Properties

Label 750.2.l.a.107.2
Level $750$
Weight $2$
Character 750.107
Analytic conductor $5.989$
Analytic rank $0$
Dimension $80$
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] = [750,2,Mod(107,750)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(750, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([10, 13]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("750.107");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 750.l (of order \(20\), degree \(8\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.98878015160\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(10\) over \(\Q(\zeta_{20})\)
Twist minimal: no (minimal twist has level 150)
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 107.2
Character \(\chi\) \(=\) 750.107
Dual form 750.2.l.a.743.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.891007 - 0.453990i) q^{2} +(-0.974581 - 1.43185i) q^{3} +(0.587785 + 0.809017i) q^{4} +(0.218312 + 1.71824i) q^{6} +(-3.13589 - 3.13589i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-1.10038 + 2.79091i) q^{9} +O(q^{10})\) \(q+(-0.891007 - 0.453990i) q^{2} +(-0.974581 - 1.43185i) q^{3} +(0.587785 + 0.809017i) q^{4} +(0.218312 + 1.71824i) q^{6} +(-3.13589 - 3.13589i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-1.10038 + 2.79091i) q^{9} +(-3.57685 + 1.16219i) q^{11} +(0.585546 - 1.63007i) q^{12} +(1.78169 + 3.49677i) q^{13} +(1.37043 + 4.21776i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(0.406920 - 0.0644499i) q^{17} +(2.24749 - 1.98715i) q^{18} +(2.93913 - 4.04536i) q^{19} +(-1.43394 + 7.54629i) q^{21} +(3.71462 + 0.588338i) q^{22} +(-2.28327 + 4.48117i) q^{23} +(-1.26176 + 1.18657i) q^{24} -3.92451i q^{26} +(5.06857 - 1.14438i) q^{27} +(0.693758 - 4.38021i) q^{28} +(-1.49299 + 1.08472i) q^{29} +(2.69808 + 1.96027i) q^{31} +(0.707107 - 0.707107i) q^{32} +(5.15001 + 3.98886i) q^{33} +(-0.391828 - 0.127313i) q^{34} +(-2.90468 + 0.750223i) q^{36} +(-4.70465 + 2.39714i) q^{37} +(-4.45534 + 2.27011i) q^{38} +(3.27044 - 5.95899i) q^{39} +(3.24600 + 1.05469i) q^{41} +(4.70360 - 6.07280i) q^{42} +(-3.71639 + 3.71639i) q^{43} +(-3.04265 - 2.21062i) q^{44} +(4.06882 - 2.95617i) q^{46} +(0.808572 - 5.10512i) q^{47} +(1.66293 - 0.484416i) q^{48} +12.6676i q^{49} +(-0.488859 - 0.519837i) q^{51} +(-1.78169 + 3.49677i) q^{52} +(8.20487 + 1.29952i) q^{53} +(-5.03567 - 1.28143i) q^{54} +(-2.60672 + 3.58784i) q^{56} +(-8.65677 - 0.265855i) q^{57} +(1.82271 - 0.288689i) q^{58} +(1.73564 - 5.34175i) q^{59} +(4.43829 + 13.6596i) q^{61} +(-1.51406 - 2.97152i) q^{62} +(12.2026 - 5.30128i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(-2.77779 - 5.89216i) q^{66} +(0.968887 + 6.11731i) q^{67} +(0.291323 + 0.291323i) q^{68} +(8.64159 - 1.09796i) q^{69} +(-0.992045 - 1.36543i) q^{71} +(2.92868 + 0.650243i) q^{72} +(-3.19175 - 1.62628i) q^{73} +5.28015 q^{74} +5.00034 q^{76} +(14.8611 + 7.57211i) q^{77} +(-5.61931 + 3.82475i) q^{78} +(6.24842 + 8.60021i) q^{79} +(-6.57831 - 6.14214i) q^{81} +(-2.41339 - 2.41339i) q^{82} +(1.10932 + 7.00394i) q^{83} +(-6.94793 + 3.27552i) q^{84} +(4.99854 - 1.62412i) q^{86} +(3.00819 + 1.08059i) q^{87} +(1.70742 + 3.35101i) q^{88} +(-0.324819 - 0.999689i) q^{89} +(5.37828 - 16.5526i) q^{91} +(-4.96742 + 0.786761i) q^{92} +(0.177314 - 5.77369i) q^{93} +(-3.03812 + 4.18162i) q^{94} +(-1.70160 - 0.323338i) q^{96} +(7.61627 + 1.20630i) q^{97} +(5.75096 - 11.2869i) q^{98} +(0.692350 - 11.2615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 4 q^{3} - 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 80 q - 4 q^{3} - 4 q^{7} - 16 q^{12} + 20 q^{16} + 8 q^{18} + 40 q^{19} - 4 q^{22} + 56 q^{27} - 4 q^{28} + 96 q^{33} + 40 q^{34} + 64 q^{37} + 40 q^{39} + 4 q^{42} + 24 q^{43} - 16 q^{48} + 64 q^{57} - 20 q^{58} - 4 q^{63} + 104 q^{67} - 140 q^{69} - 8 q^{72} + 60 q^{73} + 60 q^{78} - 80 q^{79} - 40 q^{81} - 96 q^{82} - 60 q^{84} - 80 q^{87} - 24 q^{88} - 12 q^{93} + 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(251\)
\(\chi(n)\) \(e\left(\frac{13}{20}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.891007 0.453990i −0.630037 0.321020i
\(3\) −0.974581 1.43185i −0.562674 0.826679i
\(4\) 0.587785 + 0.809017i 0.293893 + 0.404508i
\(5\) 0 0
\(6\) 0.218312 + 1.71824i 0.0891255 + 0.701467i
\(7\) −3.13589 3.13589i −1.18525 1.18525i −0.978364 0.206890i \(-0.933666\pi\)
−0.206890 0.978364i \(-0.566334\pi\)
\(8\) −0.156434 0.987688i −0.0553079 0.349201i
\(9\) −1.10038 + 2.79091i −0.366795 + 0.930302i
\(10\) 0 0
\(11\) −3.57685 + 1.16219i −1.07846 + 0.350413i −0.793778 0.608208i \(-0.791889\pi\)
−0.284684 + 0.958622i \(0.591889\pi\)
\(12\) 0.585546 1.63007i 0.169033 0.470561i
\(13\) 1.78169 + 3.49677i 0.494152 + 0.969828i 0.994573 + 0.104046i \(0.0331788\pi\)
−0.500420 + 0.865783i \(0.666821\pi\)
\(14\) 1.37043 + 4.21776i 0.366264 + 1.12724i
\(15\) 0 0
\(16\) −0.309017 + 0.951057i −0.0772542 + 0.237764i
\(17\) 0.406920 0.0644499i 0.0986927 0.0156314i −0.106893 0.994271i \(-0.534090\pi\)
0.205585 + 0.978639i \(0.434090\pi\)
\(18\) 2.24749 1.98715i 0.529739 0.468376i
\(19\) 2.93913 4.04536i 0.674282 0.928070i −0.325565 0.945520i \(-0.605555\pi\)
0.999848 + 0.0174495i \(0.00555464\pi\)
\(20\) 0 0
\(21\) −1.43394 + 7.54629i −0.312912 + 1.64674i
\(22\) 3.71462 + 0.588338i 0.791960 + 0.125434i
\(23\) −2.28327 + 4.48117i −0.476095 + 0.934389i 0.520650 + 0.853770i \(0.325690\pi\)
−0.996745 + 0.0806186i \(0.974310\pi\)
\(24\) −1.26176 + 1.18657i −0.257556 + 0.242208i
\(25\) 0 0
\(26\) 3.92451i 0.769660i
\(27\) 5.06857 1.14438i 0.975447 0.220236i
\(28\) 0.693758 4.38021i 0.131108 0.827783i
\(29\) −1.49299 + 1.08472i −0.277241 + 0.201427i −0.717713 0.696339i \(-0.754811\pi\)
0.440472 + 0.897766i \(0.354811\pi\)
\(30\) 0 0
\(31\) 2.69808 + 1.96027i 0.484590 + 0.352075i 0.803100 0.595844i \(-0.203182\pi\)
−0.318510 + 0.947920i \(0.603182\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 5.15001 + 3.98886i 0.896502 + 0.694372i
\(34\) −0.391828 0.127313i −0.0671980 0.0218340i
\(35\) 0 0
\(36\) −2.90468 + 0.750223i −0.484113 + 0.125037i
\(37\) −4.70465 + 2.39714i −0.773440 + 0.394087i −0.795720 0.605664i \(-0.792907\pi\)
0.0222802 + 0.999752i \(0.492907\pi\)
\(38\) −4.45534 + 2.27011i −0.722751 + 0.368260i
\(39\) 3.27044 5.95899i 0.523689 0.954203i
\(40\) 0 0
\(41\) 3.24600 + 1.05469i 0.506941 + 0.164715i 0.551310 0.834300i \(-0.314128\pi\)
−0.0443698 + 0.999015i \(0.514128\pi\)
\(42\) 4.70360 6.07280i 0.725781 0.937053i
\(43\) −3.71639 + 3.71639i −0.566745 + 0.566745i −0.931215 0.364470i \(-0.881250\pi\)
0.364470 + 0.931215i \(0.381250\pi\)
\(44\) −3.04265 2.21062i −0.458697 0.333263i
\(45\) 0 0
\(46\) 4.06882 2.95617i 0.599914 0.435863i
\(47\) 0.808572 5.10512i 0.117942 0.744659i −0.855851 0.517223i \(-0.826966\pi\)
0.973793 0.227436i \(-0.0730342\pi\)
\(48\) 1.66293 0.484416i 0.240023 0.0699194i
\(49\) 12.6676i 1.80965i
\(50\) 0 0
\(51\) −0.488859 0.519837i −0.0684540 0.0727917i
\(52\) −1.78169 + 3.49677i −0.247076 + 0.484914i
\(53\) 8.20487 + 1.29952i 1.12703 + 0.178503i 0.691988 0.721909i \(-0.256735\pi\)
0.435037 + 0.900412i \(0.356735\pi\)
\(54\) −5.03567 1.28143i −0.685267 0.174381i
\(55\) 0 0
\(56\) −2.60672 + 3.58784i −0.348337 + 0.479445i
\(57\) −8.65677 0.265855i −1.14662 0.0352134i
\(58\) 1.82271 0.288689i 0.239334 0.0379068i
\(59\) 1.73564 5.34175i 0.225961 0.695437i −0.772231 0.635341i \(-0.780859\pi\)
0.998193 0.0600956i \(-0.0191406\pi\)
\(60\) 0 0
\(61\) 4.43829 + 13.6596i 0.568264 + 1.74894i 0.658047 + 0.752977i \(0.271383\pi\)
−0.0897825 + 0.995961i \(0.528617\pi\)
\(62\) −1.51406 2.97152i −0.192286 0.377383i
\(63\) 12.2026 5.30128i 1.53739 0.667899i
\(64\) −0.951057 + 0.309017i −0.118882 + 0.0386271i
\(65\) 0 0
\(66\) −2.77779 5.89216i −0.341922 0.725275i
\(67\) 0.968887 + 6.11731i 0.118368 + 0.747349i 0.973458 + 0.228868i \(0.0735023\pi\)
−0.855089 + 0.518481i \(0.826498\pi\)
\(68\) 0.291323 + 0.291323i 0.0353281 + 0.0353281i
\(69\) 8.64159 1.09796i 1.04033 0.132179i
\(70\) 0 0
\(71\) −0.992045 1.36543i −0.117734 0.162047i 0.746082 0.665854i \(-0.231932\pi\)
−0.863817 + 0.503806i \(0.831932\pi\)
\(72\) 2.92868 + 0.650243i 0.345149 + 0.0766319i
\(73\) −3.19175 1.62628i −0.373567 0.190342i 0.257120 0.966380i \(-0.417227\pi\)
−0.630686 + 0.776038i \(0.717227\pi\)
\(74\) 5.28015 0.613805
\(75\) 0 0
\(76\) 5.00034 0.573579
\(77\) 14.8611 + 7.57211i 1.69358 + 0.862922i
\(78\) −5.61931 + 3.82475i −0.636262 + 0.433068i
\(79\) 6.24842 + 8.60021i 0.703002 + 0.967599i 0.999919 + 0.0126959i \(0.00404134\pi\)
−0.296918 + 0.954903i \(0.595959\pi\)
\(80\) 0 0
\(81\) −6.57831 6.14214i −0.730923 0.682460i
\(82\) −2.41339 2.41339i −0.266514 0.266514i
\(83\) 1.10932 + 7.00394i 0.121763 + 0.768782i 0.970701 + 0.240290i \(0.0772425\pi\)
−0.848938 + 0.528493i \(0.822757\pi\)
\(84\) −6.94793 + 3.27552i −0.758081 + 0.357388i
\(85\) 0 0
\(86\) 4.99854 1.62412i 0.539006 0.175134i
\(87\) 3.00819 + 1.08059i 0.322512 + 0.115851i
\(88\) 1.70742 + 3.35101i 0.182012 + 0.357219i
\(89\) −0.324819 0.999689i −0.0344307 0.105967i 0.932364 0.361521i \(-0.117742\pi\)
−0.966795 + 0.255554i \(0.917742\pi\)
\(90\) 0 0
\(91\) 5.37828 16.5526i 0.563797 1.73519i
\(92\) −4.96742 + 0.786761i −0.517889 + 0.0820255i
\(93\) 0.177314 5.77369i 0.0183866 0.598704i
\(94\) −3.03812 + 4.18162i −0.313358 + 0.431301i
\(95\) 0 0
\(96\) −1.70160 0.323338i −0.173669 0.0330005i
\(97\) 7.61627 + 1.20630i 0.773315 + 0.122481i 0.530607 0.847618i \(-0.321964\pi\)
0.242709 + 0.970099i \(0.421964\pi\)
\(98\) 5.75096 11.2869i 0.580935 1.14015i
\(99\) 0.692350 11.2615i 0.0695838 1.13182i
\(100\) 0 0
\(101\) 11.0847i 1.10297i −0.834184 0.551487i \(-0.814061\pi\)
0.834184 0.551487i \(-0.185939\pi\)
\(102\) 0.199576 + 0.685116i 0.0197609 + 0.0678366i
\(103\) −0.383628 + 2.42213i −0.0378000 + 0.238660i −0.999353 0.0359588i \(-0.988552\pi\)
0.961553 + 0.274618i \(0.0885515\pi\)
\(104\) 3.17500 2.30677i 0.311334 0.226197i
\(105\) 0 0
\(106\) −6.72062 4.88282i −0.652764 0.474261i
\(107\) −4.30681 + 4.30681i −0.416355 + 0.416355i −0.883945 0.467590i \(-0.845122\pi\)
0.467590 + 0.883945i \(0.345122\pi\)
\(108\) 3.90505 + 3.42791i 0.375764 + 0.329851i
\(109\) −4.46242 1.44993i −0.427422 0.138878i 0.0874029 0.996173i \(-0.472143\pi\)
−0.514825 + 0.857295i \(0.672143\pi\)
\(110\) 0 0
\(111\) 8.01741 + 4.40015i 0.760979 + 0.417643i
\(112\) 3.95145 2.01336i 0.373377 0.190245i
\(113\) −15.2342 + 7.76223i −1.43312 + 0.730209i −0.986384 0.164459i \(-0.947412\pi\)
−0.446732 + 0.894668i \(0.647412\pi\)
\(114\) 7.59254 + 4.16697i 0.711107 + 0.390272i
\(115\) 0 0
\(116\) −1.75511 0.570270i −0.162958 0.0529483i
\(117\) −11.7197 + 1.12475i −1.08349 + 0.103983i
\(118\) −3.97157 + 3.97157i −0.365613 + 0.365613i
\(119\) −1.47816 1.07395i −0.135503 0.0984487i
\(120\) 0 0
\(121\) 2.54399 1.84832i 0.231272 0.168029i
\(122\) 2.24681 14.1858i 0.203416 1.28432i
\(123\) −1.65334 5.67567i −0.149076 0.511758i
\(124\) 3.33501i 0.299493i
\(125\) 0 0
\(126\) −13.2794 0.816407i −1.18302 0.0727313i
\(127\) −8.90421 + 17.4755i −0.790121 + 1.55070i 0.0439442 + 0.999034i \(0.486008\pi\)
−0.834065 + 0.551666i \(0.813992\pi\)
\(128\) 0.987688 + 0.156434i 0.0873001 + 0.0138270i
\(129\) 8.94324 + 1.69939i 0.787409 + 0.149623i
\(130\) 0 0
\(131\) −12.0644 + 16.6052i −1.05407 + 1.45080i −0.168841 + 0.985643i \(0.554002\pi\)
−0.885228 + 0.465158i \(0.845998\pi\)
\(132\) −0.199959 + 6.51104i −0.0174042 + 0.566713i
\(133\) −21.9026 + 3.46903i −1.89919 + 0.300803i
\(134\) 1.91392 5.89043i 0.165337 0.508856i
\(135\) 0 0
\(136\) −0.127313 0.391828i −0.0109170 0.0335990i
\(137\) −3.28166 6.44062i −0.280371 0.550259i 0.707279 0.706935i \(-0.249922\pi\)
−0.987650 + 0.156675i \(0.949922\pi\)
\(138\) −8.19818 2.94491i −0.697875 0.250687i
\(139\) −9.21867 + 2.99533i −0.781918 + 0.254060i −0.672659 0.739953i \(-0.734848\pi\)
−0.109259 + 0.994013i \(0.534848\pi\)
\(140\) 0 0
\(141\) −8.09779 + 3.81760i −0.681957 + 0.321500i
\(142\) 0.264025 + 1.66699i 0.0221565 + 0.139891i
\(143\) −10.4367 10.4367i −0.872765 0.872765i
\(144\) −2.31427 1.90897i −0.192856 0.159080i
\(145\) 0 0
\(146\) 2.10556 + 2.89805i 0.174257 + 0.239845i
\(147\) 18.1381 12.3456i 1.49600 1.01825i
\(148\) −4.70465 2.39714i −0.386720 0.197044i
\(149\) −4.14920 −0.339915 −0.169958 0.985451i \(-0.554363\pi\)
−0.169958 + 0.985451i \(0.554363\pi\)
\(150\) 0 0
\(151\) −9.50070 −0.773156 −0.386578 0.922257i \(-0.626343\pi\)
−0.386578 + 0.922257i \(0.626343\pi\)
\(152\) −4.45534 2.27011i −0.361376 0.184130i
\(153\) −0.267895 + 1.20660i −0.0216581 + 0.0975475i
\(154\) −9.80367 13.4936i −0.790002 1.08734i
\(155\) 0 0
\(156\) 6.74324 0.856768i 0.539892 0.0685963i
\(157\) −2.98265 2.98265i −0.238041 0.238041i 0.577997 0.816039i \(-0.303834\pi\)
−0.816039 + 0.577997i \(0.803834\pi\)
\(158\) −1.66297 10.4996i −0.132299 0.835300i
\(159\) −6.13559 13.0146i −0.486584 1.03213i
\(160\) 0 0
\(161\) 21.2125 6.89237i 1.67178 0.543195i
\(162\) 3.07284 + 8.45917i 0.241425 + 0.664616i
\(163\) −4.73142 9.28593i −0.370593 0.727330i 0.628116 0.778119i \(-0.283826\pi\)
−0.998709 + 0.0507896i \(0.983826\pi\)
\(164\) 1.05469 + 3.24600i 0.0823575 + 0.253470i
\(165\) 0 0
\(166\) 2.19132 6.74418i 0.170079 0.523450i
\(167\) −13.8268 + 2.18995i −1.06995 + 0.169464i −0.666476 0.745527i \(-0.732198\pi\)
−0.403476 + 0.914990i \(0.632198\pi\)
\(168\) 7.67770 + 0.235788i 0.592348 + 0.0181914i
\(169\) −1.41174 + 1.94309i −0.108595 + 0.149469i
\(170\) 0 0
\(171\) 8.05606 + 12.6543i 0.616062 + 0.967697i
\(172\) −5.19107 0.822184i −0.395815 0.0626910i
\(173\) 3.18237 6.24576i 0.241951 0.474856i −0.737815 0.675003i \(-0.764142\pi\)
0.979766 + 0.200147i \(0.0641421\pi\)
\(174\) −2.18974 2.32850i −0.166004 0.176523i
\(175\) 0 0
\(176\) 3.76092i 0.283490i
\(177\) −9.34011 + 2.72079i −0.702045 + 0.204507i
\(178\) −0.164434 + 1.03819i −0.0123248 + 0.0778159i
\(179\) −2.28996 + 1.66375i −0.171159 + 0.124355i −0.670067 0.742301i \(-0.733735\pi\)
0.498908 + 0.866655i \(0.333735\pi\)
\(180\) 0 0
\(181\) −0.283169 0.205734i −0.0210478 0.0152921i 0.577212 0.816595i \(-0.304141\pi\)
−0.598259 + 0.801302i \(0.704141\pi\)
\(182\) −12.3068 + 12.3068i −0.912243 + 0.912243i
\(183\) 15.2331 19.6674i 1.12606 1.45386i
\(184\) 4.78318 + 1.55415i 0.352621 + 0.114573i
\(185\) 0 0
\(186\) −2.77919 + 5.06390i −0.203780 + 0.371303i
\(187\) −1.38059 + 0.703446i −0.100959 + 0.0514411i
\(188\) 4.60540 2.34657i 0.335883 0.171141i
\(189\) −19.4831 12.3058i −1.41719 0.895117i
\(190\) 0 0
\(191\) −1.07980 0.350849i −0.0781318 0.0253866i 0.269690 0.962947i \(-0.413079\pi\)
−0.347822 + 0.937561i \(0.613079\pi\)
\(192\) 1.36935 + 1.06061i 0.0988241 + 0.0765428i
\(193\) −4.16176 + 4.16176i −0.299570 + 0.299570i −0.840845 0.541275i \(-0.817942\pi\)
0.541275 + 0.840845i \(0.317942\pi\)
\(194\) −6.23850 4.53254i −0.447898 0.325417i
\(195\) 0 0
\(196\) −10.2483 + 7.44581i −0.732020 + 0.531844i
\(197\) −3.00593 + 18.9787i −0.214164 + 1.35218i 0.612941 + 0.790129i \(0.289986\pi\)
−0.827105 + 0.562048i \(0.810014\pi\)
\(198\) −5.72951 + 9.71976i −0.407178 + 0.690753i
\(199\) 12.7124i 0.901157i −0.892737 0.450579i \(-0.851218\pi\)
0.892737 0.450579i \(-0.148782\pi\)
\(200\) 0 0
\(201\) 7.81481 7.34912i 0.551214 0.518367i
\(202\) −5.03237 + 9.87658i −0.354076 + 0.694914i
\(203\) 8.08340 + 1.28028i 0.567343 + 0.0898583i
\(204\) 0.133213 0.701048i 0.00932676 0.0490832i
\(205\) 0 0
\(206\) 1.44144 1.98397i 0.100430 0.138230i
\(207\) −9.99405 11.3034i −0.694634 0.785641i
\(208\) −3.87619 + 0.613929i −0.268766 + 0.0425683i
\(209\) −5.81135 + 17.8855i −0.401979 + 1.23716i
\(210\) 0 0
\(211\) −5.38805 16.5827i −0.370929 1.14160i −0.946184 0.323628i \(-0.895097\pi\)
0.575255 0.817974i \(-0.304903\pi\)
\(212\) 3.77136 + 7.40172i 0.259018 + 0.508352i
\(213\) −0.988266 + 2.75118i −0.0677149 + 0.188508i
\(214\) 5.79265 1.88215i 0.395977 0.128661i
\(215\) 0 0
\(216\) −1.92319 4.82715i −0.130856 0.328446i
\(217\) −2.31369 14.6081i −0.157064 0.991661i
\(218\) 3.31779 + 3.31779i 0.224709 + 0.224709i
\(219\) 0.782035 + 6.15505i 0.0528450 + 0.415920i
\(220\) 0 0
\(221\) 0.950373 + 1.30808i 0.0639290 + 0.0879907i
\(222\) −5.14594 7.56039i −0.345373 0.507420i
\(223\) 20.1688 + 10.2765i 1.35060 + 0.688167i 0.971467 0.237174i \(-0.0762211\pi\)
0.379136 + 0.925341i \(0.376221\pi\)
\(224\) −4.43481 −0.296313
\(225\) 0 0
\(226\) 17.0978 1.13733
\(227\) 17.2036 + 8.76566i 1.14184 + 0.581797i 0.919468 0.393164i \(-0.128620\pi\)
0.222373 + 0.974962i \(0.428620\pi\)
\(228\) −4.87324 7.15974i −0.322738 0.474165i
\(229\) −9.58051 13.1864i −0.633098 0.871384i 0.365126 0.930958i \(-0.381026\pi\)
−0.998224 + 0.0595738i \(0.981026\pi\)
\(230\) 0 0
\(231\) −3.64122 28.6585i −0.239575 1.88559i
\(232\) 1.30492 + 1.30492i 0.0856721 + 0.0856721i
\(233\) 0.0952038 + 0.601093i 0.00623701 + 0.0393789i 0.990611 0.136714i \(-0.0436541\pi\)
−0.984374 + 0.176093i \(0.943654\pi\)
\(234\) 10.9529 + 4.31847i 0.716016 + 0.282307i
\(235\) 0 0
\(236\) 5.34175 1.73564i 0.347718 0.112981i
\(237\) 6.22461 17.3284i 0.404332 1.12560i
\(238\) 0.829491 + 1.62797i 0.0537679 + 0.105525i
\(239\) −2.47857 7.62825i −0.160325 0.493430i 0.838336 0.545154i \(-0.183529\pi\)
−0.998661 + 0.0517231i \(0.983529\pi\)
\(240\) 0 0
\(241\) −2.23962 + 6.89284i −0.144267 + 0.444007i −0.996916 0.0784767i \(-0.974994\pi\)
0.852649 + 0.522484i \(0.174994\pi\)
\(242\) −3.10583 + 0.491916i −0.199650 + 0.0316215i
\(243\) −2.38352 + 15.4052i −0.152903 + 0.988241i
\(244\) −8.44212 + 11.6196i −0.540452 + 0.743868i
\(245\) 0 0
\(246\) −1.10357 + 5.80766i −0.0703609 + 0.370283i
\(247\) 19.3823 + 3.06986i 1.23327 + 0.195330i
\(248\) 1.51406 2.97152i 0.0961432 0.188692i
\(249\) 8.94747 8.41428i 0.567023 0.533233i
\(250\) 0 0
\(251\) 14.5520i 0.918511i −0.888304 0.459256i \(-0.848116\pi\)
0.888304 0.459256i \(-0.151884\pi\)
\(252\) 11.4614 + 6.75613i 0.721998 + 0.425596i
\(253\) 2.95895 18.6821i 0.186028 1.17453i
\(254\) 15.8674 11.5284i 0.995611 0.723353i
\(255\) 0 0
\(256\) −0.809017 0.587785i −0.0505636 0.0367366i
\(257\) −1.03830 + 1.03830i −0.0647675 + 0.0647675i −0.738749 0.673981i \(-0.764583\pi\)
0.673981 + 0.738749i \(0.264583\pi\)
\(258\) −7.19698 5.57431i −0.448064 0.347042i
\(259\) 22.2704 + 7.23610i 1.38382 + 0.449629i
\(260\) 0 0
\(261\) −1.38449 5.36039i −0.0856976 0.331800i
\(262\) 18.2880 9.31821i 1.12984 0.575681i
\(263\) 19.8871 10.1330i 1.22629 0.624825i 0.283743 0.958901i \(-0.408424\pi\)
0.942546 + 0.334075i \(0.108424\pi\)
\(264\) 3.13412 5.71060i 0.192891 0.351463i
\(265\) 0 0
\(266\) 21.0902 + 6.85264i 1.29313 + 0.420162i
\(267\) −1.11484 + 1.43937i −0.0682272 + 0.0880880i
\(268\) −4.37951 + 4.37951i −0.267521 + 0.267521i
\(269\) 20.2239 + 14.6936i 1.23308 + 0.895882i 0.997117 0.0758813i \(-0.0241770\pi\)
0.235959 + 0.971763i \(0.424177\pi\)
\(270\) 0 0
\(271\) −13.1402 + 9.54690i −0.798209 + 0.579933i −0.910388 0.413755i \(-0.864217\pi\)
0.112179 + 0.993688i \(0.464217\pi\)
\(272\) −0.0644499 + 0.406920i −0.00390785 + 0.0246732i
\(273\) −28.9425 + 8.43100i −1.75168 + 0.510268i
\(274\) 7.22848i 0.436688i
\(275\) 0 0
\(276\) 5.96767 + 6.34583i 0.359212 + 0.381974i
\(277\) −3.12626 + 6.13564i −0.187839 + 0.368655i −0.965651 0.259842i \(-0.916330\pi\)
0.777812 + 0.628497i \(0.216330\pi\)
\(278\) 9.57375 + 1.51633i 0.574195 + 0.0909436i
\(279\) −8.43986 + 5.37304i −0.505281 + 0.321676i
\(280\) 0 0
\(281\) −14.3948 + 19.8128i −0.858723 + 1.18193i 0.123150 + 0.992388i \(0.460700\pi\)
−0.981873 + 0.189542i \(0.939300\pi\)
\(282\) 8.94834 + 0.274810i 0.532866 + 0.0163647i
\(283\) 7.23244 1.14551i 0.429924 0.0680933i 0.0622774 0.998059i \(-0.480164\pi\)
0.367646 + 0.929966i \(0.380164\pi\)
\(284\) 0.521549 1.60516i 0.0309482 0.0952489i
\(285\) 0 0
\(286\) 4.56103 + 14.0374i 0.269699 + 0.830049i
\(287\) −6.87171 13.4865i −0.405624 0.796083i
\(288\) 1.19538 + 2.75156i 0.0704384 + 0.162137i
\(289\) −16.0065 + 5.20084i −0.941561 + 0.305932i
\(290\) 0 0
\(291\) −5.69543 12.0810i −0.333872 0.708200i
\(292\) −0.560378 3.53809i −0.0327936 0.207051i
\(293\) −1.14628 1.14628i −0.0669662 0.0669662i 0.672830 0.739797i \(-0.265078\pi\)
−0.739797 + 0.672830i \(0.765078\pi\)
\(294\) −21.7659 + 2.76548i −1.26941 + 0.161286i
\(295\) 0 0
\(296\) 3.10360 + 4.27173i 0.180393 + 0.248290i
\(297\) −16.7995 + 9.98391i −0.974808 + 0.579325i
\(298\) 3.69696 + 1.88370i 0.214159 + 0.109120i
\(299\) −19.7377 −1.14146
\(300\) 0 0
\(301\) 23.3084 1.34347
\(302\) 8.46519 + 4.31323i 0.487117 + 0.248198i
\(303\) −15.8717 + 10.8030i −0.911804 + 0.620615i
\(304\) 2.93913 + 4.04536i 0.168571 + 0.232018i
\(305\) 0 0
\(306\) 0.786480 0.953463i 0.0449600 0.0545058i
\(307\) 8.29257 + 8.29257i 0.473282 + 0.473282i 0.902975 0.429693i \(-0.141378\pi\)
−0.429693 + 0.902975i \(0.641378\pi\)
\(308\) 2.60917 + 16.4737i 0.148671 + 0.938673i
\(309\) 3.84200 1.81126i 0.218564 0.103039i
\(310\) 0 0
\(311\) −31.4637 + 10.2232i −1.78414 + 0.579703i −0.999205 0.0398725i \(-0.987305\pi\)
−0.784937 + 0.619575i \(0.787305\pi\)
\(312\) −6.39724 2.29798i −0.362172 0.130098i
\(313\) 1.98845 + 3.90255i 0.112394 + 0.220585i 0.940351 0.340206i \(-0.110497\pi\)
−0.827957 + 0.560791i \(0.810497\pi\)
\(314\) 1.30346 + 4.01165i 0.0735587 + 0.226391i
\(315\) 0 0
\(316\) −3.28499 + 10.1102i −0.184795 + 0.568740i
\(317\) 27.6572 4.38047i 1.55338 0.246032i 0.680053 0.733163i \(-0.261957\pi\)
0.873329 + 0.487131i \(0.161957\pi\)
\(318\) −0.441669 + 14.3816i −0.0247676 + 0.806481i
\(319\) 4.07954 5.61501i 0.228411 0.314380i
\(320\) 0 0
\(321\) 10.3640 + 1.96937i 0.578464 + 0.109919i
\(322\) −22.0296 3.48914i −1.22766 0.194442i
\(323\) 0.935268 1.83557i 0.0520397 0.102134i
\(324\) 1.10246 8.93222i 0.0612479 0.496235i
\(325\) 0 0
\(326\) 10.4218i 0.577212i
\(327\) 2.27291 + 7.80259i 0.125692 + 0.431484i
\(328\) 0.533919 3.37103i 0.0294807 0.186134i
\(329\) −18.5447 + 13.4735i −1.02240 + 0.742818i
\(330\) 0 0
\(331\) 7.75360 + 5.63332i 0.426176 + 0.309635i 0.780118 0.625632i \(-0.215159\pi\)
−0.353942 + 0.935267i \(0.615159\pi\)
\(332\) −5.01427 + 5.01427i −0.275194 + 0.275194i
\(333\) −1.51327 15.7680i −0.0829264 0.864082i
\(334\) 13.3140 + 4.32598i 0.728510 + 0.236707i
\(335\) 0 0
\(336\) −6.73384 3.69569i −0.367361 0.201617i
\(337\) −13.9578 + 7.11185i −0.760329 + 0.387407i −0.790757 0.612130i \(-0.790313\pi\)
0.0304279 + 0.999537i \(0.490313\pi\)
\(338\) 2.14002 1.09039i 0.116401 0.0593095i
\(339\) 25.9613 + 14.2482i 1.41003 + 0.773856i
\(340\) 0 0
\(341\) −11.9289 3.87592i −0.645983 0.209893i
\(342\) −1.43307 14.9324i −0.0774917 0.807453i
\(343\) 17.7729 17.7729i 0.959645 0.959645i
\(344\) 4.25201 + 3.08927i 0.229253 + 0.166562i
\(345\) 0 0
\(346\) −5.67103 + 4.12024i −0.304876 + 0.221506i
\(347\) 5.77593 36.4678i 0.310068 1.95769i 0.0231773 0.999731i \(-0.492622\pi\)
0.286891 0.957963i \(-0.407378\pi\)
\(348\) 0.893957 + 3.06883i 0.0479211 + 0.164507i
\(349\) 15.0145i 0.803705i −0.915704 0.401853i \(-0.868366\pi\)
0.915704 0.401853i \(-0.131634\pi\)
\(350\) 0 0
\(351\) 13.0322 + 15.6847i 0.695610 + 0.837186i
\(352\) −1.70742 + 3.35101i −0.0910060 + 0.178609i
\(353\) −29.7348 4.70953i −1.58263 0.250663i −0.697698 0.716392i \(-0.745792\pi\)
−0.884927 + 0.465729i \(0.845792\pi\)
\(354\) 9.55731 + 1.81607i 0.507965 + 0.0965233i
\(355\) 0 0
\(356\) 0.617842 0.850386i 0.0327456 0.0450704i
\(357\) −0.0971428 + 3.16316i −0.00514134 + 0.167412i
\(358\) 2.79569 0.442795i 0.147757 0.0234024i
\(359\) 1.07807 3.31797i 0.0568986 0.175116i −0.918568 0.395263i \(-0.870654\pi\)
0.975467 + 0.220147i \(0.0706536\pi\)
\(360\) 0 0
\(361\) −1.85517 5.70961i −0.0976403 0.300506i
\(362\) 0.158904 + 0.311866i 0.00835180 + 0.0163913i
\(363\) −5.12584 1.84128i −0.269037 0.0966420i
\(364\) 16.5526 5.37828i 0.867594 0.281898i
\(365\) 0 0
\(366\) −22.5016 + 10.6081i −1.17618 + 0.554494i
\(367\) −2.44988 15.4679i −0.127882 0.807418i −0.965355 0.260939i \(-0.915968\pi\)
0.837473 0.546479i \(-0.184032\pi\)
\(368\) −3.55628 3.55628i −0.185384 0.185384i
\(369\) −6.51539 + 7.89873i −0.339178 + 0.411191i
\(370\) 0 0
\(371\) −21.6544 29.8047i −1.12424 1.54738i
\(372\) 4.77524 3.25024i 0.247585 0.168517i
\(373\) 5.68352 + 2.89590i 0.294282 + 0.149944i 0.594898 0.803801i \(-0.297192\pi\)
−0.300616 + 0.953745i \(0.597192\pi\)
\(374\) 1.54947 0.0801213
\(375\) 0 0
\(376\) −5.16876 −0.266558
\(377\) −6.45305 3.28799i −0.332349 0.169340i
\(378\) 11.7728 + 19.8097i 0.605530 + 1.01890i
\(379\) 15.8374 + 21.7983i 0.813510 + 1.11970i 0.990772 + 0.135537i \(0.0432760\pi\)
−0.177262 + 0.984164i \(0.556724\pi\)
\(380\) 0 0
\(381\) 33.7002 4.28180i 1.72651 0.219363i
\(382\) 0.802829 + 0.802829i 0.0410763 + 0.0410763i
\(383\) 4.68475 + 29.5784i 0.239380 + 1.51138i 0.755660 + 0.654964i \(0.227316\pi\)
−0.516280 + 0.856420i \(0.672684\pi\)
\(384\) −0.738592 1.56668i −0.0376911 0.0799492i
\(385\) 0 0
\(386\) 5.59756 1.81876i 0.284908 0.0925723i
\(387\) −6.28264 14.4616i −0.319365 0.735123i
\(388\) 3.50082 + 6.87074i 0.177727 + 0.348809i
\(389\) 3.57268 + 10.9956i 0.181142 + 0.557497i 0.999861 0.0166975i \(-0.00531522\pi\)
−0.818719 + 0.574195i \(0.805315\pi\)
\(390\) 0 0
\(391\) −0.640299 + 1.97064i −0.0323813 + 0.0996594i
\(392\) 12.5116 1.98165i 0.631932 0.100088i
\(393\) 35.5338 + 1.09127i 1.79244 + 0.0550472i
\(394\) 11.2945 15.5455i 0.569007 0.783170i
\(395\) 0 0
\(396\) 9.51771 6.05923i 0.478283 0.304488i
\(397\) 13.2341 + 2.09608i 0.664203 + 0.105199i 0.479427 0.877581i \(-0.340844\pi\)
0.184775 + 0.982781i \(0.440844\pi\)
\(398\) −5.77130 + 11.3268i −0.289289 + 0.567762i
\(399\) 26.3130 + 27.9803i 1.31730 + 1.40077i
\(400\) 0 0
\(401\) 22.2904i 1.11313i 0.830804 + 0.556565i \(0.187881\pi\)
−0.830804 + 0.556565i \(0.812119\pi\)
\(402\) −10.2995 + 3.00026i −0.513691 + 0.149639i
\(403\) −2.04746 + 12.9272i −0.101991 + 0.643948i
\(404\) 8.96775 6.51545i 0.446162 0.324156i
\(405\) 0 0
\(406\) −6.62112 4.81053i −0.328601 0.238742i
\(407\) 14.0419 14.0419i 0.696032 0.696032i
\(408\) −0.436963 + 0.564161i −0.0216329 + 0.0279301i
\(409\) −13.3939 4.35194i −0.662285 0.215190i −0.0414620 0.999140i \(-0.513202\pi\)
−0.620823 + 0.783951i \(0.713202\pi\)
\(410\) 0 0
\(411\) −6.02376 + 10.9757i −0.297130 + 0.541394i
\(412\) −2.18504 + 1.11333i −0.107649 + 0.0548499i
\(413\) −22.1939 + 11.3084i −1.09209 + 0.556448i
\(414\) 3.77313 + 14.6086i 0.185439 + 0.717974i
\(415\) 0 0
\(416\) 3.73243 + 1.21274i 0.182998 + 0.0594595i
\(417\) 13.2732 + 10.2806i 0.649992 + 0.503441i
\(418\) 13.2978 13.2978i 0.650416 0.650416i
\(419\) −4.58918 3.33423i −0.224196 0.162888i 0.470017 0.882657i \(-0.344248\pi\)
−0.694213 + 0.719769i \(0.744248\pi\)
\(420\) 0 0
\(421\) 5.16685 3.75393i 0.251817 0.182956i −0.454715 0.890637i \(-0.650259\pi\)
0.706532 + 0.707682i \(0.250259\pi\)
\(422\) −2.72761 + 17.2214i −0.132778 + 0.838327i
\(423\) 13.3582 + 7.87425i 0.649497 + 0.382859i
\(424\) 8.30714i 0.403431i
\(425\) 0 0
\(426\) 2.12956 2.00266i 0.103178 0.0970292i
\(427\) 28.9171 56.7531i 1.39940 2.74647i
\(428\) −6.01577 0.952804i −0.290783 0.0460555i
\(429\) −4.77240 + 25.1153i −0.230413 + 1.21258i
\(430\) 0 0
\(431\) −11.7415 + 16.1608i −0.565568 + 0.778437i −0.992021 0.126072i \(-0.959763\pi\)
0.426453 + 0.904510i \(0.359763\pi\)
\(432\) −0.477906 + 5.17413i −0.0229932 + 0.248940i
\(433\) 22.9138 3.62919i 1.10117 0.174408i 0.420710 0.907195i \(-0.361781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(434\) −4.57041 + 14.0663i −0.219387 + 0.675203i
\(435\) 0 0
\(436\) −1.44993 4.46242i −0.0694390 0.213711i
\(437\) 11.4171 + 22.4074i 0.546156 + 1.07189i
\(438\) 2.09754 5.83923i 0.100224 0.279009i
\(439\) −10.7777 + 3.50189i −0.514393 + 0.167136i −0.554699 0.832051i \(-0.687167\pi\)
0.0403065 + 0.999187i \(0.487167\pi\)
\(440\) 0 0
\(441\) −35.3540 13.9392i −1.68352 0.663772i
\(442\) −0.252934 1.59696i −0.0120309 0.0759598i
\(443\) 5.43418 + 5.43418i 0.258186 + 0.258186i 0.824316 0.566130i \(-0.191560\pi\)
−0.566130 + 0.824316i \(0.691560\pi\)
\(444\) 1.15272 + 9.07256i 0.0547057 + 0.430565i
\(445\) 0 0
\(446\) −13.3051 18.3129i −0.630015 0.867141i
\(447\) 4.04373 + 5.94102i 0.191262 + 0.281001i
\(448\) 3.95145 + 2.01336i 0.186688 + 0.0951225i
\(449\) 26.9459 1.27165 0.635827 0.771831i \(-0.280659\pi\)
0.635827 + 0.771831i \(0.280659\pi\)
\(450\) 0 0
\(451\) −12.8362 −0.604434
\(452\) −15.2342 7.76223i −0.716558 0.365104i
\(453\) 9.25920 + 13.6036i 0.435035 + 0.639152i
\(454\) −11.3490 15.6205i −0.532634 0.733108i
\(455\) 0 0
\(456\) 1.09163 + 8.59178i 0.0511205 + 0.402347i
\(457\) −24.1951 24.1951i −1.13180 1.13180i −0.989878 0.141919i \(-0.954673\pi\)
−0.141919 0.989878i \(-0.545327\pi\)
\(458\) 2.54978 + 16.0987i 0.119143 + 0.752241i
\(459\) 1.98875 0.792339i 0.0928269 0.0369832i
\(460\) 0 0
\(461\) 35.3066 11.4718i 1.64439 0.534295i 0.666877 0.745168i \(-0.267631\pi\)
0.977513 + 0.210873i \(0.0676307\pi\)
\(462\) −9.76632 + 27.1880i −0.454370 + 1.26490i
\(463\) 3.18828 + 6.25735i 0.148172 + 0.290804i 0.953149 0.302503i \(-0.0978222\pi\)
−0.804977 + 0.593307i \(0.797822\pi\)
\(464\) −0.570270 1.75511i −0.0264741 0.0814790i
\(465\) 0 0
\(466\) 0.188063 0.578799i 0.00871187 0.0268124i
\(467\) −28.3424 + 4.48899i −1.31153 + 0.207726i −0.772744 0.634718i \(-0.781116\pi\)
−0.538785 + 0.842444i \(0.681116\pi\)
\(468\) −7.79860 8.82032i −0.360490 0.407719i
\(469\) 16.1449 22.2215i 0.745502 1.02609i
\(470\) 0 0
\(471\) −1.36387 + 7.17753i −0.0628438 + 0.330723i
\(472\) −5.54750 0.878638i −0.255344 0.0404426i
\(473\) 8.97383 17.6121i 0.412617 0.809807i
\(474\) −13.4131 + 12.6138i −0.616084 + 0.579371i
\(475\) 0 0
\(476\) 1.82711i 0.0837455i
\(477\) −12.6554 + 21.4690i −0.579449 + 0.983000i
\(478\) −1.25473 + 7.92207i −0.0573901 + 0.362347i
\(479\) −10.3928 + 7.55082i −0.474860 + 0.345006i −0.799332 0.600889i \(-0.794813\pi\)
0.324473 + 0.945895i \(0.394813\pi\)
\(480\) 0 0
\(481\) −16.7645 12.1801i −0.764394 0.555365i
\(482\) 5.12480 5.12480i 0.233428 0.233428i
\(483\) −30.5421 23.6560i −1.38972 1.07638i
\(484\) 2.99064 + 0.971718i 0.135938 + 0.0441690i
\(485\) 0 0
\(486\) 9.11753 12.6440i 0.413580 0.573543i
\(487\) 18.4423 9.39682i 0.835700 0.425810i 0.0168777 0.999858i \(-0.494627\pi\)
0.818822 + 0.574047i \(0.194627\pi\)
\(488\) 12.7972 6.52048i 0.579301 0.295168i
\(489\) −8.68490 + 15.8246i −0.392745 + 0.715611i
\(490\) 0 0
\(491\) 26.5707 + 8.63333i 1.19912 + 0.389617i 0.839436 0.543459i \(-0.182886\pi\)
0.359681 + 0.933075i \(0.382886\pi\)
\(492\) 3.61991 4.67365i 0.163198 0.210704i
\(493\) −0.537617 + 0.537617i −0.0242131 + 0.0242131i
\(494\) −15.8761 11.5346i −0.714298 0.518968i
\(495\) 0 0
\(496\) −2.69808 + 1.96027i −0.121148 + 0.0880188i
\(497\) −1.17090 + 7.39279i −0.0525221 + 0.331612i
\(498\) −11.7923 + 3.43511i −0.528424 + 0.153931i
\(499\) 0.405848i 0.0181683i −0.999959 0.00908413i \(-0.997108\pi\)
0.999959 0.00908413i \(-0.00289161\pi\)
\(500\) 0 0
\(501\) 16.6110 + 17.6636i 0.742126 + 0.789153i
\(502\) −6.60645 + 12.9659i −0.294860 + 0.578696i
\(503\) 5.98816 + 0.948431i 0.266999 + 0.0422885i 0.288498 0.957480i \(-0.406844\pi\)
−0.0214995 + 0.999769i \(0.506844\pi\)
\(504\) −7.14493 11.2231i −0.318260 0.499917i
\(505\) 0 0
\(506\) −11.1179 + 15.3025i −0.494252 + 0.680280i
\(507\) 4.15807 + 0.127697i 0.184666 + 0.00567123i
\(508\) −19.3717 + 3.06818i −0.859482 + 0.136129i
\(509\) 1.17675 3.62167i 0.0521586 0.160528i −0.921584 0.388178i \(-0.873104\pi\)
0.973743 + 0.227651i \(0.0731044\pi\)
\(510\) 0 0
\(511\) 4.90915 + 15.1088i 0.217168 + 0.668375i
\(512\) 0.453990 + 0.891007i 0.0200637 + 0.0393773i
\(513\) 10.2678 23.8677i 0.453332 1.05378i
\(514\) 1.39651 0.453755i 0.0615976 0.0200143i
\(515\) 0 0
\(516\) 3.88187 + 8.23411i 0.170890 + 0.362487i
\(517\) 3.04098 + 19.2000i 0.133742 + 0.844414i
\(518\) −16.5580 16.5580i −0.727515 0.727515i
\(519\) −12.0445 + 1.53032i −0.528693 + 0.0671735i
\(520\) 0 0
\(521\) 1.70955 + 2.35299i 0.0748966 + 0.103086i 0.844822 0.535048i \(-0.179706\pi\)
−0.769925 + 0.638134i \(0.779706\pi\)
\(522\) −1.19998 + 5.40469i −0.0525217 + 0.236557i
\(523\) 7.89460 + 4.02250i 0.345207 + 0.175892i 0.617994 0.786183i \(-0.287946\pi\)
−0.272787 + 0.962074i \(0.587946\pi\)
\(524\) −20.5251 −0.896645
\(525\) 0 0
\(526\) −22.3198 −0.973188
\(527\) 1.22424 + 0.623784i 0.0533289 + 0.0271724i
\(528\) −5.38508 + 3.66532i −0.234355 + 0.159513i
\(529\) −1.34851 1.85606i −0.0586307 0.0806982i
\(530\) 0 0
\(531\) 12.9985 + 10.7220i 0.564085 + 0.465295i
\(532\) −15.6805 15.6805i −0.679837 0.679837i
\(533\) 2.09537 + 13.2296i 0.0907606 + 0.573040i
\(534\) 1.64679 0.776360i 0.0712636 0.0335964i
\(535\) 0 0
\(536\) 5.89043 1.91392i 0.254428 0.0826686i
\(537\) 4.61399 + 1.65741i 0.199108 + 0.0715227i
\(538\) −11.3489 22.2735i −0.489287 0.960280i
\(539\) −14.7221 45.3100i −0.634127 1.95164i
\(540\) 0 0
\(541\) −11.3923 + 35.0618i −0.489792 + 1.50742i 0.335128 + 0.942173i \(0.391221\pi\)
−0.824919 + 0.565251i \(0.808779\pi\)
\(542\) 16.0422 2.54083i 0.689071 0.109138i
\(543\) −0.0186094 + 0.605959i −0.000798607 + 0.0260042i
\(544\) 0.242163 0.333309i 0.0103827 0.0142905i
\(545\) 0 0
\(546\) 29.6155 + 5.62752i 1.26743 + 0.240836i
\(547\) −26.2003 4.14971i −1.12024 0.177429i −0.431274 0.902221i \(-0.641936\pi\)
−0.688968 + 0.724792i \(0.741936\pi\)
\(548\) 3.28166 6.44062i 0.140186 0.275130i
\(549\) −43.0066 2.64402i −1.83548 0.112844i
\(550\) 0 0
\(551\) 9.22780i 0.393118i
\(552\) −2.43629 8.36344i −0.103695 0.355972i
\(553\) 7.37495 46.5636i 0.313615 1.98009i
\(554\) 5.57104 4.04760i 0.236691 0.171966i
\(555\) 0 0
\(556\) −7.84187 5.69745i −0.332569 0.241626i
\(557\) 20.9449 20.9449i 0.887465 0.887465i −0.106814 0.994279i \(-0.534065\pi\)
0.994279 + 0.106814i \(0.0340648\pi\)
\(558\) 9.95928 0.955798i 0.421610 0.0404622i
\(559\) −19.6168 6.37389i −0.829703 0.269587i
\(560\) 0 0
\(561\) 2.35273 + 1.29123i 0.0993322 + 0.0545159i
\(562\) 21.8207 11.1182i 0.920450 0.468993i
\(563\) −13.4464 + 6.85128i −0.566698 + 0.288747i −0.713772 0.700378i \(-0.753015\pi\)
0.147073 + 0.989126i \(0.453015\pi\)
\(564\) −7.84827 4.30732i −0.330472 0.181371i
\(565\) 0 0
\(566\) −6.96420 2.26281i −0.292727 0.0951128i
\(567\) 1.36778 + 39.8899i 0.0574413 + 1.67522i
\(568\) −1.19343 + 1.19343i −0.0500753 + 0.0500753i
\(569\) 7.06373 + 5.13210i 0.296127 + 0.215149i 0.725921 0.687778i \(-0.241414\pi\)
−0.429794 + 0.902927i \(0.641414\pi\)
\(570\) 0 0
\(571\) 19.6305 14.2624i 0.821513 0.596864i −0.0956328 0.995417i \(-0.530487\pi\)
0.917145 + 0.398553i \(0.130487\pi\)
\(572\) 2.30894 14.5781i 0.0965416 0.609540i
\(573\) 0.549992 + 1.88805i 0.0229762 + 0.0788743i
\(574\) 15.1362i 0.631775i
\(575\) 0 0
\(576\) 0.184091 2.99435i 0.00767044 0.124764i
\(577\) 16.6187 32.6160i 0.691845 1.35782i −0.231114 0.972927i \(-0.574237\pi\)
0.922960 0.384896i \(-0.125763\pi\)
\(578\) 16.6231 + 2.63283i 0.691428 + 0.109511i
\(579\) 10.0150 + 1.90304i 0.416209 + 0.0790877i
\(580\) 0 0
\(581\) 18.4849 25.4423i 0.766882 1.05552i
\(582\) −0.409985 + 13.3499i −0.0169944 + 0.553372i
\(583\) −30.8579 + 4.88741i −1.27800 + 0.202416i
\(584\) −1.10696 + 3.40687i −0.0458062 + 0.140977i
\(585\) 0 0
\(586\) 0.500941 + 1.54174i 0.0206937 + 0.0636887i
\(587\) 5.16169 + 10.1304i 0.213046 + 0.418126i 0.972655 0.232254i \(-0.0746099\pi\)
−0.759609 + 0.650379i \(0.774610\pi\)
\(588\) 20.6491 + 7.41745i 0.851553 + 0.305890i
\(589\) 15.8600 5.15324i 0.653501 0.212335i
\(590\) 0 0
\(591\) 30.1042 14.1922i 1.23832 0.583791i
\(592\) −0.825998 5.21515i −0.0339483 0.214341i
\(593\) −16.4362 16.4362i −0.674952 0.674952i 0.283901 0.958854i \(-0.408371\pi\)
−0.958854 + 0.283901i \(0.908371\pi\)
\(594\) 19.5011 1.26890i 0.800140 0.0520636i
\(595\) 0 0
\(596\) −2.43884 3.35677i −0.0998986 0.137499i
\(597\) −18.2022 + 12.3893i −0.744968 + 0.507058i
\(598\) 17.5864 + 8.96072i 0.719162 + 0.366431i
\(599\) 16.9386 0.692094 0.346047 0.938217i \(-0.387524\pi\)
0.346047 + 0.938217i \(0.387524\pi\)
\(600\) 0 0
\(601\) −26.0220 −1.06146 −0.530730 0.847541i \(-0.678082\pi\)
−0.530730 + 0.847541i \(0.678082\pi\)
\(602\) −20.7679 10.5818i −0.846437 0.431281i
\(603\) −18.1390 4.02732i −0.738677 0.164005i
\(604\) −5.58437 7.68623i −0.227225 0.312748i
\(605\) 0 0
\(606\) 19.0462 2.41993i 0.773700 0.0983030i
\(607\) 29.4219 + 29.4219i 1.19420 + 1.19420i 0.975877 + 0.218322i \(0.0700583\pi\)
0.218322 + 0.975877i \(0.429942\pi\)
\(608\) −0.782226 4.93878i −0.0317235 0.200294i
\(609\) −6.04475 12.8219i −0.244946 0.519571i
\(610\) 0 0
\(611\) 19.2921 6.26837i 0.780473 0.253591i
\(612\) −1.13362 + 0.492487i −0.0458239 + 0.0199076i
\(613\) 2.55565 + 5.01575i 0.103222 + 0.202584i 0.936841 0.349755i \(-0.113735\pi\)
−0.833619 + 0.552339i \(0.813735\pi\)
\(614\) −3.62398 11.1535i −0.146252 0.450118i
\(615\) 0 0
\(616\) 5.15409 15.8627i 0.207664 0.639125i
\(617\) −35.1967 + 5.57460i −1.41696 + 0.224425i −0.817478 0.575960i \(-0.804628\pi\)
−0.599486 + 0.800385i \(0.704628\pi\)
\(618\) −4.24555 0.130384i −0.170781 0.00524480i
\(619\) 20.2991 27.9393i 0.815889 1.12297i −0.174499 0.984657i \(-0.555831\pi\)
0.990388 0.138317i \(-0.0441694\pi\)
\(620\) 0 0
\(621\) −6.44476 + 25.3261i −0.258619 + 1.01630i
\(622\) 32.6756 + 5.17530i 1.31017 + 0.207511i
\(623\) −2.11632 + 4.15351i −0.0847885 + 0.166407i
\(624\) 4.65672 + 4.95180i 0.186418 + 0.198231i
\(625\) 0 0
\(626\) 4.37993i 0.175057i
\(627\) 31.2729 9.10988i 1.24892 0.363814i
\(628\) 0.659856 4.16617i 0.0263311 0.166248i
\(629\) −1.75992 + 1.27866i −0.0701727 + 0.0509835i
\(630\) 0 0
\(631\) −6.95722 5.05472i −0.276963 0.201225i 0.440629 0.897689i \(-0.354755\pi\)
−0.717591 + 0.696464i \(0.754755\pi\)
\(632\) 7.51686 7.51686i 0.299005 0.299005i
\(633\) −18.4929 + 23.8761i −0.735026 + 0.948989i
\(634\) −26.6314 8.65307i −1.05767 0.343657i
\(635\) 0 0
\(636\) 6.92265 12.6136i 0.274501 0.500162i
\(637\) −44.2955 + 22.5697i −1.75505 + 0.894244i
\(638\) −6.18406 + 3.15094i −0.244829 + 0.124747i
\(639\) 4.90243 1.26620i 0.193937 0.0500902i
\(640\) 0 0
\(641\) 12.9664 + 4.21305i 0.512144 + 0.166406i 0.553677 0.832732i \(-0.313224\pi\)
−0.0415332 + 0.999137i \(0.513224\pi\)
\(642\) −8.34036 6.45990i −0.329168 0.254952i
\(643\) 11.4059 11.4059i 0.449806 0.449806i −0.445484 0.895290i \(-0.646968\pi\)
0.895290 + 0.445484i \(0.146968\pi\)
\(644\) 18.0445 + 13.1101i 0.711051 + 0.516609i
\(645\) 0 0
\(646\) −1.66666 + 1.21090i −0.0655739 + 0.0476422i
\(647\) −4.90280 + 30.9551i −0.192749 + 1.21697i 0.681619 + 0.731707i \(0.261276\pi\)
−0.874368 + 0.485263i \(0.838724\pi\)
\(648\) −5.03744 + 7.45816i −0.197889 + 0.292984i
\(649\) 21.1238i 0.829181i
\(650\) 0 0
\(651\) −18.6617 + 17.5496i −0.731409 + 0.687823i
\(652\) 4.73142 9.28593i 0.185297 0.363665i
\(653\) 37.8061 + 5.98789i 1.47947 + 0.234324i 0.843390 0.537302i \(-0.180556\pi\)
0.636076 + 0.771626i \(0.280556\pi\)
\(654\) 1.51712 7.98404i 0.0593242 0.312201i
\(655\) 0 0
\(656\) −2.00614 + 2.76122i −0.0783266 + 0.107807i
\(657\) 8.05095 7.11835i 0.314098 0.277713i
\(658\) 22.6403 3.58587i 0.882610 0.139792i
\(659\) 6.33270 19.4901i 0.246687 0.759225i −0.748667 0.662946i \(-0.769306\pi\)
0.995354 0.0962789i \(-0.0306941\pi\)
\(660\) 0 0
\(661\) −13.4948 41.5327i −0.524887 1.61544i −0.764539 0.644577i \(-0.777033\pi\)
0.239652 0.970859i \(-0.422967\pi\)
\(662\) −4.35103 8.53939i −0.169108 0.331893i
\(663\) 0.946752 2.63562i 0.0367688 0.102359i
\(664\) 6.74418 2.19132i 0.261725 0.0850395i
\(665\) 0 0
\(666\) −5.81020 + 14.7364i −0.225141 + 0.571024i
\(667\) −1.45192 9.16704i −0.0562184 0.354949i
\(668\) −9.89891 9.89891i −0.383000 0.383000i
\(669\) −4.94171 38.8940i −0.191057 1.50373i
\(670\) 0 0
\(671\) −31.7502 43.7004i −1.22570 1.68703i
\(672\) 4.32208 + 6.34998i 0.166728 + 0.244956i
\(673\) −33.0273 16.8283i −1.27311 0.648681i −0.318890 0.947792i \(-0.603310\pi\)
−0.954219 + 0.299110i \(0.903310\pi\)
\(674\) 15.6652 0.603401
\(675\) 0 0
\(676\) −2.40180 −0.0923767
\(677\) −37.1946 18.9516i −1.42951 0.728369i −0.443686 0.896182i \(-0.646330\pi\)
−0.985819 + 0.167813i \(0.946330\pi\)
\(678\) −16.6632 24.4814i −0.639945 0.940204i
\(679\) −20.1010 27.6666i −0.771404 1.06175i
\(680\) 0 0
\(681\) −4.21517 33.1758i −0.161526 1.27130i
\(682\) 8.86905 + 8.86905i 0.339614 + 0.339614i
\(683\) −7.96066 50.2616i −0.304606 1.92321i −0.377793 0.925890i \(-0.623317\pi\)
0.0731865 0.997318i \(-0.476683\pi\)
\(684\) −5.50230 + 13.9555i −0.210386 + 0.533601i
\(685\) 0 0
\(686\) −23.9045 + 7.76703i −0.912677 + 0.296547i
\(687\) −9.54401 + 26.5691i −0.364127 + 1.01367i
\(688\) −2.38607 4.68293i −0.0909681 0.178535i
\(689\) 10.0744 + 31.0059i 0.383805 + 1.18123i
\(690\) 0 0
\(691\) −9.91187 + 30.5056i −0.377065 + 1.16049i 0.565010 + 0.825084i \(0.308872\pi\)
−0.942075 + 0.335403i \(0.891128\pi\)
\(692\) 6.92347 1.09657i 0.263191 0.0416854i
\(693\) −37.4860 + 33.1437i −1.42397 + 1.25902i
\(694\) −21.7024 + 29.8708i −0.823813 + 1.13388i
\(695\) 0 0
\(696\) 0.596698 3.14020i 0.0226178 0.119029i
\(697\) 1.38884 + 0.219971i 0.0526061 + 0.00833198i
\(698\) −6.81642 + 13.3780i −0.258005 + 0.506364i
\(699\) 0.767891 0.722131i 0.0290443 0.0273135i
\(700\) 0 0
\(701\) 32.1785i 1.21536i −0.794180 0.607682i \(-0.792100\pi\)
0.794180 0.607682i \(-0.207900\pi\)
\(702\) −4.49113 19.8917i −0.169507 0.750762i
\(703\) −4.13027 + 26.0775i −0.155776 + 0.983533i
\(704\) 3.04265 2.21062i 0.114674 0.0833157i
\(705\) 0 0
\(706\) 24.3558 + 17.6956i 0.916644 + 0.665981i
\(707\) −34.7605 + 34.7605i −1.30730 + 1.30730i
\(708\) −7.69114 5.95706i −0.289051 0.223880i
\(709\) 2.62130 + 0.851713i 0.0984451 + 0.0319867i 0.357825 0.933789i \(-0.383518\pi\)
−0.259380 + 0.965775i \(0.583518\pi\)
\(710\) 0 0
\(711\) −30.8780 + 7.97521i −1.15802 + 0.299094i
\(712\) −0.936569 + 0.477205i −0.0350994 + 0.0178840i
\(713\) −14.9448 + 7.61474i −0.559686 + 0.285174i
\(714\) 1.52260 2.77429i 0.0569818 0.103825i
\(715\) 0 0
\(716\) −2.69201 0.874686i −0.100605 0.0326886i
\(717\) −8.50694 + 10.9833i −0.317697 + 0.410178i
\(718\) −2.46690 + 2.46690i −0.0920639 + 0.0920639i
\(719\) −6.94235 5.04392i −0.258906 0.188106i 0.450759 0.892646i \(-0.351154\pi\)
−0.709665 + 0.704540i \(0.751154\pi\)
\(720\) 0 0
\(721\) 8.79854 6.39251i 0.327675 0.238070i
\(722\) −0.939145 + 5.92953i −0.0349514 + 0.220674i
\(723\) 12.0522 3.51083i 0.448226 0.130569i
\(724\) 0.350016i 0.0130082i
\(725\) 0 0
\(726\) 3.73123 + 3.96767i 0.138479 + 0.147254i
\(727\) −15.5376 + 30.4942i −0.576257 + 1.13097i 0.400435 + 0.916325i \(0.368859\pi\)
−0.976692 + 0.214644i \(0.931141\pi\)
\(728\) −17.1902 2.72266i −0.637111 0.100909i
\(729\) 24.3808 11.6007i 0.902992 0.429656i
\(730\) 0 0
\(731\) −1.27276 + 1.75180i −0.0470746 + 0.0647926i
\(732\) 24.8650 + 0.763622i 0.919038 + 0.0282243i
\(733\) 39.3201 6.22770i 1.45232 0.230025i 0.620124 0.784504i \(-0.287082\pi\)
0.832198 + 0.554478i \(0.187082\pi\)
\(734\) −4.83943 + 14.8942i −0.178627 + 0.549756i
\(735\) 0 0
\(736\) 1.55415 + 4.78318i 0.0572867 + 0.176310i
\(737\) −10.5750 20.7547i −0.389537 0.764509i
\(738\) 9.39121 4.07989i 0.345695 0.150183i
\(739\) −19.6010 + 6.36874i −0.721033 + 0.234278i −0.646471 0.762939i \(-0.723756\pi\)
−0.0745620 + 0.997216i \(0.523756\pi\)
\(740\) 0 0
\(741\) −14.4941 30.7444i −0.532452 1.12942i
\(742\) 5.76314 + 36.3871i 0.211572 + 1.33581i
\(743\) 25.7253 + 25.7253i 0.943771 + 0.943771i 0.998501 0.0547306i \(-0.0174300\pi\)
−0.0547306 + 0.998501i \(0.517430\pi\)
\(744\) −5.73035 + 0.728073i −0.210085 + 0.0266925i
\(745\) 0 0
\(746\) −3.74935 5.16053i −0.137273 0.188940i
\(747\) −20.7680 4.61103i −0.759862 0.168709i
\(748\) −1.38059 0.703446i −0.0504794 0.0257205i
\(749\) 27.0114 0.986973
\(750\) 0 0
\(751\) −13.8571 −0.505654 −0.252827 0.967511i \(-0.581360\pi\)
−0.252827 + 0.967511i \(0.581360\pi\)
\(752\) 4.60540 + 2.34657i 0.167942 + 0.0855705i
\(753\) −20.8362 + 14.1821i −0.759314 + 0.516823i
\(754\) 4.25699 + 5.85925i 0.155031 + 0.213381i
\(755\) 0 0
\(756\) −1.49626 22.9953i −0.0544186 0.836332i
\(757\) 28.7075 + 28.7075i 1.04339 + 1.04339i 0.999015 + 0.0443764i \(0.0141301\pi\)
0.0443764 + 0.999015i \(0.485870\pi\)
\(758\) −4.21499 26.6124i −0.153095 0.966606i
\(759\) −29.6336 + 13.9704i −1.07563 + 0.507094i
\(760\) 0 0
\(761\) −36.3818 + 11.8212i −1.31884 + 0.428517i −0.882096 0.471069i \(-0.843868\pi\)
−0.436744 + 0.899586i \(0.643868\pi\)
\(762\) −31.9710 11.4844i −1.15819 0.416037i
\(763\) 9.44684 + 18.5405i 0.341998 + 0.671210i
\(764\) −0.350849 1.07980i −0.0126933 0.0390659i
\(765\) 0 0
\(766\) 9.25415 28.4814i 0.334366 1.02907i
\(767\) 21.7712 3.44822i 0.786114 0.124508i
\(768\) −0.0531674 + 1.73123i −0.00191851 + 0.0624705i
\(769\) −23.2438 + 31.9924i −0.838194 + 1.15368i 0.148148 + 0.988965i \(0.452669\pi\)
−0.986342 + 0.164710i \(0.947331\pi\)
\(770\) 0 0
\(771\) 2.49860 + 0.474783i 0.0899850 + 0.0170989i
\(772\) −5.81316 0.920714i −0.209220 0.0331372i
\(773\) 16.3075 32.0052i 0.586539 1.15115i −0.386883 0.922129i \(-0.626448\pi\)
0.973422 0.229019i \(-0.0735518\pi\)
\(774\) −0.967539 + 15.7376i −0.0347775 + 0.565677i
\(775\) 0 0
\(776\) 7.71121i 0.276816i
\(777\) −11.3433 38.9400i −0.406939 1.39697i
\(778\) 1.80860 11.4191i 0.0648416 0.409394i
\(779\) 13.8070 10.0314i 0.494688 0.359412i
\(780\) 0 0
\(781\) 5.13529 + 3.73101i 0.183755 + 0.133506i
\(782\) 1.46516 1.46516i 0.0523940 0.0523940i
\(783\) −6.32598 + 7.20652i −0.226072 + 0.257540i
\(784\) −12.0476 3.91450i −0.430271 0.139803i
\(785\) 0 0
\(786\) −31.1654 17.1043i −1.11163 0.610092i
\(787\) −25.5543 + 13.0206i −0.910913 + 0.464133i −0.845652 0.533735i \(-0.820788\pi\)
−0.0652610 + 0.997868i \(0.520788\pi\)
\(788\) −17.1209 + 8.72355i −0.609908 + 0.310764i
\(789\) −33.8904 18.5999i −1.20653 0.662173i
\(790\) 0 0
\(791\) 72.1143 + 23.4314i 2.56409 + 0.833123i
\(792\) −11.2312 + 1.07786i −0.399082 + 0.0383001i
\(793\) −39.8569 + 39.8569i −1.41536 + 1.41536i
\(794\) −10.8401 7.87580i −0.384701 0.279502i
\(795\) 0 0
\(796\) 10.2845 7.47216i 0.364526 0.264844i
\(797\) −1.51547 + 9.56827i −0.0536805 + 0.338926i 0.946202 + 0.323578i \(0.104886\pi\)
−0.999882 + 0.0153481i \(0.995114\pi\)
\(798\) −10.7422 36.8765i −0.380270 1.30541i
\(799\) 2.12949i 0.0753360i
\(800\) 0 0
\(801\) 3.14746 + 0.193504i 0.111210 + 0.00683713i
\(802\) 10.1196 19.8609i 0.357337 0.701313i
\(803\) 13.3065 + 2.10754i 0.469575 + 0.0743734i
\(804\) 10.5390 + 2.00261i 0.371682 + 0.0706267i
\(805\) 0 0
\(806\) 7.69311 10.5887i 0.270978 0.372970i
\(807\) 1.32909 43.2777i 0.0467861 1.52345i
\(808\) −10.9483 + 1.73404i −0.385159 + 0.0610032i
\(809\) 17.2607 53.1231i 0.606855 1.86771i 0.123359 0.992362i \(-0.460633\pi\)
0.483496 0.875346i \(-0.339367\pi\)
\(810\) 0 0
\(811\) −6.13462 18.8804i −0.215416 0.662981i −0.999124 0.0418519i \(-0.986674\pi\)
0.783708 0.621129i \(-0.213326\pi\)
\(812\) 3.71553 + 7.29214i 0.130390 + 0.255904i
\(813\) 26.4759 + 9.51053i 0.928550 + 0.333549i
\(814\) −18.8863 + 6.13654i −0.661965 + 0.215086i
\(815\) 0 0
\(816\) 0.645460 0.304294i 0.0225956 0.0106524i
\(817\) 4.11120 + 25.9571i 0.143833 + 0.908125i
\(818\) 9.95831 + 9.95831i 0.348184 + 0.348184i
\(819\) 40.2787 + 33.2245i 1.40745 + 1.16096i
\(820\) 0 0
\(821\) 22.0314 + 30.3236i 0.768899 + 1.05830i 0.996421 + 0.0845263i \(0.0269377\pi\)
−0.227522 + 0.973773i \(0.573062\pi\)
\(822\) 10.3501 7.04474i 0.361001 0.245713i
\(823\) −35.1647 17.9173i −1.22577 0.624559i −0.283355 0.959015i \(-0.591447\pi\)
−0.942411 + 0.334456i \(0.891447\pi\)
\(824\) 2.45232 0.0854307
\(825\) 0 0
\(826\) 24.9088 0.866688
\(827\) −22.4561 11.4419i −0.780874 0.397875i 0.0176456 0.999844i \(-0.494383\pi\)
−0.798519 + 0.601969i \(0.794383\pi\)
\(828\) 3.27029 14.7293i 0.113650 0.511880i
\(829\) 22.7111 + 31.2592i 0.788791 + 1.08568i 0.994258 + 0.107013i \(0.0341287\pi\)
−0.205467 + 0.978664i \(0.565871\pi\)
\(830\) 0 0
\(831\) 11.8321 1.50334i 0.410451 0.0521502i
\(832\) −2.77505 2.77505i −0.0962075 0.0962075i
\(833\) 0.816423 + 5.15469i 0.0282874 + 0.178600i
\(834\) −7.15923 15.1860i −0.247904 0.525847i
\(835\) 0 0
\(836\) −17.8855 + 5.81135i −0.618582 + 0.200990i
\(837\) 15.9187 + 6.84815i 0.550231 + 0.236707i
\(838\) 2.57528 + 5.05427i 0.0889615 + 0.174597i
\(839\) 1.11037 + 3.41736i 0.0383342 + 0.117980i 0.968392 0.249432i \(-0.0802438\pi\)
−0.930058 + 0.367412i \(0.880244\pi\)
\(840\) 0 0
\(841\) −7.90910 + 24.3417i −0.272727 + 0.839369i
\(842\) −6.30794 + 0.999080i −0.217386 + 0.0344306i
\(843\) 42.3978 + 1.30207i 1.46026 + 0.0448455i
\(844\) 10.2487 14.1061i 0.352774 0.485552i
\(845\) 0 0
\(846\) −8.32739 13.0805i −0.286302 0.449717i
\(847\) −13.7738 2.18155i −0.473273 0.0749591i
\(848\) −3.77136 + 7.40172i −0.129509 + 0.254176i
\(849\) −8.68879 9.23937i −0.298198 0.317095i
\(850\) 0 0
\(851\) 26.5557i 0.910317i
\(852\) −2.80664 + 0.817581i −0.0961540 + 0.0280099i
\(853\) −7.10018 + 44.8288i −0.243106 + 1.53491i 0.500172 + 0.865926i \(0.333270\pi\)
−0.743278 + 0.668983i \(0.766730\pi\)
\(854\) −51.5307 + 37.4393i −1.76334 + 1.28114i
\(855\) 0 0
\(856\) 4.92752 + 3.58005i 0.168419 + 0.122364i
\(857\) 5.49063 5.49063i 0.187556 0.187556i −0.607082 0.794639i \(-0.707660\pi\)
0.794639 + 0.607082i \(0.207660\pi\)
\(858\) 15.6543 20.2113i 0.534431 0.690002i
\(859\) −10.7387 3.48922i −0.366400 0.119051i 0.120030 0.992770i \(-0.461701\pi\)
−0.486430 + 0.873720i \(0.661701\pi\)
\(860\) 0 0
\(861\) −12.6136 + 22.9829i −0.429870 + 0.783256i
\(862\) 17.7986 9.06883i 0.606222 0.308886i
\(863\) −10.3665 + 5.28199i −0.352880 + 0.179801i −0.621440 0.783462i \(-0.713452\pi\)
0.268560 + 0.963263i \(0.413452\pi\)
\(864\) 2.77482 4.39322i 0.0944014 0.149460i
\(865\) 0 0
\(866\) −22.0640 7.16903i −0.749765 0.243613i
\(867\) 23.0465 + 17.8503i 0.782699 + 0.606228i
\(868\) 10.4582 10.4582i 0.354975 0.354975i
\(869\) −32.3447 23.4998i −1.09722 0.797177i
\(870\) 0 0
\(871\) −19.6646 + 14.2871i −0.666308 + 0.484101i
\(872\) −0.734001 + 4.63430i −0.0248564 + 0.156937i
\(873\) −11.7475 + 19.9289i −0.397592 + 0.674491i
\(874\) 25.1484i 0.850658i
\(875\) 0 0
\(876\) −4.51987 + 4.25053i −0.152712 + 0.143612i
\(877\) 11.2271 22.0344i 0.379112 0.744049i −0.620068 0.784548i \(-0.712895\pi\)
0.999180 + 0.0404992i \(0.0128948\pi\)
\(878\) 11.1928 + 1.77277i 0.377740 + 0.0598282i
\(879\) −0.524156 + 2.75844i −0.0176794 + 0.0930397i
\(880\) 0 0
\(881\) −7.08613 + 9.75322i −0.238738 + 0.328594i −0.911527 0.411240i \(-0.865096\pi\)
0.672790 + 0.739834i \(0.265096\pi\)
\(882\) 25.1724 + 28.4703i 0.847598 + 0.958645i
\(883\) −7.05614 + 1.11758i −0.237458 + 0.0376097i −0.274029 0.961721i \(-0.588356\pi\)
0.0365710 + 0.999331i \(0.488356\pi\)
\(884\) −0.499640 + 1.53774i −0.0168047 + 0.0517196i
\(885\) 0 0
\(886\) −2.37482 7.30895i −0.0797837 0.245549i
\(887\) 1.61555 + 3.17069i 0.0542448 + 0.106461i 0.916537 0.399949i \(-0.130972\pi\)
−0.862293 + 0.506410i \(0.830972\pi\)
\(888\) 3.09177 8.60703i 0.103753 0.288833i
\(889\) 82.7238 26.8786i 2.77447 0.901479i
\(890\) 0 0
\(891\) 30.6680 + 14.3243i 1.02742 + 0.479881i
\(892\) 3.54105 + 22.3573i 0.118563 + 0.748578i
\(893\) −18.2756 18.2756i −0.611569 0.611569i
\(894\) −0.905819 7.12930i −0.0302951 0.238440i
\(895\) 0 0
\(896\) −2.60672 3.58784i −0.0870843 0.119861i
\(897\) 19.2360 + 28.2614i 0.642270 + 0.943620i
\(898\) −24.0090 12.2332i −0.801189 0.408226i
\(899\) −6.15455 −0.205266
\(900\) 0 0
\(901\) 3.42248 0.114019
\(902\) 11.4372 + 5.82752i 0.380816 + 0.194035i
\(903\) −22.7159 33.3741i −0.755938 1.11062i
\(904\) 10.0498 + 13.8324i 0.334252 + 0.460058i
\(905\) 0 0
\(906\) −2.07412 16.3245i −0.0689079 0.542344i
\(907\) −1.89862 1.89862i −0.0630427 0.0630427i 0.674883 0.737925i \(-0.264194\pi\)
−0.737925 + 0.674883i \(0.764194\pi\)
\(908\) 3.02044 + 19.0703i 0.100237 + 0.632871i
\(909\) 30.9365 + 12.1975i 1.02610 + 0.404565i
\(910\) 0 0
\(911\) −2.38886 + 0.776187i −0.0791464 + 0.0257162i −0.348323 0.937375i \(-0.613249\pi\)
0.269176 + 0.963091i \(0.413249\pi\)
\(912\) 2.92793 8.15092i 0.0969535 0.269904i
\(913\) −12.1078 23.7628i −0.400708 0.786435i
\(914\) 10.5736 + 32.5423i 0.349744 + 1.07640i
\(915\) 0 0
\(916\) 5.03677 15.5016i 0.166420 0.512187i
\(917\) 89.9045 14.2395i 2.96891 0.470229i
\(918\) −2.13170 0.196894i −0.0703567 0.00649846i
\(919\) 5.62589 7.74338i 0.185581 0.255430i −0.706082 0.708130i \(-0.749539\pi\)
0.891663 + 0.452700i \(0.149539\pi\)
\(920\) 0 0
\(921\) 3.79193 19.9555i 0.124948 0.657555i
\(922\) −36.6665 5.80740i −1.20755 0.191256i
\(923\) 3.00708 5.90173i 0.0989793 0.194258i
\(924\) 21.0449 19.7908i 0.692328 0.651071i
\(925\) 0 0
\(926\) 7.02279i 0.230783i
\(927\) −6.33780 3.73594i −0.208161 0.122704i
\(928\) −0.288689 + 1.82271i −0.00947670 + 0.0598335i
\(929\) 28.0139 20.3533i 0.919106 0.667770i −0.0241953 0.999707i \(-0.507702\pi\)
0.943301 + 0.331938i \(0.107702\pi\)
\(930\) 0 0
\(931\) 51.2449 + 37.2316i 1.67949 + 1.22022i
\(932\) −0.430335 + 0.430335i −0.0140961 + 0.0140961i
\(933\) 45.3019 + 35.0879i 1.48312 + 1.14873i
\(934\) 27.2912 + 8.86745i 0.892995 + 0.290152i
\(935\) 0 0
\(936\) 2.94426 + 11.3995i 0.0962362 + 0.372603i
\(937\) 13.6302 6.94494i 0.445280 0.226881i −0.216949 0.976183i \(-0.569611\pi\)
0.662229 + 0.749302i \(0.269611\pi\)
\(938\) −24.4736 + 12.4699i −0.799090 + 0.407157i
\(939\) 3.64996 6.65050i 0.119112 0.217031i
\(940\) 0 0
\(941\) 27.0255 + 8.78112i 0.881006 + 0.286256i 0.714375 0.699763i \(-0.246711\pi\)
0.166631 + 0.986019i \(0.446711\pi\)
\(942\) 4.47375 5.77604i 0.145763 0.188194i
\(943\) −12.1378 + 12.1378i −0.395260 + 0.395260i
\(944\) 4.54397 + 3.30138i 0.147893 + 0.107451i
\(945\) 0 0
\(946\) −15.9915 + 11.6185i −0.519928 + 0.377750i
\(947\) −5.88298 + 37.1437i −0.191171 + 1.20701i 0.686279 + 0.727339i \(0.259243\pi\)
−0.877450 + 0.479669i \(0.840757\pi\)
\(948\) 17.6777 5.14955i 0.574145 0.167250i
\(949\) 14.0583i 0.456353i
\(950\) 0 0
\(951\) −33.2263 35.3318i −1.07744 1.14571i
\(952\) −0.829491 + 1.62797i −0.0268840 + 0.0527627i
\(953\) 26.3120 + 4.16742i 0.852331 + 0.134996i 0.567289 0.823519i \(-0.307992\pi\)
0.285042 + 0.958515i \(0.407992\pi\)
\(954\) 21.0227 13.3836i 0.680636 0.433311i
\(955\) 0 0
\(956\) 4.71452 6.48898i 0.152478 0.209868i
\(957\) −12.0157 0.369010i −0.388412 0.0119284i
\(958\) 12.6881 2.00959i 0.409933 0.0649269i
\(959\) −9.90614 + 30.4880i −0.319886 + 0.984508i
\(960\) 0 0
\(961\) −6.14254 18.9048i −0.198146 0.609832i
\(962\) 9.40760 + 18.4635i 0.303313 + 0.595286i
\(963\) −7.28076 16.7591i −0.234619 0.540053i
\(964\) −6.89284 + 2.23962i −0.222003 + 0.0721333i
\(965\) 0 0
\(966\) 16.4737 + 34.9435i 0.530032 + 1.12429i
\(967\) −6.56982 41.4802i −0.211271 1.33391i −0.834125 0.551576i \(-0.814027\pi\)
0.622853 0.782339i \(-0.285973\pi\)
\(968\) −2.22353 2.22353i −0.0714670 0.0714670i
\(969\) −3.53975 + 0.449746i −0.113713 + 0.0144479i
\(970\) 0 0
\(971\) 8.52779 + 11.7375i 0.273670 + 0.376674i 0.923624 0.383299i \(-0.125212\pi\)
−0.649955 + 0.759973i \(0.725212\pi\)
\(972\) −13.8640 + 7.12661i −0.444689 + 0.228586i
\(973\) 38.3017 + 19.5157i 1.22790 + 0.625645i
\(974\) −20.6983 −0.663215
\(975\) 0 0
\(976\) −14.3626 −0.459736
\(977\) −1.06999 0.545186i −0.0342319 0.0174420i 0.436791 0.899563i \(-0.356115\pi\)
−0.471023 + 0.882121i \(0.656115\pi\)
\(978\) 14.9225 10.1569i 0.477169 0.324783i
\(979\) 2.32366 + 3.19824i 0.0742644 + 0.102216i
\(980\) 0 0
\(981\) 8.95699 10.8587i 0.285975 0.346692i
\(982\) −19.7552 19.7552i −0.630413 0.630413i
\(983\) 2.80520 + 17.7113i 0.0894719 + 0.564903i 0.991176 + 0.132550i \(0.0423165\pi\)
−0.901704 + 0.432353i \(0.857683\pi\)
\(984\) −5.34715 + 2.52085i −0.170461 + 0.0803618i
\(985\) 0 0
\(986\) 0.723093 0.234947i 0.0230280 0.00748224i
\(987\) 37.3653 + 13.4222i 1.18935 + 0.427233i
\(988\) 8.90907 + 17.4850i 0.283435 + 0.556273i
\(989\) −8.16826 25.1393i −0.259736 0.799384i
\(990\) 0 0
\(991\) 14.9087 45.8841i 0.473589 1.45756i −0.374262 0.927323i \(-0.622104\pi\)
0.847851 0.530234i \(-0.177896\pi\)
\(992\) 3.29395 0.521711i 0.104583 0.0165643i
\(993\) 0.509555 16.5921i 0.0161702 0.526535i
\(994\) 4.39954 6.05544i 0.139545 0.192067i
\(995\) 0 0
\(996\) 12.0665 + 2.29287i 0.382341 + 0.0726523i
\(997\) −21.3791 3.38611i −0.677082 0.107239i −0.191583 0.981476i \(-0.561362\pi\)
−0.485499 + 0.874237i \(0.661362\pi\)
\(998\) −0.184251 + 0.361613i −0.00583237 + 0.0114467i
\(999\) −21.1026 + 17.5340i −0.667657 + 0.554750i
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 750.2.l.a.107.2 80
3.2 odd 2 inner 750.2.l.a.107.9 80
5.2 odd 4 150.2.l.a.83.6 yes 80
5.3 odd 4 750.2.l.b.143.5 80
5.4 even 2 750.2.l.c.107.9 80
15.2 even 4 150.2.l.a.83.2 yes 80
15.8 even 4 750.2.l.b.143.9 80
15.14 odd 2 750.2.l.c.107.2 80
25.3 odd 20 inner 750.2.l.a.743.9 80
25.4 even 10 150.2.l.a.47.2 80
25.21 even 5 750.2.l.b.257.9 80
25.22 odd 20 750.2.l.c.743.2 80
75.29 odd 10 150.2.l.a.47.6 yes 80
75.47 even 20 750.2.l.c.743.9 80
75.53 even 20 inner 750.2.l.a.743.2 80
75.71 odd 10 750.2.l.b.257.5 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
150.2.l.a.47.2 80 25.4 even 10
150.2.l.a.47.6 yes 80 75.29 odd 10
150.2.l.a.83.2 yes 80 15.2 even 4
150.2.l.a.83.6 yes 80 5.2 odd 4
750.2.l.a.107.2 80 1.1 even 1 trivial
750.2.l.a.107.9 80 3.2 odd 2 inner
750.2.l.a.743.2 80 75.53 even 20 inner
750.2.l.a.743.9 80 25.3 odd 20 inner
750.2.l.b.143.5 80 5.3 odd 4
750.2.l.b.143.9 80 15.8 even 4
750.2.l.b.257.5 80 75.71 odd 10
750.2.l.b.257.9 80 25.21 even 5
750.2.l.c.107.2 80 15.14 odd 2
750.2.l.c.107.9 80 5.4 even 2
750.2.l.c.743.2 80 25.22 odd 20
750.2.l.c.743.9 80 75.47 even 20