Properties

Label 240.2.s.c.61.2
Level $240$
Weight $2$
Character 240.61
Analytic conductor $1.916$
Analytic rank $0$
Dimension $20$
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] = [240,2,Mod(61,240)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(240, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("240.61");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 240.s (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: \(1.91640964851\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 2 x^{18} - 4 x^{17} + 7 x^{16} + 16 x^{15} + 6 x^{14} - 36 x^{13} - 42 x^{12} + 40 x^{11} + 136 x^{10} + 80 x^{9} - 168 x^{8} - 288 x^{7} + 96 x^{6} + 512 x^{5} + 448 x^{4} + \cdots + 1024 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 61.2
Root \(-1.13207 + 0.847599i\) of defining polynomial
Character \(\chi\) \(=\) 240.61
Dual form 240.2.s.c.181.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.13207 + 0.847599i) q^{2} +(0.707107 + 0.707107i) q^{3} +(0.563151 - 1.91908i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.39984 - 0.201149i) q^{6} -4.27253i q^{7} +(0.989085 + 2.64985i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(-1.13207 + 0.847599i) q^{2} +(0.707107 + 0.707107i) q^{3} +(0.563151 - 1.91908i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.39984 - 0.201149i) q^{6} -4.27253i q^{7} +(0.989085 + 2.64985i) q^{8} +1.00000i q^{9} +(-0.201149 + 1.39984i) q^{10} +(2.94281 - 2.94281i) q^{11} +(1.75520 - 0.958786i) q^{12} +(-4.05962 - 4.05962i) q^{13} +(3.62140 + 4.83679i) q^{14} +1.00000 q^{15} +(-3.36572 - 2.16146i) q^{16} +0.160060 q^{17} +(-0.847599 - 1.13207i) q^{18} +(4.32576 + 4.32576i) q^{19} +(-0.958786 - 1.75520i) q^{20} +(3.02114 - 3.02114i) q^{21} +(-0.837134 + 5.82579i) q^{22} +8.40564i q^{23} +(-1.17434 + 2.57312i) q^{24} -1.00000i q^{25} +(8.03670 + 1.15483i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-8.19933 - 2.40608i) q^{28} +(-1.78072 - 1.78072i) q^{29} +(-1.13207 + 0.847599i) q^{30} +7.17282 q^{31} +(5.64228 - 0.405867i) q^{32} +4.16177 q^{33} +(-0.181198 + 0.135667i) q^{34} +(-3.02114 - 3.02114i) q^{35} +(1.91908 + 0.563151i) q^{36} +(-0.669226 + 0.669226i) q^{37} +(-8.56355 - 1.23054i) q^{38} -5.74117i q^{39} +(2.57312 + 1.17434i) q^{40} +3.96632i q^{41} +(-0.859415 + 5.98084i) q^{42} +(-0.255733 + 0.255733i) q^{43} +(-3.99024 - 7.30473i) q^{44} +(0.707107 + 0.707107i) q^{45} +(-7.12462 - 9.51575i) q^{46} +0.0752658 q^{47} +(-0.851542 - 3.90831i) q^{48} -11.2545 q^{49} +(0.847599 + 1.13207i) q^{50} +(0.113179 + 0.113179i) q^{51} +(-10.0769 + 5.50456i) q^{52} +(-2.88214 + 2.88214i) q^{53} +(0.201149 - 1.39984i) q^{54} -4.16177i q^{55} +(11.3216 - 4.22590i) q^{56} +6.11754i q^{57} +(3.52522 + 0.506556i) q^{58} +(-5.63594 + 5.63594i) q^{59} +(0.563151 - 1.91908i) q^{60} +(-4.48857 - 4.48857i) q^{61} +(-8.12011 + 6.07968i) q^{62} +4.27253 q^{63} +(-6.04342 + 5.24186i) q^{64} -5.74117 q^{65} +(-4.71140 + 3.52751i) q^{66} +(-0.131176 - 0.131176i) q^{67} +(0.0901377 - 0.307167i) q^{68} +(-5.94369 + 5.94369i) q^{69} +(5.98084 + 0.859415i) q^{70} -12.1137i q^{71} +(-2.64985 + 0.989085i) q^{72} -0.382876i q^{73} +(0.190373 - 1.32484i) q^{74} +(0.707107 - 0.707107i) q^{75} +(10.7375 - 5.86541i) q^{76} +(-12.5733 - 12.5733i) q^{77} +(4.86622 + 6.49939i) q^{78} +15.3239 q^{79} +(-3.90831 + 0.851542i) q^{80} -1.00000 q^{81} +(-3.36185 - 4.49014i) q^{82} +(-5.54562 - 5.54562i) q^{83} +(-4.09644 - 7.49916i) q^{84} +(0.113179 - 0.113179i) q^{85} +(0.0727477 - 0.506266i) q^{86} -2.51831i q^{87} +(10.7087 + 4.88732i) q^{88} +13.8991i q^{89} +(-1.39984 - 0.201149i) q^{90} +(-17.3449 + 17.3449i) q^{91} +(16.1311 + 4.73364i) q^{92} +(5.07195 + 5.07195i) q^{93} +(-0.0852060 + 0.0637953i) q^{94} +6.11754 q^{95} +(4.27668 + 3.70270i) q^{96} +10.8999 q^{97} +(12.7409 - 9.53935i) q^{98} +(2.94281 + 2.94281i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 4 q^{4} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 4 q^{4} + 12 q^{8} + 8 q^{11} - 4 q^{14} + 20 q^{15} - 20 q^{16} - 24 q^{17} - 4 q^{18} - 4 q^{19} - 8 q^{20} + 8 q^{22} + 28 q^{26} - 8 q^{28} + 16 q^{29} - 40 q^{32} + 16 q^{33} - 44 q^{34} + 16 q^{37} - 8 q^{38} + 12 q^{40} + 12 q^{42} - 8 q^{43} + 24 q^{44} - 12 q^{46} - 16 q^{48} - 52 q^{49} + 4 q^{50} + 4 q^{51} - 56 q^{52} - 16 q^{53} + 64 q^{56} + 72 q^{58} - 16 q^{59} + 4 q^{60} - 4 q^{61} - 44 q^{62} - 8 q^{63} - 56 q^{64} - 32 q^{66} - 8 q^{67} - 32 q^{68} - 4 q^{69} + 20 q^{70} + 4 q^{72} + 60 q^{74} + 28 q^{76} - 40 q^{77} - 28 q^{78} + 56 q^{79} - 16 q^{80} - 20 q^{81} - 24 q^{82} - 48 q^{83} + 24 q^{84} + 4 q^{85} + 64 q^{86} + 40 q^{88} - 8 q^{91} + 88 q^{92} + 16 q^{93} - 20 q^{94} + 56 q^{97} - 48 q^{98} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/240\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(97\) \(161\) \(181\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.13207 + 0.847599i −0.800492 + 0.599343i
\(3\) 0.707107 + 0.707107i 0.408248 + 0.408248i
\(4\) 0.563151 1.91908i 0.281575 0.959539i
\(5\) 0.707107 0.707107i 0.316228 0.316228i
\(6\) −1.39984 0.201149i −0.571480 0.0821187i
\(7\) 4.27253i 1.61487i −0.589959 0.807433i \(-0.700856\pi\)
0.589959 0.807433i \(-0.299144\pi\)
\(8\) 0.989085 + 2.64985i 0.349695 + 0.936864i
\(9\) 1.00000i 0.333333i
\(10\) −0.201149 + 1.39984i −0.0636089 + 0.442667i
\(11\) 2.94281 2.94281i 0.887291 0.887291i −0.106971 0.994262i \(-0.534115\pi\)
0.994262 + 0.106971i \(0.0341151\pi\)
\(12\) 1.75520 0.958786i 0.506683 0.276778i
\(13\) −4.05962 4.05962i −1.12594 1.12594i −0.990831 0.135106i \(-0.956863\pi\)
−0.135106 0.990831i \(-0.543137\pi\)
\(14\) 3.62140 + 4.83679i 0.967859 + 1.29269i
\(15\) 1.00000 0.258199
\(16\) −3.36572 2.16146i −0.841431 0.540365i
\(17\) 0.160060 0.0388202 0.0194101 0.999812i \(-0.493821\pi\)
0.0194101 + 0.999812i \(0.493821\pi\)
\(18\) −0.847599 1.13207i −0.199781 0.266831i
\(19\) 4.32576 + 4.32576i 0.992396 + 0.992396i 0.999971 0.00757497i \(-0.00241121\pi\)
−0.00757497 + 0.999971i \(0.502411\pi\)
\(20\) −0.958786 1.75520i −0.214391 0.392475i
\(21\) 3.02114 3.02114i 0.659266 0.659266i
\(22\) −0.837134 + 5.82579i −0.178478 + 1.24206i
\(23\) 8.40564i 1.75270i 0.481677 + 0.876349i \(0.340028\pi\)
−0.481677 + 0.876349i \(0.659972\pi\)
\(24\) −1.17434 + 2.57312i −0.239711 + 0.525235i
\(25\) 1.00000i 0.200000i
\(26\) 8.03670 + 1.15483i 1.57613 + 0.226481i
\(27\) −0.707107 + 0.707107i −0.136083 + 0.136083i
\(28\) −8.19933 2.40608i −1.54953 0.454706i
\(29\) −1.78072 1.78072i −0.330671 0.330671i 0.522171 0.852841i \(-0.325122\pi\)
−0.852841 + 0.522171i \(0.825122\pi\)
\(30\) −1.13207 + 0.847599i −0.206686 + 0.154750i
\(31\) 7.17282 1.28828 0.644138 0.764909i \(-0.277216\pi\)
0.644138 + 0.764909i \(0.277216\pi\)
\(32\) 5.64228 0.405867i 0.997423 0.0717479i
\(33\) 4.16177 0.724470
\(34\) −0.181198 + 0.135667i −0.0310752 + 0.0232666i
\(35\) −3.02114 3.02114i −0.510666 0.510666i
\(36\) 1.91908 + 0.563151i 0.319846 + 0.0938584i
\(37\) −0.669226 + 0.669226i −0.110020 + 0.110020i −0.759974 0.649954i \(-0.774788\pi\)
0.649954 + 0.759974i \(0.274788\pi\)
\(38\) −8.56355 1.23054i −1.38919 0.199619i
\(39\) 5.74117i 0.919324i
\(40\) 2.57312 + 1.17434i 0.406845 + 0.185679i
\(41\) 3.96632i 0.619435i 0.950829 + 0.309717i \(0.100234\pi\)
−0.950829 + 0.309717i \(0.899766\pi\)
\(42\) −0.859415 + 5.98084i −0.132611 + 0.922864i
\(43\) −0.255733 + 0.255733i −0.0389989 + 0.0389989i −0.726337 0.687338i \(-0.758779\pi\)
0.687338 + 0.726337i \(0.258779\pi\)
\(44\) −3.99024 7.30473i −0.601551 1.10123i
\(45\) 0.707107 + 0.707107i 0.105409 + 0.105409i
\(46\) −7.12462 9.51575i −1.05047 1.40302i
\(47\) 0.0752658 0.0109787 0.00548933 0.999985i \(-0.498253\pi\)
0.00548933 + 0.999985i \(0.498253\pi\)
\(48\) −0.851542 3.90831i −0.122910 0.564116i
\(49\) −11.2545 −1.60779
\(50\) 0.847599 + 1.13207i 0.119869 + 0.160098i
\(51\) 0.113179 + 0.113179i 0.0158483 + 0.0158483i
\(52\) −10.0769 + 5.50456i −1.39742 + 0.763345i
\(53\) −2.88214 + 2.88214i −0.395892 + 0.395892i −0.876781 0.480889i \(-0.840314\pi\)
0.480889 + 0.876781i \(0.340314\pi\)
\(54\) 0.201149 1.39984i 0.0273729 0.190493i
\(55\) 4.16177i 0.561172i
\(56\) 11.3216 4.22590i 1.51291 0.564710i
\(57\) 6.11754i 0.810288i
\(58\) 3.52522 + 0.506556i 0.462884 + 0.0665140i
\(59\) −5.63594 + 5.63594i −0.733737 + 0.733737i −0.971358 0.237621i \(-0.923632\pi\)
0.237621 + 0.971358i \(0.423632\pi\)
\(60\) 0.563151 1.91908i 0.0727024 0.247752i
\(61\) −4.48857 4.48857i −0.574703 0.574703i 0.358736 0.933439i \(-0.383208\pi\)
−0.933439 + 0.358736i \(0.883208\pi\)
\(62\) −8.12011 + 6.07968i −1.03126 + 0.772120i
\(63\) 4.27253 0.538289
\(64\) −6.04342 + 5.24186i −0.755428 + 0.655232i
\(65\) −5.74117 −0.712105
\(66\) −4.71140 + 3.52751i −0.579933 + 0.434206i
\(67\) −0.131176 0.131176i −0.0160257 0.0160257i 0.699049 0.715074i \(-0.253607\pi\)
−0.715074 + 0.699049i \(0.753607\pi\)
\(68\) 0.0901377 0.307167i 0.0109308 0.0372495i
\(69\) −5.94369 + 5.94369i −0.715536 + 0.715536i
\(70\) 5.98084 + 0.859415i 0.714848 + 0.102720i
\(71\) 12.1137i 1.43764i −0.695199 0.718818i \(-0.744684\pi\)
0.695199 0.718818i \(-0.255316\pi\)
\(72\) −2.64985 + 0.989085i −0.312288 + 0.116565i
\(73\) 0.382876i 0.0448123i −0.999749 0.0224061i \(-0.992867\pi\)
0.999749 0.0224061i \(-0.00713269\pi\)
\(74\) 0.190373 1.32484i 0.0221304 0.154010i
\(75\) 0.707107 0.707107i 0.0816497 0.0816497i
\(76\) 10.7375 5.86541i 1.23168 0.672809i
\(77\) −12.5733 12.5733i −1.43286 1.43286i
\(78\) 4.86622 + 6.49939i 0.550990 + 0.735911i
\(79\) 15.3239 1.72408 0.862039 0.506841i \(-0.169187\pi\)
0.862039 + 0.506841i \(0.169187\pi\)
\(80\) −3.90831 + 0.851542i −0.436962 + 0.0952053i
\(81\) −1.00000 −0.111111
\(82\) −3.36185 4.49014i −0.371254 0.495853i
\(83\) −5.54562 5.54562i −0.608710 0.608710i 0.333899 0.942609i \(-0.391636\pi\)
−0.942609 + 0.333899i \(0.891636\pi\)
\(84\) −4.09644 7.49916i −0.446959 0.818225i
\(85\) 0.113179 0.113179i 0.0122760 0.0122760i
\(86\) 0.0727477 0.506266i 0.00784459 0.0545921i
\(87\) 2.51831i 0.269991i
\(88\) 10.7087 + 4.88732i 1.14155 + 0.520990i
\(89\) 13.8991i 1.47330i 0.676275 + 0.736649i \(0.263593\pi\)
−0.676275 + 0.736649i \(0.736407\pi\)
\(90\) −1.39984 0.201149i −0.147556 0.0212030i
\(91\) −17.3449 + 17.3449i −1.81824 + 1.81824i
\(92\) 16.1311 + 4.73364i 1.68178 + 0.493516i
\(93\) 5.07195 + 5.07195i 0.525937 + 0.525937i
\(94\) −0.0852060 + 0.0637953i −0.00878832 + 0.00657998i
\(95\) 6.11754 0.627647
\(96\) 4.27668 + 3.70270i 0.436487 + 0.377905i
\(97\) 10.8999 1.10672 0.553358 0.832944i \(-0.313346\pi\)
0.553358 + 0.832944i \(0.313346\pi\)
\(98\) 12.7409 9.53935i 1.28703 0.963620i
\(99\) 2.94281 + 2.94281i 0.295764 + 0.295764i
\(100\) −1.91908 0.563151i −0.191908 0.0563151i
\(101\) −2.98972 + 2.98972i −0.297489 + 0.297489i −0.840029 0.542541i \(-0.817462\pi\)
0.542541 + 0.840029i \(0.317462\pi\)
\(102\) −0.224057 0.0321958i −0.0221850 0.00318786i
\(103\) 16.8190i 1.65723i 0.559820 + 0.828615i \(0.310870\pi\)
−0.559820 + 0.828615i \(0.689130\pi\)
\(104\) 6.74208 14.7727i 0.661116 1.44858i
\(105\) 4.27253i 0.416957i
\(106\) 0.819874 5.70567i 0.0796332 0.554184i
\(107\) 1.64447 1.64447i 0.158977 0.158977i −0.623136 0.782113i \(-0.714142\pi\)
0.782113 + 0.623136i \(0.214142\pi\)
\(108\) 0.958786 + 1.75520i 0.0922592 + 0.168894i
\(109\) 4.67023 + 4.67023i 0.447327 + 0.447327i 0.894465 0.447138i \(-0.147557\pi\)
−0.447138 + 0.894465i \(0.647557\pi\)
\(110\) 3.52751 + 4.71140i 0.336335 + 0.449214i
\(111\) −0.946429 −0.0898311
\(112\) −9.23491 + 14.3802i −0.872617 + 1.35880i
\(113\) 5.00533 0.470862 0.235431 0.971891i \(-0.424350\pi\)
0.235431 + 0.971891i \(0.424350\pi\)
\(114\) −5.18522 6.92547i −0.485641 0.648629i
\(115\) 5.94369 + 5.94369i 0.554252 + 0.554252i
\(116\) −4.42014 + 2.41452i −0.410400 + 0.224183i
\(117\) 4.05962 4.05962i 0.375312 0.375312i
\(118\) 1.60324 11.1573i 0.147590 1.02711i
\(119\) 0.683861i 0.0626894i
\(120\) 0.989085 + 2.64985i 0.0902907 + 0.241897i
\(121\) 6.32029i 0.574572i
\(122\) 8.88588 + 1.27685i 0.804489 + 0.115601i
\(123\) −2.80461 + 2.80461i −0.252883 + 0.252883i
\(124\) 4.03938 13.7652i 0.362747 1.23615i
\(125\) −0.707107 0.707107i −0.0632456 0.0632456i
\(126\) −4.83679 + 3.62140i −0.430896 + 0.322620i
\(127\) 1.96679 0.174525 0.0872623 0.996185i \(-0.472188\pi\)
0.0872623 + 0.996185i \(0.472188\pi\)
\(128\) 2.39856 11.0565i 0.212005 0.977269i
\(129\) −0.361661 −0.0318425
\(130\) 6.49939 4.86622i 0.570035 0.426795i
\(131\) −0.852904 0.852904i −0.0745186 0.0745186i 0.668865 0.743384i \(-0.266780\pi\)
−0.743384 + 0.668865i \(0.766780\pi\)
\(132\) 2.34370 7.98675i 0.203993 0.695158i
\(133\) 18.4819 18.4819i 1.60259 1.60259i
\(134\) 0.259686 + 0.0373154i 0.0224334 + 0.00322356i
\(135\) 1.00000i 0.0860663i
\(136\) 0.158313 + 0.424134i 0.0135752 + 0.0363692i
\(137\) 4.12023i 0.352015i 0.984389 + 0.176007i \(0.0563183\pi\)
−0.984389 + 0.176007i \(0.943682\pi\)
\(138\) 1.69079 11.7665i 0.143929 1.00163i
\(139\) 5.73895 5.73895i 0.486771 0.486771i −0.420514 0.907286i \(-0.638150\pi\)
0.907286 + 0.420514i \(0.138150\pi\)
\(140\) −7.49916 + 4.09644i −0.633794 + 0.346213i
\(141\) 0.0532210 + 0.0532210i 0.00448202 + 0.00448202i
\(142\) 10.2676 + 13.7136i 0.861637 + 1.15082i
\(143\) −23.8934 −1.99807
\(144\) 2.16146 3.36572i 0.180122 0.280477i
\(145\) −2.51831 −0.209134
\(146\) 0.324525 + 0.433441i 0.0268579 + 0.0358719i
\(147\) −7.95817 7.95817i −0.656379 0.656379i
\(148\) 0.907422 + 1.66117i 0.0745897 + 0.136548i
\(149\) −9.96311 + 9.96311i −0.816210 + 0.816210i −0.985557 0.169346i \(-0.945834\pi\)
0.169346 + 0.985557i \(0.445834\pi\)
\(150\) −0.201149 + 1.39984i −0.0164237 + 0.114296i
\(151\) 4.01882i 0.327047i 0.986539 + 0.163524i \(0.0522860\pi\)
−0.986539 + 0.163524i \(0.947714\pi\)
\(152\) −7.18407 + 15.7411i −0.582705 + 1.27678i
\(153\) 0.160060i 0.0129401i
\(154\) 24.8909 + 3.57669i 2.00576 + 0.288218i
\(155\) 5.07195 5.07195i 0.407389 0.407389i
\(156\) −11.0178 3.23315i −0.882127 0.258859i
\(157\) −9.14459 9.14459i −0.729818 0.729818i 0.240766 0.970583i \(-0.422601\pi\)
−0.970583 + 0.240766i \(0.922601\pi\)
\(158\) −17.3477 + 12.9886i −1.38011 + 1.03332i
\(159\) −4.07596 −0.323244
\(160\) 3.70270 4.27668i 0.292724 0.338101i
\(161\) 35.9134 2.83037
\(162\) 1.13207 0.847599i 0.0889436 0.0665937i
\(163\) −0.346095 0.346095i −0.0271082 0.0271082i 0.693423 0.720531i \(-0.256102\pi\)
−0.720531 + 0.693423i \(0.756102\pi\)
\(164\) 7.61168 + 2.23363i 0.594372 + 0.174418i
\(165\) 2.94281 2.94281i 0.229098 0.229098i
\(166\) 10.9785 + 1.57755i 0.852094 + 0.122441i
\(167\) 10.9882i 0.850296i 0.905124 + 0.425148i \(0.139778\pi\)
−0.905124 + 0.425148i \(0.860222\pi\)
\(168\) 10.9937 + 5.01740i 0.848185 + 0.387101i
\(169\) 19.9611i 1.53547i
\(170\) −0.0321958 + 0.224057i −0.00246931 + 0.0171844i
\(171\) −4.32576 + 4.32576i −0.330799 + 0.330799i
\(172\) 0.346755 + 0.634788i 0.0264398 + 0.0484021i
\(173\) 2.70605 + 2.70605i 0.205737 + 0.205737i 0.802453 0.596716i \(-0.203528\pi\)
−0.596716 + 0.802453i \(0.703528\pi\)
\(174\) 2.13452 + 2.85090i 0.161818 + 0.216126i
\(175\) −4.27253 −0.322973
\(176\) −16.2655 + 3.54392i −1.22606 + 0.267133i
\(177\) −7.97042 −0.599093
\(178\) −11.7808 15.7347i −0.883012 1.17936i
\(179\) −10.4088 10.4088i −0.777990 0.777990i 0.201499 0.979489i \(-0.435419\pi\)
−0.979489 + 0.201499i \(0.935419\pi\)
\(180\) 1.75520 0.958786i 0.130825 0.0714637i
\(181\) −15.4792 + 15.4792i −1.15056 + 1.15056i −0.164119 + 0.986441i \(0.552478\pi\)
−0.986441 + 0.164119i \(0.947522\pi\)
\(182\) 4.93405 34.3371i 0.365736 2.54523i
\(183\) 6.34780i 0.469243i
\(184\) −22.2737 + 8.31390i −1.64204 + 0.612909i
\(185\) 0.946429i 0.0695828i
\(186\) −10.0408 1.44280i −0.736225 0.105792i
\(187\) 0.471026 0.471026i 0.0344448 0.0344448i
\(188\) 0.0423860 0.144441i 0.00309132 0.0105344i
\(189\) 3.02114 + 3.02114i 0.219755 + 0.219755i
\(190\) −6.92547 + 5.18522i −0.502426 + 0.376176i
\(191\) 4.75146 0.343803 0.171902 0.985114i \(-0.445009\pi\)
0.171902 + 0.985114i \(0.445009\pi\)
\(192\) −7.97990 0.566790i −0.575899 0.0409046i
\(193\) −11.7915 −0.848772 −0.424386 0.905481i \(-0.639510\pi\)
−0.424386 + 0.905481i \(0.639510\pi\)
\(194\) −12.3394 + 9.23873i −0.885917 + 0.663302i
\(195\) −4.05962 4.05962i −0.290716 0.290716i
\(196\) −6.33801 + 21.5984i −0.452715 + 1.54274i
\(197\) 4.56244 4.56244i 0.325060 0.325060i −0.525644 0.850705i \(-0.676176\pi\)
0.850705 + 0.525644i \(0.176176\pi\)
\(198\) −5.82579 0.837134i −0.414021 0.0594926i
\(199\) 3.60262i 0.255383i −0.991814 0.127691i \(-0.959243\pi\)
0.991814 0.127691i \(-0.0407567\pi\)
\(200\) 2.64985 0.989085i 0.187373 0.0699389i
\(201\) 0.185511i 0.0130850i
\(202\) 0.850479 5.91865i 0.0598395 0.416435i
\(203\) −7.60817 + 7.60817i −0.533989 + 0.533989i
\(204\) 0.280937 0.153463i 0.0196695 0.0107446i
\(205\) 2.80461 + 2.80461i 0.195883 + 0.195883i
\(206\) −14.2558 19.0403i −0.993249 1.32660i
\(207\) −8.40564 −0.584233
\(208\) 4.88885 + 22.4383i 0.338981 + 1.55582i
\(209\) 25.4598 1.76109
\(210\) 3.62140 + 4.83679i 0.249900 + 0.333771i
\(211\) −0.975389 0.975389i −0.0671486 0.0671486i 0.672735 0.739884i \(-0.265119\pi\)
−0.739884 + 0.672735i \(0.765119\pi\)
\(212\) 3.90797 + 7.15412i 0.268400 + 0.491347i
\(213\) 8.56570 8.56570i 0.586912 0.586912i
\(214\) −0.467799 + 3.25551i −0.0319781 + 0.222542i
\(215\) 0.361661i 0.0246651i
\(216\) −2.57312 1.17434i −0.175078 0.0799036i
\(217\) 30.6461i 2.08039i
\(218\) −9.24550 1.32853i −0.626184 0.0899793i
\(219\) 0.270734 0.270734i 0.0182945 0.0182945i
\(220\) −7.98675 2.34370i −0.538467 0.158012i
\(221\) −0.649782 0.649782i −0.0437091 0.0437091i
\(222\) 1.07142 0.802193i 0.0719091 0.0538396i
\(223\) 4.66343 0.312286 0.156143 0.987734i \(-0.450094\pi\)
0.156143 + 0.987734i \(0.450094\pi\)
\(224\) −1.73408 24.1068i −0.115863 1.61070i
\(225\) 1.00000 0.0666667
\(226\) −5.66637 + 4.24251i −0.376921 + 0.282208i
\(227\) −1.61701 1.61701i −0.107325 0.107325i 0.651405 0.758730i \(-0.274180\pi\)
−0.758730 + 0.651405i \(0.774180\pi\)
\(228\) 11.7400 + 3.44510i 0.777503 + 0.228157i
\(229\) 9.14882 9.14882i 0.604571 0.604571i −0.336951 0.941522i \(-0.609396\pi\)
0.941522 + 0.336951i \(0.109396\pi\)
\(230\) −11.7665 1.69079i −0.775861 0.111487i
\(231\) 17.7813i 1.16992i
\(232\) 2.95735 6.47991i 0.194160 0.425427i
\(233\) 10.3002i 0.674789i −0.941363 0.337394i \(-0.890454\pi\)
0.941363 0.337394i \(-0.109546\pi\)
\(234\) −1.15483 + 8.03670i −0.0754937 + 0.525376i
\(235\) 0.0532210 0.0532210i 0.00347175 0.00347175i
\(236\) 7.64192 + 13.9897i 0.497447 + 0.910651i
\(237\) 10.8357 + 10.8357i 0.703852 + 0.703852i
\(238\) 0.579640 + 0.774176i 0.0375725 + 0.0501824i
\(239\) 3.73825 0.241807 0.120904 0.992664i \(-0.461421\pi\)
0.120904 + 0.992664i \(0.461421\pi\)
\(240\) −3.36572 2.16146i −0.217256 0.139522i
\(241\) −9.34283 −0.601824 −0.300912 0.953652i \(-0.597291\pi\)
−0.300912 + 0.953652i \(0.597291\pi\)
\(242\) 5.35707 + 7.15499i 0.344366 + 0.459940i
\(243\) −0.707107 0.707107i −0.0453609 0.0453609i
\(244\) −11.1417 + 6.08618i −0.713272 + 0.389628i
\(245\) −7.95817 + 7.95817i −0.508429 + 0.508429i
\(246\) 0.797821 5.55219i 0.0508672 0.353995i
\(247\) 35.1219i 2.23475i
\(248\) 7.09453 + 19.0069i 0.450503 + 1.20694i
\(249\) 7.84269i 0.497010i
\(250\) 1.39984 + 0.201149i 0.0885334 + 0.0127218i
\(251\) −9.31174 + 9.31174i −0.587752 + 0.587752i −0.937022 0.349270i \(-0.886429\pi\)
0.349270 + 0.937022i \(0.386429\pi\)
\(252\) 2.40608 8.19933i 0.151569 0.516509i
\(253\) 24.7362 + 24.7362i 1.55515 + 1.55515i
\(254\) −2.22654 + 1.66705i −0.139706 + 0.104600i
\(255\) 0.160060 0.0100233
\(256\) 6.65618 + 14.5498i 0.416011 + 0.909359i
\(257\) 8.68522 0.541769 0.270885 0.962612i \(-0.412684\pi\)
0.270885 + 0.962612i \(0.412684\pi\)
\(258\) 0.409424 0.306544i 0.0254897 0.0190846i
\(259\) 2.85929 + 2.85929i 0.177668 + 0.177668i
\(260\) −3.23315 + 11.0178i −0.200511 + 0.683293i
\(261\) 1.78072 1.78072i 0.110224 0.110224i
\(262\) 1.68847 + 0.242624i 0.104314 + 0.0149893i
\(263\) 5.18971i 0.320011i 0.987116 + 0.160006i \(0.0511513\pi\)
−0.987116 + 0.160006i \(0.948849\pi\)
\(264\) 4.11634 + 11.0281i 0.253343 + 0.678730i
\(265\) 4.07596i 0.250384i
\(266\) −5.25751 + 36.5881i −0.322359 + 2.24336i
\(267\) −9.82813 + 9.82813i −0.601472 + 0.601472i
\(268\) −0.325610 + 0.177866i −0.0198898 + 0.0108649i
\(269\) −7.99426 7.99426i −0.487418 0.487418i 0.420072 0.907491i \(-0.362005\pi\)
−0.907491 + 0.420072i \(0.862005\pi\)
\(270\) −0.847599 1.13207i −0.0515833 0.0688954i
\(271\) −18.8342 −1.14410 −0.572048 0.820220i \(-0.693851\pi\)
−0.572048 + 0.820220i \(0.693851\pi\)
\(272\) −0.538717 0.345963i −0.0326645 0.0209771i
\(273\) −24.5294 −1.48458
\(274\) −3.49230 4.66437i −0.210978 0.281785i
\(275\) −2.94281 2.94281i −0.177458 0.177458i
\(276\) 8.05921 + 14.7536i 0.485107 + 0.888062i
\(277\) 3.71919 3.71919i 0.223465 0.223465i −0.586491 0.809956i \(-0.699491\pi\)
0.809956 + 0.586491i \(0.199491\pi\)
\(278\) −1.63254 + 11.3612i −0.0979135 + 0.681400i
\(279\) 7.17282i 0.429425i
\(280\) 5.01740 10.9937i 0.299847 0.657001i
\(281\) 11.0223i 0.657538i −0.944410 0.328769i \(-0.893366\pi\)
0.944410 0.328769i \(-0.106634\pi\)
\(282\) −0.105360 0.0151396i −0.00627408 0.000901552i
\(283\) 10.5210 10.5210i 0.625411 0.625411i −0.321499 0.946910i \(-0.604187\pi\)
0.946910 + 0.321499i \(0.104187\pi\)
\(284\) −23.2472 6.82186i −1.37947 0.404803i
\(285\) 4.32576 + 4.32576i 0.256236 + 0.256236i
\(286\) 27.0490 20.2521i 1.59944 1.19753i
\(287\) 16.9462 1.00030
\(288\) 0.405867 + 5.64228i 0.0239160 + 0.332474i
\(289\) −16.9744 −0.998493
\(290\) 2.85090 2.13452i 0.167410 0.125343i
\(291\) 7.70738 + 7.70738i 0.451815 + 0.451815i
\(292\) −0.734769 0.215617i −0.0429991 0.0126180i
\(293\) 15.5643 15.5643i 0.909274 0.909274i −0.0869399 0.996214i \(-0.527709\pi\)
0.996214 + 0.0869399i \(0.0277088\pi\)
\(294\) 15.7545 + 2.26384i 0.918822 + 0.132030i
\(295\) 7.97042i 0.464056i
\(296\) −2.43527 1.11143i −0.141547 0.0646004i
\(297\) 4.16177i 0.241490i
\(298\) 2.83418 19.7236i 0.164180 1.14256i
\(299\) 34.1237 34.1237i 1.97343 1.97343i
\(300\) −0.958786 1.75520i −0.0553555 0.101337i
\(301\) 1.09263 + 1.09263i 0.0629780 + 0.0629780i
\(302\) −3.40635 4.54958i −0.196014 0.261799i
\(303\) −4.22811 −0.242898
\(304\) −5.20935 23.9092i −0.298776 1.37129i
\(305\) −6.34780 −0.363474
\(306\) −0.135667 0.181198i −0.00775554 0.0103584i
\(307\) 19.6795 + 19.6795i 1.12317 + 1.12317i 0.991262 + 0.131908i \(0.0421104\pi\)
0.131908 + 0.991262i \(0.457890\pi\)
\(308\) −31.2097 + 17.0484i −1.77834 + 0.971425i
\(309\) −11.8929 + 11.8929i −0.676561 + 0.676561i
\(310\) −1.44280 + 10.0408i −0.0819458 + 0.570277i
\(311\) 11.8922i 0.674344i 0.941443 + 0.337172i \(0.109470\pi\)
−0.941443 + 0.337172i \(0.890530\pi\)
\(312\) 15.2133 5.67851i 0.861281 0.321482i
\(313\) 9.61193i 0.543298i −0.962396 0.271649i \(-0.912431\pi\)
0.962396 0.271649i \(-0.0875690\pi\)
\(314\) 18.1032 + 2.60134i 1.02162 + 0.146802i
\(315\) 3.02114 3.02114i 0.170222 0.170222i
\(316\) 8.62969 29.4079i 0.485458 1.65432i
\(317\) 8.10049 + 8.10049i 0.454969 + 0.454969i 0.897000 0.442031i \(-0.145742\pi\)
−0.442031 + 0.897000i \(0.645742\pi\)
\(318\) 4.61426 3.45478i 0.258755 0.193734i
\(319\) −10.4806 −0.586802
\(320\) −0.566790 + 7.97990i −0.0316845 + 0.446090i
\(321\) 2.32563 0.129804
\(322\) −40.6564 + 30.4402i −2.26569 + 1.69636i
\(323\) 0.692379 + 0.692379i 0.0385250 + 0.0385250i
\(324\) −0.563151 + 1.91908i −0.0312861 + 0.106615i
\(325\) −4.05962 + 4.05962i −0.225187 + 0.225187i
\(326\) 0.685152 + 0.0984526i 0.0379470 + 0.00545279i
\(327\) 6.60470i 0.365241i
\(328\) −10.5102 + 3.92303i −0.580326 + 0.216613i
\(329\) 0.321576i 0.0177291i
\(330\) −0.837134 + 5.82579i −0.0460827 + 0.320699i
\(331\) −13.3267 + 13.3267i −0.732501 + 0.732501i −0.971115 0.238613i \(-0.923307\pi\)
0.238613 + 0.971115i \(0.423307\pi\)
\(332\) −13.7655 + 7.51945i −0.755479 + 0.412684i
\(333\) −0.669226 0.669226i −0.0366734 0.0366734i
\(334\) −9.31363 12.4394i −0.509619 0.680655i
\(335\) −0.185511 −0.0101356
\(336\) −16.6984 + 3.63824i −0.910971 + 0.198482i
\(337\) 32.6763 1.77999 0.889996 0.455967i \(-0.150707\pi\)
0.889996 + 0.455967i \(0.150707\pi\)
\(338\) −16.9190 22.5973i −0.920273 1.22913i
\(339\) 3.53930 + 3.53930i 0.192229 + 0.192229i
\(340\) −0.153463 0.280937i −0.00832270 0.0152359i
\(341\) 21.1083 21.1083i 1.14308 1.14308i
\(342\) 1.23054 8.56355i 0.0665398 0.463064i
\(343\) 18.1777i 0.981504i
\(344\) −0.930596 0.424712i −0.0501744 0.0228990i
\(345\) 8.40564i 0.452545i
\(346\) −5.35708 0.769784i −0.287998 0.0413838i
\(347\) 22.4898 22.4898i 1.20732 1.20732i 0.235423 0.971893i \(-0.424352\pi\)
0.971893 0.235423i \(-0.0756477\pi\)
\(348\) −4.83284 1.41819i −0.259067 0.0760229i
\(349\) −22.6617 22.6617i −1.21305 1.21305i −0.970018 0.243032i \(-0.921858\pi\)
−0.243032 0.970018i \(-0.578142\pi\)
\(350\) 4.83679 3.62140i 0.258538 0.193572i
\(351\) 5.74117 0.306441
\(352\) 15.4098 17.7985i 0.821343 0.948666i
\(353\) −10.6347 −0.566026 −0.283013 0.959116i \(-0.591334\pi\)
−0.283013 + 0.959116i \(0.591334\pi\)
\(354\) 9.02305 6.75572i 0.479570 0.359063i
\(355\) −8.56570 8.56570i −0.454620 0.454620i
\(356\) 26.6734 + 7.82727i 1.41369 + 0.414845i
\(357\) 0.483562 0.483562i 0.0255928 0.0255928i
\(358\) 20.6059 + 2.96096i 1.08906 + 0.156492i
\(359\) 17.0191i 0.898235i 0.893473 + 0.449118i \(0.148262\pi\)
−0.893473 + 0.449118i \(0.851738\pi\)
\(360\) −1.17434 + 2.57312i −0.0618931 + 0.135615i
\(361\) 18.4243i 0.969701i
\(362\) 4.40333 30.6436i 0.231434 1.61059i
\(363\) 4.46912 4.46912i 0.234568 0.234568i
\(364\) 23.5184 + 43.0540i 1.23270 + 2.25664i
\(365\) −0.270734 0.270734i −0.0141709 0.0141709i
\(366\) 5.38039 + 7.18613i 0.281238 + 0.375625i
\(367\) −25.7040 −1.34174 −0.670868 0.741577i \(-0.734078\pi\)
−0.670868 + 0.741577i \(0.734078\pi\)
\(368\) 18.1685 28.2911i 0.947097 1.47477i
\(369\) −3.96632 −0.206478
\(370\) −0.802193 1.07142i −0.0417040 0.0557005i
\(371\) 12.3140 + 12.3140i 0.639313 + 0.639313i
\(372\) 12.5897 6.87720i 0.652747 0.356566i
\(373\) −14.7290 + 14.7290i −0.762641 + 0.762641i −0.976799 0.214158i \(-0.931299\pi\)
0.214158 + 0.976799i \(0.431299\pi\)
\(374\) −0.133991 + 0.932474i −0.00692853 + 0.0482171i
\(375\) 1.00000i 0.0516398i
\(376\) 0.0744443 + 0.199443i 0.00383917 + 0.0102855i
\(377\) 14.4581i 0.744628i
\(378\) −5.98084 0.859415i −0.307621 0.0442036i
\(379\) 10.0142 10.0142i 0.514395 0.514395i −0.401475 0.915870i \(-0.631502\pi\)
0.915870 + 0.401475i \(0.131502\pi\)
\(380\) 3.44510 11.7400i 0.176730 0.602251i
\(381\) 1.39073 + 1.39073i 0.0712494 + 0.0712494i
\(382\) −5.37897 + 4.02733i −0.275212 + 0.206056i
\(383\) −28.1834 −1.44010 −0.720052 0.693920i \(-0.755882\pi\)
−0.720052 + 0.693920i \(0.755882\pi\)
\(384\) 9.51419 6.12211i 0.485519 0.312418i
\(385\) −17.7813 −0.906218
\(386\) 13.3488 9.99448i 0.679435 0.508706i
\(387\) −0.255733 0.255733i −0.0129996 0.0129996i
\(388\) 6.13828 20.9177i 0.311624 1.06194i
\(389\) −11.1551 + 11.1551i −0.565586 + 0.565586i −0.930889 0.365303i \(-0.880965\pi\)
0.365303 + 0.930889i \(0.380965\pi\)
\(390\) 8.03670 + 1.15483i 0.406954 + 0.0584771i
\(391\) 1.34540i 0.0680400i
\(392\) −11.1317 29.8229i −0.562236 1.50628i
\(393\) 1.20619i 0.0608442i
\(394\) −1.29787 + 9.03211i −0.0653855 + 0.455031i
\(395\) 10.8357 10.8357i 0.545202 0.545202i
\(396\) 7.30473 3.99024i 0.367077 0.200517i
\(397\) 2.98216 + 2.98216i 0.149670 + 0.149670i 0.777971 0.628300i \(-0.216249\pi\)
−0.628300 + 0.777971i \(0.716249\pi\)
\(398\) 3.05358 + 4.07841i 0.153062 + 0.204432i
\(399\) 26.1374 1.30851
\(400\) −2.16146 + 3.36572i −0.108073 + 0.168286i
\(401\) −15.9896 −0.798485 −0.399242 0.916845i \(-0.630727\pi\)
−0.399242 + 0.916845i \(0.630727\pi\)
\(402\) 0.157239 + 0.210011i 0.00784239 + 0.0104744i
\(403\) −29.1189 29.1189i −1.45052 1.45052i
\(404\) 4.05385 + 7.42118i 0.201687 + 0.369217i
\(405\) −0.707107 + 0.707107i −0.0351364 + 0.0351364i
\(406\) 2.16428 15.0616i 0.107411 0.747496i
\(407\) 3.93881i 0.195240i
\(408\) −0.187964 + 0.411852i −0.00930562 + 0.0203897i
\(409\) 27.5110i 1.36033i −0.733059 0.680165i \(-0.761908\pi\)
0.733059 0.680165i \(-0.238092\pi\)
\(410\) −5.55219 0.797821i −0.274203 0.0394015i
\(411\) −2.91344 + 2.91344i −0.143709 + 0.143709i
\(412\) 32.2770 + 9.47165i 1.59018 + 0.466635i
\(413\) 24.0797 + 24.0797i 1.18489 + 1.18489i
\(414\) 9.51575 7.12462i 0.467674 0.350156i
\(415\) −7.84269 −0.384982
\(416\) −24.5532 21.2578i −1.20382 1.04225i
\(417\) 8.11610 0.397447
\(418\) −28.8222 + 21.5797i −1.40974 + 1.05550i
\(419\) 1.95916 + 1.95916i 0.0957114 + 0.0957114i 0.753341 0.657630i \(-0.228441\pi\)
−0.657630 + 0.753341i \(0.728441\pi\)
\(420\) −8.19933 2.40608i −0.400086 0.117405i
\(421\) 6.23743 6.23743i 0.303994 0.303994i −0.538580 0.842574i \(-0.681039\pi\)
0.842574 + 0.538580i \(0.181039\pi\)
\(422\) 1.93095 + 0.277467i 0.0939970 + 0.0135069i
\(423\) 0.0752658i 0.00365955i
\(424\) −10.4879 4.78655i −0.509338 0.232456i
\(425\) 0.160060i 0.00776404i
\(426\) −2.43666 + 16.9572i −0.118057 + 0.821581i
\(427\) −19.1776 + 19.1776i −0.928068 + 0.928068i
\(428\) −2.22978 4.08196i −0.107781 0.197309i
\(429\) −16.8952 16.8952i −0.815708 0.815708i
\(430\) −0.306544 0.409424i −0.0147828 0.0197442i
\(431\) 5.88180 0.283317 0.141658 0.989916i \(-0.454757\pi\)
0.141658 + 0.989916i \(0.454757\pi\)
\(432\) 3.90831 0.851542i 0.188039 0.0409698i
\(433\) −6.37830 −0.306522 −0.153261 0.988186i \(-0.548977\pi\)
−0.153261 + 0.988186i \(0.548977\pi\)
\(434\) 25.9756 + 34.6934i 1.24687 + 1.66534i
\(435\) −1.78072 1.78072i −0.0853788 0.0853788i
\(436\) 11.5926 6.33250i 0.555184 0.303272i
\(437\) −36.3608 + 36.3608i −1.73937 + 1.73937i
\(438\) −0.0770151 + 0.535963i −0.00367992 + 0.0256093i
\(439\) 37.2899i 1.77975i −0.456206 0.889874i \(-0.650792\pi\)
0.456206 0.889874i \(-0.349208\pi\)
\(440\) 11.0281 4.11634i 0.525742 0.196239i
\(441\) 11.2545i 0.535931i
\(442\) 1.28635 + 0.184842i 0.0611855 + 0.00879203i
\(443\) 28.4238 28.4238i 1.35046 1.35046i 0.465308 0.885149i \(-0.345944\pi\)
0.885149 0.465308i \(-0.154056\pi\)
\(444\) −0.532982 + 1.81627i −0.0252942 + 0.0861964i
\(445\) 9.82813 + 9.82813i 0.465898 + 0.465898i
\(446\) −5.27931 + 3.95272i −0.249983 + 0.187167i
\(447\) −14.0900 −0.666433
\(448\) 22.3960 + 25.8207i 1.05811 + 1.21991i
\(449\) 11.9658 0.564701 0.282350 0.959311i \(-0.408886\pi\)
0.282350 + 0.959311i \(0.408886\pi\)
\(450\) −1.13207 + 0.847599i −0.0533661 + 0.0399562i
\(451\) 11.6721 + 11.6721i 0.549619 + 0.549619i
\(452\) 2.81875 9.60562i 0.132583 0.451810i
\(453\) −2.84174 + 2.84174i −0.133516 + 0.133516i
\(454\) 3.20114 + 0.459986i 0.150237 + 0.0215882i
\(455\) 24.5294i 1.14995i
\(456\) −16.2106 + 6.05077i −0.759130 + 0.283353i
\(457\) 33.0504i 1.54603i 0.634385 + 0.773017i \(0.281253\pi\)
−0.634385 + 0.773017i \(0.718747\pi\)
\(458\) −2.60254 + 18.1116i −0.121609 + 0.846300i
\(459\) −0.113179 + 0.113179i −0.00528276 + 0.00528276i
\(460\) 14.7536 8.05921i 0.687890 0.375763i
\(461\) −20.7242 20.7242i −0.965221 0.965221i 0.0341939 0.999415i \(-0.489114\pi\)
−0.999415 + 0.0341939i \(0.989114\pi\)
\(462\) 15.0714 + 20.1296i 0.701185 + 0.936514i
\(463\) 14.2359 0.661599 0.330800 0.943701i \(-0.392682\pi\)
0.330800 + 0.943701i \(0.392682\pi\)
\(464\) 2.14445 + 9.84234i 0.0995536 + 0.456919i
\(465\) 7.17282 0.332632
\(466\) 8.73045 + 11.6605i 0.404430 + 0.540163i
\(467\) 18.7991 + 18.7991i 0.869918 + 0.869918i 0.992463 0.122545i \(-0.0391056\pi\)
−0.122545 + 0.992463i \(0.539106\pi\)
\(468\) −5.50456 10.0769i −0.254448 0.465806i
\(469\) −0.560456 + 0.560456i −0.0258794 + 0.0258794i
\(470\) −0.0151396 + 0.105360i −0.000698339 + 0.00485988i
\(471\) 12.9324i 0.595894i
\(472\) −20.5088 9.35997i −0.943995 0.430828i
\(473\) 1.50515i 0.0692068i
\(474\) −21.4510 3.08239i −0.985277 0.141579i
\(475\) 4.32576 4.32576i 0.198479 0.198479i
\(476\) −1.31238 0.385117i −0.0601529 0.0176518i
\(477\) −2.88214 2.88214i −0.131964 0.131964i
\(478\) −4.23195 + 3.16854i −0.193565 + 0.144926i
\(479\) −26.7178 −1.22077 −0.610384 0.792106i \(-0.708985\pi\)
−0.610384 + 0.792106i \(0.708985\pi\)
\(480\) 5.64228 0.405867i 0.257533 0.0185252i
\(481\) 5.43361 0.247751
\(482\) 10.5767 7.91897i 0.481756 0.360699i
\(483\) 25.3946 + 25.3946i 1.15549 + 1.15549i
\(484\) −12.1291 3.55928i −0.551324 0.161785i
\(485\) 7.70738 7.70738i 0.349974 0.349974i
\(486\) 1.39984 + 0.201149i 0.0634978 + 0.00912430i
\(487\) 27.0801i 1.22712i 0.789650 + 0.613558i \(0.210262\pi\)
−0.789650 + 0.613558i \(0.789738\pi\)
\(488\) 7.45447 16.3336i 0.337448 0.739389i
\(489\) 0.489452i 0.0221338i
\(490\) 2.26384 15.7545i 0.102270 0.711717i
\(491\) 1.51536 1.51536i 0.0683872 0.0683872i −0.672086 0.740473i \(-0.734601\pi\)
0.740473 + 0.672086i \(0.234601\pi\)
\(492\) 3.80285 + 6.96169i 0.171446 + 0.313857i
\(493\) −0.285021 0.285021i −0.0128367 0.0128367i
\(494\) 29.7693 + 39.7603i 1.33938 + 1.78890i
\(495\) 4.16177 0.187057
\(496\) −24.1417 15.5038i −1.08400 0.696139i
\(497\) −51.7563 −2.32159
\(498\) 6.64746 + 8.87844i 0.297880 + 0.397853i
\(499\) 7.31012 + 7.31012i 0.327246 + 0.327246i 0.851538 0.524292i \(-0.175670\pi\)
−0.524292 + 0.851538i \(0.675670\pi\)
\(500\) −1.75520 + 0.958786i −0.0784950 + 0.0428782i
\(501\) −7.76986 + 7.76986i −0.347132 + 0.347132i
\(502\) 2.64889 18.4341i 0.118226 0.822756i
\(503\) 37.4924i 1.67170i 0.548954 + 0.835852i \(0.315026\pi\)
−0.548954 + 0.835852i \(0.684974\pi\)
\(504\) 4.22590 + 11.3216i 0.188237 + 0.504303i
\(505\) 4.22811i 0.188148i
\(506\) −48.9695 7.03665i −2.17696 0.312817i
\(507\) −14.1146 + 14.1146i −0.626852 + 0.626852i
\(508\) 1.10760 3.77443i 0.0491418 0.167463i
\(509\) 27.7592 + 27.7592i 1.23040 + 1.23040i 0.963809 + 0.266595i \(0.0858987\pi\)
0.266595 + 0.963809i \(0.414101\pi\)
\(510\) −0.181198 + 0.135667i −0.00802359 + 0.00600741i
\(511\) −1.63585 −0.0723658
\(512\) −19.8676 10.8295i −0.878032 0.478602i
\(513\) −6.11754 −0.270096
\(514\) −9.83225 + 7.36159i −0.433682 + 0.324706i
\(515\) 11.8929 + 11.8929i 0.524062 + 0.524062i
\(516\) −0.203670 + 0.694056i −0.00896605 + 0.0305541i
\(517\) 0.221493 0.221493i 0.00974126 0.00974126i
\(518\) −5.66044 0.813376i −0.248706 0.0357377i
\(519\) 3.82694i 0.167984i
\(520\) −5.67851 15.2133i −0.249019 0.667145i
\(521\) 10.0782i 0.441533i −0.975327 0.220767i \(-0.929144\pi\)
0.975327 0.220767i \(-0.0708559\pi\)
\(522\) −0.506556 + 3.52522i −0.0221713 + 0.154295i
\(523\) 8.16934 8.16934i 0.357220 0.357220i −0.505567 0.862787i \(-0.668717\pi\)
0.862787 + 0.505567i \(0.168717\pi\)
\(524\) −2.11710 + 1.15648i −0.0924861 + 0.0505209i
\(525\) −3.02114 3.02114i −0.131853 0.131853i
\(526\) −4.39880 5.87510i −0.191797 0.256167i
\(527\) 1.14808 0.0500111
\(528\) −14.0073 8.99549i −0.609592 0.391478i
\(529\) −47.6548 −2.07195
\(530\) −3.45478 4.61426i −0.150066 0.200430i
\(531\) −5.63594 5.63594i −0.244579 0.244579i
\(532\) −25.0602 45.8764i −1.08650 1.98899i
\(533\) 16.1018 16.1018i 0.697445 0.697445i
\(534\) 2.79578 19.4564i 0.120985 0.841961i
\(535\) 2.32563i 0.100546i
\(536\) 0.217853 0.477343i 0.00940983 0.0206181i
\(537\) 14.7203i 0.635226i
\(538\) 15.8260 + 2.27411i 0.682306 + 0.0980437i
\(539\) −33.1200 + 33.1200i −1.42658 + 1.42658i
\(540\) 1.91908 + 0.563151i 0.0825840 + 0.0242341i
\(541\) 1.98301 + 1.98301i 0.0852564 + 0.0852564i 0.748449 0.663192i \(-0.230799\pi\)
−0.663192 + 0.748449i \(0.730799\pi\)
\(542\) 21.3216 15.9639i 0.915840 0.685707i
\(543\) −21.8909 −0.939428
\(544\) 0.903101 0.0649630i 0.0387201 0.00278526i
\(545\) 6.60470 0.282914
\(546\) 27.7689 20.7911i 1.18840 0.889776i
\(547\) −14.5464 14.5464i −0.621959 0.621959i 0.324073 0.946032i \(-0.394948\pi\)
−0.946032 + 0.324073i \(0.894948\pi\)
\(548\) 7.90704 + 2.32031i 0.337772 + 0.0991187i
\(549\) 4.48857 4.48857i 0.191568 0.191568i
\(550\) 5.82579 + 0.837134i 0.248412 + 0.0356955i
\(551\) 15.4059i 0.656313i
\(552\) −21.6287 9.87107i −0.920579 0.420141i
\(553\) 65.4721i 2.78416i
\(554\) −1.05799 + 7.36276i −0.0449496 + 0.312814i
\(555\) −0.669226 + 0.669226i −0.0284071 + 0.0284071i
\(556\) −7.78160 14.2454i −0.330013 0.604139i
\(557\) −25.6935 25.6935i −1.08867 1.08867i −0.995666 0.0930007i \(-0.970354\pi\)
−0.0930007 0.995666i \(-0.529646\pi\)
\(558\) −6.07968 8.12011i −0.257373 0.343752i
\(559\) 2.07636 0.0878206
\(560\) 3.63824 + 16.6984i 0.153744 + 0.705635i
\(561\) 0.666131 0.0281241
\(562\) 9.34253 + 12.4780i 0.394091 + 0.526354i
\(563\) −15.8673 15.8673i −0.668729 0.668729i 0.288693 0.957422i \(-0.406779\pi\)
−0.957422 + 0.288693i \(0.906779\pi\)
\(564\) 0.132107 0.0721638i 0.00556269 0.00303864i
\(565\) 3.53930 3.53930i 0.148900 0.148900i
\(566\) −2.99289 + 20.8281i −0.125801 + 0.875472i
\(567\) 4.27253i 0.179430i
\(568\) 32.0996 11.9815i 1.34687 0.502733i
\(569\) 45.0379i 1.88809i −0.329819 0.944044i \(-0.606988\pi\)
0.329819 0.944044i \(-0.393012\pi\)
\(570\) −8.56355 1.23054i −0.358688 0.0515415i
\(571\) 23.0995 23.0995i 0.966684 0.966684i −0.0327783 0.999463i \(-0.510436\pi\)
0.999463 + 0.0327783i \(0.0104355\pi\)
\(572\) −13.4556 + 45.8533i −0.562607 + 1.91722i
\(573\) 3.35979 + 3.35979i 0.140357 + 0.140357i
\(574\) −19.1843 + 14.3636i −0.800736 + 0.599526i
\(575\) 8.40564 0.350540
\(576\) −5.24186 6.04342i −0.218411 0.251809i
\(577\) −10.3572 −0.431178 −0.215589 0.976484i \(-0.569167\pi\)
−0.215589 + 0.976484i \(0.569167\pi\)
\(578\) 19.2161 14.3875i 0.799286 0.598440i
\(579\) −8.33786 8.33786i −0.346510 0.346510i
\(580\) −1.41819 + 4.83284i −0.0588871 + 0.200673i
\(581\) −23.6938 + 23.6938i −0.982986 + 0.982986i
\(582\) −15.2580 2.19250i −0.632466 0.0908820i
\(583\) 16.9632i 0.702543i
\(584\) 1.01456 0.378697i 0.0419830 0.0156706i
\(585\) 5.74117i 0.237368i
\(586\) −4.42753 + 30.8120i −0.182899 + 1.27283i
\(587\) −23.6336 + 23.6336i −0.975462 + 0.975462i −0.999706 0.0242436i \(-0.992282\pi\)
0.0242436 + 0.999706i \(0.492282\pi\)
\(588\) −19.7540 + 10.7907i −0.814641 + 0.445001i
\(589\) 31.0279 + 31.0279i 1.27848 + 1.27848i
\(590\) −6.75572 9.02305i −0.278129 0.371473i
\(591\) 6.45226 0.265411
\(592\) 3.69894 0.805924i 0.152025 0.0331233i
\(593\) −30.5649 −1.25515 −0.627575 0.778556i \(-0.715952\pi\)
−0.627575 + 0.778556i \(0.715952\pi\)
\(594\) −3.52751 4.71140i −0.144735 0.193311i
\(595\) −0.483562 0.483562i −0.0198241 0.0198241i
\(596\) 13.5093 + 24.7307i 0.553361 + 1.01301i
\(597\) 2.54744 2.54744i 0.104260 0.104260i
\(598\) −9.70710 + 67.5536i −0.396953 + 2.76247i
\(599\) 10.2816i 0.420096i −0.977691 0.210048i \(-0.932638\pi\)
0.977691 0.210048i \(-0.0673620\pi\)
\(600\) 2.57312 + 1.17434i 0.105047 + 0.0479422i
\(601\) 22.9223i 0.935021i 0.883987 + 0.467511i \(0.154849\pi\)
−0.883987 + 0.467511i \(0.845151\pi\)
\(602\) −2.16304 0.310817i −0.0881589 0.0126680i
\(603\) 0.131176 0.131176i 0.00534192 0.00534192i
\(604\) 7.71244 + 2.26320i 0.313815 + 0.0920884i
\(605\) −4.46912 4.46912i −0.181696 0.181696i
\(606\) 4.78650 3.58374i 0.194438 0.145580i
\(607\) 39.7832 1.61475 0.807374 0.590040i \(-0.200888\pi\)
0.807374 + 0.590040i \(0.200888\pi\)
\(608\) 26.1628 + 22.6514i 1.06104 + 0.918636i
\(609\) −10.7596 −0.436000
\(610\) 7.18613 5.38039i 0.290958 0.217846i
\(611\) −0.305551 0.305551i −0.0123613 0.0123613i
\(612\) 0.307167 + 0.0901377i 0.0124165 + 0.00364360i
\(613\) −26.9534 + 26.9534i −1.08864 + 1.08864i −0.0929665 + 0.995669i \(0.529635\pi\)
−0.995669 + 0.0929665i \(0.970365\pi\)
\(614\) −38.9589 5.59819i −1.57225 0.225924i
\(615\) 3.96632i 0.159937i
\(616\) 20.8812 45.7533i 0.841330 1.84345i
\(617\) 12.2306i 0.492385i −0.969221 0.246193i \(-0.920820\pi\)
0.969221 0.246193i \(-0.0791795\pi\)
\(618\) 3.38313 23.5439i 0.136089 0.947074i
\(619\) −4.13984 + 4.13984i −0.166394 + 0.166394i −0.785392 0.618998i \(-0.787539\pi\)
0.618998 + 0.785392i \(0.287539\pi\)
\(620\) −6.87720 12.5897i −0.276195 0.505616i
\(621\) −5.94369 5.94369i −0.238512 0.238512i
\(622\) −10.0798 13.4628i −0.404164 0.539807i
\(623\) 59.3843 2.37918
\(624\) −12.4093 + 19.3232i −0.496770 + 0.773547i
\(625\) −1.00000 −0.0400000
\(626\) 8.14706 + 10.8813i 0.325622 + 0.434906i
\(627\) 18.0028 + 18.0028i 0.718962 + 0.718962i
\(628\) −22.6990 + 12.3994i −0.905787 + 0.494790i
\(629\) −0.107116 + 0.107116i −0.00427100 + 0.00427100i
\(630\) −0.859415 + 5.98084i −0.0342399 + 0.238283i
\(631\) 25.3923i 1.01085i −0.862870 0.505426i \(-0.831336\pi\)
0.862870 0.505426i \(-0.168664\pi\)
\(632\) 15.1567 + 40.6062i 0.602901 + 1.61523i
\(633\) 1.37941i 0.0548266i
\(634\) −16.0363 2.30433i −0.636881 0.0915164i
\(635\) 1.39073 1.39073i 0.0551895 0.0551895i
\(636\) −2.29538 + 7.82208i −0.0910176 + 0.310166i
\(637\) 45.6892 + 45.6892i 1.81027 + 1.81027i
\(638\) 11.8648 8.88337i 0.469731 0.351696i
\(639\) 12.1137 0.479212
\(640\) −6.12211 9.51419i −0.241998 0.376081i
\(641\) 42.0683 1.66160 0.830799 0.556572i \(-0.187884\pi\)
0.830799 + 0.556572i \(0.187884\pi\)
\(642\) −2.63277 + 1.97121i −0.103907 + 0.0777973i
\(643\) −8.73724 8.73724i −0.344563 0.344563i 0.513517 0.858080i \(-0.328343\pi\)
−0.858080 + 0.513517i \(0.828343\pi\)
\(644\) 20.2247 68.9206i 0.796963 2.71585i
\(645\) −0.255733 + 0.255733i −0.0100695 + 0.0100695i
\(646\) −1.37068 0.196959i −0.0539287 0.00774926i
\(647\) 4.04843i 0.159160i −0.996828 0.0795802i \(-0.974642\pi\)
0.996828 0.0795802i \(-0.0253580\pi\)
\(648\) −0.989085 2.64985i −0.0388549 0.104096i
\(649\) 33.1710i 1.30208i
\(650\) 1.15483 8.03670i 0.0452962 0.315225i
\(651\) 21.6701 21.6701i 0.849317 0.849317i
\(652\) −0.859086 + 0.469279i −0.0336444 + 0.0183784i
\(653\) −12.8095 12.8095i −0.501275 0.501275i 0.410559 0.911834i \(-0.365334\pi\)
−0.911834 + 0.410559i \(0.865334\pi\)
\(654\) −5.59814 7.47697i −0.218905 0.292373i
\(655\) −1.20619 −0.0471297
\(656\) 8.57304 13.3495i 0.334721 0.521212i
\(657\) 0.382876 0.0149374
\(658\) 0.272568 + 0.364045i 0.0106258 + 0.0141920i
\(659\) −29.8196 29.8196i −1.16161 1.16161i −0.984124 0.177481i \(-0.943205\pi\)
−0.177481 0.984124i \(-0.556795\pi\)
\(660\) −3.99024 7.30473i −0.155320 0.284336i
\(661\) −30.2458 + 30.2458i −1.17642 + 1.17642i −0.195775 + 0.980649i \(0.562722\pi\)
−0.980649 + 0.195775i \(0.937278\pi\)
\(662\) 3.79101 26.3824i 0.147342 1.02538i
\(663\) 0.918931i 0.0356883i
\(664\) 9.20997 20.1801i 0.357416 0.783141i
\(665\) 26.1374i 1.01357i
\(666\) 1.32484 + 0.190373i 0.0513367 + 0.00737681i
\(667\) 14.9681 14.9681i 0.579566 0.579566i
\(668\) 21.0873 + 6.18804i 0.815892 + 0.239422i
\(669\) 3.29754 + 3.29754i 0.127490 + 0.127490i
\(670\) 0.210011 0.157239i 0.00811345 0.00607469i
\(671\) −26.4181 −1.01986
\(672\) 15.8199 18.2723i 0.610266 0.704868i
\(673\) 38.3587 1.47862 0.739309 0.673366i \(-0.235152\pi\)
0.739309 + 0.673366i \(0.235152\pi\)
\(674\) −36.9918 + 27.6964i −1.42487 + 1.06683i
\(675\) 0.707107 + 0.707107i 0.0272166 + 0.0272166i
\(676\) 38.3069 + 11.2411i 1.47334 + 0.432350i
\(677\) −19.3263 + 19.3263i −0.742772 + 0.742772i −0.973111 0.230339i \(-0.926017\pi\)
0.230339 + 0.973111i \(0.426017\pi\)
\(678\) −7.00664 1.00682i −0.269088 0.0386665i
\(679\) 46.5701i 1.78720i
\(680\) 0.411852 + 0.187964i 0.0157938 + 0.00720810i
\(681\) 2.28680i 0.0876302i
\(682\) −6.00461 + 41.7873i −0.229929 + 1.60012i
\(683\) 21.3741 21.3741i 0.817856 0.817856i −0.167941 0.985797i \(-0.553712\pi\)
0.985797 + 0.167941i \(0.0537119\pi\)
\(684\) 5.86541 + 10.7375i 0.224270 + 0.410559i
\(685\) 2.91344 + 2.91344i 0.111317 + 0.111317i
\(686\) −15.4074 20.5784i −0.588258 0.785686i
\(687\) 12.9384 0.493630
\(688\) 1.41348 0.307970i 0.0538885 0.0117412i
\(689\) 23.4008 0.891499
\(690\) −7.12462 9.51575i −0.271230 0.362258i
\(691\) 3.96331 + 3.96331i 0.150771 + 0.150771i 0.778462 0.627691i \(-0.216000\pi\)
−0.627691 + 0.778462i \(0.716000\pi\)
\(692\) 6.71704 3.66921i 0.255344 0.139482i
\(693\) 12.5733 12.5733i 0.477619 0.477619i
\(694\) −6.39762 + 44.5223i −0.242850 + 1.69004i
\(695\) 8.11610i 0.307861i
\(696\) 6.67315 2.49083i 0.252945 0.0944145i
\(697\) 0.634848i 0.0240466i
\(698\) 44.8625 + 6.44650i 1.69807 + 0.244004i
\(699\) 7.28334 7.28334i 0.275481 0.275481i
\(700\) −2.40608 + 8.19933i −0.0909413 + 0.309905i
\(701\) −27.4177 27.4177i −1.03555 1.03555i −0.999344 0.0362086i \(-0.988472\pi\)
−0.0362086 0.999344i \(-0.511528\pi\)
\(702\) −6.49939 + 4.86622i −0.245304 + 0.183663i
\(703\) −5.78982 −0.218367
\(704\) −2.35885 + 33.2105i −0.0889024 + 1.25167i
\(705\) 0.0752658 0.00283468
\(706\) 12.0391 9.01393i 0.453099 0.339244i
\(707\) 12.7737 + 12.7737i 0.480404 + 0.480404i
\(708\) −4.48855 + 15.2959i −0.168690 + 0.574854i
\(709\) 36.8453 36.8453i 1.38376 1.38376i 0.545915 0.837840i \(-0.316182\pi\)
0.837840 0.545915i \(-0.183818\pi\)
\(710\) 16.9572 + 2.43666i 0.636394 + 0.0914464i
\(711\) 15.3239i 0.574693i
\(712\) −36.8305 + 13.7474i −1.38028 + 0.515204i
\(713\) 60.2922i 2.25796i
\(714\) −0.137558 + 0.957292i −0.00514797 + 0.0358258i
\(715\) −16.8952 + 16.8952i −0.631845 + 0.631845i
\(716\) −25.8370 + 14.1136i −0.965575 + 0.527449i
\(717\) 2.64334 + 2.64334i 0.0987175 + 0.0987175i
\(718\) −14.4254 19.2668i −0.538351 0.719030i
\(719\) −26.8739 −1.00223 −0.501114 0.865382i \(-0.667076\pi\)
−0.501114 + 0.865382i \(0.667076\pi\)
\(720\) −0.851542 3.90831i −0.0317351 0.145654i
\(721\) 71.8599 2.67620
\(722\) −15.6164 20.8576i −0.581184 0.776238i
\(723\) −6.60638 6.60638i −0.245694 0.245694i
\(724\) 20.9887 + 38.4229i 0.780038 + 1.42798i
\(725\) −1.78072 + 1.78072i −0.0661341 + 0.0661341i
\(726\) −1.27132 + 8.84737i −0.0471831 + 0.328357i
\(727\) 9.81023i 0.363841i 0.983313 + 0.181921i \(0.0582314\pi\)
−0.983313 + 0.181921i \(0.941769\pi\)
\(728\) −63.1169 28.8058i −2.33927 1.06761i
\(729\) 1.00000i 0.0370370i
\(730\) 0.535963 + 0.0770151i 0.0198369 + 0.00285046i
\(731\) −0.0409325 + 0.0409325i −0.00151394 + 0.00151394i
\(732\) −12.1819 3.57477i −0.450257 0.132127i
\(733\) −1.66941 1.66941i −0.0616610 0.0616610i 0.675604 0.737265i \(-0.263883\pi\)
−0.737265 + 0.675604i \(0.763883\pi\)
\(734\) 29.0986 21.7867i 1.07405 0.804160i
\(735\) −11.2545 −0.415130
\(736\) 3.41157 + 47.4270i 0.125752 + 1.74818i
\(737\) −0.772055 −0.0284390
\(738\) 4.49014 3.36185i 0.165284 0.123751i
\(739\) 36.2208 + 36.2208i 1.33240 + 1.33240i 0.903214 + 0.429191i \(0.141201\pi\)
0.429191 + 0.903214i \(0.358799\pi\)
\(740\) 1.81627 + 0.532982i 0.0667675 + 0.0195928i
\(741\) 24.8349 24.8349i 0.912334 0.912334i
\(742\) −24.3777 3.50294i −0.894932 0.128597i
\(743\) 32.7601i 1.20185i −0.799305 0.600926i \(-0.794799\pi\)
0.799305 0.600926i \(-0.205201\pi\)
\(744\) −8.42332 + 18.4565i −0.308814 + 0.676648i
\(745\) 14.0900i 0.516217i
\(746\) 4.18993 29.1586i 0.153404 1.06757i
\(747\) 5.54562 5.54562i 0.202903 0.202903i
\(748\) −0.638677 1.16919i −0.0233523 0.0427500i
\(749\) −7.02606 7.02606i −0.256727 0.256727i
\(750\) 0.847599 + 1.13207i 0.0309500 + 0.0413372i
\(751\) 8.98910 0.328017 0.164008 0.986459i \(-0.447558\pi\)
0.164008 + 0.986459i \(0.447558\pi\)
\(752\) −0.253324 0.162684i −0.00923777 0.00593248i
\(753\) −13.1688 −0.479897
\(754\) −12.2547 16.3675i −0.446288 0.596069i
\(755\) 2.84174 + 2.84174i 0.103421 + 0.103421i
\(756\) 7.49916 4.09644i 0.272742 0.148986i
\(757\) 27.4805 27.4805i 0.998796 0.998796i −0.00120342 0.999999i \(-0.500383\pi\)
0.999999 + 0.00120342i \(0.000383062\pi\)
\(758\) −2.84871 + 19.8248i −0.103470 + 0.720068i
\(759\) 34.9823i 1.26978i
\(760\) 6.05077 + 16.2106i 0.219485 + 0.588019i
\(761\) 1.80961i 0.0655984i 0.999462 + 0.0327992i \(0.0104422\pi\)
−0.999462 + 0.0327992i \(0.989558\pi\)
\(762\) −2.75319 0.395618i −0.0997374 0.0143317i
\(763\) 19.9537 19.9537i 0.722373 0.722373i
\(764\) 2.67579 9.11842i 0.0968065 0.329893i
\(765\) 0.113179 + 0.113179i 0.00409201 + 0.00409201i
\(766\) 31.9055 23.8882i 1.15279 0.863117i
\(767\) 45.7596 1.65228
\(768\) −5.58160 + 14.9949i −0.201409 + 0.541080i
\(769\) 41.3952 1.49275 0.746374 0.665527i \(-0.231793\pi\)
0.746374 + 0.665527i \(0.231793\pi\)
\(770\) 20.1296 15.0714i 0.725421 0.543136i
\(771\) 6.14138 + 6.14138i 0.221176 + 0.221176i
\(772\) −6.64040 + 22.6288i −0.238993 + 0.814430i
\(773\) 20.2439 20.2439i 0.728122 0.728122i −0.242123 0.970246i \(-0.577844\pi\)
0.970246 + 0.242123i \(0.0778438\pi\)
\(774\) 0.506266 + 0.0727477i 0.0181974 + 0.00261486i
\(775\) 7.17282i 0.257655i
\(776\) 10.7809 + 28.8831i 0.387012 + 1.03684i
\(777\) 4.04365i 0.145065i
\(778\) 3.17326 22.0834i 0.113767 0.791727i
\(779\) −17.1573 + 17.1573i −0.614725 + 0.614725i
\(780\) −10.0769 + 5.50456i −0.360811 + 0.197095i
\(781\) −35.6484 35.6484i −1.27560 1.27560i
\(782\) −1.14036 1.52309i −0.0407793 0.0544655i
\(783\) 2.51831 0.0899971
\(784\) 37.8797 + 24.3263i 1.35285 + 0.868795i
\(785\) −12.9324 −0.461577
\(786\) 1.02236 + 1.36549i 0.0364665 + 0.0487053i
\(787\) −36.5446 36.5446i −1.30267 1.30267i −0.926583 0.376091i \(-0.877268\pi\)
−0.376091 0.926583i \(-0.622732\pi\)
\(788\) −6.18634 11.3250i −0.220379 0.403437i
\(789\) −3.66968 + 3.66968i −0.130644 + 0.130644i
\(790\) −3.08239 + 21.4510i −0.109667 + 0.763193i
\(791\) 21.3854i 0.760379i
\(792\) −4.88732 + 10.7087i −0.173663 + 0.380517i
\(793\) 36.4438i 1.29416i
\(794\) −5.90368 0.848328i −0.209514 0.0301060i
\(795\) −2.88214 + 2.88214i −0.102219 + 0.102219i
\(796\) −6.91371 2.02882i −0.245050 0.0719095i
\(797\) −12.7215 12.7215i −0.450619 0.450619i 0.444941 0.895560i \(-0.353225\pi\)
−0.895560 + 0.444941i \(0.853225\pi\)
\(798\) −29.5893 + 22.1541i −1.04745 + 0.784245i
\(799\) 0.0120470 0.000426193
\(800\) −0.405867 5.64228i −0.0143496 0.199485i
\(801\) −13.8991 −0.491100
\(802\) 18.1013 13.5528i 0.639181 0.478566i
\(803\) −1.12673 1.12673i −0.0397615 0.0397615i
\(804\) −0.356011 0.104471i −0.0125555 0.00368440i
\(805\) 25.3946 25.3946i 0.895042 0.895042i
\(806\) 57.6458 + 8.28339i 2.03049 + 0.291770i
\(807\) 11.3056i 0.397975i
\(808\) −10.8794 4.96523i −0.382736 0.174676i
\(809\) 5.24547i 0.184421i 0.995740 + 0.0922105i \(0.0293933\pi\)
−0.995740 + 0.0922105i \(0.970607\pi\)
\(810\) 0.201149 1.39984i 0.00706765 0.0491852i
\(811\) −2.66407 + 2.66407i −0.0935481 + 0.0935481i −0.752332 0.658784i \(-0.771071\pi\)
0.658784 + 0.752332i \(0.271071\pi\)
\(812\) 10.3161 + 18.8852i 0.362025 + 0.662741i
\(813\) −13.3178 13.3178i −0.467075 0.467075i
\(814\) −3.33854 4.45900i −0.117016 0.156288i
\(815\) −0.489452 −0.0171447
\(816\) −0.136298 0.625563i −0.00477137 0.0218991i
\(817\) −2.21248 −0.0774047
\(818\) 23.3183 + 31.1443i 0.815305 + 1.08893i
\(819\) −17.3449 17.3449i −0.606079 0.606079i
\(820\) 6.96169 3.80285i 0.243113 0.132801i
\(821\) 1.11276 1.11276i 0.0388357 0.0388357i −0.687422 0.726258i \(-0.741258\pi\)
0.726258 + 0.687422i \(0.241258\pi\)
\(822\) 0.828779 5.76764i 0.0289070 0.201170i
\(823\) 11.7558i 0.409781i 0.978785 + 0.204891i \(0.0656838\pi\)
−0.978785 + 0.204891i \(0.934316\pi\)
\(824\) −44.5679 + 16.6355i −1.55260 + 0.579524i
\(825\) 4.16177i 0.144894i
\(826\) −47.6698 6.84990i −1.65865 0.238339i
\(827\) −30.1964 + 30.1964i −1.05003 + 1.05003i −0.0513511 + 0.998681i \(0.516353\pi\)
−0.998681 + 0.0513511i \(0.983647\pi\)
\(828\) −4.73364 + 16.1311i −0.164505 + 0.560594i
\(829\) 0.0724462 + 0.0724462i 0.00251616 + 0.00251616i 0.708364 0.705848i \(-0.249434\pi\)
−0.705848 + 0.708364i \(0.749434\pi\)
\(830\) 8.87844 6.64746i 0.308175 0.230737i
\(831\) 5.25973 0.182458
\(832\) 45.8140 + 3.25404i 1.58831 + 0.112814i
\(833\) −1.80140 −0.0624148
\(834\) −9.18797 + 6.87920i −0.318153 + 0.238207i
\(835\) 7.76986 + 7.76986i 0.268887 + 0.268887i
\(836\) 14.3377 48.8593i 0.495879 1.68983i
\(837\) −5.07195 + 5.07195i −0.175312 + 0.175312i
\(838\) −3.87849 0.557318i −0.133980 0.0192522i
\(839\) 7.91971i 0.273419i −0.990611 0.136709i \(-0.956347\pi\)
0.990611 0.136709i \(-0.0436527\pi\)
\(840\) 11.3216 4.22590i 0.390632 0.145807i
\(841\) 22.6581i 0.781314i
\(842\) −1.77435 + 12.3480i −0.0611480 + 0.425541i
\(843\) 7.79397 7.79397i 0.268439 0.268439i
\(844\) −2.42114 + 1.32256i −0.0833391 + 0.0455243i
\(845\) 14.1146 + 14.1146i 0.485558 + 0.485558i
\(846\) −0.0637953 0.0852060i −0.00219333 0.00292944i
\(847\) −27.0037 −0.927857
\(848\) 15.9301 3.47085i 0.547042 0.119189i
\(849\) 14.8790 0.510646
\(850\) 0.135667 + 0.181198i 0.00465332 + 0.00621505i
\(851\) −5.62528 5.62528i −0.192832 0.192832i
\(852\) −11.6145 21.2620i −0.397905 0.728425i
\(853\) −14.1305 + 14.1305i −0.483817 + 0.483817i −0.906348 0.422531i \(-0.861142\pi\)
0.422531 + 0.906348i \(0.361142\pi\)
\(854\) 5.45540 37.9652i 0.186680 1.29914i
\(855\) 6.11754i 0.209216i
\(856\) 5.98413 + 2.73108i 0.204533 + 0.0933465i
\(857\) 4.80762i 0.164225i 0.996623 + 0.0821126i \(0.0261667\pi\)
−0.996623 + 0.0821126i \(0.973833\pi\)
\(858\) 33.4469 + 4.80613i 1.14186 + 0.164079i
\(859\) −34.8123 + 34.8123i −1.18778 + 1.18778i −0.210101 + 0.977680i \(0.567379\pi\)
−0.977680 + 0.210101i \(0.932621\pi\)
\(860\) 0.694056 + 0.203670i 0.0236671 + 0.00694508i
\(861\) 11.9828 + 11.9828i 0.408373 + 0.408373i
\(862\) −6.65859 + 4.98541i −0.226793 + 0.169804i
\(863\) −51.5605 −1.75514 −0.877570 0.479449i \(-0.840837\pi\)
−0.877570 + 0.479449i \(0.840837\pi\)
\(864\) −3.70270 + 4.27668i −0.125968 + 0.145496i
\(865\) 3.82694 0.130120
\(866\) 7.22066 5.40624i 0.245368 0.183712i
\(867\) −12.0027 12.0027i −0.407633 0.407633i
\(868\) −58.8123 17.2584i −1.99622 0.585788i
\(869\) 45.0955 45.0955i 1.52976 1.52976i
\(870\) 3.52522 + 0.506556i 0.119516 + 0.0171738i
\(871\) 1.06505i 0.0360880i
\(872\) −7.75616 + 16.9947i −0.262657 + 0.575512i
\(873\) 10.8999i 0.368905i
\(874\) 10.3435 71.9822i 0.349872 2.43483i
\(875\) −3.02114 + 3.02114i −0.102133 + 0.102133i
\(876\) −0.367096 0.672024i −0.0124030 0.0227056i
\(877\) −12.4082 12.4082i −0.418994 0.418994i 0.465863 0.884857i \(-0.345744\pi\)
−0.884857 + 0.465863i \(0.845744\pi\)
\(878\) 31.6069 + 42.2146i 1.06668 + 1.42467i
\(879\) 22.0112 0.742419
\(880\) −8.99549 + 14.0073i −0.303238 + 0.472188i
\(881\) −45.7147 −1.54017 −0.770084 0.637942i \(-0.779786\pi\)
−0.770084 + 0.637942i \(0.779786\pi\)
\(882\) 9.53935 + 12.7409i 0.321207 + 0.429009i
\(883\) −8.68322 8.68322i −0.292213 0.292213i 0.545741 0.837954i \(-0.316248\pi\)
−0.837954 + 0.545741i \(0.816248\pi\)
\(884\) −1.61291 + 0.881058i −0.0542480 + 0.0296332i
\(885\) −5.63594 + 5.63594i −0.189450 + 0.189450i
\(886\) −8.08565 + 56.2697i −0.271643 + 1.89042i
\(887\) 5.87579i 0.197290i −0.995123 0.0986449i \(-0.968549\pi\)
0.995123 0.0986449i \(-0.0314508\pi\)
\(888\) −0.936099 2.50790i −0.0314134 0.0841595i
\(889\) 8.40319i 0.281834i
\(890\) −19.4564 2.79578i −0.652180 0.0937148i
\(891\) −2.94281 + 2.94281i −0.0985879 + 0.0985879i
\(892\) 2.62621 8.94948i 0.0879321 0.299651i
\(893\) 0.325582 + 0.325582i 0.0108952 + 0.0108952i
\(894\) 15.9508 11.9427i 0.533474 0.399422i
\(895\) −14.7203 −0.492044
\(896\) −47.2394 10.2479i −1.57816 0.342359i
\(897\) 48.2583 1.61130
\(898\) −13.5461 + 10.1422i −0.452039 + 0.338450i
\(899\) −12.7727 12.7727i −0.425995 0.425995i
\(900\) 0.563151 1.91908i 0.0187717 0.0639693i
\(901\) −0.461314 + 0.461314i −0.0153686 + 0.0153686i
\(902\) −23.1069 3.32034i −0.769377 0.110555i
\(903\) 1.54521i 0.0514213i
\(904\) 4.95070 + 13.2634i 0.164658 + 0.441133i
\(905\) 21.8909i 0.727678i
\(906\) 0.808382 5.62569i 0.0268567 0.186901i
\(907\) 0.656960 0.656960i 0.0218140 0.0218140i −0.696116 0.717930i \(-0.745090\pi\)
0.717930 + 0.696116i \(0.245090\pi\)
\(908\) −4.01379 + 2.19255i −0.133202 + 0.0727622i
\(909\) −2.98972 2.98972i −0.0991629 0.0991629i
\(910\) −20.7911 27.7689i −0.689217 0.920530i
\(911\) −3.71828 −0.123192 −0.0615960 0.998101i \(-0.519619\pi\)
−0.0615960 + 0.998101i \(0.519619\pi\)
\(912\) 13.2228 20.5900i 0.437851 0.681801i
\(913\) −32.6394 −1.08021
\(914\) −28.0135 37.4153i −0.926605 1.23759i
\(915\) −4.48857 4.48857i −0.148388 0.148388i
\(916\) −12.4051 22.7095i −0.409877 0.750341i
\(917\) −3.64406 + 3.64406i −0.120338 + 0.120338i
\(918\) 0.0321958 0.224057i 0.00106262 0.00739499i
\(919\) 33.0548i 1.09038i 0.838313 + 0.545189i \(0.183542\pi\)
−0.838313 + 0.545189i \(0.816458\pi\)
\(920\) −9.87107 + 21.6287i −0.325440 + 0.713077i
\(921\) 27.8311i 0.917064i
\(922\) 41.0270 + 5.89535i 1.35115 + 0.194153i
\(923\) −49.1772 + 49.1772i −1.61869 + 1.61869i
\(924\) −34.1237 10.0135i −1.12259 0.329421i
\(925\) 0.669226 + 0.669226i 0.0220040 + 0.0220040i
\(926\) −16.1160 + 12.0664i −0.529605 + 0.396525i
\(927\) −16.8190 −0.552410
\(928\) −10.7700 9.32455i −0.353543 0.306093i
\(929\) −17.6732 −0.579839 −0.289919 0.957051i \(-0.593629\pi\)
−0.289919 + 0.957051i \(0.593629\pi\)
\(930\) −8.12011 + 6.07968i −0.266269 + 0.199360i
\(931\) −48.6844 48.6844i −1.59557 1.59557i
\(932\) −19.7669 5.80057i −0.647486 0.190004i
\(933\) −8.40905 + 8.40905i −0.275300 + 0.275300i
\(934\) −37.2159 5.34773i −1.21774 0.174983i
\(935\) 0.666131i 0.0217848i
\(936\) 14.7727 + 6.74208i 0.482861 + 0.220372i
\(937\) 25.9902i 0.849061i 0.905414 + 0.424531i \(0.139561\pi\)
−0.905414 + 0.424531i \(0.860439\pi\)
\(938\) 0.159431 1.10952i 0.00520562 0.0362270i
\(939\) 6.79666 6.79666i 0.221801 0.221801i
\(940\) −0.0721638 0.132107i −0.00235372 0.00430884i
\(941\) 29.0860 + 29.0860i 0.948176 + 0.948176i 0.998722 0.0505455i \(-0.0160960\pi\)
−0.0505455 + 0.998722i \(0.516096\pi\)
\(942\) 10.9615 + 14.6403i 0.357145 + 0.477008i
\(943\) −33.3395 −1.08568
\(944\) 31.1509 6.78715i 1.01387 0.220903i
\(945\) 4.27253 0.138986
\(946\) −1.27576 1.70393i −0.0414786 0.0553995i
\(947\) 30.8896 + 30.8896i 1.00378 + 1.00378i 0.999993 + 0.00378509i \(0.00120483\pi\)
0.00378509 + 0.999993i \(0.498795\pi\)
\(948\) 26.8966 14.6924i 0.873561 0.477186i
\(949\) −1.55433 + 1.55433i −0.0504558 + 0.0504558i
\(950\) −1.23054 + 8.56355i −0.0399239 + 0.277838i
\(951\) 11.4558i 0.371480i
\(952\) 1.81213 0.676397i 0.0587314 0.0219221i
\(953\) 51.5794i 1.67082i −0.549626 0.835411i \(-0.685230\pi\)
0.549626 0.835411i \(-0.314770\pi\)
\(954\) 5.70567 + 0.819874i 0.184728 + 0.0265444i
\(955\) 3.35979 3.35979i 0.108720 0.108720i
\(956\) 2.10520 7.17400i 0.0680870 0.232024i
\(957\) −7.41092 7.41092i −0.239561 0.239561i
\(958\) 30.2463 22.6460i 0.977215 0.731659i
\(959\) 17.6038 0.568457
\(960\) −6.04342 + 5.24186i −0.195051 + 0.169180i
\(961\) 20.4493 0.659656
\(962\) −6.15121 + 4.60553i −0.198323 + 0.148488i
\(963\) 1.64447 + 1.64447i 0.0529924 + 0.0529924i
\(964\) −5.26142 + 17.9296i −0.169459 + 0.577474i
\(965\) −8.33786 + 8.33786i −0.268405 + 0.268405i
\(966\) −50.2728 7.22394i −1.61750 0.232426i
\(967\) 5.55245i 0.178555i −0.996007 0.0892774i \(-0.971544\pi\)
0.996007 0.0892774i \(-0.0284558\pi\)
\(968\) 16.7478 6.25131i 0.538296 0.200925i
\(969\) 0.979172i 0.0314555i
\(970\) −2.19250 + 15.2580i −0.0703969 + 0.489906i
\(971\) −30.5095 + 30.5095i −0.979098 + 0.979098i −0.999786 0.0206884i \(-0.993414\pi\)
0.0206884 + 0.999786i \(0.493414\pi\)
\(972\) −1.75520 + 0.958786i −0.0562981 + 0.0307531i
\(973\) −24.5199 24.5199i −0.786071 0.786071i
\(974\) −22.9531 30.6564i −0.735463 0.982296i
\(975\) −5.74117 −0.183865
\(976\) 5.40542 + 24.8092i 0.173023 + 0.794122i
\(977\) 31.8649 1.01945 0.509723 0.860338i \(-0.329748\pi\)
0.509723 + 0.860338i \(0.329748\pi\)
\(978\) 0.414859 + 0.554092i 0.0132657 + 0.0177179i
\(979\) 40.9024 + 40.9024i 1.30725 + 1.30725i
\(980\) 10.7907 + 19.7540i 0.344696 + 0.631018i
\(981\) −4.67023 + 4.67023i −0.149109 + 0.149109i
\(982\) −0.431070 + 2.99990i −0.0137560 + 0.0957308i
\(983\) 24.2289i 0.772782i −0.922335 0.386391i \(-0.873721\pi\)
0.922335 0.386391i \(-0.126279\pi\)
\(984\) −10.2058 4.65780i −0.325349 0.148485i
\(985\) 6.45226i 0.205586i
\(986\) 0.564246 + 0.0810791i 0.0179693 + 0.00258209i
\(987\) 0.227388 0.227388i 0.00723786 0.00723786i
\(988\) −67.4016 19.7789i −2.14433 0.629251i
\(989\) −2.14960 2.14960i −0.0683533 0.0683533i
\(990\) −4.71140 + 3.52751i −0.149738 + 0.112112i
\(991\) 38.9268 1.23655 0.618276 0.785961i \(-0.287832\pi\)
0.618276 + 0.785961i \(0.287832\pi\)
\(992\) 40.4710 2.91121i 1.28496 0.0924311i
\(993\) −18.8468 −0.598085
\(994\) 58.5916 43.8686i 1.85841 1.39143i
\(995\) −2.54744 2.54744i −0.0807592 0.0807592i
\(996\) −15.0507 4.41661i −0.476901 0.139946i
\(997\) −8.00046 + 8.00046i −0.253377 + 0.253377i −0.822354 0.568977i \(-0.807340\pi\)
0.568977 + 0.822354i \(0.307340\pi\)
\(998\) −14.4716 2.07949i −0.458090 0.0658251i
\(999\) 0.946429i 0.0299437i
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 240.2.s.c.61.2 20
3.2 odd 2 720.2.t.d.541.9 20
4.3 odd 2 960.2.s.c.721.5 20
8.3 odd 2 1920.2.s.f.1441.10 20
8.5 even 2 1920.2.s.e.1441.1 20
12.11 even 2 2880.2.t.d.721.5 20
16.3 odd 4 1920.2.s.f.481.6 20
16.5 even 4 inner 240.2.s.c.181.2 yes 20
16.11 odd 4 960.2.s.c.241.1 20
16.13 even 4 1920.2.s.e.481.5 20
48.5 odd 4 720.2.t.d.181.9 20
48.11 even 4 2880.2.t.d.2161.1 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
240.2.s.c.61.2 20 1.1 even 1 trivial
240.2.s.c.181.2 yes 20 16.5 even 4 inner
720.2.t.d.181.9 20 48.5 odd 4
720.2.t.d.541.9 20 3.2 odd 2
960.2.s.c.241.1 20 16.11 odd 4
960.2.s.c.721.5 20 4.3 odd 2
1920.2.s.e.481.5 20 16.13 even 4
1920.2.s.e.1441.1 20 8.5 even 2
1920.2.s.f.481.6 20 16.3 odd 4
1920.2.s.f.1441.10 20 8.3 odd 2
2880.2.t.d.721.5 20 12.11 even 2
2880.2.t.d.2161.1 20 48.11 even 4