Properties

Label 65.2.f.b.47.2
Level $65$
Weight $2$
Character 65.47
Analytic conductor $0.519$
Analytic rank $0$
Dimension $8$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [65,2,Mod(18,65)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(65, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("65.18");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 65 = 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 65.f (of order \(4\), degree \(2\), 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: \(0.519027613138\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.619810816.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{5} + 14x^{4} - 8x^{3} + 2x^{2} + 2x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 47.2
Root \(-0.252709 - 0.252709i\) of defining polynomial
Character \(\chi\) \(=\) 65.47
Dual form 65.2.f.b.18.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.57942i q^{2} +(0.725850 - 0.725850i) q^{3} -0.494582 q^{4} +(0.146426 + 2.23127i) q^{5} +(-1.14643 - 1.14643i) q^{6} -4.24997 q^{7} -2.37769i q^{8} +1.94628i q^{9} +O(q^{10})\) \(q-1.57942i q^{2} +(0.725850 - 0.725850i) q^{3} -0.494582 q^{4} +(0.146426 + 2.23127i) q^{5} +(-1.14643 - 1.14643i) q^{6} -4.24997 q^{7} -2.37769i q^{8} +1.94628i q^{9} +(3.52412 - 0.231269i) q^{10} +(1.14643 - 1.14643i) q^{11} +(-0.358992 + 0.358992i) q^{12} +(-0.231269 + 3.59813i) q^{13} +6.71251i q^{14} +(1.72585 + 1.51328i) q^{15} -4.74455 q^{16} +(4.37769 - 4.37769i) q^{17} +3.07401 q^{18} +(-0.274150 + 0.274150i) q^{19} +(-0.0724196 - 1.10354i) q^{20} +(-3.08484 + 3.08484i) q^{21} +(-1.81069 - 1.81069i) q^{22} +(-1.64101 - 1.64101i) q^{23} +(-1.72585 - 1.72585i) q^{24} +(-4.95712 + 0.653431i) q^{25} +(5.68297 + 0.365271i) q^{26} +(3.59026 + 3.59026i) q^{27} +2.10196 q^{28} -2.79827i q^{29} +(2.39012 - 2.72585i) q^{30} +(-2.30527 - 2.30527i) q^{31} +2.73827i q^{32} -1.66427i q^{33} +(-6.91424 - 6.91424i) q^{34} +(-0.622306 - 9.48283i) q^{35} -0.962596i q^{36} -2.04288 q^{37} +(0.432999 + 0.432999i) q^{38} +(2.44384 + 2.77957i) q^{39} +(5.30527 - 0.348156i) q^{40} +(-0.883113 - 0.883113i) q^{41} +(4.87228 + 4.87228i) q^{42} +(0.944696 + 0.944696i) q^{43} +(-0.567001 + 0.567001i) q^{44} +(-4.34268 + 0.284986i) q^{45} +(-2.59185 + 2.59185i) q^{46} +0.483745 q^{47} +(-3.44384 + 3.44384i) q^{48} +11.0623 q^{49} +(1.03204 + 7.82940i) q^{50} -6.35510i q^{51} +(0.114381 - 1.77957i) q^{52} +(-7.24997 + 7.24997i) q^{53} +(5.67055 - 5.67055i) q^{54} +(2.72585 + 2.39012i) q^{55} +10.1051i q^{56} +0.397983i q^{57} -4.41966 q^{58} +(0.311554 + 0.311554i) q^{59} +(-0.853574 - 0.748443i) q^{60} +11.2857 q^{61} +(-3.64101 + 3.64101i) q^{62} -8.27164i q^{63} -5.16421 q^{64} +(-8.06225 + 0.0108364i) q^{65} -2.62858 q^{66} -7.11597i q^{67} +(-2.16513 + 2.16513i) q^{68} -2.38225 q^{69} +(-14.9774 + 0.982885i) q^{70} +(7.42752 + 7.42752i) q^{71} +4.62767 q^{72} +4.96796i q^{73} +3.22658i q^{74} +(-3.12383 + 4.07242i) q^{75} +(0.135589 - 0.135589i) q^{76} +(-4.87228 + 4.87228i) q^{77} +(4.39012 - 3.85985i) q^{78} -10.7928i q^{79} +(-0.694725 - 10.5864i) q^{80} -0.626863 q^{81} +(-1.39481 + 1.39481i) q^{82} +11.8340 q^{83} +(1.52571 - 1.52571i) q^{84} +(10.4088 + 9.12680i) q^{85} +(1.49208 - 1.49208i) q^{86} +(-2.03113 - 2.03113i) q^{87} +(-2.72585 - 2.72585i) q^{88} +(-1.10513 - 1.10513i) q^{89} +(0.450114 + 6.85893i) q^{90} +(0.982885 - 15.2919i) q^{91} +(0.811612 + 0.811612i) q^{92} -3.34657 q^{93} -0.764039i q^{94} +(-0.651844 - 0.571559i) q^{95} +(1.98758 + 1.98758i) q^{96} +10.7928i q^{97} -17.4720i q^{98} +(2.23127 + 2.23127i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 6 q^{3} - 8 q^{4} - 2 q^{5} - 6 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 6 q^{3} - 8 q^{4} - 2 q^{5} - 6 q^{6} + 6 q^{10} + 6 q^{11} - 2 q^{12} + 14 q^{13} + 2 q^{15} - 8 q^{16} + 16 q^{17} + 20 q^{18} - 14 q^{19} - 2 q^{20} - 12 q^{21} + 10 q^{22} - 14 q^{23} - 2 q^{24} - 12 q^{25} + 6 q^{26} + 12 q^{27} - 8 q^{28} - 14 q^{30} + 2 q^{31} - 24 q^{35} - 44 q^{37} - 2 q^{38} + 6 q^{39} + 22 q^{40} + 16 q^{41} + 24 q^{42} - 6 q^{43} - 10 q^{44} + 22 q^{45} + 2 q^{46} + 16 q^{47} - 14 q^{48} + 24 q^{49} + 44 q^{50} - 38 q^{52} - 24 q^{53} + 20 q^{54} + 10 q^{55} + 24 q^{58} - 22 q^{59} - 10 q^{60} + 20 q^{61} - 30 q^{62} + 48 q^{64} - 36 q^{66} + 4 q^{68} + 4 q^{69} - 68 q^{70} - 10 q^{71} - 16 q^{72} + 30 q^{75} + 6 q^{76} - 24 q^{77} + 2 q^{78} - 26 q^{80} - 20 q^{81} + 20 q^{82} + 48 q^{83} - 16 q^{84} + 32 q^{85} - 46 q^{86} + 16 q^{87} - 10 q^{88} + 28 q^{89} - 14 q^{90} + 20 q^{91} + 50 q^{92} - 40 q^{93} + 2 q^{95} + 30 q^{96} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/65\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(41\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.57942i 1.11682i −0.829565 0.558411i \(-0.811411\pi\)
0.829565 0.558411i \(-0.188589\pi\)
\(3\) 0.725850 0.725850i 0.419070 0.419070i −0.465813 0.884883i \(-0.654238\pi\)
0.884883 + 0.465813i \(0.154238\pi\)
\(4\) −0.494582 −0.247291
\(5\) 0.146426 + 2.23127i 0.0654836 + 0.997854i
\(6\) −1.14643 1.14643i −0.468026 0.468026i
\(7\) −4.24997 −1.60634 −0.803169 0.595751i \(-0.796854\pi\)
−0.803169 + 0.595751i \(0.796854\pi\)
\(8\) 2.37769i 0.840642i
\(9\) 1.94628i 0.648761i
\(10\) 3.52412 0.231269i 1.11442 0.0731335i
\(11\) 1.14643 1.14643i 0.345660 0.345660i −0.512830 0.858490i \(-0.671403\pi\)
0.858490 + 0.512830i \(0.171403\pi\)
\(12\) −0.358992 + 0.358992i −0.103632 + 0.103632i
\(13\) −0.231269 + 3.59813i −0.0641424 + 0.997941i
\(14\) 6.71251i 1.79399i
\(15\) 1.72585 + 1.51328i 0.445613 + 0.390728i
\(16\) −4.74455 −1.18614
\(17\) 4.37769 4.37769i 1.06175 1.06175i 0.0637831 0.997964i \(-0.479683\pi\)
0.997964 0.0637831i \(-0.0203166\pi\)
\(18\) 3.07401 0.724550
\(19\) −0.274150 + 0.274150i −0.0628942 + 0.0628942i −0.737854 0.674960i \(-0.764161\pi\)
0.674960 + 0.737854i \(0.264161\pi\)
\(20\) −0.0724196 1.10354i −0.0161935 0.246760i
\(21\) −3.08484 + 3.08484i −0.673168 + 0.673168i
\(22\) −1.81069 1.81069i −0.386041 0.386041i
\(23\) −1.64101 1.64101i −0.342174 0.342174i 0.515010 0.857184i \(-0.327788\pi\)
−0.857184 + 0.515010i \(0.827788\pi\)
\(24\) −1.72585 1.72585i −0.352288 0.352288i
\(25\) −4.95712 + 0.653431i −0.991424 + 0.130686i
\(26\) 5.68297 + 0.365271i 1.11452 + 0.0716356i
\(27\) 3.59026 + 3.59026i 0.690946 + 0.690946i
\(28\) 2.10196 0.397233
\(29\) 2.79827i 0.519626i −0.965659 0.259813i \(-0.916339\pi\)
0.965659 0.259813i \(-0.0836609\pi\)
\(30\) 2.39012 2.72585i 0.436374 0.497670i
\(31\) −2.30527 2.30527i −0.414040 0.414040i 0.469104 0.883143i \(-0.344577\pi\)
−0.883143 + 0.469104i \(0.844577\pi\)
\(32\) 2.73827i 0.484063i
\(33\) 1.66427i 0.289712i
\(34\) −6.91424 6.91424i −1.18578 1.18578i
\(35\) −0.622306 9.48283i −0.105189 1.60289i
\(36\) 0.962596i 0.160433i
\(37\) −2.04288 −0.335848 −0.167924 0.985800i \(-0.553706\pi\)
−0.167924 + 0.985800i \(0.553706\pi\)
\(38\) 0.432999 + 0.432999i 0.0702417 + 0.0702417i
\(39\) 2.44384 + 2.77957i 0.391327 + 0.445087i
\(40\) 5.30527 0.348156i 0.838838 0.0550483i
\(41\) −0.883113 0.883113i −0.137919 0.137919i 0.634777 0.772696i \(-0.281092\pi\)
−0.772696 + 0.634777i \(0.781092\pi\)
\(42\) 4.87228 + 4.87228i 0.751809 + 0.751809i
\(43\) 0.944696 + 0.944696i 0.144065 + 0.144065i 0.775461 0.631396i \(-0.217518\pi\)
−0.631396 + 0.775461i \(0.717518\pi\)
\(44\) −0.567001 + 0.567001i −0.0854787 + 0.0854787i
\(45\) −4.34268 + 0.284986i −0.647368 + 0.0424832i
\(46\) −2.59185 + 2.59185i −0.382147 + 0.382147i
\(47\) 0.483745 0.0705615 0.0352808 0.999377i \(-0.488767\pi\)
0.0352808 + 0.999377i \(0.488767\pi\)
\(48\) −3.44384 + 3.44384i −0.497075 + 0.497075i
\(49\) 11.0623 1.58032
\(50\) 1.03204 + 7.82940i 0.145953 + 1.10724i
\(51\) 6.35510i 0.889892i
\(52\) 0.114381 1.77957i 0.0158618 0.246782i
\(53\) −7.24997 + 7.24997i −0.995860 + 0.995860i −0.999991 0.00413141i \(-0.998685\pi\)
0.00413141 + 0.999991i \(0.498685\pi\)
\(54\) 5.67055 5.67055i 0.771664 0.771664i
\(55\) 2.72585 + 2.39012i 0.367554 + 0.322283i
\(56\) 10.1051i 1.35036i
\(57\) 0.397983i 0.0527142i
\(58\) −4.41966 −0.580329
\(59\) 0.311554 + 0.311554i 0.0405608 + 0.0405608i 0.727096 0.686535i \(-0.240869\pi\)
−0.686535 + 0.727096i \(0.740869\pi\)
\(60\) −0.853574 0.748443i −0.110196 0.0966235i
\(61\) 11.2857 1.44498 0.722490 0.691381i \(-0.242998\pi\)
0.722490 + 0.691381i \(0.242998\pi\)
\(62\) −3.64101 + 3.64101i −0.462408 + 0.462408i
\(63\) 8.27164i 1.04213i
\(64\) −5.16421 −0.645526
\(65\) −8.06225 + 0.0108364i −0.999999 + 0.00134409i
\(66\) −2.62858 −0.323556
\(67\) 7.11597i 0.869354i −0.900586 0.434677i \(-0.856863\pi\)
0.900586 0.434677i \(-0.143137\pi\)
\(68\) −2.16513 + 2.16513i −0.262560 + 0.262560i
\(69\) −2.38225 −0.286789
\(70\) −14.9774 + 0.982885i −1.79014 + 0.117477i
\(71\) 7.42752 + 7.42752i 0.881485 + 0.881485i 0.993686 0.112201i \(-0.0357900\pi\)
−0.112201 + 0.993686i \(0.535790\pi\)
\(72\) 4.62767 0.545376
\(73\) 4.96796i 0.581455i 0.956806 + 0.290728i \(0.0938973\pi\)
−0.956806 + 0.290728i \(0.906103\pi\)
\(74\) 3.22658i 0.375082i
\(75\) −3.12383 + 4.07242i −0.360709 + 0.470243i
\(76\) 0.135589 0.135589i 0.0155532 0.0155532i
\(77\) −4.87228 + 4.87228i −0.555247 + 0.555247i
\(78\) 4.39012 3.85985i 0.497083 0.437042i
\(79\) 10.7928i 1.21428i −0.794593 0.607142i \(-0.792316\pi\)
0.794593 0.607142i \(-0.207684\pi\)
\(80\) −0.694725 10.5864i −0.0776726 1.18359i
\(81\) −0.626863 −0.0696515
\(82\) −1.39481 + 1.39481i −0.154031 + 0.154031i
\(83\) 11.8340 1.29895 0.649473 0.760385i \(-0.274990\pi\)
0.649473 + 0.760385i \(0.274990\pi\)
\(84\) 1.52571 1.52571i 0.166468 0.166468i
\(85\) 10.4088 + 9.12680i 1.12900 + 0.989941i
\(86\) 1.49208 1.49208i 0.160895 0.160895i
\(87\) −2.03113 2.03113i −0.217759 0.217759i
\(88\) −2.72585 2.72585i −0.290577 0.290577i
\(89\) −1.10513 1.10513i −0.117144 0.117144i 0.646105 0.763249i \(-0.276397\pi\)
−0.763249 + 0.646105i \(0.776397\pi\)
\(90\) 0.450114 + 6.85893i 0.0474462 + 0.722995i
\(91\) 0.982885 15.2919i 0.103034 1.60303i
\(92\) 0.811612 + 0.811612i 0.0846165 + 0.0846165i
\(93\) −3.34657 −0.347023
\(94\) 0.764039i 0.0788046i
\(95\) −0.651844 0.571559i −0.0668778 0.0586407i
\(96\) 1.98758 + 1.98758i 0.202856 + 0.202856i
\(97\) 10.7928i 1.09584i 0.836530 + 0.547921i \(0.184581\pi\)
−0.836530 + 0.547921i \(0.815419\pi\)
\(98\) 17.4720i 1.76494i
\(99\) 2.23127 + 2.23127i 0.224251 + 0.224251i
\(100\) 2.45170 0.323175i 0.245170 0.0323175i
\(101\) 11.6588i 1.16009i −0.814583 0.580046i \(-0.803034\pi\)
0.814583 0.580046i \(-0.196966\pi\)
\(102\) −10.0374 −0.993851
\(103\) 3.67213 + 3.67213i 0.361826 + 0.361826i 0.864485 0.502659i \(-0.167645\pi\)
−0.502659 + 0.864485i \(0.667645\pi\)
\(104\) 8.55525 + 0.549886i 0.838911 + 0.0539208i
\(105\) −7.33481 6.43141i −0.715804 0.627642i
\(106\) 11.4508 + 11.4508i 1.11220 + 1.11220i
\(107\) −2.58729 2.58729i −0.250123 0.250123i 0.570898 0.821021i \(-0.306595\pi\)
−0.821021 + 0.570898i \(0.806595\pi\)
\(108\) −1.77568 1.77568i −0.170865 0.170865i
\(109\) 5.28110 5.28110i 0.505837 0.505837i −0.407409 0.913246i \(-0.633568\pi\)
0.913246 + 0.407409i \(0.133568\pi\)
\(110\) 3.77501 4.30527i 0.359933 0.410492i
\(111\) −1.48283 + 1.48283i −0.140744 + 0.140744i
\(112\) 20.1642 1.90534
\(113\) −1.43459 + 1.43459i −0.134954 + 0.134954i −0.771357 0.636403i \(-0.780422\pi\)
0.636403 + 0.771357i \(0.280422\pi\)
\(114\) 0.628584 0.0588723
\(115\) 3.42124 3.90181i 0.319033 0.363846i
\(116\) 1.38397i 0.128499i
\(117\) −7.00297 0.450114i −0.647425 0.0416131i
\(118\) 0.492076 0.492076i 0.0452992 0.0452992i
\(119\) −18.6051 + 18.6051i −1.70552 + 1.70552i
\(120\) 3.59813 4.10354i 0.328463 0.374601i
\(121\) 8.37142i 0.761038i
\(122\) 17.8248i 1.61378i
\(123\) −1.28202 −0.115595
\(124\) 1.14015 + 1.14015i 0.102388 + 0.102388i
\(125\) −2.18383 10.9650i −0.195328 0.980738i
\(126\) −13.0644 −1.16387
\(127\) −14.0115 + 14.0115i −1.24332 + 1.24332i −0.284705 + 0.958615i \(0.591896\pi\)
−0.958615 + 0.284705i \(0.908104\pi\)
\(128\) 13.6330i 1.20500i
\(129\) 1.37142 0.120746
\(130\) 0.0171153 + 12.7337i 0.00150111 + 1.11682i
\(131\) −12.9251 −1.12927 −0.564634 0.825341i \(-0.690983\pi\)
−0.564634 + 0.825341i \(0.690983\pi\)
\(132\) 0.823116i 0.0716431i
\(133\) 1.16513 1.16513i 0.101029 0.101029i
\(134\) −11.2391 −0.970913
\(135\) −7.48513 + 8.53654i −0.644217 + 0.734709i
\(136\) −10.4088 10.4088i −0.892549 0.892549i
\(137\) 5.62139 0.480267 0.240134 0.970740i \(-0.422809\pi\)
0.240134 + 0.970740i \(0.422809\pi\)
\(138\) 3.76259i 0.320293i
\(139\) 8.53735i 0.724128i 0.932153 + 0.362064i \(0.117928\pi\)
−0.932153 + 0.362064i \(0.882072\pi\)
\(140\) 0.307781 + 4.69003i 0.0260122 + 0.396380i
\(141\) 0.351127 0.351127i 0.0295702 0.0295702i
\(142\) 11.7312 11.7312i 0.984461 0.984461i
\(143\) 3.85985 + 4.39012i 0.322777 + 0.367120i
\(144\) 9.23424i 0.769520i
\(145\) 6.24369 0.409739i 0.518510 0.0340270i
\(146\) 7.84651 0.649382
\(147\) 8.02954 8.02954i 0.662265 0.662265i
\(148\) 1.01037 0.0830520
\(149\) 7.43141 7.43141i 0.608805 0.608805i −0.333829 0.942634i \(-0.608341\pi\)
0.942634 + 0.333829i \(0.108341\pi\)
\(150\) 6.43208 + 4.93386i 0.525177 + 0.402848i
\(151\) −13.4492 + 13.4492i −1.09448 + 1.09448i −0.0994360 + 0.995044i \(0.531704\pi\)
−0.995044 + 0.0994360i \(0.968296\pi\)
\(152\) 0.651844 + 0.651844i 0.0528715 + 0.0528715i
\(153\) 8.52023 + 8.52023i 0.688820 + 0.688820i
\(154\) 7.69539 + 7.69539i 0.620112 + 0.620112i
\(155\) 4.80614 5.48124i 0.386038 0.440264i
\(156\) −1.20868 1.37472i −0.0967716 0.110066i
\(157\) 5.65971 + 5.65971i 0.451694 + 0.451694i 0.895917 0.444222i \(-0.146520\pi\)
−0.444222 + 0.895917i \(0.646520\pi\)
\(158\) −17.0464 −1.35614
\(159\) 10.5248i 0.834670i
\(160\) −6.10982 + 0.400954i −0.483024 + 0.0316982i
\(161\) 6.97423 + 6.97423i 0.549647 + 0.549647i
\(162\) 0.990083i 0.0777883i
\(163\) 5.05372i 0.395838i 0.980218 + 0.197919i \(0.0634183\pi\)
−0.980218 + 0.197919i \(0.936582\pi\)
\(164\) 0.436771 + 0.436771i 0.0341061 + 0.0341061i
\(165\) 3.71343 0.243692i 0.289090 0.0189714i
\(166\) 18.6908i 1.45069i
\(167\) 8.81400 0.682048 0.341024 0.940055i \(-0.389226\pi\)
0.341024 + 0.940055i \(0.389226\pi\)
\(168\) 7.33481 + 7.33481i 0.565893 + 0.565893i
\(169\) −12.8930 1.66427i −0.991772 0.128021i
\(170\) 14.4151 16.4399i 1.10559 1.26089i
\(171\) −0.533573 0.533573i −0.0408033 0.0408033i
\(172\) −0.467229 0.467229i −0.0356259 0.0356259i
\(173\) −11.9251 11.9251i −0.906647 0.906647i 0.0893534 0.996000i \(-0.471520\pi\)
−0.996000 + 0.0893534i \(0.971520\pi\)
\(174\) −3.20801 + 3.20801i −0.243199 + 0.243199i
\(175\) 21.0676 2.77706i 1.59256 0.209926i
\(176\) −5.43928 + 5.43928i −0.410001 + 0.410001i
\(177\) 0.452283 0.0339957
\(178\) −1.74547 + 1.74547i −0.130829 + 0.130829i
\(179\) −2.01256 −0.150426 −0.0752128 0.997168i \(-0.523964\pi\)
−0.0752128 + 0.997168i \(0.523964\pi\)
\(180\) 2.14781 0.140949i 0.160088 0.0105057i
\(181\) 8.38225i 0.623048i −0.950238 0.311524i \(-0.899161\pi\)
0.950238 0.311524i \(-0.100839\pi\)
\(182\) −24.1525 1.55239i −1.79030 0.115071i
\(183\) 8.19170 8.19170i 0.605548 0.605548i
\(184\) −3.90181 + 3.90181i −0.287646 + 0.287646i
\(185\) −0.299131 4.55822i −0.0219925 0.335127i
\(186\) 5.28565i 0.387563i
\(187\) 10.0374i 0.734008i
\(188\) −0.239252 −0.0174492
\(189\) −15.2585 15.2585i −1.10989 1.10989i
\(190\) −0.902734 + 1.02954i −0.0654912 + 0.0746906i
\(191\) 7.97649 0.577158 0.288579 0.957456i \(-0.406817\pi\)
0.288579 + 0.957456i \(0.406817\pi\)
\(192\) −3.74844 + 3.74844i −0.270521 + 0.270521i
\(193\) 21.2368i 1.52866i −0.644825 0.764330i \(-0.723070\pi\)
0.644825 0.764330i \(-0.276930\pi\)
\(194\) 17.0464 1.22386
\(195\) −5.84412 + 5.85985i −0.418506 + 0.419633i
\(196\) −5.47119 −0.390799
\(197\) 3.55914i 0.253578i 0.991930 + 0.126789i \(0.0404671\pi\)
−0.991930 + 0.126789i \(0.959533\pi\)
\(198\) 3.52412 3.52412i 0.250448 0.250448i
\(199\) 0.607376 0.0430558 0.0215279 0.999768i \(-0.493147\pi\)
0.0215279 + 0.999768i \(0.493147\pi\)
\(200\) 1.55366 + 11.7865i 0.109860 + 0.833432i
\(201\) −5.16513 5.16513i −0.364320 0.364320i
\(202\) −18.4142 −1.29562
\(203\) 11.8926i 0.834694i
\(204\) 3.14312i 0.220062i
\(205\) 1.84115 2.09977i 0.128592 0.146654i
\(206\) 5.79986 5.79986i 0.404095 0.404095i
\(207\) 3.19386 3.19386i 0.221989 0.221989i
\(208\) 1.09727 17.0715i 0.0760817 1.18370i
\(209\) 0.628584i 0.0434801i
\(210\) −10.1579 + 11.5848i −0.700964 + 0.799426i
\(211\) −17.9890 −1.23842 −0.619209 0.785227i \(-0.712546\pi\)
−0.619209 + 0.785227i \(0.712546\pi\)
\(212\) 3.58570 3.58570i 0.246267 0.246267i
\(213\) 10.7825 0.738807
\(214\) −4.08643 + 4.08643i −0.279343 + 0.279343i
\(215\) −1.96954 + 2.24620i −0.134322 + 0.153189i
\(216\) 8.53654 8.53654i 0.580838 0.580838i
\(217\) 9.79735 + 9.79735i 0.665087 + 0.665087i
\(218\) −8.34109 8.34109i −0.564930 0.564930i
\(219\) 3.60599 + 3.60599i 0.243670 + 0.243670i
\(220\) −1.34816 1.18211i −0.0908927 0.0796977i
\(221\) 14.7391 + 16.7639i 0.991458 + 1.12766i
\(222\) 2.34201 + 2.34201i 0.157186 + 0.157186i
\(223\) 15.6643 1.04896 0.524478 0.851424i \(-0.324260\pi\)
0.524478 + 0.851424i \(0.324260\pi\)
\(224\) 11.6376i 0.777569i
\(225\) −1.27176 9.64795i −0.0847841 0.643197i
\(226\) 2.26582 + 2.26582i 0.150720 + 0.150720i
\(227\) 24.4976i 1.62597i −0.582288 0.812983i \(-0.697842\pi\)
0.582288 0.812983i \(-0.302158\pi\)
\(228\) 0.196835i 0.0130357i
\(229\) 10.7265 + 10.7265i 0.708828 + 0.708828i 0.966289 0.257461i \(-0.0828857\pi\)
−0.257461 + 0.966289i \(0.582886\pi\)
\(230\) −6.16262 5.40359i −0.406351 0.356302i
\(231\) 7.07309i 0.465375i
\(232\) −6.65343 −0.436819
\(233\) −6.63712 6.63712i −0.434812 0.434812i 0.455450 0.890262i \(-0.349479\pi\)
−0.890262 + 0.455450i \(0.849479\pi\)
\(234\) −0.710921 + 11.0607i −0.0464744 + 0.723058i
\(235\) 0.0708328 + 1.07937i 0.00462062 + 0.0704101i
\(236\) −0.154089 0.154089i −0.0100303 0.0100303i
\(237\) −7.83395 7.83395i −0.508870 0.508870i
\(238\) 29.3853 + 29.3853i 1.90477 + 1.90477i
\(239\) −18.6766 + 18.6766i −1.20809 + 1.20809i −0.236441 + 0.971646i \(0.575981\pi\)
−0.971646 + 0.236441i \(0.924019\pi\)
\(240\) −8.18839 7.17985i −0.528558 0.463458i
\(241\) 2.88629 2.88629i 0.185922 0.185922i −0.608008 0.793931i \(-0.708031\pi\)
0.793931 + 0.608008i \(0.208031\pi\)
\(242\) 13.2220 0.849944
\(243\) −11.2258 + 11.2258i −0.720135 + 0.720135i
\(244\) −5.58168 −0.357330
\(245\) 1.61980 + 24.6829i 0.103485 + 1.57693i
\(246\) 2.02485i 0.129099i
\(247\) −0.923023 1.04983i −0.0587305 0.0667989i
\(248\) −5.48124 + 5.48124i −0.348059 + 0.348059i
\(249\) 8.58968 8.58968i 0.544349 0.544349i
\(250\) −17.3184 + 3.44919i −1.09531 + 0.218146i
\(251\) 17.7801i 1.12227i −0.827724 0.561136i \(-0.810365\pi\)
0.827724 0.561136i \(-0.189635\pi\)
\(252\) 4.09100i 0.257709i
\(253\) −3.76259 −0.236552
\(254\) 22.1301 + 22.1301i 1.38857 + 1.38857i
\(255\) 14.1799 0.930551i 0.887982 0.0582734i
\(256\) 11.2039 0.700245
\(257\) −4.03204 + 4.03204i −0.251512 + 0.251512i −0.821590 0.570078i \(-0.806913\pi\)
0.570078 + 0.821590i \(0.306913\pi\)
\(258\) 2.16605i 0.134852i
\(259\) 8.68218 0.539485
\(260\) 3.98744 0.00535950i 0.247291 0.000332382i
\(261\) 5.44622 0.337113
\(262\) 20.4142i 1.26119i
\(263\) −6.17438 + 6.17438i −0.380728 + 0.380728i −0.871365 0.490636i \(-0.836764\pi\)
0.490636 + 0.871365i \(0.336764\pi\)
\(264\) −3.95712 −0.243544
\(265\) −17.2382 15.1150i −1.05894 0.928510i
\(266\) −1.84023 1.84023i −0.112832 0.112832i
\(267\) −1.60432 −0.0981828
\(268\) 3.51943i 0.214983i
\(269\) 25.1885i 1.53577i −0.640589 0.767884i \(-0.721310\pi\)
0.640589 0.767884i \(-0.278690\pi\)
\(270\) 13.4828 + 11.8222i 0.820539 + 0.719476i
\(271\) −7.43070 + 7.43070i −0.451383 + 0.451383i −0.895813 0.444431i \(-0.853406\pi\)
0.444431 + 0.895813i \(0.353406\pi\)
\(272\) −20.7702 + 20.7702i −1.25938 + 1.25938i
\(273\) −10.3862 11.8131i −0.628603 0.714960i
\(274\) 8.87856i 0.536373i
\(275\) −4.93386 + 6.43208i −0.297523 + 0.387869i
\(276\) 1.17822 0.0709204
\(277\) 0.389450 0.389450i 0.0233998 0.0233998i −0.695310 0.718710i \(-0.744733\pi\)
0.718710 + 0.695310i \(0.244733\pi\)
\(278\) 13.4841 0.808722
\(279\) 4.48672 4.48672i 0.268613 0.268613i
\(280\) −22.5473 + 1.47965i −1.34746 + 0.0884261i
\(281\) −2.39890 + 2.39890i −0.143107 + 0.143107i −0.775030 0.631924i \(-0.782266\pi\)
0.631924 + 0.775030i \(0.282266\pi\)
\(282\) −0.554578 0.554578i −0.0330246 0.0330246i
\(283\) −20.6500 20.6500i −1.22752 1.22752i −0.964901 0.262615i \(-0.915415\pi\)
−0.262615 0.964901i \(-0.584585\pi\)
\(284\) −3.67352 3.67352i −0.217983 0.217983i
\(285\) −0.888007 + 0.0582750i −0.0526010 + 0.00345192i
\(286\) 6.93386 6.09635i 0.410008 0.360485i
\(287\) 3.75320 + 3.75320i 0.221545 + 0.221545i
\(288\) −5.32945 −0.314041
\(289\) 21.3284i 1.25461i
\(290\) −0.647152 9.86144i −0.0380021 0.579084i
\(291\) 7.83395 + 7.83395i 0.459234 + 0.459234i
\(292\) 2.45706i 0.143789i
\(293\) 15.0708i 0.880445i 0.897889 + 0.440222i \(0.145100\pi\)
−0.897889 + 0.440222i \(0.854900\pi\)
\(294\) −12.6820 12.6820i −0.739632 0.739632i
\(295\) −0.649541 + 0.740780i −0.0378177 + 0.0431299i
\(296\) 4.85735i 0.282328i
\(297\) 8.23194 0.477665
\(298\) −11.7374 11.7374i −0.679927 0.679927i
\(299\) 6.28407 5.52504i 0.363417 0.319521i
\(300\) 1.54499 2.01414i 0.0892001 0.116287i
\(301\) −4.01493 4.01493i −0.231417 0.231417i
\(302\) 21.2420 + 21.2420i 1.22234 + 1.22234i
\(303\) −8.46254 8.46254i −0.486160 0.486160i
\(304\) 1.30072 1.30072i 0.0746013 0.0746013i
\(305\) 1.65251 + 25.1813i 0.0946225 + 1.44188i
\(306\) 13.4571 13.4571i 0.769289 0.769289i
\(307\) −12.2780 −0.700742 −0.350371 0.936611i \(-0.613944\pi\)
−0.350371 + 0.936611i \(0.613944\pi\)
\(308\) 2.40974 2.40974i 0.137308 0.137308i
\(309\) 5.33084 0.303261
\(310\) −8.65720 7.59093i −0.491696 0.431136i
\(311\) 21.1944i 1.20182i 0.799315 + 0.600912i \(0.205196\pi\)
−0.799315 + 0.600912i \(0.794804\pi\)
\(312\) 6.60896 5.81069i 0.374159 0.328966i
\(313\) −5.71879 + 5.71879i −0.323245 + 0.323245i −0.850011 0.526766i \(-0.823405\pi\)
0.526766 + 0.850011i \(0.323405\pi\)
\(314\) 8.93908 8.93908i 0.504462 0.504462i
\(315\) 18.4563 1.21118i 1.03989 0.0682424i
\(316\) 5.33792i 0.300281i
\(317\) 9.88047i 0.554943i −0.960734 0.277471i \(-0.910504\pi\)
0.960734 0.277471i \(-0.0894963\pi\)
\(318\) 16.6231 0.932178
\(319\) −3.20801 3.20801i −0.179614 0.179614i
\(320\) −0.756174 11.5227i −0.0422714 0.644141i
\(321\) −3.75597 −0.209638
\(322\) 11.0153 11.0153i 0.613857 0.613857i
\(323\) 2.40029i 0.133556i
\(324\) 0.310035 0.0172242
\(325\) −1.20470 17.9875i −0.0668248 0.997765i
\(326\) 7.98197 0.442080
\(327\) 7.66657i 0.423962i
\(328\) −2.09977 + 2.09977i −0.115941 + 0.115941i
\(329\) −2.05590 −0.113346
\(330\) −0.384893 5.86508i −0.0211876 0.322862i
\(331\) 3.87697 + 3.87697i 0.213097 + 0.213097i 0.805582 0.592484i \(-0.201853\pi\)
−0.592484 + 0.805582i \(0.701853\pi\)
\(332\) −5.85286 −0.321217
\(333\) 3.97602i 0.217885i
\(334\) 13.9210i 0.761726i
\(335\) 15.8776 1.04196i 0.867488 0.0569284i
\(336\) 14.6362 14.6362i 0.798470 0.798470i
\(337\) 10.6060 10.6060i 0.577745 0.577745i −0.356536 0.934281i \(-0.616042\pi\)
0.934281 + 0.356536i \(0.116042\pi\)
\(338\) −2.62858 + 20.3636i −0.142976 + 1.10763i
\(339\) 2.08259i 0.113111i
\(340\) −5.14801 4.51395i −0.279190 0.244803i
\(341\) −5.28565 −0.286234
\(342\) −0.842738 + 0.842738i −0.0455700 + 0.0455700i
\(343\) −17.2644 −0.932192
\(344\) 2.24620 2.24620i 0.121107 0.121107i
\(345\) −0.348823 5.31544i −0.0187800 0.286174i
\(346\) −18.8348 + 18.8348i −1.01256 + 1.01256i
\(347\) 9.02188 + 9.02188i 0.484320 + 0.484320i 0.906508 0.422188i \(-0.138738\pi\)
−0.422188 + 0.906508i \(0.638738\pi\)
\(348\) 1.00456 + 1.00456i 0.0538499 + 0.0538499i
\(349\) 12.4143 + 12.4143i 0.664522 + 0.664522i 0.956443 0.291921i \(-0.0942943\pi\)
−0.291921 + 0.956443i \(0.594294\pi\)
\(350\) −4.38616 33.2747i −0.234450 1.77861i
\(351\) −13.7485 + 12.0879i −0.733842 + 0.645204i
\(352\) 3.13923 + 3.13923i 0.167321 + 0.167321i
\(353\) 26.3713 1.40360 0.701801 0.712373i \(-0.252379\pi\)
0.701801 + 0.712373i \(0.252379\pi\)
\(354\) 0.714347i 0.0379671i
\(355\) −15.4852 + 17.6604i −0.821870 + 0.937315i
\(356\) 0.546578 + 0.546578i 0.0289686 + 0.0289686i
\(357\) 27.0090i 1.42947i
\(358\) 3.17868i 0.167999i
\(359\) −16.3706 16.3706i −0.864009 0.864009i 0.127792 0.991801i \(-0.459211\pi\)
−0.991801 + 0.127792i \(0.959211\pi\)
\(360\) 0.677610 + 10.3256i 0.0357132 + 0.544205i
\(361\) 18.8497i 0.992089i
\(362\) −13.2391 −0.695833
\(363\) 6.07639 + 6.07639i 0.318928 + 0.318928i
\(364\) −0.486117 + 7.56311i −0.0254794 + 0.396415i
\(365\) −11.0848 + 0.727437i −0.580207 + 0.0380758i
\(366\) −12.9382 12.9382i −0.676289 0.676289i
\(367\) 22.1292 + 22.1292i 1.15513 + 1.15513i 0.985509 + 0.169626i \(0.0542560\pi\)
0.169626 + 0.985509i \(0.445744\pi\)
\(368\) 7.78585 + 7.78585i 0.405865 + 0.405865i
\(369\) 1.71879 1.71879i 0.0894765 0.0894765i
\(370\) −7.19936 + 0.472454i −0.374277 + 0.0245617i
\(371\) 30.8122 30.8122i 1.59969 1.59969i
\(372\) 1.65515 0.0858156
\(373\) 13.4134 13.4134i 0.694518 0.694518i −0.268704 0.963223i \(-0.586595\pi\)
0.963223 + 0.268704i \(0.0865955\pi\)
\(374\) −15.8533 −0.819756
\(375\) −9.54407 6.37380i −0.492854 0.329142i
\(376\) 1.15020i 0.0593170i
\(377\) 10.0685 + 0.647152i 0.518556 + 0.0333300i
\(378\) −24.0997 + 24.0997i −1.23955 + 1.23955i
\(379\) 12.8914 12.8914i 0.662189 0.662189i −0.293707 0.955896i \(-0.594889\pi\)
0.955896 + 0.293707i \(0.0948889\pi\)
\(380\) 0.322390 + 0.282683i 0.0165383 + 0.0145013i
\(381\) 20.3405i 1.04208i
\(382\) 12.5983i 0.644583i
\(383\) −19.8962 −1.01665 −0.508324 0.861166i \(-0.669735\pi\)
−0.508324 + 0.861166i \(0.669735\pi\)
\(384\) 9.89554 + 9.89554i 0.504979 + 0.504979i
\(385\) −11.5848 10.1579i −0.590415 0.517696i
\(386\) −33.5420 −1.70724
\(387\) −1.83864 + 1.83864i −0.0934636 + 0.0934636i
\(388\) 5.33792i 0.270992i
\(389\) −13.2861 −0.673633 −0.336816 0.941570i \(-0.609350\pi\)
−0.336816 + 0.941570i \(0.609350\pi\)
\(390\) 9.25520 + 9.23035i 0.468655 + 0.467397i
\(391\) −14.3677 −0.726604
\(392\) 26.3027i 1.32848i
\(393\) −9.38167 + 9.38167i −0.473243 + 0.473243i
\(394\) 5.62139 0.283201
\(395\) 24.0816 1.58034i 1.21168 0.0795157i
\(396\) −1.10354 1.10354i −0.0554552 0.0554552i
\(397\) 3.61591 0.181477 0.0907386 0.995875i \(-0.471077\pi\)
0.0907386 + 0.995875i \(0.471077\pi\)
\(398\) 0.959305i 0.0480856i
\(399\) 1.69142i 0.0846768i
\(400\) 23.5193 3.10024i 1.17597 0.155012i
\(401\) 5.44634 5.44634i 0.271977 0.271977i −0.557918 0.829896i \(-0.688400\pi\)
0.829896 + 0.557918i \(0.188400\pi\)
\(402\) −8.15793 + 8.15793i −0.406881 + 0.406881i
\(403\) 8.82781 7.76153i 0.439744 0.386630i
\(404\) 5.76623i 0.286880i
\(405\) −0.0917890 1.39870i −0.00456103 0.0695020i
\(406\) 18.7834 0.932205
\(407\) −2.34201 + 2.34201i −0.116089 + 0.116089i
\(408\) −15.1105 −0.748081
\(409\) −27.3844 + 27.3844i −1.35407 + 1.35407i −0.473018 + 0.881053i \(0.656836\pi\)
−0.881053 + 0.473018i \(0.843164\pi\)
\(410\) −3.31643 2.90796i −0.163787 0.143614i
\(411\) 4.08029 4.08029i 0.201266 0.201266i
\(412\) −1.81617 1.81617i −0.0894763 0.0894763i
\(413\) −1.32409 1.32409i −0.0651544 0.0651544i
\(414\) −5.04447 5.04447i −0.247922 0.247922i
\(415\) 1.73280 + 26.4047i 0.0850596 + 1.29616i
\(416\) −9.85265 0.633277i −0.483066 0.0310489i
\(417\) 6.19684 + 6.19684i 0.303460 + 0.303460i
\(418\) 0.992802 0.0485595
\(419\) 31.6412i 1.54577i 0.634543 + 0.772887i \(0.281188\pi\)
−0.634543 + 0.772887i \(0.718812\pi\)
\(420\) 3.62767 + 3.18086i 0.177012 + 0.155210i
\(421\) −0.312270 0.312270i −0.0152191 0.0152191i 0.699456 0.714675i \(-0.253426\pi\)
−0.714675 + 0.699456i \(0.753426\pi\)
\(422\) 28.4123i 1.38309i
\(423\) 0.941505i 0.0457775i
\(424\) 17.2382 + 17.2382i 0.837162 + 0.837162i
\(425\) −18.8402 + 24.5613i −0.913885 + 1.19140i
\(426\) 17.0302i 0.825116i
\(427\) −47.9637 −2.32113
\(428\) 1.27963 + 1.27963i 0.0618531 + 0.0618531i
\(429\) 5.98824 + 0.384893i 0.289115 + 0.0185828i
\(430\) 3.54770 + 3.11074i 0.171085 + 0.150013i
\(431\) −13.0481 13.0481i −0.628505 0.628505i 0.319187 0.947692i \(-0.396590\pi\)
−0.947692 + 0.319187i \(0.896590\pi\)
\(432\) −17.0342 17.0342i −0.819557 0.819557i
\(433\) −0.0391255 0.0391255i −0.00188025 0.00188025i 0.706166 0.708046i \(-0.250423\pi\)
−0.708046 + 0.706166i \(0.750423\pi\)
\(434\) 15.4742 15.4742i 0.742784 0.742784i
\(435\) 4.23458 4.82940i 0.203032 0.231552i
\(436\) −2.61193 + 2.61193i −0.125089 + 0.125089i
\(437\) 0.899763 0.0430415
\(438\) 5.69539 5.69539i 0.272136 0.272136i
\(439\) 17.4097 0.830919 0.415460 0.909612i \(-0.363621\pi\)
0.415460 + 0.909612i \(0.363621\pi\)
\(440\) 5.68297 6.48124i 0.270925 0.308981i
\(441\) 21.5303i 1.02525i
\(442\) 26.4773 23.2793i 1.25940 1.10728i
\(443\) 17.8580 17.8580i 0.848460 0.848460i −0.141481 0.989941i \(-0.545186\pi\)
0.989941 + 0.141481i \(0.0451864\pi\)
\(444\) 0.733379 0.733379i 0.0348046 0.0348046i
\(445\) 2.30403 2.62767i 0.109221 0.124563i
\(446\) 24.7405i 1.17150i
\(447\) 10.7882i 0.510264i
\(448\) 21.9477 1.03693
\(449\) −9.22202 9.22202i −0.435214 0.435214i 0.455184 0.890398i \(-0.349574\pi\)
−0.890398 + 0.455184i \(0.849574\pi\)
\(450\) −15.2382 + 2.00865i −0.718336 + 0.0946887i
\(451\) −2.02485 −0.0953463
\(452\) 0.709520 0.709520i 0.0333730 0.0333730i
\(453\) 19.5242i 0.917327i
\(454\) −38.6922 −1.81591
\(455\) 34.2643 0.0460545i 1.60634 0.00215907i
\(456\) 0.946283 0.0443137
\(457\) 10.5157i 0.491902i 0.969282 + 0.245951i \(0.0791003\pi\)
−0.969282 + 0.245951i \(0.920900\pi\)
\(458\) 16.9417 16.9417i 0.791635 0.791635i
\(459\) 31.4341 1.46722
\(460\) −1.69208 + 1.92977i −0.0788938 + 0.0899758i
\(461\) −2.81936 2.81936i −0.131311 0.131311i 0.638397 0.769707i \(-0.279598\pi\)
−0.769707 + 0.638397i \(0.779598\pi\)
\(462\) 11.1714 0.519741
\(463\) 32.9570i 1.53164i −0.643054 0.765821i \(-0.722333\pi\)
0.643054 0.765821i \(-0.277667\pi\)
\(464\) 13.2765i 0.616348i
\(465\) −0.490024 7.46709i −0.0227243 0.346278i
\(466\) −10.4828 + 10.4828i −0.485608 + 0.485608i
\(467\) 7.26867 7.26867i 0.336354 0.336354i −0.518639 0.854993i \(-0.673561\pi\)
0.854993 + 0.518639i \(0.173561\pi\)
\(468\) 3.46354 + 0.222618i 0.160102 + 0.0102905i
\(469\) 30.2427i 1.39648i
\(470\) 1.70478 0.111875i 0.0786355 0.00516041i
\(471\) 8.21620 0.378583
\(472\) 0.740780 0.740780i 0.0340971 0.0340971i
\(473\) 2.16605 0.0995950
\(474\) −12.3731 + 12.3731i −0.568317 + 0.568317i
\(475\) 1.17985 1.53813i 0.0541354 0.0705743i
\(476\) 9.20173 9.20173i 0.421761 0.421761i
\(477\) −14.1105 14.1105i −0.646075 0.646075i
\(478\) 29.4982 + 29.4982i 1.34922 + 1.34922i
\(479\) −19.0701 19.0701i −0.871336 0.871336i 0.121282 0.992618i \(-0.461299\pi\)
−0.992618 + 0.121282i \(0.961299\pi\)
\(480\) −4.14379 + 4.72585i −0.189137 + 0.215705i
\(481\) 0.472454 7.35054i 0.0215421 0.335156i
\(482\) −4.55867 4.55867i −0.207642 0.207642i
\(483\) 10.1245 0.460681
\(484\) 4.14035i 0.188198i
\(485\) −24.0816 + 1.58034i −1.09349 + 0.0717597i
\(486\) 17.7303 + 17.7303i 0.804262 + 0.804262i
\(487\) 40.7729i 1.84760i −0.382879 0.923799i \(-0.625067\pi\)
0.382879 0.923799i \(-0.374933\pi\)
\(488\) 26.8338i 1.21471i
\(489\) 3.66824 + 3.66824i 0.165884 + 0.165884i
\(490\) 38.9847 2.55835i 1.76115 0.115575i
\(491\) 4.59799i 0.207504i 0.994603 + 0.103752i \(0.0330849\pi\)
−0.994603 + 0.103752i \(0.966915\pi\)
\(492\) 0.634061 0.0285857
\(493\) −12.2500 12.2500i −0.551711 0.551711i
\(494\) −1.65812 + 1.45784i −0.0746025 + 0.0655915i
\(495\) −4.65184 + 5.30527i −0.209085 + 0.238454i
\(496\) 10.9375 + 10.9375i 0.491108 + 0.491108i
\(497\) −31.5667 31.5667i −1.41596 1.41596i
\(498\) −13.5667 13.5667i −0.607941 0.607941i
\(499\) −22.8147 + 22.8147i −1.02132 + 1.02132i −0.0215572 + 0.999768i \(0.506862\pi\)
−0.999768 + 0.0215572i \(0.993138\pi\)
\(500\) 1.08008 + 5.42308i 0.0483028 + 0.242528i
\(501\) 6.39765 6.39765i 0.285826 0.285826i
\(502\) −28.0824 −1.25338
\(503\) 11.1978 11.1978i 0.499287 0.499287i −0.411929 0.911216i \(-0.635145\pi\)
0.911216 + 0.411929i \(0.135145\pi\)
\(504\) −19.6674 −0.876057
\(505\) 26.0139 1.70715i 1.15760 0.0759671i
\(506\) 5.94272i 0.264186i
\(507\) −10.5664 + 8.15040i −0.469271 + 0.361972i
\(508\) 6.92983 6.92983i 0.307462 0.307462i
\(509\) 4.71971 4.71971i 0.209197 0.209197i −0.594729 0.803926i \(-0.702741\pi\)
0.803926 + 0.594729i \(0.202741\pi\)
\(510\) −1.46974 22.3961i −0.0650810 0.991718i
\(511\) 21.1137i 0.934014i
\(512\) 9.57031i 0.422952i
\(513\) −1.96854 −0.0869131
\(514\) 6.36831 + 6.36831i 0.280894 + 0.280894i
\(515\) −7.65582 + 8.73121i −0.337356 + 0.384743i
\(516\) −0.678277 −0.0298595
\(517\) 0.554578 0.554578i 0.0243903 0.0243903i
\(518\) 13.7129i 0.602508i
\(519\) −17.3116 −0.759897
\(520\) 0.0257657 + 19.1696i 0.00112990 + 0.840641i
\(521\) −14.8279 −0.649622 −0.324811 0.945779i \(-0.605301\pi\)
−0.324811 + 0.945779i \(0.605301\pi\)
\(522\) 8.60190i 0.376495i
\(523\) −22.3472 + 22.3472i −0.977176 + 0.977176i −0.999745 0.0225689i \(-0.992815\pi\)
0.0225689 + 0.999745i \(0.492815\pi\)
\(524\) 6.39251 0.279258
\(525\) 13.2762 17.3077i 0.579421 0.755368i
\(526\) 9.75196 + 9.75196i 0.425206 + 0.425206i
\(527\) −20.1836 −0.879210
\(528\) 7.89620i 0.343638i
\(529\) 17.6142i 0.765834i
\(530\) −23.8731 + 27.2265i −1.03698 + 1.18264i
\(531\) −0.606372 + 0.606372i −0.0263143 + 0.0263143i
\(532\) −0.576251 + 0.576251i −0.0249837 + 0.0249837i
\(533\) 3.38179 2.97331i 0.146481 0.128789i
\(534\) 2.53390i 0.109653i
\(535\) 5.39409 6.15179i 0.233207 0.265965i
\(536\) −16.9196 −0.730815
\(537\) −1.46082 + 1.46082i −0.0630389 + 0.0630389i
\(538\) −39.7833 −1.71518
\(539\) 12.6820 12.6820i 0.546255 0.546255i
\(540\) 3.70201 4.22202i 0.159309 0.181687i
\(541\) 30.7281 30.7281i 1.32111 1.32111i 0.408223 0.912882i \(-0.366149\pi\)
0.912882 0.408223i \(-0.133851\pi\)
\(542\) 11.7362 + 11.7362i 0.504114 + 0.504114i
\(543\) −6.08426 6.08426i −0.261101 0.261101i
\(544\) 11.9873 + 11.9873i 0.513952 + 0.513952i
\(545\) 12.5568 + 11.0103i 0.537876 + 0.471627i
\(546\) −18.6579 + 16.4043i −0.798483 + 0.702038i
\(547\) 10.0949 + 10.0949i 0.431627 + 0.431627i 0.889181 0.457555i \(-0.151275\pi\)
−0.457555 + 0.889181i \(0.651275\pi\)
\(548\) −2.78024 −0.118766
\(549\) 21.9651i 0.937446i
\(550\) 10.1590 + 7.79266i 0.433181 + 0.332280i
\(551\) 0.767145 + 0.767145i 0.0326815 + 0.0326815i
\(552\) 5.66427i 0.241087i
\(553\) 45.8691i 1.95055i
\(554\) −0.615107 0.615107i −0.0261334 0.0261334i
\(555\) −3.52571 3.09146i −0.149658 0.131225i
\(556\) 4.22242i 0.179070i
\(557\) 37.4425 1.58649 0.793246 0.608902i \(-0.208390\pi\)
0.793246 + 0.608902i \(0.208390\pi\)
\(558\) −7.08643 7.08643i −0.299992 0.299992i
\(559\) −3.61761 + 3.18066i −0.153009 + 0.134527i
\(560\) 2.95256 + 44.9918i 0.124768 + 1.90125i
\(561\) −7.28565 7.28565i −0.307601 0.307601i
\(562\) 3.78889 + 3.78889i 0.159824 + 0.159824i
\(563\) 30.1530 + 30.1530i 1.27080 + 1.27080i 0.945670 + 0.325127i \(0.105407\pi\)
0.325127 + 0.945670i \(0.394593\pi\)
\(564\) −0.173661 + 0.173661i −0.00731244 + 0.00731244i
\(565\) −3.41101 2.99088i −0.143502 0.125827i
\(566\) −32.6151 + 32.6151i −1.37092 + 1.37092i
\(567\) 2.66415 0.111884
\(568\) 17.6604 17.6604i 0.741013 0.741013i
\(569\) 44.0021 1.84466 0.922331 0.386400i \(-0.126282\pi\)
0.922331 + 0.386400i \(0.126282\pi\)
\(570\) 0.0920410 + 1.40254i 0.00385517 + 0.0587460i
\(571\) 30.3749i 1.27115i −0.772039 0.635576i \(-0.780763\pi\)
0.772039 0.635576i \(-0.219237\pi\)
\(572\) −1.90901 2.17127i −0.0798198 0.0907855i
\(573\) 5.78974 5.78974i 0.241870 0.241870i
\(574\) 5.92790 5.92790i 0.247426 0.247426i
\(575\) 9.20695 + 7.06239i 0.383957 + 0.294522i
\(576\) 10.0510i 0.418792i
\(577\) 17.8387i 0.742636i 0.928506 + 0.371318i \(0.121094\pi\)
−0.928506 + 0.371318i \(0.878906\pi\)
\(578\) −33.6866 −1.40118
\(579\) −15.4148 15.4148i −0.640616 0.640616i
\(580\) −3.08802 + 0.202649i −0.128223 + 0.00841456i
\(581\) −50.2940 −2.08654
\(582\) 12.3731 12.3731i 0.512883 0.512883i
\(583\) 16.6231i 0.688459i
\(584\) 11.8123 0.488796
\(585\) −0.0210908 15.6914i −0.000871996 0.648760i
\(586\) 23.8032 0.983300
\(587\) 9.44899i 0.390002i 0.980803 + 0.195001i \(0.0624710\pi\)
−0.980803 + 0.195001i \(0.937529\pi\)
\(588\) −3.97126 + 3.97126i −0.163772 + 0.163772i
\(589\) 1.26398 0.0520814
\(590\) 1.17001 + 1.02590i 0.0481684 + 0.0422356i
\(591\) 2.58340 + 2.58340i 0.106267 + 0.106267i
\(592\) 9.69256 0.398362
\(593\) 31.6013i 1.29771i 0.760912 + 0.648855i \(0.224752\pi\)
−0.760912 + 0.648855i \(0.775248\pi\)
\(594\) 13.0017i 0.533467i
\(595\) −44.2372 38.7887i −1.81355 1.59018i
\(596\) −3.67544 + 3.67544i −0.150552 + 0.150552i
\(597\) 0.440864 0.440864i 0.0180434 0.0180434i
\(598\) −8.72638 9.92521i −0.356848 0.405872i
\(599\) 16.7567i 0.684661i −0.939580 0.342331i \(-0.888784\pi\)
0.939580 0.342331i \(-0.111216\pi\)
\(600\) 9.68297 + 7.42752i 0.395306 + 0.303227i
\(601\) 36.7570 1.49935 0.749675 0.661807i \(-0.230210\pi\)
0.749675 + 0.661807i \(0.230210\pi\)
\(602\) −6.34128 + 6.34128i −0.258451 + 0.258451i
\(603\) 13.8497 0.564003
\(604\) 6.65173 6.65173i 0.270655 0.270655i
\(605\) −18.6789 + 1.22579i −0.759404 + 0.0498355i
\(606\) −13.3659 + 13.3659i −0.542954 + 0.542954i
\(607\) 15.2660 + 15.2660i 0.619629 + 0.619629i 0.945436 0.325807i \(-0.105636\pi\)
−0.325807 + 0.945436i \(0.605636\pi\)
\(608\) −0.750697 0.750697i −0.0304448 0.0304448i
\(609\) 8.63222 + 8.63222i 0.349795 + 0.349795i
\(610\) 39.7720 2.61002i 1.61032 0.105677i
\(611\) −0.111875 + 1.74058i −0.00452598 + 0.0704162i
\(612\) −4.21395 4.21395i −0.170339 0.170339i
\(613\) −22.8956 −0.924745 −0.462373 0.886686i \(-0.653002\pi\)
−0.462373 + 0.886686i \(0.653002\pi\)
\(614\) 19.3922i 0.782604i
\(615\) −0.187720 2.86052i −0.00756961 0.115347i
\(616\) 11.5848 + 11.5848i 0.466764 + 0.466764i
\(617\) 14.4562i 0.581984i −0.956725 0.290992i \(-0.906015\pi\)
0.956725 0.290992i \(-0.0939854\pi\)
\(618\) 8.41966i 0.338688i
\(619\) −1.00603 1.00603i −0.0404356 0.0404356i 0.686600 0.727036i \(-0.259102\pi\)
−0.727036 + 0.686600i \(0.759102\pi\)
\(620\) −2.37703 + 2.71092i −0.0954637 + 0.108873i
\(621\) 11.7833i 0.472847i
\(622\) 33.4750 1.34222
\(623\) 4.69678 + 4.69678i 0.188172 + 0.188172i
\(624\) −11.5949 13.1878i −0.464168 0.527935i
\(625\) 24.1461 6.47827i 0.965842 0.259131i
\(626\) 9.03239 + 9.03239i 0.361007 + 0.361007i
\(627\) 0.456258 + 0.456258i 0.0182212 + 0.0182212i
\(628\) −2.79919 2.79919i −0.111700 0.111700i
\(629\) −8.94311 + 8.94311i −0.356585 + 0.356585i
\(630\) −1.91297 29.1503i −0.0762146 1.16137i
\(631\) −18.7320 + 18.7320i −0.745710 + 0.745710i −0.973670 0.227961i \(-0.926794\pi\)
0.227961 + 0.973670i \(0.426794\pi\)
\(632\) −25.6620 −1.02078
\(633\) −13.0574 + 13.0574i −0.518983 + 0.518983i
\(634\) −15.6055 −0.619772
\(635\) −33.3151 29.2118i −1.32207 1.15923i
\(636\) 5.20537i 0.206406i
\(637\) −2.55835 + 39.8034i −0.101366 + 1.57707i
\(638\) −5.06681 + 5.06681i −0.200597 + 0.200597i
\(639\) −14.4561 + 14.4561i −0.571873 + 0.571873i
\(640\) −30.4189 + 1.99623i −1.20241 + 0.0789078i
\(641\) 9.96670i 0.393661i 0.980438 + 0.196830i \(0.0630649\pi\)
−0.980438 + 0.196830i \(0.936935\pi\)
\(642\) 5.93227i 0.234128i
\(643\) 15.9115 0.627489 0.313745 0.949507i \(-0.398416\pi\)
0.313745 + 0.949507i \(0.398416\pi\)
\(644\) −3.44933 3.44933i −0.135923 0.135923i
\(645\) 0.200811 + 3.06000i 0.00790691 + 0.120487i
\(646\) 3.79107 0.149158
\(647\) 18.1067 18.1067i 0.711846 0.711846i −0.255075 0.966921i \(-0.582100\pi\)
0.966921 + 0.255075i \(0.0821003\pi\)
\(648\) 1.49049i 0.0585519i
\(649\) 0.714347 0.0280406
\(650\) −28.4098 + 1.90273i −1.11433 + 0.0746314i
\(651\) 14.2228 0.557436
\(652\) 2.49948i 0.0978871i
\(653\) 28.8486 28.8486i 1.12893 1.12893i 0.138584 0.990351i \(-0.455745\pi\)
0.990351 0.138584i \(-0.0442551\pi\)
\(654\) −12.1088 −0.473490
\(655\) −1.89257 28.8393i −0.0739486 1.12685i
\(656\) 4.18997 + 4.18997i 0.163591 + 0.163591i
\(657\) −9.66904 −0.377225
\(658\) 3.24714i 0.126587i
\(659\) 9.37689i 0.365272i 0.983181 + 0.182636i \(0.0584630\pi\)
−0.983181 + 0.182636i \(0.941537\pi\)
\(660\) −1.83659 + 0.120525i −0.0714893 + 0.00469145i
\(661\) −8.37769 + 8.37769i −0.325855 + 0.325855i −0.851008 0.525153i \(-0.824008\pi\)
0.525153 + 0.851008i \(0.324008\pi\)
\(662\) 6.12338 6.12338i 0.237992 0.237992i
\(663\) 22.8665 + 1.46974i 0.888060 + 0.0570798i
\(664\) 28.1375i 1.09195i
\(665\) 2.77032 + 2.42911i 0.107428 + 0.0941968i
\(666\) −6.27983 −0.243338
\(667\) −4.59198 + 4.59198i −0.177802 + 0.177802i
\(668\) −4.35924 −0.168664
\(669\) 11.3699 11.3699i 0.439586 0.439586i
\(670\) −1.64570 25.0775i −0.0635789 0.968829i
\(671\) 12.9382 12.9382i 0.499472 0.499472i
\(672\) −8.44714 8.44714i −0.325856 0.325856i
\(673\) −4.98824 4.98824i −0.192283 0.192283i 0.604399 0.796682i \(-0.293413\pi\)
−0.796682 + 0.604399i \(0.793413\pi\)
\(674\) −16.7514 16.7514i −0.645238 0.645238i
\(675\) −20.1433 15.4514i −0.775317 0.594723i
\(676\) 6.37666 + 0.823116i 0.245256 + 0.0316583i
\(677\) 4.95712 + 4.95712i 0.190518 + 0.190518i 0.795920 0.605402i \(-0.206988\pi\)
−0.605402 + 0.795920i \(0.706988\pi\)
\(678\) 3.28929 0.126324
\(679\) 45.8691i 1.76029i
\(680\) 21.7008 24.7490i 0.832186 0.949081i
\(681\) −17.7816 17.7816i −0.681393 0.681393i
\(682\) 8.34829i 0.319673i
\(683\) 3.52220i 0.134773i −0.997727 0.0673865i \(-0.978534\pi\)
0.997727 0.0673865i \(-0.0214661\pi\)
\(684\) 0.263895 + 0.263895i 0.0100903 + 0.0100903i
\(685\) 0.823116 + 12.5428i 0.0314497 + 0.479237i
\(686\) 27.2679i 1.04109i
\(687\) 15.5717 0.594097
\(688\) −4.48216 4.48216i −0.170881 0.170881i
\(689\) −24.4096 27.7630i −0.929933 1.05769i
\(690\) −8.39534 + 0.550940i −0.319605 + 0.0209739i
\(691\) 18.5922 + 18.5922i 0.707280 + 0.707280i 0.965962 0.258682i \(-0.0832883\pi\)
−0.258682 + 0.965962i \(0.583288\pi\)
\(692\) 5.89792 + 5.89792i 0.224205 + 0.224205i
\(693\) −9.48283 9.48283i −0.360223 0.360223i
\(694\) 14.2494 14.2494i 0.540899 0.540899i
\(695\) −19.0491 + 1.25009i −0.722574 + 0.0474185i
\(696\) −4.82940 + 4.82940i −0.183058 + 0.183058i
\(697\) −7.73199 −0.292870
\(698\) 19.6074 19.6074i 0.742153 0.742153i
\(699\) −9.63511 −0.364433
\(700\) −10.4197 + 1.37348i −0.393826 + 0.0519128i
\(701\) 4.94675i 0.186836i 0.995627 + 0.0934180i \(0.0297793\pi\)
−0.995627 + 0.0934180i \(0.970221\pi\)
\(702\) 19.0919 + 21.7148i 0.720578 + 0.819571i
\(703\) 0.560055 0.560055i 0.0211229 0.0211229i
\(704\) −5.92038 + 5.92038i −0.223133 + 0.223133i
\(705\) 0.834872 + 0.732044i 0.0314431 + 0.0275704i
\(706\) 41.6515i 1.56757i
\(707\) 49.5495i 1.86350i
\(708\) −0.223691 −0.00840682
\(709\) 14.2124 + 14.2124i 0.533760 + 0.533760i 0.921689 0.387929i \(-0.126810\pi\)
−0.387929 + 0.921689i \(0.626810\pi\)
\(710\) 27.8932 + 24.4577i 1.04681 + 0.917882i
\(711\) 21.0058 0.787780
\(712\) −2.62767 + 2.62767i −0.0984759 + 0.0984759i
\(713\) 7.56595i 0.283347i
\(714\) 42.6587 1.59646
\(715\) −9.23035 + 9.25520i −0.345195 + 0.346125i
\(716\) 0.995374 0.0371989
\(717\) 27.1128i 1.01255i
\(718\) −25.8562 + 25.8562i −0.964944 + 0.964944i
\(719\) 44.0748 1.64371 0.821856 0.569695i \(-0.192939\pi\)
0.821856 + 0.569695i \(0.192939\pi\)
\(720\) 20.6041 1.35213i 0.767868 0.0503910i
\(721\) −15.6065 15.6065i −0.581215 0.581215i
\(722\) 29.7717 1.10799
\(723\) 4.19002i 0.155829i
\(724\) 4.14571i 0.154074i
\(725\) 1.82848 + 13.8714i 0.0679079 + 0.515169i
\(726\) 9.59721 9.59721i 0.356186 0.356186i
\(727\) 18.2981 18.2981i 0.678638 0.678638i −0.281054 0.959692i \(-0.590684\pi\)
0.959692 + 0.281054i \(0.0906840\pi\)
\(728\) −36.3595 2.33700i −1.34757 0.0866150i
\(729\) 14.4159i 0.533922i
\(730\) 1.14893 + 17.5077i 0.0425239 + 0.647988i
\(731\) 8.27118 0.305921
\(732\) −4.05146 + 4.05146i −0.149746 + 0.149746i
\(733\) 19.8910 0.734691 0.367345 0.930085i \(-0.380267\pi\)
0.367345 + 0.930085i \(0.380267\pi\)
\(734\) 34.9514 34.9514i 1.29008 1.29008i
\(735\) 19.0918 + 16.7403i 0.704211 + 0.617476i
\(736\) 4.49353 4.49353i 0.165634 0.165634i
\(737\) −8.15793 8.15793i −0.300501 0.300501i
\(738\) −2.71469 2.71469i −0.0999293 0.0999293i
\(739\) 2.02107 + 2.02107i 0.0743464 + 0.0743464i 0.743302 0.668956i \(-0.233258\pi\)
−0.668956 + 0.743302i \(0.733258\pi\)
\(740\) 0.147945 + 2.25441i 0.00543855 + 0.0828738i
\(741\) −1.43199 0.0920410i −0.0526056 0.00338121i
\(742\) −48.6655 48.6655i −1.78657 1.78657i
\(743\) −1.93043 −0.0708207 −0.0354104 0.999373i \(-0.511274\pi\)
−0.0354104 + 0.999373i \(0.511274\pi\)
\(744\) 7.95712i 0.291722i
\(745\) 17.6696 + 15.4933i 0.647365 + 0.567632i
\(746\) −21.1854 21.1854i −0.775653 0.775653i
\(747\) 23.0322i 0.842705i
\(748\) 4.96432i 0.181513i
\(749\) 10.9959 + 10.9959i 0.401782 + 0.401782i
\(750\) −10.0669 + 15.0741i −0.367593 + 0.550430i
\(751\) 42.9887i 1.56868i 0.620332 + 0.784339i \(0.286998\pi\)
−0.620332 + 0.784339i \(0.713002\pi\)
\(752\) −2.29516 −0.0836957
\(753\) −12.9057 12.9057i −0.470310 0.470310i
\(754\) 1.02213 15.9025i 0.0372237 0.579134i
\(755\) −31.9781 28.0395i −1.16380 1.02046i
\(756\) 7.54658 + 7.54658i 0.274466 + 0.274466i
\(757\) −31.8767 31.8767i −1.15858 1.15858i −0.984781 0.173798i \(-0.944396\pi\)
−0.173798 0.984781i \(-0.555604\pi\)
\(758\) −20.3611 20.3611i −0.739547 0.739547i
\(759\) −2.73108 + 2.73108i −0.0991318 + 0.0991318i
\(760\) −1.35899 + 1.54989i −0.0492958 + 0.0562203i
\(761\) 19.0048 19.0048i 0.688923 0.688923i −0.273071 0.961994i \(-0.588039\pi\)
0.961994 + 0.273071i \(0.0880395\pi\)
\(762\) 32.1263 1.16381
\(763\) −22.4445 + 22.4445i −0.812546 + 0.812546i
\(764\) −3.94503 −0.142726
\(765\) −17.7633 + 20.2585i −0.642235 + 0.732448i
\(766\) 31.4246i 1.13542i
\(767\) −1.19306 + 1.04896i −0.0430790 + 0.0378757i
\(768\) 8.13237 8.13237i 0.293452 0.293452i
\(769\) −21.9349 + 21.9349i −0.790991 + 0.790991i −0.981655 0.190664i \(-0.938936\pi\)
0.190664 + 0.981655i \(0.438936\pi\)
\(770\) −16.0437 +