Properties

Label 450.2.j.c.349.1
Level $450$
Weight $2$
Character 450.349
Analytic conductor $3.593$
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] = [450,2,Mod(49,450)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(450, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("450.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 450.j (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: \(3.59326809096\)
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 90)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 349.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 450.349
Dual form 450.2.j.c.49.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.73205i q^{6} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.73205i q^{6} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +(-3.00000 + 5.19615i) q^{11} +(0.866025 - 1.50000i) q^{12} +(-1.73205 + 1.00000i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.59808 - 1.50000i) q^{18} +4.00000 q^{19} -1.73205i q^{21} +(5.19615 - 3.00000i) q^{22} +(-7.79423 + 4.50000i) q^{23} +(-1.50000 + 0.866025i) q^{24} +2.00000 q^{26} +5.19615 q^{27} +1.00000i q^{28} +(1.50000 - 2.59808i) q^{29} +(2.00000 + 3.46410i) q^{31} +(0.866025 - 0.500000i) q^{32} +10.3923 q^{33} -3.00000 q^{36} +8.00000i q^{37} +(-3.46410 - 2.00000i) q^{38} +(3.00000 + 1.73205i) q^{39} +(1.50000 + 2.59808i) q^{41} +(-0.866025 + 1.50000i) q^{42} +(6.92820 + 4.00000i) q^{43} -6.00000 q^{44} +9.00000 q^{46} +(2.59808 + 1.50000i) q^{47} +1.73205 q^{48} +(-3.00000 - 5.19615i) q^{49} +(-1.73205 - 1.00000i) q^{52} -6.00000i q^{53} +(-4.50000 - 2.59808i) q^{54} +(0.500000 - 0.866025i) q^{56} +(-3.46410 - 6.00000i) q^{57} +(-2.59808 + 1.50000i) q^{58} +(3.00000 + 5.19615i) q^{59} +(6.50000 - 11.2583i) q^{61} -4.00000i q^{62} +(-2.59808 + 1.50000i) q^{63} -1.00000 q^{64} +(-9.00000 - 5.19615i) q^{66} +(-11.2583 + 6.50000i) q^{67} +(13.5000 + 7.79423i) q^{69} -6.00000 q^{71} +(2.59808 + 1.50000i) q^{72} +4.00000i q^{73} +(4.00000 - 6.92820i) q^{74} +(2.00000 + 3.46410i) q^{76} +(-5.19615 + 3.00000i) q^{77} +(-1.73205 - 3.00000i) q^{78} +(-5.00000 + 8.66025i) q^{79} +(-4.50000 - 7.79423i) q^{81} -3.00000i q^{82} +(-7.79423 - 4.50000i) q^{83} +(1.50000 - 0.866025i) q^{84} +(-4.00000 - 6.92820i) q^{86} -5.19615 q^{87} +(5.19615 + 3.00000i) q^{88} -9.00000 q^{89} -2.00000 q^{91} +(-7.79423 - 4.50000i) q^{92} +(3.46410 - 6.00000i) q^{93} +(-1.50000 - 2.59808i) q^{94} +(-1.50000 - 0.866025i) q^{96} +(-1.73205 - 1.00000i) q^{97} +6.00000i q^{98} +(-9.00000 - 15.5885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{4} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{4} - 6 q^{9} - 12 q^{11} - 2 q^{14} - 2 q^{16} + 16 q^{19} - 6 q^{24} + 8 q^{26} + 6 q^{29} + 8 q^{31} - 12 q^{36} + 12 q^{39} + 6 q^{41} - 24 q^{44} + 36 q^{46} - 12 q^{49} - 18 q^{54} + 2 q^{56} + 12 q^{59} + 26 q^{61} - 4 q^{64} - 36 q^{66} + 54 q^{69} - 24 q^{71} + 16 q^{74} + 8 q^{76} - 20 q^{79} - 18 q^{81} + 6 q^{84} - 16 q^{86} - 36 q^{89} - 8 q^{91} - 6 q^{94} - 6 q^{96} - 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) −0.866025 1.50000i −0.500000 0.866025i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0 0
\(6\) 1.73205i 0.707107i
\(7\) 0.866025 + 0.500000i 0.327327 + 0.188982i 0.654654 0.755929i \(-0.272814\pi\)
−0.327327 + 0.944911i \(0.606148\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −1.50000 + 2.59808i −0.500000 + 0.866025i
\(10\) 0 0
\(11\) −3.00000 + 5.19615i −0.904534 + 1.56670i −0.0829925 + 0.996550i \(0.526448\pi\)
−0.821541 + 0.570149i \(0.806886\pi\)
\(12\) 0.866025 1.50000i 0.250000 0.433013i
\(13\) −1.73205 + 1.00000i −0.480384 + 0.277350i −0.720577 0.693375i \(-0.756123\pi\)
0.240192 + 0.970725i \(0.422790\pi\)
\(14\) −0.500000 0.866025i −0.133631 0.231455i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 2.59808 1.50000i 0.612372 0.353553i
\(19\) 4.00000 0.917663 0.458831 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 0 0
\(21\) 1.73205i 0.377964i
\(22\) 5.19615 3.00000i 1.10782 0.639602i
\(23\) −7.79423 + 4.50000i −1.62521 + 0.938315i −0.639713 + 0.768613i \(0.720947\pi\)
−0.985496 + 0.169701i \(0.945720\pi\)
\(24\) −1.50000 + 0.866025i −0.306186 + 0.176777i
\(25\) 0 0
\(26\) 2.00000 0.392232
\(27\) 5.19615 1.00000
\(28\) 1.00000i 0.188982i
\(29\) 1.50000 2.59808i 0.278543 0.482451i −0.692480 0.721437i \(-0.743482\pi\)
0.971023 + 0.238987i \(0.0768152\pi\)
\(30\) 0 0
\(31\) 2.00000 + 3.46410i 0.359211 + 0.622171i 0.987829 0.155543i \(-0.0497126\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 10.3923 1.80907
\(34\) 0 0
\(35\) 0 0
\(36\) −3.00000 −0.500000
\(37\) 8.00000i 1.31519i 0.753371 + 0.657596i \(0.228427\pi\)
−0.753371 + 0.657596i \(0.771573\pi\)
\(38\) −3.46410 2.00000i −0.561951 0.324443i
\(39\) 3.00000 + 1.73205i 0.480384 + 0.277350i
\(40\) 0 0
\(41\) 1.50000 + 2.59808i 0.234261 + 0.405751i 0.959058 0.283211i \(-0.0913998\pi\)
−0.724797 + 0.688963i \(0.758066\pi\)
\(42\) −0.866025 + 1.50000i −0.133631 + 0.231455i
\(43\) 6.92820 + 4.00000i 1.05654 + 0.609994i 0.924473 0.381246i \(-0.124505\pi\)
0.132068 + 0.991241i \(0.457838\pi\)
\(44\) −6.00000 −0.904534
\(45\) 0 0
\(46\) 9.00000 1.32698
\(47\) 2.59808 + 1.50000i 0.378968 + 0.218797i 0.677369 0.735643i \(-0.263120\pi\)
−0.298401 + 0.954441i \(0.596453\pi\)
\(48\) 1.73205 0.250000
\(49\) −3.00000 5.19615i −0.428571 0.742307i
\(50\) 0 0
\(51\) 0 0
\(52\) −1.73205 1.00000i −0.240192 0.138675i
\(53\) 6.00000i 0.824163i −0.911147 0.412082i \(-0.864802\pi\)
0.911147 0.412082i \(-0.135198\pi\)
\(54\) −4.50000 2.59808i −0.612372 0.353553i
\(55\) 0 0
\(56\) 0.500000 0.866025i 0.0668153 0.115728i
\(57\) −3.46410 6.00000i −0.458831 0.794719i
\(58\) −2.59808 + 1.50000i −0.341144 + 0.196960i
\(59\) 3.00000 + 5.19615i 0.390567 + 0.676481i 0.992524 0.122047i \(-0.0389457\pi\)
−0.601958 + 0.798528i \(0.705612\pi\)
\(60\) 0 0
\(61\) 6.50000 11.2583i 0.832240 1.44148i −0.0640184 0.997949i \(-0.520392\pi\)
0.896258 0.443533i \(-0.146275\pi\)
\(62\) 4.00000i 0.508001i
\(63\) −2.59808 + 1.50000i −0.327327 + 0.188982i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −9.00000 5.19615i −1.10782 0.639602i
\(67\) −11.2583 + 6.50000i −1.37542 + 0.794101i −0.991605 0.129307i \(-0.958725\pi\)
−0.383819 + 0.923408i \(0.625391\pi\)
\(68\) 0 0
\(69\) 13.5000 + 7.79423i 1.62521 + 0.938315i
\(70\) 0 0
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 2.59808 + 1.50000i 0.306186 + 0.176777i
\(73\) 4.00000i 0.468165i 0.972217 + 0.234082i \(0.0752085\pi\)
−0.972217 + 0.234082i \(0.924791\pi\)
\(74\) 4.00000 6.92820i 0.464991 0.805387i
\(75\) 0 0
\(76\) 2.00000 + 3.46410i 0.229416 + 0.397360i
\(77\) −5.19615 + 3.00000i −0.592157 + 0.341882i
\(78\) −1.73205 3.00000i −0.196116 0.339683i
\(79\) −5.00000 + 8.66025i −0.562544 + 0.974355i 0.434730 + 0.900561i \(0.356844\pi\)
−0.997274 + 0.0737937i \(0.976489\pi\)
\(80\) 0 0
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 3.00000i 0.331295i
\(83\) −7.79423 4.50000i −0.855528 0.493939i 0.00698436 0.999976i \(-0.497777\pi\)
−0.862512 + 0.506036i \(0.831110\pi\)
\(84\) 1.50000 0.866025i 0.163663 0.0944911i
\(85\) 0 0
\(86\) −4.00000 6.92820i −0.431331 0.747087i
\(87\) −5.19615 −0.557086
\(88\) 5.19615 + 3.00000i 0.553912 + 0.319801i
\(89\) −9.00000 −0.953998 −0.476999 0.878904i \(-0.658275\pi\)
−0.476999 + 0.878904i \(0.658275\pi\)
\(90\) 0 0
\(91\) −2.00000 −0.209657
\(92\) −7.79423 4.50000i −0.812605 0.469157i
\(93\) 3.46410 6.00000i 0.359211 0.622171i
\(94\) −1.50000 2.59808i −0.154713 0.267971i
\(95\) 0 0
\(96\) −1.50000 0.866025i −0.153093 0.0883883i
\(97\) −1.73205 1.00000i −0.175863 0.101535i 0.409484 0.912317i \(-0.365709\pi\)
−0.585348 + 0.810782i \(0.699042\pi\)
\(98\) 6.00000i 0.606092i
\(99\) −9.00000 15.5885i −0.904534 1.56670i
\(100\) 0 0
\(101\) −3.00000 + 5.19615i −0.298511 + 0.517036i −0.975796 0.218685i \(-0.929823\pi\)
0.677284 + 0.735721i \(0.263157\pi\)
\(102\) 0 0
\(103\) −6.92820 + 4.00000i −0.682656 + 0.394132i −0.800855 0.598858i \(-0.795621\pi\)
0.118199 + 0.992990i \(0.462288\pi\)
\(104\) 1.00000 + 1.73205i 0.0980581 + 0.169842i
\(105\) 0 0
\(106\) −3.00000 + 5.19615i −0.291386 + 0.504695i
\(107\) 3.00000i 0.290021i −0.989430 0.145010i \(-0.953678\pi\)
0.989430 0.145010i \(-0.0463216\pi\)
\(108\) 2.59808 + 4.50000i 0.250000 + 0.433013i
\(109\) 7.00000 0.670478 0.335239 0.942133i \(-0.391183\pi\)
0.335239 + 0.942133i \(0.391183\pi\)
\(110\) 0 0
\(111\) 12.0000 6.92820i 1.13899 0.657596i
\(112\) −0.866025 + 0.500000i −0.0818317 + 0.0472456i
\(113\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(114\) 6.92820i 0.648886i
\(115\) 0 0
\(116\) 3.00000 0.278543
\(117\) 6.00000i 0.554700i
\(118\) 6.00000i 0.552345i
\(119\) 0 0
\(120\) 0 0
\(121\) −12.5000 21.6506i −1.13636 1.96824i
\(122\) −11.2583 + 6.50000i −1.01928 + 0.588482i
\(123\) 2.59808 4.50000i 0.234261 0.405751i
\(124\) −2.00000 + 3.46410i −0.179605 + 0.311086i
\(125\) 0 0
\(126\) 3.00000 0.267261
\(127\) 7.00000i 0.621150i −0.950549 0.310575i \(-0.899478\pi\)
0.950549 0.310575i \(-0.100522\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 13.8564i 1.21999i
\(130\) 0 0
\(131\) 9.00000 + 15.5885i 0.786334 + 1.36197i 0.928199 + 0.372084i \(0.121357\pi\)
−0.141865 + 0.989886i \(0.545310\pi\)
\(132\) 5.19615 + 9.00000i 0.452267 + 0.783349i
\(133\) 3.46410 + 2.00000i 0.300376 + 0.173422i
\(134\) 13.0000 1.12303
\(135\) 0 0
\(136\) 0 0
\(137\) 10.3923 + 6.00000i 0.887875 + 0.512615i 0.873247 0.487278i \(-0.162010\pi\)
0.0146279 + 0.999893i \(0.495344\pi\)
\(138\) −7.79423 13.5000i −0.663489 1.14920i
\(139\) −8.00000 13.8564i −0.678551 1.17529i −0.975417 0.220366i \(-0.929275\pi\)
0.296866 0.954919i \(-0.404058\pi\)
\(140\) 0 0
\(141\) 5.19615i 0.437595i
\(142\) 5.19615 + 3.00000i 0.436051 + 0.251754i
\(143\) 12.0000i 1.00349i
\(144\) −1.50000 2.59808i −0.125000 0.216506i
\(145\) 0 0
\(146\) 2.00000 3.46410i 0.165521 0.286691i
\(147\) −5.19615 + 9.00000i −0.428571 + 0.742307i
\(148\) −6.92820 + 4.00000i −0.569495 + 0.328798i
\(149\) −1.50000 2.59808i −0.122885 0.212843i 0.798019 0.602632i \(-0.205881\pi\)
−0.920904 + 0.389789i \(0.872548\pi\)
\(150\) 0 0
\(151\) −7.00000 + 12.1244i −0.569652 + 0.986666i 0.426948 + 0.904276i \(0.359589\pi\)
−0.996600 + 0.0823900i \(0.973745\pi\)
\(152\) 4.00000i 0.324443i
\(153\) 0 0
\(154\) 6.00000 0.483494
\(155\) 0 0
\(156\) 3.46410i 0.277350i
\(157\) 12.1244 7.00000i 0.967629 0.558661i 0.0691164 0.997609i \(-0.477982\pi\)
0.898513 + 0.438948i \(0.144649\pi\)
\(158\) 8.66025 5.00000i 0.688973 0.397779i
\(159\) −9.00000 + 5.19615i −0.713746 + 0.412082i
\(160\) 0 0
\(161\) −9.00000 −0.709299
\(162\) 9.00000i 0.707107i
\(163\) 4.00000i 0.313304i 0.987654 + 0.156652i \(0.0500701\pi\)
−0.987654 + 0.156652i \(0.949930\pi\)
\(164\) −1.50000 + 2.59808i −0.117130 + 0.202876i
\(165\) 0 0
\(166\) 4.50000 + 7.79423i 0.349268 + 0.604949i
\(167\) −2.59808 + 1.50000i −0.201045 + 0.116073i −0.597143 0.802135i \(-0.703697\pi\)
0.396098 + 0.918208i \(0.370364\pi\)
\(168\) −1.73205 −0.133631
\(169\) −4.50000 + 7.79423i −0.346154 + 0.599556i
\(170\) 0 0
\(171\) −6.00000 + 10.3923i −0.458831 + 0.794719i
\(172\) 8.00000i 0.609994i
\(173\) 20.7846 + 12.0000i 1.58022 + 0.912343i 0.994826 + 0.101598i \(0.0323955\pi\)
0.585399 + 0.810745i \(0.300938\pi\)
\(174\) 4.50000 + 2.59808i 0.341144 + 0.196960i
\(175\) 0 0
\(176\) −3.00000 5.19615i −0.226134 0.391675i
\(177\) 5.19615 9.00000i 0.390567 0.676481i
\(178\) 7.79423 + 4.50000i 0.584202 + 0.337289i
\(179\) 18.0000 1.34538 0.672692 0.739923i \(-0.265138\pi\)
0.672692 + 0.739923i \(0.265138\pi\)
\(180\) 0 0
\(181\) 5.00000 0.371647 0.185824 0.982583i \(-0.440505\pi\)
0.185824 + 0.982583i \(0.440505\pi\)
\(182\) 1.73205 + 1.00000i 0.128388 + 0.0741249i
\(183\) −22.5167 −1.66448
\(184\) 4.50000 + 7.79423i 0.331744 + 0.574598i
\(185\) 0 0
\(186\) −6.00000 + 3.46410i −0.439941 + 0.254000i
\(187\) 0 0
\(188\) 3.00000i 0.218797i
\(189\) 4.50000 + 2.59808i 0.327327 + 0.188982i
\(190\) 0 0
\(191\) 6.00000 10.3923i 0.434145 0.751961i −0.563081 0.826402i \(-0.690384\pi\)
0.997225 + 0.0744412i \(0.0237173\pi\)
\(192\) 0.866025 + 1.50000i 0.0625000 + 0.108253i
\(193\) −1.73205 + 1.00000i −0.124676 + 0.0719816i −0.561041 0.827788i \(-0.689599\pi\)
0.436365 + 0.899770i \(0.356266\pi\)
\(194\) 1.00000 + 1.73205i 0.0717958 + 0.124354i
\(195\) 0 0
\(196\) 3.00000 5.19615i 0.214286 0.371154i
\(197\) 12.0000i 0.854965i −0.904024 0.427482i \(-0.859401\pi\)
0.904024 0.427482i \(-0.140599\pi\)
\(198\) 18.0000i 1.27920i
\(199\) −8.00000 −0.567105 −0.283552 0.958957i \(-0.591513\pi\)
−0.283552 + 0.958957i \(0.591513\pi\)
\(200\) 0 0
\(201\) 19.5000 + 11.2583i 1.37542 + 0.794101i
\(202\) 5.19615 3.00000i 0.365600 0.211079i
\(203\) 2.59808 1.50000i 0.182349 0.105279i
\(204\) 0 0
\(205\) 0 0
\(206\) 8.00000 0.557386
\(207\) 27.0000i 1.87663i
\(208\) 2.00000i 0.138675i
\(209\) −12.0000 + 20.7846i −0.830057 + 1.43770i
\(210\) 0 0
\(211\) −1.00000 1.73205i −0.0688428 0.119239i 0.829549 0.558433i \(-0.188597\pi\)
−0.898392 + 0.439194i \(0.855264\pi\)
\(212\) 5.19615 3.00000i 0.356873 0.206041i
\(213\) 5.19615 + 9.00000i 0.356034 + 0.616670i
\(214\) −1.50000 + 2.59808i −0.102538 + 0.177601i
\(215\) 0 0
\(216\) 5.19615i 0.353553i
\(217\) 4.00000i 0.271538i
\(218\) −6.06218 3.50000i −0.410582 0.237050i
\(219\) 6.00000 3.46410i 0.405442 0.234082i
\(220\) 0 0
\(221\) 0 0
\(222\) −13.8564 −0.929981
\(223\) −0.866025 0.500000i −0.0579934 0.0334825i 0.470723 0.882281i \(-0.343993\pi\)
−0.528716 + 0.848799i \(0.677326\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) 0 0
\(227\) 10.3923 + 6.00000i 0.689761 + 0.398234i 0.803523 0.595274i \(-0.202957\pi\)
−0.113761 + 0.993508i \(0.536290\pi\)
\(228\) 3.46410 6.00000i 0.229416 0.397360i
\(229\) −6.50000 11.2583i −0.429532 0.743971i 0.567300 0.823511i \(-0.307988\pi\)
−0.996832 + 0.0795401i \(0.974655\pi\)
\(230\) 0 0
\(231\) 9.00000 + 5.19615i 0.592157 + 0.341882i
\(232\) −2.59808 1.50000i −0.170572 0.0984798i
\(233\) 12.0000i 0.786146i 0.919507 + 0.393073i \(0.128588\pi\)
−0.919507 + 0.393073i \(0.871412\pi\)
\(234\) −3.00000 + 5.19615i −0.196116 + 0.339683i
\(235\) 0 0
\(236\) −3.00000 + 5.19615i −0.195283 + 0.338241i
\(237\) 17.3205 1.12509
\(238\) 0 0
\(239\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(240\) 0 0
\(241\) −14.5000 + 25.1147i −0.934027 + 1.61778i −0.157667 + 0.987492i \(0.550397\pi\)
−0.776360 + 0.630290i \(0.782936\pi\)
\(242\) 25.0000i 1.60706i
\(243\) −7.79423 + 13.5000i −0.500000 + 0.866025i
\(244\) 13.0000 0.832240
\(245\) 0 0
\(246\) −4.50000 + 2.59808i −0.286910 + 0.165647i
\(247\) −6.92820 + 4.00000i −0.440831 + 0.254514i
\(248\) 3.46410 2.00000i 0.219971 0.127000i
\(249\) 15.5885i 0.987878i
\(250\) 0 0
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) −2.59808 1.50000i −0.163663 0.0944911i
\(253\) 54.0000i 3.39495i
\(254\) −3.50000 + 6.06218i −0.219610 + 0.380375i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 15.5885 9.00000i 0.972381 0.561405i 0.0724199 0.997374i \(-0.476928\pi\)
0.899961 + 0.435970i \(0.143595\pi\)
\(258\) −6.92820 + 12.0000i −0.431331 + 0.747087i
\(259\) −4.00000 + 6.92820i −0.248548 + 0.430498i
\(260\) 0 0
\(261\) 4.50000 + 7.79423i 0.278543 + 0.482451i
\(262\) 18.0000i 1.11204i
\(263\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) 10.3923i 0.639602i
\(265\) 0 0
\(266\) −2.00000 3.46410i −0.122628 0.212398i
\(267\) 7.79423 + 13.5000i 0.476999 + 0.826187i
\(268\) −11.2583 6.50000i −0.687712 0.397051i
\(269\) −21.0000 −1.28039 −0.640196 0.768211i \(-0.721147\pi\)
−0.640196 + 0.768211i \(0.721147\pi\)
\(270\) 0 0
\(271\) −4.00000 −0.242983 −0.121491 0.992592i \(-0.538768\pi\)
−0.121491 + 0.992592i \(0.538768\pi\)
\(272\) 0 0
\(273\) 1.73205 + 3.00000i 0.104828 + 0.181568i
\(274\) −6.00000 10.3923i −0.362473 0.627822i
\(275\) 0 0
\(276\) 15.5885i 0.938315i
\(277\) −6.92820 4.00000i −0.416275 0.240337i 0.277207 0.960810i \(-0.410591\pi\)
−0.693482 + 0.720473i \(0.743925\pi\)
\(278\) 16.0000i 0.959616i
\(279\) −12.0000 −0.718421
\(280\) 0 0
\(281\) 7.50000 12.9904i 0.447412 0.774941i −0.550804 0.834634i \(-0.685679\pi\)
0.998217 + 0.0596933i \(0.0190123\pi\)
\(282\) −2.59808 + 4.50000i −0.154713 + 0.267971i
\(283\) 11.2583 6.50000i 0.669238 0.386385i −0.126550 0.991960i \(-0.540390\pi\)
0.795788 + 0.605575i \(0.207057\pi\)
\(284\) −3.00000 5.19615i −0.178017 0.308335i
\(285\) 0 0
\(286\) −6.00000 + 10.3923i −0.354787 + 0.614510i
\(287\) 3.00000i 0.177084i
\(288\) 3.00000i 0.176777i
\(289\) 17.0000 1.00000
\(290\) 0 0
\(291\) 3.46410i 0.203069i
\(292\) −3.46410 + 2.00000i −0.202721 + 0.117041i
\(293\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(294\) 9.00000 5.19615i 0.524891 0.303046i
\(295\) 0 0
\(296\) 8.00000 0.464991
\(297\) −15.5885 + 27.0000i −0.904534 + 1.56670i
\(298\) 3.00000i 0.173785i
\(299\) 9.00000 15.5885i 0.520483 0.901504i
\(300\) 0 0
\(301\) 4.00000 + 6.92820i 0.230556 + 0.399335i
\(302\) 12.1244 7.00000i 0.697678 0.402805i
\(303\) 10.3923 0.597022
\(304\) −2.00000 + 3.46410i −0.114708 + 0.198680i
\(305\) 0 0
\(306\) 0 0
\(307\) 7.00000i 0.399511i −0.979846 0.199756i \(-0.935985\pi\)
0.979846 0.199756i \(-0.0640148\pi\)
\(308\) −5.19615 3.00000i −0.296078 0.170941i
\(309\) 12.0000 + 6.92820i 0.682656 + 0.394132i
\(310\) 0 0
\(311\) −6.00000 10.3923i −0.340229 0.589294i 0.644246 0.764818i \(-0.277171\pi\)
−0.984475 + 0.175525i \(0.943838\pi\)
\(312\) 1.73205 3.00000i 0.0980581 0.169842i
\(313\) 1.73205 + 1.00000i 0.0979013 + 0.0565233i 0.548151 0.836379i \(-0.315332\pi\)
−0.450250 + 0.892903i \(0.648665\pi\)
\(314\) −14.0000 −0.790066
\(315\) 0 0
\(316\) −10.0000 −0.562544
\(317\) 5.19615 + 3.00000i 0.291845 + 0.168497i 0.638774 0.769395i \(-0.279442\pi\)
−0.346929 + 0.937892i \(0.612775\pi\)
\(318\) 10.3923 0.582772
\(319\) 9.00000 + 15.5885i 0.503903 + 0.872786i
\(320\) 0 0
\(321\) −4.50000 + 2.59808i −0.251166 + 0.145010i
\(322\) 7.79423 + 4.50000i 0.434355 + 0.250775i
\(323\) 0 0
\(324\) 4.50000 7.79423i 0.250000 0.433013i
\(325\) 0 0
\(326\) 2.00000 3.46410i 0.110770 0.191859i
\(327\) −6.06218 10.5000i −0.335239 0.580651i
\(328\) 2.59808 1.50000i 0.143455 0.0828236i
\(329\) 1.50000 + 2.59808i 0.0826977 + 0.143237i
\(330\) 0 0
\(331\) 5.00000 8.66025i 0.274825 0.476011i −0.695266 0.718752i \(-0.744713\pi\)
0.970091 + 0.242742i \(0.0780468\pi\)
\(332\) 9.00000i 0.493939i
\(333\) −20.7846 12.0000i −1.13899 0.657596i
\(334\) 3.00000 0.164153
\(335\) 0 0
\(336\) 1.50000 + 0.866025i 0.0818317 + 0.0472456i
\(337\) 6.92820 4.00000i 0.377403 0.217894i −0.299285 0.954164i \(-0.596748\pi\)
0.676688 + 0.736270i \(0.263415\pi\)
\(338\) 7.79423 4.50000i 0.423950 0.244768i
\(339\) 0 0
\(340\) 0 0
\(341\) −24.0000 −1.29967
\(342\) 10.3923 6.00000i 0.561951 0.324443i
\(343\) 13.0000i 0.701934i
\(344\) 4.00000 6.92820i 0.215666 0.373544i
\(345\) 0 0
\(346\) −12.0000 20.7846i −0.645124 1.11739i
\(347\) 10.3923 6.00000i 0.557888 0.322097i −0.194409 0.980921i \(-0.562279\pi\)
0.752297 + 0.658824i \(0.228946\pi\)
\(348\) −2.59808 4.50000i −0.139272 0.241225i
\(349\) 11.5000 19.9186i 0.615581 1.06622i −0.374701 0.927146i \(-0.622255\pi\)
0.990282 0.139072i \(-0.0444119\pi\)
\(350\) 0 0
\(351\) −9.00000 + 5.19615i −0.480384 + 0.277350i
\(352\) 6.00000i 0.319801i
\(353\) 20.7846 + 12.0000i 1.10625 + 0.638696i 0.937856 0.347024i \(-0.112808\pi\)
0.168397 + 0.985719i \(0.446141\pi\)
\(354\) −9.00000 + 5.19615i −0.478345 + 0.276172i
\(355\) 0 0
\(356\) −4.50000 7.79423i −0.238500 0.413093i
\(357\) 0 0
\(358\) −15.5885 9.00000i −0.823876 0.475665i
\(359\) 12.0000 0.633336 0.316668 0.948536i \(-0.397436\pi\)
0.316668 + 0.948536i \(0.397436\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) −4.33013 2.50000i −0.227586 0.131397i
\(363\) −21.6506 + 37.5000i −1.13636 + 1.96824i
\(364\) −1.00000 1.73205i −0.0524142 0.0907841i
\(365\) 0 0
\(366\) 19.5000 + 11.2583i 1.01928 + 0.588482i
\(367\) −6.92820 4.00000i −0.361649 0.208798i 0.308155 0.951336i \(-0.400289\pi\)
−0.669804 + 0.742538i \(0.733622\pi\)
\(368\) 9.00000i 0.469157i
\(369\) −9.00000 −0.468521
\(370\) 0 0
\(371\) 3.00000 5.19615i 0.155752 0.269771i
\(372\) 6.92820 0.359211
\(373\) −22.5167 + 13.0000i −1.16587 + 0.673114i −0.952703 0.303902i \(-0.901711\pi\)
−0.213165 + 0.977016i \(0.568377\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 1.50000 2.59808i 0.0773566 0.133986i
\(377\) 6.00000i 0.309016i
\(378\) −2.59808 4.50000i −0.133631 0.231455i
\(379\) 22.0000 1.13006 0.565032 0.825069i \(-0.308864\pi\)
0.565032 + 0.825069i \(0.308864\pi\)
\(380\) 0 0
\(381\) −10.5000 + 6.06218i −0.537931 + 0.310575i
\(382\) −10.3923 + 6.00000i −0.531717 + 0.306987i
\(383\) 10.3923 6.00000i 0.531022 0.306586i −0.210411 0.977613i \(-0.567480\pi\)
0.741433 + 0.671027i \(0.234147\pi\)
\(384\) 1.73205i 0.0883883i
\(385\) 0 0
\(386\) 2.00000 0.101797
\(387\) −20.7846 + 12.0000i −1.05654 + 0.609994i
\(388\) 2.00000i 0.101535i
\(389\) 10.5000 18.1865i 0.532371 0.922094i −0.466915 0.884302i \(-0.654634\pi\)
0.999286 0.0377914i \(-0.0120322\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −5.19615 + 3.00000i −0.262445 + 0.151523i
\(393\) 15.5885 27.0000i 0.786334 1.36197i
\(394\) −6.00000 + 10.3923i −0.302276 + 0.523557i
\(395\) 0 0
\(396\) 9.00000 15.5885i 0.452267 0.783349i
\(397\) 2.00000i 0.100377i 0.998740 + 0.0501886i \(0.0159822\pi\)
−0.998740 + 0.0501886i \(0.984018\pi\)
\(398\) 6.92820 + 4.00000i 0.347279 + 0.200502i
\(399\) 6.92820i 0.346844i
\(400\) 0 0
\(401\) −3.00000 5.19615i −0.149813 0.259483i 0.781345 0.624099i \(-0.214534\pi\)
−0.931158 + 0.364615i \(0.881200\pi\)
\(402\) −11.2583 19.5000i −0.561514 0.972572i
\(403\) −6.92820 4.00000i −0.345118 0.199254i
\(404\) −6.00000 −0.298511
\(405\) 0 0
\(406\) −3.00000 −0.148888
\(407\) −41.5692 24.0000i −2.06051 1.18964i
\(408\) 0 0
\(409\) −5.00000 8.66025i −0.247234 0.428222i 0.715523 0.698589i \(-0.246188\pi\)
−0.962757 + 0.270367i \(0.912855\pi\)
\(410\) 0 0
\(411\) 20.7846i 1.02523i
\(412\) −6.92820 4.00000i −0.341328 0.197066i
\(413\) 6.00000i 0.295241i
\(414\) −13.5000 + 23.3827i −0.663489 + 1.14920i
\(415\) 0 0
\(416\) −1.00000 + 1.73205i −0.0490290 + 0.0849208i
\(417\) −13.8564 + 24.0000i −0.678551 + 1.17529i
\(418\) 20.7846 12.0000i 1.01661 0.586939i
\(419\) −15.0000 25.9808i −0.732798 1.26924i −0.955683 0.294398i \(-0.904881\pi\)
0.222885 0.974845i \(-0.428453\pi\)
\(420\) 0 0
\(421\) 11.0000 19.0526i 0.536107 0.928565i −0.463002 0.886357i \(-0.653228\pi\)
0.999109 0.0422075i \(-0.0134391\pi\)
\(422\) 2.00000i 0.0973585i
\(423\) −7.79423 + 4.50000i −0.378968 + 0.218797i
\(424\) −6.00000 −0.291386
\(425\) 0 0
\(426\) 10.3923i 0.503509i
\(427\) 11.2583 6.50000i 0.544829 0.314557i
\(428\) 2.59808 1.50000i 0.125583 0.0725052i
\(429\) −18.0000 + 10.3923i −0.869048 + 0.501745i
\(430\) 0 0
\(431\) 6.00000 0.289010 0.144505 0.989504i \(-0.453841\pi\)
0.144505 + 0.989504i \(0.453841\pi\)
\(432\) −2.59808 + 4.50000i −0.125000 + 0.216506i
\(433\) 16.0000i 0.768911i 0.923144 + 0.384455i \(0.125611\pi\)
−0.923144 + 0.384455i \(0.874389\pi\)
\(434\) 2.00000 3.46410i 0.0960031 0.166282i
\(435\) 0 0
\(436\) 3.50000 + 6.06218i 0.167620 + 0.290326i
\(437\) −31.1769 + 18.0000i −1.49139 + 0.861057i
\(438\) −6.92820 −0.331042
\(439\) −14.0000 + 24.2487i −0.668184 + 1.15733i 0.310228 + 0.950662i \(0.399595\pi\)
−0.978412 + 0.206666i \(0.933739\pi\)
\(440\) 0 0
\(441\) 18.0000 0.857143
\(442\) 0 0
\(443\) 7.79423 + 4.50000i 0.370315 + 0.213801i 0.673596 0.739100i \(-0.264749\pi\)
−0.303281 + 0.952901i \(0.598082\pi\)
\(444\) 12.0000 + 6.92820i 0.569495 + 0.328798i
\(445\) 0 0
\(446\) 0.500000 + 0.866025i 0.0236757 + 0.0410075i
\(447\) −2.59808 + 4.50000i −0.122885 + 0.212843i
\(448\) −0.866025 0.500000i −0.0409159 0.0236228i
\(449\) −6.00000 −0.283158 −0.141579 0.989927i \(-0.545218\pi\)
−0.141579 + 0.989927i \(0.545218\pi\)
\(450\) 0 0
\(451\) −18.0000 −0.847587
\(452\) 0 0
\(453\) 24.2487 1.13930
\(454\) −6.00000 10.3923i −0.281594 0.487735i
\(455\) 0 0
\(456\) −6.00000 + 3.46410i −0.280976 + 0.162221i
\(457\) −6.92820 4.00000i −0.324088 0.187112i 0.329125 0.944286i \(-0.393246\pi\)
−0.653213 + 0.757174i \(0.726579\pi\)
\(458\) 13.0000i 0.607450i
\(459\) 0 0
\(460\) 0 0
\(461\) 13.5000 23.3827i 0.628758 1.08904i −0.359044 0.933321i \(-0.616897\pi\)
0.987801 0.155719i \(-0.0497696\pi\)
\(462\) −5.19615 9.00000i −0.241747 0.418718i
\(463\) 3.46410 2.00000i 0.160990 0.0929479i −0.417340 0.908750i \(-0.637038\pi\)
0.578331 + 0.815802i \(0.303704\pi\)
\(464\) 1.50000 + 2.59808i 0.0696358 + 0.120613i
\(465\) 0 0
\(466\) 6.00000 10.3923i 0.277945 0.481414i
\(467\) 36.0000i 1.66588i 0.553362 + 0.832941i \(0.313345\pi\)
−0.553362 + 0.832941i \(0.686655\pi\)
\(468\) 5.19615 3.00000i 0.240192 0.138675i
\(469\) −13.0000 −0.600284
\(470\) 0 0
\(471\) −21.0000 12.1244i −0.967629 0.558661i
\(472\) 5.19615 3.00000i 0.239172 0.138086i
\(473\) −41.5692 + 24.0000i −1.91135 + 1.10352i
\(474\) −15.0000 8.66025i −0.688973 0.397779i
\(475\) 0 0
\(476\) 0 0
\(477\) 15.5885 + 9.00000i 0.713746 + 0.412082i
\(478\) 0 0
\(479\) −15.0000 + 25.9808i −0.685367 + 1.18709i 0.287954 + 0.957644i \(0.407025\pi\)
−0.973321 + 0.229447i \(0.926308\pi\)
\(480\) 0 0
\(481\) −8.00000 13.8564i −0.364769 0.631798i
\(482\) 25.1147 14.5000i 1.14394 0.660457i
\(483\) 7.79423 + 13.5000i 0.354650 + 0.614271i
\(484\) 12.5000 21.6506i 0.568182 0.984120i
\(485\) 0 0
\(486\) 13.5000 7.79423i 0.612372 0.353553i
\(487\) 8.00000i 0.362515i 0.983436 + 0.181257i \(0.0580167\pi\)
−0.983436 + 0.181257i \(0.941983\pi\)
\(488\) −11.2583 6.50000i −0.509641 0.294241i
\(489\) 6.00000 3.46410i 0.271329 0.156652i
\(490\) 0 0
\(491\) −6.00000 10.3923i −0.270776 0.468998i 0.698285 0.715820i \(-0.253947\pi\)
−0.969061 + 0.246822i \(0.920614\pi\)
\(492\) 5.19615 0.234261
\(493\) 0 0
\(494\) 8.00000 0.359937
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) −5.19615 3.00000i −0.233079 0.134568i
\(498\) 7.79423 13.5000i 0.349268 0.604949i
\(499\) 16.0000 + 27.7128i 0.716258 + 1.24060i 0.962472 + 0.271380i \(0.0874801\pi\)
−0.246214 + 0.969216i \(0.579187\pi\)
\(500\) 0 0
\(501\) 4.50000 + 2.59808i 0.201045 + 0.116073i
\(502\) −10.3923 6.00000i −0.463831 0.267793i
\(503\) 27.0000i 1.20387i −0.798545 0.601935i \(-0.794397\pi\)
0.798545 0.601935i \(-0.205603\pi\)
\(504\) 1.50000 + 2.59808i 0.0668153 + 0.115728i
\(505\) 0 0
\(506\) −27.0000 + 46.7654i −1.20030 + 2.07897i
\(507\) 15.5885 0.692308
\(508\) 6.06218 3.50000i 0.268966 0.155287i
\(509\) 7.50000 + 12.9904i 0.332432 + 0.575789i 0.982988 0.183669i \(-0.0587976\pi\)
−0.650556 + 0.759458i \(0.725464\pi\)
\(510\) 0 0
\(511\) −2.00000 + 3.46410i −0.0884748 + 0.153243i
\(512\) 1.00000i 0.0441942i
\(513\) 20.7846 0.917663
\(514\) −18.0000 −0.793946
\(515\) 0 0
\(516\) 12.0000 6.92820i 0.528271 0.304997i
\(517\) −15.5885 + 9.00000i −0.685580 + 0.395820i
\(518\) 6.92820 4.00000i 0.304408 0.175750i
\(519\) 41.5692i 1.82469i
\(520\) 0 0
\(521\) 27.0000 1.18289 0.591446 0.806345i \(-0.298557\pi\)
0.591446 + 0.806345i \(0.298557\pi\)
\(522\) 9.00000i 0.393919i
\(523\) 19.0000i 0.830812i 0.909636 + 0.415406i \(0.136360\pi\)
−0.909636 + 0.415406i \(0.863640\pi\)
\(524\) −9.00000 + 15.5885i −0.393167 + 0.680985i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −5.19615 + 9.00000i −0.226134 + 0.391675i
\(529\) 29.0000 50.2295i 1.26087 2.18389i
\(530\) 0 0
\(531\) −18.0000 −0.781133
\(532\) 4.00000i 0.173422i
\(533\) −5.19615 3.00000i −0.225070 0.129944i
\(534\) 15.5885i 0.674579i
\(535\) 0 0
\(536\) 6.50000 + 11.2583i 0.280757 + 0.486286i
\(537\) −15.5885 27.0000i −0.672692 1.16514i
\(538\) 18.1865 + 10.5000i 0.784077 + 0.452687i
\(539\) 36.0000 1.55063
\(540\) 0 0
\(541\) 29.0000 1.24681 0.623404 0.781900i \(-0.285749\pi\)
0.623404 + 0.781900i \(0.285749\pi\)
\(542\) 3.46410 + 2.00000i 0.148796 + 0.0859074i
\(543\) −4.33013 7.50000i −0.185824 0.321856i
\(544\) 0 0
\(545\) 0 0
\(546\) 3.46410i 0.148250i
\(547\) 37.2391 + 21.5000i 1.59223 + 0.919274i 0.992924 + 0.118753i \(0.0378896\pi\)
0.599305 + 0.800521i \(0.295444\pi\)
\(548\) 12.0000i 0.512615i
\(549\) 19.5000 + 33.7750i 0.832240 + 1.44148i
\(550\) 0 0
\(551\) 6.00000 10.3923i 0.255609 0.442727i
\(552\) 7.79423 13.5000i 0.331744 0.574598i
\(553\) −8.66025 + 5.00000i −0.368271 + 0.212622i
\(554\) 4.00000 + 6.92820i 0.169944 + 0.294351i
\(555\) 0 0
\(556\) 8.00000 13.8564i 0.339276 0.587643i
\(557\) 6.00000i 0.254228i −0.991888 0.127114i \(-0.959429\pi\)
0.991888 0.127114i \(-0.0405714\pi\)
\(558\) 10.3923 + 6.00000i 0.439941 + 0.254000i
\(559\) −16.0000 −0.676728
\(560\) 0 0
\(561\) 0 0
\(562\) −12.9904 + 7.50000i −0.547966 + 0.316368i
\(563\) 2.59808 1.50000i 0.109496 0.0632175i −0.444252 0.895902i \(-0.646530\pi\)
0.553748 + 0.832684i \(0.313197\pi\)
\(564\) 4.50000 2.59808i 0.189484 0.109399i
\(565\) 0 0
\(566\) −13.0000 −0.546431
\(567\) 9.00000i 0.377964i
\(568\) 6.00000i 0.251754i
\(569\) −3.00000 + 5.19615i −0.125767 + 0.217834i −0.922032 0.387113i \(-0.873472\pi\)
0.796266 + 0.604947i \(0.206806\pi\)
\(570\) 0 0
\(571\) 20.0000 + 34.6410i 0.836974 + 1.44968i 0.892413 + 0.451219i \(0.149011\pi\)
−0.0554391 + 0.998462i \(0.517656\pi\)
\(572\) 10.3923 6.00000i 0.434524 0.250873i
\(573\) −20.7846 −0.868290
\(574\) 1.50000 2.59808i 0.0626088 0.108442i
\(575\) 0 0
\(576\) 1.50000 2.59808i 0.0625000 0.108253i
\(577\) 10.0000i 0.416305i −0.978096 0.208153i \(-0.933255\pi\)
0.978096 0.208153i \(-0.0667451\pi\)
\(578\) −14.7224 8.50000i −0.612372 0.353553i
\(579\) 3.00000 + 1.73205i 0.124676 + 0.0719816i
\(580\) 0 0
\(581\) −4.50000 7.79423i −0.186691 0.323359i
\(582\) 1.73205 3.00000i 0.0717958 0.124354i
\(583\) 31.1769 + 18.0000i 1.29122 + 0.745484i
\(584\) 4.00000 0.165521
\(585\) 0 0
\(586\) 0 0
\(587\) 12.9904 + 7.50000i 0.536170 + 0.309558i 0.743525 0.668708i \(-0.233152\pi\)
−0.207355 + 0.978266i \(0.566486\pi\)
\(588\) −10.3923 −0.428571
\(589\) 8.00000 + 13.8564i 0.329634 + 0.570943i
\(590\) 0 0
\(591\) −18.0000 + 10.3923i −0.740421 + 0.427482i
\(592\) −6.92820 4.00000i −0.284747 0.164399i
\(593\) 24.0000i 0.985562i −0.870153 0.492781i \(-0.835980\pi\)
0.870153 0.492781i \(-0.164020\pi\)
\(594\) 27.0000 15.5885i 1.10782 0.639602i
\(595\) 0 0
\(596\) 1.50000 2.59808i 0.0614424 0.106421i
\(597\) 6.92820 + 12.0000i 0.283552 + 0.491127i
\(598\) −15.5885 + 9.00000i −0.637459 + 0.368037i
\(599\) −3.00000 5.19615i −0.122577 0.212309i 0.798206 0.602384i \(-0.205782\pi\)
−0.920783 + 0.390075i \(0.872449\pi\)
\(600\) 0 0
\(601\) −13.0000 + 22.5167i −0.530281 + 0.918474i 0.469095 + 0.883148i \(0.344580\pi\)
−0.999376 + 0.0353259i \(0.988753\pi\)
\(602\) 8.00000i 0.326056i
\(603\) 39.0000i 1.58820i
\(604\) −14.0000 −0.569652
\(605\) 0 0
\(606\) −9.00000 5.19615i −0.365600 0.211079i
\(607\) 25.1147 14.5000i 1.01938 0.588537i 0.105453 0.994424i \(-0.466371\pi\)
0.913923 + 0.405887i \(0.133038\pi\)
\(608\) 3.46410 2.00000i 0.140488 0.0811107i
\(609\) −4.50000 2.59808i −0.182349 0.105279i
\(610\) 0 0
\(611\) −6.00000 −0.242734
\(612\) 0 0
\(613\) 40.0000i 1.61558i 0.589467 + 0.807792i \(0.299338\pi\)
−0.589467 + 0.807792i \(0.700662\pi\)
\(614\) −3.50000 + 6.06218i −0.141249 + 0.244650i
\(615\) 0 0
\(616\) 3.00000 + 5.19615i 0.120873 + 0.209359i
\(617\) 10.3923 6.00000i 0.418378 0.241551i −0.276005 0.961156i \(-0.589011\pi\)
0.694383 + 0.719605i \(0.255677\pi\)
\(618\) −6.92820 12.0000i −0.278693 0.482711i
\(619\) −20.0000 + 34.6410i −0.803868 + 1.39234i 0.113185 + 0.993574i \(0.463895\pi\)
−0.917053 + 0.398766i \(0.869439\pi\)
\(620\) 0 0
\(621\) −40.5000 + 23.3827i −1.62521 + 0.938315i
\(622\) 12.0000i 0.481156i
\(623\) −7.79423 4.50000i −0.312269 0.180289i
\(624\) −3.00000 + 1.73205i −0.120096 + 0.0693375i
\(625\) 0 0
\(626\) −1.00000 1.73205i −0.0399680 0.0692267i
\(627\) 41.5692 1.66011
\(628\) 12.1244 + 7.00000i 0.483814 + 0.279330i
\(629\) 0 0
\(630\) 0 0
\(631\) 32.0000 1.27390 0.636950 0.770905i \(-0.280196\pi\)
0.636950 + 0.770905i \(0.280196\pi\)
\(632\) 8.66025 + 5.00000i 0.344486 + 0.198889i
\(633\) −1.73205 + 3.00000i −0.0688428 + 0.119239i
\(634\) −3.00000 5.19615i −0.119145 0.206366i
\(635\) 0 0
\(636\) −9.00000 5.19615i −0.356873 0.206041i
\(637\) 10.3923 + 6.00000i 0.411758 + 0.237729i
\(638\) 18.0000i 0.712627i
\(639\) 9.00000 15.5885i 0.356034 0.616670i
\(640\) 0 0
\(641\) −16.5000 + 28.5788i −0.651711 + 1.12880i 0.330997 + 0.943632i \(0.392615\pi\)
−0.982708 + 0.185164i \(0.940718\pi\)
\(642\) 5.19615 0.205076
\(643\) 26.8468 15.5000i 1.05873 0.611260i 0.133652 0.991028i \(-0.457330\pi\)
0.925082 + 0.379768i \(0.123996\pi\)
\(644\) −4.50000 7.79423i −0.177325 0.307136i
\(645\) 0 0
\(646\) 0 0
\(647\) 3.00000i 0.117942i −0.998260 0.0589711i \(-0.981218\pi\)
0.998260 0.0589711i \(-0.0187820\pi\)
\(648\) −7.79423 + 4.50000i −0.306186 + 0.176777i
\(649\) −36.0000 −1.41312
\(650\) 0 0
\(651\) 6.00000 3.46410i 0.235159 0.135769i
\(652\) −3.46410 + 2.00000i −0.135665 + 0.0783260i
\(653\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(654\) 12.1244i 0.474100i
\(655\) 0 0
\(656\) −3.00000 −0.117130
\(657\) −10.3923 6.00000i −0.405442 0.234082i
\(658\) 3.00000i 0.116952i
\(659\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(660\) 0 0
\(661\) 23.0000 + 39.8372i 0.894596 + 1.54949i 0.834303 + 0.551306i \(0.185870\pi\)
0.0602929 + 0.998181i \(0.480797\pi\)
\(662\) −8.66025 + 5.00000i −0.336590 + 0.194331i
\(663\) 0 0
\(664\) −4.50000 + 7.79423i −0.174634 + 0.302475i
\(665\) 0 0
\(666\) 12.0000 + 20.7846i 0.464991 + 0.805387i
\(667\) 27.0000i 1.04544i
\(668\) −2.59808 1.50000i −0.100523 0.0580367i
\(669\) 1.73205i 0.0669650i
\(670\) 0 0
\(671\) 39.0000 + 67.5500i 1.50558 + 2.60774i
\(672\) −0.866025 1.50000i −0.0334077 0.0578638i
\(673\) −39.8372 23.0000i −1.53561 0.886585i −0.999088 0.0426985i \(-0.986405\pi\)
−0.536522 0.843886i \(-0.680262\pi\)
\(674\) −8.00000 −0.308148
\(675\) 0 0
\(676\) −9.00000 −0.346154
\(677\) −15.5885 9.00000i −0.599113 0.345898i 0.169580 0.985517i \(-0.445759\pi\)
−0.768693 + 0.639618i \(0.779092\pi\)
\(678\) 0 0
\(679\) −1.00000 1.73205i −0.0383765 0.0664700i
\(680\) 0 0
\(681\) 20.7846i 0.796468i
\(682\) 20.7846 + 12.0000i 0.795884 + 0.459504i
\(683\) 12.0000i 0.459167i −0.973289 0.229584i \(-0.926264\pi\)
0.973289 0.229584i \(-0.0737364\pi\)
\(684\) −12.0000 −0.458831
\(685\) 0 0
\(686\) −6.50000 + 11.2583i −0.248171 + 0.429845i
\(687\) −11.2583 + 19.5000i −0.429532 + 0.743971i
\(688\) −6.92820 + 4.00000i −0.264135 + 0.152499i
\(689\) 6.00000 + 10.3923i 0.228582 + 0.395915i
\(690\) 0 0
\(691\) 5.00000 8.66025i 0.190209 0.329452i −0.755110 0.655598i \(-0.772417\pi\)
0.945319 + 0.326146i \(0.105750\pi\)
\(692\) 24.0000i 0.912343i
\(693\) 18.0000i 0.683763i
\(694\) −12.0000 −0.455514
\(695\) 0 0
\(696\) 5.19615i 0.196960i
\(697\) 0 0
\(698\) −19.9186 + 11.5000i −0.753930 + 0.435281i
\(699\) 18.0000 10.3923i 0.680823 0.393073i
\(700\) 0 0
\(701\) −45.0000 −1.69963 −0.849813 0.527084i \(-0.823285\pi\)
−0.849813 + 0.527084i \(0.823285\pi\)
\(702\) 10.3923 0.392232
\(703\) 32.0000i 1.20690i
\(704\) 3.00000 5.19615i 0.113067 0.195837i
\(705\) 0 0
\(706\) −12.0000 20.7846i −0.451626 0.782239i
\(707\) −5.19615 + 3.00000i −0.195421 + 0.112827i
\(708\) 10.3923 0.390567
\(709\) 5.50000 9.52628i 0.206557 0.357767i −0.744071 0.668101i \(-0.767108\pi\)
0.950628 + 0.310334i \(0.100441\pi\)
\(710\) 0 0
\(711\) −15.0000 25.9808i −0.562544 0.974355i
\(712\) 9.00000i 0.337289i
\(713\) −31.1769 18.0000i −1.16758 0.674105i
\(714\) 0 0
\(715\) 0 0
\(716\) 9.00000 + 15.5885i 0.336346 + 0.582568i
\(717\) 0 0
\(718\) −10.3923 6.00000i −0.387837 0.223918i
\(719\) 6.00000 0.223762 0.111881 0.993722i \(-0.464312\pi\)
0.111881 + 0.993722i \(0.464312\pi\)
\(720\) 0 0
\(721\) −8.00000 −0.297936
\(722\) 2.59808 + 1.50000i 0.0966904 + 0.0558242i
\(723\) 50.2295 1.86805
\(724\) 2.50000 + 4.33013i 0.0929118 + 0.160928i
\(725\) 0 0
\(726\) 37.5000 21.6506i 1.39176 0.803530i
\(727\) −45.8993 26.5000i −1.70231 0.982831i −0.943411 0.331625i \(-0.892403\pi\)
−0.758901 0.651206i \(-0.774263\pi\)
\(728\) 2.00000i 0.0741249i
\(729\) 27.0000 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) −11.2583 19.5000i −0.416120 0.720741i
\(733\) −12.1244 + 7.00000i −0.447823 + 0.258551i −0.706910 0.707303i \(-0.749912\pi\)
0.259087 + 0.965854i \(0.416578\pi\)
\(734\) 4.00000 + 6.92820i 0.147643 + 0.255725i
\(735\) 0 0
\(736\) −4.50000 + 7.79423i −0.165872 + 0.287299i
\(737\) 78.0000i 2.87317i
\(738\) 7.79423 + 4.50000i 0.286910 + 0.165647i
\(739\) −2.00000 −0.0735712 −0.0367856 0.999323i \(-0.511712\pi\)
−0.0367856 + 0.999323i \(0.511712\pi\)
\(740\) 0 0
\(741\) 12.0000 + 6.92820i 0.440831 + 0.254514i
\(742\) −5.19615 + 3.00000i −0.190757 + 0.110133i
\(743\) 12.9904 7.50000i 0.476571 0.275148i −0.242415 0.970173i \(-0.577940\pi\)
0.718986 + 0.695024i \(0.244606\pi\)
\(744\) −6.00000 3.46410i −0.219971 0.127000i
\(745\) 0 0
\(746\) 26.0000 0.951928
\(747\) 23.3827 13.5000i 0.855528 0.493939i
\(748\) 0 0
\(749\) 1.50000 2.59808i 0.0548088 0.0949316i
\(750\) 0 0
\(751\) −1.00000 1.73205i −0.0364905 0.0632034i 0.847203 0.531269i \(-0.178285\pi\)
−0.883694 + 0.468065i \(0.844951\pi\)
\(752\) −2.59808 + 1.50000i −0.0947421 + 0.0546994i
\(753\) −10.3923 18.0000i −0.378717 0.655956i
\(754\) 3.00000 5.19615i 0.109254 0.189233i
\(755\) 0 0
\(756\) 5.19615i 0.188982i
\(757\) 46.0000i 1.67190i −0.548807 0.835949i \(-0.684918\pi\)
0.548807 0.835949i \(-0.315082\pi\)
\(758\) −19.0526 11.0000i −0.692020 0.399538i
\(759\) −81.0000 + 46.7654i −2.94011 + 1.69748i
\(760\) 0 0
\(761\) 16.5000 + 28.5788i 0.598125 + 1.03598i 0.993098 + 0.117289i \(0.0374205\pi\)
−0.394973 + 0.918693i \(0.629246\pi\)
\(762\) 12.1244 0.439219
\(763\) 6.06218 + 3.50000i 0.219466 + 0.126709i
\(764\) 12.0000 0.434145
\(765\) 0 0
\(766\) −12.0000 −0.433578
\(767\) −10.3923 6.00000i −0.375244 0.216647i
\(768\) −0.866025 + 1.50000i −0.0312500 + 0.0541266i
\(769\) 14.5000 + 25.1147i 0.522883 + 0.905661i 0.999645 + 0.0266282i \(0.00847701\pi\)
−0.476762 + 0.879032i \(0.658190\pi\)
\(770\) 0 0
\(771\) −27.0000 15.5885i −0.972381 0.561405i
\(772\) −1.73205 1.00000i −0.0623379 0.0359908i
\(773\) 48.0000i 1.72644i 0.504828 + 0.863220i \(0.331556\pi\)
−0.504828 + 0.863220i \(0.668444\pi\)
\(774\) 24.0000 0.862662
\(775\) 0 0
\(776\) −1.00000 + 1.73205i −0.0358979 + 0.0621770i
\(777\) 13.8564 0.497096
\(778\) −18.1865 + 10.5000i −0.652019 + 0.376443i
\(779\) 6.00000 + 10.3923i 0.214972 + 0.372343i
\(780\) 0 0
\(781\) 18.0000 31.1769i 0.644091 1.11560i
\(782\) 0 0
\(783\) 7.79423 13.5000i 0.278543 0.482451i
\(784\) 6.00000 0.214286
\(785\) 0 0
\(786\) −27.0000 + 15.5885i −0.963058 + 0.556022i
\(787\) 17.3205 10.0000i 0.617409 0.356462i −0.158450 0.987367i \(-0.550650\pi\)
0.775860 + 0.630905i \(0.217316\pi\)
\(788\) 10.3923 6.00000i 0.370211 0.213741i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) −15.5885 + 9.00000i −0.553912 + 0.319801i
\(793\) 26.0000i 0.923287i
\(794\) 1.00000 1.73205i 0.0354887 0.0614682i
\(795\) 0 0
\(796\) −4.00000 6.92820i −0.141776 0.245564i
\(797\) −36.3731 + 21.0000i −1.28840 + 0.743858i −0.978369 0.206868i \(-0.933673\pi\)
−0.310031 + 0.950726i \(0.600340\pi\)
\(798\) −3.46410 + 6.00000i −0.122628 + 0.212398i
\(799\) 0 0
\(800\) 0 0
\(801\) 13.5000 23.3827i 0.476999 0.826187i
\(802\) 6.00000i 0.211867i
\(803\) −20.7846 12.0000i −0.733473 0.423471i
\(804\) 22.5167i 0.794101i
\(805\) 0 0
\(806\) 4.00000 + 6.92820i 0.140894 + 0.244036i
\(807\) 18.1865 + 31.5000i 0.640196 + 1.10885i
\(808\) 5.19615 + 3.00000i 0.182800 + 0.105540i
\(809\) −18.0000 −0.632846 −0.316423 0.948618i \(-0.602482\pi\)
−0.316423 + 0.948618i \(0.602482\pi\)
\(810\) 0 0
\(811\) 2.00000 0.0702295 0.0351147 0.999383i \(-0.488820\pi\)
0.0351147 + 0.999383i \(0.488820\pi\)
\(812\) 2.59808 + 1.50000i 0.0911746 + 0.0526397i
\(813\) 3.46410 + 6.00000i 0.121491 + 0.210429i
\(814\) 24.0000 + 41.5692i 0.841200 + 1.45700i
\(815\) 0 0
\(816\) 0 0
\(817\) 27.7128 + 16.0000i 0.969549 + 0.559769i
\(818\) 10.0000i 0.349642i
\(819\) 3.00000 5.19615i 0.104828 0.181568i
\(820\) 0 0
\(821\) −13.5000 + 23.3827i −0.471153 + 0.816061i −0.999456 0.0329950i \(-0.989495\pi\)
0.528302 + 0.849056i \(0.322829\pi\)
\(822\) −10.3923 + 18.0000i −0.362473 + 0.627822i
\(823\) 21.6506 12.5000i 0.754694 0.435723i −0.0726937 0.997354i \(-0.523160\pi\)
0.827387 + 0.561632i \(0.189826\pi\)
\(824\) 4.00000 + 6.92820i 0.139347 + 0.241355i
\(825\) 0 0
\(826\) 3.00000 5.19615i 0.104383 0.180797i
\(827\) 3.00000i 0.104320i 0.998639 + 0.0521601i \(0.0166106\pi\)
−0.998639 + 0.0521601i \(0.983389\pi\)
\(828\) 23.3827 13.5000i 0.812605 0.469157i
\(829\) 7.00000 0.243120 0.121560 0.992584i \(-0.461210\pi\)
0.121560 + 0.992584i \(0.461210\pi\)
\(830\) 0 0
\(831\) 13.8564i 0.480673i
\(832\) 1.73205 1.00000i 0.0600481 0.0346688i
\(833\) 0 0
\(834\) 24.0000 13.8564i 0.831052 0.479808i
\(835\) 0 0
\(836\) −24.0000 −0.830057
\(837\) 10.3923 + 18.0000i 0.359211 + 0.622171i
\(838\) 30.0000i 1.03633i
\(839\) 18.0000 31.1769i 0.621429 1.07635i −0.367791 0.929909i \(-0.619886\pi\)
0.989220 0.146438i \(-0.0467809\pi\)
\(840\) 0 0
\(841\) 10.0000 + 17.3205i 0.344828 + 0.597259i
\(842\) −19.0526 + 11.0000i −0.656595 + 0.379085i
\(843\) −25.9808 −0.894825
\(844\) 1.00000 1.73205i 0.0344214 0.0596196i
\(845\) 0 0
\(846\) 9.00000 0.309426
\(847\) 25.0000i 0.859010i
\(848\) 5.19615 + 3.00000i 0.178437 + 0.103020i
\(849\) −19.5000 11.2583i −0.669238 0.386385i
\(850\) 0 0
\(851\) −36.0000 62.3538i −1.23406 2.13746i
\(852\) −5.19615 + 9.00000i −0.178017 + 0.308335i
\(853\) −8.66025 5.00000i −0.296521 0.171197i 0.344358 0.938839i \(-0.388097\pi\)
−0.640879 + 0.767642i \(0.721430\pi\)
\(854\) −13.0000 −0.444851
\(855\) 0 0
\(856\) −3.00000 −0.102538
\(857\) 36.3731 + 21.0000i 1.24248 + 0.717346i 0.969599 0.244701i \(-0.0786899\pi\)
0.272882 + 0.962048i \(0.412023\pi\)
\(858\) 20.7846 0.709575
\(859\) −17.0000 29.4449i −0.580033 1.00465i −0.995475 0.0950262i \(-0.969707\pi\)
0.415442 0.909620i \(-0.363627\pi\)
\(860\) 0 0
\(861\) 4.50000 2.59808i 0.153360 0.0885422i
\(862\) −5.19615 3.00000i −0.176982 0.102180i
\(863\) 3.00000i 0.102121i −0.998696 0.0510606i \(-0.983740\pi\)
0.998696 0.0510606i \(-0.0162602\pi\)
\(864\) 4.50000 2.59808i 0.153093 0.0883883i
\(865\) 0 0
\(866\) 8.00000 13.8564i 0.271851 0.470860i
\(867\) −14.7224 25.5000i −0.500000 0.866025i
\(868\) −3.46410 + 2.00000i −0.117579 + 0.0678844i
\(869\) −30.0000 51.9615i −1.01768 1.76267i
\(870\) 0 0
\(871\) 13.0000 22.5167i 0.440488 0.762948i
\(872\) 7.00000i 0.237050i
\(873\) 5.19615 3.00000i 0.175863 0.101535i
\(874\) 36.0000 1.21772
\(875\) 0 0
\(876\) 6.00000 + 3.46410i 0.202721 + 0.117041i
\(877\) −19.0526 + 11.0000i −0.643359 + 0.371444i −0.785907 0.618344i \(-0.787804\pi\)
0.142548 + 0.989788i \(0.454470\pi\)
\(878\) 24.2487 14.0000i 0.818354 0.472477i
\(879\) 0 0
\(880\) 0 0
\(881\) 21.0000 0.707508 0.353754 0.935339i \(-0.384905\pi\)
0.353754 + 0.935339i \(0.384905\pi\)
\(882\) −15.5885 9.00000i −0.524891 0.303046i
\(883\) 31.0000i 1.04323i 0.853180 + 0.521617i \(0.174671\pi\)
−0.853180 + 0.521617i \(0.825329\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −4.50000 7.79423i −0.151180 0.261852i
\(887\) 31.1769 18.0000i 1.04682 0.604381i 0.125061 0.992149i \(-0.460087\pi\)
0.921757 + 0.387768i \(0.126754\pi\)
\(888\) −6.92820 12.0000i −0.232495 0.402694i
\(889\) 3.50000 6.06218i 0.117386 0.203319i
\(890\) 0 0
\(891\) 54.0000 1.80907
\(892\) 1.00000i 0.0334825i
\(893\) 10.3923 + 6.00000i 0.347765 + 0.200782i
\(894\) 4.50000 2.59808i 0.150503 0.0868927i
\(895\) 0 0
\(896\) 0.500000 + 0.866025i 0.0167038 + 0.0289319i
\(897\) −31.1769 −1.04097
\(898\) 5.19615 + 3.00000i 0.173398 + 0.100111i
\(899\) 12.0000 0.400222
\(900\) 0 0
\(901\) 0 0
\(902\) 15.5885 + 9.00000i 0.519039 + 0.299667i
\(903\) 6.92820 12.0000i 0.230556 0.399335i
\(904\) 0 0
\(905\) 0 0
\(906\) −21.0000 12.1244i −0.697678 0.402805i
\(907\) 32.0429 + 18.5000i 1.06397 + 0.614282i 0.926527 0.376228i \(-0.122779\pi\)
0.137441 + 0.990510i \(0.456112\pi\)
\(908\) 12.0000i 0.398234i
\(909\) −9.00000 15.5885i −0.298511 0.517036i
\(910\) 0 0
\(911\) 15.0000 25.9808i 0.496972 0.860781i −0.503022 0.864274i \(-0.667778\pi\)
0.999994 + 0.00349271i \(0.00111177\pi\)
\(912\) 6.92820 0.229416
\(913\) 46.7654 27.0000i 1.54771 0.893570i
\(914\) 4.00000 + 6.92820i 0.132308 + 0.229165i
\(915\) 0 0
\(916\) 6.50000 11.2583i 0.214766 0.371986i
\(917\) 18.0000i 0.594412i
\(918\) 0 0
\(919\) −38.0000 −1.25350 −0.626752 0.779219i \(-0.715616\pi\)
−0.626752 + 0.779219i \(0.715616\pi\)
\(920\) 0 0
\(921\) −10.5000 + 6.06218i −0.345987 + 0.199756i
\(922\) −23.3827 + 13.5000i −0.770068 + 0.444599i
\(923\) 10.3923 6.00000i 0.342067 0.197492i
\(924\) 10.3923i 0.341882i
\(925\) 0 0
\(926\) −4.00000 −0.131448
\(927\) 24.0000i 0.788263i
\(928\) 3.00000i 0.0984798i
\(929\) 3.00000 5.19615i 0.0984268 0.170480i −0.812607 0.582812i \(-0.801952\pi\)
0.911034 + 0.412332i \(0.135286\pi\)
\(930\) 0 0
\(931\) −12.0000 20.7846i −0.393284 0.681188i
\(932\) −10.3923 + 6.00000i −0.340411 + 0.196537i
\(933\) −10.3923 + 18.0000i −0.340229 + 0.589294i
\(934\) 18.0000 31.1769i 0.588978 1.02014i
\(935\) 0 0
\(936\) −6.00000 −0.196116
\(937\) 56.0000i 1.82944i 0.404088 + 0.914720i \(0.367589\pi\)
−0.404088 + 0.914720i \(0.632411\pi\)
\(938\) 11.2583 + 6.50000i 0.367598 + 0.212233i
\(939\) 3.46410i 0.113047i
\(940\) 0 0
\(941\) −10.5000 18.1865i −0.342290 0.592864i 0.642567 0.766229i \(-0.277869\pi\)
−0.984858 + 0.173365i \(0.944536\pi\)
\(942\) 12.1244 + 21.0000i 0.395033 + 0.684217i
\(943\) −23.3827 13.5000i −0.761445 0.439620i
\(944\) −6.00000 −0.195283
\(945\) 0 0
\(946\) 48.0000 1.56061
\(947\) −33.7750 19.5000i −1.09754 0.633665i −0.161966 0.986796i \(-0.551783\pi\)
−0.935574 + 0.353131i \(0.885117\pi\)
\(948\) 8.66025 + 15.0000i 0.281272 + 0.487177i
\(949\) −4.00000 6.92820i −0.129845 0.224899i
\(950\) 0 0
\(951\) 10.3923i 0.336994i
\(952\) 0 0
\(953\) 6.00000i 0.194359i 0.995267 + 0.0971795i \(0.0309821\pi\)
−0.995267 + 0.0971795i \(0.969018\pi\)
\(954\) −9.00000 15.5885i −0.291386 0.504695i
\(955\) 0 0
\(956\) 0 0
\(957\) 15.5885 27.0000i 0.503903 0.872786i
\(958\) 25.9808 15.0000i 0.839400 0.484628i
\(959\) 6.00000 + 10.3923i 0.193750 + 0.335585i
\(960\) 0 0
\(961\) 7.50000 12.9904i 0.241935 0.419045i
\(962\) 16.0000i 0.515861i
\(963\) 7.79423 + 4.50000i 0.251166 + 0.145010i
\(964\) −29.0000 −0.934027
\(965\) 0 0
\(966\) 15.5885i 0.501550i
\(967\) −32.0429 + 18.5000i −1.03043 + 0.594920i −0.917108 0.398638i \(-0.869483\pi\)
−0.113323 + 0.993558i \(0.536150\pi\)
\(968\) −21.6506 + 12.5000i −0.695878 + 0.401765i
\(969\) 0 0
\(970\) 0 0
\(971\) −24.0000 −0.770197 −0.385098 0.922876i \(-0.625832\pi\)
−0.385098 + 0.922876i \(0.625832\pi\)
\(972\) −15.5885 −0.500000
\(973\) 16.0000i 0.512936i
\(974\) 4.00000 6.92820i 0.128168 0.221994i
\(975\) 0 0
\(976\) 6.50000 + 11.2583i 0.208060 + 0.360370i
\(977\) −36.3731 + 21.0000i −1.16368 + 0.671850i −0.952183 0.305530i \(-0.901167\pi\)
−0.211495 + 0.977379i \(0.567833\pi\)
\(978\) −6.92820 −0.221540
\(979\) 27.0000 46.7654i 0.862924 1.49463i
\(980\) 0 0
\(981\) −10.5000 + 18.1865i −0.335239 + 0.580651i
\(982\) 12.0000i 0.382935i
\(983\) 7.79423 + 4.50000i 0.248597 + 0.143528i 0.619122 0.785295i \(-0.287489\pi\)
−0.370525 + 0.928823i \(0.620822\pi\)
\(984\) −4.50000 2.59808i −0.143455 0.0828236i
\(985\) 0 0
\(986\) 0 0
\(987\) 2.59808 4.50000i 0.0826977 0.143237i
\(988\) −6.92820 4.00000i −0.220416 0.127257i
\(989\) −72.0000 −2.28947
\(990\) 0 0
\(991\) −10.0000 −0.317660 −0.158830 0.987306i \(-0.550772\pi\)
−0.158830 + 0.987306i \(0.550772\pi\)
\(992\) 3.46410 + 2.00000i 0.109985 + 0.0635001i
\(993\) −17.3205 −0.549650
\(994\) 3.00000 + 5.19615i 0.0951542 + 0.164812i
\(995\) 0 0
\(996\) −13.5000 + 7.79423i −0.427764 + 0.246970i
\(997\) 8.66025 + 5.00000i 0.274273 + 0.158352i 0.630828 0.775923i \(-0.282715\pi\)
−0.356555 + 0.934274i \(0.616049\pi\)
\(998\) 32.0000i 1.01294i
\(999\) 41.5692i 1.31519i
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 450.2.j.c.349.1 4
3.2 odd 2 1350.2.j.e.1099.2 4
5.2 odd 4 450.2.e.e.151.1 2
5.3 odd 4 90.2.e.a.61.1 yes 2
5.4 even 2 inner 450.2.j.c.349.2 4
9.2 odd 6 4050.2.c.a.649.1 2
9.4 even 3 inner 450.2.j.c.49.2 4
9.5 odd 6 1350.2.j.e.199.1 4
9.7 even 3 4050.2.c.t.649.2 2
15.2 even 4 1350.2.e.b.451.1 2
15.8 even 4 270.2.e.b.181.1 2
15.14 odd 2 1350.2.j.e.1099.1 4
20.3 even 4 720.2.q.b.241.1 2
45.2 even 12 4050.2.a.ba.1.1 1
45.4 even 6 inner 450.2.j.c.49.1 4
45.7 odd 12 4050.2.a.n.1.1 1
45.13 odd 12 90.2.e.a.31.1 2
45.14 odd 6 1350.2.j.e.199.2 4
45.22 odd 12 450.2.e.e.301.1 2
45.23 even 12 270.2.e.b.91.1 2
45.29 odd 6 4050.2.c.a.649.2 2
45.32 even 12 1350.2.e.b.901.1 2
45.34 even 6 4050.2.c.t.649.1 2
45.38 even 12 810.2.a.b.1.1 1
45.43 odd 12 810.2.a.g.1.1 1
60.23 odd 4 2160.2.q.b.721.1 2
180.23 odd 12 2160.2.q.b.1441.1 2
180.43 even 12 6480.2.a.g.1.1 1
180.83 odd 12 6480.2.a.v.1.1 1
180.103 even 12 720.2.q.b.481.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
90.2.e.a.31.1 2 45.13 odd 12
90.2.e.a.61.1 yes 2 5.3 odd 4
270.2.e.b.91.1 2 45.23 even 12
270.2.e.b.181.1 2 15.8 even 4
450.2.e.e.151.1 2 5.2 odd 4
450.2.e.e.301.1 2 45.22 odd 12
450.2.j.c.49.1 4 45.4 even 6 inner
450.2.j.c.49.2 4 9.4 even 3 inner
450.2.j.c.349.1 4 1.1 even 1 trivial
450.2.j.c.349.2 4 5.4 even 2 inner
720.2.q.b.241.1 2 20.3 even 4
720.2.q.b.481.1 2 180.103 even 12
810.2.a.b.1.1 1 45.38 even 12
810.2.a.g.1.1 1 45.43 odd 12
1350.2.e.b.451.1 2 15.2 even 4
1350.2.e.b.901.1 2 45.32 even 12
1350.2.j.e.199.1 4 9.5 odd 6
1350.2.j.e.199.2 4 45.14 odd 6
1350.2.j.e.1099.1 4 15.14 odd 2
1350.2.j.e.1099.2 4 3.2 odd 2
2160.2.q.b.721.1 2 60.23 odd 4
2160.2.q.b.1441.1 2 180.23 odd 12
4050.2.a.n.1.1 1 45.7 odd 12
4050.2.a.ba.1.1 1 45.2 even 12
4050.2.c.a.649.1 2 9.2 odd 6
4050.2.c.a.649.2 2 45.29 odd 6
4050.2.c.t.649.1 2 45.34 even 6
4050.2.c.t.649.2 2 9.7 even 3
6480.2.a.g.1.1 1 180.43 even 12
6480.2.a.v.1.1 1 180.83 odd 12