Properties

Label 804.2.bf.b.7.3
Level $804$
Weight $2$
Character 804.7
Analytic conductor $6.420$
Analytic rank $0$
Dimension $680$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [804,2,Mod(7,804)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(804, base_ring=CyclotomicField(66))
 
chi = DirichletCharacter(H, H._module([33, 0, 23]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("804.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 804.bf (of order \(66\), degree \(20\), 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: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(680\)
Relative dimension: \(34\) over \(\Q(\zeta_{66})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label 7.3
Character \(\chi\) \(=\) 804.7
Dual form 804.2.bf.b.115.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.39654 + 0.222851i) q^{2} +(0.959493 + 0.281733i) q^{3} +(1.90067 - 0.622444i) q^{4} +(0.851506 + 0.737834i) q^{5} +(-1.40276 - 0.179628i) q^{6} +(-0.200085 + 4.20030i) q^{7} +(-2.51566 + 1.29284i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\) \(q+(-1.39654 + 0.222851i) q^{2} +(0.959493 + 0.281733i) q^{3} +(1.90067 - 0.622444i) q^{4} +(0.851506 + 0.737834i) q^{5} +(-1.40276 - 0.179628i) q^{6} +(-0.200085 + 4.20030i) q^{7} +(-2.51566 + 1.29284i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-1.35359 - 0.840659i) q^{10} +(5.02159 + 0.967831i) q^{11} +(1.99905 - 0.0617487i) q^{12} +(-1.62754 + 4.06539i) q^{13} +(-0.656615 - 5.91049i) q^{14} +(0.609142 + 0.947844i) q^{15} +(3.22513 - 2.36613i) q^{16} +(-1.33842 - 1.87954i) q^{17} +(-1.29533 - 0.567555i) q^{18} +(-6.17296 + 0.294055i) q^{19} +(2.07770 + 0.872368i) q^{20} +(-1.37534 + 3.97378i) q^{21} +(-7.22855 - 0.232552i) q^{22} +(1.21618 + 1.27550i) q^{23} +(-2.77800 + 0.531725i) q^{24} +(-0.530911 - 3.69257i) q^{25} +(1.36695 - 6.04020i) q^{26} +(0.654861 + 0.755750i) q^{27} +(2.23415 + 8.10794i) q^{28} +(-2.11626 - 3.66547i) q^{29} +(-1.06192 - 1.18796i) q^{30} +(-2.93522 + 1.17509i) q^{31} +(-3.97674 + 4.02313i) q^{32} +(4.54551 + 2.34337i) q^{33} +(2.28802 + 2.32660i) q^{34} +(-3.26950 + 3.42895i) q^{35} +(1.93547 + 0.503949i) q^{36} +(-4.19530 + 7.26647i) q^{37} +(8.55529 - 1.78631i) q^{38} +(-2.70696 + 3.44218i) q^{39} +(-3.09601 - 0.755283i) q^{40} +(-0.329718 - 3.45297i) q^{41} +(1.03516 - 5.85606i) q^{42} +(1.49948 - 3.28341i) q^{43} +(10.1468 - 1.28612i) q^{44} +(0.317429 + 1.08106i) q^{45} +(-1.98270 - 1.51026i) q^{46} +(4.77256 - 1.15781i) q^{47} +(3.76110 - 1.36166i) q^{48} +(-10.6342 - 1.01544i) q^{49} +(1.56433 + 5.03852i) q^{50} +(-0.754673 - 2.18048i) q^{51} +(-0.562940 + 8.74003i) q^{52} +(10.8310 - 4.94636i) q^{53} +(-1.08296 - 0.909501i) q^{54} +(3.56181 + 4.52921i) q^{55} +(-4.92696 - 10.8252i) q^{56} +(-6.00576 - 1.45698i) q^{57} +(3.77230 + 4.64738i) q^{58} +(2.35946 + 0.339239i) q^{59} +(1.74776 + 1.42239i) q^{60} +(-0.554856 - 2.87886i) q^{61} +(3.83730 - 2.29518i) q^{62} +(-2.43917 + 3.42534i) q^{63} +(4.65714 - 6.50470i) q^{64} +(-4.38544 + 2.26085i) q^{65} +(-6.87023 - 2.25965i) q^{66} +(7.72643 + 2.70228i) q^{67} +(-3.71380 - 2.73931i) q^{68} +(0.807571 + 1.56647i) q^{69} +(3.80185 - 5.51729i) q^{70} +(8.66967 + 6.17364i) q^{71} +(-2.81527 - 0.272466i) q^{72} +(14.4478 - 2.78459i) q^{73} +(4.23958 - 11.0829i) q^{74} +(0.530911 - 3.69257i) q^{75} +(-11.5498 + 4.40123i) q^{76} +(-5.06992 + 20.8985i) q^{77} +(3.01330 - 5.41041i) q^{78} +(-11.8138 + 9.29050i) q^{79} +(4.49203 + 0.364838i) q^{80} +(0.415415 + 0.909632i) q^{81} +(1.22997 + 4.74874i) q^{82} +(-16.4716 + 5.70086i) q^{83} +(-0.140616 + 8.40894i) q^{84} +(0.247121 - 2.58797i) q^{85} +(-1.36238 + 4.91959i) q^{86} +(-0.997854 - 4.11321i) q^{87} +(-13.8839 + 4.05736i) q^{88} +(-11.1422 + 3.27164i) q^{89} +(-0.684221 - 1.43902i) q^{90} +(-16.7502 - 7.64956i) q^{91} +(3.10550 + 1.66730i) q^{92} +(-3.14738 + 0.300539i) q^{93} +(-6.40707 + 2.68051i) q^{94} +(-5.47328 - 4.30424i) q^{95} +(-4.94910 + 2.73978i) q^{96} +(15.8538 + 9.15322i) q^{97} +(15.0774 - 0.951731i) q^{98} +(3.70118 + 3.52907i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 680 q + 68 q^{3} + 2 q^{4} + 11 q^{6} - 4 q^{7} - 27 q^{8} - 68 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 680 q + 68 q^{3} + 2 q^{4} + 11 q^{6} - 4 q^{7} - 27 q^{8} - 68 q^{9} + 15 q^{10} + 9 q^{12} - 6 q^{13} - 10 q^{14} + 2 q^{16} + 36 q^{20} + 4 q^{21} + 33 q^{22} - 6 q^{24} + 68 q^{25} + q^{26} + 68 q^{27} + 76 q^{28} + 8 q^{29} + 18 q^{30} - 2 q^{31} + 40 q^{32} - 9 q^{36} - 12 q^{37} + 22 q^{38} + 6 q^{39} + 37 q^{40} + 10 q^{42} + 4 q^{43} - 123 q^{44} + 67 q^{46} - 2 q^{48} + 46 q^{49} + 42 q^{50} + 28 q^{52} + 11 q^{56} - 66 q^{57} - 92 q^{58} + 74 q^{60} - 6 q^{61} + 34 q^{62} + 18 q^{63} - 49 q^{64} - 22 q^{66} + 18 q^{67} + 208 q^{68} - 56 q^{70} + 36 q^{71} + 6 q^{72} - 72 q^{73} + 53 q^{74} - 68 q^{75} - 190 q^{76} + 4 q^{77} - q^{78} - 28 q^{79} + 11 q^{80} - 68 q^{81} - 84 q^{82} - 12 q^{83} + q^{84} - 89 q^{86} - 8 q^{87} + 160 q^{88} + 15 q^{90} + 166 q^{92} + 2 q^{93} + 16 q^{94} - 20 q^{95} + 15 q^{96} - 18 q^{97} + 37 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(1\) \(e\left(\frac{23}{66}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.39654 + 0.222851i −0.987506 + 0.157580i
\(3\) 0.959493 + 0.281733i 0.553964 + 0.162658i
\(4\) 1.90067 0.622444i 0.950337 0.311222i
\(5\) 0.851506 + 0.737834i 0.380805 + 0.329970i 0.824140 0.566387i \(-0.191659\pi\)
−0.443334 + 0.896356i \(0.646205\pi\)
\(6\) −1.40276 0.179628i −0.572674 0.0733327i
\(7\) −0.200085 + 4.20030i −0.0756249 + 1.58756i 0.568527 + 0.822665i \(0.307514\pi\)
−0.644152 + 0.764898i \(0.722789\pi\)
\(8\) −2.51566 + 1.29284i −0.889422 + 0.457088i
\(9\) 0.841254 + 0.540641i 0.280418 + 0.180214i
\(10\) −1.35359 0.840659i −0.428044 0.265840i
\(11\) 5.02159 + 0.967831i 1.51406 + 0.291812i 0.877562 0.479462i \(-0.159168\pi\)
0.636503 + 0.771275i \(0.280380\pi\)
\(12\) 1.99905 0.0617487i 0.577075 0.0178253i
\(13\) −1.62754 + 4.06539i −0.451397 + 1.12754i 0.511887 + 0.859053i \(0.328947\pi\)
−0.963284 + 0.268483i \(0.913478\pi\)
\(14\) −0.656615 5.91049i −0.175488 1.57965i
\(15\) 0.609142 + 0.947844i 0.157280 + 0.244732i
\(16\) 3.22513 2.36613i 0.806282 0.591532i
\(17\) −1.33842 1.87954i −0.324614 0.455856i 0.619731 0.784815i \(-0.287242\pi\)
−0.944344 + 0.328958i \(0.893302\pi\)
\(18\) −1.29533 0.567555i −0.305312 0.133774i
\(19\) −6.17296 + 0.294055i −1.41618 + 0.0674607i −0.741648 0.670789i \(-0.765956\pi\)
−0.674527 + 0.738250i \(0.735652\pi\)
\(20\) 2.07770 + 0.872368i 0.464587 + 0.195067i
\(21\) −1.37534 + 3.97378i −0.300124 + 0.867151i
\(22\) −7.22855 0.232552i −1.54113 0.0495803i
\(23\) 1.21618 + 1.27550i 0.253592 + 0.265960i 0.838208 0.545350i \(-0.183603\pi\)
−0.584616 + 0.811310i \(0.698755\pi\)
\(24\) −2.77800 + 0.531725i −0.567056 + 0.108538i
\(25\) −0.530911 3.69257i −0.106182 0.738513i
\(26\) 1.36695 6.04020i 0.268081 1.18458i
\(27\) 0.654861 + 0.755750i 0.126028 + 0.145444i
\(28\) 2.23415 + 8.10794i 0.422215 + 1.53226i
\(29\) −2.11626 3.66547i −0.392979 0.680660i 0.599862 0.800104i \(-0.295222\pi\)
−0.992841 + 0.119444i \(0.961889\pi\)
\(30\) −1.06192 1.18796i −0.193880 0.216891i
\(31\) −2.93522 + 1.17509i −0.527181 + 0.211052i −0.619957 0.784635i \(-0.712850\pi\)
0.0927761 + 0.995687i \(0.470426\pi\)
\(32\) −3.97674 + 4.02313i −0.702995 + 0.711195i
\(33\) 4.54551 + 2.34337i 0.791271 + 0.407929i
\(34\) 2.28802 + 2.32660i 0.392392 + 0.399008i
\(35\) −3.26950 + 3.42895i −0.552646 + 0.579598i
\(36\) 1.93547 + 0.503949i 0.322578 + 0.0839915i
\(37\) −4.19530 + 7.26647i −0.689703 + 1.19460i 0.282231 + 0.959347i \(0.408926\pi\)
−0.971934 + 0.235254i \(0.924408\pi\)
\(38\) 8.55529 1.78631i 1.38785 0.289778i
\(39\) −2.70696 + 3.44218i −0.433461 + 0.551190i
\(40\) −3.09601 0.755283i −0.489521 0.119421i
\(41\) −0.329718 3.45297i −0.0514934 0.539263i −0.984007 0.178129i \(-0.942996\pi\)
0.932514 0.361134i \(-0.117610\pi\)
\(42\) 1.03516 5.85606i 0.159729 0.903610i
\(43\) 1.49948 3.28341i 0.228669 0.500715i −0.760166 0.649729i \(-0.774883\pi\)
0.988835 + 0.149014i \(0.0476098\pi\)
\(44\) 10.1468 1.28612i 1.52969 0.193890i
\(45\) 0.317429 + 1.08106i 0.0473196 + 0.161156i
\(46\) −1.98270 1.51026i −0.292334 0.222676i
\(47\) 4.77256 1.15781i 0.696149 0.168884i 0.127957 0.991780i \(-0.459158\pi\)
0.568192 + 0.822896i \(0.307643\pi\)
\(48\) 3.76110 1.36166i 0.542868 0.196539i
\(49\) −10.6342 1.01544i −1.51916 0.145063i
\(50\) 1.56433 + 5.03852i 0.221230 + 0.712554i
\(51\) −0.754673 2.18048i −0.105675 0.305329i
\(52\) −0.562940 + 8.74003i −0.0780657 + 1.21202i
\(53\) 10.8310 4.94636i 1.48776 0.679435i 0.504793 0.863240i \(-0.331569\pi\)
0.982963 + 0.183805i \(0.0588416\pi\)
\(54\) −1.08296 0.909501i −0.147372 0.123767i
\(55\) 3.56181 + 4.52921i 0.480275 + 0.610719i
\(56\) −4.92696 10.8252i −0.658393 1.44658i
\(57\) −6.00576 1.45698i −0.795482 0.192982i
\(58\) 3.77230 + 4.64738i 0.495328 + 0.610231i
\(59\) 2.35946 + 0.339239i 0.307176 + 0.0441652i 0.294179 0.955750i \(-0.404954\pi\)
0.0129967 + 0.999916i \(0.495863\pi\)
\(60\) 1.74776 + 1.42239i 0.225635 + 0.183629i
\(61\) −0.554856 2.87886i −0.0710420 0.368601i 0.928957 0.370188i \(-0.120707\pi\)
−0.999999 + 0.00158742i \(0.999495\pi\)
\(62\) 3.83730 2.29518i 0.487337 0.291488i
\(63\) −2.43917 + 3.42534i −0.307307 + 0.431552i
\(64\) 4.65714 6.50470i 0.582142 0.813087i
\(65\) −4.38544 + 2.26085i −0.543947 + 0.280424i
\(66\) −6.87023 2.25965i −0.845666 0.278144i
\(67\) 7.72643 + 2.70228i 0.943933 + 0.330136i
\(68\) −3.71380 2.73931i −0.450365 0.332190i
\(69\) 0.807571 + 1.56647i 0.0972202 + 0.188581i
\(70\) 3.80185 5.51729i 0.454408 0.659443i
\(71\) 8.66967 + 6.17364i 1.02890 + 0.732677i 0.964186 0.265227i \(-0.0854470\pi\)
0.0647144 + 0.997904i \(0.479386\pi\)
\(72\) −2.81527 0.272466i −0.331783 0.0321104i
\(73\) 14.4478 2.78459i 1.69099 0.325912i 0.749260 0.662276i \(-0.230409\pi\)
0.941732 + 0.336364i \(0.109197\pi\)
\(74\) 4.23958 11.0829i 0.492841 1.28836i
\(75\) 0.530911 3.69257i 0.0613043 0.426381i
\(76\) −11.5498 + 4.40123i −1.32485 + 0.504855i
\(77\) −5.06992 + 20.8985i −0.577771 + 2.38160i
\(78\) 3.01330 5.41041i 0.341189 0.612609i
\(79\) −11.8138 + 9.29050i −1.32916 + 1.04526i −0.334464 + 0.942409i \(0.608555\pi\)
−0.994696 + 0.102854i \(0.967202\pi\)
\(80\) 4.49203 + 0.364838i 0.502224 + 0.0407901i
\(81\) 0.415415 + 0.909632i 0.0461572 + 0.101070i
\(82\) 1.22997 + 4.74874i 0.135827 + 0.524411i
\(83\) −16.4716 + 5.70086i −1.80799 + 0.625751i −0.808692 + 0.588233i \(0.799824\pi\)
−0.999296 + 0.0375181i \(0.988055\pi\)
\(84\) −0.140616 + 8.40894i −0.0153424 + 0.917491i
\(85\) 0.247121 2.58797i 0.0268041 0.280705i
\(86\) −1.36238 + 4.91959i −0.146909 + 0.530493i
\(87\) −0.997854 4.11321i −0.106981 0.440982i
\(88\) −13.8839 + 4.05736i −1.48003 + 0.432516i
\(89\) −11.1422 + 3.27164i −1.18107 + 0.346793i −0.812585 0.582842i \(-0.801941\pi\)
−0.368482 + 0.929635i \(0.620122\pi\)
\(90\) −0.684221 1.43902i −0.0721232 0.151686i
\(91\) −16.7502 7.64956i −1.75590 0.801892i
\(92\) 3.10550 + 1.66730i 0.323770 + 0.173828i
\(93\) −3.14738 + 0.300539i −0.326369 + 0.0311644i
\(94\) −6.40707 + 2.68051i −0.660839 + 0.276473i
\(95\) −5.47328 4.30424i −0.561547 0.441605i
\(96\) −4.94910 + 2.73978i −0.505115 + 0.279628i
\(97\) 15.8538 + 9.15322i 1.60971 + 0.929368i 0.989433 + 0.144988i \(0.0463143\pi\)
0.620280 + 0.784381i \(0.287019\pi\)
\(98\) 15.0774 0.951731i 1.52304 0.0961393i
\(99\) 3.70118 + 3.52907i 0.371982 + 0.354684i
\(100\) −3.30750 6.68790i −0.330750 0.668790i
\(101\) −0.478521 + 0.928201i −0.0476146 + 0.0923594i −0.911442 0.411428i \(-0.865030\pi\)
0.863828 + 0.503787i \(0.168060\pi\)
\(102\) 1.53986 + 2.87696i 0.152469 + 0.284862i
\(103\) 5.19790 + 12.9837i 0.512164 + 1.27932i 0.928911 + 0.370302i \(0.120746\pi\)
−0.416747 + 0.909023i \(0.636830\pi\)
\(104\) −1.16156 12.3313i −0.113900 1.20918i
\(105\) −4.10311 + 2.36893i −0.400422 + 0.231184i
\(106\) −14.0237 + 9.32153i −1.36210 + 0.905387i
\(107\) 2.98753 2.58871i 0.288816 0.250260i −0.498387 0.866955i \(-0.666074\pi\)
0.787203 + 0.616694i \(0.211529\pi\)
\(108\) 1.71509 + 1.02882i 0.165035 + 0.0989982i
\(109\) 9.48514 1.36376i 0.908512 0.130624i 0.327813 0.944743i \(-0.393688\pi\)
0.580699 + 0.814118i \(0.302779\pi\)
\(110\) −5.98357 5.53149i −0.570511 0.527407i
\(111\) −6.07256 + 5.79018i −0.576382 + 0.549579i
\(112\) 9.29313 + 14.0199i 0.878119 + 1.32476i
\(113\) 1.50712 + 0.521620i 0.141778 + 0.0490699i 0.397035 0.917803i \(-0.370039\pi\)
−0.255257 + 0.966873i \(0.582160\pi\)
\(114\) 8.71200 + 0.696348i 0.815954 + 0.0652190i
\(115\) 0.0944828 + 1.98344i 0.00881056 + 0.184956i
\(116\) −6.30387 5.64961i −0.585299 0.524553i
\(117\) −3.56709 + 2.54011i −0.329777 + 0.234833i
\(118\) −3.37069 + 0.0520464i −0.310297 + 0.00479126i
\(119\) 8.16243 5.24568i 0.748249 0.480871i
\(120\) −2.75781 1.59693i −0.251752 0.145780i
\(121\) 14.0676 + 5.63181i 1.27887 + 0.511983i
\(122\) 1.41644 + 3.89681i 0.128238 + 0.352801i
\(123\) 0.656451 3.40599i 0.0591902 0.307108i
\(124\) −4.84748 + 4.06047i −0.435316 + 0.364641i
\(125\) 5.31814 8.27519i 0.475669 0.740155i
\(126\) 2.64307 5.32721i 0.235464 0.474586i
\(127\) −13.8226 0.658452i −1.22656 0.0584282i −0.575721 0.817646i \(-0.695279\pi\)
−0.650837 + 0.759218i \(0.725582\pi\)
\(128\) −5.05432 + 10.1220i −0.446743 + 0.894662i
\(129\) 2.36379 2.72795i 0.208120 0.240183i
\(130\) 5.62063 4.13468i 0.492962 0.362636i
\(131\) 1.69746 5.78100i 0.148307 0.505088i −0.851507 0.524343i \(-0.824311\pi\)
0.999815 + 0.0192544i \(0.00612923\pi\)
\(132\) 10.0981 + 1.62466i 0.878931 + 0.141409i
\(133\) 25.9871i 2.25337i
\(134\) −11.3925 2.05201i −0.984163 0.177266i
\(135\) 1.12670i 0.0969713i
\(136\) 5.79695 + 2.99794i 0.497085 + 0.257071i
\(137\) 3.45684 11.7729i 0.295338 1.00583i −0.669463 0.742845i \(-0.733476\pi\)
0.964801 0.262982i \(-0.0847061\pi\)
\(138\) −1.47690 2.00768i −0.125722 0.170905i
\(139\) 0.586864 0.677277i 0.0497772 0.0574459i −0.730315 0.683111i \(-0.760627\pi\)
0.780092 + 0.625665i \(0.215172\pi\)
\(140\) −4.07992 + 8.55239i −0.344816 + 0.722809i
\(141\) 4.90543 + 0.233674i 0.413112 + 0.0196789i
\(142\) −13.4834 6.68972i −1.13150 0.561389i
\(143\) −12.1074 + 18.8395i −1.01247 + 1.57544i
\(144\) 3.99237 0.246877i 0.332698 0.0205731i
\(145\) 0.902500 4.68262i 0.0749486 0.388870i
\(146\) −19.5565 + 7.10853i −1.61851 + 0.588306i
\(147\) −9.91731 3.97029i −0.817966 0.327464i
\(148\) −3.45093 + 16.4225i −0.283665 + 1.34992i
\(149\) 7.03128 4.51873i 0.576025 0.370189i −0.219957 0.975510i \(-0.570592\pi\)
0.795982 + 0.605321i \(0.206955\pi\)
\(150\) 0.0814529 + 5.27515i 0.00665060 + 0.430714i
\(151\) 8.72026 6.20967i 0.709645 0.505336i −0.167313 0.985904i \(-0.553509\pi\)
0.876957 + 0.480568i \(0.159569\pi\)
\(152\) 15.1489 8.72039i 1.22874 0.707317i
\(153\) −0.109790 2.30477i −0.00887599 0.186330i
\(154\) 2.42311 30.3155i 0.195260 2.44289i
\(155\) −3.36638 1.16511i −0.270394 0.0935843i
\(156\) −3.00249 + 8.22740i −0.240391 + 0.658719i
\(157\) 10.9841 10.4733i 0.876624 0.835859i −0.110818 0.993841i \(-0.535347\pi\)
0.987442 + 0.157982i \(0.0504987\pi\)
\(158\) 14.4281 15.6073i 1.14784 1.24165i
\(159\) 11.7858 1.69455i 0.934678 0.134386i
\(160\) −6.35462 + 0.491542i −0.502377 + 0.0388598i
\(161\) −5.60081 + 4.85313i −0.441406 + 0.382480i
\(162\) −0.782858 1.17777i −0.0615072 0.0925340i
\(163\) −11.6275 + 6.71313i −0.910735 + 0.525813i −0.880668 0.473735i \(-0.842906\pi\)
−0.0300675 + 0.999548i \(0.509572\pi\)
\(164\) −2.77597 6.35774i −0.216767 0.496456i
\(165\) 2.14151 + 5.34923i 0.166716 + 0.416437i
\(166\) 21.7328 11.6322i 1.68679 0.902835i
\(167\) 0.801188 1.55409i 0.0619978 0.120259i −0.855800 0.517306i \(-0.826935\pi\)
0.917798 + 0.397047i \(0.129965\pi\)
\(168\) −1.67757 11.7748i −0.129427 0.908446i
\(169\) −4.46998 4.26211i −0.343844 0.327855i
\(170\) 0.231617 + 3.66929i 0.0177642 + 0.281422i
\(171\) −5.35201 3.08998i −0.409278 0.236297i
\(172\) 0.806290 7.17403i 0.0614790 0.547015i
\(173\) 3.76406 + 2.96009i 0.286176 + 0.225052i 0.750919 0.660394i \(-0.229611\pi\)
−0.464743 + 0.885446i \(0.653853\pi\)
\(174\) 2.31018 + 5.52191i 0.175134 + 0.418615i
\(175\) 15.6161 1.49116i 1.18047 0.112721i
\(176\) 18.4853 8.76033i 1.39338 0.660335i
\(177\) 2.16831 + 0.990235i 0.162980 + 0.0744306i
\(178\) 14.8314 7.05203i 1.11166 0.528572i
\(179\) 12.0426 3.53603i 0.900106 0.264295i 0.201235 0.979543i \(-0.435504\pi\)
0.698871 + 0.715248i \(0.253686\pi\)
\(180\) 1.27623 + 1.85717i 0.0951247 + 0.138425i
\(181\) −0.534276 2.20232i −0.0397124 0.163697i 0.948502 0.316770i \(-0.102598\pi\)
−0.988215 + 0.153073i \(0.951083\pi\)
\(182\) 25.0971 + 6.95015i 1.86032 + 0.515179i
\(183\) 0.278690 2.91857i 0.0206013 0.215747i
\(184\) −4.70853 1.63639i −0.347117 0.120637i
\(185\) −8.93378 + 3.09201i −0.656824 + 0.227329i
\(186\) 4.32849 1.12111i 0.317380 0.0822041i
\(187\) −4.90189 10.7336i −0.358462 0.784922i
\(188\) 8.35041 5.17127i 0.609016 0.377154i
\(189\) −3.30540 + 2.59940i −0.240432 + 0.189078i
\(190\) 8.60289 + 4.79133i 0.624119 + 0.347600i
\(191\) 4.17386 17.2049i 0.302010 1.24490i −0.595301 0.803503i \(-0.702967\pi\)
0.897311 0.441399i \(-0.145518\pi\)
\(192\) 6.30107 4.92915i 0.454741 0.355730i
\(193\) 1.52934 10.6368i 0.110085 0.765655i −0.857750 0.514067i \(-0.828138\pi\)
0.967835 0.251588i \(-0.0809527\pi\)
\(194\) −24.1804 9.24983i −1.73605 0.664099i
\(195\) −4.84476 + 0.933750i −0.346940 + 0.0668672i
\(196\) −20.8441 + 4.68915i −1.48887 + 0.334939i
\(197\) 8.15547 + 5.80748i 0.581053 + 0.413766i 0.832436 0.554122i \(-0.186946\pi\)
−0.251382 + 0.967888i \(0.580885\pi\)
\(198\) −5.95532 4.10369i −0.423226 0.291636i
\(199\) 0.524142 + 1.01669i 0.0371555 + 0.0720715i 0.906682 0.421814i \(-0.138606\pi\)
−0.869527 + 0.493886i \(0.835576\pi\)
\(200\) 6.10949 + 8.60287i 0.432006 + 0.608315i
\(201\) 6.65213 + 4.76960i 0.469205 + 0.336422i
\(202\) 0.461425 1.40291i 0.0324657 0.0987086i
\(203\) 15.8195 8.15551i 1.11031 0.572404i
\(204\) −2.79162 3.67465i −0.195452 0.257277i
\(205\) 2.26696 3.18350i 0.158331 0.222345i
\(206\) −10.1525 16.9740i −0.707361 1.18263i
\(207\) 0.333533 + 1.73054i 0.0231822 + 0.120281i
\(208\) 4.37022 + 16.9624i 0.303020 + 1.17613i
\(209\) −31.2827 4.49777i −2.16387 0.311117i
\(210\) 5.20225 4.22270i 0.358989 0.291394i
\(211\) 15.7978 + 3.83250i 1.08756 + 0.263840i 0.739177 0.673511i \(-0.235215\pi\)
0.348386 + 0.937351i \(0.386730\pi\)
\(212\) 17.5074 16.1431i 1.20241 1.10871i
\(213\) 6.57917 + 8.36609i 0.450797 + 0.573235i
\(214\) −3.59533 + 4.28103i −0.245771 + 0.292645i
\(215\) 3.69943 1.68947i 0.252299 0.115221i
\(216\) −2.62447 1.05458i −0.178573 0.0717553i
\(217\) −4.34841 12.5639i −0.295190 0.852894i
\(218\) −12.9425 + 4.01833i −0.876577 + 0.272155i
\(219\) 14.6471 + 1.39863i 0.989760 + 0.0945106i
\(220\) 9.58903 + 6.39153i 0.646492 + 0.430917i
\(221\) 9.81940 2.38216i 0.660524 0.160241i
\(222\) 7.19026 9.43952i 0.482578 0.633539i
\(223\) −1.37228 4.67354i −0.0918944 0.312964i 0.900700 0.434442i \(-0.143055\pi\)
−0.992594 + 0.121479i \(0.961236\pi\)
\(224\) −16.1026 17.5084i −1.07590 1.16983i
\(225\) 1.54972 3.39342i 0.103315 0.226228i
\(226\) −2.22101 0.392601i −0.147739 0.0261154i
\(227\) 1.98221 + 20.7587i 0.131564 + 1.37780i 0.784378 + 0.620283i \(0.212982\pi\)
−0.652814 + 0.757518i \(0.726412\pi\)
\(228\) −12.3219 + 0.969002i −0.816037 + 0.0641737i
\(229\) −12.9869 + 16.5142i −0.858199 + 1.09129i 0.136720 + 0.990610i \(0.456344\pi\)
−0.994919 + 0.100679i \(0.967898\pi\)
\(230\) −0.573961 2.74890i −0.0378459 0.181257i
\(231\) −10.7523 + 18.6236i −0.707452 + 1.22534i
\(232\) 10.0627 + 6.48510i 0.660646 + 0.425768i
\(233\) −0.174104 + 0.182595i −0.0114059 + 0.0119622i −0.729412 0.684074i \(-0.760206\pi\)
0.718006 + 0.696037i \(0.245055\pi\)
\(234\) 4.41553 4.34231i 0.288652 0.283866i
\(235\) 4.91814 + 2.53548i 0.320824 + 0.165396i
\(236\) 4.69572 0.823849i 0.305666 0.0536280i
\(237\) −13.9527 + 5.58583i −0.906327 + 0.362839i
\(238\) −10.2302 + 9.14483i −0.663125 + 0.592772i
\(239\) −14.4134 24.9647i −0.932325 1.61483i −0.779335 0.626607i \(-0.784443\pi\)
−0.152990 0.988228i \(-0.548890\pi\)
\(240\) 4.20728 + 1.61561i 0.271579 + 0.104287i
\(241\) −5.56839 6.42626i −0.358691 0.413952i 0.547509 0.836800i \(-0.315576\pi\)
−0.906201 + 0.422848i \(0.861031\pi\)
\(242\) −20.9011 4.73009i −1.34357 0.304062i
\(243\) 0.142315 + 0.989821i 0.00912950 + 0.0634971i
\(244\) −2.84653 5.12642i −0.182231 0.328185i
\(245\) −8.30582 8.71089i −0.530639 0.556519i
\(246\) −0.157733 + 4.90291i −0.0100567 + 0.312598i
\(247\) 8.85128 25.5741i 0.563193 1.62724i
\(248\) 5.86484 6.75089i 0.372417 0.428682i
\(249\) −17.4105 + 0.829362i −1.10334 + 0.0525587i
\(250\) −5.58288 + 12.7418i −0.353093 + 0.805864i
\(251\) 9.89767 + 13.8993i 0.624736 + 0.877318i 0.998744 0.0501070i \(-0.0159562\pi\)
−0.374008 + 0.927425i \(0.622017\pi\)
\(252\) −2.50399 + 8.02871i −0.157737 + 0.505761i
\(253\) 4.87271 + 7.58208i 0.306345 + 0.476681i
\(254\) 19.4506 2.16083i 1.22044 0.135583i
\(255\) 0.966227 2.41352i 0.0605075 0.151140i
\(256\) 4.80289 15.2621i 0.300181 0.953882i
\(257\) −13.5941 2.62004i −0.847974 0.163434i −0.253287 0.967391i \(-0.581512\pi\)
−0.594687 + 0.803958i \(0.702724\pi\)
\(258\) −2.69320 + 4.33648i −0.167672 + 0.269978i
\(259\) −29.6819 19.0754i −1.84435 1.18529i
\(260\) −6.92804 + 7.02684i −0.429659 + 0.435786i
\(261\) 0.201391 4.22772i 0.0124658 0.261689i
\(262\) −1.08227 + 8.45171i −0.0668627 + 0.522148i
\(263\) −11.1899 9.69611i −0.690000 0.597888i 0.237645 0.971352i \(-0.423624\pi\)
−0.927645 + 0.373464i \(0.878170\pi\)
\(264\) −14.4646 0.0185287i −0.890233 0.00114036i
\(265\) 12.8723 + 3.77964i 0.790738 + 0.232182i
\(266\) 5.79127 + 36.2922i 0.355085 + 2.22522i
\(267\) −11.6126 −0.710677
\(268\) 16.3674 + 0.326881i 0.999801 + 0.0199675i
\(269\) 17.3544 1.05812 0.529059 0.848585i \(-0.322545\pi\)
0.529059 + 0.848585i \(0.322545\pi\)
\(270\) −0.251088 1.57349i −0.0152807 0.0957597i
\(271\) 18.3208 + 5.37949i 1.11291 + 0.326780i 0.785970 0.618264i \(-0.212164\pi\)
0.326942 + 0.945045i \(0.393982\pi\)
\(272\) −8.76380 2.89490i −0.531383 0.175529i
\(273\) −13.9166 12.0588i −0.842269 0.729830i
\(274\) −2.20402 + 17.2118i −0.133150 + 1.03980i
\(275\) 0.907767 19.0564i 0.0547404 1.14914i
\(276\) 2.50997 + 2.47468i 0.151082 + 0.148958i
\(277\) −1.09523 0.703860i −0.0658058 0.0422908i 0.507324 0.861755i \(-0.330635\pi\)
−0.573130 + 0.819464i \(0.694271\pi\)
\(278\) −0.668650 + 1.07663i −0.0401030 + 0.0645721i
\(279\) −3.10456 0.598356i −0.185865 0.0358226i
\(280\) 3.79188 12.8530i 0.226608 0.768115i
\(281\) −1.84581 + 4.61061i −0.110112 + 0.275046i −0.973181 0.230039i \(-0.926115\pi\)
0.863070 + 0.505085i \(0.168539\pi\)
\(282\) −6.90273 + 0.766845i −0.411051 + 0.0456650i
\(283\) −8.20216 12.7628i −0.487568 0.758671i 0.507090 0.861893i \(-0.330721\pi\)
−0.994658 + 0.103222i \(0.967085\pi\)
\(284\) 20.3210 + 6.33770i 1.20583 + 0.376073i
\(285\) −4.03893 5.67189i −0.239246 0.335974i
\(286\) 12.7101 29.0084i 0.751567 1.71530i
\(287\) 14.5695 0.694029i 0.860008 0.0409672i
\(288\) −5.52051 + 1.23448i −0.325299 + 0.0727425i
\(289\) 3.81883 11.0338i 0.224637 0.649047i
\(290\) −0.216854 + 6.74061i −0.0127341 + 0.395822i
\(291\) 12.6329 + 13.2490i 0.740553 + 0.776670i
\(292\) 25.7274 14.2856i 1.50558 0.836000i
\(293\) 0.851508 + 5.92237i 0.0497456 + 0.345988i 0.999460 + 0.0328698i \(0.0104647\pi\)
−0.949714 + 0.313119i \(0.898626\pi\)
\(294\) 14.7348 + 3.33460i 0.859348 + 0.194478i
\(295\) 1.75879 + 2.02976i 0.102401 + 0.118177i
\(296\) 1.15959 23.7039i 0.0673997 1.37776i
\(297\) 2.55700 + 4.42886i 0.148372 + 0.256988i
\(298\) −8.81249 + 7.87754i −0.510494 + 0.456334i
\(299\) −7.16478 + 2.86835i −0.414350 + 0.165881i
\(300\) −1.28933 7.34883i −0.0744393 0.424285i
\(301\) 13.4913 + 6.95523i 0.777624 + 0.400893i
\(302\) −10.7944 + 10.6154i −0.621148 + 0.610848i
\(303\) −0.720642 + 0.755787i −0.0413998 + 0.0434188i
\(304\) −19.2128 + 15.5544i −1.10193 + 0.892105i
\(305\) 1.65166 2.86076i 0.0945739 0.163807i
\(306\) 0.666949 + 3.19425i 0.0381269 + 0.182603i
\(307\) 1.43465 1.82431i 0.0818800 0.104119i −0.743387 0.668861i \(-0.766782\pi\)
0.825267 + 0.564742i \(0.191024\pi\)
\(308\) 3.37188 + 42.8770i 0.192130 + 2.44314i
\(309\) 1.32941 + 13.9222i 0.0756275 + 0.792007i
\(310\) 4.96095 + 0.876933i 0.281763 + 0.0498064i
\(311\) −5.73608 + 12.5603i −0.325263 + 0.712228i −0.999658 0.0261433i \(-0.991677\pi\)
0.674395 + 0.738371i \(0.264405\pi\)
\(312\) 2.35962 12.1590i 0.133587 0.688370i
\(313\) 2.53047 + 8.61800i 0.143031 + 0.487118i 0.999581 0.0289457i \(-0.00921498\pi\)
−0.856550 + 0.516064i \(0.827397\pi\)
\(314\) −13.0058 + 17.0742i −0.733957 + 0.963554i
\(315\) −4.60431 + 1.11699i −0.259423 + 0.0629354i
\(316\) −16.6714 + 25.0117i −0.937842 + 1.40702i
\(317\) −18.7843 1.79368i −1.05503 0.100743i −0.446902 0.894583i \(-0.647473\pi\)
−0.608127 + 0.793840i \(0.708079\pi\)
\(318\) −16.0818 + 4.99300i −0.901824 + 0.279994i
\(319\) −7.07942 20.4546i −0.396371 1.14524i
\(320\) 8.76497 2.10260i 0.489977 0.117539i
\(321\) 3.59584 1.64217i 0.200700 0.0916568i
\(322\) 6.74025 8.02576i 0.375620 0.447258i
\(323\) 8.81469 + 11.2088i 0.490462 + 0.623673i
\(324\) 1.35576 + 1.47034i 0.0753202 + 0.0816857i
\(325\) 15.8758 + 3.85143i 0.880631 + 0.213639i
\(326\) 14.7423 11.9664i 0.816499 0.662757i
\(327\) 9.48514 + 1.36376i 0.524530 + 0.0754160i
\(328\) 5.29359 + 8.26023i 0.292290 + 0.456095i
\(329\) 3.90823 + 20.2778i 0.215468 + 1.11795i
\(330\) −4.18279 6.99320i −0.230255 0.384963i
\(331\) 17.3149 24.3154i 0.951715 1.33650i 0.0100485 0.999950i \(-0.496801\pi\)
0.941667 0.336547i \(-0.109259\pi\)
\(332\) −27.7586 + 21.0881i −1.52345 + 1.15736i
\(333\) −7.45786 + 3.84480i −0.408688 + 0.210694i
\(334\) −0.772564 + 2.34890i −0.0422728 + 0.128526i
\(335\) 4.58527 + 8.00183i 0.250520 + 0.437187i
\(336\) 4.96683 + 16.0702i 0.270963 + 0.876701i
\(337\) −2.01817 3.91470i −0.109937 0.213247i 0.827449 0.561541i \(-0.189791\pi\)
−0.937385 + 0.348294i \(0.886761\pi\)
\(338\) 7.19234 + 4.95609i 0.391212 + 0.269576i
\(339\) 1.29912 + 0.925096i 0.0705582 + 0.0502443i
\(340\) −1.14117 5.07271i −0.0618887 0.275106i
\(341\) −15.8768 + 3.05999i −0.859774 + 0.165708i
\(342\) 8.16292 + 3.12260i 0.441400 + 0.168851i
\(343\) 2.20378 15.3276i 0.118993 0.827613i
\(344\) 0.472724 + 10.1985i 0.0254876 + 0.549869i
\(345\) −0.468143 + 1.92971i −0.0252040 + 0.103892i
\(346\) −5.91634 3.29507i −0.318065 0.177144i
\(347\) 10.6358 8.36405i 0.570957 0.449006i −0.290472 0.956884i \(-0.593812\pi\)
0.861429 + 0.507878i \(0.169570\pi\)
\(348\) −4.45684 7.19676i −0.238912 0.385787i
\(349\) −10.9391 23.9532i −0.585554 1.28219i −0.938092 0.346387i \(-0.887408\pi\)
0.352537 0.935798i \(-0.385319\pi\)
\(350\) −21.4763 + 5.56254i −1.14796 + 0.297330i
\(351\) −4.13823 + 1.43225i −0.220882 + 0.0764481i
\(352\) −23.8632 + 16.3537i −1.27192 + 0.871653i
\(353\) −2.26875 + 23.7594i −0.120753 + 1.26459i 0.708498 + 0.705712i \(0.249373\pi\)
−0.829252 + 0.558875i \(0.811233\pi\)
\(354\) −3.24882 0.899696i −0.172673 0.0478183i
\(355\) 2.82715 + 11.6537i 0.150050 + 0.618513i
\(356\) −19.1412 + 13.1537i −1.01448 + 0.697144i
\(357\) 9.30968 2.73357i 0.492720 0.144676i
\(358\) −16.0300 + 7.62193i −0.847213 + 0.402832i
\(359\) 8.47324 + 3.86960i 0.447201 + 0.204230i 0.626269 0.779607i \(-0.284581\pi\)
−0.179069 + 0.983837i \(0.557308\pi\)
\(360\) −2.19619 2.30921i −0.115749 0.121706i
\(361\) 19.1051 1.82431i 1.00553 0.0960164i
\(362\) 1.23693 + 2.95657i 0.0650116 + 0.155394i
\(363\) 11.9111 + 9.36697i 0.625169 + 0.491639i
\(364\) −36.5981 4.11326i −1.91826 0.215593i
\(365\) 14.3570 + 8.28902i 0.751480 + 0.433867i
\(366\) 0.261205 + 4.13802i 0.0136534 + 0.216298i
\(367\) −14.2080 13.5473i −0.741650 0.707162i 0.221787 0.975095i \(-0.428811\pi\)
−0.963438 + 0.267933i \(0.913659\pi\)
\(368\) 6.94034 + 1.23600i 0.361790 + 0.0644307i
\(369\) 1.58944 3.08308i 0.0827428 0.160499i
\(370\) 11.7874 6.30904i 0.612796 0.327991i
\(371\) 18.6091 + 46.4832i 0.966135 + 2.41329i
\(372\) −5.79508 + 2.53030i −0.300461 + 0.131190i
\(373\) 20.0485 11.5750i 1.03807 0.599332i 0.118787 0.992920i \(-0.462100\pi\)
0.919287 + 0.393588i \(0.128766\pi\)
\(374\) 9.23772 + 13.8976i 0.477671 + 0.718629i
\(375\) 7.43411 6.44169i 0.383896 0.332647i
\(376\) −10.5093 + 9.08281i −0.541975 + 0.468410i
\(377\) 18.3458 2.63773i 0.944859 0.135850i
\(378\) 4.03686 4.36678i 0.207634 0.224603i
\(379\) −27.3114 + 26.0413i −1.40289 + 1.33765i −0.531504 + 0.847056i \(0.678373\pi\)
−0.871386 + 0.490598i \(0.836778\pi\)
\(380\) −13.0821 4.77414i −0.671096 0.244908i
\(381\) −13.0772 4.52606i −0.669965 0.231877i
\(382\) −1.99485 + 24.9575i −0.102065 + 1.27694i
\(383\) −1.27634 26.7936i −0.0652178 1.36909i −0.760025 0.649894i \(-0.774813\pi\)
0.694807 0.719197i \(-0.255490\pi\)
\(384\) −7.70126 + 8.28798i −0.393003 + 0.422944i
\(385\) −19.7367 + 14.0544i −1.00588 + 0.716281i
\(386\) 0.234633 + 15.1956i 0.0119425 + 0.773436i
\(387\) 3.03659 1.95150i 0.154359 0.0992002i
\(388\) 35.8303 + 7.52916i 1.81901 + 0.382235i
\(389\) 3.62590 + 1.45159i 0.183840 + 0.0735985i 0.461756 0.887007i \(-0.347219\pi\)
−0.277916 + 0.960605i \(0.589644\pi\)
\(390\) 6.55783 2.38368i 0.332069 0.120703i
\(391\) 0.769591 3.99302i 0.0389199 0.201936i
\(392\) 28.0648 11.1937i 1.41748 0.565369i
\(393\) 3.25739 5.06860i 0.164314 0.255677i
\(394\) −12.6837 6.29295i −0.638995 0.317034i
\(395\) −16.9144 0.805732i −0.851056 0.0405408i
\(396\) 9.23138 + 4.40383i 0.463894 + 0.221301i
\(397\) −21.4832 + 24.7929i −1.07821 + 1.24432i −0.110068 + 0.993924i \(0.535107\pi\)
−0.968143 + 0.250398i \(0.919439\pi\)
\(398\) −0.958560 1.30305i −0.0480483 0.0653162i
\(399\) 7.32142 24.9345i 0.366529 1.24828i
\(400\) −10.4493 10.6528i −0.522467 0.532640i
\(401\) 2.97366i 0.148498i 0.997240 + 0.0742488i \(0.0236559\pi\)
−0.997240 + 0.0742488i \(0.976344\pi\)
\(402\) −10.3529 5.17853i −0.516357 0.258281i
\(403\) 13.8453i 0.689684i
\(404\) −0.331759 + 2.06206i −0.0165056 + 0.102591i
\(405\) −0.317429 + 1.08106i −0.0157732 + 0.0537185i
\(406\) −20.2751 + 14.9149i −1.00624 + 0.740215i
\(407\) −28.0998 + 32.4289i −1.39285 + 1.60744i
\(408\) 4.71752 + 4.50970i 0.233552 + 0.223263i
\(409\) −17.7182 0.844020i −0.876106 0.0417341i −0.395291 0.918556i \(-0.629356\pi\)
−0.480815 + 0.876822i \(0.659659\pi\)
\(410\) −2.45646 + 4.95110i −0.121316 + 0.244517i
\(411\) 6.63362 10.3221i 0.327213 0.509153i
\(412\) 17.9612 + 21.4424i 0.884883 + 1.05639i
\(413\) −1.89700 + 9.84256i −0.0933451 + 0.484321i
\(414\) −0.851447 2.34244i −0.0418463 0.115125i
\(415\) −18.2319 7.29896i −0.894970 0.358292i
\(416\) −9.88329 22.7148i −0.484568 1.11368i
\(417\) 0.753903 0.484504i 0.0369188 0.0237263i
\(418\) 44.6900 0.690052i 2.18586 0.0337515i
\(419\) 21.6552 15.4206i 1.05793 0.753346i 0.0878473 0.996134i \(-0.472001\pi\)
0.970079 + 0.242788i \(0.0780618\pi\)
\(420\) −6.32414 + 7.05652i −0.308587 + 0.344323i
\(421\) 1.00666 + 21.1323i 0.0490614 + 1.02993i 0.880422 + 0.474192i \(0.157260\pi\)
−0.831360 + 0.555734i \(0.812437\pi\)
\(422\) −22.9164 1.83170i −1.11555 0.0891657i
\(423\) 4.64089 + 1.60623i 0.225648 + 0.0780975i
\(424\) −20.8524 + 26.4462i −1.01268 + 1.28434i
\(425\) −6.22976 + 5.94006i −0.302188 + 0.288135i
\(426\) −11.0525 10.2174i −0.535495 0.495037i
\(427\) 12.2031 1.75454i 0.590550 0.0849082i
\(428\) 4.06700 6.77987i 0.196586 0.327718i
\(429\) −16.9247 + 14.6653i −0.817132 + 0.708049i
\(430\) −4.78992 + 3.18385i −0.230990 + 0.153539i
\(431\) 17.4353 10.0663i 0.839830 0.484876i −0.0173764 0.999849i \(-0.505531\pi\)
0.857206 + 0.514973i \(0.172198\pi\)
\(432\) 3.90021 + 0.887905i 0.187649 + 0.0427193i
\(433\) −1.88948 4.71969i −0.0908026 0.226814i 0.876014 0.482286i \(-0.160193\pi\)
−0.966816 + 0.255472i \(0.917769\pi\)
\(434\) 8.87264 + 16.5770i 0.425900 + 0.795723i
\(435\) 2.18519 4.23867i 0.104772 0.203229i
\(436\) 17.1793 8.49603i 0.822740 0.406886i
\(437\) −7.88253 7.51598i −0.377073 0.359538i
\(438\) −20.7670 + 1.31088i −0.992287 + 0.0626363i
\(439\) 16.0488 + 9.26577i 0.765967 + 0.442231i 0.831434 0.555624i \(-0.187520\pi\)
−0.0654673 + 0.997855i \(0.520854\pi\)
\(440\) −14.8159 6.78913i −0.706319 0.323659i
\(441\) −8.39703 6.60350i −0.399859 0.314452i
\(442\) −13.1824 + 5.51506i −0.627021 + 0.262325i
\(443\) −29.2063 + 2.78887i −1.38763 + 0.132503i −0.761982 0.647599i \(-0.775773\pi\)
−0.625653 + 0.780102i \(0.715167\pi\)
\(444\) −7.93791 + 14.7851i −0.376716 + 0.701669i
\(445\) −11.9016 5.43526i −0.564188 0.257656i
\(446\) 2.95795 + 6.22100i 0.140063 + 0.294573i
\(447\) 8.01954 2.35475i 0.379311 0.111376i
\(448\) 26.3898 + 20.8628i 1.24680 + 0.985676i
\(449\) −7.84894 32.3538i −0.370415 1.52687i −0.786527 0.617556i \(-0.788123\pi\)
0.416112 0.909313i \(-0.363392\pi\)
\(450\) −1.40803 + 5.08442i −0.0663751 + 0.239682i
\(451\) 1.68618 17.6585i 0.0793991 0.831505i
\(452\) 3.18923 + 0.0533308i 0.150009 + 0.00250847i
\(453\) 10.1165 3.50135i 0.475315 0.164508i
\(454\) −7.39435 28.5487i −0.347034 1.33986i
\(455\) −8.61879 18.8725i −0.404055 0.884757i
\(456\) 16.9921 4.09920i 0.795729 0.191963i
\(457\) −1.09890 + 0.864187i −0.0514045 + 0.0404250i −0.643531 0.765420i \(-0.722531\pi\)
0.592126 + 0.805845i \(0.298289\pi\)
\(458\) 14.4566 25.9570i 0.675512 1.21289i
\(459\) 0.543987 2.24235i 0.0253912 0.104664i
\(460\) 1.41416 + 3.71106i 0.0659355 + 0.173029i
\(461\) 1.58593 11.0304i 0.0738642 0.513737i −0.918979 0.394308i \(-0.870984\pi\)
0.992843 0.119429i \(-0.0381065\pi\)
\(462\) 10.8658 28.4049i 0.505524 1.32151i
\(463\) 22.9943 4.43179i 1.06864 0.205963i 0.375539 0.926806i \(-0.377457\pi\)
0.693098 + 0.720843i \(0.256245\pi\)
\(464\) −15.4982 6.81426i −0.719484 0.316344i
\(465\) −2.90177 2.06634i −0.134566 0.0958241i
\(466\) 0.202453 0.293802i 0.00937844 0.0136101i
\(467\) −7.33666 14.2311i −0.339500 0.658538i 0.655847 0.754894i \(-0.272312\pi\)
−0.995347 + 0.0963558i \(0.969281\pi\)
\(468\) −5.19879 + 7.04824i −0.240314 + 0.325805i
\(469\) −12.8963 + 31.9126i −0.595496 + 1.47359i
\(470\) −7.43343 2.44489i −0.342879 0.112774i
\(471\) 13.4898 6.95447i 0.621577 0.320445i
\(472\) −6.37419 + 2.19699i −0.293396 + 0.101125i
\(473\) 10.7076 15.0367i 0.492334 0.691387i
\(474\) 18.2408 10.9102i 0.837828 0.501124i
\(475\) 4.36311 + 22.6380i 0.200193 + 1.03870i
\(476\) 12.2490 15.0510i 0.561432 0.689861i
\(477\) 11.7858 + 1.69455i 0.539637 + 0.0775880i
\(478\) 25.6924 + 31.6523i 1.17514 + 1.44774i
\(479\) −14.4585 3.50759i −0.660624 0.160266i −0.108589 0.994087i \(-0.534633\pi\)
−0.552035 + 0.833821i \(0.686148\pi\)
\(480\) −6.23570 1.31867i −0.284619 0.0601889i
\(481\) −22.7130 28.8820i −1.03563 1.31691i
\(482\) 9.20861 + 7.73364i 0.419441 + 0.352258i
\(483\) −6.74122 + 3.07861i −0.306736 + 0.140082i
\(484\) 30.2434 + 1.94796i 1.37470 + 0.0885434i
\(485\) 6.74608 + 19.4915i 0.306324 + 0.885065i
\(486\) −0.419332 1.35061i −0.0190213 0.0612651i
\(487\) −14.5978 1.39392i −0.661488 0.0631645i −0.241088 0.970503i \(-0.577504\pi\)
−0.420400 + 0.907339i \(0.638110\pi\)
\(488\) 5.11774 + 6.52492i 0.231669 + 0.295369i
\(489\) −13.0478 + 3.16536i −0.590042 + 0.143143i
\(490\) 13.5407 + 10.3142i 0.611706 + 0.465948i
\(491\) 3.32733 + 11.3318i 0.150160 + 0.511399i 0.999874 0.0158448i \(-0.00504377\pi\)
−0.849714 + 0.527243i \(0.823226\pi\)
\(492\) −0.872339 6.88228i −0.0393281 0.310277i
\(493\) −4.05697 + 8.88352i −0.182717 + 0.400094i
\(494\) −6.66198 + 37.6879i −0.299737 + 1.69566i
\(495\) 0.547710 + 5.73588i 0.0246177 + 0.257809i
\(496\) −6.68606 + 10.7349i −0.300213 + 0.482012i
\(497\) −27.6658 + 35.1799i −1.24098 + 1.57804i
\(498\) 24.1297 5.03819i 1.08128 0.225767i
\(499\) −4.56808 + 7.91215i −0.204495 + 0.354196i −0.949972 0.312336i \(-0.898889\pi\)
0.745477 + 0.666532i \(0.232222\pi\)
\(500\) 4.95721 19.0387i 0.221693 0.851436i
\(501\) 1.20657 1.26542i 0.0539056 0.0565346i
\(502\) −16.9200 17.2053i −0.755178 0.767912i
\(503\) −7.51173 3.87257i −0.334932 0.172669i 0.282554 0.959251i \(-0.408818\pi\)
−0.617486 + 0.786582i \(0.711849\pi\)
\(504\) 1.70773 11.7705i 0.0760683 0.524298i
\(505\) −1.09232 + 0.437300i −0.0486077 + 0.0194596i
\(506\) −8.49463 9.50283i −0.377632 0.422452i
\(507\) −3.08813 5.34881i −0.137149 0.237549i
\(508\) −26.6821 + 7.35230i −1.18383 + 0.326205i
\(509\) 19.7656 + 22.8107i 0.876094 + 1.01107i 0.999824 + 0.0187509i \(0.00596894\pi\)
−0.123730 + 0.992316i \(0.539486\pi\)
\(510\) −0.811524 + 3.58591i −0.0359349 + 0.158787i
\(511\) 8.80532 + 61.2424i 0.389525 + 2.70920i
\(512\) −3.30626 + 22.3846i −0.146118 + 0.989267i
\(513\) −4.26466 4.47265i −0.188290 0.197472i
\(514\) 19.5686 + 0.629548i 0.863133 + 0.0277682i
\(515\) −5.15380 + 14.8909i −0.227103 + 0.656172i
\(516\) 2.79479 6.65628i 0.123034 0.293026i
\(517\) 25.0864 1.19501i 1.10330 0.0525565i
\(518\) 45.7031 + 20.0250i 2.00808 + 0.879849i
\(519\) 2.77764 + 3.90065i 0.121925 + 0.171219i
\(520\) 8.10938 11.3572i 0.355620 0.498047i
\(521\) −14.5494 22.6393i −0.637420 0.991844i −0.998245 0.0592111i \(-0.981141\pi\)
0.360826 0.932633i \(-0.382495\pi\)
\(522\) 0.660902 + 5.94908i 0.0289269 + 0.260384i
\(523\) −2.14374 + 5.35479i −0.0937390 + 0.234149i −0.967826 0.251621i \(-0.919036\pi\)
0.874087 + 0.485770i \(0.161461\pi\)
\(524\) −0.372040 12.0444i −0.0162526 0.526161i
\(525\) 15.4036 + 2.96881i 0.672270 + 0.129569i
\(526\) 17.7880 + 11.0474i 0.775594 + 0.481688i
\(527\) 6.13717 + 3.94412i 0.267339 + 0.171809i
\(528\) 20.2045 3.19757i 0.879290 0.139157i
\(529\) 0.946595 19.8715i 0.0411563 0.863977i
\(530\) −18.8190 2.40983i −0.817446 0.104677i
\(531\) 1.80150 + 1.56101i 0.0781784 + 0.0677419i
\(532\) −16.1755 49.3930i −0.701298 2.14146i
\(533\) 14.5743 + 4.27940i 0.631282 + 0.185361i
\(534\) 16.2175 2.58788i 0.701798 0.111988i
\(535\) 4.45395 0.192561
\(536\) −22.9307 + 3.19100i −0.990456 + 0.137830i
\(537\) 12.5510 0.541616
\(538\) −24.2362 + 3.86746i −1.04490 + 0.166738i
\(539\) −52.4175 15.3912i −2.25778 0.662945i
\(540\) 0.701310 + 2.14150i 0.0301796 + 0.0921554i
\(541\) 11.7808 + 10.2082i 0.506498 + 0.438883i 0.870248 0.492614i \(-0.163958\pi\)
−0.363750 + 0.931497i \(0.618504\pi\)
\(542\) −26.7847 3.42987i −1.15050 0.147325i
\(543\) 0.107830 2.26363i 0.00462743 0.0971416i
\(544\) 12.8842 + 2.08983i 0.552404 + 0.0896009i
\(545\) 9.08289 + 5.83722i 0.389068 + 0.250039i
\(546\) 22.1224 + 13.7393i 0.946752 + 0.587987i
\(547\) 7.64281 + 1.47303i 0.326783 + 0.0629823i 0.350004 0.936748i \(-0.386180\pi\)
−0.0232212 + 0.999730i \(0.507392\pi\)
\(548\) −0.757653 24.5282i −0.0323653 1.04779i
\(549\) 1.08966 2.72183i 0.0465054 0.116165i
\(550\) 2.97900 + 26.8154i 0.127025 + 1.14341i
\(551\) 14.1414 + 22.0045i 0.602445 + 0.937423i
\(552\) −4.05677 2.89665i −0.172668 0.123290i
\(553\) −36.6591 51.4805i −1.55890 2.18917i
\(554\) 1.68639 + 0.738899i 0.0716479 + 0.0313928i
\(555\) −9.44302 + 0.449826i −0.400834 + 0.0190941i
\(556\) 0.693871 1.65257i 0.0294267 0.0700847i
\(557\) −0.199052 + 0.575124i −0.00843411 + 0.0243688i −0.949139 0.314856i \(-0.898044\pi\)
0.940705 + 0.339225i \(0.110165\pi\)
\(558\) 4.46901 + 0.143774i 0.189188 + 0.00608644i
\(559\) 10.9079 + 11.4398i 0.461354 + 0.483854i
\(560\) −2.43121 + 18.7948i −0.102737 + 0.794227i
\(561\) −1.67931 11.6799i −0.0709007 0.493125i
\(562\) 1.55027 6.85026i 0.0653944 0.288961i
\(563\) 25.1383 + 29.0111i 1.05945 + 1.22267i 0.974052 + 0.226326i \(0.0726714\pi\)
0.0854001 + 0.996347i \(0.472783\pi\)
\(564\) 9.46907 2.60922i 0.398720 0.109868i
\(565\) 0.898454 + 1.55617i 0.0377983 + 0.0654685i
\(566\) 14.2989 + 15.9960i 0.601028 + 0.672361i
\(567\) −3.90384 + 1.56286i −0.163946 + 0.0656341i
\(568\) −29.7915 4.32233i −1.25002 0.181361i
\(569\) −31.2236 16.0969i −1.30896 0.674816i −0.344436 0.938810i \(-0.611930\pi\)
−0.964524 + 0.263994i \(0.914960\pi\)
\(570\) 6.90454 + 7.02096i 0.289199 + 0.294076i
\(571\) −7.52169 + 7.88852i −0.314773 + 0.330124i −0.862046 0.506830i \(-0.830817\pi\)
0.547273 + 0.836954i \(0.315666\pi\)
\(572\) −11.2857 + 43.3440i −0.471880 + 1.81230i
\(573\) 8.85196 15.3320i 0.369796 0.640506i
\(574\) −20.1922 + 4.21607i −0.842807 + 0.175975i
\(575\) 4.06417 5.16802i 0.169488 0.215521i
\(576\) 7.43454 2.95426i 0.309772 0.123094i
\(577\) −3.45935 36.2280i −0.144015 1.50819i −0.721857 0.692043i \(-0.756711\pi\)
0.577842 0.816149i \(-0.303895\pi\)
\(578\) −2.87427 + 16.2602i −0.119554 + 0.676336i
\(579\) 4.46413 9.77508i 0.185523 0.406239i
\(580\) −1.19931 9.46188i −0.0497985 0.392883i
\(581\) −20.6496 70.3261i −0.856689 2.91762i
\(582\) −20.5949 15.6876i −0.853688 0.650270i
\(583\) 59.1762 14.3560i 2.45083 0.594564i
\(584\) −32.7459 + 25.6838i −1.35503 + 1.06280i
\(585\) −4.91158 0.468999i −0.203069 0.0193907i
\(586\) −2.50898 8.08109i −0.103645 0.333827i
\(587\) −11.8631 34.2762i −0.489642 1.41473i −0.871449 0.490486i \(-0.836819\pi\)
0.381807 0.924242i \(-0.375302\pi\)
\(588\) −21.3209 1.37326i −0.879258 0.0566324i
\(589\) 17.7735 8.11688i 0.732344 0.334450i
\(590\) −2.90857 2.44269i −0.119744 0.100564i
\(591\) 6.18896 + 7.86990i 0.254580 + 0.323724i
\(592\) 3.66302 + 33.3619i 0.150549 + 1.37117i
\(593\) −8.54040 2.07188i −0.350712 0.0850819i 0.0565330 0.998401i \(-0.481995\pi\)
−0.407245 + 0.913319i \(0.633511\pi\)
\(594\) −4.55794 5.61526i −0.187015 0.230397i
\(595\) 10.8208 + 1.55580i 0.443610 + 0.0637815i
\(596\) 10.5515 12.9652i 0.432207 0.531076i
\(597\) 0.216475 + 1.12318i 0.00885973 + 0.0459687i
\(598\) 9.36672 5.60245i 0.383034 0.229101i
\(599\) 0.0888807 0.124816i 0.00363157 0.00509982i −0.812756 0.582604i \(-0.802034\pi\)
0.816388 + 0.577504i \(0.195973\pi\)
\(600\) 3.43830 + 9.97564i 0.140368 + 0.407254i
\(601\) −4.78211 + 2.46535i −0.195066 + 0.100564i −0.552993 0.833186i \(-0.686514\pi\)
0.357926 + 0.933750i \(0.383484\pi\)
\(602\) −20.3911 6.70674i −0.831081 0.273346i
\(603\) 5.03892 + 6.45052i 0.205201 + 0.262686i
\(604\) 12.7092 17.2304i 0.517130 0.701097i
\(605\) 7.82329 + 15.1751i 0.318062 + 0.616954i
\(606\) 0.837980 1.21609i 0.0340406 0.0494001i
\(607\) 27.3249 + 19.4580i 1.10908 + 0.789776i 0.979430 0.201783i \(-0.0646737\pi\)
0.129655 + 0.991559i \(0.458613\pi\)
\(608\) 23.3653 26.0040i 0.947586 1.05460i
\(609\) 17.4763 3.36829i 0.708177 0.136490i
\(610\) −1.66910 + 4.36326i −0.0675797 + 0.176663i
\(611\) −3.06056 + 21.2867i −0.123817 + 0.861167i
\(612\) −1.64327 4.31229i −0.0664252 0.174314i
\(613\) −1.98197 + 8.16980i −0.0800511 + 0.329975i −0.997729 0.0673489i \(-0.978546\pi\)
0.917678 + 0.397324i \(0.130061\pi\)
\(614\) −1.59701 + 2.86744i −0.0644500 + 0.115721i
\(615\) 3.07203 2.41587i 0.123876 0.0974173i
\(616\) −14.2642 59.1282i −0.574720 2.38234i
\(617\) 5.35093 + 11.7169i 0.215420 + 0.471705i 0.986234 0.165356i \(-0.0528773\pi\)
−0.770814 + 0.637061i \(0.780150\pi\)
\(618\) −4.95917 19.1467i −0.199487 0.770195i
\(619\) 5.84652 2.02350i 0.234992 0.0813314i −0.207034 0.978334i \(-0.566381\pi\)
0.442026 + 0.897002i \(0.354260\pi\)
\(620\) −7.12361 0.119122i −0.286091 0.00478406i
\(621\) −0.167525 + 1.75440i −0.00672256 + 0.0704018i
\(622\) 5.21162 18.8193i 0.208967 0.754584i
\(623\) −11.5125 47.4550i −0.461237 1.90124i
\(624\) −0.585657 + 17.5065i −0.0234450 + 0.700821i
\(625\) −7.26298 + 2.13260i −0.290519 + 0.0853041i
\(626\) −5.45445 11.4715i −0.218004 0.458493i
\(627\) −28.7483 13.1289i −1.14810 0.524319i
\(628\) 14.3581 26.7433i 0.572950 1.06717i
\(629\) 19.2727 1.84032i 0.768453 0.0733784i
\(630\) 6.18119 2.58601i 0.246265 0.103029i
\(631\) −21.6241 17.0054i −0.860843 0.676974i 0.0868281 0.996223i \(-0.472327\pi\)
−0.947671 + 0.319249i \(0.896569\pi\)
\(632\) 17.7085 38.6452i 0.704407 1.53722i
\(633\) 14.0781 + 8.12800i 0.559555 + 0.323059i
\(634\) 26.6328 1.68114i 1.05772 0.0667668i
\(635\) −11.2842 10.7595i −0.447800 0.426977i
\(636\) 21.3463 10.5568i 0.846435 0.418605i
\(637\) 21.4356 41.5793i 0.849310 1.64743i
\(638\) 14.4451 + 26.9882i 0.571886 + 1.06847i
\(639\) 3.95567 + 9.88078i 0.156484 + 0.390877i
\(640\) −11.7721 + 4.88966i −0.465333 + 0.193281i
\(641\) −16.4681 + 9.50787i −0.650451 + 0.375538i −0.788629 0.614869i \(-0.789209\pi\)
0.138178 + 0.990407i \(0.455875\pi\)
\(642\) −4.65580 + 3.09470i −0.183750 + 0.122138i
\(643\) 6.78337 5.87783i 0.267510 0.231799i −0.510768 0.859719i \(-0.670639\pi\)
0.778278 + 0.627920i \(0.216093\pi\)
\(644\) −7.62451 + 12.7104i −0.300448 + 0.500860i
\(645\) 4.02556 0.578788i 0.158506 0.0227897i
\(646\) −14.8080 13.6892i −0.582613 0.538595i
\(647\) −31.2396 + 29.7869i −1.22816 + 1.17104i −0.248875 + 0.968536i \(0.580061\pi\)
−0.979281 + 0.202508i \(0.935091\pi\)
\(648\) −2.22105 1.75126i −0.0872512 0.0687962i
\(649\) 11.5199 + 3.98708i 0.452196 + 0.156507i
\(650\) −23.0296 1.84075i −0.903294 0.0722000i
\(651\) −0.632608 13.2801i −0.0247939 0.520487i
\(652\) −17.9215 + 19.9969i −0.701861 + 0.783141i
\(653\) 34.7129 24.7190i 1.35842 0.967328i 0.359000 0.933337i \(-0.383118\pi\)
0.999422 0.0339909i \(-0.0108217\pi\)
\(654\) −13.5503 + 0.209229i −0.529860 + 0.00818150i
\(655\) 5.71082 3.67012i 0.223140 0.143403i
\(656\) −9.23354 10.3561i −0.360509 0.404338i
\(657\) 13.6598 + 5.46854i 0.532918 + 0.213348i
\(658\) −9.97696 27.4479i −0.388942 1.07003i
\(659\) 5.38579 27.9441i 0.209800 1.08855i −0.712382 0.701792i \(-0.752383\pi\)
0.922182 0.386756i \(-0.126404\pi\)
\(660\) 7.39990 + 8.83417i 0.288041 + 0.343870i
\(661\) −6.22890 + 9.69236i −0.242276 + 0.376989i −0.941002 0.338400i \(-0.890114\pi\)
0.698726 + 0.715389i \(0.253751\pi\)
\(662\) −18.7624 + 37.8162i −0.729220 + 1.46977i
\(663\) 10.0928 + 0.480778i 0.391971 + 0.0186719i
\(664\) 34.0666 35.6365i 1.32204 1.38296i
\(665\) 19.1742 22.1282i 0.743543 0.858094i
\(666\) 9.55842 7.03143i 0.370381 0.272462i
\(667\) 2.10153 7.15717i 0.0813717 0.277127i
\(668\) 0.555465 3.45251i 0.0214916 0.133582i
\(669\) 4.87085i 0.188318i
\(670\) −8.18675 10.1531i −0.316282 0.392248i
\(671\) 14.9935i 0.578817i
\(672\) −10.5177 21.3359i −0.405728 0.823049i
\(673\) −11.6886 + 39.8078i −0.450564 + 1.53448i 0.350887 + 0.936418i \(0.385880\pi\)
−0.801451 + 0.598061i \(0.795938\pi\)
\(674\) 3.69086 + 5.01730i 0.142166 + 0.193259i
\(675\) 2.44298 2.81935i 0.0940304 0.108517i
\(676\) −11.1489 5.31858i −0.428804 0.204561i
\(677\) 5.23390 + 0.249321i 0.201155 + 0.00958220i 0.147918 0.989000i \(-0.452743\pi\)
0.0532374 + 0.998582i \(0.483046\pi\)
\(678\) −2.02043 1.00243i −0.0775942 0.0384980i
\(679\) −41.6183 + 64.7594i −1.59717 + 2.48524i
\(680\) 2.72416 + 6.82996i 0.104467 + 0.261917i
\(681\) −3.94647 + 20.4762i −0.151229 + 0.784651i
\(682\) 21.4907 7.81157i 0.822920 0.299121i
\(683\) 6.61174 + 2.64694i 0.252991 + 0.101282i 0.494692 0.869068i \(-0.335281\pi\)
−0.241701 + 0.970351i \(0.577705\pi\)
\(684\) −12.0958 2.54173i −0.462493 0.0971853i
\(685\) 11.6300 7.47413i 0.444359 0.285572i
\(686\) 0.338106 + 21.8968i 0.0129089 + 0.836024i
\(687\) −17.1134 + 12.1864i −0.652918 + 0.464941i
\(688\) −2.93294 14.1374i −0.111817 0.538982i
\(689\) 2.48101 + 52.0827i 0.0945188 + 1.98419i
\(690\) 0.223744 2.79926i 0.00851778 0.106566i
\(691\) −21.7914 7.54209i −0.828985 0.286915i −0.120565 0.992705i \(-0.538471\pi\)
−0.708420 + 0.705791i \(0.750592\pi\)
\(692\) 8.99675 + 3.28325i 0.342005 + 0.124811i
\(693\) −15.5637 + 14.8399i −0.591215 + 0.563722i
\(694\) −12.9894 + 14.0510i −0.493070 + 0.533367i
\(695\) 0.999437 0.143697i 0.0379108 0.00545075i
\(696\) 7.82798 + 9.05739i 0.296719 + 0.343319i
\(697\) −6.04870 + 5.24123i −0.229111 + 0.198526i
\(698\) 20.6149 + 31.0139i 0.780285 + 1.17389i
\(699\) −0.218495 + 0.126148i −0.00826423 + 0.00477136i
\(700\) 28.7530 12.5543i 1.08676 0.474510i
\(701\) 17.8609 + 44.6144i 0.674598 + 1.68506i 0.727180 + 0.686447i \(0.240830\pi\)
−0.0525828 + 0.998617i \(0.516745\pi\)
\(702\) 5.46004 2.92242i 0.206076 0.110300i
\(703\) 23.7607 46.0893i 0.896152 1.73829i
\(704\) 29.6817 28.1566i 1.11867 1.06119i
\(705\) 4.00459 + 3.81837i 0.150822 + 0.143808i
\(706\) −2.12641 33.6867i −0.0800286 1.26782i
\(707\) −3.80297 2.19565i −0.143026 0.0825758i
\(708\) 4.73762 + 0.532461i 0.178051 + 0.0200111i
\(709\) 12.2731 + 9.65167i 0.460926 + 0.362476i 0.821456 0.570271i \(-0.193162\pi\)
−0.360531 + 0.932747i \(0.617404\pi\)
\(710\) −6.54528 15.6448i −0.245640 0.587141i
\(711\) −14.9613 + 1.42863i −0.561091 + 0.0535777i
\(712\) 23.8003 22.6354i 0.891952 0.848296i
\(713\) −5.06859 2.31475i −0.189820 0.0866880i
\(714\) −12.3922 + 5.89222i −0.463766 + 0.220511i
\(715\) −24.2100 + 7.10870i −0.905402 + 0.265850i
\(716\) 20.6881 14.2167i 0.773150 0.531302i
\(717\) −6.79618 28.0142i −0.253808 1.04621i
\(718\) −12.6956 3.51580i −0.473796 0.131208i
\(719\) 2.43298 25.4793i 0.0907347 0.950217i −0.829411 0.558640i \(-0.811324\pi\)
0.920145 0.391577i \(-0.128070\pi\)
\(720\) 3.58169 + 2.73549i 0.133482 + 0.101946i
\(721\) −55.5755 + 19.2349i −2.06974 + 0.716344i
\(722\) −26.2745 + 6.80532i −0.977836 + 0.253268i
\(723\) −3.53234 7.73475i −0.131369 0.287659i
\(724\) −2.38630 3.85333i −0.0886863 0.143208i
\(725\) −12.4114 + 9.76046i −0.460949 + 0.362494i
\(726\) −18.7218 10.4270i −0.694831 0.386982i
\(727\) 0.609983 2.51439i 0.0226230 0.0932534i −0.959381 0.282114i \(-0.908964\pi\)
0.982004 + 0.188861i \(0.0604795\pi\)
\(728\) 52.0275 2.41158i 1.92827 0.0893792i
\(729\) −0.142315 + 0.989821i −0.00527092 + 0.0366601i
\(730\) −21.8974 8.37650i −0.810459 0.310028i
\(731\) −8.17824 + 1.57623i −0.302483 + 0.0582988i
\(732\) −1.28695 5.72072i −0.0475670 0.211444i
\(733\) 27.4396 + 19.5397i 1.01351 + 0.721714i 0.960898 0.276901i \(-0.0893075\pi\)
0.0526072 + 0.998615i \(0.483247\pi\)
\(734\) 22.8611 + 15.7531i 0.843819 + 0.581458i
\(735\) −5.51523 10.6981i −0.203432 0.394604i
\(736\) −9.96794 0.179458i −0.367423 0.00661491i
\(737\) 36.1836 + 21.0476i 1.33284 + 0.775298i
\(738\) −1.53265 + 4.65987i −0.0564177 + 0.171532i
\(739\) 1.79879 0.927341i 0.0661696 0.0341128i −0.424824 0.905276i \(-0.639664\pi\)
0.490994 + 0.871163i \(0.336634\pi\)
\(740\) −15.0556 + 11.4377i −0.553455 + 0.420458i
\(741\) 15.6978 22.0445i 0.576673 0.809824i
\(742\) −36.3472 60.7688i −1.33435 2.23089i
\(743\) −1.13696 5.89912i −0.0417111 0.216418i 0.955093 0.296307i \(-0.0957553\pi\)
−0.996804 + 0.0798897i \(0.974543\pi\)
\(744\) 7.52921 4.82512i 0.276034 0.176897i
\(745\) 9.32125 + 1.34019i 0.341504 + 0.0491009i
\(746\) −25.4192 + 20.6329i −0.930662 + 0.755424i
\(747\) −16.9389 4.10933i −0.619761 0.150352i
\(748\) −15.9980 17.3500i −0.584945 0.634379i
\(749\) 10.2756 + 13.0665i 0.375462 + 0.477439i
\(750\) −8.94652 + 10.6528i −0.326681 + 0.388986i
\(751\) −20.8298 + 9.51267i −0.760091 + 0.347122i −0.757466 0.652874i \(-0.773563\pi\)
−0.00262526 + 0.999997i \(0.500836\pi\)
\(752\) 12.6526 15.0266i 0.461392 0.547962i
\(753\) 5.58085 + 16.1248i 0.203378 + 0.587621i
\(754\) −25.0330 + 7.77211i −0.911647 + 0.283044i
\(755\) 12.0071 + 1.14654i 0.436982 + 0.0417267i
\(756\) −4.66451 + 6.99803i −0.169647 + 0.254516i
\(757\) −29.4835 + 7.15262i −1.07160 + 0.259967i −0.732488 0.680780i \(-0.761641\pi\)
−0.339109 + 0.940747i \(0.610126\pi\)
\(758\) 32.3382 42.4543i 1.17458 1.54201i
\(759\) 2.53921 + 8.64775i 0.0921675 + 0.313894i
\(760\) 19.3336 + 3.75194i 0.701304 + 0.136097i
\(761\) 18.7336 41.0209i 0.679094 1.48701i −0.184507 0.982831i \(-0.559069\pi\)
0.863601 0.504177i \(-0.168204\pi\)
\(762\) 19.2715 + 3.40657i 0.698133 + 0.123407i
\(763\) 3.83035 + 40.1133i 0.138668 + 1.45220i
\(764\) −2.77593 35.2989i −0.100430 1.27707i
\(765\) 1.60706 2.04354i 0.0581032 0.0738842i
\(766\) 7.75346 + 37.1341i 0.280144 + 1.34171i
\(767\) −5.21925 + 9.04000i −0.188456 + 0.326416i
\(768\) 8.90817 13.2908i 0.321446 0.479589i
\(769\) −0.0255329 + 0.0267781i −0.000920740 + 0.000965644i −0.724194 0.689596i \(-0.757788\pi\)
0.723274 + 0.690562i \(0.242637\pi\)
\(770\) 24.4311 24.0260i 0.880437 0.865837i
\(771\) −12.3053 6.34380i −0.443163 0.228466i
\(772\) −3.71404 21.1691i −0.133671 0.761891i
\(773\) 5.56591 2.22825i 0.200192 0.0801447i −0.269400 0.963028i \(-0.586825\pi\)
0.469592 + 0.882884i \(0.344401\pi\)
\(774\) −3.80584 + 3.40206i −0.136798 + 0.122285i
\(775\) 5.89742 + 10.2146i 0.211842 + 0.366920i
\(776\) −51.7166 2.52997i −1.85652 0.0908205i
\(777\) −23.1054 26.6651i −0.828903 0.956605i
\(778\) −5.38721 1.21917i −0.193141 0.0437095i
\(779\) 3.05070 + 21.2181i 0.109303 + 0.760217i
\(780\) −8.62710 + 4.79034i −0.308900 + 0.171522i
\(781\) 37.5604 + 39.3923i 1.34402 + 1.40957i
\(782\) −0.184919 + 5.74793i −0.00661268 + 0.205546i
\(783\) 1.38432 3.99973i 0.0494716 0.142939i
\(784\) −36.6991 + 21.8868i −1.31068 + 0.781673i
\(785\) 17.0805 0.813647i 0.609631 0.0290403i
\(786\) −3.41955 + 7.80444i −0.121971 + 0.278375i
\(787\) 4.42024 + 6.20737i 0.157565 + 0.221269i 0.885810 0.464048i \(-0.153603\pi\)
−0.728246 + 0.685316i \(0.759664\pi\)
\(788\) 19.1157 + 5.96181i 0.680970 + 0.212381i
\(789\) −8.00493 12.4559i −0.284983 0.443442i
\(790\) 23.8013 2.64416i 0.846812 0.0940749i
\(791\) −2.49251 + 6.22599i −0.0886234 + 0.221371i
\(792\) −13.8734 4.09292i −0.492971 0.145436i
\(793\) 12.6068 + 2.42975i 0.447679 + 0.0862831i
\(794\) 24.4771 39.4120i 0.868660 1.39868i
\(795\) 11.2860 + 7.25308i 0.400274 + 0.257240i
\(796\) 1.62906 + 1.60616i 0.0577405 + 0.0569287i
\(797\) −0.675334 + 14.1770i −0.0239215 + 0.502175i 0.954833 + 0.297142i \(0.0960334\pi\)
−0.978755 + 0.205033i \(0.934270\pi\)
\(798\) −4.66801 + 36.4537i −0.165246 + 1.29045i
\(799\) −8.56383 7.42060i −0.302966 0.262522i
\(800\) 16.9670 + 12.5485i 0.599872 + 0.443655i
\(801\) −11.1422 3.27164i −0.393689 0.115598i
\(802\) −0.662685 4.15285i −0.0234002 0.146642i
\(803\) 75.2461 2.65538
\(804\) 15.6124 + 4.92488i 0.550605 + 0.173687i
\(805\) −8.34993 −0.294296
\(806\) 3.08545 + 19.3356i 0.108680 + 0.681068i
\(807\) 16.6514 + 4.88930i 0.586159 + 0.172112i
\(808\) 0.00378359 2.95369i 0.000133106 0.103911i
\(809\) 13.8138 + 11.9697i 0.485668 + 0.420834i 0.862969 0.505257i \(-0.168602\pi\)
−0.377301 + 0.926091i \(0.623148\pi\)
\(810\) 0.202387 1.58049i 0.00711117 0.0555329i
\(811\) −0.426481 + 8.95293i −0.0149758 + 0.314380i 0.978934 + 0.204179i \(0.0654525\pi\)
−0.993909 + 0.110201i \(0.964851\pi\)
\(812\) 24.9913 25.3477i 0.877024 0.889530i
\(813\) 16.0631 + 10.3232i 0.563359 + 0.362049i
\(814\) 32.0158 51.5505i 1.12215 1.80684i
\(815\) −14.8541 2.86289i −0.520315 0.100282i
\(816\) −7.59322 5.24669i −0.265816 0.183671i
\(817\) −8.29075 + 20.7093i −0.290057 + 0.724527i
\(818\) 24.9323 2.76980i 0.871737 0.0968439i
\(819\) −9.95550 15.4911i −0.347873 0.541301i
\(820\) 2.32720 7.46185i 0.0812695 0.260579i
\(821\) −13.8604 19.4642i −0.483731 0.679305i 0.498519 0.866879i \(-0.333877\pi\)
−0.982251 + 0.187573i \(0.939938\pi\)
\(822\) −6.96385 + 15.8936i −0.242892 + 0.554354i
\(823\) −11.0272 + 0.525291i −0.384384 + 0.0183105i −0.238885 0.971048i \(-0.576782\pi\)
−0.145499 + 0.989358i \(0.546479\pi\)
\(824\) −29.8620 25.9427i −1.04029 0.903755i
\(825\) 6.23979 18.0287i 0.217242 0.627679i
\(826\) 0.455814 14.1683i 0.0158598 0.492979i
\(827\) −3.46875 3.63792i −0.120620 0.126503i 0.660655 0.750690i \(-0.270279\pi\)
−0.781275 + 0.624187i \(0.785430\pi\)
\(828\) 1.71110 + 3.08158i 0.0594648 + 0.107092i
\(829\) −0.785088 5.46041i −0.0272672 0.189648i 0.971635 0.236484i \(-0.0759951\pi\)
−0.998903 + 0.0468364i \(0.985086\pi\)
\(830\) 27.0883 + 6.13031i 0.940248 + 0.212786i
\(831\) −0.852563 0.983910i −0.0295751 0.0341315i
\(832\) 18.8645 + 29.5197i 0.654008 + 1.02341i
\(833\) 12.3244 + 21.3464i 0.427014 + 0.739610i
\(834\) −0.944887 + 0.844640i −0.0327188 + 0.0292475i
\(835\) 1.82888 0.732172i 0.0632909 0.0253378i
\(836\) −62.2578 + 10.9229i −2.15323 + 0.377777i
\(837\) −2.81023 1.44878i −0.0971358 0.0500770i
\(838\) −26.8060 + 26.3615i −0.925997 + 0.910642i
\(839\) −39.6333 + 41.5662i −1.36829 + 1.43502i −0.589451 + 0.807804i \(0.700656\pi\)
−0.778842 + 0.627220i \(0.784193\pi\)
\(840\) 7.25939 11.2641i 0.250473 0.388648i
\(841\) 5.54290 9.60059i 0.191135 0.331055i
\(842\) −6.11521 29.2879i −0.210744 1.00933i
\(843\) −3.07000 + 3.90382i −0.105736 + 0.134455i
\(844\) 32.4119 2.54890i 1.11566 0.0877366i
\(845\) −0.661479 6.92732i −0.0227556 0.238307i
\(846\) −6.83916 1.20894i −0.235135 0.0415642i
\(847\) −26.4700 + 57.9611i −0.909519 + 1.99157i
\(848\) 23.2277 41.5802i 0.797643 1.42787i
\(849\) −4.27422 14.5566i −0.146691 0.499583i
\(850\) 7.37638 9.68387i 0.253008 0.332154i
\(851\) −14.3706 + 3.48628i −0.492619 + 0.119508i
\(852\) 17.7123 + 11.8061i 0.606813 + 0.404469i
\(853\) 9.48769 + 0.905964i 0.324852 + 0.0310196i 0.256208 0.966622i \(-0.417527\pi\)
0.0686439 + 0.997641i \(0.478133\pi\)
\(854\) −16.6512 + 5.16977i −0.569792 + 0.176906i
\(855\) −2.27737 6.58003i −0.0778845 0.225032i
\(856\) −4.16884 + 10.3747i −0.142488 + 0.354601i
\(857\) 26.6362 12.1643i 0.909874 0.415526i 0.0952092 0.995457i \(-0.469648\pi\)
0.814665 + 0.579932i \(0.196921\pi\)
\(858\) 20.3679 24.2525i 0.695349 0.827966i
\(859\) −25.8233 32.8369i −0.881078 1.12038i −0.991960 0.126549i \(-0.959610\pi\)
0.110882 0.993834i \(-0.464632\pi\)
\(860\) 5.97981 5.51383i 0.203910 0.188020i
\(861\) 14.1748 + 3.43877i 0.483077 + 0.117193i
\(862\) −22.1059 + 17.9435i −0.752931 + 0.611158i
\(863\) −23.1448 3.32772i −0.787859 0.113277i −0.263371 0.964695i \(-0.584834\pi\)
−0.524488 + 0.851418i \(0.675743\pi\)
\(864\) −5.64469 0.370832i −0.192036 0.0126160i
\(865\) 1.02107 + 5.29779i 0.0347173 + 0.180130i
\(866\) 3.69053 + 6.17018i 0.125409 + 0.209671i
\(867\) 6.77272 9.51096i 0.230014 0.323009i
\(868\) −16.0853 21.1733i −0.545969 0.718668i
\(869\) −68.3158 + 35.2192i −2.31746 + 1.19473i
\(870\) −2.10712 + 6.40647i −0.0714380 + 0.217200i
\(871\) −23.5609 + 27.0129i −0.798329 + 0.915297i
\(872\) −22.0983 + 15.6935i −0.748343 + 0.531450i
\(873\) 8.38849 + 16.2714i 0.283907 + 0.550704i
\(874\) 12.6833 + 8.73977i 0.429017 + 0.295627i
\(875\) 33.6942 + 23.9935i 1.13907 + 0.811128i
\(876\) 28.7100 6.45867i 0.970020 0.218218i
\(877\) 43.7528 8.43267i 1.47743 0.284751i 0.614033 0.789280i \(-0.289546\pi\)
0.863395 + 0.504529i \(0.168334\pi\)
\(878\) −24.4777 9.36357i −0.826083 0.316005i
\(879\) −0.851508 + 5.92237i −0.0287207 + 0.199757i
\(880\) 22.2040 + 6.17959i 0.748496 + 0.208314i
\(881\) 10.1202 41.7161i 0.340959 1.40545i −0.500783 0.865573i \(-0.666955\pi\)
0.841742 0.539880i \(-0.181530\pi\)
\(882\) 13.1984 + 7.35079i 0.444414 + 0.247514i
\(883\) 6.81935 5.36280i 0.229489 0.180472i −0.496793 0.867869i \(-0.665489\pi\)
0.726282 + 0.687397i \(0.241247\pi\)
\(884\) 17.1807 10.6397i 0.577850 0.357853i
\(885\) 1.11570 + 2.44305i 0.0375039 + 0.0821221i
\(886\) 40.1664 10.4034i 1.34942 0.349511i
\(887\) −33.8630 + 11.7201i −1.13701 + 0.393523i −0.829768 0.558109i \(-0.811527\pi\)
−0.307242 + 0.951631i \(0.599406\pi\)
\(888\) 7.79077 22.4170i 0.261441 0.752265i
\(889\) 5.53139 57.9273i 0.185517 1.94282i
\(890\) 17.8323 + 4.93830i 0.597740 + 0.165532i
\(891\) 1.20567 + 4.96985i 0.0403915 + 0.166496i
\(892\) −5.51727 8.02872i −0.184732 0.268821i
\(893\) −29.1204 + 8.55051i −0.974476 + 0.286132i
\(894\) −10.6749 + 5.07568i −0.357022 + 0.169756i
\(895\) 12.8634 + 5.87450i 0.429974 + 0.196363i
\(896\) −41.5039 23.2549i −1.38655 0.776891i
\(897\) −7.68266 + 0.733605i −0.256517 + 0.0244944i
\(898\) 18.1715 + 43.4344i 0.606390 + 1.44942i
\(899\) 10.5189 + 8.27217i 0.350826 + 0.275892i
\(900\) 0.833304 7.41439i 0.0277768 0.247146i
\(901\) −23.7933 13.7371i −0.792671 0.457649i
\(902\) 1.58039 + 25.0366i 0.0526213 + 0.833628i
\(903\) 10.9853 + 10.4744i 0.365567 + 0.348567i
\(904\) −4.46578 + 0.636245i −0.148530 + 0.0211612i
\(905\) 1.17001 2.26949i 0.0388923 0.0754405i
\(906\) −13.3479 + 7.14427i −0.443453 + 0.237353i
\(907\) 9.18830 + 22.9513i 0.305093 + 0.762085i 0.999112 + 0.0421284i \(0.0134139\pi\)
−0.694020 + 0.719956i \(0.744162\pi\)
\(908\) 16.6886 + 38.2216i 0.553832 + 1.26843i
\(909\) −0.904380 + 0.522144i −0.0299964 + 0.0173184i
\(910\) 16.2423 + 24.4356i 0.538427 + 0.810032i
\(911\) 10.7161 9.28559i 0.355042 0.307645i −0.459018 0.888427i \(-0.651798\pi\)
0.814059 + 0.580782i \(0.197253\pi\)
\(912\) −22.8167 + 9.51144i −0.755538 + 0.314955i
\(913\) −88.2308 + 12.6857i −2.92001 + 0.419834i
\(914\) 1.34208 1.45177i 0.0443921 0.0480202i
\(915\) 2.39073 2.27955i 0.0790350 0.0753598i
\(916\) −14.4047 + 39.4717i −0.475946 + 1.30418i
\(917\) 23.9423 + 8.28650i 0.790644 + 0.273644i
\(918\) −0.259993 + 3.25277i −0.00858103 + 0.107357i
\(919\) −1.74435 36.6183i −0.0575407 1.20793i −0.824361 0.566065i \(-0.808465\pi\)
0.766820 0.641862i \(-0.221838\pi\)
\(920\) −2.80195 4.86751i −0.0923776 0.160477i
\(921\) 1.89051 1.34622i 0.0622943 0.0443596i
\(922\) 0.243315 + 15.7579i 0.00801316 + 0.518958i
\(923\) −39.2085 + 25.1978i −1.29056 + 0.829394i
\(924\) −8.84455 + 42.0901i −0.290964 + 1.38466i
\(925\) 29.0593 + 11.6336i 0.955463 + 0.382510i
\(926\) −31.1250 + 11.3135i −1.02283 + 0.371785i
\(927\) −2.64678 + 13.7328i −0.0869317 + 0.451045i
\(928\) 23.1624 + 6.06263i 0.760344 + 0.199016i
\(929\) 10.1368 15.7732i 0.332578 0.517502i −0.634183 0.773183i \(-0.718663\pi\)
0.966761 + 0.255681i \(0.0822997\pi\)
\(930\) 4.51293 + 2.23907i 0.147985 + 0.0734220i
\(931\) 65.9428 + 3.14124i 2.16119 + 0.102950i
\(932\) −0.217260 + 0.455424i −0.00711659 + 0.0149179i
\(933\) −9.04237 + 10.4355i −0.296034 + 0.341641i
\(934\) 13.4174 + 18.2394i 0.439031 + 0.596812i
\(935\) 3.74566 12.7566i 0.122496 0.417184i
\(936\) 5.68964 11.0017i 0.185972 0.359603i
\(937\) 20.6210i 0.673660i 0.941565 + 0.336830i \(0.109355\pi\)
−0.941565 + 0.336830i \(0.890645\pi\)
\(938\) 10.8985 47.4413i 0.355849 1.54901i
\(939\) 8.98182i 0.293111i
\(940\) 10.9260 + 1.75785i 0.356366 + 0.0573347i
\(941\) 10.1535 34.5797i 0.330995 1.12727i −0.610997 0.791633i \(-0.709231\pi\)
0.941993 0.335634i \(-0.108950\pi\)
\(942\) −17.2893 + 12.7185i −0.563316 + 0.414390i
\(943\) 4.00325 4.62000i 0.130364 0.150448i
\(944\) 8.41224 4.48869i 0.273795 0.146095i
\(945\) −4.73249 0.225436i −0.153948 0.00733345i
\(946\) −11.6027 + 23.3856i −0.377235 + 0.760331i
\(947\) 6.11000 9.50734i 0.198548 0.308947i −0.727675 0.685922i \(-0.759399\pi\)
0.926224 + 0.376975i \(0.123036\pi\)
\(948\) −23.0427 + 19.3016i −0.748393 + 0.626888i
\(949\) −12.1939 + 63.2681i −0.395832 + 2.05377i
\(950\) −11.1382 30.6426i −0.361370 0.994177i
\(951\) −17.5180 7.01316i −0.568061 0.227417i
\(952\) −13.7521 + 23.7491i −0.445709 + 0.769712i
\(953\) 31.4037 20.1819i 1.01727 0.653757i 0.0780022 0.996953i \(-0.475146\pi\)
0.939264 + 0.343196i \(0.111510\pi\)
\(954\) −16.8371 + 0.259979i −0.545121 + 0.00841714i
\(955\) 16.2484 11.5704i 0.525786 0.374411i
\(956\) −42.9343 38.4783i −1.38860 1.24448i
\(957\) −1.02992 21.6206i −0.0332924 0.698894i
\(958\) 20.9736 + 1.67641i 0.677625 + 0.0541624i
\(959\) 48.7581 + 16.8753i 1.57448 + 0.544933i
\(960\) 9.00230 + 0.451951i 0.290548 + 0.0145866i
\(961\) −15.2011 + 14.4942i −0.490357 + 0.467554i
\(962\) 38.1562 + 35.2733i 1.23020 + 1.13726i
\(963\) 3.91284 0.562581i 0.126089 0.0181289i
\(964\) −14.5837 8.74823i −0.469709 0.281761i
\(965\) 9.15045 7.92891i 0.294564 0.255241i
\(966\) 8.72834 5.80171i 0.280830 0.186667i
\(967\) −37.4363 + 21.6138i −1.20387 + 0.695054i −0.961413 0.275108i \(-0.911286\pi\)
−0.242456 + 0.970162i \(0.577953\pi\)
\(968\) −42.6703 + 4.01937i −1.37148 + 0.129187i
\(969\) 5.29975 + 13.2381i 0.170252 + 0.425270i
\(970\) −13.7649 25.7174i −0.441965 0.825736i
\(971\) 1.53836 2.98400i 0.0493682 0.0957610i −0.862861 0.505442i \(-0.831330\pi\)
0.912229 + 0.409681i \(0.134360\pi\)
\(972\) 0.886603 + 1.79275i 0.0284378 + 0.0575023i
\(973\) 2.72734 + 2.60052i 0.0874346 + 0.0833687i
\(974\) 20.6971 1.30647i 0.663177 0.0418618i
\(975\) 14.1476 + 8.16815i 0.453087 + 0.261590i
\(976\) −8.60124 7.97185i −0.275319 0.255173i
\(977\) −5.72280 4.50046i −0.183089 0.143983i 0.522408 0.852696i \(-0.325034\pi\)
−0.705497 + 0.708713i \(0.749276\pi\)
\(978\) 17.5164 7.32829i 0.560114 0.234333i
\(979\) −59.1177 + 5.64506i −1.88941 + 0.180417i
\(980\) −21.2087 11.3867i −0.677487 0.363734i
\(981\) 8.71671 + 3.98079i 0.278303 + 0.127097i
\(982\) −7.17208 15.0839i −0.228870 0.481347i
\(983\) −49.2470 + 14.4602i −1.57074 + 0.461210i −0.947216 0.320597i \(-0.896116\pi\)
−0.623521 + 0.781807i \(0.714298\pi\)
\(984\) 2.75199 + 9.41701i 0.0877301 + 0.300203i
\(985\) 2.65947 + 10.9625i 0.0847378 + 0.349294i
\(986\) 3.68603 13.3103i 0.117387 0.423887i
\(987\) −1.96300 + 20.5575i −0.0624831 + 0.654352i
\(988\) 0.904961 54.1174i 0.0287906 1.72171i
\(989\) 6.01163 2.08064i 0.191159 0.0661606i
\(990\) −2.04315 7.88835i −0.0649356 0.250708i
\(991\) −2.92208 6.39846i −0.0928229 0.203254i 0.857526 0.514441i \(-0.172001\pi\)
−0.950349 + 0.311187i \(0.899273\pi\)
\(992\) 6.94509 16.4818i 0.220507 0.523297i
\(993\) 23.4640 18.4523i 0.744608 0.585566i
\(994\) 30.7966 55.2957i 0.976810 1.75387i
\(995\) −0.303842 + 1.25245i −0.00963242 + 0.0397054i
\(996\) −32.5754 + 12.4134i −1.03219 + 0.393333i
\(997\) −6.01486 + 41.8343i −0.190493 + 1.32491i 0.640215 + 0.768196i \(0.278845\pi\)
−0.830707 + 0.556709i \(0.812064\pi\)
\(998\) 4.61629 12.0677i 0.146126 0.381995i
\(999\) −8.23897 + 1.58793i −0.260670 + 0.0502399i
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 804.2.bf.b.7.3 yes 680
4.3 odd 2 804.2.bf.a.7.26 680
67.48 odd 66 804.2.bf.a.115.26 yes 680
268.115 even 66 inner 804.2.bf.b.115.3 yes 680
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
804.2.bf.a.7.26 680 4.3 odd 2
804.2.bf.a.115.26 yes 680 67.48 odd 66
804.2.bf.b.7.3 yes 680 1.1 even 1 trivial
804.2.bf.b.115.3 yes 680 268.115 even 66 inner