Properties

Label 462.2.w.b.365.1
Level $462$
Weight $2$
Character 462.365
Analytic conductor $3.689$
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] = [462,2,Mod(29,462)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(462, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 0, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("462.29");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.w (of order \(10\), degree \(4\), 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: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 365.1
Character \(\chi\) \(=\) 462.365
Dual form 462.2.w.b.281.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.309017 + 0.951057i) q^{2} +(-1.71791 + 0.220849i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.826066 - 0.268405i) q^{5} +(0.320825 - 1.70208i) q^{6} +(-0.587785 + 0.809017i) q^{7} +(0.809017 - 0.587785i) q^{8} +(2.90245 - 0.758798i) q^{9} +O(q^{10})\) \(q+(-0.309017 + 0.951057i) q^{2} +(-1.71791 + 0.220849i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.826066 - 0.268405i) q^{5} +(0.320825 - 1.70208i) q^{6} +(-0.587785 + 0.809017i) q^{7} +(0.809017 - 0.587785i) q^{8} +(2.90245 - 0.758798i) q^{9} +0.868577i q^{10} +(2.10123 + 2.56609i) q^{11} +(1.51963 + 0.831094i) q^{12} +(-2.27068 - 0.737788i) q^{13} +(-0.587785 - 0.809017i) q^{14} +(-1.35983 + 0.643532i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.798865 + 2.45865i) q^{17} +(-0.175247 + 2.99488i) q^{18} +(-0.826882 - 1.13811i) q^{19} +(-0.826066 - 0.268405i) q^{20} +(0.831094 - 1.51963i) q^{21} +(-3.08982 + 1.20542i) q^{22} +7.05910i q^{23} +(-1.26001 + 1.18843i) q^{24} +(-3.43474 + 2.49549i) q^{25} +(1.40336 - 1.93155i) q^{26} +(-4.81858 + 1.94455i) q^{27} +(0.951057 - 0.309017i) q^{28} +(2.21175 + 1.60693i) q^{29} +(-0.191824 - 1.49214i) q^{30} +(-2.56914 + 7.90699i) q^{31} -1.00000 q^{32} +(-4.17645 - 3.94427i) q^{33} -2.58518 q^{34} +(-0.268405 + 0.826066i) q^{35} +(-2.79414 - 1.09214i) q^{36} +(-7.66547 - 5.56929i) q^{37} +(1.33792 - 0.434718i) q^{38} +(4.06377 + 0.765980i) q^{39} +(0.510537 - 0.702694i) q^{40} +(1.38502 - 1.00627i) q^{41} +(1.18843 + 1.26001i) q^{42} +8.09566i q^{43} +(-0.191619 - 3.31108i) q^{44} +(2.19395 - 1.40585i) q^{45} +(-6.71360 - 2.18138i) q^{46} +(-4.32066 - 5.94688i) q^{47} +(-0.740904 - 1.56559i) q^{48} +(-0.309017 - 0.951057i) q^{49} +(-1.31195 - 4.03778i) q^{50} +(-1.91537 - 4.04733i) q^{51} +(1.40336 + 1.93155i) q^{52} +(11.0186 + 3.58016i) q^{53} +(-0.360355 - 5.18364i) q^{54} +(2.42451 + 1.55578i) q^{55} +1.00000i q^{56} +(1.67186 + 1.77255i) q^{57} +(-2.21175 + 1.60693i) q^{58} +(-4.55709 + 6.27229i) q^{59} +(1.47839 + 0.278661i) q^{60} +(10.7299 - 3.48636i) q^{61} +(-6.72609 - 4.88679i) q^{62} +(-1.09214 + 2.79414i) q^{63} +(0.309017 - 0.951057i) q^{64} -2.07376 q^{65} +(5.04182 - 2.75319i) q^{66} +3.25130 q^{67} +(0.798865 - 2.45865i) q^{68} +(-1.55899 - 12.1269i) q^{69} +(-0.702694 - 0.510537i) q^{70} +(-1.00580 + 0.326804i) q^{71} +(1.90212 - 2.31990i) q^{72} +(-8.20257 + 11.2899i) q^{73} +(7.66547 - 5.56929i) q^{74} +(5.34946 - 5.04559i) q^{75} +1.40678i q^{76} +(-3.31108 + 0.191619i) q^{77} +(-1.98426 + 3.62817i) q^{78} +(14.0381 + 4.56125i) q^{79} +(0.510537 + 0.702694i) q^{80} +(7.84845 - 4.40475i) q^{81} +(0.529029 + 1.62818i) q^{82} +(2.40880 + 7.41353i) q^{83} +(-1.56559 + 0.740904i) q^{84} +(1.31983 + 1.81659i) q^{85} +(-7.69943 - 2.50170i) q^{86} +(-4.15448 - 2.27210i) q^{87} +(3.20824 + 0.840941i) q^{88} -4.36036i q^{89} +(0.659074 + 2.52100i) q^{90} +(1.93155 - 1.40336i) q^{91} +(4.14923 - 5.71093i) q^{92} +(2.66731 - 14.1509i) q^{93} +(6.99098 - 2.27151i) q^{94} +(-0.988533 - 0.718211i) q^{95} +(1.71791 - 0.220849i) q^{96} +(3.57219 - 10.9941i) q^{97} +1.00000 q^{98} +(8.04586 + 5.85355i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 12 q^{2} - 4 q^{3} - 12 q^{4} + 4 q^{6} + 12 q^{8} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 12 q^{2} - 4 q^{3} - 12 q^{4} + 4 q^{6} + 12 q^{8} + 10 q^{9} + 8 q^{11} + 6 q^{12} - 24 q^{15} - 12 q^{16} + 24 q^{17} + 10 q^{18} + 30 q^{19} - 8 q^{22} - 6 q^{24} + 18 q^{25} + 20 q^{26} + 38 q^{27} - 8 q^{29} - 36 q^{30} - 32 q^{31} - 48 q^{32} + 24 q^{33} - 4 q^{34} - 6 q^{35} - 20 q^{37} - 20 q^{38} - 34 q^{39} - 22 q^{44} + 12 q^{45} + 20 q^{46} - 20 q^{47} - 4 q^{48} + 12 q^{49} - 28 q^{50} + 2 q^{51} + 20 q^{52} - 20 q^{53} - 18 q^{54} + 16 q^{55} + 12 q^{57} + 8 q^{58} - 30 q^{59} - 4 q^{60} - 20 q^{61} - 8 q^{62} - 4 q^{63} - 12 q^{64} + 46 q^{66} + 36 q^{67} + 24 q^{68} + 30 q^{69} - 4 q^{70} - 10 q^{72} - 20 q^{73} + 20 q^{74} + 40 q^{75} + 16 q^{77} - 16 q^{78} - 20 q^{79} - 54 q^{81} - 10 q^{82} + 46 q^{83} - 10 q^{84} + 10 q^{85} + 30 q^{86} - 8 q^{87} - 8 q^{88} - 62 q^{90} - 36 q^{91} - 10 q^{92} + 44 q^{93} - 50 q^{95} + 4 q^{96} - 2 q^{97} + 48 q^{98} - 26 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{10}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.309017 + 0.951057i −0.218508 + 0.672499i
\(3\) −1.71791 + 0.220849i −0.991838 + 0.127507i
\(4\) −0.809017 0.587785i −0.404508 0.293893i
\(5\) 0.826066 0.268405i 0.369428 0.120034i −0.118419 0.992964i \(-0.537783\pi\)
0.487847 + 0.872929i \(0.337783\pi\)
\(6\) 0.320825 1.70208i 0.130976 0.694871i
\(7\) −0.587785 + 0.809017i −0.222162 + 0.305780i
\(8\) 0.809017 0.587785i 0.286031 0.207813i
\(9\) 2.90245 0.758798i 0.967484 0.252933i
\(10\) 0.868577i 0.274668i
\(11\) 2.10123 + 2.56609i 0.633545 + 0.773706i
\(12\) 1.51963 + 0.831094i 0.438680 + 0.239916i
\(13\) −2.27068 0.737788i −0.629773 0.204626i −0.0232985 0.999729i \(-0.507417\pi\)
−0.606475 + 0.795103i \(0.707417\pi\)
\(14\) −0.587785 0.809017i −0.157092 0.216219i
\(15\) −1.35983 + 0.643532i −0.351107 + 0.166159i
\(16\) 0.309017 + 0.951057i 0.0772542 + 0.237764i
\(17\) 0.798865 + 2.45865i 0.193753 + 0.596311i 0.999989 + 0.00471671i \(0.00150138\pi\)
−0.806236 + 0.591595i \(0.798499\pi\)
\(18\) −0.175247 + 2.99488i −0.0413062 + 0.705899i
\(19\) −0.826882 1.13811i −0.189700 0.261099i 0.703564 0.710632i \(-0.251591\pi\)
−0.893264 + 0.449532i \(0.851591\pi\)
\(20\) −0.826066 0.268405i −0.184714 0.0600172i
\(21\) 0.831094 1.51963i 0.181360 0.331611i
\(22\) −3.08982 + 1.20542i −0.658751 + 0.256997i
\(23\) 7.05910i 1.47192i 0.677023 + 0.735962i \(0.263270\pi\)
−0.677023 + 0.735962i \(0.736730\pi\)
\(24\) −1.26001 + 1.18843i −0.257198 + 0.242588i
\(25\) −3.43474 + 2.49549i −0.686948 + 0.499097i
\(26\) 1.40336 1.93155i 0.275221 0.378809i
\(27\) −4.81858 + 1.94455i −0.927336 + 0.374229i
\(28\) 0.951057 0.309017i 0.179733 0.0583987i
\(29\) 2.21175 + 1.60693i 0.410711 + 0.298399i 0.773890 0.633320i \(-0.218308\pi\)
−0.363178 + 0.931720i \(0.618308\pi\)
\(30\) −0.191824 1.49214i −0.0350221 0.272426i
\(31\) −2.56914 + 7.90699i −0.461431 + 1.42014i 0.401986 + 0.915646i \(0.368320\pi\)
−0.863417 + 0.504492i \(0.831680\pi\)
\(32\) −1.00000 −0.176777
\(33\) −4.17645 3.94427i −0.727026 0.686609i
\(34\) −2.58518 −0.443355
\(35\) −0.268405 + 0.826066i −0.0453687 + 0.139631i
\(36\) −2.79414 1.09214i −0.465690 0.182023i
\(37\) −7.66547 5.56929i −1.26020 0.915586i −0.261429 0.965223i \(-0.584194\pi\)
−0.998767 + 0.0496366i \(0.984194\pi\)
\(38\) 1.33792 0.434718i 0.217040 0.0705205i
\(39\) 4.06377 + 0.765980i 0.650724 + 0.122655i
\(40\) 0.510537 0.702694i 0.0807230 0.111106i
\(41\) 1.38502 1.00627i 0.216303 0.157154i −0.474358 0.880332i \(-0.657320\pi\)
0.690661 + 0.723179i \(0.257320\pi\)
\(42\) 1.18843 + 1.26001i 0.183379 + 0.194424i
\(43\) 8.09566i 1.23458i 0.786737 + 0.617289i \(0.211769\pi\)
−0.786737 + 0.617289i \(0.788231\pi\)
\(44\) −0.191619 3.31108i −0.0288876 0.499165i
\(45\) 2.19395 1.40585i 0.327055 0.209572i
\(46\) −6.71360 2.18138i −0.989866 0.321627i
\(47\) −4.32066 5.94688i −0.630234 0.867442i 0.367814 0.929899i \(-0.380106\pi\)
−0.998048 + 0.0624572i \(0.980106\pi\)
\(48\) −0.740904 1.56559i −0.106940 0.225973i
\(49\) −0.309017 0.951057i −0.0441453 0.135865i
\(50\) −1.31195 4.03778i −0.185538 0.571028i
\(51\) −1.91537 4.04733i −0.268206 0.566739i
\(52\) 1.40336 + 1.93155i 0.194611 + 0.267858i
\(53\) 11.0186 + 3.58016i 1.51352 + 0.491773i 0.943927 0.330154i \(-0.107101\pi\)
0.569593 + 0.821927i \(0.307101\pi\)
\(54\) −0.360355 5.18364i −0.0490381 0.705404i
\(55\) 2.42451 + 1.55578i 0.326920 + 0.209782i
\(56\) 1.00000i 0.133631i
\(57\) 1.67186 + 1.77255i 0.221443 + 0.234780i
\(58\) −2.21175 + 1.60693i −0.290417 + 0.211000i
\(59\) −4.55709 + 6.27229i −0.593282 + 0.816583i −0.995073 0.0991487i \(-0.968388\pi\)
0.401790 + 0.915732i \(0.368388\pi\)
\(60\) 1.47839 + 0.278661i 0.190859 + 0.0359750i
\(61\) 10.7299 3.48636i 1.37382 0.446383i 0.473190 0.880960i \(-0.343102\pi\)
0.900634 + 0.434578i \(0.143102\pi\)
\(62\) −6.72609 4.88679i −0.854214 0.620623i
\(63\) −1.09214 + 2.79414i −0.137596 + 0.352029i
\(64\) 0.309017 0.951057i 0.0386271 0.118882i
\(65\) −2.07376 −0.257218
\(66\) 5.04182 2.75319i 0.620605 0.338894i
\(67\) 3.25130 0.397209 0.198605 0.980080i \(-0.436359\pi\)
0.198605 + 0.980080i \(0.436359\pi\)
\(68\) 0.798865 2.45865i 0.0968766 0.298156i
\(69\) −1.55899 12.1269i −0.187681 1.45991i
\(70\) −0.702694 0.510537i −0.0839880 0.0610208i
\(71\) −1.00580 + 0.326804i −0.119367 + 0.0387845i −0.368091 0.929790i \(-0.619989\pi\)
0.248725 + 0.968574i \(0.419989\pi\)
\(72\) 1.90212 2.31990i 0.224167 0.273403i
\(73\) −8.20257 + 11.2899i −0.960038 + 1.32138i −0.0131169 + 0.999914i \(0.504175\pi\)
−0.946921 + 0.321465i \(0.895825\pi\)
\(74\) 7.66547 5.56929i 0.891093 0.647417i
\(75\) 5.34946 5.04559i 0.617703 0.582614i
\(76\) 1.40678i 0.161368i
\(77\) −3.31108 + 0.191619i −0.377333 + 0.0218370i
\(78\) −1.98426 + 3.62817i −0.224674 + 0.410810i
\(79\) 14.0381 + 4.56125i 1.57941 + 0.513181i 0.961904 0.273387i \(-0.0881441\pi\)
0.617504 + 0.786568i \(0.288144\pi\)
\(80\) 0.510537 + 0.702694i 0.0570798 + 0.0785635i
\(81\) 7.84845 4.40475i 0.872050 0.489416i
\(82\) 0.529029 + 1.62818i 0.0584215 + 0.179803i
\(83\) 2.40880 + 7.41353i 0.264400 + 0.813740i 0.991831 + 0.127559i \(0.0407142\pi\)
−0.727431 + 0.686181i \(0.759286\pi\)
\(84\) −1.56559 + 0.740904i −0.170819 + 0.0808393i
\(85\) 1.31983 + 1.81659i 0.143156 + 0.197037i
\(86\) −7.69943 2.50170i −0.830251 0.269765i
\(87\) −4.15448 2.27210i −0.445407 0.243595i
\(88\) 3.20824 + 0.840941i 0.342000 + 0.0896446i
\(89\) 4.36036i 0.462197i −0.972930 0.231099i \(-0.925768\pi\)
0.972930 0.231099i \(-0.0742320\pi\)
\(90\) 0.659074 + 2.52100i 0.0694725 + 0.265737i
\(91\) 1.93155 1.40336i 0.202482 0.147112i
\(92\) 4.14923 5.71093i 0.432587 0.595406i
\(93\) 2.66731 14.1509i 0.276587 1.46738i
\(94\) 6.99098 2.27151i 0.721065 0.234288i
\(95\) −0.988533 0.718211i −0.101421 0.0736869i
\(96\) 1.71791 0.220849i 0.175334 0.0225403i
\(97\) 3.57219 10.9941i 0.362701 1.11628i −0.588707 0.808347i \(-0.700363\pi\)
0.951408 0.307933i \(-0.0996374\pi\)
\(98\) 1.00000 0.101015
\(99\) 8.04586 + 5.85355i 0.808640 + 0.588304i
\(100\) 4.24557 0.424557
\(101\) 3.86333 11.8901i 0.384416 1.18311i −0.552488 0.833521i \(-0.686321\pi\)
0.936903 0.349589i \(-0.113679\pi\)
\(102\) 4.44112 0.570934i 0.439736 0.0565309i
\(103\) −7.10827 5.16446i −0.700398 0.508869i 0.179664 0.983728i \(-0.442499\pi\)
−0.880062 + 0.474859i \(0.842499\pi\)
\(104\) −2.27068 + 0.737788i −0.222658 + 0.0723461i
\(105\) 0.278661 1.47839i 0.0271945 0.144276i
\(106\) −6.80987 + 9.37298i −0.661433 + 0.910384i
\(107\) 5.70103 4.14204i 0.551140 0.400426i −0.277066 0.960851i \(-0.589362\pi\)
0.828205 + 0.560425i \(0.189362\pi\)
\(108\) 5.04129 + 1.25912i 0.485099 + 0.121158i
\(109\) 1.36825i 0.131055i −0.997851 0.0655274i \(-0.979127\pi\)
0.997851 0.0655274i \(-0.0208730\pi\)
\(110\) −2.22885 + 1.82508i −0.212512 + 0.174015i
\(111\) 14.3986 + 7.87465i 1.36665 + 0.747429i
\(112\) −0.951057 0.309017i −0.0898664 0.0291994i
\(113\) 3.06929 + 4.22452i 0.288735 + 0.397409i 0.928603 0.371076i \(-0.121011\pi\)
−0.639868 + 0.768485i \(0.721011\pi\)
\(114\) −2.20243 + 1.04229i −0.206276 + 0.0976190i
\(115\) 1.89470 + 5.83128i 0.176681 + 0.543770i
\(116\) −0.844812 2.60007i −0.0784389 0.241410i
\(117\) −7.15037 0.418409i −0.661052 0.0386819i
\(118\) −4.55709 6.27229i −0.419514 0.577411i
\(119\) −2.45865 0.798865i −0.225384 0.0732319i
\(120\) −0.721869 + 1.31992i −0.0658973 + 0.120491i
\(121\) −2.16967 + 10.7839i −0.197242 + 0.980355i
\(122\) 11.2821i 1.02143i
\(123\) −2.15710 + 2.03457i −0.194500 + 0.183451i
\(124\) 6.72609 4.88679i 0.604021 0.438847i
\(125\) −4.72021 + 6.49681i −0.422188 + 0.581092i
\(126\) −2.31990 1.90212i −0.206673 0.169455i
\(127\) −3.23727 + 1.05185i −0.287262 + 0.0933370i −0.449104 0.893480i \(-0.648257\pi\)
0.161842 + 0.986817i \(0.448257\pi\)
\(128\) 0.809017 + 0.587785i 0.0715077 + 0.0519534i
\(129\) −1.78792 13.9076i −0.157417 1.22450i
\(130\) 0.640826 1.97226i 0.0562042 0.172979i
\(131\) −2.32126 −0.202809 −0.101405 0.994845i \(-0.532334\pi\)
−0.101405 + 0.994845i \(0.532334\pi\)
\(132\) 1.06043 + 5.64584i 0.0922989 + 0.491407i
\(133\) 1.40678 0.121983
\(134\) −1.00471 + 3.09217i −0.0867934 + 0.267123i
\(135\) −3.45854 + 2.89966i −0.297664 + 0.249563i
\(136\) 2.09146 + 1.51953i 0.179341 + 0.130299i
\(137\) −11.5111 + 3.74017i −0.983456 + 0.319544i −0.756236 0.654299i \(-0.772964\pi\)
−0.227220 + 0.973843i \(0.572964\pi\)
\(138\) 12.0151 + 2.26473i 1.02280 + 0.192787i
\(139\) 7.37130 10.1457i 0.625225 0.860549i −0.372495 0.928034i \(-0.621498\pi\)
0.997720 + 0.0674855i \(0.0214976\pi\)
\(140\) 0.702694 0.510537i 0.0593885 0.0431482i
\(141\) 8.73589 + 9.26202i 0.735694 + 0.780003i
\(142\) 1.05756i 0.0887486i
\(143\) −2.87798 7.37704i −0.240669 0.616899i
\(144\) 1.61857 + 2.52591i 0.134881 + 0.210493i
\(145\) 2.25836 + 0.733785i 0.187546 + 0.0609375i
\(146\) −8.20257 11.2899i −0.678850 0.934356i
\(147\) 0.740904 + 1.56559i 0.0611087 + 0.129127i
\(148\) 2.92795 + 9.01131i 0.240676 + 0.740725i
\(149\) 4.39186 + 13.5168i 0.359795 + 1.10734i 0.953177 + 0.302414i \(0.0977926\pi\)
−0.593381 + 0.804921i \(0.702207\pi\)
\(150\) 3.14556 + 6.64681i 0.256834 + 0.542710i
\(151\) −5.02618 6.91794i −0.409025 0.562974i 0.553956 0.832546i \(-0.313118\pi\)
−0.962980 + 0.269572i \(0.913118\pi\)
\(152\) −1.33792 0.434718i −0.108520 0.0352603i
\(153\) 4.18429 + 6.52995i 0.338280 + 0.527915i
\(154\) 0.840941 3.20824i 0.0677650 0.258528i
\(155\) 7.22126i 0.580026i
\(156\) −2.83743 3.00831i −0.227176 0.240858i
\(157\) −7.23521 + 5.25669i −0.577433 + 0.419529i −0.837798 0.545981i \(-0.816157\pi\)
0.260365 + 0.965510i \(0.416157\pi\)
\(158\) −8.67601 + 11.9415i −0.690226 + 0.950015i
\(159\) −19.7197 3.71696i −1.56387 0.294774i
\(160\) −0.826066 + 0.268405i −0.0653062 + 0.0212193i
\(161\) −5.71093 4.14923i −0.450084 0.327005i
\(162\) 1.76386 + 8.82546i 0.138582 + 0.693394i
\(163\) 3.78357 11.6446i 0.296352 0.912077i −0.686412 0.727213i \(-0.740815\pi\)
0.982764 0.184864i \(-0.0591846\pi\)
\(164\) −1.71197 −0.133683
\(165\) −4.50868 2.13725i −0.351001 0.166385i
\(166\) −7.79504 −0.605013
\(167\) 4.04296 12.4429i 0.312853 0.962864i −0.663776 0.747932i \(-0.731047\pi\)
0.976629 0.214932i \(-0.0689530\pi\)
\(168\) −0.220849 1.71791i −0.0170388 0.132540i
\(169\) −5.90557 4.29065i −0.454275 0.330050i
\(170\) −2.13553 + 0.693876i −0.163788 + 0.0532179i
\(171\) −3.26358 2.67586i −0.249572 0.204628i
\(172\) 4.75851 6.54953i 0.362833 0.499397i
\(173\) 13.9724 10.1516i 1.06230 0.771809i 0.0877903 0.996139i \(-0.472019\pi\)
0.974513 + 0.224330i \(0.0720194\pi\)
\(174\) 3.44470 3.24903i 0.261142 0.246308i
\(175\) 4.24557i 0.320935i
\(176\) −1.79118 + 2.79135i −0.135016 + 0.210406i
\(177\) 6.44345 11.7817i 0.484320 0.885565i
\(178\) 4.14695 + 1.34743i 0.310827 + 0.100994i
\(179\) −1.60174 2.20460i −0.119719 0.164780i 0.744951 0.667119i \(-0.232473\pi\)
−0.864670 + 0.502339i \(0.832473\pi\)
\(180\) −2.60128 0.152216i −0.193888 0.0113455i
\(181\) −5.32872 16.4001i −0.396081 1.21901i −0.928117 0.372289i \(-0.878573\pi\)
0.532036 0.846722i \(-0.321427\pi\)
\(182\) 0.737788 + 2.27068i 0.0546885 + 0.168314i
\(183\) −17.6631 + 8.35895i −1.30569 + 0.617911i
\(184\) 4.14923 + 5.71093i 0.305886 + 0.421015i
\(185\) −7.82701 2.54315i −0.575454 0.186976i
\(186\) 12.6341 + 6.90963i 0.926375 + 0.506639i
\(187\) −4.63054 + 7.21616i −0.338618 + 0.527698i
\(188\) 7.35075i 0.536109i
\(189\) 1.25912 5.04129i 0.0915872 0.366700i
\(190\) 0.988533 0.718211i 0.0717157 0.0521045i
\(191\) −5.57837 + 7.67797i −0.403637 + 0.555559i −0.961652 0.274272i \(-0.911563\pi\)
0.558015 + 0.829831i \(0.311563\pi\)
\(192\) −0.320825 + 1.70208i −0.0231535 + 0.122837i
\(193\) −0.857425 + 0.278594i −0.0617188 + 0.0200537i −0.339714 0.940529i \(-0.610330\pi\)
0.277995 + 0.960583i \(0.410330\pi\)
\(194\) 9.35213 + 6.79472i 0.671444 + 0.487832i
\(195\) 3.56253 0.457986i 0.255118 0.0327971i
\(196\) −0.309017 + 0.951057i −0.0220726 + 0.0679326i
\(197\) 16.1154 1.14818 0.574088 0.818794i \(-0.305357\pi\)
0.574088 + 0.818794i \(0.305357\pi\)
\(198\) −8.05337 + 5.84322i −0.572328 + 0.415260i
\(199\) −2.39529 −0.169798 −0.0848989 0.996390i \(-0.527057\pi\)
−0.0848989 + 0.996390i \(0.527057\pi\)
\(200\) −1.31195 + 4.03778i −0.0927692 + 0.285514i
\(201\) −5.58545 + 0.718045i −0.393967 + 0.0506470i
\(202\) 10.1143 + 7.34849i 0.711642 + 0.517038i
\(203\) −2.60007 + 0.844812i −0.182489 + 0.0592942i
\(204\) −0.829391 + 4.40018i −0.0580690 + 0.308074i
\(205\) 0.874026 1.20299i 0.0610446 0.0840207i
\(206\) 7.10827 5.16446i 0.495256 0.359825i
\(207\) 5.35643 + 20.4887i 0.372297 + 1.42406i
\(208\) 2.38753i 0.165546i
\(209\) 1.18302 4.51328i 0.0818309 0.312190i
\(210\) 1.31992 + 0.721869i 0.0910830 + 0.0498137i
\(211\) −1.10512 0.359075i −0.0760796 0.0247197i 0.270730 0.962655i \(-0.412735\pi\)
−0.346809 + 0.937936i \(0.612735\pi\)
\(212\) −6.80987 9.37298i −0.467703 0.643739i
\(213\) 1.65570 0.783551i 0.113447 0.0536880i
\(214\) 2.17760 + 6.70196i 0.148858 + 0.458137i
\(215\) 2.17292 + 6.68755i 0.148192 + 0.456087i
\(216\) −2.75533 + 4.40547i −0.187477 + 0.299754i
\(217\) −4.88679 6.72609i −0.331737 0.456597i
\(218\) 1.30129 + 0.422813i 0.0881342 + 0.0286365i
\(219\) 11.5980 21.2065i 0.783717 1.43301i
\(220\) −1.04700 2.68374i −0.0705889 0.180938i
\(221\) 6.17221i 0.415188i
\(222\) −11.9386 + 11.2605i −0.801270 + 0.755753i
\(223\) −16.3441 + 11.8747i −1.09448 + 0.795188i −0.980151 0.198254i \(-0.936473\pi\)
−0.114332 + 0.993443i \(0.536473\pi\)
\(224\) 0.587785 0.809017i 0.0392731 0.0540547i
\(225\) −8.07560 + 9.84930i −0.538373 + 0.656620i
\(226\) −4.96622 + 1.61362i −0.330348 + 0.107337i
\(227\) −8.63392 6.27291i −0.573053 0.416348i 0.263160 0.964752i \(-0.415235\pi\)
−0.836213 + 0.548405i \(0.815235\pi\)
\(228\) −0.310685 2.41672i −0.0205756 0.160051i
\(229\) 0.489598 1.50683i 0.0323535 0.0995739i −0.933576 0.358380i \(-0.883329\pi\)
0.965929 + 0.258806i \(0.0833291\pi\)
\(230\) −6.13137 −0.404291
\(231\) 5.64584 1.06043i 0.371469 0.0697714i
\(232\) 2.73387 0.179487
\(233\) 3.15670 9.71532i 0.206802 0.636472i −0.792832 0.609440i \(-0.791394\pi\)
0.999635 0.0270320i \(-0.00860560\pi\)
\(234\) 2.60752 6.67111i 0.170459 0.436104i
\(235\) −5.16533 3.75283i −0.336949 0.244808i
\(236\) 7.37352 2.39580i 0.479975 0.155953i
\(237\) −25.1236 4.73554i −1.63195 0.307606i
\(238\) 1.51953 2.09146i 0.0984966 0.135569i
\(239\) 16.8321 12.2292i 1.08878 0.791041i 0.109583 0.993978i \(-0.465048\pi\)
0.979192 + 0.202936i \(0.0650484\pi\)
\(240\) −1.03225 1.09442i −0.0666313 0.0706442i
\(241\) 15.8700i 1.02228i 0.859499 + 0.511138i \(0.170776\pi\)
−0.859499 + 0.511138i \(0.829224\pi\)
\(242\) −9.58564 5.39588i −0.616188 0.346861i
\(243\) −12.5102 + 9.30030i −0.802528 + 0.596614i
\(244\) −10.7299 3.48636i −0.686912 0.223191i
\(245\) −0.510537 0.702694i −0.0326170 0.0448935i
\(246\) −1.26841 2.68024i −0.0808708 0.170886i
\(247\) 1.03790 + 3.19434i 0.0660402 + 0.203251i
\(248\) 2.56914 + 7.90699i 0.163140 + 0.502094i
\(249\) −5.77538 12.2038i −0.366000 0.773385i
\(250\) −4.72021 6.49681i −0.298532 0.410894i
\(251\) 8.08993 + 2.62858i 0.510632 + 0.165914i 0.552990 0.833188i \(-0.313487\pi\)
−0.0423578 + 0.999103i \(0.513487\pi\)
\(252\) 2.52591 1.61857i 0.159118 0.101960i
\(253\) −18.1143 + 14.8328i −1.13884 + 0.932529i
\(254\) 3.40387i 0.213578i
\(255\) −2.66855 2.82926i −0.167111 0.177175i
\(256\) −0.809017 + 0.587785i −0.0505636 + 0.0367366i
\(257\) −7.98604 + 10.9918i −0.498156 + 0.685652i −0.981866 0.189576i \(-0.939289\pi\)
0.483711 + 0.875228i \(0.339289\pi\)
\(258\) 13.7795 + 2.59729i 0.857872 + 0.161700i
\(259\) 9.01131 2.92795i 0.559935 0.181934i
\(260\) 1.67770 + 1.21892i 0.104047 + 0.0755944i
\(261\) 7.63882 + 2.98576i 0.472831 + 0.184814i
\(262\) 0.717308 2.20765i 0.0443154 0.136389i
\(263\) −24.4820 −1.50962 −0.754811 0.655942i \(-0.772271\pi\)
−0.754811 + 0.655942i \(0.772271\pi\)
\(264\) −5.69720 0.736128i −0.350639 0.0453055i
\(265\) 10.0630 0.618166
\(266\) −0.434718 + 1.33792i −0.0266543 + 0.0820334i
\(267\) 0.962980 + 7.49072i 0.0589334 + 0.458425i
\(268\) −2.63035 1.91106i −0.160674 0.116737i
\(269\) 2.86740 0.931675i 0.174828 0.0568052i −0.220295 0.975433i \(-0.570702\pi\)
0.395123 + 0.918628i \(0.370702\pi\)
\(270\) −1.68899 4.18531i −0.102789 0.254710i
\(271\) 4.85580 6.68343i 0.294969 0.405990i −0.635651 0.771976i \(-0.719268\pi\)
0.930620 + 0.365987i \(0.119268\pi\)
\(272\) −2.09146 + 1.51953i −0.126813 + 0.0921352i
\(273\) −3.00831 + 2.83743i −0.182071 + 0.171729i
\(274\) 12.1034i 0.731195i
\(275\) −13.6208 3.57028i −0.821367 0.215296i
\(276\) −5.86677 + 10.7272i −0.353138 + 0.645704i
\(277\) 5.89617 + 1.91578i 0.354267 + 0.115108i 0.480743 0.876861i \(-0.340367\pi\)
−0.126477 + 0.991970i \(0.540367\pi\)
\(278\) 7.37130 + 10.1457i 0.442101 + 0.608500i
\(279\) −1.45699 + 24.8991i −0.0872276 + 1.49067i
\(280\) 0.268405 + 0.826066i 0.0160403 + 0.0493669i
\(281\) 7.08533 + 21.8064i 0.422675 + 1.30086i 0.905203 + 0.424980i \(0.139719\pi\)
−0.482527 + 0.875881i \(0.660281\pi\)
\(282\) −11.5082 + 5.44620i −0.685306 + 0.324317i
\(283\) 0.655664 + 0.902445i 0.0389752 + 0.0536448i 0.828060 0.560640i \(-0.189445\pi\)
−0.789085 + 0.614284i \(0.789445\pi\)
\(284\) 1.00580 + 0.326804i 0.0596833 + 0.0193923i
\(285\) 1.85683 + 1.01551i 0.109989 + 0.0601535i
\(286\) 7.90532 0.457497i 0.467452 0.0270523i
\(287\) 1.71197i 0.101055i
\(288\) −2.90245 + 0.758798i −0.171029 + 0.0447126i
\(289\) 8.34649 6.06408i 0.490970 0.356711i
\(290\) −1.39574 + 1.92107i −0.0819608 + 0.112809i
\(291\) −3.70869 + 19.6758i −0.217407 + 1.15342i
\(292\) 13.2720 4.31235i 0.776687 0.252361i
\(293\) 18.4654 + 13.4159i 1.07876 + 0.783765i 0.977466 0.211091i \(-0.0677017\pi\)
0.101294 + 0.994857i \(0.467702\pi\)
\(294\) −1.71791 + 0.220849i −0.100191 + 0.0128802i
\(295\) −2.08094 + 6.40447i −0.121157 + 0.372883i
\(296\) −9.47505 −0.550726
\(297\) −15.1148 8.27898i −0.877052 0.480395i
\(298\) −14.2124 −0.823300
\(299\) 5.20812 16.0289i 0.301193 0.926978i
\(300\) −7.29353 + 0.937630i −0.421092 + 0.0541341i
\(301\) −6.54953 4.75851i −0.377509 0.274276i
\(302\) 8.13253 2.64242i 0.467974 0.152054i
\(303\) −4.01095 + 21.2794i −0.230423 + 1.22247i
\(304\) 0.826882 1.13811i 0.0474250 0.0652748i
\(305\) 7.92786 5.75993i 0.453948 0.329812i
\(306\) −7.50337 + 1.96163i −0.428939 + 0.112139i
\(307\) 24.2578i 1.38447i −0.721674 0.692233i \(-0.756627\pi\)
0.721674 0.692233i \(-0.243373\pi\)
\(308\) 2.79135 + 1.79118i 0.159052 + 0.102062i
\(309\) 13.3519 + 7.30224i 0.759566 + 0.415410i
\(310\) −6.86783 2.23149i −0.390067 0.126740i
\(311\) 14.2391 + 19.5985i 0.807428 + 1.11133i 0.991715 + 0.128457i \(0.0410024\pi\)
−0.184287 + 0.982872i \(0.558998\pi\)
\(312\) 3.73789 1.76893i 0.211616 0.100146i
\(313\) 5.95258 + 18.3202i 0.336460 + 1.03552i 0.965999 + 0.258548i \(0.0832439\pi\)
−0.629539 + 0.776969i \(0.716756\pi\)
\(314\) −2.76360 8.50550i −0.155959 0.479993i
\(315\) −0.152216 + 2.60128i −0.00857639 + 0.146566i
\(316\) −8.67601 11.9415i −0.488064 0.671762i
\(317\) −9.22231 2.99651i −0.517976 0.168301i 0.0383503 0.999264i \(-0.487790\pi\)
−0.556327 + 0.830964i \(0.687790\pi\)
\(318\) 9.62875 17.6059i 0.539953 0.987290i
\(319\) 0.523861 + 9.05208i 0.0293306 + 0.506819i
\(320\) 0.868577i 0.0485549i
\(321\) −8.87911 + 8.37473i −0.495584 + 0.467432i
\(322\) 5.71093 4.14923i 0.318258 0.231228i
\(323\) 2.13764 2.94221i 0.118942 0.163709i
\(324\) −8.93858 1.04969i −0.496588 0.0583160i
\(325\) 9.64033 3.13233i 0.534750 0.173751i
\(326\) 9.90550 + 7.19677i 0.548615 + 0.398592i
\(327\) 0.302177 + 2.35054i 0.0167104 + 0.129985i
\(328\) 0.529029 1.62818i 0.0292108 0.0899015i
\(329\) 7.35075 0.405260
\(330\) 3.42590 3.62757i 0.188590 0.199691i
\(331\) 25.6282 1.40865 0.704327 0.709876i \(-0.251249\pi\)
0.704327 + 0.709876i \(0.251249\pi\)
\(332\) 2.40880 7.41353i 0.132200 0.406870i
\(333\) −26.4746 10.3481i −1.45080 0.567070i
\(334\) 10.5846 + 7.69016i 0.579164 + 0.420787i
\(335\) 2.68579 0.872665i 0.146740 0.0476788i
\(336\) 1.70208 + 0.320825i 0.0928560 + 0.0175024i
\(337\) 11.0189 15.1662i 0.600237 0.826155i −0.395493 0.918469i \(-0.629426\pi\)
0.995730 + 0.0923139i \(0.0294263\pi\)
\(338\) 5.90557 4.29065i 0.321221 0.233380i
\(339\) −6.20575 6.57950i −0.337050 0.357350i
\(340\) 2.24543i 0.121776i
\(341\) −25.6884 + 10.0218i −1.39111 + 0.542709i
\(342\) 3.55340 2.27696i 0.192146 0.123124i
\(343\) 0.951057 + 0.309017i 0.0513522 + 0.0166853i
\(344\) 4.75851 + 6.54953i 0.256562 + 0.353127i
\(345\) −4.54276 9.59919i −0.244574 0.516803i
\(346\) 5.33699 + 16.4256i 0.286918 + 0.883044i
\(347\) −0.170339 0.524249i −0.00914426 0.0281432i 0.946380 0.323055i \(-0.104710\pi\)
−0.955525 + 0.294912i \(0.904710\pi\)
\(348\) 2.02554 + 4.28011i 0.108580 + 0.229438i
\(349\) −6.49222 8.93578i −0.347521 0.478321i 0.599099 0.800675i \(-0.295526\pi\)
−0.946619 + 0.322354i \(0.895526\pi\)
\(350\) 4.03778 + 1.31195i 0.215828 + 0.0701269i
\(351\) 12.3761 0.860360i 0.660588 0.0459226i
\(352\) −2.10123 2.56609i −0.111996 0.136773i
\(353\) 19.7791i 1.05273i 0.850257 + 0.526367i \(0.176446\pi\)
−0.850257 + 0.526367i \(0.823554\pi\)
\(354\) 9.21391 + 9.76883i 0.489714 + 0.519207i
\(355\) −0.743141 + 0.539924i −0.0394419 + 0.0286562i
\(356\) −2.56296 + 3.52761i −0.135836 + 0.186963i
\(357\) 4.40018 + 0.829391i 0.232882 + 0.0438960i
\(358\) 2.59166 0.842083i 0.136974 0.0445055i
\(359\) 7.99645 + 5.80976i 0.422036 + 0.306627i 0.778457 0.627698i \(-0.216003\pi\)
−0.356420 + 0.934326i \(0.616003\pi\)
\(360\) 0.948606 2.42693i 0.0499959 0.127910i
\(361\) 5.25977 16.1879i 0.276830 0.851996i
\(362\) 17.2441 0.906330
\(363\) 1.34569 19.0050i 0.0706303 0.997503i
\(364\) −2.38753 −0.125141
\(365\) −3.74561 + 11.5278i −0.196054 + 0.603392i
\(366\) −2.49164 19.3817i −0.130240 1.01310i
\(367\) 19.3727 + 14.0751i 1.01125 + 0.734714i 0.964470 0.264192i \(-0.0851052\pi\)
0.0467764 + 0.998905i \(0.485105\pi\)
\(368\) −6.71360 + 2.18138i −0.349971 + 0.113712i
\(369\) 3.25639 3.97161i 0.169521 0.206754i
\(370\) 4.83736 6.65806i 0.251482 0.346136i
\(371\) −9.37298 + 6.80987i −0.486621 + 0.353551i
\(372\) −10.4756 + 9.88053i −0.543134 + 0.512281i
\(373\) 6.97622i 0.361215i −0.983555 0.180607i \(-0.942194\pi\)
0.983555 0.180607i \(-0.0578063\pi\)
\(374\) −5.43206 6.63382i −0.280885 0.343027i
\(375\) 6.67409 12.2034i 0.344649 0.630181i
\(376\) −6.99098 2.27151i −0.360532 0.117144i
\(377\) −3.83660 5.28062i −0.197595 0.271966i
\(378\) 4.40547 + 2.75533i 0.226593 + 0.141719i
\(379\) −10.6387 32.7426i −0.546474 1.68187i −0.717460 0.696599i \(-0.754696\pi\)
0.170987 0.985273i \(-0.445304\pi\)
\(380\) 0.377586 + 1.16209i 0.0193697 + 0.0596140i
\(381\) 5.32906 2.52194i 0.273016 0.129203i
\(382\) −5.57837 7.67797i −0.285414 0.392839i
\(383\) −2.22861 0.724118i −0.113876 0.0370007i 0.251524 0.967851i \(-0.419068\pi\)
−0.365401 + 0.930850i \(0.619068\pi\)
\(384\) −1.51963 0.831094i −0.0775484 0.0424116i
\(385\) −2.68374 + 1.04700i −0.136776 + 0.0533602i
\(386\) 0.901550i 0.0458877i
\(387\) 6.14297 + 23.4973i 0.312265 + 1.19443i
\(388\) −9.35213 + 6.79472i −0.474782 + 0.344950i
\(389\) 6.08479 8.37499i 0.308511 0.424629i −0.626405 0.779498i \(-0.715474\pi\)
0.934916 + 0.354869i \(0.115474\pi\)
\(390\) −0.665313 + 3.52970i −0.0336894 + 0.178733i
\(391\) −17.3559 + 5.63927i −0.877725 + 0.285190i
\(392\) −0.809017 0.587785i −0.0408615 0.0296876i
\(393\) 3.98772 0.512647i 0.201154 0.0258596i
\(394\) −4.97994 + 15.3267i −0.250886 + 0.772147i
\(395\) 12.8206 0.645077
\(396\) −3.06861 9.46486i −0.154203 0.475627i
\(397\) −21.5362 −1.08087 −0.540435 0.841386i \(-0.681740\pi\)
−0.540435 + 0.841386i \(0.681740\pi\)
\(398\) 0.740186 2.27806i 0.0371022 0.114189i
\(399\) −2.41672 + 0.310685i −0.120987 + 0.0155537i
\(400\) −3.43474 2.49549i −0.171737 0.124774i
\(401\) 5.84277 1.89843i 0.291774 0.0948031i −0.159473 0.987202i \(-0.550979\pi\)
0.451247 + 0.892399i \(0.350979\pi\)
\(402\) 1.04310 5.53396i 0.0520249 0.276009i
\(403\) 11.6674 16.0588i 0.581193 0.799944i
\(404\) −10.1143 + 7.34849i −0.503207 + 0.365601i
\(405\) 5.30108 5.74518i 0.263413 0.285480i
\(406\) 2.73387i 0.135680i
\(407\) −1.81560 31.3727i −0.0899959 1.55509i
\(408\) −3.92853 2.14853i −0.194491 0.106368i
\(409\) 27.1710 + 8.82840i 1.34352 + 0.436536i 0.890508 0.454968i \(-0.150349\pi\)
0.453012 + 0.891504i \(0.350349\pi\)
\(410\) 0.874026 + 1.20299i 0.0431651 + 0.0594116i
\(411\) 18.9490 8.96749i 0.934684 0.442333i
\(412\) 2.71512 + 8.35627i 0.133764 + 0.411684i
\(413\) −2.39580 7.37352i −0.117890 0.362827i
\(414\) −21.1411 1.23709i −1.03903 0.0607995i
\(415\) 3.97966 + 5.47753i 0.195354 + 0.268881i
\(416\) 2.27068 + 0.737788i 0.111329 + 0.0361730i
\(417\) −10.4226 + 19.0574i −0.510396 + 0.933245i
\(418\) 3.92681 + 2.51979i 0.192067 + 0.123247i
\(419\) 14.0646i 0.687100i 0.939134 + 0.343550i \(0.111630\pi\)
−0.939134 + 0.343550i \(0.888370\pi\)
\(420\) −1.09442 + 1.03225i −0.0534020 + 0.0503685i
\(421\) 31.3061 22.7452i 1.52577 1.10853i 0.567231 0.823558i \(-0.308014\pi\)
0.958535 0.284976i \(-0.0919855\pi\)
\(422\) 0.683001 0.940071i 0.0332480 0.0457619i
\(423\) −17.0530 13.9820i −0.829145 0.679830i
\(424\) 11.0186 3.58016i 0.535110 0.173868i
\(425\) −8.87943 6.45129i −0.430716 0.312933i
\(426\) 0.233561 + 1.81680i 0.0113161 + 0.0880242i
\(427\) −3.48636 + 10.7299i −0.168717 + 0.519257i
\(428\) −7.04686 −0.340623
\(429\) 6.57334 + 12.0375i 0.317364 + 0.581176i
\(430\) −7.03171 −0.339099
\(431\) 0.574964 1.76956i 0.0276950 0.0852366i −0.936254 0.351325i \(-0.885731\pi\)
0.963949 + 0.266088i \(0.0857313\pi\)
\(432\) −3.33840 3.98184i −0.160619 0.191577i
\(433\) 31.9942 + 23.2452i 1.53755 + 1.11709i 0.951851 + 0.306560i \(0.0991780\pi\)
0.585694 + 0.810532i \(0.300822\pi\)
\(434\) 7.90699 2.56914i 0.379548 0.123323i
\(435\) −4.04172 0.761823i −0.193785 0.0365266i
\(436\) −0.804239 + 1.10694i −0.0385160 + 0.0530128i
\(437\) 8.03400 5.83704i 0.384318 0.279224i
\(438\) 16.5847 + 17.5835i 0.792446 + 0.840172i
\(439\) 1.37828i 0.0657816i 0.999459 + 0.0328908i \(0.0104714\pi\)
−0.999459 + 0.0328908i \(0.989529\pi\)
\(440\) 2.87593 0.166436i 0.137105 0.00793452i
\(441\) −1.61857 2.52591i −0.0770746 0.120282i
\(442\) 5.87012 + 1.90732i 0.279213 + 0.0907218i
\(443\) 19.1405 + 26.3446i 0.909391 + 1.25167i 0.967374 + 0.253352i \(0.0815332\pi\)
−0.0579827 + 0.998318i \(0.518467\pi\)
\(444\) −7.02010 14.8340i −0.333159 0.703991i
\(445\) −1.17034 3.60195i −0.0554796 0.170749i
\(446\) −6.24289 19.2137i −0.295610 0.909793i
\(447\) −10.5300 22.2507i −0.498052 1.05242i
\(448\) 0.587785 + 0.809017i 0.0277702 + 0.0382225i
\(449\) −25.9542 8.43302i −1.22485 0.397979i −0.376006 0.926617i \(-0.622703\pi\)
−0.848847 + 0.528638i \(0.822703\pi\)
\(450\) −6.87174 10.7240i −0.323937 0.505532i
\(451\) 5.49243 + 1.43967i 0.258628 + 0.0677914i
\(452\) 5.22179i 0.245612i
\(453\) 10.1624 + 10.7744i 0.477469 + 0.506225i
\(454\) 8.63392 6.27291i 0.405210 0.294402i
\(455\) 1.21892 1.67770i 0.0571440 0.0786520i
\(456\) 2.39444 + 0.451329i 0.112130 + 0.0211354i
\(457\) −8.78464 + 2.85430i −0.410928 + 0.133519i −0.507184 0.861838i \(-0.669313\pi\)
0.0962556 + 0.995357i \(0.469313\pi\)
\(458\) 1.28178 + 0.931270i 0.0598938 + 0.0435154i
\(459\) −8.63038 10.2938i −0.402832 0.480473i
\(460\) 1.89470 5.83128i 0.0883407 0.271885i
\(461\) 32.8527 1.53010 0.765051 0.643969i \(-0.222714\pi\)
0.765051 + 0.643969i \(0.222714\pi\)
\(462\) −0.736128 + 5.69720i −0.0342478 + 0.265058i
\(463\) −0.810614 −0.0376724 −0.0188362 0.999823i \(-0.505996\pi\)
−0.0188362 + 0.999823i \(0.505996\pi\)
\(464\) −0.844812 + 2.60007i −0.0392194 + 0.120705i
\(465\) −1.59481 12.4055i −0.0739574 0.575292i
\(466\) 8.26435 + 6.00440i 0.382838 + 0.278148i
\(467\) 9.31227 3.02574i 0.430920 0.140014i −0.0855224 0.996336i \(-0.527256\pi\)
0.516443 + 0.856322i \(0.327256\pi\)
\(468\) 5.53883 + 4.54138i 0.256033 + 0.209925i
\(469\) −1.91106 + 2.63035i −0.0882447 + 0.121458i
\(470\) 5.16533 3.75283i 0.238259 0.173105i
\(471\) 11.2685 10.6284i 0.519226 0.489732i
\(472\) 7.75298i 0.356860i
\(473\) −20.7742 + 17.0109i −0.955200 + 0.782160i
\(474\) 12.2674 22.4306i 0.563459 1.03027i
\(475\) 5.68025 + 1.84563i 0.260628 + 0.0846831i
\(476\) 1.51953 + 2.09146i 0.0696476 + 0.0958617i
\(477\) 34.6976 + 2.03035i 1.58869 + 0.0929634i
\(478\) 6.42927 + 19.7873i 0.294068 + 0.905049i
\(479\) −12.0460 37.0738i −0.550395 1.69394i −0.707804 0.706409i \(-0.750314\pi\)
0.157408 0.987534i \(-0.449686\pi\)
\(480\) 1.35983 0.643532i 0.0620676 0.0293731i
\(481\) 13.2969 + 18.3016i 0.606285 + 0.834480i
\(482\) −15.0932 4.90409i −0.687478 0.223375i
\(483\) 10.7272 + 5.86677i 0.488106 + 0.266947i
\(484\) 8.09392 7.44906i 0.367905 0.338594i
\(485\) 10.0406i 0.455922i
\(486\) −4.97925 14.7718i −0.225863 0.670064i
\(487\) −4.57320 + 3.32263i −0.207232 + 0.150563i −0.686560 0.727073i \(-0.740880\pi\)
0.479329 + 0.877636i \(0.340880\pi\)
\(488\) 6.63145 9.12741i 0.300192 0.413178i
\(489\) −3.92814 + 20.8400i −0.177637 + 0.942419i
\(490\) 0.826066 0.268405i 0.0373179 0.0121253i
\(491\) −26.8757 19.5264i −1.21289 0.881213i −0.217396 0.976084i \(-0.569756\pi\)
−0.995490 + 0.0948706i \(0.969756\pi\)
\(492\) 2.94102 0.378087i 0.132592 0.0170455i
\(493\) −2.18399 + 6.72164i −0.0983621 + 0.302728i
\(494\) −3.35872 −0.151116
\(495\) 8.21754 + 2.67587i 0.369351 + 0.120271i
\(496\) −8.31390 −0.373305
\(497\) 0.326804 1.00580i 0.0146592 0.0451163i
\(498\) 13.3912 1.72153i 0.600074 0.0771434i
\(499\) −14.6221 10.6236i −0.654576 0.475577i 0.210251 0.977647i \(-0.432572\pi\)
−0.864827 + 0.502070i \(0.832572\pi\)
\(500\) 7.63745 2.48156i 0.341557 0.110979i
\(501\) −4.19744 + 22.2688i −0.187528 + 0.994896i
\(502\) −4.99985 + 6.88170i −0.223154 + 0.307146i
\(503\) 29.0451 21.1025i 1.29506 0.940914i 0.295162 0.955447i \(-0.404626\pi\)
0.999894 + 0.0145334i \(0.00462627\pi\)
\(504\) 0.758798 + 2.90245i 0.0337995 + 0.129285i
\(505\) 10.8589i 0.483217i
\(506\) −8.50919 21.8113i −0.378280 0.969631i
\(507\) 11.0928 + 6.06672i 0.492650 + 0.269433i
\(508\) 3.23727 + 1.05185i 0.143631 + 0.0466685i
\(509\) −16.3147 22.4552i −0.723135 0.995310i −0.999414 0.0342328i \(-0.989101\pi\)
0.276279 0.961078i \(-0.410899\pi\)
\(510\) 3.51542 1.66365i 0.155665 0.0736676i
\(511\) −4.31235 13.2720i −0.190767 0.587120i
\(512\) −0.309017 0.951057i −0.0136568 0.0420312i
\(513\) 6.19750 + 3.87614i 0.273627 + 0.171136i
\(514\) −7.98604 10.9918i −0.352249 0.484829i
\(515\) −7.25806 2.35829i −0.319828 0.103919i
\(516\) −6.72826 + 12.3024i −0.296195 + 0.541585i
\(517\) 6.18155 23.5830i 0.271864 1.03718i
\(518\) 9.47505i 0.416310i
\(519\) −21.7614 + 20.5253i −0.955222 + 0.900960i
\(520\) −1.67770 + 1.21892i −0.0735722 + 0.0534533i
\(521\) −21.4692 + 29.5498i −0.940584 + 1.29460i 0.0150016 + 0.999887i \(0.495225\pi\)
−0.955585 + 0.294715i \(0.904775\pi\)
\(522\) −5.20016 + 6.34230i −0.227605 + 0.277595i
\(523\) −4.85366 + 1.57705i −0.212236 + 0.0689596i −0.413205 0.910638i \(-0.635591\pi\)
0.200969 + 0.979598i \(0.435591\pi\)
\(524\) 1.87794 + 1.36440i 0.0820380 + 0.0596041i
\(525\) 0.937630 + 7.29353i 0.0409215 + 0.318316i
\(526\) 7.56534 23.2837i 0.329865 1.01522i
\(527\) −21.4930 −0.936248
\(528\) 2.46063 5.19089i 0.107085 0.225904i
\(529\) −26.8309 −1.16656
\(530\) −3.10964 + 9.57050i −0.135074 + 0.415716i
\(531\) −8.46732 + 21.6629i −0.367451 + 0.940091i
\(532\) −1.13811 0.826882i −0.0493431 0.0358499i
\(533\) −3.88734 + 1.26307i −0.168380 + 0.0547098i
\(534\) −7.42168 1.39891i −0.321167 0.0605368i
\(535\) 3.59768 4.95179i 0.155541 0.214084i
\(536\) 2.63035 1.91106i 0.113614 0.0825454i
\(537\) 3.23853 + 3.43357i 0.139753 + 0.148170i
\(538\) 3.01496i 0.129984i
\(539\) 1.79118 2.79135i 0.0771517 0.120232i
\(540\) 4.50239 0.312996i 0.193752 0.0134692i
\(541\) −17.6485 5.73435i −0.758769 0.246539i −0.0960186 0.995380i \(-0.530611\pi\)
−0.662750 + 0.748841i \(0.730611\pi\)
\(542\) 4.85580 + 6.68343i 0.208574 + 0.287078i
\(543\) 12.7762 + 26.9971i 0.548280 + 1.15856i
\(544\) −0.798865 2.45865i −0.0342511 0.105414i
\(545\) −0.367246 1.13027i −0.0157311 0.0484153i
\(546\) −1.76893 3.73789i −0.0757033 0.159967i
\(547\) −0.385909 0.531158i −0.0165003 0.0227107i 0.800687 0.599083i \(-0.204468\pi\)
−0.817187 + 0.576372i \(0.804468\pi\)
\(548\) 11.5111 + 3.74017i 0.491728 + 0.159772i
\(549\) 28.4976 18.2608i 1.21625 0.779353i
\(550\) 7.60460 11.8509i 0.324261 0.505324i
\(551\) 3.84594i 0.163843i
\(552\) −8.38927 8.89453i −0.357071 0.378576i
\(553\) −11.9415 + 8.67601i −0.507804 + 0.368942i
\(554\) −3.64403 + 5.01558i −0.154820 + 0.213092i
\(555\) 14.0078 + 2.64033i 0.594597 + 0.112076i
\(556\) −11.9270 + 3.87532i −0.505818 + 0.164350i
\(557\) 32.7072 + 23.7631i 1.38585 + 1.00688i 0.996307 + 0.0858673i \(0.0273661\pi\)
0.389540 + 0.921009i \(0.372634\pi\)
\(558\) −23.2302 9.07993i −0.983414 0.384384i
\(559\) 5.97289 18.3827i 0.252626 0.777503i
\(560\) −0.868577 −0.0367041
\(561\) 6.36118 13.4194i 0.268569 0.566567i
\(562\) −22.9286 −0.967185
\(563\) 5.29868 16.3077i 0.223313 0.687286i −0.775146 0.631783i \(-0.782324\pi\)
0.998458 0.0555038i \(-0.0176765\pi\)
\(564\) −1.62340 12.6280i −0.0683577 0.531733i
\(565\) 3.66932 + 2.66592i 0.154369 + 0.112156i
\(566\) −1.06089 + 0.344703i −0.0445924 + 0.0144890i
\(567\) −1.04969 + 8.93858i −0.0440828 + 0.375385i
\(568\) −0.621619 + 0.855585i −0.0260825 + 0.0358995i
\(569\) −28.3434 + 20.5927i −1.18822 + 0.863291i −0.993075 0.117483i \(-0.962517\pi\)
−0.195144 + 0.980775i \(0.562517\pi\)
\(570\) −1.53960 + 1.45214i −0.0644866 + 0.0608235i
\(571\) 38.2259i 1.59970i 0.600199 + 0.799851i \(0.295088\pi\)
−0.600199 + 0.799851i \(0.704912\pi\)
\(572\) −2.00777 + 7.65978i −0.0839493 + 0.320272i
\(573\) 7.88749 14.4221i 0.329505 0.602490i
\(574\) −1.62818 0.529029i −0.0679591 0.0220813i
\(575\) −17.6159 24.2462i −0.734633 1.01114i
\(576\) 0.175247 2.99488i 0.00730197 0.124787i
\(577\) −6.04713 18.6111i −0.251745 0.774792i −0.994454 0.105177i \(-0.966459\pi\)
0.742708 0.669615i \(-0.233541\pi\)
\(578\) 3.18808 + 9.81189i 0.132606 + 0.408121i
\(579\) 1.41145 0.667962i 0.0586580 0.0277596i
\(580\) −1.39574 1.92107i −0.0579550 0.0797682i
\(581\) −7.41353 2.40880i −0.307565 0.0999339i
\(582\) −17.5667 9.60733i −0.728165 0.398237i
\(583\) 13.9656 + 35.7975i 0.578395 + 1.48258i
\(584\) 13.9550i 0.577464i
\(585\) −6.01898 + 1.57356i −0.248854 + 0.0650588i
\(586\) −18.4654 + 13.4159i −0.762799 + 0.554206i
\(587\) −14.4699 + 19.9161i −0.597237 + 0.822026i −0.995452 0.0952662i \(-0.969630\pi\)
0.398215 + 0.917292i \(0.369630\pi\)
\(588\) 0.320825 1.70208i 0.0132306 0.0701925i
\(589\) 11.1234 3.61420i 0.458330 0.148921i
\(590\) −5.44797 3.95818i −0.224289 0.162956i
\(591\) −27.6849 + 3.55907i −1.13880 + 0.146401i
\(592\) 2.92795 9.01131i 0.120338 0.370362i
\(593\) 3.72800 0.153091 0.0765453 0.997066i \(-0.475611\pi\)
0.0765453 + 0.997066i \(0.475611\pi\)
\(594\) 12.5445 11.8167i 0.514708 0.484846i
\(595\) −2.24543 −0.0920537
\(596\) 4.39186 13.5168i 0.179898 0.553668i
\(597\) 4.11491 0.528997i 0.168412 0.0216504i
\(598\) 13.6350 + 9.90643i 0.557578 + 0.405104i
\(599\) −10.0553 + 3.26717i −0.410849 + 0.133493i −0.507147 0.861860i \(-0.669300\pi\)
0.0962980 + 0.995353i \(0.469300\pi\)
\(600\) 1.36209 7.22630i 0.0556069 0.295012i
\(601\) −21.3749 + 29.4200i −0.871901 + 1.20007i 0.106698 + 0.994291i \(0.465972\pi\)
−0.978599 + 0.205777i \(0.934028\pi\)
\(602\) 6.54953 4.75851i 0.266939 0.193942i
\(603\) 9.43673 2.46708i 0.384293 0.100467i
\(604\) 8.55105i 0.347937i
\(605\) 1.10217 + 9.49056i 0.0448094 + 0.385846i
\(606\) −18.9984 10.3903i −0.771759 0.422078i
\(607\) 27.3432 + 8.88433i 1.10983 + 0.360604i 0.805876 0.592084i \(-0.201695\pi\)
0.303949 + 0.952688i \(0.401695\pi\)
\(608\) 0.826882 + 1.13811i 0.0335345 + 0.0461563i
\(609\) 4.28011 2.02554i 0.173439 0.0820788i
\(610\) 3.02817 + 9.31976i 0.122607 + 0.377346i
\(611\) 5.42330 + 16.6912i 0.219403 + 0.675254i
\(612\) 0.453046 7.74230i 0.0183133 0.312964i
\(613\) −23.5434 32.4047i −0.950909 1.30881i −0.951122 0.308814i \(-0.900068\pi\)
0.000213312 1.00000i \(-0.499932\pi\)
\(614\) 23.0705 + 7.49607i 0.931051 + 0.302517i
\(615\) −1.23582 + 2.25967i −0.0498331 + 0.0911185i
\(616\) −2.56609 + 2.10123i −0.103391 + 0.0846610i
\(617\) 35.0792i 1.41224i 0.708094 + 0.706118i \(0.249555\pi\)
−0.708094 + 0.706118i \(0.750445\pi\)
\(618\) −11.0708 + 10.4419i −0.445334 + 0.420036i
\(619\) −15.9766 + 11.6077i −0.642153 + 0.466551i −0.860589 0.509300i \(-0.829904\pi\)
0.218436 + 0.975851i \(0.429904\pi\)
\(620\) 4.24455 5.84213i 0.170465 0.234625i
\(621\) −13.7268 34.0148i −0.550837 1.36497i
\(622\) −23.0394 + 7.48596i −0.923797 + 0.300160i
\(623\) 3.52761 + 2.56296i 0.141331 + 0.102683i
\(624\) 0.527284 + 4.10157i 0.0211082 + 0.164194i
\(625\) 4.40435 13.5552i 0.176174 0.542207i
\(626\) −19.2630 −0.769903
\(627\) −1.03557 + 8.01469i −0.0413565 + 0.320076i
\(628\) 8.94321 0.356873
\(629\) 7.56929 23.2959i 0.301807 0.928867i
\(630\) −2.42693 0.948606i −0.0966912 0.0377934i
\(631\) −34.2584 24.8902i −1.36380 0.990862i −0.998193 0.0600943i \(-0.980860\pi\)
−0.365612 0.930768i \(-0.619140\pi\)
\(632\) 14.0381 4.56125i 0.558405 0.181437i
\(633\) 1.97780 + 0.372796i 0.0786105 + 0.0148173i
\(634\) 5.69970 7.84496i 0.226364 0.311563i
\(635\) −2.39188 + 1.73780i −0.0949188 + 0.0689626i
\(636\) 13.7688 + 14.5980i 0.545967 + 0.578849i
\(637\) 2.38753i 0.0945975i
\(638\) −8.77092 2.29902i −0.347244 0.0910192i
\(639\) −2.67131 + 1.71173i −0.105675 + 0.0677151i
\(640\) 0.826066 + 0.268405i 0.0326531 + 0.0106096i
\(641\) 19.3858 + 26.6822i 0.765692 + 1.05389i 0.996719 + 0.0809377i \(0.0257915\pi\)
−0.231027 + 0.972947i \(0.574209\pi\)
\(642\) −5.22105 11.0325i −0.206058 0.435417i
\(643\) 8.72192 + 26.8433i 0.343959 + 1.05860i 0.962139 + 0.272560i \(0.0878704\pi\)
−0.618180 + 0.786037i \(0.712130\pi\)
\(644\) 2.18138 + 6.71360i 0.0859585 + 0.264553i
\(645\) −5.20982 11.0087i −0.205137 0.433469i
\(646\) 2.13764 + 2.94221i 0.0841044 + 0.115760i
\(647\) 15.8981 + 5.16561i 0.625020 + 0.203081i 0.604368 0.796706i \(-0.293426\pi\)
0.0206520 + 0.999787i \(0.493426\pi\)
\(648\) 3.76048 8.17672i 0.147726 0.321212i
\(649\) −25.6708 + 1.48562i −1.00767 + 0.0583156i
\(650\) 10.1364i 0.397584i
\(651\) 9.88053 + 10.4756i 0.387248 + 0.410571i
\(652\) −9.90550 + 7.19677i −0.387929 + 0.281847i
\(653\) 22.8632 31.4685i 0.894707 1.23146i −0.0774182 0.996999i \(-0.524668\pi\)
0.972126 0.234460i \(-0.0753323\pi\)
\(654\) −2.32887 0.438969i −0.0910661 0.0171651i
\(655\) −1.91751 + 0.623037i −0.0749234 + 0.0243441i
\(656\) 1.38502 + 1.00627i 0.0540758 + 0.0392884i
\(657\) −15.2408 + 38.9924i −0.594602 + 1.52124i
\(658\) −2.27151 + 6.99098i −0.0885526 + 0.272537i
\(659\) −13.1507 −0.512277 −0.256138 0.966640i \(-0.582450\pi\)
−0.256138 + 0.966640i \(0.582450\pi\)
\(660\) 2.39136 + 4.37921i 0.0930835 + 0.170460i
\(661\) 21.8589 0.850214 0.425107 0.905143i \(-0.360237\pi\)
0.425107 + 0.905143i \(0.360237\pi\)
\(662\) −7.91955 + 24.3739i −0.307802 + 0.947318i
\(663\) 1.36312 + 10.6033i 0.0529394 + 0.411799i
\(664\) 6.30632 + 4.58181i 0.244733 + 0.177809i
\(665\) 1.16209 0.377586i 0.0450639 0.0146422i
\(666\) 18.0227 21.9811i 0.698365 0.851752i
\(667\) −11.3435 + 15.6129i −0.439221 + 0.604535i
\(668\) −10.5846 + 7.69016i −0.409530 + 0.297541i
\(669\) 25.4553 24.0093i 0.984157 0.928252i
\(670\) 2.82400i 0.109101i
\(671\) 31.4923 + 20.2083i 1.21575 + 0.780133i
\(672\) −0.831094 + 1.51963i −0.0320601 + 0.0586211i
\(673\) −13.5961 4.41763i −0.524090 0.170287i 0.0350107 0.999387i \(-0.488853\pi\)
−0.559101 + 0.829100i \(0.688853\pi\)
\(674\) 11.0189 + 15.1662i 0.424431 + 0.584180i
\(675\) 11.6980 18.7037i 0.450255 0.719907i
\(676\) 2.25573 + 6.94241i 0.0867587 + 0.267016i
\(677\) 12.3344 + 37.9614i 0.474050 + 1.45898i 0.847235 + 0.531218i \(0.178266\pi\)
−0.373185 + 0.927757i \(0.621734\pi\)
\(678\) 8.17516 3.86884i 0.313965 0.148582i
\(679\) 6.79472 + 9.35213i 0.260757 + 0.358902i
\(680\) 2.13553 + 0.693876i 0.0818939 + 0.0266089i
\(681\) 16.2177 + 8.86953i 0.621463 + 0.339881i
\(682\) −1.59310 27.5280i −0.0610030 1.05410i
\(683\) 48.8360i 1.86866i −0.356411 0.934329i \(-0.616000\pi\)
0.356411 0.934329i \(-0.384000\pi\)
\(684\) 1.06746 + 4.08310i 0.0408153 + 0.156121i
\(685\) −8.50501 + 6.17925i −0.324960 + 0.236097i
\(686\) −0.587785 + 0.809017i −0.0224417 + 0.0308884i
\(687\) −0.508306 + 2.69673i −0.0193931 + 0.102886i
\(688\) −7.69943 + 2.50170i −0.293538 + 0.0953763i
\(689\) −22.3783 16.2588i −0.852545 0.619410i
\(690\) 10.5332 1.35411i 0.400991 0.0515499i
\(691\) −8.48432 + 26.1120i −0.322759 + 0.993349i 0.649683 + 0.760205i \(0.274901\pi\)
−0.972442 + 0.233144i \(0.925099\pi\)
\(692\) −17.2709 −0.656540
\(693\) −9.46486 + 3.06861i −0.359540 + 0.116567i
\(694\) 0.551228 0.0209243
\(695\) 3.36601 10.3595i 0.127680 0.392959i
\(696\) −4.69655 + 0.603772i −0.178022 + 0.0228859i
\(697\) 3.58052 + 2.60140i 0.135622 + 0.0985351i
\(698\) 10.5046 3.41316i 0.397606 0.129190i
\(699\) −3.27732 + 17.3872i −0.123960 + 0.657645i
\(700\) −2.49549 + 3.43474i −0.0943205 + 0.129821i
\(701\) −29.0205 + 21.0846i −1.09609 + 0.796355i −0.980417 0.196933i \(-0.936902\pi\)
−0.115671 + 0.993288i \(0.536902\pi\)
\(702\) −3.00618 + 12.0363i −0.113461 + 0.454279i
\(703\) 13.3293i 0.502723i
\(704\) 3.08982 1.20542i 0.116452 0.0454310i
\(705\) 9.70239 + 5.30628i 0.365413 + 0.199846i
\(706\) −18.8110 6.11207i −0.707962 0.230031i
\(707\) 7.34849 + 10.1143i 0.276368 + 0.380388i
\(708\) −12.1380 + 5.74421i −0.456172 + 0.215881i
\(709\) 13.4780 + 41.4810i 0.506177 + 1.55785i 0.798783 + 0.601619i \(0.205478\pi\)
−0.292606 + 0.956233i \(0.594522\pi\)
\(710\) −0.283855 0.873615i −0.0106529 0.0327862i
\(711\) 44.2059 + 2.58674i 1.65785 + 0.0970103i
\(712\) −2.56296 3.52761i −0.0960508 0.132203i
\(713\) −55.8162 18.1358i −2.09033 0.679191i
\(714\) −2.14853 + 3.92853i −0.0804067 + 0.147021i
\(715\) −4.35744 5.32145i −0.162959 0.199011i
\(716\) 2.72504i 0.101839i
\(717\) −26.2152 + 24.7260i −0.979025 + 0.923411i
\(718\) −7.99645 + 5.80976i −0.298425 + 0.216818i
\(719\) 8.77972 12.0843i 0.327428 0.450667i −0.613289 0.789859i \(-0.710154\pi\)
0.940717 + 0.339192i \(0.110154\pi\)
\(720\) 2.01501 + 1.65214i 0.0750950 + 0.0615716i
\(721\) 8.35627 2.71512i 0.311204 0.101116i
\(722\) 13.7703 + 10.0047i 0.512476 + 0.372336i
\(723\) −3.50486 27.2632i −0.130347 1.01393i
\(724\) −5.32872 + 16.4001i −0.198040 + 0.609505i
\(725\) −11.6068 −0.431068
\(726\) 17.6590 + 7.15269i 0.655386 + 0.265461i
\(727\) −19.9614 −0.740327 −0.370163 0.928967i \(-0.620698\pi\)
−0.370163 + 0.928967i \(0.620698\pi\)
\(728\) 0.737788 2.27068i 0.0273443 0.0841570i
\(729\) 19.4374 18.7400i 0.719905 0.694072i
\(730\) −9.80612 7.12456i −0.362941 0.263692i
\(731\) −19.9044 + 6.46735i −0.736192 + 0.239203i
\(732\) 19.2030 + 3.61958i 0.709764 + 0.133783i
\(733\) −12.7126 + 17.4974i −0.469551 + 0.646282i −0.976455 0.215721i \(-0.930790\pi\)
0.506904 + 0.862003i \(0.330790\pi\)
\(734\) −19.3727 + 14.0751i −0.715059 + 0.519521i
\(735\) 1.03225 + 1.09442i 0.0380750 + 0.0403681i
\(736\) 7.05910i 0.260202i
\(737\) 6.83172 + 8.34313i 0.251650 + 0.307323i
\(738\) 2.77094 + 4.32430i 0.102000 + 0.159180i
\(739\) 12.0995 + 3.93136i 0.445086 + 0.144617i 0.522981 0.852344i \(-0.324820\pi\)
−0.0778949 + 0.996962i \(0.524820\pi\)
\(740\) 4.83736 + 6.65806i 0.177825 + 0.244755i
\(741\) −2.48849 5.25837i −0.0914171 0.193171i
\(742\) −3.58016 11.0186i −0.131432 0.404505i
\(743\) −9.87887 30.4040i −0.362421 1.11542i −0.951581 0.307399i \(-0.900541\pi\)
0.589160 0.808016i \(-0.299459\pi\)
\(744\) −6.15980 13.0161i −0.225829 0.477195i
\(745\) 7.25593 + 9.98693i 0.265837 + 0.365893i
\(746\) 6.63478 + 2.15577i 0.242916 + 0.0789283i
\(747\) 12.6168 + 19.6896i 0.461624 + 0.720405i
\(748\) 7.98774 3.11624i 0.292061 0.113941i
\(749\) 7.04686i 0.257487i
\(750\) 9.54372 + 10.1185i 0.348487 + 0.369475i
\(751\) −17.0527 + 12.3895i −0.622263 + 0.452101i −0.853711 0.520747i \(-0.825654\pi\)
0.231448 + 0.972847i \(0.425654\pi\)
\(752\) 4.32066 5.94688i 0.157558 0.216861i
\(753\) −14.4783 2.72902i −0.527619 0.0994509i
\(754\) 6.20774 2.01702i 0.226073 0.0734554i
\(755\) −6.00877 4.36562i −0.218681 0.158881i
\(756\) −3.98184 + 3.33840i −0.144818 + 0.121416i
\(757\) 4.50990 13.8800i 0.163915 0.504478i −0.835040 0.550190i \(-0.814555\pi\)
0.998955 + 0.0457113i \(0.0145554\pi\)
\(758\) 34.4276 1.25047
\(759\) 27.8430 29.4820i 1.01064 1.07013i
\(760\) −1.22189 −0.0443227
\(761\) 5.35178 16.4711i 0.194002 0.597077i −0.805985 0.591936i \(-0.798364\pi\)
0.999987 0.00514046i \(-0.00163626\pi\)
\(762\) 0.751741 + 5.84756i 0.0272327 + 0.211835i
\(763\) 1.10694 + 0.804239i 0.0400739 + 0.0291154i
\(764\) 9.02600 2.93272i 0.326549 0.106102i
\(765\) 5.20917 + 4.27108i 0.188338 + 0.154421i
\(766\) 1.37735 1.89577i 0.0497658 0.0684968i
\(767\) 14.9753 10.8802i 0.540727 0.392861i
\(768\) 1.26001 1.18843i 0.0454667 0.0428839i
\(769\) 34.3601i 1.23906i 0.784974 + 0.619528i \(0.212676\pi\)
−0.784974 + 0.619528i \(0.787324\pi\)
\(770\) −0.166436 2.87593i −0.00599793 0.103641i
\(771\) 11.2918 20.6467i 0.406664 0.743574i
\(772\) 0.857425 + 0.278594i 0.0308594 + 0.0100268i
\(773\) 11.8736 + 16.3426i 0.427065 + 0.587804i 0.967276 0.253725i \(-0.0816558\pi\)
−0.540212 + 0.841529i \(0.681656\pi\)
\(774\) −24.2455 1.41874i −0.871487 0.0509957i
\(775\) −10.9075 33.5697i −0.391808 1.20586i
\(776\) −3.57219 10.9941i −0.128234 0.394665i
\(777\) −14.8340 + 7.02010i −0.532167 + 0.251845i
\(778\) 6.08479 + 8.37499i 0.218150 + 0.300258i
\(779\) −2.29049 0.744226i −0.0820654 0.0266647i
\(780\) −3.15135 1.72349i −0.112836 0.0617107i
\(781\) −2.95203 1.89429i −0.105632 0.0677829i
\(782\) 18.2491i 0.652585i
\(783\) −13.7822 3.44226i −0.492537 0.123016i
\(784\) 0.809017 0.587785i 0.0288935 0.0209923i
\(785\) −4.56584 + 6.28434i −0.162962 + 0.224298i
\(786\) −0.744717 + 3.95096i −0.0265632 + 0.140926i
\(787\) −31.8682 + 10.3546i −1.13598 + 0.369102i −0.815845 0.578270i \(-0.803728\pi\)
−0.320134 + 0.947372i \(0.603728\pi\)
\(788\) −13.0376 9.47240i −0.464447 0.337440i
\(789\) 42.0579 5.40681i 1.49730 0.192487i
\(790\) −3.96180 + 12.1932i −0.140954 + 0.433813i
\(791\) −5.22179 −0.185665
\(792\) 9.94987 + 0.00638338i 0.353553 + 0.000226824i
\(793\) −26.9364 −0.956539
\(794\) 6.65504 20.4821i 0.236179 0.726883i
\(795\) −17.2874 + 2.22240i −0.613121 + 0.0788206i
\(796\) 1.93783 + 1.40792i 0.0686847 + 0.0499023i
\(797\) 34.8848 11.3348i 1.23568 0.401498i 0.382913 0.923784i \(-0.374921\pi\)
0.852770 + 0.522287i \(0.174921\pi\)
\(798\) 0.451329 2.39444i 0.0159769 0.0847624i
\(799\) 11.1697 15.3738i 0.395156 0.543885i
\(800\) 3.43474 2.49549i 0.121436 0.0882287i
\(801\) −3.30863 12.6557i −0.116905 0.447168i
\(802\) 6.14345i 0.216933i
\(803\) −46.2063 + 2.67405i −1.63059 + 0.0943652i
\(804\) 4.94078 + 2.70213i 0.174248 + 0.0952969i
\(805\) −5.83128 1.89470i −0.205526 0.0667793i
\(806\) 11.6674 + 16.0588i 0.410966 + 0.565646i
\(807\) −4.72019 + 2.23380i −0.166158 + 0.0786334i
\(808\) −3.86333 11.8901i −0.135911 0.418292i
\(809\) −9.69613 29.8416i −0.340898 1.04918i −0.963743 0.266831i \(-0.914024\pi\)
0.622846 0.782345i \(-0.285976\pi\)
\(810\) 3.82586 + 6.81699i 0.134427 + 0.239524i
\(811\) 14.8086 + 20.3822i 0.519999 + 0.715717i 0.985565 0.169296i \(-0.0541494\pi\)
−0.465567 + 0.885013i \(0.654149\pi\)
\(812\) 2.60007 + 0.844812i 0.0912444 + 0.0296471i
\(813\) −6.86581 + 12.5540i −0.240795 + 0.440286i
\(814\) 30.3982 + 7.96796i 1.06546 + 0.279277i
\(815\) 10.6348i 0.372519i
\(816\) 3.25735 3.07232i 0.114030 0.107553i
\(817\) 9.21372 6.69416i 0.322347 0.234199i
\(818\) −16.7926 + 23.1130i −0.587140 + 0.808129i
\(819\) 4.54138 5.53883i 0.158689 0.193543i
\(820\) −1.41420 + 0.459503i −0.0493861 + 0.0160465i
\(821\) 13.4292 + 9.75686i 0.468681 + 0.340517i 0.796927 0.604076i \(-0.206458\pi\)
−0.328246 + 0.944592i \(0.606458\pi\)
\(822\) 2.67303 + 20.7927i 0.0932326 + 0.725227i
\(823\) 3.83254 11.7953i 0.133594 0.411160i −0.861775 0.507291i \(-0.830647\pi\)
0.995369 + 0.0961313i \(0.0306469\pi\)
\(824\) −8.78630 −0.306085
\(825\) 24.1879 + 3.12528i 0.842114 + 0.108808i
\(826\) 7.75298 0.269761
\(827\) 11.3513 34.9357i 0.394723 1.21483i −0.534454 0.845197i \(-0.679483\pi\)
0.929177 0.369635i \(-0.120517\pi\)
\(828\) 7.70951 19.7241i 0.267924 0.685461i
\(829\) 3.15977 + 2.29571i 0.109743 + 0.0797332i 0.641303 0.767287i \(-0.278394\pi\)
−0.531560 + 0.847021i \(0.678394\pi\)
\(830\) −6.43922 + 2.09223i −0.223509 + 0.0726223i
\(831\) −10.5522 1.98899i −0.366052 0.0689972i
\(832\) −1.40336 + 1.93155i −0.0486526 + 0.0669646i
\(833\) 2.09146 1.51953i 0.0724647 0.0526487i
\(834\) −14.9039 15.8015i −0.516080 0.547162i
\(835\) 11.3638i 0.393262i
\(836\) −3.60992 + 2.95596i −0.124852 + 0.102234i
\(837\) −2.99596 43.0963i −0.103555 1.48963i
\(838\) −13.3762 4.34620i −0.462074 0.150137i
\(839\) −7.51313 10.3409i −0.259382 0.357009i 0.659387 0.751803i \(-0.270816\pi\)
−0.918769 + 0.394795i \(0.870816\pi\)
\(840\) −0.643532 1.35983i −0.0222040 0.0469187i
\(841\) −6.65189 20.4724i −0.229375 0.705945i
\(842\) 11.9579 + 36.8025i 0.412095 + 1.26830i
\(843\) −16.9879 35.8967i −0.585094 1.23635i
\(844\) 0.683001 + 0.940071i 0.0235099 + 0.0323586i
\(845\) −6.03002 1.95927i −0.207439 0.0674010i
\(846\) 18.5674 11.8977i 0.638359 0.409051i
\(847\) −7.44906 8.09392i −0.255953 0.278110i
\(848\) 11.5856i 0.397852i
\(849\) −1.32568 1.40552i −0.0454972 0.0482373i
\(850\) 8.87943 6.45129i 0.304562 0.221277i
\(851\) 39.3142 54.1113i 1.34767 1.85491i
\(852\) −1.80005 0.339292i −0.0616688 0.0116239i
\(853\) −28.6593 + 9.31196i −0.981275 + 0.318836i −0.755359 0.655311i \(-0.772537\pi\)
−0.225916 + 0.974147i \(0.572537\pi\)
\(854\) −9.12741 6.63145i −0.312333 0.226924i
\(855\) −3.41415 1.33448i −0.116761 0.0456381i
\(856\) 2.17760 6.70196i 0.0744288 0.229068i
\(857\) −14.2634 −0.487228 −0.243614 0.969872i \(-0.578333\pi\)
−0.243614 + 0.969872i \(0.578333\pi\)
\(858\) −13.4796 + 2.53182i −0.460187 + 0.0864349i
\(859\) −14.6371 −0.499411 −0.249705 0.968322i \(-0.580334\pi\)
−0.249705 + 0.968322i \(0.580334\pi\)
\(860\) 2.17292 6.68755i 0.0740959 0.228044i
\(861\) −0.378087 2.94102i −0.0128852 0.100230i
\(862\) 1.50528 + 1.09365i 0.0512699 + 0.0372498i
\(863\) 12.0457 3.91388i 0.410040 0.133230i −0.0967316 0.995310i \(-0.530839\pi\)
0.506771 + 0.862081i \(0.330839\pi\)
\(864\) 4.81858 1.94455i 0.163931 0.0661550i
\(865\) 8.81741 12.1361i 0.299801 0.412641i
\(866\) −31.9942 + 23.2452i −1.08721 + 0.789903i
\(867\) −12.9993 + 12.2609i −0.441480 + 0.416401i
\(868\) 8.31390i 0.282192i
\(869\) 17.7926 + 45.6073i 0.603574 + 1.54712i
\(870\) 1.97350 3.60848i 0.0669078 0.122339i
\(871\) −7.38265 2.39877i −0.250152 0.0812792i
\(872\) −0.804239 1.10694i −0.0272350 0.0374857i
\(873\) 2.02583 34.6204i 0.0685641 1.17172i
\(874\) 3.06871 + 9.44453i 0.103801 + 0.319466i
\(875\) −2.48156 7.63745i −0.0838920 0.258193i
\(876\) −21.8478 + 10.3393i −0.738170 + 0.349334i
\(877\) 24.0016 + 33.0354i 0.810477 + 1.11553i 0.991250 + 0.132001i \(0.0421401\pi\)
−0.180773 + 0.983525i \(0.557860\pi\)
\(878\) −1.31082 0.425912i −0.0442381 0.0143738i
\(879\) −34.6848 18.9693i −1.16989 0.639818i
\(880\) −0.730422 + 2.78661i −0.0246225 + 0.0939365i
\(881\) 37.5887i 1.26639i 0.773991 + 0.633197i \(0.218258\pi\)
−0.773991 + 0.633197i \(0.781742\pi\)
\(882\) 2.90245 0.758798i 0.0977306 0.0255501i
\(883\) −2.76929 + 2.01201i −0.0931942 + 0.0677095i −0.633407 0.773819i \(-0.718344\pi\)
0.540212 + 0.841529i \(0.318344\pi\)
\(884\) −3.62793 + 4.99342i −0.122021 + 0.167947i
\(885\) 2.16045 11.4619i 0.0726229 0.385288i
\(886\) −30.9699 + 10.0627i −1.04046 + 0.338064i
\(887\) 42.6860 + 31.0132i 1.43325 + 1.04132i 0.989399 + 0.145222i \(0.0463897\pi\)
0.443856 + 0.896098i \(0.353610\pi\)
\(888\) 16.2773 2.09255i 0.546231 0.0702214i
\(889\) 1.05185 3.23727i 0.0352781 0.108575i
\(890\) 3.78731 0.126951
\(891\) 27.7944 + 10.8845i 0.931147 + 0.364643i
\(892\) 20.2024 0.676427
\(893\) −3.19550 + 9.83475i −0.106933 + 0.329107i
\(894\) 24.4156 3.13878i 0.816580 0.104977i
\(895\) −1.91487 1.39123i −0.0640069 0.0465037i
\(896\) −0.951057 + 0.309017i −0.0317726 + 0.0103235i
\(897\) −5.40713 + 28.6865i −0.180539 + 0.957816i
\(898\) 16.0406 22.0779i 0.535280 0.736750i
\(899\) −18.3883 + 13.3598i −0.613283 + 0.445576i
\(900\) 12.3226 3.22153i 0.410752 0.107384i
\(901\) 29.9510i 0.997812i
\(902\) −3.06646 + 4.77873i −0.102102 + 0.159114i
\(903\) 12.3024 + 6.72826i 0.409399 + 0.223902i
\(904\) 4.96622 + 1.61362i 0.165174 + 0.0536683i
\(905\) −8.80375 12.1173i −0.292646 0.402793i
\(906\) −13.3874 + 6.33550i −0.444767 + 0.210483i
\(907\) −13.7169 42.2162i −0.455461 1.40177i −0.870593 0.492004i \(-0.836265\pi\)
0.415132 0.909761i \(-0.363735\pi\)
\(908\) 3.29786 + 10.1498i 0.109443 + 0.336832i
\(909\) 2.19094 37.4419i 0.0726689 1.24187i
\(910\) 1.21892 + 1.67770i 0.0404069 + 0.0556154i
\(911\) −44.4912 14.4561i −1.47406 0.478951i −0.541728 0.840554i \(-0.682230\pi\)
−0.932332 + 0.361602i \(0.882230\pi\)
\(912\) −1.16916 + 2.13778i −0.0387148 + 0.0707891i
\(913\) −13.9624 + 21.7587i −0.462086 + 0.720109i
\(914\) 9.23671i 0.305523i
\(915\) −12.3473 + 11.6459i −0.408189 + 0.385002i
\(916\) −1.28178 + 0.931270i −0.0423513 + 0.0307700i
\(917\) 1.36440 1.87794i 0.0450565 0.0620149i
\(918\) 12.4569 5.02702i 0.411139 0.165916i
\(919\) 26.9250 8.74845i 0.888172 0.288585i 0.170826 0.985301i \(-0.445356\pi\)
0.717346 + 0.696717i \(0.245356\pi\)
\(920\) 4.96038 + 3.60393i 0.163539 + 0.118818i
\(921\) 5.35730 + 41.6728i 0.176529 + 1.37317i
\(922\) −10.1520 + 31.2448i −0.334340 + 1.02899i
\(923\) 2.52496 0.0831101
\(924\) −5.19089 2.46063i −0.170768 0.0809488i
\(925\) 40.2270 1.32266
\(926\) 0.250493 0.770940i 0.00823173 0.0253347i
\(927\) −24.5502 9.59585i −0.806334 0.315169i
\(928\) −2.21175 1.60693i −0.0726042 0.0527500i
\(929\) −15.2962 + 4.97003i −0.501851 + 0.163061i −0.548993 0.835827i \(-0.684989\pi\)
0.0471418 + 0.998888i \(0.484989\pi\)
\(930\) 12.2912 + 2.31676i 0.403043 + 0.0759696i
\(931\) −0.826882 + 1.13811i −0.0271000 + 0.0372999i
\(932\) −8.26435 + 6.00440i −0.270708 + 0.196681i
\(933\) −28.7899 30.5238i −0.942540 0.999306i
\(934\) 9.79150i 0.320388i
\(935\) −1.88827 + 7.20388i −0.0617532 + 0.235592i
\(936\) −6.03070 + 3.86438i −0.197120 + 0.126311i
\(937\) −14.9808 4.86755i −0.489401 0.159016i 0.0539130 0.998546i \(-0.482831\pi\)
−0.543314 + 0.839530i \(0.682831\pi\)
\(938\) −1.91106 2.63035i −0.0623985 0.0858841i
\(939\) −14.2720 30.1578i −0.465749 0.984163i
\(940\) 1.97298 + 6.07221i 0.0643515 + 0.198054i
\(941\) −13.0916 40.2918i −0.426774 1.31347i −0.901286 0.433226i \(-0.857375\pi\)
0.474512 0.880249i \(-0.342625\pi\)
\(942\) 6.62606 + 14.0014i 0.215889 + 0.456189i
\(943\) 7.10338 + 9.77697i 0.231318 + 0.318382i
\(944\) −7.37352 2.39580i −0.239988 0.0779767i
\(945\) −0.312996 4.50239i −0.0101818 0.146463i
\(946\) −9.75869 25.0141i −0.317282 0.813279i
\(947\) 48.4481i 1.57435i −0.616729 0.787176i \(-0.711542\pi\)
0.616729 0.787176i \(-0.288458\pi\)
\(948\) 17.5419 + 18.5984i 0.569734 + 0.604047i
\(949\) 26.9549 19.5839i 0.874994 0.635721i
\(950\) −3.51059 + 4.83191i −0.113899 + 0.156768i
\(951\) 16.5049 + 3.11101i 0.535208 + 0.100881i
\(952\) −2.45865 + 0.798865i −0.0796855 + 0.0258914i
\(953\) −4.37076 3.17554i −0.141583 0.102866i 0.514739 0.857347i \(-0.327889\pi\)
−0.656322 + 0.754481i \(0.727889\pi\)
\(954\) −12.6531 + 32.3719i −0.409660 + 1.04808i
\(955\) −2.54730 + 7.83978i −0.0824286 + 0.253689i
\(956\) −20.8056 −0.672900
\(957\) −2.89909 15.4350i −0.0937142 0.498942i
\(958\) 38.9816 1.25944
\(959\) 3.74017 11.5111i 0.120776 0.371711i
\(960\) 0.191824 + 1.49214i 0.00619110 + 0.0481586i
\(961\) −30.8405 22.4069i −0.994855 0.722804i
\(962\) −21.5148 + 6.99058i −0.693665 + 0.225385i
\(963\) 13.4040 16.3480i 0.431938 0.526807i
\(964\) 9.32814 12.8391i 0.300439 0.413519i
\(965\) −0.633513 + 0.460274i −0.0203935 + 0.0148168i
\(966\) −8.89453 + 8.38927i −0.286177 + 0.269920i
\(967\) 25.8925i 0.832645i −0.909217 0.416323i \(-0.863319\pi\)
0.909217 0.416323i \(-0.136681\pi\)
\(968\) 4.58332 + 9.99966i 0.147314 + 0.321401i
\(969\) −3.02250 + 5.52656i −0.0970967 + 0.177539i
\(970\) 9.54921 + 3.10273i 0.306607 + 0.0996225i
\(971\) 31.9524 + 43.9787i 1.02540 + 1.41134i 0.908347 + 0.418217i \(0.137345\pi\)
0.117053 + 0.993126i \(0.462655\pi\)
\(972\) 15.5875 0.170800i 0.499970 0.00547842i
\(973\) 3.87532 + 11.9270i 0.124237 + 0.382362i
\(974\) −1.74681 5.37612i −0.0559714 0.172262i
\(975\) −15.8695 + 7.51013i −0.508230 + 0.240517i
\(976\) 6.63145 + 9.12741i 0.212268 + 0.292161i
\(977\) 18.7851 + 6.10364i 0.600988 + 0.195273i 0.593681 0.804701i \(-0.297674\pi\)
0.00730686 + 0.999973i \(0.497674\pi\)
\(978\) −18.6062 10.1758i −0.594960 0.325386i
\(979\) 11.1891 9.16212i 0.357605 0.292823i
\(980\) 0.868577i 0.0277457i
\(981\) −1.03823 3.97129i −0.0331480 0.126793i
\(982\) 26.8757 19.5264i 0.857640 0.623112i
\(983\) 22.3185 30.7188i 0.711850 0.979777i −0.287906 0.957659i \(-0.592959\pi\)
0.999755 0.0221183i \(-0.00704106\pi\)
\(984\) −0.549244 + 2.91392i −0.0175093 + 0.0928922i
\(985\) 13.3124 4.32546i 0.424168 0.137821i
\(986\) −5.71777 4.15420i −0.182091 0.132297i
\(987\) −12.6280 + 1.62340i −0.401952 + 0.0516735i
\(988\) 1.03790 3.19434i 0.0330201 0.101625i
\(989\) −57.1481 −1.81720
\(990\) −5.08426 + 6.98845i −0.161588 + 0.222108i
\(991\) −4.58569 −0.145669 −0.0728347 0.997344i \(-0.523205\pi\)
−0.0728347 + 0.997344i \(0.523205\pi\)
\(992\) 2.56914 7.90699i 0.0815702 0.251047i
\(993\) −44.0270 + 5.65996i −1.39716 + 0.179613i
\(994\) 0.855585 + 0.621619i 0.0271375 + 0.0197166i
\(995\) −1.97867 + 0.642909i −0.0627281 + 0.0203816i
\(996\) −2.50084 + 13.2678i −0.0792422 + 0.420406i
\(997\) −2.16828 + 2.98438i −0.0686701 + 0.0945162i −0.841971 0.539523i \(-0.818604\pi\)
0.773301 + 0.634040i \(0.218604\pi\)
\(998\) 14.6221 10.6236i 0.462855 0.336284i
\(999\) 47.7665 + 11.9302i 1.51126 + 0.377454i
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 462.2.w.b.365.1 yes 48
3.2 odd 2 462.2.w.a.365.5 yes 48
11.6 odd 10 462.2.w.a.281.5 48
33.17 even 10 inner 462.2.w.b.281.1 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.w.a.281.5 48 11.6 odd 10
462.2.w.a.365.5 yes 48 3.2 odd 2
462.2.w.b.281.1 yes 48 33.17 even 10 inner
462.2.w.b.365.1 yes 48 1.1 even 1 trivial