Properties

Label 210.2.x.a.23.2
Level $210$
Weight $2$
Character 210.23
Analytic conductor $1.677$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [210,2,Mod(23,210)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(210, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 9, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("210.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 210.x (of order \(12\), 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: \(1.67685844245\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 23.2
Character \(\chi\) \(=\) 210.23
Dual form 210.2.x.a.137.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.965926 + 0.258819i) q^{2} +(-1.45883 + 0.933717i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.00119 + 0.997619i) q^{5} +(1.16745 - 1.27947i) q^{6} +(-1.20893 - 2.35340i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.25635 - 2.72426i) q^{9} +O(q^{10})\) \(q+(-0.965926 + 0.258819i) q^{2} +(-1.45883 + 0.933717i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.00119 + 0.997619i) q^{5} +(1.16745 - 1.27947i) q^{6} +(-1.20893 - 2.35340i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.25635 - 2.72426i) q^{9} +(1.67480 - 1.48157i) q^{10} +(3.01159 - 1.73874i) q^{11} +(-0.796522 + 1.53804i) q^{12} +(-0.354405 - 0.354405i) q^{13} +(1.77684 + 1.96031i) q^{14} +(1.98789 - 3.32390i) q^{15} +(0.500000 - 0.866025i) q^{16} +(0.838307 - 3.12860i) q^{17} +(-0.508447 + 2.95660i) q^{18} +(-2.42435 - 1.39970i) q^{19} +(-1.23427 + 1.86456i) q^{20} +(3.96103 + 2.30440i) q^{21} +(-2.45895 + 2.45895i) q^{22} +(-1.51128 - 5.64018i) q^{23} +(0.371308 - 1.69178i) q^{24} +(3.00951 - 3.99285i) q^{25} +(0.434056 + 0.250602i) q^{26} +(0.710897 + 5.14729i) q^{27} +(-2.22367 - 1.43364i) q^{28} -1.97825 q^{29} +(-1.05987 + 3.72514i) q^{30} +(-4.44221 - 7.69413i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-2.76989 + 5.34850i) q^{33} +3.23897i q^{34} +(4.76710 + 3.50354i) q^{35} +(-0.274103 - 2.98745i) q^{36} +(2.16990 + 8.09819i) q^{37} +(2.70402 + 0.724539i) q^{38} +(0.847929 + 0.186101i) q^{39} +(0.709630 - 2.12048i) q^{40} +7.96768i q^{41} +(-4.42248 - 1.20069i) q^{42} +(-6.03572 - 6.03572i) q^{43} +(1.73874 - 3.01159i) q^{44} +(0.203590 + 6.70511i) q^{45} +(2.91957 + 5.05684i) q^{46} +(-2.30600 + 0.617891i) q^{47} +(0.0792095 + 1.73024i) q^{48} +(-4.07696 + 5.69020i) q^{49} +(-1.87354 + 4.63571i) q^{50} +(1.69829 + 5.34683i) q^{51} +(-0.484126 - 0.129721i) q^{52} +(-5.79919 - 1.55389i) q^{53} +(-2.01889 - 4.78791i) q^{54} +(-4.29216 + 6.48398i) q^{55} +(2.51895 + 0.809259i) q^{56} +(4.84364 - 0.221739i) q^{57} +(1.91084 - 0.512009i) q^{58} +(-2.18403 - 3.78284i) q^{59} +(0.0596165 - 3.87252i) q^{60} +(3.79381 - 6.57108i) q^{61} +(6.28223 + 6.28223i) q^{62} +(-7.93011 + 0.336766i) q^{63} -1.00000i q^{64} +(1.06279 + 0.355670i) q^{65} +(1.29122 - 5.88315i) q^{66} +(13.6099 + 3.64677i) q^{67} +(-0.838307 - 3.12860i) q^{68} +(7.47102 + 6.81693i) q^{69} +(-5.51145 - 2.15034i) q^{70} -3.96344i q^{71} +(1.03797 + 2.81471i) q^{72} +(-0.988062 + 3.68750i) q^{73} +(-4.19193 - 7.26063i) q^{74} +(-0.662162 + 8.63490i) q^{75} -2.79940 q^{76} +(-7.73277 - 4.98545i) q^{77} +(-0.867203 + 0.0397001i) q^{78} +(-7.48605 - 4.32207i) q^{79} +(-0.136630 + 2.23189i) q^{80} +(-5.84319 - 6.84523i) q^{81} +(-2.06219 - 7.69619i) q^{82} +(10.4891 - 10.4891i) q^{83} +(4.58255 + 0.0151515i) q^{84} +(1.44355 + 7.09724i) q^{85} +(7.39221 + 4.26790i) q^{86} +(2.88592 - 1.84713i) q^{87} +(-0.900040 + 3.35899i) q^{88} +(-3.59897 + 6.23359i) q^{89} +(-1.93206 - 6.42395i) q^{90} +(-0.405604 + 1.26251i) q^{91} +(-4.12890 - 4.12890i) q^{92} +(13.6645 + 7.07663i) q^{93} +(2.06750 - 1.19367i) q^{94} +(6.24796 + 0.382484i) q^{95} +(-0.524329 - 1.65078i) q^{96} +(11.6503 - 11.6503i) q^{97} +(2.46531 - 6.55151i) q^{98} +(-0.953188 - 10.3888i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q + 8 q^{6} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 64 q + 8 q^{6} + 4 q^{7} + 4 q^{10} - 24 q^{15} + 32 q^{16} - 8 q^{18} + 12 q^{21} - 24 q^{22} - 8 q^{25} - 72 q^{27} + 4 q^{28} - 12 q^{30} + 32 q^{31} - 20 q^{33} - 24 q^{36} - 8 q^{37} - 40 q^{42} - 64 q^{43} - 28 q^{45} + 24 q^{46} - 16 q^{55} + 24 q^{57} - 28 q^{58} + 8 q^{60} + 24 q^{61} - 88 q^{63} - 16 q^{67} - 12 q^{70} + 8 q^{72} - 56 q^{73} + 8 q^{75} - 32 q^{76} - 16 q^{78} + 4 q^{81} + 16 q^{82} + 32 q^{85} + 76 q^{87} + 12 q^{88} + 40 q^{90} - 48 q^{91} + 84 q^{93} + 4 q^{96} + 104 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.965926 + 0.258819i −0.683013 + 0.183013i
\(3\) −1.45883 + 0.933717i −0.842254 + 0.539082i
\(4\) 0.866025 0.500000i 0.433013 0.250000i
\(5\) −2.00119 + 0.997619i −0.894959 + 0.446149i
\(6\) 1.16745 1.27947i 0.476611 0.522343i
\(7\) −1.20893 2.35340i −0.456934 0.889501i
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 1.25635 2.72426i 0.418782 0.908087i
\(10\) 1.67480 1.48157i 0.529617 0.468514i
\(11\) 3.01159 1.73874i 0.908029 0.524251i 0.0282327 0.999601i \(-0.491012\pi\)
0.879797 + 0.475350i \(0.157679\pi\)
\(12\) −0.796522 + 1.53804i −0.229936 + 0.443993i
\(13\) −0.354405 0.354405i −0.0982943 0.0982943i 0.656250 0.754544i \(-0.272142\pi\)
−0.754544 + 0.656250i \(0.772142\pi\)
\(14\) 1.77684 + 1.96031i 0.474881 + 0.523916i
\(15\) 1.98789 3.32390i 0.513271 0.858226i
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 0.838307 3.12860i 0.203319 0.758798i −0.786636 0.617417i \(-0.788179\pi\)
0.989955 0.141381i \(-0.0451542\pi\)
\(18\) −0.508447 + 2.95660i −0.119842 + 0.696877i
\(19\) −2.42435 1.39970i −0.556185 0.321114i 0.195428 0.980718i \(-0.437390\pi\)
−0.751613 + 0.659604i \(0.770724\pi\)
\(20\) −1.23427 + 1.86456i −0.275991 + 0.416928i
\(21\) 3.96103 + 2.30440i 0.864368 + 0.502861i
\(22\) −2.45895 + 2.45895i −0.524251 + 0.524251i
\(23\) −1.51128 5.64018i −0.315124 1.17606i −0.923874 0.382696i \(-0.874996\pi\)
0.608750 0.793362i \(-0.291671\pi\)
\(24\) 0.371308 1.69178i 0.0757930 0.345334i
\(25\) 3.00951 3.99285i 0.601902 0.798570i
\(26\) 0.434056 + 0.250602i 0.0851254 + 0.0491471i
\(27\) 0.710897 + 5.14729i 0.136812 + 0.990597i
\(28\) −2.22367 1.43364i −0.420233 0.270932i
\(29\) −1.97825 −0.367352 −0.183676 0.982987i \(-0.558800\pi\)
−0.183676 + 0.982987i \(0.558800\pi\)
\(30\) −1.05987 + 3.72514i −0.193505 + 0.680115i
\(31\) −4.44221 7.69413i −0.797844 1.38191i −0.921018 0.389521i \(-0.872641\pi\)
0.123174 0.992385i \(-0.460693\pi\)
\(32\) −0.258819 + 0.965926i −0.0457532 + 0.170753i
\(33\) −2.76989 + 5.34850i −0.482177 + 0.931054i
\(34\) 3.23897i 0.555479i
\(35\) 4.76710 + 3.50354i 0.805787 + 0.592206i
\(36\) −0.274103 2.98745i −0.0456838 0.497909i
\(37\) 2.16990 + 8.09819i 0.356730 + 1.33133i 0.878294 + 0.478121i \(0.158682\pi\)
−0.521564 + 0.853212i \(0.674651\pi\)
\(38\) 2.70402 + 0.724539i 0.438649 + 0.117536i
\(39\) 0.847929 + 0.186101i 0.135777 + 0.0298001i
\(40\) 0.709630 2.12048i 0.112202 0.335277i
\(41\) 7.96768i 1.24434i 0.782881 + 0.622171i \(0.213749\pi\)
−0.782881 + 0.622171i \(0.786251\pi\)
\(42\) −4.42248 1.20069i −0.682404 0.185270i
\(43\) −6.03572 6.03572i −0.920438 0.920438i 0.0766219 0.997060i \(-0.475587\pi\)
−0.997060 + 0.0766219i \(0.975587\pi\)
\(44\) 1.73874 3.01159i 0.262125 0.454015i
\(45\) 0.203590 + 6.70511i 0.0303494 + 0.999539i
\(46\) 2.91957 + 5.05684i 0.430467 + 0.745591i
\(47\) −2.30600 + 0.617891i −0.336365 + 0.0901286i −0.423048 0.906107i \(-0.639040\pi\)
0.0866833 + 0.996236i \(0.472373\pi\)
\(48\) 0.0792095 + 1.73024i 0.0114329 + 0.249738i
\(49\) −4.07696 + 5.69020i −0.582423 + 0.812886i
\(50\) −1.87354 + 4.63571i −0.264958 + 0.655589i
\(51\) 1.69829 + 5.34683i 0.237808 + 0.748706i
\(52\) −0.484126 0.129721i −0.0671362 0.0179891i
\(53\) −5.79919 1.55389i −0.796580 0.213443i −0.162498 0.986709i \(-0.551955\pi\)
−0.634082 + 0.773266i \(0.718622\pi\)
\(54\) −2.01889 4.78791i −0.274736 0.651552i
\(55\) −4.29216 + 6.48398i −0.578755 + 0.874299i
\(56\) 2.51895 + 0.809259i 0.336609 + 0.108142i
\(57\) 4.84364 0.221739i 0.641555 0.0293701i
\(58\) 1.91084 0.512009i 0.250906 0.0672301i
\(59\) −2.18403 3.78284i −0.284336 0.492484i 0.688112 0.725604i \(-0.258440\pi\)
−0.972448 + 0.233120i \(0.925106\pi\)
\(60\) 0.0596165 3.87252i 0.00769645 0.499941i
\(61\) 3.79381 6.57108i 0.485748 0.841340i −0.514118 0.857720i \(-0.671881\pi\)
0.999866 + 0.0163794i \(0.00521396\pi\)
\(62\) 6.28223 + 6.28223i 0.797844 + 0.797844i
\(63\) −7.93011 + 0.336766i −0.999100 + 0.0424285i
\(64\) 1.00000i 0.125000i
\(65\) 1.06279 + 0.355670i 0.131823 + 0.0441154i
\(66\) 1.29122 5.88315i 0.158938 0.724166i
\(67\) 13.6099 + 3.64677i 1.66272 + 0.445524i 0.963133 0.269026i \(-0.0867019\pi\)
0.699584 + 0.714550i \(0.253369\pi\)
\(68\) −0.838307 3.12860i −0.101660 0.379399i
\(69\) 7.47102 + 6.81693i 0.899406 + 0.820662i
\(70\) −5.51145 2.15034i −0.658744 0.257015i
\(71\) 3.96344i 0.470374i −0.971950 0.235187i \(-0.924430\pi\)
0.971950 0.235187i \(-0.0755702\pi\)
\(72\) 1.03797 + 2.81471i 0.122326 + 0.331717i
\(73\) −0.988062 + 3.68750i −0.115644 + 0.431589i −0.999334 0.0364830i \(-0.988385\pi\)
0.883690 + 0.468072i \(0.155051\pi\)
\(74\) −4.19193 7.26063i −0.487302 0.844032i
\(75\) −0.662162 + 8.63490i −0.0764599 + 0.997073i
\(76\) −2.79940 −0.321114
\(77\) −7.73277 4.98545i −0.881231 0.568145i
\(78\) −0.867203 + 0.0397001i −0.0981915 + 0.00449516i
\(79\) −7.48605 4.32207i −0.842246 0.486271i 0.0157809 0.999875i \(-0.494977\pi\)
−0.858027 + 0.513604i \(0.828310\pi\)
\(80\) −0.136630 + 2.23189i −0.0152757 + 0.249533i
\(81\) −5.84319 6.84523i −0.649243 0.760581i
\(82\) −2.06219 7.69619i −0.227730 0.849901i
\(83\) 10.4891 10.4891i 1.15132 1.15132i 0.165037 0.986287i \(-0.447225\pi\)
0.986287 0.165037i \(-0.0527745\pi\)
\(84\) 4.58255 + 0.0151515i 0.499997 + 0.00165316i
\(85\) 1.44355 + 7.09724i 0.156575 + 0.769804i
\(86\) 7.39221 + 4.26790i 0.797123 + 0.460219i
\(87\) 2.88592 1.84713i 0.309403 0.198033i
\(88\) −0.900040 + 3.35899i −0.0959446 + 0.358070i
\(89\) −3.59897 + 6.23359i −0.381490 + 0.660760i −0.991275 0.131807i \(-0.957922\pi\)
0.609786 + 0.792566i \(0.291256\pi\)
\(90\) −1.93206 6.42395i −0.203657 0.677144i
\(91\) −0.405604 + 1.26251i −0.0425189 + 0.132347i
\(92\) −4.12890 4.12890i −0.430467 0.430467i
\(93\) 13.6645 + 7.07663i 1.41695 + 0.733812i
\(94\) 2.06750 1.19367i 0.213247 0.123118i
\(95\) 6.24796 + 0.382484i 0.641027 + 0.0392420i
\(96\) −0.524329 1.65078i −0.0535141 0.168482i
\(97\) 11.6503 11.6503i 1.18291 1.18291i 0.203919 0.978988i \(-0.434632\pi\)
0.978988 0.203919i \(-0.0653678\pi\)
\(98\) 2.46531 6.55151i 0.249034 0.661802i
\(99\) −0.953188 10.3888i −0.0957990 1.04412i
\(100\) 0.609888 4.96266i 0.0609888 0.496266i
\(101\) −2.74872 + 1.58698i −0.273508 + 0.157910i −0.630481 0.776205i \(-0.717142\pi\)
0.356973 + 0.934115i \(0.383809\pi\)
\(102\) −3.02428 4.72509i −0.299448 0.467854i
\(103\) 4.82502 1.29286i 0.475423 0.127389i −0.0131477 0.999914i \(-0.504185\pi\)
0.488571 + 0.872524i \(0.337518\pi\)
\(104\) 0.501205 0.0491471
\(105\) −10.2257 0.659932i −0.997924 0.0644028i
\(106\) 6.00376 0.583137
\(107\) −13.2839 + 3.55941i −1.28420 + 0.344101i −0.835456 0.549558i \(-0.814796\pi\)
−0.448747 + 0.893659i \(0.648130\pi\)
\(108\) 3.18930 + 4.10224i 0.306891 + 0.394738i
\(109\) 1.66115 0.959063i 0.159109 0.0918615i −0.418331 0.908294i \(-0.637385\pi\)
0.577440 + 0.816433i \(0.304052\pi\)
\(110\) 2.46773 7.37393i 0.235289 0.703077i
\(111\) −10.7269 9.78777i −1.01815 0.929014i
\(112\) −2.64257 0.129732i −0.249699 0.0122586i
\(113\) 5.10087 5.10087i 0.479850 0.479850i −0.425234 0.905084i \(-0.639808\pi\)
0.905084 + 0.425234i \(0.139808\pi\)
\(114\) −4.62120 + 1.46781i −0.432815 + 0.137473i
\(115\) 8.65111 + 9.77938i 0.806720 + 0.911931i
\(116\) −1.71321 + 0.989125i −0.159068 + 0.0918380i
\(117\) −1.41075 + 0.520236i −0.130424 + 0.0480959i
\(118\) 3.08868 + 3.08868i 0.284336 + 0.284336i
\(119\) −8.37631 + 1.80940i −0.767855 + 0.165868i
\(120\) 0.944698 + 3.75600i 0.0862387 + 0.342874i
\(121\) 0.546459 0.946494i 0.0496781 0.0860449i
\(122\) −1.96382 + 7.32908i −0.177796 + 0.663544i
\(123\) −7.43955 11.6235i −0.670802 1.04805i
\(124\) −7.69413 4.44221i −0.690953 0.398922i
\(125\) −2.03925 + 10.9928i −0.182396 + 0.983225i
\(126\) 7.57273 2.37775i 0.674633 0.211827i
\(127\) −5.65099 + 5.65099i −0.501444 + 0.501444i −0.911886 0.410443i \(-0.865374\pi\)
0.410443 + 0.911886i \(0.365374\pi\)
\(128\) 0.258819 + 0.965926i 0.0228766 + 0.0853766i
\(129\) 14.4407 + 3.16941i 1.27143 + 0.279051i
\(130\) −1.11863 0.0684798i −0.0981106 0.00600608i
\(131\) −0.812657 0.469187i −0.0710021 0.0409931i 0.464079 0.885794i \(-0.346385\pi\)
−0.535081 + 0.844801i \(0.679719\pi\)
\(132\) 0.275450 + 6.01688i 0.0239748 + 0.523702i
\(133\) −0.363173 + 7.39762i −0.0314911 + 0.641455i
\(134\) −14.0900 −1.21719
\(135\) −6.55768 9.59150i −0.564395 0.825505i
\(136\) 1.61948 + 2.80503i 0.138870 + 0.240529i
\(137\) 4.69276 17.5136i 0.400929 1.49629i −0.410513 0.911855i \(-0.634650\pi\)
0.811442 0.584433i \(-0.198683\pi\)
\(138\) −8.98081 4.65100i −0.764497 0.395920i
\(139\) 14.4400i 1.22478i 0.790555 + 0.612391i \(0.209792\pi\)
−0.790555 + 0.612391i \(0.790208\pi\)
\(140\) 5.88020 + 0.650604i 0.496967 + 0.0549860i
\(141\) 2.78712 3.05455i 0.234718 0.257239i
\(142\) 1.02581 + 3.82839i 0.0860843 + 0.321271i
\(143\) −1.68354 0.451104i −0.140785 0.0377232i
\(144\) −1.73111 2.45016i −0.144259 0.204180i
\(145\) 3.95885 1.97354i 0.328765 0.163894i
\(146\) 3.81758i 0.315945i
\(147\) 0.634544 12.1077i 0.0523363 0.998630i
\(148\) 5.92828 + 5.92828i 0.487302 + 0.487302i
\(149\) 4.55062 7.88190i 0.372801 0.645711i −0.617194 0.786811i \(-0.711731\pi\)
0.989995 + 0.141100i \(0.0450640\pi\)
\(150\) −1.59528 8.51206i −0.130254 0.695006i
\(151\) 10.0131 + 17.3431i 0.814852 + 1.41136i 0.909434 + 0.415848i \(0.136515\pi\)
−0.0945826 + 0.995517i \(0.530152\pi\)
\(152\) 2.70402 0.724539i 0.219325 0.0587679i
\(153\) −7.46993 6.21438i −0.603908 0.502403i
\(154\) 8.75961 + 2.81419i 0.705870 + 0.226774i
\(155\) 16.5655 + 10.9658i 1.33057 + 0.880792i
\(156\) 0.827379 0.262796i 0.0662433 0.0210405i
\(157\) −4.57610 1.22616i −0.365212 0.0978584i 0.0715458 0.997437i \(-0.477207\pi\)
−0.436758 + 0.899579i \(0.643873\pi\)
\(158\) 8.34960 + 2.23727i 0.664259 + 0.177988i
\(159\) 9.91090 3.14795i 0.785986 0.249649i
\(160\) −0.445681 2.19120i −0.0352342 0.173230i
\(161\) −11.4465 + 10.3752i −0.902114 + 0.817684i
\(162\) 7.41576 + 5.09965i 0.582637 + 0.400667i
\(163\) 5.68384 1.52298i 0.445193 0.119289i −0.0292565 0.999572i \(-0.509314\pi\)
0.474449 + 0.880283i \(0.342647\pi\)
\(164\) 3.98384 + 6.90021i 0.311086 + 0.538816i
\(165\) 0.207316 13.4667i 0.0161395 1.04838i
\(166\) −7.41689 + 12.8464i −0.575662 + 0.997076i
\(167\) −6.77976 6.77976i −0.524634 0.524634i 0.394334 0.918967i \(-0.370975\pi\)
−0.918967 + 0.394334i \(0.870975\pi\)
\(168\) −4.43033 + 1.17142i −0.341807 + 0.0903767i
\(169\) 12.7488i 0.980676i
\(170\) −3.23126 6.48179i −0.247826 0.497131i
\(171\) −6.85898 + 4.84606i −0.524519 + 0.370588i
\(172\) −8.24494 2.20923i −0.628671 0.168452i
\(173\) 3.45191 + 12.8827i 0.262444 + 0.979455i 0.963796 + 0.266640i \(0.0859134\pi\)
−0.701352 + 0.712815i \(0.747420\pi\)
\(174\) −2.30952 + 2.53112i −0.175084 + 0.191884i
\(175\) −13.0351 2.25549i −0.985358 0.170499i
\(176\) 3.47749i 0.262125i
\(177\) 6.71822 + 3.47925i 0.504972 + 0.261516i
\(178\) 1.86296 6.95267i 0.139635 0.521125i
\(179\) 11.6481 + 20.1751i 0.870619 + 1.50796i 0.861358 + 0.507999i \(0.169615\pi\)
0.00926137 + 0.999957i \(0.497052\pi\)
\(180\) 3.52887 + 5.70500i 0.263027 + 0.425226i
\(181\) 0.785759 0.0584050 0.0292025 0.999574i \(-0.490703\pi\)
0.0292025 + 0.999574i \(0.490703\pi\)
\(182\) 0.0650224 1.32447i 0.00481978 0.0981761i
\(183\) 0.601012 + 13.1284i 0.0444281 + 0.970479i
\(184\) 5.05684 + 2.91957i 0.372796 + 0.215234i
\(185\) −12.4213 14.0413i −0.913231 1.03233i
\(186\) −15.0305 3.29886i −1.10209 0.241884i
\(187\) −2.91520 10.8797i −0.213181 0.795601i
\(188\) −1.68811 + 1.68811i −0.123118 + 0.123118i
\(189\) 11.2542 7.89576i 0.818623 0.574332i
\(190\) −6.13406 + 1.24764i −0.445011 + 0.0905133i
\(191\) 8.94888 + 5.16664i 0.647518 + 0.373845i 0.787505 0.616309i \(-0.211373\pi\)
−0.139987 + 0.990153i \(0.544706\pi\)
\(192\) 0.933717 + 1.45883i 0.0673852 + 0.105282i
\(193\) −3.18118 + 11.8723i −0.228986 + 0.854589i 0.751782 + 0.659412i \(0.229195\pi\)
−0.980768 + 0.195177i \(0.937472\pi\)
\(194\) −8.23799 + 14.2686i −0.591453 + 1.02443i
\(195\) −1.88252 + 0.473487i −0.134810 + 0.0339071i
\(196\) −0.685653 + 6.96634i −0.0489752 + 0.497596i
\(197\) 8.78363 + 8.78363i 0.625808 + 0.625808i 0.947010 0.321203i \(-0.104087\pi\)
−0.321203 + 0.947010i \(0.604087\pi\)
\(198\) 3.60953 + 9.78813i 0.256518 + 0.695612i
\(199\) −14.0224 + 8.09584i −0.994022 + 0.573899i −0.906474 0.422262i \(-0.861236\pi\)
−0.0875478 + 0.996160i \(0.527903\pi\)
\(200\) 0.695325 + 4.95142i 0.0491669 + 0.350118i
\(201\) −23.2596 + 7.38781i −1.64060 + 0.521096i
\(202\) 2.24432 2.24432i 0.157910 0.157910i
\(203\) 2.39157 + 4.65561i 0.167855 + 0.326760i
\(204\) 4.14417 + 3.78135i 0.290150 + 0.264747i
\(205\) −7.94871 15.9448i −0.555162 1.11363i
\(206\) −4.32599 + 2.49761i −0.301406 + 0.174017i
\(207\) −17.2640 2.96889i −1.19993 0.206352i
\(208\) −0.484126 + 0.129721i −0.0335681 + 0.00899455i
\(209\) −9.73489 −0.673376
\(210\) 10.0480 2.00915i 0.693381 0.138645i
\(211\) −10.8789 −0.748933 −0.374466 0.927240i \(-0.622174\pi\)
−0.374466 + 0.927240i \(0.622174\pi\)
\(212\) −5.79919 + 1.55389i −0.398290 + 0.106722i
\(213\) 3.70073 + 5.78197i 0.253570 + 0.396174i
\(214\) 11.9100 6.87625i 0.814152 0.470051i
\(215\) 18.1000 + 6.05726i 1.23441 + 0.413102i
\(216\) −4.14237 3.13701i −0.281852 0.213446i
\(217\) −12.7370 + 19.7560i −0.864645 + 1.34112i
\(218\) −1.35632 + 1.35632i −0.0918615 + 0.0918615i
\(219\) −2.00167 6.30199i −0.135260 0.425849i
\(220\) −0.475131 + 7.76137i −0.0320333 + 0.523271i
\(221\) −1.40589 + 0.811693i −0.0945707 + 0.0546004i
\(222\) 12.8947 + 6.67793i 0.865434 + 0.448193i
\(223\) −4.82814 4.82814i −0.323316 0.323316i 0.526722 0.850038i \(-0.323421\pi\)
−0.850038 + 0.526722i \(0.823421\pi\)
\(224\) 2.58610 0.558635i 0.172791 0.0373254i
\(225\) −7.09657 13.2151i −0.473105 0.881006i
\(226\) −3.60686 + 6.24727i −0.239925 + 0.415562i
\(227\) −3.08682 + 11.5202i −0.204879 + 0.764620i 0.784607 + 0.619993i \(0.212865\pi\)
−0.989486 + 0.144627i \(0.953802\pi\)
\(228\) 4.08384 2.61385i 0.270459 0.173106i
\(229\) 11.5271 + 6.65520i 0.761735 + 0.439788i 0.829918 0.557885i \(-0.188387\pi\)
−0.0681831 + 0.997673i \(0.521720\pi\)
\(230\) −10.8874 7.20708i −0.717895 0.475221i
\(231\) 15.9358 + 0.0526891i 1.04850 + 0.00346669i
\(232\) 1.39883 1.39883i 0.0918380 0.0918380i
\(233\) −0.0494125 0.184410i −0.00323712 0.0120811i 0.964288 0.264855i \(-0.0853239\pi\)
−0.967525 + 0.252773i \(0.918657\pi\)
\(234\) 1.22803 0.867638i 0.0802788 0.0567193i
\(235\) 3.99832 3.53703i 0.260822 0.230730i
\(236\) −3.78284 2.18403i −0.246242 0.142168i
\(237\) 14.9564 0.684698i 0.971525 0.0444759i
\(238\) 7.62258 3.91570i 0.494099 0.253817i
\(239\) 7.37456 0.477020 0.238510 0.971140i \(-0.423341\pi\)
0.238510 + 0.971140i \(0.423341\pi\)
\(240\) −1.88463 3.38351i −0.121653 0.218405i
\(241\) −7.27332 12.5978i −0.468516 0.811493i 0.530837 0.847474i \(-0.321878\pi\)
−0.999352 + 0.0359810i \(0.988544\pi\)
\(242\) −0.282868 + 1.05568i −0.0181834 + 0.0678615i
\(243\) 14.9157 + 4.53011i 0.956843 + 0.290607i
\(244\) 7.58763i 0.485748i
\(245\) 2.48212 15.4544i 0.158577 0.987347i
\(246\) 10.1944 + 9.30190i 0.649973 + 0.593067i
\(247\) 0.363142 + 1.35527i 0.0231062 + 0.0862334i
\(248\) 8.58169 + 2.29946i 0.544938 + 0.146016i
\(249\) −5.50791 + 25.0955i −0.349049 + 1.59037i
\(250\) −0.875375 11.1460i −0.0553636 0.704936i
\(251\) 2.79937i 0.176694i −0.996090 0.0883472i \(-0.971842\pi\)
0.996090 0.0883472i \(-0.0281585\pi\)
\(252\) −6.69929 + 4.25670i −0.422016 + 0.268147i
\(253\) −14.3582 14.3582i −0.902691 0.902691i
\(254\) 3.99585 6.92102i 0.250722 0.434263i
\(255\) −8.73269 9.00577i −0.546863 0.563963i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 26.7017 7.15470i 1.66561 0.446298i 0.701686 0.712487i \(-0.252431\pi\)
0.963921 + 0.266189i \(0.0857644\pi\)
\(258\) −14.7690 + 0.676116i −0.919475 + 0.0420931i
\(259\) 16.4350 14.8968i 1.02122 0.925642i
\(260\) 1.09824 0.223377i 0.0681100 0.0138533i
\(261\) −2.48537 + 5.38927i −0.153840 + 0.333587i
\(262\) 0.906401 + 0.242869i 0.0559976 + 0.0150045i
\(263\) −9.41543 2.52286i −0.580580 0.155566i −0.0434357 0.999056i \(-0.513830\pi\)
−0.537145 + 0.843490i \(0.680497\pi\)
\(264\) −1.82335 5.74057i −0.112219 0.353308i
\(265\) 13.1555 2.67576i 0.808134 0.164371i
\(266\) −1.56385 7.23954i −0.0958855 0.443885i
\(267\) −0.570145 12.4541i −0.0348923 0.762181i
\(268\) 13.6099 3.64677i 0.831359 0.222762i
\(269\) −10.2899 17.8226i −0.627384 1.08666i −0.988075 0.153975i \(-0.950792\pi\)
0.360691 0.932685i \(-0.382541\pi\)
\(270\) 8.81669 + 7.56742i 0.536567 + 0.460539i
\(271\) 11.5399 19.9876i 0.700997 1.21416i −0.267120 0.963663i \(-0.586072\pi\)
0.968117 0.250499i \(-0.0805945\pi\)
\(272\) −2.29030 2.29030i −0.138870 0.138870i
\(273\) −0.587119 2.22050i −0.0355341 0.134391i
\(274\) 18.1314i 1.09536i
\(275\) 2.12088 17.2576i 0.127894 1.04067i
\(276\) 9.87856 + 2.16812i 0.594620 + 0.130506i
\(277\) −7.08871 1.89941i −0.425919 0.114125i 0.0394907 0.999220i \(-0.487426\pi\)
−0.465410 + 0.885095i \(0.654093\pi\)
\(278\) −3.73734 13.9479i −0.224151 0.836542i
\(279\) −26.5418 + 2.43524i −1.58901 + 0.145794i
\(280\) −5.84822 + 0.893472i −0.349498 + 0.0533952i
\(281\) 7.12223i 0.424877i −0.977174 0.212438i \(-0.931860\pi\)
0.977174 0.212438i \(-0.0681405\pi\)
\(282\) −1.90157 + 3.67182i −0.113237 + 0.218654i
\(283\) 3.21738 12.0074i 0.191254 0.713768i −0.801951 0.597389i \(-0.796205\pi\)
0.993205 0.116379i \(-0.0371287\pi\)
\(284\) −1.98172 3.43244i −0.117593 0.203678i
\(285\) −9.47182 + 5.27585i −0.561062 + 0.312514i
\(286\) 1.74293 0.103062
\(287\) 18.7511 9.63239i 1.10684 0.568582i
\(288\) 2.30627 + 1.91863i 0.135898 + 0.113056i
\(289\) 5.63702 + 3.25454i 0.331590 + 0.191443i
\(290\) −3.31317 + 2.93092i −0.194556 + 0.172110i
\(291\) −6.11767 + 27.8738i −0.358624 + 1.63399i
\(292\) 0.988062 + 3.68750i 0.0578219 + 0.215794i
\(293\) 4.01118 4.01118i 0.234336 0.234336i −0.580164 0.814500i \(-0.697012\pi\)
0.814500 + 0.580164i \(0.197012\pi\)
\(294\) 2.52079 + 11.8594i 0.147016 + 0.691655i
\(295\) 8.14448 + 5.39136i 0.474190 + 0.313897i
\(296\) −7.26063 4.19193i −0.422016 0.243651i
\(297\) 11.0908 + 14.2655i 0.643551 + 0.827767i
\(298\) −2.35557 + 8.79112i −0.136455 + 0.509256i
\(299\) −1.46330 + 2.53451i −0.0846249 + 0.146575i
\(300\) 3.74400 + 7.80913i 0.216160 + 0.450860i
\(301\) −6.90767 + 21.5012i −0.398151 + 1.23931i
\(302\) −14.1606 14.1606i −0.814852 0.814852i
\(303\) 2.52812 4.88165i 0.145237 0.280444i
\(304\) −2.42435 + 1.39970i −0.139046 + 0.0802784i
\(305\) −1.03670 + 16.9347i −0.0593613 + 0.969681i
\(306\) 8.82380 + 4.06927i 0.504423 + 0.232625i
\(307\) 17.5067 17.5067i 0.999159 0.999159i −0.000841117 1.00000i \(-0.500268\pi\)
1.00000 0.000841117i \(0.000267736\pi\)
\(308\) −9.18950 0.451143i −0.523620 0.0257062i
\(309\) −5.83169 + 6.39125i −0.331753 + 0.363586i
\(310\) −18.8392 6.30465i −1.06999 0.358080i
\(311\) 4.32483 2.49694i 0.245238 0.141588i −0.372344 0.928095i \(-0.621446\pi\)
0.617582 + 0.786506i \(0.288112\pi\)
\(312\) −0.731170 + 0.467983i −0.0413944 + 0.0264943i
\(313\) −10.9857 + 2.94360i −0.620946 + 0.166382i −0.555558 0.831478i \(-0.687495\pi\)
−0.0653882 + 0.997860i \(0.520829\pi\)
\(314\) 4.73752 0.267354
\(315\) 15.5337 8.58516i 0.875223 0.483719i
\(316\) −8.64414 −0.486271
\(317\) −25.9681 + 6.95813i −1.45851 + 0.390808i −0.898976 0.437998i \(-0.855688\pi\)
−0.559537 + 0.828805i \(0.689021\pi\)
\(318\) −8.75845 + 5.60582i −0.491149 + 0.314359i
\(319\) −5.95768 + 3.43967i −0.333566 + 0.192585i
\(320\) 0.997619 + 2.00119i 0.0557686 + 0.111870i
\(321\) 16.0554 17.5960i 0.896126 0.982111i
\(322\) 8.37120 12.9843i 0.466509 0.723587i
\(323\) −6.41147 + 6.41147i −0.356744 + 0.356744i
\(324\) −8.48296 3.00655i −0.471276 0.167030i
\(325\) −2.48167 + 0.348500i −0.137658 + 0.0193313i
\(326\) −5.09599 + 2.94217i −0.282241 + 0.162952i
\(327\) −1.52783 + 2.95014i −0.0844891 + 0.163143i
\(328\) −5.63400 5.63400i −0.311086 0.311086i
\(329\) 4.24194 + 4.67995i 0.233866 + 0.258014i
\(330\) 3.28518 + 13.0614i 0.180843 + 0.719009i
\(331\) 13.4191 23.2426i 0.737580 1.27753i −0.216002 0.976393i \(-0.569302\pi\)
0.953582 0.301133i \(-0.0973649\pi\)
\(332\) 3.83927 14.3283i 0.210707 0.786369i
\(333\) 24.7877 + 4.26274i 1.35836 + 0.233597i
\(334\) 8.30348 + 4.79401i 0.454346 + 0.262317i
\(335\) −30.8741 + 6.27966i −1.68683 + 0.343094i
\(336\) 3.97618 2.27815i 0.216918 0.124283i
\(337\) −10.5014 + 10.5014i −0.572050 + 0.572050i −0.932701 0.360651i \(-0.882555\pi\)
0.360651 + 0.932701i \(0.382555\pi\)
\(338\) 3.29963 + 12.3144i 0.179476 + 0.669814i
\(339\) −2.67851 + 12.2041i −0.145477 + 0.662833i
\(340\) 4.79877 + 5.42462i 0.260250 + 0.294191i
\(341\) −26.7562 15.4477i −1.44893 0.836541i
\(342\) 5.37101 6.45617i 0.290431 0.349110i
\(343\) 18.3201 + 2.71565i 0.989191 + 0.146631i
\(344\) 8.53579 0.460219
\(345\) −21.7516 6.18872i −1.17107 0.333190i
\(346\) −6.66858 11.5503i −0.358505 0.620949i
\(347\) −4.03107 + 15.0442i −0.216399 + 0.807613i 0.769270 + 0.638924i \(0.220620\pi\)
−0.985669 + 0.168689i \(0.946047\pi\)
\(348\) 1.57572 3.04262i 0.0844674 0.163101i
\(349\) 26.9797i 1.44419i −0.691794 0.722095i \(-0.743179\pi\)
0.691794 0.722095i \(-0.256821\pi\)
\(350\) 13.1747 1.19509i 0.704215 0.0638800i
\(351\) 1.57228 2.07617i 0.0839222 0.110818i
\(352\) 0.900040 + 3.35899i 0.0479723 + 0.179035i
\(353\) 22.6214 + 6.06139i 1.20402 + 0.322615i 0.804412 0.594072i \(-0.202481\pi\)
0.399605 + 0.916687i \(0.369147\pi\)
\(354\) −7.38979 1.62189i −0.392763 0.0862027i
\(355\) 3.95400 + 7.93159i 0.209857 + 0.420965i
\(356\) 7.19793i 0.381490i
\(357\) 10.5301 10.4607i 0.557312 0.553639i
\(358\) −16.4729 16.4729i −0.870619 0.870619i
\(359\) −9.51649 + 16.4830i −0.502261 + 0.869941i 0.497736 + 0.867329i \(0.334165\pi\)
−0.999997 + 0.00261263i \(0.999168\pi\)
\(360\) −4.88519 4.59727i −0.257472 0.242297i
\(361\) −5.58167 9.66774i −0.293772 0.508828i
\(362\) −0.758985 + 0.203369i −0.0398914 + 0.0106889i
\(363\) 0.0865694 + 1.89101i 0.00454372 + 0.0992522i
\(364\) 0.279991 + 1.29617i 0.0146755 + 0.0679376i
\(365\) −1.70142 8.36509i −0.0890564 0.437849i
\(366\) −3.97841 12.5255i −0.207955 0.654719i
\(367\) −8.65175 2.31823i −0.451618 0.121011i 0.0258384 0.999666i \(-0.491774\pi\)
−0.477456 + 0.878655i \(0.658441\pi\)
\(368\) −5.64018 1.51128i −0.294015 0.0787810i
\(369\) 21.7060 + 10.0102i 1.12997 + 0.521108i
\(370\) 15.6322 + 10.3479i 0.812679 + 0.537964i
\(371\) 3.35391 + 15.5264i 0.174127 + 0.806088i
\(372\) 15.3722 0.703730i 0.797009 0.0364867i
\(373\) −9.33806 + 2.50213i −0.483506 + 0.129555i −0.492335 0.870406i \(-0.663856\pi\)
0.00882841 + 0.999961i \(0.497190\pi\)
\(374\) 5.63174 + 9.75446i 0.291210 + 0.504391i
\(375\) −7.28924 17.9407i −0.376415 0.926451i
\(376\) 1.19367 2.06750i 0.0615590 0.106623i
\(377\) 0.701102 + 0.701102i 0.0361086 + 0.0361086i
\(378\) −8.82715 + 10.5395i −0.454020 + 0.542094i
\(379\) 9.63664i 0.495001i 0.968888 + 0.247500i \(0.0796092\pi\)
−0.968888 + 0.247500i \(0.920391\pi\)
\(380\) 5.60213 2.79274i 0.287383 0.143265i
\(381\) 2.96738 13.5202i 0.152024 0.692662i
\(382\) −9.98118 2.67445i −0.510681 0.136837i
\(383\) −5.07236 18.9303i −0.259185 0.967293i −0.965714 0.259609i \(-0.916406\pi\)
0.706529 0.707685i \(-0.250260\pi\)
\(384\) −1.27947 1.16745i −0.0652928 0.0595764i
\(385\) 20.4483 + 2.26247i 1.04214 + 0.115306i
\(386\) 12.2911i 0.625602i
\(387\) −24.0258 + 8.85992i −1.22130 + 0.450375i
\(388\) 4.26430 15.9146i 0.216487 0.807940i
\(389\) −5.28560 9.15493i −0.267991 0.464174i 0.700352 0.713798i \(-0.253026\pi\)
−0.968343 + 0.249624i \(0.919693\pi\)
\(390\) 1.69583 0.944586i 0.0858718 0.0478310i
\(391\) −18.9128 −0.956462
\(392\) −1.14073 6.90643i −0.0576156 0.348827i
\(393\) 1.62361 0.0743282i 0.0819004 0.00374936i
\(394\) −10.7577 6.21096i −0.541965 0.312904i
\(395\) 19.2928 + 1.18105i 0.970725 + 0.0594252i
\(396\) −6.01990 8.52039i −0.302511 0.428166i
\(397\) 4.05577 + 15.1363i 0.203553 + 0.759671i 0.989886 + 0.141868i \(0.0453107\pi\)
−0.786332 + 0.617804i \(0.788023\pi\)
\(398\) 11.4492 11.4492i 0.573899 0.573899i
\(399\) −6.37747 11.1309i −0.319273 0.557244i
\(400\) −1.95315 4.60274i −0.0976577 0.230137i
\(401\) 22.4638 + 12.9695i 1.12179 + 0.647666i 0.941857 0.336013i \(-0.109079\pi\)
0.179932 + 0.983679i \(0.442412\pi\)
\(402\) 20.5549 13.1561i 1.02519 0.656167i
\(403\) −1.15250 + 4.30118i −0.0574100 + 0.214257i
\(404\) −1.58698 + 2.74872i −0.0789551 + 0.136754i
\(405\) 18.5223 + 7.86931i 0.920378 + 0.391029i
\(406\) −3.51504 3.87799i −0.174449 0.192461i
\(407\) 20.6155 + 20.6155i 1.02187 + 1.02187i
\(408\) −4.98165 2.57991i −0.246628 0.127725i
\(409\) 5.22497 3.01664i 0.258358 0.149163i −0.365227 0.930918i \(-0.619009\pi\)
0.623585 + 0.781755i \(0.285675\pi\)
\(410\) 11.8047 + 13.3442i 0.582992 + 0.659025i
\(411\) 9.50683 + 29.9310i 0.468937 + 1.47639i
\(412\) 3.53216 3.53216i 0.174017 0.174017i
\(413\) −6.26219 + 9.71308i −0.308142 + 0.477950i
\(414\) 17.4442 1.60052i 0.857333 0.0786614i
\(415\) −10.5265 + 31.4547i −0.516726 + 1.54405i
\(416\) 0.434056 0.250602i 0.0212813 0.0122868i
\(417\) −13.4828 21.0654i −0.660258 1.03158i
\(418\) 9.40318 2.51957i 0.459925 0.123236i
\(419\) 3.42723 0.167431 0.0837157 0.996490i \(-0.473321\pi\)
0.0837157 + 0.996490i \(0.473321\pi\)
\(420\) −9.18566 + 4.54132i −0.448214 + 0.221594i
\(421\) −12.2231 −0.595718 −0.297859 0.954610i \(-0.596272\pi\)
−0.297859 + 0.954610i \(0.596272\pi\)
\(422\) 10.5082 2.81566i 0.511531 0.137064i
\(423\) −1.21384 + 7.05843i −0.0590188 + 0.343193i
\(424\) 5.19941 3.00188i 0.252506 0.145784i
\(425\) −9.96915 12.7628i −0.483575 0.619087i
\(426\) −5.07111 4.62713i −0.245696 0.224185i
\(427\) −20.0508 0.984361i −0.970327 0.0476365i
\(428\) −9.72449 + 9.72449i −0.470051 + 0.470051i
\(429\) 2.87720 0.913870i 0.138913 0.0441221i
\(430\) −19.0510 1.16625i −0.918718 0.0562415i
\(431\) 5.13623 2.96540i 0.247403 0.142838i −0.371171 0.928564i \(-0.621044\pi\)
0.618575 + 0.785726i \(0.287710\pi\)
\(432\) 4.81314 + 1.95799i 0.231572 + 0.0942039i
\(433\) 6.21844 + 6.21844i 0.298839 + 0.298839i 0.840559 0.541720i \(-0.182227\pi\)
−0.541720 + 0.840559i \(0.682227\pi\)
\(434\) 7.18979 22.3794i 0.345121 1.07424i
\(435\) −3.93255 + 6.57550i −0.188551 + 0.315271i
\(436\) 0.959063 1.66115i 0.0459308 0.0795544i
\(437\) −4.23069 + 15.7891i −0.202381 + 0.755297i
\(438\) 3.56454 + 5.56918i 0.170320 + 0.266106i
\(439\) −2.39660 1.38368i −0.114383 0.0660393i 0.441717 0.897155i \(-0.354370\pi\)
−0.556100 + 0.831115i \(0.687703\pi\)
\(440\) −1.54985 7.61988i −0.0738862 0.363263i
\(441\) 10.3795 + 18.2556i 0.494262 + 0.869313i
\(442\) 1.14791 1.14791i 0.0546004 0.0546004i
\(443\) 6.26524 + 23.3822i 0.297671 + 1.11092i 0.939073 + 0.343717i \(0.111686\pi\)
−0.641403 + 0.767204i \(0.721647\pi\)
\(444\) −14.1837 3.11300i −0.673127 0.147736i
\(445\) 0.983457 16.0650i 0.0466203 0.761554i
\(446\) 5.91324 + 3.41401i 0.280000 + 0.161658i
\(447\) 0.720904 + 15.7473i 0.0340976 + 0.744822i
\(448\) −2.35340 + 1.20893i −0.111188 + 0.0571167i
\(449\) −6.14519 −0.290010 −0.145005 0.989431i \(-0.546320\pi\)
−0.145005 + 0.989431i \(0.546320\pi\)
\(450\) 10.2751 + 10.9281i 0.484372 + 0.515154i
\(451\) 13.8537 + 23.9954i 0.652348 + 1.12990i
\(452\) 1.86705 6.96792i 0.0878186 0.327743i
\(453\) −30.8009 15.9513i −1.44715 0.749455i
\(454\) 11.9266i 0.559741i
\(455\) −0.447812 2.93116i −0.0209938 0.137415i
\(456\) −3.26817 + 3.58176i −0.153046 + 0.167731i
\(457\) 2.83485 + 10.5798i 0.132609 + 0.494903i 0.999996 0.00273047i \(-0.000869137\pi\)
−0.867387 + 0.497633i \(0.834202\pi\)
\(458\) −12.8569 3.44499i −0.600762 0.160974i
\(459\) 16.6998 + 2.09090i 0.779480 + 0.0975946i
\(460\) 12.3818 + 4.14363i 0.577303 + 0.193198i
\(461\) 0.00387108i 0.000180294i −1.00000 9.01471e-5i \(-0.999971\pi\)
1.00000 9.01471e-5i \(-2.86947e-5\pi\)
\(462\) −15.4064 + 4.07358i −0.716771 + 0.189520i
\(463\) 27.8340 + 27.8340i 1.29356 + 1.29356i 0.932571 + 0.360986i \(0.117560\pi\)
0.360986 + 0.932571i \(0.382440\pi\)
\(464\) −0.989125 + 1.71321i −0.0459190 + 0.0795340i
\(465\) −34.4051 0.529657i −1.59550 0.0245623i
\(466\) 0.0954575 + 0.165337i 0.00442199 + 0.00765910i
\(467\) 10.0261 2.68649i 0.463953 0.124316i −0.0192680 0.999814i \(-0.506134\pi\)
0.483221 + 0.875499i \(0.339467\pi\)
\(468\) −0.961625 + 1.15591i −0.0444511 + 0.0534320i
\(469\) −7.87119 36.4383i −0.363458 1.68256i
\(470\) −2.94663 + 4.45135i −0.135918 + 0.205325i
\(471\) 7.82062 2.48402i 0.360355 0.114458i
\(472\) 4.21921 + 1.13053i 0.194205 + 0.0520371i
\(473\) −28.6717 7.68255i −1.31833 0.353244i
\(474\) −14.2696 + 4.53238i −0.655424 + 0.208179i
\(475\) −12.8849 + 5.46766i −0.591201 + 0.250874i
\(476\) −6.34939 + 5.75514i −0.291024 + 0.263787i
\(477\) −11.5190 + 13.8463i −0.527418 + 0.633978i
\(478\) −7.12327 + 1.90868i −0.325811 + 0.0873008i
\(479\) −2.84062 4.92009i −0.129791 0.224805i 0.793805 0.608173i \(-0.208097\pi\)
−0.923596 + 0.383368i \(0.874764\pi\)
\(480\) 2.69613 + 2.78044i 0.123061 + 0.126909i
\(481\) 2.10101 3.63906i 0.0957980 0.165927i
\(482\) 10.2860 + 10.2860i 0.468516 + 0.468516i
\(483\) 7.01098 25.8235i 0.319011 1.17501i
\(484\) 1.09292i 0.0496781i
\(485\) −11.6919 + 34.9369i −0.530900 + 1.58640i
\(486\) −15.5799 0.515285i −0.706720 0.0233738i
\(487\) −6.53929 1.75220i −0.296324 0.0793997i 0.107594 0.994195i \(-0.465685\pi\)
−0.403918 + 0.914795i \(0.632352\pi\)
\(488\) 1.96382 + 7.32908i 0.0888980 + 0.331772i
\(489\) −6.86970 + 7.52886i −0.310659 + 0.340467i
\(490\) 1.60236 + 15.5702i 0.0723871 + 0.703392i
\(491\) 11.2931i 0.509652i 0.966987 + 0.254826i \(0.0820182\pi\)
−0.966987 + 0.254826i \(0.917982\pi\)
\(492\) −12.2546 6.34643i −0.552479 0.286119i
\(493\) −1.65838 + 6.18916i −0.0746897 + 0.278746i
\(494\) −0.701537 1.21510i −0.0315636 0.0546698i
\(495\) 12.2716 + 19.8391i 0.551568 + 0.891700i
\(496\) −8.88441 −0.398922
\(497\) −9.32755 + 4.79153i −0.418398 + 0.214930i
\(498\) −1.17498 25.6660i −0.0526519 1.15012i
\(499\) 2.82144 + 1.62896i 0.126305 + 0.0729221i 0.561821 0.827259i \(-0.310101\pi\)
−0.435516 + 0.900181i \(0.643434\pi\)
\(500\) 3.73035 + 10.5397i 0.166826 + 0.471348i
\(501\) 16.2209 + 3.56011i 0.724695 + 0.159054i
\(502\) 0.724529 + 2.70398i 0.0323373 + 0.120685i
\(503\) 29.1072 29.1072i 1.29783 1.29783i 0.368003 0.929825i \(-0.380042\pi\)
0.929825 0.368003i \(-0.119958\pi\)
\(504\) 5.36930 5.84556i 0.239168 0.260382i
\(505\) 3.91752 5.91802i 0.174327 0.263349i
\(506\) 17.5851 + 10.1528i 0.781754 + 0.451346i
\(507\) 11.9038 + 18.5983i 0.528665 + 0.825978i
\(508\) −2.06840 + 7.71939i −0.0917706 + 0.342493i
\(509\) 15.2527 26.4185i 0.676064 1.17098i −0.300092 0.953910i \(-0.597017\pi\)
0.976157 0.217068i \(-0.0696493\pi\)
\(510\) 10.7660 + 6.43872i 0.476727 + 0.285111i
\(511\) 9.87265 2.13263i 0.436740 0.0943422i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 5.48121 13.4739i 0.242001 0.594888i
\(514\) −23.9401 + 13.8218i −1.05595 + 0.609654i
\(515\) −8.36598 + 7.40078i −0.368649 + 0.326118i
\(516\) 14.0907 4.47557i 0.620310 0.197026i
\(517\) −5.87038 + 5.87038i −0.258179 + 0.258179i
\(518\) −12.0194 + 18.6429i −0.528102 + 0.819122i
\(519\) −17.0645 15.5705i −0.749051 0.683470i
\(520\) −1.00300 + 0.500011i −0.0439847 + 0.0219269i
\(521\) 37.2040 21.4798i 1.62994 0.941045i 0.645829 0.763482i \(-0.276512\pi\)
0.984109 0.177563i \(-0.0568213\pi\)
\(522\) 1.00583 5.84889i 0.0440242 0.255999i
\(523\) −34.1251 + 9.14379i −1.49219 + 0.399830i −0.910474 0.413566i \(-0.864283\pi\)
−0.581711 + 0.813396i \(0.697617\pi\)
\(524\) −0.938375 −0.0409931
\(525\) 21.1219 8.88069i 0.921834 0.387585i
\(526\) 9.74757 0.425014
\(527\) −27.7958 + 7.44787i −1.21080 + 0.324434i
\(528\) 3.24699 + 5.07305i 0.141307 + 0.220776i
\(529\) −9.60905 + 5.54779i −0.417785 + 0.241208i
\(530\) −12.0147 + 5.98947i −0.521884 + 0.260166i
\(531\) −13.0493 + 1.19729i −0.566293 + 0.0519581i
\(532\) 3.38429 + 6.58811i 0.146728 + 0.285631i
\(533\) 2.82379 2.82379i 0.122312 0.122312i
\(534\) 3.77409 + 11.8822i 0.163321 + 0.514194i
\(535\) 23.0326 20.3753i 0.995788 0.880902i
\(536\) −12.2023 + 7.04502i −0.527060 + 0.304298i
\(537\) −35.8303 18.5559i −1.54619 0.800747i
\(538\) 14.5521 + 14.5521i 0.627384 + 0.627384i
\(539\) −2.38435 + 24.2254i −0.102701 + 1.04346i
\(540\) −10.4749 5.02764i −0.450766 0.216355i
\(541\) 17.0132 29.4677i 0.731454 1.26692i −0.224807 0.974403i \(-0.572175\pi\)
0.956262 0.292513i \(-0.0944914\pi\)
\(542\) −5.97347 + 22.2933i −0.256583 + 0.957579i
\(543\) −1.14629 + 0.733677i −0.0491918 + 0.0314851i
\(544\) 2.80503 + 1.61948i 0.120265 + 0.0694348i
\(545\) −2.36749 + 3.57646i −0.101412 + 0.153199i
\(546\) 1.14182 + 1.99288i 0.0488654 + 0.0852874i
\(547\) 16.7941 16.7941i 0.718062 0.718062i −0.250146 0.968208i \(-0.580479\pi\)
0.968208 + 0.250146i \(0.0804787\pi\)
\(548\) −4.69276 17.5136i −0.200465 0.748144i
\(549\) −13.1350 18.5909i −0.560587 0.793439i
\(550\) 2.41798 + 17.2185i 0.103103 + 0.734199i
\(551\) 4.79598 + 2.76896i 0.204316 + 0.117962i
\(552\) −10.1031 + 0.462515i −0.430017 + 0.0196860i
\(553\) −1.12143 + 22.8427i −0.0476879 + 0.971372i
\(554\) 7.33877 0.311795
\(555\) 31.2311 + 8.88578i 1.32568 + 0.377181i
\(556\) 7.21999 + 12.5054i 0.306196 + 0.530347i
\(557\) 4.54543 16.9638i 0.192596 0.718778i −0.800280 0.599626i \(-0.795316\pi\)
0.992876 0.119152i \(-0.0380174\pi\)
\(558\) 25.0071 9.22177i 1.05863 0.390389i
\(559\) 4.27818i 0.180948i
\(560\) 5.41770 2.37666i 0.228940 0.100432i
\(561\) 14.4113 + 13.1496i 0.608446 + 0.555176i
\(562\) 1.84337 + 6.87955i 0.0777578 + 0.290196i
\(563\) −18.5191 4.96217i −0.780486 0.209130i −0.153487 0.988151i \(-0.549050\pi\)
−0.626999 + 0.779020i \(0.715717\pi\)
\(564\) 0.886442 4.03887i 0.0373259 0.170067i
\(565\) −5.11908 + 15.2965i −0.215361 + 0.643530i
\(566\) 12.4310i 0.522515i
\(567\) −9.04552 + 22.0268i −0.379876 + 0.925037i
\(568\) 2.80257 + 2.80257i 0.117593 + 0.117593i
\(569\) 16.9400 29.3410i 0.710164 1.23004i −0.254632 0.967038i \(-0.581954\pi\)
0.964795 0.263002i \(-0.0847124\pi\)
\(570\) 7.78358 7.54756i 0.326018 0.316133i
\(571\) 1.99106 + 3.44862i 0.0833234 + 0.144320i 0.904676 0.426101i \(-0.140113\pi\)
−0.821352 + 0.570421i \(0.806780\pi\)
\(572\) −1.68354 + 0.451104i −0.0703925 + 0.0188616i
\(573\) −17.8790 + 0.818493i −0.746907 + 0.0341930i
\(574\) −15.6191 + 14.1573i −0.651930 + 0.590915i
\(575\) −27.0686 10.9399i −1.12884 0.456224i
\(576\) −2.72426 1.25635i −0.113511 0.0523478i
\(577\) 4.71693 + 1.26390i 0.196369 + 0.0526168i 0.355663 0.934614i \(-0.384255\pi\)
−0.159294 + 0.987231i \(0.550922\pi\)
\(578\) −6.28728 1.68467i −0.261516 0.0700731i
\(579\) −6.44460 20.2900i −0.267828 0.843223i
\(580\) 2.44170 3.68856i 0.101386 0.153159i
\(581\) −37.3655 12.0044i −1.55018 0.498025i
\(582\) −1.30505 28.5074i −0.0540962 1.18167i
\(583\) −20.1666 + 5.40363i −0.835216 + 0.223795i
\(584\) −1.90879 3.30612i −0.0789862 0.136808i
\(585\) 2.30417 2.44848i 0.0952658 0.101232i
\(586\) −2.83634 + 4.91268i −0.117168 + 0.202941i
\(587\) −11.5042 11.5042i −0.474828 0.474828i 0.428645 0.903473i \(-0.358991\pi\)
−0.903473 + 0.428645i \(0.858991\pi\)
\(588\) −5.50434 10.8029i −0.226995 0.445503i
\(589\) 24.8711i 1.02479i
\(590\) −9.26235 3.09970i −0.381325 0.127613i
\(591\) −21.0152 4.61236i −0.864450 0.189727i
\(592\) 8.09819 + 2.16990i 0.332833 + 0.0891824i
\(593\) 4.21822 + 15.7426i 0.173221 + 0.646471i 0.996848 + 0.0793383i \(0.0252807\pi\)
−0.823626 + 0.567133i \(0.808053\pi\)
\(594\) −14.4050 10.9089i −0.591045 0.447597i
\(595\) 14.9575 11.9773i 0.613197 0.491022i
\(596\) 9.10124i 0.372801i
\(597\) 12.8970 24.9034i 0.527840 1.01923i
\(598\) 0.757461 2.82688i 0.0309749 0.115600i
\(599\) −8.39829 14.5463i −0.343145 0.594344i 0.641870 0.766813i \(-0.278159\pi\)
−0.985015 + 0.172469i \(0.944825\pi\)
\(600\) −5.63758 6.57402i −0.230153 0.268383i
\(601\) 10.7142 0.437041 0.218520 0.975832i \(-0.429877\pi\)
0.218520 + 0.975832i \(0.429877\pi\)
\(602\) 1.10737 22.5564i 0.0451330 0.919331i
\(603\) 27.0335 32.4954i 1.10089 1.32331i
\(604\) 17.3431 + 10.0131i 0.705682 + 0.407426i
\(605\) −0.149326 + 2.43927i −0.00607096 + 0.0991705i
\(606\) −1.17852 + 5.36964i −0.0478739 + 0.218127i
\(607\) −7.07936 26.4205i −0.287342 1.07238i −0.947111 0.320907i \(-0.896012\pi\)
0.659768 0.751469i \(-0.270654\pi\)
\(608\) 1.97948 1.97948i 0.0802784 0.0802784i
\(609\) −7.83591 4.55867i −0.317527 0.184727i
\(610\) −3.38166 16.6260i −0.136919 0.673168i
\(611\) 1.03624 + 0.598274i 0.0419219 + 0.0242036i
\(612\) −9.57634 1.64684i −0.387101 0.0665697i
\(613\) −1.20955 + 4.51412i −0.0488534 + 0.182323i −0.986041 0.166502i \(-0.946753\pi\)
0.937188 + 0.348826i \(0.113419\pi\)
\(614\) −12.3791 + 21.4412i −0.499579 + 0.865297i
\(615\) 26.4837 + 15.8389i 1.06793 + 0.638685i
\(616\) 8.99314 1.94265i 0.362344 0.0782715i
\(617\) 5.85206 + 5.85206i 0.235595 + 0.235595i 0.815023 0.579428i \(-0.196724\pi\)
−0.579428 + 0.815023i \(0.696724\pi\)
\(618\) 3.97881 7.68283i 0.160051 0.309049i
\(619\) −0.702396 + 0.405529i −0.0282317 + 0.0162996i −0.514049 0.857761i \(-0.671855\pi\)
0.485818 + 0.874060i \(0.338522\pi\)
\(620\) 19.8290 + 1.21388i 0.796353 + 0.0487507i
\(621\) 27.9573 11.7886i 1.12189 0.473060i
\(622\) −3.53121 + 3.53121i −0.141588 + 0.141588i
\(623\) 19.0210 + 0.933805i 0.762062 + 0.0374121i
\(624\) 0.585133 0.641278i 0.0234241 0.0256717i
\(625\) −6.88569 24.0330i −0.275428 0.961322i
\(626\) 9.84947 5.68659i 0.393664 0.227282i
\(627\) 14.2015 9.08963i 0.567154 0.363005i
\(628\) −4.57610 + 1.22616i −0.182606 + 0.0489292i
\(629\) 27.1551 1.08274
\(630\) −12.7824 + 12.3130i −0.509262 + 0.490563i
\(631\) 26.9516 1.07293 0.536463 0.843924i \(-0.319760\pi\)
0.536463 + 0.843924i \(0.319760\pi\)
\(632\) 8.34960 2.23727i 0.332129 0.0889938i
\(633\) 15.8704 10.1578i 0.630791 0.403736i
\(634\) 23.2824 13.4421i 0.924661 0.533853i
\(635\) 5.67115 16.9462i 0.225053 0.672490i
\(636\) 7.00912 7.68165i 0.277930 0.304597i
\(637\) 3.46153 0.571739i 0.137151 0.0226531i
\(638\) 4.86443 4.86443i 0.192585 0.192585i
\(639\) −10.7974 4.97945i −0.427140 0.196984i
\(640\) −1.48157 1.67480i −0.0585643 0.0662022i
\(641\) 36.5634 21.1099i 1.44417 0.833791i 0.446043 0.895011i \(-0.352833\pi\)
0.998124 + 0.0612207i \(0.0194993\pi\)
\(642\) −10.9542 + 21.1518i −0.432327 + 0.834796i
\(643\) 0.470316 + 0.470316i 0.0185475 + 0.0185475i 0.716320 0.697772i \(-0.245825\pi\)
−0.697772 + 0.716320i \(0.745825\pi\)
\(644\) −4.72538 + 14.7085i −0.186206 + 0.579596i
\(645\) −32.0605 + 8.06375i −1.26238 + 0.317510i
\(646\) 4.53359 7.85241i 0.178372 0.308949i
\(647\) 6.18342 23.0768i 0.243095 0.907244i −0.731236 0.682125i \(-0.761056\pi\)
0.974331 0.225119i \(-0.0722772\pi\)
\(648\) 8.97207 + 0.708548i 0.352456 + 0.0278344i
\(649\) −13.1548 7.59492i −0.516371 0.298127i
\(650\) 2.30691 0.978929i 0.0904846 0.0383968i
\(651\) 0.134612 40.7133i 0.00527587 1.59568i
\(652\) 4.16086 4.16086i 0.162952 0.162952i
\(653\) 1.57175 + 5.86586i 0.0615075 + 0.229549i 0.989836 0.142211i \(-0.0454211\pi\)
−0.928329 + 0.371760i \(0.878754\pi\)
\(654\) 0.712216 3.24505i 0.0278498 0.126892i
\(655\) 2.09435 + 0.128211i 0.0818330 + 0.00500960i
\(656\) 6.90021 + 3.98384i 0.269408 + 0.155543i
\(657\) 8.80435 + 7.32451i 0.343491 + 0.285756i
\(658\) −5.30866 3.42259i −0.206953 0.133426i
\(659\) 6.09039 0.237248 0.118624 0.992939i \(-0.462152\pi\)
0.118624 + 0.992939i \(0.462152\pi\)
\(660\) −6.55379 11.7661i −0.255106 0.457996i
\(661\) 10.6307 + 18.4129i 0.413485 + 0.716177i 0.995268 0.0971670i \(-0.0309781\pi\)
−0.581783 + 0.813344i \(0.697645\pi\)
\(662\) −6.94623 + 25.9237i −0.269973 + 1.00755i
\(663\) 1.29306 2.49683i 0.0502184 0.0969687i
\(664\) 14.8338i 0.575662i
\(665\) −6.65323 15.1663i −0.258001 0.588125i
\(666\) −25.0464 + 2.29804i −0.970527 + 0.0890471i
\(667\) 2.98969 + 11.1577i 0.115761 + 0.432027i
\(668\) −9.26132 2.48156i −0.358331 0.0960146i
\(669\) 11.5515 + 2.53530i 0.446608 + 0.0980203i
\(670\) 28.1968 14.0565i 1.08934 0.543050i
\(671\) 26.3859i 1.01862i
\(672\) −3.25107 + 3.22964i −0.125413 + 0.124586i
\(673\) 2.29463 + 2.29463i 0.0884515 + 0.0884515i 0.749948 0.661497i \(-0.230078\pi\)
−0.661497 + 0.749948i \(0.730078\pi\)
\(674\) 7.42564 12.8616i 0.286025 0.495410i
\(675\) 22.6918 + 12.6523i 0.873408 + 0.486988i
\(676\) −6.37440 11.0408i −0.245169 0.424645i
\(677\) −30.0603 + 8.05463i −1.15531 + 0.309564i −0.785091 0.619380i \(-0.787384\pi\)
−0.370219 + 0.928944i \(0.620717\pi\)
\(678\) −0.571395 12.4815i −0.0219443 0.479348i
\(679\) −41.5021 13.3333i −1.59271 0.511686i
\(680\) −6.03925 3.99776i −0.231595 0.153307i
\(681\) −6.25344 19.6881i −0.239632 0.754451i
\(682\) 29.8427 + 7.99633i 1.14274 + 0.306195i
\(683\) −22.9706 6.15496i −0.878947 0.235513i −0.208994 0.977917i \(-0.567019\pi\)
−0.669953 + 0.742404i \(0.733686\pi\)
\(684\) −3.51702 + 7.62630i −0.134477 + 0.291599i
\(685\) 8.08082 + 39.7296i 0.308752 + 1.51799i
\(686\) −18.3987 + 2.11847i −0.702466 + 0.0808837i
\(687\) −23.0302 + 1.05431i −0.878656 + 0.0402244i
\(688\) −8.24494 + 2.20923i −0.314336 + 0.0842259i
\(689\) 1.50456 + 2.60597i 0.0573190 + 0.0992795i
\(690\) 22.6122 + 0.348109i 0.860832 + 0.0132523i
\(691\) −4.20725 + 7.28718i −0.160051 + 0.277217i −0.934887 0.354946i \(-0.884499\pi\)
0.774835 + 0.632163i \(0.217833\pi\)
\(692\) 9.43080 + 9.43080i 0.358505 + 0.358505i
\(693\) −23.2967 + 14.8026i −0.884968 + 0.562305i
\(694\) 15.5749i 0.591213i
\(695\) −14.4056 28.8971i −0.546436 1.09613i
\(696\) −0.734541 + 3.34677i −0.0278427 + 0.126859i
\(697\) 24.9277 + 6.67936i 0.944204 + 0.252999i
\(698\) 6.98286 + 26.0604i 0.264305 + 0.986400i
\(699\) 0.244271 + 0.222885i 0.00923917 + 0.00843027i
\(700\) −12.4164 + 4.56422i −0.469297 + 0.172511i
\(701\) 15.9126i 0.601012i −0.953780 0.300506i \(-0.902844\pi\)
0.953780 0.300506i \(-0.0971556\pi\)
\(702\) −0.981354 + 2.41236i −0.0370388 + 0.0910488i
\(703\) 6.07443 22.6701i 0.229102 0.855019i
\(704\) −1.73874 3.01159i −0.0655314 0.113504i
\(705\) −2.53027 + 8.89320i −0.0952956 + 0.334937i
\(706\) −23.4194 −0.881401
\(707\) 7.05781 + 4.55029i 0.265436 + 0.171131i
\(708\) 7.55777 0.345991i 0.284038 0.0130031i
\(709\) 15.6443 + 9.03223i 0.587533 + 0.339213i 0.764122 0.645072i \(-0.223173\pi\)
−0.176588 + 0.984285i \(0.556506\pi\)
\(710\) −5.87212 6.63795i −0.220377 0.249118i
\(711\) −21.1795 + 14.9639i −0.794294 + 0.561191i
\(712\) −1.86296 6.95267i −0.0698175 0.260562i
\(713\) −36.6828 + 36.6828i −1.37378 + 1.37378i
\(714\) −7.46387 + 12.8297i −0.279328 + 0.480138i
\(715\) 3.81912 0.776791i 0.142827 0.0290503i
\(716\) 20.1751 + 11.6481i 0.753978 + 0.435309i
\(717\) −10.7582 + 6.88575i −0.401772 + 0.257153i
\(718\) 4.92610 18.3844i 0.183840 0.686101i
\(719\) 5.34310 9.25452i 0.199264 0.345135i −0.749026 0.662541i \(-0.769478\pi\)
0.948290 + 0.317405i \(0.102812\pi\)
\(720\) 5.90859 + 3.17624i 0.220200 + 0.118372i
\(721\) −8.87573 9.79220i −0.330550 0.364681i
\(722\) 7.89367 + 7.89367i 0.293772 + 0.293772i
\(723\) 22.3733 + 11.5867i 0.832070 + 0.430915i
\(724\) 0.680488 0.392880i 0.0252901 0.0146013i
\(725\) −5.95357 + 7.89886i −0.221110 + 0.293356i
\(726\) −0.573049 1.80417i −0.0212678 0.0669589i
\(727\) −24.1736 + 24.1736i −0.896550 + 0.896550i −0.995129 0.0985796i \(-0.968570\pi\)
0.0985796 + 0.995129i \(0.468570\pi\)
\(728\) −0.605923 1.17953i −0.0224570 0.0437164i
\(729\) −25.9893 + 7.31839i −0.962565 + 0.271052i
\(730\) 3.80849 + 7.63969i 0.140959 + 0.282758i
\(731\) −23.9432 + 13.8236i −0.885570 + 0.511284i
\(732\) 7.08469 + 11.0690i 0.261858 + 0.409123i
\(733\) 8.33762 2.23406i 0.307957 0.0825168i −0.101531 0.994832i \(-0.532374\pi\)
0.409488 + 0.912316i \(0.365707\pi\)
\(734\) 8.95696 0.330607
\(735\) 10.8091 + 24.8629i 0.398699 + 0.917082i
\(736\) 5.83914 0.215234
\(737\) 47.3283 12.6816i 1.74336 0.467132i
\(738\) −23.5572 4.05114i −0.867154 0.149124i
\(739\) −8.19770 + 4.73295i −0.301557 + 0.174104i −0.643142 0.765747i \(-0.722370\pi\)
0.341585 + 0.939851i \(0.389036\pi\)
\(740\) −17.7778 5.94944i −0.653524 0.218706i
\(741\) −1.79519 1.63802i −0.0659481 0.0601743i
\(742\) −7.25815 14.1292i −0.266455 0.518701i
\(743\) −14.3909 + 14.3909i −0.527951 + 0.527951i −0.919961 0.392010i \(-0.871780\pi\)
0.392010 + 0.919961i \(0.371780\pi\)
\(744\) −14.6662 + 4.65836i −0.537690 + 0.170784i
\(745\) −1.24351 + 20.3130i −0.0455585 + 0.744209i
\(746\) 8.37228 4.83374i 0.306531 0.176976i
\(747\) −15.3971 41.7529i −0.563349 1.52766i
\(748\) −7.96448 7.96448i −0.291210 0.291210i
\(749\) 24.4360 + 26.9592i 0.892874 + 0.985068i
\(750\) 11.6842 + 15.4427i 0.426648 + 0.563889i
\(751\) −6.73442 + 11.6644i −0.245742 + 0.425638i −0.962340 0.271848i \(-0.912365\pi\)
0.716598 + 0.697487i \(0.245698\pi\)
\(752\) −0.617891 + 2.30600i −0.0225322 + 0.0840912i
\(753\) 2.61381 + 4.08379i 0.0952527 + 0.148821i
\(754\) −0.858671 0.495754i −0.0312710 0.0180543i
\(755\) −37.3399 24.7177i −1.35894 0.899568i
\(756\) 5.79855 12.4650i 0.210891 0.453349i
\(757\) 18.0263 18.0263i 0.655177 0.655177i −0.299058 0.954235i \(-0.596672\pi\)
0.954235 + 0.299058i \(0.0966724\pi\)
\(758\) −2.49415 9.30828i −0.0905914 0.338092i
\(759\) 34.3526 + 7.53961i 1.24692 + 0.273671i
\(760\) −4.68843 + 4.14752i −0.170067 + 0.150446i
\(761\) −10.1461 5.85784i −0.367795 0.212347i 0.304700 0.952448i \(-0.401444\pi\)
−0.672495 + 0.740102i \(0.734777\pi\)
\(762\) 0.633018 + 13.8275i 0.0229318 + 0.500919i
\(763\) −4.26527 2.74989i −0.154413 0.0995528i
\(764\) 10.3333 0.373845
\(765\) 21.1483 + 4.98399i 0.764619 + 0.180197i
\(766\) 9.79904 + 16.9724i 0.354054 + 0.613239i
\(767\) −0.566629 + 2.11469i −0.0204598 + 0.0763570i
\(768\) 1.53804 + 0.796522i 0.0554991 + 0.0287420i
\(769\) 22.2703i 0.803088i 0.915840 + 0.401544i \(0.131526\pi\)
−0.915840 + 0.401544i \(0.868474\pi\)
\(770\) −20.3371 + 3.10704i −0.732899 + 0.111970i
\(771\) −32.2727 + 35.3693i −1.16227 + 1.27379i
\(772\) 3.18118 + 11.8723i 0.114493 + 0.427294i
\(773\) −19.3977 5.19759i −0.697686 0.186944i −0.107492 0.994206i \(-0.534282\pi\)
−0.590194 + 0.807261i \(0.700949\pi\)
\(774\) 20.9140 14.7764i 0.751740 0.531125i
\(775\) −44.0904 5.41850i −1.58377 0.194638i
\(776\) 16.4760i 0.591453i
\(777\) −10.0664 + 37.0775i −0.361130 + 1.33015i
\(778\) 7.47497 + 7.47497i 0.267991 + 0.267991i
\(779\) 11.1524 19.3165i 0.399575 0.692084i
\(780\) −1.39357 + 1.35131i −0.0498978 + 0.0483848i
\(781\) −6.89140 11.9363i −0.246594 0.427113i
\(782\) 18.2684 4.89499i 0.653275 0.175045i
\(783\) −1.40633 10.1826i −0.0502582 0.363898i
\(784\) 2.88938 + 6.37585i 0.103192 + 0.227709i
\(785\) 10.3809 2.11142i 0.370509 0.0753599i
\(786\) −1.54905 + 0.492017i −0.0552528 + 0.0175497i
\(787\) 16.5702 + 4.43996i 0.590663 + 0.158268i 0.541756 0.840536i \(-0.317760\pi\)
0.0489067 + 0.998803i \(0.484426\pi\)
\(788\) 11.9987 + 3.21503i 0.427435 + 0.114531i
\(789\) 16.0911 5.11094i 0.572859 0.181954i
\(790\) −18.9411 + 3.85253i −0.673893 + 0.137067i
\(791\) −18.1710 5.83777i −0.646086 0.207567i
\(792\) 8.02001 + 6.67200i 0.284979 + 0.237079i
\(793\) −3.67337 + 0.984276i −0.130445 + 0.0349527i
\(794\) −7.83515 13.5709i −0.278059 0.481612i
\(795\) −16.6931 + 16.1869i −0.592044 + 0.574092i
\(796\) −8.09584 + 14.0224i −0.286949 + 0.497011i
\(797\) 26.9706 + 26.9706i 0.955347 + 0.955347i 0.999045 0.0436979i \(-0.0139139\pi\)
−0.0436979 + 0.999045i \(0.513914\pi\)
\(798\) 9.04106 + 9.10105i 0.320050 + 0.322174i
\(799\) 7.73254i 0.273558i
\(800\) 3.07788 + 3.94039i 0.108819 + 0.139314i
\(801\) 12.4604 + 17.6361i 0.440266 + 0.623140i
\(802\) −25.0551 6.71350i −0.884728 0.237062i
\(803\) 3.43597 + 12.8232i 0.121253 + 0.452522i
\(804\) −16.4495 + 18.0278i −0.580128 + 0.635792i
\(805\) 12.5562 32.1821i 0.442546 1.13427i
\(806\) 4.45291i 0.156847i
\(807\) 31.6523 + 16.3922i 1.11421 + 0.577032i
\(808\) 0.821480 3.06580i 0.0288996 0.107855i
\(809\) −4.15287 7.19297i −0.146007 0.252891i 0.783741 0.621088i \(-0.213309\pi\)
−0.929748 + 0.368196i \(0.879976\pi\)
\(810\) −19.9279 2.80726i −0.700193 0.0986370i
\(811\) −17.0386 −0.598306 −0.299153 0.954205i \(-0.596704\pi\)
−0.299153 + 0.954205i \(0.596704\pi\)
\(812\) 4.39897 + 2.83609i 0.154373 + 0.0995273i
\(813\) 1.82813 + 39.9334i 0.0641154 + 1.40053i
\(814\) −25.2488 14.5774i −0.884969 0.510937i
\(815\) −9.85508 + 8.71808i −0.345208 + 0.305381i
\(816\) 5.47963 + 1.20266i 0.191826 + 0.0421014i
\(817\) 6.18451 + 23.0809i 0.216369 + 0.807499i
\(818\) −4.26617 + 4.26617i −0.149163 + 0.149163i
\(819\) 2.92982 + 2.69112i 0.102376 + 0.0940353i
\(820\) −14.8562 9.83427i −0.518801 0.343428i
\(821\) −9.60555 5.54577i −0.335236 0.193549i 0.322927 0.946424i \(-0.395333\pi\)
−0.658163 + 0.752875i \(0.728666\pi\)
\(822\) −16.9296 26.4506i −0.590488 0.922570i
\(823\) 10.1745 37.9719i 0.354662 1.32362i −0.526247 0.850332i \(-0.676401\pi\)
0.880909 0.473285i \(-0.156932\pi\)
\(824\) −2.49761 + 4.32599i −0.0870084 + 0.150703i
\(825\) 13.0197 + 27.1561i 0.453288 + 0.945455i
\(826\) 3.53488 11.0029i 0.122994 0.382840i
\(827\) −12.4819 12.4819i −0.434037 0.434037i 0.455962 0.889999i \(-0.349295\pi\)
−0.889999 + 0.455962i \(0.849295\pi\)
\(828\) −16.4355 + 6.06087i −0.571174 + 0.210630i
\(829\) −9.94204 + 5.74004i −0.345301 + 0.199360i −0.662614 0.748961i \(-0.730553\pi\)
0.317313 + 0.948321i \(0.397220\pi\)
\(830\) 2.02675 33.1074i 0.0703494 1.14917i
\(831\) 12.1147 3.84793i 0.420255 0.133483i
\(832\) −0.354405 + 0.354405i −0.0122868 + 0.0122868i
\(833\) 14.3846 + 17.5253i 0.498398 + 0.607217i
\(834\) 18.4756 + 16.8580i 0.639756 + 0.583745i
\(835\) 20.3312 + 6.80396i 0.703590 + 0.235461i
\(836\) −8.43066 + 4.86744i −0.291581 + 0.168344i
\(837\) 36.4460 28.3351i 1.25976 0.979404i
\(838\) −3.31045 + 0.887033i −0.114358 + 0.0306421i
\(839\) 44.5591 1.53835 0.769176 0.639037i \(-0.220667\pi\)
0.769176 + 0.639037i \(0.220667\pi\)
\(840\) 7.69729 6.76400i 0.265582 0.233380i
\(841\) −25.0865 −0.865053
\(842\) 11.8066 3.16357i 0.406883 0.109024i
\(843\) 6.65015 + 10.3901i 0.229043 + 0.357854i
\(844\) −9.42139 + 5.43944i −0.324297 + 0.187233i
\(845\) 12.7184 + 25.5127i 0.437528 + 0.877665i
\(846\) −0.654378 7.13208i −0.0224980 0.245206i
\(847\) −2.88811 0.141787i −0.0992366 0.00487185i
\(848\) −4.24530 + 4.24530i −0.145784 + 0.145784i
\(849\) 6.51795 + 20.5209i 0.223695 + 0.704275i
\(850\) 12.9327 + 9.74772i 0.443589 + 0.334344i
\(851\) 42.3959 24.4773i 1.45331 0.839070i
\(852\) 6.09591 + 3.15697i 0.208842 + 0.108156i
\(853\) −7.83980 7.83980i −0.268430 0.268430i 0.560037 0.828467i \(-0.310787\pi\)
−0.828467 + 0.560037i \(0.810787\pi\)
\(854\) 19.6224 4.23872i 0.671464 0.145046i
\(855\) 8.89159 16.5405i 0.304086 0.565674i
\(856\) 6.87625 11.9100i 0.235025 0.407076i
\(857\) −6.67783 + 24.9220i −0.228110 + 0.851319i 0.753024 + 0.657993i \(0.228594\pi\)
−0.981134 + 0.193327i \(0.938072\pi\)
\(858\) −2.54263 + 1.62741i −0.0868041 + 0.0555587i
\(859\) 26.5807 + 15.3464i 0.906923 + 0.523612i 0.879440 0.476010i \(-0.157917\pi\)
0.0274833 + 0.999622i \(0.491251\pi\)
\(860\) 18.7037 3.80424i 0.637789 0.129723i
\(861\) −18.3607 + 31.5602i −0.625731 + 1.07557i
\(862\) −4.19371 + 4.19371i −0.142838 + 0.142838i
\(863\) 4.61920 + 17.2391i 0.157240 + 0.586826i 0.998903 + 0.0468238i \(0.0149099\pi\)
−0.841664 + 0.540002i \(0.818423\pi\)
\(864\) −5.15590 0.645543i −0.175407 0.0219618i
\(865\) −19.7600 22.3370i −0.671859 0.759482i
\(866\) −7.61601 4.39710i −0.258802 0.149420i
\(867\) −11.2623 + 0.515580i −0.382486 + 0.0175100i
\(868\) −1.15260 + 23.4777i −0.0391217 + 0.796884i
\(869\) −30.0599 −1.01971
\(870\) 2.09668 7.36926i 0.0710843 0.249841i
\(871\) −3.53099 6.11586i −0.119643 0.207228i
\(872\) −0.496447 + 1.85277i −0.0168118 + 0.0627426i
\(873\) −17.1016 46.3752i −0.578802 1.56956i
\(874\) 16.3461i 0.552916i
\(875\) 28.3357 8.49037i 0.957923 0.287027i
\(876\) −4.88449 4.45685i −0.165032 0.150583i
\(877\) −0.581994 2.17203i −0.0196525 0.0733443i 0.955403 0.295305i \(-0.0954211\pi\)
−0.975056 + 0.221960i \(0.928754\pi\)
\(878\) 2.67306 + 0.716244i 0.0902113 + 0.0241720i
\(879\) −2.10631 + 9.59693i −0.0710441 + 0.323696i
\(880\) 3.46921 + 6.95911i 0.116947 + 0.234591i
\(881\) 38.0258i 1.28112i 0.767908 + 0.640560i \(0.221298\pi\)
−0.767908 + 0.640560i \(0.778702\pi\)
\(882\) −14.7507 14.9471i −0.496683 0.503295i
\(883\) −37.1733 37.1733i −1.25098 1.25098i −0.955281 0.295701i \(-0.904447\pi\)
−0.295701 0.955281i \(-0.595553\pi\)
\(884\) −0.811693 + 1.40589i −0.0273002 + 0.0472853i
\(885\) −16.9154 0.260408i −0.568604 0.00875351i
\(886\) −12.1035 20.9639i −0.406626 0.704296i
\(887\) −18.9826 + 5.08637i −0.637373 + 0.170783i −0.563013 0.826448i \(-0.690358\pi\)
−0.0743596 + 0.997231i \(0.523691\pi\)
\(888\) 14.5061 0.664081i 0.486792 0.0222851i
\(889\) 20.1307 + 6.46735i 0.675161 + 0.216908i
\(890\) 3.20798 + 15.7721i 0.107532 + 0.528683i
\(891\) −29.4994 10.4552i −0.988267 0.350263i
\(892\) −6.59536 1.76722i −0.220829 0.0591709i
\(893\) 6.45542 + 1.72973i 0.216023 + 0.0578831i
\(894\) −4.77204 15.0242i −0.159601 0.502483i
\(895\) −43.4371 28.7538i −1.45194 0.961133i
\(896\) 1.96031 1.77684i 0.0654895 0.0593602i
\(897\) −0.231815 5.06372i −0.00774007 0.169073i
\(898\) 5.93580 1.59049i 0.198080 0.0530754i
\(899\) 8.78780 + 15.2209i 0.293089 + 0.507646i
\(900\) −12.7534 7.89632i −0.425112 0.263211i
\(901\) −9.72301 + 16.8407i −0.323920 + 0.561046i
\(902\) −19.5922 19.5922i −0.652348 0.652348i
\(903\) −9.99897 37.8163i −0.332745 1.25845i
\(904\) 7.21372i 0.239925i
\(905\) −1.57245 + 0.783889i −0.0522701 + 0.0260573i
\(906\) 33.8799 + 7.43587i 1.12558 + 0.247040i
\(907\) −11.6626 3.12499i −0.387251 0.103764i 0.0599403 0.998202i \(-0.480909\pi\)
−0.447191 + 0.894438i \(0.647576\pi\)
\(908\) 3.08682 + 11.5202i 0.102440 + 0.382310i
\(909\) 0.869989 + 9.48203i 0.0288557 + 0.314499i
\(910\) 1.19119 + 2.71538i 0.0394876 + 0.0900139i
\(911\) 29.5439i 0.978834i 0.872050 + 0.489417i \(0.162790\pi\)
−0.872050 + 0.489417i \(0.837210\pi\)
\(912\) 2.22979 4.30558i 0.0738356 0.142572i
\(913\) 13.3510 49.8266i 0.441853 1.64902i
\(914\) −5.47652 9.48561i −0.181147 0.313756i
\(915\) −14.2999 25.6728i −0.472740 0.848718i
\(916\) 13.3104 0.439788
\(917\) −0.121738 + 2.47972i −0.00402013 + 0.0818876i
\(918\) −16.6719 + 2.30258i −0.550256 + 0.0759963i
\(919\) 38.4441 + 22.1957i 1.26816 + 0.732170i 0.974639 0.223784i \(-0.0718412\pi\)
0.293516 + 0.955954i \(0.405174\pi\)
\(920\) −13.0323 0.797805i −0.429663 0.0263028i
\(921\) −9.19291 + 41.8855i −0.302917 + 1.38017i
\(922\) 0.00100191 + 0.00373918i 3.29961e−5 + 0.000123143i
\(923\) −1.40466 + 1.40466i −0.0462350 + 0.0462350i
\(924\) 13.8271 7.92225i 0.454879 0.260623i
\(925\) 38.8652 + 15.7075i 1.27788 + 0.516459i
\(926\) −34.0896 19.6816i −1.12025 0.646778i
\(927\) 2.53980 14.7689i 0.0834181 0.485074i
\(928\) 0.512009 1.91084i 0.0168075 0.0627265i
\(929\) −20.6408 + 35.7508i −0.677201 + 1.17295i 0.298619 + 0.954372i \(0.403474\pi\)
−0.975820 + 0.218575i \(0.929859\pi\)
\(930\) 33.3699 8.39309i 1.09424 0.275220i
\(931\) 17.8486 8.08853i 0.584964 0.265091i
\(932\) −0.134997 0.134997i −0.00442199 0.00442199i
\(933\) −3.97774 + 7.68076i −0.130225 + 0.251457i
\(934\) −8.98915 + 5.18989i −0.294134 + 0.169818i
\(935\) 16.6877 + 18.8640i 0.545745 + 0.616920i
\(936\) 0.629686 1.36541i 0.0205819 0.0446299i
\(937\) −6.68894 + 6.68894i −0.218518 + 0.218518i −0.807874 0.589356i \(-0.799382\pi\)
0.589356 + 0.807874i \(0.299382\pi\)
\(938\) 17.0339 + 33.1594i 0.556177 + 1.08269i
\(939\) 13.2777 14.5517i 0.433300 0.474876i
\(940\) 1.69413 5.06231i 0.0552566 0.165115i
\(941\) 11.8432 6.83768i 0.386078 0.222902i −0.294382 0.955688i \(-0.595114\pi\)
0.680459 + 0.732786i \(0.261780\pi\)
\(942\) −6.91122 + 4.42351i −0.225180 + 0.144126i
\(943\) 44.9391 12.0414i 1.46342 0.392122i
\(944\) −4.36805 −0.142168
\(945\) −14.6448 + 27.0283i −0.476396 + 0.879231i
\(946\) 29.6831 0.965081
\(947\) −8.01700 + 2.14815i −0.260517 + 0.0698054i −0.386714 0.922200i \(-0.626390\pi\)
0.126196 + 0.992005i \(0.459723\pi\)
\(948\) 12.6103 8.07118i 0.409564 0.262140i
\(949\) 1.65704 0.956694i 0.0537899 0.0310556i
\(950\) 11.0307 8.61622i 0.357884 0.279547i
\(951\) 31.3860 34.3975i 1.01776 1.11542i
\(952\) 4.64350 7.20239i 0.150497 0.233431i
\(953\) 27.8231 27.8231i 0.901277 0.901277i −0.0942697 0.995547i \(-0.530052\pi\)
0.995547 + 0.0942697i \(0.0300516\pi\)
\(954\) 7.54281 16.3558i 0.244207 0.529539i
\(955\) −23.0627 1.41184i −0.746292 0.0456861i
\(956\) 6.38655 3.68728i 0.206556 0.119255i
\(957\) 5.47955 10.5807i 0.177129 0.342024i
\(958\) 4.01724 + 4.01724i 0.129791 + 0.129791i
\(959\) −46.8897 + 10.1288i −1.51415 + 0.327078i
\(960\) −3.32390 1.98789i −0.107278 0.0641589i
\(961\) −23.9664 + 41.5110i −0.773110 + 1.33907i
\(962\) −1.08756 + 4.05885i −0.0350645 + 0.130862i
\(963\) −6.99241 + 40.6606i −0.225327 + 1.31027i
\(964\) −12.5978 7.27332i −0.405747 0.234258i
\(965\) −5.47792 26.9324i −0.176341 0.866984i
\(966\) −0.0884717 + 26.7582i −0.00284653 + 0.860930i
\(967\) 18.6189 18.6189i 0.598743 0.598743i −0.341235 0.939978i \(-0.610845\pi\)
0.939978 + 0.341235i \(0.110845\pi\)
\(968\) 0.282868 + 1.05568i 0.00909172 + 0.0339308i
\(969\) 3.36672 15.3397i 0.108155 0.492782i
\(970\) 2.25112 36.7726i 0.0722791 1.18070i
\(971\) −43.2885 24.9926i −1.38920 0.802052i −0.395971 0.918263i \(-0.629592\pi\)
−0.993225 + 0.116211i \(0.962925\pi\)
\(972\) 15.1824 3.53466i 0.486977 0.113374i
\(973\) 33.9830 17.4570i 1.08945 0.559645i
\(974\) 6.76997 0.216924
\(975\) 3.29493 2.82558i 0.105522 0.0904910i
\(976\) −3.79381 6.57108i −0.121437 0.210335i
\(977\) 1.11603 4.16509i 0.0357050 0.133253i −0.945773 0.324829i \(-0.894693\pi\)
0.981478 + 0.191576i \(0.0613599\pi\)
\(978\) 4.68701 9.05033i 0.149874 0.289398i
\(979\) 25.0307i 0.799985i
\(980\) −5.57763 14.6250i −0.178171 0.467178i
\(981\) −0.525763 5.73031i −0.0167863 0.182955i
\(982\) −2.92288 10.9083i −0.0932728 0.348099i
\(983\) 2.36044 + 0.632479i 0.0752865 + 0.0201730i 0.296266 0.955106i \(-0.404259\pi\)
−0.220979 + 0.975279i \(0.570925\pi\)
\(984\) 13.4796 + 2.95846i 0.429713 + 0.0943124i
\(985\) −26.3404 8.81498i −0.839275 0.280869i
\(986\) 6.40749i 0.204056i
\(987\) −10.5580 2.86646i −0.336065 0.0912403i
\(988\) 0.992123 + 0.992123i 0.0315636 + 0.0315636i
\(989\) −24.9209 + 43.1642i −0.792437 + 1.37254i
\(990\) −16.9882 15.9870i −0.539920 0.508099i
\(991\) 17.2356 + 29.8529i 0.547506 + 0.948309i 0.998445 + 0.0557538i \(0.0177562\pi\)
−0.450938 + 0.892555i \(0.648910\pi\)
\(992\) 8.58169 2.29946i 0.272469 0.0730078i
\(993\) 2.12584 + 46.4365i 0.0674614 + 1.47362i
\(994\) 7.76958 7.04241i 0.246436 0.223372i
\(995\) 19.9849 30.1903i 0.633564 0.957097i
\(996\) 7.77778 + 24.4873i 0.246449 + 0.775911i
\(997\) −53.4053 14.3099i −1.69136 0.453199i −0.720622 0.693328i \(-0.756144\pi\)
−0.970741 + 0.240129i \(0.922810\pi\)
\(998\) −3.14690 0.843210i −0.0996135 0.0266913i
\(999\) −40.1412 + 16.9261i −1.27001 + 0.535518i
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 210.2.x.a.23.2 64
3.2 odd 2 inner 210.2.x.a.23.14 yes 64
5.2 odd 4 inner 210.2.x.a.107.5 yes 64
7.4 even 3 inner 210.2.x.a.53.15 yes 64
15.2 even 4 inner 210.2.x.a.107.15 yes 64
21.11 odd 6 inner 210.2.x.a.53.5 yes 64
35.32 odd 12 inner 210.2.x.a.137.14 yes 64
105.32 even 12 inner 210.2.x.a.137.2 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.x.a.23.2 64 1.1 even 1 trivial
210.2.x.a.23.14 yes 64 3.2 odd 2 inner
210.2.x.a.53.5 yes 64 21.11 odd 6 inner
210.2.x.a.53.15 yes 64 7.4 even 3 inner
210.2.x.a.107.5 yes 64 5.2 odd 4 inner
210.2.x.a.107.15 yes 64 15.2 even 4 inner
210.2.x.a.137.2 yes 64 105.32 even 12 inner
210.2.x.a.137.14 yes 64 35.32 odd 12 inner