Properties

Label 68.2.i.b.7.6
Level $68$
Weight $2$
Character 68.7
Analytic conductor $0.543$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [68,2,Mod(3,68)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(68, base_ring=CyclotomicField(16))
 
chi = DirichletCharacter(H, H._module([8, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("68.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 68 = 2^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 68.i (of order \(16\), degree \(8\), 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: \(0.542982733745\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(6\) over \(\Q(\zeta_{16})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label 7.6
Character \(\chi\) \(=\) 68.7
Dual form 68.2.i.b.39.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.34224 + 0.445422i) q^{2} +(-0.968913 - 0.647407i) q^{3} +(1.60320 + 1.19572i) q^{4} +(0.0404181 + 0.203195i) q^{5} +(-1.01214 - 1.30055i) q^{6} +(-2.58907 - 0.514998i) q^{7} +(1.61927 + 2.31904i) q^{8} +(-0.628394 - 1.51708i) q^{9} +O(q^{10})\) \(q+(1.34224 + 0.445422i) q^{2} +(-0.968913 - 0.647407i) q^{3} +(1.60320 + 1.19572i) q^{4} +(0.0404181 + 0.203195i) q^{5} +(-1.01214 - 1.30055i) q^{6} +(-2.58907 - 0.514998i) q^{7} +(1.61927 + 2.31904i) q^{8} +(-0.628394 - 1.51708i) q^{9} +(-0.0362570 + 0.290739i) q^{10} +(-0.166947 - 0.249854i) q^{11} +(-0.779241 - 2.19647i) q^{12} +(-2.27910 + 2.27910i) q^{13} +(-3.24575 - 1.84448i) q^{14} +(0.0923885 - 0.223045i) q^{15} +(1.14049 + 3.83396i) q^{16} +(-3.65826 - 1.90188i) q^{17} +(-0.167714 - 2.31618i) q^{18} +(4.06173 + 1.68242i) q^{19} +(-0.178167 + 0.374091i) q^{20} +(2.17517 + 2.17517i) q^{21} +(-0.112792 - 0.409726i) q^{22} +(5.73829 - 3.83420i) q^{23} +(-0.0675690 - 3.29528i) q^{24} +(4.57974 - 1.89699i) q^{25} +(-4.07426 + 2.04393i) q^{26} +(-1.05532 + 5.30547i) q^{27} +(-3.53500 - 3.92145i) q^{28} +(3.83218 - 0.762267i) q^{29} +(0.223357 - 0.258228i) q^{30} +(-3.47003 + 5.19327i) q^{31} +(-0.176917 + 5.65409i) q^{32} +0.350170i q^{33} +(-4.06311 - 4.18224i) q^{34} -0.546902i q^{35} +(0.806563 - 3.18356i) q^{36} +(-4.85288 + 7.26286i) q^{37} +(4.70242 + 4.06739i) q^{38} +(3.68376 - 0.732745i) q^{39} +(-0.405771 + 0.422760i) q^{40} +(1.40273 - 7.05199i) q^{41} +(1.95072 + 3.88846i) q^{42} +(4.20432 - 1.74149i) q^{43} +(0.0311067 - 0.600189i) q^{44} +(0.282864 - 0.189004i) q^{45} +(9.40999 - 2.59045i) q^{46} +(-3.51433 - 3.51433i) q^{47} +(1.37709 - 4.45314i) q^{48} +(-0.0291012 - 0.0120541i) q^{49} +(6.99206 - 0.506295i) q^{50} +(2.31324 + 4.21114i) q^{51} +(-6.37903 + 0.928680i) q^{52} +(-2.21996 + 5.35945i) q^{53} +(-3.77967 + 6.65114i) q^{54} +(0.0440216 - 0.0440216i) q^{55} +(-2.99810 - 6.83808i) q^{56} +(-2.84625 - 4.25972i) q^{57} +(5.48322 + 0.683791i) q^{58} +(-4.44465 - 10.7303i) q^{59} +(0.414818 - 0.247115i) q^{60} +(5.17195 + 1.02876i) q^{61} +(-6.97080 + 5.42497i) q^{62} +(0.845664 + 4.25144i) q^{63} +(-2.75592 + 7.51032i) q^{64} +(-0.555220 - 0.370986i) q^{65} +(-0.155973 + 0.470011i) q^{66} -13.4490 q^{67} +(-3.59079 - 7.42336i) q^{68} -8.04220 q^{69} +(0.243602 - 0.734072i) q^{70} +(-7.26888 - 4.85691i) q^{71} +(2.50063 - 3.91383i) q^{72} +(-0.991453 - 4.98437i) q^{73} +(-9.74875 + 7.58689i) q^{74} +(-5.66550 - 1.12694i) q^{75} +(4.50005 + 7.55396i) q^{76} +(0.303564 + 0.732868i) q^{77} +(5.27086 + 0.657308i) q^{78} +(6.48976 + 9.71261i) q^{79} +(-0.732947 + 0.386704i) q^{80} +(0.973957 - 0.973957i) q^{81} +(5.02390 - 8.84063i) q^{82} +(2.51104 - 6.06219i) q^{83} +(0.886330 + 6.08813i) q^{84} +(0.238593 - 0.820211i) q^{85} +(6.41889 - 0.464791i) q^{86} +(-4.20654 - 1.74241i) q^{87} +(0.309090 - 0.791740i) q^{88} +(6.73363 + 6.73363i) q^{89} +(0.463857 - 0.127694i) q^{90} +(7.07449 - 4.72702i) q^{91} +(13.7843 + 0.714414i) q^{92} +(6.72432 - 2.78530i) q^{93} +(-3.15170 - 6.28242i) q^{94} +(-0.177693 + 0.893325i) q^{95} +(3.83191 - 5.36378i) q^{96} +(-1.95863 + 0.389596i) q^{97} +(-0.0336916 - 0.0291418i) q^{98} +(-0.274140 + 0.410279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 8 q^{2} - 8 q^{4} - 16 q^{5} - 8 q^{6} - 8 q^{8} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 8 q^{2} - 8 q^{4} - 16 q^{5} - 8 q^{6} - 8 q^{8} - 16 q^{9} + 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{14} - 16 q^{17} - 16 q^{18} - 24 q^{20} - 16 q^{21} - 8 q^{22} + 8 q^{24} + 16 q^{25} - 16 q^{26} + 40 q^{28} + 56 q^{30} + 32 q^{32} + 56 q^{34} + 56 q^{36} - 16 q^{37} + 32 q^{38} + 56 q^{40} - 48 q^{41} + 40 q^{42} + 24 q^{44} - 64 q^{45} + 8 q^{46} - 32 q^{48} - 16 q^{49} - 16 q^{52} + 48 q^{53} - 24 q^{54} - 48 q^{56} + 64 q^{57} - 64 q^{58} - 112 q^{60} + 16 q^{61} - 64 q^{62} - 56 q^{64} + 96 q^{65} - 96 q^{66} - 32 q^{68} + 32 q^{69} - 80 q^{70} - 64 q^{72} + 64 q^{73} - 16 q^{74} - 64 q^{76} + 16 q^{77} - 112 q^{78} - 24 q^{80} + 64 q^{81} - 40 q^{82} - 80 q^{85} + 64 q^{86} + 56 q^{88} - 16 q^{89} + 48 q^{90} + 104 q^{92} - 16 q^{93} + 88 q^{94} + 144 q^{96} - 16 q^{97} + 72 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/68\mathbb{Z}\right)^\times\).

\(n\) \(35\) \(37\)
\(\chi(n)\) \(-1\) \(e\left(\frac{11}{16}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.34224 + 0.445422i 0.949105 + 0.314961i
\(3\) −0.968913 0.647407i −0.559402 0.373781i 0.243491 0.969903i \(-0.421707\pi\)
−0.802893 + 0.596123i \(0.796707\pi\)
\(4\) 1.60320 + 1.19572i 0.801599 + 0.597861i
\(5\) 0.0404181 + 0.203195i 0.0180755 + 0.0908717i 0.988770 0.149445i \(-0.0477487\pi\)
−0.970695 + 0.240317i \(0.922749\pi\)
\(6\) −1.01214 1.30055i −0.413205 0.530947i
\(7\) −2.58907 0.514998i −0.978576 0.194651i −0.320208 0.947347i \(-0.603753\pi\)
−0.658368 + 0.752696i \(0.728753\pi\)
\(8\) 1.61927 + 2.31904i 0.572499 + 0.819905i
\(9\) −0.628394 1.51708i −0.209465 0.505692i
\(10\) −0.0362570 + 0.290739i −0.0114655 + 0.0919398i
\(11\) −0.166947 0.249854i −0.0503365 0.0753340i 0.805448 0.592667i \(-0.201925\pi\)
−0.855784 + 0.517333i \(0.826925\pi\)
\(12\) −0.779241 2.19647i −0.224948 0.634067i
\(13\) −2.27910 + 2.27910i −0.632109 + 0.632109i −0.948597 0.316488i \(-0.897496\pi\)
0.316488 + 0.948597i \(0.397496\pi\)
\(14\) −3.24575 1.84448i −0.867464 0.492957i
\(15\) 0.0923885 0.223045i 0.0238546 0.0575901i
\(16\) 1.14049 + 3.83396i 0.285124 + 0.958491i
\(17\) −3.65826 1.90188i −0.887258 0.461274i
\(18\) −0.167714 2.31618i −0.0395306 0.545928i
\(19\) 4.06173 + 1.68242i 0.931825 + 0.385975i 0.796371 0.604809i \(-0.206751\pi\)
0.135454 + 0.990784i \(0.456751\pi\)
\(20\) −0.178167 + 0.374091i −0.0398394 + 0.0836494i
\(21\) 2.17517 + 2.17517i 0.474661 + 0.474661i
\(22\) −0.112792 0.409726i −0.0240474 0.0873538i
\(23\) 5.73829 3.83420i 1.19652 0.799487i 0.212430 0.977176i \(-0.431862\pi\)
0.984087 + 0.177689i \(0.0568622\pi\)
\(24\) −0.0675690 3.29528i −0.0137925 0.672646i
\(25\) 4.57974 1.89699i 0.915949 0.379398i
\(26\) −4.07426 + 2.04393i −0.799027 + 0.400848i
\(27\) −1.05532 + 5.30547i −0.203097 + 1.02104i
\(28\) −3.53500 3.92145i −0.668052 0.741085i
\(29\) 3.83218 0.762267i 0.711617 0.141549i 0.174009 0.984744i \(-0.444328\pi\)
0.537608 + 0.843195i \(0.319328\pi\)
\(30\) 0.223357 0.258228i 0.0407791 0.0471458i
\(31\) −3.47003 + 5.19327i −0.623236 + 0.932739i 0.376743 + 0.926318i \(0.377044\pi\)
−0.999979 + 0.00642140i \(0.997956\pi\)
\(32\) −0.176917 + 5.65409i −0.0312749 + 0.999511i
\(33\) 0.350170i 0.0609568i
\(34\) −4.06311 4.18224i −0.696818 0.717248i
\(35\) 0.546902i 0.0924433i
\(36\) 0.806563 3.18356i 0.134427 0.530593i
\(37\) −4.85288 + 7.26286i −0.797809 + 1.19401i 0.179826 + 0.983698i \(0.442447\pi\)
−0.977635 + 0.210308i \(0.932553\pi\)
\(38\) 4.70242 + 4.06739i 0.762833 + 0.659819i
\(39\) 3.68376 0.732745i 0.589873 0.117333i
\(40\) −0.405771 + 0.422760i −0.0641580 + 0.0668442i
\(41\) 1.40273 7.05199i 0.219069 1.10134i −0.702072 0.712106i \(-0.747741\pi\)
0.921141 0.389229i \(-0.127259\pi\)
\(42\) 1.95072 + 3.88846i 0.301003 + 0.600002i
\(43\) 4.20432 1.74149i 0.641153 0.265574i −0.0383307 0.999265i \(-0.512204\pi\)
0.679483 + 0.733691i \(0.262204\pi\)
\(44\) 0.0311067 0.600189i 0.00468952 0.0904819i
\(45\) 0.282864 0.189004i 0.0421669 0.0281750i
\(46\) 9.40999 2.59045i 1.38743 0.381941i
\(47\) −3.51433 3.51433i −0.512617 0.512617i 0.402710 0.915328i \(-0.368068\pi\)
−0.915328 + 0.402710i \(0.868068\pi\)
\(48\) 1.37709 4.45314i 0.198767 0.642755i
\(49\) −0.0291012 0.0120541i −0.00415732 0.00172202i
\(50\) 6.99206 0.506295i 0.988827 0.0716009i
\(51\) 2.31324 + 4.21114i 0.323919 + 0.589677i
\(52\) −6.37903 + 0.928680i −0.884612 + 0.128785i
\(53\) −2.21996 + 5.35945i −0.304935 + 0.736177i 0.694919 + 0.719088i \(0.255440\pi\)
−0.999854 + 0.0170896i \(0.994560\pi\)
\(54\) −3.77967 + 6.65114i −0.514348 + 0.905105i
\(55\) 0.0440216 0.0440216i 0.00593587 0.00593587i
\(56\) −2.99810 6.83808i −0.400639 0.913777i
\(57\) −2.84625 4.25972i −0.376995 0.564213i
\(58\) 5.48322 + 0.683791i 0.719982 + 0.0897862i
\(59\) −4.44465 10.7303i −0.578645 1.39697i −0.894030 0.448008i \(-0.852134\pi\)
0.315385 0.948964i \(-0.397866\pi\)
\(60\) 0.414818 0.247115i 0.0535527 0.0319024i
\(61\) 5.17195 + 1.02876i 0.662200 + 0.131720i 0.514738 0.857348i \(-0.327889\pi\)
0.147463 + 0.989068i \(0.452889\pi\)
\(62\) −6.97080 + 5.42497i −0.885293 + 0.688972i
\(63\) 0.845664 + 4.25144i 0.106544 + 0.535631i
\(64\) −2.75592 + 7.51032i −0.344490 + 0.938790i
\(65\) −0.555220 0.370986i −0.0688665 0.0460151i
\(66\) −0.155973 + 0.470011i −0.0191990 + 0.0578544i
\(67\) −13.4490 −1.64306 −0.821531 0.570164i \(-0.806880\pi\)
−0.821531 + 0.570164i \(0.806880\pi\)
\(68\) −3.59079 7.42336i −0.435448 0.900214i
\(69\) −8.04220 −0.968167
\(70\) 0.243602 0.734072i 0.0291160 0.0877384i
\(71\) −7.26888 4.85691i −0.862657 0.576409i 0.0436416 0.999047i \(-0.486104\pi\)
−0.906298 + 0.422638i \(0.861104\pi\)
\(72\) 2.50063 3.91383i 0.294702 0.461249i
\(73\) −0.991453 4.98437i −0.116041 0.583377i −0.994427 0.105425i \(-0.966380\pi\)
0.878386 0.477951i \(-0.158620\pi\)
\(74\) −9.74875 + 7.58689i −1.13327 + 0.881958i
\(75\) −5.66550 1.12694i −0.654195 0.130128i
\(76\) 4.50005 + 7.55396i 0.516191 + 0.866499i
\(77\) 0.303564 + 0.732868i 0.0345943 + 0.0835181i
\(78\) 5.27086 + 0.657308i 0.596807 + 0.0744255i
\(79\) 6.48976 + 9.71261i 0.730155 + 1.09275i 0.991826 + 0.127597i \(0.0407265\pi\)
−0.261671 + 0.965157i \(0.584274\pi\)
\(80\) −0.732947 + 0.386704i −0.0819459 + 0.0432349i
\(81\) 0.973957 0.973957i 0.108217 0.108217i
\(82\) 5.02390 8.84063i 0.554797 0.976284i
\(83\) 2.51104 6.06219i 0.275623 0.665412i −0.724082 0.689714i \(-0.757736\pi\)
0.999705 + 0.0243018i \(0.00773627\pi\)
\(84\) 0.886330 + 6.08813i 0.0967065 + 0.664269i
\(85\) 0.238593 0.820211i 0.0258791 0.0889644i
\(86\) 6.41889 0.464791i 0.692166 0.0501197i
\(87\) −4.20654 1.74241i −0.450989 0.186806i
\(88\) 0.309090 0.791740i 0.0329491 0.0843998i
\(89\) 6.73363 + 6.73363i 0.713764 + 0.713764i 0.967321 0.253557i \(-0.0816005\pi\)
−0.253557 + 0.967321i \(0.581600\pi\)
\(90\) 0.463857 0.127694i 0.0488949 0.0134601i
\(91\) 7.07449 4.72702i 0.741608 0.495526i
\(92\) 13.7843 + 0.714414i 1.43711 + 0.0744829i
\(93\) 6.72432 2.78530i 0.697280 0.288823i
\(94\) −3.15170 6.28242i −0.325073 0.647982i
\(95\) −0.177693 + 0.893325i −0.0182310 + 0.0916532i
\(96\) 3.83191 5.36378i 0.391093 0.547439i
\(97\) −1.95863 + 0.389596i −0.198869 + 0.0395574i −0.293519 0.955953i \(-0.594827\pi\)
0.0946508 + 0.995511i \(0.469827\pi\)
\(98\) −0.0336916 0.0291418i −0.00340336 0.00294377i
\(99\) −0.274140 + 0.410279i −0.0275521 + 0.0412346i
\(100\) 9.61052 + 2.43485i 0.961052 + 0.243485i
\(101\) 2.30622i 0.229477i 0.993396 + 0.114739i \(0.0366030\pi\)
−0.993396 + 0.114739i \(0.963397\pi\)
\(102\) 1.22919 + 6.68271i 0.121708 + 0.661687i
\(103\) 10.9401i 1.07796i 0.842320 + 0.538978i \(0.181189\pi\)
−0.842320 + 0.538978i \(0.818811\pi\)
\(104\) −8.97582 1.59485i −0.880152 0.156388i
\(105\) −0.354068 + 0.529900i −0.0345535 + 0.0517130i
\(106\) −5.36692 + 6.20484i −0.521282 + 0.602667i
\(107\) 6.21070 1.23539i 0.600411 0.119429i 0.114479 0.993426i \(-0.463480\pi\)
0.485932 + 0.873996i \(0.338480\pi\)
\(108\) −8.03577 + 7.24386i −0.773242 + 0.697040i
\(109\) −0.257660 + 1.29534i −0.0246793 + 0.124071i −0.991161 0.132664i \(-0.957647\pi\)
0.966482 + 0.256735i \(0.0826469\pi\)
\(110\) 0.0786955 0.0394792i 0.00750332 0.00376419i
\(111\) 9.40405 3.89528i 0.892593 0.369724i
\(112\) −0.978335 10.5137i −0.0924440 0.993456i
\(113\) −5.20115 + 3.47530i −0.489283 + 0.326928i −0.775620 0.631201i \(-0.782562\pi\)
0.286337 + 0.958129i \(0.407562\pi\)
\(114\) −1.92297 6.98533i −0.180103 0.654236i
\(115\) 1.01102 + 1.01102i 0.0942784 + 0.0942784i
\(116\) 7.05520 + 3.36015i 0.655059 + 0.311983i
\(117\) 4.88975 + 2.02540i 0.452057 + 0.187248i
\(118\) −1.18625 16.3824i −0.109203 1.50812i
\(119\) 8.49202 + 6.80809i 0.778462 + 0.624097i
\(120\) 0.666854 0.146918i 0.0608752 0.0134118i
\(121\) 4.17496 10.0792i 0.379542 0.916295i
\(122\) 6.48375 + 3.68454i 0.587011 + 0.333583i
\(123\) −5.92463 + 5.92463i −0.534205 + 0.534205i
\(124\) −11.7729 + 4.17665i −1.05723 + 0.375074i
\(125\) 1.14607 + 1.71521i 0.102507 + 0.153413i
\(126\) −0.758602 + 6.08311i −0.0675816 + 0.541927i
\(127\) −6.50849 15.7129i −0.577535 1.39429i −0.895019 0.446028i \(-0.852838\pi\)
0.317484 0.948264i \(-0.397162\pi\)
\(128\) −7.04435 + 8.85308i −0.622639 + 0.782509i
\(129\) −5.20107 1.03456i −0.457929 0.0910876i
\(130\) −0.579991 0.745258i −0.0508686 0.0653634i
\(131\) 3.32444 + 16.7131i 0.290457 + 1.46023i 0.800113 + 0.599849i \(0.204773\pi\)
−0.509656 + 0.860378i \(0.670227\pi\)
\(132\) −0.418706 + 0.561392i −0.0364437 + 0.0488629i
\(133\) −9.64966 6.44769i −0.836731 0.559086i
\(134\) −18.0518 5.99050i −1.55944 0.517500i
\(135\) −1.12070 −0.0964546
\(136\) −1.51317 11.5633i −0.129753 0.991546i
\(137\) 10.2073 0.872070 0.436035 0.899930i \(-0.356382\pi\)
0.436035 + 0.899930i \(0.356382\pi\)
\(138\) −10.7945 3.58217i −0.918892 0.304934i
\(139\) 9.89069 + 6.60875i 0.838918 + 0.560547i 0.899152 0.437637i \(-0.144185\pi\)
−0.0602338 + 0.998184i \(0.519185\pi\)
\(140\) 0.653943 0.876793i 0.0552683 0.0741025i
\(141\) 1.12988 + 5.68028i 0.0951528 + 0.478366i
\(142\) −7.59318 9.75683i −0.637206 0.818775i
\(143\) 0.949934 + 0.188954i 0.0794375 + 0.0158011i
\(144\) 5.09974 4.13946i 0.424978 0.344955i
\(145\) 0.309778 + 0.747871i 0.0257257 + 0.0621073i
\(146\) 0.889383 7.13182i 0.0736058 0.590234i
\(147\) 0.0203926 + 0.0305197i 0.00168196 + 0.00251723i
\(148\) −16.4645 + 5.84110i −1.35337 + 0.480135i
\(149\) −3.06436 + 3.06436i −0.251042 + 0.251042i −0.821398 0.570356i \(-0.806805\pi\)
0.570356 + 0.821398i \(0.306805\pi\)
\(150\) −7.10248 4.03615i −0.579915 0.329550i
\(151\) 4.76310 11.4991i 0.387615 0.935786i −0.602829 0.797871i \(-0.705960\pi\)
0.990444 0.137915i \(-0.0440402\pi\)
\(152\) 2.67543 + 12.1436i 0.217006 + 0.984978i
\(153\) −0.586472 + 6.74499i −0.0474134 + 0.545300i
\(154\) 0.0810193 + 1.11890i 0.00652872 + 0.0901632i
\(155\) −1.19550 0.495193i −0.0960249 0.0397748i
\(156\) 6.78196 + 3.23002i 0.542991 + 0.258608i
\(157\) −10.4900 10.4900i −0.837193 0.837193i 0.151295 0.988489i \(-0.451656\pi\)
−0.988489 + 0.151295i \(0.951656\pi\)
\(158\) 4.38459 + 15.9273i 0.348819 + 1.26711i
\(159\) 5.62069 3.75563i 0.445750 0.297841i
\(160\) −1.15603 + 0.192578i −0.0913926 + 0.0152247i
\(161\) −16.8314 + 6.97181i −1.32650 + 0.549456i
\(162\) 1.74110 0.873460i 0.136794 0.0686255i
\(163\) 0.684996 3.44371i 0.0536531 0.269732i −0.944642 0.328103i \(-0.893591\pi\)
0.998295 + 0.0583710i \(0.0185906\pi\)
\(164\) 10.6811 9.62846i 0.834052 0.751857i
\(165\) −0.0711529 + 0.0141532i −0.00553925 + 0.00110182i
\(166\) 6.07065 7.01843i 0.471174 0.544735i
\(167\) −6.63543 + 9.93062i −0.513465 + 0.768454i −0.994100 0.108466i \(-0.965406\pi\)
0.480635 + 0.876921i \(0.340406\pi\)
\(168\) −1.52212 + 8.56650i −0.117434 + 0.660920i
\(169\) 2.61139i 0.200876i
\(170\) 0.685589 0.994643i 0.0525823 0.0762856i
\(171\) 7.21918i 0.552065i
\(172\) 8.82269 + 2.23525i 0.672724 + 0.170436i
\(173\) 13.3175 19.9310i 1.01251 1.51532i 0.163778 0.986497i \(-0.447632\pi\)
0.848729 0.528827i \(-0.177368\pi\)
\(174\) −4.87007 4.21241i −0.369199 0.319342i
\(175\) −12.8342 + 2.55288i −0.970176 + 0.192980i
\(176\) 0.767530 0.925028i 0.0578548 0.0697266i
\(177\) −2.64042 + 13.2743i −0.198466 + 0.997755i
\(178\) 6.03882 + 12.0374i 0.452629 + 0.902244i
\(179\) 3.46317 1.43449i 0.258849 0.107219i −0.249485 0.968379i \(-0.580261\pi\)
0.508335 + 0.861160i \(0.330261\pi\)
\(180\) 0.679484 + 0.0352165i 0.0506458 + 0.00262488i
\(181\) 2.50680 1.67499i 0.186329 0.124501i −0.458907 0.888484i \(-0.651759\pi\)
0.645236 + 0.763983i \(0.276759\pi\)
\(182\) 11.6012 3.19365i 0.859935 0.236729i
\(183\) −4.34514 4.34514i −0.321202 0.321202i
\(184\) 18.1835 + 7.09873i 1.34051 + 0.523325i
\(185\) −1.67192 0.692533i −0.122922 0.0509160i
\(186\) 10.2663 0.743380i 0.752759 0.0545073i
\(187\) 0.135543 + 1.23155i 0.00991192 + 0.0900596i
\(188\) −1.43200 9.83633i −0.104440 0.717388i
\(189\) 5.46462 13.1927i 0.397492 0.959631i
\(190\) −0.636413 + 1.11991i −0.0461702 + 0.0812465i
\(191\) −3.57657 + 3.57657i −0.258792 + 0.258792i −0.824563 0.565771i \(-0.808579\pi\)
0.565771 + 0.824563i \(0.308579\pi\)
\(192\) 7.53248 5.49265i 0.543610 0.396398i
\(193\) 8.92819 + 13.3620i 0.642665 + 0.961817i 0.999616 + 0.0276937i \(0.00881630\pi\)
−0.356951 + 0.934123i \(0.616184\pi\)
\(194\) −2.80248 0.349486i −0.201206 0.0250917i
\(195\) 0.297781 + 0.718906i 0.0213245 + 0.0514819i
\(196\) −0.0322417 0.0541222i −0.00230298 0.00386587i
\(197\) −7.38428 1.46882i −0.526108 0.104649i −0.0751117 0.997175i \(-0.523931\pi\)
−0.450997 + 0.892526i \(0.648931\pi\)
\(198\) −0.550708 + 0.428584i −0.0391371 + 0.0304581i
\(199\) −2.08094 10.4616i −0.147514 0.741603i −0.981747 0.190191i \(-0.939089\pi\)
0.834233 0.551412i \(-0.185911\pi\)
\(200\) 11.8151 + 7.54887i 0.835450 + 0.533786i
\(201\) 13.0310 + 8.70700i 0.919133 + 0.614145i
\(202\) −1.02724 + 3.09549i −0.0722763 + 0.217798i
\(203\) −10.3143 −0.723924
\(204\) −1.32676 + 9.51729i −0.0928921 + 0.666344i
\(205\) 1.48963 0.104040
\(206\) −4.87294 + 14.6842i −0.339514 + 1.02309i
\(207\) −9.42269 6.29604i −0.654922 0.437605i
\(208\) −11.3373 6.13869i −0.786100 0.425642i
\(209\) −0.257734 1.29572i −0.0178279 0.0896267i
\(210\) −0.711272 + 0.553542i −0.0490824 + 0.0381980i
\(211\) −19.8266 3.94375i −1.36492 0.271499i −0.542343 0.840157i \(-0.682463\pi\)
−0.822574 + 0.568658i \(0.807463\pi\)
\(212\) −9.96745 + 5.93781i −0.684567 + 0.407811i
\(213\) 3.89851 + 9.41184i 0.267122 + 0.644889i
\(214\) 8.88650 + 1.10820i 0.607468 + 0.0757551i
\(215\) 0.523792 + 0.783910i 0.0357223 + 0.0534622i
\(216\) −14.0125 + 6.14366i −0.953428 + 0.418023i
\(217\) 11.6587 11.6587i 0.791443 0.791443i
\(218\) −0.922815 + 1.62389i −0.0625009 + 0.109984i
\(219\) −2.26629 + 5.47130i −0.153141 + 0.369716i
\(220\) 0.123213 0.0179377i 0.00830701 0.00120936i
\(221\) 12.6721 4.00296i 0.852419 0.269268i
\(222\) 14.3575 1.03963i 0.963612 0.0697751i
\(223\) 11.4037 + 4.72357i 0.763649 + 0.316314i 0.730297 0.683130i \(-0.239382\pi\)
0.0333523 + 0.999444i \(0.489382\pi\)
\(224\) 3.36989 14.5477i 0.225161 0.972010i
\(225\) −5.75576 5.75576i −0.383718 0.383718i
\(226\) −8.52915 + 2.34797i −0.567350 + 0.156184i
\(227\) −3.72939 + 2.49190i −0.247528 + 0.165393i −0.673145 0.739510i \(-0.735057\pi\)
0.425617 + 0.904903i \(0.360057\pi\)
\(228\) 0.530332 10.2325i 0.0351221 0.677664i
\(229\) −7.82438 + 3.24097i −0.517050 + 0.214169i −0.625920 0.779887i \(-0.715277\pi\)
0.108871 + 0.994056i \(0.465277\pi\)
\(230\) 0.906701 + 1.80736i 0.0597861 + 0.119174i
\(231\) 0.180337 0.906615i 0.0118653 0.0596509i
\(232\) 7.97307 + 7.65266i 0.523457 + 0.502422i
\(233\) −5.35657 + 1.06549i −0.350921 + 0.0698025i −0.367403 0.930062i \(-0.619753\pi\)
0.0164827 + 0.999864i \(0.494753\pi\)
\(234\) 5.66104 + 4.89656i 0.370074 + 0.320098i
\(235\) 0.572053 0.856137i 0.0373166 0.0558482i
\(236\) 5.70485 22.5174i 0.371354 1.46576i
\(237\) 13.6122i 0.884207i
\(238\) 8.36583 + 12.9206i 0.542276 + 0.837518i
\(239\) 6.30256i 0.407679i −0.979004 0.203839i \(-0.934658\pi\)
0.979004 0.203839i \(-0.0653420\pi\)
\(240\) 0.960517 + 0.0998319i 0.0620011 + 0.00644412i
\(241\) −1.71769 + 2.57071i −0.110646 + 0.165594i −0.882660 0.470012i \(-0.844250\pi\)
0.772014 + 0.635606i \(0.219250\pi\)
\(242\) 10.0933 11.6691i 0.648822 0.750119i
\(243\) 14.3422 2.85284i 0.920052 0.183010i
\(244\) 7.06155 + 7.83353i 0.452069 + 0.501491i
\(245\) 0.00127313 0.00640044i 8.13371e−5 0.000408909i
\(246\) −10.5912 + 5.31329i −0.675271 + 0.338763i
\(247\) −13.0915 + 5.42268i −0.832993 + 0.345037i
\(248\) −17.6623 + 0.362163i −1.12156 + 0.0229974i
\(249\) −6.35769 + 4.24807i −0.402902 + 0.269211i
\(250\) 0.774302 + 2.81271i 0.0489712 + 0.177891i
\(251\) 7.94673 + 7.94673i 0.501593 + 0.501593i 0.911933 0.410339i \(-0.134590\pi\)
−0.410339 + 0.911933i \(0.634590\pi\)
\(252\) −3.72777 + 7.82708i −0.234828 + 0.493060i
\(253\) −1.91599 0.793627i −0.120457 0.0498949i
\(254\) −1.73707 23.9894i −0.108994 1.50523i
\(255\) −0.762187 + 0.640246i −0.0477300 + 0.0400938i
\(256\) −13.3985 + 8.74522i −0.837409 + 0.546576i
\(257\) −9.99534 + 24.1309i −0.623492 + 1.50524i 0.224084 + 0.974570i \(0.428061\pi\)
−0.847576 + 0.530674i \(0.821939\pi\)
\(258\) −6.52025 3.70529i −0.405933 0.230681i
\(259\) 16.3048 16.3048i 1.01313 1.01313i
\(260\) −0.446531 1.25865i −0.0276927 0.0780584i
\(261\) −3.56453 5.33470i −0.220639 0.330210i
\(262\) −2.98218 + 23.9137i −0.184240 + 1.47739i
\(263\) 5.02015 + 12.1197i 0.309556 + 0.747333i 0.999720 + 0.0236804i \(0.00753840\pi\)
−0.690164 + 0.723653i \(0.742462\pi\)
\(264\) −0.812059 + 0.567021i −0.0499788 + 0.0348977i
\(265\) −1.17874 0.234466i −0.0724095 0.0144032i
\(266\) −10.0802 12.9525i −0.618056 0.794169i
\(267\) −2.16490 10.8837i −0.132490 0.666072i
\(268\) −21.5615 16.0813i −1.31708 0.982323i
\(269\) −8.78455 5.86965i −0.535603 0.357879i 0.258163 0.966101i \(-0.416883\pi\)
−0.793767 + 0.608223i \(0.791883\pi\)
\(270\) −1.50425 0.499185i −0.0915455 0.0303794i
\(271\) 21.2908 1.29332 0.646661 0.762778i \(-0.276165\pi\)
0.646661 + 0.762778i \(0.276165\pi\)
\(272\) 3.11952 16.1947i 0.189149 0.981948i
\(273\) −9.91487 −0.600075
\(274\) 13.7006 + 4.54656i 0.827686 + 0.274668i
\(275\) −1.23855 0.827571i −0.0746873 0.0499044i
\(276\) −12.8932 9.61624i −0.776082 0.578829i
\(277\) 0.863478 + 4.34100i 0.0518814 + 0.260825i 0.998017 0.0629454i \(-0.0200494\pi\)
−0.946136 + 0.323771i \(0.895049\pi\)
\(278\) 10.3320 + 13.2760i 0.619671 + 0.796244i
\(279\) 10.0591 + 2.00089i 0.602225 + 0.119790i
\(280\) 1.26829 0.885583i 0.0757948 0.0529237i
\(281\) −3.85099 9.29711i −0.229731 0.554619i 0.766414 0.642347i \(-0.222039\pi\)
−0.996144 + 0.0877281i \(0.972039\pi\)
\(282\) −1.01356 + 8.12755i −0.0603564 + 0.483988i
\(283\) −1.14669 1.71614i −0.0681637 0.102014i 0.795822 0.605531i \(-0.207039\pi\)
−0.863985 + 0.503517i \(0.832039\pi\)
\(284\) −5.84594 16.4781i −0.346893 0.977798i
\(285\) 0.750514 0.750514i 0.0444566 0.0444566i
\(286\) 1.19087 + 0.676742i 0.0704178 + 0.0400166i
\(287\) −7.26352 + 17.5357i −0.428752 + 1.03510i
\(288\) 8.68886 3.28460i 0.511996 0.193547i
\(289\) 9.76570 + 13.9151i 0.574453 + 0.818538i
\(290\) 0.0826778 + 1.14180i 0.00485501 + 0.0670489i
\(291\) 2.14997 + 0.890546i 0.126033 + 0.0522047i
\(292\) 4.37043 9.17645i 0.255760 0.537011i
\(293\) −6.19554 6.19554i −0.361947 0.361947i 0.502582 0.864529i \(-0.332383\pi\)
−0.864529 + 0.502582i \(0.832383\pi\)
\(294\) 0.0137776 + 0.0500480i 0.000803526 + 0.00291886i
\(295\) 2.00071 1.33683i 0.116486 0.0778334i
\(296\) −24.7010 + 0.506489i −1.43572 + 0.0294391i
\(297\) 1.50178 0.622058i 0.0871421 0.0360954i
\(298\) −5.47803 + 2.74817i −0.317334 + 0.159197i
\(299\) −4.33961 + 21.8167i −0.250966 + 1.26169i
\(300\) −7.73542 8.58107i −0.446604 0.495428i
\(301\) −11.7821 + 2.34361i −0.679111 + 0.135084i
\(302\) 11.5152 13.3130i 0.662623 0.766075i
\(303\) 1.49306 2.23452i 0.0857741 0.128370i
\(304\) −1.81797 + 17.4913i −0.104268 + 1.00320i
\(305\) 1.09250i 0.0625562i
\(306\) −3.79155 + 8.79214i −0.216748 + 0.502613i
\(307\) 8.86852i 0.506153i 0.967446 + 0.253077i \(0.0814424\pi\)
−0.967446 + 0.253077i \(0.918558\pi\)
\(308\) −0.389634 + 1.53791i −0.0222014 + 0.0876306i
\(309\) 7.08267 10.6000i 0.402919 0.603011i
\(310\) −1.38408 1.19717i −0.0786102 0.0679945i
\(311\) 6.34176 1.26146i 0.359608 0.0715306i −0.0119797 0.999928i \(-0.503813\pi\)
0.371588 + 0.928398i \(0.378813\pi\)
\(312\) 7.66427 + 7.35628i 0.433904 + 0.416467i
\(313\) 0.714940 3.59425i 0.0404108 0.203159i −0.955305 0.295621i \(-0.904474\pi\)
0.995716 + 0.0924618i \(0.0294736\pi\)
\(314\) −9.40759 18.7525i −0.530901 1.05827i
\(315\) −0.829692 + 0.343670i −0.0467479 + 0.0193636i
\(316\) −1.20922 + 23.3312i −0.0680237 + 1.31248i
\(317\) 25.3863 16.9626i 1.42584 0.952714i 0.427012 0.904246i \(-0.359566\pi\)
0.998825 0.0484675i \(-0.0154337\pi\)
\(318\) 9.21714 2.53736i 0.516871 0.142288i
\(319\) −0.830228 0.830228i −0.0464838 0.0464838i
\(320\) −1.63745 0.256437i −0.0915363 0.0143353i
\(321\) −6.81742 2.82387i −0.380512 0.157613i
\(322\) −25.6972 + 1.86073i −1.43205 + 0.103695i
\(323\) −11.6591 13.8797i −0.648729 0.772285i
\(324\) 2.72603 0.396864i 0.151446 0.0220480i
\(325\) −6.11426 + 14.7611i −0.339158 + 0.818801i
\(326\) 2.45333 4.31716i 0.135877 0.239105i
\(327\) 1.08826 1.08826i 0.0601812 0.0601812i
\(328\) 18.6253 8.16610i 1.02841 0.450897i
\(329\) 7.28897 + 10.9087i 0.401854 + 0.601416i
\(330\) −0.101808 0.0126961i −0.00560436 0.000698898i
\(331\) 2.87291 + 6.93581i 0.157909 + 0.381227i 0.982957 0.183837i \(-0.0588517\pi\)
−0.825048 + 0.565063i \(0.808852\pi\)
\(332\) 11.2744 6.71639i 0.618763 0.368610i
\(333\) 14.0678 + 2.79827i 0.770912 + 0.153344i
\(334\) −13.3296 + 10.3737i −0.729365 + 0.567622i
\(335\) −0.543584 2.73278i −0.0296992 0.149308i
\(336\) −5.85875 + 10.8203i −0.319621 + 0.590295i
\(337\) 21.9290 + 14.6525i 1.19455 + 0.798171i 0.983782 0.179366i \(-0.0574047\pi\)
0.210764 + 0.977537i \(0.432405\pi\)
\(338\) −1.16317 + 3.50510i −0.0632680 + 0.190652i
\(339\) 7.28939 0.395905
\(340\) 1.36326 1.02967i 0.0739330 0.0558417i
\(341\) 1.87688 0.101639
\(342\) 3.21558 9.68985i 0.173879 0.523967i
\(343\) 15.4335 + 10.3123i 0.833330 + 0.556813i
\(344\) 10.8465 + 6.93006i 0.584805 + 0.373644i
\(345\) −0.325050 1.63414i −0.0175001 0.0879790i
\(346\) 26.7529 20.8202i 1.43824 1.11930i
\(347\) 20.2479 + 4.02755i 1.08696 + 0.216210i 0.705880 0.708331i \(-0.250552\pi\)
0.381082 + 0.924541i \(0.375552\pi\)
\(348\) −4.66049 7.82328i −0.249828 0.419372i
\(349\) 4.21534 + 10.1767i 0.225642 + 0.544748i 0.995638 0.0933009i \(-0.0297418\pi\)
−0.769996 + 0.638049i \(0.779742\pi\)
\(350\) −18.3637 2.29006i −0.981579 0.122409i
\(351\) −9.68652 14.4969i −0.517028 0.773788i
\(352\) 1.44223 0.899732i 0.0768714 0.0479559i
\(353\) 15.0514 15.0514i 0.801103 0.801103i −0.182165 0.983268i \(-0.558311\pi\)
0.983268 + 0.182165i \(0.0583105\pi\)
\(354\) −9.45671 + 16.6411i −0.502618 + 0.884465i
\(355\) 0.693107 1.67331i 0.0367863 0.0888100i
\(356\) 2.74380 + 18.8469i 0.145421 + 0.998884i
\(357\) −3.82042 12.0942i −0.202198 0.640095i
\(358\) 5.28735 0.382857i 0.279445 0.0202346i
\(359\) −4.82742 1.99958i −0.254781 0.105534i 0.251637 0.967822i \(-0.419031\pi\)
−0.506419 + 0.862288i \(0.669031\pi\)
\(360\) 0.896343 + 0.349926i 0.0472414 + 0.0184427i
\(361\) 0.232078 + 0.232078i 0.0122146 + 0.0122146i
\(362\) 4.11079 1.13165i 0.216058 0.0594781i
\(363\) −10.5706 + 7.06302i −0.554810 + 0.370712i
\(364\) 16.9940 + 0.880770i 0.890728 + 0.0461649i
\(365\) 0.972729 0.402917i 0.0509149 0.0210897i
\(366\) −3.89679 7.76763i −0.203688 0.406020i
\(367\) 3.23267 16.2517i 0.168744 0.848334i −0.799948 0.600069i \(-0.795140\pi\)
0.968692 0.248265i \(-0.0798604\pi\)
\(368\) 21.2447 + 17.6275i 1.10746 + 0.918898i
\(369\) −11.5799 + 2.30338i −0.602824 + 0.119909i
\(370\) −1.93565 1.67425i −0.100629 0.0870403i
\(371\) 8.50773 12.7327i 0.441699 0.661050i
\(372\) 14.1109 + 3.57503i 0.731615 + 0.185356i
\(373\) 4.35156i 0.225315i −0.993634 0.112658i \(-0.964064\pi\)
0.993634 0.112658i \(-0.0359364\pi\)
\(374\) −0.366626 + 1.71340i −0.0189578 + 0.0885978i
\(375\) 2.40386i 0.124135i
\(376\) 2.45922 13.8405i 0.126825 0.713771i
\(377\) −6.99664 + 10.4712i −0.360345 + 0.539295i
\(378\) 13.2111 15.2737i 0.679508 0.785596i
\(379\) −32.5789 + 6.48036i −1.67347 + 0.332873i −0.938513 0.345243i \(-0.887797\pi\)
−0.734955 + 0.678116i \(0.762797\pi\)
\(380\) −1.35305 + 1.21971i −0.0694098 + 0.0625696i
\(381\) −3.86647 + 19.4380i −0.198085 + 0.995841i
\(382\) −6.39369 + 3.20752i −0.327130 + 0.164111i
\(383\) −7.31551 + 3.03018i −0.373805 + 0.154835i −0.561673 0.827359i \(-0.689842\pi\)
0.187868 + 0.982194i \(0.439842\pi\)
\(384\) 12.5569 4.01730i 0.640792 0.205007i
\(385\) −0.136646 + 0.0913039i −0.00696412 + 0.00465328i
\(386\) 6.03203 + 21.9118i 0.307022 + 1.11528i
\(387\) −5.28393 5.28393i −0.268597 0.268597i
\(388\) −3.60592 1.71738i −0.183063 0.0871867i
\(389\) −17.1480 7.10295i −0.869440 0.360134i −0.0970480 0.995280i \(-0.530940\pi\)
−0.772392 + 0.635146i \(0.780940\pi\)
\(390\) 0.0794758 + 1.09758i 0.00402441 + 0.0555781i
\(391\) −28.2844 + 3.11296i −1.43040 + 0.157429i
\(392\) −0.0191688 0.0870059i −0.000968169 0.00439446i
\(393\) 7.59907 18.3458i 0.383322 0.925422i
\(394\) −9.25721 5.26063i −0.466371 0.265027i
\(395\) −1.71125 + 1.71125i −0.0861025 + 0.0861025i
\(396\) −0.930080 + 0.329964i −0.0467383 + 0.0165813i
\(397\) −17.1410 25.6534i −0.860284 1.28751i −0.956377 0.292134i \(-0.905635\pi\)
0.0960934 0.995372i \(-0.469365\pi\)
\(398\) 1.86671 14.9688i 0.0935695 0.750320i
\(399\) 5.17540 + 12.4945i 0.259094 + 0.625508i
\(400\) 12.4962 + 15.3951i 0.624808 + 0.769753i
\(401\) −29.1903 5.80630i −1.45769 0.289953i −0.598301 0.801272i \(-0.704157\pi\)
−0.859391 + 0.511319i \(0.829157\pi\)
\(402\) 13.6123 + 17.4911i 0.678922 + 0.872378i
\(403\) −3.92744 19.7446i −0.195640 0.983547i
\(404\) −2.75760 + 3.69732i −0.137196 + 0.183949i
\(405\) 0.237269 + 0.158538i 0.0117900 + 0.00787782i
\(406\) −13.8443 4.59423i −0.687080 0.228008i
\(407\) 2.62483 0.130108
\(408\) −6.02004 + 12.1835i −0.298036 + 0.603172i
\(409\) 13.8906 0.686848 0.343424 0.939180i \(-0.388413\pi\)
0.343424 + 0.939180i \(0.388413\pi\)
\(410\) 1.99943 + 0.663512i 0.0987448 + 0.0327685i
\(411\) −9.89000 6.60829i −0.487838 0.325963i
\(412\) −13.0813 + 17.5391i −0.644468 + 0.864089i
\(413\) 5.98141 + 30.0706i 0.294326 + 1.47968i
\(414\) −9.84309 12.6478i −0.483761 0.621608i
\(415\) 1.33330 + 0.265210i 0.0654492 + 0.0130186i
\(416\) −12.4830 13.2895i −0.612031 0.651569i
\(417\) −5.30467 12.8066i −0.259771 0.627142i
\(418\) 0.231200 1.85396i 0.0113084 0.0906802i
\(419\) −4.80731 7.19466i −0.234853 0.351482i 0.695259 0.718760i \(-0.255290\pi\)
−0.930111 + 0.367278i \(0.880290\pi\)
\(420\) −1.20126 + 0.426168i −0.0586153 + 0.0207949i
\(421\) −27.3530 + 27.3530i −1.33310 + 1.33310i −0.430523 + 0.902580i \(0.641671\pi\)
−0.902580 + 0.430523i \(0.858329\pi\)
\(422\) −24.8553 14.1246i −1.20994 0.687576i
\(423\) −3.12312 + 7.53989i −0.151851 + 0.366602i
\(424\) −16.0235 + 3.53023i −0.778171 + 0.171443i
\(425\) −20.3617 1.77044i −0.987689 0.0858789i
\(426\) 1.04049 + 14.3694i 0.0504118 + 0.696200i
\(427\) −12.8607 5.32709i −0.622374 0.257796i
\(428\) 11.4342 + 5.44571i 0.552691 + 0.263228i
\(429\) −0.798073 0.798073i −0.0385314 0.0385314i
\(430\) 0.353882 + 1.28550i 0.0170657 + 0.0619924i
\(431\) −20.5318 + 13.7189i −0.988984 + 0.660818i −0.941133 0.338037i \(-0.890237\pi\)
−0.0478508 + 0.998854i \(0.515237\pi\)
\(432\) −21.5446 + 2.00479i −1.03656 + 0.0964553i
\(433\) 8.90292 3.68771i 0.427847 0.177220i −0.158360 0.987381i \(-0.550621\pi\)
0.586207 + 0.810161i \(0.300621\pi\)
\(434\) 20.8417 10.4557i 1.00044 0.501889i
\(435\) 0.184029 0.925174i 0.00882350 0.0443587i
\(436\) −1.96195 + 1.76860i −0.0939605 + 0.0847008i
\(437\) 29.7582 5.91927i 1.42353 0.283157i
\(438\) −5.47893 + 6.33432i −0.261793 + 0.302666i
\(439\) 11.7906 17.6458i 0.562733 0.842189i −0.435586 0.900147i \(-0.643459\pi\)
0.998319 + 0.0579578i \(0.0184589\pi\)
\(440\) 0.173371 + 0.0308050i 0.00826513 + 0.00146857i
\(441\) 0.0517235i 0.00246303i
\(442\) 18.7920 + 0.271513i 0.893844 + 0.0129146i
\(443\) 9.44084i 0.448548i −0.974526 0.224274i \(-0.927999\pi\)
0.974526 0.224274i \(-0.0720010\pi\)
\(444\) 19.7342 + 4.99972i 0.936545 + 0.237276i
\(445\) −1.09608 + 1.64040i −0.0519593 + 0.0777626i
\(446\) 13.2025 + 11.4196i 0.625157 + 0.540735i
\(447\) 4.95299 0.985211i 0.234268 0.0465989i
\(448\) 11.0031 18.0254i 0.519846 0.851622i
\(449\) 5.32246 26.7578i 0.251182 1.26278i −0.624933 0.780678i \(-0.714874\pi\)
0.876116 0.482101i \(-0.160126\pi\)
\(450\) −5.16186 10.2893i −0.243332 0.485044i
\(451\) −1.99615 + 0.826833i −0.0939951 + 0.0389341i
\(452\) −12.4940 0.647540i −0.587667 0.0304577i
\(453\) −12.0596 + 8.05800i −0.566611 + 0.378598i
\(454\) −6.11567 + 1.68357i −0.287023 + 0.0790137i
\(455\) 1.24645 + 1.24645i 0.0584343 + 0.0584343i
\(456\) 5.26961 13.4982i 0.246772 0.632112i
\(457\) 16.4293 + 6.80523i 0.768529 + 0.318335i 0.732276 0.681008i \(-0.238458\pi\)
0.0362526 + 0.999343i \(0.488458\pi\)
\(458\) −11.9458 + 0.864993i −0.558189 + 0.0404185i
\(459\) 13.9510 17.4017i 0.651178 0.812241i
\(460\) 0.411968 + 2.82977i 0.0192081 + 0.131939i
\(461\) −3.73198 + 9.00979i −0.173816 + 0.419628i −0.986647 0.162871i \(-0.947925\pi\)
0.812832 + 0.582498i \(0.197925\pi\)
\(462\) 0.645881 1.13657i 0.0300491 0.0528778i
\(463\) 5.79189 5.79189i 0.269172 0.269172i −0.559595 0.828766i \(-0.689043\pi\)
0.828766 + 0.559595i \(0.189043\pi\)
\(464\) 7.29308 + 13.8231i 0.338573 + 0.641720i
\(465\) 0.837745 + 1.25377i 0.0388495 + 0.0581424i
\(466\) −7.66438 0.955796i −0.355046 0.0442764i
\(467\) 13.6837 + 33.0353i 0.633205 + 1.52869i 0.835572 + 0.549381i \(0.185137\pi\)
−0.202367 + 0.979310i \(0.564863\pi\)
\(468\) 5.41742 + 9.09390i 0.250420 + 0.420366i
\(469\) 34.8205 + 6.92623i 1.60786 + 0.319824i
\(470\) 1.14917 0.894334i 0.0530074 0.0412526i
\(471\) 3.37260 + 16.9552i 0.155401 + 0.781254i
\(472\) 17.6870 27.6827i 0.814111 1.27420i
\(473\) −1.13702 0.759731i −0.0522801 0.0349325i
\(474\) 6.06317 18.2708i 0.278490 0.839205i
\(475\) 21.7932 0.999942
\(476\) 5.47380 + 21.0688i 0.250891 + 0.965688i
\(477\) 9.52571 0.436152
\(478\) 2.80730 8.45952i 0.128403 0.386930i
\(479\) 0.719534 + 0.480777i 0.0328763 + 0.0219673i 0.571900 0.820323i \(-0.306207\pi\)
−0.539023 + 0.842291i \(0.681207\pi\)
\(480\) 1.24477 + 0.561833i 0.0568159 + 0.0256441i
\(481\) −5.49257 27.6130i −0.250440 1.25904i
\(482\) −3.45060 + 2.68540i −0.157170 + 0.122317i
\(483\) 20.8218 + 4.14171i 0.947425 + 0.188455i
\(484\) 18.7453 11.1669i 0.852058 0.507588i
\(485\) −0.158328 0.382238i −0.00718930 0.0173565i
\(486\) 20.5213 + 2.55914i 0.930867 + 0.116085i
\(487\) 3.52366 + 5.27353i 0.159672 + 0.238966i 0.902676 0.430321i \(-0.141600\pi\)
−0.743004 + 0.669287i \(0.766600\pi\)
\(488\) 5.98904 + 13.6598i 0.271111 + 0.618351i
\(489\) −2.89318 + 2.89318i −0.130834 + 0.130834i
\(490\) 0.00455973 0.00802383i 0.000205988 0.000362479i
\(491\) 2.46559 5.95246i 0.111271 0.268631i −0.858429 0.512933i \(-0.828559\pi\)
0.969699 + 0.244302i \(0.0785589\pi\)
\(492\) −16.5826 + 2.41414i −0.747600 + 0.108838i
\(493\) −15.4688 4.49977i −0.696681 0.202659i
\(494\) −19.9873 + 1.44728i −0.899271 + 0.0651162i
\(495\) −0.0944470 0.0391212i −0.00424508 0.00175837i
\(496\) −23.8684 7.38109i −1.07172 0.331421i
\(497\) 16.3183 + 16.3183i 0.731977 + 0.731977i
\(498\) −10.4257 + 2.87007i −0.467187 + 0.128611i
\(499\) −29.0506 + 19.4110i −1.30048 + 0.868955i −0.996489 0.0837189i \(-0.973320\pi\)
−0.303994 + 0.952674i \(0.598320\pi\)
\(500\) −0.213543 + 4.12021i −0.00954994 + 0.184261i
\(501\) 12.8583 5.32608i 0.574467 0.237952i
\(502\) 7.12675 + 14.2060i 0.318082 + 0.634047i
\(503\) 7.58005 38.1075i 0.337978 1.69913i −0.321093 0.947048i \(-0.604050\pi\)
0.659071 0.752081i \(-0.270950\pi\)
\(504\) −8.48991 + 8.84536i −0.378170 + 0.394004i
\(505\) −0.468612 + 0.0932128i −0.0208530 + 0.00414791i
\(506\) −2.21821 1.91866i −0.0986114 0.0852947i
\(507\) 1.69063 2.53021i 0.0750835 0.112370i
\(508\) 8.35384 32.9732i 0.370642 1.46295i
\(509\) 13.2888i 0.589014i 0.955649 + 0.294507i \(0.0951555\pi\)
−0.955649 + 0.294507i \(0.904844\pi\)
\(510\) −1.30821 + 0.519867i −0.0579287 + 0.0230201i
\(511\) 13.4155i 0.593466i
\(512\) −21.8793 + 5.77016i −0.966939 + 0.255007i
\(513\) −13.2125 + 19.7739i −0.583346 + 0.873039i
\(514\) −24.1645 + 27.9372i −1.06585 + 1.23226i
\(515\) −2.22297 + 0.442176i −0.0979557 + 0.0194846i
\(516\) −7.10130 7.87764i −0.312617 0.346794i
\(517\) −0.291363 + 1.46478i −0.0128141 + 0.0644209i
\(518\) 29.1474 14.6224i 1.28066 0.642471i
\(519\) −25.8069 + 10.6896i −1.13280 + 0.469220i
\(520\) −0.0387193 1.88831i −0.00169795 0.0828077i
\(521\) 5.26182 3.51584i 0.230525 0.154032i −0.434944 0.900458i \(-0.643232\pi\)
0.665468 + 0.746426i \(0.268232\pi\)
\(522\) −2.40826 8.74815i −0.105407 0.382896i
\(523\) 23.7396 + 23.7396i 1.03806 + 1.03806i 0.999247 + 0.0388121i \(0.0123574\pi\)
0.0388121 + 0.999247i \(0.487643\pi\)
\(524\) −14.6545 + 30.7695i −0.640183 + 1.34417i
\(525\) 14.0880 + 5.83544i 0.614850 + 0.254679i
\(526\) 1.33985 + 18.5036i 0.0584200 + 0.806795i
\(527\) 22.5713 12.3987i 0.983220 0.540098i
\(528\) −1.34254 + 0.399367i −0.0584265 + 0.0173802i
\(529\) 9.42516 22.7543i 0.409789 0.989319i
\(530\) −1.47771 0.839746i −0.0641878 0.0364763i
\(531\) −13.4858 + 13.4858i −0.585232 + 0.585232i
\(532\) −7.76066 21.8753i −0.336467 0.948412i
\(533\) 12.8752 + 19.2692i 0.557688 + 0.834640i
\(534\) 1.94203 15.5728i 0.0840397 0.673901i
\(535\) 0.502049 + 1.21205i 0.0217055 + 0.0524016i
\(536\) −21.7777 31.1889i −0.940651 1.34716i
\(537\) −4.28421 0.852182i −0.184877 0.0367744i
\(538\) −9.17648 11.7913i −0.395626 0.508359i
\(539\) 0.00184660 + 0.00928348i 7.95386e−5 + 0.000399868i
\(540\) −1.79671 1.34005i −0.0773180 0.0576665i
\(541\) −15.8217 10.5717i −0.680228 0.454514i 0.166850 0.985982i \(-0.446640\pi\)
−0.847078 + 0.531469i \(0.821640\pi\)
\(542\) 28.5772 + 9.48336i 1.22750 + 0.407345i
\(543\) −3.51327 −0.150769
\(544\) 11.4006 20.3476i 0.488797 0.872398i
\(545\) −0.273622 −0.0117207
\(546\) −13.3081 4.41630i −0.569534 0.189000i
\(547\) 36.2785 + 24.2405i 1.55116 + 1.03645i 0.975831 + 0.218527i \(0.0701252\pi\)
0.575327 + 0.817924i \(0.304875\pi\)
\(548\) 16.3644 + 12.2051i 0.699051 + 0.521377i
\(549\) −1.68931 8.49271i −0.0720978 0.362460i
\(550\) −1.29381 1.66247i −0.0551681 0.0708881i
\(551\) 16.8477 + 3.35122i 0.717737 + 0.142767i
\(552\) −13.0225 18.6502i −0.554274 0.793805i
\(553\) −11.8005 28.4888i −0.501807 1.21147i
\(554\) −0.774582 + 6.21126i −0.0329089 + 0.263891i
\(555\) 1.17160 + 1.75342i 0.0497315 + 0.0744285i
\(556\) 7.95452 + 22.4217i 0.337347 + 0.950891i
\(557\) −19.8868 + 19.8868i −0.842632 + 0.842632i −0.989201 0.146568i \(-0.953177\pi\)
0.146568 + 0.989201i \(0.453177\pi\)
\(558\) 12.6105 + 7.16622i 0.533845 + 0.303370i
\(559\) −5.61305 + 13.5511i −0.237407 + 0.573150i
\(560\) 2.09680 0.623738i 0.0886060 0.0263578i
\(561\) 0.665982 1.28101i 0.0281178 0.0540844i
\(562\) −1.02780 14.1942i −0.0433553 0.598748i
\(563\) −23.6462 9.79456i −0.996567 0.412791i −0.176030 0.984385i \(-0.556325\pi\)
−0.820537 + 0.571593i \(0.806325\pi\)
\(564\) −4.98062 + 10.4576i −0.209722 + 0.440346i
\(565\) −0.916384 0.916384i −0.0385526 0.0385526i
\(566\) −0.774723 2.81423i −0.0325640 0.118291i
\(567\) −3.02323 + 2.02006i −0.126964 + 0.0848344i
\(568\) −0.506909 24.7215i −0.0212694 1.03729i
\(569\) 2.58622 1.07125i 0.108420 0.0449091i −0.327814 0.944742i \(-0.606312\pi\)
0.436234 + 0.899833i \(0.356312\pi\)
\(570\) 1.34166 0.673072i 0.0561961 0.0281919i
\(571\) 3.97592 19.9883i 0.166387 0.836485i −0.803944 0.594705i \(-0.797269\pi\)
0.970331 0.241780i \(-0.0777311\pi\)
\(572\) 1.29700 + 1.43879i 0.0542302 + 0.0601587i
\(573\) 5.78089 1.14989i 0.241500 0.0480373i
\(574\) −17.5601 + 20.3017i −0.732946 + 0.847377i
\(575\) 19.0065 28.4452i 0.792624 1.18625i
\(576\) 13.1255 0.538499i 0.546897 0.0224375i
\(577\) 2.06460i 0.0859505i −0.999076 0.0429752i \(-0.986316\pi\)
0.999076 0.0429752i \(-0.0136837\pi\)
\(578\) 6.90978 + 23.0273i 0.287409 + 0.957808i
\(579\) 18.7268i 0.778258i
\(580\) −0.397610 + 1.56939i −0.0165099 + 0.0651656i
\(581\) −9.62328 + 14.4023i −0.399241 + 0.597506i
\(582\) 2.48910 + 2.15297i 0.103176 + 0.0892433i
\(583\) 1.70970 0.340080i 0.0708085 0.0140847i
\(584\) 9.95354 10.3703i 0.411880 0.429125i
\(585\) −0.213918 + 1.07544i −0.00884440 + 0.0444638i
\(586\) −5.55625 11.0755i −0.229527 0.457525i
\(587\) 3.72794 1.54416i 0.153869 0.0637344i −0.304420 0.952538i \(-0.598463\pi\)
0.458289 + 0.888803i \(0.348463\pi\)
\(588\) −0.00379969 + 0.0733132i −0.000156697 + 0.00302338i
\(589\) −22.8316 + 15.2556i −0.940761 + 0.628596i
\(590\) 3.28088 0.903185i 0.135072 0.0371836i
\(591\) 6.20380 + 6.20380i 0.255190 + 0.255190i
\(592\) −33.3802 10.3225i −1.37192 0.424254i
\(593\) −10.4763 4.33943i −0.430211 0.178199i 0.157061 0.987589i \(-0.449798\pi\)
−0.587272 + 0.809390i \(0.699798\pi\)
\(594\) 2.29282 0.166023i 0.0940756 0.00681201i
\(595\) −1.04014 + 2.00071i −0.0426417 + 0.0820210i
\(596\) −8.57691 + 1.24865i −0.351324 + 0.0511469i
\(597\) −4.75666 + 11.4836i −0.194677 + 0.469992i
\(598\) −15.5424 + 27.3502i −0.635577 + 1.11843i
\(599\) −20.6575 + 20.6575i −0.844044 + 0.844044i −0.989382 0.145338i \(-0.953573\pi\)
0.145338 + 0.989382i \(0.453573\pi\)
\(600\) −6.56056 14.9633i −0.267834 0.610876i
\(601\) −14.8206 22.1806i −0.604546 0.904767i 0.395359 0.918527i \(-0.370620\pi\)
−0.999905 + 0.0137592i \(0.995620\pi\)
\(602\) −16.8583 2.10234i −0.687093 0.0856848i
\(603\) 8.45129 + 20.4032i 0.344163 + 0.830884i
\(604\) 21.3860 12.7401i 0.870182 0.518385i
\(605\) 2.21680 + 0.440949i 0.0901257 + 0.0179271i
\(606\) 2.99935 2.33422i 0.121840 0.0948211i
\(607\) −4.87713 24.5190i −0.197957 0.995196i −0.944162 0.329480i \(-0.893126\pi\)
0.746206 0.665716i \(-0.231874\pi\)
\(608\) −10.2312 + 22.6677i −0.414928 + 0.919298i
\(609\) 9.99369 + 6.67757i 0.404965 + 0.270589i
\(610\) −0.486622 + 1.46639i −0.0197027 + 0.0593724i
\(611\) 16.0190 0.648060
\(612\) −9.00537 + 10.1123i −0.364020 + 0.408765i
\(613\) −43.1667 −1.74349 −0.871743 0.489964i \(-0.837010\pi\)
−0.871743 + 0.489964i \(0.837010\pi\)
\(614\) −3.95023 + 11.9037i −0.159418 + 0.480392i
\(615\) −1.44332 0.964394i −0.0582002 0.0388881i
\(616\) −1.20800 + 1.89069i −0.0486717 + 0.0761781i
\(617\) −4.67959 23.5259i −0.188393 0.947116i −0.953081 0.302715i \(-0.902107\pi\)
0.764688 0.644401i \(-0.222893\pi\)
\(618\) 14.2281 11.0729i 0.572337 0.445417i
\(619\) −3.89440 0.774645i −0.156529 0.0311356i 0.116204 0.993225i \(-0.462928\pi\)
−0.272733 + 0.962090i \(0.587928\pi\)
\(620\) −1.32451 2.22338i −0.0531937 0.0892931i
\(621\) 14.2865 + 34.4907i 0.573298 + 1.38406i
\(622\) 9.07403 + 1.13159i 0.363835 + 0.0453725i
\(623\) −13.9660 20.9016i −0.559537 0.837407i
\(624\) 7.01062 + 13.2877i 0.280649 + 0.531934i
\(625\) 17.2237 17.2237i 0.688949 0.688949i
\(626\) 2.56057 4.50588i 0.102341 0.180091i
\(627\) −0.589135 + 1.42230i −0.0235278 + 0.0568011i
\(628\) −4.27443 29.3607i −0.170568 1.17162i
\(629\) 31.5662 17.3398i 1.25863 0.691383i
\(630\) −1.26672 + 0.0917232i −0.0504674 + 0.00365434i
\(631\) −8.69103 3.59994i −0.345985 0.143311i 0.202923 0.979195i \(-0.434956\pi\)
−0.548907 + 0.835883i \(0.684956\pi\)
\(632\) −12.0153 + 30.7774i −0.477942 + 1.22426i
\(633\) 16.6570 + 16.6570i 0.662057 + 0.662057i
\(634\) 41.6299 11.4602i 1.65334 0.455142i
\(635\) 2.92972 1.95758i 0.116262 0.0776841i
\(636\) 13.5018 + 0.699773i 0.535380 + 0.0277478i
\(637\) 0.0937973 0.0388521i 0.00371638 0.00153938i
\(638\) −0.744561 1.48416i −0.0294774 0.0587586i
\(639\) −2.80059 + 14.0795i −0.110789 + 0.556976i
\(640\) −2.08362 1.07356i −0.0823625 0.0424360i
\(641\) 16.3834 3.25887i 0.647107 0.128717i 0.139384 0.990238i \(-0.455488\pi\)
0.507722 + 0.861521i \(0.330488\pi\)
\(642\) −7.89279 6.82693i −0.311503 0.269437i
\(643\) −23.1308 + 34.6177i −0.912189 + 1.36519i 0.0186768 + 0.999826i \(0.494055\pi\)
−0.930866 + 0.365362i \(0.880945\pi\)
\(644\) −35.3205 8.94854i −1.39182 0.352622i
\(645\) 1.09865i 0.0432592i
\(646\) −9.46695 23.8230i −0.372472 0.937304i
\(647\) 27.2486i 1.07125i −0.844454 0.535627i \(-0.820075\pi\)
0.844454 0.535627i \(-0.179925\pi\)
\(648\) 3.83575 + 0.681547i 0.150682 + 0.0267737i
\(649\) −1.93900 + 2.90192i −0.0761124 + 0.113910i
\(650\) −14.7817 + 17.0895i −0.579787 + 0.670306i
\(651\) −18.8442 + 3.74834i −0.738561 + 0.146909i
\(652\) 5.21591 4.70189i 0.204271 0.184140i
\(653\) 1.56384 7.86196i 0.0611978 0.307662i −0.938047 0.346507i \(-0.887368\pi\)
0.999245 + 0.0388446i \(0.0123677\pi\)
\(654\) 1.94545 0.975972i 0.0760729 0.0381635i
\(655\) −3.26165 + 1.35102i −0.127443 + 0.0527887i
\(656\) 28.6369 2.66474i 1.11808 0.104041i
\(657\) −6.93865 + 4.63626i −0.270703 + 0.180878i
\(658\) 4.92454 + 17.8887i 0.191979 + 0.697375i
\(659\) −32.4205 32.4205i −1.26292 1.26292i −0.949669 0.313254i \(-0.898581\pi\)
−0.313254 0.949669i \(-0.601419\pi\)
\(660\) −0.130996 0.0623888i −0.00509900 0.00242848i
\(661\) 27.4450 + 11.3681i 1.06749 + 0.442167i 0.846103 0.533020i \(-0.178943\pi\)
0.221383 + 0.975187i \(0.428943\pi\)
\(662\) 0.766761 + 10.5892i 0.0298010 + 0.411559i
\(663\) −14.8697 4.32550i −0.577492 0.167988i
\(664\) 18.1245 3.99312i 0.703369 0.154963i
\(665\) 0.920121 2.22137i 0.0356808 0.0861410i
\(666\) 17.6360 + 10.0221i 0.683379 + 0.388347i
\(667\) 19.0675 19.0675i 0.738295 0.738295i
\(668\) −22.5122 + 7.98663i −0.871022 + 0.309012i
\(669\) −7.99113 11.9596i −0.308955 0.462384i
\(670\) 0.487622 3.91017i 0.0188385 0.151063i
\(671\) −0.606402 1.46398i −0.0234099 0.0565165i
\(672\) −12.6834 + 11.9138i −0.489274 + 0.459584i
\(673\) 14.1499 + 2.81459i 0.545438 + 0.108494i 0.460116 0.887859i \(-0.347808\pi\)
0.0853226 + 0.996353i \(0.472808\pi\)
\(674\) 22.9073 + 29.4347i 0.882358 + 1.13378i
\(675\) 5.23133 + 26.2996i 0.201354 + 1.01227i
\(676\) −3.12250 + 4.18657i −0.120096 + 0.161022i
\(677\) −33.2451 22.2136i −1.27771 0.853739i −0.283271 0.959040i \(-0.591420\pi\)
−0.994440 + 0.105301i \(0.966420\pi\)
\(678\) 9.78409 + 3.24685i 0.375756 + 0.124695i
\(679\) 5.27167 0.202308
\(680\) 2.28845 0.774836i 0.0877581 0.0297136i
\(681\) 5.22673 0.200289
\(682\) 2.51921 + 0.836001i 0.0964656 + 0.0320121i
\(683\) −26.0760 17.4234i −0.997769 0.666688i −0.0544296 0.998518i \(-0.517334\pi\)
−0.943339 + 0.331830i \(0.892334\pi\)
\(684\) 8.63214 11.5738i 0.330058 0.442535i
\(685\) 0.412560 + 2.07408i 0.0157631 + 0.0792465i
\(686\) 16.1221 + 20.7160i 0.615543 + 0.790940i
\(687\) 9.67937 + 1.92535i 0.369291 + 0.0734565i
\(688\) 11.4718 + 14.1330i 0.437358 + 0.538817i
\(689\) −7.15523 17.2742i −0.272592 0.658096i
\(690\) 0.291586 2.33818i 0.0111005 0.0890131i
\(691\) −5.75723 8.61631i −0.219016 0.327780i 0.705650 0.708561i \(-0.250655\pi\)
−0.924665 + 0.380781i \(0.875655\pi\)
\(692\) 45.1825 16.0293i 1.71758 0.609344i
\(693\) 0.921059 0.921059i 0.0349882 0.0349882i
\(694\) 25.3835 + 14.4248i 0.963543 + 0.547556i
\(695\) −0.943104 + 2.27686i −0.0357740 + 0.0863661i
\(696\) −2.77082 12.5766i −0.105028 0.476714i
\(697\) −18.5436 + 23.1302i −0.702388 + 0.876117i
\(698\) 1.12505 + 15.5372i 0.0425837 + 0.588091i
\(699\) 5.87986 + 2.43552i 0.222397 + 0.0921197i
\(700\) −23.6283 11.2534i −0.893068 0.425338i
\(701\) 11.5837 + 11.5837i 0.437510 + 0.437510i 0.891173 0.453663i \(-0.149883\pi\)
−0.453663 + 0.891173i \(0.649883\pi\)
\(702\) −6.54437 23.7729i −0.247001 0.897249i
\(703\) −31.9303 + 21.3352i −1.20427 + 0.804671i
\(704\) 2.33658 0.565250i 0.0880632 0.0213037i
\(705\) −1.10854 + 0.459172i −0.0417500 + 0.0172934i
\(706\) 26.9067 13.4983i 1.01265 0.508015i
\(707\) 1.18770 5.97095i 0.0446679 0.224561i
\(708\) −20.1055 + 18.1241i −0.755609 + 0.681145i
\(709\) 16.8423 3.35014i 0.632525 0.125817i 0.131593 0.991304i \(-0.457991\pi\)
0.500932 + 0.865487i \(0.332991\pi\)
\(710\) 1.67564 1.93725i 0.0628857 0.0727037i
\(711\) 10.6567 15.9488i 0.399656 0.598127i
\(712\) −4.71200 + 26.5192i −0.176590 + 0.993848i
\(713\) 43.1053i 1.61431i
\(714\) 0.259132 17.9350i 0.00969776 0.671202i
\(715\) 0.200659i 0.00750423i
\(716\) 7.26740 + 1.84121i 0.271596 + 0.0688094i
\(717\) −4.08032 + 6.10663i −0.152382 + 0.228056i
\(718\) −5.58888 4.83415i −0.208575 0.180409i
\(719\) −13.9584 + 2.77649i −0.520560 + 0.103546i −0.448375 0.893846i \(-0.647997\pi\)
−0.0721846 + 0.997391i \(0.522997\pi\)
\(720\) 1.04724 + 0.868934i 0.0390283 + 0.0323833i
\(721\) 5.63411 28.3246i 0.209825 1.05486i
\(722\) 0.208131 + 0.414876i 0.00774583 + 0.0154401i
\(723\) 3.32859 1.37875i 0.123791 0.0512761i
\(724\) 6.02171 + 0.312095i 0.223795 + 0.0115989i
\(725\) 16.1044 10.7606i 0.598101 0.399638i
\(726\) −17.3342 + 4.77189i −0.643333 + 0.177101i
\(727\) 19.1837 + 19.1837i 0.711483 + 0.711483i 0.966846 0.255362i \(-0.0821947\pi\)
−0.255362 + 0.966846i \(0.582195\pi\)
\(728\) 22.4177 + 8.75170i 0.830854 + 0.324360i
\(729\) −19.5609 8.10239i −0.724478 0.300088i
\(730\) 1.48510 0.107536i 0.0549660 0.00398009i
\(731\) −18.6926 1.62531i −0.691370 0.0601141i
\(732\) −1.77054 12.1617i −0.0654411 0.449510i
\(733\) 2.15675 5.20684i 0.0796612 0.192319i −0.879031 0.476765i \(-0.841809\pi\)
0.958692 + 0.284445i \(0.0918094\pi\)
\(734\) 11.5779 20.3738i 0.427348 0.752010i
\(735\) −0.00537724 + 0.00537724i −0.000198342 + 0.000198342i
\(736\) 20.6637 + 33.1231i 0.761675 + 1.22094i
\(737\) 2.24528 + 3.36030i 0.0827061 + 0.123778i
\(738\) −16.5689 2.06624i −0.609910 0.0760595i
\(739\) −3.71981 8.98042i −0.136835 0.330350i 0.840577 0.541693i \(-0.182216\pi\)
−0.977412 + 0.211343i \(0.932216\pi\)
\(740\) −1.85235 3.10942i −0.0680936 0.114305i
\(741\) 16.1952 + 3.22143i 0.594946 + 0.118342i
\(742\) 17.0908 13.3008i 0.627424 0.488287i
\(743\) −0.923079 4.64063i −0.0338645 0.170248i 0.960152 0.279478i \(-0.0901615\pi\)
−0.994016 + 0.109230i \(0.965161\pi\)
\(744\) 17.3477 + 11.0838i 0.635999 + 0.406353i
\(745\) −0.746519 0.498808i −0.0273504 0.0182749i
\(746\) 1.93828 5.84083i 0.0709655 0.213848i
\(747\) −10.7747 −0.394227
\(748\) −1.25528 + 2.13649i −0.0458978 + 0.0781177i
\(749\) −16.7162 −0.610795
\(750\) 1.07073 3.22656i 0.0390977 0.117817i
\(751\) 7.97875 + 5.33123i 0.291149 + 0.194539i 0.692563 0.721357i \(-0.256481\pi\)
−0.401414 + 0.915897i \(0.631481\pi\)
\(752\) 9.46573 17.4819i 0.345180 0.637498i
\(753\) −2.55492 12.8445i −0.0931066 0.468078i
\(754\) −14.0552 + 10.9384i −0.511862 + 0.398352i
\(755\) 2.52908 + 0.503066i 0.0920428 + 0.0183085i
\(756\) 24.5357 14.6164i 0.892356 0.531595i
\(757\) 12.3012 + 29.6977i 0.447094 + 1.07938i 0.973406 + 0.229088i \(0.0735745\pi\)
−0.526312 + 0.850292i \(0.676426\pi\)
\(758\) −46.6151 5.81320i −1.69314 0.211145i
\(759\) 1.34262 + 2.00938i 0.0487342 + 0.0729358i
\(760\) −2.35939 + 1.03446i −0.0855842 + 0.0375237i
\(761\) 18.1276 18.1276i 0.657126 0.657126i −0.297573 0.954699i \(-0.596177\pi\)
0.954699 + 0.297573i \(0.0961771\pi\)
\(762\) −13.8478 + 24.3682i −0.501654 + 0.882769i
\(763\) 1.33420 3.22104i 0.0483012 0.116609i
\(764\) −10.0105 + 1.45737i −0.362169 + 0.0527257i
\(765\) −1.39425 + 0.153451i −0.0504094 + 0.00554803i
\(766\) −11.1689 + 0.808736i −0.403547 + 0.0292208i
\(767\) 34.5854 + 14.3257i 1.24881 + 0.517272i
\(768\) 18.6437 + 0.200951i 0.672748 + 0.00725121i
\(769\) 19.8264 + 19.8264i 0.714959 + 0.714959i 0.967568 0.252610i \(-0.0812888\pi\)
−0.252610 + 0.967568i \(0.581289\pi\)
\(770\) −0.224080 + 0.0616863i −0.00807528 + 0.00222302i
\(771\) 25.3071 16.9097i 0.911414 0.608987i
\(772\) −1.66356 + 32.0976i −0.0598728 + 1.15522i
\(773\) 2.09682 0.868531i 0.0754173 0.0312389i −0.344656 0.938729i \(-0.612004\pi\)
0.420073 + 0.907490i \(0.362004\pi\)
\(774\) −4.73871 9.44587i −0.170329 0.339525i
\(775\) −6.04027 + 30.3665i −0.216973 + 1.09080i
\(776\) −4.07504 3.91128i −0.146285 0.140407i
\(777\) −26.3538 + 5.24209i −0.945437 + 0.188059i
\(778\) −19.8529 17.1720i −0.711762 0.615644i
\(779\) 17.5619 26.2833i 0.629221 0.941697i
\(780\) −0.382211 + 1.50861i −0.0136853 + 0.0540170i
\(781\) 2.62701i 0.0940018i
\(782\) −39.3509 8.42013i −1.40718 0.301103i
\(783\) 21.1360i 0.755337i
\(784\) 0.0130253 0.125321i 0.000465189 0.00447574i
\(785\) 1.70753 2.55550i 0.0609445 0.0912099i
\(786\) 18.3713 21.2396i 0.655284 0.757591i
\(787\) 31.5846 6.28256i 1.12587 0.223949i 0.403178 0.915121i \(-0.367905\pi\)
0.722690 + 0.691172i \(0.242905\pi\)
\(788\) −10.0822 11.1844i −0.359162 0.398427i
\(789\) 2.98230 14.9930i 0.106173 0.533766i
\(790\) −3.05914 + 1.53468i −0.108839 + 0.0546014i
\(791\) 15.2559 6.31920i 0.542438 0.224685i
\(792\) −1.39536 + 0.0286116i −0.0495820 + 0.00101667i
\(793\) −14.1321 + 9.44274i −0.501844 + 0.335322i
\(794\) −11.5808 42.0679i −0.410986 1.49293i
\(795\) 0.990303 + 0.990303i 0.0351224 + 0.0351224i
\(796\) 9.17300 19.2602i 0.325128 0.682661i
\(797\) 3.01331 + 1.24815i 0.106737 + 0.0442119i 0.435413 0.900231i \(-0.356602\pi\)
−0.328676 + 0.944443i \(0.606602\pi\)
\(798\) 1.38128 + 19.0758i 0.0488968 + 0.675277i
\(799\) 6.17249 + 19.5401i 0.218367 + 0.691281i
\(800\) 9.91552 + 26.2299i 0.350567 + 0.927366i
\(801\) 5.98407 14.4468i 0.211437 0.510453i
\(802\) −36.5940 20.7954i −1.29218 0.734312i
\(803\) −1.07985 + 1.07985i −0.0381070 + 0.0381070i
\(804\) 10.4800 + 29.5405i 0.369603 + 1.04181i
\(805\) −2.09693 3.13828i −0.0739072 0.110610i
\(806\) 3.52311 28.2512i 0.124096 0.995107i
\(807\) 4.71141 + 11.3744i 0.165850 + 0.400396i
\(808\) −5.34821 + 3.73439i −0.188150 + 0.131375i
\(809\) −40.6651 8.08880i −1.42971 0.284387i −0.581284 0.813701i \(-0.697449\pi\)
−0.848426 + 0.529314i \(0.822449\pi\)
\(810\) 0.247855 + 0.318480i 0.00870873 + 0.0111903i
\(811\) −5.63562 28.3322i −0.197894 0.994878i −0.944224 0.329303i \(-0.893186\pi\)
0.746331 0.665575i \(-0.231814\pi\)
\(812\) −16.5359 12.3331i −0.580297 0.432806i
\(813\) −20.6289 13.7838i −0.723487 0.483418i
\(814\) 3.52315 + 1.16916i 0.123486 + 0.0409790i
\(815\) 0.727432 0.0254808
\(816\) −13.5071 + 13.6717i −0.472843 + 0.478604i
\(817\) 20.0067 0.699947
\(818\) 18.6445 + 6.18719i 0.651891 + 0.216330i
\(819\) −11.6168 7.76211i −0.405924 0.271230i
\(820\) 2.38817 + 1.78118i 0.0833984 + 0.0622015i
\(821\) 3.01130 + 15.1388i 0.105095 + 0.528348i 0.997085 + 0.0762937i \(0.0243087\pi\)
−0.891990 + 0.452054i \(0.850691\pi\)
\(822\) −10.3312 13.2751i −0.360344 0.463023i
\(823\) −19.5009 3.87896i −0.679758 0.135212i −0.156877 0.987618i \(-0.550143\pi\)
−0.522881 + 0.852406i \(0.675143\pi\)
\(824\) −25.3705 + 17.7149i −0.883822 + 0.617129i
\(825\) 0.664270 + 1.60369i 0.0231269 + 0.0558333i
\(826\) −5.36562 + 43.0261i −0.186694 + 1.49707i
\(827\) 15.4683 + 23.1499i 0.537884 + 0.805000i 0.996496 0.0836361i \(-0.0266533\pi\)
−0.458612 + 0.888636i \(0.651653\pi\)
\(828\) −7.57813 21.3607i −0.263358 0.742337i
\(829\) −24.9078 + 24.9078i −0.865083 + 0.865083i −0.991923 0.126840i \(-0.959516\pi\)
0.126840 + 0.991923i \(0.459516\pi\)
\(830\) 1.67147 + 0.949856i 0.0580177 + 0.0329700i
\(831\) 1.97376 4.76507i 0.0684688 0.165298i
\(832\) −10.8358 23.3978i −0.375663 0.811173i
\(833\) 0.0835343 + 0.0994442i 0.00289429 + 0.00344554i
\(834\) −1.41578 19.5523i −0.0490245 0.677041i
\(835\) −2.28605 0.946911i −0.0791119 0.0327692i
\(836\) 1.13612 2.38547i 0.0392935 0.0825033i
\(837\) −23.8908 23.8908i −0.825785 0.825785i
\(838\) −3.24790 11.7982i −0.112197 0.407563i
\(839\) 34.5955 23.1160i 1.19437 0.798052i 0.210615 0.977569i \(-0.432453\pi\)
0.983755 + 0.179517i \(0.0574535\pi\)
\(840\) −1.80219 + 0.0369536i −0.0621816 + 0.00127502i
\(841\) −12.6880 + 5.25553i −0.437517 + 0.181225i
\(842\) −48.8978 + 24.5306i −1.68513 + 0.845379i
\(843\) −2.28774 + 11.5013i −0.0787940 + 0.396124i
\(844\) −27.0703 30.0297i −0.931798 1.03366i
\(845\) −0.530622 + 0.105547i −0.0182539 + 0.00363093i
\(846\) −7.55040 + 8.72920i −0.259588 + 0.300116i
\(847\) −16.0001 + 23.9458i −0.549768 + 0.822787i
\(848\) −23.0798 2.39881i −0.792563 0.0823756i
\(849\) 2.40517i 0.0825452i
\(850\) −26.5417 11.4459i −0.910372 0.392591i
\(851\) 60.2833i 2.06649i
\(852\) −5.00386 + 19.7506i −0.171429 + 0.676644i
\(853\) 23.4897 35.1548i 0.804272 1.20368i −0.171564 0.985173i \(-0.554882\pi\)
0.975836 0.218505i \(-0.0701179\pi\)
\(854\) −14.8893 12.8787i −0.509503 0.440699i
\(855\) 1.46690 0.291785i 0.0501671 0.00997885i
\(856\) 12.9217 + 12.4025i 0.441655 + 0.423907i
\(857\) −8.33184 + 41.8870i −0.284610 + 1.43083i 0.528604 + 0.848869i \(0.322716\pi\)
−0.813214 + 0.581964i \(0.802284\pi\)
\(858\) −0.715724 1.42668i −0.0244344 0.0487061i
\(859\) −25.4001 + 10.5211i −0.866642 + 0.358975i −0.771302 0.636470i \(-0.780394\pi\)
−0.0953404 + 0.995445i \(0.530394\pi\)
\(860\) −0.0975964 + 1.88307i −0.00332801 + 0.0642123i
\(861\) 18.3904 12.2881i 0.626744 0.418777i
\(862\) −33.6693 + 9.26873i −1.14678 + 0.315694i
\(863\) −2.73308 2.73308i −0.0930351 0.0930351i 0.659057 0.752093i \(-0.270955\pi\)
−0.752093 + 0.659057i \(0.770955\pi\)
\(864\) −29.8109 6.90553i −1.01419 0.234931i
\(865\) 4.58815 + 1.90047i 0.156002 + 0.0646180i
\(866\) 13.5924 0.984227i 0.461889 0.0334454i
\(867\) −0.453359 19.8049i −0.0153969 0.672611i
\(868\) 32.6317 4.75063i 1.10759 0.161247i
\(869\) 1.34329 3.24299i 0.0455680 0.110011i
\(870\) 0.659103 1.15983i 0.0223457 0.0393220i
\(871\) 30.6517 30.6517i 1.03859 1.03859i
\(872\) −3.42118 + 1.49999i −0.115856 + 0.0507960i
\(873\) 1.82184 + 2.72657i 0.0616598 + 0.0922804i
\(874\) 42.5791 + 5.30987i 1.44026 + 0.179609i
\(875\) −2.08392 5.03103i −0.0704493 0.170080i
\(876\) −10.1755 + 6.06173i −0.343797 + 0.204807i
\(877\) −27.2993 5.43017i −0.921832 0.183364i −0.288711 0.957416i \(-0.593227\pi\)
−0.633121 + 0.774052i \(0.718227\pi\)
\(878\) 23.6856 18.4331i 0.799349 0.622087i
\(879\) 1.99190 + 10.0140i 0.0671852 + 0.337763i
\(880\) 0.218983 + 0.118571i 0.00738193 + 0.00399702i
\(881\) 24.6326 + 16.4590i 0.829893 + 0.554517i 0.896388 0.443270i \(-0.146182\pi\)
−0.0664953 + 0.997787i \(0.521182\pi\)
\(882\) −0.0230388 + 0.0694252i −0.000775756 + 0.00233767i
\(883\) 8.24236 0.277378 0.138689 0.990336i \(-0.455711\pi\)
0.138689 + 0.990336i \(0.455711\pi\)
\(884\) 25.1024 + 8.73480i 0.844284 + 0.293783i
\(885\) −2.80399 −0.0942551
\(886\) 4.20515 12.6718i 0.141275 0.425719i
\(887\) −4.30048 2.87349i −0.144396 0.0964823i 0.481274 0.876570i \(-0.340174\pi\)
−0.625670 + 0.780088i \(0.715174\pi\)
\(888\) 24.2610 + 15.5009i 0.814147 + 0.520175i
\(889\) 8.75882 + 44.0336i 0.293761 + 1.47684i
\(890\) −2.20187 + 1.71359i −0.0738070 + 0.0574397i
\(891\) −0.405947 0.0807479i −0.0135997 0.00270516i
\(892\) 12.6343 + 21.2085i 0.423029 + 0.710113i
\(893\) −8.36166 20.1868i −0.279812 0.675527i
\(894\) 7.08692 + 0.883783i 0.237022 + 0.0295581i
\(895\) 0.431457 + 0.645720i 0.0144220 + 0.0215841i
\(896\) 22.7976 19.2934i 0.761616 0.644548i
\(897\) 18.3290 18.3290i 0.611987 0.611987i
\(898\) 19.0625 33.5446i 0.636124 1.11940i
\(899\) −9.33912 + 22.5466i −0.311477 + 0.751972i
\(900\) −2.34534 16.1099i −0.0781779 0.536998i
\(901\) 18.3142 15.3842i 0.610135 0.512521i
\(902\) −3.04760 + 0.220676i −0.101474 + 0.00734772i
\(903\) 12.9331 + 5.35708i 0.430388 + 0.178272i
\(904\) −16.4814 6.43424i −0.548164 0.214000i
\(905\) 0.441669 + 0.441669i 0.0146816 + 0.0146816i
\(906\) −19.7761 + 5.44411i −0.657017 + 0.180868i
\(907\) 8.60733 5.75124i 0.285802 0.190967i −0.404403 0.914581i \(-0.632521\pi\)
0.690204 + 0.723614i \(0.257521\pi\)
\(908\) −8.95857 0.464307i −0.297301 0.0154086i
\(909\) 3.49871 1.44921i 0.116045 0.0480673i
\(910\) 1.11783 + 2.22822i 0.0370557 + 0.0738647i
\(911\) −5.89233 + 29.6227i −0.195222 + 0.981445i 0.751584 + 0.659638i \(0.229290\pi\)
−0.946805 + 0.321807i \(0.895710\pi\)
\(912\) 13.0855 15.7706i 0.433303 0.522217i
\(913\) −1.93388 + 0.384672i −0.0640020 + 0.0127308i
\(914\) 19.0208 + 16.4522i 0.629151 + 0.544190i
\(915\) 0.707290 1.05853i 0.0233823 0.0349941i
\(916\) −16.4193 4.15988i −0.542510 0.137446i
\(917\) 44.9834i 1.48548i
\(918\) 26.4767 17.1431i 0.873860 0.565807i
\(919\) 34.1231i 1.12562i −0.826587 0.562809i \(-0.809721\pi\)
0.826587 0.562809i \(-0.190279\pi\)
\(920\) −0.707485 + 3.98173i −0.0233251 + 0.131274i
\(921\) 5.74154 8.59282i 0.189190 0.283143i
\(922\) −9.02235 + 10.4310i −0.297135 + 0.343526i
\(923\) 27.6359 5.49712i 0.909647 0.180940i
\(924\) 1.37318 1.23785i 0.0451742 0.0407223i
\(925\) −8.44739 + 42.4679i −0.277748 + 1.39634i
\(926\) 10.3539 5.19425i 0.340251 0.170694i
\(927\) 16.5969 6.87467i 0.545114 0.225794i
\(928\) 3.63195 + 21.8023i 0.119224 + 0.715696i
\(929\) −28.7558 + 19.2140i −0.943448 + 0.630392i −0.929228 0.369507i \(-0.879527\pi\)
−0.0142201 + 0.999899i \(0.504527\pi\)
\(930\) 0.565994 + 2.05601i 0.0185597 + 0.0674193i
\(931\) −0.0979212 0.0979212i −0.00320924 0.00320924i
\(932\) −9.86168 4.69679i −0.323030 0.153848i
\(933\) −6.96129 2.88346i −0.227902 0.0944003i
\(934\) 3.65208 + 50.4362i 0.119500 + 1.65032i
\(935\) −0.244766 + 0.0773185i −0.00800470 + 0.00252858i
\(936\) 3.22084 + 14.6192i 0.105276 + 0.477844i
\(937\) −2.25675 + 5.44829i −0.0737249 + 0.177988i −0.956446 0.291910i \(-0.905709\pi\)
0.882721 + 0.469898i \(0.155709\pi\)
\(938\) 43.6523 + 24.8064i 1.42530 + 0.809959i
\(939\) −3.01965 + 3.01965i −0.0985427 + 0.0985427i
\(940\) 1.94082 0.688542i 0.0633025 0.0224578i
\(941\) 7.59505 + 11.3668i 0.247592 + 0.370547i 0.934361 0.356329i \(-0.115972\pi\)
−0.686769 + 0.726876i \(0.740972\pi\)
\(942\) −3.02539 + 24.2601i −0.0985725 + 0.790437i
\(943\) −18.9895 45.8447i −0.618383 1.49291i
\(944\) 36.0706 29.2785i 1.17400 0.952935i
\(945\) 2.90157 + 0.577159i 0.0943882 + 0.0187750i
\(946\) −1.18775 1.52619i −0.0386170 0.0496208i
\(947\) 1.14465 + 5.75453i 0.0371960 + 0.186997i 0.994917 0.100703i \(-0.0321093\pi\)
−0.957720 + 0.287700i \(0.907109\pi\)
\(948\) 16.2764 21.8231i 0.528633 0.708780i
\(949\) 13.6195 + 9.10027i 0.442108 + 0.295407i
\(950\) 29.2517 + 9.70718i 0.949050 + 0.314942i
\(951\) −35.5788 −1.15372
\(952\) −2.03738 + 30.7175i −0.0660318 + 0.995560i
\(953\) 43.4782 1.40840 0.704199 0.710003i \(-0.251306\pi\)
0.704199 + 0.710003i \(0.251306\pi\)
\(954\) 12.7858 + 4.24296i 0.413954 + 0.137371i
\(955\) −0.871301 0.582185i −0.0281946 0.0188391i
\(956\) 7.53611 10.1043i 0.243735 0.326795i
\(957\) 0.266923 + 1.34191i 0.00862840 + 0.0433779i
\(958\) 0.751636 + 0.965813i 0.0242843 + 0.0312040i
\(959\) −26.4274 5.25675i −0.853387 0.169749i
\(960\) 1.42053 + 1.30856i 0.0458473 + 0.0422337i
\(961\) −3.06576 7.40139i −0.0988954 0.238755i
\(962\) 4.92711 39.5097i 0.158856 1.27384i
\(963\) −5.77694 8.64580i −0.186159 0.278607i
\(964\) −5.82765 + 2.06747i −0.187696 + 0.0665888i
\(965\) −2.35423 + 2.35423i −0.0757854 + 0.0757854i
\(966\) 26.1030 + 14.8336i 0.839850 + 0.477265i
\(967\) 2.13329 5.15021i 0.0686018 0.165619i −0.885860 0.463953i \(-0.846431\pi\)
0.954462 + 0.298333i \(0.0964307\pi\)
\(968\) 30.1346 6.63913i 0.968563 0.213390i
\(969\) 2.31085 + 20.9964i 0.0742352 + 0.674500i
\(970\) −0.0422567 0.583576i −0.00135678 0.0187375i
\(971\) 11.9212 + 4.93791i 0.382568 + 0.158465i 0.565675 0.824628i \(-0.308615\pi\)
−0.183107 + 0.983093i \(0.558615\pi\)
\(972\) 26.4046 + 12.5756i 0.846928 + 0.403363i
\(973\) −22.2042 22.2042i −0.711834 0.711834i
\(974\) 2.38064 + 8.64783i 0.0762806 + 0.277094i
\(975\) 15.4807 10.3438i 0.495778 0.331268i
\(976\) 1.95433 + 21.0024i 0.0625566 + 0.672269i
\(977\) −23.2430 + 9.62756i −0.743609 + 0.308013i −0.722131 0.691756i \(-0.756837\pi\)
−0.0214780 + 0.999769i \(0.506837\pi\)
\(978\) −5.17202 + 2.59465i −0.165383 + 0.0829678i
\(979\) 0.558266 2.80659i 0.0178422 0.0896990i
\(980\) 0.00969423 0.00873887i 0.000309671 0.000279153i
\(981\) 2.12705 0.423096i 0.0679114 0.0135084i
\(982\) 5.96076 6.89138i 0.190216 0.219913i
\(983\) −28.8266 + 43.1420i −0.919425 + 1.37602i 0.00717802 + 0.999974i \(0.497715\pi\)
−0.926603 + 0.376042i \(0.877285\pi\)
\(984\) −23.3330 4.14588i −0.743830 0.132166i
\(985\) 1.55982i 0.0496999i
\(986\) −18.7585 12.9299i −0.597394 0.411772i
\(987\) 15.2885i 0.486639i
\(988\) −27.4723 6.96018i −0.874011 0.221433i
\(989\) 17.4484 26.1134i 0.554827 0.830357i
\(990\) −0.109345 0.0945787i −0.00347520 0.00300591i
\(991\) 5.69709 1.13322i 0.180974 0.0359979i −0.103771 0.994601i \(-0.533091\pi\)
0.284745 + 0.958603i \(0.408091\pi\)
\(992\) −28.7493 20.5387i −0.912791 0.652103i
\(993\) 1.70670 8.58014i 0.0541603 0.272282i
\(994\) 14.6345 + 29.1716i 0.464179 + 0.925267i
\(995\) 2.04164 0.845675i 0.0647243 0.0268097i
\(996\) −15.2722 0.791529i −0.483917 0.0250805i
\(997\) 36.3003 24.2551i 1.14964 0.768167i 0.173401 0.984851i \(-0.444524\pi\)
0.976242 + 0.216685i \(0.0695243\pi\)
\(998\) −47.6389 + 13.1144i −1.50798 + 0.415128i
\(999\) −33.4115 33.4115i −1.05709 1.05709i
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 68.2.i.b.7.6 yes 48
3.2 odd 2 612.2.bd.d.415.1 48
4.3 odd 2 inner 68.2.i.b.7.1 48
12.11 even 2 612.2.bd.d.415.6 48
17.5 odd 16 inner 68.2.i.b.39.1 yes 48
51.5 even 16 612.2.bd.d.379.6 48
68.39 even 16 inner 68.2.i.b.39.6 yes 48
204.107 odd 16 612.2.bd.d.379.1 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
68.2.i.b.7.1 48 4.3 odd 2 inner
68.2.i.b.7.6 yes 48 1.1 even 1 trivial
68.2.i.b.39.1 yes 48 17.5 odd 16 inner
68.2.i.b.39.6 yes 48 68.39 even 16 inner
612.2.bd.d.379.1 48 204.107 odd 16
612.2.bd.d.379.6 48 51.5 even 16
612.2.bd.d.415.1 48 3.2 odd 2
612.2.bd.d.415.6 48 12.11 even 2