Properties

Label 85.2.j.a.64.1
Level $85$
Weight $2$
Character 85.64
Analytic conductor $0.679$
Analytic rank $1$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [85,2,Mod(4,85)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(85, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("85.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 85 = 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 85.j (of order \(4\), 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: \(0.678728417181\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 64.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 85.64
Dual form 85.2.j.a.4.1

$q$-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} +(-1.00000 + 1.00000i) q^{3} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} +(1.00000 - 1.00000i) q^{6} +(-3.00000 - 3.00000i) q^{7} +3.00000 q^{8} +1.00000i q^{9} +(2.00000 + 1.00000i) q^{10} +(-3.00000 + 3.00000i) q^{11} +(1.00000 - 1.00000i) q^{12} +(3.00000 + 3.00000i) q^{14} +(3.00000 - 1.00000i) q^{15} -1.00000 q^{16} +(-1.00000 + 4.00000i) q^{17} -1.00000i q^{18} -6.00000i q^{19} +(2.00000 + 1.00000i) q^{20} +6.00000 q^{21} +(3.00000 - 3.00000i) q^{22} +(1.00000 + 1.00000i) q^{23} +(-3.00000 + 3.00000i) q^{24} +(3.00000 + 4.00000i) q^{25} +(-4.00000 - 4.00000i) q^{27} +(3.00000 + 3.00000i) q^{28} +(-3.00000 - 3.00000i) q^{29} +(-3.00000 + 1.00000i) q^{30} +(-1.00000 - 1.00000i) q^{31} -5.00000 q^{32} -6.00000i q^{33} +(1.00000 - 4.00000i) q^{34} +(3.00000 + 9.00000i) q^{35} -1.00000i q^{36} +(3.00000 - 3.00000i) q^{37} +6.00000i q^{38} +(-6.00000 - 3.00000i) q^{40} +(-3.00000 + 3.00000i) q^{41} -6.00000 q^{42} -12.0000 q^{43} +(3.00000 - 3.00000i) q^{44} +(1.00000 - 2.00000i) q^{45} +(-1.00000 - 1.00000i) q^{46} +2.00000i q^{47} +(1.00000 - 1.00000i) q^{48} +11.0000i q^{49} +(-3.00000 - 4.00000i) q^{50} +(-3.00000 - 5.00000i) q^{51} +2.00000 q^{53} +(4.00000 + 4.00000i) q^{54} +(9.00000 - 3.00000i) q^{55} +(-9.00000 - 9.00000i) q^{56} +(6.00000 + 6.00000i) q^{57} +(3.00000 + 3.00000i) q^{58} -6.00000i q^{59} +(-3.00000 + 1.00000i) q^{60} +(1.00000 - 1.00000i) q^{61} +(1.00000 + 1.00000i) q^{62} +(3.00000 - 3.00000i) q^{63} +7.00000 q^{64} +6.00000i q^{66} +6.00000i q^{67} +(1.00000 - 4.00000i) q^{68} -2.00000 q^{69} +(-3.00000 - 9.00000i) q^{70} +(3.00000 + 3.00000i) q^{71} +3.00000i q^{72} +(3.00000 - 3.00000i) q^{73} +(-3.00000 + 3.00000i) q^{74} +(-7.00000 - 1.00000i) q^{75} +6.00000i q^{76} +18.0000 q^{77} +(-7.00000 + 7.00000i) q^{79} +(2.00000 + 1.00000i) q^{80} +5.00000 q^{81} +(3.00000 - 3.00000i) q^{82} -4.00000 q^{83} -6.00000 q^{84} +(6.00000 - 7.00000i) q^{85} +12.0000 q^{86} +6.00000 q^{87} +(-9.00000 + 9.00000i) q^{88} +6.00000 q^{89} +(-1.00000 + 2.00000i) q^{90} +(-1.00000 - 1.00000i) q^{92} +2.00000 q^{93} -2.00000i q^{94} +(-6.00000 + 12.0000i) q^{95} +(5.00000 - 5.00000i) q^{96} +(3.00000 - 3.00000i) q^{97} -11.0000i q^{98} +(-3.00000 - 3.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 4 q^{5} + 2 q^{6} - 6 q^{7} + 6 q^{8} + 4 q^{10} - 6 q^{11} + 2 q^{12} + 6 q^{14} + 6 q^{15} - 2 q^{16} - 2 q^{17} + 4 q^{20} + 12 q^{21} + 6 q^{22} + 2 q^{23} - 6 q^{24}+ \cdots - 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/85\mathbb{Z}\right)^\times\).

\(n\) \(52\) \(71\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107 −0.353553 0.935414i \(-0.615027\pi\)
−0.353553 + 0.935414i \(0.615027\pi\)
\(3\) −1.00000 + 1.00000i −0.577350 + 0.577350i −0.934172 0.356822i \(-0.883860\pi\)
0.356822 + 0.934172i \(0.383860\pi\)
\(4\) −1.00000 −0.500000
\(5\) −2.00000 1.00000i −0.894427 0.447214i
\(6\) 1.00000 1.00000i 0.408248 0.408248i
\(7\) −3.00000 3.00000i −1.13389 1.13389i −0.989524 0.144370i \(-0.953885\pi\)
−0.144370 0.989524i \(-0.546115\pi\)
\(8\) 3.00000 1.06066
\(9\) 1.00000i 0.333333i
\(10\) 2.00000 + 1.00000i 0.632456 + 0.316228i
\(11\) −3.00000 + 3.00000i −0.904534 + 0.904534i −0.995824 0.0912903i \(-0.970901\pi\)
0.0912903 + 0.995824i \(0.470901\pi\)
\(12\) 1.00000 1.00000i 0.288675 0.288675i
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 3.00000 + 3.00000i 0.801784 + 0.801784i
\(15\) 3.00000 1.00000i 0.774597 0.258199i
\(16\) −1.00000 −0.250000
\(17\) −1.00000 + 4.00000i −0.242536 + 0.970143i
\(18\) 1.00000i 0.235702i
\(19\) 6.00000i 1.37649i −0.725476 0.688247i \(-0.758380\pi\)
0.725476 0.688247i \(-0.241620\pi\)
\(20\) 2.00000 + 1.00000i 0.447214 + 0.223607i
\(21\) 6.00000 1.30931
\(22\) 3.00000 3.00000i 0.639602 0.639602i
\(23\) 1.00000 + 1.00000i 0.208514 + 0.208514i 0.803636 0.595121i \(-0.202896\pi\)
−0.595121 + 0.803636i \(0.702896\pi\)
\(24\) −3.00000 + 3.00000i −0.612372 + 0.612372i
\(25\) 3.00000 + 4.00000i 0.600000 + 0.800000i
\(26\) 0 0
\(27\) −4.00000 4.00000i −0.769800 0.769800i
\(28\) 3.00000 + 3.00000i 0.566947 + 0.566947i
\(29\) −3.00000 3.00000i −0.557086 0.557086i 0.371391 0.928477i \(-0.378881\pi\)
−0.928477 + 0.371391i \(0.878881\pi\)
\(30\) −3.00000 + 1.00000i −0.547723 + 0.182574i
\(31\) −1.00000 1.00000i −0.179605 0.179605i 0.611578 0.791184i \(-0.290535\pi\)
−0.791184 + 0.611578i \(0.790535\pi\)
\(32\) −5.00000 −0.883883
\(33\) 6.00000i 1.04447i
\(34\) 1.00000 4.00000i 0.171499 0.685994i
\(35\) 3.00000 + 9.00000i 0.507093 + 1.52128i
\(36\) 1.00000i 0.166667i
\(37\) 3.00000 3.00000i 0.493197 0.493197i −0.416115 0.909312i \(-0.636609\pi\)
0.909312 + 0.416115i \(0.136609\pi\)
\(38\) 6.00000i 0.973329i
\(39\) 0 0
\(40\) −6.00000 3.00000i −0.948683 0.474342i
\(41\) −3.00000 + 3.00000i −0.468521 + 0.468521i −0.901435 0.432914i \(-0.857485\pi\)
0.432914 + 0.901435i \(0.357485\pi\)
\(42\) −6.00000 −0.925820
\(43\) −12.0000 −1.82998 −0.914991 0.403473i \(-0.867803\pi\)
−0.914991 + 0.403473i \(0.867803\pi\)
\(44\) 3.00000 3.00000i 0.452267 0.452267i
\(45\) 1.00000 2.00000i 0.149071 0.298142i
\(46\) −1.00000 1.00000i −0.147442 0.147442i
\(47\) 2.00000i 0.291730i 0.989305 + 0.145865i \(0.0465965\pi\)
−0.989305 + 0.145865i \(0.953403\pi\)
\(48\) 1.00000 1.00000i 0.144338 0.144338i
\(49\) 11.0000i 1.57143i
\(50\) −3.00000 4.00000i −0.424264 0.565685i
\(51\) −3.00000 5.00000i −0.420084 0.700140i
\(52\) 0 0
\(53\) 2.00000 0.274721 0.137361 0.990521i \(-0.456138\pi\)
0.137361 + 0.990521i \(0.456138\pi\)
\(54\) 4.00000 + 4.00000i 0.544331 + 0.544331i
\(55\) 9.00000 3.00000i 1.21356 0.404520i
\(56\) −9.00000 9.00000i −1.20268 1.20268i
\(57\) 6.00000 + 6.00000i 0.794719 + 0.794719i
\(58\) 3.00000 + 3.00000i 0.393919 + 0.393919i
\(59\) 6.00000i 0.781133i −0.920575 0.390567i \(-0.872279\pi\)
0.920575 0.390567i \(-0.127721\pi\)
\(60\) −3.00000 + 1.00000i −0.387298 + 0.129099i
\(61\) 1.00000 1.00000i 0.128037 0.128037i −0.640184 0.768221i \(-0.721142\pi\)
0.768221 + 0.640184i \(0.221142\pi\)
\(62\) 1.00000 + 1.00000i 0.127000 + 0.127000i
\(63\) 3.00000 3.00000i 0.377964 0.377964i
\(64\) 7.00000 0.875000
\(65\) 0 0
\(66\) 6.00000i 0.738549i
\(67\) 6.00000i 0.733017i 0.930415 + 0.366508i \(0.119447\pi\)
−0.930415 + 0.366508i \(0.880553\pi\)
\(68\) 1.00000 4.00000i 0.121268 0.485071i
\(69\) −2.00000 −0.240772
\(70\) −3.00000 9.00000i −0.358569 1.07571i
\(71\) 3.00000 + 3.00000i 0.356034 + 0.356034i 0.862349 0.506314i \(-0.168992\pi\)
−0.506314 + 0.862349i \(0.668992\pi\)
\(72\) 3.00000i 0.353553i
\(73\) 3.00000 3.00000i 0.351123 0.351123i −0.509404 0.860527i \(-0.670134\pi\)
0.860527 + 0.509404i \(0.170134\pi\)
\(74\) −3.00000 + 3.00000i −0.348743 + 0.348743i
\(75\) −7.00000 1.00000i −0.808290 0.115470i
\(76\) 6.00000i 0.688247i
\(77\) 18.0000 2.05129
\(78\) 0 0
\(79\) −7.00000 + 7.00000i −0.787562 + 0.787562i −0.981094 0.193532i \(-0.938006\pi\)
0.193532 + 0.981094i \(0.438006\pi\)
\(80\) 2.00000 + 1.00000i 0.223607 + 0.111803i
\(81\) 5.00000 0.555556
\(82\) 3.00000 3.00000i 0.331295 0.331295i
\(83\) −4.00000 −0.439057 −0.219529 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) −6.00000 −0.654654
\(85\) 6.00000 7.00000i 0.650791 0.759257i
\(86\) 12.0000 1.29399
\(87\) 6.00000 0.643268
\(88\) −9.00000 + 9.00000i −0.959403 + 0.959403i
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) −1.00000 + 2.00000i −0.105409 + 0.210819i
\(91\) 0 0
\(92\) −1.00000 1.00000i −0.104257 0.104257i
\(93\) 2.00000 0.207390
\(94\) 2.00000i 0.206284i
\(95\) −6.00000 + 12.0000i −0.615587 + 1.23117i
\(96\) 5.00000 5.00000i 0.510310 0.510310i
\(97\) 3.00000 3.00000i 0.304604 0.304604i −0.538208 0.842812i \(-0.680899\pi\)
0.842812 + 0.538208i \(0.180899\pi\)
\(98\) 11.0000i 1.11117i
\(99\) −3.00000 3.00000i −0.301511 0.301511i
\(100\) −3.00000 4.00000i −0.300000 0.400000i
\(101\) −6.00000 −0.597022 −0.298511 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(102\) 3.00000 + 5.00000i 0.297044 + 0.495074i
\(103\) 6.00000i 0.591198i −0.955312 0.295599i \(-0.904481\pi\)
0.955312 0.295599i \(-0.0955191\pi\)
\(104\) 0 0
\(105\) −12.0000 6.00000i −1.17108 0.585540i
\(106\) −2.00000 −0.194257
\(107\) −9.00000 + 9.00000i −0.870063 + 0.870063i −0.992479 0.122416i \(-0.960936\pi\)
0.122416 + 0.992479i \(0.460936\pi\)
\(108\) 4.00000 + 4.00000i 0.384900 + 0.384900i
\(109\) −7.00000 + 7.00000i −0.670478 + 0.670478i −0.957826 0.287348i \(-0.907226\pi\)
0.287348 + 0.957826i \(0.407226\pi\)
\(110\) −9.00000 + 3.00000i −0.858116 + 0.286039i
\(111\) 6.00000i 0.569495i
\(112\) 3.00000 + 3.00000i 0.283473 + 0.283473i
\(113\) −9.00000 9.00000i −0.846649 0.846649i 0.143065 0.989713i \(-0.454304\pi\)
−0.989713 + 0.143065i \(0.954304\pi\)
\(114\) −6.00000 6.00000i −0.561951 0.561951i
\(115\) −1.00000 3.00000i −0.0932505 0.279751i
\(116\) 3.00000 + 3.00000i 0.278543 + 0.278543i
\(117\) 0 0
\(118\) 6.00000i 0.552345i
\(119\) 15.0000 9.00000i 1.37505 0.825029i
\(120\) 9.00000 3.00000i 0.821584 0.273861i
\(121\) 7.00000i 0.636364i
\(122\) −1.00000 + 1.00000i −0.0905357 + 0.0905357i
\(123\) 6.00000i 0.541002i
\(124\) 1.00000 + 1.00000i 0.0898027 + 0.0898027i
\(125\) −2.00000 11.0000i −0.178885 0.983870i
\(126\) −3.00000 + 3.00000i −0.267261 + 0.267261i
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 3.00000 0.265165
\(129\) 12.0000 12.0000i 1.05654 1.05654i
\(130\) 0 0
\(131\) 3.00000 + 3.00000i 0.262111 + 0.262111i 0.825911 0.563800i \(-0.190661\pi\)
−0.563800 + 0.825911i \(0.690661\pi\)
\(132\) 6.00000i 0.522233i
\(133\) −18.0000 + 18.0000i −1.56080 + 1.56080i
\(134\) 6.00000i 0.518321i
\(135\) 4.00000 + 12.0000i 0.344265 + 1.03280i
\(136\) −3.00000 + 12.0000i −0.257248 + 1.02899i
\(137\) 4.00000i 0.341743i 0.985293 + 0.170872i \(0.0546583\pi\)
−0.985293 + 0.170872i \(0.945342\pi\)
\(138\) 2.00000 0.170251
\(139\) 7.00000 + 7.00000i 0.593732 + 0.593732i 0.938638 0.344905i \(-0.112089\pi\)
−0.344905 + 0.938638i \(0.612089\pi\)
\(140\) −3.00000 9.00000i −0.253546 0.760639i
\(141\) −2.00000 2.00000i −0.168430 0.168430i
\(142\) −3.00000 3.00000i −0.251754 0.251754i
\(143\) 0 0
\(144\) 1.00000i 0.0833333i
\(145\) 3.00000 + 9.00000i 0.249136 + 0.747409i
\(146\) −3.00000 + 3.00000i −0.248282 + 0.248282i
\(147\) −11.0000 11.0000i −0.907265 0.907265i
\(148\) −3.00000 + 3.00000i −0.246598 + 0.246598i
\(149\) −18.0000 −1.47462 −0.737309 0.675556i \(-0.763904\pi\)
−0.737309 + 0.675556i \(0.763904\pi\)
\(150\) 7.00000 + 1.00000i 0.571548 + 0.0816497i
\(151\) 10.0000i 0.813788i −0.913475 0.406894i \(-0.866612\pi\)
0.913475 0.406894i \(-0.133388\pi\)
\(152\) 18.0000i 1.45999i
\(153\) −4.00000 1.00000i −0.323381 0.0808452i
\(154\) −18.0000 −1.45048
\(155\) 1.00000 + 3.00000i 0.0803219 + 0.240966i
\(156\) 0 0
\(157\) 12.0000i 0.957704i 0.877896 + 0.478852i \(0.158947\pi\)
−0.877896 + 0.478852i \(0.841053\pi\)
\(158\) 7.00000 7.00000i 0.556890 0.556890i
\(159\) −2.00000 + 2.00000i −0.158610 + 0.158610i
\(160\) 10.0000 + 5.00000i 0.790569 + 0.395285i
\(161\) 6.00000i 0.472866i
\(162\) −5.00000 −0.392837
\(163\) 9.00000 + 9.00000i 0.704934 + 0.704934i 0.965465 0.260531i \(-0.0838976\pi\)
−0.260531 + 0.965465i \(0.583898\pi\)
\(164\) 3.00000 3.00000i 0.234261 0.234261i
\(165\) −6.00000 + 12.0000i −0.467099 + 0.934199i
\(166\) 4.00000 0.310460
\(167\) 3.00000 3.00000i 0.232147 0.232147i −0.581441 0.813588i \(-0.697511\pi\)
0.813588 + 0.581441i \(0.197511\pi\)
\(168\) 18.0000 1.38873
\(169\) 13.0000 1.00000
\(170\) −6.00000 + 7.00000i −0.460179 + 0.536875i
\(171\) 6.00000 0.458831
\(172\) 12.0000 0.914991
\(173\) 15.0000 15.0000i 1.14043 1.14043i 0.152057 0.988372i \(-0.451410\pi\)
0.988372 0.152057i \(-0.0485898\pi\)
\(174\) −6.00000 −0.454859
\(175\) 3.00000 21.0000i 0.226779 1.58745i
\(176\) 3.00000 3.00000i 0.226134 0.226134i
\(177\) 6.00000 + 6.00000i 0.450988 + 0.450988i
\(178\) −6.00000 −0.449719
\(179\) 6.00000i 0.448461i −0.974536 0.224231i \(-0.928013\pi\)
0.974536 0.224231i \(-0.0719869\pi\)
\(180\) −1.00000 + 2.00000i −0.0745356 + 0.149071i
\(181\) −11.0000 + 11.0000i −0.817624 + 0.817624i −0.985763 0.168140i \(-0.946224\pi\)
0.168140 + 0.985763i \(0.446224\pi\)
\(182\) 0 0
\(183\) 2.00000i 0.147844i
\(184\) 3.00000 + 3.00000i 0.221163 + 0.221163i
\(185\) −9.00000 + 3.00000i −0.661693 + 0.220564i
\(186\) −2.00000 −0.146647
\(187\) −9.00000 15.0000i −0.658145 1.09691i
\(188\) 2.00000i 0.145865i
\(189\) 24.0000i 1.74574i
\(190\) 6.00000 12.0000i 0.435286 0.870572i
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) −7.00000 + 7.00000i −0.505181 + 0.505181i
\(193\) 3.00000 + 3.00000i 0.215945 + 0.215945i 0.806787 0.590842i \(-0.201204\pi\)
−0.590842 + 0.806787i \(0.701204\pi\)
\(194\) −3.00000 + 3.00000i −0.215387 + 0.215387i
\(195\) 0 0
\(196\) 11.0000i 0.785714i
\(197\) −13.0000 13.0000i −0.926212 0.926212i 0.0712470 0.997459i \(-0.477302\pi\)
−0.997459 + 0.0712470i \(0.977302\pi\)
\(198\) 3.00000 + 3.00000i 0.213201 + 0.213201i
\(199\) −1.00000 1.00000i −0.0708881 0.0708881i 0.670774 0.741662i \(-0.265962\pi\)
−0.741662 + 0.670774i \(0.765962\pi\)
\(200\) 9.00000 + 12.0000i 0.636396 + 0.848528i
\(201\) −6.00000 6.00000i −0.423207 0.423207i
\(202\) 6.00000 0.422159
\(203\) 18.0000i 1.26335i
\(204\) 3.00000 + 5.00000i 0.210042 + 0.350070i
\(205\) 9.00000 3.00000i 0.628587 0.209529i
\(206\) 6.00000i 0.418040i
\(207\) −1.00000 + 1.00000i −0.0695048 + 0.0695048i
\(208\) 0 0
\(209\) 18.0000 + 18.0000i 1.24509 + 1.24509i
\(210\) 12.0000 + 6.00000i 0.828079 + 0.414039i
\(211\) 17.0000 17.0000i 1.17033 1.17033i 0.188197 0.982131i \(-0.439736\pi\)
0.982131 0.188197i \(-0.0602643\pi\)
\(212\) −2.00000 −0.137361
\(213\) −6.00000 −0.411113
\(214\) 9.00000 9.00000i 0.615227 0.615227i
\(215\) 24.0000 + 12.0000i 1.63679 + 0.818393i
\(216\) −12.0000 12.0000i −0.816497 0.816497i
\(217\) 6.00000i 0.407307i
\(218\) 7.00000 7.00000i 0.474100 0.474100i
\(219\) 6.00000i 0.405442i
\(220\) −9.00000 + 3.00000i −0.606780 + 0.202260i
\(221\) 0 0
\(222\) 6.00000i 0.402694i
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 15.0000 + 15.0000i 1.00223 + 1.00223i
\(225\) −4.00000 + 3.00000i −0.266667 + 0.200000i
\(226\) 9.00000 + 9.00000i 0.598671 + 0.598671i
\(227\) −15.0000 15.0000i −0.995585 0.995585i 0.00440533 0.999990i \(-0.498598\pi\)
−0.999990 + 0.00440533i \(0.998598\pi\)
\(228\) −6.00000 6.00000i −0.397360 0.397360i
\(229\) 24.0000i 1.58596i −0.609245 0.792982i \(-0.708527\pi\)
0.609245 0.792982i \(-0.291473\pi\)
\(230\) 1.00000 + 3.00000i 0.0659380 + 0.197814i
\(231\) −18.0000 + 18.0000i −1.18431 + 1.18431i
\(232\) −9.00000 9.00000i −0.590879 0.590879i
\(233\) −5.00000 + 5.00000i −0.327561 + 0.327561i −0.851658 0.524097i \(-0.824403\pi\)
0.524097 + 0.851658i \(0.324403\pi\)
\(234\) 0 0
\(235\) 2.00000 4.00000i 0.130466 0.260931i
\(236\) 6.00000i 0.390567i
\(237\) 14.0000i 0.909398i
\(238\) −15.0000 + 9.00000i −0.972306 + 0.583383i
\(239\) −24.0000 −1.55243 −0.776215 0.630468i \(-0.782863\pi\)
−0.776215 + 0.630468i \(0.782863\pi\)
\(240\) −3.00000 + 1.00000i −0.193649 + 0.0645497i
\(241\) −19.0000 19.0000i −1.22390 1.22390i −0.966235 0.257663i \(-0.917048\pi\)
−0.257663 0.966235i \(-0.582952\pi\)
\(242\) 7.00000i 0.449977i
\(243\) 7.00000 7.00000i 0.449050 0.449050i
\(244\) −1.00000 + 1.00000i −0.0640184 + 0.0640184i
\(245\) 11.0000 22.0000i 0.702764 1.40553i
\(246\) 6.00000i 0.382546i
\(247\) 0 0
\(248\) −3.00000 3.00000i −0.190500 0.190500i
\(249\) 4.00000 4.00000i 0.253490 0.253490i
\(250\) 2.00000 + 11.0000i 0.126491 + 0.695701i
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) −3.00000 + 3.00000i −0.188982 + 0.188982i
\(253\) −6.00000 −0.377217
\(254\) 0 0
\(255\) 1.00000 + 13.0000i 0.0626224 + 0.814092i
\(256\) −17.0000 −1.06250
\(257\) −14.0000 −0.873296 −0.436648 0.899632i \(-0.643834\pi\)
−0.436648 + 0.899632i \(0.643834\pi\)
\(258\) −12.0000 + 12.0000i −0.747087 + 0.747087i
\(259\) −18.0000 −1.11847
\(260\) 0 0
\(261\) 3.00000 3.00000i 0.185695 0.185695i
\(262\) −3.00000 3.00000i −0.185341 0.185341i
\(263\) 16.0000 0.986602 0.493301 0.869859i \(-0.335790\pi\)
0.493301 + 0.869859i \(0.335790\pi\)
\(264\) 18.0000i 1.10782i
\(265\) −4.00000 2.00000i −0.245718 0.122859i
\(266\) 18.0000 18.0000i 1.10365 1.10365i
\(267\) −6.00000 + 6.00000i −0.367194 + 0.367194i
\(268\) 6.00000i 0.366508i
\(269\) −3.00000 3.00000i −0.182913 0.182913i 0.609711 0.792624i \(-0.291286\pi\)
−0.792624 + 0.609711i \(0.791286\pi\)
\(270\) −4.00000 12.0000i −0.243432 0.730297i
\(271\) 24.0000 1.45790 0.728948 0.684569i \(-0.240010\pi\)
0.728948 + 0.684569i \(0.240010\pi\)
\(272\) 1.00000 4.00000i 0.0606339 0.242536i
\(273\) 0 0
\(274\) 4.00000i 0.241649i
\(275\) −21.0000 3.00000i −1.26635 0.180907i
\(276\) 2.00000 0.120386
\(277\) −21.0000 + 21.0000i −1.26177 + 1.26177i −0.311532 + 0.950236i \(0.600842\pi\)
−0.950236 + 0.311532i \(0.899158\pi\)
\(278\) −7.00000 7.00000i −0.419832 0.419832i
\(279\) 1.00000 1.00000i 0.0598684 0.0598684i
\(280\) 9.00000 + 27.0000i 0.537853 + 1.61356i
\(281\) 24.0000i 1.43172i 0.698244 + 0.715860i \(0.253965\pi\)
−0.698244 + 0.715860i \(0.746035\pi\)
\(282\) 2.00000 + 2.00000i 0.119098 + 0.119098i
\(283\) 9.00000 + 9.00000i 0.534994 + 0.534994i 0.922055 0.387060i \(-0.126509\pi\)
−0.387060 + 0.922055i \(0.626509\pi\)
\(284\) −3.00000 3.00000i −0.178017 0.178017i
\(285\) −6.00000 18.0000i −0.355409 1.06623i
\(286\) 0 0
\(287\) 18.0000 1.06251
\(288\) 5.00000i 0.294628i
\(289\) −15.0000 8.00000i −0.882353 0.470588i
\(290\) −3.00000 9.00000i −0.176166 0.528498i
\(291\) 6.00000i 0.351726i
\(292\) −3.00000 + 3.00000i −0.175562 + 0.175562i
\(293\) 4.00000i 0.233682i −0.993151 0.116841i \(-0.962723\pi\)
0.993151 0.116841i \(-0.0372769\pi\)
\(294\) 11.0000 + 11.0000i 0.641533 + 0.641533i
\(295\) −6.00000 + 12.0000i −0.349334 + 0.698667i
\(296\) 9.00000 9.00000i 0.523114 0.523114i
\(297\) 24.0000 1.39262
\(298\) 18.0000 1.04271
\(299\) 0 0
\(300\) 7.00000 + 1.00000i 0.404145 + 0.0577350i
\(301\) 36.0000 + 36.0000i 2.07501 + 2.07501i
\(302\) 10.0000i 0.575435i
\(303\) 6.00000 6.00000i 0.344691 0.344691i
\(304\) 6.00000i 0.344124i
\(305\) −3.00000 + 1.00000i −0.171780 + 0.0572598i
\(306\) 4.00000 + 1.00000i 0.228665 + 0.0571662i
\(307\) 18.0000i 1.02731i −0.857996 0.513657i \(-0.828290\pi\)
0.857996 0.513657i \(-0.171710\pi\)
\(308\) −18.0000 −1.02565
\(309\) 6.00000 + 6.00000i 0.341328 + 0.341328i
\(310\) −1.00000 3.00000i −0.0567962 0.170389i
\(311\) 3.00000 + 3.00000i 0.170114 + 0.170114i 0.787030 0.616915i \(-0.211618\pi\)
−0.616915 + 0.787030i \(0.711618\pi\)
\(312\) 0 0
\(313\) 3.00000 + 3.00000i 0.169570 + 0.169570i 0.786790 0.617220i \(-0.211741\pi\)
−0.617220 + 0.786790i \(0.711741\pi\)
\(314\) 12.0000i 0.677199i
\(315\) −9.00000 + 3.00000i −0.507093 + 0.169031i
\(316\) 7.00000 7.00000i 0.393781 0.393781i
\(317\) 15.0000 + 15.0000i 0.842484 + 0.842484i 0.989181 0.146697i \(-0.0468644\pi\)
−0.146697 + 0.989181i \(0.546864\pi\)
\(318\) 2.00000 2.00000i 0.112154 0.112154i
\(319\) 18.0000 1.00781
\(320\) −14.0000 7.00000i −0.782624 0.391312i
\(321\) 18.0000i 1.00466i
\(322\) 6.00000i 0.334367i
\(323\) 24.0000 + 6.00000i 1.33540 + 0.333849i
\(324\) −5.00000 −0.277778
\(325\) 0 0
\(326\) −9.00000 9.00000i −0.498464 0.498464i
\(327\) 14.0000i 0.774202i
\(328\) −9.00000 + 9.00000i −0.496942 + 0.496942i
\(329\) 6.00000 6.00000i 0.330791 0.330791i
\(330\) 6.00000 12.0000i 0.330289 0.660578i
\(331\) 18.0000i 0.989369i 0.869072 + 0.494685i \(0.164716\pi\)
−0.869072 + 0.494685i \(0.835284\pi\)
\(332\) 4.00000 0.219529
\(333\) 3.00000 + 3.00000i 0.164399 + 0.164399i
\(334\) −3.00000 + 3.00000i −0.164153 + 0.164153i
\(335\) 6.00000 12.0000i 0.327815 0.655630i
\(336\) −6.00000 −0.327327
\(337\) 15.0000 15.0000i 0.817102 0.817102i −0.168585 0.985687i \(-0.553920\pi\)
0.985687 + 0.168585i \(0.0539198\pi\)
\(338\) −13.0000 −0.707107
\(339\) 18.0000 0.977626
\(340\) −6.00000 + 7.00000i −0.325396 + 0.379628i
\(341\) 6.00000 0.324918
\(342\) −6.00000 −0.324443
\(343\) 12.0000 12.0000i 0.647939 0.647939i
\(344\) −36.0000 −1.94099
\(345\) 4.00000 + 2.00000i 0.215353 + 0.107676i
\(346\) −15.0000 + 15.0000i −0.806405 + 0.806405i
\(347\) 9.00000 + 9.00000i 0.483145 + 0.483145i 0.906135 0.422989i \(-0.139019\pi\)
−0.422989 + 0.906135i \(0.639019\pi\)
\(348\) −6.00000 −0.321634
\(349\) 28.0000i 1.49881i −0.662114 0.749403i \(-0.730341\pi\)
0.662114 0.749403i \(-0.269659\pi\)
\(350\) −3.00000 + 21.0000i −0.160357 + 1.12250i
\(351\) 0 0
\(352\) 15.0000 15.0000i 0.799503 0.799503i
\(353\) 16.0000i 0.851594i 0.904819 + 0.425797i \(0.140006\pi\)
−0.904819 + 0.425797i \(0.859994\pi\)
\(354\) −6.00000 6.00000i −0.318896 0.318896i
\(355\) −3.00000 9.00000i −0.159223 0.477670i
\(356\) −6.00000 −0.317999
\(357\) −6.00000 + 24.0000i −0.317554 + 1.27021i
\(358\) 6.00000i 0.317110i
\(359\) 30.0000i 1.58334i 0.610949 + 0.791670i \(0.290788\pi\)
−0.610949 + 0.791670i \(0.709212\pi\)
\(360\) 3.00000 6.00000i 0.158114 0.316228i
\(361\) −17.0000 −0.894737
\(362\) 11.0000 11.0000i 0.578147 0.578147i
\(363\) 7.00000 + 7.00000i 0.367405 + 0.367405i
\(364\) 0 0
\(365\) −9.00000 + 3.00000i −0.471082 + 0.157027i
\(366\) 2.00000i 0.104542i
\(367\) −3.00000 3.00000i −0.156599 0.156599i 0.624459 0.781058i \(-0.285320\pi\)
−0.781058 + 0.624459i \(0.785320\pi\)
\(368\) −1.00000 1.00000i −0.0521286 0.0521286i
\(369\) −3.00000 3.00000i −0.156174 0.156174i
\(370\) 9.00000 3.00000i 0.467888 0.155963i
\(371\) −6.00000 6.00000i −0.311504 0.311504i
\(372\) −2.00000 −0.103695
\(373\) 24.0000i 1.24267i −0.783544 0.621336i \(-0.786590\pi\)
0.783544 0.621336i \(-0.213410\pi\)
\(374\) 9.00000 + 15.0000i 0.465379 + 0.775632i
\(375\) 13.0000 + 9.00000i 0.671317 + 0.464758i
\(376\) 6.00000i 0.309426i
\(377\) 0 0
\(378\) 24.0000i 1.23443i
\(379\) 11.0000 + 11.0000i 0.565032 + 0.565032i 0.930733 0.365701i \(-0.119171\pi\)
−0.365701 + 0.930733i \(0.619171\pi\)
\(380\) 6.00000 12.0000i 0.307794 0.615587i
\(381\) 0 0
\(382\) 0 0
\(383\) −16.0000 −0.817562 −0.408781 0.912633i \(-0.634046\pi\)
−0.408781 + 0.912633i \(0.634046\pi\)
\(384\) −3.00000 + 3.00000i −0.153093 + 0.153093i
\(385\) −36.0000 18.0000i −1.83473 0.917365i
\(386\) −3.00000 3.00000i −0.152696 0.152696i
\(387\) 12.0000i 0.609994i
\(388\) −3.00000 + 3.00000i −0.152302 + 0.152302i
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) −5.00000 + 3.00000i −0.252861 + 0.151717i
\(392\) 33.0000i 1.66675i
\(393\) −6.00000 −0.302660
\(394\) 13.0000 + 13.0000i 0.654931 + 0.654931i
\(395\) 21.0000 7.00000i 1.05662 0.352208i
\(396\) 3.00000 + 3.00000i 0.150756 + 0.150756i
\(397\) 27.0000 + 27.0000i 1.35509 + 1.35509i 0.879862 + 0.475229i \(0.157635\pi\)
0.475229 + 0.879862i \(0.342365\pi\)
\(398\) 1.00000 + 1.00000i 0.0501255 + 0.0501255i
\(399\) 36.0000i 1.80225i
\(400\) −3.00000 4.00000i −0.150000 0.200000i
\(401\) 9.00000 9.00000i 0.449439 0.449439i −0.445729 0.895168i \(-0.647056\pi\)
0.895168 + 0.445729i \(0.147056\pi\)
\(402\) 6.00000 + 6.00000i 0.299253 + 0.299253i
\(403\) 0 0
\(404\) 6.00000 0.298511
\(405\) −10.0000 5.00000i −0.496904 0.248452i
\(406\) 18.0000i 0.893325i
\(407\) 18.0000i 0.892227i
\(408\) −9.00000 15.0000i −0.445566 0.742611i
\(409\) −30.0000 −1.48340 −0.741702 0.670729i \(-0.765981\pi\)
−0.741702 + 0.670729i \(0.765981\pi\)
\(410\) −9.00000 + 3.00000i −0.444478 + 0.148159i
\(411\) −4.00000 4.00000i −0.197305 0.197305i
\(412\) 6.00000i 0.295599i
\(413\) −18.0000 + 18.0000i −0.885722 + 0.885722i
\(414\) 1.00000 1.00000i 0.0491473 0.0491473i
\(415\) 8.00000 + 4.00000i 0.392705 + 0.196352i
\(416\) 0 0
\(417\) −14.0000 −0.685583
\(418\) −18.0000 18.0000i −0.880409 0.880409i
\(419\) −15.0000 + 15.0000i −0.732798 + 0.732798i −0.971173 0.238375i \(-0.923385\pi\)
0.238375 + 0.971173i \(0.423385\pi\)
\(420\) 12.0000 + 6.00000i 0.585540 + 0.292770i
\(421\) −6.00000 −0.292422 −0.146211 0.989253i \(-0.546708\pi\)
−0.146211 + 0.989253i \(0.546708\pi\)
\(422\) −17.0000 + 17.0000i −0.827547 + 0.827547i
\(423\) −2.00000 −0.0972433
\(424\) 6.00000 0.291386
\(425\) −19.0000 + 8.00000i −0.921635 + 0.388057i
\(426\) 6.00000 0.290701
\(427\) −6.00000 −0.290360
\(428\) 9.00000 9.00000i 0.435031 0.435031i
\(429\) 0 0
\(430\) −24.0000 12.0000i −1.15738 0.578691i
\(431\) 9.00000 9.00000i 0.433515 0.433515i −0.456307 0.889822i \(-0.650828\pi\)
0.889822 + 0.456307i \(0.150828\pi\)
\(432\) 4.00000 + 4.00000i 0.192450 + 0.192450i
\(433\) −30.0000 −1.44171 −0.720854 0.693087i \(-0.756250\pi\)
−0.720854 + 0.693087i \(0.756250\pi\)
\(434\) 6.00000i 0.288009i
\(435\) −12.0000 6.00000i −0.575356 0.287678i
\(436\) 7.00000 7.00000i 0.335239 0.335239i
\(437\) 6.00000 6.00000i 0.287019 0.287019i
\(438\) 6.00000i 0.286691i
\(439\) 19.0000 + 19.0000i 0.906821 + 0.906821i 0.996014 0.0891938i \(-0.0284290\pi\)
−0.0891938 + 0.996014i \(0.528429\pi\)
\(440\) 27.0000 9.00000i 1.28717 0.429058i
\(441\) −11.0000 −0.523810
\(442\) 0 0
\(443\) 22.0000i 1.04525i 0.852562 + 0.522626i \(0.175047\pi\)
−0.852562 + 0.522626i \(0.824953\pi\)
\(444\) 6.00000i 0.284747i
\(445\) −12.0000 6.00000i −0.568855 0.284427i
\(446\) 0 0
\(447\) 18.0000 18.0000i 0.851371 0.851371i
\(448\) −21.0000 21.0000i −0.992157 0.992157i
\(449\) −15.0000 + 15.0000i −0.707894 + 0.707894i −0.966092 0.258198i \(-0.916871\pi\)
0.258198 + 0.966092i \(0.416871\pi\)
\(450\) 4.00000 3.00000i 0.188562 0.141421i
\(451\) 18.0000i 0.847587i
\(452\) 9.00000 + 9.00000i 0.423324 + 0.423324i
\(453\) 10.0000 + 10.0000i 0.469841 + 0.469841i
\(454\) 15.0000 + 15.0000i 0.703985 + 0.703985i
\(455\) 0 0
\(456\) 18.0000 + 18.0000i 0.842927 + 0.842927i
\(457\) −6.00000 −0.280668 −0.140334 0.990104i \(-0.544818\pi\)
−0.140334 + 0.990104i \(0.544818\pi\)
\(458\) 24.0000i 1.12145i
\(459\) 20.0000 12.0000i 0.933520 0.560112i
\(460\) 1.00000 + 3.00000i 0.0466252 + 0.139876i
\(461\) 12.0000i 0.558896i −0.960161 0.279448i \(-0.909849\pi\)
0.960161 0.279448i \(-0.0901514\pi\)
\(462\) 18.0000 18.0000i 0.837436 0.837436i
\(463\) 18.0000i 0.836531i 0.908325 + 0.418265i \(0.137362\pi\)
−0.908325 + 0.418265i \(0.862638\pi\)
\(464\) 3.00000 + 3.00000i 0.139272 + 0.139272i
\(465\) −4.00000 2.00000i −0.185496 0.0927478i
\(466\) 5.00000 5.00000i 0.231621 0.231621i
\(467\) −28.0000 −1.29569 −0.647843 0.761774i \(-0.724329\pi\)
−0.647843 + 0.761774i \(0.724329\pi\)
\(468\) 0 0
\(469\) 18.0000 18.0000i 0.831163 0.831163i
\(470\) −2.00000 + 4.00000i −0.0922531 + 0.184506i
\(471\) −12.0000 12.0000i −0.552931 0.552931i
\(472\) 18.0000i 0.828517i
\(473\) 36.0000 36.0000i 1.65528 1.65528i
\(474\) 14.0000i 0.643041i
\(475\) 24.0000 18.0000i 1.10120 0.825897i
\(476\) −15.0000 + 9.00000i −0.687524 + 0.412514i
\(477\) 2.00000i 0.0915737i
\(478\) 24.0000 1.09773
\(479\) −9.00000 9.00000i −0.411220 0.411220i 0.470943 0.882164i \(-0.343914\pi\)
−0.882164 + 0.470943i \(0.843914\pi\)
\(480\) −15.0000 + 5.00000i −0.684653 + 0.228218i
\(481\) 0 0
\(482\) 19.0000 + 19.0000i 0.865426 + 0.865426i
\(483\) 6.00000 + 6.00000i 0.273009 + 0.273009i
\(484\) 7.00000i 0.318182i
\(485\) −9.00000 + 3.00000i −0.408669 + 0.136223i
\(486\) −7.00000 + 7.00000i −0.317526 + 0.317526i
\(487\) −3.00000 3.00000i −0.135943 0.135943i 0.635861 0.771804i \(-0.280645\pi\)
−0.771804 + 0.635861i \(0.780645\pi\)
\(488\) 3.00000 3.00000i 0.135804 0.135804i
\(489\) −18.0000 −0.813988
\(490\) −11.0000 + 22.0000i −0.496929 + 0.993859i
\(491\) 6.00000i 0.270776i −0.990793 0.135388i \(-0.956772\pi\)
0.990793 0.135388i \(-0.0432281\pi\)
\(492\) 6.00000i 0.270501i
\(493\) 15.0000 9.00000i 0.675566 0.405340i
\(494\) 0 0
\(495\) 3.00000 + 9.00000i 0.134840 + 0.404520i
\(496\) 1.00000 + 1.00000i 0.0449013 + 0.0449013i
\(497\) 18.0000i 0.807410i
\(498\) −4.00000 + 4.00000i −0.179244 + 0.179244i
\(499\) −23.0000 + 23.0000i −1.02962 + 1.02962i −0.0300737 + 0.999548i \(0.509574\pi\)
−0.999548 + 0.0300737i \(0.990426\pi\)
\(500\) 2.00000 + 11.0000i 0.0894427 + 0.491935i
\(501\) 6.00000i 0.268060i
\(502\) 12.0000 0.535586
\(503\) −3.00000 3.00000i −0.133763 0.133763i 0.637055 0.770818i \(-0.280152\pi\)
−0.770818 + 0.637055i \(0.780152\pi\)
\(504\) 9.00000 9.00000i 0.400892 0.400892i
\(505\) 12.0000 + 6.00000i 0.533993 + 0.266996i
\(506\) 6.00000 0.266733
\(507\) −13.0000 + 13.0000i −0.577350 + 0.577350i
\(508\) 0 0
\(509\) 6.00000 0.265945 0.132973 0.991120i \(-0.457548\pi\)
0.132973 + 0.991120i \(0.457548\pi\)
\(510\) −1.00000 13.0000i −0.0442807 0.575650i
\(511\) −18.0000 −0.796273
\(512\) 11.0000 0.486136
\(513\) −24.0000 + 24.0000i −1.05963 + 1.05963i
\(514\) 14.0000 0.617514
\(515\) −6.00000 + 12.0000i −0.264392 + 0.528783i
\(516\) −12.0000 + 12.0000i −0.528271 + 0.528271i
\(517\) −6.00000 6.00000i −0.263880 0.263880i
\(518\) 18.0000 0.790875
\(519\) 30.0000i 1.31685i
\(520\) 0 0
\(521\) 9.00000 9.00000i 0.394297 0.394297i −0.481919 0.876216i \(-0.660060\pi\)
0.876216 + 0.481919i \(0.160060\pi\)
\(522\) −3.00000 + 3.00000i −0.131306 + 0.131306i
\(523\) 6.00000i 0.262362i 0.991358 + 0.131181i \(0.0418769\pi\)
−0.991358 + 0.131181i \(0.958123\pi\)
\(524\) −3.00000 3.00000i −0.131056 0.131056i
\(525\) 18.0000 + 24.0000i 0.785584 + 1.04745i
\(526\) −16.0000 −0.697633
\(527\) 5.00000 3.00000i 0.217803 0.130682i
\(528\) 6.00000i 0.261116i
\(529\) 21.0000i 0.913043i
\(530\) 4.00000 + 2.00000i 0.173749 + 0.0868744i
\(531\) 6.00000 0.260378
\(532\) 18.0000 18.0000i 0.780399 0.780399i
\(533\) 0 0
\(534\) 6.00000 6.00000i 0.259645 0.259645i
\(535\) 27.0000 9.00000i 1.16731 0.389104i
\(536\) 18.0000i 0.777482i
\(537\) 6.00000 + 6.00000i 0.258919 + 0.258919i
\(538\) 3.00000 + 3.00000i 0.129339 + 0.129339i
\(539\) −33.0000 33.0000i −1.42141 1.42141i
\(540\) −4.00000 12.0000i −0.172133 0.516398i
\(541\) 1.00000 + 1.00000i 0.0429934 + 0.0429934i 0.728277 0.685283i \(-0.240322\pi\)
−0.685283 + 0.728277i \(0.740322\pi\)
\(542\) −24.0000 −1.03089
\(543\) 22.0000i 0.944110i
\(544\) 5.00000 20.0000i 0.214373 0.857493i
\(545\) 21.0000 7.00000i 0.899541 0.299847i
\(546\) 0 0
\(547\) −9.00000 + 9.00000i −0.384812 + 0.384812i −0.872832 0.488020i \(-0.837719\pi\)
0.488020 + 0.872832i \(0.337719\pi\)
\(548\) 4.00000i 0.170872i
\(549\) 1.00000 + 1.00000i 0.0426790 + 0.0426790i
\(550\) 21.0000 + 3.00000i 0.895443 + 0.127920i
\(551\) −18.0000 + 18.0000i −0.766826 + 0.766826i
\(552\) −6.00000 −0.255377
\(553\) 42.0000 1.78602
\(554\) 21.0000 21.0000i 0.892205 0.892205i
\(555\) 6.00000 12.0000i 0.254686 0.509372i
\(556\) −7.00000 7.00000i −0.296866 0.296866i
\(557\) 32.0000i 1.35588i −0.735116 0.677942i \(-0.762872\pi\)
0.735116 0.677942i \(-0.237128\pi\)
\(558\) −1.00000 + 1.00000i −0.0423334 + 0.0423334i
\(559\) 0 0
\(560\) −3.00000 9.00000i −0.126773 0.380319i
\(561\) 24.0000 + 6.00000i 1.01328 + 0.253320i
\(562\) 24.0000i 1.01238i
\(563\) −28.0000 −1.18006 −0.590030 0.807382i \(-0.700884\pi\)
−0.590030 + 0.807382i \(0.700884\pi\)
\(564\) 2.00000 + 2.00000i 0.0842152 + 0.0842152i
\(565\) 9.00000 + 27.0000i 0.378633 + 1.13590i
\(566\) −9.00000 9.00000i −0.378298 0.378298i
\(567\) −15.0000 15.0000i −0.629941 0.629941i
\(568\) 9.00000 + 9.00000i 0.377632 + 0.377632i
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 6.00000 + 18.0000i 0.251312 + 0.753937i
\(571\) −23.0000 + 23.0000i −0.962520 + 0.962520i −0.999323 0.0368025i \(-0.988283\pi\)
0.0368025 + 0.999323i \(0.488283\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −18.0000 −0.751305
\(575\) −1.00000 + 7.00000i −0.0417029 + 0.291920i
\(576\) 7.00000i 0.291667i
\(577\) 36.0000i 1.49870i 0.662174 + 0.749350i \(0.269634\pi\)
−0.662174 + 0.749350i \(0.730366\pi\)
\(578\) 15.0000 + 8.00000i 0.623918 + 0.332756i
\(579\) −6.00000 −0.249351
\(580\) −3.00000 9.00000i −0.124568 0.373705i
\(581\) 12.0000 + 12.0000i 0.497844 + 0.497844i
\(582\) 6.00000i 0.248708i
\(583\) −6.00000 + 6.00000i −0.248495 + 0.248495i
\(584\) 9.00000 9.00000i 0.372423 0.372423i
\(585\) 0 0
\(586\) 4.00000i 0.165238i
\(587\) 4.00000 0.165098 0.0825488 0.996587i \(-0.473694\pi\)
0.0825488 + 0.996587i \(0.473694\pi\)
\(588\) 11.0000 + 11.0000i 0.453632 + 0.453632i
\(589\) −6.00000 + 6.00000i −0.247226 + 0.247226i
\(590\) 6.00000 12.0000i 0.247016 0.494032i
\(591\) 26.0000 1.06950
\(592\) −3.00000 + 3.00000i −0.123299 + 0.123299i
\(593\) −2.00000 −0.0821302 −0.0410651 0.999156i \(-0.513075\pi\)
−0.0410651 + 0.999156i \(0.513075\pi\)
\(594\) −24.0000 −0.984732
\(595\) −39.0000 + 3.00000i −1.59884 + 0.122988i
\(596\) 18.0000 0.737309
\(597\) 2.00000 0.0818546
\(598\) 0 0
\(599\) 24.0000 0.980613 0.490307 0.871550i \(-0.336885\pi\)
0.490307 + 0.871550i \(0.336885\pi\)
\(600\) −21.0000 3.00000i −0.857321 0.122474i
\(601\) 29.0000 29.0000i 1.18293 1.18293i 0.203954 0.978980i \(-0.434621\pi\)
0.978980 0.203954i \(-0.0653794\pi\)
\(602\) −36.0000 36.0000i −1.46725 1.46725i
\(603\) −6.00000 −0.244339
\(604\) 10.0000i 0.406894i
\(605\) −7.00000 + 14.0000i −0.284590 + 0.569181i
\(606\) −6.00000 + 6.00000i −0.243733 + 0.243733i
\(607\) −33.0000 + 33.0000i −1.33943 + 1.33943i −0.442816 + 0.896612i \(0.646021\pi\)
−0.896612 + 0.442816i \(0.853979\pi\)
\(608\) 30.0000i 1.21666i
\(609\) −18.0000 18.0000i −0.729397 0.729397i
\(610\) 3.00000 1.00000i 0.121466 0.0404888i
\(611\) 0 0
\(612\) 4.00000 + 1.00000i 0.161690 + 0.0404226i
\(613\) 36.0000i 1.45403i −0.686624 0.727013i \(-0.740908\pi\)
0.686624 0.727013i \(-0.259092\pi\)
\(614\) 18.0000i 0.726421i
\(615\) −6.00000 + 12.0000i −0.241943 + 0.483887i
\(616\) 54.0000 2.17572
\(617\) 15.0000 15.0000i 0.603877 0.603877i −0.337462 0.941339i \(-0.609568\pi\)
0.941339 + 0.337462i \(0.109568\pi\)
\(618\) −6.00000 6.00000i −0.241355 0.241355i
\(619\) 13.0000 13.0000i 0.522514 0.522514i −0.395816 0.918330i \(-0.629538\pi\)
0.918330 + 0.395816i \(0.129538\pi\)
\(620\) −1.00000 3.00000i −0.0401610 0.120483i
\(621\) 8.00000i 0.321029i
\(622\) −3.00000 3.00000i −0.120289 0.120289i
\(623\) −18.0000 18.0000i −0.721155 0.721155i
\(624\) 0 0
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) −3.00000 3.00000i −0.119904 0.119904i
\(627\) −36.0000 −1.43770
\(628\) 12.0000i 0.478852i
\(629\) 9.00000 + 15.0000i 0.358854 + 0.598089i
\(630\) 9.00000 3.00000i 0.358569 0.119523i
\(631\) 34.0000i 1.35352i −0.736204 0.676759i \(-0.763384\pi\)
0.736204 0.676759i \(-0.236616\pi\)
\(632\) −21.0000 + 21.0000i −0.835335 + 0.835335i
\(633\) 34.0000i 1.35138i
\(634\) −15.0000 15.0000i −0.595726 0.595726i
\(635\) 0 0
\(636\) 2.00000 2.00000i 0.0793052 0.0793052i
\(637\) 0 0
\(638\) −18.0000 −0.712627
\(639\) −3.00000 + 3.00000i −0.118678 + 0.118678i
\(640\) −6.00000 3.00000i −0.237171 0.118585i
\(641\) 9.00000 + 9.00000i 0.355479 + 0.355479i 0.862143 0.506665i \(-0.169122\pi\)
−0.506665 + 0.862143i \(0.669122\pi\)
\(642\) 18.0000i 0.710403i
\(643\) −9.00000 + 9.00000i −0.354925 + 0.354925i −0.861938 0.507013i \(-0.830750\pi\)
0.507013 + 0.861938i \(0.330750\pi\)
\(644\) 6.00000i 0.236433i
\(645\) −36.0000 + 12.0000i −1.41750 + 0.472500i
\(646\) −24.0000 6.00000i −0.944267 0.236067i
\(647\) 46.0000i 1.80845i −0.427060 0.904223i \(-0.640451\pi\)
0.427060 0.904223i \(-0.359549\pi\)
\(648\) 15.0000 0.589256
\(649\) 18.0000 + 18.0000i 0.706562 + 0.706562i
\(650\) 0 0
\(651\) −6.00000 6.00000i −0.235159 0.235159i
\(652\) −9.00000 9.00000i −0.352467 0.352467i
\(653\) −21.0000 21.0000i −0.821794 0.821794i 0.164572 0.986365i \(-0.447376\pi\)
−0.986365 + 0.164572i \(0.947376\pi\)
\(654\) 14.0000i 0.547443i
\(655\) −3.00000 9.00000i −0.117220 0.351659i
\(656\) 3.00000 3.00000i 0.117130 0.117130i
\(657\) 3.00000 + 3.00000i 0.117041 + 0.117041i
\(658\) −6.00000 + 6.00000i −0.233904 + 0.233904i
\(659\) 36.0000 1.40236 0.701180 0.712984i \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) 6.00000 12.0000i 0.233550 0.467099i
\(661\) 36.0000i 1.40024i 0.714026 + 0.700119i \(0.246870\pi\)
−0.714026 + 0.700119i \(0.753130\pi\)
\(662\) 18.0000i 0.699590i
\(663\) 0 0
\(664\) −12.0000 −0.465690
\(665\) 54.0000 18.0000i 2.09403 0.698010i
\(666\) −3.00000 3.00000i −0.116248 0.116248i
\(667\) 6.00000i 0.232321i
\(668\) −3.00000 + 3.00000i −0.116073 + 0.116073i
\(669\) 0 0
\(670\) −6.00000 + 12.0000i −0.231800 + 0.463600i
\(671\) 6.00000i 0.231627i
\(672\) −30.0000 −1.15728
\(673\) 15.0000 + 15.0000i 0.578208 + 0.578208i 0.934409 0.356202i \(-0.115928\pi\)
−0.356202 + 0.934409i \(0.615928\pi\)
\(674\) −15.0000 + 15.0000i −0.577778 + 0.577778i
\(675\) 4.00000 28.0000i 0.153960 1.07772i
\(676\) −13.0000 −0.500000
\(677\) 11.0000 11.0000i 0.422764 0.422764i −0.463390 0.886154i \(-0.653367\pi\)
0.886154 + 0.463390i \(0.153367\pi\)
\(678\) −18.0000 −0.691286
\(679\) −18.0000 −0.690777
\(680\) 18.0000 21.0000i 0.690268 0.805313i
\(681\) 30.0000 1.14960
\(682\) −6.00000 −0.229752
\(683\) 15.0000 15.0000i 0.573959 0.573959i −0.359273 0.933232i \(-0.616975\pi\)
0.933232 + 0.359273i \(0.116975\pi\)
\(684\) −6.00000 −0.229416
\(685\) 4.00000 8.00000i 0.152832 0.305664i
\(686\) −12.0000 + 12.0000i −0.458162 + 0.458162i
\(687\) 24.0000 + 24.0000i 0.915657 + 0.915657i
\(688\) 12.0000 0.457496
\(689\) 0 0
\(690\) −4.00000 2.00000i −0.152277 0.0761387i
\(691\) −19.0000 + 19.0000i −0.722794 + 0.722794i −0.969173 0.246379i \(-0.920759\pi\)
0.246379 + 0.969173i \(0.420759\pi\)
\(692\) −15.0000 + 15.0000i −0.570214 + 0.570214i
\(693\) 18.0000i 0.683763i
\(694\) −9.00000 9.00000i −0.341635 0.341635i
\(695\) −7.00000 21.0000i −0.265525 0.796575i
\(696\) 18.0000 0.682288
\(697\) −9.00000 15.0000i −0.340899 0.568166i
\(698\) 28.0000i 1.05982i
\(699\) 10.0000i 0.378235i
\(700\) −3.00000 + 21.0000i −0.113389 + 0.793725i
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 0 0
\(703\) −18.0000 18.0000i −0.678883 0.678883i
\(704\) −21.0000 + 21.0000i −0.791467 + 0.791467i
\(705\) 2.00000 + 6.00000i 0.0753244 + 0.225973i
\(706\) 16.0000i 0.602168i
\(707\) 18.0000 + 18.0000i 0.676960 + 0.676960i
\(708\) −6.00000 6.00000i −0.225494 0.225494i
\(709\) 5.00000 + 5.00000i 0.187779 + 0.187779i 0.794735 0.606956i \(-0.207610\pi\)
−0.606956 + 0.794735i \(0.707610\pi\)
\(710\) 3.00000 + 9.00000i 0.112588 + 0.337764i
\(711\) −7.00000 7.00000i −0.262521 0.262521i
\(712\) 18.0000 0.674579
\(713\) 2.00000i 0.0749006i
\(714\) 6.00000 24.0000i 0.224544 0.898177i
\(715\) 0 0
\(716\) 6.00000i 0.224231i
\(717\) 24.0000 24.0000i 0.896296 0.896296i
\(718\) 30.0000i 1.11959i
\(719\) −21.0000 21.0000i −0.783168 0.783168i 0.197196 0.980364i \(-0.436816\pi\)
−0.980364 + 0.197196i \(0.936816\pi\)
\(720\) −1.00000 + 2.00000i −0.0372678 + 0.0745356i
\(721\) −18.0000 + 18.0000i −0.670355 + 0.670355i
\(722\) 17.0000 0.632674
\(723\) 38.0000 1.41324
\(724\) 11.0000 11.0000i 0.408812 0.408812i
\(725\) 3.00000 21.0000i 0.111417 0.779920i
\(726\) −7.00000 7.00000i −0.259794 0.259794i
\(727\) 18.0000i 0.667583i 0.942647 + 0.333792i \(0.108328\pi\)
−0.942647 + 0.333792i \(0.891672\pi\)
\(728\) 0 0
\(729\) 29.0000i 1.07407i
\(730\) 9.00000 3.00000i 0.333105 0.111035i
\(731\) 12.0000 48.0000i 0.443836 1.77534i
\(732\) 2.00000i 0.0739221i
\(733\) 42.0000 1.55131 0.775653 0.631160i \(-0.217421\pi\)
0.775653 + 0.631160i \(0.217421\pi\)
\(734\) 3.00000 + 3.00000i 0.110732 + 0.110732i
\(735\) 11.0000 + 33.0000i 0.405741 + 1.21722i
\(736\) −5.00000 5.00000i −0.184302 0.184302i
\(737\) −18.0000 18.0000i −0.663039 0.663039i
\(738\) 3.00000 + 3.00000i 0.110432 + 0.110432i
\(739\) 34.0000i 1.25071i 0.780340 + 0.625355i \(0.215046\pi\)
−0.780340 + 0.625355i \(0.784954\pi\)
\(740\) 9.00000 3.00000i 0.330847 0.110282i
\(741\) 0 0
\(742\) 6.00000 + 6.00000i 0.220267 + 0.220267i
\(743\) −9.00000 + 9.00000i −0.330178 + 0.330178i −0.852654 0.522476i \(-0.825008\pi\)
0.522476 + 0.852654i \(0.325008\pi\)
\(744\) 6.00000 0.219971
\(745\) 36.0000 + 18.0000i 1.31894 + 0.659469i
\(746\) 24.0000i 0.878702i
\(747\) 4.00000i 0.146352i
\(748\) 9.00000 + 15.0000i 0.329073 + 0.548454i
\(749\) 54.0000 1.97312
\(750\) −13.0000 9.00000i −0.474693 0.328634i
\(751\) 19.0000 + 19.0000i 0.693320 + 0.693320i 0.962961 0.269641i \(-0.0869050\pi\)
−0.269641 + 0.962961i \(0.586905\pi\)
\(752\) 2.00000i 0.0729325i
\(753\) 12.0000 12.0000i 0.437304 0.437304i
\(754\) 0 0
\(755\) −10.0000 + 20.0000i −0.363937 + 0.727875i
\(756\) 24.0000i 0.872872i
\(757\) −42.0000 −1.52652 −0.763258 0.646094i \(-0.776401\pi\)
−0.763258 + 0.646094i \(0.776401\pi\)
\(758\) −11.0000 11.0000i −0.399538 0.399538i
\(759\) 6.00000 6.00000i 0.217786 0.217786i
\(760\) −18.0000 + 36.0000i −0.652929 + 1.30586i
\(761\) −42.0000 −1.52250 −0.761249 0.648459i \(-0.775414\pi\)
−0.761249 + 0.648459i \(0.775414\pi\)
\(762\) 0 0
\(763\) 42.0000 1.52050
\(764\) 0 0
\(765\) 7.00000 + 6.00000i 0.253086 + 0.216930i
\(766\) 16.0000 0.578103
\(767\) 0 0
\(768\) 17.0000 17.0000i 0.613435 0.613435i
\(769\) 14.0000 0.504853 0.252426 0.967616i \(-0.418771\pi\)
0.252426 + 0.967616i \(0.418771\pi\)
\(770\) 36.0000 + 18.0000i 1.29735 + 0.648675i
\(771\) 14.0000 14.0000i 0.504198 0.504198i
\(772\) −3.00000 3.00000i −0.107972 0.107972i
\(773\) −26.0000 −0.935155 −0.467578 0.883952i \(-0.654873\pi\)
−0.467578 + 0.883952i \(0.654873\pi\)
\(774\)