Properties

Label 462.2.ba.a.73.2
Level $462$
Weight $2$
Character 462.73
Analytic conductor $3.689$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [462,2,Mod(19,462)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(462, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([0, 25, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("462.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.ba (of order \(30\), 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: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(8\) over \(\Q(\zeta_{30})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label 73.2
Character \(\chi\) \(=\) 462.73
Dual form 462.2.ba.a.19.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.994522 - 0.104528i) q^{2} +(0.743145 - 0.669131i) q^{3} +(0.978148 + 0.207912i) q^{4} +(-0.716911 + 1.61021i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(1.87226 - 1.86939i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(0.104528 - 0.994522i) q^{9} +O(q^{10})\) \(q+(-0.994522 - 0.104528i) q^{2} +(0.743145 - 0.669131i) q^{3} +(0.978148 + 0.207912i) q^{4} +(-0.716911 + 1.61021i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(1.87226 - 1.86939i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(0.104528 - 0.994522i) q^{9} +(0.881296 - 1.52645i) q^{10} +(3.30708 + 0.251417i) q^{11} +(0.866025 - 0.500000i) q^{12} +(-4.51584 - 3.28095i) q^{13} +(-2.05741 + 1.66345i) q^{14} +(0.544671 + 1.67633i) q^{15} +(0.913545 + 0.406737i) q^{16} +(0.164901 + 1.56893i) q^{17} +(-0.207912 + 0.978148i) q^{18} +(8.01319 - 1.70326i) q^{19} +(-1.03603 + 1.42597i) q^{20} +(0.140496 - 2.64202i) q^{21} +(-3.26268 - 0.595724i) q^{22} +(1.59448 + 2.76172i) q^{23} +(-0.913545 + 0.406737i) q^{24} +(1.26684 + 1.40697i) q^{25} +(4.14815 + 3.73501i) q^{26} +(-0.587785 - 0.809017i) q^{27} +(2.22002 - 1.43928i) q^{28} +(3.68375 - 1.19692i) q^{29} +(-0.366464 - 1.72408i) q^{30} +(-2.22993 - 5.00850i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(2.62587 - 2.02603i) q^{33} -1.57757i q^{34} +(1.66786 + 4.35492i) q^{35} +(0.309017 - 0.951057i) q^{36} +(0.688318 - 0.764454i) q^{37} +(-8.14734 + 0.856320i) q^{38} +(-5.55130 + 0.583465i) q^{39} +(1.17940 - 1.30986i) q^{40} +(2.03783 - 6.27181i) q^{41} +(-0.415892 + 2.61286i) q^{42} +0.237804i q^{43} +(3.18254 + 0.933504i) q^{44} +(1.52645 + 0.881296i) q^{45} +(-1.29707 - 2.91326i) q^{46} +(0.287918 + 1.35455i) q^{47} +(0.951057 - 0.309017i) q^{48} +(0.0107455 - 6.99999i) q^{49} +(-1.11283 - 1.53168i) q^{50} +(1.17236 + 1.05560i) q^{51} +(-3.73501 - 4.14815i) q^{52} +(-6.91287 + 3.07781i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-2.77572 + 5.14485i) q^{55} +(-2.35830 + 1.19934i) q^{56} +(4.81526 - 6.62764i) q^{57} +(-3.78868 + 0.805309i) q^{58} +(1.40613 - 6.61530i) q^{59} +(0.184241 + 1.75294i) q^{60} +(4.88024 + 2.17282i) q^{61} +(1.69418 + 5.21415i) q^{62} +(-1.66345 - 2.05741i) q^{63} +(0.809017 + 0.587785i) q^{64} +(8.52046 - 4.91929i) q^{65} +(-2.82326 + 1.74045i) q^{66} +(-5.30356 + 9.18603i) q^{67} +(-0.164901 + 1.56893i) q^{68} +(3.03288 + 0.985443i) q^{69} +(-1.20351 - 4.50541i) q^{70} +(0.175328 - 0.127383i) q^{71} +(-0.406737 + 0.913545i) q^{72} +(9.80345 + 2.08379i) q^{73} +(-0.764454 + 0.688318i) q^{74} +(1.88289 + 0.197900i) q^{75} +8.19221 q^{76} +(6.66173 - 5.71151i) q^{77} +5.58188 q^{78} +(1.57504 + 0.165543i) q^{79} +(-1.30986 + 1.17940i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-2.68225 + 6.02444i) q^{82} +(-8.61257 + 6.25740i) q^{83} +(0.686732 - 2.55507i) q^{84} +(-2.64452 - 0.859256i) q^{85} +(0.0248573 - 0.236502i) q^{86} +(1.93666 - 3.35439i) q^{87} +(-3.06753 - 1.26106i) q^{88} +(-6.84058 + 3.94941i) q^{89} +(-1.42597 - 1.03603i) q^{90} +(-14.5882 + 2.29907i) q^{91} +(0.985443 + 3.03288i) q^{92} +(-5.00850 - 2.22993i) q^{93} +(-0.144752 - 1.37722i) q^{94} +(-3.00215 + 14.1240i) q^{95} +(-0.978148 + 0.207912i) q^{96} +(-4.70842 + 6.48058i) q^{97} +(-0.742385 + 6.96052i) q^{98} +(0.595724 - 3.26268i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 8 q^{4} - 22 q^{5} - 16 q^{6} + 4 q^{7} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 8 q^{4} - 22 q^{5} - 16 q^{6} + 4 q^{7} - 8 q^{9} + 2 q^{10} + 4 q^{11} + 2 q^{14} - 6 q^{15} + 8 q^{16} + 30 q^{17} + 10 q^{19} + 20 q^{20} - 4 q^{21} - 2 q^{22} + 4 q^{23} - 8 q^{24} - 12 q^{26} - 10 q^{28} - 20 q^{29} + 18 q^{30} - 16 q^{31} - 14 q^{33} + 42 q^{35} - 16 q^{36} - 14 q^{37} + 12 q^{38} + 18 q^{39} + 18 q^{40} - 28 q^{41} - 6 q^{42} + 6 q^{44} - 12 q^{45} - 42 q^{46} + 24 q^{47} + 116 q^{49} + 26 q^{51} + 32 q^{54} - 14 q^{55} - 4 q^{56} + 20 q^{58} + 30 q^{59} + 2 q^{60} - 32 q^{61} - 8 q^{62} + 4 q^{63} + 16 q^{64} + 12 q^{65} + 4 q^{66} + 16 q^{67} - 30 q^{68} - 20 q^{70} - 24 q^{71} - 64 q^{73} + 4 q^{74} + 12 q^{75} - 48 q^{77} - 60 q^{79} - 18 q^{80} + 8 q^{81} - 68 q^{82} + 8 q^{83} + 2 q^{84} - 80 q^{85} - 18 q^{86} + 10 q^{87} - 8 q^{88} - 24 q^{89} + 4 q^{90} - 172 q^{91} + 8 q^{92} - 104 q^{93} - 6 q^{94} - 118 q^{95} + 8 q^{96} + 120 q^{97} + 40 q^{98} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.994522 0.104528i −0.703233 0.0739128i
\(3\) 0.743145 0.669131i 0.429055 0.386323i
\(4\) 0.978148 + 0.207912i 0.489074 + 0.103956i
\(5\) −0.716911 + 1.61021i −0.320612 + 0.720107i −0.999905 0.0137600i \(-0.995620\pi\)
0.679293 + 0.733867i \(0.262287\pi\)
\(6\) −0.809017 + 0.587785i −0.330280 + 0.239962i
\(7\) 1.87226 1.86939i 0.707649 0.706564i
\(8\) −0.951057 0.309017i −0.336249 0.109254i
\(9\) 0.104528 0.994522i 0.0348428 0.331507i
\(10\) 0.881296 1.52645i 0.278690 0.482706i
\(11\) 3.30708 + 0.251417i 0.997123 + 0.0758050i
\(12\) 0.866025 0.500000i 0.250000 0.144338i
\(13\) −4.51584 3.28095i −1.25247 0.909971i −0.254105 0.967177i \(-0.581781\pi\)
−0.998362 + 0.0572055i \(0.981781\pi\)
\(14\) −2.05741 + 1.66345i −0.549867 + 0.444575i
\(15\) 0.544671 + 1.67633i 0.140633 + 0.432825i
\(16\) 0.913545 + 0.406737i 0.228386 + 0.101684i
\(17\) 0.164901 + 1.56893i 0.0399943 + 0.380520i 0.996150 + 0.0876624i \(0.0279397\pi\)
−0.956156 + 0.292858i \(0.905394\pi\)
\(18\) −0.207912 + 0.978148i −0.0490053 + 0.230552i
\(19\) 8.01319 1.70326i 1.83835 0.390754i 0.848077 0.529873i \(-0.177760\pi\)
0.990276 + 0.139119i \(0.0444269\pi\)
\(20\) −1.03603 + 1.42597i −0.231662 + 0.318856i
\(21\) 0.140496 2.64202i 0.0306587 0.576536i
\(22\) −3.26268 0.595724i −0.695607 0.127009i
\(23\) 1.59448 + 2.76172i 0.332472 + 0.575859i 0.982996 0.183627i \(-0.0587839\pi\)
−0.650524 + 0.759486i \(0.725451\pi\)
\(24\) −0.913545 + 0.406737i −0.186477 + 0.0830248i
\(25\) 1.26684 + 1.40697i 0.253368 + 0.281394i
\(26\) 4.14815 + 3.73501i 0.813518 + 0.732495i
\(27\) −0.587785 0.809017i −0.113119 0.155695i
\(28\) 2.22002 1.43928i 0.419544 0.271998i
\(29\) 3.68375 1.19692i 0.684055 0.222263i 0.0536851 0.998558i \(-0.482903\pi\)
0.630370 + 0.776295i \(0.282903\pi\)
\(30\) −0.366464 1.72408i −0.0669068 0.314772i
\(31\) −2.22993 5.00850i −0.400507 0.899553i −0.995405 0.0957521i \(-0.969474\pi\)
0.594898 0.803801i \(-0.297192\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 2.62587 2.02603i 0.457106 0.352687i
\(34\) 1.57757i 0.270551i
\(35\) 1.66786 + 4.35492i 0.281921 + 0.736117i
\(36\) 0.309017 0.951057i 0.0515028 0.158509i
\(37\) 0.688318 0.764454i 0.113159 0.125675i −0.683904 0.729572i \(-0.739719\pi\)
0.797063 + 0.603896i \(0.206386\pi\)
\(38\) −8.14734 + 0.856320i −1.32167 + 0.138913i
\(39\) −5.55130 + 0.583465i −0.888920 + 0.0934292i
\(40\) 1.17940 1.30986i 0.186480 0.207107i
\(41\) 2.03783 6.27181i 0.318256 0.979492i −0.656137 0.754642i \(-0.727811\pi\)
0.974393 0.224850i \(-0.0721893\pi\)
\(42\) −0.415892 + 2.61286i −0.0641736 + 0.403173i
\(43\) 0.237804i 0.0362648i 0.999836 + 0.0181324i \(0.00577204\pi\)
−0.999836 + 0.0181324i \(0.994228\pi\)
\(44\) 3.18254 + 0.933504i 0.479786 + 0.140731i
\(45\) 1.52645 + 0.881296i 0.227550 + 0.131376i
\(46\) −1.29707 2.91326i −0.191242 0.429537i
\(47\) 0.287918 + 1.35455i 0.0419972 + 0.197581i 0.994145 0.108058i \(-0.0344632\pi\)
−0.952147 + 0.305639i \(0.901130\pi\)
\(48\) 0.951057 0.309017i 0.137273 0.0446028i
\(49\) 0.0107455 6.99999i 0.00153506 0.999999i
\(50\) −1.11283 1.53168i −0.157378 0.216613i
\(51\) 1.17236 + 1.05560i 0.164163 + 0.147813i
\(52\) −3.73501 4.14815i −0.517952 0.575244i
\(53\) −6.91287 + 3.07781i −0.949556 + 0.422770i −0.822271 0.569096i \(-0.807293\pi\)
−0.127286 + 0.991866i \(0.540626\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) −2.77572 + 5.14485i −0.374278 + 0.693731i
\(56\) −2.35830 + 1.19934i −0.315141 + 0.160268i
\(57\) 4.81526 6.62764i 0.637797 0.877852i
\(58\) −3.78868 + 0.805309i −0.497478 + 0.105742i
\(59\) 1.40613 6.61530i 0.183062 0.861239i −0.786728 0.617299i \(-0.788227\pi\)
0.969790 0.243940i \(-0.0784399\pi\)
\(60\) 0.184241 + 1.75294i 0.0237854 + 0.226303i
\(61\) 4.88024 + 2.17282i 0.624851 + 0.278202i 0.694637 0.719360i \(-0.255565\pi\)
−0.0697860 + 0.997562i \(0.522232\pi\)
\(62\) 1.69418 + 5.21415i 0.215161 + 0.662198i
\(63\) −1.66345 2.05741i −0.209575 0.259210i
\(64\) 0.809017 + 0.587785i 0.101127 + 0.0734732i
\(65\) 8.52046 4.91929i 1.05683 0.610163i
\(66\) −2.82326 + 1.74045i −0.347520 + 0.214235i
\(67\) −5.30356 + 9.18603i −0.647933 + 1.12225i 0.335683 + 0.941975i \(0.391033\pi\)
−0.983616 + 0.180277i \(0.942301\pi\)
\(68\) −0.164901 + 1.56893i −0.0199972 + 0.190260i
\(69\) 3.03288 + 0.985443i 0.365116 + 0.118633i
\(70\) −1.20351 4.50541i −0.143848 0.538499i
\(71\) 0.175328 0.127383i 0.0208075 0.0151176i −0.577333 0.816509i \(-0.695906\pi\)
0.598140 + 0.801391i \(0.295906\pi\)
\(72\) −0.406737 + 0.913545i −0.0479344 + 0.107662i
\(73\) 9.80345 + 2.08379i 1.14741 + 0.243889i 0.742098 0.670291i \(-0.233831\pi\)
0.405308 + 0.914180i \(0.367164\pi\)
\(74\) −0.764454 + 0.688318i −0.0888660 + 0.0800153i
\(75\) 1.88289 + 0.197900i 0.217418 + 0.0228515i
\(76\) 8.19221 0.939711
\(77\) 6.66173 5.71151i 0.759174 0.650887i
\(78\) 5.58188 0.632024
\(79\) 1.57504 + 0.165543i 0.177206 + 0.0186251i 0.192716 0.981255i \(-0.438270\pi\)
−0.0155098 + 0.999880i \(0.504937\pi\)
\(80\) −1.30986 + 1.17940i −0.146447 + 0.131861i
\(81\) −0.978148 0.207912i −0.108683 0.0231013i
\(82\) −2.68225 + 6.02444i −0.296205 + 0.665288i
\(83\) −8.61257 + 6.25740i −0.945353 + 0.686839i −0.949703 0.313152i \(-0.898615\pi\)
0.00435058 + 0.999991i \(0.498615\pi\)
\(84\) 0.686732 2.55507i 0.0749286 0.278781i
\(85\) −2.64452 0.859256i −0.286838 0.0931994i
\(86\) 0.0248573 0.236502i 0.00268043 0.0255026i
\(87\) 1.93666 3.35439i 0.207632 0.359629i
\(88\) −3.06753 1.26106i −0.327000 0.134429i
\(89\) −6.84058 + 3.94941i −0.725100 + 0.418637i −0.816627 0.577166i \(-0.804159\pi\)
0.0915270 + 0.995803i \(0.470825\pi\)
\(90\) −1.42597 1.03603i −0.150310 0.109207i
\(91\) −14.5882 + 2.29907i −1.52926 + 0.241008i
\(92\) 0.985443 + 3.03288i 0.102740 + 0.316200i
\(93\) −5.00850 2.22993i −0.519357 0.231233i
\(94\) −0.144752 1.37722i −0.0149300 0.142050i
\(95\) −3.00215 + 14.1240i −0.308014 + 1.44909i
\(96\) −0.978148 + 0.207912i −0.0998318 + 0.0212199i
\(97\) −4.70842 + 6.48058i −0.478068 + 0.658004i −0.978132 0.207985i \(-0.933310\pi\)
0.500065 + 0.865988i \(0.333310\pi\)
\(98\) −0.742385 + 6.96052i −0.0749922 + 0.703119i
\(99\) 0.595724 3.26268i 0.0598725 0.327912i
\(100\) 0.946633 + 1.63962i 0.0946633 + 0.163962i
\(101\) −17.1166 + 7.62082i −1.70317 + 0.758300i −0.704344 + 0.709859i \(0.748759\pi\)
−0.998826 + 0.0484414i \(0.984575\pi\)
\(102\) −1.05560 1.17236i −0.104520 0.116081i
\(103\) −1.21705 1.09584i −0.119920 0.107976i 0.606989 0.794710i \(-0.292377\pi\)
−0.726909 + 0.686734i \(0.759044\pi\)
\(104\) 3.28095 + 4.51584i 0.321723 + 0.442814i
\(105\) 4.15348 + 2.12032i 0.405338 + 0.206922i
\(106\) 7.19672 2.33836i 0.699008 0.227121i
\(107\) 0.390754 + 1.83835i 0.0377756 + 0.177720i 0.992991 0.118192i \(-0.0377098\pi\)
−0.955215 + 0.295912i \(0.904376\pi\)
\(108\) −0.406737 0.913545i −0.0391383 0.0879060i
\(109\) −3.51016 2.02659i −0.336213 0.194112i 0.322383 0.946609i \(-0.395516\pi\)
−0.658596 + 0.752497i \(0.728849\pi\)
\(110\) 3.29829 4.82652i 0.314480 0.460191i
\(111\) 1.02867i 0.0976375i
\(112\) 2.47075 0.946256i 0.233464 0.0894128i
\(113\) −5.52686 + 17.0099i −0.519923 + 1.60016i 0.254219 + 0.967147i \(0.418182\pi\)
−0.774142 + 0.633012i \(0.781818\pi\)
\(114\) −5.48166 + 6.08800i −0.513405 + 0.570194i
\(115\) −5.59005 + 0.587538i −0.521275 + 0.0547882i
\(116\) 3.85210 0.404872i 0.357659 0.0375915i
\(117\) −3.73501 + 4.14815i −0.345302 + 0.383496i
\(118\) −2.08991 + 6.43208i −0.192392 + 0.592121i
\(119\) 3.24168 + 2.62918i 0.297164 + 0.241016i
\(120\) 1.76259i 0.160902i
\(121\) 10.8736 + 1.66291i 0.988507 + 0.151174i
\(122\) −4.62639 2.67105i −0.418853 0.241825i
\(123\) −2.68225 6.02444i −0.241851 0.543206i
\(124\) −1.13987 5.36268i −0.102364 0.481583i
\(125\) −11.5554 + 3.75456i −1.03354 + 0.335818i
\(126\) 1.43928 + 2.22002i 0.128221 + 0.197775i
\(127\) −6.97399 9.59887i −0.618841 0.851762i 0.378427 0.925631i \(-0.376465\pi\)
−0.997268 + 0.0738693i \(0.976465\pi\)
\(128\) −0.743145 0.669131i −0.0656853 0.0591433i
\(129\) 0.159122 + 0.176723i 0.0140099 + 0.0155596i
\(130\) −8.98799 + 4.00171i −0.788299 + 0.350973i
\(131\) −9.26215 16.0425i −0.809237 1.40164i −0.913393 0.407079i \(-0.866547\pi\)
0.104155 0.994561i \(-0.466786\pi\)
\(132\) 2.98973 1.43581i 0.260222 0.124971i
\(133\) 11.8188 18.1688i 1.02482 1.57543i
\(134\) 6.23470 8.58133i 0.538596 0.741314i
\(135\) 1.72408 0.366464i 0.148385 0.0315402i
\(136\) 0.327995 1.54309i 0.0281253 0.132319i
\(137\) 0.947755 + 9.01729i 0.0809722 + 0.770399i 0.957380 + 0.288830i \(0.0932662\pi\)
−0.876408 + 0.481569i \(0.840067\pi\)
\(138\) −2.91326 1.29707i −0.247993 0.110414i
\(139\) 3.43271 + 10.5648i 0.291159 + 0.896095i 0.984485 + 0.175471i \(0.0561447\pi\)
−0.693326 + 0.720624i \(0.743855\pi\)
\(140\) 0.725978 + 4.60653i 0.0613564 + 0.389323i
\(141\) 1.12033 + 0.813971i 0.0943492 + 0.0685487i
\(142\) −0.187682 + 0.108358i −0.0157499 + 0.00909323i
\(143\) −14.1094 11.9857i −1.17988 1.00230i
\(144\) 0.500000 0.866025i 0.0416667 0.0721688i
\(145\) −0.713625 + 6.78969i −0.0592633 + 0.563853i
\(146\) −9.53193 3.09711i −0.788868 0.256319i
\(147\) −4.67592 5.20920i −0.385664 0.429647i
\(148\) 0.832215 0.604640i 0.0684077 0.0497011i
\(149\) 5.36923 12.0595i 0.439864 0.987951i −0.548543 0.836123i \(-0.684817\pi\)
0.988407 0.151828i \(-0.0485161\pi\)
\(150\) −1.85189 0.393632i −0.151206 0.0321399i
\(151\) −15.2288 + 13.7120i −1.23930 + 1.11587i −0.250266 + 0.968177i \(0.580518\pi\)
−0.989033 + 0.147693i \(0.952815\pi\)
\(152\) −8.14734 0.856320i −0.660836 0.0694567i
\(153\) 1.57757 0.127539
\(154\) −7.22225 + 4.98389i −0.581985 + 0.401613i
\(155\) 9.66339 0.776182
\(156\) −5.55130 0.583465i −0.444460 0.0467146i
\(157\) −8.65887 + 7.79648i −0.691053 + 0.622227i −0.937932 0.346819i \(-0.887262\pi\)
0.246879 + 0.969046i \(0.420595\pi\)
\(158\) −1.54911 0.329273i −0.123240 0.0261956i
\(159\) −3.07781 + 6.91287i −0.244086 + 0.548227i
\(160\) 1.42597 1.03603i 0.112733 0.0819051i
\(161\) 8.14803 + 2.18996i 0.642155 + 0.172593i
\(162\) 0.951057 + 0.309017i 0.0747221 + 0.0242787i
\(163\) −1.93063 + 18.3687i −0.151219 + 1.43875i 0.611102 + 0.791551i \(0.290726\pi\)
−0.762321 + 0.647199i \(0.775940\pi\)
\(164\) 3.29729 5.71107i 0.257475 0.445959i
\(165\) 1.37982 + 5.68069i 0.107419 + 0.442241i
\(166\) 9.21947 5.32286i 0.715569 0.413134i
\(167\) −6.19748 4.50273i −0.479575 0.348432i 0.321586 0.946880i \(-0.395784\pi\)
−0.801161 + 0.598448i \(0.795784\pi\)
\(168\) −0.950048 + 2.46929i −0.0732978 + 0.190510i
\(169\) 5.61094 + 17.2687i 0.431611 + 1.32836i
\(170\) 2.54021 + 1.13098i 0.194825 + 0.0867419i
\(171\) −0.856320 8.14734i −0.0654844 0.623042i
\(172\) −0.0494423 + 0.232608i −0.00376994 + 0.0177362i
\(173\) 25.4570 5.41105i 1.93546 0.411394i 0.937464 0.348082i \(-0.113167\pi\)
0.997994 0.0633117i \(-0.0201662\pi\)
\(174\) −2.27668 + 3.13358i −0.172595 + 0.237556i
\(175\) 5.00204 + 0.265996i 0.378119 + 0.0201074i
\(176\) 2.91891 + 1.57479i 0.220021 + 0.118704i
\(177\) −3.38155 5.85701i −0.254172 0.440240i
\(178\) 7.21593 3.21274i 0.540857 0.240805i
\(179\) −7.88766 8.76013i −0.589551 0.654763i 0.372372 0.928084i \(-0.378545\pi\)
−0.961923 + 0.273321i \(0.911878\pi\)
\(180\) 1.30986 + 1.17940i 0.0976313 + 0.0879077i
\(181\) −10.3319 14.2206i −0.767961 1.05701i −0.996510 0.0834747i \(-0.973398\pi\)
0.228549 0.973532i \(-0.426602\pi\)
\(182\) 14.7486 0.761592i 1.09324 0.0564529i
\(183\) 5.08063 1.65080i 0.375571 0.122030i
\(184\) −0.663022 3.11927i −0.0488786 0.229956i
\(185\) 0.737468 + 1.65638i 0.0542197 + 0.121780i
\(186\) 4.74797 + 2.74124i 0.348138 + 0.200998i
\(187\) 0.150886 + 5.23002i 0.0110339 + 0.382457i
\(188\) 1.38481i 0.100998i
\(189\) −2.61286 0.415892i −0.190058 0.0302517i
\(190\) 4.46206 13.7328i 0.323712 0.996283i
\(191\) 1.65348 1.83637i 0.119642 0.132875i −0.680348 0.732889i \(-0.738171\pi\)
0.799990 + 0.600014i \(0.204838\pi\)
\(192\) 0.994522 0.104528i 0.0717734 0.00754369i
\(193\) 21.5960 2.26983i 1.55451 0.163386i 0.712044 0.702134i \(-0.247769\pi\)
0.842467 + 0.538749i \(0.181103\pi\)
\(194\) 5.36003 5.95292i 0.384828 0.427395i
\(195\) 3.04029 9.35705i 0.217720 0.670072i
\(196\) 1.46589 6.84479i 0.104706 0.488914i
\(197\) 6.69661i 0.477114i −0.971128 0.238557i \(-0.923326\pi\)
0.971128 0.238557i \(-0.0766744\pi\)
\(198\) −0.933504 + 3.18254i −0.0663412 + 0.226173i
\(199\) 10.7110 + 6.18401i 0.759284 + 0.438373i 0.829038 0.559192i \(-0.188888\pi\)
−0.0697548 + 0.997564i \(0.522222\pi\)
\(200\) −0.770061 1.72958i −0.0544515 0.122300i
\(201\) 2.20534 + 10.3753i 0.155553 + 0.731819i
\(202\) 17.8195 5.78990i 1.25377 0.407376i
\(203\) 4.65943 9.12732i 0.327028 0.640613i
\(204\) 0.927271 + 1.27628i 0.0649220 + 0.0893574i
\(205\) 8.63798 + 7.77767i 0.603303 + 0.543216i
\(206\) 1.09584 + 1.21705i 0.0763508 + 0.0847961i
\(207\) 2.91326 1.29707i 0.202486 0.0901524i
\(208\) −2.79094 4.83405i −0.193517 0.335181i
\(209\) 26.9285 3.61816i 1.86268 0.250273i
\(210\) −3.90909 2.54286i −0.269753 0.175474i
\(211\) −13.5513 + 18.6518i −0.932911 + 1.28404i 0.0258019 + 0.999667i \(0.491786\pi\)
−0.958713 + 0.284375i \(0.908214\pi\)
\(212\) −7.40172 + 1.57329i −0.508353 + 0.108054i
\(213\) 0.0450579 0.211981i 0.00308732 0.0145247i
\(214\) −0.196453 1.86913i −0.0134293 0.127771i
\(215\) −0.382915 0.170485i −0.0261146 0.0116270i
\(216\) 0.309017 + 0.951057i 0.0210259 + 0.0647112i
\(217\) −13.5379 5.20862i −0.919010 0.353584i
\(218\) 3.27910 + 2.38240i 0.222089 + 0.161357i
\(219\) 8.67971 5.01123i 0.586520 0.338628i
\(220\) −3.78474 + 4.45532i −0.255167 + 0.300377i
\(221\) 4.40290 7.62604i 0.296171 0.512983i
\(222\) −0.107526 + 1.02304i −0.00721666 + 0.0686619i
\(223\) 19.4005 + 6.30361i 1.29916 + 0.422121i 0.875288 0.483603i \(-0.160672\pi\)
0.423868 + 0.905724i \(0.360672\pi\)
\(224\) −2.55612 + 0.682809i −0.170788 + 0.0456221i
\(225\) 1.53168 1.11283i 0.102112 0.0741889i
\(226\) 7.27460 16.3390i 0.483899 1.08686i
\(227\) −8.82657 1.87615i −0.585840 0.124524i −0.0945500 0.995520i \(-0.530141\pi\)
−0.491290 + 0.870996i \(0.663475\pi\)
\(228\) 6.08800 5.48166i 0.403188 0.363032i
\(229\) −6.86643 0.721691i −0.453746 0.0476907i −0.125101 0.992144i \(-0.539925\pi\)
−0.328645 + 0.944453i \(0.606592\pi\)
\(230\) 5.62084 0.370627
\(231\) 1.12888 8.70205i 0.0742748 0.572553i
\(232\) −3.87332 −0.254296
\(233\) 2.84315 + 0.298827i 0.186261 + 0.0195768i 0.197200 0.980363i \(-0.436815\pi\)
−0.0109386 + 0.999940i \(0.503482\pi\)
\(234\) 4.14815 3.73501i 0.271173 0.244165i
\(235\) −2.38752 0.507482i −0.155744 0.0331045i
\(236\) 2.75080 6.17839i 0.179062 0.402179i
\(237\) 1.28125 0.930885i 0.0832264 0.0604675i
\(238\) −2.94909 2.95362i −0.191161 0.191455i
\(239\) 19.3686 + 6.29323i 1.25285 + 0.407075i 0.858941 0.512075i \(-0.171123\pi\)
0.393908 + 0.919150i \(0.371123\pi\)
\(240\) −0.184241 + 1.75294i −0.0118927 + 0.113152i
\(241\) 6.18718 10.7165i 0.398552 0.690311i −0.594996 0.803729i \(-0.702846\pi\)
0.993547 + 0.113417i \(0.0361797\pi\)
\(242\) −10.6402 2.79040i −0.683977 0.179374i
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) 4.32184 + 3.14000i 0.276678 + 0.201018i
\(245\) 11.2637 + 5.03567i 0.719614 + 0.321717i
\(246\) 2.03783 + 6.27181i 0.129928 + 0.399876i
\(247\) −41.7746 18.5992i −2.65805 1.18344i
\(248\) 0.573076 + 5.45245i 0.0363903 + 0.346231i
\(249\) −2.21337 + 10.4131i −0.140267 + 0.659903i
\(250\) 11.8845 2.52613i 0.751643 0.159767i
\(251\) 2.10736 2.90053i 0.133016 0.183080i −0.737314 0.675551i \(-0.763906\pi\)
0.870329 + 0.492470i \(0.163906\pi\)
\(252\) −1.19934 2.35830i −0.0755511 0.148559i
\(253\) 4.57873 + 9.53412i 0.287863 + 0.599405i
\(254\) 5.93243 + 10.2753i 0.372234 + 0.644728i
\(255\) −2.54021 + 1.13098i −0.159074 + 0.0708245i
\(256\) 0.669131 + 0.743145i 0.0418207 + 0.0464466i
\(257\) −17.8810 16.1002i −1.11539 1.00430i −0.999940 0.0109869i \(-0.996503\pi\)
−0.115449 0.993313i \(-0.536831\pi\)
\(258\) −0.139778 0.192388i −0.00870219 0.0119775i
\(259\) −0.140352 2.71800i −0.00872107 0.168888i
\(260\) 9.35705 3.04029i 0.580300 0.188551i
\(261\) −0.805309 3.78868i −0.0498474 0.234513i
\(262\) 7.53451 + 16.9228i 0.465483 + 1.04549i
\(263\) 7.36346 + 4.25129i 0.454050 + 0.262146i 0.709539 0.704666i \(-0.248903\pi\)
−0.255489 + 0.966812i \(0.582236\pi\)
\(264\) −3.12343 + 1.11543i −0.192234 + 0.0686500i
\(265\) 13.3377i 0.819328i
\(266\) −13.6532 + 16.8338i −0.837129 + 1.03215i
\(267\) −2.44087 + 7.51222i −0.149379 + 0.459741i
\(268\) −7.09754 + 7.88262i −0.433551 + 0.481508i
\(269\) −0.999386 + 0.105040i −0.0609337 + 0.00640439i −0.134946 0.990853i \(-0.543086\pi\)
0.0740126 + 0.997257i \(0.476420\pi\)
\(270\) −1.75294 + 0.184241i −0.106680 + 0.0112126i
\(271\) −10.2471 + 11.3806i −0.622468 + 0.691321i −0.969097 0.246682i \(-0.920660\pi\)
0.346629 + 0.938002i \(0.387326\pi\)
\(272\) −0.487495 + 1.50036i −0.0295587 + 0.0909724i
\(273\) −9.30278 + 11.4700i −0.563030 + 0.694194i
\(274\) 9.06696i 0.547755i
\(275\) 3.83581 + 4.97147i 0.231308 + 0.299791i
\(276\) 2.76172 + 1.59448i 0.166236 + 0.0959764i
\(277\) −3.28690 7.38251i −0.197491 0.443572i 0.787469 0.616354i \(-0.211391\pi\)
−0.984960 + 0.172782i \(0.944724\pi\)
\(278\) −2.30959 10.8657i −0.138520 0.651684i
\(279\) −5.21415 + 1.69418i −0.312163 + 0.101428i
\(280\) −0.240488 4.65718i −0.0143719 0.278320i
\(281\) −11.1060 15.2861i −0.662529 0.911892i 0.337033 0.941493i \(-0.390577\pi\)
−0.999562 + 0.0296004i \(0.990577\pi\)
\(282\) −1.02911 0.926619i −0.0612829 0.0551793i
\(283\) −16.8755 18.7421i −1.00314 1.11410i −0.993464 0.114149i \(-0.963586\pi\)
−0.00967847 0.999953i \(-0.503081\pi\)
\(284\) 0.197981 0.0881466i 0.0117480 0.00523054i
\(285\) 7.21977 + 12.5050i 0.427662 + 0.740733i
\(286\) 12.7792 + 13.3949i 0.755651 + 0.792056i
\(287\) −7.90911 15.5520i −0.466860 0.918005i
\(288\) −0.587785 + 0.809017i −0.0346356 + 0.0476718i
\(289\) 14.1942 3.01706i 0.834951 0.177474i
\(290\) 1.41943 6.67790i 0.0833519 0.392140i
\(291\) 0.837319 + 7.96656i 0.0490845 + 0.467008i
\(292\) 9.15597 + 4.07650i 0.535813 + 0.238559i
\(293\) −6.28952 19.3572i −0.367438 1.13086i −0.948440 0.316955i \(-0.897339\pi\)
0.581003 0.813902i \(-0.302661\pi\)
\(294\) 4.10580 + 5.66943i 0.239455 + 0.330648i
\(295\) 9.64395 + 7.00674i 0.561492 + 0.407948i
\(296\) −0.890858 + 0.514337i −0.0517801 + 0.0298952i
\(297\) −1.74045 2.82326i −0.100991 0.163822i
\(298\) −6.60037 + 11.4322i −0.382349 + 0.662248i
\(299\) 1.86065 17.7029i 0.107604 1.02378i
\(300\) 1.80060 + 0.585051i 0.103958 + 0.0337780i
\(301\) 0.444550 + 0.445233i 0.0256234 + 0.0256628i
\(302\) 16.5786 12.0451i 0.953994 0.693117i
\(303\) −7.62082 + 17.1166i −0.437805 + 0.983326i
\(304\) 8.01319 + 1.70326i 0.459588 + 0.0976885i
\(305\) −6.99740 + 6.30049i −0.400670 + 0.360765i
\(306\) −1.56893 0.164901i −0.0896895 0.00942675i
\(307\) −7.25267 −0.413932 −0.206966 0.978348i \(-0.566359\pi\)
−0.206966 + 0.978348i \(0.566359\pi\)
\(308\) 7.70364 4.20165i 0.438956 0.239411i
\(309\) −1.63771 −0.0931659
\(310\) −9.61045 1.01010i −0.545837 0.0573698i
\(311\) −2.51958 + 2.26864i −0.142872 + 0.128643i −0.737468 0.675382i \(-0.763979\pi\)
0.594596 + 0.804025i \(0.297312\pi\)
\(312\) 5.45990 + 1.16054i 0.309106 + 0.0657025i
\(313\) 7.26152 16.3096i 0.410445 0.921875i −0.583512 0.812105i \(-0.698322\pi\)
0.993957 0.109771i \(-0.0350116\pi\)
\(314\) 9.42639 6.84868i 0.531962 0.386493i
\(315\) 4.50541 1.20351i 0.253851 0.0678104i
\(316\) 1.50620 + 0.489395i 0.0847306 + 0.0275306i
\(317\) −1.64926 + 15.6917i −0.0926319 + 0.881334i 0.845248 + 0.534374i \(0.179453\pi\)
−0.937880 + 0.346960i \(0.887214\pi\)
\(318\) 3.78354 6.55329i 0.212170 0.367490i
\(319\) 12.4834 3.03216i 0.698935 0.169769i
\(320\) −1.52645 + 0.881296i −0.0853312 + 0.0492660i
\(321\) 1.52049 + 1.10470i 0.0848652 + 0.0616582i
\(322\) −7.87448 3.02967i −0.438828 0.168837i
\(323\) 3.99367 + 12.2912i 0.222213 + 0.683903i
\(324\) −0.913545 0.406737i −0.0507525 0.0225965i
\(325\) −1.10466 10.5101i −0.0612752 0.582995i
\(326\) 3.84011 18.0663i 0.212684 1.00060i
\(327\) −3.96462 + 0.842705i −0.219244 + 0.0466017i
\(328\) −3.87619 + 5.33512i −0.214027 + 0.294583i
\(329\) 3.07124 + 1.99784i 0.169323 + 0.110144i
\(330\) −0.778464 5.79380i −0.0428530 0.318938i
\(331\) 16.5386 + 28.6456i 0.909042 + 1.57451i 0.815398 + 0.578900i \(0.196518\pi\)
0.0936434 + 0.995606i \(0.470149\pi\)
\(332\) −9.72535 + 4.33001i −0.533748 + 0.237640i
\(333\) −0.688318 0.764454i −0.0377196 0.0418918i
\(334\) 5.69287 + 5.12588i 0.311500 + 0.280476i
\(335\) −10.9892 15.1254i −0.600407 0.826389i
\(336\) 1.20295 2.35646i 0.0656266 0.128555i
\(337\) −6.97567 + 2.26653i −0.379989 + 0.123466i −0.492782 0.870153i \(-0.664020\pi\)
0.112794 + 0.993618i \(0.464020\pi\)
\(338\) −3.77513 17.7606i −0.205340 0.966050i
\(339\) 7.27460 + 16.3390i 0.395102 + 0.887414i
\(340\) −2.40808 1.39030i −0.130596 0.0753999i
\(341\) −6.11533 17.1242i −0.331164 0.927325i
\(342\) 8.19221i 0.442984i
\(343\) −13.0656 13.1259i −0.705477 0.708733i
\(344\) 0.0734856 0.226165i 0.00396208 0.0121940i
\(345\) −3.76108 + 4.17710i −0.202490 + 0.224887i
\(346\) −25.8831 + 2.72043i −1.39149 + 0.146251i
\(347\) −6.73699 + 0.708086i −0.361661 + 0.0380121i −0.283616 0.958938i \(-0.591534\pi\)
−0.0780443 + 0.996950i \(0.524868\pi\)
\(348\) 2.59176 2.87844i 0.138933 0.154301i
\(349\) −9.52359 + 29.3106i −0.509786 + 1.56896i 0.282787 + 0.959183i \(0.408741\pi\)
−0.792573 + 0.609777i \(0.791259\pi\)
\(350\) −4.94684 0.787395i −0.264420 0.0420880i
\(351\) 5.58188i 0.297939i
\(352\) −2.73831 1.87127i −0.145952 0.0997393i
\(353\) 6.71975 + 3.87965i 0.357656 + 0.206493i 0.668052 0.744114i \(-0.267128\pi\)
−0.310396 + 0.950607i \(0.600462\pi\)
\(354\) 2.75080 + 6.17839i 0.146203 + 0.328378i
\(355\) 0.0794188 + 0.373636i 0.00421511 + 0.0198305i
\(356\) −7.51222 + 2.44087i −0.398147 + 0.129366i
\(357\) 4.16830 0.215243i 0.220610 0.0113919i
\(358\) 6.92877 + 9.53663i 0.366197 + 0.504027i
\(359\) 26.8071 + 24.1372i 1.41482 + 1.27391i 0.912405 + 0.409288i \(0.134223\pi\)
0.502418 + 0.864625i \(0.332444\pi\)
\(360\) −1.17940 1.30986i −0.0621601 0.0690358i
\(361\) 43.9528 19.5691i 2.31331 1.02995i
\(362\) 8.78880 + 15.2226i 0.461929 + 0.800085i
\(363\) 9.19335 6.04006i 0.482526 0.317021i
\(364\) −14.7474 0.784231i −0.772975 0.0411049i
\(365\) −10.3835 + 14.2917i −0.543499 + 0.748062i
\(366\) −5.22535 + 1.11068i −0.273134 + 0.0580563i
\(367\) 4.32830 20.3630i 0.225935 1.06294i −0.708197 0.706015i \(-0.750491\pi\)
0.934132 0.356927i \(-0.116176\pi\)
\(368\) 0.333337 + 3.17149i 0.0173764 + 0.165325i
\(369\) −6.02444 2.68225i −0.313620 0.139633i
\(370\) −0.560289 1.72439i −0.0291281 0.0896469i
\(371\) −7.18909 + 18.6853i −0.373239 + 0.970095i
\(372\) −4.43542 3.22252i −0.229966 0.167080i
\(373\) −32.6736 + 18.8641i −1.69177 + 0.976745i −0.738685 + 0.674051i \(0.764553\pi\)
−0.953088 + 0.302694i \(0.902114\pi\)
\(374\) 0.396627 5.21715i 0.0205091 0.269772i
\(375\) −6.07501 + 10.5222i −0.313712 + 0.543366i
\(376\) 0.144752 1.37722i 0.00746502 0.0710249i
\(377\) −20.5622 6.68108i −1.05901 0.344093i
\(378\) 2.55507 + 0.686732i 0.131419 + 0.0353217i
\(379\) −5.88551 + 4.27608i −0.302319 + 0.219647i −0.728593 0.684946i \(-0.759826\pi\)
0.426275 + 0.904594i \(0.359826\pi\)
\(380\) −5.87309 + 13.1912i −0.301283 + 0.676693i
\(381\) −11.6056 2.46684i −0.594572 0.126380i
\(382\) −1.83637 + 1.65348i −0.0939571 + 0.0845993i
\(383\) −15.9000 1.67116i −0.812452 0.0853921i −0.310815 0.950470i \(-0.600602\pi\)
−0.501637 + 0.865078i \(0.667269\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 4.42086 + 14.8214i 0.225308 + 0.755369i
\(386\) −21.7149 −1.10526
\(387\) 0.236502 + 0.0248573i 0.0120221 + 0.00126357i
\(388\) −5.95292 + 5.36003i −0.302214 + 0.272114i
\(389\) 12.2529 + 2.60444i 0.621249 + 0.132051i 0.507774 0.861490i \(-0.330469\pi\)
0.113475 + 0.993541i \(0.463802\pi\)
\(390\) −4.00171 + 8.98799i −0.202635 + 0.455125i
\(391\) −4.07000 + 2.95703i −0.205829 + 0.149543i
\(392\) −2.17334 + 6.65407i −0.109770 + 0.336081i
\(393\) −17.6176 5.72432i −0.888693 0.288754i
\(394\) −0.699987 + 6.65993i −0.0352648 + 0.335522i
\(395\) −1.39572 + 2.41746i −0.0702265 + 0.121636i
\(396\) 1.26106 3.06753i 0.0633705 0.154149i
\(397\) 3.04579 1.75849i 0.152864 0.0882558i −0.421617 0.906774i \(-0.638537\pi\)
0.574481 + 0.818518i \(0.305204\pi\)
\(398\) −10.0059 7.26974i −0.501552 0.364399i
\(399\) −3.37422 21.4103i −0.168922 1.07186i
\(400\) 0.585051 + 1.80060i 0.0292526 + 0.0900301i
\(401\) 33.4422 + 14.8894i 1.67002 + 0.743543i 0.999999 + 0.00120359i \(0.000383115\pi\)
0.670025 + 0.742339i \(0.266284\pi\)
\(402\) −1.10875 10.5490i −0.0552992 0.526137i
\(403\) −6.36263 + 29.9338i −0.316945 + 1.49111i
\(404\) −18.3271 + 3.89554i −0.911806 + 0.193810i
\(405\) 1.03603 1.42597i 0.0514806 0.0708569i
\(406\) −5.58797 + 8.59028i −0.277326 + 0.426328i
\(407\) 2.46852 2.35506i 0.122360 0.116736i
\(408\) −0.788784 1.36621i −0.0390506 0.0676377i
\(409\) 19.9169 8.86758i 0.984827 0.438473i 0.149821 0.988713i \(-0.452130\pi\)
0.835007 + 0.550240i \(0.185464\pi\)
\(410\) −7.77767 8.63798i −0.384112 0.426599i
\(411\) 6.73806 + 6.06698i 0.332364 + 0.299262i
\(412\) −0.962620 1.32493i −0.0474249 0.0652747i
\(413\) −9.73395 15.0142i −0.478977 0.738800i
\(414\) −3.03288 + 0.985443i −0.149058 + 0.0484319i
\(415\) −3.90127 18.3540i −0.191506 0.900964i
\(416\) 2.27036 + 5.09930i 0.111313 + 0.250014i
\(417\) 9.62024 + 5.55425i 0.471105 + 0.271993i
\(418\) −27.1592 + 0.783541i −1.32840 + 0.0383243i
\(419\) 11.7175i 0.572435i 0.958165 + 0.286218i \(0.0923980\pi\)
−0.958165 + 0.286218i \(0.907602\pi\)
\(420\) 3.62188 + 2.93754i 0.176729 + 0.143337i
\(421\) 9.00812 27.7241i 0.439029 1.35119i −0.449872 0.893093i \(-0.648530\pi\)
0.888901 0.458099i \(-0.151470\pi\)
\(422\) 15.4267 17.1331i 0.750961 0.834027i
\(423\) 1.37722 0.144752i 0.0669629 0.00703808i
\(424\) 7.52563 0.790976i 0.365477 0.0384132i
\(425\) −1.99853 + 2.21959i −0.0969429 + 0.107666i
\(426\) −0.0669692 + 0.206110i −0.00324467 + 0.00998606i
\(427\) 13.1990 5.05499i 0.638743 0.244628i
\(428\) 1.87942i 0.0908454i
\(429\) −18.5053 + 0.533877i −0.893445 + 0.0257758i
\(430\) 0.362997 + 0.209576i 0.0175053 + 0.0101067i
\(431\) −15.1704 34.0732i −0.730730 1.64125i −0.766790 0.641898i \(-0.778147\pi\)
0.0360598 0.999350i \(-0.488519\pi\)
\(432\) −0.207912 0.978148i −0.0100032 0.0470611i
\(433\) −5.20881 + 1.69245i −0.250320 + 0.0813337i −0.431489 0.902118i \(-0.642012\pi\)
0.181170 + 0.983452i \(0.442012\pi\)
\(434\) 12.9193 + 6.59518i 0.620144 + 0.316579i
\(435\) 4.01286 + 5.52323i 0.192402 + 0.264819i
\(436\) −3.01211 2.71211i −0.144254 0.129887i
\(437\) 17.4808 + 19.4144i 0.836220 + 0.928717i
\(438\) −9.15597 + 4.07650i −0.437489 + 0.194783i
\(439\) 7.38776 + 12.7960i 0.352599 + 0.610719i 0.986704 0.162528i \(-0.0519648\pi\)
−0.634105 + 0.773247i \(0.718631\pi\)
\(440\) 4.22971 4.03530i 0.201644 0.192375i
\(441\) −6.96052 0.742385i −0.331453 0.0353517i
\(442\) −5.17592 + 7.12404i −0.246193 + 0.338856i
\(443\) 28.8102 6.12379i 1.36881 0.290950i 0.535866 0.844303i \(-0.319985\pi\)
0.832947 + 0.553353i \(0.186652\pi\)
\(444\) 0.213873 1.00620i 0.0101500 0.0477519i
\(445\) −1.45529 13.8461i −0.0689872 0.656370i
\(446\) −18.6353 8.29699i −0.882409 0.392874i
\(447\) −4.07925 12.5547i −0.192942 0.593815i
\(448\) 2.61349 0.411881i 0.123476 0.0194595i
\(449\) 5.29202 + 3.84488i 0.249746 + 0.181451i 0.705614 0.708596i \(-0.250671\pi\)
−0.455868 + 0.890047i \(0.650671\pi\)
\(450\) −1.63962 + 0.946633i −0.0772923 + 0.0446247i
\(451\) 8.31612 20.2290i 0.391591 0.952548i
\(452\) −8.94265 + 15.4891i −0.420627 + 0.728547i
\(453\) −2.14203 + 20.3801i −0.100641 + 0.957539i
\(454\) 8.58211 + 2.78850i 0.402778 + 0.130871i
\(455\) 6.75647 25.1383i 0.316748 1.17850i
\(456\) −6.62764 + 4.81526i −0.310368 + 0.225495i
\(457\) 3.16264 7.10340i 0.147942 0.332283i −0.824340 0.566095i \(-0.808453\pi\)
0.972282 + 0.233812i \(0.0751201\pi\)
\(458\) 6.75338 + 1.43547i 0.315565 + 0.0670753i
\(459\) 1.17236 1.05560i 0.0547211 0.0492711i
\(460\) −5.59005 0.587538i −0.260637 0.0273941i
\(461\) −27.8271 −1.29604 −0.648019 0.761625i \(-0.724402\pi\)
−0.648019 + 0.761625i \(0.724402\pi\)
\(462\) −2.03231 + 8.53638i −0.0945515 + 0.397148i
\(463\) −37.6832 −1.75129 −0.875644 0.482958i \(-0.839563\pi\)
−0.875644 + 0.482958i \(0.839563\pi\)
\(464\) 3.85210 + 0.404872i 0.178829 + 0.0187957i
\(465\) 7.18130 6.46607i 0.333025 0.299857i
\(466\) −2.79634 0.594380i −0.129538 0.0275341i
\(467\) 3.09091 6.94231i 0.143030 0.321252i −0.827798 0.561026i \(-0.810407\pi\)
0.970829 + 0.239774i \(0.0770735\pi\)
\(468\) −4.51584 + 3.28095i −0.208745 + 0.151662i
\(469\) 7.24263 + 27.1131i 0.334434 + 1.25197i
\(470\) 2.32139 + 0.754266i 0.107078 + 0.0347917i
\(471\) −1.21793 + 11.5878i −0.0561193 + 0.533939i
\(472\) −3.38155 + 5.85701i −0.155648 + 0.269591i
\(473\) −0.0597880 + 0.786439i −0.00274906 + 0.0361605i
\(474\) −1.37154 + 0.791858i −0.0629969 + 0.0363713i
\(475\) 12.5479 + 9.11657i 0.575737 + 0.418297i
\(476\) 2.62420 + 3.24571i 0.120280 + 0.148767i
\(477\) 2.33836 + 7.19672i 0.107066 + 0.329515i
\(478\) −18.6046 8.28332i −0.850957 0.378870i
\(479\) 3.76156 + 35.7889i 0.171870 + 1.63524i 0.652128 + 0.758109i \(0.273876\pi\)
−0.480258 + 0.877127i \(0.659457\pi\)
\(480\) 0.366464 1.72408i 0.0167267 0.0786929i
\(481\) −5.61646 + 1.19382i −0.256089 + 0.0544333i
\(482\) −7.27347 + 10.0111i −0.331297 + 0.455992i
\(483\) 7.52054 3.82464i 0.342196 0.174027i
\(484\) 10.2902 + 3.88732i 0.467738 + 0.176696i
\(485\) −7.05957 12.2275i −0.320559 0.555224i
\(486\) 0.913545 0.406737i 0.0414393 0.0184499i
\(487\) 9.59059 + 10.6514i 0.434591 + 0.482662i 0.920164 0.391534i \(-0.128055\pi\)
−0.485572 + 0.874196i \(0.661389\pi\)
\(488\) −3.96995 3.57456i −0.179711 0.161813i
\(489\) 10.8563 + 14.9425i 0.490941 + 0.675722i
\(490\) −10.6757 6.18547i −0.482278 0.279431i
\(491\) −26.4639 + 8.59865i −1.19430 + 0.388052i −0.837661 0.546190i \(-0.816078\pi\)
−0.356639 + 0.934242i \(0.616078\pi\)
\(492\) −1.37109 6.45046i −0.0618134 0.290809i
\(493\) 2.48533 + 5.58215i 0.111934 + 0.251408i
\(494\) 39.6016 + 22.8640i 1.78176 + 1.02870i
\(495\) 4.82652 + 3.29829i 0.216936 + 0.148247i
\(496\) 5.48249i 0.246171i
\(497\) 0.0901308 0.566250i 0.00404292 0.0253998i
\(498\) 3.28971 10.1247i 0.147415 0.453698i
\(499\) 13.8244 15.3536i 0.618867 0.687321i −0.349476 0.936945i \(-0.613640\pi\)
0.968343 + 0.249624i \(0.0803070\pi\)
\(500\) −12.0835 + 1.27002i −0.540389 + 0.0567972i
\(501\) −7.61854 + 0.800741i −0.340371 + 0.0357745i
\(502\) −2.39901 + 2.66437i −0.107073 + 0.118916i
\(503\) 3.90081 12.0055i 0.173929 0.535298i −0.825654 0.564177i \(-0.809194\pi\)
0.999583 + 0.0288790i \(0.00919375\pi\)
\(504\) 0.946256 + 2.47075i 0.0421496 + 0.110056i
\(505\) 33.0248i 1.46959i
\(506\) −3.55706 9.96050i −0.158131 0.442798i
\(507\) 15.7248 + 9.07870i 0.698361 + 0.403199i
\(508\) −4.82587 10.8391i −0.214113 0.480907i
\(509\) 5.64033 + 26.5357i 0.250003 + 1.17617i 0.906620 + 0.421948i \(0.138654\pi\)
−0.656617 + 0.754225i \(0.728013\pi\)
\(510\) 2.64452 0.859256i 0.117101 0.0380485i
\(511\) 22.2501 14.4251i 0.984284 0.638128i
\(512\) −0.587785 0.809017i −0.0259767 0.0357538i
\(513\) −6.08800 5.48166i −0.268792 0.242021i
\(514\) 16.1002 + 17.8810i 0.710148 + 0.788699i
\(515\) 2.63705 1.17409i 0.116202 0.0517366i
\(516\) 0.118902 + 0.205945i 0.00523438 + 0.00906621i
\(517\) 0.611613 + 4.55199i 0.0268987 + 0.200196i
\(518\) −0.144524 + 2.71778i −0.00635004 + 0.119412i
\(519\) 15.2975 21.0552i 0.671487 0.924222i
\(520\) −9.62359 + 2.04556i −0.422022 + 0.0897036i
\(521\) −8.00913 + 37.6800i −0.350886 + 1.65079i 0.349434 + 0.936961i \(0.386374\pi\)
−0.700320 + 0.713829i \(0.746959\pi\)
\(522\) 0.404872 + 3.85210i 0.0177208 + 0.168602i
\(523\) 17.2846 + 7.69561i 0.755804 + 0.336506i 0.748207 0.663466i \(-0.230915\pi\)
0.00759710 + 0.999971i \(0.497582\pi\)
\(524\) −5.72432 17.6176i −0.250068 0.769631i
\(525\) 3.89523 3.14935i 0.170002 0.137449i
\(526\) −6.87874 4.99770i −0.299927 0.217910i
\(527\) 7.49025 4.32450i 0.326280 0.188378i
\(528\) 3.22291 0.782833i 0.140259 0.0340684i
\(529\) 6.41526 11.1116i 0.278925 0.483112i
\(530\) −1.39417 + 13.2646i −0.0605588 + 0.576178i
\(531\) −6.43208 2.08991i −0.279129 0.0906944i
\(532\) 15.3380 15.3145i 0.664986 0.663966i
\(533\) −29.7800 + 21.6364i −1.28992 + 0.937178i
\(534\) 3.21274 7.21593i 0.139029 0.312264i
\(535\) −3.24027 0.688741i −0.140089 0.0297769i
\(536\) 7.88262 7.09754i 0.340477 0.306567i
\(537\) −11.7233 1.23217i −0.505900 0.0531722i
\(538\) 1.00489 0.0433239
\(539\) 1.79545 23.1468i 0.0773356 0.997005i
\(540\) 1.76259 0.0758499
\(541\) −1.15068 0.120941i −0.0494715 0.00519967i 0.0797604 0.996814i \(-0.474584\pi\)
−0.129232 + 0.991614i \(0.541251\pi\)
\(542\) 11.3806 10.2471i 0.488837 0.440151i
\(543\) −17.1935 3.65459i −0.737843 0.156833i
\(544\) 0.641655 1.44118i 0.0275107 0.0617901i
\(545\) 5.77971 4.19921i 0.247576 0.179874i
\(546\) 10.4508 10.4347i 0.447251 0.446565i
\(547\) 13.7848 + 4.47895i 0.589395 + 0.191506i 0.588505 0.808493i \(-0.299717\pi\)
0.000890152 1.00000i \(0.499717\pi\)
\(548\) −0.947755 + 9.01729i −0.0404861 + 0.385199i
\(549\) 2.67105 4.62639i 0.113997 0.197449i
\(550\) −3.29514 5.34519i −0.140505 0.227920i
\(551\) 27.4799 15.8655i 1.17068 0.675895i
\(552\) −2.57992 1.87442i −0.109809 0.0797808i
\(553\) 3.25836 2.63443i 0.138559 0.112027i
\(554\) 2.49722 + 7.68564i 0.106097 + 0.326532i
\(555\) 1.65638 + 0.737468i 0.0703094 + 0.0313038i
\(556\) 1.16115 + 11.0476i 0.0492439 + 0.468524i
\(557\) 0.470672 2.21434i 0.0199430 0.0938244i −0.967050 0.254585i \(-0.918061\pi\)
0.986993 + 0.160760i \(0.0513946\pi\)
\(558\) 5.36268 1.13987i 0.227020 0.0482547i
\(559\) 0.780224 1.07389i 0.0329999 0.0454205i
\(560\) −0.247637 + 4.65680i −0.0104646 + 0.196786i
\(561\) 3.61170 + 3.78570i 0.152486 + 0.159833i
\(562\) 9.44733 + 16.3633i 0.398512 + 0.690242i
\(563\) 2.31898 1.03248i 0.0977335 0.0435138i −0.357288 0.933994i \(-0.616298\pi\)
0.455021 + 0.890481i \(0.349632\pi\)
\(564\) 0.926619 + 1.02911i 0.0390177 + 0.0433335i
\(565\) −23.4273 21.0940i −0.985592 0.887431i
\(566\) 14.8239 + 20.4034i 0.623096 + 0.857619i
\(567\) −2.22002 + 1.43928i −0.0932320 + 0.0604439i
\(568\) −0.206110 + 0.0669692i −0.00864818 + 0.00280996i
\(569\) −9.13198 42.9626i −0.382833 1.80109i −0.573248 0.819382i \(-0.694317\pi\)
0.190415 0.981704i \(-0.439016\pi\)
\(570\) −5.87309 13.1912i −0.245997 0.552518i
\(571\) −33.0979 19.1091i −1.38510 0.799689i −0.392344 0.919819i \(-0.628336\pi\)
−0.992758 + 0.120130i \(0.961669\pi\)
\(572\) −11.3091 14.6573i −0.472856 0.612853i
\(573\) 2.47108i 0.103231i
\(574\) 6.24016 + 16.2935i 0.260459 + 0.680079i
\(575\) −1.86571 + 5.74205i −0.0778053 + 0.239460i
\(576\) 0.669131 0.743145i 0.0278804 0.0309644i
\(577\) 25.7656 2.70808i 1.07264 0.112739i 0.448292 0.893887i \(-0.352033\pi\)
0.624345 + 0.781149i \(0.285366\pi\)
\(578\) −14.4318 + 1.51684i −0.600283 + 0.0630923i
\(579\) 14.5301 16.1373i 0.603851 0.670644i
\(580\) −2.10969 + 6.49295i −0.0876000 + 0.269605i
\(581\) −4.42747 + 27.8158i −0.183683 + 1.15399i
\(582\) 8.01044i 0.332043i
\(583\) −23.6353 + 8.44056i −0.978872 + 0.349572i
\(584\) −8.67971 5.01123i −0.359169 0.207366i
\(585\) −4.00171 8.98799i −0.165450 0.371608i
\(586\) 4.23169 + 19.9085i 0.174810 + 0.822414i
\(587\) −3.04993 + 0.990983i −0.125884 + 0.0409023i −0.371282 0.928520i \(-0.621082\pi\)
0.245397 + 0.969423i \(0.421082\pi\)
\(588\) −3.49069 6.06754i −0.143954 0.250221i
\(589\) −26.3996 36.3359i −1.08778 1.49720i
\(590\) −8.85871 7.97642i −0.364707 0.328384i
\(591\) −4.48091 4.97655i −0.184320 0.204708i
\(592\) 0.939741 0.418400i 0.0386231 0.0171961i
\(593\) 1.44076 + 2.49547i 0.0591650 + 0.102477i 0.894091 0.447886i \(-0.147823\pi\)
−0.834926 + 0.550362i \(0.814490\pi\)
\(594\) 1.43581 + 2.98973i 0.0589119 + 0.122670i
\(595\) −6.55752 + 3.33489i −0.268832 + 0.136717i
\(596\) 7.75920 10.6796i 0.317829 0.437455i
\(597\) 12.0977 2.57145i 0.495128 0.105243i
\(598\) −3.70091 + 17.4114i −0.151342 + 0.712006i
\(599\) 2.15752 + 20.5274i 0.0881538 + 0.838727i 0.945857 + 0.324583i \(0.105224\pi\)
−0.857704 + 0.514145i \(0.828110\pi\)
\(600\) −1.72958 0.770061i −0.0706100 0.0314376i
\(601\) 0.643933 + 1.98182i 0.0262666 + 0.0808402i 0.963330 0.268318i \(-0.0864677\pi\)
−0.937064 + 0.349158i \(0.886468\pi\)
\(602\) −0.395575 0.489262i −0.0161224 0.0199408i
\(603\) 8.58133 + 6.23470i 0.349459 + 0.253897i
\(604\) −17.7469 + 10.2462i −0.722110 + 0.416911i
\(605\) −10.4730 + 16.3166i −0.425789 + 0.663363i
\(606\) 9.36825 16.2263i 0.380559 0.659148i
\(607\) −3.37834 + 32.1427i −0.137122 + 1.30463i 0.682143 + 0.731219i \(0.261048\pi\)
−0.819266 + 0.573414i \(0.805619\pi\)
\(608\) −7.79126 2.53153i −0.315977 0.102667i
\(609\) −2.64474 9.90069i −0.107170 0.401196i
\(610\) 7.61765 5.53455i 0.308430 0.224087i
\(611\) 3.14401 7.06156i 0.127193 0.285680i
\(612\) 1.54309 + 0.327995i 0.0623759 + 0.0132584i
\(613\) 15.0653 13.5649i 0.608483 0.547880i −0.306244 0.951953i \(-0.599072\pi\)
0.914727 + 0.404073i \(0.132406\pi\)
\(614\) 7.21294 + 0.758110i 0.291090 + 0.0305948i
\(615\) 11.6235 0.468707
\(616\) −8.10063 + 3.37339i −0.326384 + 0.135918i
\(617\) 3.63885 0.146495 0.0732473 0.997314i \(-0.476664\pi\)
0.0732473 + 0.997314i \(0.476664\pi\)
\(618\) 1.62873 + 0.171187i 0.0655173 + 0.00688615i
\(619\) 1.28363 1.15578i 0.0515934 0.0464549i −0.642931 0.765924i \(-0.722282\pi\)
0.694524 + 0.719469i \(0.255615\pi\)
\(620\) 9.45222 + 2.00913i 0.379610 + 0.0806887i
\(621\) 1.29707 2.91326i 0.0520495 0.116905i
\(622\) 2.74292 1.99285i 0.109981 0.0799059i
\(623\) −5.42437 + 20.1821i −0.217323 + 0.808577i
\(624\) −5.30868 1.72490i −0.212517 0.0690511i
\(625\) 1.24903 11.8838i 0.0499613 0.475350i
\(626\) −8.92656 + 15.4613i −0.356777 + 0.617956i
\(627\) 17.5908 20.7075i 0.702508 0.826978i
\(628\) −10.0906 + 5.82583i −0.402660 + 0.232476i
\(629\) 1.31288 + 0.953860i 0.0523478 + 0.0380329i
\(630\) −4.60653 + 0.725978i −0.183528 + 0.0289237i
\(631\) 4.56321 + 14.0441i 0.181659 + 0.559088i 0.999875 0.0158230i \(-0.00503683\pi\)
−0.818216 + 0.574911i \(0.805037\pi\)
\(632\) −1.44680 0.644156i −0.0575505 0.0256231i
\(633\) 2.40989 + 22.9286i 0.0957846 + 0.911329i
\(634\) 3.28046 15.4333i 0.130284 0.612937i
\(635\) 20.4559 4.34804i 0.811768 0.172547i
\(636\) −4.44782 + 6.12190i −0.176368 + 0.242749i
\(637\) −23.0151 + 31.5756i −0.911893 + 1.25107i
\(638\) −12.7319 + 1.71068i −0.504062 + 0.0677266i
\(639\) −0.108358 0.187682i −0.00428659 0.00742459i
\(640\) 1.61021 0.716911i 0.0636491 0.0283384i
\(641\) −16.9045 18.7744i −0.667689 0.741544i 0.310199 0.950672i \(-0.399604\pi\)
−0.977888 + 0.209128i \(0.932938\pi\)
\(642\) −1.39668 1.25758i −0.0551227 0.0496327i
\(643\) −9.93411 13.6731i −0.391763 0.539216i 0.566890 0.823794i \(-0.308147\pi\)
−0.958653 + 0.284578i \(0.908147\pi\)
\(644\) 7.51466 + 3.83618i 0.296119 + 0.151167i
\(645\) −0.398638 + 0.129525i −0.0156963 + 0.00510005i
\(646\) −2.68700 12.6414i −0.105719 0.497368i
\(647\) −1.72634 3.87743i −0.0678696 0.152438i 0.876426 0.481537i \(-0.159921\pi\)
−0.944295 + 0.329100i \(0.893255\pi\)
\(648\) 0.866025 + 0.500000i 0.0340207 + 0.0196419i
\(649\) 6.31337 21.5238i 0.247821 0.844884i
\(650\) 10.5680i 0.414510i
\(651\) −13.5458 + 5.18784i −0.530903 + 0.203327i
\(652\) −5.70752 + 17.5659i −0.223524 + 0.687935i
\(653\) 2.89569 3.21599i 0.113317 0.125852i −0.683817 0.729653i \(-0.739681\pi\)
0.797135 + 0.603802i \(0.206348\pi\)
\(654\) 4.03098 0.423673i 0.157624 0.0165669i
\(655\) 32.4719 3.41294i 1.26878 0.133354i
\(656\) 4.41263 4.90072i 0.172284 0.191341i
\(657\) 3.09711 9.53193i 0.120830 0.371876i
\(658\) −2.84558 2.30793i −0.110932 0.0899724i
\(659\) 4.71642i 0.183726i 0.995772 + 0.0918629i \(0.0292821\pi\)
−0.995772 + 0.0918629i \(0.970718\pi\)
\(660\) 0.168583 + 5.84343i 0.00656207 + 0.227455i
\(661\) −1.32891 0.767247i −0.0516887 0.0298425i 0.473933 0.880561i \(-0.342834\pi\)
−0.525622 + 0.850718i \(0.676167\pi\)
\(662\) −13.4537 30.2175i −0.522892 1.17443i
\(663\) −1.83083 8.61337i −0.0711035 0.334515i
\(664\) 10.1247 3.28971i 0.392914 0.127665i
\(665\) 20.7825 + 32.0561i 0.805910 + 1.24308i
\(666\) 0.604640 + 0.832215i 0.0234293 + 0.0322477i
\(667\) 9.17923 + 8.26501i 0.355421 + 0.320023i
\(668\) −5.12588 5.69287i −0.198326 0.220264i
\(669\) 18.6353 8.29699i 0.720484 0.320780i
\(670\) 9.34801 + 16.1912i 0.361145 + 0.625522i
\(671\) 15.5931 + 8.41268i 0.601964 + 0.324768i
\(672\) −1.44268 + 2.21781i −0.0556527 + 0.0855538i
\(673\) 14.4958 19.9518i 0.558772 0.769084i −0.432398 0.901683i \(-0.642332\pi\)
0.991170 + 0.132599i \(0.0423323\pi\)
\(674\) 7.17437 1.52496i 0.276346 0.0587392i
\(675\) 0.393632 1.85189i 0.0151509 0.0712794i
\(676\) 1.89796 + 18.0579i 0.0729986 + 0.694536i
\(677\) −4.68527 2.08602i −0.180069 0.0801721i 0.314722 0.949184i \(-0.398089\pi\)
−0.494791 + 0.869012i \(0.664755\pi\)
\(678\) −5.52686 17.0099i −0.212258 0.653262i
\(679\) 3.29935 + 20.9352i 0.126617 + 0.803421i
\(680\) 2.24956 + 1.63440i 0.0862667 + 0.0626764i
\(681\) −7.81481 + 4.51188i −0.299464 + 0.172896i
\(682\) 4.29187 + 17.6696i 0.164344 + 0.676603i
\(683\) 12.5347 21.7107i 0.479627 0.830739i −0.520100 0.854105i \(-0.674105\pi\)
0.999727 + 0.0233669i \(0.00743860\pi\)
\(684\) 0.856320 8.14734i 0.0327422 0.311521i
\(685\) −15.1992 4.93851i −0.580730 0.188691i
\(686\) 11.6220 + 14.4197i 0.443730 + 0.550548i
\(687\) −5.58566 + 4.05822i −0.213106 + 0.154831i
\(688\) −0.0967238 + 0.217245i −0.00368756 + 0.00828239i
\(689\) 41.3155 + 8.78189i 1.57400 + 0.334563i
\(690\) 4.17710 3.76108i 0.159019 0.143182i
\(691\) −16.3307 1.71643i −0.621249 0.0652959i −0.211326 0.977416i \(-0.567778\pi\)
−0.409924 + 0.912120i \(0.634445\pi\)
\(692\) 26.0257 0.989348
\(693\) −4.98389 7.22225i −0.189322 0.274351i
\(694\) 6.77410 0.257141
\(695\) −19.4725 2.04664i −0.738634 0.0776335i
\(696\) −2.87844 + 2.59176i −0.109107 + 0.0982403i
\(697\) 10.1760 + 2.16298i 0.385445 + 0.0819289i
\(698\) 12.5352 28.1545i 0.474465 1.06566i
\(699\) 2.31283 1.68037i 0.0874792 0.0635573i
\(700\) 4.83743 + 1.30017i 0.182838 + 0.0491417i
\(701\) −31.5677 10.2570i −1.19229 0.387400i −0.355374 0.934724i \(-0.615646\pi\)
−0.836921 + 0.547324i \(0.815646\pi\)
\(702\) 0.583465 5.55130i 0.0220215 0.209520i
\(703\) 4.21356 7.29810i 0.158917 0.275253i
\(704\) 2.52771 + 2.14725i 0.0952665 + 0.0809277i
\(705\) −2.11384 + 1.22043i −0.0796119 + 0.0459640i
\(706\) −6.27741 4.56080i −0.236253 0.171648i
\(707\) −17.8006 + 46.2659i −0.669460 + 1.74001i
\(708\) −2.08991 6.43208i −0.0785436 0.241732i
\(709\) −3.67697 1.63709i −0.138092 0.0614823i 0.336527 0.941674i \(-0.390748\pi\)
−0.474619 + 0.880191i \(0.657414\pi\)
\(710\) −0.0399281 0.379891i −0.00149848 0.0142570i
\(711\) 0.329273 1.54911i 0.0123487 0.0580961i
\(712\) 7.72621 1.64226i 0.289552 0.0615462i
\(713\) 10.2765 14.1444i 0.384858 0.529712i
\(714\) −4.16796 0.221642i −0.155982 0.00829473i
\(715\) 29.4147 14.1263i 1.10005 0.528294i
\(716\) −5.89396 10.2086i −0.220268 0.381515i
\(717\) 18.6046 8.28332i 0.694803 0.309346i
\(718\) −24.1372 26.8071i −0.900792 1.00043i
\(719\) −14.1436 12.7350i −0.527468 0.474934i 0.361842 0.932239i \(-0.382148\pi\)
−0.889310 + 0.457305i \(0.848815\pi\)
\(720\) 1.03603 + 1.42597i 0.0386104 + 0.0531427i
\(721\) −4.32720 + 0.223449i −0.161153 + 0.00832166i
\(722\) −45.7576 + 14.8675i −1.70292 + 0.553313i
\(723\) −2.57278 12.1040i −0.0956826 0.450151i
\(724\) −7.14945 16.0579i −0.265707 0.596788i
\(725\) 6.35076 + 3.66661i 0.235861 + 0.136175i
\(726\) −9.77435 + 5.04601i −0.362760 + 0.187275i
\(727\) 35.0199i 1.29882i −0.760440 0.649409i \(-0.775017\pi\)
0.760440 0.649409i \(-0.224983\pi\)
\(728\) 14.5847 + 2.32146i 0.540544 + 0.0860391i
\(729\) −0.309017 + 0.951057i −0.0114451 + 0.0352243i
\(730\) 11.8205 13.1280i 0.437498 0.485891i
\(731\) −0.373097 + 0.0392141i −0.0137995 + 0.00145039i
\(732\) 5.31283 0.558401i 0.196368 0.0206391i
\(733\) −14.1345 + 15.6979i −0.522069 + 0.579816i −0.945299 0.326206i \(-0.894230\pi\)
0.423230 + 0.906022i \(0.360896\pi\)
\(734\) −6.43311 + 19.7991i −0.237450 + 0.730797i
\(735\) 11.7401 3.79468i 0.433041 0.139969i
\(736\) 3.18896i 0.117547i
\(737\) −19.8488 + 29.0455i −0.731141 + 1.06991i
\(738\) 5.71107 + 3.29729i 0.210227 + 0.121375i
\(739\) 15.2637 + 34.2828i 0.561484 + 1.26111i 0.941774 + 0.336246i \(0.109157\pi\)
−0.380291 + 0.924867i \(0.624176\pi\)
\(740\) 0.376972 + 1.77351i 0.0138578 + 0.0651956i
\(741\) −43.4899 + 14.1307i −1.59764 + 0.519105i
\(742\) 9.10286 17.8315i 0.334177 0.654616i
\(743\) 7.02101 + 9.66358i 0.257576 + 0.354523i 0.918146 0.396241i \(-0.129686\pi\)
−0.660571 + 0.750764i \(0.729686\pi\)
\(744\) 4.07428 + 3.66850i 0.149370 + 0.134494i
\(745\) 15.5690 + 17.2912i 0.570405 + 0.633499i
\(746\) 34.4664 15.3454i 1.26190 0.561836i
\(747\) 5.32286 + 9.21947i 0.194753 + 0.337323i
\(748\) −0.939794 + 5.14711i −0.0343623 + 0.188197i
\(749\) 4.16820 + 2.71141i 0.152303 + 0.0990728i
\(750\) 7.14160 9.82957i 0.260775 0.358925i
\(751\) 12.0666 2.56483i 0.440315 0.0935919i 0.0175806 0.999845i \(-0.494404\pi\)
0.422734 + 0.906254i \(0.361070\pi\)
\(752\) −0.287918 + 1.35455i −0.0104993 + 0.0493953i
\(753\) −0.374762 3.56562i −0.0136571 0.129938i
\(754\) 19.7512 + 8.79382i 0.719298 + 0.320252i
\(755\) −11.1616 34.3518i −0.406212 1.25019i
\(756\) −2.46929 0.950048i −0.0898073 0.0345529i
\(757\) 1.37458 + 0.998690i 0.0499599 + 0.0362980i 0.612485 0.790482i \(-0.290170\pi\)
−0.562525 + 0.826780i \(0.690170\pi\)
\(758\) 6.30024 3.63745i 0.228835 0.132118i
\(759\) 9.78223 + 4.02146i 0.355072 + 0.145970i
\(760\) 7.21977 12.5050i 0.261889 0.453604i
\(761\) −5.07578 + 48.2928i −0.183997 + 1.75061i 0.380138 + 0.924930i \(0.375877\pi\)
−0.564134 + 0.825683i \(0.690790\pi\)
\(762\) 11.2841 + 3.66644i 0.408782 + 0.132821i
\(763\) −10.3605 + 2.76755i −0.375074 + 0.100192i
\(764\) 1.99915 1.45247i 0.0723267 0.0525484i
\(765\) −1.13098 + 2.54021i −0.0408905 + 0.0918416i
\(766\) 15.6382 + 3.32400i 0.565031 + 0.120101i
\(767\) −28.0543 + 25.2602i −1.01298 + 0.912093i
\(768\) 0.994522 + 0.104528i 0.0358867 + 0.00377185i
\(769\) −26.3181 −0.949053 −0.474527 0.880241i \(-0.657381\pi\)
−0.474527 + 0.880241i \(0.657381\pi\)
\(770\) −2.84739 15.2023i −0.102613 0.547854i
\(771\) −24.0613 −0.866547
\(772\) 21.5960 + 2.26983i 0.777256 + 0.0816928i
\(773\) −17.5062 + 15.7626i −0.629653 + 0.566942i −0.920945 0.389692i \(-0.872581\pi\)
0.291292 + 0.956634i \(0.405915\pi\)
\(774\) −0.232608 0.0494423i −0.00836092 0.00177717i
\(775\) 4.22185 9.48242i 0.151653 0.340619i
\(776\) 6.48058 4.70842i 0.232639 0.169022i
\(777\) −1.92300 1.92595i −0.0689871 0.0690931i
\(778\) −11.9136 3.87096i −0.427123 0.138781i
\(779\) 5.64706 53.7282i 0.202327 1.92501i
\(780\) 4.91929 8.52046i 0.176139 0.305082i
\(781\) 0.611849 0.377185i 0.0218937 0.0134968i
\(782\) 4.35680 2.51540i 0.155799 0.0899505i
\(783\) −3.13358 2.27668i −0.111985 0.0813620i
\(784\) 2.85697 6.39044i 0.102035 0.228230i
\(785\) −6.34632 19.5320i −0.226510 0.697126i
\(786\) 16.9228 + 7.53451i 0.603616 + 0.268747i
\(787\) −1.44053 13.7058i −0.0513495 0.488558i −0.989730 0.142953i \(-0.954340\pi\)
0.938380 0.345605i \(-0.112326\pi\)
\(788\) 1.39230 6.55028i 0.0495988 0.233344i
\(789\) 8.31679 1.76779i 0.296085 0.0629349i
\(790\) 1.64077 2.25833i 0.0583760 0.0803477i
\(791\) 21.4505 + 42.1789i 0.762691 + 1.49971i
\(792\) −1.57479 + 2.91891i −0.0559578 + 0.103719i
\(793\) −14.9095 25.8239i −0.529450 0.917035i
\(794\) −3.21291 + 1.43048i −0.114022 + 0.0507659i
\(795\) −8.92466 9.91183i −0.316525 0.351537i
\(796\) 9.19123 + 8.27582i 0.325774 + 0.293329i
\(797\) 17.7045 + 24.3681i 0.627125 + 0.863163i 0.997847 0.0655804i \(-0.0208899\pi\)
−0.370722 + 0.928744i \(0.620890\pi\)
\(798\) 1.11775 + 21.6457i 0.0395678 + 0.766250i
\(799\) −2.07771 + 0.675088i −0.0735040 + 0.0238829i
\(800\) −0.393632 1.85189i −0.0139170 0.0654743i
\(801\) 3.21274 + 7.21593i 0.113517 + 0.254962i
\(802\) −31.7026 18.3035i −1.11946 0.646320i
\(803\) 31.8969 + 9.35600i 1.12562 + 0.330166i
\(804\) 10.6071i 0.374084i
\(805\) −9.36771 + 11.5500i −0.330168 + 0.407085i
\(806\) 9.45672 29.1048i 0.333099 1.02517i
\(807\) −0.672404 + 0.746780i −0.0236697 + 0.0262879i
\(808\) 18.6339 1.95850i 0.655537 0.0688997i
\(809\) −5.45014 + 0.572832i −0.191617 + 0.0201397i −0.199851 0.979826i \(-0.564046\pi\)
0.00823400 + 0.999966i \(0.497379\pi\)
\(810\) −1.17940 + 1.30986i −0.0414401 + 0.0460239i
\(811\) −10.6960 + 32.9190i −0.375589 + 1.15594i 0.567492 + 0.823379i \(0.307914\pi\)
−0.943081 + 0.332565i \(0.892086\pi\)
\(812\) 6.45529 7.95912i 0.226536 0.279310i
\(813\) 15.3141i 0.537088i
\(814\) −2.70117 + 2.08413i −0.0946759 + 0.0730486i
\(815\) −28.1934 16.2775i −0.987572 0.570175i
\(816\) 0.641655 + 1.44118i 0.0224624 + 0.0504514i
\(817\) 0.405042 + 1.90557i 0.0141706 + 0.0666676i
\(818\) −20.7347 + 6.73712i −0.724972 + 0.235558i
\(819\) 0.761592 + 14.7486i 0.0266122 + 0.515358i
\(820\) 6.83215 + 9.40365i 0.238589 + 0.328390i
\(821\) −14.9968 13.5032i −0.523392 0.471264i 0.364573 0.931175i \(-0.381215\pi\)
−0.887965 + 0.459910i \(0.847882\pi\)
\(822\) −6.06698 6.73806i −0.211610 0.235017i
\(823\) 48.2090 21.4640i 1.68046 0.748189i 0.680579 0.732674i \(-0.261728\pi\)
0.999880 0.0155143i \(-0.00493855\pi\)
\(824\) 0.818853 + 1.41830i 0.0285261 + 0.0494087i
\(825\) 6.17713 + 1.12786i 0.215060 + 0.0392672i
\(826\) 8.11122 + 15.9494i 0.282225 + 0.554951i
\(827\) 13.2624 18.2542i 0.461181 0.634761i −0.513573 0.858046i \(-0.671678\pi\)
0.974753 + 0.223286i \(0.0716783\pi\)
\(828\) 3.11927 0.663022i 0.108402 0.0230416i
\(829\) −0.842230 + 3.96238i −0.0292518 + 0.137619i −0.990350 0.138587i \(-0.955744\pi\)
0.961098 + 0.276206i \(0.0890773\pi\)
\(830\) 1.96138 + 18.6613i 0.0680805 + 0.647743i
\(831\) −7.38251 3.28690i −0.256096 0.114021i
\(832\) −1.72490 5.30868i −0.0598000 0.184046i
\(833\) 10.9842 1.13744i 0.380581 0.0394101i
\(834\) −8.98696 6.52941i −0.311193 0.226095i
\(835\) 11.6934 6.75118i 0.404666 0.233634i
\(836\) 27.0923 + 2.05966i 0.937008 + 0.0712348i
\(837\) −2.74124 + 4.74797i −0.0947512 + 0.164114i
\(838\) 1.22481 11.6533i 0.0423103 0.402555i
\(839\) 36.4220 + 11.8342i 1.25743 + 0.408563i 0.860577 0.509320i \(-0.170103\pi\)
0.396850 + 0.917883i \(0.370103\pi\)
\(840\) −3.29498 3.30004i −0.113688 0.113862i
\(841\) −11.3241 + 8.22745i −0.390487 + 0.283705i
\(842\) −11.8567 + 26.6307i −0.408610 + 0.917753i
\(843\) −18.4818 3.92842i −0.636546 0.135302i
\(844\) −17.1331 + 15.4267i −0.589746 + 0.531010i
\(845\) −31.8288 3.34534i −1.09494 0.115083i
\(846\) −1.38481 −0.0476107
\(847\) 23.4668 17.2136i 0.806330 0.591465i
\(848\) −7.56708 −0.259855
\(849\) −25.0818 2.63621i −0.860806 0.0904744i
\(850\) 2.21959 1.99853i 0.0761314 0.0685490i
\(851\) 3.20872 + 0.682034i 0.109993 + 0.0233798i
\(852\) 0.0881466 0.197981i 0.00301985 0.00678270i
\(853\) 35.0928 25.4964i 1.20155 0.872981i 0.207118 0.978316i \(-0.433592\pi\)
0.994437 + 0.105335i \(0.0335915\pi\)
\(854\) −13.6550 + 3.64763i −0.467266 + 0.124819i
\(855\) 13.7328 + 4.46206i 0.469652 + 0.152599i
\(856\) 0.196453 1.86913i 0.00671463 0.0638855i
\(857\) 13.1525 22.7807i 0.449279 0.778175i −0.549060 0.835783i \(-0.685014\pi\)
0.998339 + 0.0576082i \(0.0183474\pi\)
\(858\) 18.4597 + 1.40338i 0.630205 + 0.0479106i
\(859\) −30.2125 + 17.4432i −1.03084 + 0.595155i −0.917225 0.398370i \(-0.869576\pi\)
−0.113614 + 0.993525i \(0.536243\pi\)
\(860\) −0.339101 0.246372i −0.0115633 0.00840120i
\(861\) −16.2839 6.26516i −0.554955 0.213516i
\(862\) 11.5256 + 35.4723i 0.392565 + 1.20819i
\(863\) −6.42289 2.85965i −0.218638 0.0973438i 0.294495 0.955653i \(-0.404849\pi\)
−0.513133 + 0.858309i \(0.671515\pi\)
\(864\) 0.104528 + 0.994522i 0.00355613 + 0.0338343i
\(865\) −9.53747 + 44.8703i −0.324284 + 1.52564i
\(866\) 5.35719 1.13871i 0.182045 0.0386948i
\(867\) 8.52952 11.7399i 0.289678 0.398707i
\(868\) −12.1591 7.90948i −0.412707 0.268465i
\(869\) 5.16717 + 0.943458i 0.175284 + 0.0320046i
\(870\) −3.41354 5.91243i −0.115730 0.200450i
\(871\) 54.0889 24.0819i 1.83273 0.815985i
\(872\) 2.71211 + 3.01211i 0.0918437 + 0.102003i
\(873\) 5.95292 + 5.36003i 0.201476 + 0.181410i
\(874\) −15.3557 21.1353i −0.519414 0.714912i
\(875\) −14.6159 + 28.6310i −0.494109 + 0.967905i
\(876\) 9.53193 3.09711i 0.322054 0.104642i
\(877\) −7.18454 33.8006i −0.242605 1.14136i −0.915717 0.401825i \(-0.868376\pi\)
0.673112 0.739540i \(-0.264957\pi\)
\(878\) −6.00975 13.4981i −0.202819 0.455539i
\(879\) −17.6265 10.1767i −0.594527 0.343250i
\(880\) −4.62834 + 3.57107i −0.156021 + 0.120381i
\(881\) 28.4742i 0.959321i −0.877454 0.479661i \(-0.840760\pi\)
0.877454 0.479661i \(-0.159240\pi\)
\(882\) 6.84479 + 1.46589i 0.230476 + 0.0493591i
\(883\) −3.09987 + 9.54041i −0.104319 + 0.321060i −0.989570 0.144053i \(-0.953986\pi\)
0.885251 + 0.465113i \(0.153986\pi\)
\(884\) 5.89223 6.54398i 0.198177 0.220098i
\(885\) 11.8553 1.24604i 0.398511 0.0418852i
\(886\) −29.2925 + 3.07876i −0.984099 + 0.103433i
\(887\) 17.8684 19.8449i 0.599963 0.666326i −0.364297 0.931283i \(-0.618691\pi\)
0.964260 + 0.264956i \(0.0853575\pi\)
\(888\) −0.317878 + 0.978328i −0.0106673 + 0.0328305i
\(889\) −31.0012 4.93450i −1.03975 0.165498i
\(890\) 13.9224i 0.466680i
\(891\) −3.18254 0.933504i −0.106619 0.0312736i
\(892\) 17.6660 + 10.1995i 0.591501 + 0.341503i
\(893\) 4.61429 + 10.3639i 0.154411 + 0.346813i
\(894\) 2.74459 + 12.9123i 0.0917928 + 0.431851i
\(895\) 19.7604 6.42054i 0.660517 0.214615i
\(896\) −2.64223 + 0.136440i −0.0882707 + 0.00455814i
\(897\) −10.4628 14.4008i −0.349343 0.480830i
\(898\) −4.86113 4.37698i −0.162218 0.146062i
\(899\) −14.2093 15.7810i −0.473906 0.526326i
\(900\) 1.72958 0.770061i 0.0576528 0.0256687i
\(901\) −5.96879 10.3383i −0.198849 0.344417i
\(902\) −10.3851 + 19.2490i −0.345785 + 0.640920i
\(903\) 0.628284 + 0.0334105i 0.0209080 + 0.00111183i
\(904\) 10.5127 14.4695i 0.349648 0.481249i
\(905\) 30.3051 6.44155i 1.00738 0.214124i
\(906\) 4.26060 20.0445i 0.141549 0.665935i
\(907\) −2.85779 27.1900i −0.0948913 0.902830i −0.933616 0.358275i \(-0.883365\pi\)
0.838725 0.544555i \(-0.183302\pi\)
\(908\) −8.24362 3.67030i −0.273574 0.121803i
\(909\) 5.78990 + 17.8195i 0.192039 + 0.591035i
\(910\) −9.34713 + 24.2943i −0.309854 + 0.805350i
\(911\) 4.44954 + 3.23278i 0.147420 + 0.107107i 0.659050 0.752099i \(-0.270958\pi\)
−0.511631 + 0.859206i \(0.670958\pi\)
\(912\) 7.09467 4.09611i 0.234928 0.135636i
\(913\) −30.0557 + 18.5284i −0.994698 + 0.613200i
\(914\) −3.88782 + 6.73390i −0.128598 + 0.222737i
\(915\) −0.984233 + 9.36435i −0.0325377 + 0.309576i
\(916\) −6.56633 2.13353i −0.216958 0.0704938i
\(917\) −47.3309 12.7212i −1.56300 0.420092i
\(918\) −1.27628 + 0.927271i −0.0421235 + 0.0306045i
\(919\) −18.7958 + 42.2160i −0.620016 + 1.39258i 0.281386 + 0.959595i \(0.409206\pi\)
−0.901402 + 0.432984i \(0.857461\pi\)
\(920\) 5.49801 + 1.16864i 0.181264 + 0.0385289i
\(921\) −5.38978 + 4.85298i −0.177599 + 0.159911i
\(922\) 27.6747 + 2.90872i 0.911416 + 0.0957937i
\(923\) −1.20969 −0.0398173
\(924\) 2.91347 8.27718i 0.0958460 0.272299i
\(925\) 1.94755 0.0640352
\(926\) 37.4768 + 3.93897i 1.23156 + 0.129443i
\(927\) −1.21705 + 1.09584i −0.0399733 + 0.0359921i
\(928\) −3.78868 0.805309i −0.124370 0.0264356i
\(929\) 2.41358 5.42100i 0.0791871 0.177857i −0.869613 0.493734i \(-0.835632\pi\)
0.948800 + 0.315876i \(0.102298\pi\)
\(930\) −7.81785 + 5.68000i −0.256357 + 0.186254i
\(931\) −11.8367 56.1106i −0.387932 1.83895i
\(932\) 2.71889 + 0.883421i 0.0890603 + 0.0289374i
\(933\) −0.354397 + 3.37186i −0.0116024 + 0.110390i
\(934\) −3.79965 + 6.58119i −0.124328 + 0.215343i
\(935\) −8.52960 3.50650i −0.278948 0.114675i
\(936\) 4.83405 2.79094i 0.158006 0.0912247i
\(937\) 16.2313 + 11.7927i 0.530253 + 0.385252i 0.820453 0.571715i \(-0.193722\pi\)
−0.290199 + 0.956966i \(0.593722\pi\)
\(938\) −4.36887 27.7216i −0.142649 0.905143i
\(939\) −5.51692 16.9793i −0.180038 0.554099i
\(940\) −2.22983 0.992785i −0.0727291 0.0323811i
\(941\) 3.45779 + 32.8987i 0.112721 + 1.07247i 0.893933 + 0.448201i \(0.147935\pi\)
−0.781212 + 0.624266i \(0.785398\pi\)
\(942\) 2.42252 11.3970i 0.0789299 0.371336i
\(943\) 20.5703 4.37235i 0.669860 0.142383i
\(944\) 3.97524 5.47145i 0.129383 0.178081i
\(945\) 2.54286 3.90909i 0.0827193 0.127163i
\(946\) 0.141666 0.775881i 0.00460595 0.0252261i
\(947\) 15.3745 + 26.6294i 0.499604 + 0.865339i 1.00000 0.000457686i \(-0.000145686\pi\)
−0.500396 + 0.865796i \(0.666812\pi\)
\(948\) 1.44680 0.644156i 0.0469898 0.0209212i
\(949\) −37.4340 41.5746i −1.21516 1.34957i
\(950\) −11.5262 10.3782i −0.373960 0.336715i
\(951\) 9.27416 + 12.7648i 0.300735 + 0.413926i
\(952\) −2.27056 3.50223i −0.0735891 0.113508i
\(953\) −36.9208 + 11.9963i −1.19598 + 0.388598i −0.838282 0.545238i \(-0.816439\pi\)
−0.357702 + 0.933836i \(0.616439\pi\)
\(954\) −1.57329 7.40172i −0.0509370 0.239640i
\(955\) 1.77155 + 3.97896i 0.0573260 + 0.128756i
\(956\) 17.6369 + 10.1827i 0.570418 + 0.329331i
\(957\) 7.24805 10.6063i 0.234296 0.342855i
\(958\) 35.9860i 1.16266i
\(959\) 18.6313 + 15.1110i 0.601636 + 0.487960i
\(960\) −0.544671 + 1.67633i −0.0175792 + 0.0541032i
\(961\) 0.630559 0.700307i 0.0203406 0.0225905i
\(962\) 5.71048 0.600196i 0.184113 0.0193511i
\(963\) 1.86913 0.196453i 0.0602318 0.00633062i
\(964\) 8.28007 9.19595i 0.266683 0.296181i
\(965\) −11.8275 + 36.4013i −0.380740 + 1.17180i
\(966\) −7.87912 + 3.01757i −0.253507 + 0.0970889i
\(967\) 13.6406i 0.438653i 0.975651 + 0.219327i \(0.0703860\pi\)
−0.975651 + 0.219327i \(0.929614\pi\)
\(968\) −9.82752 4.94164i −0.315868 0.158830i
\(969\) 11.1923 + 6.46189i 0.359549 + 0.207586i
\(970\) 5.74277 + 12.8985i 0.184389 + 0.414145i
\(971\) 11.8314 + 55.6625i 0.379688 + 1.78629i 0.588669 + 0.808374i \(0.299652\pi\)
−0.208981 + 0.977920i \(0.567015\pi\)
\(972\) −0.951057 + 0.309017i −0.0305052 + 0.00991172i
\(973\) 26.1767 + 13.3630i 0.839187 + 0.428399i
\(974\) −8.42468 11.5956i −0.269944 0.371546i
\(975\) −7.85354 7.07136i −0.251515 0.226465i
\(976\) 3.57456 + 3.96995i 0.114419 + 0.127075i
\(977\) −27.3631 + 12.1828i −0.875424 + 0.389764i −0.794721 0.606975i \(-0.792383\pi\)
−0.0807023 + 0.996738i \(0.525716\pi\)
\(978\) −9.23496 15.9954i −0.295301 0.511477i
\(979\) −23.6153 + 11.3412i −0.754748 + 0.362466i
\(980\) 9.97063 + 7.26750i 0.318500 + 0.232152i
\(981\) −2.38240 + 3.27910i −0.0760643 + 0.104694i
\(982\) 27.2178 5.78531i 0.868554 0.184617i
\(983\) −3.56118 + 16.7540i −0.113584 + 0.534370i 0.884157 + 0.467190i \(0.154734\pi\)
−0.997741 + 0.0671802i \(0.978600\pi\)
\(984\) 0.689320 + 6.55845i 0.0219747 + 0.209076i
\(985\) 10.7829 + 4.80088i 0.343573 + 0.152969i
\(986\) −1.88823 5.81136i −0.0601334 0.185071i
\(987\) 3.61919 0.570377i 0.115200 0.0181553i
\(988\) −36.9947 26.8782i −1.17696 0.855110i
\(989\) −0.656749 + 0.379174i −0.0208834 + 0.0120570i
\(990\) −4.45532 3.78474i −0.141599 0.120287i
\(991\) −16.0095 + 27.7293i −0.508560 + 0.880851i 0.491391 + 0.870939i \(0.336489\pi\)
−0.999951 + 0.00991210i \(0.996845\pi\)
\(992\) −0.573076 + 5.45245i −0.0181952 + 0.173116i
\(993\) 31.4582 + 10.2214i 0.998296 + 0.324366i
\(994\) −0.148826 + 0.553727i −0.00472048 + 0.0175632i
\(995\) −17.6364 + 12.8136i −0.559111 + 0.406218i
\(996\) −4.33001 + 9.72535i −0.137201 + 0.308160i
\(997\) −34.2723 7.28480i −1.08541 0.230712i −0.369733 0.929138i \(-0.620551\pi\)
−0.715682 + 0.698426i \(0.753884\pi\)
\(998\) −15.3536 + 13.8244i −0.486010 + 0.437605i
\(999\) −1.02304 0.107526i −0.0323675 0.00340196i
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 462.2.ba.a.73.2 yes 64
7.5 odd 6 462.2.ba.b.271.6 yes 64
11.8 odd 10 462.2.ba.b.283.6 yes 64
77.19 even 30 inner 462.2.ba.a.19.2 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.ba.a.19.2 64 77.19 even 30 inner
462.2.ba.a.73.2 yes 64 1.1 even 1 trivial
462.2.ba.b.271.6 yes 64 7.5 odd 6
462.2.ba.b.283.6 yes 64 11.8 odd 10