Properties

Label 210.2.u.a.73.1
Level $210$
Weight $2$
Character 210.73
Analytic conductor $1.677$
Analytic rank $0$
Dimension $16$
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] = [210,2,Mod(73,210)]
 
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([0, 9, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("210.73");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 210.u (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: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} - 180 x^{7} + 358 x^{6} - 336 x^{5} + 390 x^{4} - 344 x^{3} + 164 x^{2} - 40 x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 73.1
Root \(0.277956 - 0.213283i\) of defining polynomial
Character \(\chi\) \(=\) 210.73
Dual form 210.2.u.a.187.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.965926 - 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.851088 + 2.06776i) q^{5} +1.00000i q^{6} +(-1.86367 + 1.87796i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\) \(q+(-0.965926 - 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.851088 + 2.06776i) q^{5} +1.00000i q^{6} +(-1.86367 + 1.87796i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(1.35727 - 1.77703i) q^{10} +(-2.74315 + 4.75127i) q^{11} +(0.258819 - 0.965926i) q^{12} +(2.41668 - 2.41668i) q^{13} +(2.28622 - 1.33161i) q^{14} +(2.21758 + 0.286912i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-2.04607 + 0.548242i) q^{17} +(0.965926 - 0.258819i) q^{18} +(3.49797 + 6.05866i) q^{19} +(-1.77095 + 1.36519i) q^{20} +(2.29632 + 1.31412i) q^{21} +(3.87940 - 3.87940i) q^{22} +(-0.454069 + 1.69461i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-3.55130 - 3.51970i) q^{25} +(-2.95981 + 1.70885i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-2.55297 + 0.694523i) q^{28} -0.684610i q^{29} +(-2.06776 - 0.851088i) q^{30} +(4.82932 + 2.78821i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(5.29936 + 1.41996i) q^{33} +2.11825 q^{34} +(-2.29702 - 5.45194i) q^{35} -1.00000 q^{36} +(-9.46620 - 2.53646i) q^{37} +(-1.81068 - 6.75755i) q^{38} +(-2.95981 - 1.70885i) q^{39} +(2.06394 - 0.860320i) q^{40} -2.50597i q^{41} +(-1.87796 - 1.86367i) q^{42} +(-1.95305 - 1.95305i) q^{43} +(-4.75127 + 2.74315i) q^{44} +(-0.296818 - 2.21628i) q^{45} +(0.877194 - 1.51935i) q^{46} +(-0.912383 + 3.40506i) q^{47} +(0.707107 - 0.707107i) q^{48} +(-0.0534500 - 6.99980i) q^{49} +(2.51932 + 4.31891i) q^{50} +(1.05912 + 1.83445i) q^{51} +(3.30124 - 0.884566i) q^{52} +(9.08204 - 2.43353i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-7.48985 - 9.71594i) q^{55} +(2.64573 - 0.0101012i) q^{56} +(4.94687 - 4.94687i) q^{57} +(-0.177190 + 0.661282i) q^{58} +(5.08015 - 8.79907i) q^{59} +(1.77703 + 1.35727i) q^{60} +(1.01469 - 0.585830i) q^{61} +(-3.94312 - 3.94312i) q^{62} +(0.675009 - 2.55820i) q^{63} +1.00000i q^{64} +(2.94031 + 7.05393i) q^{65} +(-4.75127 - 2.74315i) q^{66} +(2.57606 + 9.61398i) q^{67} +(-2.04607 - 0.548242i) q^{68} +1.75439 q^{69} +(0.807687 + 5.86069i) q^{70} -11.9716 q^{71} +(0.965926 + 0.258819i) q^{72} +(1.26065 + 4.70482i) q^{73} +(8.48716 + 4.90007i) q^{74} +(-2.48063 + 4.34125i) q^{75} +6.99593i q^{76} +(-3.81036 - 14.0063i) q^{77} +(2.41668 + 2.41668i) q^{78} +(-7.21474 + 4.16543i) q^{79} +(-2.21628 + 0.296818i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-0.648592 + 2.42058i) q^{82} +(4.05281 - 4.05281i) q^{83} +(1.33161 + 2.28622i) q^{84} +(0.607749 - 4.69739i) q^{85} +(1.38101 + 2.39198i) q^{86} +(-0.661282 + 0.177190i) q^{87} +(5.29936 - 1.41996i) q^{88} +(3.59178 + 6.22115i) q^{89} +(-0.286912 + 2.21758i) q^{90} +(0.0345228 + 9.04232i) q^{91} +(-1.24054 + 1.24054i) q^{92} +(1.44328 - 5.38640i) q^{93} +(1.76259 - 3.05289i) q^{94} +(-15.5049 + 2.07652i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(13.1212 + 13.1212i) q^{97} +(-1.76005 + 6.77512i) q^{98} -5.48630i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 12 q^{5} - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 12 q^{5} - 8 q^{7} + 8 q^{10} + 4 q^{11} - 16 q^{13} + 16 q^{14} + 4 q^{15} + 8 q^{16} - 12 q^{17} - 8 q^{19} - 8 q^{20} + 8 q^{21} + 4 q^{22} + 32 q^{23} - 8 q^{24} - 32 q^{25} - 12 q^{26} - 8 q^{28} - 4 q^{30} - 24 q^{31} + 8 q^{33} + 16 q^{34} + 4 q^{35} - 16 q^{36} - 8 q^{37} - 28 q^{38} - 12 q^{39} - 4 q^{42} - 24 q^{43} + 4 q^{45} - 4 q^{46} - 24 q^{47} + 52 q^{49} + 8 q^{51} - 8 q^{52} + 44 q^{53} - 8 q^{54} - 56 q^{55} + 8 q^{56} - 8 q^{57} + 48 q^{58} + 8 q^{59} + 24 q^{61} + 8 q^{62} + 4 q^{63} + 16 q^{65} + 36 q^{67} - 12 q^{68} - 8 q^{69} + 32 q^{70} - 32 q^{71} - 40 q^{73} - 24 q^{74} - 24 q^{75} - 44 q^{77} - 16 q^{78} + 12 q^{79} + 12 q^{80} + 8 q^{81} + 12 q^{82} - 16 q^{83} + 4 q^{84} + 8 q^{85} - 8 q^{86} + 12 q^{87} + 8 q^{88} - 16 q^{89} + 8 q^{91} + 8 q^{92} + 40 q^{93} + 8 q^{94} - 48 q^{95} + 44 q^{97} - 8 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.965926 0.258819i −0.683013 0.183013i
\(3\) −0.258819 0.965926i −0.149429 0.557678i
\(4\) 0.866025 + 0.500000i 0.433013 + 0.250000i
\(5\) −0.851088 + 2.06776i −0.380618 + 0.924732i
\(6\) 1.00000i 0.408248i
\(7\) −1.86367 + 1.87796i −0.704402 + 0.709801i
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) −0.866025 + 0.500000i −0.288675 + 0.166667i
\(10\) 1.35727 1.77703i 0.429205 0.561946i
\(11\) −2.74315 + 4.75127i −0.827091 + 1.43256i 0.0732202 + 0.997316i \(0.476672\pi\)
−0.900311 + 0.435247i \(0.856661\pi\)
\(12\) 0.258819 0.965926i 0.0747146 0.278839i
\(13\) 2.41668 2.41668i 0.670266 0.670266i −0.287511 0.957777i \(-0.592828\pi\)
0.957777 + 0.287511i \(0.0928279\pi\)
\(14\) 2.28622 1.33161i 0.611018 0.355889i
\(15\) 2.21758 + 0.286912i 0.572578 + 0.0740803i
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) −2.04607 + 0.548242i −0.496244 + 0.132968i −0.498256 0.867030i \(-0.666026\pi\)
0.00201209 + 0.999998i \(0.499360\pi\)
\(18\) 0.965926 0.258819i 0.227671 0.0610042i
\(19\) 3.49797 + 6.05866i 0.802489 + 1.38995i 0.917974 + 0.396642i \(0.129824\pi\)
−0.115485 + 0.993309i \(0.536842\pi\)
\(20\) −1.77095 + 1.36519i −0.395996 + 0.305266i
\(21\) 2.29632 + 1.31412i 0.501098 + 0.286764i
\(22\) 3.87940 3.87940i 0.827091 0.827091i
\(23\) −0.454069 + 1.69461i −0.0946800 + 0.353350i −0.996971 0.0777776i \(-0.975218\pi\)
0.902291 + 0.431128i \(0.141884\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) −3.55130 3.51970i −0.710259 0.703940i
\(26\) −2.95981 + 1.70885i −0.580467 + 0.335133i
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) −2.55297 + 0.694523i −0.482465 + 0.131252i
\(29\) 0.684610i 0.127129i −0.997978 0.0635644i \(-0.979753\pi\)
0.997978 0.0635644i \(-0.0202468\pi\)
\(30\) −2.06776 0.851088i −0.377520 0.155387i
\(31\) 4.82932 + 2.78821i 0.867371 + 0.500777i 0.866474 0.499223i \(-0.166381\pi\)
0.000897301 1.00000i \(0.499714\pi\)
\(32\) −0.258819 0.965926i −0.0457532 0.170753i
\(33\) 5.29936 + 1.41996i 0.922500 + 0.247183i
\(34\) 2.11825 0.363276
\(35\) −2.29702 5.45194i −0.388268 0.921547i
\(36\) −1.00000 −0.166667
\(37\) −9.46620 2.53646i −1.55623 0.416992i −0.624765 0.780813i \(-0.714805\pi\)
−0.931469 + 0.363821i \(0.881472\pi\)
\(38\) −1.81068 6.75755i −0.293731 1.09622i
\(39\) −2.95981 1.70885i −0.473950 0.273635i
\(40\) 2.06394 0.860320i 0.326338 0.136028i
\(41\) 2.50597i 0.391366i −0.980667 0.195683i \(-0.937308\pi\)
0.980667 0.195683i \(-0.0626924\pi\)
\(42\) −1.87796 1.86367i −0.289775 0.287571i
\(43\) −1.95305 1.95305i −0.297837 0.297837i 0.542329 0.840166i \(-0.317543\pi\)
−0.840166 + 0.542329i \(0.817543\pi\)
\(44\) −4.75127 + 2.74315i −0.716282 + 0.413545i
\(45\) −0.296818 2.21628i −0.0442470 0.330384i
\(46\) 0.877194 1.51935i 0.129335 0.224015i
\(47\) −0.912383 + 3.40506i −0.133085 + 0.496679i −0.999998 0.00177938i \(-0.999434\pi\)
0.866914 + 0.498458i \(0.166100\pi\)
\(48\) 0.707107 0.707107i 0.102062 0.102062i
\(49\) −0.0534500 6.99980i −0.00763571 0.999971i
\(50\) 2.51932 + 4.31891i 0.356286 + 0.610787i
\(51\) 1.05912 + 1.83445i 0.148307 + 0.256875i
\(52\) 3.30124 0.884566i 0.457800 0.122667i
\(53\) 9.08204 2.43353i 1.24751 0.334270i 0.426138 0.904658i \(-0.359874\pi\)
0.821376 + 0.570388i \(0.193207\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) −7.48985 9.71594i −1.00993 1.31010i
\(56\) 2.64573 0.0101012i 0.353551 0.00134983i
\(57\) 4.94687 4.94687i 0.655229 0.655229i
\(58\) −0.177190 + 0.661282i −0.0232662 + 0.0868306i
\(59\) 5.08015 8.79907i 0.661379 1.14554i −0.318875 0.947797i \(-0.603305\pi\)
0.980253 0.197745i \(-0.0633618\pi\)
\(60\) 1.77703 + 1.35727i 0.229413 + 0.175222i
\(61\) 1.01469 0.585830i 0.129917 0.0750079i −0.433633 0.901090i \(-0.642768\pi\)
0.563550 + 0.826082i \(0.309435\pi\)
\(62\) −3.94312 3.94312i −0.500777 0.500777i
\(63\) 0.675009 2.55820i 0.0850431 0.322302i
\(64\) 1.00000i 0.125000i
\(65\) 2.94031 + 7.05393i 0.364701 + 0.874932i
\(66\) −4.75127 2.74315i −0.584841 0.337658i
\(67\) 2.57606 + 9.61398i 0.314716 + 1.17454i 0.924254 + 0.381778i \(0.124688\pi\)
−0.609538 + 0.792757i \(0.708645\pi\)
\(68\) −2.04607 0.548242i −0.248122 0.0664841i
\(69\) 1.75439 0.211204
\(70\) 0.807687 + 5.86069i 0.0965371 + 0.700486i
\(71\) −11.9716 −1.42077 −0.710383 0.703816i \(-0.751478\pi\)
−0.710383 + 0.703816i \(0.751478\pi\)
\(72\) 0.965926 + 0.258819i 0.113835 + 0.0305021i
\(73\) 1.26065 + 4.70482i 0.147548 + 0.550657i 0.999629 + 0.0272467i \(0.00867396\pi\)
−0.852081 + 0.523411i \(0.824659\pi\)
\(74\) 8.48716 + 4.90007i 0.986613 + 0.569621i
\(75\) −2.48063 + 4.34125i −0.286438 + 0.501285i
\(76\) 6.99593i 0.802489i
\(77\) −3.81036 14.0063i −0.434231 1.59617i
\(78\) 2.41668 + 2.41668i 0.273635 + 0.273635i
\(79\) −7.21474 + 4.16543i −0.811722 + 0.468648i −0.847553 0.530710i \(-0.821925\pi\)
0.0358316 + 0.999358i \(0.488592\pi\)
\(80\) −2.21628 + 0.296818i −0.247788 + 0.0331852i
\(81\) 0.500000 0.866025i 0.0555556 0.0962250i
\(82\) −0.648592 + 2.42058i −0.0716250 + 0.267308i
\(83\) 4.05281 4.05281i 0.444854 0.444854i −0.448786 0.893639i \(-0.648143\pi\)
0.893639 + 0.448786i \(0.148143\pi\)
\(84\) 1.33161 + 2.28622i 0.145291 + 0.249447i
\(85\) 0.607749 4.69739i 0.0659197 0.509503i
\(86\) 1.38101 + 2.39198i 0.148918 + 0.257934i
\(87\) −0.661282 + 0.177190i −0.0708969 + 0.0189968i
\(88\) 5.29936 1.41996i 0.564913 0.151368i
\(89\) 3.59178 + 6.22115i 0.380728 + 0.659440i 0.991166 0.132623i \(-0.0423401\pi\)
−0.610439 + 0.792064i \(0.709007\pi\)
\(90\) −0.286912 + 2.21758i −0.0302431 + 0.233754i
\(91\) 0.0345228 + 9.04232i 0.00361897 + 0.947892i
\(92\) −1.24054 + 1.24054i −0.129335 + 0.129335i
\(93\) 1.44328 5.38640i 0.149661 0.558544i
\(94\) 1.76259 3.05289i 0.181797 0.314882i
\(95\) −15.5049 + 2.07652i −1.59077 + 0.213046i
\(96\) −0.866025 + 0.500000i −0.0883883 + 0.0510310i
\(97\) 13.1212 + 13.1212i 1.33226 + 1.33226i 0.903348 + 0.428909i \(0.141102\pi\)
0.428909 + 0.903348i \(0.358898\pi\)
\(98\) −1.76005 + 6.77512i −0.177792 + 0.684390i
\(99\) 5.48630i 0.551394i
\(100\) −1.31566 4.82380i −0.131566 0.482380i
\(101\) 7.16001 + 4.13383i 0.712447 + 0.411332i 0.811967 0.583704i \(-0.198397\pi\)
−0.0995192 + 0.995036i \(0.531730\pi\)
\(102\) −0.548242 2.04607i −0.0542841 0.202591i
\(103\) −8.98910 2.40862i −0.885722 0.237329i −0.212848 0.977085i \(-0.568274\pi\)
−0.672874 + 0.739757i \(0.734941\pi\)
\(104\) −3.41770 −0.335133
\(105\) −4.67166 + 3.62982i −0.455907 + 0.354234i
\(106\) −9.40242 −0.913244
\(107\) 11.8496 + 3.17510i 1.14555 + 0.306949i 0.781180 0.624306i \(-0.214618\pi\)
0.364369 + 0.931255i \(0.381285\pi\)
\(108\) 0.258819 + 0.965926i 0.0249049 + 0.0929463i
\(109\) 0.291523 + 0.168311i 0.0279228 + 0.0161213i 0.513896 0.857852i \(-0.328202\pi\)
−0.485974 + 0.873973i \(0.661535\pi\)
\(110\) 4.71997 + 11.3234i 0.450032 + 1.07964i
\(111\) 9.80013i 0.930188i
\(112\) −2.55820 0.675009i −0.241727 0.0637823i
\(113\) 10.1896 + 10.1896i 0.958555 + 0.958555i 0.999175 0.0406198i \(-0.0129332\pi\)
−0.0406198 + 0.999175i \(0.512933\pi\)
\(114\) −6.05866 + 3.49797i −0.567445 + 0.327615i
\(115\) −3.11760 2.38117i −0.290718 0.222045i
\(116\) 0.342305 0.592889i 0.0317822 0.0550484i
\(117\) −0.884566 + 3.30124i −0.0817781 + 0.305200i
\(118\) −7.18441 + 7.18441i −0.661379 + 0.661379i
\(119\) 2.78362 4.86417i 0.255174 0.445898i
\(120\) −1.36519 1.77095i −0.124624 0.161665i
\(121\) −9.54974 16.5406i −0.868158 1.50369i
\(122\) −1.13174 + 0.303248i −0.102463 + 0.0274548i
\(123\) −2.42058 + 0.648592i −0.218256 + 0.0584816i
\(124\) 2.78821 + 4.82932i 0.250388 + 0.433686i
\(125\) 10.3004 4.34767i 0.921294 0.388867i
\(126\) −1.31412 + 2.29632i −0.117071 + 0.204573i
\(127\) −4.77054 + 4.77054i −0.423317 + 0.423317i −0.886344 0.463027i \(-0.846763\pi\)
0.463027 + 0.886344i \(0.346763\pi\)
\(128\) 0.258819 0.965926i 0.0228766 0.0853766i
\(129\) −1.38101 + 2.39198i −0.121591 + 0.210602i
\(130\) −1.01443 7.57458i −0.0889717 0.664335i
\(131\) 15.7695 9.10455i 1.37779 0.795468i 0.385898 0.922542i \(-0.373892\pi\)
0.991893 + 0.127074i \(0.0405585\pi\)
\(132\) 3.87940 + 3.87940i 0.337658 + 0.337658i
\(133\) −17.8970 4.72232i −1.55186 0.409477i
\(134\) 9.95313i 0.859819i
\(135\) −2.06394 + 0.860320i −0.177636 + 0.0740445i
\(136\) 1.83445 + 1.05912i 0.157303 + 0.0908190i
\(137\) 0.565438 + 2.11024i 0.0483086 + 0.180290i 0.985865 0.167544i \(-0.0535837\pi\)
−0.937556 + 0.347835i \(0.886917\pi\)
\(138\) −1.69461 0.454069i −0.144255 0.0386529i
\(139\) 18.1446 1.53900 0.769501 0.638645i \(-0.220505\pi\)
0.769501 + 0.638645i \(0.220505\pi\)
\(140\) 0.736691 5.87003i 0.0622618 0.496108i
\(141\) 3.52518 0.296873
\(142\) 11.5637 + 3.09847i 0.970401 + 0.260018i
\(143\) 4.85299 + 18.1116i 0.405828 + 1.51457i
\(144\) −0.866025 0.500000i −0.0721688 0.0416667i
\(145\) 1.41561 + 0.582663i 0.117560 + 0.0483876i
\(146\) 4.87079i 0.403109i
\(147\) −6.74745 + 1.86331i −0.556520 + 0.153683i
\(148\) −6.92974 6.92974i −0.569621 0.569621i
\(149\) 0.167711 0.0968279i 0.0137394 0.00793245i −0.493115 0.869964i \(-0.664142\pi\)
0.506854 + 0.862032i \(0.330808\pi\)
\(150\) 3.51970 3.55130i 0.287382 0.289962i
\(151\) 10.6614 18.4660i 0.867610 1.50274i 0.00317777 0.999995i \(-0.498988\pi\)
0.864432 0.502750i \(-0.167678\pi\)
\(152\) 1.81068 6.75755i 0.146866 0.548110i
\(153\) 1.49783 1.49783i 0.121092 0.121092i
\(154\) 0.0554181 + 14.5153i 0.00446571 + 1.16967i
\(155\) −9.87553 + 7.61288i −0.793222 + 0.611481i
\(156\) −1.70885 2.95981i −0.136817 0.236975i
\(157\) −3.55464 + 0.952462i −0.283691 + 0.0760147i −0.397859 0.917447i \(-0.630247\pi\)
0.114168 + 0.993461i \(0.463580\pi\)
\(158\) 8.04700 2.15619i 0.640185 0.171537i
\(159\) −4.70121 8.14273i −0.372830 0.645761i
\(160\) 2.21758 + 0.286912i 0.175315 + 0.0226824i
\(161\) −2.33617 4.01092i −0.184116 0.316105i
\(162\) −0.707107 + 0.707107i −0.0555556 + 0.0555556i
\(163\) −3.64443 + 13.6012i −0.285454 + 1.06533i 0.663054 + 0.748572i \(0.269260\pi\)
−0.948507 + 0.316756i \(0.897406\pi\)
\(164\) 1.25298 2.17023i 0.0978416 0.169467i
\(165\) −7.44636 + 9.74931i −0.579699 + 0.758983i
\(166\) −4.96366 + 2.86577i −0.385255 + 0.222427i
\(167\) −6.07259 6.07259i −0.469911 0.469911i 0.431974 0.901886i \(-0.357817\pi\)
−0.901886 + 0.431974i \(0.857817\pi\)
\(168\) −0.694523 2.55297i −0.0535836 0.196966i
\(169\) 1.31933i 0.101487i
\(170\) −1.80281 + 4.38003i −0.138270 + 0.335933i
\(171\) −6.05866 3.49797i −0.463317 0.267496i
\(172\) −0.714864 2.66791i −0.0545079 0.203426i
\(173\) −3.91108 1.04797i −0.297354 0.0796757i 0.107058 0.994253i \(-0.465857\pi\)
−0.404412 + 0.914577i \(0.632524\pi\)
\(174\) 0.684610 0.0519001
\(175\) 13.2283 0.109616i 0.999966 0.00828621i
\(176\) −5.48630 −0.413545
\(177\) −9.81409 2.62968i −0.737672 0.197659i
\(178\) −1.85924 6.93879i −0.139356 0.520084i
\(179\) −3.17428 1.83267i −0.237256 0.136980i 0.376659 0.926352i \(-0.377073\pi\)
−0.613915 + 0.789372i \(0.710406\pi\)
\(180\) 0.851088 2.06776i 0.0634364 0.154122i
\(181\) 2.39985i 0.178379i 0.996015 + 0.0891896i \(0.0284277\pi\)
−0.996015 + 0.0891896i \(0.971572\pi\)
\(182\) 2.30698 8.74314i 0.171005 0.648085i
\(183\) −0.828489 0.828489i −0.0612437 0.0612437i
\(184\) 1.51935 0.877194i 0.112008 0.0646676i
\(185\) 13.3014 17.4151i 0.977937 1.28039i
\(186\) −2.78821 + 4.82932i −0.204441 + 0.354103i
\(187\) 3.00782 11.2253i 0.219954 0.820878i
\(188\) −2.49268 + 2.49268i −0.181797 + 0.181797i
\(189\) −2.64573 + 0.0101012i −0.192449 + 0.000734752i
\(190\) 15.5141 + 2.00721i 1.12551 + 0.145619i
\(191\) −4.03766 6.99344i −0.292155 0.506027i 0.682164 0.731199i \(-0.261039\pi\)
−0.974319 + 0.225172i \(0.927706\pi\)
\(192\) 0.965926 0.258819i 0.0697097 0.0186787i
\(193\) 1.66383 0.445821i 0.119765 0.0320909i −0.198439 0.980113i \(-0.563587\pi\)
0.318204 + 0.948022i \(0.396920\pi\)
\(194\) −9.27809 16.0701i −0.666128 1.15377i
\(195\) 6.05256 4.66582i 0.433433 0.334126i
\(196\) 3.45361 6.08873i 0.246686 0.434909i
\(197\) 6.01174 6.01174i 0.428319 0.428319i −0.459737 0.888055i \(-0.652056\pi\)
0.888055 + 0.459737i \(0.152056\pi\)
\(198\) −1.41996 + 5.29936i −0.100912 + 0.376609i
\(199\) −5.50897 + 9.54181i −0.390520 + 0.676401i −0.992518 0.122097i \(-0.961038\pi\)
0.601998 + 0.798498i \(0.294372\pi\)
\(200\) 0.0223420 + 4.99995i 0.00157982 + 0.353550i
\(201\) 8.61966 4.97656i 0.607984 0.351020i
\(202\) −5.84612 5.84612i −0.411332 0.411332i
\(203\) 1.28567 + 1.27589i 0.0902362 + 0.0895498i
\(204\) 2.11825i 0.148307i
\(205\) 5.18175 + 2.13280i 0.361909 + 0.148961i
\(206\) 8.05941 + 4.65310i 0.561526 + 0.324197i
\(207\) −0.454069 1.69461i −0.0315600 0.117783i
\(208\) 3.30124 + 0.884566i 0.228900 + 0.0613336i
\(209\) −38.3818 −2.65492
\(210\) 5.45194 2.29702i 0.376220 0.158510i
\(211\) 10.3323 0.711302 0.355651 0.934619i \(-0.384259\pi\)
0.355651 + 0.934619i \(0.384259\pi\)
\(212\) 9.08204 + 2.43353i 0.623757 + 0.167135i
\(213\) 3.09847 + 11.5637i 0.212304 + 0.792329i
\(214\) −10.6241 6.13383i −0.726249 0.419300i
\(215\) 5.70065 2.37622i 0.388781 0.162057i
\(216\) 1.00000i 0.0680414i
\(217\) −14.2364 + 3.87295i −0.966430 + 0.262913i
\(218\) −0.238027 0.238027i −0.0161213 0.0161213i
\(219\) 4.21822 2.43539i 0.285041 0.164569i
\(220\) −1.62843 12.1592i −0.109789 0.819772i
\(221\) −3.61976 + 6.26961i −0.243492 + 0.421740i
\(222\) 2.53646 9.46620i 0.170236 0.635330i
\(223\) −3.41183 + 3.41183i −0.228473 + 0.228473i −0.812054 0.583582i \(-0.801651\pi\)
0.583582 + 0.812054i \(0.301651\pi\)
\(224\) 2.29632 + 1.31412i 0.153429 + 0.0878032i
\(225\) 4.83536 + 1.27250i 0.322358 + 0.0848334i
\(226\) −7.20512 12.4796i −0.479277 0.830133i
\(227\) −17.4772 + 4.68301i −1.16000 + 0.310822i −0.786968 0.616994i \(-0.788350\pi\)
−0.373037 + 0.927816i \(0.621684\pi\)
\(228\) 6.75755 1.81068i 0.447530 0.119915i
\(229\) −4.82375 8.35497i −0.318762 0.552112i 0.661468 0.749973i \(-0.269934\pi\)
−0.980230 + 0.197861i \(0.936600\pi\)
\(230\) 2.39508 + 3.10693i 0.157927 + 0.204865i
\(231\) −12.5429 + 7.30563i −0.825262 + 0.480675i
\(232\) −0.484092 + 0.484092i −0.0317822 + 0.0317822i
\(233\) 3.74597 13.9801i 0.245407 0.915870i −0.727772 0.685819i \(-0.759444\pi\)
0.973179 0.230051i \(-0.0738892\pi\)
\(234\) 1.70885 2.95981i 0.111711 0.193489i
\(235\) −6.26434 4.78460i −0.408640 0.312113i
\(236\) 8.79907 5.08015i 0.572771 0.330689i
\(237\) 5.89081 + 5.89081i 0.382649 + 0.382649i
\(238\) −3.94772 + 3.97798i −0.255892 + 0.257854i
\(239\) 29.9736i 1.93883i 0.245427 + 0.969415i \(0.421072\pi\)
−0.245427 + 0.969415i \(0.578928\pi\)
\(240\) 0.860320 + 2.06394i 0.0555334 + 0.133227i
\(241\) 14.3934 + 8.31003i 0.927161 + 0.535296i 0.885912 0.463853i \(-0.153533\pi\)
0.0412481 + 0.999149i \(0.486867\pi\)
\(242\) 4.94331 + 18.4487i 0.317768 + 1.18593i
\(243\) −0.965926 0.258819i −0.0619642 0.0166032i
\(244\) 1.17166 0.0750079
\(245\) 14.5194 + 5.84692i 0.927612 + 0.373546i
\(246\) 2.50597 0.159775
\(247\) 23.0953 + 6.18836i 1.46952 + 0.393756i
\(248\) −1.44328 5.38640i −0.0916485 0.342037i
\(249\) −4.96366 2.86577i −0.314559 0.181611i
\(250\) −11.0747 + 1.53359i −0.700423 + 0.0969928i
\(251\) 10.7660i 0.679546i −0.940508 0.339773i \(-0.889650\pi\)
0.940508 0.339773i \(-0.110350\pi\)
\(252\) 1.86367 1.87796i 0.117400 0.118300i
\(253\) −6.80597 6.80597i −0.427888 0.427888i
\(254\) 5.84270 3.37328i 0.366604 0.211659i
\(255\) −4.69463 + 0.628733i −0.293989 + 0.0393728i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −3.89328 + 14.5299i −0.242856 + 0.906352i 0.731593 + 0.681742i \(0.238777\pi\)
−0.974449 + 0.224610i \(0.927889\pi\)
\(258\) 1.95305 1.95305i 0.121591 0.121591i
\(259\) 22.4053 13.0500i 1.39220 0.810887i
\(260\) −0.980578 + 7.57904i −0.0608128 + 0.470032i
\(261\) 0.342305 + 0.592889i 0.0211881 + 0.0366989i
\(262\) −17.5886 + 4.71286i −1.08663 + 0.291161i
\(263\) −21.7637 + 5.83157i −1.34201 + 0.359590i −0.857179 0.515019i \(-0.827785\pi\)
−0.484829 + 0.874609i \(0.661118\pi\)
\(264\) −2.74315 4.75127i −0.168829 0.292421i
\(265\) −2.69766 + 20.8507i −0.165716 + 1.28085i
\(266\) 16.0649 + 9.19348i 0.985003 + 0.563689i
\(267\) 5.07954 5.07954i 0.310863 0.310863i
\(268\) −2.57606 + 9.61398i −0.157358 + 0.587268i
\(269\) −5.52122 + 9.56304i −0.336635 + 0.583069i −0.983797 0.179283i \(-0.942622\pi\)
0.647163 + 0.762352i \(0.275955\pi\)
\(270\) 2.21628 0.296818i 0.134879 0.0180638i
\(271\) 4.34433 2.50820i 0.263899 0.152362i −0.362213 0.932095i \(-0.617979\pi\)
0.626112 + 0.779733i \(0.284645\pi\)
\(272\) −1.49783 1.49783i −0.0908190 0.0908190i
\(273\) 8.72527 2.37367i 0.528077 0.143661i
\(274\) 2.18468i 0.131982i
\(275\) 26.4648 7.21812i 1.59589 0.435269i
\(276\) 1.51935 + 0.877194i 0.0914538 + 0.0528009i
\(277\) 1.63963 + 6.11920i 0.0985161 + 0.367667i 0.997529 0.0702549i \(-0.0223813\pi\)
−0.899013 + 0.437922i \(0.855715\pi\)
\(278\) −17.5263 4.69616i −1.05116 0.281657i
\(279\) −5.57642 −0.333851
\(280\) −2.23087 + 5.47935i −0.133320 + 0.327454i
\(281\) −29.4723 −1.75817 −0.879085 0.476665i \(-0.841846\pi\)
−0.879085 + 0.476665i \(0.841846\pi\)
\(282\) −3.40506 0.912383i −0.202768 0.0543316i
\(283\) −0.0253192 0.0944925i −0.00150507 0.00561700i 0.965169 0.261626i \(-0.0842588\pi\)
−0.966674 + 0.256009i \(0.917592\pi\)
\(284\) −10.3677 5.98579i −0.615210 0.355191i
\(285\) 6.01874 + 14.4392i 0.356519 + 0.855304i
\(286\) 18.7505i 1.10874i
\(287\) 4.70610 + 4.67030i 0.277792 + 0.275679i
\(288\) 0.707107 + 0.707107i 0.0416667 + 0.0416667i
\(289\) −10.8366 + 6.25652i −0.637447 + 0.368030i
\(290\) −1.21657 0.929197i −0.0714395 0.0545643i
\(291\) 9.27809 16.0701i 0.543891 0.942048i
\(292\) −1.26065 + 4.70482i −0.0737741 + 0.275329i
\(293\) 14.0076 14.0076i 0.818330 0.818330i −0.167536 0.985866i \(-0.553581\pi\)
0.985866 + 0.167536i \(0.0535810\pi\)
\(294\) 6.99980 0.0534500i 0.408236 0.00311727i
\(295\) 13.8708 + 17.9933i 0.807587 + 1.04761i
\(296\) 4.90007 + 8.48716i 0.284811 + 0.493306i
\(297\) −5.29936 + 1.41996i −0.307500 + 0.0823944i
\(298\) −0.187057 + 0.0501218i −0.0108359 + 0.00290348i
\(299\) 2.99799 + 5.19266i 0.173378 + 0.300300i
\(300\) −4.31891 + 2.51932i −0.249353 + 0.145453i
\(301\) 7.30758 0.0278997i 0.421202 0.00160811i
\(302\) −15.0775 + 15.0775i −0.867610 + 0.867610i
\(303\) 2.13983 7.98595i 0.122930 0.458781i
\(304\) −3.49797 + 6.05866i −0.200622 + 0.347488i
\(305\) 0.347770 + 2.59673i 0.0199132 + 0.148688i
\(306\) −1.83445 + 1.05912i −0.104869 + 0.0605460i
\(307\) 3.05320 + 3.05320i 0.174255 + 0.174255i 0.788846 0.614591i \(-0.210679\pi\)
−0.614591 + 0.788846i \(0.710679\pi\)
\(308\) 3.70330 14.0350i 0.211015 0.799720i
\(309\) 9.30620i 0.529411i
\(310\) 11.5094 4.79750i 0.653689 0.272480i
\(311\) −7.31386 4.22266i −0.414731 0.239445i 0.278089 0.960555i \(-0.410299\pi\)
−0.692820 + 0.721110i \(0.743632\pi\)
\(312\) 0.884566 + 3.30124i 0.0500787 + 0.186896i
\(313\) −18.7482 5.02358i −1.05971 0.283949i −0.313453 0.949604i \(-0.601486\pi\)
−0.746260 + 0.665654i \(0.768153\pi\)
\(314\) 3.68003 0.207676
\(315\) 4.71525 + 3.57301i 0.265674 + 0.201316i
\(316\) −8.33087 −0.468648
\(317\) 15.0204 + 4.02471i 0.843632 + 0.226050i 0.654652 0.755931i \(-0.272815\pi\)
0.188980 + 0.981981i \(0.439482\pi\)
\(318\) 2.43353 + 9.08204i 0.136465 + 0.509296i
\(319\) 3.25277 + 1.87799i 0.182120 + 0.105147i
\(320\) −2.06776 0.851088i −0.115592 0.0475773i
\(321\) 12.2677i 0.684714i
\(322\) 1.21846 + 4.47890i 0.0679023 + 0.249599i
\(323\) −10.4787 10.4787i −0.583050 0.583050i
\(324\) 0.866025 0.500000i 0.0481125 0.0277778i
\(325\) −17.0883 + 0.0763581i −0.947890 + 0.00423559i
\(326\) 7.04050 12.1945i 0.389937 0.675391i
\(327\) 0.0871241 0.325151i 0.00481797 0.0179809i
\(328\) −1.77199 + 1.77199i −0.0978416 + 0.0978416i
\(329\) −4.69417 8.05933i −0.258798 0.444325i
\(330\) 9.71594 7.48985i 0.534845 0.412303i
\(331\) −8.09296 14.0174i −0.444830 0.770467i 0.553211 0.833041i \(-0.313402\pi\)
−0.998040 + 0.0625739i \(0.980069\pi\)
\(332\) 5.53624 1.48343i 0.303841 0.0814139i
\(333\) 9.46620 2.53646i 0.518745 0.138997i
\(334\) 4.29397 + 7.43738i 0.234956 + 0.406955i
\(335\) −22.0719 2.85567i −1.20592 0.156022i
\(336\) 0.0101012 + 2.64573i 0.000551064 + 0.144337i
\(337\) 19.2055 19.2055i 1.04619 1.04619i 0.0473073 0.998880i \(-0.484936\pi\)
0.998880 0.0473073i \(-0.0150640\pi\)
\(338\) 0.341468 1.27438i 0.0185734 0.0693169i
\(339\) 7.20512 12.4796i 0.391328 0.677801i
\(340\) 2.87502 3.76418i 0.155920 0.204142i
\(341\) −26.4951 + 15.2969i −1.43479 + 0.828376i
\(342\) 4.94687 + 4.94687i 0.267496 + 0.267496i
\(343\) 13.2449 + 12.9450i 0.715159 + 0.698962i
\(344\) 2.76202i 0.148918i
\(345\) −1.49314 + 3.62766i −0.0803880 + 0.195307i
\(346\) 3.50658 + 2.02452i 0.188515 + 0.108839i
\(347\) 2.65696 + 9.91592i 0.142633 + 0.532315i 0.999849 + 0.0173577i \(0.00552541\pi\)
−0.857216 + 0.514957i \(0.827808\pi\)
\(348\) −0.661282 0.177190i −0.0354484 0.00949838i
\(349\) −6.61441 −0.354061 −0.177031 0.984205i \(-0.556649\pi\)
−0.177031 + 0.984205i \(0.556649\pi\)
\(350\) −12.8059 3.31786i −0.684506 0.177347i
\(351\) 3.41770 0.182423
\(352\) 5.29936 + 1.41996i 0.282457 + 0.0756841i
\(353\) 3.52633 + 13.1604i 0.187688 + 0.700460i 0.994039 + 0.109023i \(0.0347723\pi\)
−0.806352 + 0.591436i \(0.798561\pi\)
\(354\) 8.79907 + 5.08015i 0.467666 + 0.270007i
\(355\) 10.1889 24.7544i 0.540769 1.31383i
\(356\) 7.18356i 0.380728i
\(357\) −5.41889 1.42983i −0.286798 0.0756749i
\(358\) 2.59178 + 2.59178i 0.136980 + 0.136980i
\(359\) 14.9791 8.64822i 0.790569 0.456435i −0.0495937 0.998769i \(-0.515793\pi\)
0.840163 + 0.542334i \(0.182459\pi\)
\(360\) −1.35727 + 1.77703i −0.0715342 + 0.0936576i
\(361\) −14.9715 + 25.9315i −0.787976 + 1.36481i
\(362\) 0.621126 2.31807i 0.0326457 0.121835i
\(363\) −13.5054 + 13.5054i −0.708848 + 0.708848i
\(364\) −4.49126 + 7.84814i −0.235406 + 0.411354i
\(365\) −10.8014 1.39749i −0.565370 0.0731477i
\(366\) 0.585830 + 1.01469i 0.0306218 + 0.0530386i
\(367\) −24.9992 + 6.69852i −1.30495 + 0.349660i −0.843319 0.537413i \(-0.819402\pi\)
−0.461629 + 0.887073i \(0.652735\pi\)
\(368\) −1.69461 + 0.454069i −0.0883376 + 0.0236700i
\(369\) 1.25298 + 2.17023i 0.0652277 + 0.112978i
\(370\) −17.3555 + 13.3791i −0.902270 + 0.695544i
\(371\) −12.3559 + 21.5910i −0.641486 + 1.12095i
\(372\) 3.94312 3.94312i 0.204441 0.204441i
\(373\) 2.37243 8.85404i 0.122840 0.458445i −0.876914 0.480648i \(-0.840401\pi\)
0.999753 + 0.0222033i \(0.00706810\pi\)
\(374\) −5.81066 + 10.0644i −0.300462 + 0.520416i
\(375\) −6.86546 8.82414i −0.354531 0.455677i
\(376\) 3.05289 1.76259i 0.157441 0.0908985i
\(377\) −1.65448 1.65448i −0.0852101 0.0852101i
\(378\) 2.55820 + 0.675009i 0.131579 + 0.0347187i
\(379\) 18.6871i 0.959891i 0.877298 + 0.479946i \(0.159344\pi\)
−0.877298 + 0.479946i \(0.840656\pi\)
\(380\) −14.4659 5.95416i −0.742087 0.305442i
\(381\) 5.84270 + 3.37328i 0.299331 + 0.172819i
\(382\) 2.09005 + 7.80016i 0.106936 + 0.399091i
\(383\) −19.1654 5.13534i −0.979304 0.262404i −0.266553 0.963820i \(-0.585885\pi\)
−0.712752 + 0.701417i \(0.752551\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 32.2048 + 4.04171i 1.64131 + 0.205984i
\(386\) −1.72252 −0.0876740
\(387\) 2.66791 + 0.714864i 0.135618 + 0.0363386i
\(388\) 4.80269 + 17.9239i 0.243820 + 0.909948i
\(389\) 4.44026 + 2.56359i 0.225130 + 0.129979i 0.608323 0.793689i \(-0.291842\pi\)
−0.383193 + 0.923668i \(0.625176\pi\)
\(390\) −7.05393 + 2.94031i −0.357190 + 0.148889i
\(391\) 3.71623i 0.187938i
\(392\) −4.91181 + 4.98740i −0.248084 + 0.251902i
\(393\) −12.8758 12.8758i −0.649497 0.649497i
\(394\) −7.36285 + 4.25094i −0.370935 + 0.214159i
\(395\) −2.47275 18.4635i −0.124418 0.929001i
\(396\) 2.74315 4.75127i 0.137848 0.238761i
\(397\) 6.83113 25.4941i 0.342844 1.27951i −0.552266 0.833668i \(-0.686237\pi\)
0.895110 0.445845i \(-0.147097\pi\)
\(398\) 7.79086 7.79086i 0.390520 0.390520i
\(399\) 0.0706671 + 18.5094i 0.00353778 + 0.926627i
\(400\) 1.27250 4.83536i 0.0636251 0.241768i
\(401\) 8.61471 + 14.9211i 0.430198 + 0.745125i 0.996890 0.0788050i \(-0.0251104\pi\)
−0.566692 + 0.823930i \(0.691777\pi\)
\(402\) −9.61398 + 2.57606i −0.479502 + 0.128482i
\(403\) 18.4091 4.93271i 0.917023 0.245716i
\(404\) 4.13383 + 7.16001i 0.205666 + 0.356224i
\(405\) 1.36519 + 1.77095i 0.0678369 + 0.0879990i
\(406\) −0.911636 1.56517i −0.0452437 0.0776780i
\(407\) 38.0186 38.0186i 1.88451 1.88451i
\(408\) 0.548242 2.04607i 0.0271420 0.101295i
\(409\) 17.8569 30.9290i 0.882967 1.52934i 0.0349400 0.999389i \(-0.488876\pi\)
0.848027 0.529954i \(-0.177791\pi\)
\(410\) −4.45318 3.40126i −0.219927 0.167976i
\(411\) 1.89199 1.09234i 0.0933251 0.0538813i
\(412\) −6.58048 6.58048i −0.324197 0.324197i
\(413\) 7.05656 + 25.9389i 0.347230 + 1.27637i
\(414\) 1.75439i 0.0862235i
\(415\) 4.93096 + 11.8296i 0.242051 + 0.580690i
\(416\) −2.95981 1.70885i −0.145117 0.0837832i
\(417\) −4.69616 17.5263i −0.229972 0.858267i
\(418\) 37.0740 + 9.93394i 1.81335 + 0.485885i
\(419\) −14.0414 −0.685966 −0.342983 0.939342i \(-0.611437\pi\)
−0.342983 + 0.939342i \(0.611437\pi\)
\(420\) −5.86069 + 0.807687i −0.285972 + 0.0394111i
\(421\) 24.4332 1.19080 0.595401 0.803429i \(-0.296993\pi\)
0.595401 + 0.803429i \(0.296993\pi\)
\(422\) −9.98020 2.67419i −0.485829 0.130177i
\(423\) −0.912383 3.40506i −0.0443616 0.165560i
\(424\) −8.14273 4.70121i −0.395446 0.228311i
\(425\) 9.19584 + 5.25458i 0.446064 + 0.254884i
\(426\) 11.9716i 0.580025i
\(427\) −0.790881 + 2.99734i −0.0382734 + 0.145051i
\(428\) 8.67454 + 8.67454i 0.419300 + 0.419300i
\(429\) 16.2384 9.37526i 0.783999 0.452642i
\(430\) −6.12142 + 0.819818i −0.295201 + 0.0395351i
\(431\) 19.3886 33.5820i 0.933914 1.61759i 0.157354 0.987542i \(-0.449704\pi\)
0.776559 0.630044i \(-0.216963\pi\)
\(432\) −0.258819 + 0.965926i −0.0124524 + 0.0464731i
\(433\) 7.85700 7.85700i 0.377583 0.377583i −0.492646 0.870230i \(-0.663970\pi\)
0.870230 + 0.492646i \(0.163970\pi\)
\(434\) 14.7537 0.0563283i 0.708200 0.00270385i
\(435\) 0.196422 1.51818i 0.00941774 0.0727911i
\(436\) 0.168311 + 0.291523i 0.00806063 + 0.0139614i
\(437\) −11.8554 + 3.17664i −0.567119 + 0.151959i
\(438\) −4.70482 + 1.26065i −0.224805 + 0.0602363i
\(439\) −10.5640 18.2973i −0.504190 0.873283i −0.999988 0.00484487i \(-0.998458\pi\)
0.495798 0.868438i \(-0.334876\pi\)
\(440\) −1.57408 + 12.1663i −0.0750415 + 0.580007i
\(441\) 3.54619 + 6.03528i 0.168866 + 0.287394i
\(442\) 5.11912 5.11912i 0.243492 0.243492i
\(443\) 1.73709 6.48289i 0.0825314 0.308011i −0.912304 0.409514i \(-0.865698\pi\)
0.994835 + 0.101503i \(0.0323650\pi\)
\(444\) −4.90007 + 8.48716i −0.232547 + 0.402783i
\(445\) −15.9208 + 2.13221i −0.754718 + 0.101076i
\(446\) 4.17862 2.41253i 0.197863 0.114236i
\(447\) −0.136935 0.136935i −0.00647682 0.00647682i
\(448\) −1.87796 1.86367i −0.0887252 0.0880502i
\(449\) 8.28979i 0.391219i −0.980682 0.195610i \(-0.937331\pi\)
0.980682 0.195610i \(-0.0626685\pi\)
\(450\) −4.34125 2.48063i −0.204649 0.116938i
\(451\) 11.9065 + 6.87424i 0.560657 + 0.323695i
\(452\) 3.72964 + 13.9192i 0.175428 + 0.654705i
\(453\) −20.5962 5.51873i −0.967693 0.259293i
\(454\) 18.0938 0.849182
\(455\) −18.7268 7.62443i −0.877924 0.357439i
\(456\) −6.99593 −0.327615
\(457\) −21.3296 5.71524i −0.997755 0.267348i −0.277250 0.960798i \(-0.589423\pi\)
−0.720505 + 0.693450i \(0.756090\pi\)
\(458\) 2.49695 + 9.31876i 0.116675 + 0.435437i
\(459\) −1.83445 1.05912i −0.0856250 0.0494356i
\(460\) −1.50933 3.62095i −0.0703731 0.168828i
\(461\) 19.0130i 0.885524i 0.896639 + 0.442762i \(0.146001\pi\)
−0.896639 + 0.442762i \(0.853999\pi\)
\(462\) 14.0063 3.81036i 0.651634 0.177274i
\(463\) −16.6091 16.6091i −0.771891 0.771891i 0.206546 0.978437i \(-0.433778\pi\)
−0.978437 + 0.206546i \(0.933778\pi\)
\(464\) 0.592889 0.342305i 0.0275242 0.0158911i
\(465\) 9.90945 + 7.56867i 0.459540 + 0.350989i
\(466\) −7.23665 + 12.5343i −0.335232 + 0.580638i
\(467\) 4.13837 15.4446i 0.191501 0.714691i −0.801644 0.597802i \(-0.796041\pi\)
0.993145 0.116889i \(-0.0372923\pi\)
\(468\) −2.41668 + 2.41668i −0.111711 + 0.111711i
\(469\) −22.8556 13.0796i −1.05537 0.603959i
\(470\) 4.81254 + 6.24290i 0.221986 + 0.287963i
\(471\) 1.84001 + 3.18700i 0.0847834 + 0.146849i
\(472\) −9.81409 + 2.62968i −0.451730 + 0.121041i
\(473\) 14.6370 3.92196i 0.673008 0.180332i
\(474\) −4.16543 7.21474i −0.191325 0.331384i
\(475\) 8.90234 33.8279i 0.408467 1.55213i
\(476\) 4.84278 2.82069i 0.221968 0.129286i
\(477\) −6.64852 + 6.64852i −0.304415 + 0.304415i
\(478\) 7.75773 28.9523i 0.354831 1.32425i
\(479\) −4.50526 + 7.80333i −0.205850 + 0.356543i −0.950403 0.311020i \(-0.899329\pi\)
0.744553 + 0.667563i \(0.232663\pi\)
\(480\) −0.296818 2.21628i −0.0135478 0.101159i
\(481\) −29.0066 + 16.7470i −1.32259 + 0.763595i
\(482\) −11.7522 11.7522i −0.535296 0.535296i
\(483\) −3.26961 + 3.29467i −0.148772 + 0.149913i
\(484\) 19.0995i 0.868158i
\(485\) −38.2989 + 15.9643i −1.73906 + 0.724899i
\(486\) 0.866025 + 0.500000i 0.0392837 + 0.0226805i
\(487\) 2.41740 + 9.02186i 0.109543 + 0.408820i 0.998821 0.0485475i \(-0.0154592\pi\)
−0.889278 + 0.457367i \(0.848793\pi\)
\(488\) −1.13174 0.303248i −0.0512313 0.0137274i
\(489\) 14.0810 0.636764
\(490\) −12.5114 9.40560i −0.565207 0.424902i
\(491\) 2.08535 0.0941107 0.0470554 0.998892i \(-0.485016\pi\)
0.0470554 + 0.998892i \(0.485016\pi\)
\(492\) −2.42058 0.648592i −0.109128 0.0292408i
\(493\) 0.375332 + 1.40076i 0.0169041 + 0.0630870i
\(494\) −20.7067 11.9550i −0.931637 0.537881i
\(495\) 11.3444 + 4.66933i 0.509892 + 0.209871i
\(496\) 5.57642i 0.250388i
\(497\) 22.3111 22.4821i 1.00079 1.00846i
\(498\) 4.05281 + 4.05281i 0.181611 + 0.181611i
\(499\) 11.6260 6.71229i 0.520452 0.300483i −0.216668 0.976245i \(-0.569519\pi\)
0.737120 + 0.675762i \(0.236185\pi\)
\(500\) 11.0942 + 1.38500i 0.496149 + 0.0619390i
\(501\) −4.29397 + 7.43738i −0.191841 + 0.332278i
\(502\) −2.78645 + 10.3992i −0.124366 + 0.464138i
\(503\) 7.19669 7.19669i 0.320885 0.320885i −0.528222 0.849106i \(-0.677141\pi\)
0.849106 + 0.528222i \(0.177141\pi\)
\(504\) −2.28622 + 1.33161i −0.101836 + 0.0593148i
\(505\) −14.6416 + 11.2869i −0.651542 + 0.502263i
\(506\) 4.81255 + 8.33558i 0.213944 + 0.370562i
\(507\) 1.27438 0.341468i 0.0565970 0.0151651i
\(508\) −6.51668 + 1.74614i −0.289131 + 0.0774724i
\(509\) −2.14078 3.70794i −0.0948884 0.164352i 0.814674 0.579920i \(-0.196916\pi\)
−0.909562 + 0.415568i \(0.863583\pi\)
\(510\) 4.69739 + 0.607749i 0.208004 + 0.0269116i
\(511\) −11.1849 6.40079i −0.494791 0.283154i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −1.81068 + 6.75755i −0.0799435 + 0.298353i
\(514\) 7.52124 13.0272i 0.331748 0.574604i
\(515\) 12.6310 16.5374i 0.556588 0.728724i
\(516\) −2.39198 + 1.38101i −0.105301 + 0.0607957i
\(517\) −13.6756 13.6756i −0.601451 0.601451i
\(518\) −25.0194 + 6.80642i −1.09929 + 0.299057i
\(519\) 4.04905i 0.177733i
\(520\) 2.90876 7.06700i 0.127558 0.309908i
\(521\) −12.6226 7.28768i −0.553007 0.319279i 0.197327 0.980338i \(-0.436774\pi\)
−0.750334 + 0.661059i \(0.770107\pi\)
\(522\) −0.177190 0.661282i −0.00775540 0.0289435i
\(523\) 36.7904 + 9.85794i 1.60873 + 0.431058i 0.947664 0.319270i \(-0.103438\pi\)
0.661066 + 0.750328i \(0.270104\pi\)
\(524\) 18.2091 0.795468
\(525\) −3.52962 12.7492i −0.154045 0.556420i
\(526\) 22.5315 0.982418
\(527\) −11.4097 3.05723i −0.497015 0.133175i
\(528\) 1.41996 + 5.29936i 0.0617958 + 0.230625i
\(529\) 17.2531 + 9.96106i 0.750133 + 0.433090i
\(530\) 8.00229 19.4420i 0.347597 0.844506i
\(531\) 10.1603i 0.440919i
\(532\) −13.1381 13.0381i −0.569607 0.565275i
\(533\) −6.05612 6.05612i −0.262319 0.262319i
\(534\) −6.22115 + 3.59178i −0.269215 + 0.155432i
\(535\) −16.6505 + 21.8000i −0.719862 + 0.942495i
\(536\) 4.97656 8.61966i 0.214955 0.372313i
\(537\) −0.948659 + 3.54044i −0.0409377 + 0.152781i
\(538\) 7.80819 7.80819i 0.336635 0.336635i
\(539\) 33.4046 + 18.9475i 1.43884 + 0.816128i
\(540\) −2.21758 0.286912i −0.0954296 0.0123467i
\(541\) −8.43016 14.6015i −0.362441 0.627766i 0.625921 0.779886i \(-0.284723\pi\)
−0.988362 + 0.152121i \(0.951390\pi\)
\(542\) −4.84547 + 1.29834i −0.208131 + 0.0557684i
\(543\) 2.31807 0.621126i 0.0994781 0.0266551i
\(544\) 1.05912 + 1.83445i 0.0454095 + 0.0786516i
\(545\) −0.596139 + 0.459553i −0.0255358 + 0.0196851i
\(546\) −9.04232 + 0.0345228i −0.386975 + 0.00147744i
\(547\) −2.04444 + 2.04444i −0.0874141 + 0.0874141i −0.749462 0.662048i \(-0.769688\pi\)
0.662048 + 0.749462i \(0.269688\pi\)
\(548\) −0.565438 + 2.11024i −0.0241543 + 0.0901451i
\(549\) −0.585830 + 1.01469i −0.0250026 + 0.0433058i
\(550\) −27.4312 + 0.122575i −1.16967 + 0.00522660i
\(551\) 4.14781 2.39474i 0.176703 0.102019i
\(552\) −1.24054 1.24054i −0.0528009 0.0528009i
\(553\) 5.62341 21.3120i 0.239132 0.906278i
\(554\) 6.33506i 0.269151i
\(555\) −20.2644 8.34078i −0.860174 0.354046i
\(556\) 15.7137 + 9.07229i 0.666408 + 0.384751i
\(557\) 1.08302 + 4.04187i 0.0458889 + 0.171260i 0.985067 0.172170i \(-0.0550779\pi\)
−0.939178 + 0.343430i \(0.888411\pi\)
\(558\) 5.38640 + 1.44328i 0.228025 + 0.0610990i
\(559\) −9.43977 −0.399260
\(560\) 3.57301 4.71525i 0.150987 0.199256i
\(561\) −11.6213 −0.490653
\(562\) 28.4681 + 7.62799i 1.20085 + 0.321767i
\(563\) 6.48217 + 24.1918i 0.273191 + 1.01956i 0.957044 + 0.289943i \(0.0936363\pi\)
−0.683853 + 0.729620i \(0.739697\pi\)
\(564\) 3.05289 + 1.76259i 0.128550 + 0.0742183i
\(565\) −29.7419 + 12.3974i −1.25125 + 0.521563i
\(566\) 0.0978259i 0.00411193i
\(567\) 0.694523 + 2.55297i 0.0291672 + 0.107215i
\(568\) 8.46519 + 8.46519i 0.355191 + 0.355191i
\(569\) 1.99827 1.15370i 0.0837720 0.0483658i −0.457529 0.889195i \(-0.651265\pi\)
0.541301 + 0.840829i \(0.317932\pi\)
\(570\) −2.07652 15.5049i −0.0869757 0.649431i
\(571\) −7.94325 + 13.7581i −0.332415 + 0.575759i −0.982985 0.183687i \(-0.941197\pi\)
0.650570 + 0.759446i \(0.274530\pi\)
\(572\) −4.85299 + 18.1116i −0.202914 + 0.757285i
\(573\) −5.71012 + 5.71012i −0.238544 + 0.238544i
\(574\) −3.33698 5.72919i −0.139283 0.239132i
\(575\) 7.57705 4.41987i 0.315985 0.184321i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 3.86453 1.03550i 0.160883 0.0431084i −0.177479 0.984125i \(-0.556794\pi\)
0.338361 + 0.941016i \(0.390127\pi\)
\(578\) 12.0867 3.23861i 0.502739 0.134709i
\(579\) −0.861260 1.49175i −0.0357928 0.0619949i
\(580\) 0.934623 + 1.21241i 0.0388081 + 0.0503425i
\(581\) 0.0578953 + 15.1641i 0.00240190 + 0.629114i
\(582\) −13.1212 + 13.1212i −0.543891 + 0.543891i
\(583\) −13.3510 + 49.8268i −0.552944 + 2.06361i
\(584\) 2.43539 4.21822i 0.100777 0.174551i
\(585\) −6.07335 4.63872i −0.251102 0.191788i
\(586\) −17.1557 + 9.90484i −0.708695 + 0.409165i
\(587\) 5.31785 + 5.31785i 0.219491 + 0.219491i 0.808284 0.588793i \(-0.200397\pi\)
−0.588793 + 0.808284i \(0.700397\pi\)
\(588\) −6.77512 1.76005i −0.279401 0.0725833i
\(589\) 39.0122i 1.60747i
\(590\) −8.74110 20.9702i −0.359865 0.863331i
\(591\) −7.36285 4.25094i −0.302867 0.174860i
\(592\) −2.53646 9.46620i −0.104248 0.389059i
\(593\) 17.0986 + 4.58156i 0.702156 + 0.188142i 0.592196 0.805794i \(-0.298261\pi\)
0.109960 + 0.993936i \(0.464928\pi\)
\(594\) 5.48630 0.225106
\(595\) 7.68885 + 9.89572i 0.315212 + 0.405685i
\(596\) 0.193656 0.00793245
\(597\) 10.6425 + 2.85165i 0.435569 + 0.116710i
\(598\) −1.55187 5.79167i −0.0634608 0.236839i
\(599\) 27.0972 + 15.6446i 1.10716 + 0.639220i 0.938093 0.346384i \(-0.112591\pi\)
0.169069 + 0.985604i \(0.445924\pi\)
\(600\) 4.82380 1.31566i 0.196931 0.0537117i
\(601\) 47.5637i 1.94016i 0.242776 + 0.970082i \(0.421942\pi\)
−0.242776 + 0.970082i \(0.578058\pi\)
\(602\) −7.06580 1.86439i −0.287980 0.0759869i
\(603\) −7.03792 7.03792i −0.286606 0.286606i
\(604\) 18.4660 10.6614i 0.751372 0.433805i
\(605\) 42.3298 5.66907i 1.72095 0.230480i
\(606\) −4.13383 + 7.16001i −0.167925 + 0.290855i
\(607\) 6.35260 23.7082i 0.257844 0.962287i −0.708642 0.705568i \(-0.750692\pi\)
0.966486 0.256719i \(-0.0826414\pi\)
\(608\) 4.94687 4.94687i 0.200622 0.200622i
\(609\) 0.899658 1.57208i 0.0364560 0.0637041i
\(610\) 0.336163 2.59826i 0.0136108 0.105200i
\(611\) 6.02400 + 10.4339i 0.243705 + 0.422109i
\(612\) 2.04607 0.548242i 0.0827074 0.0221614i
\(613\) 26.8884 7.20472i 1.08601 0.290996i 0.328955 0.944345i \(-0.393303\pi\)
0.757056 + 0.653349i \(0.226637\pi\)
\(614\) −2.15894 3.73939i −0.0871277 0.150910i
\(615\) 0.718991 5.55719i 0.0289925 0.224088i
\(616\) −7.20965 + 12.5983i −0.290485 + 0.507600i
\(617\) −24.4884 + 24.4884i −0.985865 + 0.985865i −0.999901 0.0140365i \(-0.995532\pi\)
0.0140365 + 0.999901i \(0.495532\pi\)
\(618\) 2.40862 8.98910i 0.0968890 0.361595i
\(619\) 15.9137 27.5634i 0.639627 1.10787i −0.345888 0.938276i \(-0.612422\pi\)
0.985515 0.169590i \(-0.0542445\pi\)
\(620\) −12.3589 + 1.65518i −0.496345 + 0.0664736i
\(621\) −1.51935 + 0.877194i −0.0609692 + 0.0352006i
\(622\) 5.97174 + 5.97174i 0.239445 + 0.239445i
\(623\) −18.3770 4.84897i −0.736257 0.194270i
\(624\) 3.41770i 0.136817i
\(625\) 0.223417 + 24.9990i 0.00893670 + 0.999960i
\(626\) 16.8092 + 9.70480i 0.671831 + 0.387882i
\(627\) 9.93394 + 37.0740i 0.396723 + 1.48059i
\(628\) −3.55464 0.952462i −0.141845 0.0380074i
\(629\) 20.7591 0.827719
\(630\) −3.62982 4.67166i −0.144616 0.186123i
\(631\) −34.9471 −1.39122 −0.695610 0.718419i \(-0.744866\pi\)
−0.695610 + 0.718419i \(0.744866\pi\)
\(632\) 8.04700 + 2.15619i 0.320092 + 0.0857685i
\(633\) −2.67419 9.98020i −0.106289 0.396677i
\(634\) −13.4670 7.77515i −0.534841 0.308791i
\(635\) −5.80420 13.9245i −0.230333 0.552577i
\(636\) 9.40242i 0.372830i
\(637\) −17.0454 16.7871i −0.675364 0.665128i
\(638\) −2.65587 2.65587i −0.105147 0.105147i
\(639\) 10.3677 5.98579i 0.410140 0.236794i
\(640\) 1.77703 + 1.35727i 0.0702432 + 0.0536506i
\(641\) 5.61488 9.72526i 0.221774 0.384125i −0.733572 0.679611i \(-0.762148\pi\)
0.955347 + 0.295487i \(0.0954818\pi\)
\(642\) −3.17510 + 11.8496i −0.125311 + 0.467668i
\(643\) −9.89036 + 9.89036i −0.390038 + 0.390038i −0.874701 0.484663i \(-0.838942\pi\)
0.484663 + 0.874701i \(0.338942\pi\)
\(644\) −0.0177214 4.64164i −0.000698320 0.182906i
\(645\) −3.77069 4.89140i −0.148471 0.192599i
\(646\) 7.40955 + 12.8337i 0.291525 + 0.504936i
\(647\) 15.1576 4.06147i 0.595908 0.159673i 0.0517559 0.998660i \(-0.483518\pi\)
0.544152 + 0.838987i \(0.316852\pi\)
\(648\) −0.965926 + 0.258819i −0.0379452 + 0.0101674i
\(649\) 27.8712 + 48.2744i 1.09404 + 1.89493i
\(650\) 16.5258 + 4.34903i 0.648196 + 0.170583i
\(651\) 7.42563 + 12.7489i 0.291033 + 0.499669i
\(652\) −9.95676 + 9.95676i −0.389937 + 0.389937i
\(653\) 4.12761 15.4045i 0.161526 0.602823i −0.836932 0.547307i \(-0.815653\pi\)
0.998458 0.0555160i \(-0.0176804\pi\)
\(654\) −0.168311 + 0.291523i −0.00658147 + 0.0113994i
\(655\) 5.40478 + 40.3565i 0.211182 + 1.57686i
\(656\) 2.17023 1.25298i 0.0847333 0.0489208i
\(657\) −3.44417 3.44417i −0.134370 0.134370i
\(658\) 2.44832 + 8.99966i 0.0954453 + 0.350843i
\(659\) 10.4778i 0.408157i 0.978955 + 0.204078i \(0.0654198\pi\)
−0.978955 + 0.204078i \(0.934580\pi\)
\(660\) −11.3234 + 4.71997i −0.440763 + 0.183725i
\(661\) −20.9764 12.1107i −0.815888 0.471053i 0.0331084 0.999452i \(-0.489459\pi\)
−0.848996 + 0.528399i \(0.822793\pi\)
\(662\) 4.18923 + 15.6344i 0.162819 + 0.607648i
\(663\) 6.99285 + 1.87373i 0.271580 + 0.0727695i
\(664\) −5.73154 −0.222427
\(665\) 24.9965 32.9876i 0.969324 1.27920i
\(666\) −9.80013 −0.379747
\(667\) 1.16015 + 0.310860i 0.0449210 + 0.0120366i
\(668\) −2.22272 8.29532i −0.0859998 0.320955i
\(669\) 4.17862 + 2.41253i 0.161555 + 0.0932736i
\(670\) 20.5807 + 8.47099i 0.795103 + 0.327263i
\(671\) 6.42808i 0.248153i
\(672\) 0.675009 2.55820i 0.0260390 0.0986845i
\(673\) −1.16725 1.16725i −0.0449943 0.0449943i 0.684252 0.729246i \(-0.260129\pi\)
−0.729246 + 0.684252i \(0.760129\pi\)
\(674\) −23.5218 + 13.5803i −0.906025 + 0.523094i
\(675\) −0.0223420 4.99995i −0.000859943 0.192448i
\(676\) −0.659666 + 1.14257i −0.0253718 + 0.0439452i
\(677\) −3.32260 + 12.4001i −0.127698 + 0.476575i −0.999921 0.0125322i \(-0.996011\pi\)
0.872223 + 0.489108i \(0.162677\pi\)
\(678\) −10.1896 + 10.1896i −0.391328 + 0.391328i
\(679\) −49.0947 + 0.187439i −1.88408 + 0.00719326i
\(680\) −3.75130 + 2.89181i −0.143856 + 0.110896i
\(681\) 9.04688 + 15.6697i 0.346677 + 0.600463i
\(682\) 29.5514 7.91828i 1.13158 0.303207i
\(683\) −20.6373 + 5.52974i −0.789663 + 0.211589i −0.631040 0.775750i \(-0.717372\pi\)
−0.158622 + 0.987339i \(0.550705\pi\)
\(684\) −3.49797 6.05866i −0.133748 0.231658i
\(685\) −4.84472 0.626811i −0.185107 0.0239492i
\(686\) −9.44322 15.9319i −0.360544 0.608283i
\(687\) −6.82181 + 6.82181i −0.260268 + 0.260268i
\(688\) 0.714864 2.66791i 0.0272540 0.101713i
\(689\) 16.0673 27.8294i 0.612116 1.06022i
\(690\) 2.38117 3.11760i 0.0906496 0.118685i
\(691\) −37.0127 + 21.3693i −1.40803 + 0.812927i −0.995198 0.0978797i \(-0.968794\pi\)
−0.412833 + 0.910807i \(0.635461\pi\)
\(692\) −2.86311 2.86311i −0.108839 0.108839i
\(693\) 10.3030 + 10.2247i 0.391380 + 0.388403i
\(694\) 10.2657i 0.389681i
\(695\) −15.4426 + 37.5187i −0.585773 + 1.42317i
\(696\) 0.592889 + 0.342305i 0.0224734 + 0.0129750i
\(697\) 1.37388 + 5.12738i 0.0520393 + 0.194213i
\(698\) 6.38903 + 1.71194i 0.241828 + 0.0647977i
\(699\) −14.4733 −0.547431
\(700\) 11.5109 + 6.51922i 0.435069 + 0.246403i
\(701\) 44.5959 1.68436 0.842182 0.539194i \(-0.181271\pi\)
0.842182 + 0.539194i \(0.181271\pi\)
\(702\) −3.30124 0.884566i −0.124597 0.0333858i
\(703\) −17.7449 66.2249i −0.669262 2.49772i
\(704\) −4.75127 2.74315i −0.179070 0.103386i
\(705\) −3.00024 + 7.28923i −0.112995 + 0.274528i
\(706\) 13.6247i 0.512772i
\(707\) −21.1071 + 5.74208i −0.793813 + 0.215953i
\(708\) −7.18441 7.18441i −0.270007 0.270007i
\(709\) −35.8750 + 20.7125i −1.34732 + 0.777873i −0.987869 0.155293i \(-0.950368\pi\)
−0.359447 + 0.933166i \(0.617035\pi\)
\(710\) −16.2486 + 21.2738i −0.609800 + 0.798393i
\(711\) 4.16543 7.21474i 0.156216 0.270574i
\(712\) 1.85924 6.93879i 0.0696781 0.260042i
\(713\) −6.91777 + 6.91777i −0.259072 + 0.259072i
\(714\) 4.86417 + 2.78362i 0.182037 + 0.104175i
\(715\) −41.5809 5.37974i −1.55504 0.201191i
\(716\) −1.83267 3.17428i −0.0684900 0.118628i
\(717\) 28.9523 7.75773i 1.08124 0.289718i
\(718\) −16.7071 + 4.47665i −0.623502 + 0.167067i
\(719\) 11.7839 + 20.4103i 0.439464 + 0.761174i 0.997648 0.0685431i \(-0.0218351\pi\)
−0.558184 + 0.829717i \(0.688502\pi\)
\(720\) 1.77095 1.36519i 0.0659993 0.0508777i
\(721\) 21.2760 12.3923i 0.792361 0.461512i
\(722\) 21.1730 21.1730i 0.787976 0.787976i
\(723\) 4.30159 16.0538i 0.159978 0.597046i
\(724\) −1.19992 + 2.07833i −0.0445948 + 0.0772405i
\(725\) −2.40962 + 2.43125i −0.0894911 + 0.0902944i
\(726\) 16.5406 9.54974i 0.613881 0.354424i
\(727\) −3.38556 3.38556i −0.125563 0.125563i 0.641532 0.767096i \(-0.278299\pi\)
−0.767096 + 0.641532i \(0.778299\pi\)
\(728\) 6.36947 6.41829i 0.236068 0.237878i
\(729\) 1.00000i 0.0370370i
\(730\) 10.0716 + 4.14547i 0.372768 + 0.153431i
\(731\) 5.06681 + 2.92532i 0.187403 + 0.108197i
\(732\) −0.303248 1.13174i −0.0112084 0.0418302i
\(733\) 37.9373 + 10.1653i 1.40125 + 0.375463i 0.878792 0.477204i \(-0.158350\pi\)
0.522454 + 0.852667i \(0.325017\pi\)
\(734\) 25.8811 0.955288
\(735\) 1.88979 15.5380i 0.0697061 0.573127i
\(736\) 1.75439 0.0646676
\(737\) −52.7452 14.1330i −1.94289 0.520597i
\(738\) −0.648592 2.42058i −0.0238750 0.0891027i
\(739\) −38.6211 22.2979i −1.42070 0.820242i −0.424343 0.905502i \(-0.639495\pi\)
−0.996359 + 0.0852593i \(0.972828\pi\)
\(740\) 20.2269 8.43125i 0.743555 0.309939i
\(741\) 23.9100i 0.878356i
\(742\) 17.5230 17.6573i 0.643291 0.648222i
\(743\) 24.7787 + 24.7787i 0.909041 + 0.909041i 0.996195 0.0871537i \(-0.0277771\pi\)
−0.0871537 + 0.996195i \(0.527777\pi\)
\(744\) −4.82932 + 2.78821i −0.177051 + 0.102221i
\(745\) 0.0574805 + 0.429196i 0.00210592 + 0.0157245i
\(746\) −4.58319 + 7.93832i −0.167802 + 0.290642i
\(747\) −1.48343 + 5.53624i −0.0542759 + 0.202561i
\(748\) 8.21752 8.21752i 0.300462 0.300462i
\(749\) −28.0466 + 16.3358i −1.02480 + 0.596897i
\(750\) 4.34767 + 10.3004i 0.158754 + 0.376117i
\(751\) −2.54731 4.41207i −0.0929526 0.160999i 0.815800 0.578335i \(-0.196297\pi\)
−0.908752 + 0.417336i \(0.862964\pi\)
\(752\) −3.40506 + 0.912383i −0.124170 + 0.0332712i
\(753\) −10.3992 + 2.78645i −0.378967 + 0.101544i
\(754\) 1.16989 + 2.02632i 0.0426051 + 0.0737941i
\(755\) 29.1096 + 37.7614i 1.05941 + 1.37428i
\(756\) −2.29632 1.31412i −0.0835164 0.0477940i
\(757\) 18.2623 18.2623i 0.663754 0.663754i −0.292509 0.956263i \(-0.594490\pi\)
0.956263 + 0.292509i \(0.0944900\pi\)
\(758\) 4.83657 18.0503i 0.175672 0.655618i
\(759\) −4.81255 + 8.33558i −0.174685 + 0.302562i
\(760\) 12.4320 + 9.49534i 0.450955 + 0.344432i
\(761\) 24.3626 14.0657i 0.883142 0.509882i 0.0114488 0.999934i \(-0.496356\pi\)
0.871693 + 0.490052i \(0.163022\pi\)
\(762\) −4.77054 4.77054i −0.172819 0.172819i
\(763\) −0.859384 + 0.233791i −0.0311118 + 0.00846382i
\(764\) 8.07532i 0.292155i
\(765\) 1.82237 + 4.37193i 0.0658879 + 0.158068i
\(766\) 17.1832 + 9.92072i 0.620854 + 0.358450i
\(767\) −8.98745 33.5416i −0.324518 1.21112i
\(768\) 0.965926 + 0.258819i 0.0348548 + 0.00933933i
\(769\) 3.03517 0.109451 0.0547256 0.998501i \(-0.482572\pi\)
0.0547256 + 0.998501i \(0.482572\pi\)
\(770\) −30.0613 12.2392i −1.08334 0.441070i
\(771\) 15.0425 0.541742
\(772\) 1.66383 + 0.445821i 0.0598825 + 0.0160455i
\(773\) −12.5554 46.8575i −0.451588 1.68535i −0.697930 0.716166i \(-0.745895\pi\)
0.246342 0.969183i \(-0.420771\pi\)
\(774\) −2.39198 1.38101i −0.0859781 0.0496395i
\(775\) −7.33668 26.8995i −0.263541 0.966259i
\(776\) 18.5562i 0.666128i
\(777\) −18.4042 18.2642i −0.660248 0.655226i
\(778\) −3.62546 3.62546i −0.129979 0.129979i
\(779\) 15.1828 8.76579i 0.543980 0.314067i
\(780\) 7.57458 1.01443i 0.271213 0.0363226i
\(781\) 32.8398 56.8803i 1.17510 2.03534i
\(782\) −0.961830 + 3.58960i −0.0343950 + 0.128364i
\(783\) 0.484092 0.484092i 0.0173000 0.0173000i
\(784\) 6.03528 3.54619i 0.215546 0.126650i
\(785\) 1.05584 8.16078i 0.0376847 0.291271i
\(786\) 9.10455 + 15.7695i 0.324748 + 0.562481i
\(787\) −36.6884 + 9.83063i −1.30780 + 0.350424i −0.844394 0.535722i \(-0.820039\pi\)
−0.463406 + 0.886146i \(0.653373\pi\)
\(788\) 8.21219 2.20045i 0.292547 0.0783878i
\(789\) 11.2657 + 19.5128i 0.401070 + 0.694674i
\(790\) −2.39022 + 18.4744i −0.0850403 + 0.657290i
\(791\) −38.1256 + 0.145560i −1.35559 + 0.00517553i
\(792\) −3.87940 + 3.87940i −0.137848 + 0.137848i
\(793\) 1.03641 3.86794i 0.0368040 0.137354i
\(794\) −13.1967 + 22.8574i −0.468334 + 0.811179i
\(795\) 20.8384 2.79081i 0.739062 0.0989797i
\(796\) −9.54181 + 5.50897i −0.338200 + 0.195260i
\(797\) 34.4058 + 34.4058i 1.21871 + 1.21871i 0.968082 + 0.250632i \(0.0806384\pi\)
0.250632 + 0.968082i \(0.419362\pi\)
\(798\) 4.72232 17.8970i 0.167168 0.633546i
\(799\) 7.46719i 0.264170i
\(800\) −2.48063 + 4.34125i −0.0877034 + 0.153487i
\(801\) −6.22115 3.59178i −0.219813 0.126909i
\(802\) −4.45930 16.6423i −0.157463 0.587661i
\(803\) −25.8120 6.91632i −0.910887 0.244071i
\(804\) 9.95313 0.351020
\(805\) 10.2819 1.41700i 0.362390 0.0499426i
\(806\) −19.0585 −0.671307
\(807\) 10.6662 + 2.85799i 0.375467 + 0.100606i
\(808\) −2.13983 7.98595i −0.0752789 0.280945i
\(809\) −33.6569 19.4318i −1.18331 0.683186i −0.226534 0.974003i \(-0.572740\pi\)
−0.956779 + 0.290817i \(0.906073\pi\)
\(810\) −0.860320 2.06394i −0.0302285 0.0725195i
\(811\) 15.3545i 0.539168i 0.962977 + 0.269584i \(0.0868862\pi\)
−0.962977 + 0.269584i \(0.913114\pi\)
\(812\) 0.475477 + 1.74779i 0.0166860 + 0.0613352i
\(813\) −3.54713 3.54713i −0.124403 0.124403i
\(814\) −46.5631 + 26.8832i −1.63204 + 0.942257i
\(815\) −25.0223 19.1116i −0.876494 0.669451i
\(816\) −1.05912 + 1.83445i −0.0370767 + 0.0642187i
\(817\) 5.00114 18.6645i 0.174968 0.652989i
\(818\) −25.2535 + 25.2535i −0.882967 + 0.882967i
\(819\) −4.55106 7.81361i −0.159027 0.273030i
\(820\) 3.42113 + 4.43793i 0.119471 + 0.154979i
\(821\) −11.9561 20.7086i −0.417271 0.722735i 0.578393 0.815758i \(-0.303680\pi\)
−0.995664 + 0.0930235i \(0.970347\pi\)
\(822\) −2.11024 + 0.565438i −0.0736032 + 0.0197219i
\(823\) 27.3473 7.32768i 0.953267 0.255427i 0.251519 0.967852i \(-0.419070\pi\)
0.701748 + 0.712425i \(0.252403\pi\)
\(824\) 4.65310 + 8.05941i 0.162098 + 0.280763i
\(825\) −13.8218 23.6948i −0.481212 0.824949i
\(826\) −0.102631 26.8814i −0.00357099 0.935324i
\(827\) 20.7600 20.7600i 0.721898 0.721898i −0.247094 0.968992i \(-0.579476\pi\)
0.968992 + 0.247094i \(0.0794757\pi\)
\(828\) 0.454069 1.69461i 0.0157800 0.0588917i
\(829\) 4.14106 7.17253i 0.143825 0.249112i −0.785109 0.619358i \(-0.787393\pi\)
0.928934 + 0.370246i \(0.120726\pi\)
\(830\) −1.70122 12.7027i −0.0590503 0.440917i
\(831\) 5.48632 3.16753i 0.190318 0.109880i
\(832\) 2.41668 + 2.41668i 0.0837832 + 0.0837832i
\(833\) 3.94695 + 14.2928i 0.136754 + 0.495215i
\(834\) 18.1446i 0.628295i
\(835\) 17.7250 7.38838i 0.613399 0.255685i
\(836\) −33.2396 19.1909i −1.14962 0.663731i
\(837\) 1.44328 + 5.38640i 0.0498871 + 0.186181i
\(838\) 13.5629 + 3.63417i 0.468523 + 0.125540i
\(839\) 8.03334 0.277342 0.138671 0.990339i \(-0.455717\pi\)
0.138671 + 0.990339i \(0.455717\pi\)
\(840\) 5.87003 + 0.736691i 0.202535 + 0.0254183i
\(841\) 28.5313 0.983838
\(842\) −23.6007 6.32378i −0.813333 0.217932i
\(843\) 7.62799 + 28.4681i 0.262722 + 0.980492i
\(844\) 8.94800 + 5.16613i 0.308003 + 0.177826i
\(845\) −2.72807 1.12287i −0.0938483 0.0386278i
\(846\) 3.52518i 0.121198i
\(847\) 48.8602 + 12.8923i 1.67886 + 0.442985i
\(848\) 6.64852 + 6.64852i 0.228311 + 0.228311i
\(849\) −0.0847197 + 0.0489129i −0.00290757 + 0.00167869i
\(850\) −7.52252 7.45559i −0.258020 0.255725i
\(851\) 8.59662 14.8898i 0.294688 0.510415i
\(852\) −3.09847 + 11.5637i −0.106152 + 0.396165i
\(853\) 23.8654 23.8654i 0.817136 0.817136i −0.168556 0.985692i \(-0.553911\pi\)
0.985692 + 0.168556i \(0.0539105\pi\)
\(854\) 1.53970 2.69051i 0.0526875 0.0920673i
\(855\) 12.3894 9.55079i 0.423709 0.326630i
\(856\) −6.13383 10.6241i −0.209650 0.363124i
\(857\) 23.1984 6.21598i 0.792441 0.212334i 0.160178 0.987088i \(-0.448793\pi\)
0.632263 + 0.774754i \(0.282126\pi\)
\(858\) −18.1116 + 4.85299i −0.618320 + 0.165678i
\(859\) −3.26421 5.65377i −0.111373 0.192904i 0.804951 0.593341i \(-0.202192\pi\)
−0.916324 + 0.400437i \(0.868858\pi\)
\(860\) 6.12502 + 0.792457i 0.208862 + 0.0270226i
\(861\) 3.29314 5.75451i 0.112230 0.196113i
\(862\) −27.4196 + 27.4196i −0.933914 + 0.933914i
\(863\) −4.28582 + 15.9949i −0.145891 + 0.544473i 0.853823 + 0.520563i \(0.174278\pi\)
−0.999714 + 0.0239095i \(0.992389\pi\)
\(864\) 0.500000 0.866025i 0.0170103 0.0294628i
\(865\) 5.49563 7.19527i 0.186857 0.244647i
\(866\) −9.62282 + 5.55574i −0.326997 + 0.188792i
\(867\) 8.84805 + 8.84805i 0.300496 + 0.300496i
\(868\) −14.2656 3.76413i −0.484205 0.127763i
\(869\) 45.7056i 1.55046i
\(870\) −0.582663 + 1.41561i −0.0197541 + 0.0479937i
\(871\) 29.4594 + 17.0084i 0.998194 + 0.576308i
\(872\) −0.0871241 0.325151i −0.00295039 0.0110110i
\(873\) −17.9239 4.80269i −0.606632 0.162547i
\(874\) 12.2736 0.415160
\(875\) −11.0318 + 27.4463i −0.372943 + 0.927854i
\(876\) 4.87079 0.164569
\(877\) −35.7050 9.56712i −1.20567 0.323059i −0.400609 0.916249i \(-0.631202\pi\)
−0.805062 + 0.593190i \(0.797868\pi\)
\(878\) 5.46830 + 20.4080i 0.184546 + 0.688736i
\(879\) −17.1557 9.90484i −0.578647 0.334082i
\(880\) 4.66933 11.3444i 0.157403 0.382419i
\(881\) 17.4940i 0.589386i −0.955592 0.294693i \(-0.904783\pi\)
0.955592 0.294693i \(-0.0952174\pi\)
\(882\) −1.86331 6.74745i −0.0627409 0.227198i
\(883\) −14.0857 14.0857i −0.474022 0.474022i 0.429191 0.903214i \(-0.358799\pi\)
−0.903214 + 0.429191i \(0.858799\pi\)
\(884\) −6.26961 + 3.61976i −0.210870 + 0.121746i
\(885\) 13.7902 18.0551i 0.463553 0.606917i
\(886\) −3.35579 + 5.81240i −0.112740 + 0.195271i
\(887\) −10.6152 + 39.6163i −0.356422 + 1.33018i 0.522264 + 0.852784i \(0.325088\pi\)
−0.878686 + 0.477401i \(0.841579\pi\)
\(888\) 6.92974 6.92974i 0.232547 0.232547i
\(889\) −0.0681482 17.8496i −0.00228562 0.598657i
\(890\) 15.9302 + 2.06105i 0.533980 + 0.0690865i
\(891\) 2.74315 + 4.75127i 0.0918990 + 0.159174i
\(892\) −4.66064 + 1.24882i −0.156050 + 0.0418134i
\(893\) −23.8216 + 6.38297i −0.797158 + 0.213598i
\(894\) 0.0968279 + 0.167711i 0.00323841 + 0.00560909i
\(895\) 6.49112 5.00389i 0.216974 0.167262i
\(896\) 1.33161 + 2.28622i 0.0444861 + 0.0763773i
\(897\) 4.23979 4.23979i 0.141563 0.141563i
\(898\) −2.14555 + 8.00732i −0.0715981 + 0.267208i
\(899\) 1.90883 3.30620i 0.0636632 0.110268i
\(900\) 3.55130 + 3.51970i 0.118377 + 0.117323i
\(901\) −17.2483 + 9.95832i −0.574625 + 0.331760i
\(902\) −9.72165 9.72165i −0.323695 0.323695i
\(903\) −1.91829 7.05136i −0.0638367 0.234654i
\(904\) 14.4102i 0.479277i
\(905\) −4.96232 2.04248i −0.164953 0.0678944i
\(906\) 18.4660 + 10.6614i 0.613493 + 0.354200i
\(907\) 5.17169 + 19.3010i 0.171723 + 0.640879i 0.997087 + 0.0762776i \(0.0243035\pi\)
−0.825364 + 0.564602i \(0.809030\pi\)
\(908\) −17.4772 4.68301i −0.580002 0.155411i
\(909\) −8.26766 −0.274221
\(910\) 16.1153 + 12.2115i 0.534217 + 0.404806i
\(911\) −21.3131 −0.706136 −0.353068 0.935598i \(-0.614862\pi\)
−0.353068 + 0.935598i \(0.614862\pi\)
\(912\) 6.75755 + 1.81068i 0.223765 + 0.0599576i
\(913\) 8.13855 + 30.3735i 0.269347 + 1.00522i
\(914\) 19.1236 + 11.0410i 0.632551 + 0.365204i
\(915\) 2.41824 1.00800i 0.0799445 0.0333235i
\(916\) 9.64749i 0.318762i
\(917\) −12.2913 + 46.5824i −0.405894 + 1.53829i
\(918\) 1.49783 + 1.49783i 0.0494356 + 0.0494356i
\(919\) 11.4010 6.58238i 0.376085 0.217133i −0.300029 0.953930i \(-0.596996\pi\)
0.676114 + 0.736797i \(0.263663\pi\)
\(920\) 0.520734 + 3.88822i 0.0171681 + 0.128191i
\(921\) 2.15894 3.73939i 0.0711394 0.123217i
\(922\) 4.92093 18.3652i 0.162062 0.604824i
\(923\) −28.9315 + 28.9315i −0.952291 + 0.952291i
\(924\) −14.5153 + 0.0554181i −0.477518 + 0.00182312i
\(925\) 24.6897 + 42.3259i 0.811793 + 1.39167i
\(926\) 11.7444 + 20.3419i 0.385946 + 0.668478i
\(927\) 8.98910 2.40862i 0.295241 0.0791095i
\(928\) −0.661282 + 0.177190i −0.0217076 + 0.00581655i
\(929\) −2.59922 4.50199i −0.0852777 0.147705i 0.820232 0.572031i \(-0.193844\pi\)
−0.905510 + 0.424326i \(0.860511\pi\)
\(930\) −7.61288 9.87553i −0.249636 0.323831i
\(931\) 42.2224 24.8089i 1.38378 0.813078i
\(932\) 10.2342 10.2342i 0.335232 0.335232i
\(933\) −2.18581 + 8.15755i −0.0715602 + 0.267066i
\(934\) −7.99472 + 13.8473i −0.261595 + 0.453096i
\(935\) 20.6514 + 15.7732i 0.675374 + 0.515840i
\(936\) 2.95981 1.70885i 0.0967446 0.0558555i
\(937\) 3.54515 + 3.54515i 0.115815 + 0.115815i 0.762639 0.646824i \(-0.223903\pi\)
−0.646824 + 0.762639i \(0.723903\pi\)
\(938\) 18.6916 + 18.5494i 0.610301 + 0.605658i
\(939\) 19.4096i 0.633409i
\(940\) −3.03278 7.27575i −0.0989183 0.237309i
\(941\) 8.88464 + 5.12955i 0.289631 + 0.167219i 0.637775 0.770222i \(-0.279855\pi\)
−0.348144 + 0.937441i \(0.613188\pi\)
\(942\) −0.952462 3.55464i −0.0310329 0.115816i
\(943\) 4.24663 + 1.13788i 0.138289 + 0.0370545i
\(944\) 10.1603 0.330689
\(945\) 2.23087 5.47935i 0.0725701 0.178243i
\(946\) −15.1533 −0.492676
\(947\) −27.1150 7.26545i −0.881120 0.236096i −0.210230 0.977652i \(-0.567421\pi\)
−0.670890 + 0.741556i \(0.734088\pi\)
\(948\) 2.15619 + 8.04700i 0.0700297 + 0.261354i
\(949\) 14.4166 + 8.32344i 0.467983 + 0.270190i
\(950\) −17.3543 + 30.3711i −0.563048 + 0.985369i
\(951\) 15.5503i 0.504253i
\(952\) −5.40781 + 1.47117i −0.175268 + 0.0476809i
\(953\) −29.6648 29.6648i −0.960937 0.960937i 0.0383279 0.999265i \(-0.487797\pi\)
−0.999265 + 0.0383279i \(0.987797\pi\)
\(954\) 8.14273 4.70121i 0.263631 0.152207i
\(955\) 17.8972 2.39690i 0.579139 0.0775619i
\(956\) −14.9868 + 25.9579i −0.484708 + 0.839538i
\(957\) 0.972117 3.62799i 0.0314241 0.117276i
\(958\) 6.37140 6.37140i 0.205850 0.205850i
\(959\) −5.01674 2.87093i −0.161999 0.0927073i
\(960\) −0.286912 + 2.21758i −0.00926003 + 0.0715722i
\(961\) 0.0482042 + 0.0834922i 0.00155498 + 0.00269330i
\(962\) 32.3526 8.66886i 1.04309 0.279495i
\(963\) −11.8496 + 3.17510i −0.381850 + 0.102316i
\(964\) 8.31003 + 14.3934i 0.267648 + 0.463580i
\(965\) −0.494211 + 3.81984i −0.0159092 + 0.122965i
\(966\) 4.01092 2.33617i 0.129049 0.0751650i
\(967\) −3.20889 + 3.20889i −0.103191 + 0.103191i −0.756817 0.653626i \(-0.773247\pi\)
0.653626 + 0.756817i \(0.273247\pi\)
\(968\) −4.94331 + 18.4487i −0.158884 + 0.592963i
\(969\) −7.40955 + 12.8337i −0.238029 + 0.412278i
\(970\) 41.1257 5.50781i 1.32047 0.176845i
\(971\) 51.1699 29.5430i 1.64212 0.948079i 0.662042 0.749467i \(-0.269690\pi\)
0.980078 0.198612i \(-0.0636433\pi\)
\(972\) −0.707107 0.707107i −0.0226805 0.0226805i
\(973\) −33.8155 + 34.0747i −1.08408 + 1.09239i
\(974\) 9.34012i 0.299277i
\(975\) 4.49654 + 16.4863i 0.144005 + 0.527984i
\(976\) 1.01469 + 0.585830i 0.0324794 + 0.0187520i
\(977\) −3.06089 11.4234i −0.0979266 0.365467i 0.899520 0.436879i \(-0.143916\pi\)
−0.997447 + 0.0714120i \(0.977249\pi\)
\(978\) −13.6012 3.64443i −0.434918 0.116536i
\(979\) −39.4112 −1.25959
\(980\) 9.65072 + 12.3233i 0.308281 + 0.393653i
\(981\) −0.336622 −0.0107475
\(982\) −2.01430 0.539730i −0.0642788 0.0172235i
\(983\) −9.83561 36.7070i −0.313707 1.17077i −0.925187 0.379511i \(-0.876092\pi\)
0.611480 0.791260i \(-0.290575\pi\)
\(984\) 2.17023 + 1.25298i 0.0691844 + 0.0399437i
\(985\) 7.31434 + 17.5474i 0.233054 + 0.559106i
\(986\) 1.45017i 0.0461829i
\(987\) −6.56977 + 6.62013i −0.209118 + 0.210721i
\(988\) 16.9069 + 16.9069i 0.537881 + 0.537881i
\(989\) 4.19647 2.42283i 0.133440 0.0770416i
\(990\) −9.74931 7.44636i −0.309853 0.236661i
\(991\) −4.00630 + 6.93911i −0.127264 + 0.220428i −0.922616 0.385720i \(-0.873953\pi\)
0.795352 + 0.606148i \(0.207286\pi\)
\(992\) 1.44328 5.38640i 0.0458243 0.171018i
\(993\) −11.4452 + 11.4452i −0.363202 + 0.363202i
\(994\) −27.3697 + 15.9415i −0.868114 + 0.505635i
\(995\) −15.0416 19.5122i −0.476851 0.618577i
\(996\) −2.86577 4.96366i −0.0908054 0.157280i
\(997\) 41.1086 11.0150i 1.30192 0.348849i 0.459745 0.888051i \(-0.347941\pi\)
0.842176 + 0.539202i \(0.181274\pi\)
\(998\) −12.9671 + 3.47453i −0.410468 + 0.109984i
\(999\) −4.90007 8.48716i −0.155031 0.268522i
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.u.a.73.1 16
3.2 odd 2 630.2.bv.a.73.4 16
5.2 odd 4 210.2.u.b.157.3 yes 16
5.3 odd 4 1050.2.bc.g.157.2 16
5.4 even 2 1050.2.bc.h.493.3 16
7.3 odd 6 1470.2.m.e.1273.7 16
7.4 even 3 1470.2.m.d.1273.6 16
7.5 odd 6 210.2.u.b.103.3 yes 16
15.2 even 4 630.2.bv.b.577.2 16
21.5 even 6 630.2.bv.b.523.2 16
35.12 even 12 inner 210.2.u.a.187.1 yes 16
35.17 even 12 1470.2.m.d.97.6 16
35.19 odd 6 1050.2.bc.g.943.2 16
35.32 odd 12 1470.2.m.e.97.7 16
35.33 even 12 1050.2.bc.h.607.3 16
105.47 odd 12 630.2.bv.a.397.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.u.a.73.1 16 1.1 even 1 trivial
210.2.u.a.187.1 yes 16 35.12 even 12 inner
210.2.u.b.103.3 yes 16 7.5 odd 6
210.2.u.b.157.3 yes 16 5.2 odd 4
630.2.bv.a.73.4 16 3.2 odd 2
630.2.bv.a.397.4 16 105.47 odd 12
630.2.bv.b.523.2 16 21.5 even 6
630.2.bv.b.577.2 16 15.2 even 4
1050.2.bc.g.157.2 16 5.3 odd 4
1050.2.bc.g.943.2 16 35.19 odd 6
1050.2.bc.h.493.3 16 5.4 even 2
1050.2.bc.h.607.3 16 35.33 even 12
1470.2.m.d.97.6 16 35.17 even 12
1470.2.m.d.1273.6 16 7.4 even 3
1470.2.m.e.97.7 16 35.32 odd 12
1470.2.m.e.1273.7 16 7.3 odd 6