Properties

Label 3332.1.cc.c.2447.1
Level $3332$
Weight $1$
Character 3332.2447
Analytic conductor $1.663$
Analytic rank $0$
Dimension $24$
Projective image $D_{42}$
CM discriminant -68
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3332,1,Mod(135,3332)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3332, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([21, 32, 21]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3332.135");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3332.cc (of order \(42\), degree \(12\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.66288462209\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(2\) over \(\Q(\zeta_{42})\)
Coefficient field: \(\Q(\zeta_{84})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{24} + x^{22} - x^{18} - x^{16} + x^{12} - x^{8} - x^{6} + x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{42}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{42} - \cdots)\)

Embedding invariants

Embedding label 2447.1
Root \(-0.563320 + 0.826239i\) of defining polynomial
Character \(\chi\) \(=\) 3332.2447
Dual form 3332.1.cc.c.2515.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.365341 + 0.930874i) q^{2} +(-0.149042 + 1.98883i) q^{3} +(-0.733052 - 0.680173i) q^{4} +(-1.79690 - 0.865341i) q^{6} +(-0.433884 - 0.900969i) q^{7} +(0.900969 - 0.433884i) q^{8} +(-2.94440 - 0.443797i) q^{9} +O(q^{10})\) \(q+(-0.365341 + 0.930874i) q^{2} +(-0.149042 + 1.98883i) q^{3} +(-0.733052 - 0.680173i) q^{4} +(-1.79690 - 0.865341i) q^{6} +(-0.433884 - 0.900969i) q^{7} +(0.900969 - 0.433884i) q^{8} +(-2.94440 - 0.443797i) q^{9} +(1.84095 - 0.277479i) q^{11} +(1.46200 - 1.35654i) q^{12} +(-0.455573 - 0.571270i) q^{13} +(0.997204 - 0.0747301i) q^{14} +(0.0747301 + 0.997204i) q^{16} +(0.955573 + 0.294755i) q^{17} +(1.48883 - 2.57873i) q^{18} +(1.85654 - 0.728639i) q^{21} +(-0.414278 + 1.81507i) q^{22} +(1.49419 - 0.460898i) q^{23} +(0.728639 + 1.85654i) q^{24} +(0.365341 + 0.930874i) q^{25} +(0.698220 - 0.215372i) q^{26} +(0.877681 - 3.84537i) q^{27} +(-0.294755 + 0.955573i) q^{28} +(0.433884 - 0.751509i) q^{31} +(-0.955573 - 0.294755i) q^{32} +(0.277479 + 3.70270i) q^{33} +(-0.623490 + 0.781831i) q^{34} +(1.85654 + 2.32803i) q^{36} +(1.20406 - 0.820914i) q^{39} +1.99441i q^{42} +(-1.53825 - 1.04876i) q^{44} +(-0.116853 + 1.55929i) q^{46} -1.99441 q^{48} +(-0.623490 + 0.781831i) q^{49} -1.00000 q^{50} +(-0.728639 + 1.85654i) q^{51} +(-0.0546039 + 0.728639i) q^{52} +(-1.21135 - 1.12397i) q^{53} +(3.25890 + 2.22188i) q^{54} +(-0.781831 - 0.623490i) q^{56} +(0.541044 + 0.678448i) q^{62} +(0.877681 + 2.84537i) q^{63} +(0.623490 - 0.781831i) q^{64} +(-3.54812 - 1.09445i) q^{66} +(-0.500000 - 0.866025i) q^{68} +(0.693950 + 3.04039i) q^{69} +(0.250701 - 1.09839i) q^{71} +(-2.84537 + 0.877681i) q^{72} +(-1.90580 + 0.587862i) q^{75} +(-1.04876 - 1.53825i) q^{77} +(0.324275 + 1.42074i) q^{78} +(0.149042 + 0.258149i) q^{79} +(4.67161 + 1.44100i) q^{81} +(-1.85654 - 0.728639i) q^{84} +(1.53825 - 1.04876i) q^{88} +(0.147791 + 0.0222759i) q^{89} +(-0.317031 + 0.658322i) q^{91} +(-1.40881 - 0.678448i) q^{92} +(1.42996 + 0.974928i) q^{93} +(0.728639 - 1.85654i) q^{96} +(-0.500000 - 0.866025i) q^{98} -5.54365 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 2 q^{2} + 2 q^{4} + 4 q^{8} - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 2 q^{2} + 2 q^{4} + 4 q^{8} - 24 q^{9} + 10 q^{13} + 2 q^{16} + 2 q^{17} + 10 q^{18} + 6 q^{21} + 2 q^{25} - 2 q^{26} - 2 q^{32} + 8 q^{33} + 4 q^{34} + 6 q^{36} + 4 q^{49} - 24 q^{50} + 2 q^{52} - 2 q^{53} - 4 q^{64} - 22 q^{66} - 12 q^{68} - 14 q^{69} - 4 q^{72} - 6 q^{77} + 30 q^{81} - 6 q^{84} + 2 q^{89} - 12 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3332\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(885\) \(1667\)
\(\chi(n)\) \(-1\) \(e\left(\frac{11}{21}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.365341 + 0.930874i −0.365341 + 0.930874i
\(3\) −0.149042 + 1.98883i −0.149042 + 1.98883i 1.00000i \(0.5\pi\)
−0.149042 + 0.988831i \(0.547619\pi\)
\(4\) −0.733052 0.680173i −0.733052 0.680173i
\(5\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(6\) −1.79690 0.865341i −1.79690 0.865341i
\(7\) −0.433884 0.900969i −0.433884 0.900969i
\(8\) 0.900969 0.433884i 0.900969 0.433884i
\(9\) −2.94440 0.443797i −2.94440 0.443797i
\(10\) 0 0
\(11\) 1.84095 0.277479i 1.84095 0.277479i 0.866025 0.500000i \(-0.166667\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(12\) 1.46200 1.35654i 1.46200 1.35654i
\(13\) −0.455573 0.571270i −0.455573 0.571270i 0.500000 0.866025i \(-0.333333\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(14\) 0.997204 0.0747301i 0.997204 0.0747301i
\(15\) 0 0
\(16\) 0.0747301 + 0.997204i 0.0747301 + 0.997204i
\(17\) 0.955573 + 0.294755i 0.955573 + 0.294755i
\(18\) 1.48883 2.57873i 1.48883 2.57873i
\(19\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(20\) 0 0
\(21\) 1.85654 0.728639i 1.85654 0.728639i
\(22\) −0.414278 + 1.81507i −0.414278 + 1.81507i
\(23\) 1.49419 0.460898i 1.49419 0.460898i 0.563320 0.826239i \(-0.309524\pi\)
0.930874 + 0.365341i \(0.119048\pi\)
\(24\) 0.728639 + 1.85654i 0.728639 + 1.85654i
\(25\) 0.365341 + 0.930874i 0.365341 + 0.930874i
\(26\) 0.698220 0.215372i 0.698220 0.215372i
\(27\) 0.877681 3.84537i 0.877681 3.84537i
\(28\) −0.294755 + 0.955573i −0.294755 + 0.955573i
\(29\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(30\) 0 0
\(31\) 0.433884 0.751509i 0.433884 0.751509i −0.563320 0.826239i \(-0.690476\pi\)
0.997204 + 0.0747301i \(0.0238095\pi\)
\(32\) −0.955573 0.294755i −0.955573 0.294755i
\(33\) 0.277479 + 3.70270i 0.277479 + 3.70270i
\(34\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(35\) 0 0
\(36\) 1.85654 + 2.32803i 1.85654 + 2.32803i
\(37\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(38\) 0 0
\(39\) 1.20406 0.820914i 1.20406 0.820914i
\(40\) 0 0
\(41\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(42\) 1.99441i 1.99441i
\(43\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(44\) −1.53825 1.04876i −1.53825 1.04876i
\(45\) 0 0
\(46\) −0.116853 + 1.55929i −0.116853 + 1.55929i
\(47\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(48\) −1.99441 −1.99441
\(49\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(50\) −1.00000 −1.00000
\(51\) −0.728639 + 1.85654i −0.728639 + 1.85654i
\(52\) −0.0546039 + 0.728639i −0.0546039 + 0.728639i
\(53\) −1.21135 1.12397i −1.21135 1.12397i −0.988831 0.149042i \(-0.952381\pi\)
−0.222521 0.974928i \(-0.571429\pi\)
\(54\) 3.25890 + 2.22188i 3.25890 + 2.22188i
\(55\) 0 0
\(56\) −0.781831 0.623490i −0.781831 0.623490i
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(60\) 0 0
\(61\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(62\) 0.541044 + 0.678448i 0.541044 + 0.678448i
\(63\) 0.877681 + 2.84537i 0.877681 + 2.84537i
\(64\) 0.623490 0.781831i 0.623490 0.781831i
\(65\) 0 0
\(66\) −3.54812 1.09445i −3.54812 1.09445i
\(67\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(68\) −0.500000 0.866025i −0.500000 0.866025i
\(69\) 0.693950 + 3.04039i 0.693950 + 3.04039i
\(70\) 0 0
\(71\) 0.250701 1.09839i 0.250701 1.09839i −0.680173 0.733052i \(-0.738095\pi\)
0.930874 0.365341i \(-0.119048\pi\)
\(72\) −2.84537 + 0.877681i −2.84537 + 0.877681i
\(73\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(74\) 0 0
\(75\) −1.90580 + 0.587862i −1.90580 + 0.587862i
\(76\) 0 0
\(77\) −1.04876 1.53825i −1.04876 1.53825i
\(78\) 0.324275 + 1.42074i 0.324275 + 1.42074i
\(79\) 0.149042 + 0.258149i 0.149042 + 0.258149i 0.930874 0.365341i \(-0.119048\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(80\) 0 0
\(81\) 4.67161 + 1.44100i 4.67161 + 1.44100i
\(82\) 0 0
\(83\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(84\) −1.85654 0.728639i −1.85654 0.728639i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 1.53825 1.04876i 1.53825 1.04876i
\(89\) 0.147791 + 0.0222759i 0.147791 + 0.0222759i 0.222521 0.974928i \(-0.428571\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(90\) 0 0
\(91\) −0.317031 + 0.658322i −0.317031 + 0.658322i
\(92\) −1.40881 0.678448i −1.40881 0.678448i
\(93\) 1.42996 + 0.974928i 1.42996 + 0.974928i
\(94\) 0 0
\(95\) 0 0
\(96\) 0.728639 1.85654i 0.728639 1.85654i
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) −0.500000 0.866025i −0.500000 0.866025i
\(99\) −5.54365 −5.54365
\(100\) 0.365341 0.930874i 0.365341 0.930874i
\(101\) −0.0931869 + 1.24349i −0.0931869 + 1.24349i 0.733052 + 0.680173i \(0.238095\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(102\) −1.46200 1.35654i −1.46200 1.35654i
\(103\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(104\) −0.658322 0.317031i −0.658322 0.317031i
\(105\) 0 0
\(106\) 1.48883 0.716983i 1.48883 0.716983i
\(107\) 1.34515 + 0.202749i 1.34515 + 0.202749i 0.781831 0.623490i \(-0.214286\pi\)
0.563320 + 0.826239i \(0.309524\pi\)
\(108\) −3.25890 + 2.22188i −3.25890 + 2.22188i
\(109\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.866025 0.500000i 0.866025 0.500000i
\(113\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 1.08786 + 1.88423i 1.08786 + 1.88423i
\(118\) 0 0
\(119\) −0.149042 0.988831i −0.149042 0.988831i
\(120\) 0 0
\(121\) 2.35654 0.726897i 2.35654 0.726897i
\(122\) 0 0
\(123\) 0 0
\(124\) −0.829215 + 0.255779i −0.829215 + 0.255779i
\(125\) 0 0
\(126\) −2.96934 0.222521i −2.96934 0.222521i
\(127\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(128\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(129\) 0 0
\(130\) 0 0
\(131\) 0.116853 + 1.55929i 0.116853 + 1.55929i 0.680173 + 0.733052i \(0.261905\pi\)
−0.563320 + 0.826239i \(0.690476\pi\)
\(132\) 2.31507 2.90301i 2.31507 2.90301i
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0.988831 0.149042i 0.988831 0.149042i
\(137\) −0.123490 + 0.0841939i −0.123490 + 0.0841939i −0.623490 0.781831i \(-0.714286\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(138\) −3.08375 0.464800i −3.08375 0.464800i
\(139\) 0.268565 0.129334i 0.268565 0.129334i −0.294755 0.955573i \(-0.595238\pi\)
0.563320 + 0.826239i \(0.309524\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0.930874 + 0.634659i 0.930874 + 0.634659i
\(143\) −0.997204 0.925270i −0.997204 0.925270i
\(144\) 0.222521 2.96934i 0.222521 2.96934i
\(145\) 0 0
\(146\) 0 0
\(147\) −1.46200 1.35654i −1.46200 1.35654i
\(148\) 0 0
\(149\) 0.0546039 0.139129i 0.0546039 0.139129i −0.900969 0.433884i \(-0.857143\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(150\) 0.149042 1.98883i 0.149042 1.98883i
\(151\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(152\) 0 0
\(153\) −2.68278 1.29196i −2.68278 1.29196i
\(154\) 1.81507 0.414278i 1.81507 0.414278i
\(155\) 0 0
\(156\) −1.44100 0.217196i −1.44100 0.217196i
\(157\) −1.63402 + 1.11406i −1.63402 + 1.11406i −0.733052 + 0.680173i \(0.761905\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(158\) −0.294755 + 0.0444272i −0.294755 + 0.0444272i
\(159\) 2.41593 2.24165i 2.41593 2.24165i
\(160\) 0 0
\(161\) −1.06356 1.14625i −1.06356 1.14625i
\(162\) −3.04812 + 3.82222i −3.04812 + 3.82222i
\(163\) 0 0 0.997204 0.0747301i \(-0.0238095\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0.131178 + 0.574730i 0.131178 + 0.574730i 0.997204 + 0.0747301i \(0.0238095\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(168\) 1.35654 1.46200i 1.35654 1.46200i
\(169\) 0.103718 0.454418i 0.103718 0.454418i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(174\) 0 0
\(175\) 0.680173 0.733052i 0.680173 0.733052i
\(176\) 0.414278 + 1.81507i 0.414278 + 1.81507i
\(177\) 0 0
\(178\) −0.0747301 + 0.129436i −0.0747301 + 0.129436i
\(179\) 0 0 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(180\) 0 0
\(181\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(182\) −0.496990 0.535628i −0.496990 0.535628i
\(183\) 0 0
\(184\) 1.14625 1.06356i 1.14625 1.06356i
\(185\) 0 0
\(186\) −1.42996 + 0.974928i −1.42996 + 0.974928i
\(187\) 1.84095 + 0.277479i 1.84095 + 0.277479i
\(188\) 0 0
\(189\) −3.84537 + 0.877681i −3.84537 + 0.877681i
\(190\) 0 0
\(191\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(192\) 1.46200 + 1.35654i 1.46200 + 1.35654i
\(193\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.988831 0.149042i 0.988831 0.149042i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 2.02532 5.16044i 2.02532 5.16044i
\(199\) 0.0841939 1.12349i 0.0841939 1.12349i −0.781831 0.623490i \(-0.785714\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(200\) 0.733052 + 0.680173i 0.733052 + 0.680173i
\(201\) 0 0
\(202\) −1.12349 0.541044i −1.12349 0.541044i
\(203\) 0 0
\(204\) 1.79690 0.865341i 1.79690 0.865341i
\(205\) 0 0
\(206\) 0 0
\(207\) −4.60405 + 0.693950i −4.60405 + 0.693950i
\(208\) 0.535628 0.496990i 0.535628 0.496990i
\(209\) 0 0
\(210\) 0 0
\(211\) 1.21572 1.52446i 1.21572 1.52446i 0.433884 0.900969i \(-0.357143\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(212\) 0.123490 + 1.64786i 0.123490 + 1.64786i
\(213\) 2.14715 + 0.662309i 2.14715 + 0.662309i
\(214\) −0.680173 + 1.17809i −0.680173 + 1.17809i
\(215\) 0 0
\(216\) −0.877681 3.84537i −0.877681 3.84537i
\(217\) −0.865341 0.0648483i −0.865341 0.0648483i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −0.266948 0.680173i −0.266948 0.680173i
\(222\) 0 0
\(223\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(224\) 0.149042 + 0.988831i 0.149042 + 0.988831i
\(225\) −0.662592 2.90301i −0.662592 2.90301i
\(226\) 0 0
\(227\) −0.563320 + 0.975699i −0.563320 + 0.975699i 0.433884 + 0.900969i \(0.357143\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(228\) 0 0
\(229\) 0.0332580 + 0.443797i 0.0332580 + 0.443797i 0.988831 + 0.149042i \(0.0476190\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(230\) 0 0
\(231\) 3.21562 1.85654i 3.21562 1.85654i
\(232\) 0 0
\(233\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(234\) −2.15142 + 0.324275i −2.15142 + 0.324275i
\(235\) 0 0
\(236\) 0 0
\(237\) −0.535628 + 0.257945i −0.535628 + 0.257945i
\(238\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(239\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(240\) 0 0
\(241\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(242\) −0.184292 + 2.45921i −0.184292 + 2.45921i
\(243\) −2.12117 + 5.40466i −2.12117 + 5.40466i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0.0648483 0.865341i 0.0648483 0.865341i
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(252\) 1.29196 2.68278i 1.29196 2.68278i
\(253\) 2.62285 1.26310i 2.62285 1.26310i
\(254\) 0 0
\(255\) 0 0
\(256\) −0.988831 + 0.149042i −0.988831 + 0.149042i
\(257\) −0.733052 + 0.680173i −0.733052 + 0.680173i −0.955573 0.294755i \(-0.904762\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −1.49419 0.460898i −1.49419 0.460898i
\(263\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) 1.85654 + 3.21562i 1.85654 + 3.21562i
\(265\) 0 0
\(266\) 0 0
\(267\) −0.0663300 + 0.290611i −0.0663300 + 0.290611i
\(268\) 0 0
\(269\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(270\) 0 0
\(271\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(272\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(273\) −1.26204 0.728639i −1.26204 0.728639i
\(274\) −0.0332580 0.145713i −0.0332580 0.145713i
\(275\) 0.930874 + 1.61232i 0.930874 + 1.61232i
\(276\) 1.55929 2.70077i 1.55929 2.70077i
\(277\) 0 0 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(278\) 0.0222759 + 0.297251i 0.0222759 + 0.297251i
\(279\) −1.61105 + 2.02019i −1.61105 + 2.02019i
\(280\) 0 0
\(281\) −0.623490 0.781831i −0.623490 0.781831i 0.365341 0.930874i \(-0.380952\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(282\) 0 0
\(283\) −1.84095 + 0.277479i −1.84095 + 0.277479i −0.974928 0.222521i \(-0.928571\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(284\) −0.930874 + 0.634659i −0.930874 + 0.634659i
\(285\) 0 0
\(286\) 1.22563 0.590232i 1.22563 0.590232i
\(287\) 0 0
\(288\) 2.68278 + 1.29196i 2.68278 + 1.29196i
\(289\) 0.826239 + 0.563320i 0.826239 + 0.563320i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.97766 −1.97766 −0.988831 0.149042i \(-0.952381\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(294\) 1.79690 0.865341i 1.79690 0.865341i
\(295\) 0 0
\(296\) 0 0
\(297\) 0.548760 7.32269i 0.548760 7.32269i
\(298\) 0.109562 + 0.101659i 0.109562 + 0.101659i
\(299\) −0.944011 0.643616i −0.944011 0.643616i
\(300\) 1.79690 + 0.865341i 1.79690 + 0.865341i
\(301\) 0 0
\(302\) 0 0
\(303\) −2.45921 0.370666i −2.45921 0.370666i
\(304\) 0 0
\(305\) 0 0
\(306\) 2.18278 2.02532i 2.18278 2.02532i
\(307\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(308\) −0.277479 + 1.84095i −0.277479 + 1.84095i
\(309\) 0 0
\(310\) 0 0
\(311\) 1.65510 + 0.510531i 1.65510 + 0.510531i 0.974928 0.222521i \(-0.0714286\pi\)
0.680173 + 0.733052i \(0.261905\pi\)
\(312\) 0.728639 1.26204i 0.728639 1.26204i
\(313\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(314\) −0.440071 1.92808i −0.440071 1.92808i
\(315\) 0 0
\(316\) 0.0663300 0.290611i 0.0663300 0.290611i
\(317\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(318\) 1.20406 + 3.06789i 1.20406 + 3.06789i
\(319\) 0 0
\(320\) 0 0
\(321\) −0.603718 + 2.64506i −0.603718 + 2.64506i
\(322\) 1.45557 0.571270i 1.45557 0.571270i
\(323\) 0 0
\(324\) −2.44440 4.23383i −2.44440 4.23383i
\(325\) 0.365341 0.632789i 0.365341 0.632789i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −0.582926 0.0878620i −0.582926 0.0878620i
\(335\) 0 0
\(336\) 0.865341 + 1.79690i 0.865341 + 1.79690i
\(337\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(338\) 0.385113 + 0.262566i 0.385113 + 0.262566i
\(339\) 0 0
\(340\) 0 0
\(341\) 0.590232 1.50389i 0.590232 1.50389i
\(342\) 0 0
\(343\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1.42935 1.32624i −1.42935 1.32624i −0.866025 0.500000i \(-0.833333\pi\)
−0.563320 0.826239i \(-0.690476\pi\)
\(348\) 0 0
\(349\) 0.400969 + 0.193096i 0.400969 + 0.193096i 0.623490 0.781831i \(-0.285714\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(350\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(351\) −2.59659 + 1.25045i −2.59659 + 1.25045i
\(352\) −1.84095 0.277479i −1.84095 0.277479i
\(353\) −0.826239 + 0.563320i −0.826239 + 0.563320i −0.900969 0.433884i \(-0.857143\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −0.0931869 0.116853i −0.0931869 0.116853i
\(357\) 1.98883 0.149042i 1.98883 0.149042i
\(358\) 0 0
\(359\) 0 0 −0.0747301 0.997204i \(-0.523810\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(360\) 0 0
\(361\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(362\) 0 0
\(363\) 1.09445 + 4.79510i 1.09445 + 4.79510i
\(364\) 0.680173 0.266948i 0.680173 0.266948i
\(365\) 0 0
\(366\) 0 0
\(367\) 0.496990 + 1.26631i 0.496990 + 1.26631i 0.930874 + 0.365341i \(0.119048\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(368\) 0.571270 + 1.45557i 0.571270 + 1.45557i
\(369\) 0 0
\(370\) 0 0
\(371\) −0.487076 + 1.57906i −0.487076 + 1.57906i
\(372\) −0.385113 1.68729i −0.385113 1.68729i
\(373\) 0.365341 + 0.632789i 0.365341 + 0.632789i 0.988831 0.149042i \(-0.0476190\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(374\) −0.930874 + 1.61232i −0.930874 + 1.61232i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0.587862 3.90021i 0.587862 3.90021i
\(379\) 1.07992 + 1.35417i 1.07992 + 1.35417i 0.930874 + 0.365341i \(0.119048\pi\)
0.149042 + 0.988831i \(0.452381\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(384\) −1.79690 + 0.865341i −1.79690 + 0.865341i
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −0.142820 + 1.90580i −0.142820 + 1.90580i 0.222521 + 0.974928i \(0.428571\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(390\) 0 0
\(391\) 1.56366 1.56366
\(392\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(393\) −3.11858 −3.11858
\(394\) 0 0
\(395\) 0 0
\(396\) 4.06379 + 3.77064i 4.06379 + 3.77064i
\(397\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(398\) 1.01507 + 0.488831i 1.01507 + 0.488831i
\(399\) 0 0
\(400\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(401\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(402\) 0 0
\(403\) −0.626980 + 0.0945021i −0.626980 + 0.0945021i
\(404\) 0.914101 0.848162i 0.914101 0.848162i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0.149042 + 1.98883i 0.149042 + 1.98883i
\(409\) 1.57906 + 0.487076i 1.57906 + 0.487076i 0.955573 0.294755i \(-0.0952381\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(410\) 0 0
\(411\) −0.149042 0.258149i −0.149042 0.258149i
\(412\) 0 0
\(413\) 0 0
\(414\) 1.03607 4.53932i 1.03607 4.53932i
\(415\) 0 0
\(416\) 0.266948 + 0.680173i 0.266948 + 0.680173i
\(417\) 0.217196 + 0.553406i 0.217196 + 0.553406i
\(418\) 0 0
\(419\) 0.0663300 0.290611i 0.0663300 0.290611i −0.930874 0.365341i \(-0.880952\pi\)
0.997204 + 0.0747301i \(0.0238095\pi\)
\(420\) 0 0
\(421\) −0.400969 1.75676i −0.400969 1.75676i −0.623490 0.781831i \(-0.714286\pi\)
0.222521 0.974928i \(-0.428571\pi\)
\(422\) 0.974928 + 1.68862i 0.974928 + 1.68862i
\(423\) 0 0
\(424\) −1.57906 0.487076i −1.57906 0.487076i
\(425\) 0.0747301 + 0.997204i 0.0747301 + 0.997204i
\(426\) −1.40097 + 1.75676i −1.40097 + 1.75676i
\(427\) 0 0
\(428\) −0.848162 1.06356i −0.848162 1.06356i
\(429\) 1.98883 1.84537i 1.98883 1.84537i
\(430\) 0 0
\(431\) 1.43109 0.975699i 1.43109 0.975699i 0.433884 0.900969i \(-0.357143\pi\)
0.997204 0.0747301i \(-0.0238095\pi\)
\(432\) 3.90021 + 0.587862i 3.90021 + 0.587862i
\(433\) 1.12349 0.541044i 1.12349 0.541044i 0.222521 0.974928i \(-0.428571\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(434\) 0.376510 0.781831i 0.376510 0.781831i
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0.108903 0.277479i 0.108903 0.277479i −0.866025 0.500000i \(-0.833333\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(440\) 0 0
\(441\) 2.18278 2.02532i 2.18278 2.02532i
\(442\) 0.730682 0.730682
\(443\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0.268565 + 0.129334i 0.268565 + 0.129334i
\(448\) −0.974928 0.222521i −0.974928 0.222521i
\(449\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(450\) 2.94440 + 0.443797i 2.94440 + 0.443797i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) −0.702449 0.880843i −0.702449 0.880843i
\(455\) 0 0
\(456\) 0 0
\(457\) −0.0931869 1.24349i −0.0931869 1.24349i −0.826239 0.563320i \(-0.809524\pi\)
0.733052 0.680173i \(-0.238095\pi\)
\(458\) −0.425270 0.131178i −0.425270 0.131178i
\(459\) 1.97213 3.41583i 1.97213 3.41583i
\(460\) 0 0
\(461\) −0.367711 1.61105i −0.367711 1.61105i −0.733052 0.680173i \(-0.761905\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(462\) 0.553406 + 3.67161i 0.553406 + 3.67161i
\(463\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(468\) 0.484144 2.12117i 0.484144 2.12117i
\(469\) 0 0
\(470\) 0 0
\(471\) −1.97213 3.41583i −1.97213 3.41583i
\(472\) 0 0
\(473\) 0 0
\(474\) −0.0444272 0.592840i −0.0444272 0.592840i
\(475\) 0 0
\(476\) −0.563320 + 0.826239i −0.563320 + 0.826239i
\(477\) 3.06789 + 3.84702i 3.06789 + 3.84702i
\(478\) 0 0
\(479\) 1.54620 0.233052i 1.54620 0.233052i 0.680173 0.733052i \(-0.261905\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 2.43821 1.94440i 2.43821 1.94440i
\(484\) −2.22188 1.07000i −2.22188 1.07000i
\(485\) 0 0
\(486\) −4.25611 3.94909i −4.25611 3.94909i
\(487\) −0.129436 + 1.72721i −0.129436 + 1.72721i 0.433884 + 0.900969i \(0.357143\pi\)
−0.563320 + 0.826239i \(0.690476\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0.781831 + 0.376510i 0.781831 + 0.376510i
\(497\) −1.09839 + 0.250701i −1.09839 + 0.250701i
\(498\) 0 0
\(499\) −0.294755 0.0444272i −0.294755 0.0444272i 1.00000i \(-0.5\pi\)
−0.294755 + 0.955573i \(0.595238\pi\)
\(500\) 0 0
\(501\) −1.16259 + 0.175233i −1.16259 + 0.175233i
\(502\) 0 0
\(503\) −0.848162 1.06356i −0.848162 1.06356i −0.997204 0.0747301i \(-0.976190\pi\)
0.149042 0.988831i \(-0.452381\pi\)
\(504\) 2.02532 + 2.18278i 2.02532 + 2.18278i
\(505\) 0 0
\(506\) 0.217550 + 2.90301i 0.217550 + 2.90301i
\(507\) 0.888301 + 0.274005i 0.888301 + 0.274005i
\(508\) 0 0
\(509\) −0.623490 1.07992i −0.623490 1.07992i −0.988831 0.149042i \(-0.952381\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.222521 0.974928i 0.222521 0.974928i
\(513\) 0 0
\(514\) −0.365341 0.930874i −0.365341 0.930874i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(522\) 0 0
\(523\) 0 0 −0.0747301 0.997204i \(-0.523810\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(524\) 0.974928 1.22252i 0.974928 1.22252i
\(525\) 1.35654 + 1.46200i 1.35654 + 1.46200i
\(526\) 0 0
\(527\) 0.636119 0.590232i 0.636119 0.590232i
\(528\) −3.67161 + 0.553406i −3.67161 + 0.553406i
\(529\) 1.19395 0.814021i 1.19395 0.814021i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) −0.246289 0.167917i −0.246289 0.167917i
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −0.930874 + 1.61232i −0.930874 + 1.61232i
\(540\) 0 0
\(541\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −0.826239 0.563320i −0.826239 0.563320i
\(545\) 0 0
\(546\) 1.13935 0.908598i 1.13935 0.908598i
\(547\) 0.531130 0.255779i 0.531130 0.255779i −0.149042 0.988831i \(-0.547619\pi\)
0.680173 + 0.733052i \(0.261905\pi\)
\(548\) 0.147791 + 0.0222759i 0.147791 + 0.0222759i
\(549\) 0 0
\(550\) −1.84095 + 0.277479i −1.84095 + 0.277479i
\(551\) 0 0
\(552\) 1.94440 + 2.43821i 1.94440 + 2.43821i
\(553\) 0.167917 0.246289i 0.167917 0.246289i
\(554\) 0 0
\(555\) 0 0
\(556\) −0.284841 0.0878620i −0.284841 0.0878620i
\(557\) 0.826239 1.43109i 0.826239 1.43109i −0.0747301 0.997204i \(-0.523810\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(558\) −1.29196 2.23774i −1.29196 2.23774i
\(559\) 0 0
\(560\) 0 0
\(561\) −0.826239 + 3.61999i −0.826239 + 3.61999i
\(562\) 0.955573 0.294755i 0.955573 0.294755i
\(563\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.414278 1.81507i 0.414278 1.81507i
\(567\) −0.728639 4.83420i −0.728639 4.83420i
\(568\) −0.250701 1.09839i −0.250701 1.09839i
\(569\) −0.365341 0.632789i −0.365341 0.632789i 0.623490 0.781831i \(-0.285714\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(570\) 0 0
\(571\) −0.829215 0.255779i −0.829215 0.255779i −0.149042 0.988831i \(-0.547619\pi\)
−0.680173 + 0.733052i \(0.738095\pi\)
\(572\) 0.101659 + 1.35654i 0.101659 + 1.35654i
\(573\) 0 0
\(574\) 0 0
\(575\) 0.974928 + 1.22252i 0.974928 + 1.22252i
\(576\) −2.18278 + 2.02532i −2.18278 + 2.02532i
\(577\) −1.44973 + 0.218511i −1.44973 + 0.218511i −0.826239 0.563320i \(-0.809524\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(578\) −0.826239 + 0.563320i −0.826239 + 0.563320i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −2.54192 1.73305i −2.54192 1.73305i
\(584\) 0 0
\(585\) 0 0
\(586\) 0.722521 1.84095i 0.722521 1.84095i
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 0.149042 + 1.98883i 0.149042 + 1.98883i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.21135 0.825886i −1.21135 0.825886i −0.222521 0.974928i \(-0.571429\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(594\) 6.61601 + 3.18610i 6.61601 + 3.18610i
\(595\) 0 0
\(596\) −0.134659 + 0.0648483i −0.134659 + 0.0648483i
\(597\) 2.22188 + 0.334895i 2.22188 + 0.334895i
\(598\) 0.944011 0.643616i 0.944011 0.643616i
\(599\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(600\) −1.46200 + 1.35654i −1.46200 + 1.35654i
\(601\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 1.24349 2.15379i 1.24349 2.15379i
\(607\) 0.866025 + 1.50000i 0.866025 + 1.50000i 0.866025 + 0.500000i \(0.166667\pi\)
1.00000i \(0.5\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 1.08786 + 2.77183i 1.08786 + 2.77183i
\(613\) 0.698220 + 1.77904i 0.698220 + 1.77904i 0.623490 + 0.781831i \(0.285714\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −1.61232 0.930874i −1.61232 0.930874i
\(617\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(618\) 0 0
\(619\) −0.866025 + 1.50000i −0.866025 + 1.50000i 1.00000i \(0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(620\) 0 0
\(621\) −0.460898 6.15025i −0.460898 6.15025i
\(622\) −1.07992 + 1.35417i −1.07992 + 1.35417i
\(623\) −0.0440542 0.142820i −0.0440542 0.142820i
\(624\) 0.908598 + 1.13935i 0.908598 + 1.13935i
\(625\) −0.733052 + 0.680173i −0.733052 + 0.680173i
\(626\) 0 0
\(627\) 0 0
\(628\) 1.95557 + 0.294755i 1.95557 + 0.294755i
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(632\) 0.246289 + 0.167917i 0.246289 + 0.167917i
\(633\) 2.85070 + 2.64506i 2.85070 + 2.64506i
\(634\) 0 0
\(635\) 0 0
\(636\) −3.29571 −3.29571
\(637\) 0.730682 0.730682
\(638\) 0 0
\(639\) −1.22563 + 3.12285i −1.22563 + 3.12285i
\(640\) 0 0
\(641\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(642\) −2.24165 1.52833i −2.24165 1.52833i
\(643\) 0.531130 + 0.255779i 0.531130 + 0.255779i 0.680173 0.733052i \(-0.261905\pi\)
−0.149042 + 0.988831i \(0.547619\pi\)
\(644\) 1.56366i 1.56366i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(648\) 4.83420 0.728639i 4.83420 0.728639i
\(649\) 0 0
\(650\) 0.455573 + 0.571270i 0.455573 + 0.571270i
\(651\) 0.257945 1.71135i 0.257945 1.71135i
\(652\) 0 0
\(653\) 0 0 −0.0747301 0.997204i \(-0.523810\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(660\) 0 0
\(661\) −0.658322 1.67738i −0.658322 1.67738i −0.733052 0.680173i \(-0.761905\pi\)
0.0747301 0.997204i \(-0.476190\pi\)
\(662\) 0 0
\(663\) 1.39254 0.429540i 1.39254 0.429540i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0.294755 0.510531i 0.294755 0.510531i
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) −1.98883 + 0.149042i −1.98883 + 0.149042i
\(673\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(674\) 0 0
\(675\) 3.90021 0.587862i 3.90021 0.587862i
\(676\) −0.385113 + 0.262566i −0.385113 + 0.262566i
\(677\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −1.85654 1.26577i −1.85654 1.26577i
\(682\) 1.18429 + 1.09886i 1.18429 + 1.09886i
\(683\) 0.0841939 1.12349i 0.0841939 1.12349i −0.781831 0.623490i \(-0.785714\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.563320 + 0.826239i −0.563320 + 0.826239i
\(687\) −0.887595 −0.887595
\(688\) 0 0
\(689\) −0.0902318 + 1.20406i −0.0902318 + 1.20406i
\(690\) 0 0
\(691\) 0.716983 + 0.488831i 0.716983 + 0.488831i 0.866025 0.500000i \(-0.166667\pi\)
−0.149042 + 0.988831i \(0.547619\pi\)
\(692\) 0 0
\(693\) 2.40530 + 4.99466i 2.40530 + 4.99466i
\(694\) 1.75676 0.846011i 1.75676 0.846011i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −0.326239 + 0.302705i −0.326239 + 0.302705i
\(699\) 0 0
\(700\) −0.997204 + 0.0747301i −0.997204 + 0.0747301i
\(701\) −1.03030 + 1.29196i −1.03030 + 1.29196i −0.0747301 + 0.997204i \(0.523810\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(702\) −0.215372 2.87394i −0.215372 2.87394i
\(703\) 0 0
\(704\) 0.930874 1.61232i 0.930874 1.61232i
\(705\) 0 0
\(706\) −0.222521 0.974928i −0.222521 0.974928i
\(707\) 1.16078 0.455573i 1.16078 0.455573i
\(708\) 0 0
\(709\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(710\) 0 0
\(711\) −0.324275 0.826239i −0.324275 0.826239i
\(712\) 0.142820 0.0440542i 0.142820 0.0440542i
\(713\) 0.301938 1.32288i 0.301938 1.32288i
\(714\) −0.587862 + 1.90580i −0.587862 + 1.90580i
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −0.139129 1.85654i −0.139129 1.85654i −0.433884 0.900969i \(-0.642857\pi\)
0.294755 0.955573i \(-0.404762\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.623490 0.781831i −0.623490 0.781831i
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) −4.86348 0.733052i −4.86348 0.733052i
\(727\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(728\) 0.730682i 0.730682i
\(729\) −6.02815 2.90301i −6.02815 2.90301i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −0.365341 + 0.930874i −0.365341 + 0.930874i 0.623490 + 0.781831i \(0.285714\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(734\) −1.36035 −1.36035
\(735\) 0 0
\(736\) −1.56366 −1.56366
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −1.29196 1.03030i −1.29196 1.03030i
\(743\) −1.79690 + 0.865341i −1.79690 + 0.865341i −0.866025 + 0.500000i \(0.833333\pi\)
−0.930874 + 0.365341i \(0.880952\pi\)
\(744\) 1.71135 + 0.257945i 1.71135 + 0.257945i
\(745\) 0 0
\(746\) −0.722521 + 0.108903i −0.722521 + 0.108903i
\(747\) 0 0
\(748\) −1.16078 1.45557i −1.16078 1.45557i
\(749\) −0.400969 1.29991i −0.400969 1.29991i
\(750\) 0 0
\(751\) 0.0222759 + 0.297251i 0.0222759 + 0.297251i 0.997204 + 0.0747301i \(0.0238095\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 3.41583 + 1.97213i 3.41583 + 1.97213i
\(757\) −0.222521 + 0.974928i −0.222521 + 0.974928i 0.733052 + 0.680173i \(0.238095\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(758\) −1.65510 + 0.510531i −1.65510 + 0.510531i
\(759\) 2.12117 + 5.40466i 2.12117 + 5.40466i
\(760\) 0 0
\(761\) −1.82624 + 0.563320i −1.82624 + 0.563320i −0.826239 + 0.563320i \(0.809524\pi\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −0.149042 1.98883i −0.149042 1.98883i
\(769\) 0.623490 0.781831i 0.623490 0.781831i −0.365341 0.930874i \(-0.619048\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(770\) 0 0
\(771\) −1.24349 1.55929i −1.24349 1.55929i
\(772\) 0 0
\(773\) 1.88980 0.284841i 1.88980 0.284841i 0.900969 0.433884i \(-0.142857\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(774\) 0 0
\(775\) 0.858075 + 0.129334i 0.858075 + 0.129334i
\(776\) 0 0
\(777\) 0 0
\(778\) −1.72188 0.829215i −1.72188 0.829215i
\(779\) 0 0
\(780\) 0 0
\(781\) 0.156748 2.09165i 0.156748 2.09165i
\(782\) −0.571270 + 1.45557i −0.571270 + 1.45557i
\(783\) 0 0
\(784\) −0.826239 0.563320i −0.826239 0.563320i
\(785\) 0 0
\(786\) 1.13935 2.90301i 1.13935 2.90301i
\(787\) 0.145713 1.94440i 0.145713