\) −180.317 −0.302545
\(597\) −490.139 + 131.332i −0.821004 + 0.219987i
\(598\) 1771.10 + 474.564i 2.96170 + 0.793586i
\(599\) 576.293 332.723i 0.962092 0.555464i 0.0652757 0.997867i \(-0.479207\pi\)
0.896816 + 0.442403i \(0.145874\pi\)
\(600\) 31.7687 + 256.922i 0.0529478 + 0.428204i
\(601\) 492.128 0.818849 0.409424 0.912344i \(-0.365730\pi\)
0.409424 + 0.912344i \(0.365730\pi\)
\(602\) −598.736 + 288.432i −0.994578 + 0.479123i
\(603\) −211.114 + 211.114i −0.350105 + 0.350105i
\(604\) −200.185 115.577i −0.331433 0.191353i
\(605\) 25.2115 + 409.338i 0.0416719 + 0.676591i
\(606\) 1.58615 + 2.74730i 0.00261742 + 0.00453350i
\(607\) 504.962 135.304i 0.831898 0.222906i 0.182356 0.983232i \(-0.441628\pi\)
0.649542 + 0.760326i \(0.274961\pi\)
\(608\) 401.991 401.991i 0.661170 0.661170i
\(609\) −370.999 + 319.355i −0.609194 + 0.524392i
\(610\) 163.231 + 487.156i 0.267592 + 0.798616i
\(611\) −89.7051 + 155.374i −0.146817 + 0.254294i
\(612\) −19.8124 + 73.9408i −0.0323732 + 0.120818i
\(613\) 331.820 + 88.9109i 0.541305 + 0.145042i 0.519104 0.854711i \(-0.326266\pi\)
0.0222014 + 0.999754i \(0.492932\pi\)
\(614\) −352.490 203.510i −0.574088 0.331450i
\(615\) −523.481 + 175.403i −0.851189 + 0.285208i
\(616\) −120.609 140.113i −0.195794 0.227457i
\(617\) 332.862 + 332.862i 0.539485 + 0.539485i 0.923378 0.383892i \(-0.125417\pi\)
−0.383892 + 0.923378i \(0.625417\pi\)
\(618\) −65.5453 244.618i −0.106060 0.395822i
\(619\) −60.4937 + 34.9260i −0.0977280 + 0.0564233i −0.548067 0.836434i \(-0.684636\pi\)
0.450339 + 0.892857i \(0.351303\pi\)
\(620\) −547.561 + 33.7248i −0.883163 + 0.0543949i
\(621\) −530.171 + 918.284i −0.853738 + 1.47872i
\(622\) −44.2416 44.2416i −0.0711279 0.0711279i
\(623\) −67.4434 140.001i −0.108256 0.224721i
\(624\) 348.045i 0.557764i
\(625\) −434.928 448.846i −0.695885 0.718153i
\(626\) −361.056 625.367i −0.576766 0.998989i
\(627\) 52.0962 194.426i 0.0830881 0.310089i
\(628\) 104.145 + 388.674i 0.165836 + 0.618907i
\(629\) 110.885i 0.176287i
\(630\) 310.346 + 87.5489i 0.492613 + 0.138967i
\(631\) −764.553 −1.21165 −0.605826 0.795597i \(-0.707157\pi\)
−0.605826 + 0.795597i \(0.707157\pi\)
\(632\) −170.449 + 45.6718i −0.269698 + 0.0722654i
\(633\) 339.297 + 90.9143i 0.536014 + 0.143625i
\(634\) 527.556 304.585i 0.832107 0.480417i
\(635\) −102.736 20.8562i −0.161789 0.0328444i
\(636\) 977.640 1.53717
\(637\) 745.398 + 324.983i 1.17017 + 0.510177i
\(638\) −386.281 + 386.281i −0.605457 + 0.605457i
\(639\) −172.559 99.6273i −0.270046 0.155911i
\(640\) −476.890 421.554i −0.745140 0.658678i
\(641\) −384.061 665.213i −0.599159 1.03777i −0.992945 0.118572i \(-0.962168\pi\)
0.393786 0.919202i \(-0.371165\pi\)
\(642\) −148.098 + 39.6828i −0.230683 + 0.0618112i
\(643\) −568.614 + 568.614i −0.884314 + 0.884314i −0.993970 0.109655i \(-0.965025\pi\)
0.109655 + 0.993970i \(0.465025\pi\)
\(644\) 252.795 + 1335.10i 0.392539 + 2.07314i
\(645\) −169.137 + 339.599i −0.262227 + 0.526509i
\(646\) −95.3901 + 165.220i −0.147663 + 0.255759i
\(647\) 181.932 678.979i 0.281193 1.04943i −0.670383 0.742015i \(-0.733870\pi\)
0.951576 0.307412i \(-0.0994630\pi\)
\(648\) −183.386 49.1382i −0.283003 0.0758305i
\(649\) 91.2222 + 52.6671i 0.140558 + 0.0811512i
\(650\) −765.603 1014.19i −1.17785 1.56029i
\(651\) 115.349 329.785i 0.177187 0.506583i
\(652\) 466.110 + 466.110i 0.714892 + 0.714892i
\(653\) 2.19525 + 8.19277i 0.00336179 + 0.0125464i 0.967586 0.252540i \(-0.0812661\pi\)
−0.964225 + 0.265087i \(0.914599\pi\)
\(654\) 473.968 273.646i 0.724722 0.418419i
\(655\) −13.6821 222.144i −0.0208886 0.339151i
\(656\) 193.237 334.695i 0.294568 0.510206i
\(657\) −219.942 219.942i −0.334768 0.334768i
\(658\) −231.143 17.2915i −0.351281 0.0262788i
\(659\) 365.363i 0.554420i −0.960809 0.277210i \(-0.910590\pi\)
0.960809 0.277210i \(-0.0894097\pi\)
\(660\) −402.965 81.8052i −0.610554 0.123947i
\(661\) 343.193 + 594.427i 0.519202 + 0.899285i 0.999751 + 0.0223166i \(0.00710417\pi\)
−0.480549 + 0.876968i \(0.659562\pi\)
\(662\) −22.3580 + 83.4413i −0.0337734 + 0.126044i
\(663\) 49.7222 + 185.566i 0.0749957 + 0.279888i
\(664\) 44.2379i 0.0666234i
\(665\) 396.157 + 235.724i 0.595725 + 0.354473i
\(666\) −216.018 −0.324352
\(667\) 995.447 266.729i 1.49242 0.399894i
\(668\) −752.808 201.714i −1.12696 0.301968i
\(669\) 882.711 509.634i 1.31945 0.761784i
\(670\) 839.500 + 1267.17i 1.25298 + 1.89130i
\(671\) −209.450 −0.312147
\(672\) 666.315 320.988i 0.991541 0.477660i
\(673\) 475.382 475.382i 0.706362 0.706362i −0.259406 0.965768i \(-0.583527\pi\)
0.965768 + 0.259406i \(0.0835269\pi\)
\(674\) −538.825 311.091i −0.799443 0.461559i
\(675\) 681.103 275.860i 1.00904 0.408681i
\(676\) −286.274 495.842i −0.423483 0.733493i
\(677\) −856.760 + 229.568i −1.26552 + 0.339096i −0.828315 0.560263i \(-0.810700\pi\)
−0.437210 + 0.899359i \(0.644033\pi\)
\(678\) −280.728 + 280.728i −0.414053 + 0.414053i
\(679\) −135.681 716.580i −0.199825 1.05535i
\(680\) 89.5388 + 44.5947i 0.131675 + 0.0655805i
\(681\) 184.511 319.582i 0.270941 0.469283i
\(682\) 100.911 376.606i 0.147964 0.552208i
\(683\) 361.286 + 96.8062i 0.528969 + 0.141737i 0.513412 0.858142i \(-0.328381\pi\)
0.0155567 + 0.999879i \(0.495048\pi\)
\(684\) 184.630 + 106.596i 0.269927 + 0.155842i
\(685\) −228.722 682.610i −0.333901 0.996511i
\(686\) 39.6922 + 1049.81i 0.0578604 + 1.53034i
\(687\) 743.064 + 743.064i 1.08161 + 1.08161i
\(688\) −68.7371 256.530i −0.0999086 0.372864i
\(689\) −1066.67 + 615.841i −1.54814 + 0.893818i
\(690\) 1013.20 + 895.630i 1.46840 + 1.29801i
\(691\) −606.569 + 1050.61i −0.877813 + 1.52042i −0.0240780 + 0.999710i \(0.507665\pi\)
−0.853735 + 0.520707i \(0.825668\pi\)
\(692\) −550.662 550.662i −0.795754 0.795754i
\(693\) −74.0379 + 108.624i −0.106837 + 0.156745i
\(694\) 1429.30i 2.05951i
\(695\) −528.231 797.330i −0.760045 1.14724i
\(696\) 147.915 + 256.196i 0.212521 + 0.368097i
\(697\) −55.2120 + 206.054i −0.0792138 + 0.295630i
\(698\) −463.886 1731.25i −0.664593 2.48029i
\(699\) 756.800i 1.08269i
\(700\) 430.879 837.345i 0.615542 1.19621i
\(701\) 996.400 1.42140 0.710699 0.703496i \(-0.248379\pi\)
0.710699 + 0.703496i \(0.248379\pi\)
\(702\) 1443.14 386.689i 2.05576 0.550839i
\(703\) −298.295 79.9280i −0.424318 0.113696i
\(704\) 529.494 305.703i 0.752122 0.434238i
\(705\) −110.308 + 73.0788i −0.156465 + 0.103658i
\(706\) 1381.37 1.95661
\(707\) 0.220953 2.95357i 0.000312521 0.00417761i
\(708\) 157.148 157.148i 0.221961 0.221961i
\(709\) 1158.38 + 668.789i 1.63382 + 0.943285i 0.982901 + 0.184135i \(0.0589483\pi\)
0.650916 + 0.759150i \(0.274385\pi\)
\(710\) −671.867 + 760.061i −0.946291 + 1.07051i
\(711\) 62.7377 + 108.665i 0.0882387 + 0.152834i
\(712\) −90.7122 + 24.3063i −0.127405 + 0.0341380i
\(713\) −520.096 + 520.096i −0.729448 + 0.729448i
\(714\) −188.106 + 161.921i −0.263454 + 0.226780i
\(715\) 491.192 164.584i 0.686982 0.230187i
\(716\) 165.494 286.645i 0.231137 0.400342i
\(717\) 5.10865 19.0657i 0.00712503 0.0265910i
\(718\) −1338.15 358.557i −1.86372 0.499382i
\(719\) 469.505 + 271.069i 0.652997 + 0.377008i 0.789603 0.613617i \(-0.210286\pi\)
−0.136607 + 0.990625i \(0.543620\pi\)
\(720\) −57.4476 + 115.345i −0.0797884 + 0.160202i
\(721\) −78.0636 + 223.186i −0.108271 + 0.309551i
\(722\) −406.137 406.137i −0.562517 0.562517i
\(723\) −102.040 380.819i −0.141134 0.526721i
\(724\) −450.388 + 260.032i −0.622083 + 0.359160i
\(725\) −657.670 278.502i −0.907131 0.384141i
\(726\) −307.481 + 532.572i −0.423527 + 0.733571i
\(727\) −843.507 843.507i −1.16026 1.16026i −0.984419 0.175839i \(-0.943736\pi\)
−0.175839 0.984419i \(-0.556264\pi\)
\(728\) 276.772 406.064i 0.380181 0.557780i
\(729\) 782.566i 1.07348i
\(730\) −1320.16 + 874.608i −1.80844 + 1.19809i
\(731\) 73.2965 + 126.953i 0.100269 + 0.173671i
\(732\) −114.375 + 426.855i −0.156251 + 0.583135i
\(733\) −223.944 835.772i −0.305518 1.14021i −0.932499 0.361173i \(-0.882376\pi\)
0.626981 0.779034i \(-0.284290\pi\)
\(734\) 1507.09i 2.05326i
\(735\) 385.239 + 459.631i 0.524134 + 0.625349i
\(736\) −1557.05 −2.11556
\(737\) −598.553 + 160.382i −0.812148 + 0.217614i
\(738\) 401.422 + 107.561i 0.543932 + 0.145746i
\(739\) 324.604 187.410i 0.439247 0.253600i −0.264031 0.964514i \(-0.585052\pi\)
0.703278 + 0.710915i \(0.251719\pi\)
\(740\) −125.509 + 618.245i −0.169606 + 0.835466i
\(741\) 535.038 0.722049
\(742\) −1314.88 896.222i −1.77208 1.20785i
\(743\) 789.786 789.786i 1.06297 1.06297i 0.0650901 0.997879i \(-0.479267\pi\)
0.997879 0.0650901i \(-0.0207335\pi\)
\(744\) −182.851 105.569i −0.245767 0.141894i
\(745\) 167.228 10.2997i 0.224467 0.0138251i
\(746\) 348.680 + 603.932i 0.467400 + 0.809560i
\(747\) −30.3841 + 8.14138i −0.0406748 + 0.0108988i
\(748\) −112.345 + 112.345i −0.150194 + 0.150194i
\(749\) 135.123 + 47.2617i 0.180404 + 0.0630997i
\(750\) −171.967 921.270i −0.229290 1.22836i
\(751\) −591.949 + 1025.29i −0.788215 + 1.36523i 0.138845 + 0.990314i \(0.455661\pi\)
−0.927060 + 0.374914i \(0.877672\pi\)
\(752\) 23.9735 89.4702i 0.0318796 0.118976i
\(753\) −836.175 224.052i −1.11046 0.297546i
\(754\) −1257.55 726.046i −1.66784 0.962925i
\(755\) 192.256 + 95.7528i 0.254643 + 0.126825i
\(756\) 722.329 + 839.140i 0.955461 + 1.10997i
\(757\) −250.904 250.904i −0.331446 0.331446i 0.521690 0.853135i \(-0.325302\pi\)
−0.853135 + 0.521690i \(0.825302\pi\)
\(758\) 451.012 + 1683.20i 0.595003 + 2.22058i
\(759\) −477.433 + 275.646i −0.629028 + 0.363170i
\(760\) 184.508 208.727i 0.242773 0.274641i
\(761\) 610.504 1057.42i 0.802239 1.38952i −0.115900 0.993261i \(-0.536975\pi\)
0.918139 0.396258i \(-0.129691\pi\)
\(762\) −111.153 111.153i −0.145870 0.145870i
\(763\) −509.555 38.1191i −0.667831 0.0499595i
\(764\) 1816.93i 2.37818i
\(765\) 14.1507 69.7052i 0.0184977 0.0911180i
\(766\) −34.8369 60.3393i −0.0454790 0.0787719i
\(767\) −72.4671 + 270.451i −0.0944813 + 0.352609i
\(768\) 1.15639 + 4.31571i 0.00150572 + 0.00561942i
\(769\) 625.225i 0.813037i 0.913643 + 0.406519i \(0.133257\pi\)
−0.913643 + 0.406519i \(0.866743\pi\)
\(770\) 466.979 + 479.431i 0.606467 + 0.622638i
\(771\) −1041.07 −1.35029
\(772\) 891.112 238.773i 1.15429 0.309291i
\(773\) 1159.83 + 310.776i 1.50043 + 0.402039i 0.913244 0.407414i \(-0.133569\pi\)
0.587185 + 0.809452i \(0.300236\pi\)
\(774\) 247.322 142.792i 0.319538 0.184485i
\(775\) 505.888 62.5535i 0.652759 0.0807143i
\(776\) −440.744 −0.567969
\(777\) −331.981 226.277i −0.427259 0.291219i
\(778\) −1069.22 + 1069.22i −1.37432 + 1.37432i
\(779\) 514.517 + 297.056i 0.660483 + 0.381330i
\(780\) −67.1904 1090.91i −0.0861416 1.39861i
\(781\) −206.779 358.151i −0.264762 0.458581i
\(782\) 504.718 135.239i 0.645419 0.172939i
\(783\) 593.781 593.781i 0.758341 0.758341i
\(784\) −415.149 62.4629i −0.529526 0.0796721i
\(785\) −118.786 354.511i −0.151320 0.451607i
\(786\) 166.867 289.022i 0.212299 0.367713i
\(787\) −313.785 + 1171.06i −0.398710 + 1.48801i 0.416657 + 0.909064i \(0.363202\pi\)
−0.815368 + 0.578944i \(0.803465\pi\)
\(788\) 981.493 + 262.990i 1.24555 + 0.333744i
\(789\) −119.359 68.9122i −0.151279 0.0873412i
\(790\) 605.722 202.959i 0.766737 0.256910i
\(791\) 364.196 68.9588i 0.460425 0.0871793i
\(792\) 56.1746 + 56.1746i 0.0709275 + 0.0709275i
\(793\) −144.096 537.774i −0.181710 0.678152i
\(794\) −266.652 + 153.951i −0.335833 + 0.193894i
\(795\) −906.674 + 55.8429i −1.14047 + 0.0702427i
\(796\) 557.745 966.042i 0.700684 1.21362i
\(797\) 531.274 + 531.274i 0.666592 + 0.666592i 0.956926 0.290333i \(-0.0937662\pi\)
−0.290333 + 0.956926i \(0.593766\pi\)
\(798\) 300.000 + 622.749i 0.375940 + 0.780387i
\(799\) 51.1273i 0.0639892i
\(800\) 850.893 + 663.622i 1.06362 + 0.829527i
\(801\) 33.3887 + 57.8308i 0.0416837 + 0.0721983i
\(802\) −182.448 + 680.904i −0.227491 + 0.849008i
\(803\) −167.089 623.585i −0.208081 0.776569i
\(804\) 1307.42i 1.62614i
\(805\) −310.706 1223.75i −0.385970 1.52018i
\(806\) 1036.38 1.28583
\(807\) −1047.25 + 280.609i −1.29770 + 0.347719i
\(808\) −1.72893 0.463264i −0.00213976 0.000573347i
\(809\) −367.031 + 211.905i −0.453684 + 0.261935i −0.709385 0.704821i \(-0.751027\pi\)
0.255701 + 0.966756i \(0.417694\pi\)
\(810\) 673.567 + 136.739i 0.831564 + 0.168814i
\(811\) 1447.54 1.78489 0.892443 0.451161i \(-0.148990\pi\)
0.892443 + 0.451161i \(0.148990\pi\)
\(812\) 80.2783 1073.12i 0.0988649 1.32157i
\(813\) −126.501 + 126.501i −0.155598 + 0.155598i
\(814\) −388.284 224.176i −0.477007 0.275400i
\(815\) −458.900 405.651i −0.563067 0.497731i
\(816\) −49.5920 85.8958i −0.0607745 0.105264i
\(817\) 394.356 105.667i 0.482688 0.129336i
\(818\) −1572.69 + 1572.69i −1.92260 + 1.92260i
\(819\) −329.834 115.366i −0.402728 0.140862i
\(820\) 541.068 1086.38i 0.659839 1.32485i
\(821\) −63.7478 + 110.414i −0.0776465 + 0.134488i −0.902234 0.431247i \(-0.858074\pi\)
0.824588 + 0.565734i \(0.191407\pi\)
\(822\) 279.395 1042.72i 0.339896 1.26851i
\(823\) −929.575 249.079i −1.12950 0.302648i −0.354776 0.934951i \(-0.615443\pi\)
−0.774720 + 0.632304i \(0.782109\pi\)
\(824\) 123.746 + 71.4450i 0.150178 + 0.0867051i
\(825\) 378.387 + 52.8496i 0.458651 + 0.0640601i
\(826\) −355.420 + 67.2970i −0.430290 + 0.0814733i
\(827\) −68.5400 68.5400i −0.0828779 0.0828779i 0.664453 0.747330i \(-0.268665\pi\)
−0.747330 + 0.664453i \(0.768665\pi\)
\(828\) −151.126 564.010i −0.182519 0.681172i
\(829\) 159.509 92.0928i 0.192412 0.111089i −0.400699 0.916210i \(-0.631233\pi\)
0.593111 + 0.805121i \(0.297899\pi\)
\(830\) 9.84503 + 159.845i 0.0118615 + 0.192585i
\(831\) 227.806 394.572i 0.274135 0.474816i
\(832\) 1149.19 + 1149.19i 1.38123 + 1.38123i
\(833\) 230.267 26.0056i 0.276430 0.0312192i
\(834\) 1434.16i 1.71962i
\(835\) 709.685 + 144.072i 0.849922 + 0.172541i
\(836\) 221.243 + 383.204i 0.264645 + 0.458378i
\(837\) −155.118 + 578.908i −0.185326 + 0.691646i
\(838\) 133.734 + 499.102i 0.159587 + 0.595588i
\(839\) 1364.90i 1.62681i −0.581697 0.813406i \(-0.697611\pi\)
0.581697 0.813406i \(-0.302389\pi\)
\(840\) 316.231 177.070i 0.376465 0.210798i
\(841\) 24.8511 0.0295495
\(842\) 1729.16 463.326i 2.05363 0.550268i
\(843\) 1102.42 + 295.393i 1.30774 + 0.350407i
\(844\) −668.739 + 386.097i −0.792345 + 0.457460i
\(845\) 293.816 + 443.497i 0.347712 + 0.524848i
\(846\) 99.6030 0.117734
\(847\) 517.267 249.186i 0.610705 0.294198i
\(848\) 449.646 449.646i 0.530243 0.530243i
\(849\) 498.612 + 287.874i 0.587294 + 0.339074i
\(850\) −333.456 141.208i −0.392301 0.166127i
\(851\) 422.906 + 732.495i 0.496952 + 0.860747i
\(852\) −842.821 + 225.833i −0.989226 + 0.265062i
\(853\) −453.633 + 453.633i −0.531809 + 0.531809i −0.921111 0.389301i \(-0.872717\pi\)
0.389301 + 0.921111i \(0.372717\pi\)
\(854\) 545.137 469.252i 0.638334 0.549476i
\(855\) −177.317 88.3124i −0.207388 0.103289i
\(856\) 43.2547 74.9193i 0.0505311 0.0875225i
\(857\) 223.494 834.091i 0.260786 0.973268i −0.703993 0.710207i \(-0.748601\pi\)
0.964779 0.263061i \(-0.0847320\pi\)
\(858\) 750.317 + 201.047i 0.874495 + 0.234320i
\(859\) 349.690 + 201.894i 0.407090 + 0.235034i 0.689539 0.724249i \(-0.257813\pi\)
−0.282449 + 0.959282i \(0.591147\pi\)
\(860\) −264.973 790.800i −0.308108 0.919535i
\(861\) 504.242 + 585.786i 0.585647 + 0.680355i
\(862\) 280.120 + 280.120i 0.324965 + 0.324965i
\(863\) 368.792 + 1376.35i 0.427337 + 1.59484i 0.758766 + 0.651364i \(0.225803\pi\)
−0.331429 + 0.943480i \(0.607531\pi\)
\(864\) −1098.75 + 634.366i −1.27171 + 0.734220i
\(865\) 542.144 + 479.236i 0.626756 + 0.554030i
\(866\) 174.891 302.920i 0.201953 0.349792i
\(867\) −461.517 461.517i −0.532315 0.532315i
\(868\) 333.329 + 691.935i 0.384020 + 0.797160i
\(869\) 260.427i 0.299686i
\(870\) −591.477 892.797i −0.679859 1.02620i
\(871\) −823.577 1426.48i −0.945553 1.63775i
\(872\) −79.9230 + 298.277i −0.0916548 + 0.342061i
\(873\) 81.1129 + 302.717i 0.0929128 + 0.346755i
\(874\) 1455.24i 1.66504i
\(875\) −351.773 + 801.175i −0.402026 + 0.915628i
\(876\) −1362.10 −1.55490
\(877\) −1161.08 + 311.111i −1.32392 + 0.354744i −0.850447 0.526061i \(-0.823668\pi\)
−0.473478 + 0.880806i \(0.657002\pi\)
\(878\) −1616.59 433.165i −1.84122 0.493354i
\(879\) −808.765 + 466.941i −0.920096 + 0.531218i
\(880\) −222.961 + 147.711i −0.253364 + 0.167854i
\(881\) −737.001 −0.836551 −0.418275 0.908320i \(-0.637365\pi\)
−0.418275 + 0.908320i \(0.637365\pi\)
\(882\) −50.6624 448.591i −0.0574404 0.508606i
\(883\) 177.282 177.282i 0.200773 0.200773i −0.599558 0.800331i \(-0.704657\pi\)
0.800331 + 0.599558i \(0.204657\pi\)
\(884\) −365.741 211.161i −0.413735 0.238870i
\(885\) −136.765 + 154.718i −0.154537 + 0.174822i
\(886\) −744.326 1289.21i −0.840097 1.45509i
\(887\) −902.875 + 241.925i −1.01790 + 0.272745i −0.728926 0.684593i \(-0.759980\pi\)
−0.288972 + 0.957338i \(0.593313\pi\)
\(888\) −171.683 + 171.683i −0.193336 + 0.193336i
\(889\) 27.3040 + 144.202i 0.0307131 + 0.162207i
\(890\) 322.362 108.014i 0.362204 0.121364i
\(891\) −140.097 + 242.655i −0.157235 + 0.272340i
\(892\) −579.928 + 2164.32i −0.650143 + 2.42637i
\(893\) 137.540 + 36.8537i 0.154020 + 0.0412695i
\(894\) 217.573 + 125.616i 0.243370 + 0.140510i
\(895\) −137.108 + 275.291i −0.153193 + 0.307587i
\(896\) −294.202 + 841.132i −0.328350 + 0.938763i
\(897\) −1036.19 1036.19i −1.15518 1.15518i
\(898\) −319.838 1193.65i −0.356167 1.32923i
\(899\) 504.457 291.249i 0.561132 0.323970i
\(900\) −157.797 + 372.629i −0.175329 + 0.414032i
\(901\) −175.499 + 303.973i −0.194782 + 0.337373i
\(902\) 609.916 + 609.916i 0.676182 + 0.676182i
\(903\) 529.662 + 39.6232i 0.586558 + 0.0438796i
\(904\) 224.005i 0.247793i
\(905\) 402.842 266.882i 0.445129 0.294898i
\(906\) 161.031 + 278.914i 0.177739 + 0.307852i
\(907\) 42.1435 157.282i 0.0464647 0.173409i −0.938794 0.344479i \(-0.888056\pi\)
0.985259 + 0.171070i \(0.0547224\pi\)
\(908\) 209.960 + 783.583i 0.231234 + 0.862977i
\(909\) 1.27274i 0.00140015i
\(910\) −909.694 + 1528.83i −0.999664 + 1.68003i
\(911\) −136.210 −0.149517 −0.0747583 0.997202i \(-0.523819\pi\)
−0.0747583 + 0.997202i \(0.523819\pi\)
\(912\) −266.819 + 71.4939i −0.292564 + 0.0783924i
\(913\) −63.0629 16.8976i −0.0690721 0.0185078i
\(914\) −300.909 + 173.730i −0.329222 + 0.190076i
\(915\) 81.6911 402.403i 0.0892799 0.439785i
\(916\) −2310.10 −2.52194
\(917\) −280.716 + 135.231i −0.306124 + 0.147471i
\(918\) 301.063 301.063i 0.327955 0.327955i
\(919\) 1017.63 + 587.529i 1.10732 + 0.639314i 0.938135 0.346270i \(-0.112552\pi\)
0.169189 + 0.985584i \(0.445885\pi\)
\(920\) −761.567 + 46.9057i −0.827791 + 0.0509844i
\(921\) 162.646 + 281.712i 0.176597 + 0.305876i
\(922\) −793.337 + 212.574i −0.860452 + 0.230558i
\(923\) 777.313 777.313i 0.842160 0.842160i
\(924\) 107.095 + 565.609i 0.115904 + 0.612131i
\(925\) 81.0838 580.536i 0.0876582 0.627607i
\(926\) 415.813 720.209i 0.449042 0.777763i
\(927\) 26.2969 98.1415i 0.0283678 0.105870i
\(928\) 1191.08 + 319.150i 1.28349 + 0.343911i
\(929\) 22.6987 + 13.1051i 0.0244334 + 0.0141067i 0.512167 0.858886i \(-0.328843\pi\)
−0.487734 + 0.872993i \(0.662176\pi\)
\(930\) 684.190 + 340.760i 0.735688 + 0.366409i
\(931\) 96.0223 638.195i 0.103139 0.685494i
\(932\) 1176.40 + 1176.40i 1.26223 + 1.26223i
\(933\) 12.9419 + 48.3000i 0.0138713 + 0.0517685i
\(934\) 148.642 85.8185i 0.159146 0.0918827i
\(935\) 97.7728 110.607i 0.104570 0.118296i
\(936\) −105.584 + 182.878i −0.112804 + 0.195382i
\(937\) 334.657 + 334.657i 0.357158 + 0.357158i 0.862764 0.505606i \(-0.168731\pi\)
−0.505606 + 0.862764i \(0.668731\pi\)
\(938\) 1198.54 1758.42i 1.27776 1.87465i
\(939\) 577.114i 0.614605i
\(940\) 57.8702 285.064i 0.0615641 0.303259i
\(941\) 459.123 + 795.225i 0.487910 + 0.845085i 0.999903 0.0139045i \(-0.00442610\pi\)
−0.511993 + 0.858989i \(0.671093\pi\)
\(942\) 145.103 541.531i 0.154037 0.574874i
\(943\) −421.150 1571.75i −0.446606 1.66676i
\(944\) 144.555i 0.153130i
\(945\) −717.828 736.968i −0.759606 0.779861i
\(946\) 592.735 0.626570
\(947\) 264.244 70.8040i 0.279033 0.0747667i −0.116589 0.993180i \(-0.537196\pi\)
0.395622 + 0.918414i \(0.370529\pi\)
\(948\) 530.745 + 142.213i 0.559857 + 0.150013i
\(949\) 1486.13 858.019i 1.56600 0.904130i
\(950\) −620.231 + 795.258i −0.652875 + 0.837113i
\(951\) −486.851 −0.511935
\(952\) 10.4471 139.651i 0.0109738 0.146692i
\(953\) −157.912 + 157.912i −0.165699 + 0.165699i −0.785086 0.619387i \(-0.787381\pi\)
0.619387 + 0.785086i \(0.287381\pi\)
\(954\) 592.181 + 341.896i 0.620734 + 0.358381i
\(955\) 103.783 + 1685.04i 0.108674 + 1.76444i
\(956\) 21.6955 + 37.5777i 0.0226940 + 0.0393072i
\(957\) 421.716 112.999i 0.440665 0.118076i
\(958\) 713.106 713.106i 0.744370 0.744370i
\(959\) −763.854 + 657.523i −0.796511 + 0.685634i
\(960\) 380.812 + 1136.51i 0.396679 + 1.18387i
\(961\) 272.632 472.212i 0.283696 0.491375i
\(962\) 308.454 1151.16i 0.320638 1.19664i
\(963\) −59.4174 15.9208i −0.0617003 0.0165326i
\(964\) 750.577 + 433.346i 0.778607 + 0.449529i
\(965\) −812.789 + 272.341i −0.842268 + 0.282219i
\(966\) 625.059 1787.06i 0.647059 1.84996i
\(967\) 1059.59 + 1059.59i 1.09575 + 1.09575i 0.994902 + 0.100844i \(0.0321543\pi\)
0.100844 + 0.994902i \(0.467846\pi\)
\(968\) −89.8051 335.157i −0.0927739 0.346237i
\(969\) 132.045 76.2361i 0.136269 0.0786751i
\(970\) 1592.54 98.0864i 1.64180 0.101120i
\(971\) −279.066 + 483.357i −0.287401 + 0.497793i −0.973189 0.230009i \(-0.926125\pi\)
0.685788 + 0.727802i \(0.259458\pi\)
\(972\) −588.585 588.585i −0.605540 0.605540i
\(973\) −754.145 + 1106.44i −0.775072 + 1.13714i
\(974\) 1033.29i 1.06087i
\(975\) 124.626 + 1007.89i 0.127822 + 1.03373i
\(976\) 143.719 + 248.928i 0.147253 + 0.255050i
\(977\) 465.961 1738.99i 0.476930 1.77993i −0.137004 0.990570i \(-0.543747\pi\)
0.613934 0.789357i \(-0.289586\pi\)
\(978\) −237.705 887.126i −0.243052 0.907082i
\(979\) 138.598i 0.141571i
\(980\) −1313.30 115.639i −1.34010 0.117999i
\(981\) 219.575 0.223828
\(982\) −1145.33 + 306.890i −1.16632 + 0.312516i
\(983\) −1757.33 470.876i −1.78772 0.479019i −0.795767 0.605603i \(-0.792932\pi\)
−0.991956 + 0.126584i \(0.959599\pi\)
\(984\) 404.518 233.549i 0.411096 0.237346i
\(985\) −925.269 187.837i −0.939360 0.190697i
\(986\) −413.809 −0.419684
\(987\) 153.071 + 104.333i 0.155088 + 0.105707i
\(988\) −831.687 + 831.687i −0.841788 + 0.841788i
\(989\) −968.382 559.096i −0.979153 0.565314i
\(990\) −215.478 190.475i −0.217654 0.192399i
\(991\) 36.3267 + 62.9197i 0.0366566 + 0.0634912i 0.883772 0.467918i \(-0.154996\pi\)
−0.847115 + 0.531410i \(0.821663\pi\)
\(992\) −850.093 + 227.782i −0.856949 + 0.229619i
\(993\) 48.8180 48.8180i 0.0491621 0.0491621i
\(994\) 1340.59 + 468.895i 1.34868 + 0.471725i
\(995\) −462.078 + 927.777i −0.464400 + 0.932439i
\(996\) −68.8740 + 119.293i −0.0691506 + 0.119772i
\(997\) 450.664 1681.90i 0.452020 1.68696i −0.244682 0.969603i \(-0.578684\pi\)
0.696703 0.717360i \(-0.254650\pi\)
\(998\) −1828.91 490.054i −1.83257 0.491036i
\(999\) 596.859 + 344.597i 0.597457 + 0.344942i
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 35.3.l.a.2.6 24
3.2 odd 2 315.3.ca.a.37.1 24
5.2 odd 4 175.3.p.c.93.6 24
5.3 odd 4 inner 35.3.l.a.23.1 yes 24
5.4 even 2 175.3.p.c.107.1 24
7.2 even 3 245.3.g.c.197.1 12
7.3 odd 6 245.3.m.b.67.1 24
7.4 even 3 inner 35.3.l.a.32.1 yes 24
7.5 odd 6 245.3.g.b.197.1 12
7.6 odd 2 245.3.m.b.177.6 24
15.8 even 4 315.3.ca.a.163.6 24
21.11 odd 6 315.3.ca.a.172.6 24
35.3 even 12 245.3.m.b.18.6 24
35.4 even 6 175.3.p.c.32.6 24
35.13 even 4 245.3.m.b.128.1 24
35.18 odd 12 inner 35.3.l.a.18.6 yes 24
35.23 odd 12 245.3.g.c.148.1 12
35.32 odd 12 175.3.p.c.18.1 24
35.33 even 12 245.3.g.b.148.1 12
105.53 even 12 315.3.ca.a.298.1 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.3.l.a.2.6 24 1.1 even 1 trivial
35.3.l.a.18.6 yes 24 35.18 odd 12 inner
35.3.l.a.23.1 yes 24 5.3 odd 4 inner
35.3.l.a.32.1 yes 24 7.4 even 3 inner
175.3.p.c.18.1 24 35.32 odd 12
175.3.p.c.32.6 24 35.4 even 6
175.3.p.c.93.6 24 5.2 odd 4
175.3.p.c.107.1 24 5.4 even 2
245.3.g.b.148.1 12 35.33 even 12
245.3.g.b.197.1 12 7.5 odd 6
245.3.g.c.148.1 12 35.23 odd 12
245.3.g.c.197.1 12 7.2 even 3
245.3.m.b.18.6 24 35.3 even 12
245.3.m.b.67.1 24 7.3 odd 6
245.3.m.b.128.1 24 35.13 even 4
245.3.m.b.177.6 24 7.6 odd 2
315.3.ca.a.37.1 24 3.2 odd 2
315.3.ca.a.163.6 24 15.8 even 4
315.3.ca.a.172.6 24 21.11 odd 6
315.3.ca.a.298.1 24 105.53 even 12