Properties

Label 130.2.j.a.47.1
Level $130$
Weight $2$
Character 130.47
Analytic conductor $1.038$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [130,2,Mod(47,130)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(130, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("130.47");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 130 = 2 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 130.j (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.03805522628\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 47.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 130.47
Dual form 130.2.j.a.83.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000i q^{2} +(-2.00000 + 2.00000i) q^{3} -1.00000 q^{4} +(-1.00000 - 2.00000i) q^{5} +(2.00000 + 2.00000i) q^{6} -4.00000 q^{7} +1.00000i q^{8} -5.00000i q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(-2.00000 + 2.00000i) q^{3} -1.00000 q^{4} +(-1.00000 - 2.00000i) q^{5} +(2.00000 + 2.00000i) q^{6} -4.00000 q^{7} +1.00000i q^{8} -5.00000i q^{9} +(-2.00000 + 1.00000i) q^{10} +(-2.00000 + 2.00000i) q^{11} +(2.00000 - 2.00000i) q^{12} +(-3.00000 + 2.00000i) q^{13} +4.00000i q^{14} +(6.00000 + 2.00000i) q^{15} +1.00000 q^{16} +(3.00000 - 3.00000i) q^{17} -5.00000 q^{18} +(2.00000 - 2.00000i) q^{19} +(1.00000 + 2.00000i) q^{20} +(8.00000 - 8.00000i) q^{21} +(2.00000 + 2.00000i) q^{22} +(2.00000 + 2.00000i) q^{23} +(-2.00000 - 2.00000i) q^{24} +(-3.00000 + 4.00000i) q^{25} +(2.00000 + 3.00000i) q^{26} +(4.00000 + 4.00000i) q^{27} +4.00000 q^{28} +6.00000i q^{29} +(2.00000 - 6.00000i) q^{30} +(-6.00000 - 6.00000i) q^{31} -1.00000i q^{32} -8.00000i q^{33} +(-3.00000 - 3.00000i) q^{34} +(4.00000 + 8.00000i) q^{35} +5.00000i q^{36} -4.00000 q^{37} +(-2.00000 - 2.00000i) q^{38} +(2.00000 - 10.0000i) q^{39} +(2.00000 - 1.00000i) q^{40} +(-1.00000 - 1.00000i) q^{41} +(-8.00000 - 8.00000i) q^{42} +(-2.00000 - 2.00000i) q^{43} +(2.00000 - 2.00000i) q^{44} +(-10.0000 + 5.00000i) q^{45} +(2.00000 - 2.00000i) q^{46} -4.00000 q^{47} +(-2.00000 + 2.00000i) q^{48} +9.00000 q^{49} +(4.00000 + 3.00000i) q^{50} +12.0000i q^{51} +(3.00000 - 2.00000i) q^{52} +(-1.00000 + 1.00000i) q^{53} +(4.00000 - 4.00000i) q^{54} +(6.00000 + 2.00000i) q^{55} -4.00000i q^{56} +8.00000i q^{57} +6.00000 q^{58} +(2.00000 + 2.00000i) q^{59} +(-6.00000 - 2.00000i) q^{60} -12.0000 q^{61} +(-6.00000 + 6.00000i) q^{62} +20.0000i q^{63} -1.00000 q^{64} +(7.00000 + 4.00000i) q^{65} -8.00000 q^{66} +4.00000i q^{67} +(-3.00000 + 3.00000i) q^{68} -8.00000 q^{69} +(8.00000 - 4.00000i) q^{70} +(-2.00000 - 2.00000i) q^{71} +5.00000 q^{72} -10.0000i q^{73} +4.00000i q^{74} +(-2.00000 - 14.0000i) q^{75} +(-2.00000 + 2.00000i) q^{76} +(8.00000 - 8.00000i) q^{77} +(-10.0000 - 2.00000i) q^{78} +4.00000i q^{79} +(-1.00000 - 2.00000i) q^{80} -1.00000 q^{81} +(-1.00000 + 1.00000i) q^{82} +8.00000 q^{83} +(-8.00000 + 8.00000i) q^{84} +(-9.00000 - 3.00000i) q^{85} +(-2.00000 + 2.00000i) q^{86} +(-12.0000 - 12.0000i) q^{87} +(-2.00000 - 2.00000i) q^{88} +(-5.00000 - 5.00000i) q^{89} +(5.00000 + 10.0000i) q^{90} +(12.0000 - 8.00000i) q^{91} +(-2.00000 - 2.00000i) q^{92} +24.0000 q^{93} +4.00000i q^{94} +(-6.00000 - 2.00000i) q^{95} +(2.00000 + 2.00000i) q^{96} -9.00000i q^{98} +(10.0000 + 10.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 4 q^{3} - 2 q^{4} - 2 q^{5} + 4 q^{6} - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 4 q^{3} - 2 q^{4} - 2 q^{5} + 4 q^{6} - 8 q^{7} - 4 q^{10} - 4 q^{11} + 4 q^{12} - 6 q^{13} + 12 q^{15} + 2 q^{16} + 6 q^{17} - 10 q^{18} + 4 q^{19} + 2 q^{20} + 16 q^{21} + 4 q^{22} + 4 q^{23} - 4 q^{24} - 6 q^{25} + 4 q^{26} + 8 q^{27} + 8 q^{28} + 4 q^{30} - 12 q^{31} - 6 q^{34} + 8 q^{35} - 8 q^{37} - 4 q^{38} + 4 q^{39} + 4 q^{40} - 2 q^{41} - 16 q^{42} - 4 q^{43} + 4 q^{44} - 20 q^{45} + 4 q^{46} - 8 q^{47} - 4 q^{48} + 18 q^{49} + 8 q^{50} + 6 q^{52} - 2 q^{53} + 8 q^{54} + 12 q^{55} + 12 q^{58} + 4 q^{59} - 12 q^{60} - 24 q^{61} - 12 q^{62} - 2 q^{64} + 14 q^{65} - 16 q^{66} - 6 q^{68} - 16 q^{69} + 16 q^{70} - 4 q^{71} + 10 q^{72} - 4 q^{75} - 4 q^{76} + 16 q^{77} - 20 q^{78} - 2 q^{80} - 2 q^{81} - 2 q^{82} + 16 q^{83} - 16 q^{84} - 18 q^{85} - 4 q^{86} - 24 q^{87} - 4 q^{88} - 10 q^{89} + 10 q^{90} + 24 q^{91} - 4 q^{92} + 48 q^{93} - 12 q^{95} + 4 q^{96} + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/130\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(41\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −2.00000 + 2.00000i −1.15470 + 1.15470i −0.169102 + 0.985599i \(0.554087\pi\)
−0.985599 + 0.169102i \(0.945913\pi\)
\(4\) −1.00000 −0.500000
\(5\) −1.00000 2.00000i −0.447214 0.894427i
\(6\) 2.00000 + 2.00000i 0.816497 + 0.816497i
\(7\) −4.00000 −1.51186 −0.755929 0.654654i \(-0.772814\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 5.00000i 1.66667i
\(10\) −2.00000 + 1.00000i −0.632456 + 0.316228i
\(11\) −2.00000 + 2.00000i −0.603023 + 0.603023i −0.941113 0.338091i \(-0.890219\pi\)
0.338091 + 0.941113i \(0.390219\pi\)
\(12\) 2.00000 2.00000i 0.577350 0.577350i
\(13\) −3.00000 + 2.00000i −0.832050 + 0.554700i
\(14\) 4.00000i 1.06904i
\(15\) 6.00000 + 2.00000i 1.54919 + 0.516398i
\(16\) 1.00000 0.250000
\(17\) 3.00000 3.00000i 0.727607 0.727607i −0.242536 0.970143i \(-0.577979\pi\)
0.970143 + 0.242536i \(0.0779791\pi\)
\(18\) −5.00000 −1.17851
\(19\) 2.00000 2.00000i 0.458831 0.458831i −0.439440 0.898272i \(-0.644823\pi\)
0.898272 + 0.439440i \(0.144823\pi\)
\(20\) 1.00000 + 2.00000i 0.223607 + 0.447214i
\(21\) 8.00000 8.00000i 1.74574 1.74574i
\(22\) 2.00000 + 2.00000i 0.426401 + 0.426401i
\(23\) 2.00000 + 2.00000i 0.417029 + 0.417029i 0.884178 0.467150i \(-0.154719\pi\)
−0.467150 + 0.884178i \(0.654719\pi\)
\(24\) −2.00000 2.00000i −0.408248 0.408248i
\(25\) −3.00000 + 4.00000i −0.600000 + 0.800000i
\(26\) 2.00000 + 3.00000i 0.392232 + 0.588348i
\(27\) 4.00000 + 4.00000i 0.769800 + 0.769800i
\(28\) 4.00000 0.755929
\(29\) 6.00000i 1.11417i 0.830455 + 0.557086i \(0.188081\pi\)
−0.830455 + 0.557086i \(0.811919\pi\)
\(30\) 2.00000 6.00000i 0.365148 1.09545i
\(31\) −6.00000 6.00000i −1.07763 1.07763i −0.996721 0.0809104i \(-0.974217\pi\)
−0.0809104 0.996721i \(-0.525783\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 8.00000i 1.39262i
\(34\) −3.00000 3.00000i −0.514496 0.514496i
\(35\) 4.00000 + 8.00000i 0.676123 + 1.35225i
\(36\) 5.00000i 0.833333i
\(37\) −4.00000 −0.657596 −0.328798 0.944400i \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) −2.00000 2.00000i −0.324443 0.324443i
\(39\) 2.00000 10.0000i 0.320256 1.60128i
\(40\) 2.00000 1.00000i 0.316228 0.158114i
\(41\) −1.00000 1.00000i −0.156174 0.156174i 0.624695 0.780869i \(-0.285223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) −8.00000 8.00000i −1.23443 1.23443i
\(43\) −2.00000 2.00000i −0.304997 0.304997i 0.537968 0.842965i \(-0.319192\pi\)
−0.842965 + 0.537968i \(0.819192\pi\)
\(44\) 2.00000 2.00000i 0.301511 0.301511i
\(45\) −10.0000 + 5.00000i −1.49071 + 0.745356i
\(46\) 2.00000 2.00000i 0.294884 0.294884i
\(47\) −4.00000 −0.583460 −0.291730 0.956501i \(-0.594231\pi\)
−0.291730 + 0.956501i \(0.594231\pi\)
\(48\) −2.00000 + 2.00000i −0.288675 + 0.288675i
\(49\) 9.00000 1.28571
\(50\) 4.00000 + 3.00000i 0.565685 + 0.424264i
\(51\) 12.0000i 1.68034i
\(52\) 3.00000 2.00000i 0.416025 0.277350i
\(53\) −1.00000 + 1.00000i −0.137361 + 0.137361i −0.772444 0.635083i \(-0.780966\pi\)
0.635083 + 0.772444i \(0.280966\pi\)
\(54\) 4.00000 4.00000i 0.544331 0.544331i
\(55\) 6.00000 + 2.00000i 0.809040 + 0.269680i
\(56\) 4.00000i 0.534522i
\(57\) 8.00000i 1.05963i
\(58\) 6.00000 0.787839
\(59\) 2.00000 + 2.00000i 0.260378 + 0.260378i 0.825208 0.564830i \(-0.191058\pi\)
−0.564830 + 0.825208i \(0.691058\pi\)
\(60\) −6.00000 2.00000i −0.774597 0.258199i
\(61\) −12.0000 −1.53644 −0.768221 0.640184i \(-0.778858\pi\)
−0.768221 + 0.640184i \(0.778858\pi\)
\(62\) −6.00000 + 6.00000i −0.762001 + 0.762001i
\(63\) 20.0000i 2.51976i
\(64\) −1.00000 −0.125000
\(65\) 7.00000 + 4.00000i 0.868243 + 0.496139i
\(66\) −8.00000 −0.984732
\(67\) 4.00000i 0.488678i 0.969690 + 0.244339i \(0.0785709\pi\)
−0.969690 + 0.244339i \(0.921429\pi\)
\(68\) −3.00000 + 3.00000i −0.363803 + 0.363803i
\(69\) −8.00000 −0.963087
\(70\) 8.00000 4.00000i 0.956183 0.478091i
\(71\) −2.00000 2.00000i −0.237356 0.237356i 0.578398 0.815755i \(-0.303678\pi\)
−0.815755 + 0.578398i \(0.803678\pi\)
\(72\) 5.00000 0.589256
\(73\) 10.0000i 1.17041i −0.810885 0.585206i \(-0.801014\pi\)
0.810885 0.585206i \(-0.198986\pi\)
\(74\) 4.00000i 0.464991i
\(75\) −2.00000 14.0000i −0.230940 1.61658i
\(76\) −2.00000 + 2.00000i −0.229416 + 0.229416i
\(77\) 8.00000 8.00000i 0.911685 0.911685i
\(78\) −10.0000 2.00000i −1.13228 0.226455i
\(79\) 4.00000i 0.450035i 0.974355 + 0.225018i \(0.0722440\pi\)
−0.974355 + 0.225018i \(0.927756\pi\)
\(80\) −1.00000 2.00000i −0.111803 0.223607i
\(81\) −1.00000 −0.111111
\(82\) −1.00000 + 1.00000i −0.110432 + 0.110432i
\(83\) 8.00000 0.878114 0.439057 0.898459i \(-0.355313\pi\)
0.439057 + 0.898459i \(0.355313\pi\)
\(84\) −8.00000 + 8.00000i −0.872872 + 0.872872i
\(85\) −9.00000 3.00000i −0.976187 0.325396i
\(86\) −2.00000 + 2.00000i −0.215666 + 0.215666i
\(87\) −12.0000 12.0000i −1.28654 1.28654i
\(88\) −2.00000 2.00000i −0.213201 0.213201i
\(89\) −5.00000 5.00000i −0.529999 0.529999i 0.390573 0.920572i \(-0.372277\pi\)
−0.920572 + 0.390573i \(0.872277\pi\)
\(90\) 5.00000 + 10.0000i 0.527046 + 1.05409i
\(91\) 12.0000 8.00000i 1.25794 0.838628i
\(92\) −2.00000 2.00000i −0.208514 0.208514i
\(93\) 24.0000 2.48868
\(94\) 4.00000i 0.412568i
\(95\) −6.00000 2.00000i −0.615587 0.205196i
\(96\) 2.00000 + 2.00000i 0.204124 + 0.204124i
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 9.00000i 0.909137i
\(99\) 10.0000 + 10.0000i 1.00504 + 1.00504i
\(100\) 3.00000 4.00000i 0.300000 0.400000i
\(101\) 12.0000i 1.19404i 0.802225 + 0.597022i \(0.203650\pi\)
−0.802225 + 0.597022i \(0.796350\pi\)
\(102\) 12.0000 1.18818
\(103\) −6.00000 6.00000i −0.591198 0.591198i 0.346757 0.937955i \(-0.387283\pi\)
−0.937955 + 0.346757i \(0.887283\pi\)
\(104\) −2.00000 3.00000i −0.196116 0.294174i
\(105\) −24.0000 8.00000i −2.34216 0.780720i
\(106\) 1.00000 + 1.00000i 0.0971286 + 0.0971286i
\(107\) −6.00000 6.00000i −0.580042 0.580042i 0.354873 0.934915i \(-0.384524\pi\)
−0.934915 + 0.354873i \(0.884524\pi\)
\(108\) −4.00000 4.00000i −0.384900 0.384900i
\(109\) −11.0000 + 11.0000i −1.05361 + 1.05361i −0.0551297 + 0.998479i \(0.517557\pi\)
−0.998479 + 0.0551297i \(0.982443\pi\)
\(110\) 2.00000 6.00000i 0.190693 0.572078i
\(111\) 8.00000 8.00000i 0.759326 0.759326i
\(112\) −4.00000 −0.377964
\(113\) 1.00000 1.00000i 0.0940721 0.0940721i −0.658505 0.752577i \(-0.728811\pi\)
0.752577 + 0.658505i \(0.228811\pi\)
\(114\) 8.00000 0.749269
\(115\) 2.00000 6.00000i 0.186501 0.559503i
\(116\) 6.00000i 0.557086i
\(117\) 10.0000 + 15.0000i 0.924500 + 1.38675i
\(118\) 2.00000 2.00000i 0.184115 0.184115i
\(119\) −12.0000 + 12.0000i −1.10004 + 1.10004i
\(120\) −2.00000 + 6.00000i −0.182574 + 0.547723i
\(121\) 3.00000i 0.272727i
\(122\) 12.0000i 1.08643i
\(123\) 4.00000 0.360668
\(124\) 6.00000 + 6.00000i 0.538816 + 0.538816i
\(125\) 11.0000 + 2.00000i 0.983870 + 0.178885i
\(126\) 20.0000 1.78174
\(127\) 14.0000 14.0000i 1.24230 1.24230i 0.283254 0.959045i \(-0.408586\pi\)
0.959045 0.283254i \(-0.0914140\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 8.00000 0.704361
\(130\) 4.00000 7.00000i 0.350823 0.613941i
\(131\) 4.00000 0.349482 0.174741 0.984614i \(-0.444091\pi\)
0.174741 + 0.984614i \(0.444091\pi\)
\(132\) 8.00000i 0.696311i
\(133\) −8.00000 + 8.00000i −0.693688 + 0.693688i
\(134\) 4.00000 0.345547
\(135\) 4.00000 12.0000i 0.344265 1.03280i
\(136\) 3.00000 + 3.00000i 0.257248 + 0.257248i
\(137\) 18.0000 1.53784 0.768922 0.639343i \(-0.220793\pi\)
0.768922 + 0.639343i \(0.220793\pi\)
\(138\) 8.00000i 0.681005i
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) −4.00000 8.00000i −0.338062 0.676123i
\(141\) 8.00000 8.00000i 0.673722 0.673722i
\(142\) −2.00000 + 2.00000i −0.167836 + 0.167836i
\(143\) 2.00000 10.0000i 0.167248 0.836242i
\(144\) 5.00000i 0.416667i
\(145\) 12.0000 6.00000i 0.996546 0.498273i
\(146\) −10.0000 −0.827606
\(147\) −18.0000 + 18.0000i −1.48461 + 1.48461i
\(148\) 4.00000 0.328798
\(149\) 11.0000 11.0000i 0.901155 0.901155i −0.0943810 0.995536i \(-0.530087\pi\)
0.995536 + 0.0943810i \(0.0300872\pi\)
\(150\) −14.0000 + 2.00000i −1.14310 + 0.163299i
\(151\) −14.0000 + 14.0000i −1.13930 + 1.13930i −0.150729 + 0.988575i \(0.548162\pi\)
−0.988575 + 0.150729i \(0.951838\pi\)
\(152\) 2.00000 + 2.00000i 0.162221 + 0.162221i
\(153\) −15.0000 15.0000i −1.21268 1.21268i
\(154\) −8.00000 8.00000i −0.644658 0.644658i
\(155\) −6.00000 + 18.0000i −0.481932 + 1.44579i
\(156\) −2.00000 + 10.0000i −0.160128 + 0.800641i
\(157\) 3.00000 + 3.00000i 0.239426 + 0.239426i 0.816612 0.577186i \(-0.195849\pi\)
−0.577186 + 0.816612i \(0.695849\pi\)
\(158\) 4.00000 0.318223
\(159\) 4.00000i 0.317221i
\(160\) −2.00000 + 1.00000i −0.158114 + 0.0790569i
\(161\) −8.00000 8.00000i −0.630488 0.630488i
\(162\) 1.00000i 0.0785674i
\(163\) 20.0000i 1.56652i 0.621694 + 0.783260i \(0.286445\pi\)
−0.621694 + 0.783260i \(0.713555\pi\)
\(164\) 1.00000 + 1.00000i 0.0780869 + 0.0780869i
\(165\) −16.0000 + 8.00000i −1.24560 + 0.622799i
\(166\) 8.00000i 0.620920i
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 8.00000 + 8.00000i 0.617213 + 0.617213i
\(169\) 5.00000 12.0000i 0.384615 0.923077i
\(170\) −3.00000 + 9.00000i −0.230089 + 0.690268i
\(171\) −10.0000 10.0000i −0.764719 0.764719i
\(172\) 2.00000 + 2.00000i 0.152499 + 0.152499i
\(173\) 9.00000 + 9.00000i 0.684257 + 0.684257i 0.960957 0.276699i \(-0.0892406\pi\)
−0.276699 + 0.960957i \(0.589241\pi\)
\(174\) −12.0000 + 12.0000i −0.909718 + 0.909718i
\(175\) 12.0000 16.0000i 0.907115 1.20949i
\(176\) −2.00000 + 2.00000i −0.150756 + 0.150756i
\(177\) −8.00000 −0.601317
\(178\) −5.00000 + 5.00000i −0.374766 + 0.374766i
\(179\) −20.0000 −1.49487 −0.747435 0.664335i \(-0.768715\pi\)
−0.747435 + 0.664335i \(0.768715\pi\)
\(180\) 10.0000 5.00000i 0.745356 0.372678i
\(181\) 2.00000i 0.148659i −0.997234 0.0743294i \(-0.976318\pi\)
0.997234 0.0743294i \(-0.0236816\pi\)
\(182\) −8.00000 12.0000i −0.592999 0.889499i
\(183\) 24.0000 24.0000i 1.77413 1.77413i
\(184\) −2.00000 + 2.00000i −0.147442 + 0.147442i
\(185\) 4.00000 + 8.00000i 0.294086 + 0.588172i
\(186\) 24.0000i 1.75977i
\(187\) 12.0000i 0.877527i
\(188\) 4.00000 0.291730
\(189\) −16.0000 16.0000i −1.16383 1.16383i
\(190\) −2.00000 + 6.00000i −0.145095 + 0.435286i
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 2.00000 2.00000i 0.144338 0.144338i
\(193\) 16.0000i 1.15171i 0.817554 + 0.575853i \(0.195330\pi\)
−0.817554 + 0.575853i \(0.804670\pi\)
\(194\) 0 0
\(195\) −22.0000 + 6.00000i −1.57545 + 0.429669i
\(196\) −9.00000 −0.642857
\(197\) 12.0000i 0.854965i −0.904024 0.427482i \(-0.859401\pi\)
0.904024 0.427482i \(-0.140599\pi\)
\(198\) 10.0000 10.0000i 0.710669 0.710669i
\(199\) 8.00000 0.567105 0.283552 0.958957i \(-0.408487\pi\)
0.283552 + 0.958957i \(0.408487\pi\)
\(200\) −4.00000 3.00000i −0.282843 0.212132i
\(201\) −8.00000 8.00000i −0.564276 0.564276i
\(202\) 12.0000 0.844317
\(203\) 24.0000i 1.68447i
\(204\) 12.0000i 0.840168i
\(205\) −1.00000 + 3.00000i −0.0698430 + 0.209529i
\(206\) −6.00000 + 6.00000i −0.418040 + 0.418040i
\(207\) 10.0000 10.0000i 0.695048 0.695048i
\(208\) −3.00000 + 2.00000i −0.208013 + 0.138675i
\(209\) 8.00000i 0.553372i
\(210\) −8.00000 + 24.0000i −0.552052 + 1.65616i
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 1.00000 1.00000i 0.0686803 0.0686803i
\(213\) 8.00000 0.548151
\(214\) −6.00000 + 6.00000i −0.410152 + 0.410152i
\(215\) −2.00000 + 6.00000i −0.136399 + 0.409197i
\(216\) −4.00000 + 4.00000i −0.272166 + 0.272166i
\(217\) 24.0000 + 24.0000i 1.62923 + 1.62923i
\(218\) 11.0000 + 11.0000i 0.745014 + 0.745014i
\(219\) 20.0000 + 20.0000i 1.35147 + 1.35147i
\(220\) −6.00000 2.00000i −0.404520 0.134840i
\(221\) −3.00000 + 15.0000i −0.201802 + 1.00901i
\(222\) −8.00000 8.00000i −0.536925 0.536925i
\(223\) −28.0000 −1.87502 −0.937509 0.347960i \(-0.886874\pi\)
−0.937509 + 0.347960i \(0.886874\pi\)
\(224\) 4.00000i 0.267261i
\(225\) 20.0000 + 15.0000i 1.33333 + 1.00000i
\(226\) −1.00000 1.00000i −0.0665190 0.0665190i
\(227\) 4.00000i 0.265489i −0.991150 0.132745i \(-0.957621\pi\)
0.991150 0.132745i \(-0.0423790\pi\)
\(228\) 8.00000i 0.529813i
\(229\) −1.00000 1.00000i −0.0660819 0.0660819i 0.673293 0.739375i \(-0.264879\pi\)
−0.739375 + 0.673293i \(0.764879\pi\)
\(230\) −6.00000 2.00000i −0.395628 0.131876i
\(231\) 32.0000i 2.10545i
\(232\) −6.00000 −0.393919
\(233\) −11.0000 11.0000i −0.720634 0.720634i 0.248100 0.968734i \(-0.420194\pi\)
−0.968734 + 0.248100i \(0.920194\pi\)
\(234\) 15.0000 10.0000i 0.980581 0.653720i
\(235\) 4.00000 + 8.00000i 0.260931 + 0.521862i
\(236\) −2.00000 2.00000i −0.130189 0.130189i
\(237\) −8.00000 8.00000i −0.519656 0.519656i
\(238\) 12.0000 + 12.0000i 0.777844 + 0.777844i
\(239\) 10.0000 10.0000i 0.646846 0.646846i −0.305383 0.952230i \(-0.598785\pi\)
0.952230 + 0.305383i \(0.0987846\pi\)
\(240\) 6.00000 + 2.00000i 0.387298 + 0.129099i
\(241\) −5.00000 + 5.00000i −0.322078 + 0.322078i −0.849564 0.527486i \(-0.823135\pi\)
0.527486 + 0.849564i \(0.323135\pi\)
\(242\) 3.00000 0.192847
\(243\) −10.0000 + 10.0000i −0.641500 + 0.641500i
\(244\) 12.0000 0.768221
\(245\) −9.00000 18.0000i −0.574989 1.14998i
\(246\) 4.00000i 0.255031i
\(247\) −2.00000 + 10.0000i −0.127257 + 0.636285i
\(248\) 6.00000 6.00000i 0.381000 0.381000i
\(249\) −16.0000 + 16.0000i −1.01396 + 1.01396i
\(250\) 2.00000 11.0000i 0.126491 0.695701i
\(251\) 16.0000i 1.00991i −0.863145 0.504956i \(-0.831509\pi\)
0.863145 0.504956i \(-0.168491\pi\)
\(252\) 20.0000i 1.25988i
\(253\) −8.00000 −0.502956
\(254\) −14.0000 14.0000i −0.878438 0.878438i
\(255\) 24.0000 12.0000i 1.50294 0.751469i
\(256\) 1.00000 0.0625000
\(257\) −17.0000 + 17.0000i −1.06043 + 1.06043i −0.0623783 + 0.998053i \(0.519869\pi\)
−0.998053 + 0.0623783i \(0.980131\pi\)
\(258\) 8.00000i 0.498058i
\(259\) 16.0000 0.994192
\(260\) −7.00000 4.00000i −0.434122 0.248069i
\(261\) 30.0000 1.85695
\(262\) 4.00000i 0.247121i
\(263\) 14.0000 14.0000i 0.863277 0.863277i −0.128440 0.991717i \(-0.540997\pi\)
0.991717 + 0.128440i \(0.0409971\pi\)
\(264\) 8.00000 0.492366
\(265\) 3.00000 + 1.00000i 0.184289 + 0.0614295i
\(266\) 8.00000 + 8.00000i 0.490511 + 0.490511i
\(267\) 20.0000 1.22398
\(268\) 4.00000i 0.244339i
\(269\) 20.0000i 1.21942i −0.792624 0.609711i \(-0.791286\pi\)
0.792624 0.609711i \(-0.208714\pi\)
\(270\) −12.0000 4.00000i −0.730297 0.243432i
\(271\) 6.00000 6.00000i 0.364474 0.364474i −0.500983 0.865457i \(-0.667028\pi\)
0.865457 + 0.500983i \(0.167028\pi\)
\(272\) 3.00000 3.00000i 0.181902 0.181902i
\(273\) −8.00000 + 40.0000i −0.484182 + 2.42091i
\(274\) 18.0000i 1.08742i
\(275\) −2.00000 14.0000i −0.120605 0.844232i
\(276\) 8.00000 0.481543
\(277\) −3.00000 + 3.00000i −0.180253 + 0.180253i −0.791466 0.611213i \(-0.790682\pi\)
0.611213 + 0.791466i \(0.290682\pi\)
\(278\) 0 0
\(279\) −30.0000 + 30.0000i −1.79605 + 1.79605i
\(280\) −8.00000 + 4.00000i −0.478091 + 0.239046i
\(281\) 11.0000 11.0000i 0.656205 0.656205i −0.298275 0.954480i \(-0.596411\pi\)
0.954480 + 0.298275i \(0.0964112\pi\)
\(282\) −8.00000 8.00000i −0.476393 0.476393i
\(283\) −6.00000 6.00000i −0.356663 0.356663i 0.505918 0.862581i \(-0.331154\pi\)
−0.862581 + 0.505918i \(0.831154\pi\)
\(284\) 2.00000 + 2.00000i 0.118678 + 0.118678i
\(285\) 16.0000 8.00000i 0.947758 0.473879i
\(286\) −10.0000 2.00000i −0.591312 0.118262i
\(287\) 4.00000 + 4.00000i 0.236113 + 0.236113i
\(288\) −5.00000 −0.294628
\(289\) 1.00000i 0.0588235i
\(290\) −6.00000 12.0000i −0.352332 0.704664i
\(291\) 0 0
\(292\) 10.0000i 0.585206i
\(293\) 26.0000i 1.51894i 0.650545 + 0.759468i \(0.274541\pi\)
−0.650545 + 0.759468i \(0.725459\pi\)
\(294\) 18.0000 + 18.0000i 1.04978 + 1.04978i
\(295\) 2.00000 6.00000i 0.116445 0.349334i
\(296\) 4.00000i 0.232495i
\(297\) −16.0000 −0.928414
\(298\) −11.0000 11.0000i −0.637213 0.637213i
\(299\) −10.0000 2.00000i −0.578315 0.115663i
\(300\) 2.00000 + 14.0000i 0.115470 + 0.808290i
\(301\) 8.00000 + 8.00000i 0.461112 + 0.461112i
\(302\) 14.0000 + 14.0000i 0.805609 + 0.805609i
\(303\) −24.0000 24.0000i −1.37876 1.37876i
\(304\) 2.00000 2.00000i 0.114708 0.114708i
\(305\) 12.0000 + 24.0000i 0.687118 + 1.37424i
\(306\) −15.0000 + 15.0000i −0.857493 + 0.857493i
\(307\) −8.00000 −0.456584 −0.228292 0.973593i \(-0.573314\pi\)
−0.228292 + 0.973593i \(0.573314\pi\)
\(308\) −8.00000 + 8.00000i −0.455842 + 0.455842i
\(309\) 24.0000 1.36531
\(310\) 18.0000 + 6.00000i 1.02233 + 0.340777i
\(311\) 12.0000i 0.680458i 0.940343 + 0.340229i \(0.110505\pi\)
−0.940343 + 0.340229i \(0.889495\pi\)
\(312\) 10.0000 + 2.00000i 0.566139 + 0.113228i
\(313\) −9.00000 + 9.00000i −0.508710 + 0.508710i −0.914130 0.405420i \(-0.867125\pi\)
0.405420 + 0.914130i \(0.367125\pi\)
\(314\) 3.00000 3.00000i 0.169300 0.169300i
\(315\) 40.0000 20.0000i 2.25374 1.12687i
\(316\) 4.00000i 0.225018i
\(317\) 30.0000i 1.68497i −0.538721 0.842484i \(-0.681092\pi\)
0.538721 0.842484i \(-0.318908\pi\)
\(318\) −4.00000 −0.224309
\(319\) −12.0000 12.0000i −0.671871 0.671871i
\(320\) 1.00000 + 2.00000i 0.0559017 + 0.111803i
\(321\) 24.0000 1.33955
\(322\) −8.00000 + 8.00000i −0.445823 + 0.445823i
\(323\) 12.0000i 0.667698i
\(324\) 1.00000 0.0555556
\(325\) 1.00000 18.0000i 0.0554700 0.998460i
\(326\) 20.0000 1.10770
\(327\) 44.0000i 2.43321i
\(328\) 1.00000 1.00000i 0.0552158 0.0552158i
\(329\) 16.0000 0.882109
\(330\) 8.00000 + 16.0000i 0.440386 + 0.880771i
\(331\) −6.00000 6.00000i −0.329790 0.329790i 0.522717 0.852506i \(-0.324919\pi\)
−0.852506 + 0.522717i \(0.824919\pi\)
\(332\) −8.00000 −0.439057
\(333\) 20.0000i 1.09599i
\(334\) 12.0000i 0.656611i
\(335\) 8.00000 4.00000i 0.437087 0.218543i
\(336\) 8.00000 8.00000i 0.436436 0.436436i
\(337\) −15.0000 + 15.0000i −0.817102 + 0.817102i −0.985687 0.168585i \(-0.946080\pi\)
0.168585 + 0.985687i \(0.446080\pi\)
\(338\) −12.0000 5.00000i −0.652714 0.271964i
\(339\) 4.00000i 0.217250i
\(340\) 9.00000 + 3.00000i 0.488094 + 0.162698i
\(341\) 24.0000 1.29967
\(342\) −10.0000 + 10.0000i −0.540738 + 0.540738i
\(343\) −8.00000 −0.431959
\(344\) 2.00000 2.00000i 0.107833 0.107833i
\(345\) 8.00000 + 16.0000i 0.430706 + 0.861411i
\(346\) 9.00000 9.00000i 0.483843 0.483843i
\(347\) −2.00000 2.00000i −0.107366 0.107366i 0.651383 0.758749i \(-0.274189\pi\)
−0.758749 + 0.651383i \(0.774189\pi\)
\(348\) 12.0000 + 12.0000i 0.643268 + 0.643268i
\(349\) −23.0000 23.0000i −1.23116 1.23116i −0.963518 0.267644i \(-0.913755\pi\)
−0.267644 0.963518i \(-0.586245\pi\)
\(350\) −16.0000 12.0000i −0.855236 0.641427i
\(351\) −20.0000 4.00000i −1.06752 0.213504i
\(352\) 2.00000 + 2.00000i 0.106600 + 0.106600i
\(353\) −16.0000 −0.851594 −0.425797 0.904819i \(-0.640006\pi\)
−0.425797 + 0.904819i \(0.640006\pi\)
\(354\) 8.00000i 0.425195i
\(355\) −2.00000 + 6.00000i −0.106149 + 0.318447i
\(356\) 5.00000 + 5.00000i 0.264999 + 0.264999i
\(357\) 48.0000i 2.54043i
\(358\) 20.0000i 1.05703i
\(359\) 22.0000 + 22.0000i 1.16112 + 1.16112i 0.984232 + 0.176884i \(0.0566017\pi\)
0.176884 + 0.984232i \(0.443398\pi\)
\(360\) −5.00000 10.0000i −0.263523 0.527046i
\(361\) 11.0000i 0.578947i
\(362\) −2.00000 −0.105118
\(363\) −6.00000 6.00000i −0.314918 0.314918i
\(364\) −12.0000 + 8.00000i −0.628971 + 0.419314i
\(365\) −20.0000 + 10.0000i −1.04685 + 0.523424i
\(366\) −24.0000 24.0000i −1.25450 1.25450i
\(367\) −14.0000 14.0000i −0.730794 0.730794i 0.239983 0.970777i \(-0.422858\pi\)
−0.970777 + 0.239983i \(0.922858\pi\)
\(368\) 2.00000 + 2.00000i 0.104257 + 0.104257i
\(369\) −5.00000 + 5.00000i −0.260290 + 0.260290i
\(370\) 8.00000 4.00000i 0.415900 0.207950i
\(371\) 4.00000 4.00000i 0.207670 0.207670i
\(372\) −24.0000 −1.24434
\(373\) 15.0000 15.0000i 0.776671 0.776671i −0.202593 0.979263i \(-0.564937\pi\)
0.979263 + 0.202593i \(0.0649367\pi\)
\(374\) 12.0000 0.620505
\(375\) −26.0000 + 18.0000i −1.34263 + 0.929516i
\(376\) 4.00000i 0.206284i
\(377\) −12.0000 18.0000i −0.618031 0.927047i
\(378\) −16.0000 + 16.0000i −0.822951 + 0.822951i
\(379\) −6.00000 + 6.00000i −0.308199 + 0.308199i −0.844211 0.536011i \(-0.819930\pi\)
0.536011 + 0.844211i \(0.319930\pi\)
\(380\) 6.00000 + 2.00000i 0.307794 + 0.102598i
\(381\) 56.0000i 2.86897i
\(382\) 0 0
\(383\) 4.00000 0.204390 0.102195 0.994764i \(-0.467413\pi\)
0.102195 + 0.994764i \(0.467413\pi\)
\(384\) −2.00000 2.00000i −0.102062 0.102062i
\(385\) −24.0000 8.00000i −1.22315 0.407718i
\(386\) 16.0000 0.814379
\(387\) −10.0000 + 10.0000i −0.508329 + 0.508329i
\(388\) 0 0
\(389\) −38.0000 −1.92668 −0.963338 0.268290i \(-0.913542\pi\)
−0.963338 + 0.268290i \(0.913542\pi\)
\(390\) 6.00000 + 22.0000i 0.303822 + 1.11401i
\(391\) 12.0000 0.606866
\(392\) 9.00000i 0.454569i
\(393\) −8.00000 + 8.00000i −0.403547 + 0.403547i
\(394\) −12.0000 −0.604551
\(395\) 8.00000 4.00000i 0.402524 0.201262i
\(396\) −10.0000 10.0000i −0.502519 0.502519i
\(397\) 4.00000 0.200754 0.100377 0.994949i \(-0.467995\pi\)
0.100377 + 0.994949i \(0.467995\pi\)
\(398\) 8.00000i 0.401004i
\(399\) 32.0000i 1.60200i
\(400\) −3.00000 + 4.00000i −0.150000 + 0.200000i
\(401\) −5.00000 + 5.00000i −0.249688 + 0.249688i −0.820843 0.571154i \(-0.806496\pi\)
0.571154 + 0.820843i \(0.306496\pi\)
\(402\) −8.00000 + 8.00000i −0.399004 + 0.399004i
\(403\) 30.0000 + 6.00000i 1.49441 + 0.298881i
\(404\) 12.0000i 0.597022i
\(405\) 1.00000 + 2.00000i 0.0496904 + 0.0993808i
\(406\) −24.0000 −1.19110
\(407\) 8.00000 8.00000i 0.396545 0.396545i
\(408\) −12.0000 −0.594089
\(409\) 15.0000 15.0000i 0.741702 0.741702i −0.231203 0.972905i \(-0.574266\pi\)
0.972905 + 0.231203i \(0.0742662\pi\)
\(410\) 3.00000 + 1.00000i 0.148159 + 0.0493865i
\(411\) −36.0000 + 36.0000i −1.77575 + 1.77575i
\(412\) 6.00000 + 6.00000i 0.295599 + 0.295599i
\(413\) −8.00000 8.00000i −0.393654 0.393654i
\(414\) −10.0000 10.0000i −0.491473 0.491473i
\(415\) −8.00000 16.0000i −0.392705 0.785409i
\(416\) 2.00000 + 3.00000i 0.0980581 + 0.147087i
\(417\) 0 0
\(418\) 8.00000 0.391293
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 24.0000 + 8.00000i 1.17108 + 0.390360i
\(421\) −19.0000 19.0000i −0.926003 0.926003i 0.0714415 0.997445i \(-0.477240\pi\)
−0.997445 + 0.0714415i \(0.977240\pi\)
\(422\) 4.00000i 0.194717i
\(423\) 20.0000i 0.972433i
\(424\) −1.00000 1.00000i −0.0485643 0.0485643i
\(425\) 3.00000 + 21.0000i 0.145521 + 1.01865i
\(426\) 8.00000i 0.387601i
\(427\) 48.0000 2.32288
\(428\) 6.00000 + 6.00000i 0.290021 + 0.290021i
\(429\) 16.0000 + 24.0000i 0.772487 + 1.15873i
\(430\) 6.00000 + 2.00000i 0.289346 + 0.0964486i
\(431\) 6.00000 + 6.00000i 0.289010 + 0.289010i 0.836689 0.547679i \(-0.184488\pi\)
−0.547679 + 0.836689i \(0.684488\pi\)
\(432\) 4.00000 + 4.00000i 0.192450 + 0.192450i
\(433\) −3.00000 3.00000i −0.144171 0.144171i 0.631337 0.775508i \(-0.282506\pi\)
−0.775508 + 0.631337i \(0.782506\pi\)
\(434\) 24.0000 24.0000i 1.15204 1.15204i
\(435\) −12.0000 + 36.0000i −0.575356 + 1.72607i
\(436\) 11.0000 11.0000i 0.526804 0.526804i
\(437\) 8.00000 0.382692
\(438\) 20.0000 20.0000i 0.955637 0.955637i
\(439\) 40.0000 1.90910 0.954548 0.298057i \(-0.0963387\pi\)
0.954548 + 0.298057i \(0.0963387\pi\)
\(440\) −2.00000 + 6.00000i −0.0953463 + 0.286039i
\(441\) 45.0000i 2.14286i
\(442\) 15.0000 + 3.00000i 0.713477 + 0.142695i
\(443\) −18.0000 + 18.0000i −0.855206 + 0.855206i −0.990769 0.135563i \(-0.956716\pi\)
0.135563 + 0.990769i \(0.456716\pi\)
\(444\) −8.00000 + 8.00000i −0.379663 + 0.379663i
\(445\) −5.00000 + 15.0000i −0.237023 + 0.711068i
\(446\) 28.0000i 1.32584i
\(447\) 44.0000i 2.08113i
\(448\) 4.00000 0.188982
\(449\) −11.0000 11.0000i −0.519122 0.519122i 0.398184 0.917306i \(-0.369641\pi\)
−0.917306 + 0.398184i \(0.869641\pi\)
\(450\) 15.0000 20.0000i 0.707107 0.942809i
\(451\) 4.00000 0.188353
\(452\) −1.00000 + 1.00000i −0.0470360 + 0.0470360i
\(453\) 56.0000i 2.63111i
\(454\) −4.00000 −0.187729
\(455\) −28.0000 16.0000i −1.31266 0.750092i
\(456\) −8.00000 −0.374634
\(457\) 16.0000i 0.748448i 0.927338 + 0.374224i \(0.122091\pi\)
−0.927338 + 0.374224i \(0.877909\pi\)
\(458\) −1.00000 + 1.00000i −0.0467269 + 0.0467269i
\(459\) 24.0000 1.12022
\(460\) −2.00000 + 6.00000i −0.0932505 + 0.279751i
\(461\) −11.0000 11.0000i −0.512321 0.512321i 0.402916 0.915237i \(-0.367997\pi\)
−0.915237 + 0.402916i \(0.867997\pi\)
\(462\) 32.0000 1.48877
\(463\) 8.00000i 0.371792i 0.982569 + 0.185896i \(0.0595187\pi\)
−0.982569 + 0.185896i \(0.940481\pi\)
\(464\) 6.00000i 0.278543i
\(465\) −24.0000 48.0000i −1.11297 2.22595i
\(466\) −11.0000 + 11.0000i −0.509565 + 0.509565i
\(467\) −2.00000 + 2.00000i −0.0925490 + 0.0925490i −0.751865 0.659317i \(-0.770846\pi\)
0.659317 + 0.751865i \(0.270846\pi\)
\(468\) −10.0000 15.0000i −0.462250 0.693375i
\(469\) 16.0000i 0.738811i
\(470\) 8.00000 4.00000i 0.369012 0.184506i
\(471\) −12.0000 −0.552931
\(472\) −2.00000 + 2.00000i −0.0920575 + 0.0920575i
\(473\) 8.00000 0.367840
\(474\) −8.00000 + 8.00000i −0.367452 + 0.367452i
\(475\) 2.00000 + 14.0000i 0.0917663 + 0.642364i
\(476\) 12.0000 12.0000i 0.550019 0.550019i
\(477\) 5.00000 + 5.00000i 0.228934 + 0.228934i
\(478\) −10.0000 10.0000i −0.457389 0.457389i
\(479\) 10.0000 + 10.0000i 0.456912 + 0.456912i 0.897640 0.440729i \(-0.145280\pi\)
−0.440729 + 0.897640i \(0.645280\pi\)
\(480\) 2.00000 6.00000i 0.0912871 0.273861i
\(481\) 12.0000 8.00000i 0.547153 0.364769i
\(482\) 5.00000 + 5.00000i 0.227744 + 0.227744i
\(483\) 32.0000 1.45605
\(484\) 3.00000i 0.136364i
\(485\) 0 0
\(486\) 10.0000 + 10.0000i 0.453609 + 0.453609i
\(487\) 16.0000i 0.725029i 0.931978 + 0.362515i \(0.118082\pi\)
−0.931978 + 0.362515i \(0.881918\pi\)
\(488\) 12.0000i 0.543214i
\(489\) −40.0000 40.0000i −1.80886 1.80886i
\(490\) −18.0000 + 9.00000i −0.813157 + 0.406579i
\(491\) 24.0000i 1.08310i −0.840667 0.541552i \(-0.817837\pi\)
0.840667 0.541552i \(-0.182163\pi\)
\(492\) −4.00000 −0.180334
\(493\) 18.0000 + 18.0000i 0.810679 + 0.810679i
\(494\) 10.0000 + 2.00000i 0.449921 + 0.0899843i
\(495\) 10.0000 30.0000i 0.449467 1.34840i
\(496\) −6.00000 6.00000i −0.269408 0.269408i
\(497\) 8.00000 + 8.00000i 0.358849 + 0.358849i
\(498\) 16.0000 + 16.0000i 0.716977 + 0.716977i
\(499\) 14.0000 14.0000i 0.626726 0.626726i −0.320517 0.947243i \(-0.603857\pi\)
0.947243 + 0.320517i \(0.103857\pi\)
\(500\) −11.0000 2.00000i −0.491935 0.0894427i
\(501\) 24.0000 24.0000i 1.07224 1.07224i
\(502\) −16.0000 −0.714115
\(503\) −18.0000 + 18.0000i −0.802580 + 0.802580i −0.983498 0.180918i \(-0.942093\pi\)
0.180918 + 0.983498i \(0.442093\pi\)
\(504\) −20.0000 −0.890871
\(505\) 24.0000 12.0000i 1.06799 0.533993i
\(506\) 8.00000i 0.355643i
\(507\) 14.0000 + 34.0000i 0.621762 + 1.50999i
\(508\) −14.0000 + 14.0000i −0.621150 + 0.621150i
\(509\) −3.00000 + 3.00000i −0.132973 + 0.132973i −0.770460 0.637488i \(-0.779974\pi\)
0.637488 + 0.770460i \(0.279974\pi\)
\(510\) −12.0000 24.0000i −0.531369 1.06274i
\(511\) 40.0000i 1.76950i
\(512\) 1.00000i 0.0441942i
\(513\) 16.0000 0.706417
\(514\) 17.0000 + 17.0000i 0.749838 + 0.749838i
\(515\) −6.00000 + 18.0000i −0.264392 + 0.793175i
\(516\) −8.00000 −0.352180
\(517\) 8.00000 8.00000i 0.351840 0.351840i
\(518\) 16.0000i 0.703000i
\(519\) −36.0000 −1.58022
\(520\) −4.00000 + 7.00000i −0.175412 + 0.306970i
\(521\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) 30.0000i 1.31306i
\(523\) 30.0000 30.0000i 1.31181 1.31181i 0.391727 0.920082i \(-0.371878\pi\)
0.920082 0.391727i \(-0.128122\pi\)
\(524\) −4.00000 −0.174741
\(525\) 8.00000 + 56.0000i 0.349149 + 2.44404i
\(526\) −14.0000 14.0000i −0.610429 0.610429i
\(527\) −36.0000 −1.56818
\(528\) 8.00000i 0.348155i
\(529\) 15.0000i 0.652174i
\(530\) 1.00000 3.00000i 0.0434372 0.130312i
\(531\) 10.0000 10.0000i 0.433963 0.433963i
\(532\) 8.00000 8.00000i 0.346844 0.346844i
\(533\) 5.00000 + 1.00000i 0.216574 + 0.0433148i
\(534\) 20.0000i 0.865485i
\(535\) −6.00000 + 18.0000i −0.259403 + 0.778208i
\(536\) −4.00000 −0.172774
\(537\) 40.0000 40.0000i 1.72613 1.72613i
\(538\) −20.0000 −0.862261
\(539\) −18.0000 + 18.0000i −0.775315 + 0.775315i
\(540\) −4.00000 + 12.0000i −0.172133 + 0.516398i
\(541\) 7.00000 7.00000i 0.300954 0.300954i −0.540433 0.841387i \(-0.681740\pi\)
0.841387 + 0.540433i \(0.181740\pi\)
\(542\) −6.00000 6.00000i −0.257722 0.257722i
\(543\) 4.00000 + 4.00000i 0.171656 + 0.171656i
\(544\) −3.00000 3.00000i −0.128624 0.128624i
\(545\) 33.0000 + 11.0000i 1.41356 + 0.471188i
\(546\) 40.0000 + 8.00000i 1.71184 + 0.342368i
\(547\) −30.0000 30.0000i −1.28271 1.28271i −0.939121 0.343586i \(-0.888358\pi\)
−0.343586 0.939121i \(-0.611642\pi\)
\(548\) −18.0000 −0.768922
\(549\) 60.0000i 2.56074i
\(550\) −14.0000 + 2.00000i −0.596962 + 0.0852803i
\(551\) 12.0000 + 12.0000i 0.511217 + 0.511217i
\(552\) 8.00000i 0.340503i
\(553\) 16.0000i 0.680389i
\(554\) 3.00000 + 3.00000i 0.127458 + 0.127458i
\(555\) −24.0000 8.00000i −1.01874 0.339581i
\(556\) 0 0
\(557\) 20.0000 0.847427 0.423714 0.905796i \(-0.360726\pi\)
0.423714 + 0.905796i \(0.360726\pi\)
\(558\) 30.0000 + 30.0000i 1.27000 + 1.27000i
\(559\) 10.0000 + 2.00000i 0.422955 + 0.0845910i
\(560\) 4.00000 + 8.00000i 0.169031 + 0.338062i
\(561\) −24.0000 24.0000i −1.01328 1.01328i
\(562\) −11.0000 11.0000i −0.464007 0.464007i
\(563\) 10.0000 + 10.0000i 0.421450 + 0.421450i 0.885703 0.464253i \(-0.153677\pi\)
−0.464253 + 0.885703i \(0.653677\pi\)
\(564\) −8.00000 + 8.00000i −0.336861 + 0.336861i
\(565\) −3.00000 1.00000i −0.126211 0.0420703i
\(566\) −6.00000 + 6.00000i −0.252199 + 0.252199i
\(567\) 4.00000 0.167984
\(568\) 2.00000 2.00000i 0.0839181 0.0839181i
\(569\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(570\) −8.00000 16.0000i −0.335083 0.670166i
\(571\) 32.0000i 1.33916i −0.742741 0.669579i \(-0.766474\pi\)
0.742741 0.669579i \(-0.233526\pi\)
\(572\) −2.00000 + 10.0000i −0.0836242 + 0.418121i
\(573\) 0 0
\(574\) 4.00000 4.00000i 0.166957 0.166957i
\(575\) −14.0000 + 2.00000i −0.583840 + 0.0834058i
\(576\) 5.00000i 0.208333i
\(577\) 18.0000i 0.749350i 0.927156 + 0.374675i \(0.122246\pi\)
−0.927156 + 0.374675i \(0.877754\pi\)
\(578\) −1.00000 −0.0415945
\(579\) −32.0000 32.0000i −1.32987 1.32987i
\(580\) −12.0000 + 6.00000i −0.498273 + 0.249136i
\(581\) −32.0000 −1.32758
\(582\) 0 0
\(583\) 4.00000i 0.165663i
\(584\) 10.0000 0.413803
\(585\) 20.0000 35.0000i 0.826898 1.44707i
\(586\) 26.0000 1.07405
\(587\) 12.0000i 0.495293i 0.968850 + 0.247647i \(0.0796572\pi\)
−0.968850 + 0.247647i \(0.920343\pi\)
\(588\) 18.0000 18.0000i 0.742307 0.742307i
\(589\) −24.0000 −0.988903
\(590\) −6.00000 2.00000i −0.247016 0.0823387i
\(591\) 24.0000 + 24.0000i 0.987228 + 0.987228i
\(592\) −4.00000 −0.164399
\(593\) 24.0000i 0.985562i 0.870153 + 0.492781i \(0.164020\pi\)
−0.870153 + 0.492781i \(0.835980\pi\)
\(594\) 16.0000i 0.656488i
\(595\) 36.0000 + 12.0000i 1.47586 + 0.491952i
\(596\) −11.0000 + 11.0000i −0.450578 + 0.450578i
\(597\) −16.0000 + 16.0000i −0.654836 + 0.654836i
\(598\) −2.00000 + 10.0000i −0.0817861 + 0.408930i
\(599\) 36.0000i 1.47092i 0.677568 + 0.735460i \(0.263034\pi\)
−0.677568 + 0.735460i \(0.736966\pi\)
\(600\) 14.0000 2.00000i 0.571548 0.0816497i
\(601\) −22.0000 −0.897399 −0.448699 0.893683i \(-0.648113\pi\)
−0.448699 + 0.893683i \(0.648113\pi\)
\(602\) 8.00000 8.00000i 0.326056 0.326056i
\(603\) 20.0000 0.814463
\(604\) 14.0000 14.0000i 0.569652 0.569652i
\(605\) 6.00000 3.00000i 0.243935 0.121967i
\(606\) −24.0000 + 24.0000i −0.974933 + 0.974933i
\(607\) 26.0000 + 26.0000i 1.05531 + 1.05531i 0.998378 + 0.0569292i \(0.0181309\pi\)
0.0569292 + 0.998378i \(0.481869\pi\)
\(608\) −2.00000 2.00000i −0.0811107 0.0811107i
\(609\) 48.0000 + 48.0000i 1.94506 + 1.94506i
\(610\) 24.0000 12.0000i 0.971732 0.485866i
\(611\) 12.0000 8.00000i 0.485468 0.323645i
\(612\) 15.0000 + 15.0000i 0.606339 + 0.606339i
\(613\) −18.0000 −0.727013 −0.363507 0.931592i \(-0.618421\pi\)
−0.363507 + 0.931592i \(0.618421\pi\)
\(614\) 8.00000i 0.322854i
\(615\) −4.00000 8.00000i −0.161296 0.322591i
\(616\) 8.00000 + 8.00000i 0.322329 + 0.322329i
\(617\) 40.0000i 1.61034i 0.593045 + 0.805170i \(0.297926\pi\)
−0.593045 + 0.805170i \(0.702074\pi\)
\(618\) 24.0000i 0.965422i
\(619\) 18.0000 + 18.0000i 0.723481 + 0.723481i 0.969313 0.245831i \(-0.0790610\pi\)
−0.245831 + 0.969313i \(0.579061\pi\)
\(620\) 6.00000 18.0000i 0.240966 0.722897i
\(621\) 16.0000i 0.642058i
\(622\) 12.0000 0.481156
\(623\) 20.0000 + 20.0000i 0.801283 + 0.801283i
\(624\) 2.00000 10.0000i 0.0800641 0.400320i
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 9.00000 + 9.00000i 0.359712 + 0.359712i
\(627\) −16.0000 16.0000i −0.638978 0.638978i
\(628\) −3.00000 3.00000i −0.119713 0.119713i
\(629\) −12.0000 + 12.0000i −0.478471 + 0.478471i
\(630\) −20.0000 40.0000i −0.796819 1.59364i
\(631\) 14.0000 14.0000i 0.557331 0.557331i −0.371216 0.928547i \(-0.621059\pi\)
0.928547 + 0.371216i \(0.121059\pi\)
\(632\) −4.00000 −0.159111
\(633\) 8.00000 8.00000i 0.317971 0.317971i
\(634\) −30.0000 −1.19145
\(635\) −42.0000 14.0000i −1.66672 0.555573i
\(636\) 4.00000i 0.158610i
\(637\) −27.0000 + 18.0000i −1.06978 + 0.713186i
\(638\) −12.0000 + 12.0000i −0.475085 + 0.475085i
\(639\) −10.0000 + 10.0000i −0.395594 + 0.395594i
\(640\) 2.00000 1.00000i 0.0790569 0.0395285i
\(641\) 40.0000i 1.57991i −0.613168 0.789953i \(-0.710105\pi\)
0.613168 0.789953i \(-0.289895\pi\)
\(642\) 24.0000i 0.947204i
\(643\) −32.0000 −1.26196 −0.630978 0.775800i \(-0.717346\pi\)
−0.630978 + 0.775800i \(0.717346\pi\)
\(644\) 8.00000 + 8.00000i 0.315244 + 0.315244i
\(645\) −8.00000 16.0000i −0.315000 0.629999i
\(646\) −12.0000 −0.472134
\(647\) −10.0000 + 10.0000i −0.393141 + 0.393141i −0.875805 0.482665i \(-0.839669\pi\)
0.482665 + 0.875805i \(0.339669\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −8.00000 −0.314027
\(650\) −18.0000 1.00000i −0.706018 0.0392232i
\(651\) −96.0000 −3.76254
\(652\) 20.0000i 0.783260i
\(653\) 5.00000 5.00000i 0.195665 0.195665i −0.602474 0.798139i \(-0.705818\pi\)
0.798139 + 0.602474i \(0.205818\pi\)
\(654\) −44.0000 −1.72054
\(655\) −4.00000 8.00000i −0.156293 0.312586i
\(656\) −1.00000 1.00000i −0.0390434 0.0390434i
\(657\) −50.0000 −1.95069
\(658\) 16.0000i 0.623745i
\(659\) 32.0000i 1.24654i 0.782006 + 0.623272i \(0.214197\pi\)
−0.782006 + 0.623272i \(0.785803\pi\)
\(660\) 16.0000 8.00000i 0.622799 0.311400i
\(661\) −23.0000 + 23.0000i −0.894596 + 0.894596i −0.994952 0.100355i \(-0.968002\pi\)
0.100355 + 0.994952i \(0.468002\pi\)
\(662\) −6.00000 + 6.00000i −0.233197 + 0.233197i
\(663\) −24.0000 36.0000i −0.932083 1.39812i
\(664\) 8.00000i 0.310460i
\(665\) 24.0000 + 8.00000i 0.930680 + 0.310227i
\(666\) 20.0000 0.774984
\(667\) −12.0000 + 12.0000i −0.464642 + 0.464642i
\(668\) 12.0000 0.464294
\(669\) 56.0000 56.0000i 2.16509 2.16509i
\(670\) −4.00000 8.00000i −0.154533 0.309067i
\(671\) 24.0000 24.0000i 0.926510 0.926510i
\(672\) −8.00000 8.00000i −0.308607 0.308607i
\(673\) −5.00000 5.00000i −0.192736 0.192736i 0.604141 0.796877i \(-0.293516\pi\)
−0.796877 + 0.604141i \(0.793516\pi\)
\(674\) 15.0000 + 15.0000i 0.577778 + 0.577778i
\(675\) −28.0000 + 4.00000i −1.07772 + 0.153960i
\(676\) −5.00000 + 12.0000i −0.192308 + 0.461538i
\(677\) 27.0000 + 27.0000i 1.03769 + 1.03769i 0.999261 + 0.0384331i \(0.0122367\pi\)
0.0384331 + 0.999261i \(0.487763\pi\)
\(678\) 4.00000 0.153619
\(679\) 0 0
\(680\) 3.00000 9.00000i 0.115045 0.345134i
\(681\) 8.00000 + 8.00000i 0.306561 + 0.306561i
\(682\) 24.0000i 0.919007i
\(683\) 36.0000i 1.37750i 0.724998 + 0.688751i \(0.241841\pi\)
−0.724998 + 0.688751i \(0.758159\pi\)
\(684\) 10.0000 + 10.0000i 0.382360 + 0.382360i
\(685\) −18.0000 36.0000i −0.687745 1.37549i
\(686\) 8.00000i 0.305441i
\(687\) 4.00000 0.152610
\(688\) −2.00000 2.00000i −0.0762493 0.0762493i
\(689\) 1.00000 5.00000i 0.0380970 0.190485i
\(690\) 16.0000 8.00000i 0.609110 0.304555i
\(691\) 14.0000 + 14.0000i 0.532585 + 0.532585i 0.921341 0.388756i \(-0.127095\pi\)
−0.388756 + 0.921341i \(0.627095\pi\)
\(692\) −9.00000 9.00000i −0.342129 0.342129i
\(693\) −40.0000 40.0000i −1.51947 1.51947i
\(694\) −2.00000 + 2.00000i −0.0759190 + 0.0759190i
\(695\) 0 0
\(696\) 12.0000 12.0000i 0.454859 0.454859i
\(697\) −6.00000 −0.227266
\(698\) −23.0000 + 23.0000i −0.870563 + 0.870563i
\(699\) 44.0000 1.66423
\(700\) −12.0000 + 16.0000i −0.453557 + 0.604743i
\(701\) 20.0000i 0.755390i 0.925930 + 0.377695i \(0.123283\pi\)
−0.925930 + 0.377695i \(0.876717\pi\)
\(702\) −4.00000 + 20.0000i −0.150970 + 0.754851i
\(703\) −8.00000 + 8.00000i −0.301726 + 0.301726i
\(704\) 2.00000 2.00000i 0.0753778 0.0753778i
\(705\) −24.0000 8.00000i −0.903892 0.301297i
\(706\) 16.0000i 0.602168i
\(707\) 48.0000i 1.80523i
\(708\) 8.00000 0.300658
\(709\) 7.00000 + 7.00000i 0.262891 + 0.262891i 0.826227 0.563337i \(-0.190483\pi\)
−0.563337 + 0.826227i \(0.690483\pi\)
\(710\) 6.00000 + 2.00000i 0.225176 + 0.0750587i
\(711\) 20.0000 0.750059
\(712\) 5.00000 5.00000i 0.187383 0.187383i
\(713\) 24.0000i 0.898807i
\(714\) −48.0000 −1.79635
\(715\) −22.0000 + 6.00000i −0.822753 + 0.224387i
\(716\) 20.0000 0.747435
\(717\) 40.0000i 1.49383i
\(718\) 22.0000 22.0000i 0.821033 0.821033i
\(719\) 16.0000 0.596699 0.298350 0.954457i \(-0.403564\pi\)
0.298350 + 0.954457i \(0.403564\pi\)
\(720\) −10.0000 + 5.00000i −0.372678 + 0.186339i
\(721\) 24.0000 + 24.0000i 0.893807 + 0.893807i
\(722\) 11.0000 0.409378
\(723\) 20.0000i 0.743808i
\(724\) 2.00000i 0.0743294i
\(725\) −24.0000 18.0000i −0.891338 0.668503i
\(726\) −6.00000 + 6.00000i −0.222681 + 0.222681i
\(727\) 30.0000 30.0000i 1.11264 1.11264i 0.119846 0.992793i \(-0.461760\pi\)
0.992793 0.119846i \(-0.0382401\pi\)
\(728\) 8.00000 + 12.0000i 0.296500 + 0.444750i
\(729\) 43.0000i 1.59259i
\(730\) 10.0000 + 20.0000i 0.370117 + 0.740233i
\(731\) −12.0000 −0.443836
\(732\) −24.0000 + 24.0000i −0.887066 + 0.887066i
\(733\) −6.00000 −0.221615 −0.110808 0.993842i \(-0.535344\pi\)
−0.110808 + 0.993842i \(0.535344\pi\)
\(734\) −14.0000 + 14.0000i −0.516749 + 0.516749i
\(735\) 54.0000 + 18.0000i 1.99182 + 0.663940i
\(736\) 2.00000 2.00000i 0.0737210 0.0737210i
\(737\) −8.00000 8.00000i −0.294684 0.294684i
\(738\) 5.00000 + 5.00000i 0.184053 + 0.184053i
\(739\) −18.0000 18.0000i −0.662141 0.662141i 0.293744 0.955884i \(-0.405099\pi\)
−0.955884 + 0.293744i \(0.905099\pi\)
\(740\) −4.00000 8.00000i −0.147043 0.294086i
\(741\) −16.0000 24.0000i −0.587775 0.881662i
\(742\) −4.00000 4.00000i −0.146845 0.146845i
\(743\) 44.0000 1.61420 0.807102 0.590412i \(-0.201035\pi\)
0.807102 + 0.590412i \(0.201035\pi\)
\(744\) 24.0000i 0.879883i
\(745\) −33.0000 11.0000i −1.20903 0.403009i
\(746\) −15.0000 15.0000i −0.549189 0.549189i
\(747\) 40.0000i 1.46352i
\(748\) 12.0000i 0.438763i
\(749\) 24.0000 + 24.0000i 0.876941 + 0.876941i
\(750\) 18.0000 + 26.0000i 0.657267 + 0.949386i
\(751\) 4.00000i 0.145962i 0.997333 + 0.0729810i \(0.0232513\pi\)
−0.997333 + 0.0729810i \(0.976749\pi\)
\(752\) −4.00000 −0.145865
\(753\) 32.0000 + 32.0000i 1.16614 + 1.16614i
\(754\) −18.0000 + 12.0000i −0.655521 + 0.437014i
\(755\) 42.0000 + 14.0000i 1.52854 + 0.509512i
\(756\) 16.0000 + 16.0000i 0.581914 + 0.581914i
\(757\) 9.00000 + 9.00000i 0.327111 + 0.327111i 0.851487 0.524376i \(-0.175701\pi\)
−0.524376 + 0.851487i \(0.675701\pi\)
\(758\) 6.00000 + 6.00000i 0.217930 + 0.217930i
\(759\) 16.0000 16.0000i 0.580763 0.580763i
\(760\) 2.00000 6.00000i 0.0725476 0.217643i
\(761\) 1.00000 1.00000i 0.0362500 0.0362500i −0.688749 0.724999i \(-0.741840\pi\)
0.724999 + 0.688749i \(0.241840\pi\)
\(762\) 56.0000 2.02867
\(763\) 44.0000 44.0000i 1.59291 1.59291i
\(764\) 0 0
\(765\) −15.0000 + 45.0000i −0.542326 + 1.62698i
\(766\) 4.00000i 0.144526i
\(767\) −10.0000 2.00000i −0.361079 0.0722158i
\(768\) −2.00000 + 2.00000i −0.0721688 + 0.0721688i
\(769\) −3.00000 + 3.00000i −0.108183 + 0.108183i −0.759126 0.650943i \(-0.774373\pi\)
0.650943 + 0.759126i \(0.274373\pi\)
\(770\) −8.00000 + 24.0000i −0.288300 + 0.864900i
\(771\) 68.0000i 2.44896i
\(772\) 16.0000i 0.575853i
\(773\) 4.00000 0.143870 0.0719350 0.997409i \(-0.477083\pi\)
0.0719350 + 0.997409i \(0.477083\pi\)
\(774\) 10.0000 + 10.0000i 0.359443 + 0.359443i
\(775\) 42.0000 6.00000i 1.50868 0.215526i
\(776\) 0 0
\(777\) −32.0000 + 32.0000i −1.14799 + 1.14799i
\(778\) 38.0000i 1.36237i
\(779\) −4.00000 −0.143315
\(780\) 22.0000 6.00000i 0.787726 0.214834i
\(781\) 8.00000 0.286263
\(782\) 12.0000i 0.429119i
\(783\) −24.0000 + 24.0000i −0.857690 + 0.857690i
\(784\) 9.00000 0.321429
\(785\) 3.00000 9.00000i 0.107075 0.321224i
\(786\) 8.00000 + 8.00000i 0.285351 + 0.285351i
\(787\) −8.00000 −0.285169 −0.142585 0.989783i \(-0.545541\pi\)
−0.142585 + 0.989783i \(0.545541\pi\)
\(788\) 12.0000i 0.427482i
\(789\) 56.0000i 1.99365i
\(790\) −4.00000 8.00000i −0.142314 0.284627i
\(791\) −4.00000 + 4.00000i −0.142224 + 0.142224i
\(792\) −10.0000 + 10.0000i −0.355335 + 0.355335i
\(793\) 36.0000 24.0000i 1.27840 0.852265i
\(794\) 4.00000i 0.141955i
\(795\) −8.00000 + 4.00000i −0.283731 + 0.141865i
\(796\) −8.00000 −0.283552
\(797\) 35.0000 35.0000i 1.23976 1.23976i 0.279666 0.960097i \(-0.409776\pi\)
0.960097 0.279666i \(-0.0902238\pi\)
\(798\) −32.0000 −1.13279
\(799\) −12.0000 + 12.0000i −0.424529 + 0.424529i
\(800\) 4.00000 + 3.00000i 0.141421 + 0.106066i
\(801\) −25.0000 + 25.0000i −0.883332 + 0.883332i
\(802\) 5.00000 + 5.00000i 0.176556 + 0.176556i
\(803\) 20.0000 + 20.0000i 0.705785 + 0.705785i
\(804\) 8.00000 + 8.00000i 0.282138 + 0.282138i
\(805\) −8.00000 + 24.0000i −0.281963 + 0.845889i
\(806\) 6.00000 30.0000i 0.211341 1.05670i
\(807\) 40.0000 + 40.0000i 1.40807 + 1.40807i
\(808\) −12.0000 −0.422159
\(809\) 18.0000i 0.632846i −0.948618 0.316423i \(-0.897518\pi\)
0.948618 0.316423i \(-0.102482\pi\)
\(810\) 2.00000 1.00000i 0.0702728 0.0351364i
\(811\) 14.0000 + 14.0000i 0.491606 + 0.491606i 0.908812 0.417206i \(-0.136991\pi\)
−0.417206 + 0.908812i \(0.636991\pi\)
\(812\) 24.0000i 0.842235i
\(813\) 24.0000i 0.841717i
\(814\) −8.00000 8.00000i −0.280400 0.280400i
\(815\) 40.0000 20.0000i 1.40114 0.700569i
\(816\) 12.0000i 0.420084i
\(817\) −8.00000 −0.279885
\(818\) −15.0000 15.0000i −0.524463 0.524463i
\(819\) −40.0000 60.0000i −1.39771 2.09657i
\(820\) 1.00000 3.00000i 0.0349215 0.104765i
\(821\) −29.0000 29.0000i −1.01211 1.01211i −0.999926 0.0121812i \(-0.996123\pi\)
−0.0121812 0.999926i \(-0.503877\pi\)
\(822\) 36.0000 + 36.0000i 1.25564 + 1.25564i
\(823\) −18.0000 18.0000i −0.627441 0.627441i 0.319983 0.947423i \(-0.396323\pi\)
−0.947423 + 0.319983i \(0.896323\pi\)
\(824\) 6.00000 6.00000i 0.209020 0.209020i
\(825\) 32.0000 + 24.0000i 1.11410 + 0.835573i
\(826\) −8.00000 + 8.00000i −0.278356 + 0.278356i
\(827\) −24.0000 −0.834562 −0.417281 0.908778i \(-0.637017\pi\)
−0.417281 + 0.908778i \(0.637017\pi\)
\(828\) −10.0000 + 10.0000i −0.347524 + 0.347524i
\(829\) 4.00000 0.138926 0.0694629 0.997585i \(-0.477871\pi\)
0.0694629 + 0.997585i \(0.477871\pi\)
\(830\) −16.0000 + 8.00000i −0.555368 + 0.277684i
\(831\) 12.0000i 0.416275i
\(832\) 3.00000 2.00000i 0.104006 0.0693375i
\(833\) 27.0000 27.0000i 0.935495 0.935495i
\(834\) 0 0
\(835\) 12.0000 + 24.0000i 0.415277 + 0.830554i
\(836\) 8.00000i 0.276686i
\(837\) 48.0000i 1.65912i
\(838\) 0 0
\(839\) −18.0000 18.0000i −0.621429 0.621429i 0.324468 0.945897i \(-0.394815\pi\)
−0.945897 + 0.324468i \(0.894815\pi\)
\(840\) 8.00000 24.0000i 0.276026 0.828079i
\(841\) −7.00000 −0.241379
\(842\) −19.0000 + 19.0000i −0.654783 + 0.654783i
\(843\) 44.0000i 1.51544i
\(844\) 4.00000 0.137686
\(845\) −29.0000 + 2.00000i −0.997630 + 0.0688021i
\(846\) 20.0000 0.687614
\(847\) 12.0000i 0.412325i
\(848\) −1.00000 + 1.00000i −0.0343401 + 0.0343401i
\(849\) 24.0000 0.823678
\(850\) 21.0000 3.00000i 0.720294 0.102899i
\(851\) −8.00000 8.00000i −0.274236 0.274236i
\(852\) −8.00000 −0.274075
\(853\) 22.0000i 0.753266i 0.926363 + 0.376633i \(0.122918\pi\)
−0.926363 + 0.376633i \(0.877082\pi\)
\(854\) 48.0000i 1.64253i
\(855\) −10.0000 + 30.0000i −0.341993 + 1.02598i
\(856\) 6.00000 6.00000i 0.205076 0.205076i
\(857\) 31.0000 31.0000i 1.05894 1.05894i 0.0607892 0.998151i \(-0.480638\pi\)
0.998151 0.0607892i \(-0.0193617\pi\)
\(858\) 24.0000 16.0000i 0.819346 0.546231i
\(859\) 40.0000i 1.36478i −0.730987 0.682391i \(-0.760940\pi\)
0.730987 0.682391i \(-0.239060\pi\)
\(860\) 2.00000 6.00000i 0.0681994 0.204598i
\(861\) −16.0000 −0.545279
\(862\) 6.00000 6.00000i 0.204361 0.204361i
\(863\) −52.0000 −1.77010 −0.885050 0.465495i \(-0.845876\pi\)
−0.885050 + 0.465495i \(0.845876\pi\)
\(864\) 4.00000 4.00000i 0.136083 0.136083i
\(865\) 9.00000 27.0000i 0.306009 0.918028i
\(866\) −3.00000 + 3.00000i −0.101944 + 0.101944i
\(867\) 2.00000 + 2.00000i 0.0679236 + 0.0679236i
\(868\) −24.0000 24.0000i −0.814613 0.814613i
\(869\) −8.00000 8.00000i −0.271381 0.271381i
\(870\) 36.0000 + 12.0000i 1.22051 + 0.406838i
\(871\) −8.00000 12.0000i −0.271070 0.406604i
\(872\) −11.0000 11.0000i −0.372507 0.372507i
\(873\) 0 0
\(874\) 8.00000i 0.270604i
\(875\) −44.0000 8.00000i −1.48747 0.270449i
\(876\) −20.0000 20.0000i −0.675737 0.675737i
\(877\) 20.0000i 0.675352i 0.941262 + 0.337676i \(0.109641\pi\)
−0.941262 + 0.337676i \(0.890359\pi\)
\(878\) 40.0000i 1.34993i
\(879\) −52.0000 52.0000i −1.75392 1.75392i
\(880\) 6.00000 + 2.00000i 0.202260 + 0.0674200i
\(881\) 38.0000i 1.28025i 0.768270 + 0.640126i \(0.221118\pi\)
−0.768270 + 0.640126i \(0.778882\pi\)
\(882\) −45.0000 −1.51523
\(883\) 18.0000 + 18.0000i 0.605748 + 0.605748i 0.941832 0.336084i \(-0.109103\pi\)
−0.336084 + 0.941832i \(0.609103\pi\)
\(884\) 3.00000 15.0000i 0.100901 0.504505i
\(885\) 8.00000 + 16.0000i 0.268917 + 0.537834i
\(886\) 18.0000 + 18.0000i 0.604722 + 0.604722i
\(887\) 2.00000 + 2.00000i 0.0671534 + 0.0671534i 0.739886 0.672732i \(-0.234879\pi\)
−0.672732 + 0.739886i \(0.734879\pi\)
\(888\) 8.00000 + 8.00000i 0.268462 + 0.268462i
\(889\) −56.0000 + 56.0000i −1.87818 + 1.87818i
\(890\) 15.0000 + 5.00000i 0.502801 + 0.167600i
\(891\) 2.00000 2.00000i 0.0670025 0.0670025i
\(892\) 28.0000 0.937509
\(893\) −8.00000 + 8.00000i −0.267710 + 0.267710i
\(894\) 44.0000 1.47158
\(895\) 20.0000 + 40.0000i 0.668526 + 1.33705i
\(896\) 4.00000i 0.133631i
\(897\) 24.0000 16.0000i 0.801337 0.534224i
\(898\) −11.0000 + 11.0000i −0.367075 + 0.367075i
\(899\) 36.0000 36.0000i 1.20067 1.20067i
\(900\) −20.0000 15.0000i −0.666667 0.500000i
\(901\) 6.00000i 0.199889i
\(902\) 4.00000i 0.133185i
\(903\) −32.0000 −1.06489
\(904\) 1.00000 + 1.00000i 0.0332595 + 0.0332595i
\(905\) −4.00000 + 2.00000i −0.132964 + 0.0664822i
\(906\) −56.0000 −1.86048
\(907\) −6.00000 + 6.00000i −0.199227 + 0.199227i −0.799668 0.600442i \(-0.794991\pi\)
0.600442 + 0.799668i \(0.294991\pi\)
\(908\) 4.00000i 0.132745i
\(909\) 60.0000 1.99007
\(910\) −16.0000 + 28.0000i −0.530395 + 0.928191i
\(911\) 8.00000 0.265052 0.132526 0.991180i \(-0.457691\pi\)
0.132526 + 0.991180i \(0.457691\pi\)
\(912\) 8.00000i 0.264906i
\(913\) −16.0000 + 16.0000i −0.529523 + 0.529523i
\(914\) 16.0000 0.529233
\(915\) −72.0000 24.0000i −2.38025 0.793416i
\(916\) 1.00000 + 1.00000i 0.0330409 + 0.0330409i
\(917\) −16.0000 −0.528367
\(918\) 24.0000i 0.792118i
\(919\) 28.0000i 0.923635i 0.886975 + 0.461817i \(0.152802\pi\)
−0.886975 + 0.461817i \(0.847198\pi\)
\(920\) 6.00000 + 2.00000i 0.197814 + 0.0659380i
\(921\) 16.0000 16.0000i 0.527218 0.527218i
\(922\) −11.0000 + 11.0000i −0.362266 + 0.362266i
\(923\) 10.0000 + 2.00000i 0.329154 + 0.0658308i
\(924\) 32.0000i 1.05272i
\(925\) 12.0000 16.0000i 0.394558 0.526077i
\(926\) 8.00000 0.262896
\(927\) −30.0000 + 30.0000i −0.985329 + 0.985329i
\(928\) 6.00000 0.196960
\(929\) −27.0000 + 27.0000i −0.885841 + 0.885841i −0.994121 0.108279i \(-0.965466\pi\)
0.108279 + 0.994121i \(0.465466\pi\)
\(930\) −48.0000 + 24.0000i −1.57398 + 0.786991i
\(931\) 18.0000 18.0000i 0.589926 0.589926i
\(932\) 11.0000 + 11.0000i 0.360317 + 0.360317i
\(933\) −24.0000 24.0000i −0.785725 0.785725i
\(934\) 2.00000 + 2.00000i 0.0654420 + 0.0654420i
\(935\) 24.0000 12.0000i 0.784884 0.392442i
\(936\) −15.0000 + 10.0000i −0.490290 + 0.326860i
\(937\) −35.0000 35.0000i −1.14340 1.14340i −0.987824 0.155576i \(-0.950277\pi\)
−0.155576 0.987824i \(-0.549723\pi\)
\(938\) −16.0000 −0.522419
\(939\) 36.0000i 1.17482i
\(940\) −4.00000 8.00000i −0.130466 0.260931i
\(941\) −25.0000 25.0000i −0.814977 0.814977i 0.170399 0.985375i \(-0.445494\pi\)
−0.985375 + 0.170399i \(0.945494\pi\)
\(942\) 12.0000i 0.390981i
\(943\) 4.00000i 0.130258i
\(944\) 2.00000 + 2.00000i 0.0650945 + 0.0650945i
\(945\) −16.0000 + 48.0000i −0.520480 + 1.56144i
\(946\) 8.00000i 0.260102i
\(947\) 32.0000 1.03986 0.519930 0.854209i \(-0.325958\pi\)
0.519930 + 0.854209i \(0.325958\pi\)
\(948\) 8.00000 + 8.00000i 0.259828 + 0.259828i
\(949\) 20.0000 + 30.0000i 0.649227 + 0.973841i
\(950\) 14.0000 2.00000i 0.454220 0.0648886i
\(951\) 60.0000 + 60.0000i 1.94563 + 1.94563i
\(952\) −12.0000 12.0000i −0.388922 0.388922i
\(953\) 23.0000 + 23.0000i 0.745043 + 0.745043i 0.973544 0.228501i \(-0.0733823\pi\)
−0.228501 + 0.973544i \(0.573382\pi\)
\(954\) 5.00000 5.00000i 0.161881 0.161881i
\(955\) 0 0
\(956\) −10.0000 + 10.0000i −0.323423 + 0.323423i
\(957\) 48.0000 1.55162
\(958\) 10.0000 10.0000i 0.323085 0.323085i
\(959\) −72.0000 −2.32500
\(960\) −6.00000 2.00000i −0.193649 0.0645497i
\(961\) 41.0000i 1.32258i
\(962\) −8.00000 12.0000i −0.257930 0.386896i
\(963\) −30.0000 + 30.0000i −0.966736 + 0.966736i
\(964\) 5.00000 5.00000i 0.161039 0.161039i
\(965\) 32.0000 16.0000i 1.03012 0.515058i
\(966\) 32.0000i 1.02958i
\(967\) 24.0000i 0.771788i −0.922543 0.385894i \(-0.873893\pi\)
0.922543 0.385894i \(-0.126107\pi\)
\(968\) −3.00000 −0.0964237
\(969\) 24.0000 + 24.0000i 0.770991 + 0.770991i
\(970\) 0 0
\(971\) 36.0000 1.15529 0.577647 0.816286i \(-0.303971\pi\)
0.577647 + 0.816286i \(0.303971\pi\)
\(972\) 10.0000 10.0000i 0.320750 0.320750i
\(973\) 0 0
\(974\) 16.0000 0.512673
\(975\) 34.0000 + 38.0000i 1.08887 + 1.21697i
\(976\) −12.0000 −0.384111
\(977\) 2.00000i 0.0639857i 0.999488 + 0.0319928i \(0.0101854\pi\)
−0.999488 + 0.0319928i \(0.989815\pi\)
\(978\) −40.0000 + 40.0000i −1.27906 + 1.27906i
\(979\) 20.0000 0.639203
\(980\) 9.00000 + 18.0000i 0.287494 + 0.574989i
\(981\) 55.0000 + 55.0000i 1.75601 + 1.75601i
\(982\) −24.0000 −0.765871
\(983\) 24.0000i 0.765481i −0.923856 0.382741i \(-0.874980\pi\)
0.923856 0.382741i \(-0.125020\pi\)
\(984\) 4.00000i 0.127515i
\(985\) −24.0000 + 12.0000i −0.764704 + 0.382352i
\(986\) 18.0000 18.0000i 0.573237 0.573237i
\(987\) −32.0000 + 32.0000i −1.01857 + 1.01857i
\(988\) 2.00000 10.0000i 0.0636285 0.318142i
\(989\) 8.00000i 0.254385i
\(990\) −30.0000 10.0000i −0.953463 0.317821i
\(991\) −32.0000 −1.01651 −0.508257 0.861206i \(-0.669710\pi\)
−0.508257 + 0.861206i \(0.669710\pi\)
\(992\) −6.00000 + 6.00000i −0.190500 + 0.190500i
\(993\) 24.0000 0.761617
\(994\) 8.00000 8.00000i 0.253745 0.253745i
\(995\) −8.00000 16.0000i −0.253617 0.507234i
\(996\) 16.0000 16.0000i 0.506979 0.506979i
\(997\) −37.0000 37.0000i −1.17180 1.17180i −0.981780 0.190022i \(-0.939144\pi\)
−0.190022 0.981780i \(-0.560856\pi\)
\(998\) −14.0000 14.0000i −0.443162 0.443162i
\(999\) −16.0000 16.0000i −0.506218 0.506218i
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 130.2.j.a.47.1 yes 2
3.2 odd 2 1170.2.w.b.307.1 2
4.3 odd 2 1040.2.cd.g.177.1 2
5.2 odd 4 650.2.g.e.593.1 2
5.3 odd 4 130.2.g.a.73.1 yes 2
5.4 even 2 650.2.j.e.307.1 2
13.5 odd 4 130.2.g.a.57.1 2
15.8 even 4 1170.2.m.c.73.1 2
20.3 even 4 1040.2.bg.g.593.1 2
39.5 even 4 1170.2.m.c.577.1 2
52.31 even 4 1040.2.bg.g.577.1 2
65.18 even 4 inner 130.2.j.a.83.1 yes 2
65.44 odd 4 650.2.g.e.57.1 2
65.57 even 4 650.2.j.e.343.1 2
195.83 odd 4 1170.2.w.b.343.1 2
260.83 odd 4 1040.2.cd.g.993.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
130.2.g.a.57.1 2 13.5 odd 4
130.2.g.a.73.1 yes 2 5.3 odd 4
130.2.j.a.47.1 yes 2 1.1 even 1 trivial
130.2.j.a.83.1 yes 2 65.18 even 4 inner
650.2.g.e.57.1 2 65.44 odd 4
650.2.g.e.593.1 2 5.2 odd 4
650.2.j.e.307.1 2 5.4 even 2
650.2.j.e.343.1 2 65.57 even 4
1040.2.bg.g.577.1 2 52.31 even 4
1040.2.bg.g.593.1 2 20.3 even 4
1040.2.cd.g.177.1 2 4.3 odd 2
1040.2.cd.g.993.1 2 260.83 odd 4
1170.2.m.c.73.1 2 15.8 even 4
1170.2.m.c.577.1 2 39.5 even 4
1170.2.w.b.307.1 2 3.2 odd 2
1170.2.w.b.343.1 2 195.83 odd 4