Properties

Label 825.2.bx.g.724.3
Level $825$
Weight $2$
Character 825.724
Analytic conductor $6.588$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [825,2,Mod(49,825)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(825, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 5, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("825.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.bx (of order \(10\), degree \(4\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.58765816676\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 11x^{14} + 80x^{12} - 529x^{10} + 3359x^{8} - 10729x^{6} + 15420x^{4} + 1089x^{2} + 14641 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 165)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 724.3
Root \(-0.548716 + 0.755243i\) of defining polynomial
Character \(\chi\) \(=\) 825.724
Dual form 825.2.bx.g.49.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.887841 + 0.288477i) q^{2} +(0.587785 + 0.809017i) q^{3} +(-0.912991 - 0.663327i) q^{4} +(0.288477 + 0.887841i) q^{6} +(1.19972 - 1.65127i) q^{7} +(-1.71667 - 2.36279i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\) \(q+(0.887841 + 0.288477i) q^{2} +(0.587785 + 0.809017i) q^{3} +(-0.912991 - 0.663327i) q^{4} +(0.288477 + 0.887841i) q^{6} +(1.19972 - 1.65127i) q^{7} +(-1.71667 - 2.36279i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(1.85274 - 2.75088i) q^{11} -1.12852i q^{12} +(-1.37754 - 0.447591i) q^{13} +(1.54151 - 1.11997i) q^{14} +(-0.145054 - 0.446431i) q^{16} +(0.824626 - 0.267937i) q^{17} +(-0.548716 + 0.755243i) q^{18} +(2.53103 - 1.83890i) q^{19} +2.04108 q^{21} +(2.43850 - 1.90788i) q^{22} -4.70547i q^{23} +(0.902506 - 2.77763i) q^{24} +(-1.09392 - 0.794779i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(-2.19066 + 0.711789i) q^{28} +(1.64906 + 1.19811i) q^{29} +(3.27979 - 10.0941i) q^{31} +5.40294i q^{32} +(3.31452 - 0.118034i) q^{33} +0.809430 q^{34} +(0.912991 - 0.663327i) q^{36} +(-2.44321 + 3.36279i) q^{37} +(2.77763 - 0.902506i) q^{38} +(-0.447591 - 1.37754i) q^{39} +(0.651268 - 0.473174i) q^{41} +(1.81215 + 0.588805i) q^{42} -2.34089i q^{43} +(-3.51627 + 1.28256i) q^{44} +(1.35742 - 4.17771i) q^{46} +(6.10137 + 8.39782i) q^{47} +(0.275910 - 0.379757i) q^{48} +(0.875752 + 2.69529i) q^{49} +(0.701468 + 0.509647i) q^{51} +(0.960786 + 1.32241i) q^{52} +(6.86278 + 2.22985i) q^{53} -0.933531 q^{54} -5.96112 q^{56} +(2.97540 + 0.966766i) q^{57} +(1.11847 + 1.53945i) q^{58} +(-6.73386 - 4.89243i) q^{59} +(-2.70931 - 8.33841i) q^{61} +(5.82386 - 8.01586i) q^{62} +(1.19972 + 1.65127i) q^{63} +(-1.84873 + 5.68981i) q^{64} +(2.97682 + 0.851369i) q^{66} +3.15664i q^{67} +(-0.930606 - 0.302372i) q^{68} +(3.80681 - 2.76581i) q^{69} +(3.97725 + 12.2407i) q^{71} +(2.77763 - 0.902506i) q^{72} +(-8.65128 + 11.9075i) q^{73} +(-3.13927 + 2.28081i) q^{74} -3.53059 q^{76} +(-2.31969 - 6.35965i) q^{77} -1.35216i q^{78} +(5.25303 - 16.1672i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(0.714723 - 0.232227i) q^{82} +(-5.84089 + 1.89782i) q^{83} +(-1.86349 - 1.35390i) q^{84} +(0.675292 - 2.07833i) q^{86} +2.03835i q^{87} +(-9.68030 + 0.344727i) q^{88} -3.77194 q^{89} +(-2.39175 + 1.73771i) q^{91} +(-3.12127 + 4.29606i) q^{92} +(10.0941 - 3.27979i) q^{93} +(2.99447 + 9.21604i) q^{94} +(-4.37107 + 3.17577i) q^{96} +(1.84310 + 0.598859i) q^{97} +2.64562i q^{98} +(2.04372 + 2.61213i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{4} - 4 q^{6} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 4 q^{4} - 4 q^{6} + 4 q^{9} - 6 q^{11} - 48 q^{14} + 8 q^{16} + 4 q^{19} + 32 q^{21} + 32 q^{24} + 28 q^{26} - 28 q^{29} - 10 q^{31} + 140 q^{34} - 4 q^{36} + 20 q^{39} + 2 q^{41} - 94 q^{44} + 84 q^{46} + 30 q^{49} - 16 q^{51} + 4 q^{54} - 48 q^{56} - 26 q^{59} - 6 q^{61} - 38 q^{64} + 74 q^{66} + 6 q^{69} + 18 q^{71} + 34 q^{74} - 92 q^{76} + 20 q^{79} - 4 q^{81} + 36 q^{84} + 40 q^{86} - 8 q^{89} - 86 q^{91} - 114 q^{94} + 12 q^{96} + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).

\(n\) \(376\) \(551\) \(727\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.887841 + 0.288477i 0.627798 + 0.203984i 0.605600 0.795770i \(-0.292933\pi\)
0.0221988 + 0.999754i \(0.492933\pi\)
\(3\) 0.587785 + 0.809017i 0.339358 + 0.467086i
\(4\) −0.912991 0.663327i −0.456496 0.331664i
\(5\) 0 0
\(6\) 0.288477 + 0.887841i 0.117770 + 0.362460i
\(7\) 1.19972 1.65127i 0.453450 0.624121i −0.519684 0.854358i \(-0.673950\pi\)
0.973134 + 0.230238i \(0.0739504\pi\)
\(8\) −1.71667 2.36279i −0.606934 0.835373i
\(9\) −0.309017 + 0.951057i −0.103006 + 0.317019i
\(10\) 0 0
\(11\) 1.85274 2.75088i 0.558621 0.829423i
\(12\) 1.12852i 0.325775i
\(13\) −1.37754 0.447591i −0.382062 0.124139i 0.111688 0.993743i \(-0.464374\pi\)
−0.493750 + 0.869604i \(0.664374\pi\)
\(14\) 1.54151 1.11997i 0.411986 0.299325i
\(15\) 0 0
\(16\) −0.145054 0.446431i −0.0362636 0.111608i
\(17\) 0.824626 0.267937i 0.200001 0.0649843i −0.207303 0.978277i \(-0.566469\pi\)
0.407305 + 0.913292i \(0.366469\pi\)
\(18\) −0.548716 + 0.755243i −0.129334 + 0.178012i
\(19\) 2.53103 1.83890i 0.580657 0.421872i −0.258304 0.966064i \(-0.583164\pi\)
0.838961 + 0.544192i \(0.183164\pi\)
\(20\) 0 0
\(21\) 2.04108 0.445400
\(22\) 2.43850 1.90788i 0.519891 0.406761i
\(23\) 4.70547i 0.981159i −0.871396 0.490580i \(-0.836785\pi\)
0.871396 0.490580i \(-0.163215\pi\)
\(24\) 0.902506 2.77763i 0.184223 0.566981i
\(25\) 0 0
\(26\) −1.09392 0.794779i −0.214535 0.155869i
\(27\) −0.951057 + 0.309017i −0.183031 + 0.0594703i
\(28\) −2.19066 + 0.711789i −0.413996 + 0.134516i
\(29\) 1.64906 + 1.19811i 0.306223 + 0.222484i 0.730274 0.683154i \(-0.239392\pi\)
−0.424051 + 0.905638i \(0.639392\pi\)
\(30\) 0 0
\(31\) 3.27979 10.0941i 0.589067 1.81296i 0.00678348 0.999977i \(-0.497841\pi\)
0.582284 0.812986i \(-0.302159\pi\)
\(32\) 5.40294i 0.955113i
\(33\) 3.31452 0.118034i 0.576985 0.0205471i
\(34\) 0.809430 0.138816
\(35\) 0 0
\(36\) 0.912991 0.663327i 0.152165 0.110555i
\(37\) −2.44321 + 3.36279i −0.401661 + 0.552839i −0.961160 0.275992i \(-0.910994\pi\)
0.559499 + 0.828831i \(0.310994\pi\)
\(38\) 2.77763 0.902506i 0.450591 0.146406i
\(39\) −0.447591 1.37754i −0.0716719 0.220583i
\(40\) 0 0
\(41\) 0.651268 0.473174i 0.101711 0.0738974i −0.535767 0.844366i \(-0.679978\pi\)
0.637478 + 0.770468i \(0.279978\pi\)
\(42\) 1.81215 + 0.588805i 0.279622 + 0.0908545i
\(43\) 2.34089i 0.356982i −0.983942 0.178491i \(-0.942878\pi\)
0.983942 0.178491i \(-0.0571215\pi\)
\(44\) −3.51627 + 1.28256i −0.530097 + 0.193354i
\(45\) 0 0
\(46\) 1.35742 4.17771i 0.200141 0.615970i
\(47\) 6.10137 + 8.39782i 0.889977 + 1.22495i 0.973556 + 0.228447i \(0.0733648\pi\)
−0.0835794 + 0.996501i \(0.526635\pi\)
\(48\) 0.275910 0.379757i 0.0398241 0.0548132i
\(49\) 0.875752 + 2.69529i 0.125107 + 0.385041i
\(50\) 0 0
\(51\) 0.701468 + 0.509647i 0.0982252 + 0.0713648i
\(52\) 0.960786 + 1.32241i 0.133237 + 0.183385i
\(53\) 6.86278 + 2.22985i 0.942676 + 0.306294i 0.739736 0.672897i \(-0.234950\pi\)
0.202940 + 0.979191i \(0.434950\pi\)
\(54\) −0.933531 −0.127038
\(55\) 0 0
\(56\) −5.96112 −0.796588
\(57\) 2.97540 + 0.966766i 0.394101 + 0.128051i
\(58\) 1.11847 + 1.53945i 0.146863 + 0.202139i
\(59\) −6.73386 4.89243i −0.876674 0.636941i 0.0556956 0.998448i \(-0.482262\pi\)
−0.932369 + 0.361507i \(0.882262\pi\)
\(60\) 0 0
\(61\) −2.70931 8.33841i −0.346892 1.06762i −0.960563 0.278062i \(-0.910308\pi\)
0.613671 0.789562i \(-0.289692\pi\)
\(62\) 5.82386 8.01586i 0.739631 1.01801i
\(63\) 1.19972 + 1.65127i 0.151150 + 0.208040i
\(64\) −1.84873 + 5.68981i −0.231091 + 0.711226i
\(65\) 0 0
\(66\) 2.97682 + 0.851369i 0.366421 + 0.104796i
\(67\) 3.15664i 0.385645i 0.981234 + 0.192822i \(0.0617641\pi\)
−0.981234 + 0.192822i \(0.938236\pi\)
\(68\) −0.930606 0.302372i −0.112853 0.0366680i
\(69\) 3.80681 2.76581i 0.458286 0.332964i
\(70\) 0 0
\(71\) 3.97725 + 12.2407i 0.472013 + 1.45271i 0.849944 + 0.526873i \(0.176636\pi\)
−0.377931 + 0.925834i \(0.623364\pi\)
\(72\) 2.77763 0.902506i 0.327347 0.106361i
\(73\) −8.65128 + 11.9075i −1.01256 + 1.39366i −0.0952617 + 0.995452i \(0.530369\pi\)
−0.917294 + 0.398211i \(0.869631\pi\)
\(74\) −3.13927 + 2.28081i −0.364933 + 0.265139i
\(75\) 0 0
\(76\) −3.53059 −0.404987
\(77\) −2.31969 6.35965i −0.264353 0.724749i
\(78\) 1.35216i 0.153102i
\(79\) 5.25303 16.1672i 0.591012 1.81895i 0.0173618 0.999849i \(-0.494473\pi\)
0.573651 0.819100i \(-0.305527\pi\)
\(80\) 0 0
\(81\) −0.809017 0.587785i −0.0898908 0.0653095i
\(82\) 0.714723 0.232227i 0.0789279 0.0256452i
\(83\) −5.84089 + 1.89782i −0.641121 + 0.208313i −0.611495 0.791248i \(-0.709432\pi\)
−0.0296262 + 0.999561i \(0.509432\pi\)
\(84\) −1.86349 1.35390i −0.203323 0.147723i
\(85\) 0 0
\(86\) 0.675292 2.07833i 0.0728186 0.224113i
\(87\) 2.03835i 0.218534i
\(88\) −9.68030 + 0.344727i −1.03192 + 0.0367480i
\(89\) −3.77194 −0.399825 −0.199913 0.979814i \(-0.564066\pi\)
−0.199913 + 0.979814i \(0.564066\pi\)
\(90\) 0 0
\(91\) −2.39175 + 1.73771i −0.250724 + 0.182162i
\(92\) −3.12127 + 4.29606i −0.325415 + 0.447895i
\(93\) 10.0941 3.27979i 1.04671 0.340098i
\(94\) 2.99447 + 9.21604i 0.308856 + 0.950562i
\(95\) 0 0
\(96\) −4.37107 + 3.17577i −0.446120 + 0.324125i
\(97\) 1.84310 + 0.598859i 0.187138 + 0.0608049i 0.401087 0.916040i \(-0.368633\pi\)
−0.213949 + 0.976845i \(0.568633\pi\)
\(98\) 2.64562i 0.267248i
\(99\) 2.04372 + 2.61213i 0.205402 + 0.262529i
\(100\) 0 0
\(101\) −1.62288 + 4.99472i −0.161483 + 0.496993i −0.998760 0.0497857i \(-0.984146\pi\)
0.837277 + 0.546779i \(0.184146\pi\)
\(102\) 0.475771 + 0.654843i 0.0471084 + 0.0648391i
\(103\) −7.99426 + 11.0032i −0.787698 + 1.08417i 0.206693 + 0.978406i \(0.433730\pi\)
−0.994391 + 0.105768i \(0.966270\pi\)
\(104\) 1.30722 + 4.02321i 0.128184 + 0.394508i
\(105\) 0 0
\(106\) 5.44980 + 3.95951i 0.529331 + 0.384582i
\(107\) −5.87235 8.08259i −0.567701 0.781374i 0.424579 0.905391i \(-0.360422\pi\)
−0.992280 + 0.124017i \(0.960422\pi\)
\(108\) 1.07329 + 0.348732i 0.103277 + 0.0335567i
\(109\) 6.75183 0.646708 0.323354 0.946278i \(-0.395189\pi\)
0.323354 + 0.946278i \(0.395189\pi\)
\(110\) 0 0
\(111\) −4.15664 −0.394531
\(112\) −0.911202 0.296067i −0.0861005 0.0279757i
\(113\) 3.08270 + 4.24298i 0.289996 + 0.399146i 0.929013 0.370047i \(-0.120658\pi\)
−0.639017 + 0.769193i \(0.720658\pi\)
\(114\) 2.36279 + 1.71667i 0.221296 + 0.160781i
\(115\) 0 0
\(116\) −0.710837 2.18773i −0.0659996 0.203126i
\(117\) 0.851369 1.17181i 0.0787091 0.108334i
\(118\) −4.56724 6.28627i −0.420449 0.578698i
\(119\) 0.546881 1.68313i 0.0501325 0.154292i
\(120\) 0 0
\(121\) −4.13473 10.1933i −0.375885 0.926666i
\(122\) 8.18476i 0.741013i
\(123\) 0.765612 + 0.248762i 0.0690329 + 0.0224301i
\(124\) −9.69014 + 7.04030i −0.870200 + 0.632237i
\(125\) 0 0
\(126\) 0.588805 + 1.81215i 0.0524549 + 0.161440i
\(127\) −19.6632 + 6.38897i −1.74483 + 0.566929i −0.995456 0.0952195i \(-0.969645\pi\)
−0.749372 + 0.662149i \(0.769645\pi\)
\(128\) 3.06877 4.22380i 0.271244 0.373335i
\(129\) 1.89382 1.37594i 0.166741 0.121145i
\(130\) 0 0
\(131\) 20.3089 1.77439 0.887197 0.461392i \(-0.152650\pi\)
0.887197 + 0.461392i \(0.152650\pi\)
\(132\) −3.10443 2.09085i −0.270206 0.181985i
\(133\) 6.38556i 0.553698i
\(134\) −0.910618 + 2.80259i −0.0786654 + 0.242107i
\(135\) 0 0
\(136\) −2.04869 1.48846i −0.175674 0.127634i
\(137\) −3.30950 + 1.07532i −0.282750 + 0.0918710i −0.446959 0.894555i \(-0.647493\pi\)
0.164209 + 0.986426i \(0.447493\pi\)
\(138\) 4.17771 1.35742i 0.355630 0.115551i
\(139\) 2.20931 + 1.60516i 0.187392 + 0.136148i 0.677526 0.735499i \(-0.263052\pi\)
−0.490134 + 0.871647i \(0.663052\pi\)
\(140\) 0 0
\(141\) −3.20768 + 9.87223i −0.270136 + 0.831392i
\(142\) 12.0152i 1.00829i
\(143\) −3.78350 + 2.96019i −0.316392 + 0.247544i
\(144\) 0.469405 0.0391171
\(145\) 0 0
\(146\) −11.1160 + 8.07624i −0.919966 + 0.668394i
\(147\) −1.66578 + 2.29275i −0.137391 + 0.189103i
\(148\) 4.46126 1.44955i 0.366713 0.119152i
\(149\) 2.81465 + 8.66261i 0.230585 + 0.709669i 0.997676 + 0.0681306i \(0.0217035\pi\)
−0.767091 + 0.641538i \(0.778297\pi\)
\(150\) 0 0
\(151\) −17.4541 + 12.6811i −1.42039 + 1.03198i −0.428687 + 0.903453i \(0.641024\pi\)
−0.991706 + 0.128523i \(0.958976\pi\)
\(152\) −8.68986 2.82351i −0.704841 0.229017i
\(153\) 0.867063i 0.0700979i
\(154\) −0.224903 6.31553i −0.0181232 0.508920i
\(155\) 0 0
\(156\) −0.505115 + 1.55458i −0.0404416 + 0.124466i
\(157\) −13.9857 19.2497i −1.11618 1.53629i −0.811978 0.583688i \(-0.801609\pi\)
−0.304205 0.952607i \(-0.598391\pi\)
\(158\) 9.32772 12.8385i 0.742073 1.02138i
\(159\) 2.22985 + 6.86278i 0.176839 + 0.544254i
\(160\) 0 0
\(161\) −7.77000 5.64523i −0.612362 0.444907i
\(162\) −0.548716 0.755243i −0.0431112 0.0593375i
\(163\) −1.71506 0.557258i −0.134334 0.0436478i 0.241078 0.970506i \(-0.422499\pi\)
−0.375412 + 0.926858i \(0.622499\pi\)
\(164\) −0.908472 −0.0709397
\(165\) 0 0
\(166\) −5.73326 −0.444988
\(167\) 23.3840 + 7.59792i 1.80951 + 0.587945i 1.00000 0.000837897i \(0.000266711\pi\)
0.809509 + 0.587107i \(0.199733\pi\)
\(168\) −3.50386 4.82265i −0.270328 0.372075i
\(169\) −8.81993 6.40806i −0.678456 0.492927i
\(170\) 0 0
\(171\) 0.966766 + 2.97540i 0.0739304 + 0.227534i
\(172\) −1.55277 + 2.13721i −0.118398 + 0.162961i
\(173\) 9.52890 + 13.1154i 0.724469 + 0.997146i 0.999364 + 0.0356719i \(0.0113571\pi\)
−0.274894 + 0.961474i \(0.588643\pi\)
\(174\) −0.588017 + 1.80973i −0.0445775 + 0.137195i
\(175\) 0 0
\(176\) −1.49683 0.428092i −0.112828 0.0322686i
\(177\) 8.32351i 0.625633i
\(178\) −3.34888 1.08812i −0.251010 0.0815579i
\(179\) 13.7287 9.97452i 1.02613 0.745530i 0.0586031 0.998281i \(-0.481335\pi\)
0.967531 + 0.252751i \(0.0813353\pi\)
\(180\) 0 0
\(181\) 5.67071 + 17.4526i 0.421500 + 1.29725i 0.906306 + 0.422623i \(0.138891\pi\)
−0.484805 + 0.874622i \(0.661109\pi\)
\(182\) −2.62479 + 0.852845i −0.194562 + 0.0632171i
\(183\) 5.15342 7.09308i 0.380952 0.524335i
\(184\) −11.1181 + 8.07774i −0.819634 + 0.595499i
\(185\) 0 0
\(186\) 9.90814 0.726500
\(187\) 0.790750 2.76487i 0.0578254 0.202187i
\(188\) 11.7143i 0.854356i
\(189\) −0.630728 + 1.94118i −0.0458787 + 0.141200i
\(190\) 0 0
\(191\) 12.4577 + 9.05102i 0.901405 + 0.654909i 0.938826 0.344391i \(-0.111914\pi\)
−0.0374216 + 0.999300i \(0.511914\pi\)
\(192\) −5.68981 + 1.84873i −0.410627 + 0.133421i
\(193\) 7.01824 2.28037i 0.505184 0.164144i −0.0453268 0.998972i \(-0.514433\pi\)
0.550511 + 0.834828i \(0.314433\pi\)
\(194\) 1.46362 + 1.06338i 0.105082 + 0.0763465i
\(195\) 0 0
\(196\) 0.988303 3.04168i 0.0705931 0.217263i
\(197\) 3.14676i 0.224197i −0.993697 0.112099i \(-0.964243\pi\)
0.993697 0.112099i \(-0.0357573\pi\)
\(198\) 1.06096 + 2.90872i 0.0753991 + 0.206714i
\(199\) 3.25757 0.230923 0.115462 0.993312i \(-0.463165\pi\)
0.115462 + 0.993312i \(0.463165\pi\)
\(200\) 0 0
\(201\) −2.55377 + 1.85543i −0.180129 + 0.130872i
\(202\) −2.88172 + 3.96635i −0.202757 + 0.279072i
\(203\) 3.95681 1.28564i 0.277713 0.0902346i
\(204\) −0.302372 0.930606i −0.0211703 0.0651554i
\(205\) 0 0
\(206\) −10.2718 + 7.46290i −0.715670 + 0.519965i
\(207\) 4.47517 + 1.45407i 0.311046 + 0.101065i
\(208\) 0.679903i 0.0471428i
\(209\) −0.369272 10.3696i −0.0255431 0.717277i
\(210\) 0 0
\(211\) 6.15690 18.9490i 0.423859 1.30450i −0.480224 0.877146i \(-0.659445\pi\)
0.904083 0.427357i \(-0.140555\pi\)
\(212\) −4.78654 6.58811i −0.328741 0.452473i
\(213\) −7.56518 + 10.4126i −0.518358 + 0.713458i
\(214\) −2.88207 8.87009i −0.197014 0.606347i
\(215\) 0 0
\(216\) 2.36279 + 1.71667i 0.160768 + 0.116804i
\(217\) −12.7333 17.5259i −0.864395 1.18974i
\(218\) 5.99455 + 1.94775i 0.406002 + 0.131918i
\(219\) −14.7184 −0.994580
\(220\) 0 0
\(221\) −1.25588 −0.0844799
\(222\) −3.69043 1.19909i −0.247686 0.0804780i
\(223\) −6.16008 8.47862i −0.412509 0.567770i 0.551319 0.834295i \(-0.314125\pi\)
−0.963828 + 0.266524i \(0.914125\pi\)
\(224\) 8.92170 + 6.48199i 0.596106 + 0.433096i
\(225\) 0 0
\(226\) 1.51295 + 4.65638i 0.100640 + 0.309738i
\(227\) −10.3880 + 14.2979i −0.689476 + 0.948982i −0.999999 0.00158404i \(-0.999496\pi\)
0.310523 + 0.950566i \(0.399496\pi\)
\(228\) −2.07523 2.85631i −0.137436 0.189164i
\(229\) −1.27614 + 3.92755i −0.0843297 + 0.259540i −0.984326 0.176357i \(-0.943569\pi\)
0.899997 + 0.435897i \(0.143569\pi\)
\(230\) 0 0
\(231\) 3.78158 5.61478i 0.248810 0.369425i
\(232\) 5.95314i 0.390843i
\(233\) 12.9334 + 4.20231i 0.847294 + 0.275303i 0.700312 0.713837i \(-0.253044\pi\)
0.146982 + 0.989139i \(0.453044\pi\)
\(234\) 1.09392 0.794779i 0.0715118 0.0519563i
\(235\) 0 0
\(236\) 2.90267 + 8.93350i 0.188948 + 0.581521i
\(237\) 16.1672 5.25303i 1.05017 0.341221i
\(238\) 0.971087 1.33659i 0.0629462 0.0866380i
\(239\) 6.47725 4.70600i 0.418979 0.304406i −0.358248 0.933626i \(-0.616626\pi\)
0.777227 + 0.629221i \(0.216626\pi\)
\(240\) 0 0
\(241\) −0.501943 −0.0323330 −0.0161665 0.999869i \(-0.505146\pi\)
−0.0161665 + 0.999869i \(0.505146\pi\)
\(242\) −0.730444 10.2428i −0.0469547 0.658434i
\(243\) 1.00000i 0.0641500i
\(244\) −3.05751 + 9.41006i −0.195737 + 0.602417i
\(245\) 0 0
\(246\) 0.607979 + 0.441723i 0.0387633 + 0.0281632i
\(247\) −4.30967 + 1.40030i −0.274218 + 0.0890988i
\(248\) −29.4807 + 9.57885i −1.87202 + 0.608258i
\(249\) −4.96856 3.60987i −0.314870 0.228766i
\(250\) 0 0
\(251\) −5.72933 + 17.6331i −0.361632 + 1.11299i 0.590431 + 0.807088i \(0.298958\pi\)
−0.952063 + 0.305901i \(0.901042\pi\)
\(252\) 2.30340i 0.145100i
\(253\) −12.9442 8.71800i −0.813796 0.548096i
\(254\) −19.3009 −1.21105
\(255\) 0 0
\(256\) 13.6231 9.89779i 0.851446 0.618612i
\(257\) −4.33791 + 5.97062i −0.270592 + 0.372437i −0.922589 0.385784i \(-0.873931\pi\)
0.651998 + 0.758221i \(0.273931\pi\)
\(258\) 2.07833 0.675292i 0.129391 0.0420418i
\(259\) 2.62171 + 8.06879i 0.162905 + 0.501370i
\(260\) 0 0
\(261\) −1.64906 + 1.19811i −0.102074 + 0.0741613i
\(262\) 18.0310 + 5.85864i 1.11396 + 0.361948i
\(263\) 3.05950i 0.188657i −0.995541 0.0943285i \(-0.969930\pi\)
0.995541 0.0943285i \(-0.0300704\pi\)
\(264\) −5.96883 7.62890i −0.367356 0.469527i
\(265\) 0 0
\(266\) 1.84209 5.66936i 0.112946 0.347611i
\(267\) −2.21709 3.05157i −0.135684 0.186753i
\(268\) 2.09388 2.88198i 0.127904 0.176045i
\(269\) 5.46345 + 16.8148i 0.333112 + 1.02521i 0.967644 + 0.252318i \(0.0811928\pi\)
−0.634532 + 0.772896i \(0.718807\pi\)
\(270\) 0 0
\(271\) 12.3773 + 8.99262i 0.751866 + 0.546263i 0.896405 0.443236i \(-0.146170\pi\)
−0.144538 + 0.989499i \(0.546170\pi\)
\(272\) −0.239231 0.329273i −0.0145055 0.0199651i
\(273\) −2.81168 0.913569i −0.170170 0.0552917i
\(274\) −3.24852 −0.196250
\(275\) 0 0
\(276\) −5.31022 −0.319638
\(277\) 16.9514 + 5.50785i 1.01851 + 0.330934i 0.770239 0.637756i \(-0.220137\pi\)
0.248273 + 0.968690i \(0.420137\pi\)
\(278\) 1.49847 + 2.06246i 0.0898721 + 0.123698i
\(279\) 8.58660 + 6.23853i 0.514066 + 0.373491i
\(280\) 0 0
\(281\) −5.34568 16.4523i −0.318896 0.981462i −0.974121 0.226028i \(-0.927426\pi\)
0.655224 0.755434i \(-0.272574\pi\)
\(282\) −5.69582 + 7.83963i −0.339181 + 0.466843i
\(283\) 15.1510 + 20.8535i 0.900633 + 1.23961i 0.970266 + 0.242042i \(0.0778171\pi\)
−0.0696333 + 0.997573i \(0.522183\pi\)
\(284\) 4.48840 13.8139i 0.266338 0.819704i
\(285\) 0 0
\(286\) −4.21309 + 1.53673i −0.249125 + 0.0908688i
\(287\) 1.64309i 0.0969888i
\(288\) −5.13850 1.66960i −0.302789 0.0983821i
\(289\) −13.1451 + 9.55045i −0.773240 + 0.561791i
\(290\) 0 0
\(291\) 0.598859 + 1.84310i 0.0351058 + 0.108044i
\(292\) 15.7971 5.13278i 0.924454 0.300373i
\(293\) 7.95310 10.9465i 0.464625 0.639502i −0.510835 0.859679i \(-0.670664\pi\)
0.975460 + 0.220177i \(0.0706635\pi\)
\(294\) −2.14035 + 1.55506i −0.124828 + 0.0906928i
\(295\) 0 0
\(296\) 12.1398 0.705609
\(297\) −0.911987 + 3.18877i −0.0529189 + 0.185031i
\(298\) 8.50299i 0.492565i
\(299\) −2.10613 + 6.48199i −0.121800 + 0.374863i
\(300\) 0 0
\(301\) −3.86543 2.80840i −0.222800 0.161873i
\(302\) −19.1547 + 6.22373i −1.10223 + 0.358135i
\(303\) −4.99472 + 1.62288i −0.286939 + 0.0932322i
\(304\) −1.18808 0.863188i −0.0681409 0.0495073i
\(305\) 0 0
\(306\) −0.250128 + 0.769814i −0.0142988 + 0.0440073i
\(307\) 13.0268i 0.743478i 0.928337 + 0.371739i \(0.121238\pi\)
−0.928337 + 0.371739i \(0.878762\pi\)
\(308\) −2.10067 + 7.34502i −0.119697 + 0.418521i
\(309\) −13.6007 −0.773714
\(310\) 0 0
\(311\) −1.53971 + 1.11867i −0.0873092 + 0.0634339i −0.630584 0.776121i \(-0.717184\pi\)
0.543274 + 0.839555i \(0.317184\pi\)
\(312\) −2.48648 + 3.42235i −0.140769 + 0.193752i
\(313\) −10.3973 + 3.37829i −0.587691 + 0.190952i −0.587743 0.809048i \(-0.699983\pi\)
5.23383e−5 1.00000i \(0.499983\pi\)
\(314\) −6.86401 21.1252i −0.387358 1.19217i
\(315\) 0 0
\(316\) −15.5201 + 11.2760i −0.873074 + 0.634325i
\(317\) 15.2856 + 4.96660i 0.858526 + 0.278952i 0.705013 0.709194i \(-0.250941\pi\)
0.153513 + 0.988147i \(0.450941\pi\)
\(318\) 6.73632i 0.377754i
\(319\) 6.35114 2.31659i 0.355596 0.129704i
\(320\) 0 0
\(321\) 3.08727 9.50166i 0.172315 0.530331i
\(322\) −5.27000 7.25354i −0.293686 0.404224i
\(323\) 1.59444 2.19456i 0.0887170 0.122108i
\(324\) 0.348732 + 1.07329i 0.0193740 + 0.0596270i
\(325\) 0 0
\(326\) −1.36195 0.989513i −0.0754313 0.0548040i
\(327\) 3.96863 + 5.46235i 0.219466 + 0.302069i
\(328\) −2.23602 0.726528i −0.123464 0.0401158i
\(329\) 21.1870 1.16808
\(330\) 0 0
\(331\) 1.39579 0.0767195 0.0383597 0.999264i \(-0.487787\pi\)
0.0383597 + 0.999264i \(0.487787\pi\)
\(332\) 6.59156 + 2.14173i 0.361759 + 0.117543i
\(333\) −2.44321 3.36279i −0.133887 0.184280i
\(334\) 18.5695 + 13.4915i 1.01608 + 0.738222i
\(335\) 0 0
\(336\) −0.296067 0.911202i −0.0161518 0.0497101i
\(337\) 1.62429 2.23564i 0.0884805 0.121783i −0.762482 0.647009i \(-0.776019\pi\)
0.850962 + 0.525227i \(0.176019\pi\)
\(338\) −5.98212 8.23368i −0.325384 0.447853i
\(339\) −1.62067 + 4.98792i −0.0880229 + 0.270907i
\(340\) 0 0
\(341\) −21.6913 27.7241i −1.17465 1.50135i
\(342\) 2.92057i 0.157926i
\(343\) 19.0896 + 6.20258i 1.03074 + 0.334908i
\(344\) −5.53103 + 4.01853i −0.298213 + 0.216664i
\(345\) 0 0
\(346\) 4.67666 + 14.3933i 0.251419 + 0.773787i
\(347\) −2.97379 + 0.966244i −0.159642 + 0.0518707i −0.387748 0.921766i \(-0.626747\pi\)
0.228106 + 0.973636i \(0.426747\pi\)
\(348\) 1.35209 1.86100i 0.0724798 0.0997598i
\(349\) 10.6205 7.71626i 0.568504 0.413042i −0.266058 0.963957i \(-0.585721\pi\)
0.834561 + 0.550915i \(0.185721\pi\)
\(350\) 0 0
\(351\) 1.44843 0.0773117
\(352\) 14.8629 + 10.0102i 0.792193 + 0.533546i
\(353\) 10.7984i 0.574739i 0.957820 + 0.287370i \(0.0927808\pi\)
−0.957820 + 0.287370i \(0.907219\pi\)
\(354\) 2.40114 7.38995i 0.127619 0.392771i
\(355\) 0 0
\(356\) 3.44375 + 2.50203i 0.182518 + 0.132607i
\(357\) 1.68313 0.546881i 0.0890805 0.0289440i
\(358\) 15.0664 4.89536i 0.796282 0.258728i
\(359\) 19.3934 + 14.0901i 1.02354 + 0.743649i 0.967007 0.254752i \(-0.0819937\pi\)
0.0565382 + 0.998400i \(0.481994\pi\)
\(360\) 0 0
\(361\) −2.84678 + 8.76148i −0.149830 + 0.461131i
\(362\) 17.1310i 0.900388i
\(363\) 5.81624 9.33656i 0.305274 0.490042i
\(364\) 3.33632 0.174871
\(365\) 0 0
\(366\) 6.62161 4.81088i 0.346117 0.251469i
\(367\) −5.21534 + 7.17831i −0.272239 + 0.374705i −0.923144 0.384455i \(-0.874390\pi\)
0.650905 + 0.759159i \(0.274390\pi\)
\(368\) −2.10067 + 0.682549i −0.109505 + 0.0355803i
\(369\) 0.248762 + 0.765612i 0.0129501 + 0.0398562i
\(370\) 0 0
\(371\) 11.9155 8.65711i 0.618621 0.449455i
\(372\) −11.3914 3.70130i −0.590619 0.191904i
\(373\) 26.3389i 1.36378i −0.731456 0.681888i \(-0.761159\pi\)
0.731456 0.681888i \(-0.238841\pi\)
\(374\) 1.49966 2.22665i 0.0775456 0.115137i
\(375\) 0 0
\(376\) 9.36826 28.8325i 0.483131 1.48693i
\(377\) −1.73539 2.38855i −0.0893770 0.123017i
\(378\) −1.11997 + 1.54151i −0.0576052 + 0.0792868i
\(379\) −1.45118 4.46626i −0.0745419 0.229416i 0.906843 0.421469i \(-0.138485\pi\)
−0.981385 + 0.192053i \(0.938485\pi\)
\(380\) 0 0
\(381\) −16.7265 12.1525i −0.856926 0.622593i
\(382\) 8.44941 + 11.6296i 0.432310 + 0.595023i
\(383\) −6.56163 2.13200i −0.335284 0.108940i 0.136537 0.990635i \(-0.456403\pi\)
−0.471820 + 0.881695i \(0.656403\pi\)
\(384\) 5.22091 0.266428
\(385\) 0 0
\(386\) 6.88892 0.350637
\(387\) 2.22631 + 0.723374i 0.113170 + 0.0367711i
\(388\) −1.28549 1.76933i −0.0652611 0.0898242i
\(389\) 1.94538 + 1.41340i 0.0986348 + 0.0716624i 0.636009 0.771681i \(-0.280584\pi\)
−0.537375 + 0.843344i \(0.680584\pi\)
\(390\) 0 0
\(391\) −1.26077 3.88025i −0.0637599 0.196233i
\(392\) 4.86503 6.69613i 0.245721 0.338206i
\(393\) 11.9372 + 16.4302i 0.602155 + 0.828795i
\(394\) 0.907768 2.79382i 0.0457327 0.140751i
\(395\) 0 0
\(396\) −0.133204 3.74050i −0.00669373 0.187967i
\(397\) 37.6715i 1.89068i −0.326091 0.945338i \(-0.605732\pi\)
0.326091 0.945338i \(-0.394268\pi\)
\(398\) 2.89221 + 0.939734i 0.144973 + 0.0471046i
\(399\) 5.16602 3.75334i 0.258625 0.187902i
\(400\) 0 0
\(401\) −3.86791 11.9042i −0.193154 0.594467i −0.999993 0.00369578i \(-0.998824\pi\)
0.806839 0.590771i \(-0.201176\pi\)
\(402\) −2.80259 + 0.910618i −0.139781 + 0.0454175i
\(403\) −9.03610 + 12.4371i −0.450120 + 0.619537i
\(404\) 4.79481 3.48363i 0.238551 0.173317i
\(405\) 0 0
\(406\) 3.88390 0.192754
\(407\) 4.72402 + 12.9514i 0.234161 + 0.641975i
\(408\) 2.53232i 0.125368i
\(409\) 8.17728 25.1671i 0.404340 1.24443i −0.517104 0.855922i \(-0.672990\pi\)
0.921445 0.388510i \(-0.127010\pi\)
\(410\) 0 0
\(411\) −2.81523 2.04539i −0.138865 0.100891i
\(412\) 14.5974 4.74298i 0.719162 0.233670i
\(413\) −16.1574 + 5.24987i −0.795056 + 0.258329i
\(414\) 3.55377 + 2.58197i 0.174658 + 0.126897i
\(415\) 0 0
\(416\) 2.41831 7.44278i 0.118567 0.364912i
\(417\) 2.73086i 0.133731i
\(418\) 2.66352 9.31304i 0.130277 0.455516i
\(419\) −30.9711 −1.51304 −0.756518 0.653973i \(-0.773101\pi\)
−0.756518 + 0.653973i \(0.773101\pi\)
\(420\) 0 0
\(421\) −14.7593 + 10.7232i −0.719323 + 0.522618i −0.886168 0.463365i \(-0.846642\pi\)
0.166845 + 0.985983i \(0.446642\pi\)
\(422\) 10.9327 15.0476i 0.532196 0.732505i
\(423\) −9.87223 + 3.20768i −0.480004 + 0.155963i
\(424\) −6.51245 20.0432i −0.316272 0.973386i
\(425\) 0 0
\(426\) −9.72047 + 7.06233i −0.470958 + 0.342171i
\(427\) −17.0194 5.52993i −0.823625 0.267612i
\(428\) 11.2746i 0.544979i
\(429\) −4.61873 1.32095i −0.222994 0.0637763i
\(430\) 0 0
\(431\) 9.37829 28.8634i 0.451736 1.39030i −0.423188 0.906042i \(-0.639089\pi\)
0.874924 0.484260i \(-0.160911\pi\)
\(432\) 0.275910 + 0.379757i 0.0132747 + 0.0182711i
\(433\) 7.46560 10.2755i 0.358774 0.493810i −0.591033 0.806648i \(-0.701280\pi\)
0.949807 + 0.312838i \(0.101280\pi\)
\(434\) −6.24935 19.2335i −0.299978 0.923238i
\(435\) 0 0
\(436\) −6.16436 4.47867i −0.295220 0.214490i
\(437\) −8.65288 11.9097i −0.413924 0.569717i
\(438\) −13.0676 4.24593i −0.624395 0.202878i
\(439\) 25.6564 1.22451 0.612257 0.790659i \(-0.290262\pi\)
0.612257 + 0.790659i \(0.290262\pi\)
\(440\) 0 0
\(441\) −2.83399 −0.134952
\(442\) −1.11502 0.362294i −0.0530363 0.0172325i
\(443\) 15.4087 + 21.2082i 0.732088 + 1.00763i 0.999035 + 0.0439211i \(0.0139850\pi\)
−0.266947 + 0.963711i \(0.586015\pi\)
\(444\) 3.79498 + 2.75721i 0.180102 + 0.130851i
\(445\) 0 0
\(446\) −3.02328 9.30470i −0.143157 0.440590i
\(447\) −5.35379 + 7.36886i −0.253226 + 0.348535i
\(448\) 7.17745 + 9.87891i 0.339103 + 0.466735i
\(449\) 3.71010 11.4185i 0.175091 0.538873i −0.824547 0.565793i \(-0.808570\pi\)
0.999638 + 0.0269202i \(0.00856999\pi\)
\(450\) 0 0
\(451\) −0.0950188 2.66823i −0.00447426 0.125642i
\(452\) 5.91864i 0.278390i
\(453\) −20.5185 6.66687i −0.964044 0.313237i
\(454\) −13.3475 + 9.69752i −0.626429 + 0.455127i
\(455\) 0 0
\(456\) −2.82351 8.68986i −0.132223 0.406940i
\(457\) 13.1141 4.26104i 0.613453 0.199323i 0.0142215 0.999899i \(-0.495473\pi\)
0.599231 + 0.800576i \(0.295473\pi\)
\(458\) −2.26602 + 3.11891i −0.105884 + 0.145737i
\(459\) −0.701468 + 0.509647i −0.0327417 + 0.0237883i
\(460\) 0 0
\(461\) 11.3262 0.527515 0.263758 0.964589i \(-0.415038\pi\)
0.263758 + 0.964589i \(0.415038\pi\)
\(462\) 4.97718 3.89413i 0.231559 0.181171i
\(463\) 6.18784i 0.287573i 0.989609 + 0.143787i \(0.0459279\pi\)
−0.989609 + 0.143787i \(0.954072\pi\)
\(464\) 0.295671 0.909983i 0.0137262 0.0422449i
\(465\) 0 0
\(466\) 10.2705 + 7.46197i 0.475773 + 0.345669i
\(467\) 8.06770 2.62135i 0.373328 0.121302i −0.116342 0.993209i \(-0.537117\pi\)
0.489671 + 0.871907i \(0.337117\pi\)
\(468\) −1.55458 + 0.505115i −0.0718607 + 0.0233490i
\(469\) 5.21246 + 3.78707i 0.240689 + 0.174871i
\(470\) 0 0
\(471\) 7.35274 22.6294i 0.338796 1.04271i
\(472\) 24.3094i 1.11893i
\(473\) −6.43951 4.33705i −0.296089 0.199418i
\(474\) 15.8693 0.728899
\(475\) 0 0
\(476\) −1.61576 + 1.17392i −0.0740583 + 0.0538065i
\(477\) −4.24143 + 5.83783i −0.194202 + 0.267296i
\(478\) 7.10834 2.30964i 0.325128 0.105640i
\(479\) −2.85394 8.78352i −0.130400 0.401329i 0.864446 0.502725i \(-0.167669\pi\)
−0.994846 + 0.101396i \(0.967669\pi\)
\(480\) 0 0
\(481\) 4.87078 3.53883i 0.222089 0.161357i
\(482\) −0.445645 0.144799i −0.0202986 0.00659541i
\(483\) 9.60425i 0.437008i
\(484\) −2.98654 + 12.0491i −0.135752 + 0.547686i
\(485\) 0 0
\(486\) 0.288477 0.887841i 0.0130856 0.0402733i
\(487\) 11.8561 + 16.3185i 0.537250 + 0.739461i 0.988214 0.153081i \(-0.0489196\pi\)
−0.450964 + 0.892542i \(0.648920\pi\)
\(488\) −15.0509 + 20.7158i −0.681324 + 0.937762i
\(489\) −0.557258 1.71506i −0.0252001 0.0775578i
\(490\) 0 0
\(491\) 4.31686 + 3.13638i 0.194817 + 0.141543i 0.680918 0.732360i \(-0.261581\pi\)
−0.486100 + 0.873903i \(0.661581\pi\)
\(492\) −0.533986 0.734969i −0.0240740 0.0331350i
\(493\) 1.68087 + 0.546149i 0.0757028 + 0.0245973i
\(494\) −4.23026 −0.190328
\(495\) 0 0
\(496\) −4.98209 −0.223702
\(497\) 24.9843 + 8.11789i 1.12070 + 0.364137i
\(498\) −3.36993 4.63831i −0.151010 0.207848i
\(499\) −31.7795 23.0891i −1.42265 1.03361i −0.991328 0.131412i \(-0.958049\pi\)
−0.431317 0.902200i \(-0.641951\pi\)
\(500\) 0 0
\(501\) 7.59792 + 23.3840i 0.339450 + 1.04472i
\(502\) −10.1735 + 14.0026i −0.454064 + 0.624966i
\(503\) −19.0549 26.2268i −0.849616 1.16940i −0.983947 0.178460i \(-0.942889\pi\)
0.134331 0.990936i \(-0.457111\pi\)
\(504\) 1.84209 5.66936i 0.0820531 0.252533i
\(505\) 0 0
\(506\) −8.97746 11.4743i −0.399097 0.510095i
\(507\) 10.9020i 0.484176i
\(508\) 22.1903 + 7.21007i 0.984536 + 0.319895i
\(509\) −13.8064 + 10.0309i −0.611958 + 0.444613i −0.850103 0.526616i \(-0.823461\pi\)
0.238145 + 0.971229i \(0.423461\pi\)
\(510\) 0 0
\(511\) 9.28333 + 28.5712i 0.410671 + 1.26391i
\(512\) 5.01971 1.63100i 0.221842 0.0720808i
\(513\) −1.83890 + 2.53103i −0.0811893 + 0.111747i
\(514\) −5.57376 + 4.04958i −0.245848 + 0.178619i
\(515\) 0 0
\(516\) −2.64174 −0.116296
\(517\) 34.4057 1.22523i 1.51316 0.0538854i
\(518\) 7.92011i 0.347990i
\(519\) −5.00964 + 15.4181i −0.219899 + 0.676779i
\(520\) 0 0
\(521\) 12.1733 + 8.84445i 0.533324 + 0.387482i 0.821600 0.570065i \(-0.193082\pi\)
−0.288276 + 0.957547i \(0.593082\pi\)
\(522\) −1.80973 + 0.588017i −0.0792097 + 0.0257368i
\(523\) 35.2287 11.4465i 1.54044 0.500520i 0.588945 0.808173i \(-0.299544\pi\)
0.951499 + 0.307653i \(0.0995435\pi\)
\(524\) −18.5418 13.4714i −0.810003 0.588502i
\(525\) 0 0
\(526\) 0.882596 2.71635i 0.0384830 0.118439i
\(527\) 9.20267i 0.400875i
\(528\) −0.533480 1.46259i −0.0232167 0.0636508i
\(529\) 0.858520 0.0373270
\(530\) 0 0
\(531\) 6.73386 4.89243i 0.292225 0.212314i
\(532\) −4.23571 + 5.82996i −0.183641 + 0.252761i
\(533\) −1.10894 + 0.360316i −0.0480335 + 0.0156070i
\(534\) −1.08812 3.34888i −0.0470875 0.144920i
\(535\) 0 0
\(536\) 7.45848 5.41890i 0.322157 0.234061i
\(537\) 16.1391 + 5.24391i 0.696454 + 0.226292i
\(538\) 16.5049i 0.711577i
\(539\) 9.03696 + 2.58457i 0.389250 + 0.111325i
\(540\) 0 0
\(541\) 0.0547265 0.168431i 0.00235288 0.00724141i −0.949873 0.312635i \(-0.898788\pi\)
0.952226 + 0.305394i \(0.0987882\pi\)
\(542\) 8.39489 + 11.5546i 0.360592 + 0.496312i
\(543\) −10.7863 + 14.8461i −0.462886 + 0.637108i
\(544\) 1.44765 + 4.45540i 0.0620674 + 0.191024i
\(545\) 0 0
\(546\) −2.23278 1.62221i −0.0955541 0.0694241i
\(547\) 0.712805 + 0.981092i 0.0304773 + 0.0419484i 0.823984 0.566613i \(-0.191747\pi\)
−0.793506 + 0.608562i \(0.791747\pi\)
\(548\) 3.73484 + 1.21352i 0.159544 + 0.0518391i
\(549\) 8.76752 0.374189
\(550\) 0 0
\(551\) 6.37702 0.271670
\(552\) −13.0701 4.24672i −0.556298 0.180752i
\(553\) −20.3942 28.0702i −0.867249 1.19367i
\(554\) 13.4613 + 9.78018i 0.571914 + 0.415520i
\(555\) 0 0
\(556\) −0.952338 2.93100i −0.0403881 0.124302i
\(557\) −1.13940 + 1.56825i −0.0482778 + 0.0664488i −0.832473 0.554065i \(-0.813076\pi\)
0.784196 + 0.620514i \(0.213076\pi\)
\(558\) 5.82386 + 8.01586i 0.246544 + 0.339338i
\(559\) −1.04776 + 3.22467i −0.0443155 + 0.136389i
\(560\) 0 0
\(561\) 2.70162 0.985418i 0.114062 0.0416044i
\(562\) 16.1491i 0.681210i
\(563\) −19.9682 6.48805i −0.841558 0.273439i −0.143652 0.989628i \(-0.545885\pi\)
−0.697906 + 0.716190i \(0.745885\pi\)
\(564\) 9.47710 6.88552i 0.399058 0.289933i
\(565\) 0 0
\(566\) 7.43590 + 22.8853i 0.312554 + 0.961943i
\(567\) −1.94118 + 0.630728i −0.0815220 + 0.0264881i
\(568\) 22.0946 30.4107i 0.927071 1.27600i
\(569\) −31.8556 + 23.1444i −1.33546 + 0.970265i −0.335857 + 0.941913i \(0.609026\pi\)
−0.999598 + 0.0283521i \(0.990974\pi\)
\(570\) 0 0
\(571\) 30.6796 1.28390 0.641950 0.766746i \(-0.278126\pi\)
0.641950 + 0.766746i \(0.278126\pi\)
\(572\) 5.41788 0.192937i 0.226533 0.00806709i
\(573\) 15.3985i 0.643282i
\(574\) 0.473995 1.45881i 0.0197842 0.0608894i
\(575\) 0 0
\(576\) −4.84004 3.51650i −0.201668 0.146521i
\(577\) −33.0053 + 10.7241i −1.37403 + 0.446448i −0.900701 0.434439i \(-0.856947\pi\)
−0.473326 + 0.880887i \(0.656947\pi\)
\(578\) −14.4258 + 4.68723i −0.600035 + 0.194963i
\(579\) 5.97007 + 4.33751i 0.248108 + 0.180261i
\(580\) 0 0
\(581\) −3.87361 + 11.9217i −0.160704 + 0.494597i
\(582\) 1.80914i 0.0749911i
\(583\) 18.8490 14.7474i 0.780646 0.610775i
\(584\) 42.9862 1.77878
\(585\) 0 0
\(586\) 10.2189 7.42447i 0.422139 0.306702i
\(587\) −4.73584 + 6.51833i −0.195469 + 0.269040i −0.895489 0.445083i \(-0.853174\pi\)
0.700020 + 0.714123i \(0.253174\pi\)
\(588\) 3.04168 0.988303i 0.125437 0.0407569i
\(589\) −10.2609 31.5797i −0.422792 1.30122i
\(590\) 0 0
\(591\) 2.54578 1.84962i 0.104719 0.0760832i
\(592\) 1.85565 + 0.602938i 0.0762669 + 0.0247806i
\(593\) 28.1409i 1.15561i −0.816175 0.577805i \(-0.803909\pi\)
0.816175 0.577805i \(-0.196091\pi\)
\(594\) −1.72959 + 2.56804i −0.0709658 + 0.105368i
\(595\) 0 0
\(596\) 3.17639 9.77593i 0.130110 0.400438i
\(597\) 1.91475 + 2.63543i 0.0783656 + 0.107861i
\(598\) −3.73981 + 5.14741i −0.152932 + 0.210493i
\(599\) 8.83751 + 27.1991i 0.361091 + 1.11132i 0.952393 + 0.304873i \(0.0986141\pi\)
−0.591302 + 0.806450i \(0.701386\pi\)
\(600\) 0 0
\(601\) 5.88649 + 4.27679i 0.240115 + 0.174454i 0.701335 0.712832i \(-0.252588\pi\)
−0.461219 + 0.887286i \(0.652588\pi\)
\(602\) −2.62173 3.60850i −0.106854 0.147072i
\(603\) −3.00214 0.975455i −0.122257 0.0397236i
\(604\) 24.3472 0.990672
\(605\) 0 0
\(606\) −4.90268 −0.199158
\(607\) 5.08611 + 1.65258i 0.206439 + 0.0670761i 0.410411 0.911901i \(-0.365385\pi\)
−0.203972 + 0.978977i \(0.565385\pi\)
\(608\) 9.93545 + 13.6750i 0.402936 + 0.554593i
\(609\) 3.36586 + 2.44544i 0.136392 + 0.0990943i
\(610\) 0 0
\(611\) −4.64612 14.2993i −0.187962 0.578487i
\(612\) 0.575146 0.791621i 0.0232489 0.0319994i
\(613\) 2.72790 + 3.75464i 0.110179 + 0.151648i 0.860545 0.509374i \(-0.170123\pi\)
−0.750366 + 0.661022i \(0.770123\pi\)
\(614\) −3.75793 + 11.5657i −0.151658 + 0.466754i
\(615\) 0 0
\(616\) −11.0444 + 16.3983i −0.444991 + 0.660708i
\(617\) 24.5843i 0.989727i −0.868971 0.494864i \(-0.835218\pi\)
0.868971 0.494864i \(-0.164782\pi\)
\(618\) −12.0752 3.92348i −0.485737 0.157825i
\(619\) −4.96566 + 3.60776i −0.199587 + 0.145008i −0.683090 0.730335i \(-0.739364\pi\)
0.483503 + 0.875343i \(0.339364\pi\)
\(620\) 0 0
\(621\) 1.45407 + 4.47517i 0.0583499 + 0.179582i
\(622\) −1.68973 + 0.549027i −0.0677521 + 0.0220140i
\(623\) −4.52526 + 6.22849i −0.181301 + 0.249539i
\(624\) −0.550053 + 0.399637i −0.0220197 + 0.0159983i
\(625\) 0 0
\(626\) −10.2057 −0.407902
\(627\) 8.17209 6.39382i 0.326362 0.255344i
\(628\) 26.8519i 1.07151i
\(629\) −1.11372 + 3.42767i −0.0444068 + 0.136670i
\(630\) 0 0
\(631\) 14.3265 + 10.4088i 0.570329 + 0.414368i 0.835225 0.549909i \(-0.185338\pi\)
−0.264896 + 0.964277i \(0.585338\pi\)
\(632\) −47.2174 + 15.3419i −1.87821 + 0.610266i
\(633\) 18.9490 6.15690i 0.753155 0.244715i
\(634\) 12.1385 + 8.81910i 0.482080 + 0.350251i
\(635\) 0 0
\(636\) 2.51643 7.74479i 0.0997831 0.307101i
\(637\) 4.10485i 0.162640i
\(638\) 6.30708 0.224603i 0.249700 0.00889210i
\(639\) −12.8707 −0.509155
\(640\) 0 0
\(641\) −32.2492 + 23.4304i −1.27377 + 0.925444i −0.999346 0.0361657i \(-0.988486\pi\)
−0.274419 + 0.961610i \(0.588486\pi\)
\(642\) 5.48202 7.54535i 0.216358 0.297791i
\(643\) 16.9918 5.52097i 0.670091 0.217726i 0.0458392 0.998949i \(-0.485404\pi\)
0.624252 + 0.781223i \(0.285404\pi\)
\(644\) 3.34931 + 10.3081i 0.131981 + 0.406196i
\(645\) 0 0
\(646\) 2.04869 1.48846i 0.0806045 0.0585626i
\(647\) −4.79404 1.55768i −0.188473 0.0612386i 0.213260 0.976996i \(-0.431592\pi\)
−0.401733 + 0.915757i \(0.631592\pi\)
\(648\) 2.92057i 0.114731i
\(649\) −25.9346 + 9.45968i −1.01802 + 0.371325i
\(650\) 0 0
\(651\) 6.69431 20.6030i 0.262371 0.807494i
\(652\) 1.19619 + 1.64642i 0.0468466 + 0.0644788i
\(653\) 23.9353 32.9441i 0.936661 1.28920i −0.0205434 0.999789i \(-0.506540\pi\)
0.957204 0.289414i \(-0.0934604\pi\)
\(654\) 1.94775 + 5.99455i 0.0761630 + 0.234406i
\(655\) 0 0
\(656\) −0.305709 0.222111i −0.0119359 0.00867196i
\(657\) −8.65128 11.9075i −0.337519 0.464554i
\(658\) 18.8107 + 6.11196i 0.733316 + 0.238269i
\(659\) −48.7556 −1.89925 −0.949624 0.313390i \(-0.898535\pi\)
−0.949624 + 0.313390i \(0.898535\pi\)
\(660\) 0 0
\(661\) −41.0061 −1.59495 −0.797477 0.603350i \(-0.793832\pi\)
−0.797477 + 0.603350i \(0.793832\pi\)
\(662\) 1.23924 + 0.402653i 0.0481643 + 0.0156495i
\(663\) −0.738190 1.01603i −0.0286689 0.0394594i
\(664\) 14.5110 + 10.5429i 0.563137 + 0.409143i
\(665\) 0 0
\(666\) −1.19909 3.69043i −0.0464640 0.143001i
\(667\) 5.63768 7.75960i 0.218292 0.300453i
\(668\) −16.3095 22.4481i −0.631033 0.868542i
\(669\) 3.23854 9.96721i 0.125209 0.385355i
\(670\) 0 0
\(671\) −27.9577 7.99587i −1.07929 0.308677i
\(672\) 11.0278i 0.425408i
\(673\) −29.0012 9.42305i −1.11791 0.363232i −0.308942 0.951081i \(-0.599975\pi\)
−0.808971 + 0.587849i \(0.799975\pi\)
\(674\) 2.08704 1.51632i 0.0803897 0.0584065i
\(675\) 0 0
\(676\) 3.80189 + 11.7010i 0.146226 + 0.450038i
\(677\) −41.3161 + 13.4244i −1.58791 + 0.515943i −0.964079 0.265617i \(-0.914424\pi\)
−0.623830 + 0.781560i \(0.714424\pi\)
\(678\) −2.87780 + 3.96095i −0.110521 + 0.152120i
\(679\) 3.20007 2.32499i 0.122808 0.0892249i
\(680\) 0 0
\(681\) −17.6731 −0.677235
\(682\) −11.2606 30.8720i −0.431191 1.18215i
\(683\) 43.5970i 1.66819i −0.551619 0.834096i \(-0.685990\pi\)
0.551619 0.834096i \(-0.314010\pi\)
\(684\) 1.09101 3.35779i 0.0417160 0.128388i
\(685\) 0 0
\(686\) 15.1592 + 11.0138i 0.578781 + 0.420509i
\(687\) −3.92755 + 1.27614i −0.149846 + 0.0486878i
\(688\) −1.04504 + 0.339555i −0.0398419 + 0.0129454i
\(689\) −8.45572 6.14344i −0.322137 0.234046i
\(690\) 0 0
\(691\) −2.56761 + 7.90230i −0.0976766 + 0.300618i −0.987942 0.154824i \(-0.950519\pi\)
0.890265 + 0.455442i \(0.150519\pi\)
\(692\) 18.2950i 0.695473i
\(693\) 6.76521 0.240917i 0.256989 0.00915167i
\(694\) −2.91900 −0.110804
\(695\) 0 0
\(696\) 4.81619 3.49917i 0.182557 0.132636i
\(697\) 0.410272 0.564690i 0.0155401 0.0213892i
\(698\) 11.6553 3.78704i 0.441160 0.143342i
\(699\) 4.20231 + 12.9334i 0.158946 + 0.489186i
\(700\) 0 0
\(701\) −7.35189 + 5.34146i −0.277677 + 0.201744i −0.717904 0.696143i \(-0.754898\pi\)
0.440226 + 0.897887i \(0.354898\pi\)
\(702\) 1.28598 + 0.417840i 0.0485362 + 0.0157704i
\(703\) 13.0041i 0.490460i
\(704\) 12.2268 + 15.6274i 0.460815 + 0.588979i
\(705\) 0 0
\(706\) −3.11508 + 9.58724i −0.117238 + 0.360821i
\(707\) 6.30062 + 8.67206i 0.236959 + 0.326147i
\(708\) −5.52121 + 7.59929i −0.207500 + 0.285599i
\(709\) 1.50049 + 4.61802i 0.0563520 + 0.173434i 0.975271 0.221013i \(-0.0709363\pi\)
−0.918919 + 0.394447i \(0.870936\pi\)
\(710\) 0 0
\(711\) 13.7526 + 9.99186i 0.515764 + 0.374724i
\(712\) 6.47517 + 8.91231i 0.242667 + 0.334003i
\(713\) −47.4977 15.4330i −1.77880 0.577969i
\(714\) 1.65211 0.0618287
\(715\) 0 0
\(716\) −19.1506 −0.715691
\(717\) 7.61447 + 2.47409i 0.284367 + 0.0923966i
\(718\) 13.1536 + 18.1043i 0.490887 + 0.675648i
\(719\) 19.3383 + 14.0501i 0.721196 + 0.523980i 0.886766 0.462218i \(-0.152946\pi\)
−0.165570 + 0.986198i \(0.552946\pi\)
\(720\) 0 0
\(721\) 8.57832 + 26.4014i 0.319473 + 0.983238i
\(722\) −5.05497 + 6.95757i −0.188127 + 0.258934i
\(723\) −0.295035 0.406080i −0.0109725 0.0151023i
\(724\) 6.39951 19.6957i 0.237836 0.731983i
\(725\) 0 0
\(726\) 7.85728 6.61153i 0.291611 0.245377i
\(727\) 11.3674i 0.421592i 0.977530 + 0.210796i \(0.0676055\pi\)
−0.977530 + 0.210796i \(0.932394\pi\)
\(728\) 8.21170 + 2.66814i 0.304346 + 0.0988879i
\(729\) 0.809017 0.587785i 0.0299636 0.0217698i
\(730\) 0 0
\(731\) −0.627210 1.93035i −0.0231982 0.0713967i
\(732\) −9.41006 + 3.05751i −0.347806 + 0.113009i
\(733\) −20.0539 + 27.6019i −0.740709 + 1.01950i 0.257869 + 0.966180i \(0.416980\pi\)
−0.998578 + 0.0533185i \(0.983020\pi\)
\(734\) −6.70117 + 4.86869i −0.247345 + 0.179707i
\(735\) 0 0
\(736\) 25.4234 0.937118
\(737\) 8.68355 + 5.84842i 0.319863 + 0.215429i
\(738\) 0.751504i 0.0276632i
\(739\) −0.722631 + 2.22403i −0.0265824 + 0.0818123i −0.963468 0.267825i \(-0.913695\pi\)
0.936885 + 0.349637i \(0.113695\pi\)
\(740\) 0 0
\(741\) −3.66602 2.66352i −0.134675 0.0978470i
\(742\) 13.0764 4.24879i 0.480051 0.155978i
\(743\) −13.7794 + 4.47721i −0.505518 + 0.164253i −0.550663 0.834728i \(-0.685625\pi\)
0.0451450 + 0.998980i \(0.485625\pi\)
\(744\) −25.0778 18.2201i −0.919395 0.667980i
\(745\) 0 0
\(746\) 7.59817 23.3848i 0.278189 0.856177i
\(747\) 6.14148i 0.224705i
\(748\) −2.55596 + 1.99977i −0.0934551 + 0.0731190i
\(749\) −20.3917 −0.745096
\(750\) 0 0
\(751\) −26.9567 + 19.5852i −0.983663 + 0.714673i −0.958524 0.285011i \(-0.908003\pi\)
−0.0251387 + 0.999684i \(0.508003\pi\)
\(752\) 2.86402 3.94198i 0.104440 0.143749i
\(753\) −17.6331 + 5.72933i −0.642585 + 0.208788i
\(754\) −0.851704 2.62128i −0.0310172 0.0954612i
\(755\) 0 0
\(756\) 1.86349 1.35390i 0.0677744 0.0492410i
\(757\) −38.4015 12.4774i −1.39573 0.453499i −0.487921 0.872888i \(-0.662244\pi\)
−0.907807 + 0.419389i \(0.862244\pi\)
\(758\) 4.38396i 0.159233i
\(759\) −0.555406 15.5964i −0.0201600 0.566114i
\(760\) 0 0
\(761\) −15.4190 + 47.4549i −0.558940 + 1.72024i 0.126364 + 0.991984i \(0.459669\pi\)
−0.685304 + 0.728257i \(0.740331\pi\)
\(762\) −11.3448 15.6147i −0.410978 0.565662i
\(763\) 8.10029 11.1491i 0.293250 0.403624i
\(764\) −5.36995 16.5270i −0.194278 0.597926i
\(765\) 0 0
\(766\) −5.21065 3.78576i −0.188268 0.136785i
\(767\) 7.08637 + 9.75356i 0.255874 + 0.352180i
\(768\) 16.0150 + 5.20358i 0.577890 + 0.187768i
\(769\) −4.93932 −0.178116 −0.0890582 0.996026i \(-0.528386\pi\)
−0.0890582 + 0.996026i \(0.528386\pi\)
\(770\) 0 0
\(771\) −7.38010 −0.265788
\(772\) −7.92022 2.57344i −0.285055 0.0926200i
\(773\) 19.6738 + 27.0786i 0.707616 + 0.973950i 0.999845 + 0.0176019i \(0.00560313\pi\)
−0.292229 + 0.956348i \(0.594397\pi\)
\(774\) 1.76794 + 1.28448i 0.0635472 + 0.0461697i
\(775\) 0 0
\(776\) −1.74901 5.38290i −0.0627858 0.193235i
\(777\) −4.98679 + 6.86373i −0.178900 + 0.246235i
\(778\) 1.31946 + 1.81607i 0.0473048 + 0.0651094i
\(779\) 0.778258 2.39523i 0.0278840 0.0858181i
\(780\) 0 0
\(781\) 41.0416 + 11.7379i 1.46858 + 0.420014i
\(782\) 3.80875i 0.136201i
\(783\) −1.93859 0.629885i −0.0692794 0.0225102i
\(784\) 1.07623 0.781926i 0.0384367 0.0279259i
\(785\) 0 0
\(786\) 5.85864 + 18.0310i 0.208971 + 0.643146i
\(787\) 24.6704 8.01590i 0.879405 0.285736i 0.165695 0.986177i \(-0.447013\pi\)
0.713710 + 0.700441i \(0.247013\pi\)
\(788\) −2.08733 + 2.87296i −0.0743581 + 0.102345i
\(789\) 2.47519 1.79833i 0.0881191 0.0640222i
\(790\) 0 0
\(791\) 10.7047 0.380614
\(792\) 2.66352 9.31304i 0.0946442 0.330924i
\(793\) 12.6992i 0.450961i
\(794\) 10.8674 33.4463i 0.385668 1.18696i
\(795\) 0 0
\(796\) −2.97413 2.16083i −0.105415 0.0765888i
\(797\) 9.37993 3.04772i 0.332254 0.107956i −0.138139 0.990413i \(-0.544112\pi\)
0.470393 + 0.882457i \(0.344112\pi\)
\(798\) 5.66936 1.84209i 0.200693 0.0652092i
\(799\) 7.28144 + 5.29027i 0.257599 + 0.187156i
\(800\) 0 0
\(801\) 1.16559 3.58733i 0.0411842 0.126752i
\(802\) 11.6848i 0.412606i
\(803\) 16.7275 + 45.8601i 0.590301 + 1.61837i
\(804\) 3.56233 0.125634
\(805\) 0 0
\(806\) −11.6104 + 8.43548i −0.408960 + 0.297127i
\(807\) −10.3921 + 14.3035i −0.365819 + 0.503507i
\(808\) 14.5874 4.73974i 0.513184 0.166744i
\(809\) 10.2158 + 31.4410i 0.359168 + 1.10541i 0.953553 + 0.301225i \(0.0973956\pi\)
−0.594385 + 0.804181i \(0.702604\pi\)
\(810\) 0 0
\(811\) −4.21750 + 3.06419i −0.148096 + 0.107598i −0.659366 0.751822i \(-0.729175\pi\)
0.511270 + 0.859420i \(0.329175\pi\)
\(812\) −4.46533 1.45088i −0.156703 0.0509157i
\(813\) 15.2992i 0.536565i
\(814\) 0.458013 + 12.8615i 0.0160534 + 0.450796i
\(815\) 0 0
\(816\) 0.125771 0.387084i 0.00440287 0.0135506i
\(817\) −4.30465 5.92484i −0.150601 0.207284i
\(818\) 14.5202 19.9854i 0.507689 0.698773i
\(819\) −0.913569 2.81168i −0.0319227 0.0982479i
\(820\) 0 0
\(821\) 1.32625 + 0.963576i 0.0462864 + 0.0336290i 0.610688 0.791871i \(-0.290893\pi\)
−0.564401 + 0.825500i \(0.690893\pi\)
\(822\) −1.90943 2.62811i −0.0665991 0.0916657i
\(823\) −17.0139 5.52814i −0.593066 0.192699i −0.00292037 0.999996i \(-0.500930\pi\)
−0.590145 + 0.807297i \(0.700930\pi\)
\(824\) 39.7217 1.38377
\(825\) 0 0
\(826\) −15.8597 −0.551830
\(827\) −33.8052 10.9840i −1.17552 0.381951i −0.344821 0.938668i \(-0.612061\pi\)
−0.830702 + 0.556718i \(0.812061\pi\)
\(828\) −3.12127 4.29606i −0.108472 0.149298i
\(829\) −21.8039 15.8415i −0.757282 0.550198i 0.140793 0.990039i \(-0.455035\pi\)
−0.898076 + 0.439841i \(0.855035\pi\)
\(830\) 0 0
\(831\) 5.50785 + 16.9514i 0.191065 + 0.588038i
\(832\) 5.09342 7.01049i 0.176582 0.243045i
\(833\) 1.44433 + 1.98796i 0.0500432 + 0.0688786i
\(834\) −0.787791 + 2.42457i −0.0272790 + 0.0839560i
\(835\) 0 0
\(836\) −6.54126 + 9.71226i −0.226234 + 0.335905i
\(837\) 10.6136i 0.366860i
\(838\) −27.4974 8.93444i −0.949881 0.308635i
\(839\) −9.57654 + 6.95776i −0.330619 + 0.240209i −0.740693 0.671843i \(-0.765503\pi\)
0.410074 + 0.912052i \(0.365503\pi\)
\(840\) 0 0
\(841\) −7.67757 23.6291i −0.264744 0.814797i
\(842\) −16.1973 + 5.26282i −0.558195 + 0.181369i
\(843\) 10.1681 13.9952i 0.350207 0.482019i
\(844\) −18.1906 + 13.2162i −0.626146 + 0.454922i
\(845\) 0 0
\(846\) −9.69031 −0.333160
\(847\) −21.7924 5.40155i −0.748797 0.185600i
\(848\) 3.38721i 0.116317i
\(849\) −7.96534 + 24.5148i −0.273370 + 0.841346i
\(850\) 0 0
\(851\) 15.8235 + 11.4965i 0.542423 + 0.394094i
\(852\) 13.8139 4.48840i 0.473256 0.153770i
\(853\) 28.8211 9.36453i 0.986814 0.320635i 0.229230 0.973372i \(-0.426379\pi\)
0.757585 + 0.652737i \(0.226379\pi\)
\(854\) −13.5152 9.81939i −0.462482 0.336013i
\(855\) 0 0
\(856\) −9.01660 + 27.7503i −0.308181 + 0.948484i
\(857\) 29.2318i 0.998540i 0.866446 + 0.499270i \(0.166398\pi\)
−0.866446 + 0.499270i \(0.833602\pi\)
\(858\) −3.71963 2.50519i −0.126986 0.0855259i
\(859\) 36.7151 1.25270 0.626351 0.779541i \(-0.284548\pi\)
0.626351 + 0.779541i \(0.284548\pi\)
\(860\) 0 0
\(861\) 1.32929 0.965786i 0.0453021 0.0329139i
\(862\) 16.6529 22.9207i 0.567199 0.780682i
\(863\) −41.4431 + 13.4657i −1.41074 + 0.458377i −0.912647 0.408748i \(-0.865966\pi\)
−0.498091 + 0.867125i \(0.665966\pi\)
\(864\) −1.66960 5.13850i −0.0568009 0.174815i
\(865\) 0 0
\(866\) 9.59252 6.96937i 0.325967 0.236829i
\(867\) −15.4530 5.02097i −0.524810 0.170521i
\(868\) 24.4474i 0.829798i
\(869\) −34.7415 44.4040i −1.17853 1.50630i
\(870\) 0 0
\(871\) 1.41288 4.34841i 0.0478737 0.147340i
\(872\) −11.5907 15.9532i −0.392509 0.540243i
\(873\) −1.13910 + 1.56783i −0.0385526 + 0.0530631i
\(874\) −4.24672 13.0701i −0.143647 0.442101i
\(875\) 0 0
\(876\) 13.4378 + 9.76314i 0.454021 + 0.329866i
\(877\) −6.53457 8.99407i −0.220657 0.303708i 0.684309 0.729192i \(-0.260104\pi\)
−0.904966 + 0.425484i \(0.860104\pi\)
\(878\) 22.7788 + 7.40129i 0.768748 + 0.249781i
\(879\) 13.5306 0.456377
\(880\) 0 0
\(881\) −39.1155 −1.31783 −0.658917 0.752216i \(-0.728985\pi\)
−0.658917 + 0.752216i \(0.728985\pi\)
\(882\) −2.51613 0.817542i −0.0847227 0.0275281i
\(883\) −11.4728 15.7910i −0.386091 0.531408i 0.571094 0.820884i \(-0.306519\pi\)
−0.957185 + 0.289476i \(0.906519\pi\)
\(884\) 1.14661 + 0.833061i 0.0385647 + 0.0280189i
\(885\) 0 0
\(886\) 7.56236 + 23.2746i 0.254063 + 0.781924i
\(887\) 3.05124 4.19967i 0.102451 0.141011i −0.754714 0.656054i \(-0.772224\pi\)
0.857164 + 0.515043i \(0.172224\pi\)
\(888\) 7.13557 + 9.82127i 0.239454 + 0.329580i
\(889\) −13.0404 + 40.1342i −0.437361 + 1.34606i
\(890\) 0 0
\(891\) −3.11582 + 1.13650i −0.104384 + 0.0380742i
\(892\) 11.8270i 0.395999i
\(893\) 30.8855 + 10.0353i 1.03354 + 0.335818i
\(894\) −6.87906 + 4.99793i −0.230070 + 0.167156i
\(895\) 0 0
\(896\) −3.29298 10.1347i −0.110011 0.338578i
\(897\) −6.48199 + 2.10613i −0.216427 + 0.0703215i
\(898\) 6.58796 9.06755i 0.219843 0.302588i
\(899\) 17.5025 12.7163i 0.583740 0.424112i
\(900\) 0 0
\(901\) 6.25669 0.208440
\(902\) 0.685362 2.39638i 0.0228201 0.0797906i
\(903\) 4.77794i 0.159000i
\(904\) 4.73329 14.5676i 0.157427 0.484510i
\(905\) 0 0
\(906\) −16.2939 11.8382i −0.541330 0.393299i
\(907\) −40.3608 + 13.1140i −1.34016 + 0.435444i −0.889371 0.457187i \(-0.848857\pi\)
−0.450789 + 0.892631i \(0.648857\pi\)
\(908\) 18.9683 6.16318i 0.629485 0.204532i
\(909\) −4.24876 3.08691i −0.140923 0.102386i
\(910\) 0 0
\(911\) −6.10306 + 18.7833i −0.202203 + 0.622318i 0.797613 + 0.603169i \(0.206096\pi\)
−0.999817 + 0.0191487i \(0.993904\pi\)
\(912\) 1.46854i 0.0486283i
\(913\) −5.60095 + 19.5838i −0.185364 + 0.648129i
\(914\) 12.8725 0.425783
\(915\) 0 0
\(916\) 3.77036 2.73932i 0.124576 0.0905098i
\(917\) 24.3649 33.5354i 0.804599 1.10744i
\(918\) −0.769814 + 0.250128i −0.0254076 + 0.00825544i
\(919\) 7.56638 + 23.2869i 0.249592 + 0.768165i 0.994847 + 0.101385i \(0.0323275\pi\)
−0.745255 + 0.666779i \(0.767672\pi\)
\(920\) 0 0
\(921\) −10.5389 + 7.65695i −0.347268 + 0.252305i
\(922\) 10.0559 + 3.26736i 0.331173 + 0.107605i
\(923\) 18.6423i 0.613619i
\(924\) −7.17699 + 2.61781i −0.236105 + 0.0861198i
\(925\) 0 0
\(926\) −1.78505 + 5.49382i −0.0586604 + 0.180538i
\(927\) −7.99426 11.0032i −0.262566 0.361391i
\(928\) −6.47332 + 8.90976i −0.212497 + 0.292477i
\(929\) 1.87044 + 5.75664i 0.0613673 + 0.188869i 0.977040 0.213055i \(-0.0683415\pi\)
−0.915673 + 0.401924i \(0.868341\pi\)
\(930\) 0 0
\(931\) 7.17291 + 5.21142i 0.235083 + 0.170797i
\(932\) −9.02056 12.4157i −0.295478 0.406691i
\(933\) −1.81004 0.588119i −0.0592582 0.0192541i
\(934\) 7.91903 0.259119
\(935\) 0 0
\(936\) −4.23026 −0.138270
\(937\) −6.50394 2.11326i −0.212475 0.0690372i 0.200846 0.979623i \(-0.435631\pi\)
−0.413320 + 0.910586i \(0.635631\pi\)
\(938\) 3.53535 + 4.86599i 0.115433 + 0.158880i
\(939\) −8.84448 6.42589i −0.288629 0.209701i
\(940\) 0 0
\(941\) −1.22191 3.76064i −0.0398330 0.122593i 0.929163 0.369671i \(-0.120530\pi\)
−0.968996 + 0.247078i \(0.920530\pi\)
\(942\) 13.0561 17.9702i 0.425391 0.585501i
\(943\) −2.22651 3.06453i −0.0725051 0.0997947i
\(944\) −1.20736 + 3.71587i −0.0392962 + 0.120941i
\(945\) 0 0
\(946\) −4.46612 5.70826i −0.145206 0.185591i
\(947\) 40.1742i 1.30549i 0.757579 + 0.652743i \(0.226382\pi\)
−0.757579 + 0.652743i \(0.773618\pi\)
\(948\) −18.2450 5.92815i −0.592569 0.192537i
\(949\) 17.2472 12.5308i 0.559867 0.406767i
\(950\) 0 0
\(951\) 4.96660 + 15.2856i 0.161053 + 0.495670i
\(952\) −4.91569 + 1.59720i −0.159318 + 0.0517657i
\(953\) −24.2444 + 33.3696i −0.785353 + 1.08095i 0.209318 + 0.977848i \(0.432876\pi\)
−0.994671 + 0.103098i \(0.967124\pi\)
\(954\) −5.44980 + 3.95951i −0.176444 + 0.128194i
\(955\) 0 0
\(956\) −9.03529 −0.292222
\(957\) 5.60726 + 3.77652i 0.181257 + 0.122078i
\(958\) 8.62166i 0.278553i
\(959\) −2.19482 + 6.75496i −0.0708744 + 0.218129i
\(960\) 0 0
\(961\) −66.0553 47.9920i −2.13082 1.54813i
\(962\) 5.34535 1.73681i 0.172341 0.0559970i
\(963\) 9.50166 3.08727i 0.306187 0.0994860i
\(964\) 0.458269 + 0.332952i 0.0147599 + 0.0107237i
\(965\) 0 0
\(966\) 2.77060 8.52704i 0.0891427 0.274353i
\(967\) 9.16826i 0.294831i −0.989075 0.147416i \(-0.952904\pi\)
0.989075 0.147416i \(-0.0470955\pi\)
\(968\) −16.9867 + 27.2681i −0.545975 + 0.876429i
\(969\) 2.71262 0.0871420
\(970\) 0 0
\(971\) 3.00359 2.18224i 0.0963899 0.0700313i −0.538546 0.842596i \(-0.681026\pi\)
0.634936 + 0.772565i \(0.281026\pi\)
\(972\) −0.663327 + 0.912991i −0.0212762 + 0.0292842i
\(973\) 5.30110 1.72243i 0.169946 0.0552186i
\(974\) 5.81880 + 17.9084i 0.186446 + 0.573823i
\(975\) 0 0
\(976\) −3.32953 + 2.41904i −0.106576 + 0.0774317i
\(977\) −11.7867 3.82972i −0.377089 0.122524i 0.114339 0.993442i \(-0.463525\pi\)
−0.491428 + 0.870918i \(0.663525\pi\)
\(978\) 1.68346i 0.0538311i
\(979\) −6.98842 + 10.3762i −0.223351 + 0.331624i
\(980\) 0 0
\(981\) −2.08643 + 6.42137i −0.0666146 + 0.205019i
\(982\) 2.92791 + 4.02993i 0.0934335 + 0.128600i
\(983\) 13.6924 18.8460i 0.436720 0.601093i −0.532760 0.846267i \(-0.678845\pi\)
0.969479 + 0.245174i \(0.0788450\pi\)
\(984\) −0.726528 2.23602i −0.0231609 0.0712818i
\(985\) 0 0
\(986\) 1.33480 + 0.969788i 0.0425086 + 0.0308843i
\(987\) 12.4534 + 17.1406i 0.396396 + 0.545592i
\(988\) 4.86355 + 1.58026i 0.154730 + 0.0502748i
\(989\) −11.0150 −0.350256
\(990\) 0 0
\(991\) −37.7826 −1.20020 −0.600101 0.799924i \(-0.704873\pi\)
−0.600101 + 0.799924i \(0.704873\pi\)
\(992\) 54.5380 + 17.7205i 1.73158 + 0.562626i
\(993\) 0.820424 + 1.12922i 0.0260354 + 0.0358346i
\(994\) 19.8403 + 14.4148i 0.629295 + 0.457209i
\(995\) 0 0
\(996\) 2.14173 + 6.59156i 0.0678633 + 0.208862i
\(997\) −4.62934 + 6.37174i −0.146613 + 0.201795i −0.876007 0.482299i \(-0.839802\pi\)
0.729394 + 0.684094i \(0.239802\pi\)
\(998\) −21.5544 29.6671i −0.682294 0.939097i
\(999\) 1.28447 3.95320i 0.0406389 0.125074i
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 825.2.bx.g.724.3 16
5.2 odd 4 165.2.m.b.31.1 yes 8
5.3 odd 4 825.2.n.i.526.2 8
5.4 even 2 inner 825.2.bx.g.724.2 16
11.5 even 5 inner 825.2.bx.g.49.2 16
15.2 even 4 495.2.n.b.361.2 8
55.7 even 20 1815.2.a.r.1.3 4
55.18 even 20 9075.2.a.dg.1.2 4
55.27 odd 20 165.2.m.b.16.1 8
55.37 odd 20 1815.2.a.v.1.2 4
55.38 odd 20 825.2.n.i.676.2 8
55.48 odd 20 9075.2.a.cq.1.3 4
55.49 even 10 inner 825.2.bx.g.49.3 16
165.62 odd 20 5445.2.a.br.1.2 4
165.92 even 20 5445.2.a.bk.1.3 4
165.137 even 20 495.2.n.b.181.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.2.m.b.16.1 8 55.27 odd 20
165.2.m.b.31.1 yes 8 5.2 odd 4
495.2.n.b.181.2 8 165.137 even 20
495.2.n.b.361.2 8 15.2 even 4
825.2.n.i.526.2 8 5.3 odd 4
825.2.n.i.676.2 8 55.38 odd 20
825.2.bx.g.49.2 16 11.5 even 5 inner
825.2.bx.g.49.3 16 55.49 even 10 inner
825.2.bx.g.724.2 16 5.4 even 2 inner
825.2.bx.g.724.3 16 1.1 even 1 trivial
1815.2.a.r.1.3 4 55.7 even 20
1815.2.a.v.1.2 4 55.37 odd 20
5445.2.a.bk.1.3 4 165.92 even 20
5445.2.a.br.1.2 4 165.62 odd 20
9075.2.a.cq.1.3 4 55.48 odd 20
9075.2.a.dg.1.2 4 55.18 even 20