Properties

Label 1050.3.p.f.451.5
Level $1050$
Weight $3$
Character 1050.451
Analytic conductor $28.610$
Analytic rank $0$
Dimension $12$
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] = [1050,3,Mod(451,1050)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1050, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1050.451");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1050.p (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(28.6104277578\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 4 x^{11} + 56 x^{10} + 300 x^{9} + 1007 x^{8} + 12456 x^{7} + 209990 x^{6} - 250384 x^{5} + 4799806 x^{4} + 51487320 x^{3} - 123648876 x^{2} + \cdots + 6882692292 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 451.5
Root \(-4.82374 + 1.03135i\) of defining polynomial
Character \(\chi\) \(=\) 1050.451
Dual form 1050.3.p.f.901.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 + 1.22474i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(-1.72580 - 6.78392i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(0.707107 + 1.22474i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(-1.72580 - 6.78392i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(-9.79066 + 16.9579i) q^{11} +(-3.00000 + 1.73205i) q^{12} +2.16261i q^{13} +(7.08825 - 6.91062i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(16.9975 + 9.81350i) q^{17} +(-2.12132 + 3.67423i) q^{18} +(-19.8410 + 11.4552i) q^{19} +(3.28635 - 11.6705i) q^{21} -27.6922 q^{22} +(-16.2734 - 28.1864i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(-2.64865 + 1.52920i) q^{26} +5.19615i q^{27} +(13.4759 + 3.79475i) q^{28} +27.6922 q^{29} +(-36.3761 - 21.0018i) q^{31} +(2.82843 - 4.89898i) q^{32} +(-29.3720 + 16.9579i) q^{33} +27.7568i q^{34} -6.00000 q^{36} +(30.2280 + 52.3564i) q^{37} +(-28.0594 - 16.2001i) q^{38} +(-1.87288 + 3.24392i) q^{39} -66.3893i q^{41} +(16.6171 - 4.22733i) q^{42} -73.9553 q^{43} +(-19.5813 - 33.9159i) q^{44} +(23.0141 - 39.8615i) q^{46} +(-52.7322 + 30.4450i) q^{47} -6.92820i q^{48} +(-43.0432 + 23.4154i) q^{49} +(16.9975 + 29.4405i) q^{51} +(-3.74576 - 2.16261i) q^{52} +(-46.3119 + 80.2145i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(4.88130 + 19.1878i) q^{56} -39.6819 q^{57} +(19.5813 + 33.9159i) q^{58} +(-24.9434 - 14.4011i) q^{59} +(-72.7954 + 42.0285i) q^{61} -59.4020i q^{62} +(15.0364 - 14.6596i) q^{63} +8.00000 q^{64} +(-41.5383 - 23.9821i) q^{66} +(-1.62591 + 2.81616i) q^{67} +(-33.9950 + 19.6270i) q^{68} -56.3727i q^{69} -38.9302 q^{71} +(-4.24264 - 7.34847i) q^{72} +(30.5285 + 17.6257i) q^{73} +(-42.7488 + 74.0432i) q^{74} -45.8208i q^{76} +(131.938 + 37.1531i) q^{77} -5.29730 q^{78} +(-10.7857 - 18.6813i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(81.3099 - 46.9443i) q^{82} -40.3650i q^{83} +(16.9275 + 17.3626i) q^{84} +(-52.2943 - 90.5764i) q^{86} +(41.5383 + 23.9821i) q^{87} +(27.6922 - 47.9643i) q^{88} +(42.1123 - 24.3136i) q^{89} +(14.6710 - 3.73224i) q^{91} +65.0936 q^{92} +(-36.3761 - 63.0053i) q^{93} +(-74.5746 - 43.0557i) q^{94} +(8.48528 - 4.89898i) q^{96} -25.2493i q^{97} +(-59.1141 - 36.1598i) q^{98} -58.7440 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 18 q^{3} - 12 q^{4} + 8 q^{7} + 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 18 q^{3} - 12 q^{4} + 8 q^{7} + 18 q^{9} - 4 q^{11} - 36 q^{12} + 8 q^{14} - 24 q^{16} - 24 q^{17} + 12 q^{19} + 18 q^{21} + 24 q^{22} - 60 q^{23} - 24 q^{26} + 4 q^{28} - 24 q^{29} - 198 q^{31} - 12 q^{33} - 72 q^{36} + 70 q^{37} - 60 q^{38} - 36 q^{39} + 36 q^{42} - 84 q^{43} - 8 q^{44} + 32 q^{46} - 60 q^{47} + 28 q^{49} - 24 q^{51} - 72 q^{52} + 44 q^{53} + 40 q^{56} + 24 q^{57} + 8 q^{58} - 48 q^{59} + 186 q^{61} + 30 q^{63} + 96 q^{64} + 36 q^{66} + 152 q^{67} + 48 q^{68} - 136 q^{71} + 18 q^{73} - 64 q^{74} + 132 q^{77} - 48 q^{78} - 70 q^{79} - 54 q^{81} - 84 q^{82} - 12 q^{84} - 208 q^{86} - 36 q^{87} - 24 q^{88} + 168 q^{89} + 292 q^{91} + 240 q^{92} - 198 q^{93} - 204 q^{94} + 48 q^{98} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 1.22474i 0.353553 + 0.612372i
\(3\) 1.50000 + 0.866025i 0.500000 + 0.288675i
\(4\) −1.00000 + 1.73205i −0.250000 + 0.433013i
\(5\) 0 0
\(6\) 2.44949i 0.408248i
\(7\) −1.72580 6.78392i −0.246543 0.969132i
\(8\) −2.82843 −0.353553
\(9\) 1.50000 + 2.59808i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) −9.79066 + 16.9579i −0.890060 + 1.54163i −0.0502590 + 0.998736i \(0.516005\pi\)
−0.839801 + 0.542894i \(0.817329\pi\)
\(12\) −3.00000 + 1.73205i −0.250000 + 0.144338i
\(13\) 2.16261i 0.166355i 0.996535 + 0.0831775i \(0.0265068\pi\)
−0.996535 + 0.0831775i \(0.973493\pi\)
\(14\) 7.08825 6.91062i 0.506303 0.493616i
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) 16.9975 + 9.81350i 0.999852 + 0.577265i 0.908205 0.418527i \(-0.137453\pi\)
0.0916476 + 0.995792i \(0.470787\pi\)
\(18\) −2.12132 + 3.67423i −0.117851 + 0.204124i
\(19\) −19.8410 + 11.4552i −1.04426 + 0.602905i −0.921037 0.389474i \(-0.872657\pi\)
−0.123224 + 0.992379i \(0.539323\pi\)
\(20\) 0 0
\(21\) 3.28635 11.6705i 0.156493 0.555737i
\(22\) −27.6922 −1.25874
\(23\) −16.2734 28.1864i −0.707539 1.22549i −0.965767 0.259410i \(-0.916472\pi\)
0.258228 0.966084i \(-0.416861\pi\)
\(24\) −4.24264 2.44949i −0.176777 0.102062i
\(25\) 0 0
\(26\) −2.64865 + 1.52920i −0.101871 + 0.0588153i
\(27\) 5.19615i 0.192450i
\(28\) 13.4759 + 3.79475i 0.481282 + 0.135527i
\(29\) 27.6922 0.954903 0.477451 0.878658i \(-0.341561\pi\)
0.477451 + 0.878658i \(0.341561\pi\)
\(30\) 0 0
\(31\) −36.3761 21.0018i −1.17342 0.677477i −0.218940 0.975738i \(-0.570260\pi\)
−0.954484 + 0.298262i \(0.903593\pi\)
\(32\) 2.82843 4.89898i 0.0883883 0.153093i
\(33\) −29.3720 + 16.9579i −0.890060 + 0.513877i
\(34\) 27.7568i 0.816376i
\(35\) 0 0
\(36\) −6.00000 −0.166667
\(37\) 30.2280 + 52.3564i 0.816973 + 1.41504i 0.907902 + 0.419181i \(0.137683\pi\)
−0.0909295 + 0.995857i \(0.528984\pi\)
\(38\) −28.0594 16.2001i −0.738405 0.426318i
\(39\) −1.87288 + 3.24392i −0.0480225 + 0.0831775i
\(40\) 0 0
\(41\) 66.3893i 1.61925i −0.586947 0.809625i \(-0.699670\pi\)
0.586947 0.809625i \(-0.300330\pi\)
\(42\) 16.6171 4.22733i 0.395646 0.100651i
\(43\) −73.9553 −1.71989 −0.859945 0.510386i \(-0.829502\pi\)
−0.859945 + 0.510386i \(0.829502\pi\)
\(44\) −19.5813 33.9159i −0.445030 0.770815i
\(45\) 0 0
\(46\) 23.0141 39.8615i 0.500306 0.866555i
\(47\) −52.7322 + 30.4450i −1.12196 + 0.647765i −0.941901 0.335890i \(-0.890963\pi\)
−0.180061 + 0.983655i \(0.557630\pi\)
\(48\) 6.92820i 0.144338i
\(49\) −43.0432 + 23.4154i −0.878433 + 0.477866i
\(50\) 0 0
\(51\) 16.9975 + 29.4405i 0.333284 + 0.577265i
\(52\) −3.74576 2.16261i −0.0720338 0.0415887i
\(53\) −46.3119 + 80.2145i −0.873809 + 1.51348i −0.0157830 + 0.999875i \(0.505024\pi\)
−0.858026 + 0.513606i \(0.828309\pi\)
\(54\) −6.36396 + 3.67423i −0.117851 + 0.0680414i
\(55\) 0 0
\(56\) 4.88130 + 19.1878i 0.0871662 + 0.342640i
\(57\) −39.6819 −0.696174
\(58\) 19.5813 + 33.9159i 0.337609 + 0.584756i
\(59\) −24.9434 14.4011i −0.422770 0.244086i 0.273492 0.961874i \(-0.411821\pi\)
−0.696262 + 0.717788i \(0.745155\pi\)
\(60\) 0 0
\(61\) −72.7954 + 42.0285i −1.19337 + 0.688991i −0.959069 0.283173i \(-0.908613\pi\)
−0.234299 + 0.972165i \(0.575280\pi\)
\(62\) 59.4020i 0.958097i
\(63\) 15.0364 14.6596i 0.238674 0.232693i
\(64\) 8.00000 0.125000
\(65\) 0 0
\(66\) −41.5383 23.9821i −0.629368 0.363366i
\(67\) −1.62591 + 2.81616i −0.0242673 + 0.0420322i −0.877904 0.478837i \(-0.841059\pi\)
0.853637 + 0.520869i \(0.174392\pi\)
\(68\) −33.9950 + 19.6270i −0.499926 + 0.288632i
\(69\) 56.3727i 0.816996i
\(70\) 0 0
\(71\) −38.9302 −0.548313 −0.274156 0.961685i \(-0.588399\pi\)
−0.274156 + 0.961685i \(0.588399\pi\)
\(72\) −4.24264 7.34847i −0.0589256 0.102062i
\(73\) 30.5285 + 17.6257i 0.418199 + 0.241447i 0.694307 0.719679i \(-0.255711\pi\)
−0.276107 + 0.961127i \(0.589045\pi\)
\(74\) −42.7488 + 74.0432i −0.577687 + 1.00058i
\(75\) 0 0
\(76\) 45.8208i 0.602905i
\(77\) 131.938 + 37.1531i 1.71348 + 0.482508i
\(78\) −5.29730 −0.0679141
\(79\) −10.7857 18.6813i −0.136527 0.236472i 0.789653 0.613554i \(-0.210261\pi\)
−0.926180 + 0.377082i \(0.876927\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.0555556 + 0.0962250i
\(82\) 81.3099 46.9443i 0.991585 0.572492i
\(83\) 40.3650i 0.486325i −0.969986 0.243162i \(-0.921815\pi\)
0.969986 0.243162i \(-0.0781848\pi\)
\(84\) 16.9275 + 17.3626i 0.201518 + 0.206698i
\(85\) 0 0
\(86\) −52.2943 90.5764i −0.608073 1.05321i
\(87\) 41.5383 + 23.9821i 0.477451 + 0.275657i
\(88\) 27.6922 47.9643i 0.314684 0.545048i
\(89\) 42.1123 24.3136i 0.473172 0.273186i −0.244395 0.969676i \(-0.578589\pi\)
0.717567 + 0.696490i \(0.245256\pi\)
\(90\) 0 0
\(91\) 14.6710 3.73224i 0.161220 0.0410137i
\(92\) 65.0936 0.707539
\(93\) −36.3761 63.0053i −0.391141 0.677477i
\(94\) −74.5746 43.0557i −0.793347 0.458039i
\(95\) 0 0
\(96\) 8.48528 4.89898i 0.0883883 0.0510310i
\(97\) 25.2493i 0.260302i −0.991494 0.130151i \(-0.958454\pi\)
0.991494 0.130151i \(-0.0415462\pi\)
\(98\) −59.1141 36.1598i −0.603205 0.368977i
\(99\) −58.7440 −0.593374
\(100\) 0 0
\(101\) 52.6467 + 30.3956i 0.521255 + 0.300947i 0.737448 0.675404i \(-0.236031\pi\)
−0.216193 + 0.976351i \(0.569364\pi\)
\(102\) −24.0381 + 41.6352i −0.235667 + 0.408188i
\(103\) 37.0217 21.3745i 0.359434 0.207519i −0.309399 0.950932i \(-0.600128\pi\)
0.668832 + 0.743413i \(0.266794\pi\)
\(104\) 6.11680i 0.0588153i
\(105\) 0 0
\(106\) −130.990 −1.23575
\(107\) 76.6488 + 132.760i 0.716343 + 1.24074i 0.962439 + 0.271498i \(0.0875189\pi\)
−0.246096 + 0.969246i \(0.579148\pi\)
\(108\) −9.00000 5.19615i −0.0833333 0.0481125i
\(109\) −28.8885 + 50.0364i −0.265032 + 0.459050i −0.967572 0.252595i \(-0.918716\pi\)
0.702540 + 0.711645i \(0.252049\pi\)
\(110\) 0 0
\(111\) 104.713i 0.943359i
\(112\) −20.0486 + 19.5462i −0.179005 + 0.174520i
\(113\) −149.523 −1.32322 −0.661608 0.749850i \(-0.730126\pi\)
−0.661608 + 0.749850i \(0.730126\pi\)
\(114\) −28.0594 48.6003i −0.246135 0.426318i
\(115\) 0 0
\(116\) −27.6922 + 47.9643i −0.238726 + 0.413485i
\(117\) −5.61864 + 3.24392i −0.0480225 + 0.0277258i
\(118\) 40.7325i 0.345190i
\(119\) 37.2398 132.246i 0.312939 1.11131i
\(120\) 0 0
\(121\) −131.214 227.270i −1.08442 1.87826i
\(122\) −102.948 59.4372i −0.843839 0.487190i
\(123\) 57.4948 99.5839i 0.467437 0.809625i
\(124\) 72.7523 42.0035i 0.586712 0.338738i
\(125\) 0 0
\(126\) 28.5867 + 8.04987i 0.226879 + 0.0638879i
\(127\) 176.212 1.38750 0.693749 0.720217i \(-0.255958\pi\)
0.693749 + 0.720217i \(0.255958\pi\)
\(128\) 5.65685 + 9.79796i 0.0441942 + 0.0765466i
\(129\) −110.933 64.0472i −0.859945 0.496490i
\(130\) 0 0
\(131\) 63.0502 36.4021i 0.481300 0.277878i −0.239658 0.970857i \(-0.577035\pi\)
0.720958 + 0.692979i \(0.243702\pi\)
\(132\) 67.8317i 0.513877i
\(133\) 111.953 + 114.830i 0.841750 + 0.863385i
\(134\) −4.59876 −0.0343191
\(135\) 0 0
\(136\) −48.0762 27.7568i −0.353501 0.204094i
\(137\) 74.7510 129.472i 0.545628 0.945055i −0.452940 0.891541i \(-0.649625\pi\)
0.998567 0.0535134i \(-0.0170420\pi\)
\(138\) 69.0422 39.8615i 0.500306 0.288852i
\(139\) 57.4753i 0.413491i −0.978395 0.206746i \(-0.933713\pi\)
0.978395 0.206746i \(-0.0662873\pi\)
\(140\) 0 0
\(141\) −105.464 −0.747975
\(142\) −27.5278 47.6796i −0.193858 0.335772i
\(143\) −36.6735 21.1734i −0.256458 0.148066i
\(144\) 6.00000 10.3923i 0.0416667 0.0721688i
\(145\) 0 0
\(146\) 49.8529i 0.341458i
\(147\) −84.8432 2.15340i −0.577164 0.0146490i
\(148\) −120.912 −0.816973
\(149\) 12.5813 + 21.7915i 0.0844385 + 0.146252i 0.905152 0.425088i \(-0.139757\pi\)
−0.820713 + 0.571340i \(0.806424\pi\)
\(150\) 0 0
\(151\) −11.1332 + 19.2832i −0.0737296 + 0.127703i −0.900533 0.434787i \(-0.856824\pi\)
0.826804 + 0.562491i \(0.190157\pi\)
\(152\) 56.1187 32.4002i 0.369202 0.213159i
\(153\) 58.8810i 0.384843i
\(154\) 47.7912 + 187.862i 0.310333 + 1.21988i
\(155\) 0 0
\(156\) −3.74576 6.48784i −0.0240113 0.0415887i
\(157\) 242.578 + 140.053i 1.54508 + 0.892054i 0.998506 + 0.0546460i \(0.0174030\pi\)
0.546578 + 0.837408i \(0.315930\pi\)
\(158\) 15.2532 26.4193i 0.0965393 0.167211i
\(159\) −138.936 + 80.2145i −0.873809 + 0.504494i
\(160\) 0 0
\(161\) −163.129 + 159.042i −1.01323 + 0.987836i
\(162\) −12.7279 −0.0785674
\(163\) 66.3200 + 114.870i 0.406871 + 0.704722i 0.994537 0.104382i \(-0.0332864\pi\)
−0.587666 + 0.809104i \(0.699953\pi\)
\(164\) 114.990 + 66.3893i 0.701156 + 0.404813i
\(165\) 0 0
\(166\) 49.4368 28.5423i 0.297812 0.171942i
\(167\) 119.492i 0.715520i 0.933814 + 0.357760i \(0.116459\pi\)
−0.933814 + 0.357760i \(0.883541\pi\)
\(168\) −9.29519 + 33.0091i −0.0553285 + 0.196483i
\(169\) 164.323 0.972326
\(170\) 0 0
\(171\) −59.5229 34.3656i −0.348087 0.200968i
\(172\) 73.9553 128.094i 0.429973 0.744734i
\(173\) 218.340 126.059i 1.26208 0.728664i 0.288606 0.957448i \(-0.406808\pi\)
0.973477 + 0.228784i \(0.0734750\pi\)
\(174\) 67.8317i 0.389837i
\(175\) 0 0
\(176\) 78.3253 0.445030
\(177\) −24.9434 43.2033i −0.140923 0.244086i
\(178\) 59.5558 + 34.3846i 0.334583 + 0.193172i
\(179\) −20.7738 + 35.9814i −0.116055 + 0.201013i −0.918201 0.396115i \(-0.870358\pi\)
0.802146 + 0.597128i \(0.203692\pi\)
\(180\) 0 0
\(181\) 258.208i 1.42656i 0.700878 + 0.713281i \(0.252792\pi\)
−0.700878 + 0.713281i \(0.747208\pi\)
\(182\) 14.9450 + 15.3291i 0.0821155 + 0.0842261i
\(183\) −145.591 −0.795579
\(184\) 46.0281 + 79.7230i 0.250153 + 0.433277i
\(185\) 0 0
\(186\) 51.4436 89.1030i 0.276579 0.479048i
\(187\) −332.833 + 192.161i −1.77986 + 1.02760i
\(188\) 121.780i 0.647765i
\(189\) 35.2503 8.96753i 0.186510 0.0474472i
\(190\) 0 0
\(191\) 45.1850 + 78.2627i 0.236571 + 0.409752i 0.959728 0.280931i \(-0.0906432\pi\)
−0.723157 + 0.690683i \(0.757310\pi\)
\(192\) 12.0000 + 6.92820i 0.0625000 + 0.0360844i
\(193\) −30.4605 + 52.7591i −0.157826 + 0.273363i −0.934085 0.357052i \(-0.883782\pi\)
0.776258 + 0.630415i \(0.217115\pi\)
\(194\) 30.9240 17.8540i 0.159402 0.0920307i
\(195\) 0 0
\(196\) 2.48653 97.9684i 0.0126864 0.499839i
\(197\) −74.1310 −0.376299 −0.188150 0.982140i \(-0.560249\pi\)
−0.188150 + 0.982140i \(0.560249\pi\)
\(198\) −41.5383 71.9464i −0.209789 0.363366i
\(199\) 77.5575 + 44.7778i 0.389736 + 0.225014i 0.682046 0.731309i \(-0.261090\pi\)
−0.292310 + 0.956324i \(0.594424\pi\)
\(200\) 0 0
\(201\) −4.87773 + 2.81616i −0.0242673 + 0.0140107i
\(202\) 85.9717i 0.425603i
\(203\) −47.7912 187.862i −0.235425 0.925427i
\(204\) −67.9899 −0.333284
\(205\) 0 0
\(206\) 52.3565 + 30.2281i 0.254158 + 0.146738i
\(207\) 48.8202 84.5591i 0.235846 0.408498i
\(208\) 7.49151 4.32523i 0.0360169 0.0207944i
\(209\) 448.616i 2.14649i
\(210\) 0 0
\(211\) 69.8647 0.331112 0.165556 0.986200i \(-0.447058\pi\)
0.165556 + 0.986200i \(0.447058\pi\)
\(212\) −92.6238 160.429i −0.436905 0.756741i
\(213\) −58.3953 33.7145i −0.274156 0.158284i
\(214\) −108.398 + 187.750i −0.506531 + 0.877338i
\(215\) 0 0
\(216\) 14.6969i 0.0680414i
\(217\) −79.6964 + 283.018i −0.367265 + 1.30423i
\(218\) −81.7091 −0.374812
\(219\) 30.5285 + 52.8770i 0.139400 + 0.241447i
\(220\) 0 0
\(221\) −21.2228 + 36.7590i −0.0960309 + 0.166330i
\(222\) −128.247 + 74.0432i −0.577687 + 0.333528i
\(223\) 389.679i 1.74744i 0.486430 + 0.873719i \(0.338299\pi\)
−0.486430 + 0.873719i \(0.661701\pi\)
\(224\) −38.1156 10.7332i −0.170159 0.0479159i
\(225\) 0 0
\(226\) −105.729 183.128i −0.467828 0.810301i
\(227\) 6.47172 + 3.73645i 0.0285098 + 0.0164601i 0.514187 0.857678i \(-0.328094\pi\)
−0.485677 + 0.874138i \(0.661427\pi\)
\(228\) 39.6819 68.7311i 0.174044 0.301452i
\(229\) −86.8317 + 50.1323i −0.379178 + 0.218918i −0.677460 0.735559i \(-0.736920\pi\)
0.298283 + 0.954478i \(0.403586\pi\)
\(230\) 0 0
\(231\) 165.732 + 169.991i 0.717452 + 0.735893i
\(232\) −78.3253 −0.337609
\(233\) −169.986 294.424i −0.729552 1.26362i −0.957073 0.289848i \(-0.906395\pi\)
0.227520 0.973773i \(-0.426938\pi\)
\(234\) −7.94595 4.58760i −0.0339571 0.0196051i
\(235\) 0 0
\(236\) 49.8869 28.8022i 0.211385 0.122043i
\(237\) 37.3626i 0.157648i
\(238\) 188.300 47.9027i 0.791176 0.201272i
\(239\) 37.7094 0.157780 0.0788899 0.996883i \(-0.474862\pi\)
0.0788899 + 0.996883i \(0.474862\pi\)
\(240\) 0 0
\(241\) −258.515 149.254i −1.07268 0.619310i −0.143765 0.989612i \(-0.545921\pi\)
−0.928912 + 0.370301i \(0.879254\pi\)
\(242\) 185.565 321.408i 0.766797 1.32813i
\(243\) −13.5000 + 7.79423i −0.0555556 + 0.0320750i
\(244\) 168.114i 0.688991i
\(245\) 0 0
\(246\) 162.620 0.661056
\(247\) −24.7732 42.9084i −0.100296 0.173718i
\(248\) 102.887 + 59.4020i 0.414868 + 0.239524i
\(249\) 34.9571 60.5474i 0.140390 0.243162i
\(250\) 0 0
\(251\) 251.129i 1.00051i −0.865877 0.500257i \(-0.833239\pi\)
0.865877 0.500257i \(-0.166761\pi\)
\(252\) 10.3548 + 40.7035i 0.0410905 + 0.161522i
\(253\) 637.310 2.51901
\(254\) 124.601 + 215.815i 0.490554 + 0.849665i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) −51.6733 + 29.8336i −0.201063 + 0.116084i −0.597151 0.802129i \(-0.703701\pi\)
0.396088 + 0.918213i \(0.370368\pi\)
\(258\) 181.153i 0.702142i
\(259\) 303.014 295.421i 1.16994 1.14062i
\(260\) 0 0
\(261\) 41.5383 + 71.9464i 0.159150 + 0.275657i
\(262\) 89.1665 + 51.4803i 0.340330 + 0.196490i
\(263\) −62.4039 + 108.087i −0.237277 + 0.410976i −0.959932 0.280233i \(-0.909588\pi\)
0.722655 + 0.691209i \(0.242922\pi\)
\(264\) 83.0765 47.9643i 0.314684 0.181683i
\(265\) 0 0
\(266\) −61.4752 + 218.311i −0.231110 + 0.820717i
\(267\) 84.2246 0.315448
\(268\) −3.25182 5.63231i −0.0121336 0.0210161i
\(269\) −180.299 104.096i −0.670257 0.386973i 0.125917 0.992041i \(-0.459813\pi\)
−0.796174 + 0.605068i \(0.793146\pi\)
\(270\) 0 0
\(271\) 17.1857 9.92217i 0.0634159 0.0366132i −0.467957 0.883751i \(-0.655010\pi\)
0.531373 + 0.847138i \(0.321676\pi\)
\(272\) 78.5080i 0.288632i
\(273\) 25.2387 + 7.10710i 0.0924496 + 0.0260333i
\(274\) 211.428 0.771634
\(275\) 0 0
\(276\) 97.6404 + 56.3727i 0.353770 + 0.204249i
\(277\) −43.5077 + 75.3576i −0.157068 + 0.272049i −0.933810 0.357769i \(-0.883537\pi\)
0.776742 + 0.629818i \(0.216871\pi\)
\(278\) 70.3926 40.6412i 0.253211 0.146191i
\(279\) 126.011i 0.451651i
\(280\) 0 0
\(281\) 145.993 0.519549 0.259774 0.965669i \(-0.416352\pi\)
0.259774 + 0.965669i \(0.416352\pi\)
\(282\) −74.5746 129.167i −0.264449 0.458039i
\(283\) 306.352 + 176.873i 1.08252 + 0.624991i 0.931574 0.363551i \(-0.118436\pi\)
0.150943 + 0.988543i \(0.451769\pi\)
\(284\) 38.9302 67.4291i 0.137078 0.237426i
\(285\) 0 0
\(286\) 59.8875i 0.209397i
\(287\) −450.380 + 114.575i −1.56927 + 0.399215i
\(288\) 16.9706 0.0589256
\(289\) 48.1097 + 83.3284i 0.166470 + 0.288334i
\(290\) 0 0
\(291\) 21.8665 37.8740i 0.0751428 0.130151i
\(292\) −61.0571 + 35.2513i −0.209100 + 0.120724i
\(293\) 118.997i 0.406135i 0.979165 + 0.203067i \(0.0650910\pi\)
−0.979165 + 0.203067i \(0.934909\pi\)
\(294\) −57.3558 105.434i −0.195088 0.358619i
\(295\) 0 0
\(296\) −85.4977 148.086i −0.288844 0.500292i
\(297\) −88.1160 50.8738i −0.296687 0.171292i
\(298\) −17.7927 + 30.8179i −0.0597071 + 0.103416i
\(299\) 60.9562 35.1931i 0.203867 0.117703i
\(300\) 0 0
\(301\) 127.632 + 501.707i 0.424027 + 1.66680i
\(302\) −31.4894 −0.104269
\(303\) 52.6467 + 91.1868i 0.173752 + 0.300947i
\(304\) 79.3639 + 45.8208i 0.261065 + 0.150726i
\(305\) 0 0
\(306\) −72.1142 + 41.6352i −0.235667 + 0.136063i
\(307\) 481.700i 1.56905i −0.620095 0.784527i \(-0.712906\pi\)
0.620095 0.784527i \(-0.287094\pi\)
\(308\) −196.289 + 191.370i −0.637302 + 0.621332i
\(309\) 74.0433 0.239622
\(310\) 0 0
\(311\) 498.665 + 287.904i 1.60343 + 0.925738i 0.990795 + 0.135368i \(0.0432216\pi\)
0.612630 + 0.790370i \(0.290112\pi\)
\(312\) 5.29730 9.17519i 0.0169785 0.0294077i
\(313\) −369.168 + 213.139i −1.17945 + 0.680957i −0.955888 0.293733i \(-0.905102\pi\)
−0.223564 + 0.974689i \(0.571769\pi\)
\(314\) 396.128i 1.26156i
\(315\) 0 0
\(316\) 43.1426 0.136527
\(317\) 12.6099 + 21.8410i 0.0397789 + 0.0688990i 0.885229 0.465155i \(-0.154001\pi\)
−0.845451 + 0.534054i \(0.820668\pi\)
\(318\) −196.485 113.440i −0.617876 0.356731i
\(319\) −271.125 + 469.602i −0.849921 + 1.47211i
\(320\) 0 0
\(321\) 265.519i 0.827162i
\(322\) −310.135 87.3325i −0.963153 0.271219i
\(323\) −449.662 −1.39214
\(324\) −9.00000 15.5885i −0.0277778 0.0481125i
\(325\) 0 0
\(326\) −93.7907 + 162.450i −0.287701 + 0.498313i
\(327\) −86.6656 + 50.0364i −0.265032 + 0.153017i
\(328\) 187.777i 0.572492i
\(329\) 297.542 + 305.189i 0.904382 + 0.927627i
\(330\) 0 0
\(331\) 0.955424 + 1.65484i 0.00288648 + 0.00499953i 0.867465 0.497498i \(-0.165748\pi\)
−0.864579 + 0.502498i \(0.832415\pi\)
\(332\) 69.9142 + 40.3650i 0.210585 + 0.121581i
\(333\) −90.6840 + 157.069i −0.272324 + 0.471680i
\(334\) −146.347 + 84.4935i −0.438165 + 0.252975i
\(335\) 0 0
\(336\) −47.0004 + 11.9567i −0.139882 + 0.0355854i
\(337\) −337.622 −1.00184 −0.500922 0.865492i \(-0.667006\pi\)
−0.500922 + 0.865492i \(0.667006\pi\)
\(338\) 116.194 + 201.254i 0.343769 + 0.595426i
\(339\) −224.285 129.491i −0.661608 0.381980i
\(340\) 0 0
\(341\) 712.293 411.243i 2.08884 1.20599i
\(342\) 97.2005i 0.284212i
\(343\) 233.132 + 251.591i 0.679686 + 0.733503i
\(344\) 209.177 0.608073
\(345\) 0 0
\(346\) 308.780 + 178.274i 0.892427 + 0.515243i
\(347\) 148.250 256.776i 0.427232 0.739988i −0.569394 0.822065i \(-0.692822\pi\)
0.996626 + 0.0820768i \(0.0261553\pi\)
\(348\) −83.0765 + 47.9643i −0.238726 + 0.137828i
\(349\) 367.499i 1.05300i 0.850174 + 0.526502i \(0.176497\pi\)
−0.850174 + 0.526502i \(0.823503\pi\)
\(350\) 0 0
\(351\) −11.2373 −0.0320150
\(352\) 55.3844 + 95.9285i 0.157342 + 0.272524i
\(353\) 456.656 + 263.651i 1.29364 + 0.746886i 0.979298 0.202423i \(-0.0648816\pi\)
0.314346 + 0.949309i \(0.398215\pi\)
\(354\) 35.2753 61.0987i 0.0996479 0.172595i
\(355\) 0 0
\(356\) 97.2542i 0.273186i
\(357\) 170.388 166.118i 0.477277 0.465317i
\(358\) −58.7573 −0.164127
\(359\) −294.338 509.809i −0.819884 1.42008i −0.905767 0.423775i \(-0.860705\pi\)
0.0858836 0.996305i \(-0.472629\pi\)
\(360\) 0 0
\(361\) 81.9428 141.929i 0.226988 0.393155i
\(362\) −316.239 + 182.580i −0.873587 + 0.504366i
\(363\) 454.539i 1.25217i
\(364\) −8.20657 + 29.1432i −0.0225455 + 0.0800637i
\(365\) 0 0
\(366\) −102.948 178.312i −0.281280 0.487190i
\(367\) 295.319 + 170.503i 0.804685 + 0.464585i 0.845107 0.534598i \(-0.179537\pi\)
−0.0404219 + 0.999183i \(0.512870\pi\)
\(368\) −65.0936 + 112.745i −0.176885 + 0.306373i
\(369\) 172.484 99.5839i 0.467437 0.269875i
\(370\) 0 0
\(371\) 624.094 + 175.742i 1.68219 + 0.473698i
\(372\) 145.505 0.391141
\(373\) 58.6711 + 101.621i 0.157295 + 0.272443i 0.933892 0.357554i \(-0.116389\pi\)
−0.776597 + 0.629998i \(0.783056\pi\)
\(374\) −470.697 271.757i −1.25855 0.726624i
\(375\) 0 0
\(376\) 149.149 86.1114i 0.396674 0.229020i
\(377\) 59.8875i 0.158853i
\(378\) 35.9087 + 36.8316i 0.0949965 + 0.0974381i
\(379\) −188.135 −0.496398 −0.248199 0.968709i \(-0.579839\pi\)
−0.248199 + 0.968709i \(0.579839\pi\)
\(380\) 0 0
\(381\) 264.318 + 152.604i 0.693749 + 0.400536i
\(382\) −63.9012 + 110.680i −0.167281 + 0.289739i
\(383\) 232.895 134.462i 0.608081 0.351076i −0.164133 0.986438i \(-0.552483\pi\)
0.772214 + 0.635363i \(0.219149\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0 0
\(386\) −86.1552 −0.223200
\(387\) −110.933 192.141i −0.286648 0.496490i
\(388\) 43.7331 + 25.2493i 0.112714 + 0.0650755i
\(389\) −148.182 + 256.658i −0.380930 + 0.659790i −0.991195 0.132407i \(-0.957729\pi\)
0.610265 + 0.792197i \(0.291063\pi\)
\(390\) 0 0
\(391\) 638.796i 1.63375i
\(392\) 121.745 66.2288i 0.310573 0.168951i
\(393\) 126.100 0.320866
\(394\) −52.4185 90.7915i −0.133042 0.230435i
\(395\) 0 0
\(396\) 58.7440 101.748i 0.148343 0.256938i
\(397\) −16.3455 + 9.43705i −0.0411724 + 0.0237709i −0.520445 0.853895i \(-0.674234\pi\)
0.479273 + 0.877666i \(0.340901\pi\)
\(398\) 126.651i 0.318218i
\(399\) 68.4832 + 269.199i 0.171637 + 0.674685i
\(400\) 0 0
\(401\) −171.967 297.856i −0.428845 0.742782i 0.567925 0.823080i \(-0.307746\pi\)
−0.996771 + 0.0802979i \(0.974413\pi\)
\(402\) −6.89815 3.98265i −0.0171596 0.00990708i
\(403\) 45.4187 78.6675i 0.112702 0.195205i
\(404\) −105.293 + 60.7912i −0.260627 + 0.150473i
\(405\) 0 0
\(406\) 196.289 191.370i 0.483471 0.471355i
\(407\) −1183.81 −2.90862
\(408\) −48.0762 83.2703i −0.117834 0.204094i
\(409\) 376.358 + 217.291i 0.920192 + 0.531273i 0.883696 0.468061i \(-0.155047\pi\)
0.0364954 + 0.999334i \(0.488381\pi\)
\(410\) 0 0
\(411\) 224.253 129.472i 0.545628 0.315018i
\(412\) 85.4978i 0.207519i
\(413\) −54.6485 + 194.068i −0.132321 + 0.469898i
\(414\) 138.084 0.333537
\(415\) 0 0
\(416\) 10.5946 + 6.11680i 0.0254678 + 0.0147038i
\(417\) 49.7751 86.2129i 0.119365 0.206746i
\(418\) 549.440 317.219i 1.31445 0.758898i
\(419\) 319.236i 0.761899i 0.924596 + 0.380949i \(0.124403\pi\)
−0.924596 + 0.380949i \(0.875597\pi\)
\(420\) 0 0
\(421\) −663.506 −1.57602 −0.788012 0.615660i \(-0.788889\pi\)
−0.788012 + 0.615660i \(0.788889\pi\)
\(422\) 49.4018 + 85.5664i 0.117066 + 0.202764i
\(423\) −158.197 91.3349i −0.373987 0.215922i
\(424\) 130.990 226.881i 0.308938 0.535097i
\(425\) 0 0
\(426\) 95.3591i 0.223848i
\(427\) 410.748 + 421.306i 0.961940 + 0.986665i
\(428\) −306.595 −0.716343
\(429\) −36.6735 63.5203i −0.0854859 0.148066i
\(430\) 0 0
\(431\) 50.5285 87.5179i 0.117235 0.203058i −0.801436 0.598081i \(-0.795930\pi\)
0.918671 + 0.395023i \(0.129263\pi\)
\(432\) 18.0000 10.3923i 0.0416667 0.0240563i
\(433\) 490.183i 1.13206i 0.824384 + 0.566031i \(0.191522\pi\)
−0.824384 + 0.566031i \(0.808478\pi\)
\(434\) −402.978 + 102.516i −0.928522 + 0.236212i
\(435\) 0 0
\(436\) −57.7771 100.073i −0.132516 0.229525i
\(437\) 645.760 + 372.830i 1.47771 + 0.853157i
\(438\) −43.1739 + 74.7793i −0.0985705 + 0.170729i
\(439\) 399.753 230.797i 0.910599 0.525735i 0.0299751 0.999551i \(-0.490457\pi\)
0.880624 + 0.473816i \(0.157124\pi\)
\(440\) 0 0
\(441\) −125.400 76.7064i −0.284353 0.173937i
\(442\) −60.0272 −0.135808
\(443\) −100.023 173.245i −0.225786 0.391073i 0.730769 0.682625i \(-0.239162\pi\)
−0.956555 + 0.291552i \(0.905828\pi\)
\(444\) −181.368 104.713i −0.408487 0.235840i
\(445\) 0 0
\(446\) −477.257 + 275.545i −1.07008 + 0.617813i
\(447\) 43.5830i 0.0975012i
\(448\) −13.8064 54.2714i −0.0308179 0.121141i
\(449\) −75.8015 −0.168823 −0.0844115 0.996431i \(-0.526901\pi\)
−0.0844115 + 0.996431i \(0.526901\pi\)
\(450\) 0 0
\(451\) 1125.82 + 649.995i 2.49629 + 1.44123i
\(452\) 149.523 258.982i 0.330804 0.572970i
\(453\) −33.3995 + 19.2832i −0.0737296 + 0.0425678i
\(454\) 10.5683i 0.0232781i
\(455\) 0 0
\(456\) 112.237 0.246135
\(457\) 205.573 + 356.062i 0.449831 + 0.779129i 0.998375 0.0569922i \(-0.0181510\pi\)
−0.548544 + 0.836122i \(0.684818\pi\)
\(458\) −122.799 70.8978i −0.268119 0.154799i
\(459\) −50.9925 + 88.3215i −0.111095 + 0.192422i
\(460\) 0 0
\(461\) 278.002i 0.603041i 0.953460 + 0.301521i \(0.0974942\pi\)
−0.953460 + 0.301521i \(0.902506\pi\)
\(462\) −91.0061 + 323.181i −0.196983 + 0.699526i
\(463\) −492.573 −1.06387 −0.531936 0.846784i \(-0.678535\pi\)
−0.531936 + 0.846784i \(0.678535\pi\)
\(464\) −55.3844 95.9285i −0.119363 0.206743i
\(465\) 0 0
\(466\) 240.396 416.378i 0.515871 0.893515i
\(467\) −279.726 + 161.500i −0.598985 + 0.345824i −0.768642 0.639679i \(-0.779067\pi\)
0.169657 + 0.985503i \(0.445734\pi\)
\(468\) 12.9757i 0.0277258i
\(469\) 21.9106 + 6.16991i 0.0467177 + 0.0131555i
\(470\) 0 0
\(471\) 242.578 + 420.158i 0.515028 + 0.892054i
\(472\) 70.5507 + 40.7325i 0.149472 + 0.0862976i
\(473\) 724.072 1254.13i 1.53081 2.65143i
\(474\) 45.7597 26.4193i 0.0965393 0.0557370i
\(475\) 0 0
\(476\) 191.817 + 196.747i 0.402976 + 0.413334i
\(477\) −277.871 −0.582539
\(478\) 26.6646 + 46.1844i 0.0557836 + 0.0966200i
\(479\) −267.845 154.641i −0.559176 0.322841i 0.193639 0.981073i \(-0.437971\pi\)
−0.752815 + 0.658232i \(0.771304\pi\)
\(480\) 0 0
\(481\) −113.227 + 65.3715i −0.235399 + 0.135907i
\(482\) 422.154i 0.875837i
\(483\) −382.428 + 97.2881i −0.791777 + 0.201425i
\(484\) 524.857 1.08442
\(485\) 0 0
\(486\) −19.0919 11.0227i −0.0392837 0.0226805i
\(487\) 282.854 489.918i 0.580809 1.00599i −0.414574 0.910015i \(-0.636070\pi\)
0.995384 0.0959758i \(-0.0305971\pi\)
\(488\) 205.897 118.874i 0.421919 0.243595i
\(489\) 229.739i 0.469814i
\(490\) 0 0
\(491\) −379.335 −0.772577 −0.386288 0.922378i \(-0.626243\pi\)
−0.386288 + 0.922378i \(0.626243\pi\)
\(492\) 114.990 + 199.168i 0.233719 + 0.404813i
\(493\) 470.697 + 271.757i 0.954762 + 0.551232i
\(494\) 35.0345 60.6816i 0.0709201 0.122837i
\(495\) 0 0
\(496\) 168.014i 0.338738i
\(497\) 67.1858 + 264.099i 0.135183 + 0.531387i
\(498\) 98.8736 0.198541
\(499\) 271.332 + 469.961i 0.543751 + 0.941805i 0.998684 + 0.0512794i \(0.0163299\pi\)
−0.454933 + 0.890526i \(0.650337\pi\)
\(500\) 0 0
\(501\) −103.483 + 179.238i −0.206553 + 0.357760i
\(502\) 307.569 177.575i 0.612687 0.353735i
\(503\) 281.628i 0.559896i −0.960015 0.279948i \(-0.909683\pi\)
0.960015 0.279948i \(-0.0903173\pi\)
\(504\) −42.5295 + 41.4637i −0.0843839 + 0.0822693i
\(505\) 0 0
\(506\) 450.646 + 780.542i 0.890605 + 1.54257i
\(507\) 246.485 + 142.308i 0.486163 + 0.280686i
\(508\) −176.212 + 305.208i −0.346874 + 0.600804i
\(509\) −8.88432 + 5.12937i −0.0174545 + 0.0100773i −0.508702 0.860943i \(-0.669874\pi\)
0.491247 + 0.871020i \(0.336541\pi\)
\(510\) 0 0
\(511\) 66.8849 237.522i 0.130890 0.464817i
\(512\) −22.6274 −0.0441942
\(513\) −59.5229 103.097i −0.116029 0.200968i
\(514\) −73.0771 42.1911i −0.142173 0.0820838i
\(515\) 0 0
\(516\) 221.866 128.094i 0.429973 0.248245i
\(517\) 1192.31i 2.30620i
\(518\) 576.079 + 162.221i 1.11212 + 0.313168i
\(519\) 436.681 0.841389
\(520\) 0 0
\(521\) −666.970 385.075i −1.28017 0.739108i −0.303292 0.952898i \(-0.598086\pi\)
−0.976880 + 0.213790i \(0.931419\pi\)
\(522\) −58.7440 + 101.748i −0.112536 + 0.194919i
\(523\) −260.981 + 150.678i −0.499008 + 0.288102i −0.728304 0.685254i \(-0.759691\pi\)
0.229296 + 0.973357i \(0.426358\pi\)
\(524\) 145.608i 0.277878i
\(525\) 0 0
\(526\) −176.505 −0.335561
\(527\) −412.202 713.955i −0.782167 1.35475i
\(528\) 117.488 + 67.8317i 0.222515 + 0.128469i
\(529\) −265.147 + 459.248i −0.501223 + 0.868144i
\(530\) 0 0
\(531\) 86.4066i 0.162724i
\(532\) −310.845 + 79.0776i −0.584294 + 0.148642i
\(533\) 143.574 0.269370
\(534\) 59.5558 + 103.154i 0.111528 + 0.193172i
\(535\) 0 0
\(536\) 4.59876 7.96529i 0.00857978 0.0148606i
\(537\) −62.3215 + 35.9814i −0.116055 + 0.0670044i
\(538\) 294.427i 0.547263i
\(539\) 24.3448 959.176i 0.0451666 1.77955i
\(540\) 0 0
\(541\) −488.481 846.074i −0.902922 1.56391i −0.823682 0.567052i \(-0.808084\pi\)
−0.0792400 0.996856i \(-0.525249\pi\)
\(542\) 24.3042 + 14.0321i 0.0448418 + 0.0258894i
\(543\) −223.614 + 387.311i −0.411813 + 0.713281i
\(544\) 96.1523 55.5136i 0.176751 0.102047i
\(545\) 0 0
\(546\) 9.14209 + 35.9365i 0.0167438 + 0.0658177i
\(547\) 231.665 0.423520 0.211760 0.977322i \(-0.432080\pi\)
0.211760 + 0.977322i \(0.432080\pi\)
\(548\) 149.502 + 258.945i 0.272814 + 0.472527i
\(549\) −218.386 126.085i −0.397789 0.229664i
\(550\) 0 0
\(551\) −549.440 + 317.219i −0.997168 + 0.575715i
\(552\) 159.446i 0.288852i
\(553\) −108.119 + 105.409i −0.195513 + 0.190613i
\(554\) −123.058 −0.222127
\(555\) 0 0
\(556\) 99.5501 + 57.4753i 0.179047 + 0.103373i
\(557\) −92.4015 + 160.044i −0.165891 + 0.287332i −0.936971 0.349406i \(-0.886383\pi\)
0.771080 + 0.636738i \(0.219717\pi\)
\(558\) 154.331 89.1030i 0.276579 0.159683i
\(559\) 159.937i 0.286112i
\(560\) 0 0
\(561\) −665.667 −1.18657
\(562\) 103.233 + 178.804i 0.183688 + 0.318157i
\(563\) −35.3570 20.4134i −0.0628011 0.0362582i 0.468271 0.883585i \(-0.344877\pi\)
−0.531072 + 0.847327i \(0.678211\pi\)
\(564\) 105.464 182.670i 0.186994 0.323883i
\(565\) 0 0
\(566\) 500.271i 0.883871i
\(567\) 60.6416 + 17.0764i 0.106952 + 0.0301170i
\(568\) 110.111 0.193858
\(569\) 300.722 + 520.866i 0.528509 + 0.915405i 0.999447 + 0.0332389i \(0.0105822\pi\)
−0.470938 + 0.882166i \(0.656084\pi\)
\(570\) 0 0
\(571\) −434.599 + 752.747i −0.761119 + 1.31830i 0.181156 + 0.983454i \(0.442016\pi\)
−0.942274 + 0.334842i \(0.891317\pi\)
\(572\) 73.3469 42.3469i 0.128229 0.0740330i
\(573\) 156.525i 0.273168i
\(574\) −458.791 470.584i −0.799288 0.819832i
\(575\) 0 0
\(576\) 12.0000 + 20.7846i 0.0208333 + 0.0360844i
\(577\) 54.2326 + 31.3112i 0.0939906 + 0.0542655i 0.546259 0.837617i \(-0.316052\pi\)
−0.452268 + 0.891882i \(0.649385\pi\)
\(578\) −68.0374 + 117.844i −0.117712 + 0.203883i
\(579\) −91.3814 + 52.7591i −0.157826 + 0.0911210i
\(580\) 0 0
\(581\) −273.833 + 69.6619i −0.471313 + 0.119900i
\(582\) 61.8479 0.106268
\(583\) −906.848 1570.71i −1.55549 2.69418i
\(584\) −86.3477 49.8529i −0.147856 0.0853645i
\(585\) 0 0
\(586\) −145.741 + 84.1439i −0.248706 + 0.143590i
\(587\) 112.217i 0.191170i −0.995421 0.0955852i \(-0.969528\pi\)
0.995421 0.0955852i \(-0.0304722\pi\)
\(588\) 88.5730 144.799i 0.150634 0.246257i
\(589\) 962.317 1.63382
\(590\) 0 0
\(591\) −111.196 64.1993i −0.188150 0.108628i
\(592\) 120.912 209.426i 0.204243 0.353760i
\(593\) 449.992 259.803i 0.758841 0.438117i −0.0700388 0.997544i \(-0.522312\pi\)
0.828879 + 0.559427i \(0.188979\pi\)
\(594\) 143.893i 0.242244i
\(595\) 0 0
\(596\) −50.3254 −0.0844385
\(597\) 77.5575 + 134.334i 0.129912 + 0.225014i
\(598\) 86.2051 + 49.7705i 0.144156 + 0.0832283i
\(599\) 123.317 213.591i 0.205871 0.356579i −0.744539 0.667579i \(-0.767331\pi\)
0.950410 + 0.311000i \(0.100664\pi\)
\(600\) 0 0
\(601\) 244.671i 0.407106i −0.979064 0.203553i \(-0.934751\pi\)
0.979064 0.203553i \(-0.0652489\pi\)
\(602\) −524.214 + 511.077i −0.870787 + 0.848966i
\(603\) −9.75545 −0.0161782
\(604\) −22.2663 38.5664i −0.0368648 0.0638517i
\(605\) 0 0
\(606\) −74.4537 + 128.958i −0.122861 + 0.212801i
\(607\) −35.1564 + 20.2975i −0.0579183 + 0.0334391i −0.528680 0.848822i \(-0.677313\pi\)
0.470761 + 0.882261i \(0.343979\pi\)
\(608\) 129.601i 0.213159i
\(609\) 91.0061 323.181i 0.149435 0.530675i
\(610\) 0 0
\(611\) −65.8407 114.039i −0.107759 0.186644i
\(612\) −101.985 58.8810i −0.166642 0.0962108i
\(613\) −54.9828 + 95.2330i −0.0896946 + 0.155356i −0.907382 0.420307i \(-0.861922\pi\)
0.817687 + 0.575662i \(0.195256\pi\)
\(614\) 589.959 340.613i 0.960845 0.554744i
\(615\) 0 0
\(616\) −373.177 105.085i −0.605807 0.170592i
\(617\) 168.842 0.273650 0.136825 0.990595i \(-0.456310\pi\)
0.136825 + 0.990595i \(0.456310\pi\)
\(618\) 52.3565 + 90.6842i 0.0847193 + 0.146738i
\(619\) −607.202 350.568i −0.980940 0.566346i −0.0783859 0.996923i \(-0.524977\pi\)
−0.902554 + 0.430577i \(0.858310\pi\)
\(620\) 0 0
\(621\) 146.461 84.5591i 0.235846 0.136166i
\(622\) 814.317i 1.30919i
\(623\) −237.619 243.726i −0.381411 0.391214i
\(624\) 14.9830 0.0240113
\(625\) 0 0
\(626\) −522.083 301.425i −0.833998 0.481509i
\(627\) 388.513 672.924i 0.619637 1.07324i
\(628\) −485.156 + 280.105i −0.772542 + 0.446027i
\(629\) 1186.57i 1.88644i
\(630\) 0 0
\(631\) −465.556 −0.737807 −0.368903 0.929468i \(-0.620267\pi\)
−0.368903 + 0.929468i \(0.620267\pi\)
\(632\) 30.5064 + 52.8387i 0.0482697 + 0.0836055i
\(633\) 104.797 + 60.5046i 0.165556 + 0.0955838i
\(634\) −17.8331 + 30.8878i −0.0281279 + 0.0487189i
\(635\) 0 0
\(636\) 320.858i 0.504494i
\(637\) −50.6385 93.0859i −0.0794953 0.146132i
\(638\) −766.857 −1.20197
\(639\) −58.3953 101.144i −0.0913854 0.158284i
\(640\) 0 0
\(641\) 615.260 1065.66i 0.959844 1.66250i 0.236973 0.971516i \(-0.423845\pi\)
0.722871 0.690983i \(-0.242822\pi\)
\(642\) −325.193 + 187.750i −0.506531 + 0.292446i
\(643\) 322.975i 0.502293i −0.967949 0.251147i \(-0.919192\pi\)
0.967949 0.251147i \(-0.0808076\pi\)
\(644\) −112.339 441.590i −0.174439 0.685699i
\(645\) 0 0
\(646\) −317.959 550.721i −0.492197 0.852510i
\(647\) 1025.79 + 592.243i 1.58546 + 0.915368i 0.994041 + 0.109006i \(0.0347667\pi\)
0.591422 + 0.806362i \(0.298567\pi\)
\(648\) 12.7279 22.0454i 0.0196419 0.0340207i
\(649\) 488.426 281.993i 0.752582 0.434503i
\(650\) 0 0
\(651\) −364.645 + 355.508i −0.560131 + 0.546095i
\(652\) −265.280 −0.406871
\(653\) −131.660 228.041i −0.201623 0.349221i 0.747429 0.664342i \(-0.231288\pi\)
−0.949052 + 0.315121i \(0.897955\pi\)
\(654\) −122.564 70.7622i −0.187406 0.108199i
\(655\) 0 0
\(656\) −229.979 + 132.779i −0.350578 + 0.202406i
\(657\) 105.754i 0.160965i
\(658\) −163.385 + 580.214i −0.248306 + 0.881784i
\(659\) −1199.70 −1.82049 −0.910246 0.414069i \(-0.864107\pi\)
−0.910246 + 0.414069i \(0.864107\pi\)
\(660\) 0 0
\(661\) 497.702 + 287.349i 0.752954 + 0.434718i 0.826760 0.562555i \(-0.190181\pi\)
−0.0738065 + 0.997273i \(0.523515\pi\)
\(662\) −1.35117 + 2.34030i −0.00204105 + 0.00353520i
\(663\) −63.6685 + 36.7590i −0.0960309 + 0.0554434i
\(664\) 114.169i 0.171942i
\(665\) 0 0
\(666\) −256.493 −0.385125
\(667\) −450.646 780.542i −0.675631 1.17023i
\(668\) −206.966 119.492i −0.309829 0.178880i
\(669\) −337.472 + 584.518i −0.504442 + 0.873719i
\(670\) 0 0
\(671\) 1645.95i 2.45298i
\(672\) −47.8782 49.1088i −0.0712473 0.0730786i
\(673\) 958.817 1.42469 0.712346 0.701829i \(-0.247633\pi\)
0.712346 + 0.701829i \(0.247633\pi\)
\(674\) −238.735 413.500i −0.354206 0.613502i
\(675\) 0 0
\(676\) −164.323 + 284.616i −0.243082 + 0.421030i
\(677\) −394.839 + 227.961i −0.583219 + 0.336722i −0.762412 0.647092i \(-0.775985\pi\)
0.179192 + 0.983814i \(0.442652\pi\)
\(678\) 366.256i 0.540201i
\(679\) −171.289 + 43.5753i −0.252267 + 0.0641757i
\(680\) 0 0
\(681\) 6.47172 + 11.2093i 0.00950325 + 0.0164601i
\(682\) 1007.33 + 581.585i 1.47703 + 0.852764i
\(683\) −115.479 + 200.015i −0.169076 + 0.292848i −0.938095 0.346378i \(-0.887412\pi\)
0.769019 + 0.639225i \(0.220745\pi\)
\(684\) 119.046 68.7311i 0.174044 0.100484i
\(685\) 0 0
\(686\) −143.286 + 463.430i −0.208872 + 0.675554i
\(687\) −173.663 −0.252785
\(688\) 147.911 + 256.189i 0.214986 + 0.372367i
\(689\) −173.473 100.155i −0.251775 0.145362i
\(690\) 0 0
\(691\) −92.1832 + 53.2220i −0.133405 + 0.0770217i −0.565217 0.824942i \(-0.691208\pi\)
0.431812 + 0.901964i \(0.357874\pi\)
\(692\) 504.235i 0.728664i
\(693\) 101.380 + 398.515i 0.146292 + 0.575057i
\(694\) 419.313 0.604198
\(695\) 0 0
\(696\) −117.488 67.8317i −0.168805 0.0974594i
\(697\) 651.511 1128.45i 0.934737 1.61901i
\(698\) −450.092 + 259.861i −0.644831 + 0.372293i
\(699\) 588.848i 0.842414i
\(700\) 0 0
\(701\) −623.489 −0.889429 −0.444714 0.895672i \(-0.646695\pi\)
−0.444714 + 0.895672i \(0.646695\pi\)
\(702\) −7.94595 13.7628i −0.0113190 0.0196051i
\(703\) −1199.51 692.535i −1.70627 0.985114i
\(704\) −78.3253 + 135.663i −0.111258 + 0.192704i
\(705\) 0 0
\(706\) 745.717i 1.05626i
\(707\) 115.344 409.608i 0.163145 0.579361i
\(708\) 99.7737 0.140923
\(709\) −397.184 687.943i −0.560203 0.970300i −0.997478 0.0709721i \(-0.977390\pi\)
0.437275 0.899328i \(-0.355943\pi\)
\(710\) 0 0
\(711\) 32.3570 56.0439i 0.0455091 0.0788240i
\(712\) −119.112 + 68.7691i −0.167292 + 0.0965858i
\(713\) 1367.08i 1.91736i
\(714\) 323.935 + 91.2184i 0.453690 + 0.127757i
\(715\) 0 0
\(716\) −41.5477 71.9627i −0.0580275 0.100507i
\(717\) 56.5641 + 32.6573i 0.0788899 + 0.0455471i
\(718\) 416.257 720.979i 0.579745 1.00415i
\(719\) −33.4178 + 19.2938i −0.0464782 + 0.0268342i −0.523059 0.852296i \(-0.675209\pi\)
0.476581 + 0.879131i \(0.341876\pi\)
\(720\) 0 0
\(721\) −208.895 214.264i −0.289729 0.297176i
\(722\) 231.769 0.321010
\(723\) −258.515 447.761i −0.357559 0.619310i
\(724\) −447.229 258.208i −0.617719 0.356640i
\(725\) 0 0
\(726\) 556.695 321.408i 0.766797 0.442711i
\(727\) 867.980i 1.19392i 0.802271 + 0.596960i \(0.203625\pi\)
−0.802271 + 0.596960i \(0.796375\pi\)
\(728\) −41.4959 + 10.5564i −0.0569998 + 0.0145005i
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) −1257.05 725.761i −1.71964 0.992832i
\(732\) 145.591 252.171i 0.198895 0.344496i
\(733\) −283.830 + 163.869i −0.387217 + 0.223560i −0.680954 0.732327i \(-0.738434\pi\)
0.293737 + 0.955886i \(0.405101\pi\)
\(734\) 482.254i 0.657022i
\(735\) 0 0
\(736\) −184.112 −0.250153
\(737\) −31.8375 55.1441i −0.0431987 0.0748224i
\(738\) 243.930 + 140.833i 0.330528 + 0.190831i
\(739\) −598.500 + 1036.63i −0.809878 + 1.40275i 0.103070 + 0.994674i \(0.467134\pi\)
−0.912948 + 0.408076i \(0.866200\pi\)
\(740\) 0 0
\(741\) 85.8167i 0.115812i
\(742\) 226.062 + 888.625i 0.304666 + 1.19761i
\(743\) 685.246 0.922269 0.461135 0.887330i \(-0.347443\pi\)
0.461135 + 0.887330i \(0.347443\pi\)
\(744\) 102.887 + 178.206i 0.138289 + 0.239524i
\(745\) 0 0
\(746\) −82.9735 + 143.714i −0.111225 + 0.192647i
\(747\) 104.871 60.5474i 0.140390 0.0810541i
\(748\) 768.646i 1.02760i
\(749\) 768.350 749.096i 1.02583 1.00013i
\(750\) 0 0
\(751\) −40.2714 69.7521i −0.0536237 0.0928789i 0.837968 0.545720i \(-0.183744\pi\)
−0.891591 + 0.452841i \(0.850410\pi\)
\(752\) 210.929 + 121.780i 0.280491 + 0.161941i
\(753\) 217.484 376.694i 0.288824 0.500257i
\(754\) −73.3469 + 42.3469i −0.0972771 + 0.0561629i
\(755\) 0 0
\(756\) −19.7181 + 70.0228i −0.0260821 + 0.0926228i
\(757\) −978.106 −1.29208 −0.646041 0.763303i \(-0.723576\pi\)
−0.646041 + 0.763303i \(0.723576\pi\)
\(758\) −133.031 230.417i −0.175503 0.303981i
\(759\) 955.964 + 551.926i 1.25951 + 0.727176i
\(760\) 0 0
\(761\) −514.781 + 297.209i −0.676453 + 0.390550i −0.798517 0.601972i \(-0.794382\pi\)
0.122064 + 0.992522i \(0.461049\pi\)
\(762\) 431.630i 0.566443i
\(763\) 389.299 + 109.625i 0.510221 + 0.143676i
\(764\) −180.740 −0.236571
\(765\) 0 0
\(766\) 329.363 + 190.158i 0.429978 + 0.248248i
\(767\) 31.1440 53.9430i 0.0406050 0.0703299i
\(768\) −24.0000 + 13.8564i −0.0312500 + 0.0180422i
\(769\) 1475.89i 1.91923i −0.281321 0.959614i \(-0.590772\pi\)
0.281321 0.959614i \(-0.409228\pi\)
\(770\) 0 0
\(771\) −103.347 −0.134042
\(772\) −60.9209 105.518i −0.0789131 0.136682i
\(773\) −34.0155 19.6389i −0.0440045 0.0254060i 0.477836 0.878449i \(-0.341421\pi\)
−0.521841 + 0.853043i \(0.674755\pi\)
\(774\) 156.883 271.729i 0.202691 0.351071i
\(775\) 0 0
\(776\) 71.4158i 0.0920307i
\(777\) 710.364 180.714i 0.914239 0.232579i
\(778\) −419.121 −0.538716
\(779\) 760.502 + 1317.23i 0.976254 + 1.69092i
\(780\) 0 0
\(781\) 381.153 660.176i 0.488031 0.845295i
\(782\) 782.362 451.697i 1.00046 0.577618i
\(783\) 143.893i 0.183771i
\(784\) 167.200 + 102.275i 0.213265 + 0.130453i
\(785\) 0 0
\(786\) 89.1665 + 154.441i 0.113443 + 0.196490i
\(787\) −769.456 444.246i −0.977708 0.564480i −0.0761308 0.997098i \(-0.524257\pi\)
−0.901577 + 0.432618i \(0.857590\pi\)
\(788\) 74.1310 128.399i 0.0940749 0.162942i
\(789\) −187.212 + 108.087i −0.237277 + 0.136992i
\(790\) 0 0
\(791\) 258.048 + 1014.36i 0.326230 + 1.28237i
\(792\) 166.153 0.209789
\(793\) −90.8914 157.428i −0.114617 0.198523i
\(794\) −23.1160 13.3460i −0.0291133 0.0168086i
\(795\) 0 0
\(796\) −155.115 + 89.5557i −0.194868 + 0.112507i
\(797\) 340.067i 0.426684i 0.976978 + 0.213342i \(0.0684349\pi\)
−0.976978 + 0.213342i \(0.931565\pi\)
\(798\) −281.275 + 274.227i −0.352476 + 0.343643i
\(799\) −1195.09 −1.49573
\(800\) 0 0
\(801\) 126.337 + 72.9407i 0.157724 + 0.0910620i
\(802\) 243.198 421.231i 0.303240 0.525226i
\(803\) −597.789 + 345.134i −0.744445 + 0.429806i
\(804\) 11.2646i 0.0140107i
\(805\) 0 0
\(806\) 128.464 0.159384
\(807\) −180.299 312.287i −0.223419 0.386973i
\(808\) −148.907 85.9717i −0.184291 0.106401i
\(809\) 17.5840 30.4564i 0.0217355 0.0376470i −0.854953 0.518705i \(-0.826414\pi\)
0.876689 + 0.481058i \(0.159747\pi\)
\(810\) 0 0
\(811\) 1408.87i 1.73720i 0.495511 + 0.868602i \(0.334981\pi\)
−0.495511 + 0.868602i \(0.665019\pi\)
\(812\) 373.177 + 105.085i 0.459578 + 0.129415i
\(813\) 34.3714 0.0422772
\(814\) −837.079 1449.86i −1.02835 1.78116i
\(815\) 0 0
\(816\) 67.9899 117.762i 0.0833210 0.144316i
\(817\) 1467.35 847.172i 1.79602 1.03693i
\(818\) 614.591i 0.751333i
\(819\) 31.7032 + 32.5180i 0.0387096 + 0.0397046i
\(820\) 0 0
\(821\) −218.908 379.160i −0.266636 0.461827i 0.701355 0.712812i \(-0.252579\pi\)
−0.967991 + 0.250985i \(0.919245\pi\)
\(822\) 317.141 + 183.102i 0.385817 + 0.222751i
\(823\) 394.124 682.642i 0.478887 0.829456i −0.520820 0.853666i \(-0.674374\pi\)
0.999707 + 0.0242104i \(0.00770715\pi\)
\(824\) −104.713 + 60.4561i −0.127079 + 0.0733691i
\(825\) 0 0
\(826\) −276.326 + 70.2962i −0.334535 + 0.0851043i
\(827\) −45.9270 −0.0555345 −0.0277673 0.999614i \(-0.508840\pi\)
−0.0277673 + 0.999614i \(0.508840\pi\)
\(828\) 97.6404 + 169.118i 0.117923 + 0.204249i
\(829\) 519.195 + 299.757i 0.626290 + 0.361589i 0.779314 0.626634i \(-0.215568\pi\)
−0.153024 + 0.988223i \(0.548901\pi\)
\(830\) 0 0
\(831\) −130.523 + 75.3576i −0.157068 + 0.0906830i
\(832\) 17.3009i 0.0207944i
\(833\) −961.414 24.4016i −1.15416 0.0292936i
\(834\) 140.785 0.168807
\(835\) 0 0
\(836\) 777.025 + 448.616i 0.929456 + 0.536622i
\(837\) 109.128 189.016i 0.130380 0.225826i
\(838\) −390.982 + 225.734i −0.466566 + 0.269372i
\(839\) 933.368i 1.11248i −0.831023 0.556238i \(-0.812244\pi\)
0.831023 0.556238i \(-0.187756\pi\)
\(840\) 0 0
\(841\) −74.1431 −0.0881606
\(842\) −469.170 812.626i −0.557209 0.965114i
\(843\) 218.990 + 126.434i 0.259774 + 0.149981i
\(844\) −69.8647 + 121.009i −0.0827780 + 0.143376i
\(845\) 0 0
\(846\) 258.334i 0.305359i
\(847\) −1315.33 + 1282.37i −1.55293 + 1.51401i
\(848\) 370.495 0.436905
\(849\) 306.352 + 530.618i 0.360839 + 0.624991i
\(850\) 0 0
\(851\) 983.825 1704.03i 1.15608 2.00239i
\(852\) 116.791 67.4291i 0.137078 0.0791421i
\(853\) 1336.84i 1.56722i −0.621255 0.783608i \(-0.713377\pi\)
0.621255 0.783608i \(-0.286623\pi\)
\(854\) −225.549 + 800.970i −0.264109 + 0.937904i
\(855\) 0 0
\(856\) −216.795 375.501i −0.253266 0.438669i
\(857\) 1045.96 + 603.883i 1.22049 + 0.704647i 0.965021 0.262171i \(-0.0844385\pi\)
0.255464 + 0.966819i \(0.417772\pi\)
\(858\) 51.8641 89.8313i 0.0604477 0.104698i
\(859\) −1377.37 + 795.223i −1.60345 + 0.925755i −0.612665 + 0.790343i \(0.709902\pi\)
−0.990789 + 0.135412i \(0.956764\pi\)
\(860\) 0 0
\(861\) −774.794 218.178i −0.899877 0.253401i
\(862\) 142.916 0.165796
\(863\) −28.9950 50.2209i −0.0335980 0.0581934i 0.848737 0.528814i \(-0.177363\pi\)
−0.882335 + 0.470621i \(0.844030\pi\)
\(864\) 25.4558 + 14.6969i 0.0294628 + 0.0170103i
\(865\) 0 0
\(866\) −600.349 + 346.612i −0.693243 + 0.400244i
\(867\) 166.657i 0.192222i
\(868\) −410.505 421.056i −0.472932 0.485088i
\(869\) 422.395 0.486070
\(870\) 0 0
\(871\) −6.09026 3.51621i −0.00699226 0.00403698i
\(872\) 81.7091 141.524i 0.0937031 0.162299i
\(873\) 65.5996 37.8740i 0.0751428 0.0433837i
\(874\) 1054.52i 1.20655i
\(875\) 0 0
\(876\) −122.114 −0.139400
\(877\) 255.414 + 442.389i 0.291236 + 0.504435i 0.974102 0.226108i \(-0.0726003\pi\)
−0.682867 + 0.730543i \(0.739267\pi\)
\(878\) 565.336 + 326.397i 0.643891 + 0.371750i
\(879\) −103.055 + 178.496i −0.117241 + 0.203067i
\(880\) 0 0
\(881\) 631.045i 0.716282i −0.933667 0.358141i \(-0.883411\pi\)
0.933667 0.358141i \(-0.116589\pi\)
\(882\) 5.27473 207.822i 0.00598042 0.235626i
\(883\) −918.874 −1.04063 −0.520314 0.853975i \(-0.674185\pi\)
−0.520314 + 0.853975i \(0.674185\pi\)
\(884\) −42.4456 73.5180i −0.0480154 0.0831652i
\(885\) 0 0
\(886\) 141.454 245.006i 0.159655 0.276530i
\(887\) 84.1745 48.5981i 0.0948979 0.0547893i −0.451800 0.892119i \(-0.649218\pi\)
0.546698 + 0.837330i \(0.315885\pi\)
\(888\) 296.173i 0.333528i
\(889\) −304.107 1195.41i −0.342078 1.34467i
\(890\) 0 0
\(891\) −88.1160 152.621i −0.0988956 0.171292i
\(892\) −674.944 389.679i −0.756663 0.436860i
\(893\) 697.506 1208.12i 0.781082 1.35287i
\(894\) −53.3781 + 30.8179i −0.0597071 + 0.0344719i
\(895\) 0 0
\(896\) 56.7060 55.2850i 0.0632879 0.0617020i
\(897\) 121.912 0.135911
\(898\) −53.5998 92.8375i −0.0596880 0.103383i
\(899\) −1007.33 581.585i −1.12051 0.646924i
\(900\) 0 0
\(901\) −1574.37 + 908.964i −1.74736 + 1.00884i
\(902\) 1838.46i 2.03821i
\(903\) −243.043 + 863.093i −0.269150 + 0.955806i
\(904\) 422.916 0.467828
\(905\) 0 0
\(906\) −47.2340 27.2706i −0.0521347 0.0301000i
\(907\) 293.890 509.032i 0.324024 0.561226i −0.657291 0.753637i \(-0.728298\pi\)
0.981314 + 0.192412i \(0.0616309\pi\)
\(908\) −12.9434 + 7.47289i −0.0142549 + 0.00823006i
\(909\) 182.374i 0.200631i
\(910\) 0 0
\(911\) −406.902 −0.446654 −0.223327 0.974744i \(-0.571692\pi\)
−0.223327 + 0.974744i \(0.571692\pi\)
\(912\) 79.3639 + 137.462i 0.0870218 + 0.150726i
\(913\) 684.506 + 395.200i 0.749733 + 0.432858i
\(914\) −290.724 + 503.548i −0.318078 + 0.550928i
\(915\) 0 0
\(916\) 200.529i 0.218918i
\(917\) −355.761 364.905i −0.387962 0.397934i
\(918\) −144.228 −0.157112
\(919\) 480.514 + 832.275i 0.522866 + 0.905631i 0.999646 + 0.0266079i \(0.00847057\pi\)
−0.476780 + 0.879023i \(0.658196\pi\)
\(920\) 0 0
\(921\) 417.164 722.549i 0.452947 0.784527i
\(922\) −340.481 + 196.577i −0.369286 + 0.213207i
\(923\) 84.1910i 0.0912145i
\(924\) −460.165 + 117.064i −0.498014 + 0.126693i
\(925\) 0 0
\(926\) −348.302 603.276i −0.376136 0.651486i
\(927\) 111.065 + 64.1234i 0.119811 + 0.0691730i
\(928\) 78.3253 135.663i 0.0844023 0.146189i
\(929\) 1072.91 619.447i 1.15491 0.666789i 0.204832 0.978797i \(-0.434335\pi\)
0.950079 + 0.312009i \(0.101002\pi\)
\(930\) 0 0
\(931\) 585.791 957.653i 0.629206 1.02863i
\(932\) 679.943 0.729552
\(933\) 498.665 + 863.713i 0.534475 + 0.925738i
\(934\) −395.593 228.395i −0.423547 0.244535i
\(935\) 0 0
\(936\) 15.8919 9.17519i 0.0169785 0.00980256i
\(937\) 219.917i 0.234703i 0.993090 + 0.117351i \(0.0374404\pi\)
−0.993090 + 0.117351i \(0.962560\pi\)
\(938\) 7.93656 + 31.1977i 0.00846115 + 0.0332598i
\(939\) −738.337 −0.786301
\(940\) 0 0
\(941\) 1070.33 + 617.954i 1.13744 + 0.656700i 0.945795 0.324765i \(-0.105285\pi\)
0.191642 + 0.981465i \(0.438619\pi\)
\(942\) −343.057 + 594.193i −0.364180 + 0.630778i
\(943\) −1871.27 + 1080.38i −1.98438 + 1.14568i
\(944\) 115.209i 0.122043i
\(945\) 0 0
\(946\) 2047.98 2.16489
\(947\) 288.231 + 499.231i 0.304363 + 0.527172i 0.977119 0.212692i \(-0.0682232\pi\)
−0.672757 + 0.739864i \(0.734890\pi\)
\(948\) 64.7139 + 37.3626i 0.0682636 + 0.0394120i
\(949\) −38.1175 + 66.0214i −0.0401660 + 0.0695695i
\(950\) 0 0
\(951\) 43.6820i 0.0459327i
\(952\) −105.330 + 374.048i −0.110641 + 0.392907i
\(953\) −976.945 −1.02513 −0.512563 0.858650i \(-0.671304\pi\)
−0.512563 + 0.858650i \(0.671304\pi\)
\(954\) −196.485 340.321i −0.205959 0.356731i
\(955\) 0 0
\(956\) −37.7094 + 65.3145i −0.0394449 + 0.0683207i
\(957\) −813.375 + 469.602i −0.849921 + 0.490702i
\(958\) 437.390i 0.456566i
\(959\) −1007.34 283.661i −1.05040 0.295788i
\(960\) 0 0
\(961\) 401.649 + 695.676i 0.417949 + 0.723909i
\(962\) −160.127 92.4493i −0.166452 0.0961011i
\(963\) −229.946 + 398.279i −0.238781 + 0.413581i
\(964\) 517.030 298.508i 0.536339 0.309655i
\(965\) 0 0
\(966\) −389.571 399.584i −0.403282 0.413648i
\(967\) −805.489 −0.832978 −0.416489 0.909141i \(-0.636740\pi\)
−0.416489 + 0.909141i \(0.636740\pi\)
\(968\) 371.130 + 642.816i 0.383399 + 0.664066i
\(969\) −674.493 389.419i −0.696072 0.401877i
\(970\) 0 0
\(971\) 1332.28 769.192i 1.37207 0.792165i 0.380881 0.924624i \(-0.375621\pi\)
0.991188 + 0.132459i \(0.0422873\pi\)
\(972\) 31.1769i 0.0320750i
\(973\) −389.908 + 99.1910i −0.400728 + 0.101943i
\(974\) 800.032 0.821388
\(975\) 0 0
\(976\) 291.182 + 168.114i 0.298342 + 0.172248i
\(977\) 585.004 1013.26i 0.598775 1.03711i −0.394227 0.919013i \(-0.628988\pi\)
0.993002 0.118096i \(-0.0376791\pi\)
\(978\) −281.372 + 162.450i −0.287701 + 0.166104i
\(979\) 952.183i 0.972608i
\(980\) 0 0
\(981\) −173.331 −0.176688
\(982\) −268.230 464.589i −0.273147 0.473105i
\(983\) −383.708 221.534i −0.390344 0.225365i 0.291965 0.956429i \(-0.405691\pi\)
−0.682309 + 0.731064i \(0.739024\pi\)
\(984\) −162.620 + 281.666i −0.165264 + 0.286246i
\(985\) 0 0
\(986\) 768.646i 0.779560i
\(987\) 182.011 + 715.463i 0.184408 + 0.724886i
\(988\) 99.0926 0.100296
\(989\) 1203.50 + 2084.53i 1.21689 + 2.10771i
\(990\) 0 0
\(991\) −72.4829 + 125.544i −0.0731411 + 0.126684i −0.900276 0.435319i \(-0.856636\pi\)
0.827135 + 0.562003i \(0.189969\pi\)
\(992\) −205.775 + 118.804i −0.207434 + 0.119762i
\(993\) 3.30969i 0.00333302i
\(994\) −275.947 + 269.032i −0.277613 + 0.270656i
\(995\) 0 0
\(996\) 69.9142 + 121.095i 0.0701949 + 0.121581i
\(997\) 781.912 + 451.437i 0.784265 + 0.452796i 0.837940 0.545763i \(-0.183760\pi\)
−0.0536748 + 0.998558i \(0.517093\pi\)
\(998\) −383.721 + 664.625i −0.384490 + 0.665957i
\(999\) −272.052 + 157.069i −0.272324 + 0.157227i
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 1050.3.p.f.451.5 yes 12
5.2 odd 4 1050.3.q.d.199.5 24
5.3 odd 4 1050.3.q.d.199.12 24
5.4 even 2 1050.3.p.e.451.2 12
7.5 odd 6 inner 1050.3.p.f.901.5 yes 12
35.12 even 12 1050.3.q.d.649.12 24
35.19 odd 6 1050.3.p.e.901.2 yes 12
35.33 even 12 1050.3.q.d.649.5 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1050.3.p.e.451.2 12 5.4 even 2
1050.3.p.e.901.2 yes 12 35.19 odd 6
1050.3.p.f.451.5 yes 12 1.1 even 1 trivial
1050.3.p.f.901.5 yes 12 7.5 odd 6 inner
1050.3.q.d.199.5 24 5.2 odd 4
1050.3.q.d.199.12 24 5.3 odd 4
1050.3.q.d.649.5 24 35.33 even 12
1050.3.q.d.649.12 24 35.12 even 12