Properties

Label 210.2.x.a.107.8
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 107.8
Character \(\chi\) \(=\) 210.107
Dual form 210.2.x.a.53.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.258819 - 0.965926i) q^{2} +(1.55878 + 0.755113i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.856739 + 2.06543i) q^{5} +(0.325941 - 1.70111i) q^{6} +(-0.301012 + 2.62857i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.85961 + 2.35411i) q^{9} +O(q^{10})\) \(q+(-0.258819 - 0.965926i) q^{2} +(1.55878 + 0.755113i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.856739 + 2.06543i) q^{5} +(0.325941 - 1.70111i) q^{6} +(-0.301012 + 2.62857i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.85961 + 2.35411i) q^{9} +(2.21679 + 0.292973i) q^{10} +(1.49091 - 0.860779i) q^{11} +(-1.72750 + 0.125444i) q^{12} +(1.71166 - 1.71166i) q^{13} +(2.61691 - 0.389569i) q^{14} +(-2.89510 + 2.57262i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-2.39412 - 0.641503i) q^{17} +(1.79260 - 2.40553i) q^{18} +(-3.74936 - 2.16470i) q^{19} +(-0.290757 - 2.21708i) q^{20} +(-2.45408 + 3.87008i) q^{21} +(-1.21733 - 1.21733i) q^{22} +(7.36627 - 1.97379i) q^{23} +(0.568280 + 1.63617i) q^{24} +(-3.53200 - 3.53907i) q^{25} +(-2.09634 - 1.21032i) q^{26} +(1.12110 + 5.07377i) q^{27} +(-1.05360 - 2.42692i) q^{28} +3.49141 q^{29} +(3.23427 + 2.13061i) q^{30} +(-2.74588 - 4.75601i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(2.97400 - 0.215960i) q^{33} +2.47858i q^{34} +(-5.17124 - 2.87372i) q^{35} +(-2.78753 - 1.10892i) q^{36} +(4.83348 - 1.29513i) q^{37} +(-1.12053 + 4.18187i) q^{38} +(3.96059 - 1.37561i) q^{39} +(-2.06628 + 0.854674i) q^{40} -5.76741i q^{41} +(4.37337 + 1.36881i) q^{42} +(-1.33337 + 1.33337i) q^{43} +(-0.860779 + 1.49091i) q^{44} +(-6.45546 + 1.82403i) q^{45} +(-3.81306 - 6.60442i) q^{46} +(1.56613 + 5.84489i) q^{47} +(1.43334 - 0.972389i) q^{48} +(-6.81878 - 1.58246i) q^{49} +(-2.50433 + 4.32763i) q^{50} +(-3.24751 - 2.80780i) q^{51} +(-0.626510 + 2.33817i) q^{52} +(-3.51917 + 13.1337i) q^{53} +(4.61072 - 2.39609i) q^{54} +(0.500556 + 3.81684i) q^{55} +(-2.07153 + 1.64583i) q^{56} +(-4.20985 - 6.20549i) q^{57} +(-0.903644 - 3.37245i) q^{58} +(-5.45213 - 9.44337i) q^{59} +(1.22092 - 3.67551i) q^{60} +(-4.22391 + 7.31603i) q^{61} +(-3.88326 + 3.88326i) q^{62} +(-6.74772 + 4.17950i) q^{63} +1.00000i q^{64} +(2.06886 + 5.00175i) q^{65} +(-0.978328 - 2.81677i) q^{66} +(3.54455 - 13.2284i) q^{67} +(2.39412 - 0.641503i) q^{68} +(12.9729 + 2.48566i) q^{69} +(-1.43738 + 5.73881i) q^{70} -10.9125i q^{71} +(-0.349669 + 2.97955i) q^{72} +(3.17204 + 0.849946i) q^{73} +(-2.50199 - 4.33358i) q^{74} +(-2.83322 - 8.18369i) q^{75} +4.32939 q^{76} +(1.81384 + 4.17808i) q^{77} +(-2.35381 - 3.46961i) q^{78} +(-2.97847 - 1.71962i) q^{79} +(1.36035 + 1.77467i) q^{80} +(-2.08371 + 8.75546i) q^{81} +(-5.57089 + 1.49272i) q^{82} +(-1.66979 - 1.66979i) q^{83} +(0.190259 - 4.57862i) q^{84} +(3.37612 - 4.39529i) q^{85} +(1.63304 + 0.942836i) q^{86} +(5.44236 + 2.63641i) q^{87} +(1.66290 + 0.445572i) q^{88} +(-1.63686 + 2.83513i) q^{89} +(3.43267 + 5.76340i) q^{90} +(3.98398 + 5.01444i) q^{91} +(-5.39249 + 5.39249i) q^{92} +(-0.688911 - 9.48704i) q^{93} +(5.24039 - 3.02554i) q^{94} +(7.68325 - 5.88947i) q^{95} +(-1.31023 - 1.13283i) q^{96} +(11.1959 + 11.1959i) q^{97} +(0.236290 + 6.99601i) q^{98} +(4.79889 + 1.90907i) 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
\(3\) 1.55878 + 0.755113i 0.899964 + 0.435965i
\(4\) −0.866025 + 0.500000i −0.433013 + 0.250000i
\(5\) −0.856739 + 2.06543i −0.383145 + 0.923688i
\(6\) 0.325941 1.70111i 0.133065 0.694474i
\(7\) −0.301012 + 2.62857i −0.113772 + 0.993507i
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 1.85961 + 2.35411i 0.619869 + 0.784705i
\(10\) 2.21679 + 0.292973i 0.701011 + 0.0926463i
\(11\) 1.49091 0.860779i 0.449527 0.259535i −0.258103 0.966117i \(-0.583097\pi\)
0.707631 + 0.706583i \(0.249764\pi\)
\(12\) −1.72750 + 0.125444i −0.498687 + 0.0362127i
\(13\) 1.71166 1.71166i 0.474728 0.474728i −0.428713 0.903441i \(-0.641033\pi\)
0.903441 + 0.428713i \(0.141033\pi\)
\(14\) 2.61691 0.389569i 0.699400 0.104117i
\(15\) −2.89510 + 2.57262i −0.747512 + 0.664248i
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) −2.39412 0.641503i −0.580660 0.155587i −0.0434791 0.999054i \(-0.513844\pi\)
−0.537181 + 0.843467i \(0.680511\pi\)
\(18\) 1.79260 2.40553i 0.422519 0.566990i
\(19\) −3.74936 2.16470i −0.860163 0.496615i 0.00390374 0.999992i \(-0.498757\pi\)
−0.864067 + 0.503377i \(0.832091\pi\)
\(20\) −0.290757 2.21708i −0.0650153 0.495755i
\(21\) −2.45408 + 3.87008i −0.535524 + 0.844520i
\(22\) −1.21733 1.21733i −0.259535 0.259535i
\(23\) 7.36627 1.97379i 1.53597 0.411563i 0.611012 0.791622i \(-0.290763\pi\)
0.924962 + 0.380059i \(0.124096\pi\)
\(24\) 0.568280 + 1.63617i 0.116000 + 0.333982i
\(25\) −3.53200 3.53907i −0.706400 0.707813i
\(26\) −2.09634 1.21032i −0.411126 0.237364i
\(27\) 1.12110 + 5.07377i 0.215756 + 0.976447i
\(28\) −1.05360 2.42692i −0.199112 0.458644i
\(29\) 3.49141 0.648339 0.324170 0.945999i \(-0.394915\pi\)
0.324170 + 0.945999i \(0.394915\pi\)
\(30\) 3.23427 + 2.13061i 0.590494 + 0.388994i
\(31\) −2.74588 4.75601i −0.493175 0.854204i 0.506794 0.862067i \(-0.330830\pi\)
−0.999969 + 0.00786297i \(0.997497\pi\)
\(32\) −0.965926 0.258819i −0.170753 0.0457532i
\(33\) 2.97400 0.215960i 0.517706 0.0375938i
\(34\) 2.47858i 0.425073i
\(35\) −5.17124 2.87372i −0.874099 0.485747i
\(36\) −2.78753 1.10892i −0.464588 0.184820i
\(37\) 4.83348 1.29513i 0.794619 0.212918i 0.161399 0.986889i \(-0.448399\pi\)
0.633220 + 0.773972i \(0.281733\pi\)
\(38\) −1.12053 + 4.18187i −0.181774 + 0.678389i
\(39\) 3.96059 1.37561i 0.634203 0.220273i
\(40\) −2.06628 + 0.854674i −0.326708 + 0.135136i
\(41\) 5.76741i 0.900718i −0.892848 0.450359i \(-0.851296\pi\)
0.892848 0.450359i \(-0.148704\pi\)
\(42\) 4.37337 + 1.36881i 0.674825 + 0.211212i
\(43\) −1.33337 + 1.33337i −0.203337 + 0.203337i −0.801428 0.598091i \(-0.795926\pi\)
0.598091 + 0.801428i \(0.295926\pi\)
\(44\) −0.860779 + 1.49091i −0.129767 + 0.224764i
\(45\) −6.45546 + 1.82403i −0.962323 + 0.271910i
\(46\) −3.81306 6.60442i −0.562206 0.973769i
\(47\) 1.56613 + 5.84489i 0.228444 + 0.852565i 0.980995 + 0.194031i \(0.0621563\pi\)
−0.752551 + 0.658534i \(0.771177\pi\)
\(48\) 1.43334 0.972389i 0.206885 0.140352i
\(49\) −6.81878 1.58246i −0.974112 0.226066i
\(50\) −2.50433 + 4.32763i −0.354165 + 0.612019i
\(51\) −3.24751 2.80780i −0.454742 0.393170i
\(52\) −0.626510 + 2.33817i −0.0868812 + 0.324245i
\(53\) −3.51917 + 13.1337i −0.483395 + 1.80406i 0.103784 + 0.994600i \(0.466905\pi\)
−0.587180 + 0.809457i \(0.699762\pi\)
\(54\) 4.61072 2.39609i 0.627440 0.326067i
\(55\) 0.500556 + 3.81684i 0.0674949 + 0.514663i
\(56\) −2.07153 + 1.64583i −0.276820 + 0.219934i
\(57\) −4.20985 6.20549i −0.557609 0.821937i
\(58\) −0.903644 3.37245i −0.118654 0.442824i
\(59\) −5.45213 9.44337i −0.709807 1.22942i −0.964928 0.262513i \(-0.915449\pi\)
0.255121 0.966909i \(-0.417885\pi\)
\(60\) 1.22092 3.67551i 0.157620 0.474506i
\(61\) −4.22391 + 7.31603i −0.540817 + 0.936722i 0.458041 + 0.888931i \(0.348551\pi\)
−0.998857 + 0.0477908i \(0.984782\pi\)
\(62\) −3.88326 + 3.88326i −0.493175 + 0.493175i
\(63\) −6.74772 + 4.17950i −0.850133 + 0.526567i
\(64\) 1.00000i 0.125000i
\(65\) 2.06886 + 5.00175i 0.256611 + 0.620390i
\(66\) −0.978328 2.81677i −0.120424 0.346720i
\(67\) 3.54455 13.2284i 0.433035 1.61611i −0.312689 0.949856i \(-0.601230\pi\)
0.745724 0.666255i \(-0.232104\pi\)
\(68\) 2.39412 0.641503i 0.290330 0.0777937i
\(69\) 12.9729 + 2.48566i 1.56175 + 0.299239i
\(70\) −1.43738 + 5.73881i −0.171800 + 0.685919i
\(71\) 10.9125i 1.29507i −0.762034 0.647537i \(-0.775799\pi\)
0.762034 0.647537i \(-0.224201\pi\)
\(72\) −0.349669 + 2.97955i −0.0412089 + 0.351144i
\(73\) 3.17204 + 0.849946i 0.371259 + 0.0994786i 0.439624 0.898182i \(-0.355112\pi\)
−0.0683650 + 0.997660i \(0.521778\pi\)
\(74\) −2.50199 4.33358i −0.290851 0.503768i
\(75\) −2.83322 8.18369i −0.327152 0.944972i
\(76\) 4.32939 0.496615
\(77\) 1.81384 + 4.17808i 0.206706 + 0.476136i
\(78\) −2.35381 3.46961i −0.266517 0.392856i
\(79\) −2.97847 1.71962i −0.335104 0.193472i 0.323001 0.946399i \(-0.395308\pi\)
−0.658105 + 0.752926i \(0.728642\pi\)
\(80\) 1.36035 + 1.77467i 0.152091 + 0.198414i
\(81\) −2.08371 + 8.75546i −0.231524 + 0.972829i
\(82\) −5.57089 + 1.49272i −0.615202 + 0.164843i
\(83\) −1.66979 1.66979i −0.183283 0.183283i 0.609502 0.792785i \(-0.291370\pi\)
−0.792785 + 0.609502i \(0.791370\pi\)
\(84\) 0.190259 4.57862i 0.0207590 0.499569i
\(85\) 3.37612 4.39529i 0.366191 0.476736i
\(86\) 1.63304 + 0.942836i 0.176095 + 0.101669i
\(87\) 5.44236 + 2.63641i 0.583482 + 0.282653i
\(88\) 1.66290 + 0.445572i 0.177266 + 0.0474981i
\(89\) −1.63686 + 2.83513i −0.173507 + 0.300523i −0.939644 0.342155i \(-0.888843\pi\)
0.766136 + 0.642678i \(0.222177\pi\)
\(90\) 3.43267 + 5.76340i 0.361835 + 0.607516i
\(91\) 3.98398 + 5.01444i 0.417635 + 0.525656i
\(92\) −5.39249 + 5.39249i −0.562206 + 0.562206i
\(93\) −0.688911 9.48704i −0.0714367 0.983760i
\(94\) 5.24039 3.02554i 0.540505 0.312060i
\(95\) 7.68325 5.88947i 0.788285 0.604247i
\(96\) −1.31023 1.13283i −0.133725 0.115619i
\(97\) 11.1959 + 11.1959i 1.13678 + 1.13678i 0.989025 + 0.147751i \(0.0472033\pi\)
0.147751 + 0.989025i \(0.452797\pi\)
\(98\) 0.236290 + 6.99601i 0.0238689 + 0.706704i
\(99\) 4.79889 + 1.90907i 0.482306 + 0.191869i
\(100\) 4.82833 + 1.29892i 0.482833 + 0.129892i
\(101\) 6.85108 3.95547i 0.681707 0.393584i −0.118791 0.992919i \(-0.537902\pi\)
0.800498 + 0.599335i \(0.204568\pi\)
\(102\) −1.87161 + 3.86357i −0.185317 + 0.382550i
\(103\) 3.57231 + 13.3320i 0.351990 + 1.31364i 0.884230 + 0.467051i \(0.154684\pi\)
−0.532241 + 0.846593i \(0.678650\pi\)
\(104\) 2.42065 0.237364
\(105\) −5.89086 8.38438i −0.574889 0.818231i
\(106\) 13.5970 1.32066
\(107\) −5.24240 19.5649i −0.506802 1.89141i −0.450008 0.893024i \(-0.648579\pi\)
−0.0567934 0.998386i \(-0.518088\pi\)
\(108\) −3.50779 3.83346i −0.337537 0.368875i
\(109\) 6.61391 3.81854i 0.633497 0.365750i −0.148608 0.988896i \(-0.547479\pi\)
0.782105 + 0.623146i \(0.214146\pi\)
\(110\) 3.55723 1.47137i 0.339169 0.140290i
\(111\) 8.51232 + 1.63100i 0.807953 + 0.154808i
\(112\) 2.12590 + 1.57497i 0.200879 + 0.148821i
\(113\) 4.50613 + 4.50613i 0.423901 + 0.423901i 0.886545 0.462643i \(-0.153099\pi\)
−0.462643 + 0.886545i \(0.653099\pi\)
\(114\) −4.90445 + 5.67251i −0.459344 + 0.531279i
\(115\) −2.23425 + 16.9055i −0.208345 + 1.57645i
\(116\) −3.02365 + 1.74571i −0.280739 + 0.162085i
\(117\) 7.21244 + 0.846425i 0.666791 + 0.0782520i
\(118\) −7.71048 + 7.71048i −0.709807 + 0.709807i
\(119\) 2.40690 6.10003i 0.220640 0.559188i
\(120\) −3.86626 0.228028i −0.352940 0.0208160i
\(121\) −4.01812 + 6.95958i −0.365283 + 0.632690i
\(122\) 8.15997 + 2.18646i 0.738769 + 0.197953i
\(123\) 4.35505 8.99014i 0.392681 0.810613i
\(124\) 4.75601 + 2.74588i 0.427102 + 0.246588i
\(125\) 10.3357 4.26304i 0.924452 0.381298i
\(126\) 5.78353 + 5.43607i 0.515237 + 0.484283i
\(127\) −3.77174 3.77174i −0.334688 0.334688i 0.519676 0.854364i \(-0.326053\pi\)
−0.854364 + 0.519676i \(0.826053\pi\)
\(128\) 0.965926 0.258819i 0.0853766 0.0228766i
\(129\) −3.08528 + 1.07159i −0.271644 + 0.0943483i
\(130\) 4.29585 3.29292i 0.376771 0.288808i
\(131\) −8.66142 5.00068i −0.756752 0.436911i 0.0713763 0.997449i \(-0.477261\pi\)
−0.828128 + 0.560538i \(0.810594\pi\)
\(132\) −2.46758 + 1.67402i −0.214775 + 0.145705i
\(133\) 6.81866 9.20388i 0.591253 0.798077i
\(134\) −13.6951 −1.18307
\(135\) −11.4400 2.03133i −0.984599 0.174829i
\(136\) −1.23929 2.14651i −0.106268 0.184062i
\(137\) −2.39345 0.641324i −0.204487 0.0547920i 0.155122 0.987895i \(-0.450423\pi\)
−0.359608 + 0.933103i \(0.617090\pi\)
\(138\) −0.956654 13.1742i −0.0814358 1.12146i
\(139\) 3.57912i 0.303577i −0.988413 0.151788i \(-0.951497\pi\)
0.988413 0.151788i \(-0.0485033\pi\)
\(140\) 5.91529 0.0969085i 0.499933 0.00819027i
\(141\) −1.97229 + 10.2935i −0.166097 + 0.866871i
\(142\) −10.5407 + 2.82436i −0.884552 + 0.237015i
\(143\) 1.07857 4.02529i 0.0901948 0.336612i
\(144\) 2.96853 0.433411i 0.247377 0.0361176i
\(145\) −2.99123 + 7.21127i −0.248408 + 0.598863i
\(146\) 3.28394i 0.271781i
\(147\) −9.43407 7.61567i −0.778109 0.628130i
\(148\) −3.53835 + 3.53835i −0.290851 + 0.290851i
\(149\) −6.70402 + 11.6117i −0.549215 + 0.951268i 0.449114 + 0.893475i \(0.351740\pi\)
−0.998329 + 0.0577936i \(0.981593\pi\)
\(150\) −7.17155 + 4.85478i −0.585555 + 0.396391i
\(151\) −2.73907 4.74421i −0.222903 0.386078i 0.732786 0.680460i \(-0.238220\pi\)
−0.955688 + 0.294381i \(0.904886\pi\)
\(152\) −1.12053 4.18187i −0.0908869 0.339195i
\(153\) −2.94196 6.82899i −0.237843 0.552091i
\(154\) 3.56626 2.83340i 0.287377 0.228322i
\(155\) 12.1757 1.59677i 0.977976 0.128256i
\(156\) −2.74217 + 3.17161i −0.219549 + 0.253932i
\(157\) 2.85955 10.6720i 0.228217 0.851718i −0.752873 0.658166i \(-0.771333\pi\)
0.981090 0.193552i \(-0.0620008\pi\)
\(158\) −0.890141 + 3.32205i −0.0708158 + 0.264288i
\(159\) −15.4031 + 17.8153i −1.22154 + 1.41284i
\(160\) 1.36212 1.77331i 0.107685 0.140193i
\(161\) 2.97091 + 19.9569i 0.234140 + 1.57283i
\(162\) 8.99643 0.253368i 0.706827 0.0199065i
\(163\) 1.28791 + 4.80653i 0.100877 + 0.376476i 0.997845 0.0656186i \(-0.0209021\pi\)
−0.896968 + 0.442095i \(0.854235\pi\)
\(164\) 2.88370 + 4.99472i 0.225179 + 0.390022i
\(165\) −2.10189 + 6.32760i −0.163632 + 0.492603i
\(166\) −1.18072 + 2.04507i −0.0916417 + 0.158728i
\(167\) −12.6740 + 12.6740i −0.980742 + 0.980742i −0.999818 0.0190761i \(-0.993928\pi\)
0.0190761 + 0.999818i \(0.493928\pi\)
\(168\) −4.47185 + 1.00126i −0.345011 + 0.0772488i
\(169\) 7.14047i 0.549267i
\(170\) −5.11933 2.12349i −0.392635 0.162865i
\(171\) −1.87640 12.8519i −0.143492 0.982811i
\(172\) 0.488048 1.82142i 0.0372133 0.138882i
\(173\) −7.46147 + 1.99929i −0.567285 + 0.152004i −0.531051 0.847340i \(-0.678203\pi\)
−0.0362338 + 0.999343i \(0.511536\pi\)
\(174\) 1.13799 5.93926i 0.0862710 0.450255i
\(175\) 10.3659 8.21881i 0.783586 0.621284i
\(176\) 1.72156i 0.129767i
\(177\) −1.36788 18.8371i −0.102816 1.41589i
\(178\) 3.16218 + 0.847304i 0.237015 + 0.0635081i
\(179\) −1.78392 3.08984i −0.133336 0.230945i 0.791624 0.611008i \(-0.209236\pi\)
−0.924961 + 0.380063i \(0.875902\pi\)
\(180\) 4.67857 4.80738i 0.348720 0.358321i
\(181\) −22.4506 −1.66874 −0.834371 0.551203i \(-0.814169\pi\)
−0.834371 + 0.551203i \(0.814169\pi\)
\(182\) 3.81245 5.14606i 0.282597 0.381452i
\(183\) −12.1086 + 8.21457i −0.895093 + 0.607239i
\(184\) 6.60442 + 3.81306i 0.486884 + 0.281103i
\(185\) −1.46604 + 11.0928i −0.107785 + 0.815559i
\(186\) −8.98547 + 3.12086i −0.658847 + 0.228833i
\(187\) −4.12162 + 1.10439i −0.301403 + 0.0807607i
\(188\) −4.27876 4.27876i −0.312060 0.312060i
\(189\) −13.6742 + 1.41964i −0.994654 + 0.103263i
\(190\) −7.67736 5.89715i −0.556974 0.427824i
\(191\) 20.0377 + 11.5688i 1.44988 + 0.837088i 0.998474 0.0552306i \(-0.0175894\pi\)
0.451406 + 0.892319i \(0.350923\pi\)
\(192\) −0.755113 + 1.55878i −0.0544956 + 0.112495i
\(193\) −15.5358 4.16280i −1.11829 0.299645i −0.348099 0.937458i \(-0.613173\pi\)
−0.770191 + 0.637813i \(0.779839\pi\)
\(194\) 7.91672 13.7122i 0.568388 0.984476i
\(195\) −0.551976 + 9.35886i −0.0395278 + 0.670202i
\(196\) 6.69647 2.03894i 0.478319 0.145639i
\(197\) 4.51365 4.51365i 0.321584 0.321584i −0.527791 0.849375i \(-0.676979\pi\)
0.849375 + 0.527791i \(0.176979\pi\)
\(198\) 0.601976 5.12947i 0.0427805 0.364536i
\(199\) 1.87390 1.08190i 0.132837 0.0766936i −0.432109 0.901821i \(-0.642230\pi\)
0.564946 + 0.825128i \(0.308897\pi\)
\(200\) 0.00499778 5.00000i 0.000353396 0.353553i
\(201\) 15.5141 17.9437i 1.09428 1.26565i
\(202\) −5.59388 5.59388i −0.393584 0.393584i
\(203\) −1.05096 + 9.17743i −0.0737627 + 0.644129i
\(204\) 4.21633 + 0.807869i 0.295202 + 0.0565622i
\(205\) 11.9122 + 4.94116i 0.831983 + 0.345106i
\(206\) 11.9532 6.90117i 0.832817 0.480827i
\(207\) 18.3449 + 13.6706i 1.27506 + 0.950171i
\(208\) −0.626510 2.33817i −0.0434406 0.162123i
\(209\) −7.45330 −0.515556
\(210\) −6.57402 + 7.86017i −0.453650 + 0.542403i
\(211\) 8.92286 0.614275 0.307138 0.951665i \(-0.400629\pi\)
0.307138 + 0.951665i \(0.400629\pi\)
\(212\) −3.51917 13.1337i −0.241698 0.902028i
\(213\) 8.24016 17.0102i 0.564607 1.16552i
\(214\) −17.5414 + 10.1275i −1.19911 + 0.692304i
\(215\) −1.61163 3.89634i −0.109913 0.265728i
\(216\) −2.79496 + 4.38044i −0.190173 + 0.298051i
\(217\) 13.3281 5.78614i 0.904767 0.392788i
\(218\) −5.40023 5.40023i −0.365750 0.365750i
\(219\) 4.30272 + 3.72013i 0.290751 + 0.251383i
\(220\) −2.34191 3.05520i −0.157892 0.205982i
\(221\) −5.19595 + 2.99988i −0.349517 + 0.201794i
\(222\) −0.627722 8.64440i −0.0421299 0.580174i
\(223\) 4.95541 4.95541i 0.331839 0.331839i −0.521446 0.853284i \(-0.674607\pi\)
0.853284 + 0.521446i \(0.174607\pi\)
\(224\) 0.971080 2.46110i 0.0648830 0.164439i
\(225\) 1.76323 14.8960i 0.117549 0.993067i
\(226\) 3.18632 5.51886i 0.211951 0.367109i
\(227\) −23.5933 6.32181i −1.56594 0.419593i −0.631404 0.775454i \(-0.717521\pi\)
−0.934539 + 0.355862i \(0.884187\pi\)
\(228\) 6.74858 + 3.26918i 0.446936 + 0.216507i
\(229\) 1.56910 + 0.905917i 0.103689 + 0.0598647i 0.550948 0.834540i \(-0.314266\pi\)
−0.447259 + 0.894405i \(0.647600\pi\)
\(230\) 16.9078 2.21735i 1.11486 0.146208i
\(231\) −0.327542 + 7.88237i −0.0215507 + 0.518622i
\(232\) 2.46880 + 2.46880i 0.162085 + 0.162085i
\(233\) −1.82119 + 0.487986i −0.119310 + 0.0319690i −0.317980 0.948097i \(-0.603004\pi\)
0.198670 + 0.980066i \(0.436338\pi\)
\(234\) −1.04913 7.18576i −0.0685840 0.469748i
\(235\) −13.4140 1.77280i −0.875031 0.115645i
\(236\) 9.44337 + 5.45213i 0.614711 + 0.354904i
\(237\) −3.34428 4.92960i −0.217234 0.320212i
\(238\) −6.51512 0.746081i −0.422313 0.0483613i
\(239\) −7.33694 −0.474587 −0.237294 0.971438i \(-0.576260\pi\)
−0.237294 + 0.971438i \(0.576260\pi\)
\(240\) 0.780405 + 3.79354i 0.0503749 + 0.244872i
\(241\) 7.03912 + 12.1921i 0.453430 + 0.785363i 0.998596 0.0529643i \(-0.0168669\pi\)
−0.545167 + 0.838328i \(0.683534\pi\)
\(242\) 7.76241 + 2.07993i 0.498987 + 0.133703i
\(243\) −9.85942 + 12.0744i −0.632482 + 0.774575i
\(244\) 8.44783i 0.540817i
\(245\) 9.11038 12.7280i 0.582041 0.813160i
\(246\) −9.81098 1.87983i −0.625525 0.119854i
\(247\) −10.1228 + 2.71241i −0.644101 + 0.172586i
\(248\) 1.42137 5.30464i 0.0902573 0.336845i
\(249\) −1.34196 3.86372i −0.0850433 0.244853i
\(250\) −6.79285 8.88015i −0.429618 0.561630i
\(251\) 23.2410i 1.46696i 0.679711 + 0.733480i \(0.262105\pi\)
−0.679711 + 0.733480i \(0.737895\pi\)
\(252\) 3.75395 6.99341i 0.236477 0.440544i
\(253\) 9.28348 9.28348i 0.583647 0.583647i
\(254\) −2.66703 + 4.61942i −0.167344 + 0.289848i
\(255\) 8.58158 4.30196i 0.537399 0.269399i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 3.91483 + 14.6104i 0.244201 + 0.911369i 0.973784 + 0.227477i \(0.0730476\pi\)
−0.729583 + 0.683892i \(0.760286\pi\)
\(258\) 1.83361 + 2.70281i 0.114155 + 0.168269i
\(259\) 1.94940 + 13.0950i 0.121130 + 0.813684i
\(260\) −4.29256 3.29721i −0.266213 0.204484i
\(261\) 6.49266 + 8.21919i 0.401886 + 0.508755i
\(262\) −2.58854 + 9.66056i −0.159921 + 0.596832i
\(263\) −3.46268 + 12.9229i −0.213518 + 0.796859i 0.773165 + 0.634205i \(0.218672\pi\)
−0.986683 + 0.162655i \(0.947994\pi\)
\(264\) 2.25564 + 1.95023i 0.138825 + 0.120028i
\(265\) −24.1118 18.5208i −1.48117 1.13772i
\(266\) −10.6551 4.20419i −0.653304 0.257775i
\(267\) −4.69236 + 3.18334i −0.287168 + 0.194817i
\(268\) 3.54455 + 13.2284i 0.216518 + 0.808055i
\(269\) 1.71727 + 2.97440i 0.104704 + 0.181352i 0.913617 0.406576i \(-0.133277\pi\)
−0.808913 + 0.587928i \(0.799944\pi\)
\(270\) 0.998772 + 11.5759i 0.0607833 + 0.704489i
\(271\) 7.63352 13.2217i 0.463704 0.803158i −0.535438 0.844574i \(-0.679854\pi\)
0.999142 + 0.0414162i \(0.0131870\pi\)
\(272\) −1.75262 + 1.75262i −0.106268 + 0.106268i
\(273\) 2.42369 + 10.8248i 0.146689 + 0.655145i
\(274\) 2.47789i 0.149695i
\(275\) −8.31226 2.23617i −0.501248 0.134846i
\(276\) −12.4777 + 4.33378i −0.751066 + 0.260863i
\(277\) −8.14417 + 30.3945i −0.489336 + 1.82623i 0.0703507 + 0.997522i \(0.477588\pi\)
−0.559687 + 0.828704i \(0.689079\pi\)
\(278\) −3.45716 + 0.926344i −0.207347 + 0.0555584i
\(279\) 6.08992 15.3084i 0.364594 0.916492i
\(280\) −1.62460 5.68865i −0.0970881 0.339962i
\(281\) 6.72535i 0.401201i −0.979673 0.200600i \(-0.935711\pi\)
0.979673 0.200600i \(-0.0642893\pi\)
\(282\) 10.4532 0.759073i 0.622482 0.0452021i
\(283\) −1.09393 0.293117i −0.0650272 0.0174240i 0.226159 0.974090i \(-0.427383\pi\)
−0.291186 + 0.956666i \(0.594050\pi\)
\(284\) 5.45624 + 9.45049i 0.323768 + 0.560783i
\(285\) 16.4237 3.37868i 0.972858 0.200136i
\(286\) −4.16729 −0.246417
\(287\) 15.1601 + 1.73606i 0.894870 + 0.102476i
\(288\) −1.18695 2.75520i −0.0699419 0.162352i
\(289\) −9.40213 5.42832i −0.553067 0.319313i
\(290\) 7.73974 + 1.02289i 0.454493 + 0.0600662i
\(291\) 8.99784 + 25.9062i 0.527463 + 1.51865i
\(292\) −3.17204 + 0.849946i −0.185630 + 0.0497393i
\(293\) −23.0536 23.0536i −1.34680 1.34680i −0.889110 0.457694i \(-0.848676\pi\)
−0.457694 0.889110i \(-0.651324\pi\)
\(294\) −4.91446 + 11.0837i −0.286617 + 0.646414i
\(295\) 24.1757 3.17050i 1.40756 0.184593i
\(296\) 4.33358 + 2.50199i 0.251884 + 0.145425i
\(297\) 6.03886 + 6.59953i 0.350410 + 0.382943i
\(298\) 12.9512 + 3.47026i 0.750242 + 0.201027i
\(299\) 9.23008 15.9870i 0.533789 0.924550i
\(300\) 6.54549 + 5.67068i 0.377904 + 0.327397i
\(301\) −3.10350 3.90623i −0.178883 0.225151i
\(302\) −3.87363 + 3.87363i −0.222903 + 0.222903i
\(303\) 13.6662 0.992382i 0.785101 0.0570109i
\(304\) −3.74936 + 2.16470i −0.215041 + 0.124154i
\(305\) −11.4920 14.9921i −0.658028 0.858446i
\(306\) −5.83486 + 4.60919i −0.333557 + 0.263490i
\(307\) −6.95926 6.95926i −0.397186 0.397186i 0.480054 0.877239i \(-0.340617\pi\)
−0.877239 + 0.480054i \(0.840617\pi\)
\(308\) −3.65987 2.71140i −0.208540 0.154497i
\(309\) −4.49874 + 23.4792i −0.255924 + 1.33569i
\(310\) −4.69367 11.3475i −0.266582 0.644498i
\(311\) −7.67936 + 4.43368i −0.435457 + 0.251411i −0.701669 0.712503i \(-0.747561\pi\)
0.266212 + 0.963915i \(0.414228\pi\)
\(312\) 3.77326 + 1.82786i 0.213619 + 0.103482i
\(313\) −1.49927 5.59536i −0.0847439 0.316269i 0.910522 0.413461i \(-0.135680\pi\)
−0.995266 + 0.0971927i \(0.969014\pi\)
\(314\) −11.0485 −0.623501
\(315\) −2.85142 17.5177i −0.160660 0.987010i
\(316\) 3.43924 0.193472
\(317\) −1.09948 4.10330i −0.0617527 0.230464i 0.928151 0.372203i \(-0.121397\pi\)
−0.989904 + 0.141739i \(0.954731\pi\)
\(318\) 21.1948 + 10.2673i 1.18855 + 0.575762i
\(319\) 5.20539 3.00534i 0.291446 0.168267i
\(320\) −2.06543 0.856739i −0.115461 0.0478931i
\(321\) 6.60195 34.4560i 0.368485 1.92315i
\(322\) 18.5080 8.03490i 1.03141 0.447768i
\(323\) 7.58778 + 7.58778i 0.422195 + 0.422195i
\(324\) −2.57318 8.62431i −0.142955 0.479128i
\(325\) −12.1032 0.0120979i −0.671366 0.000671068i
\(326\) 4.30942 2.48804i 0.238677 0.137800i
\(327\) 13.1931 0.958028i 0.729579 0.0529791i
\(328\) 4.07817 4.07817i 0.225179 0.225179i
\(329\) −15.8351 + 2.35731i −0.873020 + 0.129963i
\(330\) 6.65600 + 0.392564i 0.366401 + 0.0216099i
\(331\) −2.70453 + 4.68438i −0.148654 + 0.257477i −0.930730 0.365706i \(-0.880828\pi\)
0.782076 + 0.623183i \(0.214161\pi\)
\(332\) 2.28098 + 0.611186i 0.125185 + 0.0335432i
\(333\) 12.0373 + 8.97014i 0.659638 + 0.491561i
\(334\) 15.5224 + 8.96186i 0.849347 + 0.490371i
\(335\) 24.2856 + 18.6543i 1.32687 + 1.01919i
\(336\) 2.12454 + 4.06033i 0.115903 + 0.221509i
\(337\) 10.8084 + 10.8084i 0.588773 + 0.588773i 0.937299 0.348526i \(-0.113318\pi\)
−0.348526 + 0.937299i \(0.613318\pi\)
\(338\) 6.89716 1.84809i 0.375156 0.100523i
\(339\) 3.62144 + 10.4267i 0.196690 + 0.566302i
\(340\) −0.726158 + 5.49449i −0.0393814 + 0.297981i
\(341\) −8.18775 4.72720i −0.443391 0.255992i
\(342\) −11.9284 + 5.13879i −0.645012 + 0.277874i
\(343\) 6.21215 17.4473i 0.335425 0.942067i
\(344\) −1.88567 −0.101669
\(345\) −16.2483 + 24.6649i −0.874779 + 1.32792i
\(346\) 3.86234 + 6.68977i 0.207641 + 0.359644i
\(347\) 21.2748 + 5.70057i 1.14209 + 0.306023i 0.779792 0.626039i \(-0.215325\pi\)
0.362300 + 0.932061i \(0.381991\pi\)
\(348\) −6.03142 + 0.437978i −0.323318 + 0.0234781i
\(349\) 1.21120i 0.0648340i −0.999474 0.0324170i \(-0.989680\pi\)
0.999474 0.0324170i \(-0.0103205\pi\)
\(350\) −10.6216 7.88547i −0.567751 0.421496i
\(351\) 10.6035 + 6.76560i 0.565972 + 0.361121i
\(352\) −1.66290 + 0.445572i −0.0886328 + 0.0237491i
\(353\) −3.46790 + 12.9424i −0.184578 + 0.688854i 0.810143 + 0.586233i \(0.199390\pi\)
−0.994721 + 0.102621i \(0.967277\pi\)
\(354\) −17.8413 + 6.19668i −0.948252 + 0.329350i
\(355\) 22.5390 + 9.34915i 1.19624 + 0.496201i
\(356\) 3.27373i 0.173507i
\(357\) 8.35804 7.69114i 0.442354 0.407058i
\(358\) −2.52284 + 2.52284i −0.133336 + 0.133336i
\(359\) −6.11095 + 10.5845i −0.322523 + 0.558627i −0.981008 0.193967i \(-0.937864\pi\)
0.658485 + 0.752594i \(0.271198\pi\)
\(360\) −5.85448 3.27491i −0.308558 0.172603i
\(361\) −0.128177 0.222010i −0.00674618 0.0116847i
\(362\) 5.81065 + 21.6857i 0.305401 + 1.13977i
\(363\) −11.5186 + 7.81435i −0.604572 + 0.410147i
\(364\) −5.95745 2.35064i −0.312255 0.123207i
\(365\) −4.47311 + 5.82345i −0.234133 + 0.304813i
\(366\) 11.0686 + 9.56992i 0.578565 + 0.500228i
\(367\) −4.12585 + 15.3979i −0.215368 + 0.803762i 0.770669 + 0.637235i \(0.219922\pi\)
−0.986037 + 0.166527i \(0.946745\pi\)
\(368\) 1.97379 7.36627i 0.102891 0.383994i
\(369\) 13.5771 10.7251i 0.706798 0.558328i
\(370\) 11.0943 1.45495i 0.576763 0.0756391i
\(371\) −33.4636 13.2038i −1.73735 0.685507i
\(372\) 5.34013 + 7.87156i 0.276873 + 0.408121i
\(373\) −5.63264 21.0213i −0.291647 1.08844i −0.943844 0.330392i \(-0.892819\pi\)
0.652196 0.758050i \(-0.273848\pi\)
\(374\) 2.13351 + 3.69535i 0.110321 + 0.191082i
\(375\) 19.3302 + 1.15946i 0.998206 + 0.0598744i
\(376\) −3.02554 + 5.24039i −0.156030 + 0.270252i
\(377\) 5.97610 5.97610i 0.307785 0.307785i
\(378\) 4.91041 + 12.8409i 0.252564 + 0.660463i
\(379\) 20.0870i 1.03180i −0.856649 0.515900i \(-0.827457\pi\)
0.856649 0.515900i \(-0.172543\pi\)
\(380\) −3.70916 + 8.94206i −0.190276 + 0.458718i
\(381\) −3.03124 8.72742i −0.155295 0.447119i
\(382\) 5.98845 22.3492i 0.306396 1.14348i
\(383\) −0.353827 + 0.0948076i −0.0180797 + 0.00484444i −0.267848 0.963461i \(-0.586312\pi\)
0.249768 + 0.968306i \(0.419646\pi\)
\(384\) 1.70111 + 0.325941i 0.0868092 + 0.0166331i
\(385\) −10.1835 + 0.166834i −0.519000 + 0.00850263i
\(386\) 16.0838i 0.818645i
\(387\) −5.61846 0.659361i −0.285602 0.0335172i
\(388\) −15.2939 4.09800i −0.776432 0.208044i
\(389\) −6.65686 11.5300i −0.337516 0.584595i 0.646449 0.762958i \(-0.276253\pi\)
−0.983965 + 0.178362i \(0.942920\pi\)
\(390\) 9.18283 1.88908i 0.464991 0.0956575i
\(391\) −18.9020 −0.955913
\(392\) −3.70264 5.94058i −0.187011 0.300045i
\(393\) −9.72520 14.3353i −0.490572 0.723121i
\(394\) −5.52807 3.19163i −0.278500 0.160792i
\(395\) 6.10352 4.67855i 0.307102 0.235404i
\(396\) −5.11049 + 0.746142i −0.256812 + 0.0374950i
\(397\) −8.50692 + 2.27942i −0.426950 + 0.114401i −0.465894 0.884840i \(-0.654267\pi\)
0.0389441 + 0.999241i \(0.487601\pi\)
\(398\) −1.53003 1.53003i −0.0766936 0.0766936i
\(399\) 17.5788 9.19798i 0.880040 0.460475i
\(400\) −4.83092 + 1.28927i −0.241546 + 0.0644634i
\(401\) 15.4318 + 8.90955i 0.770627 + 0.444922i 0.833098 0.553125i \(-0.186565\pi\)
−0.0624713 + 0.998047i \(0.519898\pi\)
\(402\) −21.3477 10.3413i −1.06472 0.515779i
\(403\) −12.8407 3.44064i −0.639638 0.171391i
\(404\) −3.95547 + 6.85108i −0.196792 + 0.340854i
\(405\) −16.2986 11.8049i −0.809884 0.586591i
\(406\) 9.13673 1.36015i 0.453448 0.0675030i
\(407\) 6.09148 6.09148i 0.301944 0.301944i
\(408\) −0.310924 4.28175i −0.0153930 0.211978i
\(409\) 11.3497 6.55276i 0.561208 0.324013i −0.192423 0.981312i \(-0.561634\pi\)
0.753630 + 0.657299i \(0.228301\pi\)
\(410\) 1.68970 12.7851i 0.0834482 0.631413i
\(411\) −3.24660 2.80701i −0.160143 0.138460i
\(412\) −9.75972 9.75972i −0.480827 0.480827i
\(413\) 26.4637 11.4888i 1.30220 0.565325i
\(414\) 8.45676 21.2580i 0.415627 1.04477i
\(415\) 4.87941 2.01826i 0.239521 0.0990725i
\(416\) −2.09634 + 1.21032i −0.102782 + 0.0593410i
\(417\) 2.70264 5.57907i 0.132349 0.273208i
\(418\) 1.92906 + 7.19934i 0.0943533 + 0.352131i
\(419\) 12.5812 0.614634 0.307317 0.951607i \(-0.400569\pi\)
0.307317 + 0.951607i \(0.400569\pi\)
\(420\) 9.29382 + 4.31565i 0.453492 + 0.210582i
\(421\) −6.71657 −0.327346 −0.163673 0.986515i \(-0.552334\pi\)
−0.163673 + 0.986515i \(0.552334\pi\)
\(422\) −2.30941 8.61882i −0.112420 0.419558i
\(423\) −10.8471 + 14.5561i −0.527406 + 0.707740i
\(424\) −11.7754 + 6.79852i −0.571863 + 0.330165i
\(425\) 6.18572 + 10.7387i 0.300051 + 0.520906i
\(426\) −18.5633 3.55682i −0.899395 0.172329i
\(427\) −17.9593 13.3051i −0.869110 0.643878i
\(428\) 14.3225 + 14.3225i 0.692304 + 0.692304i
\(429\) 4.72081 5.46011i 0.227923 0.263616i
\(430\) −3.34645 + 2.56517i −0.161380 + 0.123703i
\(431\) 16.1423 9.31978i 0.777549 0.448918i −0.0580119 0.998316i \(-0.518476\pi\)
0.835561 + 0.549398i \(0.185143\pi\)
\(432\) 4.95456 + 1.56598i 0.238377 + 0.0753433i
\(433\) −2.13742 + 2.13742i −0.102718 + 0.102718i −0.756598 0.653880i \(-0.773140\pi\)
0.653880 + 0.756598i \(0.273140\pi\)
\(434\) −9.03853 11.3763i −0.433863 0.546082i
\(435\) −10.1080 + 8.98209i −0.484641 + 0.430658i
\(436\) −3.81854 + 6.61391i −0.182875 + 0.316749i
\(437\) −31.8915 8.54530i −1.52558 0.408777i
\(438\) 2.47974 5.11895i 0.118487 0.244593i
\(439\) −12.7163 7.34175i −0.606915 0.350403i 0.164842 0.986320i \(-0.447289\pi\)
−0.771757 + 0.635917i \(0.780622\pi\)
\(440\) −2.34497 + 3.05286i −0.111792 + 0.145539i
\(441\) −8.95497 18.9950i −0.426427 0.904522i
\(442\) 4.24247 + 4.24247i 0.201794 + 0.201794i
\(443\) 7.03018 1.88373i 0.334014 0.0894987i −0.0879143 0.996128i \(-0.528020\pi\)
0.421928 + 0.906629i \(0.361353\pi\)
\(444\) −8.18738 + 2.84367i −0.388556 + 0.134955i
\(445\) −4.45340 5.80980i −0.211112 0.275411i
\(446\) −6.06911 3.50400i −0.287381 0.165919i
\(447\) −19.2183 + 13.0378i −0.908993 + 0.616669i
\(448\) −2.62857 0.301012i −0.124188 0.0142215i
\(449\) 32.4071 1.52939 0.764694 0.644394i \(-0.222890\pi\)
0.764694 + 0.644394i \(0.222890\pi\)
\(450\) −14.8448 + 2.15222i −0.699790 + 0.101456i
\(451\) −4.96447 8.59871i −0.233768 0.404897i
\(452\) −6.15549 1.64936i −0.289530 0.0775793i
\(453\) −0.687202 9.46350i −0.0322876 0.444634i
\(454\) 24.4256i 1.14635i
\(455\) −13.7702 + 3.93257i −0.645557 + 0.184362i
\(456\) 1.41112 7.36476i 0.0660820 0.344886i
\(457\) −9.22656 + 2.47225i −0.431601 + 0.115647i −0.468077 0.883687i \(-0.655053\pi\)
0.0364769 + 0.999334i \(0.488386\pi\)
\(458\) 0.468937 1.75010i 0.0219120 0.0817767i
\(459\) 0.570782 12.8664i 0.0266418 0.600553i
\(460\) −6.51785 15.7578i −0.303896 0.734709i
\(461\) 20.6157i 0.960170i −0.877222 0.480085i \(-0.840606\pi\)
0.877222 0.480085i \(-0.159394\pi\)
\(462\) 7.69856 1.72373i 0.358169 0.0801950i
\(463\) −21.4096 + 21.4096i −0.994986 + 0.994986i −0.999987 0.00500119i \(-0.998408\pi\)
0.00500119 + 0.999987i \(0.498408\pi\)
\(464\) 1.74571 3.02365i 0.0810424 0.140370i
\(465\) 20.1850 + 6.70501i 0.936058 + 0.310937i
\(466\) 0.942716 + 1.63283i 0.0436705 + 0.0756395i
\(467\) −6.88896 25.7099i −0.318783 1.18971i −0.920416 0.390942i \(-0.872149\pi\)
0.601632 0.798773i \(-0.294517\pi\)
\(468\) −6.66937 + 2.87320i −0.308292 + 0.132814i
\(469\) 33.7049 + 13.2990i 1.55635 + 0.614091i
\(470\) 1.75940 + 13.4157i 0.0811549 + 0.618822i
\(471\) 12.5160 14.4760i 0.576706 0.667020i
\(472\) 2.82223 10.5327i 0.129904 0.484807i
\(473\) −0.840203 + 3.13568i −0.0386326 + 0.144179i
\(474\) −3.89606 + 4.50620i −0.178952 + 0.206977i
\(475\) 5.58174 + 20.9150i 0.256108 + 0.959644i
\(476\) 0.965579 + 6.48623i 0.0442572 + 0.297296i
\(477\) −37.4626 + 16.1391i −1.71529 + 0.738957i
\(478\) 1.89894 + 7.08694i 0.0868555 + 0.324149i
\(479\) 15.6629 + 27.1290i 0.715657 + 1.23955i 0.962706 + 0.270551i \(0.0872058\pi\)
−0.247049 + 0.969003i \(0.579461\pi\)
\(480\) 3.46230 1.73565i 0.158032 0.0792214i
\(481\) 6.05644 10.4901i 0.276150 0.478306i
\(482\) 9.95482 9.95482i 0.453430 0.453430i
\(483\) −10.4387 + 33.3519i −0.474979 + 1.51756i
\(484\) 8.03624i 0.365283i
\(485\) −32.7164 + 13.5324i −1.48558 + 0.614476i
\(486\) 14.2148 + 6.39838i 0.644797 + 0.290236i
\(487\) −1.02073 + 3.80941i −0.0462536 + 0.172621i −0.985189 0.171473i \(-0.945147\pi\)
0.938935 + 0.344094i \(0.111814\pi\)
\(488\) −8.15997 + 2.18646i −0.369385 + 0.0989763i
\(489\) −1.62191 + 8.46485i −0.0733452 + 0.382794i
\(490\) −14.6522 5.50571i −0.661919 0.248723i
\(491\) 17.7217i 0.799771i −0.916565 0.399886i \(-0.869050\pi\)
0.916565 0.399886i \(-0.130950\pi\)
\(492\) 0.723489 + 9.96321i 0.0326174 + 0.449176i
\(493\) −8.35887 2.23975i −0.376465 0.100873i
\(494\) 5.23997 + 9.07589i 0.235757 + 0.408343i
\(495\) −8.05444 + 8.27619i −0.362020 + 0.371987i
\(496\) −5.49176 −0.246588
\(497\) 28.6843 + 3.28479i 1.28666 + 0.147343i
\(498\) −3.38474 + 2.29624i −0.151674 + 0.102897i
\(499\) −14.7187 8.49786i −0.658901 0.380417i 0.132957 0.991122i \(-0.457553\pi\)
−0.791858 + 0.610705i \(0.790886\pi\)
\(500\) −6.81945 + 8.85975i −0.304975 + 0.396220i
\(501\) −29.3263 + 10.1857i −1.31020 + 0.455063i
\(502\) 22.4491 6.01522i 1.00195 0.268472i
\(503\) 13.9310 + 13.9310i 0.621153 + 0.621153i 0.945826 0.324673i \(-0.105254\pi\)
−0.324673 + 0.945826i \(0.605254\pi\)
\(504\) −7.72671 1.81601i −0.344175 0.0808915i
\(505\) 2.30016 + 17.5392i 0.102356 + 0.780485i
\(506\) −11.3699 6.56441i −0.505453 0.291824i
\(507\) −5.39186 + 11.1304i −0.239461 + 0.494320i
\(508\) 5.15230 + 1.38055i 0.228596 + 0.0612522i
\(509\) 8.58091 14.8626i 0.380342 0.658772i −0.610769 0.791809i \(-0.709140\pi\)
0.991111 + 0.133037i \(0.0424728\pi\)
\(510\) −6.37645 7.17574i −0.282354 0.317747i
\(511\) −3.18897 + 8.08209i −0.141072 + 0.357531i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 6.77975 21.4503i 0.299333 0.947052i
\(514\) 13.0993 7.56288i 0.577785 0.333584i
\(515\) −30.5969 4.04372i −1.34826 0.178187i
\(516\) 2.13614 2.47067i 0.0940383 0.108765i
\(517\) 7.36613 + 7.36613i 0.323962 + 0.323962i
\(518\) 12.1443 5.27221i 0.533588 0.231648i
\(519\) −13.1405 2.51779i −0.576804 0.110519i
\(520\) −2.07386 + 4.99968i −0.0909448 + 0.219250i
\(521\) −0.555645 + 0.320802i −0.0243433 + 0.0140546i −0.512122 0.858913i \(-0.671141\pi\)
0.487779 + 0.872967i \(0.337807\pi\)
\(522\) 6.25870 8.39871i 0.273936 0.367602i
\(523\) 2.95123 + 11.0142i 0.129048 + 0.481615i 0.999952 0.00983936i \(-0.00313202\pi\)
−0.870903 + 0.491455i \(0.836465\pi\)
\(524\) 10.0014 0.436911
\(525\) 22.3643 4.98394i 0.976057 0.217517i
\(526\) 13.3788 0.583341
\(527\) 3.52299 + 13.1480i 0.153464 + 0.572734i
\(528\) 1.29997 2.68354i 0.0565740 0.116786i
\(529\) 30.4476 17.5789i 1.32381 0.764300i
\(530\) −11.6491 + 28.0837i −0.506005 + 1.21988i
\(531\) 12.0919 30.3959i 0.524746 1.31907i
\(532\) −1.30320 + 11.3801i −0.0565008 + 0.493391i
\(533\) −9.87182 9.87182i −0.427596 0.427596i
\(534\) 4.28934 + 3.70857i 0.185618 + 0.160485i
\(535\) 44.9013 + 5.93420i 1.94125 + 0.256558i
\(536\) 11.8603 6.84754i 0.512286 0.295769i
\(537\) −0.447565 6.16344i −0.0193138 0.265972i
\(538\) 2.42859 2.42859i 0.104704 0.104704i
\(539\) −11.5284 + 3.51015i −0.496562 + 0.151193i
\(540\) 10.9230 3.96081i 0.470051 0.170446i
\(541\) 7.98850 13.8365i 0.343452 0.594877i −0.641619 0.767023i \(-0.721737\pi\)
0.985071 + 0.172147i \(0.0550703\pi\)
\(542\) −14.7468 3.95140i −0.633431 0.169727i
\(543\) −34.9957 16.9528i −1.50181 0.727513i
\(544\) 2.14651 + 1.23929i 0.0920310 + 0.0531341i
\(545\) 2.22054 + 16.9320i 0.0951174 + 0.725289i
\(546\) 9.82864 5.14277i 0.420627 0.220090i
\(547\) −9.35884 9.35884i −0.400155 0.400155i 0.478132 0.878288i \(-0.341314\pi\)
−0.878288 + 0.478132i \(0.841314\pi\)
\(548\) 2.39345 0.641324i 0.102243 0.0273960i
\(549\) −25.0776 + 3.66138i −1.07029 + 0.156264i
\(550\) −0.00860396 + 8.60779i −0.000366874 + 0.367037i
\(551\) −13.0906 7.55785i −0.557677 0.321975i
\(552\) 7.41556 + 10.9308i 0.315627 + 0.465247i
\(553\) 5.41670 7.31150i 0.230342 0.310916i
\(554\) 31.4667 1.33689
\(555\) −10.6615 + 16.1842i −0.452558 + 0.686983i
\(556\) 1.78956 + 3.09961i 0.0758942 + 0.131453i
\(557\) 18.7711 + 5.02971i 0.795358 + 0.213116i 0.633545 0.773706i \(-0.281599\pi\)
0.161813 + 0.986821i \(0.448266\pi\)
\(558\) −16.3630 1.92030i −0.692701 0.0812928i
\(559\) 4.56455i 0.193060i
\(560\) −5.07433 + 3.04157i −0.214430 + 0.128530i
\(561\) −7.25865 1.39079i −0.306461 0.0587194i
\(562\) −6.49619 + 1.74065i −0.274025 + 0.0734249i
\(563\) 8.19533 30.5854i 0.345392 1.28902i −0.546761 0.837288i \(-0.684140\pi\)
0.892154 0.451732i \(-0.149194\pi\)
\(564\) −3.43871 9.90060i −0.144796 0.416890i
\(565\) −13.1677 + 5.44652i −0.553968 + 0.229137i
\(566\) 1.13252i 0.0476032i
\(567\) −22.3871 8.11269i −0.940172 0.340701i
\(568\) 7.71629 7.71629i 0.323768 0.323768i
\(569\) 2.76033 4.78104i 0.115719 0.200432i −0.802348 0.596857i \(-0.796416\pi\)
0.918067 + 0.396425i \(0.129749\pi\)
\(570\) −7.51433 14.9896i −0.314741 0.627847i
\(571\) 10.0033 + 17.3262i 0.418623 + 0.725077i 0.995801 0.0915415i \(-0.0291794\pi\)
−0.577178 + 0.816618i \(0.695846\pi\)
\(572\) 1.07857 + 4.02529i 0.0450974 + 0.168306i
\(573\) 22.4987 + 33.1640i 0.939898 + 1.38545i
\(574\) −2.24681 15.0928i −0.0937799 0.629962i
\(575\) −33.0030 19.0983i −1.37632 0.796455i
\(576\) −2.35411 + 1.85961i −0.0980881 + 0.0774837i
\(577\) 1.98001 7.38948i 0.0824287 0.307628i −0.912386 0.409331i \(-0.865762\pi\)
0.994815 + 0.101702i \(0.0324290\pi\)
\(578\) −2.80991 + 10.4867i −0.116877 + 0.436190i
\(579\) −21.0735 18.2202i −0.875786 0.757205i
\(580\) −1.01515 7.74076i −0.0421520 0.321417i
\(581\) 4.89179 3.88654i 0.202946 0.161241i
\(582\) 22.6947 15.3963i 0.940725 0.638196i
\(583\) 6.05846 + 22.6105i 0.250916 + 0.936430i
\(584\) 1.64197 + 2.84397i 0.0679452 + 0.117684i
\(585\) −7.92741 + 14.1716i −0.327758 + 0.585925i
\(586\) −16.3013 + 28.2347i −0.673402 + 1.16637i
\(587\) −16.6172 + 16.6172i −0.685865 + 0.685865i −0.961315 0.275450i \(-0.911173\pi\)
0.275450 + 0.961315i \(0.411173\pi\)
\(588\) 11.9780 + 1.87833i 0.493963 + 0.0774610i
\(589\) 23.7760i 0.979673i
\(590\) −9.31959 22.5313i −0.383681 0.927600i
\(591\) 10.4441 3.62748i 0.429613 0.149215i
\(592\) 1.29513 4.83348i 0.0532294 0.198655i
\(593\) 41.0736 11.0056i 1.68669 0.451948i 0.717159 0.696909i \(-0.245442\pi\)
0.969533 + 0.244961i \(0.0787753\pi\)
\(594\) 4.81168 7.54118i 0.197426 0.309418i
\(595\) 10.5371 + 10.1974i 0.431979 + 0.418053i
\(596\) 13.4080i 0.549215i
\(597\) 3.73795 0.271435i 0.152984 0.0111091i
\(598\) −17.8311 4.77784i −0.729170 0.195380i
\(599\) 2.61599 + 4.53103i 0.106887 + 0.185133i 0.914507 0.404569i \(-0.132578\pi\)
−0.807621 + 0.589702i \(0.799245\pi\)
\(600\) 3.78335 7.79014i 0.154455 0.318031i
\(601\) 35.0786 1.43089 0.715443 0.698671i \(-0.246225\pi\)
0.715443 + 0.698671i \(0.246225\pi\)
\(602\) −2.96988 + 4.00876i −0.121043 + 0.163385i
\(603\) 37.7327 16.2554i 1.53660 0.661972i
\(604\) 4.74421 + 2.73907i 0.193039 + 0.111451i
\(605\) −10.9321 14.2617i −0.444451 0.579820i
\(606\) −4.49563 12.9437i −0.182623 0.525800i
\(607\) 14.0589 3.76707i 0.570632 0.152900i 0.0380457 0.999276i \(-0.487887\pi\)
0.532587 + 0.846376i \(0.321220\pi\)
\(608\) 3.06134 + 3.06134i 0.124154 + 0.124154i
\(609\) −8.56821 + 13.5120i −0.347201 + 0.547535i
\(610\) −11.5069 + 14.9806i −0.465902 + 0.606548i
\(611\) 12.6851 + 7.32376i 0.513185 + 0.296288i
\(612\) 5.96230 + 4.44310i 0.241012 + 0.179602i
\(613\) 27.7427 + 7.43363i 1.12052 + 0.300241i 0.771092 0.636723i \(-0.219711\pi\)
0.349424 + 0.936965i \(0.386377\pi\)
\(614\) −4.92094 + 8.52331i −0.198593 + 0.343973i
\(615\) 14.8374 + 16.6972i 0.598300 + 0.673298i
\(616\) −1.67177 + 4.23692i −0.0673575 + 0.170711i
\(617\) −24.1611 + 24.1611i −0.972689 + 0.972689i −0.999637 0.0269478i \(-0.991421\pi\)
0.0269478 + 0.999637i \(0.491421\pi\)
\(618\) 23.8436 1.73142i 0.959129 0.0696481i
\(619\) 1.28110 0.739645i 0.0514919 0.0297288i −0.474033 0.880507i \(-0.657202\pi\)
0.525525 + 0.850778i \(0.323869\pi\)
\(620\) −9.74608 + 7.47070i −0.391412 + 0.300030i
\(621\) 18.2729 + 35.1619i 0.733266 + 1.41100i
\(622\) 6.27017 + 6.27017i 0.251411 + 0.251411i
\(623\) −6.95964 5.15603i −0.278832 0.206572i
\(624\) 0.788987 4.11778i 0.0315848 0.164843i
\(625\) −0.0499777 + 25.0000i −0.00199911 + 0.999998i
\(626\) −5.01667 + 2.89637i −0.200506 + 0.115762i
\(627\) −11.6181 5.62809i −0.463982 0.224764i
\(628\) 2.85955 + 10.6720i 0.114109 + 0.425859i
\(629\) −12.4028 −0.494531
\(630\) −16.1828 + 7.28817i −0.644738 + 0.290368i
\(631\) −46.0928 −1.83492 −0.917462 0.397824i \(-0.869765\pi\)
−0.917462 + 0.397824i \(0.869765\pi\)
\(632\) −0.890141 3.32205i −0.0354079 0.132144i
\(633\) 13.9088 + 6.73777i 0.552825 + 0.267802i
\(634\) −3.67892 + 2.12403i −0.146109 + 0.0843558i
\(635\) 11.0217 4.55887i 0.437382 0.180913i
\(636\) 4.43183 23.1300i 0.175733 0.917164i
\(637\) −14.3800 + 8.96278i −0.569758 + 0.355118i
\(638\) −4.25019 4.25019i −0.168267 0.168267i
\(639\) 25.6892 20.2929i 1.01625 0.802777i
\(640\) −0.292973 + 2.21679i −0.0115808 + 0.0876264i
\(641\) −8.05187 + 4.64875i −0.318030 + 0.183614i −0.650514 0.759494i \(-0.725446\pi\)
0.332484 + 0.943109i \(0.392113\pi\)
\(642\) −34.9907 + 2.54088i −1.38097 + 0.100281i
\(643\) 18.9401 18.9401i 0.746924 0.746924i −0.226976 0.973900i \(-0.572884\pi\)
0.973900 + 0.226976i \(0.0728840\pi\)
\(644\) −12.5513 15.7977i −0.494592 0.622518i
\(645\) 0.429987 7.29051i 0.0169307 0.287064i
\(646\) 5.36537 9.29310i 0.211098 0.365632i
\(647\) 33.1966 + 8.89500i 1.30509 + 0.349698i 0.843373 0.537328i \(-0.180566\pi\)
0.461719 + 0.887026i \(0.347233\pi\)
\(648\) −7.66446 + 4.71764i −0.301088 + 0.185326i
\(649\) −16.2573 9.38617i −0.638156 0.368439i
\(650\) 3.12086 + 11.6940i 0.122410 + 0.458675i
\(651\) 25.1447 + 1.04486i 0.985500 + 0.0409512i
\(652\) −3.51862 3.51862i −0.137800 0.137800i
\(653\) −25.9190 + 6.94497i −1.01429 + 0.271778i −0.727420 0.686193i \(-0.759281\pi\)
−0.286868 + 0.957970i \(0.592614\pi\)
\(654\) −4.34000 12.4956i −0.169708 0.488616i
\(655\) 17.7491 13.6053i 0.693515 0.531603i
\(656\) −4.99472 2.88370i −0.195011 0.112590i
\(657\) 3.89788 + 9.04791i 0.152071 + 0.352993i
\(658\) 6.37543 + 14.6855i 0.248540 + 0.572499i
\(659\) 5.40014 0.210360 0.105180 0.994453i \(-0.466458\pi\)
0.105180 + 0.994453i \(0.466458\pi\)
\(660\) −1.34351 6.53081i −0.0522961 0.254211i
\(661\) 12.2794 + 21.2685i 0.477613 + 0.827250i 0.999671 0.0256598i \(-0.00816868\pi\)
−0.522057 + 0.852910i \(0.674835\pi\)
\(662\) 5.22475 + 1.39997i 0.203066 + 0.0544113i
\(663\) −10.3646 + 0.752636i −0.402528 + 0.0292300i
\(664\) 2.36144i 0.0916417i
\(665\) 13.1681 + 21.9688i 0.510639 + 0.851913i
\(666\) 5.54902 13.9487i 0.215020 0.540503i
\(667\) 25.7187 6.89131i 0.995832 0.266832i
\(668\) 4.63900 17.3130i 0.179488 0.669859i
\(669\) 11.4663 3.98251i 0.443313 0.153973i
\(670\) 11.7331 28.2862i 0.453289 1.09279i
\(671\) 14.5434i 0.561443i
\(672\) 3.37211 3.10304i 0.130082 0.119702i
\(673\) 18.8221 18.8221i 0.725540 0.725540i −0.244188 0.969728i \(-0.578521\pi\)
0.969728 + 0.244188i \(0.0785214\pi\)
\(674\) 7.64272 13.2376i 0.294386 0.509892i
\(675\) 13.9967 21.8882i 0.538732 0.842477i
\(676\) −3.57023 6.18383i −0.137317 0.237840i
\(677\) 7.35179 + 27.4373i 0.282552 + 1.05450i 0.950609 + 0.310389i \(0.100459\pi\)
−0.668057 + 0.744110i \(0.732874\pi\)
\(678\) 9.13414 6.19668i 0.350795 0.237982i
\(679\) −32.7994 + 26.0592i −1.25873 + 1.00006i
\(680\) 5.49522 0.720665i 0.210732 0.0276362i
\(681\) −32.0032 27.6699i −1.22636 1.06031i
\(682\) −2.44698 + 9.13224i −0.0936996 + 0.349692i
\(683\) 0.658859 2.45890i 0.0252106 0.0940871i −0.952174 0.305555i \(-0.901158\pi\)
0.977385 + 0.211468i \(0.0678245\pi\)
\(684\) 8.05098 + 10.1919i 0.307837 + 0.389697i
\(685\) 3.37517 4.39406i 0.128959 0.167889i
\(686\) −18.4606 1.48478i −0.704831 0.0566891i
\(687\) 1.76181 + 2.59697i 0.0672172 + 0.0990807i
\(688\) 0.488048 + 1.82142i 0.0186067 + 0.0694410i
\(689\) 16.4568 + 28.5040i 0.626955 + 1.08592i
\(690\) 28.0299 + 9.31090i 1.06708 + 0.354460i
\(691\) −2.47893 + 4.29362i −0.0943028 + 0.163337i −0.909317 0.416103i \(-0.863396\pi\)
0.815015 + 0.579440i \(0.196729\pi\)
\(692\) 5.46217 5.46217i 0.207641 0.207641i
\(693\) −6.46265 + 12.0396i −0.245496 + 0.457346i
\(694\) 22.0253i 0.836070i
\(695\) 7.39242 + 3.06637i 0.280410 + 0.116314i
\(696\) 1.98410 + 5.71255i 0.0752072 + 0.216534i
\(697\) −3.69981 + 13.8079i −0.140140 + 0.523011i
\(698\) −1.16993 + 0.313481i −0.0442824 + 0.0118654i
\(699\) −3.20732 0.614539i −0.121312 0.0232440i
\(700\) −4.86770 + 12.3006i −0.183982 + 0.464920i
\(701\) 7.09309i 0.267902i 0.990988 + 0.133951i \(0.0427665\pi\)
−0.990988 + 0.133951i \(0.957233\pi\)
\(702\) 3.79069 11.9932i 0.143070 0.452656i
\(703\) −20.9260 5.60712i −0.789241 0.211476i
\(704\) 0.860779 + 1.49091i 0.0324418 + 0.0561909i
\(705\) −19.5708 12.8925i −0.737079 0.485559i
\(706\) 13.3989 0.504276
\(707\) 8.33498 + 19.1992i 0.313469 + 0.722060i
\(708\) 10.6032 + 15.6295i 0.398492 + 0.587393i
\(709\) 24.9741 + 14.4188i 0.937921 + 0.541509i 0.889308 0.457309i \(-0.151186\pi\)
0.0486133 + 0.998818i \(0.484520\pi\)
\(710\) 3.19707 24.1907i 0.119984 0.907861i
\(711\) −1.49060 10.2095i −0.0559020 0.382885i
\(712\) −3.16218 + 0.847304i −0.118508 + 0.0317540i
\(713\) −29.6143 29.6143i −1.10906 1.10906i
\(714\) −9.59229 6.08263i −0.358982 0.227637i
\(715\) 7.38989 + 5.67634i 0.276366 + 0.212283i
\(716\) 3.08984 + 1.78392i 0.115473 + 0.0666681i
\(717\) −11.4367 5.54022i −0.427111 0.206903i
\(718\) 11.8054 + 3.16326i 0.440575 + 0.118052i
\(719\) 7.22895 12.5209i 0.269594 0.466951i −0.699163 0.714962i \(-0.746444\pi\)
0.968757 + 0.248012i \(0.0797771\pi\)
\(720\) −1.64807 + 6.50260i −0.0614200 + 0.242338i
\(721\) −36.1195 + 5.37697i −1.34516 + 0.200249i
\(722\) −0.181270 + 0.181270i −0.00674618 + 0.00674618i
\(723\) 1.76604 + 24.3202i 0.0656796 + 0.904478i
\(724\) 19.4428 11.2253i 0.722587 0.417186i
\(725\) −12.3317 12.3563i −0.457987 0.458903i
\(726\) 10.5293 + 9.10366i 0.390780 + 0.337868i
\(727\) 16.0036 + 16.0036i 0.593541 + 0.593541i 0.938586 0.345045i \(-0.112136\pi\)
−0.345045 + 0.938586i \(0.612136\pi\)
\(728\) −0.728643 + 6.36285i −0.0270053 + 0.235823i
\(729\) −24.4863 + 11.3764i −0.906898 + 0.421349i
\(730\) 6.78274 + 2.81348i 0.251041 + 0.104131i
\(731\) 4.04762 2.33689i 0.149707 0.0864332i
\(732\) 6.37907 13.1683i 0.235777 0.486715i
\(733\) −3.08877 11.5274i −0.114086 0.425775i 0.885131 0.465342i \(-0.154069\pi\)
−0.999217 + 0.0395671i \(0.987402\pi\)
\(734\) 15.9411 0.588395
\(735\) 23.8122 12.9608i 0.878325 0.478065i
\(736\) −7.62613 −0.281103
\(737\) −6.10215 22.7735i −0.224775 0.838873i
\(738\) −13.8737 10.3386i −0.510698 0.380571i
\(739\) −29.8148 + 17.2136i −1.09675 + 0.633211i −0.935366 0.353680i \(-0.884930\pi\)
−0.161387 + 0.986891i \(0.551597\pi\)
\(740\) −4.27678 10.3397i −0.157217 0.380094i
\(741\) −17.8275 3.41583i −0.654909 0.125484i
\(742\) −4.09287 + 35.7408i −0.150254 + 1.31209i
\(743\) −33.6273 33.6273i −1.23367 1.23367i −0.962545 0.271121i \(-0.912606\pi\)
−0.271121 0.962545i \(-0.587394\pi\)
\(744\) 6.22121 7.19548i 0.228081 0.263799i
\(745\) −18.2396 23.7949i −0.668246 0.871777i
\(746\) −18.8472 + 10.8814i −0.690045 + 0.398398i
\(747\) 0.825723 7.03604i 0.0302116 0.257435i
\(748\) 3.01724 3.01724i 0.110321 0.110321i
\(749\) 53.0058 7.89076i 1.93679 0.288322i
\(750\) −3.88306 18.9716i −0.141789 0.692745i
\(751\) 18.5581 32.1436i 0.677196 1.17294i −0.298626 0.954370i \(-0.596528\pi\)
0.975822 0.218567i \(-0.0701383\pi\)
\(752\) 5.84489 + 1.56613i 0.213141 + 0.0571110i
\(753\) −17.5496 + 36.2277i −0.639543 + 1.32021i
\(754\) −7.31919 4.22574i −0.266549 0.153892i
\(755\) 12.1455 1.59281i 0.442020 0.0579683i
\(756\) 11.1324 8.06656i 0.404882 0.293378i
\(757\) −8.10894 8.10894i −0.294724 0.294724i 0.544219 0.838943i \(-0.316826\pi\)
−0.838943 + 0.544219i \(0.816826\pi\)
\(758\) −19.4026 + 5.19890i −0.704733 + 0.188833i
\(759\) 21.4810 7.46085i 0.779711 0.270812i
\(760\) 9.59736 + 1.26840i 0.348133 + 0.0460096i
\(761\) −25.8264 14.9109i −0.936205 0.540518i −0.0474360 0.998874i \(-0.515105\pi\)
−0.888769 + 0.458356i \(0.848438\pi\)
\(762\) −7.64550 + 5.18677i −0.276967 + 0.187897i
\(763\) 8.04645 + 18.5346i 0.291301 + 0.670996i
\(764\) −23.1376 −0.837088
\(765\) 16.6253 0.225753i 0.601088 0.00816212i
\(766\) 0.183154 + 0.317232i 0.00661763 + 0.0114621i
\(767\) −25.4960 6.83163i −0.920606 0.246676i
\(768\) −0.125444 1.72750i −0.00452658 0.0623359i
\(769\) 11.1146i 0.400803i −0.979714 0.200401i \(-0.935775\pi\)
0.979714 0.200401i \(-0.0642246\pi\)
\(770\) 2.79684 + 9.79334i 0.100791 + 0.352927i
\(771\) −4.93010 + 25.7305i −0.177553 + 0.926662i
\(772\) 15.5358 4.16280i 0.559145 0.149822i
\(773\) −0.889057 + 3.31800i −0.0319771 + 0.119340i −0.980070 0.198655i \(-0.936343\pi\)
0.948092 + 0.317995i \(0.103009\pi\)
\(774\) 0.817271 + 5.59767i 0.0293762 + 0.201204i
\(775\) −7.13337 + 26.5161i −0.256238 + 0.952485i
\(776\) 15.8334i 0.568388i
\(777\) −6.84952 + 21.8843i −0.245725 + 0.785094i
\(778\) −9.41423 + 9.41423i −0.337516 + 0.337516i
\(779\) −12.4847 + 21.6241i −0.447310 + 0.774764i
\(780\) −4.20141 8.38100i −0.150434 0.300088i
\(781\) −9.39324 16.2696i −0.336117 0.582171i
\(782\) 4.89219 + 18.2579i 0.174944 + 0.652901i
\(783\) 3.91423 + 17.7146i 0.139883 + 0.633069i
\(784\) −4.77984 + 5.11401i −0.170709 + 0.182643i
\(785\) 19.5924 + 15.0493i 0.699281 + 0.537133i
\(786\) −11.3298 + 13.1041i −0.404120 + 0.467407i
\(787\) 13.3051 49.6552i 0.474275 1.77002i −0.149868 0.988706i \(-0.547885\pi\)
0.624142 0.781311i \(-0.285449\pi\)
\(788\) −1.65211 + 6.16576i −0.0588540 + 0.219646i
\(789\) −15.1558 + 17.5293i −0.539561 + 0.624058i
\(790\) −6.09884 4.68465i −0.216987 0.166672i
\(791\) −13.2011 + 10.4883i −0.469377 + 0.372921i
\(792\) 2.04341 + 4.74324i 0.0726094 + 0.168544i
\(793\) 5.29264 + 19.7524i 0.187947 + 0.701429i
\(794\) 4.40351 + 7.62710i 0.156275 + 0.270676i
\(795\) −23.5998 47.0770i −0.836997 1.66965i
\(796\) −1.08190 + 1.87390i −0.0383468 + 0.0664186i
\(797\) 27.0994 27.0994i 0.959910 0.959910i −0.0393164 0.999227i \(-0.512518\pi\)
0.999227 + 0.0393164i \(0.0125180\pi\)
\(798\) −13.4343 14.5992i −0.475569 0.516806i
\(799\) 14.9981i 0.530594i
\(800\) 2.49567 + 4.33262i 0.0882353 + 0.153181i
\(801\) −9.71816 + 1.41887i −0.343374 + 0.0501333i
\(802\) 4.61192 17.2119i 0.162853 0.607774i
\(803\) 5.46085 1.46323i 0.192709 0.0516363i
\(804\) −4.46378 + 23.2968i −0.157425 + 0.821614i
\(805\) −43.7649 10.9617i −1.54251 0.386348i
\(806\) 13.2936i 0.468248i
\(807\) 0.430844 + 5.93318i 0.0151664 + 0.208858i
\(808\) 7.64138 + 2.04750i 0.268823 + 0.0720309i
\(809\) −0.674354 1.16802i −0.0237090 0.0410653i 0.853927 0.520392i \(-0.174214\pi\)
−0.877636 + 0.479327i \(0.840881\pi\)
\(810\) −7.18428 + 18.7986i −0.252430 + 0.660514i
\(811\) 24.7652 0.869624 0.434812 0.900521i \(-0.356815\pi\)
0.434812 + 0.900521i \(0.356815\pi\)
\(812\) −3.67856 8.47337i −0.129092 0.297357i
\(813\) 21.8828 14.8455i 0.767465 0.520655i
\(814\) −7.46051 4.30733i −0.261491 0.150972i
\(815\) −11.0309 1.45786i −0.386397 0.0510666i
\(816\) −4.05538 + 1.40853i −0.141967 + 0.0493083i
\(817\) 7.88564 2.11295i 0.275884 0.0739228i
\(818\) −9.26701 9.26701i −0.324013 0.324013i
\(819\) −4.39592 + 18.7036i −0.153606 + 0.653558i
\(820\) −12.7868 + 1.67692i −0.446535 + 0.0585605i
\(821\) −15.4089 8.89631i −0.537773 0.310483i 0.206403 0.978467i \(-0.433824\pi\)
−0.744176 + 0.667984i \(0.767158\pi\)
\(822\) −1.87108 + 3.86249i −0.0652616 + 0.134720i
\(823\) 1.94629 + 0.521507i 0.0678434 + 0.0181786i 0.292581 0.956241i \(-0.405486\pi\)
−0.224738 + 0.974419i \(0.572153\pi\)
\(824\) −6.90117 + 11.9532i −0.240414 + 0.416408i
\(825\) −11.2684 9.76240i −0.392317 0.339883i
\(826\) −17.9466 22.5885i −0.624442 0.785954i
\(827\) 4.04681 4.04681i 0.140721 0.140721i −0.633237 0.773958i \(-0.718274\pi\)
0.773958 + 0.633237i \(0.218274\pi\)
\(828\) −22.7224 2.66662i −0.789660 0.0926714i
\(829\) −26.8242 + 15.4870i −0.931643 + 0.537884i −0.887331 0.461134i \(-0.847443\pi\)
−0.0443119 + 0.999018i \(0.514110\pi\)
\(830\) −3.21237 4.19078i −0.111503 0.145464i
\(831\) −35.6463 + 41.2286i −1.23656 + 1.43020i
\(832\) 1.71166 + 1.71166i 0.0593410 + 0.0593410i
\(833\) 15.3099 + 8.16288i 0.530455 + 0.282827i
\(834\) −6.08846 1.16658i −0.210826 0.0403954i
\(835\) −15.3189 37.0355i −0.530133 1.28167i
\(836\) 6.45475 3.72665i 0.223242 0.128889i
\(837\) 21.0525 19.2639i 0.727680 0.665859i
\(838\) −3.25627 12.1525i −0.112486 0.419803i
\(839\) −29.6641 −1.02412 −0.512060 0.858950i \(-0.671117\pi\)
−0.512060 + 0.858950i \(0.671117\pi\)
\(840\) 1.76318 10.0941i 0.0608355 0.348280i
\(841\) −16.8100 −0.579656
\(842\) 1.73838 + 6.48771i 0.0599084 + 0.223581i
\(843\) 5.07840 10.4834i 0.174909 0.361066i
\(844\) −7.72742 + 4.46143i −0.265989 + 0.153569i
\(845\) −14.7481 6.11751i −0.507351 0.210449i
\(846\) 16.8675 + 6.71015i 0.579918 + 0.230700i
\(847\) −17.0843 12.6568i −0.587022 0.434894i
\(848\) 9.61456 + 9.61456i 0.330165 + 0.330165i
\(849\) −1.48386 1.28294i −0.0509259 0.0440305i
\(850\) 8.77185 8.75434i 0.300872 0.300271i
\(851\) 33.0484 19.0805i 1.13289 0.654072i
\(852\) 1.36891 + 18.8513i 0.0468981 + 0.645836i
\(853\) −27.7032 + 27.7032i −0.948539 + 0.948539i −0.998739 0.0502004i \(-0.984014\pi\)
0.0502004 + 0.998739i \(0.484014\pi\)
\(854\) −8.20351 + 20.7909i −0.280718 + 0.711451i
\(855\) 28.1523 + 7.13515i 0.962789 + 0.244017i
\(856\) 10.1275 17.5414i 0.346152 0.599553i
\(857\) 22.5283 + 6.03643i 0.769551 + 0.206200i 0.622173 0.782880i \(-0.286250\pi\)
0.147378 + 0.989080i \(0.452917\pi\)
\(858\) −6.49589 3.14677i −0.221766 0.107429i
\(859\) −26.1491 15.0972i −0.892195 0.515109i −0.0175351 0.999846i \(-0.505582\pi\)
−0.874660 + 0.484737i \(0.838915\pi\)
\(860\) 3.34389 + 2.56851i 0.114026 + 0.0875854i
\(861\) 22.3203 + 14.1537i 0.760674 + 0.482357i
\(862\) −13.1802 13.1802i −0.448918 0.448918i
\(863\) 12.8439 3.44152i 0.437212 0.117151i −0.0334974 0.999439i \(-0.510665\pi\)
0.470710 + 0.882288i \(0.343998\pi\)
\(864\) 0.230286 5.19105i 0.00783449 0.176603i
\(865\) 2.26313 17.1240i 0.0769486 0.582234i
\(866\) 2.61779 + 1.51138i 0.0889561 + 0.0513589i
\(867\) −10.5569 15.5613i −0.358531 0.528488i
\(868\) −8.64936 + 11.6750i −0.293579 + 0.396274i
\(869\) −5.92085 −0.200851
\(870\) 11.2922 + 7.43884i 0.382840 + 0.252200i
\(871\) −16.5755 28.7096i −0.561639 0.972787i
\(872\) 7.37685 + 1.97662i 0.249812 + 0.0669369i
\(873\) −5.53646 + 47.1766i −0.187381 + 1.59669i
\(874\) 33.0165i 1.11680i
\(875\) 8.09454 + 28.4513i 0.273645 + 0.961831i
\(876\) −5.58633 1.07037i −0.188745 0.0361644i
\(877\) −24.5656 + 6.58233i −0.829521 + 0.222269i −0.648505 0.761211i \(-0.724605\pi\)
−0.181016 + 0.983480i \(0.557939\pi\)
\(878\) −3.80037 + 14.1832i −0.128256 + 0.478659i
\(879\) −18.5275 53.3436i −0.624916 1.79923i
\(880\) 3.55576 + 1.47493i 0.119865 + 0.0497197i
\(881\) 42.8833i 1.44478i 0.691488 + 0.722388i \(0.256955\pi\)
−0.691488 + 0.722388i \(0.743045\pi\)
\(882\) −16.0300 + 13.5661i −0.539758 + 0.456794i
\(883\) 2.85947 2.85947i 0.0962290 0.0962290i −0.657353 0.753582i \(-0.728324\pi\)
0.753582 + 0.657353i \(0.228324\pi\)
\(884\) 2.99988 5.19595i 0.100897 0.174759i
\(885\) 40.0787 + 13.3133i 1.34723 + 0.447520i
\(886\) −3.63909 6.30308i −0.122258 0.211756i
\(887\) −5.20994 19.4438i −0.174933 0.652858i −0.996563 0.0828372i \(-0.973602\pi\)
0.821630 0.570021i \(-0.193065\pi\)
\(888\) 4.86582 + 7.17241i 0.163286 + 0.240690i
\(889\) 11.0496 8.77896i 0.370593 0.294437i
\(890\) −4.45921 + 5.80534i −0.149473 + 0.194596i
\(891\) 4.42988 + 14.8473i 0.148407 + 0.497402i
\(892\) −1.81381 + 6.76921i −0.0607307 + 0.226650i
\(893\) 6.78041 25.3048i 0.226898 0.846794i
\(894\) 17.5676 + 15.1890i 0.587550 + 0.507996i
\(895\) 7.91019 1.03737i 0.264409 0.0346756i
\(896\) 0.389569 + 2.61691i 0.0130146 + 0.0874249i
\(897\) 26.4597 17.9505i 0.883462 0.599348i
\(898\) −8.38758 31.3029i −0.279897 1.04459i
\(899\) −9.58701 16.6052i −0.319745 0.553814i
\(900\) 5.92100 + 13.7819i 0.197367 + 0.459398i
\(901\) 16.8507 29.1862i 0.561377 0.972333i
\(902\) −7.02082 + 7.02082i −0.233768 + 0.233768i
\(903\) −1.88805 8.43245i −0.0628303 0.280614i
\(904\) 6.37263i 0.211951i
\(905\) 19.2343 46.3702i 0.639371 1.54140i
\(906\) −8.96318 + 3.11312i −0.297782 + 0.103427i
\(907\) 3.66762 13.6878i 0.121781 0.454494i −0.877923 0.478802i \(-0.841071\pi\)
0.999705 + 0.0243072i \(0.00773798\pi\)
\(908\) 23.5933 6.32181i 0.782971 0.209796i
\(909\) 22.0519 + 8.77259i 0.731417 + 0.290969i
\(910\) 7.36256 + 12.2832i 0.244067 + 0.407183i
\(911\) 8.31142i 0.275370i −0.990476 0.137685i \(-0.956034\pi\)
0.990476 0.137685i \(-0.0439661\pi\)
\(912\) −7.47904 + 0.543098i −0.247656 + 0.0179838i
\(913\) −3.92683 1.05219i −0.129959 0.0348225i
\(914\) 4.77602 + 8.27231i 0.157977 + 0.273624i
\(915\) −6.59272 32.0472i −0.217949 1.05945i
\(916\) −1.81183 −0.0598647
\(917\) 15.7518 21.2619i 0.520171 0.702130i
\(918\) −12.5757 + 2.77874i −0.415061 + 0.0917121i
\(919\) 8.31275 + 4.79937i 0.274212 + 0.158316i 0.630800 0.775945i \(-0.282727\pi\)
−0.356588 + 0.934262i \(0.616060\pi\)
\(920\) −13.5339 + 10.3742i −0.446199 + 0.342026i
\(921\) −5.59294 16.1030i −0.184294 0.530612i
\(922\) −19.9133 + 5.33574i −0.655808 + 0.175723i
\(923\) −18.6784 18.6784i −0.614808 0.614808i
\(924\) −3.65753 6.99010i −0.120324 0.229958i
\(925\) −21.6554 12.5316i −0.712025 0.412037i
\(926\) 26.2212 + 15.1388i 0.861683 + 0.497493i
\(927\) −24.7420 + 33.2020i −0.812635 + 1.09050i
\(928\) −3.37245 0.903644i −0.110706 0.0296636i
\(929\) −1.09625 + 1.89876i −0.0359667 + 0.0622962i −0.883448 0.468528i \(-0.844784\pi\)
0.847482 + 0.530825i \(0.178118\pi\)
\(930\) 1.25228 21.2326i 0.0410638 0.696245i
\(931\) 22.1406 + 20.6938i 0.725627 + 0.678213i
\(932\) 1.33320 1.33320i 0.0436705 0.0436705i
\(933\) −15.3184 + 1.11236i −0.501502 + 0.0364170i
\(934\) −23.0509 + 13.3084i −0.754249 + 0.435466i
\(935\) 1.25012 9.45909i 0.0408834 0.309345i
\(936\) 4.50146 + 5.69848i 0.147135 + 0.186261i
\(937\) 26.2254 + 26.2254i 0.856748 + 0.856748i 0.990954 0.134206i \(-0.0428482\pi\)
−0.134206 + 0.990954i \(0.542848\pi\)
\(938\) 4.12238 35.9985i 0.134601 1.17539i
\(939\) 1.88809 9.85408i 0.0616155 0.321576i
\(940\) 12.5032 5.17170i 0.407811 0.168682i
\(941\) −17.9055 + 10.3377i −0.583702 + 0.337000i −0.762603 0.646867i \(-0.776079\pi\)
0.178902 + 0.983867i \(0.442746\pi\)
\(942\) −17.2221 8.34284i −0.561128 0.271824i
\(943\) −11.3836 42.4843i −0.370702 1.38348i
\(944\) −10.9043 −0.354904
\(945\) 8.78309 29.4594i 0.285714 0.958315i
\(946\) 3.24630 0.105546
\(947\) 5.28781 + 19.7344i 0.171831 + 0.641281i 0.997070 + 0.0764972i \(0.0243736\pi\)
−0.825239 + 0.564783i \(0.808960\pi\)
\(948\) 5.36103 + 2.59702i 0.174118 + 0.0843471i
\(949\) 6.88426 3.97463i 0.223472 0.129022i
\(950\) 18.7576 10.8047i 0.608578 0.350552i
\(951\) 1.38461 7.22639i 0.0448991 0.234332i
\(952\) 6.01530 2.61144i 0.194957 0.0846371i
\(953\) 23.8399 + 23.8399i 0.772251 + 0.772251i 0.978500 0.206249i \(-0.0661257\pi\)
−0.206249 + 0.978500i \(0.566126\pi\)
\(954\) 25.2852 + 32.0090i 0.818637 + 1.03633i
\(955\) −41.0616 + 31.4751i −1.32872 + 1.01851i
\(956\) 6.35398 3.66847i 0.205502 0.118647i
\(957\) 10.3834 0.754005i 0.335649 0.0243735i
\(958\) 22.1507 22.1507i 0.715657 0.715657i
\(959\) 2.40623 6.09832i 0.0777011 0.196925i
\(960\) −2.57262 2.89510i −0.0830310 0.0934390i
\(961\) 0.420261 0.727914i 0.0135568 0.0234811i
\(962\) −11.7002 3.13505i −0.377228 0.101078i
\(963\) 36.3092 48.7243i 1.17005 1.57012i
\(964\) −12.1921 7.03912i −0.392682 0.226715i
\(965\) 21.9081 28.5216i 0.705246 0.918144i
\(966\) 34.9172 + 1.45094i 1.12344 + 0.0466832i
\(967\) 27.2454 + 27.2454i 0.876152 + 0.876152i 0.993134 0.116982i \(-0.0373219\pi\)
−0.116982 + 0.993134i \(0.537322\pi\)
\(968\) −7.76241 + 2.07993i −0.249493 + 0.0668515i
\(969\) 6.09807 + 17.5573i 0.195898 + 0.564023i
\(970\) 21.5390 + 28.0992i 0.691574 + 0.902210i
\(971\) 19.3176 + 11.1530i 0.619933 + 0.357918i 0.776843 0.629695i \(-0.216820\pi\)
−0.156910 + 0.987613i \(0.550153\pi\)
\(972\) 2.50130 15.3865i 0.0802291 0.493521i
\(973\) 9.40797 + 1.07736i 0.301606 + 0.0345385i
\(974\) 3.94379 0.126367
\(975\) −18.8572 9.15816i −0.603913 0.293296i
\(976\) 4.22391 + 7.31603i 0.135204 + 0.234181i
\(977\) −46.5829 12.4818i −1.49032 0.399330i −0.580474 0.814279i \(-0.697133\pi\)
−0.909845 + 0.414949i \(0.863799\pi\)
\(978\) 8.59620 0.624222i 0.274876 0.0199604i
\(979\) 5.63592i 0.180125i
\(980\) −1.52584 + 15.5779i −0.0487412 + 0.497619i
\(981\) 21.2886 + 8.46891i 0.679691 + 0.270391i
\(982\) −17.1179 + 4.58672i −0.546254 + 0.146368i
\(983\) −3.30152 + 12.3214i −0.105302 + 0.392993i −0.998379 0.0569107i \(-0.981875\pi\)
0.893077 + 0.449904i \(0.148542\pi\)
\(984\) 9.43647 3.27751i 0.300824 0.104483i
\(985\) 5.45560 + 13.1896i 0.173830 + 0.420257i
\(986\) 8.65374i 0.275591i
\(987\) −26.4636 8.28278i −0.842345 0.263644i
\(988\) 7.41043 7.41043i 0.235757 0.235757i
\(989\) −7.19019 + 12.4538i −0.228635 + 0.396007i
\(990\) 10.0788 + 5.63796i 0.320326 + 0.179186i
\(991\) 20.9965 + 36.3671i 0.666977 + 1.15524i 0.978745 + 0.205080i \(0.0657456\pi\)
−0.311768 + 0.950158i \(0.600921\pi\)
\(992\) 1.42137 + 5.30464i 0.0451286 + 0.168422i
\(993\) −7.75301 + 5.25971i −0.246034 + 0.166912i
\(994\) −4.25117 28.5570i −0.134839 0.905774i
\(995\) 0.629139 + 4.79731i 0.0199450 + 0.152085i
\(996\) 3.09403 + 2.67510i 0.0980382 + 0.0847638i
\(997\) 9.88552 36.8933i 0.313078 1.16842i −0.612688 0.790325i \(-0.709912\pi\)
0.925766 0.378097i \(-0.123421\pi\)
\(998\) −4.39882 + 16.4166i −0.139242 + 0.519659i
\(999\) 11.9900 + 23.0720i 0.379347 + 0.729966i
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.107.8 yes 64
3.2 odd 2 inner 210.2.x.a.107.16 yes 64
5.3 odd 4 inner 210.2.x.a.23.4 64
7.4 even 3 inner 210.2.x.a.137.11 yes 64
15.8 even 4 inner 210.2.x.a.23.11 yes 64
21.11 odd 6 inner 210.2.x.a.137.4 yes 64
35.18 odd 12 inner 210.2.x.a.53.16 yes 64
105.53 even 12 inner 210.2.x.a.53.8 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.x.a.23.4 64 5.3 odd 4 inner
210.2.x.a.23.11 yes 64 15.8 even 4 inner
210.2.x.a.53.8 yes 64 105.53 even 12 inner
210.2.x.a.53.16 yes 64 35.18 odd 12 inner
210.2.x.a.107.8 yes 64 1.1 even 1 trivial
210.2.x.a.107.16 yes 64 3.2 odd 2 inner
210.2.x.a.137.4 yes 64 21.11 odd 6 inner
210.2.x.a.137.11 yes 64 7.4 even 3 inner