Properties

Label 930.2.j.b.683.2
Level $930$
Weight $2$
Character 930.683
Analytic conductor $7.426$
Analytic rank $0$
Dimension $4$
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] = [930,2,Mod(497,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.497");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.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: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 683.2
Root \(-0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 930.683
Dual form 930.2.j.b.497.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +(1.70711 + 0.292893i) q^{3} +1.00000i q^{4} +(-2.12132 + 0.707107i) q^{5} +(1.00000 + 1.41421i) q^{6} +(-0.707107 + 0.707107i) q^{8} +(2.82843 + 1.00000i) q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +(1.70711 + 0.292893i) q^{3} +1.00000i q^{4} +(-2.12132 + 0.707107i) q^{5} +(1.00000 + 1.41421i) q^{6} +(-0.707107 + 0.707107i) q^{8} +(2.82843 + 1.00000i) q^{9} +(-2.00000 - 1.00000i) q^{10} +1.41421i q^{11} +(-0.292893 + 1.70711i) q^{12} +(3.00000 + 3.00000i) q^{13} +(-3.82843 + 0.585786i) q^{15} -1.00000 q^{16} +(-1.41421 - 1.41421i) q^{17} +(1.29289 + 2.70711i) q^{18} +4.00000i q^{19} +(-0.707107 - 2.12132i) q^{20} +(-1.00000 + 1.00000i) q^{22} +(-2.82843 + 2.82843i) q^{23} +(-1.41421 + 1.00000i) q^{24} +(4.00000 - 3.00000i) q^{25} +4.24264i q^{26} +(4.53553 + 2.53553i) q^{27} -2.82843 q^{29} +(-3.12132 - 2.29289i) q^{30} +1.00000 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.414214 + 2.41421i) q^{33} -2.00000i q^{34} +(-1.00000 + 2.82843i) q^{36} +(-3.00000 + 3.00000i) q^{37} +(-2.82843 + 2.82843i) q^{38} +(4.24264 + 6.00000i) q^{39} +(1.00000 - 2.00000i) q^{40} -5.65685i q^{41} -1.41421 q^{44} +(-6.70711 - 0.121320i) q^{45} -4.00000 q^{46} +(1.41421 + 1.41421i) q^{47} +(-1.70711 - 0.292893i) q^{48} +7.00000i q^{49} +(4.94975 + 0.707107i) q^{50} +(-2.00000 - 2.82843i) q^{51} +(-3.00000 + 3.00000i) q^{52} +(1.41421 - 1.41421i) q^{53} +(1.41421 + 5.00000i) q^{54} +(-1.00000 - 3.00000i) q^{55} +(-1.17157 + 6.82843i) q^{57} +(-2.00000 - 2.00000i) q^{58} +(-0.585786 - 3.82843i) q^{60} +8.00000 q^{61} +(0.707107 + 0.707107i) q^{62} -1.00000i q^{64} +(-8.48528 - 4.24264i) q^{65} +(-2.00000 + 1.41421i) q^{66} +(7.00000 - 7.00000i) q^{67} +(1.41421 - 1.41421i) q^{68} +(-5.65685 + 4.00000i) q^{69} -12.7279i q^{71} +(-2.70711 + 1.29289i) q^{72} +(-2.00000 - 2.00000i) q^{73} -4.24264 q^{74} +(7.70711 - 3.94975i) q^{75} -4.00000 q^{76} +(-1.24264 + 7.24264i) q^{78} -2.00000i q^{79} +(2.12132 - 0.707107i) q^{80} +(7.00000 + 5.65685i) q^{81} +(4.00000 - 4.00000i) q^{82} +(4.24264 - 4.24264i) q^{83} +(4.00000 + 2.00000i) q^{85} +(-4.82843 - 0.828427i) q^{87} +(-1.00000 - 1.00000i) q^{88} +7.07107 q^{89} +(-4.65685 - 4.82843i) q^{90} +(-2.82843 - 2.82843i) q^{92} +(1.70711 + 0.292893i) q^{93} +2.00000i q^{94} +(-2.82843 - 8.48528i) q^{95} +(-1.00000 - 1.41421i) q^{96} +(11.0000 - 11.0000i) q^{97} +(-4.94975 + 4.94975i) q^{98} +(-1.41421 + 4.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{3} + 4 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{3} + 4 q^{6} - 8 q^{10} - 4 q^{12} + 12 q^{13} - 4 q^{15} - 4 q^{16} + 8 q^{18} - 4 q^{22} + 16 q^{25} + 4 q^{27} - 4 q^{30} + 4 q^{31} + 4 q^{33} - 4 q^{36} - 12 q^{37} + 4 q^{40} - 24 q^{45} - 16 q^{46} - 4 q^{48} - 8 q^{51} - 12 q^{52} - 4 q^{55} - 16 q^{57} - 8 q^{58} - 8 q^{60} + 32 q^{61} - 8 q^{66} + 28 q^{67} - 8 q^{72} - 8 q^{73} + 28 q^{75} - 16 q^{76} + 12 q^{78} + 28 q^{81} + 16 q^{82} + 16 q^{85} - 8 q^{87} - 4 q^{88} + 4 q^{90} + 4 q^{93} - 4 q^{96} + 44 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.500000 + 0.500000i
\(3\) 1.70711 + 0.292893i 0.985599 + 0.169102i
\(4\) 1.00000i 0.500000i
\(5\) −2.12132 + 0.707107i −0.948683 + 0.316228i
\(6\) 1.00000 + 1.41421i 0.408248 + 0.577350i
\(7\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 2.82843 + 1.00000i 0.942809 + 0.333333i
\(10\) −2.00000 1.00000i −0.632456 0.316228i
\(11\) 1.41421i 0.426401i 0.977008 + 0.213201i \(0.0683888\pi\)
−0.977008 + 0.213201i \(0.931611\pi\)
\(12\) −0.292893 + 1.70711i −0.0845510 + 0.492799i
\(13\) 3.00000 + 3.00000i 0.832050 + 0.832050i 0.987797 0.155747i \(-0.0497784\pi\)
−0.155747 + 0.987797i \(0.549778\pi\)
\(14\) 0 0
\(15\) −3.82843 + 0.585786i −0.988496 + 0.151249i
\(16\) −1.00000 −0.250000
\(17\) −1.41421 1.41421i −0.342997 0.342997i 0.514496 0.857493i \(-0.327979\pi\)
−0.857493 + 0.514496i \(0.827979\pi\)
\(18\) 1.29289 + 2.70711i 0.304738 + 0.638071i
\(19\) 4.00000i 0.917663i 0.888523 + 0.458831i \(0.151732\pi\)
−0.888523 + 0.458831i \(0.848268\pi\)
\(20\) −0.707107 2.12132i −0.158114 0.474342i
\(21\) 0 0
\(22\) −1.00000 + 1.00000i −0.213201 + 0.213201i
\(23\) −2.82843 + 2.82843i −0.589768 + 0.589768i −0.937568 0.347801i \(-0.886929\pi\)
0.347801 + 0.937568i \(0.386929\pi\)
\(24\) −1.41421 + 1.00000i −0.288675 + 0.204124i
\(25\) 4.00000 3.00000i 0.800000 0.600000i
\(26\) 4.24264i 0.832050i
\(27\) 4.53553 + 2.53553i 0.872864 + 0.487964i
\(28\) 0 0
\(29\) −2.82843 −0.525226 −0.262613 0.964901i \(-0.584584\pi\)
−0.262613 + 0.964901i \(0.584584\pi\)
\(30\) −3.12132 2.29289i −0.569873 0.418623i
\(31\) 1.00000 0.179605
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) −0.414214 + 2.41421i −0.0721053 + 0.420261i
\(34\) 2.00000i 0.342997i
\(35\) 0 0
\(36\) −1.00000 + 2.82843i −0.166667 + 0.471405i
\(37\) −3.00000 + 3.00000i −0.493197 + 0.493197i −0.909312 0.416115i \(-0.863391\pi\)
0.416115 + 0.909312i \(0.363391\pi\)
\(38\) −2.82843 + 2.82843i −0.458831 + 0.458831i
\(39\) 4.24264 + 6.00000i 0.679366 + 0.960769i
\(40\) 1.00000 2.00000i 0.158114 0.316228i
\(41\) 5.65685i 0.883452i −0.897150 0.441726i \(-0.854366\pi\)
0.897150 0.441726i \(-0.145634\pi\)
\(42\) 0 0
\(43\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(44\) −1.41421 −0.213201
\(45\) −6.70711 0.121320i −0.999836 0.0180854i
\(46\) −4.00000 −0.589768
\(47\) 1.41421 + 1.41421i 0.206284 + 0.206284i 0.802686 0.596402i \(-0.203403\pi\)
−0.596402 + 0.802686i \(0.703403\pi\)
\(48\) −1.70711 0.292893i −0.246400 0.0422755i
\(49\) 7.00000i 1.00000i
\(50\) 4.94975 + 0.707107i 0.700000 + 0.100000i
\(51\) −2.00000 2.82843i −0.280056 0.396059i
\(52\) −3.00000 + 3.00000i −0.416025 + 0.416025i
\(53\) 1.41421 1.41421i 0.194257 0.194257i −0.603276 0.797533i \(-0.706138\pi\)
0.797533 + 0.603276i \(0.206138\pi\)
\(54\) 1.41421 + 5.00000i 0.192450 + 0.680414i
\(55\) −1.00000 3.00000i −0.134840 0.404520i
\(56\) 0 0
\(57\) −1.17157 + 6.82843i −0.155179 + 0.904447i
\(58\) −2.00000 2.00000i −0.262613 0.262613i
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) −0.585786 3.82843i −0.0756247 0.494248i
\(61\) 8.00000 1.02430 0.512148 0.858898i \(-0.328850\pi\)
0.512148 + 0.858898i \(0.328850\pi\)
\(62\) 0.707107 + 0.707107i 0.0898027 + 0.0898027i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) −8.48528 4.24264i −1.05247 0.526235i
\(66\) −2.00000 + 1.41421i −0.246183 + 0.174078i
\(67\) 7.00000 7.00000i 0.855186 0.855186i −0.135580 0.990766i \(-0.543290\pi\)
0.990766 + 0.135580i \(0.0432899\pi\)
\(68\) 1.41421 1.41421i 0.171499 0.171499i
\(69\) −5.65685 + 4.00000i −0.681005 + 0.481543i
\(70\) 0 0
\(71\) 12.7279i 1.51053i −0.655422 0.755263i \(-0.727509\pi\)
0.655422 0.755263i \(-0.272491\pi\)
\(72\) −2.70711 + 1.29289i −0.319036 + 0.152369i
\(73\) −2.00000 2.00000i −0.234082 0.234082i 0.580312 0.814394i \(-0.302931\pi\)
−0.814394 + 0.580312i \(0.802931\pi\)
\(74\) −4.24264 −0.493197
\(75\) 7.70711 3.94975i 0.889940 0.456078i
\(76\) −4.00000 −0.458831
\(77\) 0 0
\(78\) −1.24264 + 7.24264i −0.140701 + 0.820068i
\(79\) 2.00000i 0.225018i −0.993651 0.112509i \(-0.964111\pi\)
0.993651 0.112509i \(-0.0358886\pi\)
\(80\) 2.12132 0.707107i 0.237171 0.0790569i
\(81\) 7.00000 + 5.65685i 0.777778 + 0.628539i
\(82\) 4.00000 4.00000i 0.441726 0.441726i
\(83\) 4.24264 4.24264i 0.465690 0.465690i −0.434825 0.900515i \(-0.643190\pi\)
0.900515 + 0.434825i \(0.143190\pi\)
\(84\) 0 0
\(85\) 4.00000 + 2.00000i 0.433861 + 0.216930i
\(86\) 0 0
\(87\) −4.82843 0.828427i −0.517662 0.0888167i
\(88\) −1.00000 1.00000i −0.106600 0.106600i
\(89\) 7.07107 0.749532 0.374766 0.927119i \(-0.377723\pi\)
0.374766 + 0.927119i \(0.377723\pi\)
\(90\) −4.65685 4.82843i −0.490876 0.508961i
\(91\) 0 0
\(92\) −2.82843 2.82843i −0.294884 0.294884i
\(93\) 1.70711 + 0.292893i 0.177019 + 0.0303716i
\(94\) 2.00000i 0.206284i
\(95\) −2.82843 8.48528i −0.290191 0.870572i
\(96\) −1.00000 1.41421i −0.102062 0.144338i
\(97\) 11.0000 11.0000i 1.11688 1.11688i 0.124684 0.992196i \(-0.460208\pi\)
0.992196 0.124684i \(-0.0397918\pi\)
\(98\) −4.94975 + 4.94975i −0.500000 + 0.500000i
\(99\) −1.41421 + 4.00000i −0.142134 + 0.402015i
\(100\) 3.00000 + 4.00000i 0.300000 + 0.400000i
\(101\) 15.5563i 1.54791i −0.633238 0.773957i \(-0.718274\pi\)
0.633238 0.773957i \(-0.281726\pi\)
\(102\) 0.585786 3.41421i 0.0580015 0.338058i
\(103\) −6.00000 6.00000i −0.591198 0.591198i 0.346757 0.937955i \(-0.387283\pi\)
−0.937955 + 0.346757i \(0.887283\pi\)
\(104\) −4.24264 −0.416025
\(105\) 0 0
\(106\) 2.00000 0.194257
\(107\) 8.48528 + 8.48528i 0.820303 + 0.820303i 0.986151 0.165848i \(-0.0530362\pi\)
−0.165848 + 0.986151i \(0.553036\pi\)
\(108\) −2.53553 + 4.53553i −0.243982 + 0.436432i
\(109\) 10.0000i 0.957826i 0.877862 + 0.478913i \(0.158969\pi\)
−0.877862 + 0.478913i \(0.841031\pi\)
\(110\) 1.41421 2.82843i 0.134840 0.269680i
\(111\) −6.00000 + 4.24264i −0.569495 + 0.402694i
\(112\) 0 0
\(113\) 4.24264 4.24264i 0.399114 0.399114i −0.478806 0.877920i \(-0.658930\pi\)
0.877920 + 0.478806i \(0.158930\pi\)
\(114\) −5.65685 + 4.00000i −0.529813 + 0.374634i
\(115\) 4.00000 8.00000i 0.373002 0.746004i
\(116\) 2.82843i 0.262613i
\(117\) 5.48528 + 11.4853i 0.507114 + 1.06181i
\(118\) 0 0
\(119\) 0 0
\(120\) 2.29289 3.12132i 0.209312 0.284936i
\(121\) 9.00000 0.818182
\(122\) 5.65685 + 5.65685i 0.512148 + 0.512148i
\(123\) 1.65685 9.65685i 0.149394 0.870729i
\(124\) 1.00000i 0.0898027i
\(125\) −6.36396 + 9.19239i −0.569210 + 0.822192i
\(126\) 0 0
\(127\) 5.00000 5.00000i 0.443678 0.443678i −0.449568 0.893246i \(-0.648422\pi\)
0.893246 + 0.449568i \(0.148422\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) 0 0
\(130\) −3.00000 9.00000i −0.263117 0.789352i
\(131\) 14.1421i 1.23560i 0.786334 + 0.617802i \(0.211977\pi\)
−0.786334 + 0.617802i \(0.788023\pi\)
\(132\) −2.41421 0.414214i −0.210130 0.0360527i
\(133\) 0 0
\(134\) 9.89949 0.855186
\(135\) −11.4142 2.17157i −0.982379 0.186899i
\(136\) 2.00000 0.171499
\(137\) −7.07107 7.07107i −0.604122 0.604122i 0.337282 0.941404i \(-0.390493\pi\)
−0.941404 + 0.337282i \(0.890493\pi\)
\(138\) −6.82843 1.17157i −0.581274 0.0997309i
\(139\) 12.0000i 1.01783i −0.860818 0.508913i \(-0.830047\pi\)
0.860818 0.508913i \(-0.169953\pi\)
\(140\) 0 0
\(141\) 2.00000 + 2.82843i 0.168430 + 0.238197i
\(142\) 9.00000 9.00000i 0.755263 0.755263i
\(143\) −4.24264 + 4.24264i −0.354787 + 0.354787i
\(144\) −2.82843 1.00000i −0.235702 0.0833333i
\(145\) 6.00000 2.00000i 0.498273 0.166091i
\(146\) 2.82843i 0.234082i
\(147\) −2.05025 + 11.9497i −0.169102 + 0.985599i
\(148\) −3.00000 3.00000i −0.246598 0.246598i
\(149\) −1.41421 −0.115857 −0.0579284 0.998321i \(-0.518450\pi\)
−0.0579284 + 0.998321i \(0.518450\pi\)
\(150\) 8.24264 + 2.65685i 0.673009 + 0.216931i
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) −2.82843 2.82843i −0.229416 0.229416i
\(153\) −2.58579 5.41421i −0.209048 0.437713i
\(154\) 0 0
\(155\) −2.12132 + 0.707107i −0.170389 + 0.0567962i
\(156\) −6.00000 + 4.24264i −0.480384 + 0.339683i
\(157\) −4.00000 + 4.00000i −0.319235 + 0.319235i −0.848473 0.529238i \(-0.822478\pi\)
0.529238 + 0.848473i \(0.322478\pi\)
\(158\) 1.41421 1.41421i 0.112509 0.112509i
\(159\) 2.82843 2.00000i 0.224309 0.158610i
\(160\) 2.00000 + 1.00000i 0.158114 + 0.0790569i
\(161\) 0 0
\(162\) 0.949747 + 8.94975i 0.0746192 + 0.703159i
\(163\) −11.0000 11.0000i −0.861586 0.861586i 0.129936 0.991522i \(-0.458523\pi\)
−0.991522 + 0.129936i \(0.958523\pi\)
\(164\) 5.65685 0.441726
\(165\) −0.828427 5.41421i −0.0644930 0.421496i
\(166\) 6.00000 0.465690
\(167\) −5.65685 5.65685i −0.437741 0.437741i 0.453510 0.891251i \(-0.350171\pi\)
−0.891251 + 0.453510i \(0.850171\pi\)
\(168\) 0 0
\(169\) 5.00000i 0.384615i
\(170\) 1.41421 + 4.24264i 0.108465 + 0.325396i
\(171\) −4.00000 + 11.3137i −0.305888 + 0.865181i
\(172\) 0 0
\(173\) −14.1421 + 14.1421i −1.07521 + 1.07521i −0.0782748 + 0.996932i \(0.524941\pi\)
−0.996932 + 0.0782748i \(0.975059\pi\)
\(174\) −2.82843 4.00000i −0.214423 0.303239i
\(175\) 0 0
\(176\) 1.41421i 0.106600i
\(177\) 0 0
\(178\) 5.00000 + 5.00000i 0.374766 + 0.374766i
\(179\) 12.7279 0.951330 0.475665 0.879627i \(-0.342208\pi\)
0.475665 + 0.879627i \(0.342208\pi\)
\(180\) 0.121320 6.70711i 0.00904268 0.499918i
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 0 0
\(183\) 13.6569 + 2.34315i 1.00954 + 0.173210i
\(184\) 4.00000i 0.294884i
\(185\) 4.24264 8.48528i 0.311925 0.623850i
\(186\) 1.00000 + 1.41421i 0.0733236 + 0.103695i
\(187\) 2.00000 2.00000i 0.146254 0.146254i
\(188\) −1.41421 + 1.41421i −0.103142 + 0.103142i
\(189\) 0 0
\(190\) 4.00000 8.00000i 0.290191 0.580381i
\(191\) 21.2132i 1.53493i 0.641089 + 0.767467i \(0.278483\pi\)
−0.641089 + 0.767467i \(0.721517\pi\)
\(192\) 0.292893 1.70711i 0.0211377 0.123200i
\(193\) −9.00000 9.00000i −0.647834 0.647834i 0.304635 0.952469i \(-0.401466\pi\)
−0.952469 + 0.304635i \(0.901466\pi\)
\(194\) 15.5563 1.11688
\(195\) −13.2426 9.72792i −0.948325 0.696631i
\(196\) −7.00000 −0.500000
\(197\) 7.07107 + 7.07107i 0.503793 + 0.503793i 0.912614 0.408822i \(-0.134060\pi\)
−0.408822 + 0.912614i \(0.634060\pi\)
\(198\) −3.82843 + 1.82843i −0.272074 + 0.129941i
\(199\) 24.0000i 1.70131i 0.525720 + 0.850657i \(0.323796\pi\)
−0.525720 + 0.850657i \(0.676204\pi\)
\(200\) −0.707107 + 4.94975i −0.0500000 + 0.350000i
\(201\) 14.0000 9.89949i 0.987484 0.698257i
\(202\) 11.0000 11.0000i 0.773957 0.773957i
\(203\) 0 0
\(204\) 2.82843 2.00000i 0.198030 0.140028i
\(205\) 4.00000 + 12.0000i 0.279372 + 0.838116i
\(206\) 8.48528i 0.591198i
\(207\) −10.8284 + 5.17157i −0.752628 + 0.359449i
\(208\) −3.00000 3.00000i −0.208013 0.208013i
\(209\) −5.65685 −0.391293
\(210\) 0 0
\(211\) 10.0000 0.688428 0.344214 0.938891i \(-0.388145\pi\)
0.344214 + 0.938891i \(0.388145\pi\)
\(212\) 1.41421 + 1.41421i 0.0971286 + 0.0971286i
\(213\) 3.72792 21.7279i 0.255433 1.48877i
\(214\) 12.0000i 0.820303i
\(215\) 0 0
\(216\) −5.00000 + 1.41421i −0.340207 + 0.0962250i
\(217\) 0 0
\(218\) −7.07107 + 7.07107i −0.478913 + 0.478913i
\(219\) −2.82843 4.00000i −0.191127 0.270295i
\(220\) 3.00000 1.00000i 0.202260 0.0674200i
\(221\) 8.48528i 0.570782i
\(222\) −7.24264 1.24264i −0.486094 0.0834006i
\(223\) −11.0000 11.0000i −0.736614 0.736614i 0.235307 0.971921i \(-0.424391\pi\)
−0.971921 + 0.235307i \(0.924391\pi\)
\(224\) 0 0
\(225\) 14.3137 4.48528i 0.954247 0.299019i
\(226\) 6.00000 0.399114
\(227\) 11.3137 + 11.3137i 0.750917 + 0.750917i 0.974650 0.223733i \(-0.0718244\pi\)
−0.223733 + 0.974650i \(0.571824\pi\)
\(228\) −6.82843 1.17157i −0.452224 0.0775893i
\(229\) 26.0000i 1.71813i −0.511868 0.859064i \(-0.671046\pi\)
0.511868 0.859064i \(-0.328954\pi\)
\(230\) 8.48528 2.82843i 0.559503 0.186501i
\(231\) 0 0
\(232\) 2.00000 2.00000i 0.131306 0.131306i
\(233\) −9.89949 + 9.89949i −0.648537 + 0.648537i −0.952639 0.304102i \(-0.901644\pi\)
0.304102 + 0.952639i \(0.401644\pi\)
\(234\) −4.24264 + 12.0000i −0.277350 + 0.784465i
\(235\) −4.00000 2.00000i −0.260931 0.130466i
\(236\) 0 0
\(237\) 0.585786 3.41421i 0.0380509 0.221777i
\(238\) 0 0
\(239\) 22.6274 1.46365 0.731823 0.681495i \(-0.238670\pi\)
0.731823 + 0.681495i \(0.238670\pi\)
\(240\) 3.82843 0.585786i 0.247124 0.0378124i
\(241\) −2.00000 −0.128831 −0.0644157 0.997923i \(-0.520518\pi\)
−0.0644157 + 0.997923i \(0.520518\pi\)
\(242\) 6.36396 + 6.36396i 0.409091 + 0.409091i
\(243\) 10.2929 + 11.7071i 0.660289 + 0.751011i
\(244\) 8.00000i 0.512148i
\(245\) −4.94975 14.8492i −0.316228 0.948683i
\(246\) 8.00000 5.65685i 0.510061 0.360668i
\(247\) −12.0000 + 12.0000i −0.763542 + 0.763542i
\(248\) −0.707107 + 0.707107i −0.0449013 + 0.0449013i
\(249\) 8.48528 6.00000i 0.537733 0.380235i
\(250\) −11.0000 + 2.00000i −0.695701 + 0.126491i
\(251\) 4.24264i 0.267793i 0.990995 + 0.133897i \(0.0427490\pi\)
−0.990995 + 0.133897i \(0.957251\pi\)
\(252\) 0 0
\(253\) −4.00000 4.00000i −0.251478 0.251478i
\(254\) 7.07107 0.443678
\(255\) 6.24264 + 4.58579i 0.390929 + 0.287173i
\(256\) 1.00000 0.0625000
\(257\) −4.24264 4.24264i −0.264649 0.264649i 0.562291 0.826940i \(-0.309920\pi\)
−0.826940 + 0.562291i \(0.809920\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 4.24264 8.48528i 0.263117 0.526235i
\(261\) −8.00000 2.82843i −0.495188 0.175075i
\(262\) −10.0000 + 10.0000i −0.617802 + 0.617802i
\(263\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(264\) −1.41421 2.00000i −0.0870388 0.123091i
\(265\) −2.00000 + 4.00000i −0.122859 + 0.245718i
\(266\) 0 0
\(267\) 12.0711 + 2.07107i 0.738737 + 0.126747i
\(268\) 7.00000 + 7.00000i 0.427593 + 0.427593i
\(269\) 25.4558 1.55207 0.776035 0.630690i \(-0.217228\pi\)
0.776035 + 0.630690i \(0.217228\pi\)
\(270\) −6.53553 9.60660i −0.397740 0.584639i
\(271\) 10.0000 0.607457 0.303728 0.952759i \(-0.401768\pi\)
0.303728 + 0.952759i \(0.401768\pi\)
\(272\) 1.41421 + 1.41421i 0.0857493 + 0.0857493i
\(273\) 0 0
\(274\) 10.0000i 0.604122i
\(275\) 4.24264 + 5.65685i 0.255841 + 0.341121i
\(276\) −4.00000 5.65685i −0.240772 0.340503i
\(277\) 5.00000 5.00000i 0.300421 0.300421i −0.540758 0.841178i \(-0.681862\pi\)
0.841178 + 0.540758i \(0.181862\pi\)
\(278\) 8.48528 8.48528i 0.508913 0.508913i
\(279\) 2.82843 + 1.00000i 0.169334 + 0.0598684i
\(280\) 0 0
\(281\) 22.6274i 1.34984i −0.737892 0.674919i \(-0.764178\pi\)
0.737892 0.674919i \(-0.235822\pi\)
\(282\) −0.585786 + 3.41421i −0.0348831 + 0.203313i
\(283\) −19.0000 19.0000i −1.12943 1.12943i −0.990269 0.139163i \(-0.955559\pi\)
−0.139163 0.990269i \(-0.544441\pi\)
\(284\) 12.7279 0.755263
\(285\) −2.34315 15.3137i −0.138796 0.907106i
\(286\) −6.00000 −0.354787
\(287\) 0 0
\(288\) −1.29289 2.70711i −0.0761845 0.159518i
\(289\) 13.0000i 0.764706i
\(290\) 5.65685 + 2.82843i 0.332182 + 0.166091i
\(291\) 22.0000 15.5563i 1.28966 0.911929i
\(292\) 2.00000 2.00000i 0.117041 0.117041i
\(293\) −16.9706 + 16.9706i −0.991431 + 0.991431i −0.999964 0.00853273i \(-0.997284\pi\)
0.00853273 + 0.999964i \(0.497284\pi\)
\(294\) −9.89949 + 7.00000i −0.577350 + 0.408248i
\(295\) 0 0
\(296\) 4.24264i 0.246598i
\(297\) −3.58579 + 6.41421i −0.208068 + 0.372190i
\(298\) −1.00000 1.00000i −0.0579284 0.0579284i
\(299\) −16.9706 −0.981433
\(300\) 3.94975 + 7.70711i 0.228039 + 0.444970i
\(301\) 0 0
\(302\) −5.65685 5.65685i −0.325515 0.325515i
\(303\) 4.55635 26.5563i 0.261755 1.52562i
\(304\) 4.00000i 0.229416i
\(305\) −16.9706 + 5.65685i −0.971732 + 0.323911i
\(306\) 2.00000 5.65685i 0.114332 0.323381i
\(307\) 5.00000 5.00000i 0.285365 0.285365i −0.549879 0.835244i \(-0.685326\pi\)
0.835244 + 0.549879i \(0.185326\pi\)
\(308\) 0 0
\(309\) −8.48528 12.0000i −0.482711 0.682656i
\(310\) −2.00000 1.00000i −0.113592 0.0567962i
\(311\) 1.41421i 0.0801927i −0.999196 0.0400963i \(-0.987234\pi\)
0.999196 0.0400963i \(-0.0127665\pi\)
\(312\) −7.24264 1.24264i −0.410034 0.0703507i
\(313\) −10.0000 10.0000i −0.565233 0.565233i 0.365556 0.930789i \(-0.380879\pi\)
−0.930789 + 0.365556i \(0.880879\pi\)
\(314\) −5.65685 −0.319235
\(315\) 0 0
\(316\) 2.00000 0.112509
\(317\) 4.24264 + 4.24264i 0.238290 + 0.238290i 0.816142 0.577851i \(-0.196109\pi\)
−0.577851 + 0.816142i \(0.696109\pi\)
\(318\) 3.41421 + 0.585786i 0.191460 + 0.0328493i
\(319\) 4.00000i 0.223957i
\(320\) 0.707107 + 2.12132i 0.0395285 + 0.118585i
\(321\) 12.0000 + 16.9706i 0.669775 + 0.947204i
\(322\) 0 0
\(323\) 5.65685 5.65685i 0.314756 0.314756i
\(324\) −5.65685 + 7.00000i −0.314270 + 0.388889i
\(325\) 21.0000 + 3.00000i 1.16487 + 0.166410i
\(326\) 15.5563i 0.861586i
\(327\) −2.92893 + 17.0711i −0.161970 + 0.944032i
\(328\) 4.00000 + 4.00000i 0.220863 + 0.220863i
\(329\) 0 0
\(330\) 3.24264 4.41421i 0.178501 0.242994i
\(331\) 32.0000 1.75888 0.879440 0.476011i \(-0.157918\pi\)
0.879440 + 0.476011i \(0.157918\pi\)
\(332\) 4.24264 + 4.24264i 0.232845 + 0.232845i
\(333\) −11.4853 + 5.48528i −0.629390 + 0.300592i
\(334\) 8.00000i 0.437741i
\(335\) −9.89949 + 19.7990i −0.540867 + 1.08173i
\(336\) 0 0
\(337\) −8.00000 + 8.00000i −0.435788 + 0.435788i −0.890592 0.454804i \(-0.849709\pi\)
0.454804 + 0.890592i \(0.349709\pi\)
\(338\) −3.53553 + 3.53553i −0.192308 + 0.192308i
\(339\) 8.48528 6.00000i 0.460857 0.325875i
\(340\) −2.00000 + 4.00000i −0.108465 + 0.216930i
\(341\) 1.41421i 0.0765840i
\(342\) −10.8284 + 5.17157i −0.585534 + 0.279647i
\(343\) 0 0
\(344\) 0 0
\(345\) 9.17157 12.4853i 0.493781 0.672185i
\(346\) −20.0000 −1.07521
\(347\) 4.24264 + 4.24264i 0.227757 + 0.227757i 0.811755 0.583998i \(-0.198512\pi\)
−0.583998 + 0.811755i \(0.698512\pi\)
\(348\) 0.828427 4.82843i 0.0444084 0.258831i
\(349\) 30.0000i 1.60586i −0.596071 0.802932i \(-0.703272\pi\)
0.596071 0.802932i \(-0.296728\pi\)
\(350\) 0 0
\(351\) 6.00000 + 21.2132i 0.320256 + 1.13228i
\(352\) 1.00000 1.00000i 0.0533002 0.0533002i
\(353\) −25.4558 + 25.4558i −1.35488 + 1.35488i −0.474766 + 0.880112i \(0.657467\pi\)
−0.880112 + 0.474766i \(0.842533\pi\)
\(354\) 0 0
\(355\) 9.00000 + 27.0000i 0.477670 + 1.43301i
\(356\) 7.07107i 0.374766i
\(357\) 0 0
\(358\) 9.00000 + 9.00000i 0.475665 + 0.475665i
\(359\) 7.07107 0.373197 0.186598 0.982436i \(-0.440254\pi\)
0.186598 + 0.982436i \(0.440254\pi\)
\(360\) 4.82843 4.65685i 0.254480 0.245438i
\(361\) 3.00000 0.157895
\(362\) −7.07107 7.07107i −0.371647 0.371647i
\(363\) 15.3640 + 2.63604i 0.806399 + 0.138356i
\(364\) 0 0
\(365\) 5.65685 + 2.82843i 0.296093 + 0.148047i
\(366\) 8.00000 + 11.3137i 0.418167 + 0.591377i
\(367\) −15.0000 + 15.0000i −0.782994 + 0.782994i −0.980335 0.197341i \(-0.936769\pi\)
0.197341 + 0.980335i \(0.436769\pi\)
\(368\) 2.82843 2.82843i 0.147442 0.147442i
\(369\) 5.65685 16.0000i 0.294484 0.832927i
\(370\) 9.00000 3.00000i 0.467888 0.155963i
\(371\) 0 0
\(372\) −0.292893 + 1.70711i −0.0151858 + 0.0885094i
\(373\) −12.0000 12.0000i −0.621336 0.621336i 0.324537 0.945873i \(-0.394792\pi\)
−0.945873 + 0.324537i \(0.894792\pi\)
\(374\) 2.82843 0.146254
\(375\) −13.5563 + 13.8284i −0.700047 + 0.714097i
\(376\) −2.00000 −0.103142
\(377\) −8.48528 8.48528i −0.437014 0.437014i
\(378\) 0 0
\(379\) 34.0000i 1.74646i 0.487306 + 0.873231i \(0.337980\pi\)
−0.487306 + 0.873231i \(0.662020\pi\)
\(380\) 8.48528 2.82843i 0.435286 0.145095i
\(381\) 10.0000 7.07107i 0.512316 0.362262i
\(382\) −15.0000 + 15.0000i −0.767467 + 0.767467i
\(383\) −25.4558 + 25.4558i −1.30073 + 1.30073i −0.372835 + 0.927898i \(0.621614\pi\)
−0.927898 + 0.372835i \(0.878386\pi\)
\(384\) 1.41421 1.00000i 0.0721688 0.0510310i
\(385\) 0 0
\(386\) 12.7279i 0.647834i
\(387\) 0 0
\(388\) 11.0000 + 11.0000i 0.558440 + 0.558440i
\(389\) −5.65685 −0.286814 −0.143407 0.989664i \(-0.545806\pi\)
−0.143407 + 0.989664i \(0.545806\pi\)
\(390\) −2.48528 16.2426i −0.125847 0.822478i
\(391\) 8.00000 0.404577
\(392\) −4.94975 4.94975i −0.250000 0.250000i
\(393\) −4.14214 + 24.1421i −0.208943 + 1.21781i
\(394\) 10.0000i 0.503793i
\(395\) 1.41421 + 4.24264i 0.0711568 + 0.213470i
\(396\) −4.00000 1.41421i −0.201008 0.0710669i
\(397\) −8.00000 + 8.00000i −0.401508 + 0.401508i −0.878764 0.477256i \(-0.841631\pi\)
0.477256 + 0.878764i \(0.341631\pi\)
\(398\) −16.9706 + 16.9706i −0.850657 + 0.850657i
\(399\) 0 0
\(400\) −4.00000 + 3.00000i −0.200000 + 0.150000i
\(401\) 26.8701i 1.34183i −0.741536 0.670913i \(-0.765902\pi\)
0.741536 0.670913i \(-0.234098\pi\)
\(402\) 16.8995 + 2.89949i 0.842870 + 0.144614i
\(403\) 3.00000 + 3.00000i 0.149441 + 0.149441i
\(404\) 15.5563 0.773957
\(405\) −18.8492 7.05025i −0.936626 0.350330i
\(406\) 0 0
\(407\) −4.24264 4.24264i −0.210300 0.210300i
\(408\) 3.41421 + 0.585786i 0.169029 + 0.0290008i
\(409\) 6.00000i 0.296681i −0.988936 0.148340i \(-0.952607\pi\)
0.988936 0.148340i \(-0.0473931\pi\)
\(410\) −5.65685 + 11.3137i −0.279372 + 0.558744i
\(411\) −10.0000 14.1421i −0.493264 0.697580i
\(412\) 6.00000 6.00000i 0.295599 0.295599i
\(413\) 0 0
\(414\) −11.3137 4.00000i −0.556038 0.196589i
\(415\) −6.00000 + 12.0000i −0.294528 + 0.589057i
\(416\) 4.24264i 0.208013i
\(417\) 3.51472 20.4853i 0.172117 1.00317i
\(418\) −4.00000 4.00000i −0.195646 0.195646i
\(419\) −5.65685 −0.276355 −0.138178 0.990407i \(-0.544125\pi\)
−0.138178 + 0.990407i \(0.544125\pi\)
\(420\) 0 0
\(421\) −22.0000 −1.07221 −0.536107 0.844150i \(-0.680106\pi\)
−0.536107 + 0.844150i \(0.680106\pi\)
\(422\) 7.07107 + 7.07107i 0.344214 + 0.344214i
\(423\) 2.58579 + 5.41421i 0.125725 + 0.263248i
\(424\) 2.00000i 0.0971286i
\(425\) −9.89949 1.41421i −0.480196 0.0685994i
\(426\) 18.0000 12.7279i 0.872103 0.616670i
\(427\) 0 0
\(428\) −8.48528 + 8.48528i −0.410152 + 0.410152i
\(429\) −8.48528 + 6.00000i −0.409673 + 0.289683i
\(430\) 0 0
\(431\) 32.5269i 1.56677i 0.621539 + 0.783383i \(0.286508\pi\)
−0.621539 + 0.783383i \(0.713492\pi\)
\(432\) −4.53553 2.53553i −0.218216 0.121991i
\(433\) 2.00000 + 2.00000i 0.0961139 + 0.0961139i 0.753529 0.657415i \(-0.228350\pi\)
−0.657415 + 0.753529i \(0.728350\pi\)
\(434\) 0 0
\(435\) 10.8284 1.65685i 0.519183 0.0794401i
\(436\) −10.0000 −0.478913
\(437\) −11.3137 11.3137i −0.541208 0.541208i
\(438\) 0.828427 4.82843i 0.0395838 0.230711i
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 2.82843 + 1.41421i 0.134840 + 0.0674200i
\(441\) −7.00000 + 19.7990i −0.333333 + 0.942809i
\(442\) 6.00000 6.00000i 0.285391 0.285391i
\(443\) 16.9706 16.9706i 0.806296 0.806296i −0.177775 0.984071i \(-0.556890\pi\)
0.984071 + 0.177775i \(0.0568900\pi\)
\(444\) −4.24264 6.00000i −0.201347 0.284747i
\(445\) −15.0000 + 5.00000i −0.711068 + 0.237023i
\(446\) 15.5563i 0.736614i
\(447\) −2.41421 0.414214i −0.114188 0.0195916i
\(448\) 0 0
\(449\) 9.89949 0.467186 0.233593 0.972334i \(-0.424952\pi\)
0.233593 + 0.972334i \(0.424952\pi\)
\(450\) 13.2929 + 6.94975i 0.626633 + 0.327614i
\(451\) 8.00000 0.376705
\(452\) 4.24264 + 4.24264i 0.199557 + 0.199557i
\(453\) −13.6569 2.34315i −0.641655 0.110091i
\(454\) 16.0000i 0.750917i
\(455\) 0 0
\(456\) −4.00000 5.65685i −0.187317 0.264906i
\(457\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(458\) 18.3848 18.3848i 0.859064 0.859064i
\(459\) −2.82843 10.0000i −0.132020 0.466760i
\(460\) 8.00000 + 4.00000i 0.373002 + 0.186501i
\(461\) 2.82843i 0.131733i −0.997828 0.0658665i \(-0.979019\pi\)
0.997828 0.0658665i \(-0.0209811\pi\)
\(462\) 0 0
\(463\) −7.00000 7.00000i −0.325318 0.325318i 0.525485 0.850803i \(-0.323884\pi\)
−0.850803 + 0.525485i \(0.823884\pi\)
\(464\) 2.82843 0.131306
\(465\) −3.82843 + 0.585786i −0.177539 + 0.0271652i
\(466\) −14.0000 −0.648537
\(467\) −2.82843 2.82843i −0.130884 0.130884i 0.638630 0.769514i \(-0.279501\pi\)
−0.769514 + 0.638630i \(0.779501\pi\)
\(468\) −11.4853 + 5.48528i −0.530907 + 0.253557i
\(469\) 0 0
\(470\) −1.41421 4.24264i −0.0652328 0.195698i
\(471\) −8.00000 + 5.65685i −0.368621 + 0.260654i
\(472\) 0 0
\(473\) 0 0
\(474\) 2.82843 2.00000i 0.129914 0.0918630i
\(475\) 12.0000 + 16.0000i 0.550598 + 0.734130i
\(476\) 0 0
\(477\) 5.41421 2.58579i 0.247900 0.118395i
\(478\) 16.0000 + 16.0000i 0.731823 + 0.731823i
\(479\) −38.1838 −1.74466 −0.872330 0.488917i \(-0.837392\pi\)
−0.872330 + 0.488917i \(0.837392\pi\)
\(480\) 3.12132 + 2.29289i 0.142468 + 0.104656i
\(481\) −18.0000 −0.820729
\(482\) −1.41421 1.41421i −0.0644157 0.0644157i
\(483\) 0 0
\(484\) 9.00000i 0.409091i
\(485\) −15.5563 + 31.1127i −0.706377 + 1.41275i
\(486\) −1.00000 + 15.5563i −0.0453609 + 0.705650i
\(487\) −11.0000 + 11.0000i −0.498458 + 0.498458i −0.910958 0.412500i \(-0.864656\pi\)
0.412500 + 0.910958i \(0.364656\pi\)
\(488\) −5.65685 + 5.65685i −0.256074 + 0.256074i
\(489\) −15.5563 22.0000i −0.703482 0.994874i
\(490\) 7.00000 14.0000i 0.316228 0.632456i
\(491\) 12.7279i 0.574403i 0.957870 + 0.287202i \(0.0927249\pi\)
−0.957870 + 0.287202i \(0.907275\pi\)
\(492\) 9.65685 + 1.65685i 0.435365 + 0.0746968i
\(493\) 4.00000 + 4.00000i 0.180151 + 0.180151i
\(494\) −16.9706 −0.763542
\(495\) 0.171573 9.48528i 0.00771163 0.426332i
\(496\) −1.00000 −0.0449013
\(497\) 0 0
\(498\) 10.2426 + 1.75736i 0.458984 + 0.0787492i
\(499\) 36.0000i 1.61158i 0.592200 + 0.805791i \(0.298259\pi\)
−0.592200 + 0.805791i \(0.701741\pi\)
\(500\) −9.19239 6.36396i −0.411096 0.284605i
\(501\) −8.00000 11.3137i −0.357414 0.505459i
\(502\) −3.00000 + 3.00000i −0.133897 + 0.133897i
\(503\) −18.3848 + 18.3848i −0.819737 + 0.819737i −0.986070 0.166333i \(-0.946807\pi\)
0.166333 + 0.986070i \(0.446807\pi\)
\(504\) 0 0
\(505\) 11.0000 + 33.0000i 0.489494 + 1.46848i
\(506\) 5.65685i 0.251478i
\(507\) −1.46447 + 8.53553i −0.0650392 + 0.379076i
\(508\) 5.00000 + 5.00000i 0.221839 + 0.221839i
\(509\) 11.3137 0.501471 0.250736 0.968056i \(-0.419328\pi\)
0.250736 + 0.968056i \(0.419328\pi\)
\(510\) 1.17157 + 7.65685i 0.0518781 + 0.339051i
\(511\) 0 0
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) −10.1421 + 18.1421i −0.447786 + 0.800995i
\(514\) 6.00000i 0.264649i
\(515\) 16.9706 + 8.48528i 0.747812 + 0.373906i
\(516\) 0 0
\(517\) −2.00000 + 2.00000i −0.0879599 + 0.0879599i
\(518\) 0 0
\(519\) −28.2843 + 20.0000i −1.24154 + 0.877903i
\(520\) 9.00000 3.00000i 0.394676 0.131559i
\(521\) 14.1421i 0.619578i 0.950805 + 0.309789i \(0.100258\pi\)
−0.950805 + 0.309789i \(0.899742\pi\)
\(522\) −3.65685 7.65685i −0.160056 0.335131i
\(523\) 18.0000 + 18.0000i 0.787085 + 0.787085i 0.981015 0.193930i \(-0.0621236\pi\)
−0.193930 + 0.981015i \(0.562124\pi\)
\(524\) −14.1421 −0.617802
\(525\) 0 0
\(526\) 0 0
\(527\) −1.41421 1.41421i −0.0616041 0.0616041i
\(528\) 0.414214 2.41421i 0.0180263 0.105065i
\(529\) 7.00000i 0.304348i
\(530\) −4.24264 + 1.41421i −0.184289 + 0.0614295i
\(531\) 0 0
\(532\) 0 0
\(533\) 16.9706 16.9706i 0.735077 0.735077i
\(534\) 7.07107 + 10.0000i 0.305995 + 0.432742i
\(535\) −24.0000 12.0000i −1.03761 0.518805i
\(536\) 9.89949i 0.427593i
\(537\) 21.7279 + 3.72792i 0.937629 + 0.160872i
\(538\) 18.0000 + 18.0000i 0.776035 + 0.776035i
\(539\) −9.89949 −0.426401
\(540\) 2.17157 11.4142i 0.0934496 0.491190i
\(541\) 30.0000 1.28980 0.644900 0.764267i \(-0.276899\pi\)
0.644900 + 0.764267i \(0.276899\pi\)
\(542\) 7.07107 + 7.07107i 0.303728 + 0.303728i
\(543\) −17.0711 2.92893i −0.732590 0.125693i
\(544\) 2.00000i 0.0857493i
\(545\) −7.07107 21.2132i −0.302891 0.908674i
\(546\) 0 0
\(547\) −5.00000 + 5.00000i −0.213785 + 0.213785i −0.805873 0.592088i \(-0.798304\pi\)
0.592088 + 0.805873i \(0.298304\pi\)
\(548\) 7.07107 7.07107i 0.302061 0.302061i
\(549\) 22.6274 + 8.00000i 0.965715 + 0.341432i
\(550\) −1.00000 + 7.00000i −0.0426401 + 0.298481i
\(551\) 11.3137i 0.481980i
\(552\) 1.17157 6.82843i 0.0498655 0.290637i
\(553\) 0 0
\(554\) 7.07107 0.300421
\(555\) 9.72792 13.2426i 0.412927 0.562119i
\(556\) 12.0000 0.508913
\(557\) −26.8701 26.8701i −1.13852 1.13852i −0.988716 0.149805i \(-0.952135\pi\)
−0.149805 0.988716i \(-0.547865\pi\)
\(558\) 1.29289 + 2.70711i 0.0547325 + 0.114601i
\(559\) 0 0
\(560\) 0 0
\(561\) 4.00000 2.82843i 0.168880 0.119416i
\(562\) 16.0000 16.0000i 0.674919 0.674919i
\(563\) 11.3137 11.3137i 0.476816 0.476816i −0.427296 0.904112i \(-0.640534\pi\)
0.904112 + 0.427296i \(0.140534\pi\)
\(564\) −2.82843 + 2.00000i −0.119098 + 0.0842152i
\(565\) −6.00000 + 12.0000i −0.252422 + 0.504844i
\(566\) 26.8701i 1.12943i
\(567\) 0 0
\(568\) 9.00000 + 9.00000i 0.377632 + 0.377632i
\(569\) 26.8701 1.12645 0.563226 0.826303i \(-0.309560\pi\)
0.563226 + 0.826303i \(0.309560\pi\)
\(570\) 9.17157 12.4853i 0.384155 0.522951i
\(571\) −40.0000 −1.67395 −0.836974 0.547243i \(-0.815677\pi\)
−0.836974 + 0.547243i \(0.815677\pi\)
\(572\) −4.24264 4.24264i −0.177394 0.177394i
\(573\) −6.21320 + 36.2132i −0.259560 + 1.51283i
\(574\) 0 0
\(575\) −2.82843 + 19.7990i −0.117954 + 0.825675i
\(576\) 1.00000 2.82843i 0.0416667 0.117851i
\(577\) 21.0000 21.0000i 0.874241 0.874241i −0.118690 0.992931i \(-0.537869\pi\)
0.992931 + 0.118690i \(0.0378694\pi\)
\(578\) 9.19239 9.19239i 0.382353 0.382353i
\(579\) −12.7279 18.0000i −0.528954 0.748054i
\(580\) 2.00000 + 6.00000i 0.0830455 + 0.249136i
\(581\) 0 0
\(582\) 26.5563 + 4.55635i 1.10080 + 0.188867i
\(583\) 2.00000 + 2.00000i 0.0828315 + 0.0828315i
\(584\) 2.82843 0.117041
\(585\) −19.7574 20.4853i −0.816866 0.846962i
\(586\) −24.0000 −0.991431
\(587\) −25.4558 25.4558i −1.05068 1.05068i −0.998646 0.0520296i \(-0.983431\pi\)
−0.0520296 0.998646i \(-0.516569\pi\)
\(588\) −11.9497 2.05025i −0.492799 0.0845510i
\(589\) 4.00000i 0.164817i
\(590\) 0 0
\(591\) 10.0000 + 14.1421i 0.411345 + 0.581730i
\(592\) 3.00000 3.00000i 0.123299 0.123299i
\(593\) 4.24264 4.24264i 0.174224 0.174224i −0.614608 0.788833i \(-0.710686\pi\)
0.788833 + 0.614608i \(0.210686\pi\)
\(594\) −7.07107 + 2.00000i −0.290129 + 0.0820610i
\(595\) 0 0
\(596\) 1.41421i 0.0579284i
\(597\) −7.02944 + 40.9706i −0.287696 + 1.67681i
\(598\) −12.0000 12.0000i −0.490716 0.490716i
\(599\) 43.8406 1.79128 0.895640 0.444781i \(-0.146718\pi\)
0.895640 + 0.444781i \(0.146718\pi\)
\(600\) −2.65685 + 8.24264i −0.108466 + 0.336504i
\(601\) 2.00000 0.0815817 0.0407909 0.999168i \(-0.487012\pi\)
0.0407909 + 0.999168i \(0.487012\pi\)
\(602\) 0 0
\(603\) 26.7990 12.7990i 1.09134 0.521215i
\(604\) 8.00000i 0.325515i
\(605\) −19.0919 + 6.36396i −0.776195 + 0.258732i
\(606\) 22.0000 15.5563i 0.893689 0.631933i
\(607\) −20.0000 + 20.0000i −0.811775 + 0.811775i −0.984900 0.173125i \(-0.944614\pi\)
0.173125 + 0.984900i \(0.444614\pi\)
\(608\) 2.82843 2.82843i 0.114708 0.114708i
\(609\) 0 0
\(610\) −16.0000 8.00000i −0.647821 0.323911i
\(611\) 8.48528i 0.343278i
\(612\) 5.41421 2.58579i 0.218857 0.104524i
\(613\) −13.0000 13.0000i −0.525065 0.525065i 0.394032 0.919097i \(-0.371080\pi\)
−0.919097 + 0.394032i \(0.871080\pi\)
\(614\) 7.07107 0.285365
\(615\) 3.31371 + 21.6569i 0.133622 + 0.873289i
\(616\) 0 0
\(617\) −29.6985 29.6985i −1.19562 1.19562i −0.975466 0.220150i \(-0.929345\pi\)
−0.220150 0.975466i \(-0.570655\pi\)
\(618\) 2.48528 14.4853i 0.0999727 0.582683i
\(619\) 4.00000i 0.160774i 0.996764 + 0.0803868i \(0.0256155\pi\)
−0.996764 + 0.0803868i \(0.974384\pi\)
\(620\) −0.707107 2.12132i −0.0283981 0.0851943i
\(621\) −20.0000 + 5.65685i −0.802572 + 0.227002i
\(622\) 1.00000 1.00000i 0.0400963 0.0400963i
\(623\) 0 0
\(624\) −4.24264 6.00000i −0.169842 0.240192i
\(625\) 7.00000 24.0000i 0.280000 0.960000i
\(626\) 14.1421i 0.565233i
\(627\) −9.65685 1.65685i −0.385658 0.0661684i
\(628\) −4.00000 4.00000i −0.159617 0.159617i
\(629\) 8.48528 0.338330
\(630\) 0 0
\(631\) 32.0000 1.27390 0.636950 0.770905i \(-0.280196\pi\)
0.636950 + 0.770905i \(0.280196\pi\)
\(632\) 1.41421 + 1.41421i 0.0562544 + 0.0562544i
\(633\) 17.0711 + 2.92893i 0.678514 + 0.116415i
\(634\) 6.00000i 0.238290i
\(635\) −7.07107 + 14.1421i −0.280607 + 0.561214i
\(636\) 2.00000 + 2.82843i 0.0793052 + 0.112154i
\(637\) −21.0000 + 21.0000i −0.832050 + 0.832050i
\(638\) 2.82843 2.82843i 0.111979 0.111979i
\(639\) 12.7279 36.0000i 0.503509 1.42414i
\(640\) −1.00000 + 2.00000i −0.0395285 + 0.0790569i
\(641\) 26.8701i 1.06130i −0.847590 0.530652i \(-0.821947\pi\)
0.847590 0.530652i \(-0.178053\pi\)
\(642\) −3.51472 + 20.4853i −0.138715 + 0.808490i
\(643\) 6.00000 + 6.00000i 0.236617 + 0.236617i 0.815448 0.578831i \(-0.196491\pi\)
−0.578831 + 0.815448i \(0.696491\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 8.00000 0.314756
\(647\) 8.48528 + 8.48528i 0.333591 + 0.333591i 0.853948 0.520358i \(-0.174201\pi\)
−0.520358 + 0.853948i \(0.674201\pi\)
\(648\) −8.94975 + 0.949747i −0.351579 + 0.0373096i
\(649\) 0 0
\(650\) 12.7279 + 16.9706i 0.499230 + 0.665640i
\(651\) 0 0
\(652\) 11.0000 11.0000i 0.430793 0.430793i
\(653\) 12.7279 12.7279i 0.498082 0.498082i −0.412758 0.910841i \(-0.635435\pi\)
0.910841 + 0.412758i \(0.135435\pi\)
\(654\) −14.1421 + 10.0000i −0.553001 + 0.391031i
\(655\) −10.0000 30.0000i −0.390732 1.17220i
\(656\) 5.65685i 0.220863i
\(657\) −3.65685 7.65685i −0.142667 0.298722i
\(658\) 0 0
\(659\) 16.9706 0.661079 0.330540 0.943792i \(-0.392769\pi\)
0.330540 + 0.943792i \(0.392769\pi\)
\(660\) 5.41421 0.828427i 0.210748 0.0322465i
\(661\) −34.0000 −1.32245 −0.661223 0.750189i \(-0.729962\pi\)
−0.661223 + 0.750189i \(0.729962\pi\)
\(662\) 22.6274 + 22.6274i 0.879440 + 0.879440i
\(663\) 2.48528 14.4853i 0.0965203 0.562562i
\(664\) 6.00000i 0.232845i
\(665\) 0 0
\(666\) −12.0000 4.24264i −0.464991 0.164399i
\(667\) 8.00000 8.00000i 0.309761 0.309761i
\(668\) 5.65685 5.65685i 0.218870 0.218870i
\(669\) −15.5563 22.0000i −0.601443 0.850569i
\(670\) −21.0000 + 7.00000i −0.811301 + 0.270434i
\(671\) 11.3137i 0.436761i
\(672\) 0 0
\(673\) 24.0000 + 24.0000i 0.925132 + 0.925132i 0.997386 0.0722542i \(-0.0230193\pi\)
−0.0722542 + 0.997386i \(0.523019\pi\)
\(674\) −11.3137 −0.435788
\(675\) 25.7487 3.46447i 0.991069 0.133347i
\(676\) −5.00000 −0.192308
\(677\) −15.5563 15.5563i −0.597879 0.597879i 0.341869 0.939748i \(-0.388940\pi\)
−0.939748 + 0.341869i \(0.888940\pi\)
\(678\) 10.2426 + 1.75736i 0.393366 + 0.0674910i
\(679\) 0 0
\(680\) −4.24264 + 1.41421i −0.162698 + 0.0542326i
\(681\) 16.0000 + 22.6274i 0.613121 + 0.867085i
\(682\) −1.00000 + 1.00000i −0.0382920 + 0.0382920i
\(683\) 16.9706 16.9706i 0.649361 0.649361i −0.303478 0.952838i \(-0.598148\pi\)
0.952838 + 0.303478i \(0.0981479\pi\)
\(684\) −11.3137 4.00000i −0.432590 0.152944i
\(685\) 20.0000 + 10.0000i 0.764161 + 0.382080i
\(686\) 0 0
\(687\) 7.61522 44.3848i 0.290539 1.69338i
\(688\) 0 0
\(689\) 8.48528 0.323263
\(690\) 15.3137 2.34315i 0.582983 0.0892020i
\(691\) −14.0000 −0.532585 −0.266293 0.963892i \(-0.585799\pi\)
−0.266293 + 0.963892i \(0.585799\pi\)
\(692\) −14.1421 14.1421i −0.537603 0.537603i
\(693\) 0 0
\(694\) 6.00000i 0.227757i
\(695\) 8.48528 + 25.4558i 0.321865 + 0.965595i
\(696\) 4.00000 2.82843i 0.151620 0.107211i
\(697\) −8.00000 + 8.00000i −0.303022 + 0.303022i
\(698\) 21.2132 21.2132i 0.802932 0.802932i
\(699\) −19.7990 + 14.0000i −0.748867 + 0.529529i
\(700\) 0 0
\(701\) 4.24264i 0.160242i −0.996785 0.0801212i \(-0.974469\pi\)
0.996785 0.0801212i \(-0.0255307\pi\)
\(702\) −10.7574 + 19.2426i −0.406010 + 0.726267i
\(703\) −12.0000 12.0000i −0.452589 0.452589i
\(704\) 1.41421 0.0533002
\(705\) −6.24264 4.58579i −0.235111 0.172711i
\(706\) −36.0000 −1.35488
\(707\) 0 0
\(708\) 0 0
\(709\) 48.0000i 1.80268i −0.433114 0.901339i \(-0.642585\pi\)
0.433114 0.901339i \(-0.357415\pi\)
\(710\) −12.7279 + 25.4558i −0.477670 + 0.955341i
\(711\) 2.00000 5.65685i 0.0750059 0.212149i
\(712\) −5.00000 + 5.00000i −0.187383 + 0.187383i
\(713\) −2.82843 + 2.82843i −0.105925 + 0.105925i
\(714\) 0 0
\(715\) 6.00000 12.0000i 0.224387 0.448775i
\(716\) 12.7279i 0.475665i
\(717\) 38.6274 + 6.62742i 1.44257 + 0.247505i
\(718\) 5.00000 + 5.00000i 0.186598 + 0.186598i
\(719\) 39.5980 1.47676 0.738378 0.674387i \(-0.235592\pi\)
0.738378 + 0.674387i \(0.235592\pi\)
\(720\) 6.70711 + 0.121320i 0.249959 + 0.00452134i
\(721\) 0 0
\(722\) 2.12132 + 2.12132i 0.0789474 + 0.0789474i
\(723\) −3.41421 0.585786i −0.126976 0.0217856i
\(724\) 10.0000i 0.371647i
\(725\) −11.3137 + 8.48528i −0.420181 + 0.315135i
\(726\) 9.00000 + 12.7279i 0.334021 + 0.472377i
\(727\) −18.0000 + 18.0000i −0.667583 + 0.667583i −0.957156 0.289573i \(-0.906487\pi\)
0.289573 + 0.957156i \(0.406487\pi\)
\(728\) 0 0
\(729\) 14.1421 + 23.0000i 0.523783 + 0.851852i
\(730\) 2.00000 + 6.00000i 0.0740233 + 0.222070i
\(731\) 0 0
\(732\) −2.34315 + 13.6569i −0.0866052 + 0.504772i
\(733\) 24.0000 + 24.0000i 0.886460 + 0.886460i 0.994181 0.107721i \(-0.0343553\pi\)
−0.107721 + 0.994181i \(0.534355\pi\)
\(734\) −21.2132 −0.782994
\(735\) −4.10051 26.7990i −0.151249 0.988496i
\(736\) 4.00000 0.147442
\(737\) 9.89949 + 9.89949i 0.364653 + 0.364653i
\(738\) 15.3137 7.31371i 0.563705 0.269221i
\(739\) 40.0000i 1.47142i 0.677295 + 0.735712i \(0.263152\pi\)
−0.677295 + 0.735712i \(0.736848\pi\)
\(740\) 8.48528 + 4.24264i 0.311925 + 0.155963i
\(741\) −24.0000 + 16.9706i −0.881662 + 0.623429i
\(742\) 0 0
\(743\) 14.1421 14.1421i 0.518825 0.518825i −0.398391 0.917216i \(-0.630431\pi\)
0.917216 + 0.398391i \(0.130431\pi\)
\(744\) −1.41421 + 1.00000i −0.0518476 + 0.0366618i
\(745\) 3.00000 1.00000i 0.109911 0.0366372i
\(746\) 16.9706i 0.621336i
\(747\) 16.2426 7.75736i 0.594287 0.283827i
\(748\) 2.00000 + 2.00000i 0.0731272 + 0.0731272i
\(749\) 0 0
\(750\) −19.3640 + 0.192388i −0.707072 + 0.00702502i
\(751\) 4.00000 0.145962 0.0729810 0.997333i \(-0.476749\pi\)
0.0729810 + 0.997333i \(0.476749\pi\)
\(752\) −1.41421 1.41421i −0.0515711 0.0515711i
\(753\) −1.24264 + 7.24264i −0.0452843 + 0.263936i
\(754\) 12.0000i 0.437014i
\(755\) 16.9706 5.65685i 0.617622 0.205874i
\(756\) 0 0
\(757\) −35.0000 + 35.0000i −1.27210 + 1.27210i −0.327111 + 0.944986i \(0.606075\pi\)
−0.944986 + 0.327111i \(0.893925\pi\)
\(758\) −24.0416 + 24.0416i −0.873231 + 0.873231i
\(759\) −5.65685 8.00000i −0.205331 0.290382i
\(760\) 8.00000 + 4.00000i 0.290191 + 0.145095i
\(761\) 52.3259i 1.89681i 0.317058 + 0.948406i \(0.397305\pi\)
−0.317058 + 0.948406i \(0.602695\pi\)
\(762\) 12.0711 + 2.07107i 0.437289 + 0.0750269i
\(763\) 0 0
\(764\) −21.2132 −0.767467
\(765\) 9.31371 + 9.65685i 0.336738 + 0.349144i
\(766\) −36.0000 −1.30073
\(767\) 0 0
\(768\) 1.70711 + 0.292893i 0.0615999 + 0.0105689i
\(769\) 48.0000i 1.73092i −0.500974 0.865462i \(-0.667025\pi\)
0.500974 0.865462i \(-0.332975\pi\)
\(770\) 0 0
\(771\) −6.00000 8.48528i −0.216085 0.305590i
\(772\) 9.00000 9.00000i 0.323917 0.323917i
\(773\) 12.7279 12.7279i 0.457792 0.457792i −0.440138 0.897930i \(-0.645071\pi\)
0.897930 + 0.440138i \(0.145071\pi\)
\(774\) 0 0
\(775\) 4.00000 3.00000i 0.143684 0.107763i
\(776\) 15.5563i 0.558440i
\(777\) 0 0
\(778\) −4.00000 4.00000i −0.143407 0.143407i
\(779\) 22.6274 0.810711
\(780\) 9.72792 13.2426i 0.348315 0.474163i
\(781\) 18.0000 0.644091
\(782\) 5.65685 + 5.65685i 0.202289 + 0.202289i
\(783\) −12.8284 7.17157i −0.458451 0.256291i
\(784\) 7.00000i 0.250000i
\(785\) 5.65685 11.3137i 0.201902 0.403804i
\(786\) −20.0000 + 14.1421i −0.713376 + 0.504433i
\(787\) −24.0000 + 24.0000i −0.855508 + 0.855508i −0.990805 0.135297i \(-0.956801\pi\)
0.135297 + 0.990805i \(0.456801\pi\)
\(788\) −7.07107 + 7.07107i −0.251896 + 0.251896i
\(789\) 0 0
\(790\) −2.00000 + 4.00000i −0.0711568 + 0.142314i
\(791\) 0 0
\(792\) −1.82843 3.82843i −0.0649703 0.136037i
\(793\) 24.0000 + 24.0000i 0.852265 + 0.852265i
\(794\) −11.3137 −0.401508
\(795\) −4.58579 + 6.24264i −0.162641 + 0.221404i
\(796\) −24.0000 −0.850657
\(797\) 4.24264 + 4.24264i 0.150282 + 0.150282i 0.778244 0.627962i \(-0.216111\pi\)
−0.627962 + 0.778244i \(0.716111\pi\)
\(798\) 0 0
\(799\) 4.00000i 0.141510i
\(800\) −4.94975 0.707107i −0.175000 0.0250000i
\(801\) 20.0000 + 7.07107i 0.706665 + 0.249844i
\(802\) 19.0000 19.0000i 0.670913 0.670913i
\(803\) 2.82843 2.82843i 0.0998130 0.0998130i
\(804\) 9.89949 + 14.0000i 0.349128 + 0.493742i
\(805\) 0 0
\(806\) 4.24264i 0.149441i
\(807\) 43.4558 + 7.45584i 1.52972 + 0.262458i
\(808\) 11.0000 + 11.0000i 0.386979 + 0.386979i
\(809\) −7.07107 −0.248606 −0.124303 0.992244i \(-0.539669\pi\)
−0.124303 + 0.992244i \(0.539669\pi\)
\(810\) −8.34315 18.3137i −0.293148 0.643478i
\(811\) 6.00000 0.210688 0.105344 0.994436i \(-0.466406\pi\)
0.105344 + 0.994436i \(0.466406\pi\)
\(812\) 0 0
\(813\) 17.0711 + 2.92893i 0.598708 + 0.102722i
\(814\) 6.00000i 0.210300i
\(815\) 31.1127 + 15.5563i 1.08983 + 0.544915i
\(816\) 2.00000 + 2.82843i 0.0700140 + 0.0990148i
\(817\) 0 0
\(818\) 4.24264 4.24264i 0.148340 0.148340i
\(819\) 0 0
\(820\) −12.0000 + 4.00000i −0.419058 + 0.139686i
\(821\) 14.1421i 0.493564i −0.969071 0.246782i \(-0.920627\pi\)
0.969071 0.246782i \(-0.0793731\pi\)
\(822\) 2.92893 17.0711i 0.102158 0.595422i
\(823\) −25.0000 25.0000i −0.871445 0.871445i 0.121185 0.992630i \(-0.461331\pi\)
−0.992630 + 0.121185i \(0.961331\pi\)
\(824\) 8.48528 0.295599
\(825\) 5.58579 + 10.8995i 0.194472 + 0.379472i
\(826\) 0 0
\(827\) −25.4558 25.4558i −0.885186 0.885186i 0.108870 0.994056i \(-0.465277\pi\)
−0.994056 + 0.108870i \(0.965277\pi\)
\(828\) −5.17157 10.8284i −0.179725 0.376314i
\(829\) 28.0000i 0.972480i 0.873825 + 0.486240i \(0.161632\pi\)
−0.873825 + 0.486240i \(0.838368\pi\)
\(830\) −12.7279 + 4.24264i −0.441793 + 0.147264i
\(831\) 10.0000 7.07107i 0.346896 0.245293i
\(832\) 3.00000 3.00000i 0.104006 0.104006i
\(833\) 9.89949 9.89949i 0.342997 0.342997i
\(834\) 16.9706 12.0000i 0.587643 0.415526i
\(835\) 16.0000 + 8.00000i 0.553703 + 0.276851i
\(836\) 5.65685i 0.195646i
\(837\) 4.53553 + 2.53553i 0.156771 + 0.0876409i
\(838\) −4.00000 4.00000i −0.138178 0.138178i
\(839\) −35.3553 −1.22060 −0.610301 0.792170i \(-0.708951\pi\)
−0.610301 + 0.792170i \(0.708951\pi\)
\(840\) 0 0
\(841\) −21.0000 −0.724138
\(842\) −15.5563 15.5563i −0.536107 0.536107i
\(843\) 6.62742 38.6274i 0.228260 1.33040i
\(844\) 10.0000i 0.344214i
\(845\) −3.53553 10.6066i −0.121626 0.364878i
\(846\) −2.00000 + 5.65685i −0.0687614 + 0.194487i
\(847\) 0 0
\(848\) −1.41421 + 1.41421i −0.0485643 + 0.0485643i
\(849\) −26.8701 38.0000i −0.922178 1.30416i
\(850\) −6.00000 8.00000i −0.205798 0.274398i
\(851\) 16.9706i 0.581743i
\(852\) 21.7279 + 3.72792i 0.744386 + 0.127717i
\(853\) 8.00000 + 8.00000i 0.273915 + 0.273915i 0.830674 0.556759i \(-0.187955\pi\)
−0.556759 + 0.830674i \(0.687955\pi\)
\(854\) 0 0
\(855\) 0.485281 26.8284i 0.0165963 0.917513i
\(856\) −12.0000 −0.410152
\(857\) −21.2132 21.2132i −0.724629 0.724629i 0.244915 0.969544i \(-0.421240\pi\)
−0.969544 + 0.244915i \(0.921240\pi\)
\(858\) −10.2426 1.75736i −0.349678 0.0599953i
\(859\) 12.0000i 0.409435i 0.978821 + 0.204717i \(0.0656275\pi\)
−0.978821 + 0.204717i \(0.934372\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −23.0000 + 23.0000i −0.783383 + 0.783383i
\(863\) 16.9706 16.9706i 0.577685 0.577685i −0.356580 0.934265i \(-0.616057\pi\)
0.934265 + 0.356580i \(0.116057\pi\)
\(864\) −1.41421 5.00000i −0.0481125 0.170103i
\(865\) 20.0000 40.0000i 0.680020 1.36004i
\(866\) 2.82843i 0.0961139i
\(867\) 3.80761 22.1924i 0.129313 0.753693i
\(868\) 0 0
\(869\) 2.82843 0.0959478
\(870\) 8.82843 + 6.48528i 0.299312 + 0.219872i
\(871\) 42.0000 1.42312
\(872\) −7.07107 7.07107i −0.239457 0.239457i
\(873\) 42.1127 20.1127i 1.42530 0.680712i
\(874\) 16.0000i 0.541208i
\(875\) 0 0
\(876\) 4.00000 2.82843i 0.135147 0.0955637i
\(877\) 30.0000 30.0000i 1.01303 1.01303i 0.0131140 0.999914i \(-0.495826\pi\)
0.999914 0.0131140i \(-0.00417444\pi\)
\(878\) 0 0
\(879\) −33.9411 + 24.0000i −1.14481 + 0.809500i
\(880\) 1.00000 + 3.00000i 0.0337100 + 0.101130i
\(881\) 24.0416i 0.809983i 0.914320 + 0.404992i \(0.132726\pi\)
−0.914320 + 0.404992i \(0.867274\pi\)
\(882\) −18.9497 + 9.05025i −0.638071 + 0.304738i
\(883\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(884\) 8.48528 0.285391
\(885\) 0 0
\(886\) 24.0000 0.806296
\(887\) 1.41421 + 1.41421i 0.0474846 + 0.0474846i 0.730450 0.682966i \(-0.239310\pi\)
−0.682966 + 0.730450i \(0.739310\pi\)
\(888\) 1.24264 7.24264i 0.0417003 0.243047i
\(889\) 0 0
\(890\) −14.1421 7.07107i −0.474045 0.237023i
\(891\) −8.00000 + 9.89949i −0.268010 + 0.331646i
\(892\) 11.0000 11.0000i 0.368307 0.368307i
\(893\) −5.65685 + 5.65685i −0.189299 + 0.189299i
\(894\) −1.41421 2.00000i −0.0472984 0.0668900i
\(895\) −27.0000 + 9.00000i −0.902510 + 0.300837i
\(896\) 0 0
\(897\) −28.9706 4.97056i −0.967299 0.165962i
\(898\) 7.00000 + 7.00000i 0.233593 + 0.233593i
\(899\) −2.82843 −0.0943333
\(900\) 4.48528 + 14.3137i 0.149509 + 0.477124i
\(901\) −4.00000 −0.133259
\(902\) 5.65685 + 5.65685i 0.188353 + 0.188353i
\(903\) 0 0
\(904\) 6.00000i 0.199557i
\(905\) 21.2132 7.07107i 0.705151 0.235050i
\(906\) −8.00000 11.3137i −0.265782 0.375873i
\(907\) 25.0000 25.0000i 0.830111 0.830111i −0.157420 0.987532i \(-0.550318\pi\)
0.987532 + 0.157420i \(0.0503177\pi\)
\(908\) −11.3137 + 11.3137i −0.375459 + 0.375459i
\(909\) 15.5563 44.0000i 0.515972 1.45939i
\(910\) 0 0
\(911\) 11.3137i 0.374840i 0.982280 + 0.187420i \(0.0600125\pi\)
−0.982280 + 0.187420i \(0.939987\pi\)
\(912\) 1.17157 6.82843i 0.0387947 0.226112i
\(913\) 6.00000 + 6.00000i 0.198571 + 0.198571i
\(914\) 0 0
\(915\) −30.6274 + 4.68629i −1.01251 + 0.154924i
\(916\) 26.0000 0.859064
\(917\) 0 0
\(918\) 5.07107 9.07107i 0.167370 0.299390i
\(919\) 4.00000i 0.131948i −0.997821 0.0659739i \(-0.978985\pi\)
0.997821 0.0659739i \(-0.0210154\pi\)
\(920\) 2.82843 + 8.48528i 0.0932505 + 0.279751i
\(921\) 10.0000 7.07107i 0.329511 0.233000i
\(922\) 2.00000 2.00000i 0.0658665 0.0658665i
\(923\) 38.1838 38.1838i 1.25683 1.25683i
\(924\) 0 0
\(925\) −3.00000 + 21.0000i −0.0986394 + 0.690476i
\(926\) 9.89949i 0.325318i
\(927\) −10.9706 22.9706i −0.360321 0.754452i
\(928\) 2.00000 + 2.00000i 0.0656532 + 0.0656532i
\(929\) 1.41421 0.0463988 0.0231994 0.999731i \(-0.492615\pi\)
0.0231994 + 0.999731i \(0.492615\pi\)
\(930\) −3.12132 2.29289i −0.102352 0.0751869i
\(931\) −28.0000 −0.917663
\(932\) −9.89949 9.89949i −0.324269 0.324269i
\(933\) 0.414214 2.41421i 0.0135607 0.0790378i
\(934\) 4.00000i 0.130884i
\(935\) −2.82843 + 5.65685i −0.0924995 + 0.184999i
\(936\) −12.0000 4.24264i −0.392232 0.138675i
\(937\) 13.0000 13.0000i 0.424691 0.424691i −0.462124 0.886815i \(-0.652912\pi\)
0.886815 + 0.462124i \(0.152912\pi\)
\(938\) 0 0
\(939\) −14.1421 20.0000i −0.461511 0.652675i
\(940\) 2.00000 4.00000i 0.0652328 0.130466i
\(941\) 16.9706i 0.553225i −0.960982 0.276612i \(-0.910788\pi\)
0.960982 0.276612i \(-0.0892118\pi\)
\(942\) −9.65685 1.65685i −0.314637 0.0539832i
\(943\) 16.0000 + 16.0000i 0.521032 + 0.521032i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 25.4558 + 25.4558i 0.827204 + 0.827204i 0.987129 0.159925i \(-0.0511253\pi\)
−0.159925 + 0.987129i \(0.551125\pi\)
\(948\) 3.41421 + 0.585786i 0.110889 + 0.0190255i
\(949\) 12.0000i 0.389536i
\(950\) −2.82843 + 19.7990i −0.0917663 + 0.642364i
\(951\) 6.00000 + 8.48528i 0.194563 + 0.275154i
\(952\) 0 0
\(953\) −25.4558 + 25.4558i −0.824596 + 0.824596i −0.986763 0.162168i \(-0.948151\pi\)
0.162168 + 0.986763i \(0.448151\pi\)
\(954\) 5.65685 + 2.00000i 0.183147 + 0.0647524i
\(955\) −15.0000 45.0000i −0.485389 1.45617i
\(956\) 22.6274i 0.731823i
\(957\) 1.17157 6.82843i 0.0378716 0.220732i
\(958\) −27.0000 27.0000i −0.872330 0.872330i
\(959\) 0 0
\(960\) 0.585786 + 3.82843i 0.0189062 + 0.123562i
\(961\) 1.00000 0.0322581
\(962\) −12.7279 12.7279i −0.410365 0.410365i
\(963\) 15.5147 + 32.4853i 0.499955 + 1.04682i
\(964\) 2.00000i 0.0644157i
\(965\) 25.4558 + 12.7279i 0.819453 + 0.409726i
\(966\) 0 0
\(967\) 31.0000 31.0000i 0.996893 0.996893i −0.00310239 0.999995i \(-0.500988\pi\)
0.999995 + 0.00310239i \(0.000987524\pi\)
\(968\) −6.36396 + 6.36396i −0.204545 + 0.204545i
\(969\) 11.3137 8.00000i 0.363449 0.256997i
\(970\) −33.0000 + 11.0000i −1.05957 + 0.353189i
\(971\) 39.5980i 1.27076i −0.772200 0.635380i \(-0.780844\pi\)
0.772200 0.635380i \(-0.219156\pi\)
\(972\) −11.7071 + 10.2929i −0.375506 + 0.330145i
\(973\) 0 0
\(974\) −15.5563 −0.498458
\(975\) 34.9706 + 11.2721i 1.11995 + 0.360995i
\(976\) −8.00000 −0.256074
\(977\) −21.2132 21.2132i −0.678671 0.678671i 0.281029 0.959699i \(-0.409324\pi\)
−0.959699 + 0.281029i \(0.909324\pi\)
\(978\) 4.55635 26.5563i 0.145696 0.849178i
\(979\) 10.0000i 0.319601i
\(980\) 14.8492 4.94975i 0.474342 0.158114i
\(981\) −10.0000 + 28.2843i −0.319275 + 0.903047i
\(982\) −9.00000 + 9.00000i −0.287202 + 0.287202i
\(983\) −16.9706 + 16.9706i −0.541277 + 0.541277i −0.923903 0.382626i \(-0.875020\pi\)
0.382626 + 0.923903i \(0.375020\pi\)
\(984\) 5.65685 + 8.00000i 0.180334 + 0.255031i
\(985\) −20.0000 10.0000i −0.637253 0.318626i
\(986\) 5.65685i 0.180151i
\(987\) 0 0
\(988\) −12.0000 12.0000i −0.381771 0.381771i
\(989\) 0 0
\(990\) 6.82843 6.58579i 0.217022 0.209310i
\(991\) −22.0000 −0.698853 −0.349427 0.936964i \(-0.613624\pi\)
−0.349427 + 0.936964i \(0.613624\pi\)
\(992\) −0.707107 0.707107i −0.0224507 0.0224507i
\(993\) 54.6274 + 9.37258i 1.73355 + 0.297430i
\(994\) 0 0
\(995\) −16.9706 50.9117i −0.538003 1.61401i
\(996\) 6.00000 + 8.48528i 0.190117 + 0.268866i
\(997\) 24.0000 24.0000i 0.760088 0.760088i −0.216250 0.976338i \(-0.569383\pi\)
0.976338 + 0.216250i \(0.0693827\pi\)
\(998\) −25.4558 + 25.4558i −0.805791 + 0.805791i
\(999\) −21.2132 + 6.00000i −0.671156 + 0.189832i
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 930.2.j.b.683.2 yes 4
3.2 odd 2 inner 930.2.j.b.683.1 yes 4
5.2 odd 4 inner 930.2.j.b.497.1 4
15.2 even 4 inner 930.2.j.b.497.2 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.j.b.497.1 4 5.2 odd 4 inner
930.2.j.b.497.2 yes 4 15.2 even 4 inner
930.2.j.b.683.1 yes 4 3.2 odd 2 inner
930.2.j.b.683.2 yes 4 1.1 even 1 trivial