Properties

Label 90.2.l.b.83.1
Level $90$
Weight $2$
Character 90.83
Analytic conductor $0.719$
Analytic rank $0$
Dimension $16$
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] = [90,2,Mod(23,90)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(90, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([10, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("90.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 90.l (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.718653618192\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: 16.0.9349208943630483456.9
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + 9297 x^{8} - 11276 x^{7} + 11224 x^{6} - 9024 x^{5} + 5736 x^{4} - 2780 x^{3} + \cdots + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 83.1
Root \(0.500000 + 1.74530i\) of defining polynomial
Character \(\chi\) \(=\) 90.83
Dual form 90.2.l.b.77.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.965926 + 0.258819i) q^{2} +(-1.73022 - 0.0795432i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.51901 - 1.64092i) q^{5} +(1.69185 - 0.370982i) q^{6} +(-1.00635 - 3.75574i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.98735 + 0.275255i) q^{9} +O(q^{10})\) \(q+(-0.965926 + 0.258819i) q^{2} +(-1.73022 - 0.0795432i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.51901 - 1.64092i) q^{5} +(1.69185 - 0.370982i) q^{6} +(-1.00635 - 3.75574i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.98735 + 0.275255i) q^{9} +(1.89195 + 1.19185i) q^{10} +(-3.44125 - 1.98681i) q^{11} +(-1.53819 + 0.796225i) q^{12} +(-0.256253 + 0.956351i) q^{13} +(1.94411 + 3.36730i) q^{14} +(2.49770 + 2.95998i) q^{15} +(0.500000 - 0.866025i) q^{16} +(0.120239 + 0.120239i) q^{17} +(-2.95680 + 0.507306i) q^{18} +1.88492i q^{19} +(-2.13596 - 0.661570i) q^{20} +(1.44246 + 6.57832i) q^{21} +(3.83821 + 1.02845i) q^{22} +(5.08911 + 1.36362i) q^{23} +(1.27970 - 1.16721i) q^{24} +(-0.385214 + 4.98514i) q^{25} -0.990087i q^{26} +(-5.14688 - 0.713876i) q^{27} +(-2.74939 - 2.74939i) q^{28} +(2.15618 - 3.73461i) q^{29} +(-3.17870 - 2.21267i) q^{30} +(-4.70172 - 8.14362i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(5.79609 + 3.71134i) q^{33} +(-0.147262 - 0.0850217i) q^{34} +(-4.63420 + 7.35634i) q^{35} +(2.72474 - 1.25529i) q^{36} +(3.26863 - 3.26863i) q^{37} +(-0.487854 - 1.82070i) q^{38} +(0.519447 - 1.63432i) q^{39} +(2.23441 + 0.0862005i) q^{40} +(7.15775 - 4.13253i) q^{41} +(-3.09591 - 5.98083i) q^{42} +(-1.99285 + 0.533983i) q^{43} -3.97361 q^{44} +(-4.08614 - 5.32010i) q^{45} -5.26863 q^{46} +(3.34787 - 0.897060i) q^{47} +(-0.933998 + 1.45865i) q^{48} +(-7.03067 + 4.05916i) q^{49} +(-0.918161 - 4.91498i) q^{50} +(-0.198476 - 0.217604i) q^{51} +(0.256253 + 0.956351i) q^{52} +(3.66571 - 3.66571i) q^{53} +(5.15627 - 0.642559i) q^{54} +(1.96711 + 8.66478i) q^{55} +(3.36730 + 1.94411i) q^{56} +(0.149933 - 3.26134i) q^{57} +(-1.11612 + 4.16541i) q^{58} +(-2.72877 - 4.72637i) q^{59} +(3.64306 + 1.31457i) q^{60} +(-4.35623 + 7.54520i) q^{61} +(6.64923 + 6.64923i) q^{62} +(-1.97252 - 11.4967i) q^{63} -1.00000i q^{64} +(1.95854 - 1.03222i) q^{65} +(-6.55916 - 2.08475i) q^{66} +(7.86563 + 2.10759i) q^{67} +(0.164249 + 0.0440105i) q^{68} +(-8.69683 - 2.76418i) q^{69} +(2.57234 - 8.30510i) q^{70} +6.94911i q^{71} +(-2.30701 + 1.91774i) q^{72} +(-8.27728 - 8.27728i) q^{73} +(-2.31127 + 4.00324i) q^{74} +(1.06304 - 8.59476i) q^{75} +(0.942462 + 1.63239i) q^{76} +(-3.99883 + 14.9238i) q^{77} +(-0.0787547 + 1.71307i) q^{78} +(11.7529 + 6.78553i) q^{79} +(-2.18058 + 0.495044i) q^{80} +(8.84847 + 1.64456i) q^{81} +(-5.84428 + 5.84428i) q^{82} +(1.81110 + 6.75913i) q^{83} +(4.53837 + 4.97576i) q^{84} +(0.0146578 - 0.379946i) q^{85} +(1.78674 - 1.03157i) q^{86} +(-4.02773 + 6.29020i) q^{87} +(3.83821 - 1.02845i) q^{88} -4.87832 q^{89} +(5.32385 + 4.08125i) q^{90} +3.84968 q^{91} +(5.08911 - 1.36362i) q^{92} +(7.48725 + 14.4643i) q^{93} +(-3.00162 + 1.73299i) q^{94} +(3.09300 - 2.86322i) q^{95} +(0.524648 - 1.65068i) q^{96} +(-0.387234 - 1.44518i) q^{97} +(5.74052 - 5.74052i) q^{98} +(-9.73332 - 6.88249i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 12 q^{5} + 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 12 q^{5} + 8 q^{7} - 8 q^{10} - 24 q^{15} + 8 q^{16} - 12 q^{20} + 24 q^{21} + 8 q^{22} - 24 q^{23} - 16 q^{25} - 16 q^{28} - 12 q^{30} - 8 q^{31} + 24 q^{36} + 24 q^{38} - 4 q^{40} + 24 q^{41} + 24 q^{42} + 36 q^{45} - 32 q^{46} + 48 q^{47} + 24 q^{50} - 48 q^{51} + 24 q^{55} + 24 q^{56} + 24 q^{57} + 16 q^{58} + 12 q^{60} - 24 q^{61} - 48 q^{63} - 48 q^{66} - 16 q^{67} - 24 q^{68} + 16 q^{70} - 24 q^{72} + 16 q^{73} + 16 q^{76} - 72 q^{77} + 24 q^{81} - 16 q^{82} + 48 q^{83} - 4 q^{85} - 48 q^{86} - 48 q^{87} + 8 q^{88} + 12 q^{90} - 24 q^{92} + 72 q^{93} + 84 q^{95} - 48 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/90\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(37\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.965926 + 0.258819i −0.683013 + 0.183013i
\(3\) −1.73022 0.0795432i −0.998945 0.0459243i
\(4\) 0.866025 0.500000i 0.433013 0.250000i
\(5\) −1.51901 1.64092i −0.679322 0.733840i
\(6\) 1.69185 0.370982i 0.690697 0.151453i
\(7\) −1.00635 3.75574i −0.380364 1.41954i −0.845347 0.534217i \(-0.820606\pi\)
0.464984 0.885319i \(-0.346060\pi\)
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 2.98735 + 0.275255i 0.995782 + 0.0917517i
\(10\) 1.89195 + 1.19185i 0.598288 + 0.376898i
\(11\) −3.44125 1.98681i −1.03758 0.599044i −0.118430 0.992962i \(-0.537786\pi\)
−0.919145 + 0.393918i \(0.871119\pi\)
\(12\) −1.53819 + 0.796225i −0.444037 + 0.229850i
\(13\) −0.256253 + 0.956351i −0.0710719 + 0.265244i −0.992314 0.123746i \(-0.960509\pi\)
0.921242 + 0.388990i \(0.127176\pi\)
\(14\) 1.94411 + 3.36730i 0.519586 + 0.899950i
\(15\) 2.49770 + 2.95998i 0.644904 + 0.764263i
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 0.120239 + 0.120239i 0.0291622 + 0.0291622i 0.721538 0.692375i \(-0.243436\pi\)
−0.692375 + 0.721538i \(0.743436\pi\)
\(18\) −2.95680 + 0.507306i −0.696923 + 0.119573i
\(19\) 1.88492i 0.432431i 0.976346 + 0.216216i \(0.0693714\pi\)
−0.976346 + 0.216216i \(0.930629\pi\)
\(20\) −2.13596 0.661570i −0.477615 0.147932i
\(21\) 1.44246 + 6.57832i 0.314771 + 1.43551i
\(22\) 3.83821 + 1.02845i 0.818310 + 0.219265i
\(23\) 5.08911 + 1.36362i 1.06115 + 0.284335i 0.746853 0.664989i \(-0.231564\pi\)
0.314299 + 0.949324i \(0.398230\pi\)
\(24\) 1.27970 1.16721i 0.261217 0.238255i
\(25\) −0.385214 + 4.98514i −0.0770427 + 0.997028i
\(26\) 0.990087i 0.194172i
\(27\) −5.14688 0.713876i −0.990518 0.137386i
\(28\) −2.74939 2.74939i −0.519586 0.519586i
\(29\) 2.15618 3.73461i 0.400392 0.693499i −0.593381 0.804922i \(-0.702207\pi\)
0.993773 + 0.111422i \(0.0355406\pi\)
\(30\) −3.17870 2.21267i −0.580348 0.403976i
\(31\) −4.70172 8.14362i −0.844454 1.46264i −0.886095 0.463504i \(-0.846592\pi\)
0.0416413 0.999133i \(-0.486741\pi\)
\(32\) −0.258819 + 0.965926i −0.0457532 + 0.170753i
\(33\) 5.79609 + 3.71134i 1.00897 + 0.646062i
\(34\) −0.147262 0.0850217i −0.0252552 0.0145811i
\(35\) −4.63420 + 7.35634i −0.783323 + 1.24345i
\(36\) 2.72474 1.25529i 0.454124 0.209216i
\(37\) 3.26863 3.26863i 0.537360 0.537360i −0.385393 0.922753i \(-0.625934\pi\)
0.922753 + 0.385393i \(0.125934\pi\)
\(38\) −0.487854 1.82070i −0.0791404 0.295356i
\(39\) 0.519447 1.63432i 0.0831781 0.261700i
\(40\) 2.23441 + 0.0862005i 0.353291 + 0.0136295i
\(41\) 7.15775 4.13253i 1.11785 0.645393i 0.177001 0.984211i \(-0.443360\pi\)
0.940852 + 0.338818i \(0.110027\pi\)
\(42\) −3.09591 5.98083i −0.477709 0.922862i
\(43\) −1.99285 + 0.533983i −0.303907 + 0.0814316i −0.407550 0.913183i \(-0.633617\pi\)
0.103643 + 0.994615i \(0.466950\pi\)
\(44\) −3.97361 −0.599044
\(45\) −4.08614 5.32010i −0.609126 0.793074i
\(46\) −5.26863 −0.776818
\(47\) 3.34787 0.897060i 0.488338 0.130850i −0.00624459 0.999981i \(-0.501988\pi\)
0.494582 + 0.869131i \(0.335321\pi\)
\(48\) −0.933998 + 1.45865i −0.134811 + 0.210537i
\(49\) −7.03067 + 4.05916i −1.00438 + 0.579880i
\(50\) −0.918161 4.91498i −0.129848 0.695082i
\(51\) −0.198476 0.217604i −0.0277922 0.0304707i
\(52\) 0.256253 + 0.956351i 0.0355359 + 0.132622i
\(53\) 3.66571 3.66571i 0.503524 0.503524i −0.409007 0.912531i \(-0.634125\pi\)
0.912531 + 0.409007i \(0.134125\pi\)
\(54\) 5.15627 0.642559i 0.701679 0.0874413i
\(55\) 1.96711 + 8.66478i 0.265245 + 1.16836i
\(56\) 3.36730 + 1.94411i 0.449975 + 0.259793i
\(57\) 0.149933 3.26134i 0.0198591 0.431975i
\(58\) −1.11612 + 4.16541i −0.146554 + 0.546946i
\(59\) −2.72877 4.72637i −0.355255 0.615320i 0.631906 0.775045i \(-0.282273\pi\)
−0.987162 + 0.159724i \(0.948939\pi\)
\(60\) 3.64306 + 1.31457i 0.470318 + 0.169710i
\(61\) −4.35623 + 7.54520i −0.557758 + 0.966064i 0.439926 + 0.898034i \(0.355005\pi\)
−0.997683 + 0.0680302i \(0.978329\pi\)
\(62\) 6.64923 + 6.64923i 0.844454 + 0.844454i
\(63\) −1.97252 11.4967i −0.248514 1.44845i
\(64\) 1.00000i 0.125000i
\(65\) 1.95854 1.03222i 0.242927 0.128031i
\(66\) −6.55916 2.08475i −0.807377 0.256614i
\(67\) 7.86563 + 2.10759i 0.960940 + 0.257483i 0.704998 0.709209i \(-0.250948\pi\)
0.255942 + 0.966692i \(0.417615\pi\)
\(68\) 0.164249 + 0.0440105i 0.0199182 + 0.00533705i
\(69\) −8.69683 2.76418i −1.04698 0.332768i
\(70\) 2.57234 8.30510i 0.307453 0.992649i
\(71\) 6.94911i 0.824708i 0.911024 + 0.412354i \(0.135293\pi\)
−0.911024 + 0.412354i \(0.864707\pi\)
\(72\) −2.30701 + 1.91774i −0.271883 + 0.226008i
\(73\) −8.27728 8.27728i −0.968783 0.968783i 0.0307446 0.999527i \(-0.490212\pi\)
−0.999527 + 0.0307446i \(0.990212\pi\)
\(74\) −2.31127 + 4.00324i −0.268680 + 0.465368i
\(75\) 1.06304 8.59476i 0.122749 0.992438i
\(76\) 0.942462 + 1.63239i 0.108108 + 0.187248i
\(77\) −3.99883 + 14.9238i −0.455709 + 1.70073i
\(78\) −0.0787547 + 1.71307i −0.00891722 + 0.193967i
\(79\) 11.7529 + 6.78553i 1.32230 + 0.763431i 0.984095 0.177641i \(-0.0568465\pi\)
0.338206 + 0.941072i \(0.390180\pi\)
\(80\) −2.18058 + 0.495044i −0.243796 + 0.0553475i
\(81\) 8.84847 + 1.64456i 0.983163 + 0.182729i
\(82\) −5.84428 + 5.84428i −0.645393 + 0.645393i
\(83\) 1.81110 + 6.75913i 0.198795 + 0.741911i 0.991252 + 0.131984i \(0.0421347\pi\)
−0.792457 + 0.609927i \(0.791199\pi\)
\(84\) 4.53837 + 4.97576i 0.495176 + 0.542900i
\(85\) 0.0146578 0.379946i 0.00158986 0.0412109i
\(86\) 1.78674 1.03157i 0.192669 0.111238i
\(87\) −4.02773 + 6.29020i −0.431818 + 0.674380i
\(88\) 3.83821 1.02845i 0.409155 0.109633i
\(89\) −4.87832 −0.517100 −0.258550 0.965998i \(-0.583245\pi\)
−0.258550 + 0.965998i \(0.583245\pi\)
\(90\) 5.32385 + 4.08125i 0.561183 + 0.430202i
\(91\) 3.84968 0.403557
\(92\) 5.08911 1.36362i 0.530576 0.142168i
\(93\) 7.48725 + 14.4643i 0.776392 + 1.49987i
\(94\) −3.00162 + 1.73299i −0.309594 + 0.178744i
\(95\) 3.09300 2.86322i 0.317335 0.293760i
\(96\) 0.524648 1.65068i 0.0535466 0.168472i
\(97\) −0.387234 1.44518i −0.0393177 0.146736i 0.943477 0.331439i \(-0.107534\pi\)
−0.982794 + 0.184704i \(0.940868\pi\)
\(98\) 5.74052 5.74052i 0.579880 0.579880i
\(99\) −9.73332 6.88249i −0.978235 0.691717i
\(100\) 2.15896 + 4.50986i 0.215896 + 0.450986i
\(101\) −8.91944 5.14964i −0.887517 0.512408i −0.0143875 0.999896i \(-0.504580\pi\)
−0.873130 + 0.487488i \(0.837913\pi\)
\(102\) 0.248033 + 0.158820i 0.0245589 + 0.0157255i
\(103\) 1.67823 6.26326i 0.165361 0.617137i −0.832632 0.553826i \(-0.813167\pi\)
0.997994 0.0633111i \(-0.0201660\pi\)
\(104\) −0.495044 0.857441i −0.0485430 0.0840790i
\(105\) 8.60335 12.3595i 0.839601 1.20616i
\(106\) −2.59205 + 4.48956i −0.251762 + 0.436065i
\(107\) −3.70057 3.70057i −0.357747 0.357747i 0.505235 0.862982i \(-0.331406\pi\)
−0.862982 + 0.505235i \(0.831406\pi\)
\(108\) −4.81427 + 1.95521i −0.463253 + 0.188140i
\(109\) 7.30160i 0.699367i −0.936868 0.349683i \(-0.886289\pi\)
0.936868 0.349683i \(-0.113711\pi\)
\(110\) −4.14269 7.86041i −0.394990 0.749460i
\(111\) −5.91546 + 5.39547i −0.561471 + 0.512115i
\(112\) −3.75574 1.00635i −0.354884 0.0950909i
\(113\) −4.07557 1.09205i −0.383397 0.102731i 0.0619722 0.998078i \(-0.480261\pi\)
−0.445369 + 0.895347i \(0.646928\pi\)
\(114\) 0.699273 + 3.18902i 0.0654929 + 0.298679i
\(115\) −5.49282 10.4222i −0.512208 0.971872i
\(116\) 4.31235i 0.400392i
\(117\) −1.02876 + 2.78641i −0.0951087 + 0.257604i
\(118\) 3.85906 + 3.85906i 0.355255 + 0.355255i
\(119\) 0.330584 0.572588i 0.0303046 0.0524891i
\(120\) −3.85916 0.326878i −0.352292 0.0298397i
\(121\) 2.39479 + 4.14790i 0.217708 + 0.377081i
\(122\) 2.25495 8.41558i 0.204153 0.761911i
\(123\) −12.7132 + 6.58085i −1.14631 + 0.593375i
\(124\) −8.14362 4.70172i −0.731318 0.422227i
\(125\) 8.76534 6.94038i 0.783996 0.620766i
\(126\) 4.88087 + 10.5944i 0.434823 + 0.943827i
\(127\) 13.7871 13.7871i 1.22341 1.22341i 0.257000 0.966411i \(-0.417266\pi\)
0.966411 0.257000i \(-0.0827341\pi\)
\(128\) 0.258819 + 0.965926i 0.0228766 + 0.0853766i
\(129\) 3.49055 0.765391i 0.307326 0.0673889i
\(130\) −1.62465 + 1.50395i −0.142491 + 0.131905i
\(131\) −3.88249 + 2.24156i −0.339215 + 0.195846i −0.659925 0.751332i \(-0.729412\pi\)
0.320710 + 0.947178i \(0.396079\pi\)
\(132\) 6.87523 + 0.316074i 0.598412 + 0.0275107i
\(133\) 7.07929 1.89689i 0.613852 0.164481i
\(134\) −8.14310 −0.703457
\(135\) 6.64676 + 9.52999i 0.572062 + 0.820211i
\(136\) −0.170043 −0.0145811
\(137\) −12.0729 + 3.23492i −1.03146 + 0.276378i −0.734569 0.678534i \(-0.762616\pi\)
−0.296888 + 0.954912i \(0.595949\pi\)
\(138\) 9.11591 + 0.419084i 0.775998 + 0.0356748i
\(139\) −3.60435 + 2.08097i −0.305717 + 0.176506i −0.645008 0.764176i \(-0.723146\pi\)
0.339291 + 0.940681i \(0.389813\pi\)
\(140\) −0.335167 + 8.68788i −0.0283268 + 0.734260i
\(141\) −5.86393 + 1.28581i −0.493832 + 0.108285i
\(142\) −1.79856 6.71233i −0.150932 0.563286i
\(143\) 2.78191 2.78191i 0.232635 0.232635i
\(144\) 1.73205 2.44949i 0.144338 0.204124i
\(145\) −9.40344 + 2.13480i −0.780913 + 0.177286i
\(146\) 10.1376 + 5.85292i 0.838990 + 0.484391i
\(147\) 12.4875 6.46401i 1.02995 0.533143i
\(148\) 1.19640 4.46504i 0.0983437 0.367024i
\(149\) −0.518244 0.897625i −0.0424562 0.0735363i 0.844016 0.536317i \(-0.180185\pi\)
−0.886473 + 0.462781i \(0.846852\pi\)
\(150\) 1.19767 + 8.57704i 0.0977894 + 0.700312i
\(151\) −2.03451 + 3.52388i −0.165566 + 0.286769i −0.936856 0.349715i \(-0.886278\pi\)
0.771290 + 0.636484i \(0.219612\pi\)
\(152\) −1.33284 1.33284i −0.108108 0.108108i
\(153\) 0.326099 + 0.392291i 0.0263635 + 0.0317149i
\(154\) 15.4503i 1.24502i
\(155\) −6.22103 + 20.0854i −0.499685 + 1.61330i
\(156\) −0.367304 1.67508i −0.0294079 0.134114i
\(157\) −8.81460 2.36186i −0.703481 0.188497i −0.110692 0.993855i \(-0.535307\pi\)
−0.592789 + 0.805357i \(0.701973\pi\)
\(158\) −13.1086 3.51245i −1.04287 0.279435i
\(159\) −6.63408 + 6.05092i −0.526117 + 0.479869i
\(160\) 1.97815 1.04255i 0.156387 0.0824209i
\(161\) 20.4857i 1.61450i
\(162\) −8.97261 + 0.701625i −0.704955 + 0.0551249i
\(163\) 5.03848 + 5.03848i 0.394644 + 0.394644i 0.876339 0.481695i \(-0.159979\pi\)
−0.481695 + 0.876339i \(0.659979\pi\)
\(164\) 4.13253 7.15775i 0.322696 0.558926i
\(165\) −2.71432 15.1485i −0.211309 1.17931i
\(166\) −3.49878 6.06007i −0.271558 0.470353i
\(167\) −2.80384 + 10.4641i −0.216968 + 0.809734i 0.768497 + 0.639853i \(0.221005\pi\)
−0.985465 + 0.169881i \(0.945662\pi\)
\(168\) −5.67155 3.63160i −0.437569 0.280184i
\(169\) 10.4094 + 6.00986i 0.800722 + 0.462297i
\(170\) 0.0841789 + 0.370793i 0.00645623 + 0.0284386i
\(171\) −0.518835 + 5.63092i −0.0396763 + 0.430607i
\(172\) −1.45887 + 1.45887i −0.111238 + 0.111238i
\(173\) 0.975709 + 3.64139i 0.0741818 + 0.276850i 0.993047 0.117722i \(-0.0375593\pi\)
−0.918865 + 0.394573i \(0.870893\pi\)
\(174\) 2.26247 7.11832i 0.171517 0.539638i
\(175\) 19.1105 3.57002i 1.44462 0.269868i
\(176\) −3.44125 + 1.98681i −0.259394 + 0.149761i
\(177\) 4.34543 + 8.39472i 0.326622 + 0.630986i
\(178\) 4.71209 1.26260i 0.353186 0.0946359i
\(179\) 12.8952 0.963836 0.481918 0.876216i \(-0.339940\pi\)
0.481918 + 0.876216i \(0.339940\pi\)
\(180\) −6.19875 2.56427i −0.462028 0.191130i
\(181\) 24.3197 1.80767 0.903835 0.427881i \(-0.140740\pi\)
0.903835 + 0.427881i \(0.140740\pi\)
\(182\) −3.71851 + 0.996372i −0.275634 + 0.0738560i
\(183\) 8.13741 12.7084i 0.601535 0.939430i
\(184\) −4.56277 + 2.63432i −0.336372 + 0.194204i
\(185\) −10.3286 0.398466i −0.759377 0.0292958i
\(186\) −10.9758 12.0336i −0.804782 0.882344i
\(187\) −0.174880 0.652663i −0.0127885 0.0477274i
\(188\) 2.45081 2.45081i 0.178744 0.178744i
\(189\) 2.49842 + 20.0488i 0.181733 + 1.45833i
\(190\) −2.24656 + 3.56619i −0.162982 + 0.258718i
\(191\) 11.8036 + 6.81478i 0.854075 + 0.493100i 0.862024 0.506868i \(-0.169197\pi\)
−0.00794868 + 0.999968i \(0.502530\pi\)
\(192\) −0.0795432 + 1.73022i −0.00574054 + 0.124868i
\(193\) −4.19397 + 15.6521i −0.301889 + 1.12666i 0.633702 + 0.773577i \(0.281534\pi\)
−0.935591 + 0.353086i \(0.885132\pi\)
\(194\) 0.748079 + 1.29571i 0.0537090 + 0.0930267i
\(195\) −3.47082 + 1.63018i −0.248551 + 0.116739i
\(196\) −4.05916 + 7.03067i −0.289940 + 0.502191i
\(197\) −1.16085 1.16085i −0.0827072 0.0827072i 0.664543 0.747250i \(-0.268626\pi\)
−0.747250 + 0.664543i \(0.768626\pi\)
\(198\) 11.1830 + 4.12881i 0.794740 + 0.293422i
\(199\) 17.1733i 1.21738i 0.793407 + 0.608691i \(0.208305\pi\)
−0.793407 + 0.608691i \(0.791695\pi\)
\(200\) −3.25264 3.79741i −0.229996 0.268518i
\(201\) −13.4417 4.27226i −0.948101 0.301342i
\(202\) 9.94834 + 2.66565i 0.699963 + 0.187554i
\(203\) −16.1961 4.33973i −1.13674 0.304589i
\(204\) −0.280687 0.0892129i −0.0196520 0.00624615i
\(205\) −17.6538 5.46791i −1.23300 0.381896i
\(206\) 6.48420i 0.451776i
\(207\) 14.8276 + 5.47442i 1.03059 + 0.380498i
\(208\) 0.700097 + 0.700097i 0.0485430 + 0.0485430i
\(209\) 3.74498 6.48649i 0.259046 0.448680i
\(210\) −5.11133 + 14.1651i −0.352715 + 0.977482i
\(211\) −9.10894 15.7771i −0.627085 1.08614i −0.988134 0.153597i \(-0.950914\pi\)
0.361048 0.932547i \(-0.382419\pi\)
\(212\) 1.34174 5.00745i 0.0921513 0.343913i
\(213\) 0.552755 12.0235i 0.0378741 0.823838i
\(214\) 4.53225 + 2.61670i 0.309818 + 0.178874i
\(215\) 3.90338 + 2.45898i 0.266208 + 0.167701i
\(216\) 4.14418 3.13461i 0.281976 0.213283i
\(217\) −25.8537 + 25.8537i −1.75507 + 1.75507i
\(218\) 1.88979 + 7.05281i 0.127993 + 0.477676i
\(219\) 13.6631 + 14.9799i 0.923270 + 1.01225i
\(220\) 6.03596 + 6.52036i 0.406944 + 0.439603i
\(221\) −0.145802 + 0.0841789i −0.00980771 + 0.00566249i
\(222\) 4.31745 6.74266i 0.289768 0.452538i
\(223\) −4.53570 + 1.21534i −0.303733 + 0.0813849i −0.407466 0.913220i \(-0.633588\pi\)
0.103734 + 0.994605i \(0.466921\pi\)
\(224\) 3.88823 0.259793
\(225\) −2.52295 + 14.7863i −0.168197 + 0.985753i
\(226\) 4.21934 0.280666
\(227\) 24.1784 6.47859i 1.60478 0.429999i 0.658297 0.752758i \(-0.271277\pi\)
0.946481 + 0.322759i \(0.104610\pi\)
\(228\) −1.50082 2.89937i −0.0993945 0.192015i
\(229\) 19.7350 11.3940i 1.30412 0.752935i 0.323014 0.946394i \(-0.395304\pi\)
0.981108 + 0.193459i \(0.0619706\pi\)
\(230\) 8.00311 + 8.64539i 0.527709 + 0.570060i
\(231\) 8.10596 25.5035i 0.533333 1.67801i
\(232\) 1.11612 + 4.16541i 0.0732768 + 0.273473i
\(233\) −20.6491 + 20.6491i −1.35277 + 1.35277i −0.470214 + 0.882553i \(0.655823\pi\)
−0.882553 + 0.470214i \(0.844177\pi\)
\(234\) 0.272527 2.95773i 0.0178156 0.193353i
\(235\) −6.55746 4.13094i −0.427761 0.269473i
\(236\) −4.72637 2.72877i −0.307660 0.177628i
\(237\) −19.7954 12.6753i −1.28585 0.823352i
\(238\) −0.171123 + 0.638639i −0.0110922 + 0.0413968i
\(239\) 4.56277 + 7.90295i 0.295141 + 0.511199i 0.975018 0.222127i \(-0.0713000\pi\)
−0.679877 + 0.733327i \(0.737967\pi\)
\(240\) 3.81227 0.683085i 0.246081 0.0440930i
\(241\) 0.869654 1.50629i 0.0560194 0.0970284i −0.836656 0.547729i \(-0.815492\pi\)
0.892675 + 0.450701i \(0.148826\pi\)
\(242\) −3.38674 3.38674i −0.217708 0.217708i
\(243\) −15.1790 3.54930i −0.973734 0.227688i
\(244\) 8.71245i 0.557758i
\(245\) 17.3404 + 5.37084i 1.10784 + 0.343130i
\(246\) 10.5768 9.64703i 0.674351 0.615072i
\(247\) −1.80265 0.483018i −0.114700 0.0307337i
\(248\) 9.08302 + 2.43379i 0.576773 + 0.154546i
\(249\) −2.59597 11.8389i −0.164513 0.750258i
\(250\) −6.67037 + 8.97252i −0.421871 + 0.567472i
\(251\) 6.16751i 0.389290i 0.980874 + 0.194645i \(0.0623555\pi\)
−0.980874 + 0.194645i \(0.937645\pi\)
\(252\) −7.45660 8.97017i −0.469722 0.565068i
\(253\) −14.8036 14.8036i −0.930696 0.930696i
\(254\) −9.74898 + 16.8857i −0.611706 + 1.05951i
\(255\) −0.0555835 + 0.656226i −0.00348077 + 0.0410944i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 7.51956 28.0634i 0.469057 1.75055i −0.174018 0.984743i \(-0.555675\pi\)
0.643075 0.765803i \(-0.277658\pi\)
\(258\) −3.17351 + 1.64273i −0.197574 + 0.102272i
\(259\) −15.5655 8.98676i −0.967194 0.558410i
\(260\) 1.18004 1.87320i 0.0731830 0.116171i
\(261\) 7.46922 10.5631i 0.462333 0.653838i
\(262\) 3.17004 3.17004i 0.195846 0.195846i
\(263\) −4.82975 18.0249i −0.297815 1.11146i −0.938956 0.344038i \(-0.888205\pi\)
0.641141 0.767424i \(-0.278462\pi\)
\(264\) −6.72277 + 1.47414i −0.413758 + 0.0907269i
\(265\) −11.5834 0.446872i −0.711561 0.0274511i
\(266\) −6.34711 + 3.66451i −0.389167 + 0.224685i
\(267\) 8.44057 + 0.388037i 0.516555 + 0.0237475i
\(268\) 7.86563 2.10759i 0.480470 0.128742i
\(269\) 15.5553 0.948425 0.474212 0.880411i \(-0.342733\pi\)
0.474212 + 0.880411i \(0.342733\pi\)
\(270\) −8.88681 7.48495i −0.540834 0.455520i
\(271\) −1.87184 −0.113706 −0.0568532 0.998383i \(-0.518107\pi\)
−0.0568532 + 0.998383i \(0.518107\pi\)
\(272\) 0.164249 0.0440105i 0.00995908 0.00266853i
\(273\) −6.66081 0.306216i −0.403131 0.0185331i
\(274\) 10.8243 6.24939i 0.653918 0.377540i
\(275\) 11.2301 16.3898i 0.677201 0.988339i
\(276\) −8.91376 + 1.95457i −0.536545 + 0.117651i
\(277\) −1.06921 3.99035i −0.0642426 0.239757i 0.926337 0.376696i \(-0.122940\pi\)
−0.990579 + 0.136940i \(0.956273\pi\)
\(278\) 2.94294 2.94294i 0.176506 0.176506i
\(279\) −11.8041 25.6220i −0.706692 1.53395i
\(280\) −1.92484 8.47860i −0.115031 0.506693i
\(281\) 0.248640 + 0.143552i 0.0148326 + 0.00856361i 0.507398 0.861712i \(-0.330607\pi\)
−0.492565 + 0.870275i \(0.663941\pi\)
\(282\) 5.33132 2.75970i 0.317476 0.164338i
\(283\) −4.68527 + 17.4857i −0.278510 + 1.03941i 0.674942 + 0.737871i \(0.264169\pi\)
−0.953452 + 0.301544i \(0.902498\pi\)
\(284\) 3.47456 + 6.01811i 0.206177 + 0.357109i
\(285\) −5.57934 + 4.70798i −0.330491 + 0.278877i
\(286\) −1.96711 + 3.40713i −0.116318 + 0.201468i
\(287\) −22.7239 22.7239i −1.34135 1.34135i
\(288\) −1.03906 + 2.81431i −0.0612271 + 0.165835i
\(289\) 16.9711i 0.998299i
\(290\) 8.53050 4.49585i 0.500928 0.264005i
\(291\) 0.555048 + 2.53128i 0.0325375 + 0.148386i
\(292\) −11.3070 3.02970i −0.661691 0.177300i
\(293\) 20.6663 + 5.53752i 1.20734 + 0.323505i 0.805717 0.592300i \(-0.201780\pi\)
0.401621 + 0.915806i \(0.368447\pi\)
\(294\) −10.3890 + 9.47576i −0.605899 + 0.552637i
\(295\) −3.61054 + 11.6571i −0.210214 + 0.678702i
\(296\) 4.62255i 0.268680i
\(297\) 16.2934 + 12.6825i 0.945436 + 0.735912i
\(298\) 0.732907 + 0.732907i 0.0424562 + 0.0424562i
\(299\) −2.60820 + 4.51754i −0.150836 + 0.261256i
\(300\) −3.37676 7.97480i −0.194957 0.460425i
\(301\) 4.01100 + 6.94725i 0.231190 + 0.400433i
\(302\) 1.05314 3.93037i 0.0606014 0.226168i
\(303\) 15.0230 + 9.61951i 0.863049 + 0.552626i
\(304\) 1.63239 + 0.942462i 0.0936241 + 0.0540539i
\(305\) 18.9982 4.31304i 1.08783 0.246964i
\(306\) −0.416520 0.294524i −0.0238108 0.0168368i
\(307\) −20.2953 + 20.2953i −1.15831 + 1.15831i −0.173476 + 0.984838i \(0.555500\pi\)
−0.984838 + 0.173476i \(0.944500\pi\)
\(308\) 3.99883 + 14.9238i 0.227855 + 0.850365i
\(309\) −3.40192 + 10.7033i −0.193528 + 0.608892i
\(310\) 0.810581 21.0111i 0.0460379 1.19335i
\(311\) −11.9868 + 6.92056i −0.679707 + 0.392429i −0.799745 0.600340i \(-0.795032\pi\)
0.120038 + 0.992769i \(0.461698\pi\)
\(312\) 0.788332 + 1.52294i 0.0446305 + 0.0862196i
\(313\) 17.9081 4.79847i 1.01223 0.271226i 0.285668 0.958329i \(-0.407785\pi\)
0.726560 + 0.687103i \(0.241118\pi\)
\(314\) 9.12554 0.514984
\(315\) −15.8688 + 20.7003i −0.894108 + 1.16633i
\(316\) 13.5711 0.763431
\(317\) 0.811966 0.217566i 0.0456046 0.0122197i −0.235945 0.971766i \(-0.575818\pi\)
0.281549 + 0.959547i \(0.409152\pi\)
\(318\) 4.84194 7.56176i 0.271522 0.424043i
\(319\) −14.8399 + 8.56781i −0.830874 + 0.479705i
\(320\) −1.64092 + 1.51901i −0.0917300 + 0.0849153i
\(321\) 6.10845 + 6.69716i 0.340941 + 0.373799i
\(322\) 5.30208 + 19.7876i 0.295473 + 1.10272i
\(323\) −0.226641 + 0.226641i −0.0126107 + 0.0126107i
\(324\) 8.48528 3.00000i 0.471405 0.166667i
\(325\) −4.66883 1.64586i −0.258980 0.0912958i
\(326\) −6.17086 3.56275i −0.341772 0.197322i
\(327\) −0.580793 + 12.6334i −0.0321179 + 0.698629i
\(328\) −2.13915 + 7.98343i −0.118115 + 0.440811i
\(329\) −6.73825 11.6710i −0.371492 0.643443i
\(330\) 6.54254 + 13.9298i 0.360155 + 0.766809i
\(331\) 2.08211 3.60631i 0.114443 0.198221i −0.803114 0.595825i \(-0.796825\pi\)
0.917557 + 0.397604i \(0.130158\pi\)
\(332\) 4.94803 + 4.94803i 0.271558 + 0.271558i
\(333\) 10.6642 8.86483i 0.584397 0.485790i
\(334\) 10.8332i 0.592766i
\(335\) −8.48960 16.1083i −0.463836 0.880090i
\(336\) 6.41822 + 2.03995i 0.350143 + 0.111288i
\(337\) 3.13777 + 0.840764i 0.170925 + 0.0457993i 0.343267 0.939238i \(-0.388467\pi\)
−0.172341 + 0.985037i \(0.555133\pi\)
\(338\) −11.6102 3.11093i −0.631510 0.169213i
\(339\) 6.96478 + 2.21367i 0.378275 + 0.120230i
\(340\) −0.177279 0.336372i −0.00961430 0.0182423i
\(341\) 37.3656i 2.02346i
\(342\) −0.956233 5.57334i −0.0517072 0.301372i
\(343\) 3.07470 + 3.07470i 0.166018 + 0.166018i
\(344\) 1.03157 1.78674i 0.0556188 0.0963346i
\(345\) 8.67479 + 18.4696i 0.467035 + 0.994369i
\(346\) −1.88492 3.26478i −0.101334 0.175516i
\(347\) 1.21470 4.53334i 0.0652087 0.243362i −0.925627 0.378438i \(-0.876461\pi\)
0.990835 + 0.135076i \(0.0431279\pi\)
\(348\) −0.343019 + 7.46134i −0.0183877 + 0.399970i
\(349\) 8.42818 + 4.86601i 0.451150 + 0.260472i 0.708316 0.705896i \(-0.249455\pi\)
−0.257166 + 0.966367i \(0.582789\pi\)
\(350\) −17.5354 + 8.39455i −0.937305 + 0.448707i
\(351\) 2.00162 4.73929i 0.106839 0.252965i
\(352\) 2.80977 2.80977i 0.149761 0.149761i
\(353\) −1.32049 4.92815i −0.0702827 0.262299i 0.921840 0.387572i \(-0.126686\pi\)
−0.992122 + 0.125273i \(0.960019\pi\)
\(354\) −6.37008 6.98400i −0.338566 0.371195i
\(355\) 11.4029 10.5558i 0.605204 0.560242i
\(356\) −4.22474 + 2.43916i −0.223911 + 0.129275i
\(357\) −0.617529 + 0.964409i −0.0326831 + 0.0510420i
\(358\) −12.4559 + 3.33754i −0.658312 + 0.176394i
\(359\) 1.27697 0.0673957 0.0336978 0.999432i \(-0.489272\pi\)
0.0336978 + 0.999432i \(0.489272\pi\)
\(360\) 6.65122 + 0.872542i 0.350550 + 0.0459870i
\(361\) 15.4471 0.813003
\(362\) −23.4910 + 6.29441i −1.23466 + 0.330827i
\(363\) −3.81358 7.36727i −0.200161 0.386682i
\(364\) 3.33392 1.92484i 0.174745 0.100889i
\(365\) −1.00905 + 26.1556i −0.0528161 + 1.36905i
\(366\) −4.57097 + 14.3815i −0.238928 + 0.751731i
\(367\) −2.61063 9.74300i −0.136274 0.508581i −0.999989 0.00460117i \(-0.998535\pi\)
0.863716 0.503979i \(-0.168131\pi\)
\(368\) 3.72549 3.72549i 0.194204 0.194204i
\(369\) 22.5202 10.3751i 1.17235 0.540105i
\(370\) 10.0798 2.28836i 0.524026 0.118966i
\(371\) −17.4564 10.0785i −0.906293 0.523249i
\(372\) 13.7163 + 8.78279i 0.711156 + 0.455367i
\(373\) −3.39374 + 12.6656i −0.175721 + 0.655801i 0.820706 + 0.571350i \(0.193580\pi\)
−0.996428 + 0.0844507i \(0.973086\pi\)
\(374\) 0.337843 + 0.585162i 0.0174695 + 0.0302580i
\(375\) −15.7181 + 11.3112i −0.811677 + 0.584107i
\(376\) −1.73299 + 3.00162i −0.0893720 + 0.154797i
\(377\) 3.01907 + 3.01907i 0.155490 + 0.155490i
\(378\) −7.60229 18.7190i −0.391019 0.962800i
\(379\) 0.587648i 0.0301854i −0.999886 0.0150927i \(-0.995196\pi\)
0.999886 0.0150927i \(-0.00480434\pi\)
\(380\) 1.24701 4.02612i 0.0639702 0.206536i
\(381\) −24.9515 + 22.7582i −1.27830 + 1.16594i
\(382\) −13.1652 3.52759i −0.673588 0.180487i
\(383\) 14.0071 + 3.75319i 0.715729 + 0.191779i 0.598265 0.801298i \(-0.295857\pi\)
0.117464 + 0.993077i \(0.462524\pi\)
\(384\) −0.370982 1.69185i −0.0189316 0.0863371i
\(385\) 30.5631 16.1077i 1.55764 0.820926i
\(386\) 16.2043i 0.824775i
\(387\) −6.10031 + 1.04665i −0.310096 + 0.0532041i
\(388\) −1.05794 1.05794i −0.0537090 0.0537090i
\(389\) −10.3789 + 17.9767i −0.526230 + 0.911456i 0.473303 + 0.880899i \(0.343061\pi\)
−0.999533 + 0.0305570i \(0.990272\pi\)
\(390\) 2.93064 2.47294i 0.148399 0.125222i
\(391\) 0.447948 + 0.775869i 0.0226537 + 0.0392374i
\(392\) 2.10118 7.84169i 0.106125 0.396065i
\(393\) 6.89588 3.56957i 0.347851 0.180061i
\(394\) 1.42175 + 0.820845i 0.0716265 + 0.0413536i
\(395\) −6.71826 29.5928i −0.338032 1.48897i
\(396\) −11.8705 1.09376i −0.596517 0.0549633i
\(397\) 15.7430 15.7430i 0.790118 0.790118i −0.191395 0.981513i \(-0.561301\pi\)
0.981513 + 0.191395i \(0.0613012\pi\)
\(398\) −4.44477 16.5881i −0.222796 0.831487i
\(399\) −12.3996 + 2.71893i −0.620758 + 0.136117i
\(400\) 4.12465 + 2.82617i 0.206233 + 0.141309i
\(401\) 4.11737 2.37716i 0.205612 0.118710i −0.393659 0.919257i \(-0.628791\pi\)
0.599270 + 0.800547i \(0.295457\pi\)
\(402\) 14.0894 + 0.647729i 0.702715 + 0.0323058i
\(403\) 8.99298 2.40966i 0.447972 0.120034i
\(404\) −10.2993 −0.512408
\(405\) −10.7423 17.0177i −0.533790 0.845617i
\(406\) 16.7674 0.832153
\(407\) −17.7423 + 4.75404i −0.879454 + 0.235649i
\(408\) 0.294213 + 0.0135258i 0.0145657 + 0.000669627i
\(409\) −25.8797 + 14.9417i −1.27967 + 0.738817i −0.976787 0.214211i \(-0.931282\pi\)
−0.302882 + 0.953028i \(0.597949\pi\)
\(410\) 18.4675 + 0.712452i 0.912044 + 0.0351855i
\(411\) 21.1461 4.63682i 1.04306 0.228718i
\(412\) −1.67823 6.26326i −0.0826807 0.308568i
\(413\) −15.0049 + 15.0049i −0.738343 + 0.738343i
\(414\) −15.7392 1.45022i −0.773541 0.0712744i
\(415\) 8.34009 13.2391i 0.409399 0.649880i
\(416\) −0.857441 0.495044i −0.0420395 0.0242715i
\(417\) 6.40185 3.31384i 0.313500 0.162280i
\(418\) −1.93854 + 7.23474i −0.0948172 + 0.353863i
\(419\) 8.81638 + 15.2704i 0.430708 + 0.746009i 0.996934 0.0782412i \(-0.0249304\pi\)
−0.566226 + 0.824250i \(0.691597\pi\)
\(420\) 1.27098 15.0053i 0.0620173 0.732184i
\(421\) 13.9462 24.1555i 0.679696 1.17727i −0.295377 0.955381i \(-0.595445\pi\)
0.975072 0.221887i \(-0.0712215\pi\)
\(422\) 12.8820 + 12.8820i 0.627085 + 0.627085i
\(423\) 10.2482 1.75831i 0.498284 0.0854919i
\(424\) 5.18410i 0.251762i
\(425\) −0.645725 + 0.553090i −0.0313223 + 0.0268288i
\(426\) 2.57799 + 11.7569i 0.124904 + 0.569623i
\(427\) 32.7217 + 8.76775i 1.58351 + 0.424301i
\(428\) −5.05507 1.35450i −0.244346 0.0654723i
\(429\) −5.03461 + 4.59205i −0.243073 + 0.221706i
\(430\) −4.40681 1.36492i −0.212515 0.0658222i
\(431\) 19.2910i 0.929215i 0.885517 + 0.464608i \(0.153805\pi\)
−0.885517 + 0.464608i \(0.846195\pi\)
\(432\) −3.19168 + 4.10039i −0.153560 + 0.197280i
\(433\) 16.7154 + 16.7154i 0.803292 + 0.803292i 0.983609 0.180316i \(-0.0577122\pi\)
−0.180316 + 0.983609i \(0.557712\pi\)
\(434\) 18.2814 31.6642i 0.877533 1.51993i
\(435\) 16.4399 2.94571i 0.788231 0.141236i
\(436\) −3.65080 6.32337i −0.174842 0.302835i
\(437\) −2.57033 + 9.59259i −0.122955 + 0.458876i
\(438\) −17.0747 10.9332i −0.815860 0.522410i
\(439\) −31.1811 18.0024i −1.48819 0.859209i −0.488285 0.872684i \(-0.662377\pi\)
−0.999909 + 0.0134750i \(0.995711\pi\)
\(440\) −7.51788 4.73597i −0.358401 0.225778i
\(441\) −22.1203 + 10.1909i −1.05335 + 0.485280i
\(442\) 0.119047 0.119047i 0.00566249 0.00566249i
\(443\) −6.94511 25.9195i −0.329972 1.23147i −0.909218 0.416320i \(-0.863320\pi\)
0.579246 0.815153i \(-0.303347\pi\)
\(444\) −2.42521 + 7.63035i −0.115095 + 0.362120i
\(445\) 7.41021 + 8.00491i 0.351278 + 0.379469i
\(446\) 4.06659 2.34785i 0.192559 0.111174i
\(447\) 0.825278 + 1.59431i 0.0390343 + 0.0754085i
\(448\) −3.75574 + 1.00635i −0.177442 + 0.0475455i
\(449\) −41.3392 −1.95092 −0.975459 0.220182i \(-0.929335\pi\)
−0.975459 + 0.220182i \(0.929335\pi\)
\(450\) −1.38999 14.9355i −0.0655249 0.704064i
\(451\) −32.8421 −1.54647
\(452\) −4.07557 + 1.09205i −0.191699 + 0.0513655i
\(453\) 3.80046 5.93526i 0.178561 0.278863i
\(454\) −21.6778 + 12.5157i −1.01739 + 0.587390i
\(455\) −5.84771 6.31701i −0.274145 0.296146i
\(456\) 2.20010 + 2.41213i 0.103029 + 0.112959i
\(457\) 5.58827 + 20.8557i 0.261408 + 0.975589i 0.964412 + 0.264403i \(0.0851750\pi\)
−0.703004 + 0.711186i \(0.748158\pi\)
\(458\) −16.1135 + 16.1135i −0.752935 + 0.752935i
\(459\) −0.533019 0.704691i −0.0248792 0.0328921i
\(460\) −9.96800 6.27945i −0.464761 0.292781i
\(461\) −10.8706 6.27615i −0.506295 0.292309i 0.225015 0.974355i \(-0.427757\pi\)
−0.731309 + 0.682046i \(0.761090\pi\)
\(462\) −1.22897 + 26.7325i −0.0571767 + 1.24371i
\(463\) 5.72110 21.3514i 0.265882 0.992286i −0.695826 0.718210i \(-0.744962\pi\)
0.961708 0.274076i \(-0.0883718\pi\)
\(464\) −2.15618 3.73461i −0.100098 0.173375i
\(465\) 12.3614 34.2573i 0.573248 1.58865i
\(466\) 14.6011 25.2899i 0.676383 1.17153i
\(467\) 3.48137 + 3.48137i 0.161099 + 0.161099i 0.783053 0.621955i \(-0.213661\pi\)
−0.621955 + 0.783053i \(0.713661\pi\)
\(468\) 0.502277 + 2.92749i 0.0232178 + 0.135323i
\(469\) 31.6622i 1.46203i
\(470\) 7.40318 + 2.29299i 0.341483 + 0.105768i
\(471\) 15.0634 + 4.78769i 0.694083 + 0.220605i
\(472\) 5.27158 + 1.41251i 0.242644 + 0.0650163i
\(473\) 7.91881 + 2.12184i 0.364107 + 0.0975622i
\(474\) 22.4015 + 7.12002i 1.02893 + 0.327033i
\(475\) −9.39661 0.726099i −0.431146 0.0333157i
\(476\) 0.661168i 0.0303046i
\(477\) 11.9598 9.94174i 0.547599 0.455201i
\(478\) −6.45273 6.45273i −0.295141 0.295141i
\(479\) −1.35673 + 2.34993i −0.0619906 + 0.107371i −0.895355 0.445353i \(-0.853078\pi\)
0.833364 + 0.552724i \(0.186412\pi\)
\(480\) −3.50557 + 1.64650i −0.160007 + 0.0751520i
\(481\) 2.28836 + 3.96356i 0.104340 + 0.180723i
\(482\) −0.450166 + 1.68004i −0.0205045 + 0.0765239i
\(483\) −1.62949 + 35.4448i −0.0741446 + 1.61279i
\(484\) 4.14790 + 2.39479i 0.188541 + 0.108854i
\(485\) −1.78320 + 2.83066i −0.0809711 + 0.128534i
\(486\) 15.5804 0.500258i 0.706743 0.0226921i
\(487\) −8.20799 + 8.20799i −0.371940 + 0.371940i −0.868183 0.496244i \(-0.834712\pi\)
0.496244 + 0.868183i \(0.334712\pi\)
\(488\) −2.25495 8.41558i −0.102077 0.380955i
\(489\) −8.31692 9.11848i −0.376104 0.412352i
\(490\) −18.1396 0.699803i −0.819464 0.0316139i
\(491\) 4.28058 2.47139i 0.193180 0.111532i −0.400290 0.916388i \(-0.631091\pi\)
0.593470 + 0.804856i \(0.297757\pi\)
\(492\) −7.71955 + 12.0558i −0.348024 + 0.543517i
\(493\) 0.708301 0.189789i 0.0319003 0.00854766i
\(494\) 1.86624 0.0839661
\(495\) 3.49141 + 26.4261i 0.156927 + 1.18777i
\(496\) −9.40344 −0.422227
\(497\) 26.0991 6.99322i 1.17070 0.313689i
\(498\) 5.57164 + 10.7636i 0.249671 + 0.482328i
\(499\) 28.1148 16.2321i 1.25859 0.726649i 0.285791 0.958292i \(-0.407744\pi\)
0.972801 + 0.231643i \(0.0744102\pi\)
\(500\) 4.12082 10.3932i 0.184289 0.464799i
\(501\) 5.68361 17.8821i 0.253925 0.798915i
\(502\) −1.59627 5.95736i −0.0712450 0.265890i
\(503\) 19.6817 19.6817i 0.877565 0.877565i −0.115717 0.993282i \(-0.536917\pi\)
0.993282 + 0.115717i \(0.0369166\pi\)
\(504\) 9.52417 + 6.73461i 0.424240 + 0.299983i
\(505\) 5.09859 + 22.4584i 0.226884 + 0.999386i
\(506\) 18.1307 + 10.4677i 0.806007 + 0.465348i
\(507\) −17.5325 11.2264i −0.778647 0.498582i
\(508\) 5.04645 18.8336i 0.223900 0.835606i
\(509\) −5.25069 9.09446i −0.232733 0.403105i 0.725879 0.687823i \(-0.241433\pi\)
−0.958611 + 0.284718i \(0.908100\pi\)
\(510\) −0.116154 0.648251i −0.00514339 0.0287051i
\(511\) −22.7575 + 39.4171i −1.00673 + 1.74371i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 1.34560 9.70148i 0.0594098 0.428331i
\(514\) 29.0534i 1.28149i
\(515\) −12.8267 + 6.76011i −0.565214 + 0.297886i
\(516\) 2.64021 2.40812i 0.116229 0.106012i
\(517\) −13.3031 3.56457i −0.585072 0.156770i
\(518\) 17.3611 + 4.65189i 0.762802 + 0.204392i
\(519\) −1.39855 6.37804i −0.0613893 0.279965i
\(520\) −0.655012 + 2.11479i −0.0287242 + 0.0927395i
\(521\) 28.2545i 1.23785i −0.785450 0.618925i \(-0.787568\pi\)
0.785450 0.618925i \(-0.212432\pi\)
\(522\) −4.48079 + 12.1363i −0.196119 + 0.531192i
\(523\) 13.6590 + 13.6590i 0.597266 + 0.597266i 0.939584 0.342318i \(-0.111212\pi\)
−0.342318 + 0.939584i \(0.611212\pi\)
\(524\) −2.24156 + 3.88249i −0.0979230 + 0.169608i
\(525\) −33.3495 + 4.65682i −1.45549 + 0.203240i
\(526\) 9.33036 + 16.1607i 0.406823 + 0.704638i
\(527\) 0.413850 1.54451i 0.0180276 0.0672798i
\(528\) 6.11216 3.16389i 0.265998 0.137691i
\(529\) 4.12099 + 2.37925i 0.179173 + 0.103446i
\(530\) 11.3043 2.56635i 0.491029 0.111475i
\(531\) −6.85082 14.8704i −0.297300 0.645320i
\(532\) 5.18240 5.18240i 0.224685 0.224685i
\(533\) 2.11795 + 7.90429i 0.0917385 + 0.342373i
\(534\) −8.25340 + 1.80977i −0.357160 + 0.0783163i
\(535\) −0.451121 + 11.6935i −0.0195037 + 0.505555i
\(536\) −7.05213 + 4.07155i −0.304606 + 0.175864i
\(537\) −22.3117 1.02573i −0.962819 0.0442635i
\(538\) −15.0253 + 4.02601i −0.647786 + 0.173574i
\(539\) 32.2590 1.38949
\(540\) 10.5213 + 4.92983i 0.452763 + 0.212146i
\(541\) −26.7216 −1.14885 −0.574427 0.818556i \(-0.694775\pi\)
−0.574427 + 0.818556i \(0.694775\pi\)
\(542\) 1.80806 0.484468i 0.0776628 0.0208097i
\(543\) −42.0785 1.93447i −1.80576 0.0830160i
\(544\) −0.147262 + 0.0850217i −0.00631380 + 0.00364528i
\(545\) −11.9813 + 11.0912i −0.513223 + 0.475095i
\(546\) 6.51311 1.42816i 0.278735 0.0611197i
\(547\) 0.0627654 + 0.234244i 0.00268365 + 0.0100155i 0.967255 0.253808i \(-0.0816831\pi\)
−0.964571 + 0.263823i \(0.915016\pi\)
\(548\) −8.83798 + 8.83798i −0.377540 + 0.377540i
\(549\) −15.0904 + 21.3411i −0.644043 + 0.910814i
\(550\) −6.60548 + 18.7379i −0.281659 + 0.798985i
\(551\) 7.03946 + 4.06423i 0.299891 + 0.173142i
\(552\) 8.10415 4.19502i 0.344936 0.178552i
\(553\) 13.6572 50.9693i 0.580763 2.16744i
\(554\) 2.06556 + 3.57765i 0.0877571 + 0.152000i
\(555\) 17.8392 + 1.51101i 0.757230 + 0.0641387i
\(556\) −2.08097 + 3.60435i −0.0882528 + 0.152858i
\(557\) 31.4838 + 31.4838i 1.33401 + 1.33401i 0.901746 + 0.432266i \(0.142286\pi\)
0.432266 + 0.901746i \(0.357714\pi\)
\(558\) 18.0333 + 21.6938i 0.763412 + 0.918372i
\(559\) 2.04270i 0.0863969i
\(560\) 4.05368 + 7.69151i 0.171299 + 0.325026i
\(561\) 0.250667 + 1.14316i 0.0105832 + 0.0482644i
\(562\) −0.277322 0.0743081i −0.0116981 0.00313450i
\(563\) 31.1771 + 8.35388i 1.31396 + 0.352074i 0.846711 0.532053i \(-0.178579\pi\)
0.467247 + 0.884127i \(0.345246\pi\)
\(564\) −4.43540 + 4.04551i −0.186764 + 0.170347i
\(565\) 4.39888 + 8.34650i 0.185062 + 0.351140i
\(566\) 18.1025i 0.760904i
\(567\) −2.72808 34.8876i −0.114569 1.46514i
\(568\) −4.91376 4.91376i −0.206177 0.206177i
\(569\) −16.1545 + 27.9804i −0.677232 + 1.17300i 0.298580 + 0.954385i \(0.403487\pi\)
−0.975811 + 0.218615i \(0.929846\pi\)
\(570\) 4.17071 5.99160i 0.174692 0.250961i
\(571\) 12.9565 + 22.4413i 0.542213 + 0.939141i 0.998777 + 0.0494501i \(0.0157469\pi\)
−0.456563 + 0.889691i \(0.650920\pi\)
\(572\) 1.01825 3.80016i 0.0425752 0.158893i
\(573\) −19.8807 12.7300i −0.830529 0.531803i
\(574\) 27.8310 + 16.0682i 1.16164 + 0.670674i
\(575\) −8.75824 + 24.8446i −0.365244 + 1.03609i
\(576\) 0.275255 2.98735i 0.0114690 0.124473i
\(577\) 6.10724 6.10724i 0.254248 0.254248i −0.568462 0.822710i \(-0.692461\pi\)
0.822710 + 0.568462i \(0.192461\pi\)
\(578\) 4.39244 + 16.3928i 0.182701 + 0.681851i
\(579\) 8.50152 26.7480i 0.353311 1.11161i
\(580\) −7.07621 + 6.55051i −0.293824 + 0.271995i
\(581\) 23.5629 13.6041i 0.977556 0.564392i
\(582\) −1.19128 2.30138i −0.0493801 0.0953951i
\(583\) −19.8977 + 5.33157i −0.824077 + 0.220811i
\(584\) 11.7058 0.484391
\(585\) 6.13497 2.54449i 0.253650 0.105202i
\(586\) −21.3953 −0.883833
\(587\) 1.83025 0.490414i 0.0755424 0.0202415i −0.220850 0.975308i \(-0.570883\pi\)
0.296392 + 0.955066i \(0.404216\pi\)
\(588\) 7.58249 11.8418i 0.312697 0.488346i
\(589\) 15.3501 8.86238i 0.632490 0.365168i
\(590\) 0.470442 12.1944i 0.0193678 0.502034i
\(591\) 1.91619 + 2.10087i 0.0788217 + 0.0864182i
\(592\) −1.19640 4.46504i −0.0491719 0.183512i
\(593\) −11.0077 + 11.0077i −0.452033 + 0.452033i −0.896029 0.443996i \(-0.853561\pi\)
0.443996 + 0.896029i \(0.353561\pi\)
\(594\) −19.0206 8.03330i −0.780426 0.329610i
\(595\) −1.44173 + 0.327307i −0.0591051 + 0.0134183i
\(596\) −0.897625 0.518244i −0.0367681 0.0212281i
\(597\) 1.36602 29.7136i 0.0559074 1.21610i
\(598\) 1.35011 5.03866i 0.0552099 0.206046i
\(599\) −12.9428 22.4176i −0.528828 0.915957i −0.999435 0.0336142i \(-0.989298\pi\)
0.470607 0.882343i \(-0.344035\pi\)
\(600\) 5.32573 + 6.82910i 0.217422 + 0.278797i
\(601\) −9.79604 + 16.9672i −0.399589 + 0.692108i −0.993675 0.112293i \(-0.964180\pi\)
0.594086 + 0.804401i \(0.297514\pi\)
\(602\) −5.67241 5.67241i −0.231190 0.231190i
\(603\) 22.9172 + 8.46115i 0.933262 + 0.344565i
\(604\) 4.06902i 0.165566i
\(605\) 3.16864 10.2303i 0.128824 0.415923i
\(606\) −17.0008 5.40349i −0.690611 0.219502i
\(607\) −28.7731 7.70972i −1.16786 0.312928i −0.377761 0.925903i \(-0.623306\pi\)
−0.790102 + 0.612975i \(0.789973\pi\)
\(608\) −1.82070 0.487854i −0.0738390 0.0197851i
\(609\) 27.6776 + 8.79699i 1.12155 + 0.356472i
\(610\) −17.2346 + 9.08318i −0.697807 + 0.367767i
\(611\) 3.43162i 0.138828i
\(612\) 0.478556 + 0.176685i 0.0193445 + 0.00714207i
\(613\) −12.5028 12.5028i −0.504982 0.504982i 0.408000 0.912982i \(-0.366226\pi\)
−0.912982 + 0.408000i \(0.866226\pi\)
\(614\) 14.3510 24.8566i 0.579157 1.00313i
\(615\) 30.1101 + 10.8650i 1.21416 + 0.438117i
\(616\) −7.72515 13.3804i −0.311255 0.539110i
\(617\) −1.91482 + 7.14621i −0.0770878 + 0.287695i −0.993699 0.112085i \(-0.964247\pi\)
0.916611 + 0.399781i \(0.130914\pi\)
\(618\) 0.515774 11.2191i 0.0207475 0.451299i
\(619\) 16.4624 + 9.50460i 0.661682 + 0.382022i 0.792917 0.609329i \(-0.208561\pi\)
−0.131236 + 0.991351i \(0.541895\pi\)
\(620\) 4.65511 + 20.5050i 0.186954 + 0.823499i
\(621\) −25.2196 10.6514i −1.01203 0.427426i
\(622\) 9.78715 9.78715i 0.392429 0.392429i
\(623\) 4.90928 + 18.3217i 0.196686 + 0.734043i
\(624\) −1.15564 1.26701i −0.0462625 0.0507211i
\(625\) −24.7032 3.84069i −0.988129 0.153628i
\(626\) −16.0560 + 9.26994i −0.641727 + 0.370501i
\(627\) −6.99560 + 10.9252i −0.279378 + 0.436310i
\(628\) −8.81460 + 2.36186i −0.351741 + 0.0942486i
\(629\) 0.786034 0.0313412
\(630\) 9.97048 24.1022i 0.397233 0.960253i
\(631\) −2.22853 −0.0887165 −0.0443583 0.999016i \(-0.514124\pi\)
−0.0443583 + 0.999016i \(0.514124\pi\)
\(632\) −13.1086 + 3.51245i −0.521433 + 0.139718i
\(633\) 14.5055 + 28.0225i 0.576543 + 1.11380i
\(634\) −0.727989 + 0.420305i −0.0289121 + 0.0166924i
\(635\) −43.5664 1.68073i −1.72888 0.0666979i
\(636\) −2.71982 + 8.55729i −0.107848 + 0.339319i
\(637\) −2.08035 7.76396i −0.0824263 0.307619i
\(638\) 12.1167 12.1167i 0.479705 0.479705i
\(639\) −1.91278 + 20.7594i −0.0756683 + 0.821229i
\(640\) 1.19185 1.89195i 0.0471122 0.0747860i
\(641\) 37.8297 + 21.8410i 1.49418 + 0.862666i 0.999978 0.00667968i \(-0.00212622\pi\)
0.494204 + 0.869346i \(0.335460\pi\)
\(642\) −7.63367 4.88798i −0.301277 0.192913i
\(643\) −7.89483 + 29.4639i −0.311342 + 1.16194i 0.616006 + 0.787742i \(0.288750\pi\)
−0.927347 + 0.374202i \(0.877917\pi\)
\(644\) −10.2428 17.7411i −0.403624 0.699097i
\(645\) −6.55813 4.56506i −0.258226 0.179749i
\(646\) 0.160260 0.277578i 0.00630533 0.0109211i
\(647\) −4.02651 4.02651i −0.158298 0.158298i 0.623514 0.781812i \(-0.285704\pi\)
−0.781812 + 0.623514i \(0.785704\pi\)
\(648\) −7.41970 + 5.09393i −0.291473 + 0.200108i
\(649\) 21.6861i 0.851255i
\(650\) 4.93572 + 0.381395i 0.193595 + 0.0149595i
\(651\) 46.7892 42.6763i 1.83381 1.67261i
\(652\) 6.88270 + 1.84421i 0.269547 + 0.0722249i
\(653\) −31.5015 8.44081i −1.23275 0.330314i −0.417100 0.908861i \(-0.636954\pi\)
−0.815650 + 0.578546i \(0.803620\pi\)
\(654\) −2.70876 12.3533i −0.105921 0.483050i
\(655\) 9.57576 + 2.96590i 0.374156 + 0.115887i
\(656\) 8.26506i 0.322696i
\(657\) −22.4487 27.0055i −0.875809 1.05358i
\(658\) 9.52933 + 9.52933i 0.371492 + 0.371492i
\(659\) 7.75612 13.4340i 0.302136 0.523314i −0.674484 0.738290i \(-0.735634\pi\)
0.976619 + 0.214975i \(0.0689671\pi\)
\(660\) −9.92490 11.7618i −0.386326 0.457828i
\(661\) 11.1307 + 19.2789i 0.432933 + 0.749862i 0.997124 0.0757821i \(-0.0241453\pi\)
−0.564191 + 0.825644i \(0.690812\pi\)
\(662\) −1.07778 + 4.02232i −0.0418890 + 0.156332i
\(663\) 0.258966 0.134051i 0.0100574 0.00520610i
\(664\) −6.06007 3.49878i −0.235176 0.135779i
\(665\) −13.8661 8.73512i −0.537706 0.338734i
\(666\) −8.00649 + 11.3229i −0.310245 + 0.438753i
\(667\) 16.0656 16.0656i 0.622063 0.622063i
\(668\) 2.80384 + 10.4641i 0.108484 + 0.404867i
\(669\) 7.94444 1.74202i 0.307150 0.0673503i
\(670\) 12.3695 + 13.3621i 0.477874 + 0.516225i
\(671\) 29.9817 17.3099i 1.15743 0.668243i
\(672\) −6.72750 0.309282i −0.259519 0.0119308i
\(673\) −9.32657 + 2.49905i −0.359513 + 0.0963312i −0.434054 0.900887i \(-0.642917\pi\)
0.0745413 + 0.997218i \(0.476251\pi\)
\(674\) −3.24846 −0.125126
\(675\) 5.54142 25.3829i 0.213289 0.976989i
\(676\) 12.0197 0.462297
\(677\) 7.30994 1.95869i 0.280944 0.0752787i −0.115596 0.993296i \(-0.536878\pi\)
0.396539 + 0.918018i \(0.370211\pi\)
\(678\) −7.30040 0.335620i −0.280370 0.0128894i
\(679\) −5.03802 + 2.90870i −0.193342 + 0.111626i
\(680\) 0.258298 + 0.279027i 0.00990527 + 0.0107002i
\(681\) −42.3494 + 9.28618i −1.62283 + 0.355847i
\(682\) −9.67093 36.0924i −0.370319 1.38205i
\(683\) 7.48288 7.48288i 0.286325 0.286325i −0.549300 0.835625i \(-0.685106\pi\)
0.835625 + 0.549300i \(0.185106\pi\)
\(684\) 2.36614 + 5.13594i 0.0904715 + 0.196378i
\(685\) 23.6471 + 14.8967i 0.903509 + 0.569175i
\(686\) −3.76572 2.17414i −0.143776 0.0830090i
\(687\) −35.0522 + 18.1443i −1.33732 + 0.692250i
\(688\) −0.533983 + 1.99285i −0.0203579 + 0.0759767i
\(689\) 2.56635 + 4.44506i 0.0977703 + 0.169343i
\(690\) −13.1595 15.5950i −0.500973 0.593693i
\(691\) 21.3061 36.9033i 0.810523 1.40387i −0.101975 0.994787i \(-0.532516\pi\)
0.912498 0.409080i \(-0.134150\pi\)
\(692\) 2.66569 + 2.66569i 0.101334 + 0.101334i
\(693\) −16.0538 + 43.4820i −0.609832 + 1.65174i
\(694\) 4.69326i 0.178154i
\(695\) 8.88974 + 2.75342i 0.337207 + 0.104443i
\(696\) −1.59981 7.29588i −0.0606405 0.276550i
\(697\) 1.35753 + 0.363749i 0.0514201 + 0.0137780i
\(698\) −9.40041 2.51883i −0.355811 0.0953392i
\(699\) 37.3700 34.0850i 1.41346 1.28921i
\(700\) 14.7652 12.6470i 0.558072 0.478012i
\(701\) 36.3602i 1.37331i −0.726985 0.686653i \(-0.759079\pi\)
0.726985 0.686653i \(-0.240921\pi\)
\(702\) −0.706799 + 5.09586i −0.0266764 + 0.192331i
\(703\) 6.16113 + 6.16113i 0.232371 + 0.232371i
\(704\) −1.98681 + 3.44125i −0.0748805 + 0.129697i
\(705\) 11.0173 + 7.66905i 0.414935 + 0.288833i
\(706\) 2.55100 + 4.41846i 0.0960080 + 0.166291i
\(707\) −10.3647 + 38.6814i −0.389803 + 1.45476i
\(708\) 7.96061 + 5.09733i 0.299178 + 0.191569i
\(709\) −0.356646 0.205910i −0.0133941 0.00773310i 0.493288 0.869866i \(-0.335795\pi\)
−0.506682 + 0.862133i \(0.669128\pi\)
\(710\) −8.28233 + 13.1474i −0.310830 + 0.493413i
\(711\) 33.2421 + 23.5057i 1.24668 + 0.881534i
\(712\) 3.44949 3.44949i 0.129275 0.129275i
\(713\) −12.8227 47.8551i −0.480215 1.79219i
\(714\) 0.346880 1.09138i 0.0129817 0.0408437i
\(715\) −8.79064 0.339132i −0.328751 0.0126828i
\(716\) 11.1676 6.44762i 0.417353 0.240959i
\(717\) −7.26599 14.0368i −0.271353 0.524214i
\(718\) −1.23345 + 0.330503i −0.0460321 + 0.0123343i
\(719\) −34.4664 −1.28538 −0.642690 0.766126i \(-0.722182\pi\)
−0.642690 + 0.766126i \(0.722182\pi\)
\(720\) −6.65041 + 0.878650i −0.247846 + 0.0327454i
\(721\) −25.2120 −0.938946
\(722\) −14.9207 + 3.99799i −0.555291 + 0.148790i
\(723\) −1.62451 + 2.53704i −0.0604162 + 0.0943534i
\(724\) 21.0615 12.1599i 0.782744 0.451918i
\(725\) 17.7870 + 12.1875i 0.660591 + 0.452631i
\(726\) 5.59043 + 6.12921i 0.207480 + 0.227476i
\(727\) 3.69508 + 13.7902i 0.137043 + 0.511451i 0.999981 + 0.00614188i \(0.00195503\pi\)
−0.862938 + 0.505310i \(0.831378\pi\)
\(728\) −2.72214 + 2.72214i −0.100889 + 0.100889i
\(729\) 25.9808 + 7.34847i 0.962250 + 0.272166i
\(730\) −5.79490 25.5255i −0.214479 0.944743i
\(731\) −0.303823 0.175413i −0.0112373 0.00648787i
\(732\) 0.693017 15.0745i 0.0256146 0.557169i
\(733\) 7.94942 29.6676i 0.293618 1.09580i −0.648690 0.761053i \(-0.724683\pi\)
0.942308 0.334746i \(-0.108651\pi\)
\(734\) 5.04335 + 8.73534i 0.186153 + 0.322427i
\(735\) −29.5756 10.6721i −1.09091 0.393645i
\(736\) −2.63432 + 4.56277i −0.0971022 + 0.168186i
\(737\) −22.8802 22.8802i −0.842803 0.842803i
\(738\) −19.0675 + 15.8502i −0.701886 + 0.583454i
\(739\) 19.6312i 0.722144i 0.932538 + 0.361072i \(0.117589\pi\)
−0.932538 + 0.361072i \(0.882411\pi\)
\(740\) −9.14410 + 4.81924i −0.336144 + 0.177159i
\(741\) 3.08056 + 0.979118i 0.113167 + 0.0359688i
\(742\) 19.4701 + 5.21700i 0.714771 + 0.191522i
\(743\) −34.7672 9.31585i −1.27549 0.341765i −0.443356 0.896346i \(-0.646212\pi\)
−0.832130 + 0.554580i \(0.812879\pi\)
\(744\) −15.5221 4.93349i −0.569067 0.180871i
\(745\) −0.685709 + 2.21390i −0.0251224 + 0.0811109i
\(746\) 13.1124i 0.480080i
\(747\) 3.54991 + 20.6904i 0.129884 + 0.757022i
\(748\) −0.477782 0.477782i −0.0174695 0.0174695i
\(749\) −10.1743 + 17.6224i −0.371761 + 0.643910i
\(750\) 12.2549 14.9939i 0.447487 0.547499i
\(751\) −24.4567 42.3603i −0.892438 1.54575i −0.836944 0.547289i \(-0.815660\pi\)
−0.0554938 0.998459i \(-0.517673\pi\)
\(752\) 0.897060 3.34787i 0.0327124 0.122084i
\(753\) 0.490584 10.6712i 0.0178779 0.388879i
\(754\) −3.69759 2.13480i −0.134658 0.0777449i
\(755\) 8.87283 2.01434i 0.322915 0.0733095i
\(756\) 12.1881 + 16.1135i 0.443276 + 0.586043i
\(757\) 22.9129 22.9129i 0.832783 0.832783i −0.155114 0.987897i \(-0.549574\pi\)
0.987897 + 0.155114i \(0.0495745\pi\)
\(758\) 0.152094 + 0.567624i 0.00552432 + 0.0206170i
\(759\) 24.4361 + 26.7911i 0.886973 + 0.972456i
\(760\) −0.162481 + 4.21169i −0.00589382 + 0.152774i
\(761\) −9.19124 + 5.30657i −0.333182 + 0.192363i −0.657253 0.753670i \(-0.728282\pi\)
0.324071 + 0.946033i \(0.394948\pi\)
\(762\) 18.2111 28.4406i 0.659717 1.03030i
\(763\) −27.4229 + 7.34795i −0.992777 + 0.266014i
\(764\) 13.6296 0.493100
\(765\) 0.148370 1.13100i 0.00536433 0.0408912i
\(766\) −14.5012 −0.523950
\(767\) 5.21932 1.39851i 0.188459 0.0504974i
\(768\) 0.796225 + 1.53819i 0.0287313 + 0.0555046i
\(769\) −3.31814 + 1.91573i −0.119655 + 0.0690830i −0.558633 0.829415i \(-0.688674\pi\)
0.438978 + 0.898498i \(0.355341\pi\)
\(770\) −25.3527 + 23.4692i −0.913646 + 0.845770i
\(771\) −15.2428 + 47.9578i −0.548955 + 1.72716i
\(772\) 4.19397 + 15.6521i 0.150944 + 0.563332i
\(773\) 19.8976 19.8976i 0.715668 0.715668i −0.252047 0.967715i \(-0.581104\pi\)
0.967715 + 0.252047i \(0.0811037\pi\)
\(774\) 5.62156 2.58986i 0.202063 0.0930907i
\(775\) 42.4082 20.3017i 1.52335 0.729258i
\(776\) 1.29571 + 0.748079i 0.0465133 + 0.0268545i
\(777\) 26.2170 + 16.7872i 0.940529 + 0.602239i
\(778\) 5.37250 20.0504i 0.192613 0.718843i
\(779\) 7.78950 + 13.4918i 0.279088 + 0.483395i
\(780\) −2.19073 + 3.14719i −0.0784408 + 0.112687i
\(781\) 13.8065 23.9136i 0.494036 0.855696i
\(782\) −0.633495 0.633495i −0.0226537 0.0226537i
\(783\) −13.7636 + 17.6823i −0.491872 + 0.631915i
\(784\) 8.11832i 0.289940i
\(785\) 9.51384 + 18.0517i 0.339564 + 0.644293i
\(786\) −5.73704 + 5.23273i −0.204633 + 0.186645i
\(787\) 6.98473 + 1.87155i 0.248979 + 0.0667137i 0.381150 0.924513i \(-0.375528\pi\)
−0.132171 + 0.991227i \(0.542195\pi\)
\(788\) −1.58575 0.424901i −0.0564901 0.0151365i
\(789\) 6.92279 + 31.5712i 0.246458 + 1.12397i
\(790\) 14.1485 + 26.8456i 0.503382 + 0.955124i
\(791\) 16.4058i 0.583321i
\(792\) 11.7492 2.01584i 0.417488 0.0716296i
\(793\) −6.09956 6.09956i −0.216602 0.216602i
\(794\) −11.1320 + 19.2811i −0.395059 + 0.684262i
\(795\) 20.0063 + 1.69457i 0.709550 + 0.0601001i
\(796\) 8.58664 + 14.8725i 0.304345 + 0.527142i
\(797\) −8.96012 + 33.4396i −0.317384 + 1.18449i 0.604366 + 0.796707i \(0.293427\pi\)
−0.921750 + 0.387786i \(0.873240\pi\)
\(798\) 11.2734 5.83555i 0.399074 0.206576i
\(799\) 0.510406 + 0.294683i 0.0180569 + 0.0104251i
\(800\) −4.71557 1.66234i −0.166721 0.0587725i
\(801\) −14.5732 1.34278i −0.514919 0.0474448i
\(802\) −3.36182 + 3.36182i −0.118710 + 0.118710i
\(803\) 12.0388 + 44.9295i 0.424841 + 1.58553i
\(804\) −13.7769 + 3.02094i −0.485875 + 0.106540i
\(805\) −33.6152 + 31.1179i −1.18478 + 1.09676i
\(806\) −8.06289 + 4.65511i −0.284003 + 0.163969i
\(807\) −26.9142 1.23732i −0.947424 0.0435557i
\(808\) 9.94834 2.66565i 0.349981 0.0937772i
\(809\) 52.6028 1.84942 0.924709 0.380675i \(-0.124308\pi\)
0.924709 + 0.380675i \(0.124308\pi\)
\(810\) 14.7808 + 13.6575i 0.519344 + 0.479877i
\(811\) −13.8979 −0.488021 −0.244011 0.969773i \(-0.578463\pi\)
−0.244011 + 0.969773i \(0.578463\pi\)
\(812\) −16.1961 + 4.33973i −0.568371 + 0.152295i
\(813\) 3.23870 + 0.148892i 0.113586 + 0.00522188i
\(814\) 15.9073 9.18410i 0.557551 0.321902i
\(815\) 0.614221 15.9212i 0.0215152 0.557697i
\(816\) −0.287689 + 0.0630830i −0.0100711 + 0.00220835i
\(817\) −1.00652 3.75637i −0.0352136 0.131419i
\(818\) 21.1307 21.1307i 0.738817 0.738817i
\(819\) 11.5003 + 1.05965i 0.401854 + 0.0370270i
\(820\) −18.0226 + 4.09156i −0.629377 + 0.142884i
\(821\) −23.9657 13.8366i −0.836408 0.482900i 0.0196338 0.999807i \(-0.493750\pi\)
−0.856042 + 0.516907i \(0.827083\pi\)
\(822\) −19.2255 + 9.95185i −0.670566 + 0.347111i
\(823\) −7.80049 + 29.1118i −0.271908 + 1.01477i 0.685977 + 0.727623i \(0.259375\pi\)
−0.957885 + 0.287151i \(0.907292\pi\)
\(824\) 3.24210 + 5.61548i 0.112944 + 0.195625i
\(825\) −20.7343 + 27.4647i −0.721876 + 0.956196i
\(826\) 10.6101 18.3772i 0.369172 0.639424i
\(827\) 4.09863 + 4.09863i 0.142523 + 0.142523i 0.774768 0.632245i \(-0.217866\pi\)
−0.632245 + 0.774768i \(0.717866\pi\)
\(828\) 15.5783 2.67281i 0.541382 0.0928865i
\(829\) 37.6756i 1.30853i 0.756266 + 0.654264i \(0.227021\pi\)
−0.756266 + 0.654264i \(0.772979\pi\)
\(830\) −4.62938 + 14.9465i −0.160688 + 0.518802i
\(831\) 1.53257 + 6.98924i 0.0531642 + 0.242454i
\(832\) 0.956351 + 0.256253i 0.0331555 + 0.00888399i
\(833\) −1.33343 0.357291i −0.0462006 0.0123794i
\(834\) −5.32603 + 4.85785i −0.184425 + 0.168213i
\(835\) 21.4297 11.2942i 0.741606 0.390851i
\(836\) 7.48995i 0.259046i
\(837\) 18.3857 + 45.2707i 0.635501 + 1.56478i
\(838\) −12.4682 12.4682i −0.430708 0.430708i
\(839\) 16.5639 28.6895i 0.571849 0.990471i −0.424527 0.905415i \(-0.639560\pi\)
0.996376 0.0850559i \(-0.0271069\pi\)
\(840\) 2.65599 + 14.8230i 0.0916404 + 0.511441i
\(841\) 5.20180 + 9.00978i 0.179372 + 0.310682i
\(842\) −7.21908 + 26.9420i −0.248786 + 0.928482i
\(843\) −0.418784 0.268155i −0.0144237 0.00923575i
\(844\) −15.7771 9.10894i −0.543072 0.313543i
\(845\) −5.95029 26.2100i −0.204696 0.901651i
\(846\) −9.44390 + 4.35082i −0.324688 + 0.149584i
\(847\) 13.1684 13.1684i 0.452472 0.452472i
\(848\) −1.34174 5.00745i −0.0460757 0.171957i
\(849\) 9.49743 29.8814i 0.325951 1.02553i
\(850\) 0.480572 0.701370i 0.0164835 0.0240568i
\(851\) 21.0916 12.1773i 0.723011 0.417431i
\(852\) −5.53306 10.6890i −0.189559 0.366201i
\(853\) −2.57386 + 0.689663i −0.0881273 + 0.0236136i −0.302613 0.953113i \(-0.597859\pi\)
0.214486 + 0.976727i \(0.431192\pi\)
\(854\) −33.8760 −1.15921
\(855\) 10.0280 7.70206i 0.342950 0.263405i
\(856\) 5.23339 0.178874
\(857\) 15.1284 4.05364i 0.516776 0.138470i 0.00900123 0.999959i \(-0.497135\pi\)
0.507775 + 0.861490i \(0.330468\pi\)
\(858\) 3.67455 5.73863i 0.125447 0.195914i
\(859\) 0.691191 0.399059i 0.0235831 0.0136157i −0.488162 0.872753i \(-0.662333\pi\)
0.511745 + 0.859137i \(0.328999\pi\)
\(860\) 4.60991 + 0.177845i 0.157197 + 0.00606445i
\(861\) 37.5099 + 41.1249i 1.27833 + 1.40153i
\(862\) −4.99288 18.6337i −0.170058 0.634666i
\(863\) 30.2854 30.2854i 1.03093 1.03093i 0.0314193 0.999506i \(-0.489997\pi\)
0.999506 0.0314193i \(-0.0100027\pi\)
\(864\) 2.02166 4.78674i 0.0687783 0.162848i
\(865\) 4.49311 7.13237i 0.152770 0.242508i
\(866\) −20.4721 11.8196i −0.695671 0.401646i
\(867\) −1.34994 + 29.3638i −0.0458462 + 0.997246i
\(868\) −9.46313 + 35.3169i −0.321199 + 1.19873i
\(869\) −26.9630 46.7013i −0.914658 1.58423i
\(870\) −15.1173 + 7.10028i −0.512524 + 0.240722i
\(871\) −4.03119 + 6.98222i −0.136592 + 0.236584i
\(872\) 5.16301 + 5.16301i 0.174842 + 0.174842i
\(873\) −0.759010 4.42384i −0.0256886 0.149724i
\(874\) 9.93098i 0.335920i
\(875\) −34.8872 25.9359i −1.17940 0.876794i
\(876\) 19.3226 + 6.14144i 0.652850 + 0.207500i
\(877\) −16.7435 4.48641i −0.565388 0.151495i −0.0352074 0.999380i \(-0.511209\pi\)
−0.530180 + 0.847885i \(0.677876\pi\)
\(878\) 34.7780 + 9.31875i 1.17370 + 0.314492i
\(879\) −35.3169 11.2250i −1.19121 0.378610i
\(880\) 8.48747 + 2.62882i 0.286113 + 0.0886176i
\(881\) 15.1033i 0.508843i −0.967093 0.254421i \(-0.918115\pi\)
0.967093 0.254421i \(-0.0818850\pi\)
\(882\) 18.7290 15.5688i 0.630639 0.524229i
\(883\) −16.4678 16.4678i −0.554185 0.554185i 0.373461 0.927646i \(-0.378171\pi\)
−0.927646 + 0.373461i \(0.878171\pi\)
\(884\) −0.0841789 + 0.145802i −0.00283124 + 0.00490386i
\(885\) 7.17429 19.8822i 0.241161 0.668332i
\(886\) 13.4169 + 23.2388i 0.450750 + 0.780723i
\(887\) 7.07714 26.4123i 0.237627 0.886837i −0.739320 0.673355i \(-0.764853\pi\)
0.976947 0.213482i \(-0.0684806\pi\)
\(888\) 0.367692 7.99804i 0.0123389 0.268397i
\(889\) −65.6556 37.9063i −2.20202 1.27134i
\(890\) −9.22954 5.81424i −0.309375 0.194894i
\(891\) −27.1823 23.2395i −0.910643 0.778554i
\(892\) −3.32036 + 3.32036i −0.111174 + 0.111174i
\(893\) 1.69089 + 6.31049i 0.0565835 + 0.211173i
\(894\) −1.20980 1.32639i −0.0404616 0.0443612i
\(895\) −19.5880 21.1600i −0.654755 0.707302i
\(896\) 3.36730 1.94411i 0.112494 0.0649483i
\(897\) 4.87211 7.60889i 0.162675 0.254053i
\(898\) 39.9306 10.6994i 1.33250 0.357043i
\(899\) −40.5510 −1.35245
\(900\) 5.20821 + 14.0668i 0.173607 + 0.468893i
\(901\) 0.881522 0.0293678
\(902\) 31.7230 8.50016i 1.05626 0.283025i
\(903\) −6.38732 12.3393i −0.212557 0.410628i
\(904\) 3.65405 2.10967i 0.121532 0.0701666i
\(905\) −36.9419 39.9066i −1.22799 1.32654i
\(906\) −2.13480 + 6.71666i −0.0709241 + 0.223146i
\(907\) 6.62626 + 24.7295i 0.220021 + 0.821130i 0.984338 + 0.176290i \(0.0564096\pi\)
−0.764317 + 0.644841i \(0.776924\pi\)
\(908\) 17.6998 17.6998i 0.587390 0.587390i
\(909\) −25.2280 17.8389i −0.836759 0.591678i
\(910\) 7.28342 + 4.58826i 0.241443 + 0.152099i
\(911\) 3.55075 + 2.05003i 0.117642 + 0.0679204i 0.557666 0.830065i \(-0.311697\pi\)
−0.440025 + 0.897986i \(0.645030\pi\)
\(912\) −2.74944 1.76052i −0.0910430 0.0582965i
\(913\) 7.19662 26.8582i 0.238173 0.888875i
\(914\) −10.7957 18.6987i −0.357090 0.618499i
\(915\) −33.2142 + 5.95135i −1.09803 + 0.196746i
\(916\) 11.3940 19.7350i 0.376468 0.652061i
\(917\) 12.3259 + 12.3259i 0.407035 + 0.407035i
\(918\) 0.697245 + 0.542723i 0.0230125 + 0.0179125i
\(919\) 28.8740i 0.952464i −0.879320 0.476232i \(-0.842002\pi\)
0.879320 0.476232i \(-0.157998\pi\)
\(920\) 11.2536 + 3.48557i 0.371020 + 0.114916i
\(921\) 36.7298 33.5011i 1.21029 1.10390i
\(922\) 12.1246 + 3.24877i 0.399302 + 0.106993i
\(923\) −6.64579 1.78073i −0.218749 0.0586135i
\(924\) −5.73178 26.1397i −0.188562 0.859932i
\(925\) 15.0355 + 17.5537i 0.494363 + 0.577163i
\(926\) 22.1046i 0.726404i
\(927\) 6.73746 18.2486i 0.221287 0.599362i
\(928\) 3.04930 + 3.04930i 0.100098 + 0.100098i
\(929\) −25.1077 + 43.4879i −0.823758 + 1.42679i 0.0791067 + 0.996866i \(0.474793\pi\)
−0.902865 + 0.429925i \(0.858540\pi\)
\(930\) −3.07378 + 36.2894i −0.100793 + 1.18998i
\(931\) −7.65121 13.2523i −0.250758 0.434326i
\(932\) −7.55809 + 28.2072i −0.247573 + 0.923956i
\(933\) 21.2903 11.0206i 0.697012 0.360800i
\(934\) −4.26380 2.46170i −0.139516 0.0805494i
\(935\) −0.805320 + 1.27837i −0.0263368 + 0.0418070i
\(936\) −1.24285 2.69773i −0.0406239 0.0881782i
\(937\) −0.857094 + 0.857094i −0.0280000 + 0.0280000i −0.720968 0.692968i \(-0.756303\pi\)
0.692968 + 0.720968i \(0.256303\pi\)
\(938\) 8.19479 + 30.5834i 0.267569 + 0.998582i
\(939\) −31.3668 + 6.87796i −1.02362 + 0.224454i
\(940\) −7.74439 0.298769i −0.252594 0.00974476i
\(941\) −43.4478 + 25.0846i −1.41636 + 0.817735i −0.995977 0.0896119i \(-0.971437\pi\)
−0.420382 + 0.907347i \(0.638104\pi\)
\(942\) −15.7892 0.725875i −0.514441 0.0236503i
\(943\) 42.0618 11.2704i 1.36972 0.367015i
\(944\) −5.45754 −0.177628
\(945\) 29.1032 34.5540i 0.946727 1.12404i
\(946\) −8.19815 −0.266545
\(947\) 2.54334 0.681485i 0.0826473 0.0221453i −0.217258 0.976114i \(-0.569711\pi\)
0.299906 + 0.953969i \(0.403045\pi\)
\(948\) −23.4809 1.07949i −0.762626 0.0350601i
\(949\) 10.0371 5.79490i 0.325817 0.188111i
\(950\) 9.26436 1.73066i 0.300575 0.0561502i
\(951\) −1.42219 + 0.311851i −0.0461176 + 0.0101125i
\(952\) 0.171123 + 0.638639i 0.00554612 + 0.0206984i
\(953\) −28.1499 + 28.1499i −0.911864 + 0.911864i −0.996419 0.0845545i \(-0.973053\pi\)
0.0845545 + 0.996419i \(0.473053\pi\)
\(954\) −8.97912 + 12.6984i −0.290710 + 0.411126i
\(955\) −6.74723 29.7204i −0.218335 0.961729i
\(956\) 7.90295 + 4.56277i 0.255600 + 0.147571i
\(957\) 26.3578 13.6438i 0.852027 0.441042i
\(958\) 0.702296 2.62100i 0.0226901 0.0846808i
\(959\) 24.2991 + 42.0872i 0.784658 + 1.35907i
\(960\) 2.95998 2.49770i 0.0955329 0.0806130i
\(961\) −28.7123 + 49.7312i −0.926204 + 1.60423i
\(962\) −3.23623 3.23623i −0.104340 0.104340i
\(963\) −10.0363 12.0735i −0.323414 0.389062i
\(964\) 1.73931i 0.0560194i
\(965\) 32.0545 16.8938i 1.03187 0.543830i
\(966\) −7.59981 34.6587i −0.244520 1.11513i
\(967\) 1.28319 + 0.343829i 0.0412646 + 0.0110568i 0.279392 0.960177i \(-0.409867\pi\)
−0.238128 + 0.971234i \(0.576534\pi\)
\(968\) −4.62638 1.23963i −0.148697 0.0398433i
\(969\) 0.410168 0.374112i 0.0131765 0.0120182i
\(970\) 0.989814 3.19574i 0.0317810 0.102609i
\(971\) 38.7906i 1.24485i 0.782679 + 0.622425i \(0.213853\pi\)
−0.782679 + 0.622425i \(0.786147\pi\)
\(972\) −14.9201 + 4.51572i −0.478561 + 0.144842i
\(973\) 11.4428 + 11.4428i 0.366840 + 0.366840i
\(974\) 5.80393 10.0527i 0.185970 0.322109i
\(975\) 7.94720 + 3.21908i 0.254514 + 0.103093i
\(976\) 4.35623 + 7.54520i 0.139439 + 0.241516i
\(977\) 11.0953 41.4084i 0.354972 1.32477i −0.525548 0.850764i \(-0.676140\pi\)
0.880520 0.474009i \(-0.157193\pi\)
\(978\) 10.3936 + 6.65520i 0.332350 + 0.212810i
\(979\) 16.7875 + 9.69226i 0.536530 + 0.309766i
\(980\) 17.7026 4.01892i 0.565490 0.128380i
\(981\) 2.00980 21.8124i 0.0641681 0.696417i
\(982\) −3.49508 + 3.49508i −0.111532 + 0.111532i
\(983\) 8.34182 + 31.1321i 0.266063 + 0.992960i 0.961597 + 0.274466i \(0.0885012\pi\)
−0.695534 + 0.718493i \(0.744832\pi\)
\(984\) 4.33624 13.6430i 0.138234 0.434922i
\(985\) −0.141515 + 3.66820i −0.00450903 + 0.116879i
\(986\) −0.635046 + 0.366644i −0.0202240 + 0.0116763i
\(987\) 10.7303 + 20.7294i 0.341550 + 0.659824i
\(988\) −1.80265 + 0.483018i −0.0573499 + 0.0153669i
\(989\) −10.8700 −0.345645
\(990\) −10.2120 24.6220i −0.324560 0.782540i
\(991\) 20.1017 0.638551 0.319275 0.947662i \(-0.396561\pi\)
0.319275 + 0.947662i \(0.396561\pi\)
\(992\) 9.08302 2.43379i 0.288386 0.0772729i
\(993\) −3.88937 + 6.07411i −0.123425 + 0.192756i
\(994\) −23.3998 + 13.5099i −0.742196 + 0.428507i
\(995\) 28.1799 26.0864i 0.893364 0.826995i
\(996\) −8.16761 8.95478i −0.258801 0.283743i
\(997\) 0.763421 + 2.84912i 0.0241778 + 0.0902327i 0.976960 0.213420i \(-0.0684603\pi\)
−0.952783 + 0.303653i \(0.901794\pi\)
\(998\) −22.9557 + 22.9557i −0.726649 + 0.726649i
\(999\) −19.1567 + 14.4899i −0.606090 + 0.458439i
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 90.2.l.b.83.1 yes 16
3.2 odd 2 270.2.m.b.143.4 16
4.3 odd 2 720.2.cu.b.353.4 16
5.2 odd 4 inner 90.2.l.b.47.1 yes 16
5.3 odd 4 450.2.p.h.407.4 16
5.4 even 2 450.2.p.h.443.4 16
9.2 odd 6 810.2.f.c.323.1 16
9.4 even 3 270.2.m.b.233.3 16
9.5 odd 6 inner 90.2.l.b.23.1 16
9.7 even 3 810.2.f.c.323.8 16
15.2 even 4 270.2.m.b.197.3 16
15.8 even 4 1350.2.q.h.1007.1 16
15.14 odd 2 1350.2.q.h.143.2 16
20.7 even 4 720.2.cu.b.497.3 16
36.23 even 6 720.2.cu.b.113.3 16
45.2 even 12 810.2.f.c.647.8 16
45.4 even 6 1350.2.q.h.1043.1 16
45.7 odd 12 810.2.f.c.647.1 16
45.13 odd 12 1350.2.q.h.557.2 16
45.14 odd 6 450.2.p.h.293.4 16
45.22 odd 12 270.2.m.b.17.4 16
45.23 even 12 450.2.p.h.257.4 16
45.32 even 12 inner 90.2.l.b.77.1 yes 16
180.167 odd 12 720.2.cu.b.257.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
90.2.l.b.23.1 16 9.5 odd 6 inner
90.2.l.b.47.1 yes 16 5.2 odd 4 inner
90.2.l.b.77.1 yes 16 45.32 even 12 inner
90.2.l.b.83.1 yes 16 1.1 even 1 trivial
270.2.m.b.17.4 16 45.22 odd 12
270.2.m.b.143.4 16 3.2 odd 2
270.2.m.b.197.3 16 15.2 even 4
270.2.m.b.233.3 16 9.4 even 3
450.2.p.h.257.4 16 45.23 even 12
450.2.p.h.293.4 16 45.14 odd 6
450.2.p.h.407.4 16 5.3 odd 4
450.2.p.h.443.4 16 5.4 even 2
720.2.cu.b.113.3 16 36.23 even 6
720.2.cu.b.257.4 16 180.167 odd 12
720.2.cu.b.353.4 16 4.3 odd 2
720.2.cu.b.497.3 16 20.7 even 4
810.2.f.c.323.1 16 9.2 odd 6
810.2.f.c.323.8 16 9.7 even 3
810.2.f.c.647.1 16 45.7 odd 12
810.2.f.c.647.8 16 45.2 even 12
1350.2.q.h.143.2 16 15.14 odd 2
1350.2.q.h.557.2 16 45.13 odd 12
1350.2.q.h.1007.1 16 15.8 even 4
1350.2.q.h.1043.1 16 45.4 even 6