Properties

Label 260.2.o.a.27.17
Level $260$
Weight $2$
Character 260.27
Analytic conductor $2.076$
Analytic rank $0$
Dimension $72$
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] = [260,2,Mod(27,260)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(260, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("260.27");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 260.o (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: \(2.07611045255\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(36\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 27.17
Character \(\chi\) \(=\) 260.27
Dual form 260.2.o.a.183.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0788259 - 1.41202i) q^{2} +(1.63309 + 1.63309i) q^{3} +(-1.98757 + 0.222607i) q^{4} +(-0.963620 + 2.01778i) q^{5} +(2.17721 - 2.43467i) q^{6} +(-3.04756 + 3.04756i) q^{7} +(0.470996 + 2.78894i) q^{8} +2.33394i q^{9} +O(q^{10})\) \(q+(-0.0788259 - 1.41202i) q^{2} +(1.63309 + 1.63309i) q^{3} +(-1.98757 + 0.222607i) q^{4} +(-0.963620 + 2.01778i) q^{5} +(2.17721 - 2.43467i) q^{6} +(-3.04756 + 3.04756i) q^{7} +(0.470996 + 2.78894i) q^{8} +2.33394i q^{9} +(2.92509 + 1.20159i) q^{10} +0.497041i q^{11} +(-3.60941 - 2.88234i) q^{12} +(0.707107 - 0.707107i) q^{13} +(4.54342 + 4.06297i) q^{14} +(-4.86888 + 1.72154i) q^{15} +(3.90089 - 0.884894i) q^{16} +(-2.41342 - 2.41342i) q^{17} +(3.29556 - 0.183975i) q^{18} +5.62862 q^{19} +(1.46609 - 4.22499i) q^{20} -9.95385 q^{21} +(0.701829 - 0.0391797i) q^{22} +(4.41675 + 4.41675i) q^{23} +(-3.78540 + 5.32375i) q^{24} +(-3.14287 - 3.88875i) q^{25} +(-1.05418 - 0.942707i) q^{26} +(1.08773 - 1.08773i) q^{27} +(5.37884 - 6.73565i) q^{28} -5.13981i q^{29} +(2.81463 + 6.73924i) q^{30} +3.14912i q^{31} +(-1.55698 - 5.43837i) q^{32} +(-0.811710 + 0.811710i) q^{33} +(-3.21754 + 3.59802i) q^{34} +(-3.21261 - 9.08599i) q^{35} +(-0.519552 - 4.63888i) q^{36} +(4.40088 + 4.40088i) q^{37} +(-0.443681 - 7.94770i) q^{38} +2.30953 q^{39} +(-6.08132 - 1.73711i) q^{40} +8.49850 q^{41} +(0.784621 + 14.0550i) q^{42} +(5.16698 + 5.16698i) q^{43} +(-0.110645 - 0.987905i) q^{44} +(-4.70939 - 2.24903i) q^{45} +(5.88836 - 6.58467i) q^{46} +(-0.110788 + 0.110788i) q^{47} +(7.81560 + 4.92539i) q^{48} -11.5752i q^{49} +(-5.24323 + 4.74432i) q^{50} -7.88265i q^{51} +(-1.24802 + 1.56283i) q^{52} +(0.203180 - 0.203180i) q^{53} +(-1.62163 - 1.45015i) q^{54} +(-1.00292 - 0.478958i) q^{55} +(-9.93483 - 7.06405i) q^{56} +(9.19203 + 9.19203i) q^{57} +(-7.25749 + 0.405150i) q^{58} -7.36019 q^{59} +(9.29404 - 4.50552i) q^{60} -6.43106 q^{61} +(4.44661 - 0.248232i) q^{62} +(-7.11283 - 7.11283i) q^{63} +(-7.55632 + 2.62716i) q^{64} +(0.745404 + 2.10817i) q^{65} +(1.21013 + 1.08216i) q^{66} +(-7.40905 + 7.40905i) q^{67} +(5.33409 + 4.25960i) q^{68} +14.4259i q^{69} +(-12.5763 + 5.25247i) q^{70} -0.618858i q^{71} +(-6.50922 + 1.09928i) q^{72} +(-11.5363 + 11.5363i) q^{73} +(5.86720 - 6.56101i) q^{74} +(1.21807 - 11.4832i) q^{75} +(-11.1873 + 1.25297i) q^{76} +(-1.51476 - 1.51476i) q^{77} +(-0.182051 - 3.26110i) q^{78} -2.69514 q^{79} +(-1.97345 + 8.72385i) q^{80} +10.5545 q^{81} +(-0.669902 - 12.0000i) q^{82} +(-5.93375 - 5.93375i) q^{83} +(19.7840 - 2.21579i) q^{84} +(7.19537 - 2.54413i) q^{85} +(6.88856 - 7.70314i) q^{86} +(8.39376 - 8.39376i) q^{87} +(-1.38621 + 0.234104i) q^{88} -12.7437i q^{89} +(-2.80445 + 6.82701i) q^{90} +4.30990i q^{91} +(-9.76181 - 7.79541i) q^{92} +(-5.14279 + 5.14279i) q^{93} +(0.165168 + 0.147702i) q^{94} +(-5.42385 + 11.3573i) q^{95} +(6.33865 - 11.4240i) q^{96} +(8.15212 + 8.15212i) q^{97} +(-16.3444 + 0.912426i) q^{98} -1.16007 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q - 8 q^{6} - 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 72 q - 8 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 8 q^{16} + 28 q^{18} - 16 q^{21} - 8 q^{22} - 20 q^{28} - 32 q^{30} - 40 q^{32} + 16 q^{33} + 32 q^{36} - 12 q^{38} - 8 q^{40} - 40 q^{42} - 8 q^{46} + 60 q^{48} + 40 q^{50} + 8 q^{52} - 48 q^{53} + 8 q^{56} - 60 q^{58} + 20 q^{60} - 64 q^{61} + 60 q^{62} + 8 q^{66} - 16 q^{68} - 60 q^{70} + 40 q^{72} - 16 q^{73} - 72 q^{76} + 48 q^{77} - 20 q^{80} + 8 q^{81} - 12 q^{82} + 48 q^{85} + 48 q^{86} + 12 q^{88} + 44 q^{90} - 36 q^{92} + 16 q^{93} + 32 q^{96} - 80 q^{97} - 32 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).

\(n\) \(41\) \(131\) \(157\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0788259 1.41202i −0.0557383 0.998445i
\(3\) 1.63309 + 1.63309i 0.942863 + 0.942863i 0.998454 0.0555906i \(-0.0177042\pi\)
−0.0555906 + 0.998454i \(0.517704\pi\)
\(4\) −1.98757 + 0.222607i −0.993786 + 0.111303i
\(5\) −0.963620 + 2.01778i −0.430944 + 0.902379i
\(6\) 2.17721 2.43467i 0.888844 0.993951i
\(7\) −3.04756 + 3.04756i −1.15187 + 1.15187i −0.165690 + 0.986178i \(0.552985\pi\)
−0.986178 + 0.165690i \(0.947015\pi\)
\(8\) 0.470996 + 2.78894i 0.166522 + 0.986038i
\(9\) 2.33394i 0.777981i
\(10\) 2.92509 + 1.20159i 0.924996 + 0.379977i
\(11\) 0.497041i 0.149863i 0.997189 + 0.0749317i \(0.0238739\pi\)
−0.997189 + 0.0749317i \(0.976126\pi\)
\(12\) −3.60941 2.88234i −1.04195 0.832061i
\(13\) 0.707107 0.707107i 0.196116 0.196116i
\(14\) 4.54342 + 4.06297i 1.21428 + 1.08587i
\(15\) −4.86888 + 1.72154i −1.25714 + 0.444499i
\(16\) 3.90089 0.884894i 0.975223 0.221224i
\(17\) −2.41342 2.41342i −0.585340 0.585340i 0.351026 0.936366i \(-0.385833\pi\)
−0.936366 + 0.351026i \(0.885833\pi\)
\(18\) 3.29556 0.183975i 0.776772 0.0433634i
\(19\) 5.62862 1.29129 0.645647 0.763636i \(-0.276588\pi\)
0.645647 + 0.763636i \(0.276588\pi\)
\(20\) 1.46609 4.22499i 0.327828 0.944737i
\(21\) −9.95385 −2.17211
\(22\) 0.701829 0.0391797i 0.149630 0.00835314i
\(23\) 4.41675 + 4.41675i 0.920956 + 0.920956i 0.997097 0.0761410i \(-0.0242599\pi\)
−0.0761410 + 0.997097i \(0.524260\pi\)
\(24\) −3.78540 + 5.32375i −0.772691 + 1.08671i
\(25\) −3.14287 3.88875i −0.628575 0.777749i
\(26\) −1.05418 0.942707i −0.206742 0.184880i
\(27\) 1.08773 1.08773i 0.209333 0.209333i
\(28\) 5.37884 6.73565i 1.01650 1.27292i
\(29\) 5.13981i 0.954439i −0.878784 0.477220i \(-0.841645\pi\)
0.878784 0.477220i \(-0.158355\pi\)
\(30\) 2.81463 + 6.73924i 0.513878 + 1.23041i
\(31\) 3.14912i 0.565599i 0.959179 + 0.282800i \(0.0912631\pi\)
−0.959179 + 0.282800i \(0.908737\pi\)
\(32\) −1.55698 5.43837i −0.275237 0.961376i
\(33\) −0.811710 + 0.811710i −0.141301 + 0.141301i
\(34\) −3.21754 + 3.59802i −0.551804 + 0.617056i
\(35\) −3.21261 9.08599i −0.543031 1.53581i
\(36\) −0.519552 4.63888i −0.0865919 0.773147i
\(37\) 4.40088 + 4.40088i 0.723500 + 0.723500i 0.969316 0.245817i \(-0.0790561\pi\)
−0.245817 + 0.969316i \(0.579056\pi\)
\(38\) −0.443681 7.94770i −0.0719746 1.28929i
\(39\) 2.30953 0.369821
\(40\) −6.08132 1.73711i −0.961541 0.274661i
\(41\) 8.49850 1.32724 0.663621 0.748069i \(-0.269019\pi\)
0.663621 + 0.748069i \(0.269019\pi\)
\(42\) 0.784621 + 14.0550i 0.121070 + 2.16873i
\(43\) 5.16698 + 5.16698i 0.787957 + 0.787957i 0.981159 0.193202i \(-0.0618873\pi\)
−0.193202 + 0.981159i \(0.561887\pi\)
\(44\) −0.110645 0.987905i −0.0166803 0.148932i
\(45\) −4.70939 2.24903i −0.702034 0.335266i
\(46\) 5.88836 6.58467i 0.868192 0.970857i
\(47\) −0.110788 + 0.110788i −0.0161601 + 0.0161601i −0.715141 0.698981i \(-0.753637\pi\)
0.698981 + 0.715141i \(0.253637\pi\)
\(48\) 7.81560 + 4.92539i 1.12809 + 0.710918i
\(49\) 11.5752i 1.65360i
\(50\) −5.24323 + 4.74432i −0.741504 + 0.670948i
\(51\) 7.88265i 1.10379i
\(52\) −1.24802 + 1.56283i −0.173069 + 0.216726i
\(53\) 0.203180 0.203180i 0.0279090 0.0279090i −0.693015 0.720924i \(-0.743718\pi\)
0.720924 + 0.693015i \(0.243718\pi\)
\(54\) −1.62163 1.45015i −0.220676 0.197340i
\(55\) −1.00292 0.478958i −0.135234 0.0645827i
\(56\) −9.93483 7.06405i −1.32760 0.943974i
\(57\) 9.19203 + 9.19203i 1.21751 + 1.21751i
\(58\) −7.25749 + 0.405150i −0.952955 + 0.0531988i
\(59\) −7.36019 −0.958216 −0.479108 0.877756i \(-0.659040\pi\)
−0.479108 + 0.877756i \(0.659040\pi\)
\(60\) 9.29404 4.50552i 1.19986 0.581661i
\(61\) −6.43106 −0.823413 −0.411707 0.911316i \(-0.635067\pi\)
−0.411707 + 0.911316i \(0.635067\pi\)
\(62\) 4.44661 0.248232i 0.564720 0.0315256i
\(63\) −7.11283 7.11283i −0.896132 0.896132i
\(64\) −7.55632 + 2.62716i −0.944541 + 0.328395i
\(65\) 0.745404 + 2.10817i 0.0924560 + 0.261486i
\(66\) 1.21013 + 1.08216i 0.148957 + 0.133205i
\(67\) −7.40905 + 7.40905i −0.905159 + 0.905159i −0.995877 0.0907174i \(-0.971084\pi\)
0.0907174 + 0.995877i \(0.471084\pi\)
\(68\) 5.33409 + 4.25960i 0.646853 + 0.516553i
\(69\) 14.4259i 1.73667i
\(70\) −12.5763 + 5.25247i −1.50316 + 0.627790i
\(71\) 0.618858i 0.0734449i −0.999326 0.0367225i \(-0.988308\pi\)
0.999326 0.0367225i \(-0.0116917\pi\)
\(72\) −6.50922 + 1.09928i −0.767119 + 0.129551i
\(73\) −11.5363 + 11.5363i −1.35023 + 1.35023i −0.464820 + 0.885405i \(0.653881\pi\)
−0.885405 + 0.464820i \(0.846119\pi\)
\(74\) 5.86720 6.56101i 0.682048 0.762701i
\(75\) 1.21807 11.4832i 0.140651 1.32597i
\(76\) −11.1873 + 1.25297i −1.28327 + 0.143725i
\(77\) −1.51476 1.51476i −0.172623 0.172623i
\(78\) −0.182051 3.26110i −0.0206132 0.369246i
\(79\) −2.69514 −0.303227 −0.151613 0.988440i \(-0.548447\pi\)
−0.151613 + 0.988440i \(0.548447\pi\)
\(80\) −1.97345 + 8.72385i −0.220639 + 0.975356i
\(81\) 10.5545 1.17273
\(82\) −0.669902 12.0000i −0.0739783 1.32518i
\(83\) −5.93375 5.93375i −0.651314 0.651314i 0.301995 0.953309i \(-0.402347\pi\)
−0.953309 + 0.301995i \(0.902347\pi\)
\(84\) 19.7840 2.21579i 2.15861 0.241763i
\(85\) 7.19537 2.54413i 0.780447 0.275950i
\(86\) 6.88856 7.70314i 0.742812 0.830651i
\(87\) 8.39376 8.39376i 0.899905 0.899905i
\(88\) −1.38621 + 0.234104i −0.147771 + 0.0249556i
\(89\) 12.7437i 1.35083i −0.737440 0.675413i \(-0.763965\pi\)
0.737440 0.675413i \(-0.236035\pi\)
\(90\) −2.80445 + 6.82701i −0.295615 + 0.719630i
\(91\) 4.30990i 0.451800i
\(92\) −9.76181 7.79541i −1.01774 0.812728i
\(93\) −5.14279 + 5.14279i −0.533282 + 0.533282i
\(94\) 0.165168 + 0.147702i 0.0170357 + 0.0152343i
\(95\) −5.42385 + 11.3573i −0.556476 + 1.16524i
\(96\) 6.33865 11.4240i 0.646936 1.16596i
\(97\) 8.15212 + 8.15212i 0.827723 + 0.827723i 0.987201 0.159479i \(-0.0509814\pi\)
−0.159479 + 0.987201i \(0.550981\pi\)
\(98\) −16.3444 + 0.912426i −1.65103 + 0.0921690i
\(99\) −1.16007 −0.116591
\(100\) 7.11235 + 7.02954i 0.711235 + 0.702954i
\(101\) −4.18013 −0.415938 −0.207969 0.978135i \(-0.566685\pi\)
−0.207969 + 0.978135i \(0.566685\pi\)
\(102\) −11.1304 + 0.621357i −1.10208 + 0.0615235i
\(103\) 3.46965 + 3.46965i 0.341875 + 0.341875i 0.857072 0.515197i \(-0.172281\pi\)
−0.515197 + 0.857072i \(0.672281\pi\)
\(104\) 2.30512 + 1.63903i 0.226036 + 0.160720i
\(105\) 9.59172 20.0847i 0.936056 1.96006i
\(106\) −0.302910 0.270878i −0.0294212 0.0263100i
\(107\) 9.43408 9.43408i 0.912027 0.912027i −0.0844046 0.996432i \(-0.526899\pi\)
0.996432 + 0.0844046i \(0.0268988\pi\)
\(108\) −1.91980 + 2.40407i −0.184733 + 0.231332i
\(109\) 10.2008i 0.977061i −0.872547 0.488531i \(-0.837533\pi\)
0.872547 0.488531i \(-0.162467\pi\)
\(110\) −0.597240 + 1.45389i −0.0569446 + 0.138623i
\(111\) 14.3740i 1.36432i
\(112\) −9.19143 + 14.5850i −0.868508 + 1.37815i
\(113\) 9.50714 9.50714i 0.894357 0.894357i −0.100573 0.994930i \(-0.532068\pi\)
0.994930 + 0.100573i \(0.0320676\pi\)
\(114\) 12.2547 13.7039i 1.14776 1.28348i
\(115\) −13.1681 + 4.65596i −1.22793 + 0.434171i
\(116\) 1.14416 + 10.2158i 0.106232 + 0.948509i
\(117\) 1.65035 + 1.65035i 0.152575 + 0.152575i
\(118\) 0.580174 + 10.3927i 0.0534093 + 0.956726i
\(119\) 14.7101 1.34847
\(120\) −7.09448 12.7682i −0.647634 1.16557i
\(121\) 10.7530 0.977541
\(122\) 0.506934 + 9.08076i 0.0458957 + 0.822133i
\(123\) 13.8788 + 13.8788i 1.25141 + 1.25141i
\(124\) −0.701016 6.25911i −0.0629531 0.562085i
\(125\) 10.8752 2.59436i 0.972705 0.232046i
\(126\) −9.48274 + 10.6041i −0.844790 + 0.944688i
\(127\) −0.0846773 + 0.0846773i −0.00751389 + 0.00751389i −0.710854 0.703340i \(-0.751691\pi\)
0.703340 + 0.710854i \(0.251691\pi\)
\(128\) 4.30522 + 10.4626i 0.380531 + 0.924768i
\(129\) 16.8762i 1.48587i
\(130\) 2.91801 1.21870i 0.255926 0.106887i
\(131\) 12.2879i 1.07360i −0.843709 0.536801i \(-0.819633\pi\)
0.843709 0.536801i \(-0.180367\pi\)
\(132\) 1.43264 1.79403i 0.124695 0.156150i
\(133\) −17.1536 + 17.1536i −1.48740 + 1.48740i
\(134\) 11.0457 + 9.87766i 0.954204 + 0.853300i
\(135\) 1.14664 + 3.24295i 0.0986870 + 0.279109i
\(136\) 5.59416 7.86758i 0.479695 0.674640i
\(137\) −2.43793 2.43793i −0.208286 0.208286i 0.595253 0.803539i \(-0.297052\pi\)
−0.803539 + 0.595253i \(0.797052\pi\)
\(138\) 20.3695 1.13713i 1.73397 0.0967991i
\(139\) 2.17145 0.184180 0.0920899 0.995751i \(-0.470645\pi\)
0.0920899 + 0.995751i \(0.470645\pi\)
\(140\) 8.40791 + 17.3439i 0.710598 + 1.46583i
\(141\) −0.361854 −0.0304736
\(142\) −0.873837 + 0.0487820i −0.0733307 + 0.00409370i
\(143\) 0.351461 + 0.351461i 0.0293906 + 0.0293906i
\(144\) 2.06529 + 9.10446i 0.172108 + 0.758705i
\(145\) 10.3710 + 4.95282i 0.861266 + 0.411310i
\(146\) 17.1988 + 15.3801i 1.42339 + 1.27287i
\(147\) 18.9033 18.9033i 1.55912 1.55912i
\(148\) −9.72673 7.76740i −0.799532 0.638476i
\(149\) 0.402191i 0.0329488i 0.999864 + 0.0164744i \(0.00524420\pi\)
−0.999864 + 0.0164744i \(0.994756\pi\)
\(150\) −16.3105 0.814759i −1.33175 0.0665248i
\(151\) 11.5532i 0.940189i −0.882616 0.470095i \(-0.844220\pi\)
0.882616 0.470095i \(-0.155780\pi\)
\(152\) 2.65106 + 15.6979i 0.215029 + 1.27327i
\(153\) 5.63279 5.63279i 0.455384 0.455384i
\(154\) −2.01946 + 2.25827i −0.162733 + 0.181976i
\(155\) −6.35424 3.03456i −0.510385 0.243741i
\(156\) −4.59037 + 0.514118i −0.367523 + 0.0411624i
\(157\) 10.9364 + 10.9364i 0.872818 + 0.872818i 0.992779 0.119960i \(-0.0382767\pi\)
−0.119960 + 0.992779i \(0.538277\pi\)
\(158\) 0.212447 + 3.80557i 0.0169013 + 0.302755i
\(159\) 0.663622 0.0526287
\(160\) 12.4738 + 2.09888i 0.986137 + 0.165931i
\(161\) −26.9206 −2.12164
\(162\) −0.831971 14.9032i −0.0653658 1.17090i
\(163\) −5.15794 5.15794i −0.404001 0.404001i 0.475639 0.879640i \(-0.342217\pi\)
−0.879640 + 0.475639i \(0.842217\pi\)
\(164\) −16.8914 + 1.89182i −1.31900 + 0.147727i
\(165\) −0.855673 2.42003i −0.0666141 0.188399i
\(166\) −7.91081 + 8.84628i −0.613998 + 0.686605i
\(167\) 4.88399 4.88399i 0.377935 0.377935i −0.492422 0.870357i \(-0.663888\pi\)
0.870357 + 0.492422i \(0.163888\pi\)
\(168\) −4.68823 27.7606i −0.361705 2.14178i
\(169\) 1.00000i 0.0769231i
\(170\) −4.15953 9.95942i −0.319022 0.763853i
\(171\) 13.1369i 1.00460i
\(172\) −11.4200 9.11954i −0.870763 0.695359i
\(173\) 11.3759 11.3759i 0.864896 0.864896i −0.127006 0.991902i \(-0.540537\pi\)
0.991902 + 0.127006i \(0.0405367\pi\)
\(174\) −12.5138 11.1905i −0.948666 0.848347i
\(175\) 21.4293 + 2.27308i 1.61990 + 0.171829i
\(176\) 0.439828 + 1.93890i 0.0331533 + 0.146150i
\(177\) −12.0198 12.0198i −0.903466 0.903466i
\(178\) −17.9942 + 1.00453i −1.34873 + 0.0752928i
\(179\) −14.2199 −1.06285 −0.531423 0.847106i \(-0.678343\pi\)
−0.531423 + 0.847106i \(0.678343\pi\)
\(180\) 9.86090 + 3.42178i 0.734988 + 0.255044i
\(181\) −10.4080 −0.773624 −0.386812 0.922159i \(-0.626424\pi\)
−0.386812 + 0.922159i \(0.626424\pi\)
\(182\) 6.08564 0.339732i 0.451098 0.0251826i
\(183\) −10.5025 10.5025i −0.776366 0.776366i
\(184\) −10.2378 + 14.3983i −0.754738 + 1.06146i
\(185\) −13.1208 + 4.63923i −0.964658 + 0.341083i
\(186\) 7.66708 + 6.85631i 0.562178 + 0.502729i
\(187\) 1.19957 1.19957i 0.0877211 0.0877211i
\(188\) 0.195538 0.244862i 0.0142610 0.0178584i
\(189\) 6.62982i 0.482249i
\(190\) 16.4643 + 6.76331i 1.19444 + 0.490662i
\(191\) 7.07244i 0.511744i −0.966711 0.255872i \(-0.917637\pi\)
0.966711 0.255872i \(-0.0823626\pi\)
\(192\) −16.6305 8.04976i −1.20020 0.580941i
\(193\) 15.3297 15.3297i 1.10345 1.10345i 0.109464 0.993991i \(-0.465087\pi\)
0.993991 0.109464i \(-0.0349134\pi\)
\(194\) 10.8683 12.1535i 0.780300 0.872572i
\(195\) −2.22551 + 4.66013i −0.159372 + 0.333719i
\(196\) 2.57672 + 23.0066i 0.184051 + 1.64333i
\(197\) −3.85661 3.85661i −0.274772 0.274772i 0.556246 0.831018i \(-0.312241\pi\)
−0.831018 + 0.556246i \(0.812241\pi\)
\(198\) 0.0914432 + 1.63803i 0.00649858 + 0.116410i
\(199\) 3.17819 0.225296 0.112648 0.993635i \(-0.464067\pi\)
0.112648 + 0.993635i \(0.464067\pi\)
\(200\) 9.36518 10.5969i 0.662218 0.749311i
\(201\) −24.1992 −1.70688
\(202\) 0.329502 + 5.90240i 0.0231837 + 0.415292i
\(203\) 15.6639 + 15.6639i 1.09939 + 1.09939i
\(204\) 1.75473 + 15.6673i 0.122856 + 1.09693i
\(205\) −8.18932 + 17.1481i −0.571967 + 1.19768i
\(206\) 4.62570 5.17269i 0.322288 0.360399i
\(207\) −10.3084 + 10.3084i −0.716487 + 0.716487i
\(208\) 2.13263 3.38406i 0.147871 0.234642i
\(209\) 2.79766i 0.193518i
\(210\) −29.1159 11.9605i −2.00919 0.825351i
\(211\) 10.6465i 0.732937i 0.930430 + 0.366469i \(0.119433\pi\)
−0.930430 + 0.366469i \(0.880567\pi\)
\(212\) −0.358606 + 0.449065i −0.0246292 + 0.0308419i
\(213\) 1.01065 1.01065i 0.0692485 0.0692485i
\(214\) −14.0647 12.5774i −0.961444 0.859774i
\(215\) −15.4048 + 5.44683i −1.05060 + 0.371470i
\(216\) 3.54592 + 2.52129i 0.241269 + 0.171552i
\(217\) −9.59713 9.59713i −0.651496 0.651496i
\(218\) −14.4037 + 0.804089i −0.975542 + 0.0544598i
\(219\) −37.6796 −2.54615
\(220\) 2.09999 + 0.728708i 0.141582 + 0.0491295i
\(221\) −3.41309 −0.229589
\(222\) 20.2963 1.13305i 1.36220 0.0760450i
\(223\) −13.3536 13.3536i −0.894220 0.894220i 0.100697 0.994917i \(-0.467893\pi\)
−0.994917 + 0.100697i \(0.967893\pi\)
\(224\) 21.3187 + 11.8288i 1.42442 + 0.790342i
\(225\) 9.07611 7.33529i 0.605074 0.489020i
\(226\) −14.1736 12.6748i −0.942816 0.843116i
\(227\) −5.71415 + 5.71415i −0.379262 + 0.379262i −0.870836 0.491574i \(-0.836422\pi\)
0.491574 + 0.870836i \(0.336422\pi\)
\(228\) −20.3160 16.2236i −1.34546 1.07444i
\(229\) 12.9982i 0.858948i 0.903079 + 0.429474i \(0.141301\pi\)
−0.903079 + 0.429474i \(0.858699\pi\)
\(230\) 7.61228 + 18.2265i 0.501939 + 1.20182i
\(231\) 4.94747i 0.325519i
\(232\) 14.3346 2.42083i 0.941113 0.158935i
\(233\) 0.881833 0.881833i 0.0577708 0.0577708i −0.677631 0.735402i \(-0.736993\pi\)
0.735402 + 0.677631i \(0.236993\pi\)
\(234\) 2.20023 2.46041i 0.143833 0.160842i
\(235\) −0.116789 0.330304i −0.00761845 0.0215467i
\(236\) 14.6289 1.63843i 0.952262 0.106653i
\(237\) −4.40139 4.40139i −0.285901 0.285901i
\(238\) −1.15953 20.7708i −0.0751614 1.34637i
\(239\) 6.13684 0.396960 0.198480 0.980105i \(-0.436400\pi\)
0.198480 + 0.980105i \(0.436400\pi\)
\(240\) −17.4696 + 11.0240i −1.12766 + 0.711594i
\(241\) 23.7790 1.53174 0.765869 0.642997i \(-0.222309\pi\)
0.765869 + 0.642997i \(0.222309\pi\)
\(242\) −0.847611 15.1833i −0.0544865 0.976021i
\(243\) 13.9733 + 13.9733i 0.896387 + 0.896387i
\(244\) 12.7822 1.43160i 0.818297 0.0916487i
\(245\) 23.3562 + 11.1541i 1.49217 + 0.712609i
\(246\) 18.5030 20.6911i 1.17971 1.31921i
\(247\) 3.98004 3.98004i 0.253244 0.253244i
\(248\) −8.78270 + 1.48323i −0.557702 + 0.0941849i
\(249\) 19.3807i 1.22820i
\(250\) −4.52052 15.1514i −0.285903 0.958259i
\(251\) 21.3919i 1.35025i 0.737705 + 0.675124i \(0.235910\pi\)
−0.737705 + 0.675124i \(0.764090\pi\)
\(252\) 15.7206 + 12.5539i 0.990306 + 0.790821i
\(253\) −2.19530 + 2.19530i −0.138018 + 0.138018i
\(254\) 0.126240 + 0.112891i 0.00792103 + 0.00708340i
\(255\) 15.9054 + 7.59587i 0.996038 + 0.475672i
\(256\) 14.4339 6.90375i 0.902120 0.431485i
\(257\) 11.7799 + 11.7799i 0.734811 + 0.734811i 0.971569 0.236758i \(-0.0760847\pi\)
−0.236758 + 0.971569i \(0.576085\pi\)
\(258\) 23.8295 1.33029i 1.48356 0.0828200i
\(259\) −26.8238 −1.66675
\(260\) −1.95084 4.02421i −0.120986 0.249571i
\(261\) 11.9960 0.742536
\(262\) −17.3508 + 0.968608i −1.07193 + 0.0598408i
\(263\) −11.1802 11.1802i −0.689398 0.689398i 0.272701 0.962099i \(-0.412083\pi\)
−0.962099 + 0.272701i \(0.912083\pi\)
\(264\) −2.64612 1.88150i −0.162857 0.115798i
\(265\) 0.214185 + 0.605762i 0.0131573 + 0.0372117i
\(266\) 25.5732 + 22.8689i 1.56799 + 1.40218i
\(267\) 20.8115 20.8115i 1.27364 1.27364i
\(268\) 13.0767 16.3753i 0.798788 1.00028i
\(269\) 1.87020i 0.114028i −0.998373 0.0570141i \(-0.981842\pi\)
0.998373 0.0570141i \(-0.0181580\pi\)
\(270\) 4.48871 1.87470i 0.273174 0.114091i
\(271\) 23.6707i 1.43789i −0.695066 0.718946i \(-0.744625\pi\)
0.695066 0.718946i \(-0.255375\pi\)
\(272\) −11.5501 7.27887i −0.700328 0.441346i
\(273\) −7.03843 + 7.03843i −0.425985 + 0.425985i
\(274\) −3.25022 + 3.63456i −0.196353 + 0.219572i
\(275\) 1.93286 1.56214i 0.116556 0.0942004i
\(276\) −3.21130 28.6725i −0.193297 1.72588i
\(277\) −11.2334 11.2334i −0.674949 0.674949i 0.283903 0.958853i \(-0.408370\pi\)
−0.958853 + 0.283903i \(0.908370\pi\)
\(278\) −0.171166 3.06612i −0.0102659 0.183893i
\(279\) −7.34988 −0.440026
\(280\) 23.8271 13.2392i 1.42394 0.791196i
\(281\) 5.48143 0.326995 0.163497 0.986544i \(-0.447723\pi\)
0.163497 + 0.986544i \(0.447723\pi\)
\(282\) 0.0285234 + 0.510943i 0.00169855 + 0.0304262i
\(283\) 7.89795 + 7.89795i 0.469484 + 0.469484i 0.901747 0.432263i \(-0.142285\pi\)
−0.432263 + 0.901747i \(0.642285\pi\)
\(284\) 0.137762 + 1.23003i 0.00817467 + 0.0729886i
\(285\) −27.4051 + 9.68988i −1.62334 + 0.573979i
\(286\) 0.468564 0.523972i 0.0277068 0.0309831i
\(287\) −25.8997 + 25.8997i −1.52881 + 1.52881i
\(288\) 12.6928 3.63389i 0.747933 0.214129i
\(289\) 5.35082i 0.314754i
\(290\) 6.17596 15.0344i 0.362665 0.882852i
\(291\) 26.6262i 1.56086i
\(292\) 20.3612 25.4974i 1.19155 1.49212i
\(293\) −12.2389 + 12.2389i −0.715005 + 0.715005i −0.967578 0.252573i \(-0.918723\pi\)
0.252573 + 0.967578i \(0.418723\pi\)
\(294\) −28.1818 25.2017i −1.64360 1.46979i
\(295\) 7.09243 14.8513i 0.412937 0.864673i
\(296\) −10.2010 + 14.3466i −0.592919 + 0.833877i
\(297\) 0.540645 + 0.540645i 0.0313714 + 0.0313714i
\(298\) 0.567900 0.0317031i 0.0328976 0.00183651i
\(299\) 6.24623 0.361229
\(300\) 0.135241 + 23.0949i 0.00780812 + 1.33339i
\(301\) −31.4933 −1.81524
\(302\) −16.3133 + 0.910695i −0.938728 + 0.0524046i
\(303\) −6.82651 6.82651i −0.392173 0.392173i
\(304\) 21.9567 4.98074i 1.25930 0.285665i
\(305\) 6.19710 12.9765i 0.354845 0.743031i
\(306\) −8.39759 7.50957i −0.480058 0.429293i
\(307\) −4.60280 + 4.60280i −0.262696 + 0.262696i −0.826148 0.563453i \(-0.809473\pi\)
0.563453 + 0.826148i \(0.309473\pi\)
\(308\) 3.34789 + 2.67350i 0.190764 + 0.152337i
\(309\) 11.3325i 0.644682i
\(310\) −3.78396 + 9.21148i −0.214915 + 0.523177i
\(311\) 32.5052i 1.84320i 0.388141 + 0.921600i \(0.373118\pi\)
−0.388141 + 0.921600i \(0.626882\pi\)
\(312\) 1.08778 + 6.44114i 0.0615835 + 0.364658i
\(313\) −19.2039 + 19.2039i −1.08547 + 1.08547i −0.0894769 + 0.995989i \(0.528520\pi\)
−0.995989 + 0.0894769i \(0.971480\pi\)
\(314\) 14.5803 16.3044i 0.822812 0.920111i
\(315\) 21.2062 7.49806i 1.19483 0.422468i
\(316\) 5.35678 0.599956i 0.301342 0.0337501i
\(317\) −8.28473 8.28473i −0.465317 0.465317i 0.435077 0.900393i \(-0.356721\pi\)
−0.900393 + 0.435077i \(0.856721\pi\)
\(318\) −0.0523106 0.937045i −0.00293343 0.0525469i
\(319\) 2.55470 0.143035
\(320\) 1.98040 17.7786i 0.110708 0.993853i
\(321\) 30.8133 1.71983
\(322\) 2.12204 + 38.0123i 0.118257 + 2.11834i
\(323\) −13.5842 13.5842i −0.755847 0.755847i
\(324\) −20.9779 + 2.34951i −1.16544 + 0.130528i
\(325\) −4.97211 0.527410i −0.275803 0.0292555i
\(326\) −6.87651 + 7.68967i −0.380855 + 0.425891i
\(327\) 16.6588 16.6588i 0.921235 0.921235i
\(328\) 4.00276 + 23.7018i 0.221015 + 1.30871i
\(329\) 0.675267i 0.0372287i
\(330\) −3.34967 + 1.39898i −0.184394 + 0.0770116i
\(331\) 2.91495i 0.160220i 0.996786 + 0.0801102i \(0.0255272\pi\)
−0.996786 + 0.0801102i \(0.974473\pi\)
\(332\) 13.1147 + 10.4729i 0.719760 + 0.574774i
\(333\) −10.2714 + 10.2714i −0.562869 + 0.562869i
\(334\) −7.28126 6.51129i −0.398413 0.356282i
\(335\) −7.81033 22.0893i −0.426724 1.20687i
\(336\) −38.8289 + 8.80810i −2.11829 + 0.480521i
\(337\) −4.32305 4.32305i −0.235492 0.235492i 0.579489 0.814980i \(-0.303252\pi\)
−0.814980 + 0.579489i \(0.803252\pi\)
\(338\) −1.41202 + 0.0788259i −0.0768035 + 0.00428756i
\(339\) 31.0520 1.68651
\(340\) −13.7350 + 6.65838i −0.744884 + 0.361102i
\(341\) −1.56524 −0.0847626
\(342\) 18.5495 1.03553i 1.00304 0.0559949i
\(343\) 13.9432 + 13.9432i 0.752862 + 0.752862i
\(344\) −11.9767 + 16.8440i −0.645743 + 0.908168i
\(345\) −29.1082 13.9011i −1.56713 0.748408i
\(346\) −16.9597 15.1663i −0.911760 0.815344i
\(347\) −16.3762 + 16.3762i −0.879119 + 0.879119i −0.993443 0.114324i \(-0.963530\pi\)
0.114324 + 0.993443i \(0.463530\pi\)
\(348\) −14.8147 + 18.5517i −0.794151 + 0.994476i
\(349\) 24.6174i 1.31774i −0.752258 0.658869i \(-0.771035\pi\)
0.752258 0.658869i \(-0.228965\pi\)
\(350\) 1.52045 30.4376i 0.0812714 1.62696i
\(351\) 1.53828i 0.0821072i
\(352\) 2.70309 0.773880i 0.144075 0.0412479i
\(353\) 5.78094 5.78094i 0.307688 0.307688i −0.536324 0.844012i \(-0.680187\pi\)
0.844012 + 0.536324i \(0.180187\pi\)
\(354\) −16.0247 + 17.9197i −0.851704 + 0.952419i
\(355\) 1.24872 + 0.596344i 0.0662751 + 0.0316506i
\(356\) 2.83683 + 25.3290i 0.150351 + 1.34243i
\(357\) 24.0228 + 24.0228i 1.27142 + 1.27142i
\(358\) 1.12090 + 20.0787i 0.0592413 + 1.06119i
\(359\) 6.42788 0.339251 0.169625 0.985509i \(-0.445744\pi\)
0.169625 + 0.985509i \(0.445744\pi\)
\(360\) 4.05431 14.1935i 0.213681 0.748061i
\(361\) 12.6814 0.667443
\(362\) 0.820424 + 14.6963i 0.0431205 + 0.772422i
\(363\) 17.5605 + 17.5605i 0.921687 + 0.921687i
\(364\) −0.959412 8.56623i −0.0502869 0.448993i
\(365\) −12.1611 34.3944i −0.636543 1.80029i
\(366\) −14.0018 + 15.6575i −0.731886 + 0.818432i
\(367\) −11.7313 + 11.7313i −0.612371 + 0.612371i −0.943563 0.331192i \(-0.892549\pi\)
0.331192 + 0.943563i \(0.392549\pi\)
\(368\) 21.1376 + 13.3209i 1.10187 + 0.694400i
\(369\) 19.8350i 1.03257i
\(370\) 7.58492 + 18.1610i 0.394321 + 0.944147i
\(371\) 1.23841i 0.0642949i
\(372\) 9.07685 11.3665i 0.470613 0.589325i
\(373\) 15.7227 15.7227i 0.814091 0.814091i −0.171154 0.985244i \(-0.554749\pi\)
0.985244 + 0.171154i \(0.0547494\pi\)
\(374\) −1.78836 1.59925i −0.0924741 0.0826953i
\(375\) 21.9969 + 13.5233i 1.13592 + 0.698339i
\(376\) −0.361162 0.256800i −0.0186255 0.0132435i
\(377\) −3.63440 3.63440i −0.187181 0.187181i
\(378\) 9.36141 0.522602i 0.481499 0.0268797i
\(379\) 28.9807 1.48864 0.744319 0.667825i \(-0.232774\pi\)
0.744319 + 0.667825i \(0.232774\pi\)
\(380\) 8.25209 23.7809i 0.423323 1.21993i
\(381\) −0.276571 −0.0141691
\(382\) −9.98640 + 0.557492i −0.510948 + 0.0285238i
\(383\) −22.7875 22.7875i −1.16439 1.16439i −0.983505 0.180882i \(-0.942105\pi\)
−0.180882 0.983505i \(-0.557895\pi\)
\(384\) −10.0555 + 24.1171i −0.513141 + 1.23072i
\(385\) 4.51610 1.59680i 0.230162 0.0813805i
\(386\) −22.8541 20.4374i −1.16324 1.04023i
\(387\) −12.0594 + 12.0594i −0.613016 + 0.613016i
\(388\) −18.0177 14.3882i −0.914708 0.730451i
\(389\) 1.60674i 0.0814649i −0.999170 0.0407324i \(-0.987031\pi\)
0.999170 0.0407324i \(-0.0129691\pi\)
\(390\) 6.75560 + 2.77512i 0.342083 + 0.140524i
\(391\) 21.3189i 1.07815i
\(392\) 32.2825 5.45188i 1.63051 0.275362i
\(393\) 20.0673 20.0673i 1.01226 1.01226i
\(394\) −5.14160 + 5.74960i −0.259030 + 0.289661i
\(395\) 2.59709 5.43819i 0.130674 0.273625i
\(396\) 2.30571 0.258238i 0.115866 0.0129770i
\(397\) −12.8728 12.8728i −0.646069 0.646069i 0.305971 0.952041i \(-0.401019\pi\)
−0.952041 + 0.305971i \(0.901019\pi\)
\(398\) −0.250524 4.48766i −0.0125576 0.224946i
\(399\) −56.0265 −2.80483
\(400\) −15.7011 12.3885i −0.785057 0.619423i
\(401\) −9.91973 −0.495367 −0.247684 0.968841i \(-0.579669\pi\)
−0.247684 + 0.968841i \(0.579669\pi\)
\(402\) 1.90753 + 34.1697i 0.0951388 + 1.70423i
\(403\) 2.22677 + 2.22677i 0.110923 + 0.110923i
\(404\) 8.30831 0.930524i 0.413354 0.0462953i
\(405\) −10.1706 + 21.2967i −0.505379 + 1.05824i
\(406\) 20.8829 23.3523i 1.03640 1.15896i
\(407\) −2.18741 + 2.18741i −0.108426 + 0.108426i
\(408\) 21.9842 3.71270i 1.08838 0.183806i
\(409\) 22.7557i 1.12520i 0.826730 + 0.562599i \(0.190198\pi\)
−0.826730 + 0.562599i \(0.809802\pi\)
\(410\) 24.8589 + 10.2117i 1.22769 + 0.504321i
\(411\) 7.96269i 0.392770i
\(412\) −7.66855 6.12381i −0.377802 0.301699i
\(413\) 22.4306 22.4306i 1.10374 1.10374i
\(414\) 15.3683 + 13.7431i 0.755309 + 0.675437i
\(415\) 17.6909 6.25513i 0.868412 0.307052i
\(416\) −4.94645 2.74456i −0.242520 0.134563i
\(417\) 3.54616 + 3.54616i 0.173656 + 0.173656i
\(418\) 3.95033 0.220528i 0.193217 0.0107864i
\(419\) 6.93899 0.338992 0.169496 0.985531i \(-0.445786\pi\)
0.169496 + 0.985531i \(0.445786\pi\)
\(420\) −14.5933 + 42.0550i −0.712079 + 2.05207i
\(421\) −3.45189 −0.168235 −0.0841173 0.996456i \(-0.526807\pi\)
−0.0841173 + 0.996456i \(0.526807\pi\)
\(422\) 15.0331 0.839222i 0.731798 0.0408527i
\(423\) −0.258574 0.258574i −0.0125723 0.0125723i
\(424\) 0.662354 + 0.470960i 0.0321668 + 0.0228718i
\(425\) −1.80010 + 16.9702i −0.0873176 + 0.823178i
\(426\) −1.50672 1.34739i −0.0730006 0.0652810i
\(427\) 19.5990 19.5990i 0.948463 0.948463i
\(428\) −16.6508 + 20.8510i −0.804848 + 1.00787i
\(429\) 1.14793i 0.0554227i
\(430\) 8.90530 + 21.3225i 0.429452 + 1.02826i
\(431\) 5.69174i 0.274161i −0.990560 0.137081i \(-0.956228\pi\)
0.990560 0.137081i \(-0.0437720\pi\)
\(432\) 3.28058 5.20563i 0.157837 0.250456i
\(433\) −22.4844 + 22.4844i −1.08053 + 1.08053i −0.0840698 + 0.996460i \(0.526792\pi\)
−0.996460 + 0.0840698i \(0.973208\pi\)
\(434\) −12.7948 + 14.3078i −0.614170 + 0.686796i
\(435\) 8.84837 + 25.0252i 0.424247 + 1.19986i
\(436\) 2.27077 + 20.2749i 0.108750 + 0.970990i
\(437\) 24.8602 + 24.8602i 1.18923 + 1.18923i
\(438\) 2.97013 + 53.2042i 0.141918 + 2.54220i
\(439\) 18.8063 0.897574 0.448787 0.893639i \(-0.351856\pi\)
0.448787 + 0.893639i \(0.351856\pi\)
\(440\) 0.863412 3.02266i 0.0411616 0.144100i
\(441\) 27.0159 1.28647
\(442\) 0.269040 + 4.81933i 0.0127969 + 0.229232i
\(443\) −27.8526 27.8526i −1.32332 1.32332i −0.911073 0.412246i \(-0.864744\pi\)
−0.412246 0.911073i \(-0.635256\pi\)
\(444\) −3.19975 28.5694i −0.151854 1.35584i
\(445\) 25.7139 + 12.2800i 1.21896 + 0.582130i
\(446\) −17.8028 + 19.9080i −0.842988 + 0.942672i
\(447\) −0.656813 + 0.656813i −0.0310662 + 0.0310662i
\(448\) 15.0219 31.0347i 0.709719 1.46625i
\(449\) 18.0953i 0.853970i 0.904259 + 0.426985i \(0.140424\pi\)
−0.904259 + 0.426985i \(0.859576\pi\)
\(450\) −11.0730 12.2374i −0.521985 0.576876i
\(451\) 4.22410i 0.198905i
\(452\) −16.7798 + 21.0125i −0.789255 + 0.988344i
\(453\) 18.8674 18.8674i 0.886470 0.886470i
\(454\) 8.51890 + 7.61805i 0.399812 + 0.357533i
\(455\) −8.69642 4.15310i −0.407695 0.194700i
\(456\) −21.3066 + 29.9654i −0.997772 + 1.40326i
\(457\) 19.6055 + 19.6055i 0.917105 + 0.917105i 0.996818 0.0797133i \(-0.0254005\pi\)
−0.0797133 + 0.996818i \(0.525400\pi\)
\(458\) 18.3537 1.02460i 0.857613 0.0478763i
\(459\) −5.25028 −0.245062
\(460\) 25.1361 12.1854i 1.17198 0.568146i
\(461\) −34.9245 −1.62660 −0.813298 0.581848i \(-0.802330\pi\)
−0.813298 + 0.581848i \(0.802330\pi\)
\(462\) −6.98590 + 0.389989i −0.325013 + 0.0181439i
\(463\) 21.6671 + 21.6671i 1.00695 + 1.00695i 0.999976 + 0.00697798i \(0.00222118\pi\)
0.00697798 + 0.999976i \(0.497779\pi\)
\(464\) −4.54819 20.0499i −0.211144 0.930791i
\(465\) −5.42133 15.3327i −0.251408 0.711038i
\(466\) −1.31467 1.17565i −0.0609010 0.0544609i
\(467\) 1.42697 1.42697i 0.0660321 0.0660321i −0.673320 0.739352i \(-0.735132\pi\)
0.739352 + 0.673320i \(0.235132\pi\)
\(468\) −3.64756 2.91281i −0.168609 0.134645i
\(469\) 45.1590i 2.08525i
\(470\) −0.457188 + 0.190944i −0.0210885 + 0.00880758i
\(471\) 35.7201i 1.64590i
\(472\) −3.46662 20.5271i −0.159564 0.944837i
\(473\) −2.56820 + 2.56820i −0.118086 + 0.118086i
\(474\) −5.86789 + 6.56178i −0.269521 + 0.301392i
\(475\) −17.6901 21.8883i −0.811676 1.00430i
\(476\) −29.2373 + 3.27456i −1.34009 + 0.150089i
\(477\) 0.474212 + 0.474212i 0.0217127 + 0.0217127i
\(478\) −0.483742 8.66532i −0.0221259 0.396342i
\(479\) 27.3934 1.25163 0.625817 0.779970i \(-0.284765\pi\)
0.625817 + 0.779970i \(0.284765\pi\)
\(480\) 16.9431 + 23.7984i 0.773342 + 1.08624i
\(481\) 6.22378 0.283780
\(482\) −1.87440 33.5763i −0.0853765 1.52936i
\(483\) −43.9637 43.9637i −2.00042 2.00042i
\(484\) −21.3723 + 2.39368i −0.971467 + 0.108804i
\(485\) −24.3047 + 8.59365i −1.10362 + 0.390217i
\(486\) 18.6290 20.8320i 0.845030 0.944957i
\(487\) −8.51241 + 8.51241i −0.385734 + 0.385734i −0.873163 0.487429i \(-0.837935\pi\)
0.487429 + 0.873163i \(0.337935\pi\)
\(488\) −3.02901 17.9358i −0.137117 0.811916i
\(489\) 16.8467i 0.761835i
\(490\) 13.9087 33.8586i 0.628330 1.52957i
\(491\) 14.9696i 0.675570i 0.941223 + 0.337785i \(0.109678\pi\)
−0.941223 + 0.337785i \(0.890322\pi\)
\(492\) −30.6746 24.4956i −1.38292 1.10435i
\(493\) −12.4045 + 12.4045i −0.558672 + 0.558672i
\(494\) −5.93360 5.30614i −0.266965 0.238735i
\(495\) 1.11786 2.34076i 0.0502441 0.105209i
\(496\) 2.78664 + 12.2844i 0.125124 + 0.551585i
\(497\) 1.88600 + 1.88600i 0.0845989 + 0.0845989i
\(498\) −27.3658 + 1.52770i −1.22629 + 0.0684578i
\(499\) −15.5021 −0.693969 −0.346984 0.937871i \(-0.612794\pi\)
−0.346984 + 0.937871i \(0.612794\pi\)
\(500\) −21.0377 + 7.57736i −0.940833 + 0.338870i
\(501\) 15.9520 0.712682
\(502\) 30.2057 1.68624i 1.34815 0.0752605i
\(503\) 7.25339 + 7.25339i 0.323413 + 0.323413i 0.850075 0.526662i \(-0.176557\pi\)
−0.526662 + 0.850075i \(0.676557\pi\)
\(504\) 16.4871 23.1873i 0.734394 1.03285i
\(505\) 4.02805 8.43458i 0.179246 0.375334i
\(506\) 3.27285 + 2.92676i 0.145496 + 0.130110i
\(507\) 1.63309 1.63309i 0.0725279 0.0725279i
\(508\) 0.149453 0.187152i 0.00663089 0.00830353i
\(509\) 3.62150i 0.160520i −0.996774 0.0802602i \(-0.974425\pi\)
0.996774 0.0802602i \(-0.0255751\pi\)
\(510\) 9.47172 23.0575i 0.419415 1.02100i
\(511\) 70.3152i 3.11056i
\(512\) −10.8860 19.8367i −0.481097 0.876668i
\(513\) 6.12241 6.12241i 0.270311 0.270311i
\(514\) 15.7049 17.5620i 0.692712 0.774626i
\(515\) −10.3444 + 3.65757i −0.455829 + 0.161172i
\(516\) −3.75677 33.5428i −0.165382 1.47664i
\(517\) −0.0550663 0.0550663i −0.00242181 0.00242181i
\(518\) 2.11441 + 37.8757i 0.0929020 + 1.66416i
\(519\) 37.1558 1.63096
\(520\) −5.52846 + 3.07182i −0.242439 + 0.134708i
\(521\) 35.8853 1.57216 0.786082 0.618123i \(-0.212107\pi\)
0.786082 + 0.618123i \(0.212107\pi\)
\(522\) −0.945598 16.9386i −0.0413877 0.741381i
\(523\) 18.4185 + 18.4185i 0.805384 + 0.805384i 0.983931 0.178548i \(-0.0571399\pi\)
−0.178548 + 0.983931i \(0.557140\pi\)
\(524\) 2.73538 + 24.4232i 0.119496 + 1.06693i
\(525\) 31.2837 + 38.7080i 1.36533 + 1.68936i
\(526\) −14.9053 + 16.6678i −0.649900 + 0.726752i
\(527\) 7.60015 7.60015i 0.331068 0.331068i
\(528\) −2.44812 + 3.88467i −0.106541 + 0.169059i
\(529\) 16.0154i 0.696320i
\(530\) 0.838462 0.350182i 0.0364204 0.0152109i
\(531\) 17.1783i 0.745474i
\(532\) 30.2754 37.9124i 1.31261 1.64371i
\(533\) 6.00935 6.00935i 0.260294 0.260294i
\(534\) −31.0266 27.7457i −1.34265 1.20067i
\(535\) 9.94504 + 28.1268i 0.429961 + 1.21603i
\(536\) −24.1530 17.1737i −1.04325 0.741792i
\(537\) −23.2224 23.2224i −1.00212 1.00212i
\(538\) −2.64075 + 0.147420i −0.113851 + 0.00635574i
\(539\) 5.75335 0.247814
\(540\) −3.00093 6.19035i −0.129140 0.266390i
\(541\) −0.467513 −0.0200999 −0.0100500 0.999949i \(-0.503199\pi\)
−0.0100500 + 0.999949i \(0.503199\pi\)
\(542\) −33.4234 + 1.86586i −1.43566 + 0.0801457i
\(543\) −16.9972 16.9972i −0.729422 0.729422i
\(544\) −9.36742 + 16.8827i −0.401625 + 0.723839i
\(545\) 20.5830 + 9.82971i 0.881679 + 0.421058i
\(546\) 10.4932 + 9.38356i 0.449067 + 0.401579i
\(547\) −16.7318 + 16.7318i −0.715402 + 0.715402i −0.967660 0.252258i \(-0.918827\pi\)
0.252258 + 0.967660i \(0.418827\pi\)
\(548\) 5.38825 + 4.30286i 0.230175 + 0.183809i
\(549\) 15.0097i 0.640600i
\(550\) −2.35812 2.60610i −0.100551 0.111124i
\(551\) 28.9301i 1.23246i
\(552\) −40.2328 + 6.79453i −1.71242 + 0.289194i
\(553\) 8.21358 8.21358i 0.349277 0.349277i
\(554\) −14.9762 + 16.7472i −0.636280 + 0.711521i
\(555\) −29.0036 13.8511i −1.23114 0.587946i
\(556\) −4.31591 + 0.483379i −0.183035 + 0.0204998i
\(557\) −26.5909 26.5909i −1.12669 1.12669i −0.990711 0.135981i \(-0.956581\pi\)
−0.135981 0.990711i \(-0.543419\pi\)
\(558\) 0.579361 + 10.3781i 0.0245263 + 0.439341i
\(559\) 7.30721 0.309062
\(560\) −20.5722 32.6006i −0.869334 1.37763i
\(561\) 3.91800 0.165418
\(562\) −0.432078 7.73986i −0.0182261 0.326486i
\(563\) −0.168647 0.168647i −0.00710764 0.00710764i 0.703544 0.710652i \(-0.251600\pi\)
−0.710652 + 0.703544i \(0.751600\pi\)
\(564\) 0.719211 0.0805511i 0.0302842 0.00339181i
\(565\) 10.0221 + 28.3446i 0.421631 + 1.19247i
\(566\) 10.5295 11.7746i 0.442586 0.494923i
\(567\) −32.1656 + 32.1656i −1.35083 + 1.35083i
\(568\) 1.72595 0.291480i 0.0724194 0.0122302i
\(569\) 3.52360i 0.147717i −0.997269 0.0738586i \(-0.976469\pi\)
0.997269 0.0738586i \(-0.0235313\pi\)
\(570\) 15.8425 + 37.9326i 0.663569 + 1.58882i
\(571\) 29.6178i 1.23947i −0.784812 0.619734i \(-0.787240\pi\)
0.784812 0.619734i \(-0.212760\pi\)
\(572\) −0.776792 0.620316i −0.0324793 0.0259367i
\(573\) 11.5499 11.5499i 0.482505 0.482505i
\(574\) 38.6123 + 34.5291i 1.61164 + 1.44122i
\(575\) 3.29433 31.0569i 0.137383 1.29516i
\(576\) −6.13164 17.6360i −0.255485 0.734835i
\(577\) −6.92290 6.92290i −0.288204 0.288204i 0.548166 0.836370i \(-0.315326\pi\)
−0.836370 + 0.548166i \(0.815326\pi\)
\(578\) −7.55543 + 0.421783i −0.314265 + 0.0175439i
\(579\) 50.0694 2.08081
\(580\) −21.7157 7.53544i −0.901694 0.312892i
\(581\) 36.1669 1.50046
\(582\) 37.5967 2.09884i 1.55843 0.0869996i
\(583\) 0.100989 + 0.100989i 0.00418253 + 0.00418253i
\(584\) −37.6076 26.7405i −1.55622 1.10653i
\(585\) −4.92035 + 1.73973i −0.203431 + 0.0719290i
\(586\) 18.2463 + 16.3168i 0.753747 + 0.674040i
\(587\) −18.1217 + 18.1217i −0.747961 + 0.747961i −0.974096 0.226135i \(-0.927391\pi\)
0.226135 + 0.974096i \(0.427391\pi\)
\(588\) −33.3637 + 41.7797i −1.37590 + 1.72297i
\(589\) 17.7252i 0.730355i
\(590\) −21.5293 8.84395i −0.886346 0.364100i
\(591\) 12.5964i 0.518145i
\(592\) 21.0617 + 13.2730i 0.865629 + 0.545518i
\(593\) −16.4896 + 16.4896i −0.677147 + 0.677147i −0.959354 0.282206i \(-0.908934\pi\)
0.282206 + 0.959354i \(0.408934\pi\)
\(594\) 0.720782 0.806015i 0.0295740 0.0330712i
\(595\) −14.1749 + 29.6817i −0.581115 + 1.21683i
\(596\) −0.0895305 0.799385i −0.00366731 0.0327441i
\(597\) 5.19027 + 5.19027i 0.212423 + 0.212423i
\(598\) −0.492365 8.81977i −0.0201343 0.360667i
\(599\) 6.82062 0.278683 0.139341 0.990244i \(-0.455501\pi\)
0.139341 + 0.990244i \(0.455501\pi\)
\(600\) 32.5997 2.01144i 1.33088 0.0821167i
\(601\) 3.24618 0.132415 0.0662073 0.997806i \(-0.478910\pi\)
0.0662073 + 0.997806i \(0.478910\pi\)
\(602\) 2.48249 + 44.4690i 0.101179 + 1.81242i
\(603\) −17.2923 17.2923i −0.704197 0.704197i
\(604\) 2.57183 + 22.9629i 0.104646 + 0.934347i
\(605\) −10.3618 + 21.6971i −0.421265 + 0.882112i
\(606\) −9.10103 + 10.1772i −0.369704 + 0.413422i
\(607\) −6.52615 + 6.52615i −0.264888 + 0.264888i −0.827036 0.562148i \(-0.809975\pi\)
0.562148 + 0.827036i \(0.309975\pi\)
\(608\) −8.76363 30.6105i −0.355412 1.24142i
\(609\) 51.1609i 2.07314i
\(610\) −18.8115 7.72751i −0.761654 0.312878i
\(611\) 0.156678i 0.00633852i
\(612\) −9.94168 + 12.4495i −0.401868 + 0.503240i
\(613\) −5.59655 + 5.59655i −0.226042 + 0.226042i −0.811037 0.584995i \(-0.801097\pi\)
0.584995 + 0.811037i \(0.301097\pi\)
\(614\) 6.86205 + 6.13641i 0.276930 + 0.247645i
\(615\) −41.3782 + 14.6305i −1.66853 + 0.589957i
\(616\) 3.51112 4.93801i 0.141467 0.198958i
\(617\) −26.4213 26.4213i −1.06368 1.06368i −0.997829 0.0658511i \(-0.979024\pi\)
−0.0658511 0.997829i \(-0.520976\pi\)
\(618\) 16.0016 0.893292i 0.643680 0.0359335i
\(619\) −18.4631 −0.742093 −0.371046 0.928614i \(-0.621001\pi\)
−0.371046 + 0.928614i \(0.621001\pi\)
\(620\) 13.3050 + 4.61691i 0.534343 + 0.185419i
\(621\) 9.60844 0.385573
\(622\) 45.8978 2.56225i 1.84033 0.102737i
\(623\) 38.8370 + 38.8370i 1.55597 + 1.55597i
\(624\) 9.00924 2.04369i 0.360658 0.0818132i
\(625\) −5.24468 + 24.4437i −0.209787 + 0.977747i
\(626\) 28.6299 + 25.6024i 1.14428 + 1.02328i
\(627\) −4.56881 + 4.56881i −0.182461 + 0.182461i
\(628\) −24.1714 19.3023i −0.964543 0.770248i
\(629\) 21.2423i 0.846987i
\(630\) −12.2590 29.3524i −0.488409 1.16943i
\(631\) 23.4935i 0.935263i 0.883923 + 0.467632i \(0.154893\pi\)
−0.883923 + 0.467632i \(0.845107\pi\)
\(632\) −1.26940 7.51656i −0.0504940 0.298993i
\(633\) −17.3867 + 17.3867i −0.691059 + 0.691059i
\(634\) −11.0451 + 12.3512i −0.438657 + 0.490529i
\(635\) −0.0892635 0.252457i −0.00354231 0.0100184i
\(636\) −1.31900 + 0.147727i −0.0523017 + 0.00585775i
\(637\) −8.18491 8.18491i −0.324298 0.324298i
\(638\) −0.201376 3.60727i −0.00797256 0.142813i
\(639\) 1.44438 0.0571388
\(640\) −25.2597 1.39494i −0.998479 0.0551398i
\(641\) 23.5205 0.929004 0.464502 0.885572i \(-0.346233\pi\)
0.464502 + 0.885572i \(0.346233\pi\)
\(642\) −2.42889 43.5089i −0.0958606 1.71716i
\(643\) −21.3805 21.3805i −0.843165 0.843165i 0.146104 0.989269i \(-0.453326\pi\)
−0.989269 + 0.146104i \(0.953326\pi\)
\(644\) 53.5066 5.99271i 2.10846 0.236146i
\(645\) −34.0526 16.2623i −1.34082 0.640327i
\(646\) −18.1103 + 20.2519i −0.712542 + 0.796801i
\(647\) 20.7116 20.7116i 0.814255 0.814255i −0.171013 0.985269i \(-0.554704\pi\)
0.985269 + 0.171013i \(0.0547041\pi\)
\(648\) 4.97115 + 29.4359i 0.195285 + 1.15635i
\(649\) 3.65832i 0.143601i
\(650\) −0.352781 + 7.06226i −0.0138372 + 0.277005i
\(651\) 31.3459i 1.22854i
\(652\) 11.4000 + 9.10359i 0.446457 + 0.356524i
\(653\) 18.3070 18.3070i 0.716410 0.716410i −0.251458 0.967868i \(-0.580910\pi\)
0.967868 + 0.251458i \(0.0809101\pi\)
\(654\) −24.8356 22.2094i −0.971151 0.868455i
\(655\) 24.7944 + 11.8409i 0.968796 + 0.462662i
\(656\) 33.1517 7.52027i 1.29436 0.293617i
\(657\) −26.9251 26.9251i −1.05045 1.05045i
\(658\) −0.953487 + 0.0532285i −0.0371708 + 0.00207506i
\(659\) 21.7960 0.849050 0.424525 0.905416i \(-0.360441\pi\)
0.424525 + 0.905416i \(0.360441\pi\)
\(660\) 2.23943 + 4.61951i 0.0871696 + 0.179814i
\(661\) −8.52927 −0.331750 −0.165875 0.986147i \(-0.553045\pi\)
−0.165875 + 0.986147i \(0.553045\pi\)
\(662\) 4.11596 0.229774i 0.159971 0.00893042i
\(663\) −5.57387 5.57387i −0.216471 0.216471i
\(664\) 13.7541 19.3436i 0.533762 0.750678i
\(665\) −18.0826 51.1416i −0.701213 1.98319i
\(666\) 15.3130 + 13.6937i 0.593367 + 0.530621i
\(667\) 22.7013 22.7013i 0.878997 0.878997i
\(668\) −8.62009 + 10.7945i −0.333521 + 0.417652i
\(669\) 43.6150i 1.68625i
\(670\) −30.5748 + 12.7695i −1.18121 + 0.493329i
\(671\) 3.19650i 0.123399i
\(672\) 15.4979 + 54.1327i 0.597844 + 2.08821i
\(673\) 12.3291 12.3291i 0.475250 0.475250i −0.428358 0.903609i \(-0.640908\pi\)
0.903609 + 0.428358i \(0.140908\pi\)
\(674\) −5.76344 + 6.44498i −0.222000 + 0.248251i
\(675\) −7.64848 0.811304i −0.294390 0.0312271i
\(676\) 0.222607 + 1.98757i 0.00856180 + 0.0764451i
\(677\) 18.8117 + 18.8117i 0.722992 + 0.722992i 0.969213 0.246222i \(-0.0791892\pi\)
−0.246222 + 0.969213i \(0.579189\pi\)
\(678\) −2.44770 43.8458i −0.0940033 1.68389i
\(679\) −49.6881 −1.90685
\(680\) 10.4844 + 18.8691i 0.402059 + 0.723599i
\(681\) −18.6634 −0.715184
\(682\) 0.123382 + 2.21015i 0.00472453 + 0.0846308i
\(683\) −29.2411 29.2411i −1.11888 1.11888i −0.991906 0.126973i \(-0.959474\pi\)
−0.126973 0.991906i \(-0.540526\pi\)
\(684\) −2.92436 26.1105i −0.111816 0.998361i
\(685\) 7.26843 2.56996i 0.277712 0.0981933i
\(686\) 18.5889 20.7871i 0.709729 0.793655i
\(687\) −21.2273 + 21.2273i −0.809870 + 0.809870i
\(688\) 24.7281 + 15.5836i 0.942748 + 0.594119i
\(689\) 0.287340i 0.0109468i
\(690\) −17.3340 + 42.1970i −0.659895 + 1.60641i
\(691\) 21.6953i 0.825329i −0.910883 0.412664i \(-0.864598\pi\)
0.910883 0.412664i \(-0.135402\pi\)
\(692\) −20.0781 + 25.1429i −0.763256 + 0.955788i
\(693\) 3.53536 3.53536i 0.134297 0.134297i
\(694\) 24.4143 + 21.8325i 0.926753 + 0.828752i
\(695\) −2.09245 + 4.38150i −0.0793711 + 0.166200i
\(696\) 27.3631 + 19.4562i 1.03719 + 0.737486i
\(697\) −20.5104 20.5104i −0.776888 0.776888i
\(698\) −34.7601 + 1.94049i −1.31569 + 0.0734485i
\(699\) 2.88022 0.108940
\(700\) −43.0982 + 0.252377i −1.62896 + 0.00953896i
\(701\) −1.18461 −0.0447420 −0.0223710 0.999750i \(-0.507122\pi\)
−0.0223710 + 0.999750i \(0.507122\pi\)
\(702\) −2.17207 + 0.121256i −0.0819796 + 0.00457652i
\(703\) 24.7709 + 24.7709i 0.934251 + 0.934251i
\(704\) −1.30580 3.75580i −0.0492143 0.141552i
\(705\) 0.348689 0.730141i 0.0131324 0.0274987i
\(706\) −8.61846 7.70709i −0.324360 0.290060i
\(707\) 12.7392 12.7392i 0.479106 0.479106i
\(708\) 26.5660 + 21.2146i 0.998411 + 0.797294i
\(709\) 22.7803i 0.855532i 0.903890 + 0.427766i \(0.140699\pi\)
−0.903890 + 0.427766i \(0.859301\pi\)
\(710\) 0.743615 1.81022i 0.0279074 0.0679363i
\(711\) 6.29030i 0.235905i
\(712\) 35.5413 6.00222i 1.33197 0.224943i
\(713\) −13.9089 + 13.9089i −0.520892 + 0.520892i
\(714\) 32.0270 35.8142i 1.19858 1.34031i
\(715\) −1.04785 + 0.370496i −0.0391872 + 0.0138558i
\(716\) 28.2631 3.16545i 1.05624 0.118298i
\(717\) 10.0220 + 10.0220i 0.374278 + 0.374278i
\(718\) −0.506684 9.07627i −0.0189093 0.338723i
\(719\) −11.1110 −0.414370 −0.207185 0.978302i \(-0.566430\pi\)
−0.207185 + 0.978302i \(0.566430\pi\)
\(720\) −20.3610 4.60593i −0.758808 0.171653i
\(721\) −21.1479 −0.787589
\(722\) −0.999624 17.9063i −0.0372021 0.666405i
\(723\) 38.8331 + 38.8331i 1.44422 + 1.44422i
\(724\) 20.6868 2.31690i 0.768817 0.0861070i
\(725\) −19.9874 + 16.1538i −0.742314 + 0.599936i
\(726\) 23.4115 26.1799i 0.868881 0.971628i
\(727\) −11.9420 + 11.9420i −0.442904 + 0.442904i −0.892987 0.450083i \(-0.851394\pi\)
0.450083 + 0.892987i \(0.351394\pi\)
\(728\) −12.0200 + 2.02995i −0.445492 + 0.0752348i
\(729\) 13.9756i 0.517614i
\(730\) −47.6068 + 19.8829i −1.76201 + 0.735899i
\(731\) 24.9402i 0.922445i
\(732\) 23.2124 + 18.5365i 0.857954 + 0.685130i
\(733\) 26.1775 26.1775i 0.966887 0.966887i −0.0325820 0.999469i \(-0.510373\pi\)
0.999469 + 0.0325820i \(0.0103730\pi\)
\(734\) 17.4896 + 15.6401i 0.645552 + 0.577287i
\(735\) 19.9271 + 56.3584i 0.735023 + 2.07881i
\(736\) 17.1431 30.8967i 0.631904 1.13887i
\(737\) −3.68260 3.68260i −0.135650 0.135650i
\(738\) 28.0073 1.56351i 1.03096 0.0575537i
\(739\) −4.47304 −0.164544 −0.0822718 0.996610i \(-0.526218\pi\)
−0.0822718 + 0.996610i \(0.526218\pi\)
\(740\) 25.0458 12.1416i 0.920701 0.446333i
\(741\) 12.9995 0.477548
\(742\) 1.74865 0.0976186i 0.0641950 0.00358369i
\(743\) 33.2249 + 33.2249i 1.21890 + 1.21890i 0.968017 + 0.250885i \(0.0807217\pi\)
0.250885 + 0.968017i \(0.419278\pi\)
\(744\) −16.7651 11.9207i −0.614640 0.437033i
\(745\) −0.811534 0.387560i −0.0297323 0.0141991i
\(746\) −23.4401 20.9613i −0.858201 0.767449i
\(747\) 13.8490 13.8490i 0.506710 0.506710i
\(748\) −2.11720 + 2.65126i −0.0774124 + 0.0969397i
\(749\) 57.5018i 2.10107i
\(750\) 17.3612 32.1259i 0.633940 1.17307i
\(751\) 20.1494i 0.735264i 0.929971 + 0.367632i \(0.119831\pi\)
−0.929971 + 0.367632i \(0.880169\pi\)
\(752\) −0.334137 + 0.530209i −0.0121847 + 0.0193347i
\(753\) −34.9349 + 34.9349i −1.27310 + 1.27310i
\(754\) −4.84534 + 5.41831i −0.176457 + 0.197323i
\(755\) 23.3119 + 11.1329i 0.848407 + 0.405169i
\(756\) −1.47584 13.1773i −0.0536759 0.479252i
\(757\) 0.215715 + 0.215715i 0.00784030 + 0.00784030i 0.711016 0.703176i \(-0.248235\pi\)
−0.703176 + 0.711016i \(0.748235\pi\)
\(758\) −2.28443 40.9211i −0.0829742 1.48632i
\(759\) −7.17024 −0.260263
\(760\) −34.2295 9.77752i −1.24163 0.354668i
\(761\) −44.7165 −1.62097 −0.810485 0.585759i \(-0.800796\pi\)
−0.810485 + 0.585759i \(0.800796\pi\)
\(762\) 0.0218009 + 0.390522i 0.000789765 + 0.0141471i
\(763\) 31.0876 + 31.0876i 1.12545 + 1.12545i
\(764\) 1.57437 + 14.0570i 0.0569588 + 0.508564i
\(765\) 5.93786 + 16.7936i 0.214684 + 0.607173i
\(766\) −30.3801 + 33.9725i −1.09768 + 1.22748i
\(767\) −5.20444 + 5.20444i −0.187922 + 0.187922i
\(768\) 34.8463 + 12.2974i 1.25741 + 0.443745i
\(769\) 10.5286i 0.379672i −0.981816 0.189836i \(-0.939204\pi\)
0.981816 0.189836i \(-0.0607956\pi\)
\(770\) −2.61069 6.25094i −0.0940828 0.225268i
\(771\) 38.4753i 1.38565i
\(772\) −27.0564 + 33.8814i −0.973780 + 1.21942i
\(773\) −6.70573 + 6.70573i −0.241188 + 0.241188i −0.817342 0.576153i \(-0.804553\pi\)
0.576153 + 0.817342i \(0.304553\pi\)
\(774\) 17.9787 + 16.0775i 0.646231 + 0.577894i
\(775\) 12.2461 9.89730i 0.439894 0.355521i
\(776\) −18.8961 + 26.5754i −0.678331 + 0.954000i
\(777\) −43.8057 43.8057i −1.57152 1.57152i
\(778\) −2.26874 + 0.126653i −0.0813382 + 0.00454072i
\(779\) 47.8348 1.71386
\(780\) 3.38599 9.75776i 0.121238 0.349384i
\(781\) 0.307597 0.0110067
\(782\) −30.1027 + 1.68048i −1.07647 + 0.0600940i
\(783\) −5.59071 5.59071i −0.199796 0.199796i
\(784\) −10.2428 45.1536i −0.365816 1.61263i
\(785\) −32.6057 + 11.5287i −1.16375 + 0.411477i
\(786\) −29.9171 26.7535i −1.06711 0.954264i
\(787\) 22.3816 22.3816i 0.797818 0.797818i −0.184933 0.982751i \(-0.559207\pi\)
0.982751 + 0.184933i \(0.0592069\pi\)
\(788\) 8.52381 + 6.80679i 0.303648 + 0.242482i
\(789\) 36.5163i 1.30002i
\(790\) −7.88353 3.23845i −0.280483 0.115219i
\(791\) 57.9471i 2.06036i
\(792\) −0.546386 3.23535i −0.0194150 0.114963i
\(793\) −4.54745 + 4.54745i −0.161485 + 0.161485i
\(794\) −17.1619 + 19.1914i −0.609054 + 0.681076i
\(795\) −0.639479 + 1.33904i −0.0226800 + 0.0474910i
\(796\) −6.31689 + 0.707487i −0.223896 + 0.0250762i
\(797\) −0.328478 0.328478i −0.0116353 0.0116353i 0.701265 0.712900i \(-0.252619\pi\)
−0.712900 + 0.701265i \(0.752619\pi\)
\(798\) 4.41634 + 79.1102i 0.156337 + 2.80047i
\(799\) 0.534757 0.0189183
\(800\) −16.2550 + 23.1468i −0.574703 + 0.818362i
\(801\) 29.7430 1.05092
\(802\) 0.781931 + 14.0068i 0.0276110 + 0.494597i
\(803\) −5.73402 5.73402i −0.202349 0.202349i
\(804\) 48.0977 5.38691i 1.69628 0.189982i
\(805\) 25.9412 54.3198i 0.914308 1.91452i
\(806\) 2.96870 3.31975i 0.104568 0.116933i
\(807\) 3.05420 3.05420i 0.107513 0.107513i
\(808\) −1.96882 11.6581i −0.0692630 0.410131i
\(809\) 45.9759i 1.61643i 0.588890 + 0.808213i \(0.299565\pi\)
−0.588890 + 0.808213i \(0.700435\pi\)
\(810\) 30.8730 + 12.6822i 1.08477 + 0.445609i
\(811\) 32.3964i 1.13759i 0.822479 + 0.568796i \(0.192590\pi\)
−0.822479 + 0.568796i \(0.807410\pi\)
\(812\) −34.6200 27.6462i −1.21492 0.970192i
\(813\) 38.6563 38.6563i 1.35574 1.35574i
\(814\) 3.26109 + 2.91624i 0.114301 + 0.102214i
\(815\) 15.3779 5.43730i 0.538664 0.190460i
\(816\) −6.97531 30.7494i −0.244185 1.07644i
\(817\) 29.0830 + 29.0830i 1.01748 + 1.01748i
\(818\) 32.1314 1.79374i 1.12345 0.0627166i
\(819\) −10.0591 −0.351492
\(820\) 12.4596 35.9061i 0.435108 1.25390i
\(821\) 21.6545 0.755748 0.377874 0.925857i \(-0.376655\pi\)
0.377874 + 0.925857i \(0.376655\pi\)
\(822\) −11.2434 + 0.627666i −0.392160 + 0.0218924i
\(823\) −24.0230 24.0230i −0.837390 0.837390i 0.151124 0.988515i \(-0.451711\pi\)
−0.988515 + 0.151124i \(0.951711\pi\)
\(824\) −8.04243 + 11.3108i −0.280171 + 0.394031i
\(825\) 5.70764 + 0.605431i 0.198714 + 0.0210784i
\(826\) −33.4405 29.9042i −1.16354 1.04050i
\(827\) −14.4001 + 14.4001i −0.500740 + 0.500740i −0.911668 0.410928i \(-0.865205\pi\)
0.410928 + 0.911668i \(0.365205\pi\)
\(828\) 18.1941 22.7835i 0.632287 0.791782i
\(829\) 8.72836i 0.303149i −0.988446 0.151574i \(-0.951566\pi\)
0.988446 0.151574i \(-0.0484343\pi\)
\(830\) −10.2268 24.4867i −0.354979 0.849947i
\(831\) 36.6902i 1.27277i
\(832\) −3.48545 + 7.20081i −0.120836 + 0.249643i
\(833\) −27.9358 + 27.9358i −0.967919 + 0.967919i
\(834\) 4.72770 5.28676i 0.163707 0.183066i
\(835\) 5.14851 + 14.5611i 0.178172 + 0.503909i
\(836\) −0.622777 5.56054i −0.0215392 0.192315i
\(837\) 3.42539 + 3.42539i 0.118399 + 0.118399i
\(838\) −0.546972 9.79795i −0.0188948 0.338465i
\(839\) 11.5417 0.398462 0.199231 0.979953i \(-0.436156\pi\)
0.199231 + 0.979953i \(0.436156\pi\)
\(840\) 60.5326 + 17.2909i 2.08857 + 0.596593i
\(841\) 2.58233 0.0890459
\(842\) 0.272098 + 4.87412i 0.00937712 + 0.167973i
\(843\) 8.95165 + 8.95165i 0.308311 + 0.308311i
\(844\) −2.36999 21.1607i −0.0815784 0.728383i
\(845\) 2.01778 + 0.963620i 0.0694138 + 0.0331495i
\(846\) −0.344727 + 0.385492i −0.0118520 + 0.0132535i
\(847\) −32.7702 + 32.7702i −1.12600 + 1.12600i
\(848\) 0.612792 0.972378i 0.0210434 0.0333916i
\(849\) 25.7961i 0.885319i
\(850\) 24.1041 + 1.20407i 0.826765 + 0.0412993i
\(851\) 38.8751i 1.33262i
\(852\) −1.78376 + 2.23371i −0.0611106 + 0.0765258i
\(853\) 37.1465 37.1465i 1.27187 1.27187i 0.326767 0.945105i \(-0.394041\pi\)
0.945105 0.326767i \(-0.105959\pi\)
\(854\) −29.2190 26.1292i −0.999855 0.894123i
\(855\) −26.5074 12.6590i −0.906533 0.432928i
\(856\) 30.7545 + 21.8676i 1.05117 + 0.747420i
\(857\) −2.27770 2.27770i −0.0778048 0.0778048i 0.667133 0.744938i \(-0.267521\pi\)
−0.744938 + 0.667133i \(0.767521\pi\)
\(858\) 1.62090 0.0904868i 0.0553365 0.00308917i
\(859\) −18.7926 −0.641197 −0.320598 0.947215i \(-0.603884\pi\)
−0.320598 + 0.947215i \(0.603884\pi\)
\(860\) 29.4057 14.2552i 1.00273 0.486098i
\(861\) −84.5928 −2.88291
\(862\) −8.03682 + 0.448656i −0.273735 + 0.0152813i
\(863\) 14.2909 + 14.2909i 0.486469 + 0.486469i 0.907190 0.420721i \(-0.138223\pi\)
−0.420721 + 0.907190i \(0.638223\pi\)
\(864\) −7.60902 4.22189i −0.258864 0.143632i
\(865\) 11.9921 + 33.9162i 0.407742 + 1.15319i
\(866\) 33.5206 + 29.9759i 1.13908 + 1.01862i
\(867\) 8.73835 8.73835i 0.296770 0.296770i
\(868\) 21.2114 + 16.9386i 0.719961 + 0.574934i
\(869\) 1.33959i 0.0454426i
\(870\) 34.6384 14.4667i 1.17435 0.490466i
\(871\) 10.4780i 0.355033i
\(872\) 28.4494 4.80455i 0.963419 0.162703i
\(873\) −19.0266 + 19.0266i −0.643953 + 0.643953i
\(874\) 33.1434 37.0626i 1.12109 1.25366i
\(875\) −25.2362 + 41.0492i −0.853141 + 1.38771i
\(876\) 74.8910 8.38774i 2.53033 0.283396i
\(877\) −9.54071 9.54071i −0.322167 0.322167i 0.527431 0.849598i \(-0.323155\pi\)
−0.849598 + 0.527431i \(0.823155\pi\)
\(878\) −1.48242 26.5547i −0.0500293 0.896178i
\(879\) −39.9744 −1.34830
\(880\) −4.33611 0.980887i −0.146170 0.0330657i
\(881\) −4.19846 −0.141450 −0.0707249 0.997496i \(-0.522531\pi\)
−0.0707249 + 0.997496i \(0.522531\pi\)
\(882\) −2.12955 38.1468i −0.0717057 1.28447i
\(883\) −33.5170 33.5170i −1.12794 1.12794i −0.990512 0.137426i \(-0.956117\pi\)
−0.137426 0.990512i \(-0.543883\pi\)
\(884\) 6.78377 0.759777i 0.228163 0.0255541i
\(885\) 35.8359 12.6708i 1.20461 0.425926i
\(886\) −37.1328 + 41.5238i −1.24750 + 1.39502i
\(887\) −20.2939 + 20.2939i −0.681403 + 0.681403i −0.960316 0.278913i \(-0.910026\pi\)
0.278913 + 0.960316i \(0.410026\pi\)
\(888\) −40.0882 + 6.77011i −1.34527 + 0.227190i
\(889\) 0.516118i 0.0173100i
\(890\) 15.3127 37.2764i 0.513282 1.24951i
\(891\) 5.24603i 0.175749i
\(892\) 29.5138 + 23.5686i 0.988194 + 0.789134i
\(893\) −0.623585 + 0.623585i −0.0208675 + 0.0208675i
\(894\) 0.979204 + 0.875657i 0.0327495 + 0.0292863i
\(895\) 13.7026 28.6927i 0.458027 0.959091i
\(896\) −45.0056 18.7648i −1.50353 0.626889i
\(897\) 10.2006 + 10.2006i 0.340589 + 0.340589i
\(898\) 25.5508 1.42638i 0.852642 0.0475989i
\(899\) 16.1859 0.539830
\(900\) −16.4066 + 16.5998i −0.546885 + 0.553328i
\(901\) −0.980719 −0.0326725
\(902\) 5.96449 0.332968i 0.198596 0.0110866i
\(903\) −51.4313 51.4313i −1.71153 1.71153i
\(904\) 30.9926 + 22.0370i 1.03080 + 0.732939i
\(905\) 10.0294 21.0012i 0.333389 0.698102i
\(906\) −28.1284 25.1539i −0.934502 0.835681i
\(907\) 0.106512 0.106512i 0.00353667 0.00353667i −0.705336 0.708873i \(-0.749204\pi\)
0.708873 + 0.705336i \(0.249204\pi\)
\(908\) 10.0853 12.6293i 0.334692 0.419118i
\(909\) 9.75618i 0.323592i
\(910\) −5.17874 + 12.6069i −0.171673 + 0.417913i
\(911\) 22.3251i 0.739662i −0.929099 0.369831i \(-0.879416\pi\)
0.929099 0.369831i \(-0.120584\pi\)
\(912\) 43.9911 + 27.7231i 1.45669 + 0.918005i
\(913\) 2.94932 2.94932i 0.0976081 0.0976081i
\(914\) 26.1378 29.2286i 0.864561 0.966797i
\(915\) 31.3121 11.0713i 1.03515 0.366006i
\(916\) −2.89350 25.8350i −0.0956038 0.853611i
\(917\) 37.4482 + 37.4482i 1.23665 + 1.23665i
\(918\) 0.413858 + 7.41348i 0.0136594 + 0.244681i
\(919\) −47.8075 −1.57703 −0.788513 0.615019i \(-0.789149\pi\)
−0.788513 + 0.615019i \(0.789149\pi\)
\(920\) −19.1873 34.5320i −0.632587 1.13849i
\(921\) −15.0336 −0.495372
\(922\) 2.75295 + 49.3139i 0.0906637 + 1.62407i
\(923\) −0.437599 0.437599i −0.0144037 0.0144037i
\(924\) 1.10134 + 9.83345i 0.0362314 + 0.323497i
\(925\) 3.28249 30.9453i 0.107927 1.01747i
\(926\) 28.8863 32.3021i 0.949262 1.06151i
\(927\) −8.09796 + 8.09796i −0.265972 + 0.265972i
\(928\) −27.9522 + 8.00256i −0.917575 + 0.262697i
\(929\) 3.18424i 0.104471i −0.998635 0.0522357i \(-0.983365\pi\)
0.998635 0.0522357i \(-0.0166347\pi\)
\(930\) −21.2227 + 8.86361i −0.695919 + 0.290649i
\(931\) 65.1525i 2.13529i
\(932\) −1.55641 + 1.94901i −0.0509818 + 0.0638419i
\(933\) −53.0838 + 53.0838i −1.73789 + 1.73789i
\(934\) −2.12738 1.90242i −0.0696100 0.0622490i
\(935\) 1.26454 + 3.57639i 0.0413548 + 0.116960i
\(936\) −3.82541 + 5.38002i −0.125037 + 0.175851i
\(937\) −24.5677 24.5677i −0.802591 0.802591i 0.180909 0.983500i \(-0.442096\pi\)
−0.983500 + 0.180909i \(0.942096\pi\)
\(938\) −63.7652 + 3.55970i −2.08201 + 0.116228i
\(939\) −62.7231 −2.04689
\(940\) 0.305654 + 0.630506i 0.00996933 + 0.0205648i
\(941\) −0.415679 −0.0135508 −0.00677538 0.999977i \(-0.502157\pi\)
−0.00677538 + 0.999977i \(0.502157\pi\)
\(942\) 50.4374 2.81567i 1.64334 0.0917395i
\(943\) 37.5357 + 37.5357i 1.22233 + 1.22233i
\(944\) −28.7113 + 6.51299i −0.934474 + 0.211980i
\(945\) −13.3775 6.38863i −0.435171 0.207822i
\(946\) 3.82878 + 3.42389i 0.124484 + 0.111320i
\(947\) 4.99828 4.99828i 0.162422 0.162422i −0.621217 0.783639i \(-0.713361\pi\)
0.783639 + 0.621217i \(0.213361\pi\)
\(948\) 9.72787 + 7.76831i 0.315946 + 0.252303i
\(949\) 16.3148i 0.529602i
\(950\) −29.5122 + 26.7040i −0.957501 + 0.866392i
\(951\) 27.0594i 0.877460i
\(952\) 6.92839 + 41.0254i 0.224550 + 1.32964i
\(953\) 30.7986 30.7986i 0.997664 0.997664i −0.00233327 0.999997i \(-0.500743\pi\)
0.999997 + 0.00233327i \(0.000742703\pi\)
\(954\) 0.632214 0.706974i 0.0204687 0.0228891i
\(955\) 14.2706 + 6.81514i 0.461787 + 0.220533i
\(956\) −12.1974 + 1.36610i −0.394493 + 0.0441829i
\(957\) 4.17204 + 4.17204i 0.134863 + 0.134863i
\(958\) −2.15931 38.6798i −0.0697640 1.24969i
\(959\) 14.8594 0.479836
\(960\) 32.2681 25.7998i 1.04145 0.832685i
\(961\) 21.0830 0.680098
\(962\) −0.490595 8.78807i −0.0158174 0.283339i
\(963\) 22.0186 + 22.0186i 0.709540 + 0.709540i
\(964\) −47.2624 + 5.29336i −1.52222 + 0.170488i
\(965\) 16.1599 + 45.7039i 0.520207 + 1.47126i
\(966\) −58.6119 + 65.5428i −1.88581 + 2.10881i
\(967\) 33.8828 33.8828i 1.08960 1.08960i 0.0940276 0.995570i \(-0.470026\pi\)
0.995570 0.0940276i \(-0.0299742\pi\)
\(968\) 5.06460 + 29.9893i 0.162782 + 0.963892i
\(969\) 44.3684i 1.42532i
\(970\) 14.0502 + 33.6413i 0.451125 + 1.08016i
\(971\) 19.0484i 0.611293i −0.952145 0.305647i \(-0.901127\pi\)
0.952145 0.305647i \(-0.0988726\pi\)
\(972\) −30.8835 24.6624i −0.990588 0.791047i
\(973\) −6.61761 + 6.61761i −0.212151 + 0.212151i
\(974\) 12.6906 + 11.3487i 0.406635 + 0.363634i
\(975\) −7.25857 8.98119i −0.232460 0.287628i
\(976\) −25.0869 + 5.69081i −0.803012 + 0.182158i
\(977\) 12.1118 + 12.1118i 0.387490 + 0.387490i 0.873791 0.486301i \(-0.161654\pi\)
−0.486301 + 0.873791i \(0.661654\pi\)
\(978\) −23.7878 + 1.32796i −0.760651 + 0.0424634i
\(979\) 6.33412 0.202439
\(980\) −48.9052 16.9703i −1.56222 0.542097i
\(981\) 23.8081 0.760135
\(982\) 21.1373 1.17999i 0.674520 0.0376551i
\(983\) −24.1809 24.1809i −0.771253 0.771253i 0.207073 0.978325i \(-0.433606\pi\)
−0.978325 + 0.207073i \(0.933606\pi\)
\(984\) −32.1702 + 45.2439i −1.02555 + 1.44232i
\(985\) 11.4981 4.06549i 0.366360 0.129537i
\(986\) 18.4932 + 16.5376i 0.588942 + 0.526664i
\(987\) 1.10277 1.10277i 0.0351015 0.0351015i
\(988\) −7.02463 + 8.79660i −0.223483 + 0.279857i
\(989\) 45.6425i 1.45135i
\(990\) −3.39330 1.39392i −0.107846 0.0443018i
\(991\) 11.4017i 0.362187i 0.983466 + 0.181093i \(0.0579636\pi\)
−0.983466 + 0.181093i \(0.942036\pi\)
\(992\) 17.1261 4.90311i 0.543754 0.155674i
\(993\) −4.76037 + 4.76037i −0.151066 + 0.151066i
\(994\) 2.51440 2.81173i 0.0797519 0.0891827i
\(995\) −3.06257 + 6.41290i −0.0970900 + 0.203302i
\(996\) 4.31427 + 38.5205i 0.136703 + 1.22057i
\(997\) −37.8036 37.8036i −1.19725 1.19725i −0.974986 0.222265i \(-0.928655\pi\)
−0.222265 0.974986i \(-0.571345\pi\)
\(998\) 1.22197 + 21.8892i 0.0386806 + 0.692890i
\(999\) 9.57391 0.302905
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 260.2.o.a.27.17 yes 72
4.3 odd 2 inner 260.2.o.a.27.2 72
5.3 odd 4 inner 260.2.o.a.183.2 yes 72
20.3 even 4 inner 260.2.o.a.183.17 yes 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
260.2.o.a.27.2 72 4.3 odd 2 inner
260.2.o.a.27.17 yes 72 1.1 even 1 trivial
260.2.o.a.183.2 yes 72 5.3 odd 4 inner
260.2.o.a.183.17 yes 72 20.3 even 4 inner