Properties

Label 360.2.bm.a.11.20
Level $360$
Weight $2$
Character 360.11
Analytic conductor $2.875$
Analytic rank $0$
Dimension $48$
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] = [360,2,Mod(11,360)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(360, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 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("360.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.bm (of order \(6\), 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: \(2.87461447277\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 11.20
Character \(\chi\) \(=\) 360.11
Dual form 360.2.bm.a.131.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.20329 - 0.743030i) q^{2} +(1.46420 + 0.925262i) q^{3} +(0.895814 - 1.78816i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.44936 + 0.0254133i) q^{6} +(-0.947055 - 0.546782i) q^{7} +(-0.250732 - 2.81729i) q^{8} +(1.28778 + 2.70954i) q^{9} +O(q^{10})\) \(q+(1.20329 - 0.743030i) q^{2} +(1.46420 + 0.925262i) q^{3} +(0.895814 - 1.78816i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.44936 + 0.0254133i) q^{6} +(-0.947055 - 0.546782i) q^{7} +(-0.250732 - 2.81729i) q^{8} +(1.28778 + 2.70954i) q^{9} +(-1.24513 - 0.670565i) q^{10} +(2.31540 + 1.33679i) q^{11} +(2.96617 - 1.78937i) q^{12} +(2.12374 - 1.22614i) q^{13} +(-1.54586 + 0.0457520i) q^{14} +(0.0691995 - 1.73067i) q^{15} +(-2.39503 - 3.20372i) q^{16} -0.124711i q^{17} +(3.56284 + 2.30351i) q^{18} -5.84133 q^{19} +(-1.99650 + 0.118282i) q^{20} +(-0.880763 - 1.67687i) q^{21} +(3.77937 - 0.111856i) q^{22} +(1.21152 + 2.09842i) q^{23} +(2.23961 - 4.35708i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.64441 - 3.05340i) q^{26} +(-0.621470 + 5.15885i) q^{27} +(-1.82612 + 1.20367i) q^{28} +(-4.29490 + 7.43898i) q^{29} +(-1.20267 - 2.13391i) q^{30} +(-2.54447 + 1.46905i) q^{31} +(-5.26238 - 2.07542i) q^{32} +(2.15332 + 4.09969i) q^{33} +(-0.0926640 - 0.150064i) q^{34} +1.09356i q^{35} +(5.99871 + 0.124492i) q^{36} -2.42896i q^{37} +(-7.02882 + 4.34028i) q^{38} +(4.24408 + 0.169696i) q^{39} +(-2.31448 + 1.62579i) q^{40} +(7.57229 - 4.37186i) q^{41} +(-2.30578 - 1.36333i) q^{42} +(-2.14293 + 3.71166i) q^{43} +(4.46457 - 2.94278i) q^{44} +(1.70264 - 2.47002i) q^{45} +(3.01700 + 1.62481i) q^{46} +(-3.32459 + 5.75836i) q^{47} +(-0.542535 - 6.90693i) q^{48} +(-2.90206 - 5.02651i) q^{49} +(0.0418375 + 1.41359i) q^{50} +(0.115390 - 0.182602i) q^{51} +(-0.290061 - 4.89597i) q^{52} -2.14097 q^{53} +(3.08537 + 6.66937i) q^{54} -2.67359i q^{55} +(-1.30299 + 2.80523i) q^{56} +(-8.55289 - 5.40476i) q^{57} +(0.359375 + 12.1425i) q^{58} +(-2.34413 + 1.35338i) q^{59} +(-3.03272 - 1.67410i) q^{60} +(-9.69518 - 5.59752i) q^{61} +(-1.97018 + 3.65830i) q^{62} +(0.261933 - 3.27022i) q^{63} +(-7.87427 + 1.41277i) q^{64} +(-2.12374 - 1.22614i) q^{65} +(5.63726 + 3.33313i) q^{66} +(-0.707180 - 1.22487i) q^{67} +(-0.223003 - 0.111718i) q^{68} +(-0.167673 + 4.19348i) q^{69} +(0.812551 + 1.31588i) q^{70} +11.2346 q^{71} +(7.31069 - 4.30742i) q^{72} +5.35400 q^{73} +(-1.80479 - 2.92274i) q^{74} +(-1.53340 + 0.805405i) q^{75} +(-5.23275 + 10.4452i) q^{76} +(-1.46187 - 2.53203i) q^{77} +(5.23295 - 2.94928i) q^{78} +(-2.07178 - 1.19614i) q^{79} +(-1.57698 + 3.67602i) q^{80} +(-5.68325 + 6.97859i) q^{81} +(5.86323 - 10.8871i) q^{82} +(11.2212 + 6.47858i) q^{83} +(-3.78752 + 0.0727777i) q^{84} +(-0.108003 + 0.0623555i) q^{85} +(0.179309 + 6.05846i) q^{86} +(-13.1716 + 6.91827i) q^{87} +(3.18560 - 6.85832i) q^{88} -13.3875i q^{89} +(0.213476 - 4.23727i) q^{90} -2.68172 q^{91} +(4.83760 - 0.286603i) q^{92} +(-5.08487 - 0.203315i) q^{93} +(0.278185 + 9.39924i) q^{94} +(2.92067 + 5.05874i) q^{95} +(-5.78488 - 7.90792i) q^{96} +(7.51249 - 13.0120i) q^{97} +(-7.22687 - 3.89204i) q^{98} +(-0.640385 + 7.99516i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 24 q^{5} + 7 q^{6} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 24 q^{5} + 7 q^{6} - 6 q^{8} - 15 q^{12} + 15 q^{14} + 12 q^{16} - 11 q^{18} - 4 q^{21} + 21 q^{22} - 24 q^{24} - 24 q^{25} + 12 q^{27} - 14 q^{30} - 8 q^{33} + 33 q^{34} - 23 q^{36} - 33 q^{38} + 16 q^{39} - 6 q^{40} + 12 q^{41} - 53 q^{42} - 24 q^{44} - 6 q^{46} + 12 q^{47} + 45 q^{48} + 24 q^{49} - 20 q^{51} - 36 q^{52} - 36 q^{54} + 21 q^{56} + 4 q^{57} - 51 q^{58} - 36 q^{59} + 15 q^{60} + 12 q^{61} + 42 q^{62} + 56 q^{63} - 12 q^{64} + 24 q^{66} + 57 q^{68} - 40 q^{69} - 15 q^{70} + 46 q^{72} + 30 q^{74} + 57 q^{76} + 78 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} - 31 q^{84} + 27 q^{86} + 36 q^{87} + 57 q^{88} + 4 q^{90} - 51 q^{92} + 57 q^{94} - 119 q^{96} + 42 q^{98} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(217\) \(271\) \(281\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.20329 0.743030i 0.850855 0.525401i
\(3\) 1.46420 + 0.925262i 0.845358 + 0.534201i
\(4\) 0.895814 1.78816i 0.447907 0.894080i
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 2.44936 + 0.0254133i 0.999946 + 0.0103749i
\(7\) −0.947055 0.546782i −0.357953 0.206664i 0.310229 0.950662i \(-0.399594\pi\)
−0.668182 + 0.743997i \(0.732927\pi\)
\(8\) −0.250732 2.81729i −0.0886471 0.996063i
\(9\) 1.28778 + 2.70954i 0.429260 + 0.903181i
\(10\) −1.24513 0.670565i −0.393744 0.212051i
\(11\) 2.31540 + 1.33679i 0.698118 + 0.403059i 0.806646 0.591035i \(-0.201280\pi\)
−0.108528 + 0.994093i \(0.534614\pi\)
\(12\) 2.96617 1.78937i 0.856260 0.516545i
\(13\) 2.12374 1.22614i 0.589018 0.340070i −0.175691 0.984445i \(-0.556216\pi\)
0.764709 + 0.644376i \(0.222883\pi\)
\(14\) −1.54586 + 0.0457520i −0.413148 + 0.0122277i
\(15\) 0.0691995 1.73067i 0.0178672 0.446857i
\(16\) −2.39503 3.20372i −0.598759 0.800930i
\(17\) 0.124711i 0.0302469i −0.999886 0.0151234i \(-0.995186\pi\)
0.999886 0.0151234i \(-0.00481412\pi\)
\(18\) 3.56284 + 2.30351i 0.839770 + 0.542942i
\(19\) −5.84133 −1.34009 −0.670047 0.742319i \(-0.733726\pi\)
−0.670047 + 0.742319i \(0.733726\pi\)
\(20\) −1.99650 + 0.118282i −0.446431 + 0.0264487i
\(21\) −0.880763 1.67687i −0.192198 0.365924i
\(22\) 3.77937 0.111856i 0.805765 0.0238478i
\(23\) 1.21152 + 2.09842i 0.252620 + 0.437550i 0.964246 0.265008i \(-0.0853745\pi\)
−0.711627 + 0.702558i \(0.752041\pi\)
\(24\) 2.23961 4.35708i 0.457159 0.889385i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 1.64441 3.05340i 0.322496 0.598821i
\(27\) −0.621470 + 5.15885i −0.119602 + 0.992822i
\(28\) −1.82612 + 1.20367i −0.345104 + 0.227472i
\(29\) −4.29490 + 7.43898i −0.797542 + 1.38138i 0.123670 + 0.992323i \(0.460534\pi\)
−0.921212 + 0.389060i \(0.872800\pi\)
\(30\) −1.20267 2.13391i −0.219577 0.389597i
\(31\) −2.54447 + 1.46905i −0.457000 + 0.263849i −0.710782 0.703413i \(-0.751659\pi\)
0.253782 + 0.967261i \(0.418325\pi\)
\(32\) −5.26238 2.07542i −0.930266 0.366886i
\(33\) 2.15332 + 4.09969i 0.374845 + 0.713664i
\(34\) −0.0926640 0.150064i −0.0158917 0.0257357i
\(35\) 1.09356i 0.184846i
\(36\) 5.99871 + 0.124492i 0.999785 + 0.0207487i
\(37\) 2.42896i 0.399318i −0.979865 0.199659i \(-0.936017\pi\)
0.979865 0.199659i \(-0.0639835\pi\)
\(38\) −7.02882 + 4.34028i −1.14022 + 0.704087i
\(39\) 4.24408 + 0.169696i 0.679597 + 0.0271732i
\(40\) −2.31448 + 1.62579i −0.365951 + 0.257059i
\(41\) 7.57229 4.37186i 1.18259 0.682770i 0.225980 0.974132i \(-0.427442\pi\)
0.956613 + 0.291362i \(0.0941084\pi\)
\(42\) −2.30578 1.36333i −0.355790 0.210367i
\(43\) −2.14293 + 3.71166i −0.326793 + 0.566023i −0.981874 0.189537i \(-0.939301\pi\)
0.655080 + 0.755559i \(0.272635\pi\)
\(44\) 4.46457 2.94278i 0.673059 0.443641i
\(45\) 1.70264 2.47002i 0.253815 0.368209i
\(46\) 3.01700 + 1.62481i 0.444832 + 0.239565i
\(47\) −3.32459 + 5.75836i −0.484941 + 0.839942i −0.999850 0.0173022i \(-0.994492\pi\)
0.514909 + 0.857245i \(0.327826\pi\)
\(48\) −0.542535 6.90693i −0.0783082 0.996929i
\(49\) −2.90206 5.02651i −0.414580 0.718073i
\(50\) 0.0418375 + 1.41359i 0.00591671 + 0.199912i
\(51\) 0.115390 0.182602i 0.0161579 0.0255694i
\(52\) −0.290061 4.89597i −0.0402243 0.678949i
\(53\) −2.14097 −0.294084 −0.147042 0.989130i \(-0.546975\pi\)
−0.147042 + 0.989130i \(0.546975\pi\)
\(54\) 3.08537 + 6.66937i 0.419866 + 0.907586i
\(55\) 2.67359i 0.360507i
\(56\) −1.30299 + 2.80523i −0.174119 + 0.374864i
\(57\) −8.55289 5.40476i −1.13286 0.715879i
\(58\) 0.359375 + 12.1425i 0.0471883 + 1.59439i
\(59\) −2.34413 + 1.35338i −0.305179 + 0.176195i −0.644767 0.764379i \(-0.723046\pi\)
0.339588 + 0.940574i \(0.389712\pi\)
\(60\) −3.03272 1.67410i −0.391523 0.216125i
\(61\) −9.69518 5.59752i −1.24134 0.716688i −0.271974 0.962305i \(-0.587676\pi\)
−0.969367 + 0.245616i \(0.921010\pi\)
\(62\) −1.97018 + 3.65830i −0.250214 + 0.464605i
\(63\) 0.261933 3.27022i 0.0330005 0.412009i
\(64\) −7.87427 + 1.41277i −0.984283 + 0.176596i
\(65\) −2.12374 1.22614i −0.263417 0.152084i
\(66\) 5.63726 + 3.33313i 0.693899 + 0.410280i
\(67\) −0.707180 1.22487i −0.0863958 0.149642i 0.819589 0.572951i \(-0.194202\pi\)
−0.905985 + 0.423309i \(0.860868\pi\)
\(68\) −0.223003 0.111718i −0.0270431 0.0135478i
\(69\) −0.167673 + 4.19348i −0.0201855 + 0.504836i
\(70\) 0.812551 + 1.31588i 0.0971184 + 0.157277i
\(71\) 11.2346 1.33330 0.666648 0.745372i \(-0.267728\pi\)
0.666648 + 0.745372i \(0.267728\pi\)
\(72\) 7.31069 4.30742i 0.861573 0.507634i
\(73\) 5.35400 0.626639 0.313319 0.949648i \(-0.398559\pi\)
0.313319 + 0.949648i \(0.398559\pi\)
\(74\) −1.80479 2.92274i −0.209802 0.339762i
\(75\) −1.53340 + 0.805405i −0.177062 + 0.0930002i
\(76\) −5.23275 + 10.4452i −0.600237 + 1.19815i
\(77\) −1.46187 2.53203i −0.166596 0.288552i
\(78\) 5.23295 2.94928i 0.592515 0.333940i
\(79\) −2.07178 1.19614i −0.233093 0.134577i 0.378905 0.925436i \(-0.376301\pi\)
−0.611998 + 0.790859i \(0.709634\pi\)
\(80\) −1.57698 + 3.67602i −0.176312 + 0.410991i
\(81\) −5.68325 + 6.97859i −0.631472 + 0.775398i
\(82\) 5.86323 10.8871i 0.647486 1.20227i
\(83\) 11.2212 + 6.47858i 1.23169 + 0.711116i 0.967382 0.253322i \(-0.0815232\pi\)
0.264308 + 0.964438i \(0.414857\pi\)
\(84\) −3.78752 + 0.0727777i −0.413252 + 0.00794069i
\(85\) −0.108003 + 0.0623555i −0.0117146 + 0.00676341i
\(86\) 0.179309 + 6.05846i 0.0193354 + 0.653300i
\(87\) −13.1716 + 6.91827i −1.41214 + 0.741716i
\(88\) 3.18560 6.85832i 0.339586 0.731100i
\(89\) 13.3875i 1.41907i −0.704671 0.709535i \(-0.748905\pi\)
0.704671 0.709535i \(-0.251095\pi\)
\(90\) 0.213476 4.23727i 0.0225024 0.446647i
\(91\) −2.68172 −0.281121
\(92\) 4.83760 0.286603i 0.504355 0.0298805i
\(93\) −5.08487 0.203315i −0.527276 0.0210828i
\(94\) 0.278185 + 9.39924i 0.0286925 + 0.969457i
\(95\) 2.92067 + 5.05874i 0.299654 + 0.519016i
\(96\) −5.78488 7.90792i −0.590417 0.807099i
\(97\) 7.51249 13.0120i 0.762778 1.32117i −0.178636 0.983915i \(-0.557168\pi\)
0.941413 0.337255i \(-0.109498\pi\)
\(98\) −7.22687 3.89204i −0.730024 0.393155i
\(99\) −0.640385 + 7.99516i −0.0643611 + 0.803544i
\(100\) 1.10069 + 1.66988i 0.110069 + 0.166988i
\(101\) −9.34757 + 16.1905i −0.930117 + 1.61101i −0.147000 + 0.989136i \(0.546962\pi\)
−0.783117 + 0.621874i \(0.786371\pi\)
\(102\) 0.00316931 0.305462i 0.000313809 0.0302452i
\(103\) 13.4232 7.74987i 1.32262 0.763617i 0.338477 0.940975i \(-0.390088\pi\)
0.984147 + 0.177357i \(0.0567549\pi\)
\(104\) −3.98688 5.67575i −0.390946 0.556553i
\(105\) −1.01183 + 1.60120i −0.0987449 + 0.156261i
\(106\) −2.57620 + 1.59080i −0.250223 + 0.154512i
\(107\) 16.6662i 1.61118i 0.592474 + 0.805590i \(0.298151\pi\)
−0.592474 + 0.805590i \(0.701849\pi\)
\(108\) 8.66814 + 5.73266i 0.834092 + 0.551626i
\(109\) 9.56196i 0.915870i −0.888986 0.457935i \(-0.848589\pi\)
0.888986 0.457935i \(-0.151411\pi\)
\(110\) −1.98656 3.21710i −0.189411 0.306739i
\(111\) 2.24742 3.55649i 0.213316 0.337567i
\(112\) 0.516492 + 4.34366i 0.0488039 + 0.410437i
\(113\) 11.1943 6.46306i 1.05307 0.607993i 0.129566 0.991571i \(-0.458641\pi\)
0.923509 + 0.383578i \(0.125308\pi\)
\(114\) −14.3075 0.148447i −1.34002 0.0139034i
\(115\) 1.21152 2.09842i 0.112975 0.195678i
\(116\) 9.45466 + 14.3439i 0.877843 + 1.33180i
\(117\) 6.05718 + 4.17536i 0.559986 + 0.386012i
\(118\) −1.81506 + 3.37026i −0.167090 + 0.310258i
\(119\) −0.0681898 + 0.118108i −0.00625095 + 0.0108270i
\(120\) −4.89315 + 0.238978i −0.446681 + 0.0218156i
\(121\) −1.92596 3.33586i −0.175087 0.303260i
\(122\) −15.8252 + 0.468372i −1.43275 + 0.0424044i
\(123\) 15.1325 + 0.605061i 1.36445 + 0.0545565i
\(124\) 0.347525 + 5.86591i 0.0312087 + 0.526774i
\(125\) 1.00000 0.0894427
\(126\) −2.11469 4.12965i −0.188391 0.367898i
\(127\) 15.7987i 1.40191i 0.713205 + 0.700956i \(0.247243\pi\)
−0.713205 + 0.700956i \(0.752757\pi\)
\(128\) −8.42530 + 7.55078i −0.744698 + 0.667401i
\(129\) −6.57194 + 3.45185i −0.578627 + 0.303918i
\(130\) −3.46653 + 0.102597i −0.304035 + 0.00899836i
\(131\) −4.77387 + 2.75619i −0.417095 + 0.240810i −0.693834 0.720135i \(-0.744080\pi\)
0.276739 + 0.960945i \(0.410746\pi\)
\(132\) 9.25987 0.177930i 0.805969 0.0154868i
\(133\) 5.53206 + 3.19394i 0.479690 + 0.276949i
\(134\) −1.76106 0.948421i −0.152132 0.0819311i
\(135\) 4.77843 2.04122i 0.411262 0.175680i
\(136\) −0.351347 + 0.0312690i −0.0301278 + 0.00268130i
\(137\) −7.73347 4.46492i −0.660715 0.381464i 0.131834 0.991272i \(-0.457913\pi\)
−0.792549 + 0.609808i \(0.791247\pi\)
\(138\) 2.91412 + 5.17056i 0.248067 + 0.440147i
\(139\) −7.69083 13.3209i −0.652328 1.12987i −0.982556 0.185964i \(-0.940459\pi\)
0.330228 0.943901i \(-0.392874\pi\)
\(140\) 1.95547 + 0.979631i 0.165267 + 0.0827939i
\(141\) −10.1959 + 5.35528i −0.858646 + 0.450996i
\(142\) 13.5184 8.34761i 1.13444 0.700516i
\(143\) 6.55638 0.548272
\(144\) 5.59634 10.6151i 0.466362 0.884594i
\(145\) 8.58979 0.713344
\(146\) 6.44242 3.97818i 0.533178 0.329237i
\(147\) 0.401642 10.0450i 0.0331269 0.828497i
\(148\) −4.34336 2.17589i −0.357022 0.178857i
\(149\) −0.101779 0.176287i −0.00833810 0.0144420i 0.861826 0.507204i \(-0.169321\pi\)
−0.870164 + 0.492762i \(0.835987\pi\)
\(150\) −1.24669 + 2.10850i −0.101792 + 0.172158i
\(151\) 5.62686 + 3.24867i 0.457908 + 0.264373i 0.711164 0.703026i \(-0.248168\pi\)
−0.253256 + 0.967399i \(0.581502\pi\)
\(152\) 1.46461 + 16.4567i 0.118795 + 1.33482i
\(153\) 0.337910 0.160600i 0.0273184 0.0129838i
\(154\) −3.64043 1.96056i −0.293354 0.157986i
\(155\) 2.54447 + 1.46905i 0.204376 + 0.117997i
\(156\) 4.10535 7.43708i 0.328691 0.595443i
\(157\) 19.7645 11.4110i 1.57738 0.910700i 0.582155 0.813078i \(-0.302210\pi\)
0.995224 0.0976221i \(-0.0311237\pi\)
\(158\) −3.38172 + 0.100087i −0.269035 + 0.00796251i
\(159\) −3.13481 1.98096i −0.248606 0.157100i
\(160\) 0.833822 + 5.59506i 0.0659194 + 0.442329i
\(161\) 2.64975i 0.208830i
\(162\) −1.65331 + 12.6201i −0.129896 + 0.991528i
\(163\) −17.3974 −1.36267 −0.681334 0.731973i \(-0.738600\pi\)
−0.681334 + 0.731973i \(0.738600\pi\)
\(164\) −1.03423 17.4568i −0.0807597 1.36315i
\(165\) 2.47377 3.91468i 0.192583 0.304757i
\(166\) 18.3162 0.542094i 1.42161 0.0420747i
\(167\) −7.48004 12.9558i −0.578823 1.00255i −0.995615 0.0935486i \(-0.970179\pi\)
0.416792 0.909002i \(-0.363154\pi\)
\(168\) −4.50341 + 2.90181i −0.347446 + 0.223880i
\(169\) −3.49317 + 6.05034i −0.268705 + 0.465411i
\(170\) −0.0836269 + 0.155281i −0.00641389 + 0.0119095i
\(171\) −7.52234 15.8273i −0.575248 1.21035i
\(172\) 4.71738 + 7.15685i 0.359697 + 0.545705i
\(173\) 12.9112 22.3629i 0.981621 1.70022i 0.325539 0.945529i \(-0.394454\pi\)
0.656083 0.754689i \(-0.272212\pi\)
\(174\) −10.7088 + 18.1116i −0.811831 + 1.37304i
\(175\) 0.947055 0.546782i 0.0715906 0.0413329i
\(176\) −1.26274 10.6195i −0.0951826 0.800478i
\(177\) −4.68451 0.187307i −0.352109 0.0140788i
\(178\) −9.94729 16.1090i −0.745581 1.20742i
\(179\) 5.67678i 0.424303i −0.977237 0.212151i \(-0.931953\pi\)
0.977237 0.212151i \(-0.0680470\pi\)
\(180\) −2.89154 5.25728i −0.215523 0.391855i
\(181\) 13.3860i 0.994971i 0.867472 + 0.497485i \(0.165743\pi\)
−0.867472 + 0.497485i \(0.834257\pi\)
\(182\) −3.22689 + 1.99260i −0.239193 + 0.147701i
\(183\) −9.01654 17.1665i −0.666522 1.26898i
\(184\) 5.60808 3.93935i 0.413433 0.290413i
\(185\) −2.10354 + 1.21448i −0.154655 + 0.0892902i
\(186\) −6.26964 + 3.53356i −0.459712 + 0.259093i
\(187\) 0.166713 0.288755i 0.0121913 0.0211159i
\(188\) 7.31865 + 11.1033i 0.533767 + 0.809792i
\(189\) 3.40934 4.54591i 0.247993 0.330666i
\(190\) 7.27320 + 3.91699i 0.527654 + 0.284168i
\(191\) 2.24173 3.88280i 0.162206 0.280949i −0.773453 0.633853i \(-0.781472\pi\)
0.935660 + 0.352904i \(0.114806\pi\)
\(192\) −12.8367 5.21718i −0.926409 0.376518i
\(193\) 4.45569 + 7.71749i 0.320728 + 0.555517i 0.980638 0.195827i \(-0.0627392\pi\)
−0.659911 + 0.751344i \(0.729406\pi\)
\(194\) −0.628607 21.2392i −0.0451313 1.52489i
\(195\) −1.97508 3.76033i −0.141438 0.269283i
\(196\) −11.5879 + 0.686525i −0.827708 + 0.0490375i
\(197\) 12.0147 0.856014 0.428007 0.903775i \(-0.359216\pi\)
0.428007 + 0.903775i \(0.359216\pi\)
\(198\) 5.17007 + 10.0963i 0.367421 + 0.717514i
\(199\) 12.4401i 0.881853i −0.897543 0.440927i \(-0.854650\pi\)
0.897543 0.440927i \(-0.145350\pi\)
\(200\) 2.56521 + 1.19151i 0.181388 + 0.0842522i
\(201\) 0.0978730 2.44779i 0.00690343 0.172654i
\(202\) 0.782157 + 26.4273i 0.0550324 + 1.85942i
\(203\) 8.13501 4.69675i 0.570965 0.329647i
\(204\) −0.223154 0.369914i −0.0156239 0.0258992i
\(205\) −7.57229 4.37186i −0.528871 0.305344i
\(206\) 10.3936 19.2991i 0.724155 1.34464i
\(207\) −4.12558 + 5.98497i −0.286748 + 0.415984i
\(208\) −9.01462 3.86720i −0.625052 0.268142i
\(209\) −13.5250 7.80866i −0.935543 0.540136i
\(210\) −0.0277910 + 2.67853i −0.00191776 + 0.184836i
\(211\) −11.2044 19.4065i −0.771340 1.33600i −0.936829 0.349788i \(-0.886254\pi\)
0.165489 0.986212i \(-0.447080\pi\)
\(212\) −1.91791 + 3.82839i −0.131722 + 0.262935i
\(213\) 16.4497 + 10.3949i 1.12711 + 0.712248i
\(214\) 12.3835 + 20.0542i 0.846516 + 1.37088i
\(215\) 4.28585 0.292293
\(216\) 14.6898 + 0.457373i 0.999516 + 0.0311203i
\(217\) 3.21300 0.218113
\(218\) −7.10482 11.5058i −0.481199 0.779272i
\(219\) 7.83935 + 4.95386i 0.529734 + 0.334751i
\(220\) −4.78081 2.39504i −0.322322 0.161473i
\(221\) −0.152913 0.264853i −0.0102860 0.0178160i
\(222\) 0.0617277 5.94939i 0.00414289 0.399297i
\(223\) 6.10284 + 3.52348i 0.408677 + 0.235950i 0.690221 0.723599i \(-0.257513\pi\)
−0.281544 + 0.959548i \(0.590847\pi\)
\(224\) 3.84896 + 4.84291i 0.257169 + 0.323581i
\(225\) −2.99042 0.239523i −0.199362 0.0159682i
\(226\) 8.66780 16.0947i 0.576573 1.07060i
\(227\) 9.66735 + 5.58145i 0.641645 + 0.370454i 0.785248 0.619182i \(-0.212536\pi\)
−0.143603 + 0.989635i \(0.545869\pi\)
\(228\) −17.3264 + 10.4523i −1.14747 + 0.692219i
\(229\) 5.60858 3.23812i 0.370626 0.213981i −0.303106 0.952957i \(-0.598024\pi\)
0.673732 + 0.738976i \(0.264690\pi\)
\(230\) −0.101374 3.42520i −0.00668440 0.225851i
\(231\) 0.202321 5.06003i 0.0133118 0.332925i
\(232\) 22.0346 + 10.2348i 1.44665 + 0.671947i
\(233\) 7.74508i 0.507397i 0.967283 + 0.253699i \(0.0816471\pi\)
−0.967283 + 0.253699i \(0.918353\pi\)
\(234\) 10.3910 + 0.523503i 0.679278 + 0.0342225i
\(235\) 6.64918 0.433744
\(236\) 0.320162 + 5.40405i 0.0208408 + 0.351774i
\(237\) −1.92676 3.66834i −0.125157 0.238284i
\(238\) 0.00570578 + 0.192785i 0.000369850 + 0.0124964i
\(239\) 7.25239 + 12.5615i 0.469118 + 0.812537i 0.999377 0.0352993i \(-0.0112385\pi\)
−0.530259 + 0.847836i \(0.677905\pi\)
\(240\) −5.71031 + 3.92331i −0.368599 + 0.253249i
\(241\) −10.0033 + 17.3262i −0.644368 + 1.11608i 0.340079 + 0.940397i \(0.389546\pi\)
−0.984447 + 0.175681i \(0.943787\pi\)
\(242\) −4.79613 2.58296i −0.308307 0.166039i
\(243\) −14.7785 + 4.95956i −0.948038 + 0.318156i
\(244\) −18.6943 + 12.3222i −1.19678 + 0.788848i
\(245\) −2.90206 + 5.02651i −0.185406 + 0.321132i
\(246\) 18.6583 10.5158i 1.18961 0.670464i
\(247\) −12.4054 + 7.16228i −0.789339 + 0.455725i
\(248\) 4.77672 + 6.80017i 0.303322 + 0.431811i
\(249\) 10.4358 + 19.8685i 0.661340 + 1.25912i
\(250\) 1.20329 0.743030i 0.0761027 0.0469933i
\(251\) 20.7692i 1.31094i −0.755222 0.655469i \(-0.772471\pi\)
0.755222 0.655469i \(-0.227529\pi\)
\(252\) −5.61303 3.39789i −0.353588 0.214047i
\(253\) 6.47822i 0.407282i
\(254\) 11.7389 + 19.0105i 0.736566 + 1.19282i
\(255\) −0.215833 0.00862994i −0.0135160 0.000540428i
\(256\) −4.52762 + 15.3460i −0.282976 + 0.959127i
\(257\) 6.95814 4.01728i 0.434037 0.250591i −0.267028 0.963689i \(-0.586042\pi\)
0.701065 + 0.713097i \(0.252708\pi\)
\(258\) −5.34312 + 9.03672i −0.332648 + 0.562602i
\(259\) −1.32811 + 2.30036i −0.0825248 + 0.142937i
\(260\) −4.09500 + 2.69919i −0.253961 + 0.167396i
\(261\) −25.6871 2.05745i −1.58999 0.127353i
\(262\) −3.69642 + 6.86363i −0.228365 + 0.424036i
\(263\) 10.4995 18.1856i 0.647425 1.12137i −0.336310 0.941751i \(-0.609179\pi\)
0.983736 0.179622i \(-0.0574876\pi\)
\(264\) 11.0101 7.09446i 0.677625 0.436634i
\(265\) 1.07048 + 1.85413i 0.0657592 + 0.113898i
\(266\) 9.02986 0.267252i 0.553656 0.0163863i
\(267\) 12.3869 19.6020i 0.758067 1.19962i
\(268\) −2.82377 + 0.167294i −0.172489 + 0.0102191i
\(269\) 1.50694 0.0918795 0.0459397 0.998944i \(-0.485372\pi\)
0.0459397 + 0.998944i \(0.485372\pi\)
\(270\) 4.23316 6.00670i 0.257622 0.365556i
\(271\) 25.3685i 1.54103i 0.637423 + 0.770514i \(0.280000\pi\)
−0.637423 + 0.770514i \(0.720000\pi\)
\(272\) −0.399539 + 0.298687i −0.0242256 + 0.0181106i
\(273\) −3.92659 2.48130i −0.237648 0.150175i
\(274\) −12.6232 + 0.373602i −0.762594 + 0.0225701i
\(275\) −2.31540 + 1.33679i −0.139624 + 0.0806117i
\(276\) 7.34841 + 4.05641i 0.442323 + 0.244167i
\(277\) 11.8303 + 6.83025i 0.710816 + 0.410390i 0.811363 0.584542i \(-0.198726\pi\)
−0.100547 + 0.994932i \(0.532059\pi\)
\(278\) −19.1521 10.3144i −1.14867 0.618617i
\(279\) −7.25716 5.00253i −0.434475 0.299494i
\(280\) 3.08089 0.274191i 0.184118 0.0163861i
\(281\) 2.52130 + 1.45567i 0.150408 + 0.0868383i 0.573315 0.819335i \(-0.305657\pi\)
−0.422907 + 0.906173i \(0.638990\pi\)
\(282\) −8.28944 + 14.0198i −0.493629 + 0.834866i
\(283\) −4.83052 8.36671i −0.287145 0.497349i 0.685982 0.727618i \(-0.259373\pi\)
−0.973127 + 0.230269i \(0.926039\pi\)
\(284\) 10.0641 20.0892i 0.597193 1.19207i
\(285\) −0.404217 + 10.1094i −0.0239437 + 0.598829i
\(286\) 7.88923 4.87159i 0.466500 0.288063i
\(287\) −9.56183 −0.564417
\(288\) −1.15334 16.9313i −0.0679610 0.997688i
\(289\) 16.9844 0.999085
\(290\) 10.3360 6.38247i 0.606952 0.374792i
\(291\) 23.0393 12.1012i 1.35059 0.709385i
\(292\) 4.79619 9.57382i 0.280676 0.560265i
\(293\) −11.9028 20.6162i −0.695367 1.20441i −0.970057 0.242878i \(-0.921909\pi\)
0.274690 0.961533i \(-0.411425\pi\)
\(294\) −6.98044 12.3855i −0.407107 0.722336i
\(295\) 2.34413 + 1.35338i 0.136480 + 0.0787969i
\(296\) −6.84308 + 0.609017i −0.397746 + 0.0353984i
\(297\) −8.33528 + 11.1140i −0.483662 + 0.644900i
\(298\) −0.253457 0.136499i −0.0146824 0.00790720i
\(299\) 5.14590 + 2.97099i 0.297595 + 0.171817i
\(300\) 0.0665509 + 3.46346i 0.00384232 + 0.199963i
\(301\) 4.05894 2.34343i 0.233953 0.135073i
\(302\) 9.18461 0.271832i 0.528515 0.0156422i
\(303\) −28.6672 + 15.0572i −1.64688 + 0.865011i
\(304\) 13.9902 + 18.7140i 0.802392 + 1.07332i
\(305\) 11.1950i 0.641026i
\(306\) 0.287273 0.444326i 0.0164223 0.0254004i
\(307\) 17.7957 1.01565 0.507827 0.861459i \(-0.330449\pi\)
0.507827 + 0.861459i \(0.330449\pi\)
\(308\) −5.83725 + 0.345827i −0.332608 + 0.0197053i
\(309\) 26.8249 + 1.07257i 1.52601 + 0.0610166i
\(310\) 4.15328 0.122922i 0.235890 0.00698153i
\(311\) −8.19800 14.1993i −0.464866 0.805171i 0.534330 0.845276i \(-0.320564\pi\)
−0.999195 + 0.0401050i \(0.987231\pi\)
\(312\) −0.586041 11.9994i −0.0331781 0.679330i
\(313\) −10.7484 + 18.6168i −0.607536 + 1.05228i 0.384109 + 0.923288i \(0.374509\pi\)
−0.991645 + 0.128995i \(0.958825\pi\)
\(314\) 15.3037 28.4164i 0.863637 1.60363i
\(315\) −2.96306 + 1.40827i −0.166950 + 0.0793470i
\(316\) −3.99483 + 2.63315i −0.224726 + 0.148126i
\(317\) −7.30418 + 12.6512i −0.410244 + 0.710563i −0.994916 0.100706i \(-0.967890\pi\)
0.584672 + 0.811270i \(0.301223\pi\)
\(318\) −5.24399 0.0544089i −0.294068 0.00305110i
\(319\) −19.8888 + 11.4828i −1.11356 + 0.642913i
\(320\) 5.16063 + 6.11293i 0.288488 + 0.341723i
\(321\) −15.4206 + 24.4027i −0.860693 + 1.36202i
\(322\) −1.96885 3.18842i −0.109719 0.177684i
\(323\) 0.728479i 0.0405336i
\(324\) 7.38769 + 16.4141i 0.410427 + 0.911893i
\(325\) 2.45228i 0.136028i
\(326\) −20.9341 + 12.9268i −1.15943 + 0.715947i
\(327\) 8.84733 14.0007i 0.489258 0.774238i
\(328\) −14.2154 20.2372i −0.784915 1.11741i
\(329\) 6.29713 3.63565i 0.347172 0.200440i
\(330\) 0.0679446 6.54858i 0.00374023 0.360487i
\(331\) −15.6137 + 27.0437i −0.858207 + 1.48646i 0.0154304 + 0.999881i \(0.495088\pi\)
−0.873637 + 0.486577i \(0.838245\pi\)
\(332\) 21.6369 14.2618i 1.18748 0.782715i
\(333\) 6.58136 3.12796i 0.360657 0.171411i
\(334\) −18.6272 10.0317i −1.01924 0.548910i
\(335\) −0.707180 + 1.22487i −0.0386374 + 0.0669219i
\(336\) −3.26278 + 6.83789i −0.177999 + 0.373037i
\(337\) 5.23636 + 9.06964i 0.285243 + 0.494055i 0.972668 0.232200i \(-0.0745925\pi\)
−0.687425 + 0.726255i \(0.741259\pi\)
\(338\) 0.292290 + 9.87584i 0.0158985 + 0.537175i
\(339\) 22.3708 + 0.894480i 1.21502 + 0.0485815i
\(340\) 0.0147511 + 0.248986i 0.000799992 + 0.0135031i
\(341\) −7.85526 −0.425386
\(342\) −20.8117 13.4556i −1.12537 0.727593i
\(343\) 14.0021i 0.756044i
\(344\) 10.9941 + 5.10662i 0.592763 + 0.275330i
\(345\) 3.71550 1.95153i 0.200036 0.105067i
\(346\) −1.08034 36.5024i −0.0580797 1.96238i
\(347\) −27.8626 + 16.0865i −1.49574 + 0.863567i −0.999988 0.00489628i \(-0.998441\pi\)
−0.495754 + 0.868463i \(0.665108\pi\)
\(348\) 0.571658 + 29.7504i 0.0306441 + 1.59479i
\(349\) −14.7646 8.52433i −0.790330 0.456297i 0.0497488 0.998762i \(-0.484158\pi\)
−0.840079 + 0.542465i \(0.817491\pi\)
\(350\) 0.733306 1.36163i 0.0391969 0.0727820i
\(351\) 5.00564 + 11.7180i 0.267181 + 0.625463i
\(352\) −9.41008 11.8401i −0.501559 0.631082i
\(353\) −16.3559 9.44311i −0.870539 0.502606i −0.00301183 0.999995i \(-0.500959\pi\)
−0.867527 + 0.497389i \(0.834292\pi\)
\(354\) −5.77600 + 3.25534i −0.306991 + 0.173020i
\(355\) −5.61728 9.72941i −0.298134 0.516384i
\(356\) −23.9389 11.9927i −1.26876 0.635611i
\(357\) −0.209125 + 0.109841i −0.0110681 + 0.00581340i
\(358\) −4.21802 6.83082i −0.222929 0.361020i
\(359\) −24.5546 −1.29594 −0.647972 0.761664i \(-0.724382\pi\)
−0.647972 + 0.761664i \(0.724382\pi\)
\(360\) −7.38568 4.17753i −0.389259 0.220175i
\(361\) 15.1211 0.795850
\(362\) 9.94617 + 16.1072i 0.522759 + 0.846576i
\(363\) 0.266551 6.66640i 0.0139903 0.349895i
\(364\) −2.40233 + 4.79535i −0.125916 + 0.251345i
\(365\) −2.67700 4.63670i −0.140121 0.242696i
\(366\) −23.6047 13.9567i −1.23384 0.729529i
\(367\) −16.6622 9.61992i −0.869759 0.502156i −0.00249084 0.999997i \(-0.500793\pi\)
−0.867268 + 0.497841i \(0.834126\pi\)
\(368\) 3.82110 8.90715i 0.199189 0.464317i
\(369\) 21.5972 + 14.8874i 1.12430 + 0.775010i
\(370\) −1.62877 + 3.02436i −0.0846759 + 0.157229i
\(371\) 2.02761 + 1.17064i 0.105268 + 0.0607767i
\(372\) −4.91866 + 8.91043i −0.255020 + 0.461984i
\(373\) −13.5653 + 7.83195i −0.702386 + 0.405523i −0.808236 0.588859i \(-0.799577\pi\)
0.105849 + 0.994382i \(0.466244\pi\)
\(374\) −0.0139497 0.471329i −0.000721322 0.0243719i
\(375\) 1.46420 + 0.925262i 0.0756111 + 0.0477803i
\(376\) 17.0565 + 7.92253i 0.879624 + 0.408573i
\(377\) 21.0646i 1.08488i
\(378\) 0.724676 8.00328i 0.0372733 0.411645i
\(379\) 11.3447 0.582738 0.291369 0.956611i \(-0.405889\pi\)
0.291369 + 0.956611i \(0.405889\pi\)
\(380\) 11.6622 0.690927i 0.598259 0.0354438i
\(381\) −14.6180 + 23.1326i −0.748902 + 1.18512i
\(382\) −0.187577 6.33781i −0.00959727 0.324271i
\(383\) 8.35938 + 14.4789i 0.427145 + 0.739836i 0.996618 0.0821736i \(-0.0261862\pi\)
−0.569473 + 0.822010i \(0.692853\pi\)
\(384\) −19.3228 + 3.26027i −0.986063 + 0.166375i
\(385\) −1.46187 + 2.53203i −0.0745038 + 0.129044i
\(386\) 11.0958 + 5.97566i 0.564762 + 0.304153i
\(387\) −12.8165 1.02656i −0.651500 0.0521829i
\(388\) −16.5378 25.0899i −0.839578 1.27375i
\(389\) −6.23931 + 10.8068i −0.316346 + 0.547927i −0.979723 0.200359i \(-0.935789\pi\)
0.663377 + 0.748285i \(0.269123\pi\)
\(390\) −5.17063 3.05722i −0.261825 0.154809i
\(391\) 0.261696 0.151090i 0.0132345 0.00764096i
\(392\) −13.4335 + 9.43625i −0.678495 + 0.476603i
\(393\) −9.54011 0.381454i −0.481235 0.0192418i
\(394\) 14.4572 8.92730i 0.728344 0.449751i
\(395\) 2.39229i 0.120369i
\(396\) 13.7230 + 8.30729i 0.689605 + 0.417457i
\(397\) 0.465205i 0.0233480i −0.999932 0.0116740i \(-0.996284\pi\)
0.999932 0.0116740i \(-0.00371603\pi\)
\(398\) −9.24334 14.9690i −0.463327 0.750329i
\(399\) 5.14483 + 9.79518i 0.257564 + 0.490372i
\(400\) 3.97202 0.472301i 0.198601 0.0236151i
\(401\) −11.4982 + 6.63849i −0.574193 + 0.331510i −0.758822 0.651298i \(-0.774225\pi\)
0.184629 + 0.982808i \(0.440892\pi\)
\(402\) −1.70101 3.01812i −0.0848387 0.150530i
\(403\) −3.60251 + 6.23974i −0.179454 + 0.310823i
\(404\) 20.5775 + 31.2186i 1.02377 + 1.55318i
\(405\) 8.88526 + 1.43255i 0.441512 + 0.0711839i
\(406\) 6.29895 11.6961i 0.312612 0.580468i
\(407\) 3.24702 5.62400i 0.160949 0.278771i
\(408\) −0.543376 0.279304i −0.0269011 0.0138276i
\(409\) −0.111999 0.193987i −0.00553798 0.00959206i 0.863243 0.504788i \(-0.168429\pi\)
−0.868781 + 0.495196i \(0.835096\pi\)
\(410\) −12.3601 + 0.365815i −0.610421 + 0.0180663i
\(411\) −7.19214 13.6930i −0.354762 0.675428i
\(412\) −1.83335 30.9452i −0.0903225 1.52456i
\(413\) 2.96002 0.145653
\(414\) −0.517262 + 10.2671i −0.0254220 + 0.504599i
\(415\) 12.9572i 0.636042i
\(416\) −13.7207 + 2.04476i −0.672710 + 0.100253i
\(417\) 1.06440 26.6206i 0.0521241 1.30361i
\(418\) −22.0766 + 0.653389i −1.07980 + 0.0319583i
\(419\) −6.92393 + 3.99754i −0.338256 + 0.195292i −0.659501 0.751704i \(-0.729232\pi\)
0.321244 + 0.946996i \(0.395899\pi\)
\(420\) 1.95679 + 3.24370i 0.0954814 + 0.158276i
\(421\) 15.0227 + 8.67337i 0.732162 + 0.422714i 0.819213 0.573490i \(-0.194411\pi\)
−0.0870505 + 0.996204i \(0.527744\pi\)
\(422\) −27.9017 15.0265i −1.35823 0.731478i
\(423\) −19.8838 1.59263i −0.966786 0.0774362i
\(424\) 0.536808 + 6.03173i 0.0260697 + 0.292926i
\(425\) 0.108003 + 0.0623555i 0.00523891 + 0.00302469i
\(426\) 27.5175 + 0.285507i 1.33322 + 0.0138328i
\(427\) 6.12124 + 10.6023i 0.296228 + 0.513082i
\(428\) 29.8018 + 14.9298i 1.44052 + 0.721659i
\(429\) 9.59987 + 6.06638i 0.463486 + 0.292887i
\(430\) 5.15712 3.18452i 0.248699 0.153571i
\(431\) 3.02918 0.145910 0.0729552 0.997335i \(-0.476757\pi\)
0.0729552 + 0.997335i \(0.476757\pi\)
\(432\) 18.0160 10.3646i 0.866793 0.498668i
\(433\) 0.00546847 0.000262798 0.000131399 1.00000i \(-0.499958\pi\)
0.000131399 1.00000i \(0.499958\pi\)
\(434\) 3.86617 2.38735i 0.185582 0.114597i
\(435\) 12.5772 + 7.94781i 0.603031 + 0.381069i
\(436\) −17.0983 8.56574i −0.818861 0.410225i
\(437\) −7.07690 12.2575i −0.338534 0.586358i
\(438\) 13.1139 + 0.136063i 0.626605 + 0.00650133i
\(439\) −22.4571 12.9656i −1.07182 0.618815i −0.143141 0.989702i \(-0.545720\pi\)
−0.928678 + 0.370887i \(0.879054\pi\)
\(440\) −7.53228 + 0.670354i −0.359087 + 0.0319579i
\(441\) 9.88234 14.3363i 0.470588 0.682680i
\(442\) −0.380793 0.205076i −0.0181125 0.00975449i
\(443\) 13.0998 + 7.56316i 0.622389 + 0.359336i 0.777799 0.628514i \(-0.216336\pi\)
−0.155409 + 0.987850i \(0.549670\pi\)
\(444\) −4.34629 7.20470i −0.206266 0.341920i
\(445\) −11.5939 + 6.69374i −0.549603 + 0.317314i
\(446\) 9.96154 0.294827i 0.471693 0.0139605i
\(447\) 0.0140862 0.352293i 0.000666253 0.0166629i
\(448\) 8.22984 + 2.96754i 0.388823 + 0.140203i
\(449\) 4.83214i 0.228043i −0.993478 0.114021i \(-0.963627\pi\)
0.993478 0.114021i \(-0.0363732\pi\)
\(450\) −3.77632 + 1.93376i −0.178017 + 0.0911582i
\(451\) 23.3771 1.10079
\(452\) −1.52893 25.8070i −0.0719149 1.21386i
\(453\) 5.23299 + 9.96304i 0.245868 + 0.468104i
\(454\) 15.7798 0.467027i 0.740583 0.0219187i
\(455\) 1.34086 + 2.32244i 0.0628606 + 0.108878i
\(456\) −13.0823 + 25.4511i −0.612636 + 1.19186i
\(457\) −0.817739 + 1.41637i −0.0382522 + 0.0662548i −0.884518 0.466507i \(-0.845512\pi\)
0.846265 + 0.532761i \(0.178846\pi\)
\(458\) 4.34273 8.06374i 0.202923 0.376794i
\(459\) 0.643366 + 0.0775042i 0.0300298 + 0.00361758i
\(460\) −2.66701 4.04619i −0.124350 0.188654i
\(461\) −4.05449 + 7.02259i −0.188837 + 0.327075i −0.944863 0.327467i \(-0.893805\pi\)
0.756026 + 0.654542i \(0.227138\pi\)
\(462\) −3.51630 6.23901i −0.163593 0.290265i
\(463\) 19.0599 11.0043i 0.885790 0.511411i 0.0132272 0.999913i \(-0.495790\pi\)
0.872563 + 0.488501i \(0.162456\pi\)
\(464\) 34.1188 4.05697i 1.58393 0.188340i
\(465\) 2.36636 + 4.50528i 0.109737 + 0.208928i
\(466\) 5.75482 + 9.31958i 0.266587 + 0.431721i
\(467\) 4.66635i 0.215933i −0.994155 0.107966i \(-0.965566\pi\)
0.994155 0.107966i \(-0.0344339\pi\)
\(468\) 12.8923 7.09086i 0.595947 0.327775i
\(469\) 1.54669i 0.0714197i
\(470\) 8.00089 4.94053i 0.369053 0.227890i
\(471\) 39.4974 + 1.57928i 1.81995 + 0.0727692i
\(472\) 4.40062 + 6.26475i 0.202555 + 0.288358i
\(473\) −9.92345 + 5.72931i −0.456281 + 0.263434i
\(474\) −5.04413 2.98243i −0.231685 0.136988i
\(475\) 2.92067 5.05874i 0.134009 0.232111i
\(476\) 0.150111 + 0.227737i 0.00688033 + 0.0104383i
\(477\) −2.75709 5.80104i −0.126238 0.265611i
\(478\) 18.0603 + 9.72640i 0.826059 + 0.444875i
\(479\) −4.15142 + 7.19047i −0.189683 + 0.328541i −0.945145 0.326652i \(-0.894079\pi\)
0.755461 + 0.655193i \(0.227413\pi\)
\(480\) −3.95602 + 8.96381i −0.180567 + 0.409140i
\(481\) −2.97824 5.15846i −0.135796 0.235206i
\(482\) 0.837023 + 28.2812i 0.0381254 + 1.28817i
\(483\) 2.45172 3.87978i 0.111557 0.176536i
\(484\) −7.69036 + 0.455615i −0.349562 + 0.0207098i
\(485\) −15.0250 −0.682249
\(486\) −14.0977 + 16.9486i −0.639483 + 0.768805i
\(487\) 12.1772i 0.551800i −0.961186 0.275900i \(-0.911024\pi\)
0.961186 0.275900i \(-0.0889759\pi\)
\(488\) −13.3389 + 28.7176i −0.603826 + 1.29999i
\(489\) −25.4733 16.0971i −1.15194 0.727938i
\(490\) 0.242829 + 8.20467i 0.0109699 + 0.370649i
\(491\) −22.4724 + 12.9744i −1.01416 + 0.585528i −0.912408 0.409281i \(-0.865779\pi\)
−0.101756 + 0.994809i \(0.532446\pi\)
\(492\) 14.6378 26.5173i 0.659925 1.19549i
\(493\) 0.927723 + 0.535621i 0.0417825 + 0.0241232i
\(494\) −9.60555 + 17.8359i −0.432174 + 0.802476i
\(495\) 7.24421 3.44299i 0.325603 0.154751i
\(496\) 10.8005 + 4.63333i 0.484957 + 0.208043i
\(497\) −10.6397 6.14286i −0.477258 0.275545i
\(498\) 27.3202 + 16.1535i 1.22425 + 0.723857i
\(499\) 21.1249 + 36.5894i 0.945680 + 1.63797i 0.754384 + 0.656433i \(0.227936\pi\)
0.191296 + 0.981532i \(0.438731\pi\)
\(500\) 0.895814 1.78816i 0.0400620 0.0799690i
\(501\) 1.03523 25.8909i 0.0462506 1.15672i
\(502\) −15.4321 24.9913i −0.688769 1.11542i
\(503\) −15.7960 −0.704311 −0.352156 0.935942i \(-0.614551\pi\)
−0.352156 + 0.935942i \(0.614551\pi\)
\(504\) −9.27884 + 0.0820053i −0.413312 + 0.00365281i
\(505\) 18.6951 0.831922
\(506\) 4.81351 + 7.79518i 0.213987 + 0.346538i
\(507\) −10.7129 + 5.62683i −0.475775 + 0.249896i
\(508\) 28.2507 + 14.1527i 1.25342 + 0.627926i
\(509\) 16.1458 + 27.9654i 0.715651 + 1.23954i 0.962708 + 0.270543i \(0.0872033\pi\)
−0.247057 + 0.969001i \(0.579463\pi\)
\(510\) −0.266123 + 0.149986i −0.0117841 + 0.00664151i
\(511\) −5.07053 2.92747i −0.224307 0.129504i
\(512\) 5.95451 + 21.8299i 0.263155 + 0.964754i
\(513\) 3.63021 30.1346i 0.160278 1.33047i
\(514\) 5.38770 10.0041i 0.237641 0.441260i
\(515\) −13.4232 7.74987i −0.591495 0.341500i
\(516\) 0.285227 + 14.8439i 0.0125564 + 0.653466i
\(517\) −15.3955 + 8.88858i −0.677092 + 0.390919i
\(518\) 0.111130 + 3.75482i 0.00488275 + 0.164977i
\(519\) 39.5962 20.7975i 1.73808 0.912910i
\(520\) −2.92190 + 6.29061i −0.128134 + 0.275862i
\(521\) 10.9201i 0.478418i 0.970968 + 0.239209i \(0.0768881\pi\)
−0.970968 + 0.239209i \(0.923112\pi\)
\(522\) −32.4378 + 16.6106i −1.41976 + 0.727025i
\(523\) 5.69579 0.249059 0.124530 0.992216i \(-0.460258\pi\)
0.124530 + 0.992216i \(0.460258\pi\)
\(524\) 0.652019 + 11.0055i 0.0284836 + 0.480777i
\(525\) 1.89260 + 0.0756741i 0.0825997 + 0.00330269i
\(526\) −0.878543 29.6840i −0.0383063 1.29428i
\(527\) 0.183207 + 0.317323i 0.00798060 + 0.0138228i
\(528\) 7.97696 16.7175i 0.347153 0.727537i
\(529\) 8.56443 14.8340i 0.372367 0.644958i
\(530\) 2.66578 + 1.43566i 0.115794 + 0.0623609i
\(531\) −6.68576 4.60865i −0.290137 0.199999i
\(532\) 10.6670 7.03104i 0.462472 0.304834i
\(533\) 10.7210 18.5694i 0.464379 0.804328i
\(534\) 0.340219 32.7907i 0.0147227 1.41899i
\(535\) 14.4333 8.33308i 0.624007 0.360271i
\(536\) −3.27351 + 2.29945i −0.141394 + 0.0993210i
\(537\) 5.25251 8.31196i 0.226663 0.358688i
\(538\) 1.81328 1.11970i 0.0781761 0.0482736i
\(539\) 15.5178i 0.668400i
\(540\) 0.630562 10.3732i 0.0271351 0.446390i
\(541\) 40.7008i 1.74987i −0.484244 0.874933i \(-0.660905\pi\)
0.484244 0.874933i \(-0.339095\pi\)
\(542\) 18.8496 + 30.5257i 0.809658 + 1.31119i
\(543\) −12.3855 + 19.5998i −0.531514 + 0.841106i
\(544\) −0.258828 + 0.656277i −0.0110972 + 0.0281376i
\(545\) −8.28090 + 4.78098i −0.354715 + 0.204795i
\(546\) −6.56850 0.0681513i −0.281106 0.00291661i
\(547\) −4.03253 + 6.98454i −0.172418 + 0.298637i −0.939265 0.343193i \(-0.888491\pi\)
0.766846 + 0.641831i \(0.221825\pi\)
\(548\) −14.9117 + 9.82895i −0.636998 + 0.419872i
\(549\) 2.68146 33.4779i 0.114442 1.42880i
\(550\) −1.79282 + 3.32896i −0.0764459 + 0.141947i
\(551\) 25.0879 43.4535i 1.06878 1.85118i
\(552\) 11.8563 0.579055i 0.504638 0.0246462i
\(553\) 1.30806 + 2.26563i 0.0556243 + 0.0963442i
\(554\) 19.3104 0.571521i 0.820421 0.0242816i
\(555\) −4.20372 0.168083i −0.178438 0.00713471i
\(556\) −30.7095 + 1.81938i −1.30237 + 0.0771589i
\(557\) 33.6992 1.42788 0.713940 0.700207i \(-0.246909\pi\)
0.713940 + 0.700207i \(0.246909\pi\)
\(558\) −12.4495 0.627214i −0.527029 0.0265521i
\(559\) 10.5101i 0.444530i
\(560\) 3.50347 2.61912i 0.148049 0.110678i
\(561\) 0.511276 0.268543i 0.0215861 0.0113379i
\(562\) 4.11547 0.121803i 0.173601 0.00513797i
\(563\) −6.59410 + 3.80710i −0.277908 + 0.160450i −0.632476 0.774580i \(-0.717961\pi\)
0.354568 + 0.935030i \(0.384628\pi\)
\(564\) 0.442508 + 23.0292i 0.0186330 + 0.969703i
\(565\) −11.1943 6.46306i −0.470949 0.271903i
\(566\) −12.0292 6.47836i −0.505627 0.272306i
\(567\) 9.19812 3.50160i 0.386285 0.147053i
\(568\) −2.81686 31.6510i −0.118193 1.32805i
\(569\) −11.5746 6.68257i −0.485231 0.280148i 0.237363 0.971421i \(-0.423717\pi\)
−0.722594 + 0.691273i \(0.757050\pi\)
\(570\) 7.02520 + 12.4649i 0.294253 + 0.522097i
\(571\) 1.37959 + 2.38951i 0.0577339 + 0.0999980i 0.893448 0.449167i \(-0.148279\pi\)
−0.835714 + 0.549165i \(0.814946\pi\)
\(572\) 5.87330 11.7239i 0.245575 0.490199i
\(573\) 6.87496 3.61101i 0.287206 0.150852i
\(574\) −11.5057 + 7.10472i −0.480237 + 0.296545i
\(575\) −2.42304 −0.101048
\(576\) −13.9683 19.5163i −0.582011 0.813181i
\(577\) −5.91800 −0.246369 −0.123185 0.992384i \(-0.539311\pi\)
−0.123185 + 0.992384i \(0.539311\pi\)
\(578\) 20.4372 12.6199i 0.850076 0.524921i
\(579\) −0.616663 + 15.4226i −0.0256276 + 0.640943i
\(580\) 7.69486 15.3599i 0.319512 0.637786i
\(581\) −7.08474 12.2711i −0.293925 0.509093i
\(582\) 18.7315 31.6802i 0.776444 1.31319i
\(583\) −4.95718 2.86203i −0.205306 0.118533i
\(584\) −1.34242 15.0838i −0.0555497 0.624172i
\(585\) 0.587376 7.33335i 0.0242850 0.303197i
\(586\) −29.6409 15.9631i −1.22445 0.659432i
\(587\) −0.615419 0.355312i −0.0254011 0.0146653i 0.487246 0.873265i \(-0.338002\pi\)
−0.512647 + 0.858600i \(0.671335\pi\)
\(588\) −17.6023 9.71665i −0.725905 0.400708i
\(589\) 14.8631 8.58120i 0.612422 0.353582i
\(590\) 3.82626 0.113244i 0.157525 0.00466218i
\(591\) 17.5920 + 11.1168i 0.723638 + 0.457283i
\(592\) −7.78169 + 5.81744i −0.319826 + 0.239095i
\(593\) 5.76716i 0.236829i 0.992964 + 0.118414i \(0.0377811\pi\)
−0.992964 + 0.118414i \(0.962219\pi\)
\(594\) −1.77172 + 19.5667i −0.0726944 + 0.802833i
\(595\) 0.136380 0.00559102
\(596\) −0.406405 + 0.0240774i −0.0166470 + 0.000986250i
\(597\) 11.5103 18.2148i 0.471086 0.745481i
\(598\) 8.39954 0.248597i 0.343483 0.0101659i
\(599\) 16.9465 + 29.3522i 0.692416 + 1.19930i 0.971044 + 0.238901i \(0.0767871\pi\)
−0.278628 + 0.960399i \(0.589880\pi\)
\(600\) 2.65353 + 4.11810i 0.108330 + 0.168121i
\(601\) 1.86493 3.23015i 0.0760719 0.131760i −0.825480 0.564431i \(-0.809095\pi\)
0.901552 + 0.432671i \(0.142429\pi\)
\(602\) 3.14284 5.83574i 0.128093 0.237847i
\(603\) 2.40815 3.49350i 0.0980676 0.142266i
\(604\) 10.8498 7.15153i 0.441471 0.290992i
\(605\) −1.92596 + 3.33586i −0.0783015 + 0.135622i
\(606\) −23.3070 + 39.4187i −0.946782 + 1.60127i
\(607\) −15.0247 + 8.67454i −0.609836 + 0.352089i −0.772901 0.634526i \(-0.781195\pi\)
0.163066 + 0.986615i \(0.447862\pi\)
\(608\) 30.7393 + 12.1232i 1.24664 + 0.491662i
\(609\) 16.2570 + 0.650025i 0.658768 + 0.0263403i
\(610\) 8.31824 + 13.4709i 0.336796 + 0.545420i
\(611\) 16.3056i 0.659655i
\(612\) 0.0155256 0.748105i 0.000627584 0.0302404i
\(613\) 29.3264i 1.18448i 0.805761 + 0.592241i \(0.201757\pi\)
−0.805761 + 0.592241i \(0.798243\pi\)
\(614\) 21.4134 13.2227i 0.864174 0.533626i
\(615\) −7.04224 13.4076i −0.283971 0.540648i
\(616\) −6.76694 + 4.75338i −0.272648 + 0.191519i
\(617\) 13.3388 7.70113i 0.536998 0.310036i −0.206863 0.978370i \(-0.566326\pi\)
0.743861 + 0.668334i \(0.232992\pi\)
\(618\) 33.0751 18.6411i 1.33047 0.749854i
\(619\) 14.0738 24.3766i 0.565675 0.979778i −0.431311 0.902203i \(-0.641949\pi\)
0.996987 0.0775751i \(-0.0247178\pi\)
\(620\) 4.90626 3.23392i 0.197040 0.129877i
\(621\) −11.5783 + 4.94596i −0.464623 + 0.198475i
\(622\) −20.4151 10.9946i −0.818571 0.440843i
\(623\) −7.32003 + 12.6787i −0.293271 + 0.507960i
\(624\) −9.62106 14.0033i −0.385150 0.560579i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0.899372 + 30.3878i 0.0359461 + 1.21454i
\(627\) −12.5783 23.9476i −0.502328 0.956376i
\(628\) −2.69945 45.5643i −0.107720 1.81821i
\(629\) −0.302918 −0.0120781
\(630\) −2.51904 + 3.89620i −0.100361 + 0.155228i
\(631\) 11.3112i 0.450292i −0.974325 0.225146i \(-0.927714\pi\)
0.974325 0.225146i \(-0.0722859\pi\)
\(632\) −2.85042 + 6.13672i −0.113384 + 0.244106i
\(633\) 1.55067 38.7820i 0.0616336 1.54145i
\(634\) 0.611177 + 20.6503i 0.0242729 + 0.820129i
\(635\) 13.6821 7.89937i 0.542958 0.313477i
\(636\) −6.35047 + 3.83097i −0.251813 + 0.151908i
\(637\) −12.3264 7.11665i −0.488390 0.281972i
\(638\) −15.3999 + 28.5951i −0.609688 + 1.13209i
\(639\) 14.4676 + 30.4405i 0.572330 + 1.20421i
\(640\) 10.7518 + 3.52113i 0.425003 + 0.139185i
\(641\) 18.5045 + 10.6836i 0.730882 + 0.421975i 0.818745 0.574158i \(-0.194670\pi\)
−0.0878627 + 0.996133i \(0.528004\pi\)
\(642\) −0.423542 + 40.8214i −0.0167159 + 1.61109i
\(643\) −8.54544 14.8011i −0.336999 0.583700i 0.646867 0.762602i \(-0.276079\pi\)
−0.983867 + 0.178902i \(0.942745\pi\)
\(644\) −4.73818 2.37369i −0.186711 0.0935363i
\(645\) 6.27536 + 3.96554i 0.247092 + 0.156143i
\(646\) 0.541281 + 0.876571i 0.0212964 + 0.0344882i
\(647\) 20.5113 0.806383 0.403192 0.915116i \(-0.367901\pi\)
0.403192 + 0.915116i \(0.367901\pi\)
\(648\) 21.0857 + 14.2616i 0.828324 + 0.560250i
\(649\) −7.23677 −0.284068
\(650\) 1.82212 + 2.95080i 0.0714692 + 0.115740i
\(651\) 4.70448 + 2.97287i 0.184383 + 0.116516i
\(652\) −15.5848 + 31.1093i −0.610349 + 1.21833i
\(653\) 1.44882 + 2.50943i 0.0566968 + 0.0982017i 0.892981 0.450095i \(-0.148610\pi\)
−0.836284 + 0.548297i \(0.815277\pi\)
\(654\) 0.243001 23.4207i 0.00950208 0.915821i
\(655\) 4.77387 + 2.75619i 0.186530 + 0.107693i
\(656\) −32.1421 13.7887i −1.25494 0.538359i
\(657\) 6.89477 + 14.5069i 0.268991 + 0.565968i
\(658\) 4.87588 9.05370i 0.190082 0.352950i
\(659\) −16.4080 9.47318i −0.639166 0.369023i 0.145127 0.989413i \(-0.453641\pi\)
−0.784293 + 0.620390i \(0.786974\pi\)
\(660\) −4.78403 7.93032i −0.186218 0.308687i
\(661\) 12.1534 7.01678i 0.472713 0.272921i −0.244662 0.969608i \(-0.578677\pi\)
0.717375 + 0.696688i \(0.245344\pi\)
\(662\) 1.30648 + 44.1429i 0.0507776 + 1.71566i
\(663\) 0.0211630 0.529284i 0.000821903 0.0205557i
\(664\) 15.4385 33.2379i 0.599131 1.28988i
\(665\) 6.38787i 0.247711i
\(666\) 5.59512 8.65399i 0.216807 0.335335i
\(667\) −20.8134 −0.805899
\(668\) −29.8678 + 1.76951i −1.15562 + 0.0684646i
\(669\) 5.67566 + 10.8058i 0.219434 + 0.417777i
\(670\) 0.0591733 + 1.99933i 0.00228606 + 0.0772410i
\(671\) −14.9655 25.9209i −0.577735 1.00067i
\(672\) 1.15469 + 10.6523i 0.0445430 + 0.410921i
\(673\) −4.84513 + 8.39201i −0.186766 + 0.323488i −0.944170 0.329458i \(-0.893134\pi\)
0.757404 + 0.652946i \(0.226467\pi\)
\(674\) 13.0399 + 7.02264i 0.502277 + 0.270502i
\(675\) −4.15696 3.11764i −0.160002 0.119998i
\(676\) 7.68975 + 11.6663i 0.295760 + 0.448705i
\(677\) −9.97234 + 17.2726i −0.383268 + 0.663840i −0.991527 0.129898i \(-0.958535\pi\)
0.608259 + 0.793739i \(0.291868\pi\)
\(678\) 27.5832 15.5459i 1.05933 0.597035i
\(679\) −14.2295 + 8.21539i −0.546077 + 0.315278i
\(680\) 0.202754 + 0.288641i 0.00777524 + 0.0110689i
\(681\) 8.99066 + 17.1172i 0.344523 + 0.655933i
\(682\) −9.45216 + 5.83669i −0.361942 + 0.223498i
\(683\) 30.2801i 1.15864i −0.815101 0.579318i \(-0.803319\pi\)
0.815101 0.579318i \(-0.196681\pi\)
\(684\) −35.0404 0.727201i −1.33980 0.0278052i
\(685\) 8.92984i 0.341192i
\(686\) 10.4040 + 16.8486i 0.397226 + 0.643283i
\(687\) 11.2082 + 0.448152i 0.427620 + 0.0170981i
\(688\) 17.0235 2.02421i 0.649014 0.0771725i
\(689\) −4.54684 + 2.62512i −0.173221 + 0.100009i
\(690\) 3.02078 5.10898i 0.114999 0.194496i
\(691\) 3.89324 6.74329i 0.148106 0.256527i −0.782422 0.622749i \(-0.786016\pi\)
0.930527 + 0.366222i \(0.119349\pi\)
\(692\) −28.4224 43.1203i −1.08046 1.63919i
\(693\) 4.97809 7.22170i 0.189102 0.274330i
\(694\) −21.5740 + 40.0594i −0.818940 + 1.52063i
\(695\) −7.69083 + 13.3209i −0.291730 + 0.505291i
\(696\) 22.7933 + 35.3736i 0.863979 + 1.34083i
\(697\) −0.545220 0.944348i −0.0206517 0.0357697i
\(698\) −24.0999 + 0.713273i −0.912195 + 0.0269978i
\(699\) −7.16623 + 11.3404i −0.271052 + 0.428932i
\(700\) −0.129349 2.18330i −0.00488895 0.0825210i
\(701\) 19.9020 0.751687 0.375843 0.926683i \(-0.377353\pi\)
0.375843 + 0.926683i \(0.377353\pi\)
\(702\) 14.7301 + 10.3809i 0.555951 + 0.391801i
\(703\) 14.1883i 0.535123i
\(704\) −20.1206 7.25516i −0.758325 0.273439i
\(705\) 9.73574 + 6.15223i 0.366669 + 0.231706i
\(706\) −26.6975 + 0.790151i −1.00477 + 0.0297377i
\(707\) 17.7053 10.2222i 0.665877 0.384444i
\(708\) −4.53138 + 8.20886i −0.170300 + 0.308508i
\(709\) −33.0445 19.0782i −1.24101 0.716498i −0.271711 0.962379i \(-0.587590\pi\)
−0.969300 + 0.245881i \(0.920923\pi\)
\(710\) −13.9885 7.53350i −0.524977 0.282727i
\(711\) 0.573007 7.15395i 0.0214894 0.268294i
\(712\) −37.7164 + 3.35666i −1.41348 + 0.125796i
\(713\) −6.16535 3.55957i −0.230894 0.133307i
\(714\) −0.170023 + 0.287556i −0.00636294 + 0.0107615i
\(715\) −3.27819 5.67799i −0.122597 0.212345i
\(716\) −10.1510 5.08534i −0.379361 0.190048i
\(717\) −1.00372 + 25.1030i −0.0374847 + 0.937487i
\(718\) −29.5463 + 18.2448i −1.10266 + 0.680890i
\(719\) −42.2205 −1.57456 −0.787280 0.616596i \(-0.788511\pi\)
−0.787280 + 0.616596i \(0.788511\pi\)
\(720\) −11.9911 + 0.460993i −0.446883 + 0.0171802i
\(721\) −16.9500 −0.631250
\(722\) 18.1951 11.2355i 0.677153 0.418141i
\(723\) −30.6781 + 16.1134i −1.14093 + 0.599263i
\(724\) 23.9363 + 11.9913i 0.889584 + 0.445654i
\(725\) −4.29490 7.43898i −0.159508 0.276277i
\(726\) −4.63259 8.21967i −0.171932 0.305060i
\(727\) 22.2634 + 12.8538i 0.825703 + 0.476720i 0.852379 0.522924i \(-0.175159\pi\)
−0.0266764 + 0.999644i \(0.508492\pi\)
\(728\) 0.672394 + 7.55520i 0.0249206 + 0.280014i
\(729\) −26.2276 6.41214i −0.971391 0.237487i
\(730\) −6.66642 3.59021i −0.246735 0.132880i
\(731\) 0.462885 + 0.267247i 0.0171204 + 0.00988448i
\(732\) −38.7736 + 0.745039i −1.43311 + 0.0275374i
\(733\) −44.6422 + 25.7742i −1.64890 + 0.951991i −0.671385 + 0.741109i \(0.734300\pi\)
−0.977512 + 0.210882i \(0.932366\pi\)
\(734\) −27.1973 + 0.804946i −1.00387 + 0.0297111i
\(735\) −8.90004 + 4.67467i −0.328283 + 0.172428i
\(736\) −2.02039 13.5571i −0.0744724 0.499721i
\(737\) 3.78142i 0.139290i
\(738\) 37.0495 + 1.86658i 1.36381 + 0.0687096i
\(739\) −13.1324 −0.483085 −0.241542 0.970390i \(-0.577653\pi\)
−0.241542 + 0.970390i \(0.577653\pi\)
\(740\) 0.287303 + 4.84941i 0.0105615 + 0.178268i
\(741\) −24.7911 0.991252i −0.910723 0.0364146i
\(742\) 3.30963 0.0979534i 0.121500 0.00359598i
\(743\) 19.9804 + 34.6070i 0.733009 + 1.26961i 0.955591 + 0.294695i \(0.0952182\pi\)
−0.222582 + 0.974914i \(0.571448\pi\)
\(744\) 0.702142 + 14.3765i 0.0257418 + 0.527069i
\(745\) −0.101779 + 0.176287i −0.00372891 + 0.00645866i
\(746\) −10.5037 + 19.5036i −0.384566 + 0.714076i
\(747\) −3.10353 + 38.7474i −0.113552 + 1.41769i
\(748\) −0.366997 0.556781i −0.0134187 0.0203579i
\(749\) 9.11277 15.7838i 0.332973 0.576727i
\(750\) 2.44936 + 0.0254133i 0.0894379 + 0.000927961i
\(751\) 27.3738 15.8043i 0.998885 0.576707i 0.0909671 0.995854i \(-0.471004\pi\)
0.907918 + 0.419147i \(0.137671\pi\)
\(752\) 26.4106 3.14042i 0.963097 0.114519i
\(753\) 19.2169 30.4103i 0.700304 1.10821i
\(754\) 15.6516 + 25.3468i 0.569997 + 0.923075i
\(755\) 6.49734i 0.236462i
\(756\) −5.07468 10.1687i −0.184564 0.369833i
\(757\) 10.1899i 0.370357i 0.982705 + 0.185178i \(0.0592863\pi\)
−0.982705 + 0.185178i \(0.940714\pi\)
\(758\) 13.6510 8.42944i 0.495825 0.306171i
\(759\) −5.99405 + 9.48543i −0.217570 + 0.344299i
\(760\) 13.5196 9.49675i 0.490409 0.344483i
\(761\) 45.8686 26.4823i 1.66274 0.959981i 0.691337 0.722533i \(-0.257022\pi\)
0.971400 0.237449i \(-0.0763111\pi\)
\(762\) −0.401497 + 38.6968i −0.0145447 + 1.40184i
\(763\) −5.22831 + 9.05570i −0.189278 + 0.327838i
\(764\) −4.93489 7.48685i −0.178538 0.270865i
\(765\) −0.308039 0.212339i −0.0111372 0.00767712i
\(766\) 20.8170 + 11.2110i 0.752149 + 0.405071i
\(767\) −3.31887 + 5.74845i −0.119837 + 0.207564i
\(768\) −20.8285 + 18.2805i −0.751582 + 0.659639i
\(769\) −17.1669 29.7339i −0.619053 1.07223i −0.989659 0.143441i \(-0.954183\pi\)
0.370606 0.928790i \(-0.379150\pi\)
\(770\) 0.122322 + 4.13299i 0.00440818 + 0.148942i
\(771\) 13.9052 + 0.555988i 0.500782 + 0.0200234i
\(772\) 17.7916 1.05406i 0.640333 0.0379364i
\(773\) −49.7288 −1.78862 −0.894310 0.447447i \(-0.852333\pi\)
−0.894310 + 0.447447i \(0.852333\pi\)
\(774\) −16.1847 + 8.28780i −0.581749 + 0.297899i
\(775\) 2.93810i 0.105540i
\(776\) −38.5423 17.9024i −1.38359 0.642657i
\(777\) −4.07306 + 2.13934i −0.146120 + 0.0767482i
\(778\) 0.522074 + 17.6397i 0.0187172 + 0.632414i
\(779\) −44.2322 + 25.5375i −1.58478 + 0.914976i
\(780\) −8.49337 + 0.163201i −0.304112 + 0.00584354i
\(781\) 26.0124 + 15.0183i 0.930799 + 0.537397i
\(782\) 0.202631 0.376253i 0.00724609 0.0134548i
\(783\) −35.7075 26.7798i −1.27608 0.957034i
\(784\) −9.15300 + 21.3360i −0.326893 + 0.762002i
\(785\) −19.7645 11.4110i −0.705425 0.407277i
\(786\) −11.7630 + 6.62959i −0.419571 + 0.236470i
\(787\) 16.3098 + 28.2495i 0.581383 + 1.00698i 0.995316 + 0.0966772i \(0.0308215\pi\)
−0.413933 + 0.910307i \(0.635845\pi\)
\(788\) 10.7630 21.4843i 0.383415 0.765345i
\(789\) 32.1998 16.9127i 1.14634 0.602107i
\(790\) 1.77754 + 2.87861i 0.0632420 + 0.102416i
\(791\) −14.1355 −0.502602
\(792\) 22.6853 0.200490i 0.806086 0.00712410i
\(793\) −27.4533 −0.974896
\(794\) −0.345661 0.559777i −0.0122671 0.0198657i
\(795\) −0.148154 + 3.70530i −0.00525447 + 0.131413i
\(796\) −22.2448 11.1440i −0.788447 0.394988i
\(797\) 12.3771 + 21.4377i 0.438419 + 0.759363i 0.997568 0.0697039i \(-0.0222054\pi\)
−0.559149 + 0.829067i \(0.688872\pi\)
\(798\) 13.4688 + 7.96368i 0.476791 + 0.281911i
\(799\) 0.718131 + 0.414613i 0.0254056 + 0.0146679i
\(800\) 4.42856 3.51964i 0.156573 0.124438i
\(801\) 36.2739 17.2401i 1.28168 0.609149i
\(802\) −8.90308 + 16.5315i −0.314379 + 0.583749i
\(803\) 12.3966 + 7.15720i 0.437468 + 0.252572i
\(804\) −4.28936 2.36778i −0.151274 0.0835050i
\(805\) −2.29475 + 1.32488i −0.0808794 + 0.0466958i
\(806\) 0.301440 + 10.1850i 0.0106178 + 0.358751i
\(807\) 2.20646 + 1.39431i 0.0776710 + 0.0490821i
\(808\) 47.9570 + 22.2754i 1.68712 + 0.783644i
\(809\) 31.2048i 1.09710i 0.836116 + 0.548552i \(0.184821\pi\)
−0.836116 + 0.548552i \(0.815179\pi\)
\(810\) 11.7560 4.87824i 0.413063 0.171404i
\(811\) 37.9198 1.33155 0.665773 0.746155i \(-0.268102\pi\)
0.665773 + 0.746155i \(0.268102\pi\)
\(812\) −1.11109 18.7541i −0.0389914 0.658140i
\(813\) −23.4725 + 37.1446i −0.823218 + 1.30272i
\(814\) −0.271694 9.17993i −0.00952286 0.321756i
\(815\) 8.69869 + 15.0666i 0.304702 + 0.527759i
\(816\) −0.861370 + 0.0676602i −0.0301540 + 0.00236858i
\(817\) 12.5175 21.6810i 0.437933 0.758523i
\(818\) −0.278905 0.150205i −0.00975169 0.00525178i
\(819\) −3.45347 7.26625i −0.120674 0.253903i
\(820\) −14.6009 + 9.62409i −0.509887 + 0.336088i
\(821\) 10.9987 19.0504i 0.383859 0.664863i −0.607751 0.794127i \(-0.707928\pi\)
0.991610 + 0.129264i \(0.0412615\pi\)
\(822\) −18.8286 11.1327i −0.656722 0.388298i
\(823\) 30.4982 17.6082i 1.06310 0.613782i 0.136813 0.990597i \(-0.456314\pi\)
0.926289 + 0.376815i \(0.122981\pi\)
\(824\) −25.1993 35.8738i −0.877858 1.24972i
\(825\) −4.62709 0.185011i −0.161095 0.00644125i
\(826\) 3.56176 2.19938i 0.123930 0.0765263i
\(827\) 26.5196i 0.922178i −0.887354 0.461089i \(-0.847459\pi\)
0.887354 0.461089i \(-0.152541\pi\)
\(828\) 7.00633 + 12.7386i 0.243487 + 0.442697i
\(829\) 3.51213i 0.121981i −0.998138 0.0609907i \(-0.980574\pi\)
0.998138 0.0609907i \(-0.0194260\pi\)
\(830\) −9.62755 15.5912i −0.334177 0.541179i
\(831\) 11.0022 + 20.9470i 0.381664 + 0.726645i
\(832\) −14.9906 + 12.6553i −0.519706 + 0.438743i
\(833\) −0.626862 + 0.361919i −0.0217195 + 0.0125397i
\(834\) −18.4991 32.8231i −0.640571 1.13657i
\(835\) −7.48004 + 12.9558i −0.258857 + 0.448354i
\(836\) −26.0790 + 17.1898i −0.901962 + 0.594520i
\(837\) −5.99730 14.0395i −0.207297 0.485276i
\(838\) −5.36121 + 9.95488i −0.185200 + 0.343886i
\(839\) 6.16894 10.6849i 0.212975 0.368884i −0.739669 0.672971i \(-0.765018\pi\)
0.952644 + 0.304087i \(0.0983513\pi\)
\(840\) 4.76475 + 2.44916i 0.164399 + 0.0845041i
\(841\) −22.3923 38.7846i −0.772148 1.33740i
\(842\) 24.5212 0.725743i 0.845058 0.0250108i
\(843\) 2.34482 + 4.46427i 0.0807598 + 0.153758i
\(844\) −44.7390 + 2.65056i −1.53998 + 0.0912359i
\(845\) 6.98633 0.240337
\(846\) −25.1094 + 12.8579i −0.863279 + 0.442063i
\(847\) 4.21233i 0.144737i
\(848\) 5.12769 + 6.85905i 0.176085 + 0.235541i
\(849\) 0.668539 16.7201i 0.0229442 0.573831i
\(850\) 0.176291 0.00521759i 0.00604673 0.000178962i
\(851\) 5.09696 2.94273i 0.174722 0.100876i
\(852\) 33.3236 20.1027i 1.14165 0.688708i
\(853\) 28.9822 + 16.7329i 0.992330 + 0.572922i 0.905970 0.423342i \(-0.139143\pi\)
0.0863602 + 0.996264i \(0.472476\pi\)
\(854\) 15.2435 + 8.20939i 0.521621 + 0.280919i
\(855\) −9.94571 + 14.4282i −0.340136 + 0.493434i
\(856\) 46.9535 4.17874i 1.60484 0.142826i
\(857\) 3.00409 + 1.73441i 0.102618 + 0.0592464i 0.550431 0.834881i \(-0.314464\pi\)
−0.447813 + 0.894127i \(0.647797\pi\)
\(858\) 16.0589 + 0.166619i 0.548243 + 0.00568828i
\(859\) 11.4262 + 19.7907i 0.389855 + 0.675250i 0.992430 0.122813i \(-0.0391916\pi\)
−0.602574 + 0.798063i \(0.705858\pi\)
\(860\) 3.83933 7.66379i 0.130920 0.261333i
\(861\) −14.0005 8.84720i −0.477134 0.301512i
\(862\) 3.64498 2.25077i 0.124149 0.0766615i
\(863\) −22.0525 −0.750677 −0.375338 0.926888i \(-0.622474\pi\)
−0.375338 + 0.926888i \(0.622474\pi\)
\(864\) 13.9772 25.8580i 0.475514 0.879708i
\(865\) −25.8224 −0.877989
\(866\) 0.00658016 0.00406324i 0.000223603 0.000138074i
\(867\) 24.8687 + 15.7151i 0.844584 + 0.533712i
\(868\) 2.87825 5.74536i 0.0976941 0.195010i
\(869\) −3.19799 5.53909i −0.108485 0.187901i
\(870\) 21.0395 + 0.218295i 0.713305 + 0.00740088i
\(871\) −3.00373 1.73420i −0.101777 0.0587612i
\(872\) −26.9388 + 2.39749i −0.912264 + 0.0811892i
\(873\) 44.9310 + 3.59882i 1.52069 + 0.121802i
\(874\) −17.6233 9.49104i −0.596116 0.321039i
\(875\) −0.947055 0.546782i −0.0320163 0.0184846i
\(876\) 15.8809 9.58027i 0.536566 0.323687i
\(877\) 7.13379 4.11870i 0.240891 0.139079i −0.374695 0.927148i \(-0.622253\pi\)
0.615586 + 0.788070i \(0.288919\pi\)
\(878\) −36.6563 + 1.08490i −1.23709 + 0.0366135i
\(879\) 1.64733 41.1995i 0.0555630 1.38962i
\(880\) −8.56543 + 6.40334i −0.288740 + 0.215856i
\(881\) 32.8817i 1.10781i 0.832578 + 0.553907i \(0.186864\pi\)
−0.832578 + 0.553907i \(0.813136\pi\)
\(882\) 1.23904 24.5936i 0.0417207 0.828109i
\(883\) −11.4139 −0.384109 −0.192054 0.981384i \(-0.561515\pi\)
−0.192054 + 0.981384i \(0.561515\pi\)
\(884\) −0.610582 + 0.0361739i −0.0205361 + 0.00121666i
\(885\) 2.18004 + 4.15056i 0.0732813 + 0.139519i
\(886\) 21.3825 0.632847i 0.718358 0.0212609i
\(887\) −15.2731 26.4538i −0.512821 0.888232i −0.999889 0.0148681i \(-0.995267\pi\)
0.487069 0.873364i \(-0.338066\pi\)
\(888\) −10.5832 5.43992i −0.355148 0.182552i
\(889\) 8.63847 14.9623i 0.289725 0.501819i
\(890\) −8.97717 + 16.6691i −0.300915 + 0.558750i
\(891\) −22.4879 + 8.56085i −0.753373 + 0.286799i
\(892\) 11.7676 7.75648i 0.394007 0.259706i
\(893\) 19.4200 33.6365i 0.649866 1.12560i
\(894\) −0.244814 0.434377i −0.00818781 0.0145277i
\(895\) −4.91624 + 2.83839i −0.164332 + 0.0948770i
\(896\) 12.1079 2.54420i 0.404495 0.0849958i
\(897\) 4.78570 + 9.11144i 0.159790 + 0.304222i
\(898\) −3.59042 5.81446i −0.119814 0.194031i
\(899\) 25.2376i 0.841723i
\(900\) −3.10717 + 5.13279i −0.103572 + 0.171093i
\(901\) 0.267002i 0.00889513i
\(902\) 28.1295 17.3699i 0.936609 0.578354i
\(903\) 8.11139 + 0.324328i 0.269930 + 0.0107930i
\(904\) −21.0151 29.9172i −0.698951 0.995032i
\(905\) 11.5926 6.69298i 0.385351 0.222482i
\(906\) 13.6996 + 8.10016i 0.455140 + 0.269110i
\(907\) 7.61694 13.1929i 0.252916 0.438064i −0.711411 0.702776i \(-0.751944\pi\)
0.964328 + 0.264712i \(0.0852769\pi\)
\(908\) 18.6407 12.2868i 0.618613 0.407753i
\(909\) −55.9063 4.47791i −1.85430 0.148523i
\(910\) 3.33909 + 1.79827i 0.110690 + 0.0596121i
\(911\) 10.3048 17.8485i 0.341414 0.591346i −0.643282 0.765629i \(-0.722428\pi\)
0.984695 + 0.174284i \(0.0557610\pi\)
\(912\) 3.16913 + 40.3457i 0.104940 + 1.33598i
\(913\) 17.3211 + 30.0009i 0.573243 + 0.992887i
\(914\) 0.0684243 + 2.31190i 0.00226327 + 0.0764710i
\(915\) −10.3583 + 16.3918i −0.342436 + 0.541896i
\(916\) −0.766024 12.9298i −0.0253102 0.427212i
\(917\) 6.02815 0.199067
\(918\) 0.831744 0.384780i 0.0274516 0.0126996i
\(919\) 53.6801i 1.77074i −0.464884 0.885371i \(-0.653904\pi\)
0.464884 0.885371i \(-0.346096\pi\)
\(920\) −6.21562 2.88707i −0.204923 0.0951839i
\(921\) 26.0565 + 16.4657i 0.858591 + 0.542563i
\(922\) 0.339259 + 11.4628i 0.0111729 + 0.377508i
\(923\) 23.8592 13.7751i 0.785336 0.453414i
\(924\) −8.86690 4.89463i −0.291699 0.161021i
\(925\) 2.10354 + 1.21448i 0.0691639 + 0.0399318i
\(926\) 14.7581 27.4034i 0.484983 0.900532i
\(927\) 38.2847 + 26.3905i 1.25743 + 0.866779i
\(928\) 38.0404 30.2330i 1.24874 0.992447i
\(929\) 15.9508 + 9.20921i 0.523329 + 0.302144i 0.738296 0.674477i \(-0.235631\pi\)
−0.214966 + 0.976621i \(0.568964\pi\)
\(930\) 6.19497 + 3.66289i 0.203141 + 0.120111i
\(931\) 16.9519 + 29.3615i 0.555576 + 0.962285i
\(932\) 13.8494 + 6.93815i 0.453654 + 0.227267i
\(933\) 1.13459 28.3760i 0.0371449 0.928989i
\(934\) −3.46723 5.61497i −0.113451 0.183727i
\(935\) −0.333426 −0.0109042
\(936\) 10.2445 18.1117i 0.334851 0.592000i
\(937\) −50.9610 −1.66482 −0.832412 0.554157i \(-0.813041\pi\)
−0.832412 + 0.554157i \(0.813041\pi\)
\(938\) 1.14924 + 1.86112i 0.0375240 + 0.0607678i
\(939\) −32.9633 + 17.3137i −1.07572 + 0.565010i
\(940\) 5.95643 11.8898i 0.194277 0.387802i
\(941\) 21.4122 + 37.0870i 0.698018 + 1.20900i 0.969153 + 0.246461i \(0.0792678\pi\)
−0.271135 + 0.962541i \(0.587399\pi\)
\(942\) 48.7003 27.4474i 1.58674 0.894286i
\(943\) 18.3480 + 10.5932i 0.597492 + 0.344962i
\(944\) 9.95011 + 4.26852i 0.323849 + 0.138929i
\(945\) −5.64154 0.679617i −0.183519 0.0221080i
\(946\) −7.68374 + 14.2674i −0.249820 + 0.463874i
\(947\) −18.4862 10.6730i −0.600720 0.346826i 0.168604 0.985684i \(-0.446074\pi\)
−0.769325 + 0.638858i \(0.779407\pi\)
\(948\) −8.28559 + 0.159209i −0.269104 + 0.00517086i
\(949\) 11.3705 6.56475i 0.369102 0.213101i
\(950\) −0.244386 8.25727i −0.00792894 0.267901i
\(951\) −22.4005 + 11.7657i −0.726386 + 0.381528i
\(952\) 0.349843 + 0.162497i 0.0113385 + 0.00526656i
\(953\) 0.717198i 0.0232323i −0.999933 0.0116162i \(-0.996302\pi\)
0.999933 0.0116162i \(-0.00369762\pi\)
\(954\) −7.62792 4.93173i −0.246963 0.159671i
\(955\) −4.48347 −0.145082
\(956\) 28.9588 1.71566i 0.936594 0.0554884i
\(957\) −39.7458 1.58921i −1.28480 0.0513717i
\(958\) 0.347370 + 11.7368i 0.0112230 + 0.379200i
\(959\) 4.88268 + 8.45705i 0.157670 + 0.273092i
\(960\) 1.90014 + 13.7255i 0.0613267 + 0.442989i
\(961\) −11.1838 + 19.3709i −0.360768 + 0.624868i
\(962\) −7.41657 3.99421i −0.239120 0.128778i
\(963\) −45.1577 + 21.4623i −1.45519 + 0.691614i
\(964\) 22.0209 + 33.4085i 0.709246 + 1.07602i
\(965\) 4.45569 7.71749i 0.143434 0.248435i
\(966\) 0.0673389 6.49019i 0.00216659 0.208819i
\(967\) 1.20100 0.693395i 0.0386214 0.0222981i −0.480565 0.876959i \(-0.659568\pi\)
0.519186 + 0.854661i \(0.326235\pi\)
\(968\) −8.91520 + 6.26240i −0.286545 + 0.201281i
\(969\) −0.674034 + 1.06664i −0.0216531 + 0.0342654i
\(970\) −18.0794 + 11.1640i −0.580495 + 0.358455i
\(971\) 6.74126i 0.216337i −0.994133 0.108169i \(-0.965501\pi\)
0.994133 0.108169i \(-0.0344987\pi\)
\(972\) −4.37025 + 30.8691i −0.140176 + 0.990127i
\(973\) 16.8208i 0.539252i
\(974\) −9.04800 14.6527i −0.289917 0.469502i
\(975\) −2.26900 + 3.59063i −0.0726662 + 0.114992i
\(976\) 5.28743 + 44.4669i 0.169246 + 1.42335i
\(977\) 45.1870 26.0887i 1.44566 0.834652i 0.447441 0.894313i \(-0.352335\pi\)
0.998219 + 0.0596612i \(0.0190020\pi\)
\(978\) −42.6124 0.442124i −1.36259 0.0141376i
\(979\) 17.8963 30.9973i 0.571968 0.990678i
\(980\) 6.38851 + 9.69217i 0.204073 + 0.309605i
\(981\) 25.9086 12.3137i 0.827197 0.393146i
\(982\) −17.4004 + 32.3097i −0.555269 + 1.03104i
\(983\) −12.0449 + 20.8624i −0.384173 + 0.665407i −0.991654 0.128927i \(-0.958847\pi\)
0.607481 + 0.794334i \(0.292180\pi\)
\(984\) −2.08956 42.7843i −0.0666128 1.36391i
\(985\) −6.00737 10.4051i −0.191411 0.331533i
\(986\) 1.51430 0.0448181i 0.0482252 0.00142730i
\(987\) 12.5842 + 0.503170i 0.400560 + 0.0160161i
\(988\) 1.69434 + 28.5990i 0.0539043 + 0.909855i
\(989\) −10.3848 −0.330218
\(990\) 6.15864 9.52558i 0.195734 0.302743i
\(991\) 59.3927i 1.88667i 0.331840 + 0.943336i \(0.392331\pi\)
−0.331840 + 0.943336i \(0.607669\pi\)
\(992\) 16.4388 2.44985i 0.521934 0.0777828i
\(993\) −47.8842 + 25.1507i −1.51956 + 0.798134i
\(994\) −17.3670 + 0.514003i −0.550848 + 0.0163032i
\(995\) −10.7734 + 6.22003i −0.341540 + 0.197188i
\(996\) 44.8766 0.862310i 1.42197 0.0273233i
\(997\) 20.5450 + 11.8616i 0.650665 + 0.375662i 0.788711 0.614764i \(-0.210749\pi\)
−0.138046 + 0.990426i \(0.544082\pi\)
\(998\) 52.6064 + 28.3312i 1.66523 + 0.896809i
\(999\) 12.5306 + 1.50952i 0.396452 + 0.0477592i
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 360.2.bm.a.11.20 48
3.2 odd 2 1080.2.bm.b.251.5 48
4.3 odd 2 1440.2.cc.a.911.5 48
8.3 odd 2 360.2.bm.b.11.13 yes 48
8.5 even 2 1440.2.cc.b.911.5 48
9.4 even 3 1080.2.bm.a.611.12 48
9.5 odd 6 360.2.bm.b.131.13 yes 48
12.11 even 2 4320.2.cc.b.1871.14 48
24.5 odd 2 4320.2.cc.a.1871.11 48
24.11 even 2 1080.2.bm.a.251.12 48
36.23 even 6 1440.2.cc.b.1391.5 48
36.31 odd 6 4320.2.cc.a.3311.11 48
72.5 odd 6 1440.2.cc.a.1391.5 48
72.13 even 6 4320.2.cc.b.3311.14 48
72.59 even 6 inner 360.2.bm.a.131.20 yes 48
72.67 odd 6 1080.2.bm.b.611.5 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
360.2.bm.a.11.20 48 1.1 even 1 trivial
360.2.bm.a.131.20 yes 48 72.59 even 6 inner
360.2.bm.b.11.13 yes 48 8.3 odd 2
360.2.bm.b.131.13 yes 48 9.5 odd 6
1080.2.bm.a.251.12 48 24.11 even 2
1080.2.bm.a.611.12 48 9.4 even 3
1080.2.bm.b.251.5 48 3.2 odd 2
1080.2.bm.b.611.5 48 72.67 odd 6
1440.2.cc.a.911.5 48 4.3 odd 2
1440.2.cc.a.1391.5 48 72.5 odd 6
1440.2.cc.b.911.5 48 8.5 even 2
1440.2.cc.b.1391.5 48 36.23 even 6
4320.2.cc.a.1871.11 48 24.5 odd 2
4320.2.cc.a.3311.11 48 36.31 odd 6
4320.2.cc.b.1871.14 48 12.11 even 2
4320.2.cc.b.3311.14 48 72.13 even 6