Properties

Label 605.2.j.e.9.2
Level $605$
Weight $2$
Character 605.9
Analytic conductor $4.831$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [605,2,Mod(9,605)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(605, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("605.9");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.j (of order \(10\), degree \(4\), 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: \(4.83094932229\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: 16.0.6879707136000000000000.7
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 4x^{14} + 15x^{12} - 56x^{10} + 209x^{8} - 56x^{6} + 15x^{4} - 4x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 9.2
Root \(-0.304260 - 0.418778i\) of defining polynomial
Character \(\chi\) \(=\) 605.9
Dual form 605.2.j.e.269.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.492303 - 0.159959i) q^{2} +(-1.13551 - 1.56290i) q^{3} +(-1.40126 - 1.01807i) q^{4} +(1.88023 + 1.21026i) q^{5} +(0.309017 + 0.951057i) q^{6} +(1.96677 - 2.70702i) q^{7} +(1.13551 + 1.56290i) q^{8} +(-0.226216 + 0.696222i) q^{9} +O(q^{10})\) \(q+(-0.492303 - 0.159959i) q^{2} +(-1.13551 - 1.56290i) q^{3} +(-1.40126 - 1.01807i) q^{4} +(1.88023 + 1.21026i) q^{5} +(0.309017 + 0.951057i) q^{6} +(1.96677 - 2.70702i) q^{7} +(1.13551 + 1.56290i) q^{8} +(-0.226216 + 0.696222i) q^{9} +(-0.732051 - 0.896575i) q^{10} +3.34607i q^{12} +(4.03499 + 1.31105i) q^{13} +(-1.40126 + 1.01807i) q^{14} +(-0.243508 - 4.31288i) q^{15} +(0.761449 + 2.34350i) q^{16} +(3.67460 - 1.19395i) q^{17} +(0.222734 - 0.306567i) q^{18} +(3.39476 - 2.46644i) q^{19} +(-1.40255 - 3.61010i) q^{20} -6.46410 q^{21} -3.48477i q^{23} +(1.15327 - 3.54939i) q^{24} +(2.07053 + 4.55114i) q^{25} +(-1.77672 - 1.29087i) q^{26} +(-4.16690 + 1.35391i) q^{27} +(-5.51190 + 1.79092i) q^{28} +(-5.60503 - 4.07230i) q^{29} +(-0.570005 + 2.16220i) q^{30} +(-2.69835 + 8.30467i) q^{31} -5.13922i q^{32} -2.00000 q^{34} +(6.97418 - 2.70952i) q^{35} +(1.02579 - 0.745282i) q^{36} +(1.05399 - 1.45069i) q^{37} +(-2.06578 + 0.671212i) q^{38} +(-2.53275 - 7.79500i) q^{39} +(0.243508 + 4.31288i) q^{40} +(1.40126 - 1.01807i) q^{41} +(3.18230 + 1.03399i) q^{42} -6.45189i q^{43} +(-1.26795 + 1.03528i) q^{45} +(-0.557420 + 1.71556i) q^{46} +(-6.73156 - 9.26519i) q^{47} +(2.79802 - 3.85115i) q^{48} +(-1.29668 - 3.99078i) q^{49} +(-0.291333 - 2.57174i) q^{50} +(-6.03859 - 4.38729i) q^{51} +(-4.31932 - 5.94504i) q^{52} +(-2.06578 - 0.671212i) q^{53} +2.26795 q^{54} +6.46410 q^{56} +(-7.70959 - 2.50500i) q^{57} +(2.10798 + 2.90138i) q^{58} +(-1.02579 - 0.745282i) q^{59} +(-4.04962 + 6.29137i) q^{60} +(3.62540 + 11.1578i) q^{61} +(2.65681 - 3.65679i) q^{62} +(1.43977 + 1.98168i) q^{63} +(0.700835 - 2.15695i) q^{64} +(6.00000 + 7.34847i) q^{65} +2.20925i q^{67} +(-6.36459 - 2.06798i) q^{68} +(-5.44634 + 3.95700i) q^{69} +(-3.86682 + 0.218323i) q^{70} +(-2.53275 - 7.79500i) q^{71} +(-1.34500 + 0.437016i) q^{72} +(-2.87955 + 3.96336i) q^{73} +(-0.750932 + 0.545584i) q^{74} +(4.76187 - 8.40392i) q^{75} -7.26795 q^{76} +4.24264i q^{78} +(0.452432 - 1.39244i) q^{79} +(-1.40455 + 5.32787i) q^{80} +(8.62433 + 6.26594i) q^{81} +(-0.852694 + 0.277057i) q^{82} +(9.41498 - 3.05911i) q^{83} +(9.05788 + 6.58093i) q^{84} +(8.35409 + 2.20233i) q^{85} +(-1.03204 + 3.17629i) q^{86} +13.3843i q^{87} -0.464102 q^{89} +(0.789817 - 0.306850i) q^{90} +(11.4849 - 8.34429i) q^{91} +(-3.54775 + 4.88306i) q^{92} +(16.0434 - 5.21282i) q^{93} +(1.83192 + 5.63806i) q^{94} +(9.36796 - 0.528920i) q^{95} +(-8.03209 + 5.83565i) q^{96} +(-8.69420 - 2.82492i) q^{97} +2.17209i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 4 q^{6} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 4 q^{6} - 4 q^{9} + 16 q^{10} - 4 q^{15} + 4 q^{16} - 4 q^{19} - 12 q^{20} - 48 q^{21} - 8 q^{24} - 4 q^{25} + 12 q^{26} + 28 q^{31} - 32 q^{34} - 12 q^{35} + 12 q^{36} + 12 q^{39} + 4 q^{40} - 48 q^{45} + 28 q^{46} - 4 q^{49} + 24 q^{50} - 16 q^{51} + 64 q^{54} + 48 q^{56} - 12 q^{59} - 12 q^{60} - 40 q^{61} - 16 q^{64} + 96 q^{65} - 20 q^{69} - 12 q^{70} + 12 q^{71} + 24 q^{74} - 24 q^{75} - 144 q^{76} + 8 q^{79} - 24 q^{80} + 8 q^{81} + 24 q^{84} + 8 q^{85} + 48 q^{86} + 48 q^{89} - 16 q^{90} + 36 q^{91} + 4 q^{94} + 36 q^{95} - 12 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.492303 0.159959i −0.348111 0.113108i 0.129742 0.991548i \(-0.458585\pi\)
−0.477853 + 0.878440i \(0.658585\pi\)
\(3\) −1.13551 1.56290i −0.655589 0.902341i 0.343736 0.939066i \(-0.388307\pi\)
−0.999325 + 0.0367251i \(0.988307\pi\)
\(4\) −1.40126 1.01807i −0.700629 0.509037i
\(5\) 1.88023 + 1.21026i 0.840864 + 0.541246i
\(6\) 0.309017 + 0.951057i 0.126156 + 0.388267i
\(7\) 1.96677 2.70702i 0.743368 1.02316i −0.255049 0.966928i \(-0.582092\pi\)
0.998418 0.0562307i \(-0.0179082\pi\)
\(8\) 1.13551 + 1.56290i 0.401465 + 0.552569i
\(9\) −0.226216 + 0.696222i −0.0754054 + 0.232074i
\(10\) −0.732051 0.896575i −0.231495 0.283522i
\(11\) 0 0
\(12\) 3.34607i 0.965926i
\(13\) 4.03499 + 1.31105i 1.11911 + 0.363619i 0.809426 0.587222i \(-0.199778\pi\)
0.309679 + 0.950841i \(0.399778\pi\)
\(14\) −1.40126 + 1.01807i −0.374502 + 0.272092i
\(15\) −0.243508 4.31288i −0.0628734 1.11358i
\(16\) 0.761449 + 2.34350i 0.190362 + 0.585875i
\(17\) 3.67460 1.19395i 0.891221 0.289575i 0.172613 0.984990i \(-0.444779\pi\)
0.718609 + 0.695414i \(0.244779\pi\)
\(18\) 0.222734 0.306567i 0.0524989 0.0722585i
\(19\) 3.39476 2.46644i 0.778811 0.565839i −0.125811 0.992054i \(-0.540153\pi\)
0.904622 + 0.426215i \(0.140153\pi\)
\(20\) −1.40255 3.61010i −0.313620 0.807244i
\(21\) −6.46410 −1.41058
\(22\) 0 0
\(23\) 3.48477i 0.726624i −0.931668 0.363312i \(-0.881646\pi\)
0.931668 0.363312i \(-0.118354\pi\)
\(24\) 1.15327 3.54939i 0.235410 0.724516i
\(25\) 2.07053 + 4.55114i 0.414106 + 0.910229i
\(26\) −1.77672 1.29087i −0.348444 0.253160i
\(27\) −4.16690 + 1.35391i −0.801921 + 0.260560i
\(28\) −5.51190 + 1.79092i −1.04165 + 0.338453i
\(29\) −5.60503 4.07230i −1.04083 0.756206i −0.0703816 0.997520i \(-0.522422\pi\)
−0.970447 + 0.241314i \(0.922422\pi\)
\(30\) −0.570005 + 2.16220i −0.104068 + 0.394761i
\(31\) −2.69835 + 8.30467i −0.484638 + 1.49156i 0.347866 + 0.937544i \(0.386907\pi\)
−0.832504 + 0.554019i \(0.813093\pi\)
\(32\) 5.13922i 0.908494i
\(33\) 0 0
\(34\) −2.00000 −0.342997
\(35\) 6.97418 2.70952i 1.17885 0.457993i
\(36\) 1.02579 0.745282i 0.170965 0.124214i
\(37\) 1.05399 1.45069i 0.173275 0.238492i −0.713543 0.700611i \(-0.752911\pi\)
0.886818 + 0.462119i \(0.152911\pi\)
\(38\) −2.06578 + 0.671212i −0.335114 + 0.108885i
\(39\) −2.53275 7.79500i −0.405565 1.24820i
\(40\) 0.243508 + 4.31288i 0.0385020 + 0.681927i
\(41\) 1.40126 1.01807i 0.218840 0.158996i −0.472964 0.881082i \(-0.656816\pi\)
0.691804 + 0.722085i \(0.256816\pi\)
\(42\) 3.18230 + 1.03399i 0.491039 + 0.159548i
\(43\) 6.45189i 0.983905i −0.870622 0.491952i \(-0.836283\pi\)
0.870622 0.491952i \(-0.163717\pi\)
\(44\) 0 0
\(45\) −1.26795 + 1.03528i −0.189015 + 0.154330i
\(46\) −0.557420 + 1.71556i −0.0821870 + 0.252946i
\(47\) −6.73156 9.26519i −0.981899 1.35147i −0.935800 0.352530i \(-0.885321\pi\)
−0.0460982 0.998937i \(-0.514679\pi\)
\(48\) 2.79802 3.85115i 0.403860 0.555865i
\(49\) −1.29668 3.99078i −0.185240 0.570111i
\(50\) −0.291333 2.57174i −0.0412007 0.363699i
\(51\) −6.03859 4.38729i −0.845571 0.614343i
\(52\) −4.31932 5.94504i −0.598982 0.824428i
\(53\) −2.06578 0.671212i −0.283757 0.0921981i 0.163681 0.986513i \(-0.447663\pi\)
−0.447437 + 0.894315i \(0.647663\pi\)
\(54\) 2.26795 0.308629
\(55\) 0 0
\(56\) 6.46410 0.863802
\(57\) −7.70959 2.50500i −1.02116 0.331795i
\(58\) 2.10798 + 2.90138i 0.276791 + 0.380970i
\(59\) −1.02579 0.745282i −0.133547 0.0970274i 0.519006 0.854770i \(-0.326302\pi\)
−0.652553 + 0.757743i \(0.726302\pi\)
\(60\) −4.04962 + 6.29137i −0.522803 + 0.812213i
\(61\) 3.62540 + 11.1578i 0.464185 + 1.42862i 0.860004 + 0.510287i \(0.170461\pi\)
−0.395819 + 0.918329i \(0.629539\pi\)
\(62\) 2.65681 3.65679i 0.337416 0.464413i
\(63\) 1.43977 + 1.98168i 0.181394 + 0.249668i
\(64\) 0.700835 2.15695i 0.0876044 0.269618i
\(65\) 6.00000 + 7.34847i 0.744208 + 0.911465i
\(66\) 0 0
\(67\) 2.20925i 0.269903i 0.990852 + 0.134952i \(0.0430879\pi\)
−0.990852 + 0.134952i \(0.956912\pi\)
\(68\) −6.36459 2.06798i −0.771820 0.250780i
\(69\) −5.44634 + 3.95700i −0.655663 + 0.476367i
\(70\) −3.86682 + 0.218323i −0.462174 + 0.0260946i
\(71\) −2.53275 7.79500i −0.300582 0.925097i −0.981289 0.192541i \(-0.938327\pi\)
0.680707 0.732556i \(-0.261673\pi\)
\(72\) −1.34500 + 0.437016i −0.158509 + 0.0515028i
\(73\) −2.87955 + 3.96336i −0.337026 + 0.463876i −0.943570 0.331174i \(-0.892555\pi\)
0.606544 + 0.795050i \(0.292555\pi\)
\(74\) −0.750932 + 0.545584i −0.0872941 + 0.0634229i
\(75\) 4.76187 8.40392i 0.549853 0.970401i
\(76\) −7.26795 −0.833691
\(77\) 0 0
\(78\) 4.24264i 0.480384i
\(79\) 0.452432 1.39244i 0.0509026 0.156662i −0.922374 0.386298i \(-0.873754\pi\)
0.973277 + 0.229636i \(0.0737536\pi\)
\(80\) −1.40455 + 5.32787i −0.157033 + 0.595674i
\(81\) 8.62433 + 6.26594i 0.958259 + 0.696216i
\(82\) −0.852694 + 0.277057i −0.0941643 + 0.0305958i
\(83\) 9.41498 3.05911i 1.03343 0.335781i 0.257283 0.966336i \(-0.417173\pi\)
0.776145 + 0.630555i \(0.217173\pi\)
\(84\) 9.05788 + 6.58093i 0.988295 + 0.718039i
\(85\) 8.35409 + 2.20233i 0.906128 + 0.238876i
\(86\) −1.03204 + 3.17629i −0.111288 + 0.342508i
\(87\) 13.3843i 1.43494i
\(88\) 0 0
\(89\) −0.464102 −0.0491947 −0.0245973 0.999697i \(-0.507830\pi\)
−0.0245973 + 0.999697i \(0.507830\pi\)
\(90\) 0.789817 0.306850i 0.0832540 0.0323448i
\(91\) 11.4849 8.34429i 1.20395 0.874719i
\(92\) −3.54775 + 4.88306i −0.369878 + 0.509094i
\(93\) 16.0434 5.21282i 1.66362 0.540544i
\(94\) 1.83192 + 5.63806i 0.188948 + 0.581521i
\(95\) 9.36796 0.528920i 0.961133 0.0542661i
\(96\) −8.03209 + 5.83565i −0.819771 + 0.595599i
\(97\) −8.69420 2.82492i −0.882762 0.286827i −0.167658 0.985845i \(-0.553621\pi\)
−0.715104 + 0.699018i \(0.753621\pi\)
\(98\) 2.17209i 0.219414i
\(99\) 0 0
\(100\) 1.73205 8.48528i 0.173205 0.848528i
\(101\) −5.99255 + 18.4432i −0.596281 + 1.83516i −0.0480385 + 0.998845i \(0.515297\pi\)
−0.548243 + 0.836319i \(0.684703\pi\)
\(102\) 2.27103 + 3.12580i 0.224865 + 0.309500i
\(103\) −2.49376 + 3.43237i −0.245718 + 0.338201i −0.914006 0.405701i \(-0.867027\pi\)
0.668288 + 0.743903i \(0.267027\pi\)
\(104\) 2.53275 + 7.79500i 0.248357 + 0.764363i
\(105\) −12.1540 7.82326i −1.18611 0.763472i
\(106\) 0.909623 + 0.660880i 0.0883504 + 0.0641903i
\(107\) 1.74403 + 2.40046i 0.168602 + 0.232061i 0.884954 0.465678i \(-0.154190\pi\)
−0.716352 + 0.697739i \(0.754190\pi\)
\(108\) 7.21729 + 2.34504i 0.694484 + 0.225651i
\(109\) 9.19615 0.880832 0.440416 0.897794i \(-0.354831\pi\)
0.440416 + 0.897794i \(0.354831\pi\)
\(110\) 0 0
\(111\) −3.46410 −0.328798
\(112\) 7.84150 + 2.54786i 0.740952 + 0.240750i
\(113\) 1.66251 + 2.28825i 0.156396 + 0.215260i 0.880023 0.474930i \(-0.157527\pi\)
−0.723628 + 0.690190i \(0.757527\pi\)
\(114\) 3.39476 + 2.46644i 0.317948 + 0.231003i
\(115\) 4.21748 6.55216i 0.393282 0.610992i
\(116\) 3.70820 + 11.4127i 0.344298 + 1.05964i
\(117\) −1.82556 + 2.51267i −0.168773 + 0.232296i
\(118\) 0.385786 + 0.530989i 0.0355145 + 0.0488815i
\(119\) 3.99503 12.2955i 0.366224 1.12712i
\(120\) 6.46410 5.27792i 0.590089 0.481806i
\(121\) 0 0
\(122\) 6.07296i 0.549820i
\(123\) −3.18230 1.03399i −0.286938 0.0932318i
\(124\) 12.2359 8.88987i 1.09881 0.798334i
\(125\) −1.61500 + 11.0631i −0.144450 + 0.989512i
\(126\) −0.391818 1.20589i −0.0349059 0.107429i
\(127\) −0.852694 + 0.277057i −0.0756644 + 0.0245848i −0.346605 0.938011i \(-0.612665\pi\)
0.270940 + 0.962596i \(0.412665\pi\)
\(128\) −6.73156 + 9.26519i −0.594991 + 0.818935i
\(129\) −10.0837 + 7.32622i −0.887818 + 0.645037i
\(130\) −1.77836 4.57743i −0.155973 0.401467i
\(131\) 3.12436 0.272976 0.136488 0.990642i \(-0.456418\pi\)
0.136488 + 0.990642i \(0.456418\pi\)
\(132\) 0 0
\(133\) 14.0406i 1.21747i
\(134\) 0.353390 1.08762i 0.0305282 0.0939562i
\(135\) −9.47332 2.49739i −0.815334 0.214941i
\(136\) 6.03859 + 4.38729i 0.517804 + 0.376207i
\(137\) 8.43037 2.73919i 0.720255 0.234025i 0.0741215 0.997249i \(-0.476385\pi\)
0.646134 + 0.763224i \(0.276385\pi\)
\(138\) 3.31421 1.07685i 0.282124 0.0916677i
\(139\) 11.8023 + 8.57488i 1.00106 + 0.727312i 0.962315 0.271937i \(-0.0876643\pi\)
0.0387439 + 0.999249i \(0.487664\pi\)
\(140\) −12.5311 3.30349i −1.05907 0.279196i
\(141\) −6.83680 + 21.0415i −0.575763 + 1.77202i
\(142\) 4.24264i 0.356034i
\(143\) 0 0
\(144\) −1.80385 −0.150321
\(145\) −5.61021 14.4404i −0.465902 1.19921i
\(146\) 2.05158 1.49056i 0.169790 0.123360i
\(147\) −4.76479 + 6.55817i −0.392993 + 0.540909i
\(148\) −2.95382 + 0.959754i −0.242802 + 0.0788913i
\(149\) −3.17297 9.76540i −0.259940 0.800013i −0.992816 0.119651i \(-0.961823\pi\)
0.732876 0.680362i \(-0.238177\pi\)
\(150\) −3.68856 + 3.37557i −0.301170 + 0.275614i
\(151\) 3.39476 2.46644i 0.276262 0.200716i −0.441024 0.897495i \(-0.645384\pi\)
0.717285 + 0.696780i \(0.245384\pi\)
\(152\) 7.70959 + 2.50500i 0.625330 + 0.203182i
\(153\) 2.82843i 0.228665i
\(154\) 0 0
\(155\) −15.1244 + 12.3490i −1.21482 + 0.991894i
\(156\) −4.38685 + 13.5013i −0.351229 + 1.08097i
\(157\) 12.8546 + 17.6928i 1.02591 + 1.41204i 0.907977 + 0.419020i \(0.137626\pi\)
0.117931 + 0.993022i \(0.462374\pi\)
\(158\) −0.445468 + 0.613134i −0.0354395 + 0.0487783i
\(159\) 1.29668 + 3.99078i 0.102834 + 0.316489i
\(160\) 6.21980 9.66291i 0.491718 0.763920i
\(161\) −9.43334 6.85373i −0.743452 0.540149i
\(162\) −3.24349 4.46428i −0.254833 0.350747i
\(163\) 4.88769 + 1.58811i 0.382833 + 0.124390i 0.494110 0.869399i \(-0.335494\pi\)
−0.111277 + 0.993789i \(0.535494\pi\)
\(164\) −3.00000 −0.234261
\(165\) 0 0
\(166\) −5.12436 −0.397727
\(167\) −0.492303 0.159959i −0.0380956 0.0123780i 0.289907 0.957055i \(-0.406376\pi\)
−0.328003 + 0.944677i \(0.606376\pi\)
\(168\) −7.34008 10.1027i −0.566299 0.779444i
\(169\) 4.04508 + 2.93893i 0.311160 + 0.226071i
\(170\) −3.76046 2.42052i −0.288414 0.185646i
\(171\) 0.949237 + 2.92145i 0.0725900 + 0.223409i
\(172\) −6.56850 + 9.04077i −0.500844 + 0.689352i
\(173\) −12.7949 17.6107i −0.972779 1.33892i −0.940630 0.339433i \(-0.889765\pi\)
−0.0321489 0.999483i \(-0.510235\pi\)
\(174\) 2.14093 6.58911i 0.162304 0.499519i
\(175\) 16.3923 + 3.34607i 1.23914 + 0.252939i
\(176\) 0 0
\(177\) 2.44949i 0.184115i
\(178\) 0.228479 + 0.0742372i 0.0171252 + 0.00556431i
\(179\) −12.5107 + 9.08957i −0.935095 + 0.679386i −0.947235 0.320540i \(-0.896136\pi\)
0.0121398 + 0.999926i \(0.496136\pi\)
\(180\) 2.83071 0.159824i 0.210989 0.0119125i
\(181\) −5.37452 16.5411i −0.399485 1.22949i −0.925413 0.378959i \(-0.876282\pi\)
0.525929 0.850529i \(-0.323718\pi\)
\(182\) −6.98881 + 2.27080i −0.518045 + 0.168323i
\(183\) 13.3219 18.3360i 0.984784 1.35544i
\(184\) 5.44634 3.95700i 0.401510 0.291714i
\(185\) 3.73745 1.45203i 0.274783 0.106755i
\(186\) −8.73205 −0.640265
\(187\) 0 0
\(188\) 19.8362i 1.44670i
\(189\) −4.53027 + 13.9427i −0.329528 + 1.01418i
\(190\) −4.69648 1.23810i −0.340719 0.0898212i
\(191\) 5.87989 + 4.27199i 0.425454 + 0.309111i 0.779829 0.625993i \(-0.215306\pi\)
−0.354374 + 0.935104i \(0.615306\pi\)
\(192\) −4.16690 + 1.35391i −0.300720 + 0.0977100i
\(193\) −14.4346 + 4.69008i −1.03902 + 0.337599i −0.778352 0.627828i \(-0.783944\pi\)
−0.260672 + 0.965428i \(0.583944\pi\)
\(194\) 3.82831 + 2.78143i 0.274857 + 0.199695i
\(195\) 4.67185 17.7217i 0.334558 1.26908i
\(196\) −2.24592 + 6.91223i −0.160423 + 0.493731i
\(197\) 17.2480i 1.22887i −0.788969 0.614433i \(-0.789385\pi\)
0.788969 0.614433i \(-0.210615\pi\)
\(198\) 0 0
\(199\) 2.00000 0.141776 0.0708881 0.997484i \(-0.477417\pi\)
0.0708881 + 0.997484i \(0.477417\pi\)
\(200\) −4.76187 + 8.40392i −0.336715 + 0.594247i
\(201\) 3.45284 2.50864i 0.243545 0.176946i
\(202\) 5.90030 8.12107i 0.415144 0.571397i
\(203\) −22.0476 + 7.16370i −1.54744 + 0.502793i
\(204\) 3.99503 + 12.2955i 0.279708 + 0.860854i
\(205\) 3.86682 0.218323i 0.270071 0.0152483i
\(206\) 1.77672 1.29087i 0.123790 0.0899389i
\(207\) 2.42617 + 0.788310i 0.168630 + 0.0547914i
\(208\) 10.4543i 0.724875i
\(209\) 0 0
\(210\) 4.73205 + 5.79555i 0.326543 + 0.399931i
\(211\) 4.05565 12.4820i 0.279202 0.859297i −0.708874 0.705335i \(-0.750797\pi\)
0.988077 0.153962i \(-0.0492033\pi\)
\(212\) 2.21135 + 3.04366i 0.151876 + 0.209039i
\(213\) −9.30685 + 12.8098i −0.637695 + 0.877711i
\(214\) −0.474619 1.46073i −0.0324443 0.0998532i
\(215\) 7.80848 12.1310i 0.532534 0.827330i
\(216\) −6.84760 4.97507i −0.465920 0.338511i
\(217\) 17.1739 + 23.6379i 1.16584 + 1.60464i
\(218\) −4.52729 1.47101i −0.306627 0.0996292i
\(219\) 9.46410 0.639525
\(220\) 0 0
\(221\) 16.3923 1.10267
\(222\) 1.70539 + 0.554114i 0.114458 + 0.0371897i
\(223\) 0.912780 + 1.25633i 0.0611243 + 0.0841303i 0.838485 0.544925i \(-0.183442\pi\)
−0.777361 + 0.629055i \(0.783442\pi\)
\(224\) −13.9120 10.1076i −0.929533 0.675345i
\(225\) −3.63699 + 0.412007i −0.242466 + 0.0274671i
\(226\) −0.452432 1.39244i −0.0300953 0.0926240i
\(227\) −11.8225 + 16.2722i −0.784684 + 1.08002i 0.210066 + 0.977687i \(0.432632\pi\)
−0.994750 + 0.102337i \(0.967368\pi\)
\(228\) 8.25286 + 11.3591i 0.546559 + 0.752274i
\(229\) 1.25825 3.87251i 0.0831478 0.255903i −0.900836 0.434159i \(-0.857046\pi\)
0.983984 + 0.178256i \(0.0570456\pi\)
\(230\) −3.12436 + 2.55103i −0.206014 + 0.168210i
\(231\) 0 0
\(232\) 13.3843i 0.878720i
\(233\) 1.60882 + 0.522738i 0.105397 + 0.0342457i 0.361241 0.932473i \(-0.382353\pi\)
−0.255844 + 0.966718i \(0.582353\pi\)
\(234\) 1.30065 0.944980i 0.0850263 0.0617752i
\(235\) −1.44356 25.5676i −0.0941677 1.66785i
\(236\) 0.678648 + 2.08867i 0.0441762 + 0.135961i
\(237\) −2.68999 + 0.874032i −0.174734 + 0.0567745i
\(238\) −3.93354 + 5.41405i −0.254973 + 0.350941i
\(239\) −4.57924 + 3.32701i −0.296207 + 0.215207i −0.725955 0.687742i \(-0.758602\pi\)
0.429749 + 0.902948i \(0.358602\pi\)
\(240\) 9.92182 3.85470i 0.640451 0.248820i
\(241\) −14.1244 −0.909830 −0.454915 0.890535i \(-0.650330\pi\)
−0.454915 + 0.890535i \(0.650330\pi\)
\(242\) 0 0
\(243\) 7.45001i 0.477918i
\(244\) 6.27938 19.3260i 0.401996 1.23722i
\(245\) 2.39183 9.07291i 0.152808 0.579647i
\(246\) 1.40126 + 1.01807i 0.0893410 + 0.0649100i
\(247\) 16.9314 5.50136i 1.07732 0.350043i
\(248\) −16.0434 + 5.21282i −1.01876 + 0.331014i
\(249\) −15.4719 11.2410i −0.980494 0.712370i
\(250\) 2.56471 5.18806i 0.162206 0.328121i
\(251\) −1.17545 + 3.61767i −0.0741940 + 0.228346i −0.981276 0.192609i \(-0.938305\pi\)
0.907082 + 0.420955i \(0.138305\pi\)
\(252\) 4.24264i 0.267261i
\(253\) 0 0
\(254\) 0.464102 0.0291203
\(255\) −6.04416 15.5574i −0.378500 0.974241i
\(256\) 1.12640 0.818376i 0.0703999 0.0511485i
\(257\) 8.69833 11.9722i 0.542587 0.746806i −0.446396 0.894835i \(-0.647293\pi\)
0.988983 + 0.148029i \(0.0472929\pi\)
\(258\) 6.13612 1.99374i 0.382018 0.124125i
\(259\) −1.85410 5.70634i −0.115208 0.354575i
\(260\) −0.926266 16.4055i −0.0574446 1.01743i
\(261\) 4.10317 2.98113i 0.253980 0.184527i
\(262\) −1.53813 0.499769i −0.0950260 0.0308758i
\(263\) 6.79367i 0.418915i −0.977818 0.209458i \(-0.932830\pi\)
0.977818 0.209458i \(-0.0671699\pi\)
\(264\) 0 0
\(265\) −3.07180 3.76217i −0.188699 0.231108i
\(266\) −2.24592 + 6.91223i −0.137706 + 0.423816i
\(267\) 0.526994 + 0.725345i 0.0322515 + 0.0443904i
\(268\) 2.24918 3.09573i 0.137391 0.189102i
\(269\) 5.02707 + 15.4717i 0.306506 + 0.943329i 0.979111 + 0.203327i \(0.0651754\pi\)
−0.672605 + 0.740002i \(0.734825\pi\)
\(270\) 4.26427 + 2.74481i 0.259515 + 0.167044i
\(271\) 9.27465 + 6.73843i 0.563395 + 0.409330i 0.832700 0.553725i \(-0.186794\pi\)
−0.269305 + 0.963055i \(0.586794\pi\)
\(272\) 5.59604 + 7.70229i 0.339310 + 0.467020i
\(273\) −26.0826 8.47475i −1.57859 0.512915i
\(274\) −4.58846 −0.277199
\(275\) 0 0
\(276\) 11.6603 0.701865
\(277\) 29.6606 + 9.63732i 1.78213 + 0.579051i 0.999079 0.0429019i \(-0.0136603\pi\)
0.783055 + 0.621952i \(0.213660\pi\)
\(278\) −4.43868 6.10933i −0.266215 0.366413i
\(279\) −5.17148 3.75730i −0.309609 0.224944i
\(280\) 12.1540 + 7.82326i 0.726340 + 0.467529i
\(281\) 5.35233 + 16.4728i 0.319293 + 0.982684i 0.973951 + 0.226758i \(0.0728128\pi\)
−0.654658 + 0.755925i \(0.727187\pi\)
\(282\) 6.73156 9.26519i 0.400858 0.551734i
\(283\) 4.74294 + 6.52810i 0.281939 + 0.388055i 0.926375 0.376603i \(-0.122908\pi\)
−0.644436 + 0.764658i \(0.722908\pi\)
\(284\) −4.38685 + 13.5013i −0.260312 + 0.801157i
\(285\) −11.4641 14.0406i −0.679075 0.831693i
\(286\) 0 0
\(287\) 5.79555i 0.342101i
\(288\) 3.57803 + 1.16257i 0.210838 + 0.0685053i
\(289\) −1.67612 + 1.21777i −0.0985952 + 0.0716336i
\(290\) 0.452049 + 8.00646i 0.0265453 + 0.470156i
\(291\) 5.45732 + 16.7959i 0.319914 + 0.984593i
\(292\) 8.06998 2.62210i 0.472260 0.153447i
\(293\) 8.86138 12.1966i 0.517687 0.712535i −0.467505 0.883991i \(-0.654847\pi\)
0.985192 + 0.171455i \(0.0548469\pi\)
\(294\) 3.39476 2.46644i 0.197986 0.143845i
\(295\) −1.02674 2.64278i −0.0597791 0.153869i
\(296\) 3.46410 0.201347
\(297\) 0 0
\(298\) 5.31508i 0.307894i
\(299\) 4.56870 14.0610i 0.264214 0.813169i
\(300\) −15.2284 + 6.92813i −0.879213 + 0.399996i
\(301\) −17.4654 12.6894i −1.00669 0.731404i
\(302\) −2.06578 + 0.671212i −0.118872 + 0.0386239i
\(303\) 35.6295 11.5767i 2.04686 0.665065i
\(304\) 8.36503 + 6.07755i 0.479767 + 0.348571i
\(305\) −6.68732 + 25.3670i −0.382915 + 1.45251i
\(306\) 0.452432 1.39244i 0.0258638 0.0796007i
\(307\) 7.82894i 0.446821i 0.974724 + 0.223411i \(0.0717191\pi\)
−0.974724 + 0.223411i \(0.928281\pi\)
\(308\) 0 0
\(309\) 8.19615 0.466263
\(310\) 9.42110 3.66017i 0.535082 0.207884i
\(311\) −8.13269 + 5.90875i −0.461163 + 0.335054i −0.793987 0.607935i \(-0.791998\pi\)
0.332825 + 0.942989i \(0.391998\pi\)
\(312\) 9.30685 12.8098i 0.526896 0.725211i
\(313\) −16.3072 + 5.29854i −0.921739 + 0.299491i −0.731180 0.682185i \(-0.761030\pi\)
−0.190559 + 0.981676i \(0.561030\pi\)
\(314\) −3.49823 10.7664i −0.197417 0.607586i
\(315\) 0.308755 + 5.46852i 0.0173964 + 0.308116i
\(316\) −2.05158 + 1.49056i −0.115411 + 0.0838508i
\(317\) −12.0084 3.90177i −0.674459 0.219145i −0.0482913 0.998833i \(-0.515378\pi\)
−0.626168 + 0.779688i \(0.715378\pi\)
\(318\) 2.17209i 0.121805i
\(319\) 0 0
\(320\) 3.92820 3.20736i 0.219593 0.179297i
\(321\) 1.77130 5.45150i 0.0988644 0.304273i
\(322\) 3.54775 + 4.88306i 0.197708 + 0.272122i
\(323\) 9.52958 13.1163i 0.530240 0.729813i
\(324\) −5.70572 17.5604i −0.316985 0.975578i
\(325\) 2.38781 + 21.0784i 0.132452 + 1.16922i
\(326\) −2.15219 1.56366i −0.119199 0.0866030i
\(327\) −10.4424 14.3727i −0.577464 0.794811i
\(328\) 3.18230 + 1.03399i 0.175713 + 0.0570926i
\(329\) −38.3205 −2.11268
\(330\) 0 0
\(331\) −18.1962 −1.00015 −0.500075 0.865982i \(-0.666694\pi\)
−0.500075 + 0.865982i \(0.666694\pi\)
\(332\) −16.3072 5.29854i −0.894975 0.290795i
\(333\) 0.771573 + 1.06198i 0.0422819 + 0.0581961i
\(334\) 0.216775 + 0.157497i 0.0118614 + 0.00861783i
\(335\) −2.67378 + 4.15390i −0.146084 + 0.226952i
\(336\) −4.92209 15.1486i −0.268522 0.826425i
\(337\) 10.3608 14.2605i 0.564391 0.776817i −0.427486 0.904022i \(-0.640601\pi\)
0.991876 + 0.127205i \(0.0406006\pi\)
\(338\) −1.52130 2.09389i −0.0827478 0.113893i
\(339\) 1.68850 5.19667i 0.0917067 0.282244i
\(340\) −9.46410 11.5911i −0.513263 0.628616i
\(341\) 0 0
\(342\) 1.59008i 0.0859816i
\(343\) 8.92268 + 2.89915i 0.481779 + 0.156540i
\(344\) 10.0837 7.32622i 0.543675 0.395003i
\(345\) −15.0294 + 0.848567i −0.809155 + 0.0456853i
\(346\) 3.48199 + 10.7165i 0.187193 + 0.576120i
\(347\) −4.16690 + 1.35391i −0.223691 + 0.0726816i −0.418718 0.908116i \(-0.637521\pi\)
0.195027 + 0.980798i \(0.437521\pi\)
\(348\) 13.6262 18.7548i 0.730439 1.00536i
\(349\) 5.92242 4.30289i 0.317020 0.230328i −0.417883 0.908501i \(-0.637228\pi\)
0.734903 + 0.678173i \(0.237228\pi\)
\(350\) −7.53475 4.26937i −0.402749 0.228208i
\(351\) −18.5885 −0.992178
\(352\) 0 0
\(353\) 13.0053i 0.692204i 0.938197 + 0.346102i \(0.112495\pi\)
−0.938197 + 0.346102i \(0.887505\pi\)
\(354\) 0.391818 1.20589i 0.0208249 0.0640924i
\(355\) 4.67185 17.7217i 0.247956 0.940570i
\(356\) 0.650326 + 0.472490i 0.0344672 + 0.0250419i
\(357\) −23.7530 + 7.71781i −1.25714 + 0.408470i
\(358\) 7.61302 2.47362i 0.402361 0.130735i
\(359\) −28.8498 20.9606i −1.52263 1.10626i −0.960164 0.279437i \(-0.909852\pi\)
−0.562468 0.826819i \(-0.690148\pi\)
\(360\) −3.05781 0.806108i −0.161161 0.0424856i
\(361\) −0.430246 + 1.32416i −0.0226445 + 0.0696927i
\(362\) 9.00292i 0.473183i
\(363\) 0 0
\(364\) −24.5885 −1.28879
\(365\) −10.2109 + 3.96702i −0.534464 + 0.207643i
\(366\) −9.49143 + 6.89593i −0.496125 + 0.360456i
\(367\) −9.93721 + 13.6774i −0.518718 + 0.713954i −0.985359 0.170493i \(-0.945464\pi\)
0.466641 + 0.884447i \(0.345464\pi\)
\(368\) 8.16655 2.65347i 0.425711 0.138322i
\(369\) 0.391818 + 1.20589i 0.0203972 + 0.0627762i
\(370\) −2.07223 + 0.116999i −0.107730 + 0.00608249i
\(371\) −5.87989 + 4.27199i −0.305269 + 0.221791i
\(372\) −27.7880 9.02886i −1.44074 0.468125i
\(373\) 0.175865i 0.00910597i 0.999990 + 0.00455298i \(0.00144926\pi\)
−0.999990 + 0.00455298i \(0.998551\pi\)
\(374\) 0 0
\(375\) 19.1244 10.0382i 0.987577 0.518370i
\(376\) 6.83680 21.0415i 0.352581 1.08513i
\(377\) −17.2773 23.7801i −0.889826 1.22474i
\(378\) 4.46053 6.13939i 0.229425 0.315776i
\(379\) −0.452432 1.39244i −0.0232399 0.0715250i 0.938764 0.344561i \(-0.111972\pi\)
−0.962004 + 0.273036i \(0.911972\pi\)
\(380\) −13.6654 8.79612i −0.701021 0.451232i
\(381\) 1.40126 + 1.01807i 0.0717886 + 0.0521575i
\(382\) −2.21135 3.04366i −0.113142 0.155727i
\(383\) 36.5787 + 11.8852i 1.86909 + 0.607303i 0.991878 + 0.127194i \(0.0405969\pi\)
0.877209 + 0.480109i \(0.159403\pi\)
\(384\) 22.1244 1.12903
\(385\) 0 0
\(386\) 7.85641 0.399881
\(387\) 4.49195 + 1.45952i 0.228339 + 0.0741917i
\(388\) 9.30685 + 12.8098i 0.472483 + 0.650318i
\(389\) 4.95471 + 3.59981i 0.251214 + 0.182517i 0.706265 0.707948i \(-0.250379\pi\)
−0.455051 + 0.890465i \(0.650379\pi\)
\(390\) −5.13471 + 7.97714i −0.260006 + 0.403938i
\(391\) −4.16064 12.8051i −0.210412 0.647583i
\(392\) 4.76479 6.55817i 0.240658 0.331238i
\(393\) −3.54775 4.88306i −0.178960 0.246318i
\(394\) −2.75897 + 8.49123i −0.138995 + 0.427782i
\(395\) 2.53590 2.07055i 0.127595 0.104181i
\(396\) 0 0
\(397\) 32.9802i 1.65523i 0.561298 + 0.827614i \(0.310302\pi\)
−0.561298 + 0.827614i \(0.689698\pi\)
\(398\) −0.984606 0.319918i −0.0493538 0.0160360i
\(399\) −21.9441 + 15.9433i −1.09858 + 0.798163i
\(400\) −9.08900 + 8.31775i −0.454450 + 0.415888i
\(401\) 0.717076 + 2.20693i 0.0358091 + 0.110209i 0.967363 0.253393i \(-0.0815467\pi\)
−0.931554 + 0.363602i \(0.881547\pi\)
\(402\) −2.10112 + 0.682697i −0.104795 + 0.0340498i
\(403\) −21.7757 + 29.9716i −1.08472 + 1.49299i
\(404\) 27.1736 19.7428i 1.35194 0.982241i
\(405\) 8.63229 + 22.2191i 0.428942 + 1.10408i
\(406\) 12.0000 0.595550
\(407\) 0 0
\(408\) 14.4195i 0.713873i
\(409\) −8.07287 + 24.8457i −0.399178 + 1.22854i 0.526482 + 0.850186i \(0.323511\pi\)
−0.925660 + 0.378357i \(0.876489\pi\)
\(410\) −1.93857 0.511052i −0.0957393 0.0252391i
\(411\) −13.8539 10.0654i −0.683362 0.496492i
\(412\) 6.98881 2.27080i 0.344314 0.111874i
\(413\) −4.03499 + 1.31105i −0.198549 + 0.0645125i
\(414\) −1.06831 0.776175i −0.0525047 0.0381469i
\(415\) 21.4047 + 5.64276i 1.05071 + 0.276992i
\(416\) 6.73776 20.7367i 0.330346 1.01670i
\(417\) 28.1827i 1.38011i
\(418\) 0 0
\(419\) 12.3397 0.602836 0.301418 0.953492i \(-0.402540\pi\)
0.301418 + 0.953492i \(0.402540\pi\)
\(420\) 9.06624 + 23.3361i 0.442387 + 1.13868i
\(421\) 13.7958 10.0232i 0.672367 0.488503i −0.198450 0.980111i \(-0.563591\pi\)
0.870817 + 0.491608i \(0.163591\pi\)
\(422\) −3.99322 + 5.49619i −0.194387 + 0.267550i
\(423\) 7.97342 2.59072i 0.387681 0.125965i
\(424\) −1.29668 3.99078i −0.0629725 0.193809i
\(425\) 13.0422 + 14.2515i 0.632640 + 0.691300i
\(426\) 6.63083 4.81758i 0.321265 0.233412i
\(427\) 37.3349 + 12.1308i 1.80676 + 0.587052i
\(428\) 5.13922i 0.248413i
\(429\) 0 0
\(430\) −5.78461 + 4.72311i −0.278959 + 0.227769i
\(431\) 1.56727 4.82357i 0.0754928 0.232343i −0.906188 0.422874i \(-0.861021\pi\)
0.981681 + 0.190531i \(0.0610211\pi\)
\(432\) −6.34577 8.73420i −0.305311 0.420225i
\(433\) 16.8915 23.2492i 0.811754 1.11728i −0.179297 0.983795i \(-0.557382\pi\)
0.991050 0.133488i \(-0.0426178\pi\)
\(434\) −4.67368 14.3841i −0.224344 0.690460i
\(435\) −16.1985 + 25.1655i −0.776657 + 1.20659i
\(436\) −12.8862 9.36236i −0.617136 0.448376i
\(437\) −8.59495 11.8299i −0.411152 0.565903i
\(438\) −4.65921 1.51387i −0.222625 0.0723354i
\(439\) 28.2487 1.34824 0.674119 0.738623i \(-0.264524\pi\)
0.674119 + 0.738623i \(0.264524\pi\)
\(440\) 0 0
\(441\) 3.07180 0.146276
\(442\) −8.06998 2.62210i −0.383850 0.124720i
\(443\) 16.2015 + 22.2994i 0.769754 + 1.05948i 0.996339 + 0.0854846i \(0.0272438\pi\)
−0.226585 + 0.973991i \(0.572756\pi\)
\(444\) 4.85410 + 3.52671i 0.230365 + 0.167370i
\(445\) −0.872618 0.561685i −0.0413661 0.0266264i
\(446\) −0.248403 0.764504i −0.0117622 0.0362003i
\(447\) −11.6594 + 16.0478i −0.551471 + 0.759034i
\(448\) −4.46053 6.13939i −0.210740 0.290059i
\(449\) −10.6662 + 32.8273i −0.503371 + 1.54922i 0.300122 + 0.953901i \(0.402973\pi\)
−0.803492 + 0.595315i \(0.797027\pi\)
\(450\) 1.85641 + 0.378937i 0.0875118 + 0.0178633i
\(451\) 0 0
\(452\) 4.89898i 0.230429i
\(453\) −7.70959 2.50500i −0.362228 0.117695i
\(454\) 8.42312 6.11975i 0.395316 0.287214i
\(455\) 31.6931 1.78941i 1.48579 0.0838888i
\(456\) −4.83928 14.8938i −0.226620 0.697465i
\(457\) −20.1750 + 6.55524i −0.943745 + 0.306641i −0.740171 0.672418i \(-0.765256\pi\)
−0.203573 + 0.979060i \(0.565256\pi\)
\(458\) −1.23889 + 1.70518i −0.0578893 + 0.0796778i
\(459\) −13.6952 + 9.95015i −0.639237 + 0.464433i
\(460\) −12.5804 + 4.88757i −0.586563 + 0.227884i
\(461\) 33.0000 1.53696 0.768482 0.639872i \(-0.221013\pi\)
0.768482 + 0.639872i \(0.221013\pi\)
\(462\) 0 0
\(463\) 20.3166i 0.944194i 0.881547 + 0.472097i \(0.156503\pi\)
−0.881547 + 0.472097i \(0.843497\pi\)
\(464\) 5.27548 16.2362i 0.244908 0.753749i
\(465\) 36.4742 + 9.61542i 1.69145 + 0.445905i
\(466\) −0.708411 0.514691i −0.0328165 0.0238426i
\(467\) 0.588870 0.191335i 0.0272496 0.00885394i −0.295360 0.955386i \(-0.595440\pi\)
0.322610 + 0.946532i \(0.395440\pi\)
\(468\) 5.11616 1.66234i 0.236495 0.0768418i
\(469\) 5.98050 + 4.34509i 0.276154 + 0.200638i
\(470\) −3.37910 + 12.8179i −0.155866 + 0.591248i
\(471\) 13.0556 40.1809i 0.601569 1.85144i
\(472\) 2.44949i 0.112747i
\(473\) 0 0
\(474\) 1.46410 0.0672484
\(475\) 18.2541 + 10.3432i 0.837554 + 0.474579i
\(476\) −18.1158 + 13.1619i −0.830334 + 0.603273i
\(477\) 0.934625 1.28640i 0.0427935 0.0589003i
\(478\) 2.78656 0.905408i 0.127454 0.0414124i
\(479\) 0.783636 + 2.41178i 0.0358052 + 0.110197i 0.967362 0.253399i \(-0.0815487\pi\)
−0.931557 + 0.363597i \(0.881549\pi\)
\(480\) −22.1648 + 1.25144i −1.01168 + 0.0571201i
\(481\) 6.15475 4.47169i 0.280633 0.203892i
\(482\) 6.95346 + 2.25932i 0.316722 + 0.102909i
\(483\) 22.5259i 1.02496i
\(484\) 0 0
\(485\) −12.9282 15.8338i −0.587039 0.718974i
\(486\) −1.19170 + 3.66766i −0.0540564 + 0.166368i
\(487\) −7.48128 10.2971i −0.339009 0.466606i 0.605142 0.796117i \(-0.293116\pi\)
−0.944152 + 0.329511i \(0.893116\pi\)
\(488\) −13.3219 + 18.3360i −0.603054 + 0.830033i
\(489\) −3.06798 9.44228i −0.138739 0.426995i
\(490\) −2.62880 + 4.08403i −0.118757 + 0.184497i
\(491\) 32.1283 + 23.3426i 1.44993 + 1.05344i 0.985847 + 0.167646i \(0.0536166\pi\)
0.464084 + 0.885791i \(0.346383\pi\)
\(492\) 3.40654 + 4.68870i 0.153579 + 0.211383i
\(493\) −25.4584 8.27193i −1.14659 0.372549i
\(494\) −9.21539 −0.414620
\(495\) 0 0
\(496\) −21.5167 −0.966127
\(497\) −26.0826 8.47475i −1.16996 0.380144i
\(498\) 5.81878 + 8.00886i 0.260746 + 0.358886i
\(499\) 14.2449 + 10.3495i 0.637690 + 0.463309i 0.859056 0.511882i \(-0.171051\pi\)
−0.221366 + 0.975191i \(0.571051\pi\)
\(500\) 13.5261 13.8580i 0.604904 0.619751i
\(501\) 0.309017 + 0.951057i 0.0138059 + 0.0424901i
\(502\) 1.15736 1.59297i 0.0516555 0.0710976i
\(503\) 4.34117 + 5.97510i 0.193563 + 0.266417i 0.894756 0.446554i \(-0.147349\pi\)
−0.701193 + 0.712971i \(0.747349\pi\)
\(504\) −1.46228 + 4.50045i −0.0651353 + 0.200466i
\(505\) −33.5885 + 27.4249i −1.49467 + 1.22039i
\(506\) 0 0
\(507\) 9.65926i 0.428983i
\(508\) 1.47691 + 0.479877i 0.0655273 + 0.0212911i
\(509\) −6.53022 + 4.74448i −0.289447 + 0.210296i −0.723027 0.690819i \(-0.757250\pi\)
0.433580 + 0.901115i \(0.357250\pi\)
\(510\) 0.487015 + 8.62577i 0.0215654 + 0.381955i
\(511\) 5.06550 + 15.5900i 0.224085 + 0.689661i
\(512\) 21.0983 6.85527i 0.932424 0.302963i
\(513\) −10.8063 + 14.8736i −0.477110 + 0.656685i
\(514\) −6.19728 + 4.50258i −0.273350 + 0.198600i
\(515\) −8.84291 + 3.43554i −0.389665 + 0.151388i
\(516\) 21.5885 0.950379
\(517\) 0 0
\(518\) 3.10583i 0.136462i
\(519\) −12.9950 + 39.9944i −0.570415 + 1.75556i
\(520\) −4.67185 + 17.7217i −0.204874 + 0.777148i
\(521\) 7.48236 + 5.43626i 0.327808 + 0.238167i 0.739500 0.673156i \(-0.235062\pi\)
−0.411692 + 0.911323i \(0.635062\pi\)
\(522\) −2.49686 + 0.811279i −0.109285 + 0.0355087i
\(523\) −24.3772 + 7.92063i −1.06594 + 0.346345i −0.788905 0.614515i \(-0.789352\pi\)
−0.277035 + 0.960860i \(0.589352\pi\)
\(524\) −4.37803 3.18083i −0.191255 0.138955i
\(525\) −13.3841 29.4191i −0.584131 1.28395i
\(526\) −1.08671 + 3.34454i −0.0473827 + 0.145829i
\(527\) 33.7381i 1.46965i
\(528\) 0 0
\(529\) 10.8564 0.472018
\(530\) 0.910463 + 2.34349i 0.0395480 + 0.101795i
\(531\) 0.750932 0.545584i 0.0325877 0.0236763i
\(532\) −14.2944 + 19.6745i −0.619739 + 0.852998i
\(533\) 6.98881 2.27080i 0.302719 0.0983593i
\(534\) −0.143415 0.441387i −0.00620619 0.0191007i
\(535\) 0.374003 + 6.62415i 0.0161696 + 0.286387i
\(536\) −3.45284 + 2.50864i −0.149140 + 0.108357i
\(537\) 28.4122 + 9.23168i 1.22608 + 0.398376i
\(538\) 8.42091i 0.363051i
\(539\) 0 0
\(540\) 10.7321 + 13.1440i 0.461834 + 0.565629i
\(541\) 0.805822 2.48007i 0.0346450 0.106626i −0.932239 0.361844i \(-0.882147\pi\)
0.966884 + 0.255218i \(0.0821472\pi\)
\(542\) −3.48807 4.80091i −0.149825 0.206217i
\(543\) −19.7492 + 27.1824i −0.847519 + 1.16651i
\(544\) −6.13597 18.8846i −0.263077 0.809669i
\(545\) 17.2909 + 11.1298i 0.740660 + 0.476746i
\(546\) 11.4849 + 8.34429i 0.491510 + 0.357103i
\(547\) −16.8915 23.2492i −0.722228 0.994062i −0.999447 0.0332552i \(-0.989413\pi\)
0.277218 0.960807i \(-0.410587\pi\)
\(548\) −14.6018 4.74442i −0.623759 0.202672i
\(549\) −8.58846 −0.366546
\(550\) 0 0
\(551\) −29.0718 −1.23850
\(552\) −12.3688 4.01887i −0.526451 0.171054i
\(553\) −2.87955 3.96336i −0.122451 0.168539i
\(554\) −13.0604 9.48897i −0.554885 0.403148i
\(555\) −6.51331 4.19247i −0.276475 0.177960i
\(556\) −7.80823 24.0312i −0.331143 1.01915i
\(557\) 22.1018 30.4205i 0.936482 1.28896i −0.0207955 0.999784i \(-0.506620\pi\)
0.957277 0.289173i \(-0.0933801\pi\)
\(558\) 1.94492 + 2.67696i 0.0823352 + 0.113325i
\(559\) 8.45874 26.0333i 0.357767 1.10109i
\(560\) 11.6603 + 14.2808i 0.492736 + 0.603475i
\(561\) 0 0
\(562\) 8.96575i 0.378198i
\(563\) 15.1907 + 4.93576i 0.640212 + 0.208017i 0.611093 0.791559i \(-0.290730\pi\)
0.0291185 + 0.999576i \(0.490730\pi\)
\(564\) 31.0019 22.5242i 1.30542 0.948441i
\(565\) 0.356520 + 6.31450i 0.0149989 + 0.265653i
\(566\) −1.29074 3.97248i −0.0542537 0.166976i
\(567\) 33.9241 11.0226i 1.42468 0.462906i
\(568\) 9.30685 12.8098i 0.390507 0.537486i
\(569\) −24.3711 + 17.7067i −1.02169 + 0.742301i −0.966629 0.256181i \(-0.917536\pi\)
−0.0550616 + 0.998483i \(0.517536\pi\)
\(570\) 3.39789 + 8.74602i 0.142322 + 0.366330i
\(571\) 19.7128 0.824956 0.412478 0.910968i \(-0.364663\pi\)
0.412478 + 0.910968i \(0.364663\pi\)
\(572\) 0 0
\(573\) 14.0406i 0.586554i
\(574\) −0.927051 + 2.85317i −0.0386944 + 0.119089i
\(575\) 15.8597 7.21532i 0.661394 0.300899i
\(576\) 1.34317 + 0.975873i 0.0559656 + 0.0406614i
\(577\) 3.57803 1.16257i 0.148955 0.0483986i −0.233590 0.972335i \(-0.575047\pi\)
0.382546 + 0.923937i \(0.375047\pi\)
\(578\) 1.01995 0.331402i 0.0424244 0.0137845i
\(579\) 23.7208 + 17.2342i 0.985802 + 0.716227i
\(580\) −6.84006 + 25.9464i −0.284018 + 1.07736i
\(581\) 10.2360 31.5031i 0.424660 1.30697i
\(582\) 9.14162i 0.378932i
\(583\) 0 0
\(584\) −9.46410 −0.391627
\(585\) −6.47346 + 2.51499i −0.267645 + 0.103982i
\(586\) −6.31345 + 4.58699i −0.260806 + 0.189487i
\(587\) −11.9855 + 16.4966i −0.494695 + 0.680889i −0.981245 0.192764i \(-0.938255\pi\)
0.486551 + 0.873652i \(0.338255\pi\)
\(588\) 13.3534 4.33878i 0.550685 0.178928i
\(589\) 11.3227 + 34.8477i 0.466544 + 1.43587i
\(590\) 0.0827308 + 1.46528i 0.00340597 + 0.0603248i
\(591\) −26.9569 + 19.5853i −1.10886 + 0.805632i
\(592\) 4.20225 + 1.36539i 0.172711 + 0.0561173i
\(593\) 0.859411i 0.0352918i 0.999844 + 0.0176459i \(0.00561715\pi\)
−0.999844 + 0.0176459i \(0.994383\pi\)
\(594\) 0 0
\(595\) 22.3923 18.2832i 0.917995 0.749540i
\(596\) −5.49575 + 16.9142i −0.225115 + 0.692831i
\(597\) −2.27103 3.12580i −0.0929470 0.127931i
\(598\) −4.49837 + 6.19147i −0.183952 + 0.253188i
\(599\) 11.8801 + 36.5632i 0.485408 + 1.49393i 0.831389 + 0.555692i \(0.187546\pi\)
−0.345980 + 0.938242i \(0.612454\pi\)
\(600\) 18.5417 2.10044i 0.756960 0.0857501i
\(601\) 16.1803 + 11.7557i 0.660010 + 0.479525i 0.866666 0.498888i \(-0.166258\pi\)
−0.206656 + 0.978414i \(0.566258\pi\)
\(602\) 6.56850 + 9.04077i 0.267712 + 0.368474i
\(603\) −1.53813 0.499769i −0.0626375 0.0203522i
\(604\) −7.26795 −0.295729
\(605\) 0 0
\(606\) −19.3923 −0.787759
\(607\) −34.6095 11.2453i −1.40476 0.456433i −0.494031 0.869444i \(-0.664477\pi\)
−0.910726 + 0.413011i \(0.864477\pi\)
\(608\) −12.6756 17.4464i −0.514061 0.707545i
\(609\) 36.2315 + 26.3237i 1.46817 + 1.06669i
\(610\) 7.34987 11.4186i 0.297588 0.462324i
\(611\) −15.0147 46.2104i −0.607428 1.86947i
\(612\) 2.87955 3.96336i 0.116399 0.160209i
\(613\) −1.05399 1.45069i −0.0425702 0.0585928i 0.787201 0.616696i \(-0.211529\pi\)
−0.829771 + 0.558103i \(0.811529\pi\)
\(614\) 1.25231 3.85421i 0.0505391 0.155543i
\(615\) −4.73205 5.79555i −0.190815 0.233699i
\(616\) 0 0
\(617\) 13.0053i 0.523575i 0.965126 + 0.261787i \(0.0843119\pi\)
−0.965126 + 0.261787i \(0.915688\pi\)
\(618\) −4.03499 1.31105i −0.162311 0.0527381i
\(619\) 10.3430 7.51461i 0.415719 0.302037i −0.360194 0.932877i \(-0.617290\pi\)
0.775913 + 0.630840i \(0.217290\pi\)
\(620\) 33.7653 1.90641i 1.35605 0.0765632i
\(621\) 4.71806 + 14.5207i 0.189329 + 0.582695i
\(622\) 4.94891 1.60800i 0.198433 0.0644748i
\(623\) −0.912780 + 1.25633i −0.0365698 + 0.0503340i
\(624\) 16.3390 11.8710i 0.654085 0.475220i
\(625\) −16.4258 + 18.8466i −0.657032 + 0.753863i
\(626\) 8.87564 0.354742
\(627\) 0 0
\(628\) 37.8792i 1.51154i
\(629\) 2.14093 6.58911i 0.0853646 0.262725i
\(630\) 0.722737 2.74156i 0.0287945 0.109226i
\(631\) 12.3946 + 9.00517i 0.493419 + 0.358490i 0.806498 0.591237i \(-0.201360\pi\)
−0.313078 + 0.949727i \(0.601360\pi\)
\(632\) 2.68999 0.874032i 0.107002 0.0347671i
\(633\) −24.1134 + 7.83491i −0.958421 + 0.311410i
\(634\) 5.28765 + 3.84170i 0.210000 + 0.152574i
\(635\) −1.93857 0.511052i −0.0769299 0.0202805i
\(636\) 2.24592 6.91223i 0.0890565 0.274088i
\(637\) 17.8028i 0.705371i
\(638\) 0 0
\(639\) 6.00000 0.237356
\(640\) −23.8702 + 9.27375i −0.943552 + 0.366577i
\(641\) 6.35597 4.61788i 0.251046 0.182395i −0.455144 0.890418i \(-0.650412\pi\)
0.706190 + 0.708022i \(0.250412\pi\)
\(642\) −1.74403 + 2.40046i −0.0688315 + 0.0947385i
\(643\) −10.0038 + 3.25045i −0.394513 + 0.128185i −0.499554 0.866283i \(-0.666503\pi\)
0.105041 + 0.994468i \(0.466503\pi\)
\(644\) 6.24095 + 19.2077i 0.245928 + 0.756889i
\(645\) −27.8263 + 1.57109i −1.09566 + 0.0618615i
\(646\) −6.78952 + 4.93287i −0.267130 + 0.194081i
\(647\) −35.5329 11.5453i −1.39694 0.453894i −0.488742 0.872428i \(-0.662544\pi\)
−0.908201 + 0.418534i \(0.862544\pi\)
\(648\) 20.5940i 0.809010i
\(649\) 0 0
\(650\) 2.19615 10.7589i 0.0861402 0.421999i
\(651\) 17.4424 53.6823i 0.683622 2.10397i
\(652\) −5.23210 7.20137i −0.204905 0.282027i
\(653\) −7.13919 + 9.82625i −0.279378 + 0.384531i −0.925528 0.378680i \(-0.876378\pi\)
0.646150 + 0.763211i \(0.276378\pi\)
\(654\) 2.84177 + 8.74606i 0.111122 + 0.341998i
\(655\) 5.87451 + 3.78129i 0.229536 + 0.147747i
\(656\) 3.45284 + 2.50864i 0.134811 + 0.0979458i
\(657\) −2.10798 2.90138i −0.0822400 0.113194i
\(658\) 18.8653 + 6.12971i 0.735446 + 0.238961i
\(659\) −23.3205 −0.908438 −0.454219 0.890890i \(-0.650082\pi\)
−0.454219 + 0.890890i \(0.650082\pi\)
\(660\) 0 0
\(661\) 29.5885 1.15086 0.575429 0.817852i \(-0.304835\pi\)
0.575429 + 0.817852i \(0.304835\pi\)
\(662\) 8.95802 + 2.91064i 0.348163 + 0.113125i
\(663\) −18.6137 25.6195i −0.722896 0.994981i
\(664\) 15.4719 + 11.2410i 0.600427 + 0.436236i
\(665\) 16.9928 26.3996i 0.658953 1.02373i
\(666\) −0.209975 0.646235i −0.00813635 0.0250411i
\(667\) −14.1910 + 19.5322i −0.549478 + 0.756291i
\(668\) 0.526994 + 0.725345i 0.0203900 + 0.0280644i
\(669\) 0.927051 2.85317i 0.0358419 0.110310i
\(670\) 1.98076 1.61729i 0.0765235 0.0624812i
\(671\) 0 0
\(672\) 33.2204i 1.28151i
\(673\) −38.8118 12.6107i −1.49608 0.486107i −0.557211 0.830371i \(-0.688129\pi\)
−0.938873 + 0.344264i \(0.888129\pi\)
\(674\) −7.38176 + 5.36316i −0.284335 + 0.206581i
\(675\) −14.7895 16.1609i −0.569249 0.622032i
\(676\) −2.67617 8.23639i −0.102929 0.316784i
\(677\) 19.3576 6.28967i 0.743973 0.241732i 0.0875873 0.996157i \(-0.472084\pi\)
0.656386 + 0.754425i \(0.272084\pi\)
\(678\) −1.66251 + 2.28825i −0.0638482 + 0.0878795i
\(679\) −24.7466 + 17.9794i −0.949687 + 0.689988i
\(680\) 6.04416 + 15.5574i 0.231783 + 0.596598i
\(681\) 38.8564 1.48898
\(682\) 0 0
\(683\) 29.8372i 1.14169i −0.821058 0.570844i \(-0.806616\pi\)
0.821058 0.570844i \(-0.193384\pi\)
\(684\) 1.64413 5.06010i 0.0628648 0.193478i
\(685\) 19.1662 + 5.05265i 0.732302 + 0.193052i
\(686\) −3.92892 2.85452i −0.150007 0.108986i
\(687\) −7.48111 + 2.43076i −0.285422 + 0.0927393i
\(688\) 15.1200 4.91279i 0.576445 0.187298i
\(689\) −7.45541 5.41667i −0.284028 0.206359i
\(690\) 7.53475 + 1.98633i 0.286843 + 0.0756184i
\(691\) 11.7145 36.0536i 0.445641 1.37154i −0.436138 0.899880i \(-0.643654\pi\)
0.881779 0.471663i \(-0.156346\pi\)
\(692\) 37.7033i 1.43326i
\(693\) 0 0
\(694\) 2.26795 0.0860902
\(695\) 11.8132 + 30.4066i 0.448100 + 1.15339i
\(696\) −20.9183 + 15.1980i −0.792905 + 0.576079i
\(697\) 3.93354 5.41405i 0.148993 0.205072i
\(698\) −3.60391 + 1.17098i −0.136410 + 0.0443223i
\(699\) −1.00985 3.10800i −0.0381961 0.117556i
\(700\) −19.5633 21.3773i −0.739424 0.807985i
\(701\) 30.6265 22.2514i 1.15675 0.840425i 0.167383 0.985892i \(-0.446468\pi\)
0.989363 + 0.145467i \(0.0464684\pi\)
\(702\) 9.15115 + 2.97339i 0.345388 + 0.112223i
\(703\) 7.52433i 0.283786i
\(704\) 0 0
\(705\) −38.3205 + 31.2886i −1.44323 + 1.17840i
\(706\) 2.08032 6.40256i 0.0782938 0.240964i
\(707\) 38.1402 + 52.4954i 1.43441 + 1.97429i
\(708\) 2.49376 3.43237i 0.0937213 0.128996i
\(709\) −0.805822 2.48007i −0.0302633 0.0931408i 0.934784 0.355217i \(-0.115593\pi\)
−0.965047 + 0.262076i \(0.915593\pi\)
\(710\) −5.13471 + 7.97714i −0.192702 + 0.299377i
\(711\) 0.867102 + 0.629986i 0.0325189 + 0.0236263i
\(712\) −0.526994 0.725345i −0.0197499 0.0271834i
\(713\) 28.9398 + 9.40313i 1.08381 + 0.352150i
\(714\) 12.9282 0.483826
\(715\) 0 0
\(716\) 26.7846 1.00099
\(717\) 10.3996 + 3.37903i 0.388380 + 0.126192i
\(718\) 10.8500 + 14.9337i 0.404918 + 0.557322i
\(719\) −40.6095 29.5046i −1.51448 1.10033i −0.964140 0.265394i \(-0.914498\pi\)
−0.550340 0.834941i \(-0.685502\pi\)
\(720\) −3.39165 2.18313i −0.126399 0.0813604i
\(721\) 4.38685 + 13.5013i 0.163375 + 0.502816i
\(722\) 0.423623 0.583067i 0.0157656 0.0216995i
\(723\) 16.0384 + 22.0750i 0.596475 + 0.820977i
\(724\) −9.30894 + 28.6500i −0.345964 + 1.06477i
\(725\) 6.92820 33.9411i 0.257307 1.26054i
\(726\) 0 0
\(727\) 8.24504i 0.305792i −0.988242 0.152896i \(-0.951140\pi\)
0.988242 0.152896i \(-0.0488599\pi\)
\(728\) 26.0826 + 8.47475i 0.966685 + 0.314095i
\(729\) 14.2294 10.3382i 0.527013 0.382898i
\(730\) 5.66142 0.319647i 0.209539 0.0118307i
\(731\) −7.70324 23.7081i −0.284915 0.876877i
\(732\) −37.3349 + 12.1308i −1.37994 + 0.448369i
\(733\) −5.47668 + 7.53800i −0.202286 + 0.278423i −0.898093 0.439807i \(-0.855047\pi\)
0.695807 + 0.718229i \(0.255047\pi\)
\(734\) 7.07994 5.14388i 0.261325 0.189864i
\(735\) −16.8960 + 6.56422i −0.623219 + 0.242125i
\(736\) −17.9090 −0.660133
\(737\) 0 0
\(738\) 0.656339i 0.0241602i
\(739\) −12.0295 + 37.0229i −0.442511 + 1.36191i 0.442679 + 0.896680i \(0.354028\pi\)
−0.885190 + 0.465230i \(0.845972\pi\)
\(740\) −6.71541 1.77034i −0.246863 0.0650789i
\(741\) −27.8240 20.2153i −1.02214 0.742627i
\(742\) 3.57803 1.16257i 0.131354 0.0426794i
\(743\) −41.2733 + 13.4105i −1.51417 + 0.491984i −0.944113 0.329621i \(-0.893079\pi\)
−0.570057 + 0.821605i \(0.693079\pi\)
\(744\) 26.3646 + 19.1550i 0.966574 + 0.702257i
\(745\) 5.85278 22.2013i 0.214429 0.813394i
\(746\) 0.0281313 0.0865791i 0.00102996 0.00316989i
\(747\) 7.24693i 0.265151i
\(748\) 0 0
\(749\) 9.92820 0.362769
\(750\) −11.0207 + 1.88272i −0.402418 + 0.0687473i
\(751\) −39.3514 + 28.5905i −1.43595 + 1.04328i −0.447084 + 0.894492i \(0.647538\pi\)
−0.988869 + 0.148789i \(0.952462\pi\)
\(752\) 16.5872 22.8304i 0.604874 0.832538i
\(753\) 6.98881 2.27080i 0.254686 0.0827526i
\(754\) 4.70181 + 14.4707i 0.171230 + 0.526992i
\(755\) 9.36796 0.528920i 0.340935 0.0192494i
\(756\) 20.5428 14.9252i 0.747135 0.542825i
\(757\) −47.3387 15.3813i −1.72056 0.559042i −0.728522 0.685022i \(-0.759793\pi\)
−0.992033 + 0.125980i \(0.959793\pi\)
\(758\) 0.757875i 0.0275273i
\(759\) 0 0
\(760\) 11.4641 + 14.0406i 0.415847 + 0.509306i
\(761\) 6.13597 18.8846i 0.222429 0.684565i −0.776114 0.630593i \(-0.782812\pi\)
0.998542 0.0539721i \(-0.0171882\pi\)
\(762\) −0.526994 0.725345i −0.0190910 0.0262765i
\(763\) 18.0867 24.8942i 0.654782 0.901231i
\(764\) −3.89005 11.9723i −0.140737 0.433144i
\(765\) −3.42314 + 5.31809i −0.123764 + 0.192276i
\(766\) −16.1067 11.7022i −0.581958 0.422818i
\(767\) −3.16196 4.35207i −0.114172 0.157144i
\(768\) −2.55808 0.831171i −0.0923068 0.0299923i
\(769\) −9.85641 −0.355431 −0.177716 0.984082i \(-0.556871\pi\)
−0.177716 + 0.984082i \(0.556871\pi\)
\(770\) 0 0
\(771\) −28.5885 −1.02959
\(772\) 25.0014 + 8.12345i 0.899821 + 0.292369i
\(773\) −7.07951 9.74411i −0.254632 0.350471i 0.662495 0.749067i \(-0.269498\pi\)
−0.917127 + 0.398596i \(0.869498\pi\)
\(774\) −1.97794 1.43705i −0.0710955 0.0516539i
\(775\) −43.3828 + 4.91450i −1.55836 + 0.176534i
\(776\) −5.45732 16.7959i −0.195906 0.602938i
\(777\) −6.81308 + 9.37740i −0.244418 + 0.336413i
\(778\) −1.86340 2.56475i −0.0668060 0.0919506i
\(779\) 2.24592 6.91223i 0.0804684 0.247656i
\(780\) −24.5885 + 20.0764i −0.880408 + 0.718850i
\(781\) 0 0
\(782\) 6.96953i 0.249230i
\(783\) 28.8692 + 9.38016i 1.03170 + 0.335219i
\(784\) 8.36503 6.07755i 0.298751 0.217055i
\(785\) 2.75663 + 48.8240i 0.0983884 + 1.74260i
\(786\) 0.965479 + 2.97144i 0.0344375 + 0.105988i
\(787\) −16.5357 + 5.37277i −0.589434 + 0.191519i −0.588522 0.808481i \(-0.700290\pi\)
−0.000911585 1.00000i \(0.500290\pi\)
\(788\) −17.5597 + 24.1689i −0.625539 + 0.860980i
\(789\) −10.6178 + 7.71430i −0.378005 + 0.274636i
\(790\) −1.57963 + 0.613700i −0.0562009 + 0.0218345i
\(791\) 9.46410 0.336505
\(792\) 0 0
\(793\) 49.7749i 1.76756i
\(794\) 5.27548 16.2362i 0.187220 0.576203i
\(795\) −2.39183 + 9.07291i −0.0848293 + 0.321783i
\(796\) −2.80252 2.03615i −0.0993326 0.0721693i
\(797\) −34.4164 + 11.1826i −1.21909 + 0.396107i −0.846751 0.531989i \(-0.821445\pi\)
−0.372340 + 0.928096i \(0.621445\pi\)
\(798\) 13.3534 4.33878i 0.472705 0.153591i
\(799\) −35.7980 26.0087i −1.26644 0.920123i
\(800\) 23.3893 10.6409i 0.826937 0.376213i
\(801\) 0.104987 0.323118i 0.00370954 0.0114168i
\(802\) 1.20118i 0.0424153i
\(803\) 0 0
\(804\) −7.39230 −0.260706
\(805\) −9.44205 24.3034i −0.332789 0.856582i
\(806\) 15.5144 11.2719i 0.546473 0.397036i
\(807\) 18.4725 25.4252i 0.650262 0.895009i
\(808\) −35.6295 + 11.5767i −1.25344 + 0.407268i
\(809\) −4.49184 13.8245i −0.157925 0.486042i 0.840521 0.541779i \(-0.182249\pi\)
−0.998445 + 0.0557371i \(0.982249\pi\)
\(810\) −0.695557 12.3193i −0.0244394 0.432858i
\(811\) 15.3558 11.1566i 0.539214 0.391762i −0.284579 0.958653i \(-0.591854\pi\)
0.823793 + 0.566891i \(0.191854\pi\)
\(812\) 38.1876 + 12.4079i 1.34012 + 0.435432i
\(813\) 22.1469i 0.776727i
\(814\) 0 0
\(815\) 7.26795 + 8.90138i 0.254585 + 0.311802i
\(816\) 5.68353 17.4921i 0.198964 0.612347i
\(817\) −15.9132 21.9026i −0.556732 0.766276i
\(818\) 7.94860 10.9403i 0.277916 0.382519i
\(819\) 3.21140 + 9.88367i 0.112215 + 0.345363i
\(820\) −5.64069 3.63079i −0.196981 0.126793i
\(821\) 23.6202 + 17.1611i 0.824350 + 0.598925i 0.917955 0.396684i \(-0.129839\pi\)
−0.0936051 + 0.995609i \(0.529839\pi\)
\(822\) 5.21026 + 7.17130i 0.181729 + 0.250128i
\(823\) 6.42581 + 2.08787i 0.223990 + 0.0727787i 0.418862 0.908050i \(-0.362429\pi\)
−0.194872 + 0.980829i \(0.562429\pi\)
\(824\) −8.19615 −0.285526
\(825\) 0 0
\(826\) 2.19615 0.0764139
\(827\) 32.4118 + 10.5312i 1.12707 + 0.366207i 0.812462 0.583014i \(-0.198127\pi\)
0.314608 + 0.949222i \(0.398127\pi\)
\(828\) −2.59713 3.57465i −0.0902566 0.124228i
\(829\) −8.07461 5.86654i −0.280443 0.203754i 0.438668 0.898649i \(-0.355450\pi\)
−0.719110 + 0.694896i \(0.755450\pi\)
\(830\) −9.63497 6.20181i −0.334435 0.215268i
\(831\) −18.6179 57.2999i −0.645847 1.98771i
\(832\) 5.65572 7.78444i 0.196077 0.269877i
\(833\) −9.52958 13.1163i −0.330180 0.454454i
\(834\) −4.50808 + 13.8744i −0.156102 + 0.480433i
\(835\) −0.732051 0.896575i −0.0253337 0.0310273i
\(836\) 0 0
\(837\) 38.2581i 1.32239i
\(838\) −6.07489 1.97385i −0.209854 0.0681856i
\(839\) −31.3774 + 22.7970i −1.08327 + 0.787041i −0.978250 0.207430i \(-0.933490\pi\)
−0.105019 + 0.994470i \(0.533490\pi\)
\(840\) −1.57406 27.8789i −0.0543102 0.961914i
\(841\) 5.87132 + 18.0701i 0.202459 + 0.623106i
\(842\) −8.39503 + 2.72771i −0.289312 + 0.0940031i
\(843\) 19.6677 27.0702i 0.677391 0.932348i
\(844\) −18.3906 + 13.3616i −0.633031 + 0.459924i
\(845\) 4.04882 + 10.4215i 0.139284 + 0.358510i
\(846\) −4.33975 −0.149204
\(847\) 0 0
\(848\) 5.35225i 0.183797i
\(849\) 4.81710 14.8255i 0.165322 0.508810i
\(850\) −4.14106 9.10229i −0.142037 0.312206i
\(851\) −5.05531 3.67290i −0.173294 0.125905i
\(852\) 26.0826 8.47475i 0.893575 0.290340i
\(853\) 44.0952 14.3274i 1.50979 0.490561i 0.566935 0.823762i \(-0.308129\pi\)
0.942856 + 0.333201i \(0.108129\pi\)
\(854\) −16.4396 11.9441i −0.562553 0.408719i
\(855\) −1.75094 + 6.64183i −0.0598808 + 0.227146i
\(856\) −1.77130 + 5.45150i −0.0605418 + 0.186329i
\(857\) 29.3195i 1.00154i −0.865581 0.500768i \(-0.833051\pi\)
0.865581 0.500768i \(-0.166949\pi\)
\(858\) 0 0
\(859\) 22.1962 0.757323 0.378661 0.925535i \(-0.376384\pi\)
0.378661 + 0.925535i \(0.376384\pi\)
\(860\) −23.2920 + 9.04912i −0.794251 + 0.308572i
\(861\) −9.05788 + 6.58093i −0.308692 + 0.224278i
\(862\) −1.54315 + 2.12396i −0.0525597 + 0.0723423i
\(863\) 16.2719 5.28705i 0.553901 0.179973i −0.0186740 0.999826i \(-0.505944\pi\)
0.572575 + 0.819852i \(0.305944\pi\)
\(864\) 6.95803 + 21.4146i 0.236717 + 0.728540i
\(865\) −2.74383 48.5973i −0.0932931 1.65236i
\(866\) −12.0346 + 8.74368i −0.408954 + 0.297122i
\(867\) 3.80651 + 1.23681i 0.129276 + 0.0420043i
\(868\) 50.6071i 1.71772i
\(869\) 0 0
\(870\) 12.0000 9.79796i 0.406838 0.332182i
\(871\) −2.89644 + 8.91432i −0.0981420 + 0.302050i
\(872\) 10.4424 + 14.3727i 0.353623 + 0.486720i
\(873\) 3.93354 5.41405i 0.133130 0.183238i
\(874\) 2.33902 + 7.19876i 0.0791184 + 0.243502i
\(875\) 26.7717 + 26.1304i 0.905048 + 0.883367i
\(876\) −13.2617 9.63516i −0.448070 0.325542i
\(877\) 6.99213 + 9.62384i 0.236107 + 0.324974i 0.910585 0.413321i \(-0.135631\pi\)
−0.674478 + 0.738295i \(0.735631\pi\)
\(878\) −13.9069 4.51863i −0.469336 0.152497i
\(879\) −29.1244 −0.982340
\(880\) 0 0
\(881\) −26.9090 −0.906586 −0.453293 0.891362i \(-0.649751\pi\)
−0.453293 + 0.891362i \(0.649751\pi\)
\(882\) −1.51226 0.491361i −0.0509203 0.0165450i
\(883\) −12.6756 17.4464i −0.426566 0.587118i 0.540595 0.841283i \(-0.318199\pi\)
−0.967161 + 0.254165i \(0.918199\pi\)
\(884\) −22.9699 16.6886i −0.772560 0.561298i
\(885\) −2.96452 + 4.60560i −0.0996514 + 0.154816i
\(886\) −4.40904 13.5696i −0.148125 0.455881i
\(887\) −9.22532 + 12.6976i −0.309756 + 0.426342i −0.935305 0.353842i \(-0.884875\pi\)
0.625549 + 0.780185i \(0.284875\pi\)
\(888\) −3.93354 5.41405i −0.132001 0.181684i
\(889\) −0.927051 + 2.85317i −0.0310923 + 0.0956922i
\(890\) 0.339746 + 0.416102i 0.0113883 + 0.0139478i
\(891\) 0 0
\(892\) 2.68973i 0.0900587i
\(893\) −45.7040 14.8501i −1.52943 0.496941i
\(894\) 8.30695 6.03535i 0.277826 0.201852i
\(895\) −34.5238 + 1.94923i −1.15400 + 0.0651557i
\(896\) 11.8417 + 36.4450i 0.395603 + 1.21754i
\(897\) −27.1638 + 8.82604i −0.906972 + 0.294693i
\(898\) 10.5020 14.4548i 0.350458 0.482364i
\(899\) 48.9434 35.5595i 1.63236 1.18598i
\(900\) 5.51582 + 3.12540i 0.183861 + 0.104180i
\(901\) −8.39230 −0.279588
\(902\) 0 0
\(903\) 41.7057i 1.38788i
\(904\) −1.68850 + 5.19667i −0.0561587 + 0.172839i
\(905\) 9.91369 37.6056i 0.329542 1.25005i
\(906\) 3.39476 + 2.46644i 0.112783 + 0.0819419i
\(907\) 28.6407 9.30592i 0.950998 0.308998i 0.207877 0.978155i \(-0.433345\pi\)
0.743121 + 0.669157i \(0.233345\pi\)
\(908\) 33.1326 10.7654i 1.09954 0.357264i
\(909\) −11.4849 8.34429i −0.380931 0.276763i
\(910\) −15.8888 4.18866i −0.526710 0.138853i
\(911\) −9.34737 + 28.7682i −0.309692 + 0.953134i 0.668192 + 0.743988i \(0.267068\pi\)
−0.977885 + 0.209146i \(0.932932\pi\)
\(912\) 19.9749i 0.661434i
\(913\) 0 0
\(914\) 10.9808 0.363211
\(915\) 47.2397 18.3530i 1.56169 0.606730i
\(916\) −5.70564 + 4.14539i −0.188520 + 0.136968i
\(917\) 6.14488 8.45770i 0.202922 0.279298i
\(918\) 8.33381 2.70782i 0.275057 0.0893713i
\(919\) −5.86538 18.0518i −0.193481 0.595473i −0.999991 0.00425273i \(-0.998646\pi\)
0.806510 0.591220i \(-0.201354\pi\)
\(920\) 15.0294 0.848567i 0.495504 0.0279764i
\(921\) 12.2359 8.88987i 0.403185 0.292931i
\(922\) −16.2460 5.27865i −0.535034 0.173843i
\(923\) 34.7733i 1.14458i
\(924\) 0 0
\(925\) 8.78461 + 1.79315i 0.288836 + 0.0589584i
\(926\) 3.24983 10.0019i 0.106796 0.328684i
\(927\) −1.82556 2.51267i −0.0599593 0.0825268i
\(928\) −20.9284 + 28.8055i −0.687009 + 0.945586i
\(929\) 13.5524 + 41.7099i 0.444639 + 1.36846i 0.882879 + 0.469600i \(0.155602\pi\)
−0.438240 + 0.898858i \(0.644398\pi\)
\(930\) −16.4183 10.5681i −0.538376 0.346541i
\(931\) −14.2449 10.3495i −0.466859 0.339193i
\(932\) −1.72219 2.37039i −0.0564122 0.0776447i
\(933\) 18.4696 + 6.00113i 0.604666 + 0.196468i
\(934\) −0.320508 −0.0104873
\(935\) 0 0
\(936\) −6.00000 −0.196116
\(937\) 29.6606 + 9.63732i 0.968970 + 0.314838i 0.750400 0.660984i \(-0.229861\pi\)
0.218570 + 0.975821i \(0.429861\pi\)
\(938\) −2.24918 3.09573i −0.0734384 0.101079i
\(939\) 26.7982 + 19.4700i 0.874525 + 0.635380i
\(940\) −24.0069 + 37.2965i −0.783020 + 1.21648i
\(941\) 8.34346 + 25.6785i 0.271989 + 0.837096i 0.990000 + 0.141065i \(0.0450526\pi\)
−0.718011 + 0.696031i \(0.754947\pi\)
\(942\) −12.8546 + 17.6928i −0.418825 + 0.576464i
\(943\) −3.54775 4.88306i −0.115531 0.159014i
\(944\) 0.965479 2.97144i 0.0314237 0.0967121i
\(945\) −25.3923 + 20.7327i −0.826012 + 0.674436i
\(946\) 0 0
\(947\) 19.9749i 0.649096i −0.945869 0.324548i \(-0.894788\pi\)
0.945869 0.324548i \(-0.105212\pi\)
\(948\) 4.65921 + 1.51387i 0.151324 + 0.0491681i
\(949\) −16.8151 + 12.2169i −0.545841 + 0.396577i
\(950\) −7.33204 8.01189i −0.237883 0.259940i
\(951\) 7.53764 + 23.1985i 0.244425 + 0.752262i
\(952\) 23.7530 7.71781i 0.769839 0.250136i
\(953\) 9.81199 13.5051i 0.317842 0.437472i −0.619965 0.784629i \(-0.712853\pi\)
0.937807 + 0.347158i \(0.112853\pi\)
\(954\) −0.665890 + 0.483797i −0.0215590 + 0.0156635i
\(955\) 5.88532 + 15.1485i 0.190445 + 0.490195i
\(956\) 9.80385 0.317079
\(957\) 0 0
\(958\) 1.31268i 0.0424107i
\(959\) 9.16552 28.2086i 0.295970 0.910902i
\(960\) −9.47332 2.49739i −0.305750 0.0806028i
\(961\) −36.6070 26.5965i −1.18087 0.857952i
\(962\) −3.74529 + 1.21692i −0.120753 + 0.0392350i
\(963\) −2.06578 + 0.671212i −0.0665688 + 0.0216295i
\(964\) 19.7919 + 14.3796i 0.637453 + 0.463137i
\(965\) −32.8166 8.65120i −1.05640 0.278492i
\(966\) 3.60322 11.0896i 0.115932 0.356801i
\(967\) 4.24264i 0.136434i −0.997671 0.0682171i \(-0.978269\pi\)
0.997671 0.0682171i \(-0.0217310\pi\)
\(968\) 0 0
\(969\) −31.3205 −1.00616
\(970\) 3.83184 + 9.86299i 0.123033 + 0.316681i
\(971\) 20.1673 14.6524i 0.647201 0.470219i −0.215116 0.976589i \(-0.569013\pi\)
0.862316 + 0.506370i \(0.169013\pi\)
\(972\) −7.58466 + 10.4394i −0.243278 + 0.334843i
\(973\) 46.4248 15.0843i 1.48831 0.483582i
\(974\) 2.03595 + 6.26600i 0.0652359 + 0.200775i
\(975\) 30.2320 27.6667i 0.968200 0.886044i
\(976\) −23.3878 + 16.9923i −0.748627 + 0.543909i
\(977\) −27.6914 8.99749i −0.885927 0.287855i −0.169511 0.985528i \(-0.554219\pi\)
−0.716416 + 0.697673i \(0.754219\pi\)
\(978\) 5.13922i 0.164334i
\(979\) 0 0
\(980\) −12.5885 + 10.2784i −0.402124 + 0.328332i
\(981\) −2.08032 + 6.40256i −0.0664194 + 0.204418i
\(982\) −12.0830 16.6309i −0.385585 0.530712i
\(983\) 32.9299 45.3241i 1.05030 1.44562i 0.161753 0.986831i \(-0.448285\pi\)
0.888548 0.458784i \(-0.151715\pi\)
\(984\) −1.99752 6.14773i −0.0636785 0.195982i
\(985\) 20.8746 32.4301i 0.665119 1.03331i
\(986\) 11.2101 + 8.14459i 0.357001 + 0.259377i
\(987\) 43.5135 + 59.8912i 1.38505 + 1.90636i
\(988\) −29.3261 9.52863i −0.932988 0.303146i
\(989\) −22.4833 −0.714929
\(990\) 0 0
\(991\) 19.9090 0.632429 0.316215 0.948688i \(-0.397588\pi\)
0.316215 + 0.948688i \(0.397588\pi\)
\(992\) 42.6795 + 13.8674i 1.35508 + 0.440291i
\(993\) 20.6620 + 28.4388i 0.655688 + 0.902477i
\(994\) 11.4849 + 8.34429i 0.364280 + 0.264665i
\(995\) 3.76046 + 2.42052i 0.119215 + 0.0767358i
\(996\) 10.2360 + 31.5031i 0.324340 + 0.998215i
\(997\) 20.0535 27.6012i 0.635100 0.874140i −0.363243 0.931695i \(-0.618330\pi\)
0.998342 + 0.0575549i \(0.0183304\pi\)
\(998\) −5.35732 7.37372i −0.169583 0.233411i
\(999\) −2.42776 + 7.47189i −0.0768110 + 0.236400i
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 605.2.j.e.9.2 16
5.4 even 2 inner 605.2.j.e.9.3 16
11.2 odd 10 605.2.j.f.124.2 16
11.3 even 5 inner 605.2.j.e.444.2 16
11.4 even 5 605.2.b.e.364.2 yes 4
11.5 even 5 inner 605.2.j.e.269.3 16
11.6 odd 10 605.2.j.f.269.2 16
11.7 odd 10 605.2.b.d.364.3 yes 4
11.8 odd 10 605.2.j.f.444.3 16
11.9 even 5 inner 605.2.j.e.124.3 16
11.10 odd 2 605.2.j.f.9.3 16
55.4 even 10 605.2.b.e.364.3 yes 4
55.7 even 20 3025.2.a.y.1.2 4
55.9 even 10 inner 605.2.j.e.124.2 16
55.14 even 10 inner 605.2.j.e.444.3 16
55.18 even 20 3025.2.a.y.1.3 4
55.19 odd 10 605.2.j.f.444.2 16
55.24 odd 10 605.2.j.f.124.3 16
55.29 odd 10 605.2.b.d.364.2 4
55.37 odd 20 3025.2.a.z.1.3 4
55.39 odd 10 605.2.j.f.269.3 16
55.48 odd 20 3025.2.a.z.1.2 4
55.49 even 10 inner 605.2.j.e.269.2 16
55.54 odd 2 605.2.j.f.9.2 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
605.2.b.d.364.2 4 55.29 odd 10
605.2.b.d.364.3 yes 4 11.7 odd 10
605.2.b.e.364.2 yes 4 11.4 even 5
605.2.b.e.364.3 yes 4 55.4 even 10
605.2.j.e.9.2 16 1.1 even 1 trivial
605.2.j.e.9.3 16 5.4 even 2 inner
605.2.j.e.124.2 16 55.9 even 10 inner
605.2.j.e.124.3 16 11.9 even 5 inner
605.2.j.e.269.2 16 55.49 even 10 inner
605.2.j.e.269.3 16 11.5 even 5 inner
605.2.j.e.444.2 16 11.3 even 5 inner
605.2.j.e.444.3 16 55.14 even 10 inner
605.2.j.f.9.2 16 55.54 odd 2
605.2.j.f.9.3 16 11.10 odd 2
605.2.j.f.124.2 16 11.2 odd 10
605.2.j.f.124.3 16 55.24 odd 10
605.2.j.f.269.2 16 11.6 odd 10
605.2.j.f.269.3 16 55.39 odd 10
605.2.j.f.444.2 16 55.19 odd 10
605.2.j.f.444.3 16 11.8 odd 10
3025.2.a.y.1.2 4 55.7 even 20
3025.2.a.y.1.3 4 55.18 even 20
3025.2.a.z.1.2 4 55.48 odd 20
3025.2.a.z.1.3 4 55.37 odd 20