Properties

Label 930.2.bg.d.691.1
Level $930$
Weight $2$
Character 930.691
Analytic conductor $7.426$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [930,2,Mod(121,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([0, 0, 16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.121");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.bg (of order \(15\), 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: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(2\) over \(\Q(\zeta_{15})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 21x^{14} + 167x^{12} + 653x^{10} + 1350x^{8} + 1472x^{6} + 777x^{4} + 149x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 691.1
Root \(-2.86648i\) of defining polynomial
Character \(\chi\) \(=\) 930.691
Dual form 930.2.bg.d.751.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.309017 - 0.951057i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.461080 + 0.205286i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})\) \(q+(0.309017 - 0.951057i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.461080 + 0.205286i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +(0.978148 - 0.207912i) q^{10} +(0.111410 - 1.05999i) q^{11} +(0.669131 + 0.743145i) q^{12} +(1.28441 - 1.42648i) q^{13} +(0.0527571 + 0.501950i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.267253 - 2.54274i) q^{17} +(0.669131 - 0.743145i) q^{18} +(0.589263 + 0.654443i) q^{19} +(0.104528 - 0.994522i) q^{20} +(0.493686 - 0.104936i) q^{21} +(-0.973686 - 0.433513i) q^{22} +(3.27538 - 2.37971i) q^{23} +(0.913545 - 0.406737i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.959760 - 1.66235i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.493686 + 0.104936i) q^{28} +(0.692835 - 2.13233i) q^{29} -1.00000 q^{30} +(1.71067 - 5.29845i) q^{31} +1.00000 q^{32} +(-0.329360 + 1.01367i) q^{33} +(-2.50088 - 0.531578i) q^{34} +(-0.408323 - 0.296664i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(4.79593 - 8.30680i) q^{37} +(0.804504 - 0.358188i) q^{38} +(-1.55293 + 1.12827i) q^{39} +(-0.913545 - 0.406737i) q^{40} +(4.07758 - 0.866716i) q^{41} +(0.0527571 - 0.501950i) q^{42} +(-2.75002 - 3.05421i) q^{43} +(-0.713181 + 0.792068i) q^{44} +(0.104528 + 0.994522i) q^{45} +(-1.25109 - 3.85044i) q^{46} +(-2.99894 - 9.22979i) q^{47} +(-0.104528 - 0.994522i) q^{48} +(-4.51346 + 5.01271i) q^{49} +(0.669131 + 0.743145i) q^{50} +(-0.267253 + 2.54274i) q^{51} +(-1.87757 + 0.399091i) q^{52} +(-0.919436 - 0.409359i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(0.973686 - 0.433513i) q^{55} +(0.252358 - 0.437096i) q^{56} +(-0.440320 - 0.762656i) q^{57} +(-1.81387 - 1.31785i) q^{58} +(-9.41829 - 2.00192i) q^{59} +(-0.309017 + 0.951057i) q^{60} +11.2837 q^{61} +(-4.51050 - 3.26425i) q^{62} -0.504715 q^{63} +(0.309017 - 0.951057i) q^{64} +(1.87757 + 0.399091i) q^{65} +(0.862276 + 0.626480i) q^{66} +(1.13972 + 1.97406i) q^{67} +(-1.27837 + 2.21421i) q^{68} +(-3.69858 + 1.64671i) q^{69} +(-0.408323 + 0.296664i) q^{70} +(-8.17500 - 3.63974i) q^{71} +(-0.978148 + 0.207912i) q^{72} +(0.0271610 - 0.258420i) q^{73} +(-6.41821 - 7.12815i) q^{74} +(0.669131 - 0.743145i) q^{75} +(-0.0920519 - 0.875815i) q^{76} +(0.166233 + 0.511613i) q^{77} +(0.593165 + 1.82557i) q^{78} +(0.784025 + 7.45950i) q^{79} +(-0.669131 + 0.743145i) q^{80} +(0.669131 + 0.743145i) q^{81} +(0.435745 - 4.14584i) q^{82} +(-0.771873 + 0.164067i) q^{83} +(-0.461080 - 0.205286i) q^{84} +(2.06845 - 1.50282i) q^{85} +(-3.75453 + 1.67162i) q^{86} +(-1.12103 + 1.94168i) q^{87} +(0.532916 + 0.923038i) q^{88} +(4.82338 + 3.50439i) q^{89} +(0.978148 + 0.207912i) q^{90} +(-0.299379 + 0.921395i) q^{91} -4.04860 q^{92} +(-2.77490 + 4.82700i) q^{93} -9.70477 q^{94} +(-0.272133 + 0.837538i) q^{95} +(-0.978148 - 0.207912i) q^{96} +(7.01736 + 5.09841i) q^{97} +(3.37263 + 5.84157i) q^{98} +(0.532916 - 0.923038i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{12} - 20 q^{13} - 4 q^{14} + 4 q^{15} - 4 q^{16} - 12 q^{17} + 2 q^{18} - 7 q^{19} - 2 q^{20} - 4 q^{21} + 11 q^{22} + 11 q^{23} + 2 q^{24} - 8 q^{25} + 5 q^{26} - 4 q^{27} - 4 q^{28} + 23 q^{29} - 16 q^{30} - 17 q^{31} + 16 q^{32} - 2 q^{33} - 2 q^{34} + 7 q^{35} - 8 q^{36} + 17 q^{37} - 2 q^{38} - 5 q^{39} - 2 q^{40} + 8 q^{41} - 4 q^{42} + 32 q^{43} + q^{44} - 2 q^{45} + 11 q^{46} - 7 q^{47} + 2 q^{48} - q^{49} + 2 q^{50} - 12 q^{51} + 10 q^{52} + 54 q^{53} - 4 q^{54} - 11 q^{55} + q^{56} + 18 q^{57} - 22 q^{58} - 38 q^{59} + 4 q^{60} - 28 q^{61} - 27 q^{62} - 2 q^{63} - 4 q^{64} - 10 q^{65} - 7 q^{66} + q^{67} - 2 q^{68} - 13 q^{69} + 7 q^{70} - 11 q^{71} + 2 q^{72} + 53 q^{73} + 2 q^{74} + 2 q^{75} - 2 q^{76} + 44 q^{77} + 10 q^{78} + 48 q^{79} - 2 q^{80} + 2 q^{81} + 8 q^{82} + 56 q^{83} + 11 q^{84} - 24 q^{85} - 13 q^{86} + q^{87} - 9 q^{88} - 43 q^{89} - 2 q^{90} - 50 q^{91} - 44 q^{92} - 22 q^{93} - 72 q^{94} - 14 q^{95} + 2 q^{96} + 17 q^{97} + 29 q^{98} - 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{15}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.309017 0.951057i 0.218508 0.672499i
\(3\) −0.978148 0.207912i −0.564734 0.120038i
\(4\) −0.809017 0.587785i −0.404508 0.293893i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) −0.500000 + 0.866025i −0.204124 + 0.353553i
\(7\) −0.461080 + 0.205286i −0.174272 + 0.0775909i −0.492018 0.870585i \(-0.663741\pi\)
0.317746 + 0.948176i \(0.397074\pi\)
\(8\) −0.809017 + 0.587785i −0.286031 + 0.207813i
\(9\) 0.913545 + 0.406737i 0.304515 + 0.135579i
\(10\) 0.978148 0.207912i 0.309317 0.0657474i
\(11\) 0.111410 1.05999i 0.0335913 0.319600i −0.964804 0.262970i \(-0.915298\pi\)
0.998395 0.0566297i \(-0.0180355\pi\)
\(12\) 0.669131 + 0.743145i 0.193161 + 0.214527i
\(13\) 1.28441 1.42648i 0.356231 0.395635i −0.538217 0.842806i \(-0.680902\pi\)
0.894448 + 0.447171i \(0.147569\pi\)
\(14\) 0.0527571 + 0.501950i 0.0140999 + 0.134152i
\(15\) −0.309017 0.951057i −0.0797878 0.245562i
\(16\) 0.309017 + 0.951057i 0.0772542 + 0.237764i
\(17\) −0.267253 2.54274i −0.0648184 0.616706i −0.977921 0.208976i \(-0.932987\pi\)
0.913102 0.407730i \(-0.133680\pi\)
\(18\) 0.669131 0.743145i 0.157716 0.175161i
\(19\) 0.589263 + 0.654443i 0.135186 + 0.150139i 0.806937 0.590638i \(-0.201124\pi\)
−0.671750 + 0.740778i \(0.734457\pi\)
\(20\) 0.104528 0.994522i 0.0233733 0.222382i
\(21\) 0.493686 0.104936i 0.107731 0.0228990i
\(22\) −0.973686 0.433513i −0.207591 0.0924253i
\(23\) 3.27538 2.37971i 0.682965 0.496203i −0.191375 0.981517i \(-0.561295\pi\)
0.874340 + 0.485314i \(0.161295\pi\)
\(24\) 0.913545 0.406737i 0.186477 0.0830248i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −0.959760 1.66235i −0.188225 0.326014i
\(27\) −0.809017 0.587785i −0.155695 0.113119i
\(28\) 0.493686 + 0.104936i 0.0932979 + 0.0198311i
\(29\) 0.692835 2.13233i 0.128656 0.395963i −0.865893 0.500229i \(-0.833249\pi\)
0.994549 + 0.104266i \(0.0332492\pi\)
\(30\) −1.00000 −0.182574
\(31\) 1.71067 5.29845i 0.307245 0.951630i
\(32\) 1.00000 0.176777
\(33\) −0.329360 + 1.01367i −0.0573343 + 0.176457i
\(34\) −2.50088 0.531578i −0.428897 0.0911649i
\(35\) −0.408323 0.296664i −0.0690192 0.0501454i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) 4.79593 8.30680i 0.788447 1.36563i −0.138472 0.990366i \(-0.544219\pi\)
0.926918 0.375263i \(-0.122448\pi\)
\(38\) 0.804504 0.358188i 0.130508 0.0581058i
\(39\) −1.55293 + 1.12827i −0.248667 + 0.180667i
\(40\) −0.913545 0.406737i −0.144444 0.0643107i
\(41\) 4.07758 0.866716i 0.636811 0.135358i 0.121817 0.992553i \(-0.461128\pi\)
0.514993 + 0.857194i \(0.327794\pi\)
\(42\) 0.0527571 0.501950i 0.00814060 0.0774526i
\(43\) −2.75002 3.05421i −0.419374 0.465762i 0.496026 0.868308i \(-0.334792\pi\)
−0.915400 + 0.402546i \(0.868125\pi\)
\(44\) −0.713181 + 0.792068i −0.107516 + 0.119409i
\(45\) 0.104528 + 0.994522i 0.0155822 + 0.148255i
\(46\) −1.25109 3.85044i −0.184462 0.567717i
\(47\) −2.99894 9.22979i −0.437440 1.34630i −0.890565 0.454856i \(-0.849691\pi\)
0.453125 0.891447i \(-0.350309\pi\)
\(48\) −0.104528 0.994522i −0.0150874 0.143547i
\(49\) −4.51346 + 5.01271i −0.644780 + 0.716101i
\(50\) 0.669131 + 0.743145i 0.0946294 + 0.105097i
\(51\) −0.267253 + 2.54274i −0.0374229 + 0.356055i
\(52\) −1.87757 + 0.399091i −0.260373 + 0.0553439i
\(53\) −0.919436 0.409359i −0.126294 0.0562298i 0.342617 0.939475i \(-0.388687\pi\)
−0.468911 + 0.883245i \(0.655353\pi\)
\(54\) −0.809017 + 0.587785i −0.110093 + 0.0799874i
\(55\) 0.973686 0.433513i 0.131292 0.0584549i
\(56\) 0.252358 0.437096i 0.0337227 0.0584095i
\(57\) −0.440320 0.762656i −0.0583218 0.101016i
\(58\) −1.81387 1.31785i −0.238172 0.173042i
\(59\) −9.41829 2.00192i −1.22616 0.260628i −0.451074 0.892487i \(-0.648959\pi\)
−0.775083 + 0.631859i \(0.782292\pi\)
\(60\) −0.309017 + 0.951057i −0.0398939 + 0.122781i
\(61\) 11.2837 1.44474 0.722368 0.691509i \(-0.243054\pi\)
0.722368 + 0.691509i \(0.243054\pi\)
\(62\) −4.51050 3.26425i −0.572835 0.414561i
\(63\) −0.504715 −0.0635882
\(64\) 0.309017 0.951057i 0.0386271 0.118882i
\(65\) 1.87757 + 0.399091i 0.232884 + 0.0495011i
\(66\) 0.862276 + 0.626480i 0.106139 + 0.0771144i
\(67\) 1.13972 + 1.97406i 0.139240 + 0.241170i 0.927209 0.374544i \(-0.122201\pi\)
−0.787969 + 0.615714i \(0.788868\pi\)
\(68\) −1.27837 + 2.21421i −0.155026 + 0.268512i
\(69\) −3.69858 + 1.64671i −0.445256 + 0.198241i
\(70\) −0.408323 + 0.296664i −0.0488040 + 0.0354582i
\(71\) −8.17500 3.63974i −0.970194 0.431958i −0.140441 0.990089i \(-0.544852\pi\)
−0.829753 + 0.558131i \(0.811519\pi\)
\(72\) −0.978148 + 0.207912i −0.115276 + 0.0245026i
\(73\) 0.0271610 0.258420i 0.00317896 0.0302458i −0.992817 0.119639i \(-0.961826\pi\)
0.995996 + 0.0893935i \(0.0284929\pi\)
\(74\) −6.41821 7.12815i −0.746102 0.828630i
\(75\) 0.669131 0.743145i 0.0772645 0.0858110i
\(76\) −0.0920519 0.875815i −0.0105591 0.100463i
\(77\) 0.166233 + 0.511613i 0.0189440 + 0.0583037i
\(78\) 0.593165 + 1.82557i 0.0671627 + 0.206705i
\(79\) 0.784025 + 7.45950i 0.0882097 + 0.839260i 0.945761 + 0.324862i \(0.105318\pi\)
−0.857552 + 0.514398i \(0.828016\pi\)
\(80\) −0.669131 + 0.743145i −0.0748111 + 0.0830861i
\(81\) 0.669131 + 0.743145i 0.0743478 + 0.0825716i
\(82\) 0.435745 4.14584i 0.0481200 0.457831i
\(83\) −0.771873 + 0.164067i −0.0847240 + 0.0180086i −0.250079 0.968226i \(-0.580456\pi\)
0.165355 + 0.986234i \(0.447123\pi\)
\(84\) −0.461080 0.205286i −0.0503080 0.0223986i
\(85\) 2.06845 1.50282i 0.224355 0.163004i
\(86\) −3.75453 + 1.67162i −0.404861 + 0.180256i
\(87\) −1.12103 + 1.94168i −0.120187 + 0.208170i
\(88\) 0.532916 + 0.923038i 0.0568090 + 0.0983961i
\(89\) 4.82338 + 3.50439i 0.511277 + 0.371464i 0.813308 0.581834i \(-0.197665\pi\)
−0.302031 + 0.953298i \(0.597665\pi\)
\(90\) 0.978148 + 0.207912i 0.103106 + 0.0219158i
\(91\) −0.299379 + 0.921395i −0.0313835 + 0.0965884i
\(92\) −4.04860 −0.422095
\(93\) −2.77490 + 4.82700i −0.287743 + 0.500537i
\(94\) −9.70477 −1.00097
\(95\) −0.272133 + 0.837538i −0.0279202 + 0.0859296i
\(96\) −0.978148 0.207912i −0.0998318 0.0212199i
\(97\) 7.01736 + 5.09841i 0.712505 + 0.517665i 0.883981 0.467523i \(-0.154854\pi\)
−0.171476 + 0.985188i \(0.554854\pi\)
\(98\) 3.37263 + 5.84157i 0.340687 + 0.590088i
\(99\) 0.532916 0.923038i 0.0535601 0.0927688i
\(100\) 0.913545 0.406737i 0.0913545 0.0406737i
\(101\) 2.93695 2.13382i 0.292237 0.212323i −0.432000 0.901874i \(-0.642192\pi\)
0.724237 + 0.689551i \(0.242192\pi\)
\(102\) 2.33571 + 1.03992i 0.231269 + 0.102968i
\(103\) −3.59237 + 0.763582i −0.353967 + 0.0752380i −0.381463 0.924384i \(-0.624580\pi\)
0.0274966 + 0.999622i \(0.491246\pi\)
\(104\) −0.200645 + 1.90901i −0.0196748 + 0.187193i
\(105\) 0.337720 + 0.375077i 0.0329581 + 0.0366037i
\(106\) −0.673445 + 0.747937i −0.0654108 + 0.0726460i
\(107\) −1.81444 17.2632i −0.175408 1.66890i −0.628786 0.777579i \(-0.716448\pi\)
0.453378 0.891319i \(-0.350219\pi\)
\(108\) 0.309017 + 0.951057i 0.0297352 + 0.0915155i
\(109\) 1.87670 + 5.77590i 0.179756 + 0.553231i 0.999819 0.0190421i \(-0.00606165\pi\)
−0.820063 + 0.572273i \(0.806062\pi\)
\(110\) −0.111410 1.05999i −0.0106225 0.101066i
\(111\) −6.41821 + 7.12815i −0.609190 + 0.676574i
\(112\) −0.337720 0.375077i −0.0319116 0.0354414i
\(113\) 0.965814 9.18911i 0.0908562 0.864439i −0.850262 0.526360i \(-0.823556\pi\)
0.941118 0.338078i \(-0.109777\pi\)
\(114\) −0.861395 + 0.183095i −0.0806771 + 0.0171484i
\(115\) 3.69858 + 1.64671i 0.344894 + 0.153557i
\(116\) −1.81387 + 1.31785i −0.168413 + 0.122359i
\(117\) 1.75357 0.780740i 0.162118 0.0721794i
\(118\) −4.81435 + 8.33870i −0.443197 + 0.767640i
\(119\) 0.645215 + 1.11755i 0.0591468 + 0.102445i
\(120\) 0.809017 + 0.587785i 0.0738528 + 0.0536572i
\(121\) 9.64845 + 2.05084i 0.877132 + 0.186440i
\(122\) 3.48687 10.7315i 0.315686 0.971582i
\(123\) −4.16867 −0.375877
\(124\) −4.49831 + 3.28103i −0.403960 + 0.294646i
\(125\) −1.00000 −0.0894427
\(126\) −0.155966 + 0.480013i −0.0138945 + 0.0427629i
\(127\) 1.65331 + 0.351422i 0.146707 + 0.0311836i 0.280680 0.959801i \(-0.409440\pi\)
−0.133973 + 0.990985i \(0.542773\pi\)
\(128\) −0.809017 0.587785i −0.0715077 0.0519534i
\(129\) 2.05492 + 3.55923i 0.180926 + 0.313372i
\(130\) 0.959760 1.66235i 0.0841766 0.145798i
\(131\) 3.48702 1.55252i 0.304662 0.135644i −0.248711 0.968578i \(-0.580007\pi\)
0.553373 + 0.832933i \(0.313340\pi\)
\(132\) 0.862276 0.626480i 0.0750515 0.0545281i
\(133\) −0.406046 0.180783i −0.0352086 0.0156759i
\(134\) 2.22964 0.473924i 0.192611 0.0409408i
\(135\) 0.104528 0.994522i 0.00899638 0.0855948i
\(136\) 1.71080 + 1.90003i 0.146700 + 0.162927i
\(137\) −0.100000 + 0.111061i −0.00854358 + 0.00948861i −0.747401 0.664373i \(-0.768699\pi\)
0.738858 + 0.673861i \(0.235365\pi\)
\(138\) 0.423194 + 4.02642i 0.0360246 + 0.342751i
\(139\) 3.37890 + 10.3992i 0.286595 + 0.882048i 0.985916 + 0.167241i \(0.0534857\pi\)
−0.699321 + 0.714807i \(0.746514\pi\)
\(140\) 0.155966 + 0.480013i 0.0131815 + 0.0405685i
\(141\) 1.01442 + 9.65161i 0.0854300 + 0.812812i
\(142\) −5.98781 + 6.65014i −0.502486 + 0.558068i
\(143\) −1.36897 1.52039i −0.114479 0.127141i
\(144\) −0.104528 + 0.994522i −0.00871071 + 0.0828768i
\(145\) 2.19307 0.466151i 0.182124 0.0387117i
\(146\) −0.237379 0.105688i −0.0196456 0.00874679i
\(147\) 5.45703 3.96477i 0.450088 0.327008i
\(148\) −8.76261 + 3.90136i −0.720282 + 0.320690i
\(149\) −1.56358 + 2.70819i −0.128093 + 0.221864i −0.922938 0.384949i \(-0.874219\pi\)
0.794845 + 0.606813i \(0.207552\pi\)
\(150\) −0.500000 0.866025i −0.0408248 0.0707107i
\(151\) 13.4837 + 9.79650i 1.09729 + 0.797227i 0.980615 0.195943i \(-0.0627767\pi\)
0.116674 + 0.993170i \(0.462777\pi\)
\(152\) −0.861395 0.183095i −0.0698684 0.0148510i
\(153\) 0.790079 2.43161i 0.0638741 0.196584i
\(154\) 0.537942 0.0433486
\(155\) 5.44393 1.16775i 0.437267 0.0937956i
\(156\) 1.91952 0.153685
\(157\) 2.29856 7.07425i 0.183445 0.564586i −0.816473 0.577384i \(-0.804074\pi\)
0.999918 + 0.0127974i \(0.00407366\pi\)
\(158\) 7.33669 + 1.55946i 0.583675 + 0.124064i
\(159\) 0.814233 + 0.591575i 0.0645729 + 0.0469150i
\(160\) 0.500000 + 0.866025i 0.0395285 + 0.0684653i
\(161\) −1.02169 + 1.76963i −0.0805208 + 0.139466i
\(162\) 0.913545 0.406737i 0.0717749 0.0319562i
\(163\) 5.06115 3.67714i 0.396420 0.288016i −0.371661 0.928368i \(-0.621212\pi\)
0.768081 + 0.640352i \(0.221212\pi\)
\(164\) −3.80827 1.69555i −0.297376 0.132400i
\(165\) −1.04254 + 0.221599i −0.0811617 + 0.0172515i
\(166\) −0.0824852 + 0.784794i −0.00640209 + 0.0609118i
\(167\) 5.94465 + 6.60220i 0.460011 + 0.510894i 0.927867 0.372911i \(-0.121640\pi\)
−0.467856 + 0.883804i \(0.654974\pi\)
\(168\) −0.337720 + 0.375077i −0.0260557 + 0.0289378i
\(169\) 0.973729 + 9.26441i 0.0749022 + 0.712647i
\(170\) −0.790079 2.43161i −0.0605963 0.186496i
\(171\) 0.272133 + 0.837538i 0.0208105 + 0.0640481i
\(172\) 0.429595 + 4.08733i 0.0327563 + 0.311656i
\(173\) −10.3140 + 11.4548i −0.784158 + 0.870896i −0.994283 0.106779i \(-0.965946\pi\)
0.210125 + 0.977675i \(0.432613\pi\)
\(174\) 1.50023 + 1.66618i 0.113732 + 0.126313i
\(175\) 0.0527571 0.501950i 0.00398806 0.0379439i
\(176\) 1.04254 0.221599i 0.0785845 0.0167036i
\(177\) 8.79626 + 3.91635i 0.661167 + 0.294371i
\(178\) 4.82338 3.50439i 0.361527 0.262665i
\(179\) −11.7488 + 5.23088i −0.878143 + 0.390974i −0.795750 0.605625i \(-0.792923\pi\)
−0.0823932 + 0.996600i \(0.526256\pi\)
\(180\) 0.500000 0.866025i 0.0372678 0.0645497i
\(181\) 5.48915 + 9.50749i 0.408006 + 0.706686i 0.994666 0.103147i \(-0.0328911\pi\)
−0.586661 + 0.809833i \(0.699558\pi\)
\(182\) 0.783785 + 0.569453i 0.0580980 + 0.0422107i
\(183\) −11.0372 2.34602i −0.815891 0.173423i
\(184\) −1.25109 + 3.85044i −0.0922312 + 0.283859i
\(185\) 9.59187 0.705208
\(186\) 3.73326 + 4.13071i 0.273736 + 0.302878i
\(187\) −2.72506 −0.199276
\(188\) −2.99894 + 9.22979i −0.218720 + 0.673151i
\(189\) 0.493686 + 0.104936i 0.0359104 + 0.00763299i
\(190\) 0.712452 + 0.517627i 0.0516867 + 0.0375526i
\(191\) −2.90351 5.02903i −0.210091 0.363888i 0.741652 0.670785i \(-0.234043\pi\)
−0.951743 + 0.306897i \(0.900709\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) 9.40849 4.18893i 0.677238 0.301526i −0.0391447 0.999234i \(-0.512463\pi\)
0.716382 + 0.697708i \(0.245797\pi\)
\(194\) 7.01736 5.09841i 0.503817 0.366044i
\(195\) −1.75357 0.780740i −0.125576 0.0559099i
\(196\) 6.59786 1.40242i 0.471276 0.100173i
\(197\) −0.160245 + 1.52463i −0.0114170 + 0.108626i −0.998746 0.0500596i \(-0.984059\pi\)
0.987329 + 0.158685i \(0.0507255\pi\)
\(198\) −0.713181 0.792068i −0.0506836 0.0562898i
\(199\) −10.7569 + 11.9467i −0.762535 + 0.846881i −0.991974 0.126442i \(-0.959644\pi\)
0.229439 + 0.973323i \(0.426311\pi\)
\(200\) −0.104528 0.994522i −0.00739128 0.0703233i
\(201\) −0.704389 2.16789i −0.0496837 0.152911i
\(202\) −1.12181 3.45259i −0.0789305 0.242923i
\(203\) 0.118285 + 1.12540i 0.00830196 + 0.0789879i
\(204\) 1.71080 1.90003i 0.119780 0.133029i
\(205\) 2.78939 + 3.09793i 0.194819 + 0.216369i
\(206\) −0.383894 + 3.65251i −0.0267472 + 0.254482i
\(207\) 3.96013 0.841751i 0.275248 0.0585057i
\(208\) 1.75357 + 0.780740i 0.121588 + 0.0541345i
\(209\) 0.759355 0.551703i 0.0525257 0.0381621i
\(210\) 0.461080 0.205286i 0.0318176 0.0141661i
\(211\) 3.95374 6.84809i 0.272187 0.471442i −0.697235 0.716843i \(-0.745586\pi\)
0.969422 + 0.245401i \(0.0789197\pi\)
\(212\) 0.503224 + 0.871609i 0.0345616 + 0.0598624i
\(213\) 7.23961 + 5.25988i 0.496050 + 0.360401i
\(214\) −16.9790 3.60899i −1.16066 0.246706i
\(215\) 1.27001 3.90869i 0.0866140 0.266570i
\(216\) 1.00000 0.0680414
\(217\) 0.298945 + 2.79419i 0.0202937 + 0.189682i
\(218\) 6.07314 0.411325
\(219\) −0.0802960 + 0.247126i −0.00542590 + 0.0166992i
\(220\) −1.04254 0.221599i −0.0702881 0.0149402i
\(221\) −3.97044 2.88469i −0.267081 0.194045i
\(222\) 4.79593 + 8.30680i 0.321882 + 0.557516i
\(223\) −10.1218 + 17.5315i −0.677806 + 1.17399i 0.297835 + 0.954617i \(0.403736\pi\)
−0.975640 + 0.219376i \(0.929598\pi\)
\(224\) −0.461080 + 0.205286i −0.0308072 + 0.0137163i
\(225\) −0.809017 + 0.587785i −0.0539345 + 0.0391857i
\(226\) −8.44091 3.75813i −0.561481 0.249987i
\(227\) 21.5102 4.57213i 1.42768 0.303463i 0.571697 0.820465i \(-0.306285\pi\)
0.855984 + 0.517002i \(0.172952\pi\)
\(228\) −0.0920519 + 0.875815i −0.00609629 + 0.0580023i
\(229\) 6.02740 + 6.69411i 0.398302 + 0.442359i 0.908618 0.417628i \(-0.137138\pi\)
−0.510316 + 0.859987i \(0.670472\pi\)
\(230\) 2.70904 3.00869i 0.178629 0.198387i
\(231\) −0.0562302 0.534995i −0.00369968 0.0352001i
\(232\) 0.692835 + 2.13233i 0.0454869 + 0.139994i
\(233\) −2.40151 7.39110i −0.157328 0.484207i 0.841061 0.540940i \(-0.181931\pi\)
−0.998389 + 0.0567334i \(0.981931\pi\)
\(234\) −0.200645 1.90901i −0.0131165 0.124796i
\(235\) 6.49376 7.21205i 0.423606 0.470462i
\(236\) 6.44286 + 7.15552i 0.419394 + 0.465785i
\(237\) 0.784025 7.45950i 0.0509279 0.484547i
\(238\) 1.26223 0.268296i 0.0818183 0.0173910i
\(239\) 2.29146 + 1.02022i 0.148222 + 0.0659928i 0.479507 0.877538i \(-0.340815\pi\)
−0.331285 + 0.943531i \(0.607482\pi\)
\(240\) 0.809017 0.587785i 0.0522218 0.0379414i
\(241\) −13.9276 + 6.20099i −0.897158 + 0.399441i −0.802905 0.596108i \(-0.796713\pi\)
−0.0942538 + 0.995548i \(0.530047\pi\)
\(242\) 4.93200 8.54248i 0.317041 0.549131i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) −9.12874 6.63242i −0.584408 0.424597i
\(245\) −6.59786 1.40242i −0.421522 0.0895973i
\(246\) −1.28819 + 3.96464i −0.0821320 + 0.252776i
\(247\) 1.69041 0.107558
\(248\) 1.73039 + 5.29204i 0.109880 + 0.336045i
\(249\) 0.789117 0.0500082
\(250\) −0.309017 + 0.951057i −0.0195440 + 0.0601501i
\(251\) −21.6710 4.60630i −1.36786 0.290747i −0.535289 0.844669i \(-0.679797\pi\)
−0.832569 + 0.553921i \(0.813131\pi\)
\(252\) 0.408323 + 0.296664i 0.0257220 + 0.0186881i
\(253\) −2.15756 3.73701i −0.135645 0.234944i
\(254\) 0.845122 1.46379i 0.0530277 0.0918466i
\(255\) −2.33571 + 1.03992i −0.146268 + 0.0651225i
\(256\) −0.809017 + 0.587785i −0.0505636 + 0.0367366i
\(257\) 12.5156 + 5.57232i 0.780704 + 0.347592i 0.758088 0.652152i \(-0.226134\pi\)
0.0226163 + 0.999744i \(0.492800\pi\)
\(258\) 4.02003 0.854484i 0.250276 0.0531978i
\(259\) −0.506039 + 4.81464i −0.0314438 + 0.299167i
\(260\) −1.28441 1.42648i −0.0796557 0.0884667i
\(261\) 1.50023 1.66618i 0.0928621 0.103134i
\(262\) −0.398987 3.79611i −0.0246495 0.234524i
\(263\) −4.56839 14.0601i −0.281699 0.866981i −0.987369 0.158440i \(-0.949354\pi\)
0.705669 0.708541i \(-0.250646\pi\)
\(264\) −0.329360 1.01367i −0.0202707 0.0623869i
\(265\) −0.105202 1.00093i −0.00646254 0.0614869i
\(266\) −0.297410 + 0.330307i −0.0182354 + 0.0202524i
\(267\) −3.98937 4.43064i −0.244145 0.271151i
\(268\) 0.238267 2.26696i 0.0145545 0.138477i
\(269\) −2.10674 + 0.447800i −0.128450 + 0.0273029i −0.271688 0.962385i \(-0.587582\pi\)
0.143238 + 0.989688i \(0.454249\pi\)
\(270\) −0.913545 0.406737i −0.0555966 0.0247532i
\(271\) 13.2400 9.61939i 0.804270 0.584336i −0.107894 0.994162i \(-0.534411\pi\)
0.912164 + 0.409826i \(0.134411\pi\)
\(272\) 2.33571 1.03992i 0.141623 0.0630546i
\(273\) 0.484406 0.839016i 0.0293176 0.0507795i
\(274\) 0.0747238 + 0.129426i 0.00451423 + 0.00781888i
\(275\) 0.862276 + 0.626480i 0.0519972 + 0.0377782i
\(276\) 3.96013 + 0.841751i 0.238372 + 0.0506674i
\(277\) −3.22735 + 9.93276i −0.193913 + 0.596801i 0.806075 + 0.591813i \(0.201588\pi\)
−0.999988 + 0.00498810i \(0.998412\pi\)
\(278\) 10.9344 0.655799
\(279\) 3.71785 4.14459i 0.222582 0.248130i
\(280\) 0.504715 0.0301625
\(281\) −6.79900 + 20.9252i −0.405595 + 1.24829i 0.514803 + 0.857308i \(0.327865\pi\)
−0.920398 + 0.390983i \(0.872135\pi\)
\(282\) 9.49270 + 2.01774i 0.565282 + 0.120154i
\(283\) −0.743807 0.540407i −0.0442147 0.0321239i 0.565458 0.824777i \(-0.308699\pi\)
−0.609673 + 0.792653i \(0.708699\pi\)
\(284\) 4.47432 + 7.74976i 0.265502 + 0.459863i
\(285\) 0.440320 0.762656i 0.0260823 0.0451759i
\(286\) −1.86901 + 0.832137i −0.110517 + 0.0492053i
\(287\) −1.70217 + 1.23670i −0.100476 + 0.0729999i
\(288\) 0.913545 + 0.406737i 0.0538312 + 0.0239672i
\(289\) 10.2344 2.17539i 0.602023 0.127964i
\(290\) 0.234359 2.22978i 0.0137621 0.130937i
\(291\) −5.80399 6.44599i −0.340236 0.377870i
\(292\) −0.173869 + 0.193101i −0.0101749 + 0.0113004i
\(293\) −0.633195 6.02444i −0.0369916 0.351952i −0.997325 0.0730968i \(-0.976712\pi\)
0.960333 0.278855i \(-0.0899549\pi\)
\(294\) −2.08440 6.41513i −0.121565 0.374138i
\(295\) −2.97543 9.15744i −0.173236 0.533167i
\(296\) 1.00262 + 9.53932i 0.0582763 + 0.554462i
\(297\) −0.713181 + 0.792068i −0.0413829 + 0.0459604i
\(298\) 2.09247 + 2.32393i 0.121214 + 0.134621i
\(299\) 0.812329 7.72879i 0.0469782 0.446968i
\(300\) −0.978148 + 0.207912i −0.0564734 + 0.0120038i
\(301\) 1.89497 + 0.843693i 0.109224 + 0.0486297i
\(302\) 13.4837 9.79650i 0.775901 0.563725i
\(303\) −3.31641 + 1.47656i −0.190523 + 0.0848263i
\(304\) −0.440320 + 0.762656i −0.0252541 + 0.0437413i
\(305\) 5.64187 + 9.77201i 0.323053 + 0.559544i
\(306\) −2.06845 1.50282i −0.118246 0.0859105i
\(307\) −28.5743 6.07366i −1.63082 0.346642i −0.700576 0.713578i \(-0.747073\pi\)
−0.930246 + 0.366936i \(0.880407\pi\)
\(308\) 0.166233 0.511613i 0.00947201 0.0291519i
\(309\) 3.67263 0.208928
\(310\) 0.571674 5.53834i 0.0324689 0.314556i
\(311\) −16.6755 −0.945579 −0.472789 0.881175i \(-0.656753\pi\)
−0.472789 + 0.881175i \(0.656753\pi\)
\(312\) 0.593165 1.82557i 0.0335813 0.103353i
\(313\) −27.0192 5.74311i −1.52722 0.324620i −0.633674 0.773600i \(-0.718454\pi\)
−0.893542 + 0.448981i \(0.851787\pi\)
\(314\) −6.01771 4.37212i −0.339599 0.246733i
\(315\) −0.252358 0.437096i −0.0142187 0.0246276i
\(316\) 3.75030 6.49570i 0.210971 0.365412i
\(317\) 6.52737 2.90617i 0.366614 0.163227i −0.215158 0.976579i \(-0.569027\pi\)
0.581771 + 0.813352i \(0.302360\pi\)
\(318\) 0.814233 0.591575i 0.0456599 0.0331739i
\(319\) −2.18306 0.971963i −0.122228 0.0544195i
\(320\) 0.978148 0.207912i 0.0546801 0.0116226i
\(321\) −1.81444 + 17.2632i −0.101272 + 0.963538i
\(322\) 1.36729 + 1.51853i 0.0761963 + 0.0846246i
\(323\) 1.50660 1.67325i 0.0838293 0.0931019i
\(324\) −0.104528 0.994522i −0.00580714 0.0552512i
\(325\) 0.593165 + 1.82557i 0.0329029 + 0.101265i
\(326\) −1.93319 5.94974i −0.107069 0.329526i
\(327\) −0.634816 6.03987i −0.0351054 0.334006i
\(328\) −2.78939 + 3.09793i −0.154018 + 0.171054i
\(329\) 3.27750 + 3.64003i 0.180694 + 0.200682i
\(330\) −0.111410 + 1.05999i −0.00613291 + 0.0583507i
\(331\) 8.59690 1.82733i 0.472528 0.100439i 0.0345087 0.999404i \(-0.489013\pi\)
0.438020 + 0.898965i \(0.355680\pi\)
\(332\) 0.720894 + 0.320963i 0.0395642 + 0.0176151i
\(333\) 7.75998 5.63796i 0.425244 0.308958i
\(334\) 8.11606 3.61350i 0.444091 0.197722i
\(335\) −1.13972 + 1.97406i −0.0622698 + 0.107854i
\(336\) 0.252358 + 0.437096i 0.0137672 + 0.0238456i
\(337\) −6.37269 4.63003i −0.347143 0.252214i 0.400527 0.916285i \(-0.368827\pi\)
−0.747669 + 0.664071i \(0.768827\pi\)
\(338\) 9.11187 + 1.93679i 0.495621 + 0.105347i
\(339\) −2.85523 + 8.78750i −0.155075 + 0.477271i
\(340\) −2.55675 −0.138659
\(341\) −5.42574 2.40360i −0.293820 0.130162i
\(342\) 0.880640 0.0476195
\(343\) 2.14379 6.59790i 0.115754 0.356253i
\(344\) 4.02003 + 0.854484i 0.216745 + 0.0460707i
\(345\) −3.27538 2.37971i −0.176341 0.128119i
\(346\) 7.70701 + 13.3489i 0.414331 + 0.717643i
\(347\) 3.29994 5.71567i 0.177150 0.306833i −0.763753 0.645509i \(-0.776645\pi\)
0.940903 + 0.338675i \(0.109979\pi\)
\(348\) 2.04823 0.911929i 0.109796 0.0488845i
\(349\) −11.4181 + 8.29577i −0.611199 + 0.444062i −0.849837 0.527046i \(-0.823299\pi\)
0.238637 + 0.971109i \(0.423299\pi\)
\(350\) −0.461080 0.205286i −0.0246458 0.0109730i
\(351\) −1.87757 + 0.399091i −0.100218 + 0.0213019i
\(352\) 0.111410 1.05999i 0.00593816 0.0564978i
\(353\) 16.8455 + 18.7088i 0.896596 + 0.995771i 0.999999 + 0.00113111i \(0.000360043\pi\)
−0.103403 + 0.994639i \(0.532973\pi\)
\(354\) 6.44286 7.15552i 0.342434 0.380312i
\(355\) −0.935388 8.89963i −0.0496453 0.472343i
\(356\) −1.84237 5.67022i −0.0976452 0.300521i
\(357\) −0.398765 1.22727i −0.0211049 0.0649541i
\(358\) 1.34430 + 12.7902i 0.0710485 + 0.675981i
\(359\) −4.81254 + 5.34486i −0.253996 + 0.282091i −0.856635 0.515923i \(-0.827449\pi\)
0.602639 + 0.798014i \(0.294116\pi\)
\(360\) −0.669131 0.743145i −0.0352663 0.0391672i
\(361\) 1.90498 18.1246i 0.100262 0.953928i
\(362\) 10.7384 2.28252i 0.564398 0.119966i
\(363\) −9.01121 4.01205i −0.472966 0.210578i
\(364\) 0.783785 0.569453i 0.0410815 0.0298475i
\(365\) 0.237379 0.105688i 0.0124250 0.00553195i
\(366\) −5.64187 + 9.77201i −0.294905 + 0.510791i
\(367\) 7.50288 + 12.9954i 0.391647 + 0.678353i 0.992667 0.120881i \(-0.0385720\pi\)
−0.601020 + 0.799234i \(0.705239\pi\)
\(368\) 3.27538 + 2.37971i 0.170741 + 0.124051i
\(369\) 4.07758 + 0.866716i 0.212270 + 0.0451194i
\(370\) 2.96405 9.12241i 0.154094 0.474251i
\(371\) 0.507970 0.0263725
\(372\) 5.08218 2.27408i 0.263499 0.117906i
\(373\) −16.9266 −0.876428 −0.438214 0.898871i \(-0.644389\pi\)
−0.438214 + 0.898871i \(0.644389\pi\)
\(374\) −0.842091 + 2.59169i −0.0435435 + 0.134013i
\(375\) 0.978148 + 0.207912i 0.0505113 + 0.0107365i
\(376\) 7.85133 + 5.70432i 0.404901 + 0.294178i
\(377\) −2.15184 3.72710i −0.110826 0.191955i
\(378\) 0.252358 0.437096i 0.0129799 0.0224818i
\(379\) −17.9314 + 7.98355i −0.921072 + 0.410088i −0.811807 0.583925i \(-0.801516\pi\)
−0.109264 + 0.994013i \(0.534849\pi\)
\(380\) 0.712452 0.517627i 0.0365480 0.0265537i
\(381\) −1.54412 0.687484i −0.0791074 0.0352209i
\(382\) −5.68013 + 1.20735i −0.290621 + 0.0617734i
\(383\) −2.36503 + 22.5017i −0.120847 + 1.14978i 0.751101 + 0.660187i \(0.229523\pi\)
−0.871949 + 0.489598i \(0.837144\pi\)
\(384\) 0.669131 + 0.743145i 0.0341464 + 0.0379235i
\(385\) −0.359953 + 0.399769i −0.0183449 + 0.0203741i
\(386\) −1.07653 10.2425i −0.0547937 0.521327i
\(387\) −1.27001 3.90869i −0.0645582 0.198690i
\(388\) −2.68039 8.24940i −0.136076 0.418800i
\(389\) 0.269023 + 2.55959i 0.0136400 + 0.129776i 0.999223 0.0394176i \(-0.0125503\pi\)
−0.985583 + 0.169194i \(0.945884\pi\)
\(390\) −1.28441 + 1.42648i −0.0650386 + 0.0722327i
\(391\) −6.92634 7.69247i −0.350280 0.389025i
\(392\) 0.705072 6.70831i 0.0356115 0.338821i
\(393\) −3.73361 + 0.793602i −0.188335 + 0.0400319i
\(394\) 1.40049 + 0.623540i 0.0705559 + 0.0314135i
\(395\) −6.06811 + 4.40874i −0.305320 + 0.221828i
\(396\) −0.973686 + 0.433513i −0.0489296 + 0.0217848i
\(397\) 3.21063 5.56097i 0.161137 0.279097i −0.774140 0.633015i \(-0.781817\pi\)
0.935277 + 0.353918i \(0.115151\pi\)
\(398\) 8.03795 + 13.9221i 0.402906 + 0.697854i
\(399\) 0.359586 + 0.261254i 0.0180018 + 0.0130791i
\(400\) −0.978148 0.207912i −0.0489074 0.0103956i
\(401\) −3.26204 + 10.0395i −0.162899 + 0.501351i −0.998875 0.0474144i \(-0.984902\pi\)
0.835977 + 0.548765i \(0.184902\pi\)
\(402\) −2.27945 −0.113689
\(403\) −5.36095 9.24562i −0.267048 0.460557i
\(404\) −3.63027 −0.180612
\(405\) −0.309017 + 0.951057i −0.0153552 + 0.0472584i
\(406\) 1.10687 + 0.235274i 0.0549333 + 0.0116764i
\(407\) −8.27084 6.00912i −0.409970 0.297861i
\(408\) −1.27837 2.21421i −0.0632890 0.109620i
\(409\) 9.63076 16.6810i 0.476210 0.824820i −0.523418 0.852076i \(-0.675343\pi\)
0.999628 + 0.0272555i \(0.00867678\pi\)
\(410\) 3.80827 1.69555i 0.188077 0.0837374i
\(411\) 0.120906 0.0878432i 0.00596384 0.00433298i
\(412\) 3.35511 + 1.49379i 0.165294 + 0.0735938i
\(413\) 4.75356 1.01040i 0.233907 0.0497185i
\(414\) 0.423194 4.02642i 0.0207988 0.197888i
\(415\) −0.528022 0.586428i −0.0259196 0.0287866i
\(416\) 1.28441 1.42648i 0.0629734 0.0699390i
\(417\) −1.14295 10.8745i −0.0559706 0.532525i
\(418\) −0.290048 0.892675i −0.0141867 0.0436622i
\(419\) 0.868628 + 2.67336i 0.0424353 + 0.130602i 0.970030 0.242987i \(-0.0781271\pi\)
−0.927594 + 0.373589i \(0.878127\pi\)
\(420\) −0.0527571 0.501950i −0.00257428 0.0244927i
\(421\) −3.33125 + 3.69973i −0.162355 + 0.180314i −0.818833 0.574031i \(-0.805379\pi\)
0.656478 + 0.754345i \(0.272045\pi\)
\(422\) −5.29114 5.87641i −0.257569 0.286059i
\(423\) 1.01442 9.65161i 0.0493230 0.469277i
\(424\) 0.984455 0.209252i 0.0478093 0.0101622i
\(425\) 2.33571 + 1.03992i 0.113298 + 0.0504437i
\(426\) 7.23961 5.25988i 0.350760 0.254842i
\(427\) −5.20271 + 2.31640i −0.251777 + 0.112098i
\(428\) −8.67915 + 15.0327i −0.419522 + 0.726634i
\(429\) 1.02294 + 1.77179i 0.0493882 + 0.0855428i
\(430\) −3.32493 2.41570i −0.160342 0.116496i
\(431\) −3.70289 0.787073i −0.178362 0.0379120i 0.117865 0.993030i \(-0.462395\pi\)
−0.296227 + 0.955118i \(0.595728\pi\)
\(432\) 0.309017 0.951057i 0.0148676 0.0457577i
\(433\) 14.1918 0.682015 0.341008 0.940061i \(-0.389232\pi\)
0.341008 + 0.940061i \(0.389232\pi\)
\(434\) 2.74981 + 0.579139i 0.131995 + 0.0277996i
\(435\) −2.24206 −0.107499
\(436\) 1.87670 5.77590i 0.0898779 0.276616i
\(437\) 3.48744 + 0.741279i 0.166827 + 0.0354602i
\(438\) 0.210218 + 0.152732i 0.0100446 + 0.00729782i
\(439\) 12.3687 + 21.4232i 0.590325 + 1.02247i 0.994188 + 0.107654i \(0.0343338\pi\)
−0.403863 + 0.914819i \(0.632333\pi\)
\(440\) −0.532916 + 0.923038i −0.0254058 + 0.0440041i
\(441\) −6.16210 + 2.74355i −0.293434 + 0.130645i
\(442\) −3.97044 + 2.88469i −0.188855 + 0.137211i
\(443\) −1.13462 0.505165i −0.0539073 0.0240011i 0.379606 0.925148i \(-0.376060\pi\)
−0.433513 + 0.901147i \(0.642726\pi\)
\(444\) 9.38226 1.99426i 0.445262 0.0946435i
\(445\) −0.623201 + 5.92936i −0.0295426 + 0.281079i
\(446\) 13.5456 + 15.0439i 0.641403 + 0.712350i
\(447\) 2.09247 2.32393i 0.0989705 0.109918i
\(448\) 0.0527571 + 0.501950i 0.00249254 + 0.0237149i
\(449\) −4.62447 14.2327i −0.218242 0.671681i −0.998907 0.0467313i \(-0.985120\pi\)
0.780665 0.624950i \(-0.214880\pi\)
\(450\) 0.309017 + 0.951057i 0.0145672 + 0.0448332i
\(451\) −0.464431 4.41877i −0.0218692 0.208072i
\(452\) −6.18258 + 6.86645i −0.290804 + 0.322971i
\(453\) −11.1523 12.3858i −0.523979 0.581938i
\(454\) 2.29866 21.8703i 0.107881 1.02642i
\(455\) −0.947641 + 0.201427i −0.0444261 + 0.00944306i
\(456\) 0.804504 + 0.358188i 0.0376744 + 0.0167737i
\(457\) −5.16778 + 3.75462i −0.241739 + 0.175633i −0.702058 0.712120i \(-0.747735\pi\)
0.460319 + 0.887754i \(0.347735\pi\)
\(458\) 8.22904 3.66381i 0.384518 0.171198i
\(459\) −1.27837 + 2.21421i −0.0596694 + 0.103350i
\(460\) −2.02430 3.50619i −0.0943834 0.163477i
\(461\) −25.5244 18.5446i −1.18879 0.863706i −0.195653 0.980673i \(-0.562683\pi\)
−0.993136 + 0.116967i \(0.962683\pi\)
\(462\) −0.526186 0.111844i −0.0244804 0.00520347i
\(463\) −2.05258 + 6.31720i −0.0953916 + 0.293585i −0.987356 0.158521i \(-0.949327\pi\)
0.891964 + 0.452107i \(0.149327\pi\)
\(464\) 2.24206 0.104085
\(465\) −5.56775 + 0.0103712i −0.258198 + 0.000480954i
\(466\) −7.77146 −0.360006
\(467\) −1.84412 + 5.67563i −0.0853358 + 0.262637i −0.984615 0.174739i \(-0.944092\pi\)
0.899279 + 0.437375i \(0.144092\pi\)
\(468\) −1.87757 0.399091i −0.0867909 0.0184480i
\(469\) −0.930752 0.676231i −0.0429782 0.0312255i
\(470\) −4.85239 8.40458i −0.223824 0.387674i
\(471\) −3.71915 + 6.44176i −0.171369 + 0.296821i
\(472\) 8.79626 3.91635i 0.404881 0.180264i
\(473\) −3.54382 + 2.57473i −0.162945 + 0.118386i
\(474\) −6.85213 3.05077i −0.314729 0.140126i
\(475\) −0.861395 + 0.183095i −0.0395235 + 0.00840099i
\(476\) 0.134887 1.28336i 0.00618252 0.0588228i
\(477\) −0.673445 0.747937i −0.0308349 0.0342457i
\(478\) 1.67839 1.86404i 0.0767678 0.0852593i
\(479\) 0.780743 + 7.42827i 0.0356730 + 0.339406i 0.997773 + 0.0667078i \(0.0212495\pi\)
−0.962100 + 0.272699i \(0.912084\pi\)
\(480\) −0.309017 0.951057i −0.0141046 0.0434096i
\(481\) −5.68956 17.5107i −0.259421 0.798417i
\(482\) 1.59361 + 15.1622i 0.0725870 + 0.690619i
\(483\) 1.36729 1.51853i 0.0622140 0.0690957i
\(484\) −6.60031 7.33038i −0.300014 0.333199i
\(485\) −0.906673 + 8.62641i −0.0411699 + 0.391705i
\(486\) −0.978148 + 0.207912i −0.0443697 + 0.00943107i
\(487\) 13.4318 + 5.98020i 0.608651 + 0.270989i 0.687830 0.725872i \(-0.258563\pi\)
−0.0791794 + 0.996860i \(0.525230\pi\)
\(488\) −9.12874 + 6.63242i −0.413239 + 0.300235i
\(489\) −5.71508 + 2.54452i −0.258445 + 0.115067i
\(490\) −3.37263 + 5.84157i −0.152360 + 0.263895i
\(491\) −15.9787 27.6759i −0.721109 1.24900i −0.960556 0.278087i \(-0.910299\pi\)
0.239447 0.970909i \(-0.423034\pi\)
\(492\) 3.37253 + 2.45028i 0.152045 + 0.110467i
\(493\) −5.60712 1.19183i −0.252532 0.0536774i
\(494\) 0.522364 1.60767i 0.0235023 0.0723326i
\(495\) 1.06583 0.0479056
\(496\) 5.56775 0.0103712i 0.250000 0.000465682i
\(497\) 4.51652 0.202594
\(498\) 0.243850 0.750495i 0.0109272 0.0336305i
\(499\) −18.1957 3.86762i −0.814553 0.173138i −0.218244 0.975894i \(-0.570033\pi\)
−0.596308 + 0.802756i \(0.703366\pi\)
\(500\) 0.809017 + 0.587785i 0.0361803 + 0.0262866i
\(501\) −4.44207 7.69389i −0.198457 0.343738i
\(502\) −11.0775 + 19.1869i −0.494415 + 0.856352i
\(503\) −23.6615 + 10.5348i −1.05501 + 0.469723i −0.859584 0.510995i \(-0.829277\pi\)
−0.195430 + 0.980718i \(0.562610\pi\)
\(504\) 0.408323 0.296664i 0.0181882 0.0132145i
\(505\) 3.31641 + 1.47656i 0.147578 + 0.0657062i
\(506\) −4.22083 + 0.897165i −0.187639 + 0.0398838i
\(507\) 0.973729 9.26441i 0.0432448 0.411447i
\(508\) −1.13099 1.25610i −0.0501798 0.0557303i
\(509\) 13.4069 14.8899i 0.594250 0.659981i −0.368736 0.929534i \(-0.620209\pi\)
0.962986 + 0.269553i \(0.0868759\pi\)
\(510\) 0.267253 + 2.54274i 0.0118342 + 0.112595i
\(511\) 0.0405266 + 0.124728i 0.00179279 + 0.00551765i
\(512\) 0.309017 + 0.951057i 0.0136568 + 0.0420312i
\(513\) −0.0920519 0.875815i −0.00406419 0.0386682i
\(514\) 9.16714 10.1811i 0.404345 0.449071i
\(515\) −2.45747 2.72929i −0.108289 0.120267i
\(516\) 0.429595 4.08733i 0.0189119 0.179934i
\(517\) −10.1176 + 2.15057i −0.444973 + 0.0945818i
\(518\) 4.42262 + 1.96908i 0.194319 + 0.0865163i
\(519\) 12.4702 9.06013i 0.547381 0.397696i
\(520\) −1.75357 + 0.780740i −0.0768991 + 0.0342377i
\(521\) −15.2530 + 26.4190i −0.668246 + 1.15744i 0.310148 + 0.950688i \(0.399621\pi\)
−0.978394 + 0.206748i \(0.933712\pi\)
\(522\) −1.12103 1.94168i −0.0490662 0.0849851i
\(523\) 8.29085 + 6.02365i 0.362534 + 0.263396i 0.754108 0.656750i \(-0.228069\pi\)
−0.391575 + 0.920146i \(0.628069\pi\)
\(524\) −3.73361 0.793602i −0.163103 0.0346687i
\(525\) −0.155966 + 0.480013i −0.00680690 + 0.0209495i
\(526\) −14.7836 −0.644597
\(527\) −13.9298 2.93376i −0.606791 0.127797i
\(528\) −1.06583 −0.0463844
\(529\) −2.04225 + 6.28540i −0.0887935 + 0.273278i
\(530\) −0.984455 0.209252i −0.0427620 0.00908934i
\(531\) −7.78978 5.65961i −0.338048 0.245606i
\(532\) 0.222236 + 0.384924i 0.00963516 + 0.0166886i
\(533\) 4.00093 6.92981i 0.173299 0.300163i
\(534\) −5.44658 + 2.42497i −0.235696 + 0.104939i
\(535\) 14.0432 10.2030i 0.607139 0.441112i
\(536\) −2.08238 0.927136i −0.0899451 0.0400462i
\(537\) 12.5796 2.67387i 0.542849 0.115386i
\(538\) −0.225133 + 2.14200i −0.00970619 + 0.0923483i
\(539\) 4.81059 + 5.34270i 0.207207 + 0.230127i
\(540\) −0.669131 + 0.743145i −0.0287948 + 0.0319799i
\(541\) −3.51153 33.4100i −0.150972 1.43641i −0.763423 0.645898i \(-0.776483\pi\)
0.612451 0.790509i \(-0.290184\pi\)
\(542\) −5.05721 15.5645i −0.217226 0.668552i
\(543\) −3.39248 10.4410i −0.145585 0.448066i
\(544\) −0.267253 2.54274i −0.0114584 0.109019i
\(545\) −4.06373 + 4.51323i −0.174071 + 0.193325i
\(546\) −0.648262 0.719967i −0.0277430 0.0308118i
\(547\) 3.78410 36.0033i 0.161797 1.53939i −0.548897 0.835890i \(-0.684952\pi\)
0.710694 0.703501i \(-0.248381\pi\)
\(548\) 0.146182 0.0310719i 0.00624458 0.00132733i
\(549\) 10.3082 + 4.58951i 0.439944 + 0.195876i
\(550\) 0.862276 0.626480i 0.0367676 0.0267132i
\(551\) 1.80375 0.803081i 0.0768423 0.0342124i
\(552\) 2.02430 3.50619i 0.0861599 0.149233i
\(553\) −1.89283 3.27848i −0.0804914 0.139415i
\(554\) 8.44931 + 6.13878i 0.358977 + 0.260812i
\(555\) −9.38226 1.99426i −0.398255 0.0846517i
\(556\) 3.37890 10.3992i 0.143297 0.441024i
\(557\) 12.4171 0.526128 0.263064 0.964778i \(-0.415267\pi\)
0.263064 + 0.964778i \(0.415267\pi\)
\(558\) −2.79286 4.81663i −0.118231 0.203904i
\(559\) −7.88892 −0.333666
\(560\) 0.155966 0.480013i 0.00659075 0.0202842i
\(561\) 2.66552 + 0.566573i 0.112538 + 0.0239207i
\(562\) 17.8000 + 12.9325i 0.750849 + 0.545524i
\(563\) −13.5801 23.5214i −0.572332 0.991308i −0.996326 0.0856430i \(-0.972706\pi\)
0.423994 0.905665i \(-0.360628\pi\)
\(564\) 4.85239 8.40458i 0.204322 0.353897i
\(565\) 8.44091 3.75813i 0.355112 0.158106i
\(566\) −0.743807 + 0.540407i −0.0312645 + 0.0227150i
\(567\) −0.461080 0.205286i −0.0193636 0.00862121i
\(568\) 8.75310 1.86053i 0.367272 0.0780660i
\(569\) −1.47609 + 14.0440i −0.0618807 + 0.588756i 0.919015 + 0.394222i \(0.128986\pi\)
−0.980896 + 0.194534i \(0.937681\pi\)
\(570\) −0.589263 0.654443i −0.0246815 0.0274116i
\(571\) 11.3330 12.5865i 0.474270 0.526730i −0.457777 0.889067i \(-0.651354\pi\)
0.932047 + 0.362337i \(0.118021\pi\)
\(572\) 0.213853 + 2.03468i 0.00894166 + 0.0850742i
\(573\) 1.79447 + 5.52281i 0.0749651 + 0.230719i
\(574\) 0.650170 + 2.00102i 0.0271376 + 0.0835208i
\(575\) 0.423194 + 4.02642i 0.0176484 + 0.167913i
\(576\) 0.669131 0.743145i 0.0278804 0.0309644i
\(577\) −12.1843 13.5321i −0.507240 0.563347i 0.434075 0.900877i \(-0.357075\pi\)
−0.941315 + 0.337530i \(0.890409\pi\)
\(578\) 1.09368 10.4057i 0.0454913 0.432821i
\(579\) −10.0738 + 2.14126i −0.418654 + 0.0889875i
\(580\) −2.04823 0.911929i −0.0850479 0.0378658i
\(581\) 0.322215 0.234103i 0.0133677 0.00971222i
\(582\) −7.92403 + 3.52801i −0.328462 + 0.146241i
\(583\) −0.536352 + 0.928989i −0.0222134 + 0.0384748i
\(584\) 0.129922 + 0.225031i 0.00537620 + 0.00931185i
\(585\) 1.55293 + 1.12827i 0.0642055 + 0.0466481i
\(586\) −5.92525 1.25945i −0.244770 0.0520275i
\(587\) −7.02382 + 21.6171i −0.289904 + 0.892232i 0.694982 + 0.719027i \(0.255412\pi\)
−0.984886 + 0.173205i \(0.944588\pi\)
\(588\) −6.74526 −0.278170
\(589\) 4.47557 2.00265i 0.184413 0.0825177i
\(590\) −9.62870 −0.396407
\(591\) 0.473733 1.45800i 0.0194868 0.0599741i
\(592\) 9.38226 + 1.99426i 0.385609 + 0.0819636i
\(593\) 27.6610 + 20.0969i 1.13590 + 0.825280i 0.986543 0.163503i \(-0.0522792\pi\)
0.149358 + 0.988783i \(0.452279\pi\)
\(594\) 0.532916 + 0.923038i 0.0218658 + 0.0378727i
\(595\) −0.645215 + 1.11755i −0.0264512 + 0.0458149i
\(596\) 2.85679 1.27193i 0.117019 0.0521001i
\(597\) 13.0057 9.44918i 0.532287 0.386729i
\(598\) −7.09950 3.16090i −0.290320 0.129259i
\(599\) 36.3297 7.72211i 1.48439 0.315517i 0.606771 0.794876i \(-0.292464\pi\)
0.877619 + 0.479359i \(0.159131\pi\)
\(600\) −0.104528 + 0.994522i −0.00426736 + 0.0406012i
\(601\) 3.54171 + 3.93346i 0.144469 + 0.160449i 0.811036 0.584996i \(-0.198904\pi\)
−0.666567 + 0.745445i \(0.732237\pi\)
\(602\) 1.38798 1.54150i 0.0565697 0.0628270i
\(603\) 0.238267 + 2.26696i 0.00970300 + 0.0923178i
\(604\) −5.15032 15.8511i −0.209564 0.644971i
\(605\) 3.04814 + 9.38122i 0.123925 + 0.381401i
\(606\) 0.379466 + 3.61038i 0.0154148 + 0.146662i
\(607\) −17.9184 + 19.9004i −0.727285 + 0.807732i −0.987467 0.157828i \(-0.949551\pi\)
0.260182 + 0.965560i \(0.416218\pi\)
\(608\) 0.589263 + 0.654443i 0.0238978 + 0.0265412i
\(609\) 0.118285 1.12540i 0.00479314 0.0456037i
\(610\) 11.0372 2.34602i 0.446882 0.0949877i
\(611\) −17.0180 7.57690i −0.688474 0.306529i
\(612\) −2.06845 + 1.50282i −0.0836123 + 0.0607479i
\(613\) −30.9649 + 13.7865i −1.25066 + 0.556830i −0.921843 0.387563i \(-0.873317\pi\)
−0.328818 + 0.944393i \(0.606650\pi\)
\(614\) −14.6063 + 25.2989i −0.589464 + 1.02098i
\(615\) −2.08434 3.61018i −0.0840486 0.145576i
\(616\) −0.435204 0.316194i −0.0175349 0.0127398i
\(617\) −10.4831 2.22825i −0.422033 0.0897058i −0.00800031 0.999968i \(-0.502547\pi\)
−0.414032 + 0.910262i \(0.635880\pi\)
\(618\) 1.13490 3.49288i 0.0456525 0.140504i
\(619\) 42.4657 1.70684 0.853420 0.521225i \(-0.174525\pi\)
0.853420 + 0.521225i \(0.174525\pi\)
\(620\) −5.09062 2.25514i −0.204444 0.0905684i
\(621\) −4.04860 −0.162465
\(622\) −5.15300 + 15.8593i −0.206617 + 0.635900i
\(623\) −2.94337 0.625632i −0.117923 0.0250654i
\(624\) −1.55293 1.12827i −0.0621668 0.0451668i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −13.8114 + 23.9221i −0.552015 + 0.956118i
\(627\) −0.857466 + 0.381769i −0.0342439 + 0.0152464i
\(628\) −6.01771 + 4.37212i −0.240133 + 0.174467i
\(629\) −22.4038 9.97481i −0.893297 0.397722i
\(630\) −0.493686 + 0.104936i −0.0196689 + 0.00418076i
\(631\) 3.09666 29.4628i 0.123276 1.17289i −0.741577 0.670868i \(-0.765922\pi\)
0.864853 0.502026i \(-0.167412\pi\)
\(632\) −5.01888 5.57403i −0.199640 0.221723i
\(633\) −5.29114 + 5.87641i −0.210304 + 0.233566i
\(634\) −0.746866 7.10595i −0.0296618 0.282213i
\(635\) 0.522314 + 1.60752i 0.0207274 + 0.0637924i
\(636\) −0.311010 0.957189i −0.0123323 0.0379550i
\(637\) 1.35340 + 12.8767i 0.0536237 + 0.510195i
\(638\) −1.59900 + 1.77586i −0.0633048 + 0.0703072i
\(639\) −5.98781 6.65014i −0.236874 0.263076i
\(640\) 0.104528 0.994522i 0.00413185 0.0393119i
\(641\) 30.2300 6.42559i 1.19401 0.253795i 0.432312 0.901724i \(-0.357698\pi\)
0.761701 + 0.647928i \(0.224364\pi\)
\(642\) 15.8576 + 7.06026i 0.625849 + 0.278646i
\(643\) 30.0569 21.8376i 1.18533 0.861191i 0.192565 0.981284i \(-0.438319\pi\)
0.992763 + 0.120093i \(0.0383194\pi\)
\(644\) 1.86673 0.831121i 0.0735594 0.0327508i
\(645\) −2.05492 + 3.55923i −0.0809124 + 0.140144i
\(646\) −1.12579 1.94992i −0.0442935 0.0767186i
\(647\) 17.9864 + 13.0679i 0.707119 + 0.513752i 0.882243 0.470794i \(-0.156033\pi\)
−0.175124 + 0.984546i \(0.556033\pi\)
\(648\) −0.978148 0.207912i −0.0384253 0.00816754i
\(649\) −3.17131 + 9.76029i −0.124485 + 0.383125i
\(650\) 1.91952 0.0752898
\(651\) 0.288533 2.79528i 0.0113085 0.109556i
\(652\) −6.25593 −0.245001
\(653\) −1.19070 + 3.66459i −0.0465955 + 0.143406i −0.971647 0.236434i \(-0.924021\pi\)
0.925052 + 0.379841i \(0.124021\pi\)
\(654\) −5.94043 1.26268i −0.232289 0.0493746i
\(655\) 3.08803 + 2.24359i 0.120659 + 0.0876642i
\(656\) 2.08434 + 3.61018i 0.0813797 + 0.140954i
\(657\) 0.129922 0.225031i 0.00506873 0.00877929i
\(658\) 4.47468 1.99226i 0.174441 0.0776662i
\(659\) 20.6044 14.9700i 0.802634 0.583148i −0.109052 0.994036i \(-0.534781\pi\)
0.911686 + 0.410888i \(0.134781\pi\)
\(660\) 0.973686 + 0.433513i 0.0379007 + 0.0168745i
\(661\) 39.9028 8.48161i 1.55204 0.329896i 0.649453 0.760402i \(-0.274998\pi\)
0.902588 + 0.430505i \(0.141665\pi\)
\(662\) 0.918696 8.74081i 0.0357061 0.339721i
\(663\) 3.28391 + 3.64716i 0.127537 + 0.141644i
\(664\) 0.528022 0.586428i 0.0204912 0.0227578i
\(665\) −0.0464600 0.442037i −0.00180164 0.0171415i
\(666\) −2.96405 9.12241i −0.114855 0.353486i
\(667\) −2.80501 8.63294i −0.108610 0.334269i
\(668\) −0.928645 8.83547i −0.0359304 0.341855i
\(669\) 13.5456 15.0439i 0.523703 0.581632i
\(670\) 1.52525 + 1.69396i 0.0589255 + 0.0654434i
\(671\) 1.25712 11.9607i 0.0485306 0.461737i
\(672\) 0.493686 0.104936i 0.0190444 0.00404800i
\(673\) 6.67609 + 2.97239i 0.257344 + 0.114577i 0.531354 0.847150i \(-0.321683\pi\)
−0.274010 + 0.961727i \(0.588350\pi\)
\(674\) −6.37269 + 4.63003i −0.245467 + 0.178342i
\(675\) 0.913545 0.406737i 0.0351624 0.0156553i
\(676\) 4.65772 8.06741i 0.179143 0.310285i
\(677\) 20.9423 + 36.2731i 0.804878 + 1.39409i 0.916373 + 0.400325i \(0.131103\pi\)
−0.111495 + 0.993765i \(0.535564\pi\)
\(678\) 7.47509 + 5.43097i 0.287079 + 0.208575i
\(679\) −4.28220 0.910209i −0.164336 0.0349306i
\(680\) −0.790079 + 2.43161i −0.0302981 + 0.0932481i
\(681\) −21.9907 −0.842687
\(682\) −3.96260 + 4.41743i −0.151736 + 0.169152i
\(683\) 18.0458 0.690505 0.345253 0.938510i \(-0.387793\pi\)
0.345253 + 0.938510i \(0.387793\pi\)
\(684\) 0.272133 0.837538i 0.0104052 0.0320241i
\(685\) −0.146182 0.0310719i −0.00558532 0.00118720i
\(686\) −5.61251 4.07773i −0.214287 0.155688i
\(687\) −4.50390 7.80099i −0.171835 0.297626i
\(688\) 2.05492 3.55923i 0.0783431 0.135694i
\(689\) −1.76488 + 0.785774i −0.0672364 + 0.0299356i
\(690\) −3.27538 + 2.37971i −0.124692 + 0.0905938i
\(691\) 4.52697 + 2.01554i 0.172214 + 0.0766746i 0.491033 0.871141i \(-0.336619\pi\)
−0.318819 + 0.947816i \(0.603286\pi\)
\(692\) 15.0772 3.20475i 0.573148 0.121826i
\(693\) −0.0562302 + 0.534995i −0.00213601 + 0.0203228i
\(694\) −4.41619 4.90467i −0.167636 0.186179i
\(695\) −7.31651 + 8.12581i −0.277531 + 0.308230i
\(696\) −0.234359 2.22978i −0.00888337 0.0845196i
\(697\) −3.29358 10.1366i −0.124753 0.383951i
\(698\) 4.36134 + 13.4228i 0.165079 + 0.508062i
\(699\) 0.812339 + 7.72889i 0.0307255 + 0.292333i
\(700\) −0.337720 + 0.375077i −0.0127646 + 0.0141766i
\(701\) −0.710260 0.788824i −0.0268261 0.0297935i 0.729582 0.683893i \(-0.239714\pi\)
−0.756409 + 0.654099i \(0.773048\pi\)
\(702\) −0.200645 + 1.90901i −0.00757284 + 0.0720508i
\(703\) 8.26239 1.75623i 0.311622 0.0662373i
\(704\) −0.973686 0.433513i −0.0366972 0.0163386i
\(705\) −7.85133 + 5.70432i −0.295698 + 0.214837i
\(706\) 22.9987 10.2397i 0.865568 0.385376i
\(707\) −0.916125 + 1.58678i −0.0344544 + 0.0596768i
\(708\) −4.81435 8.33870i −0.180934 0.313388i
\(709\) −19.4117 14.1035i −0.729023 0.529667i 0.160231 0.987080i \(-0.448776\pi\)
−0.889254 + 0.457413i \(0.848776\pi\)
\(710\) −8.75310 1.86053i −0.328498 0.0698244i
\(711\) −2.31781 + 7.13349i −0.0869247 + 0.267527i
\(712\) −5.96202 −0.223436
\(713\) −7.00567 21.4254i −0.262364 0.802386i
\(714\) −1.29043 −0.0482931
\(715\) 0.632214 1.94575i 0.0236435 0.0727671i
\(716\) 12.5796 + 2.67387i 0.470121 + 0.0999273i
\(717\) −2.02927 1.47435i −0.0757845 0.0550606i
\(718\) 3.59611 + 6.22865i 0.134206 + 0.232451i
\(719\) 1.22986 2.13018i 0.0458660 0.0794422i −0.842181 0.539195i \(-0.818729\pi\)
0.888047 + 0.459753i \(0.152062\pi\)
\(720\) −0.913545 + 0.406737i −0.0340458 + 0.0151582i
\(721\) 1.49962 1.08954i 0.0558487 0.0405765i
\(722\) −16.6489 7.41256i −0.619607 0.275867i
\(723\) 14.9126 3.16976i 0.554604 0.117885i
\(724\) 1.14755 10.9182i 0.0426482 0.405770i
\(725\) 1.50023 + 1.66618i 0.0557172 + 0.0618803i
\(726\) −6.60031 + 7.33038i −0.244960 + 0.272056i
\(727\) 4.43124 + 42.1604i 0.164346 + 1.56364i 0.696850 + 0.717217i \(0.254584\pi\)
−0.532504 + 0.846427i \(0.678749\pi\)
\(728\) −0.299379 0.921395i −0.0110957 0.0341492i
\(729\) 0.309017 + 0.951057i 0.0114451 + 0.0352243i
\(730\) −0.0271610 0.258420i −0.00100527 0.00956455i
\(731\) −7.03111 + 7.80884i −0.260055 + 0.288820i
\(732\) 7.55030 + 8.38546i 0.279067 + 0.309935i
\(733\) 3.97248 37.7956i 0.146727 1.39601i −0.635058 0.772464i \(-0.719024\pi\)
0.781785 0.623548i \(-0.214309\pi\)
\(734\) 14.6779 3.11987i 0.541769 0.115157i
\(735\) 6.16210 + 2.74355i 0.227293 + 0.101197i
\(736\) 3.27538 2.37971i 0.120732 0.0877171i
\(737\) 2.21947 0.988171i 0.0817552 0.0363997i
\(738\) 2.08434 3.61018i 0.0767255 0.132892i
\(739\) 11.6260 + 20.1368i 0.427668 + 0.740743i 0.996665 0.0815965i \(-0.0260019\pi\)
−0.568997 + 0.822339i \(0.692669\pi\)
\(740\) −7.75998 5.63796i −0.285263 0.207255i
\(741\) −1.65347 0.351455i −0.0607416 0.0129110i
\(742\) 0.156971 0.483108i 0.00576260 0.0177355i
\(743\) −4.65333 −0.170714 −0.0853570 0.996350i \(-0.527203\pi\)
−0.0853570 + 0.996350i \(0.527203\pi\)
\(744\) −0.592303 5.53617i −0.0217149 0.202966i
\(745\) −3.12715 −0.114570
\(746\) −5.23062 + 16.0982i −0.191507 + 0.589397i
\(747\) −0.771873 0.164067i −0.0282413 0.00600288i
\(748\) 2.20462 + 1.60175i 0.0806090 + 0.0585659i
\(749\) 4.38050 + 7.58725i 0.160060 + 0.277232i
\(750\) 0.500000 0.866025i 0.0182574 0.0316228i
\(751\) 1.87845 0.836339i 0.0685456 0.0305185i −0.372178 0.928162i \(-0.621389\pi\)
0.440723 + 0.897643i \(0.354722\pi\)
\(752\) 7.85133 5.70432i 0.286308 0.208015i
\(753\) 20.2397 + 9.01129i 0.737575 + 0.328390i
\(754\) −4.20964 + 0.894786i −0.153306 + 0.0325862i
\(755\) −1.74215 + 16.5755i −0.0634035 + 0.603244i
\(756\) −0.337720 0.375077i −0.0122828 0.0136414i
\(757\) 15.9143 17.6747i 0.578416 0.642396i −0.380938 0.924601i \(-0.624399\pi\)
0.959354 + 0.282204i \(0.0910655\pi\)
\(758\) 2.05172 + 19.5208i 0.0745217 + 0.709027i
\(759\) 1.33345 + 4.10393i 0.0484011 + 0.148963i
\(760\) −0.272133 0.837538i −0.00987129 0.0303807i
\(761\) 3.85927 + 36.7185i 0.139898 + 1.33104i 0.808971 + 0.587848i \(0.200025\pi\)
−0.669073 + 0.743197i \(0.733309\pi\)
\(762\) −1.13099 + 1.25610i −0.0409716 + 0.0455036i
\(763\) −2.05103 2.27789i −0.0742521 0.0824653i
\(764\) −0.607000 + 5.77522i −0.0219605 + 0.208940i
\(765\) 2.50088 0.531578i 0.0904194 0.0192192i
\(766\) 20.6696 + 9.20269i 0.746822 + 0.332507i
\(767\) −14.9527 + 10.8637i −0.539909 + 0.392267i
\(768\) 0.913545 0.406737i 0.0329647 0.0146768i
\(769\) 1.49734 2.59346i 0.0539953 0.0935227i −0.837764 0.546032i \(-0.816138\pi\)
0.891760 + 0.452509i \(0.149471\pi\)
\(770\) 0.268971 + 0.465871i 0.00969304 + 0.0167888i
\(771\) −11.0836 8.05270i −0.399166 0.290011i
\(772\) −10.0738 2.14126i −0.362565 0.0770655i
\(773\) 13.0666 40.2150i 0.469974 1.44643i −0.382643 0.923896i \(-0.624986\pi\)
0.852617 0.522536i \(-0.175014\pi\)
\(774\) −4.10984 −0.147725
\(775\) 3.73326 + 4.13071i 0.134103 + 0.148379i
\(776\) −8.67393 −0.311376
\(777\) 1.49600 4.60422i 0.0536688 0.165175i
\(778\) 2.51744 + 0.535099i 0.0902548 + 0.0191842i
\(779\) 2.96998 + 2.15782i 0.106411 + 0.0773118i
\(780\) 0.959760 + 1.66235i 0.0343649 + 0.0595218i
\(781\) −4.76888 + 8.25994i −0.170644 + 0.295564i
\(782\) −9.45633 + 4.21023i −0.338158 + 0.150558i
\(783\) −1.81387 + 1.31785i −0.0648223 + 0.0470962i
\(784\) −6.16210 2.74355i −0.220075 0.0979838i
\(785\) 7.27576 1.54651i 0.259683 0.0551973i
\(786\) −0.398987 + 3.79611i −0.0142314 + 0.135403i
\(787\) 13.1611 + 14.6168i 0.469141 + 0.521034i 0.930556 0.366151i \(-0.119325\pi\)
−0.461414 + 0.887185i \(0.652658\pi\)
\(788\) 1.02580 1.13926i 0.0365426 0.0405846i
\(789\) 1.54531 + 14.7026i 0.0550145 + 0.523428i
\(790\) 2.31781 + 7.13349i 0.0824640 + 0.253798i
\(791\) 1.44108 + 4.43519i 0.0512389 + 0.157697i
\(792\) 0.111410 + 1.05999i 0.00395877 + 0.0376652i
\(793\) 14.4930 16.0961i 0.514660 0.571588i
\(794\) −4.29666 4.77192i −0.152483 0.169349i
\(795\) −0.105202 + 1.00093i −0.00373115 + 0.0354995i
\(796\) 15.7246 3.34237i 0.557344 0.118467i
\(797\) −0.496801 0.221190i −0.0175976 0.00783495i 0.397919 0.917421i \(-0.369733\pi\)
−0.415517 + 0.909586i \(0.636399\pi\)
\(798\) 0.359586 0.261254i 0.0127292 0.00924830i
\(799\) −22.6675 + 10.0922i −0.801918 + 0.357037i
\(800\) −0.500000 + 0.866025i −0.0176777 + 0.0306186i
\(801\) 2.98101 + 5.16326i 0.105329 + 0.182435i
\(802\) 8.54014 + 6.20478i 0.301563 + 0.219098i
\(803\) −0.270897 0.0575810i −0.00955976 0.00203199i
\(804\) −0.704389 + 2.16789i −0.0248419 + 0.0764554i
\(805\) −2.04339 −0.0720200
\(806\) −10.4497 + 2.24151i −0.368076 + 0.0789539i
\(807\) 2.15380 0.0758174
\(808\) −1.12181 + 3.45259i −0.0394653 + 0.121462i
\(809\) −23.5502 5.00574i −0.827979 0.175992i −0.225618 0.974216i \(-0.572440\pi\)
−0.602361 + 0.798223i \(0.705773\pi\)
\(810\) 0.809017 + 0.587785i 0.0284260 + 0.0206527i
\(811\) 0.420409 + 0.728170i 0.0147626 + 0.0255695i 0.873312 0.487161i \(-0.161967\pi\)
−0.858550 + 0.512730i \(0.828634\pi\)
\(812\) 0.565802 0.979997i 0.0198557 0.0343912i
\(813\) −14.9506 + 6.65644i −0.524341 + 0.233452i
\(814\) −8.27084 + 6.00912i −0.289893 + 0.210619i
\(815\) 5.71508 + 2.54452i 0.200190 + 0.0891305i
\(816\) −2.50088 + 0.531578i −0.0875482 + 0.0186090i
\(817\) 0.378319 3.59946i 0.0132357 0.125929i
\(818\) −12.8885 14.3141i −0.450635 0.500481i
\(819\) −0.648262 + 0.719967i −0.0226521 + 0.0251577i
\(820\) −0.435745 4.14584i −0.0152169 0.144779i
\(821\) 6.56805 + 20.2144i 0.229226 + 0.705487i 0.997835 + 0.0657671i \(0.0209494\pi\)
−0.768609 + 0.639719i \(0.779051\pi\)
\(822\) −0.0461819 0.142133i −0.00161078 0.00495746i
\(823\) 5.15435 + 49.0404i 0.179669 + 1.70944i 0.598291 + 0.801279i \(0.295847\pi\)
−0.418622 + 0.908161i \(0.637487\pi\)
\(824\) 2.45747 2.72929i 0.0856099 0.0950794i
\(825\) −0.713181 0.792068i −0.0248298 0.0275763i
\(826\) 0.507983 4.83313i 0.0176750 0.168166i
\(827\) −13.0933 + 2.78307i −0.455300 + 0.0967770i −0.429852 0.902899i \(-0.641434\pi\)
−0.0254475 + 0.999676i \(0.508101\pi\)
\(828\) −3.69858 1.64671i −0.128534 0.0572272i
\(829\) 21.1414 15.3601i 0.734272 0.533480i −0.156640 0.987656i \(-0.550066\pi\)
0.890912 + 0.454176i \(0.150066\pi\)
\(830\) −0.720894 + 0.320963i −0.0250226 + 0.0111408i
\(831\) 5.22196 9.04470i 0.181148 0.313757i
\(832\) −0.959760 1.66235i −0.0332737 0.0576318i
\(833\) 13.9523 + 10.1369i 0.483417 + 0.351223i
\(834\) −10.6954 2.27338i −0.370352 0.0787207i
\(835\) −2.74535 + 8.44932i −0.0950068 + 0.292401i
\(836\) −0.938614 −0.0324626
\(837\) −4.49831 + 3.28103i −0.155484 + 0.113409i
\(838\) 2.81094 0.0971023
\(839\) −13.3065 + 40.9531i −0.459390 + 1.41386i 0.406513 + 0.913645i \(0.366744\pi\)
−0.865903 + 0.500212i \(0.833256\pi\)
\(840\) −0.493686 0.104936i −0.0170338 0.00362064i
\(841\) 19.3947 + 14.0911i 0.668782 + 0.485899i
\(842\) 2.48924 + 4.31148i 0.0857847 + 0.148584i
\(843\) 11.0010 19.0543i 0.378895 0.656266i
\(844\) −7.22385 + 3.21627i −0.248655 + 0.110708i
\(845\) −7.53635 + 5.47548i −0.259258 + 0.188362i
\(846\) −8.86575 3.94729i −0.304811 0.135711i
\(847\) −4.86972 + 1.03509i −0.167326 + 0.0355662i
\(848\) 0.105202 1.00093i 0.00361267 0.0343722i
\(849\) 0.615196 + 0.683244i 0.0211135 + 0.0234489i
\(850\) 1.71080 1.90003i 0.0586799 0.0651707i
\(851\) −4.05922 38.6209i −0.139148 1.32391i
\(852\) −2.76528 8.51067i −0.0947371 0.291571i
\(853\) 7.79682 + 23.9962i 0.266958 + 0.821613i 0.991236 + 0.132104i \(0.0421734\pi\)
−0.724278 + 0.689508i \(0.757827\pi\)
\(854\) 0.595298 + 5.66388i 0.0203707 + 0.193814i
\(855\) −0.589263 + 0.654443i −0.0201524 + 0.0223815i
\(856\) 11.6150 + 12.8997i 0.396991 + 0.440904i
\(857\) −4.52536 + 43.0560i −0.154583 + 1.47076i 0.592251 + 0.805754i \(0.298239\pi\)
−0.746834 + 0.665010i \(0.768427\pi\)
\(858\) 2.00118 0.425364i 0.0683191 0.0145217i
\(859\) 20.7984 + 9.26004i 0.709632 + 0.315948i 0.729621 0.683852i \(-0.239696\pi\)
−0.0199891 + 0.999800i \(0.506363\pi\)
\(860\) −3.32493 + 2.41570i −0.113379 + 0.0823748i
\(861\) 1.92209 0.855771i 0.0655048 0.0291646i
\(862\) −1.89281 + 3.27844i −0.0644693 + 0.111664i
\(863\) 14.5028 + 25.1196i 0.493681 + 0.855081i 0.999973 0.00728118i \(-0.00231769\pi\)
−0.506292 + 0.862362i \(0.668984\pi\)
\(864\) −0.809017 0.587785i −0.0275233 0.0199969i
\(865\) −15.0772 3.20475i −0.512639 0.108965i
\(866\) 4.38551 13.4972i 0.149026 0.458654i
\(867\) −10.4630 −0.355343
\(868\) 1.40053 2.43626i 0.0475372 0.0826921i
\(869\) 7.99437 0.271190
\(870\) −0.692835 + 2.13233i −0.0234893 + 0.0722927i
\(871\) 4.27984 + 0.909707i 0.145017 + 0.0308243i
\(872\) −4.91328 3.56970i −0.166385 0.120885i
\(873\) 4.33697 + 7.51184i 0.146784 + 0.254237i
\(874\) 1.78268 3.08769i 0.0603000 0.104443i
\(875\) 0.461080 0.205286i 0.0155874 0.00693994i
\(876\) 0.210218 0.152732i 0.00710260 0.00516034i
\(877\) −36.3831 16.1988i −1.22857 0.546995i −0.313231 0.949677i \(-0.601411\pi\)
−0.915340 + 0.402682i \(0.868078\pi\)
\(878\) 24.1968 5.14319i 0.816603 0.173574i
\(879\) −0.633195 + 6.02444i −0.0213571 + 0.203199i
\(880\) 0.713181 + 0.792068i 0.0240413 + 0.0267006i
\(881\) −12.6947 + 14.0988i −0.427694 + 0.475002i −0.918018 0.396538i \(-0.870212\pi\)
0.490325 + 0.871540i \(0.336878\pi\)
\(882\) 0.705072 + 6.70831i 0.0237410 + 0.225881i
\(883\) −4.78390 14.7233i −0.160991 0.495479i 0.837728 0.546088i \(-0.183884\pi\)
−0.998719 + 0.0506090i \(0.983884\pi\)
\(884\) 1.51657 + 4.66753i 0.0510079 + 0.156986i
\(885\) 1.00647 + 9.57596i 0.0338322 + 0.321892i
\(886\) −0.831056 + 0.922982i −0.0279199 + 0.0310082i
\(887\) 14.0746 + 15.6314i 0.472577 + 0.524850i 0.931556 0.363597i \(-0.118451\pi\)
−0.458979 + 0.888447i \(0.651785\pi\)
\(888\) 1.00262 9.53932i 0.0336458 0.320119i
\(889\) −0.834450 + 0.177368i −0.0279866 + 0.00594873i
\(890\) 5.44658 + 2.42497i 0.182570 + 0.0812853i
\(891\) 0.862276 0.626480i 0.0288873 0.0209879i
\(892\) 18.4934 8.23381i 0.619206 0.275688i
\(893\) 4.27320 7.40140i 0.142997 0.247679i
\(894\) −1.56358 2.70819i −0.0522938 0.0905755i
\(895\) −10.4045 7.55928i −0.347783 0.252679i
\(896\) 0.493686 + 0.104936i 0.0164929 + 0.00350567i
\(897\) −2.40148 + 7.39101i −0.0801832 + 0.246779i
\(898\) −14.9651 −0.499392
\(899\) −10.1128 7.31866i −0.337282 0.244091i
\(900\) 1.00000 0.0333333
\(901\) −0.795173 + 2.44729i −0.0264911 + 0.0815311i
\(902\) −4.34601 0.923774i −0.144706 0.0307583i
\(903\) −1.67814 1.21924i −0.0558451 0.0405738i
\(904\) 4.61986 + 8.00184i 0.153654 + 0.266137i
\(905\) −5.48915 + 9.50749i −0.182466 + 0.316040i
\(906\) −15.2259 + 6.77900i −0.505846 + 0.225217i
\(907\) −46.9038 + 34.0776i −1.55742 + 1.13153i −0.619328 + 0.785132i \(0.712595\pi\)
−0.938088 + 0.346397i \(0.887405\pi\)
\(908\) −20.0895 8.94444i −0.666694 0.296832i
\(909\) 3.55094 0.754775i 0.117777 0.0250343i
\(910\) −0.101268 + 0.963504i −0.00335701 + 0.0319399i
\(911\) 17.7565 + 19.7206i 0.588298 + 0.653371i 0.961637 0.274324i \(-0.0884539\pi\)
−0.373339 + 0.927695i \(0.621787\pi\)
\(912\) 0.589263 0.654443i 0.0195124 0.0216708i
\(913\) 0.0879153 + 0.836458i 0.00290957 + 0.0276827i
\(914\) 1.97392 + 6.07510i 0.0652914 + 0.200946i
\(915\) −3.48687 10.7315i −0.115272 0.354772i
\(916\) −0.941573 8.95846i −0.0311104 0.295996i
\(917\) −1.28908 + 1.43167i −0.0425693 + 0.0472780i
\(918\) 1.71080 + 1.90003i 0.0564648 + 0.0627105i
\(919\) 4.83895 46.0395i 0.159622 1.51870i −0.562419 0.826853i \(-0.690129\pi\)
0.722041 0.691851i \(-0.243204\pi\)
\(920\) −3.96013 + 0.841751i −0.130561 + 0.0277517i
\(921\) 26.6871 + 11.8819i 0.879370 + 0.391521i
\(922\) −25.5244 + 18.5446i −0.840601 + 0.610732i
\(923\) −15.6921 + 6.98656i −0.516511 + 0.229966i
\(924\) −0.268971 + 0.465871i −0.00884849 + 0.0153260i
\(925\) 4.79593 + 8.30680i 0.157689 + 0.273126i
\(926\) 5.37373 + 3.90424i 0.176592 + 0.128301i
\(927\) −3.59237 0.763582i −0.117989 0.0250793i
\(928\) 0.692835 2.13233i 0.0227434 0.0699971i
\(929\) 52.4160 1.71971 0.859856 0.510537i \(-0.170553\pi\)
0.859856 + 0.510537i \(0.170553\pi\)
\(930\) −1.71067 + 5.29845i −0.0560950 + 0.173743i
\(931\) −5.94014 −0.194680
\(932\) −2.40151 + 7.39110i −0.0786642 + 0.242103i
\(933\) 16.3111 + 3.46702i 0.534000 + 0.113505i
\(934\) 4.82798 + 3.50773i 0.157976 + 0.114776i
\(935\) −1.36253 2.35998i −0.0445596 0.0771794i
\(936\) −0.959760 + 1.66235i −0.0313708 + 0.0543357i
\(937\) −26.9766 + 12.0108i −0.881288 + 0.392375i −0.796938 0.604062i \(-0.793548\pi\)
−0.0843500 + 0.996436i \(0.526881\pi\)
\(938\) −0.930752 + 0.676231i −0.0303901 + 0.0220797i
\(939\) 25.2347 + 11.2352i 0.823503 + 0.366647i
\(940\) −9.49270 + 2.01774i −0.309618 + 0.0658113i
\(941\) −5.91015 + 56.2313i −0.192665 + 1.83309i 0.289698 + 0.957118i \(0.406445\pi\)
−0.482363 + 0.875971i \(0.660221\pi\)
\(942\) 4.97720 + 5.52774i 0.162166 + 0.180103i
\(943\) 11.2931 12.5423i 0.367754 0.408432i
\(944\) −1.00647 9.57596i −0.0327579 0.311671i
\(945\) 0.155966 + 0.480013i 0.00507356 + 0.0156148i
\(946\) 1.35362 + 4.16601i 0.0440099 + 0.135449i
\(947\) 2.30595 + 21.9396i 0.0749333 + 0.712943i 0.965907 + 0.258888i \(0.0833561\pi\)
−0.890974 + 0.454054i \(0.849977\pi\)
\(948\) −5.01888 + 5.57403i −0.163005 + 0.181036i
\(949\) −0.333745 0.370662i −0.0108338 0.0120322i
\(950\) −0.0920519 + 0.875815i −0.00298656 + 0.0284152i
\(951\) −6.98896 + 1.48555i −0.226632 + 0.0481722i
\(952\) −1.17887 0.524865i −0.0382073 0.0170110i
\(953\) 32.9103 23.9107i 1.06607 0.774544i 0.0908674 0.995863i \(-0.471036\pi\)
0.975202 + 0.221319i \(0.0710361\pi\)
\(954\) −0.919436 + 0.409359i −0.0297678 + 0.0132535i
\(955\) 2.90351 5.02903i 0.0939555 0.162736i
\(956\) −1.25416 2.17226i −0.0405624 0.0702561i
\(957\) 1.93328 + 1.40461i 0.0624940 + 0.0454045i
\(958\) 7.30597 + 1.55293i 0.236045 + 0.0501729i
\(959\) 0.0233087 0.0717368i 0.000752677 0.00231650i
\(960\) −1.00000 −0.0322749
\(961\) −25.1472 18.1278i −0.811201 0.584767i
\(962\) −18.4118 −0.593620
\(963\) 5.36401 16.5087i 0.172853 0.531986i
\(964\) 14.9126 + 3.16976i 0.480301 + 0.102091i
\(965\) 8.33196 + 6.05352i 0.268215 + 0.194870i
\(966\) −1.02169 1.76963i −0.0328725 0.0569368i
\(967\) −5.12117 + 8.87014i −0.164686 + 0.285244i −0.936544 0.350551i \(-0.885994\pi\)
0.771858 + 0.635795i \(0.219328\pi\)
\(968\) −9.01121 + 4.01205i −0.289631 + 0.128952i
\(969\) −1.82156 + 1.32344i −0.0585170 + 0.0425151i
\(970\) 7.92403 + 3.52801i 0.254425 + 0.113277i
\(971\) 41.5371 8.82899i 1.33299 0.283336i 0.514319 0.857599i \(-0.328045\pi\)
0.818671 + 0.574263i \(0.194711\pi\)
\(972\) −0.104528 + 0.994522i −0.00335275 + 0.0318993i
\(973\) −3.69276 4.10122i −0.118384 0.131479i
\(974\) 9.83815 10.9264i 0.315235 0.350104i
\(975\) −0.200645 1.90901i −0.00642577 0.0611371i
\(976\) 3.48687 + 10.7315i 0.111612 + 0.343506i
\(977\) −9.35480 28.7911i −0.299287 0.921110i −0.981748 0.190188i \(-0.939090\pi\)
0.682461 0.730922i \(-0.260910\pi\)
\(978\) 0.653923 + 6.22166i 0.0209101 + 0.198947i
\(979\) 4.25200 4.72232i 0.135894 0.150926i
\(980\) 4.51346 + 5.01271i 0.144177 + 0.160125i
\(981\) −0.634816 + 6.03987i −0.0202681 + 0.192838i
\(982\) −31.2591 + 6.64432i −0.997517 + 0.212029i
\(983\) −17.7096 7.88482i −0.564848 0.251487i 0.104388 0.994537i \(-0.466712\pi\)
−0.669236 + 0.743050i \(0.733378\pi\)
\(984\) 3.37253 2.45028i 0.107512 0.0781122i
\(985\) −1.40049 + 0.623540i −0.0446235 + 0.0198676i
\(986\) −2.86619 + 4.96440i −0.0912782 + 0.158099i
\(987\) −2.44907 4.24192i −0.0779549 0.135022i
\(988\) −1.36757 0.993596i −0.0435081 0.0316105i
\(989\) −16.2755 3.45946i −0.517530 0.110004i
\(990\) 0.329360 1.01367i 0.0104678 0.0322164i
\(991\) 37.2609 1.18363 0.591816 0.806073i \(-0.298411\pi\)
0.591816 + 0.806073i \(0.298411\pi\)
\(992\) 1.71067 5.29845i 0.0543137 0.168226i
\(993\) −8.78896 −0.278909
\(994\) 1.39568 4.29547i 0.0442683 0.136244i
\(995\) −15.7246 3.34237i −0.498504 0.105960i
\(996\) −0.638409 0.463831i −0.0202288 0.0146971i
\(997\) −2.33752 4.04870i −0.0740299 0.128224i 0.826634 0.562740i \(-0.190253\pi\)
−0.900664 + 0.434516i \(0.856919\pi\)
\(998\) −9.30111 + 16.1100i −0.294422 + 0.509953i
\(999\) −8.76261 + 3.90136i −0.277237 + 0.123434i
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 930.2.bg.d.691.1 16
31.7 even 15 inner 930.2.bg.d.751.1 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.bg.d.691.1 16 1.1 even 1 trivial
930.2.bg.d.751.1 yes 16 31.7 even 15 inner