Properties

Label 39.2.f.a.8.2
Level $39$
Weight $2$
Character 39.8
Analytic conductor $0.311$
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] = [39,2,Mod(5,39)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(39, 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("39.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 39 = 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 39.f (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: \(0.311416567883\)
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 8.2
Root \(0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 39.8
Dual form 39.2.f.a.5.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(-1.00000 - 1.41421i) q^{3} +1.00000i q^{4} +(-1.41421 + 1.41421i) q^{5} +(-1.70711 - 0.292893i) q^{6} +(1.00000 - 1.00000i) q^{7} +(2.12132 + 2.12132i) q^{8} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(-1.00000 - 1.41421i) q^{3} +1.00000i q^{4} +(-1.41421 + 1.41421i) q^{5} +(-1.70711 - 0.292893i) q^{6} +(1.00000 - 1.00000i) q^{7} +(2.12132 + 2.12132i) q^{8} +(-1.00000 + 2.82843i) q^{9} +2.00000i q^{10} +(-2.82843 - 2.82843i) q^{11} +(1.41421 - 1.00000i) q^{12} +(-2.00000 - 3.00000i) q^{13} -1.41421i q^{14} +(3.41421 + 0.585786i) q^{15} +1.00000 q^{16} +(1.29289 + 2.70711i) q^{18} +(1.00000 + 1.00000i) q^{19} +(-1.41421 - 1.41421i) q^{20} +(-2.41421 - 0.414214i) q^{21} -4.00000 q^{22} +8.48528 q^{23} +(0.878680 - 5.12132i) q^{24} +1.00000i q^{25} +(-3.53553 - 0.707107i) q^{26} +(5.00000 - 1.41421i) q^{27} +(1.00000 + 1.00000i) q^{28} +2.82843i q^{29} +(2.82843 - 2.00000i) q^{30} +(-5.00000 - 5.00000i) q^{31} +(-3.53553 + 3.53553i) q^{32} +(-1.17157 + 6.82843i) q^{33} +2.82843i q^{35} +(-2.82843 - 1.00000i) q^{36} +(1.00000 - 1.00000i) q^{37} +1.41421 q^{38} +(-2.24264 + 5.82843i) q^{39} -6.00000 q^{40} +(-1.41421 + 1.41421i) q^{41} +(-2.00000 + 1.41421i) q^{42} +6.00000i q^{43} +(2.82843 - 2.82843i) q^{44} +(-2.58579 - 5.41421i) q^{45} +(6.00000 - 6.00000i) q^{46} +(-2.82843 - 2.82843i) q^{47} +(-1.00000 - 1.41421i) q^{48} +5.00000i q^{49} +(0.707107 + 0.707107i) q^{50} +(3.00000 - 2.00000i) q^{52} -5.65685i q^{53} +(2.53553 - 4.53553i) q^{54} +8.00000 q^{55} +4.24264 q^{56} +(0.414214 - 2.41421i) q^{57} +(2.00000 + 2.00000i) q^{58} +(-2.82843 - 2.82843i) q^{59} +(-0.585786 + 3.41421i) q^{60} +8.00000 q^{61} -7.07107 q^{62} +(1.82843 + 3.82843i) q^{63} +7.00000i q^{64} +(7.07107 + 1.41421i) q^{65} +(4.00000 + 5.65685i) q^{66} +(-5.00000 - 5.00000i) q^{67} +(-8.48528 - 12.0000i) q^{69} +(2.00000 + 2.00000i) q^{70} +(2.82843 - 2.82843i) q^{71} +(-8.12132 + 3.87868i) q^{72} +(1.00000 - 1.00000i) q^{73} -1.41421i q^{74} +(1.41421 - 1.00000i) q^{75} +(-1.00000 + 1.00000i) q^{76} -5.65685 q^{77} +(2.53553 + 5.70711i) q^{78} -10.0000 q^{79} +(-1.41421 + 1.41421i) q^{80} +(-7.00000 - 5.65685i) q^{81} +2.00000i q^{82} +(-5.65685 + 5.65685i) q^{83} +(0.414214 - 2.41421i) q^{84} +(4.24264 + 4.24264i) q^{86} +(4.00000 - 2.82843i) q^{87} -12.0000i q^{88} +(9.89949 + 9.89949i) q^{89} +(-5.65685 - 2.00000i) q^{90} +(-5.00000 - 1.00000i) q^{91} +8.48528i q^{92} +(-2.07107 + 12.0711i) q^{93} -4.00000 q^{94} -2.82843 q^{95} +(8.53553 + 1.46447i) q^{96} +(7.00000 + 7.00000i) q^{97} +(3.53553 + 3.53553i) q^{98} +(10.8284 - 5.17157i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{3} - 4 q^{6} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{3} - 4 q^{6} + 4 q^{7} - 4 q^{9} - 8 q^{13} + 8 q^{15} + 4 q^{16} + 8 q^{18} + 4 q^{19} - 4 q^{21} - 16 q^{22} + 12 q^{24} + 20 q^{27} + 4 q^{28} - 20 q^{31} - 16 q^{33} + 4 q^{37} + 8 q^{39} - 24 q^{40} - 8 q^{42} - 16 q^{45} + 24 q^{46} - 4 q^{48} + 12 q^{52} - 4 q^{54} + 32 q^{55} - 4 q^{57} + 8 q^{58} - 8 q^{60} + 32 q^{61} - 4 q^{63} + 16 q^{66} - 20 q^{67} + 8 q^{70} - 24 q^{72} + 4 q^{73} - 4 q^{76} - 4 q^{78} - 40 q^{79} - 28 q^{81} - 4 q^{84} + 16 q^{87} - 20 q^{91} + 20 q^{93} - 16 q^{94} + 20 q^{96} + 28 q^{97} + 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/39\mathbb{Z}\right)^\times\).

\(n\) \(14\) \(28\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i −0.411438 0.911438i \(-0.634973\pi\)
0.911438 + 0.411438i \(0.134973\pi\)
\(3\) −1.00000 1.41421i −0.577350 0.816497i
\(4\) 1.00000i 0.500000i
\(5\) −1.41421 + 1.41421i −0.632456 + 0.632456i −0.948683 0.316228i \(-0.897584\pi\)
0.316228 + 0.948683i \(0.397584\pi\)
\(6\) −1.70711 0.292893i −0.696923 0.119573i
\(7\) 1.00000 1.00000i 0.377964 0.377964i −0.492403 0.870367i \(-0.663881\pi\)
0.870367 + 0.492403i \(0.163881\pi\)
\(8\) 2.12132 + 2.12132i 0.750000 + 0.750000i
\(9\) −1.00000 + 2.82843i −0.333333 + 0.942809i
\(10\) 2.00000i 0.632456i
\(11\) −2.82843 2.82843i −0.852803 0.852803i 0.137675 0.990478i \(-0.456037\pi\)
−0.990478 + 0.137675i \(0.956037\pi\)
\(12\) 1.41421 1.00000i 0.408248 0.288675i
\(13\) −2.00000 3.00000i −0.554700 0.832050i
\(14\) 1.41421i 0.377964i
\(15\) 3.41421 + 0.585786i 0.881546 + 0.151249i
\(16\) 1.00000 0.250000
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 1.29289 + 2.70711i 0.304738 + 0.638071i
\(19\) 1.00000 + 1.00000i 0.229416 + 0.229416i 0.812449 0.583033i \(-0.198134\pi\)
−0.583033 + 0.812449i \(0.698134\pi\)
\(20\) −1.41421 1.41421i −0.316228 0.316228i
\(21\) −2.41421 0.414214i −0.526825 0.0903888i
\(22\) −4.00000 −0.852803
\(23\) 8.48528 1.76930 0.884652 0.466252i \(-0.154396\pi\)
0.884652 + 0.466252i \(0.154396\pi\)
\(24\) 0.878680 5.12132i 0.179360 1.04539i
\(25\) 1.00000i 0.200000i
\(26\) −3.53553 0.707107i −0.693375 0.138675i
\(27\) 5.00000 1.41421i 0.962250 0.272166i
\(28\) 1.00000 + 1.00000i 0.188982 + 0.188982i
\(29\) 2.82843i 0.525226i 0.964901 + 0.262613i \(0.0845842\pi\)
−0.964901 + 0.262613i \(0.915416\pi\)
\(30\) 2.82843 2.00000i 0.516398 0.365148i
\(31\) −5.00000 5.00000i −0.898027 0.898027i 0.0972349 0.995261i \(-0.469000\pi\)
−0.995261 + 0.0972349i \(0.969000\pi\)
\(32\) −3.53553 + 3.53553i −0.625000 + 0.625000i
\(33\) −1.17157 + 6.82843i −0.203945 + 1.18868i
\(34\) 0 0
\(35\) 2.82843i 0.478091i
\(36\) −2.82843 1.00000i −0.471405 0.166667i
\(37\) 1.00000 1.00000i 0.164399 0.164399i −0.620113 0.784512i \(-0.712913\pi\)
0.784512 + 0.620113i \(0.212913\pi\)
\(38\) 1.41421 0.229416
\(39\) −2.24264 + 5.82843i −0.359110 + 0.933295i
\(40\) −6.00000 −0.948683
\(41\) −1.41421 + 1.41421i −0.220863 + 0.220863i −0.808862 0.587999i \(-0.799916\pi\)
0.587999 + 0.808862i \(0.299916\pi\)
\(42\) −2.00000 + 1.41421i −0.308607 + 0.218218i
\(43\) 6.00000i 0.914991i 0.889212 + 0.457496i \(0.151253\pi\)
−0.889212 + 0.457496i \(0.848747\pi\)
\(44\) 2.82843 2.82843i 0.426401 0.426401i
\(45\) −2.58579 5.41421i −0.385466 0.807103i
\(46\) 6.00000 6.00000i 0.884652 0.884652i
\(47\) −2.82843 2.82843i −0.412568 0.412568i 0.470064 0.882632i \(-0.344231\pi\)
−0.882632 + 0.470064i \(0.844231\pi\)
\(48\) −1.00000 1.41421i −0.144338 0.204124i
\(49\) 5.00000i 0.714286i
\(50\) 0.707107 + 0.707107i 0.100000 + 0.100000i
\(51\) 0 0
\(52\) 3.00000 2.00000i 0.416025 0.277350i
\(53\) 5.65685i 0.777029i −0.921443 0.388514i \(-0.872988\pi\)
0.921443 0.388514i \(-0.127012\pi\)
\(54\) 2.53553 4.53553i 0.345042 0.617208i
\(55\) 8.00000 1.07872
\(56\) 4.24264 0.566947
\(57\) 0.414214 2.41421i 0.0548639 0.319770i
\(58\) 2.00000 + 2.00000i 0.262613 + 0.262613i
\(59\) −2.82843 2.82843i −0.368230 0.368230i 0.498601 0.866831i \(-0.333847\pi\)
−0.866831 + 0.498601i \(0.833847\pi\)
\(60\) −0.585786 + 3.41421i −0.0756247 + 0.440773i
\(61\) 8.00000 1.02430 0.512148 0.858898i \(-0.328850\pi\)
0.512148 + 0.858898i \(0.328850\pi\)
\(62\) −7.07107 −0.898027
\(63\) 1.82843 + 3.82843i 0.230360 + 0.482336i
\(64\) 7.00000i 0.875000i
\(65\) 7.07107 + 1.41421i 0.877058 + 0.175412i
\(66\) 4.00000 + 5.65685i 0.492366 + 0.696311i
\(67\) −5.00000 5.00000i −0.610847 0.610847i 0.332320 0.943167i \(-0.392169\pi\)
−0.943167 + 0.332320i \(0.892169\pi\)
\(68\) 0 0
\(69\) −8.48528 12.0000i −1.02151 1.44463i
\(70\) 2.00000 + 2.00000i 0.239046 + 0.239046i
\(71\) 2.82843 2.82843i 0.335673 0.335673i −0.519063 0.854736i \(-0.673719\pi\)
0.854736 + 0.519063i \(0.173719\pi\)
\(72\) −8.12132 + 3.87868i −0.957107 + 0.457107i
\(73\) 1.00000 1.00000i 0.117041 0.117041i −0.646160 0.763202i \(-0.723626\pi\)
0.763202 + 0.646160i \(0.223626\pi\)
\(74\) 1.41421i 0.164399i
\(75\) 1.41421 1.00000i 0.163299 0.115470i
\(76\) −1.00000 + 1.00000i −0.114708 + 0.114708i
\(77\) −5.65685 −0.644658
\(78\) 2.53553 + 5.70711i 0.287093 + 0.646203i
\(79\) −10.0000 −1.12509 −0.562544 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) −1.41421 + 1.41421i −0.158114 + 0.158114i
\(81\) −7.00000 5.65685i −0.777778 0.628539i
\(82\) 2.00000i 0.220863i
\(83\) −5.65685 + 5.65685i −0.620920 + 0.620920i −0.945767 0.324846i \(-0.894687\pi\)
0.324846 + 0.945767i \(0.394687\pi\)
\(84\) 0.414214 2.41421i 0.0451944 0.263412i
\(85\) 0 0
\(86\) 4.24264 + 4.24264i 0.457496 + 0.457496i
\(87\) 4.00000 2.82843i 0.428845 0.303239i
\(88\) 12.0000i 1.27920i
\(89\) 9.89949 + 9.89949i 1.04934 + 1.04934i 0.998718 + 0.0506267i \(0.0161219\pi\)
0.0506267 + 0.998718i \(0.483878\pi\)
\(90\) −5.65685 2.00000i −0.596285 0.210819i
\(91\) −5.00000 1.00000i −0.524142 0.104828i
\(92\) 8.48528i 0.884652i
\(93\) −2.07107 + 12.0711i −0.214760 + 1.25171i
\(94\) −4.00000 −0.412568
\(95\) −2.82843 −0.290191
\(96\) 8.53553 + 1.46447i 0.871154 + 0.149466i
\(97\) 7.00000 + 7.00000i 0.710742 + 0.710742i 0.966691 0.255948i \(-0.0823876\pi\)
−0.255948 + 0.966691i \(0.582388\pi\)
\(98\) 3.53553 + 3.53553i 0.357143 + 0.357143i
\(99\) 10.8284 5.17157i 1.08830 0.519763i
\(100\) −1.00000 −0.100000
\(101\) −8.48528 −0.844317 −0.422159 0.906522i \(-0.638727\pi\)
−0.422159 + 0.906522i \(0.638727\pi\)
\(102\) 0 0
\(103\) 6.00000i 0.591198i −0.955312 0.295599i \(-0.904481\pi\)
0.955312 0.295599i \(-0.0955191\pi\)
\(104\) 2.12132 10.6066i 0.208013 1.04006i
\(105\) 4.00000 2.82843i 0.390360 0.276026i
\(106\) −4.00000 4.00000i −0.388514 0.388514i
\(107\) 5.65685i 0.546869i −0.961891 0.273434i \(-0.911840\pi\)
0.961891 0.273434i \(-0.0881596\pi\)
\(108\) 1.41421 + 5.00000i 0.136083 + 0.481125i
\(109\) 1.00000 + 1.00000i 0.0957826 + 0.0957826i 0.753374 0.657592i \(-0.228425\pi\)
−0.657592 + 0.753374i \(0.728425\pi\)
\(110\) 5.65685 5.65685i 0.539360 0.539360i
\(111\) −2.41421 0.414214i −0.229147 0.0393154i
\(112\) 1.00000 1.00000i 0.0944911 0.0944911i
\(113\) 14.1421i 1.33038i −0.746674 0.665190i \(-0.768350\pi\)
0.746674 0.665190i \(-0.231650\pi\)
\(114\) −1.41421 2.00000i −0.132453 0.187317i
\(115\) −12.0000 + 12.0000i −1.11901 + 1.11901i
\(116\) −2.82843 −0.262613
\(117\) 10.4853 2.65685i 0.969365 0.245626i
\(118\) −4.00000 −0.368230
\(119\) 0 0
\(120\) 6.00000 + 8.48528i 0.547723 + 0.774597i
\(121\) 5.00000i 0.454545i
\(122\) 5.65685 5.65685i 0.512148 0.512148i
\(123\) 3.41421 + 0.585786i 0.307849 + 0.0528186i
\(124\) 5.00000 5.00000i 0.449013 0.449013i
\(125\) −8.48528 8.48528i −0.758947 0.758947i
\(126\) 4.00000 + 1.41421i 0.356348 + 0.125988i
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) −2.12132 2.12132i −0.187500 0.187500i
\(129\) 8.48528 6.00000i 0.747087 0.528271i
\(130\) 6.00000 4.00000i 0.526235 0.350823i
\(131\) 11.3137i 0.988483i 0.869325 + 0.494242i \(0.164554\pi\)
−0.869325 + 0.494242i \(0.835446\pi\)
\(132\) −6.82843 1.17157i −0.594338 0.101972i
\(133\) 2.00000 0.173422
\(134\) −7.07107 −0.610847
\(135\) −5.07107 + 9.07107i −0.436448 + 0.780713i
\(136\) 0 0
\(137\) 9.89949 + 9.89949i 0.845771 + 0.845771i 0.989602 0.143831i \(-0.0459423\pi\)
−0.143831 + 0.989602i \(0.545942\pi\)
\(138\) −14.4853 2.48528i −1.23307 0.211561i
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) −2.82843 −0.239046
\(141\) −1.17157 + 6.82843i −0.0986642 + 0.575057i
\(142\) 4.00000i 0.335673i
\(143\) −2.82843 + 14.1421i −0.236525 + 1.18262i
\(144\) −1.00000 + 2.82843i −0.0833333 + 0.235702i
\(145\) −4.00000 4.00000i −0.332182 0.332182i
\(146\) 1.41421i 0.117041i
\(147\) 7.07107 5.00000i 0.583212 0.412393i
\(148\) 1.00000 + 1.00000i 0.0821995 + 0.0821995i
\(149\) −1.41421 + 1.41421i −0.115857 + 0.115857i −0.762658 0.646802i \(-0.776106\pi\)
0.646802 + 0.762658i \(0.276106\pi\)
\(150\) 0.292893 1.70711i 0.0239146 0.139385i
\(151\) 1.00000 1.00000i 0.0813788 0.0813788i −0.665246 0.746625i \(-0.731673\pi\)
0.746625 + 0.665246i \(0.231673\pi\)
\(152\) 4.24264i 0.344124i
\(153\) 0 0
\(154\) −4.00000 + 4.00000i −0.322329 + 0.322329i
\(155\) 14.1421 1.13592
\(156\) −5.82843 2.24264i −0.466648 0.179555i
\(157\) 14.0000 1.11732 0.558661 0.829396i \(-0.311315\pi\)
0.558661 + 0.829396i \(0.311315\pi\)
\(158\) −7.07107 + 7.07107i −0.562544 + 0.562544i
\(159\) −8.00000 + 5.65685i −0.634441 + 0.448618i
\(160\) 10.0000i 0.790569i
\(161\) 8.48528 8.48528i 0.668734 0.668734i
\(162\) −8.94975 + 0.949747i −0.703159 + 0.0746192i
\(163\) 1.00000 1.00000i 0.0783260 0.0783260i −0.666858 0.745184i \(-0.732361\pi\)
0.745184 + 0.666858i \(0.232361\pi\)
\(164\) −1.41421 1.41421i −0.110432 0.110432i
\(165\) −8.00000 11.3137i −0.622799 0.880771i
\(166\) 8.00000i 0.620920i
\(167\) −2.82843 2.82843i −0.218870 0.218870i 0.589152 0.808022i \(-0.299462\pi\)
−0.808022 + 0.589152i \(0.799462\pi\)
\(168\) −4.24264 6.00000i −0.327327 0.462910i
\(169\) −5.00000 + 12.0000i −0.384615 + 0.923077i
\(170\) 0 0
\(171\) −3.82843 + 1.82843i −0.292767 + 0.139823i
\(172\) −6.00000 −0.457496
\(173\) −8.48528 −0.645124 −0.322562 0.946548i \(-0.604544\pi\)
−0.322562 + 0.946548i \(0.604544\pi\)
\(174\) 0.828427 4.82843i 0.0628029 0.366042i
\(175\) 1.00000 + 1.00000i 0.0755929 + 0.0755929i
\(176\) −2.82843 2.82843i −0.213201 0.213201i
\(177\) −1.17157 + 6.82843i −0.0880608 + 0.513256i
\(178\) 14.0000 1.04934
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 5.41421 2.58579i 0.403552 0.192733i
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) −4.24264 + 2.82843i −0.314485 + 0.209657i
\(183\) −8.00000 11.3137i −0.591377 0.836333i
\(184\) 18.0000 + 18.0000i 1.32698 + 1.32698i
\(185\) 2.82843i 0.207950i
\(186\) 7.07107 + 10.0000i 0.518476 + 0.733236i
\(187\) 0 0
\(188\) 2.82843 2.82843i 0.206284 0.206284i
\(189\) 3.58579 6.41421i 0.260828 0.466565i
\(190\) −2.00000 + 2.00000i −0.145095 + 0.145095i
\(191\) 2.82843i 0.204658i 0.994751 + 0.102329i \(0.0326294\pi\)
−0.994751 + 0.102329i \(0.967371\pi\)
\(192\) 9.89949 7.00000i 0.714435 0.505181i
\(193\) 19.0000 19.0000i 1.36765 1.36765i 0.503871 0.863779i \(-0.331909\pi\)
0.863779 0.503871i \(-0.168091\pi\)
\(194\) 9.89949 0.710742
\(195\) −5.07107 11.4142i −0.363147 0.817389i
\(196\) −5.00000 −0.357143
\(197\) 15.5563 15.5563i 1.10834 1.10834i 0.114976 0.993368i \(-0.463321\pi\)
0.993368 0.114976i \(-0.0366790\pi\)
\(198\) 4.00000 11.3137i 0.284268 0.804030i
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) −2.12132 + 2.12132i −0.150000 + 0.150000i
\(201\) −2.07107 + 12.0711i −0.146082 + 0.851427i
\(202\) −6.00000 + 6.00000i −0.422159 + 0.422159i
\(203\) 2.82843 + 2.82843i 0.198517 + 0.198517i
\(204\) 0 0
\(205\) 4.00000i 0.279372i
\(206\) −4.24264 4.24264i −0.295599 0.295599i
\(207\) −8.48528 + 24.0000i −0.589768 + 1.66812i
\(208\) −2.00000 3.00000i −0.138675 0.208013i
\(209\) 5.65685i 0.391293i
\(210\) 0.828427 4.82843i 0.0571669 0.333193i
\(211\) 14.0000 0.963800 0.481900 0.876226i \(-0.339947\pi\)
0.481900 + 0.876226i \(0.339947\pi\)
\(212\) 5.65685 0.388514
\(213\) −6.82843 1.17157i −0.467876 0.0802749i
\(214\) −4.00000 4.00000i −0.273434 0.273434i
\(215\) −8.48528 8.48528i −0.578691 0.578691i
\(216\) 13.6066 + 7.60660i 0.925812 + 0.517564i
\(217\) −10.0000 −0.678844
\(218\) 1.41421 0.0957826
\(219\) −2.41421 0.414214i −0.163137 0.0279900i
\(220\) 8.00000i 0.539360i
\(221\) 0 0
\(222\) −2.00000 + 1.41421i −0.134231 + 0.0949158i
\(223\) −11.0000 11.0000i −0.736614 0.736614i 0.235307 0.971921i \(-0.424391\pi\)
−0.971921 + 0.235307i \(0.924391\pi\)
\(224\) 7.07107i 0.472456i
\(225\) −2.82843 1.00000i −0.188562 0.0666667i
\(226\) −10.0000 10.0000i −0.665190 0.665190i
\(227\) −5.65685 + 5.65685i −0.375459 + 0.375459i −0.869461 0.494002i \(-0.835534\pi\)
0.494002 + 0.869461i \(0.335534\pi\)
\(228\) 2.41421 + 0.414214i 0.159885 + 0.0274320i
\(229\) 1.00000 1.00000i 0.0660819 0.0660819i −0.673293 0.739375i \(-0.735121\pi\)
0.739375 + 0.673293i \(0.235121\pi\)
\(230\) 16.9706i 1.11901i
\(231\) 5.65685 + 8.00000i 0.372194 + 0.526361i
\(232\) −6.00000 + 6.00000i −0.393919 + 0.393919i
\(233\) −25.4558 −1.66767 −0.833834 0.552015i \(-0.813859\pi\)
−0.833834 + 0.552015i \(0.813859\pi\)
\(234\) 5.53553 9.29289i 0.361869 0.607495i
\(235\) 8.00000 0.521862
\(236\) 2.82843 2.82843i 0.184115 0.184115i
\(237\) 10.0000 + 14.1421i 0.649570 + 0.918630i
\(238\) 0 0
\(239\) −14.1421 + 14.1421i −0.914779 + 0.914779i −0.996643 0.0818647i \(-0.973912\pi\)
0.0818647 + 0.996643i \(0.473912\pi\)
\(240\) 3.41421 + 0.585786i 0.220387 + 0.0378124i
\(241\) −17.0000 + 17.0000i −1.09507 + 1.09507i −0.100088 + 0.994979i \(0.531912\pi\)
−0.994979 + 0.100088i \(0.968088\pi\)
\(242\) 3.53553 + 3.53553i 0.227273 + 0.227273i
\(243\) −1.00000 + 15.5563i −0.0641500 + 0.997940i
\(244\) 8.00000i 0.512148i
\(245\) −7.07107 7.07107i −0.451754 0.451754i
\(246\) 2.82843 2.00000i 0.180334 0.127515i
\(247\) 1.00000 5.00000i 0.0636285 0.318142i
\(248\) 21.2132i 1.34704i
\(249\) 13.6569 + 2.34315i 0.865468 + 0.148491i
\(250\) −12.0000 −0.758947
\(251\) 25.4558 1.60676 0.803379 0.595468i \(-0.203033\pi\)
0.803379 + 0.595468i \(0.203033\pi\)
\(252\) −3.82843 + 1.82843i −0.241168 + 0.115180i
\(253\) −24.0000 24.0000i −1.50887 1.50887i
\(254\) 0 0
\(255\) 0 0
\(256\) −17.0000 −1.06250
\(257\) 8.48528 0.529297 0.264649 0.964345i \(-0.414744\pi\)
0.264649 + 0.964345i \(0.414744\pi\)
\(258\) 1.75736 10.2426i 0.109408 0.637679i
\(259\) 2.00000i 0.124274i
\(260\) −1.41421 + 7.07107i −0.0877058 + 0.438529i
\(261\) −8.00000 2.82843i −0.495188 0.175075i
\(262\) 8.00000 + 8.00000i 0.494242 + 0.494242i
\(263\) 22.6274i 1.39527i −0.716455 0.697633i \(-0.754237\pi\)
0.716455 0.697633i \(-0.245763\pi\)
\(264\) −16.9706 + 12.0000i −1.04447 + 0.738549i
\(265\) 8.00000 + 8.00000i 0.491436 + 0.491436i
\(266\) 1.41421 1.41421i 0.0867110 0.0867110i
\(267\) 4.10051 23.8995i 0.250947 1.46263i
\(268\) 5.00000 5.00000i 0.305424 0.305424i
\(269\) 19.7990i 1.20717i 0.797300 + 0.603583i \(0.206261\pi\)
−0.797300 + 0.603583i \(0.793739\pi\)
\(270\) 2.82843 + 10.0000i 0.172133 + 0.608581i
\(271\) 19.0000 19.0000i 1.15417 1.15417i 0.168459 0.985709i \(-0.446121\pi\)
0.985709 0.168459i \(-0.0538791\pi\)
\(272\) 0 0
\(273\) 3.58579 + 8.07107i 0.217022 + 0.488483i
\(274\) 14.0000 0.845771
\(275\) 2.82843 2.82843i 0.170561 0.170561i
\(276\) 12.0000 8.48528i 0.722315 0.510754i
\(277\) 12.0000i 0.721010i −0.932757 0.360505i \(-0.882604\pi\)
0.932757 0.360505i \(-0.117396\pi\)
\(278\) −2.82843 + 2.82843i −0.169638 + 0.169638i
\(279\) 19.1421 9.14214i 1.14601 0.547325i
\(280\) −6.00000 + 6.00000i −0.358569 + 0.358569i
\(281\) 9.89949 + 9.89949i 0.590554 + 0.590554i 0.937781 0.347227i \(-0.112877\pi\)
−0.347227 + 0.937781i \(0.612877\pi\)
\(282\) 4.00000 + 5.65685i 0.238197 + 0.336861i
\(283\) 12.0000i 0.713326i 0.934233 + 0.356663i \(0.116086\pi\)
−0.934233 + 0.356663i \(0.883914\pi\)
\(284\) 2.82843 + 2.82843i 0.167836 + 0.167836i
\(285\) 2.82843 + 4.00000i 0.167542 + 0.236940i
\(286\) 8.00000 + 12.0000i 0.473050 + 0.709575i
\(287\) 2.82843i 0.166957i
\(288\) −6.46447 13.5355i −0.380922 0.797589i
\(289\) −17.0000 −1.00000
\(290\) −5.65685 −0.332182
\(291\) 2.89949 16.8995i 0.169971 0.990666i
\(292\) 1.00000 + 1.00000i 0.0585206 + 0.0585206i
\(293\) 9.89949 + 9.89949i 0.578335 + 0.578335i 0.934444 0.356110i \(-0.115897\pi\)
−0.356110 + 0.934444i \(0.615897\pi\)
\(294\) 1.46447 8.53553i 0.0854094 0.497802i
\(295\) 8.00000 0.465778
\(296\) 4.24264 0.246598
\(297\) −18.1421 10.1421i −1.05271 0.588506i
\(298\) 2.00000i 0.115857i
\(299\) −16.9706 25.4558i −0.981433 1.47215i
\(300\) 1.00000 + 1.41421i 0.0577350 + 0.0816497i
\(301\) 6.00000 + 6.00000i 0.345834 + 0.345834i
\(302\) 1.41421i 0.0813788i
\(303\) 8.48528 + 12.0000i 0.487467 + 0.689382i
\(304\) 1.00000 + 1.00000i 0.0573539 + 0.0573539i
\(305\) −11.3137 + 11.3137i −0.647821 + 0.647821i
\(306\) 0 0
\(307\) −17.0000 + 17.0000i −0.970241 + 0.970241i −0.999570 0.0293286i \(-0.990663\pi\)
0.0293286 + 0.999570i \(0.490663\pi\)
\(308\) 5.65685i 0.322329i
\(309\) −8.48528 + 6.00000i −0.482711 + 0.341328i
\(310\) 10.0000 10.0000i 0.567962 0.567962i
\(311\) 8.48528 0.481156 0.240578 0.970630i \(-0.422663\pi\)
0.240578 + 0.970630i \(0.422663\pi\)
\(312\) −17.1213 + 7.60660i −0.969304 + 0.430639i
\(313\) 8.00000 0.452187 0.226093 0.974106i \(-0.427405\pi\)
0.226093 + 0.974106i \(0.427405\pi\)
\(314\) 9.89949 9.89949i 0.558661 0.558661i
\(315\) −8.00000 2.82843i −0.450749 0.159364i
\(316\) 10.0000i 0.562544i
\(317\) 7.07107 7.07107i 0.397151 0.397151i −0.480076 0.877227i \(-0.659391\pi\)
0.877227 + 0.480076i \(0.159391\pi\)
\(318\) −1.65685 + 9.65685i −0.0929118 + 0.541529i
\(319\) 8.00000 8.00000i 0.447914 0.447914i
\(320\) −9.89949 9.89949i −0.553399 0.553399i
\(321\) −8.00000 + 5.65685i −0.446516 + 0.315735i
\(322\) 12.0000i 0.668734i
\(323\) 0 0
\(324\) 5.65685 7.00000i 0.314270 0.388889i
\(325\) 3.00000 2.00000i 0.166410 0.110940i
\(326\) 1.41421i 0.0783260i
\(327\) 0.414214 2.41421i 0.0229061 0.133506i
\(328\) −6.00000 −0.331295
\(329\) −5.65685 −0.311872
\(330\) −13.6569 2.34315i −0.751785 0.128986i
\(331\) 7.00000 + 7.00000i 0.384755 + 0.384755i 0.872812 0.488057i \(-0.162294\pi\)
−0.488057 + 0.872812i \(0.662294\pi\)
\(332\) −5.65685 5.65685i −0.310460 0.310460i
\(333\) 1.82843 + 3.82843i 0.100197 + 0.209797i
\(334\) −4.00000 −0.218870
\(335\) 14.1421 0.772667
\(336\) −2.41421 0.414214i −0.131706 0.0225972i
\(337\) 6.00000i 0.326841i −0.986557 0.163420i \(-0.947747\pi\)
0.986557 0.163420i \(-0.0522527\pi\)
\(338\) 4.94975 + 12.0208i 0.269231 + 0.653846i
\(339\) −20.0000 + 14.1421i −1.08625 + 0.768095i
\(340\) 0 0
\(341\) 28.2843i 1.53168i
\(342\) −1.41421 + 4.00000i −0.0764719 + 0.216295i
\(343\) 12.0000 + 12.0000i 0.647939 + 0.647939i
\(344\) −12.7279 + 12.7279i −0.686244 + 0.686244i
\(345\) 28.9706 + 4.97056i 1.55972 + 0.267606i
\(346\) −6.00000 + 6.00000i −0.322562 + 0.322562i
\(347\) 14.1421i 0.759190i −0.925153 0.379595i \(-0.876063\pi\)
0.925153 0.379595i \(-0.123937\pi\)
\(348\) 2.82843 + 4.00000i 0.151620 + 0.214423i
\(349\) −17.0000 + 17.0000i −0.909989 + 0.909989i −0.996271 0.0862816i \(-0.972502\pi\)
0.0862816 + 0.996271i \(0.472502\pi\)
\(350\) 1.41421 0.0755929
\(351\) −14.2426 12.1716i −0.760216 0.649670i
\(352\) 20.0000 1.06600
\(353\) −18.3848 + 18.3848i −0.978523 + 0.978523i −0.999774 0.0212513i \(-0.993235\pi\)
0.0212513 + 0.999774i \(0.493235\pi\)
\(354\) 4.00000 + 5.65685i 0.212598 + 0.300658i
\(355\) 8.00000i 0.424596i
\(356\) −9.89949 + 9.89949i −0.524672 + 0.524672i
\(357\) 0 0
\(358\) 0 0
\(359\) −2.82843 2.82843i −0.149279 0.149279i 0.628517 0.777796i \(-0.283662\pi\)
−0.777796 + 0.628517i \(0.783662\pi\)
\(360\) 6.00000 16.9706i 0.316228 0.894427i
\(361\) 17.0000i 0.894737i
\(362\) 0 0
\(363\) 7.07107 5.00000i 0.371135 0.262432i
\(364\) 1.00000 5.00000i 0.0524142 0.262071i
\(365\) 2.82843i 0.148047i
\(366\) −13.6569 2.34315i −0.713855 0.122478i
\(367\) 8.00000 0.417597 0.208798 0.977959i \(-0.433045\pi\)
0.208798 + 0.977959i \(0.433045\pi\)
\(368\) 8.48528 0.442326
\(369\) −2.58579 5.41421i −0.134611 0.281853i
\(370\) 2.00000 + 2.00000i 0.103975 + 0.103975i
\(371\) −5.65685 5.65685i −0.293689 0.293689i
\(372\) −12.0711 2.07107i −0.625856 0.107380i
\(373\) −4.00000 −0.207112 −0.103556 0.994624i \(-0.533022\pi\)
−0.103556 + 0.994624i \(0.533022\pi\)
\(374\) 0 0
\(375\) −3.51472 + 20.4853i −0.181499 + 1.05786i
\(376\) 12.0000i 0.618853i
\(377\) 8.48528 5.65685i 0.437014 0.291343i
\(378\) −2.00000 7.07107i −0.102869 0.363696i
\(379\) 19.0000 + 19.0000i 0.975964 + 0.975964i 0.999718 0.0237534i \(-0.00756165\pi\)
−0.0237534 + 0.999718i \(0.507562\pi\)
\(380\) 2.82843i 0.145095i
\(381\) 0 0
\(382\) 2.00000 + 2.00000i 0.102329 + 0.102329i
\(383\) 11.3137 11.3137i 0.578103 0.578103i −0.356277 0.934380i \(-0.615954\pi\)
0.934380 + 0.356277i \(0.115954\pi\)
\(384\) −0.878680 + 5.12132i −0.0448399 + 0.261346i
\(385\) 8.00000 8.00000i 0.407718 0.407718i
\(386\) 26.8701i 1.36765i
\(387\) −16.9706 6.00000i −0.862662 0.304997i
\(388\) −7.00000 + 7.00000i −0.355371 + 0.355371i
\(389\) 16.9706 0.860442 0.430221 0.902724i \(-0.358436\pi\)
0.430221 + 0.902724i \(0.358436\pi\)
\(390\) −11.6569 4.48528i −0.590268 0.227121i
\(391\) 0 0
\(392\) −10.6066 + 10.6066i −0.535714 + 0.535714i
\(393\) 16.0000 11.3137i 0.807093 0.570701i
\(394\) 22.0000i 1.10834i
\(395\) 14.1421 14.1421i 0.711568 0.711568i
\(396\) 5.17157 + 10.8284i 0.259881 + 0.544149i
\(397\) −17.0000 + 17.0000i −0.853206 + 0.853206i −0.990527 0.137321i \(-0.956151\pi\)
0.137321 + 0.990527i \(0.456151\pi\)
\(398\) 0 0
\(399\) −2.00000 2.82843i −0.100125 0.141598i
\(400\) 1.00000i 0.0500000i
\(401\) −15.5563 15.5563i −0.776847 0.776847i 0.202446 0.979293i \(-0.435111\pi\)
−0.979293 + 0.202446i \(0.935111\pi\)
\(402\) 7.07107 + 10.0000i 0.352673 + 0.498755i
\(403\) −5.00000 + 25.0000i −0.249068 + 1.24534i
\(404\) 8.48528i 0.422159i
\(405\) 17.8995 1.89949i 0.889433 0.0943867i
\(406\) 4.00000 0.198517
\(407\) −5.65685 −0.280400
\(408\) 0 0
\(409\) −23.0000 23.0000i −1.13728 1.13728i −0.988936 0.148340i \(-0.952607\pi\)
−0.148340 0.988936i \(-0.547393\pi\)
\(410\) −2.82843 2.82843i −0.139686 0.139686i
\(411\) 4.10051 23.8995i 0.202263 1.17888i
\(412\) 6.00000 0.295599
\(413\) −5.65685 −0.278356
\(414\) 10.9706 + 22.9706i 0.539174 + 1.12894i
\(415\) 16.0000i 0.785409i
\(416\) 17.6777 + 3.53553i 0.866719 + 0.173344i
\(417\) 4.00000 + 5.65685i 0.195881 + 0.277017i
\(418\) −4.00000 4.00000i −0.195646 0.195646i
\(419\) 11.3137i 0.552711i 0.961056 + 0.276355i \(0.0891267\pi\)
−0.961056 + 0.276355i \(0.910873\pi\)
\(420\) 2.82843 + 4.00000i 0.138013 + 0.195180i
\(421\) 25.0000 + 25.0000i 1.21843 + 1.21843i 0.968183 + 0.250242i \(0.0805102\pi\)
0.250242 + 0.968183i \(0.419490\pi\)
\(422\) 9.89949 9.89949i 0.481900 0.481900i
\(423\) 10.8284 5.17157i 0.526496 0.251450i
\(424\) 12.0000 12.0000i 0.582772 0.582772i
\(425\) 0 0
\(426\) −5.65685 + 4.00000i −0.274075 + 0.193801i
\(427\) 8.00000 8.00000i 0.387147 0.387147i
\(428\) 5.65685 0.273434
\(429\) 22.8284 10.1421i 1.10217 0.489667i
\(430\) −12.0000 −0.578691
\(431\) −22.6274 + 22.6274i −1.08992 + 1.08992i −0.0943889 + 0.995535i \(0.530090\pi\)
−0.995535 + 0.0943889i \(0.969910\pi\)
\(432\) 5.00000 1.41421i 0.240563 0.0680414i
\(433\) 18.0000i 0.865025i 0.901628 + 0.432512i \(0.142373\pi\)
−0.901628 + 0.432512i \(0.857627\pi\)
\(434\) −7.07107 + 7.07107i −0.339422 + 0.339422i
\(435\) −1.65685 + 9.65685i −0.0794401 + 0.463011i
\(436\) −1.00000 + 1.00000i −0.0478913 + 0.0478913i
\(437\) 8.48528 + 8.48528i 0.405906 + 0.405906i
\(438\) −2.00000 + 1.41421i −0.0955637 + 0.0675737i
\(439\) 30.0000i 1.43182i −0.698192 0.715911i \(-0.746012\pi\)
0.698192 0.715911i \(-0.253988\pi\)
\(440\) 16.9706 + 16.9706i 0.809040 + 0.809040i
\(441\) −14.1421 5.00000i −0.673435 0.238095i
\(442\) 0 0
\(443\) 28.2843i 1.34383i 0.740630 + 0.671913i \(0.234527\pi\)
−0.740630 + 0.671913i \(0.765473\pi\)
\(444\) 0.414214 2.41421i 0.0196577 0.114574i
\(445\) −28.0000 −1.32733
\(446\) −15.5563 −0.736614
\(447\) 3.41421 + 0.585786i 0.161487 + 0.0277067i
\(448\) 7.00000 + 7.00000i 0.330719 + 0.330719i
\(449\) −15.5563 15.5563i −0.734150 0.734150i 0.237289 0.971439i \(-0.423741\pi\)
−0.971439 + 0.237289i \(0.923741\pi\)
\(450\) −2.70711 + 1.29289i −0.127614 + 0.0609476i
\(451\) 8.00000 0.376705
\(452\) 14.1421 0.665190
\(453\) −2.41421 0.414214i −0.113430 0.0194615i
\(454\) 8.00000i 0.375459i
\(455\) 8.48528 5.65685i 0.397796 0.265197i
\(456\) 6.00000 4.24264i 0.280976 0.198680i
\(457\) −29.0000 29.0000i −1.35656 1.35656i −0.878117 0.478446i \(-0.841200\pi\)
−0.478446 0.878117i \(-0.658800\pi\)
\(458\) 1.41421i 0.0660819i
\(459\) 0 0
\(460\) −12.0000 12.0000i −0.559503 0.559503i
\(461\) 7.07107 7.07107i 0.329332 0.329332i −0.523000 0.852333i \(-0.675187\pi\)
0.852333 + 0.523000i \(0.175187\pi\)
\(462\) 9.65685 + 1.65685i 0.449278 + 0.0770838i
\(463\) −17.0000 + 17.0000i −0.790057 + 0.790057i −0.981503 0.191446i \(-0.938682\pi\)
0.191446 + 0.981503i \(0.438682\pi\)
\(464\) 2.82843i 0.131306i
\(465\) −14.1421 20.0000i −0.655826 0.927478i
\(466\) −18.0000 + 18.0000i −0.833834 + 0.833834i
\(467\) −25.4558 −1.17796 −0.588978 0.808149i \(-0.700470\pi\)
−0.588978 + 0.808149i \(0.700470\pi\)
\(468\) 2.65685 + 10.4853i 0.122813 + 0.484682i
\(469\) −10.0000 −0.461757
\(470\) 5.65685 5.65685i 0.260931 0.260931i
\(471\) −14.0000 19.7990i −0.645086 0.912289i
\(472\) 12.0000i 0.552345i
\(473\) 16.9706 16.9706i 0.780307 0.780307i
\(474\) 17.0711 + 2.92893i 0.784100 + 0.134530i
\(475\) −1.00000 + 1.00000i −0.0458831 + 0.0458831i
\(476\) 0 0
\(477\) 16.0000 + 5.65685i 0.732590 + 0.259010i
\(478\) 20.0000i 0.914779i
\(479\) 22.6274 + 22.6274i 1.03387 + 1.03387i 0.999406 + 0.0344672i \(0.0109734\pi\)
0.0344672 + 0.999406i \(0.489027\pi\)
\(480\) −14.1421 + 10.0000i −0.645497 + 0.456435i
\(481\) −5.00000 1.00000i −0.227980 0.0455961i
\(482\) 24.0416i 1.09507i
\(483\) −20.4853 3.51472i −0.932113 0.159925i
\(484\) −5.00000 −0.227273
\(485\) −19.7990 −0.899026
\(486\) 10.2929 + 11.7071i 0.466895 + 0.531045i
\(487\) 19.0000 + 19.0000i 0.860972 + 0.860972i 0.991451 0.130479i \(-0.0416515\pi\)
−0.130479 + 0.991451i \(0.541651\pi\)
\(488\) 16.9706 + 16.9706i 0.768221 + 0.768221i
\(489\) −2.41421 0.414214i −0.109175 0.0187314i
\(490\) −10.0000 −0.451754
\(491\) −42.4264 −1.91468 −0.957338 0.288969i \(-0.906688\pi\)
−0.957338 + 0.288969i \(0.906688\pi\)
\(492\) −0.585786 + 3.41421i −0.0264093 + 0.153925i
\(493\) 0 0
\(494\) −2.82843 4.24264i −0.127257 0.190885i
\(495\) −8.00000 + 22.6274i −0.359573 + 1.01703i
\(496\) −5.00000 5.00000i −0.224507 0.224507i
\(497\) 5.65685i 0.253745i
\(498\) 11.3137 8.00000i 0.506979 0.358489i
\(499\) −23.0000 23.0000i −1.02962 1.02962i −0.999548 0.0300737i \(-0.990426\pi\)
−0.0300737 0.999548i \(-0.509574\pi\)
\(500\) 8.48528 8.48528i 0.379473 0.379473i
\(501\) −1.17157 + 6.82843i −0.0523420 + 0.305072i
\(502\) 18.0000 18.0000i 0.803379 0.803379i
\(503\) 5.65685i 0.252227i −0.992016 0.126113i \(-0.959750\pi\)
0.992016 0.126113i \(-0.0402503\pi\)
\(504\) −4.24264 + 12.0000i −0.188982 + 0.534522i
\(505\) 12.0000 12.0000i 0.533993 0.533993i
\(506\) −33.9411 −1.50887
\(507\) 21.9706 4.92893i 0.975747 0.218902i
\(508\) 0 0
\(509\) 24.0416 24.0416i 1.06563 1.06563i 0.0679369 0.997690i \(-0.478358\pi\)
0.997690 0.0679369i \(-0.0216417\pi\)
\(510\) 0 0
\(511\) 2.00000i 0.0884748i
\(512\) −7.77817 + 7.77817i −0.343750 + 0.343750i
\(513\) 6.41421 + 3.58579i 0.283194 + 0.158316i
\(514\) 6.00000 6.00000i 0.264649 0.264649i
\(515\) 8.48528 + 8.48528i 0.373906 + 0.373906i
\(516\) 6.00000 + 8.48528i 0.264135 + 0.373544i
\(517\) 16.0000i 0.703679i
\(518\) −1.41421 1.41421i −0.0621370 0.0621370i
\(519\) 8.48528 + 12.0000i 0.372463 + 0.526742i
\(520\) 12.0000 + 18.0000i 0.526235 + 0.789352i
\(521\) 31.1127i 1.36307i −0.731785 0.681536i \(-0.761312\pi\)
0.731785 0.681536i \(-0.238688\pi\)
\(522\) −7.65685 + 3.65685i −0.335131 + 0.160056i
\(523\) 20.0000 0.874539 0.437269 0.899331i \(-0.355946\pi\)
0.437269 + 0.899331i \(0.355946\pi\)
\(524\) −11.3137 −0.494242
\(525\) 0.414214 2.41421i 0.0180778 0.105365i
\(526\) −16.0000 16.0000i −0.697633 0.697633i
\(527\) 0 0
\(528\) −1.17157 + 6.82843i −0.0509862 + 0.297169i
\(529\) 49.0000 2.13043
\(530\) 11.3137 0.491436
\(531\) 10.8284 5.17157i 0.469914 0.224427i
\(532\) 2.00000i 0.0867110i
\(533\) 7.07107 + 1.41421i 0.306282 + 0.0612564i
\(534\) −14.0000 19.7990i −0.605839 0.856786i
\(535\) 8.00000 + 8.00000i 0.345870 + 0.345870i
\(536\) 21.2132i 0.916271i
\(537\) 0 0
\(538\) 14.0000 + 14.0000i 0.603583 + 0.603583i
\(539\) 14.1421 14.1421i 0.609145 0.609145i
\(540\) −9.07107 5.07107i −0.390357 0.218224i
\(541\) 1.00000 1.00000i 0.0429934 0.0429934i −0.685283 0.728277i \(-0.740322\pi\)
0.728277 + 0.685283i \(0.240322\pi\)
\(542\) 26.8701i 1.15417i
\(543\) 0 0
\(544\) 0 0
\(545\) −2.82843 −0.121157
\(546\) 8.24264 + 3.17157i 0.352752 + 0.135731i
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) −9.89949 + 9.89949i −0.422885 + 0.422885i
\(549\) −8.00000 + 22.6274i −0.341432 + 0.965715i
\(550\) 4.00000i 0.170561i
\(551\) −2.82843 + 2.82843i −0.120495 + 0.120495i
\(552\) 7.45584 43.4558i 0.317342 1.84960i
\(553\) −10.0000 + 10.0000i −0.425243 + 0.425243i
\(554\) −8.48528 8.48528i −0.360505 0.360505i
\(555\) 4.00000 2.82843i 0.169791 0.120060i
\(556\) 4.00000i 0.169638i
\(557\) 9.89949 + 9.89949i 0.419455 + 0.419455i 0.885016 0.465561i \(-0.154147\pi\)
−0.465561 + 0.885016i \(0.654147\pi\)
\(558\) 7.07107 20.0000i 0.299342 0.846668i
\(559\) 18.0000 12.0000i 0.761319 0.507546i
\(560\) 2.82843i 0.119523i
\(561\) 0 0
\(562\) 14.0000 0.590554
\(563\) 33.9411 1.43045 0.715224 0.698895i \(-0.246325\pi\)
0.715224 + 0.698895i \(0.246325\pi\)
\(564\) −6.82843 1.17157i −0.287529 0.0493321i
\(565\) 20.0000 + 20.0000i 0.841406 + 0.841406i
\(566\) 8.48528 + 8.48528i 0.356663 + 0.356663i
\(567\) −12.6569 + 1.34315i −0.531538 + 0.0564068i
\(568\) 12.0000 0.503509
\(569\) −8.48528 −0.355722 −0.177861 0.984056i \(-0.556918\pi\)
−0.177861 + 0.984056i \(0.556918\pi\)
\(570\) 4.82843 + 0.828427i 0.202241 + 0.0346990i
\(571\) 12.0000i 0.502184i 0.967963 + 0.251092i \(0.0807897\pi\)
−0.967963 + 0.251092i \(0.919210\pi\)
\(572\) −14.1421 2.82843i −0.591312 0.118262i
\(573\) 4.00000 2.82843i 0.167102 0.118159i
\(574\) 2.00000 + 2.00000i 0.0834784 + 0.0834784i
\(575\) 8.48528i 0.353861i
\(576\) −19.7990 7.00000i −0.824958 0.291667i
\(577\) 1.00000 + 1.00000i 0.0416305 + 0.0416305i 0.727616 0.685985i \(-0.240628\pi\)
−0.685985 + 0.727616i \(0.740628\pi\)
\(578\) −12.0208 + 12.0208i −0.500000 + 0.500000i
\(579\) −45.8701 7.87006i −1.90629 0.327068i
\(580\) 4.00000 4.00000i 0.166091 0.166091i
\(581\) 11.3137i 0.469372i
\(582\) −9.89949 14.0000i −0.410347 0.580319i
\(583\) −16.0000 + 16.0000i −0.662652 + 0.662652i
\(584\) 4.24264 0.175562
\(585\) −11.0711 + 18.5858i −0.457732 + 0.768428i
\(586\) 14.0000 0.578335
\(587\) −5.65685 + 5.65685i −0.233483 + 0.233483i −0.814145 0.580662i \(-0.802794\pi\)
0.580662 + 0.814145i \(0.302794\pi\)
\(588\) 5.00000 + 7.07107i 0.206197 + 0.291606i
\(589\) 10.0000i 0.412043i
\(590\) 5.65685 5.65685i 0.232889 0.232889i
\(591\) −37.5563 6.44365i −1.54486 0.265056i
\(592\) 1.00000 1.00000i 0.0410997 0.0410997i
\(593\) 9.89949 + 9.89949i 0.406524 + 0.406524i 0.880524 0.474001i \(-0.157191\pi\)
−0.474001 + 0.880524i \(0.657191\pi\)
\(594\) −20.0000 + 5.65685i −0.820610 + 0.232104i
\(595\) 0 0
\(596\) −1.41421 1.41421i −0.0579284 0.0579284i
\(597\) 0 0
\(598\) −30.0000 6.00000i −1.22679 0.245358i
\(599\) 11.3137i 0.462266i 0.972922 + 0.231133i \(0.0742432\pi\)
−0.972922 + 0.231133i \(0.925757\pi\)
\(600\) 5.12132 + 0.878680i 0.209077 + 0.0358719i
\(601\) 8.00000 0.326327 0.163163 0.986599i \(-0.447830\pi\)
0.163163 + 0.986599i \(0.447830\pi\)
\(602\) 8.48528 0.345834
\(603\) 19.1421 9.14214i 0.779528 0.372297i
\(604\) 1.00000 + 1.00000i 0.0406894 + 0.0406894i
\(605\) −7.07107 7.07107i −0.287480 0.287480i
\(606\) 14.4853 + 2.48528i 0.588424 + 0.100958i
\(607\) −40.0000 −1.62355 −0.811775 0.583970i \(-0.801498\pi\)
−0.811775 + 0.583970i \(0.801498\pi\)
\(608\) −7.07107 −0.286770
\(609\) 1.17157 6.82843i 0.0474745 0.276702i
\(610\) 16.0000i 0.647821i
\(611\) −2.82843 + 14.1421i −0.114426 + 0.572130i
\(612\) 0 0
\(613\) 1.00000 + 1.00000i 0.0403896 + 0.0403896i 0.727013 0.686624i \(-0.240908\pi\)
−0.686624 + 0.727013i \(0.740908\pi\)
\(614\) 24.0416i 0.970241i
\(615\) −5.65685 + 4.00000i −0.228106 + 0.161296i
\(616\) −12.0000 12.0000i −0.483494 0.483494i
\(617\) −26.8701 + 26.8701i −1.08175 + 1.08175i −0.0854011 + 0.996347i \(0.527217\pi\)
−0.996347 + 0.0854011i \(0.972783\pi\)
\(618\) −1.75736 + 10.2426i −0.0706914 + 0.412019i
\(619\) 1.00000 1.00000i 0.0401934 0.0401934i −0.686724 0.726918i \(-0.740952\pi\)
0.726918 + 0.686724i \(0.240952\pi\)
\(620\) 14.1421i 0.567962i
\(621\) 42.4264 12.0000i 1.70251 0.481543i
\(622\) 6.00000 6.00000i 0.240578 0.240578i
\(623\) 19.7990 0.793230
\(624\) −2.24264 + 5.82843i −0.0897775 + 0.233324i
\(625\) 19.0000 0.760000
\(626\) 5.65685 5.65685i 0.226093 0.226093i
\(627\) −8.00000 + 5.65685i −0.319489 + 0.225913i
\(628\) 14.0000i 0.558661i
\(629\) 0 0
\(630\) −7.65685 + 3.65685i −0.305056 + 0.145693i
\(631\) 19.0000 19.0000i 0.756378 0.756378i −0.219283 0.975661i \(-0.570372\pi\)
0.975661 + 0.219283i \(0.0703719\pi\)
\(632\) −21.2132 21.2132i −0.843816 0.843816i
\(633\) −14.0000 19.7990i −0.556450 0.786939i
\(634\) 10.0000i 0.397151i
\(635\) 0 0
\(636\) −5.65685 8.00000i −0.224309 0.317221i
\(637\) 15.0000 10.0000i 0.594322 0.396214i
\(638\) 11.3137i 0.447914i
\(639\) 5.17157 + 10.8284i 0.204584 + 0.428366i
\(640\) 6.00000 0.237171
\(641\) 16.9706 0.670297 0.335148 0.942165i \(-0.391214\pi\)
0.335148 + 0.942165i \(0.391214\pi\)
\(642\) −1.65685 + 9.65685i −0.0653908 + 0.381126i
\(643\) −5.00000 5.00000i −0.197181 0.197181i 0.601610 0.798790i \(-0.294526\pi\)
−0.798790 + 0.601610i \(0.794526\pi\)
\(644\) 8.48528 + 8.48528i 0.334367 + 0.334367i
\(645\) −3.51472 + 20.4853i −0.138392 + 0.806607i
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) −2.84924 26.8492i −0.111929 1.05474i
\(649\) 16.0000i 0.628055i
\(650\) 0.707107 3.53553i 0.0277350 0.138675i
\(651\) 10.0000 + 14.1421i 0.391931 + 0.554274i
\(652\) 1.00000 + 1.00000i 0.0391630 + 0.0391630i
\(653\) 14.1421i 0.553425i −0.960953 0.276712i \(-0.910755\pi\)
0.960953 0.276712i \(-0.0892449\pi\)
\(654\) −1.41421 2.00000i −0.0553001 0.0782062i
\(655\) −16.0000 16.0000i −0.625172 0.625172i
\(656\) −1.41421 + 1.41421i −0.0552158 + 0.0552158i
\(657\) 1.82843 + 3.82843i 0.0713337 + 0.149361i
\(658\) −4.00000 + 4.00000i −0.155936 + 0.155936i
\(659\) 2.82843i 0.110180i 0.998481 + 0.0550899i \(0.0175446\pi\)
−0.998481 + 0.0550899i \(0.982455\pi\)
\(660\) 11.3137 8.00000i 0.440386 0.311400i
\(661\) 1.00000 1.00000i 0.0388955 0.0388955i −0.687392 0.726287i \(-0.741244\pi\)
0.726287 + 0.687392i \(0.241244\pi\)
\(662\) 9.89949 0.384755
\(663\) 0 0
\(664\) −24.0000 −0.931381
\(665\) −2.82843 + 2.82843i −0.109682 + 0.109682i
\(666\) 4.00000 + 1.41421i 0.154997 + 0.0547997i
\(667\) 24.0000i 0.929284i
\(668\) 2.82843 2.82843i 0.109435 0.109435i
\(669\) −4.55635 + 26.5563i −0.176159 + 1.02673i
\(670\) 10.0000 10.0000i 0.386334 0.386334i
\(671\) −22.6274 22.6274i −0.873522 0.873522i
\(672\) 10.0000 7.07107i 0.385758 0.272772i
\(673\) 12.0000i 0.462566i −0.972887 0.231283i \(-0.925708\pi\)
0.972887 0.231283i \(-0.0742923\pi\)
\(674\) −4.24264 4.24264i −0.163420 0.163420i
\(675\) 1.41421 + 5.00000i 0.0544331 + 0.192450i
\(676\) −12.0000 5.00000i −0.461538 0.192308i
\(677\) 22.6274i 0.869642i −0.900517 0.434821i \(-0.856812\pi\)
0.900517 0.434821i \(-0.143188\pi\)
\(678\) −4.14214 + 24.1421i −0.159078 + 0.927173i
\(679\) 14.0000 0.537271
\(680\) 0 0
\(681\) 13.6569 + 2.34315i 0.523332 + 0.0897895i
\(682\) 20.0000 + 20.0000i 0.765840 + 0.765840i
\(683\) −2.82843 2.82843i −0.108227 0.108227i 0.650920 0.759147i \(-0.274383\pi\)
−0.759147 + 0.650920i \(0.774383\pi\)
\(684\) −1.82843 3.82843i −0.0699117 0.146384i
\(685\) −28.0000 −1.06983
\(686\) 16.9706 0.647939
\(687\) −2.41421 0.414214i −0.0921080 0.0158032i
\(688\) 6.00000i 0.228748i
\(689\) −16.9706 + 11.3137i −0.646527 + 0.431018i
\(690\) 24.0000 16.9706i 0.913664 0.646058i
\(691\) −11.0000 11.0000i −0.418460 0.418460i 0.466213 0.884673i \(-0.345618\pi\)
−0.884673 + 0.466213i \(0.845618\pi\)
\(692\) 8.48528i 0.322562i
\(693\) 5.65685 16.0000i 0.214886 0.607790i
\(694\) −10.0000 10.0000i −0.379595 0.379595i
\(695\) 5.65685 5.65685i 0.214577 0.214577i
\(696\) 14.4853 + 2.48528i 0.549063 + 0.0942043i
\(697\) 0 0
\(698\) 24.0416i 0.909989i
\(699\) 25.4558 + 36.0000i 0.962828 + 1.36165i
\(700\) −1.00000 + 1.00000i −0.0377964 + 0.0377964i
\(701\) 50.9117 1.92291 0.961454 0.274966i \(-0.0886666\pi\)
0.961454 + 0.274966i \(0.0886666\pi\)
\(702\) −18.6777 + 1.46447i −0.704943 + 0.0552727i
\(703\) 2.00000 0.0754314
\(704\) 19.7990 19.7990i 0.746203 0.746203i
\(705\) −8.00000 11.3137i −0.301297 0.426099i
\(706\) 26.0000i 0.978523i
\(707\) −8.48528 + 8.48528i −0.319122 + 0.319122i
\(708\) −6.82843 1.17157i −0.256628 0.0440304i
\(709\) 19.0000 19.0000i 0.713560 0.713560i −0.253718 0.967278i \(-0.581654\pi\)
0.967278 + 0.253718i \(0.0816536\pi\)
\(710\) 5.65685 + 5.65685i 0.212298 + 0.212298i
\(711\) 10.0000 28.2843i 0.375029 1.06074i
\(712\) 42.0000i 1.57402i
\(713\) −42.4264 42.4264i −1.58888 1.58888i
\(714\) 0 0
\(715\) −16.0000 24.0000i −0.598366 0.897549i
\(716\) 0 0
\(717\) 34.1421 + 5.85786i 1.27506 + 0.218766i
\(718\) −4.00000 −0.149279
\(719\) −25.4558 −0.949343 −0.474671 0.880163i \(-0.657433\pi\)
−0.474671 + 0.880163i \(0.657433\pi\)
\(720\) −2.58579 5.41421i −0.0963666 0.201776i
\(721\) −6.00000 6.00000i −0.223452 0.223452i
\(722\) −12.0208 12.0208i −0.447368 0.447368i
\(723\) 41.0416 + 7.04163i 1.52635 + 0.261881i
\(724\) 0 0
\(725\) −2.82843 −0.105045
\(726\) 1.46447 8.53553i 0.0543514 0.316783i
\(727\) 48.0000i 1.78022i −0.455744 0.890111i \(-0.650627\pi\)
0.455744 0.890111i \(-0.349373\pi\)
\(728\) −8.48528 12.7279i −0.314485 0.471728i
\(729\) 23.0000 14.1421i 0.851852 0.523783i
\(730\) 2.00000 + 2.00000i 0.0740233 + 0.0740233i
\(731\) 0 0
\(732\) 11.3137 8.00000i 0.418167 0.295689i
\(733\) −5.00000 5.00000i −0.184679 0.184679i 0.608712 0.793391i \(-0.291686\pi\)
−0.793391 + 0.608712i \(0.791686\pi\)
\(734\) 5.65685 5.65685i 0.208798 0.208798i
\(735\) −2.92893 + 17.0711i −0.108035 + 0.629676i
\(736\) −30.0000 + 30.0000i −1.10581 + 1.10581i
\(737\) 28.2843i 1.04186i
\(738\) −5.65685 2.00000i −0.208232 0.0736210i
\(739\) 1.00000 1.00000i 0.0367856 0.0367856i −0.688475 0.725260i \(-0.741719\pi\)
0.725260 + 0.688475i \(0.241719\pi\)
\(740\) −2.82843 −0.103975
\(741\) −8.07107 + 3.58579i −0.296498 + 0.131727i
\(742\) −8.00000 −0.293689
\(743\) 11.3137 11.3137i 0.415060 0.415060i −0.468437 0.883497i \(-0.655183\pi\)
0.883497 + 0.468437i \(0.155183\pi\)
\(744\) −30.0000 + 21.2132i −1.09985 + 0.777714i
\(745\) 4.00000i 0.146549i
\(746\) −2.82843 + 2.82843i −0.103556 + 0.103556i
\(747\) −10.3431 21.6569i −0.378436 0.792383i
\(748\) 0 0
\(749\) −5.65685 5.65685i −0.206697 0.206697i
\(750\) 12.0000 + 16.9706i 0.438178 + 0.619677i
\(751\) 30.0000i 1.09472i 0.836899 + 0.547358i \(0.184366\pi\)
−0.836899 + 0.547358i \(0.815634\pi\)
\(752\) −2.82843 2.82843i −0.103142 0.103142i
\(753\) −25.4558 36.0000i −0.927663 1.31191i
\(754\) 2.00000 10.0000i 0.0728357 0.364179i
\(755\) 2.82843i 0.102937i
\(756\) 6.41421 + 3.58579i 0.233283 + 0.130414i
\(757\) −16.0000 −0.581530 −0.290765 0.956795i \(-0.593910\pi\)
−0.290765 + 0.956795i \(0.593910\pi\)
\(758\) 26.8701 0.975964
\(759\) −9.94113 + 57.9411i −0.360840 + 2.10313i
\(760\) −6.00000 6.00000i −0.217643 0.217643i
\(761\) 35.3553 + 35.3553i 1.28163 + 1.28163i 0.939740 + 0.341890i \(0.111067\pi\)
0.341890 + 0.939740i \(0.388933\pi\)
\(762\) 0 0
\(763\) 2.00000 0.0724049
\(764\) −2.82843 −0.102329
\(765\) 0 0
\(766\) 16.0000i 0.578103i
\(767\) −2.82843 + 14.1421i −0.102129 + 0.510643i
\(768\) 17.0000 + 24.0416i 0.613435 + 0.867528i
\(769\) 13.0000 + 13.0000i 0.468792 + 0.468792i 0.901523 0.432731i \(-0.142450\pi\)
−0.432731 + 0.901523i \(0.642450\pi\)
\(770\) 11.3137i 0.407718i
\(771\) −8.48528 12.0000i −0.305590 0.432169i
\(772\) 19.0000 + 19.0000i 0.683825 + 0.683825i
\(773\) −9.89949 + 9.89949i −0.356060 + 0.356060i −0.862358 0.506298i \(-0.831013\pi\)
0.506298 + 0.862358i \(0.331013\pi\)
\(774\) −16.2426 + 7.75736i −0.583830 + 0.278833i
\(775\) 5.00000 5.00000i 0.179605 0.179605i
\(776\) 29.6985i 1.06611i
\(777\) −2.82843 + 2.00000i −0.101469 + 0.0717496i
\(778\) 12.0000 12.0000i 0.430221 0.430221i
\(779\) −2.82843 −0.101339
\(780\) 11.4142 5.07107i 0.408694 0.181573i
\(781\) −16.0000 −0.572525
\(782\) 0 0
\(783\) 4.00000 + 14.1421i 0.142948 + 0.505399i
\(784\) 5.00000i 0.178571i
\(785\) −19.7990 + 19.7990i −0.706656 + 0.706656i
\(786\) 3.31371 19.3137i 0.118196 0.688897i
\(787\) 19.0000 19.0000i 0.677277 0.677277i −0.282106 0.959383i \(-0.591033\pi\)
0.959383 + 0.282106i \(0.0910331\pi\)
\(788\) 15.5563 + 15.5563i 0.554172 + 0.554172i
\(789\) −32.0000 + 22.6274i −1.13923 + 0.805557i
\(790\) 20.0000i 0.711568i
\(791\) −14.1421 14.1421i −0.502836 0.502836i
\(792\) 33.9411 + 12.0000i 1.20605 + 0.426401i
\(793\) −16.0000 24.0000i −0.568177 0.852265i
\(794\) 24.0416i 0.853206i
\(795\) 3.31371 19.3137i 0.117525 0.684987i
\(796\) 0 0
\(797\) −16.9706 −0.601128 −0.300564 0.953762i \(-0.597175\pi\)
−0.300564 + 0.953762i \(0.597175\pi\)
\(798\) −3.41421 0.585786i −0.120862 0.0207366i
\(799\) 0 0
\(800\) −3.53553 3.53553i −0.125000 0.125000i
\(801\) −37.8995 + 18.1005i −1.33911 + 0.639550i
\(802\) −22.0000 −0.776847
\(803\) −5.65685 −0.199626
\(804\) −12.0711 2.07107i −0.425714 0.0730409i
\(805\) 24.0000i 0.845889i
\(806\) 14.1421 + 21.2132i 0.498135 + 0.747203i
\(807\) 28.0000 19.7990i 0.985647 0.696957i
\(808\) −18.0000 18.0000i −0.633238 0.633238i
\(809\) 31.1127i 1.09386i −0.837177 0.546932i \(-0.815796\pi\)
0.837177 0.546932i \(-0.184204\pi\)
\(810\) 11.3137 14.0000i 0.397523 0.491910i
\(811\) 1.00000 + 1.00000i 0.0351147 + 0.0351147i 0.724446 0.689331i \(-0.242096\pi\)
−0.689331 + 0.724446i \(0.742096\pi\)
\(812\) −2.82843 + 2.82843i −0.0992583 + 0.0992583i
\(813\) −45.8701 7.87006i −1.60873 0.276015i
\(814\) −4.00000 + 4.00000i −0.140200 + 0.140200i
\(815\) 2.82843i 0.0990755i
\(816\) 0 0
\(817\) −6.00000 + 6.00000i −0.209913 + 0.209913i
\(818\) −32.5269 −1.13728
\(819\) 7.82843 13.1421i 0.273547 0.459223i
\(820\) 4.00000 0.139686
\(821\) 7.07107 7.07107i 0.246782 0.246782i −0.572867 0.819649i \(-0.694169\pi\)
0.819649 + 0.572867i \(0.194169\pi\)
\(822\) −14.0000 19.7990i −0.488306 0.690569i
\(823\) 30.0000i 1.04573i 0.852414 + 0.522867i \(0.175138\pi\)
−0.852414 + 0.522867i \(0.824862\pi\)
\(824\) 12.7279 12.7279i 0.443398 0.443398i
\(825\) −6.82843 1.17157i −0.237735 0.0407889i
\(826\) −4.00000 + 4.00000i −0.139178 + 0.139178i
\(827\) 22.6274 + 22.6274i 0.786832 + 0.786832i 0.980974 0.194141i \(-0.0621920\pi\)
−0.194141 + 0.980974i \(0.562192\pi\)
\(828\) −24.0000 8.48528i −0.834058 0.294884i
\(829\) 18.0000i 0.625166i 0.949890 + 0.312583i \(0.101194\pi\)
−0.949890 + 0.312583i \(0.898806\pi\)
\(830\) −11.3137 11.3137i −0.392705 0.392705i
\(831\) −16.9706 + 12.0000i −0.588702 + 0.416275i
\(832\) 21.0000 14.0000i 0.728044 0.485363i
\(833\) 0 0
\(834\) 6.82843 + 1.17157i 0.236449 + 0.0405683i
\(835\) 8.00000 0.276851
\(836\) 5.65685 0.195646
\(837\) −32.0711 17.9289i −1.10854 0.619715i
\(838\) 8.00000 + 8.00000i 0.276355 + 0.276355i
\(839\) −2.82843 2.82843i −0.0976481 0.0976481i 0.656595 0.754243i \(-0.271996\pi\)
−0.754243 + 0.656595i \(0.771996\pi\)
\(840\) 14.4853 + 2.48528i 0.499790 + 0.0857504i
\(841\) 21.0000 0.724138
\(842\) 35.3553 1.21843
\(843\) 4.10051 23.8995i 0.141229 0.823142i
\(844\) 14.0000i 0.481900i
\(845\) −9.89949 24.0416i −0.340553 0.827057i
\(846\) 4.00000 11.3137i 0.137523 0.388973i
\(847\) 5.00000 + 5.00000i 0.171802 + 0.171802i
\(848\) 5.65685i 0.194257i
\(849\) 16.9706 12.0000i 0.582428 0.411839i
\(850\) 0 0
\(851\) 8.48528 8.48528i 0.290872 0.290872i
\(852\) 1.17157 6.82843i 0.0401374 0.233938i
\(853\) 37.0000 37.0000i 1.26686 1.26686i 0.319152 0.947703i \(-0.396602\pi\)
0.947703 0.319152i \(-0.103398\pi\)
\(854\) 11.3137i 0.387147i
\(855\) 2.82843 8.00000i 0.0967302 0.273594i
\(856\) 12.0000 12.0000i 0.410152 0.410152i
\(857\) −8.48528 −0.289852 −0.144926 0.989443i \(-0.546294\pi\)
−0.144926 + 0.989443i \(0.546294\pi\)
\(858\) 8.97056 23.3137i 0.306250 0.795917i
\(859\) 14.0000 0.477674 0.238837 0.971060i \(-0.423234\pi\)
0.238837 + 0.971060i \(0.423234\pi\)
\(860\) 8.48528 8.48528i 0.289346 0.289346i
\(861\) 4.00000 2.82843i 0.136320 0.0963925i
\(862\) 32.0000i 1.08992i
\(863\) 2.82843 2.82843i 0.0962808 0.0962808i −0.657326 0.753607i \(-0.728312\pi\)
0.753607 + 0.657326i \(0.228312\pi\)
\(864\) −12.6777 + 22.6777i −0.431303 + 0.771510i
\(865\) 12.0000 12.0000i 0.408012 0.408012i
\(866\) 12.7279 + 12.7279i 0.432512 + 0.432512i
\(867\) 17.0000 + 24.0416i 0.577350 + 0.816497i
\(868\) 10.0000i 0.339422i
\(869\) 28.2843 + 28.2843i 0.959478 + 0.959478i
\(870\) 5.65685 + 8.00000i 0.191785 + 0.271225i
\(871\) −5.00000 + 25.0000i −0.169419 + 0.847093i
\(872\) 4.24264i 0.143674i
\(873\) −26.7990 + 12.7990i −0.907008 + 0.433180i
\(874\) 12.0000 0.405906
\(875\) −16.9706 −0.573710
\(876\) 0.414214 2.41421i 0.0139950 0.0815687i
\(877\) 13.0000 + 13.0000i 0.438979 + 0.438979i 0.891668 0.452689i \(-0.149535\pi\)
−0.452689 + 0.891668i \(0.649535\pi\)
\(878\) −21.2132 21.2132i −0.715911 0.715911i
\(879\) 4.10051 23.8995i 0.138307 0.806110i
\(880\) 8.00000 0.269680
\(881\) 25.4558 0.857629 0.428815 0.903393i \(-0.358931\pi\)
0.428815 + 0.903393i \(0.358931\pi\)
\(882\) −13.5355 + 6.46447i −0.455765 + 0.217670i
\(883\) 36.0000i 1.21150i 0.795656 + 0.605748i \(0.207126\pi\)
−0.795656 + 0.605748i \(0.792874\pi\)
\(884\) 0 0
\(885\) −8.00000 11.3137i −0.268917 0.380306i
\(886\) 20.0000 + 20.0000i 0.671913 + 0.671913i
\(887\) 14.1421i 0.474846i −0.971406 0.237423i \(-0.923697\pi\)
0.971406 0.237423i \(-0.0763028\pi\)
\(888\) −4.24264 6.00000i −0.142374 0.201347i
\(889\) 0 0
\(890\) −19.7990 + 19.7990i −0.663664 + 0.663664i
\(891\) 3.79899 + 35.7990i 0.127271 + 1.19931i
\(892\) 11.0000 11.0000i 0.368307 0.368307i
\(893\) 5.65685i 0.189299i
\(894\) 2.82843 2.00000i 0.0945968 0.0668900i
\(895\) 0 0
\(896\) −4.24264 −0.141737
\(897\) −19.0294 + 49.4558i −0.635374 + 1.65128i
\(898\) −22.0000 −0.734150
\(899\) 14.1421 14.1421i 0.471667 0.471667i
\(900\) 1.00000 2.82843i 0.0333333 0.0942809i
\(901\) 0 0
\(902\) 5.65685 5.65685i 0.188353 0.188353i
\(903\) 2.48528 14.4853i 0.0827050 0.482040i
\(904\) 30.0000 30.0000i 0.997785 0.997785i
\(905\) 0 0
\(906\) −2.00000 + 1.41421i −0.0664455 + 0.0469841i
\(907\) 12.0000i 0.398453i −0.979953 0.199227i \(-0.936157\pi\)
0.979953 0.199227i \(-0.0638430\pi\)
\(908\) −5.65685 5.65685i −0.187729 0.187729i
\(909\) 8.48528 24.0000i 0.281439 0.796030i
\(910\) 2.00000 10.0000i 0.0662994 0.331497i
\(911\) 48.0833i 1.59307i −0.604593 0.796535i \(-0.706664\pi\)
0.604593 0.796535i \(-0.293336\pi\)
\(912\) 0.414214 2.41421i 0.0137160 0.0799426i
\(913\) 32.0000 1.05905
\(914\) −41.0122 −1.35656
\(915\) 27.3137 + 4.68629i 0.902963 + 0.154924i
\(916\) 1.00000 + 1.00000i 0.0330409 + 0.0330409i
\(917\) 11.3137 + 11.3137i 0.373612 + 0.373612i
\(918\) 0 0
\(919\) −34.0000 −1.12156 −0.560778 0.827966i \(-0.689498\pi\)
−0.560778 + 0.827966i \(0.689498\pi\)
\(920\) −50.9117 −1.67851
\(921\) 41.0416 + 7.04163i 1.35237 + 0.232030i
\(922\) 10.0000i 0.329332i
\(923\) −14.1421 2.82843i −0.465494 0.0930988i
\(924\) −8.00000 + 5.65685i −0.263181 + 0.186097i
\(925\) 1.00000 + 1.00000i 0.0328798 + 0.0328798i
\(926\) 24.0416i 0.790057i
\(927\) 16.9706 + 6.00000i 0.557386 + 0.197066i
\(928\) −10.0000 10.0000i −0.328266 0.328266i
\(929\) 32.5269 32.5269i 1.06717 1.06717i 0.0695983 0.997575i \(-0.477828\pi\)
0.997575 0.0695983i \(-0.0221717\pi\)
\(930\) −24.1421 4.14214i −0.791652 0.135826i
\(931\) −5.00000 + 5.00000i −0.163868 + 0.163868i
\(932\) 25.4558i 0.833834i
\(933\) −8.48528 12.0000i −0.277796 0.392862i
\(934\) −18.0000 + 18.0000i −0.588978 + 0.588978i
\(935\) 0 0
\(936\) 27.8787 + 16.6066i 0.911243 + 0.542804i
\(937\) −52.0000 −1.69877 −0.849383 0.527777i \(-0.823026\pi\)
−0.849383 + 0.527777i \(0.823026\pi\)
\(938\) −7.07107 + 7.07107i −0.230879 + 0.230879i
\(939\) −8.00000 11.3137i −0.261070 0.369209i
\(940\) 8.00000i 0.260931i
\(941\) −26.8701 + 26.8701i −0.875939 + 0.875939i −0.993112 0.117173i \(-0.962617\pi\)
0.117173 + 0.993112i \(0.462617\pi\)
\(942\) −23.8995 4.10051i −0.778688 0.133602i
\(943\) −12.0000 + 12.0000i −0.390774 + 0.390774i
\(944\) −2.82843 2.82843i −0.0920575 0.0920575i
\(945\) 4.00000 + 14.1421i 0.130120 + 0.460044i
\(946\) 24.0000i 0.780307i
\(947\) 22.6274 + 22.6274i 0.735292 + 0.735292i 0.971663 0.236371i \(-0.0759580\pi\)
−0.236371 + 0.971663i \(0.575958\pi\)
\(948\) −14.1421 + 10.0000i −0.459315 + 0.324785i
\(949\) −5.00000 1.00000i −0.162307 0.0324614i
\(950\) 1.41421i 0.0458831i
\(951\) −17.0711 2.92893i −0.553567 0.0949771i
\(952\) 0 0
\(953\) 25.4558 0.824596 0.412298 0.911049i \(-0.364726\pi\)
0.412298 + 0.911049i \(0.364726\pi\)
\(954\) 15.3137 7.31371i 0.495800 0.236790i
\(955\) −4.00000 4.00000i −0.129437 0.129437i
\(956\) −14.1421 14.1421i −0.457389 0.457389i
\(957\) −19.3137 3.31371i −0.624324 0.107117i
\(958\) 32.0000 1.03387
\(959\) 19.7990 0.639343
\(960\) −4.10051 + 23.8995i −0.132343 + 0.771353i
\(961\) 19.0000i 0.612903i
\(962\) −4.24264 + 2.82843i −0.136788 + 0.0911922i
\(963\) 16.0000 + 5.65685i 0.515593 + 0.182290i
\(964\) −17.0000 17.0000i −0.547533 0.547533i
\(965\) 53.7401i 1.72996i
\(966\) −16.9706 + 12.0000i −0.546019 + 0.386094i
\(967\) −23.0000 23.0000i −0.739630 0.739630i 0.232876 0.972506i \(-0.425186\pi\)
−0.972506 + 0.232876i \(0.925186\pi\)
\(968\) −10.6066 + 10.6066i −0.340909 + 0.340909i
\(969\) 0 0
\(970\) −14.0000 + 14.0000i −0.449513 + 0.449513i
\(971\) 31.1127i 0.998454i −0.866471 0.499227i \(-0.833617\pi\)
0.866471 0.499227i \(-0.166383\pi\)
\(972\) −15.5563 1.00000i −0.498970 0.0320750i
\(973\) −4.00000 + 4.00000i −0.128234 + 0.128234i
\(974\) 26.8701 0.860972
\(975\) −5.82843 2.24264i −0.186659 0.0718220i
\(976\) 8.00000 0.256074
\(977\) −26.8701 + 26.8701i −0.859649 + 0.859649i −0.991297 0.131647i \(-0.957973\pi\)
0.131647 + 0.991297i \(0.457973\pi\)
\(978\) −2.00000 + 1.41421i −0.0639529 + 0.0452216i
\(979\) 56.0000i 1.78977i
\(980\) 7.07107 7.07107i 0.225877 0.225877i
\(981\) −3.82843 + 1.82843i −0.122232 + 0.0583772i
\(982\) −30.0000 + 30.0000i −0.957338 + 0.957338i
\(983\) −2.82843 2.82843i −0.0902128 0.0902128i 0.660560 0.750773i \(-0.270319\pi\)
−0.750773 + 0.660560i \(0.770319\pi\)
\(984\) 6.00000 + 8.48528i 0.191273 + 0.270501i
\(985\) 44.0000i 1.40196i
\(986\) 0 0
\(987\) 5.65685 + 8.00000i 0.180060 + 0.254643i
\(988\) 5.00000 + 1.00000i 0.159071 + 0.0318142i
\(989\) 50.9117i 1.61890i
\(990\) 10.3431 + 21.6569i 0.328727 + 0.688300i
\(991\) −16.0000 −0.508257 −0.254128 0.967170i \(-0.581789\pi\)
−0.254128 + 0.967170i \(0.581789\pi\)
\(992\) 35.3553 1.12253
\(993\) 2.89949 16.8995i 0.0920127 0.536289i
\(994\) −4.00000 4.00000i −0.126872 0.126872i
\(995\) 0 0
\(996\) −2.34315 + 13.6569i −0.0742454 + 0.432734i
\(997\) 26.0000 0.823428 0.411714 0.911313i \(-0.364930\pi\)
0.411714 + 0.911313i \(0.364930\pi\)
\(998\) −32.5269 −1.02962
\(999\) 3.58579 6.41421i 0.113449 0.202937i
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 39.2.f.a.8.2 yes 4
3.2 odd 2 inner 39.2.f.a.8.1 yes 4
4.3 odd 2 624.2.bf.d.593.2 4
5.2 odd 4 975.2.n.d.749.2 4
5.3 odd 4 975.2.n.c.749.1 4
5.4 even 2 975.2.o.j.476.1 4
12.11 even 2 624.2.bf.d.593.1 4
13.2 odd 12 507.2.k.j.188.2 8
13.3 even 3 507.2.k.j.488.2 8
13.4 even 6 507.2.k.i.89.2 8
13.5 odd 4 inner 39.2.f.a.5.1 4
13.6 odd 12 507.2.k.j.80.1 8
13.7 odd 12 507.2.k.i.80.2 8
13.8 odd 4 507.2.f.a.239.2 4
13.9 even 3 507.2.k.j.89.1 8
13.10 even 6 507.2.k.i.488.1 8
13.11 odd 12 507.2.k.i.188.1 8
13.12 even 2 507.2.f.a.437.1 4
15.2 even 4 975.2.n.d.749.1 4
15.8 even 4 975.2.n.c.749.2 4
15.14 odd 2 975.2.o.j.476.2 4
39.2 even 12 507.2.k.j.188.1 8
39.5 even 4 inner 39.2.f.a.5.2 yes 4
39.8 even 4 507.2.f.a.239.1 4
39.11 even 12 507.2.k.i.188.2 8
39.17 odd 6 507.2.k.i.89.1 8
39.20 even 12 507.2.k.i.80.1 8
39.23 odd 6 507.2.k.i.488.2 8
39.29 odd 6 507.2.k.j.488.1 8
39.32 even 12 507.2.k.j.80.2 8
39.35 odd 6 507.2.k.j.89.2 8
39.38 odd 2 507.2.f.a.437.2 4
52.31 even 4 624.2.bf.d.161.2 4
65.18 even 4 975.2.n.d.824.1 4
65.44 odd 4 975.2.o.j.551.2 4
65.57 even 4 975.2.n.c.824.2 4
156.83 odd 4 624.2.bf.d.161.1 4
195.44 even 4 975.2.o.j.551.1 4
195.83 odd 4 975.2.n.d.824.2 4
195.122 odd 4 975.2.n.c.824.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.2.f.a.5.1 4 13.5 odd 4 inner
39.2.f.a.5.2 yes 4 39.5 even 4 inner
39.2.f.a.8.1 yes 4 3.2 odd 2 inner
39.2.f.a.8.2 yes 4 1.1 even 1 trivial
507.2.f.a.239.1 4 39.8 even 4
507.2.f.a.239.2 4 13.8 odd 4
507.2.f.a.437.1 4 13.12 even 2
507.2.f.a.437.2 4 39.38 odd 2
507.2.k.i.80.1 8 39.20 even 12
507.2.k.i.80.2 8 13.7 odd 12
507.2.k.i.89.1 8 39.17 odd 6
507.2.k.i.89.2 8 13.4 even 6
507.2.k.i.188.1 8 13.11 odd 12
507.2.k.i.188.2 8 39.11 even 12
507.2.k.i.488.1 8 13.10 even 6
507.2.k.i.488.2 8 39.23 odd 6
507.2.k.j.80.1 8 13.6 odd 12
507.2.k.j.80.2 8 39.32 even 12
507.2.k.j.89.1 8 13.9 even 3
507.2.k.j.89.2 8 39.35 odd 6
507.2.k.j.188.1 8 39.2 even 12
507.2.k.j.188.2 8 13.2 odd 12
507.2.k.j.488.1 8 39.29 odd 6
507.2.k.j.488.2 8 13.3 even 3
624.2.bf.d.161.1 4 156.83 odd 4
624.2.bf.d.161.2 4 52.31 even 4
624.2.bf.d.593.1 4 12.11 even 2
624.2.bf.d.593.2 4 4.3 odd 2
975.2.n.c.749.1 4 5.3 odd 4
975.2.n.c.749.2 4 15.8 even 4
975.2.n.c.824.1 4 195.122 odd 4
975.2.n.c.824.2 4 65.57 even 4
975.2.n.d.749.1 4 15.2 even 4
975.2.n.d.749.2 4 5.2 odd 4
975.2.n.d.824.1 4 65.18 even 4
975.2.n.d.824.2 4 195.83 odd 4
975.2.o.j.476.1 4 5.4 even 2
975.2.o.j.476.2 4 15.14 odd 2
975.2.o.j.551.1 4 195.44 even 4
975.2.o.j.551.2 4 65.44 odd 4