Properties

Label 177.3.h.a.107.31
Level $177$
Weight $3$
Character 177.107
Analytic conductor $4.823$
Analytic rank $0$
Dimension $1064$
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] = [177,3,Mod(5,177)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(177, base_ring=CyclotomicField(58))
 
chi = DirichletCharacter(H, H._module([29, 6]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("177.5");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 177.h (of order \(58\), degree \(28\), 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: \(4.82290067918\)
Analytic rank: \(0\)
Dimension: \(1064\)
Relative dimension: \(38\) over \(\Q(\zeta_{58})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{58}]$

Embedding invariants

Embedding label 107.31
Character \(\chi\) \(=\) 177.107
Dual form 177.3.h.a.134.31

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.574021 + 2.60780i) q^{2} +(-2.66997 + 1.36794i) q^{3} +(-2.84083 + 1.31431i) q^{4} +(7.65813 + 2.12627i) q^{5} +(-5.09993 - 6.17753i) q^{6} +(-6.92978 + 6.56424i) q^{7} +(1.40567 + 1.84913i) q^{8} +(5.25749 - 7.30471i) q^{9} +O(q^{10})\) \(q+(0.574021 + 2.60780i) q^{2} +(-2.66997 + 1.36794i) q^{3} +(-2.84083 + 1.31431i) q^{4} +(7.65813 + 2.12627i) q^{5} +(-5.09993 - 6.17753i) q^{6} +(-6.92978 + 6.56424i) q^{7} +(1.40567 + 1.84913i) q^{8} +(5.25749 - 7.30471i) q^{9} +(-1.14897 + 21.1914i) q^{10} +(-7.04832 + 5.98690i) q^{11} +(5.78704 - 7.39524i) q^{12} +(-6.51292 + 2.19446i) q^{13} +(-21.0961 - 14.3035i) q^{14} +(-23.3556 + 4.79877i) q^{15} +(-12.1209 + 14.2698i) q^{16} +(21.5904 - 22.7927i) q^{17} +(22.0671 + 9.51744i) q^{18} +(-7.52901 - 18.8964i) q^{19} +(-24.5500 + 4.02477i) q^{20} +(9.52284 - 27.0058i) q^{21} +(-19.6585 - 14.9440i) q^{22} +(0.0328185 + 0.301761i) q^{23} +(-6.28259 - 3.01425i) q^{24} +(32.7045 + 19.6777i) q^{25} +(-9.46126 - 15.7247i) q^{26} +(-4.04496 + 26.6953i) q^{27} +(11.0589 - 27.7557i) q^{28} +(-8.26086 + 37.5295i) q^{29} +(-25.9208 - 58.1522i) q^{30} +(-0.793400 + 1.99128i) q^{31} +(-35.9618 - 19.0657i) q^{32} +(10.6291 - 25.6265i) q^{33} +(71.8322 + 43.2200i) q^{34} +(-67.0265 + 35.5352i) q^{35} +(-5.33500 + 27.6614i) q^{36} +(20.2950 + 15.4279i) q^{37} +(44.9562 - 30.4811i) q^{38} +(14.3874 - 14.7684i) q^{39} +(6.83306 + 17.1497i) q^{40} +(-3.54327 + 32.5798i) q^{41} +(75.8922 + 9.33178i) q^{42} +(11.4507 - 13.4808i) q^{43} +(12.1544 - 26.2714i) q^{44} +(55.7943 - 44.7616i) q^{45} +(-0.768096 + 0.258802i) q^{46} +(82.6580 - 22.9499i) q^{47} +(12.8422 - 54.6806i) q^{48} +(2.27985 - 42.0493i) q^{49} +(-32.5424 + 96.5824i) q^{50} +(-26.4667 + 90.3902i) q^{51} +(15.6179 - 14.7941i) q^{52} +(20.5229 - 1.11272i) q^{53} +(-71.9379 + 4.77520i) q^{54} +(-66.7067 + 30.8618i) q^{55} +(-21.8791 - 3.58690i) q^{56} +(45.9513 + 40.1536i) q^{57} -102.611 q^{58} +(-37.5011 + 45.5485i) q^{59} +(60.0422 - 44.3289i) q^{60} +(5.51453 - 1.21384i) q^{61} +(-5.64830 - 0.925992i) q^{62} +(11.5166 + 85.1315i) q^{63} +(9.04130 - 32.5638i) q^{64} +(-54.5428 + 2.95722i) q^{65} +(72.9302 + 13.0085i) q^{66} +(71.1384 - 54.0780i) q^{67} +(-31.3780 + 93.1267i) q^{68} +(-0.500416 - 0.760801i) q^{69} +(-131.143 - 154.394i) q^{70} +(120.229 - 33.3815i) q^{71} +(20.8976 - 0.546243i) q^{72} +(-16.2646 + 23.9885i) q^{73} +(-28.5831 + 61.7813i) q^{74} +(-114.238 - 7.80102i) q^{75} +(46.2243 + 43.7860i) q^{76} +(9.54390 - 87.7547i) q^{77} +(46.7717 + 29.0422i) q^{78} +(11.7355 + 71.5833i) q^{79} +(-123.165 + 83.5078i) q^{80} +(-25.7176 - 76.8089i) q^{81} +(-86.9955 + 9.46134i) q^{82} +(18.6439 - 9.88435i) q^{83} +(8.44120 + 89.2349i) q^{84} +(213.806 - 128.643i) q^{85} +(41.7280 + 22.1228i) q^{86} +(-29.2817 - 111.503i) q^{87} +(-20.9781 - 4.61764i) q^{88} +(0.251811 - 1.14399i) q^{89} +(148.756 + 119.807i) q^{90} +(30.7281 - 57.9594i) q^{91} +(-0.489839 - 0.814119i) q^{92} +(-0.605598 - 6.40199i) q^{93} +(107.296 + 202.382i) q^{94} +(-17.4793 - 160.720i) q^{95} +(122.098 + 1.71145i) q^{96} +(41.3253 + 60.9503i) q^{97} +(110.965 - 18.1918i) q^{98} +(6.67607 + 82.9620i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1064 q - 29 q^{3} + 18 q^{4} - 21 q^{6} - 46 q^{7} - 49 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 1064 q - 29 q^{3} + 18 q^{4} - 21 q^{6} - 46 q^{7} - 49 q^{9} - 94 q^{10} - 29 q^{12} - 54 q^{13} - 12 q^{15} - 158 q^{16} - 27 q^{18} - 30 q^{19} - 18 q^{21} - 142 q^{22} - 23 q^{24} + 108 q^{25} - 32 q^{27} - 70 q^{28} - 131 q^{30} - 18 q^{31} + 17 q^{33} + 90 q^{34} + 67 q^{36} - 170 q^{37} - 91 q^{39} - 2 q^{40} - 43 q^{42} - 222 q^{43} - 461 q^{45} - 54 q^{46} - 1645 q^{48} - 300 q^{49} - 893 q^{51} - 66 q^{52} - 859 q^{54} + 170 q^{55} - 27 q^{57} - 36 q^{58} + 510 q^{60} - 70 q^{61} + 610 q^{63} - 106 q^{64} + 1619 q^{66} - 182 q^{67} + 1487 q^{69} - 206 q^{70} + 2241 q^{72} + 134 q^{73} + 542 q^{75} + 246 q^{76} - 273 q^{78} - 122 q^{79} + 127 q^{81} + 122 q^{82} - 329 q^{84} - 6 q^{85} + 54 q^{87} + 38 q^{88} + 347 q^{90} + 274 q^{91} - 483 q^{93} - 826 q^{94} + 693 q^{96} - 474 q^{97} - 523 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(e\left(\frac{27}{29}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.574021 + 2.60780i 0.287010 + 1.30390i 0.870656 + 0.491892i \(0.163695\pi\)
−0.583646 + 0.812008i \(0.698374\pi\)
\(3\) −2.66997 + 1.36794i −0.889990 + 0.455979i
\(4\) −2.84083 + 1.31431i −0.710207 + 0.328577i
\(5\) 7.65813 + 2.12627i 1.53163 + 0.425254i 0.928175 0.372145i \(-0.121378\pi\)
0.603452 + 0.797399i \(0.293791\pi\)
\(6\) −5.09993 6.17753i −0.849988 1.02959i
\(7\) −6.92978 + 6.56424i −0.989969 + 0.937748i −0.998063 0.0622191i \(-0.980182\pi\)
0.00809380 + 0.999967i \(0.497424\pi\)
\(8\) 1.40567 + 1.84913i 0.175709 + 0.231141i
\(9\) 5.25749 7.30471i 0.584166 0.811634i
\(10\) −1.14897 + 21.1914i −0.114897 + 2.11914i
\(11\) −7.04832 + 5.98690i −0.640756 + 0.544263i −0.907791 0.419424i \(-0.862232\pi\)
0.267034 + 0.963687i \(0.413956\pi\)
\(12\) 5.78704 7.39524i 0.482253 0.616270i
\(13\) −6.51292 + 2.19446i −0.500994 + 0.168804i −0.558441 0.829544i \(-0.688600\pi\)
0.0574476 + 0.998349i \(0.481704\pi\)
\(14\) −21.0961 14.3035i −1.50686 1.02168i
\(15\) −23.3556 + 4.79877i −1.55704 + 0.319918i
\(16\) −12.1209 + 14.2698i −0.757555 + 0.891863i
\(17\) 21.5904 22.7927i 1.27002 1.34075i 0.356322 0.934363i \(-0.384031\pi\)
0.913702 0.406385i \(-0.133211\pi\)
\(18\) 22.0671 + 9.51744i 1.22595 + 0.528747i
\(19\) −7.52901 18.8964i −0.396264 0.994547i −0.982808 0.184630i \(-0.940891\pi\)
0.586544 0.809917i \(-0.300488\pi\)
\(20\) −24.5500 + 4.02477i −1.22750 + 0.201239i
\(21\) 9.52284 27.0058i 0.453469 1.28599i
\(22\) −19.6585 14.9440i −0.893569 0.679273i
\(23\) 0.0328185 + 0.301761i 0.00142689 + 0.0131201i 0.994830 0.101557i \(-0.0323823\pi\)
−0.993403 + 0.114677i \(0.963417\pi\)
\(24\) −6.28259 3.01425i −0.261775 0.125594i
\(25\) 32.7045 + 19.6777i 1.30818 + 0.787107i
\(26\) −9.46126 15.7247i −0.363894 0.604797i
\(27\) −4.04496 + 26.6953i −0.149813 + 0.988714i
\(28\) 11.0589 27.7557i 0.394961 0.991277i
\(29\) −8.26086 + 37.5295i −0.284857 + 1.29412i 0.589077 + 0.808077i \(0.299491\pi\)
−0.873935 + 0.486043i \(0.838440\pi\)
\(30\) −25.9208 58.1522i −0.864028 1.93841i
\(31\) −0.793400 + 1.99128i −0.0255935 + 0.0642349i −0.941218 0.337799i \(-0.890317\pi\)
0.915625 + 0.402034i \(0.131697\pi\)
\(32\) −35.9618 19.0657i −1.12381 0.595804i
\(33\) 10.6291 25.6265i 0.322094 0.776561i
\(34\) 71.8322 + 43.2200i 2.11271 + 1.27118i
\(35\) −67.0265 + 35.5352i −1.91504 + 1.01529i
\(36\) −5.33500 + 27.6614i −0.148194 + 0.768372i
\(37\) 20.2950 + 15.4279i 0.548514 + 0.416970i 0.842386 0.538875i \(-0.181151\pi\)
−0.293871 + 0.955845i \(0.594944\pi\)
\(38\) 44.9562 30.4811i 1.18306 0.802134i
\(39\) 14.3874 14.7684i 0.368908 0.378677i
\(40\) 6.83306 + 17.1497i 0.170827 + 0.428742i
\(41\) −3.54327 + 32.5798i −0.0864211 + 0.794629i 0.868081 + 0.496423i \(0.165354\pi\)
−0.954502 + 0.298206i \(0.903612\pi\)
\(42\) 75.8922 + 9.33178i 1.80696 + 0.222185i
\(43\) 11.4507 13.4808i 0.266294 0.313506i −0.612721 0.790299i \(-0.709925\pi\)
0.879015 + 0.476793i \(0.158201\pi\)
\(44\) 12.1544 26.2714i 0.276237 0.597077i
\(45\) 55.7943 44.7616i 1.23987 0.994702i
\(46\) −0.768096 + 0.258802i −0.0166977 + 0.00562612i
\(47\) 82.6580 22.9499i 1.75868 0.488296i 0.769964 0.638087i \(-0.220274\pi\)
0.988718 + 0.149792i \(0.0478603\pi\)
\(48\) 12.8422 54.6806i 0.267546 1.13918i
\(49\) 2.27985 42.0493i 0.0465275 0.858149i
\(50\) −32.5424 + 96.5824i −0.650848 + 1.93165i
\(51\) −26.4667 + 90.3902i −0.518956 + 1.77236i
\(52\) 15.6179 14.7941i 0.300344 0.284501i
\(53\) 20.5229 1.11272i 0.387224 0.0209947i 0.140500 0.990081i \(-0.455129\pi\)
0.246723 + 0.969086i \(0.420646\pi\)
\(54\) −71.9379 + 4.77520i −1.33218 + 0.0884297i
\(55\) −66.7067 + 30.8618i −1.21285 + 0.561124i
\(56\) −21.8791 3.58690i −0.390698 0.0640517i
\(57\) 45.9513 + 40.1536i 0.806164 + 0.704449i
\(58\) −102.611 −1.76916
\(59\) −37.5011 + 45.5485i −0.635611 + 0.772009i
\(60\) 60.0422 44.3289i 1.00070 0.738816i
\(61\) 5.51453 1.21384i 0.0904021 0.0198990i −0.169539 0.985523i \(-0.554228\pi\)
0.259941 + 0.965624i \(0.416297\pi\)
\(62\) −5.64830 0.925992i −0.0911016 0.0149353i
\(63\) 11.5166 + 85.1315i 0.182803 + 1.35129i
\(64\) 9.04130 32.5638i 0.141270 0.508810i
\(65\) −54.5428 + 2.95722i −0.839120 + 0.0454958i
\(66\) 72.9302 + 13.0085i 1.10500 + 0.197098i
\(67\) 71.1384 54.0780i 1.06177 0.807135i 0.0799190 0.996801i \(-0.474534\pi\)
0.981849 + 0.189667i \(0.0607407\pi\)
\(68\) −31.3780 + 93.1267i −0.461442 + 1.36951i
\(69\) −0.500416 0.760801i −0.00725240 0.0110261i
\(70\) −131.143 154.394i −1.87348 2.20563i
\(71\) 120.229 33.3815i 1.69337 0.470163i 0.718983 0.695028i \(-0.244608\pi\)
0.974390 + 0.224865i \(0.0721942\pi\)
\(72\) 20.8976 0.546243i 0.290245 0.00758671i
\(73\) −16.2646 + 23.9885i −0.222803 + 0.328610i −0.922618 0.385714i \(-0.873955\pi\)
0.699815 + 0.714324i \(0.253266\pi\)
\(74\) −28.5831 + 61.7813i −0.386258 + 0.834883i
\(75\) −114.238 7.80102i −1.52317 0.104014i
\(76\) 46.2243 + 43.7860i 0.608215 + 0.576131i
\(77\) 9.54390 87.7547i 0.123947 1.13967i
\(78\) 46.7717 + 29.0422i 0.599638 + 0.372335i
\(79\) 11.7355 + 71.5833i 0.148550 + 0.906118i 0.950953 + 0.309335i \(0.100106\pi\)
−0.802403 + 0.596783i \(0.796445\pi\)
\(80\) −123.165 + 83.5078i −1.53956 + 1.04385i
\(81\) −25.7176 76.8089i −0.317501 0.948258i
\(82\) −86.9955 + 9.46134i −1.06092 + 0.115382i
\(83\) 18.6439 9.88435i 0.224625 0.119089i −0.352296 0.935889i \(-0.614599\pi\)
0.576921 + 0.816800i \(0.304254\pi\)
\(84\) 8.44120 + 89.2349i 0.100490 + 1.06232i
\(85\) 213.806 128.643i 2.51536 1.51344i
\(86\) 41.7280 + 22.1228i 0.485210 + 0.257242i
\(87\) −29.2817 111.503i −0.336572 1.28164i
\(88\) −20.9781 4.61764i −0.238388 0.0524732i
\(89\) 0.251811 1.14399i 0.00282934 0.0128538i −0.975185 0.221393i \(-0.928940\pi\)
0.978014 + 0.208539i \(0.0668708\pi\)
\(90\) 148.756 + 119.807i 1.65285 + 1.33118i
\(91\) 30.7281 57.9594i 0.337672 0.636917i
\(92\) −0.489839 0.814119i −0.00532434 0.00884912i
\(93\) −0.605598 6.40199i −0.00651181 0.0688386i
\(94\) 107.296 + 202.382i 1.14145 + 2.15300i
\(95\) −17.4793 160.720i −0.183993 1.69179i
\(96\) 122.098 + 1.71145i 1.27185 + 0.0178276i
\(97\) 41.3253 + 60.9503i 0.426034 + 0.628353i 0.978760 0.205010i \(-0.0657227\pi\)
−0.552726 + 0.833363i \(0.686412\pi\)
\(98\) 110.965 18.1918i 1.13230 0.185630i
\(99\) 6.67607 + 82.9620i 0.0674351 + 0.838000i
\(100\) −118.771 12.9171i −1.18771 0.129171i
\(101\) 105.971 111.872i 1.04921 1.10764i 0.0551899 0.998476i \(-0.482424\pi\)
0.994024 0.109165i \(-0.0348178\pi\)
\(102\) −250.912 17.1342i −2.45992 0.167982i
\(103\) −21.6500 10.0163i −0.210194 0.0972460i 0.311967 0.950093i \(-0.399012\pi\)
−0.522161 + 0.852847i \(0.674874\pi\)
\(104\) −13.2128 8.95853i −0.127047 0.0861397i
\(105\) 130.349 186.566i 1.24142 1.77682i
\(106\) 14.6823 + 52.8808i 0.138512 + 0.498876i
\(107\) 18.2595 15.5098i 0.170650 0.144951i −0.557992 0.829847i \(-0.688428\pi\)
0.728642 + 0.684895i \(0.240152\pi\)
\(108\) −23.5948 81.1531i −0.218470 0.751417i
\(109\) −189.432 63.8270i −1.73791 0.585569i −0.741553 0.670894i \(-0.765911\pi\)
−0.996353 + 0.0853251i \(0.972807\pi\)
\(110\) −118.773 156.243i −1.07975 1.42039i
\(111\) −75.2915 13.4296i −0.678302 0.120988i
\(112\) −9.67533 178.451i −0.0863869 1.59331i
\(113\) −162.400 45.0902i −1.43717 0.399029i −0.540357 0.841436i \(-0.681711\pi\)
−0.896814 + 0.442407i \(0.854125\pi\)
\(114\) −78.3356 + 142.881i −0.687154 + 1.25334i
\(115\) −0.390298 + 2.38071i −0.00339389 + 0.0207018i
\(116\) −25.8576 117.472i −0.222910 1.01269i
\(117\) −18.2117 + 59.1123i −0.155656 + 0.505233i
\(118\) −140.308 71.6496i −1.18905 0.607200i
\(119\) 299.673i 2.51826i
\(120\) −41.7038 36.4420i −0.347532 0.303683i
\(121\) −5.73975 + 35.0109i −0.0474359 + 0.289346i
\(122\) 6.33090 + 13.6840i 0.0518926 + 0.112164i
\(123\) −35.1067 91.8341i −0.285420 0.746618i
\(124\) −0.363245 6.69967i −0.00292940 0.0540296i
\(125\) 71.9727 + 75.9807i 0.575782 + 0.607846i
\(126\) −215.395 + 78.9002i −1.70949 + 0.626192i
\(127\) 98.9532 + 33.3412i 0.779159 + 0.262529i 0.680652 0.732607i \(-0.261697\pi\)
0.0985070 + 0.995136i \(0.468593\pi\)
\(128\) −72.4641 3.92889i −0.566126 0.0306944i
\(129\) −12.1321 + 51.6570i −0.0940471 + 0.400442i
\(130\) −39.0205 140.539i −0.300158 1.08107i
\(131\) −33.4632 99.3154i −0.255445 0.758132i −0.996259 0.0864223i \(-0.972457\pi\)
0.740814 0.671710i \(-0.234440\pi\)
\(132\) 3.48564 + 86.7704i 0.0264063 + 0.657352i
\(133\) 176.215 + 81.5256i 1.32492 + 0.612975i
\(134\) 181.860 + 154.473i 1.35716 + 1.15278i
\(135\) −87.7382 + 195.835i −0.649913 + 1.45063i
\(136\) 72.4956 + 7.88437i 0.533056 + 0.0579733i
\(137\) 60.3288 24.0372i 0.440356 0.175454i −0.139414 0.990234i \(-0.544522\pi\)
0.579770 + 0.814780i \(0.303142\pi\)
\(138\) 1.69677 1.74170i 0.0122954 0.0126210i
\(139\) −67.2308 99.1579i −0.483674 0.713367i 0.505054 0.863088i \(-0.331473\pi\)
−0.988728 + 0.149721i \(0.952162\pi\)
\(140\) 143.707 189.043i 1.02648 1.35031i
\(141\) −189.301 + 174.347i −1.34256 + 1.23650i
\(142\) 156.067 + 294.373i 1.09906 + 2.07305i
\(143\) 32.7671 54.4594i 0.229141 0.380835i
\(144\) 40.5114 + 163.563i 0.281329 + 1.13585i
\(145\) −143.061 + 269.841i −0.986625 + 1.86097i
\(146\) −71.8935 28.6450i −0.492422 0.196199i
\(147\) 51.4337 + 115.389i 0.349889 + 0.784960i
\(148\) −77.9317 17.1541i −0.526566 0.115906i
\(149\) −86.1008 34.3057i −0.577858 0.230240i 0.0628518 0.998023i \(-0.479980\pi\)
−0.640710 + 0.767783i \(0.721360\pi\)
\(150\) −45.2315 302.388i −0.301543 2.01592i
\(151\) 36.4106 21.9075i 0.241130 0.145083i −0.389860 0.920874i \(-0.627477\pi\)
0.630990 + 0.775791i \(0.282649\pi\)
\(152\) 24.3585 40.4842i 0.160253 0.266343i
\(153\) −52.9828 277.544i −0.346293 1.81401i
\(154\) 234.325 25.4844i 1.52159 0.165483i
\(155\) −10.3100 + 13.5625i −0.0665159 + 0.0875002i
\(156\) −21.4620 + 60.8640i −0.137577 + 0.390154i
\(157\) −15.5601 94.9123i −0.0991088 0.604537i −0.988948 0.148263i \(-0.952632\pi\)
0.889839 0.456274i \(-0.150816\pi\)
\(158\) −179.939 + 71.6941i −1.13885 + 0.453760i
\(159\) −53.2733 + 31.0449i −0.335052 + 0.195251i
\(160\) −234.861 222.472i −1.46788 1.39045i
\(161\) −2.20826 1.87571i −0.0137159 0.0116504i
\(162\) 185.540 111.156i 1.14531 0.686150i
\(163\) −66.4968 + 98.0754i −0.407956 + 0.601690i −0.975056 0.221959i \(-0.928755\pi\)
0.567100 + 0.823649i \(0.308065\pi\)
\(164\) −32.7541 97.2106i −0.199720 0.592747i
\(165\) 135.888 173.651i 0.823563 1.05243i
\(166\) 36.4784 + 42.9457i 0.219749 + 0.258709i
\(167\) 173.320 + 9.39714i 1.03784 + 0.0562703i 0.565176 0.824970i \(-0.308808\pi\)
0.472668 + 0.881240i \(0.343291\pi\)
\(168\) 63.3232 20.3523i 0.376924 0.121145i
\(169\) −96.9373 + 73.6898i −0.573593 + 0.436034i
\(170\) 458.203 + 483.719i 2.69531 + 2.84541i
\(171\) −177.616 44.3504i −1.03869 0.259359i
\(172\) −14.8115 + 53.3462i −0.0861134 + 0.310152i
\(173\) 90.7418 + 196.135i 0.524519 + 1.13373i 0.971031 + 0.238952i \(0.0768039\pi\)
−0.446512 + 0.894778i \(0.647334\pi\)
\(174\) 273.969 140.366i 1.57454 0.806701i
\(175\) −355.804 + 78.3184i −2.03317 + 0.447534i
\(176\) 173.145i 0.983776i
\(177\) 37.8192 172.912i 0.213668 0.976906i
\(178\) 3.12785 0.0175722
\(179\) −72.9996 331.641i −0.407819 1.85274i −0.513144 0.858303i \(-0.671519\pi\)
0.105325 0.994438i \(-0.466412\pi\)
\(180\) −99.6717 + 200.491i −0.553732 + 1.11384i
\(181\) −187.859 + 86.9130i −1.03790 + 0.480182i −0.863424 0.504479i \(-0.831684\pi\)
−0.174474 + 0.984662i \(0.555822\pi\)
\(182\) 168.785 + 46.8630i 0.927392 + 0.257489i
\(183\) −13.0632 + 10.7844i −0.0713834 + 0.0589314i
\(184\) −0.511863 + 0.484863i −0.00278187 + 0.00263512i
\(185\) 122.618 + 161.301i 0.662801 + 0.871900i
\(186\) 16.3475 5.25415i 0.0878898 0.0282481i
\(187\) −15.7185 + 289.910i −0.0840559 + 1.55032i
\(188\) −204.654 + 173.835i −1.08859 + 0.924653i
\(189\) −147.204 211.545i −0.778855 1.11928i
\(190\) 409.092 137.839i 2.15312 0.725469i
\(191\) −64.2905 43.5901i −0.336600 0.228220i 0.381163 0.924508i \(-0.375524\pi\)
−0.717763 + 0.696287i \(0.754834\pi\)
\(192\) 20.4053 + 99.3124i 0.106278 + 0.517252i
\(193\) 184.098 216.737i 0.953875 1.12299i −0.0384407 0.999261i \(-0.512239\pi\)
0.992316 0.123728i \(-0.0394851\pi\)
\(194\) −135.225 + 142.755i −0.697034 + 0.735850i
\(195\) 141.582 82.5069i 0.726063 0.423112i
\(196\) 48.7891 + 122.451i 0.248924 + 0.624752i
\(197\) −160.754 + 26.3543i −0.816010 + 0.133778i −0.555312 0.831642i \(-0.687401\pi\)
−0.260698 + 0.965420i \(0.583953\pi\)
\(198\) −212.516 + 65.0318i −1.07331 + 0.328443i
\(199\) 92.2683 + 70.1406i 0.463660 + 0.352465i 0.810775 0.585357i \(-0.199046\pi\)
−0.347116 + 0.937822i \(0.612839\pi\)
\(200\) 9.58528 + 88.1352i 0.0479264 + 0.440676i
\(201\) −115.962 + 241.700i −0.576926 + 1.20249i
\(202\) 352.569 + 212.134i 1.74539 + 1.05017i
\(203\) −189.106 314.297i −0.931559 1.54826i
\(204\) −43.6131 291.569i −0.213790 1.42926i
\(205\) −96.4082 + 241.966i −0.470284 + 1.18032i
\(206\) 13.6931 62.2084i 0.0664714 0.301983i
\(207\) 2.37682 + 1.34678i 0.0114822 + 0.00650617i
\(208\) 47.6278 119.537i 0.228980 0.574696i
\(209\) 166.198 + 88.1124i 0.795204 + 0.421590i
\(210\) 561.350 + 232.831i 2.67310 + 1.10872i
\(211\) −75.4581 45.4016i −0.357621 0.215173i 0.325393 0.945579i \(-0.394504\pi\)
−0.683014 + 0.730405i \(0.739331\pi\)
\(212\) −56.8395 + 30.1344i −0.268111 + 0.142143i
\(213\) −275.345 + 253.594i −1.29270 + 1.19058i
\(214\) 50.9278 + 38.7143i 0.237980 + 0.180908i
\(215\) 116.354 78.8902i 0.541183 0.366931i
\(216\) −55.0488 + 30.0451i −0.254856 + 0.139098i
\(217\) −7.57317 19.0072i −0.0348994 0.0875909i
\(218\) 57.7104 530.639i 0.264727 2.43412i
\(219\) 10.6113 86.2977i 0.0484532 0.394053i
\(220\) 148.940 175.346i 0.677002 0.797029i
\(221\) −90.5989 + 195.826i −0.409950 + 0.886092i
\(222\) −8.19703 204.054i −0.0369235 0.919164i
\(223\) 67.3288 22.6857i 0.301923 0.101730i −0.164263 0.986417i \(-0.552524\pi\)
0.466185 + 0.884687i \(0.345628\pi\)
\(224\) 374.359 103.940i 1.67125 0.464019i
\(225\) 315.684 135.442i 1.40304 0.601965i
\(226\) 24.3653 449.391i 0.107811 1.98845i
\(227\) 30.3016 89.9320i 0.133487 0.396176i −0.859975 0.510336i \(-0.829521\pi\)
0.993462 + 0.114160i \(0.0364176\pi\)
\(228\) −183.314 53.6753i −0.804009 0.235418i
\(229\) 231.649 219.430i 1.01157 0.958210i 0.0124400 0.999923i \(-0.496040\pi\)
0.999130 + 0.0417130i \(0.0132815\pi\)
\(230\) −6.43246 + 0.348758i −0.0279672 + 0.00151634i
\(231\) 94.5611 + 247.358i 0.409355 + 1.07081i
\(232\) −81.0088 + 37.4787i −0.349176 + 0.161546i
\(233\) 60.9032 + 9.98457i 0.261387 + 0.0428522i 0.291050 0.956708i \(-0.405995\pi\)
−0.0296633 + 0.999560i \(0.509444\pi\)
\(234\) −164.607 13.5609i −0.703449 0.0579525i
\(235\) 681.804 2.90129
\(236\) 46.6693 178.684i 0.197751 0.757134i
\(237\) −129.255 175.072i −0.545380 0.738700i
\(238\) −781.488 + 172.019i −3.28356 + 0.722767i
\(239\) 35.9724 + 5.89738i 0.150512 + 0.0246752i 0.236567 0.971615i \(-0.423978\pi\)
−0.0860548 + 0.996290i \(0.527426\pi\)
\(240\) 214.613 391.445i 0.894221 1.63102i
\(241\) 18.0106 64.8685i 0.0747330 0.269164i −0.916738 0.399488i \(-0.869188\pi\)
0.991471 + 0.130324i \(0.0416018\pi\)
\(242\) −94.5963 + 5.12886i −0.390894 + 0.0211936i
\(243\) 173.735 + 169.897i 0.714959 + 0.699166i
\(244\) −14.0705 + 10.6961i −0.0576659 + 0.0438364i
\(245\) 106.868 317.172i 0.436194 1.29458i
\(246\) 219.333 144.266i 0.891598 0.586447i
\(247\) 90.5031 + 106.549i 0.366409 + 0.431370i
\(248\) −4.79739 + 1.33199i −0.0193443 + 0.00537093i
\(249\) −36.2574 + 51.8946i −0.145612 + 0.208412i
\(250\) −156.829 + 231.305i −0.627315 + 0.925221i
\(251\) −58.4016 + 126.233i −0.232676 + 0.502920i −0.988382 0.151991i \(-0.951432\pi\)
0.755706 + 0.654911i \(0.227294\pi\)
\(252\) −144.606 226.708i −0.573832 0.899633i
\(253\) −2.03793 1.93043i −0.00805506 0.00763016i
\(254\) −30.1461 + 277.189i −0.118685 + 1.09129i
\(255\) −394.880 + 635.945i −1.54855 + 2.49390i
\(256\) −53.2202 324.629i −0.207892 1.26808i
\(257\) 341.941 231.842i 1.33051 0.902108i 0.331366 0.943502i \(-0.392490\pi\)
0.999143 + 0.0413945i \(0.0131801\pi\)
\(258\) −141.675 1.98588i −0.549129 0.00769719i
\(259\) −241.912 + 26.3096i −0.934025 + 0.101581i
\(260\) 151.060 80.0870i 0.581000 0.308027i
\(261\) 230.711 + 257.654i 0.883949 + 0.987180i
\(262\) 239.786 144.275i 0.915214 0.550666i
\(263\) −58.1042 30.8049i −0.220928 0.117129i 0.354269 0.935144i \(-0.384730\pi\)
−0.575197 + 0.818015i \(0.695075\pi\)
\(264\) 62.3277 16.3678i 0.236090 0.0619994i
\(265\) 159.533 + 35.1158i 0.602010 + 0.132512i
\(266\) −111.452 + 506.331i −0.418992 + 1.90350i
\(267\) 0.892579 + 3.39888i 0.00334299 + 0.0127299i
\(268\) −131.017 + 247.124i −0.488869 + 0.922105i
\(269\) 208.607 + 346.708i 0.775492 + 1.28888i 0.952461 + 0.304662i \(0.0985434\pi\)
−0.176968 + 0.984217i \(0.556629\pi\)
\(270\) −561.063 116.390i −2.07801 0.431075i
\(271\) −156.410 295.021i −0.577159 1.08864i −0.984504 0.175363i \(-0.943890\pi\)
0.407344 0.913275i \(-0.366455\pi\)
\(272\) 63.5529 + 584.359i 0.233650 + 2.14838i
\(273\) −2.75834 + 196.784i −0.0101038 + 0.720821i
\(274\) 97.3143 + 143.528i 0.355162 + 0.523824i
\(275\) −348.320 + 57.1042i −1.26662 + 0.207652i
\(276\) 2.42152 + 1.50360i 0.00877363 + 0.00544784i
\(277\) −158.282 17.2142i −0.571414 0.0621451i −0.182149 0.983271i \(-0.558305\pi\)
−0.389265 + 0.921126i \(0.627271\pi\)
\(278\) 219.992 232.243i 0.791340 0.835407i
\(279\) 10.3745 + 16.2647i 0.0371844 + 0.0582964i
\(280\) −159.926 73.9898i −0.571165 0.264249i
\(281\) −45.8095 31.0596i −0.163023 0.110533i 0.476947 0.878932i \(-0.341743\pi\)
−0.639971 + 0.768399i \(0.721054\pi\)
\(282\) −563.324 393.580i −1.99760 1.39567i
\(283\) −48.6661 175.279i −0.171965 0.619362i −0.998411 0.0563463i \(-0.982055\pi\)
0.826446 0.563016i \(-0.190359\pi\)
\(284\) −297.678 + 252.850i −1.04816 + 0.890316i
\(285\) 266.524 + 405.207i 0.935172 + 1.42178i
\(286\) 160.828 + 54.1894i 0.562337 + 0.189473i
\(287\) −189.307 249.030i −0.659608 0.867699i
\(288\) −328.338 + 162.452i −1.14006 + 0.564071i
\(289\) −37.7161 695.632i −0.130505 2.40703i
\(290\) −785.811 218.179i −2.70969 0.752343i
\(291\) −193.714 106.205i −0.665682 0.364966i
\(292\) 14.6767 89.5240i 0.0502627 0.306589i
\(293\) 17.2431 + 78.3360i 0.0588500 + 0.267358i 0.996853 0.0792680i \(-0.0252583\pi\)
−0.938003 + 0.346626i \(0.887327\pi\)
\(294\) −271.388 + 200.365i −0.923088 + 0.681513i
\(295\) −384.037 + 269.079i −1.30182 + 0.912134i
\(296\) 59.2146i 0.200049i
\(297\) −131.312 212.374i −0.442127 0.715063i
\(298\) 40.0388 244.226i 0.134359 0.819551i
\(299\) −0.875947 1.89333i −0.00292959 0.00633220i
\(300\) 334.784 127.983i 1.11595 0.426609i
\(301\) 9.14033 + 168.583i 0.0303665 + 0.560078i
\(302\) 78.0309 + 82.3762i 0.258380 + 0.272769i
\(303\) −129.905 + 443.656i −0.428728 + 1.46421i
\(304\) 360.906 + 121.603i 1.18719 + 0.400011i
\(305\) 44.8119 + 2.42963i 0.146924 + 0.00796601i
\(306\) 693.367 297.485i 2.26591 0.972173i
\(307\) 153.204 + 551.789i 0.499034 + 1.79736i 0.597085 + 0.802178i \(0.296325\pi\)
−0.0980507 + 0.995181i \(0.531261\pi\)
\(308\) 88.2241 + 261.840i 0.286442 + 0.850129i
\(309\) 71.5065 2.87247i 0.231413 0.00929604i
\(310\) −41.2865 19.1012i −0.133182 0.0616167i
\(311\) 42.1309 + 35.7863i 0.135469 + 0.115069i 0.712559 0.701612i \(-0.247536\pi\)
−0.577090 + 0.816681i \(0.695812\pi\)
\(312\) 47.5326 + 5.84466i 0.152348 + 0.0187329i
\(313\) −131.301 14.2798i −0.419491 0.0456224i −0.104060 0.994571i \(-0.533183\pi\)
−0.315431 + 0.948949i \(0.602149\pi\)
\(314\) 238.581 95.0592i 0.759811 0.302736i
\(315\) −92.8169 + 676.435i −0.294657 + 2.14741i
\(316\) −127.421 187.932i −0.403231 0.594721i
\(317\) 165.215 217.337i 0.521184 0.685606i −0.457914 0.888997i \(-0.651403\pi\)
0.979098 + 0.203391i \(0.0651962\pi\)
\(318\) −111.539 121.106i −0.350752 0.380836i
\(319\) −166.460 313.977i −0.521818 0.984253i
\(320\) 138.479 230.154i 0.432747 0.719231i
\(321\) −27.5360 + 66.3886i −0.0857819 + 0.206818i
\(322\) 3.62390 6.83540i 0.0112543 0.0212279i
\(323\) −593.255 236.374i −1.83670 0.731809i
\(324\) 174.010 + 184.400i 0.537067 + 0.569136i
\(325\) −256.184 56.3903i −0.788258 0.173509i
\(326\) −293.932 117.113i −0.901631 0.359243i
\(327\) 593.089 88.7147i 1.81373 0.271299i
\(328\) −65.2248 + 39.2445i −0.198856 + 0.119648i
\(329\) −422.154 + 701.625i −1.28314 + 2.13260i
\(330\) 530.849 + 254.690i 1.60863 + 0.771787i
\(331\) −543.502 + 59.1094i −1.64200 + 0.178578i −0.881968 0.471309i \(-0.843782\pi\)
−0.760031 + 0.649887i \(0.774816\pi\)
\(332\) −39.9729 + 52.5835i −0.120400 + 0.158384i
\(333\) 219.397 67.1374i 0.658850 0.201614i
\(334\) 74.9834 + 457.378i 0.224501 + 1.36940i
\(335\) 659.772 262.877i 1.96947 0.784708i
\(336\) 269.943 + 463.224i 0.803401 + 1.37864i
\(337\) −394.194 373.401i −1.16972 1.10801i −0.992297 0.123879i \(-0.960467\pi\)
−0.177419 0.984135i \(-0.556775\pi\)
\(338\) −247.812 210.494i −0.733173 0.622763i
\(339\) 495.285 101.764i 1.46102 0.300189i
\(340\) −438.310 + 646.458i −1.28915 + 1.90135i
\(341\) −6.32947 18.7852i −0.0185615 0.0550886i
\(342\) 13.7015 488.646i 0.0400628 1.42879i
\(343\) −42.5697 50.1169i −0.124110 0.146113i
\(344\) 41.0235 + 2.22423i 0.119254 + 0.00646578i
\(345\) −2.21458 6.89033i −0.00641908 0.0199720i
\(346\) −459.394 + 349.222i −1.32773 + 1.00931i
\(347\) 137.752 + 145.423i 0.396980 + 0.419086i 0.893588 0.448889i \(-0.148180\pi\)
−0.496608 + 0.867975i \(0.665421\pi\)
\(348\) 229.734 + 278.276i 0.660154 + 0.799643i
\(349\) 6.14129 22.1189i 0.0175968 0.0633780i −0.954230 0.299073i \(-0.903323\pi\)
0.971827 + 0.235695i \(0.0757365\pi\)
\(350\) −408.478 882.911i −1.16708 2.52260i
\(351\) −32.2372 182.741i −0.0918439 0.520629i
\(352\) 367.614 80.9181i 1.04436 0.229881i
\(353\) 136.972i 0.388023i −0.980999 0.194012i \(-0.937850\pi\)
0.980999 0.194012i \(-0.0621499\pi\)
\(354\) 472.630 0.630395i 1.33511 0.00178078i
\(355\) 991.711 2.79355
\(356\) 0.788202 + 3.58084i 0.00221405 + 0.0100585i
\(357\) −409.934 800.119i −1.14828 2.24123i
\(358\) 822.950 380.737i 2.29874 1.06351i
\(359\) −231.925 64.3936i −0.646030 0.179369i −0.0709671 0.997479i \(-0.522609\pi\)
−0.575063 + 0.818109i \(0.695022\pi\)
\(360\) 161.198 + 40.2508i 0.447773 + 0.111808i
\(361\) −38.3032 + 36.2827i −0.106103 + 0.100506i
\(362\) −334.487 440.010i −0.923998 1.21550i
\(363\) −32.5678 101.330i −0.0897185 0.279145i
\(364\) −11.1169 + 205.039i −0.0305409 + 0.563294i
\(365\) −175.563 + 149.124i −0.480994 + 0.408560i
\(366\) −35.6222 27.8757i −0.0973285 0.0761630i
\(367\) −224.010 + 75.4779i −0.610382 + 0.205662i −0.607481 0.794334i \(-0.707820\pi\)
−0.00290114 + 0.999996i \(0.500923\pi\)
\(368\) −4.70387 3.18930i −0.0127823 0.00866658i
\(369\) 219.357 + 197.170i 0.594464 + 0.534337i
\(370\) −350.257 + 412.354i −0.946640 + 1.11447i
\(371\) −134.915 + 142.428i −0.363652 + 0.383902i
\(372\) 10.1346 + 17.3910i 0.0272435 + 0.0467500i
\(373\) −112.262 281.756i −0.300970 0.755379i −0.999219 0.0395230i \(-0.987416\pi\)
0.698248 0.715856i \(-0.253963\pi\)
\(374\) −765.050 + 125.424i −2.04559 + 0.335357i
\(375\) −296.102 104.412i −0.789605 0.278432i
\(376\) 158.627 + 120.585i 0.421881 + 0.320705i
\(377\) −28.5545 262.554i −0.0757414 0.696431i
\(378\) 467.168 505.309i 1.23590 1.33680i
\(379\) 181.751 + 109.356i 0.479555 + 0.288539i 0.734734 0.678355i \(-0.237307\pi\)
−0.255179 + 0.966894i \(0.582135\pi\)
\(380\) 260.891 + 433.604i 0.686555 + 1.14106i
\(381\) −309.811 + 46.3418i −0.813152 + 0.121632i
\(382\) 76.7702 192.679i 0.200969 0.504394i
\(383\) −43.6446 + 198.280i −0.113955 + 0.517701i 0.884715 + 0.466133i \(0.154353\pi\)
−0.998669 + 0.0515686i \(0.983578\pi\)
\(384\) 198.851 88.6364i 0.517842 0.230824i
\(385\) 259.679 651.744i 0.674490 1.69284i
\(386\) 670.883 + 355.680i 1.73804 + 0.921450i
\(387\) −38.2713 154.519i −0.0988922 0.399273i
\(388\) −197.506 118.835i −0.509035 0.306276i
\(389\) 77.5468 41.1127i 0.199349 0.105688i −0.365743 0.930716i \(-0.619185\pi\)
0.565093 + 0.825027i \(0.308840\pi\)
\(390\) 296.433 + 321.858i 0.760084 + 0.825277i
\(391\) 7.58653 + 5.76713i 0.0194029 + 0.0147497i
\(392\) 80.9592 54.8917i 0.206529 0.140030i
\(393\) 225.203 + 219.393i 0.573036 + 0.558253i
\(394\) −161.003 404.086i −0.408636 1.02560i
\(395\) −62.3335 + 573.147i −0.157806 + 1.45101i
\(396\) −128.003 226.906i −0.323240 0.572996i
\(397\) −326.467 + 384.346i −0.822334 + 0.968126i −0.999872 0.0159876i \(-0.994911\pi\)
0.177538 + 0.984114i \(0.443187\pi\)
\(398\) −129.949 + 280.880i −0.326504 + 0.705728i
\(399\) −582.010 + 23.3798i −1.45867 + 0.0585961i
\(400\) −677.205 + 228.177i −1.69301 + 0.570442i
\(401\) −312.119 + 86.6595i −0.778353 + 0.216109i −0.633912 0.773405i \(-0.718552\pi\)
−0.144440 + 0.989514i \(0.546138\pi\)
\(402\) −696.870 163.666i −1.73351 0.407129i
\(403\) 0.797561 14.7101i 0.00197906 0.0365016i
\(404\) −154.010 + 457.087i −0.381214 + 1.13140i
\(405\) −33.6323 642.895i −0.0830426 1.58740i
\(406\) 711.074 673.565i 1.75141 1.65903i
\(407\) −235.411 + 12.7636i −0.578405 + 0.0313602i
\(408\) −204.347 + 78.1185i −0.500849 + 0.191467i
\(409\) 288.161 133.318i 0.704551 0.325960i −0.0346927 0.999398i \(-0.511045\pi\)
0.739244 + 0.673438i \(0.235183\pi\)
\(410\) −686.341 112.520i −1.67400 0.274439i
\(411\) −128.195 + 146.705i −0.311910 + 0.356946i
\(412\) 74.6684 0.181234
\(413\) −39.1173 561.807i −0.0947149 1.36031i
\(414\) −2.14779 + 6.97136i −0.00518789 + 0.0168390i
\(415\) 163.794 36.0538i 0.394684 0.0868766i
\(416\) 276.055 + 45.2569i 0.663593 + 0.108791i
\(417\) 315.146 + 172.781i 0.755746 + 0.414344i
\(418\) −134.379 + 483.989i −0.321480 + 1.15787i
\(419\) 496.188 26.9025i 1.18422 0.0642065i 0.548516 0.836140i \(-0.315193\pi\)
0.635703 + 0.771933i \(0.280710\pi\)
\(420\) −125.094 + 701.321i −0.297842 + 1.66981i
\(421\) 403.048 306.389i 0.957358 0.727765i −0.00487597 0.999988i \(-0.501552\pi\)
0.962234 + 0.272223i \(0.0877590\pi\)
\(422\) 75.0839 222.841i 0.177924 0.528060i
\(423\) 266.932 724.452i 0.631044 1.71265i
\(424\) 30.9059 + 36.3853i 0.0728913 + 0.0858143i
\(425\) 1154.61 320.577i 2.71673 0.754298i
\(426\) −819.377 572.478i −1.92342 1.34384i
\(427\) −30.2465 + 44.6103i −0.0708350 + 0.104474i
\(428\) −31.4876 + 68.0593i −0.0735691 + 0.159017i
\(429\) −12.9902 + 190.228i −0.0302802 + 0.443423i
\(430\) 272.520 + 258.145i 0.633767 + 0.600336i
\(431\) −32.9435 + 302.910i −0.0764349 + 0.702808i 0.891743 + 0.452543i \(0.149483\pi\)
−0.968177 + 0.250265i \(0.919482\pi\)
\(432\) −331.908 381.291i −0.768306 0.882619i
\(433\) 38.2686 + 233.428i 0.0883801 + 0.539095i 0.993490 + 0.113918i \(0.0363400\pi\)
−0.905110 + 0.425177i \(0.860212\pi\)
\(434\) 45.2199 30.6599i 0.104193 0.0706448i
\(435\) 12.8420 916.166i 0.0295218 2.10613i
\(436\) 622.032 67.6500i 1.42668 0.155161i
\(437\) 5.45511 2.89212i 0.0124831 0.00661812i
\(438\) 231.138 21.8646i 0.527713 0.0499191i
\(439\) 190.207 114.444i 0.433274 0.260692i −0.282167 0.959365i \(-0.591053\pi\)
0.715441 + 0.698673i \(0.246226\pi\)
\(440\) −150.835 79.9677i −0.342807 0.181745i
\(441\) −295.172 237.728i −0.669324 0.539065i
\(442\) −562.682 123.856i −1.27304 0.280216i
\(443\) −88.8461 + 403.632i −0.200556 + 0.911133i 0.763578 + 0.645715i \(0.223441\pi\)
−0.964134 + 0.265417i \(0.914490\pi\)
\(444\) 231.541 60.8049i 0.521489 0.136948i
\(445\) 4.36084 8.22541i 0.00979963 0.0184841i
\(446\) 97.8079 + 162.558i 0.219300 + 0.364480i
\(447\) 276.815 26.1854i 0.619273 0.0585802i
\(448\) 151.102 + 285.010i 0.337282 + 0.636182i
\(449\) −33.4925 307.959i −0.0745936 0.685877i −0.970412 0.241456i \(-0.922375\pi\)
0.895818 0.444421i \(-0.146590\pi\)
\(450\) 534.415 + 745.494i 1.18759 + 1.65665i
\(451\) −170.078 250.846i −0.377112 0.556199i
\(452\) 520.614 85.3504i 1.15180 0.188828i
\(453\) −67.2470 + 108.300i −0.148448 + 0.239072i
\(454\) 251.918 + 27.3978i 0.554887 + 0.0603475i
\(455\) 358.558 378.525i 0.788039 0.831922i
\(456\) −9.65670 + 141.413i −0.0211770 + 0.310115i
\(457\) −570.439 263.913i −1.24823 0.577491i −0.319264 0.947666i \(-0.603436\pi\)
−0.928962 + 0.370175i \(0.879298\pi\)
\(458\) 705.202 + 478.139i 1.53974 + 1.04397i
\(459\) 521.126 + 668.558i 1.13535 + 1.45655i
\(460\) −2.02022 7.27616i −0.00439178 0.0158177i
\(461\) 204.431 173.645i 0.443451 0.376671i −0.397660 0.917533i \(-0.630178\pi\)
0.841111 + 0.540862i \(0.181902\pi\)
\(462\) −590.781 + 388.585i −1.27875 + 0.841093i
\(463\) 429.573 + 144.740i 0.927802 + 0.312613i 0.742328 0.670036i \(-0.233721\pi\)
0.185474 + 0.982649i \(0.440618\pi\)
\(464\) −435.410 572.772i −0.938383 1.23442i
\(465\) 8.97461 50.3150i 0.0193002 0.108204i
\(466\) 8.92190 + 164.555i 0.0191457 + 0.353122i
\(467\) 510.318 + 141.689i 1.09276 + 0.303403i 0.766738 0.641960i \(-0.221878\pi\)
0.326020 + 0.945363i \(0.394292\pi\)
\(468\) −25.9554 191.864i −0.0554602 0.409965i
\(469\) −137.993 + 841.718i −0.294228 + 1.79471i
\(470\) 391.370 + 1778.01i 0.832701 + 3.78300i
\(471\) 171.379 + 232.128i 0.363862 + 0.492840i
\(472\) −136.939 5.31802i −0.290125 0.0112670i
\(473\) 163.571i 0.345815i
\(474\) 382.358 437.566i 0.806662 0.923135i
\(475\) 125.604 766.151i 0.264430 1.61295i
\(476\) −393.863 851.320i −0.827443 1.78849i
\(477\) 99.7707 155.764i 0.209163 0.326548i
\(478\) 5.26971 + 97.1941i 0.0110245 + 0.203335i
\(479\) −105.744 111.633i −0.220760 0.233054i 0.606203 0.795310i \(-0.292692\pi\)
−0.826963 + 0.562257i \(0.809933\pi\)
\(480\) 931.401 + 272.719i 1.94042 + 0.568165i
\(481\) −166.036 55.9439i −0.345188 0.116308i
\(482\) 179.503 + 9.73235i 0.372412 + 0.0201916i
\(483\) 8.46185 + 1.98734i 0.0175194 + 0.00411457i
\(484\) −29.7095 107.004i −0.0613832 0.221082i
\(485\) 186.878 + 554.634i 0.385315 + 1.14358i
\(486\) −343.331 + 550.591i −0.706443 + 1.13290i
\(487\) −8.08201 3.73914i −0.0165955 0.00767790i 0.411574 0.911376i \(-0.364979\pi\)
−0.428169 + 0.903699i \(0.640841\pi\)
\(488\) 9.99614 + 8.49080i 0.0204839 + 0.0173992i
\(489\) 43.3834 352.822i 0.0887186 0.721517i
\(490\) 888.465 + 96.6264i 1.81319 + 0.197197i
\(491\) −61.8947 + 24.6611i −0.126058 + 0.0502263i −0.432314 0.901723i \(-0.642303\pi\)
0.306256 + 0.951949i \(0.400924\pi\)
\(492\) 220.430 + 214.744i 0.448029 + 0.436471i
\(493\) 677.043 + 998.564i 1.37331 + 2.02549i
\(494\) −225.907 + 297.175i −0.457301 + 0.601569i
\(495\) −125.273 + 649.529i −0.253077 + 1.31218i
\(496\) −18.7985 35.4578i −0.0379003 0.0714875i
\(497\) −614.039 + 1020.54i −1.23549 + 2.05340i
\(498\) −156.143 64.7635i −0.313541 0.130047i
\(499\) −234.419 + 442.161i −0.469777 + 0.886094i 0.529508 + 0.848305i \(0.322376\pi\)
−0.999286 + 0.0377893i \(0.987968\pi\)
\(500\) −304.324 121.254i −0.608649 0.242508i
\(501\) −475.614 + 212.001i −0.949330 + 0.423156i
\(502\) −362.714 79.8394i −0.722538 0.159043i
\(503\) −843.055 335.904i −1.67605 0.667801i −0.678299 0.734786i \(-0.737283\pi\)
−0.997754 + 0.0669855i \(0.978662\pi\)
\(504\) −141.230 + 140.962i −0.280219 + 0.279687i
\(505\) 1049.41 631.407i 2.07803 1.25031i
\(506\) 3.86436 6.42262i 0.00763708 0.0126929i
\(507\) 158.017 329.354i 0.311670 0.649613i
\(508\) −324.930 + 35.3382i −0.639625 + 0.0695634i
\(509\) −1.25888 + 1.65603i −0.00247325 + 0.00325350i −0.797328 0.603546i \(-0.793754\pi\)
0.794855 + 0.606800i \(0.207547\pi\)
\(510\) −1885.09 664.723i −3.69625 1.30338i
\(511\) −44.7561 273.000i −0.0875853 0.534247i
\(512\) 546.354 217.687i 1.06710 0.425170i
\(513\) 534.899 124.554i 1.04269 0.242795i
\(514\) 800.878 + 758.632i 1.55813 + 1.47594i
\(515\) −144.501 122.740i −0.280584 0.238330i
\(516\) −33.4280 162.694i −0.0647830 0.315299i
\(517\) −445.202 + 656.623i −0.861125 + 1.27006i
\(518\) −207.473 615.757i −0.400527 1.18872i
\(519\) −510.579 399.546i −0.983774 0.769839i
\(520\) −82.1374 96.6997i −0.157957 0.185961i
\(521\) −603.086 32.6983i −1.15755 0.0627607i −0.534660 0.845067i \(-0.679560\pi\)
−0.622894 + 0.782306i \(0.714043\pi\)
\(522\) −539.478 + 749.546i −1.03348 + 1.43591i
\(523\) −417.320 + 317.238i −0.797934 + 0.606574i −0.922659 0.385617i \(-0.873988\pi\)
0.124724 + 0.992191i \(0.460195\pi\)
\(524\) 225.594 + 238.157i 0.430523 + 0.454498i
\(525\) 842.852 695.826i 1.60543 1.32538i
\(526\) 46.9800 169.207i 0.0893157 0.321686i
\(527\) 28.2569 + 61.0764i 0.0536185 + 0.115894i
\(528\) 236.851 + 462.291i 0.448582 + 0.875552i
\(529\) 516.542 113.700i 0.976450 0.214933i
\(530\) 436.187i 0.822994i
\(531\) 135.557 + 513.405i 0.255287 + 0.966865i
\(532\) −607.746 −1.14238
\(533\) −48.4179 219.965i −0.0908404 0.412692i
\(534\) −8.35126 + 4.27870i −0.0156391 + 0.00801254i
\(535\) 172.812 79.9513i 0.323013 0.149442i
\(536\) 199.994 + 55.5281i 0.373124 + 0.103597i
\(537\) 648.571 + 785.612i 1.20777 + 1.46296i
\(538\) −784.401 + 743.025i −1.45800 + 1.38109i
\(539\) 235.676 + 310.026i 0.437246 + 0.575188i
\(540\) −8.13870 671.650i −0.0150717 1.24380i
\(541\) 10.4697 193.103i 0.0193526 0.356937i −0.972779 0.231736i \(-0.925560\pi\)
0.992131 0.125201i \(-0.0399577\pi\)
\(542\) 679.573 577.235i 1.25383 1.06501i
\(543\) 382.688 489.035i 0.704765 0.900617i
\(544\) −1210.99 + 408.030i −2.22608 + 0.750054i
\(545\) −1314.98 891.579i −2.41281 1.63592i
\(546\) −514.758 + 105.765i −0.942779 + 0.193709i
\(547\) 15.3897 18.1181i 0.0281347 0.0331228i −0.747915 0.663795i \(-0.768945\pi\)
0.776049 + 0.630672i \(0.217221\pi\)
\(548\) −139.792 + 147.576i −0.255094 + 0.269300i
\(549\) 20.1258 46.6638i 0.0366591 0.0849977i
\(550\) −348.859 875.571i −0.634290 1.59195i
\(551\) 771.368 126.459i 1.39994 0.229509i
\(552\) 0.703398 1.99477i 0.00127427 0.00361371i
\(553\) −551.214 419.022i −0.996771 0.757725i
\(554\) −45.9658 422.649i −0.0829708 0.762904i
\(555\) −548.038 262.936i −0.987455 0.473759i
\(556\) 321.315 + 193.329i 0.577905 + 0.347714i
\(557\) 188.784 + 313.761i 0.338929 + 0.563305i 0.978709 0.205254i \(-0.0658020\pi\)
−0.639780 + 0.768558i \(0.720974\pi\)
\(558\) −36.4600 + 36.3908i −0.0653405 + 0.0652165i
\(559\) −44.9942 + 112.927i −0.0804906 + 0.202016i
\(560\) 305.340 1387.17i 0.545250 2.47710i
\(561\) −354.611 795.553i −0.632105 1.41810i
\(562\) 54.7018 137.291i 0.0973341 0.244290i
\(563\) −920.840 488.198i −1.63559 0.867137i −0.995067 0.0992017i \(-0.968371\pi\)
−0.640527 0.767936i \(-0.721284\pi\)
\(564\) 308.625 744.088i 0.547208 1.31931i
\(565\) −1147.81 690.614i −2.03152 1.22233i
\(566\) 429.159 227.525i 0.758231 0.401988i
\(567\) 682.409 + 363.452i 1.20354 + 0.641010i
\(568\) 230.730 + 175.396i 0.406214 + 0.308796i
\(569\) −478.264 + 324.271i −0.840534 + 0.569896i −0.903729 0.428105i \(-0.859181\pi\)
0.0631950 + 0.998001i \(0.479871\pi\)
\(570\) −903.708 + 927.639i −1.58545 + 1.62744i
\(571\) −154.998 389.015i −0.271449 0.681286i 0.728544 0.684999i \(-0.240197\pi\)
−0.999993 + 0.00371279i \(0.998818\pi\)
\(572\) −21.5094 + 197.776i −0.0376039 + 0.345762i
\(573\) 231.282 + 28.4387i 0.403634 + 0.0496313i
\(574\) 540.754 636.624i 0.942079 1.10910i
\(575\) −4.86465 + 10.5148i −0.00846026 + 0.0182865i
\(576\) −190.335 237.248i −0.330442 0.411889i
\(577\) 976.330 328.964i 1.69208 0.570128i 0.702193 0.711987i \(-0.252204\pi\)
0.989887 + 0.141859i \(0.0453078\pi\)
\(578\) 1792.42 497.663i 3.10107 0.861009i
\(579\) −195.054 + 830.516i −0.336880 + 1.43440i
\(580\) 51.7568 954.598i 0.0892358 1.64586i
\(581\) −64.3146 + 190.879i −0.110696 + 0.328535i
\(582\) 165.766 566.130i 0.284821 0.972733i
\(583\) −137.990 + 130.711i −0.236689 + 0.224204i
\(584\) −67.2205 + 3.64459i −0.115104 + 0.00624074i
\(585\) −265.157 + 413.967i −0.453259 + 0.707636i
\(586\) −194.387 + 89.9329i −0.331718 + 0.153469i
\(587\) 234.252 + 38.4037i 0.399067 + 0.0654236i 0.357974 0.933732i \(-0.383468\pi\)
0.0410929 + 0.999155i \(0.486916\pi\)
\(588\) −297.771 260.201i −0.506414 0.442519i
\(589\) 43.6016 0.0740264
\(590\) −922.151 847.034i −1.56297 1.43565i
\(591\) 393.157 290.266i 0.665241 0.491145i
\(592\) −466.147 + 102.607i −0.787410 + 0.173322i
\(593\) 768.482 + 125.986i 1.29592 + 0.212456i 0.769982 0.638066i \(-0.220265\pi\)
0.525940 + 0.850522i \(0.323714\pi\)
\(594\) 478.453 464.342i 0.805476 0.781720i
\(595\) −637.186 + 2294.94i −1.07090 + 3.85704i
\(596\) 289.686 15.7063i 0.486050 0.0263529i
\(597\) −342.302 61.0559i −0.573370 0.102271i
\(598\) 4.43461 3.37111i 0.00741574 0.00563730i
\(599\) 280.008 831.035i 0.467460 1.38737i −0.411907 0.911226i \(-0.635137\pi\)
0.879367 0.476145i \(-0.157966\pi\)
\(600\) −146.156 222.206i −0.243593 0.370344i
\(601\) 295.249 + 347.594i 0.491263 + 0.578359i 0.950802 0.309798i \(-0.100261\pi\)
−0.459540 + 0.888157i \(0.651986\pi\)
\(602\) −434.386 + 120.607i −0.721571 + 0.200343i
\(603\) −21.0147 803.960i −0.0348503 1.33327i
\(604\) −74.6430 + 110.090i −0.123581 + 0.182269i
\(605\) −118.398 + 255.914i −0.195700 + 0.422998i
\(606\) −1231.53 84.0982i −2.03223 0.138776i
\(607\) 358.334 + 339.432i 0.590335 + 0.559195i 0.923464 0.383686i \(-0.125346\pi\)
−0.333128 + 0.942882i \(0.608104\pi\)
\(608\) −89.5168 + 823.094i −0.147232 + 1.35377i
\(609\) 934.848 + 580.479i 1.53505 + 0.953167i
\(610\) 19.3870 + 118.255i 0.0317819 + 0.193861i
\(611\) −487.982 + 330.860i −0.798662 + 0.541506i
\(612\) 515.294 + 718.820i 0.841983 + 1.17454i
\(613\) −230.025 + 25.0167i −0.375244 + 0.0408102i −0.293798 0.955868i \(-0.594919\pi\)
−0.0814459 + 0.996678i \(0.525954\pi\)
\(614\) −1351.02 + 716.263i −2.20035 + 1.16655i
\(615\) −73.5879 777.924i −0.119655 1.26492i
\(616\) 175.685 105.706i 0.285203 0.171601i
\(617\) 636.956 + 337.693i 1.03234 + 0.547314i 0.896328 0.443393i \(-0.146225\pi\)
0.136016 + 0.990707i \(0.456570\pi\)
\(618\) 48.5371 + 184.826i 0.0785389 + 0.299071i
\(619\) 40.2554 + 8.86088i 0.0650329 + 0.0143148i 0.247368 0.968922i \(-0.420434\pi\)
−0.182335 + 0.983237i \(0.558365\pi\)
\(620\) 11.4635 52.0793i 0.0184895 0.0839989i
\(621\) −8.18836 0.344511i −0.0131858 0.000554769i
\(622\) −69.1396 + 130.411i −0.111157 + 0.209664i
\(623\) 5.76443 + 9.58055i 0.00925269 + 0.0153781i
\(624\) 36.3541 + 384.312i 0.0582597 + 0.615884i
\(625\) −57.3343 108.144i −0.0917349 0.173030i
\(626\) −38.1304 350.603i −0.0609111 0.560069i
\(627\) −564.275 7.90949i −0.899960 0.0126148i
\(628\) 168.947 + 249.179i 0.269025 + 0.396782i
\(629\) 789.821 129.485i 1.25568 0.205858i
\(630\) −1817.29 + 146.240i −2.88458 + 0.232127i
\(631\) 30.3350 + 3.29913i 0.0480745 + 0.00522842i 0.132125 0.991233i \(-0.457820\pi\)
−0.0840502 + 0.996462i \(0.526786\pi\)
\(632\) −115.870 + 122.323i −0.183339 + 0.193549i
\(633\) 263.577 + 17.9990i 0.416394 + 0.0284345i
\(634\) 661.609 + 306.093i 1.04355 + 0.482796i
\(635\) 686.904 + 465.732i 1.08174 + 0.733437i
\(636\) 110.538 158.211i 0.173802 0.248759i
\(637\) 77.4270 + 278.867i 0.121549 + 0.437781i
\(638\) 723.237 614.323i 1.13360 0.962889i
\(639\) 388.263 1053.74i 0.607610 1.64905i
\(640\) −546.586 184.166i −0.854040 0.287760i
\(641\) 487.930 + 641.861i 0.761201 + 1.00134i 0.999545 + 0.0301622i \(0.00960239\pi\)
−0.238344 + 0.971181i \(0.576605\pi\)
\(642\) −188.935 33.7000i −0.294291 0.0524922i
\(643\) 34.9387 + 644.406i 0.0543370 + 1.00219i 0.890867 + 0.454265i \(0.150098\pi\)
−0.836530 + 0.547922i \(0.815419\pi\)
\(644\) 8.73855 + 2.42625i 0.0135692 + 0.00376746i
\(645\) −202.746 + 369.800i −0.314335 + 0.573334i
\(646\) 275.877 1682.77i 0.427054 2.60491i
\(647\) −2.24026 10.1776i −0.00346253 0.0157304i 0.974858 0.222829i \(-0.0715291\pi\)
−0.978320 + 0.207098i \(0.933598\pi\)
\(648\) 105.879 155.523i 0.163393 0.240005i
\(649\) −8.37492 545.556i −0.0129043 0.840610i
\(650\) 700.446i 1.07761i
\(651\) 46.2208 + 40.3891i 0.0709998 + 0.0620416i
\(652\) 60.0047 366.013i 0.0920318 0.561369i
\(653\) 61.3449 + 132.595i 0.0939432 + 0.203055i 0.948850 0.315726i \(-0.102248\pi\)
−0.854907 + 0.518781i \(0.826386\pi\)
\(654\) 571.796 + 1495.73i 0.874305 + 2.28706i
\(655\) −45.0947 831.722i −0.0688468 1.26980i
\(656\) −421.960 445.458i −0.643232 0.679051i
\(657\) 89.7181 + 244.928i 0.136557 + 0.372797i
\(658\) −2072.02 698.146i −3.14897 1.06101i
\(659\) −775.337 42.0376i −1.17654 0.0637900i −0.544522 0.838747i \(-0.683289\pi\)
−0.632014 + 0.774957i \(0.717772\pi\)
\(660\) −157.804 + 671.911i −0.239097 + 1.01805i
\(661\) 25.0205 + 90.1158i 0.0378525 + 0.136332i 0.980062 0.198692i \(-0.0636693\pi\)
−0.942210 + 0.335024i \(0.891255\pi\)
\(662\) −466.127 1383.41i −0.704119 2.08975i
\(663\) −25.9818 646.784i −0.0391883 0.975542i
\(664\) 44.4845 + 20.5807i 0.0669948 + 0.0309951i
\(665\) 1176.13 + 999.014i 1.76862 + 1.50228i
\(666\) 301.019 + 533.606i 0.451981 + 0.801210i
\(667\) −11.5961 1.26115i −0.0173854 0.00189078i
\(668\) −504.723 + 201.100i −0.755574 + 0.301048i
\(669\) −148.733 + 152.672i −0.222322 + 0.228209i
\(670\) 1064.25 + 1569.66i 1.58844 + 2.34277i
\(671\) −31.6010 + 41.5704i −0.0470954 + 0.0619529i
\(672\) −857.344 + 789.618i −1.27581 + 1.17503i
\(673\) −265.993 501.716i −0.395235 0.745492i 0.603415 0.797427i \(-0.293806\pi\)
−0.998650 + 0.0519345i \(0.983461\pi\)
\(674\) 747.479 1242.32i 1.10902 1.84321i
\(675\) −657.590 + 793.462i −0.974207 + 1.17550i
\(676\) 178.531 336.746i 0.264099 0.498144i
\(677\) −1127.65 449.297i −1.66566 0.663659i −0.668843 0.743404i \(-0.733210\pi\)
−0.996815 + 0.0797451i \(0.974589\pi\)
\(678\) 549.684 + 1233.19i 0.810744 + 1.81886i
\(679\) −686.467 151.103i −1.01100 0.222537i
\(680\) 538.417 + 214.525i 0.791789 + 0.315478i
\(681\) 42.1170 + 281.566i 0.0618457 + 0.413460i
\(682\) 45.3548 27.2891i 0.0665027 0.0400133i
\(683\) 559.401 929.731i 0.819035 1.36125i −0.111018 0.993818i \(-0.535411\pi\)
0.930052 0.367428i \(-0.119761\pi\)
\(684\) 562.868 107.451i 0.822906 0.157092i
\(685\) 513.116 55.8047i 0.749074 0.0814667i
\(686\) 106.259 139.781i 0.154897 0.203763i
\(687\) −318.331 + 902.754i −0.463363 + 1.31405i
\(688\) 53.5757 + 326.797i 0.0778717 + 0.474996i
\(689\) −131.222 + 52.2836i −0.190453 + 0.0758832i
\(690\) 16.6974 9.73038i 0.0241991 0.0141020i
\(691\) −804.228 761.806i −1.16386 1.10247i −0.993114 0.117154i \(-0.962623\pi\)
−0.170748 0.985315i \(-0.554618\pi\)
\(692\) −515.564 437.924i −0.745035 0.632838i
\(693\) −590.846 531.085i −0.852591 0.766356i
\(694\) −300.162 + 442.705i −0.432510 + 0.637904i
\(695\) −304.025 902.315i −0.437447 1.29830i
\(696\) 165.023 210.882i 0.237102 0.302991i
\(697\) 666.081 + 784.172i 0.955640 + 1.12507i
\(698\) 61.2070 + 3.31855i 0.0876892 + 0.00475437i
\(699\) −176.268 + 56.6533i −0.252172 + 0.0810491i
\(700\) 907.845 690.126i 1.29692 0.985894i
\(701\) 219.908 + 232.154i 0.313706 + 0.331175i 0.863712 0.503985i \(-0.168133\pi\)
−0.550006 + 0.835160i \(0.685375\pi\)
\(702\) 458.047 188.965i 0.652488 0.269181i
\(703\) 138.730 499.660i 0.197340 0.710753i
\(704\) 131.230 + 283.650i 0.186407 + 0.402911i
\(705\) −1820.40 + 932.666i −2.58212 + 1.32293i
\(706\) 357.196 78.6248i 0.505944 0.111367i
\(707\) 1470.86i 2.08043i
\(708\) 119.822 + 540.921i 0.169241 + 0.764012i
\(709\) 856.218 1.20764 0.603821 0.797120i \(-0.293644\pi\)
0.603821 + 0.797120i \(0.293644\pi\)
\(710\) 569.263 + 2586.19i 0.801779 + 3.64252i
\(711\) 584.595 + 290.624i 0.822215 + 0.408754i
\(712\) 2.46935 1.14244i 0.00346818 0.00160455i
\(713\) −0.626931 0.174066i −0.000879286 0.000244132i
\(714\) 1851.24 1528.31i 2.59277 2.14049i
\(715\) 366.730 347.385i 0.512910 0.485854i
\(716\) 643.257 + 846.190i 0.898404 + 1.18183i
\(717\) −104.113 + 33.4622i −0.145206 + 0.0466697i
\(718\) 34.7961 641.777i 0.0484626 0.893840i
\(719\) 627.407 532.924i 0.872611 0.741202i −0.0945091 0.995524i \(-0.530128\pi\)
0.967120 + 0.254322i \(0.0818523\pi\)
\(720\) −37.5374 + 1338.73i −0.0521353 + 1.85934i
\(721\) 215.779 72.7045i 0.299278 0.100838i
\(722\) −116.605 79.0602i −0.161503 0.109502i
\(723\) 40.6482 + 197.834i 0.0562215 + 0.273630i
\(724\) 419.446 493.810i 0.579345 0.682058i
\(725\) −1008.66 + 1064.83i −1.39126 + 1.46873i
\(726\) 245.553 143.096i 0.338228 0.197102i
\(727\) 40.2144 + 100.930i 0.0553155 + 0.138831i 0.954037 0.299688i \(-0.0968825\pi\)
−0.898722 + 0.438519i \(0.855503\pi\)
\(728\) 150.368 24.6516i 0.206549 0.0338621i
\(729\) −696.277 215.962i −0.955112 0.296245i
\(730\) −489.663 372.232i −0.670772 0.509907i
\(731\) −60.0387 552.047i −0.0821323 0.755194i
\(732\) 22.9362 47.8058i 0.0313335 0.0653085i
\(733\) −158.965 95.6463i −0.216869 0.130486i 0.402974 0.915211i \(-0.367976\pi\)
−0.619844 + 0.784725i \(0.712804\pi\)
\(734\) −325.418 540.849i −0.443349 0.736851i
\(735\) 148.538 + 993.027i 0.202092 + 1.35106i
\(736\) 4.57309 11.4776i 0.00621343 0.0155945i
\(737\) −177.647 + 807.057i −0.241040 + 1.09506i
\(738\) −388.266 + 685.220i −0.526106 + 0.928483i
\(739\) −469.819 + 1179.16i −0.635750 + 1.59561i 0.158049 + 0.987431i \(0.449480\pi\)
−0.793799 + 0.608181i \(0.791900\pi\)
\(740\) −560.337 297.072i −0.757212 0.401449i
\(741\) −387.392 160.679i −0.522797 0.216840i
\(742\) −448.867 270.075i −0.604942 0.363982i
\(743\) 963.404 510.765i 1.29664 0.687435i 0.330099 0.943946i \(-0.392918\pi\)
0.966541 + 0.256511i \(0.0825729\pi\)
\(744\) 10.9868 10.1189i 0.0147672 0.0136007i
\(745\) −586.428 445.791i −0.787152 0.598378i
\(746\) 670.324 454.491i 0.898557 0.609237i
\(747\) 25.8176 188.155i 0.0345617 0.251881i
\(748\) −336.377 844.243i −0.449702 1.12867i
\(749\) −24.7246 + 227.339i −0.0330102 + 0.303524i
\(750\) 102.317 832.110i 0.136423 1.10948i
\(751\) −412.003 + 485.048i −0.548606 + 0.645869i −0.964668 0.263467i \(-0.915134\pi\)
0.416062 + 0.909336i \(0.363410\pi\)
\(752\) −674.398 + 1457.69i −0.896806 + 1.93841i
\(753\) −16.7483 416.928i −0.0222421 0.553689i
\(754\) 668.299 225.176i 0.886338 0.298642i
\(755\) 325.418 90.3519i 0.431018 0.119671i
\(756\) 696.215 + 407.491i 0.920919 + 0.539010i
\(757\) −34.8181 + 642.182i −0.0459948 + 0.848324i 0.880969 + 0.473174i \(0.156892\pi\)
−0.926964 + 0.375151i \(0.877591\pi\)
\(758\) −180.850 + 536.744i −0.238588 + 0.708105i
\(759\) 8.08192 + 2.36643i 0.0106481 + 0.00311783i
\(760\) 272.621 258.240i 0.358712 0.339790i
\(761\) −49.8486 + 2.70271i −0.0655041 + 0.00355153i −0.0868618 0.996220i \(-0.527684\pi\)
0.0213577 + 0.999772i \(0.493201\pi\)
\(762\) −298.688 781.324i −0.391979 1.02536i
\(763\) 1731.70 801.168i 2.26959 1.05002i
\(764\) 239.929 + 39.3344i 0.314043 + 0.0514848i
\(765\) 184.384 2238.13i 0.241025 2.92566i
\(766\) −542.127 −0.707738
\(767\) 144.287 378.948i 0.188119 0.494066i
\(768\) 586.169 + 793.948i 0.763241 + 1.03379i
\(769\) 10.0841 2.21969i 0.0131133 0.00288646i −0.208409 0.978042i \(-0.566828\pi\)
0.221522 + 0.975155i \(0.428897\pi\)
\(770\) 1848.68 + 303.076i 2.40088 + 0.393605i
\(771\) −595.827 + 1086.76i −0.772798 + 1.40955i
\(772\) −238.132 + 857.674i −0.308461 + 1.11098i
\(773\) −1162.93 + 63.0524i −1.50444 + 0.0815685i −0.787825 0.615899i \(-0.788793\pi\)
−0.716617 + 0.697467i \(0.754310\pi\)
\(774\) 380.986 188.501i 0.492229 0.243541i
\(775\) −65.1316 + 49.5118i −0.0840408 + 0.0638861i
\(776\) −54.6150 + 162.092i −0.0703802 + 0.208881i
\(777\) 609.909 401.167i 0.784954 0.516302i
\(778\) 151.727 + 178.627i 0.195022 + 0.229598i
\(779\) 642.318 178.339i 0.824541 0.228933i
\(780\) −293.772 + 420.471i −0.376631 + 0.539065i
\(781\) −647.564 + 955.085i −0.829147 + 1.22290i
\(782\) −10.6847 + 23.0946i −0.0136633 + 0.0295328i
\(783\) −968.445 372.331i −1.23684 0.475519i
\(784\) 572.402 + 542.208i 0.730105 + 0.691592i
\(785\) 82.6480 759.936i 0.105284 0.968071i
\(786\) −442.863 + 713.222i −0.563440 + 0.907407i
\(787\) −0.436373 2.66176i −0.000554477 0.00338216i 0.986548 0.163473i \(-0.0522696\pi\)
−0.987102 + 0.160091i \(0.948821\pi\)
\(788\) 422.037 286.148i 0.535580 0.363132i
\(789\) 197.276 + 2.76523i 0.250032 + 0.00350473i
\(790\) −1530.44 + 166.445i −1.93726 + 0.210690i
\(791\) 1421.38 753.569i 1.79694 0.952679i
\(792\) −144.023 + 128.962i −0.181847 + 0.162831i
\(793\) −33.2519 + 20.0070i −0.0419318 + 0.0252295i
\(794\) −1189.70 630.737i −1.49836 0.794380i
\(795\) −473.984 + 124.473i −0.596206 + 0.156569i
\(796\) −354.305 77.9884i −0.445107 0.0979754i
\(797\) −324.335 + 1473.47i −0.406944 + 1.84877i 0.111653 + 0.993747i \(0.464386\pi\)
−0.518597 + 0.855019i \(0.673545\pi\)
\(798\) −395.056 1504.35i −0.495058 1.88515i
\(799\) 1261.53 2379.50i 1.57889 2.97810i
\(800\) −800.944 1331.18i −1.00118 1.66397i
\(801\) −7.03262 7.85393i −0.00877980 0.00980515i
\(802\) −405.154 764.201i −0.505179 0.952869i
\(803\) −28.9785 266.453i −0.0360879 0.331822i
\(804\) 11.7609 839.038i 0.0146279 1.04358i
\(805\) −12.9229 19.0598i −0.0160533 0.0236768i
\(806\) 38.8189 6.36404i 0.0481625 0.00789584i
\(807\) −1031.25 640.339i −1.27788 0.793481i
\(808\) 355.825 + 38.6983i 0.440377 + 0.0478939i
\(809\) −484.977 + 511.984i −0.599477 + 0.632860i −0.953146 0.302511i \(-0.902175\pi\)
0.353669 + 0.935371i \(0.384934\pi\)
\(810\) 1657.24 456.741i 2.04597 0.563878i
\(811\) 218.094 + 100.901i 0.268920 + 0.124416i 0.549716 0.835352i \(-0.314736\pi\)
−0.280795 + 0.959768i \(0.590598\pi\)
\(812\) 950.303 + 644.321i 1.17032 + 0.793499i
\(813\) 821.181 + 573.738i 1.01006 + 0.705705i
\(814\) −168.416 606.579i −0.206899 0.745183i
\(815\) −717.776 + 609.684i −0.880707 + 0.748079i
\(816\) −969.051 1473.29i −1.18756 1.80550i
\(817\) −340.950 114.879i −0.417319 0.140611i
\(818\) 513.077 + 674.941i 0.627233 + 0.825111i
\(819\) −261.824 529.181i −0.319687 0.646131i
\(820\) −44.1390 814.095i −0.0538280 0.992799i
\(821\) −786.761 218.443i −0.958296 0.266070i −0.247042 0.969005i \(-0.579459\pi\)
−0.711254 + 0.702935i \(0.751872\pi\)
\(822\) −456.163 250.095i −0.554943 0.304252i
\(823\) −130.161 + 793.948i −0.158155 + 0.964700i 0.781832 + 0.623489i \(0.214285\pi\)
−0.939987 + 0.341211i \(0.889163\pi\)
\(824\) −11.9112 54.1132i −0.0144554 0.0656714i
\(825\) 851.890 628.947i 1.03259 0.762360i
\(826\) 1442.63 424.499i 1.74652 0.513921i
\(827\) 65.1681i 0.0788006i 0.999224 + 0.0394003i \(0.0125448\pi\)
−0.999224 + 0.0394003i \(0.987455\pi\)
\(828\) −8.52223 0.702090i −0.0102925 0.000847935i
\(829\) −186.780 + 1139.31i −0.225307 + 1.37431i 0.595613 + 0.803272i \(0.296909\pi\)
−0.820920 + 0.571043i \(0.806539\pi\)
\(830\) 188.042 + 406.447i 0.226557 + 0.489695i
\(831\) 446.156 170.558i 0.536890 0.205245i
\(832\) 12.5747 + 231.926i 0.0151138 + 0.278758i
\(833\) −909.195 959.826i −1.09147 1.15225i
\(834\) −269.679 + 921.019i −0.323356 + 1.10434i
\(835\) 1307.33 + 440.490i 1.56566 + 0.527533i
\(836\) −587.946 31.8775i −0.703284 0.0381310i
\(837\) −49.9486 29.2347i −0.0596758 0.0349279i
\(838\) 354.979 + 1278.52i 0.423602 + 1.52568i
\(839\) 167.284 + 496.480i 0.199384 + 0.591752i 0.999972 0.00746359i \(-0.00237576\pi\)
−0.800588 + 0.599216i \(0.795479\pi\)
\(840\) 528.212 21.2187i 0.628824 0.0252604i
\(841\) −576.949 266.925i −0.686027 0.317390i
\(842\) 1030.36 + 875.195i 1.22370 + 1.03942i
\(843\) 164.798 + 20.2637i 0.195490 + 0.0240376i
\(844\) 274.035 + 29.8031i 0.324686 + 0.0353118i
\(845\) −899.043 + 358.212i −1.06396 + 0.423919i
\(846\) 2042.45 + 280.254i 2.41424 + 0.331270i
\(847\) −190.045 280.295i −0.224374 0.330927i
\(848\) −232.877 + 306.344i −0.274619 + 0.361255i
\(849\) 369.708 + 401.419i 0.435463 + 0.472814i
\(850\) 1498.77 + 2826.98i 1.76326 + 3.32586i
\(851\) −3.98949 + 6.63058i −0.00468800 + 0.00779151i
\(852\) 448.908 1082.31i 0.526888 1.27031i
\(853\) 202.476 381.909i 0.237369 0.447725i −0.735996 0.676985i \(-0.763286\pi\)
0.973365 + 0.229261i \(0.0736308\pi\)
\(854\) −133.697 53.2697i −0.156554 0.0623767i
\(855\) −1265.91 717.301i −1.48060 0.838949i
\(856\) 54.3464 + 11.9626i 0.0634888 + 0.0139749i
\(857\) 1206.76 + 480.817i 1.40812 + 0.561047i 0.945533 0.325527i \(-0.105542\pi\)
0.462588 + 0.886573i \(0.346921\pi\)
\(858\) −503.534 + 75.3191i −0.586870 + 0.0877845i
\(859\) −409.242 + 246.233i −0.476417 + 0.286651i −0.733440 0.679755i \(-0.762086\pi\)
0.257022 + 0.966405i \(0.417259\pi\)
\(860\) −226.857 + 377.039i −0.263787 + 0.438418i
\(861\) 846.102 + 405.941i 0.982697 + 0.471476i
\(862\) −808.840 + 87.9666i −0.938329 + 0.102049i
\(863\) 443.575 583.513i 0.513992 0.676145i −0.463747 0.885968i \(-0.653495\pi\)
0.977740 + 0.209822i \(0.0672885\pi\)
\(864\) 654.429 882.890i 0.757440 1.02186i
\(865\) 277.876 + 1694.97i 0.321244 + 1.95950i
\(866\) −586.767 + 233.789i −0.677560 + 0.269965i
\(867\) 1052.28 + 1805.72i 1.21371 + 2.08273i
\(868\) 46.4954 + 44.0428i 0.0535661 + 0.0507405i
\(869\) −511.277 434.283i −0.588351 0.499750i
\(870\) 2396.55 492.409i 2.75465 0.565987i
\(871\) −344.647 + 508.316i −0.395691 + 0.583600i
\(872\) −148.254 440.003i −0.170016 0.504591i
\(873\) 662.491 + 18.5761i 0.758868 + 0.0212784i
\(874\) 10.6734 + 12.5657i 0.0122121 + 0.0143772i
\(875\) −997.511 54.0835i −1.14001 0.0618097i
\(876\) 83.2769 + 259.103i 0.0950650 + 0.295780i
\(877\) 280.493 213.225i 0.319832 0.243130i −0.432923 0.901431i \(-0.642518\pi\)
0.752755 + 0.658301i \(0.228725\pi\)
\(878\) 407.630 + 430.330i 0.464271 + 0.490125i
\(879\) −153.197 185.567i −0.174286 0.211112i
\(880\) 368.152 1325.96i 0.418355 1.50678i
\(881\) −425.234 919.127i −0.482672 1.04328i −0.984024 0.178034i \(-0.943026\pi\)
0.501353 0.865243i \(-0.332836\pi\)
\(882\) 450.512 906.210i 0.510784 1.02745i
\(883\) −1002.02 + 220.560i −1.13479 + 0.249785i −0.742362 0.669999i \(-0.766294\pi\)
−0.392424 + 0.919784i \(0.628363\pi\)
\(884\) 675.384i 0.764009i
\(885\) 657.283 1243.77i 0.742692 1.40539i
\(886\) −1103.59 −1.24559
\(887\) −159.997 726.871i −0.180379 0.819472i −0.976702 0.214600i \(-0.931155\pi\)
0.796323 0.604872i \(-0.206776\pi\)
\(888\) −81.0019 158.101i −0.0912184 0.178042i
\(889\) −904.583 + 418.505i −1.01753 + 0.470759i
\(890\) 23.9535 + 6.65064i 0.0269140 + 0.00747263i
\(891\) 641.113 + 387.405i 0.719543 + 0.434798i
\(892\) −161.454 + 152.937i −0.181002 + 0.171454i
\(893\) −1056.00 1389.15i −1.18253 1.55560i
\(894\) 227.184 + 706.847i 0.254120 + 0.790657i
\(895\) 146.117 2694.96i 0.163259 3.01113i
\(896\) 527.950 448.445i 0.589230 0.500497i
\(897\) 4.92871 + 3.85689i 0.00549466 + 0.00429977i
\(898\) 783.870 264.117i 0.872906 0.294116i
\(899\) −68.1776 46.2256i −0.0758372 0.0514189i
\(900\) −718.791 + 799.673i −0.798656 + 0.888526i
\(901\) 417.735 491.796i 0.463635 0.545833i
\(902\) 556.528 587.520i 0.616994 0.651352i
\(903\) −255.016 437.610i −0.282410 0.484617i
\(904\) −144.904 363.681i −0.160292 0.402302i
\(905\) −1623.45 + 266.152i −1.79387 + 0.294090i
\(906\) −321.026 113.201i −0.354333 0.124946i
\(907\) 931.966 + 708.462i 1.02753 + 0.781105i 0.976045 0.217569i \(-0.0698127\pi\)
0.0514810 + 0.998674i \(0.483606\pi\)
\(908\) 32.1166 + 295.307i 0.0353707 + 0.325228i
\(909\) −260.052 1362.25i −0.286085 1.49862i
\(910\) 1192.94 + 717.766i 1.31092 + 0.788754i
\(911\) −682.960 1135.09i −0.749681 1.24598i −0.963133 0.269026i \(-0.913298\pi\)
0.213452 0.976954i \(-0.431529\pi\)
\(912\) −1129.96 + 169.020i −1.23899 + 0.185329i
\(913\) −72.2313 + 181.287i −0.0791142 + 0.198562i
\(914\) 360.790 1639.08i 0.394737 1.79331i
\(915\) −122.970 + 54.8129i −0.134394 + 0.0599048i
\(916\) −369.678 + 927.822i −0.403579 + 1.01291i
\(917\) 883.822 + 468.573i 0.963820 + 0.510985i
\(918\) −1444.33 + 1742.76i −1.57334 + 1.89843i
\(919\) −346.932 208.742i −0.377511 0.227141i 0.314134 0.949379i \(-0.398286\pi\)
−0.691645 + 0.722238i \(0.743114\pi\)
\(920\) −4.95087 + 2.62478i −0.00538138 + 0.00285302i
\(921\) −1163.86 1263.69i −1.26369 1.37208i
\(922\) 570.180 + 433.440i 0.618417 + 0.470108i
\(923\) −709.790 + 481.250i −0.769003 + 0.521397i
\(924\) −593.736 578.420i −0.642572 0.625995i
\(925\) 360.155 + 903.921i 0.389357 + 0.977212i
\(926\) −130.869 + 1203.32i −0.141328 + 1.29949i
\(927\) −186.991 + 105.486i −0.201716 + 0.113793i
\(928\) 1012.60 1192.13i 1.09117 1.28462i
\(929\) 60.6294 131.048i 0.0652631 0.141064i −0.872199 0.489151i \(-0.837307\pi\)
0.937462 + 0.348087i \(0.113169\pi\)
\(930\) 136.363 5.47781i 0.146627 0.00589012i
\(931\) −811.745 + 273.509i −0.871907 + 0.293780i
\(932\) −186.138 + 51.6811i −0.199719 + 0.0554518i
\(933\) −161.442 37.9160i −0.173035 0.0406388i
\(934\) −76.5641 + 1412.14i −0.0819744 + 1.51193i
\(935\) −736.801 + 2186.75i −0.788022 + 2.33877i
\(936\) −134.906 + 49.4166i −0.144130 + 0.0527955i
\(937\) −732.485 + 693.846i −0.781734 + 0.740498i −0.970389 0.241546i \(-0.922346\pi\)
0.188656 + 0.982043i \(0.439587\pi\)
\(938\) −2274.25 + 123.306i −2.42457 + 0.131456i
\(939\) 370.103 141.484i 0.394146 0.150676i
\(940\) −1936.89 + 896.100i −2.06052 + 0.953298i
\(941\) −21.8821 3.58739i −0.0232541 0.00381231i 0.150144 0.988664i \(-0.452026\pi\)
−0.173398 + 0.984852i \(0.555475\pi\)
\(942\) −506.968 + 580.169i −0.538183 + 0.615891i
\(943\) −9.94761 −0.0105489
\(944\) −195.423 1087.22i −0.207016 1.15172i
\(945\) −677.503 1933.03i −0.716935 2.04554i
\(946\) −426.559 + 93.8928i −0.450909 + 0.0992525i
\(947\) −54.8189 8.98711i −0.0578869 0.00949008i 0.132769 0.991147i \(-0.457613\pi\)
−0.190656 + 0.981657i \(0.561061\pi\)
\(948\) 597.290 + 327.469i 0.630052 + 0.345431i
\(949\) 53.2883 191.927i 0.0561521 0.202242i
\(950\) 2070.07 112.236i 2.17902 0.118143i
\(951\) −143.817 + 806.288i −0.151227 + 0.847832i
\(952\) −554.134 + 421.241i −0.582073 + 0.442481i
\(953\) −267.435 + 793.718i −0.280624 + 0.832862i 0.710941 + 0.703252i \(0.248269\pi\)
−0.991565 + 0.129611i \(0.958627\pi\)
\(954\) 463.471 + 170.771i 0.485819 + 0.179005i
\(955\) −399.661 470.518i −0.418493 0.492689i
\(956\) −109.942 + 30.5254i −0.115003 + 0.0319303i
\(957\) 873.944 + 610.602i 0.913212 + 0.638037i
\(958\) 230.417 339.839i 0.240518 0.354738i
\(959\) −260.280 + 562.585i −0.271407 + 0.586638i
\(960\) −54.8986 + 803.935i −0.0571861 + 0.837432i
\(961\) 694.346 + 657.719i 0.722524 + 0.684411i
\(962\) 50.5828 465.101i 0.0525809 0.483473i
\(963\) −17.2952 214.923i −0.0179597 0.223181i
\(964\) 34.0920 + 207.952i 0.0353651 + 0.215718i
\(965\) 1870.69 1268.36i 1.93854 1.31436i
\(966\) −0.325303 + 23.2076i −0.000336752 + 0.0240244i
\(967\) −420.025 + 45.6805i −0.434359 + 0.0472394i −0.322687 0.946506i \(-0.604586\pi\)
−0.111672 + 0.993745i \(0.535621\pi\)
\(968\) −72.8078 + 38.6003i −0.0752147 + 0.0398763i
\(969\) 1907.32 180.423i 1.96834 0.186195i
\(970\) −1339.10 + 805.712i −1.38052 + 0.830631i
\(971\) −580.818 307.930i −0.598164 0.317127i 0.141672 0.989914i \(-0.454752\pi\)
−0.739836 + 0.672787i \(0.765097\pi\)
\(972\) −716.849 254.308i −0.737499 0.261634i
\(973\) 1116.79 + 245.824i 1.14778 + 0.252646i
\(974\) 5.11169 23.2226i 0.00524814 0.0238425i
\(975\) 761.142 199.883i 0.780658 0.205008i
\(976\) −49.5197 + 93.4041i −0.0507374 + 0.0957009i
\(977\) −699.717 1162.94i −0.716189 1.19032i −0.974529 0.224261i \(-0.928003\pi\)
0.258340 0.966054i \(-0.416824\pi\)
\(978\) 944.993 89.3918i 0.966250 0.0914027i
\(979\) 5.07410 + 9.57078i 0.00518295 + 0.00977607i
\(980\) 113.269 + 1041.49i 0.115580 + 1.06274i
\(981\) −1462.17 + 1048.17i −1.49049 + 1.06848i
\(982\) −99.8401 147.253i −0.101670 0.149952i
\(983\) 295.982 48.5238i 0.301101 0.0493630i −0.00933766 0.999956i \(-0.502972\pi\)
0.310439 + 0.950593i \(0.399524\pi\)
\(984\) 120.464 194.005i 0.122423 0.197160i
\(985\) −1287.11 139.982i −1.30671 0.142113i
\(986\) −2215.42 + 2338.79i −2.24688 + 2.37200i
\(987\) 167.359 2450.80i 0.169563 2.48308i
\(988\) −397.141 183.737i −0.401965 0.185969i
\(989\) 4.44377 + 3.01295i 0.00449319 + 0.00304646i
\(990\) −1765.75 + 46.1550i −1.78359 + 0.0466212i
\(991\) 442.572 + 1594.00i 0.446591 + 1.60847i 0.753984 + 0.656892i \(0.228129\pi\)
−0.307393 + 0.951583i \(0.599457\pi\)
\(992\) 66.4973 56.4833i 0.0670336 0.0569388i
\(993\) 1370.28 901.297i 1.37993 0.907650i
\(994\) −3013.84 1015.48i −3.03203 1.02161i
\(995\) 557.465 + 733.333i 0.560267 + 0.737018i
\(996\) 34.7956 195.077i 0.0349354 0.195860i
\(997\) 4.65993 + 85.9474i 0.00467395 + 0.0862060i 0.999940 0.0109854i \(-0.00349684\pi\)
−0.995266 + 0.0971915i \(0.969014\pi\)
\(998\) −1287.63 357.508i −1.29021 0.358225i
\(999\) −493.944 + 479.377i −0.494439 + 0.479856i
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 177.3.h.a.107.31 yes 1064
3.2 odd 2 inner 177.3.h.a.107.8 1064
59.16 even 29 inner 177.3.h.a.134.8 yes 1064
177.134 odd 58 inner 177.3.h.a.134.31 yes 1064
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.3.h.a.107.8 1064 3.2 odd 2 inner
177.3.h.a.107.31 yes 1064 1.1 even 1 trivial
177.3.h.a.134.8 yes 1064 59.16 even 29 inner
177.3.h.a.134.31 yes 1064 177.134 odd 58 inner