Properties

Label 735.2.i.k.226.1
Level $735$
Weight $2$
Character 735.226
Analytic conductor $5.869$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [735,2,Mod(226,735)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(735, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("735.226");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 735.i (of order \(3\), 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: \(5.86900454856\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{5})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + 2x^{2} + x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.1
Root \(0.809017 - 1.40126i\) of defining polynomial
Character \(\chi\) \(=\) 735.226
Dual form 735.2.i.k.361.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.11803 + 1.93649i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.50000 - 2.59808i) q^{4} +(0.500000 - 0.866025i) q^{5} -2.23607 q^{6} +2.23607 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-1.11803 + 1.93649i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.50000 - 2.59808i) q^{4} +(0.500000 - 0.866025i) q^{5} -2.23607 q^{6} +2.23607 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.11803 + 1.93649i) q^{10} +(1.23607 + 2.14093i) q^{11} +(1.50000 - 2.59808i) q^{12} -4.47214 q^{13} +1.00000 q^{15} +(0.500000 - 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(-1.11803 - 1.93649i) q^{18} +(-3.23607 + 5.60503i) q^{19} -3.00000 q^{20} -5.52786 q^{22} +(-2.00000 + 3.46410i) q^{23} +(1.11803 + 1.93649i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(5.00000 - 8.66025i) q^{26} -1.00000 q^{27} -2.00000 q^{29} +(-1.11803 + 1.93649i) q^{30} +(-5.23607 - 9.06914i) q^{31} +(3.35410 + 5.80948i) q^{32} +(-1.23607 + 2.14093i) q^{33} -4.47214 q^{34} +3.00000 q^{36} +(-5.47214 + 9.47802i) q^{37} +(-7.23607 - 12.5332i) q^{38} +(-2.23607 - 3.87298i) q^{39} +(1.11803 - 1.93649i) q^{40} -2.00000 q^{41} -8.94427 q^{43} +(3.70820 - 6.42280i) q^{44} +(0.500000 + 0.866025i) q^{45} +(-4.47214 - 7.74597i) q^{46} +(2.47214 - 4.28187i) q^{47} +1.00000 q^{48} +2.23607 q^{50} +(-1.00000 + 1.73205i) q^{51} +(6.70820 + 11.6190i) q^{52} +(6.23607 + 10.8012i) q^{53} +(1.11803 - 1.93649i) q^{54} +2.47214 q^{55} -6.47214 q^{57} +(2.23607 - 3.87298i) q^{58} +(-4.47214 - 7.74597i) q^{59} +(-1.50000 - 2.59808i) q^{60} +(1.00000 - 1.73205i) q^{61} +23.4164 q^{62} -13.0000 q^{64} +(-2.23607 + 3.87298i) q^{65} +(-2.76393 - 4.78727i) q^{66} +(2.00000 + 3.46410i) q^{67} +(3.00000 - 5.19615i) q^{68} -4.00000 q^{69} +14.4721 q^{71} +(-1.11803 + 1.93649i) q^{72} +(1.76393 + 3.05522i) q^{73} +(-12.2361 - 21.1935i) q^{74} +(0.500000 - 0.866025i) q^{75} +19.4164 q^{76} +10.0000 q^{78} +(2.47214 - 4.28187i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.23607 - 3.87298i) q^{82} +0.944272 q^{83} +2.00000 q^{85} +(10.0000 - 17.3205i) q^{86} +(-1.00000 - 1.73205i) q^{87} +(2.76393 + 4.78727i) q^{88} +(1.00000 - 1.73205i) q^{89} -2.23607 q^{90} +12.0000 q^{92} +(5.23607 - 9.06914i) q^{93} +(5.52786 + 9.57454i) q^{94} +(3.23607 + 5.60503i) q^{95} +(-3.35410 + 5.80948i) q^{96} -0.472136 q^{97} -2.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{3} - 6 q^{4} + 2 q^{5} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{3} - 6 q^{4} + 2 q^{5} - 2 q^{9} - 4 q^{11} + 6 q^{12} + 4 q^{15} + 2 q^{16} + 4 q^{17} - 4 q^{19} - 12 q^{20} - 40 q^{22} - 8 q^{23} - 2 q^{25} + 20 q^{26} - 4 q^{27} - 8 q^{29} - 12 q^{31} + 4 q^{33} + 12 q^{36} - 4 q^{37} - 20 q^{38} - 8 q^{41} - 12 q^{44} + 2 q^{45} - 8 q^{47} + 4 q^{48} - 4 q^{51} + 16 q^{53} - 8 q^{55} - 8 q^{57} - 6 q^{60} + 4 q^{61} + 40 q^{62} - 52 q^{64} - 20 q^{66} + 8 q^{67} + 12 q^{68} - 16 q^{69} + 40 q^{71} + 16 q^{73} - 40 q^{74} + 2 q^{75} + 24 q^{76} + 40 q^{78} - 8 q^{79} - 2 q^{80} - 2 q^{81} - 32 q^{83} + 8 q^{85} + 40 q^{86} - 4 q^{87} + 20 q^{88} + 4 q^{89} + 48 q^{92} + 12 q^{93} + 40 q^{94} + 4 q^{95} + 16 q^{97} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).

\(n\) \(346\) \(442\) \(491\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.11803 + 1.93649i −0.790569 + 1.36931i 0.135045 + 0.990839i \(0.456882\pi\)
−0.925615 + 0.378467i \(0.876451\pi\)
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −1.50000 2.59808i −0.750000 1.29904i
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) −2.23607 −0.912871
\(7\) 0 0
\(8\) 2.23607 0.790569
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 1.11803 + 1.93649i 0.353553 + 0.612372i
\(11\) 1.23607 + 2.14093i 0.372689 + 0.645515i 0.989978 0.141221i \(-0.0451027\pi\)
−0.617290 + 0.786736i \(0.711769\pi\)
\(12\) 1.50000 2.59808i 0.433013 0.750000i
\(13\) −4.47214 −1.24035 −0.620174 0.784465i \(-0.712938\pi\)
−0.620174 + 0.784465i \(0.712938\pi\)
\(14\) 0 0
\(15\) 1.00000 0.258199
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 1.00000 + 1.73205i 0.242536 + 0.420084i 0.961436 0.275029i \(-0.0886875\pi\)
−0.718900 + 0.695113i \(0.755354\pi\)
\(18\) −1.11803 1.93649i −0.263523 0.456435i
\(19\) −3.23607 + 5.60503i −0.742405 + 1.28588i 0.208993 + 0.977917i \(0.432982\pi\)
−0.951397 + 0.307966i \(0.900352\pi\)
\(20\) −3.00000 −0.670820
\(21\) 0 0
\(22\) −5.52786 −1.17854
\(23\) −2.00000 + 3.46410i −0.417029 + 0.722315i −0.995639 0.0932891i \(-0.970262\pi\)
0.578610 + 0.815604i \(0.303595\pi\)
\(24\) 1.11803 + 1.93649i 0.228218 + 0.395285i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 5.00000 8.66025i 0.980581 1.69842i
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) −1.11803 + 1.93649i −0.204124 + 0.353553i
\(31\) −5.23607 9.06914i −0.940426 1.62886i −0.764661 0.644433i \(-0.777094\pi\)
−0.175764 0.984432i \(-0.556240\pi\)
\(32\) 3.35410 + 5.80948i 0.592927 + 1.02698i
\(33\) −1.23607 + 2.14093i −0.215172 + 0.372689i
\(34\) −4.47214 −0.766965
\(35\) 0 0
\(36\) 3.00000 0.500000
\(37\) −5.47214 + 9.47802i −0.899614 + 1.55818i −0.0716249 + 0.997432i \(0.522818\pi\)
−0.827989 + 0.560745i \(0.810515\pi\)
\(38\) −7.23607 12.5332i −1.17385 2.03316i
\(39\) −2.23607 3.87298i −0.358057 0.620174i
\(40\) 1.11803 1.93649i 0.176777 0.306186i
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) −8.94427 −1.36399 −0.681994 0.731357i \(-0.738887\pi\)
−0.681994 + 0.731357i \(0.738887\pi\)
\(44\) 3.70820 6.42280i 0.559033 0.968273i
\(45\) 0.500000 + 0.866025i 0.0745356 + 0.129099i
\(46\) −4.47214 7.74597i −0.659380 1.14208i
\(47\) 2.47214 4.28187i 0.360598 0.624574i −0.627461 0.778648i \(-0.715906\pi\)
0.988059 + 0.154074i \(0.0492393\pi\)
\(48\) 1.00000 0.144338
\(49\) 0 0
\(50\) 2.23607 0.316228
\(51\) −1.00000 + 1.73205i −0.140028 + 0.242536i
\(52\) 6.70820 + 11.6190i 0.930261 + 1.61126i
\(53\) 6.23607 + 10.8012i 0.856590 + 1.48366i 0.875162 + 0.483830i \(0.160755\pi\)
−0.0185724 + 0.999828i \(0.505912\pi\)
\(54\) 1.11803 1.93649i 0.152145 0.263523i
\(55\) 2.47214 0.333343
\(56\) 0 0
\(57\) −6.47214 −0.857255
\(58\) 2.23607 3.87298i 0.293610 0.508548i
\(59\) −4.47214 7.74597i −0.582223 1.00844i −0.995215 0.0977047i \(-0.968850\pi\)
0.412993 0.910734i \(-0.364483\pi\)
\(60\) −1.50000 2.59808i −0.193649 0.335410i
\(61\) 1.00000 1.73205i 0.128037 0.221766i −0.794879 0.606768i \(-0.792466\pi\)
0.922916 + 0.385002i \(0.125799\pi\)
\(62\) 23.4164 2.97389
\(63\) 0 0
\(64\) −13.0000 −1.62500
\(65\) −2.23607 + 3.87298i −0.277350 + 0.480384i
\(66\) −2.76393 4.78727i −0.340217 0.589272i
\(67\) 2.00000 + 3.46410i 0.244339 + 0.423207i 0.961946 0.273241i \(-0.0880957\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) 3.00000 5.19615i 0.363803 0.630126i
\(69\) −4.00000 −0.481543
\(70\) 0 0
\(71\) 14.4721 1.71753 0.858763 0.512373i \(-0.171233\pi\)
0.858763 + 0.512373i \(0.171233\pi\)
\(72\) −1.11803 + 1.93649i −0.131762 + 0.228218i
\(73\) 1.76393 + 3.05522i 0.206453 + 0.357586i 0.950595 0.310435i \(-0.100475\pi\)
−0.744142 + 0.668022i \(0.767141\pi\)
\(74\) −12.2361 21.1935i −1.42241 2.46369i
\(75\) 0.500000 0.866025i 0.0577350 0.100000i
\(76\) 19.4164 2.22721
\(77\) 0 0
\(78\) 10.0000 1.13228
\(79\) 2.47214 4.28187i 0.278137 0.481747i −0.692785 0.721144i \(-0.743616\pi\)
0.970922 + 0.239397i \(0.0769497\pi\)
\(80\) −0.500000 0.866025i −0.0559017 0.0968246i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 2.23607 3.87298i 0.246932 0.427699i
\(83\) 0.944272 0.103647 0.0518237 0.998656i \(-0.483497\pi\)
0.0518237 + 0.998656i \(0.483497\pi\)
\(84\) 0 0
\(85\) 2.00000 0.216930
\(86\) 10.0000 17.3205i 1.07833 1.86772i
\(87\) −1.00000 1.73205i −0.107211 0.185695i
\(88\) 2.76393 + 4.78727i 0.294636 + 0.510325i
\(89\) 1.00000 1.73205i 0.106000 0.183597i −0.808146 0.588982i \(-0.799529\pi\)
0.914146 + 0.405385i \(0.132862\pi\)
\(90\) −2.23607 −0.235702
\(91\) 0 0
\(92\) 12.0000 1.25109
\(93\) 5.23607 9.06914i 0.542955 0.940426i
\(94\) 5.52786 + 9.57454i 0.570156 + 0.987539i
\(95\) 3.23607 + 5.60503i 0.332014 + 0.575064i
\(96\) −3.35410 + 5.80948i −0.342327 + 0.592927i
\(97\) −0.472136 −0.0479381 −0.0239691 0.999713i \(-0.507630\pi\)
−0.0239691 + 0.999713i \(0.507630\pi\)
\(98\) 0 0
\(99\) −2.47214 −0.248459
\(100\) −1.50000 + 2.59808i −0.150000 + 0.259808i
\(101\) 7.00000 + 12.1244i 0.696526 + 1.20642i 0.969664 + 0.244443i \(0.0786053\pi\)
−0.273138 + 0.961975i \(0.588061\pi\)
\(102\) −2.23607 3.87298i −0.221404 0.383482i
\(103\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(104\) −10.0000 −0.980581
\(105\) 0 0
\(106\) −27.8885 −2.70877
\(107\) −2.47214 + 4.28187i −0.238990 + 0.413944i −0.960425 0.278539i \(-0.910150\pi\)
0.721434 + 0.692483i \(0.243483\pi\)
\(108\) 1.50000 + 2.59808i 0.144338 + 0.250000i
\(109\) 1.00000 + 1.73205i 0.0957826 + 0.165900i 0.909935 0.414751i \(-0.136131\pi\)
−0.814152 + 0.580651i \(0.802798\pi\)
\(110\) −2.76393 + 4.78727i −0.263531 + 0.456448i
\(111\) −10.9443 −1.03878
\(112\) 0 0
\(113\) −8.47214 −0.796992 −0.398496 0.917170i \(-0.630468\pi\)
−0.398496 + 0.917170i \(0.630468\pi\)
\(114\) 7.23607 12.5332i 0.677720 1.17385i
\(115\) 2.00000 + 3.46410i 0.186501 + 0.323029i
\(116\) 3.00000 + 5.19615i 0.278543 + 0.482451i
\(117\) 2.23607 3.87298i 0.206725 0.358057i
\(118\) 20.0000 1.84115
\(119\) 0 0
\(120\) 2.23607 0.204124
\(121\) 2.44427 4.23360i 0.222207 0.384873i
\(122\) 2.23607 + 3.87298i 0.202444 + 0.350643i
\(123\) −1.00000 1.73205i −0.0901670 0.156174i
\(124\) −15.7082 + 27.2074i −1.41064 + 2.44330i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 12.9443 1.14862 0.574309 0.818638i \(-0.305271\pi\)
0.574309 + 0.818638i \(0.305271\pi\)
\(128\) 7.82624 13.5554i 0.691748 1.19814i
\(129\) −4.47214 7.74597i −0.393750 0.681994i
\(130\) −5.00000 8.66025i −0.438529 0.759555i
\(131\) −2.00000 + 3.46410i −0.174741 + 0.302660i −0.940072 0.340977i \(-0.889242\pi\)
0.765331 + 0.643637i \(0.222575\pi\)
\(132\) 7.41641 0.645515
\(133\) 0 0
\(134\) −8.94427 −0.772667
\(135\) −0.500000 + 0.866025i −0.0430331 + 0.0745356i
\(136\) 2.23607 + 3.87298i 0.191741 + 0.332106i
\(137\) −6.23607 10.8012i −0.532783 0.922808i −0.999267 0.0382780i \(-0.987813\pi\)
0.466484 0.884530i \(-0.345521\pi\)
\(138\) 4.47214 7.74597i 0.380693 0.659380i
\(139\) −19.4164 −1.64688 −0.823439 0.567405i \(-0.807948\pi\)
−0.823439 + 0.567405i \(0.807948\pi\)
\(140\) 0 0
\(141\) 4.94427 0.416383
\(142\) −16.1803 + 28.0252i −1.35782 + 2.35182i
\(143\) −5.52786 9.57454i −0.462263 0.800663i
\(144\) 0.500000 + 0.866025i 0.0416667 + 0.0721688i
\(145\) −1.00000 + 1.73205i −0.0830455 + 0.143839i
\(146\) −7.88854 −0.652861
\(147\) 0 0
\(148\) 32.8328 2.69884
\(149\) −1.47214 + 2.54981i −0.120602 + 0.208889i −0.920005 0.391906i \(-0.871816\pi\)
0.799403 + 0.600795i \(0.205149\pi\)
\(150\) 1.11803 + 1.93649i 0.0912871 + 0.158114i
\(151\) 8.00000 + 13.8564i 0.651031 + 1.12762i 0.982873 + 0.184284i \(0.0589965\pi\)
−0.331842 + 0.943335i \(0.607670\pi\)
\(152\) −7.23607 + 12.5332i −0.586923 + 1.01658i
\(153\) −2.00000 −0.161690
\(154\) 0 0
\(155\) −10.4721 −0.841142
\(156\) −6.70820 + 11.6190i −0.537086 + 0.930261i
\(157\) −4.23607 7.33708i −0.338075 0.585563i 0.645996 0.763341i \(-0.276442\pi\)
−0.984071 + 0.177778i \(0.943109\pi\)
\(158\) 5.52786 + 9.57454i 0.439773 + 0.761710i
\(159\) −6.23607 + 10.8012i −0.494552 + 0.856590i
\(160\) 6.70820 0.530330
\(161\) 0 0
\(162\) 2.23607 0.175682
\(163\) −0.472136 + 0.817763i −0.0369805 + 0.0640522i −0.883923 0.467632i \(-0.845107\pi\)
0.846943 + 0.531684i \(0.178441\pi\)
\(164\) 3.00000 + 5.19615i 0.234261 + 0.405751i
\(165\) 1.23607 + 2.14093i 0.0962278 + 0.166671i
\(166\) −1.05573 + 1.82857i −0.0819404 + 0.141925i
\(167\) −8.00000 −0.619059 −0.309529 0.950890i \(-0.600171\pi\)
−0.309529 + 0.950890i \(0.600171\pi\)
\(168\) 0 0
\(169\) 7.00000 0.538462
\(170\) −2.23607 + 3.87298i −0.171499 + 0.297044i
\(171\) −3.23607 5.60503i −0.247468 0.428628i
\(172\) 13.4164 + 23.2379i 1.02299 + 1.77187i
\(173\) −7.47214 + 12.9421i −0.568096 + 0.983971i 0.428658 + 0.903467i \(0.358986\pi\)
−0.996754 + 0.0805044i \(0.974347\pi\)
\(174\) 4.47214 0.339032
\(175\) 0 0
\(176\) 2.47214 0.186344
\(177\) 4.47214 7.74597i 0.336146 0.582223i
\(178\) 2.23607 + 3.87298i 0.167600 + 0.290292i
\(179\) 1.23607 + 2.14093i 0.0923881 + 0.160021i 0.908516 0.417851i \(-0.137217\pi\)
−0.816127 + 0.577872i \(0.803883\pi\)
\(180\) 1.50000 2.59808i 0.111803 0.193649i
\(181\) 18.9443 1.40812 0.704058 0.710142i \(-0.251369\pi\)
0.704058 + 0.710142i \(0.251369\pi\)
\(182\) 0 0
\(183\) 2.00000 0.147844
\(184\) −4.47214 + 7.74597i −0.329690 + 0.571040i
\(185\) 5.47214 + 9.47802i 0.402319 + 0.696838i
\(186\) 11.7082 + 20.2792i 0.858487 + 1.48694i
\(187\) −2.47214 + 4.28187i −0.180780 + 0.313121i
\(188\) −14.8328 −1.08179
\(189\) 0 0
\(190\) −14.4721 −1.04992
\(191\) −13.7082 + 23.7433i −0.991891 + 1.71801i −0.385880 + 0.922549i \(0.626102\pi\)
−0.606011 + 0.795456i \(0.707231\pi\)
\(192\) −6.50000 11.2583i −0.469097 0.812500i
\(193\) 7.00000 + 12.1244i 0.503871 + 0.872730i 0.999990 + 0.00447566i \(0.00142465\pi\)
−0.496119 + 0.868255i \(0.665242\pi\)
\(194\) 0.527864 0.914287i 0.0378984 0.0656420i
\(195\) −4.47214 −0.320256
\(196\) 0 0
\(197\) 24.4721 1.74357 0.871784 0.489891i \(-0.162963\pi\)
0.871784 + 0.489891i \(0.162963\pi\)
\(198\) 2.76393 4.78727i 0.196424 0.340217i
\(199\) −0.291796 0.505406i −0.0206849 0.0358273i 0.855498 0.517807i \(-0.173251\pi\)
−0.876183 + 0.481979i \(0.839918\pi\)
\(200\) −1.11803 1.93649i −0.0790569 0.136931i
\(201\) −2.00000 + 3.46410i −0.141069 + 0.244339i
\(202\) −31.3050 −2.20261
\(203\) 0 0
\(204\) 6.00000 0.420084
\(205\) −1.00000 + 1.73205i −0.0698430 + 0.120972i
\(206\) 0 0
\(207\) −2.00000 3.46410i −0.139010 0.240772i
\(208\) −2.23607 + 3.87298i −0.155043 + 0.268543i
\(209\) −16.0000 −1.10674
\(210\) 0 0
\(211\) 0.944272 0.0650064 0.0325032 0.999472i \(-0.489652\pi\)
0.0325032 + 0.999472i \(0.489652\pi\)
\(212\) 18.7082 32.4036i 1.28488 2.22549i
\(213\) 7.23607 + 12.5332i 0.495807 + 0.858763i
\(214\) −5.52786 9.57454i −0.377877 0.654502i
\(215\) −4.47214 + 7.74597i −0.304997 + 0.528271i
\(216\) −2.23607 −0.152145
\(217\) 0 0
\(218\) −4.47214 −0.302891
\(219\) −1.76393 + 3.05522i −0.119195 + 0.206453i
\(220\) −3.70820 6.42280i −0.250007 0.433025i
\(221\) −4.47214 7.74597i −0.300828 0.521050i
\(222\) 12.2361 21.1935i 0.821231 1.42241i
\(223\) 4.94427 0.331093 0.165546 0.986202i \(-0.447061\pi\)
0.165546 + 0.986202i \(0.447061\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 9.47214 16.4062i 0.630077 1.09133i
\(227\) 8.47214 + 14.6742i 0.562315 + 0.973959i 0.997294 + 0.0735180i \(0.0234226\pi\)
−0.434978 + 0.900441i \(0.643244\pi\)
\(228\) 9.70820 + 16.8151i 0.642942 + 1.11361i
\(229\) 5.94427 10.2958i 0.392809 0.680364i −0.600010 0.799992i \(-0.704837\pi\)
0.992819 + 0.119628i \(0.0381702\pi\)
\(230\) −8.94427 −0.589768
\(231\) 0 0
\(232\) −4.47214 −0.293610
\(233\) −8.70820 + 15.0831i −0.570493 + 0.988124i 0.426022 + 0.904713i \(0.359915\pi\)
−0.996515 + 0.0834107i \(0.973419\pi\)
\(234\) 5.00000 + 8.66025i 0.326860 + 0.566139i
\(235\) −2.47214 4.28187i −0.161264 0.279318i
\(236\) −13.4164 + 23.2379i −0.873334 + 1.51266i
\(237\) 4.94427 0.321165
\(238\) 0 0
\(239\) −1.52786 −0.0988293 −0.0494147 0.998778i \(-0.515736\pi\)
−0.0494147 + 0.998778i \(0.515736\pi\)
\(240\) 0.500000 0.866025i 0.0322749 0.0559017i
\(241\) 0.527864 + 0.914287i 0.0340027 + 0.0588944i 0.882526 0.470264i \(-0.155841\pi\)
−0.848523 + 0.529158i \(0.822508\pi\)
\(242\) 5.46556 + 9.46662i 0.351339 + 0.608538i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −6.00000 −0.384111
\(245\) 0 0
\(246\) 4.47214 0.285133
\(247\) 14.4721 25.0665i 0.920840 1.59494i
\(248\) −11.7082 20.2792i −0.743472 1.28773i
\(249\) 0.472136 + 0.817763i 0.0299204 + 0.0518237i
\(250\) 1.11803 1.93649i 0.0707107 0.122474i
\(251\) −0.944272 −0.0596019 −0.0298010 0.999556i \(-0.509487\pi\)
−0.0298010 + 0.999556i \(0.509487\pi\)
\(252\) 0 0
\(253\) −9.88854 −0.621687
\(254\) −14.4721 + 25.0665i −0.908063 + 1.57281i
\(255\) 1.00000 + 1.73205i 0.0626224 + 0.108465i
\(256\) 4.50000 + 7.79423i 0.281250 + 0.487139i
\(257\) −0.527864 + 0.914287i −0.0329273 + 0.0570317i −0.882019 0.471213i \(-0.843816\pi\)
0.849092 + 0.528245i \(0.177150\pi\)
\(258\) 20.0000 1.24515
\(259\) 0 0
\(260\) 13.4164 0.832050
\(261\) 1.00000 1.73205i 0.0618984 0.107211i
\(262\) −4.47214 7.74597i −0.276289 0.478547i
\(263\) −12.4721 21.6024i −0.769065 1.33206i −0.938071 0.346444i \(-0.887389\pi\)
0.169006 0.985615i \(-0.445944\pi\)
\(264\) −2.76393 + 4.78727i −0.170108 + 0.294636i
\(265\) 12.4721 0.766157
\(266\) 0 0
\(267\) 2.00000 0.122398
\(268\) 6.00000 10.3923i 0.366508 0.634811i
\(269\) 11.9443 + 20.6881i 0.728255 + 1.26137i 0.957620 + 0.288034i \(0.0930017\pi\)
−0.229365 + 0.973340i \(0.573665\pi\)
\(270\) −1.11803 1.93649i −0.0680414 0.117851i
\(271\) 5.23607 9.06914i 0.318068 0.550911i −0.662017 0.749489i \(-0.730299\pi\)
0.980085 + 0.198578i \(0.0636325\pi\)
\(272\) 2.00000 0.121268
\(273\) 0 0
\(274\) 27.8885 1.68481
\(275\) 1.23607 2.14093i 0.0745377 0.129103i
\(276\) 6.00000 + 10.3923i 0.361158 + 0.625543i
\(277\) −0.527864 0.914287i −0.0317163 0.0549342i 0.849732 0.527216i \(-0.176764\pi\)
−0.881448 + 0.472281i \(0.843431\pi\)
\(278\) 21.7082 37.5997i 1.30197 2.25508i
\(279\) 10.4721 0.626950
\(280\) 0 0
\(281\) 6.94427 0.414261 0.207130 0.978313i \(-0.433588\pi\)
0.207130 + 0.978313i \(0.433588\pi\)
\(282\) −5.52786 + 9.57454i −0.329180 + 0.570156i
\(283\) −6.00000 10.3923i −0.356663 0.617758i 0.630738 0.775996i \(-0.282752\pi\)
−0.987401 + 0.158237i \(0.949419\pi\)
\(284\) −21.7082 37.5997i −1.28814 2.23113i
\(285\) −3.23607 + 5.60503i −0.191688 + 0.332014i
\(286\) 24.7214 1.46180
\(287\) 0 0
\(288\) −6.70820 −0.395285
\(289\) 6.50000 11.2583i 0.382353 0.662255i
\(290\) −2.23607 3.87298i −0.131306 0.227429i
\(291\) −0.236068 0.408882i −0.0138385 0.0239691i
\(292\) 5.29180 9.16566i 0.309679 0.536380i
\(293\) 22.9443 1.34042 0.670209 0.742172i \(-0.266204\pi\)
0.670209 + 0.742172i \(0.266204\pi\)
\(294\) 0 0
\(295\) −8.94427 −0.520756
\(296\) −12.2361 + 21.1935i −0.711207 + 1.23185i
\(297\) −1.23607 2.14093i −0.0717239 0.124230i
\(298\) −3.29180 5.70156i −0.190689 0.330282i
\(299\) 8.94427 15.4919i 0.517261 0.895922i
\(300\) −3.00000 −0.173205
\(301\) 0 0
\(302\) −35.7771 −2.05874
\(303\) −7.00000 + 12.1244i −0.402139 + 0.696526i
\(304\) 3.23607 + 5.60503i 0.185601 + 0.321471i
\(305\) −1.00000 1.73205i −0.0572598 0.0991769i
\(306\) 2.23607 3.87298i 0.127827 0.221404i
\(307\) −32.9443 −1.88023 −0.940114 0.340859i \(-0.889282\pi\)
−0.940114 + 0.340859i \(0.889282\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 11.7082 20.2792i 0.664981 1.15178i
\(311\) 4.94427 + 8.56373i 0.280364 + 0.485605i 0.971474 0.237145i \(-0.0762115\pi\)
−0.691110 + 0.722749i \(0.742878\pi\)
\(312\) −5.00000 8.66025i −0.283069 0.490290i
\(313\) −4.70820 + 8.15485i −0.266123 + 0.460939i −0.967857 0.251500i \(-0.919076\pi\)
0.701734 + 0.712439i \(0.252410\pi\)
\(314\) 18.9443 1.06909
\(315\) 0 0
\(316\) −14.8328 −0.834411
\(317\) 15.1803 26.2931i 0.852613 1.47677i −0.0262292 0.999656i \(-0.508350\pi\)
0.878842 0.477113i \(-0.158317\pi\)
\(318\) −13.9443 24.1522i −0.781956 1.35439i
\(319\) −2.47214 4.28187i −0.138413 0.239738i
\(320\) −6.50000 + 11.2583i −0.363361 + 0.629360i
\(321\) −4.94427 −0.275962
\(322\) 0 0
\(323\) −12.9443 −0.720239
\(324\) −1.50000 + 2.59808i −0.0833333 + 0.144338i
\(325\) 2.23607 + 3.87298i 0.124035 + 0.214834i
\(326\) −1.05573 1.82857i −0.0584714 0.101275i
\(327\) −1.00000 + 1.73205i −0.0553001 + 0.0957826i
\(328\) −4.47214 −0.246932
\(329\) 0 0
\(330\) −5.52786 −0.304299
\(331\) 8.47214 14.6742i 0.465671 0.806565i −0.533561 0.845762i \(-0.679146\pi\)
0.999232 + 0.0391964i \(0.0124798\pi\)
\(332\) −1.41641 2.45329i −0.0777355 0.134642i
\(333\) −5.47214 9.47802i −0.299871 0.519392i
\(334\) 8.94427 15.4919i 0.489409 0.847681i
\(335\) 4.00000 0.218543
\(336\) 0 0
\(337\) 11.8885 0.647610 0.323805 0.946124i \(-0.395038\pi\)
0.323805 + 0.946124i \(0.395038\pi\)
\(338\) −7.82624 + 13.5554i −0.425691 + 0.737319i
\(339\) −4.23607 7.33708i −0.230072 0.398496i
\(340\) −3.00000 5.19615i −0.162698 0.281801i
\(341\) 12.9443 22.4201i 0.700972 1.21412i
\(342\) 14.4721 0.782563
\(343\) 0 0
\(344\) −20.0000 −1.07833
\(345\) −2.00000 + 3.46410i −0.107676 + 0.186501i
\(346\) −16.7082 28.9395i −0.898239 1.55579i
\(347\) 4.00000 + 6.92820i 0.214731 + 0.371925i 0.953189 0.302374i \(-0.0977791\pi\)
−0.738458 + 0.674299i \(0.764446\pi\)
\(348\) −3.00000 + 5.19615i −0.160817 + 0.278543i
\(349\) 23.8885 1.27872 0.639362 0.768906i \(-0.279198\pi\)
0.639362 + 0.768906i \(0.279198\pi\)
\(350\) 0 0
\(351\) 4.47214 0.238705
\(352\) −8.29180 + 14.3618i −0.441954 + 0.765487i
\(353\) 13.9443 + 24.1522i 0.742179 + 1.28549i 0.951501 + 0.307645i \(0.0995408\pi\)
−0.209323 + 0.977847i \(0.567126\pi\)
\(354\) 10.0000 + 17.3205i 0.531494 + 0.920575i
\(355\) 7.23607 12.5332i 0.384051 0.665195i
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) −5.52786 −0.292157
\(359\) −4.76393 + 8.25137i −0.251431 + 0.435491i −0.963920 0.266192i \(-0.914234\pi\)
0.712489 + 0.701683i \(0.247568\pi\)
\(360\) 1.11803 + 1.93649i 0.0589256 + 0.102062i
\(361\) −11.4443 19.8221i −0.602330 1.04327i
\(362\) −21.1803 + 36.6854i −1.11321 + 1.92814i
\(363\) 4.88854 0.256582
\(364\) 0 0
\(365\) 3.52786 0.184657
\(366\) −2.23607 + 3.87298i −0.116881 + 0.202444i
\(367\) −10.4721 18.1383i −0.546641 0.946810i −0.998502 0.0547215i \(-0.982573\pi\)
0.451861 0.892089i \(-0.350760\pi\)
\(368\) 2.00000 + 3.46410i 0.104257 + 0.180579i
\(369\) 1.00000 1.73205i 0.0520579 0.0901670i
\(370\) −24.4721 −1.27225
\(371\) 0 0
\(372\) −31.4164 −1.62886
\(373\) −3.00000 + 5.19615i −0.155334 + 0.269047i −0.933181 0.359408i \(-0.882979\pi\)
0.777847 + 0.628454i \(0.216312\pi\)
\(374\) −5.52786 9.57454i −0.285839 0.495088i
\(375\) −0.500000 0.866025i −0.0258199 0.0447214i
\(376\) 5.52786 9.57454i 0.285078 0.493769i
\(377\) 8.94427 0.460653
\(378\) 0 0
\(379\) −2.11146 −0.108458 −0.0542291 0.998529i \(-0.517270\pi\)
−0.0542291 + 0.998529i \(0.517270\pi\)
\(380\) 9.70820 16.8151i 0.498020 0.862597i
\(381\) 6.47214 + 11.2101i 0.331578 + 0.574309i
\(382\) −30.6525 53.0916i −1.56832 2.71640i
\(383\) 4.00000 6.92820i 0.204390 0.354015i −0.745548 0.666452i \(-0.767812\pi\)
0.949938 + 0.312437i \(0.101145\pi\)
\(384\) 15.6525 0.798762
\(385\) 0 0
\(386\) −31.3050 −1.59338
\(387\) 4.47214 7.74597i 0.227331 0.393750i
\(388\) 0.708204 + 1.22665i 0.0359536 + 0.0622735i
\(389\) −5.47214 9.47802i −0.277448 0.480555i 0.693302 0.720648i \(-0.256155\pi\)
−0.970750 + 0.240093i \(0.922822\pi\)
\(390\) 5.00000 8.66025i 0.253185 0.438529i
\(391\) −8.00000 −0.404577
\(392\) 0 0
\(393\) −4.00000 −0.201773
\(394\) −27.3607 + 47.3901i −1.37841 + 2.38748i
\(395\) −2.47214 4.28187i −0.124387 0.215444i
\(396\) 3.70820 + 6.42280i 0.186344 + 0.322758i
\(397\) −6.70820 + 11.6190i −0.336675 + 0.583138i −0.983805 0.179241i \(-0.942636\pi\)
0.647130 + 0.762380i \(0.275969\pi\)
\(398\) 1.30495 0.0654113
\(399\) 0 0
\(400\) −1.00000 −0.0500000
\(401\) −5.00000 + 8.66025i −0.249688 + 0.432472i −0.963439 0.267927i \(-0.913661\pi\)
0.713751 + 0.700399i \(0.246995\pi\)
\(402\) −4.47214 7.74597i −0.223050 0.386334i
\(403\) 23.4164 + 40.5584i 1.16645 + 2.02036i
\(404\) 21.0000 36.3731i 1.04479 1.80963i
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) −27.0557 −1.34110
\(408\) −2.23607 + 3.87298i −0.110702 + 0.191741i
\(409\) 11.9443 + 20.6881i 0.590606 + 1.02296i 0.994151 + 0.108000i \(0.0344447\pi\)
−0.403545 + 0.914960i \(0.632222\pi\)
\(410\) −2.23607 3.87298i −0.110432 0.191273i
\(411\) 6.23607 10.8012i 0.307603 0.532783i
\(412\) 0 0
\(413\) 0 0
\(414\) 8.94427 0.439587
\(415\) 0.472136 0.817763i 0.0231762 0.0401424i
\(416\) −15.0000 25.9808i −0.735436 1.27381i
\(417\) −9.70820 16.8151i −0.475413 0.823439i
\(418\) 17.8885 30.9839i 0.874957 1.51547i
\(419\) 5.88854 0.287674 0.143837 0.989601i \(-0.454056\pi\)
0.143837 + 0.989601i \(0.454056\pi\)
\(420\) 0 0
\(421\) 22.0000 1.07221 0.536107 0.844150i \(-0.319894\pi\)
0.536107 + 0.844150i \(0.319894\pi\)
\(422\) −1.05573 + 1.82857i −0.0513920 + 0.0890136i
\(423\) 2.47214 + 4.28187i 0.120199 + 0.208191i
\(424\) 13.9443 + 24.1522i 0.677194 + 1.17293i
\(425\) 1.00000 1.73205i 0.0485071 0.0840168i
\(426\) −32.3607 −1.56788
\(427\) 0 0
\(428\) 14.8328 0.716971
\(429\) 5.52786 9.57454i 0.266888 0.462263i
\(430\) −10.0000 17.3205i −0.482243 0.835269i
\(431\) 4.76393 + 8.25137i 0.229471 + 0.397455i 0.957651 0.287930i \(-0.0929672\pi\)
−0.728181 + 0.685385i \(0.759634\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) 7.52786 0.361766 0.180883 0.983505i \(-0.442104\pi\)
0.180883 + 0.983505i \(0.442104\pi\)
\(434\) 0 0
\(435\) −2.00000 −0.0958927
\(436\) 3.00000 5.19615i 0.143674 0.248851i
\(437\) −12.9443 22.4201i −0.619208 1.07250i
\(438\) −3.94427 6.83168i −0.188465 0.326430i
\(439\) −5.23607 + 9.06914i −0.249904 + 0.432846i −0.963499 0.267712i \(-0.913732\pi\)
0.713595 + 0.700558i \(0.247066\pi\)
\(440\) 5.52786 0.263531
\(441\) 0 0
\(442\) 20.0000 0.951303
\(443\) 4.00000 6.92820i 0.190046 0.329169i −0.755219 0.655472i \(-0.772470\pi\)
0.945265 + 0.326303i \(0.105803\pi\)
\(444\) 16.4164 + 28.4341i 0.779088 + 1.34942i
\(445\) −1.00000 1.73205i −0.0474045 0.0821071i
\(446\) −5.52786 + 9.57454i −0.261752 + 0.453368i
\(447\) −2.94427 −0.139259
\(448\) 0 0
\(449\) −14.0000 −0.660701 −0.330350 0.943858i \(-0.607167\pi\)
−0.330350 + 0.943858i \(0.607167\pi\)
\(450\) −1.11803 + 1.93649i −0.0527046 + 0.0912871i
\(451\) −2.47214 4.28187i −0.116408 0.201625i
\(452\) 12.7082 + 22.0113i 0.597744 + 1.03532i
\(453\) −8.00000 + 13.8564i −0.375873 + 0.651031i
\(454\) −37.8885 −1.77820
\(455\) 0 0
\(456\) −14.4721 −0.677720
\(457\) 5.47214 9.47802i 0.255976 0.443363i −0.709184 0.705023i \(-0.750937\pi\)
0.965160 + 0.261660i \(0.0842699\pi\)
\(458\) 13.2918 + 23.0221i 0.621085 + 1.07575i
\(459\) −1.00000 1.73205i −0.0466760 0.0808452i
\(460\) 6.00000 10.3923i 0.279751 0.484544i
\(461\) −31.8885 −1.48520 −0.742599 0.669737i \(-0.766407\pi\)
−0.742599 + 0.669737i \(0.766407\pi\)
\(462\) 0 0
\(463\) 3.05573 0.142012 0.0710059 0.997476i \(-0.477379\pi\)
0.0710059 + 0.997476i \(0.477379\pi\)
\(464\) −1.00000 + 1.73205i −0.0464238 + 0.0804084i
\(465\) −5.23607 9.06914i −0.242817 0.420571i
\(466\) −19.4721 33.7267i −0.902029 1.56236i
\(467\) −4.47214 + 7.74597i −0.206946 + 0.358441i −0.950751 0.309956i \(-0.899686\pi\)
0.743805 + 0.668397i \(0.233019\pi\)
\(468\) −13.4164 −0.620174
\(469\) 0 0
\(470\) 11.0557 0.509963
\(471\) 4.23607 7.33708i 0.195188 0.338075i
\(472\) −10.0000 17.3205i −0.460287 0.797241i
\(473\) −11.0557 19.1491i −0.508343 0.880476i
\(474\) −5.52786 + 9.57454i −0.253903 + 0.439773i
\(475\) 6.47214 0.296962
\(476\) 0 0
\(477\) −12.4721 −0.571060
\(478\) 1.70820 2.95870i 0.0781314 0.135328i
\(479\) −8.94427 15.4919i −0.408674 0.707845i 0.586067 0.810262i \(-0.300675\pi\)
−0.994741 + 0.102418i \(0.967342\pi\)
\(480\) 3.35410 + 5.80948i 0.153093 + 0.265165i
\(481\) 24.4721 42.3870i 1.11583 1.93268i
\(482\) −2.36068 −0.107526
\(483\) 0 0
\(484\) −14.6656 −0.666620
\(485\) −0.236068 + 0.408882i −0.0107193 + 0.0185664i
\(486\) 1.11803 + 1.93649i 0.0507151 + 0.0878410i
\(487\) 1.52786 + 2.64634i 0.0692341 + 0.119917i 0.898564 0.438842i \(-0.144611\pi\)
−0.829330 + 0.558759i \(0.811278\pi\)
\(488\) 2.23607 3.87298i 0.101222 0.175322i
\(489\) −0.944272 −0.0427015
\(490\) 0 0
\(491\) 41.3050 1.86407 0.932033 0.362373i \(-0.118033\pi\)
0.932033 + 0.362373i \(0.118033\pi\)
\(492\) −3.00000 + 5.19615i −0.135250 + 0.234261i
\(493\) −2.00000 3.46410i −0.0900755 0.156015i
\(494\) 32.3607 + 56.0503i 1.45598 + 2.52182i
\(495\) −1.23607 + 2.14093i −0.0555571 + 0.0962278i
\(496\) −10.4721 −0.470213
\(497\) 0 0
\(498\) −2.11146 −0.0946166
\(499\) −10.9443 + 18.9560i −0.489933 + 0.848589i −0.999933 0.0115857i \(-0.996312\pi\)
0.510000 + 0.860174i \(0.329645\pi\)
\(500\) 1.50000 + 2.59808i 0.0670820 + 0.116190i
\(501\) −4.00000 6.92820i −0.178707 0.309529i
\(502\) 1.05573 1.82857i 0.0471195 0.0816133i
\(503\) 32.0000 1.42681 0.713405 0.700752i \(-0.247152\pi\)
0.713405 + 0.700752i \(0.247152\pi\)
\(504\) 0 0
\(505\) 14.0000 0.622992
\(506\) 11.0557 19.1491i 0.491487 0.851281i
\(507\) 3.50000 + 6.06218i 0.155440 + 0.269231i
\(508\) −19.4164 33.6302i −0.861464 1.49210i
\(509\) −5.94427 + 10.2958i −0.263475 + 0.456352i −0.967163 0.254157i \(-0.918202\pi\)
0.703688 + 0.710509i \(0.251535\pi\)
\(510\) −4.47214 −0.198030
\(511\) 0 0
\(512\) 11.1803 0.494106
\(513\) 3.23607 5.60503i 0.142876 0.247468i
\(514\) −1.18034 2.04441i −0.0520626 0.0901750i
\(515\) 0 0
\(516\) −13.4164 + 23.2379i −0.590624 + 1.02299i
\(517\) 12.2229 0.537563
\(518\) 0 0
\(519\) −14.9443 −0.655981
\(520\) −5.00000 + 8.66025i −0.219265 + 0.379777i
\(521\) −7.94427 13.7599i −0.348045 0.602831i 0.637857 0.770155i \(-0.279821\pi\)
−0.985902 + 0.167323i \(0.946488\pi\)
\(522\) 2.23607 + 3.87298i 0.0978700 + 0.169516i
\(523\) −4.47214 + 7.74597i −0.195553 + 0.338707i −0.947082 0.320993i \(-0.895983\pi\)
0.751529 + 0.659700i \(0.229317\pi\)
\(524\) 12.0000 0.524222
\(525\) 0 0
\(526\) 55.7771 2.43200
\(527\) 10.4721 18.1383i 0.456173 0.790116i
\(528\) 1.23607 + 2.14093i 0.0537930 + 0.0931721i
\(529\) 3.50000 + 6.06218i 0.152174 + 0.263573i
\(530\) −13.9443 + 24.1522i −0.605700 + 1.04910i
\(531\) 8.94427 0.388148
\(532\) 0 0
\(533\) 8.94427 0.387419
\(534\) −2.23607 + 3.87298i −0.0967641 + 0.167600i
\(535\) 2.47214 + 4.28187i 0.106880 + 0.185121i
\(536\) 4.47214 + 7.74597i 0.193167 + 0.334575i
\(537\) −1.23607 + 2.14093i −0.0533403 + 0.0923881i
\(538\) −53.4164 −2.30294
\(539\) 0 0
\(540\) 3.00000 0.129099
\(541\) −11.9443 + 20.6881i −0.513524 + 0.889450i 0.486353 + 0.873763i \(0.338327\pi\)
−0.999877 + 0.0156876i \(0.995006\pi\)
\(542\) 11.7082 + 20.2792i 0.502910 + 0.871066i
\(543\) 9.47214 + 16.4062i 0.406488 + 0.704058i
\(544\) −6.70820 + 11.6190i −0.287612 + 0.498158i
\(545\) 2.00000 0.0856706
\(546\) 0 0
\(547\) −29.8885 −1.27794 −0.638971 0.769231i \(-0.720640\pi\)
−0.638971 + 0.769231i \(0.720640\pi\)
\(548\) −18.7082 + 32.4036i −0.799175 + 1.38421i
\(549\) 1.00000 + 1.73205i 0.0426790 + 0.0739221i
\(550\) 2.76393 + 4.78727i 0.117854 + 0.204130i
\(551\) 6.47214 11.2101i 0.275722 0.477565i
\(552\) −8.94427 −0.380693
\(553\) 0 0
\(554\) 2.36068 0.100296
\(555\) −5.47214 + 9.47802i −0.232279 + 0.402319i
\(556\) 29.1246 + 50.4453i 1.23516 + 2.13936i
\(557\) −5.76393 9.98342i −0.244226 0.423011i 0.717688 0.696365i \(-0.245200\pi\)
−0.961914 + 0.273354i \(0.911867\pi\)
\(558\) −11.7082 + 20.2792i −0.495648 + 0.858487i
\(559\) 40.0000 1.69182
\(560\) 0 0
\(561\) −4.94427 −0.208747
\(562\) −7.76393 + 13.4475i −0.327502 + 0.567250i
\(563\) 10.9443 + 18.9560i 0.461246 + 0.798902i 0.999023 0.0441853i \(-0.0140692\pi\)
−0.537777 + 0.843087i \(0.680736\pi\)
\(564\) −7.41641 12.8456i −0.312287 0.540897i
\(565\) −4.23607 + 7.33708i −0.178213 + 0.308673i
\(566\) 26.8328 1.12787
\(567\) 0 0
\(568\) 32.3607 1.35782
\(569\) 2.05573 3.56063i 0.0861806 0.149269i −0.819713 0.572774i \(-0.805867\pi\)
0.905894 + 0.423505i \(0.139200\pi\)
\(570\) −7.23607 12.5332i −0.303086 0.524960i
\(571\) 2.00000 + 3.46410i 0.0836974 + 0.144968i 0.904835 0.425762i \(-0.139994\pi\)
−0.821138 + 0.570730i \(0.806660\pi\)
\(572\) −16.5836 + 28.7236i −0.693395 + 1.20100i
\(573\) −27.4164 −1.14534
\(574\) 0 0
\(575\) 4.00000 0.166812
\(576\) 6.50000 11.2583i 0.270833 0.469097i
\(577\) 17.1803 + 29.7572i 0.715227 + 1.23881i 0.962872 + 0.269959i \(0.0870100\pi\)
−0.247645 + 0.968851i \(0.579657\pi\)
\(578\) 14.5344 + 25.1744i 0.604553 + 1.04712i
\(579\) −7.00000 + 12.1244i −0.290910 + 0.503871i
\(580\) 6.00000 0.249136
\(581\) 0 0
\(582\) 1.05573 0.0437613
\(583\) −15.4164 + 26.7020i −0.638482 + 1.10588i
\(584\) 3.94427 + 6.83168i 0.163215 + 0.282697i
\(585\) −2.23607 3.87298i −0.0924500 0.160128i
\(586\) −25.6525 + 44.4314i −1.05969 + 1.83544i
\(587\) −4.00000 −0.165098 −0.0825488 0.996587i \(-0.526306\pi\)
−0.0825488 + 0.996587i \(0.526306\pi\)
\(588\) 0 0
\(589\) 67.7771 2.79271
\(590\) 10.0000 17.3205i 0.411693 0.713074i
\(591\) 12.2361 + 21.1935i 0.503325 + 0.871784i
\(592\) 5.47214 + 9.47802i 0.224903 + 0.389544i
\(593\) 5.94427 10.2958i 0.244102 0.422797i −0.717777 0.696273i \(-0.754840\pi\)
0.961879 + 0.273476i \(0.0881735\pi\)
\(594\) 5.52786 0.226811
\(595\) 0 0
\(596\) 8.83282 0.361806
\(597\) 0.291796 0.505406i 0.0119424 0.0206849i
\(598\) 20.0000 + 34.6410i 0.817861 + 1.41658i
\(599\) 16.1803 + 28.0252i 0.661111 + 1.14508i 0.980324 + 0.197395i \(0.0632480\pi\)
−0.319213 + 0.947683i \(0.603419\pi\)
\(600\) 1.11803 1.93649i 0.0456435 0.0790569i
\(601\) 21.0557 0.858881 0.429441 0.903095i \(-0.358711\pi\)
0.429441 + 0.903095i \(0.358711\pi\)
\(602\) 0 0
\(603\) −4.00000 −0.162893
\(604\) 24.0000 41.5692i 0.976546 1.69143i
\(605\) −2.44427 4.23360i −0.0993738 0.172120i
\(606\) −15.6525 27.1109i −0.635838 1.10130i
\(607\) 7.41641 12.8456i 0.301023 0.521387i −0.675345 0.737502i \(-0.736005\pi\)
0.976368 + 0.216115i \(0.0693387\pi\)
\(608\) −43.4164 −1.76077
\(609\) 0 0
\(610\) 4.47214 0.181071
\(611\) −11.0557 + 19.1491i −0.447267 + 0.774689i
\(612\) 3.00000 + 5.19615i 0.121268 + 0.210042i
\(613\) −5.47214 9.47802i −0.221017 0.382814i 0.734100 0.679042i \(-0.237604\pi\)
−0.955117 + 0.296228i \(0.904271\pi\)
\(614\) 36.8328 63.7963i 1.48645 2.57461i
\(615\) −2.00000 −0.0806478
\(616\) 0 0
\(617\) 7.52786 0.303060 0.151530 0.988453i \(-0.451580\pi\)
0.151530 + 0.988453i \(0.451580\pi\)
\(618\) 0 0
\(619\) −6.29180 10.8977i −0.252889 0.438016i 0.711431 0.702756i \(-0.248047\pi\)
−0.964320 + 0.264740i \(0.914714\pi\)
\(620\) 15.7082 + 27.2074i 0.630857 + 1.09268i
\(621\) 2.00000 3.46410i 0.0802572 0.139010i
\(622\) −22.1115 −0.886589
\(623\) 0 0
\(624\) −4.47214 −0.179029
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −10.5279 18.2348i −0.420778 0.728809i
\(627\) −8.00000 13.8564i −0.319489 0.553372i
\(628\) −12.7082 + 22.0113i −0.507113 + 0.878345i
\(629\) −21.8885 −0.872753
\(630\) 0 0
\(631\) −22.8328 −0.908960 −0.454480 0.890757i \(-0.650175\pi\)
−0.454480 + 0.890757i \(0.650175\pi\)
\(632\) 5.52786 9.57454i 0.219887 0.380855i
\(633\) 0.472136 + 0.817763i 0.0187657 + 0.0325032i
\(634\) 33.9443 + 58.7932i 1.34810 + 2.33498i
\(635\) 6.47214 11.2101i 0.256839 0.444858i
\(636\) 37.4164 1.48366
\(637\) 0 0
\(638\) 11.0557 0.437700
\(639\) −7.23607 + 12.5332i −0.286254 + 0.495807i
\(640\) −7.82624 13.5554i −0.309359 0.535826i
\(641\) 18.4164 + 31.8982i 0.727404 + 1.25990i 0.957977 + 0.286846i \(0.0926068\pi\)
−0.230572 + 0.973055i \(0.574060\pi\)
\(642\) 5.52786 9.57454i 0.218167 0.377877i
\(643\) −32.9443 −1.29920 −0.649598 0.760278i \(-0.725063\pi\)
−0.649598 + 0.760278i \(0.725063\pi\)
\(644\) 0 0
\(645\) −8.94427 −0.352180
\(646\) 14.4721 25.0665i 0.569399 0.986227i
\(647\) −16.9443 29.3483i −0.666148 1.15380i −0.978973 0.203991i \(-0.934609\pi\)
0.312825 0.949811i \(-0.398725\pi\)
\(648\) −1.11803 1.93649i −0.0439205 0.0760726i
\(649\) 11.0557 19.1491i 0.433975 0.751667i
\(650\) −10.0000 −0.392232
\(651\) 0 0
\(652\) 2.83282 0.110942
\(653\) 24.7082 42.7959i 0.966907 1.67473i 0.262504 0.964931i \(-0.415452\pi\)
0.704403 0.709801i \(-0.251215\pi\)
\(654\) −2.23607 3.87298i −0.0874372 0.151446i
\(655\) 2.00000 + 3.46410i 0.0781465 + 0.135354i
\(656\) −1.00000 + 1.73205i −0.0390434 + 0.0676252i
\(657\) −3.52786 −0.137635
\(658\) 0 0
\(659\) −41.3050 −1.60901 −0.804506 0.593944i \(-0.797570\pi\)
−0.804506 + 0.593944i \(0.797570\pi\)
\(660\) 3.70820 6.42280i 0.144342 0.250007i
\(661\) 0.0557281 + 0.0965239i 0.00216757 + 0.00375434i 0.867107 0.498122i \(-0.165977\pi\)
−0.864940 + 0.501876i \(0.832643\pi\)
\(662\) 18.9443 + 32.8124i 0.736290 + 1.27529i
\(663\) 4.47214 7.74597i 0.173683 0.300828i
\(664\) 2.11146 0.0819404
\(665\) 0 0
\(666\) 24.4721 0.948276
\(667\) 4.00000 6.92820i 0.154881 0.268261i
\(668\) 12.0000 + 20.7846i 0.464294 + 0.804181i
\(669\) 2.47214 + 4.28187i 0.0955783 + 0.165546i
\(670\) −4.47214 + 7.74597i −0.172774 + 0.299253i
\(671\) 4.94427 0.190872
\(672\) 0 0
\(673\) −44.8328 −1.72818 −0.864089 0.503339i \(-0.832105\pi\)
−0.864089 + 0.503339i \(0.832105\pi\)
\(674\) −13.2918 + 23.0221i −0.511981 + 0.886777i
\(675\) 0.500000 + 0.866025i 0.0192450 + 0.0333333i
\(676\) −10.5000 18.1865i −0.403846 0.699482i
\(677\) −19.4721 + 33.7267i −0.748375 + 1.29622i 0.200226 + 0.979750i \(0.435832\pi\)
−0.948601 + 0.316474i \(0.897501\pi\)
\(678\) 18.9443 0.727550
\(679\) 0 0
\(680\) 4.47214 0.171499
\(681\) −8.47214 + 14.6742i −0.324653 + 0.562315i
\(682\) 28.9443 + 50.1329i 1.10833 + 1.91969i
\(683\) −16.9443 29.3483i −0.648355 1.12298i −0.983516 0.180822i \(-0.942124\pi\)
0.335161 0.942161i \(-0.391209\pi\)
\(684\) −9.70820 + 16.8151i −0.371202 + 0.642942i
\(685\) −12.4721 −0.476536
\(686\) 0 0
\(687\) 11.8885 0.453576
\(688\) −4.47214 + 7.74597i −0.170499 + 0.295312i
\(689\) −27.8885 48.3044i −1.06247 1.84025i
\(690\) −4.47214 7.74597i −0.170251 0.294884i
\(691\) 0.180340 0.312358i 0.00686045 0.0118827i −0.862575 0.505930i \(-0.831150\pi\)
0.869435 + 0.494047i \(0.164483\pi\)
\(692\) 44.8328 1.70429
\(693\) 0 0
\(694\) −17.8885 −0.679040
\(695\) −9.70820 + 16.8151i −0.368253 + 0.637833i
\(696\) −2.23607 3.87298i −0.0847579 0.146805i
\(697\) −2.00000 3.46410i −0.0757554 0.131212i
\(698\) −26.7082 + 46.2600i −1.01092 + 1.75097i
\(699\) −17.4164 −0.658749
\(700\) 0 0
\(701\) −34.0000 −1.28416 −0.642081 0.766637i \(-0.721929\pi\)
−0.642081 + 0.766637i \(0.721929\pi\)
\(702\) −5.00000 + 8.66025i −0.188713 + 0.326860i
\(703\) −35.4164 61.3430i −1.33576 2.31360i
\(704\) −16.0689 27.8321i −0.605619 1.04896i
\(705\) 2.47214 4.28187i 0.0931060 0.161264i
\(706\) −62.3607 −2.34698
\(707\) 0 0
\(708\) −26.8328 −1.00844
\(709\) 22.8885 39.6441i 0.859597 1.48887i −0.0127162 0.999919i \(-0.504048\pi\)
0.872313 0.488947i \(-0.162619\pi\)
\(710\) 16.1803 + 28.0252i 0.607237 + 1.05177i
\(711\) 2.47214 + 4.28187i 0.0927123 + 0.160582i
\(712\) 2.23607 3.87298i 0.0838002 0.145146i
\(713\) 41.8885 1.56874
\(714\) 0 0
\(715\) −11.0557 −0.413461
\(716\) 3.70820 6.42280i 0.138582 0.240031i
\(717\) −0.763932 1.32317i −0.0285296 0.0494147i
\(718\) −10.6525 18.4506i −0.397547 0.688571i
\(719\) −23.4164 + 40.5584i −0.873285 + 1.51257i −0.0147058 + 0.999892i \(0.504681\pi\)
−0.858579 + 0.512682i \(0.828652\pi\)
\(720\) 1.00000 0.0372678
\(721\) 0 0
\(722\) 51.1803 1.90474
\(723\) −0.527864 + 0.914287i −0.0196315 + 0.0340027i
\(724\) −28.4164 49.2187i −1.05609 1.82920i
\(725\) 1.00000 + 1.73205i 0.0371391 + 0.0643268i
\(726\) −5.46556 + 9.46662i −0.202846 + 0.351339i
\(727\) 14.8328 0.550119 0.275059 0.961427i \(-0.411302\pi\)
0.275059 + 0.961427i \(0.411302\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −3.94427 + 6.83168i −0.145984 + 0.252852i
\(731\) −8.94427 15.4919i −0.330816 0.572990i
\(732\) −3.00000 5.19615i −0.110883 0.192055i
\(733\) −18.7082 + 32.4036i −0.691003 + 1.19685i 0.280506 + 0.959852i \(0.409498\pi\)
−0.971510 + 0.237001i \(0.923836\pi\)
\(734\) 46.8328 1.72863
\(735\) 0 0
\(736\) −26.8328 −0.989071
\(737\) −4.94427 + 8.56373i −0.182125 + 0.315449i
\(738\) 2.23607 + 3.87298i 0.0823108 + 0.142566i
\(739\) −14.9443 25.8842i −0.549734 0.952167i −0.998292 0.0584136i \(-0.981396\pi\)
0.448559 0.893753i \(-0.351938\pi\)
\(740\) 16.4164 28.4341i 0.603479 1.04526i
\(741\) 28.9443 1.06329
\(742\) 0 0
\(743\) −18.8328 −0.690909 −0.345455 0.938436i \(-0.612275\pi\)
−0.345455 + 0.938436i \(0.612275\pi\)
\(744\) 11.7082 20.2792i 0.429244 0.743472i
\(745\) 1.47214 + 2.54981i 0.0539349 + 0.0934180i
\(746\) −6.70820 11.6190i −0.245605 0.425400i
\(747\) −0.472136 + 0.817763i −0.0172746 + 0.0299204i
\(748\) 14.8328 0.542341
\(749\) 0 0
\(750\) 2.23607 0.0816497
\(751\) 1.52786 2.64634i 0.0557526 0.0965663i −0.836802 0.547505i \(-0.815578\pi\)
0.892555 + 0.450939i \(0.148911\pi\)
\(752\) −2.47214 4.28187i −0.0901495 0.156144i
\(753\) −0.472136 0.817763i −0.0172056 0.0298010i
\(754\) −10.0000 + 17.3205i −0.364179 + 0.630776i
\(755\) 16.0000 0.582300
\(756\) 0 0
\(757\) −3.88854 −0.141332 −0.0706658 0.997500i \(-0.522512\pi\)
−0.0706658 + 0.997500i \(0.522512\pi\)
\(758\) 2.36068 4.08882i 0.0857438 0.148513i
\(759\) −4.94427 8.56373i −0.179466 0.310844i
\(760\) 7.23607 + 12.5332i 0.262480 + 0.454628i
\(761\) −3.94427 + 6.83168i −0.142980 + 0.247648i −0.928617 0.371039i \(-0.879002\pi\)
0.785638 + 0.618687i \(0.212335\pi\)
\(762\) −28.9443 −1.04854
\(763\) 0 0
\(764\) 82.2492 2.97567
\(765\) −1.00000 + 1.73205i −0.0361551 + 0.0626224i
\(766\) 8.94427 + 15.4919i 0.323170 + 0.559746i
\(767\) 20.0000 + 34.6410i 0.722158 + 1.25081i
\(768\) −4.50000 + 7.79423i −0.162380 + 0.281250i
\(769\) 0.832816 0.0300321 0.0150161 0.999887i \(-0.495220\pi\)
0.0150161 + 0.999887i \(0.495220\pi\)
\(770\) 0 0
\(771\) −1.05573 −0.0380211
\(772\) 21.0000 36.3731i 0.755807 1.30910i
\(773\) 12.5279 + 21.6989i 0.450596 + 0.780455i 0.998423 0.0561365i \(-0.0178782\pi\)
−0.547827 + 0.836592i \(0.684545\pi\)
\(774\) 10.0000 + 17.3205i 0.359443 + 0.622573i
\(775\) −5.23607 + 9.06914i −0.188085 + 0.325773i
\(776\) −1.05573 −0.0378984
\(777\) 0 0
\(778\) 24.4721 0.877369
\(779\) 6.47214 11.2101i 0.231888 0.401642i
\(780\) 6.70820 + 11.6190i 0.240192 + 0.416025i
\(781\) 17.8885 + 30.9839i 0.640102 + 1.10869i
\(782\) 8.94427 15.4919i 0.319847 0.553990i
\(783\) 2.00000 0.0714742
\(784\) 0 0
\(785\) −8.47214 −0.302383
\(786\) 4.47214 7.74597i 0.159516 0.276289i
\(787\) −24.4721 42.3870i −0.872337 1.51093i −0.859572 0.511014i \(-0.829270\pi\)
−0.0127652 0.999919i \(-0.504063\pi\)
\(788\) −36.7082 63.5805i −1.30768 2.26496i
\(789\) 12.4721 21.6024i 0.444020 0.769065i
\(790\) 11.0557 0.393345
\(791\) 0 0
\(792\) −5.52786 −0.196424
\(793\) −4.47214 + 7.74597i −0.158810 + 0.275067i
\(794\) −15.0000 25.9808i −0.532330 0.922023i
\(795\) 6.23607 + 10.8012i 0.221171 + 0.383079i
\(796\) −0.875388 + 1.51622i −0.0310273 + 0.0537409i
\(797\) −1.05573 −0.0373958 −0.0186979 0.999825i \(-0.505952\pi\)
−0.0186979 + 0.999825i \(0.505952\pi\)
\(798\) 0 0
\(799\) 9.88854 0.349832
\(800\) 3.35410 5.80948i 0.118585 0.205396i
\(801\) 1.00000 + 1.73205i 0.0353333 + 0.0611990i
\(802\) −11.1803 19.3649i −0.394792 0.683799i
\(803\) −4.36068 + 7.55292i −0.153885 + 0.266537i
\(804\) 12.0000 0.423207
\(805\) 0 0
\(806\) −104.721 −3.68865
\(807\) −11.9443 + 20.6881i −0.420458 + 0.728255i
\(808\) 15.6525 + 27.1109i 0.550652 + 0.953758i
\(809\) −10.5279 18.2348i −0.370140 0.641101i 0.619447 0.785039i \(-0.287357\pi\)
−0.989587 + 0.143937i \(0.954024\pi\)
\(810\) 1.11803 1.93649i 0.0392837 0.0680414i
\(811\) 28.5836 1.00371 0.501853 0.864953i \(-0.332652\pi\)
0.501853 + 0.864953i \(0.332652\pi\)
\(812\) 0 0
\(813\) 10.4721 0.367274
\(814\) 30.2492 52.3932i 1.06023 1.83638i
\(815\) 0.472136 + 0.817763i 0.0165382 + 0.0286450i
\(816\) 1.00000 + 1.73205i 0.0350070 + 0.0606339i
\(817\) 28.9443 50.1329i 1.01263 1.75393i
\(818\) −53.4164 −1.86766
\(819\) 0 0
\(820\) 6.00000 0.209529
\(821\) 18.8885 32.7159i 0.659215 1.14179i −0.321605 0.946874i \(-0.604222\pi\)
0.980819 0.194919i \(-0.0624445\pi\)
\(822\) 13.9443 + 24.1522i 0.486362 + 0.842404i
\(823\) −13.5279 23.4309i −0.471552 0.816751i 0.527919 0.849295i \(-0.322973\pi\)
−0.999470 + 0.0325435i \(0.989639\pi\)
\(824\) 0 0
\(825\) 2.47214 0.0860687
\(826\) 0 0
\(827\) −4.94427 −0.171929 −0.0859646 0.996298i \(-0.527397\pi\)
−0.0859646 + 0.996298i \(0.527397\pi\)
\(828\) −6.00000 + 10.3923i −0.208514 + 0.361158i
\(829\) 15.4721 + 26.7985i 0.537369 + 0.930751i 0.999045 + 0.0437022i \(0.0139153\pi\)
−0.461675 + 0.887049i \(0.652751\pi\)
\(830\) 1.05573 + 1.82857i 0.0366449 + 0.0634708i
\(831\) 0.527864 0.914287i 0.0183114 0.0317163i
\(832\) 58.1378 2.01556
\(833\) 0 0
\(834\) 43.4164 1.50339
\(835\) −4.00000 + 6.92820i −0.138426 + 0.239760i
\(836\) 24.0000 + 41.5692i 0.830057 + 1.43770i
\(837\) 5.23607 + 9.06914i 0.180985 + 0.313475i
\(838\) −6.58359 + 11.4031i −0.227426 + 0.393914i
\(839\) 1.16718 0.0402957 0.0201478 0.999797i \(-0.493586\pi\)
0.0201478 + 0.999797i \(0.493586\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) −24.5967 + 42.6028i −0.847660 + 1.46819i
\(843\) 3.47214 + 6.01392i 0.119587 + 0.207130i
\(844\) −1.41641 2.45329i −0.0487548 0.0844457i
\(845\) 3.50000 6.06218i 0.120404 0.208545i
\(846\) −11.0557 −0.380104
\(847\) 0 0
\(848\) 12.4721 0.428295
\(849\) 6.00000 10.3923i 0.205919 0.356663i
\(850\) 2.23607 + 3.87298i 0.0766965 + 0.132842i
\(851\) −21.8885 37.9121i −0.750330 1.29961i
\(852\) 21.7082 37.5997i 0.743711 1.28814i
\(853\) 31.3050 1.07186 0.535931 0.844262i \(-0.319961\pi\)
0.535931 + 0.844262i \(0.319961\pi\)
\(854\) 0 0
\(855\) −6.47214 −0.221342
\(856\) −5.52786 + 9.57454i −0.188939 + 0.327251i
\(857\) 8.41641 + 14.5776i 0.287499 + 0.497963i 0.973212 0.229909i \(-0.0738429\pi\)
−0.685713 + 0.727872i \(0.740510\pi\)
\(858\) 12.3607 + 21.4093i 0.421987 + 0.730902i
\(859\) −20.7639 + 35.9642i −0.708456 + 1.22708i 0.256973 + 0.966418i \(0.417275\pi\)
−0.965430 + 0.260664i \(0.916059\pi\)
\(860\) 26.8328 0.914991
\(861\) 0 0
\(862\) −21.3050 −0.725650
\(863\) 6.94427 12.0278i 0.236386 0.409432i −0.723289 0.690546i \(-0.757370\pi\)
0.959675 + 0.281114i \(0.0907038\pi\)
\(864\) −3.35410 5.80948i −0.114109 0.197642i
\(865\) 7.47214 + 12.9421i 0.254060 + 0.440045i
\(866\) −8.41641 + 14.5776i −0.286001 + 0.495369i
\(867\) 13.0000 0.441503
\(868\) 0 0
\(869\) 12.2229 0.414634
\(870\) 2.23607 3.87298i 0.0758098 0.131306i
\(871\) −8.94427 15.4919i −0.303065 0.524924i
\(872\) 2.23607 + 3.87298i 0.0757228 + 0.131156i
\(873\) 0.236068 0.408882i 0.00798969 0.0138385i
\(874\) 57.8885 1.95811
\(875\) 0 0
\(876\) 10.5836 0.357586
\(877\) 1.58359 2.74286i 0.0534741 0.0926199i −0.838049 0.545595i \(-0.816304\pi\)
0.891523 + 0.452975i \(0.149637\pi\)
\(878\) −11.7082 20.2792i −0.395133 0.684390i
\(879\) 11.4721 + 19.8703i 0.386946 + 0.670209i
\(880\) 1.23607 2.14093i 0.0416678 0.0721708i
\(881\) 7.88854 0.265772 0.132886 0.991131i \(-0.457576\pi\)
0.132886 + 0.991131i \(0.457576\pi\)
\(882\) 0 0
\(883\) −2.11146 −0.0710562 −0.0355281 0.999369i \(-0.511311\pi\)
−0.0355281 + 0.999369i \(0.511311\pi\)
\(884\) −13.4164 + 23.2379i −0.451243 + 0.781575i
\(885\) −4.47214 7.74597i −0.150329 0.260378i
\(886\) 8.94427 + 15.4919i 0.300489 + 0.520462i
\(887\) −11.4164 + 19.7738i −0.383325 + 0.663939i −0.991535 0.129837i \(-0.958555\pi\)
0.608210 + 0.793776i \(0.291888\pi\)
\(888\) −24.4721 −0.821231
\(889\) 0 0
\(890\) 4.47214 0.149906
\(891\) 1.23607 2.14093i 0.0414098 0.0717239i
\(892\) −7.41641 12.8456i −0.248320 0.430102i
\(893\) 16.0000 + 27.7128i 0.535420 + 0.927374i
\(894\) 3.29180 5.70156i 0.110094 0.190689i
\(895\) 2.47214 0.0826344
\(896\) 0 0
\(897\) 17.8885 0.597281
\(898\) 15.6525 27.1109i 0.522330 0.904702i
\(899\) 10.4721 + 18.1383i 0.349265 + 0.604945i
\(900\) −1.50000 2.59808i −0.0500000 0.0866025i
\(901\) −12.4721 + 21.6024i −0.415507 + 0.719679i
\(902\) 11.0557 0.368115
\(903\) 0 0
\(904\) −18.9443 −0.630077
\(905\) 9.47214 16.4062i 0.314864 0.545361i
\(906\) −17.8885 30.9839i −0.594307 1.02937i
\(907\) −9.05573 15.6850i −0.300691 0.520811i 0.675602 0.737267i \(-0.263884\pi\)
−0.976293 + 0.216455i \(0.930550\pi\)
\(908\) 25.4164 44.0225i 0.843473 1.46094i
\(909\) −14.0000 −0.464351
\(910\) 0 0
\(911\) −34.2492 −1.13473 −0.567364 0.823467i \(-0.692037\pi\)
−0.567364 + 0.823467i \(0.692037\pi\)
\(912\) −3.23607 + 5.60503i −0.107157 + 0.185601i
\(913\) 1.16718 + 2.02162i 0.0386282 + 0.0669059i
\(914\) 12.2361 + 21.1935i 0.404733 + 0.701018i
\(915\) 1.00000 1.73205i 0.0330590 0.0572598i
\(916\) −35.6656 −1.17843
\(917\) 0 0
\(918\) 4.47214 0.147602
\(919\) 26.4721 45.8511i 0.873235 1.51249i 0.0146043 0.999893i \(-0.495351\pi\)
0.858631 0.512594i \(-0.171316\pi\)
\(920\) 4.47214 + 7.74597i 0.147442 + 0.255377i
\(921\) −16.4721 28.5306i −0.542775 0.940114i
\(922\) 35.6525 61.7519i 1.17415 2.03369i
\(923\) −64.7214 −2.13033
\(924\) 0 0
\(925\) 10.9443 0.359845
\(926\) −3.41641 + 5.91739i −0.112270 + 0.194458i
\(927\) 0 0
\(928\) −6.70820 11.6190i −0.220208 0.381411i
\(929\) 25.9443 44.9368i 0.851204 1.47433i −0.0289185 0.999582i \(-0.509206\pi\)
0.880122 0.474747i \(-0.157460\pi\)
\(930\) 23.4164 0.767854
\(931\) 0 0
\(932\) 52.2492 1.71148
\(933\) −4.94427 + 8.56373i −0.161868 + 0.280364i
\(934\) −10.0000 17.3205i −0.327210 0.566744i
\(935\) 2.47214 + 4.28187i 0.0808475 + 0.140032i
\(936\) 5.00000 8.66025i 0.163430 0.283069i
\(937\) −43.5279 −1.42199 −0.710997 0.703195i \(-0.751756\pi\)
−0.710997 + 0.703195i \(0.751756\pi\)
\(938\) 0 0
\(939\) −9.41641 −0.307293
\(940\) −7.41641 + 12.8456i −0.241897 + 0.418977i
\(941\) 15.0000 + 25.9808i 0.488986 + 0.846949i 0.999920 0.0126715i \(-0.00403357\pi\)
−0.510934 + 0.859620i \(0.670700\pi\)
\(942\) 9.47214 + 16.4062i 0.308619 + 0.534544i
\(943\) 4.00000 6.92820i 0.130258 0.225613i
\(944\) −8.94427 −0.291111
\(945\) 0 0
\(946\) 49.4427 1.60752
\(947\) −8.94427 + 15.4919i −0.290650 + 0.503420i −0.973964 0.226705i \(-0.927205\pi\)
0.683314 + 0.730125i \(0.260538\pi\)
\(948\) −7.41641 12.8456i −0.240874 0.417206i
\(949\) −7.88854 13.6634i −0.256073 0.443531i
\(950\) −7.23607 + 12.5332i −0.234769 + 0.406632i
\(951\) 30.3607 0.984512
\(952\) 0 0
\(953\) −6.58359 −0.213263 −0.106632 0.994299i \(-0.534007\pi\)
−0.106632 + 0.994299i \(0.534007\pi\)
\(954\) 13.9443 24.1522i 0.451462 0.781956i
\(955\) 13.7082 + 23.7433i 0.443587 + 0.768315i
\(956\) 2.29180 + 3.96951i 0.0741220 + 0.128383i
\(957\) 2.47214 4.28187i 0.0799128 0.138413i
\(958\) 40.0000 1.29234
\(959\) 0 0
\(960\) −13.0000 −0.419573
\(961\) −39.3328 + 68.1264i −1.26880 + 2.19763i
\(962\) 54.7214 + 94.7802i 1.76429 + 3.05584i
\(963\) −2.47214 4.28187i −0.0796635 0.137981i
\(964\) 1.58359 2.74286i 0.0510041 0.0883416i
\(965\) 14.0000 0.450676
\(966\) 0 0
\(967\) −9.88854 −0.317994 −0.158997 0.987279i \(-0.550826\pi\)
−0.158997 + 0.987279i \(0.550826\pi\)
\(968\) 5.46556 9.46662i 0.175670 0.304269i
\(969\) −6.47214 11.2101i −0.207915 0.360119i
\(970\) −0.527864 0.914287i −0.0169487 0.0293560i
\(971\) −11.5279 + 19.9668i −0.369947 + 0.640767i −0.989557 0.144143i \(-0.953957\pi\)
0.619610 + 0.784910i \(0.287291\pi\)
\(972\) −3.00000 −0.0962250
\(973\) 0 0
\(974\) −6.83282 −0.218938
\(975\) −2.23607 + 3.87298i −0.0716115 + 0.124035i
\(976\) −1.00000 1.73205i −0.0320092 0.0554416i
\(977\) −28.7082 49.7241i −0.918457 1.59081i −0.801760 0.597646i \(-0.796103\pi\)
−0.116697 0.993168i \(-0.537231\pi\)
\(978\) 1.05573 1.82857i 0.0337585 0.0584714i
\(979\) 4.94427 0.158020
\(980\) 0 0
\(981\) −2.00000 −0.0638551
\(982\) −46.1803 + 79.9867i −1.47367 + 2.55248i
\(983\) −15.4164 26.7020i −0.491707 0.851662i 0.508247 0.861211i \(-0.330294\pi\)
−0.999954 + 0.00954955i \(0.996960\pi\)
\(984\) −2.23607 3.87298i −0.0712832 0.123466i
\(985\) 12.2361 21.1935i 0.389874 0.675281i
\(986\) 8.94427 0.284844
\(987\) 0 0
\(988\) −86.8328 −2.76252
\(989\) 17.8885 30.9839i 0.568823 0.985230i
\(990\) −2.76393 4.78727i −0.0878435 0.152149i
\(991\) 6.47214 + 11.2101i 0.205594 + 0.356100i 0.950322 0.311269i \(-0.100754\pi\)
−0.744728 + 0.667368i \(0.767421\pi\)
\(992\) 35.1246 60.8376i 1.11521 1.93160i
\(993\) 16.9443 0.537710
\(994\) 0 0
\(995\) −0.583592 −0.0185011
\(996\) 1.41641 2.45329i 0.0448806 0.0777355i
\(997\) −10.7082 18.5472i −0.339132 0.587394i 0.645138 0.764066i \(-0.276800\pi\)
−0.984270 + 0.176672i \(0.943467\pi\)
\(998\) −24.4721 42.3870i −0.774652 1.34174i
\(999\) 5.47214 9.47802i 0.173131 0.299871i
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 735.2.i.k.226.1 4
7.2 even 3 105.2.a.b.1.2 2
7.3 odd 6 735.2.i.i.361.1 4
7.4 even 3 inner 735.2.i.k.361.1 4
7.5 odd 6 735.2.a.k.1.2 2
7.6 odd 2 735.2.i.i.226.1 4
21.2 odd 6 315.2.a.d.1.1 2
21.5 even 6 2205.2.a.w.1.1 2
28.23 odd 6 1680.2.a.v.1.2 2
35.2 odd 12 525.2.d.c.274.4 4
35.9 even 6 525.2.a.g.1.1 2
35.19 odd 6 3675.2.a.y.1.1 2
35.23 odd 12 525.2.d.c.274.1 4
56.37 even 6 6720.2.a.cx.1.2 2
56.51 odd 6 6720.2.a.cs.1.1 2
84.23 even 6 5040.2.a.bw.1.1 2
105.2 even 12 1575.2.d.d.1324.2 4
105.23 even 12 1575.2.d.d.1324.3 4
105.44 odd 6 1575.2.a.r.1.2 2
140.79 odd 6 8400.2.a.cx.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.a.b.1.2 2 7.2 even 3
315.2.a.d.1.1 2 21.2 odd 6
525.2.a.g.1.1 2 35.9 even 6
525.2.d.c.274.1 4 35.23 odd 12
525.2.d.c.274.4 4 35.2 odd 12
735.2.a.k.1.2 2 7.5 odd 6
735.2.i.i.226.1 4 7.6 odd 2
735.2.i.i.361.1 4 7.3 odd 6
735.2.i.k.226.1 4 1.1 even 1 trivial
735.2.i.k.361.1 4 7.4 even 3 inner
1575.2.a.r.1.2 2 105.44 odd 6
1575.2.d.d.1324.2 4 105.2 even 12
1575.2.d.d.1324.3 4 105.23 even 12
1680.2.a.v.1.2 2 28.23 odd 6
2205.2.a.w.1.1 2 21.5 even 6
3675.2.a.y.1.1 2 35.19 odd 6
5040.2.a.bw.1.1 2 84.23 even 6
6720.2.a.cs.1.1 2 56.51 odd 6
6720.2.a.cx.1.2 2 56.37 even 6
8400.2.a.cx.1.2 2 140.79 odd 6