Properties

Label 784.2.x.h.557.1
Level $784$
Weight $2$
Character 784.557
Analytic conductor $6.260$
Analytic rank $0$
Dimension $4$
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] = [784,2,Mod(165,784)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(784, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("784.165");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 784.x (of order \(12\), degree \(4\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.26027151847\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 112)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 557.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 784.557
Dual form 784.2.x.h.373.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 - 1.00000i) q^{2} +(-0.500000 + 0.133975i) q^{3} -2.00000i q^{4} +(0.866025 + 0.232051i) q^{5} +(-0.366025 + 0.633975i) q^{6} +(-2.00000 - 2.00000i) q^{8} +(-2.36603 + 1.36603i) q^{9} +O(q^{10})\) \(q+(1.00000 - 1.00000i) q^{2} +(-0.500000 + 0.133975i) q^{3} -2.00000i q^{4} +(0.866025 + 0.232051i) q^{5} +(-0.366025 + 0.633975i) q^{6} +(-2.00000 - 2.00000i) q^{8} +(-2.36603 + 1.36603i) q^{9} +(1.09808 - 0.633975i) q^{10} +(-0.767949 - 2.86603i) q^{11} +(0.267949 + 1.00000i) q^{12} +(-3.73205 - 3.73205i) q^{13} -0.464102 q^{15} -4.00000 q^{16} +(3.23205 - 5.59808i) q^{17} +(-1.00000 + 3.73205i) q^{18} +(-0.767949 + 2.86603i) q^{19} +(0.464102 - 1.73205i) q^{20} +(-3.63397 - 2.09808i) q^{22} +(3.86603 - 2.23205i) q^{23} +(1.26795 + 0.732051i) q^{24} +(-3.63397 - 2.09808i) q^{25} -7.46410 q^{26} +(2.09808 - 2.09808i) q^{27} +(-0.267949 - 0.267949i) q^{29} +(-0.464102 + 0.464102i) q^{30} +(1.86603 - 3.23205i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(0.767949 + 1.33013i) q^{33} +(-2.36603 - 8.83013i) q^{34} +(2.73205 + 4.73205i) q^{36} +(-1.13397 - 0.303848i) q^{37} +(2.09808 + 3.63397i) q^{38} +(2.36603 + 1.36603i) q^{39} +(-1.26795 - 2.19615i) q^{40} +4.92820i q^{41} +(6.46410 - 6.46410i) q^{43} +(-5.73205 + 1.53590i) q^{44} +(-2.36603 + 0.633975i) q^{45} +(1.63397 - 6.09808i) q^{46} +(2.13397 + 3.69615i) q^{47} +(2.00000 - 0.535898i) q^{48} +(-5.73205 + 1.53590i) q^{50} +(-0.866025 + 3.23205i) q^{51} +(-7.46410 + 7.46410i) q^{52} +(-1.06218 - 3.96410i) q^{53} -4.19615i q^{54} -2.66025i q^{55} -1.53590i q^{57} -0.535898 q^{58} +(3.03590 + 11.3301i) q^{59} +0.928203i q^{60} +(-1.86603 + 6.96410i) q^{61} +(-1.36603 - 5.09808i) q^{62} +8.00000i q^{64} +(-2.36603 - 4.09808i) q^{65} +(2.09808 + 0.562178i) q^{66} +(-4.96410 + 1.33013i) q^{67} +(-11.1962 - 6.46410i) q^{68} +(-1.63397 + 1.63397i) q^{69} +0.535898i q^{71} +(7.46410 + 2.00000i) q^{72} +(-6.23205 - 3.59808i) q^{73} +(-1.43782 + 0.830127i) q^{74} +(2.09808 + 0.562178i) q^{75} +(5.73205 + 1.53590i) q^{76} +(3.73205 - 1.00000i) q^{78} +(8.33013 + 14.4282i) q^{79} +(-3.46410 - 0.928203i) q^{80} +(3.33013 - 5.76795i) q^{81} +(4.92820 + 4.92820i) q^{82} +(-1.53590 - 1.53590i) q^{83} +(4.09808 - 4.09808i) q^{85} -12.9282i q^{86} +(0.169873 + 0.0980762i) q^{87} +(-4.19615 + 7.26795i) q^{88} +(4.50000 - 2.59808i) q^{89} +(-1.73205 + 3.00000i) q^{90} +(-4.46410 - 7.73205i) q^{92} +(-0.500000 + 1.86603i) q^{93} +(5.83013 + 1.56218i) q^{94} +(-1.33013 + 2.30385i) q^{95} +(1.46410 - 2.53590i) q^{96} +2.92820 q^{97} +(5.73205 + 5.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{2} - 2 q^{3} + 2 q^{6} - 8 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{2} - 2 q^{3} + 2 q^{6} - 8 q^{8} - 6 q^{9} - 6 q^{10} - 10 q^{11} + 8 q^{12} - 8 q^{13} + 12 q^{15} - 16 q^{16} + 6 q^{17} - 4 q^{18} - 10 q^{19} - 12 q^{20} - 18 q^{22} + 12 q^{23} + 12 q^{24} - 18 q^{25} - 16 q^{26} - 2 q^{27} - 8 q^{29} + 12 q^{30} + 4 q^{31} - 16 q^{32} + 10 q^{33} - 6 q^{34} + 4 q^{36} - 8 q^{37} - 2 q^{38} + 6 q^{39} - 12 q^{40} + 12 q^{43} - 16 q^{44} - 6 q^{45} + 10 q^{46} + 12 q^{47} + 8 q^{48} - 16 q^{50} - 16 q^{52} + 20 q^{53} - 16 q^{58} + 26 q^{59} - 4 q^{61} - 2 q^{62} - 6 q^{65} - 2 q^{66} - 6 q^{67} - 24 q^{68} - 10 q^{69} + 16 q^{72} - 18 q^{73} - 30 q^{74} - 2 q^{75} + 16 q^{76} + 8 q^{78} + 16 q^{79} - 4 q^{81} - 8 q^{82} - 20 q^{83} + 6 q^{85} + 18 q^{87} + 4 q^{88} + 18 q^{89} - 4 q^{92} - 2 q^{93} + 6 q^{94} + 12 q^{95} - 8 q^{96} - 16 q^{97} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(687\) \(689\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.00000i 0.707107 0.707107i
\(3\) −0.500000 + 0.133975i −0.288675 + 0.0773503i −0.400251 0.916406i \(-0.631077\pi\)
0.111576 + 0.993756i \(0.464410\pi\)
\(4\) 2.00000i 1.00000i
\(5\) 0.866025 + 0.232051i 0.387298 + 0.103776i 0.447214 0.894427i \(-0.352416\pi\)
−0.0599153 + 0.998203i \(0.519083\pi\)
\(6\) −0.366025 + 0.633975i −0.149429 + 0.258819i
\(7\) 0 0
\(8\) −2.00000 2.00000i −0.707107 0.707107i
\(9\) −2.36603 + 1.36603i −0.788675 + 0.455342i
\(10\) 1.09808 0.633975i 0.347242 0.200480i
\(11\) −0.767949 2.86603i −0.231545 0.864139i −0.979676 0.200587i \(-0.935715\pi\)
0.748130 0.663552i \(-0.230952\pi\)
\(12\) 0.267949 + 1.00000i 0.0773503 + 0.288675i
\(13\) −3.73205 3.73205i −1.03508 1.03508i −0.999362 0.0357229i \(-0.988627\pi\)
−0.0357229 0.999362i \(-0.511373\pi\)
\(14\) 0 0
\(15\) −0.464102 −0.119831
\(16\) −4.00000 −1.00000
\(17\) 3.23205 5.59808i 0.783887 1.35773i −0.145774 0.989318i \(-0.546567\pi\)
0.929661 0.368415i \(-0.120099\pi\)
\(18\) −1.00000 + 3.73205i −0.235702 + 0.879653i
\(19\) −0.767949 + 2.86603i −0.176180 + 0.657511i 0.820168 + 0.572123i \(0.193880\pi\)
−0.996348 + 0.0853887i \(0.972787\pi\)
\(20\) 0.464102 1.73205i 0.103776 0.387298i
\(21\) 0 0
\(22\) −3.63397 2.09808i −0.774766 0.447311i
\(23\) 3.86603 2.23205i 0.806122 0.465415i −0.0394853 0.999220i \(-0.512572\pi\)
0.845607 + 0.533805i \(0.179239\pi\)
\(24\) 1.26795 + 0.732051i 0.258819 + 0.149429i
\(25\) −3.63397 2.09808i −0.726795 0.419615i
\(26\) −7.46410 −1.46383
\(27\) 2.09808 2.09808i 0.403775 0.403775i
\(28\) 0 0
\(29\) −0.267949 0.267949i −0.0497569 0.0497569i 0.681791 0.731547i \(-0.261202\pi\)
−0.731547 + 0.681791i \(0.761202\pi\)
\(30\) −0.464102 + 0.464102i −0.0847330 + 0.0847330i
\(31\) 1.86603 3.23205i 0.335148 0.580493i −0.648365 0.761329i \(-0.724547\pi\)
0.983513 + 0.180836i \(0.0578803\pi\)
\(32\) −4.00000 + 4.00000i −0.707107 + 0.707107i
\(33\) 0.767949 + 1.33013i 0.133683 + 0.231545i
\(34\) −2.36603 8.83013i −0.405770 1.51435i
\(35\) 0 0
\(36\) 2.73205 + 4.73205i 0.455342 + 0.788675i
\(37\) −1.13397 0.303848i −0.186424 0.0499522i 0.164399 0.986394i \(-0.447432\pi\)
−0.350823 + 0.936442i \(0.614098\pi\)
\(38\) 2.09808 + 3.63397i 0.340353 + 0.589509i
\(39\) 2.36603 + 1.36603i 0.378867 + 0.218739i
\(40\) −1.26795 2.19615i −0.200480 0.347242i
\(41\) 4.92820i 0.769656i 0.922988 + 0.384828i \(0.125739\pi\)
−0.922988 + 0.384828i \(0.874261\pi\)
\(42\) 0 0
\(43\) 6.46410 6.46410i 0.985766 0.985766i −0.0141339 0.999900i \(-0.504499\pi\)
0.999900 + 0.0141339i \(0.00449910\pi\)
\(44\) −5.73205 + 1.53590i −0.864139 + 0.231545i
\(45\) −2.36603 + 0.633975i −0.352706 + 0.0945074i
\(46\) 1.63397 6.09808i 0.240916 0.899112i
\(47\) 2.13397 + 3.69615i 0.311272 + 0.539139i 0.978638 0.205591i \(-0.0659116\pi\)
−0.667366 + 0.744730i \(0.732578\pi\)
\(48\) 2.00000 0.535898i 0.288675 0.0773503i
\(49\) 0 0
\(50\) −5.73205 + 1.53590i −0.810634 + 0.217209i
\(51\) −0.866025 + 3.23205i −0.121268 + 0.452578i
\(52\) −7.46410 + 7.46410i −1.03508 + 1.03508i
\(53\) −1.06218 3.96410i −0.145901 0.544511i −0.999714 0.0239302i \(-0.992382\pi\)
0.853812 0.520581i \(-0.174285\pi\)
\(54\) 4.19615i 0.571024i
\(55\) 2.66025i 0.358709i
\(56\) 0 0
\(57\) 1.53590i 0.203435i
\(58\) −0.535898 −0.0703669
\(59\) 3.03590 + 11.3301i 0.395240 + 1.47506i 0.821370 + 0.570395i \(0.193210\pi\)
−0.426130 + 0.904662i \(0.640123\pi\)
\(60\) 0.928203i 0.119831i
\(61\) −1.86603 + 6.96410i −0.238920 + 0.891662i 0.737422 + 0.675432i \(0.236043\pi\)
−0.976342 + 0.216230i \(0.930624\pi\)
\(62\) −1.36603 5.09808i −0.173485 0.647456i
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) −2.36603 4.09808i −0.293469 0.508304i
\(66\) 2.09808 + 0.562178i 0.258255 + 0.0691993i
\(67\) −4.96410 + 1.33013i −0.606462 + 0.162501i −0.548966 0.835845i \(-0.684978\pi\)
−0.0574958 + 0.998346i \(0.518312\pi\)
\(68\) −11.1962 6.46410i −1.35773 0.783887i
\(69\) −1.63397 + 1.63397i −0.196707 + 0.196707i
\(70\) 0 0
\(71\) 0.535898i 0.0635994i 0.999494 + 0.0317997i \(0.0101239\pi\)
−0.999494 + 0.0317997i \(0.989876\pi\)
\(72\) 7.46410 + 2.00000i 0.879653 + 0.235702i
\(73\) −6.23205 3.59808i −0.729406 0.421123i 0.0887986 0.996050i \(-0.471697\pi\)
−0.818205 + 0.574927i \(0.805031\pi\)
\(74\) −1.43782 + 0.830127i −0.167143 + 0.0965003i
\(75\) 2.09808 + 0.562178i 0.242265 + 0.0649147i
\(76\) 5.73205 + 1.53590i 0.657511 + 0.176180i
\(77\) 0 0
\(78\) 3.73205 1.00000i 0.422572 0.113228i
\(79\) 8.33013 + 14.4282i 0.937213 + 1.62330i 0.770640 + 0.637270i \(0.219937\pi\)
0.166572 + 0.986029i \(0.446730\pi\)
\(80\) −3.46410 0.928203i −0.387298 0.103776i
\(81\) 3.33013 5.76795i 0.370014 0.640883i
\(82\) 4.92820 + 4.92820i 0.544229 + 0.544229i
\(83\) −1.53590 1.53590i −0.168587 0.168587i 0.617771 0.786358i \(-0.288036\pi\)
−0.786358 + 0.617771i \(0.788036\pi\)
\(84\) 0 0
\(85\) 4.09808 4.09808i 0.444499 0.444499i
\(86\) 12.9282i 1.39408i
\(87\) 0.169873 + 0.0980762i 0.0182123 + 0.0105149i
\(88\) −4.19615 + 7.26795i −0.447311 + 0.774766i
\(89\) 4.50000 2.59808i 0.476999 0.275396i −0.242166 0.970235i \(-0.577858\pi\)
0.719165 + 0.694839i \(0.244525\pi\)
\(90\) −1.73205 + 3.00000i −0.182574 + 0.316228i
\(91\) 0 0
\(92\) −4.46410 7.73205i −0.465415 0.806122i
\(93\) −0.500000 + 1.86603i −0.0518476 + 0.193498i
\(94\) 5.83013 + 1.56218i 0.601332 + 0.161126i
\(95\) −1.33013 + 2.30385i −0.136468 + 0.236370i
\(96\) 1.46410 2.53590i 0.149429 0.258819i
\(97\) 2.92820 0.297314 0.148657 0.988889i \(-0.452505\pi\)
0.148657 + 0.988889i \(0.452505\pi\)
\(98\) 0 0
\(99\) 5.73205 + 5.73205i 0.576093 + 0.576093i
\(100\) −4.19615 + 7.26795i −0.419615 + 0.726795i
\(101\) −5.06218 18.8923i −0.503706 1.87985i −0.474450 0.880283i \(-0.657353\pi\)
−0.0292559 0.999572i \(-0.509314\pi\)
\(102\) 2.36603 + 4.09808i 0.234271 + 0.405770i
\(103\) 5.59808 3.23205i 0.551595 0.318463i −0.198170 0.980168i \(-0.563500\pi\)
0.749765 + 0.661704i \(0.230167\pi\)
\(104\) 14.9282i 1.46383i
\(105\) 0 0
\(106\) −5.02628 2.90192i −0.488195 0.281860i
\(107\) 3.23205 + 0.866025i 0.312454 + 0.0837218i 0.411638 0.911347i \(-0.364957\pi\)
−0.0991843 + 0.995069i \(0.531623\pi\)
\(108\) −4.19615 4.19615i −0.403775 0.403775i
\(109\) −2.13397 + 0.571797i −0.204398 + 0.0547682i −0.359565 0.933120i \(-0.617075\pi\)
0.155167 + 0.987888i \(0.450408\pi\)
\(110\) −2.66025 2.66025i −0.253645 0.253645i
\(111\) 0.607695 0.0576799
\(112\) 0 0
\(113\) −1.46410 −0.137731 −0.0688655 0.997626i \(-0.521938\pi\)
−0.0688655 + 0.997626i \(0.521938\pi\)
\(114\) −1.53590 1.53590i −0.143850 0.143850i
\(115\) 3.86603 1.03590i 0.360509 0.0965980i
\(116\) −0.535898 + 0.535898i −0.0497569 + 0.0497569i
\(117\) 13.9282 + 3.73205i 1.28766 + 0.345028i
\(118\) 14.3660 + 8.29423i 1.32250 + 0.763546i
\(119\) 0 0
\(120\) 0.928203 + 0.928203i 0.0847330 + 0.0847330i
\(121\) 1.90192 1.09808i 0.172902 0.0998251i
\(122\) 5.09808 + 8.83013i 0.461558 + 0.799442i
\(123\) −0.660254 2.46410i −0.0595331 0.222181i
\(124\) −6.46410 3.73205i −0.580493 0.335148i
\(125\) −5.83013 5.83013i −0.521462 0.521462i
\(126\) 0 0
\(127\) 9.46410 0.839803 0.419902 0.907570i \(-0.362065\pi\)
0.419902 + 0.907570i \(0.362065\pi\)
\(128\) 8.00000 + 8.00000i 0.707107 + 0.707107i
\(129\) −2.36603 + 4.09808i −0.208317 + 0.360815i
\(130\) −6.46410 1.73205i −0.566939 0.151911i
\(131\) 2.03590 7.59808i 0.177877 0.663847i −0.818166 0.574982i \(-0.805009\pi\)
0.996044 0.0888654i \(-0.0283241\pi\)
\(132\) 2.66025 1.53590i 0.231545 0.133683i
\(133\) 0 0
\(134\) −3.63397 + 6.29423i −0.313928 + 0.543739i
\(135\) 2.30385 1.33013i 0.198284 0.114479i
\(136\) −17.6603 + 4.73205i −1.51435 + 0.405770i
\(137\) 15.2321 + 8.79423i 1.30136 + 0.751342i 0.980638 0.195831i \(-0.0627404\pi\)
0.320724 + 0.947173i \(0.396074\pi\)
\(138\) 3.26795i 0.278186i
\(139\) 11.9282 11.9282i 1.01174 1.01174i 0.0118067 0.999930i \(-0.496242\pi\)
0.999930 0.0118067i \(-0.00375827\pi\)
\(140\) 0 0
\(141\) −1.56218 1.56218i −0.131559 0.131559i
\(142\) 0.535898 + 0.535898i 0.0449716 + 0.0449716i
\(143\) −7.83013 + 13.5622i −0.654788 + 1.13413i
\(144\) 9.46410 5.46410i 0.788675 0.455342i
\(145\) −0.169873 0.294229i −0.0141072 0.0244344i
\(146\) −9.83013 + 2.63397i −0.813547 + 0.217989i
\(147\) 0 0
\(148\) −0.607695 + 2.26795i −0.0499522 + 0.186424i
\(149\) −7.59808 2.03590i −0.622459 0.166787i −0.0662134 0.997805i \(-0.521092\pi\)
−0.556245 + 0.831018i \(0.687758\pi\)
\(150\) 2.66025 1.53590i 0.217209 0.125406i
\(151\) 9.86603 + 5.69615i 0.802886 + 0.463546i 0.844479 0.535588i \(-0.179910\pi\)
−0.0415935 + 0.999135i \(0.513243\pi\)
\(152\) 7.26795 4.19615i 0.589509 0.340353i
\(153\) 17.6603i 1.42775i
\(154\) 0 0
\(155\) 2.36603 2.36603i 0.190044 0.190044i
\(156\) 2.73205 4.73205i 0.218739 0.378867i
\(157\) 18.2583 4.89230i 1.45717 0.390448i 0.558661 0.829396i \(-0.311315\pi\)
0.898513 + 0.438948i \(0.144649\pi\)
\(158\) 22.7583 + 6.09808i 1.81056 + 0.485137i
\(159\) 1.06218 + 1.83975i 0.0842362 + 0.145901i
\(160\) −4.39230 + 2.53590i −0.347242 + 0.200480i
\(161\) 0 0
\(162\) −2.43782 9.09808i −0.191533 0.714812i
\(163\) 3.23205 12.0622i 0.253154 0.944783i −0.715954 0.698147i \(-0.754008\pi\)
0.969108 0.246636i \(-0.0793251\pi\)
\(164\) 9.85641 0.769656
\(165\) 0.356406 + 1.33013i 0.0277462 + 0.103550i
\(166\) −3.07180 −0.238418
\(167\) 21.8564i 1.69130i 0.533738 + 0.845650i \(0.320787\pi\)
−0.533738 + 0.845650i \(0.679213\pi\)
\(168\) 0 0
\(169\) 14.8564i 1.14280i
\(170\) 8.19615i 0.628616i
\(171\) −2.09808 7.83013i −0.160444 0.598785i
\(172\) −12.9282 12.9282i −0.985766 0.985766i
\(173\) −0.598076 + 2.23205i −0.0454709 + 0.169700i −0.984927 0.172969i \(-0.944664\pi\)
0.939456 + 0.342668i \(0.111331\pi\)
\(174\) 0.267949 0.0717968i 0.0203132 0.00544290i
\(175\) 0 0
\(176\) 3.07180 + 11.4641i 0.231545 + 0.864139i
\(177\) −3.03590 5.25833i −0.228192 0.395240i
\(178\) 1.90192 7.09808i 0.142555 0.532023i
\(179\) 8.96410 2.40192i 0.670008 0.179528i 0.0922498 0.995736i \(-0.470594\pi\)
0.577759 + 0.816208i \(0.303928\pi\)
\(180\) 1.26795 + 4.73205i 0.0945074 + 0.352706i
\(181\) −13.3923 + 13.3923i −0.995442 + 0.995442i −0.999990 0.00454748i \(-0.998552\pi\)
0.00454748 + 0.999990i \(0.498552\pi\)
\(182\) 0 0
\(183\) 3.73205i 0.275881i
\(184\) −12.1962 3.26795i −0.899112 0.240916i
\(185\) −0.911543 0.526279i −0.0670180 0.0386928i
\(186\) 1.36603 + 2.36603i 0.100162 + 0.173485i
\(187\) −18.5263 4.96410i −1.35478 0.363011i
\(188\) 7.39230 4.26795i 0.539139 0.311272i
\(189\) 0 0
\(190\) 0.973721 + 3.63397i 0.0706411 + 0.263636i
\(191\) −4.33013 7.50000i −0.313317 0.542681i 0.665761 0.746165i \(-0.268107\pi\)
−0.979078 + 0.203484i \(0.934774\pi\)
\(192\) −1.07180 4.00000i −0.0773503 0.288675i
\(193\) 11.5000 19.9186i 0.827788 1.43377i −0.0719816 0.997406i \(-0.522932\pi\)
0.899770 0.436365i \(-0.143734\pi\)
\(194\) 2.92820 2.92820i 0.210233 0.210233i
\(195\) 1.73205 + 1.73205i 0.124035 + 0.124035i
\(196\) 0 0
\(197\) −16.6603 + 16.6603i −1.18699 + 1.18699i −0.209100 + 0.977894i \(0.567053\pi\)
−0.977894 + 0.209100i \(0.932947\pi\)
\(198\) 11.4641 0.814718
\(199\) 10.3301 + 5.96410i 0.732283 + 0.422784i 0.819257 0.573427i \(-0.194386\pi\)
−0.0869736 + 0.996211i \(0.527720\pi\)
\(200\) 3.07180 + 11.4641i 0.217209 + 0.810634i
\(201\) 2.30385 1.33013i 0.162501 0.0938199i
\(202\) −23.9545 13.8301i −1.68543 0.973084i
\(203\) 0 0
\(204\) 6.46410 + 1.73205i 0.452578 + 0.121268i
\(205\) −1.14359 + 4.26795i −0.0798720 + 0.298087i
\(206\) 2.36603 8.83013i 0.164849 0.615224i
\(207\) −6.09808 + 10.5622i −0.423846 + 0.734122i
\(208\) 14.9282 + 14.9282i 1.03508 + 1.03508i
\(209\) 8.80385 0.608975
\(210\) 0 0
\(211\) −15.9282 15.9282i −1.09654 1.09654i −0.994812 0.101731i \(-0.967562\pi\)
−0.101731 0.994812i \(-0.532438\pi\)
\(212\) −7.92820 + 2.12436i −0.544511 + 0.145901i
\(213\) −0.0717968 0.267949i −0.00491943 0.0183596i
\(214\) 4.09808 2.36603i 0.280139 0.161738i
\(215\) 7.09808 4.09808i 0.484085 0.279486i
\(216\) −8.39230 −0.571024
\(217\) 0 0
\(218\) −1.56218 + 2.70577i −0.105804 + 0.183258i
\(219\) 3.59808 + 0.964102i 0.243135 + 0.0651479i
\(220\) −5.32051 −0.358709
\(221\) −32.9545 + 8.83013i −2.21676 + 0.593979i
\(222\) 0.607695 0.607695i 0.0407858 0.0407858i
\(223\) −9.85641 −0.660034 −0.330017 0.943975i \(-0.607054\pi\)
−0.330017 + 0.943975i \(0.607054\pi\)
\(224\) 0 0
\(225\) 11.4641 0.764273
\(226\) −1.46410 + 1.46410i −0.0973906 + 0.0973906i
\(227\) −11.1603 + 2.99038i −0.740732 + 0.198479i −0.609403 0.792860i \(-0.708591\pi\)
−0.131329 + 0.991339i \(0.541924\pi\)
\(228\) −3.07180 −0.203435
\(229\) −13.3301 3.57180i −0.880880 0.236031i −0.210093 0.977681i \(-0.567377\pi\)
−0.670787 + 0.741650i \(0.734043\pi\)
\(230\) 2.83013 4.90192i 0.186613 0.323223i
\(231\) 0 0
\(232\) 1.07180i 0.0703669i
\(233\) 0.696152 0.401924i 0.0456065 0.0263309i −0.477023 0.878891i \(-0.658284\pi\)
0.522630 + 0.852560i \(0.324951\pi\)
\(234\) 17.6603 10.1962i 1.15449 0.666543i
\(235\) 0.990381 + 3.69615i 0.0646053 + 0.241110i
\(236\) 22.6603 6.07180i 1.47506 0.395240i
\(237\) −6.09808 6.09808i −0.396113 0.396113i
\(238\) 0 0
\(239\) −8.53590 −0.552141 −0.276071 0.961137i \(-0.589032\pi\)
−0.276071 + 0.961137i \(0.589032\pi\)
\(240\) 1.85641 0.119831
\(241\) 6.96410 12.0622i 0.448597 0.776993i −0.549698 0.835364i \(-0.685257\pi\)
0.998295 + 0.0583704i \(0.0185905\pi\)
\(242\) 0.803848 3.00000i 0.0516733 0.192847i
\(243\) −3.19615 + 11.9282i −0.205033 + 0.765195i
\(244\) 13.9282 + 3.73205i 0.891662 + 0.238920i
\(245\) 0 0
\(246\) −3.12436 1.80385i −0.199202 0.115009i
\(247\) 13.5622 7.83013i 0.862941 0.498219i
\(248\) −10.1962 + 2.73205i −0.647456 + 0.173485i
\(249\) 0.973721 + 0.562178i 0.0617070 + 0.0356266i
\(250\) −11.6603 −0.737459
\(251\) 17.5885 17.5885i 1.11017 1.11017i 0.117047 0.993126i \(-0.462657\pi\)
0.993126 0.117047i \(-0.0373429\pi\)
\(252\) 0 0
\(253\) −9.36603 9.36603i −0.588837 0.588837i
\(254\) 9.46410 9.46410i 0.593831 0.593831i
\(255\) −1.50000 + 2.59808i −0.0939336 + 0.162698i
\(256\) 16.0000 1.00000
\(257\) −9.69615 16.7942i −0.604829 1.04760i −0.992078 0.125620i \(-0.959908\pi\)
0.387249 0.921975i \(-0.373425\pi\)
\(258\) 1.73205 + 6.46410i 0.107833 + 0.402437i
\(259\) 0 0
\(260\) −8.19615 + 4.73205i −0.508304 + 0.293469i
\(261\) 1.00000 + 0.267949i 0.0618984 + 0.0165856i
\(262\) −5.56218 9.63397i −0.343632 0.595189i
\(263\) 3.99038 + 2.30385i 0.246057 + 0.142061i 0.617958 0.786211i \(-0.287960\pi\)
−0.371900 + 0.928273i \(0.621294\pi\)
\(264\) 1.12436 4.19615i 0.0691993 0.258255i
\(265\) 3.67949i 0.226029i
\(266\) 0 0
\(267\) −1.90192 + 1.90192i −0.116396 + 0.116396i
\(268\) 2.66025 + 9.92820i 0.162501 + 0.606462i
\(269\) −9.79423 + 2.62436i −0.597165 + 0.160010i −0.544726 0.838614i \(-0.683366\pi\)
−0.0524390 + 0.998624i \(0.516700\pi\)
\(270\) 0.973721 3.63397i 0.0592587 0.221157i
\(271\) 6.06218 + 10.5000i 0.368251 + 0.637830i 0.989292 0.145948i \(-0.0466233\pi\)
−0.621041 + 0.783778i \(0.713290\pi\)
\(272\) −12.9282 + 22.3923i −0.783887 + 1.35773i
\(273\) 0 0
\(274\) 24.0263 6.43782i 1.45148 0.388923i
\(275\) −3.22243 + 12.0263i −0.194320 + 0.725212i
\(276\) 3.26795 + 3.26795i 0.196707 + 0.196707i
\(277\) −1.20577 4.50000i −0.0724478 0.270379i 0.920195 0.391461i \(-0.128030\pi\)
−0.992642 + 0.121082i \(0.961364\pi\)
\(278\) 23.8564i 1.43081i
\(279\) 10.1962i 0.610428i
\(280\) 0 0
\(281\) 0.928203i 0.0553720i −0.999617 0.0276860i \(-0.991186\pi\)
0.999617 0.0276860i \(-0.00881385\pi\)
\(282\) −3.12436 −0.186053
\(283\) 3.89230 + 14.5263i 0.231374 + 0.863498i 0.979750 + 0.200224i \(0.0641669\pi\)
−0.748377 + 0.663274i \(0.769166\pi\)
\(284\) 1.07180 0.0635994
\(285\) 0.356406 1.33013i 0.0211117 0.0787899i
\(286\) 5.73205 + 21.3923i 0.338943 + 1.26495i
\(287\) 0 0
\(288\) 4.00000 14.9282i 0.235702 0.879653i
\(289\) −12.3923 21.4641i −0.728959 1.26259i
\(290\) −0.464102 0.124356i −0.0272530 0.00730242i
\(291\) −1.46410 + 0.392305i −0.0858272 + 0.0229973i
\(292\) −7.19615 + 12.4641i −0.421123 + 0.729406i
\(293\) 7.92820 7.92820i 0.463171 0.463171i −0.436523 0.899693i \(-0.643790\pi\)
0.899693 + 0.436523i \(0.143790\pi\)
\(294\) 0 0
\(295\) 10.5167i 0.612304i
\(296\) 1.66025 + 2.87564i 0.0965003 + 0.167143i
\(297\) −7.62436 4.40192i −0.442410 0.255426i
\(298\) −9.63397 + 5.56218i −0.558081 + 0.322208i
\(299\) −22.7583 6.09808i −1.31615 0.352661i
\(300\) 1.12436 4.19615i 0.0649147 0.242265i
\(301\) 0 0
\(302\) 15.5622 4.16987i 0.895503 0.239949i
\(303\) 5.06218 + 8.76795i 0.290815 + 0.503706i
\(304\) 3.07180 11.4641i 0.176180 0.657511i
\(305\) −3.23205 + 5.59808i −0.185067 + 0.320545i
\(306\) 17.6603 + 17.6603i 1.00957 + 1.00957i
\(307\) −9.00000 9.00000i −0.513657 0.513657i 0.401988 0.915645i \(-0.368319\pi\)
−0.915645 + 0.401988i \(0.868319\pi\)
\(308\) 0 0
\(309\) −2.36603 + 2.36603i −0.134598 + 0.134598i
\(310\) 4.73205i 0.268762i
\(311\) −5.59808 3.23205i −0.317438 0.183273i 0.332812 0.942993i \(-0.392002\pi\)
−0.650250 + 0.759720i \(0.725336\pi\)
\(312\) −2.00000 7.46410i −0.113228 0.422572i
\(313\) 18.6962 10.7942i 1.05677 0.610126i 0.132232 0.991219i \(-0.457786\pi\)
0.924537 + 0.381093i \(0.124452\pi\)
\(314\) 13.3660 23.1506i 0.754288 1.30647i
\(315\) 0 0
\(316\) 28.8564 16.6603i 1.62330 0.937213i
\(317\) −3.79423 + 14.1603i −0.213105 + 0.795319i 0.773720 + 0.633528i \(0.218394\pi\)
−0.986825 + 0.161791i \(0.948273\pi\)
\(318\) 2.90192 + 0.777568i 0.162732 + 0.0436039i
\(319\) −0.562178 + 0.973721i −0.0314759 + 0.0545179i
\(320\) −1.85641 + 6.92820i −0.103776 + 0.387298i
\(321\) −1.73205 −0.0966736
\(322\) 0 0
\(323\) 13.5622 + 13.5622i 0.754620 + 0.754620i
\(324\) −11.5359 6.66025i −0.640883 0.370014i
\(325\) 5.73205 + 21.3923i 0.317957 + 1.18663i
\(326\) −8.83013 15.2942i −0.489056 0.847069i
\(327\) 0.990381 0.571797i 0.0547682 0.0316204i
\(328\) 9.85641 9.85641i 0.544229 0.544229i
\(329\) 0 0
\(330\) 1.68653 + 0.973721i 0.0928406 + 0.0536016i
\(331\) −19.6244 5.25833i −1.07865 0.289024i −0.324609 0.945848i \(-0.605233\pi\)
−0.754044 + 0.656824i \(0.771899\pi\)
\(332\) −3.07180 + 3.07180i −0.168587 + 0.168587i
\(333\) 3.09808 0.830127i 0.169774 0.0454907i
\(334\) 21.8564 + 21.8564i 1.19593 + 1.19593i
\(335\) −4.60770 −0.251745
\(336\) 0 0
\(337\) −6.14359 −0.334663 −0.167331 0.985901i \(-0.553515\pi\)
−0.167331 + 0.985901i \(0.553515\pi\)
\(338\) 14.8564 + 14.8564i 0.808082 + 0.808082i
\(339\) 0.732051 0.196152i 0.0397595 0.0106535i
\(340\) −8.19615 8.19615i −0.444499 0.444499i
\(341\) −10.6962 2.86603i −0.579229 0.155204i
\(342\) −9.92820 5.73205i −0.536856 0.309954i
\(343\) 0 0
\(344\) −25.8564 −1.39408
\(345\) −1.79423 + 1.03590i −0.0965980 + 0.0557709i
\(346\) 1.63397 + 2.83013i 0.0878430 + 0.152149i
\(347\) −6.30385 23.5263i −0.338408 1.26296i −0.900127 0.435628i \(-0.856526\pi\)
0.561718 0.827329i \(-0.310140\pi\)
\(348\) 0.196152 0.339746i 0.0105149 0.0182123i
\(349\) −6.12436 6.12436i −0.327829 0.327829i 0.523931 0.851761i \(-0.324465\pi\)
−0.851761 + 0.523931i \(0.824465\pi\)
\(350\) 0 0
\(351\) −15.6603 −0.835883
\(352\) 14.5359 + 8.39230i 0.774766 + 0.447311i
\(353\) −13.8923 + 24.0622i −0.739413 + 1.28070i 0.213347 + 0.976976i \(0.431563\pi\)
−0.952760 + 0.303724i \(0.901770\pi\)
\(354\) −8.29423 2.22243i −0.440833 0.118121i
\(355\) −0.124356 + 0.464102i −0.00660011 + 0.0246320i
\(356\) −5.19615 9.00000i −0.275396 0.476999i
\(357\) 0 0
\(358\) 6.56218 11.3660i 0.346822 0.600713i
\(359\) −3.86603 + 2.23205i −0.204041 + 0.117803i −0.598539 0.801094i \(-0.704252\pi\)
0.394498 + 0.918897i \(0.370919\pi\)
\(360\) 6.00000 + 3.46410i 0.316228 + 0.182574i
\(361\) 8.83013 + 5.09808i 0.464744 + 0.268320i
\(362\) 26.7846i 1.40777i
\(363\) −0.803848 + 0.803848i −0.0421911 + 0.0421911i
\(364\) 0 0
\(365\) −4.56218 4.56218i −0.238795 0.238795i
\(366\) −3.73205 3.73205i −0.195077 0.195077i
\(367\) 3.06218 5.30385i 0.159844 0.276859i −0.774968 0.632000i \(-0.782234\pi\)
0.934812 + 0.355142i \(0.115567\pi\)
\(368\) −15.4641 + 8.92820i −0.806122 + 0.465415i
\(369\) −6.73205 11.6603i −0.350457 0.607009i
\(370\) −1.43782 + 0.385263i −0.0747488 + 0.0200289i
\(371\) 0 0
\(372\) 3.73205 + 1.00000i 0.193498 + 0.0518476i
\(373\) 0.866025 + 0.232051i 0.0448411 + 0.0120151i 0.281170 0.959658i \(-0.409278\pi\)
−0.236329 + 0.971673i \(0.575944\pi\)
\(374\) −23.4904 + 13.5622i −1.21466 + 0.701284i
\(375\) 3.69615 + 2.13397i 0.190868 + 0.110198i
\(376\) 3.12436 11.6603i 0.161126 0.601332i
\(377\) 2.00000i 0.103005i
\(378\) 0 0
\(379\) 0.124356 0.124356i 0.00638772 0.00638772i −0.703906 0.710293i \(-0.748562\pi\)
0.710293 + 0.703906i \(0.248562\pi\)
\(380\) 4.60770 + 2.66025i 0.236370 + 0.136468i
\(381\) −4.73205 + 1.26795i −0.242430 + 0.0649590i
\(382\) −11.8301 3.16987i −0.605282 0.162185i
\(383\) −12.5981 21.8205i −0.643732 1.11498i −0.984593 0.174862i \(-0.944052\pi\)
0.340861 0.940114i \(-0.389281\pi\)
\(384\) −5.07180 2.92820i −0.258819 0.149429i
\(385\) 0 0
\(386\) −8.41858 31.4186i −0.428495 1.59916i
\(387\) −6.46410 + 24.1244i −0.328589 + 1.22631i
\(388\) 5.85641i 0.297314i
\(389\) 5.99038 + 22.3564i 0.303724 + 1.13351i 0.934038 + 0.357174i \(0.116260\pi\)
−0.630313 + 0.776341i \(0.717074\pi\)
\(390\) 3.46410 0.175412
\(391\) 28.8564i 1.45933i
\(392\) 0 0
\(393\) 4.07180i 0.205395i
\(394\) 33.3205i 1.67866i
\(395\) 3.86603 + 14.4282i 0.194521 + 0.725962i
\(396\) 11.4641 11.4641i 0.576093 0.576093i
\(397\) −6.86603 + 25.6244i −0.344596 + 1.28605i 0.548488 + 0.836159i \(0.315204\pi\)
−0.893084 + 0.449891i \(0.851463\pi\)
\(398\) 16.2942 4.36603i 0.816756 0.218849i
\(399\) 0 0
\(400\) 14.5359 + 8.39230i 0.726795 + 0.419615i
\(401\) 7.50000 + 12.9904i 0.374532 + 0.648709i 0.990257 0.139253i \(-0.0444700\pi\)
−0.615725 + 0.787961i \(0.711137\pi\)
\(402\) 0.973721 3.63397i 0.0485648 0.181246i
\(403\) −19.0263 + 5.09808i −0.947766 + 0.253953i
\(404\) −37.7846 + 10.1244i −1.87985 + 0.503706i
\(405\) 4.22243 4.22243i 0.209814 0.209814i
\(406\) 0 0
\(407\) 3.48334i 0.172663i
\(408\) 8.19615 4.73205i 0.405770 0.234271i
\(409\) 7.50000 + 4.33013i 0.370851 + 0.214111i 0.673830 0.738886i \(-0.264648\pi\)
−0.302979 + 0.952997i \(0.597981\pi\)
\(410\) 3.12436 + 5.41154i 0.154301 + 0.267257i
\(411\) −8.79423 2.35641i −0.433787 0.116233i
\(412\) −6.46410 11.1962i −0.318463 0.551595i
\(413\) 0 0
\(414\) 4.46410 + 16.6603i 0.219399 + 0.818807i
\(415\) −0.973721 1.68653i −0.0477981 0.0827887i
\(416\) 29.8564 1.46383
\(417\) −4.36603 + 7.56218i −0.213805 + 0.370321i
\(418\) 8.80385 8.80385i 0.430610 0.430610i
\(419\) 19.0000 + 19.0000i 0.928211 + 0.928211i 0.997590 0.0693796i \(-0.0221020\pi\)
−0.0693796 + 0.997590i \(0.522102\pi\)
\(420\) 0 0
\(421\) 8.66025 8.66025i 0.422075 0.422075i −0.463843 0.885918i \(-0.653530\pi\)
0.885918 + 0.463843i \(0.153530\pi\)
\(422\) −31.8564 −1.55075
\(423\) −10.0981 5.83013i −0.490985 0.283470i
\(424\) −5.80385 + 10.0526i −0.281860 + 0.488195i
\(425\) −23.4904 + 13.5622i −1.13945 + 0.657862i
\(426\) −0.339746 0.196152i −0.0164607 0.00950362i
\(427\) 0 0
\(428\) 1.73205 6.46410i 0.0837218 0.312454i
\(429\) 2.09808 7.83013i 0.101296 0.378042i
\(430\) 3.00000 11.1962i 0.144673 0.539926i
\(431\) −15.3301 + 26.5526i −0.738426 + 1.27899i 0.214777 + 0.976663i \(0.431097\pi\)
−0.953204 + 0.302329i \(0.902236\pi\)
\(432\) −8.39230 + 8.39230i −0.403775 + 0.403775i
\(433\) 33.1769 1.59438 0.797190 0.603728i \(-0.206319\pi\)
0.797190 + 0.603728i \(0.206319\pi\)
\(434\) 0 0
\(435\) 0.124356 + 0.124356i 0.00596240 + 0.00596240i
\(436\) 1.14359 + 4.26795i 0.0547682 + 0.204398i
\(437\) 3.42820 + 12.7942i 0.163993 + 0.612031i
\(438\) 4.56218 2.63397i 0.217989 0.125856i
\(439\) −6.52628 + 3.76795i −0.311482 + 0.179834i −0.647590 0.761989i \(-0.724223\pi\)
0.336107 + 0.941824i \(0.390890\pi\)
\(440\) −5.32051 + 5.32051i −0.253645 + 0.253645i
\(441\) 0 0
\(442\) −24.1244 + 41.7846i −1.14748 + 1.98749i
\(443\) −10.4282 2.79423i −0.495459 0.132758i 0.00243278 0.999997i \(-0.499226\pi\)
−0.497892 + 0.867239i \(0.665892\pi\)
\(444\) 1.21539i 0.0576799i
\(445\) 4.50000 1.20577i 0.213320 0.0571590i
\(446\) −9.85641 + 9.85641i −0.466714 + 0.466714i
\(447\) 4.07180 0.192589
\(448\) 0 0
\(449\) −23.3205 −1.10056 −0.550281 0.834979i \(-0.685480\pi\)
−0.550281 + 0.834979i \(0.685480\pi\)
\(450\) 11.4641 11.4641i 0.540423 0.540423i
\(451\) 14.1244 3.78461i 0.665090 0.178210i
\(452\) 2.92820i 0.137731i
\(453\) −5.69615 1.52628i −0.267629 0.0717109i
\(454\) −8.16987 + 14.1506i −0.383431 + 0.664122i
\(455\) 0 0
\(456\) −3.07180 + 3.07180i −0.143850 + 0.143850i
\(457\) 16.2846 9.40192i 0.761762 0.439803i −0.0681661 0.997674i \(-0.521715\pi\)
0.829928 + 0.557871i \(0.188381\pi\)
\(458\) −16.9019 + 9.75833i −0.789775 + 0.455977i
\(459\) −4.96410 18.5263i −0.231704 0.864733i
\(460\) −2.07180 7.73205i −0.0965980 0.360509i
\(461\) −18.6603 18.6603i −0.869095 0.869095i 0.123278 0.992372i \(-0.460659\pi\)
−0.992372 + 0.123278i \(0.960659\pi\)
\(462\) 0 0
\(463\) 2.14359 0.0996212 0.0498106 0.998759i \(-0.484138\pi\)
0.0498106 + 0.998759i \(0.484138\pi\)
\(464\) 1.07180 + 1.07180i 0.0497569 + 0.0497569i
\(465\) −0.866025 + 1.50000i −0.0401610 + 0.0695608i
\(466\) 0.294229 1.09808i 0.0136299 0.0508674i
\(467\) 6.96410 25.9904i 0.322260 1.20269i −0.594777 0.803890i \(-0.702760\pi\)
0.917038 0.398801i \(-0.130574\pi\)
\(468\) 7.46410 27.8564i 0.345028 1.28766i
\(469\) 0 0
\(470\) 4.68653 + 2.70577i 0.216174 + 0.124808i
\(471\) −8.47372 + 4.89230i −0.390448 + 0.225426i
\(472\) 16.5885 28.7321i 0.763546 1.32250i
\(473\) −23.4904 13.5622i −1.08009 0.623590i
\(474\) −12.1962 −0.560188
\(475\) 8.80385 8.80385i 0.403948 0.403948i
\(476\) 0 0
\(477\) 7.92820 + 7.92820i 0.363007 + 0.363007i
\(478\) −8.53590 + 8.53590i −0.390423 + 0.390423i
\(479\) 7.79423 13.5000i 0.356127 0.616831i −0.631183 0.775634i \(-0.717430\pi\)
0.987310 + 0.158803i \(0.0507636\pi\)
\(480\) 1.85641 1.85641i 0.0847330 0.0847330i
\(481\) 3.09808 + 5.36603i 0.141260 + 0.244670i
\(482\) −5.09808 19.0263i −0.232211 0.866623i
\(483\) 0 0
\(484\) −2.19615 3.80385i −0.0998251 0.172902i
\(485\) 2.53590 + 0.679492i 0.115149 + 0.0308541i
\(486\) 8.73205 + 15.1244i 0.396094 + 0.686055i
\(487\) 10.6699 + 6.16025i 0.483498 + 0.279148i 0.721873 0.692025i \(-0.243281\pi\)
−0.238375 + 0.971173i \(0.576615\pi\)
\(488\) 17.6603 10.1962i 0.799442 0.461558i
\(489\) 6.46410i 0.292317i
\(490\) 0 0
\(491\) −3.58846 + 3.58846i −0.161945 + 0.161945i −0.783428 0.621483i \(-0.786531\pi\)
0.621483 + 0.783428i \(0.286531\pi\)
\(492\) −4.92820 + 1.32051i −0.222181 + 0.0595331i
\(493\) −2.36603 + 0.633975i −0.106560 + 0.0285528i
\(494\) 5.73205 21.3923i 0.257897 0.962485i
\(495\) 3.63397 + 6.29423i 0.163335 + 0.282905i
\(496\) −7.46410 + 12.9282i −0.335148 + 0.580493i
\(497\) 0 0
\(498\) 1.53590 0.411543i 0.0688253 0.0184417i
\(499\) 6.69615 24.9904i 0.299761 1.11872i −0.637601 0.770367i \(-0.720073\pi\)
0.937362 0.348356i \(-0.113260\pi\)
\(500\) −11.6603 + 11.6603i −0.521462 + 0.521462i
\(501\) −2.92820 10.9282i −0.130822 0.488236i
\(502\) 35.1769i 1.57002i
\(503\) 31.8564i 1.42041i 0.703996 + 0.710203i \(0.251397\pi\)
−0.703996 + 0.710203i \(0.748603\pi\)
\(504\) 0 0
\(505\) 17.5359i 0.780337i
\(506\) −18.7321 −0.832741
\(507\) −1.99038 7.42820i −0.0883959 0.329898i
\(508\) 18.9282i 0.839803i
\(509\) −2.52628 + 9.42820i −0.111975 + 0.417898i −0.999043 0.0437420i \(-0.986072\pi\)
0.887067 + 0.461640i \(0.152739\pi\)
\(510\) 1.09808 + 4.09808i 0.0486236 + 0.181466i
\(511\) 0 0
\(512\) 16.0000 16.0000i 0.707107 0.707107i
\(513\) 4.40192 + 7.62436i 0.194350 + 0.336624i
\(514\) −26.4904 7.09808i −1.16844 0.313083i
\(515\) 5.59808 1.50000i 0.246681 0.0660979i
\(516\) 8.19615 + 4.73205i 0.360815 + 0.208317i
\(517\) 8.95448 8.95448i 0.393818 0.393818i
\(518\) 0 0
\(519\) 1.19615i 0.0525053i
\(520\) −3.46410 + 12.9282i −0.151911 + 0.566939i
\(521\) 13.3756 + 7.72243i 0.585998 + 0.338326i 0.763513 0.645792i \(-0.223473\pi\)
−0.177516 + 0.984118i \(0.556806\pi\)
\(522\) 1.26795 0.732051i 0.0554966 0.0320410i
\(523\) 32.2846 + 8.65064i 1.41171 + 0.378266i 0.882534 0.470248i \(-0.155836\pi\)
0.529173 + 0.848514i \(0.322502\pi\)
\(524\) −15.1962 4.07180i −0.663847 0.177877i
\(525\) 0 0
\(526\) 6.29423 1.68653i 0.274441 0.0735364i
\(527\) −12.0622 20.8923i −0.525437 0.910083i
\(528\) −3.07180 5.32051i −0.133683 0.231545i
\(529\) −1.53590 + 2.66025i −0.0667782 + 0.115663i
\(530\) −3.67949 3.67949i −0.159827 0.159827i
\(531\) −22.6603 22.6603i −0.983371 0.983371i
\(532\) 0 0
\(533\) 18.3923 18.3923i 0.796659 0.796659i
\(534\) 3.80385i 0.164609i
\(535\) 2.59808 + 1.50000i 0.112325 + 0.0648507i
\(536\) 12.5885 + 7.26795i 0.543739 + 0.313928i
\(537\) −4.16025 + 2.40192i −0.179528 + 0.103651i
\(538\) −7.16987 + 12.4186i −0.309115 + 0.535403i
\(539\) 0 0
\(540\) −2.66025 4.60770i −0.114479 0.198284i
\(541\) 2.47372 9.23205i 0.106354 0.396917i −0.892142 0.451756i \(-0.850798\pi\)
0.998495 + 0.0548389i \(0.0174645\pi\)
\(542\) 16.5622 + 4.43782i 0.711406 + 0.190621i
\(543\) 4.90192 8.49038i 0.210362 0.364357i
\(544\) 9.46410 + 35.3205i 0.405770 + 1.51435i
\(545\) −1.98076 −0.0848465
\(546\) 0 0
\(547\) −23.0526 23.0526i −0.985656 0.985656i 0.0142423 0.999899i \(-0.495466\pi\)
−0.999899 + 0.0142423i \(0.995466\pi\)
\(548\) 17.5885 30.4641i 0.751342 1.30136i
\(549\) −5.09808 19.0263i −0.217581 0.812022i
\(550\) 8.80385 + 15.2487i 0.375397 + 0.650207i
\(551\) 0.973721 0.562178i 0.0414819 0.0239496i
\(552\) 6.53590 0.278186
\(553\) 0 0
\(554\) −5.70577 3.29423i −0.242415 0.139958i
\(555\) 0.526279 + 0.141016i 0.0223393 + 0.00598580i
\(556\) −23.8564 23.8564i −1.01174 1.01174i
\(557\) 6.59808 1.76795i 0.279569 0.0749104i −0.116310 0.993213i \(-0.537107\pi\)
0.395879 + 0.918303i \(0.370440\pi\)
\(558\) 10.1962 + 10.1962i 0.431638 + 0.431638i
\(559\) −48.2487 −2.04070
\(560\) 0 0
\(561\) 9.92820 0.419169
\(562\) −0.928203 0.928203i −0.0391539 0.0391539i
\(563\) 2.42820 0.650635i 0.102337 0.0274210i −0.207287 0.978280i \(-0.566464\pi\)
0.309624 + 0.950859i \(0.399797\pi\)
\(564\) −3.12436 + 3.12436i −0.131559 + 0.131559i
\(565\) −1.26795 0.339746i −0.0533430 0.0142932i
\(566\) 18.4186 + 10.6340i 0.774191 + 0.446979i
\(567\) 0 0
\(568\) 1.07180 1.07180i 0.0449716 0.0449716i
\(569\) −5.08846 + 2.93782i −0.213319 + 0.123160i −0.602853 0.797852i \(-0.705969\pi\)
0.389534 + 0.921012i \(0.372636\pi\)
\(570\) −0.973721 1.68653i −0.0407847 0.0706411i
\(571\) −7.16025 26.7224i −0.299647 1.11830i −0.937456 0.348104i \(-0.886826\pi\)
0.637809 0.770195i \(-0.279841\pi\)
\(572\) 27.1244 + 15.6603i 1.13413 + 0.654788i
\(573\) 3.16987 + 3.16987i 0.132423 + 0.132423i
\(574\) 0 0
\(575\) −18.7321 −0.781181
\(576\) −10.9282 18.9282i −0.455342 0.788675i
\(577\) 6.62436 11.4737i 0.275776 0.477657i −0.694555 0.719440i \(-0.744399\pi\)
0.970330 + 0.241782i \(0.0777320\pi\)
\(578\) −33.8564 9.07180i −1.40824 0.377337i
\(579\) −3.08142 + 11.5000i −0.128059 + 0.477924i
\(580\) −0.588457 + 0.339746i −0.0244344 + 0.0141072i
\(581\) 0 0
\(582\) −1.07180 + 1.85641i −0.0444274 + 0.0769505i
\(583\) −10.5455 + 6.08846i −0.436751 + 0.252158i
\(584\) 5.26795 + 19.6603i 0.217989 + 0.813547i
\(585\) 11.1962 + 6.46410i 0.462904 + 0.267258i
\(586\) 15.8564i 0.655022i
\(587\) −21.9282 + 21.9282i −0.905074 + 0.905074i −0.995870 0.0907957i \(-0.971059\pi\)
0.0907957 + 0.995870i \(0.471059\pi\)
\(588\) 0 0
\(589\) 7.83013 + 7.83013i 0.322635 + 0.322635i
\(590\) 10.5167 + 10.5167i 0.432964 + 0.432964i
\(591\) 6.09808 10.5622i 0.250841 0.434470i
\(592\) 4.53590 + 1.21539i 0.186424 + 0.0499522i
\(593\) −5.69615 9.86603i −0.233913 0.405149i 0.725043 0.688703i \(-0.241820\pi\)
−0.958956 + 0.283554i \(0.908486\pi\)
\(594\) −12.0263 + 3.22243i −0.493444 + 0.132218i
\(595\) 0 0
\(596\) −4.07180 + 15.1962i −0.166787 + 0.622459i
\(597\) −5.96410 1.59808i −0.244094 0.0654049i
\(598\) −28.8564 + 16.6603i −1.18003 + 0.681288i
\(599\) 16.6699 + 9.62436i 0.681113 + 0.393241i 0.800274 0.599634i \(-0.204687\pi\)
−0.119162 + 0.992875i \(0.538021\pi\)
\(600\) −3.07180 5.32051i −0.125406 0.217209i
\(601\) 10.0000i 0.407909i −0.978980 0.203954i \(-0.934621\pi\)
0.978980 0.203954i \(-0.0653794\pi\)
\(602\) 0 0
\(603\) 9.92820 9.92820i 0.404308 0.404308i
\(604\) 11.3923 19.7321i 0.463546 0.802886i
\(605\) 1.90192 0.509619i 0.0773242 0.0207190i
\(606\) 13.8301 + 3.70577i 0.561811 + 0.150537i
\(607\) 8.52628 + 14.7679i 0.346071 + 0.599413i 0.985548 0.169398i \(-0.0541823\pi\)
−0.639477 + 0.768810i \(0.720849\pi\)
\(608\) −8.39230 14.5359i −0.340353 0.589509i
\(609\) 0 0
\(610\) 2.36603 + 8.83013i 0.0957976 + 0.357521i
\(611\) 5.83013 21.7583i 0.235862 0.880248i
\(612\) 35.3205 1.42775
\(613\) 2.47372 + 9.23205i 0.0999126 + 0.372879i 0.997718 0.0675126i \(-0.0215063\pi\)
−0.897806 + 0.440392i \(0.854840\pi\)
\(614\) −18.0000 −0.726421
\(615\) 2.28719i 0.0922283i
\(616\) 0 0
\(617\) 0.535898i 0.0215745i 0.999942 + 0.0107872i \(0.00343375\pi\)
−0.999942 + 0.0107872i \(0.996566\pi\)
\(618\) 4.73205i 0.190351i
\(619\) −5.10770 19.0622i −0.205296 0.766174i −0.989359 0.145493i \(-0.953523\pi\)
0.784064 0.620680i \(-0.213144\pi\)
\(620\) −4.73205 4.73205i −0.190044 0.190044i
\(621\) 3.42820 12.7942i 0.137569 0.513415i
\(622\) −8.83013 + 2.36603i −0.354056 + 0.0948690i
\(623\) 0 0
\(624\) −9.46410 5.46410i −0.378867 0.218739i
\(625\) 6.79423 + 11.7679i 0.271769 + 0.470718i
\(626\) 7.90192 29.4904i 0.315824 1.17867i
\(627\) −4.40192 + 1.17949i −0.175796 + 0.0471044i
\(628\) −9.78461 36.5167i −0.390448 1.45717i
\(629\) −5.36603 + 5.36603i −0.213957 + 0.213957i
\(630\) 0 0
\(631\) 32.2487i 1.28380i 0.766788 + 0.641900i \(0.221854\pi\)
−0.766788 + 0.641900i \(0.778146\pi\)
\(632\) 12.1962 45.5167i 0.485137 1.81056i
\(633\) 10.0981 + 5.83013i 0.401362 + 0.231727i
\(634\) 10.3660 + 17.9545i 0.411687 + 0.713064i
\(635\) 8.19615 + 2.19615i 0.325254 + 0.0871517i
\(636\) 3.67949 2.12436i 0.145901 0.0842362i
\(637\) 0 0
\(638\) 0.411543 + 1.53590i 0.0162931 + 0.0608068i
\(639\) −0.732051 1.26795i −0.0289595 0.0501593i
\(640\) 5.07180 + 8.78461i 0.200480 + 0.347242i
\(641\) 5.57180 9.65064i 0.220073 0.381177i −0.734757 0.678330i \(-0.762704\pi\)
0.954830 + 0.297153i \(0.0960372\pi\)
\(642\) −1.73205 + 1.73205i −0.0683586 + 0.0683586i
\(643\) 5.39230 + 5.39230i 0.212652 + 0.212652i 0.805393 0.592741i \(-0.201954\pi\)
−0.592741 + 0.805393i \(0.701954\pi\)
\(644\) 0 0
\(645\) −3.00000 + 3.00000i −0.118125 + 0.118125i
\(646\) 27.1244 1.06719
\(647\) −30.8660 17.8205i −1.21347 0.700596i −0.249955 0.968257i \(-0.580416\pi\)
−0.963513 + 0.267661i \(0.913749\pi\)
\(648\) −18.1962 + 4.87564i −0.714812 + 0.191533i
\(649\) 30.1410 17.4019i 1.18314 0.683085i
\(650\) 27.1244 + 15.6603i 1.06390 + 0.614246i
\(651\) 0 0
\(652\) −24.1244 6.46410i −0.944783 0.253154i
\(653\) −8.72243 + 32.5526i −0.341335 + 1.27388i 0.555501 + 0.831516i \(0.312527\pi\)
−0.896836 + 0.442364i \(0.854140\pi\)
\(654\) 0.418584 1.56218i 0.0163679 0.0610860i
\(655\) 3.52628 6.10770i 0.137783 0.238647i
\(656\) 19.7128i 0.769656i
\(657\) 19.6603 0.767020
\(658\) 0 0
\(659\) 18.8564 + 18.8564i 0.734541 + 0.734541i 0.971516 0.236975i \(-0.0761558\pi\)
−0.236975 + 0.971516i \(0.576156\pi\)
\(660\) 2.66025 0.712813i 0.103550 0.0277462i
\(661\) 5.93782 + 22.1603i 0.230955 + 0.861934i 0.979931 + 0.199337i \(0.0638789\pi\)
−0.748976 + 0.662597i \(0.769454\pi\)
\(662\) −24.8827 + 14.3660i −0.967093 + 0.558351i
\(663\) 15.2942 8.83013i 0.593979 0.342934i
\(664\) 6.14359i 0.238418i
\(665\) 0 0
\(666\) 2.26795 3.92820i 0.0878812 0.152215i
\(667\) −1.63397 0.437822i −0.0632677 0.0169525i
\(668\) 43.7128 1.69130
\(669\) 4.92820 1.32051i 0.190535 0.0510538i
\(670\) −4.60770 + 4.60770i −0.178011 + 0.178011i
\(671\) 21.3923 0.825841
\(672\) 0 0
\(673\) 40.7846 1.57213 0.786066 0.618143i \(-0.212115\pi\)
0.786066 + 0.618143i \(0.212115\pi\)
\(674\) −6.14359 + 6.14359i −0.236642 + 0.236642i
\(675\) −12.0263 + 3.22243i −0.462892 + 0.124031i
\(676\) 29.7128 1.14280
\(677\) 42.7224 + 11.4474i 1.64196 + 0.439961i 0.957345 0.288947i \(-0.0933052\pi\)
0.684611 + 0.728908i \(0.259972\pi\)
\(678\) 0.535898 0.928203i 0.0205811 0.0356474i
\(679\) 0 0
\(680\) −16.3923 −0.628616
\(681\) 5.17949 2.99038i 0.198479 0.114592i
\(682\) −13.5622 + 7.83013i −0.519323 + 0.299831i
\(683\) 12.2128 + 45.5788i 0.467310 + 1.74403i 0.649114 + 0.760691i \(0.275140\pi\)
−0.181804 + 0.983335i \(0.558194\pi\)
\(684\) −15.6603 + 4.19615i −0.598785 + 0.160444i
\(685\) 11.1506 + 11.1506i 0.426044 + 0.426044i
\(686\) 0 0
\(687\) 7.14359 0.272545
\(688\) −25.8564 + 25.8564i −0.985766 + 0.985766i
\(689\) −10.8301 + 18.7583i −0.412595 + 0.714635i
\(690\) −0.758330 + 2.83013i −0.0288691 + 0.107741i
\(691\) −6.16025 + 22.9904i −0.234347 + 0.874595i 0.744095 + 0.668074i \(0.232881\pi\)
−0.978442 + 0.206521i \(0.933786\pi\)
\(692\) 4.46410 + 1.19615i 0.169700 + 0.0454709i
\(693\) 0 0
\(694\) −29.8301 17.2224i −1.13234 0.653755i
\(695\) 13.0981 7.56218i 0.496838 0.286850i
\(696\) −0.143594 0.535898i −0.00544290 0.0203132i
\(697\) 27.5885 + 15.9282i 1.04499 + 0.603324i
\(698\) −12.2487 −0.463621
\(699\) −0.294229 + 0.294229i −0.0111287 + 0.0111287i
\(700\) 0 0
\(701\) −13.3923 13.3923i −0.505820 0.505820i 0.407420 0.913241i \(-0.366428\pi\)
−0.913241 + 0.407420i \(0.866428\pi\)
\(702\) −15.6603 + 15.6603i −0.591058 + 0.591058i
\(703\) 1.74167 3.01666i 0.0656883 0.113776i
\(704\) 22.9282 6.14359i 0.864139 0.231545i
\(705\) −0.990381 1.71539i −0.0372999 0.0646053i
\(706\) 10.1699 + 37.9545i 0.382748 + 1.42844i
\(707\) 0 0
\(708\) −10.5167 + 6.07180i −0.395240 + 0.228192i
\(709\) 45.6506 + 12.2321i 1.71445 + 0.459384i 0.976507 0.215484i \(-0.0691329\pi\)
0.737938 + 0.674868i \(0.235800\pi\)
\(710\) 0.339746 + 0.588457i 0.0127504 + 0.0220844i
\(711\) −39.4186 22.7583i −1.47831 0.853504i
\(712\) −14.1962 3.80385i −0.532023 0.142555i
\(713\) 16.6603i 0.623931i
\(714\) 0 0
\(715\) −9.92820 + 9.92820i −0.371294 + 0.371294i
\(716\) −4.80385 17.9282i −0.179528 0.670008i
\(717\) 4.26795 1.14359i 0.159389 0.0427083i
\(718\) −1.63397 + 6.09808i −0.0609794 + 0.227578i
\(719\) 0.205771 + 0.356406i 0.00767398 + 0.0132917i 0.869837 0.493339i \(-0.164224\pi\)
−0.862163 + 0.506631i \(0.830891\pi\)
\(720\) 9.46410 2.53590i 0.352706 0.0945074i
\(721\) 0 0
\(722\) 13.9282 3.73205i 0.518354 0.138893i
\(723\) −1.86603 + 6.96410i −0.0693982 + 0.258998i
\(724\) 26.7846 + 26.7846i 0.995442 + 0.995442i
\(725\) 0.411543 + 1.53590i 0.0152843 + 0.0570418i
\(726\) 1.60770i 0.0596672i
\(727\) 41.3205i 1.53249i 0.642547 + 0.766246i \(0.277878\pi\)
−0.642547 + 0.766246i \(0.722122\pi\)
\(728\) 0 0
\(729\) 13.5885i 0.503276i
\(730\) −9.12436 −0.337708
\(731\) −15.2942 57.0788i −0.565677 2.11114i
\(732\) −7.46410 −0.275881
\(733\) 8.81347 32.8923i 0.325533 1.21490i −0.588242 0.808685i \(-0.700180\pi\)
0.913775 0.406220i \(-0.133153\pi\)
\(734\) −2.24167 8.36603i −0.0827415 0.308796i
\(735\) 0 0
\(736\) −6.53590 + 24.3923i −0.240916 + 0.899112i
\(737\) 7.62436 + 13.2058i 0.280847 + 0.486441i
\(738\) −18.3923 4.92820i −0.677030 0.181410i
\(739\) 38.4808 10.3109i 1.41554 0.379292i 0.531639 0.846971i \(-0.321576\pi\)
0.883899 + 0.467679i \(0.154910\pi\)
\(740\) −1.05256 + 1.82309i −0.0386928 + 0.0670180i
\(741\) −5.73205 + 5.73205i −0.210572 + 0.210572i
\(742\) 0 0
\(743\) 11.0718i 0.406185i −0.979160 0.203092i \(-0.934901\pi\)
0.979160 0.203092i \(-0.0650992\pi\)
\(744\) 4.73205 2.73205i 0.173485 0.100162i
\(745\) −6.10770 3.52628i −0.223769 0.129193i
\(746\) 1.09808 0.633975i 0.0402034 0.0232115i
\(747\) 5.73205 + 1.53590i 0.209725 + 0.0561956i
\(748\) −9.92820 + 37.0526i −0.363011 + 1.35478i
\(749\) 0 0
\(750\) 5.83013 1.56218i 0.212886 0.0570427i
\(751\) −6.52628 11.3038i −0.238147 0.412483i 0.722035 0.691856i \(-0.243207\pi\)
−0.960183 + 0.279373i \(0.909873\pi\)
\(752\) −8.53590 14.7846i −0.311272 0.539139i
\(753\) −6.43782 + 11.1506i −0.234607 + 0.406352i
\(754\) 2.00000 + 2.00000i 0.0728357 + 0.0728357i
\(755\) 7.22243 + 7.22243i 0.262851 + 0.262851i
\(756\) 0 0
\(757\) −18.6603 + 18.6603i −0.678218 + 0.678218i −0.959597 0.281378i \(-0.909208\pi\)
0.281378 + 0.959597i \(0.409208\pi\)
\(758\) 0.248711i 0.00903360i
\(759\) 5.93782 + 3.42820i 0.215529 + 0.124436i
\(760\) 7.26795 1.94744i 0.263636 0.0706411i
\(761\) −11.7679 + 6.79423i −0.426588 + 0.246291i −0.697892 0.716203i \(-0.745878\pi\)
0.271304 + 0.962494i \(0.412545\pi\)
\(762\) −3.46410 + 6.00000i −0.125491 + 0.217357i
\(763\) 0 0
\(764\) −15.0000 + 8.66025i −0.542681 + 0.313317i
\(765\) −4.09808 + 15.2942i −0.148166 + 0.552964i
\(766\) −34.4186 9.22243i −1.24359 0.333220i
\(767\) 30.9545 53.6147i 1.11770 1.93592i
\(768\) −8.00000 + 2.14359i −0.288675 + 0.0773503i
\(769\) −9.85641 −0.355431 −0.177716 0.984082i \(-0.556871\pi\)
−0.177716 + 0.984082i \(0.556871\pi\)
\(770\) 0 0
\(771\) 7.09808 + 7.09808i 0.255631 + 0.255631i
\(772\) −39.8372 23.0000i −1.43377 0.827788i
\(773\) 2.93782 + 10.9641i 0.105666 + 0.394351i 0.998420 0.0561936i \(-0.0178964\pi\)
−0.892754 + 0.450545i \(0.851230\pi\)
\(774\) 17.6603 + 30.5885i 0.634785 + 1.09948i
\(775\) −13.5622 + 7.83013i −0.487168 + 0.281266i
\(776\) −5.85641 5.85641i −0.210233 0.210233i
\(777\) 0 0
\(778\) 28.3468 + 16.3660i 1.01628 + 0.586750i
\(779\) −14.1244 3.78461i −0.506058 0.135598i
\(780\) 3.46410 3.46410i 0.124035 0.124035i
\(781\) 1.53590 0.411543i 0.0549588 0.0147262i
\(782\) −28.8564 28.8564i −1.03190 1.03190i
\(783\) −1.12436 −0.0401812
\(784\) 0 0
\(785\) 16.9474 0.604880
\(786\) 4.07180 + 4.07180i 0.145236 + 0.145236i
\(787\) 13.1603 3.52628i 0.469112 0.125698i −0.0165161 0.999864i \(-0.505257\pi\)
0.485628 + 0.874165i \(0.338591\pi\)
\(788\) 33.3205 + 33.3205i 1.18699 + 1.18699i
\(789\) −2.30385 0.617314i −0.0820191 0.0219770i
\(790\) 18.2942 + 10.5622i 0.650879 + 0.375785i
\(791\) 0 0
\(792\) 22.9282i 0.814718i
\(793\) 32.9545 19.0263i 1.17025 0.675643i
\(794\) 18.7583 + 32.4904i 0.665708 + 1.15304i
\(795\) 0.492958 + 1.83975i 0.0174834 + 0.0652491i
\(796\) 11.9282 20.6603i 0.422784 0.732283i
\(797\) 13.3397 + 13.3397i 0.472518 + 0.472518i 0.902729 0.430211i \(-0.141561\pi\)
−0.430211 + 0.902729i \(0.641561\pi\)
\(798\) 0 0
\(799\) 27.5885 0.976009
\(800\) 22.9282 6.14359i 0.810634 0.217209i
\(801\) −7.09808 + 12.2942i −0.250798 + 0.434395i
\(802\) 20.4904 + 5.49038i 0.723541 + 0.193872i
\(803\) −5.52628 + 20.6244i −0.195018 + 0.727818i
\(804\) −2.66025 4.60770i −0.0938199 0.162501i
\(805\) 0 0
\(806\) −13.9282 + 24.1244i −0.490600 + 0.849744i
\(807\) 4.54552 2.62436i 0.160010 0.0923817i
\(808\) −27.6603 + 47.9090i −0.973084 + 1.68543i
\(809\) −29.4282 16.9904i −1.03464 0.597350i −0.116330 0.993211i \(-0.537113\pi\)
−0.918311 + 0.395861i \(0.870446\pi\)
\(810\) 8.44486i 0.296722i
\(811\) −24.3205 + 24.3205i −0.854009 + 0.854009i −0.990624 0.136616i \(-0.956377\pi\)
0.136616 + 0.990624i \(0.456377\pi\)
\(812\) 0 0
\(813\) −4.43782 4.43782i −0.155641 0.155641i
\(814\) 3.48334 + 3.48334i 0.122091 + 0.122091i
\(815\) 5.59808 9.69615i 0.196092 0.339641i
\(816\) 3.46410 12.9282i 0.121268 0.452578i
\(817\) 13.5622 + 23.4904i 0.474481 + 0.821824i
\(818\) 11.8301 3.16987i 0.413631 0.110832i
\(819\) 0 0
\(820\) 8.53590 + 2.28719i 0.298087 + 0.0798720i
\(821\) 0.598076 + 0.160254i 0.0208730 + 0.00559290i 0.269240 0.963073i \(-0.413227\pi\)
−0.248367 + 0.968666i \(0.579894\pi\)
\(822\) −11.1506 + 6.43782i −0.388923 + 0.224545i
\(823\) −14.9378 8.62436i −0.520700 0.300626i 0.216521 0.976278i \(-0.430529\pi\)
−0.737221 + 0.675652i \(0.763862\pi\)
\(824\) −17.6603 4.73205i −0.615224 0.164849i
\(825\) 6.44486i 0.224381i
\(826\) 0 0
\(827\) −3.78461 + 3.78461i −0.131604 + 0.131604i −0.769840 0.638237i \(-0.779664\pi\)
0.638237 + 0.769840i \(0.279664\pi\)
\(828\) 21.1244 + 12.1962i 0.734122 + 0.423846i
\(829\) 3.06218 0.820508i 0.106354 0.0284974i −0.205250 0.978710i \(-0.565801\pi\)
0.311603 + 0.950212i \(0.399134\pi\)
\(830\) −2.66025 0.712813i −0.0923388 0.0247421i
\(831\) 1.20577 + 2.08846i 0.0418277 + 0.0724478i
\(832\) 29.8564 29.8564i 1.03508 1.03508i
\(833\) 0 0
\(834\) 3.19615 + 11.9282i 0.110674 + 0.413040i
\(835\) −5.07180 + 18.9282i −0.175517 + 0.655037i
\(836\) 17.6077i 0.608975i
\(837\) −2.86603 10.6962i −0.0990643 0.369713i
\(838\) 38.0000 1.31269
\(839\) 17.7128i 0.611514i −0.952110 0.305757i \(-0.901090\pi\)
0.952110 0.305757i \(-0.0989096\pi\)
\(840\) 0 0
\(841\) 28.8564i 0.995048i
\(842\) 17.3205i 0.596904i
\(843\) 0.124356 + 0.464102i 0.00428304 + 0.0159845i
\(844\) −31.8564 + 31.8564i −1.09654 + 1.09654i
\(845\) −3.44744 + 12.8660i −0.118596 + 0.442605i
\(846\) −15.9282 + 4.26795i −0.547623 + 0.146735i
\(847\) 0 0
\(848\) 4.24871 + 15.8564i 0.145901 + 0.544511i
\(849\) −3.89230 6.74167i −0.133584 0.231374i
\(850\) −9.92820 + 37.0526i −0.340535 + 1.27089i
\(851\) −5.06218 + 1.35641i −0.173529 + 0.0464970i
\(852\) −0.535898 + 0.143594i −0.0183596 + 0.00491943i
\(853\) 11.8756 11.8756i 0.406614 0.406614i −0.473942 0.880556i \(-0.657169\pi\)
0.880556 + 0.473942i \(0.157169\pi\)
\(854\) 0 0
\(855\) 7.26795i 0.248559i
\(856\) −4.73205 8.19615i −0.161738 0.280139i
\(857\) −11.8923 6.86603i −0.406233 0.234539i 0.282937 0.959139i \(-0.408691\pi\)
−0.689170 + 0.724600i \(0.742025\pi\)
\(858\) −5.73205 9.92820i −0.195689 0.338943i
\(859\) −13.6244 3.65064i −0.464857 0.124558i 0.0187858 0.999824i \(-0.494020\pi\)
−0.483643 + 0.875265i \(0.660687\pi\)
\(860\) −8.19615 14.1962i −0.279486 0.484085i
\(861\) 0 0
\(862\) 11.2224 + 41.8827i 0.382238 + 1.42653i
\(863\) 16.3301 + 28.2846i 0.555884 + 0.962819i 0.997834 + 0.0657797i \(0.0209535\pi\)
−0.441950 + 0.897040i \(0.645713\pi\)
\(864\) 16.7846i 0.571024i
\(865\) −1.03590 + 1.79423i −0.0352216 + 0.0610056i
\(866\) 33.1769 33.1769i 1.12740 1.12740i
\(867\) 9.07180 + 9.07180i 0.308094 + 0.308094i
\(868\) 0 0
\(869\) 34.9545 34.9545i 1.18575 1.18575i
\(870\) 0.248711 0.00843210
\(871\) 23.4904 + 13.5622i 0.795941 + 0.459537i
\(872\) 5.41154 + 3.12436i 0.183258 + 0.105804i
\(873\) −6.92820 + 4.00000i −0.234484 + 0.135379i
\(874\) 16.2224 + 9.36603i 0.548732 + 0.316811i
\(875\) 0 0
\(876\) 1.92820 7.19615i 0.0651479 0.243135i
\(877\) 8.18653 30.5526i 0.276440 1.03169i −0.678431 0.734664i \(-0.737340\pi\)
0.954871 0.297022i \(-0.0959936\pi\)
\(878\) −2.75833 + 10.2942i −0.0930891 + 0.347413i
\(879\) −2.90192 + 5.02628i −0.0978795 + 0.169532i
\(880\) 10.6410i 0.358709i
\(881\) −50.0000 −1.68454 −0.842271 0.539054i \(-0.818782\pi\)
−0.842271 + 0.539054i \(0.818782\pi\)
\(882\) 0 0
\(883\) −5.00000 5.00000i −0.168263 0.168263i 0.617952 0.786216i \(-0.287963\pi\)
−0.786216 + 0.617952i \(0.787963\pi\)
\(884\) 17.6603 + 65.9090i 0.593979 + 2.21676i
\(885\) −1.40897 5.25833i −0.0473619 0.176757i
\(886\) −13.2224 + 7.63397i −0.444216 + 0.256468i
\(887\) 39.7750 22.9641i 1.33551 0.771059i 0.349375 0.936983i \(-0.386394\pi\)
0.986139 + 0.165924i \(0.0530606\pi\)
\(888\) −1.21539 1.21539i −0.0407858 0.0407858i
\(889\) 0 0
\(890\) 3.29423 5.70577i 0.110423 0.191258i
\(891\) −19.0885 5.11474i −0.639487 0.171350i
\(892\) 19.7128i 0.660034i
\(893\) −12.2321 + 3.27757i −0.409330 + 0.109680i
\(894\) 4.07180 4.07180i 0.136181 0.136181i
\(895\) 8.32051 0.278124
\(896\) 0 0
\(897\) 12.1962 0.407218
\(898\) −23.3205 + 23.3205i −0.778215 + 0.778215i
\(899\) −1.36603 + 0.366025i −0.0455595 + 0.0122076i
\(900\) 22.9282i 0.764273i
\(901\) −25.6244 6.86603i −0.853671 0.228740i
\(902\) 10.3397 17.9090i 0.344276 0.596303i
\(903\) 0 0
\(904\) 2.92820 + 2.92820i 0.0973906 + 0.0973906i
\(905\) −14.7058 + 8.49038i −0.488836 + 0.282230i
\(906\) −7.22243 + 4.16987i −0.239949 + 0.138535i
\(907\) 7.16025 + 26.7224i 0.237752 + 0.887304i 0.976889 + 0.213748i \(0.0685672\pi\)
−0.739136 + 0.673556i \(0.764766\pi\)
\(908\) 5.98076 + 22.3205i 0.198479 + 0.740732i
\(909\) 37.7846 + 37.7846i 1.25324 + 1.25324i
\(910\) 0 0
\(911\) 7.32051 0.242539 0.121270 0.992620i \(-0.461303\pi\)
0.121270 + 0.992620i \(0.461303\pi\)
\(912\) 6.14359i 0.203435i
\(913\) −3.22243 + 5.58142i −0.106647 + 0.184718i
\(914\) 6.88269 25.6865i 0.227659 0.849635i
\(915\) 0.866025 3.23205i 0.0286299 0.106848i
\(916\) −7.14359 + 26.6603i −0.236031 + 0.880880i
\(917\) 0 0
\(918\) −23.4904 13.5622i −0.775298 0.447619i
\(919\) −15.8660 + 9.16025i −0.523372 + 0.302169i −0.738313 0.674458i \(-0.764377\pi\)
0.214941 + 0.976627i \(0.431044\pi\)
\(920\) −9.80385 5.66025i −0.323223 0.186613i
\(921\) 5.70577 + 3.29423i 0.188012 + 0.108549i
\(922\) −37.3205 −1.22909
\(923\) 2.00000 2.00000i 0.0658308 0.0658308i
\(924\) 0 0
\(925\) 3.48334 + 3.48334i 0.114531 + 0.114531i
\(926\) 2.14359 2.14359i 0.0704429 0.0704429i
\(927\) −8.83013 + 15.2942i −0.290019 + 0.502328i
\(928\) 2.14359 0.0703669
\(929\) 25.0167 + 43.3301i 0.820770 + 1.42162i 0.905110 + 0.425178i \(0.139789\pi\)
−0.0843396 + 0.996437i \(0.526878\pi\)
\(930\) 0.633975 + 2.36603i 0.0207888 + 0.0775850i
\(931\) 0 0
\(932\) −0.803848 1.39230i −0.0263309 0.0456065i
\(933\) 3.23205 + 0.866025i 0.105813 + 0.0283524i
\(934\) −19.0263 32.9545i −0.622559 1.07830i
\(935\) −14.8923 8.59808i −0.487030 0.281187i
\(936\) −20.3923 35.3205i −0.666543 1.15449i
\(937\) 29.0718i 0.949734i 0.880058 + 0.474867i \(0.157504\pi\)
−0.880058 + 0.474867i \(0.842496\pi\)
\(938\) 0 0
\(939\) −7.90192 + 7.90192i −0.257870 + 0.257870i
\(940\) 7.39230 1.98076i 0.241110 0.0646053i
\(941\) 23.5263 6.30385i 0.766935 0.205500i 0.145918 0.989297i \(-0.453386\pi\)
0.621017 + 0.783797i \(0.286720\pi\)
\(942\) −3.58142 + 13.3660i −0.116689 + 0.435489i
\(943\) 11.0000 + 19.0526i 0.358209 + 0.620437i
\(944\) −12.1436 45.3205i −0.395240 1.47506i
\(945\) 0 0
\(946\) −37.0526 + 9.92820i −1.20468 + 0.322794i
\(947\) −1.44744 + 5.40192i −0.0470355 + 0.175539i −0.985448 0.169979i \(-0.945630\pi\)
0.938412 + 0.345518i \(0.112297\pi\)
\(948\) −12.1962 + 12.1962i −0.396113 + 0.396113i
\(949\) 9.83013 + 36.6865i 0.319099 + 1.19090i
\(950\) 17.6077i 0.571269i
\(951\) 7.58846i 0.246073i
\(952\) 0 0
\(953\) 16.5359i 0.535650i 0.963468 + 0.267825i \(0.0863050\pi\)
−0.963468 + 0.267825i \(0.913695\pi\)
\(954\) 15.8564 0.513370
\(955\) −2.00962 7.50000i −0.0650297 0.242694i
\(956\) 17.0718i 0.552141i
\(957\) 0.150635 0.562178i 0.00486934 0.0181726i
\(958\) −5.70577 21.2942i −0.184345 0.687985i
\(959\) 0 0
\(960\) 3.71281i 0.119831i
\(961\) 8.53590 + 14.7846i 0.275352 + 0.476923i
\(962\) 8.46410 + 2.26795i 0.272894 + 0.0731216i
\(963\) −8.83013 + 2.36603i −0.284547 + 0.0762441i
\(964\) −24.1244 13.9282i −0.776993 0.448597i
\(965\) 14.5814 14.5814i 0.469392 0.469392i
\(966\) 0 0
\(967\) 60.2487i 1.93747i −0.248102 0.968734i \(-0.579807\pi\)
0.248102 0.968734i \(-0.420193\pi\)
\(968\) −6.00000 1.60770i −0.192847 0.0516733i
\(969\) −8.59808 4.96410i −0.276210 0.159470i
\(970\) 3.21539 1.85641i 0.103240 0.0596056i
\(971\) 52.4090 + 14.0429i 1.68188 + 0.450659i 0.968275 0.249885i \(-0.0803930\pi\)
0.713608 + 0.700545i \(0.247060\pi\)
\(972\) 23.8564 + 6.39230i 0.765195 + 0.205033i
\(973\) 0 0
\(974\) 16.8301 4.50962i 0.539272 0.144498i
\(975\) −5.73205 9.92820i −0.183573 0.317957i
\(976\) 7.46410 27.8564i 0.238920 0.891662i
\(977\) 8.57180 14.8468i 0.274236 0.474991i −0.695706 0.718327i \(-0.744908\pi\)
0.969942 + 0.243336i \(0.0782417\pi\)
\(978\) 6.46410 + 6.46410i 0.206699 + 0.206699i
\(979\) −10.9019 10.9019i −0.348427 0.348427i
\(980\) 0 0
\(981\) 4.26795 4.26795i 0.136265 0.136265i
\(982\) 7.17691i 0.229025i
\(983\) −17.1340 9.89230i −0.546489 0.315516i 0.201216 0.979547i \(-0.435511\pi\)
−0.747705 + 0.664031i \(0.768844\pi\)
\(984\) −3.60770 + 6.24871i −0.115009 + 0.199202i
\(985\) −18.2942 + 10.5622i −0.582903 + 0.336539i
\(986\) −1.73205 + 3.00000i −0.0551597 + 0.0955395i
\(987\) 0 0
\(988\) −15.6603 27.1244i −0.498219 0.862941i
\(989\) 10.5622 39.4186i 0.335858 1.25344i
\(990\) 9.92820 + 2.66025i 0.315539 + 0.0845484i
\(991\) 4.20577 7.28461i 0.133601 0.231403i −0.791461 0.611219i \(-0.790679\pi\)
0.925062 + 0.379816i \(0.124013\pi\)
\(992\) 5.46410 + 20.3923i 0.173485 + 0.647456i
\(993\) 10.5167 0.333736
\(994\) 0 0
\(995\) 7.56218 + 7.56218i 0.239737 + 0.239737i
\(996\) 1.12436 1.94744i 0.0356266 0.0617070i
\(997\) −0.401924 1.50000i −0.0127291 0.0475055i 0.959269 0.282494i \(-0.0911616\pi\)
−0.971998 + 0.234988i \(0.924495\pi\)
\(998\) −18.2942 31.6865i −0.579094 1.00302i
\(999\) −3.01666 + 1.74167i −0.0954429 + 0.0551040i
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 784.2.x.h.557.1 4
7.2 even 3 784.2.x.a.765.1 4
7.3 odd 6 784.2.m.e.589.2 4
7.4 even 3 784.2.m.d.589.2 4
7.5 odd 6 112.2.w.a.93.1 yes 4
7.6 odd 2 112.2.w.b.109.1 yes 4
16.5 even 4 784.2.x.a.165.1 4
28.19 even 6 448.2.ba.b.401.1 4
28.27 even 2 448.2.ba.a.81.1 4
56.5 odd 6 896.2.ba.d.289.1 4
56.13 odd 2 896.2.ba.b.417.1 4
56.19 even 6 896.2.ba.a.289.1 4
56.27 even 2 896.2.ba.c.417.1 4
112.5 odd 12 112.2.w.b.37.1 yes 4
112.13 odd 4 896.2.ba.d.865.1 4
112.19 even 12 896.2.ba.c.737.1 4
112.27 even 4 448.2.ba.b.305.1 4
112.37 even 12 inner 784.2.x.h.373.1 4
112.53 even 12 784.2.m.d.197.2 4
112.61 odd 12 896.2.ba.b.737.1 4
112.69 odd 4 112.2.w.a.53.1 4
112.75 even 12 448.2.ba.a.177.1 4
112.83 even 4 896.2.ba.a.865.1 4
112.101 odd 12 784.2.m.e.197.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
112.2.w.a.53.1 4 112.69 odd 4
112.2.w.a.93.1 yes 4 7.5 odd 6
112.2.w.b.37.1 yes 4 112.5 odd 12
112.2.w.b.109.1 yes 4 7.6 odd 2
448.2.ba.a.81.1 4 28.27 even 2
448.2.ba.a.177.1 4 112.75 even 12
448.2.ba.b.305.1 4 112.27 even 4
448.2.ba.b.401.1 4 28.19 even 6
784.2.m.d.197.2 4 112.53 even 12
784.2.m.d.589.2 4 7.4 even 3
784.2.m.e.197.2 4 112.101 odd 12
784.2.m.e.589.2 4 7.3 odd 6
784.2.x.a.165.1 4 16.5 even 4
784.2.x.a.765.1 4 7.2 even 3
784.2.x.h.373.1 4 112.37 even 12 inner
784.2.x.h.557.1 4 1.1 even 1 trivial
896.2.ba.a.289.1 4 56.19 even 6
896.2.ba.a.865.1 4 112.83 even 4
896.2.ba.b.417.1 4 56.13 odd 2
896.2.ba.b.737.1 4 112.61 odd 12
896.2.ba.c.417.1 4 56.27 even 2
896.2.ba.c.737.1 4 112.19 even 12
896.2.ba.d.289.1 4 56.5 odd 6
896.2.ba.d.865.1 4 112.13 odd 4