Properties

Label 1950.2.z.h.1699.1
Level $1950$
Weight $2$
Character 1950.1699
Analytic conductor $15.571$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1950,2,Mod(1699,1950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1950.1699");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.z (of order \(6\), degree \(2\), 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: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1699.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1950.1699
Dual form 1950.2.z.h.1849.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(1.73205 - 1.00000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(1.73205 - 1.00000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{11} -1.00000i q^{12} +(-3.46410 + 1.00000i) q^{13} -2.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.73205 - 1.00000i) q^{17} -1.00000i q^{18} +(3.00000 + 5.19615i) q^{19} -2.00000 q^{21} +(0.866025 - 0.500000i) q^{22} +(-2.59808 - 1.50000i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(3.50000 + 0.866025i) q^{26} -1.00000i q^{27} +(1.73205 + 1.00000i) q^{28} +(-0.500000 + 0.866025i) q^{29} -3.00000 q^{31} +(0.866025 - 0.500000i) q^{32} +(0.866025 - 0.500000i) q^{33} -2.00000 q^{34} +(-0.500000 + 0.866025i) q^{36} +(4.33013 + 2.50000i) q^{37} -6.00000i q^{38} +(3.50000 + 0.866025i) q^{39} +(-5.00000 + 8.66025i) q^{41} +(1.73205 + 1.00000i) q^{42} +(-4.33013 + 2.50000i) q^{43} -1.00000 q^{44} +(1.50000 + 2.59808i) q^{46} +3.00000i q^{47} +(0.866025 - 0.500000i) q^{48} +(-1.50000 + 2.59808i) q^{49} -2.00000 q^{51} +(-2.59808 - 2.50000i) q^{52} -14.0000i q^{53} +(-0.500000 + 0.866025i) q^{54} +(-1.00000 - 1.73205i) q^{56} -6.00000i q^{57} +(0.866025 - 0.500000i) q^{58} +(-2.50000 - 4.33013i) q^{59} +(5.00000 + 8.66025i) q^{61} +(2.59808 + 1.50000i) q^{62} +(1.73205 + 1.00000i) q^{63} -1.00000 q^{64} -1.00000 q^{66} +(1.73205 + 1.00000i) q^{68} +(1.50000 + 2.59808i) q^{69} +(-2.00000 - 3.46410i) q^{71} +(0.866025 - 0.500000i) q^{72} +2.00000i q^{73} +(-2.50000 - 4.33013i) q^{74} +(-3.00000 + 5.19615i) q^{76} +2.00000i q^{77} +(-2.59808 - 2.50000i) q^{78} -5.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(8.66025 - 5.00000i) q^{82} +6.00000i q^{83} +(-1.00000 - 1.73205i) q^{84} +5.00000 q^{86} +(0.866025 - 0.500000i) q^{87} +(0.866025 + 0.500000i) q^{88} +(5.00000 - 8.66025i) q^{89} +(-5.00000 + 5.19615i) q^{91} -3.00000i q^{92} +(2.59808 + 1.50000i) q^{93} +(1.50000 - 2.59808i) q^{94} -1.00000 q^{96} +(-8.66025 + 5.00000i) q^{97} +(2.59808 - 1.50000i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{4} + 2 q^{6} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{4} + 2 q^{6} + 2 q^{9} - 2 q^{11} - 8 q^{14} - 2 q^{16} + 12 q^{19} - 8 q^{21} - 2 q^{24} + 14 q^{26} - 2 q^{29} - 12 q^{31} - 8 q^{34} - 2 q^{36} + 14 q^{39} - 20 q^{41} - 4 q^{44} + 6 q^{46} - 6 q^{49} - 8 q^{51} - 2 q^{54} - 4 q^{56} - 10 q^{59} + 20 q^{61} - 4 q^{64} - 4 q^{66} + 6 q^{69} - 8 q^{71} - 10 q^{74} - 12 q^{76} - 20 q^{79} - 2 q^{81} - 4 q^{84} + 20 q^{86} + 20 q^{89} - 20 q^{91} + 6 q^{94} - 4 q^{96} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) −0.866025 0.500000i −0.500000 0.288675i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0 0
\(6\) 0.500000 + 0.866025i 0.204124 + 0.353553i
\(7\) 1.73205 1.00000i 0.654654 0.377964i −0.135583 0.990766i \(-0.543291\pi\)
0.790237 + 0.612801i \(0.209957\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) −0.500000 + 0.866025i −0.150756 + 0.261116i −0.931505 0.363727i \(-0.881504\pi\)
0.780750 + 0.624844i \(0.214837\pi\)
\(12\) 1.00000i 0.288675i
\(13\) −3.46410 + 1.00000i −0.960769 + 0.277350i
\(14\) −2.00000 −0.534522
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.73205 1.00000i 0.420084 0.242536i −0.275029 0.961436i \(-0.588688\pi\)
0.695113 + 0.718900i \(0.255354\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 3.00000 + 5.19615i 0.688247 + 1.19208i 0.972404 + 0.233301i \(0.0749529\pi\)
−0.284157 + 0.958778i \(0.591714\pi\)
\(20\) 0 0
\(21\) −2.00000 −0.436436
\(22\) 0.866025 0.500000i 0.184637 0.106600i
\(23\) −2.59808 1.50000i −0.541736 0.312772i 0.204046 0.978961i \(-0.434591\pi\)
−0.745782 + 0.666190i \(0.767924\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) 0 0
\(26\) 3.50000 + 0.866025i 0.686406 + 0.169842i
\(27\) 1.00000i 0.192450i
\(28\) 1.73205 + 1.00000i 0.327327 + 0.188982i
\(29\) −0.500000 + 0.866025i −0.0928477 + 0.160817i −0.908708 0.417432i \(-0.862930\pi\)
0.815861 + 0.578249i \(0.196264\pi\)
\(30\) 0 0
\(31\) −3.00000 −0.538816 −0.269408 0.963026i \(-0.586828\pi\)
−0.269408 + 0.963026i \(0.586828\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 0.866025 0.500000i 0.150756 0.0870388i
\(34\) −2.00000 −0.342997
\(35\) 0 0
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) 4.33013 + 2.50000i 0.711868 + 0.410997i 0.811752 0.584002i \(-0.198514\pi\)
−0.0998840 + 0.994999i \(0.531847\pi\)
\(38\) 6.00000i 0.973329i
\(39\) 3.50000 + 0.866025i 0.560449 + 0.138675i
\(40\) 0 0
\(41\) −5.00000 + 8.66025i −0.780869 + 1.35250i 0.150567 + 0.988600i \(0.451890\pi\)
−0.931436 + 0.363905i \(0.881443\pi\)
\(42\) 1.73205 + 1.00000i 0.267261 + 0.154303i
\(43\) −4.33013 + 2.50000i −0.660338 + 0.381246i −0.792406 0.609994i \(-0.791172\pi\)
0.132068 + 0.991241i \(0.457838\pi\)
\(44\) −1.00000 −0.150756
\(45\) 0 0
\(46\) 1.50000 + 2.59808i 0.221163 + 0.383065i
\(47\) 3.00000i 0.437595i 0.975770 + 0.218797i \(0.0702134\pi\)
−0.975770 + 0.218797i \(0.929787\pi\)
\(48\) 0.866025 0.500000i 0.125000 0.0721688i
\(49\) −1.50000 + 2.59808i −0.214286 + 0.371154i
\(50\) 0 0
\(51\) −2.00000 −0.280056
\(52\) −2.59808 2.50000i −0.360288 0.346688i
\(53\) 14.0000i 1.92305i −0.274721 0.961524i \(-0.588586\pi\)
0.274721 0.961524i \(-0.411414\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 0 0
\(56\) −1.00000 1.73205i −0.133631 0.231455i
\(57\) 6.00000i 0.794719i
\(58\) 0.866025 0.500000i 0.113715 0.0656532i
\(59\) −2.50000 4.33013i −0.325472 0.563735i 0.656136 0.754643i \(-0.272190\pi\)
−0.981608 + 0.190909i \(0.938857\pi\)
\(60\) 0 0
\(61\) 5.00000 + 8.66025i 0.640184 + 1.10883i 0.985391 + 0.170305i \(0.0544754\pi\)
−0.345207 + 0.938527i \(0.612191\pi\)
\(62\) 2.59808 + 1.50000i 0.329956 + 0.190500i
\(63\) 1.73205 + 1.00000i 0.218218 + 0.125988i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −1.00000 −0.123091
\(67\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(68\) 1.73205 + 1.00000i 0.210042 + 0.121268i
\(69\) 1.50000 + 2.59808i 0.180579 + 0.312772i
\(70\) 0 0
\(71\) −2.00000 3.46410i −0.237356 0.411113i 0.722599 0.691268i \(-0.242948\pi\)
−0.959955 + 0.280155i \(0.909614\pi\)
\(72\) 0.866025 0.500000i 0.102062 0.0589256i
\(73\) 2.00000i 0.234082i 0.993127 + 0.117041i \(0.0373409\pi\)
−0.993127 + 0.117041i \(0.962659\pi\)
\(74\) −2.50000 4.33013i −0.290619 0.503367i
\(75\) 0 0
\(76\) −3.00000 + 5.19615i −0.344124 + 0.596040i
\(77\) 2.00000i 0.227921i
\(78\) −2.59808 2.50000i −0.294174 0.283069i
\(79\) −5.00000 −0.562544 −0.281272 0.959628i \(-0.590756\pi\)
−0.281272 + 0.959628i \(0.590756\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 8.66025 5.00000i 0.956365 0.552158i
\(83\) 6.00000i 0.658586i 0.944228 + 0.329293i \(0.106810\pi\)
−0.944228 + 0.329293i \(0.893190\pi\)
\(84\) −1.00000 1.73205i −0.109109 0.188982i
\(85\) 0 0
\(86\) 5.00000 0.539164
\(87\) 0.866025 0.500000i 0.0928477 0.0536056i
\(88\) 0.866025 + 0.500000i 0.0923186 + 0.0533002i
\(89\) 5.00000 8.66025i 0.529999 0.917985i −0.469389 0.882992i \(-0.655526\pi\)
0.999388 0.0349934i \(-0.0111410\pi\)
\(90\) 0 0
\(91\) −5.00000 + 5.19615i −0.524142 + 0.544705i
\(92\) 3.00000i 0.312772i
\(93\) 2.59808 + 1.50000i 0.269408 + 0.155543i
\(94\) 1.50000 2.59808i 0.154713 0.267971i
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) −8.66025 + 5.00000i −0.879316 + 0.507673i −0.870433 0.492287i \(-0.836161\pi\)
−0.00888289 + 0.999961i \(0.502828\pi\)
\(98\) 2.59808 1.50000i 0.262445 0.151523i
\(99\) −1.00000 −0.100504
\(100\) 0 0
\(101\) −7.00000 + 12.1244i −0.696526 + 1.20642i 0.273138 + 0.961975i \(0.411939\pi\)
−0.969664 + 0.244443i \(0.921395\pi\)
\(102\) 1.73205 + 1.00000i 0.171499 + 0.0990148i
\(103\) 6.00000i 0.591198i 0.955312 + 0.295599i \(0.0955191\pi\)
−0.955312 + 0.295599i \(0.904481\pi\)
\(104\) 1.00000 + 3.46410i 0.0980581 + 0.339683i
\(105\) 0 0
\(106\) −7.00000 + 12.1244i −0.679900 + 1.17762i
\(107\) 5.19615 + 3.00000i 0.502331 + 0.290021i 0.729676 0.683793i \(-0.239671\pi\)
−0.227345 + 0.973814i \(0.573004\pi\)
\(108\) 0.866025 0.500000i 0.0833333 0.0481125i
\(109\) 6.00000 0.574696 0.287348 0.957826i \(-0.407226\pi\)
0.287348 + 0.957826i \(0.407226\pi\)
\(110\) 0 0
\(111\) −2.50000 4.33013i −0.237289 0.410997i
\(112\) 2.00000i 0.188982i
\(113\) −14.7224 + 8.50000i −1.38497 + 0.799613i −0.992743 0.120256i \(-0.961629\pi\)
−0.392227 + 0.919868i \(0.628295\pi\)
\(114\) −3.00000 + 5.19615i −0.280976 + 0.486664i
\(115\) 0 0
\(116\) −1.00000 −0.0928477
\(117\) −2.59808 2.50000i −0.240192 0.231125i
\(118\) 5.00000i 0.460287i
\(119\) 2.00000 3.46410i 0.183340 0.317554i
\(120\) 0 0
\(121\) 5.00000 + 8.66025i 0.454545 + 0.787296i
\(122\) 10.0000i 0.905357i
\(123\) 8.66025 5.00000i 0.780869 0.450835i
\(124\) −1.50000 2.59808i −0.134704 0.233314i
\(125\) 0 0
\(126\) −1.00000 1.73205i −0.0890871 0.154303i
\(127\) 12.1244 + 7.00000i 1.07586 + 0.621150i 0.929777 0.368122i \(-0.119999\pi\)
0.146085 + 0.989272i \(0.453333\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 5.00000 0.440225
\(130\) 0 0
\(131\) 13.0000 1.13582 0.567908 0.823092i \(-0.307753\pi\)
0.567908 + 0.823092i \(0.307753\pi\)
\(132\) 0.866025 + 0.500000i 0.0753778 + 0.0435194i
\(133\) 10.3923 + 6.00000i 0.901127 + 0.520266i
\(134\) 0 0
\(135\) 0 0
\(136\) −1.00000 1.73205i −0.0857493 0.148522i
\(137\) −7.79423 + 4.50000i −0.665906 + 0.384461i −0.794524 0.607233i \(-0.792279\pi\)
0.128618 + 0.991694i \(0.458946\pi\)
\(138\) 3.00000i 0.255377i
\(139\) 5.00000 + 8.66025i 0.424094 + 0.734553i 0.996335 0.0855324i \(-0.0272591\pi\)
−0.572241 + 0.820086i \(0.693926\pi\)
\(140\) 0 0
\(141\) 1.50000 2.59808i 0.126323 0.218797i
\(142\) 4.00000i 0.335673i
\(143\) 0.866025 3.50000i 0.0724207 0.292685i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) 1.00000 1.73205i 0.0827606 0.143346i
\(147\) 2.59808 1.50000i 0.214286 0.123718i
\(148\) 5.00000i 0.410997i
\(149\) 5.50000 + 9.52628i 0.450578 + 0.780423i 0.998422 0.0561570i \(-0.0178847\pi\)
−0.547844 + 0.836580i \(0.684551\pi\)
\(150\) 0 0
\(151\) 24.0000 1.95309 0.976546 0.215308i \(-0.0690756\pi\)
0.976546 + 0.215308i \(0.0690756\pi\)
\(152\) 5.19615 3.00000i 0.421464 0.243332i
\(153\) 1.73205 + 1.00000i 0.140028 + 0.0808452i
\(154\) 1.00000 1.73205i 0.0805823 0.139573i
\(155\) 0 0
\(156\) 1.00000 + 3.46410i 0.0800641 + 0.277350i
\(157\) 25.0000i 1.99522i 0.0691164 + 0.997609i \(0.477982\pi\)
−0.0691164 + 0.997609i \(0.522018\pi\)
\(158\) 4.33013 + 2.50000i 0.344486 + 0.198889i
\(159\) −7.00000 + 12.1244i −0.555136 + 0.961524i
\(160\) 0 0
\(161\) −6.00000 −0.472866
\(162\) 0.866025 0.500000i 0.0680414 0.0392837i
\(163\) −14.7224 + 8.50000i −1.15315 + 0.665771i −0.949653 0.313304i \(-0.898564\pi\)
−0.203497 + 0.979076i \(0.565231\pi\)
\(164\) −10.0000 −0.780869
\(165\) 0 0
\(166\) 3.00000 5.19615i 0.232845 0.403300i
\(167\) 6.06218 + 3.50000i 0.469105 + 0.270838i 0.715865 0.698239i \(-0.246033\pi\)
−0.246760 + 0.969077i \(0.579366\pi\)
\(168\) 2.00000i 0.154303i
\(169\) 11.0000 6.92820i 0.846154 0.532939i
\(170\) 0 0
\(171\) −3.00000 + 5.19615i −0.229416 + 0.397360i
\(172\) −4.33013 2.50000i −0.330169 0.190623i
\(173\) −3.46410 + 2.00000i −0.263371 + 0.152057i −0.625871 0.779926i \(-0.715256\pi\)
0.362500 + 0.931984i \(0.381923\pi\)
\(174\) −1.00000 −0.0758098
\(175\) 0 0
\(176\) −0.500000 0.866025i −0.0376889 0.0652791i
\(177\) 5.00000i 0.375823i
\(178\) −8.66025 + 5.00000i −0.649113 + 0.374766i
\(179\) −3.50000 + 6.06218i −0.261602 + 0.453108i −0.966668 0.256034i \(-0.917584\pi\)
0.705066 + 0.709142i \(0.250918\pi\)
\(180\) 0 0
\(181\) 16.0000 1.18927 0.594635 0.803996i \(-0.297296\pi\)
0.594635 + 0.803996i \(0.297296\pi\)
\(182\) 6.92820 2.00000i 0.513553 0.148250i
\(183\) 10.0000i 0.739221i
\(184\) −1.50000 + 2.59808i −0.110581 + 0.191533i
\(185\) 0 0
\(186\) −1.50000 2.59808i −0.109985 0.190500i
\(187\) 2.00000i 0.146254i
\(188\) −2.59808 + 1.50000i −0.189484 + 0.109399i
\(189\) −1.00000 1.73205i −0.0727393 0.125988i
\(190\) 0 0
\(191\) −12.0000 20.7846i −0.868290 1.50392i −0.863743 0.503932i \(-0.831886\pi\)
−0.00454614 0.999990i \(-0.501447\pi\)
\(192\) 0.866025 + 0.500000i 0.0625000 + 0.0360844i
\(193\) −3.46410 2.00000i −0.249351 0.143963i 0.370116 0.928986i \(-0.379318\pi\)
−0.619467 + 0.785022i \(0.712651\pi\)
\(194\) 10.0000 0.717958
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) 10.3923 + 6.00000i 0.740421 + 0.427482i 0.822222 0.569166i \(-0.192734\pi\)
−0.0818013 + 0.996649i \(0.526067\pi\)
\(198\) 0.866025 + 0.500000i 0.0615457 + 0.0355335i
\(199\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 12.1244 7.00000i 0.853067 0.492518i
\(203\) 2.00000i 0.140372i
\(204\) −1.00000 1.73205i −0.0700140 0.121268i
\(205\) 0 0
\(206\) 3.00000 5.19615i 0.209020 0.362033i
\(207\) 3.00000i 0.208514i
\(208\) 0.866025 3.50000i 0.0600481 0.242681i
\(209\) −6.00000 −0.415029
\(210\) 0 0
\(211\) 4.00000 6.92820i 0.275371 0.476957i −0.694857 0.719148i \(-0.744533\pi\)
0.970229 + 0.242190i \(0.0778659\pi\)
\(212\) 12.1244 7.00000i 0.832704 0.480762i
\(213\) 4.00000i 0.274075i
\(214\) −3.00000 5.19615i −0.205076 0.355202i
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) −5.19615 + 3.00000i −0.352738 + 0.203653i
\(218\) −5.19615 3.00000i −0.351928 0.203186i
\(219\) 1.00000 1.73205i 0.0675737 0.117041i
\(220\) 0 0
\(221\) −5.00000 + 5.19615i −0.336336 + 0.349531i
\(222\) 5.00000i 0.335578i
\(223\) 8.66025 + 5.00000i 0.579934 + 0.334825i 0.761107 0.648626i \(-0.224656\pi\)
−0.181173 + 0.983451i \(0.557990\pi\)
\(224\) 1.00000 1.73205i 0.0668153 0.115728i
\(225\) 0 0
\(226\) 17.0000 1.13082
\(227\) 17.3205 10.0000i 1.14960 0.663723i 0.200812 0.979630i \(-0.435642\pi\)
0.948790 + 0.315906i \(0.102309\pi\)
\(228\) 5.19615 3.00000i 0.344124 0.198680i
\(229\) −22.0000 −1.45380 −0.726900 0.686743i \(-0.759040\pi\)
−0.726900 + 0.686743i \(0.759040\pi\)
\(230\) 0 0
\(231\) 1.00000 1.73205i 0.0657952 0.113961i
\(232\) 0.866025 + 0.500000i 0.0568574 + 0.0328266i
\(233\) 3.00000i 0.196537i −0.995160 0.0982683i \(-0.968670\pi\)
0.995160 0.0982683i \(-0.0313303\pi\)
\(234\) 1.00000 + 3.46410i 0.0653720 + 0.226455i
\(235\) 0 0
\(236\) 2.50000 4.33013i 0.162736 0.281867i
\(237\) 4.33013 + 2.50000i 0.281272 + 0.162392i
\(238\) −3.46410 + 2.00000i −0.224544 + 0.129641i
\(239\) 8.00000 0.517477 0.258738 0.965947i \(-0.416693\pi\)
0.258738 + 0.965947i \(0.416693\pi\)
\(240\) 0 0
\(241\) 3.50000 + 6.06218i 0.225455 + 0.390499i 0.956456 0.291877i \(-0.0942799\pi\)
−0.731001 + 0.682376i \(0.760947\pi\)
\(242\) 10.0000i 0.642824i
\(243\) 0.866025 0.500000i 0.0555556 0.0320750i
\(244\) −5.00000 + 8.66025i −0.320092 + 0.554416i
\(245\) 0 0
\(246\) −10.0000 −0.637577
\(247\) −15.5885 15.0000i −0.991870 0.954427i
\(248\) 3.00000i 0.190500i
\(249\) 3.00000 5.19615i 0.190117 0.329293i
\(250\) 0 0
\(251\) −1.50000 2.59808i −0.0946792 0.163989i 0.814795 0.579748i \(-0.196849\pi\)
−0.909475 + 0.415759i \(0.863516\pi\)
\(252\) 2.00000i 0.125988i
\(253\) 2.59808 1.50000i 0.163340 0.0943042i
\(254\) −7.00000 12.1244i −0.439219 0.760750i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −18.1865 10.5000i −1.13444 0.654972i −0.189396 0.981901i \(-0.560653\pi\)
−0.945049 + 0.326929i \(0.893986\pi\)
\(258\) −4.33013 2.50000i −0.269582 0.155643i
\(259\) 10.0000 0.621370
\(260\) 0 0
\(261\) −1.00000 −0.0618984
\(262\) −11.2583 6.50000i −0.695542 0.401571i
\(263\) 19.9186 + 11.5000i 1.22823 + 0.709120i 0.966660 0.256063i \(-0.0824256\pi\)
0.261573 + 0.965184i \(0.415759\pi\)
\(264\) −0.500000 0.866025i −0.0307729 0.0533002i
\(265\) 0 0
\(266\) −6.00000 10.3923i −0.367884 0.637193i
\(267\) −8.66025 + 5.00000i −0.529999 + 0.305995i
\(268\) 0 0
\(269\) 9.00000 + 15.5885i 0.548740 + 0.950445i 0.998361 + 0.0572259i \(0.0182255\pi\)
−0.449622 + 0.893219i \(0.648441\pi\)
\(270\) 0 0
\(271\) 14.5000 25.1147i 0.880812 1.52561i 0.0303728 0.999539i \(-0.490331\pi\)
0.850439 0.526073i \(-0.176336\pi\)
\(272\) 2.00000i 0.121268i
\(273\) 6.92820 2.00000i 0.419314 0.121046i
\(274\) 9.00000 0.543710
\(275\) 0 0
\(276\) −1.50000 + 2.59808i −0.0902894 + 0.156386i
\(277\) −16.4545 + 9.50000i −0.988654 + 0.570800i −0.904872 0.425684i \(-0.860033\pi\)
−0.0837823 + 0.996484i \(0.526700\pi\)
\(278\) 10.0000i 0.599760i
\(279\) −1.50000 2.59808i −0.0898027 0.155543i
\(280\) 0 0
\(281\) −30.0000 −1.78965 −0.894825 0.446417i \(-0.852700\pi\)
−0.894825 + 0.446417i \(0.852700\pi\)
\(282\) −2.59808 + 1.50000i −0.154713 + 0.0893237i
\(283\) −11.2583 6.50000i −0.669238 0.386385i 0.126550 0.991960i \(-0.459610\pi\)
−0.795788 + 0.605575i \(0.792943\pi\)
\(284\) 2.00000 3.46410i 0.118678 0.205557i
\(285\) 0 0
\(286\) −2.50000 + 2.59808i −0.147828 + 0.153627i
\(287\) 20.0000i 1.18056i
\(288\) 0.866025 + 0.500000i 0.0510310 + 0.0294628i
\(289\) −6.50000 + 11.2583i −0.382353 + 0.662255i
\(290\) 0 0
\(291\) 10.0000 0.586210
\(292\) −1.73205 + 1.00000i −0.101361 + 0.0585206i
\(293\) 12.1244 7.00000i 0.708312 0.408944i −0.102123 0.994772i \(-0.532564\pi\)
0.810436 + 0.585827i \(0.199230\pi\)
\(294\) −3.00000 −0.174964
\(295\) 0 0
\(296\) 2.50000 4.33013i 0.145310 0.251684i
\(297\) 0.866025 + 0.500000i 0.0502519 + 0.0290129i
\(298\) 11.0000i 0.637213i
\(299\) 10.5000 + 2.59808i 0.607231 + 0.150251i
\(300\) 0 0
\(301\) −5.00000 + 8.66025i −0.288195 + 0.499169i
\(302\) −20.7846 12.0000i −1.19602 0.690522i
\(303\) 12.1244 7.00000i 0.696526 0.402139i
\(304\) −6.00000 −0.344124
\(305\) 0 0
\(306\) −1.00000 1.73205i −0.0571662 0.0990148i
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) −1.73205 + 1.00000i −0.0986928 + 0.0569803i
\(309\) 3.00000 5.19615i 0.170664 0.295599i
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0.866025 3.50000i 0.0490290 0.198148i
\(313\) 12.0000i 0.678280i 0.940736 + 0.339140i \(0.110136\pi\)
−0.940736 + 0.339140i \(0.889864\pi\)
\(314\) 12.5000 21.6506i 0.705416 1.22182i
\(315\) 0 0
\(316\) −2.50000 4.33013i −0.140636 0.243589i
\(317\) 12.0000i 0.673987i 0.941507 + 0.336994i \(0.109410\pi\)
−0.941507 + 0.336994i \(0.890590\pi\)
\(318\) 12.1244 7.00000i 0.679900 0.392541i
\(319\) −0.500000 0.866025i −0.0279946 0.0484881i
\(320\) 0 0
\(321\) −3.00000 5.19615i −0.167444 0.290021i
\(322\) 5.19615 + 3.00000i 0.289570 + 0.167183i
\(323\) 10.3923 + 6.00000i 0.578243 + 0.333849i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) 17.0000 0.941543
\(327\) −5.19615 3.00000i −0.287348 0.165900i
\(328\) 8.66025 + 5.00000i 0.478183 + 0.276079i
\(329\) 3.00000 + 5.19615i 0.165395 + 0.286473i
\(330\) 0 0
\(331\) −2.00000 3.46410i −0.109930 0.190404i 0.805812 0.592172i \(-0.201729\pi\)
−0.915742 + 0.401768i \(0.868396\pi\)
\(332\) −5.19615 + 3.00000i −0.285176 + 0.164646i
\(333\) 5.00000i 0.273998i
\(334\) −3.50000 6.06218i −0.191511 0.331708i
\(335\) 0 0
\(336\) 1.00000 1.73205i 0.0545545 0.0944911i
\(337\) 22.0000i 1.19842i −0.800593 0.599208i \(-0.795482\pi\)
0.800593 0.599208i \(-0.204518\pi\)
\(338\) −12.9904 + 0.500000i −0.706584 + 0.0271964i
\(339\) 17.0000 0.923313
\(340\) 0 0
\(341\) 1.50000 2.59808i 0.0812296 0.140694i
\(342\) 5.19615 3.00000i 0.280976 0.162221i
\(343\) 20.0000i 1.07990i
\(344\) 2.50000 + 4.33013i 0.134791 + 0.233465i
\(345\) 0 0
\(346\) 4.00000 0.215041
\(347\) −15.5885 + 9.00000i −0.836832 + 0.483145i −0.856186 0.516667i \(-0.827172\pi\)
0.0193540 + 0.999813i \(0.493839\pi\)
\(348\) 0.866025 + 0.500000i 0.0464238 + 0.0268028i
\(349\) 4.00000 6.92820i 0.214115 0.370858i −0.738883 0.673833i \(-0.764647\pi\)
0.952998 + 0.302975i \(0.0979799\pi\)
\(350\) 0 0
\(351\) 1.00000 + 3.46410i 0.0533761 + 0.184900i
\(352\) 1.00000i 0.0533002i
\(353\) −12.1244 7.00000i −0.645314 0.372572i 0.141344 0.989960i \(-0.454858\pi\)
−0.786659 + 0.617388i \(0.788191\pi\)
\(354\) 2.50000 4.33013i 0.132874 0.230144i
\(355\) 0 0
\(356\) 10.0000 0.529999
\(357\) −3.46410 + 2.00000i −0.183340 + 0.105851i
\(358\) 6.06218 3.50000i 0.320396 0.184981i
\(359\) −12.0000 −0.633336 −0.316668 0.948536i \(-0.602564\pi\)
−0.316668 + 0.948536i \(0.602564\pi\)
\(360\) 0 0
\(361\) −8.50000 + 14.7224i −0.447368 + 0.774865i
\(362\) −13.8564 8.00000i −0.728277 0.420471i
\(363\) 10.0000i 0.524864i
\(364\) −7.00000 1.73205i −0.366900 0.0907841i
\(365\) 0 0
\(366\) −5.00000 + 8.66025i −0.261354 + 0.452679i
\(367\) −31.1769 18.0000i −1.62742 0.939592i −0.984859 0.173360i \(-0.944538\pi\)
−0.642563 0.766233i \(-0.722129\pi\)
\(368\) 2.59808 1.50000i 0.135434 0.0781929i
\(369\) −10.0000 −0.520579
\(370\) 0 0
\(371\) −14.0000 24.2487i −0.726844 1.25893i
\(372\) 3.00000i 0.155543i
\(373\) −32.0429 + 18.5000i −1.65912 + 0.957894i −0.685999 + 0.727603i \(0.740634\pi\)
−0.973122 + 0.230291i \(0.926032\pi\)
\(374\) 1.00000 1.73205i 0.0517088 0.0895622i
\(375\) 0 0
\(376\) 3.00000 0.154713
\(377\) 0.866025 3.50000i 0.0446026 0.180259i
\(378\) 2.00000i 0.102869i
\(379\) −15.0000 + 25.9808i −0.770498 + 1.33454i 0.166792 + 0.985992i \(0.446659\pi\)
−0.937290 + 0.348550i \(0.886674\pi\)
\(380\) 0 0
\(381\) −7.00000 12.1244i −0.358621 0.621150i
\(382\) 24.0000i 1.22795i
\(383\) 23.3827 13.5000i 1.19480 0.689818i 0.235408 0.971897i \(-0.424357\pi\)
0.959391 + 0.282079i \(0.0910240\pi\)
\(384\) −0.500000 0.866025i −0.0255155 0.0441942i
\(385\) 0 0
\(386\) 2.00000 + 3.46410i 0.101797 + 0.176318i
\(387\) −4.33013 2.50000i −0.220113 0.127082i
\(388\) −8.66025 5.00000i −0.439658 0.253837i
\(389\) 1.00000 0.0507020 0.0253510 0.999679i \(-0.491930\pi\)
0.0253510 + 0.999679i \(0.491930\pi\)
\(390\) 0 0
\(391\) −6.00000 −0.303433
\(392\) 2.59808 + 1.50000i 0.131223 + 0.0757614i
\(393\) −11.2583 6.50000i −0.567908 0.327882i
\(394\) −6.00000 10.3923i −0.302276 0.523557i
\(395\) 0 0
\(396\) −0.500000 0.866025i −0.0251259 0.0435194i
\(397\) −11.2583 + 6.50000i −0.565039 + 0.326226i −0.755166 0.655534i \(-0.772444\pi\)
0.190126 + 0.981760i \(0.439110\pi\)
\(398\) 0 0
\(399\) −6.00000 10.3923i −0.300376 0.520266i
\(400\) 0 0
\(401\) 6.00000 10.3923i 0.299626 0.518967i −0.676425 0.736512i \(-0.736472\pi\)
0.976050 + 0.217545i \(0.0698049\pi\)
\(402\) 0 0
\(403\) 10.3923 3.00000i 0.517678 0.149441i
\(404\) −14.0000 −0.696526
\(405\) 0 0
\(406\) 1.00000 1.73205i 0.0496292 0.0859602i
\(407\) −4.33013 + 2.50000i −0.214636 + 0.123920i
\(408\) 2.00000i 0.0990148i
\(409\) −13.0000 22.5167i −0.642809 1.11338i −0.984803 0.173675i \(-0.944436\pi\)
0.341994 0.939702i \(-0.388898\pi\)
\(410\) 0 0
\(411\) 9.00000 0.443937
\(412\) −5.19615 + 3.00000i −0.255996 + 0.147799i
\(413\) −8.66025 5.00000i −0.426143 0.246034i
\(414\) −1.50000 + 2.59808i −0.0737210 + 0.127688i
\(415\) 0 0
\(416\) −2.50000 + 2.59808i −0.122573 + 0.127381i
\(417\) 10.0000i 0.489702i
\(418\) 5.19615 + 3.00000i 0.254152 + 0.146735i
\(419\) 2.00000 3.46410i 0.0977064 0.169232i −0.813029 0.582224i \(-0.802183\pi\)
0.910735 + 0.412991i \(0.135516\pi\)
\(420\) 0 0
\(421\) 28.0000 1.36464 0.682318 0.731055i \(-0.260972\pi\)
0.682318 + 0.731055i \(0.260972\pi\)
\(422\) −6.92820 + 4.00000i −0.337260 + 0.194717i
\(423\) −2.59808 + 1.50000i −0.126323 + 0.0729325i
\(424\) −14.0000 −0.679900
\(425\) 0 0
\(426\) 2.00000 3.46410i 0.0969003 0.167836i
\(427\) 17.3205 + 10.0000i 0.838198 + 0.483934i
\(428\) 6.00000i 0.290021i
\(429\) −2.50000 + 2.59808i −0.120701 + 0.125436i
\(430\) 0 0
\(431\) −6.00000 + 10.3923i −0.289010 + 0.500580i −0.973574 0.228373i \(-0.926659\pi\)
0.684564 + 0.728953i \(0.259993\pi\)
\(432\) 0.866025 + 0.500000i 0.0416667 + 0.0240563i
\(433\) −13.8564 + 8.00000i −0.665896 + 0.384455i −0.794520 0.607238i \(-0.792277\pi\)
0.128624 + 0.991693i \(0.458944\pi\)
\(434\) 6.00000 0.288009
\(435\) 0 0
\(436\) 3.00000 + 5.19615i 0.143674 + 0.248851i
\(437\) 18.0000i 0.861057i
\(438\) −1.73205 + 1.00000i −0.0827606 + 0.0477818i
\(439\) 14.0000 24.2487i 0.668184 1.15733i −0.310228 0.950662i \(-0.600405\pi\)
0.978412 0.206666i \(-0.0662612\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.142857
\(442\) 6.92820 2.00000i 0.329541 0.0951303i
\(443\) 16.0000i 0.760183i −0.924949 0.380091i \(-0.875893\pi\)
0.924949 0.380091i \(-0.124107\pi\)
\(444\) 2.50000 4.33013i 0.118645 0.205499i
\(445\) 0 0
\(446\) −5.00000 8.66025i −0.236757 0.410075i
\(447\) 11.0000i 0.520282i
\(448\) −1.73205 + 1.00000i −0.0818317 + 0.0472456i
\(449\) −18.0000 31.1769i −0.849473 1.47133i −0.881680 0.471848i \(-0.843587\pi\)
0.0322072 0.999481i \(-0.489746\pi\)
\(450\) 0 0
\(451\) −5.00000 8.66025i −0.235441 0.407795i
\(452\) −14.7224 8.50000i −0.692485 0.399806i
\(453\) −20.7846 12.0000i −0.976546 0.563809i
\(454\) −20.0000 −0.938647
\(455\) 0 0
\(456\) −6.00000 −0.280976
\(457\) −12.1244 7.00000i −0.567153 0.327446i 0.188858 0.982004i \(-0.439521\pi\)
−0.756012 + 0.654558i \(0.772855\pi\)
\(458\) 19.0526 + 11.0000i 0.890268 + 0.513996i
\(459\) −1.00000 1.73205i −0.0466760 0.0808452i
\(460\) 0 0
\(461\) −13.5000 23.3827i −0.628758 1.08904i −0.987801 0.155719i \(-0.950230\pi\)
0.359044 0.933321i \(-0.383103\pi\)
\(462\) −1.73205 + 1.00000i −0.0805823 + 0.0465242i
\(463\) 10.0000i 0.464739i −0.972628 0.232370i \(-0.925352\pi\)
0.972628 0.232370i \(-0.0746479\pi\)
\(464\) −0.500000 0.866025i −0.0232119 0.0402042i
\(465\) 0 0
\(466\) −1.50000 + 2.59808i −0.0694862 + 0.120354i
\(467\) 2.00000i 0.0925490i −0.998929 0.0462745i \(-0.985265\pi\)
0.998929 0.0462745i \(-0.0147349\pi\)
\(468\) 0.866025 3.50000i 0.0400320 0.161788i
\(469\) 0 0
\(470\) 0 0
\(471\) 12.5000 21.6506i 0.575970 0.997609i
\(472\) −4.33013 + 2.50000i −0.199310 + 0.115072i
\(473\) 5.00000i 0.229900i
\(474\) −2.50000 4.33013i −0.114829 0.198889i
\(475\) 0 0
\(476\) 4.00000 0.183340
\(477\) 12.1244 7.00000i 0.555136 0.320508i
\(478\) −6.92820 4.00000i −0.316889 0.182956i
\(479\) −2.00000 + 3.46410i −0.0913823 + 0.158279i −0.908093 0.418769i \(-0.862462\pi\)
0.816711 + 0.577047i \(0.195795\pi\)
\(480\) 0 0
\(481\) −17.5000 4.33013i −0.797931 0.197437i
\(482\) 7.00000i 0.318841i
\(483\) 5.19615 + 3.00000i 0.236433 + 0.136505i
\(484\) −5.00000 + 8.66025i −0.227273 + 0.393648i
\(485\) 0 0
\(486\) −1.00000 −0.0453609
\(487\) 1.73205 1.00000i 0.0784867 0.0453143i −0.460243 0.887793i \(-0.652238\pi\)
0.538730 + 0.842479i \(0.318904\pi\)
\(488\) 8.66025 5.00000i 0.392031 0.226339i
\(489\) 17.0000 0.768767
\(490\) 0 0
\(491\) −12.0000 + 20.7846i −0.541552 + 0.937996i 0.457263 + 0.889332i \(0.348830\pi\)
−0.998815 + 0.0486647i \(0.984503\pi\)
\(492\) 8.66025 + 5.00000i 0.390434 + 0.225417i
\(493\) 2.00000i 0.0900755i
\(494\) 6.00000 + 20.7846i 0.269953 + 0.935144i
\(495\) 0 0
\(496\) 1.50000 2.59808i 0.0673520 0.116657i
\(497\) −6.92820 4.00000i −0.310772 0.179425i
\(498\) −5.19615 + 3.00000i −0.232845 + 0.134433i
\(499\) 40.0000 1.79065 0.895323 0.445418i \(-0.146945\pi\)
0.895323 + 0.445418i \(0.146945\pi\)
\(500\) 0 0
\(501\) −3.50000 6.06218i −0.156368 0.270838i
\(502\) 3.00000i 0.133897i
\(503\) −34.6410 + 20.0000i −1.54457 + 0.891756i −0.546025 + 0.837769i \(0.683860\pi\)
−0.998542 + 0.0539870i \(0.982807\pi\)
\(504\) 1.00000 1.73205i 0.0445435 0.0771517i
\(505\) 0 0
\(506\) −3.00000 −0.133366
\(507\) −12.9904 + 0.500000i −0.576923 + 0.0222058i
\(508\) 14.0000i 0.621150i
\(509\) −4.50000 + 7.79423i −0.199459 + 0.345473i −0.948353 0.317217i \(-0.897252\pi\)
0.748894 + 0.662690i \(0.230585\pi\)
\(510\) 0 0
\(511\) 2.00000 + 3.46410i 0.0884748 + 0.153243i
\(512\) 1.00000i 0.0441942i
\(513\) 5.19615 3.00000i 0.229416 0.132453i
\(514\) 10.5000 + 18.1865i 0.463135 + 0.802174i
\(515\) 0 0
\(516\) 2.50000 + 4.33013i 0.110056 + 0.190623i
\(517\) −2.59808 1.50000i −0.114263 0.0659699i
\(518\) −8.66025 5.00000i −0.380510 0.219687i
\(519\) 4.00000 0.175581
\(520\) 0 0
\(521\) 22.0000 0.963837 0.481919 0.876216i \(-0.339940\pi\)
0.481919 + 0.876216i \(0.339940\pi\)
\(522\) 0.866025 + 0.500000i 0.0379049 + 0.0218844i
\(523\) 28.5788 + 16.5000i 1.24967 + 0.721495i 0.971043 0.238906i \(-0.0767888\pi\)
0.278623 + 0.960401i \(0.410122\pi\)
\(524\) 6.50000 + 11.2583i 0.283954 + 0.491822i
\(525\) 0 0
\(526\) −11.5000 19.9186i −0.501424 0.868492i
\(527\) −5.19615 + 3.00000i −0.226348 + 0.130682i
\(528\) 1.00000i 0.0435194i
\(529\) −7.00000 12.1244i −0.304348 0.527146i
\(530\) 0 0
\(531\) 2.50000 4.33013i 0.108491 0.187912i
\(532\) 12.0000i 0.520266i
\(533\) 8.66025 35.0000i 0.375117 1.51602i
\(534\) 10.0000 0.432742
\(535\) 0 0
\(536\) 0 0
\(537\) 6.06218 3.50000i 0.261602 0.151036i
\(538\) 18.0000i 0.776035i
\(539\) −1.50000 2.59808i −0.0646096 0.111907i
\(540\) 0 0
\(541\) −8.00000 −0.343947 −0.171973 0.985102i \(-0.555014\pi\)
−0.171973 + 0.985102i \(0.555014\pi\)
\(542\) −25.1147 + 14.5000i −1.07877 + 0.622828i
\(543\) −13.8564 8.00000i −0.594635 0.343313i
\(544\) 1.00000 1.73205i 0.0428746 0.0742611i
\(545\) 0 0
\(546\) −7.00000 1.73205i −0.299572 0.0741249i
\(547\) 20.0000i 0.855138i −0.903983 0.427569i \(-0.859370\pi\)
0.903983 0.427569i \(-0.140630\pi\)
\(548\) −7.79423 4.50000i −0.332953 0.192230i
\(549\) −5.00000 + 8.66025i −0.213395 + 0.369611i
\(550\) 0 0
\(551\) −6.00000 −0.255609
\(552\) 2.59808 1.50000i 0.110581 0.0638442i
\(553\) −8.66025 + 5.00000i −0.368271 + 0.212622i
\(554\) 19.0000 0.807233
\(555\) 0 0
\(556\) −5.00000 + 8.66025i −0.212047 + 0.367277i
\(557\) 29.4449 + 17.0000i 1.24762 + 0.720313i 0.970634 0.240561i \(-0.0773315\pi\)
0.276985 + 0.960874i \(0.410665\pi\)
\(558\) 3.00000i 0.127000i
\(559\) 12.5000 12.9904i 0.528694 0.549435i
\(560\) 0 0
\(561\) 1.00000 1.73205i 0.0422200 0.0731272i
\(562\) 25.9808 + 15.0000i 1.09593 + 0.632737i
\(563\) 20.7846 12.0000i 0.875967 0.505740i 0.00664037 0.999978i \(-0.497886\pi\)
0.869326 + 0.494238i \(0.164553\pi\)
\(564\) 3.00000 0.126323
\(565\) 0 0
\(566\) 6.50000 + 11.2583i 0.273215 + 0.473223i
\(567\) 2.00000i 0.0839921i
\(568\) −3.46410 + 2.00000i −0.145350 + 0.0839181i
\(569\) −9.00000 + 15.5885i −0.377300 + 0.653502i −0.990668 0.136295i \(-0.956481\pi\)
0.613369 + 0.789797i \(0.289814\pi\)
\(570\) 0 0
\(571\) 4.00000 0.167395 0.0836974 0.996491i \(-0.473327\pi\)
0.0836974 + 0.996491i \(0.473327\pi\)
\(572\) 3.46410 1.00000i 0.144841 0.0418121i
\(573\) 24.0000i 1.00261i
\(574\) 10.0000 17.3205i 0.417392 0.722944i
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 18.0000i 0.749350i −0.927156 0.374675i \(-0.877754\pi\)
0.927156 0.374675i \(-0.122246\pi\)
\(578\) 11.2583 6.50000i 0.468285 0.270364i
\(579\) 2.00000 + 3.46410i 0.0831172 + 0.143963i
\(580\) 0 0
\(581\) 6.00000 + 10.3923i 0.248922 + 0.431145i
\(582\) −8.66025 5.00000i −0.358979 0.207257i
\(583\) 12.1244 + 7.00000i 0.502140 + 0.289910i
\(584\) 2.00000 0.0827606
\(585\) 0 0
\(586\) −14.0000 −0.578335
\(587\) 15.5885 + 9.00000i 0.643404 + 0.371470i 0.785925 0.618322i \(-0.212187\pi\)
−0.142520 + 0.989792i \(0.545521\pi\)
\(588\) 2.59808 + 1.50000i 0.107143 + 0.0618590i
\(589\) −9.00000 15.5885i −0.370839 0.642311i
\(590\) 0 0
\(591\) −6.00000 10.3923i −0.246807 0.427482i
\(592\) −4.33013 + 2.50000i −0.177967 + 0.102749i
\(593\) 35.0000i 1.43728i 0.695383 + 0.718639i \(0.255235\pi\)
−0.695383 + 0.718639i \(0.744765\pi\)
\(594\) −0.500000 0.866025i −0.0205152 0.0355335i
\(595\) 0 0
\(596\) −5.50000 + 9.52628i −0.225289 + 0.390212i
\(597\) 0 0
\(598\) −7.79423 7.50000i −0.318730 0.306698i
\(599\) −30.0000 −1.22577 −0.612883 0.790173i \(-0.709990\pi\)
−0.612883 + 0.790173i \(0.709990\pi\)
\(600\) 0 0
\(601\) 5.50000 9.52628i 0.224350 0.388585i −0.731774 0.681547i \(-0.761308\pi\)
0.956124 + 0.292962i \(0.0946409\pi\)
\(602\) 8.66025 5.00000i 0.352966 0.203785i
\(603\) 0 0
\(604\) 12.0000 + 20.7846i 0.488273 + 0.845714i
\(605\) 0 0
\(606\) −14.0000 −0.568711
\(607\) −8.66025 + 5.00000i −0.351509 + 0.202944i −0.665350 0.746532i \(-0.731718\pi\)
0.313841 + 0.949476i \(0.398384\pi\)
\(608\) 5.19615 + 3.00000i 0.210732 + 0.121666i
\(609\) 1.00000 1.73205i 0.0405220 0.0701862i
\(610\) 0 0
\(611\) −3.00000 10.3923i −0.121367 0.420428i
\(612\) 2.00000i 0.0808452i
\(613\) −32.0429 18.5000i −1.29420 0.747208i −0.314806 0.949156i \(-0.601939\pi\)
−0.979396 + 0.201948i \(0.935273\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 2.00000 0.0805823
\(617\) 2.59808 1.50000i 0.104595 0.0603877i −0.446790 0.894639i \(-0.647433\pi\)
0.551385 + 0.834251i \(0.314100\pi\)
\(618\) −5.19615 + 3.00000i −0.209020 + 0.120678i
\(619\) 10.0000 0.401934 0.200967 0.979598i \(-0.435592\pi\)
0.200967 + 0.979598i \(0.435592\pi\)
\(620\) 0 0
\(621\) −1.50000 + 2.59808i −0.0601929 + 0.104257i
\(622\) 0 0
\(623\) 20.0000i 0.801283i
\(624\) −2.50000 + 2.59808i −0.100080 + 0.104006i
\(625\) 0 0
\(626\) 6.00000 10.3923i 0.239808 0.415360i
\(627\) 5.19615 + 3.00000i 0.207514 + 0.119808i
\(628\) −21.6506 + 12.5000i −0.863954 + 0.498804i
\(629\) 10.0000 0.398726
\(630\) 0 0
\(631\) −24.0000 41.5692i −0.955425 1.65484i −0.733393 0.679805i \(-0.762064\pi\)
−0.222032 0.975039i \(-0.571269\pi\)
\(632\) 5.00000i 0.198889i
\(633\) −6.92820 + 4.00000i −0.275371 + 0.158986i
\(634\) 6.00000 10.3923i 0.238290 0.412731i
\(635\) 0 0
\(636\) −14.0000 −0.555136
\(637\) 2.59808 10.5000i 0.102940 0.416025i
\(638\) 1.00000i 0.0395904i
\(639\) 2.00000 3.46410i 0.0791188 0.137038i
\(640\) 0 0
\(641\) 15.0000 + 25.9808i 0.592464 + 1.02618i 0.993899 + 0.110291i \(0.0351782\pi\)
−0.401435 + 0.915888i \(0.631488\pi\)
\(642\) 6.00000i 0.236801i
\(643\) 34.6410 20.0000i 1.36611 0.788723i 0.375680 0.926750i \(-0.377409\pi\)
0.990429 + 0.138027i \(0.0440759\pi\)
\(644\) −3.00000 5.19615i −0.118217 0.204757i
\(645\) 0 0
\(646\) −6.00000 10.3923i −0.236067 0.408880i
\(647\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(648\) 0.866025 + 0.500000i 0.0340207 + 0.0196419i
\(649\) 5.00000 0.196267
\(650\) 0 0
\(651\) 6.00000 0.235159
\(652\) −14.7224 8.50000i −0.576575 0.332886i
\(653\) −15.5885 9.00000i −0.610023 0.352197i 0.162951 0.986634i \(-0.447899\pi\)
−0.772975 + 0.634437i \(0.781232\pi\)
\(654\) 3.00000 + 5.19615i 0.117309 + 0.203186i
\(655\) 0 0
\(656\) −5.00000 8.66025i −0.195217 0.338126i
\(657\) −1.73205 + 1.00000i −0.0675737 + 0.0390137i
\(658\) 6.00000i 0.233904i
\(659\) −6.50000 11.2583i −0.253204 0.438562i 0.711202 0.702988i \(-0.248151\pi\)
−0.964406 + 0.264425i \(0.914818\pi\)
\(660\) 0 0
\(661\) 6.00000 10.3923i 0.233373 0.404214i −0.725426 0.688301i \(-0.758357\pi\)
0.958799 + 0.284087i \(0.0916904\pi\)
\(662\) 4.00000i 0.155464i
\(663\) 6.92820 2.00000i 0.269069 0.0776736i
\(664\) 6.00000 0.232845
\(665\) 0 0
\(666\) 2.50000 4.33013i 0.0968730 0.167789i
\(667\) 2.59808 1.50000i 0.100598 0.0580802i
\(668\) 7.00000i 0.270838i
\(669\) −5.00000 8.66025i −0.193311 0.334825i
\(670\) 0 0
\(671\) −10.0000 −0.386046
\(672\) −1.73205 + 1.00000i −0.0668153 + 0.0385758i
\(673\) −13.8564 8.00000i −0.534125 0.308377i 0.208569 0.978008i \(-0.433119\pi\)
−0.742695 + 0.669630i \(0.766453\pi\)
\(674\) −11.0000 + 19.0526i −0.423704 + 0.733877i
\(675\) 0 0
\(676\) 11.5000 + 6.06218i 0.442308 + 0.233161i
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) −14.7224 8.50000i −0.565412 0.326441i
\(679\) −10.0000 + 17.3205i −0.383765 + 0.664700i
\(680\) 0 0
\(681\) −20.0000 −0.766402
\(682\) −2.59808 + 1.50000i −0.0994855 + 0.0574380i
\(683\) 38.1051 22.0000i 1.45805 0.841807i 0.459136 0.888366i \(-0.348159\pi\)
0.998916 + 0.0465592i \(0.0148256\pi\)
\(684\) −6.00000 −0.229416
\(685\) 0 0
\(686\) 10.0000 17.3205i 0.381802 0.661300i
\(687\) 19.0526 + 11.0000i 0.726900 + 0.419676i
\(688\) 5.00000i 0.190623i
\(689\) 14.0000 + 48.4974i 0.533358 + 1.84760i
\(690\) 0 0
\(691\) 7.00000 12.1244i 0.266293 0.461232i −0.701609 0.712562i \(-0.747535\pi\)
0.967901 + 0.251330i \(0.0808679\pi\)
\(692\) −3.46410 2.00000i −0.131685 0.0760286i
\(693\) −1.73205 + 1.00000i −0.0657952 + 0.0379869i
\(694\) 18.0000 0.683271
\(695\) 0 0
\(696\) −0.500000 0.866025i −0.0189525 0.0328266i
\(697\) 20.0000i 0.757554i
\(698\) −6.92820 + 4.00000i −0.262236 + 0.151402i
\(699\) −1.50000 + 2.59808i −0.0567352 + 0.0982683i
\(700\) 0 0
\(701\) 23.0000 0.868698 0.434349 0.900745i \(-0.356978\pi\)
0.434349 + 0.900745i \(0.356978\pi\)
\(702\) 0.866025 3.50000i 0.0326860 0.132099i
\(703\) 30.0000i 1.13147i
\(704\) 0.500000 0.866025i 0.0188445 0.0326396i
\(705\) 0 0
\(706\) 7.00000 + 12.1244i 0.263448 + 0.456306i
\(707\) 28.0000i 1.05305i
\(708\) −4.33013 + 2.50000i −0.162736 + 0.0939558i
\(709\) −8.00000 13.8564i −0.300446 0.520388i 0.675791 0.737093i \(-0.263802\pi\)
−0.976237 + 0.216705i \(0.930469\pi\)
\(710\) 0 0
\(711\) −2.50000 4.33013i −0.0937573 0.162392i
\(712\) −8.66025 5.00000i −0.324557 0.187383i
\(713\) 7.79423 + 4.50000i 0.291896 + 0.168526i
\(714\) 4.00000 0.149696
\(715\) 0 0
\(716\) −7.00000 −0.261602
\(717\) −6.92820 4.00000i −0.258738 0.149383i
\(718\) 10.3923 + 6.00000i 0.387837 + 0.223918i
\(719\) −24.0000 41.5692i −0.895049 1.55027i −0.833744 0.552151i \(-0.813807\pi\)
−0.0613050 0.998119i \(-0.519526\pi\)
\(720\) 0 0
\(721\) 6.00000 + 10.3923i 0.223452 + 0.387030i
\(722\) 14.7224 8.50000i 0.547912 0.316337i
\(723\) 7.00000i 0.260333i
\(724\) 8.00000 + 13.8564i 0.297318 + 0.514969i
\(725\) 0 0
\(726\) −5.00000 + 8.66025i −0.185567 + 0.321412i
\(727\) 32.0000i 1.18681i −0.804902 0.593407i \(-0.797782\pi\)
0.804902 0.593407i \(-0.202218\pi\)
\(728\) 5.19615 + 5.00000i 0.192582 + 0.185312i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −5.00000 + 8.66025i −0.184932 + 0.320311i
\(732\) 8.66025 5.00000i 0.320092 0.184805i
\(733\) 14.0000i 0.517102i −0.965998 0.258551i \(-0.916755\pi\)
0.965998 0.258551i \(-0.0832450\pi\)
\(734\) 18.0000 + 31.1769i 0.664392 + 1.15076i
\(735\) 0 0
\(736\) −3.00000 −0.110581
\(737\) 0 0
\(738\) 8.66025 + 5.00000i 0.318788 + 0.184053i
\(739\) 12.0000 20.7846i 0.441427 0.764574i −0.556369 0.830936i \(-0.687806\pi\)
0.997796 + 0.0663614i \(0.0211390\pi\)
\(740\) 0 0
\(741\) 6.00000 + 20.7846i 0.220416 + 0.763542i
\(742\) 28.0000i 1.02791i
\(743\) −12.9904 7.50000i −0.476571 0.275148i 0.242415 0.970173i \(-0.422060\pi\)
−0.718986 + 0.695024i \(0.755394\pi\)
\(744\) 1.50000 2.59808i 0.0549927 0.0952501i
\(745\) 0 0
\(746\) 37.0000 1.35467
\(747\) −5.19615 + 3.00000i −0.190117 + 0.109764i
\(748\) −1.73205 + 1.00000i −0.0633300 + 0.0365636i
\(749\) 12.0000 0.438470
\(750\) 0 0
\(751\) −20.5000 + 35.5070i −0.748056 + 1.29567i 0.200698 + 0.979653i \(0.435679\pi\)
−0.948753 + 0.316017i \(0.897654\pi\)
\(752\) −2.59808 1.50000i −0.0947421 0.0546994i
\(753\) 3.00000i 0.109326i
\(754\) −2.50000 + 2.59808i −0.0910446 + 0.0946164i
\(755\) 0 0
\(756\) 1.00000 1.73205i 0.0363696 0.0629941i
\(757\) 46.7654 + 27.0000i 1.69972 + 0.981332i 0.946020 + 0.324109i \(0.105065\pi\)
0.753697 + 0.657222i \(0.228269\pi\)
\(758\) 25.9808 15.0000i 0.943664 0.544825i
\(759\) −3.00000 −0.108893
\(760\) 0 0
\(761\) 10.0000 + 17.3205i 0.362500 + 0.627868i 0.988372 0.152058i \(-0.0485900\pi\)
−0.625872 + 0.779926i \(0.715257\pi\)
\(762\) 14.0000i 0.507166i
\(763\) 10.3923 6.00000i 0.376227 0.217215i
\(764\) 12.0000 20.7846i 0.434145 0.751961i
\(765\) 0 0
\(766\) −27.0000 −0.975550
\(767\) 12.9904 + 12.5000i 0.469055 + 0.451349i
\(768\) 1.00000i 0.0360844i
\(769\) −14.5000 + 25.1147i −0.522883 + 0.905661i 0.476762 + 0.879032i \(0.341810\pi\)
−0.999645 + 0.0266282i \(0.991523\pi\)
\(770\) 0 0
\(771\) 10.5000 + 18.1865i 0.378148 + 0.654972i
\(772\) 4.00000i 0.143963i
\(773\) 13.8564 8.00000i 0.498380 0.287740i −0.229664 0.973270i \(-0.573763\pi\)
0.728044 + 0.685530i \(0.240429\pi\)
\(774\) 2.50000 + 4.33013i 0.0898606 + 0.155643i
\(775\) 0 0
\(776\) 5.00000 + 8.66025i 0.179490 + 0.310885i
\(777\) −8.66025 5.00000i −0.310685 0.179374i
\(778\) −0.866025 0.500000i −0.0310485 0.0179259i
\(779\) −60.0000 −2.14972
\(780\) 0 0
\(781\) 4.00000 0.143131
\(782\) 5.19615 + 3.00000i 0.185814 + 0.107280i
\(783\) 0.866025 + 0.500000i 0.0309492 + 0.0178685i
\(784\) −1.50000 2.59808i −0.0535714 0.0927884i
\(785\) 0 0
\(786\) 6.50000 + 11.2583i 0.231847 + 0.401571i
\(787\) 21.6506 12.5000i 0.771762 0.445577i −0.0617409 0.998092i \(-0.519665\pi\)
0.833503 + 0.552515i \(0.186332\pi\)
\(788\) 12.0000i 0.427482i
\(789\) −11.5000 19.9186i −0.409411 0.709120i
\(790\) 0 0
\(791\) −17.0000 + 29.4449i −0.604450 + 1.04694i
\(792\) 1.00000i 0.0355335i
\(793\) −25.9808 25.0000i −0.922604 0.887776i
\(794\) 13.0000 0.461353
\(795\) 0 0
\(796\) 0 0
\(797\) −45.0333 + 26.0000i −1.59516 + 0.920967i −0.602761 + 0.797922i \(0.705933\pi\)
−0.992401 + 0.123045i \(0.960734\pi\)
\(798\) 12.0000i 0.424795i
\(799\) 3.00000 + 5.19615i 0.106132 + 0.183827i
\(800\) 0 0
\(801\) 10.0000 0.353333
\(802\) −10.3923 + 6.00000i −0.366965 + 0.211867i
\(803\) −1.73205 1.00000i −0.0611227 0.0352892i
\(804\) 0 0
\(805\) 0 0
\(806\) −10.5000 2.59808i −0.369847 0.0915133i
\(807\) 18.0000i 0.633630i
\(808\) 12.1244 + 7.00000i 0.426533 + 0.246259i
\(809\) 1.00000 1.73205i 0.0351581 0.0608957i −0.847911 0.530139i \(-0.822140\pi\)
0.883069 + 0.469243i \(0.155473\pi\)
\(810\) 0 0
\(811\) 52.0000 1.82597 0.912983 0.407997i \(-0.133772\pi\)
0.912983 + 0.407997i \(0.133772\pi\)
\(812\) −1.73205 + 1.00000i −0.0607831 + 0.0350931i
\(813\) −25.1147 + 14.5000i −0.880812 + 0.508537i
\(814\) 5.00000 0.175250
\(815\) 0 0
\(816\) 1.00000 1.73205i 0.0350070 0.0606339i
\(817\) −25.9808 15.0000i −0.908952 0.524784i
\(818\) 26.0000i 0.909069i
\(819\) −7.00000 1.73205i −0.244600 0.0605228i
\(820\) 0 0
\(821\) −11.5000 + 19.9186i −0.401353 + 0.695163i −0.993889 0.110380i \(-0.964793\pi\)
0.592537 + 0.805543i \(0.298127\pi\)
\(822\) −7.79423 4.50000i −0.271855 0.156956i
\(823\) 19.0526 11.0000i 0.664130 0.383436i −0.129719 0.991551i \(-0.541407\pi\)
0.793849 + 0.608115i \(0.208074\pi\)
\(824\) 6.00000 0.209020
\(825\) 0 0
\(826\) 5.00000 + 8.66025i 0.173972 + 0.301329i
\(827\) 18.0000i 0.625921i −0.949766 0.312961i \(-0.898679\pi\)
0.949766 0.312961i \(-0.101321\pi\)
\(828\) 2.59808 1.50000i 0.0902894 0.0521286i
\(829\) 13.0000 22.5167i 0.451509 0.782036i −0.546971 0.837151i \(-0.684219\pi\)
0.998480 + 0.0551154i \(0.0175527\pi\)
\(830\) 0 0
\(831\) 19.0000 0.659103
\(832\) 3.46410 1.00000i 0.120096 0.0346688i
\(833\) 6.00000i 0.207888i
\(834\) −5.00000 + 8.66025i −0.173136 + 0.299880i
\(835\) 0 0
\(836\) −3.00000 5.19615i −0.103757 0.179713i
\(837\) 3.00000i 0.103695i
\(838\) −3.46410 + 2.00000i −0.119665 + 0.0690889i
\(839\) 19.0000 + 32.9090i 0.655953 + 1.13614i 0.981654 + 0.190671i \(0.0610663\pi\)
−0.325701 + 0.945473i \(0.605600\pi\)
\(840\) 0 0
\(841\) 14.0000 + 24.2487i 0.482759 + 0.836162i
\(842\) −24.2487 14.0000i −0.835666 0.482472i
\(843\) 25.9808 + 15.0000i 0.894825 + 0.516627i
\(844\) 8.00000 0.275371
\(845\) 0 0
\(846\) 3.00000 0.103142
\(847\) 17.3205 + 10.0000i 0.595140 + 0.343604i
\(848\) 12.1244 + 7.00000i 0.416352 + 0.240381i
\(849\) 6.50000 + 11.2583i 0.223079 + 0.386385i
\(850\) 0 0
\(851\) −7.50000 12.9904i −0.257097 0.445305i
\(852\) −3.46410 + 2.00000i −0.118678 + 0.0685189i
\(853\) 7.00000i 0.239675i −0.992793 0.119838i \(-0.961763\pi\)
0.992793 0.119838i \(-0.0382374\pi\)
\(854\) −10.0000 17.3205i −0.342193 0.592696i
\(855\) 0 0
\(856\) 3.00000 5.19615i 0.102538 0.177601i
\(857\) 35.0000i 1.19558i −0.801654 0.597789i \(-0.796046\pi\)
0.801654 0.597789i \(-0.203954\pi\)
\(858\) 3.46410 1.00000i 0.118262 0.0341394i
\(859\) −18.0000 −0.614152 −0.307076 0.951685i \(-0.599351\pi\)
−0.307076 + 0.951685i \(0.599351\pi\)
\(860\) 0 0
\(861\) 10.0000 17.3205i 0.340799 0.590281i
\(862\) 10.3923 6.00000i 0.353963 0.204361i
\(863\) 51.0000i 1.73606i 0.496512 + 0.868030i \(0.334614\pi\)
−0.496512 + 0.868030i \(0.665386\pi\)
\(864\) −0.500000 0.866025i −0.0170103 0.0294628i
\(865\) 0 0
\(866\) 16.0000 0.543702
\(867\) 11.2583 6.50000i 0.382353 0.220752i
\(868\) −5.19615 3.00000i −0.176369 0.101827i
\(869\) 2.50000 4.33013i 0.0848067 0.146889i
\(870\) 0 0
\(871\) 0 0
\(872\) 6.00000i 0.203186i
\(873\) −8.66025 5.00000i −0.293105 0.169224i
\(874\) −9.00000 + 15.5885i −0.304430 + 0.527287i
\(875\) 0 0
\(876\) 2.00000 0.0675737
\(877\) 11.2583 6.50000i 0.380167 0.219489i −0.297724 0.954652i \(-0.596228\pi\)
0.677891 + 0.735163i \(0.262894\pi\)
\(878\) −24.2487 + 14.0000i −0.818354 + 0.472477i
\(879\) −14.0000 −0.472208
\(880\) 0 0
\(881\) −27.0000 + 46.7654i −0.909653 + 1.57557i −0.0951067 + 0.995467i \(0.530319\pi\)
−0.814546 + 0.580098i \(0.803014\pi\)
\(882\) 2.59808 + 1.50000i 0.0874818 + 0.0505076i
\(883\) 1.00000i 0.0336527i 0.999858 + 0.0168263i \(0.00535624\pi\)
−0.999858 + 0.0168263i \(0.994644\pi\)
\(884\) −7.00000 1.73205i −0.235435 0.0582552i
\(885\) 0 0
\(886\) −8.00000 + 13.8564i −0.268765 + 0.465515i
\(887\) −0.866025 0.500000i −0.0290783 0.0167884i 0.485390 0.874298i \(-0.338677\pi\)
−0.514469 + 0.857509i \(0.672011\pi\)
\(888\) −4.33013 + 2.50000i −0.145310 + 0.0838945i
\(889\) 28.0000 0.939090
\(890\) 0 0
\(891\) −0.500000 0.866025i −0.0167506 0.0290129i
\(892\) 10.0000i 0.334825i
\(893\) −15.5885 + 9.00000i −0.521648 + 0.301174i
\(894\) −5.50000 + 9.52628i −0.183948 + 0.318606i
\(895\) 0 0
\(896\) 2.00000 0.0668153
\(897\) −7.79423 7.50000i −0.260242 0.250418i
\(898\) 36.0000i 1.20134i
\(899\) 1.50000 2.59808i 0.0500278 0.0866507i
\(900\) 0 0
\(901\) −14.0000 24.2487i −0.466408 0.807842i
\(902\) 10.0000i 0.332964i
\(903\) 8.66025 5.00000i 0.288195 0.166390i
\(904\) 8.50000 + 14.7224i 0.282706 + 0.489661i
\(905\) 0 0
\(906\) 12.0000 + 20.7846i 0.398673 + 0.690522i
\(907\) 45.8993 + 26.5000i 1.52406 + 0.879918i 0.999594 + 0.0284883i \(0.00906934\pi\)
0.524469 + 0.851430i \(0.324264\pi\)
\(908\) 17.3205 + 10.0000i 0.574801 + 0.331862i
\(909\) −14.0000 −0.464351
\(910\) 0 0
\(911\) 34.0000 1.12647 0.563235 0.826297i \(-0.309557\pi\)
0.563235 + 0.826297i \(0.309557\pi\)
\(912\) 5.19615 + 3.00000i 0.172062 + 0.0993399i
\(913\) −5.19615 3.00000i −0.171968 0.0992855i
\(914\) 7.00000 + 12.1244i 0.231539 + 0.401038i
\(915\) 0 0
\(916\) −11.0000 19.0526i −0.363450 0.629514i
\(917\) 22.5167 13.0000i 0.743566 0.429298i
\(918\) 2.00000i 0.0660098i
\(919\) −28.0000 48.4974i −0.923635 1.59978i −0.793742 0.608254i \(-0.791870\pi\)
−0.129893 0.991528i \(-0.541463\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 27.0000i 0.889198i
\(923\) 10.3923 + 10.0000i 0.342067 + 0.329154i
\(924\) 2.00000 0.0657952
\(925\) 0 0
\(926\) −5.00000 + 8.66025i −0.164310 + 0.284594i
\(927\) −5.19615 + 3.00000i −0.170664 + 0.0985329i
\(928\) 1.00000i 0.0328266i
\(929\) 12.0000 + 20.7846i 0.393707 + 0.681921i 0.992935 0.118657i \(-0.0378590\pi\)
−0.599228 + 0.800578i \(0.704526\pi\)
\(930\) 0 0
\(931\) −18.0000 −0.589926
\(932\) 2.59808 1.50000i 0.0851028 0.0491341i
\(933\) 0 0
\(934\) −1.00000 + 1.73205i −0.0327210 + 0.0566744i
\(935\) 0 0
\(936\) −2.50000 + 2.59808i −0.0817151 + 0.0849208i
\(937\) 18.0000i 0.588034i −0.955800 0.294017i \(-0.905008\pi\)
0.955800 0.294017i \(-0.0949923\pi\)
\(938\) 0 0
\(939\) 6.00000 10.3923i 0.195803 0.339140i
\(940\) 0 0
\(941\) 26.0000 0.847576 0.423788 0.905761i \(-0.360700\pi\)
0.423788 + 0.905761i \(0.360700\pi\)
\(942\) −21.6506 + 12.5000i −0.705416 + 0.407272i
\(943\) 25.9808 15.0000i 0.846050 0.488467i
\(944\) 5.00000 0.162736
\(945\) 0 0
\(946\) −2.50000 + 4.33013i −0.0812820 + 0.140785i
\(947\) −45.0333 26.0000i −1.46339 0.844886i −0.464220 0.885720i \(-0.653665\pi\)
−0.999166 + 0.0408333i \(0.986999\pi\)
\(948\) 5.00000i 0.162392i
\(949\) −2.00000 6.92820i −0.0649227 0.224899i
\(950\) 0 0
\(951\) 6.00000 10.3923i 0.194563 0.336994i
\(952\) −3.46410 2.00000i −0.112272 0.0648204i
\(953\) −12.9904 + 7.50000i −0.420800 + 0.242949i −0.695419 0.718604i \(-0.744781\pi\)
0.274620 + 0.961553i \(0.411448\pi\)
\(954\) −14.0000 −0.453267
\(955\) 0 0
\(956\) 4.00000 + 6.92820i 0.129369 + 0.224074i
\(957\) 1.00000i 0.0323254i
\(958\) 3.46410 2.00000i 0.111920 0.0646171i
\(959\) −9.00000 + 15.5885i −0.290625 + 0.503378i
\(960\) 0 0
\(961\) −22.0000 −0.709677
\(962\) 12.9904 + 12.5000i 0.418827 + 0.403016i
\(963\) 6.00000i 0.193347i
\(964\) −3.50000 + 6.06218i −0.112727 + 0.195250i
\(965\) 0 0
\(966\) −3.00000 5.19615i −0.0965234 0.167183i
\(967\) 16.0000i 0.514525i 0.966342 + 0.257263i \(0.0828206\pi\)
−0.966342 + 0.257263i \(0.917179\pi\)
\(968\) 8.66025 5.00000i 0.278351 0.160706i
\(969\) −6.00000 10.3923i −0.192748 0.333849i
\(970\) 0 0
\(971\) 20.0000 + 34.6410i 0.641831 + 1.11168i 0.985024 + 0.172418i \(0.0551581\pi\)
−0.343193 + 0.939265i \(0.611509\pi\)
\(972\) 0.866025 + 0.500000i 0.0277778 + 0.0160375i
\(973\) 17.3205 + 10.0000i 0.555270 + 0.320585i
\(974\) −2.00000 −0.0640841
\(975\) 0 0
\(976\) −10.0000 −0.320092
\(977\) 33.7750 + 19.5000i 1.08056 + 0.623860i 0.931047 0.364900i \(-0.118897\pi\)
0.149511 + 0.988760i \(0.452230\pi\)
\(978\) −14.7224 8.50000i −0.470771 0.271800i
\(979\) 5.00000 + 8.66025i 0.159801 + 0.276783i
\(980\) 0 0
\(981\) 3.00000 + 5.19615i 0.0957826 + 0.165900i
\(982\) 20.7846 12.0000i 0.663264 0.382935i
\(983\) 25.0000i 0.797376i 0.917087 + 0.398688i \(0.130534\pi\)
−0.917087 + 0.398688i \(0.869466\pi\)
\(984\) −5.00000 8.66025i −0.159394 0.276079i
\(985\) 0 0
\(986\) 1.00000 1.73205i 0.0318465 0.0551597i
\(987\) 6.00000i 0.190982i
\(988\) 5.19615 21.0000i 0.165312 0.668099i
\(989\) 15.0000 0.476972
\(990\) 0 0
\(991\) −19.5000 + 33.7750i −0.619438 + 1.07290i 0.370151 + 0.928972i \(0.379306\pi\)
−0.989588 + 0.143926i \(0.954027\pi\)
\(992\) −2.59808 + 1.50000i −0.0824890 + 0.0476250i
\(993\) 4.00000i 0.126936i
\(994\) 4.00000 + 6.92820i 0.126872 + 0.219749i
\(995\) 0 0
\(996\) 6.00000 0.190117
\(997\) −1.73205 + 1.00000i −0.0548546 + 0.0316703i −0.527176 0.849756i \(-0.676749\pi\)
0.472322 + 0.881426i \(0.343416\pi\)
\(998\) −34.6410 20.0000i −1.09654 0.633089i
\(999\) 2.50000 4.33013i 0.0790965 0.136999i
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 1950.2.z.h.1699.1 4
5.2 odd 4 1950.2.i.s.451.1 2
5.3 odd 4 390.2.i.a.61.1 2
5.4 even 2 inner 1950.2.z.h.1699.2 4
13.3 even 3 inner 1950.2.z.h.1849.2 4
15.8 even 4 1170.2.i.k.451.1 2
65.3 odd 12 390.2.i.a.211.1 yes 2
65.29 even 6 inner 1950.2.z.h.1849.1 4
65.33 even 12 5070.2.b.g.1351.2 2
65.42 odd 12 1950.2.i.s.601.1 2
65.43 odd 12 5070.2.a.f.1.1 1
65.48 odd 12 5070.2.a.o.1.1 1
65.58 even 12 5070.2.b.g.1351.1 2
195.68 even 12 1170.2.i.k.991.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
390.2.i.a.61.1 2 5.3 odd 4
390.2.i.a.211.1 yes 2 65.3 odd 12
1170.2.i.k.451.1 2 15.8 even 4
1170.2.i.k.991.1 2 195.68 even 12
1950.2.i.s.451.1 2 5.2 odd 4
1950.2.i.s.601.1 2 65.42 odd 12
1950.2.z.h.1699.1 4 1.1 even 1 trivial
1950.2.z.h.1699.2 4 5.4 even 2 inner
1950.2.z.h.1849.1 4 65.29 even 6 inner
1950.2.z.h.1849.2 4 13.3 even 3 inner
5070.2.a.f.1.1 1 65.43 odd 12
5070.2.a.o.1.1 1 65.48 odd 12
5070.2.b.g.1351.1 2 65.58 even 12
5070.2.b.g.1351.2 2 65.33 even 12