Properties

Label 429.2.bv.a.20.10
Level $429$
Weight $2$
Character 429.20
Analytic conductor $3.426$
Analytic rank $0$
Dimension $832$
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] = [429,2,Mod(20,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(60))
 
chi = DirichletCharacter(H, H._module([30, 36, 55]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.20");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.bv (of order \(60\), degree \(16\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(832\)
Relative dimension: \(52\) over \(\Q(\zeta_{60})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label 20.10
Character \(\chi\) \(=\) 429.20
Dual form 429.2.bv.a.236.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.99540 - 0.104575i) q^{2} +(1.06644 + 1.36481i) q^{3} +(1.98165 + 0.208280i) q^{4} +(-2.39161 - 1.21859i) q^{5} +(-1.98525 - 2.83487i) q^{6} +(-0.280750 - 0.346697i) q^{7} +(0.0146712 + 0.00232369i) q^{8} +(-0.725421 + 2.91097i) q^{9} +O(q^{10})\) \(q+(-1.99540 - 0.104575i) q^{2} +(1.06644 + 1.36481i) q^{3} +(1.98165 + 0.208280i) q^{4} +(-2.39161 - 1.21859i) q^{5} +(-1.98525 - 2.83487i) q^{6} +(-0.280750 - 0.346697i) q^{7} +(0.0146712 + 0.00232369i) q^{8} +(-0.725421 + 2.91097i) q^{9} +(4.64480 + 2.68168i) q^{10} +(-2.03583 - 2.61828i) q^{11} +(1.82904 + 2.92670i) q^{12} +(3.56305 + 0.551950i) q^{13} +(0.523954 + 0.721160i) q^{14} +(-0.887364 - 4.56365i) q^{15} +(-3.92708 - 0.834726i) q^{16} +(0.551154 - 0.612119i) q^{17} +(1.75192 - 5.73270i) q^{18} +(-1.63336 - 4.25506i) q^{19} +(-4.48554 - 2.91294i) q^{20} +(0.173774 - 0.752902i) q^{21} +(3.78850 + 5.43741i) q^{22} +(4.15235 - 7.19209i) q^{23} +(0.0124745 + 0.0225015i) q^{24} +(1.29594 + 1.78370i) q^{25} +(-7.05201 - 1.47397i) q^{26} +(-4.74655 + 2.11431i) q^{27} +(-0.484138 - 0.745508i) q^{28} +(2.65777 + 5.96945i) q^{29} +(1.29341 + 9.19912i) q^{30} +(4.57729 - 2.33224i) q^{31} +(7.72012 + 2.06860i) q^{32} +(1.40236 - 5.57076i) q^{33} +(-1.16379 + 1.16379i) q^{34} +(0.248964 + 1.17129i) q^{35} +(-2.04383 + 5.61744i) q^{36} +(1.78250 - 4.64358i) q^{37} +(2.81425 + 8.66136i) q^{38} +(3.04647 + 5.45152i) q^{39} +(-0.0322562 - 0.0234355i) q^{40} +(3.57022 + 2.89111i) q^{41} +(-0.425484 + 1.48417i) q^{42} +(7.29386 - 4.21111i) q^{43} +(-3.48898 - 5.61253i) q^{44} +(5.28221 - 6.07794i) q^{45} +(-9.03772 + 13.9169i) q^{46} +(-5.83595 - 0.924323i) q^{47} +(-3.04874 - 6.24991i) q^{48} +(1.41400 - 6.65236i) q^{49} +(-2.39938 - 3.69472i) q^{50} +(1.42320 + 0.0994351i) q^{51} +(6.94577 + 1.83588i) q^{52} +(-7.27331 - 2.36324i) q^{53} +(9.69237 - 3.72253i) q^{54} +(1.67833 + 8.74275i) q^{55} +(-0.00331332 - 0.00573884i) q^{56} +(4.06547 - 6.76699i) q^{57} +(-4.67907 - 12.1894i) q^{58} +(11.4235 - 9.25061i) q^{59} +(-0.807929 - 9.22838i) q^{60} +(4.79430 - 5.32460i) q^{61} +(-9.37742 + 4.17510i) q^{62} +(1.21289 - 0.565754i) q^{63} +(-7.55179 - 2.45372i) q^{64} +(-7.84885 - 5.66195i) q^{65} +(-3.38084 + 10.9693i) q^{66} +(-3.11297 + 0.834117i) q^{67} +(1.21969 - 1.09821i) q^{68} +(14.2441 - 2.00273i) q^{69} +(-0.374297 - 2.36322i) q^{70} +(0.256322 + 4.89091i) q^{71} +(-0.0174070 + 0.0410218i) q^{72} +(-7.96795 + 1.26200i) q^{73} +(-4.04241 + 9.07941i) q^{74} +(-1.05238 + 3.67091i) q^{75} +(-2.35051 - 8.77224i) q^{76} +(-0.336190 + 1.44090i) q^{77} +(-5.50884 - 11.1966i) q^{78} +(-0.755592 + 2.32547i) q^{79} +(8.37487 + 6.78184i) q^{80} +(-7.94753 - 4.22336i) q^{81} +(-6.82170 - 6.14228i) q^{82} +(8.74621 + 4.45642i) q^{83} +(0.501174 - 1.45580i) q^{84} +(-2.06407 + 0.792322i) q^{85} +(-14.9946 + 7.64011i) q^{86} +(-5.31283 + 9.99340i) q^{87} +(-0.0237841 - 0.0431439i) q^{88} +(-8.18563 + 2.19333i) q^{89} +(-11.1757 + 11.5755i) q^{90} +(-0.808968 - 1.39026i) q^{91} +(9.72648 - 13.3874i) q^{92} +(8.06447 + 3.75994i) q^{93} +(11.5484 + 2.45469i) q^{94} +(-1.27879 + 12.1669i) q^{95} +(5.40978 + 12.7425i) q^{96} +(-12.5445 - 8.14648i) q^{97} +(-3.51717 + 13.1263i) q^{98} +(9.09857 - 4.02691i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 832 q - 6 q^{3} - 36 q^{4} - 4 q^{6} - 24 q^{7} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 832 q - 6 q^{3} - 36 q^{4} - 4 q^{6} - 24 q^{7} - 6 q^{9} - 96 q^{10} - 40 q^{13} + 12 q^{15} - 68 q^{16} - 20 q^{18} - 32 q^{19} - 84 q^{21} - 24 q^{22} - 72 q^{24} - 114 q^{30} - 8 q^{31} + 14 q^{33} - 24 q^{34} + 78 q^{36} - 24 q^{37} - 72 q^{39} - 112 q^{40} + 2 q^{42} - 96 q^{43} + 4 q^{45} - 16 q^{46} + 14 q^{48} - 36 q^{49} + 8 q^{52} + 32 q^{54} - 24 q^{55} - 12 q^{57} + 112 q^{58} - 120 q^{60} + 12 q^{61} + 28 q^{63} - 300 q^{66} - 32 q^{67} - 18 q^{69} - 140 q^{70} + 204 q^{72} - 24 q^{73} + 66 q^{75} + 176 q^{76} - 28 q^{78} - 224 q^{79} - 58 q^{81} - 264 q^{82} + 20 q^{84} - 168 q^{85} + 72 q^{87} - 120 q^{88} - 146 q^{93} - 4 q^{94} - 10 q^{96} - 88 q^{97} + 40 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{3}{5}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.99540 0.104575i −1.41096 0.0739454i −0.668440 0.743766i \(-0.733038\pi\)
−0.742523 + 0.669821i \(0.766371\pi\)
\(3\) 1.06644 + 1.36481i 0.615708 + 0.787974i
\(4\) 1.98165 + 0.208280i 0.990825 + 0.104140i
\(5\) −2.39161 1.21859i −1.06956 0.544969i −0.171657 0.985157i \(-0.554912\pi\)
−0.897906 + 0.440188i \(0.854912\pi\)
\(6\) −1.98525 2.83487i −0.810474 1.15733i
\(7\) −0.280750 0.346697i −0.106114 0.131039i 0.721322 0.692600i \(-0.243535\pi\)
−0.827436 + 0.561560i \(0.810201\pi\)
\(8\) 0.0146712 + 0.00232369i 0.00518705 + 0.000821548i
\(9\) −0.725421 + 2.91097i −0.241807 + 0.970324i
\(10\) 4.64480 + 2.68168i 1.46881 + 0.848020i
\(11\) −2.03583 2.61828i −0.613827 0.789440i
\(12\) 1.82904 + 2.92670i 0.528000 + 0.844865i
\(13\) 3.56305 + 0.551950i 0.988213 + 0.153083i
\(14\) 0.523954 + 0.721160i 0.140032 + 0.192738i
\(15\) −0.887364 4.56365i −0.229116 1.17833i
\(16\) −3.92708 0.834726i −0.981770 0.208682i
\(17\) 0.551154 0.612119i 0.133675 0.148461i −0.672591 0.740014i \(-0.734819\pi\)
0.806265 + 0.591554i \(0.201485\pi\)
\(18\) 1.75192 5.73270i 0.412932 1.35121i
\(19\) −1.63336 4.25506i −0.374719 0.976177i −0.983187 0.182599i \(-0.941549\pi\)
0.608468 0.793578i \(-0.291784\pi\)
\(20\) −4.48554 2.91294i −1.00300 0.651354i
\(21\) 0.173774 0.752902i 0.0379206 0.164297i
\(22\) 3.78850 + 5.43741i 0.807712 + 1.15926i
\(23\) 4.15235 7.19209i 0.865825 1.49965i −0.000399713 1.00000i \(-0.500127\pi\)
0.866225 0.499654i \(-0.166539\pi\)
\(24\) 0.0124745 + 0.0225015i 0.00254635 + 0.00459310i
\(25\) 1.29594 + 1.78370i 0.259187 + 0.356740i
\(26\) −7.05201 1.47397i −1.38301 0.289069i
\(27\) −4.74655 + 2.11431i −0.913473 + 0.406899i
\(28\) −0.484138 0.745508i −0.0914936 0.140888i
\(29\) 2.65777 + 5.96945i 0.493536 + 1.10850i 0.972972 + 0.230923i \(0.0741744\pi\)
−0.479437 + 0.877577i \(0.659159\pi\)
\(30\) 1.29341 + 9.19912i 0.236143 + 1.67952i
\(31\) 4.57729 2.33224i 0.822105 0.418883i 0.00826031 0.999966i \(-0.497371\pi\)
0.813845 + 0.581082i \(0.197371\pi\)
\(32\) 7.72012 + 2.06860i 1.36474 + 0.365680i
\(33\) 1.40236 5.57076i 0.244120 0.969745i
\(34\) −1.16379 + 1.16379i −0.199588 + 0.199588i
\(35\) 0.248964 + 1.17129i 0.0420827 + 0.197983i
\(36\) −2.04383 + 5.61744i −0.340638 + 0.936240i
\(37\) 1.78250 4.64358i 0.293042 0.763400i −0.705464 0.708746i \(-0.749261\pi\)
0.998505 0.0546538i \(-0.0174055\pi\)
\(38\) 2.81425 + 8.66136i 0.456531 + 1.40506i
\(39\) 3.04647 + 5.45152i 0.487825 + 0.872941i
\(40\) −0.0322562 0.0234355i −0.00510016 0.00370548i
\(41\) 3.57022 + 2.89111i 0.557575 + 0.451516i 0.866221 0.499662i \(-0.166542\pi\)
−0.308645 + 0.951177i \(0.599876\pi\)
\(42\) −0.425484 + 1.48417i −0.0656536 + 0.229012i
\(43\) 7.29386 4.21111i 1.11230 0.642188i 0.172878 0.984943i \(-0.444693\pi\)
0.939425 + 0.342755i \(0.111360\pi\)
\(44\) −3.48898 5.61253i −0.525983 0.846121i
\(45\) 5.28221 6.07794i 0.787425 0.906045i
\(46\) −9.03772 + 13.9169i −1.33254 + 2.05193i
\(47\) −5.83595 0.924323i −0.851260 0.134826i −0.284466 0.958686i \(-0.591816\pi\)
−0.566794 + 0.823860i \(0.691816\pi\)
\(48\) −3.04874 6.24991i −0.440048 0.902096i
\(49\) 1.41400 6.65236i 0.202000 0.950338i
\(50\) −2.39938 3.69472i −0.339324 0.522513i
\(51\) 1.42320 + 0.0994351i 0.199288 + 0.0139237i
\(52\) 6.94577 + 1.83588i 0.963205 + 0.254591i
\(53\) −7.27331 2.36324i −0.999066 0.324616i −0.236574 0.971614i \(-0.576025\pi\)
−0.762492 + 0.646997i \(0.776025\pi\)
\(54\) 9.69237 3.72253i 1.31896 0.506572i
\(55\) 1.67833 + 8.74275i 0.226306 + 1.17887i
\(56\) −0.00331332 0.00573884i −0.000442761 0.000766885i
\(57\) 4.06547 6.76699i 0.538485 0.896310i
\(58\) −4.67907 12.1894i −0.614392 1.60055i
\(59\) 11.4235 9.25061i 1.48722 1.20433i 0.560733 0.827996i \(-0.310519\pi\)
0.926486 0.376330i \(-0.122814\pi\)
\(60\) −0.807929 9.22838i −0.104303 1.19138i
\(61\) 4.79430 5.32460i 0.613847 0.681746i −0.353433 0.935460i \(-0.614986\pi\)
0.967279 + 0.253714i \(0.0816523\pi\)
\(62\) −9.37742 + 4.17510i −1.19093 + 0.530238i
\(63\) 1.21289 0.565754i 0.152810 0.0712783i
\(64\) −7.55179 2.45372i −0.943973 0.306716i
\(65\) −7.84885 5.66195i −0.973530 0.702278i
\(66\) −3.38084 + 10.9693i −0.416153 + 1.35022i
\(67\) −3.11297 + 0.834117i −0.380309 + 0.101904i −0.443909 0.896072i \(-0.646409\pi\)
0.0635996 + 0.997975i \(0.479742\pi\)
\(68\) 1.21969 1.09821i 0.147909 0.133178i
\(69\) 14.2441 2.00273i 1.71478 0.241101i
\(70\) −0.374297 2.36322i −0.0447371 0.282459i
\(71\) 0.256322 + 4.89091i 0.0304198 + 0.580445i 0.970737 + 0.240145i \(0.0771951\pi\)
−0.940317 + 0.340299i \(0.889472\pi\)
\(72\) −0.0174070 + 0.0410218i −0.00205143 + 0.00483447i
\(73\) −7.96795 + 1.26200i −0.932578 + 0.147706i −0.604193 0.796838i \(-0.706504\pi\)
−0.328385 + 0.944544i \(0.606504\pi\)
\(74\) −4.04241 + 9.07941i −0.469921 + 1.05546i
\(75\) −1.05238 + 3.67091i −0.121519 + 0.423881i
\(76\) −2.35051 8.77224i −0.269622 1.00624i
\(77\) −0.336190 + 1.44090i −0.0383124 + 0.164206i
\(78\) −5.50884 11.1966i −0.623753 1.26776i
\(79\) −0.755592 + 2.32547i −0.0850108 + 0.261636i −0.984522 0.175262i \(-0.943923\pi\)
0.899511 + 0.436898i \(0.143923\pi\)
\(80\) 8.37487 + 6.78184i 0.936339 + 0.758232i
\(81\) −7.94753 4.22336i −0.883059 0.469263i
\(82\) −6.82170 6.14228i −0.753330 0.678302i
\(83\) 8.74621 + 4.45642i 0.960021 + 0.489155i 0.862488 0.506077i \(-0.168905\pi\)
0.0975330 + 0.995232i \(0.468905\pi\)
\(84\) 0.501174 1.45580i 0.0546826 0.158840i
\(85\) −2.06407 + 0.792322i −0.223880 + 0.0859394i
\(86\) −14.9946 + 7.64011i −1.61690 + 0.823854i
\(87\) −5.31283 + 9.99340i −0.569595 + 1.07141i
\(88\) −0.0237841 0.0431439i −0.00253539 0.00459916i
\(89\) −8.18563 + 2.19333i −0.867675 + 0.232493i −0.665082 0.746770i \(-0.731603\pi\)
−0.202593 + 0.979263i \(0.564937\pi\)
\(90\) −11.1757 + 11.5755i −1.17802 + 1.22017i
\(91\) −0.808968 1.39026i −0.0848029 0.145739i
\(92\) 9.72648 13.3874i 1.01406 1.39573i
\(93\) 8.06447 + 3.75994i 0.836246 + 0.389888i
\(94\) 11.5484 + 2.45469i 1.19113 + 0.253182i
\(95\) −1.27879 + 12.1669i −0.131201 + 1.24829i
\(96\) 5.40978 + 12.7425i 0.552133 + 1.30053i
\(97\) −12.5445 8.14648i −1.27370 0.827150i −0.282466 0.959277i \(-0.591152\pi\)
−0.991233 + 0.132128i \(0.957819\pi\)
\(98\) −3.51717 + 13.1263i −0.355288 + 1.32595i
\(99\) 9.09857 4.02691i 0.914441 0.404719i
\(100\) 2.19658 + 3.80459i 0.219658 + 0.380459i
\(101\) −0.807796 0.897149i −0.0803787 0.0892696i 0.701614 0.712557i \(-0.252463\pi\)
−0.781993 + 0.623288i \(0.785797\pi\)
\(102\) −2.82946 0.347243i −0.280158 0.0343822i
\(103\) −8.91242 + 12.2669i −0.878167 + 1.20869i 0.0987588 + 0.995111i \(0.468513\pi\)
−0.976925 + 0.213581i \(0.931487\pi\)
\(104\) 0.0509917 + 0.0163772i 0.00500015 + 0.00160592i
\(105\) −1.33308 + 1.58889i −0.130095 + 0.155060i
\(106\) 14.2660 + 5.47622i 1.38564 + 0.531898i
\(107\) −1.01530 + 0.106712i −0.0981525 + 0.0103162i −0.153477 0.988152i \(-0.549047\pi\)
0.0553249 + 0.998468i \(0.482381\pi\)
\(108\) −9.84636 + 3.20121i −0.947467 + 0.308037i
\(109\) 0.0313750 + 0.0313750i 0.00300518 + 0.00300518i 0.708608 0.705603i \(-0.249324\pi\)
−0.705603 + 0.708608i \(0.749324\pi\)
\(110\) −2.43467 17.6208i −0.232137 1.68008i
\(111\) 8.23854 2.51931i 0.781968 0.239122i
\(112\) 0.813130 + 1.59586i 0.0768336 + 0.150794i
\(113\) 4.08785 9.18146i 0.384552 0.863719i −0.612747 0.790279i \(-0.709936\pi\)
0.997300 0.0734399i \(-0.0233977\pi\)
\(114\) −8.81991 + 13.0777i −0.826060 + 1.22484i
\(115\) −18.6950 + 12.1407i −1.74332 + 1.13213i
\(116\) 4.02346 + 12.3829i 0.373569 + 1.14973i
\(117\) −4.19143 + 9.97156i −0.387497 + 0.921871i
\(118\) −23.7619 + 17.2641i −2.18746 + 1.58929i
\(119\) −0.366957 0.0192314i −0.0336389 0.00176294i
\(120\) −0.00241419 0.0690162i −0.000220384 0.00630029i
\(121\) −2.71076 + 10.6608i −0.246432 + 0.969160i
\(122\) −10.1234 + 10.1234i −0.916526 + 0.916526i
\(123\) −0.138399 + 7.95587i −0.0124790 + 0.717357i
\(124\) 9.55634 3.66834i 0.858185 0.329426i
\(125\) 1.17371 + 7.41049i 0.104979 + 0.662814i
\(126\) −2.47936 + 1.00207i −0.220879 + 0.0892715i
\(127\) 0.170711 0.803134i 0.0151482 0.0712666i −0.969924 0.243407i \(-0.921735\pi\)
0.985072 + 0.172140i \(0.0550683\pi\)
\(128\) −0.110939 0.0425855i −0.00980571 0.00376406i
\(129\) 13.5258 + 5.46385i 1.19088 + 0.481066i
\(130\) 15.0695 + 12.1187i 1.32168 + 1.06288i
\(131\) 2.71318i 0.237052i −0.992951 0.118526i \(-0.962183\pi\)
0.992951 0.118526i \(-0.0378168\pi\)
\(132\) 3.93927 10.7472i 0.342870 0.935425i
\(133\) −1.01665 + 1.76089i −0.0881548 + 0.152689i
\(134\) 6.29885 1.33886i 0.544137 0.115660i
\(135\) 13.9284 + 0.727476i 1.19876 + 0.0626111i
\(136\) 0.00950846 0.00769980i 0.000815344 0.000660253i
\(137\) −10.3500 + 0.542420i −0.884260 + 0.0463421i −0.489057 0.872252i \(-0.662659\pi\)
−0.395203 + 0.918594i \(0.629326\pi\)
\(138\) −28.6321 + 2.50669i −2.43732 + 0.213384i
\(139\) 0.183769 1.74844i 0.0155871 0.148301i −0.983960 0.178388i \(-0.942912\pi\)
0.999547 + 0.0300870i \(0.00957843\pi\)
\(140\) 0.249405 + 2.37293i 0.0210786 + 0.200549i
\(141\) −4.96215 8.95070i −0.417888 0.753785i
\(142\) 9.78615i 0.821235i
\(143\) −5.80863 10.4527i −0.485742 0.874102i
\(144\) 5.27865 10.8261i 0.439888 0.902174i
\(145\) 0.917941 17.5154i 0.0762308 1.45457i
\(146\) 16.0312 1.68495i 1.32675 0.139448i
\(147\) 10.5872 5.16448i 0.873215 0.425959i
\(148\) 4.49946 8.83069i 0.369854 0.725879i
\(149\) −0.712890 13.6028i −0.0584022 1.11438i −0.857935 0.513758i \(-0.828253\pi\)
0.799533 0.600622i \(-0.205081\pi\)
\(150\) 2.48381 7.21490i 0.202802 0.589094i
\(151\) −2.95558 + 18.6608i −0.240522 + 1.51859i 0.511400 + 0.859343i \(0.329127\pi\)
−0.751922 + 0.659252i \(0.770873\pi\)
\(152\) −0.0140760 0.0662222i −0.00114171 0.00537133i
\(153\) 1.38204 + 2.04844i 0.111732 + 0.165606i
\(154\) 0.821515 2.84002i 0.0661996 0.228855i
\(155\) −13.7892 −1.10757
\(156\) 4.90159 + 11.4375i 0.392441 + 0.915734i
\(157\) −7.64239 + 5.55252i −0.609929 + 0.443139i −0.849389 0.527767i \(-0.823029\pi\)
0.239460 + 0.970906i \(0.423029\pi\)
\(158\) 1.75090 4.56124i 0.139294 0.362873i
\(159\) −4.53115 12.4470i −0.359344 0.987107i
\(160\) −15.9428 14.3549i −1.26039 1.13486i
\(161\) −3.65925 + 0.579568i −0.288389 + 0.0456764i
\(162\) 15.4169 + 9.25842i 1.21126 + 0.727410i
\(163\) −4.21379 + 6.48867i −0.330049 + 0.508232i −0.964270 0.264920i \(-0.914654\pi\)
0.634221 + 0.773152i \(0.281321\pi\)
\(164\) 6.47278 + 6.47278i 0.505439 + 0.505439i
\(165\) −10.1424 + 11.6142i −0.789583 + 0.904165i
\(166\) −16.9862 9.80697i −1.31838 0.761169i
\(167\) 0.821019 15.6660i 0.0635324 1.21227i −0.761872 0.647728i \(-0.775719\pi\)
0.825404 0.564542i \(-0.190947\pi\)
\(168\) 0.00429899 0.0106422i 0.000331674 0.000821062i
\(169\) 12.3907 + 3.93326i 0.953131 + 0.302558i
\(170\) 4.20151 1.36515i 0.322241 0.104702i
\(171\) 13.5712 1.66797i 1.03782 0.127553i
\(172\) 15.3310 6.82579i 1.16898 0.520461i
\(173\) −5.51980 2.45758i −0.419663 0.186846i 0.186031 0.982544i \(-0.440438\pi\)
−0.605694 + 0.795698i \(0.707104\pi\)
\(174\) 11.6463 19.3853i 0.882903 1.46959i
\(175\) 0.254571 0.950072i 0.0192438 0.0718187i
\(176\) 5.80934 + 11.9815i 0.437895 + 0.903143i
\(177\) 24.8078 + 5.72579i 1.86467 + 0.430377i
\(178\) 16.5630 3.52057i 1.24145 0.263878i
\(179\) −1.42247 13.5339i −0.106321 1.01157i −0.909463 0.415786i \(-0.863507\pi\)
0.803142 0.595788i \(-0.203160\pi\)
\(180\) 11.7334 10.9442i 0.874556 0.815730i
\(181\) −11.8427 + 3.84793i −0.880261 + 0.286014i −0.714066 0.700079i \(-0.753148\pi\)
−0.166195 + 0.986093i \(0.553148\pi\)
\(182\) 1.46883 + 2.85873i 0.108877 + 0.211903i
\(183\) 12.3799 + 0.864951i 0.915148 + 0.0639390i
\(184\) 0.0776321 0.0958677i 0.00572312 0.00706746i
\(185\) −9.92167 + 8.93352i −0.729456 + 0.656805i
\(186\) −15.6987 8.34593i −1.15108 0.611953i
\(187\) −2.72476 0.196902i −0.199254 0.0143989i
\(188\) −11.3723 3.04720i −0.829409 0.222240i
\(189\) 2.06562 + 1.05202i 0.150252 + 0.0765234i
\(190\) 3.82404 24.1440i 0.277425 1.75159i
\(191\) 13.7573 + 1.44595i 0.995444 + 0.104625i 0.588218 0.808702i \(-0.299830\pi\)
0.407226 + 0.913328i \(0.366496\pi\)
\(192\) −4.70464 12.9235i −0.339528 0.932674i
\(193\) 20.9415 13.5996i 1.50740 0.978918i 0.514826 0.857295i \(-0.327857\pi\)
0.992576 0.121623i \(-0.0388100\pi\)
\(194\) 24.1794 + 17.5673i 1.73598 + 1.26126i
\(195\) −0.642819 16.7503i −0.0460332 1.19952i
\(196\) 4.18761 12.8881i 0.299115 0.920582i
\(197\) 0.115816 + 0.432230i 0.00825153 + 0.0307951i 0.969929 0.243389i \(-0.0782590\pi\)
−0.961677 + 0.274184i \(0.911592\pi\)
\(198\) −18.5764 + 7.08382i −1.32017 + 0.503425i
\(199\) 14.8850 8.59388i 1.05517 0.609204i 0.131079 0.991372i \(-0.458156\pi\)
0.924093 + 0.382168i \(0.124823\pi\)
\(200\) 0.0148681 + 0.0291804i 0.00105134 + 0.00206336i
\(201\) −4.45820 3.35908i −0.314457 0.236931i
\(202\) 1.51806 + 1.87465i 0.106810 + 0.131900i
\(203\) 1.32342 2.59737i 0.0928861 0.182299i
\(204\) 2.79957 + 0.493469i 0.196009 + 0.0345498i
\(205\) −5.01552 11.2651i −0.350299 0.786785i
\(206\) 19.0667 23.5454i 1.32844 1.64048i
\(207\) 17.9238 + 17.3047i 1.24579 + 1.20276i
\(208\) −13.5317 5.14173i −0.938252 0.356515i
\(209\) −7.81567 + 12.9392i −0.540621 + 0.895023i
\(210\) 2.82619 3.03107i 0.195025 0.209164i
\(211\) 0.723115 + 0.803101i 0.0497813 + 0.0552877i 0.767521 0.641024i \(-0.221490\pi\)
−0.717740 + 0.696311i \(0.754823\pi\)
\(212\) −13.9209 6.19800i −0.956095 0.425681i
\(213\) −6.40183 + 5.56569i −0.438646 + 0.381355i
\(214\) 2.03709 0.106759i 0.139252 0.00729791i
\(215\) −22.5757 + 1.18314i −1.53965 + 0.0806897i
\(216\) −0.0745505 + 0.0199899i −0.00507252 + 0.00136014i
\(217\) −2.09366 0.932156i −0.142127 0.0632789i
\(218\) −0.0593247 0.0658867i −0.00401797 0.00446241i
\(219\) −10.2197 9.52891i −0.690584 0.643904i
\(220\) 1.50492 + 17.6746i 0.101462 + 1.19162i
\(221\) 2.30165 1.87680i 0.154826 0.126247i
\(222\) −16.7027 + 4.16549i −1.12101 + 0.279569i
\(223\) −4.48671 + 5.54062i −0.300452 + 0.371028i −0.904905 0.425613i \(-0.860058\pi\)
0.604453 + 0.796641i \(0.293392\pi\)
\(224\) −1.45025 3.25730i −0.0968986 0.217638i
\(225\) −6.13241 + 2.47850i −0.408827 + 0.165233i
\(226\) −9.11705 + 17.8932i −0.606457 + 1.19024i
\(227\) 10.2855 + 12.7016i 0.682675 + 0.843033i 0.994238 0.107192i \(-0.0341860\pi\)
−0.311563 + 0.950225i \(0.600853\pi\)
\(228\) 9.46577 12.5631i 0.626886 0.832008i
\(229\) 8.82252 + 17.3152i 0.583008 + 1.14422i 0.974574 + 0.224068i \(0.0719337\pi\)
−0.391565 + 0.920150i \(0.628066\pi\)
\(230\) 38.5737 22.2705i 2.54347 1.46848i
\(231\) −2.32508 + 1.07779i −0.152979 + 0.0709137i
\(232\) 0.0251215 + 0.0937548i 0.00164931 + 0.00615530i
\(233\) 1.19609 3.68118i 0.0783582 0.241162i −0.904202 0.427104i \(-0.859534\pi\)
0.982561 + 0.185942i \(0.0595338\pi\)
\(234\) 9.40635 19.4590i 0.614913 1.27207i
\(235\) 12.8310 + 9.32224i 0.837000 + 0.608116i
\(236\) 24.5642 15.9522i 1.59899 1.03840i
\(237\) −3.97963 + 1.44873i −0.258504 + 0.0941053i
\(238\) 0.730215 + 0.0767487i 0.0473328 + 0.00497488i
\(239\) −4.11423 + 25.9762i −0.266128 + 1.68026i 0.386269 + 0.922386i \(0.373764\pi\)
−0.652397 + 0.757878i \(0.726236\pi\)
\(240\) −0.324651 + 18.6625i −0.0209561 + 1.20466i
\(241\) −23.1610 6.20598i −1.49193 0.399763i −0.581544 0.813515i \(-0.697551\pi\)
−0.910390 + 0.413752i \(0.864218\pi\)
\(242\) 6.52389 20.9890i 0.419372 1.34923i
\(243\) −2.71145 15.3508i −0.173940 0.984756i
\(244\) 10.6096 9.55295i 0.679212 0.611565i
\(245\) −11.4882 + 14.1868i −0.733957 + 0.906361i
\(246\) 1.10814 15.8607i 0.0706527 1.01124i
\(247\) −3.47118 16.0625i −0.220866 1.02203i
\(248\) 0.0725737 0.0235806i 0.00460843 0.00149737i
\(249\) 3.24512 + 16.6894i 0.205651 + 1.05765i
\(250\) −1.56707 14.9096i −0.0991100 0.942968i
\(251\) 24.2848 5.16189i 1.53284 0.325816i 0.637238 0.770667i \(-0.280077\pi\)
0.895604 + 0.444852i \(0.146744\pi\)
\(252\) 2.52136 0.868507i 0.158831 0.0547108i
\(253\) −27.2844 + 3.76988i −1.71535 + 0.237011i
\(254\) −0.424625 + 1.58472i −0.0266434 + 0.0994344i
\(255\) −3.28257 1.97210i −0.205563 0.123498i
\(256\) 14.7248 + 6.55589i 0.920299 + 0.409743i
\(257\) −1.13873 + 0.506995i −0.0710320 + 0.0316255i −0.441945 0.897042i \(-0.645711\pi\)
0.370913 + 0.928668i \(0.379045\pi\)
\(258\) −26.4181 12.3170i −1.64472 0.766826i
\(259\) −2.11036 + 0.685696i −0.131131 + 0.0426071i
\(260\) −14.3744 12.8548i −0.891463 0.797218i
\(261\) −19.3049 + 3.40633i −1.19494 + 0.210847i
\(262\) −0.283730 + 5.41389i −0.0175289 + 0.334471i
\(263\) −6.67543 3.85406i −0.411625 0.237652i 0.279863 0.960040i \(-0.409711\pi\)
−0.691488 + 0.722388i \(0.743044\pi\)
\(264\) 0.0335191 0.0784710i 0.00206296 0.00482956i
\(265\) 14.5151 + 14.5151i 0.891658 + 0.891658i
\(266\) 2.21277 3.40737i 0.135674 0.208919i
\(267\) −11.7229 8.83279i −0.717433 0.540558i
\(268\) −6.34254 + 1.00456i −0.387432 + 0.0613633i
\(269\) 17.3552 + 15.6267i 1.05816 + 0.952775i 0.998966 0.0454716i \(-0.0144790\pi\)
0.0591979 + 0.998246i \(0.481146\pi\)
\(270\) −27.7166 2.90816i −1.68678 0.176985i
\(271\) −2.33130 + 6.07325i −0.141617 + 0.368924i −0.985984 0.166841i \(-0.946643\pi\)
0.844367 + 0.535765i \(0.179977\pi\)
\(272\) −2.67538 + 1.94378i −0.162219 + 0.117859i
\(273\) 1.03473 2.58672i 0.0626248 0.156555i
\(274\) 20.7091 1.25108
\(275\) 2.03192 7.02444i 0.122529 0.423590i
\(276\) 28.6439 1.00196i 1.72416 0.0603112i
\(277\) −1.44670 6.80620i −0.0869240 0.408945i −0.999999 0.00115429i \(-0.999633\pi\)
0.913075 0.407791i \(-0.133701\pi\)
\(278\) −0.549536 + 3.46963i −0.0329590 + 0.208095i
\(279\) 3.46864 + 15.0162i 0.207662 + 0.898997i
\(280\) 0.000930902 0.0177627i 5.56320e−5 0.00106152i
\(281\) 5.93276 11.6437i 0.353919 0.694605i −0.643573 0.765385i \(-0.722549\pi\)
0.997492 + 0.0707798i \(0.0225488\pi\)
\(282\) 8.96546 + 18.3792i 0.533885 + 1.09446i
\(283\) 19.5091 2.05049i 1.15970 0.121889i 0.494926 0.868935i \(-0.335195\pi\)
0.664772 + 0.747046i \(0.268528\pi\)
\(284\) −0.510738 + 9.74547i −0.0303068 + 0.578287i
\(285\) −17.9692 + 11.2299i −1.06440 + 0.665201i
\(286\) 10.4975 + 21.4649i 0.620728 + 1.26924i
\(287\) 2.04947i 0.120976i
\(288\) −11.6220 + 20.9724i −0.684831 + 1.23581i
\(289\) 1.70607 + 16.2321i 0.100357 + 0.954831i
\(290\) −3.66332 + 34.8542i −0.215118 + 2.04671i
\(291\) −2.25950 25.8086i −0.132454 1.51292i
\(292\) −16.0525 + 0.841278i −0.939404 + 0.0492321i
\(293\) −11.0700 + 8.96430i −0.646716 + 0.523700i −0.895615 0.444829i \(-0.853264\pi\)
0.248900 + 0.968529i \(0.419931\pi\)
\(294\) −21.6657 + 9.19807i −1.26357 + 0.536442i
\(295\) −38.5934 + 8.20328i −2.24699 + 0.477613i
\(296\) 0.0369417 0.0639849i 0.00214719 0.00371905i
\(297\) 15.1990 + 8.12339i 0.881937 + 0.471367i
\(298\) 27.2175i 1.57667i
\(299\) 18.7647 23.3339i 1.08519 1.34943i
\(300\) −2.85003 + 7.05528i −0.164547 + 0.407337i
\(301\) −3.50773 1.34649i −0.202182 0.0776105i
\(302\) 7.84902 36.9267i 0.451660 2.12489i
\(303\) 0.362974 2.05924i 0.0208523 0.118300i
\(304\) 2.86254 + 18.0734i 0.164178 + 1.03658i
\(305\) −17.9546 + 6.89213i −1.02808 + 0.394642i
\(306\) −2.54352 4.23199i −0.145403 0.241927i
\(307\) 18.1499 18.1499i 1.03587 1.03587i 0.0365348 0.999332i \(-0.488368\pi\)
0.999332 0.0365348i \(-0.0116320\pi\)
\(308\) −0.966321 + 2.78534i −0.0550612 + 0.158709i
\(309\) −26.2465 + 0.918104i −1.49311 + 0.0522291i
\(310\) 27.5149 + 1.44199i 1.56274 + 0.0818998i
\(311\) 1.85674 1.34900i 0.105286 0.0764946i −0.533897 0.845550i \(-0.679273\pi\)
0.639182 + 0.769055i \(0.279273\pi\)
\(312\) 0.0320277 + 0.0870593i 0.00181321 + 0.00492876i
\(313\) −4.06484 12.5103i −0.229759 0.707124i −0.997774 0.0666924i \(-0.978755\pi\)
0.768015 0.640432i \(-0.221245\pi\)
\(314\) 15.8303 10.2803i 0.893355 0.580151i
\(315\) −3.59018 0.124947i −0.202284 0.00703994i
\(316\) −1.98167 + 4.45090i −0.111478 + 0.250383i
\(317\) −3.09990 6.08389i −0.174107 0.341705i 0.787419 0.616419i \(-0.211417\pi\)
−0.961526 + 0.274713i \(0.911417\pi\)
\(318\) 7.73984 + 25.3105i 0.434029 + 1.41934i
\(319\) 10.2189 19.1116i 0.572148 1.07004i
\(320\) 15.0709 + 15.0709i 0.842488 + 0.842488i
\(321\) −1.22839 1.27189i −0.0685622 0.0709899i
\(322\) 7.36229 0.773808i 0.410284 0.0431226i
\(323\) −3.50484 1.34538i −0.195014 0.0748590i
\(324\) −14.8696 10.0245i −0.826088 0.556919i
\(325\) 3.63297 + 7.07072i 0.201521 + 0.392213i
\(326\) 9.08675 12.5068i 0.503269 0.692690i
\(327\) −0.00936147 + 0.0762804i −0.000517691 + 0.00421832i
\(328\) 0.0456614 + 0.0507121i 0.00252123 + 0.00280011i
\(329\) 1.31798 + 2.28281i 0.0726627 + 0.125855i
\(330\) 21.4527 22.1144i 1.18093 1.21736i
\(331\) 1.81184 6.76186i 0.0995875 0.371665i −0.898088 0.439817i \(-0.855043\pi\)
0.997675 + 0.0681513i \(0.0217101\pi\)
\(332\) 16.4037 + 10.6527i 0.900273 + 0.584644i
\(333\) 12.2243 + 8.55737i 0.669886 + 0.468941i
\(334\) −3.27653 + 31.1741i −0.179284 + 1.70577i
\(335\) 8.46146 + 1.79854i 0.462299 + 0.0982647i
\(336\) −1.31089 + 2.81165i −0.0715150 + 0.153388i
\(337\) 14.9325 20.5529i 0.813426 1.11959i −0.177359 0.984146i \(-0.556756\pi\)
0.990786 0.135439i \(-0.0432445\pi\)
\(338\) −24.3131 9.14418i −1.32246 0.497378i
\(339\) 16.8904 4.21231i 0.917360 0.228781i
\(340\) −4.25529 + 1.14020i −0.230775 + 0.0618361i
\(341\) −15.4251 7.23655i −0.835314 0.391881i
\(342\) −27.2545 + 1.90906i −1.47375 + 0.103230i
\(343\) −5.48579 + 2.79515i −0.296205 + 0.150924i
\(344\) 0.116795 0.0448334i 0.00629716 0.00241725i
\(345\) −36.5068 12.5679i −1.96546 0.676633i
\(346\) 10.7572 + 5.48108i 0.578312 + 0.294665i
\(347\) 3.73590 + 3.36382i 0.200553 + 0.180579i 0.763288 0.646059i \(-0.223584\pi\)
−0.562734 + 0.826638i \(0.690251\pi\)
\(348\) −12.6096 + 18.6969i −0.675945 + 1.00226i
\(349\) 15.4214 + 12.4880i 0.825489 + 0.668468i 0.945972 0.324248i \(-0.105111\pi\)
−0.120484 + 0.992715i \(0.538445\pi\)
\(350\) −0.607325 + 1.86915i −0.0324629 + 0.0999105i
\(351\) −18.0792 + 4.91354i −0.964996 + 0.262265i
\(352\) −10.3007 24.4247i −0.549030 1.30184i
\(353\) −1.32053 4.92829i −0.0702848 0.262307i 0.921838 0.387575i \(-0.126687\pi\)
−0.992123 + 0.125269i \(0.960021\pi\)
\(354\) −48.9028 14.0195i −2.59916 0.745130i
\(355\) 5.34699 12.0095i 0.283789 0.637400i
\(356\) −16.6779 + 2.64152i −0.883926 + 0.140000i
\(357\) −0.365089 0.521336i −0.0193226 0.0275920i
\(358\) 1.42310 + 27.1544i 0.0752132 + 1.43515i
\(359\) 0.483010 + 3.04961i 0.0254923 + 0.160952i 0.997150 0.0754383i \(-0.0240356\pi\)
−0.971658 + 0.236390i \(0.924036\pi\)
\(360\) 0.0916195 0.0768964i 0.00482877 0.00405279i
\(361\) −1.31789 + 1.18664i −0.0693628 + 0.0624545i
\(362\) 24.0334 6.43972i 1.26316 0.338464i
\(363\) −17.4408 + 7.66937i −0.915404 + 0.402537i
\(364\) −1.31353 2.92350i −0.0688476 0.153233i
\(365\) 20.5941 + 6.69143i 1.07795 + 0.350246i
\(366\) −24.6124 3.02055i −1.28651 0.157887i
\(367\) 11.6582 5.19059i 0.608555 0.270946i −0.0792346 0.996856i \(-0.525248\pi\)
0.687790 + 0.725910i \(0.258581\pi\)
\(368\) −22.3100 + 24.7778i −1.16299 + 1.29163i
\(369\) −11.0059 + 8.29555i −0.572942 + 0.431849i
\(370\) 20.7319 16.7884i 1.07780 0.872787i
\(371\) 1.22265 + 3.18512i 0.0634770 + 0.165363i
\(372\) 15.1978 + 9.13055i 0.787971 + 0.473397i
\(373\) 4.39972 + 7.62054i 0.227809 + 0.394577i 0.957158 0.289565i \(-0.0935105\pi\)
−0.729349 + 0.684141i \(0.760177\pi\)
\(374\) 5.41639 + 0.677840i 0.280075 + 0.0350502i
\(375\) −8.86223 + 9.50471i −0.457644 + 0.490821i
\(376\) −0.0834724 0.0271218i −0.00430476 0.00139870i
\(377\) 6.17494 + 22.7364i 0.318026 + 1.17099i
\(378\) −4.01172 2.31522i −0.206341 0.119082i
\(379\) −3.44152 5.29948i −0.176779 0.272216i 0.739163 0.673527i \(-0.235221\pi\)
−0.915942 + 0.401311i \(0.868555\pi\)
\(380\) −5.06822 + 23.8441i −0.259994 + 1.22318i
\(381\) 1.27818 0.623503i 0.0654831 0.0319431i
\(382\) −27.3002 4.32392i −1.39680 0.221231i
\(383\) 9.70905 14.9506i 0.496109 0.763941i −0.498582 0.866842i \(-0.666146\pi\)
0.994692 + 0.102901i \(0.0328125\pi\)
\(384\) −0.0601884 0.196826i −0.00307147 0.0100442i
\(385\) 2.55990 3.03640i 0.130465 0.154749i
\(386\) −43.2089 + 24.9467i −2.19927 + 1.26975i
\(387\) 6.96731 + 24.2871i 0.354168 + 1.23458i
\(388\) −23.1620 18.7562i −1.17587 0.952204i
\(389\) 11.2768 + 8.19305i 0.571754 + 0.415404i 0.835742 0.549122i \(-0.185038\pi\)
−0.263988 + 0.964526i \(0.585038\pi\)
\(390\) −0.468976 + 33.4908i −0.0237475 + 1.69587i
\(391\) −2.11382 6.50568i −0.106901 0.329006i
\(392\) 0.0362031 0.0943124i 0.00182853 0.00476350i
\(393\) 3.70298 2.89344i 0.186791 0.145955i
\(394\) −0.185899 0.874584i −0.00936544 0.0440609i
\(395\) 4.64088 4.64088i 0.233508 0.233508i
\(396\) 18.8689 6.08487i 0.948199 0.305776i
\(397\) 13.5590 + 3.63312i 0.680506 + 0.182341i 0.582483 0.812843i \(-0.302081\pi\)
0.0980231 + 0.995184i \(0.468748\pi\)
\(398\) −30.6003 + 15.5916i −1.53386 + 0.781538i
\(399\) −3.48748 + 0.490344i −0.174592 + 0.0245479i
\(400\) −3.60034 8.08649i −0.180017 0.404325i
\(401\) 15.8426 + 24.3955i 0.791143 + 1.21825i 0.972055 + 0.234754i \(0.0754286\pi\)
−0.180912 + 0.983499i \(0.557905\pi\)
\(402\) 8.54462 + 7.16893i 0.426167 + 0.357554i
\(403\) 17.5964 5.78348i 0.876539 0.288096i
\(404\) −1.41391 1.94608i −0.0703448 0.0968213i
\(405\) 13.8609 + 19.7854i 0.688753 + 0.983145i
\(406\) −2.91238 + 5.04439i −0.144539 + 0.250349i
\(407\) −15.7871 + 4.78647i −0.782536 + 0.237257i
\(408\) 0.0206490 + 0.00476590i 0.00102228 + 0.000235947i
\(409\) 16.1289 + 10.4742i 0.797523 + 0.517918i 0.877898 0.478847i \(-0.158945\pi\)
−0.0803750 + 0.996765i \(0.525612\pi\)
\(410\) 8.82995 + 23.0028i 0.436080 + 1.13603i
\(411\) −11.7779 13.5473i −0.580962 0.668241i
\(412\) −20.2162 + 22.4524i −0.995983 + 1.10615i
\(413\) −6.41432 1.36341i −0.315628 0.0670888i
\(414\) −33.9555 36.4042i −1.66882 1.78917i
\(415\) −15.4870 21.3161i −0.760228 1.04636i
\(416\) 26.3654 + 11.6316i 1.29267 + 0.570288i
\(417\) 2.58227 1.61380i 0.126455 0.0790280i
\(418\) 16.9485 25.0016i 0.828979 1.22287i
\(419\) 5.10316 + 2.94631i 0.249306 + 0.143937i 0.619446 0.785039i \(-0.287357\pi\)
−0.370141 + 0.928976i \(0.620691\pi\)
\(420\) −2.97263 + 2.87098i −0.145050 + 0.140089i
\(421\) −26.5998 4.21299i −1.29639 0.205329i −0.530164 0.847895i \(-0.677870\pi\)
−0.766230 + 0.642566i \(0.777870\pi\)
\(422\) −1.35892 1.67813i −0.0661513 0.0816900i
\(423\) 6.92420 16.3178i 0.336666 0.793396i
\(424\) −0.101217 0.0515725i −0.00491552 0.00250458i
\(425\) 1.80610 + 0.189829i 0.0876086 + 0.00920804i
\(426\) 13.3562 10.4363i 0.647112 0.505641i
\(427\) −3.19203 0.167287i −0.154473 0.00809558i
\(428\) −2.03419 −0.0983263
\(429\) 8.07148 19.0749i 0.389695 0.920944i
\(430\) 45.1713 2.17836
\(431\) −2.29038 0.120034i −0.110324 0.00578182i −0.00290579 0.999996i \(-0.500925\pi\)
−0.107418 + 0.994214i \(0.534258\pi\)
\(432\) 20.4049 4.34099i 0.981733 0.208856i
\(433\) −27.8659 2.92883i −1.33915 0.140751i −0.592287 0.805727i \(-0.701775\pi\)
−0.746864 + 0.664976i \(0.768442\pi\)
\(434\) 4.08021 + 2.07897i 0.195856 + 0.0997937i
\(435\) 24.8841 17.4262i 1.19310 0.835523i
\(436\) 0.0556395 + 0.0687090i 0.00266465 + 0.00329057i
\(437\) −37.3851 5.92121i −1.78837 0.283250i
\(438\) 19.3960 + 20.0827i 0.926775 + 0.959590i
\(439\) −9.95847 5.74952i −0.475292 0.274410i 0.243161 0.969986i \(-0.421816\pi\)
−0.718452 + 0.695576i \(0.755149\pi\)
\(440\) 0.00430764 + 0.132167i 0.000205358 + 0.00630079i
\(441\) 18.3391 + 8.94189i 0.873290 + 0.425804i
\(442\) −4.78899 + 3.50428i −0.227789 + 0.166682i
\(443\) −6.27655 8.63893i −0.298208 0.410448i 0.633451 0.773783i \(-0.281638\pi\)
−0.931659 + 0.363335i \(0.881638\pi\)
\(444\) 16.8506 3.27647i 0.799696 0.155494i
\(445\) 22.2496 + 4.72931i 1.05473 + 0.224191i
\(446\) 9.53219 10.5866i 0.451363 0.501289i
\(447\) 17.8049 15.4794i 0.842145 0.732153i
\(448\) 1.26946 + 3.30707i 0.0599766 + 0.156244i
\(449\) −18.7742 12.1921i −0.886008 0.575381i 0.0194523 0.999811i \(-0.493808\pi\)
−0.905461 + 0.424430i \(0.860474\pi\)
\(450\) 12.4958 4.30431i 0.589058 0.202907i
\(451\) 0.301345 15.2337i 0.0141898 0.717325i
\(452\) 10.0130 17.3430i 0.470972 0.815747i
\(453\) −28.6204 + 15.8668i −1.34470 + 0.745486i
\(454\) −19.1955 26.4204i −0.900890 1.23997i
\(455\) 0.240582 + 4.31077i 0.0112787 + 0.202092i
\(456\) 0.0753697 0.0898329i 0.00352951 0.00420681i
\(457\) 11.0801 + 17.0618i 0.518305 + 0.798119i 0.996797 0.0799725i \(-0.0254833\pi\)
−0.478492 + 0.878092i \(0.658817\pi\)
\(458\) −15.7937 35.4733i −0.737993 1.65756i
\(459\) −1.32187 + 4.07076i −0.0616997 + 0.190007i
\(460\) −39.5757 + 20.1648i −1.84522 + 0.940189i
\(461\) −3.76396 1.00855i −0.175305 0.0469728i 0.170099 0.985427i \(-0.445591\pi\)
−0.345404 + 0.938454i \(0.612258\pi\)
\(462\) 4.75218 1.90749i 0.221092 0.0887445i
\(463\) −14.3095 + 14.3095i −0.665019 + 0.665019i −0.956559 0.291540i \(-0.905832\pi\)
0.291540 + 0.956559i \(0.405832\pi\)
\(464\) −5.45442 25.6610i −0.253215 1.19128i
\(465\) −14.7053 18.8196i −0.681941 0.872738i
\(466\) −2.77163 + 7.22035i −0.128393 + 0.334476i
\(467\) −2.02330 6.22708i −0.0936271 0.288155i 0.893266 0.449528i \(-0.148408\pi\)
−0.986893 + 0.161373i \(0.948408\pi\)
\(468\) −10.3828 + 18.8872i −0.479946 + 0.873059i
\(469\) 1.16315 + 0.845079i 0.0537093 + 0.0390221i
\(470\) −24.6281 19.9434i −1.13601 0.919921i
\(471\) −15.7283 4.50900i −0.724721 0.207764i
\(472\) 0.189093 0.109173i 0.00870369 0.00502508i
\(473\) −25.8749 10.5242i −1.18973 0.483904i
\(474\) 8.09245 2.47464i 0.371699 0.113664i
\(475\) 5.47302 8.42771i 0.251119 0.386690i
\(476\) −0.723174 0.114540i −0.0331466 0.00524991i
\(477\) 12.1555 19.4581i 0.556564 0.890924i
\(478\) 10.9260 51.4028i 0.499744 2.35111i
\(479\) 6.97857 + 10.7460i 0.318859 + 0.490999i 0.961363 0.275282i \(-0.0887713\pi\)
−0.642505 + 0.766282i \(0.722105\pi\)
\(480\) 2.58981 37.0675i 0.118208 1.69189i
\(481\) 8.91418 15.5615i 0.406452 0.709542i
\(482\) 45.5666 + 14.8055i 2.07550 + 0.674372i
\(483\) −4.69337 4.37611i −0.213556 0.199120i
\(484\) −7.59219 + 20.5613i −0.345100 + 0.934605i
\(485\) 20.0743 + 34.7698i 0.911529 + 1.57882i
\(486\) 3.80513 + 30.9146i 0.172604 + 1.40232i
\(487\) 4.28606 + 11.1656i 0.194220 + 0.505960i 0.995761 0.0919796i \(-0.0293194\pi\)
−0.801541 + 0.597940i \(0.795986\pi\)
\(488\) 0.0827108 0.0669778i 0.00374414 0.00303194i
\(489\) −13.3496 + 1.16873i −0.603688 + 0.0528518i
\(490\) 24.4072 27.1070i 1.10261 1.22457i
\(491\) 3.28434 1.46228i 0.148220 0.0659918i −0.331286 0.943530i \(-0.607483\pi\)
0.479506 + 0.877539i \(0.340816\pi\)
\(492\) −1.93131 + 15.7369i −0.0870700 + 0.709476i
\(493\) 5.11885 + 1.66322i 0.230542 + 0.0749075i
\(494\) 5.24667 + 32.4142i 0.236059 + 1.45838i
\(495\) −26.6674 1.45661i −1.19861 0.0654698i
\(496\) −19.9222 + 5.33813i −0.894531 + 0.239689i
\(497\) 1.62371 1.46199i 0.0728331 0.0655792i
\(498\) −4.73003 33.6415i −0.211958 1.50751i
\(499\) −1.61097 10.1712i −0.0721167 0.455327i −0.997150 0.0754415i \(-0.975963\pi\)
0.925034 0.379886i \(-0.124037\pi\)
\(500\) 0.782419 + 14.9295i 0.0349909 + 0.667665i
\(501\) 22.2567 15.5863i 0.994355 0.696343i
\(502\) −48.9977 + 7.76047i −2.18687 + 0.346367i
\(503\) −17.2771 + 38.8050i −0.770348 + 1.73023i −0.0916737 + 0.995789i \(0.529222\pi\)
−0.678674 + 0.734440i \(0.737445\pi\)
\(504\) 0.0191092 0.00548191i 0.000851190 0.000244184i
\(505\) 0.838682 + 3.13001i 0.0373209 + 0.139283i
\(506\) 54.8376 4.66918i 2.43783 0.207570i
\(507\) 7.84576 + 21.1055i 0.348442 + 0.937330i
\(508\) 0.505567 1.55598i 0.0224309 0.0690352i
\(509\) 3.43176 + 2.77898i 0.152110 + 0.123176i 0.702354 0.711827i \(-0.252132\pi\)
−0.550245 + 0.835004i \(0.685465\pi\)
\(510\) 6.34382 + 4.27841i 0.280909 + 0.189451i
\(511\) 2.67453 + 2.40816i 0.118314 + 0.106531i
\(512\) −28.4845 14.5136i −1.25885 0.641416i
\(513\) 16.7493 + 16.7434i 0.739502 + 0.739239i
\(514\) 2.32524 0.892577i 0.102562 0.0393699i
\(515\) 36.2634 18.4771i 1.59795 0.814198i
\(516\) 25.6654 + 13.6446i 1.12986 + 0.600670i
\(517\) 9.46088 + 17.1619i 0.416089 + 0.754779i
\(518\) 4.28271 1.14755i 0.188172 0.0504204i
\(519\) −2.53240 10.1543i −0.111160 0.445726i
\(520\) −0.101995 0.101306i −0.00447279 0.00444255i
\(521\) 1.75826 2.42004i 0.0770310 0.106024i −0.768763 0.639534i \(-0.779127\pi\)
0.845794 + 0.533510i \(0.179127\pi\)
\(522\) 38.8773 4.77820i 1.70161 0.209136i
\(523\) 30.1507 + 6.40873i 1.31840 + 0.280234i 0.812804 0.582538i \(-0.197940\pi\)
0.505594 + 0.862772i \(0.331273\pi\)
\(524\) 0.565101 5.37657i 0.0246865 0.234877i
\(525\) 1.56815 0.665751i 0.0684398 0.0290558i
\(526\) 12.9171 + 8.38848i 0.563214 + 0.365755i
\(527\) 1.09518 4.08727i 0.0477068 0.178044i
\(528\) −10.1573 + 20.7062i −0.442038 + 0.901123i
\(529\) −22.9841 39.8096i −0.999308 1.73085i
\(530\) −27.4456 30.4815i −1.19216 1.32403i
\(531\) 18.6414 + 39.9642i 0.808967 + 1.73430i
\(532\) −2.38140 + 3.27772i −0.103247 + 0.142107i
\(533\) 11.1251 + 12.2718i 0.481884 + 0.531549i
\(534\) 22.4683 + 18.8509i 0.972299 + 0.815758i
\(535\) 2.55824 + 0.982015i 0.110602 + 0.0424562i
\(536\) −0.0476092 + 0.00500392i −0.00205640 + 0.000216137i
\(537\) 16.9543 16.3745i 0.731631 0.706612i
\(538\) −32.9964 32.9964i −1.42258 1.42258i
\(539\) −20.2964 + 9.84086i −0.874228 + 0.423876i
\(540\) 27.4497 + 4.34260i 1.18125 + 0.186876i
\(541\) 14.6085 + 28.6708i 0.628069 + 1.23266i 0.957488 + 0.288472i \(0.0931471\pi\)
−0.329419 + 0.944184i \(0.606853\pi\)
\(542\) 5.28700 11.8748i 0.227096 0.510066i
\(543\) −17.8812 12.0595i −0.767356 0.517522i
\(544\) 5.52120 3.58551i 0.236720 0.153728i
\(545\) −0.0368037 0.113270i −0.00157650 0.00485196i
\(546\) −2.33521 + 5.05333i −0.0999378 + 0.216263i
\(547\) −15.1684 + 11.0205i −0.648552 + 0.471201i −0.862778 0.505584i \(-0.831277\pi\)
0.214226 + 0.976784i \(0.431277\pi\)
\(548\) −20.6231 1.08081i −0.880973 0.0461698i
\(549\) 12.0219 + 17.8186i 0.513082 + 0.760481i
\(550\) −4.78907 + 13.8041i −0.204207 + 0.588609i
\(551\) 21.0593 21.0593i 0.897154 0.897154i
\(552\) 0.213631 + 0.00371630i 0.00909275 + 0.000158176i
\(553\) 1.01837 0.390915i 0.0433054 0.0166234i
\(554\) 2.17500 + 13.7324i 0.0924069 + 0.583434i
\(555\) −22.7734 4.01418i −0.966678 0.170392i
\(556\) 0.728331 3.42653i 0.0308881 0.145317i
\(557\) −28.7182 11.0239i −1.21683 0.467097i −0.336602 0.941647i \(-0.609278\pi\)
−0.880229 + 0.474550i \(0.842611\pi\)
\(558\) −5.35102 30.3261i −0.226527 1.28381i
\(559\) 28.3127 10.9786i 1.19750 0.464344i
\(560\) 4.80755i 0.203156i
\(561\) −2.63705 3.92876i −0.111336 0.165872i
\(562\) −13.0559 + 22.6134i −0.550729 + 0.953891i
\(563\) −38.9034 + 8.26917i −1.63958 + 0.348504i −0.933209 0.359335i \(-0.883003\pi\)
−0.706374 + 0.707839i \(0.749670\pi\)
\(564\) −7.96899 18.7707i −0.335555 0.790388i
\(565\) −20.9650 + 16.9771i −0.882003 + 0.714232i
\(566\) −39.1430 + 2.05140i −1.64530 + 0.0862267i
\(567\) 0.767040 + 3.94110i 0.0322127 + 0.165511i
\(568\) −0.00760441 + 0.0723512i −0.000319074 + 0.00303579i
\(569\) 0.343988 + 3.27283i 0.0144207 + 0.137204i 0.999363 0.0356775i \(-0.0113589\pi\)
−0.984943 + 0.172881i \(0.944692\pi\)
\(570\) 37.0302 20.5290i 1.55102 0.859866i
\(571\) 16.4635i 0.688974i 0.938791 + 0.344487i \(0.111947\pi\)
−0.938791 + 0.344487i \(0.888053\pi\)
\(572\) −9.33358 21.9235i −0.390256 0.916668i
\(573\) 12.6979 + 20.3182i 0.530461 + 0.848803i
\(574\) −0.214322 + 4.08951i −0.00894563 + 0.170693i
\(575\) 18.2097 1.91392i 0.759398 0.0798159i
\(576\) 12.6210 20.2031i 0.525873 0.841794i
\(577\) −12.3660 + 24.2696i −0.514803 + 1.01036i 0.476551 + 0.879147i \(0.341887\pi\)
−0.991354 + 0.131211i \(0.958113\pi\)
\(578\) −1.70682 32.5680i −0.0709943 1.35465i
\(579\) 40.8936 + 14.0781i 1.69948 + 0.585066i
\(580\) 5.46713 34.5181i 0.227010 1.43329i
\(581\) −0.910471 4.28343i −0.0377727 0.177707i
\(582\) 1.80968 + 51.7348i 0.0750138 + 2.14447i
\(583\) 8.61963 + 23.8547i 0.356989 + 0.987962i
\(584\) −0.119832 −0.00495868
\(585\) 22.1755 18.7405i 0.916844 0.774824i
\(586\) 23.0265 16.7297i 0.951217 0.691099i
\(587\) −5.90206 + 15.3754i −0.243604 + 0.634611i −0.999805 0.0197285i \(-0.993720\pi\)
0.756201 + 0.654339i \(0.227053\pi\)
\(588\) 22.0557 8.02911i 0.909563 0.331115i
\(589\) −17.4002 15.6672i −0.716963 0.645557i
\(590\) 77.8672 12.3330i 3.20574 0.507740i
\(591\) −0.466402 + 0.619013i −0.0191852 + 0.0254628i
\(592\) −10.8762 + 16.7478i −0.447007 + 0.688331i
\(593\) 10.4722 + 10.4722i 0.430041 + 0.430041i 0.888642 0.458601i \(-0.151649\pi\)
−0.458601 + 0.888642i \(0.651649\pi\)
\(594\) −29.4787 17.7989i −1.20952 0.730297i
\(595\) 0.854184 + 0.493163i 0.0350181 + 0.0202177i
\(596\) 1.42048 27.1044i 0.0581851 1.11024i
\(597\) 27.6030 + 11.1504i 1.12971 + 0.456357i
\(598\) −39.8833 + 44.5982i −1.63095 + 1.82376i
\(599\) −14.1215 + 4.58835i −0.576989 + 0.187475i −0.582951 0.812507i \(-0.698102\pi\)
0.00596233 + 0.999982i \(0.498102\pi\)
\(600\) −0.0239698 + 0.0514113i −0.000978562 + 0.00209886i
\(601\) −33.5370 + 14.9316i −1.36800 + 0.609074i −0.953616 0.301027i \(-0.902671\pi\)
−0.414387 + 0.910101i \(0.636004\pi\)
\(602\) 6.85853 + 3.05361i 0.279533 + 0.124456i
\(603\) −0.169880 9.66685i −0.00691805 0.393664i
\(604\) −9.74360 + 36.3636i −0.396461 + 1.47961i
\(605\) 19.4742 22.1931i 0.791737 0.902279i
\(606\) −0.939625 + 4.07106i −0.0381696 + 0.165376i
\(607\) −35.8686 + 7.62411i −1.45586 + 0.309453i −0.866808 0.498641i \(-0.833832\pi\)
−0.589053 + 0.808094i \(0.700499\pi\)
\(608\) −3.80775 36.2283i −0.154425 1.46925i
\(609\) 4.95626 0.963704i 0.200838 0.0390513i
\(610\) 36.5474 11.8750i 1.47976 0.480804i
\(611\) −20.2836 6.51456i −0.820587 0.263551i
\(612\) 2.31208 + 4.34714i 0.0934602 + 0.175723i
\(613\) 27.0711 33.4300i 1.09339 1.35022i 0.161755 0.986831i \(-0.448285\pi\)
0.931636 0.363394i \(-0.118382\pi\)
\(614\) −38.1143 + 34.3183i −1.53817 + 1.38497i
\(615\) 10.0259 18.8587i 0.404285 0.760457i
\(616\) −0.00828051 + 0.0203585i −0.000333631 + 0.000820268i
\(617\) −33.8145 9.06057i −1.36132 0.364765i −0.497019 0.867739i \(-0.665572\pi\)
−0.864301 + 0.502975i \(0.832239\pi\)
\(618\) 52.4684 + 0.912733i 2.11059 + 0.0367155i
\(619\) −6.50049 + 41.0425i −0.261277 + 1.64964i 0.412687 + 0.910873i \(0.364590\pi\)
−0.673964 + 0.738764i \(0.735410\pi\)
\(620\) −27.3253 2.87200i −1.09741 0.115342i
\(621\) −4.50305 + 42.9169i −0.180701 + 1.72220i
\(622\) −3.84601 + 2.49762i −0.154211 + 0.100146i
\(623\) 3.05854 + 2.22216i 0.122538 + 0.0890289i
\(624\) −7.41319 23.9515i −0.296765 0.958828i
\(625\) 9.62985 29.6376i 0.385194 1.18551i
\(626\) 6.80274 + 25.3882i 0.271892 + 1.01472i
\(627\) −25.9945 + 3.13193i −1.03812 + 0.125077i
\(628\) −16.3010 + 9.41140i −0.650481 + 0.375556i
\(629\) −1.85999 3.65043i −0.0741626 0.145552i
\(630\) 7.15080 + 0.624761i 0.284894 + 0.0248911i
\(631\) −3.59462 4.43898i −0.143099 0.176713i 0.700557 0.713596i \(-0.252935\pi\)
−0.843657 + 0.536883i \(0.819602\pi\)
\(632\) −0.0164891 + 0.0323617i −0.000655902 + 0.00128728i
\(633\) −0.324924 + 1.84337i −0.0129146 + 0.0732675i
\(634\) 5.54932 + 12.4640i 0.220392 + 0.495008i
\(635\) −1.38697 + 1.71276i −0.0550400 + 0.0679688i
\(636\) −6.38671 25.6093i −0.253250 1.01547i
\(637\) 8.70994 22.9223i 0.345100 0.908213i
\(638\) −22.3894 + 37.0667i −0.886405 + 1.46748i
\(639\) −14.4233 2.80183i −0.570575 0.110839i
\(640\) 0.213429 + 0.237037i 0.00843653 + 0.00936971i
\(641\) −2.07937 0.925794i −0.0821301 0.0365667i 0.365260 0.930905i \(-0.380980\pi\)
−0.447391 + 0.894339i \(0.647647\pi\)
\(642\) 2.31813 + 2.66639i 0.0914893 + 0.105234i
\(643\) 34.6512 1.81599i 1.36651 0.0716158i 0.645087 0.764109i \(-0.276821\pi\)
0.721424 + 0.692493i \(0.243488\pi\)
\(644\) −7.37207 + 0.386354i −0.290500 + 0.0152245i
\(645\) −25.6904 29.5498i −1.01156 1.16352i
\(646\) 6.85287 + 3.05109i 0.269622 + 0.120044i
\(647\) 16.3798 + 18.1917i 0.643958 + 0.715188i 0.973432 0.228977i \(-0.0735379\pi\)
−0.329474 + 0.944165i \(0.606871\pi\)
\(648\) −0.106786 0.0804294i −0.00419495 0.00315956i
\(649\) −47.4771 11.0773i −1.86364 0.434823i
\(650\) −6.50982 14.4888i −0.255336 0.568299i
\(651\) −0.960537 3.85153i −0.0376464 0.150953i
\(652\) −9.70172 + 11.9806i −0.379949 + 0.469197i
\(653\) 8.47212 + 19.0287i 0.331540 + 0.744650i 1.00000 0.000901968i \(0.000287105\pi\)
−0.668460 + 0.743748i \(0.733046\pi\)
\(654\) 0.0266569 0.151231i 0.00104237 0.00591360i
\(655\) −3.30625 + 6.48888i −0.129186 + 0.253542i
\(656\) −11.6073 14.3338i −0.453188 0.559640i
\(657\) 2.10647 24.1100i 0.0821813 0.940619i
\(658\) −2.39118 4.69295i −0.0932179 0.182950i
\(659\) 30.0583 17.3542i 1.17090 0.676022i 0.217011 0.976169i \(-0.430369\pi\)
0.953893 + 0.300147i \(0.0970358\pi\)
\(660\) −22.5177 + 20.9028i −0.876499 + 0.813642i
\(661\) −3.93487 14.6851i −0.153049 0.571186i −0.999265 0.0383456i \(-0.987791\pi\)
0.846216 0.532840i \(-0.178875\pi\)
\(662\) −4.32246 + 13.3032i −0.167997 + 0.517042i
\(663\) 5.01605 + 1.13983i 0.194807 + 0.0442672i
\(664\) 0.117962 + 0.0857044i 0.00457781 + 0.00332598i
\(665\) 4.57724 2.97249i 0.177498 0.115268i
\(666\) −23.4975 18.3537i −0.910508 0.711193i
\(667\) 53.9688 + 5.67235i 2.08968 + 0.219634i
\(668\) 4.88988 30.8735i 0.189195 1.19453i
\(669\) −12.3467 0.214781i −0.477351 0.00830393i
\(670\) −16.6959 4.47366i −0.645020 0.172833i
\(671\) −23.7017 1.71278i −0.914993 0.0661213i
\(672\) 2.89901 5.45302i 0.111832 0.210355i
\(673\) −18.2357 + 16.4195i −0.702934 + 0.632925i −0.941032 0.338316i \(-0.890143\pi\)
0.238098 + 0.971241i \(0.423476\pi\)
\(674\) −31.9457 + 39.4496i −1.23050 + 1.51954i
\(675\) −9.92251 5.72642i −0.381918 0.220410i
\(676\) 23.7348 + 10.3751i 0.912878 + 0.399041i
\(677\) 5.42273 1.76195i 0.208412 0.0677173i −0.202950 0.979189i \(-0.565053\pi\)
0.411363 + 0.911472i \(0.365053\pi\)
\(678\) −34.1436 + 6.63895i −1.31128 + 0.254967i
\(679\) 0.697499 + 6.63626i 0.0267676 + 0.254676i
\(680\) −0.0321235 + 0.00682805i −0.00123188 + 0.000261844i
\(681\) −6.36638 + 27.5833i −0.243960 + 1.05699i
\(682\) 30.0224 + 16.0529i 1.14962 + 0.614697i
\(683\) 4.77003 17.8020i 0.182520 0.681175i −0.812628 0.582783i \(-0.801964\pi\)
0.995148 0.0983913i \(-0.0313697\pi\)
\(684\) 27.2409 0.478716i 1.04158 0.0183042i
\(685\) 25.4142 + 11.3151i 0.971026 + 0.432329i
\(686\) 11.2387 5.00377i 0.429094 0.191045i
\(687\) −14.2233 + 30.5066i −0.542652 + 1.16390i
\(688\) −32.1587 + 10.4490i −1.22604 + 0.398364i
\(689\) −24.6108 12.4349i −0.937597 0.473731i
\(690\) 71.5315 + 28.8957i 2.72316 + 1.10004i
\(691\) 1.77059 33.7848i 0.0673563 1.28523i −0.730720 0.682678i \(-0.760815\pi\)
0.798076 0.602557i \(-0.205851\pi\)
\(692\) −10.4265 6.01972i −0.396355 0.228835i
\(693\) −3.95054 2.02390i −0.150069 0.0768815i
\(694\) −7.10285 7.10285i −0.269620 0.269620i
\(695\) −2.57014 + 3.95766i −0.0974909 + 0.150123i
\(696\) −0.101167 + 0.134270i −0.00383473 + 0.00508948i
\(697\) 3.73745 0.591953i 0.141566 0.0224218i
\(698\) −29.4660 26.5313i −1.11530 1.00422i
\(699\) 6.29966 2.29331i 0.238275 0.0867410i
\(700\) 0.702352 1.82969i 0.0265464 0.0691557i
\(701\) 22.9192 16.6518i 0.865646 0.628928i −0.0637694 0.997965i \(-0.520312\pi\)
0.929415 + 0.369036i \(0.120312\pi\)
\(702\) 36.5891 7.91386i 1.38097 0.298689i
\(703\) −22.6702 −0.855022
\(704\) 8.94966 + 24.7681i 0.337303 + 0.933481i
\(705\) 0.960322 + 27.4534i 0.0361678 + 1.03396i
\(706\) 2.11962 + 9.97202i 0.0797729 + 0.375302i
\(707\) −0.0842503 + 0.531936i −0.00316856 + 0.0200055i
\(708\) 47.9679 + 16.5135i 1.80274 + 0.620615i
\(709\) 0.930440 + 17.7539i 0.0349434 + 0.666760i 0.958810 + 0.284047i \(0.0916771\pi\)
−0.923867 + 0.382714i \(0.874990\pi\)
\(710\) −11.9253 + 23.4047i −0.447548 + 0.878362i
\(711\) −6.22127 3.88646i −0.233316 0.145754i
\(712\) −0.125190 + 0.0131580i −0.00469168 + 0.000493115i
\(713\) 2.23281 42.6045i 0.0836194 1.59555i
\(714\) 0.673981 + 1.07845i 0.0252231 + 0.0403601i
\(715\) 1.15441 + 32.0773i 0.0431724 + 1.19962i
\(716\) 27.1158i 1.01336i
\(717\) −39.8403 + 22.0869i −1.48786 + 0.824850i
\(718\) −0.644888 6.13570i −0.0240670 0.228982i
\(719\) −2.20805 + 21.0082i −0.0823462 + 0.783472i 0.872948 + 0.487814i \(0.162206\pi\)
−0.955294 + 0.295658i \(0.904461\pi\)
\(720\) −25.8171 + 19.4593i −0.962145 + 0.725207i
\(721\) 6.75506 0.354018i 0.251572 0.0131843i
\(722\) 2.75382 2.23000i 0.102487 0.0829919i
\(723\) −16.2298 38.2288i −0.603593 1.42174i
\(724\) −24.2695 + 5.15865i −0.901971 + 0.191720i
\(725\) −7.20342 + 12.4767i −0.267528 + 0.463373i
\(726\) 35.6034 13.4796i 1.32137 0.500275i
\(727\) 46.5047i 1.72476i −0.506257 0.862382i \(-0.668971\pi\)
0.506257 0.862382i \(-0.331029\pi\)
\(728\) −0.00863799 0.0222766i −0.000320145 0.000825625i
\(729\) 18.0594 20.0713i 0.668867 0.743382i
\(730\) −40.3938 15.5057i −1.49504 0.573893i
\(731\) 1.44234 6.78568i 0.0533469 0.250977i
\(732\) 24.3525 + 4.29251i 0.900094 + 0.158656i
\(733\) 0.810261 + 5.11578i 0.0299277 + 0.188956i 0.998123 0.0612392i \(-0.0195053\pi\)
−0.968195 + 0.250195i \(0.919505\pi\)
\(734\) −23.8057 + 9.13815i −0.878684 + 0.337295i
\(735\) −31.6138 0.549949i −1.16609 0.0202852i
\(736\) 46.9342 46.9342i 1.73002 1.73002i
\(737\) 8.52143 + 6.45249i 0.313891 + 0.237680i
\(738\) 22.8286 15.4020i 0.840333 0.566957i
\(739\) 53.1479 + 2.78536i 1.95508 + 0.102461i 0.988238 0.152924i \(-0.0488691\pi\)
0.966839 + 0.255386i \(0.0822024\pi\)
\(740\) −21.5220 + 15.6366i −0.791163 + 0.574814i
\(741\) 18.2205 21.8672i 0.669348 0.803312i
\(742\) −2.10660 6.48345i −0.0773358 0.238015i
\(743\) −18.9640 + 12.3154i −0.695722 + 0.451807i −0.843441 0.537222i \(-0.819474\pi\)
0.147719 + 0.989029i \(0.452807\pi\)
\(744\) 0.109578 + 0.0739021i 0.00401734 + 0.00270938i
\(745\) −14.8712 + 33.4013i −0.544838 + 1.22373i
\(746\) −7.98230 15.6661i −0.292253 0.573578i
\(747\) −19.3172 + 22.2272i −0.706779 + 0.813251i
\(748\) −5.35850 0.957703i −0.195926 0.0350171i
\(749\) 0.322042 + 0.322042i 0.0117671 + 0.0117671i
\(750\) 18.6777 18.0390i 0.682012 0.658689i
\(751\) 51.7300 5.43704i 1.88765 0.198400i 0.910879 0.412673i \(-0.135405\pi\)
0.976774 + 0.214272i \(0.0687379\pi\)
\(752\) 22.1467 + 8.50131i 0.807606 + 0.310011i
\(753\) 32.9432 + 27.6393i 1.20052 + 1.00723i
\(754\) −9.94384 46.0141i −0.362133 1.67573i
\(755\) 29.8084 41.0278i 1.08484 1.49315i
\(756\) 3.87422 + 2.51497i 0.140904 + 0.0914685i
\(757\) −18.5330 20.5829i −0.673592 0.748100i 0.305349 0.952240i \(-0.401227\pi\)
−0.978942 + 0.204141i \(0.934560\pi\)
\(758\) 6.31303 + 10.9345i 0.229299 + 0.397158i
\(759\) −34.2423 33.2177i −1.24292 1.20573i
\(760\) −0.0470333 + 0.175531i −0.00170608 + 0.00636717i
\(761\) 9.12350 + 5.92487i 0.330726 + 0.214776i 0.699310 0.714818i \(-0.253491\pi\)
−0.368584 + 0.929595i \(0.620157\pi\)
\(762\) −2.61569 + 1.11048i −0.0947563 + 0.0402283i
\(763\) 0.00206910 0.0196862i 7.49064e−5 0.000712687i
\(764\) 26.9610 + 5.73074i 0.975416 + 0.207331i
\(765\) −0.809108 6.58322i −0.0292534 0.238017i
\(766\) −20.9369 + 28.8172i −0.756482 + 1.04121i
\(767\) 45.8086 26.6552i 1.65405 0.962463i
\(768\) 6.75550 + 27.0880i 0.243768 + 0.977454i
\(769\) 20.9843 5.62272i 0.756713 0.202761i 0.140219 0.990121i \(-0.455219\pi\)
0.616494 + 0.787360i \(0.288553\pi\)
\(770\) −5.42556 + 5.79114i −0.195524 + 0.208698i
\(771\) −1.90634 1.01347i −0.0686551 0.0364993i
\(772\) 44.3312 22.5879i 1.59552 0.812956i
\(773\) −16.4487 + 6.31407i −0.591619 + 0.227101i −0.635712 0.771926i \(-0.719294\pi\)
0.0440930 + 0.999027i \(0.485960\pi\)
\(774\) −11.3628 49.1910i −0.408427 1.76814i
\(775\) 10.0919 + 5.14208i 0.362512 + 0.184709i
\(776\) −0.165113 0.148668i −0.00592720 0.00533687i
\(777\) −3.18641 2.14899i −0.114312 0.0770944i
\(778\) −21.6449 17.5277i −0.776007 0.628398i
\(779\) 6.47037 19.9137i 0.231825 0.713484i
\(780\) 2.21491 33.3272i 0.0793066 1.19330i
\(781\) 12.2839 10.6282i 0.439554 0.380307i
\(782\) 3.53760 + 13.2025i 0.126504 + 0.472121i
\(783\) −25.2365 22.7149i −0.901879 0.811765i
\(784\) −11.1058 + 24.9440i −0.396636 + 0.890859i
\(785\) 25.0439 3.96656i 0.893854 0.141573i
\(786\) −7.69151 + 5.38633i −0.274347 + 0.192124i
\(787\) −1.18351 22.5827i −0.0421876 0.804988i −0.935019 0.354597i \(-0.884618\pi\)
0.892832 0.450391i \(-0.148715\pi\)
\(788\) 0.139481 + 0.880651i 0.00496882 + 0.0313719i
\(789\) −1.85886 13.2208i −0.0661773 0.470674i
\(790\) −9.74574 + 8.77511i −0.346738 + 0.312204i
\(791\) −4.33085 + 1.16045i −0.153987 + 0.0412608i
\(792\) 0.142844 0.0379373i 0.00507575 0.00134804i
\(793\) 20.0212 16.3256i 0.710975 0.579740i
\(794\) −26.6757 8.66746i −0.946685 0.307596i
\(795\) −4.33094 + 35.2899i −0.153603 + 1.25160i
\(796\) 31.2869 13.9298i 1.10893 0.493729i
\(797\) 16.2886 18.0903i 0.576972 0.640792i −0.382044 0.924144i \(-0.624780\pi\)
0.959016 + 0.283352i \(0.0914465\pi\)
\(798\) 7.01020 0.613731i 0.248158 0.0217258i
\(799\) −3.78230 + 3.06285i −0.133808 + 0.108356i
\(800\) 6.31501 + 16.4512i 0.223269 + 0.581636i
\(801\) −0.446704 25.4192i −0.0157835 0.898144i
\(802\) −29.0613 50.3356i −1.02619 1.77741i
\(803\) 19.5257 + 18.2931i 0.689047 + 0.645549i
\(804\) −8.13496 7.58507i −0.286898 0.267505i
\(805\) 9.45777 + 3.07302i 0.333343 + 0.108310i
\(806\) −35.7167 + 9.70023i −1.25807 + 0.341676i
\(807\) −2.81925 + 40.3514i −0.0992421 + 1.42044i
\(808\) −0.00976664 0.0150393i −0.000343589 0.000529081i
\(809\) 2.28537 10.7518i 0.0803495 0.378015i −0.919538 0.393001i \(-0.871437\pi\)
0.999888 + 0.0149860i \(0.00477037\pi\)
\(810\) −25.5890 40.9294i −0.899105 1.43811i
\(811\) 13.0379 + 2.06501i 0.457824 + 0.0725122i 0.381087 0.924539i \(-0.375550\pi\)
0.0767369 + 0.997051i \(0.475550\pi\)
\(812\) 3.16354 4.87143i 0.111019 0.170954i
\(813\) −10.7750 + 3.29496i −0.377897 + 0.115559i
\(814\) 32.0021 7.90001i 1.12167 0.276895i
\(815\) 17.9848 10.3835i 0.629979 0.363719i
\(816\) −5.50601 1.57847i −0.192749 0.0552575i
\(817\) −29.8320 24.1575i −1.04369 0.845165i
\(818\) −31.0883 22.5870i −1.08698 0.789736i
\(819\) 4.63386 1.34636i 0.161920 0.0470456i
\(820\) −7.59273 23.3680i −0.265150 0.816047i
\(821\) −18.1060 + 47.1678i −0.631904 + 1.64617i 0.124623 + 0.992204i \(0.460228\pi\)
−0.756527 + 0.653962i \(0.773106\pi\)
\(822\) 22.0850 + 28.2641i 0.770303 + 0.985822i
\(823\) 6.99148 + 32.8923i 0.243708 + 1.14655i 0.914398 + 0.404817i \(0.132665\pi\)
−0.670690 + 0.741738i \(0.734002\pi\)
\(824\) −0.159260 + 0.159260i −0.00554809 + 0.00554809i
\(825\) 11.7540 4.71794i 0.409220 0.164258i
\(826\) 12.6566 + 3.39132i 0.440379 + 0.117999i
\(827\) 43.7123 22.2725i 1.52002 0.774491i 0.523056 0.852298i \(-0.324792\pi\)
0.996968 + 0.0778074i \(0.0247919\pi\)
\(828\) 31.9144 + 38.0250i 1.10910 + 1.32146i
\(829\) 4.18819 + 9.40683i 0.145462 + 0.326713i 0.971552 0.236825i \(-0.0761067\pi\)
−0.826090 + 0.563538i \(0.809440\pi\)
\(830\) 28.6737 + 44.1537i 0.995279 + 1.53260i
\(831\) 7.74637 9.23287i 0.268718 0.320285i
\(832\) −25.5531 12.9110i −0.885894 0.447607i
\(833\) −3.29270 4.53202i −0.114085 0.157025i
\(834\) −5.32144 + 2.95013i −0.184266 + 0.102155i
\(835\) −21.0539 + 36.4665i −0.728602 + 1.26198i
\(836\) −18.1829 + 24.0131i −0.628868 + 0.830511i
\(837\) −16.7952 + 20.7479i −0.580528 + 0.717152i
\(838\) −9.87474 6.41273i −0.341117 0.221524i
\(839\) −0.00522152 0.0136025i −0.000180267 0.000469611i 0.933490 0.358603i \(-0.116747\pi\)
−0.933671 + 0.358133i \(0.883413\pi\)
\(840\) −0.0232499 + 0.0202133i −0.000802199 + 0.000697425i
\(841\) −9.16580 + 10.1797i −0.316062 + 0.351023i
\(842\) 52.6367 + 11.1883i 1.81398 + 0.385573i
\(843\) 22.2184 4.32018i 0.765242 0.148795i
\(844\) 1.26569 + 1.74208i 0.0435669 + 0.0599647i
\(845\) −24.8408 24.5060i −0.854548 0.843032i
\(846\) −15.5230 + 31.8364i −0.533691 + 1.09456i
\(847\) 4.45710 2.05320i 0.153148 0.0705487i
\(848\) 26.5902 + 15.3519i 0.913112 + 0.527185i
\(849\) 23.6038 + 24.4396i 0.810081 + 0.838764i
\(850\) −3.58404 0.567656i −0.122932 0.0194704i
\(851\) −25.9954 32.1017i −0.891112 1.10043i
\(852\) −13.8454 + 9.69588i −0.474336 + 0.332175i
\(853\) 9.04920 + 4.61080i 0.309839 + 0.157871i 0.601995 0.798500i \(-0.294373\pi\)
−0.292156 + 0.956371i \(0.594373\pi\)
\(854\) 6.35188 + 0.667610i 0.217357 + 0.0228451i
\(855\) −34.4897 12.5486i −1.17952 0.429154i
\(856\) −0.0151436 0.000793642i −0.000517597 2.71261e-5i
\(857\) −20.5452 −0.701810 −0.350905 0.936411i \(-0.614126\pi\)
−0.350905 + 0.936411i \(0.614126\pi\)
\(858\) −18.1006 + 37.2180i −0.617944 + 1.27060i
\(859\) −49.0548 −1.67373 −0.836864 0.547411i \(-0.815613\pi\)
−0.836864 + 0.547411i \(0.815613\pi\)
\(860\) −44.9836 2.35749i −1.53393 0.0803897i
\(861\) 2.79714 2.18563i 0.0953261 0.0744860i
\(862\) 4.55767 + 0.479031i 0.155235 + 0.0163159i
\(863\) −28.1465 14.3413i −0.958117 0.488185i −0.0962710 0.995355i \(-0.530692\pi\)
−0.861846 + 0.507170i \(0.830692\pi\)
\(864\) −41.0175 + 6.50401i −1.39545 + 0.221271i
\(865\) 10.2065 + 12.6039i 0.347030 + 0.428547i
\(866\) 55.2975 + 8.75826i 1.87908 + 0.297618i
\(867\) −20.3344 + 19.6390i −0.690592 + 0.666976i
\(868\) −3.95475 2.28327i −0.134233 0.0774994i
\(869\) 7.62700 2.75593i 0.258728 0.0934885i
\(870\) −51.4761 + 32.1701i −1.74520 + 1.09067i
\(871\) −11.5521 + 1.25380i −0.391426 + 0.0424834i
\(872\) 0.000387403 0 0.000533214i 1.31191e−5 0 1.80569e-5i
\(873\) 32.8142 30.6070i 1.11059 1.03589i
\(874\) 73.9790 + 15.7247i 2.50238 + 0.531897i
\(875\) 2.23968 2.48742i 0.0757150 0.0840900i
\(876\) −18.2672 21.0115i −0.617192 0.709913i
\(877\) −13.6623 35.5914i −0.461342 1.20184i −0.945142 0.326659i \(-0.894077\pi\)
0.483800 0.875179i \(-0.339256\pi\)
\(878\) 19.2699 + 12.5140i 0.650327 + 0.422328i
\(879\) −24.0400 5.54858i −0.810850 0.187149i
\(880\) 0.706881 35.7344i 0.0238290 1.20461i
\(881\) 5.41857 9.38524i 0.182556 0.316197i −0.760194 0.649696i \(-0.774896\pi\)
0.942750 + 0.333499i \(0.108230\pi\)
\(882\) −35.6588 19.7605i −1.20069 0.665370i
\(883\) −2.77235 3.81581i −0.0932970 0.128412i 0.759817 0.650137i \(-0.225289\pi\)
−0.853114 + 0.521725i \(0.825289\pi\)
\(884\) 4.95197 3.23978i 0.166553 0.108966i
\(885\) −52.3534 43.9244i −1.75984 1.47650i
\(886\) 11.6208 + 17.8945i 0.390410 + 0.601178i
\(887\) 22.1294 + 49.7034i 0.743032 + 1.66888i 0.743372 + 0.668878i \(0.233225\pi\)
−0.000339775 1.00000i \(0.500108\pi\)
\(888\) 0.126723 0.0178174i 0.00425256 0.000597914i
\(889\) −0.326372 + 0.166295i −0.0109462 + 0.00557735i
\(890\) −43.9024 11.7636i −1.47161 0.394317i
\(891\) 5.12192 + 29.4069i 0.171591 + 0.985168i
\(892\) −10.0451 + 10.0451i −0.336334 + 0.336334i
\(893\) 5.59917 + 26.3420i 0.187369 + 0.881503i
\(894\) −37.1468 + 29.0258i −1.24237 + 0.970767i
\(895\) −13.0903 + 34.1014i −0.437560 + 1.13988i
\(896\) 0.0163818 + 0.0504181i 0.000547279 + 0.00168435i
\(897\) 51.8578 + 0.726170i 1.73148 + 0.0242461i
\(898\) 36.1871 + 26.2914i 1.20758 + 0.877357i
\(899\) 26.0876 + 21.1253i 0.870070 + 0.704569i
\(900\) −12.6685 + 3.63426i −0.422284 + 0.121142i
\(901\) −5.45530 + 3.14962i −0.181742 + 0.104929i
\(902\) −2.19436 + 30.3658i −0.0730641 + 1.01107i
\(903\) −1.90307 6.22334i −0.0633302 0.207100i
\(904\) 0.0813085 0.125204i 0.00270428 0.00416423i
\(905\) 33.0122 + 5.22862i 1.09736 + 0.173805i
\(906\) 58.7685 28.6676i 1.95245 0.952418i
\(907\) −2.45028 + 11.5277i −0.0813601 + 0.382769i −0.999922 0.0125084i \(-0.996018\pi\)
0.918562 + 0.395278i \(0.129352\pi\)
\(908\) 17.7369 + 27.3124i 0.588618 + 0.906393i
\(909\) 3.19757 1.70066i 0.106057 0.0564074i
\(910\) −0.0292618 8.62688i −0.000970019 0.285978i
\(911\) −12.1291 3.94100i −0.401856 0.130571i 0.101114 0.994875i \(-0.467759\pi\)
−0.502970 + 0.864304i \(0.667759\pi\)
\(912\) −21.6140 + 23.1809i −0.715712 + 0.767598i
\(913\) −6.13770 31.9725i −0.203128 1.05814i
\(914\) −20.3250 35.2039i −0.672291 1.16444i
\(915\) −28.5539 17.1546i −0.943964 0.567115i
\(916\) 13.8767 + 36.1502i 0.458501 + 1.19443i
\(917\) −0.940653 + 0.761725i −0.0310631 + 0.0251544i
\(918\) 3.06336 7.98457i 0.101106 0.263530i
\(919\) −2.35536 + 2.61589i −0.0776960 + 0.0862902i −0.780739 0.624857i \(-0.785157\pi\)
0.703043 + 0.711147i \(0.251824\pi\)
\(920\) −0.302489 + 0.134677i −0.00997278 + 0.00444017i
\(921\) 44.1268 + 5.41544i 1.45403 + 0.178445i
\(922\) 7.40514 + 2.40608i 0.243875 + 0.0792399i
\(923\) −1.78625 + 17.5681i −0.0587952 + 0.578260i
\(924\) −4.83198 + 1.65155i −0.158961 + 0.0543318i
\(925\) 10.5928 2.83832i 0.348288 0.0933235i
\(926\) 30.0496 27.0568i 0.987491 0.889141i
\(927\) −29.2433 34.8425i −0.960477 1.14438i
\(928\) 8.16990 + 51.5827i 0.268190 + 1.69329i
\(929\) 1.03653 + 19.7781i 0.0340074 + 0.648899i 0.961458 + 0.274953i \(0.0886623\pi\)
−0.927450 + 0.373946i \(0.878004\pi\)
\(930\) 27.3749 + 39.0905i 0.897658 + 1.28183i
\(931\) −30.6158 + 4.84906i −1.00339 + 0.158922i
\(932\) 3.13694 7.04568i 0.102754 0.230789i
\(933\) 3.82122 + 1.09547i 0.125101 + 0.0358642i
\(934\) 3.38610 + 12.6371i 0.110797 + 0.413499i
\(935\) 6.27662 + 3.79127i 0.205267 + 0.123988i
\(936\) −0.0846640 + 0.136555i −0.00276733 + 0.00446344i
\(937\) 7.26589 22.3621i 0.237366 0.730539i −0.759432 0.650586i \(-0.774523\pi\)
0.996799 0.0799523i \(-0.0254768\pi\)
\(938\) −2.23258 1.80791i −0.0728964 0.0590303i
\(939\) 12.7393 18.8892i 0.415732 0.616426i
\(940\) 23.4848 + 21.1459i 0.765991 + 0.689702i
\(941\) −16.0983 8.20249i −0.524790 0.267394i 0.171463 0.985191i \(-0.445151\pi\)
−0.696253 + 0.717797i \(0.745151\pi\)
\(942\) 30.9127 + 10.6421i 1.00719 + 0.346737i
\(943\) 35.6179 13.6724i 1.15988 0.445236i
\(944\) −52.5829 + 26.7923i −1.71143 + 0.872016i
\(945\) −3.65818 5.03317i −0.119001 0.163729i
\(946\) 50.5304 + 23.7059i 1.64288 + 0.770746i
\(947\) −27.3555 + 7.32988i −0.888933 + 0.238189i −0.674257 0.738496i \(-0.735536\pi\)
−0.214676 + 0.976685i \(0.568870\pi\)
\(948\) −8.18797 + 2.04200i −0.265933 + 0.0663212i
\(949\) −29.0868 + 0.0986605i −0.944197 + 0.00320265i
\(950\) −11.8022 + 16.2443i −0.382914 + 0.527036i
\(951\) 4.99751 10.7189i 0.162055 0.347583i
\(952\) −0.00533900 0.00113484i −0.000173038 3.67804e-5i
\(953\) 5.62138 53.4839i 0.182094 1.73251i −0.397495 0.917604i \(-0.630121\pi\)
0.579590 0.814908i \(-0.303213\pi\)
\(954\) −26.2900 + 37.5555i −0.851171 + 1.21590i
\(955\) −31.1402 20.2227i −1.00767 0.654390i
\(956\) −13.5633 + 50.6189i −0.438669 + 1.63713i
\(957\) 36.9815 6.43445i 1.19544 0.207996i
\(958\) −12.8013 22.1725i −0.413591 0.716360i
\(959\) 3.09382 + 3.43603i 0.0999046 + 0.110955i
\(960\) −4.49676 + 36.6411i −0.145132 + 1.18259i
\(961\) −2.70915 + 3.72883i −0.0873920 + 0.120285i
\(962\) −19.4147 + 30.1192i −0.625955 + 0.971082i
\(963\) 0.425882 3.03291i 0.0137239 0.0977343i
\(964\) −44.6045 17.1221i −1.43661 0.551465i
\(965\) −66.6563 + 7.00586i −2.14574 + 0.225526i
\(966\) 8.90752 + 9.22292i 0.286595 + 0.296742i
\(967\) 31.3623 + 31.3623i 1.00854 + 1.00854i 0.999963 + 0.00857908i \(0.00273084\pi\)
0.00857908 + 0.999963i \(0.497269\pi\)
\(968\) −0.0645423 + 0.150107i −0.00207447 + 0.00482463i
\(969\) −1.90150 6.21821i −0.0610849 0.199758i
\(970\) −36.4204 71.4790i −1.16939 2.29505i
\(971\) −10.2283 + 22.9731i −0.328241 + 0.737242i −0.999994 0.00353382i \(-0.998875\pi\)
0.671753 + 0.740776i \(0.265542\pi\)
\(972\) −2.17588 30.9847i −0.0697913 0.993836i
\(973\) −0.657774 + 0.427164i −0.0210873 + 0.0136942i
\(974\) −7.38478 22.7280i −0.236624 0.728253i
\(975\) −5.77586 + 12.4988i −0.184975 + 0.400282i
\(976\) −23.2722 + 16.9082i −0.744924 + 0.541219i
\(977\) −51.6613 2.70746i −1.65279 0.0866192i −0.797014 0.603961i \(-0.793588\pi\)
−0.855779 + 0.517342i \(0.826922\pi\)
\(978\) 26.7599 0.936063i 0.855689 0.0299320i
\(979\) 22.4073 + 16.9670i 0.716142 + 0.542267i
\(980\) −25.7205 + 25.7205i −0.821611 + 0.821611i
\(981\) −0.114092 + 0.0685716i −0.00364267 + 0.00218932i
\(982\) −6.70649 + 2.57438i −0.214013 + 0.0821518i
\(983\) 1.95124 + 12.3197i 0.0622349 + 0.392936i 0.999068 + 0.0431596i \(0.0137424\pi\)
−0.936833 + 0.349776i \(0.886258\pi\)
\(984\) −0.0205175 + 0.116401i −0.000654072 + 0.00371071i
\(985\) 0.249724 1.17486i 0.00795687 0.0374341i
\(986\) −10.0402 3.85409i −0.319746 0.122739i
\(987\) −1.71006 + 4.23327i −0.0544319 + 0.134747i
\(988\) −3.53317 32.5533i −0.112405 1.03566i
\(989\) 69.9441i 2.22409i
\(990\) 53.0599 + 5.69526i 1.68635 + 0.181007i
\(991\) 20.4641 35.4448i 0.650062 1.12594i −0.333045 0.942911i \(-0.608076\pi\)
0.983107 0.183030i \(-0.0585906\pi\)
\(992\) 40.1617 8.53662i 1.27513 0.271038i
\(993\) 11.1609 4.73829i 0.354180 0.150365i
\(994\) −3.39283 + 2.74746i −0.107614 + 0.0871442i
\(995\) −46.0716 + 2.41451i −1.46057 + 0.0765452i
\(996\) 2.95462 + 33.7485i 0.0936208 + 1.06936i
\(997\) −3.09389 + 29.4364i −0.0979844 + 0.932260i 0.829527 + 0.558466i \(0.188610\pi\)
−0.927512 + 0.373794i \(0.878057\pi\)
\(998\) 2.15087 + 20.4642i 0.0680846 + 0.647782i
\(999\) 1.35723 + 25.8097i 0.0429407 + 0.816584i
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 429.2.bv.a.20.10 832
3.2 odd 2 inner 429.2.bv.a.20.43 yes 832
11.5 even 5 inner 429.2.bv.a.137.43 yes 832
13.2 odd 12 inner 429.2.bv.a.119.10 yes 832
33.5 odd 10 inner 429.2.bv.a.137.10 yes 832
39.2 even 12 inner 429.2.bv.a.119.43 yes 832
143.93 odd 60 inner 429.2.bv.a.236.43 yes 832
429.236 even 60 inner 429.2.bv.a.236.10 yes 832
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.bv.a.20.10 832 1.1 even 1 trivial
429.2.bv.a.20.43 yes 832 3.2 odd 2 inner
429.2.bv.a.119.10 yes 832 13.2 odd 12 inner
429.2.bv.a.119.43 yes 832 39.2 even 12 inner
429.2.bv.a.137.10 yes 832 33.5 odd 10 inner
429.2.bv.a.137.43 yes 832 11.5 even 5 inner
429.2.bv.a.236.10 yes 832 429.236 even 60 inner
429.2.bv.a.236.43 yes 832 143.93 odd 60 inner