Properties

Label 210.2.x.a.107.4
Level $210$
Weight $2$
Character 210.107
Analytic conductor $1.677$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [210,2,Mod(23,210)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(210, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 9, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("210.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 210.x (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.67685844245\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 107.4
Character \(\chi\) \(=\) 210.107
Dual form 210.2.x.a.53.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.258819 - 0.965926i) q^{2} +(-0.530415 + 1.64884i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.50442 + 1.65430i) q^{5} +(1.72993 + 0.0855915i) q^{6} +(-1.18680 - 2.36464i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.43732 - 1.74913i) q^{9} +O(q^{10})\) \(q+(-0.258819 - 0.965926i) q^{2} +(-0.530415 + 1.64884i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.50442 + 1.65430i) q^{5} +(1.72993 + 0.0855915i) q^{6} +(-1.18680 - 2.36464i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.43732 - 1.74913i) q^{9} +(1.98730 + 1.02500i) q^{10} +(-2.97095 + 1.71528i) q^{11} +(-0.365065 - 1.69314i) q^{12} +(-3.87719 + 3.87719i) q^{13} +(-1.97690 + 1.75837i) q^{14} +(-1.92970 - 3.35801i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.70825 - 0.993622i) q^{17} +(-1.05871 + 2.80698i) q^{18} +(5.97063 + 3.44715i) q^{19} +(0.475719 - 2.18488i) q^{20} +(4.52839 - 0.702601i) q^{21} +(2.42577 + 2.42577i) q^{22} +(-1.11339 + 0.298332i) q^{23} +(-1.54096 + 0.790843i) q^{24} +(-0.473417 - 4.97754i) q^{25} +(4.74857 + 2.74159i) q^{26} +(4.17683 - 3.09097i) q^{27} +(2.21012 + 1.45443i) q^{28} +2.35616 q^{29} +(-2.74415 + 2.73307i) q^{30} +(3.58502 + 6.20943i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-1.25238 - 5.80841i) q^{33} +3.83906i q^{34} +(5.69727 + 1.59409i) q^{35} +(2.98535 + 0.296136i) q^{36} +(-4.77836 + 1.28036i) q^{37} +(1.78437 - 6.65937i) q^{38} +(-4.33633 - 8.44937i) q^{39} +(-2.23356 + 0.105978i) q^{40} -7.73718i q^{41} +(-1.85070 - 4.19225i) q^{42} +(-0.576172 + 0.576172i) q^{43} +(1.71528 - 2.97095i) q^{44} +(6.56036 - 1.40062i) q^{45} +(0.576333 + 0.998238i) q^{46} +(2.28227 + 8.51756i) q^{47} +(1.16273 + 1.28377i) q^{48} +(-4.18301 + 5.61270i) q^{49} +(-4.68540 + 1.74557i) q^{50} +(3.60523 - 5.58726i) q^{51} +(1.41915 - 5.29634i) q^{52} +(-0.246904 + 0.921459i) q^{53} +(-4.06669 - 3.23450i) q^{54} +(1.63198 - 7.49534i) q^{55} +(0.832855 - 2.51125i) q^{56} +(-8.85069 + 8.01617i) q^{57} +(-0.609819 - 2.27587i) q^{58} +(2.74415 + 4.75301i) q^{59} +(3.35018 + 1.94328i) q^{60} +(0.442564 - 0.766543i) q^{61} +(5.06998 - 5.06998i) q^{62} +(-1.24345 + 7.83925i) q^{63} +1.00000i q^{64} +(-0.581098 - 12.2470i) q^{65} +(-5.28636 + 2.71303i) q^{66} +(1.15816 - 4.32230i) q^{67} +(3.70825 - 0.993622i) q^{68} +(0.0986585 - 1.99404i) q^{69} +(0.0652109 - 5.91572i) q^{70} -1.76324i q^{71} +(-0.486620 - 2.96027i) q^{72} +(-6.82973 - 1.83002i) q^{73} +(2.47346 + 4.28416i) q^{74} +(8.45825 + 1.85957i) q^{75} -6.89429 q^{76} +(7.58193 + 4.98952i) q^{77} +(-7.03914 + 6.37543i) q^{78} +(4.97633 + 2.87309i) q^{79} +(0.680454 + 2.13002i) q^{80} +(2.88105 + 8.52640i) q^{81} +(-7.47354 + 2.00253i) q^{82} +(-7.09854 - 7.09854i) q^{83} +(-3.57040 + 2.87267i) q^{84} +(7.22252 - 4.63972i) q^{85} +(0.705664 + 0.407415i) q^{86} +(-1.24974 + 3.88492i) q^{87} +(-3.31366 - 0.887893i) q^{88} +(0.641651 - 1.11137i) q^{89} +(-3.05084 - 5.97431i) q^{90} +(13.7696 + 4.56669i) q^{91} +(0.815058 - 0.815058i) q^{92} +(-12.1399 + 2.61753i) q^{93} +(7.63664 - 4.40902i) q^{94} +(-14.6850 + 4.69125i) q^{95} +(0.939092 - 1.45537i) q^{96} +(2.15837 + 2.15837i) q^{97} +(6.50410 + 2.58780i) q^{98} +(10.2414 + 1.01591i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q + 8 q^{6} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 64 q + 8 q^{6} + 4 q^{7} + 4 q^{10} - 24 q^{15} + 32 q^{16} - 8 q^{18} + 12 q^{21} - 24 q^{22} - 8 q^{25} - 72 q^{27} + 4 q^{28} - 12 q^{30} + 32 q^{31} - 20 q^{33} - 24 q^{36} - 8 q^{37} - 40 q^{42} - 64 q^{43} - 28 q^{45} + 24 q^{46} - 16 q^{55} + 24 q^{57} - 28 q^{58} + 8 q^{60} + 24 q^{61} - 88 q^{63} - 16 q^{67} - 12 q^{70} + 8 q^{72} - 56 q^{73} + 8 q^{75} - 32 q^{76} - 16 q^{78} + 4 q^{81} + 16 q^{82} + 32 q^{85} + 76 q^{87} + 12 q^{88} + 40 q^{90} - 48 q^{91} + 84 q^{93} + 4 q^{96} + 104 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.258819 0.965926i −0.183013 0.683013i
\(3\) −0.530415 + 1.64884i −0.306235 + 0.951956i
\(4\) −0.866025 + 0.500000i −0.433013 + 0.250000i
\(5\) −1.50442 + 1.65430i −0.672799 + 0.739825i
\(6\) 1.72993 + 0.0855915i 0.706243 + 0.0349426i
\(7\) −1.18680 2.36464i −0.448569 0.893748i
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) −2.43732 1.74913i −0.812440 0.583045i
\(10\) 1.98730 + 1.02500i 0.628441 + 0.324133i
\(11\) −2.97095 + 1.71528i −0.895774 + 0.517175i −0.875827 0.482626i \(-0.839683\pi\)
−0.0199474 + 0.999801i \(0.506350\pi\)
\(12\) −0.365065 1.69314i −0.105385 0.488768i
\(13\) −3.87719 + 3.87719i −1.07534 + 1.07534i −0.0784181 + 0.996921i \(0.524987\pi\)
−0.996921 + 0.0784181i \(0.975013\pi\)
\(14\) −1.97690 + 1.75837i −0.528348 + 0.469945i
\(15\) −1.92970 3.35801i −0.498246 0.867035i
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) −3.70825 0.993622i −0.899382 0.240989i −0.220631 0.975357i \(-0.570812\pi\)
−0.678751 + 0.734369i \(0.737478\pi\)
\(18\) −1.05871 + 2.80698i −0.249540 + 0.661611i
\(19\) 5.97063 + 3.44715i 1.36976 + 0.790829i 0.990897 0.134625i \(-0.0429829\pi\)
0.378860 + 0.925454i \(0.376316\pi\)
\(20\) 0.475719 2.18488i 0.106374 0.488554i
\(21\) 4.52839 0.702601i 0.988177 0.153320i
\(22\) 2.42577 + 2.42577i 0.517175 + 0.517175i
\(23\) −1.11339 + 0.298332i −0.232158 + 0.0622065i −0.373022 0.927822i \(-0.621678\pi\)
0.140864 + 0.990029i \(0.455012\pi\)
\(24\) −1.54096 + 0.790843i −0.314548 + 0.161430i
\(25\) −0.473417 4.97754i −0.0946835 0.995507i
\(26\) 4.74857 + 2.74159i 0.931271 + 0.537669i
\(27\) 4.17683 3.09097i 0.803831 0.594858i
\(28\) 2.21012 + 1.45443i 0.417673 + 0.274862i
\(29\) 2.35616 0.437528 0.218764 0.975778i \(-0.429798\pi\)
0.218764 + 0.975778i \(0.429798\pi\)
\(30\) −2.74415 + 2.73307i −0.501011 + 0.498987i
\(31\) 3.58502 + 6.20943i 0.643888 + 1.11525i 0.984557 + 0.175063i \(0.0560130\pi\)
−0.340669 + 0.940183i \(0.610654\pi\)
\(32\) −0.965926 0.258819i −0.170753 0.0457532i
\(33\) −1.25238 5.80841i −0.218011 1.01111i
\(34\) 3.83906i 0.658393i
\(35\) 5.69727 + 1.59409i 0.963014 + 0.269450i
\(36\) 2.98535 + 0.296136i 0.497558 + 0.0493559i
\(37\) −4.77836 + 1.28036i −0.785557 + 0.210489i −0.629233 0.777217i \(-0.716631\pi\)
−0.156324 + 0.987706i \(0.549964\pi\)
\(38\) 1.78437 6.65937i 0.289464 1.08029i
\(39\) −4.33633 8.44937i −0.694368 1.35298i
\(40\) −2.23356 + 0.105978i −0.353156 + 0.0167567i
\(41\) 7.73718i 1.20834i −0.796854 0.604172i \(-0.793504\pi\)
0.796854 0.604172i \(-0.206496\pi\)
\(42\) −1.85070 4.19225i −0.285568 0.646878i
\(43\) −0.576172 + 0.576172i −0.0878654 + 0.0878654i −0.749673 0.661808i \(-0.769789\pi\)
0.661808 + 0.749673i \(0.269789\pi\)
\(44\) 1.71528 2.97095i 0.258588 0.447887i
\(45\) 6.56036 1.40062i 0.977960 0.208792i
\(46\) 0.576333 + 0.998238i 0.0849757 + 0.147182i
\(47\) 2.28227 + 8.51756i 0.332904 + 1.24241i 0.906124 + 0.423013i \(0.139027\pi\)
−0.573220 + 0.819402i \(0.694306\pi\)
\(48\) 1.16273 + 1.28377i 0.167825 + 0.185296i
\(49\) −4.18301 + 5.61270i −0.597572 + 0.801815i
\(50\) −4.68540 + 1.74557i −0.662616 + 0.246861i
\(51\) 3.60523 5.58726i 0.504833 0.782372i
\(52\) 1.41915 5.29634i 0.196801 0.734470i
\(53\) −0.246904 + 0.921459i −0.0339149 + 0.126572i −0.980808 0.194977i \(-0.937537\pi\)
0.946893 + 0.321549i \(0.104203\pi\)
\(54\) −4.06669 3.23450i −0.553407 0.440160i
\(55\) 1.63198 7.49534i 0.220056 1.01067i
\(56\) 0.832855 2.51125i 0.111295 0.335579i
\(57\) −8.85069 + 8.01617i −1.17230 + 1.06177i
\(58\) −0.609819 2.27587i −0.0800731 0.298837i
\(59\) 2.74415 + 4.75301i 0.357258 + 0.618789i 0.987502 0.157609i \(-0.0503784\pi\)
−0.630244 + 0.776397i \(0.717045\pi\)
\(60\) 3.35018 + 1.94328i 0.432506 + 0.250876i
\(61\) 0.442564 0.766543i 0.0566645 0.0981458i −0.836302 0.548270i \(-0.815287\pi\)
0.892966 + 0.450124i \(0.148620\pi\)
\(62\) 5.06998 5.06998i 0.643888 0.643888i
\(63\) −1.24345 + 7.83925i −0.156661 + 0.987653i
\(64\) 1.00000i 0.125000i
\(65\) −0.581098 12.2470i −0.0720763 1.51905i
\(66\) −5.28636 + 2.71303i −0.650706 + 0.333951i
\(67\) 1.15816 4.32230i 0.141491 0.528053i −0.858395 0.512989i \(-0.828538\pi\)
0.999887 0.0150642i \(-0.00479526\pi\)
\(68\) 3.70825 0.993622i 0.449691 0.120494i
\(69\) 0.0986585 1.99404i 0.0118771 0.240054i
\(70\) 0.0652109 5.91572i 0.00779420 0.707064i
\(71\) 1.76324i 0.209258i −0.994511 0.104629i \(-0.966635\pi\)
0.994511 0.104629i \(-0.0333655\pi\)
\(72\) −0.486620 2.96027i −0.0573487 0.348871i
\(73\) −6.82973 1.83002i −0.799360 0.214188i −0.164057 0.986451i \(-0.552458\pi\)
−0.635303 + 0.772263i \(0.719125\pi\)
\(74\) 2.47346 + 4.28416i 0.287534 + 0.498023i
\(75\) 8.45825 + 1.85957i 0.976675 + 0.214725i
\(76\) −6.89429 −0.790829
\(77\) 7.58193 + 4.98952i 0.864041 + 0.568608i
\(78\) −7.03914 + 6.37543i −0.797025 + 0.721875i
\(79\) 4.97633 + 2.87309i 0.559881 + 0.323248i 0.753098 0.657909i \(-0.228559\pi\)
−0.193217 + 0.981156i \(0.561892\pi\)
\(80\) 0.680454 + 2.13002i 0.0760771 + 0.238143i
\(81\) 2.88105 + 8.52640i 0.320117 + 0.947378i
\(82\) −7.47354 + 2.00253i −0.825315 + 0.221142i
\(83\) −7.09854 7.09854i −0.779166 0.779166i 0.200523 0.979689i \(-0.435736\pi\)
−0.979689 + 0.200523i \(0.935736\pi\)
\(84\) −3.57040 + 2.87267i −0.389563 + 0.313434i
\(85\) 7.22252 4.63972i 0.783392 0.503249i
\(86\) 0.705664 + 0.407415i 0.0760937 + 0.0439327i
\(87\) −1.24974 + 3.88492i −0.133986 + 0.416507i
\(88\) −3.31366 0.887893i −0.353237 0.0946497i
\(89\) 0.641651 1.11137i 0.0680149 0.117805i −0.830013 0.557745i \(-0.811667\pi\)
0.898027 + 0.439940i \(0.145000\pi\)
\(90\) −3.05084 5.97431i −0.321587 0.629748i
\(91\) 13.7696 + 4.56669i 1.44345 + 0.478719i
\(92\) 0.815058 0.815058i 0.0849757 0.0849757i
\(93\) −12.1399 + 2.61753i −1.25885 + 0.271425i
\(94\) 7.63664 4.40902i 0.787659 0.454755i
\(95\) −14.6850 + 4.69125i −1.50665 + 0.481312i
\(96\) 0.939092 1.45537i 0.0958457 0.148538i
\(97\) 2.15837 + 2.15837i 0.219150 + 0.219150i 0.808140 0.588990i \(-0.200474\pi\)
−0.588990 + 0.808140i \(0.700474\pi\)
\(98\) 6.50410 + 2.58780i 0.657013 + 0.261407i
\(99\) 10.2414 + 1.01591i 1.02930 + 0.102103i
\(100\) 2.89876 + 4.07396i 0.289876 + 0.407396i
\(101\) −16.2068 + 9.35702i −1.61264 + 0.931059i −0.623885 + 0.781516i \(0.714447\pi\)
−0.988755 + 0.149543i \(0.952220\pi\)
\(102\) −6.32998 2.03629i −0.626761 0.201623i
\(103\) 2.29867 + 8.57874i 0.226494 + 0.845288i 0.981800 + 0.189916i \(0.0608215\pi\)
−0.755306 + 0.655372i \(0.772512\pi\)
\(104\) −5.48317 −0.537669
\(105\) −5.65031 + 8.54833i −0.551414 + 0.834232i
\(106\) 0.953965 0.0926572
\(107\) 1.75308 + 6.54257i 0.169476 + 0.632494i 0.997427 + 0.0716931i \(0.0228402\pi\)
−0.827950 + 0.560801i \(0.810493\pi\)
\(108\) −2.07175 + 4.76527i −0.199354 + 0.458539i
\(109\) −12.2546 + 7.07519i −1.17378 + 0.677680i −0.954566 0.297998i \(-0.903681\pi\)
−0.219209 + 0.975678i \(0.570348\pi\)
\(110\) −7.66233 + 0.363565i −0.730575 + 0.0346645i
\(111\) 0.423414 8.55785i 0.0401887 0.812275i
\(112\) −2.64124 0.154518i −0.249573 0.0146006i
\(113\) 3.82501 + 3.82501i 0.359827 + 0.359827i 0.863749 0.503922i \(-0.168110\pi\)
−0.503922 + 0.863749i \(0.668110\pi\)
\(114\) 10.0338 + 6.47437i 0.939747 + 0.606380i
\(115\) 1.18148 2.29070i 0.110174 0.213609i
\(116\) −2.04049 + 1.17808i −0.189455 + 0.109382i
\(117\) 16.2317 2.66822i 1.50062 0.246677i
\(118\) 3.88081 3.88081i 0.357258 0.357258i
\(119\) 2.05140 + 9.94788i 0.188051 + 0.911921i
\(120\) 1.00997 3.73898i 0.0921973 0.341320i
\(121\) 0.384350 0.665714i 0.0349409 0.0605195i
\(122\) −0.854968 0.229088i −0.0774052 0.0207407i
\(123\) 12.7573 + 4.10392i 1.15029 + 0.370038i
\(124\) −6.20943 3.58502i −0.557623 0.321944i
\(125\) 8.94656 + 6.70515i 0.800205 + 0.599727i
\(126\) 7.89396 0.827862i 0.703250 0.0737518i
\(127\) −4.52922 4.52922i −0.401903 0.401903i 0.477000 0.878903i \(-0.341724\pi\)
−0.878903 + 0.477000i \(0.841724\pi\)
\(128\) 0.965926 0.258819i 0.0853766 0.0228766i
\(129\) −0.644403 1.25562i −0.0567365 0.110552i
\(130\) −11.6793 + 3.73105i −1.02434 + 0.327234i
\(131\) −10.5767 6.10644i −0.924088 0.533522i −0.0391509 0.999233i \(-0.512465\pi\)
−0.884937 + 0.465711i \(0.845799\pi\)
\(132\) 3.98880 + 4.40405i 0.347180 + 0.383323i
\(133\) 1.06529 18.2094i 0.0923726 1.57896i
\(134\) −4.47478 −0.386562
\(135\) −1.17032 + 11.5599i −0.100725 + 0.994914i
\(136\) −1.91953 3.32472i −0.164598 0.285093i
\(137\) 3.39968 + 0.910941i 0.290454 + 0.0778270i 0.401104 0.916032i \(-0.368627\pi\)
−0.110650 + 0.993859i \(0.535293\pi\)
\(138\) −1.95163 + 0.420798i −0.166133 + 0.0358207i
\(139\) 9.33303i 0.791618i −0.918333 0.395809i \(-0.870464\pi\)
0.918333 0.395809i \(-0.129536\pi\)
\(140\) −5.73102 + 1.46811i −0.484360 + 0.124078i
\(141\) −15.2546 0.754749i −1.28467 0.0635613i
\(142\) −1.70316 + 0.456359i −0.142926 + 0.0382968i
\(143\) 4.86847 18.1694i 0.407122 1.51940i
\(144\) −2.73346 + 1.23621i −0.227788 + 0.103018i
\(145\) −3.54466 + 3.89779i −0.294368 + 0.323694i
\(146\) 7.07066i 0.585172i
\(147\) −7.03570 9.87416i −0.580295 0.814407i
\(148\) 3.49800 3.49800i 0.287534 0.287534i
\(149\) 1.00095 1.73369i 0.0820008 0.142029i −0.822108 0.569331i \(-0.807202\pi\)
0.904109 + 0.427301i \(0.140536\pi\)
\(150\) −0.392946 8.65133i −0.0320839 0.706379i
\(151\) −7.46876 12.9363i −0.607799 1.05274i −0.991602 0.129324i \(-0.958719\pi\)
0.383803 0.923415i \(-0.374614\pi\)
\(152\) 1.78437 + 6.65937i 0.144732 + 0.540146i
\(153\) 7.30020 + 8.90800i 0.590186 + 0.720169i
\(154\) 2.85715 8.61496i 0.230236 0.694213i
\(155\) −15.6656 3.41092i −1.25829 0.273972i
\(156\) 7.98005 + 5.14920i 0.638916 + 0.412266i
\(157\) −3.64642 + 13.6086i −0.291016 + 1.08609i 0.653313 + 0.757088i \(0.273378\pi\)
−0.944330 + 0.329000i \(0.893288\pi\)
\(158\) 1.48722 5.55038i 0.118317 0.441564i
\(159\) −1.38837 0.895860i −0.110105 0.0710464i
\(160\) 1.88133 1.20856i 0.148732 0.0955449i
\(161\) 2.02682 + 2.27870i 0.159736 + 0.179587i
\(162\) 7.49020 4.98968i 0.588486 0.392026i
\(163\) −1.56120 5.82648i −0.122283 0.456365i 0.877446 0.479676i \(-0.159246\pi\)
−0.999728 + 0.0233112i \(0.992579\pi\)
\(164\) 3.86859 + 6.70060i 0.302086 + 0.523229i
\(165\) 11.4930 + 6.66651i 0.894726 + 0.518987i
\(166\) −5.01942 + 8.69390i −0.389583 + 0.674777i
\(167\) 5.93525 5.93525i 0.459284 0.459284i −0.439137 0.898420i \(-0.644716\pi\)
0.898420 + 0.439137i \(0.144716\pi\)
\(168\) 3.69887 + 2.70524i 0.285374 + 0.208714i
\(169\) 17.0652i 1.31271i
\(170\) −6.35095 5.77557i −0.487096 0.442966i
\(171\) −8.52281 18.8452i −0.651756 1.44113i
\(172\) 0.210894 0.787066i 0.0160805 0.0600132i
\(173\) 11.8097 3.16440i 0.897875 0.240585i 0.219772 0.975551i \(-0.429469\pi\)
0.678104 + 0.734966i \(0.262802\pi\)
\(174\) 4.07600 + 0.201667i 0.309001 + 0.0152884i
\(175\) −11.2082 + 7.02681i −0.847261 + 0.531177i
\(176\) 3.43055i 0.258588i
\(177\) −9.29246 + 2.00359i −0.698464 + 0.150599i
\(178\) −1.23958 0.332143i −0.0929101 0.0248952i
\(179\) 0.740048 + 1.28180i 0.0553138 + 0.0958063i 0.892356 0.451331i \(-0.149051\pi\)
−0.837043 + 0.547138i \(0.815717\pi\)
\(180\) −4.98113 + 4.49315i −0.371271 + 0.334900i
\(181\) −15.6223 −1.16120 −0.580599 0.814189i \(-0.697182\pi\)
−0.580599 + 0.814189i \(0.697182\pi\)
\(182\) 0.847250 14.4823i 0.0628023 1.07350i
\(183\) 1.02916 + 1.13630i 0.0760778 + 0.0839978i
\(184\) −0.998238 0.576333i −0.0735911 0.0424878i
\(185\) 5.07058 9.83103i 0.372796 0.722792i
\(186\) 5.67037 + 11.0488i 0.415772 + 0.810134i
\(187\) 12.7213 3.40867i 0.930276 0.249267i
\(188\) −6.23529 6.23529i −0.454755 0.454755i
\(189\) −12.2661 6.20831i −0.892227 0.451588i
\(190\) 8.33215 + 12.9704i 0.604477 + 0.940972i
\(191\) 13.1103 + 7.56922i 0.948627 + 0.547690i 0.892654 0.450743i \(-0.148841\pi\)
0.0559725 + 0.998432i \(0.482174\pi\)
\(192\) −1.64884 0.530415i −0.118994 0.0382794i
\(193\) 16.2631 + 4.35769i 1.17065 + 0.313673i 0.791210 0.611545i \(-0.209452\pi\)
0.379436 + 0.925218i \(0.376118\pi\)
\(194\) 1.52620 2.64346i 0.109575 0.189789i
\(195\) 20.5015 + 5.53784i 1.46814 + 0.396573i
\(196\) 0.816238 6.95225i 0.0583027 0.496589i
\(197\) −3.26809 + 3.26809i −0.232842 + 0.232842i −0.813878 0.581036i \(-0.802648\pi\)
0.581036 + 0.813878i \(0.302648\pi\)
\(198\) −1.66938 10.1554i −0.118637 0.721711i
\(199\) −4.35724 + 2.51565i −0.308876 + 0.178330i −0.646424 0.762979i \(-0.723736\pi\)
0.337547 + 0.941309i \(0.390403\pi\)
\(200\) 3.18489 3.85441i 0.225206 0.272548i
\(201\) 6.51246 + 4.20223i 0.459354 + 0.296402i
\(202\) 13.2328 + 13.2328i 0.931059 + 0.931059i
\(203\) −2.79629 5.57146i −0.196261 0.391040i
\(204\) −0.328591 + 6.64132i −0.0230060 + 0.464985i
\(205\) 12.7996 + 11.6400i 0.893964 + 0.812973i
\(206\) 7.69148 4.44068i 0.535891 0.309397i
\(207\) 3.23551 + 1.22034i 0.224883 + 0.0848194i
\(208\) 1.41915 + 5.29634i 0.0984003 + 0.367235i
\(209\) −23.6512 −1.63599
\(210\) 9.71946 + 3.24531i 0.670707 + 0.223948i
\(211\) 2.58896 0.178231 0.0891156 0.996021i \(-0.471596\pi\)
0.0891156 + 0.996021i \(0.471596\pi\)
\(212\) −0.246904 0.921459i −0.0169575 0.0632861i
\(213\) 2.90729 + 0.935247i 0.199204 + 0.0640821i
\(214\) 5.86591 3.38669i 0.400985 0.231509i
\(215\) −0.0863545 1.81997i −0.00588933 0.124121i
\(216\) 5.13911 + 0.767816i 0.349672 + 0.0522432i
\(217\) 10.4283 15.8466i 0.707922 1.07574i
\(218\) 10.0058 + 10.0058i 0.677680 + 0.677680i
\(219\) 6.64000 10.2904i 0.448690 0.695364i
\(220\) 2.33433 + 7.30715i 0.157381 + 0.492648i
\(221\) 18.2300 10.5251i 1.22628 0.707996i
\(222\) −8.37583 + 1.80595i −0.562149 + 0.121207i
\(223\) −7.72857 + 7.72857i −0.517543 + 0.517543i −0.916827 0.399284i \(-0.869259\pi\)
0.399284 + 0.916827i \(0.369259\pi\)
\(224\) 0.534349 + 2.59123i 0.0357027 + 0.173134i
\(225\) −7.55251 + 12.9599i −0.503501 + 0.863995i
\(226\) 2.70469 4.68466i 0.179913 0.311619i
\(227\) 7.32054 + 1.96153i 0.485881 + 0.130191i 0.493440 0.869780i \(-0.335739\pi\)
−0.00755864 + 0.999971i \(0.502406\pi\)
\(228\) 3.65684 11.3676i 0.242180 0.752835i
\(229\) 4.05881 + 2.34336i 0.268214 + 0.154853i 0.628076 0.778152i \(-0.283843\pi\)
−0.359862 + 0.933006i \(0.617176\pi\)
\(230\) −2.51843 0.548345i −0.166061 0.0361568i
\(231\) −12.2485 + 9.85484i −0.805890 + 0.648401i
\(232\) 1.66606 + 1.66606i 0.109382 + 0.109382i
\(233\) 1.81510 0.486355i 0.118911 0.0318622i −0.198873 0.980025i \(-0.563728\pi\)
0.317784 + 0.948163i \(0.397061\pi\)
\(234\) −6.77837 14.9880i −0.443116 0.979797i
\(235\) −17.5241 9.03846i −1.14315 0.589604i
\(236\) −4.75301 2.74415i −0.309394 0.178629i
\(237\) −7.37677 + 6.68123i −0.479173 + 0.433992i
\(238\) 9.07798 4.55620i 0.588438 0.295334i
\(239\) 18.5117 1.19742 0.598712 0.800964i \(-0.295679\pi\)
0.598712 + 0.800964i \(0.295679\pi\)
\(240\) −3.87298 0.00783764i −0.249999 0.000505917i
\(241\) −4.18303 7.24521i −0.269452 0.466705i 0.699268 0.714859i \(-0.253509\pi\)
−0.968721 + 0.248154i \(0.920176\pi\)
\(242\) −0.742508 0.198954i −0.0477302 0.0127893i
\(243\) −15.5868 + 0.227852i −0.999893 + 0.0146167i
\(244\) 0.885128i 0.0566645i
\(245\) −2.99208 15.3638i −0.191157 0.981559i
\(246\) 0.662237 13.3848i 0.0422227 0.853385i
\(247\) −36.5145 + 9.78403i −2.32336 + 0.622543i
\(248\) −1.85574 + 6.92572i −0.117840 + 0.439784i
\(249\) 15.4695 7.93915i 0.980339 0.503123i
\(250\) 4.16114 10.3771i 0.263174 0.656308i
\(251\) 29.1045i 1.83706i 0.395355 + 0.918528i \(0.370622\pi\)
−0.395355 + 0.918528i \(0.629378\pi\)
\(252\) −2.84276 7.41072i −0.179077 0.466831i
\(253\) 2.79610 2.79610i 0.175789 0.175789i
\(254\) −3.20264 + 5.54713i −0.200951 + 0.348058i
\(255\) 3.81921 + 14.3697i 0.239168 + 0.899868i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −4.97152 18.5540i −0.310115 1.15737i −0.928452 0.371452i \(-0.878860\pi\)
0.618337 0.785913i \(-0.287807\pi\)
\(258\) −1.04606 + 0.947425i −0.0651246 + 0.0589841i
\(259\) 8.69853 + 9.77954i 0.540501 + 0.607671i
\(260\) 6.62673 + 10.3156i 0.410972 + 0.639749i
\(261\) −5.74271 4.12124i −0.355465 0.255098i
\(262\) −3.16093 + 11.7967i −0.195283 + 0.728805i
\(263\) −2.13414 + 7.96472i −0.131597 + 0.491126i −0.999989 0.00475276i \(-0.998487\pi\)
0.868392 + 0.495878i \(0.165154\pi\)
\(264\) 3.22161 4.99273i 0.198276 0.307281i
\(265\) −1.15292 1.79472i −0.0708234 0.110249i
\(266\) −17.8647 + 3.68396i −1.09535 + 0.225878i
\(267\) 1.49213 + 1.64747i 0.0913169 + 0.100823i
\(268\) 1.15816 + 4.32230i 0.0707457 + 0.264027i
\(269\) 2.64417 + 4.57984i 0.161218 + 0.279238i 0.935306 0.353841i \(-0.115124\pi\)
−0.774088 + 0.633078i \(0.781791\pi\)
\(270\) 11.4689 1.86147i 0.697973 0.113285i
\(271\) −11.2806 + 19.5386i −0.685247 + 1.18688i 0.288112 + 0.957597i \(0.406973\pi\)
−0.973359 + 0.229286i \(0.926361\pi\)
\(272\) −2.71462 + 2.71462i −0.164598 + 0.164598i
\(273\) −14.8333 + 20.2816i −0.897753 + 1.22750i
\(274\) 3.51961i 0.212627i
\(275\) 9.94435 + 13.9760i 0.599667 + 0.842782i
\(276\) 0.911578 + 1.77622i 0.0548705 + 0.106916i
\(277\) 6.51359 24.3091i 0.391364 1.46059i −0.436522 0.899693i \(-0.643790\pi\)
0.827886 0.560896i \(-0.189543\pi\)
\(278\) −9.01502 + 2.41557i −0.540685 + 0.144876i
\(279\) 2.12330 21.4050i 0.127119 1.28149i
\(280\) 2.90139 + 5.15577i 0.173391 + 0.308116i
\(281\) 29.4678i 1.75790i −0.476910 0.878952i \(-0.658243\pi\)
0.476910 0.878952i \(-0.341757\pi\)
\(282\) 3.21915 + 14.9302i 0.191698 + 0.889079i
\(283\) −1.00552 0.269428i −0.0597719 0.0160158i 0.228809 0.973471i \(-0.426517\pi\)
−0.288581 + 0.957455i \(0.593183\pi\)
\(284\) 0.881618 + 1.52701i 0.0523144 + 0.0906112i
\(285\) 0.0540349 26.7014i 0.00320075 1.58166i
\(286\) −18.8103 −1.11228
\(287\) −18.2956 + 9.18249i −1.07996 + 0.542025i
\(288\) 1.90156 + 2.32036i 0.112051 + 0.136728i
\(289\) −1.95863 1.13081i −0.115213 0.0665185i
\(290\) 4.68241 + 2.41506i 0.274960 + 0.141817i
\(291\) −4.70364 + 2.41397i −0.275732 + 0.141509i
\(292\) 6.82973 1.83002i 0.399680 0.107094i
\(293\) 12.5118 + 12.5118i 0.730947 + 0.730947i 0.970807 0.239860i \(-0.0771017\pi\)
−0.239860 + 0.970807i \(0.577102\pi\)
\(294\) −7.71673 + 9.35158i −0.450049 + 0.545395i
\(295\) −11.9913 2.61089i −0.698158 0.152012i
\(296\) −4.28416 2.47346i −0.249012 0.143767i
\(297\) −7.10726 + 16.3475i −0.412405 + 0.948580i
\(298\) −1.93368 0.518128i −0.112015 0.0300144i
\(299\) 3.16013 5.47351i 0.182755 0.316541i
\(300\) −8.25485 + 2.61869i −0.476594 + 0.151190i
\(301\) 2.04624 + 0.678636i 0.117943 + 0.0391159i
\(302\) −10.5624 + 10.5624i −0.607799 + 0.607799i
\(303\) −6.83184 31.6855i −0.392479 1.82029i
\(304\) 5.97063 3.44715i 0.342439 0.197707i
\(305\) 0.602289 + 1.88534i 0.0344870 + 0.107954i
\(306\) 6.71503 9.35701i 0.383873 0.534905i
\(307\) 21.9524 + 21.9524i 1.25289 + 1.25289i 0.954419 + 0.298469i \(0.0964760\pi\)
0.298469 + 0.954419i \(0.403524\pi\)
\(308\) −9.06090 0.530083i −0.516293 0.0302043i
\(309\) −15.3642 0.760169i −0.874037 0.0432445i
\(310\) 0.759869 + 16.0147i 0.0431576 + 0.909572i
\(311\) −9.54424 + 5.51037i −0.541204 + 0.312465i −0.745567 0.666431i \(-0.767821\pi\)
0.204362 + 0.978895i \(0.434488\pi\)
\(312\) 2.90836 9.04085i 0.164653 0.511837i
\(313\) 2.37746 + 8.87281i 0.134382 + 0.501521i 1.00000 0.000815167i \(0.000259476\pi\)
−0.865618 + 0.500706i \(0.833074\pi\)
\(314\) 14.0887 0.795071
\(315\) −11.0978 13.8506i −0.625289 0.780393i
\(316\) −5.74617 −0.323248
\(317\) −1.31728 4.91615i −0.0739857 0.276118i 0.919016 0.394221i \(-0.128986\pi\)
−0.993001 + 0.118103i \(0.962319\pi\)
\(318\) −0.505997 + 1.57293i −0.0283749 + 0.0882056i
\(319\) −7.00002 + 4.04147i −0.391926 + 0.226279i
\(320\) −1.65430 1.50442i −0.0924782 0.0840999i
\(321\) −11.7175 0.579743i −0.654006 0.0323581i
\(322\) 1.67648 2.54753i 0.0934264 0.141968i
\(323\) −18.7154 18.7154i −1.04135 1.04135i
\(324\) −6.75827 5.94355i −0.375459 0.330197i
\(325\) 21.1344 + 17.4633i 1.17232 + 0.968691i
\(326\) −5.22388 + 3.01601i −0.289324 + 0.167041i
\(327\) −5.16580 23.9586i −0.285670 1.32491i
\(328\) 5.47101 5.47101i 0.302086 0.302086i
\(329\) 17.4323 15.5054i 0.961076 0.854840i
\(330\) 3.46476 12.8268i 0.190729 0.706090i
\(331\) 17.0080 29.4586i 0.934842 1.61919i 0.159925 0.987129i \(-0.448875\pi\)
0.774916 0.632064i \(-0.217792\pi\)
\(332\) 9.69678 + 2.59824i 0.532180 + 0.142597i
\(333\) 13.8859 + 5.23735i 0.760942 + 0.287005i
\(334\) −7.26917 4.19686i −0.397751 0.229642i
\(335\) 5.40803 + 8.41852i 0.295472 + 0.459953i
\(336\) 1.65573 4.27300i 0.0903273 0.233112i
\(337\) 19.0320 + 19.0320i 1.03674 + 1.03674i 0.999299 + 0.0374412i \(0.0119207\pi\)
0.0374412 + 0.999299i \(0.488079\pi\)
\(338\) −16.4837 + 4.41679i −0.896595 + 0.240242i
\(339\) −8.33566 + 4.27797i −0.452731 + 0.232347i
\(340\) −3.93503 + 7.62938i −0.213407 + 0.413761i
\(341\) −21.3018 12.2986i −1.15356 0.666006i
\(342\) −15.9972 + 13.1099i −0.865031 + 0.708903i
\(343\) 18.2364 + 3.23013i 0.984673 + 0.174410i
\(344\) −0.814830 −0.0439327
\(345\) 3.15031 + 3.16309i 0.169607 + 0.170295i
\(346\) −6.11315 10.5883i −0.328645 0.569230i
\(347\) 26.4308 + 7.08212i 1.41888 + 0.380188i 0.885087 0.465425i \(-0.154099\pi\)
0.533795 + 0.845614i \(0.320765\pi\)
\(348\) −0.860151 3.98931i −0.0461089 0.213849i
\(349\) 7.53522i 0.403351i 0.979452 + 0.201675i \(0.0646386\pi\)
−0.979452 + 0.201675i \(0.935361\pi\)
\(350\) 9.68827 + 9.00763i 0.517860 + 0.481478i
\(351\) −4.21007 + 28.1786i −0.224717 + 1.50406i
\(352\) 3.31366 0.887893i 0.176619 0.0473248i
\(353\) −3.86404 + 14.4208i −0.205662 + 0.767542i 0.783584 + 0.621285i \(0.213389\pi\)
−0.989247 + 0.146257i \(0.953277\pi\)
\(354\) 4.34038 + 8.45726i 0.230689 + 0.449499i
\(355\) 2.91692 + 2.65266i 0.154814 + 0.140788i
\(356\) 1.28330i 0.0680149i
\(357\) −17.4905 1.89409i −0.925696 0.100246i
\(358\) 1.04659 1.04659i 0.0553138 0.0553138i
\(359\) −15.4927 + 26.8342i −0.817675 + 1.41625i 0.0897169 + 0.995967i \(0.471404\pi\)
−0.907391 + 0.420287i \(0.861930\pi\)
\(360\) 5.62926 + 3.64849i 0.296688 + 0.192292i
\(361\) 14.2656 + 24.7088i 0.750822 + 1.30046i
\(362\) 4.04336 + 15.0900i 0.212514 + 0.793113i
\(363\) 0.893789 + 0.986836i 0.0469117 + 0.0517954i
\(364\) −14.2082 + 2.92993i −0.744710 + 0.153570i
\(365\) 13.3022 8.54530i 0.696270 0.447282i
\(366\) 0.831216 1.28819i 0.0434484 0.0673348i
\(367\) 2.59090 9.66937i 0.135244 0.504737i −0.864753 0.502197i \(-0.832525\pi\)
0.999997 0.00253931i \(-0.000808289\pi\)
\(368\) −0.298332 + 1.11339i −0.0155516 + 0.0580395i
\(369\) −13.5334 + 18.8580i −0.704519 + 0.981707i
\(370\) −10.8084 2.35334i −0.561903 0.122345i
\(371\) 2.47194 0.509750i 0.128337 0.0264649i
\(372\) 9.20468 8.33678i 0.477240 0.432242i
\(373\) 3.70262 + 13.8184i 0.191715 + 0.715489i 0.993093 + 0.117331i \(0.0374338\pi\)
−0.801378 + 0.598158i \(0.795900\pi\)
\(374\) −6.58505 11.4056i −0.340505 0.589772i
\(375\) −15.8011 + 11.1949i −0.815965 + 0.578102i
\(376\) −4.40902 + 7.63664i −0.227378 + 0.393830i
\(377\) −9.13527 + 9.13527i −0.470490 + 0.470490i
\(378\) −2.82207 + 13.4550i −0.145152 + 0.692048i
\(379\) 2.99621i 0.153905i 0.997035 + 0.0769524i \(0.0245189\pi\)
−0.997035 + 0.0769524i \(0.975481\pi\)
\(380\) 10.3719 11.4052i 0.532069 0.585076i
\(381\) 9.87030 5.06557i 0.505671 0.259517i
\(382\) 3.91812 14.6226i 0.200468 0.748158i
\(383\) 8.09984 2.17034i 0.413882 0.110899i −0.0458683 0.998947i \(-0.514605\pi\)
0.459751 + 0.888048i \(0.347939\pi\)
\(384\) −0.0855915 + 1.72993i −0.00436782 + 0.0882804i
\(385\) −19.6606 + 5.03644i −1.00200 + 0.256681i
\(386\) 16.8368i 0.856972i
\(387\) 2.41212 0.396513i 0.122615 0.0201559i
\(388\) −2.94839 0.790020i −0.149682 0.0401072i
\(389\) −13.0941 22.6796i −0.663895 1.14990i −0.979584 0.201037i \(-0.935569\pi\)
0.315688 0.948863i \(-0.397765\pi\)
\(390\) 0.0429751 21.2362i 0.00217613 1.07534i
\(391\) 4.42515 0.223790
\(392\) −6.92661 + 1.01095i −0.349847 + 0.0510606i
\(393\) 15.6785 14.2002i 0.790878 0.716307i
\(394\) 4.00258 + 2.31089i 0.201647 + 0.116421i
\(395\) −12.2395 + 3.91001i −0.615834 + 0.196734i
\(396\) −9.37727 + 4.24090i −0.471225 + 0.213113i
\(397\) −6.73010 + 1.80333i −0.337774 + 0.0905063i −0.423719 0.905794i \(-0.639276\pi\)
0.0859451 + 0.996300i \(0.472609\pi\)
\(398\) 3.55767 + 3.55767i 0.178330 + 0.178330i
\(399\) 29.4593 + 11.4151i 1.47481 + 0.571468i
\(400\) −4.54738 2.07878i −0.227369 0.103939i
\(401\) 16.7034 + 9.64369i 0.834126 + 0.481583i 0.855263 0.518193i \(-0.173395\pi\)
−0.0211370 + 0.999777i \(0.506729\pi\)
\(402\) 2.37349 7.37817i 0.118379 0.367990i
\(403\) −37.9749 10.1753i −1.89167 0.506870i
\(404\) 9.35702 16.2068i 0.465529 0.806320i
\(405\) −18.4396 8.06120i −0.916269 0.400564i
\(406\) −4.65788 + 4.14301i −0.231167 + 0.205614i
\(407\) 12.0001 12.0001i 0.594822 0.594822i
\(408\) 6.50007 1.40151i 0.321801 0.0693849i
\(409\) 30.3259 17.5087i 1.49952 0.865747i 0.499519 0.866303i \(-0.333510\pi\)
1.00000 0.000555857i \(0.000176935\pi\)
\(410\) 7.93059 15.3761i 0.391664 0.759373i
\(411\) −3.30523 + 5.12234i −0.163035 + 0.252666i
\(412\) −6.28007 6.28007i −0.309397 0.309397i
\(413\) 7.98237 12.1298i 0.392787 0.596868i
\(414\) 0.341345 3.44111i 0.0167762 0.169121i
\(415\) 22.4223 1.06390i 1.10067 0.0522249i
\(416\) 4.74857 2.74159i 0.232818 0.134417i
\(417\) 15.3886 + 4.95038i 0.753585 + 0.242421i
\(418\) 6.12139 + 22.8453i 0.299407 + 1.11740i
\(419\) −8.91090 −0.435326 −0.217663 0.976024i \(-0.569843\pi\)
−0.217663 + 0.976024i \(0.569843\pi\)
\(420\) 0.619146 10.2282i 0.0302112 0.499086i
\(421\) 18.8014 0.916324 0.458162 0.888869i \(-0.348508\pi\)
0.458162 + 0.888869i \(0.348508\pi\)
\(422\) −0.670072 2.50074i −0.0326186 0.121734i
\(423\) 9.33574 24.7520i 0.453919 1.20348i
\(424\) −0.826158 + 0.476982i −0.0401218 + 0.0231643i
\(425\) −3.19024 + 18.9283i −0.154749 + 0.918159i
\(426\) 0.150918 3.05028i 0.00731201 0.147787i
\(427\) −2.33783 0.136768i −0.113136 0.00661869i
\(428\) −4.78950 4.78950i −0.231509 0.231509i
\(429\) 27.3760 + 17.6646i 1.32173 + 0.852856i
\(430\) −1.73560 + 0.554455i −0.0836983 + 0.0267382i
\(431\) 28.5894 16.5061i 1.37710 0.795069i 0.385291 0.922795i \(-0.374101\pi\)
0.991810 + 0.127726i \(0.0407677\pi\)
\(432\) −0.588447 5.16273i −0.0283117 0.248392i
\(433\) −27.9007 + 27.9007i −1.34082 + 1.34082i −0.445581 + 0.895242i \(0.647003\pi\)
−0.895242 + 0.445581i \(0.852997\pi\)
\(434\) −18.0057 5.97160i −0.864302 0.286646i
\(435\) −4.54668 7.91201i −0.217997 0.379352i
\(436\) 7.07519 12.2546i 0.338840 0.586888i
\(437\) −7.67603 2.05679i −0.367194 0.0983895i
\(438\) −11.6584 3.75039i −0.557058 0.179200i
\(439\) −13.8443 7.99298i −0.660750 0.381484i 0.131813 0.991275i \(-0.457920\pi\)
−0.792563 + 0.609790i \(0.791254\pi\)
\(440\) 6.45399 4.14602i 0.307682 0.197654i
\(441\) 20.0127 6.36331i 0.952986 0.303015i
\(442\) −14.8848 14.8848i −0.707996 0.707996i
\(443\) 18.2487 4.88974i 0.867024 0.232318i 0.202224 0.979339i \(-0.435183\pi\)
0.664801 + 0.747021i \(0.268517\pi\)
\(444\) 3.91224 + 7.62302i 0.185666 + 0.361772i
\(445\) 0.873228 + 2.73346i 0.0413950 + 0.129578i
\(446\) 9.46552 + 5.46492i 0.448205 + 0.258772i
\(447\) 2.32765 + 2.56997i 0.110094 + 0.121556i
\(448\) 2.36464 1.18680i 0.111719 0.0560711i
\(449\) 6.78726 0.320311 0.160155 0.987092i \(-0.448801\pi\)
0.160155 + 0.987092i \(0.448801\pi\)
\(450\) 14.4731 + 3.94090i 0.682266 + 0.185776i
\(451\) 13.2714 + 22.9868i 0.624926 + 1.08240i
\(452\) −5.22506 1.40005i −0.245766 0.0658528i
\(453\) 25.2913 5.45317i 1.18829 0.256212i
\(454\) 7.57878i 0.355690i
\(455\) −28.2700 + 15.9088i −1.32532 + 0.745816i
\(456\) −11.9267 0.590093i −0.558518 0.0276336i
\(457\) −5.13040 + 1.37469i −0.239990 + 0.0643051i −0.376809 0.926291i \(-0.622979\pi\)
0.136819 + 0.990596i \(0.456312\pi\)
\(458\) 1.21301 4.52702i 0.0566803 0.211534i
\(459\) −18.5600 + 7.31190i −0.866305 + 0.341290i
\(460\) 0.122158 + 2.57454i 0.00569563 + 0.120039i
\(461\) 28.0988i 1.30869i 0.756195 + 0.654347i \(0.227056\pi\)
−0.756195 + 0.654347i \(0.772944\pi\)
\(462\) 12.6892 + 9.28049i 0.590354 + 0.431767i
\(463\) −7.61828 + 7.61828i −0.354051 + 0.354051i −0.861615 0.507563i \(-0.830546\pi\)
0.507563 + 0.861615i \(0.330546\pi\)
\(464\) 1.17808 2.04049i 0.0546910 0.0947275i
\(465\) 13.9333 24.0209i 0.646143 1.11394i
\(466\) −0.939566 1.62738i −0.0435246 0.0753867i
\(467\) −2.37036 8.84631i −0.109687 0.409358i 0.889147 0.457621i \(-0.151298\pi\)
−0.998835 + 0.0482625i \(0.984632\pi\)
\(468\) −12.7229 + 10.4266i −0.588118 + 0.481969i
\(469\) −11.5952 + 2.39109i −0.535416 + 0.110410i
\(470\) −4.19491 + 19.2663i −0.193497 + 0.888689i
\(471\) −20.5043 13.2306i −0.944788 0.609633i
\(472\) −1.42048 + 5.30129i −0.0653827 + 0.244012i
\(473\) 0.723482 2.70007i 0.0332657 0.124149i
\(474\) 8.36282 + 5.39618i 0.384117 + 0.247855i
\(475\) 14.3317 31.3510i 0.657583 1.43848i
\(476\) −6.75050 7.58942i −0.309409 0.347861i
\(477\) 2.21354 1.81402i 0.101351 0.0830583i
\(478\) −4.79119 17.8810i −0.219144 0.817856i
\(479\) −7.76447 13.4485i −0.354768 0.614476i 0.632310 0.774715i \(-0.282107\pi\)
−0.987078 + 0.160239i \(0.948773\pi\)
\(480\) 0.994829 + 3.74304i 0.0454075 + 0.170845i
\(481\) 13.5624 23.4908i 0.618392 1.07109i
\(482\) −5.91569 + 5.91569i −0.269452 + 0.269452i
\(483\) −4.83226 + 2.13323i −0.219875 + 0.0970655i
\(484\) 0.768701i 0.0349409i
\(485\) −6.81771 + 0.323489i −0.309576 + 0.0146889i
\(486\) 4.25425 + 14.9967i 0.192977 + 0.680265i
\(487\) −0.850498 + 3.17410i −0.0385397 + 0.143832i −0.982515 0.186185i \(-0.940388\pi\)
0.943975 + 0.330017i \(0.107054\pi\)
\(488\) 0.854968 0.229088i 0.0387026 0.0103703i
\(489\) 10.4350 + 0.516289i 0.471886 + 0.0233474i
\(490\) −14.0659 + 6.86658i −0.635433 + 0.310201i
\(491\) 11.6805i 0.527133i 0.964641 + 0.263567i \(0.0848989\pi\)
−0.964641 + 0.263567i \(0.915101\pi\)
\(492\) −13.1001 + 2.82457i −0.590600 + 0.127342i
\(493\) −8.73722 2.34113i −0.393504 0.105439i
\(494\) 18.9013 + 32.7380i 0.850409 + 1.47295i
\(495\) −17.0880 + 15.4140i −0.768049 + 0.692807i
\(496\) 7.17003 0.321944
\(497\) −4.16941 + 2.09261i −0.187024 + 0.0938664i
\(498\) −11.6724 12.8876i −0.523054 0.577506i
\(499\) −2.51013 1.44922i −0.112369 0.0648762i 0.442762 0.896639i \(-0.353999\pi\)
−0.555131 + 0.831763i \(0.687332\pi\)
\(500\) −11.1005 1.33355i −0.496431 0.0596382i
\(501\) 6.63811 + 12.9344i 0.296569 + 0.577867i
\(502\) 28.1127 7.53279i 1.25473 0.336205i
\(503\) −14.8328 14.8328i −0.661362 0.661362i 0.294339 0.955701i \(-0.404901\pi\)
−0.955701 + 0.294339i \(0.904901\pi\)
\(504\) −6.42244 + 4.66393i −0.286078 + 0.207748i
\(505\) 8.90263 40.8879i 0.396162 1.81949i
\(506\) −3.42451 1.97714i −0.152238 0.0878947i
\(507\) 28.1377 + 9.05163i 1.24964 + 0.401997i
\(508\) 6.18702 + 1.65781i 0.274505 + 0.0735533i
\(509\) −9.66165 + 16.7345i −0.428245 + 0.741742i −0.996717 0.0809602i \(-0.974201\pi\)
0.568472 + 0.822702i \(0.307535\pi\)
\(510\) 12.8916 7.40823i 0.570850 0.328042i
\(511\) 3.77820 + 18.3217i 0.167138 + 0.810505i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 35.5933 4.05692i 1.57148 0.179118i
\(514\) −16.6350 + 9.60425i −0.733740 + 0.423625i
\(515\) −17.6500 9.10337i −0.777751 0.401143i
\(516\) 1.18588 + 0.765201i 0.0522055 + 0.0336861i
\(517\) −21.3905 21.3905i −0.940753 0.940753i
\(518\) 7.19497 10.9333i 0.316129 0.480380i
\(519\) −1.04647 + 21.1507i −0.0459349 + 0.928413i
\(520\) 8.24902 9.07081i 0.361743 0.397781i
\(521\) 27.4522 15.8496i 1.20270 0.694382i 0.241549 0.970389i \(-0.422345\pi\)
0.961156 + 0.276007i \(0.0890112\pi\)
\(522\) −2.49449 + 6.61369i −0.109181 + 0.289473i
\(523\) −4.17483 15.5807i −0.182552 0.681295i −0.995141 0.0984575i \(-0.968609\pi\)
0.812589 0.582837i \(-0.198058\pi\)
\(524\) 12.2129 0.533522
\(525\) −5.64104 22.2076i −0.246195 0.969220i
\(526\) 8.24568 0.359529
\(527\) −7.12430 26.5882i −0.310339 1.15820i
\(528\) −5.65642 1.81962i −0.246164 0.0791887i
\(529\) −18.7679 + 10.8357i −0.815998 + 0.471117i
\(530\) −1.43517 + 1.57814i −0.0623397 + 0.0685502i
\(531\) 1.62528 16.3845i 0.0705311 0.711026i
\(532\) 8.18215 + 16.3025i 0.354741 + 0.706802i
\(533\) 29.9985 + 29.9985i 1.29938 + 1.29938i
\(534\) 1.20514 1.86768i 0.0521515 0.0808225i
\(535\) −13.4608 6.94269i −0.581959 0.300159i
\(536\) 3.87527 2.23739i 0.167386 0.0966405i
\(537\) −2.50601 + 0.540331i −0.108142 + 0.0233170i
\(538\) 3.73942 3.73942i 0.161218 0.161218i
\(539\) 2.80015 23.8501i 0.120611 1.02729i
\(540\) −4.76640 10.5963i −0.205113 0.455992i
\(541\) 3.17726 5.50318i 0.136601 0.236600i −0.789607 0.613613i \(-0.789715\pi\)
0.926208 + 0.377013i \(0.123049\pi\)
\(542\) 21.7924 + 5.83926i 0.936065 + 0.250818i
\(543\) 8.28632 25.7587i 0.355600 1.10541i
\(544\) 3.32472 + 1.91953i 0.142546 + 0.0822991i
\(545\) 6.73160 30.9168i 0.288350 1.32433i
\(546\) 23.4296 + 9.07863i 1.00270 + 0.388530i
\(547\) −1.75965 1.75965i −0.0752374 0.0752374i 0.668487 0.743724i \(-0.266942\pi\)
−0.743724 + 0.668487i \(0.766942\pi\)
\(548\) −3.39968 + 0.910941i −0.145227 + 0.0389135i
\(549\) −2.41946 + 1.09421i −0.103260 + 0.0466996i
\(550\) 10.9259 13.2228i 0.465884 0.563820i
\(551\) 14.0678 + 8.12202i 0.599307 + 0.346010i
\(552\) 1.47976 1.34024i 0.0629827 0.0570442i
\(553\) 0.887888 15.1770i 0.0377569 0.645392i
\(554\) −25.1666 −1.06923
\(555\) 13.5202 + 13.5751i 0.573903 + 0.576230i
\(556\) 4.66652 + 8.08264i 0.197904 + 0.342780i
\(557\) −44.9860 12.0540i −1.90612 0.510742i −0.995164 0.0982317i \(-0.968681\pi\)
−0.910953 0.412511i \(-0.864652\pi\)
\(558\) −21.2252 + 3.48908i −0.898536 + 0.147705i
\(559\) 4.46786i 0.188970i
\(560\) 4.22916 4.13693i 0.178715 0.174817i
\(561\) −1.12725 + 22.7834i −0.0475925 + 0.961916i
\(562\) −28.4638 + 7.62684i −1.20067 + 0.321719i
\(563\) −10.7103 + 39.9714i −0.451386 + 1.68459i 0.247115 + 0.968986i \(0.420517\pi\)
−0.698501 + 0.715609i \(0.746149\pi\)
\(564\) 13.5883 6.97368i 0.572169 0.293645i
\(565\) −12.0821 + 0.573278i −0.508300 + 0.0241180i
\(566\) 1.04099i 0.0437561i
\(567\) 16.7426 16.9318i 0.703123 0.711068i
\(568\) 1.24680 1.24680i 0.0523144 0.0523144i
\(569\) −16.0682 + 27.8309i −0.673614 + 1.16673i 0.303258 + 0.952908i \(0.401926\pi\)
−0.976872 + 0.213825i \(0.931408\pi\)
\(570\) −25.8056 + 6.85864i −1.08088 + 0.287277i
\(571\) 0.490240 + 0.849121i 0.0205159 + 0.0355346i 0.876101 0.482127i \(-0.160136\pi\)
−0.855585 + 0.517662i \(0.826802\pi\)
\(572\) 4.86847 + 18.1694i 0.203561 + 0.759700i
\(573\) −19.4343 + 17.6019i −0.811879 + 0.735329i
\(574\) 13.6049 + 15.2956i 0.567856 + 0.638426i
\(575\) 2.01206 + 5.40070i 0.0839085 + 0.225225i
\(576\) 1.74913 2.43732i 0.0728806 0.101555i
\(577\) 6.45735 24.0992i 0.268823 1.00326i −0.691046 0.722811i \(-0.742850\pi\)
0.959869 0.280450i \(-0.0904837\pi\)
\(578\) −0.585353 + 2.18457i −0.0243475 + 0.0908659i
\(579\) −15.8113 + 24.5038i −0.657096 + 1.01834i
\(580\) 1.12087 5.14792i 0.0465416 0.213756i
\(581\) −8.36091 + 25.2100i −0.346869 + 1.04589i
\(582\) 3.54911 + 3.91858i 0.147115 + 0.162431i
\(583\) −0.847018 3.16112i −0.0350799 0.130920i
\(584\) −3.53533 6.12337i −0.146293 0.253387i
\(585\) −20.0053 + 30.8662i −0.827117 + 1.27616i
\(586\) 8.84718 15.3238i 0.365473 0.633019i
\(587\) 26.5508 26.5508i 1.09587 1.09587i 0.100982 0.994888i \(-0.467801\pi\)
0.994888 0.100982i \(-0.0321986\pi\)
\(588\) 11.0302 + 5.03342i 0.454877 + 0.207575i
\(589\) 49.4323i 2.03682i
\(590\) 0.581641 + 12.2584i 0.0239458 + 0.504671i
\(591\) −3.65511 7.12200i −0.150351 0.292960i
\(592\) −1.28036 + 4.77836i −0.0526223 + 0.196389i
\(593\) −20.1433 + 5.39739i −0.827188 + 0.221644i −0.647487 0.762077i \(-0.724180\pi\)
−0.179701 + 0.983721i \(0.557513\pi\)
\(594\) 17.6300 + 2.63403i 0.723368 + 0.108076i
\(595\) −19.5430 11.5722i −0.801183 0.474414i
\(596\) 2.00189i 0.0820008i
\(597\) −1.83675 8.51871i −0.0751733 0.348648i
\(598\) −6.10491 1.63581i −0.249648 0.0668931i
\(599\) 14.8838 + 25.7795i 0.608134 + 1.05332i 0.991548 + 0.129743i \(0.0414152\pi\)
−0.383413 + 0.923577i \(0.625251\pi\)
\(600\) 4.66597 + 7.29580i 0.190487 + 0.297850i
\(601\) 13.1980 0.538359 0.269180 0.963090i \(-0.413247\pi\)
0.269180 + 0.963090i \(0.413247\pi\)
\(602\) 0.125906 2.15216i 0.00513155 0.0877155i
\(603\) −10.3831 + 8.50906i −0.422832 + 0.346516i
\(604\) 12.9363 + 7.46876i 0.526369 + 0.303900i
\(605\) 0.523065 + 1.63735i 0.0212656 + 0.0665676i
\(606\) −28.8377 + 14.7999i −1.17145 + 0.601204i
\(607\) −31.1269 + 8.34043i −1.26340 + 0.338528i −0.827500 0.561466i \(-0.810237\pi\)
−0.435903 + 0.899994i \(0.643571\pi\)
\(608\) −4.87500 4.87500i −0.197707 0.197707i
\(609\) 10.6696 1.65544i 0.432355 0.0670818i
\(610\) 1.66521 1.06973i 0.0674226 0.0433120i
\(611\) −41.8730 24.1754i −1.69400 0.978032i
\(612\) −10.7762 4.06445i −0.435600 0.164296i
\(613\) 38.3608 + 10.2788i 1.54938 + 0.415155i 0.929282 0.369370i \(-0.120427\pi\)
0.620097 + 0.784525i \(0.287093\pi\)
\(614\) 15.5227 26.8861i 0.626444 1.08503i
\(615\) −25.9816 + 14.9304i −1.04768 + 0.602053i
\(616\) 1.83311 + 8.88935i 0.0738582 + 0.358162i
\(617\) 7.74923 7.74923i 0.311972 0.311972i −0.533701 0.845673i \(-0.679199\pi\)
0.845673 + 0.533701i \(0.179199\pi\)
\(618\) 3.24227 + 15.0374i 0.130423 + 0.604893i
\(619\) −1.24931 + 0.721289i −0.0502140 + 0.0289911i −0.524897 0.851166i \(-0.675896\pi\)
0.474683 + 0.880157i \(0.342563\pi\)
\(620\) 15.2723 4.87888i 0.613351 0.195940i
\(621\) −3.72830 + 4.68754i −0.149612 + 0.188104i
\(622\) 7.79284 + 7.79284i 0.312465 + 0.312465i
\(623\) −3.38950 0.198294i −0.135798 0.00794447i
\(624\) −9.48553 0.469313i −0.379725 0.0187876i
\(625\) −24.5518 + 4.71290i −0.982070 + 0.188516i
\(626\) 7.95515 4.59291i 0.317952 0.183569i
\(627\) 12.5450 38.9970i 0.500998 1.55739i
\(628\) −3.64642 13.6086i −0.145508 0.543044i
\(629\) 18.9915 0.757241
\(630\) −10.5063 + 14.3044i −0.418582 + 0.569902i
\(631\) −17.0499 −0.678748 −0.339374 0.940652i \(-0.610215\pi\)
−0.339374 + 0.940652i \(0.610215\pi\)
\(632\) 1.48722 + 5.55038i 0.0591584 + 0.220782i
\(633\) −1.37322 + 4.26877i −0.0545807 + 0.169668i
\(634\) −4.40770 + 2.54478i −0.175052 + 0.101066i
\(635\) 14.3065 0.678821i 0.567738 0.0269382i
\(636\) 1.65030 + 0.0816513i 0.0654385 + 0.00323768i
\(637\) −5.54321 37.9798i −0.219630 1.50482i
\(638\) 5.71550 + 5.71550i 0.226279 + 0.226279i
\(639\) −3.08414 + 4.29757i −0.122007 + 0.170009i
\(640\) −1.02500 + 1.98730i −0.0405166 + 0.0785551i
\(641\) −14.6651 + 8.46692i −0.579238 + 0.334423i −0.760831 0.648951i \(-0.775208\pi\)
0.181592 + 0.983374i \(0.441875\pi\)
\(642\) 2.47272 + 11.4683i 0.0975905 + 0.452617i
\(643\) 22.8061 22.8061i 0.899385 0.899385i −0.0959964 0.995382i \(-0.530604\pi\)
0.995382 + 0.0959964i \(0.0306037\pi\)
\(644\) −2.89463 0.960004i −0.114064 0.0378295i
\(645\) 3.04663 + 0.822955i 0.119961 + 0.0324038i
\(646\) −13.2338 + 22.9216i −0.520677 + 0.901838i
\(647\) −38.0837 10.2045i −1.49723 0.401181i −0.585056 0.810993i \(-0.698928\pi\)
−0.912170 + 0.409812i \(0.865594\pi\)
\(648\) −3.99186 + 8.06629i −0.156815 + 0.316874i
\(649\) −16.3054 9.41395i −0.640045 0.369530i
\(650\) 11.3983 24.9341i 0.447078 0.977995i
\(651\) 20.5971 + 25.5999i 0.807265 + 1.00334i
\(652\) 4.26528 + 4.26528i 0.167041 + 0.167041i
\(653\) −31.6844 + 8.48981i −1.23991 + 0.332232i −0.818429 0.574607i \(-0.805155\pi\)
−0.421477 + 0.906839i \(0.638488\pi\)
\(654\) −21.8052 + 11.1907i −0.852651 + 0.437592i
\(655\) 26.0137 8.31030i 1.01644 0.324710i
\(656\) −6.70060 3.86859i −0.261614 0.151043i
\(657\) 13.4453 + 16.4065i 0.524551 + 0.640078i
\(658\) −19.4889 12.8252i −0.759756 0.499980i
\(659\) −9.95001 −0.387597 −0.193799 0.981041i \(-0.562081\pi\)
−0.193799 + 0.981041i \(0.562081\pi\)
\(660\) −13.2865 0.0268874i −0.517174 0.00104659i
\(661\) −17.3986 30.1353i −0.676727 1.17213i −0.975961 0.217946i \(-0.930064\pi\)
0.299233 0.954180i \(-0.403269\pi\)
\(662\) −32.8568 8.80396i −1.27702 0.342176i
\(663\) 7.68470 + 35.6410i 0.298449 + 1.38418i
\(664\) 10.0388i 0.389583i
\(665\) 28.5212 + 29.1570i 1.10601 + 1.13066i
\(666\) 1.46496 14.7683i 0.0567660 0.572259i
\(667\) −2.62332 + 0.702917i −0.101575 + 0.0272171i
\(668\) −2.17245 + 8.10770i −0.0840547 + 0.313697i
\(669\) −8.64379 16.8425i −0.334188 0.651168i
\(670\) 6.73196 7.40263i 0.260078 0.285988i
\(671\) 3.03648i 0.117222i
\(672\) −4.55594 0.493374i −0.175749 0.0190323i
\(673\) −27.9121 + 27.9121i −1.07593 + 1.07593i −0.0790609 + 0.996870i \(0.525192\pi\)
−0.996870 + 0.0790609i \(0.974808\pi\)
\(674\) 13.4577 23.3094i 0.518370 0.897843i
\(675\) −17.3628 19.3270i −0.668295 0.743896i
\(676\) 8.53259 + 14.7789i 0.328177 + 0.568419i
\(677\) 3.05281 + 11.3933i 0.117329 + 0.437878i 0.999451 0.0331437i \(-0.0105519\pi\)
−0.882121 + 0.471022i \(0.843885\pi\)
\(678\) 6.28963 + 6.94440i 0.241552 + 0.266698i
\(679\) 2.54221 7.66533i 0.0975610 0.294168i
\(680\) 8.38787 + 1.82631i 0.321660 + 0.0700360i
\(681\) −7.11717 + 11.0299i −0.272730 + 0.422668i
\(682\) −6.36622 + 23.7591i −0.243775 + 0.909781i
\(683\) −9.54542 + 35.6240i −0.365245 + 1.36311i 0.501843 + 0.864959i \(0.332656\pi\)
−0.867088 + 0.498155i \(0.834011\pi\)
\(684\) 16.8036 + 12.0590i 0.642501 + 0.461089i
\(685\) −6.62153 + 4.25365i −0.252996 + 0.162524i
\(686\) −1.59987 18.4510i −0.0610832 0.704464i
\(687\) −6.01667 + 5.44937i −0.229550 + 0.207906i
\(688\) 0.210894 + 0.787066i 0.00804024 + 0.0300066i
\(689\) −2.61538 4.52997i −0.0996379 0.172578i
\(690\) 2.23995 3.86163i 0.0852733 0.147010i
\(691\) −7.51839 + 13.0222i −0.286013 + 0.495389i −0.972854 0.231418i \(-0.925663\pi\)
0.686841 + 0.726807i \(0.258997\pi\)
\(692\) −8.64531 + 8.64531i −0.328645 + 0.328645i
\(693\) −9.75225 25.4229i −0.370457 0.965735i
\(694\) 27.3632i 1.03869i
\(695\) 15.4396 + 14.0408i 0.585659 + 0.532599i
\(696\) −3.63075 + 1.86335i −0.137623 + 0.0706302i
\(697\) −7.68783 + 28.6914i −0.291197 + 1.08676i
\(698\) 7.27846 1.95026i 0.275494 0.0738183i
\(699\) −0.160838 + 3.25078i −0.00608344 + 0.122956i
\(700\) 6.19319 11.6895i 0.234081 0.441821i
\(701\) 7.15756i 0.270337i 0.990823 + 0.135169i \(0.0431576\pi\)
−0.990823 + 0.135169i \(0.956842\pi\)
\(702\) 28.3081 3.22656i 1.06842 0.121778i
\(703\) −32.9434 8.82715i −1.24248 0.332922i
\(704\) −1.71528 2.97095i −0.0646469 0.111972i
\(705\) 24.1980 24.1003i 0.911349 0.907668i
\(706\) 14.9295 0.561880
\(707\) 41.3602 + 27.2183i 1.55551 + 1.02365i
\(708\) 7.04572 6.38139i 0.264794 0.239827i
\(709\) −13.4922 7.78971i −0.506709 0.292549i 0.224771 0.974412i \(-0.427837\pi\)
−0.731480 + 0.681863i \(0.761170\pi\)
\(710\) 1.80731 3.50409i 0.0678273 0.131506i
\(711\) −7.10350 15.7069i −0.266402 0.589055i
\(712\) 1.23958 0.332143i 0.0464550 0.0124476i
\(713\) −5.84399 5.84399i −0.218859 0.218859i
\(714\) 2.69733 + 17.3848i 0.100945 + 0.650609i
\(715\) 22.7334 + 35.3883i 0.850179 + 1.32345i
\(716\) −1.28180 0.740048i −0.0479032 0.0276569i
\(717\) −9.81890 + 30.5228i −0.366694 + 1.13990i
\(718\) 29.9296 + 8.01962i 1.11696 + 0.299290i
\(719\) 2.68898 4.65745i 0.100282 0.173694i −0.811519 0.584326i \(-0.801359\pi\)
0.911801 + 0.410633i \(0.134692\pi\)
\(720\) 2.06721 6.38174i 0.0770403 0.237834i
\(721\) 17.5575 15.6168i 0.653877 0.581599i
\(722\) 20.1746 20.1746i 0.750822 0.750822i
\(723\) 14.1649 3.05415i 0.526799 0.113585i
\(724\) 13.5293 7.81117i 0.502814 0.290300i
\(725\) −1.11545 11.7279i −0.0414266 0.435562i
\(726\) 0.721881 1.11875i 0.0267915 0.0415205i
\(727\) 26.8316 + 26.8316i 0.995128 + 0.995128i 0.999988 0.00486049i \(-0.00154715\pi\)
−0.00486049 + 0.999988i \(0.501547\pi\)
\(728\) 6.50743 + 12.9657i 0.241182 + 0.480541i
\(729\) 7.89178 25.8209i 0.292288 0.956330i
\(730\) −11.6970 10.6373i −0.432925 0.393703i
\(731\) 2.70909 1.56409i 0.100199 0.0578500i
\(732\) −1.45943 0.469485i −0.0539421 0.0173527i
\(733\) −7.10691 26.5233i −0.262500 0.979662i −0.963763 0.266760i \(-0.914047\pi\)
0.701263 0.712902i \(-0.252620\pi\)
\(734\) −10.0105 −0.369493
\(735\) 26.9195 + 3.21576i 0.992940 + 0.118615i
\(736\) 1.15267 0.0424878
\(737\) 3.97312 + 14.8279i 0.146352 + 0.546193i
\(738\) 21.7181 + 8.19143i 0.799455 + 0.301531i
\(739\) 31.1498 17.9843i 1.14586 0.661565i 0.197988 0.980205i \(-0.436559\pi\)
0.947876 + 0.318640i \(0.103226\pi\)
\(740\) 0.524267 + 11.0492i 0.0192724 + 0.406177i
\(741\) 3.23558 65.3960i 0.118862 2.40238i
\(742\) −1.13217 2.25578i −0.0415631 0.0828123i
\(743\) −11.3545 11.3545i −0.416555 0.416555i 0.467459 0.884015i \(-0.345169\pi\)
−0.884015 + 0.467459i \(0.845169\pi\)
\(744\) −10.4351 6.73332i −0.382568 0.246855i
\(745\) 1.36220 + 4.26407i 0.0499070 + 0.156224i
\(746\) 12.3892 7.15292i 0.453602 0.261887i
\(747\) 4.88510 + 29.7177i 0.178737 + 1.08731i
\(748\) −9.31267 + 9.31267i −0.340505 + 0.340505i
\(749\) 13.3903 11.9101i 0.489269 0.435186i
\(750\) 14.9031 + 12.3652i 0.544183 + 0.451514i
\(751\) −1.62249 + 2.81024i −0.0592056 + 0.102547i −0.894109 0.447849i \(-0.852190\pi\)
0.834903 + 0.550396i \(0.185523\pi\)
\(752\) 8.51756 + 2.28227i 0.310604 + 0.0832260i
\(753\) −47.9885 15.4374i −1.74880 0.562572i
\(754\) 11.1884 + 6.45961i 0.407457 + 0.235245i
\(755\) 32.6367 + 7.10607i 1.18777 + 0.258616i
\(756\) 13.7269 0.756491i 0.499242 0.0275133i
\(757\) −3.87448 3.87448i −0.140820 0.140820i 0.633182 0.774003i \(-0.281748\pi\)
−0.774003 + 0.633182i \(0.781748\pi\)
\(758\) 2.89411 0.775475i 0.105119 0.0281665i
\(759\) 3.12722 + 6.09340i 0.113511 + 0.221177i
\(760\) −13.7011 7.06663i −0.496990 0.256334i
\(761\) −9.71823 5.61082i −0.352286 0.203392i 0.313406 0.949619i \(-0.398530\pi\)
−0.665691 + 0.746227i \(0.731863\pi\)
\(762\) −7.44759 8.22291i −0.269798 0.297885i
\(763\) 31.2740 + 20.5808i 1.13219 + 0.745074i
\(764\) −15.1384 −0.547690
\(765\) −25.7191 1.32468i −0.929876 0.0478938i
\(766\) −4.19278 7.26211i −0.151491 0.262391i
\(767\) −29.0679 7.78872i −1.04958 0.281234i
\(768\) 1.69314 0.365065i 0.0610960 0.0131731i
\(769\) 23.3486i 0.841972i 0.907067 + 0.420986i \(0.138316\pi\)
−0.907067 + 0.420986i \(0.861684\pi\)
\(770\) 9.95336 + 17.6871i 0.358694 + 0.637400i
\(771\) 33.2294 + 1.64408i 1.19673 + 0.0592103i
\(772\) −16.2631 + 4.35769i −0.585323 + 0.156837i
\(773\) −5.68254 + 21.2075i −0.204387 + 0.762782i 0.785249 + 0.619181i \(0.212535\pi\)
−0.989636 + 0.143602i \(0.954132\pi\)
\(774\) −1.00730 2.22730i −0.0362068 0.0800587i
\(775\) 29.2105 20.7842i 1.04927 0.746591i
\(776\) 3.05240i 0.109575i
\(777\) −20.7387 + 9.15524i −0.743997 + 0.328442i
\(778\) −18.5178 + 18.5178i −0.663895 + 0.663895i
\(779\) 26.6712 46.1958i 0.955594 1.65514i
\(780\) −20.5237 + 5.45482i −0.734867 + 0.195314i
\(781\) 3.02444 + 5.23848i 0.108223 + 0.187448i
\(782\) −1.14531 4.27437i −0.0409563 0.152851i
\(783\) 9.84127 7.28282i 0.351698 0.260267i
\(784\) 2.76924 + 6.42894i 0.0989015 + 0.229605i
\(785\) −17.0270 26.5054i −0.607720 0.946020i
\(786\) −17.7743 11.4690i −0.633988 0.409086i
\(787\) 10.9946 41.0323i 0.391914 1.46264i −0.435060 0.900402i \(-0.643273\pi\)
0.826973 0.562241i \(-0.190061\pi\)
\(788\) 1.19621 4.46430i 0.0426131 0.159034i
\(789\) −12.0005 7.74345i −0.427230 0.275674i
\(790\) 6.94458 + 10.8104i 0.247077 + 0.384618i
\(791\) 4.50523 13.5843i 0.160188 0.483001i
\(792\) 6.52341 + 7.96012i 0.231799 + 0.282850i
\(793\) 1.25613 + 4.68794i 0.0446064 + 0.166474i
\(794\) 3.48376 + 6.03404i 0.123634 + 0.214140i
\(795\) 3.57072 0.949032i 0.126641 0.0336587i
\(796\) 2.51565 4.35724i 0.0891649 0.154438i
\(797\) 7.12389 7.12389i 0.252341 0.252341i −0.569589 0.821930i \(-0.692897\pi\)
0.821930 + 0.569589i \(0.192897\pi\)
\(798\) 3.40146 31.4100i 0.120410 1.11190i
\(799\) 33.8529i 1.19763i
\(800\) −0.830995 + 4.93046i −0.0293801 + 0.174318i
\(801\) −3.50785 + 1.58644i −0.123944 + 0.0560539i
\(802\) 4.99194 18.6302i 0.176272 0.657855i
\(803\) 23.4298 6.27799i 0.826819 0.221545i
\(804\) −7.74107 0.383003i −0.273007 0.0135075i
\(805\) −6.81885 0.0751664i −0.240333 0.00264927i
\(806\) 39.3145i 1.38479i
\(807\) −8.95390 + 1.93059i −0.315192 + 0.0679599i
\(808\) −18.0764 4.84355i −0.635925 0.170396i
\(809\) −23.4131 40.5526i −0.823159 1.42575i −0.903318 0.428971i \(-0.858876\pi\)
0.0801590 0.996782i \(-0.474457\pi\)
\(810\) −3.01401 + 19.8976i −0.105902 + 0.699132i
\(811\) −18.0213 −0.632815 −0.316408 0.948623i \(-0.602477\pi\)
−0.316408 + 0.948623i \(0.602477\pi\)
\(812\) 5.20739 + 3.42688i 0.182744 + 0.120260i
\(813\) −26.2325 28.9634i −0.920013 1.01579i
\(814\) −14.6970 8.48533i −0.515131 0.297411i
\(815\) 11.9874 + 6.18280i 0.419902 + 0.216574i
\(816\) −3.03609 5.91585i −0.106284 0.207096i
\(817\) −5.42626 + 1.45396i −0.189841 + 0.0508677i
\(818\) −24.7610 24.7610i −0.865747 0.865747i
\(819\) −25.5731 35.2154i −0.893598 1.23052i
\(820\) −16.9048 3.68073i −0.590341 0.128537i
\(821\) 27.1356 + 15.6667i 0.947039 + 0.546773i 0.892160 0.451720i \(-0.149189\pi\)
0.0548791 + 0.998493i \(0.482523\pi\)
\(822\) 5.80326 + 1.86685i 0.202412 + 0.0651140i
\(823\) 0.312415 + 0.0837114i 0.0108901 + 0.00291799i 0.264260 0.964451i \(-0.414872\pi\)
−0.253370 + 0.967369i \(0.581539\pi\)
\(824\) −4.44068 + 7.69148i −0.154698 + 0.267946i
\(825\) −28.3187 + 8.98355i −0.985930 + 0.312767i
\(826\) −13.7825 4.57096i −0.479553 0.159044i
\(827\) −31.9770 + 31.9770i −1.11195 + 1.11195i −0.119062 + 0.992887i \(0.537989\pi\)
−0.992887 + 0.119062i \(0.962011\pi\)
\(828\) −3.41220 + 0.560910i −0.118582 + 0.0194930i
\(829\) −35.8756 + 20.7128i −1.24601 + 0.719385i −0.970311 0.241859i \(-0.922243\pi\)
−0.275700 + 0.961244i \(0.588910\pi\)
\(830\) −6.83097 21.3829i −0.237107 0.742213i
\(831\) 36.6267 + 23.6337i 1.27057 + 0.819845i
\(832\) −3.87719 3.87719i −0.134417 0.134417i
\(833\) 21.0885 16.6570i 0.730674 0.577130i
\(834\) 0.798829 16.1455i 0.0276612 0.559074i
\(835\) 0.889553 + 18.7478i 0.0307842 + 0.648795i
\(836\) 20.4826 11.8256i 0.708405 0.408998i
\(837\) 34.1672 + 14.8545i 1.18099 + 0.513448i
\(838\) 2.30631 + 8.60727i 0.0796702 + 0.297333i
\(839\) −17.8925 −0.617717 −0.308858 0.951108i \(-0.599947\pi\)
−0.308858 + 0.951108i \(0.599947\pi\)
\(840\) −10.0400 + 2.04921i −0.346411 + 0.0707045i
\(841\) −23.4485 −0.808569
\(842\) −4.86616 18.1608i −0.167699 0.625861i
\(843\) 48.5876 + 15.6302i 1.67345 + 0.538332i
\(844\) −2.24210 + 1.29448i −0.0771764 + 0.0445578i
\(845\) 28.2309 + 25.6733i 0.971174 + 0.883187i
\(846\) −26.3249 2.61133i −0.905068 0.0897794i
\(847\) −2.03032 0.118778i −0.0697626 0.00408127i
\(848\) 0.674555 + 0.674555i 0.0231643 + 0.0231643i
\(849\) 0.977585 1.51503i 0.0335506 0.0519956i
\(850\) 19.1091 1.81748i 0.655435 0.0623389i
\(851\) 4.93820 2.85107i 0.169279 0.0977335i
\(852\) −2.98541 + 0.643696i −0.102278 + 0.0220527i
\(853\) 38.0442 38.0442i 1.30261 1.30261i 0.375983 0.926627i \(-0.377305\pi\)
0.926627 0.375983i \(-0.122695\pi\)
\(854\) 0.472967 + 2.29357i 0.0161846 + 0.0784844i
\(855\) 43.9976 + 14.2519i 1.50469 + 0.487406i
\(856\) −3.38669 + 5.86591i −0.115755 + 0.200493i
\(857\) −4.07290 1.09133i −0.139127 0.0372791i 0.188583 0.982057i \(-0.439610\pi\)
−0.327711 + 0.944778i \(0.606277\pi\)
\(858\) 9.97728 31.0151i 0.340619 1.05884i
\(859\) 34.2434 + 19.7704i 1.16837 + 0.674558i 0.953295 0.302040i \(-0.0976677\pi\)
0.215073 + 0.976598i \(0.431001\pi\)
\(860\) 0.984770 + 1.53296i 0.0335804 + 0.0522736i
\(861\) −5.43615 35.0370i −0.185264 1.19406i
\(862\) −23.3431 23.3431i −0.795069 0.795069i
\(863\) −18.0311 + 4.83143i −0.613787 + 0.164464i −0.552302 0.833644i \(-0.686250\pi\)
−0.0614855 + 0.998108i \(0.519584\pi\)
\(864\) −4.83451 + 1.90461i −0.164473 + 0.0647961i
\(865\) −12.5319 + 24.2974i −0.426099 + 0.826136i
\(866\) 34.1713 + 19.7288i 1.16119 + 0.670411i
\(867\) 2.90341 2.62965i 0.0986051 0.0893078i
\(868\) −1.10790 + 18.9377i −0.0376046 + 0.642789i
\(869\) −19.7126 −0.668703
\(870\) −6.46565 + 6.43954i −0.219206 + 0.218321i
\(871\) 12.2680 + 21.2488i 0.415685 + 0.719988i
\(872\) −13.6682 3.66239i −0.462864 0.124024i
\(873\) −1.48536 9.03593i −0.0502718 0.305820i
\(874\) 7.94681i 0.268805i
\(875\) 5.23746 29.1130i 0.177058 0.984200i
\(876\) −0.605189 + 12.2318i −0.0204474 + 0.413274i
\(877\) 47.6148 12.7584i 1.60784 0.430819i 0.660440 0.750878i \(-0.270370\pi\)
0.947397 + 0.320060i \(0.103703\pi\)
\(878\) −4.13747 + 15.4413i −0.139633 + 0.521117i
\(879\) −27.2663 + 13.9935i −0.919671 + 0.471987i
\(880\) −5.67517 5.16101i −0.191310 0.173978i
\(881\) 58.4991i 1.97089i −0.170007 0.985443i \(-0.554379\pi\)
0.170007 0.985443i \(-0.445621\pi\)
\(882\) −11.3262 17.6838i −0.381371 0.595446i
\(883\) −4.87858 + 4.87858i −0.164177 + 0.164177i −0.784414 0.620237i \(-0.787036\pi\)
0.620237 + 0.784414i \(0.287036\pi\)
\(884\) −10.5251 + 18.2300i −0.353998 + 0.613142i
\(885\) 10.6653 18.3868i 0.358509 0.618064i
\(886\) −9.44625 16.3614i −0.317353 0.549671i
\(887\) −11.6286 43.3986i −0.390451 1.45718i −0.829393 0.558666i \(-0.811313\pi\)
0.438942 0.898515i \(-0.355353\pi\)
\(888\) 6.35071 5.75191i 0.213116 0.193022i
\(889\) −5.33467 + 16.0852i −0.178919 + 0.539481i
\(890\) 2.41431 1.55095i 0.0809279 0.0519878i
\(891\) −23.1846 20.3897i −0.776713 0.683080i
\(892\) 2.82885 10.5574i 0.0947169 0.353488i
\(893\) −15.7347 + 58.7226i −0.526540 + 1.96508i
\(894\) 1.87996 2.91350i 0.0628753 0.0974420i
\(895\) −3.23383 0.704110i −0.108095 0.0235358i
\(896\) −1.75837 1.97690i −0.0587432 0.0660435i
\(897\) 7.34874 + 8.11378i 0.245367 + 0.270911i
\(898\) −1.75667 6.55599i −0.0586209 0.218776i
\(899\) 8.44687 + 14.6304i 0.281719 + 0.487951i
\(900\) 0.0607099 14.9999i 0.00202366 0.499996i
\(901\) 1.83116 3.17167i 0.0610049 0.105664i
\(902\) 18.7686 18.7686i 0.624926 0.624926i
\(903\) −2.20432 + 3.01395i −0.0733550 + 0.100298i
\(904\) 5.40938i 0.179913i
\(905\) 23.5026 25.8440i 0.781253 0.859084i
\(906\) −11.8132 23.0182i −0.392468 0.764727i
\(907\) −14.0941 + 52.6001i −0.467988 + 1.74656i 0.178798 + 0.983886i \(0.442779\pi\)
−0.646787 + 0.762671i \(0.723888\pi\)
\(908\) −7.32054 + 1.96153i −0.242941 + 0.0650957i
\(909\) 55.8679 + 5.54189i 1.85302 + 0.183813i
\(910\) 22.6835 + 23.1892i 0.751952 + 0.768714i
\(911\) 7.37432i 0.244322i 0.992510 + 0.122161i \(0.0389824\pi\)
−0.992510 + 0.122161i \(0.961018\pi\)
\(912\) 2.51686 + 11.6730i 0.0833417 + 0.386532i
\(913\) 33.2653 + 8.91342i 1.10092 + 0.294991i
\(914\) 2.65569 + 4.59979i 0.0878424 + 0.152147i
\(915\) −3.42808 0.00693731i −0.113329 0.000229340i
\(916\) −4.68671 −0.154853
\(917\) −1.88711 + 32.2571i −0.0623180 + 1.06522i
\(918\) 11.8664 + 16.0351i 0.391650 + 0.529237i
\(919\) 39.9069 + 23.0403i 1.31641 + 0.760028i 0.983149 0.182808i \(-0.0585186\pi\)
0.333258 + 0.942836i \(0.391852\pi\)
\(920\) 2.45520 0.784336i 0.0809456 0.0258588i
\(921\) −47.8397 + 24.5520i −1.57637 + 0.809016i
\(922\) 27.1414 7.27251i 0.893854 0.239507i
\(923\) 6.83640 + 6.83640i 0.225023 + 0.225023i
\(924\) 5.68006 14.6588i 0.186860 0.482238i
\(925\) 8.63518 + 23.1783i 0.283923 + 0.762098i
\(926\) 9.33045 + 5.38694i 0.306617 + 0.177026i
\(927\) 9.40279 24.9298i 0.308828 0.818802i
\(928\) −2.27587 0.609819i −0.0747093 0.0200183i
\(929\) −1.40166 + 2.42774i −0.0459869 + 0.0796516i −0.888103 0.459645i \(-0.847977\pi\)
0.842116 + 0.539297i \(0.181310\pi\)
\(930\) −26.8086 7.24152i −0.879088 0.237459i
\(931\) −44.3230 + 19.0920i −1.45263 + 0.625714i
\(932\) −1.32875 + 1.32875i −0.0435246 + 0.0435246i
\(933\) −4.02329 18.6597i −0.131717 0.610890i
\(934\) −7.93138 + 4.57919i −0.259523 + 0.149836i
\(935\) −13.4993 + 26.1730i −0.441475 + 0.855949i
\(936\) 13.3642 + 9.59081i 0.436824 + 0.313485i
\(937\) 9.16753 + 9.16753i 0.299490 + 0.299490i 0.840814 0.541324i \(-0.182077\pi\)
−0.541324 + 0.840814i \(0.682077\pi\)
\(938\) 5.31067 + 10.5812i 0.173400 + 0.345489i
\(939\) −15.8909 0.786228i −0.518578 0.0256576i
\(940\) 19.6956 0.934521i 0.642398 0.0304807i
\(941\) 16.1104 9.30133i 0.525183 0.303215i −0.213869 0.976862i \(-0.568607\pi\)
0.739053 + 0.673648i \(0.235273\pi\)
\(942\) −7.47286 + 23.2300i −0.243479 + 0.756873i
\(943\) 2.30825 + 8.61450i 0.0751669 + 0.280527i
\(944\) 5.48830 0.178629
\(945\) 28.7238 10.9519i 0.934385 0.356264i
\(946\) −2.79532 −0.0908837
\(947\) 1.20259 + 4.48811i 0.0390788 + 0.145844i 0.982709 0.185158i \(-0.0592798\pi\)
−0.943630 + 0.331002i \(0.892613\pi\)
\(948\) 3.04786 9.47450i 0.0989898 0.307717i
\(949\) 33.5755 19.3848i 1.08991 0.629258i
\(950\) −33.9920 5.72912i −1.10285 0.185877i
\(951\) 8.80462 + 0.435624i 0.285509 + 0.0141261i
\(952\) −5.58366 + 8.48477i −0.180967 + 0.274993i
\(953\) −12.6014 12.6014i −0.408198 0.408198i 0.472912 0.881110i \(-0.343203\pi\)
−0.881110 + 0.472912i \(0.843203\pi\)
\(954\) −2.32512 1.66861i −0.0752784 0.0540233i
\(955\) −32.2452 + 10.3010i −1.04343 + 0.333333i
\(956\) −16.0316 + 9.25587i −0.518500 + 0.299356i
\(957\) −2.95079 13.6855i −0.0953857 0.442391i
\(958\) −10.9806 + 10.9806i −0.354768 + 0.354768i
\(959\) −1.88070 9.12011i −0.0607309 0.294504i
\(960\) 3.35801 1.92970i 0.108379 0.0622808i
\(961\) −10.2047 + 17.6750i −0.329183 + 0.570162i
\(962\) −26.2006 7.02042i −0.844740 0.226347i
\(963\) 7.17103 19.0127i 0.231083 0.612676i
\(964\) 7.24521 + 4.18303i 0.233353 + 0.134726i
\(965\) −31.6756 + 20.3483i −1.01967 + 0.655034i
\(966\) 3.31123 + 4.11548i 0.106537 + 0.132413i
\(967\) 22.1599 + 22.1599i 0.712613 + 0.712613i 0.967081 0.254468i \(-0.0819003\pi\)
−0.254468 + 0.967081i \(0.581900\pi\)
\(968\) 0.742508 0.198954i 0.0238651 0.00639464i
\(969\) 40.7856 20.9317i 1.31022 0.672423i
\(970\) 2.07702 + 6.50167i 0.0666890 + 0.208756i
\(971\) −13.6776 7.89677i −0.438935 0.253419i 0.264211 0.964465i \(-0.414889\pi\)
−0.703146 + 0.711046i \(0.748222\pi\)
\(972\) 13.3846 7.99072i 0.429312 0.256303i
\(973\) −22.0692 + 11.0765i −0.707507 + 0.355095i
\(974\) 3.28607 0.105292
\(975\) −40.0041 + 25.5843i −1.28116 + 0.819354i
\(976\) −0.442564 0.766543i −0.0141661 0.0245365i
\(977\) 45.5260 + 12.1987i 1.45651 + 0.390270i 0.898282 0.439420i \(-0.144816\pi\)
0.558225 + 0.829690i \(0.311483\pi\)
\(978\) −2.20208 10.2130i −0.0704146 0.326577i
\(979\) 4.40244i 0.140703i
\(980\) 10.2731 + 11.8094i 0.328163 + 0.377238i
\(981\) 42.2438 + 4.19043i 1.34874 + 0.133790i
\(982\) 11.2825 3.02313i 0.360039 0.0964721i
\(983\) 10.9653 40.9232i 0.349740 1.30525i −0.537236 0.843432i \(-0.680531\pi\)
0.886976 0.461816i \(-0.152802\pi\)
\(984\) 6.11889 + 11.9227i 0.195063 + 0.380082i
\(985\) −0.489809 10.3230i −0.0156066 0.328918i
\(986\) 9.04543i 0.288065i
\(987\) 16.3195 + 36.9674i 0.519455 + 1.17668i
\(988\) 26.7305 26.7305i 0.850409 0.850409i
\(989\) 0.469614 0.813395i 0.0149328 0.0258645i
\(990\) 19.3115 + 12.5163i 0.613759 + 0.397795i
\(991\) 0.654060 + 1.13287i 0.0207769 + 0.0359867i 0.876227 0.481899i \(-0.160053\pi\)
−0.855450 + 0.517885i \(0.826719\pi\)
\(992\) −1.85574 6.92572i −0.0589198 0.219892i
\(993\) 39.5512 + 43.6686i 1.25512 + 1.38578i
\(994\) 3.10043 + 3.48574i 0.0983397 + 0.110561i
\(995\) 2.39349 10.9928i 0.0758787 0.348495i
\(996\) −9.42740 + 14.6103i −0.298719 + 0.462944i
\(997\) −13.1718 + 49.1577i −0.417154 + 1.55684i 0.363327 + 0.931662i \(0.381641\pi\)
−0.780482 + 0.625179i \(0.785026\pi\)
\(998\) −0.750174 + 2.79969i −0.0237463 + 0.0886225i
\(999\) −16.0008 + 20.1176i −0.506244 + 0.636493i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 210.2.x.a.107.4 yes 64
3.2 odd 2 inner 210.2.x.a.107.13 yes 64
5.3 odd 4 inner 210.2.x.a.23.1 64
7.4 even 3 inner 210.2.x.a.137.16 yes 64
15.8 even 4 inner 210.2.x.a.23.16 yes 64
21.11 odd 6 inner 210.2.x.a.137.1 yes 64
35.18 odd 12 inner 210.2.x.a.53.13 yes 64
105.53 even 12 inner 210.2.x.a.53.4 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.x.a.23.1 64 5.3 odd 4 inner
210.2.x.a.23.16 yes 64 15.8 even 4 inner
210.2.x.a.53.4 yes 64 105.53 even 12 inner
210.2.x.a.53.13 yes 64 35.18 odd 12 inner
210.2.x.a.107.4 yes 64 1.1 even 1 trivial
210.2.x.a.107.13 yes 64 3.2 odd 2 inner
210.2.x.a.137.1 yes 64 21.11 odd 6 inner
210.2.x.a.137.16 yes 64 7.4 even 3 inner