Properties

Label 1950.2.y.m.49.3
Level $1950$
Weight $2$
Character 1950.49
Analytic conductor $15.571$
Analytic rank $0$
Dimension $12$
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] = [1950,2,Mod(49,1950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1950.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.y (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 6 x^{11} + 87 x^{10} - 380 x^{9} + 2556 x^{8} - 8010 x^{7} + 29687 x^{6} - 62556 x^{5} + 115386 x^{4} - 135130 x^{3} + 113253 x^{2} - 54888 x + 14089 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.3
Root \(0.500000 - 1.72434i\) of defining polynomial
Character \(\chi\) \(=\) 1950.49
Dual form 1950.2.y.m.199.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(1.79518 - 3.10934i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(1.79518 - 3.10934i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-4.72163 + 2.72603i) q^{11} -1.00000i q^{12} +(-3.60494 + 0.0664404i) q^{13} -3.59036 q^{14} +(-0.500000 - 0.866025i) q^{16} +(6.33097 + 3.65519i) q^{17} -1.00000 q^{18} +(3.34713 + 1.93247i) q^{19} +3.59036i q^{21} +(4.72163 + 2.72603i) q^{22} +(1.60934 - 0.929155i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(1.86001 + 3.08875i) q^{26} +1.00000i q^{27} +(1.79518 + 3.10934i) q^{28} +(-2.67578 - 4.63459i) q^{29} -2.23338i q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.72603 - 4.72163i) q^{33} -7.31038i q^{34} +(0.500000 + 0.866025i) q^{36} +(1.06644 + 1.84713i) q^{37} -3.86493i q^{38} +(3.08875 - 1.86001i) q^{39} +(-6.33097 + 3.65519i) q^{41} +(3.10934 - 1.79518i) q^{42} +(7.10996 + 4.10494i) q^{43} -5.45207i q^{44} +(-1.60934 - 0.929155i) q^{46} +5.07700 q^{47} +(0.866025 + 0.500000i) q^{48} +(-2.94535 - 5.10149i) q^{49} -7.31038 q^{51} +(1.74493 - 3.15519i) q^{52} +2.23338i q^{53} +(0.866025 - 0.500000i) q^{54} +(1.79518 - 3.10934i) q^{56} -3.86493 q^{57} +(-2.67578 + 4.63459i) q^{58} +(0.237785 + 0.137285i) q^{59} +(2.06644 - 3.57918i) q^{61} +(-1.93416 + 1.11669i) q^{62} +(-1.79518 - 3.10934i) q^{63} +1.00000 q^{64} -5.45207 q^{66} +(-7.39851 - 12.8146i) q^{67} +(-6.33097 + 3.65519i) q^{68} +(-0.929155 + 1.60934i) q^{69} +(12.3804 + 7.14784i) q^{71} +(0.500000 - 0.866025i) q^{72} +14.8975 q^{73} +(1.06644 - 1.84713i) q^{74} +(-3.34713 + 1.93247i) q^{76} +19.5749i q^{77} +(-3.15519 - 1.74493i) q^{78} -2.62105 q^{79} +(-0.500000 - 0.866025i) q^{81} +(6.33097 + 3.65519i) q^{82} +7.15988 q^{83} +(-3.10934 - 1.79518i) q^{84} -8.20988i q^{86} +(4.63459 + 2.67578i) q^{87} +(-4.72163 + 2.72603i) q^{88} +(-8.30844 + 4.79688i) q^{89} +(-6.26493 + 11.3283i) q^{91} +1.85831i q^{92} +(1.11669 + 1.93416i) q^{93} +(-2.53850 - 4.39681i) q^{94} -1.00000i q^{96} +(-0.954155 + 1.65264i) q^{97} +(-2.94535 + 5.10149i) q^{98} +5.45207i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 6 q^{2} - 6 q^{4} + 4 q^{7} + 12 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 6 q^{2} - 6 q^{4} + 4 q^{7} + 12 q^{8} + 6 q^{9} - 12 q^{11} - 4 q^{13} - 8 q^{14} - 6 q^{16} - 12 q^{18} + 6 q^{19} + 12 q^{22} - 12 q^{23} - 4 q^{26} + 4 q^{28} - 6 q^{32} - 4 q^{33} + 6 q^{36} + 12 q^{37} - 6 q^{39} + 6 q^{42} - 12 q^{43} + 12 q^{46} - 16 q^{47} - 32 q^{49} + 8 q^{52} + 4 q^{56} - 24 q^{57} + 24 q^{61} - 4 q^{63} + 12 q^{64} + 8 q^{66} - 24 q^{67} - 4 q^{69} + 12 q^{71} + 6 q^{72} + 40 q^{73} + 12 q^{74} - 6 q^{76} + 6 q^{78} - 52 q^{79} - 6 q^{81} - 32 q^{83} - 6 q^{84} - 12 q^{88} - 24 q^{89} - 54 q^{91} + 8 q^{93} + 8 q^{94} - 24 q^{97} - 32 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) −0.866025 + 0.500000i −0.500000 + 0.288675i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0
\(6\) 0.866025 + 0.500000i 0.353553 + 0.204124i
\(7\) 1.79518 3.10934i 0.678514 1.17522i −0.296914 0.954904i \(-0.595957\pi\)
0.975428 0.220317i \(-0.0707092\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 0 0
\(11\) −4.72163 + 2.72603i −1.42362 + 0.821930i −0.996607 0.0823128i \(-0.973769\pi\)
−0.427018 + 0.904243i \(0.640436\pi\)
\(12\) 1.00000i 0.288675i
\(13\) −3.60494 + 0.0664404i −0.999830 + 0.0184272i
\(14\) −3.59036 −0.959564
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 6.33097 + 3.65519i 1.53549 + 0.886514i 0.999095 + 0.0425445i \(0.0135464\pi\)
0.536392 + 0.843969i \(0.319787\pi\)
\(18\) −1.00000 −0.235702
\(19\) 3.34713 + 1.93247i 0.767884 + 0.443338i 0.832119 0.554597i \(-0.187127\pi\)
−0.0642352 + 0.997935i \(0.520461\pi\)
\(20\) 0 0
\(21\) 3.59036i 0.783481i
\(22\) 4.72163 + 2.72603i 1.00665 + 0.581192i
\(23\) 1.60934 0.929155i 0.335571 0.193742i −0.322741 0.946487i \(-0.604604\pi\)
0.658312 + 0.752745i \(0.271271\pi\)
\(24\) −0.866025 + 0.500000i −0.176777 + 0.102062i
\(25\) 0 0
\(26\) 1.86001 + 3.08875i 0.364778 + 0.605753i
\(27\) 1.00000i 0.192450i
\(28\) 1.79518 + 3.10934i 0.339257 + 0.587611i
\(29\) −2.67578 4.63459i −0.496881 0.860622i 0.503113 0.864221i \(-0.332188\pi\)
−0.999994 + 0.00359821i \(0.998855\pi\)
\(30\) 0 0
\(31\) 2.23338i 0.401127i −0.979681 0.200563i \(-0.935723\pi\)
0.979681 0.200563i \(-0.0642773\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 2.72603 4.72163i 0.474542 0.821930i
\(34\) 7.31038i 1.25372i
\(35\) 0 0
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) 1.06644 + 1.84713i 0.175322 + 0.303666i 0.940273 0.340423i \(-0.110570\pi\)
−0.764951 + 0.644089i \(0.777237\pi\)
\(38\) 3.86493i 0.626975i
\(39\) 3.08875 1.86001i 0.494596 0.297840i
\(40\) 0 0
\(41\) −6.33097 + 3.65519i −0.988732 + 0.570845i −0.904895 0.425635i \(-0.860051\pi\)
−0.0838369 + 0.996479i \(0.526717\pi\)
\(42\) 3.10934 1.79518i 0.479782 0.277002i
\(43\) 7.10996 + 4.10494i 1.08426 + 0.625997i 0.932042 0.362350i \(-0.118025\pi\)
0.152217 + 0.988347i \(0.451359\pi\)
\(44\) 5.45207i 0.821930i
\(45\) 0 0
\(46\) −1.60934 0.929155i −0.237285 0.136996i
\(47\) 5.07700 0.740556 0.370278 0.928921i \(-0.379262\pi\)
0.370278 + 0.928921i \(0.379262\pi\)
\(48\) 0.866025 + 0.500000i 0.125000 + 0.0721688i
\(49\) −2.94535 5.10149i −0.420764 0.728784i
\(50\) 0 0
\(51\) −7.31038 −1.02366
\(52\) 1.74493 3.15519i 0.241978 0.437546i
\(53\) 2.23338i 0.306778i 0.988166 + 0.153389i \(0.0490188\pi\)
−0.988166 + 0.153389i \(0.950981\pi\)
\(54\) 0.866025 0.500000i 0.117851 0.0680414i
\(55\) 0 0
\(56\) 1.79518 3.10934i 0.239891 0.415504i
\(57\) −3.86493 −0.511923
\(58\) −2.67578 + 4.63459i −0.351348 + 0.608552i
\(59\) 0.237785 + 0.137285i 0.0309570 + 0.0178730i 0.515399 0.856951i \(-0.327644\pi\)
−0.484442 + 0.874824i \(0.660977\pi\)
\(60\) 0 0
\(61\) 2.06644 3.57918i 0.264581 0.458267i −0.702873 0.711315i \(-0.748100\pi\)
0.967454 + 0.253048i \(0.0814332\pi\)
\(62\) −1.93416 + 1.11669i −0.245639 + 0.141820i
\(63\) −1.79518 3.10934i −0.226171 0.391740i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −5.45207 −0.671103
\(67\) −7.39851 12.8146i −0.903872 1.56555i −0.822425 0.568874i \(-0.807379\pi\)
−0.0814466 0.996678i \(-0.525954\pi\)
\(68\) −6.33097 + 3.65519i −0.767743 + 0.443257i
\(69\) −0.929155 + 1.60934i −0.111857 + 0.193742i
\(70\) 0 0
\(71\) 12.3804 + 7.14784i 1.46929 + 0.848293i 0.999407 0.0344378i \(-0.0109641\pi\)
0.469879 + 0.882731i \(0.344297\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) 14.8975 1.74362 0.871811 0.489842i \(-0.162946\pi\)
0.871811 + 0.489842i \(0.162946\pi\)
\(74\) 1.06644 1.84713i 0.123971 0.214724i
\(75\) 0 0
\(76\) −3.34713 + 1.93247i −0.383942 + 0.221669i
\(77\) 19.5749i 2.23077i
\(78\) −3.15519 1.74493i −0.357255 0.197574i
\(79\) −2.62105 −0.294891 −0.147446 0.989070i \(-0.547105\pi\)
−0.147446 + 0.989070i \(0.547105\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 6.33097 + 3.65519i 0.699139 + 0.403648i
\(83\) 7.15988 0.785899 0.392949 0.919560i \(-0.371455\pi\)
0.392949 + 0.919560i \(0.371455\pi\)
\(84\) −3.10934 1.79518i −0.339257 0.195870i
\(85\) 0 0
\(86\) 8.20988i 0.885294i
\(87\) 4.63459 + 2.67578i 0.496881 + 0.286874i
\(88\) −4.72163 + 2.72603i −0.503327 + 0.290596i
\(89\) −8.30844 + 4.79688i −0.880693 + 0.508468i −0.870887 0.491484i \(-0.836455\pi\)
−0.00980594 + 0.999952i \(0.503121\pi\)
\(90\) 0 0
\(91\) −6.26493 + 11.3283i −0.656743 + 1.18753i
\(92\) 1.85831i 0.193742i
\(93\) 1.11669 + 1.93416i 0.115795 + 0.200563i
\(94\) −2.53850 4.39681i −0.261826 0.453496i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) −0.954155 + 1.65264i −0.0968797 + 0.167801i −0.910392 0.413748i \(-0.864220\pi\)
0.813512 + 0.581548i \(0.197553\pi\)
\(98\) −2.94535 + 5.10149i −0.297525 + 0.515328i
\(99\) 5.45207i 0.547953i
\(100\) 0 0
\(101\) 8.12785 + 14.0779i 0.808752 + 1.40080i 0.913729 + 0.406324i \(0.133190\pi\)
−0.104978 + 0.994475i \(0.533477\pi\)
\(102\) 3.65519 + 6.33097i 0.361918 + 0.626860i
\(103\) 12.9760i 1.27857i −0.768971 0.639284i \(-0.779231\pi\)
0.768971 0.639284i \(-0.220769\pi\)
\(104\) −3.60494 + 0.0664404i −0.353493 + 0.00651501i
\(105\) 0 0
\(106\) 1.93416 1.11669i 0.187863 0.108463i
\(107\) 8.58814 4.95837i 0.830247 0.479343i −0.0236901 0.999719i \(-0.507541\pi\)
0.853937 + 0.520376i \(0.174208\pi\)
\(108\) −0.866025 0.500000i −0.0833333 0.0481125i
\(109\) 7.41088i 0.709833i −0.934898 0.354917i \(-0.884509\pi\)
0.934898 0.354917i \(-0.115491\pi\)
\(110\) 0 0
\(111\) −1.84713 1.06644i −0.175322 0.101222i
\(112\) −3.59036 −0.339257
\(113\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(114\) 1.93247 + 3.34713i 0.180992 + 0.313487i
\(115\) 0 0
\(116\) 5.35157 0.496881
\(117\) −1.74493 + 3.15519i −0.161319 + 0.291697i
\(118\) 0.274571i 0.0252763i
\(119\) 22.7305 13.1234i 2.08370 1.20302i
\(120\) 0 0
\(121\) 9.36252 16.2164i 0.851138 1.47421i
\(122\) −4.13288 −0.374173
\(123\) 3.65519 6.33097i 0.329577 0.570845i
\(124\) 1.93416 + 1.11669i 0.173693 + 0.100282i
\(125\) 0 0
\(126\) −1.79518 + 3.10934i −0.159927 + 0.277002i
\(127\) 15.5772 8.99351i 1.38225 0.798045i 0.389828 0.920888i \(-0.372534\pi\)
0.992426 + 0.122843i \(0.0392011\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) −8.20988 −0.722839
\(130\) 0 0
\(131\) 20.3462 1.77765 0.888827 0.458242i \(-0.151521\pi\)
0.888827 + 0.458242i \(0.151521\pi\)
\(132\) 2.72603 + 4.72163i 0.237271 + 0.410965i
\(133\) 12.0174 6.93825i 1.04204 0.601623i
\(134\) −7.39851 + 12.8146i −0.639134 + 1.10701i
\(135\) 0 0
\(136\) 6.33097 + 3.65519i 0.542876 + 0.313430i
\(137\) 5.52037 9.56156i 0.471637 0.816899i −0.527837 0.849346i \(-0.676997\pi\)
0.999473 + 0.0324469i \(0.0103300\pi\)
\(138\) 1.85831 0.158190
\(139\) 4.85096 8.40212i 0.411453 0.712658i −0.583596 0.812044i \(-0.698355\pi\)
0.995049 + 0.0993864i \(0.0316880\pi\)
\(140\) 0 0
\(141\) −4.39681 + 2.53850i −0.370278 + 0.213780i
\(142\) 14.2957i 1.19967i
\(143\) 16.8401 10.1409i 1.40824 0.848024i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) −7.44876 12.9016i −0.616464 1.06775i
\(147\) 5.10149 + 2.94535i 0.420764 + 0.242928i
\(148\) −2.13288 −0.175322
\(149\) 4.70959 + 2.71908i 0.385825 + 0.222756i 0.680350 0.732888i \(-0.261828\pi\)
−0.294525 + 0.955644i \(0.595161\pi\)
\(150\) 0 0
\(151\) 17.8010i 1.44862i 0.689472 + 0.724312i \(0.257843\pi\)
−0.689472 + 0.724312i \(0.742157\pi\)
\(152\) 3.34713 + 1.93247i 0.271488 + 0.156744i
\(153\) 6.33097 3.65519i 0.511829 0.295505i
\(154\) 16.9524 9.78745i 1.36606 0.788695i
\(155\) 0 0
\(156\) 0.0664404 + 3.60494i 0.00531949 + 0.288626i
\(157\) 5.93652i 0.473786i −0.971536 0.236893i \(-0.923871\pi\)
0.971536 0.236893i \(-0.0761290\pi\)
\(158\) 1.31052 + 2.26990i 0.104260 + 0.180583i
\(159\) −1.11669 1.93416i −0.0885593 0.153389i
\(160\) 0 0
\(161\) 6.67200i 0.525828i
\(162\) −0.500000 + 0.866025i −0.0392837 + 0.0680414i
\(163\) −7.79688 + 13.5046i −0.610699 + 1.05776i 0.380424 + 0.924812i \(0.375778\pi\)
−0.991123 + 0.132949i \(0.957555\pi\)
\(164\) 7.31038i 0.570845i
\(165\) 0 0
\(166\) −3.57994 6.20064i −0.277857 0.481263i
\(167\) 0.929155 + 1.60934i 0.0719002 + 0.124535i 0.899734 0.436439i \(-0.143760\pi\)
−0.827834 + 0.560973i \(0.810427\pi\)
\(168\) 3.59036i 0.277002i
\(169\) 12.9912 0.479027i 0.999321 0.0368482i
\(170\) 0 0
\(171\) 3.34713 1.93247i 0.255961 0.147779i
\(172\) −7.10996 + 4.10494i −0.542130 + 0.312999i
\(173\) 21.0768 + 12.1687i 1.60244 + 0.925168i 0.990998 + 0.133878i \(0.0427430\pi\)
0.611441 + 0.791290i \(0.290590\pi\)
\(174\) 5.35157i 0.405701i
\(175\) 0 0
\(176\) 4.72163 + 2.72603i 0.355906 + 0.205483i
\(177\) −0.274571 −0.0206380
\(178\) 8.30844 + 4.79688i 0.622744 + 0.359541i
\(179\) −1.53429 2.65746i −0.114678 0.198628i 0.802973 0.596015i \(-0.203250\pi\)
−0.917651 + 0.397387i \(0.869917\pi\)
\(180\) 0 0
\(181\) −4.59376 −0.341451 −0.170726 0.985319i \(-0.554611\pi\)
−0.170726 + 0.985319i \(0.554611\pi\)
\(182\) 12.9430 0.238545i 0.959401 0.0176821i
\(183\) 4.13288i 0.305511i
\(184\) 1.60934 0.929155i 0.118642 0.0684982i
\(185\) 0 0
\(186\) 1.11669 1.93416i 0.0818797 0.141820i
\(187\) −39.8567 −2.91461
\(188\) −2.53850 + 4.39681i −0.185139 + 0.320670i
\(189\) 3.10934 + 1.79518i 0.226171 + 0.130580i
\(190\) 0 0
\(191\) −7.03007 + 12.1764i −0.508678 + 0.881056i 0.491272 + 0.871006i \(0.336532\pi\)
−0.999950 + 0.0100494i \(0.996801\pi\)
\(192\) −0.866025 + 0.500000i −0.0625000 + 0.0360844i
\(193\) −12.5444 21.7276i −0.902966 1.56398i −0.823624 0.567136i \(-0.808051\pi\)
−0.0793424 0.996847i \(-0.525282\pi\)
\(194\) 1.90831 0.137009
\(195\) 0 0
\(196\) 5.89069 0.420764
\(197\) 4.59737 + 7.96287i 0.327549 + 0.567331i 0.982025 0.188752i \(-0.0604441\pi\)
−0.654476 + 0.756083i \(0.727111\pi\)
\(198\) 4.72163 2.72603i 0.335552 0.193731i
\(199\) 11.8396 20.5068i 0.839286 1.45369i −0.0512060 0.998688i \(-0.516306\pi\)
0.890492 0.454998i \(-0.150360\pi\)
\(200\) 0 0
\(201\) 12.8146 + 7.39851i 0.903872 + 0.521850i
\(202\) 8.12785 14.0779i 0.571874 0.990514i
\(203\) −19.2141 −1.34856
\(204\) 3.65519 6.33097i 0.255914 0.443257i
\(205\) 0 0
\(206\) −11.2376 + 6.48802i −0.782960 + 0.452042i
\(207\) 1.85831i 0.129161i
\(208\) 1.86001 + 3.08875i 0.128968 + 0.214166i
\(209\) −21.0719 −1.45757
\(210\) 0 0
\(211\) 4.99303 + 8.64818i 0.343734 + 0.595366i 0.985123 0.171851i \(-0.0549747\pi\)
−0.641389 + 0.767216i \(0.721641\pi\)
\(212\) −1.93416 1.11669i −0.132839 0.0766946i
\(213\) −14.2957 −0.979524
\(214\) −8.58814 4.95837i −0.587073 0.338947i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) −6.94435 4.00932i −0.471413 0.272170i
\(218\) −6.41801 + 3.70544i −0.434682 + 0.250964i
\(219\) −12.9016 + 7.44876i −0.871811 + 0.503340i
\(220\) 0 0
\(221\) −23.0656 12.7561i −1.55156 0.858068i
\(222\) 2.13288i 0.143150i
\(223\) 11.1910 + 19.3833i 0.749404 + 1.29801i 0.948109 + 0.317946i \(0.102993\pi\)
−0.198705 + 0.980059i \(0.563674\pi\)
\(224\) 1.79518 + 3.10934i 0.119946 + 0.207752i
\(225\) 0 0
\(226\) 0 0
\(227\) −6.49265 + 11.2456i −0.430933 + 0.746397i −0.996954 0.0779935i \(-0.975149\pi\)
0.566021 + 0.824391i \(0.308482\pi\)
\(228\) 1.93247 3.34713i 0.127981 0.221669i
\(229\) 14.4455i 0.954587i 0.878744 + 0.477293i \(0.158382\pi\)
−0.878744 + 0.477293i \(0.841618\pi\)
\(230\) 0 0
\(231\) −9.78745 16.9524i −0.643967 1.11538i
\(232\) −2.67578 4.63459i −0.175674 0.304276i
\(233\) 12.4374i 0.814800i −0.913250 0.407400i \(-0.866436\pi\)
0.913250 0.407400i \(-0.133564\pi\)
\(234\) 3.60494 0.0664404i 0.235662 0.00434334i
\(235\) 0 0
\(236\) −0.237785 + 0.137285i −0.0154785 + 0.00893652i
\(237\) 2.26990 1.31052i 0.147446 0.0851277i
\(238\) −22.7305 13.1234i −1.47340 0.850667i
\(239\) 4.16983i 0.269724i 0.990864 + 0.134862i \(0.0430591\pi\)
−0.990864 + 0.134862i \(0.956941\pi\)
\(240\) 0 0
\(241\) 1.63165 + 0.942035i 0.105104 + 0.0606818i 0.551631 0.834089i \(-0.314006\pi\)
−0.446527 + 0.894770i \(0.647339\pi\)
\(242\) −18.7250 −1.20369
\(243\) 0.866025 + 0.500000i 0.0555556 + 0.0320750i
\(244\) 2.06644 + 3.57918i 0.132290 + 0.229134i
\(245\) 0 0
\(246\) −7.31038 −0.466093
\(247\) −12.1946 6.74404i −0.775923 0.429113i
\(248\) 2.23338i 0.141820i
\(249\) −6.20064 + 3.57994i −0.392949 + 0.226869i
\(250\) 0 0
\(251\) 3.57502 6.19212i 0.225653 0.390843i −0.730862 0.682525i \(-0.760882\pi\)
0.956515 + 0.291682i \(0.0942150\pi\)
\(252\) 3.59036 0.226171
\(253\) −5.06582 + 8.77425i −0.318485 + 0.551632i
\(254\) −15.5772 8.99351i −0.977401 0.564303i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −17.7517 + 10.2489i −1.10732 + 0.639312i −0.938134 0.346272i \(-0.887447\pi\)
−0.169186 + 0.985584i \(0.554114\pi\)
\(258\) 4.10494 + 7.10996i 0.255562 + 0.442647i
\(259\) 7.65781 0.475833
\(260\) 0 0
\(261\) −5.35157 −0.331254
\(262\) −10.1731 17.6203i −0.628496 1.08859i
\(263\) 15.3313 8.85153i 0.945369 0.545809i 0.0537296 0.998556i \(-0.482889\pi\)
0.891639 + 0.452747i \(0.149556\pi\)
\(264\) 2.72603 4.72163i 0.167776 0.290596i
\(265\) 0 0
\(266\) −12.0174 6.93825i −0.736834 0.425411i
\(267\) 4.79688 8.30844i 0.293564 0.508468i
\(268\) 14.7970 0.903872
\(269\) −9.09319 + 15.7499i −0.554421 + 0.960286i 0.443527 + 0.896261i \(0.353727\pi\)
−0.997948 + 0.0640250i \(0.979606\pi\)
\(270\) 0 0
\(271\) 19.7188 11.3847i 1.19783 0.691569i 0.237762 0.971324i \(-0.423586\pi\)
0.960072 + 0.279754i \(0.0902529\pi\)
\(272\) 7.31038i 0.443257i
\(273\) −0.238545 12.9430i −0.0144374 0.783348i
\(274\) −11.0407 −0.666995
\(275\) 0 0
\(276\) −0.929155 1.60934i −0.0559286 0.0968711i
\(277\) −14.1649 8.17814i −0.851089 0.491377i 0.00992898 0.999951i \(-0.496839\pi\)
−0.861018 + 0.508574i \(0.830173\pi\)
\(278\) −9.70193 −0.581883
\(279\) −1.93416 1.11669i −0.115795 0.0668545i
\(280\) 0 0
\(281\) 7.82221i 0.466634i −0.972401 0.233317i \(-0.925042\pi\)
0.972401 0.233317i \(-0.0749580\pi\)
\(282\) 4.39681 + 2.53850i 0.261826 + 0.151165i
\(283\) 6.01483 3.47266i 0.357544 0.206428i −0.310459 0.950587i \(-0.600483\pi\)
0.668003 + 0.744159i \(0.267149\pi\)
\(284\) −12.3804 + 7.14784i −0.734643 + 0.424146i
\(285\) 0 0
\(286\) −17.2023 9.51348i −1.01719 0.562544i
\(287\) 26.2469i 1.54931i
\(288\) 0.500000 + 0.866025i 0.0294628 + 0.0510310i
\(289\) 18.2208 + 31.5594i 1.07181 + 1.85643i
\(290\) 0 0
\(291\) 1.90831i 0.111867i
\(292\) −7.44876 + 12.9016i −0.435906 + 0.755011i
\(293\) −13.2122 + 22.8841i −0.771863 + 1.33691i 0.164678 + 0.986347i \(0.447341\pi\)
−0.936541 + 0.350558i \(0.885992\pi\)
\(294\) 5.89069i 0.343552i
\(295\) 0 0
\(296\) 1.06644 + 1.84713i 0.0619856 + 0.107362i
\(297\) −2.72603 4.72163i −0.158181 0.273977i
\(298\) 5.43817i 0.315025i
\(299\) −5.73985 + 3.45647i −0.331944 + 0.199893i
\(300\) 0 0
\(301\) 25.5273 14.7382i 1.47137 0.849496i
\(302\) 15.4161 8.90050i 0.887098 0.512166i
\(303\) −14.0779 8.12785i −0.808752 0.466933i
\(304\) 3.86493i 0.221669i
\(305\) 0 0
\(306\) −6.33097 3.65519i −0.361918 0.208953i
\(307\) −7.08581 −0.404408 −0.202204 0.979343i \(-0.564810\pi\)
−0.202204 + 0.979343i \(0.564810\pi\)
\(308\) −16.9524 9.78745i −0.965950 0.557691i
\(309\) 6.48802 + 11.2376i 0.369091 + 0.639284i
\(310\) 0 0
\(311\) −1.83017 −0.103780 −0.0518898 0.998653i \(-0.516524\pi\)
−0.0518898 + 0.998653i \(0.516524\pi\)
\(312\) 3.08875 1.86001i 0.174866 0.105302i
\(313\) 12.2499i 0.692403i 0.938160 + 0.346201i \(0.112529\pi\)
−0.938160 + 0.346201i \(0.887471\pi\)
\(314\) −5.14117 + 2.96826i −0.290133 + 0.167509i
\(315\) 0 0
\(316\) 1.31052 2.26990i 0.0737228 0.127692i
\(317\) −6.25100 −0.351091 −0.175546 0.984471i \(-0.556169\pi\)
−0.175546 + 0.984471i \(0.556169\pi\)
\(318\) −1.11669 + 1.93416i −0.0626209 + 0.108463i
\(319\) 25.2681 + 14.5886i 1.41474 + 0.816802i
\(320\) 0 0
\(321\) −4.95837 + 8.58814i −0.276749 + 0.479343i
\(322\) −5.77812 + 3.33600i −0.322002 + 0.185908i
\(323\) 14.1271 + 24.4688i 0.786050 + 1.36148i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 15.5938 0.863658
\(327\) 3.70544 + 6.41801i 0.204911 + 0.354917i
\(328\) −6.33097 + 3.65519i −0.349570 + 0.201824i
\(329\) 9.11413 15.7861i 0.502478 0.870318i
\(330\) 0 0
\(331\) −16.6067 9.58790i −0.912789 0.526999i −0.0314613 0.999505i \(-0.510016\pi\)
−0.881327 + 0.472506i \(0.843349\pi\)
\(332\) −3.57994 + 6.20064i −0.196475 + 0.340304i
\(333\) 2.13288 0.116881
\(334\) 0.929155 1.60934i 0.0508411 0.0880594i
\(335\) 0 0
\(336\) 3.10934 1.79518i 0.169629 0.0979351i
\(337\) 16.5450i 0.901262i −0.892710 0.450631i \(-0.851199\pi\)
0.892710 0.450631i \(-0.148801\pi\)
\(338\) −6.91044 11.0112i −0.375878 0.598929i
\(339\) 0 0
\(340\) 0 0
\(341\) 6.08827 + 10.5452i 0.329698 + 0.571054i
\(342\) −3.34713 1.93247i −0.180992 0.104496i
\(343\) 3.98282 0.215052
\(344\) 7.10996 + 4.10494i 0.383344 + 0.221323i
\(345\) 0 0
\(346\) 24.3374i 1.30839i
\(347\) −5.16489 2.98195i −0.277266 0.160079i 0.354919 0.934897i \(-0.384508\pi\)
−0.632185 + 0.774818i \(0.717842\pi\)
\(348\) −4.63459 + 2.67578i −0.248440 + 0.143437i
\(349\) −2.76302 + 1.59523i −0.147901 + 0.0853906i −0.572124 0.820167i \(-0.693880\pi\)
0.424223 + 0.905558i \(0.360547\pi\)
\(350\) 0 0
\(351\) −0.0664404 3.60494i −0.00354632 0.192417i
\(352\) 5.45207i 0.290596i
\(353\) −14.0524 24.3395i −0.747934 1.29546i −0.948811 0.315844i \(-0.897712\pi\)
0.200877 0.979616i \(-0.435621\pi\)
\(354\) 0.137285 + 0.237785i 0.00729663 + 0.0126381i
\(355\) 0 0
\(356\) 9.59376i 0.508468i
\(357\) −13.1234 + 22.7305i −0.694566 + 1.20302i
\(358\) −1.53429 + 2.65746i −0.0810895 + 0.140451i
\(359\) 22.7404i 1.20019i −0.799927 0.600097i \(-0.795128\pi\)
0.799927 0.600097i \(-0.204872\pi\)
\(360\) 0 0
\(361\) −2.03115 3.51806i −0.106903 0.185161i
\(362\) 2.29688 + 3.97831i 0.120721 + 0.209095i
\(363\) 18.7250i 0.982810i
\(364\) −6.67810 11.0897i −0.350028 0.581259i
\(365\) 0 0
\(366\) 3.57918 2.06644i 0.187087 0.108015i
\(367\) 26.1824 15.1164i 1.36671 0.789072i 0.376206 0.926536i \(-0.377229\pi\)
0.990507 + 0.137464i \(0.0438952\pi\)
\(368\) −1.60934 0.929155i −0.0838928 0.0484356i
\(369\) 7.31038i 0.380563i
\(370\) 0 0
\(371\) 6.94435 + 4.00932i 0.360533 + 0.208154i
\(372\) −2.23338 −0.115795
\(373\) 4.04965 + 2.33807i 0.209683 + 0.121061i 0.601164 0.799126i \(-0.294704\pi\)
−0.391481 + 0.920186i \(0.628037\pi\)
\(374\) 19.9283 + 34.5169i 1.03047 + 1.78483i
\(375\) 0 0
\(376\) 5.07700 0.261826
\(377\) 9.95396 + 16.5296i 0.512655 + 0.851320i
\(378\) 3.59036i 0.184668i
\(379\) −18.5598 + 10.7155i −0.953353 + 0.550419i −0.894121 0.447826i \(-0.852199\pi\)
−0.0592321 + 0.998244i \(0.518865\pi\)
\(380\) 0 0
\(381\) −8.99351 + 15.5772i −0.460751 + 0.798045i
\(382\) 14.0601 0.719379
\(383\) 0.0256044 0.0443481i 0.00130832 0.00226608i −0.865371 0.501133i \(-0.832917\pi\)
0.866679 + 0.498867i \(0.166250\pi\)
\(384\) 0.866025 + 0.500000i 0.0441942 + 0.0255155i
\(385\) 0 0
\(386\) −12.5444 + 21.7276i −0.638494 + 1.10590i
\(387\) 7.10996 4.10494i 0.361420 0.208666i
\(388\) −0.954155 1.65264i −0.0484399 0.0839003i
\(389\) 5.35157 0.271335 0.135668 0.990754i \(-0.456682\pi\)
0.135668 + 0.990754i \(0.456682\pi\)
\(390\) 0 0
\(391\) 13.5849 0.687020
\(392\) −2.94535 5.10149i −0.148762 0.257664i
\(393\) −17.6203 + 10.1731i −0.888827 + 0.513165i
\(394\) 4.59737 7.96287i 0.231612 0.401164i
\(395\) 0 0
\(396\) −4.72163 2.72603i −0.237271 0.136988i
\(397\) −4.25359 + 7.36744i −0.213482 + 0.369761i −0.952802 0.303593i \(-0.901814\pi\)
0.739320 + 0.673354i \(0.235147\pi\)
\(398\) −23.6792 −1.18693
\(399\) −6.93825 + 12.0174i −0.347347 + 0.601623i
\(400\) 0 0
\(401\) −20.2467 + 11.6894i −1.01107 + 0.583741i −0.911505 0.411290i \(-0.865078\pi\)
−0.0995649 + 0.995031i \(0.531745\pi\)
\(402\) 14.7970i 0.738008i
\(403\) 0.148387 + 8.05120i 0.00739166 + 0.401059i
\(404\) −16.2557 −0.808752
\(405\) 0 0
\(406\) 9.60703 + 16.6399i 0.476789 + 0.825823i
\(407\) −10.0707 5.81431i −0.499185 0.288204i
\(408\) −7.31038 −0.361918
\(409\) 4.51511 + 2.60680i 0.223258 + 0.128898i 0.607458 0.794352i \(-0.292189\pi\)
−0.384200 + 0.923250i \(0.625523\pi\)
\(410\) 0 0
\(411\) 11.0407i 0.544599i
\(412\) 11.2376 + 6.48802i 0.553636 + 0.319642i
\(413\) 0.853735 0.492904i 0.0420095 0.0242542i
\(414\) −1.60934 + 0.929155i −0.0790949 + 0.0456655i
\(415\) 0 0
\(416\) 1.74493 3.15519i 0.0855523 0.154696i
\(417\) 9.70193i 0.475105i
\(418\) 10.5359 + 18.2488i 0.515329 + 0.892577i
\(419\) 9.10066 + 15.7628i 0.444596 + 0.770064i 0.998024 0.0628337i \(-0.0200138\pi\)
−0.553428 + 0.832897i \(0.686680\pi\)
\(420\) 0 0
\(421\) 25.6463i 1.24992i 0.780656 + 0.624961i \(0.214885\pi\)
−0.780656 + 0.624961i \(0.785115\pi\)
\(422\) 4.99303 8.64818i 0.243057 0.420987i
\(423\) 2.53850 4.39681i 0.123426 0.213780i
\(424\) 2.23338i 0.108463i
\(425\) 0 0
\(426\) 7.14784 + 12.3804i 0.346314 + 0.599834i
\(427\) −7.41927 12.8505i −0.359043 0.621882i
\(428\) 9.91673i 0.479343i
\(429\) −9.51348 + 17.2023i −0.459315 + 0.830535i
\(430\) 0 0
\(431\) −1.79193 + 1.03457i −0.0863142 + 0.0498335i −0.542536 0.840033i \(-0.682536\pi\)
0.456222 + 0.889866i \(0.349202\pi\)
\(432\) 0.866025 0.500000i 0.0416667 0.0240563i
\(433\) 0.815649 + 0.470915i 0.0391976 + 0.0226307i 0.519471 0.854488i \(-0.326129\pi\)
−0.480273 + 0.877119i \(0.659462\pi\)
\(434\) 8.01864i 0.384907i
\(435\) 0 0
\(436\) 6.41801 + 3.70544i 0.307367 + 0.177458i
\(437\) 7.18224 0.343573
\(438\) 12.9016 + 7.44876i 0.616464 + 0.355915i
\(439\) 1.80132 + 3.11997i 0.0859722 + 0.148908i 0.905805 0.423695i \(-0.139267\pi\)
−0.819833 + 0.572603i \(0.805934\pi\)
\(440\) 0 0
\(441\) −5.89069 −0.280509
\(442\) 0.485704 + 26.3535i 0.0231026 + 1.25351i
\(443\) 5.05095i 0.239978i 0.992775 + 0.119989i \(0.0382859\pi\)
−0.992775 + 0.119989i \(0.961714\pi\)
\(444\) 1.84713 1.06644i 0.0876609 0.0506110i
\(445\) 0 0
\(446\) 11.1910 19.3833i 0.529908 0.917828i
\(447\) −5.43817 −0.257217
\(448\) 1.79518 3.10934i 0.0848143 0.146903i
\(449\) 4.70017 + 2.71364i 0.221815 + 0.128065i 0.606790 0.794862i \(-0.292457\pi\)
−0.384976 + 0.922927i \(0.625790\pi\)
\(450\) 0 0
\(451\) 19.9283 34.5169i 0.938389 1.62534i
\(452\) 0 0
\(453\) −8.90050 15.4161i −0.418182 0.724312i
\(454\) 12.9853 0.609431
\(455\) 0 0
\(456\) −3.86493 −0.180992
\(457\) 10.8416 + 18.7782i 0.507147 + 0.878405i 0.999966 + 0.00827291i \(0.00263338\pi\)
−0.492818 + 0.870132i \(0.664033\pi\)
\(458\) 12.5102 7.22276i 0.584562 0.337497i
\(459\) −3.65519 + 6.33097i −0.170610 + 0.295505i
\(460\) 0 0
\(461\) −25.6364 14.8012i −1.19401 0.689359i −0.234793 0.972045i \(-0.575441\pi\)
−0.959212 + 0.282686i \(0.908775\pi\)
\(462\) −9.78745 + 16.9524i −0.455353 + 0.788695i
\(463\) −28.2075 −1.31091 −0.655457 0.755232i \(-0.727524\pi\)
−0.655457 + 0.755232i \(0.727524\pi\)
\(464\) −2.67578 + 4.63459i −0.124220 + 0.215156i
\(465\) 0 0
\(466\) −10.7711 + 6.21869i −0.498961 + 0.288075i
\(467\) 8.17371i 0.378234i −0.981955 0.189117i \(-0.939437\pi\)
0.981955 0.189117i \(-0.0605626\pi\)
\(468\) −1.86001 3.08875i −0.0859789 0.142777i
\(469\) −53.1266 −2.45316
\(470\) 0 0
\(471\) 2.96826 + 5.14117i 0.136770 + 0.236893i
\(472\) 0.237785 + 0.137285i 0.0109450 + 0.00631907i
\(473\) −44.7608 −2.05810
\(474\) −2.26990 1.31052i −0.104260 0.0601944i
\(475\) 0 0
\(476\) 26.2469i 1.20302i
\(477\) 1.93416 + 1.11669i 0.0885593 + 0.0511297i
\(478\) 3.61118 2.08491i 0.165171 0.0953618i
\(479\) −10.1231 + 5.84458i −0.462537 + 0.267046i −0.713110 0.701052i \(-0.752714\pi\)
0.250573 + 0.968098i \(0.419381\pi\)
\(480\) 0 0
\(481\) −3.96718 6.58793i −0.180888 0.300384i
\(482\) 1.88407i 0.0858170i
\(483\) 3.33600 + 5.77812i 0.151793 + 0.262914i
\(484\) 9.36252 + 16.2164i 0.425569 + 0.737107i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) 15.9438 27.6154i 0.722481 1.25137i −0.237522 0.971382i \(-0.576335\pi\)
0.960003 0.279991i \(-0.0903316\pi\)
\(488\) 2.06644 3.57918i 0.0935434 0.162022i
\(489\) 15.5938i 0.705174i
\(490\) 0 0
\(491\) 9.77506 + 16.9309i 0.441142 + 0.764080i 0.997775 0.0666784i \(-0.0212402\pi\)
−0.556632 + 0.830759i \(0.687907\pi\)
\(492\) 3.65519 + 6.33097i 0.164789 + 0.285422i
\(493\) 39.1220i 1.76197i
\(494\) 0.256787 + 13.9328i 0.0115534 + 0.626868i
\(495\) 0 0
\(496\) −1.93416 + 1.11669i −0.0868465 + 0.0501409i
\(497\) 44.4502 25.6633i 1.99386 1.15116i
\(498\) 6.20064 + 3.57994i 0.277857 + 0.160421i
\(499\) 39.3428i 1.76123i 0.473836 + 0.880613i \(0.342869\pi\)
−0.473836 + 0.880613i \(0.657131\pi\)
\(500\) 0 0
\(501\) −1.60934 0.929155i −0.0719002 0.0415116i
\(502\) −7.15005 −0.319122
\(503\) −12.4127 7.16650i −0.553457 0.319538i 0.197058 0.980392i \(-0.436861\pi\)
−0.750515 + 0.660853i \(0.770194\pi\)
\(504\) −1.79518 3.10934i −0.0799637 0.138501i
\(505\) 0 0
\(506\) 10.1316 0.450406
\(507\) −11.0112 + 6.91044i −0.489023 + 0.306903i
\(508\) 17.9870i 0.798045i
\(509\) 3.23839 1.86968i 0.143539 0.0828723i −0.426511 0.904483i \(-0.640257\pi\)
0.570050 + 0.821610i \(0.306924\pi\)
\(510\) 0 0
\(511\) 26.7437 46.3215i 1.18307 2.04914i
\(512\) 1.00000 0.0441942
\(513\) −1.93247 + 3.34713i −0.0853204 + 0.147779i
\(514\) 17.7517 + 10.2489i 0.782994 + 0.452062i
\(515\) 0 0
\(516\) 4.10494 7.10996i 0.180710 0.312999i
\(517\) −23.9717 + 13.8401i −1.05427 + 0.608685i
\(518\) −3.82891 6.63186i −0.168232 0.291387i
\(519\) −24.3374 −1.06829
\(520\) 0 0
\(521\) −40.2722 −1.76436 −0.882178 0.470915i \(-0.843924\pi\)
−0.882178 + 0.470915i \(0.843924\pi\)
\(522\) 2.67578 + 4.63459i 0.117116 + 0.202851i
\(523\) −19.7853 + 11.4230i −0.865150 + 0.499495i −0.865734 0.500505i \(-0.833148\pi\)
0.000583330 1.00000i \(0.499814\pi\)
\(524\) −10.1731 + 17.6203i −0.444414 + 0.769747i
\(525\) 0 0
\(526\) −15.3313 8.85153i −0.668477 0.385945i
\(527\) 8.16343 14.1395i 0.355605 0.615925i
\(528\) −5.45207 −0.237271
\(529\) −9.77334 + 16.9279i −0.424928 + 0.735997i
\(530\) 0 0
\(531\) 0.237785 0.137285i 0.0103190 0.00595768i
\(532\) 13.8765i 0.601623i
\(533\) 22.5799 13.5974i 0.978045 0.588967i
\(534\) −9.59376 −0.415163
\(535\) 0 0
\(536\) −7.39851 12.8146i −0.319567 0.553506i
\(537\) 2.65746 + 1.53429i 0.114678 + 0.0662093i
\(538\) 18.1864 0.784070
\(539\) 27.8137 + 16.0582i 1.19802 + 0.691677i
\(540\) 0 0
\(541\) 18.9610i 0.815196i 0.913162 + 0.407598i \(0.133633\pi\)
−0.913162 + 0.407598i \(0.866367\pi\)
\(542\) −19.7188 11.3847i −0.846996 0.489013i
\(543\) 3.97831 2.29688i 0.170726 0.0985685i
\(544\) −6.33097 + 3.65519i −0.271438 + 0.156715i
\(545\) 0 0
\(546\) −11.0897 + 6.67810i −0.474596 + 0.285796i
\(547\) 26.7863i 1.14530i 0.819801 + 0.572649i \(0.194084\pi\)
−0.819801 + 0.572649i \(0.805916\pi\)
\(548\) 5.52037 + 9.56156i 0.235818 + 0.408450i
\(549\) −2.06644 3.57918i −0.0881935 0.152756i
\(550\) 0 0
\(551\) 20.6834i 0.881144i
\(552\) −0.929155 + 1.60934i −0.0395475 + 0.0684982i
\(553\) −4.70526 + 8.14974i −0.200088 + 0.346562i
\(554\) 16.3563i 0.694911i
\(555\) 0 0
\(556\) 4.85096 + 8.40212i 0.205727 + 0.356329i
\(557\) −13.1189 22.7227i −0.555867 0.962791i −0.997835 0.0657599i \(-0.979053\pi\)
0.441968 0.897031i \(-0.354280\pi\)
\(558\) 2.23338i 0.0945465i
\(559\) −25.9037 14.3257i −1.09561 0.605911i
\(560\) 0 0
\(561\) 34.5169 19.9283i 1.45730 0.841375i
\(562\) −6.77423 + 3.91110i −0.285754 + 0.164980i
\(563\) −14.0452 8.10900i −0.591935 0.341754i 0.173927 0.984758i \(-0.444354\pi\)
−0.765862 + 0.643005i \(0.777688\pi\)
\(564\) 5.07700i 0.213780i
\(565\) 0 0
\(566\) −6.01483 3.47266i −0.252822 0.145967i
\(567\) −3.59036 −0.150781
\(568\) 12.3804 + 7.14784i 0.519471 + 0.299917i
\(569\) −17.1092 29.6340i −0.717255 1.24232i −0.962083 0.272755i \(-0.912065\pi\)
0.244829 0.969566i \(-0.421268\pi\)
\(570\) 0 0
\(571\) 0.151070 0.00632206 0.00316103 0.999995i \(-0.498994\pi\)
0.00316103 + 0.999995i \(0.498994\pi\)
\(572\) 0.362237 + 19.6544i 0.0151459 + 0.821791i
\(573\) 14.0601i 0.587371i
\(574\) 22.7305 13.1234i 0.948752 0.547762i
\(575\) 0 0
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) −33.7742 −1.40604 −0.703019 0.711171i \(-0.748165\pi\)
−0.703019 + 0.711171i \(0.748165\pi\)
\(578\) 18.2208 31.5594i 0.757886 1.31270i
\(579\) 21.7276 + 12.5444i 0.902966 + 0.521328i
\(580\) 0 0
\(581\) 12.8533 22.2625i 0.533244 0.923605i
\(582\) −1.65264 + 0.954155i −0.0685043 + 0.0395510i
\(583\) −6.08827 10.5452i −0.252150 0.436737i
\(584\) 14.8975 0.616464
\(585\) 0 0
\(586\) 26.4243 1.09158
\(587\) −16.8030 29.1037i −0.693535 1.20124i −0.970672 0.240408i \(-0.922719\pi\)
0.277137 0.960831i \(-0.410615\pi\)
\(588\) −5.10149 + 2.94535i −0.210382 + 0.121464i
\(589\) 4.31593 7.47541i 0.177835 0.308019i
\(590\) 0 0
\(591\) −7.96287 4.59737i −0.327549 0.189110i
\(592\) 1.06644 1.84713i 0.0438304 0.0759165i
\(593\) 36.7529 1.50926 0.754630 0.656150i \(-0.227816\pi\)
0.754630 + 0.656150i \(0.227816\pi\)
\(594\) −2.72603 + 4.72163i −0.111851 + 0.193731i
\(595\) 0 0
\(596\) −4.70959 + 2.71908i −0.192912 + 0.111378i
\(597\) 23.6792i 0.969124i
\(598\) 5.86332 + 3.24262i 0.239769 + 0.132601i
\(599\) 24.5241 1.00203 0.501015 0.865439i \(-0.332960\pi\)
0.501015 + 0.865439i \(0.332960\pi\)
\(600\) 0 0
\(601\) 18.7548 + 32.4843i 0.765025 + 1.32506i 0.940233 + 0.340531i \(0.110607\pi\)
−0.175208 + 0.984531i \(0.556060\pi\)
\(602\) −25.5273 14.7382i −1.04042 0.600685i
\(603\) −14.7970 −0.602581
\(604\) −15.4161 8.90050i −0.627273 0.362156i
\(605\) 0 0
\(606\) 16.2557i 0.660343i
\(607\) 40.2796 + 23.2554i 1.63490 + 0.943909i 0.982552 + 0.185988i \(0.0595484\pi\)
0.652346 + 0.757921i \(0.273785\pi\)
\(608\) −3.34713 + 1.93247i −0.135744 + 0.0783718i
\(609\) 16.6399 9.60703i 0.674281 0.389297i
\(610\) 0 0
\(611\) −18.3023 + 0.337318i −0.740430 + 0.0136464i
\(612\) 7.31038i 0.295505i
\(613\) −5.14785 8.91634i −0.207920 0.360128i 0.743139 0.669137i \(-0.233336\pi\)
−0.951059 + 0.309009i \(0.900003\pi\)
\(614\) 3.54290 + 6.13649i 0.142980 + 0.247649i
\(615\) 0 0
\(616\) 19.5749i 0.788695i
\(617\) −17.8404 + 30.9005i −0.718228 + 1.24401i 0.243473 + 0.969908i \(0.421713\pi\)
−0.961701 + 0.274100i \(0.911620\pi\)
\(618\) 6.48802 11.2376i 0.260987 0.452042i
\(619\) 12.9815i 0.521772i −0.965370 0.260886i \(-0.915985\pi\)
0.965370 0.260886i \(-0.0840146\pi\)
\(620\) 0 0
\(621\) 0.929155 + 1.60934i 0.0372857 + 0.0645807i
\(622\) 0.915086 + 1.58498i 0.0366916 + 0.0635517i
\(623\) 34.4451i 1.38001i
\(624\) −3.15519 1.74493i −0.126309 0.0698531i
\(625\) 0 0
\(626\) 10.6087 6.12493i 0.424008 0.244801i
\(627\) 18.2488 10.5359i 0.728786 0.420765i
\(628\) 5.14117 + 2.96826i 0.205155 + 0.118446i
\(629\) 15.5922i 0.621700i
\(630\) 0 0
\(631\) −18.4953 10.6783i −0.736287 0.425096i 0.0844307 0.996429i \(-0.473093\pi\)
−0.820718 + 0.571334i \(0.806426\pi\)
\(632\) −2.62105 −0.104260
\(633\) −8.64818 4.99303i −0.343734 0.198455i
\(634\) 3.12550 + 5.41352i 0.124129 + 0.214999i
\(635\) 0 0
\(636\) 2.23338 0.0885593
\(637\) 10.9567 + 18.1949i 0.434122 + 0.720907i
\(638\) 29.1771i 1.15513i
\(639\) 12.3804 7.14784i 0.489762 0.282764i
\(640\) 0 0
\(641\) −6.49169 + 11.2439i −0.256407 + 0.444109i −0.965277 0.261230i \(-0.915872\pi\)
0.708870 + 0.705339i \(0.249205\pi\)
\(642\) 9.91673 0.391382
\(643\) 7.90323 13.6888i 0.311673 0.539834i −0.667052 0.745012i \(-0.732444\pi\)
0.978725 + 0.205178i \(0.0657773\pi\)
\(644\) 5.77812 + 3.33600i 0.227690 + 0.131457i
\(645\) 0 0
\(646\) 14.1271 24.4688i 0.555822 0.962711i
\(647\) −19.8219 + 11.4442i −0.779277 + 0.449916i −0.836174 0.548464i \(-0.815213\pi\)
0.0568967 + 0.998380i \(0.481879\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) −1.49698 −0.0587615
\(650\) 0 0
\(651\) 8.01864 0.314275
\(652\) −7.79688 13.5046i −0.305349 0.528881i
\(653\) 1.87183 1.08070i 0.0732504 0.0422911i −0.462927 0.886396i \(-0.653201\pi\)
0.536178 + 0.844105i \(0.319868\pi\)
\(654\) 3.70544 6.41801i 0.144894 0.250964i
\(655\) 0 0
\(656\) 6.33097 + 3.65519i 0.247183 + 0.142711i
\(657\) 7.44876 12.9016i 0.290604 0.503340i
\(658\) −18.2283 −0.710611
\(659\) 9.79863 16.9717i 0.381700 0.661124i −0.609605 0.792705i \(-0.708672\pi\)
0.991305 + 0.131581i \(0.0420053\pi\)
\(660\) 0 0
\(661\) −24.8286 + 14.3348i −0.965719 + 0.557558i −0.897929 0.440141i \(-0.854928\pi\)
−0.0677909 + 0.997700i \(0.521595\pi\)
\(662\) 19.1758i 0.745289i
\(663\) 26.3535 0.485704i 1.02348 0.0188632i
\(664\) 7.15988 0.277857
\(665\) 0 0
\(666\) −1.06644 1.84713i −0.0413237 0.0715748i
\(667\) −8.61251 4.97244i −0.333478 0.192534i
\(668\) −1.85831 −0.0719002
\(669\) −19.3833 11.1910i −0.749404 0.432668i
\(670\) 0 0
\(671\) 22.5327i 0.869867i
\(672\) −3.10934 1.79518i −0.119946 0.0692506i
\(673\) −44.0166 + 25.4130i −1.69672 + 0.979599i −0.747878 + 0.663837i \(0.768927\pi\)
−0.948838 + 0.315763i \(0.897740\pi\)
\(674\) −14.3284 + 8.27248i −0.551908 + 0.318644i
\(675\) 0 0
\(676\) −6.08074 + 11.4902i −0.233874 + 0.441931i
\(677\) 15.4058i 0.592093i 0.955174 + 0.296046i \(0.0956683\pi\)
−0.955174 + 0.296046i \(0.904332\pi\)
\(678\) 0 0
\(679\) 3.42576 + 5.93359i 0.131469 + 0.227710i
\(680\) 0 0
\(681\) 12.9853i 0.497598i
\(682\) 6.08827 10.5452i 0.233132 0.403796i
\(683\) 11.1227 19.2650i 0.425597 0.737155i −0.570879 0.821034i \(-0.693398\pi\)
0.996476 + 0.0838788i \(0.0267309\pi\)
\(684\) 3.86493i 0.147779i
\(685\) 0 0
\(686\) −1.99141 3.44922i −0.0760324 0.131692i
\(687\) −7.22276 12.5102i −0.275565 0.477293i
\(688\) 8.20988i 0.312999i
\(689\) −0.148387 8.05120i −0.00565308 0.306726i
\(690\) 0 0
\(691\) 5.31663 3.06956i 0.202254 0.116771i −0.395452 0.918486i \(-0.629412\pi\)
0.597706 + 0.801715i \(0.296079\pi\)
\(692\) −21.0768 + 12.1687i −0.801219 + 0.462584i
\(693\) 16.9524 + 9.78745i 0.643967 + 0.371794i
\(694\) 5.96390i 0.226387i
\(695\) 0 0
\(696\) 4.63459 + 2.67578i 0.175674 + 0.101425i
\(697\) −53.4416 −2.02425
\(698\) 2.76302 + 1.59523i 0.104582 + 0.0603803i
\(699\) 6.21869 + 10.7711i 0.235212 + 0.407400i
\(700\) 0 0
\(701\) −24.7793 −0.935902 −0.467951 0.883754i \(-0.655008\pi\)
−0.467951 + 0.883754i \(0.655008\pi\)
\(702\) −3.08875 + 1.86001i −0.116577 + 0.0702015i
\(703\) 8.24344i 0.310907i
\(704\) −4.72163 + 2.72603i −0.177953 + 0.102741i
\(705\) 0 0
\(706\) −14.0524 + 24.3395i −0.528869 + 0.916029i
\(707\) 58.3638 2.19500
\(708\) 0.137285 0.237785i 0.00515950 0.00893652i
\(709\) −22.3507 12.9042i −0.839398 0.484627i 0.0176613 0.999844i \(-0.494378\pi\)
−0.857060 + 0.515217i \(0.827711\pi\)
\(710\) 0 0
\(711\) −1.31052 + 2.26990i −0.0491485 + 0.0851277i
\(712\) −8.30844 + 4.79688i −0.311372 + 0.179771i
\(713\) −2.07516 3.59428i −0.0777152 0.134607i
\(714\) 26.2469 0.982265
\(715\) 0 0
\(716\) 3.06857 0.114678
\(717\) −2.08491 3.61118i −0.0778625 0.134862i
\(718\) −19.6938 + 11.3702i −0.734966 + 0.424333i
\(719\) 11.7949 20.4293i 0.439874 0.761884i −0.557806 0.829972i \(-0.688357\pi\)
0.997679 + 0.0680879i \(0.0216898\pi\)
\(720\) 0 0
\(721\) −40.3470 23.2943i −1.50260 0.867527i
\(722\) −2.03115 + 3.51806i −0.0755917 + 0.130929i
\(723\) −1.88407 −0.0700693
\(724\) 2.29688 3.97831i 0.0853628 0.147853i
\(725\) 0 0
\(726\) 16.2164 9.36252i 0.601846 0.347476i
\(727\) 31.4651i 1.16698i −0.812121 0.583489i \(-0.801687\pi\)
0.812121 0.583489i \(-0.198313\pi\)
\(728\) −6.26493 + 11.3283i −0.232194 + 0.419854i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 30.0087 + 51.9765i 1.10991 + 1.92242i
\(732\) −3.57918 2.06644i −0.132290 0.0763778i
\(733\) 32.2822 1.19237 0.596186 0.802847i \(-0.296682\pi\)
0.596186 + 0.802847i \(0.296682\pi\)
\(734\) −26.1824 15.1164i −0.966412 0.557958i
\(735\) 0 0
\(736\) 1.85831i 0.0684982i
\(737\) 69.8660 + 40.3372i 2.57355 + 1.48584i
\(738\) 6.33097 3.65519i 0.233046 0.134549i
\(739\) 13.2643 7.65817i 0.487936 0.281710i −0.235782 0.971806i \(-0.575765\pi\)
0.723718 + 0.690096i \(0.242432\pi\)
\(740\) 0 0
\(741\) 13.9328 0.256787i 0.511836 0.00943332i
\(742\) 8.01864i 0.294374i
\(743\) 12.6161 + 21.8518i 0.462841 + 0.801663i 0.999101 0.0423891i \(-0.0134969\pi\)
−0.536261 + 0.844052i \(0.680164\pi\)
\(744\) 1.11669 + 1.93416i 0.0409399 + 0.0709099i
\(745\) 0 0
\(746\) 4.67614i 0.171206i
\(747\) 3.57994 6.20064i 0.130983 0.226869i
\(748\) 19.9283 34.5169i 0.728652 1.26206i
\(749\) 35.6047i 1.30097i
\(750\) 0 0
\(751\) 7.69444 + 13.3272i 0.280774 + 0.486315i 0.971576 0.236729i \(-0.0760755\pi\)
−0.690802 + 0.723044i \(0.742742\pi\)
\(752\) −2.53850 4.39681i −0.0925695 0.160335i
\(753\) 7.15005i 0.260562i
\(754\) 9.33811 16.8852i 0.340074 0.614923i
\(755\) 0 0
\(756\) −3.10934 + 1.79518i −0.113086 + 0.0652901i
\(757\) 31.4879 18.1796i 1.14445 0.660747i 0.196920 0.980420i \(-0.436906\pi\)
0.947528 + 0.319673i \(0.103573\pi\)
\(758\) 18.5598 + 10.7155i 0.674122 + 0.389205i
\(759\) 10.1316i 0.367755i
\(760\) 0 0
\(761\) −27.4056 15.8226i −0.993453 0.573570i −0.0871481 0.996195i \(-0.527775\pi\)
−0.906305 + 0.422625i \(0.861109\pi\)
\(762\) 17.9870 0.651601
\(763\) −23.0430 13.3039i −0.834211 0.481632i
\(764\) −7.03007 12.1764i −0.254339 0.440528i
\(765\) 0 0
\(766\) −0.0512087 −0.00185025
\(767\) −0.866322 0.479107i −0.0312811 0.0172995i
\(768\) 1.00000i 0.0360844i
\(769\) 10.0722 5.81521i 0.363214 0.209702i −0.307276 0.951621i \(-0.599417\pi\)
0.670490 + 0.741919i \(0.266084\pi\)
\(770\) 0 0
\(771\) 10.2489 17.7517i 0.369107 0.639312i
\(772\) 25.0888 0.902966
\(773\) 14.5823 25.2573i 0.524490 0.908443i −0.475104 0.879930i \(-0.657590\pi\)
0.999593 0.0285128i \(-0.00907714\pi\)
\(774\) −7.10996 4.10494i −0.255562 0.147549i
\(775\) 0 0
\(776\) −0.954155 + 1.65264i −0.0342522 + 0.0593265i
\(777\) −6.63186 + 3.82891i −0.237917 + 0.137361i
\(778\) −2.67578 4.63459i −0.0959315 0.166158i
\(779\) −28.2541 −1.01231
\(780\) 0 0
\(781\) −77.9410 −2.78895
\(782\) −6.79247 11.7649i −0.242898 0.420712i
\(783\) 4.63459 2.67578i 0.165627 0.0956247i
\(784\) −2.94535 + 5.10149i −0.105191 + 0.182196i
\(785\) 0 0
\(786\) 17.6203 + 10.1731i 0.628496 + 0.362862i
\(787\) 8.03414 13.9155i 0.286386 0.496035i −0.686558 0.727075i \(-0.740879\pi\)
0.972944 + 0.231039i \(0.0742127\pi\)
\(788\) −9.19473 −0.327549
\(789\) −8.85153 + 15.3313i −0.315123 + 0.545809i
\(790\) 0 0
\(791\) 0 0
\(792\) 5.45207i 0.193731i
\(793\) −7.21159 + 13.0400i −0.256091 + 0.463065i
\(794\) 8.50719 0.301909
\(795\) 0 0
\(796\) 11.8396 + 20.5068i 0.419643 + 0.726843i
\(797\) −33.8249 19.5288i −1.19814 0.691745i −0.237998 0.971266i \(-0.576491\pi\)
−0.960140 + 0.279520i \(0.909825\pi\)
\(798\) 13.8765 0.491223
\(799\) 32.1423 + 18.5574i 1.13711 + 0.656513i
\(800\) 0 0
\(801\) 9.59376i 0.338979i
\(802\) 20.2467 + 11.6894i 0.714934 + 0.412767i
\(803\) −70.3405 + 40.6111i −2.48226 + 1.43314i
\(804\) −12.8146 + 7.39851i −0.451936 + 0.260925i
\(805\) 0 0
\(806\) 6.89835 4.15411i 0.242984 0.146322i
\(807\) 18.1864i 0.640191i
\(808\) 8.12785 + 14.0779i 0.285937 + 0.495257i
\(809\) 7.04891 + 12.2091i 0.247827 + 0.429248i 0.962923 0.269778i \(-0.0869503\pi\)
−0.715096 + 0.699026i \(0.753617\pi\)
\(810\) 0 0
\(811\) 11.3869i 0.399846i −0.979812 0.199923i \(-0.935931\pi\)
0.979812 0.199923i \(-0.0640693\pi\)
\(812\) 9.60703 16.6399i 0.337141 0.583945i
\(813\) −11.3847 + 19.7188i −0.399278 + 0.691569i
\(814\) 11.6286i 0.407583i
\(815\) 0 0
\(816\) 3.65519 + 6.33097i 0.127957 + 0.221628i
\(817\) 15.8653 + 27.4795i 0.555057 + 0.961387i
\(818\) 5.21360i 0.182289i
\(819\) 6.67810 + 11.0897i 0.233352 + 0.387506i
\(820\) 0 0
\(821\) 25.2924 14.6026i 0.882710 0.509633i 0.0111593 0.999938i \(-0.496448\pi\)
0.871551 + 0.490305i \(0.163114\pi\)
\(822\) 9.56156 5.52037i 0.333498 0.192545i
\(823\) 24.4617 + 14.1230i 0.852681 + 0.492296i 0.861555 0.507665i \(-0.169491\pi\)
−0.00887332 + 0.999961i \(0.502825\pi\)
\(824\) 12.9760i 0.452042i
\(825\) 0 0
\(826\) −0.853735 0.492904i −0.0297052 0.0171503i
\(827\) −37.3963 −1.30040 −0.650198 0.759765i \(-0.725314\pi\)
−0.650198 + 0.759765i \(0.725314\pi\)
\(828\) 1.60934 + 0.929155i 0.0559286 + 0.0322904i
\(829\) 0.925320 + 1.60270i 0.0321377 + 0.0556641i 0.881647 0.471910i \(-0.156435\pi\)
−0.849509 + 0.527574i \(0.823102\pi\)
\(830\) 0 0
\(831\) 16.3563 0.567393
\(832\) −3.60494 + 0.0664404i −0.124979 + 0.00230341i
\(833\) 43.0632i 1.49205i
\(834\) 8.40212 4.85096i 0.290941 0.167975i
\(835\) 0 0
\(836\) 10.5359 18.2488i 0.364393 0.631147i
\(837\) 2.23338 0.0771969
\(838\) 9.10066 15.7628i 0.314377 0.544517i
\(839\) 38.8940 + 22.4555i 1.34277 + 0.775249i 0.987213 0.159406i \(-0.0509578\pi\)
0.355557 + 0.934655i \(0.384291\pi\)
\(840\) 0 0
\(841\) 0.180359 0.312392i 0.00621929 0.0107721i
\(842\) 22.2103 12.8231i 0.765418 0.441914i
\(843\) 3.91110 + 6.77423i 0.134706 + 0.233317i
\(844\) −9.98606 −0.343734
\(845\) 0 0
\(846\) −5.07700 −0.174551
\(847\) −33.6148 58.2226i −1.15502 2.00055i
\(848\) 1.93416 1.11669i 0.0664195 0.0383473i
\(849\) −3.47266 + 6.01483i −0.119181 + 0.206428i
\(850\) 0 0
\(851\) 3.43254 + 1.98178i 0.117666 + 0.0679344i
\(852\) 7.14784 12.3804i 0.244881 0.424146i
\(853\) 6.75772 0.231380 0.115690 0.993285i \(-0.463092\pi\)
0.115690 + 0.993285i \(0.463092\pi\)
\(854\) −7.41927 + 12.8505i −0.253882 + 0.439737i
\(855\) 0 0
\(856\) 8.58814 4.95837i 0.293537 0.169474i
\(857\) 9.16177i 0.312960i 0.987681 + 0.156480i \(0.0500147\pi\)
−0.987681 + 0.156480i \(0.949985\pi\)
\(858\) 19.6544 0.362237i 0.670989 0.0123666i
\(859\) −11.9538 −0.407857 −0.203928 0.978986i \(-0.565371\pi\)
−0.203928 + 0.978986i \(0.565371\pi\)
\(860\) 0 0
\(861\) −13.1234 22.7305i −0.447246 0.774653i
\(862\) 1.79193 + 1.03457i 0.0610334 + 0.0352376i
\(863\) 31.6465 1.07726 0.538630 0.842542i \(-0.318942\pi\)
0.538630 + 0.842542i \(0.318942\pi\)
\(864\) −0.866025 0.500000i −0.0294628 0.0170103i
\(865\) 0 0
\(866\) 0.941830i 0.0320047i
\(867\) −31.5594 18.2208i −1.07181 0.618811i
\(868\) 6.94435 4.00932i 0.235707 0.136085i
\(869\) 12.3756 7.14507i 0.419814 0.242380i
\(870\) 0 0
\(871\) 27.5226 + 45.7043i 0.932567 + 1.54863i
\(872\) 7.41088i 0.250964i
\(873\) 0.954155 + 1.65264i 0.0322932 + 0.0559335i
\(874\) −3.59112 6.22000i −0.121471 0.210395i
\(875\) 0 0
\(876\) 14.8975i 0.503340i
\(877\) −7.06515 + 12.2372i −0.238573 + 0.413221i −0.960305 0.278952i \(-0.910013\pi\)
0.721732 + 0.692173i \(0.243346\pi\)
\(878\) 1.80132 3.11997i 0.0607915 0.105294i
\(879\) 26.4243i 0.891270i
\(880\) 0 0
\(881\) −9.56417 16.5656i −0.322225 0.558110i 0.658722 0.752387i \(-0.271097\pi\)
−0.980947 + 0.194276i \(0.937764\pi\)
\(882\) 2.94535 + 5.10149i 0.0991749 + 0.171776i
\(883\) 7.19528i 0.242140i 0.992644 + 0.121070i \(0.0386326\pi\)
−0.992644 + 0.121070i \(0.961367\pi\)
\(884\) 22.5799 13.5974i 0.759445 0.457329i
\(885\) 0 0
\(886\) 4.37425 2.52548i 0.146956 0.0848451i
\(887\) 24.9453 14.4022i 0.837580 0.483577i −0.0188611 0.999822i \(-0.506004\pi\)
0.856441 + 0.516245i \(0.172671\pi\)
\(888\) −1.84713 1.06644i −0.0619856 0.0357874i
\(889\) 64.5799i 2.16594i
\(890\) 0 0
\(891\) 4.72163 + 2.72603i 0.158181 + 0.0913256i
\(892\) −22.3820 −0.749404
\(893\) 16.9934 + 9.81112i 0.568661 + 0.328317i
\(894\) 2.71908 + 4.70959i 0.0909398 + 0.157512i
\(895\) 0 0
\(896\) −3.59036 −0.119946
\(897\) 3.24262 5.86332i 0.108268 0.195771i
\(898\) 5.42729i 0.181111i
\(899\) −10.3508 + 5.97604i −0.345219 + 0.199312i
\(900\) 0 0
\(901\) −8.16343 + 14.1395i −0.271963 + 0.471054i
\(902\) −39.8567 −1.32708
\(903\) −14.7382 + 25.5273i −0.490457 + 0.849496i
\(904\) 0 0
\(905\) 0 0
\(906\) −8.90050 + 15.4161i −0.295699 + 0.512166i
\(907\) 33.9233 19.5856i 1.12641 0.650331i 0.183377 0.983043i \(-0.441297\pi\)
0.943029 + 0.332712i \(0.107964\pi\)
\(908\) −6.49265 11.2456i −0.215466 0.373199i
\(909\) 16.2557 0.539168
\(910\) 0 0
\(911\) 26.3352 0.872526 0.436263 0.899819i \(-0.356302\pi\)
0.436263 + 0.899819i \(0.356302\pi\)
\(912\) 1.93247 + 3.34713i 0.0639903 + 0.110835i
\(913\) −33.8063 + 19.5181i −1.11883 + 0.645954i
\(914\) 10.8416 18.7782i 0.358607 0.621126i
\(915\) 0 0
\(916\) −12.5102 7.22276i −0.413348 0.238647i
\(917\) 36.5251 63.2633i 1.20616 2.08914i
\(918\) 7.31038 0.241278
\(919\) 4.85456 8.40834i 0.160137 0.277365i −0.774781 0.632230i \(-0.782140\pi\)
0.934918 + 0.354865i \(0.115473\pi\)
\(920\) 0 0
\(921\) 6.13649 3.54290i 0.202204 0.116743i
\(922\) 29.6023i 0.974901i
\(923\) −45.1056 24.9450i −1.48467 0.821074i
\(924\) 19.5749 0.643967
\(925\) 0 0
\(926\) 14.1038 + 24.4284i 0.463478 + 0.802768i
\(927\) −11.2376 6.48802i −0.369091 0.213095i
\(928\) 5.35157 0.175674
\(929\) −2.68782 1.55181i −0.0881844 0.0509133i 0.455259 0.890359i \(-0.349547\pi\)
−0.543444 + 0.839446i \(0.682880\pi\)
\(930\) 0 0
\(931\) 22.7671i 0.746162i
\(932\) 10.7711 + 6.21869i 0.352819 + 0.203700i
\(933\) 1.58498 0.915086i 0.0518898 0.0299586i
\(934\) −7.07864 + 4.08685i −0.231620 + 0.133726i
\(935\) 0 0
\(936\) −1.74493 + 3.15519i −0.0570348 + 0.103131i
\(937\) 53.5929i 1.75080i 0.483396 + 0.875402i \(0.339403\pi\)
−0.483396 + 0.875402i \(0.660597\pi\)
\(938\) 26.5633 + 46.0090i 0.867323 + 1.50225i
\(939\) −6.12493 10.6087i −0.199880 0.346201i
\(940\) 0 0
\(941\) 42.9758i 1.40097i −0.713667 0.700485i \(-0.752967\pi\)
0.713667 0.700485i \(-0.247033\pi\)
\(942\) 2.96826 5.14117i 0.0967111 0.167509i
\(943\) −6.79247 + 11.7649i −0.221193 + 0.383118i
\(944\) 0.274571i 0.00893652i
\(945\) 0 0
\(946\) 22.3804 + 38.7640i 0.727650 + 1.26033i
\(947\) 5.54457 + 9.60349i 0.180174 + 0.312071i 0.941940 0.335782i \(-0.109000\pi\)
−0.761765 + 0.647853i \(0.775667\pi\)
\(948\) 2.62105i 0.0851277i
\(949\) −53.7046 + 0.989796i −1.74333 + 0.0321301i
\(950\) 0 0
\(951\) 5.41352 3.12550i 0.175546 0.101351i
\(952\) 22.7305 13.1234i 0.736699 0.425333i
\(953\) 49.9313 + 28.8278i 1.61743 + 0.933825i 0.987581 + 0.157110i \(0.0502177\pi\)
0.629852 + 0.776715i \(0.283116\pi\)
\(954\) 2.23338i 0.0723084i
\(955\) 0 0
\(956\) −3.61118 2.08491i −0.116794 0.0674309i
\(957\) −29.1771 −0.943162
\(958\) 10.1231 + 5.84458i 0.327063 + 0.188830i
\(959\) −19.8201 34.3294i −0.640025 1.10856i
\(960\) 0 0
\(961\) 26.0120 0.839097
\(962\) −3.72173 + 6.72964i −0.119993 + 0.216972i
\(963\) 9.91673i 0.319562i
\(964\) −1.63165 + 0.942035i −0.0525520 + 0.0303409i
\(965\) 0 0
\(966\) 3.33600 5.77812i 0.107334 0.185908i
\(967\) −30.5218 −0.981516 −0.490758 0.871296i \(-0.663280\pi\)
−0.490758 + 0.871296i \(0.663280\pi\)
\(968\) 9.36252 16.2164i 0.300923 0.521214i
\(969\) −24.4688 14.1271i −0.786050 0.453826i
\(970\) 0 0
\(971\) −13.9787 + 24.2119i −0.448599 + 0.776996i −0.998295 0.0583686i \(-0.981410\pi\)
0.549696 + 0.835365i \(0.314743\pi\)
\(972\) −0.866025 + 0.500000i −0.0277778 + 0.0160375i
\(973\) −17.4167 30.1666i −0.558354 0.967098i
\(974\) −31.8875 −1.02174
\(975\) 0 0
\(976\) −4.13288 −0.132290
\(977\) 0.986516 + 1.70870i 0.0315614 + 0.0546660i 0.881375 0.472418i \(-0.156619\pi\)
−0.849813 + 0.527084i \(0.823285\pi\)
\(978\) −13.5046 + 7.79688i −0.431829 + 0.249317i
\(979\) 26.1529 45.2982i 0.835851 1.44774i
\(980\) 0 0
\(981\) −6.41801 3.70544i −0.204911 0.118306i
\(982\) 9.77506 16.9309i 0.311935 0.540286i
\(983\) −8.00792 −0.255413 −0.127707 0.991812i \(-0.540762\pi\)
−0.127707 + 0.991812i \(0.540762\pi\)
\(984\) 3.65519 6.33097i 0.116523 0.201824i
\(985\) 0 0
\(986\) −33.8806 + 19.5610i −1.07898 + 0.622949i
\(987\) 18.2283i 0.580212i
\(988\) 11.9378 7.18881i 0.379792 0.228706i
\(989\) 15.2565 0.485128
\(990\) 0 0
\(991\) −18.0138 31.2007i −0.572226 0.991124i −0.996337 0.0855139i \(-0.972747\pi\)
0.424111 0.905610i \(-0.360587\pi\)
\(992\) 1.93416 + 1.11669i 0.0614098 + 0.0354550i
\(993\) 19.1758 0.608526
\(994\) −44.4502 25.6633i −1.40987 0.813992i
\(995\) 0 0
\(996\) 7.15988i 0.226869i
\(997\) 44.3242 + 25.5906i 1.40376 + 0.810463i 0.994776 0.102078i \(-0.0325492\pi\)
0.408986 + 0.912541i \(0.365883\pi\)
\(998\) 34.0719 19.6714i 1.07853 0.622688i
\(999\) −1.84713 + 1.06644i −0.0584406 + 0.0337407i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1950.2.y.m.49.3 12
5.2 odd 4 1950.2.bc.k.751.6 yes 12
5.3 odd 4 1950.2.bc.h.751.1 12
5.4 even 2 1950.2.y.n.49.4 12
13.4 even 6 1950.2.y.n.199.4 12
65.4 even 6 inner 1950.2.y.m.199.3 12
65.17 odd 12 1950.2.bc.k.901.6 yes 12
65.43 odd 12 1950.2.bc.h.901.1 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1950.2.y.m.49.3 12 1.1 even 1 trivial
1950.2.y.m.199.3 12 65.4 even 6 inner
1950.2.y.n.49.4 12 5.4 even 2
1950.2.y.n.199.4 12 13.4 even 6
1950.2.bc.h.751.1 12 5.3 odd 4
1950.2.bc.h.901.1 yes 12 65.43 odd 12
1950.2.bc.k.751.6 yes 12 5.2 odd 4
1950.2.bc.k.901.6 yes 12 65.17 odd 12