Properties

Label 150.3.i.a.29.19
Level $150$
Weight $3$
Character 150.29
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(29,150)]
 
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, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("150.29");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 150.i (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 29.19
Character \(\chi\) \(=\) 150.29
Dual form 150.3.i.a.119.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.437016 - 1.34500i) q^{2} +(2.06877 + 2.17260i) q^{3} +(-1.61803 - 1.17557i) q^{4} +(2.68239 + 4.21957i) q^{5} +(3.82622 - 1.83303i) q^{6} +8.88015i q^{7} +(-2.28825 + 1.66251i) q^{8} +(-0.440370 + 8.98922i) q^{9} +O(q^{10})\) \(q+(0.437016 - 1.34500i) q^{2} +(2.06877 + 2.17260i) q^{3} +(-1.61803 - 1.17557i) q^{4} +(2.68239 + 4.21957i) q^{5} +(3.82622 - 1.83303i) q^{6} +8.88015i q^{7} +(-2.28825 + 1.66251i) q^{8} +(-0.440370 + 8.98922i) q^{9} +(6.84756 - 1.76378i) q^{10} +(-16.5303 - 5.37102i) q^{11} +(-0.793300 - 5.94733i) q^{12} +(14.5516 - 4.72811i) q^{13} +(11.9438 + 3.88077i) q^{14} +(-3.61819 + 14.5571i) q^{15} +(1.23607 + 3.80423i) q^{16} +(8.28643 - 6.02044i) q^{17} +(11.8980 + 4.52073i) q^{18} +(14.2114 - 10.3252i) q^{19} +(0.620212 - 9.98075i) q^{20} +(-19.2930 + 18.3710i) q^{21} +(-14.4480 + 19.8860i) q^{22} +(8.91122 - 27.4259i) q^{23} +(-8.34582 - 1.53209i) q^{24} +(-10.6096 + 22.6371i) q^{25} -21.6381i q^{26} +(-20.4410 + 17.6399i) q^{27} +(10.4392 - 14.3684i) q^{28} +(6.68922 - 9.20692i) q^{29} +(17.9980 + 11.2281i) q^{30} +(33.0715 - 24.0278i) q^{31} +5.65685 q^{32} +(-22.5283 - 47.0251i) q^{33} +(-4.47618 - 13.7763i) q^{34} +(-37.4705 + 23.8200i) q^{35} +(11.2800 - 14.0272i) q^{36} +(1.47164 - 0.478166i) q^{37} +(-7.67675 - 23.6266i) q^{38} +(40.3763 + 21.8335i) q^{39} +(-13.1530 - 5.19593i) q^{40} +(-5.18186 + 1.68369i) q^{41} +(16.2776 + 33.9775i) q^{42} +27.1575i q^{43} +(20.4326 + 28.1230i) q^{44} +(-39.1119 + 22.2544i) q^{45} +(-32.9934 - 23.9711i) q^{46} +(-73.3819 - 53.3151i) q^{47} +(-5.70791 + 10.5556i) q^{48} -29.8571 q^{49} +(25.8102 + 24.1626i) q^{50} +(30.2227 + 5.54816i) q^{51} +(-29.1032 - 9.45621i) q^{52} +(15.4590 + 11.2316i) q^{53} +(14.7926 + 35.2020i) q^{54} +(-21.6772 - 84.1579i) q^{55} +(-14.7633 - 20.3200i) q^{56} +(51.8327 + 9.51523i) q^{57} +(-9.45998 - 13.0205i) q^{58} +(-36.4710 + 11.8502i) q^{59} +(22.9672 - 19.3004i) q^{60} +(-23.6592 + 72.8155i) q^{61} +(-17.8646 - 54.9816i) q^{62} +(-79.8257 - 3.91055i) q^{63} +(2.47214 - 7.60845i) q^{64} +(58.9837 + 48.7190i) q^{65} +(-73.0939 + 9.74982i) q^{66} +(-29.7411 - 40.9351i) q^{67} -20.4852 q^{68} +(78.0208 - 37.3775i) q^{69} +(15.6627 + 60.8074i) q^{70} +(-47.1092 + 64.8403i) q^{71} +(-13.9370 - 21.3017i) q^{72} +(-20.6289 - 6.70273i) q^{73} -2.18832i q^{74} +(-71.1301 + 23.7805i) q^{75} -35.1326 q^{76} +(47.6955 - 146.792i) q^{77} +(47.0110 - 44.7644i) q^{78} +(56.9806 + 41.3989i) q^{79} +(-12.7366 + 15.4201i) q^{80} +(-80.6121 - 7.91716i) q^{81} +7.70539i q^{82} +(94.9893 - 69.0138i) q^{83} +(52.8132 - 7.04462i) q^{84} +(47.6311 + 18.8160i) q^{85} +(36.5267 + 11.8682i) q^{86} +(33.8414 - 4.51402i) q^{87} +(46.7547 - 15.1915i) q^{88} +(135.505 + 44.0283i) q^{89} +(12.8396 + 62.3309i) q^{90} +(41.9863 + 129.221i) q^{91} +(-46.6598 + 33.9003i) q^{92} +(120.620 + 22.1430i) q^{93} +(-103.778 + 75.3989i) q^{94} +(81.6885 + 32.2699i) q^{95} +(11.7027 + 12.2901i) q^{96} +(102.989 - 141.752i) q^{97} +(-13.0480 + 40.1577i) q^{98} +(55.5607 - 146.229i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 40 q^{4} + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 80 q - 40 q^{4} + 20 q^{9} + 16 q^{10} + 20 q^{12} + 32 q^{15} - 80 q^{16} + 60 q^{19} - 60 q^{21} + 40 q^{22} + 116 q^{25} - 210 q^{27} - 40 q^{28} - 68 q^{30} + 180 q^{31} - 50 q^{33} - 120 q^{34} + 40 q^{36} - 40 q^{37} + 220 q^{39} + 32 q^{40} + 468 q^{45} + 120 q^{46} - 40 q^{48} - 680 q^{49} + 20 q^{51} - 120 q^{54} - 272 q^{55} - 156 q^{60} - 200 q^{61} - 830 q^{63} - 160 q^{64} + 160 q^{66} + 500 q^{67} - 280 q^{69} - 584 q^{70} + 120 q^{73} - 138 q^{75} - 80 q^{76} + 620 q^{78} + 400 q^{79} - 420 q^{81} + 180 q^{84} + 1632 q^{85} + 750 q^{87} + 160 q^{88} + 472 q^{90} - 340 q^{91} + 160 q^{94} + 20 q^{97} - 260 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(101\) \(127\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.437016 1.34500i 0.218508 0.672499i
\(3\) 2.06877 + 2.17260i 0.689590 + 0.724200i
\(4\) −1.61803 1.17557i −0.404508 0.293893i
\(5\) 2.68239 + 4.21957i 0.536477 + 0.843915i
\(6\) 3.82622 1.83303i 0.637704 0.305505i
\(7\) 8.88015i 1.26859i 0.773090 + 0.634297i \(0.218710\pi\)
−0.773090 + 0.634297i \(0.781290\pi\)
\(8\) −2.28825 + 1.66251i −0.286031 + 0.207813i
\(9\) −0.440370 + 8.98922i −0.0489300 + 0.998802i
\(10\) 6.84756 1.76378i 0.684756 0.176378i
\(11\) −16.5303 5.37102i −1.50275 0.488274i −0.561934 0.827182i \(-0.689943\pi\)
−0.940820 + 0.338908i \(0.889943\pi\)
\(12\) −0.793300 5.94733i −0.0661083 0.495610i
\(13\) 14.5516 4.72811i 1.11936 0.363701i 0.309834 0.950791i \(-0.399727\pi\)
0.809522 + 0.587090i \(0.199727\pi\)
\(14\) 11.9438 + 3.88077i 0.853127 + 0.277198i
\(15\) −3.61819 + 14.5571i −0.241213 + 0.970472i
\(16\) 1.23607 + 3.80423i 0.0772542 + 0.237764i
\(17\) 8.28643 6.02044i 0.487437 0.354144i −0.316761 0.948505i \(-0.602595\pi\)
0.804198 + 0.594362i \(0.202595\pi\)
\(18\) 11.8980 + 4.52073i 0.661001 + 0.251152i
\(19\) 14.2114 10.3252i 0.747970 0.543432i −0.147227 0.989103i \(-0.547035\pi\)
0.895197 + 0.445671i \(0.147035\pi\)
\(20\) 0.620212 9.98075i 0.0310106 0.499037i
\(21\) −19.2930 + 18.3710i −0.918715 + 0.874810i
\(22\) −14.4480 + 19.8860i −0.656728 + 0.903908i
\(23\) 8.91122 27.4259i 0.387444 1.19243i −0.547247 0.836971i \(-0.684324\pi\)
0.934691 0.355460i \(-0.115676\pi\)
\(24\) −8.34582 1.53209i −0.347742 0.0638371i
\(25\) −10.6096 + 22.6371i −0.424384 + 0.905482i
\(26\) 21.6381i 0.832236i
\(27\) −20.4410 + 17.6399i −0.757074 + 0.653329i
\(28\) 10.4392 14.3684i 0.372830 0.513157i
\(29\) 6.68922 9.20692i 0.230663 0.317480i −0.677959 0.735099i \(-0.737135\pi\)
0.908622 + 0.417619i \(0.137135\pi\)
\(30\) 17.9980 + 11.2281i 0.599934 + 0.374271i
\(31\) 33.0715 24.0278i 1.06682 0.775092i 0.0914841 0.995807i \(-0.470839\pi\)
0.975338 + 0.220715i \(0.0708389\pi\)
\(32\) 5.65685 0.176777
\(33\) −22.5283 47.0251i −0.682677 1.42500i
\(34\) −4.47618 13.7763i −0.131652 0.405184i
\(35\) −37.4705 + 23.8200i −1.07058 + 0.680572i
\(36\) 11.2800 14.0272i 0.313333 0.389644i
\(37\) 1.47164 0.478166i 0.0397741 0.0129234i −0.289062 0.957310i \(-0.593343\pi\)
0.328836 + 0.944387i \(0.393343\pi\)
\(38\) −7.67675 23.6266i −0.202020 0.621753i
\(39\) 40.3763 + 21.8335i 1.03529 + 0.559832i
\(40\) −13.1530 5.19593i −0.328826 0.129898i
\(41\) −5.18186 + 1.68369i −0.126387 + 0.0410656i −0.371528 0.928422i \(-0.621166\pi\)
0.245141 + 0.969488i \(0.421166\pi\)
\(42\) 16.2776 + 33.9775i 0.387562 + 0.808987i
\(43\) 27.1575i 0.631569i 0.948831 + 0.315784i \(0.102268\pi\)
−0.948831 + 0.315784i \(0.897732\pi\)
\(44\) 20.4326 + 28.1230i 0.464376 + 0.639159i
\(45\) −39.1119 + 22.2544i −0.869154 + 0.494542i
\(46\) −32.9934 23.9711i −0.717249 0.521112i
\(47\) −73.3819 53.3151i −1.56132 1.13436i −0.934920 0.354859i \(-0.884529\pi\)
−0.626397 0.779504i \(-0.715471\pi\)
\(48\) −5.70791 + 10.5556i −0.118915 + 0.219907i
\(49\) −29.8571 −0.609329
\(50\) 25.8102 + 24.1626i 0.516204 + 0.483253i
\(51\) 30.2227 + 5.54816i 0.592603 + 0.108788i
\(52\) −29.1032 9.45621i −0.559678 0.181850i
\(53\) 15.4590 + 11.2316i 0.291680 + 0.211918i 0.723996 0.689804i \(-0.242303\pi\)
−0.432316 + 0.901722i \(0.642303\pi\)
\(54\) 14.7926 + 35.2020i 0.273936 + 0.651889i
\(55\) −21.6772 84.1579i −0.394132 1.53014i
\(56\) −14.7633 20.3200i −0.263631 0.362857i
\(57\) 51.8327 + 9.51523i 0.909346 + 0.166934i
\(58\) −9.45998 13.0205i −0.163103 0.224492i
\(59\) −36.4710 + 11.8502i −0.618153 + 0.200850i −0.601320 0.799008i \(-0.705358\pi\)
−0.0168331 + 0.999858i \(0.505358\pi\)
\(60\) 22.9672 19.3004i 0.382787 0.321674i
\(61\) −23.6592 + 72.8155i −0.387856 + 1.19370i 0.546532 + 0.837438i \(0.315948\pi\)
−0.934387 + 0.356258i \(0.884052\pi\)
\(62\) −17.8646 54.9816i −0.288139 0.886800i
\(63\) −79.8257 3.91055i −1.26707 0.0620723i
\(64\) 2.47214 7.60845i 0.0386271 0.118882i
\(65\) 58.9837 + 48.7190i 0.907441 + 0.749523i
\(66\) −73.0939 + 9.74982i −1.10748 + 0.147724i
\(67\) −29.7411 40.9351i −0.443897 0.610972i 0.527175 0.849756i \(-0.323251\pi\)
−0.971073 + 0.238784i \(0.923251\pi\)
\(68\) −20.4852 −0.301253
\(69\) 78.0208 37.3775i 1.13074 0.541702i
\(70\) 15.6627 + 60.8074i 0.223752 + 0.868677i
\(71\) −47.1092 + 64.8403i −0.663510 + 0.913244i −0.999591 0.0285896i \(-0.990898\pi\)
0.336081 + 0.941833i \(0.390898\pi\)
\(72\) −13.9370 21.3017i −0.193569 0.295856i
\(73\) −20.6289 6.70273i −0.282587 0.0918182i 0.164294 0.986411i \(-0.447465\pi\)
−0.446881 + 0.894593i \(0.647465\pi\)
\(74\) 2.18832i 0.0295719i
\(75\) −71.1301 + 23.7805i −0.948401 + 0.317073i
\(76\) −35.1326 −0.462271
\(77\) 47.6955 146.792i 0.619422 1.90638i
\(78\) 47.0110 44.7644i 0.602705 0.573902i
\(79\) 56.9806 + 41.3989i 0.721274 + 0.524036i 0.886791 0.462171i \(-0.152929\pi\)
−0.165517 + 0.986207i \(0.552929\pi\)
\(80\) −12.7366 + 15.4201i −0.159207 + 0.192751i
\(81\) −80.6121 7.91716i −0.995212 0.0977428i
\(82\) 7.70539i 0.0939682i
\(83\) 94.9893 69.0138i 1.14445 0.831491i 0.156717 0.987644i \(-0.449909\pi\)
0.987733 + 0.156152i \(0.0499091\pi\)
\(84\) 52.8132 7.04462i 0.628728 0.0838645i
\(85\) 47.6311 + 18.8160i 0.560366 + 0.221365i
\(86\) 36.5267 + 11.8682i 0.424729 + 0.138003i
\(87\) 33.8414 4.51402i 0.388982 0.0518853i
\(88\) 46.7547 15.1915i 0.531304 0.172631i
\(89\) 135.505 + 44.0283i 1.52253 + 0.494701i 0.946494 0.322722i \(-0.104598\pi\)
0.576038 + 0.817423i \(0.304598\pi\)
\(90\) 12.8396 + 62.3309i 0.142662 + 0.692566i
\(91\) 41.9863 + 129.221i 0.461388 + 1.42001i
\(92\) −46.6598 + 33.9003i −0.507171 + 0.368482i
\(93\) 120.620 + 22.1430i 1.29699 + 0.238096i
\(94\) −103.778 + 75.3989i −1.10402 + 0.802116i
\(95\) 81.6885 + 32.2699i 0.859879 + 0.339684i
\(96\) 11.7027 + 12.2901i 0.121904 + 0.128022i
\(97\) 102.989 141.752i 1.06174 1.46136i 0.183580 0.983005i \(-0.441231\pi\)
0.878164 0.478360i \(-0.158769\pi\)
\(98\) −13.0480 + 40.1577i −0.133143 + 0.409773i
\(99\) 55.5607 146.229i 0.561219 1.47706i
\(100\) 43.7781 24.1552i 0.437781 0.241552i
\(101\) 67.3023i 0.666359i −0.942863 0.333180i \(-0.891878\pi\)
0.942863 0.333180i \(-0.108122\pi\)
\(102\) 20.6701 38.2248i 0.202648 0.374753i
\(103\) −50.7074 + 69.7927i −0.492305 + 0.677599i −0.980811 0.194961i \(-0.937542\pi\)
0.488506 + 0.872560i \(0.337542\pi\)
\(104\) −25.4372 + 35.0112i −0.244588 + 0.336647i
\(105\) −129.269 32.1301i −1.23113 0.306001i
\(106\) 21.8624 15.8839i 0.206249 0.149849i
\(107\) −116.245 −1.08640 −0.543201 0.839603i \(-0.682788\pi\)
−0.543201 + 0.839603i \(0.682788\pi\)
\(108\) 53.8112 4.51212i 0.498251 0.0417789i
\(109\) −17.6420 54.2965i −0.161853 0.498133i 0.836937 0.547299i \(-0.184344\pi\)
−0.998791 + 0.0491655i \(0.984344\pi\)
\(110\) −122.665 7.62253i −1.11514 0.0692957i
\(111\) 4.08335 + 2.20807i 0.0367870 + 0.0198926i
\(112\) −33.7821 + 10.9765i −0.301626 + 0.0980042i
\(113\) 2.96339 + 9.12036i 0.0262247 + 0.0807112i 0.963312 0.268383i \(-0.0864893\pi\)
−0.937088 + 0.349094i \(0.886489\pi\)
\(114\) 35.4497 65.5565i 0.310962 0.575057i
\(115\) 139.629 35.9654i 1.21417 0.312743i
\(116\) −21.6468 + 7.03346i −0.186610 + 0.0606333i
\(117\) 36.0939 + 132.890i 0.308495 + 1.13581i
\(118\) 54.2322i 0.459595i
\(119\) 53.4625 + 73.5848i 0.449264 + 0.618359i
\(120\) −15.9220 39.3255i −0.132683 0.327712i
\(121\) 146.512 + 106.447i 1.21084 + 0.879727i
\(122\) 87.5972 + 63.6431i 0.718010 + 0.521665i
\(123\) −14.3781 7.77494i −0.116895 0.0632109i
\(124\) −81.7572 −0.659333
\(125\) −123.978 + 15.9534i −0.991822 + 0.127627i
\(126\) −40.1448 + 105.656i −0.318609 + 0.838542i
\(127\) −130.689 42.4634i −1.02905 0.334357i −0.254633 0.967038i \(-0.581955\pi\)
−0.774413 + 0.632681i \(0.781955\pi\)
\(128\) −9.15298 6.65003i −0.0715077 0.0519534i
\(129\) −59.0023 + 56.1826i −0.457382 + 0.435524i
\(130\) 91.3037 58.0419i 0.702336 0.446476i
\(131\) −33.6017 46.2488i −0.256502 0.353044i 0.661273 0.750145i \(-0.270016\pi\)
−0.917775 + 0.397101i \(0.870016\pi\)
\(132\) −18.8297 + 102.572i −0.142649 + 0.777059i
\(133\) 91.6894 + 126.200i 0.689394 + 0.948869i
\(134\) −68.0550 + 22.1124i −0.507873 + 0.165018i
\(135\) −129.263 38.9352i −0.957507 0.288409i
\(136\) −8.95235 + 27.5525i −0.0658261 + 0.202592i
\(137\) 51.2370 + 157.691i 0.373992 + 1.15103i 0.944156 + 0.329499i \(0.106880\pi\)
−0.570164 + 0.821531i \(0.693120\pi\)
\(138\) −16.1762 121.272i −0.117219 0.878785i
\(139\) −1.12127 + 3.45092i −0.00806671 + 0.0248268i −0.955009 0.296577i \(-0.904155\pi\)
0.946942 + 0.321404i \(0.104155\pi\)
\(140\) 88.6306 + 5.50757i 0.633076 + 0.0393398i
\(141\) −35.9781 269.726i −0.255164 1.91295i
\(142\) 66.6225 + 91.6980i 0.469173 + 0.645761i
\(143\) −265.937 −1.85970
\(144\) −34.7414 + 9.43602i −0.241259 + 0.0655279i
\(145\) 56.7923 + 3.52912i 0.391671 + 0.0243388i
\(146\) −18.0303 + 24.8166i −0.123495 + 0.169977i
\(147\) −61.7676 64.8676i −0.420188 0.441276i
\(148\) −2.94329 0.956332i −0.0198871 0.00646170i
\(149\) 30.0596i 0.201742i 0.994900 + 0.100871i \(0.0321630\pi\)
−0.994900 + 0.100871i \(0.967837\pi\)
\(150\) 0.899735 + 106.062i 0.00599823 + 0.707081i
\(151\) −239.756 −1.58779 −0.793893 0.608058i \(-0.791949\pi\)
−0.793893 + 0.608058i \(0.791949\pi\)
\(152\) −15.3535 + 47.2532i −0.101010 + 0.310876i
\(153\) 50.4700 + 77.1397i 0.329869 + 0.504181i
\(154\) −176.591 128.301i −1.14669 0.833120i
\(155\) 190.098 + 75.0956i 1.22644 + 0.484488i
\(156\) −39.6634 82.7924i −0.254252 0.530720i
\(157\) 285.668i 1.81954i −0.415108 0.909772i \(-0.636256\pi\)
0.415108 0.909772i \(-0.363744\pi\)
\(158\) 80.5828 58.5468i 0.510018 0.370550i
\(159\) 7.57935 + 56.8220i 0.0476689 + 0.357371i
\(160\) 15.1739 + 23.8695i 0.0948367 + 0.149184i
\(161\) 243.546 + 79.1330i 1.51271 + 0.491510i
\(162\) −45.8774 + 104.963i −0.283194 + 0.647921i
\(163\) 111.924 36.3663i 0.686650 0.223106i 0.0551454 0.998478i \(-0.482438\pi\)
0.631504 + 0.775372i \(0.282438\pi\)
\(164\) 10.3637 + 3.36738i 0.0631935 + 0.0205328i
\(165\) 137.996 221.199i 0.836340 1.34060i
\(166\) −51.3115 157.920i −0.309105 0.951328i
\(167\) 16.3909 11.9087i 0.0981492 0.0713096i −0.537628 0.843182i \(-0.680680\pi\)
0.635777 + 0.771872i \(0.280680\pi\)
\(168\) 13.6052 74.1122i 0.0809833 0.441144i
\(169\) 52.6707 38.2675i 0.311661 0.226435i
\(170\) 46.1231 55.8408i 0.271312 0.328475i
\(171\) 86.5572 + 132.297i 0.506183 + 0.773664i
\(172\) 31.9255 43.9417i 0.185613 0.255475i
\(173\) −38.6233 + 118.870i −0.223256 + 0.687111i 0.775208 + 0.631706i \(0.217645\pi\)
−0.998464 + 0.0554049i \(0.982355\pi\)
\(174\) 8.71789 47.4893i 0.0501028 0.272927i
\(175\) −201.021 94.2148i −1.14869 0.538370i
\(176\) 69.5239i 0.395022i
\(177\) −101.196 54.7217i −0.571728 0.309162i
\(178\) 118.436 163.013i 0.665371 0.915804i
\(179\) 56.5615 77.8503i 0.315986 0.434918i −0.621250 0.783612i \(-0.713375\pi\)
0.937236 + 0.348695i \(0.113375\pi\)
\(180\) 89.4460 + 9.97044i 0.496922 + 0.0553913i
\(181\) −68.8447 + 50.0186i −0.380357 + 0.276346i −0.761493 0.648173i \(-0.775533\pi\)
0.381135 + 0.924519i \(0.375533\pi\)
\(182\) 192.150 1.05577
\(183\) −207.144 + 99.2367i −1.13194 + 0.542277i
\(184\) 25.2047 + 77.5722i 0.136982 + 0.421588i
\(185\) 5.96517 + 4.92708i 0.0322442 + 0.0266329i
\(186\) 82.4952 152.557i 0.443523 0.820199i
\(187\) −169.313 + 55.0131i −0.905417 + 0.294188i
\(188\) 56.0588 + 172.531i 0.298185 + 0.917719i
\(189\) −156.645 181.519i −0.828809 0.960419i
\(190\) 79.1022 95.7683i 0.416327 0.504044i
\(191\) −115.633 + 37.5714i −0.605407 + 0.196709i −0.595651 0.803244i \(-0.703106\pi\)
−0.00975672 + 0.999952i \(0.503106\pi\)
\(192\) 21.6444 10.3692i 0.112731 0.0540062i
\(193\) 67.7539i 0.351056i −0.984474 0.175528i \(-0.943837\pi\)
0.984474 0.175528i \(-0.0561633\pi\)
\(194\) −145.649 200.468i −0.750766 1.03334i
\(195\) 16.1769 + 228.936i 0.0829585 + 1.17403i
\(196\) 48.3098 + 35.0992i 0.246479 + 0.179077i
\(197\) −133.793 97.2065i −0.679154 0.493434i 0.193923 0.981017i \(-0.437879\pi\)
−0.873077 + 0.487583i \(0.837879\pi\)
\(198\) −172.397 138.633i −0.870692 0.700169i
\(199\) −299.615 −1.50561 −0.752803 0.658246i \(-0.771298\pi\)
−0.752803 + 0.658246i \(0.771298\pi\)
\(200\) −13.3569 69.4377i −0.0667846 0.347188i
\(201\) 27.4080 149.301i 0.136358 0.742791i
\(202\) −90.5214 29.4122i −0.448126 0.145605i
\(203\) 81.7588 + 59.4013i 0.402753 + 0.292617i
\(204\) −42.3791 44.5061i −0.207741 0.218167i
\(205\) −21.0042 17.3489i −0.102460 0.0846290i
\(206\) 71.7111 + 98.7018i 0.348112 + 0.479135i
\(207\) 242.613 + 92.1825i 1.17205 + 0.445326i
\(208\) 35.9736 + 49.5134i 0.172950 + 0.238045i
\(209\) −290.376 + 94.3488i −1.38936 + 0.451430i
\(210\) −99.7076 + 159.825i −0.474798 + 0.761073i
\(211\) −45.0795 + 138.740i −0.213647 + 0.657538i 0.785600 + 0.618735i \(0.212354\pi\)
−0.999247 + 0.0388029i \(0.987646\pi\)
\(212\) −11.8097 36.3464i −0.0557059 0.171445i
\(213\) −238.330 + 31.7903i −1.11892 + 0.149250i
\(214\) −50.8009 + 156.349i −0.237387 + 0.730603i
\(215\) −114.593 + 72.8468i −0.532990 + 0.338823i
\(216\) 17.4475 74.3477i 0.0807757 0.344202i
\(217\) 213.371 + 293.680i 0.983276 + 1.35336i
\(218\) −80.7385 −0.370360
\(219\) −28.1141 58.6847i −0.128375 0.267967i
\(220\) −63.8591 + 161.654i −0.290268 + 0.734789i
\(221\) 92.1156 126.786i 0.416813 0.573694i
\(222\) 4.75434 4.52714i 0.0214160 0.0203925i
\(223\) 338.042 + 109.836i 1.51588 + 0.492540i 0.944603 0.328216i \(-0.106447\pi\)
0.571279 + 0.820756i \(0.306447\pi\)
\(224\) 50.2337i 0.224258i
\(225\) −198.817 105.341i −0.883633 0.468181i
\(226\) 13.5619 0.0600085
\(227\) −115.661 + 355.968i −0.509519 + 1.56814i 0.283518 + 0.958967i \(0.408498\pi\)
−0.793038 + 0.609173i \(0.791502\pi\)
\(228\) −72.6813 76.3290i −0.318777 0.334776i
\(229\) 145.582 + 105.771i 0.635729 + 0.461884i 0.858380 0.513014i \(-0.171471\pi\)
−0.222651 + 0.974898i \(0.571471\pi\)
\(230\) 12.6468 203.518i 0.0549860 0.884861i
\(231\) 417.590 200.055i 1.80775 0.866039i
\(232\) 32.1886i 0.138744i
\(233\) −20.8576 + 15.1539i −0.0895177 + 0.0650384i −0.631644 0.775259i \(-0.717619\pi\)
0.542126 + 0.840297i \(0.317619\pi\)
\(234\) 194.510 + 9.52879i 0.831239 + 0.0407213i
\(235\) 28.1282 452.652i 0.119694 1.92618i
\(236\) 72.9421 + 23.7003i 0.309077 + 0.100425i
\(237\) 27.9368 + 209.441i 0.117877 + 0.883717i
\(238\) 122.335 39.7491i 0.514014 0.167013i
\(239\) −56.1423 18.2417i −0.234905 0.0763253i 0.189199 0.981939i \(-0.439411\pi\)
−0.424104 + 0.905613i \(0.639411\pi\)
\(240\) −59.8508 + 4.22912i −0.249378 + 0.0176213i
\(241\) −45.3121 139.456i −0.188017 0.578657i 0.811970 0.583699i \(-0.198395\pi\)
−0.999987 + 0.00504186i \(0.998395\pi\)
\(242\) 207.199 150.539i 0.856193 0.622061i
\(243\) −149.567 191.517i −0.615503 0.788134i
\(244\) 123.881 90.0049i 0.507710 0.368873i
\(245\) −80.0884 125.984i −0.326891 0.514222i
\(246\) −16.7407 + 15.9407i −0.0680517 + 0.0647996i
\(247\) 157.981 217.442i 0.639597 0.880330i
\(248\) −35.7292 + 109.963i −0.144069 + 0.443400i
\(249\) 346.450 + 63.5999i 1.39137 + 0.255421i
\(250\) −32.7230 + 173.722i −0.130892 + 0.694887i
\(251\) 101.467i 0.404252i −0.979359 0.202126i \(-0.935215\pi\)
0.979359 0.202126i \(-0.0647851\pi\)
\(252\) 124.563 + 100.168i 0.494300 + 0.397492i
\(253\) −294.610 + 405.496i −1.16447 + 1.60275i
\(254\) −114.226 + 157.219i −0.449709 + 0.618972i
\(255\) 57.6582 + 142.409i 0.226111 + 0.558468i
\(256\) −12.9443 + 9.40456i −0.0505636 + 0.0367366i
\(257\) 125.099 0.486765 0.243383 0.969930i \(-0.421743\pi\)
0.243383 + 0.969930i \(0.421743\pi\)
\(258\) 49.7805 + 103.911i 0.192948 + 0.402754i
\(259\) 4.24619 + 13.0684i 0.0163945 + 0.0504572i
\(260\) −38.1650 148.168i −0.146788 0.569879i
\(261\) 79.8173 + 64.1853i 0.305813 + 0.245921i
\(262\) −76.8890 + 24.9827i −0.293469 + 0.0953540i
\(263\) −66.7110 205.315i −0.253654 0.780667i −0.994092 0.108542i \(-0.965382\pi\)
0.740438 0.672125i \(-0.234618\pi\)
\(264\) 129.730 + 70.1515i 0.491401 + 0.265725i
\(265\) −5.92563 + 95.3582i −0.0223609 + 0.359842i
\(266\) 209.808 68.1707i 0.788751 0.256281i
\(267\) 184.674 + 385.483i 0.691661 + 1.44376i
\(268\) 101.197i 0.377601i
\(269\) −14.5225 19.9886i −0.0539871 0.0743069i 0.781170 0.624319i \(-0.214623\pi\)
−0.835157 + 0.550012i \(0.814623\pi\)
\(270\) −108.858 + 156.844i −0.403178 + 0.580903i
\(271\) 375.863 + 273.080i 1.38695 + 1.00768i 0.996192 + 0.0871815i \(0.0277860\pi\)
0.390755 + 0.920495i \(0.372214\pi\)
\(272\) 33.1457 + 24.0818i 0.121859 + 0.0885359i
\(273\) −193.884 + 358.547i −0.710199 + 1.31336i
\(274\) 234.485 0.855786
\(275\) 296.964 317.213i 1.07987 1.15350i
\(276\) −170.180 31.2410i −0.616595 0.113192i
\(277\) −225.091 73.1364i −0.812601 0.264030i −0.126902 0.991915i \(-0.540503\pi\)
−0.685699 + 0.727885i \(0.740503\pi\)
\(278\) 4.15147 + 3.01622i 0.0149333 + 0.0108497i
\(279\) 201.428 + 307.868i 0.721964 + 1.10347i
\(280\) 46.1407 116.801i 0.164788 0.417146i
\(281\) 52.7516 + 72.6064i 0.187728 + 0.258386i 0.892499 0.451049i \(-0.148950\pi\)
−0.704771 + 0.709435i \(0.748950\pi\)
\(282\) −378.504 69.4842i −1.34221 0.246398i
\(283\) −296.551 408.168i −1.04789 1.44229i −0.890628 0.454732i \(-0.849735\pi\)
−0.157257 0.987558i \(-0.550265\pi\)
\(284\) 152.449 49.5336i 0.536791 0.174414i
\(285\) 98.8852 + 244.235i 0.346966 + 0.856966i
\(286\) −116.219 + 357.685i −0.406360 + 1.25065i
\(287\) −14.9514 46.0157i −0.0520955 0.160334i
\(288\) −2.49111 + 50.8507i −0.00864968 + 0.176565i
\(289\) −56.8867 + 175.079i −0.196840 + 0.605811i
\(290\) 29.5658 74.8432i 0.101951 0.258080i
\(291\) 521.032 69.4992i 1.79049 0.238829i
\(292\) 25.4987 + 35.0959i 0.0873243 + 0.120192i
\(293\) −45.9329 −0.156768 −0.0783838 0.996923i \(-0.524976\pi\)
−0.0783838 + 0.996923i \(0.524976\pi\)
\(294\) −114.240 + 54.7290i −0.388572 + 0.186153i
\(295\) −147.832 122.106i −0.501126 0.413917i
\(296\) −2.57253 + 3.54078i −0.00869097 + 0.0119621i
\(297\) 432.640 181.804i 1.45670 0.612134i
\(298\) 40.4300 + 13.1365i 0.135671 + 0.0440823i
\(299\) 441.225i 1.47567i
\(300\) 143.047 + 45.1407i 0.476822 + 0.150469i
\(301\) −241.162 −0.801204
\(302\) −104.777 + 322.471i −0.346944 + 1.06778i
\(303\) 146.221 139.233i 0.482577 0.459515i
\(304\) 56.8457 + 41.3008i 0.186992 + 0.135858i
\(305\) −370.713 + 95.4877i −1.21545 + 0.313074i
\(306\) 125.809 34.1707i 0.411140 0.111669i
\(307\) 110.694i 0.360567i 0.983615 + 0.180284i \(0.0577015\pi\)
−0.983615 + 0.180284i \(0.942298\pi\)
\(308\) −249.737 + 181.444i −0.810833 + 0.589105i
\(309\) −256.534 + 34.2184i −0.830206 + 0.110739i
\(310\) 184.079 222.863i 0.593804 0.718913i
\(311\) 320.823 + 104.242i 1.03159 + 0.335182i 0.775417 0.631450i \(-0.217540\pi\)
0.256169 + 0.966632i \(0.417540\pi\)
\(312\) −128.689 + 17.1655i −0.412465 + 0.0550177i
\(313\) 27.0113 8.77650i 0.0862981 0.0280399i −0.265550 0.964097i \(-0.585553\pi\)
0.351848 + 0.936057i \(0.385553\pi\)
\(314\) −384.223 124.842i −1.22364 0.397585i
\(315\) −197.622 347.320i −0.627373 1.10260i
\(316\) −43.5293 133.970i −0.137751 0.423954i
\(317\) 19.4846 14.1564i 0.0614655 0.0446573i −0.556628 0.830762i \(-0.687905\pi\)
0.618094 + 0.786104i \(0.287905\pi\)
\(318\) 79.7377 + 14.6379i 0.250747 + 0.0460312i
\(319\) −160.025 + 116.265i −0.501647 + 0.364468i
\(320\) 38.7356 9.97746i 0.121049 0.0311796i
\(321\) −240.484 252.554i −0.749172 0.786772i
\(322\) 212.867 292.987i 0.661079 0.909897i
\(323\) 55.5996 171.118i 0.172135 0.529777i
\(324\) 121.126 + 107.576i 0.373846 + 0.332023i
\(325\) −47.3563 + 379.569i −0.145712 + 1.16791i
\(326\) 166.430i 0.510521i
\(327\) 81.4673 150.656i 0.249135 0.460722i
\(328\) 9.05823 12.4676i 0.0276166 0.0380109i
\(329\) 473.446 651.643i 1.43905 1.98068i
\(330\) −237.206 282.272i −0.718806 0.855370i
\(331\) 201.740 146.572i 0.609486 0.442817i −0.239748 0.970835i \(-0.577065\pi\)
0.849233 + 0.528018i \(0.177065\pi\)
\(332\) −234.826 −0.707309
\(333\) 3.65027 + 13.4395i 0.0109618 + 0.0403588i
\(334\) −8.85407 27.2500i −0.0265092 0.0815869i
\(335\) 92.9516 235.299i 0.277467 0.702384i
\(336\) −93.7349 50.6872i −0.278973 0.150855i
\(337\) −108.391 + 35.2183i −0.321634 + 0.104505i −0.465384 0.885109i \(-0.654084\pi\)
0.143750 + 0.989614i \(0.454084\pi\)
\(338\) −28.4517 87.5655i −0.0841768 0.259069i
\(339\) −13.6843 + 25.3062i −0.0403667 + 0.0746496i
\(340\) −54.9492 86.4387i −0.161615 0.254231i
\(341\) −675.736 + 219.560i −1.98163 + 0.643870i
\(342\) 215.765 58.6035i 0.630893 0.171355i
\(343\) 169.992i 0.495602i
\(344\) −45.1495 62.1430i −0.131249 0.180648i
\(345\) 366.999 + 228.954i 1.06377 + 0.663634i
\(346\) 143.001 + 103.896i 0.413298 + 0.300278i
\(347\) 293.966 + 213.579i 0.847166 + 0.615502i 0.924363 0.381514i \(-0.124597\pi\)
−0.0771974 + 0.997016i \(0.524597\pi\)
\(348\) −60.0631 32.4791i −0.172595 0.0933308i
\(349\) −188.390 −0.539799 −0.269899 0.962889i \(-0.586990\pi\)
−0.269899 + 0.962889i \(0.586990\pi\)
\(350\) −214.568 + 229.199i −0.613051 + 0.654853i
\(351\) −214.046 + 353.336i −0.609818 + 1.00666i
\(352\) −93.5095 30.3831i −0.265652 0.0863155i
\(353\) 146.982 + 106.789i 0.416380 + 0.302518i 0.776180 0.630512i \(-0.217155\pi\)
−0.359799 + 0.933030i \(0.617155\pi\)
\(354\) −117.825 + 112.194i −0.332838 + 0.316932i
\(355\) −399.964 24.8541i −1.12666 0.0700114i
\(356\) −167.494 230.535i −0.470488 0.647571i
\(357\) −49.2685 + 268.382i −0.138007 + 0.751772i
\(358\) −79.9901 110.097i −0.223436 0.307533i
\(359\) 274.660 89.2425i 0.765070 0.248586i 0.0996170 0.995026i \(-0.468238\pi\)
0.665453 + 0.746439i \(0.268238\pi\)
\(360\) 52.4996 115.947i 0.145832 0.322076i
\(361\) −16.2004 + 49.8598i −0.0448765 + 0.138116i
\(362\) 37.1886 + 114.455i 0.102731 + 0.316174i
\(363\) 71.8326 + 538.526i 0.197886 + 1.48354i
\(364\) 83.9726 258.441i 0.230694 0.710003i
\(365\) −27.0520 105.024i −0.0741151 0.287738i
\(366\) 42.9477 + 321.977i 0.117343 + 0.879717i
\(367\) −104.081 143.255i −0.283598 0.390340i 0.643323 0.765595i \(-0.277555\pi\)
−0.926922 + 0.375255i \(0.877555\pi\)
\(368\) 115.349 0.313449
\(369\) −12.8531 47.3224i −0.0348323 0.128245i
\(370\) 9.23378 5.86993i 0.0249562 0.0158647i
\(371\) −99.7387 + 137.279i −0.268838 + 0.370023i
\(372\) −169.137 177.626i −0.454669 0.477488i
\(373\) 278.407 + 90.4598i 0.746399 + 0.242520i 0.657431 0.753515i \(-0.271643\pi\)
0.0889679 + 0.996034i \(0.471643\pi\)
\(374\) 251.767i 0.673174i
\(375\) −291.142 236.350i −0.776379 0.630267i
\(376\) 256.553 0.682321
\(377\) 53.8076 165.603i 0.142726 0.439265i
\(378\) −312.599 + 131.360i −0.826982 + 0.347514i
\(379\) −456.223 331.465i −1.20375 0.874579i −0.209106 0.977893i \(-0.567055\pi\)
−0.994649 + 0.103314i \(0.967055\pi\)
\(380\) −94.2392 148.244i −0.247998 0.390117i
\(381\) −178.109 371.781i −0.467479 0.975804i
\(382\) 171.945i 0.450118i
\(383\) 363.176 263.863i 0.948241 0.688937i −0.00214932 0.999998i \(-0.500684\pi\)
0.950390 + 0.311060i \(0.100684\pi\)
\(384\) −4.48758 33.6432i −0.0116864 0.0876124i
\(385\) 747.335 192.497i 1.94113 0.499993i
\(386\) −91.1288 29.6095i −0.236085 0.0767086i
\(387\) −244.124 11.9593i −0.630813 0.0309027i
\(388\) −333.280 + 108.289i −0.858969 + 0.279096i
\(389\) −512.841 166.632i −1.31836 0.428360i −0.436427 0.899740i \(-0.643756\pi\)
−0.881931 + 0.471379i \(0.843756\pi\)
\(390\) 314.988 + 78.2910i 0.807662 + 0.200746i
\(391\) −91.2740 280.912i −0.233437 0.718446i
\(392\) 68.3204 49.6377i 0.174287 0.126627i
\(393\) 30.9658 168.681i 0.0787934 0.429214i
\(394\) −189.212 + 137.471i −0.480234 + 0.348911i
\(395\) −21.8414 + 351.482i −0.0552946 + 0.889827i
\(396\) −261.802 + 171.288i −0.661116 + 0.432546i
\(397\) 311.278 428.438i 0.784076 1.07919i −0.210744 0.977541i \(-0.567589\pi\)
0.994821 0.101647i \(-0.0324112\pi\)
\(398\) −130.937 + 402.982i −0.328987 + 1.01252i
\(399\) −84.4967 + 460.282i −0.211771 + 1.15359i
\(400\) −99.2307 12.3804i −0.248077 0.0309509i
\(401\) 362.105i 0.903006i 0.892270 + 0.451503i \(0.149112\pi\)
−0.892270 + 0.451503i \(0.850888\pi\)
\(402\) −188.832 102.111i −0.469730 0.254007i
\(403\) 367.638 506.010i 0.912252 1.25561i
\(404\) −79.1186 + 108.897i −0.195838 + 0.269548i
\(405\) −182.826 361.386i −0.451422 0.892311i
\(406\) 115.624 84.0061i 0.284789 0.206912i
\(407\) −26.8949 −0.0660809
\(408\) −78.3809 + 37.5500i −0.192110 + 0.0920342i
\(409\) −118.845 365.769i −0.290576 0.894300i −0.984672 0.174418i \(-0.944196\pi\)
0.694096 0.719882i \(-0.255804\pi\)
\(410\) −32.5135 + 20.6688i −0.0793011 + 0.0504118i
\(411\) −236.602 + 437.544i −0.575674 + 1.06458i
\(412\) 164.093 53.3169i 0.398283 0.129410i
\(413\) −105.231 323.868i −0.254797 0.784185i
\(414\) 230.011 286.029i 0.555582 0.690892i
\(415\) 546.007 + 215.693i 1.31568 + 0.519741i
\(416\) 82.3164 26.7462i 0.197876 0.0642938i
\(417\) −9.81713 + 4.70310i −0.0235423 + 0.0112784i
\(418\) 431.787i 1.03298i
\(419\) 476.023 + 655.189i 1.13609 + 1.56370i 0.775943 + 0.630804i \(0.217275\pi\)
0.360150 + 0.932894i \(0.382725\pi\)
\(420\) 171.391 + 203.953i 0.408073 + 0.485601i
\(421\) −501.538 364.388i −1.19130 0.865531i −0.197899 0.980222i \(-0.563412\pi\)
−0.993401 + 0.114692i \(0.963412\pi\)
\(422\) 166.905 + 121.264i 0.395510 + 0.287355i
\(423\) 511.576 636.168i 1.20940 1.50394i
\(424\) −54.0468 −0.127469
\(425\) 48.3695 + 251.455i 0.113811 + 0.591658i
\(426\) −61.3962 + 334.446i −0.144123 + 0.785085i
\(427\) −646.613 210.097i −1.51432 0.492031i
\(428\) 188.088 + 136.654i 0.439459 + 0.319285i
\(429\) −550.163 577.775i −1.28243 1.34679i
\(430\) 47.8999 + 185.962i 0.111395 + 0.432471i
\(431\) −57.0800 78.5638i −0.132436 0.182283i 0.737649 0.675185i \(-0.235936\pi\)
−0.870085 + 0.492902i \(0.835936\pi\)
\(432\) −92.3726 55.9580i −0.213825 0.129533i
\(433\) 47.8218 + 65.8210i 0.110443 + 0.152012i 0.860660 0.509180i \(-0.170051\pi\)
−0.750217 + 0.661191i \(0.770051\pi\)
\(434\) 488.245 158.640i 1.12499 0.365531i
\(435\) 109.823 + 130.688i 0.252467 + 0.300432i
\(436\) −35.2840 + 108.593i −0.0809266 + 0.249067i
\(437\) −156.537 481.772i −0.358208 1.10245i
\(438\) −91.2171 + 12.1672i −0.208258 + 0.0277791i
\(439\) −176.553 + 543.374i −0.402171 + 1.23775i 0.521064 + 0.853518i \(0.325535\pi\)
−0.923235 + 0.384236i \(0.874465\pi\)
\(440\) 189.516 + 156.535i 0.430718 + 0.355762i
\(441\) 13.1482 268.392i 0.0298145 0.608599i
\(442\) −130.271 179.303i −0.294731 0.405663i
\(443\) 307.905 0.695044 0.347522 0.937672i \(-0.387023\pi\)
0.347522 + 0.937672i \(0.387023\pi\)
\(444\) −4.01126 8.37301i −0.00903437 0.0188581i
\(445\) 177.697 + 689.876i 0.399319 + 1.55028i
\(446\) 295.459 406.665i 0.662465 0.911805i
\(447\) −65.3074 + 62.1864i −0.146102 + 0.139119i
\(448\) 67.5642 + 21.9529i 0.150813 + 0.0490021i
\(449\) 730.520i 1.62699i 0.581570 + 0.813497i \(0.302439\pi\)
−0.581570 + 0.813497i \(0.697561\pi\)
\(450\) −228.569 + 221.373i −0.507932 + 0.491940i
\(451\) 94.7008 0.209980
\(452\) 5.92677 18.2407i 0.0131123 0.0403556i
\(453\) −496.000 520.893i −1.09492 1.14987i
\(454\) 428.230 + 311.127i 0.943237 + 0.685302i
\(455\) −432.632 + 523.784i −0.950840 + 1.15117i
\(456\) −134.425 + 64.3991i −0.294792 + 0.141226i
\(457\) 334.758i 0.732513i 0.930514 + 0.366256i \(0.119361\pi\)
−0.930514 + 0.366256i \(0.880639\pi\)
\(458\) 205.884 149.583i 0.449528 0.326601i
\(459\) −63.1828 + 269.236i −0.137653 + 0.586570i
\(460\) −268.204 105.951i −0.583053 0.230327i
\(461\) −385.182 125.153i −0.835536 0.271482i −0.140160 0.990129i \(-0.544762\pi\)
−0.695375 + 0.718647i \(0.744762\pi\)
\(462\) −86.5799 649.085i −0.187402 1.40495i
\(463\) 403.917 131.241i 0.872392 0.283457i 0.161597 0.986857i \(-0.448336\pi\)
0.710795 + 0.703400i \(0.248336\pi\)
\(464\) 43.2935 + 14.0669i 0.0933050 + 0.0303166i
\(465\) 230.116 + 568.362i 0.494874 + 1.22228i
\(466\) 11.2669 + 34.6759i 0.0241779 + 0.0744119i
\(467\) −251.589 + 182.790i −0.538734 + 0.391413i −0.823615 0.567150i \(-0.808046\pi\)
0.284881 + 0.958563i \(0.408046\pi\)
\(468\) 97.8202 257.451i 0.209017 0.550109i
\(469\) 363.510 264.106i 0.775075 0.563125i
\(470\) −596.523 235.648i −1.26920 0.501380i
\(471\) 620.643 590.983i 1.31771 1.25474i
\(472\) 63.7537 87.7495i 0.135071 0.185910i
\(473\) 145.863 448.921i 0.308379 0.949093i
\(474\) 293.906 + 53.9541i 0.620055 + 0.113827i
\(475\) 82.9548 + 431.251i 0.174642 + 0.907897i
\(476\) 181.912i 0.382167i
\(477\) −107.771 + 134.019i −0.225936 + 0.280961i
\(478\) −49.0702 + 67.5393i −0.102657 + 0.141296i
\(479\) −113.399 + 156.080i −0.236741 + 0.325846i −0.910813 0.412820i \(-0.864544\pi\)
0.674071 + 0.738666i \(0.264544\pi\)
\(480\) −20.4676 + 82.3473i −0.0426408 + 0.171557i
\(481\) 19.1540 13.9162i 0.0398211 0.0289317i
\(482\) −207.370 −0.430229
\(483\) 331.918 + 692.837i 0.687200 + 1.43444i
\(484\) −111.925 344.470i −0.231250 0.711714i
\(485\) 874.391 + 54.3354i 1.80287 + 0.112032i
\(486\) −322.953 + 117.472i −0.664512 + 0.241711i
\(487\) −485.583 + 157.776i −0.997091 + 0.323974i −0.761702 0.647927i \(-0.775636\pi\)
−0.235388 + 0.971901i \(0.575636\pi\)
\(488\) −66.9183 205.953i −0.137128 0.422036i
\(489\) 310.554 + 167.932i 0.635080 + 0.343420i
\(490\) −204.448 + 52.6615i −0.417242 + 0.107472i
\(491\) −553.144 + 179.727i −1.12657 + 0.366043i −0.812270 0.583282i \(-0.801768\pi\)
−0.314296 + 0.949325i \(0.601768\pi\)
\(492\) 14.1242 + 29.4826i 0.0287078 + 0.0599239i
\(493\) 116.565i 0.236439i
\(494\) −223.418 307.509i −0.452264 0.622487i
\(495\) 766.060 157.801i 1.54760 0.318790i
\(496\) 132.286 + 96.1114i 0.266706 + 0.193773i
\(497\) −575.792 418.337i −1.15853 0.841725i
\(498\) 236.946 438.181i 0.475795 0.879881i
\(499\) 281.894 0.564918 0.282459 0.959279i \(-0.408850\pi\)
0.282459 + 0.959279i \(0.408850\pi\)
\(500\) 219.355 + 119.931i 0.438709 + 0.239863i
\(501\) 59.7819 + 10.9745i 0.119325 + 0.0219052i
\(502\) −136.473 44.3429i −0.271859 0.0883324i
\(503\) 78.1333 + 56.7672i 0.155335 + 0.112857i 0.662738 0.748852i \(-0.269394\pi\)
−0.507403 + 0.861709i \(0.669394\pi\)
\(504\) 189.162 123.762i 0.375321 0.245560i
\(505\) 283.987 180.531i 0.562350 0.357487i
\(506\) 416.642 + 573.458i 0.823403 + 1.13332i
\(507\) 192.104 + 35.2656i 0.378903 + 0.0695574i
\(508\) 161.540 + 222.341i 0.317993 + 0.437679i
\(509\) 42.5947 13.8399i 0.0836832 0.0271903i −0.266876 0.963731i \(-0.585991\pi\)
0.350559 + 0.936541i \(0.385991\pi\)
\(510\) 216.738 15.3149i 0.424976 0.0300293i
\(511\) 59.5213 183.188i 0.116480 0.358489i
\(512\) 6.99226 + 21.5200i 0.0136568 + 0.0420312i
\(513\) −108.360 + 461.745i −0.211228 + 0.900088i
\(514\) 54.6701 168.257i 0.106362 0.327349i
\(515\) −430.512 26.7524i −0.835946 0.0519464i
\(516\) 161.514 21.5440i 0.313012 0.0417519i
\(517\) 926.668 + 1275.45i 1.79239 + 2.46702i
\(518\) 19.4326 0.0375147
\(519\) −338.160 + 162.002i −0.651560 + 0.312143i
\(520\) −215.965 13.4202i −0.415317 0.0258081i
\(521\) −437.726 + 602.478i −0.840164 + 1.15639i 0.145781 + 0.989317i \(0.453431\pi\)
−0.985945 + 0.167070i \(0.946569\pi\)
\(522\) 121.210 79.3040i 0.232204 0.151923i
\(523\) −427.802 139.001i −0.817977 0.265777i −0.130005 0.991513i \(-0.541499\pi\)
−0.687973 + 0.725736i \(0.741499\pi\)
\(524\) 114.333i 0.218193i
\(525\) −211.175 631.646i −0.402237 1.20314i
\(526\) −305.302 −0.580423
\(527\) 129.386 398.210i 0.245515 0.755617i
\(528\) 151.048 143.829i 0.286075 0.272404i
\(529\) −244.801 177.859i −0.462763 0.336217i
\(530\) 125.667 + 49.6430i 0.237107 + 0.0936660i
\(531\) −90.4630 333.065i −0.170363 0.627240i
\(532\) 311.983i 0.586433i
\(533\) −67.4438 + 49.0008i −0.126536 + 0.0919340i
\(534\) 599.179 79.9231i 1.12206 0.149669i
\(535\) −311.814 490.504i −0.582830 0.916830i
\(536\) 136.110 + 44.2248i 0.253936 + 0.0825089i
\(537\) 286.150 38.1689i 0.532868 0.0710780i
\(538\) −33.2311 + 10.7975i −0.0617679 + 0.0200696i
\(539\) 493.547 + 160.363i 0.915672 + 0.297520i
\(540\) 163.382 + 214.957i 0.302559 + 0.398068i
\(541\) 52.9898 + 163.086i 0.0979480 + 0.301453i 0.988011 0.154385i \(-0.0493397\pi\)
−0.890063 + 0.455838i \(0.849340\pi\)
\(542\) 531.550 386.194i 0.980720 0.712535i
\(543\) −251.094 46.0949i −0.462420 0.0848892i
\(544\) 46.8751 34.0568i 0.0861675 0.0626043i
\(545\) 181.785 220.086i 0.333551 0.403828i
\(546\) 397.514 + 417.465i 0.728048 + 0.764588i
\(547\) −223.225 + 307.243i −0.408090 + 0.561687i −0.962751 0.270389i \(-0.912848\pi\)
0.554661 + 0.832076i \(0.312848\pi\)
\(548\) 102.474 315.382i 0.186996 0.575515i
\(549\) −644.136 244.743i −1.17329 0.445799i
\(550\) −296.872 538.042i −0.539768 0.978259i
\(551\) 199.911i 0.362815i
\(552\) −116.390 + 215.239i −0.210852 + 0.389926i
\(553\) −367.628 + 505.997i −0.664789 + 0.915003i
\(554\) −196.736 + 270.784i −0.355120 + 0.488780i
\(555\) 1.63601 + 23.1529i 0.00294777 + 0.0417170i
\(556\) 5.87106 4.26558i 0.0105595 0.00767190i
\(557\) −162.914 −0.292485 −0.146243 0.989249i \(-0.546718\pi\)
−0.146243 + 0.989249i \(0.546718\pi\)
\(558\) 502.109 136.377i 0.899837 0.244403i
\(559\) 128.403 + 395.185i 0.229702 + 0.706950i
\(560\) −136.933 113.103i −0.244523 0.201970i
\(561\) −469.791 254.040i −0.837418 0.452833i
\(562\) 120.709 39.2206i 0.214784 0.0697876i
\(563\) 18.6650 + 57.4448i 0.0331527 + 0.102033i 0.966264 0.257555i \(-0.0829170\pi\)
−0.933111 + 0.359589i \(0.882917\pi\)
\(564\) −258.868 + 478.721i −0.458986 + 0.848796i
\(565\) −30.5351 + 36.9686i −0.0540444 + 0.0654311i
\(566\) −678.583 + 220.485i −1.19891 + 0.389549i
\(567\) 70.3056 715.848i 0.123996 1.26252i
\(568\) 226.690i 0.399102i
\(569\) 306.353 + 421.658i 0.538405 + 0.741051i 0.988382 0.151989i \(-0.0485678\pi\)
−0.449977 + 0.893040i \(0.648568\pi\)
\(570\) 371.710 26.2655i 0.652123 0.0460798i
\(571\) 438.487 + 318.579i 0.767928 + 0.557932i 0.901332 0.433129i \(-0.142591\pi\)
−0.133404 + 0.991062i \(0.542591\pi\)
\(572\) 430.296 + 312.628i 0.752265 + 0.546552i
\(573\) −320.845 173.497i −0.559940 0.302787i
\(574\) −68.4251 −0.119207
\(575\) 526.298 + 492.702i 0.915301 + 0.856873i
\(576\) 67.3054 + 25.5731i 0.116850 + 0.0443978i
\(577\) 789.861 + 256.641i 1.36891 + 0.444786i 0.899008 0.437933i \(-0.144289\pi\)
0.469902 + 0.882719i \(0.344289\pi\)
\(578\) 210.621 + 153.025i 0.364396 + 0.264749i
\(579\) 147.202 140.167i 0.254235 0.242085i
\(580\) −87.7432 72.4736i −0.151281 0.124955i
\(581\) 612.853 + 843.520i 1.05482 + 1.45184i
\(582\) 134.223 731.159i 0.230624 1.25629i
\(583\) −195.217 268.693i −0.334849 0.460880i
\(584\) 58.3473 18.9582i 0.0999097 0.0324626i
\(585\) −463.920 + 508.763i −0.793026 + 0.869680i
\(586\) −20.0734 + 61.7796i −0.0342550 + 0.105426i
\(587\) 87.1657 + 268.268i 0.148494 + 0.457016i 0.997444 0.0714568i \(-0.0227648\pi\)
−0.848950 + 0.528473i \(0.822765\pi\)
\(588\) 23.6856 + 177.570i 0.0402817 + 0.301990i
\(589\) 221.901 682.940i 0.376741 1.15949i
\(590\) −228.837 + 145.472i −0.387859 + 0.246562i
\(591\) −65.5970 491.777i −0.110993 0.832111i
\(592\) 3.63810 + 5.00742i 0.00614544 + 0.00845847i
\(593\) 737.541 1.24374 0.621872 0.783119i \(-0.286372\pi\)
0.621872 + 0.783119i \(0.286372\pi\)
\(594\) −55.4549 661.350i −0.0933584 1.11338i
\(595\) −167.089 + 422.972i −0.280822 + 0.710877i
\(596\) 35.3372 48.6374i 0.0592905 0.0816064i
\(597\) −619.836 650.944i −1.03825 1.09036i
\(598\) −593.446 192.822i −0.992385 0.322445i
\(599\) 494.412i 0.825396i −0.910868 0.412698i \(-0.864586\pi\)
0.910868 0.412698i \(-0.135414\pi\)
\(600\) 123.228 172.670i 0.205380 0.287783i
\(601\) −547.684 −0.911288 −0.455644 0.890162i \(-0.650591\pi\)
−0.455644 + 0.890162i \(0.650591\pi\)
\(602\) −105.392 + 324.363i −0.175070 + 0.538809i
\(603\) 381.072 249.323i 0.631960 0.413471i
\(604\) 387.933 + 281.850i 0.642273 + 0.466639i
\(605\) −56.1597 + 903.749i −0.0928259 + 1.49380i
\(606\) −123.367 257.514i −0.203576 0.424940i
\(607\) 414.860i 0.683459i 0.939798 + 0.341729i \(0.111013\pi\)
−0.939798 + 0.341729i \(0.888987\pi\)
\(608\) 80.3919 58.4082i 0.132224 0.0960661i
\(609\) 40.0852 + 300.517i 0.0658214 + 0.493459i
\(610\) −33.5770 + 540.338i −0.0550443 + 0.885800i
\(611\) −1319.90 428.863i −2.16024 0.701903i
\(612\) 9.02106 184.146i 0.0147403 0.300892i
\(613\) 569.176 184.937i 0.928509 0.301691i 0.194556 0.980891i \(-0.437673\pi\)
0.733953 + 0.679200i \(0.237673\pi\)
\(614\) 148.883 + 48.3751i 0.242481 + 0.0787868i
\(615\) −5.76063 81.5247i −0.00936688 0.132561i
\(616\) 134.903 + 415.189i 0.218999 + 0.674008i
\(617\) −95.2613 + 69.2114i −0.154394 + 0.112174i −0.662300 0.749238i \(-0.730420\pi\)
0.507906 + 0.861412i \(0.330420\pi\)
\(618\) −66.0856 + 359.991i −0.106935 + 0.582509i
\(619\) 279.977 203.415i 0.452305 0.328619i −0.338200 0.941074i \(-0.609818\pi\)
0.790505 + 0.612455i \(0.209818\pi\)
\(620\) −219.305 344.981i −0.353717 0.556420i
\(621\) 301.636 + 717.806i 0.485727 + 1.15589i
\(622\) 280.410 385.951i 0.450819 0.620500i
\(623\) −390.979 + 1203.31i −0.627574 + 1.93147i
\(624\) −33.1516 + 180.588i −0.0531276 + 0.289404i
\(625\) −399.873 480.340i −0.639797 0.768544i
\(626\) 40.1656i 0.0641623i
\(627\) −805.703 435.684i −1.28501 0.694871i
\(628\) −335.823 + 462.221i −0.534751 + 0.736021i
\(629\) 9.31589 12.8222i 0.0148106 0.0203851i
\(630\) −553.508 + 114.017i −0.878585 + 0.180980i
\(631\) −70.4052 + 51.1524i −0.111577 + 0.0810656i −0.642175 0.766558i \(-0.721968\pi\)
0.530597 + 0.847624i \(0.321968\pi\)
\(632\) −199.212 −0.315208
\(633\) −394.687 + 189.083i −0.623517 + 0.298709i
\(634\) −10.5252 32.3932i −0.0166013 0.0510934i
\(635\) −171.381 665.354i −0.269891 1.04780i
\(636\) 54.5346 100.850i 0.0857462 0.158569i
\(637\) −434.470 + 141.168i −0.682056 + 0.221613i
\(638\) 86.4427 + 266.043i 0.135490 + 0.416996i
\(639\) −562.118 452.029i −0.879684 0.707401i
\(640\) 3.50845 56.4596i 0.00548195 0.0882182i
\(641\) 564.370 183.375i 0.880452 0.286076i 0.166307 0.986074i \(-0.446816\pi\)
0.714145 + 0.699998i \(0.246816\pi\)
\(642\) −444.779 + 213.081i −0.692803 + 0.331901i
\(643\) 555.696i 0.864224i −0.901820 0.432112i \(-0.857768\pi\)
0.901820 0.432112i \(-0.142232\pi\)
\(644\) −301.040 414.346i −0.467453 0.643394i
\(645\) −395.334 98.2609i −0.612920 0.152343i
\(646\) −205.855 149.563i −0.318662 0.231521i
\(647\) −862.659 626.758i −1.33332 0.968715i −0.999661 0.0260212i \(-0.991716\pi\)
−0.333660 0.942693i \(-0.608284\pi\)
\(648\) 197.623 115.902i 0.304973 0.178861i
\(649\) 666.524 1.02700
\(650\) 489.824 + 229.572i 0.753575 + 0.353188i
\(651\) −196.633 + 1071.13i −0.302048 + 1.64536i
\(652\) −223.848 72.7326i −0.343325 0.111553i
\(653\) −636.997 462.806i −0.975494 0.708738i −0.0187968 0.999823i \(-0.505984\pi\)
−0.956697 + 0.291086i \(0.905984\pi\)
\(654\) −167.029 175.412i −0.255397 0.268215i
\(655\) 105.017 265.842i 0.160332 0.405866i
\(656\) −12.8103 17.6318i −0.0195279 0.0268778i
\(657\) 69.3367 182.486i 0.105535 0.277756i
\(658\) −669.554 921.562i −1.01756 1.40055i
\(659\) 233.655 75.9192i 0.354560 0.115204i −0.126321 0.991989i \(-0.540317\pi\)
0.480881 + 0.876786i \(0.340317\pi\)
\(660\) −483.318 + 195.684i −0.732300 + 0.296491i
\(661\) 177.145 545.195i 0.267995 0.824804i −0.722993 0.690855i \(-0.757234\pi\)
0.990988 0.133949i \(-0.0427657\pi\)
\(662\) −108.976 335.394i −0.164616 0.506637i
\(663\) 466.022 62.1616i 0.702899 0.0937580i
\(664\) −102.623 + 315.841i −0.154553 + 0.475664i
\(665\) −286.562 + 725.406i −0.430920 + 1.09084i
\(666\) 19.6713 + 0.963671i 0.0295365 + 0.00144695i
\(667\) −192.899 265.503i −0.289204 0.398055i
\(668\) −40.5206 −0.0606595
\(669\) 460.701 + 961.655i 0.688641 + 1.43745i
\(670\) −275.855 227.849i −0.411723 0.340073i
\(671\) 782.187 1076.59i 1.16570 1.60445i
\(672\) −109.138 + 103.922i −0.162407 + 0.154646i
\(673\) −1217.43 395.567i −1.80896 0.587767i −0.808961 0.587862i \(-0.799970\pi\)
−1.00000 9.49759e-5i \(0.999970\pi\)
\(674\) 161.176i 0.239134i
\(675\) −182.445 649.876i −0.270288 0.962779i
\(676\) −130.209 −0.192617
\(677\) 21.7680 66.9952i 0.0321537 0.0989589i −0.933692 0.358078i \(-0.883432\pi\)
0.965845 + 0.259119i \(0.0834322\pi\)
\(678\) 28.0565 + 29.4646i 0.0413813 + 0.0434581i
\(679\) 1258.78 + 914.559i 1.85388 + 1.34692i
\(680\) −140.273 + 36.1314i −0.206285 + 0.0531344i
\(681\) −1012.65 + 485.131i −1.48701 + 0.712380i
\(682\) 1004.81i 1.47333i
\(683\) −50.6807 + 36.8217i −0.0742031 + 0.0539117i −0.624268 0.781210i \(-0.714603\pi\)
0.550065 + 0.835122i \(0.314603\pi\)
\(684\) 15.4713 315.814i 0.0226189 0.461717i
\(685\) −527.952 + 639.187i −0.770733 + 0.933119i
\(686\) 228.638 + 74.2891i 0.333292 + 0.108293i
\(687\) 71.3768 + 535.108i 0.103896 + 0.778906i
\(688\) −103.313 + 33.5685i −0.150164 + 0.0487914i
\(689\) 278.058 + 90.3467i 0.403568 + 0.131127i
\(690\) 468.326 393.556i 0.678734 0.570371i
\(691\) −293.365 902.886i −0.424552 1.30664i −0.903423 0.428751i \(-0.858954\pi\)
0.478871 0.877885i \(-0.341046\pi\)
\(692\) 202.234 146.932i 0.292246 0.212329i
\(693\) 1298.54 + 493.388i 1.87379 + 0.711959i
\(694\) 415.731 302.047i 0.599037 0.435226i
\(695\) −17.5691 + 4.52542i −0.0252793 + 0.00651140i
\(696\) −69.9328 + 66.5908i −0.100478 + 0.0956764i
\(697\) −32.8026 + 45.1489i −0.0470625 + 0.0647760i
\(698\) −82.3293 + 253.384i −0.117950 + 0.363014i
\(699\) −76.0731 13.9652i −0.108831 0.0199788i
\(700\) 214.502 + 388.757i 0.306431 + 0.555367i
\(701\) 1169.75i 1.66868i −0.551247 0.834342i \(-0.685848\pi\)
0.551247 0.834342i \(-0.314152\pi\)
\(702\) 381.695 + 442.305i 0.543724 + 0.630064i
\(703\) 15.9770 21.9904i 0.0227269 0.0312808i
\(704\) −81.7303 + 112.492i −0.116094 + 0.159790i
\(705\) 1041.62 875.322i 1.47748 1.24159i
\(706\) 207.864 151.022i 0.294425 0.213913i
\(707\) 597.655 0.845339
\(708\) 99.4092 + 207.504i 0.140409 + 0.293085i
\(709\) −153.546 472.565i −0.216566 0.666523i −0.999039 0.0438374i \(-0.986042\pi\)
0.782472 0.622685i \(-0.213958\pi\)
\(710\) −208.219 + 527.088i −0.293266 + 0.742378i
\(711\) −397.236 + 493.981i −0.558700 + 0.694769i
\(712\) −383.267 + 124.531i −0.538296 + 0.174903i
\(713\) −364.279 1121.13i −0.510910 1.57242i
\(714\) 339.443 + 183.553i 0.475410 + 0.257078i
\(715\) −713.347 1122.14i −0.997688 1.56943i
\(716\) −183.037 + 59.4723i −0.255638 + 0.0830619i
\(717\) −76.5136 159.713i −0.106714 0.222751i
\(718\) 408.418i 0.568827i
\(719\) 404.305 + 556.477i 0.562315 + 0.773960i 0.991619 0.129200i \(-0.0412409\pi\)
−0.429303 + 0.903160i \(0.641241\pi\)
\(720\) −133.006 121.283i −0.184730 0.168448i
\(721\) −619.770 450.289i −0.859598 0.624534i
\(722\) 59.9814 + 43.5790i 0.0830767 + 0.0603588i
\(723\) 209.242 386.948i 0.289408 0.535198i
\(724\) 170.193 0.235074
\(725\) 137.448 + 249.106i 0.189583 + 0.343594i
\(726\) 755.707 + 138.730i 1.04092 + 0.191088i
\(727\) 883.026 + 286.913i 1.21462 + 0.394653i 0.845119 0.534579i \(-0.179530\pi\)
0.369498 + 0.929232i \(0.379530\pi\)
\(728\) −310.905 225.886i −0.427068 0.310283i
\(729\) 106.668 721.154i 0.146321 0.989237i
\(730\) −153.080 9.51249i −0.209698 0.0130308i
\(731\) 163.500 + 225.038i 0.223666 + 0.307850i
\(732\) 451.826 + 82.9444i 0.617249 + 0.113312i
\(733\) −143.420 197.401i −0.195662 0.269306i 0.699902 0.714239i \(-0.253227\pi\)
−0.895563 + 0.444934i \(0.853227\pi\)
\(734\) −238.162 + 77.3835i −0.324471 + 0.105427i
\(735\) 108.029 434.633i 0.146978 0.591337i
\(736\) 50.4095 155.144i 0.0684912 0.210794i
\(737\) 271.766 + 836.410i 0.368746 + 1.13488i
\(738\) −69.2654 3.39322i −0.0938556 0.00459786i
\(739\) −349.812 + 1076.61i −0.473359 + 1.45685i 0.374800 + 0.927106i \(0.377711\pi\)
−0.848159 + 0.529742i \(0.822289\pi\)
\(740\) −3.85972 14.9847i −0.00521584 0.0202495i
\(741\) 799.239 106.609i 1.07859 0.143871i
\(742\) 141.052 + 194.141i 0.190097 + 0.261646i
\(743\) −711.688 −0.957857 −0.478929 0.877854i \(-0.658975\pi\)
−0.478929 + 0.877854i \(0.658975\pi\)
\(744\) −312.822 + 149.864i −0.420459 + 0.201430i
\(745\) −126.839 + 80.6314i −0.170253 + 0.108230i
\(746\) 243.336 334.924i 0.326188 0.448960i
\(747\) 578.550 + 884.271i 0.774497 + 1.18376i
\(748\) 338.626 + 110.026i 0.452709 + 0.147094i
\(749\) 1032.27i 1.37820i
\(750\) −445.124 + 288.296i −0.593498 + 0.384395i
\(751\) 1293.60 1.72251 0.861254 0.508175i \(-0.169680\pi\)
0.861254 + 0.508175i \(0.169680\pi\)
\(752\) 112.118 345.062i 0.149092 0.458860i
\(753\) 220.448 209.913i 0.292759 0.278769i
\(754\) −199.221 144.742i −0.264218 0.191966i
\(755\) −643.118 1011.67i −0.851811 1.33996i
\(756\) 40.0683 + 477.851i 0.0530004 + 0.632079i
\(757\) 1171.95i 1.54815i −0.633092 0.774076i \(-0.718215\pi\)
0.633092 0.774076i \(-0.281785\pi\)
\(758\) −645.197 + 468.763i −0.851183 + 0.618421i
\(759\) −1490.46 + 198.809i −1.96372 + 0.261936i
\(760\) −240.572 + 61.9662i −0.316543 + 0.0815345i
\(761\) 929.297 + 301.947i 1.22115 + 0.396776i 0.847502 0.530793i \(-0.178106\pi\)
0.373651 + 0.927569i \(0.378106\pi\)
\(762\) −577.881 + 77.0822i −0.758375 + 0.101158i
\(763\) 482.161 156.664i 0.631928 0.205326i
\(764\) 231.266 + 75.1428i 0.302704 + 0.0983544i
\(765\) −190.117 + 419.880i −0.248519 + 0.548863i
\(766\) −196.181 603.783i −0.256111 0.788229i
\(767\) −474.684 + 344.878i −0.618884 + 0.449645i
\(768\) −47.2111 8.66681i −0.0614728 0.0112849i
\(769\) −6.70121 + 4.86871i −0.00871418 + 0.00633122i −0.592134 0.805840i \(-0.701714\pi\)
0.583420 + 0.812171i \(0.301714\pi\)
\(770\) 67.6892 1089.29i 0.0879081 1.41466i
\(771\) 258.801 + 271.789i 0.335669 + 0.352515i
\(772\) −79.6494 + 109.628i −0.103173 + 0.142005i
\(773\) 182.178 560.686i 0.235676 0.725337i −0.761355 0.648336i \(-0.775465\pi\)
0.997031 0.0770017i \(-0.0245347\pi\)
\(774\) −122.772 + 323.120i −0.158620 + 0.417468i
\(775\) 193.045 + 1003.57i 0.249090 + 1.29493i
\(776\) 495.585i 0.638640i
\(777\) −19.6080 + 36.2608i −0.0252356 + 0.0466677i
\(778\) −448.240 + 616.949i −0.576143 + 0.792993i
\(779\) −56.2572 + 77.4314i −0.0722172 + 0.0993985i
\(780\) 242.956 389.444i 0.311482 0.499287i
\(781\) 1126.99 818.804i 1.44301 1.04841i
\(782\) −417.715 −0.534162
\(783\) 25.6748 + 306.196i 0.0327903 + 0.391054i
\(784\) −36.9054 113.583i −0.0470733 0.144877i
\(785\) 1205.40 766.273i 1.53554 0.976145i
\(786\) −213.343 115.365i −0.271429 0.146775i
\(787\) 1289.88 419.107i 1.63898 0.532538i 0.662672 0.748909i \(-0.269422\pi\)
0.976311 + 0.216371i \(0.0694222\pi\)
\(788\) 102.209 + 314.567i 0.129707 + 0.399197i
\(789\) 308.058 569.687i 0.390441 0.722037i
\(790\) 463.197 + 182.980i 0.586325 + 0.231620i
\(791\) −80.9902 + 26.3153i −0.102390 + 0.0332684i
\(792\) 115.971 + 426.978i 0.146428 + 0.539114i
\(793\) 1171.45i 1.47723i
\(794\) −440.214 605.902i −0.554426 0.763101i
\(795\) −219.434 + 184.400i −0.276017 + 0.231950i
\(796\) 484.788 + 352.219i 0.609030 + 0.442486i
\(797\) 273.643 + 198.813i 0.343342 + 0.249452i 0.746070 0.665867i \(-0.231938\pi\)
−0.402729 + 0.915319i \(0.631938\pi\)
\(798\) 582.152 + 314.799i 0.729514 + 0.394484i
\(799\) −929.054 −1.16277
\(800\) −60.0169 + 128.055i −0.0750212 + 0.160068i
\(801\) −455.453 + 1198.70i −0.568605 + 1.49650i
\(802\) 487.031 + 158.246i 0.607270 + 0.197314i
\(803\) 305.001 + 221.596i 0.379827 + 0.275960i
\(804\) −219.861 + 209.354i −0.273459 + 0.260390i
\(805\) 319.378 + 1239.93i 0.396743 + 1.54028i
\(806\) −519.918 715.606i −0.645060 0.887848i
\(807\) 13.3833 72.9034i 0.0165840 0.0903388i
\(808\) 111.891 + 154.004i 0.138478 + 0.190599i
\(809\) −1309.19 + 425.381i −1.61828 + 0.525811i −0.971535 0.236895i \(-0.923870\pi\)
−0.646745 + 0.762706i \(0.723870\pi\)
\(810\) −565.961 + 87.9690i −0.698717 + 0.108604i
\(811\) −90.6930 + 279.124i −0.111829 + 0.344173i −0.991272 0.131830i \(-0.957915\pi\)
0.879444 + 0.476003i \(0.157915\pi\)
\(812\) −62.4582 192.227i −0.0769190 0.236732i
\(813\) 184.280 + 1381.54i 0.226667 + 1.69931i
\(814\) −11.7535 + 36.1736i −0.0144392 + 0.0444393i
\(815\) 453.673 + 374.723i 0.556655 + 0.459782i
\(816\) 16.2509 + 121.832i 0.0199153 + 0.149304i
\(817\) 280.406 + 385.946i 0.343215 + 0.472394i
\(818\) −543.895 −0.664909
\(819\) −1180.08 + 320.519i −1.44088 + 0.391355i
\(820\) 13.5906 + 52.7631i 0.0165739 + 0.0643453i
\(821\) 212.728 292.795i 0.259108 0.356632i −0.659567 0.751646i \(-0.729260\pi\)
0.918675 + 0.395014i \(0.129260\pi\)
\(822\) 485.097 + 509.443i 0.590142 + 0.619760i
\(823\) −255.585 83.0445i −0.310553 0.100905i 0.149594 0.988747i \(-0.452203\pi\)
−0.460147 + 0.887843i \(0.652203\pi\)
\(824\) 244.004i 0.296122i
\(825\) 1303.53 11.0579i 1.58003 0.0134035i
\(826\) −481.590 −0.583039
\(827\) 268.822 827.349i 0.325057 1.00042i −0.646358 0.763034i \(-0.723709\pi\)
0.971415 0.237388i \(-0.0762912\pi\)
\(828\) −284.190 434.364i −0.343224 0.524594i
\(829\) 498.059 + 361.861i 0.600795 + 0.436503i 0.846161 0.532927i \(-0.178908\pi\)
−0.245366 + 0.969431i \(0.578908\pi\)
\(830\) 528.720 640.116i 0.637012 0.771225i
\(831\) −306.765 640.334i −0.369152 0.770558i
\(832\) 122.404i 0.147120i
\(833\) −247.409 + 179.753i −0.297010 + 0.215790i
\(834\) 2.03541 + 15.2593i 0.00244054 + 0.0182966i
\(835\) 94.2164 + 37.2189i 0.112834 + 0.0445736i
\(836\) 580.752 + 188.698i 0.694679 + 0.225715i
\(837\) −252.166 + 1074.53i −0.301273 + 1.28379i
\(838\) 1089.26 353.921i 1.29983 0.422340i
\(839\) −383.519 124.613i −0.457115 0.148526i 0.0714035 0.997448i \(-0.477252\pi\)
−0.528518 + 0.848922i \(0.677252\pi\)
\(840\) 349.216 141.389i 0.415733 0.168321i
\(841\) 219.862 + 676.664i 0.261429 + 0.804595i
\(842\) −709.281 + 515.323i −0.842377 + 0.612023i
\(843\) −48.6135 + 264.814i −0.0576672 + 0.314133i
\(844\) 236.039 171.493i 0.279667 0.203190i
\(845\) 302.756 + 119.600i 0.358291 + 0.141538i
\(846\) −632.077 966.084i −0.747136 1.14194i
\(847\) −945.265 + 1301.05i −1.11602 + 1.53606i
\(848\) −23.6193 + 72.6927i −0.0278530 + 0.0857226i
\(849\) 273.288 1488.69i 0.321894 1.75347i
\(850\) 359.344 + 44.8330i 0.422758 + 0.0527447i
\(851\) 44.6222i 0.0524350i
\(852\) 422.998 + 228.736i 0.496477 + 0.268470i
\(853\) 384.635 529.404i 0.450920 0.620638i −0.521675 0.853144i \(-0.674693\pi\)
0.972595 + 0.232506i \(0.0746927\pi\)
\(854\) −565.160 + 777.876i −0.661780 + 0.910862i
\(855\) −326.055 + 720.105i −0.381351 + 0.842228i
\(856\) 265.997 193.258i 0.310744 0.225769i
\(857\) 668.295 0.779808 0.389904 0.920856i \(-0.372508\pi\)
0.389904 + 0.920856i \(0.372508\pi\)
\(858\) −1017.54 + 487.471i −1.18594 + 0.568148i
\(859\) 161.884 + 498.228i 0.188456 + 0.580009i 0.999991 0.00429551i \(-0.00136731\pi\)
−0.811534 + 0.584305i \(0.801367\pi\)
\(860\) 271.052 + 16.8434i 0.315177 + 0.0195853i
\(861\) 69.0427 127.679i 0.0801889 0.148292i
\(862\) −130.613 + 42.4387i −0.151523 + 0.0492329i
\(863\) −74.8592 230.393i −0.0867430 0.266967i 0.898271 0.439442i \(-0.144824\pi\)
−0.985014 + 0.172474i \(0.944824\pi\)
\(864\) −115.632 + 99.7863i −0.133833 + 0.115493i
\(865\) −605.184 + 155.882i −0.699635 + 0.180211i
\(866\) 109.428 35.5553i 0.126360 0.0410569i
\(867\) −498.063 + 238.607i −0.574467 + 0.275210i
\(868\) 726.017i 0.836425i
\(869\) −719.553 990.379i −0.828024 1.13968i
\(870\) 223.769 90.5989i 0.257206 0.104137i
\(871\) −626.327 455.053i −0.719089 0.522449i
\(872\) 130.638 + 94.9138i 0.149814 + 0.108846i
\(873\) 1228.89 + 988.215i 1.40766 + 1.13198i
\(874\) −716.391 −0.819669
\(875\) −141.669 1100.94i −0.161907 1.25822i
\(876\) −23.4984 + 128.004i −0.0268247 + 0.146123i
\(877\) −521.873 169.567i −0.595066 0.193349i −0.00402732 0.999992i \(-0.501282\pi\)
−0.591039 + 0.806643i \(0.701282\pi\)
\(878\) 653.680 + 474.926i 0.744510 + 0.540918i
\(879\) −95.0247 99.7938i −0.108105 0.113531i
\(880\) 293.361 186.490i 0.333365 0.211921i
\(881\) 659.986 + 908.393i 0.749133 + 1.03109i 0.998041 + 0.0625660i \(0.0199284\pi\)
−0.248908 + 0.968527i \(0.580072\pi\)
\(882\) −355.241 134.976i −0.402767 0.153034i
\(883\) 252.897 + 348.083i 0.286407 + 0.394205i 0.927843 0.372972i \(-0.121661\pi\)
−0.641436 + 0.767176i \(0.721661\pi\)
\(884\) −298.092 + 96.8561i −0.337209 + 0.109566i
\(885\) −40.5445 573.788i −0.0458130 0.648348i
\(886\) 134.559 414.131i 0.151873 0.467416i
\(887\) 98.4617 + 303.034i 0.111005 + 0.341639i 0.991093 0.133172i \(-0.0425163\pi\)
−0.880088 + 0.474811i \(0.842516\pi\)
\(888\) −13.0147 + 1.73599i −0.0146561 + 0.00195495i
\(889\) 377.081 1160.54i 0.424163 1.30544i
\(890\) 1005.54 + 62.4849i 1.12982 + 0.0702077i
\(891\) 1290.02 + 563.842i 1.44783 + 0.632820i
\(892\) −417.843 575.111i −0.468433 0.644743i
\(893\) −1593.35 −1.78427
\(894\) 55.1001 + 115.015i 0.0616333 + 0.128652i
\(895\) 480.215 + 29.8409i 0.536553 + 0.0333418i
\(896\) 59.0533 81.2799i 0.0659077 0.0907142i
\(897\) 958.604 912.793i 1.06868 1.01761i
\(898\) 982.547 + 319.249i 1.09415 + 0.355511i
\(899\) 465.214i 0.517480i
\(900\) 197.858 + 404.169i 0.219842 + 0.449076i
\(901\) 195.720 0.217225
\(902\) 41.3858 127.372i 0.0458822 0.141211i
\(903\) −498.910 523.949i −0.552503 0.580232i
\(904\) −21.9436 15.9430i −0.0242739 0.0176360i
\(905\) −395.725 156.326i −0.437266 0.172736i
\(906\) −917.359 + 439.480i −1.01254 + 0.485077i
\(907\) 87.2255i 0.0961692i −0.998843 0.0480846i \(-0.984688\pi\)
0.998843 0.0480846i \(-0.0153117\pi\)
\(908\) 605.608 440.000i 0.666970 0.484582i
\(909\) 604.995 + 29.6379i 0.665561 + 0.0326050i
\(910\) 515.421 + 810.791i 0.566396 + 0.890979i
\(911\) 1467.29 + 476.753i 1.61064 + 0.523329i 0.969708 0.244267i \(-0.0785472\pi\)
0.640934 + 0.767596i \(0.278547\pi\)
\(912\) 27.8706 + 208.945i 0.0305599 + 0.229106i
\(913\) −1940.88 + 630.629i −2.12582 + 0.690721i
\(914\) 450.249 + 146.295i 0.492614 + 0.160060i
\(915\) −974.378 607.869i −1.06489 0.664338i
\(916\) −111.215 342.284i −0.121413 0.373672i
\(917\) 410.696 298.388i 0.447870 0.325396i
\(918\) 334.509 + 202.641i 0.364389 + 0.220742i
\(919\) 851.640 618.753i 0.926703 0.673289i −0.0184806 0.999829i \(-0.505883\pi\)
0.945183 + 0.326540i \(0.105883\pi\)
\(920\) −259.713 + 314.432i −0.282297 + 0.341774i
\(921\) −240.494 + 229.001i −0.261123 + 0.248644i
\(922\) −336.661 + 463.375i −0.365142 + 0.502575i
\(923\) −378.944 + 1166.27i −0.410556 + 1.26356i
\(924\) −910.854 167.211i −0.985773 0.180964i
\(925\) −4.78927 + 38.3868i −0.00517759 + 0.0414993i
\(926\) 600.622i 0.648620i
\(927\) −605.052 486.554i −0.652699 0.524870i
\(928\) 37.8399 52.0822i 0.0407758 0.0561231i
\(929\) −495.358 + 681.801i −0.533216 + 0.733909i −0.987616 0.156889i \(-0.949854\pi\)
0.454400 + 0.890798i \(0.349854\pi\)
\(930\) 865.010 61.1226i 0.930118 0.0657232i
\(931\) −424.312 + 308.281i −0.455760 + 0.331129i
\(932\) 51.5629 0.0553250
\(933\) 437.234 + 912.672i 0.468632 + 0.978212i
\(934\) 135.904 + 418.268i 0.145507 + 0.447825i
\(935\) −686.295 566.862i −0.734005 0.606270i
\(936\) −303.522 244.078i −0.324276 0.260767i
\(937\) 869.531 282.528i 0.927995 0.301524i 0.194252 0.980952i \(-0.437772\pi\)
0.733742 + 0.679428i \(0.237772\pi\)
\(938\) −196.361 604.338i −0.209341 0.644284i
\(939\) 74.9480 + 40.5281i 0.0798168 + 0.0431610i
\(940\) −577.637 + 699.340i −0.614507 + 0.743978i
\(941\) −1446.35 + 469.947i −1.53703 + 0.499412i −0.950556 0.310553i \(-0.899486\pi\)
−0.586477 + 0.809966i \(0.699486\pi\)
\(942\) −523.639 1093.03i −0.555880 1.16033i
\(943\) 157.121i 0.166618i
\(944\) −90.1614 124.096i −0.0955099 0.131458i
\(945\) 345.751 1147.88i 0.365874 1.21469i
\(946\) −540.053 392.371i −0.570880 0.414769i
\(947\) 418.835 + 304.301i 0.442276 + 0.321332i 0.786539 0.617541i \(-0.211871\pi\)
−0.344263 + 0.938873i \(0.611871\pi\)
\(948\) 201.010 371.724i 0.212036 0.392114i
\(949\) −331.875 −0.349710
\(950\) 616.284 + 76.8897i 0.648720 + 0.0809365i
\(951\) 71.0652 + 13.0459i 0.0747268 + 0.0137180i
\(952\) −244.670 79.4982i −0.257007 0.0835066i
\(953\) 801.548 + 582.359i 0.841079 + 0.611080i 0.922672 0.385586i \(-0.126001\pi\)
−0.0815929 + 0.996666i \(0.526001\pi\)
\(954\) 133.157 + 203.521i 0.139577 + 0.213334i
\(955\) −468.707 387.140i −0.490793 0.405382i
\(956\) 69.3957 + 95.5150i 0.0725897 + 0.0999111i
\(957\) −583.653 107.145i −0.609878 0.111959i
\(958\) 160.371 + 220.731i 0.167401 + 0.230408i
\(959\) −1400.32 + 454.992i −1.46019 + 0.474444i
\(960\) 101.812 + 63.5159i 0.106054 + 0.0661624i
\(961\) 219.421 675.309i 0.228326 0.702715i
\(962\) −10.3466 31.8436i −0.0107553 0.0331015i
\(963\) 51.1908 1044.95i 0.0531576 1.08510i
\(964\) −90.6242 + 278.913i −0.0940085 + 0.289328i
\(965\) 285.892 181.742i 0.296262 0.188334i
\(966\) 1076.92 143.647i 1.11482 0.148703i
\(967\) −933.969 1285.50i −0.965842 1.32937i −0.944119 0.329603i \(-0.893085\pi\)
−0.0217225 0.999764i \(-0.506915\pi\)
\(968\) −512.224 −0.529157
\(969\) 486.794 233.209i 0.502367 0.240669i
\(970\) 455.204 1152.31i 0.469282 1.18795i
\(971\) −53.6223 + 73.8048i −0.0552238 + 0.0760091i −0.835736 0.549132i \(-0.814958\pi\)
0.780512 + 0.625141i \(0.214958\pi\)
\(972\) 16.8636 + 485.707i 0.0173494 + 0.499699i
\(973\) −30.6447 9.95708i −0.0314951 0.0102334i
\(974\) 722.058i 0.741333i
\(975\) −922.621 + 682.356i −0.946278 + 0.699852i
\(976\) −306.251 −0.313782
\(977\) −29.4896 + 90.7596i −0.0301838 + 0.0928962i −0.965014 0.262200i \(-0.915552\pi\)
0.934830 + 0.355096i \(0.115552\pi\)
\(978\) 361.586 344.306i 0.369719 0.352051i
\(979\) −2003.47 1455.60i −2.04644 1.48683i
\(980\) −18.5177 + 297.996i −0.0188957 + 0.304078i
\(981\) 495.852 134.677i 0.505456 0.137286i
\(982\) 822.520i 0.837597i
\(983\) 566.239 411.397i 0.576031 0.418511i −0.261260 0.965269i \(-0.584138\pi\)
0.837291 + 0.546757i \(0.184138\pi\)
\(984\) 45.8265 6.11268i 0.0465716 0.00621208i
\(985\) 51.2846 825.296i 0.0520656 0.837864i
\(986\) −156.779 50.9406i −0.159005 0.0516639i
\(987\) 2395.21 319.491i 2.42676 0.323699i
\(988\) −511.236 + 166.111i −0.517445 + 0.168128i
\(989\) 744.819 + 242.006i 0.753103 + 0.244698i
\(990\) 122.539 1099.31i 0.123777 1.11041i
\(991\) 410.128 + 1262.24i 0.413852 + 1.27371i 0.913273 + 0.407347i \(0.133546\pi\)
−0.499421 + 0.866359i \(0.666454\pi\)
\(992\) 187.081 135.922i 0.188589 0.137018i
\(993\) 735.796 + 135.074i 0.740983 + 0.136027i
\(994\) −814.292 + 591.618i −0.819208 + 0.595189i
\(995\) −803.685 1264.25i −0.807723 1.27060i
\(996\) −485.802 510.184i −0.487753 0.512233i
\(997\) −873.173 + 1201.82i −0.875800 + 1.20544i 0.101766 + 0.994808i \(0.467551\pi\)
−0.977566 + 0.210628i \(0.932449\pi\)
\(998\) 123.192 379.146i 0.123439 0.379906i
\(999\) −21.6470 + 35.7338i −0.0216687 + 0.0357696i
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.i.a.29.19 yes 80
3.2 odd 2 inner 150.3.i.a.29.3 80
25.19 even 10 inner 150.3.i.a.119.3 yes 80
75.44 odd 10 inner 150.3.i.a.119.19 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
150.3.i.a.29.3 80 3.2 odd 2 inner
150.3.i.a.29.19 yes 80 1.1 even 1 trivial
150.3.i.a.119.3 yes 80 25.19 even 10 inner
150.3.i.a.119.19 yes 80 75.44 odd 10 inner