Properties

Label 260.2.j.a.31.20
Level $260$
Weight $2$
Character 260.31
Analytic conductor $2.076$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [260,2,Mod(31,260)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(260, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("260.31");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 260.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: \(2.07611045255\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(28\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 31.20
Character \(\chi\) \(=\) 260.31
Dual form 260.2.j.a.151.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.723264 - 1.21527i) q^{2} +1.80245i q^{3} +(-0.953778 - 1.75793i) q^{4} +(0.707107 - 0.707107i) q^{5} +(2.19047 + 1.30365i) q^{6} +(1.20463 - 1.20463i) q^{7} +(-2.82620 - 0.112344i) q^{8} -0.248815 q^{9} +O(q^{10})\) \(q+(0.723264 - 1.21527i) q^{2} +1.80245i q^{3} +(-0.953778 - 1.75793i) q^{4} +(0.707107 - 0.707107i) q^{5} +(2.19047 + 1.30365i) q^{6} +(1.20463 - 1.20463i) q^{7} +(-2.82620 - 0.112344i) q^{8} -0.248815 q^{9} +(-0.347903 - 1.37075i) q^{10} +(2.81846 - 2.81846i) q^{11} +(3.16857 - 1.71913i) q^{12} +(2.45611 + 2.63961i) q^{13} +(-0.592687 - 2.33521i) q^{14} +(1.27452 + 1.27452i) q^{15} +(-2.18061 + 3.35334i) q^{16} +0.129940i q^{17} +(-0.179959 + 0.302379i) q^{18} +(0.145035 + 0.145035i) q^{19} +(-1.91747 - 0.568619i) q^{20} +(2.17127 + 2.17127i) q^{21} +(-1.38671 - 5.46368i) q^{22} -4.57371 q^{23} +(0.202494 - 5.09407i) q^{24} -1.00000i q^{25} +(4.98426 - 1.07571i) q^{26} +4.95886i q^{27} +(-3.26659 - 0.968698i) q^{28} -3.84278 q^{29} +(2.47071 - 0.627077i) q^{30} +(-2.42671 - 2.42671i) q^{31} +(2.49807 + 5.07540i) q^{32} +(5.08012 + 5.08012i) q^{33} +(0.157913 + 0.0939810i) q^{34} -1.70360i q^{35} +(0.237315 + 0.437399i) q^{36} +(-1.25170 - 1.25170i) q^{37} +(0.281155 - 0.0713584i) q^{38} +(-4.75776 + 4.42700i) q^{39} +(-2.07786 + 1.91898i) q^{40} +(-4.46917 + 4.46917i) q^{41} +(4.20910 - 1.06829i) q^{42} -7.63599 q^{43} +(-7.64283 - 2.26646i) q^{44} +(-0.175939 + 0.175939i) q^{45} +(-3.30800 + 5.55830i) q^{46} +(-4.07898 + 4.07898i) q^{47} +(-6.04423 - 3.93044i) q^{48} +4.09775i q^{49} +(-1.21527 - 0.723264i) q^{50} -0.234210 q^{51} +(2.29766 - 6.83526i) q^{52} +3.15397 q^{53} +(6.02638 + 3.58657i) q^{54} -3.98590i q^{55} +(-3.53984 + 3.26917i) q^{56} +(-0.261417 + 0.261417i) q^{57} +(-2.77935 + 4.67003i) q^{58} +(9.66305 - 9.66305i) q^{59} +(1.02491 - 3.45613i) q^{60} -5.89106 q^{61} +(-4.70428 + 1.19397i) q^{62} +(-0.299729 + 0.299729i) q^{63} +(7.97476 + 0.635013i) q^{64} +(3.60322 + 0.129757i) q^{65} +(9.84800 - 2.49947i) q^{66} +(6.46816 + 6.46816i) q^{67} +(0.228425 - 0.123934i) q^{68} -8.24386i q^{69} +(-2.07034 - 1.23215i) q^{70} +(-6.42532 - 6.42532i) q^{71} +(0.703201 + 0.0279530i) q^{72} +(11.6298 + 11.6298i) q^{73} +(-2.42646 + 0.615847i) q^{74} +1.80245 q^{75} +(0.116630 - 0.393292i) q^{76} -6.79037i q^{77} +(1.93890 + 8.98387i) q^{78} +3.11122i q^{79} +(0.829246 + 3.91310i) q^{80} -9.68454 q^{81} +(2.19887 + 8.66365i) q^{82} +(11.2681 + 11.2681i) q^{83} +(1.74603 - 5.88785i) q^{84} +(0.0918816 + 0.0918816i) q^{85} +(-5.52284 + 9.27982i) q^{86} -6.92641i q^{87} +(-8.28215 + 7.64887i) q^{88} +(-10.5657 - 10.5657i) q^{89} +(0.0865637 + 0.341064i) q^{90} +(6.13843 + 0.221053i) q^{91} +(4.36230 + 8.04024i) q^{92} +(4.37402 - 4.37402i) q^{93} +(2.00690 + 7.90726i) q^{94} +0.205110 q^{95} +(-9.14813 + 4.50264i) q^{96} +(-9.62350 + 9.62350i) q^{97} +(4.97989 + 2.96376i) q^{98} +(-0.701276 + 0.701276i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q - 12 q^{6} + 12 q^{8} - 56 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 56 q - 12 q^{6} + 12 q^{8} - 56 q^{9} + 16 q^{14} - 12 q^{18} - 8 q^{20} - 16 q^{21} - 40 q^{24} - 16 q^{26} - 44 q^{28} + 40 q^{32} - 4 q^{34} + 16 q^{37} + 8 q^{41} + 8 q^{42} + 28 q^{44} - 12 q^{46} + 104 q^{48} + 56 q^{52} - 16 q^{53} + 20 q^{54} - 48 q^{57} - 4 q^{58} + 16 q^{61} - 8 q^{65} + 64 q^{66} + 24 q^{68} - 8 q^{70} - 32 q^{72} + 48 q^{73} - 136 q^{74} - 88 q^{76} + 52 q^{78} - 32 q^{80} + 56 q^{81} - 20 q^{84} - 64 q^{86} - 8 q^{89} - 88 q^{92} - 48 q^{93} - 16 q^{94} - 4 q^{96} - 32 q^{97} + 16 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).

\(n\) \(41\) \(131\) \(157\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.723264 1.21527i 0.511425 0.859328i
\(3\) 1.80245i 1.04064i 0.853970 + 0.520322i \(0.174188\pi\)
−0.853970 + 0.520322i \(0.825812\pi\)
\(4\) −0.953778 1.75793i −0.476889 0.878963i
\(5\) 0.707107 0.707107i 0.316228 0.316228i
\(6\) 2.19047 + 1.30365i 0.894254 + 0.532211i
\(7\) 1.20463 1.20463i 0.455306 0.455306i −0.441805 0.897111i \(-0.645662\pi\)
0.897111 + 0.441805i \(0.145662\pi\)
\(8\) −2.82620 0.112344i −0.999211 0.0397196i
\(9\) −0.248815 −0.0829385
\(10\) −0.347903 1.37075i −0.110017 0.433470i
\(11\) 2.81846 2.81846i 0.849797 0.849797i −0.140311 0.990108i \(-0.544810\pi\)
0.990108 + 0.140311i \(0.0448101\pi\)
\(12\) 3.16857 1.71913i 0.914687 0.496271i
\(13\) 2.45611 + 2.63961i 0.681201 + 0.732096i
\(14\) −0.592687 2.33521i −0.158402 0.624112i
\(15\) 1.27452 + 1.27452i 0.329080 + 0.329080i
\(16\) −2.18061 + 3.35334i −0.545154 + 0.838336i
\(17\) 0.129940i 0.0315151i 0.999876 + 0.0157576i \(0.00501599\pi\)
−0.999876 + 0.0157576i \(0.994984\pi\)
\(18\) −0.179959 + 0.302379i −0.0424168 + 0.0712714i
\(19\) 0.145035 + 0.145035i 0.0332733 + 0.0332733i 0.723548 0.690274i \(-0.242510\pi\)
−0.690274 + 0.723548i \(0.742510\pi\)
\(20\) −1.91747 0.568619i −0.428758 0.127147i
\(21\) 2.17127 + 2.17127i 0.473811 + 0.473811i
\(22\) −1.38671 5.46368i −0.295647 1.16486i
\(23\) −4.57371 −0.953684 −0.476842 0.878989i \(-0.658219\pi\)
−0.476842 + 0.878989i \(0.658219\pi\)
\(24\) 0.202494 5.09407i 0.0413340 1.03982i
\(25\) 1.00000i 0.200000i
\(26\) 4.98426 1.07571i 0.977494 0.210963i
\(27\) 4.95886i 0.954334i
\(28\) −3.26659 0.968698i −0.617327 0.183067i
\(29\) −3.84278 −0.713587 −0.356793 0.934183i \(-0.616130\pi\)
−0.356793 + 0.934183i \(0.616130\pi\)
\(30\) 2.47071 0.627077i 0.451088 0.114488i
\(31\) −2.42671 2.42671i −0.435851 0.435851i 0.454762 0.890613i \(-0.349724\pi\)
−0.890613 + 0.454762i \(0.849724\pi\)
\(32\) 2.49807 + 5.07540i 0.441601 + 0.897212i
\(33\) 5.08012 + 5.08012i 0.884335 + 0.884335i
\(34\) 0.157913 + 0.0939810i 0.0270818 + 0.0161176i
\(35\) 1.70360i 0.287961i
\(36\) 0.237315 + 0.437399i 0.0395525 + 0.0728999i
\(37\) −1.25170 1.25170i −0.205778 0.205778i 0.596692 0.802470i \(-0.296481\pi\)
−0.802470 + 0.596692i \(0.796481\pi\)
\(38\) 0.281155 0.0713584i 0.0456094 0.0115759i
\(39\) −4.75776 + 4.42700i −0.761851 + 0.708888i
\(40\) −2.07786 + 1.91898i −0.328539 + 0.303418i
\(41\) −4.46917 + 4.46917i −0.697967 + 0.697967i −0.963972 0.266005i \(-0.914296\pi\)
0.266005 + 0.963972i \(0.414296\pi\)
\(42\) 4.20910 1.06829i 0.649477 0.164840i
\(43\) −7.63599 −1.16448 −0.582239 0.813018i \(-0.697823\pi\)
−0.582239 + 0.813018i \(0.697823\pi\)
\(44\) −7.64283 2.26646i −1.15220 0.341682i
\(45\) −0.175939 + 0.175939i −0.0262275 + 0.0262275i
\(46\) −3.30800 + 5.55830i −0.487738 + 0.819527i
\(47\) −4.07898 + 4.07898i −0.594981 + 0.594981i −0.938973 0.343992i \(-0.888221\pi\)
0.343992 + 0.938973i \(0.388221\pi\)
\(48\) −6.04423 3.93044i −0.872409 0.567310i
\(49\) 4.09775i 0.585394i
\(50\) −1.21527 0.723264i −0.171866 0.102285i
\(51\) −0.234210 −0.0327960
\(52\) 2.29766 6.83526i 0.318628 0.947880i
\(53\) 3.15397 0.433231 0.216616 0.976257i \(-0.430498\pi\)
0.216616 + 0.976257i \(0.430498\pi\)
\(54\) 6.02638 + 3.58657i 0.820086 + 0.488070i
\(55\) 3.98590i 0.537459i
\(56\) −3.53984 + 3.26917i −0.473031 + 0.436862i
\(57\) −0.261417 + 0.261417i −0.0346256 + 0.0346256i
\(58\) −2.77935 + 4.67003i −0.364946 + 0.613205i
\(59\) 9.66305 9.66305i 1.25802 1.25802i 0.305986 0.952036i \(-0.401014\pi\)
0.952036 0.305986i \(-0.0989861\pi\)
\(60\) 1.02491 3.45613i 0.132315 0.446184i
\(61\) −5.89106 −0.754273 −0.377136 0.926158i \(-0.623091\pi\)
−0.377136 + 0.926158i \(0.623091\pi\)
\(62\) −4.70428 + 1.19397i −0.597444 + 0.151634i
\(63\) −0.299729 + 0.299729i −0.0377624 + 0.0377624i
\(64\) 7.97476 + 0.635013i 0.996845 + 0.0793766i
\(65\) 3.60322 + 0.129757i 0.446924 + 0.0160943i
\(66\) 9.84800 2.49947i 1.21221 0.307663i
\(67\) 6.46816 + 6.46816i 0.790212 + 0.790212i 0.981528 0.191317i \(-0.0612757\pi\)
−0.191317 + 0.981528i \(0.561276\pi\)
\(68\) 0.228425 0.123934i 0.0277006 0.0150292i
\(69\) 8.24386i 0.992444i
\(70\) −2.07034 1.23215i −0.247453 0.147270i
\(71\) −6.42532 6.42532i −0.762545 0.762545i 0.214237 0.976782i \(-0.431274\pi\)
−0.976782 + 0.214237i \(0.931274\pi\)
\(72\) 0.703201 + 0.0279530i 0.0828730 + 0.00329429i
\(73\) 11.6298 + 11.6298i 1.36117 + 1.36117i 0.872433 + 0.488734i \(0.162541\pi\)
0.488734 + 0.872433i \(0.337459\pi\)
\(74\) −2.42646 + 0.615847i −0.282071 + 0.0715908i
\(75\) 1.80245 0.208129
\(76\) 0.116630 0.393292i 0.0133783 0.0451136i
\(77\) 6.79037i 0.773835i
\(78\) 1.93890 + 8.98387i 0.219537 + 1.01722i
\(79\) 3.11122i 0.350040i 0.984565 + 0.175020i \(0.0559989\pi\)
−0.984565 + 0.175020i \(0.944001\pi\)
\(80\) 0.829246 + 3.91310i 0.0927125 + 0.437498i
\(81\) −9.68454 −1.07606
\(82\) 2.19887 + 8.66365i 0.242825 + 0.956740i
\(83\) 11.2681 + 11.2681i 1.23684 + 1.23684i 0.961287 + 0.275548i \(0.0888594\pi\)
0.275548 + 0.961287i \(0.411141\pi\)
\(84\) 1.74603 5.88785i 0.190507 0.642418i
\(85\) 0.0918816 + 0.0918816i 0.00996595 + 0.00996595i
\(86\) −5.52284 + 9.27982i −0.595543 + 1.00067i
\(87\) 6.92641i 0.742589i
\(88\) −8.28215 + 7.64887i −0.882880 + 0.815373i
\(89\) −10.5657 10.5657i −1.11996 1.11996i −0.991746 0.128215i \(-0.959075\pi\)
−0.128215 0.991746i \(-0.540925\pi\)
\(90\) 0.0865637 + 0.341064i 0.00912461 + 0.0359514i
\(91\) 6.13843 + 0.221053i 0.643482 + 0.0231727i
\(92\) 4.36230 + 8.04024i 0.454801 + 0.838253i
\(93\) 4.37402 4.37402i 0.453565 0.453565i
\(94\) 2.00690 + 7.90726i 0.206996 + 0.815572i
\(95\) 0.205110 0.0210439
\(96\) −9.14813 + 4.50264i −0.933677 + 0.459549i
\(97\) −9.62350 + 9.62350i −0.977118 + 0.977118i −0.999744 0.0226260i \(-0.992797\pi\)
0.0226260 + 0.999744i \(0.492797\pi\)
\(98\) 4.97989 + 2.96376i 0.503045 + 0.299385i
\(99\) −0.701276 + 0.701276i −0.0704809 + 0.0704809i
\(100\) −1.75793 + 0.953778i −0.175793 + 0.0953778i
\(101\) 13.6153i 1.35477i −0.735629 0.677384i \(-0.763113\pi\)
0.735629 0.677384i \(-0.236887\pi\)
\(102\) −0.169396 + 0.284629i −0.0167727 + 0.0281825i
\(103\) 10.0009 0.985416 0.492708 0.870195i \(-0.336007\pi\)
0.492708 + 0.870195i \(0.336007\pi\)
\(104\) −6.64489 7.73598i −0.651585 0.758575i
\(105\) 3.07064 0.299664
\(106\) 2.28115 3.83294i 0.221565 0.372288i
\(107\) 11.8232i 1.14299i −0.820606 0.571494i \(-0.806364\pi\)
0.820606 0.571494i \(-0.193636\pi\)
\(108\) 8.71732 4.72966i 0.838825 0.455111i
\(109\) 2.62846 2.62846i 0.251761 0.251761i −0.569931 0.821692i \(-0.693030\pi\)
0.821692 + 0.569931i \(0.193030\pi\)
\(110\) −4.84396 2.88286i −0.461853 0.274870i
\(111\) 2.25612 2.25612i 0.214141 0.214141i
\(112\) 1.41270 + 6.66635i 0.133488 + 0.629911i
\(113\) 3.29753 0.310206 0.155103 0.987898i \(-0.450429\pi\)
0.155103 + 0.987898i \(0.450429\pi\)
\(114\) 0.128620 + 0.506768i 0.0120463 + 0.0474631i
\(115\) −3.23410 + 3.23410i −0.301581 + 0.301581i
\(116\) 3.66516 + 6.75533i 0.340302 + 0.627217i
\(117\) −0.611117 0.656776i −0.0564978 0.0607189i
\(118\) −4.75431 18.7322i −0.437670 1.72444i
\(119\) 0.156529 + 0.156529i 0.0143490 + 0.0143490i
\(120\) −3.45886 3.74523i −0.315750 0.341892i
\(121\) 4.88740i 0.444309i
\(122\) −4.26079 + 7.15924i −0.385754 + 0.648168i
\(123\) −8.05544 8.05544i −0.726334 0.726334i
\(124\) −1.95144 + 6.58053i −0.175244 + 0.590949i
\(125\) −0.707107 0.707107i −0.0632456 0.0632456i
\(126\) 0.147470 + 0.581037i 0.0131376 + 0.0517629i
\(127\) −11.7740 −1.04478 −0.522389 0.852707i \(-0.674959\pi\)
−0.522389 + 0.852707i \(0.674959\pi\)
\(128\) 6.53957 9.23223i 0.578022 0.816021i
\(129\) 13.7635i 1.21181i
\(130\) 2.76377 4.28504i 0.242398 0.375823i
\(131\) 7.98436i 0.697597i 0.937198 + 0.348798i \(0.113410\pi\)
−0.937198 + 0.348798i \(0.886590\pi\)
\(132\) 4.08517 13.7758i 0.355569 1.19903i
\(133\) 0.349425 0.0302990
\(134\) 12.5388 3.18240i 1.08319 0.274917i
\(135\) 3.50645 + 3.50645i 0.301787 + 0.301787i
\(136\) 0.0145980 0.367236i 0.00125177 0.0314902i
\(137\) −14.0186 14.0186i −1.19769 1.19769i −0.974857 0.222833i \(-0.928470\pi\)
−0.222833 0.974857i \(-0.571530\pi\)
\(138\) −10.0185 5.96249i −0.852835 0.507561i
\(139\) 11.8700i 1.00680i −0.864053 0.503402i \(-0.832082\pi\)
0.864053 0.503402i \(-0.167918\pi\)
\(140\) −2.99480 + 1.62485i −0.253107 + 0.137325i
\(141\) −7.35215 7.35215i −0.619163 0.619163i
\(142\) −12.4557 + 3.16132i −1.04526 + 0.265292i
\(143\) 14.3621 + 0.517197i 1.20102 + 0.0432502i
\(144\) 0.542570 0.834364i 0.0452142 0.0695303i
\(145\) −2.71726 + 2.71726i −0.225656 + 0.225656i
\(146\) 22.5448 5.72198i 1.86582 0.473554i
\(147\) −7.38599 −0.609186
\(148\) −1.00655 + 3.39424i −0.0827380 + 0.279005i
\(149\) 1.95014 1.95014i 0.159762 0.159762i −0.622699 0.782461i \(-0.713964\pi\)
0.782461 + 0.622699i \(0.213964\pi\)
\(150\) 1.30365 2.19047i 0.106442 0.178851i
\(151\) −6.31578 + 6.31578i −0.513971 + 0.513971i −0.915741 0.401770i \(-0.868395\pi\)
0.401770 + 0.915741i \(0.368395\pi\)
\(152\) −0.393603 0.426190i −0.0319254 0.0345686i
\(153\) 0.0323311i 0.00261382i
\(154\) −8.25216 4.91123i −0.664978 0.395758i
\(155\) −3.43189 −0.275656
\(156\) 12.3202 + 4.14141i 0.986405 + 0.331578i
\(157\) −0.134883 −0.0107648 −0.00538240 0.999986i \(-0.501713\pi\)
−0.00538240 + 0.999986i \(0.501713\pi\)
\(158\) 3.78098 + 2.25023i 0.300799 + 0.179019i
\(159\) 5.68486i 0.450839i
\(160\) 5.35525 + 1.82244i 0.423370 + 0.144077i
\(161\) −5.50960 + 5.50960i −0.434218 + 0.434218i
\(162\) −7.00448 + 11.7694i −0.550324 + 0.924688i
\(163\) −13.3308 + 13.3308i −1.04415 + 1.04415i −0.0451734 + 0.998979i \(0.514384\pi\)
−0.998979 + 0.0451734i \(0.985616\pi\)
\(164\) 12.1191 + 3.59387i 0.946340 + 0.280634i
\(165\) 7.18437 0.559303
\(166\) 21.8436 5.54401i 1.69540 0.430299i
\(167\) 11.9297 11.9297i 0.923150 0.923150i −0.0741008 0.997251i \(-0.523609\pi\)
0.997251 + 0.0741008i \(0.0236087\pi\)
\(168\) −5.89251 6.38037i −0.454617 0.492256i
\(169\) −0.935082 + 12.9663i −0.0719294 + 0.997410i
\(170\) 0.178116 0.0452066i 0.0136609 0.00346719i
\(171\) −0.0360869 0.0360869i −0.00275963 0.00275963i
\(172\) 7.28305 + 13.4235i 0.555327 + 1.02353i
\(173\) 22.1130i 1.68122i −0.541641 0.840610i \(-0.682197\pi\)
0.541641 0.840610i \(-0.317803\pi\)
\(174\) −8.41748 5.00963i −0.638128 0.379779i
\(175\) −1.20463 1.20463i −0.0910611 0.0910611i
\(176\) 3.30529 + 15.5972i 0.249146 + 1.17569i
\(177\) 17.4171 + 17.4171i 1.30915 + 1.30915i
\(178\) −20.4820 + 5.19842i −1.53519 + 0.389638i
\(179\) 12.1902 0.911140 0.455570 0.890200i \(-0.349435\pi\)
0.455570 + 0.890200i \(0.349435\pi\)
\(180\) 0.477095 + 0.141481i 0.0355606 + 0.0105454i
\(181\) 8.93090i 0.663828i −0.943310 0.331914i \(-0.892306\pi\)
0.943310 0.331914i \(-0.107694\pi\)
\(182\) 4.70835 7.29999i 0.349006 0.541111i
\(183\) 10.6183i 0.784929i
\(184\) 12.9262 + 0.513829i 0.952931 + 0.0378800i
\(185\) −1.77017 −0.130145
\(186\) −2.15206 8.47921i −0.157797 0.621726i
\(187\) 0.366231 + 0.366231i 0.0267814 + 0.0267814i
\(188\) 11.0610 + 3.28011i 0.806706 + 0.239227i
\(189\) 5.97357 + 5.97357i 0.434514 + 0.434514i
\(190\) 0.148349 0.249265i 0.0107624 0.0180836i
\(191\) 27.1472i 1.96430i 0.188098 + 0.982150i \(0.439768\pi\)
−0.188098 + 0.982150i \(0.560232\pi\)
\(192\) −1.14458 + 14.3741i −0.0826027 + 1.03736i
\(193\) 11.0899 + 11.0899i 0.798266 + 0.798266i 0.982822 0.184556i \(-0.0590846\pi\)
−0.184556 + 0.982822i \(0.559085\pi\)
\(194\) 4.73485 + 18.6555i 0.339942 + 1.33939i
\(195\) −0.233879 + 6.49461i −0.0167485 + 0.465088i
\(196\) 7.20355 3.90835i 0.514540 0.279168i
\(197\) 0.674322 0.674322i 0.0480434 0.0480434i −0.682677 0.730720i \(-0.739184\pi\)
0.730720 + 0.682677i \(0.239184\pi\)
\(198\) 0.345034 + 1.35945i 0.0245205 + 0.0966118i
\(199\) 18.1270 1.28499 0.642495 0.766290i \(-0.277899\pi\)
0.642495 + 0.766290i \(0.277899\pi\)
\(200\) −0.112344 + 2.82620i −0.00794393 + 0.199842i
\(201\) −11.6585 + 11.6585i −0.822329 + 0.822329i
\(202\) −16.5463 9.84743i −1.16419 0.692863i
\(203\) −4.62911 + 4.62911i −0.324900 + 0.324900i
\(204\) 0.223385 + 0.411724i 0.0156401 + 0.0288265i
\(205\) 6.32036i 0.441433i
\(206\) 7.23328 12.1538i 0.503966 0.846796i
\(207\) 1.13801 0.0790971
\(208\) −14.2073 + 2.48020i −0.985102 + 0.171971i
\(209\) 0.817549 0.0565510
\(210\) 2.22089 3.73167i 0.153256 0.257510i
\(211\) 16.9704i 1.16829i −0.811649 0.584146i \(-0.801430\pi\)
0.811649 0.584146i \(-0.198570\pi\)
\(212\) −3.00819 5.54445i −0.206603 0.380794i
\(213\) 11.5813 11.5813i 0.793538 0.793538i
\(214\) −14.3684 8.55126i −0.982201 0.584552i
\(215\) −5.39946 + 5.39946i −0.368240 + 0.368240i
\(216\) 0.557099 14.0147i 0.0379058 0.953581i
\(217\) −5.84656 −0.396891
\(218\) −1.29323 5.09537i −0.0875884 0.345102i
\(219\) −20.9621 + 20.9621i −1.41649 + 1.41649i
\(220\) −7.00692 + 3.80167i −0.472407 + 0.256308i
\(221\) −0.342991 + 0.319147i −0.0230721 + 0.0214681i
\(222\) −1.11003 4.37357i −0.0745005 0.293535i
\(223\) −15.0119 15.0119i −1.00527 1.00527i −0.999986 0.00528284i \(-0.998318\pi\)
−0.00528284 0.999986i \(-0.501682\pi\)
\(224\) 9.12319 + 3.10471i 0.609569 + 0.207442i
\(225\) 0.248815i 0.0165877i
\(226\) 2.38499 4.00740i 0.158647 0.266569i
\(227\) −3.96857 3.96857i −0.263403 0.263403i 0.563032 0.826435i \(-0.309635\pi\)
−0.826435 + 0.563032i \(0.809635\pi\)
\(228\) 0.708887 + 0.210219i 0.0469472 + 0.0139221i
\(229\) 18.9098 + 18.9098i 1.24959 + 1.24959i 0.955900 + 0.293692i \(0.0948841\pi\)
0.293692 + 0.955900i \(0.405116\pi\)
\(230\) 1.59121 + 6.26942i 0.104921 + 0.413393i
\(231\) 12.2393 0.805286
\(232\) 10.8605 + 0.431714i 0.713024 + 0.0283434i
\(233\) 1.37159i 0.0898559i −0.998990 0.0449280i \(-0.985694\pi\)
0.998990 0.0449280i \(-0.0143058\pi\)
\(234\) −1.24016 + 0.267652i −0.0810719 + 0.0174970i
\(235\) 5.76855i 0.376299i
\(236\) −26.2033 7.77053i −1.70569 0.505818i
\(237\) −5.60781 −0.364266
\(238\) 0.303438 0.0770138i 0.0196689 0.00499206i
\(239\) −14.1896 14.1896i −0.917847 0.917847i 0.0790252 0.996873i \(-0.474819\pi\)
−0.996873 + 0.0790252i \(0.974819\pi\)
\(240\) −7.05316 + 1.49467i −0.455279 + 0.0964807i
\(241\) 3.26599 + 3.26599i 0.210381 + 0.210381i 0.804429 0.594048i \(-0.202471\pi\)
−0.594048 + 0.804429i \(0.702471\pi\)
\(242\) −5.93953 3.53488i −0.381807 0.227231i
\(243\) 2.57927i 0.165460i
\(244\) 5.61876 + 10.3560i 0.359704 + 0.662978i
\(245\) 2.89755 + 2.89755i 0.185118 + 0.185118i
\(246\) −15.6158 + 3.96335i −0.995625 + 0.252694i
\(247\) −0.0266144 + 0.739056i −0.00169343 + 0.0470250i
\(248\) 6.58574 + 7.13099i 0.418195 + 0.452819i
\(249\) −20.3102 + 20.3102i −1.28710 + 1.28710i
\(250\) −1.37075 + 0.347903i −0.0866940 + 0.0220033i
\(251\) 11.0760 0.699108 0.349554 0.936916i \(-0.386333\pi\)
0.349554 + 0.936916i \(0.386333\pi\)
\(252\) 0.812778 + 0.241027i 0.0512002 + 0.0151833i
\(253\) −12.8908 + 12.8908i −0.810437 + 0.810437i
\(254\) −8.51574 + 14.3087i −0.534325 + 0.897807i
\(255\) −0.165612 + 0.165612i −0.0103710 + 0.0103710i
\(256\) −6.48984 14.6247i −0.405615 0.914044i
\(257\) 4.31539i 0.269187i 0.990901 + 0.134593i \(0.0429728\pi\)
−0.990901 + 0.134593i \(0.957027\pi\)
\(258\) −16.7264 9.95463i −1.04134 0.619748i
\(259\) −3.01566 −0.187384
\(260\) −3.20857 6.45795i −0.198987 0.400505i
\(261\) 0.956144 0.0591838
\(262\) 9.70318 + 5.77480i 0.599464 + 0.356768i
\(263\) 5.51741i 0.340218i 0.985425 + 0.170109i \(0.0544120\pi\)
−0.985425 + 0.170109i \(0.945588\pi\)
\(264\) −13.7867 14.9281i −0.848512 0.918763i
\(265\) 2.23019 2.23019i 0.137000 0.137000i
\(266\) 0.252727 0.424647i 0.0154957 0.0260368i
\(267\) 19.0441 19.0441i 1.16548 1.16548i
\(268\) 5.20136 17.5397i 0.317724 1.07141i
\(269\) 4.03912 0.246270 0.123135 0.992390i \(-0.460705\pi\)
0.123135 + 0.992390i \(0.460705\pi\)
\(270\) 6.79738 1.72520i 0.413675 0.104993i
\(271\) 7.11595 7.11595i 0.432263 0.432263i −0.457134 0.889398i \(-0.651124\pi\)
0.889398 + 0.457134i \(0.151124\pi\)
\(272\) −0.435734 0.283349i −0.0264203 0.0171806i
\(273\) −0.398436 + 11.0642i −0.0241145 + 0.669636i
\(274\) −27.1756 + 6.89728i −1.64174 + 0.416680i
\(275\) −2.81846 2.81846i −0.169959 0.169959i
\(276\) −14.4921 + 7.86282i −0.872322 + 0.473286i
\(277\) 3.87573i 0.232870i 0.993198 + 0.116435i \(0.0371467\pi\)
−0.993198 + 0.116435i \(0.962853\pi\)
\(278\) −14.4253 8.58517i −0.865174 0.514904i
\(279\) 0.603804 + 0.603804i 0.0361488 + 0.0361488i
\(280\) −0.191389 + 4.81470i −0.0114377 + 0.287733i
\(281\) 11.0563 + 11.0563i 0.659561 + 0.659561i 0.955276 0.295715i \(-0.0955580\pi\)
−0.295715 + 0.955276i \(0.595558\pi\)
\(282\) −14.2524 + 3.61733i −0.848719 + 0.215409i
\(283\) −7.53745 −0.448055 −0.224027 0.974583i \(-0.571920\pi\)
−0.224027 + 0.974583i \(0.571920\pi\)
\(284\) −5.16691 + 17.4236i −0.306600 + 1.03390i
\(285\) 0.369700i 0.0218991i
\(286\) 11.0161 17.0798i 0.651395 1.00995i
\(287\) 10.7673i 0.635576i
\(288\) −0.621559 1.26284i −0.0366257 0.0744134i
\(289\) 16.9831 0.999007
\(290\) 1.33692 + 5.26751i 0.0785064 + 0.309319i
\(291\) −17.3458 17.3458i −1.01683 1.01683i
\(292\) 9.35210 31.5366i 0.547290 1.84554i
\(293\) −8.60612 8.60612i −0.502775 0.502775i 0.409524 0.912299i \(-0.365695\pi\)
−0.912299 + 0.409524i \(0.865695\pi\)
\(294\) −5.34202 + 8.97599i −0.311553 + 0.523490i
\(295\) 13.6656i 0.795643i
\(296\) 3.39692 + 3.67817i 0.197442 + 0.213789i
\(297\) 13.9763 + 13.9763i 0.810990 + 0.810990i
\(298\) −0.959488 3.78042i −0.0555816 0.218994i
\(299\) −11.2335 12.0728i −0.649651 0.698188i
\(300\) −1.71913 3.16857i −0.0992543 0.182937i
\(301\) −9.19851 + 9.19851i −0.530194 + 0.530194i
\(302\) 3.10742 + 12.2434i 0.178812 + 0.704527i
\(303\) 24.5408 1.40983
\(304\) −0.802616 + 0.170087i −0.0460332 + 0.00975514i
\(305\) −4.16561 + 4.16561i −0.238522 + 0.238522i
\(306\) −0.0392911 0.0233839i −0.00224612 0.00133677i
\(307\) −1.42049 + 1.42049i −0.0810716 + 0.0810716i −0.746480 0.665408i \(-0.768258\pi\)
0.665408 + 0.746480i \(0.268258\pi\)
\(308\) −11.9370 + 6.47651i −0.680172 + 0.369033i
\(309\) 18.0261i 1.02547i
\(310\) −2.48216 + 4.17069i −0.140977 + 0.236879i
\(311\) −20.6745 −1.17234 −0.586172 0.810186i \(-0.699366\pi\)
−0.586172 + 0.810186i \(0.699366\pi\)
\(312\) 13.9437 11.9771i 0.789406 0.678068i
\(313\) −24.9530 −1.41043 −0.705213 0.708996i \(-0.749149\pi\)
−0.705213 + 0.708996i \(0.749149\pi\)
\(314\) −0.0975557 + 0.163919i −0.00550539 + 0.00925049i
\(315\) 0.423881i 0.0238830i
\(316\) 5.46930 2.96741i 0.307672 0.166930i
\(317\) 19.1560 19.1560i 1.07591 1.07591i 0.0790380 0.996872i \(-0.474815\pi\)
0.996872 0.0790380i \(-0.0251848\pi\)
\(318\) 6.90866 + 4.11166i 0.387419 + 0.230570i
\(319\) −10.8307 + 10.8307i −0.606404 + 0.606404i
\(320\) 6.08803 5.18998i 0.340331 0.290129i
\(321\) 21.3106 1.18944
\(322\) 2.71078 + 10.6806i 0.151066 + 0.595205i
\(323\) −0.0188458 + 0.0188458i −0.00104861 + 0.00104861i
\(324\) 9.23690 + 17.0247i 0.513161 + 0.945817i
\(325\) 2.63961 2.45611i 0.146419 0.136240i
\(326\) 6.55890 + 25.8423i 0.363264 + 1.43128i
\(327\) 4.73766 + 4.73766i 0.261993 + 0.261993i
\(328\) 13.1328 12.1287i 0.725139 0.669693i
\(329\) 9.82730i 0.541796i
\(330\) 5.19620 8.73098i 0.286041 0.480625i
\(331\) 10.3712 + 10.3712i 0.570053 + 0.570053i 0.932143 0.362090i \(-0.117937\pi\)
−0.362090 + 0.932143i \(0.617937\pi\)
\(332\) 9.06123 30.5558i 0.497300 1.67697i
\(333\) 0.311442 + 0.311442i 0.0170669 + 0.0170669i
\(334\) −5.86954 23.1262i −0.321167 1.26541i
\(335\) 9.14736 0.499774
\(336\) −12.0157 + 2.54632i −0.655512 + 0.138913i
\(337\) 8.81143i 0.479989i −0.970774 0.239995i \(-0.922854\pi\)
0.970774 0.239995i \(-0.0771457\pi\)
\(338\) 15.0813 + 10.5145i 0.820316 + 0.571911i
\(339\) 5.94363i 0.322814i
\(340\) 0.0738864 0.249156i 0.00400705 0.0135124i
\(341\) −13.6792 −0.740769
\(342\) −0.0699558 + 0.0177551i −0.00378278 + 0.000960085i
\(343\) 13.3686 + 13.3686i 0.721839 + 0.721839i
\(344\) 21.5808 + 0.857859i 1.16356 + 0.0462527i
\(345\) −5.82929 5.82929i −0.313838 0.313838i
\(346\) −26.8733 15.9935i −1.44472 0.859818i
\(347\) 26.6526i 1.43078i 0.698723 + 0.715392i \(0.253752\pi\)
−0.698723 + 0.715392i \(0.746248\pi\)
\(348\) −12.1761 + 6.60626i −0.652709 + 0.354133i
\(349\) −1.40597 1.40597i −0.0752601 0.0752601i 0.668475 0.743735i \(-0.266947\pi\)
−0.743735 + 0.668475i \(0.766947\pi\)
\(350\) −2.33521 + 0.592687i −0.124822 + 0.0316804i
\(351\) −13.0895 + 12.1795i −0.698664 + 0.650094i
\(352\) 21.3455 + 7.26408i 1.13772 + 0.387177i
\(353\) 1.08177 1.08177i 0.0575770 0.0575770i −0.677732 0.735309i \(-0.737037\pi\)
0.735309 + 0.677732i \(0.237037\pi\)
\(354\) 33.7638 8.56939i 1.79452 0.455458i
\(355\) −9.08677 −0.482276
\(356\) −8.49639 + 28.6510i −0.450308 + 1.51850i
\(357\) −0.282136 + 0.282136i −0.0149322 + 0.0149322i
\(358\) 8.81675 14.8145i 0.465980 0.782968i
\(359\) −2.87994 + 2.87994i −0.151998 + 0.151998i −0.779010 0.627012i \(-0.784278\pi\)
0.627012 + 0.779010i \(0.284278\pi\)
\(360\) 0.517004 0.477472i 0.0272485 0.0251650i
\(361\) 18.9579i 0.997786i
\(362\) −10.8535 6.45940i −0.570446 0.339498i
\(363\) 8.80929 0.462368
\(364\) −5.46611 11.0017i −0.286502 0.576648i
\(365\) 16.4470 0.860877
\(366\) −12.9042 7.67985i −0.674511 0.401432i
\(367\) 14.7250i 0.768639i 0.923200 + 0.384319i \(0.125564\pi\)
−0.923200 + 0.384319i \(0.874436\pi\)
\(368\) 9.97349 15.3372i 0.519904 0.799508i
\(369\) 1.11200 1.11200i 0.0578883 0.0578883i
\(370\) −1.28030 + 2.15124i −0.0665596 + 0.111838i
\(371\) 3.79935 3.79935i 0.197253 0.197253i
\(372\) −11.8611 3.51736i −0.614967 0.182367i
\(373\) 5.16533 0.267450 0.133725 0.991018i \(-0.457306\pi\)
0.133725 + 0.991018i \(0.457306\pi\)
\(374\) 0.709952 0.180189i 0.0367107 0.00931735i
\(375\) 1.27452 1.27452i 0.0658161 0.0658161i
\(376\) 11.9863 11.0698i 0.618144 0.570879i
\(377\) −9.43828 10.1434i −0.486096 0.522414i
\(378\) 11.5800 2.93905i 0.595611 0.151169i
\(379\) −7.51825 7.51825i −0.386187 0.386187i 0.487138 0.873325i \(-0.338041\pi\)
−0.873325 + 0.487138i \(0.838041\pi\)
\(380\) −0.195630 0.360569i −0.0100356 0.0184968i
\(381\) 21.2221i 1.08724i
\(382\) 32.9912 + 19.6346i 1.68798 + 1.00459i
\(383\) 8.07375 + 8.07375i 0.412549 + 0.412549i 0.882626 0.470076i \(-0.155774\pi\)
−0.470076 + 0.882626i \(0.655774\pi\)
\(384\) 16.6406 + 11.7872i 0.849187 + 0.601514i
\(385\) −4.80152 4.80152i −0.244708 0.244708i
\(386\) 21.4981 5.45632i 1.09423 0.277719i
\(387\) 1.89995 0.0965801
\(388\) 26.0961 + 7.73872i 1.32483 + 0.392874i
\(389\) 18.5117i 0.938578i −0.883045 0.469289i \(-0.844510\pi\)
0.883045 0.469289i \(-0.155490\pi\)
\(390\) 7.72356 + 4.98154i 0.391098 + 0.252250i
\(391\) 0.594308i 0.0300554i
\(392\) 0.460359 11.5811i 0.0232516 0.584932i
\(393\) −14.3914 −0.725949
\(394\) −0.331773 1.30720i −0.0167145 0.0658557i
\(395\) 2.19996 + 2.19996i 0.110692 + 0.110692i
\(396\) 1.90165 + 0.563930i 0.0955617 + 0.0283385i
\(397\) −23.7739 23.7739i −1.19318 1.19318i −0.976170 0.217008i \(-0.930370\pi\)
−0.217008 0.976170i \(-0.569630\pi\)
\(398\) 13.1106 22.0293i 0.657176 1.10423i
\(399\) 0.629820i 0.0315305i
\(400\) 3.35334 + 2.18061i 0.167667 + 0.109031i
\(401\) 18.0427 + 18.0427i 0.901011 + 0.901011i 0.995524 0.0945126i \(-0.0301292\pi\)
−0.0945126 + 0.995524i \(0.530129\pi\)
\(402\) 5.73610 + 22.6005i 0.286091 + 1.12721i
\(403\) 0.445311 12.3658i 0.0221825 0.615987i
\(404\) −23.9346 + 12.9859i −1.19079 + 0.646075i
\(405\) −6.84800 + 6.84800i −0.340280 + 0.340280i
\(406\) 2.27757 + 8.97371i 0.113034 + 0.445358i
\(407\) −7.05572 −0.349739
\(408\) 0.661924 + 0.0263121i 0.0327701 + 0.00130265i
\(409\) 20.2935 20.2935i 1.00345 1.00345i 0.00345338 0.999994i \(-0.498901\pi\)
0.999994 0.00345338i \(-0.00109925\pi\)
\(410\) 7.68096 + 4.57129i 0.379336 + 0.225760i
\(411\) 25.2678 25.2678i 1.24637 1.24637i
\(412\) −9.53862 17.5808i −0.469934 0.866145i
\(413\) 23.2807i 1.14557i
\(414\) 0.823081 1.38299i 0.0404522 0.0679703i
\(415\) 15.9355 0.782243
\(416\) −7.26154 + 19.0596i −0.356026 + 0.934476i
\(417\) 21.3951 1.04772
\(418\) 0.591304 0.993545i 0.0289216 0.0485959i
\(419\) 9.76105i 0.476858i 0.971160 + 0.238429i \(0.0766325\pi\)
−0.971160 + 0.238429i \(0.923367\pi\)
\(420\) −2.92871 5.39797i −0.142907 0.263394i
\(421\) 15.5421 15.5421i 0.757477 0.757477i −0.218385 0.975863i \(-0.570079\pi\)
0.975863 + 0.218385i \(0.0700790\pi\)
\(422\) −20.6237 12.2741i −1.00395 0.597493i
\(423\) 1.01491 1.01491i 0.0493468 0.0493468i
\(424\) −8.91374 0.354330i −0.432889 0.0172078i
\(425\) 0.129940 0.00630302
\(426\) −5.69811 22.4508i −0.276074 1.08774i
\(427\) −7.09652 + 7.09652i −0.343425 + 0.343425i
\(428\) −20.7842 + 11.2767i −1.00464 + 0.545078i
\(429\) −0.932220 + 25.8869i −0.0450080 + 1.24983i
\(430\) 2.65659 + 10.4671i 0.128112 + 0.504767i
\(431\) −18.6396 18.6396i −0.897836 0.897836i 0.0974082 0.995245i \(-0.468945\pi\)
−0.995245 + 0.0974082i \(0.968945\pi\)
\(432\) −16.6288 10.8134i −0.800053 0.520259i
\(433\) 17.1797i 0.825602i −0.910821 0.412801i \(-0.864550\pi\)
0.910821 0.412801i \(-0.135450\pi\)
\(434\) −4.22861 + 7.10517i −0.202980 + 0.341059i
\(435\) −4.89771 4.89771i −0.234827 0.234827i
\(436\) −7.12761 2.11367i −0.341351 0.101227i
\(437\) −0.663346 0.663346i −0.0317322 0.0317322i
\(438\) 10.3136 + 40.6359i 0.492801 + 1.94166i
\(439\) −15.3214 −0.731251 −0.365626 0.930762i \(-0.619145\pi\)
−0.365626 + 0.930762i \(0.619145\pi\)
\(440\) −0.447793 + 11.2649i −0.0213477 + 0.537035i
\(441\) 1.01958i 0.0485517i
\(442\) 0.139777 + 0.647656i 0.00664853 + 0.0308058i
\(443\) 28.2978i 1.34447i −0.740339 0.672233i \(-0.765335\pi\)
0.740339 0.672233i \(-0.234665\pi\)
\(444\) −6.11793 1.81426i −0.290344 0.0861008i
\(445\) −14.9421 −0.708326
\(446\) −29.1011 + 7.38598i −1.37798 + 0.349736i
\(447\) 3.51503 + 3.51503i 0.166255 + 0.166255i
\(448\) 10.3715 8.84164i 0.490010 0.417728i
\(449\) −17.5795 17.5795i −0.829629 0.829629i 0.157836 0.987465i \(-0.449548\pi\)
−0.987465 + 0.157836i \(0.949548\pi\)
\(450\) 0.302379 + 0.179959i 0.0142543 + 0.00848336i
\(451\) 25.1923i 1.18626i
\(452\) −3.14512 5.79682i −0.147934 0.272660i
\(453\) −11.3839 11.3839i −0.534860 0.534860i
\(454\) −7.69321 + 1.95257i −0.361060 + 0.0916387i
\(455\) 4.49683 4.18422i 0.210815 0.196159i
\(456\) 0.768186 0.709448i 0.0359736 0.0332230i
\(457\) 6.18802 6.18802i 0.289463 0.289463i −0.547405 0.836868i \(-0.684384\pi\)
0.836868 + 0.547405i \(0.184384\pi\)
\(458\) 36.6573 9.30378i 1.71288 0.434737i
\(459\) −0.644356 −0.0300759
\(460\) 8.76992 + 2.60070i 0.408900 + 0.121258i
\(461\) −5.70215 + 5.70215i −0.265576 + 0.265576i −0.827315 0.561739i \(-0.810133\pi\)
0.561739 + 0.827315i \(0.310133\pi\)
\(462\) 8.85223 14.8741i 0.411843 0.692005i
\(463\) −12.6056 + 12.6056i −0.585831 + 0.585831i −0.936500 0.350668i \(-0.885954\pi\)
0.350668 + 0.936500i \(0.385954\pi\)
\(464\) 8.37963 12.8862i 0.389014 0.598226i
\(465\) 6.18580i 0.286860i
\(466\) −1.66686 0.992022i −0.0772157 0.0459545i
\(467\) 2.92501 0.135353 0.0676766 0.997707i \(-0.478441\pi\)
0.0676766 + 0.997707i \(0.478441\pi\)
\(468\) −0.571693 + 1.70072i −0.0264265 + 0.0786157i
\(469\) 15.5834 0.719576
\(470\) 7.01037 + 4.17219i 0.323364 + 0.192449i
\(471\) 0.243119i 0.0112023i
\(472\) −28.3953 + 26.2241i −1.30700 + 1.20706i
\(473\) −21.5217 + 21.5217i −0.989570 + 0.989570i
\(474\) −4.05593 + 6.81502i −0.186295 + 0.313024i
\(475\) 0.145035 0.145035i 0.00665465 0.00665465i
\(476\) 0.125873 0.424461i 0.00576937 0.0194551i
\(477\) −0.784757 −0.0359315
\(478\) −27.5070 + 6.98140i −1.25814 + 0.319322i
\(479\) 16.7931 16.7931i 0.767298 0.767298i −0.210332 0.977630i \(-0.567454\pi\)
0.977630 + 0.210332i \(0.0674545\pi\)
\(480\) −3.28486 + 9.65255i −0.149933 + 0.440577i
\(481\) 0.229691 6.37830i 0.0104730 0.290825i
\(482\) 6.33125 1.60690i 0.288381 0.0731922i
\(483\) −9.93077 9.93077i −0.451866 0.451866i
\(484\) −8.59170 + 4.66150i −0.390532 + 0.211886i
\(485\) 13.6097i 0.617984i
\(486\) −3.13452 1.86549i −0.142185 0.0846206i
\(487\) −1.21797 1.21797i −0.0551916 0.0551916i 0.678972 0.734164i \(-0.262426\pi\)
−0.734164 + 0.678972i \(0.762426\pi\)
\(488\) 16.6493 + 0.661826i 0.753677 + 0.0299594i
\(489\) −24.0281 24.0281i −1.08659 1.08659i
\(490\) 5.61701 1.42562i 0.253751 0.0644030i
\(491\) 1.56917 0.0708155 0.0354077 0.999373i \(-0.488727\pi\)
0.0354077 + 0.999373i \(0.488727\pi\)
\(492\) −6.47777 + 21.8440i −0.292040 + 0.984802i
\(493\) 0.499332i 0.0224888i
\(494\) 0.878906 + 0.566876i 0.0395438 + 0.0255050i
\(495\) 0.991754i 0.0445760i
\(496\) 13.4293 2.84588i 0.602995 0.127784i
\(497\) −15.4802 −0.694382
\(498\) 9.99279 + 39.3720i 0.447788 + 1.76430i
\(499\) 24.2108 + 24.2108i 1.08383 + 1.08383i 0.996149 + 0.0876770i \(0.0279443\pi\)
0.0876770 + 0.996149i \(0.472056\pi\)
\(500\) −0.568619 + 1.91747i −0.0254294 + 0.0857516i
\(501\) 21.5027 + 21.5027i 0.960670 + 0.960670i
\(502\) 8.01084 13.4603i 0.357541 0.600763i
\(503\) 29.3584i 1.30902i −0.756052 0.654512i \(-0.772874\pi\)
0.756052 0.654512i \(-0.227126\pi\)
\(504\) 0.880767 0.813421i 0.0392325 0.0362327i
\(505\) −9.62744 9.62744i −0.428416 0.428416i
\(506\) 6.34239 + 24.9893i 0.281954 + 1.11091i
\(507\) −23.3711 1.68544i −1.03795 0.0748528i
\(508\) 11.2298 + 20.6979i 0.498243 + 0.918321i
\(509\) −26.9394 + 26.9394i −1.19407 + 1.19407i −0.218152 + 0.975915i \(0.570003\pi\)
−0.975915 + 0.218152i \(0.929997\pi\)
\(510\) 0.0814825 + 0.321044i 0.00360810 + 0.0142161i
\(511\) 28.0191 1.23949
\(512\) −22.4669 2.69059i −0.992905 0.118908i
\(513\) −0.719208 + 0.719208i −0.0317538 + 0.0317538i
\(514\) 5.24438 + 3.12117i 0.231320 + 0.137669i
\(515\) 7.07169 7.07169i 0.311616 0.311616i
\(516\) −24.1952 + 13.1273i −1.06513 + 0.577897i
\(517\) 22.9929i 1.01123i
\(518\) −2.18112 + 3.66485i −0.0958327 + 0.161024i
\(519\) 39.8575 1.74955
\(520\) −10.1688 0.771518i −0.445932 0.0338333i
\(521\) 6.81322 0.298493 0.149246 0.988800i \(-0.452315\pi\)
0.149246 + 0.988800i \(0.452315\pi\)
\(522\) 0.691544 1.16198i 0.0302681 0.0508583i
\(523\) 15.8116i 0.691395i 0.938346 + 0.345697i \(0.112358\pi\)
−0.938346 + 0.345697i \(0.887642\pi\)
\(524\) 14.0359 7.61531i 0.613162 0.332676i
\(525\) 2.17127 2.17127i 0.0947622 0.0947622i
\(526\) 6.70516 + 3.99054i 0.292359 + 0.173996i
\(527\) 0.315328 0.315328i 0.0137359 0.0137359i
\(528\) −28.1132 + 5.95761i −1.22347 + 0.259272i
\(529\) −2.08122 −0.0904876
\(530\) −1.09728 4.32331i −0.0476626 0.187793i
\(531\) −2.40432 + 2.40432i −0.104338 + 0.104338i
\(532\) −0.333274 0.614264i −0.0144493 0.0266317i
\(533\) −22.7736 0.820108i −0.986434 0.0355228i
\(534\) −9.36987 36.9177i −0.405474 1.59759i
\(535\) −8.36023 8.36023i −0.361444 0.361444i
\(536\) −17.5536 19.0069i −0.758201 0.820975i
\(537\) 21.9722i 0.948172i
\(538\) 2.92135 4.90864i 0.125948 0.211626i
\(539\) 11.5493 + 11.5493i 0.497466 + 0.497466i
\(540\) 2.81970 9.50845i 0.121341 0.409179i
\(541\) 3.68712 + 3.68712i 0.158522 + 0.158522i 0.781911 0.623390i \(-0.214245\pi\)
−0.623390 + 0.781911i \(0.714245\pi\)
\(542\) −3.50111 13.7945i −0.150386 0.592526i
\(543\) 16.0975 0.690809
\(544\) −0.659498 + 0.324600i −0.0282757 + 0.0139171i
\(545\) 3.71720i 0.159228i
\(546\) 13.1578 + 8.48654i 0.563104 + 0.363191i
\(547\) 34.5492i 1.47722i −0.674135 0.738608i \(-0.735483\pi\)
0.674135 0.738608i \(-0.264517\pi\)
\(548\) −11.2730 + 38.0143i −0.481560 + 1.62389i
\(549\) 1.46579 0.0625582
\(550\) −5.46368 + 1.38671i −0.232972 + 0.0591294i
\(551\) −0.557337 0.557337i −0.0237434 0.0237434i
\(552\) −0.926150 + 23.2988i −0.0394195 + 0.991661i
\(553\) 3.74785 + 3.74785i 0.159375 + 0.159375i
\(554\) 4.71008 + 2.80318i 0.200112 + 0.119096i
\(555\) 3.19064i 0.135435i
\(556\) −20.8666 + 11.3214i −0.884943 + 0.480133i
\(557\) 3.70923 + 3.70923i 0.157165 + 0.157165i 0.781309 0.624144i \(-0.214552\pi\)
−0.624144 + 0.781309i \(0.714552\pi\)
\(558\) 1.17050 0.297077i 0.0495511 0.0125763i
\(559\) −18.7548 20.1560i −0.793244 0.852510i
\(560\) 5.71275 + 3.71489i 0.241408 + 0.156983i
\(561\) −0.660112 + 0.660112i −0.0278699 + 0.0278699i
\(562\) 21.4330 5.43978i 0.904095 0.229463i
\(563\) −32.6926 −1.37783 −0.688914 0.724843i \(-0.741912\pi\)
−0.688914 + 0.724843i \(0.741912\pi\)
\(564\) −5.91222 + 19.9369i −0.248950 + 0.839494i
\(565\) 2.33171 2.33171i 0.0980957 0.0980957i
\(566\) −5.45156 + 9.16006i −0.229146 + 0.385026i
\(567\) −11.6662 + 11.6662i −0.489936 + 0.489936i
\(568\) 17.4374 + 18.8811i 0.731655 + 0.792231i
\(569\) 23.3490i 0.978840i −0.872048 0.489420i \(-0.837208\pi\)
0.872048 0.489420i \(-0.162792\pi\)
\(570\) 0.449287 + 0.267391i 0.0188186 + 0.0111998i
\(571\) −0.790107 −0.0330649 −0.0165325 0.999863i \(-0.505263\pi\)
−0.0165325 + 0.999863i \(0.505263\pi\)
\(572\) −12.7890 25.7407i −0.534736 1.07627i
\(573\) −48.9313 −2.04414
\(574\) 13.0853 + 7.78763i 0.546168 + 0.325050i
\(575\) 4.57371i 0.190737i
\(576\) −1.98424 0.158001i −0.0826768 0.00658338i
\(577\) 18.5877 18.5877i 0.773815 0.773815i −0.204956 0.978771i \(-0.565705\pi\)
0.978771 + 0.204956i \(0.0657051\pi\)
\(578\) 12.2833 20.6391i 0.510917 0.858474i
\(579\) −19.9889 + 19.9889i −0.830711 + 0.830711i
\(580\) 7.36840 + 2.18508i 0.305956 + 0.0907305i
\(581\) 27.1477 1.12628
\(582\) −33.6256 + 8.53431i −1.39382 + 0.353759i
\(583\) 8.88933 8.88933i 0.368158 0.368158i
\(584\) −31.5616 34.1747i −1.30603 1.41416i
\(585\) −0.896536 0.0322854i −0.0370672 0.00133484i
\(586\) −16.6833 + 4.23429i −0.689180 + 0.174917i
\(587\) 22.8998 + 22.8998i 0.945178 + 0.945178i 0.998573 0.0533956i \(-0.0170044\pi\)
−0.0533956 + 0.998573i \(0.517004\pi\)
\(588\) 7.04459 + 12.9840i 0.290514 + 0.535452i
\(589\) 0.703916i 0.0290043i
\(590\) −16.6075 9.88385i −0.683718 0.406912i
\(591\) 1.21543 + 1.21543i 0.0499961 + 0.0499961i
\(592\) 6.92685 1.46791i 0.284692 0.0603305i
\(593\) 9.11235 + 9.11235i 0.374199 + 0.374199i 0.869004 0.494805i \(-0.164760\pi\)
−0.494805 + 0.869004i \(0.664760\pi\)
\(594\) 27.0937 6.87649i 1.11167 0.282146i
\(595\) 0.221366 0.00907511
\(596\) −5.28821 1.56820i −0.216614 0.0642361i
\(597\) 32.6730i 1.33722i
\(598\) −22.7965 + 4.91996i −0.932220 + 0.201192i
\(599\) 14.7206i 0.601467i −0.953708 0.300733i \(-0.902769\pi\)
0.953708 0.300733i \(-0.0972314\pi\)
\(600\) −5.09407 0.202494i −0.207964 0.00826680i
\(601\) 12.8224 0.523037 0.261519 0.965198i \(-0.415777\pi\)
0.261519 + 0.965198i \(0.415777\pi\)
\(602\) 4.52575 + 17.8317i 0.184456 + 0.726764i
\(603\) −1.60938 1.60938i −0.0655390 0.0655390i
\(604\) 17.1265 + 5.07883i 0.696869 + 0.206654i
\(605\) −3.45592 3.45592i −0.140503 0.140503i
\(606\) 17.7495 29.8238i 0.721023 1.21151i
\(607\) 19.7681i 0.802362i −0.915999 0.401181i \(-0.868600\pi\)
0.915999 0.401181i \(-0.131400\pi\)
\(608\) −0.373802 + 1.09842i −0.0151597 + 0.0445467i
\(609\) −8.34373 8.34373i −0.338105 0.338105i
\(610\) 2.04952 + 8.07518i 0.0829825 + 0.326955i
\(611\) −20.7853 0.748508i −0.840885 0.0302814i
\(612\) −0.0568357 + 0.0308367i −0.00229745 + 0.00124650i
\(613\) 17.7152 17.7152i 0.715509 0.715509i −0.252173 0.967682i \(-0.581145\pi\)
0.967682 + 0.252173i \(0.0811452\pi\)
\(614\) 0.698894 + 2.75367i 0.0282051 + 0.111129i
\(615\) −11.3921 −0.459374
\(616\) −0.762858 + 19.1909i −0.0307364 + 0.773224i
\(617\) −18.7927 + 18.7927i −0.756566 + 0.756566i −0.975696 0.219130i \(-0.929678\pi\)
0.219130 + 0.975696i \(0.429678\pi\)
\(618\) 21.9066 + 13.0376i 0.881212 + 0.524449i
\(619\) 9.62828 9.62828i 0.386993 0.386993i −0.486620 0.873614i \(-0.661770\pi\)
0.873614 + 0.486620i \(0.161770\pi\)
\(620\) 3.27326 + 6.03301i 0.131457 + 0.242292i
\(621\) 22.6804i 0.910133i
\(622\) −14.9531 + 25.1252i −0.599566 + 1.00743i
\(623\) −25.4554 −1.01985
\(624\) −4.47043 25.6080i −0.178960 1.02514i
\(625\) −1.00000 −0.0400000
\(626\) −18.0476 + 30.3247i −0.721327 + 1.21202i
\(627\) 1.47359i 0.0588494i
\(628\) 0.128648 + 0.237114i 0.00513361 + 0.00946186i
\(629\) 0.162646 0.162646i 0.00648512 0.00648512i
\(630\) 0.515132 + 0.306578i 0.0205233 + 0.0122144i
\(631\) 0.441905 0.441905i 0.0175920 0.0175920i −0.698256 0.715848i \(-0.746040\pi\)
0.715848 + 0.698256i \(0.246040\pi\)
\(632\) 0.349527 8.79291i 0.0139034 0.349763i
\(633\) 30.5883 1.21577
\(634\) −9.42494 37.1347i −0.374312 1.47481i
\(635\) −8.32551 + 8.32551i −0.330388 + 0.330388i
\(636\) 9.99358 5.42210i 0.396271 0.215000i
\(637\) −10.8165 + 10.0645i −0.428564 + 0.398771i
\(638\) 5.32881 + 20.9958i 0.210970 + 0.831230i
\(639\) 1.59872 + 1.59872i 0.0632443 + 0.0632443i
\(640\) −1.90400 11.1523i −0.0752621 0.440835i
\(641\) 38.3959i 1.51655i 0.651936 + 0.758274i \(0.273957\pi\)
−0.651936 + 0.758274i \(0.726043\pi\)
\(642\) 15.4132 25.8982i 0.608310 1.02212i
\(643\) 27.0409 + 27.0409i 1.06639 + 1.06639i 0.997633 + 0.0687573i \(0.0219034\pi\)
0.0687573 + 0.997633i \(0.478097\pi\)
\(644\) 14.9404 + 4.43054i 0.588735 + 0.174588i
\(645\) −9.73225 9.73225i −0.383207 0.383207i
\(646\) 0.00927233 + 0.0365334i 0.000364815 + 0.00143739i
\(647\) −17.6171 −0.692600 −0.346300 0.938124i \(-0.612562\pi\)
−0.346300 + 0.938124i \(0.612562\pi\)
\(648\) 27.3704 + 1.08800i 1.07521 + 0.0427407i
\(649\) 54.4698i 2.13813i
\(650\) −1.07571 4.98426i −0.0421926 0.195499i
\(651\) 10.5381i 0.413021i
\(652\) 36.1493 + 10.7200i 1.41572 + 0.419827i
\(653\) −35.9748 −1.40780 −0.703902 0.710297i \(-0.748560\pi\)
−0.703902 + 0.710297i \(0.748560\pi\)
\(654\) 9.18413 2.33097i 0.359128 0.0911483i
\(655\) 5.64580 + 5.64580i 0.220599 + 0.220599i
\(656\) −5.24113 24.7322i −0.204632 0.965630i
\(657\) −2.89368 2.89368i −0.112893 0.112893i
\(658\) 11.9429 + 7.10773i 0.465581 + 0.277088i
\(659\) 0.973268i 0.0379131i −0.999820 0.0189566i \(-0.993966\pi\)
0.999820 0.0189566i \(-0.00603442\pi\)
\(660\) −6.85230 12.6296i −0.266725 0.491607i
\(661\) 14.7847 + 14.7847i 0.575059 + 0.575059i 0.933538 0.358479i \(-0.116705\pi\)
−0.358479 + 0.933538i \(0.616705\pi\)
\(662\) 20.1050 5.10273i 0.781402 0.198323i
\(663\) −0.575245 0.618224i −0.0223407 0.0240098i
\(664\) −30.5800 33.1118i −1.18673 1.28499i
\(665\) 0.247081 0.247081i 0.00958139 0.00958139i
\(666\) 0.603742 0.153232i 0.0233945 0.00593763i
\(667\) 17.5758 0.680536
\(668\) −32.3499 9.59327i −1.25166 0.371175i
\(669\) 27.0581 27.0581i 1.04613 1.04613i
\(670\) 6.61596 11.1165i 0.255597 0.429470i
\(671\) −16.6037 + 16.6037i −0.640978 + 0.640978i
\(672\) −5.59608 + 16.4441i −0.215873 + 0.634344i
\(673\) 1.67990i 0.0647555i 0.999476 + 0.0323777i \(0.0103080\pi\)
−0.999476 + 0.0323777i \(0.989692\pi\)
\(674\) −10.7083 6.37299i −0.412468 0.245478i
\(675\) 4.95886 0.190867
\(676\) 23.6857 10.7232i 0.910989 0.412431i
\(677\) 42.4579 1.63179 0.815896 0.578199i \(-0.196244\pi\)
0.815896 + 0.578199i \(0.196244\pi\)
\(678\) 7.22314 + 4.29881i 0.277403 + 0.165095i
\(679\) 23.1854i 0.889775i
\(680\) −0.249353 0.269998i −0.00956225 0.0103539i
\(681\) 7.15313 7.15313i 0.274109 0.274109i
\(682\) −9.89366 + 16.6239i −0.378848 + 0.636564i
\(683\) −24.8104 + 24.8104i −0.949345 + 0.949345i −0.998777 0.0494324i \(-0.984259\pi\)
0.0494324 + 0.998777i \(0.484259\pi\)
\(684\) −0.0290192 + 0.0978570i −0.00110958 + 0.00374166i
\(685\) −19.8253 −0.757485
\(686\) 25.9156 6.57749i 0.989462 0.251130i
\(687\) −34.0838 + 34.0838i −1.30038 + 1.30038i
\(688\) 16.6512 25.6061i 0.634819 0.976224i
\(689\) 7.74649 + 8.32525i 0.295118 + 0.317167i
\(690\) −11.3003 + 2.86807i −0.430195 + 0.109185i
\(691\) 21.9436 + 21.9436i 0.834774 + 0.834774i 0.988165 0.153392i \(-0.0490196\pi\)
−0.153392 + 0.988165i \(0.549020\pi\)
\(692\) −38.8730 + 21.0909i −1.47773 + 0.801755i
\(693\) 1.68955i 0.0641807i
\(694\) 32.3901 + 19.2768i 1.22951 + 0.731739i
\(695\) −8.39338 8.39338i −0.318379 0.318379i
\(696\) −0.778142 + 19.5754i −0.0294954 + 0.742003i
\(697\) −0.580724 0.580724i −0.0219965 0.0219965i
\(698\) −2.72553 + 0.691752i −0.103163 + 0.0261832i
\(699\) 2.47222 0.0935079
\(700\) −0.968698 + 3.26659i −0.0366133 + 0.123465i
\(701\) 46.8970i 1.77128i 0.464377 + 0.885638i \(0.346278\pi\)
−0.464377 + 0.885638i \(0.653722\pi\)
\(702\) 5.33428 + 24.7163i 0.201329 + 0.932856i
\(703\) 0.363080i 0.0136938i
\(704\) 24.2663 20.6868i 0.914569 0.779662i
\(705\) −10.3975 −0.391593
\(706\) −0.532243 2.09706i −0.0200312 0.0789238i
\(707\) −16.4013 16.4013i −0.616834 0.616834i
\(708\) 14.0060 47.2301i 0.526377 1.77502i
\(709\) 32.2745 + 32.2745i 1.21209 + 1.21209i 0.970337 + 0.241755i \(0.0777231\pi\)
0.241755 + 0.970337i \(0.422277\pi\)
\(710\) −6.57214 + 11.0429i −0.246648 + 0.414433i
\(711\) 0.774120i 0.0290318i
\(712\) 28.6737 + 31.0477i 1.07459 + 1.16356i
\(713\) 11.0991 + 11.0991i 0.415664 + 0.415664i
\(714\) 0.138813 + 0.546930i 0.00519496 + 0.0204684i
\(715\) 10.5212 9.78980i 0.393471 0.366118i
\(716\) −11.6268 21.4295i −0.434513 0.800859i
\(717\) 25.5760 25.5760i 0.955152 0.955152i
\(718\) 1.41696 + 5.58288i 0.0528805 + 0.208351i
\(719\) 13.4055 0.499939 0.249970 0.968254i \(-0.419579\pi\)
0.249970 + 0.968254i \(0.419579\pi\)
\(720\) −0.206329 0.973640i −0.00768943 0.0362854i
\(721\) 12.0473 12.0473i 0.448666 0.448666i
\(722\) −23.0391 13.7116i −0.857425 0.510293i
\(723\) −5.88678 + 5.88678i −0.218932 + 0.218932i
\(724\) −15.6999 + 8.51810i −0.583481 + 0.316573i
\(725\) 3.84278i 0.142717i
\(726\) 6.37144 10.7057i 0.236466 0.397325i
\(727\) −15.7815 −0.585305 −0.292653 0.956219i \(-0.594538\pi\)
−0.292653 + 0.956219i \(0.594538\pi\)
\(728\) −17.3236 1.31436i −0.642054 0.0487133i
\(729\) −24.4046 −0.903874
\(730\) 11.8956 19.9876i 0.440274 0.739776i
\(731\) 0.992222i 0.0366987i
\(732\) −18.6662 + 10.1275i −0.689924 + 0.374324i
\(733\) −7.78597 + 7.78597i −0.287582 + 0.287582i −0.836123 0.548542i \(-0.815183\pi\)
0.548542 + 0.836123i \(0.315183\pi\)
\(734\) 17.8949 + 10.6501i 0.660513 + 0.393101i
\(735\) −5.22268 + 5.22268i −0.192641 + 0.192641i
\(736\) −11.4254 23.2134i −0.421147 0.855656i
\(737\) 36.4605 1.34304
\(738\) −0.547113 2.15565i −0.0201395 0.0793505i
\(739\) 32.4954 32.4954i 1.19536 1.19536i 0.219823 0.975540i \(-0.429452\pi\)
0.975540 0.219823i \(-0.0705481\pi\)
\(740\) 1.68835 + 3.11183i 0.0620649 + 0.114393i
\(741\) −1.33211 0.0479710i −0.0489363 0.00176226i
\(742\) −1.86932 7.36519i −0.0686248 0.270385i
\(743\) 11.9167 + 11.9167i 0.437183 + 0.437183i 0.891063 0.453880i \(-0.149961\pi\)
−0.453880 + 0.891063i \(0.649961\pi\)
\(744\) −12.8532 + 11.8704i −0.471223 + 0.435192i
\(745\) 2.75792i 0.101042i
\(746\) 3.73589 6.27728i 0.136781 0.229828i
\(747\) −2.80368 2.80368i −0.102581 0.102581i
\(748\) 0.294504 0.993110i 0.0107681 0.0363117i
\(749\) −14.2425 14.2425i −0.520409 0.520409i
\(750\) −0.627077 2.47071i −0.0228976 0.0902176i
\(751\) −26.1761 −0.955181 −0.477591 0.878582i \(-0.658490\pi\)
−0.477591 + 0.878582i \(0.658490\pi\)
\(752\) −4.78355 22.5729i −0.174438 0.823150i
\(753\) 19.9638i 0.727522i
\(754\) −19.1534 + 4.13370i −0.697527 + 0.150541i
\(755\) 8.93186i 0.325064i
\(756\) 4.80364 16.1986i 0.174707 0.589136i
\(757\) −22.1030 −0.803347 −0.401673 0.915783i \(-0.631571\pi\)
−0.401673 + 0.915783i \(0.631571\pi\)
\(758\) −14.5744 + 3.69905i −0.529367 + 0.134356i
\(759\) −23.2350 23.2350i −0.843376 0.843376i
\(760\) −0.579681 0.0230429i −0.0210272 0.000835855i
\(761\) 9.16654 + 9.16654i 0.332287 + 0.332287i 0.853454 0.521168i \(-0.174503\pi\)
−0.521168 + 0.853454i \(0.674503\pi\)
\(762\) −25.7906 15.3492i −0.934297 0.556042i
\(763\) 6.33262i 0.229256i
\(764\) 47.7227 25.8924i 1.72655 0.936753i
\(765\) −0.0228616 0.0228616i −0.000826561 0.000826561i
\(766\) 15.6513 3.97236i 0.565503 0.143527i
\(767\) 49.2402 + 1.77320i 1.77796 + 0.0640267i
\(768\) 26.3603 11.6976i 0.951194 0.422101i
\(769\) 5.20162 5.20162i 0.187575 0.187575i −0.607072 0.794647i \(-0.707656\pi\)
0.794647 + 0.607072i \(0.207656\pi\)
\(770\) −9.30792 + 2.36239i −0.335434 + 0.0851347i
\(771\) −7.77826 −0.280127
\(772\) 8.91790 30.0725i 0.320962 1.08233i
\(773\) −7.88292 + 7.88292i −0.283529 + 0.283529i −0.834515 0.550986i \(-0.814252\pi\)
0.550986 + 0.834515i \(0.314252\pi\)
\(774\) 1.37417 2.30896i 0.0493934 0.0829939i
\(775\) −2.42671 + 2.42671i −0.0871701 + 0.0871701i
\(776\) 28.2790 26.1167i 1.01516 0.937536i
\(777\) 5.43556i 0.195000i
\(778\) −22.4967 13.3888i −0.806546 0.480012i
\(779\) −1.29637 −0.0464472
\(780\) 11.6401 5.78327i 0.416783 0.207074i
\(781\) −36.2190 −1.29602
\(782\) −0.722247 0.429842i −0.0258275 0.0153711i
\(783\) 19.0558i 0.681000i
\(784\) −13.7412 8.93562i −0.490757 0.319129i
\(785\) −0.0953763 + 0.0953763i −0.00340413 + 0.00340413i
\(786\) −10.4088 + 17.4895i −0.371269 + 0.623829i
\(787\) 34.6472 34.6472i 1.23504 1.23504i 0.273034 0.962004i \(-0.411973\pi\)
0.962004 0.273034i \(-0.0880272\pi\)
\(788\) −1.82856 0.542255i −0.0651398 0.0193170i
\(789\) −9.94484 −0.354046
\(790\) 4.26471 1.08240i 0.151732 0.0385102i
\(791\) 3.97229 3.97229i 0.141238 0.141238i
\(792\) 2.06073 1.90316i 0.0732247 0.0676258i
\(793\) −14.4691 15.5501i −0.513812 0.552200i
\(794\) −46.0866 + 11.6970i −1.63555 + 0.415110i
\(795\) 4.01981 + 4.01981i 0.142568 + 0.142568i
\(796\) −17.2892 31.8660i −0.612798 1.12946i
\(797\) 43.1803i 1.52952i 0.644313 + 0.764762i \(0.277143\pi\)
−0.644313 + 0.764762i \(0.722857\pi\)
\(798\) 0.765404 + 0.455526i 0.0270950 + 0.0161255i
\(799\) −0.530024 0.530024i −0.0187509 0.0187509i
\(800\) 5.07540 2.49807i 0.179442 0.0883201i
\(801\) 2.62891 + 2.62891i 0.0928879 + 0.0928879i
\(802\) 34.9765 8.87719i 1.23506 0.313465i
\(803\) 65.5563 2.31343
\(804\) 31.6145 + 9.37518i 1.11496 + 0.330637i
\(805\) 7.79175i 0.274623i
\(806\) −14.7058 9.48495i −0.517990 0.334093i
\(807\) 7.28031i 0.256279i
\(808\) −1.52959 + 38.4794i −0.0538109 + 1.35370i
\(809\) 1.93088 0.0678860 0.0339430 0.999424i \(-0.489194\pi\)
0.0339430 + 0.999424i \(0.489194\pi\)
\(810\) 3.36928 + 13.2751i 0.118384 + 0.466440i
\(811\) 1.00517 + 1.00517i 0.0352961 + 0.0352961i 0.724535 0.689238i \(-0.242055\pi\)
−0.689238 + 0.724535i \(0.742055\pi\)
\(812\) 12.5528 + 3.72250i 0.440517 + 0.130634i
\(813\) 12.8261 + 12.8261i 0.449832 + 0.449832i
\(814\) −5.10315 + 8.57462i −0.178865 + 0.300540i
\(815\) 18.8527i 0.660380i
\(816\) 0.510722 0.785388i 0.0178789 0.0274941i
\(817\) −1.10748 1.10748i −0.0387460 0.0387460i
\(818\) −9.98457 39.3396i −0.349102 1.37548i
\(819\) −1.52734 0.0550014i −0.0533694 0.00192190i
\(820\) 11.1107 6.02822i 0.388003 0.210515i
\(821\) 21.8955 21.8955i 0.764157 0.764157i −0.212914 0.977071i \(-0.568295\pi\)
0.977071 + 0.212914i \(0.0682954\pi\)
\(822\) −12.4320 48.9825i −0.433615 1.70846i
\(823\) −48.9301 −1.70560 −0.852798 0.522241i \(-0.825096\pi\)
−0.852798 + 0.522241i \(0.825096\pi\)
\(824\) −28.2644 1.12354i −0.984639 0.0391404i
\(825\) 5.08012 5.08012i 0.176867 0.176867i
\(826\) −28.2924 16.8381i −0.984420 0.585873i
\(827\) 15.7484 15.7484i 0.547626 0.547626i −0.378128 0.925753i \(-0.623432\pi\)
0.925753 + 0.378128i \(0.123432\pi\)
\(828\) −1.08541 2.00054i −0.0377205 0.0695234i
\(829\) 46.9223i 1.62968i 0.579686 + 0.814840i \(0.303175\pi\)
−0.579686 + 0.814840i \(0.696825\pi\)
\(830\) 11.5256 19.3660i 0.400059 0.672204i
\(831\) −6.98581 −0.242335
\(832\) 17.9107 + 22.6099i 0.620941 + 0.783858i
\(833\) −0.532463 −0.0184487
\(834\) 15.4743 26.0009i 0.535832 0.900338i
\(835\) 16.8712i 0.583851i
\(836\) −0.779760 1.43719i −0.0269686 0.0497063i
\(837\) 12.0337 12.0337i 0.415947 0.415947i
\(838\) 11.8623 + 7.05982i 0.409778 + 0.243877i
\(839\) 0.862157 0.862157i 0.0297650 0.0297650i −0.692068 0.721833i \(-0.743300\pi\)
0.721833 + 0.692068i \(0.243300\pi\)
\(840\) −8.67824 0.344969i −0.299428 0.0119026i
\(841\) −14.2330 −0.490794
\(842\) −7.64687 30.1290i −0.263529 1.03831i
\(843\) −19.9283 + 19.9283i −0.686367 + 0.686367i
\(844\) −29.8328 + 16.1860i −1.02689 + 0.557146i
\(845\) 8.50737 + 9.82978i 0.292663 + 0.338155i
\(846\) −0.499347 1.96745i −0.0171679 0.0676423i
\(847\) −5.88749 5.88749i −0.202297 0.202297i
\(848\) −6.87759 + 10.5764i −0.236177 + 0.363193i
\(849\) 13.5858i 0.466265i
\(850\) 0.0939810 0.157913i 0.00322352 0.00541636i
\(851\) 5.72490 + 5.72490i 0.196247 + 0.196247i
\(852\) −31.4051 9.31309i −1.07592 0.319061i
\(853\) 19.3938 + 19.3938i 0.664031 + 0.664031i 0.956328 0.292296i \(-0.0944194\pi\)
−0.292296 + 0.956328i \(0.594419\pi\)
\(854\) 3.49155 + 13.7569i 0.119478 + 0.470750i
\(855\) −0.0510346 −0.00174535
\(856\) −1.32826 + 33.4145i −0.0453991 + 1.14209i
\(857\) 4.80900i 0.164272i −0.996621 0.0821362i \(-0.973826\pi\)
0.996621 0.0821362i \(-0.0261742\pi\)
\(858\) 30.7854 + 19.8559i 1.05099 + 0.677870i
\(859\) 5.64419i 0.192577i −0.995353 0.0962887i \(-0.969303\pi\)
0.995353 0.0962887i \(-0.0306972\pi\)
\(860\) 14.6418 + 4.34197i 0.499280 + 0.148060i
\(861\) −19.4076 −0.661408
\(862\) −36.1335 + 9.17084i −1.23071 + 0.312360i
\(863\) −2.84941 2.84941i −0.0969951 0.0969951i 0.656944 0.753939i \(-0.271849\pi\)
−0.753939 + 0.656944i \(0.771849\pi\)
\(864\) −25.1682 + 12.3876i −0.856240 + 0.421435i
\(865\) −15.6362 15.6362i −0.531648 0.531648i
\(866\) −20.8780 12.4254i −0.709463 0.422233i
\(867\) 30.6112i 1.03961i
\(868\) 5.57632 + 10.2778i 0.189273 + 0.348852i
\(869\) 8.76884 + 8.76884i 0.297463 + 0.297463i
\(870\) −9.49440 + 2.40972i −0.321890 + 0.0816972i
\(871\) −1.18693 + 32.9599i −0.0402176 + 1.11680i
\(872\) −7.72384 + 7.13325i −0.261562 + 0.241562i
\(873\) 2.39447 2.39447i 0.0810407 0.0810407i
\(874\) −1.28592 + 0.326373i −0.0434970 + 0.0110397i
\(875\) −1.70360 −0.0575921
\(876\) 56.8431 + 16.8567i 1.92055 + 0.569534i
\(877\) −1.22498 + 1.22498i −0.0413645 + 0.0413645i −0.727487 0.686122i \(-0.759312\pi\)
0.686122 + 0.727487i \(0.259312\pi\)
\(878\) −11.0814 + 18.6197i −0.373980 + 0.628385i
\(879\) 15.5121 15.5121i 0.523209 0.523209i
\(880\) 13.3661 + 8.69171i 0.450571 + 0.292998i
\(881\) 6.78568i 0.228615i 0.993445 + 0.114308i \(0.0364650\pi\)
−0.993445 + 0.114308i \(0.963535\pi\)
\(882\) −1.23907 0.737429i −0.0417218 0.0248305i
\(883\) 19.0036 0.639523 0.319761 0.947498i \(-0.396397\pi\)
0.319761 + 0.947498i \(0.396397\pi\)
\(884\) 0.888174 + 0.298558i 0.0298725 + 0.0100416i
\(885\) 24.6316 0.827981
\(886\) −34.3895 20.4667i −1.15534 0.687594i
\(887\) 47.7807i 1.60432i −0.597110 0.802159i \(-0.703684\pi\)
0.597110 0.802159i \(-0.296316\pi\)
\(888\) −6.62970 + 6.12277i −0.222478 + 0.205467i
\(889\) −14.1833 + 14.1833i −0.475693 + 0.475693i
\(890\) −10.8071 + 18.1588i −0.362255 + 0.608684i
\(891\) −27.2955 + 27.2955i −0.914432 + 0.914432i
\(892\) −12.0718 + 40.7078i −0.404193 + 1.36300i
\(893\) −1.18319 −0.0395939
\(894\) 6.81401 1.72943i 0.227895 0.0578407i
\(895\) 8.61979 8.61979i 0.288128 0.288128i
\(896\) −3.24364 18.9991i −0.108363 0.634716i
\(897\) 21.7606 20.2478i 0.726565 0.676055i
\(898\) −34.0786 + 8.64929i −1.13722 + 0.288630i
\(899\) 9.32533 + 9.32533i 0.311017 + 0.311017i
\(900\) 0.437399 0.237315i 0.0145800 0.00791049i
\(901\) 0.409827i 0.0136533i
\(902\) 30.6155 + 18.2207i 1.01939 + 0.606683i
\(903\) −16.5798 16.5798i −0.551742 0.551742i
\(904\) −9.31947 0.370459i −0.309961 0.0123213i
\(905\) −6.31510 6.31510i −0.209921 0.209921i
\(906\) −22.0680 + 5.60096i −0.733161 + 0.186080i
\(907\) −18.1020 −0.601067 −0.300534 0.953771i \(-0.597165\pi\)
−0.300534 + 0.953771i \(0.597165\pi\)
\(908\) −3.19132 + 10.7616i −0.105908 + 0.357136i
\(909\) 3.38769i 0.112362i
\(910\) −1.83257 8.49118i −0.0607491 0.281480i
\(911\) 15.6842i 0.519641i 0.965657 + 0.259821i \(0.0836634\pi\)
−0.965657 + 0.259821i \(0.916337\pi\)
\(912\) −0.306572 1.44667i −0.0101516 0.0479042i
\(913\) 63.5174 2.10212
\(914\) −3.04456 11.9957i −0.100705 0.396783i
\(915\) −7.50829 7.50829i −0.248216 0.248216i
\(916\) 15.2063 51.2777i 0.502429 1.69426i
\(917\) 9.61816 + 9.61816i 0.317620 + 0.317620i
\(918\) −0.466039 + 0.783068i −0.0153816 + 0.0258451i
\(919\) 38.7998i 1.27989i 0.768422 + 0.639943i \(0.221042\pi\)
−0.768422 + 0.639943i \(0.778958\pi\)
\(920\) 9.50353 8.77686i 0.313322 0.289365i
\(921\) −2.56036 2.56036i −0.0843667 0.0843667i
\(922\) 2.80551 + 11.0538i 0.0923946 + 0.364039i
\(923\) 1.17907 32.7416i 0.0388095 1.07770i
\(924\) −11.6736 21.5158i −0.384032 0.707817i
\(925\) −1.25170 + 1.25170i −0.0411556 + 0.0411556i
\(926\) 6.20207 + 24.4364i 0.203813 + 0.803030i
\(927\) −2.48837 −0.0817289
\(928\) −9.59954 19.5036i −0.315120 0.640238i
\(929\) 24.4927 24.4927i 0.803580 0.803580i −0.180073 0.983653i \(-0.557633\pi\)
0.983653 + 0.180073i \(0.0576334\pi\)
\(930\) −7.51744 4.47397i −0.246507 0.146707i
\(931\) −0.594317 + 0.594317i −0.0194780 + 0.0194780i
\(932\) −2.41116 + 1.30819i −0.0789801 + 0.0428513i
\(933\) 37.2647i 1.21999i
\(934\) 2.11555 3.55468i 0.0692230 0.116313i
\(935\) 0.517928 0.0169381
\(936\) 1.65335 + 1.92483i 0.0540415 + 0.0629151i
\(937\) −49.8771 −1.62942 −0.814708 0.579872i \(-0.803103\pi\)
−0.814708 + 0.579872i \(0.803103\pi\)
\(938\) 11.2709 18.9381i 0.368009 0.618352i
\(939\) 44.9764i 1.46775i
\(940\) 10.1407 5.50192i 0.330753 0.179453i
\(941\) 1.82125 1.82125i 0.0593711 0.0593711i −0.676798 0.736169i \(-0.736633\pi\)
0.736169 + 0.676798i \(0.236633\pi\)
\(942\) −0.295456 0.175839i −0.00962646 0.00572914i
\(943\) 20.4407 20.4407i 0.665639 0.665639i
\(944\) 11.3322 + 53.4749i 0.368830 + 1.74046i
\(945\) 8.44791 0.274811
\(946\) 10.5889 + 41.7207i 0.344274 + 1.35646i
\(947\) 10.0728 10.0728i 0.327321 0.327321i −0.524246 0.851567i \(-0.675653\pi\)
0.851567 + 0.524246i \(0.175653\pi\)
\(948\) 5.34861 + 9.85812i 0.173715 + 0.320177i
\(949\) −2.13411 + 59.2622i −0.0692762 + 1.92373i
\(950\) −0.0713584 0.281155i −0.00231517 0.00912188i
\(951\) 34.5277 + 34.5277i 1.11964 + 1.11964i
\(952\) −0.424797 0.459967i −0.0137677 0.0149076i
\(953\) 22.7318i 0.736357i 0.929755 + 0.368178i \(0.120018\pi\)
−0.929755 + 0.368178i \(0.879982\pi\)
\(954\) −0.567586 + 0.953694i −0.0183763 + 0.0308770i
\(955\) 19.1959 + 19.1959i 0.621166 + 0.621166i
\(956\) −11.4105 + 38.4779i −0.369043 + 1.24447i
\(957\) −19.5218 19.5218i −0.631050 0.631050i
\(958\) −8.26238 32.5541i −0.266945 1.05178i
\(959\) −33.7743 −1.09063
\(960\) 9.35467 + 10.9733i 0.301921 + 0.354163i
\(961\) 19.2221i 0.620068i
\(962\) −7.58525 4.89233i −0.244558 0.157735i
\(963\) 2.94178i 0.0947977i
\(964\) 2.62634 8.85641i 0.0845889 0.285246i
\(965\) 15.6834 0.504868
\(966\) −19.2512 + 4.88603i −0.619396 + 0.157205i
\(967\) 16.9691 + 16.9691i 0.545691 + 0.545691i 0.925192 0.379500i \(-0.123904\pi\)
−0.379500 + 0.925192i \(0.623904\pi\)
\(968\) −0.549071 + 13.8128i −0.0176478 + 0.443959i
\(969\) −0.0339686 0.0339686i −0.00109123 0.00109123i
\(970\) 16.5395 + 9.84339i 0.531051 + 0.316052i
\(971\) 11.8306i 0.379662i 0.981817 + 0.189831i \(0.0607940\pi\)
−0.981817 + 0.189831i \(0.939206\pi\)
\(972\) −4.53417 + 2.46005i −0.145434 + 0.0789063i
\(973\) −14.2989 14.2989i −0.458403 0.458403i
\(974\) −2.36108 + 0.599253i −0.0756540 + 0.0192013i
\(975\) 4.42700 + 4.75776i 0.141778 + 0.152370i
\(976\) 12.8461 19.7547i 0.411194 0.632334i
\(977\) 20.7800 20.7800i 0.664812 0.664812i −0.291699 0.956510i \(-0.594220\pi\)
0.956510 + 0.291699i \(0.0942205\pi\)
\(978\) −46.5795 + 11.8221i −1.48945 + 0.378028i
\(979\) −59.5579 −1.90348
\(980\) 2.33006 7.85730i 0.0744311 0.250992i
\(981\) −0.654002 + 0.654002i −0.0208807 + 0.0208807i
\(982\) 1.13492 1.90697i 0.0362168 0.0608537i
\(983\) −16.0481 + 16.0481i −0.511854 + 0.511854i −0.915094 0.403240i \(-0.867884\pi\)
0.403240 + 0.915094i \(0.367884\pi\)
\(984\) 21.8613 + 23.6712i 0.696911 + 0.754611i
\(985\) 0.953635i 0.0303853i
\(986\) −0.606825 0.361149i −0.0193252 0.0115013i
\(987\) −17.7132 −0.563817
\(988\) 1.32459 0.658109i 0.0421408 0.0209373i
\(989\) 34.9248 1.11054
\(990\) 1.20525 + 0.717300i 0.0383054 + 0.0227973i
\(991\) 32.8640i 1.04396i −0.852958 0.521980i \(-0.825194\pi\)
0.852958 0.521980i \(-0.174806\pi\)
\(992\) 6.25443 18.3786i 0.198578 0.583522i
\(993\) −18.6936 + 18.6936i −0.593222 + 0.593222i
\(994\) −11.1963 + 18.8127i −0.355124 + 0.596702i
\(995\) 12.8177 12.8177i 0.406350 0.406350i
\(996\) 55.0752 + 16.3324i 1.74512 + 0.517512i
\(997\) −47.9078 −1.51726 −0.758628 0.651524i \(-0.774130\pi\)
−0.758628 + 0.651524i \(0.774130\pi\)
\(998\) 46.9336 11.9120i 1.48566 0.377066i
\(999\) 6.20700 6.20700i 0.196381 0.196381i
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 260.2.j.a.31.20 56
4.3 odd 2 inner 260.2.j.a.31.23 yes 56
13.8 odd 4 inner 260.2.j.a.151.23 yes 56
52.47 even 4 inner 260.2.j.a.151.20 yes 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
260.2.j.a.31.20 56 1.1 even 1 trivial
260.2.j.a.31.23 yes 56 4.3 odd 2 inner
260.2.j.a.151.20 yes 56 52.47 even 4 inner
260.2.j.a.151.23 yes 56 13.8 odd 4 inner