Properties

Label 950.2.bb.c.243.4
Level $950$
Weight $2$
Character 950.243
Analytic conductor $7.586$
Analytic rank $0$
Dimension $72$
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] = [950,2,Mod(143,950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(950, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([27, 34]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.143");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.bb (of order \(36\), degree \(12\), 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: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(6\) over \(\Q(\zeta_{36})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 243.4
Character \(\chi\) \(=\) 950.243
Dual form 950.2.bb.c.907.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.422618 + 0.906308i) q^{2} +(-1.84087 - 1.28899i) q^{3} +(-0.642788 + 0.766044i) q^{4} +(0.390238 - 2.21315i) q^{6} +(0.947246 + 3.53517i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(0.701247 + 1.92666i) q^{9} +O(q^{10})\) \(q+(0.422618 + 0.906308i) q^{2} +(-1.84087 - 1.28899i) q^{3} +(-0.642788 + 0.766044i) q^{4} +(0.390238 - 2.21315i) q^{6} +(0.947246 + 3.53517i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(0.701247 + 1.92666i) q^{9} +(-1.01780 - 1.76288i) q^{11} +(2.17071 - 0.581641i) q^{12} +(-0.228201 - 0.325905i) q^{13} +(-2.80363 + 2.35253i) q^{14} +(-0.173648 - 0.984808i) q^{16} +(-3.29740 + 1.53760i) q^{17} +(-1.44979 + 1.44979i) q^{18} +(2.20191 - 3.76186i) q^{19} +(2.81305 - 7.72879i) q^{21} +(1.16757 - 1.66746i) q^{22} +(0.331390 + 3.78781i) q^{23} +(1.44453 + 1.72152i) q^{24} +(0.198929 - 0.344554i) q^{26} +(-0.552380 + 2.06151i) q^{27} +(-3.31698 - 1.54673i) q^{28} +(-4.56508 + 1.66155i) q^{29} +(-3.28120 - 1.89440i) q^{31} +(0.819152 - 0.573576i) q^{32} +(-0.398700 + 4.55716i) q^{33} +(-2.78709 - 2.33864i) q^{34} +(-1.92666 - 0.701247i) q^{36} +(-7.90769 - 7.90769i) q^{37} +(4.33997 + 0.405773i) q^{38} +0.894100i q^{39} +(-1.75160 + 0.308853i) q^{41} +(8.19351 - 0.716839i) q^{42} +(0.840994 + 0.0735774i) q^{43} +(2.00467 + 0.353477i) q^{44} +(-3.29287 + 1.90114i) q^{46} +(-1.80812 + 3.87752i) q^{47} +(-0.949745 + 2.03674i) q^{48} +(-5.53799 + 3.19736i) q^{49} +(8.05206 + 1.41979i) q^{51} +(0.396343 + 0.0346755i) q^{52} +(-11.2417 + 0.983524i) q^{53} +(-2.10181 + 0.370605i) q^{54} -3.65988i q^{56} +(-8.90244 + 4.08686i) q^{57} +(-3.43516 - 3.43516i) q^{58} +(-5.19883 - 1.89222i) q^{59} +(-7.06628 - 5.92932i) q^{61} +(0.330216 - 3.77439i) q^{62} +(-6.14682 + 4.30405i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-4.29869 + 1.56459i) q^{66} +(-13.1012 - 6.10920i) q^{67} +(0.941657 - 3.51431i) q^{68} +(4.27241 - 7.40003i) q^{69} +(5.65737 + 6.74219i) q^{71} +(-0.178696 - 2.04251i) q^{72} +(-6.07023 + 8.66918i) q^{73} +(3.82487 - 10.5087i) q^{74} +(1.46640 + 4.10484i) q^{76} +(5.26797 - 5.26797i) q^{77} +(-0.810330 + 0.377863i) q^{78} +(-0.813612 - 4.61423i) q^{79} +(8.38601 - 7.03670i) q^{81} +(-1.02017 - 1.45696i) q^{82} +(-1.85941 + 0.498229i) q^{83} +(4.11240 + 7.12289i) q^{84} +(0.288736 + 0.793294i) q^{86} +(10.5454 + 2.82564i) q^{87} +(0.526850 + 1.96623i) q^{88} +(-1.99769 + 11.3295i) q^{89} +(0.935969 - 1.11544i) q^{91} +(-3.11464 - 2.18090i) q^{92} +(3.59840 + 7.71679i) q^{93} -4.27837 q^{94} -2.24729 q^{96} +(-3.74799 - 8.03759i) q^{97} +(-5.23825 - 3.66786i) q^{98} +(2.68274 - 3.19716i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + 24 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 72 q + 24 q^{6} + 24 q^{21} + 12 q^{26} + 36 q^{31} - 24 q^{36} + 48 q^{41} - 36 q^{46} + 156 q^{51} + 168 q^{61} - 36 q^{66} - 84 q^{71} - 48 q^{76} - 60 q^{81} - 60 q^{86} - 264 q^{91} + 24 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{11}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.422618 + 0.906308i 0.298836 + 0.640856i
\(3\) −1.84087 1.28899i −1.06283 0.744200i −0.0949146 0.995485i \(-0.530258\pi\)
−0.967913 + 0.251285i \(0.919147\pi\)
\(4\) −0.642788 + 0.766044i −0.321394 + 0.383022i
\(5\) 0 0
\(6\) 0.390238 2.21315i 0.159314 0.903514i
\(7\) 0.947246 + 3.53517i 0.358026 + 1.33617i 0.876634 + 0.481158i \(0.159784\pi\)
−0.518609 + 0.855012i \(0.673550\pi\)
\(8\) −0.965926 0.258819i −0.341506 0.0915064i
\(9\) 0.701247 + 1.92666i 0.233749 + 0.642220i
\(10\) 0 0
\(11\) −1.01780 1.76288i −0.306877 0.531527i 0.670800 0.741638i \(-0.265951\pi\)
−0.977678 + 0.210111i \(0.932617\pi\)
\(12\) 2.17071 0.581641i 0.626631 0.167905i
\(13\) −0.228201 0.325905i −0.0632917 0.0903899i 0.786258 0.617898i \(-0.212015\pi\)
−0.849550 + 0.527508i \(0.823127\pi\)
\(14\) −2.80363 + 2.35253i −0.749302 + 0.628739i
\(15\) 0 0
\(16\) −0.173648 0.984808i −0.0434120 0.246202i
\(17\) −3.29740 + 1.53760i −0.799738 + 0.372924i −0.779129 0.626864i \(-0.784338\pi\)
−0.0206090 + 0.999788i \(0.506560\pi\)
\(18\) −1.44979 + 1.44979i −0.341718 + 0.341718i
\(19\) 2.20191 3.76186i 0.505152 0.863030i
\(20\) 0 0
\(21\) 2.81305 7.72879i 0.613858 1.68656i
\(22\) 1.16757 1.66746i 0.248926 0.355504i
\(23\) 0.331390 + 3.78781i 0.0690997 + 0.789813i 0.949128 + 0.314891i \(0.101968\pi\)
−0.880028 + 0.474922i \(0.842476\pi\)
\(24\) 1.44453 + 1.72152i 0.294863 + 0.351404i
\(25\) 0 0
\(26\) 0.198929 0.344554i 0.0390131 0.0675727i
\(27\) −0.552380 + 2.06151i −0.106306 + 0.396738i
\(28\) −3.31698 1.54673i −0.626850 0.292305i
\(29\) −4.56508 + 1.66155i −0.847714 + 0.308542i −0.729108 0.684399i \(-0.760065\pi\)
−0.118606 + 0.992941i \(0.537842\pi\)
\(30\) 0 0
\(31\) −3.28120 1.89440i −0.589321 0.340245i 0.175508 0.984478i \(-0.443843\pi\)
−0.764829 + 0.644233i \(0.777177\pi\)
\(32\) 0.819152 0.573576i 0.144807 0.101395i
\(33\) −0.398700 + 4.55716i −0.0694047 + 0.793300i
\(34\) −2.78709 2.33864i −0.477981 0.401074i
\(35\) 0 0
\(36\) −1.92666 0.701247i −0.321110 0.116874i
\(37\) −7.90769 7.90769i −1.30002 1.30002i −0.928378 0.371638i \(-0.878796\pi\)
−0.371638 0.928378i \(-0.621204\pi\)
\(38\) 4.33997 + 0.405773i 0.704036 + 0.0658251i
\(39\) 0.894100i 0.143171i
\(40\) 0 0
\(41\) −1.75160 + 0.308853i −0.273553 + 0.0482348i −0.308742 0.951146i \(-0.599908\pi\)
0.0351886 + 0.999381i \(0.488797\pi\)
\(42\) 8.19351 0.716839i 1.26429 0.110611i
\(43\) 0.840994 + 0.0735774i 0.128250 + 0.0112205i 0.151100 0.988518i \(-0.451718\pi\)
−0.0228498 + 0.999739i \(0.507274\pi\)
\(44\) 2.00467 + 0.353477i 0.302215 + 0.0532887i
\(45\) 0 0
\(46\) −3.29287 + 1.90114i −0.485507 + 0.280308i
\(47\) −1.80812 + 3.87752i −0.263741 + 0.565595i −0.992928 0.118720i \(-0.962121\pi\)
0.729186 + 0.684315i \(0.239899\pi\)
\(48\) −0.949745 + 2.03674i −0.137084 + 0.293977i
\(49\) −5.53799 + 3.19736i −0.791141 + 0.456765i
\(50\) 0 0
\(51\) 8.05206 + 1.41979i 1.12751 + 0.198811i
\(52\) 0.396343 + 0.0346755i 0.0549629 + 0.00480863i
\(53\) −11.2417 + 0.983524i −1.54417 + 0.135097i −0.827160 0.561966i \(-0.810045\pi\)
−0.717010 + 0.697063i \(0.754490\pi\)
\(54\) −2.10181 + 0.370605i −0.286020 + 0.0504330i
\(55\) 0 0
\(56\) 3.65988i 0.489072i
\(57\) −8.90244 + 4.08686i −1.17916 + 0.541318i
\(58\) −3.43516 3.43516i −0.451059 0.451059i
\(59\) −5.19883 1.89222i −0.676830 0.246346i −0.0193440 0.999813i \(-0.506158\pi\)
−0.657486 + 0.753467i \(0.728380\pi\)
\(60\) 0 0
\(61\) −7.06628 5.92932i −0.904745 0.759171i 0.0663671 0.997795i \(-0.478859\pi\)
−0.971112 + 0.238624i \(0.923304\pi\)
\(62\) 0.330216 3.77439i 0.0419375 0.479347i
\(63\) −6.14682 + 4.30405i −0.774426 + 0.542259i
\(64\) 0.866025 + 0.500000i 0.108253 + 0.0625000i
\(65\) 0 0
\(66\) −4.29869 + 1.56459i −0.529132 + 0.192588i
\(67\) −13.1012 6.10920i −1.60057 0.746358i −0.601933 0.798547i \(-0.705603\pi\)
−0.998637 + 0.0521887i \(0.983380\pi\)
\(68\) 0.941657 3.51431i 0.114193 0.426173i
\(69\) 4.27241 7.40003i 0.514338 0.890859i
\(70\) 0 0
\(71\) 5.65737 + 6.74219i 0.671406 + 0.800150i 0.988975 0.148085i \(-0.0473109\pi\)
−0.317569 + 0.948235i \(0.602866\pi\)
\(72\) −0.178696 2.04251i −0.0210595 0.240712i
\(73\) −6.07023 + 8.66918i −0.710466 + 1.01465i 0.287908 + 0.957658i \(0.407040\pi\)
−0.998375 + 0.0569931i \(0.981849\pi\)
\(74\) 3.82487 10.5087i 0.444632 1.22162i
\(75\) 0 0
\(76\) 1.46640 + 4.10484i 0.168207 + 0.470857i
\(77\) 5.26797 5.26797i 0.600340 0.600340i
\(78\) −0.810330 + 0.377863i −0.0917518 + 0.0427845i
\(79\) −0.813612 4.61423i −0.0915386 0.519141i −0.995753 0.0920627i \(-0.970654\pi\)
0.904215 0.427078i \(-0.140457\pi\)
\(80\) 0 0
\(81\) 8.38601 7.03670i 0.931779 0.781855i
\(82\) −1.02017 1.45696i −0.112659 0.160894i
\(83\) −1.85941 + 0.498229i −0.204097 + 0.0546877i −0.359419 0.933176i \(-0.617025\pi\)
0.155322 + 0.987864i \(0.450359\pi\)
\(84\) 4.11240 + 7.12289i 0.448700 + 0.777171i
\(85\) 0 0
\(86\) 0.288736 + 0.793294i 0.0311352 + 0.0855431i
\(87\) 10.5454 + 2.82564i 1.13059 + 0.302941i
\(88\) 0.526850 + 1.96623i 0.0561624 + 0.209601i
\(89\) −1.99769 + 11.3295i −0.211755 + 1.20092i 0.674694 + 0.738097i \(0.264275\pi\)
−0.886450 + 0.462825i \(0.846836\pi\)
\(90\) 0 0
\(91\) 0.935969 1.11544i 0.0981162 0.116930i
\(92\) −3.11464 2.18090i −0.324724 0.227374i
\(93\) 3.59840 + 7.71679i 0.373136 + 0.800194i
\(94\) −4.27837 −0.441281
\(95\) 0 0
\(96\) −2.24729 −0.229363
\(97\) −3.74799 8.03759i −0.380551 0.816094i −0.999529 0.0306856i \(-0.990231\pi\)
0.618978 0.785408i \(-0.287547\pi\)
\(98\) −5.23825 3.66786i −0.529143 0.370510i
\(99\) 2.68274 3.19716i 0.269625 0.321327i
\(100\) 0 0
\(101\) −1.12745 + 6.39408i −0.112185 + 0.636235i 0.875920 + 0.482456i \(0.160255\pi\)
−0.988105 + 0.153778i \(0.950856\pi\)
\(102\) 2.11618 + 7.89767i 0.209533 + 0.781986i
\(103\) 15.6168 + 4.18451i 1.53877 + 0.412312i 0.925868 0.377847i \(-0.123335\pi\)
0.612902 + 0.790159i \(0.290002\pi\)
\(104\) 0.136075 + 0.373863i 0.0133433 + 0.0366603i
\(105\) 0 0
\(106\) −5.64233 9.77281i −0.548032 0.949219i
\(107\) 12.3055 3.29724i 1.18961 0.318756i 0.390881 0.920441i \(-0.372170\pi\)
0.798733 + 0.601685i \(0.205504\pi\)
\(108\) −1.22415 1.74826i −0.117793 0.168226i
\(109\) −7.69581 + 6.45755i −0.737124 + 0.618521i −0.932064 0.362294i \(-0.881993\pi\)
0.194939 + 0.980815i \(0.437549\pi\)
\(110\) 0 0
\(111\) 4.36409 + 24.7500i 0.414221 + 2.34916i
\(112\) 3.31698 1.54673i 0.313425 0.146152i
\(113\) 11.5628 11.5628i 1.08774 1.08774i 0.0919767 0.995761i \(-0.470681\pi\)
0.995761 0.0919767i \(-0.0293185\pi\)
\(114\) −7.46629 6.34116i −0.699282 0.593904i
\(115\) 0 0
\(116\) 1.66155 4.56508i 0.154271 0.423857i
\(117\) 0.467883 0.668206i 0.0432558 0.0617757i
\(118\) −0.482187 5.51142i −0.0443889 0.507368i
\(119\) −8.55915 10.2004i −0.784616 0.935069i
\(120\) 0 0
\(121\) 3.42818 5.93778i 0.311653 0.539798i
\(122\) 2.38744 8.91006i 0.216149 0.806679i
\(123\) 3.62257 + 1.68923i 0.326636 + 0.152313i
\(124\) 3.56031 1.29585i 0.319725 0.116370i
\(125\) 0 0
\(126\) −6.49855 3.75194i −0.578937 0.334249i
\(127\) −4.21307 + 2.95002i −0.373849 + 0.261772i −0.745368 0.666653i \(-0.767726\pi\)
0.371518 + 0.928426i \(0.378837\pi\)
\(128\) −0.0871557 + 0.996195i −0.00770355 + 0.0880520i
\(129\) −1.45332 1.21948i −0.127958 0.107369i
\(130\) 0 0
\(131\) 7.43460 + 2.70597i 0.649564 + 0.236422i 0.645724 0.763571i \(-0.276556\pi\)
0.00383987 + 0.999993i \(0.498778\pi\)
\(132\) −3.23471 3.23471i −0.281545 0.281545i
\(133\) 15.3846 + 4.22071i 1.33401 + 0.365982i
\(134\) 14.4556i 1.24877i
\(135\) 0 0
\(136\) 3.58301 0.631781i 0.307240 0.0541748i
\(137\) 0.0646282 0.00565423i 0.00552156 0.000483074i −0.0843946 0.996432i \(-0.526896\pi\)
0.0899162 + 0.995949i \(0.471340\pi\)
\(138\) 8.51230 + 0.744730i 0.724615 + 0.0633956i
\(139\) 17.1262 + 3.01982i 1.45263 + 0.256137i 0.843583 0.536998i \(-0.180442\pi\)
0.609045 + 0.793136i \(0.291553\pi\)
\(140\) 0 0
\(141\) 8.32661 4.80737i 0.701227 0.404854i
\(142\) −3.71959 + 7.97669i −0.312141 + 0.669389i
\(143\) −0.342268 + 0.733996i −0.0286219 + 0.0613798i
\(144\) 1.77562 1.02515i 0.147968 0.0854295i
\(145\) 0 0
\(146\) −10.4223 1.83774i −0.862559 0.152092i
\(147\) 14.3161 + 1.25250i 1.18077 + 0.103304i
\(148\) 11.1406 0.974677i 0.915752 0.0801179i
\(149\) −15.4981 + 2.73273i −1.26965 + 0.223874i −0.767582 0.640951i \(-0.778540\pi\)
−0.502073 + 0.864825i \(0.667429\pi\)
\(150\) 0 0
\(151\) 9.12444i 0.742536i 0.928526 + 0.371268i \(0.121077\pi\)
−0.928526 + 0.371268i \(0.878923\pi\)
\(152\) −3.10052 + 3.06378i −0.251485 + 0.248506i
\(153\) −5.27473 5.27473i −0.426437 0.426437i
\(154\) 7.00074 + 2.54806i 0.564135 + 0.205328i
\(155\) 0 0
\(156\) −0.684920 0.574716i −0.0548375 0.0460141i
\(157\) −1.49617 + 17.1013i −0.119407 + 1.36483i 0.666045 + 0.745911i \(0.267986\pi\)
−0.785453 + 0.618922i \(0.787570\pi\)
\(158\) 3.83806 2.68744i 0.305340 0.213801i
\(159\) 21.9623 + 12.6800i 1.74173 + 1.00559i
\(160\) 0 0
\(161\) −13.0766 + 4.75951i −1.03058 + 0.375102i
\(162\) 9.92150 + 4.62647i 0.779506 + 0.363490i
\(163\) 4.17250 15.5720i 0.326816 1.21969i −0.585659 0.810558i \(-0.699164\pi\)
0.912474 0.409134i \(-0.134169\pi\)
\(164\) 0.889308 1.54033i 0.0694433 0.120279i
\(165\) 0 0
\(166\) −1.23737 1.47464i −0.0960386 0.114454i
\(167\) 0.984333 + 11.2510i 0.0761700 + 0.870627i 0.934135 + 0.356919i \(0.116173\pi\)
−0.857965 + 0.513708i \(0.828272\pi\)
\(168\) −4.71756 + 6.73737i −0.363967 + 0.519799i
\(169\) 4.39212 12.0673i 0.337856 0.928251i
\(170\) 0 0
\(171\) 8.79191 + 1.60433i 0.672334 + 0.122686i
\(172\) −0.596944 + 0.596944i −0.0455165 + 0.0455165i
\(173\) 19.6625 9.16877i 1.49491 0.697088i 0.508451 0.861091i \(-0.330218\pi\)
0.986460 + 0.164003i \(0.0524406\pi\)
\(174\) 1.89580 + 10.7516i 0.143720 + 0.815076i
\(175\) 0 0
\(176\) −1.55936 + 1.30845i −0.117541 + 0.0986285i
\(177\) 7.13132 + 10.1846i 0.536023 + 0.765520i
\(178\) −11.1123 + 2.97752i −0.832899 + 0.223175i
\(179\) 11.0624 + 19.1607i 0.826843 + 1.43213i 0.900503 + 0.434851i \(0.143199\pi\)
−0.0736594 + 0.997283i \(0.523468\pi\)
\(180\) 0 0
\(181\) −4.62297 12.7015i −0.343623 0.944096i −0.984334 0.176314i \(-0.943583\pi\)
0.640711 0.767782i \(-0.278640\pi\)
\(182\) 1.40649 + 0.376869i 0.104256 + 0.0279354i
\(183\) 5.36528 + 20.0235i 0.396613 + 1.48018i
\(184\) 0.660259 3.74451i 0.0486749 0.276049i
\(185\) 0 0
\(186\) −5.47304 + 6.52251i −0.401303 + 0.478254i
\(187\) 6.06669 + 4.24794i 0.443641 + 0.310640i
\(188\) −1.80812 3.87752i −0.131871 0.282798i
\(189\) −7.81103 −0.568169
\(190\) 0 0
\(191\) −14.2634 −1.03207 −0.516033 0.856569i \(-0.672592\pi\)
−0.516033 + 0.856569i \(0.672592\pi\)
\(192\) −0.949745 2.03674i −0.0685420 0.146989i
\(193\) −4.09257 2.86565i −0.294590 0.206274i 0.416933 0.908937i \(-0.363105\pi\)
−0.711522 + 0.702664i \(0.751994\pi\)
\(194\) 5.70056 6.79366i 0.409276 0.487757i
\(195\) 0 0
\(196\) 1.11043 6.29757i 0.0793165 0.449826i
\(197\) 2.56441 + 9.57051i 0.182707 + 0.681870i 0.995110 + 0.0987743i \(0.0314922\pi\)
−0.812403 + 0.583096i \(0.801841\pi\)
\(198\) 4.03138 + 1.08021i 0.286498 + 0.0767669i
\(199\) 3.43559 + 9.43920i 0.243542 + 0.669127i 0.999888 + 0.0149552i \(0.00476057\pi\)
−0.756346 + 0.654172i \(0.773017\pi\)
\(200\) 0 0
\(201\) 16.2430 + 28.1336i 1.14569 + 1.98439i
\(202\) −6.27148 + 1.68044i −0.441260 + 0.118235i
\(203\) −10.1981 14.5644i −0.715768 1.02222i
\(204\) −6.26339 + 5.25561i −0.438525 + 0.367966i
\(205\) 0 0
\(206\) 2.80749 + 15.9221i 0.195607 + 1.10934i
\(207\) −7.06543 + 3.29467i −0.491082 + 0.228995i
\(208\) −0.281327 + 0.281327i −0.0195065 + 0.0195065i
\(209\) −8.87279 0.0528762i −0.613744 0.00365753i
\(210\) 0 0
\(211\) 5.63145 15.4723i 0.387685 1.06516i −0.580356 0.814363i \(-0.697086\pi\)
0.968041 0.250793i \(-0.0806913\pi\)
\(212\) 6.47262 9.24386i 0.444541 0.634871i
\(213\) −1.72386 19.7038i −0.118117 1.35008i
\(214\) 8.18883 + 9.75907i 0.559777 + 0.667116i
\(215\) 0 0
\(216\) 1.06712 1.84830i 0.0726080 0.125761i
\(217\) 3.58893 13.3941i 0.243632 0.909249i
\(218\) −9.10491 4.24569i −0.616663 0.287554i
\(219\) 22.3490 8.13438i 1.51021 0.549670i
\(220\) 0 0
\(221\) 1.25359 + 0.723758i 0.0843253 + 0.0486852i
\(222\) −20.5868 + 14.4150i −1.38169 + 0.967472i
\(223\) 1.76268 20.1475i 0.118038 1.34918i −0.674011 0.738721i \(-0.735430\pi\)
0.792049 0.610457i \(-0.209014\pi\)
\(224\) 2.80363 + 2.35253i 0.187325 + 0.157185i
\(225\) 0 0
\(226\) 15.3661 + 5.59281i 1.02214 + 0.372028i
\(227\) −16.9824 16.9824i −1.12716 1.12716i −0.990637 0.136525i \(-0.956407\pi\)
−0.136525 0.990637i \(-0.543593\pi\)
\(228\) 2.59166 9.44665i 0.171637 0.625620i
\(229\) 8.20517i 0.542213i 0.962549 + 0.271107i \(0.0873896\pi\)
−0.962549 + 0.271107i \(0.912610\pi\)
\(230\) 0 0
\(231\) −16.4880 + 2.90728i −1.08483 + 0.191285i
\(232\) 4.83957 0.423407i 0.317733 0.0277980i
\(233\) −9.93045 0.868802i −0.650566 0.0569171i −0.242904 0.970050i \(-0.578100\pi\)
−0.407661 + 0.913133i \(0.633656\pi\)
\(234\) 0.803337 + 0.141650i 0.0525158 + 0.00925995i
\(235\) 0 0
\(236\) 4.79127 2.76624i 0.311885 0.180067i
\(237\) −4.44994 + 9.54294i −0.289055 + 0.619880i
\(238\) 5.62745 12.0681i 0.364773 0.782259i
\(239\) −9.17350 + 5.29632i −0.593384 + 0.342591i −0.766435 0.642322i \(-0.777971\pi\)
0.173050 + 0.984913i \(0.444638\pi\)
\(240\) 0 0
\(241\) −5.98759 1.05577i −0.385695 0.0680084i −0.0225612 0.999745i \(-0.507182\pi\)
−0.363134 + 0.931737i \(0.618293\pi\)
\(242\) 6.83027 + 0.597571i 0.439066 + 0.0384133i
\(243\) −18.1295 + 1.58612i −1.16301 + 0.101750i
\(244\) 9.08424 1.60180i 0.581559 0.102545i
\(245\) 0 0
\(246\) 3.99707i 0.254844i
\(247\) −1.72849 + 0.140849i −0.109981 + 0.00896201i
\(248\) 2.67909 + 2.67909i 0.170122 + 0.170122i
\(249\) 4.06516 + 1.47960i 0.257619 + 0.0937656i
\(250\) 0 0
\(251\) 4.99608 + 4.19221i 0.315350 + 0.264610i 0.786699 0.617337i \(-0.211788\pi\)
−0.471349 + 0.881947i \(0.656233\pi\)
\(252\) 0.654006 7.47533i 0.0411985 0.470901i
\(253\) 6.34015 4.43942i 0.398602 0.279104i
\(254\) −4.45415 2.57160i −0.279478 0.161357i
\(255\) 0 0
\(256\) −0.939693 + 0.342020i −0.0587308 + 0.0213763i
\(257\) −14.0201 6.53770i −0.874553 0.407811i −0.0671022 0.997746i \(-0.521375\pi\)
−0.807450 + 0.589936i \(0.799153\pi\)
\(258\) 0.491025 1.83253i 0.0305699 0.114088i
\(259\) 20.4645 35.4456i 1.27160 2.20248i
\(260\) 0 0
\(261\) −6.40249 7.63019i −0.396304 0.472297i
\(262\) 0.689553 + 7.88163i 0.0426008 + 0.486929i
\(263\) −11.4410 + 16.3395i −0.705484 + 1.00754i 0.293190 + 0.956054i \(0.405283\pi\)
−0.998674 + 0.0514815i \(0.983606\pi\)
\(264\) 1.56459 4.29869i 0.0962941 0.264566i
\(265\) 0 0
\(266\) 2.67654 + 15.7269i 0.164109 + 0.964279i
\(267\) 18.2811 18.2811i 1.11879 1.11879i
\(268\) 13.1012 6.10920i 0.800285 0.373179i
\(269\) 2.78396 + 15.7886i 0.169741 + 0.962651i 0.944040 + 0.329831i \(0.106992\pi\)
−0.774299 + 0.632820i \(0.781897\pi\)
\(270\) 0 0
\(271\) −0.427071 + 0.358355i −0.0259427 + 0.0217685i −0.655667 0.755050i \(-0.727612\pi\)
0.629724 + 0.776819i \(0.283168\pi\)
\(272\) 2.08683 + 2.98031i 0.126533 + 0.180708i
\(273\) −3.16080 + 0.846933i −0.191300 + 0.0512587i
\(274\) 0.0324375 + 0.0561834i 0.00195962 + 0.00339416i
\(275\) 0 0
\(276\) 2.92250 + 8.02950i 0.175914 + 0.483319i
\(277\) −23.4935 6.29506i −1.41159 0.378233i −0.529095 0.848563i \(-0.677468\pi\)
−0.882491 + 0.470330i \(0.844135\pi\)
\(278\) 4.50097 + 16.7979i 0.269950 + 1.00747i
\(279\) 1.34894 7.65020i 0.0807587 0.458005i
\(280\) 0 0
\(281\) −16.7044 + 19.9075i −0.996502 + 1.18758i −0.0142727 + 0.999898i \(0.504543\pi\)
−0.982229 + 0.187686i \(0.939901\pi\)
\(282\) 7.87594 + 5.51479i 0.469005 + 0.328401i
\(283\) 10.6442 + 22.8265i 0.632730 + 1.35689i 0.917284 + 0.398233i \(0.130377\pi\)
−0.284554 + 0.958660i \(0.591846\pi\)
\(284\) −8.80130 −0.522261
\(285\) 0 0
\(286\) −0.809875 −0.0478889
\(287\) −2.75104 5.89963i −0.162389 0.348244i
\(288\) 1.67951 + 1.17601i 0.0989663 + 0.0692970i
\(289\) −2.41875 + 2.88255i −0.142279 + 0.169562i
\(290\) 0 0
\(291\) −3.46082 + 19.6273i −0.202877 + 1.15057i
\(292\) −2.73911 10.2225i −0.160294 0.598227i
\(293\) −15.6986 4.20642i −0.917121 0.245742i −0.230767 0.973009i \(-0.574123\pi\)
−0.686354 + 0.727267i \(0.740790\pi\)
\(294\) 4.91510 + 13.5041i 0.286654 + 0.787576i
\(295\) 0 0
\(296\) 5.59158 + 9.68490i 0.325004 + 0.562923i
\(297\) 4.19640 1.12442i 0.243500 0.0652455i
\(298\) −9.02648 12.8912i −0.522890 0.746764i
\(299\) 1.15884 0.972385i 0.0670177 0.0562345i
\(300\) 0 0
\(301\) 0.536520 + 3.04275i 0.0309245 + 0.175381i
\(302\) −8.26955 + 3.85615i −0.475859 + 0.221897i
\(303\) 10.3174 10.3174i 0.592719 0.592719i
\(304\) −4.08707 1.51521i −0.234409 0.0869035i
\(305\) 0 0
\(306\) 2.55133 7.00973i 0.145850 0.400720i
\(307\) −13.4826 + 19.2552i −0.769494 + 1.09895i 0.222778 + 0.974869i \(0.428488\pi\)
−0.992272 + 0.124082i \(0.960401\pi\)
\(308\) 0.649313 + 7.42168i 0.0369980 + 0.422889i
\(309\) −23.3547 27.8331i −1.32860 1.58337i
\(310\) 0 0
\(311\) −5.83904 + 10.1135i −0.331102 + 0.573485i −0.982728 0.185055i \(-0.940754\pi\)
0.651626 + 0.758540i \(0.274087\pi\)
\(312\) 0.231410 0.863634i 0.0131010 0.0488936i
\(313\) −4.39298 2.04848i −0.248306 0.115787i 0.294481 0.955657i \(-0.404853\pi\)
−0.542787 + 0.839870i \(0.682631\pi\)
\(314\) −16.1314 + 5.87133i −0.910345 + 0.331338i
\(315\) 0 0
\(316\) 4.05768 + 2.34270i 0.228262 + 0.131787i
\(317\) 23.5662 16.5012i 1.32361 0.926802i 0.323797 0.946127i \(-0.395041\pi\)
0.999813 + 0.0193247i \(0.00615163\pi\)
\(318\) −2.21026 + 25.2634i −0.123945 + 1.41670i
\(319\) 7.57543 + 6.35654i 0.424143 + 0.355898i
\(320\) 0 0
\(321\) −26.9029 9.79185i −1.50157 0.546528i
\(322\) −9.84001 9.84001i −0.548362 0.548362i
\(323\) −1.47632 + 15.7900i −0.0821445 + 0.878581i
\(324\) 10.9472i 0.608176i
\(325\) 0 0
\(326\) 15.8764 2.79944i 0.879312 0.155046i
\(327\) 22.4907 1.96768i 1.24374 0.108813i
\(328\) 1.77185 + 0.155017i 0.0978339 + 0.00855936i
\(329\) −15.4204 2.71904i −0.850157 0.149906i
\(330\) 0 0
\(331\) 16.3599 9.44539i 0.899221 0.519166i 0.0222740 0.999752i \(-0.492909\pi\)
0.876948 + 0.480586i \(0.159576\pi\)
\(332\) 0.813543 1.74465i 0.0446490 0.0957501i
\(333\) 9.69018 20.7807i 0.531019 1.13877i
\(334\) −9.78085 + 5.64698i −0.535184 + 0.308989i
\(335\) 0 0
\(336\) −8.09985 1.42822i −0.441883 0.0779159i
\(337\) −4.83922 0.423377i −0.263609 0.0230628i −0.0454151 0.998968i \(-0.514461\pi\)
−0.218194 + 0.975905i \(0.570017\pi\)
\(338\) 12.7928 1.11923i 0.695839 0.0608780i
\(339\) −36.1900 + 6.38128i −1.96557 + 0.346583i
\(340\) 0 0
\(341\) 7.71246i 0.417653i
\(342\) 2.26160 + 8.64619i 0.122294 + 0.467533i
\(343\) 1.56643 + 1.56643i 0.0845791 + 0.0845791i
\(344\) −0.793294 0.288736i −0.0427716 0.0155676i
\(345\) 0 0
\(346\) 16.6194 + 13.9454i 0.893467 + 0.749708i
\(347\) 2.05622 23.5028i 0.110384 1.26169i −0.715805 0.698300i \(-0.753940\pi\)
0.826189 0.563394i \(-0.190504\pi\)
\(348\) −8.94305 + 6.26199i −0.479398 + 0.335678i
\(349\) 27.7330 + 16.0117i 1.48451 + 0.857085i 0.999845 0.0176130i \(-0.00560669\pi\)
0.484669 + 0.874698i \(0.338940\pi\)
\(350\) 0 0
\(351\) 0.797911 0.290416i 0.0425893 0.0155013i
\(352\) −1.84487 0.860279i −0.0983321 0.0458530i
\(353\) 1.43103 5.34067i 0.0761660 0.284255i −0.917329 0.398130i \(-0.869659\pi\)
0.993495 + 0.113874i \(0.0363261\pi\)
\(354\) −6.21654 + 10.7674i −0.330405 + 0.572279i
\(355\) 0 0
\(356\) −7.39479 8.81277i −0.391923 0.467076i
\(357\) 2.60806 + 29.8103i 0.138033 + 1.57773i
\(358\) −12.6903 + 18.1236i −0.670702 + 0.957861i
\(359\) 9.48616 26.0630i 0.500660 1.37555i −0.389971 0.920827i \(-0.627515\pi\)
0.890631 0.454726i \(-0.150263\pi\)
\(360\) 0 0
\(361\) −9.30322 16.5665i −0.489643 0.871923i
\(362\) 9.55773 9.55773i 0.502343 0.502343i
\(363\) −13.9646 + 6.51179i −0.732951 + 0.341781i
\(364\) 0.252851 + 1.43399i 0.0132530 + 0.0751613i
\(365\) 0 0
\(366\) −15.8800 + 13.3249i −0.830060 + 0.696503i
\(367\) 5.06478 + 7.23325i 0.264379 + 0.377573i 0.929291 0.369350i \(-0.120420\pi\)
−0.664911 + 0.746922i \(0.731531\pi\)
\(368\) 3.67272 0.984102i 0.191454 0.0512999i
\(369\) −1.82336 3.15815i −0.0949201 0.164406i
\(370\) 0 0
\(371\) −14.1256 38.8098i −0.733365 2.01490i
\(372\) −8.22441 2.20372i −0.426416 0.114258i
\(373\) 2.17694 + 8.12447i 0.112718 + 0.420669i 0.999106 0.0422739i \(-0.0134602\pi\)
−0.886388 + 0.462943i \(0.846794\pi\)
\(374\) −1.28605 + 7.29355i −0.0665000 + 0.377141i
\(375\) 0 0
\(376\) 2.75009 3.27742i 0.141825 0.169020i
\(377\) 1.58327 + 1.10861i 0.0815423 + 0.0570966i
\(378\) −3.30108 7.07920i −0.169789 0.364115i
\(379\) 37.0435 1.90280 0.951399 0.307962i \(-0.0996471\pi\)
0.951399 + 0.307962i \(0.0996471\pi\)
\(380\) 0 0
\(381\) 11.5583 0.592148
\(382\) −6.02799 12.9271i −0.308419 0.661406i
\(383\) 21.8129 + 15.2735i 1.11459 + 0.780442i 0.977671 0.210141i \(-0.0673923\pi\)
0.136915 + 0.990583i \(0.456281\pi\)
\(384\) 1.44453 1.72152i 0.0737158 0.0878511i
\(385\) 0 0
\(386\) 0.867564 4.92020i 0.0441579 0.250432i
\(387\) 0.447985 + 1.67190i 0.0227724 + 0.0849877i
\(388\) 8.56631 + 2.29534i 0.434889 + 0.116528i
\(389\) 10.3560 + 28.4529i 0.525071 + 1.44262i 0.864810 + 0.502100i \(0.167439\pi\)
−0.339739 + 0.940520i \(0.610339\pi\)
\(390\) 0 0
\(391\) −6.91688 11.9804i −0.349802 0.605874i
\(392\) 6.17682 1.65507i 0.311977 0.0835939i
\(393\) −10.1982 14.5645i −0.514430 0.734682i
\(394\) −7.59006 + 6.36881i −0.382382 + 0.320856i
\(395\) 0 0
\(396\) 0.724737 + 4.11019i 0.0364194 + 0.206545i
\(397\) −12.9106 + 6.02029i −0.647962 + 0.302150i −0.718674 0.695347i \(-0.755251\pi\)
0.0707119 + 0.997497i \(0.477473\pi\)
\(398\) −7.10288 + 7.10288i −0.356035 + 0.356035i
\(399\) −22.8806 27.6004i −1.14546 1.38175i
\(400\) 0 0
\(401\) −2.57197 + 7.06642i −0.128438 + 0.352880i −0.987198 0.159497i \(-0.949013\pi\)
0.858761 + 0.512377i \(0.171235\pi\)
\(402\) −18.6332 + 26.6109i −0.929338 + 1.32723i
\(403\) 0.131379 + 1.50167i 0.00654444 + 0.0748033i
\(404\) −4.17344 4.97371i −0.207636 0.247451i
\(405\) 0 0
\(406\) 8.88995 15.3978i 0.441201 0.764182i
\(407\) −5.89185 + 21.9887i −0.292048 + 1.08994i
\(408\) −7.41022 3.45544i −0.366861 0.171070i
\(409\) −9.23982 + 3.36302i −0.456880 + 0.166291i −0.560200 0.828358i \(-0.689276\pi\)
0.103320 + 0.994648i \(0.467053\pi\)
\(410\) 0 0
\(411\) −0.126260 0.0728965i −0.00622797 0.00359572i
\(412\) −13.2438 + 9.27342i −0.652476 + 0.456868i
\(413\) 1.76475 20.1711i 0.0868375 0.992557i
\(414\) −5.97196 5.01107i −0.293506 0.246281i
\(415\) 0 0
\(416\) −0.373863 0.136075i −0.0183302 0.00667163i
\(417\) −27.6347 27.6347i −1.35328 1.35328i
\(418\) −3.70188 8.06383i −0.181065 0.394415i
\(419\) 22.6846i 1.10821i 0.832446 + 0.554107i \(0.186940\pi\)
−0.832446 + 0.554107i \(0.813060\pi\)
\(420\) 0 0
\(421\) 15.7480 2.77679i 0.767510 0.135333i 0.223833 0.974627i \(-0.428143\pi\)
0.543677 + 0.839295i \(0.317032\pi\)
\(422\) 16.4026 1.43504i 0.798466 0.0698568i
\(423\) −8.73861 0.764529i −0.424886 0.0371727i
\(424\) 11.1132 + 1.95956i 0.539706 + 0.0951648i
\(425\) 0 0
\(426\) 17.1292 9.88953i 0.829911 0.479149i
\(427\) 14.2676 30.5971i 0.690459 1.48070i
\(428\) −5.38397 + 11.5460i −0.260244 + 0.558095i
\(429\) 1.57619 0.910012i 0.0760990 0.0439358i
\(430\) 0 0
\(431\) −11.1562 1.96715i −0.537377 0.0947541i −0.101628 0.994822i \(-0.532405\pi\)
−0.435749 + 0.900068i \(0.643516\pi\)
\(432\) 2.12611 + 0.186011i 0.102293 + 0.00894944i
\(433\) −0.262954 + 0.0230055i −0.0126367 + 0.00110557i −0.0934724 0.995622i \(-0.529797\pi\)
0.0808356 + 0.996727i \(0.474241\pi\)
\(434\) 13.6559 2.40790i 0.655504 0.115583i
\(435\) 0 0
\(436\) 10.0462i 0.481124i
\(437\) 14.9789 + 7.09376i 0.716538 + 0.339340i
\(438\) 16.8174 + 16.8174i 0.803564 + 0.803564i
\(439\) −13.1779 4.79637i −0.628948 0.228918i 0.00782562 0.999969i \(-0.497509\pi\)
−0.636773 + 0.771051i \(0.719731\pi\)
\(440\) 0 0
\(441\) −10.0437 8.42768i −0.478272 0.401318i
\(442\) −0.126159 + 1.44201i −0.00600079 + 0.0685893i
\(443\) −20.6262 + 14.4427i −0.979983 + 0.686191i −0.949638 0.313348i \(-0.898549\pi\)
−0.0303444 + 0.999540i \(0.509660\pi\)
\(444\) −21.7648 12.5659i −1.03291 0.596351i
\(445\) 0 0
\(446\) 19.0048 6.91718i 0.899904 0.327538i
\(447\) 32.0525 + 14.9463i 1.51603 + 0.706937i
\(448\) −0.947246 + 3.53517i −0.0447532 + 0.167021i
\(449\) 8.85846 15.3433i 0.418057 0.724095i −0.577687 0.816258i \(-0.696045\pi\)
0.995744 + 0.0921629i \(0.0293780\pi\)
\(450\) 0 0
\(451\) 2.32724 + 2.77349i 0.109585 + 0.130599i
\(452\) 1.42520 + 16.2901i 0.0670356 + 0.766220i
\(453\) 11.7613 16.7969i 0.552595 0.789188i
\(454\) 8.21421 22.5683i 0.385512 1.05919i
\(455\) 0 0
\(456\) 9.65685 1.64349i 0.452224 0.0769634i
\(457\) 22.0911 22.0911i 1.03338 1.03338i 0.0339529 0.999423i \(-0.489190\pi\)
0.999423 0.0339529i \(-0.0108096\pi\)
\(458\) −7.43641 + 3.46766i −0.347481 + 0.162033i
\(459\) −1.34837 7.64697i −0.0629364 0.356930i
\(460\) 0 0
\(461\) 8.00960 6.72085i 0.373044 0.313021i −0.436920 0.899500i \(-0.643931\pi\)
0.809964 + 0.586479i \(0.199486\pi\)
\(462\) −9.60303 13.7145i −0.446773 0.638058i
\(463\) −22.5965 + 6.05471i −1.05015 + 0.281386i −0.742312 0.670054i \(-0.766271\pi\)
−0.307835 + 0.951440i \(0.599604\pi\)
\(464\) 2.42903 + 4.20720i 0.112765 + 0.195314i
\(465\) 0 0
\(466\) −3.40939 9.36722i −0.157937 0.433928i
\(467\) 25.3644 + 6.79636i 1.17372 + 0.314498i 0.792434 0.609958i \(-0.208814\pi\)
0.381289 + 0.924456i \(0.375480\pi\)
\(468\) 0.211126 + 0.787934i 0.00975932 + 0.0364223i
\(469\) 9.18699 52.1020i 0.424216 2.40585i
\(470\) 0 0
\(471\) 24.7977 29.5528i 1.14262 1.36172i
\(472\) 4.53194 + 3.17330i 0.208599 + 0.146063i
\(473\) −0.726253 1.55745i −0.0333931 0.0716118i
\(474\) −10.5295 −0.483634
\(475\) 0 0
\(476\) 13.3157 0.610323
\(477\) −9.77814 20.9693i −0.447710 0.960118i
\(478\) −8.67698 6.07569i −0.396876 0.277896i
\(479\) −10.6969 + 12.7481i −0.488755 + 0.582475i −0.952900 0.303284i \(-0.901917\pi\)
0.464146 + 0.885759i \(0.346361\pi\)
\(480\) 0 0
\(481\) −0.772613 + 4.38170i −0.0352281 + 0.199788i
\(482\) −1.57361 5.87279i −0.0716760 0.267498i
\(483\) 30.2074 + 8.09405i 1.37448 + 0.368292i
\(484\) 2.34501 + 6.44287i 0.106591 + 0.292858i
\(485\) 0 0
\(486\) −9.09937 15.7606i −0.412756 0.714914i
\(487\) 3.93208 1.05360i 0.178180 0.0477431i −0.168626 0.985680i \(-0.553933\pi\)
0.346806 + 0.937937i \(0.387266\pi\)
\(488\) 5.29089 + 7.55617i 0.239507 + 0.342052i
\(489\) −27.7532 + 23.2877i −1.25504 + 1.05311i
\(490\) 0 0
\(491\) −5.77015 32.7241i −0.260403 1.47682i −0.781813 0.623513i \(-0.785705\pi\)
0.521409 0.853307i \(-0.325406\pi\)
\(492\) −3.62257 + 1.68923i −0.163318 + 0.0761565i
\(493\) 12.4981 12.4981i 0.562886 0.562886i
\(494\) −0.858144 1.50702i −0.0386097 0.0678039i
\(495\) 0 0
\(496\) −1.29585 + 3.56031i −0.0581852 + 0.159863i
\(497\) −18.4759 + 26.3863i −0.828756 + 1.18359i
\(498\) 0.377040 + 4.30959i 0.0168956 + 0.193117i
\(499\) 0.189710 + 0.226087i 0.00849258 + 0.0101211i 0.770274 0.637713i \(-0.220119\pi\)
−0.761781 + 0.647834i \(0.775675\pi\)
\(500\) 0 0
\(501\) 12.6904 21.9804i 0.566965 0.982012i
\(502\) −1.68800 + 6.29969i −0.0753390 + 0.281169i
\(503\) −31.4925 14.6852i −1.40418 0.654781i −0.434843 0.900506i \(-0.643196\pi\)
−0.969340 + 0.245725i \(0.920974\pi\)
\(504\) 7.05134 2.56648i 0.314092 0.114320i
\(505\) 0 0
\(506\) 6.70294 + 3.86995i 0.297982 + 0.172040i
\(507\) −23.6399 + 16.5529i −1.04989 + 0.735138i
\(508\) 0.448260 5.12364i 0.0198883 0.227325i
\(509\) −7.54692 6.33262i −0.334512 0.280689i 0.460024 0.887907i \(-0.347841\pi\)
−0.794535 + 0.607218i \(0.792285\pi\)
\(510\) 0 0
\(511\) −36.3971 13.2474i −1.61011 0.586032i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 6.53883 + 6.61723i 0.288696 + 0.292158i
\(514\) 15.4695i 0.682331i
\(515\) 0 0
\(516\) 1.86835 0.329441i 0.0822497 0.0145028i
\(517\) 8.67589 0.759042i 0.381565 0.0333826i
\(518\) 40.7733 + 3.56720i 1.79147 + 0.156734i
\(519\) −48.0146 8.46626i −2.10761 0.371628i
\(520\) 0 0
\(521\) 22.9420 13.2456i 1.00511 0.580300i 0.0953526 0.995444i \(-0.469602\pi\)
0.909756 + 0.415144i \(0.136269\pi\)
\(522\) 4.20949 9.02729i 0.184244 0.395114i
\(523\) −13.7727 + 29.5357i −0.602239 + 1.29151i 0.334803 + 0.942288i \(0.391330\pi\)
−0.937042 + 0.349218i \(0.886447\pi\)
\(524\) −6.85177 + 3.95587i −0.299321 + 0.172813i
\(525\) 0 0
\(526\) −19.6438 3.46373i −0.856510 0.151026i
\(527\) 13.7323 + 1.20142i 0.598187 + 0.0523346i
\(528\) 4.55716 0.398700i 0.198325 0.0173512i
\(529\) 8.41290 1.48342i 0.365778 0.0644966i
\(530\) 0 0
\(531\) 11.3433i 0.492257i
\(532\) −13.1223 + 9.07225i −0.568922 + 0.393332i
\(533\) 0.500373 + 0.500373i 0.0216736 + 0.0216736i
\(534\) 24.2942 + 8.84238i 1.05131 + 0.382647i
\(535\) 0 0
\(536\) 11.0736 + 9.29189i 0.478308 + 0.401348i
\(537\) 4.33346 49.5316i 0.187003 2.13745i
\(538\) −13.1328 + 9.19570i −0.566196 + 0.396455i
\(539\) 11.2731 + 6.50852i 0.485566 + 0.280342i
\(540\) 0 0
\(541\) −13.6337 + 4.96227i −0.586160 + 0.213345i −0.618039 0.786147i \(-0.712073\pi\)
0.0318799 + 0.999492i \(0.489851\pi\)
\(542\) −0.505268 0.235610i −0.0217031 0.0101203i
\(543\) −7.86185 + 29.3408i −0.337384 + 1.25914i
\(544\) −1.81914 + 3.15085i −0.0779950 + 0.135091i
\(545\) 0 0
\(546\) −2.10339 2.50672i −0.0900169 0.107278i
\(547\) −0.899184 10.2777i −0.0384463 0.439444i −0.990885 0.134712i \(-0.956989\pi\)
0.952438 0.304731i \(-0.0985666\pi\)
\(548\) −0.0372108 + 0.0531425i −0.00158957 + 0.00227014i
\(549\) 6.46856 17.7722i 0.276072 0.758501i
\(550\) 0 0
\(551\) −3.80134 + 20.8318i −0.161943 + 0.887463i
\(552\) −6.04210 + 6.04210i −0.257169 + 0.257169i
\(553\) 15.5414 7.24707i 0.660887 0.308177i
\(554\) −4.22351 23.9527i −0.179440 1.01765i
\(555\) 0 0
\(556\) −13.3218 + 11.1784i −0.564972 + 0.474068i
\(557\) 21.4053 + 30.5699i 0.906970 + 1.29529i 0.955050 + 0.296444i \(0.0958009\pi\)
−0.0480799 + 0.998843i \(0.515310\pi\)
\(558\) 7.50352 2.01056i 0.317649 0.0851139i
\(559\) −0.167937 0.290875i −0.00710296 0.0123027i
\(560\) 0 0
\(561\) −5.69244 15.6398i −0.240335 0.660315i
\(562\) −25.1020 6.72605i −1.05886 0.283721i
\(563\) 2.49018 + 9.29350i 0.104949 + 0.391674i 0.998339 0.0576067i \(-0.0183469\pi\)
−0.893391 + 0.449281i \(0.851680\pi\)
\(564\) −1.66958 + 9.46867i −0.0703021 + 0.398703i
\(565\) 0 0
\(566\) −16.1894 + 19.2938i −0.680491 + 0.810978i
\(567\) 32.8196 + 22.9805i 1.37829 + 0.965090i
\(568\) −3.71959 7.97669i −0.156071 0.334694i
\(569\) −19.0127 −0.797055 −0.398527 0.917156i \(-0.630479\pi\)
−0.398527 + 0.917156i \(0.630479\pi\)
\(570\) 0 0
\(571\) 0.873418 0.0365514 0.0182757 0.999833i \(-0.494182\pi\)
0.0182757 + 0.999833i \(0.494182\pi\)
\(572\) −0.342268 0.733996i −0.0143109 0.0306899i
\(573\) 26.2571 + 18.3854i 1.09691 + 0.768063i
\(574\) 4.18424 4.98658i 0.174647 0.208136i
\(575\) 0 0
\(576\) −0.356032 + 2.01916i −0.0148347 + 0.0841316i
\(577\) −2.00055 7.46617i −0.0832841 0.310821i 0.911700 0.410857i \(-0.134771\pi\)
−0.994984 + 0.100037i \(0.968104\pi\)
\(578\) −3.63468 0.973910i −0.151183 0.0405093i
\(579\) 3.84010 + 10.5506i 0.159589 + 0.438467i
\(580\) 0 0
\(581\) −3.52265 6.10141i −0.146144 0.253129i
\(582\) −19.2510 + 5.15828i −0.797979 + 0.213818i
\(583\) 13.1756 + 18.8167i 0.545679 + 0.779310i
\(584\) 8.10714 6.80270i 0.335476 0.281498i
\(585\) 0 0
\(586\) −2.82219 16.0055i −0.116584 0.661179i
\(587\) −31.1379 + 14.5198i −1.28520 + 0.599297i −0.940620 0.339461i \(-0.889755\pi\)
−0.344577 + 0.938758i \(0.611978\pi\)
\(588\) −10.1617 + 10.1617i −0.419060 + 0.419060i
\(589\) −14.3514 + 8.17213i −0.591338 + 0.336727i
\(590\) 0 0
\(591\) 7.61556 20.9236i 0.313262 0.860681i
\(592\) −6.41440 + 9.16071i −0.263630 + 0.376503i
\(593\) −0.638147 7.29405i −0.0262055 0.299531i −0.997975 0.0636002i \(-0.979742\pi\)
0.971770 0.235931i \(-0.0758138\pi\)
\(594\) 2.79255 + 3.32803i 0.114580 + 0.136551i
\(595\) 0 0
\(596\) 7.86860 13.6288i 0.322310 0.558258i
\(597\) 5.84258 21.8048i 0.239121 0.892411i
\(598\) 1.37103 + 0.639321i 0.0560655 + 0.0261438i
\(599\) 0.0335506 0.0122114i 0.00137084 0.000498945i −0.341335 0.939942i \(-0.610879\pi\)
0.342705 + 0.939443i \(0.388657\pi\)
\(600\) 0 0
\(601\) 27.8767 + 16.0946i 1.13711 + 0.656512i 0.945714 0.325000i \(-0.105364\pi\)
0.191399 + 0.981512i \(0.438698\pi\)
\(602\) −2.53093 + 1.77218i −0.103153 + 0.0722285i
\(603\) 2.58316 29.5257i 0.105194 1.20238i
\(604\) −6.98972 5.86508i −0.284408 0.238647i
\(605\) 0 0
\(606\) 13.7111 + 4.99042i 0.556974 + 0.202722i
\(607\) −18.1942 18.1942i −0.738478 0.738478i 0.233806 0.972283i \(-0.424882\pi\)
−0.972283 + 0.233806i \(0.924882\pi\)
\(608\) −0.354019 4.34450i −0.0143574 0.176193i
\(609\) 39.9566i 1.61912i
\(610\) 0 0
\(611\) 1.67632 0.295581i 0.0678167 0.0119579i
\(612\) 7.43121 0.650147i 0.300389 0.0262806i
\(613\) −47.8974 4.19048i −1.93456 0.169252i −0.946433 0.322899i \(-0.895342\pi\)
−0.988126 + 0.153647i \(0.950898\pi\)
\(614\) −23.1491 4.08182i −0.934223 0.164729i
\(615\) 0 0
\(616\) −6.45191 + 3.72501i −0.259955 + 0.150085i
\(617\) 13.5042 28.9599i 0.543659 1.16588i −0.422126 0.906537i \(-0.638716\pi\)
0.965785 0.259343i \(-0.0835061\pi\)
\(618\) 15.3552 32.9294i 0.617677 1.32461i
\(619\) −6.33757 + 3.65900i −0.254728 + 0.147067i −0.621927 0.783075i \(-0.713650\pi\)
0.367199 + 0.930142i \(0.380317\pi\)
\(620\) 0 0
\(621\) −7.99166 1.40915i −0.320694 0.0565470i
\(622\) −11.6337 1.01781i −0.466467 0.0408106i
\(623\) −41.9440 + 3.66962i −1.68045 + 0.147020i
\(624\) 0.880516 0.155259i 0.0352489 0.00621533i
\(625\) 0 0
\(626\) 4.84712i 0.193730i
\(627\) 16.2655 + 11.5343i 0.649582 + 0.460635i
\(628\) −12.1386 12.1386i −0.484384 0.484384i
\(629\) 38.2337 + 13.9159i 1.52448 + 0.554865i
\(630\) 0 0
\(631\) −3.97788 3.33784i −0.158357 0.132877i 0.560166 0.828380i \(-0.310737\pi\)
−0.718523 + 0.695503i \(0.755182\pi\)
\(632\) −0.408360 + 4.66758i −0.0162437 + 0.185666i
\(633\) −30.3104 + 21.2236i −1.20473 + 0.843562i
\(634\) 24.9147 + 14.3845i 0.989490 + 0.571282i
\(635\) 0 0
\(636\) −23.8305 + 8.67360i −0.944942 + 0.343931i
\(637\) 2.30581 + 1.07522i 0.0913596 + 0.0426017i
\(638\) −2.55947 + 9.55206i −0.101330 + 0.378170i
\(639\) −9.02269 + 15.6278i −0.356932 + 0.618224i
\(640\) 0 0
\(641\) 7.52712 + 8.97047i 0.297303 + 0.354312i 0.893930 0.448207i \(-0.147937\pi\)
−0.596627 + 0.802519i \(0.703493\pi\)
\(642\) −2.49522 28.5205i −0.0984786 1.12562i
\(643\) 1.15385 1.64787i 0.0455035 0.0649858i −0.795756 0.605618i \(-0.792926\pi\)
0.841259 + 0.540632i \(0.181815\pi\)
\(644\) 4.75951 13.0766i 0.187551 0.515292i
\(645\) 0 0
\(646\) −14.9346 + 5.33516i −0.587592 + 0.209909i
\(647\) −19.1316 + 19.1316i −0.752140 + 0.752140i −0.974878 0.222739i \(-0.928500\pi\)
0.222739 + 0.974878i \(0.428500\pi\)
\(648\) −9.92150 + 4.62647i −0.389753 + 0.181745i
\(649\) 1.95560 + 11.0908i 0.0767642 + 0.435351i
\(650\) 0 0
\(651\) −23.8716 + 20.0307i −0.935602 + 0.785063i
\(652\) 9.24680 + 13.2058i 0.362133 + 0.517179i
\(653\) 5.77046 1.54619i 0.225816 0.0605071i −0.144137 0.989558i \(-0.546041\pi\)
0.369953 + 0.929051i \(0.379374\pi\)
\(654\) 11.2883 + 19.5519i 0.441408 + 0.764541i
\(655\) 0 0
\(656\) 0.608323 + 1.67135i 0.0237510 + 0.0652554i
\(657\) −20.9593 5.61602i −0.817700 0.219102i
\(658\) −4.05268 15.1248i −0.157990 0.589626i
\(659\) 2.71452 15.3948i 0.105743 0.599697i −0.885178 0.465252i \(-0.845964\pi\)
0.990921 0.134445i \(-0.0429252\pi\)
\(660\) 0 0
\(661\) −0.941384 + 1.12190i −0.0366156 + 0.0436368i −0.784041 0.620708i \(-0.786845\pi\)
0.747426 + 0.664345i \(0.231290\pi\)
\(662\) 15.4744 + 10.8353i 0.601431 + 0.421126i
\(663\) −1.37477 2.94821i −0.0533917 0.114499i
\(664\) 1.92501 0.0747048
\(665\) 0 0
\(666\) 22.9289 0.888478
\(667\) −7.80647 16.7410i −0.302268 0.648215i
\(668\) −9.25147 6.47795i −0.357950 0.250639i
\(669\) −29.2149 + 34.8169i −1.12951 + 1.34610i
\(670\) 0 0
\(671\) −3.26061 + 18.4918i −0.125874 + 0.713869i
\(672\) −2.12874 7.94455i −0.0821178 0.306468i
\(673\) 22.5231 + 6.03504i 0.868201 + 0.232634i 0.665310 0.746567i \(-0.268300\pi\)
0.202891 + 0.979201i \(0.434966\pi\)
\(674\) −1.66143 4.56475i −0.0639961 0.175828i
\(675\) 0 0
\(676\) 6.42085 + 11.1212i 0.246956 + 0.427740i
\(677\) −19.4948 + 5.22361i −0.749245 + 0.200760i −0.613183 0.789941i \(-0.710111\pi\)
−0.136062 + 0.990700i \(0.543445\pi\)
\(678\) −21.0780 30.1025i −0.809494 1.15608i
\(679\) 24.8640 20.8634i 0.954192 0.800663i
\(680\) 0 0
\(681\) 9.37223 + 53.1526i 0.359145 + 2.03681i
\(682\) −6.98987 + 3.25943i −0.267656 + 0.124810i
\(683\) −8.02116 + 8.02116i −0.306921 + 0.306921i −0.843714 0.536793i \(-0.819636\pi\)
0.536793 + 0.843714i \(0.319636\pi\)
\(684\) −6.88032 + 5.70375i −0.263076 + 0.218088i
\(685\) 0 0
\(686\) −0.757665 + 2.08167i −0.0289278 + 0.0794784i
\(687\) 10.5764 15.1047i 0.403515 0.576279i
\(688\) −0.0735774 0.840994i −0.00280511 0.0320626i
\(689\) 2.88591 + 3.43930i 0.109945 + 0.131027i
\(690\) 0 0
\(691\) −6.21068 + 10.7572i −0.236265 + 0.409223i −0.959640 0.281233i \(-0.909257\pi\)
0.723374 + 0.690456i \(0.242590\pi\)
\(692\) −5.61512 + 20.9559i −0.213455 + 0.796624i
\(693\) 13.8437 + 6.45543i 0.525879 + 0.245222i
\(694\) 22.1697 8.06912i 0.841551 0.306300i
\(695\) 0 0
\(696\) −9.45479 5.45873i −0.358383 0.206912i
\(697\) 5.30082 3.71168i 0.200783 0.140590i
\(698\) −2.79102 + 31.9015i −0.105642 + 1.20749i
\(699\) 17.1608 + 14.3996i 0.649081 + 0.544644i
\(700\) 0 0
\(701\) −19.8105 7.21044i −0.748233 0.272334i −0.0603709 0.998176i \(-0.519228\pi\)
−0.687862 + 0.725842i \(0.741451\pi\)
\(702\) 0.600418 + 0.600418i 0.0226613 + 0.0226613i
\(703\) −47.1596 + 12.3356i −1.77866 + 0.465248i
\(704\) 2.03559i 0.0767193i
\(705\) 0 0
\(706\) 5.44507 0.960113i 0.204928 0.0361343i
\(707\) −23.6721 + 2.07104i −0.890282 + 0.0778896i
\(708\) −12.3858 1.08361i −0.465486 0.0407247i
\(709\) −11.4026 2.01058i −0.428232 0.0755088i −0.0446217 0.999004i \(-0.514208\pi\)
−0.383610 + 0.923495i \(0.625319\pi\)
\(710\) 0 0
\(711\) 8.31950 4.80326i 0.312006 0.180137i
\(712\) 4.86191 10.4264i 0.182208 0.390746i
\(713\) 6.08827 13.0563i 0.228008 0.488964i
\(714\) −25.9151 + 14.9621i −0.969848 + 0.559942i
\(715\) 0 0
\(716\) −21.7887 3.84193i −0.814281 0.143580i
\(717\) 23.7141 + 2.07472i 0.885621 + 0.0774818i
\(718\) 27.6301 2.41732i 1.03115 0.0902137i
\(719\) −27.0863 + 4.77604i −1.01015 + 0.178116i −0.654145 0.756369i \(-0.726972\pi\)
−0.356002 + 0.934485i \(0.615860\pi\)
\(720\) 0 0
\(721\) 59.1719i 2.20368i
\(722\) 11.0827 15.4329i 0.412454 0.574353i
\(723\) 9.66151 + 9.66151i 0.359315 + 0.359315i
\(724\) 12.7015 + 4.62297i 0.472048 + 0.171811i
\(725\) 0 0
\(726\) −11.8034 9.90421i −0.438065 0.367580i
\(727\) −0.752266 + 8.59844i −0.0279000 + 0.318899i 0.969401 + 0.245481i \(0.0789460\pi\)
−0.997301 + 0.0734172i \(0.976610\pi\)
\(728\) −1.19277 + 0.835190i −0.0442072 + 0.0309542i
\(729\) 6.97700 + 4.02817i 0.258407 + 0.149192i
\(730\) 0 0
\(731\) −2.88623 + 1.05050i −0.106751 + 0.0388542i
\(732\) −18.7876 8.76081i −0.694410 0.323809i
\(733\) 2.61866 9.77299i 0.0967226 0.360974i −0.900552 0.434747i \(-0.856838\pi\)
0.997275 + 0.0737739i \(0.0235043\pi\)
\(734\) −4.41509 + 7.64715i −0.162964 + 0.282262i
\(735\) 0 0
\(736\) 2.44406 + 2.91271i 0.0900891 + 0.107364i
\(737\) 2.56462 + 29.3138i 0.0944691 + 1.07979i
\(738\) 2.09167 2.98721i 0.0769954 0.109961i
\(739\) −5.21626 + 14.3316i −0.191883 + 0.527195i −0.997905 0.0646905i \(-0.979394\pi\)
0.806022 + 0.591885i \(0.201616\pi\)
\(740\) 0 0
\(741\) 3.36348 + 1.96872i 0.123561 + 0.0723229i
\(742\) 29.2039 29.2039i 1.07211 1.07211i
\(743\) 12.9587 6.04272i 0.475407 0.221686i −0.170120 0.985423i \(-0.554416\pi\)
0.645527 + 0.763737i \(0.276638\pi\)
\(744\) −1.47853 8.38518i −0.0542057 0.307416i
\(745\) 0 0
\(746\) −6.44325 + 5.40653i −0.235904 + 0.197947i
\(747\) −2.26383 3.23308i −0.0828290 0.118292i
\(748\) −7.15371 + 1.91683i −0.261566 + 0.0700863i
\(749\) 23.3126 + 40.3786i 0.851824 + 1.47540i
\(750\) 0 0
\(751\) −0.373454 1.02606i −0.0136275 0.0374414i 0.932692 0.360673i \(-0.117453\pi\)
−0.946320 + 0.323232i \(0.895231\pi\)
\(752\) 4.13259 + 1.10732i 0.150700 + 0.0403800i
\(753\) −3.79342 14.1572i −0.138240 0.515918i
\(754\) −0.335629 + 1.90345i −0.0122229 + 0.0693194i
\(755\) 0 0
\(756\) 5.02083 5.98360i 0.182606 0.217621i
\(757\) 15.3020 + 10.7146i 0.556160 + 0.389428i 0.817595 0.575793i \(-0.195307\pi\)
−0.261435 + 0.965221i \(0.584196\pi\)
\(758\) 15.6553 + 33.5728i 0.568625 + 1.21942i
\(759\) −17.3938 −0.631354
\(760\) 0 0
\(761\) 33.7464 1.22330 0.611652 0.791127i \(-0.290505\pi\)
0.611652 + 0.791127i \(0.290505\pi\)
\(762\) 4.88474 + 10.4754i 0.176955 + 0.379482i
\(763\) −30.1184 21.0891i −1.09036 0.763477i
\(764\) 9.16835 10.9264i 0.331699 0.395304i
\(765\) 0 0
\(766\) −4.62401 + 26.2241i −0.167072 + 0.947514i
\(767\) 0.569696 + 2.12613i 0.0205705 + 0.0767702i
\(768\) 2.17071 + 0.581641i 0.0783289 + 0.0209882i
\(769\) −10.2512 28.1649i −0.369667 1.01565i −0.975488 0.220051i \(-0.929377\pi\)
0.605821 0.795601i \(-0.292845\pi\)
\(770\) 0 0
\(771\) 17.3822 + 30.1069i 0.626006 + 1.08427i
\(772\) 4.82587 1.29309i 0.173687 0.0465392i
\(773\) −8.28226 11.8283i −0.297892 0.425434i 0.642105 0.766617i \(-0.278061\pi\)
−0.939997 + 0.341183i \(0.889172\pi\)
\(774\) −1.32593 + 1.11259i −0.0476597 + 0.0399912i
\(775\) 0 0
\(776\) 1.54000 + 8.73377i 0.0552827 + 0.313524i
\(777\) −83.3616 + 38.8721i −2.99058 + 1.39453i
\(778\) −21.4104 + 21.4104i −0.767602 + 0.767602i
\(779\) −2.69498 + 7.26933i −0.0965578 + 0.260451i
\(780\) 0 0
\(781\) 6.12759 16.8354i 0.219262 0.602418i
\(782\) 7.93472 11.3320i 0.283745 0.405230i
\(783\) −0.903649 10.3288i −0.0322938 0.369120i
\(784\) 4.11044 + 4.89864i 0.146802 + 0.174951i
\(785\) 0 0
\(786\) 8.88998 15.3979i 0.317095 0.549225i
\(787\) 5.87046 21.9089i 0.209259 0.780967i −0.778849 0.627211i \(-0.784196\pi\)
0.988109 0.153756i \(-0.0491369\pi\)
\(788\) −8.97980 4.18735i −0.319892 0.149168i
\(789\) 42.1229 15.3315i 1.49962 0.545816i
\(790\) 0 0
\(791\) 51.8294 + 29.9237i 1.84284 + 1.06396i
\(792\) −3.41881 + 2.39388i −0.121482 + 0.0850627i
\(793\) −0.319860 + 3.65602i −0.0113586 + 0.129829i
\(794\) −10.9125 9.15665i −0.387269 0.324957i
\(795\) 0 0
\(796\) −9.43920 3.43559i −0.334564 0.121771i
\(797\) 37.2856 + 37.2856i 1.32072 + 1.32072i 0.913190 + 0.407534i \(0.133611\pi\)
0.407534 + 0.913190i \(0.366389\pi\)
\(798\) 15.3447 32.4013i 0.543196 1.14699i
\(799\) 15.5659i 0.550683i
\(800\) 0 0
\(801\) −23.2289 + 4.09589i −0.820754 + 0.144721i
\(802\) −7.49131 + 0.655405i −0.264527 + 0.0231431i
\(803\) 21.4610 + 1.87759i 0.757341 + 0.0662587i
\(804\) −31.9924 5.64112i −1.12828 0.198947i
\(805\) 0 0
\(806\) −1.30545 + 0.753701i −0.0459825 + 0.0265480i
\(807\) 15.2265 32.6534i 0.535999 1.14945i
\(808\) 2.74394 5.88440i 0.0965315 0.207012i
\(809\) 32.1500 18.5618i 1.13033 0.652598i 0.186314 0.982490i \(-0.440346\pi\)
0.944019 + 0.329892i \(0.107012\pi\)
\(810\) 0 0
\(811\) −33.1066 5.83759i −1.16253 0.204985i −0.441090 0.897463i \(-0.645408\pi\)
−0.721440 + 0.692477i \(0.756519\pi\)
\(812\) 17.7122 + 1.54962i 0.621577 + 0.0543810i
\(813\) 1.24810 0.109195i 0.0437728 0.00382962i
\(814\) −22.4185 + 3.95299i −0.785769 + 0.138552i
\(815\) 0 0
\(816\) 8.17627i 0.286227i
\(817\) 2.12858 3.00169i 0.0744695 0.105016i
\(818\) −6.95285 6.95285i −0.243101 0.243101i
\(819\) 2.80543 + 1.02109i 0.0980295 + 0.0356798i
\(820\) 0 0
\(821\) −36.4020 30.5449i −1.27044 1.06602i −0.994488 0.104852i \(-0.966563\pi\)
−0.275950 0.961172i \(-0.588992\pi\)
\(822\) 0.0127067 0.145238i 0.000443197 0.00506576i
\(823\) 44.5572 31.1993i 1.55317 1.08754i 0.594086 0.804402i \(-0.297514\pi\)
0.959080 0.283137i \(-0.0913750\pi\)
\(824\) −14.0016 8.08385i −0.487771 0.281614i
\(825\) 0 0
\(826\) 19.0271 6.92529i 0.662037 0.240962i
\(827\) −36.4111 16.9788i −1.26614 0.590410i −0.330646 0.943755i \(-0.607267\pi\)
−0.935493 + 0.353345i \(0.885044\pi\)
\(828\) 2.01771 7.53021i 0.0701204 0.261693i
\(829\) 1.42975 2.47640i 0.0496573 0.0860089i −0.840128 0.542388i \(-0.817520\pi\)
0.889786 + 0.456379i \(0.150854\pi\)
\(830\) 0 0
\(831\) 35.1342 + 41.8713i 1.21879 + 1.45250i
\(832\) −0.0346755 0.396343i −0.00120216 0.0137407i
\(833\) 13.3447 19.0582i 0.462367 0.660328i
\(834\) 13.3666 36.7244i 0.462847 1.27166i
\(835\) 0 0
\(836\) 5.74383 6.76296i 0.198654 0.233902i
\(837\) 5.71780 5.71780i 0.197636 0.197636i
\(838\) −20.5592 + 9.58691i −0.710206 + 0.331174i
\(839\) −5.21072 29.5514i −0.179894 1.02023i −0.932342 0.361578i \(-0.882238\pi\)
0.752448 0.658652i \(-0.228873\pi\)
\(840\) 0 0
\(841\) −4.13612 + 3.47061i −0.142625 + 0.119676i
\(842\) 9.17202 + 13.0990i 0.316089 + 0.451421i
\(843\) 56.4113 15.1154i 1.94291 0.520601i
\(844\) 8.23263 + 14.2593i 0.283379 + 0.490827i
\(845\) 0 0
\(846\) −3.00020 8.24297i −0.103149 0.283399i
\(847\) 24.2384 + 6.49466i 0.832841 + 0.223159i
\(848\) 2.92069 + 10.9002i 0.100297 + 0.374313i
\(849\) 9.82862 55.7408i 0.337317 1.91302i
\(850\) 0 0
\(851\) 27.3323 32.5733i 0.936939 1.11660i
\(852\) 16.2021 + 11.3448i 0.555073 + 0.388667i
\(853\) −15.0441 32.2621i −0.515100 1.10463i −0.976117 0.217244i \(-0.930293\pi\)
0.461018 0.887391i \(-0.347484\pi\)
\(854\) 33.7601 1.15525
\(855\) 0 0
\(856\) −12.7396 −0.435429
\(857\) −3.36904 7.22494i −0.115084 0.246799i 0.840325 0.542082i \(-0.182364\pi\)
−0.955410 + 0.295283i \(0.904586\pi\)
\(858\) 1.49088 + 1.04392i 0.0508977 + 0.0356389i
\(859\) 3.63063 4.32681i 0.123875 0.147629i −0.700542 0.713611i \(-0.747058\pi\)
0.824418 + 0.565982i \(0.191503\pi\)
\(860\) 0 0
\(861\) −2.54026 + 14.4065i −0.0865718 + 0.490973i
\(862\) −2.93199 10.9423i −0.0998640 0.372698i
\(863\) 3.20720 + 0.859366i 0.109174 + 0.0292532i 0.312993 0.949756i \(-0.398669\pi\)
−0.203818 + 0.979009i \(0.565335\pi\)
\(864\) 0.729950 + 2.00552i 0.0248334 + 0.0682292i
\(865\) 0 0
\(866\) −0.131979 0.228594i −0.00448483 0.00776795i
\(867\) 8.16818 2.18866i 0.277406 0.0743307i
\(868\) 7.95353 + 11.3588i 0.269960 + 0.385544i
\(869\) −7.30621 + 6.13064i −0.247846 + 0.207968i
\(870\) 0 0
\(871\) 0.998697 + 5.66389i 0.0338395 + 0.191914i
\(872\) 9.10491 4.24569i 0.308331 0.143777i
\(873\) 12.8574 12.8574i 0.435158 0.435158i
\(874\) −0.0987673 + 16.5735i −0.00334085 + 0.560605i
\(875\) 0 0
\(876\) −8.13438 + 22.3490i −0.274835 + 0.755103i
\(877\) −3.89826 + 5.56729i −0.131635 + 0.187994i −0.879559 0.475791i \(-0.842162\pi\)
0.747924 + 0.663785i \(0.231051\pi\)
\(878\) −1.22224 13.9703i −0.0412486 0.471474i
\(879\) 23.4770 + 27.9788i 0.791860 + 0.943702i
\(880\) 0 0
\(881\) −17.0976 + 29.6140i −0.576034 + 0.997720i 0.419895 + 0.907573i \(0.362067\pi\)
−0.995928 + 0.0901468i \(0.971266\pi\)
\(882\) 3.39341 12.6644i 0.114262 0.426432i
\(883\) 49.4000 + 23.0356i 1.66244 + 0.775210i 0.999651 + 0.0264069i \(0.00840654\pi\)
0.662792 + 0.748803i \(0.269371\pi\)
\(884\) −1.36022 + 0.495080i −0.0457492 + 0.0166513i
\(885\) 0 0
\(886\) −21.8065 12.5900i −0.732604 0.422969i
\(887\) −33.3094 + 23.3235i −1.11842 + 0.783127i −0.978338 0.207013i \(-0.933626\pi\)
−0.140083 + 0.990140i \(0.544737\pi\)
\(888\) 2.19038 25.0362i 0.0735043 0.840159i
\(889\) −14.4197 12.0995i −0.483620 0.405805i
\(890\) 0 0
\(891\) −20.9401 7.62157i −0.701519 0.255332i
\(892\) 14.3009 + 14.3009i 0.478829 + 0.478829i
\(893\) 10.6054 + 15.3398i 0.354896 + 0.513328i
\(894\) 35.3660i 1.18282i
\(895\) 0 0
\(896\) −3.60428 + 0.635531i −0.120410 + 0.0212316i
\(897\) −3.38668 + 0.296296i −0.113078 + 0.00989304i
\(898\) 17.6495 + 1.54413i 0.588972 + 0.0515283i
\(899\) 18.1266 + 3.19620i 0.604555 + 0.106599i
\(900\) 0 0
\(901\) 35.5562 20.5284i 1.18455 0.683900i
\(902\) −1.53011 + 3.28132i −0.0509470 + 0.109256i
\(903\) 2.93442 6.29289i 0.0976514 0.209414i
\(904\) −14.1615 + 8.17614i −0.471004 + 0.271934i
\(905\) 0 0
\(906\) 20.1937 + 3.56070i 0.670892 + 0.118296i
\(907\) −38.0915 3.33257i −1.26481 0.110656i −0.565062 0.825048i \(-0.691148\pi\)
−0.699746 + 0.714392i \(0.746703\pi\)
\(908\) 23.9253 2.09320i 0.793990 0.0694652i
\(909\) −13.1098 + 2.31162i −0.434826 + 0.0766715i
\(910\) 0 0
\(911\) 10.9349i 0.362288i −0.983457 0.181144i \(-0.942020\pi\)
0.983457 0.181144i \(-0.0579801\pi\)
\(912\) 5.57067 + 8.05751i 0.184463 + 0.266811i
\(913\) 2.77082 + 2.77082i 0.0917008 + 0.0917008i
\(914\) 29.3574 + 10.6852i 0.971056 + 0.353436i
\(915\) 0 0
\(916\) −6.28553 5.27418i −0.207680 0.174264i
\(917\) −2.52368 + 28.8458i −0.0833393 + 0.952573i
\(918\) 6.36067 4.45379i 0.209933 0.146997i
\(919\) 41.8138 + 24.1412i 1.37931 + 0.796345i 0.992076 0.125636i \(-0.0400972\pi\)
0.387234 + 0.921981i \(0.373431\pi\)
\(920\) 0 0
\(921\) 49.6396 18.0673i 1.63568 0.595339i
\(922\) 9.47616 + 4.41881i 0.312081 + 0.145526i
\(923\) 0.906296 3.38234i 0.0298311 0.111331i
\(924\) 8.37118 14.4993i 0.275392 0.476992i
\(925\) 0 0
\(926\) −15.0371 17.9205i −0.494150 0.588905i
\(927\) 2.88911 + 33.0226i 0.0948907 + 1.08461i
\(928\) −2.78647 + 3.97948i −0.0914702 + 0.130633i
\(929\) 2.79049 7.66681i 0.0915530 0.251540i −0.885461 0.464713i \(-0.846158\pi\)
0.977014 + 0.213173i \(0.0683798\pi\)
\(930\) 0 0
\(931\) −0.166108 + 27.8734i −0.00544397 + 0.913515i
\(932\) 7.04871 7.04871i 0.230888 0.230888i
\(933\) 23.7852 11.0912i 0.778692 0.363110i
\(934\) 4.55985 + 25.8602i 0.149203 + 0.846171i
\(935\) 0 0
\(936\) −0.624885 + 0.524341i −0.0204250 + 0.0171386i
\(937\) 4.79704 + 6.85088i 0.156712 + 0.223809i 0.889829 0.456295i \(-0.150824\pi\)
−0.733116 + 0.680103i \(0.761935\pi\)
\(938\) 51.1031 13.6930i 1.66857 0.447093i
\(939\) 5.44644 + 9.43350i 0.177738 + 0.307851i
\(940\) 0 0
\(941\) 9.65059 + 26.5148i 0.314600 + 0.864357i 0.991712 + 0.128477i \(0.0410089\pi\)
−0.677112 + 0.735880i \(0.736769\pi\)
\(942\) 37.2639 + 9.98482i 1.21412 + 0.325323i
\(943\) −1.75034 6.53236i −0.0569989 0.212723i
\(944\) −0.960705 + 5.44843i −0.0312683 + 0.177331i
\(945\) 0 0
\(946\) 1.10461 1.31642i 0.0359138 0.0428004i
\(947\) −11.1199 7.78627i −0.361350 0.253020i 0.378776 0.925488i \(-0.376345\pi\)
−0.740126 + 0.672469i \(0.765234\pi\)
\(948\) −4.44994 9.54294i −0.144527 0.309940i
\(949\) 4.21057 0.136681
\(950\) 0 0
\(951\) −64.6523 −2.09650
\(952\) 5.62745 + 12.0681i 0.182387 + 0.391129i
\(953\) 14.4384 + 10.1098i 0.467704 + 0.327490i 0.783559 0.621318i \(-0.213402\pi\)
−0.315855 + 0.948808i \(0.602291\pi\)
\(954\) 14.8722 17.7240i 0.481506 0.573836i
\(955\) 0 0
\(956\) 1.83939 10.4317i 0.0594902 0.337386i
\(957\) −5.75186 21.4662i −0.185931 0.693905i
\(958\) −16.0744 4.30712i −0.519341 0.139157i
\(959\) 0.0812075 + 0.223116i 0.00262233 + 0.00720478i
\(960\) 0 0
\(961\) −8.32249 14.4150i −0.268467 0.464999i
\(962\) −4.29769 + 1.15156i −0.138563 + 0.0371279i
\(963\) 14.9818 + 21.3963i 0.482783 + 0.689485i
\(964\) 4.65752 3.90812i 0.150009 0.125872i
\(965\) 0 0
\(966\) 5.43050 + 30.7979i 0.174723 + 0.990906i
\(967\) −21.6762 + 10.1078i −0.697059 + 0.325044i −0.738648 0.674091i \(-0.764536\pi\)
0.0415896 + 0.999135i \(0.486758\pi\)
\(968\) −4.84818 + 4.84818i −0.155826 + 0.155826i
\(969\) 23.0709 27.1645i 0.741146 0.872649i
\(970\) 0 0
\(971\) 1.15941 3.18546i 0.0372073 0.102226i −0.919698 0.392627i \(-0.871566\pi\)
0.956905 + 0.290401i \(0.0937886\pi\)
\(972\) 10.4384 14.9075i 0.334811 0.478159i
\(973\) 5.54719 + 63.4047i 0.177835 + 2.03266i
\(974\) 2.61666 + 3.11841i 0.0838431 + 0.0999203i
\(975\) 0 0
\(976\) −4.61219 + 7.98855i −0.147633 + 0.255707i
\(977\) 7.39660 27.6045i 0.236638 0.883146i −0.740765 0.671764i \(-0.765537\pi\)
0.977404 0.211382i \(-0.0677963\pi\)
\(978\) −32.8348 15.3111i −1.04994 0.489596i
\(979\) 22.0057 8.00942i 0.703306 0.255982i
\(980\) 0 0
\(981\) −17.8382 10.2989i −0.569528 0.328817i
\(982\) 27.2196 19.0594i 0.868612 0.608208i
\(983\) −2.03577 + 23.2689i −0.0649309 + 0.742164i 0.892036 + 0.451965i \(0.149277\pi\)
−0.956966 + 0.290198i \(0.906279\pi\)
\(984\) −3.06193 2.56926i −0.0976107 0.0819051i
\(985\) 0 0
\(986\) 16.6090 + 6.04520i 0.528940 + 0.192518i
\(987\) 24.8822 + 24.8822i 0.792010 + 0.792010i
\(988\) 1.00315 1.41464i 0.0319146 0.0450056i
\(989\) 3.20991i 0.102069i
\(990\) 0 0
\(991\) 27.9141 4.92201i 0.886721 0.156353i 0.288305 0.957539i \(-0.406908\pi\)
0.598416 + 0.801186i \(0.295797\pi\)
\(992\) −3.77439 + 0.330216i −0.119837 + 0.0104844i
\(993\) −42.2915 3.70003i −1.34208 0.117417i
\(994\) −31.7223 5.59350i −1.00617 0.177415i
\(995\) 0 0
\(996\) −3.74647 + 2.16302i −0.118711 + 0.0685381i
\(997\) −11.7072 + 25.1061i −0.370770 + 0.795119i 0.629072 + 0.777347i \(0.283435\pi\)
−0.999842 + 0.0177719i \(0.994343\pi\)
\(998\) −0.124730 + 0.267484i −0.00394826 + 0.00846706i
\(999\) 20.6698 11.9337i 0.653964 0.377566i
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 950.2.bb.c.243.4 yes 72
5.2 odd 4 inner 950.2.bb.c.357.1 yes 72
5.3 odd 4 inner 950.2.bb.c.357.6 yes 72
5.4 even 2 inner 950.2.bb.c.243.3 72
19.14 odd 18 inner 950.2.bb.c.793.1 yes 72
95.14 odd 18 inner 950.2.bb.c.793.6 yes 72
95.33 even 36 inner 950.2.bb.c.907.3 yes 72
95.52 even 36 inner 950.2.bb.c.907.4 yes 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
950.2.bb.c.243.3 72 5.4 even 2 inner
950.2.bb.c.243.4 yes 72 1.1 even 1 trivial
950.2.bb.c.357.1 yes 72 5.2 odd 4 inner
950.2.bb.c.357.6 yes 72 5.3 odd 4 inner
950.2.bb.c.793.1 yes 72 19.14 odd 18 inner
950.2.bb.c.793.6 yes 72 95.14 odd 18 inner
950.2.bb.c.907.3 yes 72 95.33 even 36 inner
950.2.bb.c.907.4 yes 72 95.52 even 36 inner