Properties

Label 1110.2.l.a.43.10
Level $1110$
Weight $2$
Character 1110.43
Analytic conductor $8.863$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1110,2,Mod(43,1110)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1110.43");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.l (of order \(4\), degree \(2\), 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: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.10
Character \(\chi\) \(=\) 1110.43
Dual form 1110.2.l.a.697.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(1.87641 + 1.21617i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-2.24767 + 2.24767i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(1.87641 + 1.21617i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-2.24767 + 2.24767i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +(-1.21617 + 1.87641i) q^{10} +5.65930i q^{11} +(-0.707107 + 0.707107i) q^{12} -4.81453i q^{13} +(-2.24767 - 2.24767i) q^{14} +(2.18679 - 0.466864i) q^{15} +1.00000 q^{16} -7.58373 q^{17} +1.00000 q^{18} +(-3.73408 + 3.73408i) q^{19} +(-1.87641 - 1.21617i) q^{20} +3.17868i q^{21} -5.65930 q^{22} +4.23021i q^{23} +(-0.707107 - 0.707107i) q^{24} +(2.04186 + 4.56408i) q^{25} +4.81453 q^{26} +(-0.707107 - 0.707107i) q^{27} +(2.24767 - 2.24767i) q^{28} +(3.26498 + 3.26498i) q^{29} +(0.466864 + 2.18679i) q^{30} +(1.98809 - 1.98809i) q^{31} +1.00000i q^{32} +(4.00173 + 4.00173i) q^{33} -7.58373i q^{34} +(-6.95110 + 1.48401i) q^{35} +1.00000i q^{36} +(-4.17208 - 4.42648i) q^{37} +(-3.73408 - 3.73408i) q^{38} +(-3.40439 - 3.40439i) q^{39} +(1.21617 - 1.87641i) q^{40} -2.43043i q^{41} -3.17868 q^{42} -3.34656i q^{43} -5.65930i q^{44} +(1.21617 - 1.87641i) q^{45} -4.23021 q^{46} +(6.04560 - 6.04560i) q^{47} +(0.707107 - 0.707107i) q^{48} -3.10403i q^{49} +(-4.56408 + 2.04186i) q^{50} +(-5.36251 + 5.36251i) q^{51} +4.81453i q^{52} +(8.02058 + 8.02058i) q^{53} +(0.707107 - 0.707107i) q^{54} +(-6.88266 + 10.6192i) q^{55} +(2.24767 + 2.24767i) q^{56} +5.28079i q^{57} +(-3.26498 + 3.26498i) q^{58} +(-9.84721 + 9.84721i) q^{59} +(-2.18679 + 0.466864i) q^{60} +(-1.11855 + 1.11855i) q^{61} +(1.98809 + 1.98809i) q^{62} +(2.24767 + 2.24767i) q^{63} -1.00000 q^{64} +(5.85528 - 9.03405i) q^{65} +(-4.00173 + 4.00173i) q^{66} +(6.91167 + 6.91167i) q^{67} +7.58373 q^{68} +(2.99121 + 2.99121i) q^{69} +(-1.48401 - 6.95110i) q^{70} -6.12087 q^{71} -1.00000 q^{72} +(-2.58794 + 2.58794i) q^{73} +(4.42648 - 4.17208i) q^{74} +(4.67110 + 1.78347i) q^{75} +(3.73408 - 3.73408i) q^{76} +(-12.7202 - 12.7202i) q^{77} +(3.40439 - 3.40439i) q^{78} +(-2.85317 + 2.85317i) q^{79} +(1.87641 + 1.21617i) q^{80} -1.00000 q^{81} +2.43043 q^{82} +(0.906248 + 0.906248i) q^{83} -3.17868i q^{84} +(-14.2302 - 9.22310i) q^{85} +3.34656 q^{86} +4.61737 q^{87} +5.65930 q^{88} +(10.1878 + 10.1878i) q^{89} +(1.87641 + 1.21617i) q^{90} +(10.8215 + 10.8215i) q^{91} -4.23021i q^{92} -2.81158i q^{93} +(6.04560 + 6.04560i) q^{94} +(-11.5480 + 2.46541i) q^{95} +(0.707107 + 0.707107i) q^{96} -2.87834 q^{97} +3.10403 q^{98} +5.65930 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 36 q^{4} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 36 q - 36 q^{4} + 4 q^{7} - 4 q^{10} + 4 q^{14} + 36 q^{16} - 32 q^{17} + 36 q^{18} + 4 q^{19} + 8 q^{22} - 4 q^{25} + 8 q^{26} - 4 q^{28} + 36 q^{29} - 4 q^{31} + 4 q^{33} - 12 q^{35} - 4 q^{37} + 4 q^{38} + 4 q^{39} + 4 q^{40} - 16 q^{42} + 4 q^{45} + 16 q^{47} - 16 q^{50} - 8 q^{53} + 16 q^{55} - 4 q^{56} - 36 q^{58} - 4 q^{59} - 4 q^{61} - 4 q^{62} - 4 q^{63} - 36 q^{64} + 52 q^{65} - 4 q^{66} + 16 q^{67} + 32 q^{68} - 8 q^{69} - 28 q^{70} - 8 q^{71} - 36 q^{72} - 4 q^{73} + 28 q^{74} + 16 q^{75} - 4 q^{76} + 8 q^{77} - 4 q^{78} - 12 q^{79} - 36 q^{81} - 8 q^{82} + 8 q^{83} + 8 q^{85} + 32 q^{86} - 8 q^{87} - 8 q^{88} - 24 q^{89} + 56 q^{91} + 16 q^{94} - 20 q^{95} + 40 q^{97} - 12 q^{98} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0.707107 0.707107i 0.408248 0.408248i
\(4\) −1.00000 −0.500000
\(5\) 1.87641 + 1.21617i 0.839158 + 0.543888i
\(6\) 0.707107 + 0.707107i 0.288675 + 0.288675i
\(7\) −2.24767 + 2.24767i −0.849539 + 0.849539i −0.990075 0.140537i \(-0.955117\pi\)
0.140537 + 0.990075i \(0.455117\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 1.00000i 0.333333i
\(10\) −1.21617 + 1.87641i −0.384587 + 0.593374i
\(11\) 5.65930i 1.70634i 0.521632 + 0.853171i \(0.325324\pi\)
−0.521632 + 0.853171i \(0.674676\pi\)
\(12\) −0.707107 + 0.707107i −0.204124 + 0.204124i
\(13\) 4.81453i 1.33531i −0.744471 0.667655i \(-0.767298\pi\)
0.744471 0.667655i \(-0.232702\pi\)
\(14\) −2.24767 2.24767i −0.600715 0.600715i
\(15\) 2.18679 0.466864i 0.564626 0.120544i
\(16\) 1.00000 0.250000
\(17\) −7.58373 −1.83932 −0.919662 0.392710i \(-0.871537\pi\)
−0.919662 + 0.392710i \(0.871537\pi\)
\(18\) 1.00000 0.235702
\(19\) −3.73408 + 3.73408i −0.856657 + 0.856657i −0.990943 0.134285i \(-0.957126\pi\)
0.134285 + 0.990943i \(0.457126\pi\)
\(20\) −1.87641 1.21617i −0.419579 0.271944i
\(21\) 3.17868i 0.693646i
\(22\) −5.65930 −1.20657
\(23\) 4.23021i 0.882059i 0.897493 + 0.441030i \(0.145387\pi\)
−0.897493 + 0.441030i \(0.854613\pi\)
\(24\) −0.707107 0.707107i −0.144338 0.144338i
\(25\) 2.04186 + 4.56408i 0.408373 + 0.912815i
\(26\) 4.81453 0.944207
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) 2.24767 2.24767i 0.424769 0.424769i
\(29\) 3.26498 + 3.26498i 0.606291 + 0.606291i 0.941975 0.335684i \(-0.108967\pi\)
−0.335684 + 0.941975i \(0.608967\pi\)
\(30\) 0.466864 + 2.18679i 0.0852373 + 0.399251i
\(31\) 1.98809 1.98809i 0.357071 0.357071i −0.505661 0.862732i \(-0.668751\pi\)
0.862732 + 0.505661i \(0.168751\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 4.00173 + 4.00173i 0.696611 + 0.696611i
\(34\) 7.58373i 1.30060i
\(35\) −6.95110 + 1.48401i −1.17495 + 0.250844i
\(36\) 1.00000i 0.166667i
\(37\) −4.17208 4.42648i −0.685886 0.727709i
\(38\) −3.73408 3.73408i −0.605748 0.605748i
\(39\) −3.40439 3.40439i −0.545138 0.545138i
\(40\) 1.21617 1.87641i 0.192293 0.296687i
\(41\) 2.43043i 0.379570i −0.981826 0.189785i \(-0.939221\pi\)
0.981826 0.189785i \(-0.0607791\pi\)
\(42\) −3.17868 −0.490482
\(43\) 3.34656i 0.510346i −0.966895 0.255173i \(-0.917868\pi\)
0.966895 0.255173i \(-0.0821324\pi\)
\(44\) 5.65930i 0.853171i
\(45\) 1.21617 1.87641i 0.181296 0.279719i
\(46\) −4.23021 −0.623710
\(47\) 6.04560 6.04560i 0.881842 0.881842i −0.111880 0.993722i \(-0.535687\pi\)
0.993722 + 0.111880i \(0.0356873\pi\)
\(48\) 0.707107 0.707107i 0.102062 0.102062i
\(49\) 3.10403i 0.443433i
\(50\) −4.56408 + 2.04186i −0.645458 + 0.288763i
\(51\) −5.36251 + 5.36251i −0.750901 + 0.750901i
\(52\) 4.81453i 0.667655i
\(53\) 8.02058 + 8.02058i 1.10171 + 1.10171i 0.994204 + 0.107507i \(0.0342868\pi\)
0.107507 + 0.994204i \(0.465713\pi\)
\(54\) 0.707107 0.707107i 0.0962250 0.0962250i
\(55\) −6.88266 + 10.6192i −0.928058 + 1.43189i
\(56\) 2.24767 + 2.24767i 0.300357 + 0.300357i
\(57\) 5.28079i 0.699458i
\(58\) −3.26498 + 3.26498i −0.428712 + 0.428712i
\(59\) −9.84721 + 9.84721i −1.28200 + 1.28200i −0.342468 + 0.939530i \(0.611263\pi\)
−0.939530 + 0.342468i \(0.888737\pi\)
\(60\) −2.18679 + 0.466864i −0.282313 + 0.0602718i
\(61\) −1.11855 + 1.11855i −0.143216 + 0.143216i −0.775080 0.631864i \(-0.782290\pi\)
0.631864 + 0.775080i \(0.282290\pi\)
\(62\) 1.98809 + 1.98809i 0.252487 + 0.252487i
\(63\) 2.24767 + 2.24767i 0.283180 + 0.283180i
\(64\) −1.00000 −0.125000
\(65\) 5.85528 9.03405i 0.726259 1.12054i
\(66\) −4.00173 + 4.00173i −0.492578 + 0.492578i
\(67\) 6.91167 + 6.91167i 0.844395 + 0.844395i 0.989427 0.145032i \(-0.0463284\pi\)
−0.145032 + 0.989427i \(0.546328\pi\)
\(68\) 7.58373 0.919662
\(69\) 2.99121 + 2.99121i 0.360099 + 0.360099i
\(70\) −1.48401 6.95110i −0.177373 0.830816i
\(71\) −6.12087 −0.726413 −0.363207 0.931709i \(-0.618318\pi\)
−0.363207 + 0.931709i \(0.618318\pi\)
\(72\) −1.00000 −0.117851
\(73\) −2.58794 + 2.58794i −0.302896 + 0.302896i −0.842146 0.539250i \(-0.818708\pi\)
0.539250 + 0.842146i \(0.318708\pi\)
\(74\) 4.42648 4.17208i 0.514568 0.484995i
\(75\) 4.67110 + 1.78347i 0.539373 + 0.205938i
\(76\) 3.73408 3.73408i 0.428329 0.428329i
\(77\) −12.7202 12.7202i −1.44960 1.44960i
\(78\) 3.40439 3.40439i 0.385471 0.385471i
\(79\) −2.85317 + 2.85317i −0.321007 + 0.321007i −0.849153 0.528146i \(-0.822887\pi\)
0.528146 + 0.849153i \(0.322887\pi\)
\(80\) 1.87641 + 1.21617i 0.209790 + 0.135972i
\(81\) −1.00000 −0.111111
\(82\) 2.43043 0.268396
\(83\) 0.906248 + 0.906248i 0.0994737 + 0.0994737i 0.755092 0.655619i \(-0.227592\pi\)
−0.655619 + 0.755092i \(0.727592\pi\)
\(84\) 3.17868i 0.346823i
\(85\) −14.2302 9.22310i −1.54348 1.00039i
\(86\) 3.34656 0.360869
\(87\) 4.61737 0.495034
\(88\) 5.65930 0.603283
\(89\) 10.1878 + 10.1878i 1.07990 + 1.07990i 0.996518 + 0.0833830i \(0.0265725\pi\)
0.0833830 + 0.996518i \(0.473428\pi\)
\(90\) 1.87641 + 1.21617i 0.197791 + 0.128196i
\(91\) 10.8215 + 10.8215i 1.13440 + 1.13440i
\(92\) 4.23021i 0.441030i
\(93\) 2.81158i 0.291547i
\(94\) 6.04560 + 6.04560i 0.623556 + 0.623556i
\(95\) −11.5480 + 2.46541i −1.18480 + 0.252946i
\(96\) 0.707107 + 0.707107i 0.0721688 + 0.0721688i
\(97\) −2.87834 −0.292251 −0.146125 0.989266i \(-0.546680\pi\)
−0.146125 + 0.989266i \(0.546680\pi\)
\(98\) 3.10403 0.313554
\(99\) 5.65930 0.568781
\(100\) −2.04186 4.56408i −0.204186 0.456408i
\(101\) 16.0893i 1.60095i −0.599367 0.800474i \(-0.704581\pi\)
0.599367 0.800474i \(-0.295419\pi\)
\(102\) −5.36251 5.36251i −0.530967 0.530967i
\(103\) 11.0997 1.09369 0.546845 0.837234i \(-0.315829\pi\)
0.546845 + 0.837234i \(0.315829\pi\)
\(104\) −4.81453 −0.472103
\(105\) −3.86582 + 5.96453i −0.377265 + 0.582078i
\(106\) −8.02058 + 8.02058i −0.779028 + 0.779028i
\(107\) 8.64549 8.64549i 0.835791 0.835791i −0.152511 0.988302i \(-0.548736\pi\)
0.988302 + 0.152511i \(0.0487359\pi\)
\(108\) 0.707107 + 0.707107i 0.0680414 + 0.0680414i
\(109\) −13.7592 + 13.7592i −1.31790 + 1.31790i −0.402458 + 0.915438i \(0.631844\pi\)
−0.915438 + 0.402458i \(0.868156\pi\)
\(110\) −10.6192 6.88266i −1.01250 0.656236i
\(111\) −6.08010 0.179886i −0.577098 0.0170740i
\(112\) −2.24767 + 2.24767i −0.212385 + 0.212385i
\(113\) 4.68689 0.440906 0.220453 0.975398i \(-0.429246\pi\)
0.220453 + 0.975398i \(0.429246\pi\)
\(114\) −5.28079 −0.494591
\(115\) −5.14465 + 7.93762i −0.479741 + 0.740187i
\(116\) −3.26498 3.26498i −0.303145 0.303145i
\(117\) −4.81453 −0.445103
\(118\) −9.84721 9.84721i −0.906509 0.906509i
\(119\) 17.0457 17.0457i 1.56258 1.56258i
\(120\) −0.466864 2.18679i −0.0426186 0.199625i
\(121\) −21.0276 −1.91160
\(122\) −1.11855 1.11855i −0.101269 0.101269i
\(123\) −1.71858 1.71858i −0.154959 0.154959i
\(124\) −1.98809 + 1.98809i −0.178535 + 0.178535i
\(125\) −1.71931 + 11.0474i −0.153780 + 0.988105i
\(126\) −2.24767 + 2.24767i −0.200238 + 0.200238i
\(127\) −14.6086 + 14.6086i −1.29630 + 1.29630i −0.365488 + 0.930816i \(0.619098\pi\)
−0.930816 + 0.365488i \(0.880902\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −2.36638 2.36638i −0.208348 0.208348i
\(130\) 9.03405 + 5.85528i 0.792339 + 0.513542i
\(131\) 9.26219 9.26219i 0.809241 0.809241i −0.175278 0.984519i \(-0.556082\pi\)
0.984519 + 0.175278i \(0.0560824\pi\)
\(132\) −4.00173 4.00173i −0.348306 0.348306i
\(133\) 16.7860i 1.45553i
\(134\) −6.91167 + 6.91167i −0.597078 + 0.597078i
\(135\) −0.466864 2.18679i −0.0401812 0.188209i
\(136\) 7.58373i 0.650299i
\(137\) 1.63948 1.63948i 0.140071 0.140071i −0.633595 0.773665i \(-0.718421\pi\)
0.773665 + 0.633595i \(0.218421\pi\)
\(138\) −2.99121 + 2.99121i −0.254629 + 0.254629i
\(139\) 17.9432 1.52192 0.760959 0.648800i \(-0.224729\pi\)
0.760959 + 0.648800i \(0.224729\pi\)
\(140\) 6.95110 1.48401i 0.587476 0.125422i
\(141\) 8.54977i 0.720021i
\(142\) 6.12087i 0.513652i
\(143\) 27.2468 2.27850
\(144\) 1.00000i 0.0833333i
\(145\) 2.15568 + 10.0972i 0.179020 + 0.838528i
\(146\) −2.58794 2.58794i −0.214180 0.214180i
\(147\) −2.19488 2.19488i −0.181031 0.181031i
\(148\) 4.17208 + 4.42648i 0.342943 + 0.363854i
\(149\) 9.20482i 0.754088i −0.926195 0.377044i \(-0.876941\pi\)
0.926195 0.377044i \(-0.123059\pi\)
\(150\) −1.78347 + 4.67110i −0.145620 + 0.381394i
\(151\) 5.59713i 0.455488i 0.973721 + 0.227744i \(0.0731349\pi\)
−0.973721 + 0.227744i \(0.926865\pi\)
\(152\) 3.73408 + 3.73408i 0.302874 + 0.302874i
\(153\) 7.58373i 0.613108i
\(154\) 12.7202 12.7202i 1.02502 1.02502i
\(155\) 6.14832 1.31262i 0.493845 0.105432i
\(156\) 3.40439 + 3.40439i 0.272569 + 0.272569i
\(157\) −0.998661 + 0.998661i −0.0797019 + 0.0797019i −0.745834 0.666132i \(-0.767949\pi\)
0.666132 + 0.745834i \(0.267949\pi\)
\(158\) −2.85317 2.85317i −0.226986 0.226986i
\(159\) 11.3428 0.899543
\(160\) −1.21617 + 1.87641i −0.0961466 + 0.148344i
\(161\) −9.50811 9.50811i −0.749344 0.749344i
\(162\) 1.00000i 0.0785674i
\(163\) −7.74976 −0.607008 −0.303504 0.952830i \(-0.598157\pi\)
−0.303504 + 0.952830i \(0.598157\pi\)
\(164\) 2.43043i 0.189785i
\(165\) 2.64212 + 12.3757i 0.205689 + 0.963445i
\(166\) −0.906248 + 0.906248i −0.0703385 + 0.0703385i
\(167\) 19.2547 1.48997 0.744985 0.667081i \(-0.232457\pi\)
0.744985 + 0.667081i \(0.232457\pi\)
\(168\) 3.17868 0.245241
\(169\) −10.1797 −0.783053
\(170\) 9.22310 14.2302i 0.707379 1.09141i
\(171\) 3.73408 + 3.73408i 0.285552 + 0.285552i
\(172\) 3.34656i 0.255173i
\(173\) 8.58579 8.58579i 0.652765 0.652765i −0.300893 0.953658i \(-0.597285\pi\)
0.953658 + 0.300893i \(0.0972846\pi\)
\(174\) 4.61737i 0.350042i
\(175\) −14.8480 5.66910i −1.12240 0.428544i
\(176\) 5.65930i 0.426585i
\(177\) 13.9261i 1.04675i
\(178\) −10.1878 + 10.1878i −0.763605 + 0.763605i
\(179\) −14.0961 14.0961i −1.05359 1.05359i −0.998480 0.0551080i \(-0.982450\pi\)
−0.0551080 0.998480i \(-0.517550\pi\)
\(180\) −1.21617 + 1.87641i −0.0906479 + 0.139860i
\(181\) 13.7831 1.02449 0.512245 0.858839i \(-0.328814\pi\)
0.512245 + 0.858839i \(0.328814\pi\)
\(182\) −10.8215 + 10.8215i −0.802140 + 0.802140i
\(183\) 1.58187i 0.116935i
\(184\) 4.23021 0.311855
\(185\) −2.44521 13.3799i −0.179775 0.983708i
\(186\) 2.81158 0.206155
\(187\) 42.9186i 3.13852i
\(188\) −6.04560 + 6.04560i −0.440921 + 0.440921i
\(189\) 3.17868 0.231215
\(190\) −2.46541 11.5480i −0.178860 0.837777i
\(191\) 18.4453 + 18.4453i 1.33466 + 1.33466i 0.901149 + 0.433509i \(0.142725\pi\)
0.433509 + 0.901149i \(0.357275\pi\)
\(192\) −0.707107 + 0.707107i −0.0510310 + 0.0510310i
\(193\) 22.9897i 1.65484i −0.561585 0.827419i \(-0.689808\pi\)
0.561585 0.827419i \(-0.310192\pi\)
\(194\) 2.87834i 0.206652i
\(195\) −2.24773 10.5284i −0.160963 0.753951i
\(196\) 3.10403i 0.221716i
\(197\) −1.69341 + 1.69341i −0.120650 + 0.120650i −0.764854 0.644204i \(-0.777189\pi\)
0.644204 + 0.764854i \(0.277189\pi\)
\(198\) 5.65930i 0.402189i
\(199\) 7.33672 + 7.33672i 0.520087 + 0.520087i 0.917597 0.397511i \(-0.130126\pi\)
−0.397511 + 0.917597i \(0.630126\pi\)
\(200\) 4.56408 2.04186i 0.322729 0.144382i
\(201\) 9.77458 0.689446
\(202\) 16.0893 1.13204
\(203\) −14.6772 −1.03014
\(204\) 5.36251 5.36251i 0.375451 0.375451i
\(205\) 2.95582 4.56050i 0.206443 0.318519i
\(206\) 11.0997i 0.773355i
\(207\) 4.23021 0.294020
\(208\) 4.81453i 0.333828i
\(209\) −21.1323 21.1323i −1.46175 1.46175i
\(210\) −5.96453 3.86582i −0.411592 0.266767i
\(211\) 11.9466 0.822435 0.411218 0.911537i \(-0.365104\pi\)
0.411218 + 0.911537i \(0.365104\pi\)
\(212\) −8.02058 8.02058i −0.550856 0.550856i
\(213\) −4.32811 + 4.32811i −0.296557 + 0.296557i
\(214\) 8.64549 + 8.64549i 0.590993 + 0.590993i
\(215\) 4.06999 6.27954i 0.277571 0.428261i
\(216\) −0.707107 + 0.707107i −0.0481125 + 0.0481125i
\(217\) 8.93712i 0.606691i
\(218\) −13.7592 13.7592i −0.931894 0.931894i
\(219\) 3.65991i 0.247314i
\(220\) 6.88266 10.6192i 0.464029 0.715945i
\(221\) 36.5121i 2.45607i
\(222\) 0.179886 6.08010i 0.0120732 0.408070i
\(223\) 11.0520 + 11.0520i 0.740100 + 0.740100i 0.972597 0.232497i \(-0.0746896\pi\)
−0.232497 + 0.972597i \(0.574690\pi\)
\(224\) −2.24767 2.24767i −0.150179 0.150179i
\(225\) 4.56408 2.04186i 0.304272 0.136124i
\(226\) 4.68689i 0.311768i
\(227\) −6.40168 −0.424894 −0.212447 0.977173i \(-0.568143\pi\)
−0.212447 + 0.977173i \(0.568143\pi\)
\(228\) 5.28079i 0.349729i
\(229\) 16.3225i 1.07862i −0.842107 0.539310i \(-0.818685\pi\)
0.842107 0.539310i \(-0.181315\pi\)
\(230\) −7.93762 5.14465i −0.523391 0.339228i
\(231\) −17.9891 −1.18360
\(232\) 3.26498 3.26498i 0.214356 0.214356i
\(233\) 0.738837 0.738837i 0.0484028 0.0484028i −0.682491 0.730894i \(-0.739103\pi\)
0.730894 + 0.682491i \(0.239103\pi\)
\(234\) 4.81453i 0.314736i
\(235\) 18.6965 3.99158i 1.21963 0.260382i
\(236\) 9.84721 9.84721i 0.640999 0.640999i
\(237\) 4.03499i 0.262101i
\(238\) 17.0457 + 17.0457i 1.10491 + 1.10491i
\(239\) 5.10981 5.10981i 0.330526 0.330526i −0.522260 0.852786i \(-0.674911\pi\)
0.852786 + 0.522260i \(0.174911\pi\)
\(240\) 2.18679 0.466864i 0.141157 0.0301359i
\(241\) −8.22613 8.22613i −0.529892 0.529892i 0.390648 0.920540i \(-0.372251\pi\)
−0.920540 + 0.390648i \(0.872251\pi\)
\(242\) 21.0276i 1.35171i
\(243\) −0.707107 + 0.707107i −0.0453609 + 0.0453609i
\(244\) 1.11855 1.11855i 0.0716080 0.0716080i
\(245\) 3.77503 5.82445i 0.241178 0.372110i
\(246\) 1.71858 1.71858i 0.109572 0.109572i
\(247\) 17.9778 + 17.9778i 1.14390 + 1.14390i
\(248\) −1.98809 1.98809i −0.126244 0.126244i
\(249\) 1.28163 0.0812199
\(250\) −11.0474 1.71931i −0.698696 0.108739i
\(251\) −10.0396 + 10.0396i −0.633694 + 0.633694i −0.948992 0.315299i \(-0.897895\pi\)
0.315299 + 0.948992i \(0.397895\pi\)
\(252\) −2.24767 2.24767i −0.141590 0.141590i
\(253\) −23.9400 −1.50509
\(254\) −14.6086 14.6086i −0.916626 0.916626i
\(255\) −16.5840 + 3.54057i −1.03853 + 0.221719i
\(256\) 1.00000 0.0625000
\(257\) 15.5767 0.971645 0.485823 0.874057i \(-0.338520\pi\)
0.485823 + 0.874057i \(0.338520\pi\)
\(258\) 2.36638 2.36638i 0.147324 0.147324i
\(259\) 19.3267 + 0.571801i 1.20090 + 0.0355300i
\(260\) −5.85528 + 9.03405i −0.363129 + 0.560268i
\(261\) 3.26498 3.26498i 0.202097 0.202097i
\(262\) 9.26219 + 9.26219i 0.572220 + 0.572220i
\(263\) 17.2063 17.2063i 1.06099 1.06099i 0.0629697 0.998015i \(-0.479943\pi\)
0.998015 0.0629697i \(-0.0200571\pi\)
\(264\) 4.00173 4.00173i 0.246289 0.246289i
\(265\) 5.29555 + 24.8043i 0.325303 + 1.52372i
\(266\) 16.7860 1.02921
\(267\) 14.4077 0.881735
\(268\) −6.91167 6.91167i −0.422198 0.422198i
\(269\) 16.7896i 1.02368i 0.859080 + 0.511841i \(0.171036\pi\)
−0.859080 + 0.511841i \(0.828964\pi\)
\(270\) 2.18679 0.466864i 0.133084 0.0284124i
\(271\) −3.47058 −0.210823 −0.105411 0.994429i \(-0.533616\pi\)
−0.105411 + 0.994429i \(0.533616\pi\)
\(272\) −7.58373 −0.459831
\(273\) 15.3039 0.926232
\(274\) 1.63948 + 1.63948i 0.0990449 + 0.0990449i
\(275\) −25.8295 + 11.5555i −1.55757 + 0.696823i
\(276\) −2.99121 2.99121i −0.180050 0.180050i
\(277\) 5.08835i 0.305730i 0.988247 + 0.152865i \(0.0488499\pi\)
−0.988247 + 0.152865i \(0.951150\pi\)
\(278\) 17.9432i 1.07616i
\(279\) −1.98809 1.98809i −0.119024 0.119024i
\(280\) 1.48401 + 6.95110i 0.0886867 + 0.415408i
\(281\) 22.3585 + 22.3585i 1.33380 + 1.33380i 0.901943 + 0.431856i \(0.142141\pi\)
0.431856 + 0.901943i \(0.357859\pi\)
\(282\) 8.54977 0.509131
\(283\) −4.97011 −0.295442 −0.147721 0.989029i \(-0.547194\pi\)
−0.147721 + 0.989029i \(0.547194\pi\)
\(284\) 6.12087 0.363207
\(285\) −6.42234 + 9.90895i −0.380426 + 0.586956i
\(286\) 27.2468i 1.61114i
\(287\) 5.46281 + 5.46281i 0.322459 + 0.322459i
\(288\) 1.00000 0.0589256
\(289\) 40.5129 2.38311
\(290\) −10.0972 + 2.15568i −0.592929 + 0.126586i
\(291\) −2.03529 + 2.03529i −0.119311 + 0.119311i
\(292\) 2.58794 2.58794i 0.151448 0.151448i
\(293\) −3.76385 3.76385i −0.219886 0.219886i 0.588564 0.808450i \(-0.299693\pi\)
−0.808450 + 0.588564i \(0.799693\pi\)
\(294\) 2.19488 2.19488i 0.128008 0.128008i
\(295\) −30.4533 + 6.50157i −1.77306 + 0.378536i
\(296\) −4.42648 + 4.17208i −0.257284 + 0.242497i
\(297\) 4.00173 4.00173i 0.232204 0.232204i
\(298\) 9.20482 0.533221
\(299\) 20.3665 1.17782
\(300\) −4.67110 1.78347i −0.269686 0.102969i
\(301\) 7.52196 + 7.52196i 0.433559 + 0.433559i
\(302\) −5.59713 −0.322078
\(303\) −11.3769 11.3769i −0.653584 0.653584i
\(304\) −3.73408 + 3.73408i −0.214164 + 0.214164i
\(305\) −3.45922 + 0.738519i −0.198074 + 0.0422875i
\(306\) −7.58373 −0.433533
\(307\) −10.3413 10.3413i −0.590210 0.590210i 0.347478 0.937688i \(-0.387038\pi\)
−0.937688 + 0.347478i \(0.887038\pi\)
\(308\) 12.7202 + 12.7202i 0.724802 + 0.724802i
\(309\) 7.84870 7.84870i 0.446497 0.446497i
\(310\) 1.31262 + 6.14832i 0.0745520 + 0.349201i
\(311\) 2.08224 2.08224i 0.118073 0.118073i −0.645601 0.763675i \(-0.723393\pi\)
0.763675 + 0.645601i \(0.223393\pi\)
\(312\) −3.40439 + 3.40439i −0.192735 + 0.192735i
\(313\) 5.86237i 0.331361i −0.986179 0.165681i \(-0.947018\pi\)
0.986179 0.165681i \(-0.0529820\pi\)
\(314\) −0.998661 0.998661i −0.0563577 0.0563577i
\(315\) 1.48401 + 6.95110i 0.0836146 + 0.391650i
\(316\) 2.85317 2.85317i 0.160503 0.160503i
\(317\) −3.30695 3.30695i −0.185737 0.185737i 0.608113 0.793850i \(-0.291927\pi\)
−0.793850 + 0.608113i \(0.791927\pi\)
\(318\) 11.3428i 0.636073i
\(319\) −18.4775 + 18.4775i −1.03454 + 1.03454i
\(320\) −1.87641 1.21617i −0.104895 0.0679859i
\(321\) 12.2266i 0.682421i
\(322\) 9.50811 9.50811i 0.529866 0.529866i
\(323\) 28.3183 28.3183i 1.57567 1.57567i
\(324\) 1.00000 0.0555556
\(325\) 21.9739 9.83061i 1.21889 0.545304i
\(326\) 7.74976i 0.429220i
\(327\) 19.4585i 1.07606i
\(328\) −2.43043 −0.134198
\(329\) 27.1770i 1.49832i
\(330\) −12.3757 + 2.64212i −0.681258 + 0.145444i
\(331\) 2.03744 + 2.03744i 0.111988 + 0.111988i 0.760880 0.648892i \(-0.224768\pi\)
−0.648892 + 0.760880i \(0.724768\pi\)
\(332\) −0.906248 0.906248i −0.0497368 0.0497368i
\(333\) −4.42648 + 4.17208i −0.242570 + 0.228629i
\(334\) 19.2547i 1.05357i
\(335\) 4.56340 + 21.3749i 0.249325 + 1.16784i
\(336\) 3.17868i 0.173411i
\(337\) 4.38679 + 4.38679i 0.238963 + 0.238963i 0.816421 0.577457i \(-0.195955\pi\)
−0.577457 + 0.816421i \(0.695955\pi\)
\(338\) 10.1797i 0.553702i
\(339\) 3.31414 3.31414i 0.179999 0.179999i
\(340\) 14.2302 + 9.22310i 0.771742 + 0.500193i
\(341\) 11.2512 + 11.2512i 0.609285 + 0.609285i
\(342\) −3.73408 + 3.73408i −0.201916 + 0.201916i
\(343\) −8.75685 8.75685i −0.472826 0.472826i
\(344\) −3.34656 −0.180435
\(345\) 1.97493 + 9.25056i 0.106327 + 0.498034i
\(346\) 8.58579 + 8.58579i 0.461575 + 0.461575i
\(347\) 6.84918i 0.367683i −0.982956 0.183842i \(-0.941147\pi\)
0.982956 0.183842i \(-0.0588533\pi\)
\(348\) −4.61737 −0.247517
\(349\) 11.3003i 0.604891i 0.953167 + 0.302445i \(0.0978030\pi\)
−0.953167 + 0.302445i \(0.902197\pi\)
\(350\) 5.66910 14.8480i 0.303026 0.793657i
\(351\) −3.40439 + 3.40439i −0.181713 + 0.181713i
\(352\) −5.65930 −0.301641
\(353\) −21.3525 −1.13648 −0.568240 0.822863i \(-0.692375\pi\)
−0.568240 + 0.822863i \(0.692375\pi\)
\(354\) −13.9261 −0.740162
\(355\) −11.4853 7.44401i −0.609576 0.395087i
\(356\) −10.1878 10.1878i −0.539950 0.539950i
\(357\) 24.1063i 1.27584i
\(358\) 14.0961 14.0961i 0.745000 0.745000i
\(359\) 5.23042i 0.276051i −0.990429 0.138025i \(-0.955924\pi\)
0.990429 0.138025i \(-0.0440756\pi\)
\(360\) −1.87641 1.21617i −0.0988957 0.0640978i
\(361\) 8.88674i 0.467723i
\(362\) 13.7831i 0.724424i
\(363\) −14.8688 + 14.8688i −0.780408 + 0.780408i
\(364\) −10.8215 10.8215i −0.567199 0.567199i
\(365\) −8.00344 + 1.70868i −0.418919 + 0.0894362i
\(366\) −1.58187 −0.0826858
\(367\) −0.560713 + 0.560713i −0.0292690 + 0.0292690i −0.721590 0.692321i \(-0.756588\pi\)
0.692321 + 0.721590i \(0.256588\pi\)
\(368\) 4.23021i 0.220515i
\(369\) −2.43043 −0.126523
\(370\) 13.3799 2.44521i 0.695586 0.127120i
\(371\) −36.0552 −1.87189
\(372\) 2.81158i 0.145774i
\(373\) 3.16048 3.16048i 0.163643 0.163643i −0.620535 0.784179i \(-0.713085\pi\)
0.784179 + 0.620535i \(0.213085\pi\)
\(374\) 42.9186 2.21927
\(375\) 6.59592 + 9.02739i 0.340612 + 0.466173i
\(376\) −6.04560 6.04560i −0.311778 0.311778i
\(377\) 15.7193 15.7193i 0.809586 0.809586i
\(378\) 3.17868i 0.163494i
\(379\) 1.59897i 0.0821335i −0.999156 0.0410667i \(-0.986924\pi\)
0.999156 0.0410667i \(-0.0130756\pi\)
\(380\) 11.5480 2.46541i 0.592398 0.126473i
\(381\) 20.6597i 1.05843i
\(382\) −18.4453 + 18.4453i −0.943746 + 0.943746i
\(383\) 1.83857i 0.0939464i 0.998896 + 0.0469732i \(0.0149575\pi\)
−0.998896 + 0.0469732i \(0.985042\pi\)
\(384\) −0.707107 0.707107i −0.0360844 0.0360844i
\(385\) −8.39846 39.3384i −0.428025 2.00487i
\(386\) 22.9897 1.17015
\(387\) −3.34656 −0.170115
\(388\) 2.87834 0.146125
\(389\) −21.9756 + 21.9756i −1.11421 + 1.11421i −0.121630 + 0.992575i \(0.538812\pi\)
−0.992575 + 0.121630i \(0.961188\pi\)
\(390\) 10.5284 2.24773i 0.533124 0.113818i
\(391\) 32.0807i 1.62239i
\(392\) −3.10403 −0.156777
\(393\) 13.0987i 0.660743i
\(394\) −1.69341 1.69341i −0.0853126 0.0853126i
\(395\) −8.82367 + 1.88379i −0.443967 + 0.0947838i
\(396\) −5.65930 −0.284390
\(397\) −14.3901 14.3901i −0.722218 0.722218i 0.246838 0.969057i \(-0.420608\pi\)
−0.969057 + 0.246838i \(0.920608\pi\)
\(398\) −7.33672 + 7.33672i −0.367757 + 0.367757i
\(399\) −11.8695 11.8695i −0.594217 0.594217i
\(400\) 2.04186 + 4.56408i 0.102093 + 0.228204i
\(401\) −1.56403 + 1.56403i −0.0781040 + 0.0781040i −0.745080 0.666976i \(-0.767589\pi\)
0.666976 + 0.745080i \(0.267589\pi\)
\(402\) 9.77458i 0.487512i
\(403\) −9.57170 9.57170i −0.476800 0.476800i
\(404\) 16.0893i 0.800474i
\(405\) −1.87641 1.21617i −0.0932398 0.0604320i
\(406\) 14.6772i 0.728416i
\(407\) 25.0508 23.6110i 1.24172 1.17036i
\(408\) 5.36251 + 5.36251i 0.265484 + 0.265484i
\(409\) −6.64945 6.64945i −0.328794 0.328794i 0.523334 0.852128i \(-0.324688\pi\)
−0.852128 + 0.523334i \(0.824688\pi\)
\(410\) 4.56050 + 2.95582i 0.225227 + 0.145978i
\(411\) 2.31858i 0.114367i
\(412\) −11.0997 −0.546845
\(413\) 44.2665i 2.17821i
\(414\) 4.23021i 0.207903i
\(415\) 0.598346 + 2.80265i 0.0293716 + 0.137577i
\(416\) 4.81453 0.236052
\(417\) 12.6877 12.6877i 0.621321 0.621321i
\(418\) 21.1323 21.1323i 1.03361 1.03361i
\(419\) 22.2951i 1.08919i 0.838701 + 0.544593i \(0.183316\pi\)
−0.838701 + 0.544593i \(0.816684\pi\)
\(420\) 3.86582 5.96453i 0.188633 0.291039i
\(421\) −1.74485 + 1.74485i −0.0850387 + 0.0850387i −0.748347 0.663308i \(-0.769152\pi\)
0.663308 + 0.748347i \(0.269152\pi\)
\(422\) 11.9466i 0.581549i
\(423\) −6.04560 6.04560i −0.293947 0.293947i
\(424\) 8.02058 8.02058i 0.389514 0.389514i
\(425\) −15.4849 34.6127i −0.751130 1.67896i
\(426\) −4.32811 4.32811i −0.209697 0.209697i
\(427\) 5.02827i 0.243335i
\(428\) −8.64549 + 8.64549i −0.417896 + 0.417896i
\(429\) 19.2664 19.2664i 0.930192 0.930192i
\(430\) 6.27954 + 4.06999i 0.302826 + 0.196272i
\(431\) −23.7856 + 23.7856i −1.14571 + 1.14571i −0.158327 + 0.987387i \(0.550610\pi\)
−0.987387 + 0.158327i \(0.949390\pi\)
\(432\) −0.707107 0.707107i −0.0340207 0.0340207i
\(433\) −9.00285 9.00285i −0.432649 0.432649i 0.456879 0.889529i \(-0.348967\pi\)
−0.889529 + 0.456879i \(0.848967\pi\)
\(434\) −8.93712 −0.428995
\(435\) 8.66411 + 5.61551i 0.415412 + 0.269243i
\(436\) 13.7592 13.7592i 0.658948 0.658948i
\(437\) −15.7959 15.7959i −0.755622 0.755622i
\(438\) −3.65991 −0.174877
\(439\) −4.79636 4.79636i −0.228918 0.228918i 0.583323 0.812240i \(-0.301752\pi\)
−0.812240 + 0.583323i \(0.801752\pi\)
\(440\) 10.6192 + 6.88266i 0.506250 + 0.328118i
\(441\) −3.10403 −0.147811
\(442\) −36.5121 −1.73670
\(443\) 7.85980 7.85980i 0.373430 0.373430i −0.495295 0.868725i \(-0.664940\pi\)
0.868725 + 0.495295i \(0.164940\pi\)
\(444\) 6.08010 + 0.179886i 0.288549 + 0.00853702i
\(445\) 6.72642 + 31.5065i 0.318863 + 1.49355i
\(446\) −11.0520 + 11.0520i −0.523330 + 0.523330i
\(447\) −6.50879 6.50879i −0.307855 0.307855i
\(448\) 2.24767 2.24767i 0.106192 0.106192i
\(449\) 16.4657 16.4657i 0.777066 0.777066i −0.202265 0.979331i \(-0.564830\pi\)
0.979331 + 0.202265i \(0.0648303\pi\)
\(450\) 2.04186 + 4.56408i 0.0962543 + 0.215153i
\(451\) 13.7545 0.647676
\(452\) −4.68689 −0.220453
\(453\) 3.95777 + 3.95777i 0.185952 + 0.185952i
\(454\) 6.40168i 0.300446i
\(455\) 7.14482 + 33.4663i 0.334954 + 1.56892i
\(456\) 5.28079 0.247296
\(457\) −5.42876 −0.253947 −0.126973 0.991906i \(-0.540526\pi\)
−0.126973 + 0.991906i \(0.540526\pi\)
\(458\) 16.3225 0.762699
\(459\) 5.36251 + 5.36251i 0.250300 + 0.250300i
\(460\) 5.14465 7.93762i 0.239871 0.370094i
\(461\) 12.8604 + 12.8604i 0.598967 + 0.598967i 0.940038 0.341071i \(-0.110790\pi\)
−0.341071 + 0.940038i \(0.610790\pi\)
\(462\) 17.9891i 0.836929i
\(463\) 36.1282i 1.67902i 0.543345 + 0.839509i \(0.317157\pi\)
−0.543345 + 0.839509i \(0.682843\pi\)
\(464\) 3.26498 + 3.26498i 0.151573 + 0.151573i
\(465\) 3.41936 5.27569i 0.158569 0.244654i
\(466\) 0.738837 + 0.738837i 0.0342260 + 0.0342260i
\(467\) 4.96873 0.229925 0.114963 0.993370i \(-0.463325\pi\)
0.114963 + 0.993370i \(0.463325\pi\)
\(468\) 4.81453 0.222552
\(469\) −31.0703 −1.43469
\(470\) 3.99158 + 18.6965i 0.184118 + 0.862407i
\(471\) 1.41232i 0.0650763i
\(472\) 9.84721 + 9.84721i 0.453255 + 0.453255i
\(473\) 18.9392 0.870825
\(474\) −4.03499 −0.185333
\(475\) −24.6671 9.41815i −1.13181 0.432135i
\(476\) −17.0457 + 17.0457i −0.781289 + 0.781289i
\(477\) 8.02058 8.02058i 0.367237 0.367237i
\(478\) 5.10981 + 5.10981i 0.233717 + 0.233717i
\(479\) −21.0873 + 21.0873i −0.963504 + 0.963504i −0.999357 0.0358527i \(-0.988585\pi\)
0.0358527 + 0.999357i \(0.488585\pi\)
\(480\) 0.466864 + 2.18679i 0.0213093 + 0.0998127i
\(481\) −21.3114 + 20.0866i −0.971717 + 0.915871i
\(482\) 8.22613 8.22613i 0.374690 0.374690i
\(483\) −13.4465 −0.611837
\(484\) 21.0276 0.955801
\(485\) −5.40095 3.50054i −0.245245 0.158952i
\(486\) −0.707107 0.707107i −0.0320750 0.0320750i
\(487\) −10.6041 −0.480519 −0.240259 0.970709i \(-0.577233\pi\)
−0.240259 + 0.970709i \(0.577233\pi\)
\(488\) 1.11855 + 1.11855i 0.0506345 + 0.0506345i
\(489\) −5.47991 + 5.47991i −0.247810 + 0.247810i
\(490\) 5.82445 + 3.77503i 0.263122 + 0.170538i
\(491\) 2.33716 0.105475 0.0527373 0.998608i \(-0.483205\pi\)
0.0527373 + 0.998608i \(0.483205\pi\)
\(492\) 1.71858 + 1.71858i 0.0774794 + 0.0774794i
\(493\) −24.7607 24.7607i −1.11517 1.11517i
\(494\) −17.9778 + 17.9778i −0.808862 + 0.808862i
\(495\) 10.6192 + 6.88266i 0.477297 + 0.309353i
\(496\) 1.98809 1.98809i 0.0892677 0.0892677i
\(497\) 13.7577 13.7577i 0.617116 0.617116i
\(498\) 1.28163i 0.0574312i
\(499\) 15.9396 + 15.9396i 0.713555 + 0.713555i 0.967277 0.253723i \(-0.0816550\pi\)
−0.253723 + 0.967277i \(0.581655\pi\)
\(500\) 1.71931 11.0474i 0.0768899 0.494053i
\(501\) 13.6151 13.6151i 0.608278 0.608278i
\(502\) −10.0396 10.0396i −0.448089 0.448089i
\(503\) 18.1285i 0.808309i 0.914691 + 0.404155i \(0.132434\pi\)
−0.914691 + 0.404155i \(0.867566\pi\)
\(504\) 2.24767 2.24767i 0.100119 0.100119i
\(505\) 19.5674 30.1903i 0.870736 1.34345i
\(506\) 23.9400i 1.06426i
\(507\) −7.19813 + 7.19813i −0.319680 + 0.319680i
\(508\) 14.6086 14.6086i 0.648152 0.648152i
\(509\) −14.6649 −0.650010 −0.325005 0.945712i \(-0.605366\pi\)
−0.325005 + 0.945712i \(0.605366\pi\)
\(510\) −3.54057 16.5840i −0.156779 0.734352i
\(511\) 11.6337i 0.514644i
\(512\) 1.00000i 0.0441942i
\(513\) 5.28079 0.233153
\(514\) 15.5767i 0.687057i
\(515\) 20.8277 + 13.4992i 0.917778 + 0.594844i
\(516\) 2.36638 + 2.36638i 0.104174 + 0.104174i
\(517\) 34.2138 + 34.2138i 1.50472 + 1.50472i
\(518\) −0.571801 + 19.3267i −0.0251235 + 0.849167i
\(519\) 12.1421i 0.532981i
\(520\) −9.03405 5.85528i −0.396169 0.256771i
\(521\) 13.9917i 0.612988i −0.951873 0.306494i \(-0.900844\pi\)
0.951873 0.306494i \(-0.0991560\pi\)
\(522\) 3.26498 + 3.26498i 0.142904 + 0.142904i
\(523\) 16.6140i 0.726479i 0.931696 + 0.363239i \(0.118329\pi\)
−0.931696 + 0.363239i \(0.881671\pi\)
\(524\) −9.26219 + 9.26219i −0.404621 + 0.404621i
\(525\) −14.5078 + 6.49044i −0.633170 + 0.283266i
\(526\) 17.2063 + 17.2063i 0.750230 + 0.750230i
\(527\) −15.0771 + 15.0771i −0.656769 + 0.656769i
\(528\) 4.00173 + 4.00173i 0.174153 + 0.174153i
\(529\) 5.10534 0.221971
\(530\) −24.8043 + 5.29555i −1.07743 + 0.230024i
\(531\) 9.84721 + 9.84721i 0.427332 + 0.427332i
\(532\) 16.7860i 0.727764i
\(533\) −11.7014 −0.506844
\(534\) 14.4077i 0.623481i
\(535\) 26.7369 5.70814i 1.15594 0.246784i
\(536\) 6.91167 6.91167i 0.298539 0.298539i
\(537\) −19.9348 −0.860251
\(538\) −16.7896 −0.723853
\(539\) 17.5666 0.756648
\(540\) 0.466864 + 2.18679i 0.0200906 + 0.0941043i
\(541\) −15.0297 15.0297i −0.646177 0.646177i 0.305890 0.952067i \(-0.401046\pi\)
−0.952067 + 0.305890i \(0.901046\pi\)
\(542\) 3.47058i 0.149074i
\(543\) 9.74613 9.74613i 0.418246 0.418246i
\(544\) 7.58373i 0.325150i
\(545\) −42.5516 + 9.08447i −1.82271 + 0.389136i
\(546\) 15.3039i 0.654945i
\(547\) 1.60901i 0.0687964i 0.999408 + 0.0343982i \(0.0109514\pi\)
−0.999408 + 0.0343982i \(0.989049\pi\)
\(548\) −1.63948 + 1.63948i −0.0700353 + 0.0700353i
\(549\) 1.11855 + 1.11855i 0.0477387 + 0.0477387i
\(550\) −11.5555 25.8295i −0.492728 1.10137i
\(551\) −24.3834 −1.03877
\(552\) 2.99121 2.99121i 0.127314 0.127314i
\(553\) 12.8260i 0.545416i
\(554\) −5.08835 −0.216183
\(555\) −11.1900 7.73198i −0.474990 0.328204i
\(556\) −17.9432 −0.760959
\(557\) 13.8846i 0.588309i 0.955758 + 0.294155i \(0.0950381\pi\)
−0.955758 + 0.294155i \(0.904962\pi\)
\(558\) 1.98809 1.98809i 0.0841624 0.0841624i
\(559\) −16.1121 −0.681470
\(560\) −6.95110 + 1.48401i −0.293738 + 0.0627109i
\(561\) −30.3480 30.3480i −1.28129 1.28129i
\(562\) −22.3585 + 22.3585i −0.943138 + 0.943138i
\(563\) 36.2994i 1.52984i −0.644126 0.764919i \(-0.722779\pi\)
0.644126 0.764919i \(-0.277221\pi\)
\(564\) 8.54977i 0.360010i
\(565\) 8.79456 + 5.70006i 0.369990 + 0.239803i
\(566\) 4.97011i 0.208909i
\(567\) 2.24767 2.24767i 0.0943932 0.0943932i
\(568\) 6.12087i 0.256826i
\(569\) −4.09043 4.09043i −0.171480 0.171480i 0.616149 0.787629i \(-0.288692\pi\)
−0.787629 + 0.616149i \(0.788692\pi\)
\(570\) −9.90895 6.42234i −0.415040 0.269002i
\(571\) 9.17017 0.383760 0.191880 0.981418i \(-0.438542\pi\)
0.191880 + 0.981418i \(0.438542\pi\)
\(572\) −27.2468 −1.13925
\(573\) 26.0857 1.08974
\(574\) −5.46281 + 5.46281i −0.228013 + 0.228013i
\(575\) −19.3070 + 8.63750i −0.805157 + 0.360209i
\(576\) 1.00000i 0.0416667i
\(577\) −35.0406 −1.45876 −0.729381 0.684108i \(-0.760192\pi\)
−0.729381 + 0.684108i \(0.760192\pi\)
\(578\) 40.5129i 1.68512i
\(579\) −16.2562 16.2562i −0.675585 0.675585i
\(580\) −2.15568 10.0972i −0.0895099 0.419264i
\(581\) −4.07389 −0.169014
\(582\) −2.03529 2.03529i −0.0843655 0.0843655i
\(583\) −45.3908 + 45.3908i −1.87990 + 1.87990i
\(584\) 2.58794 + 2.58794i 0.107090 + 0.107090i
\(585\) −9.03405 5.85528i −0.373512 0.242086i
\(586\) 3.76385 3.76385i 0.155483 0.155483i
\(587\) 33.5312i 1.38398i −0.721907 0.691990i \(-0.756734\pi\)
0.721907 0.691990i \(-0.243266\pi\)
\(588\) 2.19488 + 2.19488i 0.0905153 + 0.0905153i
\(589\) 14.8474i 0.611775i
\(590\) −6.50157 30.4533i −0.267665 1.25374i
\(591\) 2.39484i 0.0985106i
\(592\) −4.17208 4.42648i −0.171472 0.181927i
\(593\) 1.10793 + 1.10793i 0.0454971 + 0.0454971i 0.729489 0.683992i \(-0.239758\pi\)
−0.683992 + 0.729489i \(0.739758\pi\)
\(594\) 4.00173 + 4.00173i 0.164193 + 0.164193i
\(595\) 52.7153 11.2543i 2.16112 0.461383i
\(596\) 9.20482i 0.377044i
\(597\) 10.3757 0.424649
\(598\) 20.3665i 0.832846i
\(599\) 0.823976i 0.0336668i 0.999858 + 0.0168334i \(0.00535848\pi\)
−0.999858 + 0.0168334i \(0.994642\pi\)
\(600\) 1.78347 4.67110i 0.0728100 0.190697i
\(601\) 7.88760 0.321742 0.160871 0.986975i \(-0.448570\pi\)
0.160871 + 0.986975i \(0.448570\pi\)
\(602\) −7.52196 + 7.52196i −0.306572 + 0.306572i
\(603\) 6.91167 6.91167i 0.281465 0.281465i
\(604\) 5.59713i 0.227744i
\(605\) −39.4565 25.5732i −1.60414 1.03970i
\(606\) 11.3769 11.3769i 0.462154 0.462154i
\(607\) 1.34105i 0.0544316i −0.999630 0.0272158i \(-0.991336\pi\)
0.999630 0.0272158i \(-0.00866413\pi\)
\(608\) −3.73408 3.73408i −0.151437 0.151437i
\(609\) −10.3783 + 10.3783i −0.420551 + 0.420551i
\(610\) −0.738519 3.45922i −0.0299018 0.140060i
\(611\) −29.1067 29.1067i −1.17753 1.17753i
\(612\) 7.58373i 0.306554i
\(613\) 3.50859 3.50859i 0.141711 0.141711i −0.632693 0.774403i \(-0.718050\pi\)
0.774403 + 0.632693i \(0.218050\pi\)
\(614\) 10.3413 10.3413i 0.417342 0.417342i
\(615\) −1.13468 5.31484i −0.0457548 0.214315i
\(616\) −12.7202 + 12.7202i −0.512512 + 0.512512i
\(617\) 1.91217 + 1.91217i 0.0769810 + 0.0769810i 0.744549 0.667568i \(-0.232665\pi\)
−0.667568 + 0.744549i \(0.732665\pi\)
\(618\) 7.84870 + 7.84870i 0.315721 + 0.315721i
\(619\) 19.7786 0.794968 0.397484 0.917609i \(-0.369883\pi\)
0.397484 + 0.917609i \(0.369883\pi\)
\(620\) −6.14832 + 1.31262i −0.246923 + 0.0527162i
\(621\) 2.99121 2.99121i 0.120033 0.120033i
\(622\) 2.08224 + 2.08224i 0.0834904 + 0.0834904i
\(623\) −45.7974 −1.83484
\(624\) −3.40439 3.40439i −0.136285 0.136285i
\(625\) −16.6616 + 18.6384i −0.666464 + 0.745538i
\(626\) 5.86237 0.234308
\(627\) −29.8855 −1.19351
\(628\) 0.998661 0.998661i 0.0398509 0.0398509i
\(629\) 31.6399 + 33.5692i 1.26157 + 1.33849i
\(630\) −6.95110 + 1.48401i −0.276939 + 0.0591244i
\(631\) −2.64808 + 2.64808i −0.105418 + 0.105418i −0.757849 0.652430i \(-0.773749\pi\)
0.652430 + 0.757849i \(0.273749\pi\)
\(632\) 2.85317 + 2.85317i 0.113493 + 0.113493i
\(633\) 8.44749 8.44749i 0.335758 0.335758i
\(634\) 3.30695 3.30695i 0.131336 0.131336i
\(635\) −45.1783 + 9.64526i −1.79285 + 0.382760i
\(636\) −11.3428 −0.449772
\(637\) −14.9444 −0.592120
\(638\) −18.4775 18.4775i −0.731530 0.731530i
\(639\) 6.12087i 0.242138i
\(640\) 1.21617 1.87641i 0.0480733 0.0741718i
\(641\) −25.9245 −1.02395 −0.511977 0.858999i \(-0.671087\pi\)
−0.511977 + 0.858999i \(0.671087\pi\)
\(642\) 12.2266 0.482544
\(643\) −6.75346 −0.266331 −0.133165 0.991094i \(-0.542514\pi\)
−0.133165 + 0.991094i \(0.542514\pi\)
\(644\) 9.50811 + 9.50811i 0.374672 + 0.374672i
\(645\) −1.56239 7.31822i −0.0615190 0.288155i
\(646\) 28.3183 + 28.3183i 1.11417 + 1.11417i
\(647\) 17.0199i 0.669122i −0.942374 0.334561i \(-0.891412\pi\)
0.942374 0.334561i \(-0.108588\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −55.7283 55.7283i −2.18753 2.18753i
\(650\) 9.83061 + 21.9739i 0.385588 + 0.861886i
\(651\) 6.31950 + 6.31950i 0.247681 + 0.247681i
\(652\) 7.74976 0.303504
\(653\) 2.21356 0.0866234 0.0433117 0.999062i \(-0.486209\pi\)
0.0433117 + 0.999062i \(0.486209\pi\)
\(654\) −19.4585 −0.760888
\(655\) 28.6441 6.11531i 1.11922 0.238945i
\(656\) 2.43043i 0.0948925i
\(657\) 2.58794 + 2.58794i 0.100965 + 0.100965i
\(658\) −27.1770 −1.05947
\(659\) −10.5454 −0.410790 −0.205395 0.978679i \(-0.565848\pi\)
−0.205395 + 0.978679i \(0.565848\pi\)
\(660\) −2.64212 12.3757i −0.102844 0.481722i
\(661\) 26.5280 26.5280i 1.03182 1.03182i 0.0323414 0.999477i \(-0.489704\pi\)
0.999477 0.0323414i \(-0.0102964\pi\)
\(662\) −2.03744 + 2.03744i −0.0791872 + 0.0791872i
\(663\) 25.8179 + 25.8179i 1.00269 + 1.00269i
\(664\) 0.906248 0.906248i 0.0351693 0.0351693i
\(665\) 20.4146 31.4974i 0.791643 1.22142i
\(666\) −4.17208 4.42648i −0.161665 0.171523i
\(667\) −13.8115 + 13.8115i −0.534784 + 0.534784i
\(668\) −19.2547 −0.744985
\(669\) 15.6300 0.604289
\(670\) −21.3749 + 4.56340i −0.825786 + 0.176299i
\(671\) −6.33022 6.33022i −0.244375 0.244375i
\(672\) −3.17868 −0.122620
\(673\) −18.5100 18.5100i −0.713507 0.713507i 0.253760 0.967267i \(-0.418333\pi\)
−0.967267 + 0.253760i \(0.918333\pi\)
\(674\) −4.38679 + 4.38679i −0.168973 + 0.168973i
\(675\) 1.78347 4.67110i 0.0686460 0.179791i
\(676\) 10.1797 0.391527
\(677\) 19.4458 + 19.4458i 0.747364 + 0.747364i 0.973983 0.226620i \(-0.0727674\pi\)
−0.226620 + 0.973983i \(0.572767\pi\)
\(678\) 3.31414 + 3.31414i 0.127279 + 0.127279i
\(679\) 6.46955 6.46955i 0.248278 0.248278i
\(680\) −9.22310 + 14.2302i −0.353690 + 0.545704i
\(681\) −4.52667 + 4.52667i −0.173462 + 0.173462i
\(682\) −11.2512 + 11.2512i −0.430830 + 0.430830i
\(683\) 45.5661i 1.74354i 0.489916 + 0.871770i \(0.337028\pi\)
−0.489916 + 0.871770i \(0.662972\pi\)
\(684\) −3.73408 3.73408i −0.142776 0.142776i
\(685\) 5.07024 1.08246i 0.193724 0.0413587i
\(686\) 8.75685 8.75685i 0.334338 0.334338i
\(687\) −11.5417 11.5417i −0.440345 0.440345i
\(688\) 3.34656i 0.127587i
\(689\) 38.6153 38.6153i 1.47113 1.47113i
\(690\) −9.25056 + 1.97493i −0.352163 + 0.0751843i
\(691\) 14.6674i 0.557973i 0.960295 + 0.278986i \(0.0899984\pi\)
−0.960295 + 0.278986i \(0.910002\pi\)
\(692\) −8.58579 + 8.58579i −0.326383 + 0.326383i
\(693\) −12.7202 + 12.7202i −0.483201 + 0.483201i
\(694\) 6.84918 0.259991
\(695\) 33.6688 + 21.8219i 1.27713 + 0.827753i
\(696\) 4.61737i 0.175021i
\(697\) 18.4317i 0.698152i
\(698\) −11.3003 −0.427722
\(699\) 1.04487i 0.0395207i
\(700\) 14.8480 + 5.66910i 0.561200 + 0.214272i
\(701\) −2.72887 2.72887i −0.103068 0.103068i 0.653692 0.756760i \(-0.273219\pi\)
−0.756760 + 0.653692i \(0.773219\pi\)
\(702\) −3.40439 3.40439i −0.128490 0.128490i
\(703\) 32.1077 + 0.949941i 1.21097 + 0.0358277i
\(704\) 5.65930i 0.213293i
\(705\) 10.3980 16.0429i 0.391610 0.604211i
\(706\) 21.3525i 0.803612i
\(707\) 36.1635 + 36.1635i 1.36007 + 1.36007i
\(708\) 13.9261i 0.523373i
\(709\) −1.20334 + 1.20334i −0.0451926 + 0.0451926i −0.729342 0.684149i \(-0.760174\pi\)
0.684149 + 0.729342i \(0.260174\pi\)
\(710\) 7.44401 11.4853i 0.279369 0.431035i
\(711\) 2.85317 + 2.85317i 0.107002 + 0.107002i
\(712\) 10.1878 10.1878i 0.381803 0.381803i
\(713\) 8.41002 + 8.41002i 0.314958 + 0.314958i
\(714\) 24.1063 0.902155
\(715\) 51.1264 + 33.1368i 1.91202 + 1.23925i
\(716\) 14.0961 + 14.0961i 0.526794 + 0.526794i
\(717\) 7.22636i 0.269873i
\(718\) 5.23042 0.195197
\(719\) 34.8068i 1.29807i −0.760757 0.649037i \(-0.775172\pi\)
0.760757 0.649037i \(-0.224828\pi\)
\(720\) 1.21617 1.87641i 0.0453240 0.0699298i
\(721\) −24.9485 + 24.9485i −0.929131 + 0.929131i
\(722\) 8.88674 0.330730
\(723\) −11.6335 −0.432655
\(724\) −13.7831 −0.512245
\(725\) −8.23497 + 21.5682i −0.305839 + 0.801024i
\(726\) −14.8688 14.8688i −0.551832 0.551832i
\(727\) 29.0229i 1.07640i 0.842817 + 0.538200i \(0.180895\pi\)
−0.842817 + 0.538200i \(0.819105\pi\)
\(728\) 10.8215 10.8215i 0.401070 0.401070i
\(729\) 1.00000i 0.0370370i
\(730\) −1.70868 8.00344i −0.0632410 0.296220i
\(731\) 25.3794i 0.938692i
\(732\) 1.58187i 0.0584677i
\(733\) −6.55654 + 6.55654i −0.242171 + 0.242171i −0.817748 0.575577i \(-0.804778\pi\)
0.575577 + 0.817748i \(0.304778\pi\)
\(734\) −0.560713 0.560713i −0.0206963 0.0206963i
\(735\) −1.44916 6.78785i −0.0534530 0.250374i
\(736\) −4.23021 −0.155928
\(737\) −39.1152 + 39.1152i −1.44083 + 1.44083i
\(738\) 2.43043i 0.0894655i
\(739\) −3.57785 −0.131613 −0.0658067 0.997832i \(-0.520962\pi\)
−0.0658067 + 0.997832i \(0.520962\pi\)
\(740\) 2.44521 + 13.3799i 0.0898876 + 0.491854i
\(741\) 25.4245 0.933993
\(742\) 36.0552i 1.32363i
\(743\) −29.2655 + 29.2655i −1.07365 + 1.07365i −0.0765832 + 0.997063i \(0.524401\pi\)
−0.997063 + 0.0765832i \(0.975599\pi\)
\(744\) −2.81158 −0.103077
\(745\) 11.1946 17.2720i 0.410139 0.632799i
\(746\) 3.16048 + 3.16048i 0.115713 + 0.115713i
\(747\) 0.906248 0.906248i 0.0331579 0.0331579i
\(748\) 42.9186i 1.56926i
\(749\) 38.8644i 1.42007i
\(750\) −9.02739 + 6.59592i −0.329634 + 0.240849i
\(751\) 17.5101i 0.638951i −0.947595 0.319476i \(-0.896493\pi\)
0.947595 0.319476i \(-0.103507\pi\)
\(752\) 6.04560 6.04560i 0.220460 0.220460i
\(753\) 14.1981i 0.517409i
\(754\) 15.7193 + 15.7193i 0.572464 + 0.572464i
\(755\) −6.80705 + 10.5025i −0.247734 + 0.382226i
\(756\) −3.17868 −0.115608
\(757\) −15.4393 −0.561153 −0.280576 0.959832i \(-0.590526\pi\)
−0.280576 + 0.959832i \(0.590526\pi\)
\(758\) 1.59897 0.0580771
\(759\) −16.9281 + 16.9281i −0.614452 + 0.614452i
\(760\) 2.46541 + 11.5480i 0.0894298 + 0.418889i
\(761\) 19.6274i 0.711492i −0.934583 0.355746i \(-0.884227\pi\)
0.934583 0.355746i \(-0.115773\pi\)
\(762\) −20.6597 −0.748422
\(763\) 61.8524i 2.23921i
\(764\) −18.4453 18.4453i −0.667329 0.667329i
\(765\) −9.22310 + 14.2302i −0.333462 + 0.514495i
\(766\) −1.83857 −0.0664301
\(767\) 47.4097 + 47.4097i 1.71186 + 1.71186i
\(768\) 0.707107 0.707107i 0.0255155 0.0255155i
\(769\) 38.3252 + 38.3252i 1.38204 + 1.38204i 0.840985 + 0.541058i \(0.181976\pi\)
0.541058 + 0.840985i \(0.318024\pi\)
\(770\) 39.3384 8.39846i 1.41766 0.302660i
\(771\) 11.0144 11.0144i 0.396672 0.396672i
\(772\) 22.9897i 0.827419i
\(773\) 13.6080 + 13.6080i 0.489445 + 0.489445i 0.908131 0.418686i \(-0.137509\pi\)
−0.418686 + 0.908131i \(0.637509\pi\)
\(774\) 3.34656i 0.120290i
\(775\) 13.1332 + 5.01438i 0.471758 + 0.180122i
\(776\) 2.87834i 0.103326i
\(777\) 14.0704 13.2617i 0.504772 0.475762i
\(778\) −21.9756 21.9756i −0.787862 0.787862i
\(779\) 9.07544 + 9.07544i 0.325161 + 0.325161i
\(780\) 2.24773 + 10.5284i 0.0804816 + 0.376975i
\(781\) 34.6398i 1.23951i
\(782\) 32.0807 1.14721
\(783\) 4.61737i 0.165011i
\(784\) 3.10403i 0.110858i
\(785\) −3.08844 + 0.659361i −0.110231 + 0.0235336i
\(786\) 13.0987 0.467216
\(787\) 0.848326 0.848326i 0.0302396 0.0302396i −0.691825 0.722065i \(-0.743193\pi\)
0.722065 + 0.691825i \(0.243193\pi\)
\(788\) 1.69341 1.69341i 0.0603251 0.0603251i
\(789\) 24.3334i 0.866291i
\(790\) −1.88379 8.82367i −0.0670223 0.313932i
\(791\) −10.5346 + 10.5346i −0.374567 + 0.374567i
\(792\) 5.65930i 0.201094i
\(793\) 5.38530 + 5.38530i 0.191238 + 0.191238i
\(794\) 14.3901 14.3901i 0.510686 0.510686i
\(795\) 21.2838 + 13.7948i 0.754859 + 0.489251i
\(796\) −7.33672 7.33672i −0.260043 0.260043i
\(797\) 54.9817i 1.94755i 0.227510 + 0.973776i \(0.426942\pi\)
−0.227510 + 0.973776i \(0.573058\pi\)
\(798\) 11.8695 11.8695i 0.420175 0.420175i
\(799\) −45.8482 + 45.8482i −1.62199 + 1.62199i
\(800\) −4.56408 + 2.04186i −0.161364 + 0.0721908i
\(801\) 10.1878 10.1878i 0.359967 0.359967i
\(802\) −1.56403 1.56403i −0.0552279 0.0552279i
\(803\) −14.6459 14.6459i −0.516844 0.516844i
\(804\) −9.77458 −0.344723
\(805\) −6.27768 29.4046i −0.221259 1.03638i
\(806\) 9.57170 9.57170i 0.337149 0.337149i
\(807\) 11.8721 + 11.8721i 0.417916 + 0.417916i
\(808\) −16.0893 −0.566021
\(809\) −4.86721 4.86721i −0.171122 0.171122i 0.616350 0.787472i \(-0.288611\pi\)
−0.787472 + 0.616350i \(0.788611\pi\)
\(810\) 1.21617 1.87641i 0.0427318 0.0659305i
\(811\) −13.3290 −0.468044 −0.234022 0.972231i \(-0.575189\pi\)
−0.234022 + 0.972231i \(0.575189\pi\)
\(812\) 14.6772 0.515068
\(813\) −2.45407 + 2.45407i −0.0860680 + 0.0860680i
\(814\) 23.6110 + 25.0508i 0.827567 + 0.878029i
\(815\) −14.5418 9.42503i −0.509376 0.330144i
\(816\) −5.36251 + 5.36251i −0.187725 + 0.187725i
\(817\) 12.4963 + 12.4963i 0.437192 + 0.437192i
\(818\) 6.64945 6.64945i 0.232493 0.232493i
\(819\) 10.8215 10.8215i 0.378133 0.378133i
\(820\) −2.95582 + 4.56050i −0.103222 + 0.159260i
\(821\) 43.5087 1.51846 0.759232 0.650820i \(-0.225575\pi\)
0.759232 + 0.650820i \(0.225575\pi\)
\(822\) 2.31858 0.0808698
\(823\) −0.673165 0.673165i −0.0234651 0.0234651i 0.695277 0.718742i \(-0.255282\pi\)
−0.718742 + 0.695277i \(0.755282\pi\)
\(824\) 11.0997i 0.386677i
\(825\) −10.0932 + 26.4352i −0.351400 + 0.920354i
\(826\) 44.2665 1.54023
\(827\) 33.1455 1.15258 0.576290 0.817245i \(-0.304500\pi\)
0.576290 + 0.817245i \(0.304500\pi\)
\(828\) −4.23021 −0.147010
\(829\) −17.7173 17.7173i −0.615349 0.615349i 0.328986 0.944335i \(-0.393293\pi\)
−0.944335 + 0.328986i \(0.893293\pi\)
\(830\) −2.80265 + 0.598346i −0.0972814 + 0.0207689i
\(831\) 3.59801 + 3.59801i 0.124814 + 0.124814i
\(832\) 4.81453i 0.166914i
\(833\) 23.5401i 0.815617i
\(834\) 12.6877 + 12.6877i 0.439340 + 0.439340i
\(835\) 36.1297 + 23.4169i 1.25032 + 0.810376i
\(836\) 21.1323 + 21.1323i 0.730875 + 0.730875i
\(837\) −2.81158 −0.0971824
\(838\) −22.2951 −0.770170
\(839\) −40.9132 −1.41248 −0.706240 0.707973i \(-0.749610\pi\)
−0.706240 + 0.707973i \(0.749610\pi\)
\(840\) 5.96453 + 3.86582i 0.205796 + 0.133383i
\(841\) 7.67986i 0.264823i
\(842\) −1.74485 1.74485i −0.0601315 0.0601315i
\(843\) 31.6197 1.08904
\(844\) −11.9466 −0.411218
\(845\) −19.1013 12.3802i −0.657105 0.425893i
\(846\) 6.04560 6.04560i 0.207852 0.207852i
\(847\) 47.2631 47.2631i 1.62398 1.62398i
\(848\) 8.02058 + 8.02058i 0.275428 + 0.275428i
\(849\) −3.51440 + 3.51440i −0.120614 + 0.120614i
\(850\) 34.6127 15.4849i 1.18721 0.531129i
\(851\) 18.7249 17.6488i 0.641882 0.604992i
\(852\) 4.32811 4.32811i 0.148279 0.148279i
\(853\) −42.0289 −1.43904 −0.719520 0.694471i \(-0.755638\pi\)
−0.719520 + 0.694471i \(0.755638\pi\)
\(854\) 5.02827 0.172064
\(855\) 2.46541 + 11.5480i 0.0843152 + 0.394932i
\(856\) −8.64549 8.64549i −0.295497 0.295497i
\(857\) 34.3759 1.17426 0.587129 0.809494i \(-0.300258\pi\)
0.587129 + 0.809494i \(0.300258\pi\)
\(858\) 19.2664 + 19.2664i 0.657745 + 0.657745i
\(859\) 29.2733 29.2733i 0.998794 0.998794i −0.00120570 0.999999i \(-0.500384\pi\)
0.999999 + 0.00120570i \(0.000383786\pi\)
\(860\) −4.06999 + 6.27954i −0.138785 + 0.214130i
\(861\) 7.72558 0.263287
\(862\) −23.7856 23.7856i −0.810142 0.810142i
\(863\) 11.0183 + 11.0183i 0.375069 + 0.375069i 0.869319 0.494251i \(-0.164558\pi\)
−0.494251 + 0.869319i \(0.664558\pi\)
\(864\) 0.707107 0.707107i 0.0240563 0.0240563i
\(865\) 26.5523 5.66872i 0.902804 0.192742i
\(866\) 9.00285 9.00285i 0.305929 0.305929i
\(867\) 28.6470 28.6470i 0.972902 0.972902i
\(868\) 8.93712i 0.303346i
\(869\) −16.1469 16.1469i −0.547747 0.547747i
\(870\) −5.61551 + 8.66411i −0.190384 + 0.293741i
\(871\) 33.2765 33.2765i 1.12753 1.12753i
\(872\) 13.7592 + 13.7592i 0.465947 + 0.465947i
\(873\) 2.87834i 0.0974169i
\(874\) 15.7959 15.7959i 0.534306 0.534306i
\(875\) −20.9663 28.6952i −0.708792 0.970076i
\(876\) 3.65991i 0.123657i
\(877\) −5.02653 + 5.02653i −0.169734 + 0.169734i −0.786862 0.617129i \(-0.788296\pi\)
0.617129 + 0.786862i \(0.288296\pi\)
\(878\) 4.79636 4.79636i 0.161869 0.161869i
\(879\) −5.32288 −0.179536
\(880\) −6.88266 + 10.6192i −0.232015 + 0.357973i
\(881\) 29.2467i 0.985345i −0.870215 0.492673i \(-0.836020\pi\)
0.870215 0.492673i \(-0.163980\pi\)
\(882\) 3.10403i 0.104518i
\(883\) −28.8964 −0.972441 −0.486220 0.873836i \(-0.661625\pi\)
−0.486220 + 0.873836i \(0.661625\pi\)
\(884\) 36.5121i 1.22803i
\(885\) −16.9364 + 26.1311i −0.569312 + 0.878386i
\(886\) 7.85980 + 7.85980i 0.264055 + 0.264055i
\(887\) 8.58020 + 8.58020i 0.288095 + 0.288095i 0.836327 0.548232i \(-0.184699\pi\)
−0.548232 + 0.836327i \(0.684699\pi\)
\(888\) −0.179886 + 6.08010i −0.00603658 + 0.204035i
\(889\) 65.6706i 2.20252i
\(890\) −31.5065 + 6.72642i −1.05610 + 0.225470i
\(891\) 5.65930i 0.189594i
\(892\) −11.0520 11.0520i −0.370050 0.370050i
\(893\) 45.1495i 1.51087i
\(894\) 6.50879 6.50879i 0.217686 0.217686i
\(895\) −9.30685 43.5932i −0.311094 1.45716i
\(896\) 2.24767 + 2.24767i 0.0750893 + 0.0750893i
\(897\) 14.4013 14.4013i 0.480844 0.480844i
\(898\) 16.4657 + 16.4657i 0.549468 + 0.549468i
\(899\) 12.9821 0.432978
\(900\) −4.56408 + 2.04186i −0.152136 + 0.0680621i
\(901\) −60.8259 60.8259i −2.02640 2.02640i
\(902\) 13.7545i 0.457976i
\(903\) 10.6377 0.353999
\(904\) 4.68689i 0.155884i
\(905\) 25.8628 + 16.7626i 0.859709 + 0.557208i
\(906\) −3.95777 + 3.95777i −0.131488 + 0.131488i
\(907\) 0.367882 0.0122153 0.00610766 0.999981i \(-0.498056\pi\)
0.00610766 + 0.999981i \(0.498056\pi\)
\(908\) 6.40168 0.212447
\(909\) −16.0893 −0.533649
\(910\) −33.4663 + 7.14482i −1.10940 + 0.236848i
\(911\) −28.3530 28.3530i −0.939377 0.939377i 0.0588872 0.998265i \(-0.481245\pi\)
−0.998265 + 0.0588872i \(0.981245\pi\)
\(912\) 5.28079i 0.174864i
\(913\) −5.12873 + 5.12873i −0.169736 + 0.169736i
\(914\) 5.42876i 0.179568i
\(915\) −1.92383 + 2.96825i −0.0635997 + 0.0981273i
\(916\) 16.3225i 0.539310i
\(917\) 41.6367i 1.37496i
\(918\) −5.36251 + 5.36251i −0.176989 + 0.176989i
\(919\) 6.98899 + 6.98899i 0.230546 + 0.230546i 0.812920 0.582375i \(-0.197876\pi\)
−0.582375 + 0.812920i \(0.697876\pi\)
\(920\) 7.93762 + 5.14465i 0.261696 + 0.169614i
\(921\) −14.6248 −0.481905
\(922\) −12.8604 + 12.8604i −0.423534 + 0.423534i
\(923\) 29.4691i 0.969987i
\(924\) 17.9891 0.591798
\(925\) 11.6840 28.0800i 0.384167 0.923264i
\(926\) −36.1282 −1.18725
\(927\) 11.0997i 0.364563i
\(928\) −3.26498 + 3.26498i −0.107178 + 0.107178i
\(929\) 31.4501 1.03184 0.515922 0.856636i \(-0.327450\pi\)
0.515922 + 0.856636i \(0.327450\pi\)
\(930\) 5.27569 + 3.41936i 0.172997 + 0.112125i
\(931\) 11.5907 + 11.5907i 0.379870 + 0.379870i
\(932\) −0.738837 + 0.738837i −0.0242014 + 0.0242014i
\(933\) 2.94474i 0.0964064i
\(934\) 4.96873i 0.162582i
\(935\) 52.1962 80.5330i 1.70700 2.63371i
\(936\) 4.81453i 0.157368i
\(937\) 16.7719 16.7719i 0.547915 0.547915i −0.377922 0.925837i \(-0.623361\pi\)
0.925837 + 0.377922i \(0.123361\pi\)
\(938\) 31.0703i 1.01448i
\(939\) −4.14532 4.14532i −0.135278 0.135278i
\(940\) −18.6965 + 3.99158i −0.609814 + 0.130191i
\(941\) 16.4771 0.537139 0.268570 0.963260i \(-0.413449\pi\)
0.268570 + 0.963260i \(0.413449\pi\)
\(942\) −1.41232 −0.0460159
\(943\) 10.2812 0.334803
\(944\) −9.84721 + 9.84721i −0.320499 + 0.320499i
\(945\) 5.96453 + 3.86582i 0.194026 + 0.125755i
\(946\) 18.9392i 0.615766i
\(947\) −56.8823 −1.84843 −0.924214 0.381876i \(-0.875278\pi\)
−0.924214 + 0.381876i \(0.875278\pi\)
\(948\) 4.03499i 0.131050i
\(949\) 12.4597 + 12.4597i 0.404460 + 0.404460i
\(950\) 9.41815 24.6671i 0.305565 0.800307i
\(951\) −4.67673 −0.151653
\(952\) −17.0457 17.0457i −0.552455 0.552455i
\(953\) 3.27877 3.27877i 0.106210 0.106210i −0.652005 0.758215i \(-0.726072\pi\)
0.758215 + 0.652005i \(0.226072\pi\)
\(954\) 8.02058 + 8.02058i 0.259676 + 0.259676i
\(955\) 12.1784 + 57.0438i 0.394085 + 1.84589i
\(956\) −5.10981 + 5.10981i −0.165263 + 0.165263i
\(957\) 26.1311i 0.844698i
\(958\) −21.0873 21.0873i −0.681300 0.681300i
\(959\) 7.37004i 0.237991i
\(960\) −2.18679 + 0.466864i −0.0705783 + 0.0150680i
\(961\) 23.0950i 0.745001i
\(962\) −20.0866 21.3114i −0.647618 0.687108i
\(963\) −8.64549 8.64549i −0.278597 0.278597i
\(964\) 8.22613 + 8.22613i 0.264946 + 0.264946i
\(965\) 27.9594 43.1383i 0.900046 1.38867i
\(966\) 13.4465i 0.432634i
\(967\) −38.2625 −1.23044 −0.615219 0.788356i \(-0.710932\pi\)
−0.615219 + 0.788356i \(0.710932\pi\)
\(968\) 21.0276i 0.675853i
\(969\) 40.0481i 1.28653i
\(970\) 3.50054 5.40095i 0.112396 0.173414i
\(971\) −30.0272 −0.963620 −0.481810 0.876276i \(-0.660020\pi\)
−0.481810 + 0.876276i \(0.660020\pi\)
\(972\) 0.707107 0.707107i 0.0226805 0.0226805i
\(973\) −40.3303 + 40.3303i −1.29293 + 1.29293i
\(974\) 10.6041i 0.339778i
\(975\) 8.58659 22.4892i 0.274991 0.720230i
\(976\) −1.11855 + 1.11855i −0.0358040 + 0.0358040i
\(977\) 23.6886i 0.757865i −0.925424 0.378932i \(-0.876291\pi\)
0.925424 0.378932i \(-0.123709\pi\)
\(978\) −5.47991 5.47991i −0.175228 0.175228i
\(979\) −57.6556 + 57.6556i −1.84268 + 1.84268i
\(980\) −3.77503 + 5.82445i −0.120589 + 0.186055i
\(981\) 13.7592 + 13.7592i 0.439299 + 0.439299i
\(982\) 2.33716i 0.0745819i
\(983\) 29.2431 29.2431i 0.932711 0.932711i −0.0651639 0.997875i \(-0.520757\pi\)
0.997875 + 0.0651639i \(0.0207570\pi\)
\(984\) −1.71858 + 1.71858i −0.0547862 + 0.0547862i
\(985\) −5.23701 + 1.11806i −0.166865 + 0.0356245i
\(986\) 24.7607 24.7607i 0.788541 0.788541i
\(987\) 19.2171 + 19.2171i 0.611686 + 0.611686i
\(988\) −17.9778 17.9778i −0.571952 0.571952i
\(989\) 14.1567 0.450155
\(990\) −6.88266 + 10.6192i −0.218745 + 0.337500i
\(991\) 6.15758 6.15758i 0.195602 0.195602i −0.602510 0.798112i \(-0.705833\pi\)
0.798112 + 0.602510i \(0.205833\pi\)
\(992\) 1.98809 + 1.98809i 0.0631218 + 0.0631218i
\(993\) 2.88137 0.0914375
\(994\) 13.7577 + 13.7577i 0.436367 + 0.436367i
\(995\) 4.84403 + 22.6894i 0.153566 + 0.719303i
\(996\) −1.28163 −0.0406100
\(997\) 14.2061 0.449913 0.224957 0.974369i \(-0.427776\pi\)
0.224957 + 0.974369i \(0.427776\pi\)
\(998\) −15.9396 + 15.9396i −0.504559 + 0.504559i
\(999\) −0.179886 + 6.08010i −0.00569134 + 0.192366i
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 1110.2.l.a.43.10 36
5.2 odd 4 1110.2.o.a.487.9 yes 36
37.31 odd 4 1110.2.o.a.253.9 yes 36
185.142 even 4 inner 1110.2.l.a.697.10 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1110.2.l.a.43.10 36 1.1 even 1 trivial
1110.2.l.a.697.10 yes 36 185.142 even 4 inner
1110.2.o.a.253.9 yes 36 37.31 odd 4
1110.2.o.a.487.9 yes 36 5.2 odd 4