Properties

Label 210.2.d.a.209.5
Level $210$
Weight $2$
Character 210.209
Analytic conductor $1.677$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [210,2,Mod(209,210)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(210, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("210.209");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 210.d (of order \(2\), degree \(1\), 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: \(1.67685844245\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.10070523904.11
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 10x^{4} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 209.5
Root \(0.420861 + 1.68014i\) of defining polynomial
Character \(\chi\) \(=\) 210.209
Dual form 210.2.d.a.209.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +(0.420861 - 1.68014i) q^{3} +1.00000 q^{4} +(-1.95522 - 1.08495i) q^{5} +(-0.420861 + 1.68014i) q^{6} +(-2.37608 - 1.16372i) q^{7} -1.00000 q^{8} +(-2.64575 - 1.41421i) q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(0.420861 - 1.68014i) q^{3} +1.00000 q^{4} +(-1.95522 - 1.08495i) q^{5} +(-0.420861 + 1.68014i) q^{6} +(-2.37608 - 1.16372i) q^{7} -1.00000 q^{8} +(-2.64575 - 1.41421i) q^{9} +(1.95522 + 1.08495i) q^{10} +2.82843i q^{11} +(0.420861 - 1.68014i) q^{12} -0.841723 q^{13} +(2.37608 + 1.16372i) q^{14} +(-2.64575 + 2.82843i) q^{15} +1.00000 q^{16} -1.19038i q^{17} +(2.64575 + 1.41421i) q^{18} -4.55066i q^{19} +(-1.95522 - 1.08495i) q^{20} +(-2.95522 + 3.50238i) q^{21} -2.82843i q^{22} -3.29150 q^{23} +(-0.420861 + 1.68014i) q^{24} +(2.64575 + 4.24264i) q^{25} +0.841723 q^{26} +(-3.48957 + 3.85005i) q^{27} +(-2.37608 - 1.16372i) q^{28} -7.98430i q^{29} +(2.64575 - 2.82843i) q^{30} -5.53019i q^{31} -1.00000 q^{32} +(4.75216 + 1.19038i) q^{33} +1.19038i q^{34} +(3.38317 + 4.85326i) q^{35} +(-2.64575 - 1.41421i) q^{36} -10.8127i q^{37} +4.55066i q^{38} +(-0.354249 + 1.41421i) q^{39} +(1.95522 + 1.08495i) q^{40} +7.82087 q^{41} +(2.95522 - 3.50238i) q^{42} +4.65489i q^{43} +2.82843i q^{44} +(3.63866 + 5.63561i) q^{45} +3.29150 q^{46} +4.33981i q^{47} +(0.420861 - 1.68014i) q^{48} +(4.29150 + 5.53019i) q^{49} +(-2.64575 - 4.24264i) q^{50} +(-2.00000 - 0.500983i) q^{51} -0.841723 q^{52} +12.5830 q^{53} +(3.48957 - 3.85005i) q^{54} +(3.06871 - 5.53019i) q^{55} +(2.37608 + 1.16372i) q^{56} +(-7.64575 - 1.91520i) q^{57} +7.98430i q^{58} -3.91044 q^{59} +(-2.64575 + 2.82843i) q^{60} +10.0808i q^{61} +5.53019i q^{62} +(4.64076 + 6.43920i) q^{63} +1.00000 q^{64} +(1.64575 + 0.913230i) q^{65} +(-4.75216 - 1.19038i) q^{66} -4.65489i q^{67} -1.19038i q^{68} +(-1.38527 + 5.53019i) q^{69} +(-3.38317 - 4.85326i) q^{70} -12.6392i q^{71} +(2.64575 + 1.41421i) q^{72} +3.06871 q^{73} +10.8127i q^{74} +(8.24173 - 2.65967i) q^{75} -4.55066i q^{76} +(3.29150 - 6.72057i) q^{77} +(0.354249 - 1.41421i) q^{78} -7.29150 q^{79} +(-1.95522 - 1.08495i) q^{80} +(5.00000 + 7.48331i) q^{81} -7.82087 q^{82} -7.70010i q^{83} +(-2.95522 + 3.50238i) q^{84} +(-1.29150 + 2.32744i) q^{85} -4.65489i q^{86} +(-13.4148 - 3.36028i) q^{87} -2.82843i q^{88} -12.8712 q^{89} +(-3.63866 - 5.63561i) q^{90} +(2.00000 + 0.979531i) q^{91} -3.29150 q^{92} +(-9.29150 - 2.32744i) q^{93} -4.33981i q^{94} +(-4.93725 + 8.89753i) q^{95} +(-0.420861 + 1.68014i) q^{96} +8.11905 q^{97} +(-4.29150 - 5.53019i) q^{98} +(4.00000 - 7.48331i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} + 8 q^{16} - 8 q^{21} + 16 q^{23} - 8 q^{32} + 16 q^{35} - 24 q^{39} + 8 q^{42} - 16 q^{46} - 8 q^{49} - 16 q^{51} + 16 q^{53} - 40 q^{57} + 8 q^{63} + 8 q^{64} - 8 q^{65} - 16 q^{70} - 16 q^{77} + 24 q^{78} - 16 q^{79} + 40 q^{81} - 8 q^{84} + 32 q^{85} + 16 q^{91} + 16 q^{92} - 32 q^{93} + 24 q^{95} + 8 q^{98} + 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0.420861 1.68014i 0.242984 0.970030i
\(4\) 1.00000 0.500000
\(5\) −1.95522 1.08495i −0.874400 0.485206i
\(6\) −0.420861 + 1.68014i −0.171816 + 0.685915i
\(7\) −2.37608 1.16372i −0.898073 0.439846i
\(8\) −1.00000 −0.353553
\(9\) −2.64575 1.41421i −0.881917 0.471405i
\(10\) 1.95522 + 1.08495i 0.618294 + 0.343092i
\(11\) 2.82843i 0.852803i 0.904534 + 0.426401i \(0.140219\pi\)
−0.904534 + 0.426401i \(0.859781\pi\)
\(12\) 0.420861 1.68014i 0.121492 0.485015i
\(13\) −0.841723 −0.233452 −0.116726 0.993164i \(-0.537240\pi\)
−0.116726 + 0.993164i \(0.537240\pi\)
\(14\) 2.37608 + 1.16372i 0.635034 + 0.311018i
\(15\) −2.64575 + 2.82843i −0.683130 + 0.730297i
\(16\) 1.00000 0.250000
\(17\) 1.19038i 0.288709i −0.989526 0.144354i \(-0.953890\pi\)
0.989526 0.144354i \(-0.0461105\pi\)
\(18\) 2.64575 + 1.41421i 0.623610 + 0.333333i
\(19\) 4.55066i 1.04399i −0.852948 0.521996i \(-0.825187\pi\)
0.852948 0.521996i \(-0.174813\pi\)
\(20\) −1.95522 1.08495i −0.437200 0.242603i
\(21\) −2.95522 + 3.50238i −0.644881 + 0.764283i
\(22\) 2.82843i 0.603023i
\(23\) −3.29150 −0.686326 −0.343163 0.939276i \(-0.611498\pi\)
−0.343163 + 0.939276i \(0.611498\pi\)
\(24\) −0.420861 + 1.68014i −0.0859080 + 0.342957i
\(25\) 2.64575 + 4.24264i 0.529150 + 0.848528i
\(26\) 0.841723 0.165075
\(27\) −3.48957 + 3.85005i −0.671569 + 0.740942i
\(28\) −2.37608 1.16372i −0.449037 0.219923i
\(29\) 7.98430i 1.48265i −0.671148 0.741323i \(-0.734198\pi\)
0.671148 0.741323i \(-0.265802\pi\)
\(30\) 2.64575 2.82843i 0.483046 0.516398i
\(31\) 5.53019i 0.993252i −0.867965 0.496626i \(-0.834572\pi\)
0.867965 0.496626i \(-0.165428\pi\)
\(32\) −1.00000 −0.176777
\(33\) 4.75216 + 1.19038i 0.827245 + 0.207218i
\(34\) 1.19038i 0.204148i
\(35\) 3.38317 + 4.85326i 0.571860 + 0.820352i
\(36\) −2.64575 1.41421i −0.440959 0.235702i
\(37\) 10.8127i 1.77760i −0.458294 0.888801i \(-0.651539\pi\)
0.458294 0.888801i \(-0.348461\pi\)
\(38\) 4.55066i 0.738214i
\(39\) −0.354249 + 1.41421i −0.0567252 + 0.226455i
\(40\) 1.95522 + 1.08495i 0.309147 + 0.171546i
\(41\) 7.82087 1.22141 0.610707 0.791856i \(-0.290885\pi\)
0.610707 + 0.791856i \(0.290885\pi\)
\(42\) 2.95522 3.50238i 0.456000 0.540429i
\(43\) 4.65489i 0.709864i 0.934892 + 0.354932i \(0.115496\pi\)
−0.934892 + 0.354932i \(0.884504\pi\)
\(44\) 2.82843i 0.426401i
\(45\) 3.63866 + 5.63561i 0.542420 + 0.840108i
\(46\) 3.29150 0.485306
\(47\) 4.33981i 0.633027i 0.948588 + 0.316513i \(0.102512\pi\)
−0.948588 + 0.316513i \(0.897488\pi\)
\(48\) 0.420861 1.68014i 0.0607461 0.242508i
\(49\) 4.29150 + 5.53019i 0.613072 + 0.790027i
\(50\) −2.64575 4.24264i −0.374166 0.600000i
\(51\) −2.00000 0.500983i −0.280056 0.0701517i
\(52\) −0.841723 −0.116726
\(53\) 12.5830 1.72841 0.864204 0.503141i \(-0.167822\pi\)
0.864204 + 0.503141i \(0.167822\pi\)
\(54\) 3.48957 3.85005i 0.474871 0.523925i
\(55\) 3.06871 5.53019i 0.413785 0.745691i
\(56\) 2.37608 + 1.16372i 0.317517 + 0.155509i
\(57\) −7.64575 1.91520i −1.01270 0.253674i
\(58\) 7.98430i 1.04839i
\(59\) −3.91044 −0.509095 −0.254548 0.967060i \(-0.581927\pi\)
−0.254548 + 0.967060i \(0.581927\pi\)
\(60\) −2.64575 + 2.82843i −0.341565 + 0.365148i
\(61\) 10.0808i 1.29072i 0.763878 + 0.645360i \(0.223293\pi\)
−0.763878 + 0.645360i \(0.776707\pi\)
\(62\) 5.53019i 0.702335i
\(63\) 4.64076 + 6.43920i 0.584681 + 0.811263i
\(64\) 1.00000 0.125000
\(65\) 1.64575 + 0.913230i 0.204130 + 0.113272i
\(66\) −4.75216 1.19038i −0.584950 0.146525i
\(67\) 4.65489i 0.568685i −0.958723 0.284343i \(-0.908225\pi\)
0.958723 0.284343i \(-0.0917753\pi\)
\(68\) 1.19038i 0.144354i
\(69\) −1.38527 + 5.53019i −0.166766 + 0.665757i
\(70\) −3.38317 4.85326i −0.404366 0.580076i
\(71\) 12.6392i 1.50000i −0.661440 0.749998i \(-0.730055\pi\)
0.661440 0.749998i \(-0.269945\pi\)
\(72\) 2.64575 + 1.41421i 0.311805 + 0.166667i
\(73\) 3.06871 0.359166 0.179583 0.983743i \(-0.442525\pi\)
0.179583 + 0.983743i \(0.442525\pi\)
\(74\) 10.8127i 1.25695i
\(75\) 8.24173 2.65967i 0.951673 0.307113i
\(76\) 4.55066i 0.521996i
\(77\) 3.29150 6.72057i 0.375102 0.765880i
\(78\) 0.354249 1.41421i 0.0401108 0.160128i
\(79\) −7.29150 −0.820358 −0.410179 0.912005i \(-0.634534\pi\)
−0.410179 + 0.912005i \(0.634534\pi\)
\(80\) −1.95522 1.08495i −0.218600 0.121302i
\(81\) 5.00000 + 7.48331i 0.555556 + 0.831479i
\(82\) −7.82087 −0.863671
\(83\) 7.70010i 0.845196i −0.906317 0.422598i \(-0.861118\pi\)
0.906317 0.422598i \(-0.138882\pi\)
\(84\) −2.95522 + 3.50238i −0.322441 + 0.382141i
\(85\) −1.29150 + 2.32744i −0.140083 + 0.252447i
\(86\) 4.65489i 0.501949i
\(87\) −13.4148 3.36028i −1.43821 0.360260i
\(88\) 2.82843i 0.301511i
\(89\) −12.8712 −1.36435 −0.682173 0.731191i \(-0.738965\pi\)
−0.682173 + 0.731191i \(0.738965\pi\)
\(90\) −3.63866 5.63561i −0.383549 0.594046i
\(91\) 2.00000 + 0.979531i 0.209657 + 0.102683i
\(92\) −3.29150 −0.343163
\(93\) −9.29150 2.32744i −0.963484 0.241345i
\(94\) 4.33981i 0.447618i
\(95\) −4.93725 + 8.89753i −0.506552 + 0.912867i
\(96\) −0.420861 + 1.68014i −0.0429540 + 0.171479i
\(97\) 8.11905 0.824365 0.412182 0.911101i \(-0.364767\pi\)
0.412182 + 0.911101i \(0.364767\pi\)
\(98\) −4.29150 5.53019i −0.433507 0.558634i
\(99\) 4.00000 7.48331i 0.402015 0.752101i
\(100\) 2.64575 + 4.24264i 0.264575 + 0.424264i
\(101\) 3.91044 0.389103 0.194551 0.980892i \(-0.437675\pi\)
0.194551 + 0.980892i \(0.437675\pi\)
\(102\) 2.00000 + 0.500983i 0.198030 + 0.0496047i
\(103\) −12.5730 −1.23886 −0.619429 0.785053i \(-0.712636\pi\)
−0.619429 + 0.785053i \(0.712636\pi\)
\(104\) 0.841723 0.0825377
\(105\) 9.57802 3.64165i 0.934719 0.355388i
\(106\) −12.5830 −1.22217
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) −3.48957 + 3.85005i −0.335784 + 0.370471i
\(109\) 2.00000 0.191565 0.0957826 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) −3.06871 + 5.53019i −0.292590 + 0.527283i
\(111\) −18.1669 4.55066i −1.72433 0.431929i
\(112\) −2.37608 1.16372i −0.224518 0.109961i
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 7.64575 + 1.91520i 0.716090 + 0.179375i
\(115\) 6.43560 + 3.57113i 0.600123 + 0.333009i
\(116\) 7.98430i 0.741323i
\(117\) 2.22699 + 1.19038i 0.205885 + 0.110050i
\(118\) 3.91044 0.359985
\(119\) −1.38527 + 2.82843i −0.126987 + 0.259281i
\(120\) 2.64575 2.82843i 0.241523 0.258199i
\(121\) 3.00000 0.272727
\(122\) 10.0808i 0.912677i
\(123\) 3.29150 13.1402i 0.296785 1.18481i
\(124\) 5.53019i 0.496626i
\(125\) −0.569951 11.1658i −0.0509780 0.998700i
\(126\) −4.64076 6.43920i −0.413432 0.573650i
\(127\) 10.8127i 0.959474i 0.877412 + 0.479737i \(0.159268\pi\)
−0.877412 + 0.479737i \(0.840732\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 7.82087 + 1.95906i 0.688589 + 0.172486i
\(130\) −1.64575 0.913230i −0.144342 0.0800956i
\(131\) 8.96077 0.782906 0.391453 0.920198i \(-0.371973\pi\)
0.391453 + 0.920198i \(0.371973\pi\)
\(132\) 4.75216 + 1.19038i 0.413622 + 0.103609i
\(133\) −5.29570 + 10.8127i −0.459196 + 0.937582i
\(134\) 4.65489i 0.402121i
\(135\) 11.0000 3.74166i 0.946729 0.322031i
\(136\) 1.19038i 0.102074i
\(137\) −9.29150 −0.793827 −0.396913 0.917856i \(-0.629919\pi\)
−0.396913 + 0.917856i \(0.629919\pi\)
\(138\) 1.38527 5.53019i 0.117922 0.470761i
\(139\) 15.6110i 1.32411i 0.749455 + 0.662056i \(0.230316\pi\)
−0.749455 + 0.662056i \(0.769684\pi\)
\(140\) 3.38317 + 4.85326i 0.285930 + 0.410176i
\(141\) 7.29150 + 1.82646i 0.614055 + 0.153816i
\(142\) 12.6392i 1.06066i
\(143\) 2.38075i 0.199088i
\(144\) −2.64575 1.41421i −0.220479 0.117851i
\(145\) −8.66259 + 15.6110i −0.719389 + 1.29643i
\(146\) −3.06871 −0.253968
\(147\) 11.0976 4.88289i 0.915317 0.402734i
\(148\) 10.8127i 0.888801i
\(149\) 3.32941i 0.272756i −0.990657 0.136378i \(-0.956454\pi\)
0.990657 0.136378i \(-0.0435462\pi\)
\(150\) −8.24173 + 2.65967i −0.672935 + 0.217161i
\(151\) −22.5830 −1.83778 −0.918889 0.394515i \(-0.870913\pi\)
−0.918889 + 0.394515i \(0.870913\pi\)
\(152\) 4.55066i 0.369107i
\(153\) −1.68345 + 3.14944i −0.136099 + 0.254617i
\(154\) −3.29150 + 6.72057i −0.265237 + 0.541559i
\(155\) −6.00000 + 10.8127i −0.481932 + 0.868499i
\(156\) −0.354249 + 1.41421i −0.0283626 + 0.113228i
\(157\) 22.6209 1.80534 0.902672 0.430330i \(-0.141603\pi\)
0.902672 + 0.430330i \(0.141603\pi\)
\(158\) 7.29150 0.580081
\(159\) 5.29570 21.1412i 0.419976 1.67661i
\(160\) 1.95522 + 1.08495i 0.154574 + 0.0857731i
\(161\) 7.82087 + 3.83039i 0.616371 + 0.301877i
\(162\) −5.00000 7.48331i −0.392837 0.587945i
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 7.82087 0.610707
\(165\) −8.00000 7.48331i −0.622799 0.582575i
\(166\) 7.70010i 0.597643i
\(167\) 11.4821i 0.888509i 0.895901 + 0.444255i \(0.146531\pi\)
−0.895901 + 0.444255i \(0.853469\pi\)
\(168\) 2.95522 3.50238i 0.228000 0.270215i
\(169\) −12.2915 −0.945500
\(170\) 1.29150 2.32744i 0.0990537 0.178507i
\(171\) −6.43560 + 12.0399i −0.492143 + 0.920715i
\(172\) 4.65489i 0.354932i
\(173\) 8.89047i 0.675930i 0.941159 + 0.337965i \(0.109739\pi\)
−0.941159 + 0.337965i \(0.890261\pi\)
\(174\) 13.4148 + 3.36028i 1.01697 + 0.254742i
\(175\) −1.34926 13.1598i −0.101994 0.994785i
\(176\) 2.82843i 0.213201i
\(177\) −1.64575 + 6.57008i −0.123702 + 0.493838i
\(178\) 12.8712 0.964738
\(179\) 9.48725i 0.709110i −0.935035 0.354555i \(-0.884632\pi\)
0.935035 0.354555i \(-0.115368\pi\)
\(180\) 3.63866 + 5.63561i 0.271210 + 0.420054i
\(181\) 12.0399i 0.894920i −0.894304 0.447460i \(-0.852329\pi\)
0.894304 0.447460i \(-0.147671\pi\)
\(182\) −2.00000 0.979531i −0.148250 0.0726077i
\(183\) 16.9373 + 4.24264i 1.25204 + 0.313625i
\(184\) 3.29150 0.242653
\(185\) −11.7313 + 21.1412i −0.862503 + 1.55433i
\(186\) 9.29150 + 2.32744i 0.681286 + 0.170656i
\(187\) 3.36689 0.246211
\(188\) 4.33981i 0.316513i
\(189\) 12.7719 5.08713i 0.929018 0.370034i
\(190\) 4.93725 8.89753i 0.358186 0.645495i
\(191\) 7.98430i 0.577724i −0.957371 0.288862i \(-0.906723\pi\)
0.957371 0.288862i \(-0.0932768\pi\)
\(192\) 0.420861 1.68014i 0.0303731 0.121254i
\(193\) 8.48528i 0.610784i −0.952227 0.305392i \(-0.901213\pi\)
0.952227 0.305392i \(-0.0987875\pi\)
\(194\) −8.11905 −0.582914
\(195\) 2.22699 2.38075i 0.159478 0.170489i
\(196\) 4.29150 + 5.53019i 0.306536 + 0.395014i
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) −4.00000 + 7.48331i −0.284268 + 0.531816i
\(199\) 16.5906i 1.17607i −0.808834 0.588037i \(-0.799901\pi\)
0.808834 0.588037i \(-0.200099\pi\)
\(200\) −2.64575 4.24264i −0.187083 0.300000i
\(201\) −7.82087 1.95906i −0.551642 0.138182i
\(202\) −3.91044 −0.275137
\(203\) −9.29150 + 18.9713i −0.652136 + 1.33153i
\(204\) −2.00000 0.500983i −0.140028 0.0350758i
\(205\) −15.2915 8.48528i −1.06800 0.592638i
\(206\) 12.5730 0.876004
\(207\) 8.70850 + 4.65489i 0.605282 + 0.323537i
\(208\) −0.841723 −0.0583630
\(209\) 12.8712 0.890320
\(210\) −9.57802 + 3.64165i −0.660946 + 0.251298i
\(211\) 21.1660 1.45713 0.728564 0.684978i \(-0.240188\pi\)
0.728564 + 0.684978i \(0.240188\pi\)
\(212\) 12.5830 0.864204
\(213\) −21.2356 5.31935i −1.45504 0.364476i
\(214\) 0 0
\(215\) 5.05034 9.10132i 0.344430 0.620705i
\(216\) 3.48957 3.85005i 0.237435 0.261963i
\(217\) −6.43560 + 13.1402i −0.436877 + 0.892013i
\(218\) −2.00000 −0.135457
\(219\) 1.29150 5.15587i 0.0872717 0.348401i
\(220\) 3.06871 5.53019i 0.206893 0.372845i
\(221\) 1.00197i 0.0673996i
\(222\) 18.1669 + 4.55066i 1.21928 + 0.305420i
\(223\) −4.75216 −0.318228 −0.159114 0.987260i \(-0.550864\pi\)
−0.159114 + 0.987260i \(0.550864\pi\)
\(224\) 2.37608 + 1.16372i 0.158758 + 0.0777544i
\(225\) −1.00000 14.9666i −0.0666667 0.997775i
\(226\) 6.00000 0.399114
\(227\) 1.40122i 0.0930023i 0.998918 + 0.0465011i \(0.0148071\pi\)
−0.998918 + 0.0465011i \(0.985193\pi\)
\(228\) −7.64575 1.91520i −0.506352 0.126837i
\(229\) 28.2835i 1.86903i −0.355930 0.934513i \(-0.615836\pi\)
0.355930 0.934513i \(-0.384164\pi\)
\(230\) −6.43560 3.57113i −0.424351 0.235473i
\(231\) −9.90624 8.35862i −0.651782 0.549957i
\(232\) 7.98430i 0.524195i
\(233\) 2.70850 0.177440 0.0887198 0.996057i \(-0.471722\pi\)
0.0887198 + 0.996057i \(0.471722\pi\)
\(234\) −2.22699 1.19038i −0.145583 0.0778173i
\(235\) 4.70850 8.48528i 0.307149 0.553519i
\(236\) −3.91044 −0.254548
\(237\) −3.06871 + 12.2508i −0.199334 + 0.795772i
\(238\) 1.38527 2.82843i 0.0897935 0.183340i
\(239\) 22.1264i 1.43124i 0.698490 + 0.715620i \(0.253856\pi\)
−0.698490 + 0.715620i \(0.746144\pi\)
\(240\) −2.64575 + 2.82843i −0.170783 + 0.182574i
\(241\) 1.95906i 0.126194i −0.998007 0.0630972i \(-0.979902\pi\)
0.998007 0.0630972i \(-0.0200978\pi\)
\(242\) −3.00000 −0.192847
\(243\) 14.6773 5.25127i 0.941551 0.336869i
\(244\) 10.0808i 0.645360i
\(245\) −2.39082 15.4688i −0.152744 0.988266i
\(246\) −3.29150 + 13.1402i −0.209859 + 0.837787i
\(247\) 3.83039i 0.243722i
\(248\) 5.53019i 0.351167i
\(249\) −12.9373 3.24067i −0.819865 0.205369i
\(250\) 0.569951 + 11.1658i 0.0360469 + 0.706187i
\(251\) 11.7313 0.740473 0.370237 0.928937i \(-0.379277\pi\)
0.370237 + 0.928937i \(0.379277\pi\)
\(252\) 4.64076 + 6.43920i 0.292341 + 0.405632i
\(253\) 9.30978i 0.585301i
\(254\) 10.8127i 0.678451i
\(255\) 3.36689 + 3.14944i 0.210843 + 0.197225i
\(256\) 1.00000 0.0625000
\(257\) 14.2098i 0.886384i −0.896427 0.443192i \(-0.853846\pi\)
0.896427 0.443192i \(-0.146154\pi\)
\(258\) −7.82087 1.95906i −0.486906 0.121966i
\(259\) −12.5830 + 25.6919i −0.781870 + 1.59642i
\(260\) 1.64575 + 0.913230i 0.102065 + 0.0566361i
\(261\) −11.2915 + 21.1245i −0.698926 + 1.30757i
\(262\) −8.96077 −0.553598
\(263\) −6.58301 −0.405925 −0.202963 0.979186i \(-0.565057\pi\)
−0.202963 + 0.979186i \(0.565057\pi\)
\(264\) −4.75216 1.19038i −0.292475 0.0732626i
\(265\) −24.6025 13.6520i −1.51132 0.838634i
\(266\) 5.29570 10.8127i 0.324700 0.662971i
\(267\) −5.41699 + 21.6255i −0.331515 + 1.32346i
\(268\) 4.65489i 0.284343i
\(269\) −24.6025 −1.50004 −0.750021 0.661414i \(-0.769957\pi\)
−0.750021 + 0.661414i \(0.769957\pi\)
\(270\) −11.0000 + 3.74166i −0.669439 + 0.227710i
\(271\) 7.48925i 0.454940i 0.973785 + 0.227470i \(0.0730453\pi\)
−0.973785 + 0.227470i \(0.926955\pi\)
\(272\) 1.19038i 0.0721771i
\(273\) 2.48747 2.94804i 0.150549 0.178423i
\(274\) 9.29150 0.561320
\(275\) −12.0000 + 7.48331i −0.723627 + 0.451261i
\(276\) −1.38527 + 5.53019i −0.0833832 + 0.332878i
\(277\) 15.4676i 0.929359i 0.885479 + 0.464679i \(0.153830\pi\)
−0.885479 + 0.464679i \(0.846170\pi\)
\(278\) 15.6110i 0.936288i
\(279\) −7.82087 + 14.6315i −0.468223 + 0.875965i
\(280\) −3.38317 4.85326i −0.202183 0.290038i
\(281\) 20.6235i 1.23029i 0.788412 + 0.615147i \(0.210903\pi\)
−0.788412 + 0.615147i \(0.789097\pi\)
\(282\) −7.29150 1.82646i −0.434203 0.108764i
\(283\) 9.74968 0.579558 0.289779 0.957094i \(-0.406418\pi\)
0.289779 + 0.957094i \(0.406418\pi\)
\(284\) 12.6392i 0.749998i
\(285\) 12.8712 + 12.0399i 0.762425 + 0.713183i
\(286\) 2.38075i 0.140777i
\(287\) −18.5830 9.10132i −1.09692 0.537234i
\(288\) 2.64575 + 1.41421i 0.155902 + 0.0833333i
\(289\) 15.5830 0.916647
\(290\) 8.66259 15.6110i 0.508685 0.916712i
\(291\) 3.41699 13.6412i 0.200308 0.799659i
\(292\) 3.06871 0.179583
\(293\) 11.2712i 0.658472i −0.944248 0.329236i \(-0.893209\pi\)
0.944248 0.329236i \(-0.106791\pi\)
\(294\) −11.0976 + 4.88289i −0.647227 + 0.284776i
\(295\) 7.64575 + 4.24264i 0.445153 + 0.247016i
\(296\) 10.8127i 0.628477i
\(297\) −10.8896 9.87000i −0.631878 0.572716i
\(298\) 3.32941i 0.192868i
\(299\) 2.77053 0.160224
\(300\) 8.24173 2.65967i 0.475837 0.153556i
\(301\) 5.41699 11.0604i 0.312230 0.637510i
\(302\) 22.5830 1.29951
\(303\) 1.64575 6.57008i 0.0945459 0.377441i
\(304\) 4.55066i 0.260998i
\(305\) 10.9373 19.7103i 0.626265 1.12861i
\(306\) 1.68345 3.14944i 0.0962362 0.180041i
\(307\) 14.8000 0.844682 0.422341 0.906437i \(-0.361209\pi\)
0.422341 + 0.906437i \(0.361209\pi\)
\(308\) 3.29150 6.72057i 0.187551 0.382940i
\(309\) −5.29150 + 21.1245i −0.301023 + 1.20173i
\(310\) 6.00000 10.8127i 0.340777 0.614122i
\(311\) −2.77053 −0.157103 −0.0785513 0.996910i \(-0.525029\pi\)
−0.0785513 + 0.996910i \(0.525029\pi\)
\(312\) 0.354249 1.41421i 0.0200554 0.0800641i
\(313\) 8.11905 0.458916 0.229458 0.973319i \(-0.426305\pi\)
0.229458 + 0.973319i \(0.426305\pi\)
\(314\) −22.6209 −1.27657
\(315\) −2.08747 17.6251i −0.117615 0.993059i
\(316\) −7.29150 −0.410179
\(317\) 6.00000 0.336994 0.168497 0.985702i \(-0.446109\pi\)
0.168497 + 0.985702i \(0.446109\pi\)
\(318\) −5.29570 + 21.1412i −0.296968 + 1.18554i
\(319\) 22.5830 1.26441
\(320\) −1.95522 1.08495i −0.109300 0.0606508i
\(321\) 0 0
\(322\) −7.82087 3.83039i −0.435840 0.213459i
\(323\) −5.41699 −0.301410
\(324\) 5.00000 + 7.48331i 0.277778 + 0.415740i
\(325\) −2.22699 3.57113i −0.123531 0.198091i
\(326\) 0 0
\(327\) 0.841723 3.36028i 0.0465474 0.185824i
\(328\) −7.82087 −0.431835
\(329\) 5.05034 10.3117i 0.278434 0.568505i
\(330\) 8.00000 + 7.48331i 0.440386 + 0.411943i
\(331\) 8.00000 0.439720 0.219860 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) 7.70010i 0.422598i
\(333\) −15.2915 + 28.6078i −0.837969 + 1.56770i
\(334\) 11.4821i 0.628271i
\(335\) −5.05034 + 9.10132i −0.275929 + 0.497258i
\(336\) −2.95522 + 3.50238i −0.161220 + 0.191071i
\(337\) 22.4499i 1.22293i −0.791273 0.611463i \(-0.790581\pi\)
0.791273 0.611463i \(-0.209419\pi\)
\(338\) 12.2915 0.668570
\(339\) −2.52517 + 10.0808i −0.137148 + 0.547517i
\(340\) −1.29150 + 2.32744i −0.0700416 + 0.126223i
\(341\) 15.6417 0.847048
\(342\) 6.43560 12.0399i 0.347998 0.651044i
\(343\) −3.76135 18.1343i −0.203094 0.979159i
\(344\) 4.65489i 0.250975i
\(345\) 8.70850 9.30978i 0.468850 0.501221i
\(346\) 8.89047i 0.477955i
\(347\) −24.0000 −1.28839 −0.644194 0.764862i \(-0.722807\pi\)
−0.644194 + 0.764862i \(0.722807\pi\)
\(348\) −13.4148 3.36028i −0.719106 0.180130i
\(349\) 19.1822i 1.02680i 0.858150 + 0.513399i \(0.171614\pi\)
−0.858150 + 0.513399i \(0.828386\pi\)
\(350\) 1.34926 + 13.1598i 0.0721210 + 0.703419i
\(351\) 2.93725 3.24067i 0.156779 0.172974i
\(352\) 2.82843i 0.150756i
\(353\) 21.3521i 1.13646i −0.822871 0.568228i \(-0.807629\pi\)
0.822871 0.568228i \(-0.192371\pi\)
\(354\) 1.64575 6.57008i 0.0874707 0.349196i
\(355\) −13.7129 + 24.7124i −0.727807 + 1.31160i
\(356\) −12.8712 −0.682173
\(357\) 4.16915 + 3.51782i 0.220655 + 0.186183i
\(358\) 9.48725i 0.501417i
\(359\) 26.7813i 1.41346i 0.707481 + 0.706732i \(0.249831\pi\)
−0.707481 + 0.706732i \(0.750169\pi\)
\(360\) −3.63866 5.63561i −0.191774 0.297023i
\(361\) −1.70850 −0.0899209
\(362\) 12.0399i 0.632804i
\(363\) 1.26258 5.04042i 0.0662685 0.264554i
\(364\) 2.00000 + 0.979531i 0.104828 + 0.0513414i
\(365\) −6.00000 3.32941i −0.314054 0.174269i
\(366\) −16.9373 4.24264i −0.885324 0.221766i
\(367\) 8.11905 0.423811 0.211905 0.977290i \(-0.432033\pi\)
0.211905 + 0.977290i \(0.432033\pi\)
\(368\) −3.29150 −0.171581
\(369\) −20.6921 11.0604i −1.07719 0.575780i
\(370\) 11.7313 21.1412i 0.609882 1.09908i
\(371\) −29.8982 14.6431i −1.55224 0.760233i
\(372\) −9.29150 2.32744i −0.481742 0.120672i
\(373\) 15.4676i 0.800883i −0.916322 0.400441i \(-0.868857\pi\)
0.916322 0.400441i \(-0.131143\pi\)
\(374\) −3.36689 −0.174098
\(375\) −19.0000 3.74166i −0.981156 0.193218i
\(376\) 4.33981i 0.223809i
\(377\) 6.72057i 0.346127i
\(378\) −12.7719 + 5.08713i −0.656915 + 0.261654i
\(379\) 14.5830 0.749079 0.374539 0.927211i \(-0.377801\pi\)
0.374539 + 0.927211i \(0.377801\pi\)
\(380\) −4.93725 + 8.89753i −0.253276 + 0.456434i
\(381\) 18.1669 + 4.55066i 0.930719 + 0.233137i
\(382\) 7.98430i 0.408512i
\(383\) 11.4821i 0.586706i 0.956004 + 0.293353i \(0.0947712\pi\)
−0.956004 + 0.293353i \(0.905229\pi\)
\(384\) −0.420861 + 1.68014i −0.0214770 + 0.0857394i
\(385\) −13.7271 + 9.56904i −0.699598 + 0.487684i
\(386\) 8.48528i 0.431889i
\(387\) 6.58301 12.3157i 0.334633 0.626041i
\(388\) 8.11905 0.412182
\(389\) 0.323511i 0.0164026i −0.999966 0.00820132i \(-0.997389\pi\)
0.999966 0.00820132i \(-0.00261059\pi\)
\(390\) −2.22699 + 2.38075i −0.112768 + 0.120554i
\(391\) 3.91813i 0.198148i
\(392\) −4.29150 5.53019i −0.216754 0.279317i
\(393\) 3.77124 15.0554i 0.190234 0.759443i
\(394\) −18.0000 −0.906827
\(395\) 14.2565 + 7.91094i 0.717321 + 0.398043i
\(396\) 4.00000 7.48331i 0.201008 0.376051i
\(397\) −21.5338 −1.08075 −0.540375 0.841424i \(-0.681718\pi\)
−0.540375 + 0.841424i \(0.681718\pi\)
\(398\) 16.5906i 0.831610i
\(399\) 15.9382 + 13.4482i 0.797906 + 0.673251i
\(400\) 2.64575 + 4.24264i 0.132288 + 0.212132i
\(401\) 7.48331i 0.373699i 0.982389 + 0.186849i \(0.0598277\pi\)
−0.982389 + 0.186849i \(0.940172\pi\)
\(402\) 7.82087 + 1.95906i 0.390070 + 0.0977092i
\(403\) 4.65489i 0.231876i
\(404\) 3.91044 0.194551
\(405\) −1.65704 20.0563i −0.0823389 0.996604i
\(406\) 9.29150 18.9713i 0.461130 0.941531i
\(407\) 30.5830 1.51594
\(408\) 2.00000 + 0.500983i 0.0990148 + 0.0248024i
\(409\) 13.0194i 0.643770i −0.946779 0.321885i \(-0.895684\pi\)
0.946779 0.321885i \(-0.104316\pi\)
\(410\) 15.2915 + 8.48528i 0.755193 + 0.419058i
\(411\) −3.91044 + 15.6110i −0.192888 + 0.770036i
\(412\) −12.5730 −0.619429
\(413\) 9.29150 + 4.55066i 0.457205 + 0.223923i
\(414\) −8.70850 4.65489i −0.427999 0.228775i
\(415\) −8.35425 + 15.0554i −0.410094 + 0.739039i
\(416\) 0.841723 0.0412689
\(417\) 26.2288 + 6.57008i 1.28443 + 0.321738i
\(418\) −12.8712 −0.629551
\(419\) 21.8320 1.06656 0.533281 0.845938i \(-0.320959\pi\)
0.533281 + 0.845938i \(0.320959\pi\)
\(420\) 9.57802 3.64165i 0.467359 0.177694i
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) −21.1660 −1.03035
\(423\) 6.13742 11.4821i 0.298412 0.558277i
\(424\) −12.5830 −0.611085
\(425\) 5.05034 3.14944i 0.244977 0.152770i
\(426\) 21.2356 + 5.31935i 1.02887 + 0.257723i
\(427\) 11.7313 23.9529i 0.567718 1.15916i
\(428\) 0 0
\(429\) −4.00000 1.00197i −0.193122 0.0483754i
\(430\) −5.05034 + 9.10132i −0.243549 + 0.438905i
\(431\) 16.4696i 0.793312i −0.917967 0.396656i \(-0.870171\pi\)
0.917967 0.396656i \(-0.129829\pi\)
\(432\) −3.48957 + 3.85005i −0.167892 + 0.185236i
\(433\) 26.5313 1.27501 0.637507 0.770445i \(-0.279966\pi\)
0.637507 + 0.770445i \(0.279966\pi\)
\(434\) 6.43560 13.1402i 0.308919 0.630748i
\(435\) 22.5830 + 21.1245i 1.08277 + 1.01284i
\(436\) 2.00000 0.0957826
\(437\) 14.9785i 0.716519i
\(438\) −1.29150 + 5.15587i −0.0617104 + 0.246357i
\(439\) 18.5496i 0.885326i −0.896688 0.442663i \(-0.854034\pi\)
0.896688 0.442663i \(-0.145966\pi\)
\(440\) −3.06871 + 5.53019i −0.146295 + 0.263641i
\(441\) −3.53338 20.7006i −0.168256 0.985743i
\(442\) 1.00197i 0.0476587i
\(443\) 13.1660 0.625536 0.312768 0.949830i \(-0.398744\pi\)
0.312768 + 0.949830i \(0.398744\pi\)
\(444\) −18.1669 4.55066i −0.862163 0.215965i
\(445\) 25.1660 + 13.9647i 1.19298 + 0.661989i
\(446\) 4.75216 0.225021
\(447\) −5.59388 1.40122i −0.264581 0.0662755i
\(448\) −2.37608 1.16372i −0.112259 0.0549807i
\(449\) 8.30781i 0.392070i 0.980597 + 0.196035i \(0.0628066\pi\)
−0.980597 + 0.196035i \(0.937193\pi\)
\(450\) 1.00000 + 14.9666i 0.0471405 + 0.705534i
\(451\) 22.1208i 1.04163i
\(452\) −6.00000 −0.282216
\(453\) −9.50432 + 37.9426i −0.446552 + 1.78270i
\(454\) 1.40122i 0.0657625i
\(455\) −2.84769 4.08510i −0.133502 0.191513i
\(456\) 7.64575 + 1.91520i 0.358045 + 0.0896873i
\(457\) 8.48528i 0.396925i 0.980109 + 0.198462i \(0.0635948\pi\)
−0.980109 + 0.198462i \(0.936405\pi\)
\(458\) 28.2835i 1.32160i
\(459\) 4.58301 + 4.15390i 0.213916 + 0.193888i
\(460\) 6.43560 + 3.57113i 0.300062 + 0.166505i
\(461\) −8.96077 −0.417345 −0.208672 0.977986i \(-0.566914\pi\)
−0.208672 + 0.977986i \(0.566914\pi\)
\(462\) 9.90624 + 8.35862i 0.460880 + 0.388878i
\(463\) 23.9529i 1.11319i 0.830786 + 0.556593i \(0.187892\pi\)
−0.830786 + 0.556593i \(0.812108\pi\)
\(464\) 7.98430i 0.370662i
\(465\) 15.6417 + 14.6315i 0.725368 + 0.678520i
\(466\) −2.70850 −0.125469
\(467\) 3.36028i 0.155495i 0.996973 + 0.0777477i \(0.0247729\pi\)
−0.996973 + 0.0777477i \(0.975227\pi\)
\(468\) 2.22699 + 1.19038i 0.102943 + 0.0550251i
\(469\) −5.41699 + 11.0604i −0.250134 + 0.510721i
\(470\) −4.70850 + 8.48528i −0.217187 + 0.391397i
\(471\) 9.52026 38.0063i 0.438670 1.75124i
\(472\) 3.91044 0.179992
\(473\) −13.1660 −0.605374
\(474\) 3.06871 12.2508i 0.140951 0.562696i
\(475\) 19.3068 12.0399i 0.885857 0.552429i
\(476\) −1.38527 + 2.82843i −0.0634936 + 0.129641i
\(477\) −33.2915 17.7951i −1.52431 0.814780i
\(478\) 22.1264i 1.01204i
\(479\) 39.1044 1.78672 0.893362 0.449338i \(-0.148340\pi\)
0.893362 + 0.449338i \(0.148340\pi\)
\(480\) 2.64575 2.82843i 0.120761 0.129099i
\(481\) 9.10132i 0.414984i
\(482\) 1.95906i 0.0892329i
\(483\) 9.72711 11.5281i 0.442599 0.524547i
\(484\) 3.00000 0.136364
\(485\) −15.8745 8.80879i −0.720824 0.399987i
\(486\) −14.6773 + 5.25127i −0.665777 + 0.238202i
\(487\) 32.4382i 1.46991i −0.678114 0.734957i \(-0.737202\pi\)
0.678114 0.734957i \(-0.262798\pi\)
\(488\) 10.0808i 0.456339i
\(489\) 0 0
\(490\) 2.39082 + 15.4688i 0.108006 + 0.698809i
\(491\) 14.1421i 0.638226i −0.947717 0.319113i \(-0.896615\pi\)
0.947717 0.319113i \(-0.103385\pi\)
\(492\) 3.29150 13.1402i 0.148392 0.592405i
\(493\) −9.50432 −0.428053
\(494\) 3.83039i 0.172338i
\(495\) −15.9399 + 10.2917i −0.716446 + 0.462577i
\(496\) 5.53019i 0.248313i
\(497\) −14.7085 + 30.0317i −0.659766 + 1.34711i
\(498\) 12.9373 + 3.24067i 0.579732 + 0.145218i
\(499\) 1.41699 0.0634334 0.0317167 0.999497i \(-0.489903\pi\)
0.0317167 + 0.999497i \(0.489903\pi\)
\(500\) −0.569951 11.1658i −0.0254890 0.499350i
\(501\) 19.2915 + 4.83236i 0.861881 + 0.215894i
\(502\) −11.7313 −0.523594
\(503\) 8.67963i 0.387006i −0.981100 0.193503i \(-0.938015\pi\)
0.981100 0.193503i \(-0.0619848\pi\)
\(504\) −4.64076 6.43920i −0.206716 0.286825i
\(505\) −7.64575 4.24264i −0.340231 0.188795i
\(506\) 9.30978i 0.413870i
\(507\) −5.17302 + 20.6515i −0.229742 + 0.917164i
\(508\) 10.8127i 0.479737i
\(509\) 30.1436 1.33609 0.668045 0.744121i \(-0.267131\pi\)
0.668045 + 0.744121i \(0.267131\pi\)
\(510\) −3.36689 3.14944i −0.149088 0.139459i
\(511\) −7.29150 3.57113i −0.322557 0.157977i
\(512\) −1.00000 −0.0441942
\(513\) 17.5203 + 15.8799i 0.773538 + 0.701113i
\(514\) 14.2098i 0.626768i
\(515\) 24.5830 + 13.6412i 1.08326 + 0.601101i
\(516\) 7.82087 + 1.95906i 0.344295 + 0.0862429i
\(517\) −12.2748 −0.539847
\(518\) 12.5830 25.6919i 0.552866 1.12884i
\(519\) 14.9373 + 3.74166i 0.655673 + 0.164241i
\(520\) −1.64575 0.913230i −0.0721710 0.0400478i
\(521\) −23.4626 −1.02792 −0.513958 0.857815i \(-0.671821\pi\)
−0.513958 + 0.857815i \(0.671821\pi\)
\(522\) 11.2915 21.1245i 0.494216 0.924593i
\(523\) 4.20861 0.184030 0.0920149 0.995758i \(-0.470669\pi\)
0.0920149 + 0.995758i \(0.470669\pi\)
\(524\) 8.96077 0.391453
\(525\) −22.6781 3.27149i −0.989755 0.142780i
\(526\) 6.58301 0.287033
\(527\) −6.58301 −0.286760
\(528\) 4.75216 + 1.19038i 0.206811 + 0.0518045i
\(529\) −12.1660 −0.528957
\(530\) 24.6025 + 13.6520i 1.06866 + 0.593004i
\(531\) 10.3460 + 5.53019i 0.448980 + 0.239990i
\(532\) −5.29570 + 10.8127i −0.229598 + 0.468791i
\(533\) −6.58301 −0.285142
\(534\) 5.41699 21.6255i 0.234416 0.935825i
\(535\) 0 0
\(536\) 4.65489i 0.201061i
\(537\) −15.9399 3.99282i −0.687858 0.172303i
\(538\) 24.6025 1.06069
\(539\) −15.6417 + 12.1382i −0.673737 + 0.522829i
\(540\) 11.0000 3.74166i 0.473365 0.161015i
\(541\) 2.00000 0.0859867 0.0429934 0.999075i \(-0.486311\pi\)
0.0429934 + 0.999075i \(0.486311\pi\)
\(542\) 7.48925i 0.321691i
\(543\) −20.2288 5.06713i −0.868099 0.217452i
\(544\) 1.19038i 0.0510369i
\(545\) −3.91044 2.16991i −0.167505 0.0929486i
\(546\) −2.48747 + 2.94804i −0.106454 + 0.126164i
\(547\) 16.9706i 0.725609i −0.931865 0.362804i \(-0.881819\pi\)
0.931865 0.362804i \(-0.118181\pi\)
\(548\) −9.29150 −0.396913
\(549\) 14.2565 26.6714i 0.608451 1.13831i
\(550\) 12.0000 7.48331i 0.511682 0.319090i
\(551\) −36.3338 −1.54787
\(552\) 1.38527 5.53019i 0.0589609 0.235381i
\(553\) 17.3252 + 8.48528i 0.736742 + 0.360831i
\(554\) 15.4676i 0.657156i
\(555\) 30.5830 + 28.6078i 1.29818 + 1.21433i
\(556\) 15.6110i 0.662056i
\(557\) 7.16601 0.303634 0.151817 0.988409i \(-0.451488\pi\)
0.151817 + 0.988409i \(0.451488\pi\)
\(558\) 7.82087 14.6315i 0.331084 0.619401i
\(559\) 3.91813i 0.165719i
\(560\) 3.38317 + 4.85326i 0.142965 + 0.205088i
\(561\) 1.41699 5.65685i 0.0598256 0.238833i
\(562\) 20.6235i 0.869949i
\(563\) 18.7605i 0.790660i −0.918539 0.395330i \(-0.870630\pi\)
0.918539 0.395330i \(-0.129370\pi\)
\(564\) 7.29150 + 1.82646i 0.307028 + 0.0769079i
\(565\) 11.7313 + 6.50972i 0.493540 + 0.273866i
\(566\) −9.74968 −0.409810
\(567\) −3.17190 23.5996i −0.133207 0.991088i
\(568\) 12.6392i 0.530328i
\(569\) 11.1362i 0.466855i −0.972374 0.233428i \(-0.925006\pi\)
0.972374 0.233428i \(-0.0749942\pi\)
\(570\) −12.8712 12.0399i −0.539116 0.504296i
\(571\) −34.5830 −1.44725 −0.723627 0.690191i \(-0.757526\pi\)
−0.723627 + 0.690191i \(0.757526\pi\)
\(572\) 2.38075i 0.0995442i
\(573\) −13.4148 3.36028i −0.560409 0.140378i
\(574\) 18.5830 + 9.10132i 0.775640 + 0.379882i
\(575\) −8.70850 13.9647i −0.363169 0.582367i
\(576\) −2.64575 1.41421i −0.110240 0.0589256i
\(577\) −30.9853 −1.28993 −0.644967 0.764210i \(-0.723129\pi\)
−0.644967 + 0.764210i \(0.723129\pi\)
\(578\) −15.5830 −0.648168
\(579\) −14.2565 3.57113i −0.592479 0.148411i
\(580\) −8.66259 + 15.6110i −0.359695 + 0.648213i
\(581\) −8.96077 + 18.2960i −0.371755 + 0.759048i
\(582\) −3.41699 + 13.6412i −0.141639 + 0.565444i
\(583\) 35.5901i 1.47399i
\(584\) −3.06871 −0.126984
\(585\) −3.06275 4.74362i −0.126629 0.196125i
\(586\) 11.2712i 0.465610i
\(587\) 44.1054i 1.82042i −0.414143 0.910212i \(-0.635919\pi\)
0.414143 0.910212i \(-0.364081\pi\)
\(588\) 11.0976 4.88289i 0.457659 0.201367i
\(589\) −25.1660 −1.03695
\(590\) −7.64575 4.24264i −0.314771 0.174667i
\(591\) 7.57551 30.2425i 0.311615 1.24401i
\(592\) 10.8127i 0.444400i
\(593\) 7.91094i 0.324863i 0.986720 + 0.162432i \(0.0519337\pi\)
−0.986720 + 0.162432i \(0.948066\pi\)
\(594\) 10.8896 + 9.87000i 0.446805 + 0.404971i
\(595\) 5.77721 4.02724i 0.236843 0.165101i
\(596\) 3.32941i 0.136378i
\(597\) −27.8745 6.98233i −1.14083 0.285768i
\(598\) −2.77053 −0.113296
\(599\) 18.2960i 0.747556i 0.927518 + 0.373778i \(0.121938\pi\)
−0.927518 + 0.373778i \(0.878062\pi\)
\(600\) −8.24173 + 2.65967i −0.336467 + 0.108581i
\(601\) 11.0604i 0.451162i −0.974224 0.225581i \(-0.927572\pi\)
0.974224 0.225581i \(-0.0724281\pi\)
\(602\) −5.41699 + 11.0604i −0.220780 + 0.450787i
\(603\) −6.58301 + 12.3157i −0.268081 + 0.501533i
\(604\) −22.5830 −0.918889
\(605\) −5.86565 3.25486i −0.238473 0.132329i
\(606\) −1.64575 + 6.57008i −0.0668541 + 0.266891i
\(607\) 23.7608 0.964421 0.482210 0.876055i \(-0.339834\pi\)
0.482210 + 0.876055i \(0.339834\pi\)
\(608\) 4.55066i 0.184554i
\(609\) 27.9641 + 23.5953i 1.13316 + 0.956131i
\(610\) −10.9373 + 19.7103i −0.442836 + 0.798045i
\(611\) 3.65292i 0.147781i
\(612\) −1.68345 + 3.14944i −0.0680493 + 0.127309i
\(613\) 40.0990i 1.61958i 0.586719 + 0.809791i \(0.300419\pi\)
−0.586719 + 0.809791i \(0.699581\pi\)
\(614\) −14.8000 −0.597280
\(615\) −20.6921 + 22.1208i −0.834385 + 0.891995i
\(616\) −3.29150 + 6.72057i −0.132618 + 0.270779i
\(617\) 4.83399 0.194609 0.0973045 0.995255i \(-0.468978\pi\)
0.0973045 + 0.995255i \(0.468978\pi\)
\(618\) 5.29150 21.1245i 0.212855 0.849751i
\(619\) 0.632534i 0.0254237i −0.999919 0.0127118i \(-0.995954\pi\)
0.999919 0.0127118i \(-0.00404641\pi\)
\(620\) −6.00000 + 10.8127i −0.240966 + 0.434249i
\(621\) 11.4859 12.6724i 0.460915 0.508528i
\(622\) 2.77053 0.111088
\(623\) 30.5830 + 14.9785i 1.22528 + 0.600101i
\(624\) −0.354249 + 1.41421i −0.0141813 + 0.0566139i
\(625\) −11.0000 + 22.4499i −0.440000 + 0.897998i
\(626\) −8.11905 −0.324502
\(627\) 5.41699 21.6255i 0.216334 0.863637i
\(628\) 22.6209 0.902672
\(629\) −12.8712 −0.513209
\(630\) 2.08747 + 17.6251i 0.0831666 + 0.702199i
\(631\) −20.4575 −0.814401 −0.407200 0.913339i \(-0.633495\pi\)
−0.407200 + 0.913339i \(0.633495\pi\)
\(632\) 7.29150 0.290040
\(633\) 8.90796 35.5619i 0.354060 1.41346i
\(634\) −6.00000 −0.238290
\(635\) 11.7313 21.1412i 0.465543 0.838964i
\(636\) 5.29570 21.1412i 0.209988 0.838304i
\(637\) −3.61226 4.65489i −0.143123 0.184433i
\(638\) −22.5830 −0.894070
\(639\) −17.8745 + 33.4401i −0.707105 + 1.32287i
\(640\) 1.95522 + 1.08495i 0.0772868 + 0.0428866i
\(641\) 16.7931i 0.663287i 0.943405 + 0.331644i \(0.107603\pi\)
−0.943405 + 0.331644i \(0.892397\pi\)
\(642\) 0 0
\(643\) −47.7669 −1.88374 −0.941872 0.335971i \(-0.890935\pi\)
−0.941872 + 0.335971i \(0.890935\pi\)
\(644\) 7.82087 + 3.83039i 0.308185 + 0.150939i
\(645\) −13.1660 12.3157i −0.518411 0.484929i
\(646\) 5.41699 0.213129
\(647\) 15.4002i 0.605444i 0.953079 + 0.302722i \(0.0978954\pi\)
−0.953079 + 0.302722i \(0.902105\pi\)
\(648\) −5.00000 7.48331i −0.196419 0.293972i
\(649\) 11.0604i 0.434158i
\(650\) 2.22699 + 3.57113i 0.0873497 + 0.140071i
\(651\) 19.3688 + 16.3429i 0.759125 + 0.640529i
\(652\) 0 0
\(653\) 19.1660 0.750024 0.375012 0.927020i \(-0.377639\pi\)
0.375012 + 0.927020i \(0.377639\pi\)
\(654\) −0.841723 + 3.36028i −0.0329140 + 0.131397i
\(655\) −17.5203 9.72202i −0.684573 0.379871i
\(656\) 7.82087 0.305354
\(657\) −8.11905 4.33981i −0.316754 0.169312i
\(658\) −5.05034 + 10.3117i −0.196883 + 0.401994i
\(659\) 32.7617i 1.27621i −0.769948 0.638107i \(-0.779718\pi\)
0.769948 0.638107i \(-0.220282\pi\)
\(660\) −8.00000 7.48331i −0.311400 0.291288i
\(661\) 0.979531i 0.0380994i −0.999819 0.0190497i \(-0.993936\pi\)
0.999819 0.0190497i \(-0.00606407\pi\)
\(662\) −8.00000 −0.310929
\(663\) 1.68345 + 0.421689i 0.0653796 + 0.0163770i
\(664\) 7.70010i 0.298822i
\(665\) 22.0856 15.3956i 0.856441 0.597017i
\(666\) 15.2915 28.6078i 0.592534 1.10853i
\(667\) 26.2803i 1.01758i
\(668\) 11.4821i 0.444255i
\(669\) −2.00000 + 7.98430i −0.0773245 + 0.308691i
\(670\) 5.05034 9.10132i 0.195112 0.351615i
\(671\) −28.5129 −1.10073
\(672\) 2.95522 3.50238i 0.114000 0.135107i
\(673\) 38.5960i 1.48777i −0.668309 0.743883i \(-0.732982\pi\)
0.668309 0.743883i \(-0.267018\pi\)
\(674\) 22.4499i 0.864740i
\(675\) −25.5669 4.61874i −0.984071 0.177775i
\(676\) −12.2915 −0.472750
\(677\) 42.4933i 1.63315i −0.577239 0.816575i \(-0.695870\pi\)
0.577239 0.816575i \(-0.304130\pi\)
\(678\) 2.52517 10.0808i 0.0969785 0.387153i
\(679\) −19.2915 9.44832i −0.740340 0.362593i
\(680\) 1.29150 2.32744i 0.0495269 0.0892534i
\(681\) 2.35425 + 0.589720i 0.0902150 + 0.0225981i
\(682\) −15.6417 −0.598953
\(683\) 5.41699 0.207276 0.103638 0.994615i \(-0.466952\pi\)
0.103638 + 0.994615i \(0.466952\pi\)
\(684\) −6.43560 + 12.0399i −0.246071 + 0.460358i
\(685\) 18.1669 + 10.0808i 0.694122 + 0.385169i
\(686\) 3.76135 + 18.1343i 0.143609 + 0.692370i
\(687\) −47.5203 11.9034i −1.81301 0.454144i
\(688\) 4.65489i 0.177466i
\(689\) −10.5914 −0.403500
\(690\) −8.70850 + 9.30978i −0.331527 + 0.354417i
\(691\) 6.50972i 0.247641i −0.992305 0.123821i \(-0.960485\pi\)
0.992305 0.123821i \(-0.0395148\pi\)
\(692\) 8.89047i 0.337965i
\(693\) −18.2128 + 13.1261i −0.691848 + 0.498618i
\(694\) 24.0000 0.911028
\(695\) 16.9373 30.5230i 0.642467 1.15780i
\(696\) 13.4148 + 3.36028i 0.508485 + 0.127371i
\(697\) 9.30978i 0.352633i
\(698\) 19.1822i 0.726056i
\(699\) 1.13990 4.55066i 0.0431151 0.172122i
\(700\) −1.34926 13.1598i −0.0509972 0.497392i
\(701\) 1.32548i 0.0500626i 0.999687 + 0.0250313i \(0.00796854\pi\)
−0.999687 + 0.0250313i \(0.992031\pi\)
\(702\) −2.93725 + 3.24067i −0.110860 + 0.122311i
\(703\) −49.2050 −1.85580
\(704\) 2.82843i 0.106600i
\(705\) −12.2748 11.4821i −0.462298 0.432440i
\(706\) 21.3521i 0.803596i
\(707\) −9.29150 4.55066i −0.349443 0.171145i
\(708\) −1.64575 + 6.57008i −0.0618511 + 0.246919i
\(709\) 20.5830 0.773011 0.386505 0.922287i \(-0.373682\pi\)
0.386505 + 0.922287i \(0.373682\pi\)
\(710\) 13.7129 24.7124i 0.514637 0.927438i
\(711\) 19.2915 + 10.3117i 0.723488 + 0.386721i
\(712\) 12.8712 0.482369
\(713\) 18.2026i 0.681694i
\(714\) −4.16915 3.51782i −0.156027 0.131651i
\(715\) −2.58301 + 4.65489i −0.0965989 + 0.174083i
\(716\) 9.48725i 0.354555i
\(717\) 37.1755 + 9.31216i 1.38835 + 0.347769i
\(718\) 26.7813i 0.999470i
\(719\) −36.3338 −1.35502 −0.677511 0.735512i \(-0.736942\pi\)
−0.677511 + 0.735512i \(0.736942\pi\)
\(720\) 3.63866 + 5.63561i 0.135605 + 0.210027i
\(721\) 29.8745 + 14.6315i 1.11258 + 0.544906i
\(722\) 1.70850 0.0635837
\(723\) −3.29150 0.824494i −0.122412 0.0306633i
\(724\) 12.0399i 0.447460i
\(725\) 33.8745 21.1245i 1.25807 0.784543i
\(726\) −1.26258 + 5.04042i −0.0468589 + 0.187068i
\(727\) −7.03196 −0.260801 −0.130401 0.991461i \(-0.541626\pi\)
−0.130401 + 0.991461i \(0.541626\pi\)
\(728\) −2.00000 0.979531i −0.0741249 0.0363038i
\(729\) −2.64575 26.8701i −0.0979908 0.995187i
\(730\) 6.00000 + 3.32941i 0.222070 + 0.123227i
\(731\) 5.54107 0.204944
\(732\) 16.9373 + 4.24264i 0.626019 + 0.156813i
\(733\) 24.9007 0.919728 0.459864 0.887989i \(-0.347898\pi\)
0.459864 + 0.887989i \(0.347898\pi\)
\(734\) −8.11905 −0.299680
\(735\) −26.9960 2.49331i −0.995762 0.0919670i
\(736\) 3.29150 0.121326
\(737\) 13.1660 0.484976
\(738\) 20.6921 + 11.0604i 0.761686 + 0.407138i
\(739\) 9.16601 0.337177 0.168589 0.985687i \(-0.446079\pi\)
0.168589 + 0.985687i \(0.446079\pi\)
\(740\) −11.7313 + 21.1412i −0.431251 + 0.777167i
\(741\) 6.43560 + 1.61206i 0.236418 + 0.0592207i
\(742\) 29.8982 + 14.6431i 1.09760 + 0.537566i
\(743\) −33.8745 −1.24274 −0.621368 0.783519i \(-0.713423\pi\)
−0.621368 + 0.783519i \(0.713423\pi\)
\(744\) 9.29150 + 2.32744i 0.340643 + 0.0853282i
\(745\) −3.61226 + 6.50972i −0.132343 + 0.238498i
\(746\) 15.4676i 0.566310i
\(747\) −10.8896 + 20.3725i −0.398429 + 0.745392i
\(748\) 3.36689 0.123106
\(749\) 0 0
\(750\) 19.0000 + 3.74166i 0.693782 + 0.136626i
\(751\) 21.1660 0.772359 0.386179 0.922424i \(-0.373795\pi\)
0.386179 + 0.922424i \(0.373795\pi\)
\(752\) 4.33981i 0.158257i
\(753\) 4.93725 19.7103i 0.179924 0.718282i
\(754\) 6.72057i 0.244749i
\(755\) 44.1547 + 24.5015i 1.60695 + 0.891701i
\(756\) 12.7719 5.08713i 0.464509 0.185017i
\(757\) 3.15194i 0.114559i 0.998358 + 0.0572796i \(0.0182426\pi\)
−0.998358 + 0.0572796i \(0.981757\pi\)
\(758\) −14.5830 −0.529679
\(759\) −15.6417 3.91813i −0.567759 0.142219i
\(760\) 4.93725 8.89753i 0.179093 0.322747i
\(761\) 20.6921 0.750087 0.375044 0.927007i \(-0.377628\pi\)
0.375044 + 0.927007i \(0.377628\pi\)
\(762\) −18.1669 4.55066i −0.658118 0.164853i
\(763\) −4.75216 2.32744i −0.172040 0.0842591i
\(764\) 7.98430i 0.288862i
\(765\) 6.70850 4.33138i 0.242546 0.156601i
\(766\) 11.4821i 0.414864i
\(767\) 3.29150 0.118849
\(768\) 0.420861 1.68014i 0.0151865 0.0606269i
\(769\) 35.1402i 1.26719i 0.773666 + 0.633594i \(0.218421\pi\)
−0.773666 + 0.633594i \(0.781579\pi\)
\(770\) 13.7271 9.56904i 0.494691 0.344844i
\(771\) −23.8745 5.98036i −0.859819 0.215378i
\(772\) 8.48528i 0.305392i
\(773\) 7.35310i 0.264473i −0.991218 0.132236i \(-0.957784\pi\)
0.991218 0.132236i \(-0.0422158\pi\)
\(774\) −6.58301 + 12.3157i −0.236621 + 0.442678i
\(775\) 23.4626 14.6315i 0.842802 0.525579i
\(776\) −8.11905 −0.291457
\(777\) 37.8703 + 31.9540i 1.35859 + 1.14634i
\(778\) 0.323511i 0.0115984i
\(779\) 35.5901i 1.27515i
\(780\) 2.22699 2.38075i 0.0797390 0.0852446i
\(781\) 35.7490 1.27920
\(782\) 3.91813i 0.140112i
\(783\) 30.7399 + 27.8618i 1.09856 + 0.995699i
\(784\) 4.29150 + 5.53019i 0.153268 + 0.197507i
\(785\) −44.2288 24.5426i −1.57859 0.875963i
\(786\) −3.77124 + 15.0554i −0.134516 + 0.537007i
\(787\) 24.9007 0.887614 0.443807 0.896122i \(-0.353628\pi\)
0.443807 + 0.896122i \(0.353628\pi\)
\(788\) 18.0000 0.641223
\(789\) −2.77053 + 11.0604i −0.0986336 + 0.393760i
\(790\) −14.2565 7.91094i −0.507223 0.281459i
\(791\) 14.2565 + 6.98233i 0.506902 + 0.248263i
\(792\) −4.00000 + 7.48331i −0.142134 + 0.265908i
\(793\) 8.48528i 0.301321i
\(794\) 21.5338 0.764206
\(795\) −33.2915 + 35.5901i −1.18073 + 1.26225i
\(796\) 16.5906i 0.588037i
\(797\) 6.93141i 0.245523i 0.992436 + 0.122762i \(0.0391750\pi\)
−0.992436 + 0.122762i \(0.960825\pi\)
\(798\) −15.9382 13.4482i −0.564204 0.476061i
\(799\) 5.16601 0.182760
\(800\) −2.64575 4.24264i −0.0935414 0.150000i
\(801\) 34.0540 + 18.2026i 1.20324 + 0.643159i
\(802\) 7.48331i 0.264245i
\(803\) 8.67963i 0.306297i
\(804\) −7.82087 1.95906i −0.275821 0.0690908i
\(805\) −11.1357 15.9745i −0.392482 0.563028i
\(806\) 4.65489i 0.163961i
\(807\) −10.3542 + 41.3357i −0.364487 + 1.45509i
\(808\) −3.91044 −0.137569
\(809\) 33.7637i 1.18707i 0.804809 + 0.593533i \(0.202268\pi\)
−0.804809 + 0.593533i \(0.797732\pi\)
\(810\) 1.65704 + 20.0563i 0.0582224 + 0.704706i
\(811\) 28.6305i 1.00535i −0.864475 0.502676i \(-0.832349\pi\)
0.864475 0.502676i \(-0.167651\pi\)
\(812\) −9.29150 + 18.9713i −0.326068 + 0.665763i
\(813\) 12.5830 + 3.15194i 0.441305 + 0.110543i
\(814\) −30.5830 −1.07193
\(815\) 0 0
\(816\) −2.00000 0.500983i −0.0700140 0.0175379i
\(817\) 21.1828 0.741093
\(818\) 13.0194i 0.455214i
\(819\) −3.90624 5.42002i −0.136495 0.189391i
\(820\) −15.2915 8.48528i −0.534002 0.296319i
\(821\) 5.98036i 0.208716i 0.994540 + 0.104358i \(0.0332788\pi\)
−0.994540 + 0.104358i \(0.966721\pi\)
\(822\) 3.91044 15.6110i 0.136392 0.544498i
\(823\) 19.2980i 0.672686i −0.941740 0.336343i \(-0.890810\pi\)
0.941740 0.336343i \(-0.109190\pi\)
\(824\) 12.5730 0.438002
\(825\) 7.52269 + 23.3111i 0.261906 + 0.811590i
\(826\) −9.29150 4.55066i −0.323293 0.158338i
\(827\) 36.0000 1.25184 0.625921 0.779886i \(-0.284723\pi\)
0.625921 + 0.779886i \(0.284723\pi\)
\(828\) 8.70850 + 4.65489i 0.302641 + 0.161769i
\(829\) 45.2211i 1.57059i 0.619120 + 0.785296i \(0.287489\pi\)
−0.619120 + 0.785296i \(0.712511\pi\)
\(830\) 8.35425 15.0554i 0.289980 0.522579i
\(831\) 25.9878 + 6.50972i 0.901506 + 0.225820i
\(832\) −0.841723 −0.0291815
\(833\) 6.58301 5.10850i 0.228088 0.176999i
\(834\) −26.2288 6.57008i −0.908228 0.227503i
\(835\) 12.4575 22.4499i 0.431110 0.776912i
\(836\) 12.8712 0.445160
\(837\) 21.2915 + 19.2980i 0.735942 + 0.667037i
\(838\) −21.8320 −0.754173
\(839\) 26.2331 0.905669 0.452834 0.891595i \(-0.350413\pi\)
0.452834 + 0.891595i \(0.350413\pi\)
\(840\) −9.57802 + 3.64165i −0.330473 + 0.125649i
\(841\) −34.7490 −1.19824
\(842\) 10.0000 0.344623
\(843\) 34.6504 + 8.67963i 1.19342 + 0.298942i
\(844\) 21.1660 0.728564
\(845\) 24.0326 + 13.3357i 0.826745 + 0.458762i
\(846\) −6.13742 + 11.4821i −0.211009 + 0.394762i
\(847\) −7.12824 3.49117i −0.244929 0.119958i
\(848\) 12.5830 0.432102
\(849\) 4.10326 16.3808i 0.140824 0.562189i
\(850\) −5.05034 + 3.14944i −0.173225 + 0.108025i
\(851\) 35.5901i 1.22001i
\(852\) −21.2356 5.31935i −0.727520 0.182238i
\(853\) −5.89206 −0.201740 −0.100870 0.994900i \(-0.532163\pi\)
−0.100870 + 0.994900i \(0.532163\pi\)
\(854\) −11.7313 + 23.9529i −0.401437 + 0.819651i
\(855\) 25.6458 16.5583i 0.877066 0.566282i
\(856\) 0 0
\(857\) 24.1545i 0.825103i 0.910934 + 0.412551i \(0.135362\pi\)
−0.910934 + 0.412551i \(0.864638\pi\)
\(858\) 4.00000 + 1.00197i 0.136558 + 0.0342066i
\(859\) 2.59160i 0.0884241i −0.999022 0.0442121i \(-0.985922\pi\)
0.999022 0.0442121i \(-0.0140777\pi\)
\(860\) 5.05034 9.10132i 0.172215 0.310352i
\(861\) −23.1124 + 27.3917i −0.787668 + 0.933506i
\(862\) 16.4696i 0.560956i
\(863\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) 3.48957 3.85005i 0.118718 0.130981i
\(865\) 9.64575 17.3828i 0.327965 0.591033i
\(866\) −26.5313 −0.901571
\(867\) 6.55829 26.1817i 0.222731 0.889176i
\(868\) −6.43560 + 13.1402i −0.218439 + 0.446006i
\(869\) 20.6235i 0.699604i
\(870\) −22.5830 21.1245i −0.765636 0.716187i
\(871\) 3.91813i 0.132761i
\(872\) −2.00000 −0.0677285
\(873\) −21.4810 11.4821i −0.727021 0.388609i
\(874\) 14.9785i 0.506656i
\(875\) −11.6396 + 27.1941i −0.393492 + 0.919328i
\(876\) 1.29150 5.15587i 0.0436358 0.174201i
\(877\) 1.50295i 0.0507510i −0.999678 0.0253755i \(-0.991922\pi\)
0.999678 0.0253755i \(-0.00807814\pi\)
\(878\) 18.5496i 0.626020i
\(879\) −18.9373 4.74362i −0.638738 0.159998i
\(880\) 3.06871 5.53019i 0.103446 0.186423i
\(881\) 12.8712 0.433642 0.216821 0.976211i \(-0.430431\pi\)
0.216821 + 0.976211i \(0.430431\pi\)
\(882\) 3.53338 + 20.7006i 0.118975 + 0.697026i
\(883\) 13.9647i 0.469948i 0.972002 + 0.234974i \(0.0755006\pi\)
−0.972002 + 0.234974i \(0.924499\pi\)
\(884\) 1.00197i 0.0336998i
\(885\) 10.3460 11.0604i 0.347778 0.371791i
\(886\) −13.1660 −0.442321
\(887\) 44.6632i 1.49964i 0.661640 + 0.749822i \(0.269861\pi\)
−0.661640 + 0.749822i \(0.730139\pi\)
\(888\) 18.1669 + 4.55066i 0.609642 + 0.152710i
\(889\) 12.5830 25.6919i 0.422020 0.861678i
\(890\) −25.1660 13.9647i −0.843567 0.468097i
\(891\) −21.1660 + 14.1421i −0.709088 + 0.473779i
\(892\) −4.75216 −0.159114
\(893\) 19.7490 0.660876
\(894\) 5.59388 + 1.40122i 0.187087 + 0.0468638i
\(895\) −10.2932 + 18.5496i −0.344065 + 0.620046i
\(896\) 2.37608 + 1.16372i 0.0793792 + 0.0388772i
\(897\) 1.16601 4.65489i 0.0389320 0.155422i
\(898\) 8.30781i 0.277235i
\(899\) −44.1547 −1.47264
\(900\) −1.00000 14.9666i −0.0333333 0.498888i
\(901\) 14.9785i 0.499006i
\(902\) 22.1208i 0.736541i
\(903\) −16.3032 13.7562i −0.542537 0.457778i
\(904\) 6.00000 0.199557
\(905\) −13.0627 + 23.5406i −0.434220 + 0.782518i
\(906\) 9.50432 37.9426i 0.315760 1.26056i
\(907\) 33.9411i 1.12700i 0.826117 + 0.563498i \(0.190545\pi\)
−0.826117 + 0.563498i \(0.809455\pi\)
\(908\) 1.40122i 0.0465011i
\(909\) −10.3460 5.53019i −0.343156 0.183425i
\(910\) 2.84769 + 4.08510i 0.0944000 + 0.135420i
\(911\) 4.15390i 0.137625i −0.997630 0.0688125i \(-0.978079\pi\)
0.997630 0.0688125i \(-0.0219210\pi\)
\(912\) −7.64575 1.91520i −0.253176 0.0634185i
\(913\) 21.7792 0.720785
\(914\) 8.48528i 0.280668i
\(915\) −28.5129 26.6714i −0.942609 0.881730i
\(916\) 28.2835i 0.934513i
\(917\) −21.2915 10.4278i −0.703107 0.344358i
\(918\) −4.58301 4.15390i −0.151262 0.137099i
\(919\) 10.1255 0.334009 0.167005 0.985956i \(-0.446591\pi\)
0.167005 + 0.985956i \(0.446591\pi\)
\(920\) −6.43560 3.57113i −0.212176 0.117737i
\(921\) 6.22876 24.8661i 0.205245 0.819367i
\(922\) 8.96077 0.295107
\(923\) 10.6387i 0.350177i
\(924\) −9.90624 8.35862i −0.325891 0.274978i
\(925\) 45.8745 28.6078i 1.50834 0.940618i
\(926\) 23.9529i 0.787141i
\(927\) 33.2651 + 17.7809i 1.09257 + 0.584003i
\(928\) 7.98430i 0.262097i
\(929\) 30.7928 1.01028 0.505139 0.863038i \(-0.331441\pi\)
0.505139 + 0.863038i \(0.331441\pi\)
\(930\) −15.6417 14.6315i −0.512913 0.479786i
\(931\) 25.1660 19.5292i 0.824783 0.640043i
\(932\) 2.70850 0.0887198
\(933\) −1.16601 + 4.65489i −0.0381735 + 0.152394i
\(934\) 3.36028i 0.109952i
\(935\) −6.58301 3.65292i −0.215287 0.119463i
\(936\) −2.22699 1.19038i −0.0727914 0.0389087i
\(937\) 3.06871 0.100250 0.0501252 0.998743i \(-0.484038\pi\)
0.0501252 + 0.998743i \(0.484038\pi\)
\(938\) 5.41699 11.0604i 0.176871 0.361134i
\(939\) 3.41699 13.6412i 0.111509 0.445162i
\(940\) 4.70850 8.48528i 0.153574 0.276759i
\(941\) −40.2443 −1.31193 −0.655963 0.754793i \(-0.727737\pi\)
−0.655963 + 0.754793i \(0.727737\pi\)
\(942\) −9.52026 + 38.0063i −0.310187 + 1.23831i
\(943\) −25.7424 −0.838288
\(944\) −3.91044 −0.127274
\(945\) −30.4911 3.91047i −0.991876 0.127208i
\(946\) 13.1660 0.428064
\(947\) 24.0000 0.779895 0.389948 0.920837i \(-0.372493\pi\)
0.389948 + 0.920837i \(0.372493\pi\)
\(948\) −3.06871 + 12.2508i −0.0996671 + 0.397886i
\(949\) −2.58301 −0.0838479
\(950\) −19.3068 + 12.0399i −0.626396 + 0.390626i
\(951\) 2.52517 10.0808i 0.0818842 0.326894i
\(952\) 1.38527 2.82843i 0.0448967 0.0916698i
\(953\) −27.8745 −0.902944 −0.451472 0.892285i \(-0.649101\pi\)
−0.451472 + 0.892285i \(0.649101\pi\)
\(954\) 33.2915 + 17.7951i 1.07785 + 0.576136i
\(955\) −8.66259 + 15.6110i −0.280315 + 0.505161i
\(956\) 22.1264i 0.715620i
\(957\) 9.50432 37.9426i 0.307231 1.22651i
\(958\) −39.1044 −1.26340
\(959\) 22.0773 + 10.8127i 0.712915 + 0.349161i
\(960\) −2.64575 + 2.82843i −0.0853913 + 0.0912871i
\(961\) 0.416995 0.0134514
\(962\) 9.10132i 0.293438i
\(963\) 0 0
\(964\) 1.95906i 0.0630972i
\(965\) −9.20614 + 16.5906i −0.296356 + 0.534069i
\(966\) −9.72711 + 11.5281i −0.312965 + 0.370911i
\(967\) 49.4087i 1.58888i 0.607344 + 0.794439i \(0.292235\pi\)
−0.607344 + 0.794439i \(0.707765\pi\)
\(968\) −3.00000 −0.0964237
\(969\) −2.27980 + 9.10132i −0.0732379 + 0.292376i
\(970\) 15.8745 + 8.80879i 0.509700 + 0.282833i
\(971\) −24.6025 −0.789532 −0.394766 0.918782i \(-0.629174\pi\)
−0.394766 + 0.918782i \(0.629174\pi\)
\(972\) 14.6773 5.25127i 0.470776 0.168435i
\(973\) 18.1669 37.0931i 0.582404 1.18915i
\(974\) 32.4382i 1.03939i
\(975\) −6.93725 + 2.23871i −0.222170 + 0.0716960i
\(976\) 10.0808i 0.322680i
\(977\) −51.8745 −1.65961 −0.829806 0.558052i \(-0.811549\pi\)
−0.829806 + 0.558052i \(0.811549\pi\)
\(978\) 0 0
\(979\) 36.4053i 1.16352i
\(980\) −2.39082 15.4688i −0.0763720 0.494133i
\(981\) −5.29150 2.82843i −0.168945 0.0903047i
\(982\) 14.1421i 0.451294i
\(983\) 62.0225i 1.97821i −0.147213 0.989105i \(-0.547030\pi\)
0.147213 0.989105i \(-0.452970\pi\)
\(984\) −3.29150 + 13.1402i −0.104929 + 0.418893i
\(985\) −35.1939 19.5292i −1.12137 0.622251i
\(986\) 9.50432 0.302679
\(987\) −15.1997 12.8251i −0.483812 0.408227i
\(988\) 3.83039i 0.121861i
\(989\) 15.3216i 0.487198i
\(990\) 15.9399 10.2917i 0.506604 0.327092i
\(991\) −0.708497 −0.0225062 −0.0112531 0.999937i \(-0.503582\pi\)
−0.0112531 + 0.999937i \(0.503582\pi\)
\(992\) 5.53019i 0.175584i
\(993\) 3.36689 13.4411i 0.106845 0.426541i
\(994\) 14.7085 30.0317i 0.466525 0.952548i
\(995\) −18.0000 + 32.4382i −0.570638 + 1.02836i
\(996\) −12.9373 3.24067i −0.409933 0.102685i
\(997\) −42.2259 −1.33731 −0.668653 0.743574i \(-0.733129\pi\)
−0.668653 + 0.743574i \(0.733129\pi\)
\(998\) −1.41699 −0.0448542
\(999\) 41.6295 + 37.7318i 1.31710 + 1.19378i
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 210.2.d.a.209.5 yes 8
3.2 odd 2 210.2.d.b.209.6 yes 8
4.3 odd 2 1680.2.k.e.209.4 8
5.2 odd 4 1050.2.b.f.251.1 16
5.3 odd 4 1050.2.b.f.251.16 16
5.4 even 2 210.2.d.b.209.4 yes 8
7.6 odd 2 inner 210.2.d.a.209.4 yes 8
12.11 even 2 1680.2.k.f.209.3 8
15.2 even 4 1050.2.b.f.251.15 16
15.8 even 4 1050.2.b.f.251.2 16
15.14 odd 2 inner 210.2.d.a.209.3 8
20.19 odd 2 1680.2.k.f.209.5 8
21.20 even 2 210.2.d.b.209.3 yes 8
28.27 even 2 1680.2.k.e.209.5 8
35.13 even 4 1050.2.b.f.251.9 16
35.27 even 4 1050.2.b.f.251.8 16
35.34 odd 2 210.2.d.b.209.5 yes 8
60.59 even 2 1680.2.k.e.209.6 8
84.83 odd 2 1680.2.k.f.209.6 8
105.62 odd 4 1050.2.b.f.251.10 16
105.83 odd 4 1050.2.b.f.251.7 16
105.104 even 2 inner 210.2.d.a.209.6 yes 8
140.139 even 2 1680.2.k.f.209.4 8
420.419 odd 2 1680.2.k.e.209.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.d.a.209.3 8 15.14 odd 2 inner
210.2.d.a.209.4 yes 8 7.6 odd 2 inner
210.2.d.a.209.5 yes 8 1.1 even 1 trivial
210.2.d.a.209.6 yes 8 105.104 even 2 inner
210.2.d.b.209.3 yes 8 21.20 even 2
210.2.d.b.209.4 yes 8 5.4 even 2
210.2.d.b.209.5 yes 8 35.34 odd 2
210.2.d.b.209.6 yes 8 3.2 odd 2
1050.2.b.f.251.1 16 5.2 odd 4
1050.2.b.f.251.2 16 15.8 even 4
1050.2.b.f.251.7 16 105.83 odd 4
1050.2.b.f.251.8 16 35.27 even 4
1050.2.b.f.251.9 16 35.13 even 4
1050.2.b.f.251.10 16 105.62 odd 4
1050.2.b.f.251.15 16 15.2 even 4
1050.2.b.f.251.16 16 5.3 odd 4
1680.2.k.e.209.3 8 420.419 odd 2
1680.2.k.e.209.4 8 4.3 odd 2
1680.2.k.e.209.5 8 28.27 even 2
1680.2.k.e.209.6 8 60.59 even 2
1680.2.k.f.209.3 8 12.11 even 2
1680.2.k.f.209.4 8 140.139 even 2
1680.2.k.f.209.5 8 20.19 odd 2
1680.2.k.f.209.6 8 84.83 odd 2