Properties

Label 1470.2.n.k.79.4
Level $1470$
Weight $2$
Character 1470.79
Analytic conductor $11.738$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1470,2,Mod(79,1470)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1470, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1470.79");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.n (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: \(11.7380090971\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 18x^{14} + 227x^{12} - 1394x^{10} + 6177x^{8} - 14768x^{6} + 24768x^{4} - 11264x^{2} + 4096 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 79.4
Root \(-0.599547 - 0.346149i\) of defining polynomial
Character \(\chi\) \(=\) 1470.79
Dual form 1470.2.n.k.949.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.98078 - 1.03755i) q^{5} +1.00000 q^{6} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.98078 - 1.03755i) q^{5} +1.00000 q^{6} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.23418 - 0.0918501i) q^{10} +(-0.489528 - 0.847888i) q^{11} +(-0.866025 - 0.500000i) q^{12} -0.435157i q^{13} +(-1.19663 + 1.88893i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.42384 + 1.39940i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(3.67135 - 6.35897i) q^{19} +(1.88893 + 1.19663i) q^{20} +0.979056i q^{22} +(-2.89487 - 1.67135i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.84700 - 4.11030i) q^{25} +(-0.217579 + 0.376857i) q^{26} +1.00000i q^{27} -3.74825 q^{29} +(1.98078 - 1.03755i) q^{30} +(-2.48953 - 4.31199i) q^{31} +(0.866025 - 0.500000i) q^{32} +(0.847888 + 0.489528i) q^{33} +2.79881 q^{34} +1.00000 q^{36} +(-4.01482 - 2.31796i) q^{37} +(-6.35897 + 3.67135i) q^{38} +(0.217579 + 0.376857i) q^{39} +(-1.03755 - 1.98078i) q^{40} +4.94944 q^{41} +9.97862i q^{43} +(0.489528 - 0.847888i) q^{44} +(0.0918501 - 2.23418i) q^{45} +(1.67135 + 2.89487i) q^{46} +(-3.81531 - 2.20277i) q^{47} -1.00000i q^{48} +(-4.52072 + 2.13613i) q^{50} +(1.39940 - 2.42384i) q^{51} +(0.376857 - 0.217579i) q^{52} +(-0.569232 + 0.328646i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-1.84937 - 1.17157i) q^{55} +7.34271i q^{57} +(3.24608 + 1.87412i) q^{58} +(4.13613 + 7.16399i) q^{59} +(-2.23418 - 0.0918501i) q^{60} +(5.66680 - 9.81518i) q^{61} +4.97906i q^{62} -1.00000 q^{64} +(-0.451496 - 0.861952i) q^{65} +(-0.489528 - 0.847888i) q^{66} +(2.04698 - 1.18183i) q^{67} +(-2.42384 - 1.39940i) q^{68} +3.34271 q^{69} -14.1119 q^{71} +(-0.866025 - 0.500000i) q^{72} +(13.3306 - 7.69642i) q^{73} +(2.31796 + 4.01482i) q^{74} +(-0.410420 + 4.98313i) q^{75} +7.34271 q^{76} -0.435157i q^{78} +(-1.44383 + 2.50079i) q^{79} +(-0.0918501 + 2.23418i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.28634 - 2.47472i) q^{82} -14.3842i q^{83} +(-3.34915 + 5.28676i) q^{85} +(4.98931 - 8.64174i) q^{86} +(3.24608 - 1.87412i) q^{87} +(-0.847888 + 0.489528i) q^{88} +(5.06051 - 8.76505i) q^{89} +(-1.19663 + 1.88893i) q^{90} -3.34271i q^{92} +(4.31199 + 2.48953i) q^{93} +(2.20277 + 3.81531i) q^{94} +(0.674429 - 16.4049i) q^{95} +(-0.500000 + 0.866025i) q^{96} +10.6655i q^{97} -0.979056 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4} - 4 q^{5} + 16 q^{6} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{4} - 4 q^{5} + 16 q^{6} + 8 q^{9} - 8 q^{16} + 24 q^{19} - 8 q^{20} + 8 q^{24} - 4 q^{25} + 32 q^{29} - 4 q^{30} - 32 q^{31} - 16 q^{34} + 16 q^{36} + 48 q^{41} + 4 q^{45} - 8 q^{46} - 8 q^{50} - 8 q^{51} + 8 q^{54} + 40 q^{59} - 24 q^{61} - 16 q^{64} - 28 q^{65} - 16 q^{69} - 80 q^{71} - 16 q^{74} - 4 q^{75} + 48 q^{76} - 16 q^{79} - 4 q^{80} - 8 q^{81} + 56 q^{85} - 8 q^{86} + 88 q^{89} + 24 q^{94} - 24 q^{95} - 8 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).

\(n\) \(491\) \(1081\) \(1177\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) −0.866025 + 0.500000i −0.500000 + 0.288675i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 1.98078 1.03755i 0.885833 0.464005i
\(6\) 1.00000 0.408248
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) −2.23418 0.0918501i −0.706510 0.0290456i
\(11\) −0.489528 0.847888i −0.147598 0.255648i 0.782741 0.622348i \(-0.213821\pi\)
−0.930339 + 0.366700i \(0.880488\pi\)
\(12\) −0.866025 0.500000i −0.250000 0.144338i
\(13\) 0.435157i 0.120691i −0.998178 0.0603455i \(-0.980780\pi\)
0.998178 0.0603455i \(-0.0192202\pi\)
\(14\) 0 0
\(15\) −1.19663 + 1.88893i −0.308970 + 0.487720i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.42384 + 1.39940i −0.587867 + 0.339405i −0.764254 0.644916i \(-0.776892\pi\)
0.176386 + 0.984321i \(0.443559\pi\)
\(18\) −0.866025 + 0.500000i −0.204124 + 0.117851i
\(19\) 3.67135 6.35897i 0.842266 1.45885i −0.0457080 0.998955i \(-0.514554\pi\)
0.887974 0.459893i \(-0.152112\pi\)
\(20\) 1.88893 + 1.19663i 0.422378 + 0.267576i
\(21\) 0 0
\(22\) 0.979056i 0.208735i
\(23\) −2.89487 1.67135i −0.603622 0.348501i 0.166843 0.985983i \(-0.446643\pi\)
−0.770465 + 0.637482i \(0.779976\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) 2.84700 4.11030i 0.569399 0.822061i
\(26\) −0.217579 + 0.376857i −0.0426707 + 0.0739078i
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) −3.74825 −0.696032 −0.348016 0.937489i \(-0.613144\pi\)
−0.348016 + 0.937489i \(0.613144\pi\)
\(30\) 1.98078 1.03755i 0.361640 0.189429i
\(31\) −2.48953 4.31199i −0.447132 0.774456i 0.551066 0.834462i \(-0.314221\pi\)
−0.998198 + 0.0600058i \(0.980888\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 0.847888 + 0.489528i 0.147598 + 0.0852159i
\(34\) 2.79881 0.479992
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −4.01482 2.31796i −0.660032 0.381069i 0.132257 0.991215i \(-0.457777\pi\)
−0.792289 + 0.610146i \(0.791111\pi\)
\(38\) −6.35897 + 3.67135i −1.03156 + 0.595572i
\(39\) 0.217579 + 0.376857i 0.0348405 + 0.0603455i
\(40\) −1.03755 1.98078i −0.164050 0.313189i
\(41\) 4.94944 0.772972 0.386486 0.922295i \(-0.373689\pi\)
0.386486 + 0.922295i \(0.373689\pi\)
\(42\) 0 0
\(43\) 9.97862i 1.52172i 0.648913 + 0.760862i \(0.275224\pi\)
−0.648913 + 0.760862i \(0.724776\pi\)
\(44\) 0.489528 0.847888i 0.0737991 0.127824i
\(45\) 0.0918501 2.23418i 0.0136922 0.333052i
\(46\) 1.67135 + 2.89487i 0.246428 + 0.426825i
\(47\) −3.81531 2.20277i −0.556520 0.321307i 0.195228 0.980758i \(-0.437455\pi\)
−0.751748 + 0.659451i \(0.770789\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 0 0
\(50\) −4.52072 + 2.13613i −0.639327 + 0.302094i
\(51\) 1.39940 2.42384i 0.195956 0.339405i
\(52\) 0.376857 0.217579i 0.0522607 0.0301727i
\(53\) −0.569232 + 0.328646i −0.0781901 + 0.0451431i −0.538585 0.842571i \(-0.681041\pi\)
0.460395 + 0.887714i \(0.347708\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) −1.84937 1.17157i −0.249369 0.157975i
\(56\) 0 0
\(57\) 7.34271i 0.972565i
\(58\) 3.24608 + 1.87412i 0.426231 + 0.246084i
\(59\) 4.13613 + 7.16399i 0.538478 + 0.932672i 0.998986 + 0.0450161i \(0.0143339\pi\)
−0.460508 + 0.887656i \(0.652333\pi\)
\(60\) −2.23418 0.0918501i −0.288431 0.0118578i
\(61\) 5.66680 9.81518i 0.725559 1.25670i −0.233185 0.972432i \(-0.574915\pi\)
0.958744 0.284272i \(-0.0917520\pi\)
\(62\) 4.97906i 0.632341i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −0.451496 0.861952i −0.0560011 0.106912i
\(66\) −0.489528 0.847888i −0.0602567 0.104368i
\(67\) 2.04698 1.18183i 0.250079 0.144383i −0.369722 0.929143i \(-0.620547\pi\)
0.619800 + 0.784760i \(0.287214\pi\)
\(68\) −2.42384 1.39940i −0.293934 0.169703i
\(69\) 3.34271 0.402415
\(70\) 0 0
\(71\) −14.1119 −1.67477 −0.837387 0.546610i \(-0.815918\pi\)
−0.837387 + 0.546610i \(0.815918\pi\)
\(72\) −0.866025 0.500000i −0.102062 0.0589256i
\(73\) 13.3306 7.69642i 1.56023 0.900797i 0.562993 0.826461i \(-0.309650\pi\)
0.997233 0.0743360i \(-0.0236837\pi\)
\(74\) 2.31796 + 4.01482i 0.269457 + 0.466713i
\(75\) −0.410420 + 4.98313i −0.0473912 + 0.575402i
\(76\) 7.34271 0.842266
\(77\) 0 0
\(78\) 0.435157i 0.0492719i
\(79\) −1.44383 + 2.50079i −0.162444 + 0.281361i −0.935745 0.352678i \(-0.885271\pi\)
0.773301 + 0.634039i \(0.218604\pi\)
\(80\) −0.0918501 + 2.23418i −0.0102692 + 0.249789i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −4.28634 2.47472i −0.473347 0.273287i
\(83\) 14.3842i 1.57887i −0.613837 0.789433i \(-0.710375\pi\)
0.613837 0.789433i \(-0.289625\pi\)
\(84\) 0 0
\(85\) −3.34915 + 5.28676i −0.363266 + 0.573430i
\(86\) 4.98931 8.64174i 0.538011 0.931862i
\(87\) 3.24608 1.87412i 0.348016 0.200927i
\(88\) −0.847888 + 0.489528i −0.0903851 + 0.0521839i
\(89\) 5.06051 8.76505i 0.536412 0.929094i −0.462681 0.886525i \(-0.653112\pi\)
0.999094 0.0425688i \(-0.0135542\pi\)
\(90\) −1.19663 + 1.88893i −0.126136 + 0.199111i
\(91\) 0 0
\(92\) 3.34271i 0.348501i
\(93\) 4.31199 + 2.48953i 0.447132 + 0.258152i
\(94\) 2.20277 + 3.81531i 0.227198 + 0.393519i
\(95\) 0.674429 16.4049i 0.0691949 1.68311i
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) 10.6655i 1.08292i 0.840726 + 0.541460i \(0.182128\pi\)
−0.840726 + 0.541460i \(0.817872\pi\)
\(98\) 0 0
\(99\) −0.979056 −0.0983989
\(100\) 4.98313 + 0.410420i 0.498313 + 0.0410420i
\(101\) −7.01639 12.1527i −0.698157 1.20924i −0.969105 0.246649i \(-0.920671\pi\)
0.270948 0.962594i \(-0.412663\pi\)
\(102\) −2.42384 + 1.39940i −0.239996 + 0.138562i
\(103\) −8.99294 5.19208i −0.886101 0.511591i −0.0134358 0.999910i \(-0.504277\pi\)
−0.872665 + 0.488319i \(0.837610\pi\)
\(104\) −0.435157 −0.0426707
\(105\) 0 0
\(106\) 0.657293 0.0638419
\(107\) −17.3560 10.0205i −1.67787 0.968719i −0.963016 0.269446i \(-0.913160\pi\)
−0.714855 0.699273i \(-0.753507\pi\)
\(108\) −0.866025 + 0.500000i −0.0833333 + 0.0481125i
\(109\) 9.32821 + 16.1569i 0.893480 + 1.54755i 0.835674 + 0.549225i \(0.185077\pi\)
0.0578060 + 0.998328i \(0.481590\pi\)
\(110\) 1.01582 + 1.93930i 0.0968542 + 0.184905i
\(111\) 4.63591 0.440021
\(112\) 0 0
\(113\) 10.4132i 0.979587i −0.871838 0.489794i \(-0.837072\pi\)
0.871838 0.489794i \(-0.162928\pi\)
\(114\) 3.67135 6.35897i 0.343854 0.595572i
\(115\) −7.46821 0.307028i −0.696414 0.0286305i
\(116\) −1.87412 3.24608i −0.174008 0.301391i
\(117\) −0.376857 0.217579i −0.0348405 0.0201152i
\(118\) 8.27226i 0.761523i
\(119\) 0 0
\(120\) 1.88893 + 1.19663i 0.172435 + 0.109237i
\(121\) 5.02072 8.69615i 0.456429 0.790559i
\(122\) −9.81518 + 5.66680i −0.888625 + 0.513048i
\(123\) −4.28634 + 2.47472i −0.386486 + 0.223138i
\(124\) 2.48953 4.31199i 0.223566 0.387228i
\(125\) 1.37465 11.0955i 0.122953 0.992413i
\(126\) 0 0
\(127\) 11.6987i 1.03810i −0.854745 0.519048i \(-0.826287\pi\)
0.854745 0.519048i \(-0.173713\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) −4.98931 8.64174i −0.439284 0.760862i
\(130\) −0.0399693 + 0.972220i −0.00350554 + 0.0852693i
\(131\) −2.69230 + 4.66320i −0.235227 + 0.407425i −0.959339 0.282258i \(-0.908917\pi\)
0.724112 + 0.689683i \(0.242250\pi\)
\(132\) 0.979056i 0.0852159i
\(133\) 0 0
\(134\) −2.36365 −0.204188
\(135\) 1.03755 + 1.98078i 0.0892977 + 0.170479i
\(136\) 1.39940 + 2.42384i 0.119998 + 0.207842i
\(137\) 3.19204 1.84293i 0.272715 0.157452i −0.357406 0.933949i \(-0.616339\pi\)
0.630121 + 0.776497i \(0.283005\pi\)
\(138\) −2.89487 1.67135i −0.246428 0.142275i
\(139\) −8.15378 −0.691595 −0.345797 0.938309i \(-0.612392\pi\)
−0.345797 + 0.938309i \(0.612392\pi\)
\(140\) 0 0
\(141\) 4.40554 0.371013
\(142\) 12.2213 + 7.05595i 1.02559 + 0.592122i
\(143\) −0.368964 + 0.213022i −0.0308544 + 0.0178138i
\(144\) 0.500000 + 0.866025i 0.0416667 + 0.0721688i
\(145\) −7.42446 + 3.88898i −0.616568 + 0.322962i
\(146\) −15.3928 −1.27392
\(147\) 0 0
\(148\) 4.63591i 0.381069i
\(149\) −7.83868 + 13.5770i −0.642170 + 1.11227i 0.342778 + 0.939417i \(0.388632\pi\)
−0.984947 + 0.172854i \(0.944701\pi\)
\(150\) 2.84700 4.11030i 0.232456 0.335605i
\(151\) −2.13613 3.69989i −0.173836 0.301092i 0.765922 0.642934i \(-0.222283\pi\)
−0.939758 + 0.341841i \(0.888950\pi\)
\(152\) −6.35897 3.67135i −0.515781 0.297786i
\(153\) 2.79881i 0.226270i
\(154\) 0 0
\(155\) −9.40510 5.95811i −0.755436 0.478567i
\(156\) −0.217579 + 0.376857i −0.0174202 + 0.0301727i
\(157\) 13.2067 7.62491i 1.05401 0.608534i 0.130242 0.991482i \(-0.458425\pi\)
0.923770 + 0.382948i \(0.125091\pi\)
\(158\) 2.50079 1.44383i 0.198952 0.114865i
\(159\) 0.328646 0.569232i 0.0260634 0.0451431i
\(160\) 1.19663 1.88893i 0.0946023 0.149333i
\(161\) 0 0
\(162\) 1.00000i 0.0785674i
\(163\) −6.47439 3.73799i −0.507114 0.292782i 0.224533 0.974467i \(-0.427914\pi\)
−0.731646 + 0.681684i \(0.761248\pi\)
\(164\) 2.47472 + 4.28634i 0.193243 + 0.334707i
\(165\) 2.18739 + 0.0899264i 0.170288 + 0.00700076i
\(166\) −7.19208 + 12.4570i −0.558214 + 0.966854i
\(167\) 12.6640i 0.979972i −0.871730 0.489986i \(-0.837002\pi\)
0.871730 0.489986i \(-0.162998\pi\)
\(168\) 0 0
\(169\) 12.8106 0.985434
\(170\) 5.54383 2.90389i 0.425192 0.222718i
\(171\) −3.67135 6.35897i −0.280755 0.486283i
\(172\) −8.64174 + 4.98931i −0.658926 + 0.380431i
\(173\) 6.16660 + 3.56029i 0.468838 + 0.270684i 0.715753 0.698354i \(-0.246084\pi\)
−0.246915 + 0.969037i \(0.579417\pi\)
\(174\) −3.74825 −0.284154
\(175\) 0 0
\(176\) 0.979056 0.0737991
\(177\) −7.16399 4.13613i −0.538478 0.310891i
\(178\) −8.76505 + 5.06051i −0.656968 + 0.379301i
\(179\) 1.63210 + 2.82688i 0.121989 + 0.211291i 0.920552 0.390620i \(-0.127739\pi\)
−0.798563 + 0.601911i \(0.794406\pi\)
\(180\) 1.98078 1.03755i 0.147639 0.0773341i
\(181\) 1.93823 0.144067 0.0720337 0.997402i \(-0.477051\pi\)
0.0720337 + 0.997402i \(0.477051\pi\)
\(182\) 0 0
\(183\) 11.3336i 0.837803i
\(184\) −1.67135 + 2.89487i −0.123214 + 0.213413i
\(185\) −10.3575 0.425809i −0.761496 0.0313061i
\(186\) −2.48953 4.31199i −0.182541 0.316170i
\(187\) 2.37307 + 1.37010i 0.173536 + 0.100191i
\(188\) 4.40554i 0.321307i
\(189\) 0 0
\(190\) −8.78654 + 13.8699i −0.637443 + 1.00623i
\(191\) −4.03500 + 6.98883i −0.291963 + 0.505694i −0.974274 0.225368i \(-0.927642\pi\)
0.682311 + 0.731062i \(0.260975\pi\)
\(192\) 0.866025 0.500000i 0.0625000 0.0360844i
\(193\) −1.69578 + 0.979056i −0.122065 + 0.0704740i −0.559789 0.828635i \(-0.689118\pi\)
0.437725 + 0.899109i \(0.355785\pi\)
\(194\) 5.33276 9.23662i 0.382870 0.663151i
\(195\) 0.821983 + 0.520724i 0.0588634 + 0.0372899i
\(196\) 0 0
\(197\) 17.3418i 1.23555i −0.786353 0.617777i \(-0.788033\pi\)
0.786353 0.617777i \(-0.211967\pi\)
\(198\) 0.847888 + 0.489528i 0.0602567 + 0.0347892i
\(199\) 1.29745 + 2.24725i 0.0919738 + 0.159303i 0.908342 0.418229i \(-0.137349\pi\)
−0.816368 + 0.577532i \(0.804016\pi\)
\(200\) −4.11030 2.84700i −0.290642 0.201313i
\(201\) −1.18183 + 2.04698i −0.0833595 + 0.144383i
\(202\) 14.0328i 0.987343i
\(203\) 0 0
\(204\) 2.79881 0.195956
\(205\) 9.80376 5.13527i 0.684724 0.358663i
\(206\) 5.19208 + 8.99294i 0.361749 + 0.626568i
\(207\) −2.89487 + 1.67135i −0.201207 + 0.116167i
\(208\) 0.376857 + 0.217579i 0.0261304 + 0.0150864i
\(209\) −7.18892 −0.497268
\(210\) 0 0
\(211\) 15.4127 1.06106 0.530528 0.847668i \(-0.321994\pi\)
0.530528 + 0.847668i \(0.321994\pi\)
\(212\) −0.569232 0.328646i −0.0390950 0.0225715i
\(213\) 12.2213 7.05595i 0.837387 0.483466i
\(214\) 10.0205 + 17.3560i 0.684988 + 1.18643i
\(215\) 10.3533 + 19.7655i 0.706087 + 1.34799i
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) 18.6564i 1.26357i
\(219\) −7.69642 + 13.3306i −0.520076 + 0.900797i
\(220\) 0.0899264 2.18739i 0.00606284 0.147474i
\(221\) 0.608961 + 1.05475i 0.0409631 + 0.0709502i
\(222\) −4.01482 2.31796i −0.269457 0.155571i
\(223\) 7.61497i 0.509936i −0.966950 0.254968i \(-0.917935\pi\)
0.966950 0.254968i \(-0.0820649\pi\)
\(224\) 0 0
\(225\) −2.13613 4.52072i −0.142409 0.301382i
\(226\) −5.20658 + 9.01806i −0.346336 + 0.599872i
\(227\) −7.22462 + 4.17113i −0.479515 + 0.276848i −0.720214 0.693752i \(-0.755956\pi\)
0.240700 + 0.970600i \(0.422623\pi\)
\(228\) −6.35897 + 3.67135i −0.421133 + 0.243141i
\(229\) 9.34503 16.1861i 0.617537 1.06961i −0.372396 0.928074i \(-0.621464\pi\)
0.989934 0.141532i \(-0.0452028\pi\)
\(230\) 6.31415 + 4.00000i 0.416343 + 0.263752i
\(231\) 0 0
\(232\) 3.74825i 0.246084i
\(233\) 17.3923 + 10.0414i 1.13941 + 0.657837i 0.946284 0.323337i \(-0.104805\pi\)
0.193124 + 0.981174i \(0.438138\pi\)
\(234\) 0.217579 + 0.376857i 0.0142236 + 0.0246359i
\(235\) −9.84277 0.404649i −0.642071 0.0263964i
\(236\) −4.13613 + 7.16399i −0.269239 + 0.466336i
\(237\) 2.88767i 0.187574i
\(238\) 0 0
\(239\) 22.2714 1.44062 0.720308 0.693654i \(-0.244000\pi\)
0.720308 + 0.693654i \(0.244000\pi\)
\(240\) −1.03755 1.98078i −0.0669733 0.127859i
\(241\) 3.10038 + 5.37001i 0.199713 + 0.345913i 0.948435 0.316971i \(-0.102666\pi\)
−0.748722 + 0.662884i \(0.769332\pi\)
\(242\) −8.69615 + 5.02072i −0.559010 + 0.322744i
\(243\) 0.866025 + 0.500000i 0.0555556 + 0.0320750i
\(244\) 11.3336 0.725559
\(245\) 0 0
\(246\) 4.94944 0.315565
\(247\) −2.76715 1.59762i −0.176070 0.101654i
\(248\) −4.31199 + 2.48953i −0.273812 + 0.158085i
\(249\) 7.19208 + 12.4570i 0.455779 + 0.789433i
\(250\) −6.73824 + 8.92167i −0.426164 + 0.564256i
\(251\) −27.6560 −1.74563 −0.872815 0.488051i \(-0.837708\pi\)
−0.872815 + 0.488051i \(0.837708\pi\)
\(252\) 0 0
\(253\) 3.27270i 0.205753i
\(254\) −5.84937 + 10.1314i −0.367022 + 0.635701i
\(255\) 0.257071 6.25304i 0.0160984 0.391581i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 10.1915 + 5.88407i 0.635728 + 0.367038i 0.782967 0.622063i \(-0.213705\pi\)
−0.147239 + 0.989101i \(0.547039\pi\)
\(258\) 9.97862i 0.621242i
\(259\) 0 0
\(260\) 0.520724 0.821983i 0.0322940 0.0509772i
\(261\) −1.87412 + 3.24608i −0.116005 + 0.200927i
\(262\) 4.66320 2.69230i 0.288093 0.166331i
\(263\) 0.394078 0.227521i 0.0242999 0.0140295i −0.487801 0.872955i \(-0.662201\pi\)
0.512101 + 0.858925i \(0.328867\pi\)
\(264\) 0.489528 0.847888i 0.0301284 0.0521839i
\(265\) −0.786540 + 1.24158i −0.0483167 + 0.0762698i
\(266\) 0 0
\(267\) 10.1210i 0.619396i
\(268\) 2.04698 + 1.18183i 0.125039 + 0.0721915i
\(269\) 13.0687 + 22.6357i 0.796815 + 1.38012i 0.921680 + 0.387951i \(0.126817\pi\)
−0.124865 + 0.992174i \(0.539850\pi\)
\(270\) 0.0918501 2.23418i 0.00558982 0.135968i
\(271\) −8.38840 + 14.5291i −0.509559 + 0.882582i 0.490380 + 0.871509i \(0.336858\pi\)
−0.999939 + 0.0110734i \(0.996475\pi\)
\(272\) 2.79881i 0.169703i
\(273\) 0 0
\(274\) −3.68585 −0.222671
\(275\) −4.87876 0.401824i −0.294200 0.0242309i
\(276\) 1.67135 + 2.89487i 0.100604 + 0.174251i
\(277\) −17.9681 + 10.3739i −1.07960 + 0.623307i −0.930789 0.365558i \(-0.880878\pi\)
−0.148812 + 0.988866i \(0.547545\pi\)
\(278\) 7.06138 + 4.07689i 0.423514 + 0.244516i
\(279\) −4.97906 −0.298088
\(280\) 0 0
\(281\) −18.3141 −1.09253 −0.546265 0.837612i \(-0.683951\pi\)
−0.546265 + 0.837612i \(0.683951\pi\)
\(282\) −3.81531 2.20277i −0.227198 0.131173i
\(283\) 10.2646 5.92626i 0.610166 0.352280i −0.162864 0.986649i \(-0.552073\pi\)
0.773031 + 0.634369i \(0.218740\pi\)
\(284\) −7.05595 12.2213i −0.418693 0.725198i
\(285\) 7.61840 + 14.5443i 0.451275 + 0.861530i
\(286\) 0.426043 0.0251925
\(287\) 0 0
\(288\) 1.00000i 0.0589256i
\(289\) −4.58334 + 7.93857i −0.269608 + 0.466975i
\(290\) 8.37426 + 0.344277i 0.491753 + 0.0202166i
\(291\) −5.33276 9.23662i −0.312612 0.541460i
\(292\) 13.3306 + 7.69642i 0.780113 + 0.450399i
\(293\) 14.4770i 0.845758i 0.906186 + 0.422879i \(0.138980\pi\)
−0.906186 + 0.422879i \(0.861020\pi\)
\(294\) 0 0
\(295\) 15.6257 + 9.89887i 0.909766 + 0.576335i
\(296\) −2.31796 + 4.01482i −0.134728 + 0.233356i
\(297\) 0.847888 0.489528i 0.0491994 0.0284053i
\(298\) 13.5770 7.83868i 0.786494 0.454083i
\(299\) −0.727302 + 1.25972i −0.0420609 + 0.0728517i
\(300\) −4.52072 + 2.13613i −0.261004 + 0.123330i
\(301\) 0 0
\(302\) 4.27226i 0.245841i
\(303\) 12.1527 + 7.01639i 0.698157 + 0.403081i
\(304\) 3.67135 + 6.35897i 0.210567 + 0.364712i
\(305\) 1.04099 25.3213i 0.0596070 1.44989i
\(306\) 1.39940 2.42384i 0.0799986 0.138562i
\(307\) 30.4252i 1.73646i 0.496165 + 0.868228i \(0.334741\pi\)
−0.496165 + 0.868228i \(0.665259\pi\)
\(308\) 0 0
\(309\) 10.3842 0.590734
\(310\) 5.16600 + 9.86243i 0.293409 + 0.560148i
\(311\) 4.51428 + 7.81896i 0.255981 + 0.443373i 0.965162 0.261655i \(-0.0842681\pi\)
−0.709180 + 0.705027i \(0.750935\pi\)
\(312\) 0.376857 0.217579i 0.0213353 0.0123180i
\(313\) 14.8725 + 8.58662i 0.840641 + 0.485344i 0.857482 0.514514i \(-0.172028\pi\)
−0.0168412 + 0.999858i \(0.505361\pi\)
\(314\) −15.2498 −0.860597
\(315\) 0 0
\(316\) −2.88767 −0.162444
\(317\) −2.26501 1.30770i −0.127215 0.0734479i 0.435042 0.900410i \(-0.356734\pi\)
−0.562257 + 0.826962i \(0.690067\pi\)
\(318\) −0.569232 + 0.328646i −0.0319210 + 0.0184296i
\(319\) 1.83487 + 3.17809i 0.102733 + 0.177939i
\(320\) −1.98078 + 1.03755i −0.110729 + 0.0580006i
\(321\) 20.0410 1.11858
\(322\) 0 0
\(323\) 20.5508i 1.14348i
\(324\) 0.500000 0.866025i 0.0277778 0.0481125i
\(325\) −1.78863 1.23889i −0.0992153 0.0687213i
\(326\) 3.73799 + 6.47439i 0.207028 + 0.358584i
\(327\) −16.1569 9.32821i −0.893480 0.515851i
\(328\) 4.94944i 0.273287i
\(329\) 0 0
\(330\) −1.84937 1.17157i −0.101805 0.0644930i
\(331\) 8.87793 15.3770i 0.487975 0.845198i −0.511929 0.859028i \(-0.671069\pi\)
0.999904 + 0.0138298i \(0.00440231\pi\)
\(332\) 12.4570 7.19208i 0.683669 0.394717i
\(333\) −4.01482 + 2.31796i −0.220011 + 0.127023i
\(334\) −6.33202 + 10.9674i −0.346472 + 0.600108i
\(335\) 2.82843 4.46478i 0.154533 0.243937i
\(336\) 0 0
\(337\) 24.2304i 1.31991i −0.751304 0.659956i \(-0.770575\pi\)
0.751304 0.659956i \(-0.229425\pi\)
\(338\) −11.0943 6.40532i −0.603452 0.348403i
\(339\) 5.20658 + 9.01806i 0.282782 + 0.489794i
\(340\) −6.25304 0.257071i −0.339119 0.0139416i
\(341\) −2.43739 + 4.22168i −0.131992 + 0.228617i
\(342\) 7.34271i 0.397048i
\(343\) 0 0
\(344\) 9.97862 0.538011
\(345\) 6.62118 3.46821i 0.356472 0.186722i
\(346\) −3.56029 6.16660i −0.191402 0.331518i
\(347\) 26.3490 15.2126i 1.41449 0.816654i 0.418680 0.908134i \(-0.362493\pi\)
0.995807 + 0.0914797i \(0.0291597\pi\)
\(348\) 3.24608 + 1.87412i 0.174008 + 0.100464i
\(349\) −30.2623 −1.61990 −0.809951 0.586497i \(-0.800506\pi\)
−0.809951 + 0.586497i \(0.800506\pi\)
\(350\) 0 0
\(351\) 0.435157 0.0232270
\(352\) −0.847888 0.489528i −0.0451926 0.0260919i
\(353\) −3.78617 + 2.18594i −0.201517 + 0.116346i −0.597363 0.801971i \(-0.703785\pi\)
0.395846 + 0.918317i \(0.370451\pi\)
\(354\) 4.13613 + 7.16399i 0.219833 + 0.380762i
\(355\) −27.9526 + 14.6417i −1.48357 + 0.777103i
\(356\) 10.1210 0.536412
\(357\) 0 0
\(358\) 3.26420i 0.172519i
\(359\) −7.84249 + 13.5836i −0.413911 + 0.716914i −0.995313 0.0967016i \(-0.969171\pi\)
0.581403 + 0.813616i \(0.302504\pi\)
\(360\) −2.23418 0.0918501i −0.117752 0.00484093i
\(361\) −17.4577 30.2376i −0.918825 1.59145i
\(362\) −1.67855 0.969114i −0.0882229 0.0509355i
\(363\) 10.0414i 0.527039i
\(364\) 0 0
\(365\) 18.4196 29.0760i 0.964126 1.52191i
\(366\) 5.66680 9.81518i 0.296208 0.513048i
\(367\) −4.28231 + 2.47239i −0.223535 + 0.129058i −0.607586 0.794254i \(-0.707862\pi\)
0.384051 + 0.923312i \(0.374529\pi\)
\(368\) 2.89487 1.67135i 0.150905 0.0871253i
\(369\) 2.47472 4.28634i 0.128829 0.223138i
\(370\) 8.75692 + 5.54749i 0.455251 + 0.288400i
\(371\) 0 0
\(372\) 4.97906i 0.258152i
\(373\) −5.21467 3.01069i −0.270005 0.155888i 0.358885 0.933382i \(-0.383157\pi\)
−0.628890 + 0.777494i \(0.716490\pi\)
\(374\) −1.37010 2.37307i −0.0708459 0.122709i
\(375\) 4.35727 + 10.2963i 0.225009 + 0.531700i
\(376\) −2.20277 + 3.81531i −0.113599 + 0.196759i
\(377\) 1.63108i 0.0840047i
\(378\) 0 0
\(379\) 36.8030 1.89044 0.945222 0.326429i \(-0.105845\pi\)
0.945222 + 0.326429i \(0.105845\pi\)
\(380\) 14.5443 7.61840i 0.746107 0.390815i
\(381\) 5.84937 + 10.1314i 0.299672 + 0.519048i
\(382\) 6.98883 4.03500i 0.357580 0.206449i
\(383\) 7.82353 + 4.51692i 0.399764 + 0.230804i 0.686382 0.727241i \(-0.259198\pi\)
−0.286618 + 0.958045i \(0.592531\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 1.95811 0.0996653
\(387\) 8.64174 + 4.98931i 0.439284 + 0.253621i
\(388\) −9.23662 + 5.33276i −0.468918 + 0.270730i
\(389\) 16.7823 + 29.0678i 0.850896 + 1.47380i 0.880401 + 0.474231i \(0.157274\pi\)
−0.0295047 + 0.999565i \(0.509393\pi\)
\(390\) −0.451496 0.861952i −0.0228624 0.0436466i
\(391\) 9.35560 0.473133
\(392\) 0 0
\(393\) 5.38459i 0.271617i
\(394\) −8.67091 + 15.0185i −0.436834 + 0.756619i
\(395\) −0.265232 + 6.45157i −0.0133453 + 0.324613i
\(396\) −0.489528 0.847888i −0.0245997 0.0426080i
\(397\) 29.4269 + 16.9896i 1.47689 + 0.852685i 0.999660 0.0260921i \(-0.00830630\pi\)
0.477233 + 0.878777i \(0.341640\pi\)
\(398\) 2.59490i 0.130071i
\(399\) 0 0
\(400\) 2.13613 + 4.52072i 0.106806 + 0.226036i
\(401\) 2.13613 3.69989i 0.106673 0.184763i −0.807747 0.589529i \(-0.799313\pi\)
0.914421 + 0.404765i \(0.132647\pi\)
\(402\) 2.04698 1.18183i 0.102094 0.0589441i
\(403\) −1.87639 + 1.08334i −0.0934698 + 0.0539648i
\(404\) 7.01639 12.1527i 0.349078 0.604621i
\(405\) −1.88893 1.19663i −0.0938618 0.0594613i
\(406\) 0 0
\(407\) 4.53882i 0.224981i
\(408\) −2.42384 1.39940i −0.119998 0.0692808i
\(409\) 1.81944 + 3.15137i 0.0899656 + 0.155825i 0.907496 0.420060i \(-0.137991\pi\)
−0.817531 + 0.575885i \(0.804658\pi\)
\(410\) −11.0579 0.454606i −0.546113 0.0224514i
\(411\) −1.84293 + 3.19204i −0.0909049 + 0.157452i
\(412\) 10.3842i 0.511591i
\(413\) 0 0
\(414\) 3.34271 0.164285
\(415\) −14.9242 28.4919i −0.732601 1.39861i
\(416\) −0.217579 0.376857i −0.0106677 0.0184769i
\(417\) 7.06138 4.07689i 0.345797 0.199646i
\(418\) 6.22579 + 3.59446i 0.304513 + 0.175811i
\(419\) 26.6274 1.30083 0.650417 0.759577i \(-0.274594\pi\)
0.650417 + 0.759577i \(0.274594\pi\)
\(420\) 0 0
\(421\) −15.1880 −0.740220 −0.370110 0.928988i \(-0.620680\pi\)
−0.370110 + 0.928988i \(0.620680\pi\)
\(422\) −13.3478 7.70636i −0.649761 0.375140i
\(423\) −3.81531 + 2.20277i −0.185507 + 0.107102i
\(424\) 0.328646 + 0.569232i 0.0159605 + 0.0276444i
\(425\) −1.14869 + 13.9468i −0.0557194 + 0.676520i
\(426\) −14.1119 −0.683724
\(427\) 0 0
\(428\) 20.0410i 0.968719i
\(429\) 0.213022 0.368964i 0.0102848 0.0178138i
\(430\) 0.916537 22.2940i 0.0441993 1.07511i
\(431\) 2.11562 + 3.66437i 0.101906 + 0.176506i 0.912470 0.409144i \(-0.134173\pi\)
−0.810564 + 0.585650i \(0.800839\pi\)
\(432\) −0.866025 0.500000i −0.0416667 0.0240563i
\(433\) 33.9352i 1.63082i 0.578882 + 0.815412i \(0.303489\pi\)
−0.578882 + 0.815412i \(0.696511\pi\)
\(434\) 0 0
\(435\) 4.48528 7.08018i 0.215053 0.339469i
\(436\) −9.32821 + 16.1569i −0.446740 + 0.773777i
\(437\) −21.2562 + 12.2723i −1.01682 + 0.587062i
\(438\) 13.3306 7.69642i 0.636960 0.367749i
\(439\) 2.74128 4.74804i 0.130834 0.226612i −0.793164 0.609008i \(-0.791568\pi\)
0.923998 + 0.382396i \(0.124901\pi\)
\(440\) −1.17157 + 1.84937i −0.0558525 + 0.0881653i
\(441\) 0 0
\(442\) 1.21792i 0.0579306i
\(443\) 1.06591 + 0.615405i 0.0506431 + 0.0292388i 0.525108 0.851036i \(-0.324025\pi\)
−0.474465 + 0.880275i \(0.657358\pi\)
\(444\) 2.31796 + 4.01482i 0.110005 + 0.190535i
\(445\) 0.929616 22.6122i 0.0440680 1.07192i
\(446\) −3.80748 + 6.59475i −0.180290 + 0.312271i
\(447\) 15.6774i 0.741514i
\(448\) 0 0
\(449\) −14.6435 −0.691071 −0.345535 0.938406i \(-0.612303\pi\)
−0.345535 + 0.938406i \(0.612303\pi\)
\(450\) −0.410420 + 4.98313i −0.0193474 + 0.234907i
\(451\) −2.42289 4.19657i −0.114089 0.197609i
\(452\) 9.01806 5.20658i 0.424174 0.244897i
\(453\) 3.69989 + 2.13613i 0.173836 + 0.100364i
\(454\) 8.34227 0.391522
\(455\) 0 0
\(456\) 7.34271 0.343854
\(457\) 27.1317 + 15.6645i 1.26917 + 0.732753i 0.974830 0.222949i \(-0.0715684\pi\)
0.294335 + 0.955702i \(0.404902\pi\)
\(458\) −16.1861 + 9.34503i −0.756325 + 0.436665i
\(459\) −1.39940 2.42384i −0.0653186 0.113135i
\(460\) −3.46821 6.62118i −0.161706 0.308714i
\(461\) −12.7667 −0.594602 −0.297301 0.954784i \(-0.596087\pi\)
−0.297301 + 0.954784i \(0.596087\pi\)
\(462\) 0 0
\(463\) 26.7112i 1.24137i 0.784058 + 0.620687i \(0.213146\pi\)
−0.784058 + 0.620687i \(0.786854\pi\)
\(464\) 1.87412 3.24608i 0.0870040 0.150695i
\(465\) 11.1241 + 0.457327i 0.515868 + 0.0212080i
\(466\) −10.0414 17.3923i −0.465161 0.805683i
\(467\) −32.5748 18.8070i −1.50738 0.870286i −0.999963 0.00858551i \(-0.997267\pi\)
−0.507417 0.861701i \(-0.669400\pi\)
\(468\) 0.435157i 0.0201152i
\(469\) 0 0
\(470\) 8.32176 + 5.27182i 0.383854 + 0.243171i
\(471\) −7.62491 + 13.2067i −0.351337 + 0.608534i
\(472\) 7.16399 4.13613i 0.329749 0.190381i
\(473\) 8.46075 4.88481i 0.389026 0.224604i
\(474\) −1.44383 + 2.50079i −0.0663174 + 0.114865i
\(475\) −15.6850 33.1944i −0.719676 1.52306i
\(476\) 0 0
\(477\) 0.657293i 0.0300954i
\(478\) −19.2876 11.1357i −0.882194 0.509335i
\(479\) 11.9118 + 20.6318i 0.544262 + 0.942690i 0.998653 + 0.0518875i \(0.0165237\pi\)
−0.454391 + 0.890803i \(0.650143\pi\)
\(480\) −0.0918501 + 2.23418i −0.00419237 + 0.101976i
\(481\) −1.00868 + 1.74708i −0.0459916 + 0.0796598i
\(482\) 6.20075i 0.282437i
\(483\) 0 0
\(484\) 10.0414 0.456429
\(485\) 11.0660 + 21.1261i 0.502480 + 0.959286i
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) −3.25343 + 1.87837i −0.147427 + 0.0851170i −0.571899 0.820324i \(-0.693793\pi\)
0.424472 + 0.905441i \(0.360460\pi\)
\(488\) −9.81518 5.66680i −0.444312 0.256524i
\(489\) 7.47599 0.338076
\(490\) 0 0
\(491\) 2.00762 0.0906025 0.0453012 0.998973i \(-0.485575\pi\)
0.0453012 + 0.998973i \(0.485575\pi\)
\(492\) −4.28634 2.47472i −0.193243 0.111569i
\(493\) 9.08514 5.24531i 0.409174 0.236237i
\(494\) 1.59762 + 2.76715i 0.0718802 + 0.124500i
\(495\) −1.93930 + 1.01582i −0.0871649 + 0.0456575i
\(496\) 4.97906 0.223566
\(497\) 0 0
\(498\) 14.3842i 0.644569i
\(499\) −0.314147 + 0.544119i −0.0140632 + 0.0243581i −0.872971 0.487772i \(-0.837810\pi\)
0.858908 + 0.512130i \(0.171143\pi\)
\(500\) 10.2963 4.35727i 0.460465 0.194863i
\(501\) 6.33202 + 10.9674i 0.282894 + 0.489986i
\(502\) 23.9508 + 13.8280i 1.06898 + 0.617173i
\(503\) 28.9911i 1.29265i 0.763063 + 0.646324i \(0.223695\pi\)
−0.763063 + 0.646324i \(0.776305\pi\)
\(504\) 0 0
\(505\) −26.5070 16.7921i −1.17954 0.747239i
\(506\) 1.63635 2.83424i 0.0727446 0.125997i
\(507\) −11.0943 + 6.40532i −0.492717 + 0.284470i
\(508\) 10.1314 5.84937i 0.449509 0.259524i
\(509\) 7.75280 13.4282i 0.343637 0.595197i −0.641468 0.767150i \(-0.721674\pi\)
0.985105 + 0.171953i \(0.0550077\pi\)
\(510\) −3.34915 + 5.28676i −0.148303 + 0.234102i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 6.35897 + 3.67135i 0.280755 + 0.162094i
\(514\) −5.88407 10.1915i −0.259535 0.449528i
\(515\) −23.2001 0.953786i −1.02232 0.0420288i
\(516\) 4.98931 8.64174i 0.219642 0.380431i
\(517\) 4.31327i 0.189697i
\(518\) 0 0
\(519\) −7.12057 −0.312558
\(520\) −0.861952 + 0.451496i −0.0377991 + 0.0197994i
\(521\) −6.77660 11.7374i −0.296888 0.514225i 0.678534 0.734569i \(-0.262616\pi\)
−0.975422 + 0.220343i \(0.929282\pi\)
\(522\) 3.24608 1.87412i 0.142077 0.0820281i
\(523\) −19.4459 11.2271i −0.850309 0.490926i 0.0104462 0.999945i \(-0.496675\pi\)
−0.860755 + 0.509019i \(0.830008\pi\)
\(524\) −5.38459 −0.235227
\(525\) 0 0
\(526\) −0.455042 −0.0198408
\(527\) 12.0684 + 6.96771i 0.525709 + 0.303518i
\(528\) −0.847888 + 0.489528i −0.0368996 + 0.0213040i
\(529\) −5.91315 10.2419i −0.257094 0.445299i
\(530\) 1.30195 0.681971i 0.0565533 0.0296229i
\(531\) 8.27226 0.358985
\(532\) 0 0
\(533\) 2.15378i 0.0932907i
\(534\) 5.06051 8.76505i 0.218989 0.379301i
\(535\) −44.7752 1.84077i −1.93580 0.0795834i
\(536\) −1.18183 2.04698i −0.0510471 0.0884161i
\(537\) −2.82688 1.63210i −0.121989 0.0704304i
\(538\) 26.1375i 1.12687i
\(539\) 0 0
\(540\) −1.19663 + 1.88893i −0.0514950 + 0.0812867i
\(541\) −5.40554 + 9.36267i −0.232402 + 0.402532i −0.958515 0.285044i \(-0.907992\pi\)
0.726112 + 0.687576i \(0.241325\pi\)
\(542\) 14.5291 8.38840i 0.624080 0.360313i
\(543\) −1.67855 + 0.969114i −0.0720337 + 0.0415887i
\(544\) −1.39940 + 2.42384i −0.0599990 + 0.103921i
\(545\) 35.2407 + 22.3249i 1.50955 + 0.956294i
\(546\) 0 0
\(547\) 24.1881i 1.03421i −0.855923 0.517103i \(-0.827010\pi\)
0.855923 0.517103i \(-0.172990\pi\)
\(548\) 3.19204 + 1.84293i 0.136357 + 0.0787259i
\(549\) −5.66680 9.81518i −0.241853 0.418902i
\(550\) 4.02422 + 2.78737i 0.171593 + 0.118854i
\(551\) −13.7611 + 23.8350i −0.586244 + 1.01540i
\(552\) 3.34271i 0.142275i
\(553\) 0 0
\(554\) 20.7478 0.881490
\(555\) 9.18273 4.80997i 0.389785 0.204172i
\(556\) −4.07689 7.06138i −0.172899 0.299469i
\(557\) −22.6491 + 13.0765i −0.959672 + 0.554067i −0.896072 0.443908i \(-0.853592\pi\)
−0.0636002 + 0.997975i \(0.520258\pi\)
\(558\) 4.31199 + 2.48953i 0.182541 + 0.105390i
\(559\) 4.34227 0.183658
\(560\) 0 0
\(561\) −2.74019 −0.115691
\(562\) 15.8605 + 9.15707i 0.669036 + 0.386268i
\(563\) 9.16810 5.29320i 0.386389 0.223082i −0.294205 0.955742i \(-0.595055\pi\)
0.680594 + 0.732660i \(0.261722\pi\)
\(564\) 2.20277 + 3.81531i 0.0927533 + 0.160653i
\(565\) −10.8041 20.6262i −0.454533 0.867750i
\(566\) −11.8525 −0.498199
\(567\) 0 0
\(568\) 14.1119i 0.592122i
\(569\) 7.82198 13.5481i 0.327915 0.567965i −0.654183 0.756336i \(-0.726988\pi\)
0.982098 + 0.188371i \(0.0603208\pi\)
\(570\) 0.674429 16.4049i 0.0282487 0.687127i
\(571\) −4.25491 7.36972i −0.178062 0.308413i 0.763154 0.646216i \(-0.223650\pi\)
−0.941217 + 0.337803i \(0.890316\pi\)
\(572\) −0.368964 0.213022i −0.0154272 0.00890689i
\(573\) 8.07001i 0.337129i
\(574\) 0 0
\(575\) −15.1115 + 7.14046i −0.630191 + 0.297778i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 8.38138 4.83899i 0.348921 0.201450i −0.315289 0.948996i \(-0.602101\pi\)
0.664210 + 0.747546i \(0.268768\pi\)
\(578\) 7.93857 4.58334i 0.330201 0.190642i
\(579\) 0.979056 1.69578i 0.0406882 0.0704740i
\(580\) −7.08018 4.48528i −0.293989 0.186241i
\(581\) 0 0
\(582\) 10.6655i 0.442100i
\(583\) 0.557310 + 0.321763i 0.0230814 + 0.0133261i
\(584\) −7.69642 13.3306i −0.318480 0.551623i
\(585\) −0.972220 0.0399693i −0.0401964 0.00165253i
\(586\) 7.23852 12.5375i 0.299021 0.517919i
\(587\) 16.3013i 0.672825i −0.941715 0.336412i \(-0.890786\pi\)
0.941715 0.336412i \(-0.109214\pi\)
\(588\) 0 0
\(589\) −36.5598 −1.50642
\(590\) −8.58285 16.3855i −0.353350 0.674582i
\(591\) 8.67091 + 15.0185i 0.356674 + 0.617777i
\(592\) 4.01482 2.31796i 0.165008 0.0952674i
\(593\) −10.8082 6.24010i −0.443838 0.256250i 0.261386 0.965234i \(-0.415820\pi\)
−0.705224 + 0.708984i \(0.749154\pi\)
\(594\) −0.979056 −0.0401712
\(595\) 0 0
\(596\) −15.6774 −0.642170
\(597\) −2.24725 1.29745i −0.0919738 0.0531011i
\(598\) 1.25972 0.727302i 0.0515139 0.0297416i
\(599\) 20.3773 + 35.2945i 0.832593 + 1.44209i 0.895975 + 0.444104i \(0.146478\pi\)
−0.0633826 + 0.997989i \(0.520189\pi\)
\(600\) 4.98313 + 0.410420i 0.203435 + 0.0167553i
\(601\) −4.94541 −0.201727 −0.100864 0.994900i \(-0.532161\pi\)
−0.100864 + 0.994900i \(0.532161\pi\)
\(602\) 0 0
\(603\) 2.36365i 0.0962553i
\(604\) 2.13613 3.69989i 0.0869179 0.150546i
\(605\) 0.922308 22.4344i 0.0374972 0.912089i
\(606\) −7.01639 12.1527i −0.285021 0.493671i
\(607\) 0.754789 + 0.435778i 0.0306359 + 0.0176877i 0.515240 0.857046i \(-0.327703\pi\)
−0.484604 + 0.874734i \(0.661036\pi\)
\(608\) 7.34271i 0.297786i
\(609\) 0 0
\(610\) −13.5622 + 21.4084i −0.549116 + 0.866800i
\(611\) −0.958551 + 1.66026i −0.0387788 + 0.0671669i
\(612\) −2.42384 + 1.39940i −0.0979779 + 0.0565676i
\(613\) −31.9570 + 18.4504i −1.29073 + 0.745203i −0.978784 0.204897i \(-0.934314\pi\)
−0.311946 + 0.950100i \(0.600981\pi\)
\(614\) 15.2126 26.3490i 0.613930 1.06336i
\(615\) −5.92267 + 9.34915i −0.238825 + 0.376994i
\(616\) 0 0
\(617\) 28.6911i 1.15506i 0.816369 + 0.577530i \(0.195984\pi\)
−0.816369 + 0.577530i \(0.804016\pi\)
\(618\) −8.99294 5.19208i −0.361749 0.208856i
\(619\) 3.15707 + 5.46821i 0.126894 + 0.219786i 0.922472 0.386065i \(-0.126166\pi\)
−0.795578 + 0.605851i \(0.792833\pi\)
\(620\) 0.457327 11.1241i 0.0183667 0.446755i
\(621\) 1.67135 2.89487i 0.0670691 0.116167i
\(622\) 9.02856i 0.362012i
\(623\) 0 0
\(624\) −0.435157 −0.0174202
\(625\) −8.78921 23.4041i −0.351569 0.936162i
\(626\) −8.58662 14.8725i −0.343190 0.594423i
\(627\) 6.22579 3.59446i 0.248634 0.143549i
\(628\) 13.2067 + 7.62491i 0.527006 + 0.304267i
\(629\) 12.9750 0.517348
\(630\) 0 0
\(631\) −0.237559 −0.00945707 −0.00472853 0.999989i \(-0.501505\pi\)
−0.00472853 + 0.999989i \(0.501505\pi\)
\(632\) 2.50079 + 1.44383i 0.0994761 + 0.0574326i
\(633\) −13.3478 + 7.70636i −0.530528 + 0.306300i
\(634\) 1.30770 + 2.26501i 0.0519355 + 0.0899549i
\(635\) −12.1380 23.1727i −0.481681 0.919579i
\(636\) 0.657293 0.0260634
\(637\) 0 0
\(638\) 3.66974i 0.145287i
\(639\) −7.05595 + 12.2213i −0.279129 + 0.483466i
\(640\) 2.23418 + 0.0918501i 0.0883137 + 0.00363069i
\(641\) 7.67451 + 13.2926i 0.303125 + 0.525028i 0.976842 0.213962i \(-0.0686367\pi\)
−0.673717 + 0.738989i \(0.735303\pi\)
\(642\) −17.3560 10.0205i −0.684988 0.395478i
\(643\) 8.77577i 0.346083i 0.984915 + 0.173041i \(0.0553594\pi\)
−0.984915 + 0.173041i \(0.944641\pi\)
\(644\) 0 0
\(645\) −18.8489 11.9408i −0.742176 0.470167i
\(646\) 10.2754 17.7975i 0.404281 0.700235i
\(647\) 16.6714 9.62522i 0.655419 0.378406i −0.135110 0.990831i \(-0.543139\pi\)
0.790529 + 0.612424i \(0.209806\pi\)
\(648\) −0.866025 + 0.500000i −0.0340207 + 0.0196419i
\(649\) 4.04950 7.01395i 0.158957 0.275321i
\(650\) 0.929553 + 1.96723i 0.0364600 + 0.0771610i
\(651\) 0 0
\(652\) 7.47599i 0.292782i
\(653\) 6.45588 + 3.72730i 0.252638 + 0.145861i 0.620972 0.783833i \(-0.286738\pi\)
−0.368334 + 0.929694i \(0.620072\pi\)
\(654\) 9.32821 + 16.1569i 0.364762 + 0.631786i
\(655\) −0.494576 + 12.0302i −0.0193247 + 0.470057i
\(656\) −2.47472 + 4.28634i −0.0966215 + 0.167353i
\(657\) 15.3928i 0.600532i
\(658\) 0 0
\(659\) −2.93717 −0.114416 −0.0572079 0.998362i \(-0.518220\pi\)
−0.0572079 + 0.998362i \(0.518220\pi\)
\(660\) 1.01582 + 1.93930i 0.0395406 + 0.0754870i
\(661\) 11.8180 + 20.4695i 0.459669 + 0.796170i 0.998943 0.0459604i \(-0.0146348\pi\)
−0.539275 + 0.842130i \(0.681301\pi\)
\(662\) −15.3770 + 8.87793i −0.597645 + 0.345051i
\(663\) −1.05475 0.608961i −0.0409631 0.0236501i
\(664\) −14.3842 −0.558214
\(665\) 0 0
\(666\) 4.63591 0.179638
\(667\) 10.8507 + 6.26464i 0.420140 + 0.242568i
\(668\) 10.9674 6.33202i 0.424340 0.244993i
\(669\) 3.80748 + 6.59475i 0.147206 + 0.254968i
\(670\) −4.68188 + 2.45240i −0.180877 + 0.0947443i
\(671\) −11.0962 −0.428365
\(672\) 0 0
\(673\) 50.9568i 1.96424i 0.188256 + 0.982120i \(0.439717\pi\)
−0.188256 + 0.982120i \(0.560283\pi\)
\(674\) −12.1152 + 20.9841i −0.466660 + 0.808278i
\(675\) 4.11030 + 2.84700i 0.158206 + 0.109581i
\(676\) 6.40532 + 11.0943i 0.246358 + 0.426705i
\(677\) 4.53791 + 2.61996i 0.174406 + 0.100693i 0.584662 0.811277i \(-0.301227\pi\)
−0.410256 + 0.911971i \(0.634561\pi\)
\(678\) 10.4132i 0.399915i
\(679\) 0 0
\(680\) 5.28676 + 3.34915i 0.202738 + 0.128434i
\(681\) 4.17113 7.22462i 0.159838 0.276848i
\(682\) 4.22168 2.43739i 0.161656 0.0933324i
\(683\) −27.9421 + 16.1324i −1.06918 + 0.617289i −0.927956 0.372689i \(-0.878436\pi\)
−0.141220 + 0.989978i \(0.545102\pi\)
\(684\) 3.67135 6.35897i 0.140378 0.243141i
\(685\) 4.41062 6.96233i 0.168521 0.266017i
\(686\) 0 0
\(687\) 18.6901i 0.713071i
\(688\) −8.64174 4.98931i −0.329463 0.190216i
\(689\) 0.143013 + 0.247706i 0.00544836 + 0.00943683i
\(690\) −7.46821 0.307028i −0.284310 0.0116884i
\(691\) 10.2235 17.7076i 0.388920 0.673629i −0.603385 0.797450i \(-0.706182\pi\)
0.992305 + 0.123821i \(0.0395150\pi\)
\(692\) 7.12057i 0.270684i
\(693\) 0 0
\(694\) −30.4252 −1.15492
\(695\) −16.1509 + 8.45992i −0.612637 + 0.320903i
\(696\) −1.87412 3.24608i −0.0710384 0.123042i
\(697\) −11.9966 + 6.92626i −0.454405 + 0.262351i
\(698\) 26.2079 + 15.1311i 0.991983 + 0.572722i
\(699\) −20.0829 −0.759605
\(700\) 0 0
\(701\) −15.4969 −0.585311 −0.292655 0.956218i \(-0.594539\pi\)
−0.292655 + 0.956218i \(0.594539\pi\)
\(702\) −0.376857 0.217579i −0.0142236 0.00821198i
\(703\) −29.4796 + 17.0201i −1.11184 + 0.641924i
\(704\) 0.489528 + 0.847888i 0.0184498 + 0.0319560i
\(705\) 8.72641 4.57095i 0.328656 0.172152i
\(706\) 4.37189 0.164538
\(707\) 0 0
\(708\) 8.27226i 0.310891i
\(709\) 19.4606 33.7068i 0.730859 1.26588i −0.225658 0.974207i \(-0.572453\pi\)
0.956517 0.291678i \(-0.0942134\pi\)
\(710\) 31.5285 + 1.29618i 1.18324 + 0.0486447i
\(711\) 1.44383 + 2.50079i 0.0541479 + 0.0937870i
\(712\) −8.76505 5.06051i −0.328484 0.189650i
\(713\) 16.6435i 0.623305i
\(714\) 0 0
\(715\) −0.509819 + 0.804767i −0.0190661 + 0.0300966i
\(716\) −1.63210 + 2.82688i −0.0609945 + 0.105646i
\(717\) −19.2876 + 11.1357i −0.720308 + 0.415870i
\(718\) 13.5836 7.84249i 0.506935 0.292679i
\(719\) 1.76560 3.05810i 0.0658456 0.114048i −0.831223 0.555939i \(-0.812359\pi\)
0.897069 + 0.441891i \(0.145692\pi\)
\(720\) 1.88893 + 1.19663i 0.0703963 + 0.0445959i
\(721\) 0 0
\(722\) 34.9153i 1.29941i
\(723\) −5.37001 3.10038i −0.199713 0.115304i
\(724\) 0.969114 + 1.67855i 0.0360168 + 0.0623830i
\(725\) −10.6712 + 15.4064i −0.396320 + 0.572181i
\(726\) 5.02072 8.69615i 0.186337 0.322744i
\(727\) 45.2934i 1.67984i −0.542712 0.839919i \(-0.682602\pi\)
0.542712 0.839919i \(-0.317398\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) −30.4898 + 15.9708i −1.12848 + 0.591105i
\(731\) −13.9641 24.1866i −0.516482 0.894572i
\(732\) −9.81518 + 5.66680i −0.362779 + 0.209451i
\(733\) −42.0422 24.2731i −1.55286 0.896547i −0.997907 0.0646687i \(-0.979401\pi\)
−0.554958 0.831878i \(-0.687266\pi\)
\(734\) 4.94478 0.182515
\(735\) 0 0
\(736\) −3.34271 −0.123214
\(737\) −2.00411 1.15707i −0.0738223 0.0426214i
\(738\) −4.28634 + 2.47472i −0.157782 + 0.0910957i
\(739\) 12.8984 + 22.3407i 0.474477 + 0.821818i 0.999573 0.0292252i \(-0.00930400\pi\)
−0.525096 + 0.851043i \(0.675971\pi\)
\(740\) −4.80997 9.18273i −0.176818 0.337564i
\(741\) 3.19523 0.117380
\(742\) 0 0
\(743\) 28.7192i 1.05361i 0.849987 + 0.526803i \(0.176610\pi\)
−0.849987 + 0.526803i \(0.823390\pi\)
\(744\) 2.48953 4.31199i 0.0912705 0.158085i
\(745\) −1.43997 + 35.0261i −0.0527563 + 1.28326i
\(746\) 3.01069 + 5.21467i 0.110229 + 0.190923i
\(747\) −12.4570 7.19208i −0.455779 0.263144i
\(748\) 2.74019i 0.100191i
\(749\) 0 0
\(750\) 1.37465 11.0955i 0.0501952 0.405151i
\(751\) 17.0938 29.6073i 0.623762 1.08039i −0.365017 0.931001i \(-0.618937\pi\)
0.988779 0.149386i \(-0.0477298\pi\)
\(752\) 3.81531 2.20277i 0.139130 0.0803267i
\(753\) 23.9508 13.8280i 0.872815 0.503920i
\(754\) 0.815538 1.41255i 0.0297002 0.0514422i
\(755\) −8.07001 5.11233i −0.293698 0.186057i
\(756\) 0 0
\(757\) 41.4622i 1.50697i −0.657465 0.753485i \(-0.728371\pi\)
0.657465 0.753485i \(-0.271629\pi\)
\(758\) −31.8723 18.4015i −1.15766 0.668373i
\(759\) −1.63635 2.83424i −0.0593957 0.102876i
\(760\) −16.4049 0.674429i −0.595070 0.0244641i
\(761\) 13.8470 23.9838i 0.501955 0.869412i −0.498042 0.867153i \(-0.665948\pi\)
0.999997 0.00225889i \(-0.000719027\pi\)
\(762\) 11.6987i 0.423801i
\(763\) 0 0
\(764\) −8.07001 −0.291963
\(765\) 2.90389 + 5.54383i 0.104990 + 0.200438i
\(766\) −4.51692 7.82353i −0.163203 0.282676i
\(767\) 3.11746 1.79987i 0.112565 0.0649894i
\(768\) 0.866025 + 0.500000i 0.0312500 + 0.0180422i
\(769\) 9.74001 0.351234 0.175617 0.984459i \(-0.443808\pi\)
0.175617 + 0.984459i \(0.443808\pi\)
\(770\) 0 0
\(771\) −11.7681 −0.423819
\(772\) −1.69578 0.979056i −0.0610323 0.0352370i
\(773\) 26.5152 15.3085i 0.953684 0.550610i 0.0594605 0.998231i \(-0.481062\pi\)
0.894223 + 0.447621i \(0.147729\pi\)
\(774\) −4.98931 8.64174i −0.179337 0.310621i
\(775\) −24.8113 2.04350i −0.891247 0.0734048i
\(776\) 10.6655 0.382870
\(777\) 0 0
\(778\) 33.5646i 1.20335i
\(779\) 18.1711 31.4733i 0.651048 1.12765i
\(780\) −0.0399693 + 0.972220i −0.00143113 + 0.0348111i
\(781\) 6.90817 + 11.9653i 0.247194 + 0.428152i
\(782\) −8.10218 4.67780i −0.289734 0.167278i
\(783\) 3.74825i 0.133951i
\(784\) 0 0
\(785\) 18.2485 28.8059i 0.651316 1.02813i
\(786\) −2.69230 + 4.66320i −0.0960311 + 0.166331i
\(787\) −13.6813 + 7.89887i −0.487684 + 0.281564i −0.723613 0.690206i \(-0.757520\pi\)
0.235929 + 0.971770i \(0.424187\pi\)
\(788\) 15.0185 8.67091i 0.535011 0.308889i
\(789\) −0.227521 + 0.394078i −0.00809996 + 0.0140295i
\(790\) 3.45548 5.45460i 0.122940 0.194066i
\(791\) 0 0
\(792\) 0.979056i 0.0347892i
\(793\) −4.27115 2.46595i −0.151673 0.0875684i
\(794\) −16.9896 29.4269i −0.602939 1.04432i
\(795\) 0.0603724 1.46851i 0.00214119 0.0520827i
\(796\) −1.29745 + 2.24725i −0.0459869 + 0.0796516i
\(797\) 47.6651i 1.68838i −0.536041 0.844192i \(-0.680081\pi\)
0.536041 0.844192i \(-0.319919\pi\)
\(798\) 0 0
\(799\) 12.3303 0.436213
\(800\) 0.410420 4.98313i 0.0145105 0.176180i
\(801\) −5.06051 8.76505i −0.178804 0.309698i
\(802\) −3.69989 + 2.13613i −0.130647 + 0.0754294i
\(803\) −13.0514 7.53522i −0.460574 0.265912i
\(804\) −2.36365 −0.0833595
\(805\) 0 0
\(806\) 2.16667 0.0763178
\(807\) −22.6357 13.0687i −0.796815 0.460041i
\(808\) −12.1527 + 7.01639i −0.427532 + 0.246836i
\(809\) −8.63547 14.9571i −0.303607 0.525863i 0.673343 0.739330i \(-0.264858\pi\)
−0.976950 + 0.213467i \(0.931524\pi\)
\(810\) 1.03755 + 1.98078i 0.0364556 + 0.0695976i
\(811\) 14.7901 0.519351 0.259676 0.965696i \(-0.416384\pi\)
0.259676 + 0.965696i \(0.416384\pi\)
\(812\) 0 0
\(813\) 16.7768i 0.588388i
\(814\) 2.26941 3.93073i 0.0795427 0.137772i
\(815\) −16.7027 0.686670i −0.585070 0.0240530i
\(816\) 1.39940 + 2.42384i 0.0489889 + 0.0848513i
\(817\) 63.4537 + 36.6350i 2.21997 + 1.28170i
\(818\) 3.63888i 0.127231i
\(819\) 0 0
\(820\) 9.34915 + 5.92267i 0.326487 + 0.206829i
\(821\) 22.8459 39.5702i 0.797326 1.38101i −0.124026 0.992279i \(-0.539581\pi\)
0.921352 0.388730i \(-0.127086\pi\)
\(822\) 3.19204 1.84293i 0.111335 0.0642794i
\(823\) 4.32481 2.49693i 0.150753 0.0870375i −0.422726 0.906258i \(-0.638927\pi\)
0.573479 + 0.819220i \(0.305593\pi\)
\(824\) −5.19208 + 8.99294i −0.180875 + 0.313284i
\(825\) 4.42604 2.09139i 0.154095 0.0728129i
\(826\) 0 0
\(827\) 53.5946i 1.86367i 0.362885 + 0.931834i \(0.381792\pi\)
−0.362885 + 0.931834i \(0.618208\pi\)
\(828\) −2.89487 1.67135i −0.100604 0.0580836i
\(829\) 0.583460 + 1.01058i 0.0202644 + 0.0350990i 0.875980 0.482348i \(-0.160216\pi\)
−0.855715 + 0.517447i \(0.826883\pi\)
\(830\) −1.32119 + 32.1368i −0.0458591 + 1.11548i
\(831\) 10.3739 17.9681i 0.359867 0.623307i
\(832\) 0.435157i 0.0150864i
\(833\) 0 0
\(834\) −8.15378 −0.282342
\(835\) −13.1395 25.0847i −0.454712 0.868092i
\(836\) −3.59446 6.22579i −0.124317 0.215323i
\(837\) 4.31199 2.48953i 0.149044 0.0860507i
\(838\) −23.0600 13.3137i −0.796595 0.459914i
\(839\) 31.2709 1.07959 0.539796 0.841796i \(-0.318501\pi\)
0.539796 + 0.841796i \(0.318501\pi\)
\(840\) 0 0
\(841\) −14.9507 −0.515540
\(842\) 13.1532 + 7.59402i 0.453290 + 0.261707i
\(843\) 15.8605 9.15707i 0.546265 0.315386i
\(844\) 7.70636 + 13.3478i 0.265264 + 0.459450i
\(845\) 25.3751 13.2916i 0.872929 0.457246i
\(846\) 4.40554 0.151466
\(847\) 0 0
\(848\) 0.657293i 0.0225715i
\(849\) −5.92626 + 10.2646i −0.203389 + 0.352280i
\(850\) 7.96820 11.5040i 0.273307 0.394582i
\(851\) 7.74825 + 13.4204i 0.265606 + 0.460044i
\(852\) 12.2213 + 7.05595i 0.418693 + 0.241733i
\(853\) 11.3154i 0.387431i −0.981058 0.193715i \(-0.937946\pi\)
0.981058 0.193715i \(-0.0620538\pi\)
\(854\) 0 0
\(855\) −13.8699 8.78654i −0.474340 0.300493i
\(856\) −10.0205 + 17.3560i −0.342494 + 0.593217i
\(857\) −31.9192 + 18.4286i −1.09034 + 0.629508i −0.933667 0.358142i \(-0.883410\pi\)
−0.156673 + 0.987650i \(0.550077\pi\)
\(858\) −0.368964 + 0.213022i −0.0125962 + 0.00727244i
\(859\) 9.34871 16.1924i 0.318974 0.552479i −0.661300 0.750121i \(-0.729995\pi\)
0.980274 + 0.197642i \(0.0633284\pi\)
\(860\) −11.9408 + 18.8489i −0.407177 + 0.642743i
\(861\) 0 0
\(862\) 4.23125i 0.144117i
\(863\) 25.5810 + 14.7692i 0.870787 + 0.502749i 0.867610 0.497246i \(-0.165655\pi\)
0.00317724 + 0.999995i \(0.498989\pi\)
\(864\) 0.500000 + 0.866025i 0.0170103 + 0.0294628i
\(865\) 15.9086 + 0.654025i 0.540910 + 0.0222375i
\(866\) 16.9676 29.3888i 0.576583 0.998671i
\(867\) 9.16667i 0.311317i
\(868\) 0 0
\(869\) 2.82719 0.0959057
\(870\) −7.42446 + 3.88898i −0.251713 + 0.131849i
\(871\) −0.514280 0.890759i −0.0174257 0.0301822i
\(872\) 16.1569 9.32821i 0.547143 0.315893i
\(873\) 9.23662 + 5.33276i 0.312612 + 0.180487i
\(874\) 24.5445 0.830231
\(875\) 0 0
\(876\) −15.3928 −0.520076
\(877\) 12.3478 + 7.12903i 0.416957 + 0.240730i 0.693775 0.720192i \(-0.255946\pi\)
−0.276817 + 0.960923i \(0.589280\pi\)
\(878\) −4.74804 + 2.74128i −0.160239 + 0.0925138i
\(879\) −7.23852 12.5375i −0.244149 0.422879i
\(880\) 1.93930 1.01582i 0.0653737 0.0342431i
\(881\) 31.2744 1.05366 0.526830 0.849971i \(-0.323380\pi\)
0.526830 + 0.849971i \(0.323380\pi\)
\(882\) 0 0
\(883\) 33.3566i 1.12254i −0.827633 0.561270i \(-0.810313\pi\)
0.827633 0.561270i \(-0.189687\pi\)
\(884\) −0.608961 + 1.05475i −0.0204816 + 0.0354751i
\(885\) −18.4817 0.759808i −0.621256 0.0255407i
\(886\) −0.615405 1.06591i −0.0206749 0.0358101i
\(887\) −36.4981 21.0722i −1.22549 0.707535i −0.259405 0.965769i \(-0.583526\pi\)
−0.966083 + 0.258233i \(0.916860\pi\)
\(888\) 4.63591i 0.155571i
\(889\) 0 0
\(890\) −12.1112 + 19.1179i −0.405967 + 0.640834i
\(891\) −0.489528 + 0.847888i −0.0163998 + 0.0284053i
\(892\) 6.59475 3.80748i 0.220809 0.127484i
\(893\) −28.0147 + 16.1743i −0.937476 + 0.541252i
\(894\) −7.83868 + 13.5770i −0.262165 + 0.454083i
\(895\) 6.16586 + 3.90606i 0.206102 + 0.130565i
\(896\) 0 0
\(897\) 1.45460i 0.0485678i
\(898\) 12.6817 + 7.32176i 0.423193 + 0.244330i
\(899\) 9.33136 + 16.1624i 0.311218 + 0.539046i
\(900\) 2.84700 4.11030i 0.0948999 0.137010i
\(901\) 0.919818 1.59317i 0.0306436 0.0530763i
\(902\) 4.84578i 0.161347i
\(903\) 0 0
\(904\) −10.4132 −0.346336
\(905\) 3.83921 2.01100i 0.127620 0.0668479i
\(906\) −2.13613 3.69989i −0.0709682 0.122920i
\(907\) 48.4836 27.9920i 1.60987 0.929460i 0.620474 0.784227i \(-0.286940\pi\)
0.989397 0.145233i \(-0.0463932\pi\)
\(908\) −7.22462 4.17113i −0.239757 0.138424i
\(909\) −14.0328 −0.465438
\(910\) 0 0
\(911\) 30.4389 1.00849 0.504243 0.863562i \(-0.331771\pi\)
0.504243 + 0.863562i \(0.331771\pi\)
\(912\) −6.35897 3.67135i −0.210567 0.121571i
\(913\) −12.1961 + 7.04145i −0.403634 + 0.233038i
\(914\) −15.6645 27.1317i −0.518135 0.897436i
\(915\) 11.7591 + 22.4494i 0.388745 + 0.742154i
\(916\) 18.6901 0.617537
\(917\) 0 0
\(918\) 2.79881i 0.0923744i
\(919\) −14.0769 + 24.3819i −0.464354 + 0.804284i −0.999172 0.0406827i \(-0.987047\pi\)
0.534818 + 0.844967i \(0.320380\pi\)
\(920\) −0.307028 + 7.46821i −0.0101224 + 0.246220i
\(921\) −15.2126 26.3490i −0.501272 0.868228i
\(922\) 11.0562 + 6.38333i 0.364118 + 0.210224i
\(923\) 6.14089i 0.202130i
\(924\) 0 0
\(925\) −20.9577 + 9.90291i −0.689084 + 0.325606i
\(926\) 13.3556 23.1326i 0.438892 0.760183i
\(927\) −8.99294 + 5.19208i −0.295367 + 0.170530i
\(928\) −3.24608 + 1.87412i −0.106558 + 0.0615211i
\(929\) −12.9477 + 22.4261i −0.424801 + 0.735777i −0.996402 0.0847546i \(-0.972989\pi\)
0.571601 + 0.820532i \(0.306323\pi\)
\(930\) −9.40510 5.95811i −0.308405 0.195374i
\(931\) 0 0
\(932\) 20.0829i 0.657837i
\(933\) −7.81896 4.51428i −0.255981 0.147791i
\(934\) 18.8070 + 32.5748i 0.615385 + 1.06588i
\(935\) 6.12208 + 0.251687i 0.200213 + 0.00823104i
\(936\) −0.217579 + 0.376857i −0.00711178 + 0.0123180i
\(937\) 48.1184i 1.57196i 0.618253 + 0.785979i \(0.287841\pi\)
−0.618253 + 0.785979i \(0.712159\pi\)
\(938\) 0 0
\(939\) −17.1732 −0.560427
\(940\) −4.57095 8.72641i −0.149088 0.284624i
\(941\) −26.1033 45.2123i −0.850944 1.47388i −0.880358 0.474310i \(-0.842698\pi\)
0.0294144 0.999567i \(-0.490636\pi\)
\(942\) 13.2067 7.62491i 0.430299 0.248433i
\(943\) −14.3280 8.27226i −0.466583 0.269382i
\(944\) −8.27226 −0.269239
\(945\) 0 0
\(946\) −9.76963 −0.317638
\(947\) 17.5799 + 10.1498i 0.571270 + 0.329823i 0.757656 0.652654i \(-0.226344\pi\)
−0.186387 + 0.982476i \(0.559678\pi\)
\(948\) 2.50079 1.44383i 0.0812219 0.0468935i
\(949\) −3.34915 5.80090i −0.108718 0.188305i
\(950\) −3.01359 + 36.5896i −0.0977738 + 1.18712i
\(951\) 2.61541 0.0848103
\(952\) 0 0
\(953\) 16.9511i 0.549100i 0.961573 + 0.274550i \(0.0885289\pi\)
−0.961573 + 0.274550i \(0.911471\pi\)
\(954\) 0.328646 0.569232i 0.0106403 0.0184296i
\(955\) −0.741231 + 18.0299i −0.0239857 + 0.583433i
\(956\) 11.1357 + 19.2876i 0.360154 + 0.623805i
\(957\) −3.17809 1.83487i −0.102733 0.0593130i
\(958\) 23.8235i 0.769703i
\(959\) 0 0
\(960\) 1.19663 1.88893i 0.0386212 0.0609650i
\(961\) 3.10450 5.37715i 0.100145 0.173456i
\(962\) 1.74708 1.00868i 0.0563280 0.0325210i
\(963\) −17.3560 + 10.0205i −0.559290 + 0.322906i
\(964\) −3.10038 + 5.37001i −0.0998564 + 0.172956i
\(965\) −2.34315 + 3.69874i −0.0754285 + 0.119067i
\(966\) 0 0
\(967\) 23.0294i 0.740577i −0.928917 0.370288i \(-0.879259\pi\)
0.928917 0.370288i \(-0.120741\pi\)
\(968\) −8.69615 5.02072i −0.279505 0.161372i
\(969\) −10.2754 17.7975i −0.330094 0.571739i
\(970\) 0.979630 23.8287i 0.0314540 0.765094i
\(971\) −6.18848 + 10.7188i −0.198598 + 0.343982i −0.948074 0.318050i \(-0.896972\pi\)
0.749476 + 0.662031i \(0.230305\pi\)
\(972\) 1.00000i 0.0320750i
\(973\) 0 0
\(974\) 3.75674 0.120374
\(975\) 2.16844 + 0.178597i 0.0694458 + 0.00571968i
\(976\) 5.66680 + 9.81518i 0.181390 + 0.314176i
\(977\) −0.871343 + 0.503070i −0.0278767 + 0.0160946i −0.513874 0.857866i \(-0.671790\pi\)
0.485997 + 0.873961i \(0.338457\pi\)
\(978\) −6.47439 3.73799i −0.207028 0.119528i
\(979\) −9.90904 −0.316694
\(980\) 0 0
\(981\) 18.6564 0.595654
\(982\) −1.73865 1.00381i −0.0554824 0.0320328i
\(983\) 36.4981 21.0722i 1.16411 0.672099i 0.211824 0.977308i \(-0.432060\pi\)
0.952285 + 0.305209i \(0.0987263\pi\)
\(984\) 2.47472 + 4.28634i 0.0788911 + 0.136643i
\(985\) −17.9929 34.3504i −0.573303 1.09449i
\(986\) −10.4906 −0.334089
\(987\) 0 0
\(988\) 3.19523i 0.101654i
\(989\) 16.6778 28.8868i 0.530323 0.918547i
\(990\) 2.18739 + 0.0899264i 0.0695198 + 0.00285805i
\(991\) 17.0346 + 29.5047i 0.541121 + 0.937249i 0.998840 + 0.0481519i \(0.0153332\pi\)
−0.457719 + 0.889097i \(0.651333\pi\)
\(992\) −4.31199 2.48953i −0.136906 0.0790426i
\(993\) 17.7559i 0.563465i
\(994\) 0 0
\(995\) 4.90159 + 3.10515i 0.155391 + 0.0984398i
\(996\) −7.19208 + 12.4570i −0.227890 + 0.394717i
\(997\) −5.21413 + 3.01038i −0.165133 + 0.0953397i −0.580289 0.814411i \(-0.697060\pi\)
0.415156 + 0.909750i \(0.363727\pi\)
\(998\) 0.544119 0.314147i 0.0172238 0.00994415i
\(999\) 2.31796 4.01482i 0.0733369 0.127023i
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 1470.2.n.k.79.4 16
5.4 even 2 inner 1470.2.n.k.79.7 16
7.2 even 3 1470.2.g.k.589.5 yes 8
7.3 odd 6 1470.2.n.l.949.6 16
7.4 even 3 inner 1470.2.n.k.949.7 16
7.5 odd 6 1470.2.g.j.589.8 yes 8
7.6 odd 2 1470.2.n.l.79.1 16
35.2 odd 12 7350.2.a.dr.1.3 4
35.4 even 6 inner 1470.2.n.k.949.4 16
35.9 even 6 1470.2.g.k.589.1 yes 8
35.12 even 12 7350.2.a.ds.1.3 4
35.19 odd 6 1470.2.g.j.589.4 8
35.23 odd 12 7350.2.a.du.1.3 4
35.24 odd 6 1470.2.n.l.949.1 16
35.33 even 12 7350.2.a.dt.1.3 4
35.34 odd 2 1470.2.n.l.79.6 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1470.2.g.j.589.4 8 35.19 odd 6
1470.2.g.j.589.8 yes 8 7.5 odd 6
1470.2.g.k.589.1 yes 8 35.9 even 6
1470.2.g.k.589.5 yes 8 7.2 even 3
1470.2.n.k.79.4 16 1.1 even 1 trivial
1470.2.n.k.79.7 16 5.4 even 2 inner
1470.2.n.k.949.4 16 35.4 even 6 inner
1470.2.n.k.949.7 16 7.4 even 3 inner
1470.2.n.l.79.1 16 7.6 odd 2
1470.2.n.l.79.6 16 35.34 odd 2
1470.2.n.l.949.1 16 35.24 odd 6
1470.2.n.l.949.6 16 7.3 odd 6
7350.2.a.dr.1.3 4 35.2 odd 12
7350.2.a.ds.1.3 4 35.12 even 12
7350.2.a.dt.1.3 4 35.33 even 12
7350.2.a.du.1.3 4 35.23 odd 12