Properties

Label 150.3.j.a.11.11
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 11.11
Character \(\chi\) \(=\) 150.11
Dual form 150.3.j.a.41.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.831254 + 1.14412i) q^{2} +(-2.90622 - 0.744235i) q^{3} +(-0.618034 + 1.90211i) q^{4} +(4.36319 - 2.44184i) q^{5} +(-1.56431 - 3.94372i) q^{6} +4.66363 q^{7} +(-2.68999 + 0.874032i) q^{8} +(7.89223 + 4.32582i) q^{9} +O(q^{10})\) \(q+(0.831254 + 1.14412i) q^{2} +(-2.90622 - 0.744235i) q^{3} +(-0.618034 + 1.90211i) q^{4} +(4.36319 - 2.44184i) q^{5} +(-1.56431 - 3.94372i) q^{6} +4.66363 q^{7} +(-2.68999 + 0.874032i) q^{8} +(7.89223 + 4.32582i) q^{9} +(6.42068 + 2.96224i) q^{10} +(-2.09360 - 2.88160i) q^{11} +(3.21176 - 5.06800i) q^{12} +(18.2244 + 13.2408i) q^{13} +(3.87666 + 5.33576i) q^{14} +(-14.4977 + 3.84927i) q^{15} +(-3.23607 - 2.35114i) q^{16} +(11.5884 - 3.76531i) q^{17} +(1.61117 + 12.6255i) q^{18} +(3.82708 + 11.7786i) q^{19} +(1.94805 + 9.80842i) q^{20} +(-13.5535 - 3.47084i) q^{21} +(1.55659 - 4.79068i) q^{22} +(7.54792 + 10.3888i) q^{23} +(8.46820 - 0.538141i) q^{24} +(13.0749 - 21.3084i) q^{25} +31.8575i q^{26} +(-19.7171 - 18.4455i) q^{27} +(-2.88228 + 8.87075i) q^{28} +(-26.8199 - 8.71430i) q^{29} +(-16.4553 - 13.3874i) q^{30} +(-16.6071 - 51.1114i) q^{31} -5.65685i q^{32} +(3.93989 + 9.93269i) q^{33} +(13.9409 + 10.1287i) q^{34} +(20.3483 - 11.3878i) q^{35} +(-13.1059 + 12.3384i) q^{36} +(-12.3397 - 8.96535i) q^{37} +(-10.2948 + 14.1696i) q^{38} +(-43.1099 - 52.0440i) q^{39} +(-9.60272 + 10.3821i) q^{40} +(-14.9764 + 20.6133i) q^{41} +(-7.29536 - 18.3920i) q^{42} -31.9780 q^{43} +(6.77504 - 2.20135i) q^{44} +(44.9982 - 0.397129i) q^{45} +(-5.61185 + 17.2715i) q^{46} +(18.9392 + 6.15370i) q^{47} +(7.65492 + 9.24133i) q^{48} -27.2506 q^{49} +(35.2480 - 2.75341i) q^{50} +(-36.4808 + 2.31830i) q^{51} +(-36.4488 + 26.4816i) q^{52} +(82.7402 + 26.8839i) q^{53} +(4.71394 - 37.8917i) q^{54} +(-16.1712 - 7.46073i) q^{55} +(-12.5451 + 4.07616i) q^{56} +(-2.35633 - 37.0793i) q^{57} +(-12.3239 - 37.9290i) q^{58} +(-34.5936 + 47.6140i) q^{59} +(1.63832 - 29.9552i) q^{60} +(59.7663 - 43.4227i) q^{61} +(44.6730 - 61.4871i) q^{62} +(36.8064 + 20.1740i) q^{63} +(6.47214 - 4.70228i) q^{64} +(111.849 + 13.2712i) q^{65} +(-8.08918 + 12.7643i) q^{66} +(9.87401 + 30.3891i) q^{67} +24.3696i q^{68} +(-14.2042 - 35.8096i) q^{69} +(29.9437 + 13.8148i) q^{70} +(-106.852 - 34.7184i) q^{71} +(-25.0110 - 4.73838i) q^{72} +(-109.480 + 79.5417i) q^{73} -21.5707i q^{74} +(-53.8569 + 52.1961i) q^{75} -24.7694 q^{76} +(-9.76379 - 13.4387i) q^{77} +(23.7094 - 92.5848i) q^{78} +(4.15564 - 12.7898i) q^{79} +(-19.8607 - 2.35653i) q^{80} +(43.5745 + 68.2808i) q^{81} -36.0333 q^{82} +(-83.2577 + 27.0521i) q^{83} +(14.9785 - 23.6352i) q^{84} +(41.3683 - 44.7258i) q^{85} +(-26.5818 - 36.5868i) q^{86} +(71.4589 + 45.2860i) q^{87} +(8.15039 + 5.92161i) q^{88} +(-54.4702 - 74.9718i) q^{89} +(37.8593 + 51.1534i) q^{90} +(84.9919 + 61.7502i) q^{91} +(-24.4256 + 7.93635i) q^{92} +(10.2250 + 160.901i) q^{93} +(8.70265 + 26.7840i) q^{94} +(45.4596 + 42.0470i) q^{95} +(-4.21003 + 16.4401i) q^{96} +(20.7609 - 63.8956i) q^{97} +(-22.6521 - 31.1780i) q^{98} +(-4.05792 - 31.7988i) 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
\(3\) −2.90622 0.744235i −0.968740 0.248078i
\(4\) −0.618034 + 1.90211i −0.154508 + 0.475528i
\(5\) 4.36319 2.44184i 0.872638 0.488367i
\(6\) −1.56431 3.94372i −0.260718 0.657287i
\(7\) 4.66363 0.666233 0.333116 0.942886i \(-0.391900\pi\)
0.333116 + 0.942886i \(0.391900\pi\)
\(8\) −2.68999 + 0.874032i −0.336249 + 0.109254i
\(9\) 7.89223 + 4.32582i 0.876914 + 0.480647i
\(10\) 6.42068 + 2.96224i 0.642068 + 0.296224i
\(11\) −2.09360 2.88160i −0.190328 0.261964i 0.703180 0.711012i \(-0.251763\pi\)
−0.893507 + 0.449049i \(0.851763\pi\)
\(12\) 3.21176 5.06800i 0.267647 0.422333i
\(13\) 18.2244 + 13.2408i 1.40188 + 1.01852i 0.994441 + 0.105291i \(0.0335775\pi\)
0.407437 + 0.913233i \(0.366423\pi\)
\(14\) 3.87666 + 5.33576i 0.276904 + 0.381126i
\(15\) −14.4977 + 3.84927i −0.966513 + 0.256618i
\(16\) −3.23607 2.35114i −0.202254 0.146946i
\(17\) 11.5884 3.76531i 0.681672 0.221489i 0.0523448 0.998629i \(-0.483331\pi\)
0.629327 + 0.777140i \(0.283331\pi\)
\(18\) 1.61117 + 12.6255i 0.0895096 + 0.701419i
\(19\) 3.82708 + 11.7786i 0.201425 + 0.619924i 0.999841 + 0.0178173i \(0.00567174\pi\)
−0.798416 + 0.602106i \(0.794328\pi\)
\(20\) 1.94805 + 9.80842i 0.0974023 + 0.490421i
\(21\) −13.5535 3.47084i −0.645406 0.165278i
\(22\) 1.55659 4.79068i 0.0707539 0.217758i
\(23\) 7.54792 + 10.3888i 0.328170 + 0.451688i 0.940940 0.338574i \(-0.109945\pi\)
−0.612769 + 0.790262i \(0.709945\pi\)
\(24\) 8.46820 0.538141i 0.352842 0.0224225i
\(25\) 13.0749 21.3084i 0.522995 0.852336i
\(26\) 31.8575i 1.22529i
\(27\) −19.7171 18.4455i −0.730264 0.683165i
\(28\) −2.88228 + 8.87075i −0.102939 + 0.316812i
\(29\) −26.8199 8.71430i −0.924823 0.300493i −0.192379 0.981321i \(-0.561620\pi\)
−0.732444 + 0.680828i \(0.761620\pi\)
\(30\) −16.4553 13.3874i −0.548510 0.446247i
\(31\) −16.6071 51.1114i −0.535713 1.64876i −0.742103 0.670285i \(-0.766172\pi\)
0.206390 0.978470i \(-0.433828\pi\)
\(32\) 5.65685i 0.176777i
\(33\) 3.93989 + 9.93269i 0.119390 + 0.300991i
\(34\) 13.9409 + 10.1287i 0.410026 + 0.297902i
\(35\) 20.3483 11.3878i 0.581380 0.325366i
\(36\) −13.1059 + 12.3384i −0.364052 + 0.342733i
\(37\) −12.3397 8.96535i −0.333506 0.242307i 0.408411 0.912798i \(-0.366083\pi\)
−0.741917 + 0.670492i \(0.766083\pi\)
\(38\) −10.2948 + 14.1696i −0.270917 + 0.372885i
\(39\) −43.1099 52.0440i −1.10538 1.33446i
\(40\) −9.60272 + 10.3821i −0.240068 + 0.259552i
\(41\) −14.9764 + 20.6133i −0.365279 + 0.502763i −0.951610 0.307308i \(-0.900572\pi\)
0.586331 + 0.810071i \(0.300572\pi\)
\(42\) −7.29536 18.3920i −0.173699 0.437906i
\(43\) −31.9780 −0.743675 −0.371837 0.928298i \(-0.621272\pi\)
−0.371837 + 0.928298i \(0.621272\pi\)
\(44\) 6.77504 2.20135i 0.153978 0.0500306i
\(45\) 44.9982 0.397129i 0.999961 0.00882508i
\(46\) −5.61185 + 17.2715i −0.121997 + 0.375467i
\(47\) 18.9392 + 6.15370i 0.402961 + 0.130930i 0.503483 0.864005i \(-0.332052\pi\)
−0.100523 + 0.994935i \(0.532052\pi\)
\(48\) 7.65492 + 9.24133i 0.159478 + 0.192528i
\(49\) −27.2506 −0.556134
\(50\) 35.2480 2.75341i 0.704959 0.0550682i
\(51\) −36.4808 + 2.31830i −0.715310 + 0.0454568i
\(52\) −36.4488 + 26.4816i −0.700939 + 0.509262i
\(53\) 82.7402 + 26.8839i 1.56114 + 0.507244i 0.957111 0.289722i \(-0.0935627\pi\)
0.604025 + 0.796965i \(0.293563\pi\)
\(54\) 4.71394 37.8917i 0.0872953 0.701698i
\(55\) −16.1712 7.46073i −0.294022 0.135650i
\(56\) −12.5451 + 4.07616i −0.224020 + 0.0727886i
\(57\) −2.35633 37.0793i −0.0413392 0.650514i
\(58\) −12.3239 37.9290i −0.212481 0.653949i
\(59\) −34.5936 + 47.6140i −0.586333 + 0.807017i −0.994372 0.105947i \(-0.966213\pi\)
0.408039 + 0.912964i \(0.366213\pi\)
\(60\) 1.63832 29.9552i 0.0273054 0.499254i
\(61\) 59.7663 43.4227i 0.979775 0.711848i 0.0221165 0.999755i \(-0.492960\pi\)
0.957658 + 0.287907i \(0.0929595\pi\)
\(62\) 44.6730 61.4871i 0.720532 0.991728i
\(63\) 36.8064 + 20.1740i 0.584229 + 0.320223i
\(64\) 6.47214 4.70228i 0.101127 0.0734732i
\(65\) 111.849 + 13.2712i 1.72075 + 0.204172i
\(66\) −8.08918 + 12.7643i −0.122563 + 0.193399i
\(67\) 9.87401 + 30.3891i 0.147373 + 0.453568i 0.997309 0.0733189i \(-0.0233591\pi\)
−0.849935 + 0.526887i \(0.823359\pi\)
\(68\) 24.3696i 0.358376i
\(69\) −14.2042 35.8096i −0.205858 0.518980i
\(70\) 29.9437 + 13.8148i 0.427767 + 0.197354i
\(71\) −106.852 34.7184i −1.50496 0.488992i −0.563502 0.826115i \(-0.690546\pi\)
−0.941461 + 0.337123i \(0.890546\pi\)
\(72\) −25.0110 4.73838i −0.347374 0.0658108i
\(73\) −109.480 + 79.5417i −1.49972 + 1.08961i −0.529230 + 0.848478i \(0.677519\pi\)
−0.970492 + 0.241134i \(0.922481\pi\)
\(74\) 21.5707i 0.291495i
\(75\) −53.8569 + 52.1961i −0.718092 + 0.695948i
\(76\) −24.7694 −0.325913
\(77\) −9.76379 13.4387i −0.126802 0.174529i
\(78\) 23.7094 92.5848i 0.303967 1.18698i
\(79\) 4.15564 12.7898i 0.0526031 0.161896i −0.921304 0.388843i \(-0.872875\pi\)
0.973907 + 0.226948i \(0.0728747\pi\)
\(80\) −19.8607 2.35653i −0.248259 0.0294567i
\(81\) 43.5745 + 68.2808i 0.537957 + 0.842972i
\(82\) −36.0333 −0.439431
\(83\) −83.2577 + 27.0521i −1.00311 + 0.325929i −0.764106 0.645091i \(-0.776819\pi\)
−0.238999 + 0.971020i \(0.576819\pi\)
\(84\) 14.9785 23.6352i 0.178315 0.281372i
\(85\) 41.3683 44.7258i 0.486685 0.526186i
\(86\) −26.5818 36.5868i −0.309091 0.425427i
\(87\) 71.4589 + 45.2860i 0.821367 + 0.520528i
\(88\) 8.15039 + 5.92161i 0.0926181 + 0.0672910i
\(89\) −54.4702 74.9718i −0.612025 0.842380i 0.384717 0.923034i \(-0.374299\pi\)
−0.996742 + 0.0806546i \(0.974299\pi\)
\(90\) 37.8593 + 51.1534i 0.420659 + 0.568371i
\(91\) 84.9919 + 61.7502i 0.933977 + 0.678574i
\(92\) −24.4256 + 7.93635i −0.265495 + 0.0862647i
\(93\) 10.2250 + 160.901i 0.109946 + 1.73011i
\(94\) 8.70265 + 26.7840i 0.0925814 + 0.284936i
\(95\) 45.4596 + 42.0470i 0.478522 + 0.442600i
\(96\) −4.21003 + 16.4401i −0.0438545 + 0.171251i
\(97\) 20.7609 63.8956i 0.214030 0.658717i −0.785191 0.619254i \(-0.787435\pi\)
0.999221 0.0394634i \(-0.0125649\pi\)
\(98\) −22.6521 31.1780i −0.231144 0.318143i
\(99\) −4.05792 31.7988i −0.0409890 0.321200i
\(100\) 32.4502 + 38.0392i 0.324502 + 0.380392i
\(101\) 161.288i 1.59691i 0.602055 + 0.798454i \(0.294349\pi\)
−0.602055 + 0.798454i \(0.705651\pi\)
\(102\) −32.9772 39.8114i −0.323306 0.390308i
\(103\) 26.2153 80.6825i 0.254518 0.783325i −0.739406 0.673259i \(-0.764894\pi\)
0.993924 0.110066i \(-0.0351062\pi\)
\(104\) −60.5965 19.6890i −0.582659 0.189317i
\(105\) −67.6118 + 17.9516i −0.643922 + 0.170967i
\(106\) 38.0196 + 117.012i 0.358676 + 1.10389i
\(107\) 23.5373i 0.219975i 0.993933 + 0.109987i \(0.0350810\pi\)
−0.993933 + 0.109987i \(0.964919\pi\)
\(108\) 47.2712 26.1043i 0.437696 0.241706i
\(109\) −57.1806 41.5441i −0.524593 0.381139i 0.293739 0.955886i \(-0.405101\pi\)
−0.818331 + 0.574747i \(0.805101\pi\)
\(110\) −4.90637 24.7036i −0.0446033 0.224578i
\(111\) 29.1897 + 35.2389i 0.262970 + 0.317468i
\(112\) −15.0918 10.9648i −0.134748 0.0979004i
\(113\) 21.7772 29.9738i 0.192719 0.265255i −0.701712 0.712460i \(-0.747581\pi\)
0.894431 + 0.447206i \(0.147581\pi\)
\(114\) 40.4646 33.5183i 0.354952 0.294020i
\(115\) 58.3008 + 26.8976i 0.506963 + 0.233892i
\(116\) 33.1512 45.6287i 0.285786 0.393351i
\(117\) 86.5539 + 183.335i 0.739777 + 1.56697i
\(118\) −83.2324 −0.705359
\(119\) 54.0441 17.5600i 0.454152 0.147563i
\(120\) 35.6343 23.0260i 0.296953 0.191883i
\(121\) 33.4706 103.012i 0.276617 0.851339i
\(122\) 99.3619 + 32.2846i 0.814442 + 0.264628i
\(123\) 58.8659 48.7607i 0.478585 0.396429i
\(124\) 107.483 0.866802
\(125\) 5.01664 124.899i 0.0401331 0.999194i
\(126\) 7.51391 + 58.8808i 0.0596342 + 0.467308i
\(127\) 152.346 110.686i 1.19958 0.871542i 0.205332 0.978692i \(-0.434173\pi\)
0.994243 + 0.107150i \(0.0341725\pi\)
\(128\) 10.7600 + 3.49613i 0.0840623 + 0.0273135i
\(129\) 92.9351 + 23.7992i 0.720427 + 0.184490i
\(130\) 77.7907 + 139.000i 0.598390 + 1.06923i
\(131\) −35.7337 + 11.6106i −0.272777 + 0.0886305i −0.442211 0.896911i \(-0.645806\pi\)
0.169435 + 0.985541i \(0.445806\pi\)
\(132\) −21.3281 + 1.35537i −0.161576 + 0.0102679i
\(133\) 17.8481 + 54.9308i 0.134196 + 0.413013i
\(134\) −26.5610 + 36.5581i −0.198217 + 0.272822i
\(135\) −131.070 32.3351i −0.970892 0.239520i
\(136\) −27.8818 + 20.2573i −0.205013 + 0.148951i
\(137\) 98.3704 135.395i 0.718032 0.988286i −0.281555 0.959545i \(-0.590850\pi\)
0.999587 0.0287412i \(-0.00914986\pi\)
\(138\) 29.1633 46.0182i 0.211328 0.333465i
\(139\) −189.477 + 137.663i −1.36314 + 0.990381i −0.364905 + 0.931045i \(0.618898\pi\)
−0.998238 + 0.0593363i \(0.981102\pi\)
\(140\) 9.08496 + 45.7428i 0.0648926 + 0.326734i
\(141\) −50.4615 31.9792i −0.357883 0.226803i
\(142\) −49.0993 151.112i −0.345770 1.06417i
\(143\) 80.2365i 0.561094i
\(144\) −15.3692 32.5544i −0.106730 0.226072i
\(145\) −138.299 + 27.4675i −0.953787 + 0.189431i
\(146\) −182.011 59.1389i −1.24665 0.405061i
\(147\) 79.1962 + 20.2808i 0.538749 + 0.137965i
\(148\) 24.6795 17.9307i 0.166753 0.121153i
\(149\) 177.561i 1.19169i 0.803101 + 0.595843i \(0.203182\pi\)
−0.803101 + 0.595843i \(0.796818\pi\)
\(150\) −104.488 18.2308i −0.696583 0.121538i
\(151\) 63.2956 0.419176 0.209588 0.977790i \(-0.432788\pi\)
0.209588 + 0.977790i \(0.432788\pi\)
\(152\) −20.5897 28.3392i −0.135458 0.186442i
\(153\) 107.747 + 20.4128i 0.704226 + 0.133417i
\(154\) 7.25934 22.3419i 0.0471386 0.145078i
\(155\) −197.266 182.457i −1.27268 1.17714i
\(156\) 125.637 49.8349i 0.805365 0.319455i
\(157\) −78.2396 −0.498341 −0.249171 0.968460i \(-0.580158\pi\)
−0.249171 + 0.968460i \(0.580158\pi\)
\(158\) 18.0874 5.87697i 0.114477 0.0371960i
\(159\) −220.453 139.709i −1.38650 0.878671i
\(160\) −13.8131 24.6819i −0.0863319 0.154262i
\(161\) 35.2007 + 48.4496i 0.218638 + 0.300929i
\(162\) −41.9001 + 106.613i −0.258642 + 0.658106i
\(163\) 118.920 + 86.4004i 0.729570 + 0.530064i 0.889428 0.457076i \(-0.151103\pi\)
−0.159857 + 0.987140i \(0.551103\pi\)
\(164\) −29.9529 41.2266i −0.182639 0.251381i
\(165\) 41.4445 + 33.7177i 0.251179 + 0.204350i
\(166\) −100.159 72.7699i −0.603369 0.438373i
\(167\) −210.662 + 68.4483i −1.26145 + 0.409870i −0.862011 0.506890i \(-0.830795\pi\)
−0.399439 + 0.916760i \(0.630795\pi\)
\(168\) 39.4925 2.50969i 0.235075 0.0149386i
\(169\) 104.586 + 321.884i 0.618855 + 1.90464i
\(170\) 85.5593 + 10.1519i 0.503290 + 0.0597170i
\(171\) −20.7477 + 109.514i −0.121332 + 0.640435i
\(172\) 19.7635 60.8258i 0.114904 0.353638i
\(173\) −103.751 142.801i −0.599716 0.825438i 0.395966 0.918265i \(-0.370410\pi\)
−0.995682 + 0.0928267i \(0.970410\pi\)
\(174\) 7.58781 + 119.402i 0.0436081 + 0.686218i
\(175\) 60.9764 99.3744i 0.348436 0.567854i
\(176\) 14.2474i 0.0809512i
\(177\) 135.973 112.631i 0.768207 0.636334i
\(178\) 40.4984 124.641i 0.227519 0.700231i
\(179\) 27.3759 + 8.89497i 0.152938 + 0.0496926i 0.384486 0.923131i \(-0.374379\pi\)
−0.231547 + 0.972824i \(0.574379\pi\)
\(180\) −27.0551 + 85.8372i −0.150306 + 0.476873i
\(181\) −103.786 319.421i −0.573404 1.76476i −0.641550 0.767081i \(-0.721708\pi\)
0.0681457 0.997675i \(-0.478292\pi\)
\(182\) 148.571i 0.816326i
\(183\) −206.011 + 81.7158i −1.12574 + 0.446535i
\(184\) −29.3840 21.3487i −0.159696 0.116026i
\(185\) −75.7325 8.98591i −0.409365 0.0485725i
\(186\) −175.590 + 145.448i −0.944035 + 0.781978i
\(187\) −35.1117 25.5101i −0.187763 0.136418i
\(188\) −23.4101 + 32.2212i −0.124522 + 0.171389i
\(189\) −91.9533 86.0228i −0.486525 0.455147i
\(190\) −10.3184 + 86.9631i −0.0543076 + 0.457700i
\(191\) 204.306 281.203i 1.06966 1.47227i 0.199248 0.979949i \(-0.436150\pi\)
0.870416 0.492317i \(-0.163850\pi\)
\(192\) −22.3091 + 8.84907i −0.116193 + 0.0460889i
\(193\) −281.011 −1.45601 −0.728007 0.685569i \(-0.759553\pi\)
−0.728007 + 0.685569i \(0.759553\pi\)
\(194\) 90.3620 29.3604i 0.465784 0.151342i
\(195\) −315.180 121.811i −1.61631 0.624670i
\(196\) 16.8418 51.8337i 0.0859275 0.264458i
\(197\) −73.9465 24.0267i −0.375363 0.121963i 0.115259 0.993336i \(-0.463230\pi\)
−0.490622 + 0.871373i \(0.663230\pi\)
\(198\) 33.0086 31.0756i 0.166710 0.156948i
\(199\) 136.028 0.683558 0.341779 0.939780i \(-0.388971\pi\)
0.341779 + 0.939780i \(0.388971\pi\)
\(200\) −16.5471 + 68.7473i −0.0827357 + 0.343737i
\(201\) −6.07942 95.6659i −0.0302459 0.475950i
\(202\) −184.533 + 134.071i −0.913530 + 0.663718i
\(203\) −125.078 40.6403i −0.616147 0.200198i
\(204\) 18.1367 70.8234i 0.0889054 0.347173i
\(205\) −15.0108 + 126.510i −0.0732233 + 0.617120i
\(206\) 114.102 37.0741i 0.553895 0.179971i
\(207\) 14.6297 + 114.642i 0.0706749 + 0.553825i
\(208\) −27.8444 85.6964i −0.133867 0.412002i
\(209\) 25.9287 35.6877i 0.124061 0.170755i
\(210\) −76.7414 62.4340i −0.365435 0.297305i
\(211\) 129.439 94.0430i 0.613456 0.445702i −0.237174 0.971467i \(-0.576221\pi\)
0.850629 + 0.525766i \(0.176221\pi\)
\(212\) −102.273 + 140.766i −0.482418 + 0.663991i
\(213\) 284.698 + 180.423i 1.33661 + 0.847055i
\(214\) −26.9295 + 19.5655i −0.125839 + 0.0914274i
\(215\) −139.526 + 78.0850i −0.648959 + 0.363186i
\(216\) 69.1609 + 32.3848i 0.320189 + 0.149930i
\(217\) −77.4494 238.365i −0.356909 1.09845i
\(218\) 99.9554i 0.458511i
\(219\) 377.370 149.687i 1.72315 0.683502i
\(220\) 24.1855 26.1484i 0.109934 0.118857i
\(221\) 261.048 + 84.8197i 1.18121 + 0.383799i
\(222\) −16.0536 + 62.6891i −0.0723137 + 0.282383i
\(223\) −148.135 + 107.626i −0.664281 + 0.482629i −0.868106 0.496379i \(-0.834663\pi\)
0.203825 + 0.979007i \(0.434663\pi\)
\(224\) 26.3815i 0.117774i
\(225\) 195.366 111.611i 0.868294 0.496049i
\(226\) 52.3961 0.231841
\(227\) 42.7138 + 58.7905i 0.188167 + 0.258989i 0.892669 0.450712i \(-0.148830\pi\)
−0.704503 + 0.709701i \(0.748830\pi\)
\(228\) 71.9853 + 18.4343i 0.315725 + 0.0808520i
\(229\) −13.8705 + 42.6891i −0.0605700 + 0.186415i −0.976763 0.214322i \(-0.931246\pi\)
0.916193 + 0.400737i \(0.131246\pi\)
\(230\) 17.6886 + 89.0620i 0.0769068 + 0.387226i
\(231\) 18.3742 + 46.3224i 0.0795418 + 0.200530i
\(232\) 79.7619 0.343801
\(233\) 147.069 47.7856i 0.631197 0.205088i 0.0240918 0.999710i \(-0.492331\pi\)
0.607105 + 0.794621i \(0.292331\pi\)
\(234\) −137.810 + 251.426i −0.588930 + 1.07447i
\(235\) 97.6615 19.3965i 0.415581 0.0825383i
\(236\) −69.1872 95.2281i −0.293166 0.403509i
\(237\) −21.5958 + 34.0771i −0.0911215 + 0.143785i
\(238\) 65.0152 + 47.2363i 0.273173 + 0.198472i
\(239\) 147.954 + 203.641i 0.619053 + 0.852053i 0.997284 0.0736580i \(-0.0234673\pi\)
−0.378230 + 0.925711i \(0.623467\pi\)
\(240\) 55.9657 + 21.6296i 0.233190 + 0.0901234i
\(241\) 27.3940 + 19.9029i 0.113668 + 0.0825846i 0.643167 0.765726i \(-0.277620\pi\)
−0.529499 + 0.848311i \(0.677620\pi\)
\(242\) 145.681 47.3346i 0.601987 0.195598i
\(243\) −75.8202 230.869i −0.312017 0.950076i
\(244\) 45.6574 + 140.519i 0.187120 + 0.575897i
\(245\) −118.899 + 66.5414i −0.485304 + 0.271598i
\(246\) 104.721 + 26.8173i 0.425694 + 0.109013i
\(247\) −86.2113 + 265.331i −0.349034 + 1.07421i
\(248\) 89.3460 + 122.974i 0.360266 + 0.495864i
\(249\) 262.098 16.6559i 1.05260 0.0668913i
\(250\) 147.070 98.0834i 0.588281 0.392333i
\(251\) 268.503i 1.06973i −0.844937 0.534866i \(-0.820362\pi\)
0.844937 0.534866i \(-0.179638\pi\)
\(252\) −61.1209 + 57.5417i −0.242543 + 0.228340i
\(253\) 14.1341 43.5001i 0.0558658 0.171937i
\(254\) 253.276 + 82.2945i 0.997151 + 0.323994i
\(255\) −153.512 + 99.1952i −0.602007 + 0.389001i
\(256\) 4.94427 + 15.2169i 0.0193136 + 0.0594410i
\(257\) 273.017i 1.06232i 0.847271 + 0.531161i \(0.178244\pi\)
−0.847271 + 0.531161i \(0.821756\pi\)
\(258\) 50.0235 + 126.112i 0.193890 + 0.488807i
\(259\) −57.5480 41.8110i −0.222193 0.161433i
\(260\) −94.3695 + 204.547i −0.362960 + 0.786717i
\(261\) −173.972 184.793i −0.666559 0.708020i
\(262\) −42.9877 31.2324i −0.164075 0.119208i
\(263\) 196.807 270.881i 0.748315 1.02997i −0.249782 0.968302i \(-0.580359\pi\)
0.998097 0.0616647i \(-0.0196409\pi\)
\(264\) −19.2798 23.2753i −0.0730294 0.0881640i
\(265\) 426.657 84.7382i 1.61003 0.319767i
\(266\) −48.0113 + 66.0818i −0.180493 + 0.248428i
\(267\) 102.506 + 258.423i 0.383917 + 0.967877i
\(268\) −63.9059 −0.238455
\(269\) −101.592 + 33.0091i −0.377664 + 0.122710i −0.491697 0.870767i \(-0.663623\pi\)
0.114033 + 0.993477i \(0.463623\pi\)
\(270\) −71.9574 176.839i −0.266509 0.654960i
\(271\) −40.2056 + 123.740i −0.148360 + 0.456606i −0.997428 0.0716785i \(-0.977164\pi\)
0.849068 + 0.528284i \(0.177164\pi\)
\(272\) −46.3537 15.0612i −0.170418 0.0553722i
\(273\) −201.048 242.714i −0.736441 0.889061i
\(274\) 236.680 0.863794
\(275\) −88.7759 + 6.93477i −0.322821 + 0.0252173i
\(276\) 76.8926 4.88641i 0.278596 0.0177044i
\(277\) −252.767 + 183.646i −0.912518 + 0.662983i −0.941650 0.336593i \(-0.890725\pi\)
0.0291326 + 0.999576i \(0.490725\pi\)
\(278\) −315.007 102.352i −1.13312 0.368172i
\(279\) 90.0318 475.222i 0.322695 1.70331i
\(280\) −44.7835 + 48.4182i −0.159941 + 0.172922i
\(281\) 80.2975 26.0902i 0.285756 0.0928478i −0.162632 0.986687i \(-0.551998\pi\)
0.448388 + 0.893839i \(0.351998\pi\)
\(282\) −5.35822 84.3170i −0.0190008 0.298997i
\(283\) 69.7774 + 214.753i 0.246563 + 0.758844i 0.995375 + 0.0960613i \(0.0306245\pi\)
−0.748812 + 0.662782i \(0.769376\pi\)
\(284\) 132.077 181.788i 0.465059 0.640099i
\(285\) −100.823 156.030i −0.353764 0.547475i
\(286\) 91.8004 66.6969i 0.320980 0.233206i
\(287\) −69.8445 + 96.1327i −0.243361 + 0.334957i
\(288\) 24.4705 44.6452i 0.0849672 0.155018i
\(289\) −113.692 + 82.6020i −0.393397 + 0.285820i
\(290\) −146.388 135.399i −0.504786 0.466892i
\(291\) −107.889 + 170.244i −0.370753 + 0.585030i
\(292\) −83.6351 257.402i −0.286421 0.881515i
\(293\) 177.444i 0.605610i 0.953053 + 0.302805i \(0.0979231\pi\)
−0.953053 + 0.302805i \(0.902077\pi\)
\(294\) 42.6284 + 107.469i 0.144994 + 0.365540i
\(295\) −34.6730 + 292.221i −0.117535 + 0.990580i
\(296\) 41.0298 + 13.3314i 0.138614 + 0.0450385i
\(297\) −11.8726 + 95.4343i −0.0399750 + 0.321328i
\(298\) −203.152 + 147.599i −0.681718 + 0.495297i
\(299\) 289.271i 0.967461i
\(300\) −65.9974 134.701i −0.219991 0.449003i
\(301\) −149.134 −0.495460
\(302\) 52.6147 + 72.4180i 0.174221 + 0.239795i
\(303\) 120.036 468.738i 0.396159 1.54699i
\(304\) 15.3083 47.1142i 0.0503564 0.154981i
\(305\) 154.740 335.401i 0.507346 1.09968i
\(306\) 66.2100 + 140.244i 0.216372 + 0.458312i
\(307\) 244.240 0.795571 0.397786 0.917478i \(-0.369779\pi\)
0.397786 + 0.917478i \(0.369779\pi\)
\(308\) 31.5963 10.2663i 0.102585 0.0333320i
\(309\) −136.234 + 214.971i −0.440888 + 0.695698i
\(310\) 44.7755 377.364i 0.144437 1.21730i
\(311\) 297.138 + 408.975i 0.955427 + 1.31503i 0.949074 + 0.315053i \(0.102022\pi\)
0.00635277 + 0.999980i \(0.497978\pi\)
\(312\) 161.453 + 102.319i 0.517479 + 0.327944i
\(313\) 159.930 + 116.196i 0.510960 + 0.371234i 0.813188 0.582002i \(-0.197730\pi\)
−0.302228 + 0.953236i \(0.597730\pi\)
\(314\) −65.0370 89.5157i −0.207124 0.285082i
\(315\) 209.855 1.85206i 0.666207 0.00587955i
\(316\) 21.7592 + 15.8090i 0.0688583 + 0.0500285i
\(317\) −405.215 + 131.662i −1.27828 + 0.415339i −0.867975 0.496608i \(-0.834579\pi\)
−0.410307 + 0.911947i \(0.634579\pi\)
\(318\) −23.4086 368.359i −0.0736121 1.15836i
\(319\) 31.0391 + 95.5284i 0.0973011 + 0.299462i
\(320\) 16.7570 36.3208i 0.0523655 0.113503i
\(321\) 17.5173 68.4045i 0.0545710 0.213098i
\(322\) −26.1716 + 80.5478i −0.0812782 + 0.250148i
\(323\) 88.6997 + 122.085i 0.274612 + 0.377971i
\(324\) −156.808 + 40.6838i −0.483976 + 0.125567i
\(325\) 520.423 215.211i 1.60130 0.662188i
\(326\) 207.880i 0.637668i
\(327\) 135.261 + 163.292i 0.413642 + 0.499365i
\(328\) 22.2698 68.5395i 0.0678958 0.208962i
\(329\) 88.3251 + 28.6986i 0.268465 + 0.0872297i
\(330\) −4.12629 + 75.4455i −0.0125039 + 0.228623i
\(331\) 96.7776 + 297.851i 0.292379 + 0.899851i 0.984089 + 0.177676i \(0.0568578\pi\)
−0.691710 + 0.722176i \(0.743142\pi\)
\(332\) 175.085i 0.527364i
\(333\) −58.6055 124.136i −0.175993 0.372781i
\(334\) −253.427 184.125i −0.758763 0.551274i
\(335\) 117.287 + 108.483i 0.350111 + 0.323829i
\(336\) 35.6997 + 43.0981i 0.106249 + 0.128268i
\(337\) −344.340 250.178i −1.02178 0.742367i −0.0551333 0.998479i \(-0.517558\pi\)
−0.966647 + 0.256112i \(0.917558\pi\)
\(338\) −281.337 + 387.227i −0.832358 + 1.14564i
\(339\) −85.5970 + 70.9031i −0.252499 + 0.209154i
\(340\) 59.5065 + 106.329i 0.175019 + 0.312733i
\(341\) −112.514 + 154.862i −0.329953 + 0.454141i
\(342\) −142.544 + 67.2963i −0.416797 + 0.196773i
\(343\) −355.604 −1.03675
\(344\) 86.0206 27.9498i 0.250060 0.0812494i
\(345\) −149.417 121.560i −0.433092 0.352348i
\(346\) 77.1384 237.407i 0.222943 0.686149i
\(347\) 306.116 + 99.4631i 0.882178 + 0.286637i 0.714861 0.699266i \(-0.246490\pi\)
0.167317 + 0.985903i \(0.446490\pi\)
\(348\) −130.303 + 107.935i −0.374434 + 0.310157i
\(349\) −5.04126 −0.0144449 −0.00722244 0.999974i \(-0.502299\pi\)
−0.00722244 + 0.999974i \(0.502299\pi\)
\(350\) 164.383 12.8409i 0.469667 0.0366882i
\(351\) −115.100 597.229i −0.327920 1.70151i
\(352\) −16.3008 + 11.8432i −0.0463090 + 0.0336455i
\(353\) 49.4739 + 16.0750i 0.140153 + 0.0455384i 0.378253 0.925702i \(-0.376525\pi\)
−0.238101 + 0.971240i \(0.576525\pi\)
\(354\) 241.892 + 61.9445i 0.683310 + 0.174984i
\(355\) −550.994 + 109.433i −1.55210 + 0.308261i
\(356\) 176.269 57.2734i 0.495138 0.160880i
\(357\) −170.133 + 10.8117i −0.476562 + 0.0302848i
\(358\) 12.5794 + 38.7154i 0.0351380 + 0.108144i
\(359\) 168.495 231.914i 0.469346 0.645999i −0.507068 0.861906i \(-0.669271\pi\)
0.976414 + 0.215907i \(0.0692707\pi\)
\(360\) −120.698 + 40.3982i −0.335272 + 0.112217i
\(361\) 167.967 122.035i 0.465284 0.338048i
\(362\) 279.184 384.264i 0.771227 1.06150i
\(363\) −173.938 + 274.465i −0.479168 + 0.756103i
\(364\) −169.984 + 123.500i −0.466989 + 0.339287i
\(365\) −283.453 + 614.387i −0.776585 + 1.68325i
\(366\) −264.740 167.775i −0.723334 0.458401i
\(367\) −36.9975 113.866i −0.100811 0.310263i 0.887914 0.460010i \(-0.152154\pi\)
−0.988724 + 0.149747i \(0.952154\pi\)
\(368\) 51.3651i 0.139579i
\(369\) −207.367 + 97.8994i −0.561970 + 0.265310i
\(370\) −52.6720 94.1169i −0.142357 0.254370i
\(371\) 385.869 + 125.377i 1.04008 + 0.337942i
\(372\) −312.371 79.9930i −0.839706 0.215035i
\(373\) −508.990 + 369.803i −1.36458 + 0.991428i −0.366445 + 0.930440i \(0.619425\pi\)
−0.998138 + 0.0609884i \(0.980575\pi\)
\(374\) 61.3775i 0.164111i
\(375\) −107.534 + 359.251i −0.286757 + 0.958003i
\(376\) −56.3247 −0.149800
\(377\) −373.392 513.930i −0.990430 1.36321i
\(378\) 21.9841 176.713i 0.0581589 0.467494i
\(379\) 113.910 350.578i 0.300553 0.925008i −0.680746 0.732520i \(-0.738344\pi\)
0.981299 0.192488i \(-0.0616557\pi\)
\(380\) −108.074 + 60.4828i −0.284404 + 0.159165i
\(381\) −525.127 + 208.296i −1.37829 + 0.546709i
\(382\) 491.561 1.28681
\(383\) 436.426 141.804i 1.13949 0.370244i 0.322318 0.946632i \(-0.395538\pi\)
0.817177 + 0.576387i \(0.195538\pi\)
\(384\) −28.6689 18.1685i −0.0746586 0.0473137i
\(385\) −75.4164 34.7941i −0.195887 0.0903742i
\(386\) −233.591 321.511i −0.605159 0.832930i
\(387\) −252.378 138.331i −0.652139 0.357445i
\(388\) 108.706 + 78.9793i 0.280169 + 0.203555i
\(389\) 123.011 + 169.310i 0.316223 + 0.435244i 0.937309 0.348498i \(-0.113308\pi\)
−0.621086 + 0.783742i \(0.713308\pi\)
\(390\) −122.628 461.860i −0.314431 1.18426i
\(391\) 126.586 + 91.9698i 0.323748 + 0.235217i
\(392\) 73.3039 23.8179i 0.187000 0.0607599i
\(393\) 112.491 7.14863i 0.286237 0.0181899i
\(394\) −33.9789 104.576i −0.0862408 0.265422i
\(395\) −13.0986 65.9515i −0.0331610 0.166966i
\(396\) 62.9928 + 11.9341i 0.159073 + 0.0301367i
\(397\) 21.4074 65.8852i 0.0539229 0.165958i −0.920468 0.390817i \(-0.872192\pi\)
0.974391 + 0.224860i \(0.0721924\pi\)
\(398\) 113.074 + 155.633i 0.284105 + 0.391037i
\(399\) −10.9891 172.924i −0.0275415 0.433394i
\(400\) −92.4102 + 38.2145i −0.231026 + 0.0955363i
\(401\) 426.250i 1.06297i −0.847068 0.531484i \(-0.821635\pi\)
0.847068 0.531484i \(-0.178365\pi\)
\(402\) 104.400 86.4782i 0.259701 0.215120i
\(403\) 374.102 1151.37i 0.928293 2.85699i
\(404\) −306.788 99.6813i −0.759375 0.246736i
\(405\) 356.854 + 191.520i 0.881122 + 0.472889i
\(406\) −57.4740 176.887i −0.141562 0.435682i
\(407\) 54.3281i 0.133484i
\(408\) 96.1068 38.1216i 0.235556 0.0934353i
\(409\) 212.282 + 154.232i 0.519028 + 0.377096i 0.816238 0.577716i \(-0.196056\pi\)
−0.297210 + 0.954812i \(0.596056\pi\)
\(410\) −157.220 + 87.9875i −0.383464 + 0.214604i
\(411\) −386.652 + 320.278i −0.940759 + 0.779264i
\(412\) 137.265 + 99.7291i 0.333168 + 0.242061i
\(413\) −161.332 + 222.054i −0.390634 + 0.537661i
\(414\) −119.003 + 112.035i −0.287448 + 0.270615i
\(415\) −297.213 + 321.335i −0.716175 + 0.774301i
\(416\) 74.9014 103.093i 0.180051 0.247819i
\(417\) 653.115 259.064i 1.56622 0.621256i
\(418\) 62.3845 0.149245
\(419\) −366.810 + 119.184i −0.875441 + 0.284448i −0.712063 0.702115i \(-0.752239\pi\)
−0.163378 + 0.986564i \(0.552239\pi\)
\(420\) 7.64053 139.700i 0.0181917 0.332619i
\(421\) −44.8041 + 137.893i −0.106423 + 0.327536i −0.990062 0.140633i \(-0.955086\pi\)
0.883639 + 0.468169i \(0.155086\pi\)
\(422\) 215.194 + 69.9206i 0.509937 + 0.165689i
\(423\) 122.852 + 130.494i 0.290431 + 0.308496i
\(424\) −246.068 −0.580349
\(425\) 71.2846 296.162i 0.167729 0.696851i
\(426\) 30.2304 + 475.706i 0.0709634 + 1.11668i
\(427\) 278.728 202.507i 0.652758 0.474256i
\(428\) −44.7706 14.5468i −0.104604 0.0339880i
\(429\) −59.7148 + 233.185i −0.139195 + 0.543555i
\(430\) −205.321 94.7266i −0.477490 0.220294i
\(431\) −577.048 + 187.494i −1.33886 + 0.435021i −0.888930 0.458043i \(-0.848551\pi\)
−0.449928 + 0.893065i \(0.648551\pi\)
\(432\) 20.4381 + 106.049i 0.0473103 + 0.245483i
\(433\) −97.5441 300.210i −0.225275 0.693325i −0.998264 0.0589054i \(-0.981239\pi\)
0.772988 0.634420i \(-0.218761\pi\)
\(434\) 208.338 286.753i 0.480042 0.660721i
\(435\) 422.370 + 23.1004i 0.970965 + 0.0531044i
\(436\) 114.361 83.0883i 0.262296 0.190569i
\(437\) −93.4787 + 128.662i −0.213910 + 0.294422i
\(438\) 484.950 + 307.330i 1.10719 + 0.701666i
\(439\) −77.1960 + 56.0861i −0.175845 + 0.127759i −0.672226 0.740346i \(-0.734662\pi\)
0.496381 + 0.868105i \(0.334662\pi\)
\(440\) 50.0213 + 5.93519i 0.113685 + 0.0134891i
\(441\) −215.068 117.881i −0.487682 0.267304i
\(442\) 119.953 + 369.178i 0.271387 + 0.835244i
\(443\) 24.1612i 0.0545400i 0.999628 + 0.0272700i \(0.00868139\pi\)
−0.999628 + 0.0272700i \(0.991319\pi\)
\(444\) −85.0686 + 33.7432i −0.191596 + 0.0759982i
\(445\) −420.733 194.109i −0.945467 0.436200i
\(446\) −246.275 80.0196i −0.552186 0.179416i
\(447\) 132.147 516.032i 0.295632 1.15443i
\(448\) 30.1836 21.9297i 0.0673742 0.0489502i
\(449\) 667.584i 1.48682i −0.668834 0.743412i \(-0.733206\pi\)
0.668834 0.743412i \(-0.266794\pi\)
\(450\) 290.096 + 130.746i 0.644657 + 0.290546i
\(451\) 90.7539 0.201228
\(452\) 43.5545 + 59.9476i 0.0963595 + 0.132627i
\(453\) −183.951 47.1068i −0.406073 0.103989i
\(454\) −31.7576 + 97.7397i −0.0699506 + 0.215286i
\(455\) 521.620 + 61.8919i 1.14642 + 0.136026i
\(456\) 38.7470 + 97.6836i 0.0849716 + 0.214218i
\(457\) −266.490 −0.583129 −0.291564 0.956551i \(-0.594176\pi\)
−0.291564 + 0.956551i \(0.594176\pi\)
\(458\) −60.3715 + 19.6159i −0.131815 + 0.0428294i
\(459\) −297.943 139.513i −0.649114 0.303950i
\(460\) −87.1942 + 94.2711i −0.189553 + 0.204937i
\(461\) 81.0450 + 111.549i 0.175803 + 0.241971i 0.887821 0.460190i \(-0.152219\pi\)
−0.712018 + 0.702161i \(0.752219\pi\)
\(462\) −37.7249 + 59.5280i −0.0816556 + 0.128848i
\(463\) 714.083 + 518.812i 1.54230 + 1.12054i 0.948875 + 0.315652i \(0.102223\pi\)
0.593422 + 0.804892i \(0.297777\pi\)
\(464\) 66.3023 + 91.2574i 0.142893 + 0.196675i
\(465\) 437.506 + 677.072i 0.940874 + 1.45607i
\(466\) 176.924 + 128.543i 0.379666 + 0.275843i
\(467\) 205.045 66.6230i 0.439067 0.142662i −0.0811379 0.996703i \(-0.525855\pi\)
0.520205 + 0.854041i \(0.325855\pi\)
\(468\) −402.217 + 51.3279i −0.859439 + 0.109675i
\(469\) 46.0487 + 141.723i 0.0981848 + 0.302182i
\(470\) 103.373 + 95.6133i 0.219944 + 0.203433i
\(471\) 227.381 + 58.2287i 0.482763 + 0.123628i
\(472\) 51.4404 158.317i 0.108984 0.335418i
\(473\) 66.9493 + 92.1478i 0.141542 + 0.194816i
\(474\) −56.9399 + 3.61844i −0.120126 + 0.00763385i
\(475\) 301.021 + 72.4542i 0.633728 + 0.152535i
\(476\) 113.651i 0.238762i
\(477\) 536.709 + 570.093i 1.12518 + 1.19516i
\(478\) −110.003 + 338.554i −0.230132 + 0.708273i
\(479\) −745.417 242.201i −1.55619 0.505638i −0.600406 0.799696i \(-0.704994\pi\)
−0.955788 + 0.294058i \(0.904994\pi\)
\(480\) 21.7748 + 82.0113i 0.0453641 + 0.170857i
\(481\) −106.176 326.776i −0.220740 0.679369i
\(482\) 47.8865i 0.0993495i
\(483\) −66.2430 167.003i −0.137149 0.345761i
\(484\) 175.254 + 127.330i 0.362096 + 0.263078i
\(485\) −65.4386 329.483i −0.134925 0.679347i
\(486\) 201.116 278.658i 0.413819 0.573370i
\(487\) 577.902 + 419.871i 1.18666 + 0.862157i 0.992907 0.118894i \(-0.0379348\pi\)
0.193750 + 0.981051i \(0.437935\pi\)
\(488\) −122.818 + 169.045i −0.251676 + 0.346403i
\(489\) −281.305 339.603i −0.575267 0.694485i
\(490\) −174.967 80.7228i −0.357076 0.164740i
\(491\) −368.869 + 507.705i −0.751261 + 1.03402i 0.246629 + 0.969110i \(0.420677\pi\)
−0.997891 + 0.0649129i \(0.979323\pi\)
\(492\) 56.3673 + 142.105i 0.114568 + 0.288832i
\(493\) −343.612 −0.696982
\(494\) −375.235 + 121.921i −0.759584 + 0.246804i
\(495\) −95.3529 128.835i −0.192632 0.260274i
\(496\) −66.4284 + 204.446i −0.133928 + 0.412189i
\(497\) −498.320 161.914i −1.00266 0.325782i
\(498\) 236.927 + 286.027i 0.475756 + 0.574352i
\(499\) 358.686 0.718809 0.359405 0.933182i \(-0.382980\pi\)
0.359405 + 0.933182i \(0.382980\pi\)
\(500\) 234.472 + 86.7342i 0.468944 + 0.173468i
\(501\) 663.172 42.1436i 1.32370 0.0841189i
\(502\) 307.200 223.194i 0.611952 0.444609i
\(503\) 751.655 + 244.227i 1.49434 + 0.485542i 0.938362 0.345653i \(-0.112343\pi\)
0.555981 + 0.831195i \(0.312343\pi\)
\(504\) −116.642 22.0980i −0.231432 0.0438453i
\(505\) 393.838 + 703.730i 0.779878 + 1.39352i
\(506\) 61.5185 19.9886i 0.121578 0.0395031i
\(507\) −64.3938 1013.30i −0.127009 1.99862i
\(508\) 116.382 + 358.187i 0.229098 + 0.705093i
\(509\) 40.5836 55.8585i 0.0797319 0.109742i −0.767288 0.641303i \(-0.778394\pi\)
0.847020 + 0.531561i \(0.178394\pi\)
\(510\) −241.099 93.1799i −0.472743 0.182706i
\(511\) −510.573 + 370.953i −0.999164 + 0.725935i
\(512\) −13.3001 + 18.3060i −0.0259767 + 0.0357538i
\(513\) 141.802 302.831i 0.276417 0.590315i
\(514\) −312.365 + 226.946i −0.607714 + 0.441530i
\(515\) −82.6308 416.047i −0.160448 0.807858i
\(516\) −102.706 + 162.064i −0.199042 + 0.314078i
\(517\) −21.9186 67.4584i −0.0423957 0.130481i
\(518\) 100.598i 0.194204i
\(519\) 195.245 + 492.226i 0.376195 + 0.948412i
\(520\) −312.471 + 62.0598i −0.600906 + 0.119346i
\(521\) 118.199 + 38.4050i 0.226869 + 0.0737141i 0.420245 0.907410i \(-0.361944\pi\)
−0.193377 + 0.981125i \(0.561944\pi\)
\(522\) 66.8113 352.655i 0.127991 0.675585i
\(523\) 763.636 554.814i 1.46011 1.06083i 0.476773 0.879026i \(-0.341806\pi\)
0.983335 0.181804i \(-0.0581937\pi\)
\(524\) 75.1453i 0.143407i
\(525\) −251.169 + 243.423i −0.478417 + 0.463663i
\(526\) 473.518 0.900224
\(527\) −384.900 529.770i −0.730361 1.00526i
\(528\) 10.6034 41.4061i 0.0200822 0.0784206i
\(529\) 112.514 346.281i 0.212691 0.654595i
\(530\) 451.612 + 417.710i 0.852097 + 0.788131i
\(531\) −478.991 + 226.135i −0.902054 + 0.425866i
\(532\) −115.515 −0.217134
\(533\) −545.873 + 177.365i −1.02415 + 0.332767i
\(534\) −210.460 + 332.094i −0.394119 + 0.621900i
\(535\) 57.4742 + 102.698i 0.107428 + 0.191958i
\(536\) −53.1220 73.1162i −0.0991083 0.136411i
\(537\) −72.9405 46.2249i −0.135830 0.0860798i
\(538\) −122.215 88.7943i −0.227165 0.165045i
\(539\) 57.0519 + 78.5252i 0.105848 + 0.145687i
\(540\) 142.511 229.326i 0.263909 0.424679i
\(541\) −43.8048 31.8260i −0.0809701 0.0588282i 0.546564 0.837417i \(-0.315936\pi\)
−0.627534 + 0.778589i \(0.715936\pi\)
\(542\) −174.995 + 56.8593i −0.322869 + 0.104906i
\(543\) 63.9011 + 1005.55i 0.117682 + 1.85184i
\(544\) −21.2998 65.5540i −0.0391540 0.120504i
\(545\) −350.934 41.6394i −0.643915 0.0764026i
\(546\) 110.572 431.781i 0.202513 0.790808i
\(547\) −40.6958 + 125.249i −0.0743981 + 0.228974i −0.981340 0.192283i \(-0.938411\pi\)
0.906941 + 0.421257i \(0.138411\pi\)
\(548\) 196.741 + 270.790i 0.359016 + 0.494143i
\(549\) 659.528 84.1639i 1.20133 0.153304i
\(550\) −81.7295 95.8059i −0.148599 0.174193i
\(551\) 349.250i 0.633847i
\(552\) 69.5079 + 83.9127i 0.125920 + 0.152016i
\(553\) 19.3804 59.6466i 0.0350459 0.107860i
\(554\) −420.228 136.540i −0.758534 0.246463i
\(555\) 213.408 + 82.4779i 0.384519 + 0.148609i
\(556\) −144.747 445.487i −0.260337 0.801235i
\(557\) 852.525i 1.53056i −0.643695 0.765282i \(-0.722599\pi\)
0.643695 0.765282i \(-0.277401\pi\)
\(558\) 618.552 292.023i 1.10852 0.523339i
\(559\) −582.781 423.415i −1.04254 0.757451i
\(560\) −92.6228 10.9900i −0.165398 0.0196250i
\(561\) 83.0567 + 100.269i 0.148051 + 0.178733i
\(562\) 96.5980 + 70.1826i 0.171883 + 0.124880i
\(563\) −45.8350 + 63.0864i −0.0814121 + 0.112054i −0.847781 0.530347i \(-0.822062\pi\)
0.766369 + 0.642401i \(0.222062\pi\)
\(564\) 92.0150 76.2193i 0.163147 0.135141i
\(565\) 21.8272 183.958i 0.0386322 0.325589i
\(566\) −187.701 + 258.348i −0.331627 + 0.456445i
\(567\) 203.215 + 318.436i 0.358404 + 0.561616i
\(568\) 317.777 0.559467
\(569\) −219.995 + 71.4808i −0.386635 + 0.125625i −0.495883 0.868389i \(-0.665156\pi\)
0.109248 + 0.994014i \(0.465156\pi\)
\(570\) 94.7086 245.054i 0.166156 0.429920i
\(571\) −260.678 + 802.284i −0.456529 + 1.40505i 0.412802 + 0.910821i \(0.364550\pi\)
−0.869331 + 0.494231i \(0.835450\pi\)
\(572\) 152.619 + 49.5889i 0.266816 + 0.0866939i
\(573\) −803.039 + 665.186i −1.40146 + 1.16088i
\(574\) −168.046 −0.292763
\(575\) 320.057 25.0014i 0.556621 0.0434807i
\(576\) 71.4208 9.11417i 0.123994 0.0158232i
\(577\) −485.648 + 352.844i −0.841678 + 0.611515i −0.922839 0.385186i \(-0.874137\pi\)
0.0811607 + 0.996701i \(0.474137\pi\)
\(578\) −189.014 61.4142i −0.327013 0.106253i
\(579\) 816.679 + 209.138i 1.41050 + 0.361206i
\(580\) 33.2272 280.036i 0.0572883 0.482821i
\(581\) −388.283 + 126.161i −0.668301 + 0.217144i
\(582\) −284.463 + 18.0772i −0.488768 + 0.0310604i
\(583\) −95.7565 294.708i −0.164248 0.505503i
\(584\) 224.978 309.655i 0.385236 0.530232i
\(585\) 825.325 + 588.576i 1.41081 + 1.00611i
\(586\) −203.017 + 147.501i −0.346446 + 0.251708i
\(587\) 271.879 374.209i 0.463167 0.637495i −0.511995 0.858989i \(-0.671093\pi\)
0.975162 + 0.221494i \(0.0710933\pi\)
\(588\) −87.5224 + 138.106i −0.148848 + 0.234874i
\(589\) 538.462 391.215i 0.914196 0.664203i
\(590\) −363.159 + 203.240i −0.615523 + 0.344474i
\(591\) 197.023 + 124.860i 0.333373 + 0.211270i
\(592\) 18.8534 + 58.0249i 0.0318470 + 0.0980151i
\(593\) 28.8883i 0.0487155i −0.999703 0.0243578i \(-0.992246\pi\)
0.999703 0.0243578i \(-0.00775409\pi\)
\(594\) −119.058 + 65.7465i −0.200434 + 0.110684i
\(595\) 192.926 208.584i 0.324246 0.350562i
\(596\) −337.742 109.739i −0.566681 0.184126i
\(597\) −395.327 101.237i −0.662190 0.169576i
\(598\) −330.961 + 240.457i −0.553447 + 0.402103i
\(599\) 109.613i 0.182993i 0.995805 + 0.0914967i \(0.0291651\pi\)
−0.995805 + 0.0914967i \(0.970835\pi\)
\(600\) 99.2538 187.480i 0.165423 0.312466i
\(601\) −900.859 −1.49893 −0.749467 0.662042i \(-0.769690\pi\)
−0.749467 + 0.662042i \(0.769690\pi\)
\(602\) −123.968 170.627i −0.205927 0.283434i
\(603\) −53.5298 + 282.551i −0.0887725 + 0.468575i
\(604\) −39.1189 + 120.395i −0.0647663 + 0.199330i
\(605\) −105.500 531.191i −0.174379 0.878001i
\(606\) 636.074 252.304i 1.04963 0.416343i
\(607\) 160.798 0.264906 0.132453 0.991189i \(-0.457715\pi\)
0.132453 + 0.991189i \(0.457715\pi\)
\(608\) 66.6296 21.6493i 0.109588 0.0356073i
\(609\) 333.258 + 211.197i 0.547221 + 0.346793i
\(610\) 512.369 101.761i 0.839949 0.166822i
\(611\) 263.675 + 362.918i 0.431547 + 0.593973i
\(612\) −105.418 + 192.330i −0.172252 + 0.314265i
\(613\) −42.1118 30.5960i −0.0686979 0.0499120i 0.552906 0.833243i \(-0.313519\pi\)
−0.621604 + 0.783332i \(0.713519\pi\)
\(614\) 203.026 + 279.441i 0.330661 + 0.455116i
\(615\) 137.778 356.493i 0.224029 0.579664i
\(616\) 38.0104 + 27.6162i 0.0617052 + 0.0448314i
\(617\) 619.626 201.329i 1.00426 0.326302i 0.239691 0.970849i \(-0.422954\pi\)
0.764565 + 0.644547i \(0.222954\pi\)
\(618\) −359.198 + 22.8265i −0.581227 + 0.0369361i
\(619\) −234.129 720.573i −0.378237 1.16409i −0.941269 0.337658i \(-0.890365\pi\)
0.563032 0.826435i \(-0.309635\pi\)
\(620\) 468.971 262.457i 0.756405 0.423317i
\(621\) 42.8034 344.062i 0.0689265 0.554046i
\(622\) −220.921 + 679.924i −0.355178 + 1.09313i
\(623\) −254.029 349.641i −0.407751 0.561221i
\(624\) 17.1438 + 269.775i 0.0274740 + 0.432332i
\(625\) −283.095 557.209i −0.452952 0.891535i
\(626\) 279.569i 0.446595i
\(627\) −101.914 + 84.4194i −0.162543 + 0.134640i
\(628\) 48.3547 148.821i 0.0769980 0.236975i
\(629\) −176.755 57.4313i −0.281010 0.0913058i
\(630\) 176.562 + 238.560i 0.280257 + 0.378667i
\(631\) 131.351 + 404.256i 0.208163 + 0.640659i 0.999569 + 0.0293681i \(0.00934951\pi\)
−0.791406 + 0.611291i \(0.790650\pi\)
\(632\) 38.0365i 0.0601844i
\(633\) −446.169 + 176.977i −0.704848 + 0.279584i
\(634\) −487.475 354.171i −0.768888 0.558630i
\(635\) 394.438 854.948i 0.621163 1.34637i
\(636\) 401.989 332.982i 0.632059 0.523557i
\(637\) −496.626 360.820i −0.779633 0.566436i
\(638\) −83.4949 + 114.921i −0.130870 + 0.180127i
\(639\) −693.117 736.230i −1.08469 1.15216i
\(640\) 55.4848 11.0198i 0.0866950 0.0172185i
\(641\) 204.784 281.862i 0.319476 0.439722i −0.618831 0.785524i \(-0.712393\pi\)
0.938307 + 0.345803i \(0.112393\pi\)
\(642\) 92.8245 36.8196i 0.144586 0.0573514i
\(643\) −486.965 −0.757333 −0.378667 0.925533i \(-0.623617\pi\)
−0.378667 + 0.925533i \(0.623617\pi\)
\(644\) −113.912 + 37.0122i −0.176882 + 0.0574723i
\(645\) 463.607 123.092i 0.718771 0.190840i
\(646\) −65.9479 + 202.967i −0.102087 + 0.314190i
\(647\) 143.119 + 46.5021i 0.221204 + 0.0718735i 0.417522 0.908667i \(-0.362899\pi\)
−0.196318 + 0.980540i \(0.562899\pi\)
\(648\) −176.895 145.589i −0.272986 0.224675i
\(649\) 209.630 0.323004
\(650\) 678.831 + 416.532i 1.04436 + 0.640819i
\(651\) 47.6855 + 750.380i 0.0732496 + 1.15266i
\(652\) −237.840 + 172.801i −0.364785 + 0.265032i
\(653\) 167.961 + 54.5739i 0.257215 + 0.0835741i 0.434786 0.900534i \(-0.356824\pi\)
−0.177571 + 0.984108i \(0.556824\pi\)
\(654\) −74.3903 + 290.492i −0.113747 + 0.444178i
\(655\) −127.562 + 137.915i −0.194751 + 0.210557i
\(656\) 96.9295 31.4943i 0.147758 0.0480096i
\(657\) −1208.12 + 154.171i −1.83885 + 0.234659i
\(658\) 40.5859 + 124.911i 0.0616807 + 0.189834i
\(659\) 305.539 420.538i 0.463640 0.638146i −0.511618 0.859213i \(-0.670954\pi\)
0.975259 + 0.221067i \(0.0709538\pi\)
\(660\) −89.7490 + 57.9934i −0.135983 + 0.0878688i
\(661\) 405.623 294.703i 0.613651 0.445843i −0.237047 0.971498i \(-0.576180\pi\)
0.850698 + 0.525655i \(0.176180\pi\)
\(662\) −260.331 + 358.315i −0.393249 + 0.541261i
\(663\) −695.537 440.786i −1.04908 0.664835i
\(664\) 200.318 145.540i 0.301684 0.219187i
\(665\) 212.007 + 196.091i 0.318807 + 0.294874i
\(666\) 93.3108 170.241i 0.140106 0.255616i
\(667\) −111.903 344.402i −0.167770 0.516344i
\(668\) 443.007i 0.663183i
\(669\) 510.611 202.538i 0.763246 0.302748i
\(670\) −26.6219 + 224.368i −0.0397342 + 0.334877i
\(671\) −250.254 81.3124i −0.372956 0.121181i
\(672\) −19.6340 + 76.6703i −0.0292173 + 0.114093i
\(673\) 251.174 182.489i 0.373216 0.271157i −0.385327 0.922780i \(-0.625912\pi\)
0.758543 + 0.651623i \(0.225912\pi\)
\(674\) 601.928i 0.893069i
\(675\) −650.842 + 178.968i −0.964211 + 0.265138i
\(676\) −676.898 −1.00133
\(677\) 642.987 + 884.995i 0.949759 + 1.30723i 0.951635 + 0.307232i \(0.0994029\pi\)
−0.00187587 + 0.999998i \(0.500597\pi\)
\(678\) −152.275 38.9950i −0.224594 0.0575148i
\(679\) 96.8213 297.985i 0.142594 0.438859i
\(680\) −72.1886 + 156.469i −0.106160 + 0.230102i
\(681\) −80.3818 202.647i −0.118035 0.297573i
\(682\) −270.709 −0.396934
\(683\) −563.740 + 183.170i −0.825388 + 0.268185i −0.691101 0.722758i \(-0.742874\pi\)
−0.134287 + 0.990943i \(0.542874\pi\)
\(684\) −195.486 107.148i −0.285798 0.156649i
\(685\) 98.5960 830.960i 0.143936 1.21308i
\(686\) −295.597 406.855i −0.430900 0.593083i
\(687\) 72.0815 113.741i 0.104922 0.165562i
\(688\) 103.483 + 75.1848i 0.150411 + 0.109280i
\(689\) 1151.93 + 1585.49i 1.67188 + 2.30115i
\(690\) 14.8762 271.998i 0.0215598 0.394200i
\(691\) −238.484 173.269i −0.345129 0.250751i 0.401694 0.915774i \(-0.368422\pi\)
−0.746823 + 0.665023i \(0.768422\pi\)
\(692\) 335.745 109.090i 0.485180 0.157645i
\(693\) −18.9246 148.298i −0.0273082 0.213994i
\(694\) 140.662 + 432.913i 0.202683 + 0.623794i
\(695\) −490.573 + 1063.32i −0.705861 + 1.52996i
\(696\) −231.805 59.3616i −0.333054 0.0852896i
\(697\) −95.9378 + 295.266i −0.137644 + 0.423625i
\(698\) −4.19057 5.76782i −0.00600368 0.00826335i
\(699\) −462.978 + 29.4216i −0.662344 + 0.0420909i
\(700\) 151.336 + 177.401i 0.216194 + 0.253430i
\(701\) 41.8045i 0.0596356i 0.999555 + 0.0298178i \(0.00949270\pi\)
−0.999555 + 0.0298178i \(0.990507\pi\)
\(702\) 587.626 628.137i 0.837074 0.894783i
\(703\) 58.3736 179.655i 0.0830350 0.255555i
\(704\) −27.1002 8.80538i −0.0384946 0.0125076i
\(705\) −298.261 16.3126i −0.423066 0.0231385i
\(706\) 22.7335 + 69.9667i 0.0322005 + 0.0991029i
\(707\) 752.186i 1.06391i
\(708\) 130.201 + 328.245i 0.183900 + 0.463623i
\(709\) 435.324 + 316.281i 0.613997 + 0.446095i 0.850820 0.525458i \(-0.176106\pi\)
−0.236822 + 0.971553i \(0.576106\pi\)
\(710\) −583.220 539.439i −0.821437 0.759773i
\(711\) 88.1235 82.9631i 0.123943 0.116685i
\(712\) 212.052 + 154.065i 0.297826 + 0.216383i
\(713\) 405.638 558.313i 0.568917 0.783048i
\(714\) −153.793 185.666i −0.215397 0.260036i
\(715\) −195.924 350.087i −0.274020 0.489632i
\(716\) −33.8385 + 46.5747i −0.0472605 + 0.0650484i
\(717\) −278.429 701.937i −0.388325 0.978992i
\(718\) 405.400 0.564624
\(719\) −1195.70 + 388.505i −1.66300 + 0.540341i −0.981497 0.191477i \(-0.938672\pi\)
−0.681501 + 0.731817i \(0.738672\pi\)
\(720\) −146.551 104.512i −0.203543 0.145156i
\(721\) 122.259 376.273i 0.169568 0.521877i
\(722\) 279.247 + 90.7329i 0.386769 + 0.125669i
\(723\) −64.8005 78.2298i −0.0896273 0.108202i
\(724\) 671.718 0.927787
\(725\) −536.354 + 457.550i −0.739799 + 0.631103i
\(726\) −458.609 + 29.1439i −0.631693 + 0.0401431i
\(727\) −833.074 + 605.263i −1.14591 + 0.832549i −0.987931 0.154894i \(-0.950496\pi\)
−0.157975 + 0.987443i \(0.550496\pi\)
\(728\) −282.599 91.8221i −0.388186 0.126129i
\(729\) 48.5297 + 727.383i 0.0665702 + 0.997782i
\(730\) −938.556 + 186.406i −1.28569 + 0.255351i
\(731\) −370.575 + 120.407i −0.506942 + 0.164715i
\(732\) −28.1112 442.359i −0.0384033 0.604315i
\(733\) 146.382 + 450.517i 0.199702 + 0.614620i 0.999889 + 0.0148698i \(0.00473339\pi\)
−0.800187 + 0.599750i \(0.795267\pi\)
\(734\) 99.5230 136.982i 0.135590 0.186623i
\(735\) 395.071 104.895i 0.537511 0.142714i
\(736\) 58.7680 42.6975i 0.0798479 0.0580129i
\(737\) 66.8968 92.0756i 0.0907691 0.124933i
\(738\) −284.383 155.874i −0.385343 0.211211i
\(739\) 143.758 104.447i 0.194531 0.141335i −0.486256 0.873816i \(-0.661638\pi\)
0.680787 + 0.732481i \(0.261638\pi\)
\(740\) 63.8975 138.498i 0.0863480 0.187160i
\(741\) 448.018 706.949i 0.604612 0.954047i
\(742\) 177.309 + 545.702i 0.238961 + 0.735447i
\(743\) 82.0021i 0.110366i −0.998476 0.0551831i \(-0.982426\pi\)
0.998476 0.0551831i \(-0.0175743\pi\)
\(744\) −168.137 423.885i −0.225991 0.569737i
\(745\) 433.576 + 774.734i 0.581981 + 1.03991i
\(746\) −846.199 274.947i −1.13432 0.368561i
\(747\) −774.111 146.657i −1.03629 0.196328i
\(748\) 70.2234 51.0203i 0.0938815 0.0682089i
\(749\) 109.769i 0.146554i
\(750\) −500.416 + 175.597i −0.667221 + 0.234129i
\(751\) −301.529 −0.401504 −0.200752 0.979642i \(-0.564339\pi\)
−0.200752 + 0.979642i \(0.564339\pi\)
\(752\) −46.8202 64.4424i −0.0622608 0.0856947i
\(753\) −199.829 + 780.328i −0.265377 + 1.03629i
\(754\) 277.615 854.413i 0.368190 1.13317i
\(755\) 276.171 154.558i 0.365789 0.204712i
\(756\) 220.455 121.741i 0.291608 0.161033i
\(757\) 1243.83 1.64310 0.821552 0.570134i \(-0.193109\pi\)
0.821552 + 0.570134i \(0.193109\pi\)
\(758\) 495.792 161.093i 0.654079 0.212523i
\(759\) −73.4510 + 115.902i −0.0967734 + 0.152703i
\(760\) −159.036 73.3730i −0.209258 0.0965434i
\(761\) 251.014 + 345.491i 0.329847 + 0.453996i 0.941442 0.337176i \(-0.109472\pi\)
−0.611595 + 0.791171i \(0.709472\pi\)
\(762\) −674.831 427.663i −0.885604 0.561238i
\(763\) −266.669 193.746i −0.349501 0.253927i
\(764\) 408.612 + 562.406i 0.534832 + 0.736133i
\(765\) 519.964 174.034i 0.679691 0.227496i
\(766\) 525.022 + 381.451i 0.685407 + 0.497977i
\(767\) −1260.90 + 409.690i −1.64393 + 0.534147i
\(768\) −3.04419 47.9034i −0.00396378 0.0623742i
\(769\) 95.9167 + 295.201i 0.124729 + 0.383877i 0.993852 0.110720i \(-0.0353157\pi\)
−0.869122 + 0.494597i \(0.835316\pi\)
\(770\) −22.8815 115.208i −0.0297162 0.149621i
\(771\) 203.189 793.447i 0.263539 1.02911i
\(772\) 173.674 534.514i 0.224967 0.692376i
\(773\) −69.2751 95.3490i −0.0896185 0.123349i 0.761853 0.647749i \(-0.224290\pi\)
−0.851472 + 0.524400i \(0.824290\pi\)
\(774\) −51.5221 403.739i −0.0665660 0.521627i
\(775\) −1306.24 314.405i −1.68547 0.405684i
\(776\) 190.024i 0.244877i
\(777\) 136.130 + 164.341i 0.175199 + 0.211507i
\(778\) −91.4580 + 281.479i −0.117555 + 0.361798i
\(779\) −300.111 97.5119i −0.385251 0.125176i
\(780\) 426.489 524.224i 0.546781 0.672082i
\(781\) 123.662 + 380.592i 0.158338 + 0.487314i
\(782\) 221.280i 0.282966i
\(783\) 368.071 + 666.526i 0.470078 + 0.851246i
\(784\) 88.1847 + 64.0700i 0.112481 + 0.0817219i
\(785\) −341.374 + 191.048i −0.434872 + 0.243374i
\(786\) 101.688 + 122.761i 0.129373 + 0.156185i
\(787\) 1245.43 + 904.861i 1.58251 + 1.14976i 0.913747 + 0.406284i \(0.133176\pi\)
0.668763 + 0.743476i \(0.266824\pi\)
\(788\) 91.4029 125.805i 0.115994 0.159651i
\(789\) −773.563 + 640.770i −0.980435 + 0.812129i
\(790\) 64.5684 69.8089i 0.0817321 0.0883657i
\(791\) 101.561 139.787i 0.128396 0.176721i
\(792\) 38.7089 + 81.9918i 0.0488749 + 0.103525i
\(793\) 1664.16 2.09856
\(794\) 93.1757 30.2746i 0.117350 0.0381293i
\(795\) −1303.03 71.2655i −1.63903 0.0896422i
\(796\) −84.0700 + 258.741i −0.105616 + 0.325051i
\(797\) 623.127 + 202.466i 0.781840 + 0.254035i 0.672626 0.739983i \(-0.265166\pi\)
0.109215 + 0.994018i \(0.465166\pi\)
\(798\) 188.712 156.317i 0.236481 0.195886i
\(799\) 242.646 0.303687
\(800\) −120.538 73.9627i −0.150673 0.0924534i
\(801\) −105.577 827.323i −0.131806 1.03286i
\(802\) 487.683 354.322i 0.608083 0.441798i
\(803\) 458.414 + 148.948i 0.570877 + 0.185489i
\(804\) 185.725 + 47.5610i 0.231001 + 0.0591555i
\(805\) 271.893 + 125.441i 0.337756 + 0.155827i
\(806\) 1628.28 529.060i 2.02020 0.656402i
\(807\) 319.814 20.3237i 0.396300 0.0251842i
\(808\) −140.971 433.863i −0.174469 0.536959i
\(809\) 446.943 615.165i 0.552464 0.760401i −0.437880 0.899033i \(-0.644271\pi\)
0.990344 + 0.138632i \(0.0442705\pi\)
\(810\) 77.5139 + 567.487i 0.0956962 + 0.700601i
\(811\) 224.956 163.440i 0.277380 0.201529i −0.440394 0.897805i \(-0.645161\pi\)
0.717774 + 0.696276i \(0.245161\pi\)
\(812\) 154.605 212.795i 0.190400 0.262063i
\(813\) 208.938 329.694i 0.256996 0.405527i
\(814\) −62.1580 + 45.1604i −0.0763612 + 0.0554796i
\(815\) 729.846 + 86.5986i 0.895517 + 0.106256i
\(816\) 123.505 + 78.2693i 0.151354 + 0.0959183i
\(817\) −122.383 376.655i −0.149795 0.461022i
\(818\) 371.083i 0.453647i
\(819\) 403.655 + 855.007i 0.492863 + 1.04396i
\(820\) −231.358 106.739i −0.282145 0.130170i
\(821\) 1257.86 + 408.702i 1.53210 + 0.497810i 0.949184 0.314721i \(-0.101911\pi\)
0.582918 + 0.812531i \(0.301911\pi\)
\(822\) −687.843 176.145i −0.836792 0.214289i
\(823\) 826.934 600.803i 1.00478 0.730015i 0.0416721 0.999131i \(-0.486732\pi\)
0.963108 + 0.269116i \(0.0867315\pi\)
\(824\) 239.948i 0.291200i
\(825\) 263.163 + 45.9162i 0.318986 + 0.0556559i
\(826\) −388.165 −0.469933
\(827\) −108.957 149.966i −0.131750 0.181338i 0.738045 0.674751i \(-0.235749\pi\)
−0.869795 + 0.493413i \(0.835749\pi\)
\(828\) −227.103 43.0252i −0.274280 0.0519628i
\(829\) −292.067 + 898.891i −0.352313 + 1.08431i 0.605238 + 0.796044i \(0.293078\pi\)
−0.957551 + 0.288263i \(0.906922\pi\)
\(830\) −614.706 72.9368i −0.740610 0.0878757i
\(831\) 871.274 345.598i 1.04846 0.415882i
\(832\) 180.213 0.216602
\(833\) −315.791 + 102.607i −0.379101 + 0.123177i
\(834\) 839.305 + 531.896i 1.00636 + 0.637765i
\(835\) −752.020 + 813.055i −0.900622 + 0.973719i
\(836\) 51.8573 + 71.3755i 0.0620303 + 0.0853774i
\(837\) −615.329 + 1314.10i −0.735161 + 1.57001i
\(838\) −441.273 320.604i −0.526579 0.382582i
\(839\) 442.697 + 609.320i 0.527648 + 0.726245i 0.986770 0.162128i \(-0.0518358\pi\)
−0.459122 + 0.888373i \(0.651836\pi\)
\(840\) 166.185 107.385i 0.197840 0.127839i
\(841\) −37.0173 26.8946i −0.0440158 0.0319793i
\(842\) −195.010 + 63.3625i −0.231603 + 0.0752524i
\(843\) −252.779 + 16.0637i −0.299857 + 0.0190554i
\(844\) 98.8827 + 304.330i 0.117160 + 0.360580i
\(845\) 1242.32 + 1149.06i 1.47020 + 1.35983i
\(846\) −47.1795 + 249.032i −0.0557678 + 0.294364i
\(847\) 156.095 480.410i 0.184291 0.567190i
\(848\) −204.545 281.532i −0.241209 0.331995i
\(849\) −42.9619 676.049i −0.0506029 0.796289i
\(850\) 398.101 164.627i 0.468354 0.193679i
\(851\) 195.865i 0.230159i
\(852\) −519.137 + 430.020i −0.609316 + 0.504718i
\(853\) −258.973 + 797.036i −0.303602 + 0.934392i 0.676593 + 0.736357i \(0.263456\pi\)
−0.980195 + 0.198034i \(0.936544\pi\)
\(854\) 463.387 + 150.563i 0.542607 + 0.176304i
\(855\) 176.890 + 528.494i 0.206888 + 0.618122i
\(856\) −20.5723 63.3152i −0.0240331 0.0739663i
\(857\) 1264.09i 1.47502i 0.675335 + 0.737511i \(0.263999\pi\)
−0.675335 + 0.737511i \(0.736001\pi\)
\(858\) −316.430 + 125.515i −0.368800 + 0.146288i
\(859\) −458.500 333.120i −0.533760 0.387800i 0.288002 0.957630i \(-0.407009\pi\)
−0.821762 + 0.569830i \(0.807009\pi\)
\(860\) −62.2946 313.654i −0.0724356 0.364714i
\(861\) 274.529 227.402i 0.318849 0.264114i
\(862\) −694.190 504.358i −0.805325 0.585103i
\(863\) 660.107 908.560i 0.764898 1.05279i −0.231892 0.972741i \(-0.574492\pi\)
0.996791 0.0800508i \(-0.0255082\pi\)
\(864\) −104.343 + 111.537i −0.120768 + 0.129094i
\(865\) −801.381 369.725i −0.926452 0.427428i
\(866\) 262.393 361.153i 0.302994 0.417036i
\(867\) 391.889 155.446i 0.452006 0.179292i
\(868\) 501.263 0.577492
\(869\) −45.5552 + 14.8018i −0.0524226 + 0.0170331i
\(870\) 324.667 + 502.445i 0.373180 + 0.577523i
\(871\) −222.428 + 684.563i −0.255371 + 0.785951i
\(872\) 190.126 + 61.7758i 0.218035 + 0.0708438i
\(873\) 440.251 414.470i 0.504297 0.474766i
\(874\) −224.910 −0.257334
\(875\) 23.3957 582.484i 0.0267380 0.665696i
\(876\) 51.4941 + 810.312i 0.0587832 + 0.925013i
\(877\) 177.895 129.248i 0.202845 0.147375i −0.481726 0.876322i \(-0.659990\pi\)
0.684570 + 0.728947i \(0.259990\pi\)
\(878\) −128.339 41.6998i −0.146172 0.0474941i
\(879\) 132.060 515.691i 0.150239 0.586679i
\(880\) 34.7898 + 62.1642i 0.0395339 + 0.0706411i
\(881\) 613.682 199.397i 0.696574 0.226331i 0.0607369 0.998154i \(-0.480655\pi\)
0.635837 + 0.771823i \(0.280655\pi\)
\(882\) −43.9054 344.053i −0.0497794 0.390083i
\(883\) 248.363 + 764.384i 0.281272 + 0.865667i 0.987491 + 0.157674i \(0.0503994\pi\)
−0.706219 + 0.707993i \(0.749601\pi\)
\(884\) −322.673 + 444.122i −0.365015 + 0.502400i
\(885\) 318.248 823.454i 0.359603 0.930456i
\(886\) −27.6434 + 20.0841i −0.0312003 + 0.0226683i
\(887\) −541.528 + 745.350i −0.610517 + 0.840304i −0.996620 0.0821515i \(-0.973821\pi\)
0.386103 + 0.922456i \(0.373821\pi\)
\(888\) −109.320 69.2798i −0.123108 0.0780178i
\(889\) 710.485 516.198i 0.799196 0.580650i
\(890\) −127.651 642.724i −0.143428 0.722162i
\(891\) 105.530 268.517i 0.118440 0.301366i
\(892\) −113.165 348.286i −0.126866 0.390455i
\(893\) 246.627i 0.276178i
\(894\) 700.252 277.761i 0.783280 0.310695i
\(895\) 141.166 28.0370i 0.157728 0.0313263i
\(896\) 50.1805 + 16.3046i 0.0560050 + 0.0181971i
\(897\) 215.286 840.685i 0.240006 0.937218i
\(898\) 763.798 554.932i 0.850555 0.617964i
\(899\) 1515.52i 1.68578i
\(900\) 91.5539 + 440.588i 0.101727 + 0.489542i
\(901\) 1060.05 1.17653
\(902\) 75.4395 + 103.834i 0.0836359 + 0.115115i
\(903\) 433.415 + 110.990i 0.479972 + 0.122913i
\(904\) −32.3826 + 99.6634i −0.0358214 + 0.110247i
\(905\) −1232.81 1140.27i −1.36222 1.25996i
\(906\) −99.0140 249.620i −0.109287 0.275519i
\(907\) 867.563 0.956519 0.478259 0.878219i \(-0.341268\pi\)
0.478259 + 0.878219i \(0.341268\pi\)
\(908\) −138.225 + 44.9120i −0.152230 + 0.0494625i
\(909\) −697.702 + 1272.92i −0.767549 + 1.40035i
\(910\) 362.787 + 648.245i 0.398667 + 0.712357i
\(911\) −832.732 1146.16i −0.914086 1.25813i −0.965752 0.259467i \(-0.916453\pi\)
0.0516657 0.998664i \(-0.483547\pi\)
\(912\) −79.5534 + 125.531i −0.0872297 + 0.137644i
\(913\) 252.262 + 183.279i 0.276300 + 0.200744i
\(914\) −221.521 304.897i −0.242364 0.333585i
\(915\) −699.327 + 859.586i −0.764292 + 0.939438i
\(916\) −72.6270 52.7666i −0.0792871 0.0576055i
\(917\) −166.649 + 54.1475i −0.181733 + 0.0590485i
\(918\) −88.0466 456.854i −0.0959113 0.497663i
\(919\) −492.313 1515.18i −0.535705 1.64873i −0.742121 0.670266i \(-0.766180\pi\)
0.206417 0.978464i \(-0.433820\pi\)
\(920\) −180.338 21.3977i −0.196020 0.0232584i
\(921\) −709.816 181.772i −0.770702 0.197364i
\(922\) −60.2566 + 185.451i −0.0653543 + 0.201140i
\(923\) −1487.62 2047.54i −1.61172 2.21835i
\(924\) −99.4663 + 6.32093i −0.107647 + 0.00684083i
\(925\) −352.378 + 145.719i −0.380949 + 0.157534i
\(926\) 1248.26i 1.34802i
\(927\) 555.916 523.362i 0.599693 0.564576i
\(928\) −49.2955 + 151.716i −0.0531202 + 0.163487i
\(929\) 892.560 + 290.010i 0.960775 + 0.312175i 0.747086 0.664727i \(-0.231452\pi\)
0.213689 + 0.976902i \(0.431452\pi\)
\(930\) −410.975 + 1063.38i −0.441909 + 1.14342i
\(931\) −104.290 320.972i −0.112020 0.344761i
\(932\) 309.275i 0.331840i
\(933\) −559.174 1409.71i −0.599329 1.51095i
\(934\) 246.669 + 179.215i 0.264099 + 0.191880i
\(935\) −215.491 25.5686i −0.230471 0.0273461i
\(936\) −393.070 417.520i −0.419947 0.446068i
\(937\) 107.188 + 77.8769i 0.114395 + 0.0831131i 0.643512 0.765436i \(-0.277477\pi\)
−0.529117 + 0.848549i \(0.677477\pi\)
\(938\) −123.871 + 170.493i −0.132058 + 0.181763i
\(939\) −378.316 456.718i −0.402892 0.486387i
\(940\) −23.4638 + 197.751i −0.0249615 + 0.210373i
\(941\) 383.224 527.463i 0.407252 0.560534i −0.555293 0.831654i \(-0.687394\pi\)
0.962546 + 0.271120i \(0.0873941\pi\)
\(942\) 122.391 + 308.555i 0.129927 + 0.327553i
\(943\) −327.188 −0.346966
\(944\) 223.895 72.7478i 0.237176 0.0770633i
\(945\) −611.263 150.799i −0.646840 0.159576i
\(946\) −49.7765 + 153.196i −0.0526179 + 0.161941i
\(947\) 734.823 + 238.758i 0.775948 + 0.252121i 0.670109 0.742262i \(-0.266247\pi\)
0.105839 + 0.994383i \(0.466247\pi\)
\(948\) −51.4715 62.1384i −0.0542948 0.0655469i
\(949\) −3048.40 −3.21223
\(950\) 167.328 + 404.632i 0.176135 + 0.425929i
\(951\) 1275.63 81.0645i 1.34136 0.0852413i
\(952\) −130.030 + 94.4725i −0.136586 + 0.0992359i
\(953\) −152.706 49.6172i −0.160237 0.0520642i 0.227800 0.973708i \(-0.426847\pi\)
−0.388037 + 0.921644i \(0.626847\pi\)
\(954\) −206.115 + 1087.95i −0.216054 + 1.14041i
\(955\) 204.774 1725.82i 0.214424 1.80714i
\(956\) −478.788 + 155.568i −0.500824 + 0.162728i
\(957\) −19.1107 300.727i −0.0199694 0.314239i
\(958\) −342.523 1054.18i −0.357540 1.10039i
\(959\) 458.763 631.433i 0.478376 0.658428i
\(960\) −75.7307 + 93.0852i −0.0788861 + 0.0969638i
\(961\) −1559.12 + 1132.76i −1.62239 + 1.17873i
\(962\) 285.613 393.113i 0.296895 0.408641i
\(963\) −101.818 + 185.762i −0.105730 + 0.192899i
\(964\) −54.7880 + 39.8058i −0.0568340 + 0.0412923i
\(965\) −1226.10 + 686.182i −1.27057 + 0.711070i
\(966\) 136.007 214.612i 0.140794 0.222165i
\(967\) 142.320 + 438.017i 0.147177 + 0.452965i 0.997285 0.0736448i \(-0.0234631\pi\)
−0.850107 + 0.526609i \(0.823463\pi\)
\(968\) 306.356i 0.316483i
\(969\) −166.921 420.819i −0.172261 0.434281i
\(970\) 322.573 348.754i 0.332550 0.359540i
\(971\) −882.638 286.786i −0.908999 0.295352i −0.183053 0.983103i \(-0.558598\pi\)
−0.725946 + 0.687752i \(0.758598\pi\)
\(972\) 485.998 1.53397i 0.499998 0.00157816i
\(973\) −883.649 + 642.009i −0.908170 + 0.659824i
\(974\) 1010.21i 1.03718i
\(975\) −1672.63 + 238.134i −1.71552 + 0.244240i
\(976\) −295.501 −0.302767
\(977\) −401.777 552.998i −0.411235 0.566016i 0.552284 0.833656i \(-0.313756\pi\)
−0.963519 + 0.267640i \(0.913756\pi\)
\(978\) 154.711 604.144i 0.158192 0.617734i
\(979\) −102.000 + 313.923i −0.104188 + 0.320656i
\(980\) −53.0854 267.285i −0.0541688 0.272740i
\(981\) −271.570 575.229i −0.276830 0.586370i
\(982\) −887.501 −0.903769
\(983\) −26.4273 + 8.58674i −0.0268843 + 0.00873524i −0.322428 0.946594i \(-0.604499\pi\)
0.295544 + 0.955329i \(0.404499\pi\)
\(984\) −115.731 + 182.617i −0.117612 + 0.185586i
\(985\) −381.312 + 75.7322i −0.387119 + 0.0768855i
\(986\) −285.629 393.134i −0.289684 0.398716i
\(987\) −235.334 149.139i −0.238433 0.151103i
\(988\) −451.408 327.967i −0.456891 0.331951i
\(989\) −241.367 332.214i −0.244052 0.335909i
\(990\) 68.1411 216.190i 0.0688294 0.218374i
\(991\) 343.216 + 249.361i 0.346333 + 0.251625i 0.747329 0.664454i \(-0.231336\pi\)
−0.400996 + 0.916080i \(0.631336\pi\)
\(992\) −289.130 + 93.9440i −0.291462 + 0.0947016i
\(993\) −59.5859 937.645i −0.0600059 0.944255i
\(994\) −228.981 704.730i −0.230363 0.708984i
\(995\) 593.516 332.158i 0.596499 0.333827i
\(996\) −130.304 + 508.835i −0.130828 + 0.510878i
\(997\) −256.672 + 789.957i −0.257445 + 0.792334i 0.735893 + 0.677097i \(0.236762\pi\)
−0.993338 + 0.115236i \(0.963238\pi\)
\(998\) 298.159 + 410.381i 0.298757 + 0.411203i
\(999\) 77.9342 + 404.383i 0.0780122 + 0.404788i
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.11.11 yes 80
3.2 odd 2 inner 150.3.j.a.11.9 80
25.16 even 5 inner 150.3.j.a.41.9 yes 80
75.41 odd 10 inner 150.3.j.a.41.11 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
150.3.j.a.11.9 80 3.2 odd 2 inner
150.3.j.a.11.11 yes 80 1.1 even 1 trivial
150.3.j.a.41.9 yes 80 25.16 even 5 inner
150.3.j.a.41.11 yes 80 75.41 odd 10 inner