Properties

Label 150.3.j.a.11.1
Level $150$
Weight $3$
Character 150.11
Analytic conductor $4.087$
Analytic rank $0$
Dimension $80$
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] = [150,3,Mod(11,150)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(150, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 8]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("150.11");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 150.j (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.08720396540\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(20\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 11.1
Character \(\chi\) \(=\) 150.11
Dual form 150.3.j.a.41.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.831254 - 1.14412i) q^{2} +(-2.89929 + 0.770808i) q^{3} +(-0.618034 + 1.90211i) q^{4} +(4.91294 - 0.928983i) q^{5} +(3.29194 + 2.67640i) q^{6} -5.64982 q^{7} +(2.68999 - 0.874032i) q^{8} +(7.81171 - 4.46959i) q^{9} +O(q^{10})\) \(q+(-0.831254 - 1.14412i) q^{2} +(-2.89929 + 0.770808i) q^{3} +(-0.618034 + 1.90211i) q^{4} +(4.91294 - 0.928983i) q^{5} +(3.29194 + 2.67640i) q^{6} -5.64982 q^{7} +(2.68999 - 0.874032i) q^{8} +(7.81171 - 4.46959i) q^{9} +(-5.14677 - 4.84879i) q^{10} +(-9.35064 - 12.8700i) q^{11} +(0.325692 - 5.99115i) q^{12} +(-1.90792 - 1.38619i) q^{13} +(4.69644 + 6.46409i) q^{14} +(-13.5279 + 6.48032i) q^{15} +(-3.23607 - 2.35114i) q^{16} +(-27.0787 + 8.79841i) q^{17} +(-11.6073 - 5.22219i) q^{18} +(-4.36382 - 13.4305i) q^{19} +(-1.26933 + 9.91911i) q^{20} +(16.3804 - 4.35493i) q^{21} +(-6.95216 + 21.3966i) q^{22} +(-26.2815 - 36.1733i) q^{23} +(-7.12535 + 4.60754i) q^{24} +(23.2740 - 9.12808i) q^{25} +3.33517i q^{26} +(-19.2032 + 18.9799i) q^{27} +(3.49178 - 10.7466i) q^{28} +(21.0526 + 6.84041i) q^{29} +(18.6594 + 10.0908i) q^{30} +(-2.10324 - 6.47312i) q^{31} +5.65685i q^{32} +(37.0305 + 30.1064i) q^{33} +(32.5758 + 23.6677i) q^{34} +(-27.7573 + 5.24859i) q^{35} +(3.67376 + 17.6211i) q^{36} +(-12.0598 - 8.76194i) q^{37} +(-11.7387 + 16.1569i) q^{38} +(6.60010 + 2.54831i) q^{39} +(12.4038 - 6.79303i) q^{40} +(12.0302 - 16.5581i) q^{41} +(-18.5989 - 15.1212i) q^{42} +76.3844 q^{43} +(30.2593 - 9.83184i) q^{44} +(34.2263 - 29.2158i) q^{45} +(-19.5402 + 60.1384i) q^{46} +(25.6756 + 8.34249i) q^{47} +(11.1946 + 4.32224i) q^{48} -17.0795 q^{49} +(-29.7902 - 19.0405i) q^{50} +(71.7271 - 46.3816i) q^{51} +(3.81584 - 2.77237i) q^{52} +(-56.9921 - 18.5179i) q^{53} +(37.6781 + 6.19365i) q^{54} +(-57.8952 - 54.5432i) q^{55} +(-15.1980 + 4.93813i) q^{56} +(23.0043 + 35.5751i) q^{57} +(-9.67381 - 29.7729i) q^{58} +(-51.1291 + 70.3732i) q^{59} +(-3.96557 - 29.7367i) q^{60} +(7.99848 - 5.81124i) q^{61} +(-5.65771 + 7.78717i) q^{62} +(-44.1348 + 25.2524i) q^{63} +(6.47214 - 4.70228i) q^{64} +(-10.6613 - 5.03783i) q^{65} +(3.66366 - 67.3935i) q^{66} +(0.784981 + 2.41592i) q^{67} -56.9445i q^{68} +(104.080 + 84.6188i) q^{69} +(29.0784 + 27.3948i) q^{70} +(81.3782 + 26.4414i) q^{71} +(17.1069 - 18.8508i) q^{72} +(11.3556 - 8.25034i) q^{73} +21.0813i q^{74} +(-60.4419 + 44.4047i) q^{75} +28.2432 q^{76} +(52.8294 + 72.7135i) q^{77} +(-2.57078 - 9.66961i) q^{78} +(-20.8939 + 64.3048i) q^{79} +(-18.0828 - 8.54476i) q^{80} +(41.0456 - 69.8302i) q^{81} -28.9447 q^{82} +(-45.2531 + 14.7036i) q^{83} +(-1.84010 + 33.8490i) q^{84} +(-124.863 + 68.3818i) q^{85} +(-63.4949 - 87.3932i) q^{86} +(-66.3102 - 3.60477i) q^{87} +(-36.4020 - 26.4476i) q^{88} +(-2.51715 - 3.46456i) q^{89} +(-61.8772 - 14.8734i) q^{90} +(10.7794 + 7.83171i) q^{91} +(85.0486 - 27.6340i) q^{92} +(11.0874 + 17.1462i) q^{93} +(-11.7981 - 36.3107i) q^{94} +(-33.9159 - 61.9292i) q^{95} +(-4.36035 - 16.4008i) q^{96} +(-18.0333 + 55.5008i) q^{97} +(14.1974 + 19.5410i) q^{98} +(-130.568 - 58.7436i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 4 q^{3} + 40 q^{4} - 8 q^{7} + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 80 q - 4 q^{3} + 40 q^{4} - 8 q^{7} + 20 q^{9} - 12 q^{12} + 40 q^{13} - 60 q^{15} - 80 q^{16} - 32 q^{18} + 60 q^{19} + 60 q^{21} - 8 q^{22} - 180 q^{25} + 182 q^{27} - 24 q^{28} + 20 q^{30} - 180 q^{31} + 26 q^{33} - 120 q^{34} - 40 q^{36} + 128 q^{37} + 220 q^{39} + 128 q^{42} - 56 q^{43} - 100 q^{45} - 120 q^{46} + 24 q^{48} + 440 q^{49} - 20 q^{51} - 80 q^{52} - 120 q^{54} - 792 q^{57} - 100 q^{60} + 200 q^{61} - 574 q^{63} + 160 q^{64} - 160 q^{66} - 732 q^{67} - 220 q^{69} + 280 q^{70} + 64 q^{72} - 400 q^{73} + 590 q^{75} + 80 q^{76} - 260 q^{78} + 400 q^{79} + 140 q^{81} + 448 q^{82} + 180 q^{84} - 200 q^{85} + 310 q^{87} - 64 q^{88} + 440 q^{90} + 340 q^{91} + 348 q^{93} + 160 q^{94} - 276 q^{97} + 180 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(-1\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.831254 1.14412i −0.415627 0.572061i
\(3\) −2.89929 + 0.770808i −0.966428 + 0.256936i
\(4\) −0.618034 + 1.90211i −0.154508 + 0.475528i
\(5\) 4.91294 0.928983i 0.982588 0.185797i
\(6\) 3.29194 + 2.67640i 0.548657 + 0.446067i
\(7\) −5.64982 −0.807118 −0.403559 0.914954i \(-0.632227\pi\)
−0.403559 + 0.914954i \(0.632227\pi\)
\(8\) 2.68999 0.874032i 0.336249 0.109254i
\(9\) 7.81171 4.46959i 0.867968 0.496621i
\(10\) −5.14677 4.84879i −0.514677 0.484879i
\(11\) −9.35064 12.8700i −0.850058 1.17000i −0.983850 0.178995i \(-0.942715\pi\)
0.133792 0.991009i \(-0.457285\pi\)
\(12\) 0.325692 5.99115i 0.0271410 0.499263i
\(13\) −1.90792 1.38619i −0.146763 0.106630i 0.511981 0.858997i \(-0.328912\pi\)
−0.658744 + 0.752367i \(0.728912\pi\)
\(14\) 4.69644 + 6.46409i 0.335460 + 0.461721i
\(15\) −13.5279 + 6.48032i −0.901863 + 0.432022i
\(16\) −3.23607 2.35114i −0.202254 0.146946i
\(17\) −27.0787 + 8.79841i −1.59287 + 0.517554i −0.965330 0.261033i \(-0.915937\pi\)
−0.627537 + 0.778587i \(0.715937\pi\)
\(18\) −11.6073 5.22219i −0.644848 0.290122i
\(19\) −4.36382 13.4305i −0.229675 0.706866i −0.997783 0.0665467i \(-0.978802\pi\)
0.768108 0.640320i \(-0.221198\pi\)
\(20\) −1.26933 + 9.91911i −0.0634667 + 0.495956i
\(21\) 16.3804 4.35493i 0.780021 0.207378i
\(22\) −6.95216 + 21.3966i −0.316007 + 0.972571i
\(23\) −26.2815 36.1733i −1.14267 1.57275i −0.761389 0.648295i \(-0.775482\pi\)
−0.381283 0.924458i \(-0.624518\pi\)
\(24\) −7.12535 + 4.60754i −0.296890 + 0.191981i
\(25\) 23.2740 9.12808i 0.930959 0.365123i
\(26\) 3.33517i 0.128276i
\(27\) −19.2032 + 18.9799i −0.711229 + 0.702961i
\(28\) 3.49178 10.7466i 0.124707 0.383807i
\(29\) 21.0526 + 6.84041i 0.725953 + 0.235876i 0.648602 0.761128i \(-0.275354\pi\)
0.0773505 + 0.997004i \(0.475354\pi\)
\(30\) 18.6594 + 10.0908i 0.621982 + 0.336361i
\(31\) −2.10324 6.47312i −0.0678466 0.208810i 0.911385 0.411554i \(-0.135014\pi\)
−0.979232 + 0.202744i \(0.935014\pi\)
\(32\) 5.65685i 0.176777i
\(33\) 37.0305 + 30.1064i 1.12214 + 0.912315i
\(34\) 32.5758 + 23.6677i 0.958111 + 0.696108i
\(35\) −27.7573 + 5.24859i −0.793064 + 0.149960i
\(36\) 3.67376 + 17.6211i 0.102049 + 0.489475i
\(37\) −12.0598 8.76194i −0.325940 0.236809i 0.412766 0.910837i \(-0.364563\pi\)
−0.738706 + 0.674028i \(0.764563\pi\)
\(38\) −11.7387 + 16.1569i −0.308912 + 0.425181i
\(39\) 6.60010 + 2.54831i 0.169233 + 0.0653412i
\(40\) 12.4038 6.79303i 0.310096 0.169826i
\(41\) 12.0302 16.5581i 0.293419 0.403857i −0.636702 0.771110i \(-0.719702\pi\)
0.930121 + 0.367253i \(0.119702\pi\)
\(42\) −18.5989 15.1212i −0.442831 0.360028i
\(43\) 76.3844 1.77638 0.888191 0.459474i \(-0.151962\pi\)
0.888191 + 0.459474i \(0.151962\pi\)
\(44\) 30.2593 9.83184i 0.687711 0.223451i
\(45\) 34.2263 29.2158i 0.760584 0.649239i
\(46\) −19.5402 + 60.1384i −0.424786 + 1.30736i
\(47\) 25.6756 + 8.34249i 0.546288 + 0.177500i 0.569142 0.822239i \(-0.307275\pi\)
−0.0228540 + 0.999739i \(0.507275\pi\)
\(48\) 11.1946 + 4.32224i 0.233220 + 0.0900467i
\(49\) −17.0795 −0.348561
\(50\) −29.7902 19.0405i −0.595805 0.380811i
\(51\) 71.7271 46.3816i 1.40641 0.909444i
\(52\) 3.81584 2.77237i 0.0733816 0.0533149i
\(53\) −56.9921 18.5179i −1.07532 0.349394i −0.282765 0.959189i \(-0.591252\pi\)
−0.792559 + 0.609796i \(0.791252\pi\)
\(54\) 37.6781 + 6.19365i 0.697742 + 0.114697i
\(55\) −57.8952 54.5432i −1.05264 0.991694i
\(56\) −15.1980 + 4.93813i −0.271393 + 0.0881808i
\(57\) 23.0043 + 35.5751i 0.403584 + 0.624124i
\(58\) −9.67381 29.7729i −0.166790 0.513326i
\(59\) −51.1291 + 70.3732i −0.866596 + 1.19277i 0.113361 + 0.993554i \(0.463838\pi\)
−0.979956 + 0.199213i \(0.936162\pi\)
\(60\) −3.96557 29.7367i −0.0660929 0.495612i
\(61\) 7.99848 5.81124i 0.131123 0.0952662i −0.520291 0.853989i \(-0.674176\pi\)
0.651413 + 0.758723i \(0.274176\pi\)
\(62\) −5.65771 + 7.78717i −0.0912534 + 0.125600i
\(63\) −44.1348 + 25.2524i −0.700552 + 0.400831i
\(64\) 6.47214 4.70228i 0.101127 0.0734732i
\(65\) −10.6613 5.03783i −0.164019 0.0775050i
\(66\) 3.66366 67.3935i 0.0555100 1.02111i
\(67\) 0.784981 + 2.41592i 0.0117161 + 0.0360585i 0.956744 0.290932i \(-0.0939654\pi\)
−0.945028 + 0.326991i \(0.893965\pi\)
\(68\) 56.9445i 0.837420i
\(69\) 104.080 + 84.6188i 1.50841 + 1.22636i
\(70\) 29.0784 + 27.3948i 0.415405 + 0.391354i
\(71\) 81.3782 + 26.4414i 1.14617 + 0.372414i 0.819700 0.572793i \(-0.194140\pi\)
0.326472 + 0.945207i \(0.394140\pi\)
\(72\) 17.1069 18.8508i 0.237596 0.261817i
\(73\) 11.3556 8.25034i 0.155556 0.113018i −0.507284 0.861779i \(-0.669351\pi\)
0.662841 + 0.748760i \(0.269351\pi\)
\(74\) 21.0813i 0.284882i
\(75\) −60.4419 + 44.4047i −0.805892 + 0.592062i
\(76\) 28.2432 0.371622
\(77\) 52.8294 + 72.7135i 0.686097 + 0.944331i
\(78\) −2.57078 9.66961i −0.0329587 0.123969i
\(79\) −20.8939 + 64.3048i −0.264480 + 0.813984i 0.727333 + 0.686284i \(0.240759\pi\)
−0.991813 + 0.127700i \(0.959241\pi\)
\(80\) −18.0828 8.54476i −0.226035 0.106810i
\(81\) 41.0456 69.8302i 0.506736 0.862101i
\(82\) −28.9447 −0.352984
\(83\) −45.2531 + 14.7036i −0.545218 + 0.177152i −0.568659 0.822573i \(-0.692538\pi\)
0.0234411 + 0.999725i \(0.492538\pi\)
\(84\) −1.84010 + 33.8490i −0.0219060 + 0.402964i
\(85\) −124.863 + 68.3818i −1.46897 + 0.804492i
\(86\) −63.4949 87.3932i −0.738312 1.01620i
\(87\) −66.3102 3.60477i −0.762186 0.0414341i
\(88\) −36.4020 26.4476i −0.413659 0.300541i
\(89\) −2.51715 3.46456i −0.0282826 0.0389276i 0.794642 0.607079i \(-0.207659\pi\)
−0.822924 + 0.568151i \(0.807659\pi\)
\(90\) −61.8772 14.8734i −0.687524 0.165260i
\(91\) 10.7794 + 7.83171i 0.118455 + 0.0860628i
\(92\) 85.0486 27.6340i 0.924441 0.300369i
\(93\) 11.0874 + 17.1462i 0.119220 + 0.184368i
\(94\) −11.7981 36.3107i −0.125511 0.386284i
\(95\) −33.9159 61.9292i −0.357009 0.651886i
\(96\) −4.36035 16.4008i −0.0454203 0.170842i
\(97\) −18.0333 + 55.5008i −0.185910 + 0.572173i −0.999963 0.00861800i \(-0.997257\pi\)
0.814052 + 0.580791i \(0.197257\pi\)
\(98\) 14.1974 + 19.5410i 0.144871 + 0.199398i
\(99\) −130.568 58.7436i −1.31887 0.593370i
\(100\) 2.97853 + 49.9112i 0.0297853 + 0.499112i
\(101\) 89.9015i 0.890114i −0.895502 0.445057i \(-0.853183\pi\)
0.895502 0.445057i \(-0.146817\pi\)
\(102\) −112.690 43.5097i −1.10480 0.426566i
\(103\) 22.8962 70.4672i 0.222293 0.684148i −0.776262 0.630411i \(-0.782887\pi\)
0.998555 0.0537375i \(-0.0171134\pi\)
\(104\) −6.34387 2.06125i −0.0609988 0.0198197i
\(105\) 76.4305 36.6127i 0.727910 0.348692i
\(106\) 26.1882 + 80.5990i 0.247059 + 0.760368i
\(107\) 163.495i 1.52799i 0.645224 + 0.763993i \(0.276764\pi\)
−0.645224 + 0.763993i \(0.723236\pi\)
\(108\) −24.2338 48.2569i −0.224387 0.446823i
\(109\) −99.5480 72.3259i −0.913285 0.663540i 0.0285589 0.999592i \(-0.490908\pi\)
−0.941843 + 0.336052i \(0.890908\pi\)
\(110\) −14.2785 + 111.578i −0.129805 + 1.01435i
\(111\) 41.7185 + 16.1076i 0.375842 + 0.145113i
\(112\) 18.2832 + 13.2835i 0.163243 + 0.118603i
\(113\) 90.9811 125.225i 0.805143 1.10818i −0.186912 0.982377i \(-0.559848\pi\)
0.992055 0.125807i \(-0.0401521\pi\)
\(114\) 21.5799 55.8916i 0.189297 0.490277i
\(115\) −162.724 153.302i −1.41499 1.33306i
\(116\) −26.0225 + 35.8169i −0.224332 + 0.308766i
\(117\) −21.0998 2.30086i −0.180340 0.0196655i
\(118\) 123.017 1.04252
\(119\) 152.990 49.7095i 1.28563 0.417727i
\(120\) −30.7261 + 29.2559i −0.256051 + 0.243799i
\(121\) −40.8126 + 125.608i −0.337295 + 1.03809i
\(122\) −13.2975 4.32063i −0.108996 0.0354150i
\(123\) −22.1158 + 57.2797i −0.179803 + 0.465689i
\(124\) 13.6125 0.109778
\(125\) 105.864 66.4668i 0.846911 0.531735i
\(126\) 65.5790 + 29.5045i 0.520468 + 0.234162i
\(127\) 116.992 84.9997i 0.921197 0.669289i −0.0226245 0.999744i \(-0.507202\pi\)
0.943822 + 0.330455i \(0.107202\pi\)
\(128\) −10.7600 3.49613i −0.0840623 0.0273135i
\(129\) −221.460 + 58.8778i −1.71675 + 0.456417i
\(130\) 3.09832 + 16.3855i 0.0238332 + 0.126042i
\(131\) −72.7163 + 23.6270i −0.555086 + 0.180358i −0.573109 0.819479i \(-0.694263\pi\)
0.0180228 + 0.999838i \(0.494263\pi\)
\(132\) −80.1519 + 51.8294i −0.607211 + 0.392647i
\(133\) 24.6548 + 75.8797i 0.185375 + 0.570524i
\(134\) 2.11159 2.90636i 0.0157582 0.0216892i
\(135\) −76.7120 + 111.087i −0.568237 + 0.822865i
\(136\) −65.1515 + 47.3354i −0.479055 + 0.348054i
\(137\) 91.6175 126.101i 0.668741 0.920443i −0.330990 0.943634i \(-0.607383\pi\)
0.999731 + 0.0231911i \(0.00738262\pi\)
\(138\) 10.2973 189.420i 0.0746181 1.37261i
\(139\) 24.4182 17.7409i 0.175671 0.127632i −0.496475 0.868051i \(-0.665373\pi\)
0.672146 + 0.740419i \(0.265373\pi\)
\(140\) 7.17151 56.0412i 0.0512251 0.400295i
\(141\) −80.8712 4.39634i −0.573555 0.0311797i
\(142\) −37.3938 115.086i −0.263336 0.810466i
\(143\) 37.5168i 0.262355i
\(144\) −35.7878 3.90255i −0.248527 0.0271010i
\(145\) 109.785 + 14.0490i 0.757138 + 0.0968897i
\(146\) −18.8788 6.13410i −0.129307 0.0420144i
\(147\) 49.5183 13.1650i 0.336859 0.0895579i
\(148\) 24.1195 17.5239i 0.162970 0.118405i
\(149\) 40.8159i 0.273932i 0.990576 + 0.136966i \(0.0437351\pi\)
−0.990576 + 0.136966i \(0.956265\pi\)
\(150\) 101.047 + 32.2414i 0.673647 + 0.214943i
\(151\) 169.123 1.12002 0.560010 0.828486i \(-0.310797\pi\)
0.560010 + 0.828486i \(0.310797\pi\)
\(152\) −23.4773 32.3137i −0.154456 0.212590i
\(153\) −172.206 + 189.761i −1.12553 + 1.24027i
\(154\) 39.2785 120.887i 0.255055 0.784979i
\(155\) −16.3465 29.8482i −0.105461 0.192569i
\(156\) −8.92625 + 10.9792i −0.0572196 + 0.0703794i
\(157\) 199.715 1.27207 0.636036 0.771660i \(-0.280573\pi\)
0.636036 + 0.771660i \(0.280573\pi\)
\(158\) 90.9407 29.5484i 0.575574 0.187015i
\(159\) 179.510 + 9.75857i 1.12899 + 0.0613746i
\(160\) 5.25512 + 27.7918i 0.0328445 + 0.173699i
\(161\) 148.486 + 204.373i 0.922271 + 1.26940i
\(162\) −114.014 + 11.0854i −0.703788 + 0.0684286i
\(163\) −135.433 98.3978i −0.830877 0.603667i 0.0889306 0.996038i \(-0.471655\pi\)
−0.919807 + 0.392371i \(0.871655\pi\)
\(164\) 24.0604 + 33.1163i 0.146710 + 0.201928i
\(165\) 209.897 + 113.510i 1.27210 + 0.687941i
\(166\) 54.4396 + 39.5527i 0.327949 + 0.238269i
\(167\) −152.395 + 49.5162i −0.912546 + 0.296504i −0.727405 0.686208i \(-0.759274\pi\)
−0.185140 + 0.982712i \(0.559274\pi\)
\(168\) 40.2570 26.0318i 0.239625 0.154951i
\(169\) −50.5052 155.439i −0.298847 0.919758i
\(170\) 182.030 + 86.0156i 1.07076 + 0.505974i
\(171\) −94.1175 85.4104i −0.550395 0.499476i
\(172\) −47.2082 + 145.292i −0.274466 + 0.844720i
\(173\) 77.8819 + 107.195i 0.450185 + 0.619626i 0.972437 0.233165i \(-0.0749082\pi\)
−0.522253 + 0.852791i \(0.674908\pi\)
\(174\) 50.9963 + 78.8635i 0.293082 + 0.453239i
\(175\) −131.494 + 51.5720i −0.751394 + 0.294697i
\(176\) 63.6330i 0.361551i
\(177\) 93.9937 243.443i 0.531038 1.37538i
\(178\) −1.87149 + 5.75986i −0.0105140 + 0.0323587i
\(179\) 27.7472 + 9.01560i 0.155012 + 0.0503665i 0.385495 0.922710i \(-0.374031\pi\)
−0.230483 + 0.973076i \(0.574031\pi\)
\(180\) 34.4187 + 83.1586i 0.191215 + 0.461992i
\(181\) −46.9691 144.556i −0.259498 0.798652i −0.992910 0.118868i \(-0.962073\pi\)
0.733412 0.679784i \(-0.237927\pi\)
\(182\) 18.8431i 0.103534i
\(183\) −18.7105 + 23.0137i −0.102243 + 0.125758i
\(184\) −102.314 74.3352i −0.556052 0.403996i
\(185\) −67.3886 31.8436i −0.364263 0.172127i
\(186\) 10.4009 26.9382i 0.0559188 0.144829i
\(187\) 366.439 + 266.234i 1.95957 + 1.42371i
\(188\) −31.7367 + 43.6819i −0.168812 + 0.232350i
\(189\) 108.495 107.233i 0.574045 0.567372i
\(190\) −42.6619 + 90.2828i −0.224536 + 0.475172i
\(191\) −95.8679 + 131.951i −0.501926 + 0.690842i −0.982532 0.186095i \(-0.940417\pi\)
0.480605 + 0.876937i \(0.340417\pi\)
\(192\) −15.1400 + 18.6220i −0.0788542 + 0.0969898i
\(193\) 99.7147 0.516657 0.258328 0.966057i \(-0.416828\pi\)
0.258328 + 0.966057i \(0.416828\pi\)
\(194\) 78.4900 25.5029i 0.404588 0.131458i
\(195\) 34.7932 + 6.38831i 0.178427 + 0.0327606i
\(196\) 10.5557 32.4871i 0.0538557 0.165751i
\(197\) −101.616 33.0171i −0.515818 0.167599i 0.0395285 0.999218i \(-0.487414\pi\)
−0.555347 + 0.831619i \(0.687414\pi\)
\(198\) 41.3255 + 198.217i 0.208714 + 1.00110i
\(199\) −136.426 −0.685556 −0.342778 0.939416i \(-0.611368\pi\)
−0.342778 + 0.939416i \(0.611368\pi\)
\(200\) 54.6286 44.8967i 0.273143 0.224483i
\(201\) −4.13809 6.39938i −0.0205875 0.0318377i
\(202\) −102.858 + 74.7309i −0.509200 + 0.369955i
\(203\) −118.944 38.6471i −0.585929 0.190380i
\(204\) 43.8933 + 165.098i 0.215163 + 0.809306i
\(205\) 43.7214 92.5249i 0.213275 0.451341i
\(206\) −99.6557 + 32.3801i −0.483766 + 0.157185i
\(207\) −366.983 165.108i −1.77286 0.797625i
\(208\) 2.91505 + 8.97159i 0.0140146 + 0.0431326i
\(209\) −132.046 + 181.746i −0.631800 + 0.869598i
\(210\) −105.423 57.0115i −0.502012 0.271483i
\(211\) −97.4307 + 70.7876i −0.461757 + 0.335486i −0.794220 0.607630i \(-0.792120\pi\)
0.332463 + 0.943116i \(0.392120\pi\)
\(212\) 70.4461 96.9608i 0.332293 0.457362i
\(213\) −256.320 13.9341i −1.20338 0.0654184i
\(214\) 187.058 135.905i 0.874102 0.635072i
\(215\) 375.272 70.9598i 1.74545 0.330046i
\(216\) −35.0674 + 67.8401i −0.162349 + 0.314075i
\(217\) 11.8830 + 36.5720i 0.0547602 + 0.168534i
\(218\) 174.016i 0.798240i
\(219\) −26.5638 + 32.6731i −0.121296 + 0.149192i
\(220\) 139.529 76.4136i 0.634221 0.347335i
\(221\) 63.8604 + 20.7495i 0.288961 + 0.0938891i
\(222\) −16.2496 61.1206i −0.0731964 0.275318i
\(223\) 316.423 229.895i 1.41894 1.03092i 0.426994 0.904255i \(-0.359573\pi\)
0.991946 0.126665i \(-0.0404273\pi\)
\(224\) 31.9602i 0.142680i
\(225\) 141.011 175.331i 0.626715 0.779249i
\(226\) −218.901 −0.968588
\(227\) 30.9174 + 42.5541i 0.136200 + 0.187463i 0.871669 0.490095i \(-0.163038\pi\)
−0.735469 + 0.677558i \(0.763038\pi\)
\(228\) −81.8852 + 21.7701i −0.359146 + 0.0954830i
\(229\) −31.9950 + 98.4705i −0.139716 + 0.430002i −0.996294 0.0860161i \(-0.972586\pi\)
0.856578 + 0.516018i \(0.172586\pi\)
\(230\) −40.1321 + 313.609i −0.174487 + 1.36352i
\(231\) −209.216 170.096i −0.905696 0.736345i
\(232\) 62.6102 0.269871
\(233\) −3.15189 + 1.02411i −0.0135274 + 0.00439533i −0.315773 0.948835i \(-0.602264\pi\)
0.302245 + 0.953230i \(0.402264\pi\)
\(234\) 14.9068 + 26.0534i 0.0637044 + 0.111339i
\(235\) 133.893 + 17.1340i 0.569755 + 0.0729107i
\(236\) −102.258 140.746i −0.433298 0.596383i
\(237\) 11.0107 202.543i 0.0464586 0.854612i
\(238\) −184.047 133.718i −0.773308 0.561841i
\(239\) −276.082 379.994i −1.15515 1.58993i −0.727700 0.685896i \(-0.759410\pi\)
−0.427454 0.904037i \(-0.640590\pi\)
\(240\) 59.0135 + 10.8354i 0.245890 + 0.0451473i
\(241\) −172.479 125.313i −0.715681 0.519972i 0.169321 0.985561i \(-0.445843\pi\)
−0.885001 + 0.465589i \(0.845843\pi\)
\(242\) 177.637 57.7178i 0.734038 0.238503i
\(243\) −65.1772 + 234.096i −0.268219 + 0.963358i
\(244\) 6.11030 + 18.8056i 0.0250422 + 0.0770720i
\(245\) −83.9106 + 15.8666i −0.342492 + 0.0647615i
\(246\) 83.9188 22.3108i 0.341134 0.0906943i
\(247\) −10.2913 + 31.6734i −0.0416652 + 0.128232i
\(248\) −11.3154 15.5743i −0.0456267 0.0627998i
\(249\) 119.868 77.5115i 0.481398 0.311291i
\(250\) −164.046 65.8704i −0.656184 0.263482i
\(251\) 10.9692i 0.0437021i 0.999761 + 0.0218511i \(0.00695596\pi\)
−0.999761 + 0.0218511i \(0.993044\pi\)
\(252\) −20.7561 99.5562i −0.0823654 0.395064i
\(253\) −219.804 + 676.487i −0.868791 + 2.67386i
\(254\) −194.500 63.1969i −0.765749 0.248807i
\(255\) 309.303 294.503i 1.21295 1.15492i
\(256\) 4.94427 + 15.2169i 0.0193136 + 0.0594410i
\(257\) 505.126i 1.96547i −0.185019 0.982735i \(-0.559235\pi\)
0.185019 0.982735i \(-0.440765\pi\)
\(258\) 251.453 + 204.435i 0.974624 + 0.792385i
\(259\) 68.1356 + 49.5034i 0.263072 + 0.191133i
\(260\) 16.1715 17.1654i 0.0621982 0.0660206i
\(261\) 195.031 40.6612i 0.747245 0.155790i
\(262\) 87.4779 + 63.5564i 0.333885 + 0.242582i
\(263\) 237.193 326.468i 0.901875 1.24132i −0.0679914 0.997686i \(-0.521659\pi\)
0.969866 0.243638i \(-0.0783410\pi\)
\(264\) 125.926 + 48.6202i 0.476992 + 0.184167i
\(265\) −297.202 38.0325i −1.12152 0.143519i
\(266\) 66.3213 91.2835i 0.249328 0.343171i
\(267\) 9.96844 + 8.10450i 0.0373350 + 0.0303540i
\(268\) −5.08050 −0.0189571
\(269\) −149.906 + 48.7073i −0.557270 + 0.181068i −0.574093 0.818790i \(-0.694645\pi\)
0.0168222 + 0.999858i \(0.494645\pi\)
\(270\) 190.864 4.57327i 0.706904 0.0169380i
\(271\) −102.819 + 316.444i −0.379405 + 1.16769i 0.561053 + 0.827780i \(0.310396\pi\)
−0.940458 + 0.339909i \(0.889604\pi\)
\(272\) 108.315 + 35.1937i 0.398217 + 0.129388i
\(273\) −37.2894 14.3975i −0.136591 0.0527381i
\(274\) −220.432 −0.804497
\(275\) −335.105 214.184i −1.21856 0.778850i
\(276\) −225.280 + 145.675i −0.816231 + 0.527808i
\(277\) −182.750 + 132.775i −0.659746 + 0.479334i −0.866577 0.499043i \(-0.833685\pi\)
0.206831 + 0.978377i \(0.433685\pi\)
\(278\) −40.5955 13.1903i −0.146027 0.0474470i
\(279\) −45.3621 41.1655i −0.162588 0.147547i
\(280\) −70.0794 + 38.3794i −0.250284 + 0.137069i
\(281\) 113.418 36.8517i 0.403622 0.131145i −0.100169 0.994970i \(-0.531938\pi\)
0.503791 + 0.863826i \(0.331938\pi\)
\(282\) 62.1946 + 96.1811i 0.220548 + 0.341068i
\(283\) −46.0024 141.581i −0.162553 0.500285i 0.836295 0.548280i \(-0.184717\pi\)
−0.998848 + 0.0479943i \(0.984717\pi\)
\(284\) −100.589 + 138.449i −0.354187 + 0.487496i
\(285\) 146.067 + 153.408i 0.512517 + 0.538272i
\(286\) 42.9238 31.1860i 0.150083 0.109042i
\(287\) −67.9684 + 93.5505i −0.236824 + 0.325960i
\(288\) 25.2838 + 44.1897i 0.0877910 + 0.153436i
\(289\) 422.040 306.630i 1.46035 1.06100i
\(290\) −75.1854 137.286i −0.259260 0.473399i
\(291\) 9.50321 174.813i 0.0326571 0.600732i
\(292\) 8.67492 + 26.6987i 0.0297086 + 0.0914338i
\(293\) 499.212i 1.70379i 0.523709 + 0.851897i \(0.324548\pi\)
−0.523709 + 0.851897i \(0.675452\pi\)
\(294\) −56.2247 45.7116i −0.191240 0.155482i
\(295\) −185.819 + 393.238i −0.629895 + 1.33301i
\(296\) −40.0989 13.0289i −0.135469 0.0440167i
\(297\) 423.835 + 69.6713i 1.42705 + 0.234584i
\(298\) 46.6984 33.9284i 0.156706 0.113854i
\(299\) 105.447i 0.352665i
\(300\) −47.1076 142.411i −0.157025 0.474703i
\(301\) −431.559 −1.43375
\(302\) −140.584 193.498i −0.465511 0.640721i
\(303\) 69.2968 + 260.650i 0.228702 + 0.860231i
\(304\) −17.4553 + 53.7218i −0.0574187 + 0.176717i
\(305\) 33.8975 35.9807i 0.111139 0.117970i
\(306\) 360.257 + 39.2848i 1.17731 + 0.128382i
\(307\) 267.959 0.872832 0.436416 0.899745i \(-0.356248\pi\)
0.436416 + 0.899745i \(0.356248\pi\)
\(308\) −170.960 + 55.5482i −0.555064 + 0.180351i
\(309\) −12.0659 + 221.953i −0.0390481 + 0.718295i
\(310\) −20.5619 + 43.5138i −0.0663286 + 0.140367i
\(311\) −125.541 172.792i −0.403668 0.555601i 0.557992 0.829846i \(-0.311572\pi\)
−0.961660 + 0.274245i \(0.911572\pi\)
\(312\) 19.9815 + 1.08624i 0.0640433 + 0.00348154i
\(313\) 103.175 + 74.9608i 0.329632 + 0.239491i 0.740274 0.672305i \(-0.234696\pi\)
−0.410643 + 0.911796i \(0.634696\pi\)
\(314\) −166.014 228.499i −0.528707 0.727703i
\(315\) −193.373 + 165.064i −0.613881 + 0.524012i
\(316\) −109.402 79.4851i −0.346208 0.251535i
\(317\) −326.909 + 106.219i −1.03126 + 0.335076i −0.775287 0.631609i \(-0.782395\pi\)
−0.255970 + 0.966685i \(0.582395\pi\)
\(318\) −138.054 213.494i −0.434131 0.671363i
\(319\) −108.819 334.911i −0.341125 1.04988i
\(320\) 27.4289 29.1145i 0.0857153 0.0909829i
\(321\) −126.023 474.017i −0.392595 1.47669i
\(322\) 110.398 339.772i 0.342852 1.05519i
\(323\) 236.334 + 325.285i 0.731683 + 1.00708i
\(324\) 107.457 + 121.231i 0.331659 + 0.374169i
\(325\) −57.0582 14.8464i −0.175564 0.0456813i
\(326\) 236.745i 0.726213i
\(327\) 344.367 + 132.961i 1.05311 + 0.406608i
\(328\) 17.8888 55.0560i 0.0545390 0.167854i
\(329\) −145.062 47.1336i −0.440919 0.143263i
\(330\) −44.6081 334.504i −0.135176 1.01365i
\(331\) 5.51443 + 16.9717i 0.0166599 + 0.0512739i 0.959041 0.283268i \(-0.0914185\pi\)
−0.942381 + 0.334542i \(0.891419\pi\)
\(332\) 95.1639i 0.286638i
\(333\) −133.370 14.5435i −0.400510 0.0436742i
\(334\) 183.332 + 133.198i 0.548897 + 0.398797i
\(335\) 6.10091 + 11.1400i 0.0182117 + 0.0332539i
\(336\) −63.2473 24.4199i −0.188236 0.0726783i
\(337\) −421.225 306.038i −1.24993 0.908125i −0.251709 0.967803i \(-0.580993\pi\)
−0.998218 + 0.0596779i \(0.980993\pi\)
\(338\) −135.859 + 186.994i −0.401949 + 0.553235i
\(339\) −167.256 + 433.191i −0.493380 + 1.27785i
\(340\) −52.9005 279.765i −0.155590 0.822839i
\(341\) −63.6427 + 87.5966i −0.186635 + 0.256882i
\(342\) −19.4844 + 178.680i −0.0569720 + 0.522455i
\(343\) 373.337 1.08845
\(344\) 205.474 66.7624i 0.597307 0.194077i
\(345\) 589.949 + 319.039i 1.71000 + 0.924750i
\(346\) 57.9049 178.213i 0.167355 0.515066i
\(347\) −194.612 63.2332i −0.560840 0.182228i 0.0148588 0.999890i \(-0.495270\pi\)
−0.575699 + 0.817661i \(0.695270\pi\)
\(348\) 47.8386 123.902i 0.137467 0.356039i
\(349\) −433.831 −1.24307 −0.621535 0.783386i \(-0.713491\pi\)
−0.621535 + 0.783386i \(0.713491\pi\)
\(350\) 168.310 + 107.576i 0.480884 + 0.307359i
\(351\) 62.9479 9.59305i 0.179339 0.0273306i
\(352\) 72.8040 52.8952i 0.206829 0.150270i
\(353\) 16.3190 + 5.30236i 0.0462294 + 0.0150208i 0.332040 0.943265i \(-0.392263\pi\)
−0.285811 + 0.958286i \(0.592263\pi\)
\(354\) −356.661 + 94.8225i −1.00752 + 0.267860i
\(355\) 424.370 + 54.3060i 1.19541 + 0.152975i
\(356\) 8.14567 2.64669i 0.0228811 0.00743452i
\(357\) −405.245 + 262.048i −1.13514 + 0.734028i
\(358\) −12.7500 39.2404i −0.0356145 0.109610i
\(359\) −180.188 + 248.007i −0.501916 + 0.690828i −0.982530 0.186104i \(-0.940414\pi\)
0.480614 + 0.876932i \(0.340414\pi\)
\(360\) 66.5330 108.505i 0.184814 0.301403i
\(361\) 130.721 94.9742i 0.362107 0.263086i
\(362\) −126.347 + 173.901i −0.349024 + 0.480390i
\(363\) 21.5075 395.633i 0.0592493 1.08990i
\(364\) −21.5588 + 15.6634i −0.0592276 + 0.0430314i
\(365\) 48.1251 51.0826i 0.131850 0.139952i
\(366\) 41.8837 + 2.27689i 0.114436 + 0.00622102i
\(367\) 49.8975 + 153.569i 0.135960 + 0.418443i 0.995738 0.0922252i \(-0.0293980\pi\)
−0.859778 + 0.510668i \(0.829398\pi\)
\(368\) 178.851i 0.486008i
\(369\) 19.9683 183.117i 0.0541147 0.496253i
\(370\) 19.5841 + 103.571i 0.0529301 + 0.279922i
\(371\) 321.995 + 104.623i 0.867912 + 0.282002i
\(372\) −39.4665 + 10.4926i −0.106093 + 0.0282059i
\(373\) 85.5056 62.1234i 0.229237 0.166551i −0.467238 0.884132i \(-0.654751\pi\)
0.696475 + 0.717581i \(0.254751\pi\)
\(374\) 640.560i 1.71273i
\(375\) −255.696 + 274.307i −0.681857 + 0.731486i
\(376\) 76.3587 0.203082
\(377\) −30.6847 42.2339i −0.0813917 0.112026i
\(378\) −212.875 34.9930i −0.563160 0.0925742i
\(379\) 91.4803 281.547i 0.241373 0.742869i −0.754839 0.655910i \(-0.772285\pi\)
0.996212 0.0869589i \(-0.0277149\pi\)
\(380\) 138.757 26.2375i 0.365151 0.0690460i
\(381\) −273.675 + 336.617i −0.718307 + 0.883509i
\(382\) 230.659 0.603818
\(383\) −19.5390 + 6.34860i −0.0510156 + 0.0165760i −0.334414 0.942426i \(-0.608538\pi\)
0.283398 + 0.959002i \(0.408538\pi\)
\(384\) 33.8911 + 1.84239i 0.0882580 + 0.00479790i
\(385\) 327.098 + 308.159i 0.849604 + 0.800414i
\(386\) −82.8882 114.086i −0.214736 0.295559i
\(387\) 596.693 341.407i 1.54184 0.882188i
\(388\) −94.4236 68.6028i −0.243360 0.176811i
\(389\) 373.336 + 513.853i 0.959732 + 1.32096i 0.947066 + 0.321039i \(0.104032\pi\)
0.0126663 + 0.999920i \(0.495968\pi\)
\(390\) −21.6130 45.1180i −0.0554179 0.115687i
\(391\) 1029.94 + 748.293i 2.63411 + 1.91379i
\(392\) −45.9437 + 14.9280i −0.117203 + 0.0380817i
\(393\) 192.613 124.552i 0.490111 0.316925i
\(394\) 46.6932 + 143.707i 0.118511 + 0.364739i
\(395\) −42.9124 + 335.336i −0.108639 + 0.848951i
\(396\) 192.433 212.050i 0.485941 0.535480i
\(397\) −10.6054 + 32.6401i −0.0267139 + 0.0822169i −0.963525 0.267620i \(-0.913763\pi\)
0.936811 + 0.349837i \(0.113763\pi\)
\(398\) 113.404 + 156.088i 0.284935 + 0.392180i
\(399\) −129.970 200.993i −0.325740 0.503742i
\(400\) −96.7776 25.1813i −0.241944 0.0629533i
\(401\) 493.949i 1.23179i −0.787827 0.615897i \(-0.788794\pi\)
0.787827 0.615897i \(-0.211206\pi\)
\(402\) −3.88187 + 10.0540i −0.00965638 + 0.0250099i
\(403\) −4.96012 + 15.2657i −0.0123080 + 0.0378801i
\(404\) 171.003 + 55.5622i 0.423274 + 0.137530i
\(405\) 136.784 381.202i 0.337737 0.941240i
\(406\) 54.6553 + 168.212i 0.134619 + 0.414315i
\(407\) 237.140i 0.582652i
\(408\) 152.406 187.458i 0.373545 0.459456i
\(409\) 561.548 + 407.988i 1.37298 + 0.997526i 0.997498 + 0.0706956i \(0.0225219\pi\)
0.375479 + 0.926831i \(0.377478\pi\)
\(410\) −142.203 + 26.8891i −0.346838 + 0.0655832i
\(411\) −168.426 + 436.221i −0.409795 + 1.06137i
\(412\) 119.886 + 87.1023i 0.290986 + 0.211413i
\(413\) 288.871 397.596i 0.699445 0.962703i
\(414\) 116.152 + 557.120i 0.280560 + 1.34570i
\(415\) −208.666 + 114.277i −0.502811 + 0.275367i
\(416\) 7.84146 10.7928i 0.0188497 0.0259443i
\(417\) −57.1206 + 70.2577i −0.136980 + 0.168484i
\(418\) 317.704 0.760056
\(419\) 596.421 193.789i 1.42344 0.462503i 0.506746 0.862095i \(-0.330848\pi\)
0.916693 + 0.399592i \(0.130848\pi\)
\(420\) 22.4048 + 168.007i 0.0533447 + 0.400018i
\(421\) 44.3241 136.416i 0.105283 0.324027i −0.884514 0.466514i \(-0.845510\pi\)
0.989797 + 0.142487i \(0.0455098\pi\)
\(422\) 161.979 + 52.6303i 0.383837 + 0.124716i
\(423\) 237.857 49.5900i 0.562311 0.117234i
\(424\) −169.494 −0.399749
\(425\) −549.917 + 451.951i −1.29392 + 1.06341i
\(426\) 197.125 + 304.844i 0.462734 + 0.715597i
\(427\) −45.1900 + 32.8325i −0.105831 + 0.0768910i
\(428\) −310.985 101.045i −0.726601 0.236087i
\(429\) −28.9182 108.772i −0.0674085 0.253547i
\(430\) −393.133 370.372i −0.914263 0.861330i
\(431\) 27.5173 8.94092i 0.0638453 0.0207446i −0.276920 0.960893i \(-0.589314\pi\)
0.340766 + 0.940148i \(0.389314\pi\)
\(432\) 106.767 16.2710i 0.247147 0.0376643i
\(433\) −236.987 729.370i −0.547313 1.68446i −0.715426 0.698689i \(-0.753767\pi\)
0.168113 0.985768i \(-0.446233\pi\)
\(434\) 31.9651 43.9962i 0.0736522 0.101374i
\(435\) −329.127 + 43.8911i −0.756614 + 0.100899i
\(436\) 199.096 144.652i 0.456642 0.331770i
\(437\) −371.137 + 510.826i −0.849284 + 1.16894i
\(438\) 59.4633 + 3.23255i 0.135761 + 0.00738026i
\(439\) 120.739 87.7218i 0.275031 0.199822i −0.441716 0.897155i \(-0.645630\pi\)
0.716747 + 0.697333i \(0.245630\pi\)
\(440\) −203.410 96.1186i −0.462296 0.218451i
\(441\) −133.420 + 76.3383i −0.302540 + 0.173103i
\(442\) −29.3442 90.3122i −0.0663896 0.204326i
\(443\) 573.807i 1.29528i −0.761948 0.647638i \(-0.775757\pi\)
0.761948 0.647638i \(-0.224243\pi\)
\(444\) −56.4219 + 69.3983i −0.127076 + 0.156302i
\(445\) −15.5851 14.6828i −0.0350227 0.0329950i
\(446\) −526.056 170.926i −1.17950 0.383242i
\(447\) −31.4612 118.337i −0.0703831 0.264736i
\(448\) −36.5664 + 26.5671i −0.0816215 + 0.0593015i
\(449\) 455.314i 1.01406i −0.861928 0.507031i \(-0.830743\pi\)
0.861928 0.507031i \(-0.169257\pi\)
\(450\) −317.816 15.5892i −0.706258 0.0346426i
\(451\) −325.594 −0.721937
\(452\) 181.962 + 250.450i 0.402571 + 0.554092i
\(453\) −490.336 + 130.362i −1.08242 + 0.287774i
\(454\) 22.9869 70.7465i 0.0506320 0.155829i
\(455\) 60.2342 + 28.4628i 0.132383 + 0.0625557i
\(456\) 92.9751 + 75.5903i 0.203893 + 0.165768i
\(457\) −258.541 −0.565736 −0.282868 0.959159i \(-0.591286\pi\)
−0.282868 + 0.959159i \(0.591286\pi\)
\(458\) 139.258 45.2478i 0.304057 0.0987943i
\(459\) 353.004 682.910i 0.769073 1.48782i
\(460\) 392.167 214.773i 0.852538 0.466897i
\(461\) 390.543 + 537.536i 0.847165 + 1.16602i 0.984480 + 0.175495i \(0.0561527\pi\)
−0.137315 + 0.990527i \(0.543847\pi\)
\(462\) −20.6990 + 380.761i −0.0448031 + 0.824159i
\(463\) −474.353 344.638i −1.02452 0.744358i −0.0573161 0.998356i \(-0.518254\pi\)
−0.967205 + 0.253998i \(0.918254\pi\)
\(464\) −52.0450 71.6337i −0.112166 0.154383i
\(465\) 70.4005 + 73.9383i 0.151399 + 0.159007i
\(466\) 3.79173 + 2.75486i 0.00813677 + 0.00591171i
\(467\) 656.254 213.230i 1.40526 0.456595i 0.494369 0.869252i \(-0.335399\pi\)
0.910886 + 0.412657i \(0.135399\pi\)
\(468\) 17.4169 38.7122i 0.0372156 0.0827184i
\(469\) −4.43500 13.6495i −0.00945629 0.0291035i
\(470\) −91.6953 167.432i −0.195096 0.356239i
\(471\) −579.031 + 153.942i −1.22937 + 0.326841i
\(472\) −76.0286 + 233.992i −0.161078 + 0.495746i
\(473\) −714.243 983.071i −1.51003 2.07837i
\(474\) −240.887 + 155.767i −0.508200 + 0.328623i
\(475\) −224.158 272.747i −0.471911 0.574204i
\(476\) 321.727i 0.675896i
\(477\) −527.973 + 110.075i −1.10686 + 0.230765i
\(478\) −205.266 + 631.743i −0.429426 + 1.32164i
\(479\) 381.302 + 123.893i 0.796038 + 0.258648i 0.678673 0.734440i \(-0.262555\pi\)
0.117365 + 0.993089i \(0.462555\pi\)
\(480\) −36.6582 76.5256i −0.0763713 0.159428i
\(481\) 10.8634 + 33.4342i 0.0225851 + 0.0695098i
\(482\) 301.504i 0.625528i
\(483\) −588.035 478.081i −1.21746 0.989817i
\(484\) −213.698 155.261i −0.441524 0.320786i
\(485\) −37.0373 + 289.425i −0.0763655 + 0.596752i
\(486\) 322.013 120.022i 0.662579 0.246960i
\(487\) −402.543 292.464i −0.826576 0.600543i 0.0920122 0.995758i \(-0.470670\pi\)
−0.918589 + 0.395215i \(0.870670\pi\)
\(488\) 16.4367 22.6231i 0.0336817 0.0463589i
\(489\) 468.504 + 180.890i 0.958087 + 0.369919i
\(490\) 87.9043 + 82.8148i 0.179396 + 0.169010i
\(491\) 67.4505 92.8376i 0.137374 0.189079i −0.734787 0.678298i \(-0.762718\pi\)
0.872161 + 0.489219i \(0.162718\pi\)
\(492\) −95.2842 77.4675i −0.193667 0.157454i
\(493\) −630.263 −1.27842
\(494\) 44.7929 14.5541i 0.0906739 0.0294617i
\(495\) −696.046 167.308i −1.40615 0.337996i
\(496\) −8.41297 + 25.8925i −0.0169616 + 0.0522026i
\(497\) −459.772 149.389i −0.925095 0.300582i
\(498\) −188.323 72.7120i −0.378159 0.146008i
\(499\) −33.5081 −0.0671505 −0.0335752 0.999436i \(-0.510689\pi\)
−0.0335752 + 0.999436i \(0.510689\pi\)
\(500\) 61.0000 + 242.444i 0.122000 + 0.484888i
\(501\) 403.669 261.029i 0.805727 0.521016i
\(502\) 12.5501 9.11821i 0.0250003 0.0181638i
\(503\) 761.956 + 247.575i 1.51482 + 0.492196i 0.944300 0.329086i \(-0.106741\pi\)
0.570523 + 0.821282i \(0.306741\pi\)
\(504\) −96.6509 + 106.504i −0.191768 + 0.211317i
\(505\) −83.5169 441.681i −0.165380 0.874615i
\(506\) 956.697 310.850i 1.89071 0.614328i
\(507\) 266.243 + 411.732i 0.525134 + 0.812095i
\(508\) 89.3740 + 275.065i 0.175933 + 0.541466i
\(509\) −224.981 + 309.660i −0.442007 + 0.608370i −0.970657 0.240470i \(-0.922698\pi\)
0.528650 + 0.848840i \(0.322698\pi\)
\(510\) −594.058 109.074i −1.16482 0.213870i
\(511\) −64.1573 + 46.6130i −0.125552 + 0.0912191i
\(512\) 13.3001 18.3060i 0.0259767 0.0357538i
\(513\) 338.709 + 175.083i 0.660251 + 0.341291i
\(514\) −577.926 + 419.888i −1.12437 + 0.816902i
\(515\) 47.0248 367.472i 0.0913103 0.713537i
\(516\) 24.8778 457.631i 0.0482128 0.886882i
\(517\) −132.715 408.453i −0.256701 0.790045i
\(518\) 119.105i 0.229933i
\(519\) −308.429 250.758i −0.594275 0.483155i
\(520\) −33.0819 4.23344i −0.0636191 0.00814124i
\(521\) 124.759 + 40.5367i 0.239461 + 0.0778056i 0.426289 0.904587i \(-0.359821\pi\)
−0.186828 + 0.982393i \(0.559821\pi\)
\(522\) −208.642 189.339i −0.399696 0.362719i
\(523\) 680.823 494.647i 1.30176 0.945787i 0.301793 0.953373i \(-0.402415\pi\)
0.999971 + 0.00758609i \(0.00241475\pi\)
\(524\) 152.917i 0.291826i
\(525\) 341.486 250.879i 0.650450 0.477864i
\(526\) −570.687 −1.08496
\(527\) 113.906 + 156.779i 0.216141 + 0.297493i
\(528\) −49.0488 184.490i −0.0928955 0.349413i
\(529\) −454.324 + 1398.27i −0.858836 + 2.64323i
\(530\) 203.536 + 371.650i 0.384031 + 0.701226i
\(531\) −84.8668 + 778.261i −0.159824 + 1.46565i
\(532\) −159.569 −0.299942
\(533\) −45.9053 + 14.9155i −0.0861263 + 0.0279841i
\(534\) 0.986241 18.1420i 0.00184689 0.0339738i
\(535\) 151.884 + 803.239i 0.283895 + 1.50138i
\(536\) 4.22319 + 5.81272i 0.00787908 + 0.0108446i
\(537\) −87.3963 4.75105i −0.162749 0.00884740i
\(538\) 180.337 + 131.022i 0.335199 + 0.243536i
\(539\) 159.704 + 219.814i 0.296297 + 0.407818i
\(540\) −163.889 214.570i −0.303498 0.397353i
\(541\) −232.993 169.279i −0.430671 0.312901i 0.351246 0.936283i \(-0.385758\pi\)
−0.781917 + 0.623382i \(0.785758\pi\)
\(542\) 447.519 145.408i 0.825680 0.268280i
\(543\) 247.602 + 382.905i 0.455989 + 0.705166i
\(544\) −49.7714 153.180i −0.0914915 0.281582i
\(545\) −556.263 262.854i −1.02067 0.482301i
\(546\) 14.5244 + 54.6316i 0.0266015 + 0.100058i
\(547\) −4.27436 + 13.1551i −0.00781418 + 0.0240496i −0.954888 0.296968i \(-0.904025\pi\)
0.947073 + 0.321017i \(0.104025\pi\)
\(548\) 183.235 + 252.201i 0.334371 + 0.460222i
\(549\) 36.5080 81.1456i 0.0664991 0.147806i
\(550\) 33.5049 + 561.443i 0.0609181 + 1.02081i
\(551\) 312.597i 0.567326i
\(552\) 353.935 + 136.655i 0.641186 + 0.247563i
\(553\) 118.047 363.311i 0.213466 0.656981i
\(554\) 303.823 + 98.7180i 0.548416 + 0.178191i
\(555\) 219.924 + 40.3798i 0.396260 + 0.0727565i
\(556\) 18.6539 + 57.4107i 0.0335501 + 0.103257i
\(557\) 727.686i 1.30644i −0.757169 0.653219i \(-0.773418\pi\)
0.757169 0.653219i \(-0.226582\pi\)
\(558\) −9.39096 + 86.1188i −0.0168297 + 0.154335i
\(559\) −145.736 105.883i −0.260708 0.189415i
\(560\) 102.165 + 48.2764i 0.182437 + 0.0862079i
\(561\) −1267.63 489.433i −2.25959 0.872430i
\(562\) −136.442 99.1308i −0.242779 0.176389i
\(563\) 234.264 322.437i 0.416099 0.572712i −0.548593 0.836089i \(-0.684837\pi\)
0.964693 + 0.263378i \(0.0848365\pi\)
\(564\) 58.3435 151.109i 0.103446 0.267924i
\(565\) 330.653 699.742i 0.585227 1.23848i
\(566\) −123.746 + 170.322i −0.218633 + 0.300922i
\(567\) −231.900 + 394.528i −0.408995 + 0.695817i
\(568\) 242.017 0.426087
\(569\) 261.900 85.0964i 0.460281 0.149554i −0.0696926 0.997569i \(-0.522202\pi\)
0.529974 + 0.848014i \(0.322202\pi\)
\(570\) 54.0982 294.640i 0.0949091 0.516912i
\(571\) 37.3570 114.973i 0.0654237 0.201354i −0.913001 0.407958i \(-0.866241\pi\)
0.978425 + 0.206604i \(0.0662411\pi\)
\(572\) −71.3612 23.1866i −0.124757 0.0405361i
\(573\) 176.240 456.459i 0.307574 0.796613i
\(574\) 163.532 0.284899
\(575\) −941.867 601.998i −1.63803 1.04695i
\(576\) 29.5412 65.6606i 0.0512868 0.113994i
\(577\) −707.477 + 514.012i −1.22613 + 0.890835i −0.996594 0.0824652i \(-0.973721\pi\)
−0.229535 + 0.973300i \(0.573721\pi\)
\(578\) −701.645 227.978i −1.21392 0.394426i
\(579\) −289.101 + 76.8609i −0.499312 + 0.132748i
\(580\) −94.5736 + 200.141i −0.163058 + 0.345070i
\(581\) 255.672 83.0729i 0.440055 0.142983i
\(582\) −207.907 + 134.441i −0.357229 + 0.230998i
\(583\) 294.587 + 906.645i 0.505295 + 1.55514i
\(584\) 23.3355 32.1185i 0.0399580 0.0549975i
\(585\) −105.800 + 8.29736i −0.180854 + 0.0141835i
\(586\) 571.160 414.972i 0.974675 0.708143i
\(587\) −478.838 + 659.063i −0.815737 + 1.12277i 0.174676 + 0.984626i \(0.444112\pi\)
−0.990413 + 0.138140i \(0.955888\pi\)
\(588\) −5.56266 + 102.326i −0.00946031 + 0.174024i
\(589\) −77.7588 + 56.4951i −0.132018 + 0.0959169i
\(590\) 604.375 114.281i 1.02436 0.193696i
\(591\) 320.064 + 17.3994i 0.541564 + 0.0294406i
\(592\) 18.4257 + 56.7085i 0.0311245 + 0.0957913i
\(593\) 881.612i 1.48670i 0.668904 + 0.743349i \(0.266764\pi\)
−0.668904 + 0.743349i \(0.733236\pi\)
\(594\) −272.602 542.833i −0.458925 0.913861i
\(595\) 705.452 386.345i 1.18563 0.649319i
\(596\) −77.6365 25.2256i −0.130263 0.0423249i
\(597\) 395.537 105.158i 0.662541 0.176144i
\(598\) 120.644 87.6532i 0.201746 0.146577i
\(599\) 803.017i 1.34060i 0.742092 + 0.670298i \(0.233834\pi\)
−0.742092 + 0.670298i \(0.766166\pi\)
\(600\) −123.777 + 172.276i −0.206295 + 0.287127i
\(601\) 644.414 1.07224 0.536118 0.844143i \(-0.319890\pi\)
0.536118 + 0.844143i \(0.319890\pi\)
\(602\) 358.735 + 493.756i 0.595905 + 0.820193i
\(603\) 16.9302 + 15.3639i 0.0280766 + 0.0254792i
\(604\) −104.524 + 321.691i −0.173053 + 0.532601i
\(605\) −83.8220 + 655.021i −0.138549 + 1.08268i
\(606\) 240.612 295.950i 0.397050 0.488367i
\(607\) 257.316 0.423915 0.211957 0.977279i \(-0.432016\pi\)
0.211957 + 0.977279i \(0.432016\pi\)
\(608\) 75.9742 24.6855i 0.124958 0.0406012i
\(609\) 374.641 + 20.3663i 0.615174 + 0.0334422i
\(610\) −69.3438 8.87382i −0.113678 0.0145473i
\(611\) −37.4227 51.5080i −0.0612483 0.0843011i
\(612\) −254.519 444.834i −0.415880 0.726853i
\(613\) −167.683 121.829i −0.273544 0.198742i 0.442552 0.896743i \(-0.354073\pi\)
−0.716097 + 0.698001i \(0.754073\pi\)
\(614\) −222.742 306.579i −0.362773 0.499314i
\(615\) −55.4417 + 301.957i −0.0901491 + 0.490987i
\(616\) 205.665 + 149.424i 0.333871 + 0.242572i
\(617\) 670.741 217.937i 1.08710 0.353220i 0.289975 0.957034i \(-0.406353\pi\)
0.797125 + 0.603814i \(0.206353\pi\)
\(618\) 263.972 170.695i 0.427138 0.276205i
\(619\) −47.5058 146.208i −0.0767460 0.236200i 0.905322 0.424725i \(-0.139629\pi\)
−0.982068 + 0.188525i \(0.939629\pi\)
\(620\) 66.8773 12.6458i 0.107867 0.0203964i
\(621\) 1191.26 + 195.822i 1.91829 + 0.315334i
\(622\) −93.3390 + 287.268i −0.150063 + 0.461846i
\(623\) 14.2214 + 19.5741i 0.0228274 + 0.0314192i
\(624\) −15.3669 23.7643i −0.0246265 0.0380837i
\(625\) 458.356 424.893i 0.733370 0.679830i
\(626\) 180.356i 0.288109i
\(627\) 242.748 628.716i 0.387158 1.00274i
\(628\) −123.431 + 379.881i −0.196546 + 0.604906i
\(629\) 403.655 + 131.155i 0.641740 + 0.208514i
\(630\) 349.595 + 84.0319i 0.554913 + 0.133384i
\(631\) −173.034 532.544i −0.274222 0.843969i −0.989424 0.145051i \(-0.953665\pi\)
0.715202 0.698918i \(-0.246335\pi\)
\(632\) 191.241i 0.302597i
\(633\) 227.916 280.334i 0.360057 0.442865i
\(634\) 393.272 + 285.729i 0.620302 + 0.450676i
\(635\) 495.812 526.282i 0.780806 0.828791i
\(636\) −129.505 + 335.418i −0.203625 + 0.527386i
\(637\) 32.5864 + 23.6754i 0.0511560 + 0.0371670i
\(638\) −292.723 + 402.898i −0.458813 + 0.631502i
\(639\) 753.885 157.174i 1.17979 0.245969i
\(640\) −56.1110 7.18044i −0.0876734 0.0112194i
\(641\) 690.314 950.136i 1.07693 1.48227i 0.214081 0.976816i \(-0.431324\pi\)
0.862852 0.505456i \(-0.168676\pi\)
\(642\) −437.577 + 538.214i −0.681584 + 0.838340i
\(643\) −725.893 −1.12892 −0.564458 0.825462i \(-0.690915\pi\)
−0.564458 + 0.825462i \(0.690915\pi\)
\(644\) −480.510 + 156.127i −0.746133 + 0.242433i
\(645\) −1033.32 + 494.996i −1.60205 + 0.767435i
\(646\) 175.713 540.789i 0.272002 0.837135i
\(647\) −229.134 74.4503i −0.354149 0.115070i 0.126539 0.991962i \(-0.459613\pi\)
−0.480688 + 0.876892i \(0.659613\pi\)
\(648\) 49.3786 223.718i 0.0762015 0.345244i
\(649\) 1383.80 2.13220
\(650\) 30.4437 + 77.6227i 0.0468365 + 0.119420i
\(651\) −62.6421 96.8731i −0.0962243 0.148807i
\(652\) 270.866 196.796i 0.415438 0.301834i
\(653\) −579.210 188.197i −0.886998 0.288203i −0.170138 0.985420i \(-0.554421\pi\)
−0.716860 + 0.697217i \(0.754421\pi\)
\(654\) −134.133 504.523i −0.205097 0.771442i
\(655\) −335.302 + 183.630i −0.511911 + 0.280351i
\(656\) −77.8610 + 25.2986i −0.118691 + 0.0385649i
\(657\) 51.8312 115.204i 0.0788907 0.175349i
\(658\) 66.6570 + 205.149i 0.101302 + 0.311777i
\(659\) 21.5009 29.5935i 0.0326266 0.0449066i −0.792392 0.610012i \(-0.791165\pi\)
0.825019 + 0.565106i \(0.191165\pi\)
\(660\) −345.633 + 329.095i −0.523686 + 0.498628i
\(661\) −157.492 + 114.425i −0.238263 + 0.173108i −0.700509 0.713643i \(-0.747044\pi\)
0.462246 + 0.886752i \(0.347044\pi\)
\(662\) 14.8338 20.4170i 0.0224075 0.0308413i
\(663\) −201.143 10.9346i −0.303384 0.0164926i
\(664\) −108.879 + 79.1054i −0.163975 + 0.119135i
\(665\) 191.619 + 349.889i 0.288148 + 0.526149i
\(666\) 94.2245 + 164.681i 0.141478 + 0.247268i
\(667\) −305.853 941.320i −0.458551 1.41127i
\(668\) 320.475i 0.479754i
\(669\) −740.197 + 910.433i −1.10642 + 1.36089i
\(670\) 7.67417 16.2404i 0.0114540 0.0242394i
\(671\) −149.582 48.6021i −0.222924 0.0724323i
\(672\) 24.6352 + 92.6618i 0.0366595 + 0.137890i
\(673\) −450.133 + 327.041i −0.668846 + 0.485945i −0.869639 0.493689i \(-0.835648\pi\)
0.200793 + 0.979634i \(0.435648\pi\)
\(674\) 736.329i 1.09248i
\(675\) −273.684 + 617.027i −0.405458 + 0.914114i
\(676\) 326.877 0.483545
\(677\) 372.843 + 513.175i 0.550729 + 0.758013i 0.990111 0.140287i \(-0.0448026\pi\)
−0.439382 + 0.898300i \(0.644803\pi\)
\(678\) 634.656 168.731i 0.936071 0.248865i
\(679\) 101.885 313.570i 0.150052 0.461811i
\(680\) −276.112 + 293.081i −0.406047 + 0.431001i
\(681\) −122.439 99.5452i −0.179793 0.146175i
\(682\) 153.124 0.224523
\(683\) −28.6524 + 9.30972i −0.0419508 + 0.0136306i −0.329917 0.944010i \(-0.607021\pi\)
0.287966 + 0.957640i \(0.407021\pi\)
\(684\) 220.628 126.236i 0.322556 0.184555i
\(685\) 332.966 704.637i 0.486082 1.02867i
\(686\) −310.338 427.144i −0.452388 0.622659i
\(687\) 16.8608 310.156i 0.0245426 0.451464i
\(688\) −247.185 179.591i −0.359281 0.261033i
\(689\) 83.0673 + 114.332i 0.120562 + 0.165940i
\(690\) −125.378 940.176i −0.181707 1.36257i
\(691\) −874.500 635.361i −1.26556 0.919481i −0.266541 0.963824i \(-0.585881\pi\)
−0.999016 + 0.0443425i \(0.985881\pi\)
\(692\) −252.031 + 81.8899i −0.364207 + 0.118338i
\(693\) 737.687 + 331.891i 1.06448 + 0.478919i
\(694\) 89.4252 + 275.222i 0.128855 + 0.396574i
\(695\) 103.484 109.844i 0.148898 0.158049i
\(696\) −181.525 + 48.2604i −0.260811 + 0.0693397i
\(697\) −180.077 + 554.220i −0.258360 + 0.795150i
\(698\) 360.624 + 496.356i 0.516653 + 0.711112i
\(699\) 8.34884 5.39870i 0.0119440 0.00772346i
\(700\) −16.8281 281.989i −0.0240402 0.402842i
\(701\) 66.0320i 0.0941969i −0.998890 0.0470985i \(-0.985003\pi\)
0.998890 0.0470985i \(-0.0149975\pi\)
\(702\) −63.3013 64.0459i −0.0901728 0.0912334i
\(703\) −65.0502 + 200.204i −0.0925323 + 0.284785i
\(704\) −121.037 39.3274i −0.171928 0.0558627i
\(705\) −401.400 + 53.5291i −0.569361 + 0.0759277i
\(706\) −7.49866 23.0785i −0.0106213 0.0326891i
\(707\) 507.927i 0.718426i
\(708\) 404.964 + 329.243i 0.571984 + 0.465032i
\(709\) 393.486 + 285.884i 0.554987 + 0.403222i 0.829621 0.558327i \(-0.188557\pi\)
−0.274634 + 0.961549i \(0.588557\pi\)
\(710\) −290.626 530.673i −0.409333 0.747427i
\(711\) 124.199 + 595.717i 0.174682 + 0.837858i
\(712\) −9.79925 7.11957i −0.0137630 0.00999940i
\(713\) −178.878 + 246.204i −0.250881 + 0.345308i
\(714\) 636.677 + 245.822i 0.891704 + 0.344289i
\(715\) 34.8525 + 184.318i 0.0487447 + 0.257787i
\(716\) −34.2974 + 47.2063i −0.0479014 + 0.0659306i
\(717\) 1093.34 + 888.905i 1.52488 + 1.23976i
\(718\) 433.533 0.603806
\(719\) −826.077 + 268.409i −1.14892 + 0.373308i −0.820738 0.571305i \(-0.806438\pi\)
−0.328187 + 0.944613i \(0.606438\pi\)
\(720\) −179.449 + 14.0733i −0.249235 + 0.0195463i
\(721\) −129.359 + 398.128i −0.179417 + 0.552188i
\(722\) −217.324 70.6129i −0.301003 0.0978019i
\(723\) 596.658 + 230.371i 0.825254 + 0.318632i
\(724\) 303.990 0.419876
\(725\) 552.418 32.9664i 0.761956 0.0454709i
\(726\) −470.531 + 304.264i −0.648115 + 0.419097i
\(727\) 89.1626 64.7804i 0.122645 0.0891065i −0.524772 0.851243i \(-0.675849\pi\)
0.647417 + 0.762136i \(0.275849\pi\)
\(728\) 35.8418 + 11.6457i 0.0492332 + 0.0159968i
\(729\) 8.52416 728.950i 0.0116930 0.999932i
\(730\) −98.4489 12.5984i −0.134862 0.0172580i
\(731\) −2068.39 + 672.062i −2.82954 + 0.919373i
\(732\) −32.2110 49.8128i −0.0440041 0.0680503i
\(733\) 141.605 + 435.814i 0.193185 + 0.594562i 0.999993 + 0.00374852i \(0.00119319\pi\)
−0.806808 + 0.590814i \(0.798807\pi\)
\(734\) 134.224 184.743i 0.182866 0.251694i
\(735\) 231.051 110.681i 0.314354 0.150586i
\(736\) 204.627 148.670i 0.278026 0.201998i
\(737\) 23.7530 32.6931i 0.0322292 0.0443598i
\(738\) −226.107 + 129.371i −0.306378 + 0.175299i
\(739\) −439.130 + 319.046i −0.594221 + 0.431727i −0.843823 0.536621i \(-0.819700\pi\)
0.249602 + 0.968349i \(0.419700\pi\)
\(740\) 102.219 108.500i 0.138133 0.146622i
\(741\) 5.42332 99.7627i 0.00731892 0.134633i
\(742\) −147.959 455.370i −0.199405 0.613707i
\(743\) 353.834i 0.476224i −0.971238 0.238112i \(-0.923472\pi\)
0.971238 0.238112i \(-0.0765285\pi\)
\(744\) 44.8115 + 36.4324i 0.0602305 + 0.0489683i
\(745\) 37.9173 + 200.526i 0.0508957 + 0.269163i
\(746\) −142.154 46.1885i −0.190554 0.0619149i
\(747\) −287.785 + 317.123i −0.385254 + 0.424529i
\(748\) −732.879 + 532.468i −0.979785 + 0.711855i
\(749\) 923.715i 1.23326i
\(750\) 526.390 + 64.5292i 0.701853 + 0.0860389i
\(751\) 590.148 0.785816 0.392908 0.919578i \(-0.371469\pi\)
0.392908 + 0.919578i \(0.371469\pi\)
\(752\) −63.4735 87.3637i −0.0844062 0.116175i
\(753\) −8.45517 31.8029i −0.0112286 0.0422350i
\(754\) −22.8139 + 70.2141i −0.0302572 + 0.0931222i
\(755\) 830.892 157.113i 1.10052 0.208096i
\(756\) 136.916 + 272.643i 0.181106 + 0.360639i
\(757\) −150.334 −0.198592 −0.0992961 0.995058i \(-0.531659\pi\)
−0.0992961 + 0.995058i \(0.531659\pi\)
\(758\) −398.168 + 129.373i −0.525288 + 0.170676i
\(759\) 115.833 2130.76i 0.152612 2.80732i
\(760\) −145.362 136.945i −0.191265 0.180191i
\(761\) 468.319 + 644.586i 0.615400 + 0.847025i 0.997008 0.0772992i \(-0.0246297\pi\)
−0.381608 + 0.924324i \(0.624630\pi\)
\(762\) 612.624 + 33.3036i 0.803969 + 0.0437055i
\(763\) 562.429 + 408.628i 0.737128 + 0.535555i
\(764\) −191.736 263.902i −0.250963 0.345421i
\(765\) −669.753 + 1092.26i −0.875494 + 1.42779i
\(766\) 23.5054 + 17.0777i 0.0306859 + 0.0222946i
\(767\) 195.101 63.3921i 0.254369 0.0826494i
\(768\) −26.0642 40.3071i −0.0339377 0.0524832i
\(769\) −78.4957 241.585i −0.102075 0.314155i 0.886958 0.461850i \(-0.152814\pi\)
−0.989033 + 0.147696i \(0.952814\pi\)
\(770\) 80.6711 630.398i 0.104768 0.818699i
\(771\) 389.355 + 1464.50i 0.505000 + 1.89949i
\(772\) −61.6271 + 189.669i −0.0798278 + 0.245685i
\(773\) 146.432 + 201.546i 0.189433 + 0.260732i 0.893161 0.449737i \(-0.148482\pi\)
−0.703728 + 0.710470i \(0.748482\pi\)
\(774\) −886.615 398.894i −1.14550 0.515367i
\(775\) −108.038 131.457i −0.139404 0.169621i
\(776\) 165.059i 0.212704i
\(777\) −235.702 91.0050i −0.303349 0.117124i
\(778\) 277.574 854.284i 0.356779 1.09805i
\(779\) −274.881 89.3142i −0.352864 0.114652i
\(780\) −33.6547 + 62.2324i −0.0431470 + 0.0797852i
\(781\) −420.636 1294.58i −0.538587 1.65760i
\(782\) 1800.40i 2.30230i
\(783\) −534.108 + 268.220i −0.682130 + 0.342554i
\(784\) 55.2704 + 40.1563i 0.0704980 + 0.0512198i
\(785\) 981.189 185.532i 1.24992 0.236347i
\(786\) −302.613 116.839i −0.385004 0.148651i
\(787\) 155.382 + 112.892i 0.197436 + 0.143446i 0.682111 0.731249i \(-0.261062\pi\)
−0.484675 + 0.874694i \(0.661062\pi\)
\(788\) 125.605 172.880i 0.159397 0.219391i
\(789\) −436.046 + 1129.35i −0.552656 + 1.43138i
\(790\) 419.336 229.652i 0.530805 0.290699i
\(791\) −514.027 + 707.498i −0.649845 + 0.894435i
\(792\) −402.572 43.8991i −0.508297 0.0554281i
\(793\) −23.3159 −0.0294022
\(794\) 46.1601 14.9983i 0.0581361 0.0188896i
\(795\) 890.988 118.819i 1.12074 0.149457i
\(796\) 84.3157 259.497i 0.105924 0.326001i
\(797\) −387.304 125.843i −0.485952 0.157895i 0.0557862 0.998443i \(-0.482233\pi\)
−0.541738 + 0.840547i \(0.682233\pi\)
\(798\) −121.922 + 315.778i −0.152785 + 0.395712i
\(799\) −768.662 −0.962031
\(800\) 51.6362 + 131.658i 0.0645453 + 0.164572i
\(801\) −35.1484 15.8135i −0.0438806 0.0197422i
\(802\) −565.139 + 410.597i −0.704662 + 0.511967i
\(803\) −212.365 69.0014i −0.264464 0.0859295i
\(804\) 14.7298 3.91609i 0.0183207 0.00487076i
\(805\) 919.360 + 866.132i 1.14206 + 1.07594i
\(806\) 21.5890 7.01468i 0.0267853 0.00870307i
\(807\) 397.076 256.765i 0.492039 0.318172i
\(808\) −78.5768 241.834i −0.0972485 0.299300i
\(809\) −940.341 + 1294.27i −1.16235 + 1.59984i −0.460187 + 0.887822i \(0.652218\pi\)
−0.702163 + 0.712016i \(0.747782\pi\)
\(810\) −549.844 + 160.379i −0.678820 + 0.197999i
\(811\) 153.080 111.219i 0.188755 0.137139i −0.489394 0.872063i \(-0.662782\pi\)
0.678150 + 0.734924i \(0.262782\pi\)
\(812\) 147.022 202.359i 0.181062 0.249211i
\(813\) 54.1836 996.714i 0.0666464 1.22597i
\(814\) 271.317 197.123i 0.333313 0.242166i
\(815\) −756.784 357.608i −0.928569 0.438782i
\(816\) −341.163 18.5464i −0.418093 0.0227284i
\(817\) −333.328 1025.88i −0.407990 1.25566i
\(818\) 981.621i 1.20003i
\(819\) 119.210 + 12.9995i 0.145556 + 0.0158724i
\(820\) 148.972 + 140.347i 0.181673 + 0.171154i
\(821\) 276.418 + 89.8136i 0.336684 + 0.109395i 0.472480 0.881342i \(-0.343359\pi\)
−0.135796 + 0.990737i \(0.543359\pi\)
\(822\) 639.096 169.911i 0.777489 0.206704i
\(823\) −1259.18 + 914.845i −1.52998 + 1.11160i −0.573734 + 0.819042i \(0.694506\pi\)
−0.956248 + 0.292556i \(0.905494\pi\)
\(824\) 209.568i 0.254331i
\(825\) 1136.66 + 362.678i 1.37777 + 0.439610i
\(826\) −695.024 −0.841433
\(827\) −510.807 703.065i −0.617662 0.850139i 0.379518 0.925184i \(-0.376090\pi\)
−0.997180 + 0.0750451i \(0.976090\pi\)
\(828\) 540.863 596.001i 0.653216 0.719807i
\(829\) 184.881 569.005i 0.223017 0.686375i −0.775470 0.631384i \(-0.782487\pi\)
0.998487 0.0549909i \(-0.0175130\pi\)
\(830\) 304.202 + 143.747i 0.366509 + 0.173189i
\(831\) 427.499 525.819i 0.514439 0.632754i
\(832\) −18.8666 −0.0226762
\(833\) 462.491 150.272i 0.555211 0.180399i
\(834\) 127.865 + 6.95103i 0.153315 + 0.00833457i
\(835\) −702.709 + 384.843i −0.841567 + 0.460889i
\(836\) −264.092 363.492i −0.315900 0.434799i
\(837\) 163.248 + 84.3850i 0.195040 + 0.100818i
\(838\) −717.496 521.291i −0.856200 0.622066i
\(839\) −632.940 871.167i −0.754398 1.03834i −0.997659 0.0683793i \(-0.978217\pi\)
0.243261 0.969961i \(-0.421783\pi\)
\(840\) 173.597 165.291i 0.206663 0.196775i
\(841\) −283.961 206.310i −0.337647 0.245315i
\(842\) −192.921 + 62.6837i −0.229122 + 0.0744462i
\(843\) −300.425 + 194.267i −0.356376 + 0.230447i
\(844\) −74.4304 229.073i −0.0881877 0.271414i
\(845\) −392.529 716.745i −0.464532 0.848218i
\(846\) −254.457 230.916i −0.300777 0.272951i
\(847\) 230.584 709.665i 0.272236 0.837857i
\(848\) 140.892 + 193.922i 0.166147 + 0.228681i
\(849\) 242.506 + 375.024i 0.285637 + 0.441724i
\(850\) 974.208 + 253.487i 1.14613 + 0.298220i
\(851\) 666.519i 0.783218i
\(852\) 184.919 478.937i 0.217041 0.562133i
\(853\) −379.639 + 1168.41i −0.445063 + 1.36976i 0.437352 + 0.899291i \(0.355917\pi\)
−0.882415 + 0.470472i \(0.844083\pi\)
\(854\) 75.1288 + 24.4108i 0.0879728 + 0.0285841i
\(855\) −541.739 332.183i −0.633612 0.388518i
\(856\) 142.899 + 439.799i 0.166939 + 0.513784i
\(857\) 982.101i 1.14598i −0.819564 0.572988i \(-0.805784\pi\)
0.819564 0.572988i \(-0.194216\pi\)
\(858\) −100.410 + 123.503i −0.117028 + 0.143943i
\(859\) −262.341 190.602i −0.305403 0.221888i 0.424519 0.905419i \(-0.360443\pi\)
−0.729921 + 0.683531i \(0.760443\pi\)
\(860\) −96.9573 + 757.666i −0.112741 + 0.881007i
\(861\) 124.950 323.620i 0.145122 0.375865i
\(862\) −33.1034 24.0510i −0.0384030 0.0279014i
\(863\) −149.813 + 206.200i −0.173595 + 0.238934i −0.886945 0.461874i \(-0.847177\pi\)
0.713350 + 0.700808i \(0.247177\pi\)
\(864\) −107.367 108.630i −0.124267 0.125729i
\(865\) 482.212 + 454.293i 0.557470 + 0.525194i
\(866\) −637.492 + 877.433i −0.736134 + 1.01320i
\(867\) −987.261 + 1214.32i −1.13871 + 1.40060i
\(868\) −76.9081 −0.0886038
\(869\) 1022.98 332.385i 1.17719 0.382492i
\(870\) 323.805 + 340.077i 0.372189 + 0.390893i
\(871\) 1.85124 5.69752i 0.00212542 0.00654136i
\(872\) −330.999 107.548i −0.379586 0.123335i
\(873\) 107.195 + 514.158i 0.122789 + 0.588955i
\(874\) 892.957 1.02169
\(875\) −598.112 + 375.526i −0.683557 + 0.429173i
\(876\) −45.7306 70.7203i −0.0522039 0.0807310i
\(877\) −205.709 + 149.456i −0.234560 + 0.170417i −0.698856 0.715262i \(-0.746307\pi\)
0.464297 + 0.885680i \(0.346307\pi\)
\(878\) −200.729 65.2208i −0.228621 0.0742834i
\(879\) −384.797 1447.36i −0.437766 1.64660i
\(880\) 59.1140 + 312.625i 0.0671750 + 0.355256i
\(881\) −780.496 + 253.598i −0.885920 + 0.287853i −0.716413 0.697676i \(-0.754217\pi\)
−0.169507 + 0.985529i \(0.554217\pi\)
\(882\) 198.246 + 89.1924i 0.224769 + 0.101125i
\(883\) −333.191 1025.46i −0.377340 1.16133i −0.941887 0.335931i \(-0.890949\pi\)
0.564547 0.825401i \(-0.309051\pi\)
\(884\) −78.9358 + 108.646i −0.0892939 + 0.122902i
\(885\) 235.631 1283.34i 0.266250 1.45010i
\(886\) −656.506 + 476.979i −0.740977 + 0.538351i
\(887\) −60.8675 + 83.7769i −0.0686217 + 0.0944497i −0.841948 0.539558i \(-0.818591\pi\)
0.773327 + 0.634008i \(0.218591\pi\)
\(888\) 126.301 + 6.86600i 0.142231 + 0.00773199i
\(889\) −660.984 + 480.233i −0.743515 + 0.540195i
\(890\) −3.84371 + 30.0364i −0.00431878 + 0.0337488i
\(891\) −1282.52 + 124.698i −1.43942 + 0.139953i
\(892\) 241.726 + 743.956i 0.270993 + 0.834031i
\(893\) 381.240i 0.426920i
\(894\) −109.240 + 134.364i −0.122192 + 0.150295i
\(895\) 144.696 + 18.5165i 0.161671 + 0.0206888i
\(896\) 60.7920 + 19.7525i 0.0678482 + 0.0220452i
\(897\) −81.2794 305.721i −0.0906124 0.340826i
\(898\) −520.935 + 378.482i −0.580106 + 0.421472i
\(899\) 150.663i 0.167590i
\(900\) 246.350 + 376.579i 0.273722 + 0.418421i
\(901\) 1706.20 1.89368
\(902\) 270.651 + 372.519i 0.300057 + 0.412992i
\(903\) 1251.21 332.649i 1.38562 0.368382i
\(904\) 135.288 416.374i 0.149655 0.460591i
\(905\) −365.047 666.562i −0.403366 0.736532i
\(906\) 556.743 + 452.641i 0.614507 + 0.499604i
\(907\) 1152.59 1.27078 0.635388 0.772193i \(-0.280840\pi\)
0.635388 + 0.772193i \(0.280840\pi\)
\(908\) −100.051 + 32.5085i −0.110188 + 0.0358023i
\(909\) −401.822 702.284i −0.442049 0.772590i
\(910\) −17.5049 92.5752i −0.0192362 0.101731i
\(911\) −356.521 490.709i −0.391351 0.538649i 0.567196 0.823583i \(-0.308028\pi\)
−0.958547 + 0.284934i \(0.908028\pi\)
\(912\) 9.19861 169.210i 0.0100862 0.185537i
\(913\) 612.382 + 444.921i 0.670736 + 0.487318i
\(914\) 214.914 + 295.803i 0.235135 + 0.323636i
\(915\) −70.5444 + 130.447i −0.0770977 + 0.142565i
\(916\) −167.528 121.716i −0.182891 0.132878i
\(917\) 410.834 133.488i 0.448020 0.145571i
\(918\) −1074.77 + 163.791i −1.17077 + 0.178422i
\(919\) 183.613 + 565.101i 0.199796 + 0.614909i 0.999887 + 0.0150304i \(0.00478451\pi\)
−0.800091 + 0.599879i \(0.795215\pi\)
\(920\) −571.717 270.157i −0.621431 0.293649i
\(921\) −776.891 + 206.545i −0.843530 + 0.224262i
\(922\) 290.367 893.659i 0.314932 0.969261i
\(923\) −118.611 163.253i −0.128506 0.176873i
\(924\) 452.844 292.827i 0.490091 0.316912i
\(925\) −360.659 93.8426i −0.389901 0.101451i
\(926\) 829.200i 0.895464i
\(927\) −136.101 652.806i −0.146819 0.704214i
\(928\) −38.6952 + 119.092i −0.0416974 + 0.128332i
\(929\) 972.668 + 316.039i 1.04701 + 0.340193i 0.781493 0.623915i \(-0.214459\pi\)
0.265513 + 0.964107i \(0.414459\pi\)
\(930\) 26.0739 142.008i 0.0280364 0.152697i
\(931\) 74.5319 + 229.385i 0.0800557 + 0.246386i
\(932\) 6.62819i 0.00711180i
\(933\) 497.168 + 404.205i 0.532870 + 0.433232i
\(934\) −789.475 573.587i −0.845262 0.614119i
\(935\) 2047.62 + 967.575i 2.18997 + 1.03484i
\(936\) −58.7694 + 12.2526i −0.0627878 + 0.0130904i
\(937\) 238.925 + 173.589i 0.254990 + 0.185261i 0.707935 0.706277i \(-0.249627\pi\)
−0.452946 + 0.891538i \(0.649627\pi\)
\(938\) −11.9301 + 16.4204i −0.0127187 + 0.0175058i
\(939\) −356.913 137.805i −0.380099 0.146757i
\(940\) −115.341 + 244.089i −0.122703 + 0.259670i
\(941\) −360.338 + 495.963i −0.382931 + 0.527060i −0.956358 0.292197i \(-0.905614\pi\)
0.573427 + 0.819257i \(0.305614\pi\)
\(942\) 657.451 + 534.518i 0.697931 + 0.567429i
\(943\) −915.133 −0.970449
\(944\) 330.915 107.521i 0.350545 0.113899i
\(945\) 433.410 627.620i 0.458634 0.664149i
\(946\) −531.037 + 1634.36i −0.561350 + 1.72766i
\(947\) 843.070 + 273.930i 0.890253 + 0.289261i 0.718208 0.695828i \(-0.244963\pi\)
0.172045 + 0.985089i \(0.444963\pi\)
\(948\) 378.455 + 146.122i 0.399214 + 0.154137i
\(949\) −33.1022 −0.0348811
\(950\) −125.724 + 483.186i −0.132341 + 0.508617i
\(951\) 865.927 559.943i 0.910544 0.588794i
\(952\) 368.095 267.436i 0.386654 0.280921i
\(953\) 992.168 + 322.375i 1.04110 + 0.338274i 0.779170 0.626813i \(-0.215641\pi\)
0.261930 + 0.965087i \(0.415641\pi\)
\(954\) 564.819 + 512.566i 0.592054 + 0.537281i
\(955\) −348.413 + 737.327i −0.364831 + 0.772070i
\(956\) 893.419 290.290i 0.934539 0.303650i
\(957\) 573.649 + 887.122i 0.599424 + 0.926983i
\(958\) −175.211 539.243i −0.182892 0.562884i
\(959\) −517.623 + 712.447i −0.539753 + 0.742906i
\(960\) −57.0824 + 105.554i −0.0594609 + 0.109952i
\(961\) 739.988 537.633i 0.770018 0.559451i
\(962\) 29.2226 40.2214i 0.0303769 0.0418102i
\(963\) 730.753 + 1277.17i 0.758830 + 1.32624i
\(964\) 344.958 250.627i 0.357840 0.259986i
\(965\) 489.893 92.6333i 0.507661 0.0959930i
\(966\) −58.1779 + 1070.19i −0.0602256 + 1.10786i
\(967\) 118.040 + 363.291i 0.122069 + 0.375688i 0.993356 0.115085i \(-0.0367141\pi\)
−0.871287 + 0.490774i \(0.836714\pi\)
\(968\) 373.557i 0.385906i
\(969\) −935.931 760.927i −0.965873 0.785270i
\(970\) 361.925 198.210i 0.373118 0.204341i
\(971\) −76.9820 25.0130i −0.0792811 0.0257600i 0.269108 0.963110i \(-0.413271\pi\)
−0.348389 + 0.937350i \(0.613271\pi\)
\(972\) −404.995 268.654i −0.416662 0.276393i
\(973\) −137.959 + 100.233i −0.141787 + 0.103014i
\(974\) 703.671i 0.722454i
\(975\) 176.872 0.936909i 0.181407 0.000960933i
\(976\) −39.5467 −0.0405191
\(977\) 190.135 + 261.699i 0.194611 + 0.267859i 0.895160 0.445745i \(-0.147061\pi\)
−0.700549 + 0.713605i \(0.747061\pi\)
\(978\) −182.485 686.392i −0.186590 0.701833i
\(979\) −21.0521 + 64.7917i −0.0215037 + 0.0661815i
\(980\) 21.6796 169.413i 0.0221220 0.172871i
\(981\) −1100.91 120.050i −1.12223 0.122375i
\(982\) −162.286 −0.165261
\(983\) −10.0362 + 3.26097i −0.0102098 + 0.00331737i −0.314117 0.949384i \(-0.601709\pi\)
0.303908 + 0.952701i \(0.401709\pi\)
\(984\) −9.42706 + 173.412i −0.00958034 + 0.176232i
\(985\) −529.907 67.8114i −0.537976 0.0688440i
\(986\) 523.909 + 721.099i 0.531348 + 0.731337i
\(987\) 456.908 + 24.8385i 0.462926 + 0.0251657i
\(988\) −53.8859 39.1504i −0.0545404 0.0396259i
\(989\) −2007.49 2763.08i −2.02982 2.79381i
\(990\) 387.170 + 935.437i 0.391081 + 0.944886i
\(991\) −112.830 81.9761i −0.113855 0.0827206i 0.529401 0.848372i \(-0.322417\pi\)
−0.643256 + 0.765651i \(0.722417\pi\)
\(992\) 36.6175 11.8977i 0.0369128 0.0119937i
\(993\) −29.0698 44.9552i −0.0292747 0.0452721i
\(994\) 211.268 + 650.216i 0.212543 + 0.654141i
\(995\) −670.251 + 126.737i −0.673619 + 0.127374i
\(996\) 73.3531 + 275.907i 0.0736477 + 0.277015i
\(997\) −8.62044 + 26.5310i −0.00864638 + 0.0266108i −0.955287 0.295681i \(-0.904453\pi\)
0.946640 + 0.322292i \(0.104453\pi\)
\(998\) 27.8537 + 38.3374i 0.0279095 + 0.0384142i
\(999\) 397.887 60.6366i 0.398285 0.0606973i
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 150.3.j.a.11.1 80
3.2 odd 2 inner 150.3.j.a.11.18 yes 80
25.16 even 5 inner 150.3.j.a.41.18 yes 80
75.41 odd 10 inner 150.3.j.a.41.1 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
150.3.j.a.11.1 80 1.1 even 1 trivial
150.3.j.a.11.18 yes 80 3.2 odd 2 inner
150.3.j.a.41.1 yes 80 75.41 odd 10 inner
150.3.j.a.41.18 yes 80 25.16 even 5 inner