Properties

Label 370.2.q.f.97.8
Level $370$
Weight $2$
Character 370.97
Analytic conductor $2.954$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [370,2,Mod(97,370)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(370, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("370.97");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.q (of order \(12\), 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: \(2.95446487479\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 97.8
Character \(\chi\) \(=\) 370.97
Dual form 370.2.q.f.103.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.686833 - 2.56329i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.84814 + 1.25873i) q^{5} +(-1.87646 - 1.87646i) q^{6} +(0.524210 - 1.95638i) q^{7} -1.00000 q^{8} +(-3.50066 - 2.02111i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(0.686833 - 2.56329i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.84814 + 1.25873i) q^{5} +(-1.87646 - 1.87646i) q^{6} +(0.524210 - 1.95638i) q^{7} -1.00000 q^{8} +(-3.50066 - 2.02111i) q^{9} +(0.166021 + 2.22990i) q^{10} +1.12383i q^{11} +(-2.56329 + 0.686833i) q^{12} +(-2.37951 - 4.12143i) q^{13} +(-1.43217 - 1.43217i) q^{14} +(1.95713 + 5.60185i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.528152 + 0.304929i) q^{17} +(-3.50066 + 2.02111i) q^{18} +(-0.968309 - 0.259458i) q^{19} +(2.01416 + 0.971170i) q^{20} +(-4.65473 - 2.68741i) q^{21} +(0.973266 + 0.561916i) q^{22} +5.88152 q^{23} +(-0.686833 + 2.56329i) q^{24} +(1.83122 - 4.65260i) q^{25} -4.75902 q^{26} +(-1.95568 + 1.95568i) q^{27} +(-1.95638 + 0.524210i) q^{28} +(2.37706 + 2.37706i) q^{29} +(5.82991 + 1.10601i) q^{30} +(-3.83799 + 3.83799i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.88071 + 0.771884i) q^{33} +(0.528152 - 0.304929i) q^{34} +(1.49373 + 4.27549i) q^{35} +4.04222i q^{36} +(4.85045 - 3.67057i) q^{37} +(-0.708852 + 0.708852i) q^{38} +(-12.1988 + 3.26865i) q^{39} +(1.84814 - 1.25873i) q^{40} +(7.57396 - 4.37283i) q^{41} +(-4.65473 + 2.68741i) q^{42} -2.52967 q^{43} +(0.973266 - 0.561916i) q^{44} +(9.01373 - 0.671093i) q^{45} +(2.94076 - 5.09355i) q^{46} +(4.16660 + 4.16660i) q^{47} +(1.87646 + 1.87646i) q^{48} +(2.50956 + 1.44889i) q^{49} +(-3.11366 - 3.91218i) q^{50} +(1.14437 - 1.14437i) q^{51} +(-2.37951 + 4.12143i) q^{52} +(-0.917679 - 3.42482i) q^{53} +(0.715830 + 2.67152i) q^{54} +(-1.41460 - 2.07699i) q^{55} +(-0.524210 + 1.95638i) q^{56} +(-1.33013 + 2.30386i) q^{57} +(3.24712 - 0.870063i) q^{58} +(-1.81426 - 6.77090i) q^{59} +(3.87278 - 4.49585i) q^{60} +(-13.4578 - 3.60599i) q^{61} +(1.40480 + 5.24279i) q^{62} +(-5.78914 + 5.78914i) q^{63} +1.00000 q^{64} +(9.58541 + 4.62181i) q^{65} +(2.10883 - 2.10883i) q^{66} +(14.0161 + 3.75560i) q^{67} -0.609858i q^{68} +(4.03962 - 15.0761i) q^{69} +(4.44955 + 0.844134i) q^{70} +(-3.54588 - 6.14164i) q^{71} +(3.50066 + 2.02111i) q^{72} +(-8.20562 - 8.20562i) q^{73} +(-0.753581 - 6.03590i) q^{74} +(-10.6682 - 7.88950i) q^{75} +(0.259458 + 0.968309i) q^{76} +(2.19864 + 0.589123i) q^{77} +(-3.26865 + 12.1988i) q^{78} +(4.51070 + 1.20864i) q^{79} +(-0.166021 - 2.22990i) q^{80} +(-2.39356 - 4.14577i) q^{81} -8.74566i q^{82} +(-0.924178 - 3.44908i) q^{83} +5.37482i q^{84} +(-1.35992 + 0.101249i) q^{85} +(-1.26483 + 2.19076i) q^{86} +(7.72573 - 4.46045i) q^{87} -1.12383i q^{88} +(13.2615 - 3.55341i) q^{89} +(3.92568 - 8.14167i) q^{90} +(-9.31044 + 2.49472i) q^{91} +(-2.94076 - 5.09355i) q^{92} +(7.20184 + 12.4740i) q^{93} +(5.69169 - 1.52508i) q^{94} +(2.11615 - 0.739323i) q^{95} +(2.56329 - 0.686833i) q^{96} +10.8045i q^{97} +(2.50956 - 1.44889i) q^{98} +(2.27139 - 3.93416i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 16 q^{2} - 2 q^{3} - 16 q^{4} + 6 q^{5} + 8 q^{6} - 10 q^{7} - 32 q^{8} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 16 q^{2} - 2 q^{3} - 16 q^{4} + 6 q^{5} + 8 q^{6} - 10 q^{7} - 32 q^{8} + 12 q^{9} + 6 q^{10} + 10 q^{12} + 10 q^{13} - 8 q^{14} - 8 q^{15} - 16 q^{16} - 12 q^{17} + 12 q^{18} + 2 q^{19} - 54 q^{21} + 6 q^{22} + 12 q^{23} + 2 q^{24} - 16 q^{25} + 20 q^{26} + 40 q^{27} + 2 q^{28} + 6 q^{29} + 8 q^{30} - 4 q^{31} + 16 q^{32} + 26 q^{33} - 12 q^{34} - 12 q^{35} + 20 q^{37} - 26 q^{38} - 58 q^{39} - 6 q^{40} + 18 q^{41} - 54 q^{42} - 32 q^{43} + 6 q^{44} + 56 q^{45} + 6 q^{46} + 18 q^{47} - 8 q^{48} - 12 q^{49} - 14 q^{50} - 4 q^{51} + 10 q^{52} - 24 q^{53} + 20 q^{54} - 32 q^{55} + 10 q^{56} + 8 q^{57} + 36 q^{58} + 42 q^{59} + 16 q^{60} - 46 q^{61} - 14 q^{62} + 32 q^{64} - 18 q^{65} + 4 q^{66} + 50 q^{67} - 66 q^{69} + 12 q^{70} - 12 q^{71} - 12 q^{72} - 28 q^{73} + 16 q^{74} - 20 q^{75} - 28 q^{76} + 12 q^{77} - 26 q^{78} + 38 q^{79} - 6 q^{80} + 56 q^{81} - 8 q^{85} - 16 q^{86} + 18 q^{87} + 18 q^{89} + 4 q^{90} + 4 q^{91} - 6 q^{92} + 32 q^{93} + 30 q^{94} + 96 q^{95} - 10 q^{96} - 12 q^{98} - 26 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(297\)
\(\chi(n)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0.686833 2.56329i 0.396543 1.47992i −0.422593 0.906320i \(-0.638880\pi\)
0.819136 0.573599i \(-0.194453\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −1.84814 + 1.25873i −0.826512 + 0.562920i
\(6\) −1.87646 1.87646i −0.766062 0.766062i
\(7\) 0.524210 1.95638i 0.198133 0.739441i −0.793301 0.608830i \(-0.791639\pi\)
0.991434 0.130612i \(-0.0416941\pi\)
\(8\) −1.00000 −0.353553
\(9\) −3.50066 2.02111i −1.16689 0.673703i
\(10\) 0.166021 + 2.22990i 0.0525004 + 0.705155i
\(11\) 1.12383i 0.338848i 0.985543 + 0.169424i \(0.0541907\pi\)
−0.985543 + 0.169424i \(0.945809\pi\)
\(12\) −2.56329 + 0.686833i −0.739959 + 0.198272i
\(13\) −2.37951 4.12143i −0.659957 1.14308i −0.980626 0.195888i \(-0.937241\pi\)
0.320669 0.947191i \(-0.396092\pi\)
\(14\) −1.43217 1.43217i −0.382763 0.382763i
\(15\) 1.95713 + 5.60185i 0.505328 + 1.44639i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0.528152 + 0.304929i 0.128096 + 0.0739561i 0.562679 0.826676i \(-0.309771\pi\)
−0.434583 + 0.900632i \(0.643104\pi\)
\(18\) −3.50066 + 2.02111i −0.825115 + 0.476380i
\(19\) −0.968309 0.259458i −0.222145 0.0595237i 0.146029 0.989280i \(-0.453351\pi\)
−0.368175 + 0.929757i \(0.620017\pi\)
\(20\) 2.01416 + 0.971170i 0.450379 + 0.217160i
\(21\) −4.65473 2.68741i −1.01575 0.586441i
\(22\) 0.973266 + 0.561916i 0.207501 + 0.119801i
\(23\) 5.88152 1.22638 0.613191 0.789934i \(-0.289885\pi\)
0.613191 + 0.789934i \(0.289885\pi\)
\(24\) −0.686833 + 2.56329i −0.140199 + 0.523230i
\(25\) 1.83122 4.65260i 0.366243 0.930519i
\(26\) −4.75902 −0.933320
\(27\) −1.95568 + 1.95568i −0.376372 + 0.376372i
\(28\) −1.95638 + 0.524210i −0.369721 + 0.0990664i
\(29\) 2.37706 + 2.37706i 0.441408 + 0.441408i 0.892485 0.451077i \(-0.148960\pi\)
−0.451077 + 0.892485i \(0.648960\pi\)
\(30\) 5.82991 + 1.10601i 1.06439 + 0.201928i
\(31\) −3.83799 + 3.83799i −0.689323 + 0.689323i −0.962082 0.272759i \(-0.912064\pi\)
0.272759 + 0.962082i \(0.412064\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 2.88071 + 0.771884i 0.501467 + 0.134368i
\(34\) 0.528152 0.304929i 0.0905774 0.0522949i
\(35\) 1.49373 + 4.27549i 0.252487 + 0.722690i
\(36\) 4.04222i 0.673703i
\(37\) 4.85045 3.67057i 0.797410 0.603438i
\(38\) −0.708852 + 0.708852i −0.114991 + 0.114991i
\(39\) −12.1988 + 3.26865i −1.95337 + 0.523403i
\(40\) 1.84814 1.25873i 0.292216 0.199022i
\(41\) 7.57396 4.37283i 1.18285 0.682921i 0.226181 0.974085i \(-0.427376\pi\)
0.956673 + 0.291164i \(0.0940425\pi\)
\(42\) −4.65473 + 2.68741i −0.718240 + 0.414676i
\(43\) −2.52967 −0.385771 −0.192885 0.981221i \(-0.561785\pi\)
−0.192885 + 0.981221i \(0.561785\pi\)
\(44\) 0.973266 0.561916i 0.146725 0.0847120i
\(45\) 9.01373 0.671093i 1.34369 0.100041i
\(46\) 2.94076 5.09355i 0.433592 0.751003i
\(47\) 4.16660 + 4.16660i 0.607762 + 0.607762i 0.942361 0.334599i \(-0.108601\pi\)
−0.334599 + 0.942361i \(0.608601\pi\)
\(48\) 1.87646 + 1.87646i 0.270844 + 0.270844i
\(49\) 2.50956 + 1.44889i 0.358508 + 0.206985i
\(50\) −3.11366 3.91218i −0.440338 0.553265i
\(51\) 1.14437 1.14437i 0.160245 0.160245i
\(52\) −2.37951 + 4.12143i −0.329979 + 0.571540i
\(53\) −0.917679 3.42482i −0.126053 0.470436i 0.873822 0.486246i \(-0.161634\pi\)
−0.999875 + 0.0158099i \(0.994967\pi\)
\(54\) 0.715830 + 2.67152i 0.0974122 + 0.363547i
\(55\) −1.41460 2.07699i −0.190744 0.280062i
\(56\) −0.524210 + 1.95638i −0.0700505 + 0.261432i
\(57\) −1.33013 + 2.30386i −0.176180 + 0.305153i
\(58\) 3.24712 0.870063i 0.426368 0.114245i
\(59\) −1.81426 6.77090i −0.236196 0.881496i −0.977606 0.210443i \(-0.932509\pi\)
0.741410 0.671052i \(-0.234157\pi\)
\(60\) 3.87278 4.49585i 0.499974 0.580411i
\(61\) −13.4578 3.60599i −1.72309 0.461700i −0.744516 0.667604i \(-0.767320\pi\)
−0.978572 + 0.205904i \(0.933987\pi\)
\(62\) 1.40480 + 5.24279i 0.178410 + 0.665835i
\(63\) −5.78914 + 5.78914i −0.729363 + 0.729363i
\(64\) 1.00000 0.125000
\(65\) 9.58541 + 4.62181i 1.18892 + 0.573266i
\(66\) 2.10883 2.10883i 0.259579 0.259579i
\(67\) 14.0161 + 3.75560i 1.71234 + 0.458820i 0.975996 0.217789i \(-0.0698845\pi\)
0.736343 + 0.676609i \(0.236551\pi\)
\(68\) 0.609858i 0.0739561i
\(69\) 4.03962 15.0761i 0.486314 1.81495i
\(70\) 4.44955 + 0.844134i 0.531823 + 0.100893i
\(71\) −3.54588 6.14164i −0.420818 0.728878i 0.575202 0.818012i \(-0.304924\pi\)
−0.996020 + 0.0891333i \(0.971590\pi\)
\(72\) 3.50066 + 2.02111i 0.412557 + 0.238190i
\(73\) −8.20562 8.20562i −0.960395 0.960395i 0.0388501 0.999245i \(-0.487631\pi\)
−0.999245 + 0.0388501i \(0.987631\pi\)
\(74\) −0.753581 6.03590i −0.0876020 0.701659i
\(75\) −10.6682 7.88950i −1.23186 0.911001i
\(76\) 0.259458 + 0.968309i 0.0297618 + 0.111073i
\(77\) 2.19864 + 0.589123i 0.250558 + 0.0671368i
\(78\) −3.26865 + 12.1988i −0.370102 + 1.38124i
\(79\) 4.51070 + 1.20864i 0.507493 + 0.135982i 0.503476 0.864009i \(-0.332054\pi\)
0.00401787 + 0.999992i \(0.498721\pi\)
\(80\) −0.166021 2.22990i −0.0185617 0.249310i
\(81\) −2.39356 4.14577i −0.265951 0.460641i
\(82\) 8.74566i 0.965797i
\(83\) −0.924178 3.44908i −0.101442 0.378586i 0.896475 0.443093i \(-0.146119\pi\)
−0.997917 + 0.0645076i \(0.979452\pi\)
\(84\) 5.37482i 0.586441i
\(85\) −1.35992 + 0.101249i −0.147504 + 0.0109820i
\(86\) −1.26483 + 2.19076i −0.136391 + 0.236235i
\(87\) 7.72573 4.46045i 0.828286 0.478211i
\(88\) 1.12383i 0.119801i
\(89\) 13.2615 3.55341i 1.40572 0.376661i 0.525322 0.850903i \(-0.323945\pi\)
0.880394 + 0.474243i \(0.157278\pi\)
\(90\) 3.92568 8.14167i 0.413803 0.858207i
\(91\) −9.31044 + 2.49472i −0.975999 + 0.261518i
\(92\) −2.94076 5.09355i −0.306596 0.531039i
\(93\) 7.20184 + 12.4740i 0.746796 + 1.29349i
\(94\) 5.69169 1.52508i 0.587053 0.157300i
\(95\) 2.11615 0.739323i 0.217113 0.0758530i
\(96\) 2.56329 0.686833i 0.261615 0.0700996i
\(97\) 10.8045i 1.09703i 0.836142 + 0.548513i \(0.184806\pi\)
−0.836142 + 0.548513i \(0.815194\pi\)
\(98\) 2.50956 1.44889i 0.253504 0.146360i
\(99\) 2.27139 3.93416i 0.228283 0.395398i
\(100\) −4.94487 + 0.740419i −0.494487 + 0.0740419i
\(101\) 13.7754i 1.37071i 0.728210 + 0.685354i \(0.240352\pi\)
−0.728210 + 0.685354i \(0.759648\pi\)
\(102\) −0.418870 1.56324i −0.0414743 0.154784i
\(103\) 18.0233i 1.77589i 0.459953 + 0.887943i \(0.347866\pi\)
−0.459953 + 0.887943i \(0.652134\pi\)
\(104\) 2.37951 + 4.12143i 0.233330 + 0.404140i
\(105\) 11.9853 0.892332i 1.16964 0.0870827i
\(106\) −3.42482 0.917679i −0.332648 0.0891329i
\(107\) −0.739316 + 2.75917i −0.0714724 + 0.266739i −0.992410 0.122971i \(-0.960758\pi\)
0.920938 + 0.389709i \(0.127425\pi\)
\(108\) 2.67152 + 0.715830i 0.257067 + 0.0688808i
\(109\) 4.32210 + 16.1303i 0.413982 + 1.54500i 0.786866 + 0.617124i \(0.211702\pi\)
−0.372884 + 0.927878i \(0.621631\pi\)
\(110\) −2.50603 + 0.186579i −0.238940 + 0.0177897i
\(111\) −6.07731 14.9542i −0.576832 1.41939i
\(112\) 1.43217 + 1.43217i 0.135327 + 0.135327i
\(113\) −4.26128 2.46025i −0.400868 0.231441i 0.285991 0.958232i \(-0.407677\pi\)
−0.686858 + 0.726791i \(0.741011\pi\)
\(114\) 1.33013 + 2.30386i 0.124578 + 0.215776i
\(115\) −10.8699 + 7.40323i −1.01362 + 0.690355i
\(116\) 0.870063 3.24712i 0.0807833 0.301487i
\(117\) 19.2370i 1.77846i
\(118\) −6.77090 1.81426i −0.623312 0.167016i
\(119\) 0.873419 0.873419i 0.0800662 0.0800662i
\(120\) −1.95713 5.60185i −0.178660 0.511377i
\(121\) 9.73700 0.885182
\(122\) −9.85176 + 9.85176i −0.891936 + 0.891936i
\(123\) −6.00681 22.4177i −0.541615 2.02134i
\(124\) 5.24279 + 1.40480i 0.470817 + 0.126155i
\(125\) 2.47201 + 10.9036i 0.221103 + 0.975250i
\(126\) 2.11897 + 7.90811i 0.188773 + 0.704510i
\(127\) −6.90268 + 1.84957i −0.612514 + 0.164123i −0.551722 0.834028i \(-0.686029\pi\)
−0.0607917 + 0.998150i \(0.519363\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) −1.73746 + 6.48429i −0.152975 + 0.570910i
\(130\) 8.79531 5.99030i 0.771400 0.525384i
\(131\) 5.25720 + 19.6201i 0.459324 + 1.71422i 0.675056 + 0.737767i \(0.264120\pi\)
−0.215732 + 0.976453i \(0.569214\pi\)
\(132\) −0.771884 2.88071i −0.0671839 0.250734i
\(133\) −1.01519 + 1.75837i −0.0880285 + 0.152470i
\(134\) 10.2605 10.2605i 0.886372 0.886372i
\(135\) 1.15270 6.07604i 0.0992086 0.522943i
\(136\) −0.528152 0.304929i −0.0452887 0.0261474i
\(137\) 4.18991 + 4.18991i 0.357968 + 0.357968i 0.863064 0.505095i \(-0.168543\pi\)
−0.505095 + 0.863064i \(0.668543\pi\)
\(138\) −11.0365 11.0365i −0.939486 0.939486i
\(139\) 5.56954 9.64673i 0.472402 0.818225i −0.527099 0.849804i \(-0.676720\pi\)
0.999501 + 0.0315791i \(0.0100536\pi\)
\(140\) 2.95582 3.43136i 0.249812 0.290003i
\(141\) 13.5420 7.81847i 1.14044 0.658434i
\(142\) −7.09175 −0.595127
\(143\) 4.63179 2.67417i 0.387330 0.223625i
\(144\) 3.50066 2.02111i 0.291722 0.168426i
\(145\) −7.38519 1.40106i −0.613306 0.116352i
\(146\) −11.2091 + 3.00346i −0.927670 + 0.248569i
\(147\) 5.43759 5.43759i 0.448485 0.448485i
\(148\) −5.60404 2.36533i −0.460649 0.194429i
\(149\) 1.58834i 0.130122i −0.997881 0.0650611i \(-0.979276\pi\)
0.997881 0.0650611i \(-0.0207242\pi\)
\(150\) −12.1666 + 5.29421i −0.993401 + 0.432271i
\(151\) −10.3991 + 6.00392i −0.846266 + 0.488592i −0.859389 0.511322i \(-0.829156\pi\)
0.0131234 + 0.999914i \(0.495823\pi\)
\(152\) 0.968309 + 0.259458i 0.0785403 + 0.0210448i
\(153\) −1.23259 2.13491i −0.0996489 0.172597i
\(154\) 1.60952 1.60952i 0.129698 0.129698i
\(155\) 2.26215 11.9241i 0.181700 0.957767i
\(156\) 8.93012 + 8.93012i 0.714982 + 0.714982i
\(157\) −7.06880 + 1.89408i −0.564152 + 0.151164i −0.529613 0.848239i \(-0.677663\pi\)
−0.0345386 + 0.999403i \(0.510996\pi\)
\(158\) 3.30206 3.30206i 0.262698 0.262698i
\(159\) −9.40913 −0.746192
\(160\) −2.01416 0.971170i −0.159233 0.0767777i
\(161\) 3.08315 11.5065i 0.242986 0.906838i
\(162\) −4.78712 −0.376112
\(163\) 3.61734 + 2.08847i 0.283332 + 0.163582i 0.634931 0.772569i \(-0.281029\pi\)
−0.351599 + 0.936151i \(0.614362\pi\)
\(164\) −7.57396 4.37283i −0.591427 0.341461i
\(165\) −6.29554 + 2.19948i −0.490107 + 0.171229i
\(166\) −3.44908 0.924178i −0.267701 0.0717301i
\(167\) −4.69835 + 2.71259i −0.363569 + 0.209907i −0.670645 0.741778i \(-0.733983\pi\)
0.307076 + 0.951685i \(0.400649\pi\)
\(168\) 4.65473 + 2.68741i 0.359120 + 0.207338i
\(169\) −4.82413 + 8.35563i −0.371087 + 0.642741i
\(170\) −0.592275 + 1.22835i −0.0454254 + 0.0942101i
\(171\) 2.86533 + 2.86533i 0.219118 + 0.219118i
\(172\) 1.26483 + 2.19076i 0.0964427 + 0.167044i
\(173\) −3.85906 + 1.03403i −0.293399 + 0.0786159i −0.402516 0.915413i \(-0.631864\pi\)
0.109117 + 0.994029i \(0.465198\pi\)
\(174\) 8.92091i 0.676292i
\(175\) −8.14229 6.02149i −0.615500 0.455182i
\(176\) −0.973266 0.561916i −0.0733627 0.0423560i
\(177\) −18.6019 −1.39820
\(178\) 3.55341 13.2615i 0.266339 0.993992i
\(179\) −14.1223 14.1223i −1.05555 1.05555i −0.998363 0.0571889i \(-0.981786\pi\)
−0.0571889 0.998363i \(-0.518214\pi\)
\(180\) −5.08805 7.47057i −0.379241 0.556824i
\(181\) −5.83408 10.1049i −0.433644 0.751093i 0.563540 0.826089i \(-0.309439\pi\)
−0.997184 + 0.0749959i \(0.976106\pi\)
\(182\) −2.49472 + 9.31044i −0.184921 + 0.690136i
\(183\) −18.4865 + 32.0195i −1.36656 + 2.36695i
\(184\) −5.88152 −0.433592
\(185\) −4.34406 + 12.8891i −0.319381 + 0.947626i
\(186\) 14.4037 1.05613
\(187\) −0.342689 + 0.593554i −0.0250599 + 0.0434050i
\(188\) 1.52508 5.69169i 0.111228 0.415109i
\(189\) 2.80087 + 4.85125i 0.203733 + 0.352876i
\(190\) 0.417804 2.20230i 0.0303107 0.159772i
\(191\) 13.5165 + 13.5165i 0.978021 + 0.978021i 0.999764 0.0217424i \(-0.00692136\pi\)
−0.0217424 + 0.999764i \(0.506921\pi\)
\(192\) 0.686833 2.56329i 0.0495679 0.184990i
\(193\) 12.8185 0.922693 0.461347 0.887220i \(-0.347366\pi\)
0.461347 + 0.887220i \(0.347366\pi\)
\(194\) 9.35694 + 5.40223i 0.671789 + 0.387858i
\(195\) 18.4306 21.3958i 1.31985 1.53219i
\(196\) 2.89779i 0.206985i
\(197\) −0.822836 + 0.220478i −0.0586246 + 0.0157084i −0.288012 0.957627i \(-0.592994\pi\)
0.229388 + 0.973335i \(0.426328\pi\)
\(198\) −2.27139 3.93416i −0.161420 0.279588i
\(199\) −11.2815 11.2815i −0.799726 0.799726i 0.183326 0.983052i \(-0.441314\pi\)
−0.983052 + 0.183326i \(0.941314\pi\)
\(200\) −1.83122 + 4.65260i −0.129486 + 0.328988i
\(201\) 19.2534 33.3479i 1.35803 2.35218i
\(202\) 11.9299 + 6.88772i 0.839384 + 0.484618i
\(203\) 5.89650 3.40434i 0.413853 0.238938i
\(204\) −1.56324 0.418870i −0.109449 0.0293268i
\(205\) −8.49352 + 17.6151i −0.593213 + 1.23029i
\(206\) 15.6086 + 9.01164i 1.08750 + 0.627871i
\(207\) −20.5892 11.8872i −1.43105 0.826218i
\(208\) 4.75902 0.329979
\(209\) 0.291587 1.08822i 0.0201695 0.0752735i
\(210\) 5.21986 10.8257i 0.360205 0.747046i
\(211\) −8.38969 −0.577570 −0.288785 0.957394i \(-0.593251\pi\)
−0.288785 + 0.957394i \(0.593251\pi\)
\(212\) −2.50715 + 2.50715i −0.172191 + 0.172191i
\(213\) −18.1783 + 4.87085i −1.24555 + 0.333745i
\(214\) 2.01985 + 2.01985i 0.138074 + 0.138074i
\(215\) 4.67517 3.18416i 0.318844 0.217158i
\(216\) 1.95568 1.95568i 0.133067 0.133067i
\(217\) 5.49665 + 9.52047i 0.373137 + 0.646292i
\(218\) 16.1303 + 4.32210i 1.09248 + 0.292729i
\(219\) −26.6693 + 15.3975i −1.80214 + 1.04047i
\(220\) −1.09143 + 2.26357i −0.0735843 + 0.152610i
\(221\) 2.90232i 0.195231i
\(222\) −15.9894 2.21401i −1.07314 0.148594i
\(223\) 12.2726 12.2726i 0.821834 0.821834i −0.164537 0.986371i \(-0.552613\pi\)
0.986371 + 0.164537i \(0.0526130\pi\)
\(224\) 1.95638 0.524210i 0.130716 0.0350252i
\(225\) −15.8139 + 12.5861i −1.05426 + 0.839073i
\(226\) −4.26128 + 2.46025i −0.283456 + 0.163653i
\(227\) 7.24577 4.18335i 0.480919 0.277659i −0.239881 0.970802i \(-0.577108\pi\)
0.720799 + 0.693144i \(0.243775\pi\)
\(228\) 2.66027 0.176180
\(229\) 1.15819 0.668684i 0.0765356 0.0441879i −0.461244 0.887273i \(-0.652597\pi\)
0.537779 + 0.843086i \(0.319263\pi\)
\(230\) 0.976456 + 13.1152i 0.0643856 + 0.864790i
\(231\) 3.02019 5.23113i 0.198714 0.344183i
\(232\) −2.37706 2.37706i −0.156061 0.156061i
\(233\) 1.84053 + 1.84053i 0.120577 + 0.120577i 0.764821 0.644243i \(-0.222828\pi\)
−0.644243 + 0.764821i \(0.722828\pi\)
\(234\) 16.6597 + 9.61850i 1.08908 + 0.628781i
\(235\) −12.9451 2.45584i −0.844443 0.160201i
\(236\) −4.95664 + 4.95664i −0.322650 + 0.322650i
\(237\) 6.19619 10.7321i 0.402486 0.697126i
\(238\) −0.319693 1.19311i −0.0207226 0.0773380i
\(239\) 5.49007 + 20.4892i 0.355123 + 1.32534i 0.880329 + 0.474363i \(0.157322\pi\)
−0.525206 + 0.850975i \(0.676012\pi\)
\(240\) −5.82991 1.10601i −0.376319 0.0713923i
\(241\) 2.12638 7.93574i 0.136972 0.511186i −0.863010 0.505187i \(-0.831424\pi\)
0.999982 0.00599947i \(-0.00190970\pi\)
\(242\) 4.86850 8.43249i 0.312959 0.542061i
\(243\) −20.2853 + 5.43544i −1.30131 + 0.348684i
\(244\) 3.60599 + 13.4578i 0.230850 + 0.861544i
\(245\) −6.46177 + 0.481094i −0.412827 + 0.0307360i
\(246\) −22.4177 6.00681i −1.42930 0.382980i
\(247\) 1.23476 + 4.60820i 0.0785661 + 0.293213i
\(248\) 3.83799 3.83799i 0.243713 0.243713i
\(249\) −9.47577 −0.600502
\(250\) 10.6788 + 3.31099i 0.675388 + 0.209406i
\(251\) −13.6105 + 13.6105i −0.859084 + 0.859084i −0.991230 0.132146i \(-0.957813\pi\)
0.132146 + 0.991230i \(0.457813\pi\)
\(252\) 7.90811 + 2.11897i 0.498164 + 0.133483i
\(253\) 6.60984i 0.415557i
\(254\) −1.84957 + 6.90268i −0.116052 + 0.433113i
\(255\) −0.674506 + 3.55542i −0.0422392 + 0.222649i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −6.00922 3.46942i −0.374845 0.216417i 0.300728 0.953710i \(-0.402770\pi\)
−0.675573 + 0.737293i \(0.736104\pi\)
\(258\) 4.74683 + 4.74683i 0.295525 + 0.295525i
\(259\) −4.63837 11.4135i −0.288214 0.709199i
\(260\) −0.790097 10.6121i −0.0489997 0.658136i
\(261\) −3.51698 13.1256i −0.217696 0.812452i
\(262\) 19.6201 + 5.25720i 1.21214 + 0.324791i
\(263\) −8.10871 + 30.2621i −0.500005 + 1.86604i −3.36436e−5 1.00000i \(0.500011\pi\)
−0.499971 + 0.866042i \(0.666656\pi\)
\(264\) −2.88071 0.771884i −0.177295 0.0475062i
\(265\) 6.00691 + 5.17444i 0.369002 + 0.317863i
\(266\) 1.01519 + 1.75837i 0.0622456 + 0.107812i
\(267\) 36.4337i 2.22971i
\(268\) −3.75560 14.0161i −0.229410 0.856169i
\(269\) 17.3508i 1.05789i 0.848655 + 0.528947i \(0.177413\pi\)
−0.848655 + 0.528947i \(0.822587\pi\)
\(270\) −4.68566 4.03629i −0.285160 0.245641i
\(271\) −8.45565 + 14.6456i −0.513644 + 0.889658i 0.486231 + 0.873830i \(0.338371\pi\)
−0.999875 + 0.0158271i \(0.994962\pi\)
\(272\) −0.528152 + 0.304929i −0.0320239 + 0.0184890i
\(273\) 25.5789i 1.54810i
\(274\) 5.72353 1.53361i 0.345771 0.0926490i
\(275\) 5.22873 + 2.05798i 0.315304 + 0.124101i
\(276\) −15.0761 + 4.03962i −0.907473 + 0.243157i
\(277\) −11.9817 20.7529i −0.719912 1.24692i −0.961034 0.276429i \(-0.910849\pi\)
0.241122 0.970495i \(-0.422484\pi\)
\(278\) −5.56954 9.64673i −0.334039 0.578572i
\(279\) 21.1925 5.67852i 1.26876 0.339964i
\(280\) −1.49373 4.27549i −0.0892676 0.255509i
\(281\) 23.0722 6.18218i 1.37637 0.368798i 0.506571 0.862198i \(-0.330913\pi\)
0.869802 + 0.493400i \(0.164246\pi\)
\(282\) 15.6369i 0.931167i
\(283\) −4.68580 + 2.70535i −0.278542 + 0.160816i −0.632763 0.774345i \(-0.718079\pi\)
0.354221 + 0.935162i \(0.384746\pi\)
\(284\) −3.54588 + 6.14164i −0.210409 + 0.364439i
\(285\) −0.441660 5.93212i −0.0261617 0.351388i
\(286\) 5.34833i 0.316254i
\(287\) −4.58456 17.1098i −0.270618 1.00996i
\(288\) 4.04222i 0.238190i
\(289\) −8.31404 14.4003i −0.489061 0.847078i
\(290\) −4.90595 + 5.69523i −0.288087 + 0.334435i
\(291\) 27.6950 + 7.42086i 1.62351 + 0.435018i
\(292\) −3.00346 + 11.2091i −0.175764 + 0.655962i
\(293\) 4.01883 + 1.07684i 0.234783 + 0.0629098i 0.374292 0.927311i \(-0.377886\pi\)
−0.139509 + 0.990221i \(0.544552\pi\)
\(294\) −1.99030 7.42789i −0.116076 0.433203i
\(295\) 11.8757 + 10.2299i 0.691430 + 0.595607i
\(296\) −4.85045 + 3.67057i −0.281927 + 0.213348i
\(297\) −2.19786 2.19786i −0.127533 0.127533i
\(298\) −1.37555 0.794171i −0.0796832 0.0460051i
\(299\) −13.9951 24.2403i −0.809360 1.40185i
\(300\) −1.49839 + 13.1837i −0.0865096 + 0.761162i
\(301\) −1.32608 + 4.94899i −0.0764338 + 0.285255i
\(302\) 12.0078i 0.690973i
\(303\) 35.3105 + 9.46143i 2.02854 + 0.543545i
\(304\) 0.708852 0.708852i 0.0406554 0.0406554i
\(305\) 29.4107 10.2753i 1.68405 0.588360i
\(306\) −2.46518 −0.140925
\(307\) 19.1402 19.1402i 1.09239 1.09239i 0.0971133 0.995273i \(-0.469039\pi\)
0.995273 0.0971133i \(-0.0309609\pi\)
\(308\) −0.589123 2.19864i −0.0335684 0.125279i
\(309\) 46.1990 + 12.3790i 2.62817 + 0.704215i
\(310\) −9.19551 7.92113i −0.522270 0.449890i
\(311\) −1.52724 5.69972i −0.0866016 0.323202i 0.909011 0.416772i \(-0.136839\pi\)
−0.995613 + 0.0935704i \(0.970172\pi\)
\(312\) 12.1988 3.26865i 0.690619 0.185051i
\(313\) 14.8031 25.6397i 0.836719 1.44924i −0.0559040 0.998436i \(-0.517804\pi\)
0.892623 0.450804i \(-0.148863\pi\)
\(314\) −1.89408 + 7.06880i −0.106889 + 0.398915i
\(315\) 3.41217 17.9861i 0.192254 1.01340i
\(316\) −1.20864 4.51070i −0.0679912 0.253747i
\(317\) 2.55646 + 9.54085i 0.143585 + 0.535868i 0.999814 + 0.0192712i \(0.00613459\pi\)
−0.856229 + 0.516596i \(0.827199\pi\)
\(318\) −4.70456 + 8.14854i −0.263819 + 0.456948i
\(319\) −2.67141 + 2.67141i −0.149570 + 0.149570i
\(320\) −1.84814 + 1.25873i −0.103314 + 0.0703649i
\(321\) 6.56477 + 3.79017i 0.366410 + 0.211547i
\(322\) −8.42333 8.42333i −0.469414 0.469414i
\(323\) −0.432299 0.432299i −0.0240537 0.0240537i
\(324\) −2.39356 + 4.14577i −0.132976 + 0.230320i
\(325\) −23.5327 + 3.52367i −1.30536 + 0.195458i
\(326\) 3.61734 2.08847i 0.200346 0.115670i
\(327\) 44.3152 2.45064
\(328\) −7.57396 + 4.37283i −0.418202 + 0.241449i
\(329\) 10.3356 5.96728i 0.569822 0.328987i
\(330\) −1.24296 + 6.55183i −0.0684229 + 0.360667i
\(331\) −5.18854 + 1.39026i −0.285188 + 0.0764159i −0.398577 0.917135i \(-0.630496\pi\)
0.113389 + 0.993551i \(0.463829\pi\)
\(332\) −2.52490 + 2.52490i −0.138572 + 0.138572i
\(333\) −24.3984 + 3.04614i −1.33703 + 0.166927i
\(334\) 5.42518i 0.296853i
\(335\) −30.6309 + 10.7016i −1.67355 + 0.584689i
\(336\) 4.65473 2.68741i 0.253936 0.146610i
\(337\) 24.0356 + 6.44031i 1.30930 + 0.350826i 0.844959 0.534831i \(-0.179625\pi\)
0.464341 + 0.885657i \(0.346291\pi\)
\(338\) 4.82413 + 8.35563i 0.262398 + 0.454486i
\(339\) −9.23314 + 9.23314i −0.501475 + 0.501475i
\(340\) 0.767644 + 1.12710i 0.0416313 + 0.0611256i
\(341\) −4.31325 4.31325i −0.233576 0.233576i
\(342\) 3.91412 1.04878i 0.211651 0.0567118i
\(343\) 14.1753 14.1753i 0.765394 0.765394i
\(344\) 2.52967 0.136391
\(345\) 11.5109 + 32.9474i 0.619725 + 1.77383i
\(346\) −1.03403 + 3.85906i −0.0555898 + 0.207464i
\(347\) −24.0293 −1.28996 −0.644981 0.764198i \(-0.723135\pi\)
−0.644981 + 0.764198i \(0.723135\pi\)
\(348\) −7.72573 4.46045i −0.414143 0.239105i
\(349\) −28.9043 16.6879i −1.54721 0.893283i −0.998353 0.0573673i \(-0.981729\pi\)
−0.548858 0.835916i \(-0.684937\pi\)
\(350\) −9.28591 + 4.04069i −0.496353 + 0.215984i
\(351\) 12.7138 + 3.40665i 0.678612 + 0.181833i
\(352\) −0.973266 + 0.561916i −0.0518753 + 0.0299502i
\(353\) 25.7151 + 14.8466i 1.36867 + 0.790205i 0.990759 0.135635i \(-0.0433075\pi\)
0.377916 + 0.925840i \(0.376641\pi\)
\(354\) −9.30095 + 16.1097i −0.494340 + 0.856222i
\(355\) 14.2839 + 6.88730i 0.758111 + 0.365540i
\(356\) −9.70810 9.70810i −0.514528 0.514528i
\(357\) −1.63894 2.83872i −0.0867417 0.150241i
\(358\) −19.2915 + 5.16913i −1.01959 + 0.273197i
\(359\) 8.36739i 0.441614i 0.975318 + 0.220807i \(0.0708691\pi\)
−0.975318 + 0.220807i \(0.929131\pi\)
\(360\) −9.01373 + 0.671093i −0.475065 + 0.0353697i
\(361\) −15.5842 8.99753i −0.820220 0.473554i
\(362\) −11.6682 −0.613265
\(363\) 6.68769 24.9588i 0.351013 1.31000i
\(364\) 6.81571 + 6.81571i 0.357240 + 0.357240i
\(365\) 25.4937 + 4.83647i 1.33440 + 0.253153i
\(366\) 18.4865 + 32.0195i 0.966302 + 1.67368i
\(367\) 0.472693 1.76411i 0.0246744 0.0920860i −0.952491 0.304568i \(-0.901488\pi\)
0.977165 + 0.212482i \(0.0681546\pi\)
\(368\) −2.94076 + 5.09355i −0.153298 + 0.265520i
\(369\) −35.3519 −1.84035
\(370\) 8.99027 + 10.2066i 0.467382 + 0.530617i
\(371\) −7.18131 −0.372835
\(372\) 7.20184 12.4740i 0.373398 0.646744i
\(373\) 8.64253 32.2544i 0.447493 1.67007i −0.261774 0.965129i \(-0.584308\pi\)
0.709268 0.704939i \(-0.249026\pi\)
\(374\) 0.342689 + 0.593554i 0.0177200 + 0.0306919i
\(375\) 29.6471 + 1.15248i 1.53097 + 0.0595139i
\(376\) −4.16660 4.16660i −0.214876 0.214876i
\(377\) 4.14064 15.4531i 0.213254 0.795875i
\(378\) 5.60174 0.288122
\(379\) 10.4144 + 6.01276i 0.534952 + 0.308855i 0.743031 0.669257i \(-0.233388\pi\)
−0.208079 + 0.978112i \(0.566721\pi\)
\(380\) −1.69835 1.46298i −0.0871235 0.0750494i
\(381\) 18.9640i 0.971553i
\(382\) 18.4639 4.94739i 0.944696 0.253131i
\(383\) −0.0359998 0.0623535i −0.00183950 0.00318611i 0.865104 0.501592i \(-0.167252\pi\)
−0.866944 + 0.498406i \(0.833919\pi\)
\(384\) −1.87646 1.87646i −0.0957578 0.0957578i
\(385\) −4.80493 + 1.67870i −0.244882 + 0.0855547i
\(386\) 6.40923 11.1011i 0.326221 0.565032i
\(387\) 8.85552 + 5.11274i 0.450151 + 0.259895i
\(388\) 9.35694 5.40223i 0.475027 0.274257i
\(389\) −18.5818 4.97897i −0.942132 0.252444i −0.245112 0.969495i \(-0.578825\pi\)
−0.697020 + 0.717051i \(0.745491\pi\)
\(390\) −9.31400 26.6593i −0.471633 1.34995i
\(391\) 3.10634 + 1.79345i 0.157094 + 0.0906985i
\(392\) −2.50956 1.44889i −0.126752 0.0731802i
\(393\) 53.9030 2.71905
\(394\) −0.220478 + 0.822836i −0.0111075 + 0.0414539i
\(395\) −9.85773 + 3.44401i −0.495996 + 0.173287i
\(396\) −4.54277 −0.228283
\(397\) −9.99150 + 9.99150i −0.501459 + 0.501459i −0.911891 0.410432i \(-0.865378\pi\)
0.410432 + 0.911891i \(0.365378\pi\)
\(398\) −15.4109 + 4.12933i −0.772476 + 0.206984i
\(399\) 3.80995 + 3.80995i 0.190736 + 0.190736i
\(400\) 3.11366 + 3.91218i 0.155683 + 0.195609i
\(401\) −22.6392 + 22.6392i −1.13055 + 1.13055i −0.140461 + 0.990086i \(0.544859\pi\)
−0.990086 + 0.140461i \(0.955141\pi\)
\(402\) −19.2534 33.3479i −0.960274 1.66324i
\(403\) 24.9505 + 6.68548i 1.24287 + 0.333027i
\(404\) 11.9299 6.88772i 0.593534 0.342677i
\(405\) 9.64202 + 4.64911i 0.479116 + 0.231016i
\(406\) 6.80869i 0.337909i
\(407\) 4.12510 + 5.45109i 0.204474 + 0.270201i
\(408\) −1.14437 + 1.14437i −0.0566550 + 0.0566550i
\(409\) −21.4024 + 5.73477i −1.05828 + 0.283566i −0.745670 0.666315i \(-0.767871\pi\)
−0.312612 + 0.949881i \(0.601204\pi\)
\(410\) 11.0084 + 16.1632i 0.543666 + 0.798242i
\(411\) 13.6177 7.86221i 0.671714 0.387814i
\(412\) 15.6086 9.01164i 0.768981 0.443972i
\(413\) −14.1975 −0.698613
\(414\) −20.5892 + 11.8872i −1.01191 + 0.584224i
\(415\) 6.04946 + 5.21108i 0.296956 + 0.255802i
\(416\) 2.37951 4.12143i 0.116665 0.202070i
\(417\) −20.9021 20.9021i −1.02358 1.02358i
\(418\) −0.796629 0.796629i −0.0389644 0.0389644i
\(419\) −0.594991 0.343518i −0.0290672 0.0167820i 0.485396 0.874294i \(-0.338675\pi\)
−0.514463 + 0.857512i \(0.672009\pi\)
\(420\) −6.76543 9.93340i −0.330119 0.484700i
\(421\) 21.9676 21.9676i 1.07064 1.07064i 0.0733291 0.997308i \(-0.476638\pi\)
0.997308 0.0733291i \(-0.0233623\pi\)
\(422\) −4.19484 + 7.26568i −0.204202 + 0.353688i
\(423\) −6.16472 23.0070i −0.299739 1.11864i
\(424\) 0.917679 + 3.42482i 0.0445664 + 0.166324i
\(425\) 2.38587 1.89889i 0.115732 0.0921096i
\(426\) −4.87085 + 18.1783i −0.235993 + 0.880739i
\(427\) −14.1094 + 24.4382i −0.682800 + 1.18265i
\(428\) 2.75917 0.739316i 0.133369 0.0357362i
\(429\) −3.67341 13.7094i −0.177354 0.661894i
\(430\) −0.419978 5.64090i −0.0202531 0.272028i
\(431\) 25.8534 + 6.92740i 1.24531 + 0.333681i 0.820525 0.571611i \(-0.193681\pi\)
0.424790 + 0.905292i \(0.360348\pi\)
\(432\) −0.715830 2.67152i −0.0344404 0.128533i
\(433\) 15.2715 15.2715i 0.733900 0.733900i −0.237490 0.971390i \(-0.576325\pi\)
0.971390 + 0.237490i \(0.0763247\pi\)
\(434\) 10.9933 0.527695
\(435\) −8.66372 + 17.9681i −0.415393 + 0.861505i
\(436\) 11.8082 11.8082i 0.565510 0.565510i
\(437\) −5.69513 1.52601i −0.272435 0.0729988i
\(438\) 30.7951i 1.47144i
\(439\) −7.17501 + 26.7775i −0.342445 + 1.27802i 0.553124 + 0.833099i \(0.313435\pi\)
−0.895569 + 0.444922i \(0.853231\pi\)
\(440\) 1.41460 + 2.07699i 0.0674382 + 0.0990168i
\(441\) −5.85675 10.1442i −0.278893 0.483057i
\(442\) −2.51349 1.45116i −0.119554 0.0690247i
\(443\) 0.994977 + 0.994977i 0.0472728 + 0.0472728i 0.730348 0.683075i \(-0.239358\pi\)
−0.683075 + 0.730348i \(0.739358\pi\)
\(444\) −9.91208 + 12.7402i −0.470406 + 0.604623i
\(445\) −20.0363 + 23.2598i −0.949812 + 1.10262i
\(446\) −4.49208 16.7647i −0.212706 0.793830i
\(447\) −4.07139 1.09093i −0.192570 0.0515990i
\(448\) 0.524210 1.95638i 0.0247666 0.0924302i
\(449\) 20.6726 + 5.53920i 0.975598 + 0.261411i 0.711190 0.703000i \(-0.248157\pi\)
0.264408 + 0.964411i \(0.414823\pi\)
\(450\) 2.99294 + 19.9883i 0.141088 + 0.942256i
\(451\) 4.91432 + 8.51186i 0.231406 + 0.400808i
\(452\) 4.92050i 0.231441i
\(453\) 8.24737 + 30.7796i 0.387495 + 1.44615i
\(454\) 8.36669i 0.392668i
\(455\) 14.0668 16.3299i 0.659461 0.765557i
\(456\) 1.33013 2.30386i 0.0622892 0.107888i
\(457\) 13.9056 8.02843i 0.650479 0.375554i −0.138161 0.990410i \(-0.544119\pi\)
0.788640 + 0.614856i \(0.210786\pi\)
\(458\) 1.33737i 0.0624911i
\(459\) −1.62924 + 0.436555i −0.0760466 + 0.0203766i
\(460\) 11.8463 + 5.71196i 0.552337 + 0.266321i
\(461\) −9.28681 + 2.48839i −0.432530 + 0.115896i −0.468513 0.883456i \(-0.655210\pi\)
0.0359836 + 0.999352i \(0.488544\pi\)
\(462\) −3.02019 5.23113i −0.140512 0.243374i
\(463\) 7.67172 + 13.2878i 0.356535 + 0.617536i 0.987379 0.158373i \(-0.0506248\pi\)
−0.630845 + 0.775909i \(0.717291\pi\)
\(464\) −3.24712 + 0.870063i −0.150744 + 0.0403917i
\(465\) −29.0113 13.9884i −1.34537 0.648698i
\(466\) 2.51421 0.673681i 0.116469 0.0312077i
\(467\) 3.94300i 0.182460i −0.995830 0.0912301i \(-0.970920\pi\)
0.995830 0.0912301i \(-0.0290799\pi\)
\(468\) 16.6597 9.61850i 0.770096 0.444615i
\(469\) 14.6947 25.4521i 0.678540 1.17527i
\(470\) −8.59935 + 9.98284i −0.396658 + 0.460474i
\(471\) 19.4203i 0.894842i
\(472\) 1.81426 + 6.77090i 0.0835079 + 0.311656i
\(473\) 2.84292i 0.130718i
\(474\) −6.19619 10.7321i −0.284601 0.492943i
\(475\) −2.98033 + 4.03003i −0.136747 + 0.184910i
\(476\) −1.19311 0.319693i −0.0546862 0.0146531i
\(477\) −3.70946 + 13.8439i −0.169844 + 0.633868i
\(478\) 20.4892 + 5.49007i 0.937156 + 0.251110i
\(479\) −3.81670 14.2441i −0.174389 0.650830i −0.996655 0.0817257i \(-0.973957\pi\)
0.822266 0.569104i \(-0.192710\pi\)
\(480\) −3.87278 + 4.49585i −0.176768 + 0.205206i
\(481\) −26.6697 11.2567i −1.21603 0.513259i
\(482\) −5.80937 5.80937i −0.264609 0.264609i
\(483\) −27.3769 15.8061i −1.24569 0.719201i
\(484\) −4.86850 8.43249i −0.221296 0.383295i
\(485\) −13.5999 19.9681i −0.617538 0.906706i
\(486\) −5.43544 + 20.2853i −0.246557 + 0.920162i
\(487\) 40.5464i 1.83733i −0.395035 0.918666i \(-0.629267\pi\)
0.395035 0.918666i \(-0.370733\pi\)
\(488\) 13.4578 + 3.60599i 0.609204 + 0.163236i
\(489\) 7.83787 7.83787i 0.354441 0.354441i
\(490\) −2.81425 + 5.83660i −0.127135 + 0.263671i
\(491\) −2.02704 −0.0914790 −0.0457395 0.998953i \(-0.514564\pi\)
−0.0457395 + 0.998953i \(0.514564\pi\)
\(492\) −16.4109 + 16.4109i −0.739860 + 0.739860i
\(493\) 0.530614 + 1.98028i 0.0238977 + 0.0891873i
\(494\) 4.60820 + 1.23476i 0.207333 + 0.0555547i
\(495\) 0.754195 + 10.1299i 0.0338986 + 0.455306i
\(496\) −1.40480 5.24279i −0.0630775 0.235408i
\(497\) −13.8742 + 3.71757i −0.622341 + 0.166756i
\(498\) −4.73788 + 8.20625i −0.212310 + 0.367731i
\(499\) −10.0374 + 37.4600i −0.449335 + 1.67694i 0.254894 + 0.966969i \(0.417959\pi\)
−0.704229 + 0.709973i \(0.748707\pi\)
\(500\) 8.20682 7.59264i 0.367020 0.339553i
\(501\) 3.72619 + 13.9063i 0.166474 + 0.621290i
\(502\) 4.98177 + 18.5922i 0.222347 + 0.829812i
\(503\) −1.86775 + 3.23504i −0.0832789 + 0.144243i −0.904657 0.426141i \(-0.859873\pi\)
0.821378 + 0.570385i \(0.193206\pi\)
\(504\) 5.78914 5.78914i 0.257869 0.257869i
\(505\) −17.3395 25.4589i −0.771598 1.13291i
\(506\) 5.72429 + 3.30492i 0.254476 + 0.146922i
\(507\) 18.1046 + 18.1046i 0.804053 + 0.804053i
\(508\) 5.05311 + 5.05311i 0.224196 + 0.224196i
\(509\) 14.5825 25.2577i 0.646360 1.11953i −0.337626 0.941280i \(-0.609624\pi\)
0.983986 0.178248i \(-0.0570428\pi\)
\(510\) 2.74183 + 2.36185i 0.121410 + 0.104584i
\(511\) −20.3548 + 11.7518i −0.900441 + 0.519870i
\(512\) −1.00000 −0.0441942
\(513\) 2.40113 1.38629i 0.106012 0.0612062i
\(514\) −6.00922 + 3.46942i −0.265055 + 0.153030i
\(515\) −22.6864 33.3095i −0.999681 1.46779i
\(516\) 6.48429 1.73746i 0.285455 0.0764874i
\(517\) −4.68256 + 4.68256i −0.205939 + 0.205939i
\(518\) −12.2035 1.68979i −0.536193 0.0742451i
\(519\) 10.6021i 0.465381i
\(520\) −9.58541 4.62181i −0.420348 0.202680i
\(521\) 14.2125 8.20557i 0.622659 0.359492i −0.155244 0.987876i \(-0.549617\pi\)
0.777904 + 0.628384i \(0.216283\pi\)
\(522\) −13.1256 3.51698i −0.574490 0.153934i
\(523\) −17.0300 29.4968i −0.744668 1.28980i −0.950350 0.311184i \(-0.899274\pi\)
0.205681 0.978619i \(-0.434059\pi\)
\(524\) 14.3629 14.3629i 0.627448 0.627448i
\(525\) −21.0272 + 16.7353i −0.917704 + 0.730390i
\(526\) 22.1534 + 22.1534i 0.965935 + 0.965935i
\(527\) −3.19736 + 0.856729i −0.139279 + 0.0373197i
\(528\) −2.10883 + 2.10883i −0.0917749 + 0.0917749i
\(529\) 11.5923 0.504014
\(530\) 7.48465 2.61492i 0.325112 0.113585i
\(531\) −7.33362 + 27.3695i −0.318252 + 1.18773i
\(532\) 2.03039 0.0880285
\(533\) −36.0446 20.8104i −1.56127 0.901398i
\(534\) −31.5525 18.2169i −1.36541 0.788321i
\(535\) −2.10668 6.02991i −0.0910796 0.260696i
\(536\) −14.0161 3.75560i −0.605403 0.162217i
\(537\) −45.8994 + 26.5000i −1.98070 + 1.14356i
\(538\) 15.0262 + 8.67538i 0.647825 + 0.374022i
\(539\) −1.62831 + 2.82032i −0.0701364 + 0.121480i
\(540\) −5.83836 + 2.03975i −0.251243 + 0.0877771i
\(541\) 8.61393 + 8.61393i 0.370342 + 0.370342i 0.867602 0.497260i \(-0.165660\pi\)
−0.497260 + 0.867602i \(0.665660\pi\)
\(542\) 8.45565 + 14.6456i 0.363201 + 0.629083i
\(543\) −29.9089 + 8.01407i −1.28351 + 0.343917i
\(544\) 0.609858i 0.0261474i
\(545\) −28.2914 24.3706i −1.21187 1.04392i
\(546\) 22.1519 + 12.7894i 0.948015 + 0.547337i
\(547\) −1.86737 −0.0798431 −0.0399215 0.999203i \(-0.512711\pi\)
−0.0399215 + 0.999203i \(0.512711\pi\)
\(548\) 1.53361 5.72353i 0.0655128 0.244497i
\(549\) 39.8230 + 39.8230i 1.69960 + 1.69960i
\(550\) 4.39663 3.49923i 0.187473 0.149208i
\(551\) −1.68498 2.91847i −0.0717826 0.124331i
\(552\) −4.03962 + 15.0761i −0.171938 + 0.641681i
\(553\) 4.72911 8.19105i 0.201102 0.348319i
\(554\) −23.9634 −1.01811
\(555\) 30.0550 + 19.9878i 1.27576 + 0.848433i
\(556\) −11.1391 −0.472402
\(557\) 20.3530 35.2525i 0.862386 1.49370i −0.00723424 0.999974i \(-0.502303\pi\)
0.869620 0.493722i \(-0.164364\pi\)
\(558\) 5.67852 21.1925i 0.240391 0.897151i
\(559\) 6.01937 + 10.4259i 0.254592 + 0.440967i
\(560\) −4.44955 0.844134i −0.188028 0.0356712i
\(561\) 1.28608 + 1.28608i 0.0542985 + 0.0542985i
\(562\) 6.18218 23.0722i 0.260780 0.973243i
\(563\) −12.4306 −0.523887 −0.261943 0.965083i \(-0.584363\pi\)
−0.261943 + 0.965083i \(0.584363\pi\)
\(564\) −13.5420 7.81847i −0.570221 0.329217i
\(565\) 10.9722 0.816906i 0.461604 0.0343675i
\(566\) 5.41070i 0.227429i
\(567\) −9.36542 + 2.50946i −0.393311 + 0.105387i
\(568\) 3.54588 + 6.14164i 0.148782 + 0.257697i
\(569\) 0.758462 + 0.758462i 0.0317964 + 0.0317964i 0.722826 0.691030i \(-0.242843\pi\)
−0.691030 + 0.722826i \(0.742843\pi\)
\(570\) −5.35819 2.58357i −0.224430 0.108214i
\(571\) −1.95838 + 3.39202i −0.0819558 + 0.141952i −0.904090 0.427342i \(-0.859450\pi\)
0.822134 + 0.569294i \(0.192783\pi\)
\(572\) −4.63179 2.67417i −0.193665 0.111813i
\(573\) 43.9304 25.3632i 1.83522 1.05956i
\(574\) −17.1098 4.58456i −0.714150 0.191356i
\(575\) 10.7703 27.3644i 0.449154 1.14117i
\(576\) −3.50066 2.02111i −0.145861 0.0842129i
\(577\) −7.95453 4.59255i −0.331151 0.191190i 0.325201 0.945645i \(-0.394568\pi\)
−0.656352 + 0.754455i \(0.727901\pi\)
\(578\) −16.6281 −0.691637
\(579\) 8.80414 32.8575i 0.365888 1.36551i
\(580\) 2.47924 + 7.09629i 0.102945 + 0.294657i
\(581\) −7.23217 −0.300041
\(582\) 20.2742 20.2742i 0.840391 0.840391i
\(583\) 3.84892 1.03132i 0.159406 0.0427128i
\(584\) 8.20562 + 8.20562i 0.339551 + 0.339551i
\(585\) −24.2141 35.5526i −1.00113 1.46992i
\(586\) 2.94199 2.94199i 0.121532 0.121532i
\(587\) 7.19146 + 12.4560i 0.296823 + 0.514113i 0.975407 0.220410i \(-0.0707395\pi\)
−0.678584 + 0.734523i \(0.737406\pi\)
\(588\) −7.42789 1.99030i −0.306321 0.0820785i
\(589\) 4.71216 2.72056i 0.194161 0.112099i
\(590\) 14.7972 5.16972i 0.609191 0.212834i
\(591\) 2.26060i 0.0929887i
\(592\) 0.753581 + 6.03590i 0.0309720 + 0.248074i
\(593\) −17.4500 + 17.4500i −0.716584 + 0.716584i −0.967904 0.251320i \(-0.919135\pi\)
0.251320 + 0.967904i \(0.419135\pi\)
\(594\) −3.00233 + 0.804472i −0.123187 + 0.0330079i
\(595\) −0.514802 + 2.71359i −0.0211048 + 0.111246i
\(596\) −1.37555 + 0.794171i −0.0563445 + 0.0325305i
\(597\) −36.6664 + 21.1694i −1.50066 + 0.866404i
\(598\) −27.9903 −1.14461
\(599\) 12.7512 7.36193i 0.521001 0.300800i −0.216343 0.976317i \(-0.569413\pi\)
0.737344 + 0.675517i \(0.236080\pi\)
\(600\) 10.6682 + 7.88950i 0.435529 + 0.322088i
\(601\) −13.4916 + 23.3682i −0.550336 + 0.953209i 0.447914 + 0.894076i \(0.352167\pi\)
−0.998250 + 0.0591330i \(0.981166\pi\)
\(602\) 3.62291 + 3.62291i 0.147659 + 0.147659i
\(603\) −41.4752 41.4752i −1.68900 1.68900i
\(604\) 10.3991 + 6.00392i 0.423133 + 0.244296i
\(605\) −17.9953 + 12.2562i −0.731613 + 0.498286i
\(606\) 25.8491 25.8491i 1.05005 1.05005i
\(607\) 0.945249 1.63722i 0.0383665 0.0664527i −0.846205 0.532858i \(-0.821118\pi\)
0.884571 + 0.466406i \(0.154451\pi\)
\(608\) −0.259458 0.968309i −0.0105224 0.0392701i
\(609\) −4.67643 17.4527i −0.189498 0.707218i
\(610\) 5.80672 30.6081i 0.235107 1.23928i
\(611\) 7.25790 27.0868i 0.293623 1.09582i
\(612\) −1.23259 + 2.13491i −0.0498245 + 0.0862985i
\(613\) −24.2316 + 6.49283i −0.978704 + 0.262243i −0.712499 0.701673i \(-0.752437\pi\)
−0.266205 + 0.963916i \(0.585770\pi\)
\(614\) −7.00578 26.1459i −0.282730 1.05516i
\(615\) 39.3192 + 33.8700i 1.58550 + 1.36577i
\(616\) −2.19864 0.589123i −0.0885857 0.0237365i
\(617\) 1.23831 + 4.62145i 0.0498526 + 0.186052i 0.986362 0.164590i \(-0.0526300\pi\)
−0.936510 + 0.350642i \(0.885963\pi\)
\(618\) 33.8200 33.8200i 1.36044 1.36044i
\(619\) 2.92309 0.117489 0.0587445 0.998273i \(-0.481290\pi\)
0.0587445 + 0.998273i \(0.481290\pi\)
\(620\) −11.4577 + 4.00298i −0.460150 + 0.160763i
\(621\) −11.5024 + 11.5024i −0.461576 + 0.461576i
\(622\) −5.69972 1.52724i −0.228538 0.0612366i
\(623\) 27.8072i 1.11407i
\(624\) 3.26865 12.1988i 0.130851 0.488341i
\(625\) −18.2933 17.0398i −0.731732 0.681592i
\(626\) −14.8031 25.6397i −0.591650 1.02477i
\(627\) −2.58915 1.49484i −0.103401 0.0596984i
\(628\) 5.17472 + 5.17472i 0.206494 + 0.206494i
\(629\) 3.68104 0.459577i 0.146773 0.0183245i
\(630\) −13.8703 11.9481i −0.552606 0.476022i
\(631\) 9.97860 + 37.2406i 0.397242 + 1.48253i 0.817928 + 0.575320i \(0.195123\pi\)
−0.420687 + 0.907206i \(0.638211\pi\)
\(632\) −4.51070 1.20864i −0.179426 0.0480771i
\(633\) −5.76231 + 21.5052i −0.229031 + 0.854757i
\(634\) 9.54085 + 2.55646i 0.378916 + 0.101530i
\(635\) 10.4290 12.1068i 0.413862 0.480445i
\(636\) 4.70456 + 8.14854i 0.186548 + 0.323111i
\(637\) 13.7906i 0.546405i
\(638\) 0.977804 + 3.64921i 0.0387116 + 0.144474i
\(639\) 28.6664i 1.13403i
\(640\) 0.166021 + 2.22990i 0.00656255 + 0.0881444i
\(641\) −16.5248 + 28.6217i −0.652689 + 1.13049i 0.329779 + 0.944058i \(0.393026\pi\)
−0.982468 + 0.186432i \(0.940307\pi\)
\(642\) 6.56477 3.79017i 0.259091 0.149586i
\(643\) 11.6270i 0.458523i 0.973365 + 0.229262i \(0.0736311\pi\)
−0.973365 + 0.229262i \(0.926369\pi\)
\(644\) −11.5065 + 3.08315i −0.453419 + 0.121493i
\(645\) −4.95088 14.1708i −0.194941 0.557976i
\(646\) −0.590531 + 0.158232i −0.0232341 + 0.00622556i
\(647\) −4.49154 7.77957i −0.176581 0.305847i 0.764127 0.645066i \(-0.223170\pi\)
−0.940707 + 0.339220i \(0.889837\pi\)
\(648\) 2.39356 + 4.14577i 0.0940279 + 0.162861i
\(649\) 7.60935 2.03892i 0.298693 0.0800345i
\(650\) −8.71479 + 22.1418i −0.341822 + 0.868472i
\(651\) 28.1790 7.55055i 1.10442 0.295930i
\(652\) 4.17694i 0.163582i
\(653\) 32.6893 18.8732i 1.27923 0.738563i 0.302523 0.953142i \(-0.402171\pi\)
0.976707 + 0.214579i \(0.0688378\pi\)
\(654\) 22.1576 38.3781i 0.866431 1.50070i
\(655\) −34.4124 29.6433i −1.34460 1.15826i
\(656\) 8.74566i 0.341461i
\(657\) 12.1407 + 45.3096i 0.473652 + 1.76769i
\(658\) 11.9346i 0.465257i
\(659\) 17.7677 + 30.7746i 0.692132 + 1.19881i 0.971138 + 0.238518i \(0.0766617\pi\)
−0.279006 + 0.960289i \(0.590005\pi\)
\(660\) 5.05257 + 4.35235i 0.196671 + 0.169415i
\(661\) −32.5227 8.71443i −1.26499 0.338952i −0.436879 0.899521i \(-0.643916\pi\)
−0.828108 + 0.560568i \(0.810583\pi\)
\(662\) −1.39026 + 5.18854i −0.0540342 + 0.201658i
\(663\) −7.43951 1.99341i −0.288927 0.0774177i
\(664\) 0.924178 + 3.44908i 0.0358651 + 0.133850i
\(665\) −0.337087 4.52756i −0.0130717 0.175571i
\(666\) −9.56119 + 22.6527i −0.370488 + 0.877776i
\(667\) 13.9807 + 13.9807i 0.541335 + 0.541335i
\(668\) 4.69835 + 2.71259i 0.181785 + 0.104953i
\(669\) −23.0291 39.8875i −0.890355 1.54214i
\(670\) −6.04764 + 31.8779i −0.233641 + 1.23155i
\(671\) 4.05253 15.1242i 0.156446 0.583865i
\(672\) 5.37482i 0.207338i
\(673\) −15.6901 4.20415i −0.604809 0.162058i −0.0565967 0.998397i \(-0.518025\pi\)
−0.548213 + 0.836339i \(0.684692\pi\)
\(674\) 17.5953 17.5953i 0.677744 0.677744i
\(675\) 5.51773 + 12.6803i 0.212378 + 0.488065i
\(676\) 9.64825 0.371087
\(677\) 16.5260 16.5260i 0.635145 0.635145i −0.314209 0.949354i \(-0.601739\pi\)
0.949354 + 0.314209i \(0.101739\pi\)
\(678\) 3.37956 + 12.6127i 0.129791 + 0.484388i
\(679\) 21.1376 + 5.66381i 0.811187 + 0.217357i
\(680\) 1.35992 0.101249i 0.0521505 0.00388273i
\(681\) −5.74652 21.4463i −0.220207 0.821824i
\(682\) −5.89201 + 1.57876i −0.225617 + 0.0604538i
\(683\) −15.8504 + 27.4537i −0.606499 + 1.05049i 0.385314 + 0.922786i \(0.374093\pi\)
−0.991813 + 0.127701i \(0.959240\pi\)
\(684\) 1.04878 3.91412i 0.0401013 0.149660i
\(685\) −13.0175 2.46958i −0.497372 0.0943576i
\(686\) −5.18852 19.3638i −0.198099 0.739314i
\(687\) −0.918548 3.42807i −0.0350448 0.130789i
\(688\) 1.26483 2.19076i 0.0482214 0.0835218i
\(689\) −11.9316 + 11.9316i −0.454556 + 0.454556i
\(690\) 34.2888 + 6.50500i 1.30535 + 0.247641i
\(691\) 37.5818 + 21.6979i 1.42968 + 0.825426i 0.997095 0.0761670i \(-0.0242682\pi\)
0.432585 + 0.901593i \(0.357602\pi\)
\(692\) 2.82502 + 2.82502i 0.107391 + 0.107391i
\(693\) −6.50601 6.50601i −0.247143 0.247143i
\(694\) −12.0147 + 20.8100i −0.456071 + 0.789937i
\(695\) 1.84932 + 24.8390i 0.0701487 + 0.942197i
\(696\) −7.72573 + 4.46045i −0.292843 + 0.169073i
\(697\) 5.33361 0.202025
\(698\) −28.9043 + 16.6879i −1.09404 + 0.631646i
\(699\) 5.98196 3.45369i 0.226259 0.130630i
\(700\) −1.14361 + 10.0622i −0.0432245 + 0.380315i
\(701\) 7.31445 1.95990i 0.276263 0.0740244i −0.118027 0.993010i \(-0.537657\pi\)
0.394290 + 0.918986i \(0.370990\pi\)
\(702\) 9.30714 9.30714i 0.351275 0.351275i
\(703\) −5.64910 + 2.29576i −0.213060 + 0.0865863i
\(704\) 1.12383i 0.0423560i
\(705\) −15.1861 + 31.4953i −0.571943 + 1.18618i
\(706\) 25.7151 14.8466i 0.967799 0.558759i
\(707\) 26.9500 + 7.22122i 1.01356 + 0.271582i
\(708\) 9.30095 + 16.1097i 0.349551 + 0.605440i
\(709\) 22.7969 22.7969i 0.856155 0.856155i −0.134728 0.990883i \(-0.543016\pi\)
0.990883 + 0.134728i \(0.0430159\pi\)
\(710\) 13.1065 8.92658i 0.491879 0.335009i
\(711\) −13.3477 13.3477i −0.500576 0.500576i
\(712\) −13.2615 + 3.55341i −0.496996 + 0.133170i
\(713\) −22.5732 + 22.5732i −0.845374 + 0.845374i
\(714\) −3.27787 −0.122671
\(715\) −5.19414 + 10.7724i −0.194250 + 0.402864i
\(716\) −5.16913 + 19.2915i −0.193179 + 0.720956i
\(717\) 56.2907 2.10221
\(718\) 7.24637 + 4.18369i 0.270432 + 0.156134i
\(719\) −34.5568 19.9514i −1.28875 0.744062i −0.310321 0.950632i \(-0.600437\pi\)
−0.978432 + 0.206570i \(0.933770\pi\)
\(720\) −3.92568 + 8.14167i −0.146301 + 0.303422i
\(721\) 35.2603 + 9.44798i 1.31316 + 0.351861i
\(722\) −15.5842 + 8.99753i −0.579983 + 0.334853i
\(723\) −18.8812 10.9011i −0.702199 0.405415i
\(724\) −5.83408 + 10.1049i −0.216822 + 0.375546i
\(725\) 15.4124 6.70658i 0.572402 0.249076i
\(726\) −18.2711 18.2711i −0.678105 0.678105i
\(727\) 9.28337 + 16.0793i 0.344301 + 0.596347i 0.985227 0.171256i \(-0.0547825\pi\)
−0.640925 + 0.767603i \(0.721449\pi\)
\(728\) 9.31044 2.49472i 0.345068 0.0924606i
\(729\) 41.3692i 1.53219i
\(730\) 16.9354 19.6600i 0.626806 0.727649i
\(731\) −1.33605 0.771369i −0.0494156 0.0285301i
\(732\) 36.9729 1.36656
\(733\) 7.18267 26.8061i 0.265298 0.990106i −0.696770 0.717295i \(-0.745380\pi\)
0.962068 0.272811i \(-0.0879534\pi\)
\(734\) −1.29142 1.29142i −0.0476672 0.0476672i
\(735\) −3.20497 + 16.8939i −0.118217 + 0.623139i
\(736\) 2.94076 + 5.09355i 0.108398 + 0.187751i
\(737\) −4.22066 + 15.7517i −0.155470 + 0.580222i
\(738\) −17.6759 + 30.6156i −0.650660 + 1.12698i
\(739\) 3.93004 0.144569 0.0722845 0.997384i \(-0.476971\pi\)
0.0722845 + 0.997384i \(0.476971\pi\)
\(740\) 13.3343 2.68249i 0.490180 0.0986104i
\(741\) 12.6603 0.465086
\(742\) −3.59065 + 6.21919i −0.131817 + 0.228314i
\(743\) −6.15599 + 22.9745i −0.225841 + 0.842851i 0.756224 + 0.654312i \(0.227042\pi\)
−0.982066 + 0.188539i \(0.939625\pi\)
\(744\) −7.20184 12.4740i −0.264032 0.457317i
\(745\) 1.99929 + 2.93547i 0.0732483 + 0.107547i
\(746\) −23.6118 23.6118i −0.864491 0.864491i
\(747\) −3.73573 + 13.9419i −0.136683 + 0.510109i
\(748\) 0.685377 0.0250599
\(749\) 5.01041 + 2.89276i 0.183077 + 0.105699i
\(750\) 15.8216 25.0989i 0.577724 0.916482i
\(751\) 17.4262i 0.635893i −0.948109 0.317946i \(-0.897007\pi\)
0.948109 0.317946i \(-0.102993\pi\)
\(752\) −5.69169 + 1.52508i −0.207554 + 0.0556141i
\(753\) 25.5395 + 44.2357i 0.930711 + 1.61204i
\(754\) −11.3125 11.3125i −0.411975 0.411975i
\(755\) 11.6616 24.1857i 0.424411 0.880206i
\(756\) 2.80087 4.85125i 0.101867 0.176438i
\(757\) −2.28616 1.31992i −0.0830919 0.0479731i 0.457878 0.889015i \(-0.348610\pi\)
−0.540970 + 0.841042i \(0.681943\pi\)
\(758\) 10.4144 6.01276i 0.378268 0.218393i
\(759\) 16.9430 + 4.53985i 0.614991 + 0.164786i
\(760\) −2.11615 + 0.739323i −0.0767610 + 0.0268181i
\(761\) −27.4751 15.8628i −0.995972 0.575025i −0.0889182 0.996039i \(-0.528341\pi\)
−0.907054 + 0.421014i \(0.861674\pi\)
\(762\) 16.4233 + 9.48198i 0.594952 + 0.343496i
\(763\) 33.8226 1.22446
\(764\) 4.94739 18.4639i 0.178990 0.668001i
\(765\) 4.96526 + 2.39411i 0.179519 + 0.0865591i
\(766\) −0.0719996 −0.00260145
\(767\) −23.5887 + 23.5887i −0.851740 + 0.851740i
\(768\) −2.56329 + 0.686833i −0.0924949 + 0.0247839i
\(769\) 16.8239 + 16.8239i 0.606685 + 0.606685i 0.942078 0.335393i \(-0.108869\pi\)
−0.335393 + 0.942078i \(0.608869\pi\)
\(770\) −0.948664 + 5.00054i −0.0341875 + 0.180207i
\(771\) −13.0205 + 13.0205i −0.468921 + 0.468921i
\(772\) −6.40923 11.1011i −0.230673 0.399538i
\(773\) −5.03647 1.34952i −0.181149 0.0485388i 0.167104 0.985939i \(-0.446558\pi\)
−0.348253 + 0.937400i \(0.613225\pi\)
\(774\) 8.85552 5.11274i 0.318305 0.183774i
\(775\) 10.8284 + 24.8848i 0.388969 + 0.893888i
\(776\) 10.8045i 0.387858i
\(777\) −32.4419 + 4.05036i −1.16385 + 0.145306i
\(778\) −13.6028 + 13.6028i −0.487684 + 0.487684i
\(779\) −8.46850 + 2.26913i −0.303416 + 0.0813000i
\(780\) −27.7446 5.26350i −0.993418 0.188463i
\(781\) 6.90217 3.98497i 0.246979 0.142593i
\(782\) 3.10634 1.79345i 0.111082 0.0641335i
\(783\) −9.29754 −0.332267
\(784\) −2.50956 + 1.44889i −0.0896271 + 0.0517462i
\(785\) 10.6800 12.3982i 0.381185 0.442511i
\(786\) 26.9515 46.6814i 0.961328 1.66507i
\(787\) 18.5831 + 18.5831i 0.662417 + 0.662417i 0.955949 0.293532i \(-0.0948307\pi\)
−0.293532 + 0.955949i \(0.594831\pi\)
\(788\) 0.602358 + 0.602358i 0.0214581 + 0.0214581i
\(789\) 72.0014 + 41.5700i 2.56332 + 1.47993i
\(790\) −1.94627 + 10.2591i −0.0692451 + 0.365001i
\(791\) −7.04699 + 7.04699i −0.250562 + 0.250562i
\(792\) −2.27139 + 3.93416i −0.0807102 + 0.139794i
\(793\) 17.1610 + 64.0457i 0.609405 + 2.27433i
\(794\) 3.65714 + 13.6486i 0.129787 + 0.484372i
\(795\) 17.3893 11.8435i 0.616737 0.420046i
\(796\) −4.12933 + 15.4109i −0.146360 + 0.546223i
\(797\) 7.44208 12.8901i 0.263612 0.456590i −0.703587 0.710609i \(-0.748419\pi\)
0.967199 + 0.254020i \(0.0817528\pi\)
\(798\) 5.20449 1.39454i 0.184237 0.0493661i
\(799\) 0.930083 + 3.47112i 0.0329040 + 0.122799i
\(800\) 4.94487 0.740419i 0.174828 0.0261778i
\(801\) −53.6059 14.3637i −1.89407 0.507515i
\(802\) 8.28652 + 30.9257i 0.292607 + 1.09202i
\(803\) 9.22173 9.22173i 0.325428 0.325428i
\(804\) −38.5068 −1.35803
\(805\) 8.78543 + 25.1464i 0.309646 + 0.886294i
\(806\) 18.2651 18.2651i 0.643359 0.643359i
\(807\) 44.4751 + 11.9171i 1.56560 + 0.419501i
\(808\) 13.7754i 0.484618i
\(809\) −2.88353 + 10.7615i −0.101380 + 0.378354i −0.997909 0.0646299i \(-0.979413\pi\)
0.896530 + 0.442984i \(0.146080\pi\)
\(810\) 8.84725 6.02568i 0.310861 0.211721i
\(811\) 9.76382 + 16.9114i 0.342854 + 0.593841i 0.984962 0.172774i \(-0.0552730\pi\)
−0.642107 + 0.766615i \(0.721940\pi\)
\(812\) −5.89650 3.40434i −0.206926 0.119469i
\(813\) 31.7334 + 31.7334i 1.11294 + 1.11294i
\(814\) 6.78334 0.846898i 0.237756 0.0296838i
\(815\) −9.31415 + 0.693460i −0.326260 + 0.0242908i
\(816\) 0.418870 + 1.56324i 0.0146634 + 0.0547245i
\(817\) 2.44950 + 0.656342i 0.0856972 + 0.0229625i
\(818\) −5.73477 + 21.4024i −0.200511 + 0.748319i
\(819\) 37.6348 + 10.0842i 1.31507 + 0.352371i
\(820\) 19.5019 1.45196i 0.681036 0.0507047i
\(821\) 23.9527 + 41.4873i 0.835955 + 1.44792i 0.893251 + 0.449559i \(0.148419\pi\)
−0.0572956 + 0.998357i \(0.518248\pi\)
\(822\) 15.7244i 0.548452i
\(823\) 13.0529 + 48.7140i 0.454994 + 1.69806i 0.688104 + 0.725612i \(0.258443\pi\)
−0.233110 + 0.972450i \(0.574890\pi\)
\(824\) 18.0233i 0.627871i
\(825\) 8.86647 11.9893i 0.308691 0.417414i
\(826\) −7.09874 + 12.2954i −0.246997 + 0.427811i
\(827\) −44.1318 + 25.4795i −1.53461 + 0.886009i −0.535472 + 0.844553i \(0.679866\pi\)
−0.999140 + 0.0414556i \(0.986801\pi\)
\(828\) 23.7744i 0.826218i
\(829\) −42.8774 + 11.4890i −1.48919 + 0.399028i −0.909465 0.415781i \(-0.863508\pi\)
−0.579730 + 0.814809i \(0.696842\pi\)
\(830\) 7.53766 2.63344i 0.261636 0.0914081i
\(831\) −61.4254 + 16.4589i −2.13082 + 0.570952i
\(832\) −2.37951 4.12143i −0.0824946 0.142885i
\(833\) 0.883620 + 1.53047i 0.0306156 + 0.0530278i
\(834\) −28.5528 + 7.65069i −0.988701 + 0.264922i
\(835\) 5.26877 10.9272i 0.182333 0.378150i
\(836\) −1.08822 + 0.291587i −0.0376367 + 0.0100847i
\(837\) 15.0118i 0.518884i
\(838\) −0.594991 + 0.343518i −0.0205536 + 0.0118666i
\(839\) 5.28192 9.14855i 0.182352 0.315843i −0.760329 0.649538i \(-0.774962\pi\)
0.942681 + 0.333695i \(0.108296\pi\)
\(840\) −11.9853 + 0.892332i −0.413532 + 0.0307884i
\(841\) 17.6992i 0.610318i
\(842\) −8.04071 30.0083i −0.277101 1.03416i
\(843\) 63.3870i 2.18317i
\(844\) 4.19484 + 7.26568i 0.144392 + 0.250095i
\(845\) −1.60181 21.5146i −0.0551040 0.740125i
\(846\) −23.0070 6.16472i −0.790999 0.211947i
\(847\) 5.10423 19.0493i 0.175384 0.654540i
\(848\) 3.42482 + 0.917679i 0.117609 + 0.0315132i
\(849\) 3.71624 + 13.8692i 0.127541 + 0.475990i
\(850\) −0.451550 3.01567i −0.0154880 0.103437i
\(851\) 28.5281 21.5886i 0.977929 0.740046i
\(852\) 13.3074 + 13.3074i 0.455904 + 0.455904i
\(853\) −41.4433 23.9273i −1.41899 0.819255i −0.422782 0.906232i \(-0.638946\pi\)
−0.996210 + 0.0869761i \(0.972280\pi\)
\(854\) 14.1094 + 24.4382i 0.482813 + 0.836256i
\(855\) −8.90220 1.68886i −0.304449 0.0577576i
\(856\) 0.739316 2.75917i 0.0252693 0.0943064i
\(857\) 55.7201i 1.90336i −0.307086 0.951682i \(-0.599354\pi\)
0.307086 0.951682i \(-0.400646\pi\)
\(858\) −13.7094 3.67341i −0.468030 0.125408i
\(859\) 1.81741 1.81741i 0.0620093 0.0620093i −0.675422 0.737431i \(-0.736039\pi\)
0.737431 + 0.675422i \(0.236039\pi\)
\(860\) −5.09515 2.45674i −0.173743 0.0837741i
\(861\) −47.0063 −1.60197
\(862\) 18.9260 18.9260i 0.644622 0.644622i
\(863\) −9.45286 35.2786i −0.321779 1.20090i −0.917510 0.397712i \(-0.869804\pi\)
0.595731 0.803184i \(-0.296862\pi\)
\(864\) −2.67152 0.715830i −0.0908868 0.0243530i
\(865\) 5.83050 6.76853i 0.198243 0.230137i
\(866\) −5.58975 20.8612i −0.189947 0.708893i
\(867\) −42.6227 + 11.4207i −1.44754 + 0.387868i
\(868\) 5.49665 9.52047i 0.186568 0.323146i
\(869\) −1.35831 + 5.06927i −0.0460774 + 0.171963i
\(870\) 11.2290 + 16.4871i 0.380698 + 0.558964i
\(871\) −17.8730 66.7028i −0.605603 2.26014i
\(872\) −4.32210 16.1303i −0.146365 0.546240i
\(873\) 21.8370 37.8228i 0.739071 1.28011i
\(874\) −4.16913 + 4.16913i −0.141023 + 0.141023i
\(875\) 22.6275 + 0.879606i 0.764948 + 0.0297361i
\(876\) 26.6693 + 15.3975i 0.901072 + 0.520234i
\(877\) 11.8338 + 11.8338i 0.399598 + 0.399598i 0.878091 0.478493i \(-0.158817\pi\)
−0.478493 + 0.878091i \(0.658817\pi\)
\(878\) 19.6025 + 19.6025i 0.661552 + 0.661552i
\(879\) 5.52053 9.56184i 0.186203 0.322513i
\(880\) 2.50603 0.186579i 0.0844781 0.00628959i
\(881\) −2.66244 + 1.53716i −0.0897000 + 0.0517883i −0.544179 0.838969i \(-0.683159\pi\)
0.454479 + 0.890757i \(0.349825\pi\)
\(882\) −11.7135 −0.394414
\(883\) 19.3218 11.1555i 0.650231 0.375411i −0.138314 0.990388i \(-0.544168\pi\)
0.788545 + 0.614978i \(0.210835\pi\)
\(884\) −2.51349 + 1.45116i −0.0845377 + 0.0488079i
\(885\) 34.3788 23.4147i 1.15563 0.787077i
\(886\) 1.35916 0.364187i 0.0456620 0.0122351i
\(887\) 23.8478 23.8478i 0.800731 0.800731i −0.182479 0.983210i \(-0.558412\pi\)
0.983210 + 0.182479i \(0.0584121\pi\)
\(888\) 6.07731 + 14.9542i 0.203941 + 0.501831i
\(889\) 14.4738i 0.485436i
\(890\) 10.1254 + 28.9818i 0.339405 + 0.971473i
\(891\) 4.65914 2.68996i 0.156087 0.0901170i
\(892\) −16.7647 4.49208i −0.561323 0.150406i
\(893\) −2.95350 5.11562i −0.0988352 0.171188i
\(894\) −2.98047 + 2.98047i −0.0996817 + 0.0996817i
\(895\) 43.8761 + 8.32384i 1.46662 + 0.278235i
\(896\) −1.43217 1.43217i −0.0478454 0.0478454i
\(897\) −71.7473 + 19.2246i −2.39557 + 0.641892i
\(898\) 15.1334 15.1334i 0.505007 0.505007i
\(899\) −18.2462 −0.608546
\(900\) 18.8068 + 7.40217i 0.626894 + 0.246739i
\(901\) 0.559654 2.08866i 0.0186448 0.0695832i
\(902\) 9.82865 0.327258
\(903\) 11.7749 + 6.79825i 0.391845 + 0.226232i
\(904\) 4.26128 + 2.46025i 0.141728 + 0.0818267i
\(905\) 23.5015 + 11.3318i 0.781216 + 0.376680i
\(906\) 30.7796 + 8.24737i 1.02258 + 0.274001i
\(907\) −5.91862 + 3.41712i −0.196525 + 0.113463i −0.595033 0.803701i \(-0.702861\pi\)
0.398509 + 0.917164i \(0.369528\pi\)
\(908\) −7.24577 4.18335i −0.240459 0.138829i
\(909\) 27.8417 48.2232i 0.923450 1.59946i
\(910\) −7.10870 20.3471i −0.235651 0.674501i
\(911\) 27.5788 + 27.5788i 0.913726 + 0.913726i 0.996563 0.0828368i \(-0.0263980\pi\)
−0.0828368 + 0.996563i \(0.526398\pi\)
\(912\) −1.33013 2.30386i −0.0440451 0.0762884i
\(913\) 3.87618 1.03862i 0.128283 0.0343733i
\(914\) 16.0569i 0.531114i
\(915\) −6.13828 82.4457i −0.202925 2.72557i
\(916\) −1.15819 0.668684i −0.0382678 0.0220939i
\(917\) 41.1403 1.35857
\(918\) −0.436555 + 1.62924i −0.0144084 + 0.0537731i
\(919\) −10.4313 10.4313i −0.344098 0.344098i 0.513808 0.857905i \(-0.328235\pi\)
−0.857905 + 0.513808i \(0.828235\pi\)
\(920\) 10.8699 7.40323i 0.358369 0.244077i
\(921\) −35.9158 62.2080i −1.18347 2.04982i
\(922\) −2.48839 + 9.28681i −0.0819509 + 0.305845i
\(923\) −16.8749 + 29.2282i −0.555444 + 0.962057i
\(924\) −6.04039 −0.198714
\(925\) −8.19546 29.2888i −0.269465 0.963010i
\(926\) 15.3434 0.504216
\(927\) 36.4270 63.0934i 1.19642 2.07226i
\(928\) −0.870063 + 3.24712i −0.0285612 + 0.106592i
\(929\) −2.69845 4.67386i −0.0885333 0.153344i 0.818358 0.574709i \(-0.194885\pi\)
−0.906891 + 0.421364i \(0.861551\pi\)
\(930\) −26.6200 + 18.1303i −0.872903 + 0.594516i
\(931\) −2.05410 2.05410i −0.0673205 0.0673205i
\(932\) 0.673681 2.51421i 0.0220672 0.0823558i
\(933\) −15.6590 −0.512653
\(934\) −3.41474 1.97150i −0.111734 0.0645094i
\(935\) −0.113787 1.52832i −0.00372123 0.0499814i
\(936\) 19.2370i 0.628781i
\(937\) −33.8072 + 9.05860i −1.10443 + 0.295932i −0.764568 0.644543i \(-0.777048\pi\)
−0.339864 + 0.940475i \(0.610381\pi\)
\(938\) −14.6947 25.4521i −0.479801 0.831039i
\(939\) −55.5548 55.5548i −1.81296 1.81296i
\(940\) 4.34572 + 12.4387i 0.141742 + 0.405705i
\(941\) −4.99991 + 8.66010i −0.162992 + 0.282311i −0.935941 0.352158i \(-0.885448\pi\)
0.772948 + 0.634469i \(0.218781\pi\)
\(942\) 16.8185 + 9.71017i 0.547976 + 0.316374i
\(943\) 44.5465 25.7189i 1.45063 0.837523i
\(944\) 6.77090 + 1.81426i 0.220374 + 0.0590490i
\(945\) −11.2828 5.44024i −0.367029 0.176971i
\(946\) −2.46204 1.42146i −0.0800479 0.0462157i
\(947\) −25.6738 14.8228i −0.834287 0.481676i 0.0210312 0.999779i \(-0.493305\pi\)
−0.855318 + 0.518103i \(0.826638\pi\)
\(948\) −12.3924 −0.402486
\(949\) −14.2935 + 53.3442i −0.463988 + 1.73163i
\(950\) 1.99994 + 4.59606i 0.0648866 + 0.149116i
\(951\) 26.2119 0.849978
\(952\) −0.873419 + 0.873419i −0.0283077 + 0.0283077i
\(953\) −57.8810 + 15.5092i −1.87495 + 0.502391i −0.875119 + 0.483907i \(0.839217\pi\)
−0.999829 + 0.0184834i \(0.994116\pi\)
\(954\) 10.1344 + 10.1344i 0.328114 + 0.328114i
\(955\) −41.9940 7.96677i −1.35889 0.257799i
\(956\) 14.9992 14.9992i 0.485107 0.485107i
\(957\) 5.01280 + 8.68242i 0.162041 + 0.280663i
\(958\) −14.2441 3.81670i −0.460206 0.123312i
\(959\) 10.3934 6.00066i 0.335622 0.193771i
\(960\) 1.95713 + 5.60185i 0.0631660 + 0.180799i
\(961\) 1.53967i 0.0496668i
\(962\) −23.0834 + 17.4683i −0.744239 + 0.563201i
\(963\) 8.16468 8.16468i 0.263103 0.263103i
\(964\) −7.93574 + 2.12638i −0.255593 + 0.0684860i
\(965\) −23.6903 + 16.1349i −0.762617 + 0.519402i
\(966\) −27.3769 + 15.8061i −0.880837 + 0.508552i
\(967\) −11.8792 + 6.85847i −0.382010 + 0.220553i −0.678692 0.734423i \(-0.737453\pi\)
0.296683 + 0.954976i \(0.404120\pi\)
\(968\) −9.73700 −0.312959
\(969\) −1.40503 + 0.811192i −0.0451359 + 0.0260592i
\(970\) −24.0928 + 1.79377i −0.773574 + 0.0575944i
\(971\) 13.3529 23.1279i 0.428516 0.742211i −0.568226 0.822873i \(-0.692370\pi\)
0.996742 + 0.0806615i \(0.0257033\pi\)
\(972\) 14.8499 + 14.8499i 0.476311 + 0.476311i
\(973\) −15.9530 15.9530i −0.511431 0.511431i
\(974\) −35.1142 20.2732i −1.12513 0.649595i
\(975\) −7.13086 + 62.7415i −0.228370 + 2.00934i
\(976\) 9.85176 9.85176i 0.315347 0.315347i
\(977\) −9.32041 + 16.1434i −0.298186 + 0.516474i −0.975721 0.219017i \(-0.929715\pi\)
0.677535 + 0.735491i \(0.263048\pi\)
\(978\) −2.86886 10.7067i −0.0917360 0.342364i
\(979\) 3.99343 + 14.9037i 0.127631 + 0.476324i
\(980\) 3.64752 + 5.35551i 0.116516 + 0.171075i
\(981\) 17.4709 65.2022i 0.557802 2.08174i
\(982\) −1.01352 + 1.75547i −0.0323427 + 0.0560192i
\(983\) 1.56521 0.419397i 0.0499225 0.0133767i −0.233771 0.972292i \(-0.575107\pi\)
0.283694 + 0.958915i \(0.408440\pi\)
\(984\) 6.00681 + 22.4177i 0.191490 + 0.714650i
\(985\) 1.24319 1.44320i 0.0396114 0.0459841i
\(986\) 1.98028 + 0.530614i 0.0630650 + 0.0168982i
\(987\) −8.19704 30.5918i −0.260915 0.973747i
\(988\) 3.37344 3.37344i 0.107323 0.107323i
\(989\) −14.8783 −0.473103
\(990\) 9.14986 + 4.41180i 0.290802 + 0.140216i
\(991\) −14.0976 + 14.0976i −0.447824 + 0.447824i −0.894630 0.446807i \(-0.852561\pi\)
0.446807 + 0.894630i \(0.352561\pi\)
\(992\) −5.24279 1.40480i −0.166459 0.0446025i
\(993\) 14.2546i 0.452357i
\(994\) −3.71757 + 13.8742i −0.117914 + 0.440061i
\(995\) 35.0502 + 6.64944i 1.11116 + 0.210802i
\(996\) 4.73788 + 8.20625i 0.150126 + 0.260025i
\(997\) 15.2117 + 8.78251i 0.481761 + 0.278145i 0.721150 0.692779i \(-0.243614\pi\)
−0.239389 + 0.970924i \(0.576947\pi\)
\(998\) 27.4226 + 27.4226i 0.868049 + 0.868049i
\(999\) −2.30748 + 16.6644i −0.0730054 + 0.527240i
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 370.2.q.f.97.8 32
5.3 odd 4 370.2.r.f.23.8 yes 32
37.29 odd 12 370.2.r.f.177.8 yes 32
185.103 even 12 inner 370.2.q.f.103.8 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
370.2.q.f.97.8 32 1.1 even 1 trivial
370.2.q.f.103.8 yes 32 185.103 even 12 inner
370.2.r.f.23.8 yes 32 5.3 odd 4
370.2.r.f.177.8 yes 32 37.29 odd 12