Properties

Label 430.2.g.a.343.1
Level $430$
Weight $2$
Character 430.343
Analytic conductor $3.434$
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] = [430,2,Mod(257,430)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(430, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("430.257");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 430 = 2 \cdot 5 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 430.g (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: \(3.43356728692\)
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 343.1
Root \(-0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 430.343
Dual form 430.2.g.a.257.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +(-1.41421 + 1.41421i) q^{3} +1.00000i q^{4} +(-0.707107 + 2.12132i) q^{5} +2.00000 q^{6} +(-2.82843 - 2.82843i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +(-1.41421 + 1.41421i) q^{3} +1.00000i q^{4} +(-0.707107 + 2.12132i) q^{5} +2.00000 q^{6} +(-2.82843 - 2.82843i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +(2.00000 - 1.00000i) q^{10} -4.00000 q^{11} +(-1.41421 - 1.41421i) q^{12} +(2.00000 + 2.00000i) q^{13} +4.00000i q^{14} +(-2.00000 - 4.00000i) q^{15} -1.00000 q^{16} +(5.00000 - 5.00000i) q^{17} +(-0.707107 + 0.707107i) q^{18} +4.24264 q^{19} +(-2.12132 - 0.707107i) q^{20} +8.00000 q^{21} +(2.82843 + 2.82843i) q^{22} +(-5.00000 - 5.00000i) q^{23} +2.00000i q^{24} +(-4.00000 - 3.00000i) q^{25} -2.82843i q^{26} +(-2.82843 - 2.82843i) q^{27} +(2.82843 - 2.82843i) q^{28} +4.24264 q^{29} +(-1.41421 + 4.24264i) q^{30} +8.00000 q^{31} +(0.707107 + 0.707107i) q^{32} +(5.65685 - 5.65685i) q^{33} -7.07107 q^{34} +(8.00000 - 4.00000i) q^{35} +1.00000 q^{36} +(-4.24264 - 4.24264i) q^{37} +(-3.00000 - 3.00000i) q^{38} -5.65685 q^{39} +(1.00000 + 2.00000i) q^{40} -12.0000 q^{41} +(-5.65685 - 5.65685i) q^{42} +(0.535534 - 6.53553i) q^{43} -4.00000i q^{44} +(2.12132 + 0.707107i) q^{45} +7.07107i q^{46} +(-5.00000 + 5.00000i) q^{47} +(1.41421 - 1.41421i) q^{48} +9.00000i q^{49} +(0.707107 + 4.94975i) q^{50} +14.1421i q^{51} +(-2.00000 + 2.00000i) q^{52} +4.00000i q^{54} +(2.82843 - 8.48528i) q^{55} -4.00000 q^{56} +(-6.00000 + 6.00000i) q^{57} +(-3.00000 - 3.00000i) q^{58} +(4.00000 - 2.00000i) q^{60} -4.24264i q^{61} +(-5.65685 - 5.65685i) q^{62} +(-2.82843 + 2.82843i) q^{63} -1.00000i q^{64} +(-5.65685 + 2.82843i) q^{65} -8.00000 q^{66} +(-2.00000 + 2.00000i) q^{67} +(5.00000 + 5.00000i) q^{68} +14.1421 q^{69} +(-8.48528 - 2.82843i) q^{70} -5.65685i q^{71} +(-0.707107 - 0.707107i) q^{72} +(1.41421 - 1.41421i) q^{73} +6.00000i q^{74} +(9.89949 - 1.41421i) q^{75} +4.24264i q^{76} +(11.3137 + 11.3137i) q^{77} +(4.00000 + 4.00000i) q^{78} -10.0000i q^{79} +(0.707107 - 2.12132i) q^{80} +11.0000 q^{81} +(8.48528 + 8.48528i) q^{82} +(6.00000 + 6.00000i) q^{83} +8.00000i q^{84} +(7.07107 + 14.1421i) q^{85} +(-5.00000 + 4.24264i) q^{86} +(-6.00000 + 6.00000i) q^{87} +(-2.82843 + 2.82843i) q^{88} -14.1421 q^{89} +(-1.00000 - 2.00000i) q^{90} -11.3137i q^{91} +(5.00000 - 5.00000i) q^{92} +(-11.3137 + 11.3137i) q^{93} +7.07107 q^{94} +(-3.00000 + 9.00000i) q^{95} -2.00000 q^{96} +(9.00000 - 9.00000i) q^{97} +(6.36396 - 6.36396i) q^{98} +4.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 8 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 8 q^{6} + 8 q^{10} - 16 q^{11} + 8 q^{13} - 8 q^{15} - 4 q^{16} + 20 q^{17} + 32 q^{21} - 20 q^{23} - 16 q^{25} + 32 q^{31} + 32 q^{35} + 4 q^{36} - 12 q^{38} + 4 q^{40} - 48 q^{41} - 12 q^{43} - 20 q^{47} - 8 q^{52} - 16 q^{56} - 24 q^{57} - 12 q^{58} + 16 q^{60} - 32 q^{66} - 8 q^{67} + 20 q^{68} + 16 q^{78} + 44 q^{81} + 24 q^{83} - 20 q^{86} - 24 q^{87} - 4 q^{90} + 20 q^{92} - 12 q^{95} - 8 q^{96} + 36 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/430\mathbb{Z}\right)^\times\).

\(n\) \(87\) \(261\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 0.707107i −0.500000 0.500000i
\(3\) −1.41421 + 1.41421i −0.816497 + 0.816497i −0.985599 0.169102i \(-0.945913\pi\)
0.169102 + 0.985599i \(0.445913\pi\)
\(4\) 1.00000i 0.500000i
\(5\) −0.707107 + 2.12132i −0.316228 + 0.948683i
\(6\) 2.00000 0.816497
\(7\) −2.82843 2.82843i −1.06904 1.06904i −0.997433 0.0716124i \(-0.977186\pi\)
−0.0716124 0.997433i \(-0.522814\pi\)
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 1.00000i 0.333333i
\(10\) 2.00000 1.00000i 0.632456 0.316228i
\(11\) −4.00000 −1.20605 −0.603023 0.797724i \(-0.706037\pi\)
−0.603023 + 0.797724i \(0.706037\pi\)
\(12\) −1.41421 1.41421i −0.408248 0.408248i
\(13\) 2.00000 + 2.00000i 0.554700 + 0.554700i 0.927794 0.373094i \(-0.121703\pi\)
−0.373094 + 0.927794i \(0.621703\pi\)
\(14\) 4.00000i 1.06904i
\(15\) −2.00000 4.00000i −0.516398 1.03280i
\(16\) −1.00000 −0.250000
\(17\) 5.00000 5.00000i 1.21268 1.21268i 0.242536 0.970143i \(-0.422021\pi\)
0.970143 0.242536i \(-0.0779791\pi\)
\(18\) −0.707107 + 0.707107i −0.166667 + 0.166667i
\(19\) 4.24264 0.973329 0.486664 0.873589i \(-0.338214\pi\)
0.486664 + 0.873589i \(0.338214\pi\)
\(20\) −2.12132 0.707107i −0.474342 0.158114i
\(21\) 8.00000 1.74574
\(22\) 2.82843 + 2.82843i 0.603023 + 0.603023i
\(23\) −5.00000 5.00000i −1.04257 1.04257i −0.999053 0.0435195i \(-0.986143\pi\)
−0.0435195 0.999053i \(-0.513857\pi\)
\(24\) 2.00000i 0.408248i
\(25\) −4.00000 3.00000i −0.800000 0.600000i
\(26\) 2.82843i 0.554700i
\(27\) −2.82843 2.82843i −0.544331 0.544331i
\(28\) 2.82843 2.82843i 0.534522 0.534522i
\(29\) 4.24264 0.787839 0.393919 0.919145i \(-0.371119\pi\)
0.393919 + 0.919145i \(0.371119\pi\)
\(30\) −1.41421 + 4.24264i −0.258199 + 0.774597i
\(31\) 8.00000 1.43684 0.718421 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) 5.65685 5.65685i 0.984732 0.984732i
\(34\) −7.07107 −1.21268
\(35\) 8.00000 4.00000i 1.35225 0.676123i
\(36\) 1.00000 0.166667
\(37\) −4.24264 4.24264i −0.697486 0.697486i 0.266382 0.963868i \(-0.414172\pi\)
−0.963868 + 0.266382i \(0.914172\pi\)
\(38\) −3.00000 3.00000i −0.486664 0.486664i
\(39\) −5.65685 −0.905822
\(40\) 1.00000 + 2.00000i 0.158114 + 0.316228i
\(41\) −12.0000 −1.87409 −0.937043 0.349215i \(-0.886448\pi\)
−0.937043 + 0.349215i \(0.886448\pi\)
\(42\) −5.65685 5.65685i −0.872872 0.872872i
\(43\) 0.535534 6.53553i 0.0816682 0.996660i
\(44\) 4.00000i 0.603023i
\(45\) 2.12132 + 0.707107i 0.316228 + 0.105409i
\(46\) 7.07107i 1.04257i
\(47\) −5.00000 + 5.00000i −0.729325 + 0.729325i −0.970485 0.241160i \(-0.922472\pi\)
0.241160 + 0.970485i \(0.422472\pi\)
\(48\) 1.41421 1.41421i 0.204124 0.204124i
\(49\) 9.00000i 1.28571i
\(50\) 0.707107 + 4.94975i 0.100000 + 0.700000i
\(51\) 14.1421i 1.98030i
\(52\) −2.00000 + 2.00000i −0.277350 + 0.277350i
\(53\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(54\) 4.00000i 0.544331i
\(55\) 2.82843 8.48528i 0.381385 1.14416i
\(56\) −4.00000 −0.534522
\(57\) −6.00000 + 6.00000i −0.794719 + 0.794719i
\(58\) −3.00000 3.00000i −0.393919 0.393919i
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 4.00000 2.00000i 0.516398 0.258199i
\(61\) 4.24264i 0.543214i −0.962408 0.271607i \(-0.912445\pi\)
0.962408 0.271607i \(-0.0875552\pi\)
\(62\) −5.65685 5.65685i −0.718421 0.718421i
\(63\) −2.82843 + 2.82843i −0.356348 + 0.356348i
\(64\) 1.00000i 0.125000i
\(65\) −5.65685 + 2.82843i −0.701646 + 0.350823i
\(66\) −8.00000 −0.984732
\(67\) −2.00000 + 2.00000i −0.244339 + 0.244339i −0.818642 0.574304i \(-0.805273\pi\)
0.574304 + 0.818642i \(0.305273\pi\)
\(68\) 5.00000 + 5.00000i 0.606339 + 0.606339i
\(69\) 14.1421 1.70251
\(70\) −8.48528 2.82843i −1.01419 0.338062i
\(71\) 5.65685i 0.671345i −0.941979 0.335673i \(-0.891036\pi\)
0.941979 0.335673i \(-0.108964\pi\)
\(72\) −0.707107 0.707107i −0.0833333 0.0833333i
\(73\) 1.41421 1.41421i 0.165521 0.165521i −0.619486 0.785007i \(-0.712659\pi\)
0.785007 + 0.619486i \(0.212659\pi\)
\(74\) 6.00000i 0.697486i
\(75\) 9.89949 1.41421i 1.14310 0.163299i
\(76\) 4.24264i 0.486664i
\(77\) 11.3137 + 11.3137i 1.28932 + 1.28932i
\(78\) 4.00000 + 4.00000i 0.452911 + 0.452911i
\(79\) 10.0000i 1.12509i −0.826767 0.562544i \(-0.809823\pi\)
0.826767 0.562544i \(-0.190177\pi\)
\(80\) 0.707107 2.12132i 0.0790569 0.237171i
\(81\) 11.0000 1.22222
\(82\) 8.48528 + 8.48528i 0.937043 + 0.937043i
\(83\) 6.00000 + 6.00000i 0.658586 + 0.658586i 0.955045 0.296460i \(-0.0958061\pi\)
−0.296460 + 0.955045i \(0.595806\pi\)
\(84\) 8.00000i 0.872872i
\(85\) 7.07107 + 14.1421i 0.766965 + 1.53393i
\(86\) −5.00000 + 4.24264i −0.539164 + 0.457496i
\(87\) −6.00000 + 6.00000i −0.643268 + 0.643268i
\(88\) −2.82843 + 2.82843i −0.301511 + 0.301511i
\(89\) −14.1421 −1.49906 −0.749532 0.661968i \(-0.769721\pi\)
−0.749532 + 0.661968i \(0.769721\pi\)
\(90\) −1.00000 2.00000i −0.105409 0.210819i
\(91\) 11.3137i 1.18600i
\(92\) 5.00000 5.00000i 0.521286 0.521286i
\(93\) −11.3137 + 11.3137i −1.17318 + 1.17318i
\(94\) 7.07107 0.729325
\(95\) −3.00000 + 9.00000i −0.307794 + 0.923381i
\(96\) −2.00000 −0.204124
\(97\) 9.00000 9.00000i 0.913812 0.913812i −0.0827581 0.996570i \(-0.526373\pi\)
0.996570 + 0.0827581i \(0.0263729\pi\)
\(98\) 6.36396 6.36396i 0.642857 0.642857i
\(99\) 4.00000i 0.402015i
\(100\) 3.00000 4.00000i 0.300000 0.400000i
\(101\) 2.00000 0.199007 0.0995037 0.995037i \(-0.468274\pi\)
0.0995037 + 0.995037i \(0.468274\pi\)
\(102\) 10.0000 10.0000i 0.990148 0.990148i
\(103\) −9.00000 9.00000i −0.886796 0.886796i 0.107418 0.994214i \(-0.465742\pi\)
−0.994214 + 0.107418i \(0.965742\pi\)
\(104\) 2.82843 0.277350
\(105\) −5.65685 + 16.9706i −0.552052 + 1.65616i
\(106\) 0 0
\(107\) −12.0000 + 12.0000i −1.16008 + 1.16008i −0.175627 + 0.984457i \(0.556195\pi\)
−0.984457 + 0.175627i \(0.943805\pi\)
\(108\) 2.82843 2.82843i 0.272166 0.272166i
\(109\) 2.00000i 0.191565i −0.995402 0.0957826i \(-0.969465\pi\)
0.995402 0.0957826i \(-0.0305354\pi\)
\(110\) −8.00000 + 4.00000i −0.762770 + 0.381385i
\(111\) 12.0000 1.13899
\(112\) 2.82843 + 2.82843i 0.267261 + 0.267261i
\(113\) −7.07107 + 7.07107i −0.665190 + 0.665190i −0.956599 0.291409i \(-0.905876\pi\)
0.291409 + 0.956599i \(0.405876\pi\)
\(114\) 8.48528 0.794719
\(115\) 14.1421 7.07107i 1.31876 0.659380i
\(116\) 4.24264i 0.393919i
\(117\) 2.00000 2.00000i 0.184900 0.184900i
\(118\) 0 0
\(119\) −28.2843 −2.59281
\(120\) −4.24264 1.41421i −0.387298 0.129099i
\(121\) 5.00000 0.454545
\(122\) −3.00000 + 3.00000i −0.271607 + 0.271607i
\(123\) 16.9706 16.9706i 1.53018 1.53018i
\(124\) 8.00000i 0.718421i
\(125\) 9.19239 6.36396i 0.822192 0.569210i
\(126\) 4.00000 0.356348
\(127\) −5.00000 + 5.00000i −0.443678 + 0.443678i −0.893246 0.449568i \(-0.851578\pi\)
0.449568 + 0.893246i \(0.351578\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) 8.48528 + 10.0000i 0.747087 + 0.880451i
\(130\) 6.00000 + 2.00000i 0.526235 + 0.175412i
\(131\) 1.41421i 0.123560i 0.998090 + 0.0617802i \(0.0196778\pi\)
−0.998090 + 0.0617802i \(0.980322\pi\)
\(132\) 5.65685 + 5.65685i 0.492366 + 0.492366i
\(133\) −12.0000 12.0000i −1.04053 1.04053i
\(134\) 2.82843 0.244339
\(135\) 8.00000 4.00000i 0.688530 0.344265i
\(136\) 7.07107i 0.606339i
\(137\) 7.07107 + 7.07107i 0.604122 + 0.604122i 0.941404 0.337282i \(-0.109507\pi\)
−0.337282 + 0.941404i \(0.609507\pi\)
\(138\) −10.0000 10.0000i −0.851257 0.851257i
\(139\) 4.00000i 0.339276i 0.985506 + 0.169638i \(0.0542598\pi\)
−0.985506 + 0.169638i \(0.945740\pi\)
\(140\) 4.00000 + 8.00000i 0.338062 + 0.676123i
\(141\) 14.1421i 1.19098i
\(142\) −4.00000 + 4.00000i −0.335673 + 0.335673i
\(143\) −8.00000 8.00000i −0.668994 0.668994i
\(144\) 1.00000i 0.0833333i
\(145\) −3.00000 + 9.00000i −0.249136 + 0.747409i
\(146\) −2.00000 −0.165521
\(147\) −12.7279 12.7279i −1.04978 1.04978i
\(148\) 4.24264 4.24264i 0.348743 0.348743i
\(149\) −9.89949 −0.810998 −0.405499 0.914095i \(-0.632902\pi\)
−0.405499 + 0.914095i \(0.632902\pi\)
\(150\) −8.00000 6.00000i −0.653197 0.489898i
\(151\) 8.48528i 0.690522i 0.938507 + 0.345261i \(0.112210\pi\)
−0.938507 + 0.345261i \(0.887790\pi\)
\(152\) 3.00000 3.00000i 0.243332 0.243332i
\(153\) −5.00000 5.00000i −0.404226 0.404226i
\(154\) 16.0000i 1.28932i
\(155\) −5.65685 + 16.9706i −0.454369 + 1.36311i
\(156\) 5.65685i 0.452911i
\(157\) −1.41421 1.41421i −0.112867 0.112867i 0.648418 0.761285i \(-0.275431\pi\)
−0.761285 + 0.648418i \(0.775431\pi\)
\(158\) −7.07107 + 7.07107i −0.562544 + 0.562544i
\(159\) 0 0
\(160\) −2.00000 + 1.00000i −0.158114 + 0.0790569i
\(161\) 28.2843i 2.22911i
\(162\) −7.77817 7.77817i −0.611111 0.611111i
\(163\) 2.82843 2.82843i 0.221540 0.221540i −0.587607 0.809146i \(-0.699930\pi\)
0.809146 + 0.587607i \(0.199930\pi\)
\(164\) 12.0000i 0.937043i
\(165\) 8.00000 + 16.0000i 0.622799 + 1.24560i
\(166\) 8.48528i 0.658586i
\(167\) 11.0000 11.0000i 0.851206 0.851206i −0.139076 0.990282i \(-0.544413\pi\)
0.990282 + 0.139076i \(0.0444133\pi\)
\(168\) 5.65685 5.65685i 0.436436 0.436436i
\(169\) 5.00000i 0.384615i
\(170\) 5.00000 15.0000i 0.383482 1.15045i
\(171\) 4.24264i 0.324443i
\(172\) 6.53553 + 0.535534i 0.498330 + 0.0408341i
\(173\) −16.0000 16.0000i −1.21646 1.21646i −0.968864 0.247593i \(-0.920360\pi\)
−0.247593 0.968864i \(-0.579640\pi\)
\(174\) 8.48528 0.643268
\(175\) 2.82843 + 19.7990i 0.213809 + 1.49666i
\(176\) 4.00000 0.301511
\(177\) 0 0
\(178\) 10.0000 + 10.0000i 0.749532 + 0.749532i
\(179\) −1.41421 −0.105703 −0.0528516 0.998602i \(-0.516831\pi\)
−0.0528516 + 0.998602i \(0.516831\pi\)
\(180\) −0.707107 + 2.12132i −0.0527046 + 0.158114i
\(181\) 6.00000 0.445976 0.222988 0.974821i \(-0.428419\pi\)
0.222988 + 0.974821i \(0.428419\pi\)
\(182\) −8.00000 + 8.00000i −0.592999 + 0.592999i
\(183\) 6.00000 + 6.00000i 0.443533 + 0.443533i
\(184\) −7.07107 −0.521286
\(185\) 12.0000 6.00000i 0.882258 0.441129i
\(186\) 16.0000 1.17318
\(187\) −20.0000 + 20.0000i −1.46254 + 1.46254i
\(188\) −5.00000 5.00000i −0.364662 0.364662i
\(189\) 16.0000i 1.16383i
\(190\) 8.48528 4.24264i 0.615587 0.307794i
\(191\) 19.7990i 1.43260i −0.697790 0.716302i \(-0.745833\pi\)
0.697790 0.716302i \(-0.254167\pi\)
\(192\) 1.41421 + 1.41421i 0.102062 + 0.102062i
\(193\) 11.0000 + 11.0000i 0.791797 + 0.791797i 0.981786 0.189989i \(-0.0608452\pi\)
−0.189989 + 0.981786i \(0.560845\pi\)
\(194\) −12.7279 −0.913812
\(195\) 4.00000 12.0000i 0.286446 0.859338i
\(196\) −9.00000 −0.642857
\(197\) 2.00000 2.00000i 0.142494 0.142494i −0.632261 0.774755i \(-0.717873\pi\)
0.774755 + 0.632261i \(0.217873\pi\)
\(198\) 2.82843 2.82843i 0.201008 0.201008i
\(199\) −11.3137 −0.802008 −0.401004 0.916076i \(-0.631339\pi\)
−0.401004 + 0.916076i \(0.631339\pi\)
\(200\) −4.94975 + 0.707107i −0.350000 + 0.0500000i
\(201\) 5.65685i 0.399004i
\(202\) −1.41421 1.41421i −0.0995037 0.0995037i
\(203\) −12.0000 12.0000i −0.842235 0.842235i
\(204\) −14.1421 −0.990148
\(205\) 8.48528 25.4558i 0.592638 1.77791i
\(206\) 12.7279i 0.886796i
\(207\) −5.00000 + 5.00000i −0.347524 + 0.347524i
\(208\) −2.00000 2.00000i −0.138675 0.138675i
\(209\) −16.9706 −1.17388
\(210\) 16.0000 8.00000i 1.10410 0.552052i
\(211\) 12.7279i 0.876226i −0.898920 0.438113i \(-0.855647\pi\)
0.898920 0.438113i \(-0.144353\pi\)
\(212\) 0 0
\(213\) 8.00000 + 8.00000i 0.548151 + 0.548151i
\(214\) 16.9706 1.16008
\(215\) 13.4853 + 5.75736i 0.919689 + 0.392649i
\(216\) −4.00000 −0.272166
\(217\) −22.6274 22.6274i −1.53605 1.53605i
\(218\) −1.41421 + 1.41421i −0.0957826 + 0.0957826i
\(219\) 4.00000i 0.270295i
\(220\) 8.48528 + 2.82843i 0.572078 + 0.190693i
\(221\) 20.0000 1.34535
\(222\) −8.48528 8.48528i −0.569495 0.569495i
\(223\) −14.1421 + 14.1421i −0.947027 + 0.947027i −0.998666 0.0516384i \(-0.983556\pi\)
0.0516384 + 0.998666i \(0.483556\pi\)
\(224\) 4.00000i 0.267261i
\(225\) −3.00000 + 4.00000i −0.200000 + 0.266667i
\(226\) 10.0000 0.665190
\(227\) −14.1421 14.1421i −0.938647 0.938647i 0.0595772 0.998224i \(-0.481025\pi\)
−0.998224 + 0.0595772i \(0.981025\pi\)
\(228\) −6.00000 6.00000i −0.397360 0.397360i
\(229\) 26.0000i 1.71813i −0.511868 0.859064i \(-0.671046\pi\)
0.511868 0.859064i \(-0.328954\pi\)
\(230\) −15.0000 5.00000i −0.989071 0.329690i
\(231\) −32.0000 −2.10545
\(232\) 3.00000 3.00000i 0.196960 0.196960i
\(233\) −9.89949 + 9.89949i −0.648537 + 0.648537i −0.952639 0.304102i \(-0.901644\pi\)
0.304102 + 0.952639i \(0.401644\pi\)
\(234\) −2.82843 −0.184900
\(235\) −7.07107 14.1421i −0.461266 0.922531i
\(236\) 0 0
\(237\) 14.1421 + 14.1421i 0.918630 + 0.918630i
\(238\) 20.0000 + 20.0000i 1.29641 + 1.29641i
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 2.00000 + 4.00000i 0.129099 + 0.258199i
\(241\) 16.9706i 1.09317i −0.837404 0.546585i \(-0.815928\pi\)
0.837404 0.546585i \(-0.184072\pi\)
\(242\) −3.53553 3.53553i −0.227273 0.227273i
\(243\) −7.07107 + 7.07107i −0.453609 + 0.453609i
\(244\) 4.24264 0.271607
\(245\) −19.0919 6.36396i −1.21974 0.406579i
\(246\) −24.0000 −1.53018
\(247\) 8.48528 + 8.48528i 0.539906 + 0.539906i
\(248\) 5.65685 5.65685i 0.359211 0.359211i
\(249\) −16.9706 −1.07547
\(250\) −11.0000 2.00000i −0.695701 0.126491i
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) −2.82843 2.82843i −0.178174 0.178174i
\(253\) 20.0000 + 20.0000i 1.25739 + 1.25739i
\(254\) 7.07107 0.443678
\(255\) −30.0000 10.0000i −1.87867 0.626224i
\(256\) 1.00000 0.0625000
\(257\) −4.24264 4.24264i −0.264649 0.264649i 0.562291 0.826940i \(-0.309920\pi\)
−0.826940 + 0.562291i \(0.809920\pi\)
\(258\) 1.07107 13.0711i 0.0666818 0.813769i
\(259\) 24.0000i 1.49129i
\(260\) −2.82843 5.65685i −0.175412 0.350823i
\(261\) 4.24264i 0.262613i
\(262\) 1.00000 1.00000i 0.0617802 0.0617802i
\(263\) 16.9706 16.9706i 1.04645 1.04645i 0.0475824 0.998867i \(-0.484848\pi\)
0.998867 0.0475824i \(-0.0151517\pi\)
\(264\) 8.00000i 0.492366i
\(265\) 0 0
\(266\) 16.9706i 1.04053i
\(267\) 20.0000 20.0000i 1.22398 1.22398i
\(268\) −2.00000 2.00000i −0.122169 0.122169i
\(269\) 6.00000i 0.365826i −0.983129 0.182913i \(-0.941447\pi\)
0.983129 0.182913i \(-0.0585527\pi\)
\(270\) −8.48528 2.82843i −0.516398 0.172133i
\(271\) 8.00000 0.485965 0.242983 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) −5.00000 + 5.00000i −0.303170 + 0.303170i
\(273\) 16.0000 + 16.0000i 0.968364 + 0.968364i
\(274\) 10.0000i 0.604122i
\(275\) 16.0000 + 12.0000i 0.964836 + 0.723627i
\(276\) 14.1421i 0.851257i
\(277\) 5.65685 + 5.65685i 0.339887 + 0.339887i 0.856325 0.516437i \(-0.172742\pi\)
−0.516437 + 0.856325i \(0.672742\pi\)
\(278\) 2.82843 2.82843i 0.169638 0.169638i
\(279\) 8.00000i 0.478947i
\(280\) 2.82843 8.48528i 0.169031 0.507093i
\(281\) 10.0000 0.596550 0.298275 0.954480i \(-0.403589\pi\)
0.298275 + 0.954480i \(0.403589\pi\)
\(282\) −10.0000 + 10.0000i −0.595491 + 0.595491i
\(283\) 6.00000 + 6.00000i 0.356663 + 0.356663i 0.862581 0.505918i \(-0.168846\pi\)
−0.505918 + 0.862581i \(0.668846\pi\)
\(284\) 5.65685 0.335673
\(285\) −8.48528 16.9706i −0.502625 1.00525i
\(286\) 11.3137i 0.668994i
\(287\) 33.9411 + 33.9411i 2.00348 + 2.00348i
\(288\) 0.707107 0.707107i 0.0416667 0.0416667i
\(289\) 33.0000i 1.94118i
\(290\) 8.48528 4.24264i 0.498273 0.249136i
\(291\) 25.4558i 1.49225i
\(292\) 1.41421 + 1.41421i 0.0827606 + 0.0827606i
\(293\) −10.0000 10.0000i −0.584206 0.584206i 0.351850 0.936056i \(-0.385553\pi\)
−0.936056 + 0.351850i \(0.885553\pi\)
\(294\) 18.0000i 1.04978i
\(295\) 0 0
\(296\) −6.00000 −0.348743
\(297\) 11.3137 + 11.3137i 0.656488 + 0.656488i
\(298\) 7.00000 + 7.00000i 0.405499 + 0.405499i
\(299\) 20.0000i 1.15663i
\(300\) 1.41421 + 9.89949i 0.0816497 + 0.571548i
\(301\) −20.0000 + 16.9706i −1.15278 + 0.978167i
\(302\) 6.00000 6.00000i 0.345261 0.345261i
\(303\) −2.82843 + 2.82843i −0.162489 + 0.162489i
\(304\) −4.24264 −0.243332
\(305\) 9.00000 + 3.00000i 0.515339 + 0.171780i
\(306\) 7.07107i 0.404226i
\(307\) −16.0000 + 16.0000i −0.913168 + 0.913168i −0.996520 0.0833519i \(-0.973437\pi\)
0.0833519 + 0.996520i \(0.473437\pi\)
\(308\) −11.3137 + 11.3137i −0.644658 + 0.644658i
\(309\) 25.4558 1.44813
\(310\) 16.0000 8.00000i 0.908739 0.454369i
\(311\) 2.00000 0.113410 0.0567048 0.998391i \(-0.481941\pi\)
0.0567048 + 0.998391i \(0.481941\pi\)
\(312\) −4.00000 + 4.00000i −0.226455 + 0.226455i
\(313\) −7.07107 + 7.07107i −0.399680 + 0.399680i −0.878120 0.478440i \(-0.841202\pi\)
0.478440 + 0.878120i \(0.341202\pi\)
\(314\) 2.00000i 0.112867i
\(315\) −4.00000 8.00000i −0.225374 0.450749i
\(316\) 10.0000 0.562544
\(317\) 8.00000 8.00000i 0.449325 0.449325i −0.445805 0.895130i \(-0.647083\pi\)
0.895130 + 0.445805i \(0.147083\pi\)
\(318\) 0 0
\(319\) −16.9706 −0.950169
\(320\) 2.12132 + 0.707107i 0.118585 + 0.0395285i
\(321\) 33.9411i 1.89441i
\(322\) 20.0000 20.0000i 1.11456 1.11456i
\(323\) 21.2132 21.2132i 1.18033 1.18033i
\(324\) 11.0000i 0.611111i
\(325\) −2.00000 14.0000i −0.110940 0.776580i
\(326\) −4.00000 −0.221540
\(327\) 2.82843 + 2.82843i 0.156412 + 0.156412i
\(328\) −8.48528 + 8.48528i −0.468521 + 0.468521i
\(329\) 28.2843 1.55936
\(330\) 5.65685 16.9706i 0.311400 0.934199i
\(331\) 26.8701i 1.47691i 0.674302 + 0.738456i \(0.264445\pi\)
−0.674302 + 0.738456i \(0.735555\pi\)
\(332\) −6.00000 + 6.00000i −0.329293 + 0.329293i
\(333\) −4.24264 + 4.24264i −0.232495 + 0.232495i
\(334\) −15.5563 −0.851206
\(335\) −2.82843 5.65685i −0.154533 0.309067i
\(336\) −8.00000 −0.436436
\(337\) 9.00000 9.00000i 0.490261 0.490261i −0.418127 0.908388i \(-0.637313\pi\)
0.908388 + 0.418127i \(0.137313\pi\)
\(338\) −3.53553 + 3.53553i −0.192308 + 0.192308i
\(339\) 20.0000i 1.08625i
\(340\) −14.1421 + 7.07107i −0.766965 + 0.383482i
\(341\) −32.0000 −1.73290
\(342\) −3.00000 + 3.00000i −0.162221 + 0.162221i
\(343\) 5.65685 5.65685i 0.305441 0.305441i
\(344\) −4.24264 5.00000i −0.228748 0.269582i
\(345\) −10.0000 + 30.0000i −0.538382 + 1.61515i
\(346\) 22.6274i 1.21646i
\(347\) 8.48528 + 8.48528i 0.455514 + 0.455514i 0.897180 0.441666i \(-0.145612\pi\)
−0.441666 + 0.897180i \(0.645612\pi\)
\(348\) −6.00000 6.00000i −0.321634 0.321634i
\(349\) 4.24264 0.227103 0.113552 0.993532i \(-0.463777\pi\)
0.113552 + 0.993532i \(0.463777\pi\)
\(350\) 12.0000 16.0000i 0.641427 0.855236i
\(351\) 11.3137i 0.603881i
\(352\) −2.82843 2.82843i −0.150756 0.150756i
\(353\) 11.0000 + 11.0000i 0.585471 + 0.585471i 0.936401 0.350931i \(-0.114135\pi\)
−0.350931 + 0.936401i \(0.614135\pi\)
\(354\) 0 0
\(355\) 12.0000 + 4.00000i 0.636894 + 0.212298i
\(356\) 14.1421i 0.749532i
\(357\) 40.0000 40.0000i 2.11702 2.11702i
\(358\) 1.00000 + 1.00000i 0.0528516 + 0.0528516i
\(359\) 14.0000i 0.738892i −0.929252 0.369446i \(-0.879548\pi\)
0.929252 0.369446i \(-0.120452\pi\)
\(360\) 2.00000 1.00000i 0.105409 0.0527046i
\(361\) −1.00000 −0.0526316
\(362\) −4.24264 4.24264i −0.222988 0.222988i
\(363\) −7.07107 + 7.07107i −0.371135 + 0.371135i
\(364\) 11.3137 0.592999
\(365\) 2.00000 + 4.00000i 0.104685 + 0.209370i
\(366\) 8.48528i 0.443533i
\(367\) 1.00000 1.00000i 0.0521996 0.0521996i −0.680525 0.732725i \(-0.738248\pi\)
0.732725 + 0.680525i \(0.238248\pi\)
\(368\) 5.00000 + 5.00000i 0.260643 + 0.260643i
\(369\) 12.0000i 0.624695i
\(370\) −12.7279 4.24264i −0.661693 0.220564i
\(371\) 0 0
\(372\) −11.3137 11.3137i −0.586588 0.586588i
\(373\) −2.82843 + 2.82843i −0.146450 + 0.146450i −0.776530 0.630080i \(-0.783022\pi\)
0.630080 + 0.776530i \(0.283022\pi\)
\(374\) 28.2843 1.46254
\(375\) −4.00000 + 22.0000i −0.206559 + 1.13608i
\(376\) 7.07107i 0.364662i
\(377\) 8.48528 + 8.48528i 0.437014 + 0.437014i
\(378\) 11.3137 11.3137i 0.581914 0.581914i
\(379\) 28.0000i 1.43826i 0.694874 + 0.719132i \(0.255460\pi\)
−0.694874 + 0.719132i \(0.744540\pi\)
\(380\) −9.00000 3.00000i −0.461690 0.153897i
\(381\) 14.1421i 0.724524i
\(382\) −14.0000 + 14.0000i −0.716302 + 0.716302i
\(383\) −19.7990 + 19.7990i −1.01168 + 1.01168i −0.0117502 + 0.999931i \(0.503740\pi\)
−0.999931 + 0.0117502i \(0.996260\pi\)
\(384\) 2.00000i 0.102062i
\(385\) −32.0000 + 16.0000i −1.63087 + 0.815436i
\(386\) 15.5563i 0.791797i
\(387\) −6.53553 0.535534i −0.332220 0.0272227i
\(388\) 9.00000 + 9.00000i 0.456906 + 0.456906i
\(389\) 7.07107 0.358517 0.179259 0.983802i \(-0.442630\pi\)
0.179259 + 0.983802i \(0.442630\pi\)
\(390\) −11.3137 + 5.65685i −0.572892 + 0.286446i
\(391\) −50.0000 −2.52861
\(392\) 6.36396 + 6.36396i 0.321429 + 0.321429i
\(393\) −2.00000 2.00000i −0.100887 0.100887i
\(394\) −2.82843 −0.142494
\(395\) 21.2132 + 7.07107i 1.06735 + 0.355784i
\(396\) −4.00000 −0.201008
\(397\) −20.0000 + 20.0000i −1.00377 + 1.00377i −0.00377836 + 0.999993i \(0.501203\pi\)
−0.999993 + 0.00377836i \(0.998797\pi\)
\(398\) 8.00000 + 8.00000i 0.401004 + 0.401004i
\(399\) 33.9411 1.69918
\(400\) 4.00000 + 3.00000i 0.200000 + 0.150000i
\(401\) 16.0000 0.799002 0.399501 0.916733i \(-0.369183\pi\)
0.399501 + 0.916733i \(0.369183\pi\)
\(402\) −4.00000 + 4.00000i −0.199502 + 0.199502i
\(403\) 16.0000 + 16.0000i 0.797017 + 0.797017i
\(404\) 2.00000i 0.0995037i
\(405\) −7.77817 + 23.3345i −0.386501 + 1.15950i
\(406\) 16.9706i 0.842235i
\(407\) 16.9706 + 16.9706i 0.841200 + 0.841200i
\(408\) 10.0000 + 10.0000i 0.495074 + 0.495074i
\(409\) 31.1127 1.53842 0.769212 0.638994i \(-0.220649\pi\)
0.769212 + 0.638994i \(0.220649\pi\)
\(410\) −24.0000 + 12.0000i −1.18528 + 0.592638i
\(411\) −20.0000 −0.986527
\(412\) 9.00000 9.00000i 0.443398 0.443398i
\(413\) 0 0
\(414\) 7.07107 0.347524
\(415\) −16.9706 + 8.48528i −0.833052 + 0.416526i
\(416\) 2.82843i 0.138675i
\(417\) −5.65685 5.65685i −0.277017 0.277017i
\(418\) 12.0000 + 12.0000i 0.586939 + 0.586939i
\(419\) −4.24264 −0.207267 −0.103633 0.994616i \(-0.533047\pi\)
−0.103633 + 0.994616i \(0.533047\pi\)
\(420\) −16.9706 5.65685i −0.828079 0.276026i
\(421\) 9.89949i 0.482472i 0.970466 + 0.241236i \(0.0775528\pi\)
−0.970466 + 0.241236i \(0.922447\pi\)
\(422\) −9.00000 + 9.00000i −0.438113 + 0.438113i
\(423\) 5.00000 + 5.00000i 0.243108 + 0.243108i
\(424\) 0 0
\(425\) −35.0000 + 5.00000i −1.69775 + 0.242536i
\(426\) 11.3137i 0.548151i
\(427\) −12.0000 + 12.0000i −0.580721 + 0.580721i
\(428\) −12.0000 12.0000i −0.580042 0.580042i
\(429\) 22.6274 1.09246
\(430\) −5.46447 13.6066i −0.263520 0.656169i
\(431\) −24.0000 −1.15604 −0.578020 0.816023i \(-0.696174\pi\)
−0.578020 + 0.816023i \(0.696174\pi\)
\(432\) 2.82843 + 2.82843i 0.136083 + 0.136083i
\(433\) −9.89949 + 9.89949i −0.475739 + 0.475739i −0.903766 0.428027i \(-0.859209\pi\)
0.428027 + 0.903766i \(0.359209\pi\)
\(434\) 32.0000i 1.53605i
\(435\) −8.48528 16.9706i −0.406838 0.813676i
\(436\) 2.00000 0.0957826
\(437\) −21.2132 21.2132i −1.01477 1.01477i
\(438\) 2.82843 2.82843i 0.135147 0.135147i
\(439\) 6.00000i 0.286364i 0.989696 + 0.143182i \(0.0457335\pi\)
−0.989696 + 0.143182i \(0.954267\pi\)
\(440\) −4.00000 8.00000i −0.190693 0.381385i
\(441\) 9.00000 0.428571
\(442\) −14.1421 14.1421i −0.672673 0.672673i
\(443\) 10.0000 + 10.0000i 0.475114 + 0.475114i 0.903565 0.428451i \(-0.140940\pi\)
−0.428451 + 0.903565i \(0.640940\pi\)
\(444\) 12.0000i 0.569495i
\(445\) 10.0000 30.0000i 0.474045 1.42214i
\(446\) 20.0000 0.947027
\(447\) 14.0000 14.0000i 0.662177 0.662177i
\(448\) −2.82843 + 2.82843i −0.133631 + 0.133631i
\(449\) −36.7696 −1.73526 −0.867631 0.497208i \(-0.834358\pi\)
−0.867631 + 0.497208i \(0.834358\pi\)
\(450\) 4.94975 0.707107i 0.233333 0.0333333i
\(451\) 48.0000 2.26023
\(452\) −7.07107 7.07107i −0.332595 0.332595i
\(453\) −12.0000 12.0000i −0.563809 0.563809i
\(454\) 20.0000i 0.938647i
\(455\) 24.0000 + 8.00000i 1.12514 + 0.375046i
\(456\) 8.48528i 0.397360i
\(457\) 9.89949 + 9.89949i 0.463079 + 0.463079i 0.899663 0.436584i \(-0.143812\pi\)
−0.436584 + 0.899663i \(0.643812\pi\)
\(458\) −18.3848 + 18.3848i −0.859064 + 0.859064i
\(459\) −28.2843 −1.32020
\(460\) 7.07107 + 14.1421i 0.329690 + 0.659380i
\(461\) −6.00000 −0.279448 −0.139724 0.990190i \(-0.544622\pi\)
−0.139724 + 0.990190i \(0.544622\pi\)
\(462\) 22.6274 + 22.6274i 1.05272 + 1.05272i
\(463\) 16.9706 16.9706i 0.788689 0.788689i −0.192590 0.981279i \(-0.561689\pi\)
0.981279 + 0.192590i \(0.0616888\pi\)
\(464\) −4.24264 −0.196960
\(465\) −16.0000 32.0000i −0.741982 1.48396i
\(466\) 14.0000 0.648537
\(467\) −14.1421 14.1421i −0.654420 0.654420i 0.299634 0.954054i \(-0.403135\pi\)
−0.954054 + 0.299634i \(0.903135\pi\)
\(468\) 2.00000 + 2.00000i 0.0924500 + 0.0924500i
\(469\) 11.3137 0.522419
\(470\) −5.00000 + 15.0000i −0.230633 + 0.691898i
\(471\) 4.00000 0.184310
\(472\) 0 0
\(473\) −2.14214 + 26.1421i −0.0984955 + 1.20202i
\(474\) 20.0000i 0.918630i
\(475\) −16.9706 12.7279i −0.778663 0.583997i
\(476\) 28.2843i 1.29641i
\(477\) 0 0
\(478\) 0 0
\(479\) 6.00000i 0.274147i 0.990561 + 0.137073i \(0.0437697\pi\)
−0.990561 + 0.137073i \(0.956230\pi\)
\(480\) 1.41421 4.24264i 0.0645497 0.193649i
\(481\) 16.9706i 0.773791i
\(482\) −12.0000 + 12.0000i −0.546585 + 0.546585i
\(483\) −40.0000 40.0000i −1.82006 1.82006i
\(484\) 5.00000i 0.227273i
\(485\) 12.7279 + 25.4558i 0.577945 + 1.15589i
\(486\) 10.0000 0.453609
\(487\) 1.00000 1.00000i 0.0453143 0.0453143i −0.684087 0.729401i \(-0.739799\pi\)
0.729401 + 0.684087i \(0.239799\pi\)
\(488\) −3.00000 3.00000i −0.135804 0.135804i
\(489\) 8.00000i 0.361773i
\(490\) 9.00000 + 18.0000i 0.406579 + 0.813157i
\(491\) 1.41421i 0.0638226i −0.999491 0.0319113i \(-0.989841\pi\)
0.999491 0.0319113i \(-0.0101594\pi\)
\(492\) 16.9706 + 16.9706i 0.765092 + 0.765092i
\(493\) 21.2132 21.2132i 0.955395 0.955395i
\(494\) 12.0000i 0.539906i
\(495\) −8.48528 2.82843i −0.381385 0.127128i
\(496\) −8.00000 −0.359211
\(497\) −16.0000 + 16.0000i −0.717698 + 0.717698i
\(498\) 12.0000 + 12.0000i 0.537733 + 0.537733i
\(499\) 12.7279 0.569780 0.284890 0.958560i \(-0.408043\pi\)
0.284890 + 0.958560i \(0.408043\pi\)
\(500\) 6.36396 + 9.19239i 0.284605 + 0.411096i
\(501\) 31.1127i 1.39001i
\(502\) −8.48528 8.48528i −0.378717 0.378717i
\(503\) 5.65685 5.65685i 0.252227 0.252227i −0.569656 0.821883i \(-0.692924\pi\)
0.821883 + 0.569656i \(0.192924\pi\)
\(504\) 4.00000i 0.178174i
\(505\) −1.41421 + 4.24264i −0.0629317 + 0.188795i
\(506\) 28.2843i 1.25739i
\(507\) 7.07107 + 7.07107i 0.314037 + 0.314037i
\(508\) −5.00000 5.00000i −0.221839 0.221839i
\(509\) 6.00000i 0.265945i 0.991120 + 0.132973i \(0.0424523\pi\)
−0.991120 + 0.132973i \(0.957548\pi\)
\(510\) 14.1421 + 28.2843i 0.626224 + 1.25245i
\(511\) −8.00000 −0.353899
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) −12.0000 12.0000i −0.529813 0.529813i
\(514\) 6.00000i 0.264649i
\(515\) 25.4558 12.7279i 1.12172 0.560859i
\(516\) −10.0000 + 8.48528i −0.440225 + 0.373544i
\(517\) 20.0000 20.0000i 0.879599 0.879599i
\(518\) 16.9706 16.9706i 0.745644 0.745644i
\(519\) 45.2548 1.98647
\(520\) −2.00000 + 6.00000i −0.0877058 + 0.263117i
\(521\) 19.7990i 0.867409i 0.901055 + 0.433705i \(0.142794\pi\)
−0.901055 + 0.433705i \(0.857206\pi\)
\(522\) −3.00000 + 3.00000i −0.131306 + 0.131306i
\(523\) 8.48528 8.48528i 0.371035 0.371035i −0.496819 0.867854i \(-0.665499\pi\)
0.867854 + 0.496819i \(0.165499\pi\)
\(524\) −1.41421 −0.0617802
\(525\) −32.0000 24.0000i −1.39659 1.04745i
\(526\) −24.0000 −1.04645
\(527\) 40.0000 40.0000i 1.74243 1.74243i
\(528\) −5.65685 + 5.65685i −0.246183 + 0.246183i
\(529\) 27.0000i 1.17391i
\(530\) 0 0
\(531\) 0 0
\(532\) 12.0000 12.0000i 0.520266 0.520266i
\(533\) −24.0000 24.0000i −1.03956 1.03956i
\(534\) −28.2843 −1.22398
\(535\) −16.9706 33.9411i −0.733701 1.46740i
\(536\) 2.82843i 0.122169i
\(537\) 2.00000 2.00000i 0.0863064 0.0863064i
\(538\) −4.24264 + 4.24264i −0.182913 + 0.182913i
\(539\) 36.0000i 1.55063i
\(540\) 4.00000 + 8.00000i 0.172133 + 0.344265i
\(541\) −10.0000 −0.429934 −0.214967 0.976621i \(-0.568964\pi\)
−0.214967 + 0.976621i \(0.568964\pi\)
\(542\) −5.65685 5.65685i −0.242983 0.242983i
\(543\) −8.48528 + 8.48528i −0.364138 + 0.364138i
\(544\) 7.07107 0.303170
\(545\) 4.24264 + 1.41421i 0.181735 + 0.0605783i
\(546\) 22.6274i 0.968364i
\(547\) 16.0000 16.0000i 0.684111 0.684111i −0.276813 0.960924i \(-0.589278\pi\)
0.960924 + 0.276813i \(0.0892783\pi\)
\(548\) −7.07107 + 7.07107i −0.302061 + 0.302061i
\(549\) −4.24264 −0.181071
\(550\) −2.82843 19.7990i −0.120605 0.844232i
\(551\) 18.0000 0.766826
\(552\) 10.0000 10.0000i 0.425628 0.425628i
\(553\) −28.2843 + 28.2843i −1.20277 + 1.20277i
\(554\) 8.00000i 0.339887i
\(555\) −8.48528 + 25.4558i −0.360180 + 1.08054i
\(556\) −4.00000 −0.169638
\(557\) −10.0000 + 10.0000i −0.423714 + 0.423714i −0.886480 0.462767i \(-0.846857\pi\)
0.462767 + 0.886480i \(0.346857\pi\)
\(558\) −5.65685 + 5.65685i −0.239474 + 0.239474i
\(559\) 14.1421 12.0000i 0.598149 0.507546i
\(560\) −8.00000 + 4.00000i −0.338062 + 0.169031i
\(561\) 56.5685i 2.38833i
\(562\) −7.07107 7.07107i −0.298275 0.298275i
\(563\) −14.0000 14.0000i −0.590030 0.590030i 0.347610 0.937639i \(-0.386993\pi\)
−0.937639 + 0.347610i \(0.886993\pi\)
\(564\) 14.1421 0.595491
\(565\) −10.0000 20.0000i −0.420703 0.841406i
\(566\) 8.48528i 0.356663i
\(567\) −31.1127 31.1127i −1.30661 1.30661i
\(568\) −4.00000 4.00000i −0.167836 0.167836i
\(569\) 32.0000i 1.34151i 0.741679 + 0.670755i \(0.234030\pi\)
−0.741679 + 0.670755i \(0.765970\pi\)
\(570\) −6.00000 + 18.0000i −0.251312 + 0.753937i
\(571\) 7.07107i 0.295915i 0.988994 + 0.147957i \(0.0472699\pi\)
−0.988994 + 0.147957i \(0.952730\pi\)
\(572\) 8.00000 8.00000i 0.334497 0.334497i
\(573\) 28.0000 + 28.0000i 1.16972 + 1.16972i
\(574\) 48.0000i 2.00348i
\(575\) 5.00000 + 35.0000i 0.208514 + 1.45960i
\(576\) −1.00000 −0.0416667
\(577\) −15.5563 15.5563i −0.647619 0.647619i 0.304798 0.952417i \(-0.401411\pi\)
−0.952417 + 0.304798i \(0.901411\pi\)
\(578\) −23.3345 + 23.3345i −0.970588 + 0.970588i
\(579\) −31.1127 −1.29300
\(580\) −9.00000 3.00000i −0.373705 0.124568i
\(581\) 33.9411i 1.40812i
\(582\) 18.0000 18.0000i 0.746124 0.746124i
\(583\) 0 0
\(584\) 2.00000i 0.0827606i
\(585\) 2.82843 + 5.65685i 0.116941 + 0.233882i
\(586\) 14.1421i 0.584206i
\(587\) 29.6985 + 29.6985i 1.22579 + 1.22579i 0.965543 + 0.260245i \(0.0838034\pi\)
0.260245 + 0.965543i \(0.416197\pi\)
\(588\) 12.7279 12.7279i 0.524891 0.524891i
\(589\) 33.9411 1.39852
\(590\) 0 0
\(591\) 5.65685i 0.232692i
\(592\) 4.24264 + 4.24264i 0.174371 + 0.174371i
\(593\) −4.24264 + 4.24264i −0.174224 + 0.174224i −0.788833 0.614608i \(-0.789314\pi\)
0.614608 + 0.788833i \(0.289314\pi\)
\(594\) 16.0000i 0.656488i
\(595\) 20.0000 60.0000i 0.819920 2.45976i
\(596\) 9.89949i 0.405499i
\(597\) 16.0000 16.0000i 0.654836 0.654836i
\(598\) −14.1421 + 14.1421i −0.578315 + 0.578315i
\(599\) 30.0000i 1.22577i −0.790173 0.612883i \(-0.790010\pi\)
0.790173 0.612883i \(-0.209990\pi\)
\(600\) 6.00000 8.00000i 0.244949 0.326599i
\(601\) 8.48528i 0.346122i −0.984911 0.173061i \(-0.944634\pi\)
0.984911 0.173061i \(-0.0553658\pi\)
\(602\) 26.1421 + 2.14214i 1.06547 + 0.0873069i
\(603\) 2.00000 + 2.00000i 0.0814463 + 0.0814463i
\(604\) −8.48528 −0.345261
\(605\) −3.53553 + 10.6066i −0.143740 + 0.431220i
\(606\) 4.00000 0.162489
\(607\) 5.65685 + 5.65685i 0.229605 + 0.229605i 0.812527 0.582923i \(-0.198091\pi\)
−0.582923 + 0.812527i \(0.698091\pi\)
\(608\) 3.00000 + 3.00000i 0.121666 + 0.121666i
\(609\) 33.9411 1.37536
\(610\) −4.24264 8.48528i −0.171780 0.343559i
\(611\) −20.0000 −0.809113
\(612\) 5.00000 5.00000i 0.202113 0.202113i
\(613\) 8.00000 + 8.00000i 0.323117 + 0.323117i 0.849962 0.526845i \(-0.176625\pi\)
−0.526845 + 0.849962i \(0.676625\pi\)
\(614\) 22.6274 0.913168
\(615\) 24.0000 + 48.0000i 0.967773 + 1.93555i
\(616\) 16.0000 0.644658
\(617\) −33.0000 + 33.0000i −1.32853 + 1.32853i −0.421877 + 0.906653i \(0.638629\pi\)
−0.906653 + 0.421877i \(0.861371\pi\)
\(618\) −18.0000 18.0000i −0.724066 0.724066i
\(619\) 4.00000i 0.160774i 0.996764 + 0.0803868i \(0.0256155\pi\)
−0.996764 + 0.0803868i \(0.974384\pi\)
\(620\) −16.9706 5.65685i −0.681554 0.227185i
\(621\) 28.2843i 1.13501i
\(622\) −1.41421 1.41421i −0.0567048 0.0567048i
\(623\) 40.0000 + 40.0000i 1.60257 + 1.60257i
\(624\) 5.65685 0.226455
\(625\) 7.00000 + 24.0000i 0.280000 + 0.960000i
\(626\) 10.0000 0.399680
\(627\) 24.0000 24.0000i 0.958468 0.958468i
\(628\) 1.41421 1.41421i 0.0564333 0.0564333i
\(629\) −42.4264 −1.69165
\(630\) −2.82843 + 8.48528i −0.112687 + 0.338062i
\(631\) 8.48528i 0.337794i 0.985634 + 0.168897i \(0.0540205\pi\)
−0.985634 + 0.168897i \(0.945980\pi\)
\(632\) −7.07107 7.07107i −0.281272 0.281272i
\(633\) 18.0000 + 18.0000i 0.715436 + 0.715436i
\(634\) −11.3137 −0.449325
\(635\) −7.07107 14.1421i −0.280607 0.561214i
\(636\) 0 0
\(637\) −18.0000 + 18.0000i −0.713186 + 0.713186i
\(638\) 12.0000 + 12.0000i 0.475085 + 0.475085i
\(639\) −5.65685 −0.223782
\(640\) −1.00000 2.00000i −0.0395285 0.0790569i
\(641\) 39.5980i 1.56403i −0.623262 0.782013i \(-0.714193\pi\)
0.623262 0.782013i \(-0.285807\pi\)
\(642\) −24.0000 + 24.0000i −0.947204 + 0.947204i
\(643\) −2.00000 2.00000i −0.0788723 0.0788723i 0.666570 0.745442i \(-0.267762\pi\)
−0.745442 + 0.666570i \(0.767762\pi\)
\(644\) −28.2843 −1.11456
\(645\) −27.2132 + 10.9289i −1.07152 + 0.430326i
\(646\) −30.0000 −1.18033
\(647\) 5.65685 + 5.65685i 0.222394 + 0.222394i 0.809506 0.587112i \(-0.199735\pi\)
−0.587112 + 0.809506i \(0.699735\pi\)
\(648\) 7.77817 7.77817i 0.305556 0.305556i
\(649\) 0 0
\(650\) −8.48528 + 11.3137i −0.332820 + 0.443760i
\(651\) 64.0000 2.50836
\(652\) 2.82843 + 2.82843i 0.110770 + 0.110770i
\(653\) 24.0416 24.0416i 0.940822 0.940822i −0.0575225 0.998344i \(-0.518320\pi\)
0.998344 + 0.0575225i \(0.0183201\pi\)
\(654\) 4.00000i 0.156412i
\(655\) −3.00000 1.00000i −0.117220 0.0390732i
\(656\) 12.0000 0.468521
\(657\) −1.41421 1.41421i −0.0551737 0.0551737i
\(658\) −20.0000 20.0000i −0.779681 0.779681i
\(659\) 8.00000i 0.311636i 0.987786 + 0.155818i \(0.0498013\pi\)
−0.987786 + 0.155818i \(0.950199\pi\)
\(660\) −16.0000 + 8.00000i −0.622799 + 0.311400i
\(661\) 18.0000 0.700119 0.350059 0.936727i \(-0.386161\pi\)
0.350059 + 0.936727i \(0.386161\pi\)
\(662\) 19.0000 19.0000i 0.738456 0.738456i
\(663\) −28.2843 + 28.2843i −1.09847 + 1.09847i
\(664\) 8.48528 0.329293
\(665\) 33.9411 16.9706i 1.31618 0.658090i
\(666\) 6.00000 0.232495
\(667\) −21.2132 21.2132i −0.821379 0.821379i
\(668\) 11.0000 + 11.0000i 0.425603 + 0.425603i
\(669\) 40.0000i 1.54649i
\(670\) −2.00000 + 6.00000i −0.0772667 + 0.231800i
\(671\) 16.9706i 0.655141i
\(672\) 5.65685 + 5.65685i 0.218218 + 0.218218i
\(673\) −1.41421 + 1.41421i −0.0545139 + 0.0545139i −0.733838 0.679324i \(-0.762273\pi\)
0.679324 + 0.733838i \(0.262273\pi\)
\(674\) −12.7279 −0.490261
\(675\) 2.82843 + 19.7990i 0.108866 + 0.762063i
\(676\) 5.00000 0.192308
\(677\) −8.48528 8.48528i −0.326116 0.326116i 0.524992 0.851107i \(-0.324068\pi\)
−0.851107 + 0.524992i \(0.824068\pi\)
\(678\) −14.1421 + 14.1421i −0.543125 + 0.543125i
\(679\) −50.9117 −1.95381
\(680\) 15.0000 + 5.00000i 0.575224 + 0.191741i
\(681\) 40.0000 1.53280
\(682\) 22.6274 + 22.6274i 0.866449 + 0.866449i
\(683\) 26.0000 + 26.0000i 0.994862 + 0.994862i 0.999987 0.00512452i \(-0.00163119\pi\)
−0.00512452 + 0.999987i \(0.501631\pi\)
\(684\) 4.24264 0.162221
\(685\) −20.0000 + 10.0000i −0.764161 + 0.382080i
\(686\) −8.00000 −0.305441
\(687\) 36.7696 + 36.7696i 1.40285 + 1.40285i
\(688\) −0.535534 + 6.53553i −0.0204170 + 0.249165i
\(689\) 0 0
\(690\) 28.2843 14.1421i 1.07676 0.538382i
\(691\) 18.3848i 0.699390i −0.936864 0.349695i \(-0.886285\pi\)
0.936864 0.349695i \(-0.113715\pi\)
\(692\) 16.0000 16.0000i 0.608229 0.608229i
\(693\) 11.3137 11.3137i 0.429772 0.429772i
\(694\) 12.0000i 0.455514i
\(695\) −8.48528 2.82843i −0.321865 0.107288i
\(696\) 8.48528i 0.321634i
\(697\) −60.0000 + 60.0000i −2.27266 + 2.27266i
\(698\) −3.00000 3.00000i −0.113552 0.113552i
\(699\) 28.0000i 1.05906i
\(700\) −19.7990 + 2.82843i −0.748331 + 0.106904i
\(701\) −2.00000 −0.0755390 −0.0377695 0.999286i \(-0.512025\pi\)
−0.0377695 + 0.999286i \(0.512025\pi\)
\(702\) −8.00000 + 8.00000i −0.301941 + 0.301941i
\(703\) −18.0000 18.0000i −0.678883 0.678883i
\(704\) 4.00000i 0.150756i
\(705\) 30.0000 + 10.0000i 1.12987 + 0.376622i
\(706\) 15.5563i 0.585471i
\(707\) −5.65685 5.65685i −0.212748 0.212748i
\(708\) 0 0
\(709\) 30.0000i 1.12667i −0.826227 0.563337i \(-0.809517\pi\)
0.826227 0.563337i \(-0.190483\pi\)
\(710\) −5.65685 11.3137i −0.212298 0.424596i
\(711\) −10.0000 −0.375029
\(712\) −10.0000 + 10.0000i −0.374766 + 0.374766i
\(713\) −40.0000 40.0000i −1.49801 1.49801i
\(714\) −56.5685 −2.11702
\(715\) 22.6274 11.3137i 0.846217 0.423109i
\(716\) 1.41421i 0.0528516i
\(717\) 0 0
\(718\) −9.89949 + 9.89949i −0.369446 + 0.369446i
\(719\) 16.0000i 0.596699i 0.954457 + 0.298350i \(0.0964361\pi\)
−0.954457 + 0.298350i \(0.903564\pi\)
\(720\) −2.12132 0.707107i −0.0790569 0.0263523i
\(721\) 50.9117i 1.89605i
\(722\) 0.707107 + 0.707107i 0.0263158 + 0.0263158i
\(723\) 24.0000 + 24.0000i 0.892570 + 0.892570i
\(724\) 6.00000i 0.222988i
\(725\) −16.9706 12.7279i −0.630271 0.472703i
\(726\) 10.0000 0.371135
\(727\) −36.7696 36.7696i −1.36371 1.36371i −0.869139 0.494569i \(-0.835326\pi\)
−0.494569 0.869139i \(-0.664674\pi\)
\(728\) −8.00000 8.00000i −0.296500 0.296500i
\(729\) 13.0000i 0.481481i
\(730\) 1.41421 4.24264i 0.0523424 0.157027i
\(731\) −30.0000 35.3553i −1.10959 1.30766i
\(732\) −6.00000 + 6.00000i −0.221766 + 0.221766i
\(733\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(734\) −1.41421 −0.0521996
\(735\) 36.0000 18.0000i 1.32788 0.663940i
\(736\) 7.07107i 0.260643i
\(737\) 8.00000 8.00000i 0.294684 0.294684i
\(738\) 8.48528 8.48528i 0.312348 0.312348i
\(739\) −21.2132 −0.780340 −0.390170 0.920743i \(-0.627584\pi\)
−0.390170 + 0.920743i \(0.627584\pi\)
\(740\) 6.00000 + 12.0000i 0.220564 + 0.441129i
\(741\) −24.0000 −0.881662
\(742\) 0 0
\(743\) 5.65685 5.65685i 0.207530 0.207530i −0.595687 0.803217i \(-0.703120\pi\)
0.803217 + 0.595687i \(0.203120\pi\)
\(744\) 16.0000i 0.586588i
\(745\) 7.00000 21.0000i 0.256460 0.769380i
\(746\) 4.00000 0.146450
\(747\) 6.00000 6.00000i 0.219529 0.219529i
\(748\) −20.0000 20.0000i −0.731272 0.731272i
\(749\) 67.8823 2.48036
\(750\) 18.3848 12.7279i 0.671317 0.464758i
\(751\) 11.3137i 0.412843i 0.978463 + 0.206422i \(0.0661818\pi\)
−0.978463 + 0.206422i \(0.933818\pi\)
\(752\) 5.00000 5.00000i 0.182331 0.182331i
\(753\) −16.9706 + 16.9706i −0.618442 + 0.618442i
\(754\) 12.0000i 0.437014i
\(755\) −18.0000 6.00000i −0.655087 0.218362i
\(756\) −16.0000 −0.581914
\(757\) −11.3137 11.3137i −0.411204 0.411204i 0.470954 0.882158i \(-0.343910\pi\)
−0.882158 + 0.470954i \(0.843910\pi\)
\(758\) 19.7990 19.7990i 0.719132 0.719132i
\(759\) −56.5685 −2.05331
\(760\) 4.24264 + 8.48528i 0.153897 + 0.307794i
\(761\) 2.82843i 0.102530i −0.998685 0.0512652i \(-0.983675\pi\)
0.998685 0.0512652i \(-0.0163254\pi\)
\(762\) −10.0000 + 10.0000i −0.362262 + 0.362262i
\(763\) −5.65685 + 5.65685i −0.204792 + 0.204792i
\(764\) 19.7990 0.716302
\(765\) 14.1421 7.07107i 0.511310 0.255655i
\(766\) 28.0000 1.01168
\(767\) 0 0
\(768\) −1.41421 + 1.41421i −0.0510310 + 0.0510310i
\(769\) 18.0000i 0.649097i −0.945869 0.324548i \(-0.894788\pi\)
0.945869 0.324548i \(-0.105212\pi\)
\(770\) 33.9411 + 11.3137i 1.22315 + 0.407718i
\(771\) 12.0000 0.432169
\(772\) −11.0000 + 11.0000i −0.395899 + 0.395899i
\(773\) 16.9706 16.9706i 0.610389 0.610389i −0.332659 0.943047i \(-0.607946\pi\)
0.943047 + 0.332659i \(0.107946\pi\)
\(774\) 4.24264 + 5.00000i 0.152499 + 0.179721i
\(775\) −32.0000 24.0000i −1.14947 0.862105i
\(776\) 12.7279i 0.456906i
\(777\) −33.9411 33.9411i −1.21763 1.21763i
\(778\) −5.00000 5.00000i −0.179259 0.179259i
\(779\) −50.9117 −1.82410
\(780\) 12.0000 + 4.00000i 0.429669 + 0.143223i
\(781\) 22.6274i 0.809673i
\(782\) 35.3553 + 35.3553i 1.26430 + 1.26430i
\(783\) −12.0000 12.0000i −0.428845 0.428845i
\(784\) 9.00000i 0.321429i
\(785\) 4.00000 2.00000i 0.142766 0.0713831i
\(786\) 2.82843i 0.100887i
\(787\) −20.0000 + 20.0000i −0.712923 + 0.712923i −0.967146 0.254223i \(-0.918180\pi\)
0.254223 + 0.967146i \(0.418180\pi\)
\(788\) 2.00000 + 2.00000i 0.0712470 + 0.0712470i
\(789\) 48.0000i 1.70885i
\(790\) −10.0000 20.0000i −0.355784 0.711568i
\(791\) 40.0000 1.42224
\(792\) 2.82843 + 2.82843i 0.100504 + 0.100504i
\(793\) 8.48528 8.48528i 0.301321 0.301321i
\(794\) 28.2843 1.00377
\(795\) 0 0
\(796\) 11.3137i 0.401004i
\(797\) 28.0000 28.0000i 0.991811 0.991811i −0.00815585 0.999967i \(-0.502596\pi\)
0.999967 + 0.00815585i \(0.00259612\pi\)
\(798\) −24.0000 24.0000i −0.849591 0.849591i
\(799\) 50.0000i 1.76887i
\(800\) −0.707107 4.94975i −0.0250000 0.175000i
\(801\) 14.1421i 0.499688i
\(802\) −11.3137 11.3137i −0.399501 0.399501i
\(803\) −5.65685 + 5.65685i −0.199626 + 0.199626i
\(804\) 5.65685 0.199502
\(805\) −60.0000 20.0000i −2.11472 0.704907i
\(806\) 22.6274i 0.797017i
\(807\) 8.48528 + 8.48528i 0.298696 + 0.298696i
\(808\) 1.41421 1.41421i 0.0497519 0.0497519i
\(809\) 4.00000i 0.140633i −0.997525 0.0703163i \(-0.977599\pi\)
0.997525 0.0703163i \(-0.0224008\pi\)
\(810\) 22.0000 11.0000i 0.773001 0.386501i
\(811\) 29.6985i 1.04285i 0.853296 + 0.521427i \(0.174600\pi\)
−0.853296 + 0.521427i \(0.825400\pi\)
\(812\) 12.0000 12.0000i 0.421117 0.421117i
\(813\) −11.3137 + 11.3137i −0.396789 + 0.396789i
\(814\) 24.0000i 0.841200i
\(815\) 4.00000 + 8.00000i 0.140114 + 0.280228i
\(816\) 14.1421i 0.495074i
\(817\) 2.27208 27.7279i 0.0794899 0.970077i
\(818\) −22.0000 22.0000i −0.769212 0.769212i
\(819\) −11.3137 −0.395333
\(820\) 25.4558 + 8.48528i 0.888957 + 0.296319i
\(821\) 38.0000 1.32621 0.663105 0.748527i \(-0.269238\pi\)
0.663105 + 0.748527i \(0.269238\pi\)
\(822\) 14.1421 + 14.1421i 0.493264 + 0.493264i
\(823\) 21.0000 + 21.0000i 0.732014 + 0.732014i 0.971018 0.239004i \(-0.0768211\pi\)
−0.239004 + 0.971018i \(0.576821\pi\)
\(824\) −12.7279 −0.443398
\(825\) −39.5980 + 5.65685i −1.37862 + 0.196946i
\(826\) 0 0
\(827\) −26.0000 + 26.0000i −0.904109 + 0.904109i −0.995789 0.0916799i \(-0.970776\pi\)
0.0916799 + 0.995789i \(0.470776\pi\)
\(828\) −5.00000 5.00000i −0.173762 0.173762i
\(829\) −7.07107 −0.245588 −0.122794 0.992432i \(-0.539185\pi\)
−0.122794 + 0.992432i \(0.539185\pi\)
\(830\) 18.0000 + 6.00000i 0.624789 + 0.208263i
\(831\) −16.0000 −0.555034
\(832\) 2.00000 2.00000i 0.0693375 0.0693375i
\(833\) 45.0000 + 45.0000i 1.55916 + 1.55916i
\(834\) 8.00000i 0.277017i
\(835\) 15.5563 + 31.1127i 0.538350 + 1.07670i
\(836\) 16.9706i 0.586939i
\(837\) −22.6274 22.6274i −0.782118 0.782118i
\(838\) 3.00000 + 3.00000i 0.103633 + 0.103633i
\(839\) 53.7401 1.85531 0.927657 0.373432i \(-0.121819\pi\)
0.927657 + 0.373432i \(0.121819\pi\)
\(840\) 8.00000 + 16.0000i 0.276026 + 0.552052i
\(841\) −11.0000 −0.379310
\(842\) 7.00000 7.00000i 0.241236 0.241236i
\(843\) −14.1421 + 14.1421i −0.487081 + 0.487081i
\(844\) 12.7279 0.438113
\(845\) 10.6066 + 3.53553i 0.364878 + 0.121626i
\(846\) 7.07107i 0.243108i
\(847\) −14.1421 14.1421i −0.485930 0.485930i
\(848\) 0 0
\(849\) −16.9706 −0.582428
\(850\) 28.2843 + 21.2132i 0.970143 + 0.727607i
\(851\) 42.4264i 1.45436i
\(852\) −8.00000 + 8.00000i −0.274075 + 0.274075i
\(853\) −4.00000 4.00000i −0.136957 0.136957i 0.635304 0.772262i \(-0.280875\pi\)
−0.772262 + 0.635304i \(0.780875\pi\)
\(854\) 16.9706 0.580721
\(855\) 9.00000 + 3.00000i 0.307794 + 0.102598i
\(856\) 16.9706i 0.580042i
\(857\) 7.00000 7.00000i 0.239115 0.239115i −0.577368 0.816484i \(-0.695920\pi\)
0.816484 + 0.577368i \(0.195920\pi\)
\(858\) −16.0000 16.0000i −0.546231 0.546231i
\(859\) 15.5563 0.530776 0.265388 0.964142i \(-0.414500\pi\)
0.265388 + 0.964142i \(0.414500\pi\)
\(860\) −5.75736 + 13.4853i −0.196324 + 0.459844i
\(861\) −96.0000 −3.27167
\(862\) 16.9706 + 16.9706i 0.578020 + 0.578020i
\(863\) −33.9411 + 33.9411i −1.15537 + 1.15537i −0.169910 + 0.985460i \(0.554348\pi\)
−0.985460 + 0.169910i \(0.945652\pi\)
\(864\) 4.00000i 0.136083i
\(865\) 45.2548 22.6274i 1.53871 0.769355i
\(866\) 14.0000 0.475739
\(867\) 46.6690 + 46.6690i 1.58496 + 1.58496i
\(868\) 22.6274 22.6274i 0.768025 0.768025i
\(869\) 40.0000i 1.35691i
\(870\) −6.00000 + 18.0000i −0.203419 + 0.610257i
\(871\) −8.00000 −0.271070
\(872\) −1.41421 1.41421i −0.0478913 0.0478913i
\(873\) −9.00000 9.00000i −0.304604 0.304604i
\(874\) 30.0000i 1.01477i
\(875\) −44.0000 8.00000i −1.48747 0.270449i
\(876\) −4.00000 −0.135147
\(877\) −18.0000 + 18.0000i −0.607817 + 0.607817i −0.942375 0.334558i \(-0.891413\pi\)
0.334558 + 0.942375i \(0.391413\pi\)
\(878\) 4.24264 4.24264i 0.143182 0.143182i
\(879\) 28.2843 0.954005
\(880\) −2.82843 + 8.48528i −0.0953463 + 0.286039i
\(881\) −24.0000 −0.808581 −0.404290 0.914631i \(-0.632481\pi\)
−0.404290 + 0.914631i \(0.632481\pi\)
\(882\) −6.36396 6.36396i −0.214286 0.214286i
\(883\) −12.0000 12.0000i −0.403832 0.403832i 0.475749 0.879581i \(-0.342177\pi\)
−0.879581 + 0.475749i \(0.842177\pi\)
\(884\) 20.0000i 0.672673i
\(885\) 0 0
\(886\) 14.1421i 0.475114i
\(887\) 33.9411 + 33.9411i 1.13963 + 1.13963i 0.988516 + 0.151115i \(0.0482865\pi\)
0.151115 + 0.988516i \(0.451714\pi\)
\(888\) 8.48528 8.48528i 0.284747 0.284747i
\(889\) 28.2843 0.948624
\(890\) −28.2843 + 14.1421i −0.948091 + 0.474045i
\(891\) −44.0000 −1.47406
\(892\) −14.1421 14.1421i −0.473514 0.473514i
\(893\) −21.2132 + 21.2132i −0.709873 + 0.709873i
\(894\) −19.7990 −0.662177
\(895\) 1.00000 3.00000i 0.0334263 0.100279i
\(896\) 4.00000 0.133631
\(897\) 28.2843 + 28.2843i 0.944384 + 0.944384i
\(898\) 26.0000 + 26.0000i 0.867631 + 0.867631i
\(899\) 33.9411 1.13200
\(900\) −4.00000 3.00000i −0.133333 0.100000i
\(901\) 0 0
\(902\) −33.9411 33.9411i −1.13012 1.13012i
\(903\) 4.28427 52.2843i 0.142572 1.73991i
\(904\) 10.0000i 0.332595i
\(905\) −4.24264 + 12.7279i −0.141030 + 0.423090i
\(906\) 16.9706i 0.563809i
\(907\) −18.0000 + 18.0000i −0.597680 + 0.597680i −0.939695 0.342014i \(-0.888891\pi\)
0.342014 + 0.939695i \(0.388891\pi\)
\(908\) 14.1421 14.1421i 0.469323 0.469323i
\(909\) 2.00000i 0.0663358i
\(910\) −11.3137 22.6274i −0.375046 0.750092i
\(911\) 53.7401i 1.78049i −0.455483 0.890245i \(-0.650533\pi\)
0.455483 0.890245i \(-0.349467\pi\)
\(912\) 6.00000 6.00000i 0.198680 0.198680i
\(913\) −24.0000 24.0000i −0.794284 0.794284i
\(914\) 14.0000i 0.463079i
\(915\) −16.9706 + 8.48528i −0.561029 + 0.280515i
\(916\) 26.0000 0.859064
\(917\) 4.00000 4.00000i 0.132092 0.132092i
\(918\) 20.0000 + 20.0000i 0.660098 + 0.660098i
\(919\) 42.0000i 1.38545i −0.721201 0.692726i \(-0.756409\pi\)
0.721201 0.692726i \(-0.243591\pi\)
\(920\) 5.00000 15.0000i 0.164845 0.494535i
\(921\) 45.2548i 1.49120i
\(922\) 4.24264 + 4.24264i 0.139724 + 0.139724i
\(923\) 11.3137 11.3137i 0.372395 0.372395i
\(924\) 32.0000i 1.05272i
\(925\) 4.24264 + 29.6985i 0.139497 + 0.976480i
\(926\) −24.0000 −0.788689
\(927\) −9.00000 + 9.00000i −0.295599 + 0.295599i
\(928\) 3.00000 + 3.00000i 0.0984798 + 0.0984798i
\(929\) 2.82843 0.0927977 0.0463988 0.998923i \(-0.485225\pi\)
0.0463988 + 0.998923i \(0.485225\pi\)
\(930\) −11.3137 + 33.9411i −0.370991 + 1.11297i
\(931\) 38.1838i 1.25142i
\(932\) −9.89949 9.89949i −0.324269 0.324269i
\(933\) −2.82843 + 2.82843i −0.0925985 + 0.0925985i
\(934\) 20.0000i 0.654420i
\(935\) −28.2843 56.5685i −0.924995 1.84999i
\(936\) 2.82843i 0.0924500i
\(937\) −15.5563 15.5563i −0.508204 0.508204i 0.405771 0.913975i \(-0.367003\pi\)
−0.913975 + 0.405771i \(0.867003\pi\)
\(938\) −8.00000 8.00000i −0.261209 0.261209i
\(939\) 20.0000i 0.652675i
\(940\) 14.1421 7.07107i 0.461266 0.230633i
\(941\) 42.0000 1.36916 0.684580 0.728937i \(-0.259985\pi\)
0.684580 + 0.728937i \(0.259985\pi\)
\(942\) −2.82843 2.82843i −0.0921551 0.0921551i
\(943\) 60.0000 + 60.0000i 1.95387 + 1.95387i
\(944\) 0 0
\(945\) −33.9411 11.3137i −1.10410 0.368035i
\(946\) 20.0000 16.9706i 0.650256 0.551761i
\(947\) −20.0000 + 20.0000i −0.649913 + 0.649913i −0.952972 0.303059i \(-0.901992\pi\)
0.303059 + 0.952972i \(0.401992\pi\)
\(948\) −14.1421 + 14.1421i −0.459315 + 0.459315i
\(949\) 5.65685 0.183629
\(950\) 3.00000 + 21.0000i 0.0973329 + 0.681330i
\(951\) 22.6274i 0.733744i
\(952\) −20.0000 + 20.0000i −0.648204 + 0.648204i
\(953\) 24.0416 24.0416i 0.778785 0.778785i −0.200839 0.979624i \(-0.564367\pi\)
0.979624 + 0.200839i \(0.0643669\pi\)
\(954\) 0 0
\(955\) 42.0000 + 14.0000i 1.35909 + 0.453029i
\(956\) 0 0
\(957\) 24.0000 24.0000i 0.775810 0.775810i
\(958\) 4.24264 4.24264i 0.137073 0.137073i
\(959\) 40.0000i 1.29167i
\(960\) −4.00000 + 2.00000i −0.129099 + 0.0645497i
\(961\) 33.0000 1.06452
\(962\) −12.0000 + 12.0000i −0.386896 + 0.386896i
\(963\) 12.0000 + 12.0000i 0.386695 + 0.386695i
\(964\) 16.9706 0.546585
\(965\) −31.1127 + 15.5563i −1.00155 + 0.500777i
\(966\) 56.5685i 1.82006i
\(967\) 9.00000 9.00000i 0.289420 0.289420i −0.547431 0.836851i \(-0.684394\pi\)
0.836851 + 0.547431i \(0.184394\pi\)
\(968\) 3.53553 3.53553i 0.113636 0.113636i
\(969\) 60.0000i 1.92748i
\(970\) 9.00000 27.0000i 0.288973 0.866918i
\(971\) 4.00000 0.128366 0.0641831 0.997938i \(-0.479556\pi\)
0.0641831 + 0.997938i \(0.479556\pi\)
\(972\) −7.07107 7.07107i −0.226805 0.226805i
\(973\) 11.3137 11.3137i 0.362701 0.362701i
\(974\) −1.41421 −0.0453143
\(975\) 22.6274 + 16.9706i 0.724657 + 0.543493i
\(976\) 4.24264i 0.135804i
\(977\) −11.0000 + 11.0000i −0.351921 + 0.351921i −0.860824 0.508903i \(-0.830051\pi\)
0.508903 + 0.860824i \(0.330051\pi\)
\(978\) 5.65685 5.65685i 0.180886 0.180886i
\(979\) 56.5685 1.80794
\(980\) 6.36396 19.0919i 0.203289 0.609868i
\(981\) −2.00000 −0.0638551
\(982\) −1.00000 + 1.00000i −0.0319113 + 0.0319113i
\(983\) 16.9706 16.9706i 0.541277 0.541277i −0.382626 0.923903i \(-0.624980\pi\)
0.923903 + 0.382626i \(0.124980\pi\)
\(984\) 24.0000i 0.765092i
\(985\) 2.82843 + 5.65685i 0.0901212 + 0.180242i
\(986\) −30.0000 −0.955395
\(987\) −40.0000 + 40.0000i −1.27321 + 1.27321i
\(988\) −8.48528 + 8.48528i −0.269953 + 0.269953i
\(989\) −35.3553 + 30.0000i −1.12423 + 0.953945i
\(990\) 4.00000 + 8.00000i 0.127128 + 0.254257i
\(991\) 5.65685i 0.179696i −0.995955 0.0898479i \(-0.971362\pi\)
0.995955 0.0898479i \(-0.0286381\pi\)
\(992\) 5.65685 + 5.65685i 0.179605 + 0.179605i
\(993\) −38.0000 38.0000i −1.20589 1.20589i
\(994\) 22.6274 0.717698
\(995\) 8.00000 24.0000i 0.253617 0.760851i
\(996\) 16.9706i 0.537733i
\(997\) −31.1127 31.1127i −0.985349 0.985349i 0.0145452 0.999894i \(-0.495370\pi\)
−0.999894 + 0.0145452i \(0.995370\pi\)
\(998\) −9.00000 9.00000i −0.284890 0.284890i
\(999\) 24.0000i 0.759326i
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 430.2.g.a.343.1 yes 4
5.2 odd 4 inner 430.2.g.a.257.2 yes 4
43.42 odd 2 inner 430.2.g.a.343.2 yes 4
215.42 even 4 inner 430.2.g.a.257.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
430.2.g.a.257.1 4 215.42 even 4 inner
430.2.g.a.257.2 yes 4 5.2 odd 4 inner
430.2.g.a.343.1 yes 4 1.1 even 1 trivial
430.2.g.a.343.2 yes 4 43.42 odd 2 inner