Properties

Label 231.2.y.a.4.7
Level $231$
Weight $2$
Character 231.4
Analytic conductor $1.845$
Analytic rank $0$
Dimension $64$
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] = [231,2,Mod(4,231)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(231, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([0, 20, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("231.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 231 = 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 231.y (of order \(15\), degree \(8\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.84454428669\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(8\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 4.7
Character \(\chi\) \(=\) 231.4
Dual form 231.2.y.a.58.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.194840 - 1.85378i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(-1.44224 - 0.306558i) q^{4} +(-3.17278 - 1.41261i) q^{5} +(-1.50800 + 1.09563i) q^{6} +(-2.04677 + 1.67652i) q^{7} +(0.302713 - 0.931655i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})\) \(q+(0.194840 - 1.85378i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(-1.44224 - 0.306558i) q^{4} +(-3.17278 - 1.41261i) q^{5} +(-1.50800 + 1.09563i) q^{6} +(-2.04677 + 1.67652i) q^{7} +(0.302713 - 0.931655i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(-3.23685 + 5.60640i) q^{10} +(2.62222 + 2.03075i) q^{11} +(0.737230 + 1.27692i) q^{12} +(-1.79406 - 1.30346i) q^{13} +(2.70911 + 4.12092i) q^{14} +(1.07323 + 3.30305i) q^{15} +(-4.36208 - 1.94212i) q^{16} +(-0.524640 - 4.99162i) q^{17} +(1.82326 + 0.387545i) q^{18} +(-1.02552 + 0.217981i) q^{19} +(4.14286 + 3.00996i) q^{20} +(2.61546 + 0.399238i) q^{21} +(4.27547 - 4.46535i) q^{22} +(-3.39430 - 5.87909i) q^{23} +(-0.894909 + 0.398439i) q^{24} +(4.72539 + 5.24808i) q^{25} +(-2.76588 + 3.07182i) q^{26} +(0.809017 - 0.587785i) q^{27} +(3.46589 - 1.79049i) q^{28} +(-0.131329 - 0.404189i) q^{29} +(6.33224 - 1.34596i) q^{30} +(0.785857 - 0.349886i) q^{31} +(-3.47057 + 6.01121i) q^{32} +(-0.245470 - 3.30753i) q^{33} -9.35558 q^{34} +(8.86223 - 2.42793i) q^{35} +(0.455633 - 1.40230i) q^{36} +(0.687941 - 0.764036i) q^{37} +(0.204276 + 1.94356i) q^{38} +(0.231800 + 2.20543i) q^{39} +(-2.27651 + 2.52832i) q^{40} +(2.02483 - 6.23179i) q^{41} +(1.24969 - 4.77069i) q^{42} +3.02146 q^{43} +(-3.15934 - 3.73269i) q^{44} +(1.73652 - 3.00774i) q^{45} +(-11.5599 + 5.14679i) q^{46} +(3.19612 - 0.679355i) q^{47} +(1.47552 + 4.54119i) q^{48} +(1.37856 - 6.86291i) q^{49} +(10.6495 - 7.73730i) q^{50} +(-3.35844 + 3.72993i) q^{51} +(2.18788 + 2.42988i) q^{52} +(-11.1909 + 4.98252i) q^{53} +(-0.931995 - 1.61426i) q^{54} +(-5.45107 - 10.1473i) q^{55} +(0.942354 + 2.41439i) q^{56} +(0.848199 + 0.616252i) q^{57} +(-0.774866 + 0.164703i) q^{58} +(1.04318 + 0.221734i) q^{59} +(-0.535275 - 5.09280i) q^{60} +(6.60222 + 2.93950i) q^{61} +(-0.495495 - 1.52498i) q^{62} +(-1.45339 - 2.21080i) q^{63} +(2.74132 + 1.99168i) q^{64} +(3.85087 + 6.66989i) q^{65} +(-6.17926 - 0.189392i) q^{66} +(6.86264 - 11.8864i) q^{67} +(-0.773561 + 7.35994i) q^{68} +(-2.09779 + 6.45633i) q^{69} +(-2.77413 - 16.9017i) q^{70} +(13.1390 - 9.54608i) q^{71} +(0.894909 + 0.398439i) q^{72} +(-4.98262 - 1.05909i) q^{73} +(-1.28232 - 1.42416i) q^{74} +(0.738178 - 7.02330i) q^{75} +1.54587 q^{76} +(-8.77169 + 0.239731i) q^{77} +4.13354 q^{78} +(-0.600949 + 5.71765i) q^{79} +(11.0964 + 12.3238i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-11.1578 - 4.96779i) q^{82} +(-11.1912 + 8.13092i) q^{83} +(-3.64973 - 1.37758i) q^{84} +(-5.38665 + 16.5784i) q^{85} +(0.588701 - 5.60112i) q^{86} +(-0.212495 + 0.368052i) q^{87} +(2.68574 - 1.82827i) q^{88} +(1.78299 + 3.08823i) q^{89} +(-5.23734 - 3.80515i) q^{90} +(5.85731 - 0.339889i) q^{91} +(3.09311 + 9.51961i) q^{92} +(-0.785857 - 0.349886i) q^{93} +(-0.636644 - 6.05726i) q^{94} +(3.56167 + 0.757056i) q^{95} +(6.78946 - 1.44314i) q^{96} +(14.7992 + 10.7522i) q^{97} +(-12.4537 - 3.89272i) q^{98} +(-2.29372 + 2.39559i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9} - 22 q^{10} - 13 q^{11} + 30 q^{12} - 8 q^{13} - 26 q^{14} + 4 q^{17} - 5 q^{18} + 10 q^{19} + 24 q^{20} + 2 q^{21} - 38 q^{22} - 8 q^{23} + 14 q^{24} - 2 q^{25} + 4 q^{26} + 16 q^{27} - 67 q^{28} + 2 q^{29} - 3 q^{30} + 25 q^{31} + 72 q^{32} - 12 q^{33} - 56 q^{34} + 19 q^{35} - 20 q^{36} - 12 q^{37} - 37 q^{38} - 4 q^{39} - 9 q^{40} + 20 q^{41} + 9 q^{42} - 100 q^{43} - 5 q^{44} - 33 q^{46} - 18 q^{47} + 10 q^{48} + 29 q^{49} - 46 q^{50} + 6 q^{51} + 26 q^{52} - 49 q^{53} - 10 q^{54} - 24 q^{55} - 48 q^{56} + 20 q^{57} - 40 q^{58} + q^{59} + 12 q^{60} + 3 q^{61} + 4 q^{62} - 7 q^{63} - 24 q^{64} + 82 q^{65} + 11 q^{66} + 76 q^{67} - 39 q^{68} - 16 q^{69} + 59 q^{70} + 70 q^{71} - 14 q^{72} - 3 q^{73} + 32 q^{74} - 28 q^{75} + 104 q^{76} + 38 q^{77} - 12 q^{78} - 15 q^{79} - 83 q^{80} + 8 q^{81} + 42 q^{82} + 68 q^{83} + 27 q^{84} + 62 q^{85} - 47 q^{86} - 54 q^{87} - 64 q^{88} + 82 q^{89} - 16 q^{90} - 10 q^{91} + 190 q^{92} - 25 q^{93} - 6 q^{94} - 53 q^{95} + 8 q^{96} - 32 q^{97} - 152 q^{98} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/231\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.194840 1.85378i 0.137773 1.31082i −0.679119 0.734028i \(-0.737638\pi\)
0.816891 0.576792i \(-0.195695\pi\)
\(3\) −0.669131 0.743145i −0.386323 0.429055i
\(4\) −1.44224 0.306558i −0.721120 0.153279i
\(5\) −3.17278 1.41261i −1.41891 0.631739i −0.453210 0.891404i \(-0.649721\pi\)
−0.965699 + 0.259665i \(0.916388\pi\)
\(6\) −1.50800 + 1.09563i −0.615638 + 0.447288i
\(7\) −2.04677 + 1.67652i −0.773607 + 0.633665i
\(8\) 0.302713 0.931655i 0.107025 0.329390i
\(9\) −0.104528 + 0.994522i −0.0348428 + 0.331507i
\(10\) −3.23685 + 5.60640i −1.02358 + 1.77290i
\(11\) 2.62222 + 2.03075i 0.790630 + 0.612294i
\(12\) 0.737230 + 1.27692i 0.212820 + 0.368615i
\(13\) −1.79406 1.30346i −0.497582 0.361515i 0.310510 0.950570i \(-0.399500\pi\)
−0.808093 + 0.589055i \(0.799500\pi\)
\(14\) 2.70911 + 4.12092i 0.724039 + 1.10136i
\(15\) 1.07323 + 3.30305i 0.277106 + 0.852845i
\(16\) −4.36208 1.94212i −1.09052 0.485530i
\(17\) −0.524640 4.99162i −0.127244 1.21064i −0.852709 0.522386i \(-0.825042\pi\)
0.725465 0.688259i \(-0.241625\pi\)
\(18\) 1.82326 + 0.387545i 0.429746 + 0.0913453i
\(19\) −1.02552 + 0.217981i −0.235271 + 0.0500083i −0.324038 0.946044i \(-0.605041\pi\)
0.0887674 + 0.996052i \(0.471707\pi\)
\(20\) 4.14286 + 3.00996i 0.926372 + 0.673048i
\(21\) 2.61546 + 0.399238i 0.570739 + 0.0871208i
\(22\) 4.27547 4.46535i 0.911534 0.952017i
\(23\) −3.39430 5.87909i −0.707760 1.22588i −0.965686 0.259711i \(-0.916373\pi\)
0.257927 0.966164i \(-0.416961\pi\)
\(24\) −0.894909 + 0.398439i −0.182673 + 0.0813311i
\(25\) 4.72539 + 5.24808i 0.945078 + 1.04962i
\(26\) −2.76588 + 3.07182i −0.542434 + 0.602434i
\(27\) 0.809017 0.587785i 0.155695 0.113119i
\(28\) 3.46589 1.79049i 0.654991 0.338371i
\(29\) −0.131329 0.404189i −0.0243872 0.0750561i 0.938122 0.346304i \(-0.112564\pi\)
−0.962509 + 0.271248i \(0.912564\pi\)
\(30\) 6.33224 1.34596i 1.15610 0.245737i
\(31\) 0.785857 0.349886i 0.141144 0.0628414i −0.334949 0.942236i \(-0.608719\pi\)
0.476093 + 0.879395i \(0.342052\pi\)
\(32\) −3.47057 + 6.01121i −0.613516 + 1.06264i
\(33\) −0.245470 3.30753i −0.0427309 0.575767i
\(34\) −9.35558 −1.60447
\(35\) 8.86223 2.42793i 1.49799 0.410395i
\(36\) 0.455633 1.40230i 0.0759389 0.233716i
\(37\) 0.687941 0.764036i 0.113097 0.125607i −0.683938 0.729540i \(-0.739734\pi\)
0.797035 + 0.603933i \(0.206401\pi\)
\(38\) 0.204276 + 1.94356i 0.0331380 + 0.315287i
\(39\) 0.231800 + 2.20543i 0.0371177 + 0.353151i
\(40\) −2.27651 + 2.52832i −0.359947 + 0.399762i
\(41\) 2.02483 6.23179i 0.316225 0.973242i −0.659022 0.752124i \(-0.729029\pi\)
0.975247 0.221118i \(-0.0709706\pi\)
\(42\) 1.24969 4.77069i 0.192832 0.736134i
\(43\) 3.02146 0.460768 0.230384 0.973100i \(-0.426002\pi\)
0.230384 + 0.973100i \(0.426002\pi\)
\(44\) −3.15934 3.73269i −0.476288 0.562724i
\(45\) 1.73652 3.00774i 0.258865 0.448367i
\(46\) −11.5599 + 5.14679i −1.70441 + 0.758853i
\(47\) 3.19612 0.679355i 0.466201 0.0990942i 0.0311791 0.999514i \(-0.490074\pi\)
0.435022 + 0.900420i \(0.356740\pi\)
\(48\) 1.47552 + 4.54119i 0.212973 + 0.655464i
\(49\) 1.37856 6.86291i 0.196937 0.980416i
\(50\) 10.6495 7.73730i 1.50606 1.09422i
\(51\) −3.35844 + 3.72993i −0.470276 + 0.522294i
\(52\) 2.18788 + 2.42988i 0.303404 + 0.336964i
\(53\) −11.1909 + 4.98252i −1.53719 + 0.684402i −0.988444 0.151586i \(-0.951562\pi\)
−0.548748 + 0.835988i \(0.684895\pi\)
\(54\) −0.931995 1.61426i −0.126828 0.219673i
\(55\) −5.45107 10.1473i −0.735023 1.36826i
\(56\) 0.942354 + 2.41439i 0.125927 + 0.322637i
\(57\) 0.848199 + 0.616252i 0.112347 + 0.0816246i
\(58\) −0.774866 + 0.164703i −0.101745 + 0.0216265i
\(59\) 1.04318 + 0.221734i 0.135810 + 0.0288673i 0.275315 0.961354i \(-0.411218\pi\)
−0.139505 + 0.990221i \(0.544551\pi\)
\(60\) −0.535275 5.09280i −0.0691037 0.657478i
\(61\) 6.60222 + 2.93950i 0.845328 + 0.376364i 0.783250 0.621707i \(-0.213561\pi\)
0.0620780 + 0.998071i \(0.480227\pi\)
\(62\) −0.495495 1.52498i −0.0629280 0.193672i
\(63\) −1.45339 2.21080i −0.183110 0.278535i
\(64\) 2.74132 + 1.99168i 0.342664 + 0.248960i
\(65\) 3.85087 + 6.66989i 0.477641 + 0.827299i
\(66\) −6.17926 0.189392i −0.760614 0.0233125i
\(67\) 6.86264 11.8864i 0.838405 1.45216i −0.0528226 0.998604i \(-0.516822\pi\)
0.891228 0.453556i \(-0.149845\pi\)
\(68\) −0.773561 + 7.35994i −0.0938081 + 0.892524i
\(69\) −2.09779 + 6.45633i −0.252544 + 0.777251i
\(70\) −2.77413 16.9017i −0.331572 2.02014i
\(71\) 13.1390 9.54608i 1.55932 1.13291i 0.622753 0.782419i \(-0.286014\pi\)
0.936566 0.350492i \(-0.113986\pi\)
\(72\) 0.894909 + 0.398439i 0.105466 + 0.0469565i
\(73\) −4.98262 1.05909i −0.583172 0.123957i −0.0931271 0.995654i \(-0.529686\pi\)
−0.490045 + 0.871697i \(0.663020\pi\)
\(74\) −1.28232 1.42416i −0.149066 0.165555i
\(75\) 0.738178 7.02330i 0.0852375 0.810981i
\(76\) 1.54587 0.177324
\(77\) −8.77169 + 0.239731i −0.999627 + 0.0273199i
\(78\) 4.13354 0.468032
\(79\) −0.600949 + 5.71765i −0.0676121 + 0.643286i 0.907268 + 0.420554i \(0.138164\pi\)
−0.974880 + 0.222732i \(0.928502\pi\)
\(80\) 11.0964 + 12.3238i 1.24062 + 1.37785i
\(81\) −0.978148 0.207912i −0.108683 0.0231013i
\(82\) −11.1578 4.96779i −1.23218 0.548601i
\(83\) −11.1912 + 8.13092i −1.22840 + 0.892484i −0.996769 0.0803198i \(-0.974406\pi\)
−0.231630 + 0.972804i \(0.574406\pi\)
\(84\) −3.64973 1.37758i −0.398218 0.150307i
\(85\) −5.38665 + 16.5784i −0.584264 + 1.79818i
\(86\) 0.588701 5.60112i 0.0634813 0.603984i
\(87\) −0.212495 + 0.368052i −0.0227818 + 0.0394593i
\(88\) 2.68574 1.82827i 0.286301 0.194895i
\(89\) 1.78299 + 3.08823i 0.188997 + 0.327352i 0.944916 0.327313i \(-0.106143\pi\)
−0.755919 + 0.654665i \(0.772810\pi\)
\(90\) −5.23734 3.80515i −0.552064 0.401098i
\(91\) 5.85731 0.339889i 0.614013 0.0356301i
\(92\) 3.09311 + 9.51961i 0.322479 + 0.992488i
\(93\) −0.785857 0.349886i −0.0814896 0.0362815i
\(94\) −0.636644 6.05726i −0.0656648 0.624759i
\(95\) 3.56167 + 0.757056i 0.365420 + 0.0776723i
\(96\) 6.78946 1.44314i 0.692947 0.147290i
\(97\) 14.7992 + 10.7522i 1.50263 + 1.09172i 0.969320 + 0.245803i \(0.0790515\pi\)
0.533309 + 0.845921i \(0.320948\pi\)
\(98\) −12.4537 3.89272i −1.25802 0.393224i
\(99\) −2.29372 + 2.39559i −0.230528 + 0.240766i
\(100\) −5.20631 9.01759i −0.520631 0.901759i
\(101\) −14.6986 + 6.54422i −1.46256 + 0.651175i −0.975059 0.221947i \(-0.928759\pi\)
−0.487503 + 0.873121i \(0.662092\pi\)
\(102\) 6.26010 + 6.95255i 0.619843 + 0.688405i
\(103\) 8.35526 9.27945i 0.823268 0.914332i −0.174253 0.984701i \(-0.555751\pi\)
0.997521 + 0.0703691i \(0.0224177\pi\)
\(104\) −1.75746 + 1.27687i −0.172333 + 0.125207i
\(105\) −7.73429 4.96131i −0.754789 0.484175i
\(106\) 7.05606 + 21.7163i 0.685345 + 2.10927i
\(107\) 15.9930 3.39941i 1.54610 0.328634i 0.645664 0.763622i \(-0.276581\pi\)
0.900436 + 0.434988i \(0.143247\pi\)
\(108\) −1.34699 + 0.599717i −0.129614 + 0.0577078i
\(109\) −1.11126 + 1.92477i −0.106440 + 0.184359i −0.914326 0.404980i \(-0.867278\pi\)
0.807886 + 0.589339i \(0.200612\pi\)
\(110\) −19.8729 + 8.12799i −1.89481 + 0.774973i
\(111\) −1.02811 −0.0975841
\(112\) 12.1842 3.33803i 1.15130 0.315414i
\(113\) −0.572048 + 1.76058i −0.0538137 + 0.165622i −0.974351 0.225033i \(-0.927751\pi\)
0.920538 + 0.390654i \(0.127751\pi\)
\(114\) 1.30766 1.45230i 0.122473 0.136021i
\(115\) 2.46447 + 23.4479i 0.229813 + 2.18653i
\(116\) 0.0655007 + 0.623198i 0.00608159 + 0.0578625i
\(117\) 1.48385 1.64798i 0.137182 0.152356i
\(118\) 0.614298 1.89062i 0.0565507 0.174045i
\(119\) 9.44237 + 9.33714i 0.865580 + 0.855934i
\(120\) 3.40219 0.310576
\(121\) 2.75212 + 10.6502i 0.250193 + 0.968196i
\(122\) 6.73556 11.6663i 0.609809 1.05622i
\(123\) −5.98600 + 2.66514i −0.539739 + 0.240307i
\(124\) −1.24066 + 0.263709i −0.111414 + 0.0236818i
\(125\) −2.21298 6.81085i −0.197935 0.609181i
\(126\) −4.38152 + 2.26351i −0.390337 + 0.201650i
\(127\) −8.85144 + 6.43095i −0.785438 + 0.570654i −0.906606 0.421978i \(-0.861336\pi\)
0.121168 + 0.992632i \(0.461336\pi\)
\(128\) −5.06281 + 5.62281i −0.447493 + 0.496991i
\(129\) −2.02175 2.24538i −0.178005 0.197695i
\(130\) 13.1148 5.83909i 1.15025 0.512122i
\(131\) 7.51089 + 13.0092i 0.656230 + 1.13662i 0.981584 + 0.191031i \(0.0611830\pi\)
−0.325355 + 0.945592i \(0.605484\pi\)
\(132\) −0.659921 + 4.84550i −0.0574388 + 0.421747i
\(133\) 1.73356 2.16546i 0.150319 0.187770i
\(134\) −20.6977 15.0378i −1.78801 1.29907i
\(135\) −3.39714 + 0.722085i −0.292379 + 0.0621472i
\(136\) −4.80928 1.02224i −0.412392 0.0876567i
\(137\) −2.13232 20.2877i −0.182177 1.73330i −0.578936 0.815373i \(-0.696532\pi\)
0.396759 0.917923i \(-0.370135\pi\)
\(138\) 11.5599 + 5.14679i 0.984043 + 0.438124i
\(139\) −2.75479 8.47836i −0.233658 0.719125i −0.997297 0.0734814i \(-0.976589\pi\)
0.763639 0.645644i \(-0.223411\pi\)
\(140\) −13.5258 + 0.784876i −1.14314 + 0.0663341i
\(141\) −2.64348 1.92060i −0.222621 0.161744i
\(142\) −15.1363 26.2169i −1.27021 2.20007i
\(143\) −2.05742 7.06125i −0.172050 0.590491i
\(144\) 2.38744 4.13517i 0.198954 0.344598i
\(145\) −0.154285 + 1.46792i −0.0128126 + 0.121904i
\(146\) −2.93413 + 9.03033i −0.242831 + 0.747356i
\(147\) −6.02257 + 3.56772i −0.496734 + 0.294260i
\(148\) −1.22640 + 0.891030i −0.100809 + 0.0732422i
\(149\) −21.1602 9.42114i −1.73351 0.771810i −0.995256 0.0972921i \(-0.968982\pi\)
−0.738258 0.674518i \(-0.764351\pi\)
\(150\) −12.8758 2.73684i −1.05131 0.223462i
\(151\) 2.47293 + 2.74647i 0.201244 + 0.223505i 0.835316 0.549769i \(-0.185284\pi\)
−0.634072 + 0.773274i \(0.718618\pi\)
\(152\) −0.107355 + 1.02142i −0.00870766 + 0.0828479i
\(153\) 5.01911 0.405771
\(154\) −1.26467 + 16.3075i −0.101910 + 1.31409i
\(155\) −2.98760 −0.239970
\(156\) 0.341780 3.25182i 0.0273643 0.260354i
\(157\) 5.62229 + 6.24419i 0.448708 + 0.498340i 0.924481 0.381227i \(-0.124498\pi\)
−0.475774 + 0.879568i \(0.657832\pi\)
\(158\) 10.4822 + 2.22806i 0.833917 + 0.177255i
\(159\) 11.1909 + 4.98252i 0.887498 + 0.395140i
\(160\) 19.5029 14.1697i 1.54184 1.12021i
\(161\) 16.8038 + 6.34256i 1.32432 + 0.499864i
\(162\) −0.576005 + 1.77276i −0.0452552 + 0.139281i
\(163\) −0.00965020 + 0.0918155i −0.000755862 + 0.00719155i −0.994893 0.100932i \(-0.967818\pi\)
0.994137 + 0.108124i \(0.0344842\pi\)
\(164\) −4.83070 + 8.36701i −0.377214 + 0.653354i
\(165\) −3.89343 + 10.8408i −0.303103 + 0.843955i
\(166\) 12.8924 + 22.3303i 1.00065 + 1.73317i
\(167\) −6.71124 4.87600i −0.519331 0.377316i 0.297021 0.954871i \(-0.404007\pi\)
−0.816352 + 0.577555i \(0.804007\pi\)
\(168\) 1.16368 2.31585i 0.0897802 0.178672i
\(169\) −2.49758 7.68677i −0.192122 0.591290i
\(170\) 29.6832 + 13.2158i 2.27659 + 1.01361i
\(171\) −0.109591 1.04269i −0.00838063 0.0797363i
\(172\) −4.35767 0.926251i −0.332269 0.0706260i
\(173\) −3.59446 + 0.764026i −0.273282 + 0.0580878i −0.342514 0.939513i \(-0.611278\pi\)
0.0692322 + 0.997601i \(0.477945\pi\)
\(174\) 0.640885 + 0.465630i 0.0485853 + 0.0352993i
\(175\) −18.4703 2.81941i −1.39622 0.213127i
\(176\) −7.49438 13.9510i −0.564910 1.05159i
\(177\) −0.533241 0.923600i −0.0400808 0.0694220i
\(178\) 6.07229 2.70356i 0.455138 0.202640i
\(179\) −12.0863 13.4232i −0.903373 1.00330i −0.999968 0.00797377i \(-0.997462\pi\)
0.0965950 0.995324i \(-0.469205\pi\)
\(180\) −3.42652 + 3.80554i −0.255398 + 0.283648i
\(181\) −2.17999 + 1.58386i −0.162038 + 0.117727i −0.665849 0.746086i \(-0.731931\pi\)
0.503812 + 0.863814i \(0.331931\pi\)
\(182\) 0.511158 10.9244i 0.0378896 0.809769i
\(183\) −2.23328 6.87331i −0.165088 0.508090i
\(184\) −6.50478 + 1.38263i −0.479539 + 0.101929i
\(185\) −3.26197 + 1.45232i −0.239825 + 0.106777i
\(186\) −0.801728 + 1.38863i −0.0587856 + 0.101820i
\(187\) 8.76100 14.1546i 0.640667 1.03508i
\(188\) −4.81783 −0.351376
\(189\) −0.670440 + 2.55940i −0.0487673 + 0.186169i
\(190\) 2.09737 6.45505i 0.152159 0.468298i
\(191\) 7.63592 8.48055i 0.552516 0.613631i −0.400594 0.916256i \(-0.631196\pi\)
0.953110 + 0.302625i \(0.0978629\pi\)
\(192\) −0.354190 3.36989i −0.0255614 0.243201i
\(193\) −0.509153 4.84427i −0.0366496 0.348698i −0.997445 0.0714393i \(-0.977241\pi\)
0.960795 0.277259i \(-0.0894259\pi\)
\(194\) 22.8157 25.3394i 1.63807 1.81927i
\(195\) 2.37997 7.32478i 0.170433 0.524538i
\(196\) −4.09209 + 9.47536i −0.292292 + 0.676812i
\(197\) −4.10130 −0.292206 −0.146103 0.989269i \(-0.546673\pi\)
−0.146103 + 0.989269i \(0.546673\pi\)
\(198\) 3.99398 + 4.71881i 0.283840 + 0.335351i
\(199\) −0.829726 + 1.43713i −0.0588177 + 0.101875i −0.893935 0.448197i \(-0.852066\pi\)
0.835117 + 0.550072i \(0.185400\pi\)
\(200\) 6.31984 2.81377i 0.446880 0.198964i
\(201\) −13.4254 + 2.85365i −0.946951 + 0.201281i
\(202\) 9.26768 + 28.5230i 0.652072 + 2.00687i
\(203\) 0.946432 + 0.607108i 0.0664265 + 0.0426106i
\(204\) 5.98712 4.34990i 0.419182 0.304554i
\(205\) −15.2274 + 16.9118i −1.06353 + 1.18117i
\(206\) −15.5741 17.2968i −1.08510 1.20513i
\(207\) 6.20169 2.76117i 0.431047 0.191914i
\(208\) 5.29434 + 9.17007i 0.367097 + 0.635830i
\(209\) −3.13181 1.51098i −0.216632 0.104517i
\(210\) −10.7041 + 13.3710i −0.738655 + 0.922687i
\(211\) 10.1590 + 7.38097i 0.699376 + 0.508127i 0.879729 0.475475i \(-0.157724\pi\)
−0.180353 + 0.983602i \(0.557724\pi\)
\(212\) 17.6674 3.75533i 1.21340 0.257917i
\(213\) −15.8859 3.37664i −1.08848 0.231364i
\(214\) −3.18569 30.3098i −0.217769 2.07194i
\(215\) −9.58642 4.26815i −0.653788 0.291085i
\(216\) −0.302713 0.931655i −0.0205970 0.0633911i
\(217\) −1.02188 + 2.03364i −0.0693697 + 0.138053i
\(218\) 3.35157 + 2.43506i 0.226997 + 0.164923i
\(219\) 2.54697 + 4.41148i 0.172108 + 0.298100i
\(220\) 4.75103 + 16.3059i 0.320314 + 1.09934i
\(221\) −5.56514 + 9.63910i −0.374352 + 0.648396i
\(222\) −0.200317 + 1.90589i −0.0134444 + 0.127915i
\(223\) 7.26071 22.3462i 0.486213 1.49641i −0.344002 0.938969i \(-0.611783\pi\)
0.830216 0.557442i \(-0.188217\pi\)
\(224\) −2.97444 18.1221i −0.198738 1.21083i
\(225\) −5.71327 + 4.15093i −0.380884 + 0.276729i
\(226\) 3.15227 + 1.40348i 0.209686 + 0.0933583i
\(227\) 22.1157 + 4.70084i 1.46787 + 0.312005i 0.871377 0.490613i \(-0.163227\pi\)
0.596493 + 0.802619i \(0.296561\pi\)
\(228\) −1.03439 1.14881i −0.0685041 0.0760815i
\(229\) 1.54641 14.7131i 0.102189 0.972267i −0.816516 0.577323i \(-0.804097\pi\)
0.918705 0.394944i \(-0.129236\pi\)
\(230\) 43.9474 2.89780
\(231\) 6.04756 + 6.35822i 0.397900 + 0.418340i
\(232\) −0.416320 −0.0273327
\(233\) 0.323062 3.07373i 0.0211645 0.201367i −0.978830 0.204675i \(-0.934386\pi\)
0.999995 + 0.00330806i \(0.00105299\pi\)
\(234\) −2.76588 3.07182i −0.180811 0.200811i
\(235\) −11.1002 2.35943i −0.724099 0.153912i
\(236\) −1.43654 0.639587i −0.0935106 0.0416336i
\(237\) 4.65116 3.37926i 0.302125 0.219507i
\(238\) 19.1487 15.6848i 1.24123 1.01670i
\(239\) −6.89040 + 21.2065i −0.445703 + 1.37173i 0.436008 + 0.899943i \(0.356392\pi\)
−0.881711 + 0.471790i \(0.843608\pi\)
\(240\) 1.73343 16.4925i 0.111893 1.06459i
\(241\) −2.66332 + 4.61301i −0.171560 + 0.297150i −0.938965 0.344012i \(-0.888214\pi\)
0.767406 + 0.641162i \(0.221547\pi\)
\(242\) 20.2793 3.02675i 1.30360 0.194567i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −8.62086 6.26342i −0.551894 0.400975i
\(245\) −14.0685 + 19.8271i −0.898803 + 1.26671i
\(246\) 3.77427 + 11.6160i 0.240638 + 0.740609i
\(247\) 2.12397 + 0.945654i 0.135145 + 0.0601705i
\(248\) −0.0880840 0.838063i −0.00559334 0.0532171i
\(249\) 13.5309 + 2.87607i 0.857483 + 0.182264i
\(250\) −13.0570 + 2.77535i −0.825797 + 0.175528i
\(251\) −17.0453 12.3842i −1.07589 0.781682i −0.0989307 0.995094i \(-0.531542\pi\)
−0.976962 + 0.213412i \(0.931542\pi\)
\(252\) 1.41840 + 3.63406i 0.0893507 + 0.228924i
\(253\) 3.03835 22.3093i 0.191020 1.40257i
\(254\) 10.1969 + 17.6616i 0.639813 + 1.10819i
\(255\) 15.9245 7.09006i 0.997232 0.443996i
\(256\) 13.9717 + 15.5171i 0.873229 + 0.969819i
\(257\) −2.98221 + 3.31208i −0.186025 + 0.206602i −0.828943 0.559334i \(-0.811057\pi\)
0.642918 + 0.765935i \(0.277724\pi\)
\(258\) −4.55636 + 3.31039i −0.283667 + 0.206096i
\(259\) −0.127137 + 2.71716i −0.00789994 + 0.168836i
\(260\) −3.50917 10.8001i −0.217629 0.669794i
\(261\) 0.415703 0.0883603i 0.0257314 0.00546937i
\(262\) 25.5797 11.3888i 1.58032 0.703603i
\(263\) 7.47232 12.9424i 0.460763 0.798064i −0.538236 0.842794i \(-0.680909\pi\)
0.998999 + 0.0447295i \(0.0142426\pi\)
\(264\) −3.15578 0.772539i −0.194225 0.0475465i
\(265\) 42.5447 2.61350
\(266\) −3.67653 3.63555i −0.225422 0.222910i
\(267\) 1.10195 3.39145i 0.0674382 0.207553i
\(268\) −13.5415 + 15.0393i −0.827176 + 0.918672i
\(269\) 1.55712 + 14.8150i 0.0949392 + 0.903286i 0.933524 + 0.358515i \(0.116717\pi\)
−0.838585 + 0.544771i \(0.816617\pi\)
\(270\) 0.676687 + 6.43824i 0.0411818 + 0.391819i
\(271\) 15.1619 16.8390i 0.921022 1.02290i −0.0786402 0.996903i \(-0.525058\pi\)
0.999662 0.0259953i \(-0.00827549\pi\)
\(272\) −7.40581 + 22.7927i −0.449043 + 1.38201i
\(273\) −4.17189 4.12540i −0.252494 0.249680i
\(274\) −38.0244 −2.29714
\(275\) 1.73351 + 23.3577i 0.104534 + 1.40852i
\(276\) 5.00476 8.66849i 0.301251 0.521782i
\(277\) −13.2626 + 5.90490i −0.796874 + 0.354791i −0.764450 0.644683i \(-0.776989\pi\)
−0.0324242 + 0.999474i \(0.510323\pi\)
\(278\) −16.2538 + 3.45484i −0.974836 + 0.207208i
\(279\) 0.265825 + 0.818125i 0.0159145 + 0.0489799i
\(280\) 0.420718 8.99150i 0.0251427 0.537345i
\(281\) −1.22012 + 0.886467i −0.0727861 + 0.0528822i −0.623583 0.781757i \(-0.714324\pi\)
0.550797 + 0.834639i \(0.314324\pi\)
\(282\) −4.07542 + 4.52622i −0.242688 + 0.269532i
\(283\) 9.18557 + 10.2016i 0.546026 + 0.606423i 0.951487 0.307689i \(-0.0995558\pi\)
−0.405461 + 0.914112i \(0.632889\pi\)
\(284\) −21.8761 + 9.73986i −1.29811 + 0.577955i
\(285\) −1.82062 3.15341i −0.107844 0.186792i
\(286\) −13.4909 + 2.43820i −0.797731 + 0.144174i
\(287\) 6.30335 + 16.1497i 0.372075 + 0.953288i
\(288\) −5.61550 4.07990i −0.330897 0.240411i
\(289\) −8.01248 + 1.70311i −0.471323 + 0.100183i
\(290\) 2.69114 + 0.572019i 0.158029 + 0.0335901i
\(291\) −1.91212 18.1926i −0.112090 1.06647i
\(292\) 6.86147 + 3.05492i 0.401537 + 0.178776i
\(293\) −0.716316 2.20459i −0.0418476 0.128794i 0.927950 0.372705i \(-0.121570\pi\)
−0.969798 + 0.243911i \(0.921570\pi\)
\(294\) 5.44032 + 11.8597i 0.317286 + 0.691669i
\(295\) −2.99654 2.17711i −0.174465 0.126757i
\(296\) −0.503570 0.872208i −0.0292694 0.0506961i
\(297\) 3.31507 + 0.101605i 0.192360 + 0.00589574i
\(298\) −21.5876 + 37.3908i −1.25054 + 2.16599i
\(299\) −1.57360 + 14.9718i −0.0910034 + 0.865839i
\(300\) −3.21768 + 9.90299i −0.185773 + 0.571749i
\(301\) −6.18424 + 5.06554i −0.356454 + 0.291973i
\(302\) 5.57317 4.04915i 0.320700 0.233002i
\(303\) 14.6986 + 6.54422i 0.844411 + 0.375956i
\(304\) 4.89674 + 1.04084i 0.280848 + 0.0596960i
\(305\) −16.7950 18.6527i −0.961679 1.06805i
\(306\) 0.977924 9.30433i 0.0559042 0.531893i
\(307\) −19.8671 −1.13387 −0.566937 0.823761i \(-0.691872\pi\)
−0.566937 + 0.823761i \(0.691872\pi\)
\(308\) 12.7244 + 2.34328i 0.725039 + 0.133521i
\(309\) −12.4867 −0.710346
\(310\) −0.582105 + 5.53836i −0.0330613 + 0.314558i
\(311\) −8.09647 8.99205i −0.459109 0.509892i 0.468490 0.883469i \(-0.344798\pi\)
−0.927599 + 0.373576i \(0.878131\pi\)
\(312\) 2.12487 + 0.451655i 0.120297 + 0.0255699i
\(313\) −5.64206 2.51201i −0.318908 0.141987i 0.241039 0.970515i \(-0.422512\pi\)
−0.559947 + 0.828528i \(0.689178\pi\)
\(314\) 12.6708 9.20587i 0.715054 0.519517i
\(315\) 1.48828 + 9.06747i 0.0838548 + 0.510894i
\(316\) 2.61950 8.06200i 0.147359 0.453523i
\(317\) −0.0688763 + 0.655314i −0.00386848 + 0.0368061i −0.996286 0.0861075i \(-0.972557\pi\)
0.992417 + 0.122914i \(0.0392238\pi\)
\(318\) 11.4169 19.7747i 0.640230 1.10891i
\(319\) 0.476433 1.32657i 0.0266751 0.0742737i
\(320\) −5.88411 10.1916i −0.328932 0.569727i
\(321\) −13.2277 9.61045i −0.738296 0.536403i
\(322\) 15.0318 29.9147i 0.837687 1.66708i
\(323\) 1.62611 + 5.00464i 0.0904790 + 0.278466i
\(324\) 1.34699 + 0.599717i 0.0748326 + 0.0333176i
\(325\) −1.63697 15.5747i −0.0908027 0.863930i
\(326\) 0.168325 + 0.0357787i 0.00932269 + 0.00198160i
\(327\) 2.17396 0.462090i 0.120220 0.0255536i
\(328\) −5.19293 3.77289i −0.286732 0.208323i
\(329\) −5.40277 + 6.74884i −0.297864 + 0.372076i
\(330\) 19.3379 + 9.32978i 1.06451 + 0.513588i
\(331\) −3.91416 6.77953i −0.215142 0.372637i 0.738175 0.674610i \(-0.235688\pi\)
−0.953316 + 0.301973i \(0.902355\pi\)
\(332\) 18.6331 8.29597i 1.02262 0.455301i
\(333\) 0.687941 + 0.764036i 0.0376990 + 0.0418689i
\(334\) −10.3466 + 11.4911i −0.566143 + 0.628766i
\(335\) −38.5646 + 28.0188i −2.10701 + 1.53083i
\(336\) −10.6334 6.82104i −0.580102 0.372118i
\(337\) −2.51962 7.75460i −0.137253 0.422420i 0.858681 0.512511i \(-0.171284\pi\)
−0.995934 + 0.0900903i \(0.971284\pi\)
\(338\) −14.7362 + 3.13228i −0.801544 + 0.170373i
\(339\) 1.69114 0.752945i 0.0918502 0.0408944i
\(340\) 12.8511 22.2587i 0.696948 1.20715i
\(341\) 2.77122 + 0.678398i 0.150070 + 0.0367373i
\(342\) −1.95427 −0.105675
\(343\) 8.68422 + 16.3580i 0.468904 + 0.883249i
\(344\) 0.914635 2.81496i 0.0493138 0.151772i
\(345\) 15.7761 17.5211i 0.849357 0.943307i
\(346\) 0.715991 + 6.81220i 0.0384919 + 0.366226i
\(347\) 1.49369 + 14.2115i 0.0801853 + 0.762913i 0.958551 + 0.284922i \(0.0919678\pi\)
−0.878365 + 0.477990i \(0.841365\pi\)
\(348\) 0.419298 0.465677i 0.0224767 0.0249629i
\(349\) 8.55755 26.3374i 0.458075 1.40981i −0.409411 0.912350i \(-0.634266\pi\)
0.867486 0.497461i \(-0.165734\pi\)
\(350\) −8.82532 + 33.6905i −0.471733 + 1.80084i
\(351\) −2.21758 −0.118366
\(352\) −21.3079 + 8.71487i −1.13571 + 0.464504i
\(353\) 6.73552 11.6663i 0.358495 0.620932i −0.629214 0.777232i \(-0.716623\pi\)
0.987710 + 0.156300i \(0.0499565\pi\)
\(354\) −1.81605 + 0.808556i −0.0965218 + 0.0429743i
\(355\) −55.1722 + 11.7272i −2.92824 + 0.622416i
\(356\) −1.62478 5.00056i −0.0861132 0.265029i
\(357\) 0.620669 13.2648i 0.0328493 0.702048i
\(358\) −27.2386 + 19.7900i −1.43960 + 1.04593i
\(359\) −8.76127 + 9.73037i −0.462402 + 0.513550i −0.928575 0.371144i \(-0.878966\pi\)
0.466173 + 0.884693i \(0.345632\pi\)
\(360\) −2.27651 2.52832i −0.119982 0.133254i
\(361\) −16.3532 + 7.28091i −0.860694 + 0.383206i
\(362\) 2.51137 + 4.34983i 0.131995 + 0.228622i
\(363\) 6.07308 9.17157i 0.318754 0.481383i
\(364\) −8.55184 1.30540i −0.448238 0.0684216i
\(365\) 14.3127 + 10.3988i 0.749160 + 0.544296i
\(366\) −13.1767 + 2.80080i −0.688759 + 0.146400i
\(367\) 19.1656 + 4.07378i 1.00044 + 0.212650i 0.678887 0.734242i \(-0.262462\pi\)
0.321551 + 0.946892i \(0.395796\pi\)
\(368\) 3.38826 + 32.2372i 0.176625 + 1.68048i
\(369\) 5.98600 + 2.66514i 0.311619 + 0.138742i
\(370\) 2.05672 + 6.32995i 0.106924 + 0.329078i
\(371\) 14.5520 28.9599i 0.755502 1.50352i
\(372\) 1.02613 + 0.745530i 0.0532026 + 0.0386540i
\(373\) −7.57666 13.1232i −0.392304 0.679491i 0.600449 0.799663i \(-0.294989\pi\)
−0.992753 + 0.120172i \(0.961655\pi\)
\(374\) −24.5324 18.9988i −1.26854 0.982406i
\(375\) −3.58068 + 6.20191i −0.184905 + 0.320265i
\(376\) 0.334581 3.18333i 0.0172547 0.164168i
\(377\) −0.291232 + 0.896321i −0.0149992 + 0.0461629i
\(378\) 4.61393 + 1.74152i 0.237315 + 0.0895742i
\(379\) −9.29592 + 6.75388i −0.477499 + 0.346924i −0.800357 0.599524i \(-0.795357\pi\)
0.322857 + 0.946448i \(0.395357\pi\)
\(380\) −4.90470 2.18371i −0.251606 0.112022i
\(381\) 10.7019 + 2.27476i 0.548275 + 0.116539i
\(382\) −14.2333 15.8077i −0.728238 0.808790i
\(383\) 0.327657 3.11744i 0.0167425 0.159294i −0.982956 0.183840i \(-0.941147\pi\)
0.999699 + 0.0245457i \(0.00781394\pi\)
\(384\) 7.56624 0.386113
\(385\) 28.1693 + 11.6304i 1.43564 + 0.592739i
\(386\) −9.07940 −0.462130
\(387\) −0.315828 + 3.00491i −0.0160545 + 0.152748i
\(388\) −18.0478 20.0441i −0.916238 1.01758i
\(389\) 21.6169 + 4.59482i 1.09602 + 0.232967i 0.720229 0.693737i \(-0.244037\pi\)
0.375794 + 0.926703i \(0.377370\pi\)
\(390\) −13.1148 5.83909i −0.664095 0.295674i
\(391\) −27.5654 + 20.0274i −1.39404 + 1.01283i
\(392\) −5.97656 3.36184i −0.301862 0.169798i
\(393\) 4.64199 14.2866i 0.234157 0.720662i
\(394\) −0.799098 + 7.60291i −0.0402580 + 0.383029i
\(395\) 9.98350 17.2919i 0.502324 0.870051i
\(396\) 4.04248 2.75186i 0.203142 0.138286i
\(397\) −13.1278 22.7381i −0.658867 1.14119i −0.980909 0.194466i \(-0.937703\pi\)
0.322043 0.946725i \(-0.395631\pi\)
\(398\) 2.50245 + 1.81814i 0.125437 + 0.0911351i
\(399\) −2.76923 + 0.160694i −0.138635 + 0.00804474i
\(400\) −10.4201 32.0698i −0.521005 1.60349i
\(401\) 19.6706 + 8.75792i 0.982304 + 0.437350i 0.834104 0.551608i \(-0.185985\pi\)
0.148200 + 0.988957i \(0.452652\pi\)
\(402\) 2.67423 + 25.4436i 0.133379 + 1.26901i
\(403\) −1.86594 0.396617i −0.0929489 0.0197569i
\(404\) 23.2050 4.93239i 1.15449 0.245395i
\(405\) 2.80975 + 2.04140i 0.139617 + 0.101438i
\(406\) 1.30985 1.63619i 0.0650066 0.0812026i
\(407\) 3.35550 0.606439i 0.166326 0.0300600i
\(408\) 2.45836 + 4.25801i 0.121707 + 0.210803i
\(409\) −10.2397 + 4.55902i −0.506321 + 0.225429i −0.643968 0.765053i \(-0.722713\pi\)
0.137646 + 0.990481i \(0.456046\pi\)
\(410\) 28.3838 + 31.5234i 1.40178 + 1.55683i
\(411\) −13.6499 + 15.1598i −0.673300 + 0.747775i
\(412\) −14.8950 + 10.8218i −0.733823 + 0.533154i
\(413\) −2.50689 + 1.29507i −0.123356 + 0.0637261i
\(414\) −3.91026 12.0345i −0.192179 0.591466i
\(415\) 46.9932 9.98871i 2.30680 0.490326i
\(416\) 14.0618 6.26071i 0.689435 0.306956i
\(417\) −4.45734 + 7.72034i −0.218277 + 0.378067i
\(418\) −3.41122 + 5.51128i −0.166848 + 0.269566i
\(419\) 22.4366 1.09610 0.548050 0.836445i \(-0.315370\pi\)
0.548050 + 0.836445i \(0.315370\pi\)
\(420\) 9.63378 + 9.52641i 0.470080 + 0.464841i
\(421\) −3.89935 + 12.0010i −0.190043 + 0.584891i −0.999999 0.00159963i \(-0.999491\pi\)
0.809956 + 0.586490i \(0.199491\pi\)
\(422\) 15.6621 17.3945i 0.762418 0.846751i
\(423\) 0.341549 + 3.24962i 0.0166067 + 0.158002i
\(424\) 1.25435 + 11.9344i 0.0609167 + 0.579584i
\(425\) 23.7173 26.3407i 1.15046 1.27771i
\(426\) −9.35475 + 28.7910i −0.453239 + 1.39493i
\(427\) −18.4414 + 5.05227i −0.892441 + 0.244497i
\(428\) −24.1078 −1.16530
\(429\) −3.87084 + 6.25386i −0.186886 + 0.301939i
\(430\) −9.78002 + 16.9395i −0.471635 + 0.816895i
\(431\) 34.3179 15.2793i 1.65303 0.735978i 0.653258 0.757135i \(-0.273402\pi\)
0.999776 + 0.0211570i \(0.00673499\pi\)
\(432\) −4.67054 + 0.992755i −0.224712 + 0.0477639i
\(433\) 7.40552 + 22.7918i 0.355886 + 1.09531i 0.955494 + 0.295011i \(0.0953234\pi\)
−0.599607 + 0.800294i \(0.704677\pi\)
\(434\) 3.57082 + 2.29058i 0.171405 + 0.109951i
\(435\) 1.19411 0.867574i 0.0572533 0.0415970i
\(436\) 2.19276 2.43531i 0.105014 0.116630i
\(437\) 4.76245 + 5.28924i 0.227819 + 0.253019i
\(438\) 8.67416 3.86199i 0.414468 0.184533i
\(439\) −0.208627 0.361352i −0.00995721 0.0172464i 0.861004 0.508598i \(-0.169836\pi\)
−0.870961 + 0.491352i \(0.836503\pi\)
\(440\) −11.1039 + 2.00680i −0.529357 + 0.0956705i
\(441\) 6.68122 + 2.08838i 0.318153 + 0.0994465i
\(442\) 16.7845 + 12.1946i 0.798355 + 0.580039i
\(443\) −9.20536 + 1.95666i −0.437360 + 0.0929637i −0.421329 0.906908i \(-0.638436\pi\)
−0.0160307 + 0.999871i \(0.505103\pi\)
\(444\) 1.48279 + 0.315176i 0.0703699 + 0.0149576i
\(445\) −1.29456 12.3169i −0.0613681 0.583879i
\(446\) −40.0102 17.8137i −1.89454 0.843503i
\(447\) 7.15769 + 22.0291i 0.338547 + 1.04194i
\(448\) −8.94995 + 0.519350i −0.422845 + 0.0245370i
\(449\) 14.4666 + 10.5106i 0.682720 + 0.496025i 0.874259 0.485460i \(-0.161348\pi\)
−0.191539 + 0.981485i \(0.561348\pi\)
\(450\) 6.58174 + 11.3999i 0.310266 + 0.537397i
\(451\) 17.9648 12.2292i 0.845927 0.575852i
\(452\) 1.36475 2.36382i 0.0641925 0.111185i
\(453\) 0.386310 3.67549i 0.0181504 0.172690i
\(454\) 13.0233 40.0817i 0.611215 1.88113i
\(455\) −19.0641 7.19571i −0.893737 0.337340i
\(456\) 0.830895 0.603681i 0.0389102 0.0282699i
\(457\) 25.3173 + 11.2720i 1.18430 + 0.527282i 0.901870 0.432007i \(-0.142194\pi\)
0.282425 + 0.959289i \(0.408861\pi\)
\(458\) −26.9735 5.73339i −1.26039 0.267904i
\(459\) −3.35844 3.72993i −0.156759 0.174098i
\(460\) 3.63377 34.5730i 0.169425 1.61197i
\(461\) 31.1388 1.45028 0.725140 0.688602i \(-0.241775\pi\)
0.725140 + 0.688602i \(0.241775\pi\)
\(462\) 12.9651 9.97201i 0.603189 0.463940i
\(463\) 14.7614 0.686020 0.343010 0.939332i \(-0.388554\pi\)
0.343010 + 0.939332i \(0.388554\pi\)
\(464\) −0.212117 + 2.01816i −0.00984730 + 0.0936908i
\(465\) 1.99910 + 2.22022i 0.0927059 + 0.102960i
\(466\) −5.63507 1.19777i −0.261040 0.0554857i
\(467\) 21.3849 + 9.52117i 0.989575 + 0.440587i 0.836702 0.547659i \(-0.184481\pi\)
0.152873 + 0.988246i \(0.451147\pi\)
\(468\) −2.64527 + 1.92190i −0.122278 + 0.0888399i
\(469\) 5.88160 + 35.8342i 0.271587 + 1.65467i
\(470\) −6.53663 + 20.1177i −0.301512 + 0.927959i
\(471\) 0.878288 8.35636i 0.0404694 0.385041i
\(472\) 0.522363 0.904759i 0.0240437 0.0416449i
\(473\) 7.92294 + 6.13582i 0.364297 + 0.282126i
\(474\) −5.35818 9.28064i −0.246109 0.426274i
\(475\) −5.98997 4.35197i −0.274839 0.199682i
\(476\) −10.7558 16.3610i −0.492991 0.749906i
\(477\) −3.78546 11.6504i −0.173324 0.533437i
\(478\) 37.9696 + 16.9051i 1.73669 + 0.773223i
\(479\) −0.912225 8.67924i −0.0416806 0.396565i −0.995396 0.0958524i \(-0.969442\pi\)
0.953715 0.300712i \(-0.0972244\pi\)
\(480\) −23.5801 5.01210i −1.07628 0.228770i
\(481\) −2.23010 + 0.474022i −0.101684 + 0.0216135i
\(482\) 8.03259 + 5.83602i 0.365874 + 0.265823i
\(483\) −6.53047 16.7316i −0.297147 0.761316i
\(484\) −0.704332 16.2038i −0.0320151 0.736535i
\(485\) −31.7658 55.0199i −1.44241 2.49833i
\(486\) 1.70284 0.758153i 0.0772424 0.0343905i
\(487\) 2.14624 + 2.38364i 0.0972556 + 0.108013i 0.789808 0.613355i \(-0.210180\pi\)
−0.692552 + 0.721368i \(0.743514\pi\)
\(488\) 4.73718 5.26117i 0.214442 0.238162i
\(489\) 0.0746895 0.0542651i 0.00337757 0.00245395i
\(490\) 34.0140 + 29.9430i 1.53660 + 1.35269i
\(491\) −1.37204 4.22269i −0.0619191 0.190567i 0.915312 0.402746i \(-0.131944\pi\)
−0.977231 + 0.212179i \(0.931944\pi\)
\(492\) 9.45027 2.00872i 0.426051 0.0905599i
\(493\) −1.94866 + 0.867598i −0.0877631 + 0.0390747i
\(494\) 2.16687 3.75313i 0.0974920 0.168861i
\(495\) 10.6615 4.36053i 0.479199 0.195991i
\(496\) −4.10749 −0.184432
\(497\) −10.8885 + 41.5665i −0.488414 + 1.86451i
\(498\) 7.96796 24.5228i 0.357053 1.09890i
\(499\) −4.32193 + 4.79999i −0.193476 + 0.214877i −0.832075 0.554662i \(-0.812847\pi\)
0.638599 + 0.769539i \(0.279514\pi\)
\(500\) 1.10373 + 10.5013i 0.0493603 + 0.469632i
\(501\) 0.867120 + 8.25010i 0.0387401 + 0.368587i
\(502\) −26.2786 + 29.1854i −1.17287 + 1.30261i
\(503\) −5.77237 + 17.7655i −0.257377 + 0.792126i 0.735975 + 0.677009i \(0.236724\pi\)
−0.993352 + 0.115117i \(0.963276\pi\)
\(504\) −2.49967 + 0.684819i −0.111344 + 0.0305043i
\(505\) 55.8797 2.48662
\(506\) −40.7645 9.97918i −1.81220 0.443629i
\(507\) −4.04117 + 6.99952i −0.179475 + 0.310860i
\(508\) 14.7374 6.56150i 0.653865 0.291119i
\(509\) 40.0113 8.50466i 1.77347 0.376962i 0.798972 0.601368i \(-0.205377\pi\)
0.974496 + 0.224406i \(0.0720441\pi\)
\(510\) −10.0407 30.9020i −0.444608 1.36836i
\(511\) 11.9739 6.18576i 0.529694 0.273642i
\(512\) 19.2451 13.9824i 0.850520 0.617939i
\(513\) −0.701537 + 0.779136i −0.0309736 + 0.0343997i
\(514\) 5.55881 + 6.17368i 0.245188 + 0.272309i
\(515\) −39.6176 + 17.6389i −1.74576 + 0.777263i
\(516\) 2.22751 + 3.85816i 0.0980607 + 0.169846i
\(517\) 9.76053 + 4.70909i 0.429268 + 0.207105i
\(518\) 5.01224 + 0.765096i 0.220225 + 0.0336164i
\(519\) 2.97295 + 2.15997i 0.130498 + 0.0948122i
\(520\) 7.37975 1.56861i 0.323623 0.0687883i
\(521\) 1.99956 + 0.425021i 0.0876025 + 0.0186205i 0.251504 0.967856i \(-0.419075\pi\)
−0.163902 + 0.986477i \(0.552408\pi\)
\(522\) −0.0828050 0.787837i −0.00362428 0.0344827i
\(523\) −5.71039 2.54243i −0.249698 0.111173i 0.278071 0.960560i \(-0.410305\pi\)
−0.527769 + 0.849388i \(0.676971\pi\)
\(524\) −6.84443 21.0650i −0.299000 0.920228i
\(525\) 10.2638 + 15.6127i 0.447950 + 0.681393i
\(526\) −22.5365 16.3737i −0.982638 0.713929i
\(527\) −2.15879 3.73913i −0.0940384 0.162879i
\(528\) −5.35286 + 14.9044i −0.232953 + 0.648632i
\(529\) −11.5425 + 19.9922i −0.501847 + 0.869225i
\(530\) 8.28941 78.8685i 0.360069 3.42583i
\(531\) −0.329561 + 1.01428i −0.0143017 + 0.0440162i
\(532\) −3.16405 + 2.59168i −0.137179 + 0.112364i
\(533\) −11.7556 + 8.54091i −0.509189 + 0.369948i
\(534\) −6.07229 2.70356i −0.262774 0.116994i
\(535\) −55.5442 11.8063i −2.40139 0.510431i
\(536\) −8.99665 9.99180i −0.388596 0.431580i
\(537\) −1.88807 + 17.9638i −0.0814761 + 0.775193i
\(538\) 27.7671 1.19713
\(539\) 17.5517 15.1966i 0.756007 0.654563i
\(540\) 5.12086 0.220367
\(541\) 0.509227 4.84497i 0.0218934 0.208302i −0.978107 0.208105i \(-0.933271\pi\)
1.00000 0.000197135i \(-6.27500e-5\pi\)
\(542\) −28.2617 31.3878i −1.21394 1.34822i
\(543\) 2.63574 + 0.560243i 0.113110 + 0.0240423i
\(544\) 31.8264 + 14.1700i 1.36455 + 0.607536i
\(545\) 6.24474 4.53707i 0.267495 0.194347i
\(546\) −8.46043 + 6.92997i −0.362073 + 0.296575i
\(547\) −5.37326 + 16.5372i −0.229744 + 0.707080i 0.768031 + 0.640413i \(0.221237\pi\)
−0.997775 + 0.0666674i \(0.978763\pi\)
\(548\) −3.14403 + 29.9134i −0.134306 + 1.27784i
\(549\) −3.61352 + 6.25879i −0.154221 + 0.267119i
\(550\) 43.6378 + 1.33748i 1.86072 + 0.0570303i
\(551\) 0.222786 + 0.385877i 0.00949101 + 0.0164389i
\(552\) 5.38005 + 3.90883i 0.228990 + 0.166371i
\(553\) −8.35575 12.7102i −0.355323 0.540494i
\(554\) 8.36230 + 25.7365i 0.355280 + 1.09344i
\(555\) 3.26197 + 1.45232i 0.138463 + 0.0616477i
\(556\) 1.37396 + 13.0723i 0.0582688 + 0.554391i
\(557\) −16.8112 3.57334i −0.712315 0.151407i −0.162518 0.986706i \(-0.551962\pi\)
−0.549797 + 0.835298i \(0.685295\pi\)
\(558\) 1.56842 0.333377i 0.0663964 0.0141130i
\(559\) −5.42067 3.93835i −0.229270 0.166574i
\(560\) −43.3730 6.62070i −1.83285 0.279776i
\(561\) −16.3811 + 2.96056i −0.691612 + 0.124995i
\(562\) 1.40559 + 2.43455i 0.0592911 + 0.102695i
\(563\) −29.5272 + 13.1463i −1.24442 + 0.554052i −0.920021 0.391868i \(-0.871829\pi\)
−0.324400 + 0.945920i \(0.605162\pi\)
\(564\) 3.22376 + 3.58034i 0.135745 + 0.150760i
\(565\) 4.30200 4.77785i 0.180986 0.201006i
\(566\) 20.7013 15.0403i 0.870139 0.632193i
\(567\) 2.35061 1.21434i 0.0987165 0.0509973i
\(568\) −4.91629 15.1308i −0.206283 0.634874i
\(569\) −20.0273 + 4.25694i −0.839589 + 0.178460i −0.607585 0.794255i \(-0.707862\pi\)
−0.232004 + 0.972715i \(0.574528\pi\)
\(570\) −6.20045 + 2.76062i −0.259708 + 0.115630i
\(571\) 4.54476 7.87175i 0.190192 0.329422i −0.755122 0.655585i \(-0.772422\pi\)
0.945314 + 0.326162i \(0.105756\pi\)
\(572\) 0.802622 + 10.8147i 0.0335593 + 0.452187i
\(573\) −11.4117 −0.476731
\(574\) 31.1662 8.53841i 1.30085 0.356386i
\(575\) 14.8146 45.5945i 0.617810 1.90142i
\(576\) −2.26732 + 2.51811i −0.0944716 + 0.104921i
\(577\) −2.92720 27.8504i −0.121861 1.15943i −0.869018 0.494781i \(-0.835248\pi\)
0.747157 0.664647i \(-0.231418\pi\)
\(578\) 1.59603 + 15.1852i 0.0663861 + 0.631622i
\(579\) −3.25930 + 3.61982i −0.135452 + 0.150435i
\(580\) 0.672517 2.06980i 0.0279248 0.0859436i
\(581\) 9.27430 35.4045i 0.384763 1.46883i
\(582\) −34.0976 −1.41339
\(583\) −39.4634 9.66067i −1.63441 0.400104i
\(584\) −2.49501 + 4.32149i −0.103244 + 0.178824i
\(585\) −7.03588 + 3.13258i −0.290898 + 0.129516i
\(586\) −4.22640 + 0.898348i −0.174591 + 0.0371104i
\(587\) 4.77233 + 14.6877i 0.196975 + 0.606227i 0.999948 + 0.0102110i \(0.00325033\pi\)
−0.802973 + 0.596016i \(0.796750\pi\)
\(588\) 9.77971 3.29924i 0.403308 0.136058i
\(589\) −0.729644 + 0.530117i −0.0300645 + 0.0218431i
\(590\) −4.61974 + 5.13074i −0.190192 + 0.211229i
\(591\) 2.74431 + 3.04786i 0.112886 + 0.125372i
\(592\) −4.48470 + 1.99672i −0.184320 + 0.0820647i
\(593\) 11.9567 + 20.7096i 0.491002 + 0.850440i 0.999946 0.0103595i \(-0.00329760\pi\)
−0.508945 + 0.860799i \(0.669964\pi\)
\(594\) 0.834262 6.12561i 0.0342302 0.251337i
\(595\) −16.7688 42.9630i −0.687453 1.76131i
\(596\) 27.6300 + 20.0744i 1.13177 + 0.822279i
\(597\) 1.62319 0.345020i 0.0664327 0.0141207i
\(598\) 27.4477 + 5.83420i 1.12242 + 0.238578i
\(599\) −0.230848 2.19637i −0.00943219 0.0897413i 0.988793 0.149293i \(-0.0476996\pi\)
−0.998225 + 0.0595514i \(0.981033\pi\)
\(600\) −6.31984 2.81377i −0.258006 0.114872i
\(601\) −9.84703 30.3061i −0.401669 1.23621i −0.923645 0.383249i \(-0.874805\pi\)
0.521976 0.852960i \(-0.325195\pi\)
\(602\) 8.18545 + 12.4512i 0.333614 + 0.507473i
\(603\) 11.1040 + 8.06752i 0.452189 + 0.328535i
\(604\) −2.72461 4.71917i −0.110863 0.192020i
\(605\) 6.31267 37.6782i 0.256646 1.53184i
\(606\) 14.9954 25.9728i 0.609147 1.05507i
\(607\) 1.28745 12.2493i 0.0522560 0.497182i −0.936824 0.349801i \(-0.886249\pi\)
0.989080 0.147381i \(-0.0470843\pi\)
\(608\) 2.24881 6.92113i 0.0912014 0.280689i
\(609\) −0.182118 1.10957i −0.00737978 0.0449621i
\(610\) −37.8504 + 27.4999i −1.53252 + 1.11344i
\(611\) −6.61953 2.94721i −0.267798 0.119231i
\(612\) −7.23877 1.53865i −0.292610 0.0621961i
\(613\) 10.4214 + 11.5741i 0.420915 + 0.467473i 0.915887 0.401435i \(-0.131489\pi\)
−0.494972 + 0.868909i \(0.664822\pi\)
\(614\) −3.87090 + 36.8292i −0.156217 + 1.48631i
\(615\) 22.7570 0.917652
\(616\) −2.43196 + 8.24476i −0.0979864 + 0.332191i
\(617\) −30.3050 −1.22003 −0.610016 0.792389i \(-0.708837\pi\)
−0.610016 + 0.792389i \(0.708837\pi\)
\(618\) −2.43292 + 23.1477i −0.0978663 + 0.931135i
\(619\) 17.7153 + 19.6749i 0.712040 + 0.790800i 0.985244 0.171156i \(-0.0547501\pi\)
−0.273204 + 0.961956i \(0.588083\pi\)
\(620\) 4.30884 + 0.915873i 0.173047 + 0.0367823i
\(621\) −6.20169 2.76117i −0.248865 0.110802i
\(622\) −18.2468 + 13.2571i −0.731629 + 0.531560i
\(623\) −8.82686 3.33169i −0.353641 0.133481i
\(624\) 3.27208 10.0704i 0.130988 0.403140i
\(625\) 1.09110 10.3811i 0.0436439 0.415244i
\(626\) −5.75600 + 9.96969i −0.230056 + 0.398469i
\(627\) 0.972713 + 3.33843i 0.0388464 + 0.133324i
\(628\) −6.19449 10.7292i −0.247187 0.428141i
\(629\) −4.17470 3.03310i −0.166456 0.120937i
\(630\) 17.0991 0.992228i 0.681243 0.0395313i
\(631\) 0.304170 + 0.936140i 0.0121088 + 0.0372672i 0.956928 0.290324i \(-0.0937631\pi\)
−0.944820 + 0.327591i \(0.893763\pi\)
\(632\) 5.14496 + 2.29069i 0.204656 + 0.0911186i
\(633\) −1.31259 12.4885i −0.0521708 0.496372i
\(634\) 1.20139 + 0.255363i 0.0477132 + 0.0101418i
\(635\) 37.1681 7.90032i 1.47497 0.313515i
\(636\) −14.6126 10.6167i −0.579426 0.420978i
\(637\) −11.4187 + 10.5156i −0.452427 + 0.416642i
\(638\) −2.36634 1.14167i −0.0936844 0.0451992i
\(639\) 8.12038 + 14.0649i 0.321237 + 0.556399i
\(640\) 24.0060 10.6882i 0.948921 0.422487i
\(641\) 4.85014 + 5.38662i 0.191569 + 0.212759i 0.831276 0.555860i \(-0.187611\pi\)
−0.639707 + 0.768619i \(0.720944\pi\)
\(642\) −20.3929 + 22.6487i −0.804845 + 0.893871i
\(643\) 8.05300 5.85085i 0.317579 0.230735i −0.417563 0.908648i \(-0.637116\pi\)
0.735142 + 0.677913i \(0.237116\pi\)
\(644\) −22.2907 14.2988i −0.878377 0.563453i
\(645\) 3.24271 + 9.98004i 0.127682 + 0.392964i
\(646\) 9.59434 2.03934i 0.377484 0.0802367i
\(647\) −4.29378 + 1.91172i −0.168806 + 0.0751573i −0.489400 0.872059i \(-0.662784\pi\)
0.320594 + 0.947217i \(0.396118\pi\)
\(648\) −0.489800 + 0.848359i −0.0192412 + 0.0333267i
\(649\) 2.28516 + 2.69986i 0.0897002 + 0.105979i
\(650\) −29.1910 −1.14497
\(651\) 2.19506 0.601368i 0.0860313 0.0235695i
\(652\) 0.0420647 0.129462i 0.00164738 0.00507011i
\(653\) 5.78504 6.42494i 0.226386 0.251427i −0.619241 0.785201i \(-0.712560\pi\)
0.845628 + 0.533773i \(0.179226\pi\)
\(654\) −0.433038 4.12008i −0.0169331 0.161108i
\(655\) −5.45338 51.8854i −0.213081 2.02733i
\(656\) −20.9354 + 23.2511i −0.817388 + 0.907802i
\(657\) 1.57411 4.84462i 0.0614120 0.189007i
\(658\) 11.4582 + 11.3305i 0.446687 + 0.441708i
\(659\) −4.04586 −0.157604 −0.0788022 0.996890i \(-0.525110\pi\)
−0.0788022 + 0.996890i \(0.525110\pi\)
\(660\) 8.93859 14.4415i 0.347934 0.562134i
\(661\) 8.32331 14.4164i 0.323739 0.560732i −0.657517 0.753439i \(-0.728393\pi\)
0.981256 + 0.192707i \(0.0617267\pi\)
\(662\) −13.3304 + 5.93507i −0.518100 + 0.230673i
\(663\) 10.8871 2.31411i 0.422818 0.0898727i
\(664\) 4.18747 + 12.8877i 0.162505 + 0.500140i
\(665\) −8.55915 + 4.42169i −0.331910 + 0.171466i
\(666\) 1.55039 1.12643i 0.0600765 0.0436482i
\(667\) −1.93050 + 2.14403i −0.0747491 + 0.0830173i
\(668\) 8.18444 + 9.08974i 0.316665 + 0.351693i
\(669\) −21.4648 + 9.55675i −0.829878 + 0.369485i
\(670\) 44.4267 + 76.9494i 1.71635 + 2.97281i
\(671\) 11.3431 + 21.1155i 0.437896 + 0.815154i
\(672\) −11.4770 + 14.3365i −0.442736 + 0.553041i
\(673\) −3.01328 2.18928i −0.116154 0.0843905i 0.528192 0.849125i \(-0.322870\pi\)
−0.644346 + 0.764734i \(0.722870\pi\)
\(674\) −14.8662 + 3.15992i −0.572627 + 0.121716i
\(675\) 6.90766 + 1.46827i 0.265876 + 0.0565137i
\(676\) 1.24568 + 11.8518i 0.0479106 + 0.455839i
\(677\) 22.3019 + 9.92944i 0.857131 + 0.381619i 0.787768 0.615972i \(-0.211237\pi\)
0.0693630 + 0.997591i \(0.477903\pi\)
\(678\) −1.06629 3.28171i −0.0409507 0.126033i
\(679\) −48.3169 + 2.80374i −1.85423 + 0.107598i
\(680\) 13.8147 + 10.0370i 0.529771 + 0.384901i
\(681\) −11.3049 19.5806i −0.433204 0.750332i
\(682\) 1.79755 5.00506i 0.0688316 0.191654i
\(683\) 6.37357 11.0394i 0.243878 0.422409i −0.717938 0.696108i \(-0.754914\pi\)
0.961816 + 0.273698i \(0.0882470\pi\)
\(684\) −0.161587 + 1.53740i −0.00617845 + 0.0587840i
\(685\) −21.8933 + 67.3805i −0.836498 + 2.57448i
\(686\) 32.0162 12.9114i 1.22238 0.492960i
\(687\) −11.9687 + 8.69576i −0.456634 + 0.331764i
\(688\) −13.1798 5.86804i −0.502477 0.223717i
\(689\) 26.5717 + 5.64799i 1.01230 + 0.215171i
\(690\) −29.4065 32.6593i −1.11949 1.24332i
\(691\) −1.74662 + 16.6180i −0.0664445 + 0.632177i 0.909731 + 0.415197i \(0.136287\pi\)
−0.976176 + 0.216980i \(0.930379\pi\)
\(692\) 5.41829 0.205973
\(693\) 0.678474 8.74870i 0.0257731 0.332335i
\(694\) 26.6360 1.01109
\(695\) −3.23631 + 30.7914i −0.122760 + 1.16798i
\(696\) 0.278572 + 0.309386i 0.0105593 + 0.0117272i
\(697\) −32.1690 6.83773i −1.21849 0.258998i
\(698\) −47.1564 20.9954i −1.78490 0.794688i
\(699\) −2.50040 + 1.81664i −0.0945737 + 0.0687118i
\(700\) 25.7743 + 9.72848i 0.974178 + 0.367702i
\(701\) −7.93645 + 24.4259i −0.299756 + 0.922553i 0.681827 + 0.731514i \(0.261186\pi\)
−0.981582 + 0.191039i \(0.938814\pi\)
\(702\) −0.432073 + 4.11090i −0.0163075 + 0.155156i
\(703\) −0.538953 + 0.933493i −0.0203270 + 0.0352074i
\(704\) 3.14374 + 10.7896i 0.118484 + 0.406647i
\(705\) 5.67411 + 9.82784i 0.213699 + 0.370138i
\(706\) −20.3143 14.7592i −0.764540 0.555470i
\(707\) 19.1131 38.0370i 0.718822 1.43053i
\(708\) 0.485925 + 1.49552i 0.0182622 + 0.0562052i
\(709\) −39.3767 17.5316i −1.47882 0.658414i −0.500545 0.865711i \(-0.666867\pi\)
−0.978278 + 0.207296i \(0.933534\pi\)
\(710\) 10.9899 + 104.562i 0.412444 + 3.92414i
\(711\) −5.62351 1.19531i −0.210898 0.0448278i
\(712\) 3.41690 0.726284i 0.128054 0.0272187i
\(713\) −4.72444 3.43251i −0.176932 0.128549i
\(714\) −24.4691 3.73510i −0.915733 0.139783i
\(715\) −3.44705 + 25.3101i −0.128912 + 0.946544i
\(716\) 13.3164 + 23.0646i 0.497656 + 0.861966i
\(717\) 20.3700 9.06933i 0.760733 0.338700i
\(718\) 16.3309 + 18.1373i 0.609465 + 0.676879i
\(719\) −20.7502 + 23.0455i −0.773854 + 0.859451i −0.993227 0.116189i \(-0.962932\pi\)
0.219373 + 0.975641i \(0.429599\pi\)
\(720\) −13.4162 + 9.74745i −0.499993 + 0.363266i
\(721\) −1.54412 + 33.0007i −0.0575061 + 1.22901i
\(722\) 10.3109 + 31.7338i 0.383734 + 1.18101i
\(723\) 5.21025 1.10747i 0.193771 0.0411874i
\(724\) 3.62962 1.61601i 0.134894 0.0600585i
\(725\) 1.50064 2.59918i 0.0557322 0.0965310i
\(726\) −15.8188 13.0451i −0.587090 0.484151i
\(727\) 3.36801 0.124913 0.0624563 0.998048i \(-0.480107\pi\)
0.0624563 + 0.998048i \(0.480107\pi\)
\(728\) 1.45642 5.55988i 0.0539787 0.206063i
\(729\) 0.309017 0.951057i 0.0114451 0.0352243i
\(730\) 22.0657 24.5064i 0.816688 0.907024i
\(731\) −1.58518 15.0820i −0.0586300 0.557827i
\(732\) 1.11385 + 10.5976i 0.0411692 + 0.391699i
\(733\) −6.82826 + 7.58355i −0.252207 + 0.280105i −0.855932 0.517088i \(-0.827016\pi\)
0.603725 + 0.797193i \(0.293683\pi\)
\(734\) 11.2861 34.7351i 0.416579 1.28210i
\(735\) 24.1481 2.81201i 0.890715 0.103723i
\(736\) 47.1206 1.73689
\(737\) 42.1338 17.2326i 1.55202 0.634772i
\(738\) 6.10689 10.5774i 0.224798 0.389361i
\(739\) 20.6291 9.18465i 0.758853 0.337863i 0.00943060 0.999956i \(-0.496998\pi\)
0.749422 + 0.662093i \(0.230331\pi\)
\(740\) 5.14977 1.09462i 0.189309 0.0402389i
\(741\) −0.718458 2.21119i −0.0263932 0.0812299i
\(742\) −50.8500 32.6187i −1.86676 1.19747i
\(743\) −20.2308 + 14.6985i −0.742194 + 0.539236i −0.893398 0.449267i \(-0.851685\pi\)
0.151203 + 0.988503i \(0.451685\pi\)
\(744\) −0.563862 + 0.626233i −0.0206722 + 0.0229588i
\(745\) 53.8283 + 59.7824i 1.97212 + 2.19026i
\(746\) −25.8037 + 11.4885i −0.944740 + 0.420625i
\(747\) −6.91657 11.9799i −0.253064 0.438320i
\(748\) −16.9746 + 17.7285i −0.620655 + 0.648219i
\(749\) −27.0348 + 33.7704i −0.987831 + 1.23394i
\(750\) 10.7993 + 7.84616i 0.394335 + 0.286501i
\(751\) 21.6854 4.60937i 0.791310 0.168198i 0.205511 0.978655i \(-0.434114\pi\)
0.585799 + 0.810457i \(0.300781\pi\)
\(752\) −15.2611 3.24385i −0.556515 0.118291i
\(753\) 2.20233 + 20.9538i 0.0802574 + 0.763599i
\(754\) 1.60484 + 0.714520i 0.0584448 + 0.0260213i
\(755\) −3.96637 12.2072i −0.144351 0.444266i
\(756\) 1.75154 3.48574i 0.0637028 0.126775i
\(757\) 34.0443 + 24.7347i 1.23736 + 0.898996i 0.997420 0.0717908i \(-0.0228714\pi\)
0.239943 + 0.970787i \(0.422871\pi\)
\(758\) 10.7090 + 18.5485i 0.388968 + 0.673712i
\(759\) −18.6121 + 12.6699i −0.675575 + 0.459887i
\(760\) 1.78348 3.08908i 0.0646936 0.112053i
\(761\) 4.27124 40.6382i 0.154832 1.47313i −0.590823 0.806801i \(-0.701197\pi\)
0.745656 0.666331i \(-0.232136\pi\)
\(762\) 6.30206 19.3957i 0.228300 0.702634i
\(763\) −0.952404 5.80262i −0.0344793 0.210069i
\(764\) −13.6126 + 9.89014i −0.492487 + 0.357813i
\(765\) −15.9245 7.09006i −0.575752 0.256341i
\(766\) −5.71521 1.21481i −0.206499 0.0438927i
\(767\) −1.58250 1.75754i −0.0571407 0.0634612i
\(768\) 2.18259 20.7659i 0.0787573 0.749326i
\(769\) −3.87395 −0.139698 −0.0698490 0.997558i \(-0.522252\pi\)
−0.0698490 + 0.997558i \(0.522252\pi\)
\(770\) 27.0487 49.9535i 0.974766 1.80020i
\(771\) 4.45684 0.160509
\(772\) −0.750726 + 7.14268i −0.0270192 + 0.257071i
\(773\) −8.39256 9.32088i −0.301859 0.335249i 0.573064 0.819511i \(-0.305755\pi\)
−0.874923 + 0.484262i \(0.839088\pi\)
\(774\) 5.50890 + 1.17095i 0.198013 + 0.0420890i
\(775\) 5.54971 + 2.47089i 0.199352 + 0.0887570i
\(776\) 14.4973 10.5329i 0.520422 0.378109i
\(777\) 2.10431 1.72365i 0.0754918 0.0618356i
\(778\) 12.7296 39.1778i 0.456379 1.40459i
\(779\) −0.718093 + 6.83220i −0.0257284 + 0.244789i
\(780\) −5.67795 + 9.83450i −0.203303 + 0.352132i
\(781\) 53.8392 + 1.65015i 1.92652 + 0.0590470i
\(782\) 31.7556 + 55.0023i 1.13558 + 1.96688i
\(783\) −0.343824 0.249803i −0.0122873 0.00892722i
\(784\) −19.3420 + 27.2592i −0.690785 + 0.973544i
\(785\) −9.01767 27.7535i −0.321854 0.990566i
\(786\) −25.5797 11.3888i −0.912397 0.406225i
\(787\) −1.32147 12.5730i −0.0471055 0.448179i −0.992499 0.122249i \(-0.960989\pi\)
0.945394 0.325930i \(-0.105677\pi\)
\(788\) 5.91506 + 1.25729i 0.210715 + 0.0447889i
\(789\) −14.6181 + 3.10716i −0.520417 + 0.110618i
\(790\) −30.1102 21.8764i −1.07127 0.778326i
\(791\) −1.78080 4.56256i −0.0633179 0.162226i
\(792\) 1.53752 + 2.86213i 0.0546335 + 0.101701i
\(793\) −8.01325 13.8794i −0.284559 0.492871i
\(794\) −44.7092 + 19.9058i −1.58667 + 0.706431i
\(795\) −28.4679 31.6169i −1.00965 1.12133i
\(796\) 1.63723 1.81833i 0.0580300 0.0644488i
\(797\) −25.3544 + 18.4211i −0.898100 + 0.652508i −0.937977 0.346697i \(-0.887303\pi\)
0.0398776 + 0.999205i \(0.487303\pi\)
\(798\) −0.241667 + 5.16485i −0.00855490 + 0.182834i
\(799\) −5.06789 15.5974i −0.179289 0.551795i
\(800\) −47.9471 + 10.1915i −1.69519 + 0.360323i
\(801\) −3.25769 + 1.45041i −0.115105 + 0.0512479i
\(802\) 20.0679 34.7586i 0.708622 1.22737i
\(803\) −10.9148 12.8956i −0.385175 0.455077i
\(804\) 20.2374 0.713718
\(805\) −44.3550 43.8607i −1.56331 1.54589i
\(806\) −1.09880 + 3.38176i −0.0387036 + 0.119117i
\(807\) 9.96777 11.0703i 0.350882 0.389694i
\(808\) 1.64751 + 15.6750i 0.0579592 + 0.551445i
\(809\) −3.23013 30.7326i −0.113565 1.08050i −0.891769 0.452490i \(-0.850536\pi\)
0.778204 0.628011i \(-0.216131\pi\)
\(810\) 4.33176 4.81090i 0.152202 0.169038i
\(811\) 15.6393 48.1327i 0.549169 1.69017i −0.161698 0.986840i \(-0.551697\pi\)
0.710867 0.703327i \(-0.248303\pi\)
\(812\) −1.17887 1.16573i −0.0413702 0.0409092i
\(813\) −22.6592 −0.794691
\(814\) −0.470417 6.33852i −0.0164881 0.222165i
\(815\) 0.160318 0.277678i 0.00561568 0.00972664i
\(816\) 21.8938 9.74773i 0.766435 0.341239i
\(817\) −3.09857 + 0.658621i −0.108405 + 0.0230422i
\(818\) 6.45630 + 19.8705i 0.225739 + 0.694754i
\(819\) −0.274228 + 5.86075i −0.00958230 + 0.204791i
\(820\) 27.1461 19.7228i 0.947981 0.688749i
\(821\) 14.6550 16.2761i 0.511464 0.568039i −0.430997 0.902353i \(-0.641838\pi\)
0.942462 + 0.334315i \(0.108505\pi\)
\(822\) 25.4433 + 28.2576i 0.887437 + 0.985598i
\(823\) −35.6816 + 15.8865i −1.24378 + 0.553768i −0.919834 0.392307i \(-0.871677\pi\)
−0.323948 + 0.946075i \(0.605010\pi\)
\(824\) −6.11600 10.5932i −0.213061 0.369033i
\(825\) 16.1982 16.9176i 0.563950 0.588996i
\(826\) 1.91233 + 4.89954i 0.0665384 + 0.170477i
\(827\) 12.3679 + 8.98580i 0.430074 + 0.312467i 0.781678 0.623682i \(-0.214364\pi\)
−0.351605 + 0.936149i \(0.614364\pi\)
\(828\) −9.79078 + 2.08109i −0.340253 + 0.0723230i
\(829\) −25.7848 5.48073i −0.895544 0.190354i −0.262924 0.964816i \(-0.584687\pi\)
−0.632619 + 0.774463i \(0.718020\pi\)
\(830\) −9.36071 89.0612i −0.324915 3.09136i
\(831\) 13.2626 + 5.90490i 0.460076 + 0.204839i
\(832\) −2.32200 7.14639i −0.0805010 0.247756i
\(833\) −34.9803 3.28068i −1.21199 0.113669i
\(834\) 13.4433 + 9.76715i 0.465505 + 0.338209i
\(835\) 14.4054 + 24.9508i 0.498518 + 0.863459i
\(836\) 4.05362 + 3.13927i 0.140197 + 0.108574i
\(837\) 0.430114 0.744979i 0.0148669 0.0257502i
\(838\) 4.37155 41.5925i 0.151013 1.43679i
\(839\) 3.06478 9.43243i 0.105808 0.325644i −0.884111 0.467277i \(-0.845235\pi\)
0.989919 + 0.141633i \(0.0452352\pi\)
\(840\) −6.96351 + 5.70384i −0.240264 + 0.196801i
\(841\) 23.3154 16.9396i 0.803978 0.584124i
\(842\) 21.4874 + 9.56680i 0.740504 + 0.329694i
\(843\) 1.47519 + 0.313562i 0.0508083 + 0.0107996i
\(844\) −12.3891 13.7595i −0.426449 0.473620i
\(845\) −2.93414 + 27.9165i −0.100938 + 0.960357i
\(846\) 6.09062 0.209400
\(847\) −23.4882 17.1845i −0.807063 0.590465i
\(848\) 58.4923 2.00864
\(849\) 1.43493 13.6524i 0.0492466 0.468550i
\(850\) −44.2088 49.0988i −1.51635 1.68408i
\(851\) −6.82692 1.45111i −0.234024 0.0497433i
\(852\) 21.8761 + 9.73986i 0.749463 + 0.333682i
\(853\) 21.1701 15.3810i 0.724850 0.526635i −0.163080 0.986613i \(-0.552143\pi\)
0.887930 + 0.459978i \(0.152143\pi\)
\(854\) 5.77268 + 35.1706i 0.197537 + 1.20351i
\(855\) −1.12521 + 3.46303i −0.0384812 + 0.118433i
\(856\) 1.67420 15.9290i 0.0572231 0.544442i
\(857\) −21.7863 + 37.7349i −0.744204 + 1.28900i 0.206361 + 0.978476i \(0.433838\pi\)
−0.950566 + 0.310524i \(0.899496\pi\)
\(858\) 10.8391 + 8.39419i 0.370040 + 0.286573i
\(859\) −10.1360 17.5560i −0.345834 0.599002i 0.639671 0.768649i \(-0.279071\pi\)
−0.985505 + 0.169647i \(0.945737\pi\)
\(860\) 12.5175 + 9.09448i 0.426843 + 0.310119i
\(861\) 7.78382 15.4906i 0.265272 0.527918i
\(862\) −21.6380 66.5948i −0.736992 2.26823i
\(863\) 15.1628 + 6.75091i 0.516147 + 0.229804i 0.648243 0.761433i \(-0.275504\pi\)
−0.132096 + 0.991237i \(0.542171\pi\)
\(864\) 0.725547 + 6.90312i 0.0246836 + 0.234849i
\(865\) 12.4837 + 2.65349i 0.424458 + 0.0902214i
\(866\) 43.6939 9.28743i 1.48478 0.315600i
\(867\) 6.62705 + 4.81484i 0.225067 + 0.163520i
\(868\) 2.09723 2.61974i 0.0711845 0.0889197i
\(869\) −13.1869 + 13.7726i −0.447336 + 0.467203i
\(870\) −1.37563 2.38266i −0.0466382 0.0807798i
\(871\) −27.8055 + 12.3798i −0.942153 + 0.419473i
\(872\) 1.45682 + 1.61797i 0.0493343 + 0.0547913i
\(873\) −12.2403 + 13.5942i −0.414270 + 0.460094i
\(874\) 10.7330 7.79798i 0.363049 0.263771i
\(875\) 15.9480 + 10.2302i 0.539141 + 0.345843i
\(876\) −2.32097 7.14321i −0.0784183 0.241347i
\(877\) 30.5726 6.49840i 1.03236 0.219435i 0.339576 0.940579i \(-0.389716\pi\)
0.692786 + 0.721143i \(0.256383\pi\)
\(878\) −0.710516 + 0.316342i −0.0239787 + 0.0106760i
\(879\) −1.15902 + 2.00749i −0.0390929 + 0.0677109i
\(880\) 4.07072 + 54.8499i 0.137224 + 1.84899i
\(881\) −12.5333 −0.422257 −0.211129 0.977458i \(-0.567714\pi\)
−0.211129 + 0.977458i \(0.567714\pi\)
\(882\) 5.17316 11.9786i 0.174189 0.403341i
\(883\) −6.28545 + 19.3446i −0.211522 + 0.650999i 0.787860 + 0.615854i \(0.211189\pi\)
−0.999382 + 0.0351443i \(0.988811\pi\)
\(884\) 10.9812 12.1959i 0.369338 0.410191i
\(885\) 0.387166 + 3.68364i 0.0130144 + 0.123824i
\(886\) 1.83364 + 17.4459i 0.0616024 + 0.586108i
\(887\) −28.2392 + 31.3628i −0.948178 + 1.05306i 0.0503448 + 0.998732i \(0.483968\pi\)
−0.998523 + 0.0543269i \(0.982699\pi\)
\(888\) −0.311223 + 0.957846i −0.0104440 + 0.0321432i
\(889\) 7.33528 28.0023i 0.246017 0.939168i
\(890\) −23.0851 −0.773815
\(891\) −2.14271 2.53156i −0.0717834 0.0848106i
\(892\) −17.3221 + 30.0027i −0.579986 + 1.00457i
\(893\) −3.12960 + 1.39339i −0.104728 + 0.0466279i
\(894\) 42.2317 8.97662i 1.41244 0.300223i
\(895\) 19.3854 + 59.6621i 0.647982 + 1.99428i
\(896\) 0.935650 19.9965i 0.0312579 0.668037i
\(897\) 12.1791 8.84866i 0.406649 0.295448i
\(898\) 22.3030 24.7699i 0.744259 0.826584i
\(899\) −0.244626 0.271685i −0.00815874 0.00906120i
\(900\) 9.51240 4.23519i 0.317080 0.141173i
\(901\) 30.7420 + 53.2468i 1.02417 + 1.77391i
\(902\) −19.1700 35.6854i −0.638292 1.18820i
\(903\) 7.90249 + 1.20628i 0.262979 + 0.0401425i
\(904\) 1.46709 + 1.06590i 0.0487946 + 0.0354514i
\(905\) 9.15401 1.94574i 0.304290 0.0646787i
\(906\) −6.73829 1.43227i −0.223865 0.0475839i
\(907\) 0.160512 + 1.52717i 0.00532972 + 0.0507089i 0.996864 0.0791400i \(-0.0252174\pi\)
−0.991534 + 0.129849i \(0.958551\pi\)
\(908\) −30.4551 13.5595i −1.01069 0.449987i
\(909\) −4.97196 15.3021i −0.164909 0.507539i
\(910\) −17.0537 + 33.9386i −0.565324 + 1.12505i
\(911\) −21.1533 15.3688i −0.700839 0.509190i 0.179366 0.983782i \(-0.442595\pi\)
−0.880205 + 0.474593i \(0.842595\pi\)
\(912\) −2.50307 4.33544i −0.0828849 0.143561i
\(913\) −45.8578 1.40552i −1.51767 0.0465160i
\(914\) 25.8287 44.7365i 0.854336 1.47975i
\(915\) −2.62364 + 24.9622i −0.0867348 + 0.825226i
\(916\) −6.74069 + 20.7457i −0.222719 + 0.685458i
\(917\) −37.1833 14.0348i −1.22790 0.463470i
\(918\) −7.56882 + 5.49907i −0.249808 + 0.181496i
\(919\) 32.5798 + 14.5055i 1.07471 + 0.478491i 0.866286 0.499548i \(-0.166501\pi\)
0.208422 + 0.978039i \(0.433167\pi\)
\(920\) 22.5914 + 4.80194i 0.744815 + 0.158315i
\(921\) 13.2937 + 14.7641i 0.438041 + 0.486494i
\(922\) 6.06709 57.7245i 0.199809 1.90105i
\(923\) −36.0152 −1.18545
\(924\) −6.77287 11.0240i −0.222811 0.362663i
\(925\) 7.26051 0.238724
\(926\) 2.87611 27.3644i 0.0945148 0.899249i
\(927\) 8.35526 + 9.27945i 0.274423 + 0.304777i
\(928\) 2.88545 + 0.613322i 0.0947196 + 0.0201333i
\(929\) 45.3178 + 20.1768i 1.48683 + 0.661979i 0.979806 0.199952i \(-0.0640787\pi\)
0.507024 + 0.861932i \(0.330745\pi\)
\(930\) 4.50531 3.27330i 0.147735 0.107336i
\(931\) 0.0822447 + 7.33856i 0.00269546 + 0.240511i
\(932\) −1.40821 + 4.33402i −0.0461274 + 0.141966i
\(933\) −1.26479 + 12.0337i −0.0414075 + 0.393966i
\(934\) 21.8168 37.7878i 0.713867 1.23645i
\(935\) −47.7916 + 32.5334i −1.56295 + 1.06395i
\(936\) −1.08617 1.88130i −0.0355026 0.0614923i
\(937\) 38.6661 + 28.0926i 1.26317 + 0.917744i 0.998909 0.0467082i \(-0.0148731\pi\)
0.264258 + 0.964452i \(0.414873\pi\)
\(938\) 67.5747 3.92124i 2.20639 0.128033i
\(939\) 1.90849 + 5.87372i 0.0622812 + 0.191682i
\(940\) 15.2859 + 6.80572i 0.498571 + 0.221978i
\(941\) 0.536830 + 5.10760i 0.0175002 + 0.166503i 0.999781 0.0209101i \(-0.00665638\pi\)
−0.982281 + 0.187413i \(0.939990\pi\)
\(942\) −15.3197 3.25631i −0.499143 0.106096i
\(943\) −43.5101 + 9.24836i −1.41688 + 0.301168i
\(944\) −4.11978 2.99320i −0.134087 0.0974202i
\(945\) 5.74259 7.17332i 0.186806 0.233348i
\(946\) 12.9182 13.4919i 0.420006 0.438659i
\(947\) −20.0586 34.7425i −0.651816 1.12898i −0.982682 0.185301i \(-0.940674\pi\)
0.330866 0.943678i \(-0.392659\pi\)
\(948\) −7.74403 + 3.44786i −0.251514 + 0.111981i
\(949\) 7.55864 + 8.39472i 0.245364 + 0.272504i
\(950\) −9.23467 + 10.2561i −0.299612 + 0.332753i
\(951\) 0.533080 0.387306i 0.0172863 0.0125592i
\(952\) 11.5573 5.97056i 0.374575 0.193507i
\(953\) −8.91613 27.4410i −0.288822 0.888902i −0.985227 0.171253i \(-0.945218\pi\)
0.696405 0.717649i \(-0.254782\pi\)
\(954\) −22.3349 + 4.74743i −0.723119 + 0.153704i
\(955\) −36.2068 + 16.1203i −1.17162 + 0.521641i
\(956\) 16.4386 28.4725i 0.531663 0.920867i
\(957\) −1.30463 + 0.533591i −0.0421727 + 0.0172485i
\(958\) −16.2671 −0.525567
\(959\) 38.3771 + 37.9494i 1.23926 + 1.22545i
\(960\) −3.63658 + 11.1922i −0.117370 + 0.361228i
\(961\) −20.2479 + 22.4876i −0.653158 + 0.725405i
\(962\) 0.444220 + 4.22647i 0.0143222 + 0.136267i
\(963\) 1.70907 + 16.2607i 0.0550740 + 0.523994i
\(964\) 5.25531 5.83661i 0.169262 0.187985i
\(965\) −5.22764 + 16.0890i −0.168284 + 0.517924i
\(966\) −32.2892 + 8.84607i −1.03889 + 0.284618i
\(967\) −35.8128 −1.15166 −0.575831 0.817569i \(-0.695321\pi\)
−0.575831 + 0.817569i \(0.695321\pi\)
\(968\) 10.7554 + 0.659915i 0.345691 + 0.0212105i
\(969\) 2.63110 4.55719i 0.0845230 0.146398i
\(970\) −108.184 + 48.1666i −3.47358 + 1.54654i
\(971\) −36.5795 + 7.77522i −1.17389 + 0.249519i −0.753267 0.657715i \(-0.771523\pi\)
−0.420627 + 0.907234i \(0.638190\pi\)
\(972\) −0.455633 1.40230i −0.0146144 0.0449787i
\(973\) 19.8526 + 12.7348i 0.636444 + 0.408260i
\(974\) 4.83693 3.51423i 0.154985 0.112603i
\(975\) −10.4789 + 11.6380i −0.335594 + 0.372715i
\(976\) −23.0905 25.6446i −0.739110 0.820865i
\(977\) 24.1227 10.7401i 0.771754 0.343607i 0.0172060 0.999852i \(-0.494523\pi\)
0.754548 + 0.656245i \(0.227856\pi\)
\(978\) −0.0860430 0.149031i −0.00275135 0.00476548i
\(979\) −1.59602 + 11.7188i −0.0510090 + 0.374536i
\(980\) 26.3683 24.2827i 0.842304 0.775682i
\(981\) −1.79806 1.30637i −0.0574077 0.0417092i
\(982\) −8.09526 + 1.72070i −0.258330 + 0.0549098i
\(983\) 43.4165 + 9.22847i 1.38477 + 0.294342i 0.839246 0.543752i \(-0.182997\pi\)
0.545526 + 0.838094i \(0.316330\pi\)
\(984\) 0.670949 + 6.38366i 0.0213891 + 0.203504i
\(985\) 13.0125 + 5.79355i 0.414613 + 0.184598i
\(986\) 1.22866 + 3.78142i 0.0391285 + 0.120425i
\(987\) 8.63052 0.500814i 0.274713 0.0159411i
\(988\) −2.77338 2.01498i −0.0882330 0.0641051i
\(989\) −10.2557 17.7634i −0.326113 0.564844i
\(990\) −6.00618 20.6137i −0.190889 0.655146i
\(991\) −9.41079 + 16.3000i −0.298944 + 0.517786i −0.975895 0.218243i \(-0.929968\pi\)
0.676951 + 0.736028i \(0.263301\pi\)
\(992\) −0.624136 + 5.93826i −0.0198163 + 0.188540i
\(993\) −2.41909 + 7.44518i −0.0767673 + 0.236266i
\(994\) 74.9337 + 28.2836i 2.37675 + 0.897102i
\(995\) 4.66264 3.38761i 0.147816 0.107394i
\(996\) −18.6331 8.29597i −0.590411 0.262868i
\(997\) −5.10426 1.08494i −0.161653 0.0343605i 0.126374 0.991983i \(-0.459666\pi\)
−0.288027 + 0.957622i \(0.592999\pi\)
\(998\) 8.05603 + 8.94713i 0.255009 + 0.283216i
\(999\) 0.107467 1.02248i 0.00340011 0.0323498i
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 231.2.y.a.4.7 64
3.2 odd 2 693.2.by.d.235.2 64
7.2 even 3 inner 231.2.y.a.37.2 yes 64
11.3 even 5 inner 231.2.y.a.25.2 yes 64
21.2 odd 6 693.2.by.d.37.7 64
33.14 odd 10 693.2.by.d.487.7 64
77.58 even 15 inner 231.2.y.a.58.7 yes 64
231.212 odd 30 693.2.by.d.289.2 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
231.2.y.a.4.7 64 1.1 even 1 trivial
231.2.y.a.25.2 yes 64 11.3 even 5 inner
231.2.y.a.37.2 yes 64 7.2 even 3 inner
231.2.y.a.58.7 yes 64 77.58 even 15 inner
693.2.by.d.37.7 64 21.2 odd 6
693.2.by.d.235.2 64 3.2 odd 2
693.2.by.d.289.2 64 231.212 odd 30
693.2.by.d.487.7 64 33.14 odd 10