Properties

Label 170.2.g.d.149.1
Level $170$
Weight $2$
Character 170.149
Analytic conductor $1.357$
Analytic rank $0$
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] = [170,2,Mod(89,170)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(170, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("170.89");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 170 = 2 \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 170.g (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.35745683436\)
Analytic rank: \(0\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 149.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 170.149
Dual form 170.2.g.d.89.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +(-1.00000 + 1.00000i) q^{3} +1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} +(-1.00000 + 1.00000i) q^{6} +(-1.00000 - 1.00000i) q^{7} +1.00000 q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(-1.00000 + 1.00000i) q^{3} +1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} +(-1.00000 + 1.00000i) q^{6} +(-1.00000 - 1.00000i) q^{7} +1.00000 q^{8} +1.00000i q^{9} +(2.00000 + 1.00000i) q^{10} +(1.00000 - 1.00000i) q^{11} +(-1.00000 + 1.00000i) q^{12} +4.00000i q^{13} +(-1.00000 - 1.00000i) q^{14} +(-3.00000 + 1.00000i) q^{15} +1.00000 q^{16} +(-1.00000 - 4.00000i) q^{17} +1.00000i q^{18} -6.00000i q^{19} +(2.00000 + 1.00000i) q^{20} +2.00000 q^{21} +(1.00000 - 1.00000i) q^{22} +(-1.00000 - 1.00000i) q^{23} +(-1.00000 + 1.00000i) q^{24} +(3.00000 + 4.00000i) q^{25} +4.00000i q^{26} +(-4.00000 - 4.00000i) q^{27} +(-1.00000 - 1.00000i) q^{28} +(-5.00000 - 5.00000i) q^{29} +(-3.00000 + 1.00000i) q^{30} +(-3.00000 - 3.00000i) q^{31} +1.00000 q^{32} +2.00000i q^{33} +(-1.00000 - 4.00000i) q^{34} +(-1.00000 - 3.00000i) q^{35} +1.00000i q^{36} +(1.00000 - 1.00000i) q^{37} -6.00000i q^{38} +(-4.00000 - 4.00000i) q^{39} +(2.00000 + 1.00000i) q^{40} +(-7.00000 + 7.00000i) q^{41} +2.00000 q^{42} +4.00000 q^{43} +(1.00000 - 1.00000i) q^{44} +(-1.00000 + 2.00000i) q^{45} +(-1.00000 - 1.00000i) q^{46} +6.00000i q^{47} +(-1.00000 + 1.00000i) q^{48} -5.00000i q^{49} +(3.00000 + 4.00000i) q^{50} +(5.00000 + 3.00000i) q^{51} +4.00000i q^{52} +10.0000 q^{53} +(-4.00000 - 4.00000i) q^{54} +(3.00000 - 1.00000i) q^{55} +(-1.00000 - 1.00000i) q^{56} +(6.00000 + 6.00000i) q^{57} +(-5.00000 - 5.00000i) q^{58} +10.0000i q^{59} +(-3.00000 + 1.00000i) q^{60} +(3.00000 - 3.00000i) q^{61} +(-3.00000 - 3.00000i) q^{62} +(1.00000 - 1.00000i) q^{63} +1.00000 q^{64} +(-4.00000 + 8.00000i) q^{65} +2.00000i q^{66} -2.00000i q^{67} +(-1.00000 - 4.00000i) q^{68} +2.00000 q^{69} +(-1.00000 - 3.00000i) q^{70} +(5.00000 + 5.00000i) q^{71} +1.00000i q^{72} +(-1.00000 + 1.00000i) q^{73} +(1.00000 - 1.00000i) q^{74} +(-7.00000 - 1.00000i) q^{75} -6.00000i q^{76} -2.00000 q^{77} +(-4.00000 - 4.00000i) q^{78} +(-1.00000 + 1.00000i) q^{79} +(2.00000 + 1.00000i) q^{80} +5.00000 q^{81} +(-7.00000 + 7.00000i) q^{82} -12.0000 q^{83} +2.00000 q^{84} +(2.00000 - 9.00000i) q^{85} +4.00000 q^{86} +10.0000 q^{87} +(1.00000 - 1.00000i) q^{88} +6.00000 q^{89} +(-1.00000 + 2.00000i) q^{90} +(4.00000 - 4.00000i) q^{91} +(-1.00000 - 1.00000i) q^{92} +6.00000 q^{93} +6.00000i q^{94} +(6.00000 - 12.0000i) q^{95} +(-1.00000 + 1.00000i) q^{96} +(3.00000 - 3.00000i) q^{97} -5.00000i q^{98} +(1.00000 + 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 4 q^{10} + 2 q^{11} - 2 q^{12} - 2 q^{14} - 6 q^{15} + 2 q^{16} - 2 q^{17} + 4 q^{20} + 4 q^{21} + 2 q^{22} - 2 q^{23} - 2 q^{24} + 6 q^{25} - 8 q^{27} - 2 q^{28} - 10 q^{29} - 6 q^{30} - 6 q^{31} + 2 q^{32} - 2 q^{34} - 2 q^{35} + 2 q^{37} - 8 q^{39} + 4 q^{40} - 14 q^{41} + 4 q^{42} + 8 q^{43} + 2 q^{44} - 2 q^{45} - 2 q^{46} - 2 q^{48} + 6 q^{50} + 10 q^{51} + 20 q^{53} - 8 q^{54} + 6 q^{55} - 2 q^{56} + 12 q^{57} - 10 q^{58} - 6 q^{60} + 6 q^{61} - 6 q^{62} + 2 q^{63} + 2 q^{64} - 8 q^{65} - 2 q^{68} + 4 q^{69} - 2 q^{70} + 10 q^{71} - 2 q^{73} + 2 q^{74} - 14 q^{75} - 4 q^{77} - 8 q^{78} - 2 q^{79} + 4 q^{80} + 10 q^{81} - 14 q^{82} - 24 q^{83} + 4 q^{84} + 4 q^{85} + 8 q^{86} + 20 q^{87} + 2 q^{88} + 12 q^{89} - 2 q^{90} + 8 q^{91} - 2 q^{92} + 12 q^{93} + 12 q^{95} - 2 q^{96} + 6 q^{97} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/170\mathbb{Z}\right)^\times\).

\(n\) \(71\) \(137\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.00000 + 1.00000i −0.577350 + 0.577350i −0.934172 0.356822i \(-0.883860\pi\)
0.356822 + 0.934172i \(0.383860\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.00000 + 1.00000i 0.894427 + 0.447214i
\(6\) −1.00000 + 1.00000i −0.408248 + 0.408248i
\(7\) −1.00000 1.00000i −0.377964 0.377964i 0.492403 0.870367i \(-0.336119\pi\)
−0.870367 + 0.492403i \(0.836119\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000i 0.333333i
\(10\) 2.00000 + 1.00000i 0.632456 + 0.316228i
\(11\) 1.00000 1.00000i 0.301511 0.301511i −0.540094 0.841605i \(-0.681611\pi\)
0.841605 + 0.540094i \(0.181611\pi\)
\(12\) −1.00000 + 1.00000i −0.288675 + 0.288675i
\(13\) 4.00000i 1.10940i 0.832050 + 0.554700i \(0.187167\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) −1.00000 1.00000i −0.267261 0.267261i
\(15\) −3.00000 + 1.00000i −0.774597 + 0.258199i
\(16\) 1.00000 0.250000
\(17\) −1.00000 4.00000i −0.242536 0.970143i
\(18\) 1.00000i 0.235702i
\(19\) 6.00000i 1.37649i −0.725476 0.688247i \(-0.758380\pi\)
0.725476 0.688247i \(-0.241620\pi\)
\(20\) 2.00000 + 1.00000i 0.447214 + 0.223607i
\(21\) 2.00000 0.436436
\(22\) 1.00000 1.00000i 0.213201 0.213201i
\(23\) −1.00000 1.00000i −0.208514 0.208514i 0.595121 0.803636i \(-0.297104\pi\)
−0.803636 + 0.595121i \(0.797104\pi\)
\(24\) −1.00000 + 1.00000i −0.204124 + 0.204124i
\(25\) 3.00000 + 4.00000i 0.600000 + 0.800000i
\(26\) 4.00000i 0.784465i
\(27\) −4.00000 4.00000i −0.769800 0.769800i
\(28\) −1.00000 1.00000i −0.188982 0.188982i
\(29\) −5.00000 5.00000i −0.928477 0.928477i 0.0691309 0.997608i \(-0.477977\pi\)
−0.997608 + 0.0691309i \(0.977977\pi\)
\(30\) −3.00000 + 1.00000i −0.547723 + 0.182574i
\(31\) −3.00000 3.00000i −0.538816 0.538816i 0.384365 0.923181i \(-0.374420\pi\)
−0.923181 + 0.384365i \(0.874420\pi\)
\(32\) 1.00000 0.176777
\(33\) 2.00000i 0.348155i
\(34\) −1.00000 4.00000i −0.171499 0.685994i
\(35\) −1.00000 3.00000i −0.169031 0.507093i
\(36\) 1.00000i 0.166667i
\(37\) 1.00000 1.00000i 0.164399 0.164399i −0.620113 0.784512i \(-0.712913\pi\)
0.784512 + 0.620113i \(0.212913\pi\)
\(38\) 6.00000i 0.973329i
\(39\) −4.00000 4.00000i −0.640513 0.640513i
\(40\) 2.00000 + 1.00000i 0.316228 + 0.158114i
\(41\) −7.00000 + 7.00000i −1.09322 + 1.09322i −0.0980332 + 0.995183i \(0.531255\pi\)
−0.995183 + 0.0980332i \(0.968745\pi\)
\(42\) 2.00000 0.308607
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 1.00000 1.00000i 0.150756 0.150756i
\(45\) −1.00000 + 2.00000i −0.149071 + 0.298142i
\(46\) −1.00000 1.00000i −0.147442 0.147442i
\(47\) 6.00000i 0.875190i 0.899172 + 0.437595i \(0.144170\pi\)
−0.899172 + 0.437595i \(0.855830\pi\)
\(48\) −1.00000 + 1.00000i −0.144338 + 0.144338i
\(49\) 5.00000i 0.714286i
\(50\) 3.00000 + 4.00000i 0.424264 + 0.565685i
\(51\) 5.00000 + 3.00000i 0.700140 + 0.420084i
\(52\) 4.00000i 0.554700i
\(53\) 10.0000 1.37361 0.686803 0.726844i \(-0.259014\pi\)
0.686803 + 0.726844i \(0.259014\pi\)
\(54\) −4.00000 4.00000i −0.544331 0.544331i
\(55\) 3.00000 1.00000i 0.404520 0.134840i
\(56\) −1.00000 1.00000i −0.133631 0.133631i
\(57\) 6.00000 + 6.00000i 0.794719 + 0.794719i
\(58\) −5.00000 5.00000i −0.656532 0.656532i
\(59\) 10.0000i 1.30189i 0.759125 + 0.650945i \(0.225627\pi\)
−0.759125 + 0.650945i \(0.774373\pi\)
\(60\) −3.00000 + 1.00000i −0.387298 + 0.129099i
\(61\) 3.00000 3.00000i 0.384111 0.384111i −0.488470 0.872581i \(-0.662445\pi\)
0.872581 + 0.488470i \(0.162445\pi\)
\(62\) −3.00000 3.00000i −0.381000 0.381000i
\(63\) 1.00000 1.00000i 0.125988 0.125988i
\(64\) 1.00000 0.125000
\(65\) −4.00000 + 8.00000i −0.496139 + 0.992278i
\(66\) 2.00000i 0.246183i
\(67\) 2.00000i 0.244339i −0.992509 0.122169i \(-0.961015\pi\)
0.992509 0.122169i \(-0.0389851\pi\)
\(68\) −1.00000 4.00000i −0.121268 0.485071i
\(69\) 2.00000 0.240772
\(70\) −1.00000 3.00000i −0.119523 0.358569i
\(71\) 5.00000 + 5.00000i 0.593391 + 0.593391i 0.938546 0.345155i \(-0.112174\pi\)
−0.345155 + 0.938546i \(0.612174\pi\)
\(72\) 1.00000i 0.117851i
\(73\) −1.00000 + 1.00000i −0.117041 + 0.117041i −0.763202 0.646160i \(-0.776374\pi\)
0.646160 + 0.763202i \(0.276374\pi\)
\(74\) 1.00000 1.00000i 0.116248 0.116248i
\(75\) −7.00000 1.00000i −0.808290 0.115470i
\(76\) 6.00000i 0.688247i
\(77\) −2.00000 −0.227921
\(78\) −4.00000 4.00000i −0.452911 0.452911i
\(79\) −1.00000 + 1.00000i −0.112509 + 0.112509i −0.761120 0.648611i \(-0.775350\pi\)
0.648611 + 0.761120i \(0.275350\pi\)
\(80\) 2.00000 + 1.00000i 0.223607 + 0.111803i
\(81\) 5.00000 0.555556
\(82\) −7.00000 + 7.00000i −0.773021 + 0.773021i
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 2.00000 0.218218
\(85\) 2.00000 9.00000i 0.216930 0.976187i
\(86\) 4.00000 0.431331
\(87\) 10.0000 1.07211
\(88\) 1.00000 1.00000i 0.106600 0.106600i
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) −1.00000 + 2.00000i −0.105409 + 0.210819i
\(91\) 4.00000 4.00000i 0.419314 0.419314i
\(92\) −1.00000 1.00000i −0.104257 0.104257i
\(93\) 6.00000 0.622171
\(94\) 6.00000i 0.618853i
\(95\) 6.00000 12.0000i 0.615587 1.23117i
\(96\) −1.00000 + 1.00000i −0.102062 + 0.102062i
\(97\) 3.00000 3.00000i 0.304604 0.304604i −0.538208 0.842812i \(-0.680899\pi\)
0.842812 + 0.538208i \(0.180899\pi\)
\(98\) 5.00000i 0.505076i
\(99\) 1.00000 + 1.00000i 0.100504 + 0.100504i
\(100\) 3.00000 + 4.00000i 0.300000 + 0.400000i
\(101\) −14.0000 −1.39305 −0.696526 0.717532i \(-0.745272\pi\)
−0.696526 + 0.717532i \(0.745272\pi\)
\(102\) 5.00000 + 3.00000i 0.495074 + 0.297044i
\(103\) 14.0000i 1.37946i 0.724066 + 0.689730i \(0.242271\pi\)
−0.724066 + 0.689730i \(0.757729\pi\)
\(104\) 4.00000i 0.392232i
\(105\) 4.00000 + 2.00000i 0.390360 + 0.195180i
\(106\) 10.0000 0.971286
\(107\) −13.0000 + 13.0000i −1.25676 + 1.25676i −0.304125 + 0.952632i \(0.598364\pi\)
−0.952632 + 0.304125i \(0.901636\pi\)
\(108\) −4.00000 4.00000i −0.384900 0.384900i
\(109\) 7.00000 7.00000i 0.670478 0.670478i −0.287348 0.957826i \(-0.592774\pi\)
0.957826 + 0.287348i \(0.0927736\pi\)
\(110\) 3.00000 1.00000i 0.286039 0.0953463i
\(111\) 2.00000i 0.189832i
\(112\) −1.00000 1.00000i −0.0944911 0.0944911i
\(113\) 11.0000 + 11.0000i 1.03479 + 1.03479i 0.999372 + 0.0354205i \(0.0112770\pi\)
0.0354205 + 0.999372i \(0.488723\pi\)
\(114\) 6.00000 + 6.00000i 0.561951 + 0.561951i
\(115\) −1.00000 3.00000i −0.0932505 0.279751i
\(116\) −5.00000 5.00000i −0.464238 0.464238i
\(117\) −4.00000 −0.369800
\(118\) 10.0000i 0.920575i
\(119\) −3.00000 + 5.00000i −0.275010 + 0.458349i
\(120\) −3.00000 + 1.00000i −0.273861 + 0.0912871i
\(121\) 9.00000i 0.818182i
\(122\) 3.00000 3.00000i 0.271607 0.271607i
\(123\) 14.0000i 1.26234i
\(124\) −3.00000 3.00000i −0.269408 0.269408i
\(125\) 2.00000 + 11.0000i 0.178885 + 0.983870i
\(126\) 1.00000 1.00000i 0.0890871 0.0890871i
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 1.00000 0.0883883
\(129\) −4.00000 + 4.00000i −0.352180 + 0.352180i
\(130\) −4.00000 + 8.00000i −0.350823 + 0.701646i
\(131\) −9.00000 9.00000i −0.786334 0.786334i 0.194557 0.980891i \(-0.437673\pi\)
−0.980891 + 0.194557i \(0.937673\pi\)
\(132\) 2.00000i 0.174078i
\(133\) −6.00000 + 6.00000i −0.520266 + 0.520266i
\(134\) 2.00000i 0.172774i
\(135\) −4.00000 12.0000i −0.344265 1.03280i
\(136\) −1.00000 4.00000i −0.0857493 0.342997i
\(137\) 12.0000i 1.02523i −0.858619 0.512615i \(-0.828677\pi\)
0.858619 0.512615i \(-0.171323\pi\)
\(138\) 2.00000 0.170251
\(139\) 3.00000 + 3.00000i 0.254457 + 0.254457i 0.822795 0.568338i \(-0.192414\pi\)
−0.568338 + 0.822795i \(0.692414\pi\)
\(140\) −1.00000 3.00000i −0.0845154 0.253546i
\(141\) −6.00000 6.00000i −0.505291 0.505291i
\(142\) 5.00000 + 5.00000i 0.419591 + 0.419591i
\(143\) 4.00000 + 4.00000i 0.334497 + 0.334497i
\(144\) 1.00000i 0.0833333i
\(145\) −5.00000 15.0000i −0.415227 1.24568i
\(146\) −1.00000 + 1.00000i −0.0827606 + 0.0827606i
\(147\) 5.00000 + 5.00000i 0.412393 + 0.412393i
\(148\) 1.00000 1.00000i 0.0821995 0.0821995i
\(149\) 6.00000 0.491539 0.245770 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) −7.00000 1.00000i −0.571548 0.0816497i
\(151\) 2.00000i 0.162758i 0.996683 + 0.0813788i \(0.0259324\pi\)
−0.996683 + 0.0813788i \(0.974068\pi\)
\(152\) 6.00000i 0.486664i
\(153\) 4.00000 1.00000i 0.323381 0.0808452i
\(154\) −2.00000 −0.161165
\(155\) −3.00000 9.00000i −0.240966 0.722897i
\(156\) −4.00000 4.00000i −0.320256 0.320256i
\(157\) 16.0000i 1.27694i −0.769647 0.638470i \(-0.779568\pi\)
0.769647 0.638470i \(-0.220432\pi\)
\(158\) −1.00000 + 1.00000i −0.0795557 + 0.0795557i
\(159\) −10.0000 + 10.0000i −0.793052 + 0.793052i
\(160\) 2.00000 + 1.00000i 0.158114 + 0.0790569i
\(161\) 2.00000i 0.157622i
\(162\) 5.00000 0.392837
\(163\) −15.0000 15.0000i −1.17489 1.17489i −0.981029 0.193862i \(-0.937899\pi\)
−0.193862 0.981029i \(-0.562101\pi\)
\(164\) −7.00000 + 7.00000i −0.546608 + 0.546608i
\(165\) −2.00000 + 4.00000i −0.155700 + 0.311400i
\(166\) −12.0000 −0.931381
\(167\) −7.00000 + 7.00000i −0.541676 + 0.541676i −0.924020 0.382344i \(-0.875117\pi\)
0.382344 + 0.924020i \(0.375117\pi\)
\(168\) 2.00000 0.154303
\(169\) −3.00000 −0.230769
\(170\) 2.00000 9.00000i 0.153393 0.690268i
\(171\) 6.00000 0.458831
\(172\) 4.00000 0.304997
\(173\) −7.00000 + 7.00000i −0.532200 + 0.532200i −0.921227 0.389026i \(-0.872811\pi\)
0.389026 + 0.921227i \(0.372811\pi\)
\(174\) 10.0000 0.758098
\(175\) 1.00000 7.00000i 0.0755929 0.529150i
\(176\) 1.00000 1.00000i 0.0753778 0.0753778i
\(177\) −10.0000 10.0000i −0.751646 0.751646i
\(178\) 6.00000 0.449719
\(179\) 6.00000i 0.448461i −0.974536 0.224231i \(-0.928013\pi\)
0.974536 0.224231i \(-0.0719869\pi\)
\(180\) −1.00000 + 2.00000i −0.0745356 + 0.149071i
\(181\) 7.00000 7.00000i 0.520306 0.520306i −0.397358 0.917664i \(-0.630073\pi\)
0.917664 + 0.397358i \(0.130073\pi\)
\(182\) 4.00000 4.00000i 0.296500 0.296500i
\(183\) 6.00000i 0.443533i
\(184\) −1.00000 1.00000i −0.0737210 0.0737210i
\(185\) 3.00000 1.00000i 0.220564 0.0735215i
\(186\) 6.00000 0.439941
\(187\) −5.00000 3.00000i −0.365636 0.219382i
\(188\) 6.00000i 0.437595i
\(189\) 8.00000i 0.581914i
\(190\) 6.00000 12.0000i 0.435286 0.870572i
\(191\) −24.0000 −1.73658 −0.868290 0.496058i \(-0.834780\pi\)
−0.868290 + 0.496058i \(0.834780\pi\)
\(192\) −1.00000 + 1.00000i −0.0721688 + 0.0721688i
\(193\) −13.0000 13.0000i −0.935760 0.935760i 0.0622972 0.998058i \(-0.480157\pi\)
−0.998058 + 0.0622972i \(0.980157\pi\)
\(194\) 3.00000 3.00000i 0.215387 0.215387i
\(195\) −4.00000 12.0000i −0.286446 0.859338i
\(196\) 5.00000i 0.357143i
\(197\) −7.00000 7.00000i −0.498729 0.498729i 0.412313 0.911042i \(-0.364721\pi\)
−0.911042 + 0.412313i \(0.864721\pi\)
\(198\) 1.00000 + 1.00000i 0.0710669 + 0.0710669i
\(199\) 17.0000 + 17.0000i 1.20510 + 1.20510i 0.972596 + 0.232502i \(0.0746913\pi\)
0.232502 + 0.972596i \(0.425309\pi\)
\(200\) 3.00000 + 4.00000i 0.212132 + 0.282843i
\(201\) 2.00000 + 2.00000i 0.141069 + 0.141069i
\(202\) −14.0000 −0.985037
\(203\) 10.0000i 0.701862i
\(204\) 5.00000 + 3.00000i 0.350070 + 0.210042i
\(205\) −21.0000 + 7.00000i −1.46670 + 0.488901i
\(206\) 14.0000i 0.975426i
\(207\) 1.00000 1.00000i 0.0695048 0.0695048i
\(208\) 4.00000i 0.277350i
\(209\) −6.00000 6.00000i −0.415029 0.415029i
\(210\) 4.00000 + 2.00000i 0.276026 + 0.138013i
\(211\) 13.0000 13.0000i 0.894957 0.894957i −0.100028 0.994985i \(-0.531893\pi\)
0.994985 + 0.100028i \(0.0318932\pi\)
\(212\) 10.0000 0.686803
\(213\) −10.0000 −0.685189
\(214\) −13.0000 + 13.0000i −0.888662 + 0.888662i
\(215\) 8.00000 + 4.00000i 0.545595 + 0.272798i
\(216\) −4.00000 4.00000i −0.272166 0.272166i
\(217\) 6.00000i 0.407307i
\(218\) 7.00000 7.00000i 0.474100 0.474100i
\(219\) 2.00000i 0.135147i
\(220\) 3.00000 1.00000i 0.202260 0.0674200i
\(221\) 16.0000 4.00000i 1.07628 0.269069i
\(222\) 2.00000i 0.134231i
\(223\) 24.0000 1.60716 0.803579 0.595198i \(-0.202926\pi\)
0.803579 + 0.595198i \(0.202926\pi\)
\(224\) −1.00000 1.00000i −0.0668153 0.0668153i
\(225\) −4.00000 + 3.00000i −0.266667 + 0.200000i
\(226\) 11.0000 + 11.0000i 0.731709 + 0.731709i
\(227\) 9.00000 + 9.00000i 0.597351 + 0.597351i 0.939607 0.342256i \(-0.111191\pi\)
−0.342256 + 0.939607i \(0.611191\pi\)
\(228\) 6.00000 + 6.00000i 0.397360 + 0.397360i
\(229\) 28.0000i 1.85029i 0.379611 + 0.925146i \(0.376058\pi\)
−0.379611 + 0.925146i \(0.623942\pi\)
\(230\) −1.00000 3.00000i −0.0659380 0.197814i
\(231\) 2.00000 2.00000i 0.131590 0.131590i
\(232\) −5.00000 5.00000i −0.328266 0.328266i
\(233\) −1.00000 + 1.00000i −0.0655122 + 0.0655122i −0.739104 0.673592i \(-0.764751\pi\)
0.673592 + 0.739104i \(0.264751\pi\)
\(234\) −4.00000 −0.261488
\(235\) −6.00000 + 12.0000i −0.391397 + 0.782794i
\(236\) 10.0000i 0.650945i
\(237\) 2.00000i 0.129914i
\(238\) −3.00000 + 5.00000i −0.194461 + 0.324102i
\(239\) 16.0000 1.03495 0.517477 0.855697i \(-0.326871\pi\)
0.517477 + 0.855697i \(0.326871\pi\)
\(240\) −3.00000 + 1.00000i −0.193649 + 0.0645497i
\(241\) 9.00000 + 9.00000i 0.579741 + 0.579741i 0.934832 0.355091i \(-0.115550\pi\)
−0.355091 + 0.934832i \(0.615550\pi\)
\(242\) 9.00000i 0.578542i
\(243\) 7.00000 7.00000i 0.449050 0.449050i
\(244\) 3.00000 3.00000i 0.192055 0.192055i
\(245\) 5.00000 10.0000i 0.319438 0.638877i
\(246\) 14.0000i 0.892607i
\(247\) 24.0000 1.52708
\(248\) −3.00000 3.00000i −0.190500 0.190500i
\(249\) 12.0000 12.0000i 0.760469 0.760469i
\(250\) 2.00000 + 11.0000i 0.126491 + 0.695701i
\(251\) −20.0000 −1.26239 −0.631194 0.775625i \(-0.717435\pi\)
−0.631194 + 0.775625i \(0.717435\pi\)
\(252\) 1.00000 1.00000i 0.0629941 0.0629941i
\(253\) −2.00000 −0.125739
\(254\) 8.00000 0.501965
\(255\) 7.00000 + 11.0000i 0.438357 + 0.688847i
\(256\) 1.00000 0.0625000
\(257\) −30.0000 −1.87135 −0.935674 0.352865i \(-0.885208\pi\)
−0.935674 + 0.352865i \(0.885208\pi\)
\(258\) −4.00000 + 4.00000i −0.249029 + 0.249029i
\(259\) −2.00000 −0.124274
\(260\) −4.00000 + 8.00000i −0.248069 + 0.496139i
\(261\) 5.00000 5.00000i 0.309492 0.309492i
\(262\) −9.00000 9.00000i −0.556022 0.556022i
\(263\) 24.0000 1.47990 0.739952 0.672660i \(-0.234848\pi\)
0.739952 + 0.672660i \(0.234848\pi\)
\(264\) 2.00000i 0.123091i
\(265\) 20.0000 + 10.0000i 1.22859 + 0.614295i
\(266\) −6.00000 + 6.00000i −0.367884 + 0.367884i
\(267\) −6.00000 + 6.00000i −0.367194 + 0.367194i
\(268\) 2.00000i 0.122169i
\(269\) 11.0000 + 11.0000i 0.670682 + 0.670682i 0.957873 0.287191i \(-0.0927216\pi\)
−0.287191 + 0.957873i \(0.592722\pi\)
\(270\) −4.00000 12.0000i −0.243432 0.730297i
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) −1.00000 4.00000i −0.0606339 0.242536i
\(273\) 8.00000i 0.484182i
\(274\) 12.0000i 0.724947i
\(275\) 7.00000 + 1.00000i 0.422116 + 0.0603023i
\(276\) 2.00000 0.120386
\(277\) 5.00000 5.00000i 0.300421 0.300421i −0.540758 0.841178i \(-0.681862\pi\)
0.841178 + 0.540758i \(0.181862\pi\)
\(278\) 3.00000 + 3.00000i 0.179928 + 0.179928i
\(279\) 3.00000 3.00000i 0.179605 0.179605i
\(280\) −1.00000 3.00000i −0.0597614 0.179284i
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) −6.00000 6.00000i −0.357295 0.357295i
\(283\) −19.0000 19.0000i −1.12943 1.12943i −0.990269 0.139163i \(-0.955559\pi\)
−0.139163 0.990269i \(-0.544441\pi\)
\(284\) 5.00000 + 5.00000i 0.296695 + 0.296695i
\(285\) 6.00000 + 18.0000i 0.355409 + 1.06623i
\(286\) 4.00000 + 4.00000i 0.236525 + 0.236525i
\(287\) 14.0000 0.826394
\(288\) 1.00000i 0.0589256i
\(289\) −15.0000 + 8.00000i −0.882353 + 0.470588i
\(290\) −5.00000 15.0000i −0.293610 0.880830i
\(291\) 6.00000i 0.351726i
\(292\) −1.00000 + 1.00000i −0.0585206 + 0.0585206i
\(293\) 24.0000i 1.40209i −0.713115 0.701047i \(-0.752716\pi\)
0.713115 0.701047i \(-0.247284\pi\)
\(294\) 5.00000 + 5.00000i 0.291606 + 0.291606i
\(295\) −10.0000 + 20.0000i −0.582223 + 1.16445i
\(296\) 1.00000 1.00000i 0.0581238 0.0581238i
\(297\) −8.00000 −0.464207
\(298\) 6.00000 0.347571
\(299\) 4.00000 4.00000i 0.231326 0.231326i
\(300\) −7.00000 1.00000i −0.404145 0.0577350i
\(301\) −4.00000 4.00000i −0.230556 0.230556i
\(302\) 2.00000i 0.115087i
\(303\) 14.0000 14.0000i 0.804279 0.804279i
\(304\) 6.00000i 0.344124i
\(305\) 9.00000 3.00000i 0.515339 0.171780i
\(306\) 4.00000 1.00000i 0.228665 0.0571662i
\(307\) 2.00000i 0.114146i −0.998370 0.0570730i \(-0.981823\pi\)
0.998370 0.0570730i \(-0.0181768\pi\)
\(308\) −2.00000 −0.113961
\(309\) −14.0000 14.0000i −0.796432 0.796432i
\(310\) −3.00000 9.00000i −0.170389 0.511166i
\(311\) 17.0000 + 17.0000i 0.963982 + 0.963982i 0.999374 0.0353919i \(-0.0112680\pi\)
−0.0353919 + 0.999374i \(0.511268\pi\)
\(312\) −4.00000 4.00000i −0.226455 0.226455i
\(313\) 3.00000 + 3.00000i 0.169570 + 0.169570i 0.786790 0.617220i \(-0.211741\pi\)
−0.617220 + 0.786790i \(0.711741\pi\)
\(314\) 16.0000i 0.902932i
\(315\) 3.00000 1.00000i 0.169031 0.0563436i
\(316\) −1.00000 + 1.00000i −0.0562544 + 0.0562544i
\(317\) 5.00000 + 5.00000i 0.280828 + 0.280828i 0.833439 0.552611i \(-0.186369\pi\)
−0.552611 + 0.833439i \(0.686369\pi\)
\(318\) −10.0000 + 10.0000i −0.560772 + 0.560772i
\(319\) −10.0000 −0.559893
\(320\) 2.00000 + 1.00000i 0.111803 + 0.0559017i
\(321\) 26.0000i 1.45118i
\(322\) 2.00000i 0.111456i
\(323\) −24.0000 + 6.00000i −1.33540 + 0.333849i
\(324\) 5.00000 0.277778
\(325\) −16.0000 + 12.0000i −0.887520 + 0.665640i
\(326\) −15.0000 15.0000i −0.830773 0.830773i
\(327\) 14.0000i 0.774202i
\(328\) −7.00000 + 7.00000i −0.386510 + 0.386510i
\(329\) 6.00000 6.00000i 0.330791 0.330791i
\(330\) −2.00000 + 4.00000i −0.110096 + 0.220193i
\(331\) 10.0000i 0.549650i 0.961494 + 0.274825i \(0.0886199\pi\)
−0.961494 + 0.274825i \(0.911380\pi\)
\(332\) −12.0000 −0.658586
\(333\) 1.00000 + 1.00000i 0.0547997 + 0.0547997i
\(334\) −7.00000 + 7.00000i −0.383023 + 0.383023i
\(335\) 2.00000 4.00000i 0.109272 0.218543i
\(336\) 2.00000 0.109109
\(337\) −5.00000 + 5.00000i −0.272367 + 0.272367i −0.830053 0.557685i \(-0.811690\pi\)
0.557685 + 0.830053i \(0.311690\pi\)
\(338\) −3.00000 −0.163178
\(339\) −22.0000 −1.19488
\(340\) 2.00000 9.00000i 0.108465 0.488094i
\(341\) −6.00000 −0.324918
\(342\) 6.00000 0.324443
\(343\) −12.0000 + 12.0000i −0.647939 + 0.647939i
\(344\) 4.00000 0.215666
\(345\) 4.00000 + 2.00000i 0.215353 + 0.107676i
\(346\) −7.00000 + 7.00000i −0.376322 + 0.376322i
\(347\) 25.0000 + 25.0000i 1.34207 + 1.34207i 0.893997 + 0.448074i \(0.147890\pi\)
0.448074 + 0.893997i \(0.352110\pi\)
\(348\) 10.0000 0.536056
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 1.00000 7.00000i 0.0534522 0.374166i
\(351\) 16.0000 16.0000i 0.854017 0.854017i
\(352\) 1.00000 1.00000i 0.0533002 0.0533002i
\(353\) 24.0000i 1.27739i −0.769460 0.638696i \(-0.779474\pi\)
0.769460 0.638696i \(-0.220526\pi\)
\(354\) −10.0000 10.0000i −0.531494 0.531494i
\(355\) 5.00000 + 15.0000i 0.265372 + 0.796117i
\(356\) 6.00000 0.317999
\(357\) −2.00000 8.00000i −0.105851 0.423405i
\(358\) 6.00000i 0.317110i
\(359\) 6.00000i 0.316668i −0.987386 0.158334i \(-0.949388\pi\)
0.987386 0.158334i \(-0.0506123\pi\)
\(360\) −1.00000 + 2.00000i −0.0527046 + 0.105409i
\(361\) −17.0000 −0.894737
\(362\) 7.00000 7.00000i 0.367912 0.367912i
\(363\) −9.00000 9.00000i −0.472377 0.472377i
\(364\) 4.00000 4.00000i 0.209657 0.209657i
\(365\) −3.00000 + 1.00000i −0.157027 + 0.0523424i
\(366\) 6.00000i 0.313625i
\(367\) 19.0000 + 19.0000i 0.991792 + 0.991792i 0.999967 0.00817466i \(-0.00260210\pi\)
−0.00817466 + 0.999967i \(0.502602\pi\)
\(368\) −1.00000 1.00000i −0.0521286 0.0521286i
\(369\) −7.00000 7.00000i −0.364405 0.364405i
\(370\) 3.00000 1.00000i 0.155963 0.0519875i
\(371\) −10.0000 10.0000i −0.519174 0.519174i
\(372\) 6.00000 0.311086
\(373\) 20.0000i 1.03556i 0.855514 + 0.517780i \(0.173242\pi\)
−0.855514 + 0.517780i \(0.826758\pi\)
\(374\) −5.00000 3.00000i −0.258544 0.155126i
\(375\) −13.0000 9.00000i −0.671317 0.464758i
\(376\) 6.00000i 0.309426i
\(377\) 20.0000 20.0000i 1.03005 1.03005i
\(378\) 8.00000i 0.411476i
\(379\) −5.00000 5.00000i −0.256833 0.256833i 0.566932 0.823765i \(-0.308130\pi\)
−0.823765 + 0.566932i \(0.808130\pi\)
\(380\) 6.00000 12.0000i 0.307794 0.615587i
\(381\) −8.00000 + 8.00000i −0.409852 + 0.409852i
\(382\) −24.0000 −1.22795
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) −1.00000 + 1.00000i −0.0510310 + 0.0510310i
\(385\) −4.00000 2.00000i −0.203859 0.101929i
\(386\) −13.0000 13.0000i −0.661683 0.661683i
\(387\) 4.00000i 0.203331i
\(388\) 3.00000 3.00000i 0.152302 0.152302i
\(389\) 12.0000i 0.608424i −0.952604 0.304212i \(-0.901607\pi\)
0.952604 0.304212i \(-0.0983931\pi\)
\(390\) −4.00000 12.0000i −0.202548 0.607644i
\(391\) −3.00000 + 5.00000i −0.151717 + 0.252861i
\(392\) 5.00000i 0.252538i
\(393\) 18.0000 0.907980
\(394\) −7.00000 7.00000i −0.352655 0.352655i
\(395\) −3.00000 + 1.00000i −0.150946 + 0.0503155i
\(396\) 1.00000 + 1.00000i 0.0502519 + 0.0502519i
\(397\) −7.00000 7.00000i −0.351320 0.351320i 0.509281 0.860601i \(-0.329912\pi\)
−0.860601 + 0.509281i \(0.829912\pi\)
\(398\) 17.0000 + 17.0000i 0.852133 + 0.852133i
\(399\) 12.0000i 0.600751i
\(400\) 3.00000 + 4.00000i 0.150000 + 0.200000i
\(401\) −19.0000 + 19.0000i −0.948815 + 0.948815i −0.998752 0.0499376i \(-0.984098\pi\)
0.0499376 + 0.998752i \(0.484098\pi\)
\(402\) 2.00000 + 2.00000i 0.0997509 + 0.0997509i
\(403\) 12.0000 12.0000i 0.597763 0.597763i
\(404\) −14.0000 −0.696526
\(405\) 10.0000 + 5.00000i 0.496904 + 0.248452i
\(406\) 10.0000i 0.496292i
\(407\) 2.00000i 0.0991363i
\(408\) 5.00000 + 3.00000i 0.247537 + 0.148522i
\(409\) −22.0000 −1.08783 −0.543915 0.839140i \(-0.683059\pi\)
−0.543915 + 0.839140i \(0.683059\pi\)
\(410\) −21.0000 + 7.00000i −1.03712 + 0.345705i
\(411\) 12.0000 + 12.0000i 0.591916 + 0.591916i
\(412\) 14.0000i 0.689730i
\(413\) 10.0000 10.0000i 0.492068 0.492068i
\(414\) 1.00000 1.00000i 0.0491473 0.0491473i
\(415\) −24.0000 12.0000i −1.17811 0.589057i
\(416\) 4.00000i 0.196116i
\(417\) −6.00000 −0.293821
\(418\) −6.00000 6.00000i −0.293470 0.293470i
\(419\) 17.0000 17.0000i 0.830504 0.830504i −0.157081 0.987586i \(-0.550208\pi\)
0.987586 + 0.157081i \(0.0502085\pi\)
\(420\) 4.00000 + 2.00000i 0.195180 + 0.0975900i
\(421\) 26.0000 1.26716 0.633581 0.773676i \(-0.281584\pi\)
0.633581 + 0.773676i \(0.281584\pi\)
\(422\) 13.0000 13.0000i 0.632830 0.632830i
\(423\) −6.00000 −0.291730
\(424\) 10.0000 0.485643
\(425\) 13.0000 16.0000i 0.630593 0.776114i
\(426\) −10.0000 −0.484502
\(427\) −6.00000 −0.290360
\(428\) −13.0000 + 13.0000i −0.628379 + 0.628379i
\(429\) −8.00000 −0.386244
\(430\) 8.00000 + 4.00000i 0.385794 + 0.192897i
\(431\) 7.00000 7.00000i 0.337178 0.337178i −0.518126 0.855304i \(-0.673370\pi\)
0.855304 + 0.518126i \(0.173370\pi\)
\(432\) −4.00000 4.00000i −0.192450 0.192450i
\(433\) −30.0000 −1.44171 −0.720854 0.693087i \(-0.756250\pi\)
−0.720854 + 0.693087i \(0.756250\pi\)
\(434\) 6.00000i 0.288009i
\(435\) 20.0000 + 10.0000i 0.958927 + 0.479463i
\(436\) 7.00000 7.00000i 0.335239 0.335239i
\(437\) −6.00000 + 6.00000i −0.287019 + 0.287019i
\(438\) 2.00000i 0.0955637i
\(439\) −11.0000 11.0000i −0.525001 0.525001i 0.394076 0.919078i \(-0.371065\pi\)
−0.919078 + 0.394076i \(0.871065\pi\)
\(440\) 3.00000 1.00000i 0.143019 0.0476731i
\(441\) 5.00000 0.238095
\(442\) 16.0000 4.00000i 0.761042 0.190261i
\(443\) 10.0000i 0.475114i −0.971374 0.237557i \(-0.923653\pi\)
0.971374 0.237557i \(-0.0763467\pi\)
\(444\) 2.00000i 0.0949158i
\(445\) 12.0000 + 6.00000i 0.568855 + 0.284427i
\(446\) 24.0000 1.13643
\(447\) −6.00000 + 6.00000i −0.283790 + 0.283790i
\(448\) −1.00000 1.00000i −0.0472456 0.0472456i
\(449\) 5.00000 5.00000i 0.235965 0.235965i −0.579212 0.815177i \(-0.696640\pi\)
0.815177 + 0.579212i \(0.196640\pi\)
\(450\) −4.00000 + 3.00000i −0.188562 + 0.141421i
\(451\) 14.0000i 0.659234i
\(452\) 11.0000 + 11.0000i 0.517396 + 0.517396i
\(453\) −2.00000 2.00000i −0.0939682 0.0939682i
\(454\) 9.00000 + 9.00000i 0.422391 + 0.422391i
\(455\) 12.0000 4.00000i 0.562569 0.187523i
\(456\) 6.00000 + 6.00000i 0.280976 + 0.280976i
\(457\) 10.0000 0.467780 0.233890 0.972263i \(-0.424854\pi\)
0.233890 + 0.972263i \(0.424854\pi\)
\(458\) 28.0000i 1.30835i
\(459\) −12.0000 + 20.0000i −0.560112 + 0.933520i
\(460\) −1.00000 3.00000i −0.0466252 0.139876i
\(461\) 8.00000i 0.372597i −0.982493 0.186299i \(-0.940351\pi\)
0.982493 0.186299i \(-0.0596492\pi\)
\(462\) 2.00000 2.00000i 0.0930484 0.0930484i
\(463\) 30.0000i 1.39422i 0.716965 + 0.697109i \(0.245531\pi\)
−0.716965 + 0.697109i \(0.754469\pi\)
\(464\) −5.00000 5.00000i −0.232119 0.232119i
\(465\) 12.0000 + 6.00000i 0.556487 + 0.278243i
\(466\) −1.00000 + 1.00000i −0.0463241 + 0.0463241i
\(467\) −28.0000 −1.29569 −0.647843 0.761774i \(-0.724329\pi\)
−0.647843 + 0.761774i \(0.724329\pi\)
\(468\) −4.00000 −0.184900
\(469\) −2.00000 + 2.00000i −0.0923514 + 0.0923514i
\(470\) −6.00000 + 12.0000i −0.276759 + 0.553519i
\(471\) 16.0000 + 16.0000i 0.737241 + 0.737241i
\(472\) 10.0000i 0.460287i
\(473\) 4.00000 4.00000i 0.183920 0.183920i
\(474\) 2.00000i 0.0918630i
\(475\) 24.0000 18.0000i 1.10120 0.825897i
\(476\) −3.00000 + 5.00000i −0.137505 + 0.229175i
\(477\) 10.0000i 0.457869i
\(478\) 16.0000 0.731823
\(479\) −15.0000 15.0000i −0.685367 0.685367i 0.275837 0.961204i \(-0.411045\pi\)
−0.961204 + 0.275837i \(0.911045\pi\)
\(480\) −3.00000 + 1.00000i −0.136931 + 0.0456435i
\(481\) 4.00000 + 4.00000i 0.182384 + 0.182384i
\(482\) 9.00000 + 9.00000i 0.409939 + 0.409939i
\(483\) −2.00000 2.00000i −0.0910032 0.0910032i
\(484\) 9.00000i 0.409091i
\(485\) 9.00000 3.00000i 0.408669 0.136223i
\(486\) 7.00000 7.00000i 0.317526 0.317526i
\(487\) −5.00000 5.00000i −0.226572 0.226572i 0.584687 0.811259i \(-0.301217\pi\)
−0.811259 + 0.584687i \(0.801217\pi\)
\(488\) 3.00000 3.00000i 0.135804 0.135804i
\(489\) 30.0000 1.35665
\(490\) 5.00000 10.0000i 0.225877 0.451754i
\(491\) 18.0000i 0.812329i 0.913800 + 0.406164i \(0.133134\pi\)
−0.913800 + 0.406164i \(0.866866\pi\)
\(492\) 14.0000i 0.631169i
\(493\) −15.0000 + 25.0000i −0.675566 + 1.12594i
\(494\) 24.0000 1.07981
\(495\) 1.00000 + 3.00000i 0.0449467 + 0.134840i
\(496\) −3.00000 3.00000i −0.134704 0.134704i
\(497\) 10.0000i 0.448561i
\(498\) 12.0000 12.0000i 0.537733 0.537733i
\(499\) 21.0000 21.0000i 0.940089 0.940089i −0.0582150 0.998304i \(-0.518541\pi\)
0.998304 + 0.0582150i \(0.0185409\pi\)
\(500\) 2.00000 + 11.0000i 0.0894427 + 0.491935i
\(501\) 14.0000i 0.625474i
\(502\) −20.0000 −0.892644
\(503\) −5.00000 5.00000i −0.222939 0.222939i 0.586796 0.809735i \(-0.300389\pi\)
−0.809735 + 0.586796i \(0.800389\pi\)
\(504\) 1.00000 1.00000i 0.0445435 0.0445435i
\(505\) −28.0000 14.0000i −1.24598 0.622992i
\(506\) −2.00000 −0.0889108
\(507\) 3.00000 3.00000i 0.133235 0.133235i
\(508\) 8.00000 0.354943
\(509\) 14.0000 0.620539 0.310270 0.950649i \(-0.399581\pi\)
0.310270 + 0.950649i \(0.399581\pi\)
\(510\) 7.00000 + 11.0000i 0.309965 + 0.487088i
\(511\) 2.00000 0.0884748
\(512\) 1.00000 0.0441942
\(513\) −24.0000 + 24.0000i −1.05963 + 1.05963i
\(514\) −30.0000 −1.32324
\(515\) −14.0000 + 28.0000i −0.616914 + 1.23383i
\(516\) −4.00000 + 4.00000i −0.176090 + 0.176090i
\(517\) 6.00000 + 6.00000i 0.263880 + 0.263880i
\(518\) −2.00000 −0.0878750
\(519\) 14.0000i 0.614532i
\(520\) −4.00000 + 8.00000i −0.175412 + 0.350823i
\(521\) −11.0000 + 11.0000i −0.481919 + 0.481919i −0.905744 0.423825i \(-0.860687\pi\)
0.423825 + 0.905744i \(0.360687\pi\)
\(522\) 5.00000 5.00000i 0.218844 0.218844i
\(523\) 42.0000i 1.83653i −0.395964 0.918266i \(-0.629590\pi\)
0.395964 0.918266i \(-0.370410\pi\)
\(524\) −9.00000 9.00000i −0.393167 0.393167i
\(525\) 6.00000 + 8.00000i 0.261861 + 0.349149i
\(526\) 24.0000 1.04645
\(527\) −9.00000 + 15.0000i −0.392046 + 0.653410i
\(528\) 2.00000i 0.0870388i
\(529\) 21.0000i 0.913043i
\(530\) 20.0000 + 10.0000i 0.868744 + 0.434372i
\(531\) −10.0000 −0.433963
\(532\) −6.00000 + 6.00000i −0.260133 + 0.260133i
\(533\) −28.0000 28.0000i −1.21281 1.21281i
\(534\) −6.00000 + 6.00000i −0.259645 + 0.259645i
\(535\) −39.0000 + 13.0000i −1.68612 + 0.562039i
\(536\) 2.00000i 0.0863868i
\(537\) 6.00000 + 6.00000i 0.258919 + 0.258919i
\(538\) 11.0000 + 11.0000i 0.474244 + 0.474244i
\(539\) −5.00000 5.00000i −0.215365 0.215365i
\(540\) −4.00000 12.0000i −0.172133 0.516398i
\(541\) 3.00000 + 3.00000i 0.128980 + 0.128980i 0.768650 0.639670i \(-0.220929\pi\)
−0.639670 + 0.768650i \(0.720929\pi\)
\(542\) −8.00000 −0.343629
\(543\) 14.0000i 0.600798i
\(544\) −1.00000 4.00000i −0.0428746 0.171499i
\(545\) 21.0000 7.00000i 0.899541 0.299847i
\(546\) 8.00000i 0.342368i
\(547\) 3.00000 3.00000i 0.128271 0.128271i −0.640057 0.768328i \(-0.721089\pi\)
0.768328 + 0.640057i \(0.221089\pi\)
\(548\) 12.0000i 0.512615i
\(549\) 3.00000 + 3.00000i 0.128037 + 0.128037i
\(550\) 7.00000 + 1.00000i 0.298481 + 0.0426401i
\(551\) −30.0000 + 30.0000i −1.27804 + 1.27804i
\(552\) 2.00000 0.0851257
\(553\) 2.00000 0.0850487
\(554\) 5.00000 5.00000i 0.212430 0.212430i
\(555\) −2.00000 + 4.00000i −0.0848953 + 0.169791i
\(556\) 3.00000 + 3.00000i 0.127228 + 0.127228i
\(557\) 20.0000i 0.847427i −0.905796 0.423714i \(-0.860726\pi\)
0.905796 0.423714i \(-0.139274\pi\)
\(558\) 3.00000 3.00000i 0.127000 0.127000i
\(559\) 16.0000i 0.676728i
\(560\) −1.00000 3.00000i −0.0422577 0.126773i
\(561\) 8.00000 2.00000i 0.337760 0.0844401i
\(562\) 0 0
\(563\) −4.00000 −0.168580 −0.0842900 0.996441i \(-0.526862\pi\)
−0.0842900 + 0.996441i \(0.526862\pi\)
\(564\) −6.00000 6.00000i −0.252646 0.252646i
\(565\) 11.0000 + 33.0000i 0.462773 + 1.38832i
\(566\) −19.0000 19.0000i −0.798630 0.798630i
\(567\) −5.00000 5.00000i −0.209980 0.209980i
\(568\) 5.00000 + 5.00000i 0.209795 + 0.209795i
\(569\) 8.00000i 0.335377i 0.985840 + 0.167689i \(0.0536304\pi\)
−0.985840 + 0.167689i \(0.946370\pi\)
\(570\) 6.00000 + 18.0000i 0.251312 + 0.753937i
\(571\) 25.0000 25.0000i 1.04622 1.04622i 0.0473385 0.998879i \(-0.484926\pi\)
0.998879 0.0473385i \(-0.0150740\pi\)
\(572\) 4.00000 + 4.00000i 0.167248 + 0.167248i
\(573\) 24.0000 24.0000i 1.00261 1.00261i
\(574\) 14.0000 0.584349
\(575\) 1.00000 7.00000i 0.0417029 0.291920i
\(576\) 1.00000i 0.0416667i
\(577\) 20.0000i 0.832611i −0.909225 0.416305i \(-0.863325\pi\)
0.909225 0.416305i \(-0.136675\pi\)
\(578\) −15.0000 + 8.00000i −0.623918 + 0.332756i
\(579\) 26.0000 1.08052
\(580\) −5.00000 15.0000i −0.207614 0.622841i
\(581\) 12.0000 + 12.0000i 0.497844 + 0.497844i
\(582\) 6.00000i 0.248708i
\(583\) 10.0000 10.0000i 0.414158 0.414158i
\(584\) −1.00000 + 1.00000i −0.0413803 + 0.0413803i
\(585\) −8.00000 4.00000i −0.330759 0.165380i
\(586\) 24.0000i 0.991431i
\(587\) 4.00000 0.165098 0.0825488 0.996587i \(-0.473694\pi\)
0.0825488 + 0.996587i \(0.473694\pi\)
\(588\) 5.00000 + 5.00000i 0.206197 + 0.206197i
\(589\) −18.0000 + 18.0000i −0.741677 + 0.741677i
\(590\) −10.0000 + 20.0000i −0.411693 + 0.823387i
\(591\) 14.0000 0.575883
\(592\) 1.00000 1.00000i 0.0410997 0.0410997i
\(593\) 38.0000 1.56047 0.780236 0.625485i \(-0.215099\pi\)
0.780236 + 0.625485i \(0.215099\pi\)
\(594\) −8.00000 −0.328244
\(595\) −11.0000 + 7.00000i −0.450956 + 0.286972i
\(596\) 6.00000 0.245770
\(597\) −34.0000 −1.39153
\(598\) 4.00000 4.00000i 0.163572 0.163572i
\(599\) 16.0000 0.653742 0.326871 0.945069i \(-0.394006\pi\)
0.326871 + 0.945069i \(0.394006\pi\)
\(600\) −7.00000 1.00000i −0.285774 0.0408248i
\(601\) −11.0000 + 11.0000i −0.448699 + 0.448699i −0.894922 0.446223i \(-0.852769\pi\)
0.446223 + 0.894922i \(0.352769\pi\)
\(602\) −4.00000 4.00000i −0.163028 0.163028i
\(603\) 2.00000 0.0814463
\(604\) 2.00000i 0.0813788i
\(605\) −9.00000 + 18.0000i −0.365902 + 0.731804i
\(606\) 14.0000 14.0000i 0.568711 0.568711i
\(607\) −3.00000 + 3.00000i −0.121766 + 0.121766i −0.765364 0.643598i \(-0.777441\pi\)
0.643598 + 0.765364i \(0.277441\pi\)
\(608\) 6.00000i 0.243332i
\(609\) −10.0000 10.0000i −0.405220 0.405220i
\(610\) 9.00000 3.00000i 0.364399 0.121466i
\(611\) −24.0000 −0.970936
\(612\) 4.00000 1.00000i 0.161690 0.0404226i
\(613\) 8.00000i 0.323117i 0.986863 + 0.161558i \(0.0516520\pi\)
−0.986863 + 0.161558i \(0.948348\pi\)
\(614\) 2.00000i 0.0807134i
\(615\) 14.0000 28.0000i 0.564534 1.12907i
\(616\) −2.00000 −0.0805823
\(617\) −5.00000 + 5.00000i −0.201292 + 0.201292i −0.800554 0.599261i \(-0.795461\pi\)
0.599261 + 0.800554i \(0.295461\pi\)
\(618\) −14.0000 14.0000i −0.563163 0.563163i
\(619\) 5.00000 5.00000i 0.200967 0.200967i −0.599447 0.800414i \(-0.704613\pi\)
0.800414 + 0.599447i \(0.204613\pi\)
\(620\) −3.00000 9.00000i −0.120483 0.361449i
\(621\) 8.00000i 0.321029i
\(622\) 17.0000 + 17.0000i 0.681638 + 0.681638i
\(623\) −6.00000 6.00000i −0.240385 0.240385i
\(624\) −4.00000 4.00000i −0.160128 0.160128i
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) 3.00000 + 3.00000i 0.119904 + 0.119904i
\(627\) 12.0000 0.479234
\(628\) 16.0000i 0.638470i
\(629\) −5.00000 3.00000i −0.199363 0.119618i
\(630\) 3.00000 1.00000i 0.119523 0.0398410i
\(631\) 46.0000i 1.83123i −0.402055 0.915616i \(-0.631704\pi\)
0.402055 0.915616i \(-0.368296\pi\)
\(632\) −1.00000 + 1.00000i −0.0397779 + 0.0397779i
\(633\) 26.0000i 1.03341i
\(634\) 5.00000 + 5.00000i 0.198575 + 0.198575i
\(635\) 16.0000 + 8.00000i 0.634941 + 0.317470i
\(636\) −10.0000 + 10.0000i −0.396526 + 0.396526i
\(637\) 20.0000 0.792429
\(638\) −10.0000 −0.395904
\(639\) −5.00000 + 5.00000i −0.197797 + 0.197797i
\(640\) 2.00000 + 1.00000i 0.0790569 + 0.0395285i
\(641\) −3.00000 3.00000i −0.118493 0.118493i 0.645374 0.763867i \(-0.276702\pi\)
−0.763867 + 0.645374i \(0.776702\pi\)
\(642\) 26.0000i 1.02614i
\(643\) 31.0000 31.0000i 1.22252 1.22252i 0.255788 0.966733i \(-0.417665\pi\)
0.966733 0.255788i \(-0.0823348\pi\)
\(644\) 2.00000i 0.0788110i
\(645\) −12.0000 + 4.00000i −0.472500 + 0.157500i
\(646\) −24.0000 + 6.00000i −0.944267 + 0.236067i
\(647\) 26.0000i 1.02217i −0.859532 0.511083i \(-0.829245\pi\)
0.859532 0.511083i \(-0.170755\pi\)
\(648\) 5.00000 0.196419
\(649\) 10.0000 + 10.0000i 0.392534 + 0.392534i
\(650\) −16.0000 + 12.0000i −0.627572 + 0.470679i
\(651\) −6.00000 6.00000i −0.235159 0.235159i
\(652\) −15.0000 15.0000i −0.587445 0.587445i
\(653\) 29.0000 + 29.0000i 1.13486 + 1.13486i 0.989358 + 0.145499i \(0.0464789\pi\)
0.145499 + 0.989358i \(0.453521\pi\)
\(654\) 14.0000i 0.547443i
\(655\) −9.00000 27.0000i −0.351659 1.05498i
\(656\) −7.00000 + 7.00000i −0.273304 + 0.273304i
\(657\) −1.00000 1.00000i −0.0390137 0.0390137i
\(658\) 6.00000 6.00000i 0.233904 0.233904i
\(659\) −36.0000 −1.40236 −0.701180 0.712984i \(-0.747343\pi\)
−0.701180 + 0.712984i \(0.747343\pi\)
\(660\) −2.00000 + 4.00000i −0.0778499 + 0.155700i
\(661\) 40.0000i 1.55582i −0.628376 0.777910i \(-0.716280\pi\)
0.628376 0.777910i \(-0.283720\pi\)
\(662\) 10.0000i 0.388661i
\(663\) −12.0000 + 20.0000i −0.466041 + 0.776736i
\(664\) −12.0000 −0.465690
\(665\) −18.0000 + 6.00000i −0.698010 + 0.232670i
\(666\) 1.00000 + 1.00000i 0.0387492 + 0.0387492i
\(667\) 10.0000i 0.387202i
\(668\) −7.00000 + 7.00000i −0.270838 + 0.270838i
\(669\) −24.0000 + 24.0000i −0.927894 + 0.927894i
\(670\) 2.00000 4.00000i 0.0772667 0.154533i
\(671\) 6.00000i 0.231627i
\(672\) 2.00000 0.0771517
\(673\) −1.00000 1.00000i −0.0385472 0.0385472i 0.687570 0.726118i \(-0.258677\pi\)
−0.726118 + 0.687570i \(0.758677\pi\)
\(674\) −5.00000 + 5.00000i −0.192593 + 0.192593i
\(675\) 4.00000 28.0000i 0.153960 1.07772i
\(676\) −3.00000 −0.115385
\(677\) 17.0000 17.0000i 0.653363 0.653363i −0.300438 0.953801i \(-0.597133\pi\)
0.953801 + 0.300438i \(0.0971329\pi\)
\(678\) −22.0000 −0.844905
\(679\) −6.00000 −0.230259
\(680\) 2.00000 9.00000i 0.0766965 0.345134i
\(681\) −18.0000 −0.689761
\(682\) −6.00000 −0.229752
\(683\) −17.0000 + 17.0000i −0.650487 + 0.650487i −0.953110 0.302623i \(-0.902138\pi\)
0.302623 + 0.953110i \(0.402138\pi\)
\(684\) 6.00000 0.229416
\(685\) 12.0000 24.0000i 0.458496 0.916993i
\(686\) −12.0000 + 12.0000i −0.458162 + 0.458162i
\(687\) −28.0000 28.0000i −1.06827 1.06827i
\(688\) 4.00000 0.152499
\(689\) 40.0000i 1.52388i
\(690\) 4.00000 + 2.00000i 0.152277 + 0.0761387i
\(691\) −31.0000 + 31.0000i −1.17930 + 1.17930i −0.199372 + 0.979924i \(0.563890\pi\)
−0.979924 + 0.199372i \(0.936110\pi\)
\(692\) −7.00000 + 7.00000i −0.266100 + 0.266100i
\(693\) 2.00000i 0.0759737i
\(694\) 25.0000 + 25.0000i 0.948987 + 0.948987i
\(695\) 3.00000 + 9.00000i 0.113796 + 0.341389i
\(696\) 10.0000 0.379049
\(697\) 35.0000 + 21.0000i 1.32572 + 0.795432i
\(698\) 0 0
\(699\) 2.00000i 0.0756469i
\(700\) 1.00000 7.00000i 0.0377964 0.264575i
\(701\) 2.00000 0.0755390 0.0377695 0.999286i \(-0.487975\pi\)
0.0377695 + 0.999286i \(0.487975\pi\)
\(702\) 16.0000 16.0000i 0.603881 0.603881i
\(703\) −6.00000 6.00000i −0.226294 0.226294i
\(704\) 1.00000 1.00000i 0.0376889 0.0376889i
\(705\) −6.00000 18.0000i −0.225973 0.677919i
\(706\) 24.0000i 0.903252i
\(707\) 14.0000 + 14.0000i 0.526524 + 0.526524i
\(708\) −10.0000 10.0000i −0.375823 0.375823i
\(709\) −13.0000 13.0000i −0.488225 0.488225i 0.419521 0.907746i \(-0.362198\pi\)
−0.907746 + 0.419521i \(0.862198\pi\)
\(710\) 5.00000 + 15.0000i 0.187647 + 0.562940i
\(711\) −1.00000 1.00000i −0.0375029 0.0375029i
\(712\) 6.00000 0.224860
\(713\) 6.00000i 0.224702i
\(714\) −2.00000 8.00000i −0.0748481 0.299392i
\(715\) 4.00000 + 12.0000i 0.149592 + 0.448775i
\(716\) 6.00000i 0.224231i
\(717\) −16.0000 + 16.0000i −0.597531 + 0.597531i
\(718\) 6.00000i 0.223918i
\(719\) −3.00000 3.00000i −0.111881 0.111881i 0.648950 0.760831i \(-0.275208\pi\)
−0.760831 + 0.648950i \(0.775208\pi\)
\(720\) −1.00000 + 2.00000i −0.0372678 + 0.0745356i
\(721\) 14.0000 14.0000i 0.521387 0.521387i
\(722\) −17.0000 −0.632674
\(723\) −18.0000 −0.669427
\(724\) 7.00000 7.00000i 0.260153 0.260153i
\(725\) 5.00000 35.0000i 0.185695 1.29987i
\(726\) −9.00000 9.00000i −0.334021 0.334021i
\(727\) 2.00000i 0.0741759i −0.999312 0.0370879i \(-0.988192\pi\)
0.999312 0.0370879i \(-0.0118082\pi\)
\(728\) 4.00000 4.00000i 0.148250 0.148250i
\(729\) 29.0000i 1.07407i
\(730\) −3.00000 + 1.00000i −0.111035 + 0.0370117i
\(731\) −4.00000 16.0000i −0.147945 0.591781i
\(732\) 6.00000i 0.221766i
\(733\) 50.0000 1.84679 0.923396 0.383849i \(-0.125402\pi\)
0.923396 + 0.383849i \(0.125402\pi\)
\(734\) 19.0000 + 19.0000i 0.701303 + 0.701303i
\(735\) 5.00000 + 15.0000i 0.184428 + 0.553283i
\(736\) −1.00000 1.00000i −0.0368605 0.0368605i
\(737\) −2.00000 2.00000i −0.0736709 0.0736709i
\(738\) −7.00000 7.00000i −0.257674 0.257674i
\(739\) 14.0000i 0.514998i −0.966279 0.257499i \(-0.917102\pi\)
0.966279 0.257499i \(-0.0828985\pi\)
\(740\) 3.00000 1.00000i 0.110282 0.0367607i
\(741\) −24.0000 + 24.0000i −0.881662 + 0.881662i
\(742\) −10.0000 10.0000i −0.367112 0.367112i
\(743\) −19.0000 + 19.0000i −0.697042 + 0.697042i −0.963772 0.266729i \(-0.914057\pi\)
0.266729 + 0.963772i \(0.414057\pi\)
\(744\) 6.00000 0.219971
\(745\) 12.0000 + 6.00000i 0.439646 + 0.219823i
\(746\) 20.0000i 0.732252i
\(747\) 12.0000i 0.439057i
\(748\) −5.00000 3.00000i −0.182818 0.109691i
\(749\) 26.0000 0.950019
\(750\) −13.0000 9.00000i −0.474693 0.328634i
\(751\) −11.0000 11.0000i −0.401396 0.401396i 0.477329 0.878725i \(-0.341605\pi\)
−0.878725 + 0.477329i \(0.841605\pi\)
\(752\) 6.00000i 0.218797i
\(753\) 20.0000 20.0000i 0.728841 0.728841i
\(754\) 20.0000 20.0000i 0.728357 0.728357i
\(755\) −2.00000 + 4.00000i −0.0727875 + 0.145575i
\(756\) 8.00000i 0.290957i
\(757\) −18.0000 −0.654221 −0.327111 0.944986i \(-0.606075\pi\)
−0.327111 + 0.944986i \(0.606075\pi\)
\(758\) −5.00000 5.00000i −0.181608 0.181608i
\(759\) 2.00000 2.00000i 0.0725954 0.0725954i
\(760\) 6.00000 12.0000i 0.217643 0.435286i
\(761\) 22.0000 0.797499 0.398750 0.917060i \(-0.369444\pi\)
0.398750 + 0.917060i \(0.369444\pi\)
\(762\) −8.00000 + 8.00000i −0.289809 + 0.289809i
\(763\) −14.0000 −0.506834
\(764\) −24.0000 −0.868290
\(765\) 9.00000 + 2.00000i 0.325396 + 0.0723102i
\(766\) 0 0
\(767\) −40.0000 −1.44432
\(768\) −1.00000 + 1.00000i −0.0360844 + 0.0360844i
\(769\) 30.0000 1.08183 0.540914 0.841078i \(-0.318079\pi\)
0.540914 + 0.841078i \(0.318079\pi\)
\(770\) −4.00000 2.00000i −0.144150 0.0720750i
\(771\) 30.0000 30.0000i 1.08042 1.08042i
\(772\) −13.0000 13.0000i −0.467880 0.467880i
\(773\) 6.00000 0.215805 0.107903 0.994161i \(-0.465587\pi\)
0.107903 + 0.994161i \(0.465587\pi\)
\(774\) 4.00000i 0.143777i
\(775\) 3.00000 21.0000i 0.107763 0.754342i
\(776\) 3.00000 3.00000i 0.107694 0.107694i
\(777\) 2.00000 2.00000i 0.0717496 0.0717496i
\(778\) 12.0000i 0.430221i
\(779\) 42.0000 + 42.0000i 1.50481 + 1.50481i
\(780\) −4.00000 12.0000i −0.143223 0.429669i
\(781\) 10.0000 0.357828
\(782\) −3.00000 + 5.00000i −0.107280 + 0.178800i
\(783\) 40.0000i 1.42948i
\(784\) 5.00000i 0.178571i
\(785\) 16.0000 32.0000i 0.571064 1.14213i
\(786\) 18.0000 0.642039
\(787\) 15.0000 15.0000i 0.534692 0.534692i −0.387273 0.921965i \(-0.626583\pi\)
0.921965 + 0.387273i \(0.126583\pi\)
\(788\) −7.00000 7.00000i −0.249365 0.249365i
\(789\) −24.0000 + 24.0000i −0.854423 + 0.854423i
\(790\) −3.00000 + 1.00000i −0.106735 + 0.0355784i
\(791\) 22.0000i 0.782230i
\(792\) 1.00000 + 1.00000i 0.0355335 + 0.0355335i
\(793\) 12.0000 + 12.0000i 0.426132 + 0.426132i
\(794\) −7.00000 7.00000i −0.248421 0.248421i
\(795\) −30.0000 + 10.0000i −1.06399 + 0.354663i
\(796\) 17.0000 + 17.0000i 0.602549 + 0.602549i
\(797\) 18.0000 0.637593 0.318796 0.947823i \(-0.396721\pi\)
0.318796 + 0.947823i \(0.396721\pi\)
\(798\) 12.0000i 0.424795i
\(799\) 24.0000 6.00000i 0.849059 0.212265i
\(800\) 3.00000 + 4.00000i 0.106066 + 0.141421i
\(801\) 6.00000i 0.212000i
\(802\) −19.0000 + 19.0000i −0.670913 + 0.670913i
\(803\) 2.00000i 0.0705785i
\(804\) 2.00000 + 2.00000i 0.0705346 + 0.0705346i
\(805\) −2.00000 + 4.00000i −0.0704907 + 0.140981i
\(806\) 12.0000 12.0000i 0.422682 0.422682i
\(807\) −22.0000 −0.774437
\(808\) −14.0000 −0.492518
\(809\) −23.0000 + 23.0000i −0.808637 + 0.808637i −0.984428 0.175791i \(-0.943752\pi\)
0.175791 + 0.984428i \(0.443752\pi\)
\(810\) 10.0000 + 5.00000i 0.351364 + 0.175682i
\(811\) 39.0000 + 39.0000i 1.36948 + 1.36948i 0.861187 + 0.508288i \(0.169722\pi\)
0.508288 + 0.861187i \(0.330278\pi\)
\(812\) 10.0000i 0.350931i
\(813\) 8.00000 8.00000i 0.280572 0.280572i
\(814\) 2.00000i 0.0701000i
\(815\) −15.0000 45.0000i −0.525427 1.57628i
\(816\) 5.00000 + 3.00000i 0.175035 + 0.105021i
\(817\) 24.0000i 0.839654i
\(818\) −22.0000 −0.769212
\(819\) 4.00000 + 4.00000i 0.139771 + 0.139771i
\(820\) −21.0000 + 7.00000i −0.733352 + 0.244451i
\(821\) −5.00000 5.00000i −0.174501 0.174501i 0.614453 0.788954i \(-0.289377\pi\)
−0.788954 + 0.614453i \(0.789377\pi\)
\(822\) 12.0000 + 12.0000i 0.418548 + 0.418548i
\(823\) 15.0000 + 15.0000i 0.522867 + 0.522867i 0.918436 0.395569i \(-0.129453\pi\)
−0.395569 + 0.918436i \(0.629453\pi\)
\(824\) 14.0000i 0.487713i
\(825\) −8.00000 + 6.00000i −0.278524 + 0.208893i
\(826\) 10.0000 10.0000i 0.347945 0.347945i
\(827\) 9.00000 + 9.00000i 0.312961 + 0.312961i 0.846055 0.533095i \(-0.178971\pi\)
−0.533095 + 0.846055i \(0.678971\pi\)
\(828\) 1.00000 1.00000i 0.0347524 0.0347524i
\(829\) 14.0000 0.486240 0.243120 0.969996i \(-0.421829\pi\)
0.243120 + 0.969996i \(0.421829\pi\)
\(830\) −24.0000 12.0000i −0.833052 0.416526i
\(831\) 10.0000i 0.346896i
\(832\) 4.00000i 0.138675i
\(833\) −20.0000 + 5.00000i −0.692959 + 0.173240i
\(834\) −6.00000 −0.207763
\(835\) −21.0000 + 7.00000i −0.726735 + 0.242245i
\(836\) −6.00000 6.00000i −0.207514 0.207514i
\(837\) 24.0000i 0.829561i
\(838\) 17.0000 17.0000i 0.587255 0.587255i
\(839\) −9.00000 + 9.00000i −0.310715 + 0.310715i −0.845186 0.534472i \(-0.820511\pi\)
0.534472 + 0.845186i \(0.320511\pi\)
\(840\) 4.00000 + 2.00000i 0.138013 + 0.0690066i
\(841\) 21.0000i 0.724138i
\(842\) 26.0000 0.896019
\(843\) 0 0
\(844\) 13.0000 13.0000i 0.447478 0.447478i
\(845\) −6.00000 3.00000i −0.206406 0.103203i
\(846\) −6.00000 −0.206284
\(847\) 9.00000 9.00000i 0.309244 0.309244i
\(848\) 10.0000 0.343401
\(849\) 38.0000 1.30416
\(850\) 13.0000 16.0000i 0.445896 0.548795i
\(851\) −2.00000 −0.0685591
\(852\) −10.0000 −0.342594
\(853\) −35.0000 + 35.0000i −1.19838 + 1.19838i −0.223725 + 0.974652i \(0.571822\pi\)
−0.974652 + 0.223725i \(0.928178\pi\)
\(854\) −6.00000 −0.205316
\(855\) 12.0000 + 6.00000i 0.410391 + 0.205196i
\(856\) −13.0000 + 13.0000i −0.444331 + 0.444331i
\(857\) 27.0000 + 27.0000i 0.922302 + 0.922302i 0.997192 0.0748894i \(-0.0238604\pi\)
−0.0748894 + 0.997192i \(0.523860\pi\)
\(858\) −8.00000 −0.273115
\(859\) 6.00000i 0.204717i −0.994748 0.102359i \(-0.967361\pi\)
0.994748 0.102359i \(-0.0326389\pi\)
\(860\) 8.00000 + 4.00000i 0.272798 + 0.136399i
\(861\) −14.0000 + 14.0000i −0.477119 + 0.477119i
\(862\) 7.00000 7.00000i 0.238421 0.238421i
\(863\) 14.0000i 0.476566i 0.971196 + 0.238283i \(0.0765845\pi\)
−0.971196 + 0.238283i \(0.923415\pi\)
\(864\) −4.00000 4.00000i −0.136083 0.136083i
\(865\) −21.0000 + 7.00000i −0.714021 + 0.238007i
\(866\) −30.0000 −1.01944
\(867\) 7.00000 23.0000i 0.237732 0.781121i
\(868\) 6.00000i 0.203653i
\(869\) 2.00000i 0.0678454i
\(870\) 20.0000 + 10.0000i 0.678064 + 0.339032i
\(871\) 8.00000 0.271070
\(872\) 7.00000 7.00000i 0.237050 0.237050i
\(873\) 3.00000 + 3.00000i 0.101535 + 0.101535i
\(874\) −6.00000 + 6.00000i −0.202953 + 0.202953i
\(875\) 9.00000 13.0000i 0.304256 0.439480i
\(876\) 2.00000i 0.0675737i
\(877\) 21.0000 + 21.0000i 0.709120 + 0.709120i 0.966350 0.257230i \(-0.0828100\pi\)
−0.257230 + 0.966350i \(0.582810\pi\)
\(878\) −11.0000 11.0000i −0.371232 0.371232i
\(879\) 24.0000 + 24.0000i 0.809500 + 0.809500i
\(880\) 3.00000 1.00000i 0.101130 0.0337100i
\(881\) 13.0000 + 13.0000i 0.437981 + 0.437981i 0.891332 0.453351i \(-0.149772\pi\)
−0.453351 + 0.891332i \(0.649772\pi\)
\(882\) 5.00000 0.168359
\(883\) 14.0000i 0.471138i 0.971858 + 0.235569i \(0.0756953\pi\)
−0.971858 + 0.235569i \(0.924305\pi\)
\(884\) 16.0000 4.00000i 0.538138 0.134535i
\(885\) −10.0000 30.0000i −0.336146 1.00844i
\(886\) 10.0000i 0.335957i
\(887\) 17.0000 17.0000i 0.570804 0.570804i −0.361549 0.932353i \(-0.617752\pi\)
0.932353 + 0.361549i \(0.117752\pi\)
\(888\) 2.00000i 0.0671156i
\(889\) −8.00000 8.00000i −0.268311 0.268311i
\(890\) 12.0000 + 6.00000i 0.402241 + 0.201120i
\(891\) 5.00000 5.00000i 0.167506 0.167506i
\(892\) 24.0000 0.803579
\(893\) 36.0000 1.20469
\(894\) −6.00000 + 6.00000i −0.200670 + 0.200670i
\(895\) 6.00000 12.0000i 0.200558 0.401116i
\(896\) −1.00000 1.00000i −0.0334077 0.0334077i
\(897\) 8.00000i 0.267112i
\(898\) 5.00000 5.00000i 0.166852 0.166852i
\(899\) 30.0000i 1.00056i
\(900\) −4.00000 + 3.00000i −0.133333 + 0.100000i
\(901\) −10.0000 40.0000i −0.333148 1.33259i
\(902\) 14.0000i 0.466149i
\(903\) 8.00000 0.266223
\(904\) 11.0000 + 11.0000i 0.365855 + 0.365855i
\(905\) 21.0000 7.00000i 0.698064 0.232688i
\(906\) −2.00000 2.00000i −0.0664455 0.0664455i
\(907\) 21.0000 + 21.0000i 0.697294 + 0.697294i 0.963826 0.266532i \(-0.0858779\pi\)
−0.266532 + 0.963826i \(0.585878\pi\)
\(908\) 9.00000 + 9.00000i 0.298675 + 0.298675i
\(909\) 14.0000i 0.464351i
\(910\) 12.0000 4.00000i 0.397796 0.132599i
\(911\) 7.00000 7.00000i 0.231920 0.231920i −0.581574 0.813494i \(-0.697563\pi\)
0.813494 + 0.581574i \(0.197563\pi\)
\(912\) 6.00000 + 6.00000i 0.198680 + 0.198680i
\(913\) −12.0000 + 12.0000i −0.397142 + 0.397142i
\(914\) 10.0000 0.330771
\(915\) −6.00000 + 12.0000i −0.198354 + 0.396708i
\(916\) 28.0000i 0.925146i
\(917\) 18.0000i 0.594412i
\(918\) −12.0000 + 20.0000i −0.396059 + 0.660098i
\(919\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(920\) −1.00000 3.00000i −0.0329690 0.0989071i
\(921\) 2.00000 + 2.00000i 0.0659022 + 0.0659022i
\(922\) 8.00000i 0.263466i
\(923\) −20.0000 + 20.0000i −0.658308 + 0.658308i
\(924\) 2.00000 2.00000i 0.0657952 0.0657952i
\(925\) 7.00000 + 1.00000i 0.230159 + 0.0328798i
\(926\) 30.0000i 0.985861i
\(927\) −14.0000 −0.459820
\(928\) −5.00000 5.00000i −0.164133 0.164133i
\(929\) 9.00000 9.00000i 0.295280 0.295280i −0.543882 0.839162i \(-0.683046\pi\)
0.839162 + 0.543882i \(0.183046\pi\)
\(930\) 12.0000 + 6.00000i 0.393496 + 0.196748i
\(931\) −30.0000 −0.983210
\(932\) −1.00000 + 1.00000i −0.0327561 + 0.0327561i
\(933\) −34.0000 −1.11311
\(934\) −28.0000 −0.916188
\(935\) −7.00000 11.0000i −0.228924 0.359738i
\(936\) −4.00000 −0.130744
\(937\) −2.00000 −0.0653372 −0.0326686 0.999466i \(-0.510401\pi\)
−0.0326686 + 0.999466i \(0.510401\pi\)
\(938\) −2.00000 + 2.00000i −0.0653023 + 0.0653023i
\(939\) −6.00000 −0.195803
\(940\) −6.00000 + 12.0000i −0.195698 + 0.391397i
\(941\) 19.0000 19.0000i 0.619382 0.619382i −0.325991 0.945373i \(-0.605698\pi\)
0.945373 + 0.325991i \(0.105698\pi\)
\(942\) 16.0000 + 16.0000i 0.521308 + 0.521308i
\(943\) 14.0000 0.455903
\(944\) 10.0000i 0.325472i
\(945\) −8.00000 + 16.0000i −0.260240 + 0.520480i
\(946\) 4.00000 4.00000i 0.130051 0.130051i
\(947\) −25.0000 + 25.0000i −0.812391 + 0.812391i −0.984992 0.172601i \(-0.944783\pi\)
0.172601 + 0.984992i \(0.444783\pi\)
\(948\) 2.00000i 0.0649570i
\(949\) −4.00000 4.00000i −0.129845 0.129845i
\(950\) 24.0000 18.0000i 0.778663 0.583997i
\(951\) −10.0000 −0.324272
\(952\) −3.00000 + 5.00000i −0.0972306 + 0.162051i
\(953\) 12.0000i 0.388718i −0.980930 0.194359i \(-0.937737\pi\)
0.980930 0.194359i \(-0.0622627\pi\)
\(954\) 10.0000i 0.323762i
\(955\) −48.0000 24.0000i −1.55324 0.776622i
\(956\) 16.0000 0.517477
\(957\) 10.0000 10.0000i 0.323254 0.323254i
\(958\) −15.0000 15.0000i −0.484628 0.484628i
\(959\) −12.0000 + 12.0000i −0.387500 + 0.387500i
\(960\) −3.00000 + 1.00000i −0.0968246 + 0.0322749i
\(961\) 13.0000i 0.419355i
\(962\) 4.00000 + 4.00000i 0.128965 + 0.128965i
\(963\) −13.0000 13.0000i −0.418919 0.418919i
\(964\) 9.00000 + 9.00000i 0.289870 + 0.289870i
\(965\) −13.0000 39.0000i −0.418485 1.25545i
\(966\) −2.00000 2.00000i −0.0643489 0.0643489i
\(967\) −48.0000 −1.54358 −0.771788 0.635880i \(-0.780637\pi\)
−0.771788 + 0.635880i \(0.780637\pi\)
\(968\) 9.00000i 0.289271i
\(969\) 18.0000 30.0000i 0.578243 0.963739i
\(970\) 9.00000 3.00000i 0.288973 0.0963242i
\(971\) 38.0000i 1.21948i −0.792602 0.609739i \(-0.791274\pi\)
0.792602 0.609739i \(-0.208726\pi\)
\(972\) 7.00000 7.00000i 0.224525 0.224525i
\(973\) 6.00000i 0.192351i
\(974\) −5.00000 5.00000i −0.160210 0.160210i
\(975\) 4.00000 28.0000i 0.128103 0.896718i
\(976\) 3.00000 3.00000i 0.0960277 0.0960277i
\(977\) −10.0000 −0.319928 −0.159964 0.987123i \(-0.551138\pi\)
−0.159964 + 0.987123i \(0.551138\pi\)
\(978\) 30.0000 0.959294
\(979\) 6.00000 6.00000i 0.191761 0.191761i
\(980\) 5.00000 10.0000i 0.159719 0.319438i
\(981\) 7.00000 + 7.00000i 0.223493 + 0.223493i
\(982\) 18.0000i 0.574403i
\(983\) 21.0000 21.0000i 0.669796 0.669796i −0.287873 0.957669i \(-0.592948\pi\)
0.957669 + 0.287873i \(0.0929480\pi\)
\(984\) 14.0000i 0.446304i
\(985\) −7.00000 21.0000i −0.223039 0.669116i
\(986\) −15.0000 + 25.0000i −0.477697 + 0.796162i
\(987\) 12.0000i 0.381964i
\(988\) 24.0000 0.763542
\(989\) −4.00000 4.00000i −0.127193 0.127193i
\(990\) 1.00000 + 3.00000i 0.0317821 + 0.0953463i
\(991\) −3.00000 3.00000i −0.0952981 0.0952981i 0.657850 0.753149i \(-0.271466\pi\)
−0.753149 + 0.657850i \(0.771466\pi\)
\(992\) −3.00000 3.00000i −0.0952501 0.0952501i
\(993\) −10.0000 10.0000i −0.317340 0.317340i
\(994\) 10.0000i 0.317181i
\(995\) 17.0000 + 51.0000i 0.538936 + 1.61681i
\(996\) 12.0000 12.0000i 0.380235 0.380235i
\(997\) −15.0000 15.0000i −0.475055 0.475055i 0.428491 0.903546i \(-0.359045\pi\)
−0.903546 + 0.428491i \(0.859045\pi\)
\(998\) 21.0000 21.0000i 0.664743 0.664743i
\(999\) −8.00000 −0.253109
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 170.2.g.d.149.1 yes 2
3.2 odd 2 1530.2.n.a.829.1 2
5.2 odd 4 850.2.h.e.251.1 2
5.3 odd 4 850.2.h.a.251.1 2
5.4 even 2 170.2.g.b.149.1 yes 2
15.14 odd 2 1530.2.n.g.829.1 2
17.4 even 4 170.2.g.b.89.1 2
51.38 odd 4 1530.2.n.g.1279.1 2
85.4 even 4 inner 170.2.g.d.89.1 yes 2
85.38 odd 4 850.2.h.a.701.1 2
85.72 odd 4 850.2.h.e.701.1 2
255.89 odd 4 1530.2.n.a.1279.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
170.2.g.b.89.1 2 17.4 even 4
170.2.g.b.149.1 yes 2 5.4 even 2
170.2.g.d.89.1 yes 2 85.4 even 4 inner
170.2.g.d.149.1 yes 2 1.1 even 1 trivial
850.2.h.a.251.1 2 5.3 odd 4
850.2.h.a.701.1 2 85.38 odd 4
850.2.h.e.251.1 2 5.2 odd 4
850.2.h.e.701.1 2 85.72 odd 4
1530.2.n.a.829.1 2 3.2 odd 2
1530.2.n.a.1279.1 2 255.89 odd 4
1530.2.n.g.829.1 2 15.14 odd 2
1530.2.n.g.1279.1 2 51.38 odd 4