Properties

Label 315.2.be.b.236.6
Level $315$
Weight $2$
Character 315.236
Analytic conductor $2.515$
Analytic rank $0$
Dimension $30$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [315,2,Mod(236,315)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(315, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.236");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.be (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.51528766367\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(15\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 236.6
Character \(\chi\) \(=\) 315.236
Dual form 315.2.be.b.311.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.804799 + 0.464651i) q^{2} +(1.68100 + 0.417423i) q^{3} +(-0.568200 + 0.984151i) q^{4} +1.00000 q^{5} +(-1.54682 + 0.445136i) q^{6} +(-2.32336 + 1.26570i) q^{7} -2.91466i q^{8} +(2.65152 + 1.40338i) q^{9} +O(q^{10})\) \(q+(-0.804799 + 0.464651i) q^{2} +(1.68100 + 0.417423i) q^{3} +(-0.568200 + 0.984151i) q^{4} +1.00000 q^{5} +(-1.54682 + 0.445136i) q^{6} +(-2.32336 + 1.26570i) q^{7} -2.91466i q^{8} +(2.65152 + 1.40338i) q^{9} +(-0.804799 + 0.464651i) q^{10} +5.24269i q^{11} +(-1.36595 + 1.41718i) q^{12} +(0.516376 - 0.298130i) q^{13} +(1.28173 - 2.09819i) q^{14} +(1.68100 + 0.417423i) q^{15} +(0.217899 + 0.377413i) q^{16} +(1.80401 + 3.12464i) q^{17} +(-2.78602 + 0.102593i) q^{18} +(-2.80984 - 1.62226i) q^{19} +(-0.568200 + 0.984151i) q^{20} +(-4.43390 + 1.15782i) q^{21} +(-2.43602 - 4.21931i) q^{22} -2.75560i q^{23} +(1.21665 - 4.89954i) q^{24} +1.00000 q^{25} +(-0.277052 + 0.479869i) q^{26} +(3.87139 + 3.46588i) q^{27} +(0.0744906 - 3.00571i) q^{28} +(3.53879 + 2.04312i) q^{29} +(-1.54682 + 0.445136i) q^{30} +(-5.53812 - 3.19744i) q^{31} +(4.69761 + 2.71217i) q^{32} +(-2.18842 + 8.81296i) q^{33} +(-2.90373 - 1.67647i) q^{34} +(-2.32336 + 1.26570i) q^{35} +(-2.88772 + 1.81209i) q^{36} +(0.988179 - 1.71158i) q^{37} +3.01514 q^{38} +(0.992473 - 0.285608i) q^{39} -2.91466i q^{40} +(4.89572 + 8.47964i) q^{41} +(3.03041 - 2.99202i) q^{42} +(0.604036 - 1.04622i) q^{43} +(-5.15960 - 2.97889i) q^{44} +(2.65152 + 1.40338i) q^{45} +(1.28039 + 2.21770i) q^{46} +(-2.86588 - 4.96386i) q^{47} +(0.208748 + 0.725387i) q^{48} +(3.79600 - 5.88136i) q^{49} +(-0.804799 + 0.464651i) q^{50} +(1.72824 + 6.00554i) q^{51} +0.677589i q^{52} +(8.79935 - 5.08031i) q^{53} +(-4.72611 - 0.990490i) q^{54} +5.24269i q^{55} +(3.68909 + 6.77180i) q^{56} +(-4.04617 - 3.89992i) q^{57} -3.79735 q^{58} +(0.664164 - 1.15037i) q^{59} +(-1.36595 + 1.41718i) q^{60} +(-8.71808 + 5.03339i) q^{61} +5.94277 q^{62} +(-7.93668 + 0.0954797i) q^{63} -5.91244 q^{64} +(0.516376 - 0.298130i) q^{65} +(-2.33371 - 8.10951i) q^{66} +(4.63278 - 8.02422i) q^{67} -4.10015 q^{68} +(1.15025 - 4.63215i) q^{69} +(1.28173 - 2.09819i) q^{70} -11.6581i q^{71} +(4.09037 - 7.72827i) q^{72} +(12.2136 - 7.05152i) q^{73} +1.83663i q^{74} +(1.68100 + 0.417423i) q^{75} +(3.19310 - 1.84354i) q^{76} +(-6.63568 - 12.1807i) q^{77} +(-0.666033 + 0.691011i) q^{78} +(6.48343 + 11.2296i) q^{79} +(0.217899 + 0.377413i) q^{80} +(5.06107 + 7.44215i) q^{81} +(-7.88014 - 4.54960i) q^{82} +(5.40645 - 9.36424i) q^{83} +(1.37987 - 5.02150i) q^{84} +(1.80401 + 3.12464i) q^{85} +1.12266i q^{86} +(5.09586 + 4.91166i) q^{87} +15.2807 q^{88} +(4.26740 - 7.39135i) q^{89} +(-2.78602 + 0.102593i) q^{90} +(-0.822383 + 1.34624i) q^{91} +(2.71192 + 1.56573i) q^{92} +(-7.97490 - 7.68663i) q^{93} +(4.61292 + 2.66327i) q^{94} +(-2.80984 - 1.62226i) q^{95} +(6.76455 + 6.52004i) q^{96} +(-11.2557 - 6.49848i) q^{97} +(-0.322235 + 6.49712i) q^{98} +(-7.35747 + 13.9011i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 30 q + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9} + 3 q^{10} - 18 q^{12} + 12 q^{13} - 9 q^{14} - q^{15} - 21 q^{16} + 3 q^{17} - 22 q^{18} + 15 q^{20} - 10 q^{21} + 15 q^{22} + 2 q^{24} + 30 q^{25} - 24 q^{26} + 5 q^{27} + 27 q^{28} + q^{30} + 6 q^{31} + 9 q^{32} - 17 q^{33} - 48 q^{34} + 6 q^{35} + 21 q^{36} - 3 q^{37} - 60 q^{38} + 12 q^{39} + 18 q^{41} - 47 q^{42} + 12 q^{43} - 15 q^{44} - 5 q^{45} + 9 q^{46} - 30 q^{47} + 40 q^{48} - 24 q^{49} + 3 q^{50} + 33 q^{51} + 30 q^{53} + 13 q^{54} + 72 q^{56} - 21 q^{57} + 15 q^{59} - 18 q^{60} - 30 q^{61} - 12 q^{62} + 10 q^{63} - 138 q^{64} + 12 q^{65} + 44 q^{66} - 6 q^{67} - 42 q^{68} - 32 q^{69} - 9 q^{70} - 137 q^{72} + 6 q^{73} - q^{75} + 54 q^{76} - 21 q^{77} - 18 q^{78} - 12 q^{79} - 21 q^{80} - 17 q^{81} + 6 q^{82} + 6 q^{83} - 12 q^{84} + 3 q^{85} - 47 q^{87} + 96 q^{88} + 3 q^{89} - 22 q^{90} + 15 q^{91} - 3 q^{92} - 18 q^{93} + 3 q^{94} + 60 q^{96} - 36 q^{97} - 24 q^{98} - q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.804799 + 0.464651i −0.569078 + 0.328558i −0.756781 0.653668i \(-0.773229\pi\)
0.187703 + 0.982226i \(0.439896\pi\)
\(3\) 1.68100 + 0.417423i 0.970525 + 0.241000i
\(4\) −0.568200 + 0.984151i −0.284100 + 0.492075i
\(5\) 1.00000 0.447214
\(6\) −1.54682 + 0.445136i −0.631487 + 0.181726i
\(7\) −2.32336 + 1.26570i −0.878147 + 0.478390i
\(8\) 2.91466i 1.03049i
\(9\) 2.65152 + 1.40338i 0.883838 + 0.467792i
\(10\) −0.804799 + 0.464651i −0.254500 + 0.146935i
\(11\) 5.24269i 1.58073i 0.612636 + 0.790365i \(0.290109\pi\)
−0.612636 + 0.790365i \(0.709891\pi\)
\(12\) −1.36595 + 1.41718i −0.394316 + 0.409104i
\(13\) 0.516376 0.298130i 0.143217 0.0826863i −0.426679 0.904403i \(-0.640317\pi\)
0.569896 + 0.821717i \(0.306983\pi\)
\(14\) 1.28173 2.09819i 0.342556 0.560764i
\(15\) 1.68100 + 0.417423i 0.434032 + 0.107778i
\(16\) 0.217899 + 0.377413i 0.0544748 + 0.0943532i
\(17\) 1.80401 + 3.12464i 0.437536 + 0.757835i 0.997499 0.0706826i \(-0.0225178\pi\)
−0.559962 + 0.828518i \(0.689184\pi\)
\(18\) −2.78602 + 0.102593i −0.656670 + 0.0241814i
\(19\) −2.80984 1.62226i −0.644622 0.372173i 0.141771 0.989900i \(-0.454720\pi\)
−0.786393 + 0.617727i \(0.788054\pi\)
\(20\) −0.568200 + 0.984151i −0.127053 + 0.220063i
\(21\) −4.43390 + 1.15782i −0.967556 + 0.252657i
\(22\) −2.43602 4.21931i −0.519361 0.899560i
\(23\) 2.75560i 0.574582i −0.957843 0.287291i \(-0.907245\pi\)
0.957843 0.287291i \(-0.0927546\pi\)
\(24\) 1.21665 4.89954i 0.248347 1.00011i
\(25\) 1.00000 0.200000
\(26\) −0.277052 + 0.479869i −0.0543344 + 0.0941100i
\(27\) 3.87139 + 3.46588i 0.745050 + 0.667009i
\(28\) 0.0744906 3.00571i 0.0140774 0.568025i
\(29\) 3.53879 + 2.04312i 0.657137 + 0.379398i 0.791185 0.611576i \(-0.209464\pi\)
−0.134048 + 0.990975i \(0.542798\pi\)
\(30\) −1.54682 + 0.445136i −0.282410 + 0.0812703i
\(31\) −5.53812 3.19744i −0.994677 0.574277i −0.0880076 0.996120i \(-0.528050\pi\)
−0.906669 + 0.421843i \(0.861383\pi\)
\(32\) 4.69761 + 2.71217i 0.830428 + 0.479448i
\(33\) −2.18842 + 8.81296i −0.380955 + 1.53414i
\(34\) −2.90373 1.67647i −0.497985 0.287512i
\(35\) −2.32336 + 1.26570i −0.392719 + 0.213943i
\(36\) −2.88772 + 1.81209i −0.481287 + 0.302015i
\(37\) 0.988179 1.71158i 0.162456 0.281381i −0.773293 0.634049i \(-0.781392\pi\)
0.935749 + 0.352667i \(0.114725\pi\)
\(38\) 3.01514 0.489121
\(39\) 0.992473 0.285608i 0.158923 0.0457339i
\(40\) 2.91466i 0.460848i
\(41\) 4.89572 + 8.47964i 0.764583 + 1.32430i 0.940467 + 0.339886i \(0.110388\pi\)
−0.175884 + 0.984411i \(0.556278\pi\)
\(42\) 3.03041 2.99202i 0.467603 0.461679i
\(43\) 0.604036 1.04622i 0.0921146 0.159547i −0.816286 0.577648i \(-0.803971\pi\)
0.908401 + 0.418101i \(0.137304\pi\)
\(44\) −5.15960 2.97889i −0.777838 0.449085i
\(45\) 2.65152 + 1.40338i 0.395265 + 0.209203i
\(46\) 1.28039 + 2.21770i 0.188783 + 0.326982i
\(47\) −2.86588 4.96386i −0.418032 0.724053i 0.577709 0.816242i \(-0.303947\pi\)
−0.995741 + 0.0921898i \(0.970613\pi\)
\(48\) 0.208748 + 0.725387i 0.0301301 + 0.104701i
\(49\) 3.79600 5.88136i 0.542285 0.840194i
\(50\) −0.804799 + 0.464651i −0.113816 + 0.0657115i
\(51\) 1.72824 + 6.00554i 0.242002 + 0.840944i
\(52\) 0.677589i 0.0939646i
\(53\) 8.79935 5.08031i 1.20868 0.697834i 0.246212 0.969216i \(-0.420814\pi\)
0.962472 + 0.271382i \(0.0874806\pi\)
\(54\) −4.72611 0.990490i −0.643143 0.134789i
\(55\) 5.24269i 0.706924i
\(56\) 3.68909 + 6.77180i 0.492975 + 0.904920i
\(57\) −4.04617 3.89992i −0.535928 0.516556i
\(58\) −3.79735 −0.498617
\(59\) 0.664164 1.15037i 0.0864668 0.149765i −0.819549 0.573010i \(-0.805776\pi\)
0.906015 + 0.423245i \(0.139109\pi\)
\(60\) −1.36595 + 1.41718i −0.176343 + 0.182957i
\(61\) −8.71808 + 5.03339i −1.11624 + 0.644459i −0.940437 0.339967i \(-0.889584\pi\)
−0.175799 + 0.984426i \(0.556251\pi\)
\(62\) 5.94277 0.754732
\(63\) −7.93668 + 0.0954797i −0.999928 + 0.0120293i
\(64\) −5.91244 −0.739054
\(65\) 0.516376 0.298130i 0.0640485 0.0369784i
\(66\) −2.33371 8.10951i −0.287260 0.998211i
\(67\) 4.63278 8.02422i 0.565985 0.980314i −0.430973 0.902365i \(-0.641829\pi\)
0.996957 0.0779491i \(-0.0248372\pi\)
\(68\) −4.10015 −0.497216
\(69\) 1.15025 4.63215i 0.138474 0.557646i
\(70\) 1.28173 2.09819i 0.153196 0.250781i
\(71\) 11.6581i 1.38357i −0.722105 0.691784i \(-0.756825\pi\)
0.722105 0.691784i \(-0.243175\pi\)
\(72\) 4.09037 7.72827i 0.482054 0.910785i
\(73\) 12.2136 7.05152i 1.42949 0.825318i 0.432413 0.901676i \(-0.357662\pi\)
0.997081 + 0.0763575i \(0.0243290\pi\)
\(74\) 1.83663i 0.213504i
\(75\) 1.68100 + 0.417423i 0.194105 + 0.0481999i
\(76\) 3.19310 1.84354i 0.366274 0.211468i
\(77\) −6.63568 12.1807i −0.756206 1.38811i
\(78\) −0.666033 + 0.691011i −0.0754134 + 0.0782415i
\(79\) 6.48343 + 11.2296i 0.729442 + 1.26343i 0.957119 + 0.289695i \(0.0935537\pi\)
−0.227677 + 0.973737i \(0.573113\pi\)
\(80\) 0.217899 + 0.377413i 0.0243619 + 0.0421960i
\(81\) 5.06107 + 7.44215i 0.562341 + 0.826906i
\(82\) −7.88014 4.54960i −0.870215 0.502419i
\(83\) 5.40645 9.36424i 0.593435 1.02786i −0.400331 0.916371i \(-0.631105\pi\)
0.993766 0.111489i \(-0.0355619\pi\)
\(84\) 1.37987 5.02150i 0.150556 0.547890i
\(85\) 1.80401 + 3.12464i 0.195672 + 0.338914i
\(86\) 1.12266i 0.121060i
\(87\) 5.09586 + 4.91166i 0.546333 + 0.526585i
\(88\) 15.2807 1.62892
\(89\) 4.26740 7.39135i 0.452343 0.783481i −0.546188 0.837663i \(-0.683922\pi\)
0.998531 + 0.0541814i \(0.0172549\pi\)
\(90\) −2.78602 + 0.102593i −0.293672 + 0.0108142i
\(91\) −0.822383 + 1.34624i −0.0862092 + 0.141124i
\(92\) 2.71192 + 1.56573i 0.282737 + 0.163239i
\(93\) −7.97490 7.68663i −0.826958 0.797067i
\(94\) 4.61292 + 2.66327i 0.475786 + 0.274695i
\(95\) −2.80984 1.62226i −0.288284 0.166441i
\(96\) 6.76455 + 6.52004i 0.690404 + 0.665449i
\(97\) −11.2557 6.49848i −1.14284 0.659820i −0.195709 0.980662i \(-0.562701\pi\)
−0.947133 + 0.320842i \(0.896034\pi\)
\(98\) −0.322235 + 6.49712i −0.0325507 + 0.656309i
\(99\) −7.35747 + 13.9011i −0.739453 + 1.39711i
\(100\) −0.568200 + 0.984151i −0.0568200 + 0.0984151i
\(101\) 4.15057 0.412997 0.206498 0.978447i \(-0.433793\pi\)
0.206498 + 0.978447i \(0.433793\pi\)
\(102\) −4.18137 4.03022i −0.414017 0.399052i
\(103\) 11.5483i 1.13789i −0.822375 0.568946i \(-0.807351\pi\)
0.822375 0.568946i \(-0.192649\pi\)
\(104\) −0.868946 1.50506i −0.0852072 0.147583i
\(105\) −4.43390 + 1.15782i −0.432704 + 0.112992i
\(106\) −4.72114 + 8.17725i −0.458557 + 0.794245i
\(107\) −0.875674 0.505571i −0.0846546 0.0488753i 0.457075 0.889428i \(-0.348897\pi\)
−0.541730 + 0.840553i \(0.682230\pi\)
\(108\) −5.61067 + 1.84072i −0.539887 + 0.177124i
\(109\) 3.13405 + 5.42833i 0.300187 + 0.519940i 0.976178 0.216970i \(-0.0696175\pi\)
−0.675991 + 0.736910i \(0.736284\pi\)
\(110\) −2.43602 4.21931i −0.232265 0.402295i
\(111\) 2.37558 2.46467i 0.225480 0.233936i
\(112\) −0.983951 0.601070i −0.0929746 0.0567958i
\(113\) −11.5944 + 6.69401i −1.09071 + 0.629719i −0.933764 0.357888i \(-0.883497\pi\)
−0.156942 + 0.987608i \(0.550163\pi\)
\(114\) 5.06845 + 1.25859i 0.474704 + 0.117878i
\(115\) 2.75560i 0.256961i
\(116\) −4.02148 + 2.32180i −0.373385 + 0.215574i
\(117\) 1.78757 0.0658257i 0.165261 0.00608559i
\(118\) 1.23442i 0.113637i
\(119\) −8.14622 4.97631i −0.746763 0.456178i
\(120\) 1.21665 4.89954i 0.111064 0.447265i
\(121\) −16.4858 −1.49871
\(122\) 4.67753 8.10172i 0.423484 0.733496i
\(123\) 4.69010 + 16.2978i 0.422892 + 1.46953i
\(124\) 6.29352 3.63357i 0.565175 0.326304i
\(125\) 1.00000 0.0894427
\(126\) 6.34306 3.76463i 0.565085 0.335379i
\(127\) 12.6328 1.12098 0.560488 0.828162i \(-0.310613\pi\)
0.560488 + 0.828162i \(0.310613\pi\)
\(128\) −4.63690 + 2.67711i −0.409848 + 0.236626i
\(129\) 1.45210 1.50656i 0.127850 0.132645i
\(130\) −0.277052 + 0.479869i −0.0242991 + 0.0420873i
\(131\) 4.98386 0.435442 0.217721 0.976011i \(-0.430138\pi\)
0.217721 + 0.976011i \(0.430138\pi\)
\(132\) −7.42982 7.16125i −0.646682 0.623307i
\(133\) 8.58157 + 0.212678i 0.744117 + 0.0184415i
\(134\) 8.61050i 0.743834i
\(135\) 3.87139 + 3.46588i 0.333196 + 0.298295i
\(136\) 9.10725 5.25807i 0.780940 0.450876i
\(137\) 12.1794i 1.04055i 0.853998 + 0.520277i \(0.174171\pi\)
−0.853998 + 0.520277i \(0.825829\pi\)
\(138\) 1.22661 + 4.26242i 0.104416 + 0.362841i
\(139\) −14.5703 + 8.41218i −1.23584 + 0.713512i −0.968241 0.250019i \(-0.919563\pi\)
−0.267598 + 0.963531i \(0.586230\pi\)
\(140\) 0.0744906 3.00571i 0.00629560 0.254029i
\(141\) −2.74552 9.54052i −0.231214 0.803457i
\(142\) 5.41697 + 9.38246i 0.454582 + 0.787358i
\(143\) 1.56300 + 2.70720i 0.130705 + 0.226387i
\(144\) 0.0481112 + 1.30651i 0.00400927 + 0.108876i
\(145\) 3.53879 + 2.04312i 0.293881 + 0.169672i
\(146\) −6.55299 + 11.3501i −0.542329 + 0.939342i
\(147\) 8.83609 8.30202i 0.728788 0.684739i
\(148\) 1.12297 + 1.94503i 0.0923072 + 0.159881i
\(149\) 4.74043i 0.388351i −0.980967 0.194175i \(-0.937797\pi\)
0.980967 0.194175i \(-0.0622031\pi\)
\(150\) −1.54682 + 0.445136i −0.126297 + 0.0363452i
\(151\) −17.8242 −1.45051 −0.725257 0.688478i \(-0.758279\pi\)
−0.725257 + 0.688478i \(0.758279\pi\)
\(152\) −4.72834 + 8.18973i −0.383519 + 0.664275i
\(153\) 0.398317 + 10.8167i 0.0322021 + 0.874480i
\(154\) 11.0001 + 6.71970i 0.886416 + 0.541489i
\(155\) −5.53812 3.19744i −0.444833 0.256824i
\(156\) −0.282841 + 1.13903i −0.0226454 + 0.0911950i
\(157\) 5.13244 + 2.96322i 0.409613 + 0.236490i 0.690624 0.723214i \(-0.257336\pi\)
−0.281010 + 0.959705i \(0.590670\pi\)
\(158\) −10.4357 6.02506i −0.830220 0.479328i
\(159\) 16.9123 4.86694i 1.34124 0.385973i
\(160\) 4.69761 + 2.71217i 0.371379 + 0.214416i
\(161\) 3.48776 + 6.40224i 0.274874 + 0.504567i
\(162\) −7.53114 3.63780i −0.591702 0.285813i
\(163\) −7.24254 + 12.5444i −0.567279 + 0.982556i 0.429554 + 0.903041i \(0.358671\pi\)
−0.996834 + 0.0795155i \(0.974663\pi\)
\(164\) −11.1270 −0.868871
\(165\) −2.18842 + 8.81296i −0.170368 + 0.686088i
\(166\) 10.0484i 0.779910i
\(167\) 6.15227 + 10.6560i 0.476077 + 0.824589i 0.999624 0.0274071i \(-0.00872503\pi\)
−0.523547 + 0.851997i \(0.675392\pi\)
\(168\) 3.37465 + 12.9233i 0.260360 + 0.997055i
\(169\) −6.32224 + 10.9504i −0.486326 + 0.842341i
\(170\) −2.90373 1.67647i −0.222706 0.128579i
\(171\) −5.17369 8.24472i −0.395642 0.630490i
\(172\) 0.686426 + 1.18892i 0.0523395 + 0.0906546i
\(173\) −1.12513 1.94878i −0.0855418 0.148163i 0.820080 0.572249i \(-0.193929\pi\)
−0.905622 + 0.424086i \(0.860595\pi\)
\(174\) −6.38335 1.58510i −0.483920 0.120166i
\(175\) −2.32336 + 1.26570i −0.175629 + 0.0956781i
\(176\) −1.97866 + 1.14238i −0.149147 + 0.0861101i
\(177\) 1.59665 1.65653i 0.120011 0.124512i
\(178\) 7.93139i 0.594483i
\(179\) −11.4279 + 6.59789i −0.854159 + 0.493149i −0.862052 0.506820i \(-0.830821\pi\)
0.00789264 + 0.999969i \(0.497488\pi\)
\(180\) −2.88772 + 1.81209i −0.215238 + 0.135065i
\(181\) 6.74629i 0.501448i −0.968059 0.250724i \(-0.919331\pi\)
0.968059 0.250724i \(-0.0806687\pi\)
\(182\) 0.0363214 1.46557i 0.00269232 0.108635i
\(183\) −16.7561 + 4.82199i −1.23865 + 0.356452i
\(184\) −8.03163 −0.592099
\(185\) 0.988179 1.71158i 0.0726523 0.125838i
\(186\) 9.98978 + 2.48065i 0.732486 + 0.181890i
\(187\) −16.3815 + 9.45786i −1.19793 + 0.691627i
\(188\) 6.51357 0.475051
\(189\) −13.3814 3.15245i −0.973354 0.229307i
\(190\) 3.01514 0.218741
\(191\) 8.50532 4.91055i 0.615424 0.355315i −0.159662 0.987172i \(-0.551040\pi\)
0.775085 + 0.631857i \(0.217707\pi\)
\(192\) −9.93880 2.46799i −0.717271 0.178112i
\(193\) −4.68248 + 8.11029i −0.337052 + 0.583792i −0.983877 0.178847i \(-0.942763\pi\)
0.646825 + 0.762639i \(0.276097\pi\)
\(194\) 12.0781 0.867156
\(195\) 0.992473 0.285608i 0.0710725 0.0204528i
\(196\) 3.63126 + 7.07762i 0.259376 + 0.505544i
\(197\) 4.31693i 0.307569i 0.988104 + 0.153784i \(0.0491461\pi\)
−0.988104 + 0.153784i \(0.950854\pi\)
\(198\) −0.537863 14.6062i −0.0382242 1.03802i
\(199\) 14.8590 8.57887i 1.05333 0.608140i 0.129749 0.991547i \(-0.458583\pi\)
0.923579 + 0.383407i \(0.125249\pi\)
\(200\) 2.91466i 0.206098i
\(201\) 11.1372 11.5549i 0.785558 0.815018i
\(202\) −3.34037 + 1.92856i −0.235028 + 0.135693i
\(203\) −10.8079 0.267852i −0.758564 0.0187995i
\(204\) −6.89235 1.71150i −0.482561 0.119829i
\(205\) 4.89572 + 8.47964i 0.341932 + 0.592243i
\(206\) 5.36594 + 9.29408i 0.373863 + 0.647549i
\(207\) 3.86714 7.30651i 0.268785 0.507837i
\(208\) 0.225036 + 0.129925i 0.0156034 + 0.00900864i
\(209\) 8.50502 14.7311i 0.588305 1.01897i
\(210\) 3.03041 2.99202i 0.209118 0.206469i
\(211\) 10.0158 + 17.3479i 0.689519 + 1.19428i 0.971994 + 0.235007i \(0.0755113\pi\)
−0.282475 + 0.959275i \(0.591155\pi\)
\(212\) 11.5465i 0.793018i
\(213\) 4.86638 19.5973i 0.333439 1.34279i
\(214\) 0.939655 0.0642335
\(215\) 0.604036 1.04622i 0.0411949 0.0713517i
\(216\) 10.1019 11.2838i 0.687344 0.767765i
\(217\) 16.9141 + 0.419182i 1.14820 + 0.0284559i
\(218\) −5.04455 2.91247i −0.341660 0.197258i
\(219\) 23.4745 6.75536i 1.58626 0.456485i
\(220\) −5.15960 2.97889i −0.347860 0.200837i
\(221\) 1.86309 + 1.07566i 0.125325 + 0.0723565i
\(222\) −0.766653 + 3.08738i −0.0514544 + 0.207211i
\(223\) −13.5808 7.84086i −0.909435 0.525063i −0.0291859 0.999574i \(-0.509291\pi\)
−0.880249 + 0.474511i \(0.842625\pi\)
\(224\) −14.3470 0.355563i −0.958601 0.0237571i
\(225\) 2.65152 + 1.40338i 0.176768 + 0.0935584i
\(226\) 6.22075 10.7747i 0.413798 0.716720i
\(227\) −4.29396 −0.285000 −0.142500 0.989795i \(-0.545514\pi\)
−0.142500 + 0.989795i \(0.545514\pi\)
\(228\) 6.13714 1.76611i 0.406442 0.116964i
\(229\) 8.42278i 0.556593i −0.960495 0.278297i \(-0.910230\pi\)
0.960495 0.278297i \(-0.0897698\pi\)
\(230\) 1.28039 + 2.21770i 0.0844264 + 0.146231i
\(231\) −6.07009 23.2456i −0.399382 1.52945i
\(232\) 5.95501 10.3144i 0.390965 0.677172i
\(233\) −13.0808 7.55221i −0.856953 0.494762i 0.00603784 0.999982i \(-0.498078\pi\)
−0.862991 + 0.505220i \(0.831411\pi\)
\(234\) −1.40804 + 0.883570i −0.0920468 + 0.0577608i
\(235\) −2.86588 4.96386i −0.186950 0.323806i
\(236\) 0.754755 + 1.30727i 0.0491304 + 0.0850963i
\(237\) 6.21113 + 21.5833i 0.403456 + 1.40199i
\(238\) 8.86831 + 0.219784i 0.574847 + 0.0142465i
\(239\) −7.72892 + 4.46229i −0.499942 + 0.288642i −0.728690 0.684844i \(-0.759870\pi\)
0.228748 + 0.973486i \(0.426537\pi\)
\(240\) 0.208748 + 0.725387i 0.0134746 + 0.0468235i
\(241\) 30.4936i 1.96426i −0.188194 0.982132i \(-0.560263\pi\)
0.188194 0.982132i \(-0.439737\pi\)
\(242\) 13.2677 7.66014i 0.852883 0.492412i
\(243\) 5.40112 + 14.6229i 0.346482 + 0.938057i
\(244\) 11.4399i 0.732363i
\(245\) 3.79600 5.88136i 0.242517 0.375746i
\(246\) −11.3474 10.9372i −0.723483 0.697332i
\(247\) −1.93458 −0.123094
\(248\) −9.31944 + 16.1417i −0.591785 + 1.02500i
\(249\) 12.9971 13.4845i 0.823657 0.854546i
\(250\) −0.804799 + 0.464651i −0.0508999 + 0.0293871i
\(251\) −9.76019 −0.616058 −0.308029 0.951377i \(-0.599669\pi\)
−0.308029 + 0.951377i \(0.599669\pi\)
\(252\) 4.41565 7.86514i 0.278160 0.495457i
\(253\) 14.4467 0.908259
\(254\) −10.1668 + 5.86982i −0.637924 + 0.368305i
\(255\) 1.72824 + 6.00554i 0.108227 + 0.376082i
\(256\) 8.40028 14.5497i 0.525018 0.909357i
\(257\) −10.4201 −0.649987 −0.324993 0.945716i \(-0.605362\pi\)
−0.324993 + 0.945716i \(0.605362\pi\)
\(258\) −0.468626 + 1.88719i −0.0291754 + 0.117492i
\(259\) −0.129550 + 5.22735i −0.00804982 + 0.324811i
\(260\) 0.677589i 0.0420223i
\(261\) 6.51589 + 10.3836i 0.403324 + 0.642731i
\(262\) −4.01100 + 2.31575i −0.247801 + 0.143068i
\(263\) 23.1446i 1.42716i −0.700575 0.713579i \(-0.747073\pi\)
0.700575 0.713579i \(-0.252927\pi\)
\(264\) 25.6868 + 6.37850i 1.58091 + 0.392570i
\(265\) 8.79935 5.08031i 0.540540 0.312081i
\(266\) −7.00526 + 3.81627i −0.429520 + 0.233991i
\(267\) 10.2588 10.6435i 0.627829 0.651374i
\(268\) 5.26469 + 9.11871i 0.321592 + 0.557014i
\(269\) 15.6437 + 27.0957i 0.953815 + 1.65206i 0.737056 + 0.675831i \(0.236215\pi\)
0.216759 + 0.976225i \(0.430451\pi\)
\(270\) −4.72611 0.990490i −0.287622 0.0602793i
\(271\) −16.0145 9.24600i −0.972814 0.561654i −0.0727211 0.997352i \(-0.523168\pi\)
−0.900093 + 0.435698i \(0.856502\pi\)
\(272\) −0.786185 + 1.36171i −0.0476695 + 0.0825659i
\(273\) −1.94438 + 1.91975i −0.117679 + 0.116188i
\(274\) −5.65915 9.80193i −0.341882 0.592156i
\(275\) 5.24269i 0.316146i
\(276\) 3.90517 + 3.76401i 0.235063 + 0.226567i
\(277\) −17.4674 −1.04952 −0.524758 0.851252i \(-0.675844\pi\)
−0.524758 + 0.851252i \(0.675844\pi\)
\(278\) 7.81745 13.5402i 0.468859 0.812088i
\(279\) −10.1972 16.2501i −0.610491 0.972870i
\(280\) 3.68909 + 6.77180i 0.220465 + 0.404693i
\(281\) 17.7776 + 10.2639i 1.06052 + 0.612292i 0.925576 0.378561i \(-0.123581\pi\)
0.134945 + 0.990853i \(0.456914\pi\)
\(282\) 6.64260 + 6.40249i 0.395561 + 0.381263i
\(283\) −19.8142 11.4397i −1.17783 0.680021i −0.222319 0.974974i \(-0.571363\pi\)
−0.955512 + 0.294953i \(0.904696\pi\)
\(284\) 11.4734 + 6.62415i 0.680819 + 0.393071i
\(285\) −4.04617 3.89992i −0.239674 0.231011i
\(286\) −2.51580 1.45250i −0.148763 0.0858881i
\(287\) −22.1072 13.5047i −1.30495 0.797158i
\(288\) 8.64959 + 13.7839i 0.509682 + 0.812222i
\(289\) 1.99110 3.44869i 0.117124 0.202864i
\(290\) −3.79735 −0.222988
\(291\) −16.2082 15.6223i −0.950141 0.915797i
\(292\) 16.0267i 0.937891i
\(293\) −6.87701 11.9113i −0.401759 0.695868i 0.592179 0.805806i \(-0.298268\pi\)
−0.993938 + 0.109939i \(0.964934\pi\)
\(294\) −3.25373 + 10.7871i −0.189761 + 0.629119i
\(295\) 0.664164 1.15037i 0.0386691 0.0669769i
\(296\) −4.98866 2.88020i −0.289960 0.167409i
\(297\) −18.1705 + 20.2965i −1.05436 + 1.17772i
\(298\) 2.20264 + 3.81509i 0.127596 + 0.221002i
\(299\) −0.821525 1.42292i −0.0475100 0.0822898i
\(300\) −1.36595 + 1.41718i −0.0788632 + 0.0818207i
\(301\) −0.0791887 + 3.19528i −0.00456436 + 0.184173i
\(302\) 14.3449 8.28203i 0.825457 0.476578i
\(303\) 6.97710 + 1.73254i 0.400824 + 0.0995320i
\(304\) 1.41396i 0.0810962i
\(305\) −8.71808 + 5.03339i −0.499196 + 0.288211i
\(306\) −5.34656 8.52020i −0.305643 0.487068i
\(307\) 21.7512i 1.24141i 0.784046 + 0.620703i \(0.213153\pi\)
−0.784046 + 0.620703i \(0.786847\pi\)
\(308\) 15.7580 + 0.390531i 0.897895 + 0.0222526i
\(309\) 4.82055 19.4127i 0.274231 1.10435i
\(310\) 5.94277 0.337526
\(311\) −5.74473 + 9.95016i −0.325754 + 0.564222i −0.981665 0.190616i \(-0.938951\pi\)
0.655911 + 0.754838i \(0.272285\pi\)
\(312\) −0.832451 2.89272i −0.0471283 0.163768i
\(313\) 24.5684 14.1846i 1.38869 0.801758i 0.395519 0.918458i \(-0.370565\pi\)
0.993167 + 0.116699i \(0.0372314\pi\)
\(314\) −5.50744 −0.310803
\(315\) −7.93668 + 0.0954797i −0.447181 + 0.00537967i
\(316\) −14.7355 −0.828938
\(317\) −11.7960 + 6.81041i −0.662528 + 0.382511i −0.793240 0.608909i \(-0.791607\pi\)
0.130711 + 0.991420i \(0.458274\pi\)
\(318\) −11.3496 + 11.7752i −0.636454 + 0.660322i
\(319\) −10.7115 + 18.5528i −0.599727 + 1.03876i
\(320\) −5.91244 −0.330515
\(321\) −1.26097 1.21539i −0.0703805 0.0678365i
\(322\) −5.78175 3.53192i −0.322204 0.196826i
\(323\) 11.7063i 0.651356i
\(324\) −10.1999 + 0.752226i −0.566661 + 0.0417903i
\(325\) 0.516376 0.298130i 0.0286434 0.0165373i
\(326\) 13.4610i 0.745536i
\(327\) 3.00242 + 10.4332i 0.166034 + 0.576959i
\(328\) 24.7153 14.2694i 1.36467 0.787893i
\(329\) 12.9412 + 7.90547i 0.713473 + 0.435842i
\(330\) −2.33371 8.10951i −0.128466 0.446414i
\(331\) 11.5126 + 19.9404i 0.632789 + 1.09602i 0.986979 + 0.160849i \(0.0514232\pi\)
−0.354190 + 0.935173i \(0.615244\pi\)
\(332\) 6.14388 + 10.6415i 0.337189 + 0.584029i
\(333\) 5.02216 3.15148i 0.275212 0.172700i
\(334\) −9.90268 5.71731i −0.541850 0.312837i
\(335\) 4.63278 8.02422i 0.253116 0.438410i
\(336\) −1.40312 1.42112i −0.0765464 0.0775286i
\(337\) 5.15757 + 8.93317i 0.280951 + 0.486621i 0.971619 0.236551i \(-0.0760169\pi\)
−0.690668 + 0.723172i \(0.742684\pi\)
\(338\) 11.7505i 0.639144i
\(339\) −22.2844 + 6.41286i −1.21032 + 0.348299i
\(340\) −4.10015 −0.222362
\(341\) 16.7632 29.0347i 0.907777 1.57232i
\(342\) 7.99469 + 4.23138i 0.432304 + 0.228807i
\(343\) −1.37542 + 18.4691i −0.0742655 + 0.997239i
\(344\) −3.04938 1.76056i −0.164411 0.0949230i
\(345\) 1.15025 4.63215i 0.0619274 0.249387i
\(346\) 1.81100 + 1.04558i 0.0973600 + 0.0562108i
\(347\) 21.6894 + 12.5224i 1.16435 + 0.672237i 0.952343 0.305031i \(-0.0986667\pi\)
0.212007 + 0.977268i \(0.432000\pi\)
\(348\) −7.72928 + 2.22429i −0.414333 + 0.119234i
\(349\) −2.42311 1.39898i −0.129706 0.0748859i 0.433743 0.901037i \(-0.357193\pi\)
−0.563449 + 0.826151i \(0.690526\pi\)
\(350\) 1.28173 2.09819i 0.0685112 0.112153i
\(351\) 3.03237 + 0.635519i 0.161856 + 0.0339215i
\(352\) −14.2190 + 24.6281i −0.757878 + 1.31268i
\(353\) −0.787634 −0.0419215 −0.0209608 0.999780i \(-0.506673\pi\)
−0.0209608 + 0.999780i \(0.506673\pi\)
\(354\) −0.515274 + 2.07505i −0.0273865 + 0.110288i
\(355\) 11.6581i 0.618750i
\(356\) 4.84946 + 8.39952i 0.257021 + 0.445174i
\(357\) −11.6166 11.7656i −0.614813 0.622702i
\(358\) 6.13142 10.6199i 0.324056 0.561281i
\(359\) 3.14705 + 1.81695i 0.166095 + 0.0958950i 0.580743 0.814087i \(-0.302762\pi\)
−0.414648 + 0.909982i \(0.636095\pi\)
\(360\) 4.09037 7.72827i 0.215581 0.407315i
\(361\) −4.23653 7.33788i −0.222975 0.386204i
\(362\) 3.13467 + 5.42941i 0.164755 + 0.285363i
\(363\) −27.7126 6.88156i −1.45454 0.361188i
\(364\) −0.857625 1.57428i −0.0449518 0.0825148i
\(365\) 12.2136 7.05152i 0.639289 0.369094i
\(366\) 11.2448 11.6665i 0.587774 0.609817i
\(367\) 12.4626i 0.650545i 0.945620 + 0.325272i \(0.105456\pi\)
−0.945620 + 0.325272i \(0.894544\pi\)
\(368\) 1.04000 0.600443i 0.0542136 0.0313002i
\(369\) 1.08095 + 29.3544i 0.0562722 + 1.52813i
\(370\) 1.83663i 0.0954819i
\(371\) −14.0139 + 22.9407i −0.727565 + 1.19102i
\(372\) 12.0961 3.48096i 0.627155 0.180479i
\(373\) 10.2662 0.531562 0.265781 0.964033i \(-0.414370\pi\)
0.265781 + 0.964033i \(0.414370\pi\)
\(374\) 8.78920 15.2233i 0.454479 0.787180i
\(375\) 1.68100 + 0.417423i 0.0868064 + 0.0215557i
\(376\) −14.4679 + 8.35307i −0.746127 + 0.430777i
\(377\) 2.43646 0.125484
\(378\) 12.2341 3.68059i 0.629256 0.189309i
\(379\) −21.1937 −1.08864 −0.544322 0.838876i \(-0.683213\pi\)
−0.544322 + 0.838876i \(0.683213\pi\)
\(380\) 3.19310 1.84354i 0.163803 0.0945715i
\(381\) 21.2357 + 5.27321i 1.08794 + 0.270155i
\(382\) −4.56338 + 7.90401i −0.233483 + 0.404404i
\(383\) −6.97284 −0.356296 −0.178148 0.984004i \(-0.557011\pi\)
−0.178148 + 0.984004i \(0.557011\pi\)
\(384\) −8.91211 + 2.56468i −0.454794 + 0.130878i
\(385\) −6.63568 12.1807i −0.338186 0.620784i
\(386\) 8.70287i 0.442964i
\(387\) 3.06985 1.92638i 0.156049 0.0979234i
\(388\) 12.7910 7.38486i 0.649362 0.374910i
\(389\) 18.9856i 0.962610i −0.876553 0.481305i \(-0.840163\pi\)
0.876553 0.481305i \(-0.159837\pi\)
\(390\) −0.666033 + 0.691011i −0.0337259 + 0.0349907i
\(391\) 8.61023 4.97112i 0.435438 0.251400i
\(392\) −17.1422 11.0640i −0.865810 0.558818i
\(393\) 8.37787 + 2.08038i 0.422607 + 0.104941i
\(394\) −2.00587 3.47426i −0.101054 0.175031i
\(395\) 6.48343 + 11.2296i 0.326217 + 0.565024i
\(396\) −9.50024 15.1394i −0.477405 0.760786i
\(397\) −20.5199 11.8472i −1.02987 0.594593i −0.112919 0.993604i \(-0.536020\pi\)
−0.916946 + 0.399011i \(0.869353\pi\)
\(398\) −7.97235 + 13.8085i −0.399618 + 0.692158i
\(399\) 14.3368 + 3.93966i 0.717740 + 0.197230i
\(400\) 0.217899 + 0.377413i 0.0108950 + 0.0188706i
\(401\) 27.1825i 1.35743i −0.734403 0.678714i \(-0.762538\pi\)
0.734403 0.678714i \(-0.237462\pi\)
\(402\) −3.59423 + 14.4742i −0.179264 + 0.721910i
\(403\) −3.81300 −0.189939
\(404\) −2.35835 + 4.08478i −0.117332 + 0.203226i
\(405\) 5.06107 + 7.44215i 0.251486 + 0.369803i
\(406\) 8.82262 4.80632i 0.437859 0.238533i
\(407\) 8.97326 + 5.18072i 0.444788 + 0.256799i
\(408\) 17.5041 5.03724i 0.866583 0.249380i
\(409\) 3.00100 + 1.73263i 0.148390 + 0.0856729i 0.572357 0.820005i \(-0.306029\pi\)
−0.423967 + 0.905678i \(0.639363\pi\)
\(410\) −7.88014 4.54960i −0.389172 0.224689i
\(411\) −5.08395 + 20.4735i −0.250773 + 1.00988i
\(412\) 11.3653 + 6.56176i 0.559928 + 0.323275i
\(413\) −0.0870715 + 3.51335i −0.00428451 + 0.172880i
\(414\) 0.282705 + 7.67713i 0.0138942 + 0.377311i
\(415\) 5.40645 9.36424i 0.265392 0.459673i
\(416\) 3.23431 0.158575
\(417\) −28.0041 + 8.05887i −1.37137 + 0.394645i
\(418\) 15.8075i 0.773168i
\(419\) −0.596980 1.03400i −0.0291644 0.0505142i 0.851075 0.525044i \(-0.175951\pi\)
−0.880239 + 0.474530i \(0.842618\pi\)
\(420\) 1.37987 5.02150i 0.0673308 0.245024i
\(421\) 15.3249 26.5435i 0.746889 1.29365i −0.202417 0.979299i \(-0.564880\pi\)
0.949307 0.314351i \(-0.101787\pi\)
\(422\) −16.1215 9.30773i −0.784781 0.453093i
\(423\) −0.632775 17.1837i −0.0307666 0.835498i
\(424\) −14.8074 25.6471i −0.719109 1.24553i
\(425\) 1.80401 + 3.12464i 0.0875073 + 0.151567i
\(426\) 5.18946 + 18.0331i 0.251430 + 0.873705i
\(427\) 13.8845 22.7289i 0.671917 1.09993i
\(428\) 0.995115 0.574530i 0.0481007 0.0277710i
\(429\) 1.49736 + 5.20323i 0.0722930 + 0.251214i
\(430\) 1.12266i 0.0541396i
\(431\) −21.2265 + 12.2551i −1.02244 + 0.590307i −0.914811 0.403883i \(-0.867660\pi\)
−0.107632 + 0.994191i \(0.534327\pi\)
\(432\) −0.464493 + 2.21633i −0.0223479 + 0.106633i
\(433\) 21.7966i 1.04748i 0.851879 + 0.523739i \(0.175463\pi\)
−0.851879 + 0.523739i \(0.824537\pi\)
\(434\) −13.8072 + 7.52177i −0.662766 + 0.361057i
\(435\) 5.09586 + 4.91166i 0.244328 + 0.235496i
\(436\) −7.12306 −0.341133
\(437\) −4.47030 + 7.74279i −0.213844 + 0.370388i
\(438\) −15.7534 + 16.3442i −0.752725 + 0.780954i
\(439\) 0.662694 0.382607i 0.0316287 0.0182608i −0.484102 0.875011i \(-0.660854\pi\)
0.515731 + 0.856751i \(0.327520\pi\)
\(440\) 15.2807 0.728477
\(441\) 18.3189 10.2673i 0.872329 0.488919i
\(442\) −1.99922 −0.0950932
\(443\) 0.478086 0.276023i 0.0227145 0.0131142i −0.488600 0.872508i \(-0.662492\pi\)
0.511314 + 0.859394i \(0.329159\pi\)
\(444\) 1.07580 + 3.73835i 0.0510553 + 0.177414i
\(445\) 4.26740 7.39135i 0.202294 0.350383i
\(446\) 14.5730 0.690053
\(447\) 1.97876 7.96865i 0.0935924 0.376904i
\(448\) 13.7367 7.48338i 0.648999 0.353557i
\(449\) 38.0738i 1.79681i 0.439164 + 0.898407i \(0.355275\pi\)
−0.439164 + 0.898407i \(0.644725\pi\)
\(450\) −2.78602 + 0.102593i −0.131334 + 0.00483627i
\(451\) −44.4561 + 25.6667i −2.09336 + 1.20860i
\(452\) 15.2141i 0.715613i
\(453\) −29.9625 7.44025i −1.40776 0.349573i
\(454\) 3.45577 1.99519i 0.162187 0.0936389i
\(455\) −0.822383 + 1.34624i −0.0385539 + 0.0631127i
\(456\) −11.3669 + 11.7932i −0.532305 + 0.552268i
\(457\) −15.2716 26.4512i −0.714375 1.23733i −0.963200 0.268786i \(-0.913378\pi\)
0.248825 0.968549i \(-0.419956\pi\)
\(458\) 3.91365 + 6.77864i 0.182873 + 0.316745i
\(459\) −3.84558 + 18.3492i −0.179496 + 0.856466i
\(460\) 2.71192 + 1.56573i 0.126444 + 0.0730025i
\(461\) 16.1726 28.0117i 0.753232 1.30464i −0.193016 0.981196i \(-0.561827\pi\)
0.946248 0.323441i \(-0.104840\pi\)
\(462\) 15.6863 + 15.8875i 0.729791 + 0.739154i
\(463\) −0.0238247 0.0412655i −0.00110723 0.00191777i 0.865471 0.500959i \(-0.167019\pi\)
−0.866578 + 0.499041i \(0.833686\pi\)
\(464\) 1.78078i 0.0826707i
\(465\) −7.97490 7.68663i −0.369827 0.356459i
\(466\) 14.0366 0.650231
\(467\) 8.92449 15.4577i 0.412976 0.715296i −0.582237 0.813019i \(-0.697823\pi\)
0.995214 + 0.0977230i \(0.0311559\pi\)
\(468\) −0.950912 + 1.79664i −0.0439559 + 0.0830495i
\(469\) −0.607355 + 24.5069i −0.0280450 + 1.13162i
\(470\) 4.61292 + 2.66327i 0.212778 + 0.122847i
\(471\) 7.39071 + 7.12356i 0.340546 + 0.328236i
\(472\) −3.35292 1.93581i −0.154331 0.0891030i
\(473\) 5.48501 + 3.16677i 0.252201 + 0.145608i
\(474\) −15.0274 14.4842i −0.690232 0.665282i
\(475\) −2.80984 1.62226i −0.128924 0.0744345i
\(476\) 9.52612 5.18957i 0.436629 0.237863i
\(477\) 30.4612 1.12171i 1.39472 0.0513596i
\(478\) 4.14681 7.18249i 0.189671 0.328520i
\(479\) −0.813442 −0.0371671 −0.0185835 0.999827i \(-0.505916\pi\)
−0.0185835 + 0.999827i \(0.505916\pi\)
\(480\) 6.76455 + 6.52004i 0.308758 + 0.297598i
\(481\) 1.17842i 0.0537314i
\(482\) 14.1689 + 24.5412i 0.645374 + 1.11782i
\(483\) 3.19048 + 12.2180i 0.145172 + 0.555940i
\(484\) 9.36722 16.2245i 0.425783 0.737478i
\(485\) −11.2557 6.49848i −0.511095 0.295081i
\(486\) −11.1413 9.25882i −0.505381 0.419988i
\(487\) −1.30232 2.25568i −0.0590137 0.102215i 0.835009 0.550236i \(-0.185462\pi\)
−0.894023 + 0.448021i \(0.852129\pi\)
\(488\) 14.6706 + 25.4102i 0.664107 + 1.15027i
\(489\) −17.4110 + 18.0640i −0.787354 + 0.816882i
\(490\) −0.322235 + 6.49712i −0.0145571 + 0.293510i
\(491\) 14.8669 8.58341i 0.670934 0.387364i −0.125496 0.992094i \(-0.540052\pi\)
0.796430 + 0.604730i \(0.206719\pi\)
\(492\) −18.7044 4.64466i −0.843262 0.209398i
\(493\) 14.7432i 0.664002i
\(494\) 1.55695 0.898903i 0.0700503 0.0404436i
\(495\) −7.35747 + 13.9011i −0.330694 + 0.624807i
\(496\) 2.78688i 0.125135i
\(497\) 14.7557 + 27.0861i 0.661885 + 1.21498i
\(498\) −4.19445 + 16.8914i −0.187958 + 0.756923i
\(499\) −3.58235 −0.160368 −0.0801840 0.996780i \(-0.525551\pi\)
−0.0801840 + 0.996780i \(0.525551\pi\)
\(500\) −0.568200 + 0.984151i −0.0254107 + 0.0440125i
\(501\) 5.89388 + 20.4809i 0.263319 + 0.915019i
\(502\) 7.85498 4.53508i 0.350585 0.202410i
\(503\) −9.90167 −0.441494 −0.220747 0.975331i \(-0.570849\pi\)
−0.220747 + 0.975331i \(0.570849\pi\)
\(504\) 0.278291 + 23.1327i 0.0123961 + 1.03041i
\(505\) 4.15057 0.184698
\(506\) −11.6267 + 6.71269i −0.516870 + 0.298415i
\(507\) −15.1986 + 15.7686i −0.674995 + 0.700309i
\(508\) −7.17793 + 12.4325i −0.318469 + 0.551605i
\(509\) 33.4933 1.48457 0.742283 0.670086i \(-0.233743\pi\)
0.742283 + 0.670086i \(0.233743\pi\)
\(510\) −4.18137 4.03022i −0.185154 0.178461i
\(511\) −19.4514 + 31.8420i −0.860481 + 1.40861i
\(512\) 4.90433i 0.216743i
\(513\) −5.25543 16.0190i −0.232033 0.707256i
\(514\) 8.38606 4.84170i 0.369893 0.213558i
\(515\) 11.5483i 0.508880i
\(516\) 0.657596 + 2.28511i 0.0289491 + 0.100596i
\(517\) 26.0240 15.0249i 1.14453 0.660796i
\(518\) −2.32463 4.26716i −0.102138 0.187488i
\(519\) −1.07787 3.74554i −0.0473133 0.164411i
\(520\) −0.868946 1.50506i −0.0381058 0.0660012i
\(521\) 1.46842 + 2.54339i 0.0643329 + 0.111428i 0.896398 0.443250i \(-0.146175\pi\)
−0.832065 + 0.554678i \(0.812841\pi\)
\(522\) −10.0687 5.32912i −0.440697 0.233249i
\(523\) −6.60049 3.81080i −0.288619 0.166634i 0.348700 0.937234i \(-0.386623\pi\)
−0.637319 + 0.770600i \(0.719957\pi\)
\(524\) −2.83183 + 4.90487i −0.123709 + 0.214270i
\(525\) −4.43390 + 1.15782i −0.193511 + 0.0505314i
\(526\) 10.7542 + 18.6268i 0.468904 + 0.812165i
\(527\) 23.0728i 1.00507i
\(528\) −3.80298 + 1.09440i −0.165503 + 0.0476276i
\(529\) 15.4067 0.669856
\(530\) −4.72114 + 8.17725i −0.205073 + 0.355197i
\(531\) 3.37544 2.11814i 0.146481 0.0919195i
\(532\) −5.08535 + 8.32472i −0.220478 + 0.360922i
\(533\) 5.05606 + 2.91912i 0.219002 + 0.126441i
\(534\) −3.31075 + 13.3327i −0.143270 + 0.576961i
\(535\) −0.875674 0.505571i −0.0378587 0.0218577i
\(536\) −23.3879 13.5030i −1.01020 0.583240i
\(537\) −21.9644 + 6.32078i −0.947832 + 0.272762i
\(538\) −25.1801 14.5377i −1.08559 0.626767i
\(539\) 30.8342 + 19.9012i 1.32812 + 0.857207i
\(540\) −5.61067 + 1.84072i −0.241445 + 0.0792121i
\(541\) 2.00276 3.46888i 0.0861053 0.149139i −0.819756 0.572712i \(-0.805891\pi\)
0.905862 + 0.423574i \(0.139225\pi\)
\(542\) 17.1846 0.738143
\(543\) 2.81606 11.3405i 0.120849 0.486668i
\(544\) 19.5711i 0.839103i
\(545\) 3.13405 + 5.42833i 0.134248 + 0.232524i
\(546\) 0.672821 2.44846i 0.0287941 0.104785i
\(547\) 19.4542 33.6956i 0.831800 1.44072i −0.0648089 0.997898i \(-0.520644\pi\)
0.896609 0.442823i \(-0.146023\pi\)
\(548\) −11.9863 6.92031i −0.512030 0.295621i
\(549\) −30.1799 + 1.11135i −1.28805 + 0.0474313i
\(550\) −2.43602 4.21931i −0.103872 0.179912i
\(551\) −6.62896 11.4817i −0.282403 0.489137i
\(552\) −13.5012 3.35259i −0.574647 0.142696i
\(553\) −29.2767 17.8844i −1.24497 0.760521i
\(554\) 14.0578 8.11625i 0.597257 0.344826i
\(555\) 2.37558 2.46467i 0.100838 0.104619i
\(556\) 19.1192i 0.810834i
\(557\) −6.65261 + 3.84089i −0.281880 + 0.162744i −0.634274 0.773108i \(-0.718701\pi\)
0.352394 + 0.935852i \(0.385368\pi\)
\(558\) 15.7573 + 8.33994i 0.667061 + 0.353058i
\(559\) 0.720324i 0.0304665i
\(560\) −0.983951 0.601070i −0.0415795 0.0253998i
\(561\) −31.4852 + 9.06064i −1.32931 + 0.382540i
\(562\) −19.0765 −0.804693
\(563\) 17.3061 29.9751i 0.729367 1.26330i −0.227784 0.973712i \(-0.573148\pi\)
0.957151 0.289589i \(-0.0935187\pi\)
\(564\) 10.9493 + 2.71892i 0.461049 + 0.114487i
\(565\) −11.5944 + 6.69401i −0.487779 + 0.281619i
\(566\) 21.2619 0.893704
\(567\) −21.1782 10.8850i −0.889402 0.457126i
\(568\) −33.9795 −1.42575
\(569\) 9.90288 5.71743i 0.415150 0.239687i −0.277850 0.960625i \(-0.589622\pi\)
0.693000 + 0.720937i \(0.256288\pi\)
\(570\) 5.06845 + 1.25859i 0.212294 + 0.0527166i
\(571\) 16.7798 29.0635i 0.702215 1.21627i −0.265473 0.964118i \(-0.585528\pi\)
0.967687 0.252153i \(-0.0811387\pi\)
\(572\) −3.55239 −0.148533
\(573\) 16.3472 4.70431i 0.682915 0.196525i
\(574\) 24.0668 + 0.596449i 1.00453 + 0.0248953i
\(575\) 2.75560i 0.114916i
\(576\) −15.6769 8.29737i −0.653205 0.345724i
\(577\) 11.4056 6.58501i 0.474820 0.274137i −0.243435 0.969917i \(-0.578274\pi\)
0.718255 + 0.695780i \(0.244941\pi\)
\(578\) 3.70067i 0.153927i
\(579\) −11.2567 + 11.6788i −0.467811 + 0.485355i
\(580\) −4.02148 + 2.32180i −0.166983 + 0.0964076i
\(581\) −0.708782 + 28.5995i −0.0294052 + 1.18651i
\(582\) 20.3032 + 5.04168i 0.841597 + 0.208984i
\(583\) 26.6345 + 46.1323i 1.10309 + 1.91060i
\(584\) −20.5528 35.5985i −0.850480 1.47308i
\(585\) 1.78757 0.0658257i 0.0739068 0.00272156i
\(586\) 11.0692 + 6.39082i 0.457265 + 0.264002i
\(587\) −14.3135 + 24.7917i −0.590781 + 1.02326i 0.403346 + 0.915047i \(0.367847\pi\)
−0.994127 + 0.108215i \(0.965486\pi\)
\(588\) 3.14978 + 13.4132i 0.129895 + 0.553153i
\(589\) 10.3742 + 17.9686i 0.427460 + 0.740383i
\(590\) 1.23442i 0.0508201i
\(591\) −1.80199 + 7.25676i −0.0741239 + 0.298503i
\(592\) 0.861294 0.0353990
\(593\) 10.6177 18.3904i 0.436016 0.755202i −0.561362 0.827571i \(-0.689722\pi\)
0.997378 + 0.0723683i \(0.0230557\pi\)
\(594\) 5.19283 24.7776i 0.213064 1.01664i
\(595\) −8.14622 4.97631i −0.333962 0.204009i
\(596\) 4.66529 + 2.69351i 0.191098 + 0.110330i
\(597\) 28.5590 8.21856i 1.16884 0.336363i
\(598\) 1.32232 + 0.763444i 0.0540739 + 0.0312196i
\(599\) 41.7758 + 24.1193i 1.70691 + 0.985486i 0.938334 + 0.345729i \(0.112368\pi\)
0.768577 + 0.639757i \(0.220965\pi\)
\(600\) 1.21665 4.89954i 0.0496694 0.200023i
\(601\) −14.1137 8.14853i −0.575708 0.332385i 0.183718 0.982979i \(-0.441187\pi\)
−0.759426 + 0.650594i \(0.774520\pi\)
\(602\) −1.42096 2.60835i −0.0579138 0.106308i
\(603\) 23.5449 14.7748i 0.958822 0.601676i
\(604\) 10.1277 17.5417i 0.412091 0.713762i
\(605\) −16.4858 −0.670243
\(606\) −6.42019 + 1.84756i −0.260802 + 0.0750522i
\(607\) 8.09904i 0.328730i −0.986400 0.164365i \(-0.947443\pi\)
0.986400 0.164365i \(-0.0525574\pi\)
\(608\) −8.79969 15.2415i −0.356875 0.618125i
\(609\) −18.0562 4.96172i −0.731675 0.201059i
\(610\) 4.67753 8.10172i 0.189388 0.328029i
\(611\) −2.95974 1.70881i −0.119738 0.0691310i
\(612\) −10.8716 5.75405i −0.439459 0.232594i
\(613\) −18.0545 31.2713i −0.729215 1.26304i −0.957215 0.289376i \(-0.906552\pi\)
0.228001 0.973661i \(-0.426781\pi\)
\(614\) −10.1067 17.5053i −0.407873 0.706457i
\(615\) 4.69010 + 16.2978i 0.189123 + 0.657193i
\(616\) −35.5025 + 19.3408i −1.43043 + 0.779261i
\(617\) −34.0805 + 19.6764i −1.37203 + 0.792141i −0.991183 0.132499i \(-0.957700\pi\)
−0.380844 + 0.924639i \(0.624367\pi\)
\(618\) 5.14057 + 17.8632i 0.206784 + 0.718564i
\(619\) 6.16025i 0.247601i −0.992307 0.123801i \(-0.960492\pi\)
0.992307 0.123801i \(-0.0395084\pi\)
\(620\) 6.29352 3.63357i 0.252754 0.145927i
\(621\) 9.55057 10.6680i 0.383251 0.428092i
\(622\) 10.6772i 0.428115i
\(623\) −0.559453 + 22.5740i −0.0224140 + 0.904408i
\(624\) 0.324052 + 0.312338i 0.0129724 + 0.0125035i
\(625\) 1.00000 0.0400000
\(626\) −13.1817 + 22.8314i −0.526848 + 0.912527i
\(627\) 20.4460 21.2128i 0.816537 0.847158i
\(628\) −5.83250 + 3.36740i −0.232742 + 0.134374i
\(629\) 7.13073 0.284321
\(630\) 6.34306 3.76463i 0.252714 0.149986i
\(631\) 22.3970 0.891610 0.445805 0.895130i \(-0.352917\pi\)
0.445805 + 0.895130i \(0.352917\pi\)
\(632\) 32.7305 18.8970i 1.30195 0.751682i
\(633\) 9.59518 + 33.3427i 0.381374 + 1.32525i
\(634\) 6.32893 10.9620i 0.251354 0.435358i
\(635\) 12.6328 0.501316
\(636\) −4.81979 + 19.4097i −0.191117 + 0.769644i
\(637\) 0.206753 4.16869i 0.00819184 0.165170i
\(638\) 19.9083i 0.788179i
\(639\) 16.3608 30.9118i 0.647222 1.22285i
\(640\) −4.63690 + 2.67711i −0.183289 + 0.105822i
\(641\) 44.4010i 1.75374i 0.480732 + 0.876868i \(0.340371\pi\)
−0.480732 + 0.876868i \(0.659629\pi\)
\(642\) 1.57956 + 0.392234i 0.0623402 + 0.0154802i
\(643\) 3.06913 1.77196i 0.121035 0.0698794i −0.438260 0.898848i \(-0.644405\pi\)
0.559295 + 0.828969i \(0.311072\pi\)
\(644\) −8.28251 0.205266i −0.326377 0.00808861i
\(645\) 1.45210 1.50656i 0.0571764 0.0593206i
\(646\) 5.43934 + 9.42122i 0.214008 + 0.370673i
\(647\) −10.3018 17.8432i −0.405005 0.701489i 0.589317 0.807902i \(-0.299397\pi\)
−0.994322 + 0.106413i \(0.966063\pi\)
\(648\) 21.6913 14.7513i 0.852116 0.579485i
\(649\) 6.03101 + 3.48201i 0.236738 + 0.136681i
\(650\) −0.277052 + 0.479869i −0.0108669 + 0.0188220i
\(651\) 28.2575 + 7.76497i 1.10750 + 0.304333i
\(652\) −8.23041 14.2555i −0.322328 0.558288i
\(653\) 42.7103i 1.67138i 0.549200 + 0.835691i \(0.314933\pi\)
−0.549200 + 0.835691i \(0.685067\pi\)
\(654\) −7.26415 7.00158i −0.284051 0.273783i
\(655\) 4.98386 0.194736
\(656\) −2.13355 + 3.69541i −0.0833011 + 0.144282i
\(657\) 42.2805 1.55695i 1.64952 0.0607422i
\(658\) −14.0884 0.349153i −0.549222 0.0136114i
\(659\) −25.4695 14.7048i −0.992152 0.572819i −0.0862351 0.996275i \(-0.527484\pi\)
−0.905917 + 0.423456i \(0.860817\pi\)
\(660\) −7.42982 7.16125i −0.289205 0.278751i
\(661\) −6.66816 3.84986i −0.259361 0.149742i 0.364682 0.931132i \(-0.381178\pi\)
−0.624043 + 0.781390i \(0.714511\pi\)
\(662\) −18.5306 10.6987i −0.720213 0.415815i
\(663\) 2.68285 + 2.58588i 0.104193 + 0.100427i
\(664\) −27.2936 15.7580i −1.05920 0.611527i
\(665\) 8.58157 + 0.212678i 0.332779 + 0.00824728i
\(666\) −2.57749 + 4.86986i −0.0998756 + 0.188703i
\(667\) 5.63002 9.75148i 0.217995 0.377579i
\(668\) −13.9829 −0.541013
\(669\) −19.5563 18.8494i −0.756090 0.728760i
\(670\) 8.61050i 0.332653i
\(671\) −26.3885 45.7062i −1.01872 1.76447i
\(672\) −23.9689 6.58649i −0.924621 0.254079i
\(673\) −15.3084 + 26.5148i −0.590094 + 1.02207i 0.404126 + 0.914703i \(0.367576\pi\)
−0.994219 + 0.107369i \(0.965757\pi\)
\(674\) −8.30161 4.79294i −0.319766 0.184617i
\(675\) 3.87139 + 3.46588i 0.149010 + 0.133402i
\(676\) −7.18459 12.4441i −0.276330 0.478618i
\(677\) −14.3069 24.7802i −0.549857 0.952381i −0.998284 0.0585609i \(-0.981349\pi\)
0.448427 0.893820i \(-0.351985\pi\)
\(678\) 14.9547 15.5155i 0.574331 0.595869i
\(679\) 34.3761 + 0.851946i 1.31924 + 0.0326947i
\(680\) 9.10725 5.25807i 0.349247 0.201638i
\(681\) −7.21814 1.79240i −0.276600 0.0686849i
\(682\) 31.1561i 1.19303i
\(683\) 12.4676 7.19817i 0.477059 0.275430i −0.242131 0.970244i \(-0.577846\pi\)
0.719190 + 0.694813i \(0.244513\pi\)
\(684\) 11.0537 0.407045i 0.422650 0.0155638i
\(685\) 12.1794i 0.465349i
\(686\) −7.47475 15.5030i −0.285387 0.591907i
\(687\) 3.51587 14.1587i 0.134139 0.540188i
\(688\) 0.526476 0.0200717
\(689\) 3.02918 5.24670i 0.115403 0.199883i
\(690\) 1.22661 + 4.26242i 0.0466964 + 0.162267i
\(691\) 8.95724 5.17146i 0.340749 0.196732i −0.319854 0.947467i \(-0.603634\pi\)
0.660603 + 0.750735i \(0.270301\pi\)
\(692\) 2.55718 0.0972096
\(693\) −0.500571 41.6096i −0.0190151 1.58062i
\(694\) −23.2742 −0.883475
\(695\) −14.5703 + 8.41218i −0.552684 + 0.319092i
\(696\) 14.3158 14.8527i 0.542640 0.562990i
\(697\) −17.6638 + 30.5947i −0.669066 + 1.15886i
\(698\) 2.60016 0.0984173
\(699\) −18.8364 18.1555i −0.712457 0.686704i
\(700\) 0.0744906 3.00571i 0.00281548 0.113605i
\(701\) 13.7649i 0.519894i 0.965623 + 0.259947i \(0.0837052\pi\)
−0.965623 + 0.259947i \(0.916295\pi\)
\(702\) −2.73574 + 0.897530i −0.103254 + 0.0338751i
\(703\) −5.55325 + 3.20617i −0.209445 + 0.120923i
\(704\) 30.9971i 1.16825i
\(705\) −2.74552 9.54052i −0.103402 0.359317i
\(706\) 0.633886 0.365974i 0.0238566 0.0137736i
\(707\) −9.64326 + 5.25338i −0.362672 + 0.197574i
\(708\) 0.723056 + 2.51258i 0.0271741 + 0.0944285i
\(709\) −17.6097 30.5008i −0.661345 1.14548i −0.980262 0.197701i \(-0.936653\pi\)
0.318917 0.947783i \(-0.396681\pi\)
\(710\) 5.41697 + 9.38246i 0.203295 + 0.352117i
\(711\) 1.43151 + 38.8742i 0.0536859 + 1.45790i
\(712\) −21.5433 12.4380i −0.807368 0.466134i
\(713\) −8.81085 + 15.2608i −0.329969 + 0.571523i
\(714\) 14.8159 + 4.07130i 0.554470 + 0.152364i
\(715\) 1.56300 + 2.70720i 0.0584529 + 0.101243i
\(716\) 14.9957i 0.560414i
\(717\) −14.8550 + 4.27488i −0.554769 + 0.159648i
\(718\) −3.37699 −0.126028
\(719\) −4.86513 + 8.42665i −0.181439 + 0.314261i −0.942371 0.334571i \(-0.891409\pi\)
0.760932 + 0.648832i \(0.224742\pi\)
\(720\) 0.0481112 + 1.30651i 0.00179300 + 0.0486908i
\(721\) 14.6168 + 26.8309i 0.544356 + 0.999236i
\(722\) 6.81910 + 3.93701i 0.253781 + 0.146520i
\(723\) 12.7287 51.2597i 0.473387 1.90637i
\(724\) 6.63937 + 3.83324i 0.246750 + 0.142461i
\(725\) 3.53879 + 2.04312i 0.131427 + 0.0758797i
\(726\) 25.5006 7.33842i 0.946416 0.272354i
\(727\) 25.3316 + 14.6252i 0.939495 + 0.542418i 0.889802 0.456347i \(-0.150842\pi\)
0.0496933 + 0.998765i \(0.484176\pi\)
\(728\) 3.92383 + 2.39697i 0.145427 + 0.0888375i
\(729\) 2.97536 + 26.8356i 0.110199 + 0.993910i
\(730\) −6.55299 + 11.3501i −0.242537 + 0.420086i
\(731\) 4.35874 0.161214
\(732\) 4.77527 19.2304i 0.176499 0.710777i
\(733\) 7.11527i 0.262809i −0.991329 0.131404i \(-0.958051\pi\)
0.991329 0.131404i \(-0.0419486\pi\)
\(734\) −5.79078 10.0299i −0.213741 0.370211i
\(735\) 8.83609 8.30202i 0.325924 0.306225i
\(736\) 7.47363 12.9447i 0.275482 0.477148i
\(737\) 42.0685 + 24.2882i 1.54961 + 0.894669i
\(738\) −14.5095 23.1221i −0.534102 0.851137i
\(739\) 5.44572 + 9.43227i 0.200324 + 0.346972i 0.948633 0.316379i \(-0.102467\pi\)
−0.748309 + 0.663351i \(0.769134\pi\)
\(740\) 1.12297 + 1.94503i 0.0412810 + 0.0715008i
\(741\) −3.25202 0.807538i −0.119466 0.0296657i
\(742\) 0.618938 24.9742i 0.0227219 0.916833i
\(743\) −43.0548 + 24.8577i −1.57953 + 0.911941i −0.584604 + 0.811319i \(0.698750\pi\)
−0.994925 + 0.100623i \(0.967917\pi\)
\(744\) −22.4039 + 23.2441i −0.821367 + 0.852170i
\(745\) 4.74043i 0.173676i
\(746\) −8.26219 + 4.77018i −0.302500 + 0.174649i
\(747\) 27.4768 17.2422i 1.00533 0.630857i
\(748\) 21.4958i 0.785965i
\(749\) 2.67441 + 0.0662800i 0.0977207 + 0.00242182i
\(750\) −1.54682 + 0.445136i −0.0564819 + 0.0162541i
\(751\) 12.2123 0.445634 0.222817 0.974860i \(-0.428475\pi\)
0.222817 + 0.974860i \(0.428475\pi\)
\(752\) 1.24895 2.16324i 0.0455445 0.0788853i
\(753\) −16.4069 4.07413i −0.597899 0.148470i
\(754\) −1.96086 + 1.13210i −0.0714103 + 0.0412288i
\(755\) −17.8242 −0.648690
\(756\) 10.7058 11.3781i 0.389366 0.413817i
\(757\) −27.4472 −0.997587 −0.498794 0.866721i \(-0.666223\pi\)
−0.498794 + 0.866721i \(0.666223\pi\)
\(758\) 17.0566 9.84764i 0.619524 0.357683i
\(759\) 24.2850 + 6.03041i 0.881488 + 0.218890i
\(760\) −4.72834 + 8.18973i −0.171515 + 0.297073i
\(761\) 6.07967 0.220388 0.110194 0.993910i \(-0.464853\pi\)
0.110194 + 0.993910i \(0.464853\pi\)
\(762\) −19.5406 + 5.62329i −0.707882 + 0.203710i
\(763\) −14.1522 8.64519i −0.512343 0.312977i
\(764\) 11.1607i 0.403780i
\(765\) 0.398317 + 10.8167i 0.0144012 + 0.391079i
\(766\) 5.61173 3.23994i 0.202760 0.117064i
\(767\) 0.792028i 0.0285985i
\(768\) 20.1943 20.9516i 0.728697 0.756025i
\(769\) 14.1929 8.19430i 0.511811 0.295494i −0.221767 0.975100i \(-0.571182\pi\)
0.733578 + 0.679606i \(0.237849\pi\)
\(770\) 11.0001 + 6.71970i 0.396417 + 0.242161i
\(771\) −17.5161 4.34958i −0.630828 0.156646i
\(772\) −5.32117 9.21653i −0.191513 0.331710i
\(773\) −8.90571 15.4251i −0.320316 0.554804i 0.660237 0.751057i \(-0.270456\pi\)
−0.980553 + 0.196253i \(0.937123\pi\)
\(774\) −1.57552 + 2.97676i −0.0566308 + 0.106997i
\(775\) −5.53812 3.19744i −0.198935 0.114855i
\(776\) −18.9408 + 32.8065i −0.679937 + 1.17769i
\(777\) −2.39979 + 8.73309i −0.0860920 + 0.313298i
\(778\) 8.82169 + 15.2796i 0.316273 + 0.547801i
\(779\) 31.7686i 1.13823i
\(780\) −0.282841 + 1.13903i −0.0101273 + 0.0407837i
\(781\) 61.1201 2.18705
\(782\) −4.61967 + 8.00150i −0.165199 + 0.286133i
\(783\) 6.61884 + 20.1748i 0.236538 + 0.720987i
\(784\) 3.04685 + 0.151113i 0.108816 + 0.00539690i
\(785\) 5.13244 + 2.96322i 0.183185 + 0.105762i
\(786\) −7.70915 + 2.21849i −0.274976 + 0.0791311i
\(787\) 41.1137 + 23.7370i 1.46555 + 0.846133i 0.999259 0.0385008i \(-0.0122582\pi\)
0.466287 + 0.884634i \(0.345592\pi\)
\(788\) −4.24851 2.45288i −0.151347 0.0873802i
\(789\) 9.66110 38.9061i 0.343944 1.38509i
\(790\) −10.4357 6.02506i −0.371286 0.214362i
\(791\) 18.4653 30.2276i 0.656549 1.07477i
\(792\) 40.5169 + 21.4445i 1.43971 + 0.761998i
\(793\) −3.00120 + 5.19824i −0.106576 + 0.184595i
\(794\) 22.0192 0.781432
\(795\) 16.9123 4.86694i 0.599819 0.172612i
\(796\) 19.4980i 0.691089i
\(797\) −8.92350 15.4560i −0.316087 0.547478i 0.663581 0.748104i \(-0.269036\pi\)
−0.979668 + 0.200626i \(0.935702\pi\)
\(798\) −13.3688 + 3.49099i −0.473251 + 0.123580i
\(799\) 10.3402 17.9097i 0.365809 0.633599i
\(800\) 4.69761 + 2.71217i 0.166086 + 0.0958895i
\(801\) 21.6879 13.6095i 0.766305 0.480868i
\(802\) 12.6304 + 21.8764i 0.445993 + 0.772483i
\(803\) 36.9689 + 64.0321i 1.30461 + 2.25964i
\(804\) 5.04358 + 17.5262i 0.177873 + 0.618100i
\(805\) 3.48776 + 6.40224i 0.122928 + 0.225649i
\(806\) 3.06870 1.77171i 0.108090 0.0624060i
\(807\) 14.9867 + 52.0780i 0.527557 + 1.83323i
\(808\) 12.0975i 0.425588i
\(809\) 4.88185 2.81854i 0.171637 0.0990944i −0.411721 0.911310i \(-0.635072\pi\)
0.583357 + 0.812216i \(0.301739\pi\)
\(810\) −7.53114 3.63780i −0.264617 0.127819i
\(811\) 20.3541i 0.714729i 0.933965 + 0.357364i \(0.116325\pi\)
−0.933965 + 0.357364i \(0.883675\pi\)
\(812\) 6.40463 10.4844i 0.224759 0.367930i
\(813\) −23.0609 22.2274i −0.808782 0.779548i
\(814\) −9.62889 −0.337492
\(815\) −7.24254 + 12.5444i −0.253695 + 0.439413i
\(816\) −1.88999 + 1.96086i −0.0661628 + 0.0686440i
\(817\) −3.39449 + 1.95981i −0.118758 + 0.0685650i
\(818\) −3.22027 −0.112594
\(819\) −4.06984 + 2.41546i −0.142212 + 0.0844031i
\(820\) −11.1270 −0.388571
\(821\) 5.05686 2.91958i 0.176486 0.101894i −0.409155 0.912465i \(-0.634176\pi\)
0.585640 + 0.810571i \(0.300843\pi\)
\(822\) −5.42147 18.8393i −0.189095 0.657096i
\(823\) −23.5677 + 40.8205i −0.821518 + 1.42291i 0.0830328 + 0.996547i \(0.473539\pi\)
−0.904551 + 0.426365i \(0.859794\pi\)
\(824\) −33.6595 −1.17258
\(825\) −2.18842 + 8.81296i −0.0761911 + 0.306828i
\(826\) −1.56240 2.86799i −0.0543630 0.0997903i
\(827\) 35.6635i 1.24014i −0.784546 0.620070i \(-0.787104\pi\)
0.784546 0.620070i \(-0.212896\pi\)
\(828\) 4.99339 + 7.95740i 0.173532 + 0.276539i
\(829\) 0.0501046 0.0289279i 0.00174020 0.00100471i −0.499130 0.866527i \(-0.666347\pi\)
0.500870 + 0.865523i \(0.333014\pi\)
\(830\) 10.0484i 0.348786i
\(831\) −29.3627 7.29131i −1.01858 0.252933i
\(832\) −3.05304 + 1.76267i −0.105845 + 0.0611097i
\(833\) 25.2251 + 1.25108i 0.873999 + 0.0433473i
\(834\) 18.7931 19.4979i 0.650753 0.675157i
\(835\) 6.15227 + 10.6560i 0.212908 + 0.368768i
\(836\) 9.66510 + 16.7404i 0.334274 + 0.578980i
\(837\) −10.3583 31.5730i −0.358036 1.09132i
\(838\) 0.960897 + 0.554774i 0.0331936 + 0.0191644i
\(839\) 5.35115 9.26846i 0.184742 0.319983i −0.758747 0.651385i \(-0.774188\pi\)
0.943490 + 0.331402i \(0.107522\pi\)
\(840\) 3.37465 + 12.9233i 0.116436 + 0.445896i
\(841\) −6.15130 10.6544i −0.212114 0.367392i
\(842\) 28.4829i 0.981585i
\(843\) 25.5997 + 24.6744i 0.881701 + 0.849830i
\(844\) −22.7640 −0.783569
\(845\) −6.32224 + 10.9504i −0.217492 + 0.376706i
\(846\) 8.49365 + 13.5354i 0.292018 + 0.465355i
\(847\) 38.3024 20.8661i 1.31609 0.716968i
\(848\) 3.83475 + 2.21399i 0.131686 + 0.0760288i
\(849\) −28.5324 27.5011i −0.979229 0.943834i
\(850\) −2.90373 1.67647i −0.0995970 0.0575024i
\(851\) −4.71641 2.72302i −0.161677 0.0933440i
\(852\) 16.5216 + 15.9244i 0.566022 + 0.545563i
\(853\) −26.8003 15.4732i −0.917625 0.529791i −0.0347485 0.999396i \(-0.511063\pi\)
−0.882877 + 0.469605i \(0.844396\pi\)
\(854\) −0.613221 + 24.7436i −0.0209840 + 0.846708i
\(855\) −5.17369 8.24472i −0.176937 0.281963i
\(856\) −1.47357 + 2.55229i −0.0503654 + 0.0872355i
\(857\) −35.7192 −1.22014 −0.610072 0.792346i \(-0.708859\pi\)
−0.610072 + 0.792346i \(0.708859\pi\)
\(858\) −3.62275 3.49180i −0.123679 0.119208i
\(859\) 0.664661i 0.0226779i 0.999936 + 0.0113390i \(0.00360938\pi\)
−0.999936 + 0.0113390i \(0.996391\pi\)
\(860\) 0.686426 + 1.18892i 0.0234069 + 0.0405420i
\(861\) −31.5250 31.9295i −1.07437 1.08815i
\(862\) 11.3887 19.7258i 0.387900 0.671863i
\(863\) −1.34228 0.774964i −0.0456916 0.0263801i 0.476980 0.878914i \(-0.341731\pi\)
−0.522672 + 0.852534i \(0.675065\pi\)
\(864\) 8.78625 + 26.7812i 0.298914 + 0.911115i
\(865\) −1.12513 1.94878i −0.0382554 0.0662604i
\(866\) −10.1278 17.5419i −0.344157 0.596097i
\(867\) 4.78660 4.96611i 0.162562 0.168658i
\(868\) −10.0231 + 16.4078i −0.340206 + 0.556917i
\(869\) −58.8734 + 33.9906i −1.99714 + 1.15305i
\(870\) −6.38335 1.58510i −0.216416 0.0537401i
\(871\) 5.52468i 0.187197i
\(872\) 15.8217 9.13468i 0.535791 0.309339i
\(873\) −20.7248 33.0268i −0.701429 1.11779i
\(874\) 8.30851i 0.281040i
\(875\) −2.32336 + 1.26570i −0.0785439 + 0.0427885i
\(876\) −6.68991 + 26.9408i −0.226031 + 0.910247i
\(877\) 7.17466 0.242271 0.121136 0.992636i \(-0.461346\pi\)
0.121136 + 0.992636i \(0.461346\pi\)
\(878\) −0.355557 + 0.615842i −0.0119995 + 0.0207837i
\(879\) −6.58818 22.8936i −0.222214 0.772181i
\(880\) −1.97866 + 1.14238i −0.0667006 + 0.0385096i
\(881\) −28.8710 −0.972690 −0.486345 0.873767i \(-0.661670\pi\)
−0.486345 + 0.873767i \(0.661670\pi\)
\(882\) −9.97232 + 16.7750i −0.335786 + 0.564844i
\(883\) 19.1653 0.644964 0.322482 0.946576i \(-0.395483\pi\)
0.322482 + 0.946576i \(0.395483\pi\)
\(884\) −2.11722 + 1.22238i −0.0712097 + 0.0411130i
\(885\) 1.59665 1.65653i 0.0536708 0.0556835i
\(886\) −0.256508 + 0.444286i −0.00861757 + 0.0149261i
\(887\) −27.8814 −0.936165 −0.468083 0.883685i \(-0.655055\pi\)
−0.468083 + 0.883685i \(0.655055\pi\)
\(888\) −7.18367 6.92401i −0.241068 0.232354i
\(889\) −29.3505 + 15.9893i −0.984383 + 0.536264i
\(890\) 7.93139i 0.265861i
\(891\) −39.0169 + 26.5336i −1.30711 + 0.888909i
\(892\) 15.4332 8.91035i 0.516741 0.298340i
\(893\) 18.5969i 0.622320i
\(894\) 2.11013 + 7.33259i 0.0705734 + 0.245239i
\(895\) −11.4279 + 6.59789i −0.381992 + 0.220543i
\(896\) 7.38475 12.0888i 0.246707 0.403859i
\(897\) −0.787021 2.73486i −0.0262779 0.0913142i
\(898\) −17.6910 30.6417i −0.590357 1.02253i
\(899\) −13.0655 22.6301i −0.435759 0.754757i
\(900\) −2.88772 + 1.81209i −0.0962575 + 0.0604031i
\(901\) 31.7482 + 18.3298i 1.05769 + 0.610656i
\(902\) 23.8521 41.3131i 0.794189 1.37558i
\(903\) −1.46690 + 5.33820i −0.0488153 + 0.177644i
\(904\) 19.5108 + 33.7936i 0.648918 + 1.12396i
\(905\) 6.74629i 0.224254i
\(906\) 27.5709 7.93419i 0.915981 0.263596i
\(907\) −11.8171 −0.392380 −0.196190 0.980566i \(-0.562857\pi\)
−0.196190 + 0.980566i \(0.562857\pi\)
\(908\) 2.43982 4.22590i 0.0809684 0.140241i
\(909\) 11.0053 + 5.82481i 0.365023 + 0.193197i
\(910\) 0.0363214 1.46557i 0.00120404 0.0485833i
\(911\) −8.86875 5.12037i −0.293835 0.169646i 0.345835 0.938295i \(-0.387596\pi\)
−0.639670 + 0.768650i \(0.720929\pi\)
\(912\) 0.590220 2.37687i 0.0195441 0.0787059i
\(913\) 49.0938 + 28.3443i 1.62477 + 0.938061i
\(914\) 24.5811 + 14.1919i 0.813071 + 0.469427i
\(915\) −16.7561 + 4.82199i −0.553941 + 0.159410i
\(916\) 8.28929 + 4.78582i 0.273886 + 0.158128i
\(917\) −11.5793 + 6.30808i −0.382382 + 0.208311i
\(918\) −5.43103 16.5542i −0.179251 0.546371i
\(919\) −7.52608 + 13.0355i −0.248262 + 0.430003i −0.963044 0.269345i \(-0.913193\pi\)
0.714781 + 0.699348i \(0.246526\pi\)
\(920\) −8.03163 −0.264795
\(921\) −9.07945 + 36.5637i −0.299178 + 1.20482i
\(922\) 30.0584i 0.989921i
\(923\) −3.47564 6.01998i −0.114402 0.198150i
\(924\) 26.3261 + 7.23424i 0.866067 + 0.237989i
\(925\) 0.988179 1.71158i 0.0324911 0.0562763i
\(926\) 0.0383481 + 0.0221403i 0.00126020 + 0.000727575i
\(927\) 16.2067 30.6206i 0.532297 1.00571i
\(928\) 11.0826 + 19.1956i 0.363803 + 0.630126i
\(929\) −1.58065 2.73777i −0.0518596 0.0898235i 0.838930 0.544239i \(-0.183181\pi\)
−0.890790 + 0.454415i \(0.849848\pi\)
\(930\) 9.98978 + 2.48065i 0.327578 + 0.0813437i
\(931\) −20.2073 + 10.3676i −0.662266 + 0.339784i
\(932\) 14.8650 8.58233i 0.486920 0.281124i
\(933\) −13.8103 + 14.3282i −0.452129 + 0.469085i
\(934\) 16.5871i 0.542746i
\(935\) −16.3815 + 9.45786i −0.535732 + 0.309305i
\(936\) −0.191860 5.21015i −0.00627113 0.170299i
\(937\) 25.7818i 0.842255i 0.907001 + 0.421128i \(0.138366\pi\)
−0.907001 + 0.421128i \(0.861634\pi\)
\(938\) −10.8983 20.0053i −0.355843 0.653196i
\(939\) 47.2204 13.5888i 1.54098 0.443454i
\(940\) 6.51357 0.212449
\(941\) −26.9751 + 46.7222i −0.879362 + 1.52310i −0.0273203 + 0.999627i \(0.508697\pi\)
−0.852042 + 0.523473i \(0.824636\pi\)
\(942\) −9.25800 2.29893i −0.301642 0.0749033i
\(943\) 23.3665 13.4906i 0.760916 0.439315i
\(944\) 0.578884 0.0188411
\(945\) −13.3814 3.15245i −0.435297 0.102549i
\(946\) −5.88577 −0.191363
\(947\) 5.26239 3.03824i 0.171005 0.0987296i −0.412055 0.911159i \(-0.635189\pi\)
0.583059 + 0.812429i \(0.301855\pi\)
\(948\) −24.7704 6.15095i −0.804505 0.199774i
\(949\) 4.20454 7.28247i 0.136485 0.236399i
\(950\) 3.01514 0.0978241
\(951\) −22.6719 + 6.52438i −0.735186 + 0.211568i
\(952\) −14.5043 + 23.7435i −0.470086 + 0.769530i
\(953\) 32.7280i 1.06016i 0.847947 + 0.530082i \(0.177839\pi\)
−0.847947 + 0.530082i \(0.822161\pi\)
\(954\) −23.9939 + 15.0566i −0.776832 + 0.487474i
\(955\) 8.50532 4.91055i 0.275226 0.158902i
\(956\) 10.1419i 0.328012i
\(957\) −25.7503 + 26.7160i −0.832390 + 0.863606i
\(958\) 0.654657 0.377966i 0.0211510 0.0122115i
\(959\) −15.4154 28.2970i −0.497791 0.913759i
\(960\) −9.93880 2.46799i −0.320773 0.0796540i
\(961\) 4.94722 + 8.56883i 0.159588 + 0.276414i
\(962\) 0.547554 + 0.948392i 0.0176539 + 0.0305774i
\(963\) −1.61236 2.56943i −0.0519575 0.0827987i
\(964\) 30.0103 + 17.3264i 0.966566 + 0.558047i
\(965\) −4.68248 + 8.11029i −0.150734 + 0.261080i
\(966\) −8.24481 8.35060i −0.265273 0.268676i
\(967\) −10.6606 18.4646i −0.342821 0.593783i 0.642135 0.766592i \(-0.278049\pi\)
−0.984955 + 0.172809i \(0.944716\pi\)
\(968\) 48.0505i 1.54440i
\(969\) 4.88649 19.6783i 0.156977 0.632158i
\(970\) 12.0781 0.387804
\(971\) 0.486914 0.843360i 0.0156258 0.0270647i −0.858107 0.513471i \(-0.828359\pi\)
0.873733 + 0.486407i \(0.161693\pi\)
\(972\) −17.4600 2.99318i −0.560030 0.0960064i
\(973\) 23.2048 37.9862i 0.743911 1.21778i
\(974\) 2.09621 + 1.21025i 0.0671669 + 0.0387788i
\(975\) 0.992473 0.285608i 0.0317846 0.00914679i
\(976\) −3.79933 2.19354i −0.121614 0.0702136i
\(977\) −18.6445 10.7644i −0.596490 0.344383i 0.171170 0.985242i \(-0.445245\pi\)
−0.767659 + 0.640858i \(0.778579\pi\)
\(978\) 5.61894 22.6279i 0.179674 0.723561i
\(979\) 38.7505 + 22.3726i 1.23847 + 0.715033i
\(980\) 3.63126 + 7.07762i 0.115996 + 0.226086i
\(981\) 0.691984 + 18.7915i 0.0220933 + 0.599968i
\(982\) −7.97658 + 13.8158i −0.254543 + 0.440881i
\(983\) 8.07739 0.257629 0.128814 0.991669i \(-0.458883\pi\)
0.128814 + 0.991669i \(0.458883\pi\)
\(984\) 47.5027 13.6701i 1.51433 0.435785i
\(985\) 4.31693i 0.137549i
\(986\) −6.85046 11.8653i −0.218163 0.377870i
\(987\) 18.4543 + 18.6911i 0.587406 + 0.594943i
\(988\) 1.09923 1.90392i 0.0349711 0.0605716i
\(989\) −2.88296 1.66448i −0.0916729 0.0529273i
\(990\) −0.537863 14.6062i −0.0170944 0.464216i
\(991\) 19.8268 + 34.3411i 0.629820 + 1.09088i 0.987587 + 0.157070i \(0.0502049\pi\)
−0.357767 + 0.933811i \(0.616462\pi\)
\(992\) −17.3440 30.0406i −0.550671 0.953791i
\(993\) 11.0291 + 38.3254i 0.349997 + 1.21622i
\(994\) −24.4610 14.9426i −0.775854 0.473949i
\(995\) 14.8590 8.57887i 0.471063 0.271968i
\(996\) 5.88584 + 20.4530i 0.186500 + 0.648078i
\(997\) 21.9609i 0.695509i −0.937586 0.347755i \(-0.886944\pi\)
0.937586 0.347755i \(-0.113056\pi\)
\(998\) 2.88307 1.66454i 0.0912619 0.0526901i
\(999\) 9.75774 3.20127i 0.308721 0.101284i
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 315.2.be.b.236.6 yes 30
3.2 odd 2 945.2.be.b.656.10 30
7.3 odd 6 315.2.t.b.101.6 30
9.4 even 3 945.2.t.b.341.6 30
9.5 odd 6 315.2.t.b.131.10 yes 30
21.17 even 6 945.2.t.b.521.10 30
63.31 odd 6 945.2.be.b.206.10 30
63.59 even 6 inner 315.2.be.b.311.6 yes 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.2.t.b.101.6 30 7.3 odd 6
315.2.t.b.131.10 yes 30 9.5 odd 6
315.2.be.b.236.6 yes 30 1.1 even 1 trivial
315.2.be.b.311.6 yes 30 63.59 even 6 inner
945.2.t.b.341.6 30 9.4 even 3
945.2.t.b.521.10 30 21.17 even 6
945.2.be.b.206.10 30 63.31 odd 6
945.2.be.b.656.10 30 3.2 odd 2