Properties

Label 770.2.m.c.197.1
Level $770$
Weight $2$
Character 770.197
Analytic conductor $6.148$
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] = [770,2,Mod(43,770)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(770, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("770.43");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 770.m (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: \(6.14848095564\)
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 197.1
Root \(-0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 770.197
Dual form 770.2.m.c.43.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(2.00000 - 2.00000i) q^{3} -1.00000i q^{4} +(-1.00000 - 2.00000i) q^{5} +2.82843i q^{6} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} -5.00000i q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(2.00000 - 2.00000i) q^{3} -1.00000i q^{4} +(-1.00000 - 2.00000i) q^{5} +2.82843i q^{6} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} -5.00000i q^{9} +(2.12132 + 0.707107i) q^{10} +(3.00000 - 1.41421i) q^{11} +(-2.00000 - 2.00000i) q^{12} +(1.41421 + 1.41421i) q^{13} +1.00000i q^{14} +(-6.00000 - 2.00000i) q^{15} -1.00000 q^{16} +(1.41421 - 1.41421i) q^{17} +(3.53553 + 3.53553i) q^{18} -4.24264 q^{19} +(-2.00000 + 1.00000i) q^{20} -2.82843i q^{21} +(-1.12132 + 3.12132i) q^{22} +2.82843 q^{24} +(-3.00000 + 4.00000i) q^{25} -2.00000 q^{26} +(-4.00000 - 4.00000i) q^{27} +(-0.707107 - 0.707107i) q^{28} +1.41421 q^{29} +(5.65685 - 2.82843i) q^{30} +2.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +(3.17157 - 8.82843i) q^{33} +2.00000i q^{34} +(-2.12132 - 0.707107i) q^{35} -5.00000 q^{36} +(-4.00000 - 4.00000i) q^{37} +(3.00000 - 3.00000i) q^{38} +5.65685 q^{39} +(0.707107 - 2.12132i) q^{40} +4.24264i q^{41} +(2.00000 + 2.00000i) q^{42} +(-5.65685 - 5.65685i) q^{43} +(-1.41421 - 3.00000i) q^{44} +(-10.0000 + 5.00000i) q^{45} +(5.00000 + 5.00000i) q^{47} +(-2.00000 + 2.00000i) q^{48} -1.00000i q^{49} +(-0.707107 - 4.94975i) q^{50} -5.65685i q^{51} +(1.41421 - 1.41421i) q^{52} +(-6.00000 + 6.00000i) q^{53} +5.65685 q^{54} +(-5.82843 - 4.58579i) q^{55} +1.00000 q^{56} +(-8.48528 + 8.48528i) q^{57} +(-1.00000 + 1.00000i) q^{58} -8.00000i q^{59} +(-2.00000 + 6.00000i) q^{60} +5.65685i q^{61} +(-1.41421 + 1.41421i) q^{62} +(-3.53553 - 3.53553i) q^{63} +1.00000i q^{64} +(1.41421 - 4.24264i) q^{65} +(4.00000 + 8.48528i) q^{66} +(3.00000 + 3.00000i) q^{67} +(-1.41421 - 1.41421i) q^{68} +(2.00000 - 1.00000i) q^{70} +8.00000 q^{71} +(3.53553 - 3.53553i) q^{72} +(-11.3137 - 11.3137i) q^{73} +5.65685 q^{74} +(2.00000 + 14.0000i) q^{75} +4.24264i q^{76} +(1.12132 - 3.12132i) q^{77} +(-4.00000 + 4.00000i) q^{78} -7.07107 q^{79} +(1.00000 + 2.00000i) q^{80} -1.00000 q^{81} +(-3.00000 - 3.00000i) q^{82} +(7.07107 + 7.07107i) q^{83} -2.82843 q^{84} +(-4.24264 - 1.41421i) q^{85} +8.00000 q^{86} +(2.82843 - 2.82843i) q^{87} +(3.12132 + 1.12132i) q^{88} +6.00000i q^{89} +(3.53553 - 10.6066i) q^{90} +2.00000 q^{91} +(4.00000 - 4.00000i) q^{93} -7.07107 q^{94} +(4.24264 + 8.48528i) q^{95} -2.82843i q^{96} +(2.00000 + 2.00000i) q^{97} +(0.707107 + 0.707107i) q^{98} +(-7.07107 - 15.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 8 q^{3} - 4 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 8 q^{3} - 4 q^{5} + 12 q^{11} - 8 q^{12} - 24 q^{15} - 4 q^{16} - 8 q^{20} + 4 q^{22} - 12 q^{25} - 8 q^{26} - 16 q^{27} + 8 q^{31} + 24 q^{33} - 20 q^{36} - 16 q^{37} + 12 q^{38} + 8 q^{42} - 40 q^{45} + 20 q^{47} - 8 q^{48} - 24 q^{53} - 12 q^{55} + 4 q^{56} - 4 q^{58} - 8 q^{60} + 16 q^{66} + 12 q^{67} + 8 q^{70} + 32 q^{71} + 8 q^{75} - 4 q^{77} - 16 q^{78} + 4 q^{80} - 4 q^{81} - 12 q^{82} + 32 q^{86} + 4 q^{88} + 8 q^{91} + 16 q^{93} + 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(617\) \(661\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(1\)

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
\(3\) 2.00000 2.00000i 1.15470 1.15470i 0.169102 0.985599i \(-0.445913\pi\)
0.985599 0.169102i \(-0.0540867\pi\)
\(4\) 1.00000i 0.500000i
\(5\) −1.00000 2.00000i −0.447214 0.894427i
\(6\) 2.82843i 1.15470i
\(7\) 0.707107 0.707107i 0.267261 0.267261i
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 5.00000i 1.66667i
\(10\) 2.12132 + 0.707107i 0.670820 + 0.223607i
\(11\) 3.00000 1.41421i 0.904534 0.426401i
\(12\) −2.00000 2.00000i −0.577350 0.577350i
\(13\) 1.41421 + 1.41421i 0.392232 + 0.392232i 0.875482 0.483250i \(-0.160544\pi\)
−0.483250 + 0.875482i \(0.660544\pi\)
\(14\) 1.00000i 0.267261i
\(15\) −6.00000 2.00000i −1.54919 0.516398i
\(16\) −1.00000 −0.250000
\(17\) 1.41421 1.41421i 0.342997 0.342997i −0.514496 0.857493i \(-0.672021\pi\)
0.857493 + 0.514496i \(0.172021\pi\)
\(18\) 3.53553 + 3.53553i 0.833333 + 0.833333i
\(19\) −4.24264 −0.973329 −0.486664 0.873589i \(-0.661786\pi\)
−0.486664 + 0.873589i \(0.661786\pi\)
\(20\) −2.00000 + 1.00000i −0.447214 + 0.223607i
\(21\) 2.82843i 0.617213i
\(22\) −1.12132 + 3.12132i −0.239066 + 0.665468i
\(23\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(24\) 2.82843 0.577350
\(25\) −3.00000 + 4.00000i −0.600000 + 0.800000i
\(26\) −2.00000 −0.392232
\(27\) −4.00000 4.00000i −0.769800 0.769800i
\(28\) −0.707107 0.707107i −0.133631 0.133631i
\(29\) 1.41421 0.262613 0.131306 0.991342i \(-0.458083\pi\)
0.131306 + 0.991342i \(0.458083\pi\)
\(30\) 5.65685 2.82843i 1.03280 0.516398i
\(31\) 2.00000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 3.17157 8.82843i 0.552100 1.53683i
\(34\) 2.00000i 0.342997i
\(35\) −2.12132 0.707107i −0.358569 0.119523i
\(36\) −5.00000 −0.833333
\(37\) −4.00000 4.00000i −0.657596 0.657596i 0.297215 0.954811i \(-0.403942\pi\)
−0.954811 + 0.297215i \(0.903942\pi\)
\(38\) 3.00000 3.00000i 0.486664 0.486664i
\(39\) 5.65685 0.905822
\(40\) 0.707107 2.12132i 0.111803 0.335410i
\(41\) 4.24264i 0.662589i 0.943527 + 0.331295i \(0.107485\pi\)
−0.943527 + 0.331295i \(0.892515\pi\)
\(42\) 2.00000 + 2.00000i 0.308607 + 0.308607i
\(43\) −5.65685 5.65685i −0.862662 0.862662i 0.128984 0.991647i \(-0.458828\pi\)
−0.991647 + 0.128984i \(0.958828\pi\)
\(44\) −1.41421 3.00000i −0.213201 0.452267i
\(45\) −10.0000 + 5.00000i −1.49071 + 0.745356i
\(46\) 0 0
\(47\) 5.00000 + 5.00000i 0.729325 + 0.729325i 0.970485 0.241160i \(-0.0775280\pi\)
−0.241160 + 0.970485i \(0.577528\pi\)
\(48\) −2.00000 + 2.00000i −0.288675 + 0.288675i
\(49\) 1.00000i 0.142857i
\(50\) −0.707107 4.94975i −0.100000 0.700000i
\(51\) 5.65685i 0.792118i
\(52\) 1.41421 1.41421i 0.196116 0.196116i
\(53\) −6.00000 + 6.00000i −0.824163 + 0.824163i −0.986702 0.162539i \(-0.948032\pi\)
0.162539 + 0.986702i \(0.448032\pi\)
\(54\) 5.65685 0.769800
\(55\) −5.82843 4.58579i −0.785905 0.618347i
\(56\) 1.00000 0.133631
\(57\) −8.48528 + 8.48528i −1.12390 + 1.12390i
\(58\) −1.00000 + 1.00000i −0.131306 + 0.131306i
\(59\) 8.00000i 1.04151i −0.853706 0.520756i \(-0.825650\pi\)
0.853706 0.520756i \(-0.174350\pi\)
\(60\) −2.00000 + 6.00000i −0.258199 + 0.774597i
\(61\) 5.65685i 0.724286i 0.932123 + 0.362143i \(0.117955\pi\)
−0.932123 + 0.362143i \(0.882045\pi\)
\(62\) −1.41421 + 1.41421i −0.179605 + 0.179605i
\(63\) −3.53553 3.53553i −0.445435 0.445435i
\(64\) 1.00000i 0.125000i
\(65\) 1.41421 4.24264i 0.175412 0.526235i
\(66\) 4.00000 + 8.48528i 0.492366 + 1.04447i
\(67\) 3.00000 + 3.00000i 0.366508 + 0.366508i 0.866202 0.499694i \(-0.166554\pi\)
−0.499694 + 0.866202i \(0.666554\pi\)
\(68\) −1.41421 1.41421i −0.171499 0.171499i
\(69\) 0 0
\(70\) 2.00000 1.00000i 0.239046 0.119523i
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) 3.53553 3.53553i 0.416667 0.416667i
\(73\) −11.3137 11.3137i −1.32417 1.32417i −0.910366 0.413803i \(-0.864200\pi\)
−0.413803 0.910366i \(-0.635800\pi\)
\(74\) 5.65685 0.657596
\(75\) 2.00000 + 14.0000i 0.230940 + 1.61658i
\(76\) 4.24264i 0.486664i
\(77\) 1.12132 3.12132i 0.127786 0.355707i
\(78\) −4.00000 + 4.00000i −0.452911 + 0.452911i
\(79\) −7.07107 −0.795557 −0.397779 0.917481i \(-0.630219\pi\)
−0.397779 + 0.917481i \(0.630219\pi\)
\(80\) 1.00000 + 2.00000i 0.111803 + 0.223607i
\(81\) −1.00000 −0.111111
\(82\) −3.00000 3.00000i −0.331295 0.331295i
\(83\) 7.07107 + 7.07107i 0.776151 + 0.776151i 0.979174 0.203023i \(-0.0650767\pi\)
−0.203023 + 0.979174i \(0.565077\pi\)
\(84\) −2.82843 −0.308607
\(85\) −4.24264 1.41421i −0.460179 0.153393i
\(86\) 8.00000 0.862662
\(87\) 2.82843 2.82843i 0.303239 0.303239i
\(88\) 3.12132 + 1.12132i 0.332734 + 0.119533i
\(89\) 6.00000i 0.635999i 0.948091 + 0.317999i \(0.103011\pi\)
−0.948091 + 0.317999i \(0.896989\pi\)
\(90\) 3.53553 10.6066i 0.372678 1.11803i
\(91\) 2.00000 0.209657
\(92\) 0 0
\(93\) 4.00000 4.00000i 0.414781 0.414781i
\(94\) −7.07107 −0.729325
\(95\) 4.24264 + 8.48528i 0.435286 + 0.870572i
\(96\) 2.82843i 0.288675i
\(97\) 2.00000 + 2.00000i 0.203069 + 0.203069i 0.801314 0.598244i \(-0.204135\pi\)
−0.598244 + 0.801314i \(0.704135\pi\)
\(98\) 0.707107 + 0.707107i 0.0714286 + 0.0714286i
\(99\) −7.07107 15.0000i −0.710669 1.50756i
\(100\) 4.00000 + 3.00000i 0.400000 + 0.300000i
\(101\) 19.7990i 1.97007i 0.172345 + 0.985037i \(0.444865\pi\)
−0.172345 + 0.985037i \(0.555135\pi\)
\(102\) 4.00000 + 4.00000i 0.396059 + 0.396059i
\(103\) 3.00000 3.00000i 0.295599 0.295599i −0.543688 0.839287i \(-0.682973\pi\)
0.839287 + 0.543688i \(0.182973\pi\)
\(104\) 2.00000i 0.196116i
\(105\) −5.65685 + 2.82843i −0.552052 + 0.276026i
\(106\) 8.48528i 0.824163i
\(107\) 14.1421 14.1421i 1.36717 1.36717i 0.502726 0.864446i \(-0.332330\pi\)
0.864446 0.502726i \(-0.167670\pi\)
\(108\) −4.00000 + 4.00000i −0.384900 + 0.384900i
\(109\) 18.3848 1.76094 0.880471 0.474100i \(-0.157226\pi\)
0.880471 + 0.474100i \(0.157226\pi\)
\(110\) 7.36396 0.878680i 0.702126 0.0837788i
\(111\) −16.0000 −1.51865
\(112\) −0.707107 + 0.707107i −0.0668153 + 0.0668153i
\(113\) 13.0000 13.0000i 1.22294 1.22294i 0.256354 0.966583i \(-0.417479\pi\)
0.966583 0.256354i \(-0.0825214\pi\)
\(114\) 12.0000i 1.12390i
\(115\) 0 0
\(116\) 1.41421i 0.131306i
\(117\) 7.07107 7.07107i 0.653720 0.653720i
\(118\) 5.65685 + 5.65685i 0.520756 + 0.520756i
\(119\) 2.00000i 0.183340i
\(120\) −2.82843 5.65685i −0.258199 0.516398i
\(121\) 7.00000 8.48528i 0.636364 0.771389i
\(122\) −4.00000 4.00000i −0.362143 0.362143i
\(123\) 8.48528 + 8.48528i 0.765092 + 0.765092i
\(124\) 2.00000i 0.179605i
\(125\) 11.0000 + 2.00000i 0.983870 + 0.178885i
\(126\) 5.00000 0.445435
\(127\) 9.89949 9.89949i 0.878438 0.878438i −0.114935 0.993373i \(-0.536666\pi\)
0.993373 + 0.114935i \(0.0366659\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) −22.6274 −1.99223
\(130\) 2.00000 + 4.00000i 0.175412 + 0.350823i
\(131\) 15.5563i 1.35916i 0.733599 + 0.679582i \(0.237839\pi\)
−0.733599 + 0.679582i \(0.762161\pi\)
\(132\) −8.82843 3.17157i −0.768416 0.276050i
\(133\) −3.00000 + 3.00000i −0.260133 + 0.260133i
\(134\) −4.24264 −0.366508
\(135\) −4.00000 + 12.0000i −0.344265 + 1.03280i
\(136\) 2.00000 0.171499
\(137\) −5.00000 5.00000i −0.427179 0.427179i 0.460487 0.887666i \(-0.347675\pi\)
−0.887666 + 0.460487i \(0.847675\pi\)
\(138\) 0 0
\(139\) 1.41421 0.119952 0.0599760 0.998200i \(-0.480898\pi\)
0.0599760 + 0.998200i \(0.480898\pi\)
\(140\) −0.707107 + 2.12132i −0.0597614 + 0.179284i
\(141\) 20.0000 1.68430
\(142\) −5.65685 + 5.65685i −0.474713 + 0.474713i
\(143\) 6.24264 + 2.24264i 0.522036 + 0.187539i
\(144\) 5.00000i 0.416667i
\(145\) −1.41421 2.82843i −0.117444 0.234888i
\(146\) 16.0000 1.32417
\(147\) −2.00000 2.00000i −0.164957 0.164957i
\(148\) −4.00000 + 4.00000i −0.328798 + 0.328798i
\(149\) 1.41421 0.115857 0.0579284 0.998321i \(-0.481550\pi\)
0.0579284 + 0.998321i \(0.481550\pi\)
\(150\) −11.3137 8.48528i −0.923760 0.692820i
\(151\) 9.89949i 0.805609i 0.915286 + 0.402805i \(0.131965\pi\)
−0.915286 + 0.402805i \(0.868035\pi\)
\(152\) −3.00000 3.00000i −0.243332 0.243332i
\(153\) −7.07107 7.07107i −0.571662 0.571662i
\(154\) 1.41421 + 3.00000i 0.113961 + 0.241747i
\(155\) −2.00000 4.00000i −0.160644 0.321288i
\(156\) 5.65685i 0.452911i
\(157\) 13.0000 + 13.0000i 1.03751 + 1.03751i 0.999268 + 0.0382445i \(0.0121766\pi\)
0.0382445 + 0.999268i \(0.487823\pi\)
\(158\) 5.00000 5.00000i 0.397779 0.397779i
\(159\) 24.0000i 1.90332i
\(160\) −2.12132 0.707107i −0.167705 0.0559017i
\(161\) 0 0
\(162\) 0.707107 0.707107i 0.0555556 0.0555556i
\(163\) −15.0000 + 15.0000i −1.17489 + 1.17489i −0.193862 + 0.981029i \(0.562101\pi\)
−0.981029 + 0.193862i \(0.937899\pi\)
\(164\) 4.24264 0.331295
\(165\) −20.8284 + 2.48528i −1.62149 + 0.193479i
\(166\) −10.0000 −0.776151
\(167\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(168\) 2.00000 2.00000i 0.154303 0.154303i
\(169\) 9.00000i 0.692308i
\(170\) 4.00000 2.00000i 0.306786 0.153393i
\(171\) 21.2132i 1.62221i
\(172\) −5.65685 + 5.65685i −0.431331 + 0.431331i
\(173\) −7.07107 7.07107i −0.537603 0.537603i 0.385221 0.922824i \(-0.374125\pi\)
−0.922824 + 0.385221i \(0.874125\pi\)
\(174\) 4.00000i 0.303239i
\(175\) 0.707107 + 4.94975i 0.0534522 + 0.374166i
\(176\) −3.00000 + 1.41421i −0.226134 + 0.106600i
\(177\) −16.0000 16.0000i −1.20263 1.20263i
\(178\) −4.24264 4.24264i −0.317999 0.317999i
\(179\) 18.0000i 1.34538i 0.739923 + 0.672692i \(0.234862\pi\)
−0.739923 + 0.672692i \(0.765138\pi\)
\(180\) 5.00000 + 10.0000i 0.372678 + 0.745356i
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) −1.41421 + 1.41421i −0.104828 + 0.104828i
\(183\) 11.3137 + 11.3137i 0.836333 + 0.836333i
\(184\) 0 0
\(185\) −4.00000 + 12.0000i −0.294086 + 0.882258i
\(186\) 5.65685i 0.414781i
\(187\) 2.24264 6.24264i 0.163998 0.456507i
\(188\) 5.00000 5.00000i 0.364662 0.364662i
\(189\) −5.65685 −0.411476
\(190\) −9.00000 3.00000i −0.652929 0.217643i
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 2.00000 + 2.00000i 0.144338 + 0.144338i
\(193\) −12.7279 12.7279i −0.916176 0.916176i 0.0805728 0.996749i \(-0.474325\pi\)
−0.996749 + 0.0805728i \(0.974325\pi\)
\(194\) −2.82843 −0.203069
\(195\) −5.65685 11.3137i −0.405096 0.810191i
\(196\) −1.00000 −0.0714286
\(197\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(198\) 15.6066 + 5.60660i 1.10911 + 0.398444i
\(199\) 16.0000i 1.13421i 0.823646 + 0.567105i \(0.191937\pi\)
−0.823646 + 0.567105i \(0.808063\pi\)
\(200\) −4.94975 + 0.707107i −0.350000 + 0.0500000i
\(201\) 12.0000 0.846415
\(202\) −14.0000 14.0000i −0.985037 0.985037i
\(203\) 1.00000 1.00000i 0.0701862 0.0701862i
\(204\) −5.65685 −0.396059
\(205\) 8.48528 4.24264i 0.592638 0.296319i
\(206\) 4.24264i 0.295599i
\(207\) 0 0
\(208\) −1.41421 1.41421i −0.0980581 0.0980581i
\(209\) −12.7279 + 6.00000i −0.880409 + 0.415029i
\(210\) 2.00000 6.00000i 0.138013 0.414039i
\(211\) 11.3137i 0.778868i 0.921054 + 0.389434i \(0.127329\pi\)
−0.921054 + 0.389434i \(0.872671\pi\)
\(212\) 6.00000 + 6.00000i 0.412082 + 0.412082i
\(213\) 16.0000 16.0000i 1.09630 1.09630i
\(214\) 20.0000i 1.36717i
\(215\) −5.65685 + 16.9706i −0.385794 + 1.15738i
\(216\) 5.65685i 0.384900i
\(217\) 1.41421 1.41421i 0.0960031 0.0960031i
\(218\) −13.0000 + 13.0000i −0.880471 + 0.880471i
\(219\) −45.2548 −3.05804
\(220\) −4.58579 + 5.82843i −0.309174 + 0.392952i
\(221\) 4.00000 0.269069
\(222\) 11.3137 11.3137i 0.759326 0.759326i
\(223\) 1.00000 1.00000i 0.0669650 0.0669650i −0.672831 0.739796i \(-0.734922\pi\)
0.739796 + 0.672831i \(0.234922\pi\)
\(224\) 1.00000i 0.0668153i
\(225\) 20.0000 + 15.0000i 1.33333 + 1.00000i
\(226\) 18.3848i 1.22294i
\(227\) 8.48528 8.48528i 0.563188 0.563188i −0.367024 0.930212i \(-0.619623\pi\)
0.930212 + 0.367024i \(0.119623\pi\)
\(228\) 8.48528 + 8.48528i 0.561951 + 0.561951i
\(229\) 20.0000i 1.32164i 0.750546 + 0.660819i \(0.229791\pi\)
−0.750546 + 0.660819i \(0.770209\pi\)
\(230\) 0 0
\(231\) −4.00000 8.48528i −0.263181 0.558291i
\(232\) 1.00000 + 1.00000i 0.0656532 + 0.0656532i
\(233\) 9.89949 + 9.89949i 0.648537 + 0.648537i 0.952639 0.304102i \(-0.0983564\pi\)
−0.304102 + 0.952639i \(0.598356\pi\)
\(234\) 10.0000i 0.653720i
\(235\) 5.00000 15.0000i 0.326164 0.978492i
\(236\) −8.00000 −0.520756
\(237\) −14.1421 + 14.1421i −0.918630 + 0.918630i
\(238\) 1.41421 + 1.41421i 0.0916698 + 0.0916698i
\(239\) −1.41421 −0.0914779 −0.0457389 0.998953i \(-0.514564\pi\)
−0.0457389 + 0.998953i \(0.514564\pi\)
\(240\) 6.00000 + 2.00000i 0.387298 + 0.129099i
\(241\) 24.0416i 1.54866i −0.632783 0.774329i \(-0.718088\pi\)
0.632783 0.774329i \(-0.281912\pi\)
\(242\) 1.05025 + 10.9497i 0.0675128 + 0.703876i
\(243\) 10.0000 10.0000i 0.641500 0.641500i
\(244\) 5.65685 0.362143
\(245\) −2.00000 + 1.00000i −0.127775 + 0.0638877i
\(246\) −12.0000 −0.765092
\(247\) −6.00000 6.00000i −0.381771 0.381771i
\(248\) 1.41421 + 1.41421i 0.0898027 + 0.0898027i
\(249\) 28.2843 1.79244
\(250\) −9.19239 + 6.36396i −0.581378 + 0.402492i
\(251\) 4.00000 0.252478 0.126239 0.992000i \(-0.459709\pi\)
0.126239 + 0.992000i \(0.459709\pi\)
\(252\) −3.53553 + 3.53553i −0.222718 + 0.222718i
\(253\) 0 0
\(254\) 14.0000i 0.878438i
\(255\) −11.3137 + 5.65685i −0.708492 + 0.354246i
\(256\) 1.00000 0.0625000
\(257\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(258\) 16.0000 16.0000i 0.996116 0.996116i
\(259\) −5.65685 −0.351500
\(260\) −4.24264 1.41421i −0.263117 0.0877058i
\(261\) 7.07107i 0.437688i
\(262\) −11.0000 11.0000i −0.679582 0.679582i
\(263\) 7.07107 + 7.07107i 0.436021 + 0.436021i 0.890670 0.454650i \(-0.150236\pi\)
−0.454650 + 0.890670i \(0.650236\pi\)
\(264\) 8.48528 4.00000i 0.522233 0.246183i
\(265\) 18.0000 + 6.00000i 1.10573 + 0.368577i
\(266\) 4.24264i 0.260133i
\(267\) 12.0000 + 12.0000i 0.734388 + 0.734388i
\(268\) 3.00000 3.00000i 0.183254 0.183254i
\(269\) 24.0000i 1.46331i 0.681677 + 0.731653i \(0.261251\pi\)
−0.681677 + 0.731653i \(0.738749\pi\)
\(270\) −5.65685 11.3137i −0.344265 0.688530i
\(271\) 8.48528i 0.515444i 0.966219 + 0.257722i \(0.0829719\pi\)
−0.966219 + 0.257722i \(0.917028\pi\)
\(272\) −1.41421 + 1.41421i −0.0857493 + 0.0857493i
\(273\) 4.00000 4.00000i 0.242091 0.242091i
\(274\) 7.07107 0.427179
\(275\) −3.34315 + 16.2426i −0.201599 + 0.979468i
\(276\) 0 0
\(277\) 19.7990 19.7990i 1.18961 1.18961i 0.212430 0.977176i \(-0.431862\pi\)
0.977176 0.212430i \(-0.0681376\pi\)
\(278\) −1.00000 + 1.00000i −0.0599760 + 0.0599760i
\(279\) 10.0000i 0.598684i
\(280\) −1.00000 2.00000i −0.0597614 0.119523i
\(281\) 28.2843i 1.68730i −0.536895 0.843649i \(-0.680403\pi\)
0.536895 0.843649i \(-0.319597\pi\)
\(282\) −14.1421 + 14.1421i −0.842152 + 0.842152i
\(283\) −19.7990 19.7990i −1.17693 1.17693i −0.980523 0.196405i \(-0.937073\pi\)
−0.196405 0.980523i \(-0.562927\pi\)
\(284\) 8.00000i 0.474713i
\(285\) 25.4558 + 8.48528i 1.50787 + 0.502625i
\(286\) −6.00000 + 2.82843i −0.354787 + 0.167248i
\(287\) 3.00000 + 3.00000i 0.177084 + 0.177084i
\(288\) −3.53553 3.53553i −0.208333 0.208333i
\(289\) 13.0000i 0.764706i
\(290\) 3.00000 + 1.00000i 0.176166 + 0.0587220i
\(291\) 8.00000 0.468968
\(292\) −11.3137 + 11.3137i −0.662085 + 0.662085i
\(293\) −1.41421 1.41421i −0.0826192 0.0826192i 0.664589 0.747209i \(-0.268606\pi\)
−0.747209 + 0.664589i \(0.768606\pi\)
\(294\) 2.82843 0.164957
\(295\) −16.0000 + 8.00000i −0.931556 + 0.465778i
\(296\) 5.65685i 0.328798i
\(297\) −17.6569 6.34315i −1.02455 0.368067i
\(298\) −1.00000 + 1.00000i −0.0579284 + 0.0579284i
\(299\) 0 0
\(300\) 14.0000 2.00000i 0.808290 0.115470i
\(301\) −8.00000 −0.461112
\(302\) −7.00000 7.00000i −0.402805 0.402805i
\(303\) 39.5980 + 39.5980i 2.27484 + 2.27484i
\(304\) 4.24264 0.243332
\(305\) 11.3137 5.65685i 0.647821 0.323911i
\(306\) 10.0000 0.571662
\(307\) −19.7990 + 19.7990i −1.12999 + 1.12999i −0.139810 + 0.990178i \(0.544649\pi\)
−0.990178 + 0.139810i \(0.955351\pi\)
\(308\) −3.12132 1.12132i −0.177854 0.0638932i
\(309\) 12.0000i 0.682656i
\(310\) 4.24264 + 1.41421i 0.240966 + 0.0803219i
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 4.00000 + 4.00000i 0.226455 + 0.226455i
\(313\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(314\) −18.3848 −1.03751
\(315\) −3.53553 + 10.6066i −0.199205 + 0.597614i
\(316\) 7.07107i 0.397779i
\(317\) −22.0000 22.0000i −1.23564 1.23564i −0.961764 0.273879i \(-0.911693\pi\)
−0.273879 0.961764i \(-0.588307\pi\)
\(318\) −16.9706 16.9706i −0.951662 0.951662i
\(319\) 4.24264 2.00000i 0.237542 0.111979i
\(320\) 2.00000 1.00000i 0.111803 0.0559017i
\(321\) 56.5685i 3.15735i
\(322\) 0 0
\(323\) −6.00000 + 6.00000i −0.333849 + 0.333849i
\(324\) 1.00000i 0.0555556i
\(325\) −9.89949 + 1.41421i −0.549125 + 0.0784465i
\(326\) 21.2132i 1.17489i
\(327\) 36.7696 36.7696i 2.03336 2.03336i
\(328\) −3.00000 + 3.00000i −0.165647 + 0.165647i
\(329\) 7.07107 0.389841
\(330\) 12.9706 16.4853i 0.714006 0.907485i
\(331\) −28.0000 −1.53902 −0.769510 0.638635i \(-0.779499\pi\)
−0.769510 + 0.638635i \(0.779499\pi\)
\(332\) 7.07107 7.07107i 0.388075 0.388075i
\(333\) −20.0000 + 20.0000i −1.09599 + 1.09599i
\(334\) 0 0
\(335\) 3.00000 9.00000i 0.163908 0.491723i
\(336\) 2.82843i 0.154303i
\(337\) 1.41421 1.41421i 0.0770371 0.0770371i −0.667538 0.744575i \(-0.732652\pi\)
0.744575 + 0.667538i \(0.232652\pi\)
\(338\) 6.36396 + 6.36396i 0.346154 + 0.346154i
\(339\) 52.0000i 2.82425i
\(340\) −1.41421 + 4.24264i −0.0766965 + 0.230089i
\(341\) 6.00000 2.82843i 0.324918 0.153168i
\(342\) −15.0000 15.0000i −0.811107 0.811107i
\(343\) −0.707107 0.707107i −0.0381802 0.0381802i
\(344\) 8.00000i 0.431331i
\(345\) 0 0
\(346\) 10.0000 0.537603
\(347\) 8.48528 8.48528i 0.455514 0.455514i −0.441666 0.897180i \(-0.645612\pi\)
0.897180 + 0.441666i \(0.145612\pi\)
\(348\) −2.82843 2.82843i −0.151620 0.151620i
\(349\) −8.48528 −0.454207 −0.227103 0.973871i \(-0.572926\pi\)
−0.227103 + 0.973871i \(0.572926\pi\)
\(350\) −4.00000 3.00000i −0.213809 0.160357i
\(351\) 11.3137i 0.603881i
\(352\) 1.12132 3.12132i 0.0597666 0.166367i
\(353\) 12.0000 12.0000i 0.638696 0.638696i −0.311538 0.950234i \(-0.600844\pi\)
0.950234 + 0.311538i \(0.100844\pi\)
\(354\) 22.6274 1.20263
\(355\) −8.00000 16.0000i −0.424596 0.849192i
\(356\) 6.00000 0.317999
\(357\) −4.00000 4.00000i −0.211702 0.211702i
\(358\) −12.7279 12.7279i −0.672692 0.672692i
\(359\) −1.41421 −0.0746393 −0.0373197 0.999303i \(-0.511882\pi\)
−0.0373197 + 0.999303i \(0.511882\pi\)
\(360\) −10.6066 3.53553i −0.559017 0.186339i
\(361\) −1.00000 −0.0526316
\(362\) 7.07107 7.07107i 0.371647 0.371647i
\(363\) −2.97056 30.9706i −0.155914 1.62553i
\(364\) 2.00000i 0.104828i
\(365\) −11.3137 + 33.9411i −0.592187 + 1.77656i
\(366\) −16.0000 −0.836333
\(367\) −9.00000 9.00000i −0.469796 0.469796i 0.432052 0.901849i \(-0.357790\pi\)
−0.901849 + 0.432052i \(0.857790\pi\)
\(368\) 0 0
\(369\) 21.2132 1.10432
\(370\) −5.65685 11.3137i −0.294086 0.588172i
\(371\) 8.48528i 0.440534i
\(372\) −4.00000 4.00000i −0.207390 0.207390i
\(373\) 22.6274 + 22.6274i 1.17160 + 1.17160i 0.981827 + 0.189776i \(0.0607761\pi\)
0.189776 + 0.981827i \(0.439224\pi\)
\(374\) 2.82843 + 6.00000i 0.146254 + 0.310253i
\(375\) 26.0000 18.0000i 1.34263 0.929516i
\(376\) 7.07107i 0.364662i
\(377\) 2.00000 + 2.00000i 0.103005 + 0.103005i
\(378\) 4.00000 4.00000i 0.205738 0.205738i
\(379\) 14.0000i 0.719132i 0.933120 + 0.359566i \(0.117075\pi\)
−0.933120 + 0.359566i \(0.882925\pi\)
\(380\) 8.48528 4.24264i 0.435286 0.217643i
\(381\) 39.5980i 2.02867i
\(382\) 0 0
\(383\) −23.0000 + 23.0000i −1.17525 + 1.17525i −0.194304 + 0.980941i \(0.562245\pi\)
−0.980941 + 0.194304i \(0.937755\pi\)
\(384\) −2.82843 −0.144338
\(385\) −7.36396 + 0.878680i −0.375302 + 0.0447817i
\(386\) 18.0000 0.916176
\(387\) −28.2843 + 28.2843i −1.43777 + 1.43777i
\(388\) 2.00000 2.00000i 0.101535 0.101535i
\(389\) 2.00000i 0.101404i −0.998714 0.0507020i \(-0.983854\pi\)
0.998714 0.0507020i \(-0.0161459\pi\)
\(390\) 12.0000 + 4.00000i 0.607644 + 0.202548i
\(391\) 0 0
\(392\) 0.707107 0.707107i 0.0357143 0.0357143i
\(393\) 31.1127 + 31.1127i 1.56943 + 1.56943i
\(394\) 0 0
\(395\) 7.07107 + 14.1421i 0.355784 + 0.711568i
\(396\) −15.0000 + 7.07107i −0.753778 + 0.355335i
\(397\) −23.0000 23.0000i −1.15434 1.15434i −0.985674 0.168663i \(-0.946055\pi\)
−0.168663 0.985674i \(-0.553945\pi\)
\(398\) −11.3137 11.3137i −0.567105 0.567105i
\(399\) 12.0000i 0.600751i
\(400\) 3.00000 4.00000i 0.150000 0.200000i
\(401\) 34.0000 1.69788 0.848939 0.528490i \(-0.177242\pi\)
0.848939 + 0.528490i \(0.177242\pi\)
\(402\) −8.48528 + 8.48528i −0.423207 + 0.423207i
\(403\) 2.82843 + 2.82843i 0.140894 + 0.140894i
\(404\) 19.7990 0.985037
\(405\) 1.00000 + 2.00000i 0.0496904 + 0.0993808i
\(406\) 1.41421i 0.0701862i
\(407\) −17.6569 6.34315i −0.875218 0.314418i
\(408\) 4.00000 4.00000i 0.198030 0.198030i
\(409\) 29.6985 1.46850 0.734248 0.678882i \(-0.237535\pi\)
0.734248 + 0.678882i \(0.237535\pi\)
\(410\) −3.00000 + 9.00000i −0.148159 + 0.444478i
\(411\) −20.0000 −0.986527
\(412\) −3.00000 3.00000i −0.147799 0.147799i
\(413\) −5.65685 5.65685i −0.278356 0.278356i
\(414\) 0 0
\(415\) 7.07107 21.2132i 0.347105 1.04132i
\(416\) 2.00000 0.0980581
\(417\) 2.82843 2.82843i 0.138509 0.138509i
\(418\) 4.75736 13.2426i 0.232690 0.647719i
\(419\) 40.0000i 1.95413i −0.212946 0.977064i \(-0.568306\pi\)
0.212946 0.977064i \(-0.431694\pi\)
\(420\) 2.82843 + 5.65685i 0.138013 + 0.276026i
\(421\) 10.0000 0.487370 0.243685 0.969854i \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) −8.00000 8.00000i −0.389434 0.389434i
\(423\) 25.0000 25.0000i 1.21554 1.21554i
\(424\) −8.48528 −0.412082
\(425\) 1.41421 + 9.89949i 0.0685994 + 0.480196i
\(426\) 22.6274i 1.09630i
\(427\) 4.00000 + 4.00000i 0.193574 + 0.193574i
\(428\) −14.1421 14.1421i −0.683586 0.683586i
\(429\) 16.9706 8.00000i 0.819346 0.386244i
\(430\) −8.00000 16.0000i −0.385794 0.771589i
\(431\) 1.41421i 0.0681203i 0.999420 + 0.0340601i \(0.0108438\pi\)
−0.999420 + 0.0340601i \(0.989156\pi\)
\(432\) 4.00000 + 4.00000i 0.192450 + 0.192450i
\(433\) −24.0000 + 24.0000i −1.15337 + 1.15337i −0.167493 + 0.985873i \(0.553567\pi\)
−0.985873 + 0.167493i \(0.946433\pi\)
\(434\) 2.00000i 0.0960031i
\(435\) −8.48528 2.82843i −0.406838 0.135613i
\(436\) 18.3848i 0.880471i
\(437\) 0 0
\(438\) 32.0000 32.0000i 1.52902 1.52902i
\(439\) −25.4558 −1.21494 −0.607471 0.794342i \(-0.707816\pi\)
−0.607471 + 0.794342i \(0.707816\pi\)
\(440\) −0.878680 7.36396i −0.0418894 0.351063i
\(441\) −5.00000 −0.238095
\(442\) −2.82843 + 2.82843i −0.134535 + 0.134535i
\(443\) −15.0000 + 15.0000i −0.712672 + 0.712672i −0.967093 0.254422i \(-0.918115\pi\)
0.254422 + 0.967093i \(0.418115\pi\)
\(444\) 16.0000i 0.759326i
\(445\) 12.0000 6.00000i 0.568855 0.284427i
\(446\) 1.41421i 0.0669650i
\(447\) 2.82843 2.82843i 0.133780 0.133780i
\(448\) 0.707107 + 0.707107i 0.0334077 + 0.0334077i
\(449\) 40.0000i 1.88772i −0.330350 0.943858i \(-0.607167\pi\)
0.330350 0.943858i \(-0.392833\pi\)
\(450\) −24.7487 + 3.53553i −1.16667 + 0.166667i
\(451\) 6.00000 + 12.7279i 0.282529 + 0.599334i
\(452\) −13.0000 13.0000i −0.611469 0.611469i
\(453\) 19.7990 + 19.7990i 0.930238 + 0.930238i
\(454\) 12.0000i 0.563188i
\(455\) −2.00000 4.00000i −0.0937614 0.187523i
\(456\) −12.0000 −0.561951
\(457\) 9.89949 9.89949i 0.463079 0.463079i −0.436584 0.899663i \(-0.643812\pi\)
0.899663 + 0.436584i \(0.143812\pi\)
\(458\) −14.1421 14.1421i −0.660819 0.660819i
\(459\) −11.3137 −0.528079
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 8.82843 + 3.17157i 0.410736 + 0.147555i
\(463\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(464\) −1.41421 −0.0656532
\(465\) −12.0000 4.00000i −0.556487 0.185496i
\(466\) −14.0000 −0.648537
\(467\) −8.00000 8.00000i −0.370196 0.370196i 0.497353 0.867548i \(-0.334306\pi\)
−0.867548 + 0.497353i \(0.834306\pi\)
\(468\) −7.07107 7.07107i −0.326860 0.326860i
\(469\) 4.24264 0.195907
\(470\) 7.07107 + 14.1421i 0.326164 + 0.652328i
\(471\) 52.0000 2.39603
\(472\) 5.65685 5.65685i 0.260378 0.260378i
\(473\) −24.9706 8.97056i −1.14815 0.412467i
\(474\) 20.0000i 0.918630i
\(475\) 12.7279 16.9706i 0.583997 0.778663i
\(476\) −2.00000 −0.0916698
\(477\) 30.0000 + 30.0000i 1.37361 + 1.37361i
\(478\) 1.00000 1.00000i 0.0457389 0.0457389i
\(479\) 36.7696 1.68004 0.840022 0.542553i \(-0.182542\pi\)
0.840022 + 0.542553i \(0.182542\pi\)
\(480\) −5.65685 + 2.82843i −0.258199 + 0.129099i
\(481\) 11.3137i 0.515861i
\(482\) 17.0000 + 17.0000i 0.774329 + 0.774329i
\(483\) 0 0
\(484\) −8.48528 7.00000i −0.385695 0.318182i
\(485\) 2.00000 6.00000i 0.0908153 0.272446i
\(486\) 14.1421i 0.641500i
\(487\) 10.0000 + 10.0000i 0.453143 + 0.453143i 0.896396 0.443253i \(-0.146176\pi\)
−0.443253 + 0.896396i \(0.646176\pi\)
\(488\) −4.00000 + 4.00000i −0.181071 + 0.181071i
\(489\) 60.0000i 2.71329i
\(490\) 0.707107 2.12132i 0.0319438 0.0958315i
\(491\) 36.7696i 1.65939i 0.558219 + 0.829693i \(0.311485\pi\)
−0.558219 + 0.829693i \(0.688515\pi\)
\(492\) 8.48528 8.48528i 0.382546 0.382546i
\(493\) 2.00000 2.00000i 0.0900755 0.0900755i
\(494\) 8.48528 0.381771
\(495\) −22.9289 + 29.1421i −1.03058 + 1.30984i
\(496\) −2.00000 −0.0898027
\(497\) 5.65685 5.65685i 0.253745 0.253745i
\(498\) −20.0000 + 20.0000i −0.896221 + 0.896221i
\(499\) 20.0000i 0.895323i 0.894203 + 0.447661i \(0.147743\pi\)
−0.894203 + 0.447661i \(0.852257\pi\)
\(500\) 2.00000 11.0000i 0.0894427 0.491935i
\(501\) 0 0
\(502\) −2.82843 + 2.82843i −0.126239 + 0.126239i
\(503\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(504\) 5.00000i 0.222718i
\(505\) 39.5980 19.7990i 1.76209 0.881043i
\(506\) 0 0
\(507\) −18.0000 18.0000i −0.799408 0.799408i
\(508\) −9.89949 9.89949i −0.439219 0.439219i
\(509\) 18.0000i 0.797836i −0.916987 0.398918i \(-0.869386\pi\)
0.916987 0.398918i \(-0.130614\pi\)
\(510\) 4.00000 12.0000i 0.177123 0.531369i
\(511\) −16.0000 −0.707798
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 16.9706 + 16.9706i 0.749269 + 0.749269i
\(514\) 0 0
\(515\) −9.00000 3.00000i −0.396587 0.132196i
\(516\) 22.6274i 0.996116i
\(517\) 22.0711 + 7.92893i 0.970684 + 0.348714i
\(518\) 4.00000 4.00000i 0.175750 0.175750i
\(519\) −28.2843 −1.24154
\(520\) 4.00000 2.00000i 0.175412 0.0877058i
\(521\) 2.00000 0.0876216 0.0438108 0.999040i \(-0.486050\pi\)
0.0438108 + 0.999040i \(0.486050\pi\)
\(522\) 5.00000 + 5.00000i 0.218844 + 0.218844i
\(523\) 14.1421 + 14.1421i 0.618392 + 0.618392i 0.945119 0.326727i \(-0.105946\pi\)
−0.326727 + 0.945119i \(0.605946\pi\)
\(524\) 15.5563 0.679582
\(525\) 11.3137 + 8.48528i 0.493771 + 0.370328i
\(526\) −10.0000 −0.436021
\(527\) 2.82843 2.82843i 0.123208 0.123208i
\(528\) −3.17157 + 8.82843i −0.138025 + 0.384208i
\(529\) 23.0000i 1.00000i
\(530\) −16.9706 + 8.48528i −0.737154 + 0.368577i
\(531\) −40.0000 −1.73585
\(532\) 3.00000 + 3.00000i 0.130066 + 0.130066i
\(533\) −6.00000 + 6.00000i −0.259889 + 0.259889i
\(534\) −16.9706 −0.734388
\(535\) −42.4264 14.1421i −1.83425 0.611418i
\(536\) 4.24264i 0.183254i
\(537\) 36.0000 + 36.0000i 1.55351 + 1.55351i
\(538\) −16.9706 16.9706i −0.731653 0.731653i
\(539\) −1.41421 3.00000i −0.0609145 0.129219i
\(540\) 12.0000 + 4.00000i 0.516398 + 0.172133i
\(541\) 24.0416i 1.03363i −0.856097 0.516815i \(-0.827117\pi\)
0.856097 0.516815i \(-0.172883\pi\)
\(542\) −6.00000 6.00000i −0.257722 0.257722i
\(543\) −20.0000 + 20.0000i −0.858282 + 0.858282i
\(544\) 2.00000i 0.0857493i
\(545\) −18.3848 36.7696i −0.787517 1.57503i
\(546\) 5.65685i 0.242091i
\(547\) −8.48528 + 8.48528i −0.362804 + 0.362804i −0.864844 0.502040i \(-0.832583\pi\)
0.502040 + 0.864844i \(0.332583\pi\)
\(548\) −5.00000 + 5.00000i −0.213589 + 0.213589i
\(549\) 28.2843 1.20714
\(550\) −9.12132 13.8492i −0.388934 0.590534i
\(551\) −6.00000 −0.255609
\(552\) 0 0
\(553\) −5.00000 + 5.00000i −0.212622 + 0.212622i
\(554\) 28.0000i 1.18961i
\(555\) 16.0000 + 32.0000i 0.679162 + 1.35832i
\(556\) 1.41421i 0.0599760i
\(557\) −12.7279 + 12.7279i −0.539299 + 0.539299i −0.923323 0.384024i \(-0.874538\pi\)
0.384024 + 0.923323i \(0.374538\pi\)
\(558\) 7.07107 + 7.07107i 0.299342 + 0.299342i
\(559\) 16.0000i 0.676728i
\(560\) 2.12132 + 0.707107i 0.0896421 + 0.0298807i
\(561\) −8.00000 16.9706i −0.337760 0.716498i
\(562\) 20.0000 + 20.0000i 0.843649 + 0.843649i
\(563\) 21.2132 + 21.2132i 0.894030 + 0.894030i 0.994900 0.100870i \(-0.0321625\pi\)
−0.100870 + 0.994900i \(0.532163\pi\)
\(564\) 20.0000i 0.842152i
\(565\) −39.0000 13.0000i −1.64074 0.546914i
\(566\) 28.0000 1.17693
\(567\) −0.707107 + 0.707107i −0.0296957 + 0.0296957i
\(568\) 5.65685 + 5.65685i 0.237356 + 0.237356i
\(569\) −33.9411 −1.42289 −0.711443 0.702744i \(-0.751958\pi\)
−0.711443 + 0.702744i \(0.751958\pi\)
\(570\) −24.0000 + 12.0000i −1.00525 + 0.502625i
\(571\) 16.9706i 0.710196i 0.934829 + 0.355098i \(0.115552\pi\)
−0.934829 + 0.355098i \(0.884448\pi\)
\(572\) 2.24264 6.24264i 0.0937695 0.261018i
\(573\) 0 0
\(574\) −4.24264 −0.177084
\(575\) 0 0
\(576\) 5.00000 0.208333
\(577\) −6.00000 6.00000i −0.249783 0.249783i 0.571098 0.820882i \(-0.306517\pi\)
−0.820882 + 0.571098i \(0.806517\pi\)
\(578\) −9.19239 9.19239i −0.382353 0.382353i
\(579\) −50.9117 −2.11582
\(580\) −2.82843 + 1.41421i −0.117444 + 0.0587220i
\(581\) 10.0000 0.414870
\(582\) −5.65685 + 5.65685i −0.234484 + 0.234484i
\(583\) −9.51472 + 26.4853i −0.394059 + 1.09691i
\(584\) 16.0000i 0.662085i
\(585\) −21.2132 7.07107i −0.877058 0.292353i
\(586\) 2.00000 0.0826192
\(587\) 4.00000 + 4.00000i 0.165098 + 0.165098i 0.784821 0.619723i \(-0.212755\pi\)
−0.619723 + 0.784821i \(0.712755\pi\)
\(588\) −2.00000 + 2.00000i −0.0824786 + 0.0824786i
\(589\) −8.48528 −0.349630
\(590\) 5.65685 16.9706i 0.232889 0.698667i
\(591\) 0 0
\(592\) 4.00000 + 4.00000i 0.164399 + 0.164399i
\(593\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(594\) 16.9706 8.00000i 0.696311 0.328244i
\(595\) −4.00000 + 2.00000i −0.163984 + 0.0819920i
\(596\) 1.41421i 0.0579284i
\(597\) 32.0000 + 32.0000i 1.30967 + 1.30967i
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) −8.48528 + 11.3137i −0.346410 + 0.461880i
\(601\) 21.2132i 0.865305i 0.901561 + 0.432652i \(0.142422\pi\)
−0.901561 + 0.432652i \(0.857578\pi\)
\(602\) 5.65685 5.65685i 0.230556 0.230556i
\(603\) 15.0000 15.0000i 0.610847 0.610847i
\(604\) 9.89949 0.402805
\(605\) −23.9706 5.51472i −0.974542 0.224205i
\(606\) −56.0000 −2.27484
\(607\) −19.7990 + 19.7990i −0.803616 + 0.803616i −0.983659 0.180043i \(-0.942376\pi\)
0.180043 + 0.983659i \(0.442376\pi\)
\(608\) −3.00000 + 3.00000i −0.121666 + 0.121666i
\(609\) 4.00000i 0.162088i
\(610\) −4.00000 + 12.0000i −0.161955 + 0.485866i
\(611\) 14.1421i 0.572130i
\(612\) −7.07107 + 7.07107i −0.285831 + 0.285831i
\(613\) −9.89949 9.89949i −0.399837 0.399837i 0.478339 0.878175i \(-0.341239\pi\)
−0.878175 + 0.478339i \(0.841239\pi\)
\(614\) 28.0000i 1.12999i
\(615\) 8.48528 25.4558i 0.342160 1.02648i
\(616\) 3.00000 1.41421i 0.120873 0.0569803i
\(617\) −17.0000 17.0000i −0.684394 0.684394i 0.276593 0.960987i \(-0.410795\pi\)
−0.960987 + 0.276593i \(0.910795\pi\)
\(618\) 8.48528 + 8.48528i 0.341328 + 0.341328i
\(619\) 4.00000i 0.160774i 0.996764 + 0.0803868i \(0.0256155\pi\)
−0.996764 + 0.0803868i \(0.974384\pi\)
\(620\) −4.00000 + 2.00000i −0.160644 + 0.0803219i
\(621\) 0 0
\(622\) 0 0
\(623\) 4.24264 + 4.24264i 0.169978 + 0.169978i
\(624\) −5.65685 −0.226455
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 0 0
\(627\) −13.4558 + 37.4558i −0.537375 + 1.49584i
\(628\) 13.0000 13.0000i 0.518756 0.518756i
\(629\) −11.3137 −0.451107
\(630\) −5.00000 10.0000i −0.199205 0.398410i
\(631\) −20.0000 −0.796187 −0.398094 0.917345i \(-0.630328\pi\)
−0.398094 + 0.917345i \(0.630328\pi\)
\(632\) −5.00000 5.00000i −0.198889 0.198889i
\(633\) 22.6274 + 22.6274i 0.899359 + 0.899359i
\(634\) 31.1127 1.23564
\(635\) −29.6985 9.89949i −1.17855 0.392849i
\(636\) 24.0000 0.951662
\(637\) 1.41421 1.41421i 0.0560332 0.0560332i
\(638\) −1.58579 + 4.41421i −0.0627819 + 0.174760i
\(639\) 40.0000i 1.58238i
\(640\) −0.707107 + 2.12132i −0.0279508 + 0.0838525i
\(641\) 24.0000 0.947943 0.473972 0.880540i \(-0.342820\pi\)
0.473972 + 0.880540i \(0.342820\pi\)
\(642\) 40.0000 + 40.0000i 1.57867 + 1.57867i
\(643\) 6.00000 6.00000i 0.236617 0.236617i −0.578831 0.815448i \(-0.696491\pi\)
0.815448 + 0.578831i \(0.196491\pi\)
\(644\) 0 0
\(645\) 22.6274 + 45.2548i 0.890954 + 1.78191i
\(646\) 8.48528i 0.333849i
\(647\) 5.00000 + 5.00000i 0.196570 + 0.196570i 0.798528 0.601958i \(-0.205612\pi\)
−0.601958 + 0.798528i \(0.705612\pi\)
\(648\) −0.707107 0.707107i −0.0277778 0.0277778i
\(649\) −11.3137 24.0000i −0.444102 0.942082i
\(650\) 6.00000 8.00000i 0.235339 0.313786i
\(651\) 5.65685i 0.221710i
\(652\) 15.0000 + 15.0000i 0.587445 + 0.587445i
\(653\) −10.0000 + 10.0000i −0.391330 + 0.391330i −0.875161 0.483831i \(-0.839245\pi\)
0.483831 + 0.875161i \(0.339245\pi\)
\(654\) 52.0000i 2.03336i
\(655\) 31.1127 15.5563i 1.21567 0.607837i
\(656\) 4.24264i 0.165647i
\(657\) −56.5685 + 56.5685i −2.20695 + 2.20695i
\(658\) −5.00000 + 5.00000i −0.194920 + 0.194920i
\(659\) −36.7696 −1.43234 −0.716169 0.697927i \(-0.754106\pi\)
−0.716169 + 0.697927i \(0.754106\pi\)
\(660\) 2.48528 + 20.8284i 0.0967394 + 0.810745i
\(661\) 16.0000 0.622328 0.311164 0.950356i \(-0.399281\pi\)
0.311164 + 0.950356i \(0.399281\pi\)
\(662\) 19.7990 19.7990i 0.769510 0.769510i
\(663\) 8.00000 8.00000i 0.310694 0.310694i
\(664\) 10.0000i 0.388075i
\(665\) 9.00000 + 3.00000i 0.349005 + 0.116335i
\(666\) 28.2843i 1.09599i
\(667\) 0 0
\(668\) 0 0
\(669\) 4.00000i 0.154649i
\(670\) 4.24264 + 8.48528i 0.163908 + 0.327815i
\(671\) 8.00000 + 16.9706i 0.308837 + 0.655141i
\(672\) −2.00000 2.00000i −0.0771517 0.0771517i
\(673\) −21.2132 21.2132i −0.817709 0.817709i 0.168067 0.985776i \(-0.446248\pi\)
−0.985776 + 0.168067i \(0.946248\pi\)
\(674\) 2.00000i 0.0770371i
\(675\) 28.0000 4.00000i 1.07772 0.153960i
\(676\) −9.00000 −0.346154
\(677\) −12.7279 + 12.7279i −0.489174 + 0.489174i −0.908045 0.418872i \(-0.862426\pi\)
0.418872 + 0.908045i \(0.362426\pi\)
\(678\) 36.7696 + 36.7696i 1.41213 + 1.41213i
\(679\) 2.82843 0.108545
\(680\) −2.00000 4.00000i −0.0766965 0.153393i
\(681\) 33.9411i 1.30063i
\(682\) −2.24264 + 6.24264i −0.0858752 + 0.239043i
\(683\) 5.00000 5.00000i 0.191320 0.191320i −0.604946 0.796266i \(-0.706805\pi\)
0.796266 + 0.604946i \(0.206805\pi\)
\(684\) 21.2132 0.811107
\(685\) −5.00000 + 15.0000i −0.191040 + 0.573121i
\(686\) 1.00000 0.0381802
\(687\) 40.0000 + 40.0000i 1.52610 + 1.52610i
\(688\) 5.65685 + 5.65685i 0.215666 + 0.215666i
\(689\) −16.9706 −0.646527
\(690\) 0 0
\(691\) −28.0000 −1.06517 −0.532585 0.846376i \(-0.678779\pi\)
−0.532585 + 0.846376i \(0.678779\pi\)
\(692\) −7.07107 + 7.07107i −0.268802 + 0.268802i
\(693\) −15.6066 5.60660i −0.592846 0.212977i
\(694\) 12.0000i 0.455514i
\(695\) −1.41421 2.82843i −0.0536442 0.107288i
\(696\) 4.00000 0.151620
\(697\) 6.00000 + 6.00000i 0.227266 + 0.227266i
\(698\) 6.00000 6.00000i 0.227103 0.227103i
\(699\) 39.5980 1.49773
\(700\) 4.94975 0.707107i 0.187083 0.0267261i
\(701\) 7.07107i 0.267071i 0.991044 + 0.133535i \(0.0426329\pi\)
−0.991044 + 0.133535i \(0.957367\pi\)
\(702\) 8.00000 + 8.00000i 0.301941 + 0.301941i
\(703\) 16.9706 + 16.9706i 0.640057 + 0.640057i
\(704\) 1.41421 + 3.00000i 0.0533002 + 0.113067i
\(705\) −20.0000 40.0000i −0.753244 1.50649i
\(706\) 16.9706i 0.638696i
\(707\) 14.0000 + 14.0000i 0.526524 + 0.526524i
\(708\) −16.0000 + 16.0000i −0.601317 + 0.601317i
\(709\) 10.0000i 0.375558i 0.982211 + 0.187779i \(0.0601289\pi\)
−0.982211 + 0.187779i \(0.939871\pi\)
\(710\) 16.9706 + 5.65685i 0.636894 + 0.212298i
\(711\) 35.3553i 1.32593i
\(712\) −4.24264 + 4.24264i −0.159000 + 0.159000i
\(713\) 0 0
\(714\) 5.65685 0.211702
\(715\) −1.75736 14.7279i −0.0657215 0.550793i
\(716\) 18.0000 0.672692
\(717\) −2.82843 + 2.82843i −0.105630 + 0.105630i
\(718\) 1.00000 1.00000i 0.0373197 0.0373197i
\(719\) 10.0000i 0.372937i 0.982461 + 0.186469i \(0.0597042\pi\)
−0.982461 + 0.186469i \(0.940296\pi\)
\(720\) 10.0000 5.00000i 0.372678 0.186339i
\(721\) 4.24264i 0.158004i
\(722\) 0.707107 0.707107i 0.0263158 0.0263158i
\(723\) −48.0833 48.0833i −1.78824 1.78824i
\(724\) 10.0000i 0.371647i
\(725\) −4.24264 + 5.65685i −0.157568 + 0.210090i
\(726\) 24.0000 + 19.7990i 0.890724 + 0.734809i
\(727\) −5.00000 5.00000i −0.185440 0.185440i 0.608282 0.793721i \(-0.291859\pi\)
−0.793721 + 0.608282i \(0.791859\pi\)
\(728\) 1.41421 + 1.41421i 0.0524142 + 0.0524142i
\(729\) 43.0000i 1.59259i
\(730\) −16.0000 32.0000i −0.592187 1.18437i
\(731\) −16.0000 −0.591781
\(732\) 11.3137 11.3137i 0.418167 0.418167i
\(733\) −32.5269 32.5269i −1.20141 1.20141i −0.973738 0.227671i \(-0.926889\pi\)
−0.227671 0.973738i \(-0.573111\pi\)
\(734\) 12.7279 0.469796
\(735\) −2.00000 + 6.00000i −0.0737711 + 0.221313i
\(736\) 0 0
\(737\) 13.2426 + 4.75736i 0.487799 + 0.175240i
\(738\) −15.0000 + 15.0000i −0.552158 + 0.552158i
\(739\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(740\) 12.0000 + 4.00000i 0.441129 + 0.147043i
\(741\) −24.0000 −0.881662
\(742\) −6.00000 6.00000i −0.220267 0.220267i
\(743\) 1.41421 + 1.41421i 0.0518825 + 0.0518825i 0.732572 0.680690i \(-0.238320\pi\)
−0.680690 + 0.732572i \(0.738320\pi\)
\(744\) 5.65685 0.207390
\(745\) −1.41421 2.82843i −0.0518128 0.103626i
\(746\) −32.0000 −1.17160
\(747\) 35.3553 35.3553i 1.29358 1.29358i
\(748\) −6.24264 2.24264i −0.228254 0.0819991i
\(749\) 20.0000i 0.730784i
\(750\) −5.65685 + 31.1127i −0.206559 + 1.13608i
\(751\) 40.0000 1.45962 0.729810 0.683650i \(-0.239608\pi\)
0.729810 + 0.683650i \(0.239608\pi\)
\(752\) −5.00000 5.00000i −0.182331 0.182331i
\(753\) 8.00000 8.00000i 0.291536 0.291536i
\(754\) −2.82843 −0.103005
\(755\) 19.7990 9.89949i 0.720559 0.360280i
\(756\) 5.65685i 0.205738i
\(757\) 12.0000 + 12.0000i 0.436147 + 0.436147i 0.890713 0.454566i \(-0.150206\pi\)
−0.454566 + 0.890713i \(0.650206\pi\)
\(758\) −9.89949 9.89949i −0.359566 0.359566i
\(759\) 0 0
\(760\) −3.00000 + 9.00000i −0.108821 + 0.326464i
\(761\) 24.0416i 0.871508i −0.900066 0.435754i \(-0.856482\pi\)
0.900066 0.435754i \(-0.143518\pi\)
\(762\) 28.0000 + 28.0000i 1.01433 + 1.01433i
\(763\) 13.0000 13.0000i 0.470632 0.470632i
\(764\) 0 0
\(765\) −7.07107 + 21.2132i −0.255655 + 0.766965i
\(766\) 32.5269i 1.17525i
\(767\) 11.3137 11.3137i 0.408514 0.408514i
\(768\) 2.00000 2.00000i 0.0721688 0.0721688i
\(769\) 4.24264 0.152994 0.0764968 0.997070i \(-0.475627\pi\)
0.0764968 + 0.997070i \(0.475627\pi\)
\(770\) 4.58579 5.82843i 0.165260 0.210042i
\(771\) 0 0
\(772\) −12.7279 + 12.7279i −0.458088 + 0.458088i
\(773\) −25.0000 + 25.0000i −0.899188 + 0.899188i −0.995364 0.0961768i \(-0.969339\pi\)
0.0961768 + 0.995364i \(0.469339\pi\)
\(774\) 40.0000i 1.43777i
\(775\) −6.00000 + 8.00000i −0.215526 + 0.287368i
\(776\) 2.82843i 0.101535i
\(777\) −11.3137 + 11.3137i −0.405877 + 0.405877i
\(778\) 1.41421 + 1.41421i 0.0507020 + 0.0507020i
\(779\) 18.0000i 0.644917i
\(780\) −11.3137 + 5.65685i −0.405096 + 0.202548i
\(781\) 24.0000 11.3137i 0.858788 0.404836i
\(782\) 0 0
\(783\) −5.65685 5.65685i −0.202159 0.202159i
\(784\) 1.00000i 0.0357143i
\(785\) 13.0000 39.0000i 0.463990 1.39197i
\(786\) −44.0000 −1.56943
\(787\) 15.5563 15.5563i 0.554524 0.554524i −0.373219 0.927743i \(-0.621746\pi\)
0.927743 + 0.373219i \(0.121746\pi\)
\(788\) 0 0
\(789\) 28.2843 1.00695
\(790\) −15.0000 5.00000i −0.533676 0.177892i
\(791\) 18.3848i 0.653687i
\(792\) 5.60660 15.6066i 0.199222 0.554556i
\(793\) −8.00000 + 8.00000i −0.284088 + 0.284088i
\(794\) 32.5269 1.15434
\(795\) 48.0000 24.0000i 1.70238 0.851192i
\(796\) 16.0000 0.567105
\(797\) −25.0000 25.0000i −0.885545 0.885545i 0.108546 0.994091i \(-0.465381\pi\)
−0.994091 + 0.108546i \(0.965381\pi\)
\(798\) −8.48528 8.48528i −0.300376 0.300376i
\(799\) 14.1421 0.500313
\(800\) 0.707107 + 4.94975i 0.0250000 + 0.175000i
\(801\) 30.0000 1.06000
\(802\) −24.0416 + 24.0416i −0.848939 + 0.848939i
\(803\) −49.9411 17.9411i −1.76238 0.633129i
\(804\) 12.0000i 0.423207i
\(805\) 0 0
\(806\) −4.00000 −0.140894
\(807\) 48.0000 + 48.0000i 1.68968 + 1.68968i
\(808\) −14.0000 + 14.0000i −0.492518 + 0.492518i
\(809\) 16.9706 0.596653 0.298327 0.954464i \(-0.403572\pi\)
0.298327 + 0.954464i \(0.403572\pi\)
\(810\) −2.12132 0.707107i −0.0745356 0.0248452i
\(811\) 41.0122i 1.44013i 0.693905 + 0.720066i \(0.255889\pi\)
−0.693905 + 0.720066i \(0.744111\pi\)
\(812\) −1.00000 1.00000i −0.0350931 0.0350931i
\(813\) 16.9706 + 16.9706i 0.595184 + 0.595184i
\(814\) 16.9706 8.00000i 0.594818 0.280400i
\(815\) 45.0000 + 15.0000i 1.57628 + 0.525427i
\(816\) 5.65685i 0.198030i
\(817\) 24.0000 + 24.0000i 0.839654 + 0.839654i
\(818\) −21.0000 + 21.0000i −0.734248 + 0.734248i
\(819\) 10.0000i 0.349428i
\(820\) −4.24264 8.48528i −0.148159 0.296319i
\(821\) 29.6985i 1.03648i −0.855234 0.518242i \(-0.826587\pi\)
0.855234 0.518242i \(-0.173413\pi\)
\(822\) 14.1421 14.1421i 0.493264 0.493264i
\(823\) 18.0000 18.0000i 0.627441 0.627441i −0.319983 0.947423i \(-0.603677\pi\)
0.947423 + 0.319983i \(0.103677\pi\)
\(824\) 4.24264 0.147799
\(825\) 25.7990 + 39.1716i 0.898206 + 1.36378i
\(826\) 8.00000 0.278356
\(827\) 5.65685 5.65685i 0.196708 0.196708i −0.601879 0.798587i \(-0.705581\pi\)
0.798587 + 0.601879i \(0.205581\pi\)
\(828\) 0 0
\(829\) 2.00000i 0.0694629i −0.999397 0.0347314i \(-0.988942\pi\)
0.999397 0.0347314i \(-0.0110576\pi\)
\(830\) 10.0000 + 20.0000i 0.347105 + 0.694210i
\(831\) 79.1960i 2.74728i
\(832\) −1.41421 + 1.41421i −0.0490290 + 0.0490290i
\(833\) −1.41421 1.41421i −0.0489996 0.0489996i
\(834\) 4.00000i 0.138509i
\(835\) 0 0
\(836\) 6.00000 + 12.7279i 0.207514 + 0.440204i
\(837\) −8.00000 8.00000i −0.276520 0.276520i
\(838\) 28.2843 + 28.2843i 0.977064 + 0.977064i
\(839\) 42.0000i 1.45000i −0.688748 0.725001i \(-0.741839\pi\)
0.688748 0.725001i \(-0.258161\pi\)
\(840\) −6.00000 2.00000i −0.207020 0.0690066i
\(841\) −27.0000 −0.931034
\(842\) −7.07107 + 7.07107i −0.243685 + 0.243685i
\(843\) −56.5685 56.5685i −1.94832 1.94832i
\(844\) 11.3137 0.389434
\(845\) −18.0000 + 9.00000i −0.619219 + 0.309609i
\(846\) 35.3553i 1.21554i
\(847\) −1.05025 10.9497i −0.0360871 0.376238i
\(848\) 6.00000 6.00000i 0.206041 0.206041i
\(849\) −79.1960 −2.71800
\(850\) −8.00000 6.00000i −0.274398 0.205798i
\(851\) 0 0
\(852\) −16.0000 16.0000i −0.548151 0.548151i
\(853\) −4.24264 4.24264i −0.145265 0.145265i 0.630734 0.775999i \(-0.282754\pi\)
−0.775999 + 0.630734i \(0.782754\pi\)
\(854\) −5.65685 −0.193574
\(855\) 42.4264 21.2132i 1.45095 0.725476i
\(856\) 20.0000 0.683586
\(857\) −14.1421 + 14.1421i −0.483086 + 0.483086i −0.906116 0.423030i \(-0.860967\pi\)
0.423030 + 0.906116i \(0.360967\pi\)
\(858\) −6.34315 + 17.6569i −0.216551 + 0.602795i
\(859\) 16.0000i 0.545913i 0.962026 + 0.272956i \(0.0880015\pi\)
−0.962026 + 0.272956i \(0.911998\pi\)
\(860\) 16.9706 + 5.65685i 0.578691 + 0.192897i
\(861\) 12.0000 0.408959
\(862\) −1.00000 1.00000i −0.0340601 0.0340601i
\(863\) −14.0000 + 14.0000i −0.476566 + 0.476566i −0.904031 0.427466i \(-0.859406\pi\)
0.427466 + 0.904031i \(0.359406\pi\)
\(864\) −5.65685 −0.192450
\(865\) −7.07107 + 21.2132i −0.240424 + 0.721271i
\(866\) 33.9411i 1.15337i
\(867\) 26.0000 + 26.0000i 0.883006 + 0.883006i
\(868\) −1.41421 1.41421i −0.0480015 0.0480015i
\(869\) −21.2132 + 10.0000i −0.719609 + 0.339227i
\(870\) 8.00000 4.00000i 0.271225 0.135613i
\(871\) 8.48528i 0.287513i
\(872\) 13.0000 + 13.0000i 0.440236 + 0.440236i
\(873\) 10.0000 10.0000i 0.338449 0.338449i
\(874\) 0 0
\(875\) 9.19239 6.36396i 0.310759 0.215141i
\(876\) 45.2548i 1.52902i
\(877\) −19.7990 + 19.7990i −0.668564 + 0.668564i −0.957384 0.288819i \(-0.906737\pi\)
0.288819 + 0.957384i \(0.406737\pi\)
\(878\) 18.0000 18.0000i 0.607471 0.607471i
\(879\) −5.65685 −0.190801
\(880\) 5.82843 + 4.58579i 0.196476 + 0.154587i
\(881\) 18.0000 0.606435 0.303218 0.952921i \(-0.401939\pi\)
0.303218 + 0.952921i \(0.401939\pi\)
\(882\) 3.53553 3.53553i 0.119048 0.119048i
\(883\) 9.00000 9.00000i 0.302874 0.302874i −0.539263 0.842137i \(-0.681297\pi\)
0.842137 + 0.539263i \(0.181297\pi\)
\(884\) 4.00000i 0.134535i
\(885\) −16.0000 + 48.0000i −0.537834 + 1.61350i
\(886\) 21.2132i 0.712672i
\(887\) −5.65685 + 5.65685i −0.189939 + 0.189939i −0.795670 0.605731i \(-0.792881\pi\)
0.605731 + 0.795670i \(0.292881\pi\)
\(888\) −11.3137 11.3137i −0.379663 0.379663i
\(889\) 14.0000i 0.469545i
\(890\) −4.24264 + 12.7279i −0.142214 + 0.426641i
\(891\) −3.00000 + 1.41421i −0.100504 + 0.0473779i
\(892\) −1.00000 1.00000i −0.0334825 0.0334825i
\(893\) −21.2132 21.2132i −0.709873 0.709873i
\(894\) 4.00000i 0.133780i
\(895\) 36.0000 18.0000i 1.20335 0.601674i
\(896\) −1.00000 −0.0334077
\(897\) 0 0
\(898\) 28.2843 + 28.2843i 0.943858 + 0.943858i
\(899\) 2.82843 0.0943333
\(900\) 15.0000 20.0000i 0.500000 0.666667i
\(901\) 16.9706i 0.565371i
\(902\) −13.2426 4.75736i −0.440932 0.158403i
\(903\) −16.0000 + 16.0000i −0.532447 + 0.532447i
\(904\) 18.3848 0.611469
\(905\) 10.0000 + 20.0000i 0.332411 + 0.664822i
\(906\) −28.0000 −0.930238
\(907\) −1.00000 1.00000i −0.0332045 0.0332045i 0.690310 0.723514i \(-0.257474\pi\)
−0.723514 + 0.690310i \(0.757474\pi\)
\(908\) −8.48528 8.48528i −0.281594 0.281594i
\(909\) 98.9949 3.28346
\(910\) 4.24264 + 1.41421i 0.140642 + 0.0468807i
\(911\) −20.0000 −0.662630 −0.331315 0.943520i \(-0.607492\pi\)
−0.331315 + 0.943520i \(0.607492\pi\)
\(912\) 8.48528 8.48528i 0.280976 0.280976i
\(913\) 31.2132 + 11.2132i 1.03301 + 0.371103i
\(914\) 14.0000i 0.463079i
\(915\) 11.3137 33.9411i 0.374020 1.12206i
\(916\) 20.0000 0.660819
\(917\) 11.0000 + 11.0000i 0.363252 + 0.363252i
\(918\) 8.00000 8.00000i 0.264039 0.264039i
\(919\) −24.0416 −0.793060 −0.396530 0.918022i \(-0.629786\pi\)
−0.396530 + 0.918022i \(0.629786\pi\)
\(920\) 0 0
\(921\) 79.1960i 2.60960i
\(922\) 0 0
\(923\) 11.3137 + 11.3137i 0.372395 + 0.372395i
\(924\) −8.48528 + 4.00000i −0.279145 + 0.131590i
\(925\) 28.0000 4.00000i 0.920634 0.131519i
\(926\) 0 0
\(927\) −15.0000 15.0000i −0.492665 0.492665i
\(928\) 1.00000 1.00000i 0.0328266 0.0328266i
\(929\) 38.0000i 1.24674i −0.781927 0.623370i \(-0.785763\pi\)
0.781927 0.623370i \(-0.214237\pi\)
\(930\) 11.3137 5.65685i 0.370991 0.185496i
\(931\) 4.24264i 0.139047i
\(932\) 9.89949 9.89949i 0.324269 0.324269i
\(933\) 0 0
\(934\) 11.3137 0.370196
\(935\) −14.7279 + 1.75736i −0.481655 + 0.0574718i
\(936\) 10.0000 0.326860
\(937\) −29.6985 + 29.6985i −0.970207 + 0.970207i −0.999569 0.0293616i \(-0.990653\pi\)
0.0293616 + 0.999569i \(0.490653\pi\)
\(938\) −3.00000 + 3.00000i −0.0979535 + 0.0979535i
\(939\) 0 0
\(940\) −15.0000 5.00000i −0.489246 0.163082i
\(941\) 59.3970i 1.93629i 0.250398 + 0.968143i \(0.419438\pi\)
−0.250398 + 0.968143i \(0.580562\pi\)
\(942\) −36.7696 + 36.7696i −1.19802 + 1.19802i
\(943\) 0 0
\(944\) 8.00000i 0.260378i
\(945\) 5.65685 + 11.3137i 0.184017 + 0.368035i
\(946\) 24.0000 11.3137i 0.780307 0.367840i
\(947\) −19.0000 19.0000i −0.617417 0.617417i 0.327451 0.944868i \(-0.393810\pi\)
−0.944868 + 0.327451i \(0.893810\pi\)
\(948\) 14.1421 + 14.1421i 0.459315 + 0.459315i
\(949\) 32.0000i 1.03876i
\(950\) 3.00000 + 21.0000i 0.0973329 + 0.681330i
\(951\) −88.0000 −2.85360
\(952\) 1.41421 1.41421i 0.0458349 0.0458349i
\(953\) 1.41421 + 1.41421i 0.0458109 + 0.0458109i 0.729641 0.683830i \(-0.239687\pi\)
−0.683830 + 0.729641i \(0.739687\pi\)
\(954\) −42.4264 −1.37361
\(955\) 0 0
\(956\) 1.41421i 0.0457389i
\(957\) 4.48528 12.4853i 0.144989 0.403592i
\(958\) −26.0000 + 26.0000i −0.840022 + 0.840022i
\(959\) −7.07107 −0.228337
\(960\) 2.00000 6.00000i 0.0645497 0.193649i
\(961\) −27.0000 −0.870968
\(962\) 8.00000 + 8.00000i 0.257930 + 0.257930i
\(963\) −70.7107 70.7107i −2.27862 2.27862i
\(964\) −24.0416 −0.774329
\(965\) −12.7279 + 38.1838i −0.409726 + 1.22918i
\(966\) 0 0
\(967\) 21.2132 21.2132i 0.682171 0.682171i −0.278318 0.960489i \(-0.589777\pi\)
0.960489 + 0.278318i \(0.0897770\pi\)
\(968\) 10.9497 1.05025i 0.351938 0.0337564i
\(969\) 24.0000i 0.770991i
\(970\) 2.82843 + 5.65685i 0.0908153 + 0.181631i
\(971\) 28.0000 0.898563 0.449281 0.893390i \(-0.351680\pi\)
0.449281 + 0.893390i \(0.351680\pi\)
\(972\) −10.0000 10.0000i −0.320750 0.320750i
\(973\) 1.00000 1.00000i 0.0320585 0.0320585i
\(974\) −14.1421 −0.453143
\(975\) −16.9706 + 22.6274i −0.543493 + 0.724657i
\(976\) 5.65685i 0.181071i
\(977\) −35.0000 35.0000i −1.11975 1.11975i −0.991778 0.127971i \(-0.959153\pi\)
−0.127971 0.991778i \(-0.540847\pi\)
\(978\) −42.4264 42.4264i −1.35665 1.35665i
\(979\) 8.48528 + 18.0000i 0.271191 + 0.575282i
\(980\) 1.00000 + 2.00000i 0.0319438 + 0.0638877i
\(981\) 91.9239i 2.93490i
\(982\) −26.0000 26.0000i −0.829693 0.829693i
\(983\) −39.0000 + 39.0000i −1.24391 + 1.24391i −0.285540 + 0.958367i \(0.592173\pi\)
−0.958367 + 0.285540i \(0.907827\pi\)
\(984\) 12.0000i 0.382546i
\(985\) 0 0
\(986\) 2.82843i 0.0900755i
\(987\) 14.1421 14.1421i 0.450149 0.450149i
\(988\) −6.00000 + 6.00000i −0.190885 + 0.190885i
\(989\) 0 0
\(990\) −4.39340 36.8198i −0.139631 1.17021i
\(991\) −8.00000 −0.254128 −0.127064 0.991894i \(-0.540555\pi\)
−0.127064 + 0.991894i \(0.540555\pi\)
\(992\) 1.41421 1.41421i 0.0449013 0.0449013i
\(993\) −56.0000 + 56.0000i −1.77711 + 1.77711i
\(994\) 8.00000i 0.253745i
\(995\) 32.0000 16.0000i 1.01447 0.507234i
\(996\) 28.2843i 0.896221i
\(997\) 7.07107 7.07107i 0.223943 0.223943i −0.586214 0.810157i \(-0.699382\pi\)
0.810157 + 0.586214i \(0.199382\pi\)
\(998\) −14.1421 14.1421i −0.447661 0.447661i
\(999\) 32.0000i 1.01244i
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 770.2.m.c.197.1 yes 4
5.3 odd 4 inner 770.2.m.c.43.2 yes 4
11.10 odd 2 inner 770.2.m.c.197.2 yes 4
55.43 even 4 inner 770.2.m.c.43.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
770.2.m.c.43.1 4 55.43 even 4 inner
770.2.m.c.43.2 yes 4 5.3 odd 4 inner
770.2.m.c.197.1 yes 4 1.1 even 1 trivial
770.2.m.c.197.2 yes 4 11.10 odd 2 inner