Properties

Label 930.2.j.c.683.3
Level $930$
Weight $2$
Character 930.683
Analytic conductor $7.426$
Analytic rank $0$
Dimension $8$
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] = [930,2,Mod(497,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.497");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.j (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.1698758656.6
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 683.3
Root \(1.69230i\) of defining polynomial
Character \(\chi\) \(=\) 930.683
Dual form 930.2.j.c.497.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +(-0.292893 + 1.70711i) q^{3} +1.00000i q^{4} +(-0.489528 - 2.18183i) q^{5} +(-1.41421 + 1.00000i) q^{6} +(-0.474719 + 0.474719i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.82843 - 1.00000i) q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +(-0.292893 + 1.70711i) q^{3} +1.00000i q^{4} +(-0.489528 - 2.18183i) q^{5} +(-1.41421 + 1.00000i) q^{6} +(-0.474719 + 0.474719i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.82843 - 1.00000i) q^{9} +(1.19663 - 1.88893i) q^{10} -4.08557i q^{11} +(-1.70711 - 0.292893i) q^{12} +(-3.10651 - 3.10651i) q^{13} -0.671354 q^{14} +(3.86799 - 0.196635i) q^{15} -1.00000 q^{16} +(-4.06462 - 4.06462i) q^{17} +(-1.29289 - 2.70711i) q^{18} +1.57129i q^{19} +(2.18183 - 0.489528i) q^{20} +(-0.671354 - 0.949437i) q^{21} +(2.88893 - 2.88893i) q^{22} +(-1.06051 + 1.06051i) q^{23} +(-1.00000 - 1.41421i) q^{24} +(-4.52072 + 2.13613i) q^{25} -4.39327i q^{26} +(2.53553 - 4.53553i) q^{27} +(-0.474719 - 0.474719i) q^{28} -1.87899 q^{29} +(2.87412 + 2.59604i) q^{30} +1.00000 q^{31} +(-0.707107 - 0.707107i) q^{32} +(6.97450 + 1.19663i) q^{33} -5.74825i q^{34} +(1.26814 + 0.803365i) q^{35} +(1.00000 - 2.82843i) q^{36} +(-2.00000 + 2.00000i) q^{37} +(-1.11107 + 1.11107i) q^{38} +(6.21302 - 4.39327i) q^{39} +(1.88893 + 1.19663i) q^{40} -7.26358i q^{41} +(0.196635 - 1.14607i) q^{42} +(1.16702 + 1.16702i) q^{43} +4.08557 q^{44} +(-0.797231 + 6.66066i) q^{45} -1.49978 q^{46} +(-0.520724 - 0.520724i) q^{47} +(0.292893 - 1.70711i) q^{48} +6.54928i q^{49} +(-4.70711 - 1.68616i) q^{50} +(8.12925 - 5.74825i) q^{51} +(3.10651 - 3.10651i) q^{52} +(-2.48339 + 2.48339i) q^{53} +(5.00000 - 1.41421i) q^{54} +(-8.91399 + 2.00000i) q^{55} -0.671354i q^{56} +(-2.68235 - 0.460219i) q^{57} +(-1.32865 - 1.32865i) q^{58} +4.40554 q^{59} +(0.196635 + 3.86799i) q^{60} +11.2340 q^{61} +(0.707107 + 0.707107i) q^{62} +(1.81743 - 0.867988i) q^{63} -1.00000i q^{64} +(-5.25714 + 8.29859i) q^{65} +(4.08557 + 5.77786i) q^{66} +(-5.37233 + 5.37233i) q^{67} +(4.06462 - 4.06462i) q^{68} +(-1.49978 - 2.12101i) q^{69} +(0.328646 + 1.46478i) q^{70} -4.42871i q^{71} +(2.70711 - 1.29289i) q^{72} +(-7.86799 - 7.86799i) q^{73} -2.82843 q^{74} +(-2.32251 - 8.34302i) q^{75} -1.57129 q^{76} +(1.93949 + 1.93949i) q^{77} +(7.49978 + 1.28676i) q^{78} -9.12702i q^{79} +(0.489528 + 2.18183i) q^{80} +(7.00000 + 5.65685i) q^{81} +(5.13613 - 5.13613i) q^{82} +(-8.35783 + 8.35783i) q^{83} +(0.949437 - 0.671354i) q^{84} +(-6.87855 + 10.8580i) q^{85} +1.65041i q^{86} +(0.550343 - 3.20764i) q^{87} +(2.88893 + 2.88893i) q^{88} +5.69230 q^{89} +(-5.27353 + 4.14607i) q^{90} +2.94944 q^{91} +(-1.06051 - 1.06051i) q^{92} +(-0.292893 + 1.70711i) q^{93} -0.736416i q^{94} +(3.42827 - 0.769189i) q^{95} +(1.41421 - 1.00000i) q^{96} +(8.34915 - 8.34915i) q^{97} +(-4.63104 + 4.63104i) q^{98} +(-4.08557 + 11.5557i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{3} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{3} + 4 q^{7} - 8 q^{12} - 4 q^{13} + 12 q^{14} + 4 q^{15} - 8 q^{16} + 4 q^{17} - 16 q^{18} + 4 q^{20} + 12 q^{21} + 4 q^{22} - 12 q^{23} - 8 q^{24} - 4 q^{25} - 8 q^{27} + 4 q^{28} - 8 q^{29} + 8 q^{31} + 8 q^{33} + 24 q^{35} + 8 q^{36} - 16 q^{37} - 28 q^{38} + 8 q^{39} - 4 q^{40} - 8 q^{42} - 8 q^{43} + 4 q^{44} - 12 q^{45} + 28 q^{46} + 28 q^{47} + 8 q^{48} - 32 q^{50} - 8 q^{51} + 4 q^{52} - 12 q^{53} + 40 q^{54} - 20 q^{55} - 24 q^{57} - 28 q^{58} + 24 q^{59} - 8 q^{60} + 56 q^{61} - 28 q^{63} - 36 q^{65} + 4 q^{66} - 16 q^{67} - 4 q^{68} + 28 q^{69} + 20 q^{70} + 16 q^{72} - 36 q^{73} - 32 q^{75} + 4 q^{76} + 12 q^{77} + 20 q^{78} + 56 q^{81} + 28 q^{82} - 12 q^{83} - 8 q^{84} + 32 q^{85} - 20 q^{87} + 4 q^{88} + 36 q^{89} - 4 q^{90} + 8 q^{91} - 12 q^{92} - 8 q^{93} - 36 q^{95} + 12 q^{97} + 32 q^{98} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.500000 + 0.500000i
\(3\) −0.292893 + 1.70711i −0.169102 + 0.985599i
\(4\) 1.00000i 0.500000i
\(5\) −0.489528 2.18183i −0.218924 0.975742i
\(6\) −1.41421 + 1.00000i −0.577350 + 0.408248i
\(7\) −0.474719 + 0.474719i −0.179427 + 0.179427i −0.791106 0.611679i \(-0.790494\pi\)
0.611679 + 0.791106i \(0.290494\pi\)
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) −2.82843 1.00000i −0.942809 0.333333i
\(10\) 1.19663 1.88893i 0.378409 0.597333i
\(11\) 4.08557i 1.23184i −0.787807 0.615922i \(-0.788783\pi\)
0.787807 0.615922i \(-0.211217\pi\)
\(12\) −1.70711 0.292893i −0.492799 0.0845510i
\(13\) −3.10651 3.10651i −0.861591 0.861591i 0.129932 0.991523i \(-0.458524\pi\)
−0.991523 + 0.129932i \(0.958524\pi\)
\(14\) −0.671354 −0.179427
\(15\) 3.86799 0.196635i 0.998710 0.0507709i
\(16\) −1.00000 −0.250000
\(17\) −4.06462 4.06462i −0.985816 0.985816i 0.0140848 0.999901i \(-0.495517\pi\)
−0.999901 + 0.0140848i \(0.995517\pi\)
\(18\) −1.29289 2.70711i −0.304738 0.638071i
\(19\) 1.57129i 0.360478i 0.983623 + 0.180239i \(0.0576871\pi\)
−0.983623 + 0.180239i \(0.942313\pi\)
\(20\) 2.18183 0.489528i 0.487871 0.109462i
\(21\) −0.671354 0.949437i −0.146501 0.207184i
\(22\) 2.88893 2.88893i 0.615922 0.615922i
\(23\) −1.06051 + 1.06051i −0.221131 + 0.221131i −0.808974 0.587844i \(-0.799977\pi\)
0.587844 + 0.808974i \(0.299977\pi\)
\(24\) −1.00000 1.41421i −0.204124 0.288675i
\(25\) −4.52072 + 2.13613i −0.904145 + 0.427226i
\(26\) 4.39327i 0.861591i
\(27\) 2.53553 4.53553i 0.487964 0.872864i
\(28\) −0.474719 0.474719i −0.0897134 0.0897134i
\(29\) −1.87899 −0.348920 −0.174460 0.984664i \(-0.555818\pi\)
−0.174460 + 0.984664i \(0.555818\pi\)
\(30\) 2.87412 + 2.59604i 0.524741 + 0.473970i
\(31\) 1.00000 0.179605
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) 6.97450 + 1.19663i 1.21410 + 0.208307i
\(34\) 5.74825i 0.985816i
\(35\) 1.26814 + 0.803365i 0.214355 + 0.135793i
\(36\) 1.00000 2.82843i 0.166667 0.471405i
\(37\) −2.00000 + 2.00000i −0.328798 + 0.328798i −0.852129 0.523331i \(-0.824689\pi\)
0.523331 + 0.852129i \(0.324689\pi\)
\(38\) −1.11107 + 1.11107i −0.180239 + 0.180239i
\(39\) 6.21302 4.39327i 0.994880 0.703486i
\(40\) 1.88893 + 1.19663i 0.298666 + 0.189205i
\(41\) 7.26358i 1.13438i −0.823587 0.567191i \(-0.808030\pi\)
0.823587 0.567191i \(-0.191970\pi\)
\(42\) 0.196635 1.14607i 0.0303414 0.176843i
\(43\) 1.16702 + 1.16702i 0.177968 + 0.177968i 0.790470 0.612501i \(-0.209837\pi\)
−0.612501 + 0.790470i \(0.709837\pi\)
\(44\) 4.08557 0.615922
\(45\) −0.797231 + 6.66066i −0.118844 + 0.992913i
\(46\) −1.49978 −0.221131
\(47\) −0.520724 0.520724i −0.0759555 0.0759555i 0.668108 0.744064i \(-0.267104\pi\)
−0.744064 + 0.668108i \(0.767104\pi\)
\(48\) 0.292893 1.70711i 0.0422755 0.246400i
\(49\) 6.54928i 0.935612i
\(50\) −4.70711 1.68616i −0.665685 0.238459i
\(51\) 8.12925 5.74825i 1.13832 0.804915i
\(52\) 3.10651 3.10651i 0.430796 0.430796i
\(53\) −2.48339 + 2.48339i −0.341120 + 0.341120i −0.856788 0.515668i \(-0.827544\pi\)
0.515668 + 0.856788i \(0.327544\pi\)
\(54\) 5.00000 1.41421i 0.680414 0.192450i
\(55\) −8.91399 + 2.00000i −1.20196 + 0.269680i
\(56\) 0.671354i 0.0897134i
\(57\) −2.68235 0.460219i −0.355287 0.0609575i
\(58\) −1.32865 1.32865i −0.174460 0.174460i
\(59\) 4.40554 0.573552 0.286776 0.957998i \(-0.407416\pi\)
0.286776 + 0.957998i \(0.407416\pi\)
\(60\) 0.196635 + 3.86799i 0.0253855 + 0.499355i
\(61\) 11.2340 1.43836 0.719181 0.694823i \(-0.244517\pi\)
0.719181 + 0.694823i \(0.244517\pi\)
\(62\) 0.707107 + 0.707107i 0.0898027 + 0.0898027i
\(63\) 1.81743 0.867988i 0.228974 0.109356i
\(64\) 1.00000i 0.125000i
\(65\) −5.25714 + 8.29859i −0.652068 + 1.02931i
\(66\) 4.08557 + 5.77786i 0.502899 + 0.711206i
\(67\) −5.37233 + 5.37233i −0.656334 + 0.656334i −0.954511 0.298177i \(-0.903622\pi\)
0.298177 + 0.954511i \(0.403622\pi\)
\(68\) 4.06462 4.06462i 0.492908 0.492908i
\(69\) −1.49978 2.12101i −0.180552 0.255340i
\(70\) 0.328646 + 1.46478i 0.0392808 + 0.175074i
\(71\) 4.42871i 0.525592i −0.964851 0.262796i \(-0.915355\pi\)
0.964851 0.262796i \(-0.0846445\pi\)
\(72\) 2.70711 1.29289i 0.319036 0.152369i
\(73\) −7.86799 7.86799i −0.920878 0.920878i 0.0762132 0.997092i \(-0.475717\pi\)
−0.997092 + 0.0762132i \(0.975717\pi\)
\(74\) −2.82843 −0.328798
\(75\) −2.32251 8.34302i −0.268181 0.963369i
\(76\) −1.57129 −0.180239
\(77\) 1.93949 + 1.93949i 0.221026 + 0.221026i
\(78\) 7.49978 + 1.28676i 0.849183 + 0.145697i
\(79\) 9.12702i 1.02687i −0.858129 0.513435i \(-0.828373\pi\)
0.858129 0.513435i \(-0.171627\pi\)
\(80\) 0.489528 + 2.18183i 0.0547309 + 0.243935i
\(81\) 7.00000 + 5.65685i 0.777778 + 0.628539i
\(82\) 5.13613 5.13613i 0.567191 0.567191i
\(83\) −8.35783 + 8.35783i −0.917391 + 0.917391i −0.996839 0.0794483i \(-0.974684\pi\)
0.0794483 + 0.996839i \(0.474684\pi\)
\(84\) 0.949437 0.671354i 0.103592 0.0732507i
\(85\) −6.87855 + 10.8580i −0.746084 + 1.17772i
\(86\) 1.65041i 0.177968i
\(87\) 0.550343 3.20764i 0.0590030 0.343895i
\(88\) 2.88893 + 2.88893i 0.307961 + 0.307961i
\(89\) 5.69230 0.603382 0.301691 0.953406i \(-0.402449\pi\)
0.301691 + 0.953406i \(0.402449\pi\)
\(90\) −5.27353 + 4.14607i −0.555879 + 0.437034i
\(91\) 2.94944 0.309185
\(92\) −1.06051 1.06051i −0.110565 0.110565i
\(93\) −0.292893 + 1.70711i −0.0303716 + 0.177019i
\(94\) 0.736416i 0.0759555i
\(95\) 3.42827 0.769189i 0.351734 0.0789172i
\(96\) 1.41421 1.00000i 0.144338 0.102062i
\(97\) 8.34915 8.34915i 0.847728 0.847728i −0.142121 0.989849i \(-0.545392\pi\)
0.989849 + 0.142121i \(0.0453923\pi\)
\(98\) −4.63104 + 4.63104i −0.467806 + 0.467806i
\(99\) −4.08557 + 11.5557i −0.410615 + 1.16139i
\(100\) −2.13613 4.52072i −0.213613 0.452072i
\(101\) 12.5702i 1.25078i 0.780311 + 0.625392i \(0.215061\pi\)
−0.780311 + 0.625392i \(0.784939\pi\)
\(102\) 9.81287 + 1.68362i 0.971619 + 0.166703i
\(103\) −0.449657 0.449657i −0.0443060 0.0443060i 0.684607 0.728913i \(-0.259974\pi\)
−0.728913 + 0.684607i \(0.759974\pi\)
\(104\) 4.39327 0.430796
\(105\) −1.74286 + 1.92955i −0.170086 + 0.188305i
\(106\) −3.51205 −0.341120
\(107\) −5.00412 5.00412i −0.483766 0.483766i 0.422566 0.906332i \(-0.361130\pi\)
−0.906332 + 0.422566i \(0.861130\pi\)
\(108\) 4.53553 + 2.53553i 0.436432 + 0.243982i
\(109\) 7.47661i 0.716129i −0.933697 0.358064i \(-0.883437\pi\)
0.933697 0.358064i \(-0.116563\pi\)
\(110\) −7.71736 4.88893i −0.735821 0.466141i
\(111\) −2.82843 4.00000i −0.268462 0.379663i
\(112\) 0.474719 0.474719i 0.0448567 0.0448567i
\(113\) −6.30315 + 6.30315i −0.592950 + 0.592950i −0.938427 0.345477i \(-0.887717\pi\)
0.345477 + 0.938427i \(0.387717\pi\)
\(114\) −1.57129 2.22214i −0.147165 0.208122i
\(115\) 2.83298 + 1.79469i 0.264177 + 0.167356i
\(116\) 1.87899i 0.174460i
\(117\) 5.68003 + 11.8931i 0.525119 + 1.09951i
\(118\) 3.11519 + 3.11519i 0.286776 + 0.286776i
\(119\) 3.85911 0.353764
\(120\) −2.59604 + 2.87412i −0.236985 + 0.262370i
\(121\) −5.69186 −0.517442
\(122\) 7.94361 + 7.94361i 0.719181 + 0.719181i
\(123\) 12.3997 + 2.12745i 1.11804 + 0.191826i
\(124\) 1.00000i 0.0898027i
\(125\) 6.87368 + 8.81774i 0.614801 + 0.788682i
\(126\) 1.89887 + 0.671354i 0.169165 + 0.0598089i
\(127\) 13.5138 13.5138i 1.19916 1.19916i 0.224741 0.974419i \(-0.427846\pi\)
0.974419 0.224741i \(-0.0721536\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) −2.33403 + 1.65041i −0.205500 + 0.145310i
\(130\) −9.58535 + 2.15063i −0.840691 + 0.188623i
\(131\) 14.5940i 1.27509i −0.770415 0.637543i \(-0.779951\pi\)
0.770415 0.637543i \(-0.220049\pi\)
\(132\) −1.19663 + 6.97450i −0.104154 + 0.607052i
\(133\) −0.745919 0.745919i −0.0646794 0.0646794i
\(134\) −7.59762 −0.656334
\(135\) −11.1370 3.31182i −0.958517 0.285036i
\(136\) 5.74825 0.492908
\(137\) 6.22752 + 6.22752i 0.532053 + 0.532053i 0.921183 0.389130i \(-0.127224\pi\)
−0.389130 + 0.921183i \(0.627224\pi\)
\(138\) 0.439276 2.56029i 0.0373936 0.217946i
\(139\) 1.35498i 0.114928i 0.998348 + 0.0574638i \(0.0183014\pi\)
−0.998348 + 0.0574638i \(0.981699\pi\)
\(140\) −0.803365 + 1.26814i −0.0678967 + 0.107178i
\(141\) 1.04145 0.736416i 0.0877058 0.0620174i
\(142\) 3.13157 3.13157i 0.262796 0.262796i
\(143\) −12.6919 + 12.6919i −1.06135 + 1.06135i
\(144\) 2.82843 + 1.00000i 0.235702 + 0.0833333i
\(145\) 0.919818 + 4.09963i 0.0763868 + 0.340456i
\(146\) 11.1270i 0.920878i
\(147\) −11.1803 1.91824i −0.922138 0.158214i
\(148\) −2.00000 2.00000i −0.164399 0.164399i
\(149\) −20.3809 −1.66967 −0.834833 0.550504i \(-0.814436\pi\)
−0.834833 + 0.550504i \(0.814436\pi\)
\(150\) 4.25714 7.54167i 0.347594 0.615775i
\(151\) −19.4720 −1.58461 −0.792303 0.610128i \(-0.791118\pi\)
−0.792303 + 0.610128i \(0.791118\pi\)
\(152\) −1.11107 1.11107i −0.0901195 0.0901195i
\(153\) 7.43187 + 15.5611i 0.600831 + 1.25804i
\(154\) 2.74286i 0.221026i
\(155\) −0.489528 2.18183i −0.0393198 0.175248i
\(156\) 4.39327 + 6.21302i 0.351743 + 0.497440i
\(157\) −1.46245 + 1.46245i −0.116716 + 0.116716i −0.763053 0.646336i \(-0.776300\pi\)
0.646336 + 0.763053i \(0.276300\pi\)
\(158\) 6.45377 6.45377i 0.513435 0.513435i
\(159\) −3.51205 4.96679i −0.278524 0.393892i
\(160\) −1.19663 + 1.88893i −0.0946023 + 0.149333i
\(161\) 1.00688i 0.0793535i
\(162\) 0.949747 + 8.94975i 0.0746192 + 0.703159i
\(163\) −2.67135 2.67135i −0.209237 0.209237i 0.594706 0.803943i \(-0.297268\pi\)
−0.803943 + 0.594706i \(0.797268\pi\)
\(164\) 7.26358 0.567191
\(165\) −0.803365 15.8029i −0.0625419 1.23026i
\(166\) −11.8198 −0.917391
\(167\) −3.37465 3.37465i −0.261138 0.261138i 0.564378 0.825516i \(-0.309116\pi\)
−0.825516 + 0.564378i \(0.809116\pi\)
\(168\) 1.14607 + 0.196635i 0.0884214 + 0.0151707i
\(169\) 6.30082i 0.484678i
\(170\) −12.5417 + 2.81393i −0.961902 + 0.215818i
\(171\) 1.57129 4.44427i 0.120159 0.339862i
\(172\) −1.16702 + 1.16702i −0.0889841 + 0.0889841i
\(173\) −12.6186 + 12.6186i −0.959371 + 0.959371i −0.999206 0.0398349i \(-0.987317\pi\)
0.0398349 + 0.999206i \(0.487317\pi\)
\(174\) 2.65729 1.87899i 0.201449 0.142446i
\(175\) 1.13201 3.16013i 0.0855720 0.238884i
\(176\) 4.08557i 0.307961i
\(177\) −1.29035 + 7.52072i −0.0969888 + 0.565292i
\(178\) 4.02506 + 4.02506i 0.301691 + 0.301691i
\(179\) 22.7264 1.69865 0.849326 0.527868i \(-0.177008\pi\)
0.849326 + 0.527868i \(0.177008\pi\)
\(180\) −6.66066 0.797231i −0.496456 0.0594221i
\(181\) −10.6295 −0.790082 −0.395041 0.918663i \(-0.629270\pi\)
−0.395041 + 0.918663i \(0.629270\pi\)
\(182\) 2.08557 + 2.08557i 0.154593 + 0.154593i
\(183\) −3.29035 + 19.1776i −0.243230 + 1.41765i
\(184\) 1.49978i 0.110565i
\(185\) 5.34271 + 3.38459i 0.392804 + 0.248840i
\(186\) −1.41421 + 1.00000i −0.103695 + 0.0733236i
\(187\) −16.6063 + 16.6063i −1.21437 + 1.21437i
\(188\) 0.520724 0.520724i 0.0379777 0.0379777i
\(189\) 0.949437 + 3.35677i 0.0690614 + 0.244169i
\(190\) 2.96805 + 1.88026i 0.215325 + 0.136408i
\(191\) 0.815538i 0.0590103i 0.999565 + 0.0295051i \(0.00939314\pi\)
−0.999565 + 0.0295051i \(0.990607\pi\)
\(192\) 1.70711 + 0.292893i 0.123200 + 0.0211377i
\(193\) −5.68362 5.68362i −0.409116 0.409116i 0.472314 0.881430i \(-0.343419\pi\)
−0.881430 + 0.472314i \(0.843419\pi\)
\(194\) 11.8075 0.847728
\(195\) −12.6268 11.4051i −0.904224 0.816736i
\(196\) −6.54928 −0.467806
\(197\) −18.3545 18.3545i −1.30771 1.30771i −0.923067 0.384640i \(-0.874326\pi\)
−0.384640 0.923067i \(-0.625674\pi\)
\(198\) −11.0601 + 5.28220i −0.786005 + 0.375390i
\(199\) 16.1137i 1.14227i −0.820856 0.571135i \(-0.806503\pi\)
0.820856 0.571135i \(-0.193497\pi\)
\(200\) 1.68616 4.70711i 0.119230 0.332843i
\(201\) −7.59762 10.7447i −0.535895 0.757869i
\(202\) −8.88849 + 8.88849i −0.625392 + 0.625392i
\(203\) 0.891992 0.891992i 0.0626055 0.0626055i
\(204\) 5.74825 + 8.12925i 0.402458 + 0.569161i
\(205\) −15.8479 + 3.55573i −1.10686 + 0.248343i
\(206\) 0.635910i 0.0443060i
\(207\) 4.06007 1.93906i 0.282194 0.134774i
\(208\) 3.10651 + 3.10651i 0.215398 + 0.215398i
\(209\) 6.41960 0.444053
\(210\) −2.59679 + 0.132012i −0.179195 + 0.00910966i
\(211\) −25.1270 −1.72982 −0.864908 0.501931i \(-0.832623\pi\)
−0.864908 + 0.501931i \(0.832623\pi\)
\(212\) −2.48339 2.48339i −0.170560 0.170560i
\(213\) 7.56029 + 1.29714i 0.518022 + 0.0888786i
\(214\) 7.07689i 0.483766i
\(215\) 1.97494 3.11751i 0.134690 0.212613i
\(216\) 1.41421 + 5.00000i 0.0962250 + 0.340207i
\(217\) −0.474719 + 0.474719i −0.0322260 + 0.0322260i
\(218\) 5.28676 5.28676i 0.358064 0.358064i
\(219\) 15.7360 11.1270i 1.06334 0.751894i
\(220\) −2.00000 8.91399i −0.134840 0.600981i
\(221\) 25.2536i 1.69874i
\(222\) 0.828427 4.82843i 0.0556004 0.324063i
\(223\) −3.60852 3.60852i −0.241645 0.241645i 0.575886 0.817530i \(-0.304657\pi\)
−0.817530 + 0.575886i \(0.804657\pi\)
\(224\) 0.671354 0.0448567
\(225\) 14.9227 1.52116i 0.994845 0.101411i
\(226\) −8.91399 −0.592950
\(227\) 16.2085 + 16.2085i 1.07579 + 1.07579i 0.996882 + 0.0789120i \(0.0251446\pi\)
0.0789120 + 0.996882i \(0.474855\pi\)
\(228\) 0.460219 2.68235i 0.0304788 0.177643i
\(229\) 6.64235i 0.438939i −0.975619 0.219470i \(-0.929567\pi\)
0.975619 0.219470i \(-0.0704327\pi\)
\(230\) 0.734185 + 3.27226i 0.0484107 + 0.215766i
\(231\) −3.87899 + 2.74286i −0.255219 + 0.180467i
\(232\) 1.32865 1.32865i 0.0872299 0.0872299i
\(233\) −9.15146 + 9.15146i −0.599532 + 0.599532i −0.940188 0.340656i \(-0.889351\pi\)
0.340656 + 0.940188i \(0.389351\pi\)
\(234\) −4.39327 + 12.4260i −0.287197 + 0.812316i
\(235\) −0.881221 + 1.39104i −0.0574845 + 0.0907414i
\(236\) 4.40554i 0.286776i
\(237\) 15.5808 + 2.67324i 1.01208 + 0.173646i
\(238\) 2.72880 + 2.72880i 0.176882 + 0.176882i
\(239\) 26.5471 1.71719 0.858593 0.512658i \(-0.171339\pi\)
0.858593 + 0.512658i \(0.171339\pi\)
\(240\) −3.86799 + 0.196635i −0.249678 + 0.0126927i
\(241\) −3.60673 −0.232330 −0.116165 0.993230i \(-0.537060\pi\)
−0.116165 + 0.993230i \(0.537060\pi\)
\(242\) −4.02475 4.02475i −0.258721 0.258721i
\(243\) −11.7071 + 10.2929i −0.751011 + 0.660289i
\(244\) 11.2340i 0.719181i
\(245\) 14.2894 3.20606i 0.912916 0.204828i
\(246\) 7.26358 + 10.2723i 0.463109 + 0.654935i
\(247\) 4.88122 4.88122i 0.310585 0.310585i
\(248\) −0.707107 + 0.707107i −0.0449013 + 0.0449013i
\(249\) −11.8198 16.7157i −0.749046 1.05931i
\(250\) −1.37465 + 11.0955i −0.0869406 + 0.701742i
\(251\) 18.2657i 1.15292i −0.817126 0.576460i \(-0.804434\pi\)
0.817126 0.576460i \(-0.195566\pi\)
\(252\) 0.867988 + 1.81743i 0.0546781 + 0.114487i
\(253\) 4.33276 + 4.33276i 0.272399 + 0.272399i
\(254\) 19.1115 1.19916
\(255\) −16.5212 14.9227i −1.03460 0.934494i
\(256\) 1.00000 0.0625000
\(257\) 17.9380 + 17.9380i 1.11894 + 1.11894i 0.991897 + 0.127045i \(0.0405491\pi\)
0.127045 + 0.991897i \(0.459451\pi\)
\(258\) −2.81743 0.483394i −0.175405 0.0300948i
\(259\) 1.89887i 0.117990i
\(260\) −8.29859 5.25714i −0.514657 0.326034i
\(261\) 5.31459 + 1.87899i 0.328965 + 0.116307i
\(262\) 10.3195 10.3195i 0.637543 0.637543i
\(263\) −9.29859 + 9.29859i −0.573376 + 0.573376i −0.933070 0.359695i \(-0.882881\pi\)
0.359695 + 0.933070i \(0.382881\pi\)
\(264\) −5.77786 + 4.08557i −0.355603 + 0.251449i
\(265\) 6.63402 + 4.20264i 0.407525 + 0.258166i
\(266\) 1.05489i 0.0646794i
\(267\) −1.66724 + 9.71736i −0.102033 + 0.594693i
\(268\) −5.37233 5.37233i −0.328167 0.328167i
\(269\) 9.25447 0.564255 0.282128 0.959377i \(-0.408960\pi\)
0.282128 + 0.959377i \(0.408960\pi\)
\(270\) −5.53321 10.2168i −0.336740 0.621776i
\(271\) 28.8012 1.74955 0.874775 0.484530i \(-0.161009\pi\)
0.874775 + 0.484530i \(0.161009\pi\)
\(272\) 4.06462 + 4.06462i 0.246454 + 0.246454i
\(273\) −0.863870 + 5.03500i −0.0522838 + 0.304732i
\(274\) 8.80704i 0.532053i
\(275\) 8.72730 + 18.4697i 0.526276 + 1.11377i
\(276\) 2.12101 1.49978i 0.127670 0.0902762i
\(277\) 18.8334 18.8334i 1.13159 1.13159i 0.141674 0.989913i \(-0.454751\pi\)
0.989913 0.141674i \(-0.0452486\pi\)
\(278\) −0.958112 + 0.958112i −0.0574638 + 0.0574638i
\(279\) −2.82843 1.00000i −0.169334 0.0598684i
\(280\) −1.46478 + 0.328646i −0.0875371 + 0.0196404i
\(281\) 12.6435i 0.754250i 0.926162 + 0.377125i \(0.123087\pi\)
−0.926162 + 0.377125i \(0.876913\pi\)
\(282\) 1.25714 + 0.215691i 0.0748616 + 0.0128442i
\(283\) 13.8139 + 13.8139i 0.821153 + 0.821153i 0.986273 0.165121i \(-0.0528013\pi\)
−0.165121 + 0.986273i \(0.552801\pi\)
\(284\) 4.42871 0.262796
\(285\) 0.308970 + 6.07772i 0.0183018 + 0.360013i
\(286\) −17.9490 −1.06135
\(287\) 3.44816 + 3.44816i 0.203538 + 0.203538i
\(288\) 1.29289 + 2.70711i 0.0761845 + 0.159518i
\(289\) 16.0423i 0.943666i
\(290\) −2.24846 + 3.54928i −0.132034 + 0.208421i
\(291\) 11.8075 + 16.6983i 0.692167 + 0.978872i
\(292\) 7.86799 7.86799i 0.460439 0.460439i
\(293\) 20.2335 20.2335i 1.18206 1.18206i 0.202844 0.979211i \(-0.434981\pi\)
0.979211 0.202844i \(-0.0650185\pi\)
\(294\) −6.54928 9.26209i −0.381962 0.540176i
\(295\) −2.15663 9.61212i −0.125564 0.559639i
\(296\) 2.82843i 0.164399i
\(297\) −18.5302 10.3591i −1.07523 0.601096i
\(298\) −14.4114 14.4114i −0.834833 0.834833i
\(299\) 6.58894 0.381048
\(300\) 8.34302 2.32251i 0.481684 0.134090i
\(301\) −1.10801 −0.0638645
\(302\) −13.7688 13.7688i −0.792303 0.792303i
\(303\) −21.4587 3.68173i −1.23277 0.211510i
\(304\) 1.57129i 0.0901195i
\(305\) −5.49934 24.5106i −0.314891 1.40347i
\(306\) −5.74825 + 16.2585i −0.328605 + 0.929436i
\(307\) −7.66447 + 7.66447i −0.437434 + 0.437434i −0.891148 0.453713i \(-0.850099\pi\)
0.453713 + 0.891148i \(0.350099\pi\)
\(308\) −1.93949 + 1.93949i −0.110513 + 0.110513i
\(309\) 0.899313 0.635910i 0.0511601 0.0361757i
\(310\) 1.19663 1.88893i 0.0679643 0.107284i
\(311\) 28.5308i 1.61783i −0.587925 0.808915i \(-0.700055\pi\)
0.587925 0.808915i \(-0.299945\pi\)
\(312\) −1.28676 + 7.49978i −0.0728484 + 0.424591i
\(313\) 23.0992 + 23.0992i 1.30564 + 1.30564i 0.924527 + 0.381116i \(0.124460\pi\)
0.381116 + 0.924527i \(0.375540\pi\)
\(314\) −2.06822 −0.116716
\(315\) −2.78348 3.54040i −0.156831 0.199479i
\(316\) 9.12702 0.513435
\(317\) −11.3278 11.3278i −0.636231 0.636231i 0.313393 0.949624i \(-0.398534\pi\)
−0.949624 + 0.313393i \(0.898534\pi\)
\(318\) 1.02866 5.99544i 0.0576841 0.336208i
\(319\) 7.67674i 0.429815i
\(320\) −2.18183 + 0.489528i −0.121968 + 0.0273655i
\(321\) 10.0082 7.07689i 0.558605 0.394994i
\(322\) 0.711974 0.711974i 0.0396768 0.0396768i
\(323\) 6.38669 6.38669i 0.355365 0.355365i
\(324\) −5.65685 + 7.00000i −0.314270 + 0.388889i
\(325\) 20.6796 + 7.40777i 1.14710 + 0.410909i
\(326\) 3.77786i 0.209237i
\(327\) 12.7634 + 2.18985i 0.705816 + 0.121099i
\(328\) 5.13613 + 5.13613i 0.283595 + 0.283595i
\(329\) 0.494395 0.0272569
\(330\) 10.6063 11.7424i 0.583857 0.646399i
\(331\) −19.6774 −1.08157 −0.540783 0.841162i \(-0.681872\pi\)
−0.540783 + 0.841162i \(0.681872\pi\)
\(332\) −8.35783 8.35783i −0.458695 0.458695i
\(333\) 7.65685 3.65685i 0.419593 0.200394i
\(334\) 4.77248i 0.261138i
\(335\) 14.3514 + 9.09157i 0.784100 + 0.496726i
\(336\) 0.671354 + 0.949437i 0.0366253 + 0.0517961i
\(337\) −3.40510 + 3.40510i −0.185488 + 0.185488i −0.793742 0.608254i \(-0.791870\pi\)
0.608254 + 0.793742i \(0.291870\pi\)
\(338\) −4.45535 + 4.45535i −0.242339 + 0.242339i
\(339\) −8.91399 12.6063i −0.484142 0.684680i
\(340\) −10.8580 6.87855i −0.588860 0.373042i
\(341\) 4.08557i 0.221246i
\(342\) 4.25364 2.03151i 0.230011 0.109851i
\(343\) −6.43210 6.43210i −0.347301 0.347301i
\(344\) −1.65041 −0.0889841
\(345\) −3.89349 + 4.31055i −0.209618 + 0.232072i
\(346\) −17.8453 −0.959371
\(347\) 8.75110 + 8.75110i 0.469783 + 0.469783i 0.901844 0.432061i \(-0.142213\pi\)
−0.432061 + 0.901844i \(0.642213\pi\)
\(348\) 3.20764 + 0.550343i 0.171947 + 0.0295015i
\(349\) 30.6845i 1.64251i −0.570564 0.821253i \(-0.693276\pi\)
0.570564 0.821253i \(-0.306724\pi\)
\(350\) 3.03500 1.43410i 0.162228 0.0766558i
\(351\) −21.9663 + 6.21302i −1.17248 + 0.331627i
\(352\) −2.88893 + 2.88893i −0.153981 + 0.153981i
\(353\) 4.19208 4.19208i 0.223122 0.223122i −0.586690 0.809812i \(-0.699569\pi\)
0.809812 + 0.586690i \(0.199569\pi\)
\(354\) −6.23037 + 4.40554i −0.331141 + 0.234152i
\(355\) −9.66268 + 2.16798i −0.512842 + 0.115064i
\(356\) 5.69230i 0.301691i
\(357\) −1.13031 + 6.58790i −0.0598221 + 0.348669i
\(358\) 16.0700 + 16.0700i 0.849326 + 0.849326i
\(359\) 6.95588 0.367117 0.183559 0.983009i \(-0.441238\pi\)
0.183559 + 0.983009i \(0.441238\pi\)
\(360\) −4.14607 5.27353i −0.218517 0.277939i
\(361\) 16.5311 0.870056
\(362\) −7.51617 7.51617i −0.395041 0.395041i
\(363\) 1.66711 9.71661i 0.0875004 0.509990i
\(364\) 2.94944i 0.154593i
\(365\) −13.3150 + 21.0182i −0.696938 + 1.10014i
\(366\) −15.8872 + 11.2340i −0.830439 + 0.587209i
\(367\) 3.72774 3.72774i 0.194586 0.194586i −0.603088 0.797675i \(-0.706063\pi\)
0.797675 + 0.603088i \(0.206063\pi\)
\(368\) 1.06051 1.06051i 0.0552826 0.0552826i
\(369\) −7.26358 + 20.5445i −0.378127 + 1.06950i
\(370\) 1.38459 + 6.17113i 0.0719816 + 0.320822i
\(371\) 2.35783i 0.122412i
\(372\) −1.70711 0.292893i −0.0885094 0.0151858i
\(373\) 2.93906 + 2.93906i 0.152179 + 0.152179i 0.779090 0.626912i \(-0.215681\pi\)
−0.626912 + 0.779090i \(0.715681\pi\)
\(374\) −23.4848 −1.21437
\(375\) −17.0661 + 9.15146i −0.881288 + 0.472579i
\(376\) 0.736416 0.0379777
\(377\) 5.83710 + 5.83710i 0.300626 + 0.300626i
\(378\) −1.70224 + 3.04495i −0.0875538 + 0.156615i
\(379\) 19.7134i 1.01261i −0.862354 0.506305i \(-0.831011\pi\)
0.862354 0.506305i \(-0.168989\pi\)
\(380\) 0.769189 + 3.42827i 0.0394586 + 0.175867i
\(381\) 19.1115 + 27.0277i 0.979110 + 1.38467i
\(382\) −0.576673 + 0.576673i −0.0295051 + 0.0295051i
\(383\) 1.75110 1.75110i 0.0894769 0.0894769i −0.660952 0.750428i \(-0.729847\pi\)
0.750428 + 0.660952i \(0.229847\pi\)
\(384\) 1.00000 + 1.41421i 0.0510310 + 0.0721688i
\(385\) 3.28220 5.18108i 0.167277 0.264052i
\(386\) 8.03786i 0.409116i
\(387\) −2.13380 4.46784i −0.108467 0.227113i
\(388\) 8.34915 + 8.34915i 0.423864 + 0.423864i
\(389\) 13.1089 0.664649 0.332324 0.943165i \(-0.392167\pi\)
0.332324 + 0.943165i \(0.392167\pi\)
\(390\) −0.863870 16.9931i −0.0437438 0.860480i
\(391\) 8.62111 0.435988
\(392\) −4.63104 4.63104i −0.233903 0.233903i
\(393\) 24.9136 + 4.27449i 1.25672 + 0.215620i
\(394\) 25.9572i 1.30771i
\(395\) −19.9136 + 4.46793i −1.00196 + 0.224806i
\(396\) −11.5557 4.08557i −0.580697 0.205307i
\(397\) −5.49522 + 5.49522i −0.275797 + 0.275797i −0.831429 0.555631i \(-0.812477\pi\)
0.555631 + 0.831429i \(0.312477\pi\)
\(398\) 11.3941 11.3941i 0.571135 0.571135i
\(399\) 1.49184 1.05489i 0.0746853 0.0528105i
\(400\) 4.52072 2.13613i 0.226036 0.106806i
\(401\) 2.83575i 0.141611i −0.997490 0.0708053i \(-0.977443\pi\)
0.997490 0.0708053i \(-0.0225569\pi\)
\(402\) 2.22529 12.9699i 0.110987 0.646882i
\(403\) −3.10651 3.10651i −0.154746 0.154746i
\(404\) −12.5702 −0.625392
\(405\) 8.91557 18.0420i 0.443018 0.896513i
\(406\) 1.26147 0.0626055
\(407\) 8.17113 + 8.17113i 0.405028 + 0.405028i
\(408\) −1.68362 + 9.81287i −0.0833517 + 0.485809i
\(409\) 3.01333i 0.148999i −0.997221 0.0744997i \(-0.976264\pi\)
0.997221 0.0744997i \(-0.0237360\pi\)
\(410\) −13.7204 8.69186i −0.677603 0.429260i
\(411\) −12.4550 + 8.80704i −0.614362 + 0.434419i
\(412\) 0.449657 0.449657i 0.0221530 0.0221530i
\(413\) −2.09139 + 2.09139i −0.102911 + 0.102911i
\(414\) 4.24202 + 1.49978i 0.208484 + 0.0737102i
\(415\) 22.3267 + 14.1439i 1.09598 + 0.694298i
\(416\) 4.39327i 0.215398i
\(417\) −2.31309 0.396863i −0.113272 0.0194345i
\(418\) 4.53934 + 4.53934i 0.222026 + 0.222026i
\(419\) −39.6972 −1.93934 −0.969669 0.244423i \(-0.921401\pi\)
−0.969669 + 0.244423i \(0.921401\pi\)
\(420\) −1.92955 1.74286i −0.0941525 0.0850429i
\(421\) 6.85743 0.334210 0.167105 0.985939i \(-0.446558\pi\)
0.167105 + 0.985939i \(0.446558\pi\)
\(422\) −17.7675 17.7675i −0.864908 0.864908i
\(423\) 0.952107 + 1.99356i 0.0462930 + 0.0969300i
\(424\) 3.51205i 0.170560i
\(425\) 27.0576 + 9.69248i 1.31249 + 0.470154i
\(426\) 4.42871 + 6.26315i 0.214572 + 0.303450i
\(427\) −5.33297 + 5.33297i −0.258081 + 0.258081i
\(428\) 5.00412 5.00412i 0.241883 0.241883i
\(429\) −17.9490 25.3837i −0.866586 1.22554i
\(430\) 3.60091 0.807922i 0.173651 0.0389615i
\(431\) 7.58473i 0.365343i −0.983174 0.182672i \(-0.941525\pi\)
0.983174 0.182672i \(-0.0584746\pi\)
\(432\) −2.53553 + 4.53553i −0.121991 + 0.218216i
\(433\) 6.55340 + 6.55340i 0.314936 + 0.314936i 0.846818 0.531882i \(-0.178515\pi\)
−0.531882 + 0.846818i \(0.678515\pi\)
\(434\) −0.671354 −0.0322260
\(435\) −7.26791 + 0.369475i −0.348470 + 0.0177150i
\(436\) 7.47661 0.358064
\(437\) −1.66636 1.66636i −0.0797127 0.0797127i
\(438\) 18.9950 + 3.25903i 0.907616 + 0.155722i
\(439\) 11.1508i 0.532199i 0.963946 + 0.266100i \(0.0857350\pi\)
−0.963946 + 0.266100i \(0.914265\pi\)
\(440\) 4.88893 7.71736i 0.233071 0.367911i
\(441\) 6.54928 18.5242i 0.311871 0.882104i
\(442\) −17.8570 + 17.8570i −0.849370 + 0.849370i
\(443\) 3.68595 3.68595i 0.175125 0.175125i −0.614102 0.789227i \(-0.710482\pi\)
0.789227 + 0.614102i \(0.210482\pi\)
\(444\) 4.00000 2.82843i 0.189832 0.134231i
\(445\) −2.78654 12.4196i −0.132095 0.588745i
\(446\) 5.10322i 0.241645i
\(447\) 5.96942 34.7923i 0.282344 1.64562i
\(448\) 0.474719 + 0.474719i 0.0224283 + 0.0224283i
\(449\) −12.8111 −0.604592 −0.302296 0.953214i \(-0.597753\pi\)
−0.302296 + 0.953214i \(0.597753\pi\)
\(450\) 11.6275 + 9.47630i 0.548128 + 0.446717i
\(451\) −29.6759 −1.39738
\(452\) −6.30315 6.30315i −0.296475 0.296475i
\(453\) 5.70320 33.2407i 0.267960 1.56178i
\(454\) 22.9222i 1.07579i
\(455\) −1.44383 6.43516i −0.0676879 0.301685i
\(456\) 2.22214 1.57129i 0.104061 0.0735823i
\(457\) 20.8096 20.8096i 0.973431 0.973431i −0.0262250 0.999656i \(-0.508349\pi\)
0.999656 + 0.0262250i \(0.00834864\pi\)
\(458\) 4.69685 4.69685i 0.219470 0.219470i
\(459\) −28.7412 + 8.12925i −1.34153 + 0.379441i
\(460\) −1.79469 + 2.83298i −0.0836778 + 0.132089i
\(461\) 10.0281i 0.467056i −0.972350 0.233528i \(-0.924973\pi\)
0.972350 0.233528i \(-0.0750271\pi\)
\(462\) −4.68235 0.803365i −0.217843 0.0373759i
\(463\) −3.28991 3.28991i −0.152895 0.152895i 0.626515 0.779410i \(-0.284481\pi\)
−0.779410 + 0.626515i \(0.784481\pi\)
\(464\) 1.87899 0.0872299
\(465\) 3.86799 0.196635i 0.179374 0.00911873i
\(466\) −12.9421 −0.599532
\(467\) 11.2120 + 11.2120i 0.518828 + 0.518828i 0.917217 0.398389i \(-0.130431\pi\)
−0.398389 + 0.917217i \(0.630431\pi\)
\(468\) −11.8931 + 5.68003i −0.549756 + 0.262559i
\(469\) 5.10069i 0.235528i
\(470\) −1.60673 + 0.360496i −0.0741129 + 0.0166284i
\(471\) −2.06822 2.92490i −0.0952984 0.134772i
\(472\) −3.11519 + 3.11519i −0.143388 + 0.143388i
\(473\) 4.76792 4.76792i 0.219229 0.219229i
\(474\) 9.12702 + 12.9075i 0.419218 + 0.592863i
\(475\) −3.35647 7.10336i −0.154006 0.325924i
\(476\) 3.85911i 0.176882i
\(477\) 9.50749 4.54070i 0.435318 0.207905i
\(478\) 18.7716 + 18.7716i 0.858593 + 0.858593i
\(479\) −5.88990 −0.269116 −0.134558 0.990906i \(-0.542961\pi\)
−0.134558 + 0.990906i \(0.542961\pi\)
\(480\) −2.87412 2.59604i −0.131185 0.118492i
\(481\) 12.4260 0.566579
\(482\) −2.55034 2.55034i −0.116165 0.116165i
\(483\) 1.71886 + 0.294909i 0.0782107 + 0.0134188i
\(484\) 5.69186i 0.258721i
\(485\) −22.3035 14.1292i −1.01275 0.641576i
\(486\) −15.5563 1.00000i −0.705650 0.0453609i
\(487\) 24.5134 24.5134i 1.11081 1.11081i 0.117767 0.993041i \(-0.462426\pi\)
0.993041 0.117767i \(-0.0375736\pi\)
\(488\) −7.94361 + 7.94361i −0.359590 + 0.359590i
\(489\) 5.34271 3.77786i 0.241606 0.170841i
\(490\) 12.3712 + 7.83710i 0.558872 + 0.354044i
\(491\) 24.6711i 1.11339i −0.830717 0.556696i \(-0.812069\pi\)
0.830717 0.556696i \(-0.187931\pi\)
\(492\) −2.12745 + 12.3997i −0.0959131 + 0.559022i
\(493\) 7.63739 + 7.63739i 0.343971 + 0.343971i
\(494\) 6.90309 0.310585
\(495\) 27.2126 + 3.25714i 1.22311 + 0.146398i
\(496\) −1.00000 −0.0449013
\(497\) 2.10239 + 2.10239i 0.0943052 + 0.0943052i
\(498\) 3.46193 20.1776i 0.155133 0.904179i
\(499\) 38.4311i 1.72041i 0.509945 + 0.860207i \(0.329666\pi\)
−0.509945 + 0.860207i \(0.670334\pi\)
\(500\) −8.81774 + 6.87368i −0.394341 + 0.307400i
\(501\) 6.74930 4.77248i 0.301537 0.213219i
\(502\) 12.9158 12.9158i 0.576460 0.576460i
\(503\) 17.8215 17.8215i 0.794623 0.794623i −0.187619 0.982242i \(-0.560077\pi\)
0.982242 + 0.187619i \(0.0600769\pi\)
\(504\) −0.671354 + 1.89887i −0.0299045 + 0.0845826i
\(505\) 27.4260 6.15348i 1.22044 0.273826i
\(506\) 6.12745i 0.272399i
\(507\) −10.7562 1.84547i −0.477698 0.0819601i
\(508\) 13.5138 + 13.5138i 0.599580 + 0.599580i
\(509\) −26.2585 −1.16389 −0.581944 0.813229i \(-0.697708\pi\)
−0.581944 + 0.813229i \(0.697708\pi\)
\(510\) −1.13031 22.2341i −0.0500508 0.984545i
\(511\) 7.47016 0.330460
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 7.12663 + 3.98405i 0.314648 + 0.175900i
\(514\) 25.3682i 1.11894i
\(515\) −0.760953 + 1.20119i −0.0335316 + 0.0529308i
\(516\) −1.65041 2.33403i −0.0726552 0.102750i
\(517\) −2.12745 + 2.12745i −0.0935653 + 0.0935653i
\(518\) 1.34271 1.34271i 0.0589952 0.0589952i
\(519\) −17.8453 25.2371i −0.783323 1.10779i
\(520\) −2.15063 9.58535i −0.0943113 0.420345i
\(521\) 27.7886i 1.21744i 0.793384 + 0.608721i \(0.208317\pi\)
−0.793384 + 0.608721i \(0.791683\pi\)
\(522\) 2.42933 + 5.08663i 0.106329 + 0.222636i
\(523\) −18.1124 18.1124i −0.792001 0.792001i 0.189818 0.981819i \(-0.439210\pi\)
−0.981819 + 0.189818i \(0.939210\pi\)
\(524\) 14.5940 0.637543
\(525\) 5.06313 + 2.85805i 0.220973 + 0.124735i
\(526\) −13.1502 −0.573376
\(527\) −4.06462 4.06462i −0.177058 0.177058i
\(528\) −6.97450 1.19663i −0.303526 0.0520768i
\(529\) 20.7507i 0.902203i
\(530\) 1.71925 + 7.66268i 0.0746793 + 0.332845i
\(531\) −12.4607 4.40554i −0.540750 0.191184i
\(532\) 0.745919 0.745919i 0.0323397 0.0323397i
\(533\) −22.5644 + 22.5644i −0.977373 + 0.977373i
\(534\) −8.05012 + 5.69230i −0.348363 + 0.246330i
\(535\) −8.46846 + 13.3678i −0.366123 + 0.577939i
\(536\) 7.59762i 0.328167i
\(537\) −6.65642 + 38.7964i −0.287246 + 1.67419i
\(538\) 6.54390 + 6.54390i 0.282128 + 0.282128i
\(539\) 26.7575 1.15253
\(540\) 3.31182 11.1370i 0.142518 0.479258i
\(541\) 28.7637 1.23665 0.618323 0.785924i \(-0.287812\pi\)
0.618323 + 0.785924i \(0.287812\pi\)
\(542\) 20.3655 + 20.3655i 0.874775 + 0.874775i
\(543\) 3.11330 18.1456i 0.133604 0.778704i
\(544\) 5.74825i 0.246454i
\(545\) −16.3126 + 3.66001i −0.698757 + 0.156778i
\(546\) −4.17113 + 2.94944i −0.178508 + 0.126224i
\(547\) −10.2072 + 10.2072i −0.436428 + 0.436428i −0.890808 0.454380i \(-0.849861\pi\)
0.454380 + 0.890808i \(0.349861\pi\)
\(548\) −6.22752 + 6.22752i −0.266027 + 0.266027i
\(549\) −31.7745 11.2340i −1.35610 0.479454i
\(550\) −6.88893 + 19.2312i −0.293745 + 0.820021i
\(551\) 2.95243i 0.125778i
\(552\) 2.56029 + 0.439276i 0.108973 + 0.0186968i
\(553\) 4.33276 + 4.33276i 0.184248 + 0.184248i
\(554\) 26.6344 1.13159
\(555\) −7.34271 + 8.12925i −0.311681 + 0.345067i
\(556\) −1.35498 −0.0574638
\(557\) −12.7383 12.7383i −0.539739 0.539739i 0.383713 0.923452i \(-0.374645\pi\)
−0.923452 + 0.383713i \(0.874645\pi\)
\(558\) −1.29289 2.70711i −0.0547325 0.114601i
\(559\) 7.25070i 0.306672i
\(560\) −1.26814 0.803365i −0.0535888 0.0339484i
\(561\) −23.4848 33.2126i −0.991531 1.40224i
\(562\) −8.94032 + 8.94032i −0.377125 + 0.377125i
\(563\) −1.84999 + 1.84999i −0.0779678 + 0.0779678i −0.745015 0.667047i \(-0.767558\pi\)
0.667047 + 0.745015i \(0.267558\pi\)
\(564\) 0.736416 + 1.04145i 0.0310087 + 0.0438529i
\(565\) 16.8379 + 10.6668i 0.708377 + 0.448756i
\(566\) 19.5358i 0.821153i
\(567\) −6.00844 + 0.637616i −0.252331 + 0.0267774i
\(568\) 3.13157 + 3.13157i 0.131398 + 0.131398i
\(569\) −28.0100 −1.17424 −0.587121 0.809499i \(-0.699739\pi\)
−0.587121 + 0.809499i \(0.699739\pi\)
\(570\) −4.07912 + 4.51607i −0.170856 + 0.189157i
\(571\) 41.3740 1.73145 0.865724 0.500522i \(-0.166859\pi\)
0.865724 + 0.500522i \(0.166859\pi\)
\(572\) −12.6919 12.6919i −0.530673 0.530673i
\(573\) −1.39221 0.238866i −0.0581604 0.00997875i
\(574\) 4.87643i 0.203538i
\(575\) 2.52887 7.05963i 0.105461 0.294407i
\(576\) −1.00000 + 2.82843i −0.0416667 + 0.117851i
\(577\) −3.56082 + 3.56082i −0.148239 + 0.148239i −0.777331 0.629092i \(-0.783427\pi\)
0.629092 + 0.777331i \(0.283427\pi\)
\(578\) −11.3436 + 11.3436i −0.471833 + 0.471833i
\(579\) 11.3672 8.03786i 0.472407 0.334042i
\(580\) −4.09963 + 0.919818i −0.170228 + 0.0381934i
\(581\) 7.93523i 0.329209i
\(582\) −3.45833 + 20.1566i −0.143352 + 0.835519i
\(583\) 10.1461 + 10.1461i 0.420207 + 0.420207i
\(584\) 11.1270 0.460439
\(585\) 23.1680 18.2148i 0.957880 0.753090i
\(586\) 28.6145 1.18206
\(587\) 17.7934 + 17.7934i 0.734413 + 0.734413i 0.971491 0.237078i \(-0.0761896\pi\)
−0.237078 + 0.971491i \(0.576190\pi\)
\(588\) 1.91824 11.1803i 0.0791069 0.461069i
\(589\) 1.57129i 0.0647438i
\(590\) 5.27182 8.32176i 0.217037 0.342602i
\(591\) 36.7091 25.9572i 1.51001 1.06774i
\(592\) 2.00000 2.00000i 0.0821995 0.0821995i
\(593\) −33.6090 + 33.6090i −1.38016 + 1.38016i −0.535832 + 0.844325i \(0.680002\pi\)
−0.844325 + 0.535832i \(0.819998\pi\)
\(594\) −5.77786 20.4278i −0.237069 0.838164i
\(595\) −1.88914 8.41989i −0.0774472 0.345182i
\(596\) 20.3809i 0.834833i
\(597\) 27.5078 + 4.71959i 1.12582 + 0.193160i
\(598\) 4.65908 + 4.65908i 0.190524 + 0.190524i
\(599\) 6.77010 0.276619 0.138309 0.990389i \(-0.455833\pi\)
0.138309 + 0.990389i \(0.455833\pi\)
\(600\) 7.54167 + 4.25714i 0.307887 + 0.173797i
\(601\) 45.8051 1.86843 0.934215 0.356711i \(-0.116102\pi\)
0.934215 + 0.356711i \(0.116102\pi\)
\(602\) −0.783480 0.783480i −0.0319323 0.0319323i
\(603\) 20.5676 9.82291i 0.837576 0.400020i
\(604\) 19.4720i 0.792303i
\(605\) 2.78632 + 12.4186i 0.113280 + 0.504890i
\(606\) −12.5702 17.7770i −0.510631 0.722141i
\(607\) 20.7241 20.7241i 0.841165 0.841165i −0.147845 0.989010i \(-0.547234\pi\)
0.989010 + 0.147845i \(0.0472338\pi\)
\(608\) 1.11107 1.11107i 0.0450597 0.0450597i
\(609\) 1.26147 + 1.78398i 0.0511172 + 0.0722906i
\(610\) 13.4430 21.2202i 0.544289 0.859181i
\(611\) 3.23527i 0.130885i
\(612\) −15.5611 + 7.43187i −0.629021 + 0.300415i
\(613\) −25.8175 25.8175i −1.04276 1.04276i −0.999044 0.0437155i \(-0.986080\pi\)
−0.0437155 0.999044i \(-0.513920\pi\)
\(614\) −10.8392 −0.437434
\(615\) −1.42827 28.0955i −0.0575936 1.13292i
\(616\) −2.74286 −0.110513
\(617\) −13.0922 13.0922i −0.527073 0.527073i 0.392626 0.919698i \(-0.371567\pi\)
−0.919698 + 0.392626i \(0.871567\pi\)
\(618\) 1.08557 + 0.186254i 0.0436679 + 0.00749223i
\(619\) 6.70426i 0.269467i −0.990882 0.134734i \(-0.956982\pi\)
0.990882 0.134734i \(-0.0430178\pi\)
\(620\) 2.18183 0.489528i 0.0876242 0.0196599i
\(621\) 2.12101 + 7.49890i 0.0851132 + 0.300921i
\(622\) 20.1743 20.1743i 0.808915 0.808915i
\(623\) −2.70224 + 2.70224i −0.108263 + 0.108263i
\(624\) −6.21302 + 4.39327i −0.248720 + 0.175872i
\(625\) 15.8739 19.3137i 0.634956 0.772548i
\(626\) 32.6672i 1.30564i
\(627\) −1.88026 + 10.9589i −0.0750902 + 0.437658i
\(628\) −1.46245 1.46245i −0.0583581 0.0583581i
\(629\) 16.2585 0.648269
\(630\) 0.535224 4.47166i 0.0213238 0.178155i
\(631\) −20.5580 −0.818399 −0.409200 0.912445i \(-0.634192\pi\)
−0.409200 + 0.912445i \(0.634192\pi\)
\(632\) 6.45377 + 6.45377i 0.256717 + 0.256717i
\(633\) 7.35953 42.8945i 0.292515 1.70490i
\(634\) 16.0199i 0.636231i
\(635\) −36.1002 22.8694i −1.43259 0.907546i
\(636\) 4.96679 3.51205i 0.196946 0.139262i
\(637\) 20.3454 20.3454i 0.806115 0.806115i
\(638\) −5.42827 + 5.42827i −0.214907 + 0.214907i
\(639\) −4.42871 + 12.5263i −0.175197 + 0.495532i
\(640\) −1.88893 1.19663i −0.0746666 0.0473011i
\(641\) 21.5740i 0.852120i 0.904695 + 0.426060i \(0.140099\pi\)
−0.904695 + 0.426060i \(0.859901\pi\)
\(642\) 12.0810 + 2.07277i 0.476799 + 0.0818059i
\(643\) −21.5307 21.5307i −0.849087 0.849087i 0.140933 0.990019i \(-0.454990\pi\)
−0.990019 + 0.140933i \(0.954990\pi\)
\(644\) 1.00688 0.0396768
\(645\) 4.74348 + 4.28453i 0.186774 + 0.168703i
\(646\) 9.03214 0.355365
\(647\) 10.5743 + 10.5743i 0.415720 + 0.415720i 0.883726 0.468005i \(-0.155027\pi\)
−0.468005 + 0.883726i \(0.655027\pi\)
\(648\) −8.94975 + 0.949747i −0.351579 + 0.0373096i
\(649\) 17.9991i 0.706527i
\(650\) 9.38459 + 19.8608i 0.368094 + 0.779003i
\(651\) −0.671354 0.949437i −0.0263124 0.0372114i
\(652\) 2.67135 2.67135i 0.104618 0.104618i
\(653\) −21.0078 + 21.0078i −0.822099 + 0.822099i −0.986409 0.164310i \(-0.947460\pi\)
0.164310 + 0.986409i \(0.447460\pi\)
\(654\) 7.47661 + 10.5735i 0.292358 + 0.413457i
\(655\) −31.8416 + 7.14418i −1.24415 + 0.279146i
\(656\) 7.26358i 0.283595i
\(657\) 14.3860 + 30.1220i 0.561253 + 1.17517i
\(658\) 0.349590 + 0.349590i 0.0136284 + 0.0136284i
\(659\) 26.4009 1.02843 0.514216 0.857661i \(-0.328083\pi\)
0.514216 + 0.857661i \(0.328083\pi\)
\(660\) 15.8029 0.803365i 0.615128 0.0312709i
\(661\) −29.3162 −1.14027 −0.570135 0.821551i \(-0.693109\pi\)
−0.570135 + 0.821551i \(0.693109\pi\)
\(662\) −13.9140 13.9140i −0.540783 0.540783i
\(663\) −43.1106 7.39661i −1.67428 0.287260i
\(664\) 11.8198i 0.458695i
\(665\) −1.26232 + 1.99261i −0.0489506 + 0.0772703i
\(666\) 8.00000 + 2.82843i 0.309994 + 0.109599i
\(667\) 1.99268 1.99268i 0.0771568 0.0771568i
\(668\) 3.37465 3.37465i 0.130569 0.130569i
\(669\) 7.21704 5.10322i 0.279027 0.197302i
\(670\) 3.71925 + 16.5767i 0.143687 + 0.640413i
\(671\) 45.8971i 1.77184i
\(672\) −0.196635 + 1.14607i −0.00758536 + 0.0442107i
\(673\) −21.6844 21.6844i −0.835870 0.835870i 0.152442 0.988312i \(-0.451286\pi\)
−0.988312 + 0.152442i \(0.951286\pi\)
\(674\) −4.81554 −0.185488
\(675\) −1.77396 + 25.9201i −0.0682798 + 0.997666i
\(676\) −6.30082 −0.242339
\(677\) −31.1572 31.1572i −1.19747 1.19747i −0.974923 0.222544i \(-0.928564\pi\)
−0.222544 0.974923i \(-0.571436\pi\)
\(678\) 2.61085 15.2171i 0.100269 0.584411i
\(679\) 7.92700i 0.304210i
\(680\) −2.81393 12.5417i −0.107909 0.480951i
\(681\) −32.4169 + 22.9222i −1.24222 + 0.878382i
\(682\) 2.88893 2.88893i 0.110623 0.110623i
\(683\) 27.6523 27.6523i 1.05809 1.05809i 0.0598802 0.998206i \(-0.480928\pi\)
0.998206 0.0598802i \(-0.0190719\pi\)
\(684\) 4.44427 + 1.57129i 0.169931 + 0.0600797i
\(685\) 10.5388 16.6359i 0.402668 0.635625i
\(686\) 9.09636i 0.347301i
\(687\) 11.3392 + 1.94550i 0.432618 + 0.0742255i
\(688\) −1.16702 1.16702i −0.0444921 0.0444921i
\(689\) 15.4294 0.587813
\(690\) −5.80113 + 0.294909i −0.220845 + 0.0112270i
\(691\) −13.4710 −0.512462 −0.256231 0.966616i \(-0.582481\pi\)
−0.256231 + 0.966616i \(0.582481\pi\)
\(692\) −12.6186 12.6186i −0.479686 0.479686i
\(693\) −3.54623 7.42521i −0.134710 0.282061i
\(694\) 12.3759i 0.469783i
\(695\) 2.95632 0.663299i 0.112140 0.0251604i
\(696\) 1.87899 + 2.65729i 0.0712229 + 0.100724i
\(697\) −29.5237 + 29.5237i −1.11829 + 1.11829i
\(698\) 21.6972 21.6972i 0.821253 0.821253i
\(699\) −12.9421 18.3029i −0.489516 0.692280i
\(700\) 3.16013 + 1.13201i 0.119442 + 0.0427860i
\(701\) 6.91995i 0.261363i −0.991424 0.130682i \(-0.958283\pi\)
0.991424 0.130682i \(-0.0417165\pi\)
\(702\) −19.9258 11.1393i −0.752052 0.420425i
\(703\) −3.14257 3.14257i −0.118524 0.118524i
\(704\) −4.08557 −0.153981
\(705\) −2.11655 1.91176i −0.0797138 0.0720012i
\(706\) 5.92849 0.223122
\(707\) −5.96732 5.96732i −0.224424 0.224424i
\(708\) −7.52072 1.29035i −0.282646 0.0484944i
\(709\) 19.1112i 0.717735i 0.933389 + 0.358867i \(0.116837\pi\)
−0.933389 + 0.358867i \(0.883163\pi\)
\(710\) −8.36554 5.29955i −0.313953 0.198889i
\(711\) −9.12702 + 25.8151i −0.342290 + 0.968142i
\(712\) −4.02506 + 4.02506i −0.150846 + 0.150846i
\(713\) −1.06051 + 1.06051i −0.0397162 + 0.0397162i
\(714\) −5.45760 + 3.85911i −0.204245 + 0.144423i
\(715\) 33.9044 + 21.4784i 1.26795 + 0.803247i
\(716\) 22.7264i 0.849326i
\(717\) −7.77545 + 45.3187i −0.290380 + 1.69246i
\(718\) 4.91855 + 4.91855i 0.183559 + 0.183559i
\(719\) 40.0027 1.49185 0.745925 0.666030i \(-0.232008\pi\)
0.745925 + 0.666030i \(0.232008\pi\)
\(720\) 0.797231 6.66066i 0.0297110 0.248228i
\(721\) 0.426921 0.0158994
\(722\) 11.6892 + 11.6892i 0.435028 + 0.435028i
\(723\) 1.05639 6.15707i 0.0392874 0.228984i
\(724\) 10.6295i 0.395041i
\(725\) 8.49440 4.01377i 0.315474 0.149068i
\(726\) 8.04950 5.69186i 0.298745 0.211245i
\(727\) −13.2741 + 13.2741i −0.492311 + 0.492311i −0.909034 0.416723i \(-0.863179\pi\)
0.416723 + 0.909034i \(0.363179\pi\)
\(728\) −2.08557 + 2.08557i −0.0772963 + 0.0772963i
\(729\) −14.1421 23.0000i −0.523783 0.851852i
\(730\) −24.2772 + 5.44699i −0.898540 + 0.201602i
\(731\) 9.48696i 0.350888i
\(732\) −19.1776 3.29035i −0.708824 0.121615i
\(733\) −8.25491 8.25491i −0.304902 0.304902i 0.538026 0.842928i \(-0.319170\pi\)
−0.842928 + 0.538026i \(0.819170\pi\)
\(734\) 5.27182 0.194586
\(735\) 1.28782 + 25.3326i 0.0475019 + 0.934405i
\(736\) 1.49978 0.0552826
\(737\) 21.9490 + 21.9490i 0.808502 + 0.808502i
\(738\) −19.6633 + 9.39104i −0.723816 + 0.345689i
\(739\) 27.7673i 1.02143i 0.859749 + 0.510717i \(0.170620\pi\)
−0.859749 + 0.510717i \(0.829380\pi\)
\(740\) −3.38459 + 5.34271i −0.124420 + 0.196402i
\(741\) 6.90309 + 9.76244i 0.253591 + 0.358632i
\(742\) 1.66724 1.66724i 0.0612061 0.0612061i
\(743\) −22.1612 + 22.1612i −0.813015 + 0.813015i −0.985085 0.172070i \(-0.944955\pi\)
0.172070 + 0.985085i \(0.444955\pi\)
\(744\) −1.00000 1.41421i −0.0366618 0.0518476i
\(745\) 9.97701 + 44.4675i 0.365529 + 1.62916i
\(746\) 4.15645i 0.152179i
\(747\) 31.9973 15.2817i 1.17072 0.559127i
\(748\) −16.6063 16.6063i −0.607186 0.607186i
\(749\) 4.75110 0.173601
\(750\) −18.5386 5.59648i −0.676934 0.204354i
\(751\) −14.3357 −0.523117 −0.261558 0.965188i \(-0.584236\pi\)
−0.261558 + 0.965188i \(0.584236\pi\)
\(752\) 0.520724 + 0.520724i 0.0189889 + 0.0189889i
\(753\) 31.1815 + 5.34989i 1.13632 + 0.194961i
\(754\) 8.25491i 0.300626i
\(755\) 9.53207 + 42.4844i 0.346908 + 1.54617i
\(756\) −3.35677 + 0.949437i −0.122084 + 0.0345307i
\(757\) −32.6821 + 32.6821i −1.18785 + 1.18785i −0.210192 + 0.977660i \(0.567409\pi\)
−0.977660 + 0.210192i \(0.932591\pi\)
\(758\) 13.9395 13.9395i 0.506305 0.506305i
\(759\) −8.66553 + 6.12745i −0.314539 + 0.222413i
\(760\) −1.88026 + 2.96805i −0.0682041 + 0.107663i
\(761\) 15.8679i 0.575211i −0.957749 0.287605i \(-0.907141\pi\)
0.957749 0.287605i \(-0.0928591\pi\)
\(762\) −5.59762 + 32.6253i −0.202780 + 1.18189i
\(763\) 3.54928 + 3.54928i 0.128493 + 0.128493i
\(764\) −0.815538 −0.0295051
\(765\) 30.3135 23.8326i 1.09599 0.861671i
\(766\) 2.47642 0.0894769
\(767\) −13.6859 13.6859i −0.494168 0.494168i
\(768\) −0.292893 + 1.70711i −0.0105689 + 0.0615999i
\(769\) 25.7022i 0.926845i 0.886138 + 0.463422i \(0.153379\pi\)
−0.886138 + 0.463422i \(0.846621\pi\)
\(770\) 5.98444 1.34271i 0.215664 0.0483878i
\(771\) −35.8760 + 25.3682i −1.29204 + 0.913612i
\(772\) 5.68362 5.68362i 0.204558 0.204558i
\(773\) 29.4146 29.4146i 1.05797 1.05797i 0.0597568 0.998213i \(-0.480967\pi\)
0.998213 0.0597568i \(-0.0190325\pi\)
\(774\) 1.65041 4.66806i 0.0593228 0.167790i
\(775\) −4.52072 + 2.13613i −0.162389 + 0.0767320i
\(776\) 11.8075i 0.423864i
\(777\) 3.24158 + 0.556167i 0.116291 + 0.0199524i
\(778\) 9.26941 + 9.26941i 0.332324 + 0.332324i
\(779\) 11.4132 0.408919
\(780\) 11.4051 12.6268i 0.408368 0.452112i
\(781\) −18.0938 −0.647447
\(782\) 6.09604 + 6.09604i 0.217994 + 0.217994i
\(783\) −4.76424 + 8.52222i −0.170260 + 0.304559i
\(784\) 6.54928i 0.233903i
\(785\) 3.90672 + 2.47490i 0.139437 + 0.0883330i
\(786\) 14.5940 + 20.6391i 0.520552 + 0.736171i
\(787\) 5.55205 5.55205i 0.197909 0.197909i −0.601194 0.799103i \(-0.705308\pi\)
0.799103 + 0.601194i \(0.205308\pi\)
\(788\) 18.3545 18.3545i 0.653853 0.653853i
\(789\) −13.1502 18.5972i −0.468159 0.662077i
\(790\) −17.2403 10.9217i −0.613383 0.388577i
\(791\) 5.98444i 0.212782i
\(792\) −5.28220 11.0601i −0.187695 0.393002i
\(793\) −34.8984 34.8984i −1.23928 1.23928i
\(794\) −7.77142 −0.275797
\(795\) −9.11742 + 10.0941i −0.323361 + 0.357999i
\(796\) 16.1137 0.571135
\(797\) −1.64459 1.64459i −0.0582542 0.0582542i 0.677380 0.735634i \(-0.263116\pi\)
−0.735634 + 0.677380i \(0.763116\pi\)
\(798\) 1.80081 + 0.308970i 0.0637479 + 0.0109374i
\(799\) 4.23310i 0.149756i
\(800\) 4.70711 + 1.68616i 0.166421 + 0.0596149i
\(801\) −16.1002 5.69230i −0.568874 0.201127i
\(802\) 2.00518 2.00518i 0.0708053 0.0708053i
\(803\) −32.1452 + 32.1452i −1.13438 + 1.13438i
\(804\) 10.7447 7.59762i 0.378935 0.267947i
\(805\) −2.19684 + 0.492898i −0.0774285 + 0.0173724i
\(806\) 4.39327i 0.154746i
\(807\) −2.71057 + 15.7984i −0.0954166 + 0.556129i
\(808\) −8.88849 8.88849i −0.312696 0.312696i
\(809\) −36.8202 −1.29453 −0.647265 0.762265i \(-0.724087\pi\)
−0.647265 + 0.762265i \(0.724087\pi\)
\(810\) 19.0619 6.45334i 0.669765 0.226747i
\(811\) 51.4403 1.80631 0.903156 0.429312i \(-0.141244\pi\)
0.903156 + 0.429312i \(0.141244\pi\)
\(812\) 0.891992 + 0.891992i 0.0313028 + 0.0313028i
\(813\) −8.43568 + 49.1668i −0.295852 + 1.72435i
\(814\) 11.5557i 0.405028i
\(815\) −4.52072 + 7.13613i −0.158354 + 0.249968i
\(816\) −8.12925 + 5.74825i −0.284581 + 0.201229i
\(817\) −1.83372 + 1.83372i −0.0641536 + 0.0641536i
\(818\) 2.13074 2.13074i 0.0744997 0.0744997i
\(819\) −8.34227 2.94944i −0.291502 0.103062i
\(820\) −3.55573 15.8479i −0.124171 0.553432i
\(821\) 26.0911i 0.910587i 0.890341 + 0.455293i \(0.150466\pi\)
−0.890341 + 0.455293i \(0.849534\pi\)
\(822\) −15.0346 2.57952i −0.524391 0.0899712i
\(823\) 1.58219 + 1.58219i 0.0551518 + 0.0551518i 0.734145 0.678993i \(-0.237583\pi\)
−0.678993 + 0.734145i \(0.737583\pi\)
\(824\) 0.635910 0.0221530
\(825\) −34.0860 + 9.48878i −1.18672 + 0.330357i
\(826\) −2.95767 −0.102911
\(827\) −32.0545 32.0545i −1.11464 1.11464i −0.992514 0.122128i \(-0.961028\pi\)
−0.122128 0.992514i \(-0.538972\pi\)
\(828\) 1.93906 + 4.06007i 0.0673869 + 0.141097i
\(829\) 19.2021i 0.666917i −0.942765 0.333458i \(-0.891784\pi\)
0.942765 0.333458i \(-0.108216\pi\)
\(830\) 5.78610 + 25.7886i 0.200838 + 0.895137i
\(831\) 26.6344 + 37.6667i 0.923938 + 1.30665i
\(832\) −3.10651 + 3.10651i −0.107699 + 0.107699i
\(833\) 26.6204 26.6204i 0.922341 0.922341i
\(834\) −1.35498 1.91622i −0.0469190 0.0663534i
\(835\) −5.71091 + 9.01489i −0.197634 + 0.311973i
\(836\) 6.41960i 0.222026i
\(837\) 2.53553 4.53553i 0.0876409 0.156771i
\(838\) −28.0702 28.0702i −0.969669 0.969669i
\(839\) −4.58696 −0.158359 −0.0791797 0.996860i \(-0.525230\pi\)
−0.0791797 + 0.996860i \(0.525230\pi\)
\(840\) −0.132012 2.59679i −0.00455483 0.0895977i
\(841\) −25.4694 −0.878255
\(842\) 4.84893 + 4.84893i 0.167105 + 0.167105i
\(843\) −21.5839 3.70320i −0.743387 0.127545i
\(844\) 25.1270i 0.864908i
\(845\) 13.7473 3.08443i 0.472921 0.106108i
\(846\) −0.736416 + 2.08290i −0.0253185 + 0.0716115i
\(847\) 2.70203 2.70203i 0.0928429 0.0928429i
\(848\) 2.48339 2.48339i 0.0852801 0.0852801i
\(849\) −27.6279 + 19.5358i −0.948186 + 0.670468i
\(850\) 12.2790 + 25.9862i 0.421166 + 0.891320i
\(851\) 4.24202i 0.145415i
\(852\) −1.29714 + 7.56029i −0.0444393 + 0.259011i
\(853\) −28.9519 28.9519i −0.991296 0.991296i 0.00866672 0.999962i \(-0.497241\pi\)
−0.999962 + 0.00866672i \(0.997241\pi\)
\(854\) −7.54196 −0.258081
\(855\) −10.4658 1.25268i −0.357923 0.0428407i
\(856\) 7.07689 0.241883
\(857\) 20.9236 + 20.9236i 0.714736 + 0.714736i 0.967522 0.252786i \(-0.0813468\pi\)
−0.252786 + 0.967522i \(0.581347\pi\)
\(858\) 5.25714 30.6409i 0.179476 1.04606i
\(859\) 41.8628i 1.42834i 0.699971 + 0.714171i \(0.253196\pi\)
−0.699971 + 0.714171i \(0.746804\pi\)
\(860\) 3.11751 + 1.97494i 0.106306 + 0.0673448i
\(861\) −6.89632 + 4.87643i −0.235026 + 0.166188i
\(862\) 5.36321 5.36321i 0.182672 0.182672i
\(863\) −14.0730 + 14.0730i −0.479049 + 0.479049i −0.904827 0.425778i \(-0.860000\pi\)
0.425778 + 0.904827i \(0.360000\pi\)
\(864\) −5.00000 + 1.41421i −0.170103 + 0.0481125i
\(865\) 33.7086 + 21.3544i 1.14613 + 0.726070i
\(866\) 9.26791i 0.314936i
\(867\) −27.3860 4.69869i −0.930076 0.159576i
\(868\) −0.474719 0.474719i −0.0161130 0.0161130i
\(869\) −37.2890 −1.26494
\(870\) −5.40045 4.87793i −0.183092 0.165377i
\(871\) 33.3784 1.13098
\(872\) 5.28676 + 5.28676i 0.179032 + 0.179032i
\(873\) −31.9641 + 15.2658i −1.08182 + 0.516670i
\(874\) 2.35659i 0.0797127i
\(875\) −7.44901 0.922878i −0.251822 0.0311990i
\(876\) 11.1270 + 15.7360i 0.375947 + 0.531669i
\(877\) −25.1682 + 25.1682i −0.849868 + 0.849868i −0.990116 0.140248i \(-0.955210\pi\)
0.140248 + 0.990116i \(0.455210\pi\)
\(878\) −7.88481 + 7.88481i −0.266100 + 0.266100i
\(879\) 28.6145 + 40.4671i 0.965144 + 1.36492i
\(880\) 8.91399 2.00000i 0.300491 0.0674200i
\(881\) 55.8080i 1.88022i −0.340872 0.940110i \(-0.610722\pi\)
0.340872 0.940110i \(-0.389278\pi\)
\(882\) 17.7296 8.46753i 0.596987 0.285116i
\(883\) 11.1283 + 11.1283i 0.374497 + 0.374497i 0.869112 0.494615i \(-0.164691\pi\)
−0.494615 + 0.869112i \(0.664691\pi\)
\(884\) −25.2536 −0.849370
\(885\) 17.0406 0.866283i 0.572813 0.0291198i
\(886\) 5.21272 0.175125
\(887\) 27.8846 + 27.8846i 0.936272 + 0.936272i 0.998088 0.0618158i \(-0.0196891\pi\)
−0.0618158 + 0.998088i \(0.519689\pi\)
\(888\) 4.82843 + 0.828427i 0.162031 + 0.0278002i
\(889\) 12.8305i 0.430323i
\(890\) 6.81160 10.7524i 0.228325 0.360420i
\(891\) 23.1115 28.5990i 0.774263 0.958102i
\(892\) 3.60852 3.60852i 0.120822 0.120822i
\(893\) 0.818208 0.818208i 0.0273803 0.0273803i
\(894\) 28.8229 20.3809i 0.963982 0.681638i
\(895\) −11.1252 49.5851i −0.371875 1.65745i
\(896\) 0.671354i 0.0224283i
\(897\) −1.92986 + 11.2480i −0.0644360 + 0.375561i
\(898\) −9.05880 9.05880i −0.302296 0.302296i
\(899\) −1.87899 −0.0626678
\(900\) 1.52116 + 14.9227i 0.0507054 + 0.497422i
\(901\) 20.1881 0.672564
\(902\) −20.9840 20.9840i −0.698691 0.698691i
\(903\) 0.324528 1.89149i 0.0107996 0.0629448i
\(904\) 8.91399i 0.296475i
\(905\) 5.20342 + 23.1916i 0.172968 + 0.770916i
\(906\) 27.5375 19.4720i 0.914872 0.646912i
\(907\) −23.9940 + 23.9940i −0.796709 + 0.796709i −0.982575 0.185866i \(-0.940491\pi\)
0.185866 + 0.982575i \(0.440491\pi\)
\(908\) −16.2085 + 16.2085i −0.537897 + 0.537897i
\(909\) 12.5702 35.5540i 0.416928 1.17925i
\(910\) 3.52940 5.57129i 0.116998 0.184686i
\(911\) 5.18069i 0.171644i −0.996310 0.0858219i \(-0.972648\pi\)
0.996310 0.0858219i \(-0.0273516\pi\)
\(912\) 2.68235 + 0.460219i 0.0888216 + 0.0152394i
\(913\) 34.1465 + 34.1465i 1.13008 + 1.13008i
\(914\) 29.4292 0.973431
\(915\) 43.4528 2.20899i 1.43651 0.0730269i
\(916\) 6.64235 0.219470
\(917\) 6.92805 + 6.92805i 0.228785 + 0.228785i
\(918\) −26.0714 14.5749i −0.860483 0.481042i
\(919\) 37.4389i 1.23500i −0.786573 0.617498i \(-0.788146\pi\)
0.786573 0.617498i \(-0.211854\pi\)
\(920\) −3.27226 + 0.734185i −0.107883 + 0.0242054i
\(921\) −10.8392 15.3289i −0.357164 0.505106i
\(922\) 7.09095 7.09095i 0.233528 0.233528i
\(923\) −13.7578 + 13.7578i −0.452845 + 0.452845i
\(924\) −2.74286 3.87899i −0.0902335 0.127609i
\(925\) 4.76919 13.3137i 0.156810 0.437752i
\(926\) 4.65264i 0.152895i
\(927\) 0.822164 + 1.72148i 0.0270034 + 0.0565407i
\(928\) 1.32865 + 1.32865i 0.0436150 + 0.0436150i
\(929\) 10.3349 0.339079 0.169539 0.985523i \(-0.445772\pi\)
0.169539 + 0.985523i \(0.445772\pi\)
\(930\) 2.87412 + 2.59604i 0.0942462 + 0.0851275i
\(931\) −10.2908 −0.337268
\(932\) −9.15146 9.15146i −0.299766 0.299766i
\(933\) 48.7050 + 8.35646i 1.59453 + 0.273578i
\(934\) 15.8561i 0.518828i
\(935\) 44.3613 + 28.1028i 1.45077 + 0.919059i
\(936\) −12.4260 4.39327i −0.406158 0.143599i
\(937\) 15.8855 15.8855i 0.518958 0.518958i −0.398298 0.917256i \(-0.630399\pi\)
0.917256 + 0.398298i \(0.130399\pi\)
\(938\) 3.60673 3.60673i 0.117764 0.117764i
\(939\) −46.1984 + 32.6672i −1.50763 + 1.06605i
\(940\) −1.39104 0.881221i −0.0453707 0.0287422i
\(941\) 28.9714i 0.944442i 0.881480 + 0.472221i \(0.156548\pi\)
−0.881480 + 0.472221i \(0.843452\pi\)
\(942\) 0.605767 3.53067i 0.0197369 0.115035i
\(943\) 7.70307 + 7.70307i 0.250846 + 0.250846i
\(944\) −4.40554 −0.143388
\(945\) 6.85911 3.71474i 0.223127 0.120840i
\(946\) 6.74286 0.219229
\(947\) −34.7182 34.7182i −1.12819 1.12819i −0.990471 0.137718i \(-0.956023\pi\)
−0.137718 0.990471i \(-0.543977\pi\)
\(948\) −2.67324 + 15.5808i −0.0868228 + 0.506041i
\(949\) 48.8840i 1.58684i
\(950\) 2.64945 7.39622i 0.0859594 0.239965i
\(951\) 22.6555 16.0199i 0.734656 0.519480i
\(952\) −2.72880 + 2.72880i −0.0884409 + 0.0884409i
\(953\) 3.05595 3.05595i 0.0989919 0.0989919i −0.655876 0.754868i \(-0.727701\pi\)
0.754868 + 0.655876i \(0.227701\pi\)
\(954\) 9.93358 + 3.51205i 0.321611 + 0.113707i
\(955\) 1.77936 0.399229i 0.0575788 0.0129187i
\(956\) 26.5471i 0.858593i
\(957\) −13.1050 2.24846i −0.423625 0.0726825i
\(958\) −4.16479 4.16479i −0.134558 0.134558i
\(959\) −5.91264 −0.190929
\(960\) −0.196635 3.86799i −0.00634636 0.124839i
\(961\) 1.00000 0.0322581
\(962\) 8.78654 + 8.78654i 0.283289 + 0.283289i
\(963\) 9.14967 + 19.1579i 0.294844 + 0.617355i
\(964\) 3.60673i 0.116165i
\(965\) −9.61838 + 15.1830i −0.309627 + 0.488757i
\(966\) 1.00688 + 1.42395i 0.0323959 + 0.0458148i
\(967\) −33.8479 + 33.8479i −1.08847 + 1.08847i −0.0927884 + 0.995686i \(0.529578\pi\)
−0.995686 + 0.0927884i \(0.970422\pi\)
\(968\) 4.02475 4.02475i 0.129360 0.129360i
\(969\) 9.03214 + 12.7734i 0.290154 + 0.410340i
\(970\) −5.78010 25.7619i −0.185588 0.827164i
\(971\) 58.2910i 1.87065i 0.353793 + 0.935324i \(0.384892\pi\)
−0.353793 + 0.935324i \(0.615108\pi\)
\(972\) −10.2929 11.7071i −0.330145 0.375506i
\(973\) −0.643232 0.643232i −0.0206211 0.0206211i
\(974\) 34.6672 1.11081
\(975\) −18.7028 + 33.1326i −0.598968 + 1.06109i
\(976\) −11.2340 −0.359590
\(977\) 1.11995 + 1.11995i 0.0358304 + 0.0358304i 0.724795 0.688965i \(-0.241934\pi\)
−0.688965 + 0.724795i \(0.741934\pi\)
\(978\) 6.44922 + 1.10651i 0.206223 + 0.0353823i
\(979\) 23.2563i 0.743273i
\(980\) 3.20606 + 14.2894i 0.102414 + 0.456458i
\(981\) −7.47661 + 21.1470i −0.238710 + 0.675173i
\(982\) 17.4451 17.4451i 0.556696 0.556696i
\(983\) 36.6650 36.6650i 1.16943 1.16943i 0.187087 0.982343i \(-0.440095\pi\)
0.982343 0.187087i \(-0.0599047\pi\)
\(984\) −10.2723 + 7.26358i −0.327468 + 0.231555i
\(985\) −31.0613 + 49.0315i −0.989696 + 1.56227i
\(986\) 10.8009i 0.343971i
\(987\) −0.144805 + 0.843985i −0.00460919 + 0.0268644i
\(988\) 4.88122 + 4.88122i 0.155292 + 0.155292i
\(989\) −2.47525 −0.0787085
\(990\) 16.9391 + 21.5453i 0.538359 + 0.684756i
\(991\) 60.1248 1.90993 0.954964 0.296722i \(-0.0958934\pi\)
0.954964 + 0.296722i \(0.0958934\pi\)
\(992\) −0.707107 0.707107i −0.0224507 0.0224507i
\(993\) 5.76337 33.5914i 0.182895 1.06599i
\(994\) 2.97323i 0.0943052i
\(995\) −35.1573 + 7.88810i −1.11456 + 0.250070i
\(996\) 16.7157 11.8198i 0.529656 0.374523i
\(997\) −15.0323 + 15.0323i −0.476079 + 0.476079i −0.903875 0.427796i \(-0.859290\pi\)
0.427796 + 0.903875i \(0.359290\pi\)
\(998\) −27.1749 + 27.1749i −0.860207 + 0.860207i
\(999\) 4.00000 + 14.1421i 0.126554 + 0.447437i
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 930.2.j.c.683.3 yes 8
3.2 odd 2 930.2.j.f.683.2 yes 8
5.2 odd 4 930.2.j.f.497.2 yes 8
15.2 even 4 inner 930.2.j.c.497.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.j.c.497.3 8 15.2 even 4 inner
930.2.j.c.683.3 yes 8 1.1 even 1 trivial
930.2.j.f.497.2 yes 8 5.2 odd 4
930.2.j.f.683.2 yes 8 3.2 odd 2