Properties

Label 1470.2.n.l.79.1
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 79.1
Root \(0.599547 + 0.346149i\) of defining polynomial
Character \(\chi\) \(=\) 1470.79
Dual form 1470.2.n.l.949.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.98078 + 1.03755i) q^{5} -1.00000 q^{6} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(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 \(0.0192202\pi\)
−0.998178 + 0.0603455i \(0.980780\pi\)
\(14\) 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 −0.176386 0.984321i \(-0.556441\pi\)
0.764254 + 0.644916i \(0.223108\pi\)
\(18\) −0.866025 + 0.500000i −0.204124 + 0.117851i
\(19\) −3.67135 + 6.35897i −0.842266 + 1.45885i 0.0457080 + 0.998955i \(0.485446\pi\)
−0.887974 + 0.459893i \(0.847888\pi\)
\(20\) −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 0.998198 0.0600058i \(-0.0191119\pi\)
−0.551066 + 0.834462i \(0.685779\pi\)
\(32\) 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 \(-0.626311\pi\)
−0.386486 + 0.922295i \(0.626311\pi\)
\(42\) 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 0.751748 0.659451i \(-0.229211\pi\)
−0.195228 + 0.980758i \(0.562545\pi\)
\(48\) 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 \(-0.985666\pi\)
0.460508 0.887656i \(-0.347667\pi\)
\(60\) −2.23418 0.0918501i −0.288431 0.0118578i
\(61\) −5.66680 + 9.81518i −0.725559 + 1.25670i 0.233185 + 0.972432i \(0.425085\pi\)
−0.958744 + 0.284272i \(0.908248\pi\)
\(62\) 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 \(0.690350\pi\)
−0.997233 + 0.0743360i \(0.976316\pi\)
\(74\) 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 \(0.289625\pi\)
−0.613837 + 0.789433i \(0.710375\pi\)
\(84\) 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 \(0.346888\pi\)
−0.999094 + 0.0425688i \(0.986446\pi\)
\(90\) 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 \(-0.817872\pi\)
0.840726 0.541460i \(-0.182128\pi\)
\(98\) 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 \(0.0793294\pi\)
−0.270948 + 0.962594i \(0.587337\pi\)
\(102\) −2.42384 + 1.39940i −0.239996 + 0.138562i
\(103\) 8.99294 + 5.19208i 0.886101 + 0.511591i 0.872665 0.488319i \(-0.162390\pi\)
0.0134358 + 0.999910i \(0.495723\pi\)
\(104\) 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 −0.724112 0.689683i \(-0.757750\pi\)
0.959339 + 0.282258i \(0.0910833\pi\)
\(132\) 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 \(-0.387608\pi\)
0.345797 + 0.938309i \(0.387608\pi\)
\(140\) 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 −0.923770 0.382948i \(-0.874909\pi\)
−0.130242 + 0.991482i \(0.541575\pi\)
\(158\) 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 \(0.162998\pi\)
−0.871730 + 0.489986i \(0.837002\pi\)
\(168\) 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 0.246915 0.969037i \(-0.420583\pi\)
−0.715753 + 0.698354i \(0.753916\pi\)
\(174\) 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 \(-0.522949\pi\)
−0.0720337 + 0.997402i \(0.522949\pi\)
\(182\) 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 0.816368 0.577532i \(-0.195984\pi\)
−0.908342 + 0.418229i \(0.862651\pi\)
\(200\) −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 \(0.0820649\pi\)
−0.966950 + 0.254968i \(0.917935\pi\)
\(224\) 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 −0.240700 0.970600i \(-0.577377\pi\)
0.720214 + 0.693752i \(0.244044\pi\)
\(228\) −6.35897 + 3.67135i −0.421133 + 0.243141i
\(229\) −9.34503 + 16.1861i −0.617537 + 1.06961i 0.372396 + 0.928074i \(0.378536\pi\)
−0.989934 + 0.141532i \(0.954797\pi\)
\(230\) −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 0.748722 0.662884i \(-0.230668\pi\)
−0.948435 + 0.316971i \(0.897334\pi\)
\(242\) −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 \(-0.162292\pi\)
0.872815 + 0.488051i \(0.162292\pi\)
\(252\) 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 0.147239 0.989101i \(-0.452961\pi\)
−0.782967 + 0.622063i \(0.786295\pi\)
\(258\) 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 \(-0.873183\pi\)
0.124865 0.992174i \(-0.460150\pi\)
\(270\) 0.0918501 2.23418i 0.00558982 0.135968i
\(271\) 8.38840 14.5291i 0.509559 0.882582i −0.490380 0.871509i \(-0.663142\pi\)
0.999939 0.0110734i \(-0.00352484\pi\)
\(272\) 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 −0.773031 0.634369i \(-0.781260\pi\)
0.162864 + 0.986649i \(0.447927\pi\)
\(284\) −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 \(-0.861020\pi\)
0.906186 0.422879i \(-0.138980\pi\)
\(294\) 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 \(-0.665259\pi\)
0.496165 0.868228i \(-0.334741\pi\)
\(308\) 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 0.709180 0.705027i \(-0.249065\pi\)
−0.965162 + 0.261655i \(0.915732\pi\)
\(312\) 0.376857 0.217579i 0.0213353 0.0123180i
\(313\) −14.8725 8.58662i −0.840641 0.485344i 0.0168412 0.999858i \(-0.494639\pi\)
−0.857482 + 0.514514i \(0.827972\pi\)
\(314\) 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 \(-0.199494\pi\)
0.809951 + 0.586497i \(0.199494\pi\)
\(350\) 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 −0.395846 0.918317i \(-0.629549\pi\)
0.597363 + 0.801971i \(0.296215\pi\)
\(354\) 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 −0.384051 0.923312i \(-0.625471\pi\)
0.607586 + 0.794254i \(0.292138\pi\)
\(368\) 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 0.286618 0.958045i \(-0.407469\pi\)
−0.686382 + 0.727241i \(0.740802\pi\)
\(384\) 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 −0.477233 0.878777i \(-0.658360\pi\)
−0.999660 + 0.0260921i \(0.991694\pi\)
\(398\) 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 0.817531 0.575885i \(-0.195342\pi\)
−0.907496 + 0.420060i \(0.862009\pi\)
\(410\) −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 \(-0.725406\pi\)
−0.650417 + 0.759577i \(0.725406\pi\)
\(420\) 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 \(-0.696511\pi\)
0.578882 0.815412i \(-0.303489\pi\)
\(434\) 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 −0.923998 0.382396i \(-0.875099\pi\)
0.793164 + 0.609008i \(0.208432\pi\)
\(440\) 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 \(-0.403913\pi\)
0.297301 + 0.954784i \(0.403913\pi\)
\(462\) 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 \(0.00273289\pi\)
0.507417 + 0.861701i \(0.330600\pi\)
\(468\) 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 \(-0.983476\pi\)
0.454391 0.890803i \(-0.349857\pi\)
\(480\) −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 \(-0.776305\pi\)
0.763063 0.646324i \(-0.223695\pi\)
\(504\) 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 −0.985105 0.171953i \(-0.944992\pi\)
0.641468 + 0.767150i \(0.278326\pi\)
\(510\) 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 0.975422 0.220343i \(-0.0707178\pi\)
−0.678534 + 0.734569i \(0.737384\pi\)
\(522\) 3.24608 1.87412i 0.142077 0.0820281i
\(523\) 19.4459 + 11.2271i 0.850309 + 0.490926i 0.860755 0.509019i \(-0.169992\pi\)
−0.0104462 + 0.999945i \(0.503325\pi\)
\(524\) 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 −0.680594 0.732660i \(-0.738278\pi\)
0.294205 + 0.955742i \(0.404945\pi\)
\(564\) 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 −0.664210 0.747546i \(-0.731232\pi\)
0.315289 + 0.948996i \(0.397899\pi\)
\(578\) 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 \(0.109214\pi\)
−0.941715 + 0.336412i \(0.890786\pi\)
\(588\) 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 0.705224 0.708984i \(-0.250846\pi\)
−0.261386 + 0.965234i \(0.584180\pi\)
\(594\) 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 \(-0.467839\pi\)
0.100864 + 0.994900i \(0.467839\pi\)
\(602\) 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 0.484604 0.874734i \(-0.338964\pi\)
−0.515240 + 0.857046i \(0.672297\pi\)
\(608\) 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 0.795578 0.605851i \(-0.207167\pi\)
−0.922472 + 0.386065i \(0.873834\pi\)
\(620\) 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 \(-0.944641\pi\)
0.984915 0.173041i \(-0.0553594\pi\)
\(644\) 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 −0.790529 0.612424i \(-0.790194\pi\)
0.135110 + 0.990831i \(0.456861\pi\)
\(648\) −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 0.539275 0.842130i \(-0.318699\pi\)
−0.998943 + 0.0459604i \(0.985365\pi\)
\(662\) −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 0.410256 0.911971i \(-0.365439\pi\)
−0.584662 + 0.811277i \(0.698773\pi\)
\(678\) 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 −0.992305 0.123821i \(-0.960485\pi\)
0.603385 + 0.797450i \(0.293818\pi\)
\(692\) 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 −0.897069 0.441891i \(-0.854308\pi\)
0.831223 + 0.555939i \(0.187641\pi\)
\(720\) −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 \(0.317398\pi\)
−0.542712 + 0.839919i \(0.682602\pi\)
\(728\) 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 \(0.0205991\pi\)
0.554958 + 0.831878i \(0.312734\pi\)
\(734\) −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 \(0.334052\pi\)
−0.999997 + 0.00225889i \(0.999281\pi\)
\(762\) 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 \(-0.556192\pi\)
−0.175617 + 0.984459i \(0.556192\pi\)
\(770\) 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 −0.894223 0.447621i \(-0.852271\pi\)
−0.0594605 + 0.998231i \(0.518938\pi\)
\(774\) −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 −0.235929 0.971770i \(-0.575813\pi\)
0.723613 + 0.690206i \(0.242480\pi\)
\(788\) 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 \(0.319919\pi\)
−0.536041 + 0.844192i \(0.680081\pi\)
\(798\) 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 \(-0.583616\pi\)
−0.259676 + 0.965696i \(0.583616\pi\)
\(812\) 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 0.855715 0.517447i \(-0.173117\pi\)
−0.875980 + 0.482348i \(0.839784\pi\)
\(830\) −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 \(-0.681499\pi\)
−0.539796 + 0.841796i \(0.681499\pi\)
\(840\) 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 \(0.0620538\pi\)
−0.981058 + 0.193715i \(0.937946\pi\)
\(854\) 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 0.156673 0.987650i \(-0.449923\pi\)
0.933667 + 0.358142i \(0.116590\pi\)
\(858\) −0.368964 + 0.213022i −0.0125962 + 0.00727244i
\(859\) −9.34871 + 16.1924i −0.318974 + 0.552479i −0.980274 0.197642i \(-0.936672\pi\)
0.661300 + 0.750121i \(0.270005\pi\)
\(860\) 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 \(-0.676620\pi\)
−0.526830 + 0.849971i \(0.676620\pi\)
\(882\) 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 0.966083 0.258233i \(-0.0831403\pi\)
0.259405 + 0.965769i \(0.416474\pi\)
\(888\) 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 −0.571601 0.820532i \(-0.693677\pi\)
0.996402 + 0.0847546i \(0.0270106\pi\)
\(930\) 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 \(-0.712159\pi\)
0.618253 0.785979i \(-0.287841\pi\)
\(938\) 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 \(0.157302\pi\)
−0.0294144 + 0.999567i \(0.509364\pi\)
\(942\) 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 −0.749476 0.662031i \(-0.769695\pi\)
0.948074 + 0.318050i \(0.103028\pi\)
\(972\) 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 −0.952285 0.305209i \(-0.901274\pi\)
−0.211824 + 0.977308i \(0.567940\pi\)
\(984\) 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 −0.415156 0.909750i \(-0.636273\pi\)
0.580289 + 0.814411i \(0.302940\pi\)
\(998\) 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.l.79.1 16
5.4 even 2 inner 1470.2.n.l.79.6 16
7.2 even 3 1470.2.g.j.589.8 yes 8
7.3 odd 6 1470.2.n.k.949.7 16
7.4 even 3 inner 1470.2.n.l.949.6 16
7.5 odd 6 1470.2.g.k.589.5 yes 8
7.6 odd 2 1470.2.n.k.79.4 16
35.2 odd 12 7350.2.a.ds.1.3 4
35.4 even 6 inner 1470.2.n.l.949.1 16
35.9 even 6 1470.2.g.j.589.4 8
35.12 even 12 7350.2.a.dr.1.3 4
35.19 odd 6 1470.2.g.k.589.1 yes 8
35.23 odd 12 7350.2.a.dt.1.3 4
35.24 odd 6 1470.2.n.k.949.4 16
35.33 even 12 7350.2.a.du.1.3 4
35.34 odd 2 1470.2.n.k.79.7 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1470.2.g.j.589.4 8 35.9 even 6
1470.2.g.j.589.8 yes 8 7.2 even 3
1470.2.g.k.589.1 yes 8 35.19 odd 6
1470.2.g.k.589.5 yes 8 7.5 odd 6
1470.2.n.k.79.4 16 7.6 odd 2
1470.2.n.k.79.7 16 35.34 odd 2
1470.2.n.k.949.4 16 35.24 odd 6
1470.2.n.k.949.7 16 7.3 odd 6
1470.2.n.l.79.1 16 1.1 even 1 trivial
1470.2.n.l.79.6 16 5.4 even 2 inner
1470.2.n.l.949.1 16 35.4 even 6 inner
1470.2.n.l.949.6 16 7.4 even 3 inner
7350.2.a.dr.1.3 4 35.12 even 12
7350.2.a.ds.1.3 4 35.2 odd 12
7350.2.a.dt.1.3 4 35.23 odd 12
7350.2.a.du.1.3 4 35.33 even 12