Properties

Label 756.2.bs.a.11.3
Level $756$
Weight $2$
Character 756.11
Analytic conductor $6.037$
Analytic rank $0$
Dimension $840$
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] = [756,2,Mod(11,756)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(756, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 13, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("756.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.bs (of order \(18\), degree \(6\), 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: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(840\)
Relative dimension: \(140\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 11.3
Character \(\chi\) \(=\) 756.11
Dual form 756.2.bs.a.275.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.41197 + 0.0796147i) q^{2} +(-1.59653 + 0.671641i) q^{3} +(1.98732 - 0.224827i) q^{4} +(0.781464 - 0.137793i) q^{5} +(2.20078 - 1.07544i) q^{6} +(2.60906 + 0.439114i) q^{7} +(-2.78814 + 0.475670i) q^{8} +(2.09780 - 2.14459i) q^{9} +O(q^{10})\) \(q+(-1.41197 + 0.0796147i) q^{2} +(-1.59653 + 0.671641i) q^{3} +(1.98732 - 0.224827i) q^{4} +(0.781464 - 0.137793i) q^{5} +(2.20078 - 1.07544i) q^{6} +(2.60906 + 0.439114i) q^{7} +(-2.78814 + 0.475670i) q^{8} +(2.09780 - 2.14459i) q^{9} +(-1.09243 + 0.256776i) q^{10} +(0.353158 - 2.00286i) q^{11} +(-3.02181 + 1.69371i) q^{12} +(1.21854 - 1.02247i) q^{13} +(-3.71887 - 0.412297i) q^{14} +(-1.15508 + 0.744854i) q^{15} +(3.89891 - 0.893609i) q^{16} -7.32143i q^{17} +(-2.79129 + 3.19511i) q^{18} +1.77070i q^{19} +(1.52204 - 0.449534i) q^{20} +(-4.46036 + 1.05129i) q^{21} +(-0.339192 + 2.85609i) q^{22} +(-4.09564 + 3.43665i) q^{23} +(4.13186 - 2.63205i) q^{24} +(-4.10676 + 1.49474i) q^{25} +(-1.63913 + 1.54072i) q^{26} +(-1.90880 + 4.83286i) q^{27} +(5.28376 + 0.286074i) q^{28} +(3.78690 - 4.51305i) q^{29} +(1.57164 - 1.14367i) q^{30} +(0.584932 - 1.60709i) q^{31} +(-5.43400 + 1.57216i) q^{32} +(0.781376 + 3.43481i) q^{33} +(0.582894 + 10.3376i) q^{34} +(2.09939 - 0.0163586i) q^{35} +(3.68684 - 4.73363i) q^{36} +(1.80601 - 3.12811i) q^{37} +(-0.140974 - 2.50018i) q^{38} +(-1.25869 + 2.45083i) q^{39} +(-2.11329 + 0.755906i) q^{40} +(-5.62796 - 6.70714i) q^{41} +(6.21420 - 1.83951i) q^{42} +(-3.21899 - 8.84410i) q^{43} +(0.251542 - 4.05973i) q^{44} +(1.34384 - 1.96498i) q^{45} +(5.50931 - 5.17852i) q^{46} +(-10.3369 + 3.76233i) q^{47} +(-5.62452 + 4.04534i) q^{48} +(6.61436 + 2.29135i) q^{49} +(5.67963 - 2.43749i) q^{50} +(4.91737 + 11.6889i) q^{51} +(2.19175 - 2.30595i) q^{52} +(12.5895 + 7.26858i) q^{53} +(2.31040 - 6.97582i) q^{54} -1.61382i q^{55} +(-7.48330 + 0.0167377i) q^{56} +(-1.18927 - 2.82697i) q^{57} +(-4.98769 + 6.67379i) q^{58} +(10.9126 - 9.15677i) q^{59} +(-2.12806 + 1.73996i) q^{60} +(5.24505 - 1.90904i) q^{61} +(-0.697959 + 2.31573i) q^{62} +(6.41499 - 4.67418i) q^{63} +(7.54748 - 2.65247i) q^{64} +(0.811353 - 0.966933i) q^{65} +(-1.37674 - 4.78765i) q^{66} +(11.5769 - 2.04132i) q^{67} +(-1.64606 - 14.5500i) q^{68} +(4.23060 - 8.23750i) q^{69} +(-2.96298 + 0.190240i) q^{70} +(2.22729 + 3.85778i) q^{71} +(-4.82884 + 6.97727i) q^{72} +(-1.79740 - 3.11319i) q^{73} +(-2.30100 + 4.56058i) q^{74} +(5.55263 - 5.14466i) q^{75} +(0.398102 + 3.51895i) q^{76} +(1.80089 - 5.07049i) q^{77} +(1.58211 - 3.56071i) q^{78} +(9.17505 + 1.61781i) q^{79} +(2.92372 - 1.23557i) q^{80} +(-0.198502 - 8.99781i) q^{81} +(8.48050 + 9.02222i) q^{82} +(-3.13441 - 2.63008i) q^{83} +(-8.62781 + 3.09207i) q^{84} +(-1.00884 - 5.72143i) q^{85} +(5.24924 + 12.2313i) q^{86} +(-3.01474 + 9.74865i) q^{87} +(-0.0319553 + 5.75224i) q^{88} -7.90916i q^{89} +(-1.74103 + 2.88148i) q^{90} +(3.62822 - 2.13262i) q^{91} +(-7.36670 + 7.75054i) q^{92} +(0.145526 + 2.95862i) q^{93} +(14.2959 - 6.13527i) q^{94} +(0.243990 + 1.38374i) q^{95} +(7.61959 - 6.15969i) q^{96} +(-5.76063 + 2.09670i) q^{97} +(-9.52171 - 2.70871i) q^{98} +(-3.55445 - 4.95897i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} - 6 q^{10} - 3 q^{12} - 24 q^{13} - 21 q^{14} - 3 q^{16} - 3 q^{18} - 12 q^{20} - 12 q^{21} - 12 q^{22} - 15 q^{24} - 6 q^{25} - 12 q^{28} - 12 q^{29} + 33 q^{30} + 27 q^{32} - 6 q^{33} - 6 q^{34} - 42 q^{36} + 6 q^{37} - 9 q^{38} + 12 q^{40} - 24 q^{41} - 21 q^{42} - 9 q^{44} - 30 q^{45} + 3 q^{46} - 78 q^{48} - 12 q^{49} - 27 q^{50} - 3 q^{52} + 39 q^{54} - 27 q^{56} - 6 q^{57} - 3 q^{58} + 27 q^{60} - 6 q^{61} - 117 q^{62} - 6 q^{64} + 18 q^{65} - 3 q^{66} + 60 q^{68} - 48 q^{69} + 24 q^{70} - 63 q^{72} + 6 q^{73} - 75 q^{74} + 12 q^{77} + 6 q^{78} + 18 q^{81} - 6 q^{82} + 132 q^{84} + 6 q^{85} - 81 q^{86} + 45 q^{88} - 39 q^{90} + 48 q^{92} - 6 q^{93} - 3 q^{94} - 111 q^{96} - 24 q^{97} - 9 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41197 + 0.0796147i −0.998414 + 0.0562961i
\(3\) −1.59653 + 0.671641i −0.921755 + 0.387772i
\(4\) 1.98732 0.224827i 0.993661 0.112414i
\(5\) 0.781464 0.137793i 0.349481 0.0616230i 0.00384796 0.999993i \(-0.498775\pi\)
0.345634 + 0.938370i \(0.387664\pi\)
\(6\) 2.20078 1.07544i 0.898463 0.439048i
\(7\) 2.60906 + 0.439114i 0.986131 + 0.165969i
\(8\) −2.78814 + 0.475670i −0.985757 + 0.168175i
\(9\) 2.09780 2.14459i 0.699265 0.714862i
\(10\) −1.09243 + 0.256776i −0.345458 + 0.0811997i
\(11\) 0.353158 2.00286i 0.106481 0.603884i −0.884137 0.467227i \(-0.845253\pi\)
0.990618 0.136657i \(-0.0436359\pi\)
\(12\) −3.02181 + 1.69371i −0.872322 + 0.488932i
\(13\) 1.21854 1.02247i 0.337961 0.283583i −0.457973 0.888966i \(-0.651424\pi\)
0.795934 + 0.605383i \(0.206980\pi\)
\(14\) −3.71887 0.412297i −0.993910 0.110191i
\(15\) −1.15508 + 0.744854i −0.298241 + 0.192321i
\(16\) 3.89891 0.893609i 0.974726 0.223402i
\(17\) 7.32143i 1.77571i −0.460126 0.887854i \(-0.652196\pi\)
0.460126 0.887854i \(-0.347804\pi\)
\(18\) −2.79129 + 3.19511i −0.657913 + 0.753094i
\(19\) 1.77070i 0.406226i 0.979155 + 0.203113i \(0.0651059\pi\)
−0.979155 + 0.203113i \(0.934894\pi\)
\(20\) 1.52204 0.449534i 0.340339 0.100519i
\(21\) −4.46036 + 1.05129i −0.973330 + 0.229411i
\(22\) −0.339192 + 2.85609i −0.0723159 + 0.608921i
\(23\) −4.09564 + 3.43665i −0.854000 + 0.716591i −0.960667 0.277704i \(-0.910427\pi\)
0.106667 + 0.994295i \(0.465982\pi\)
\(24\) 4.13186 2.63205i 0.843413 0.537265i
\(25\) −4.10676 + 1.49474i −0.821353 + 0.298948i
\(26\) −1.63913 + 1.54072i −0.321461 + 0.302159i
\(27\) −1.90880 + 4.83286i −0.367348 + 0.930084i
\(28\) 5.28376 + 0.286074i 0.998538 + 0.0540629i
\(29\) 3.78690 4.51305i 0.703210 0.838053i −0.289676 0.957125i \(-0.593547\pi\)
0.992886 + 0.119072i \(0.0379919\pi\)
\(30\) 1.57164 1.14367i 0.286941 0.208805i
\(31\) 0.584932 1.60709i 0.105057 0.288641i −0.876015 0.482283i \(-0.839808\pi\)
0.981072 + 0.193642i \(0.0620299\pi\)
\(32\) −5.43400 + 1.57216i −0.960604 + 0.277921i
\(33\) 0.781376 + 3.43481i 0.136020 + 0.597924i
\(34\) 0.582894 + 10.3376i 0.0999654 + 1.77289i
\(35\) 2.09939 0.0163586i 0.354862 0.00276510i
\(36\) 3.68684 4.73363i 0.614473 0.788938i
\(37\) 1.80601 3.12811i 0.296907 0.514258i −0.678520 0.734582i \(-0.737378\pi\)
0.975427 + 0.220324i \(0.0707115\pi\)
\(38\) −0.140974 2.50018i −0.0228690 0.405582i
\(39\) −1.25869 + 2.45083i −0.201552 + 0.392446i
\(40\) −2.11329 + 0.755906i −0.334140 + 0.119519i
\(41\) −5.62796 6.70714i −0.878940 1.04748i −0.998505 0.0546532i \(-0.982595\pi\)
0.119566 0.992826i \(-0.461850\pi\)
\(42\) 6.21420 1.83951i 0.958871 0.283842i
\(43\) −3.21899 8.84410i −0.490891 1.34871i −0.899866 0.436166i \(-0.856336\pi\)
0.408975 0.912546i \(-0.365886\pi\)
\(44\) 0.251542 4.05973i 0.0379213 0.612027i
\(45\) 1.34384 1.96498i 0.200328 0.292922i
\(46\) 5.50931 5.17852i 0.812304 0.763531i
\(47\) −10.3369 + 3.76233i −1.50779 + 0.548792i −0.958065 0.286552i \(-0.907491\pi\)
−0.549728 + 0.835344i \(0.685269\pi\)
\(48\) −5.62452 + 4.04534i −0.811830 + 0.583894i
\(49\) 6.61436 + 2.29135i 0.944908 + 0.327335i
\(50\) 5.67963 2.43749i 0.803221 0.344713i
\(51\) 4.91737 + 11.6889i 0.688570 + 1.63677i
\(52\) 2.19175 2.30595i 0.303941 0.319777i
\(53\) 12.5895 + 7.26858i 1.72931 + 0.998416i 0.892785 + 0.450483i \(0.148748\pi\)
0.836522 + 0.547933i \(0.184585\pi\)
\(54\) 2.31040 6.97582i 0.314405 0.949289i
\(55\) 1.61382i 0.217608i
\(56\) −7.48330 + 0.0167377i −0.999997 + 0.00223667i
\(57\) −1.18927 2.82697i −0.157523 0.374441i
\(58\) −4.98769 + 6.67379i −0.654916 + 0.876312i
\(59\) 10.9126 9.15677i 1.42070 1.19211i 0.469738 0.882806i \(-0.344349\pi\)
0.950963 0.309304i \(-0.100096\pi\)
\(60\) −2.12806 + 1.73996i −0.274731 + 0.224628i
\(61\) 5.24505 1.90904i 0.671560 0.244428i 0.0163406 0.999866i \(-0.494798\pi\)
0.655219 + 0.755439i \(0.272576\pi\)
\(62\) −0.697959 + 2.31573i −0.0886408 + 0.294098i
\(63\) 6.41499 4.67418i 0.808213 0.588891i
\(64\) 7.54748 2.65247i 0.943435 0.331559i
\(65\) 0.811353 0.966933i 0.100636 0.119933i
\(66\) −1.37674 4.78765i −0.169465 0.589318i
\(67\) 11.5769 2.04132i 1.41435 0.249388i 0.586322 0.810078i \(-0.300575\pi\)
0.828025 + 0.560691i \(0.189464\pi\)
\(68\) −1.64606 14.5500i −0.199614 1.76445i
\(69\) 4.23060 8.23750i 0.509305 0.991679i
\(70\) −2.96298 + 0.190240i −0.354144 + 0.0227381i
\(71\) 2.22729 + 3.85778i 0.264331 + 0.457835i 0.967388 0.253299i \(-0.0815155\pi\)
−0.703057 + 0.711133i \(0.748182\pi\)
\(72\) −4.82884 + 6.97727i −0.569084 + 0.822279i
\(73\) −1.79740 3.11319i −0.210370 0.364371i 0.741460 0.670997i \(-0.234133\pi\)
−0.951830 + 0.306625i \(0.900800\pi\)
\(74\) −2.30100 + 4.56058i −0.267485 + 0.530157i
\(75\) 5.55263 5.14466i 0.641162 0.594055i
\(76\) 0.398102 + 3.51895i 0.0456654 + 0.403651i
\(77\) 1.80089 5.07049i 0.205231 0.577836i
\(78\) 1.58211 3.56071i 0.179139 0.403171i
\(79\) 9.17505 + 1.61781i 1.03227 + 0.182018i 0.664026 0.747710i \(-0.268846\pi\)
0.368248 + 0.929727i \(0.379958\pi\)
\(80\) 2.92372 1.23557i 0.326882 0.138141i
\(81\) −0.198502 8.99781i −0.0220557 0.999757i
\(82\) 8.48050 + 9.02222i 0.936515 + 0.996337i
\(83\) −3.13441 2.63008i −0.344046 0.288689i 0.454348 0.890824i \(-0.349872\pi\)
−0.798394 + 0.602135i \(0.794317\pi\)
\(84\) −8.62781 + 3.09207i −0.941371 + 0.337372i
\(85\) −1.00884 5.72143i −0.109424 0.620577i
\(86\) 5.24924 + 12.2313i 0.566040 + 1.31894i
\(87\) −3.01474 + 9.74865i −0.323214 + 1.04517i
\(88\) −0.0319553 + 5.75224i −0.00340645 + 0.613191i
\(89\) 7.90916i 0.838369i −0.907901 0.419185i \(-0.862316\pi\)
0.907901 0.419185i \(-0.137684\pi\)
\(90\) −1.74103 + 2.88148i −0.183520 + 0.303735i
\(91\) 3.62822 2.13262i 0.380340 0.223559i
\(92\) −7.36670 + 7.75054i −0.768032 + 0.808050i
\(93\) 0.145526 + 2.95862i 0.0150904 + 0.306795i
\(94\) 14.2959 6.13527i 1.47451 0.632804i
\(95\) 0.243990 + 1.38374i 0.0250329 + 0.141969i
\(96\) 7.61959 6.15969i 0.777671 0.628671i
\(97\) −5.76063 + 2.09670i −0.584903 + 0.212887i −0.617486 0.786582i \(-0.711849\pi\)
0.0325829 + 0.999469i \(0.489627\pi\)
\(98\) −9.52171 2.70871i −0.961837 0.273621i
\(99\) −3.55445 4.95897i −0.357236 0.498395i
\(100\) −7.82541 + 3.89384i −0.782541 + 0.389384i
\(101\) −6.02171 + 7.17639i −0.599183 + 0.714078i −0.977343 0.211662i \(-0.932112\pi\)
0.378160 + 0.925740i \(0.376557\pi\)
\(102\) −7.87379 16.1128i −0.779622 1.59541i
\(103\) 0.0898087 0.0158357i 0.00884911 0.00156034i −0.169222 0.985578i \(-0.554125\pi\)
0.178071 + 0.984018i \(0.443014\pi\)
\(104\) −2.91110 + 3.43042i −0.285456 + 0.336381i
\(105\) −3.34075 + 1.43615i −0.326024 + 0.140154i
\(106\) −18.3548 9.26071i −1.78277 0.899479i
\(107\) 1.07821 + 1.86751i 0.104234 + 0.180539i 0.913425 0.407007i \(-0.133427\pi\)
−0.809191 + 0.587546i \(0.800094\pi\)
\(108\) −2.70684 + 10.0336i −0.260465 + 0.965483i
\(109\) 0.392658 0.680104i 0.0376099 0.0651422i −0.846608 0.532217i \(-0.821359\pi\)
0.884218 + 0.467075i \(0.154692\pi\)
\(110\) 0.128484 + 2.27867i 0.0122505 + 0.217263i
\(111\) −0.782384 + 6.20710i −0.0742606 + 0.589152i
\(112\) 10.5649 0.619414i 0.998286 0.0585291i
\(113\) 1.09959 3.02109i 0.103440 0.284200i −0.877166 0.480187i \(-0.840569\pi\)
0.980606 + 0.195987i \(0.0627911\pi\)
\(114\) 1.90429 + 3.89691i 0.178353 + 0.364979i
\(115\) −2.72705 + 3.24997i −0.254299 + 0.303061i
\(116\) 6.51114 9.82029i 0.604544 0.911791i
\(117\) 0.363459 4.75820i 0.0336018 0.439896i
\(118\) −14.6793 + 13.7979i −1.35134 + 1.27020i
\(119\) 3.21494 19.1020i 0.294713 1.75108i
\(120\) 2.86623 2.62620i 0.261649 0.239738i
\(121\) 6.44990 + 2.34757i 0.586354 + 0.213416i
\(122\) −7.25387 + 3.11310i −0.656735 + 0.281846i
\(123\) 13.4900 + 6.92816i 1.21635 + 0.624691i
\(124\) 0.801131 3.32531i 0.0719437 0.298621i
\(125\) −6.43937 + 3.71777i −0.575954 + 0.332527i
\(126\) −8.68564 + 7.11053i −0.773779 + 0.633456i
\(127\) −10.2587 5.92288i −0.910315 0.525571i −0.0297826 0.999556i \(-0.509481\pi\)
−0.880533 + 0.473986i \(0.842815\pi\)
\(128\) −10.4456 + 4.34610i −0.923273 + 0.384145i
\(129\) 11.0793 + 11.9578i 0.975474 + 1.05283i
\(130\) −1.06863 + 1.42988i −0.0937246 + 0.125409i
\(131\) 5.81334 4.87797i 0.507914 0.426190i −0.352481 0.935819i \(-0.614662\pi\)
0.860394 + 0.509629i \(0.170217\pi\)
\(132\) 2.32509 + 6.65041i 0.202373 + 0.578844i
\(133\) −0.777539 + 4.61985i −0.0674211 + 0.400592i
\(134\) −16.1838 + 3.80399i −1.39806 + 0.328614i
\(135\) −0.825721 + 4.03972i −0.0710667 + 0.347684i
\(136\) 3.48258 + 20.4132i 0.298629 + 1.75042i
\(137\) 7.39408 + 20.3151i 0.631719 + 1.73563i 0.676299 + 0.736627i \(0.263583\pi\)
−0.0445801 + 0.999006i \(0.514195\pi\)
\(138\) −5.31766 + 11.9679i −0.452669 + 1.01878i
\(139\) −7.93738 + 1.39957i −0.673240 + 0.118710i −0.499809 0.866136i \(-0.666596\pi\)
−0.173431 + 0.984846i \(0.555485\pi\)
\(140\) 4.16849 0.504511i 0.352302 0.0426389i
\(141\) 13.9762 12.9493i 1.17701 1.09053i
\(142\) −3.45201 5.26975i −0.289686 0.442228i
\(143\) −1.61753 2.80165i −0.135265 0.234286i
\(144\) 6.26269 10.2361i 0.521891 0.853012i
\(145\) 2.33746 4.04860i 0.194116 0.336218i
\(146\) 2.78573 + 4.25263i 0.230549 + 0.351950i
\(147\) −12.0990 + 0.784279i −0.997906 + 0.0646862i
\(148\) 2.88585 6.62260i 0.237215 0.544375i
\(149\) 2.75061 7.55724i 0.225339 0.619113i −0.774572 0.632486i \(-0.782035\pi\)
0.999911 + 0.0133727i \(0.00425678\pi\)
\(150\) −7.43056 + 7.70619i −0.606703 + 0.629207i
\(151\) −8.68644 1.53165i −0.706893 0.124644i −0.191367 0.981519i \(-0.561292\pi\)
−0.515525 + 0.856874i \(0.672403\pi\)
\(152\) −0.842268 4.93696i −0.0683170 0.400440i
\(153\) −15.7014 15.3589i −1.26939 1.24169i
\(154\) −2.13912 + 7.30277i −0.172375 + 0.588474i
\(155\) 0.235658 1.33648i 0.0189285 0.107349i
\(156\) −1.95041 + 5.15357i −0.156158 + 0.412616i
\(157\) −5.46900 + 4.58904i −0.436474 + 0.366245i −0.834388 0.551178i \(-0.814179\pi\)
0.397914 + 0.917423i \(0.369734\pi\)
\(158\) −13.0837 1.55383i −1.04088 0.123616i
\(159\) −24.9814 3.14882i −1.98116 0.249718i
\(160\) −4.02984 + 1.97736i −0.318587 + 0.156324i
\(161\) −12.1948 + 7.16796i −0.961088 + 0.564915i
\(162\) 0.996637 + 12.6888i 0.0783032 + 0.996930i
\(163\) 5.72570 3.30573i 0.448471 0.258925i −0.258713 0.965954i \(-0.583298\pi\)
0.707184 + 0.707029i \(0.249965\pi\)
\(164\) −12.6925 12.0639i −0.991120 0.942035i
\(165\) 1.08391 + 2.57651i 0.0843824 + 0.200581i
\(166\) 4.63509 + 3.46405i 0.359752 + 0.268863i
\(167\) 15.5382 + 5.65545i 1.20238 + 0.437632i 0.864056 0.503396i \(-0.167916\pi\)
0.338329 + 0.941028i \(0.390138\pi\)
\(168\) 11.9360 5.05281i 0.920886 0.389833i
\(169\) −1.81805 + 10.3107i −0.139850 + 0.793127i
\(170\) 1.87997 + 7.99818i 0.144187 + 0.613432i
\(171\) 3.79742 + 3.71457i 0.290396 + 0.284060i
\(172\) −8.38556 16.8524i −0.639393 1.28498i
\(173\) −10.9709 + 13.0746i −0.834104 + 0.994046i 0.165865 + 0.986148i \(0.446958\pi\)
−0.999969 + 0.00789745i \(0.997486\pi\)
\(174\) 3.48059 14.0048i 0.263862 1.06170i
\(175\) −11.3711 + 2.09652i −0.859578 + 0.158482i
\(176\) −0.412843 8.12454i −0.0311192 0.612410i
\(177\) −11.2722 + 21.9484i −0.847272 + 1.64974i
\(178\) 0.629686 + 11.1675i 0.0471969 + 0.837040i
\(179\) 5.73321 0.428520 0.214260 0.976777i \(-0.431266\pi\)
0.214260 + 0.976777i \(0.431266\pi\)
\(180\) 2.22887 4.20718i 0.166130 0.313585i
\(181\) 1.65561 2.86761i 0.123061 0.213148i −0.797912 0.602773i \(-0.794062\pi\)
0.920973 + 0.389626i \(0.127396\pi\)
\(182\) −4.95315 + 3.30005i −0.367152 + 0.244616i
\(183\) −7.09167 + 6.57063i −0.524232 + 0.485715i
\(184\) 9.78451 11.5300i 0.721324 0.850006i
\(185\) 0.980304 2.69336i 0.0720734 0.198020i
\(186\) −0.441029 4.16590i −0.0323378 0.305459i
\(187\) −14.6638 2.58562i −1.07232 0.189079i
\(188\) −19.6969 + 9.80098i −1.43654 + 0.714810i
\(189\) −7.10233 + 11.7710i −0.516619 + 0.856216i
\(190\) −0.454673 1.93437i −0.0329855 0.140334i
\(191\) −1.38407 + 7.84945i −0.100148 + 0.567966i 0.892900 + 0.450255i \(0.148667\pi\)
−0.993048 + 0.117711i \(0.962444\pi\)
\(192\) −10.2682 + 9.30394i −0.741046 + 0.671454i
\(193\) 17.0879 + 6.21947i 1.23001 + 0.447687i 0.873601 0.486643i \(-0.161779\pi\)
0.356410 + 0.934330i \(0.384001\pi\)
\(194\) 7.96691 3.41911i 0.571991 0.245478i
\(195\) −0.645915 + 2.08867i −0.0462549 + 0.149573i
\(196\) 13.6600 + 3.06656i 0.975716 + 0.219040i
\(197\) −1.72623 0.996638i −0.122989 0.0710075i 0.437244 0.899343i \(-0.355955\pi\)
−0.560232 + 0.828336i \(0.689288\pi\)
\(198\) 5.41358 + 6.71893i 0.384727 + 0.477493i
\(199\) 19.3083i 1.36873i −0.729141 0.684363i \(-0.760080\pi\)
0.729141 0.684363i \(-0.239920\pi\)
\(200\) 10.7392 6.12101i 0.759379 0.432821i
\(201\) −17.1118 + 11.0346i −1.20698 + 0.778319i
\(202\) 7.93113 10.6123i 0.558032 0.746677i
\(203\) 11.8620 10.1119i 0.832548 0.709719i
\(204\) 12.4004 + 22.1240i 0.868200 + 1.54899i
\(205\) −5.32225 4.46590i −0.371722 0.311912i
\(206\) −0.125546 + 0.0295096i −0.00874723 + 0.00205603i
\(207\) −1.22163 + 15.9928i −0.0849088 + 1.11158i
\(208\) 3.83727 5.07543i 0.266067 0.351917i
\(209\) 3.54646 + 0.625336i 0.245314 + 0.0432554i
\(210\) 4.60270 2.29378i 0.317617 0.158286i
\(211\) 3.86008 10.6055i 0.265739 0.730111i −0.733015 0.680212i \(-0.761888\pi\)
0.998754 0.0498994i \(-0.0158901\pi\)
\(212\) 26.6537 + 11.6145i 1.83058 + 0.797690i
\(213\) −6.14698 4.66311i −0.421184 0.319511i
\(214\) −1.67108 2.55103i −0.114233 0.174385i
\(215\) −3.73418 6.46779i −0.254669 0.441100i
\(216\) 3.02315 14.3826i 0.205699 0.978615i
\(217\) 2.23181 3.93613i 0.151505 0.267202i
\(218\) −0.500276 + 0.991549i −0.0338830 + 0.0671562i
\(219\) 4.96054 + 3.76308i 0.335203 + 0.254286i
\(220\) −0.362832 3.20719i −0.0244621 0.216229i
\(221\) −7.48597 8.92143i −0.503561 0.600120i
\(222\) 0.610526 8.82654i 0.0409758 0.592398i
\(223\) −13.9172 2.45397i −0.931962 0.164330i −0.313002 0.949753i \(-0.601335\pi\)
−0.618960 + 0.785423i \(0.712446\pi\)
\(224\) −14.8680 + 1.71571i −0.993408 + 0.114636i
\(225\) −5.40955 + 11.9430i −0.360637 + 0.796198i
\(226\) −1.31206 + 4.35323i −0.0872769 + 0.289572i
\(227\) 0.262542 1.48895i 0.0174255 0.0988251i −0.974855 0.222842i \(-0.928467\pi\)
0.992280 + 0.124017i \(0.0395777\pi\)
\(228\) −2.99905 5.35072i −0.198617 0.354360i
\(229\) 23.2497 + 8.46219i 1.53638 + 0.559197i 0.965174 0.261608i \(-0.0842527\pi\)
0.571208 + 0.820805i \(0.306475\pi\)
\(230\) 3.59177 4.80598i 0.236834 0.316897i
\(231\) 0.530380 + 9.30473i 0.0348965 + 0.612207i
\(232\) −8.41170 + 14.3844i −0.552255 + 0.944379i
\(233\) 5.65175 + 3.26304i 0.370258 + 0.213769i 0.673571 0.739122i \(-0.264759\pi\)
−0.303313 + 0.952891i \(0.598093\pi\)
\(234\) −0.134370 + 6.74738i −0.00878405 + 0.441090i
\(235\) −7.55950 + 4.36448i −0.493127 + 0.284707i
\(236\) 19.6282 20.6509i 1.27769 1.34426i
\(237\) −15.7348 + 3.57947i −1.02209 + 0.232511i
\(238\) −3.01860 + 27.2275i −0.195667 + 1.76489i
\(239\) −1.05591 5.98839i −0.0683014 0.387357i −0.999726 0.0234214i \(-0.992544\pi\)
0.931424 0.363935i \(-0.118567\pi\)
\(240\) −3.83794 + 3.93631i −0.247738 + 0.254088i
\(241\) −3.93623 + 1.43267i −0.253555 + 0.0922865i −0.465671 0.884958i \(-0.654187\pi\)
0.212116 + 0.977245i \(0.431965\pi\)
\(242\) −9.29397 2.80120i −0.597439 0.180068i
\(243\) 6.36021 + 14.2319i 0.408008 + 0.912978i
\(244\) 9.99441 4.97312i 0.639826 0.318371i
\(245\) 5.48462 + 0.879192i 0.350399 + 0.0561695i
\(246\) −19.5990 8.70836i −1.24959 0.555225i
\(247\) 1.81049 + 2.15766i 0.115199 + 0.137289i
\(248\) −0.866430 + 4.75902i −0.0550184 + 0.302198i
\(249\) 6.77064 + 2.09380i 0.429072 + 0.132689i
\(250\) 8.79621 5.76205i 0.556321 0.364424i
\(251\) −7.38095 + 12.7842i −0.465881 + 0.806930i −0.999241 0.0389585i \(-0.987596\pi\)
0.533360 + 0.845889i \(0.320929\pi\)
\(252\) 11.6978 10.7314i 0.736890 0.676012i
\(253\) 5.43671 + 9.41666i 0.341803 + 0.592021i
\(254\) 14.9566 + 7.54619i 0.938459 + 0.473490i
\(255\) 5.45340 + 8.45684i 0.341505 + 0.529588i
\(256\) 14.4029 6.96820i 0.900183 0.435512i
\(257\) 1.06961 2.93873i 0.0667204 0.183313i −0.901852 0.432046i \(-0.857792\pi\)
0.968572 + 0.248733i \(0.0800141\pi\)
\(258\) −16.5956 16.0020i −1.03320 0.996243i
\(259\) 6.08559 7.36837i 0.378140 0.457848i
\(260\) 1.39503 2.10402i 0.0865160 0.130486i
\(261\) −1.73449 17.5888i −0.107362 1.08872i
\(262\) −7.81991 + 7.35038i −0.483115 + 0.454108i
\(263\) −0.508983 0.427088i −0.0313852 0.0263353i 0.626960 0.779051i \(-0.284299\pi\)
−0.658345 + 0.752716i \(0.728743\pi\)
\(264\) −3.81242 9.20507i −0.234638 0.566533i
\(265\) 10.8398 + 3.94538i 0.665886 + 0.242363i
\(266\) 0.730053 6.58500i 0.0447624 0.403752i
\(267\) 5.31212 + 12.6272i 0.325096 + 0.772771i
\(268\) 22.5482 6.65958i 1.37735 0.406799i
\(269\) 22.7943 + 13.1603i 1.38979 + 0.802397i 0.993292 0.115637i \(-0.0368908\pi\)
0.396502 + 0.918034i \(0.370224\pi\)
\(270\) 0.844272 5.76971i 0.0513808 0.351133i
\(271\) −5.91037 + 3.41235i −0.359029 + 0.207286i −0.668655 0.743573i \(-0.733130\pi\)
0.309625 + 0.950859i \(0.399796\pi\)
\(272\) −6.54250 28.5456i −0.396697 1.73083i
\(273\) −4.36019 + 5.84164i −0.263891 + 0.353552i
\(274\) −12.0576 28.0956i −0.728426 1.69732i
\(275\) 1.54342 + 8.75314i 0.0930714 + 0.527834i
\(276\) 6.55556 17.3217i 0.394598 1.04265i
\(277\) −16.5301 13.8704i −0.993200 0.833394i −0.00717226 0.999974i \(-0.502283\pi\)
−0.986028 + 0.166580i \(0.946727\pi\)
\(278\) 11.0959 2.60809i 0.665489 0.156423i
\(279\) −2.21947 4.62578i −0.132876 0.276938i
\(280\) −5.84562 + 1.04423i −0.349343 + 0.0624045i
\(281\) 5.22589 + 14.3580i 0.311750 + 0.856527i 0.992304 + 0.123828i \(0.0395172\pi\)
−0.680553 + 0.732699i \(0.738261\pi\)
\(282\) −18.7031 + 19.3968i −1.11375 + 1.15506i
\(283\) −26.4423 + 4.66249i −1.57183 + 0.277156i −0.890556 0.454873i \(-0.849685\pi\)
−0.681273 + 0.732029i \(0.738574\pi\)
\(284\) 5.29368 + 7.16591i 0.314122 + 0.425218i
\(285\) −1.31891 2.04530i −0.0781256 0.121153i
\(286\) 2.50696 + 3.82707i 0.148240 + 0.226299i
\(287\) −11.7385 19.9706i −0.692900 1.17883i
\(288\) −8.02778 + 14.9517i −0.473042 + 0.881040i
\(289\) −36.6033 −2.15314
\(290\) −2.97810 + 5.90260i −0.174880 + 0.346613i
\(291\) 7.78877 7.21651i 0.456586 0.423039i
\(292\) −4.27195 5.78281i −0.249997 0.338413i
\(293\) 14.0756 2.48191i 0.822306 0.144995i 0.253363 0.967371i \(-0.418463\pi\)
0.568943 + 0.822377i \(0.307352\pi\)
\(294\) 17.0209 2.07063i 0.992682 0.120762i
\(295\) 7.26608 8.65937i 0.423047 0.504168i
\(296\) −3.54748 + 9.58068i −0.206193 + 0.556866i
\(297\) 9.00542 + 5.52981i 0.522547 + 0.320872i
\(298\) −3.28211 + 10.8896i −0.190128 + 0.630817i
\(299\) −1.47680 + 8.37537i −0.0854058 + 0.484360i
\(300\) 9.87821 11.4725i 0.570319 0.662365i
\(301\) −4.51496 24.4883i −0.260238 1.41148i
\(302\) 12.3869 + 1.47108i 0.712789 + 0.0846513i
\(303\) 4.79386 15.5017i 0.275400 0.890551i
\(304\) 1.58231 + 6.90379i 0.0907519 + 0.395959i
\(305\) 3.83577 2.21458i 0.219635 0.126807i
\(306\) 23.3928 + 20.4362i 1.33728 + 1.16826i
\(307\) −18.2767 + 10.5521i −1.04311 + 0.602238i −0.920712 0.390243i \(-0.872391\pi\)
−0.122395 + 0.992481i \(0.539058\pi\)
\(308\) 2.43897 10.4816i 0.138973 0.597245i
\(309\) −0.132746 + 0.0856013i −0.00755166 + 0.00486969i
\(310\) −0.226338 + 1.90583i −0.0128551 + 0.108244i
\(311\) −1.51848 8.61172i −0.0861050 0.488326i −0.997113 0.0759365i \(-0.975805\pi\)
0.911008 0.412390i \(-0.135306\pi\)
\(312\) 2.34363 7.43198i 0.132682 0.420753i
\(313\) −24.3635 20.4434i −1.37710 1.15553i −0.970270 0.242026i \(-0.922188\pi\)
−0.406835 0.913502i \(-0.633367\pi\)
\(314\) 7.35672 6.91500i 0.415164 0.390236i
\(315\) 4.36901 4.53664i 0.246166 0.255611i
\(316\) 18.5975 + 1.15231i 1.04619 + 0.0648223i
\(317\) 8.12140 + 22.3133i 0.456143 + 1.25324i 0.928334 + 0.371746i \(0.121241\pi\)
−0.472191 + 0.881496i \(0.656537\pi\)
\(318\) 35.5237 + 2.45716i 1.99207 + 0.137790i
\(319\) −7.70163 9.17845i −0.431209 0.513894i
\(320\) 5.53259 3.11280i 0.309281 0.174011i
\(321\) −2.97569 2.25736i −0.166087 0.125994i
\(322\) 16.6481 11.0918i 0.927761 0.618124i
\(323\) 12.9640 0.721339
\(324\) −2.41744 17.8369i −0.134302 0.990940i
\(325\) −3.47591 + 6.02046i −0.192809 + 0.333955i
\(326\) −7.82133 + 5.12345i −0.433184 + 0.283762i
\(327\) −0.170104 + 1.34953i −0.00940676 + 0.0746292i
\(328\) 18.8819 + 16.0234i 1.04258 + 0.884745i
\(329\) −28.6217 + 5.27704i −1.57796 + 0.290933i
\(330\) −1.73558 3.55167i −0.0955405 0.195513i
\(331\) −6.89119 18.9334i −0.378774 1.04067i −0.971865 0.235538i \(-0.924315\pi\)
0.593091 0.805136i \(-0.297908\pi\)
\(332\) −6.82040 4.52212i −0.374318 0.248184i
\(333\) −2.91985 10.4353i −0.160007 0.571850i
\(334\) −22.3898 6.74826i −1.22511 0.369249i
\(335\) 8.76568 3.19045i 0.478920 0.174313i
\(336\) −16.4511 + 8.08471i −0.897479 + 0.441057i
\(337\) 0.0389681 0.0326981i 0.00212273 0.00178118i −0.641726 0.766934i \(-0.721781\pi\)
0.643848 + 0.765153i \(0.277337\pi\)
\(338\) 1.74615 14.7031i 0.0949780 0.799743i
\(339\) 0.273568 + 5.56177i 0.0148582 + 0.302074i
\(340\) −3.29123 11.1435i −0.178492 0.604342i
\(341\) −3.01219 1.73909i −0.163119 0.0941770i
\(342\) −5.65758 4.94253i −0.305927 0.267261i
\(343\) 16.2511 + 8.88271i 0.877476 + 0.479621i
\(344\) 13.1819 + 23.1274i 0.710719 + 1.24695i
\(345\) 2.17099 7.02026i 0.116882 0.377958i
\(346\) 14.4497 19.3344i 0.776820 1.03943i
\(347\) 10.5556 + 3.84191i 0.566652 + 0.206244i 0.609429 0.792840i \(-0.291399\pi\)
−0.0427779 + 0.999085i \(0.513621\pi\)
\(348\) −3.79949 + 20.0515i −0.203674 + 1.07487i
\(349\) 4.43558 + 3.72189i 0.237431 + 0.199228i 0.753738 0.657176i \(-0.228249\pi\)
−0.516306 + 0.856404i \(0.672693\pi\)
\(350\) 15.8888 3.86554i 0.849292 0.206622i
\(351\) 2.61553 + 7.84071i 0.139607 + 0.418506i
\(352\) 1.22976 + 11.4387i 0.0655462 + 0.609687i
\(353\) −7.53448 20.7008i −0.401020 1.10179i −0.961782 0.273816i \(-0.911714\pi\)
0.560762 0.827977i \(-0.310508\pi\)
\(354\) 14.1686 31.8879i 0.753054 1.69482i
\(355\) 2.27213 + 2.70781i 0.120592 + 0.143716i
\(356\) −1.77820 15.7181i −0.0942442 0.833055i
\(357\) 7.69697 + 32.6562i 0.407367 + 1.72835i
\(358\) −8.09513 + 0.456448i −0.427841 + 0.0241240i
\(359\) 24.0906 1.27145 0.635726 0.771915i \(-0.280701\pi\)
0.635726 + 0.771915i \(0.280701\pi\)
\(360\) −2.81215 + 6.11787i −0.148213 + 0.322440i
\(361\) 15.8646 0.834980
\(362\) −2.10937 + 4.18079i −0.110866 + 0.219737i
\(363\) −11.8742 + 0.584057i −0.623232 + 0.0306550i
\(364\) 6.73097 5.05392i 0.352798 0.264897i
\(365\) −1.83358 2.18518i −0.0959740 0.114377i
\(366\) 9.49012 9.84214i 0.496056 0.514457i
\(367\) −1.80198 0.317738i −0.0940626 0.0165858i 0.126419 0.991977i \(-0.459652\pi\)
−0.220481 + 0.975391i \(0.570763\pi\)
\(368\) −12.8975 + 17.0591i −0.672328 + 0.889265i
\(369\) −26.1904 2.00057i −1.36342 0.104146i
\(370\) −1.16973 + 3.88100i −0.0608113 + 0.201763i
\(371\) 29.6551 + 24.4924i 1.53962 + 1.27158i
\(372\) 0.954387 + 5.84702i 0.0494826 + 0.303154i
\(373\) 1.64898 + 9.35184i 0.0853810 + 0.484220i 0.997274 + 0.0737912i \(0.0235098\pi\)
−0.911893 + 0.410429i \(0.865379\pi\)
\(374\) 20.9107 + 2.48337i 1.08127 + 0.128412i
\(375\) 7.78361 10.2605i 0.401944 0.529848i
\(376\) 27.0311 15.4069i 1.39402 0.794548i
\(377\) 9.37133i 0.482648i
\(378\) 9.09114 17.1858i 0.467598 0.883941i
\(379\) 18.4607i 0.948262i −0.880454 0.474131i \(-0.842762\pi\)
0.880454 0.474131i \(-0.157238\pi\)
\(380\) 0.795990 + 2.69508i 0.0408334 + 0.138255i
\(381\) 20.3564 + 2.56585i 1.04289 + 0.131453i
\(382\) 1.32933 11.1934i 0.0680147 0.572704i
\(383\) −1.43266 8.12503i −0.0732056 0.415170i −0.999284 0.0378383i \(-0.987953\pi\)
0.926078 0.377332i \(-0.123158\pi\)
\(384\) 13.7577 13.9544i 0.702071 0.712107i
\(385\) 0.708653 4.21056i 0.0361163 0.214590i
\(386\) −24.6227 7.42127i −1.25326 0.377732i
\(387\) −25.7197 11.6497i −1.30741 0.592188i
\(388\) −10.9768 + 5.46196i −0.557265 + 0.277289i
\(389\) −6.43740 1.13509i −0.326389 0.0575512i 0.00805290 0.999968i \(-0.497437\pi\)
−0.334442 + 0.942416i \(0.608548\pi\)
\(390\) 0.745724 3.00057i 0.0377612 0.151940i
\(391\) 25.1612 + 29.9859i 1.27246 + 1.51645i
\(392\) −19.5317 3.24235i −0.986500 0.163763i
\(393\) −6.00491 + 11.6923i −0.302907 + 0.589798i
\(394\) 2.51673 + 1.26979i 0.126791 + 0.0639711i
\(395\) 7.39290 0.371977
\(396\) −8.17875 9.05593i −0.410998 0.455078i
\(397\) 15.6028 0.783084 0.391542 0.920160i \(-0.371942\pi\)
0.391542 + 0.920160i \(0.371942\pi\)
\(398\) 1.53722 + 27.2627i 0.0770540 + 1.36656i
\(399\) −1.86152 7.89795i −0.0931927 0.395392i
\(400\) −14.6762 + 9.49769i −0.733808 + 0.474885i
\(401\) −17.7020 21.0964i −0.883994 1.05350i −0.998196 0.0600456i \(-0.980875\pi\)
0.114201 0.993458i \(-0.463569\pi\)
\(402\) 23.2829 16.9428i 1.16125 0.845033i
\(403\) −0.930443 2.55637i −0.0463487 0.127342i
\(404\) −10.3536 + 15.6157i −0.515112 + 0.776908i
\(405\) −1.39496 7.00412i −0.0693161 0.348037i
\(406\) −15.9437 + 15.2221i −0.791274 + 0.755462i
\(407\) −5.62735 4.72191i −0.278937 0.234056i
\(408\) −19.2704 30.2512i −0.954026 1.49766i
\(409\) −9.54873 3.47545i −0.472154 0.171850i 0.0949736 0.995480i \(-0.469723\pi\)
−0.567128 + 0.823630i \(0.691946\pi\)
\(410\) 7.87041 + 5.88199i 0.388692 + 0.290491i
\(411\) −25.4493 27.4674i −1.25532 1.35487i
\(412\) 0.174919 0.0516621i 0.00861762 0.00254521i
\(413\) 32.4925 19.0987i 1.59885 0.939783i
\(414\) 0.451633 22.6787i 0.0221966 1.11460i
\(415\) −2.81184 1.62341i −0.138028 0.0796903i
\(416\) −5.01403 + 7.47186i −0.245833 + 0.366338i
\(417\) 11.7322 7.56553i 0.574529 0.370485i
\(418\) −5.05728 0.600606i −0.247360 0.0293766i
\(419\) −13.9545 + 11.7092i −0.681724 + 0.572034i −0.916509 0.400013i \(-0.869006\pi\)
0.234786 + 0.972047i \(0.424561\pi\)
\(420\) −6.31626 + 3.60520i −0.308202 + 0.175916i
\(421\) −27.8943 + 10.1527i −1.35948 + 0.494812i −0.915895 0.401419i \(-0.868517\pi\)
−0.443589 + 0.896230i \(0.646295\pi\)
\(422\) −4.60597 + 15.2819i −0.224215 + 0.743914i
\(423\) −13.6161 + 30.0610i −0.662037 + 1.46162i
\(424\) −38.5589 14.2774i −1.87259 0.693370i
\(425\) 10.9436 + 30.0674i 0.530844 + 1.45848i
\(426\) 9.05061 + 6.09479i 0.438503 + 0.295294i
\(427\) 14.5229 2.67763i 0.702814 0.129579i
\(428\) 2.56262 + 3.46894i 0.123869 + 0.167677i
\(429\) 4.46414 + 3.38651i 0.215531 + 0.163502i
\(430\) 5.78749 + 8.83504i 0.279097 + 0.426063i
\(431\) 3.76944 6.52886i 0.181567 0.314484i −0.760847 0.648931i \(-0.775216\pi\)
0.942414 + 0.334447i \(0.108550\pi\)
\(432\) −3.12353 + 20.5486i −0.150281 + 0.988643i
\(433\) 15.7137 0.755152 0.377576 0.925979i \(-0.376758\pi\)
0.377576 + 0.925979i \(0.376758\pi\)
\(434\) −2.83788 + 5.73538i −0.136223 + 0.275307i
\(435\) −1.01261 + 8.03363i −0.0485510 + 0.385183i
\(436\) 0.627433 1.43987i 0.0300486 0.0689571i
\(437\) −6.08527 7.25214i −0.291098 0.346917i
\(438\) −7.30374 4.91843i −0.348986 0.235012i
\(439\) 6.38320 + 17.5377i 0.304653 + 0.837029i 0.993676 + 0.112288i \(0.0358180\pi\)
−0.689022 + 0.724740i \(0.741960\pi\)
\(440\) 0.767648 + 4.49957i 0.0365962 + 0.214509i
\(441\) 18.7896 9.37828i 0.894741 0.446585i
\(442\) 11.2802 + 12.0008i 0.536547 + 0.570820i
\(443\) 1.13338 + 0.951018i 0.0538484 + 0.0451842i 0.669315 0.742979i \(-0.266588\pi\)
−0.615466 + 0.788163i \(0.711032\pi\)
\(444\) −0.159323 + 12.5114i −0.00756113 + 0.593766i
\(445\) −1.08983 6.18073i −0.0516628 0.292995i
\(446\) 19.8460 + 2.35692i 0.939735 + 0.111604i
\(447\) 0.684330 + 13.9128i 0.0323677 + 0.658051i
\(448\) 20.8565 3.60625i 0.985379 0.170379i
\(449\) −30.7406 + 17.7481i −1.45074 + 0.837584i −0.998523 0.0543258i \(-0.982699\pi\)
−0.452214 + 0.891909i \(0.649366\pi\)
\(450\) 6.68730 17.2938i 0.315242 0.815238i
\(451\) −15.4210 + 8.90332i −0.726147 + 0.419241i
\(452\) 1.50601 6.25109i 0.0708367 0.294026i
\(453\) 14.8969 3.38885i 0.699916 0.159222i
\(454\) −0.252159 + 2.12326i −0.0118344 + 0.0996494i
\(455\) 2.54146 2.16651i 0.119146 0.101567i
\(456\) 4.66057 + 7.31629i 0.218251 + 0.342617i
\(457\) −2.52347 + 14.3113i −0.118043 + 0.669456i 0.867155 + 0.498038i \(0.165946\pi\)
−0.985198 + 0.171418i \(0.945165\pi\)
\(458\) −33.5016 10.0974i −1.56543 0.471818i
\(459\) 35.3834 + 13.9751i 1.65156 + 0.652302i
\(460\) −4.68884 + 7.07186i −0.218618 + 0.329727i
\(461\) 7.16036 8.53339i 0.333491 0.397440i −0.573075 0.819503i \(-0.694250\pi\)
0.906566 + 0.422063i \(0.138694\pi\)
\(462\) −1.48968 13.0958i −0.0693060 0.609271i
\(463\) −16.2732 + 2.86940i −0.756278 + 0.133352i −0.538476 0.842641i \(-0.681000\pi\)
−0.217802 + 0.975993i \(0.569889\pi\)
\(464\) 10.7319 20.9800i 0.498214 0.973971i
\(465\) 0.521402 + 2.29200i 0.0241794 + 0.106289i
\(466\) −8.23989 4.15735i −0.381706 0.192586i
\(467\) −19.1575 −0.886502 −0.443251 0.896398i \(-0.646175\pi\)
−0.443251 + 0.896398i \(0.646175\pi\)
\(468\) −0.347464 9.53780i −0.0160615 0.440885i
\(469\) 31.1012 0.242342i 1.43612 0.0111903i
\(470\) 10.3263 6.76437i 0.476318 0.312017i
\(471\) 5.64922 10.9997i 0.260302 0.506841i
\(472\) −26.0703 + 30.7212i −1.19998 + 1.41406i
\(473\) −18.8503 + 3.32381i −0.866737 + 0.152829i
\(474\) 21.9321 6.30683i 1.00738 0.289682i
\(475\) −2.64673 7.27184i −0.121440 0.333655i
\(476\) 2.09447 38.6847i 0.0959998 1.77311i
\(477\) 41.9984 11.7514i 1.92297 0.538058i
\(478\) 1.96768 + 8.37136i 0.0899998 + 0.382897i
\(479\) 1.71312 + 1.43748i 0.0782747 + 0.0656802i 0.681085 0.732204i \(-0.261508\pi\)
−0.602811 + 0.797884i \(0.705953\pi\)
\(480\) 5.10568 5.86351i 0.233041 0.267631i
\(481\) −0.997714 5.65832i −0.0454919 0.257997i
\(482\) 5.44378 2.33627i 0.247957 0.106414i
\(483\) 14.6551 19.6344i 0.666829 0.893396i
\(484\) 13.3458 + 3.21527i 0.606629 + 0.146149i
\(485\) −4.21282 + 2.43227i −0.191294 + 0.110444i
\(486\) −10.1135 19.5887i −0.458758 0.888561i
\(487\) 36.2296 + 20.9172i 1.64172 + 0.947849i 0.980221 + 0.197904i \(0.0634134\pi\)
0.661500 + 0.749945i \(0.269920\pi\)
\(488\) −13.7159 + 7.81760i −0.620889 + 0.353886i
\(489\) −6.92096 + 9.12331i −0.312977 + 0.412570i
\(490\) −7.81412 0.804737i −0.353006 0.0363543i
\(491\) 4.24457 + 1.54490i 0.191555 + 0.0697203i 0.436016 0.899939i \(-0.356389\pi\)
−0.244461 + 0.969659i \(0.578611\pi\)
\(492\) 28.3666 + 10.7356i 1.27886 + 0.483997i
\(493\) −33.0420 27.7255i −1.48814 1.24869i
\(494\) −2.72815 2.90241i −0.122745 0.130586i
\(495\) −3.46099 3.38548i −0.155560 0.152166i
\(496\) 0.844486 6.78858i 0.0379185 0.304816i
\(497\) 4.11713 + 11.0432i 0.184678 + 0.495356i
\(498\) −9.72664 2.41734i −0.435861 0.108323i
\(499\) −13.1423 + 36.1083i −0.588332 + 1.61643i 0.185220 + 0.982697i \(0.440700\pi\)
−0.773552 + 0.633732i \(0.781522\pi\)
\(500\) −11.9612 + 8.83615i −0.534923 + 0.395165i
\(501\) −28.6056 + 1.40703i −1.27801 + 0.0628615i
\(502\) 9.40387 18.6385i 0.419715 0.831878i
\(503\) −0.622584 1.07835i −0.0277596 0.0480811i 0.851812 0.523848i \(-0.175504\pi\)
−0.879571 + 0.475767i \(0.842171\pi\)
\(504\) −15.6625 + 16.0837i −0.697665 + 0.716424i
\(505\) −3.71689 + 6.43785i −0.165400 + 0.286480i
\(506\) −8.42618 12.8632i −0.374590 0.571839i
\(507\) −4.02250 17.6823i −0.178646 0.785299i
\(508\) −21.7190 9.46423i −0.963626 0.419907i
\(509\) 5.02606 + 5.98983i 0.222776 + 0.265494i 0.865843 0.500316i \(-0.166783\pi\)
−0.643067 + 0.765810i \(0.722338\pi\)
\(510\) −8.37333 11.5066i −0.370777 0.509523i
\(511\) −3.32248 8.91175i −0.146978 0.394233i
\(512\) −19.7817 + 10.9856i −0.874238 + 0.485498i
\(513\) −8.55753 3.37990i −0.377824 0.149226i
\(514\) −1.27629 + 4.23456i −0.0562948 + 0.186778i
\(515\) 0.0680002 0.0247501i 0.00299645 0.00109062i
\(516\) 24.7065 + 21.2732i 1.08764 + 0.936498i
\(517\) 3.88485 + 22.0321i 0.170855 + 0.968969i
\(518\) −8.00605 + 10.8884i −0.351765 + 0.478410i
\(519\) 8.73391 28.2425i 0.383376 1.23971i
\(520\) −1.80223 + 3.08188i −0.0790329 + 0.135150i
\(521\) −9.97306 + 5.75795i −0.436928 + 0.252260i −0.702294 0.711887i \(-0.747841\pi\)
0.265366 + 0.964148i \(0.414507\pi\)
\(522\) 3.84937 + 24.6968i 0.168482 + 1.08095i
\(523\) −17.0473 9.84224i −0.745425 0.430371i 0.0786137 0.996905i \(-0.474951\pi\)
−0.824038 + 0.566534i \(0.808284\pi\)
\(524\) 10.4563 11.0011i 0.456785 0.480585i
\(525\) 16.7462 10.9845i 0.730865 0.479402i
\(526\) 0.752672 + 0.562513i 0.0328181 + 0.0245267i
\(527\) −11.7662 4.28253i −0.512542 0.186550i
\(528\) 6.11589 + 12.6938i 0.266160 + 0.552425i
\(529\) 0.969793 5.49997i 0.0421649 0.239129i
\(530\) −15.6197 4.70775i −0.678474 0.204492i
\(531\) 3.25495 42.6121i 0.141253 1.84921i
\(532\) −0.506551 + 9.35595i −0.0219617 + 0.405632i
\(533\) −13.7158 2.41846i −0.594095 0.104755i
\(534\) −8.50586 17.4063i −0.368085 0.753244i
\(535\) 1.09991 + 1.31082i 0.0475533 + 0.0566719i
\(536\) −31.3071 + 11.1983i −1.35226 + 0.483693i
\(537\) −9.15322 + 3.85066i −0.394991 + 0.166168i
\(538\) −33.2326 16.7672i −1.43276 0.722885i
\(539\) 6.92515 12.4384i 0.298288 0.535760i
\(540\) −0.732733 + 8.21388i −0.0315318 + 0.353469i
\(541\) −3.54794 6.14521i −0.152538 0.264203i 0.779622 0.626250i \(-0.215411\pi\)
−0.932160 + 0.362047i \(0.882078\pi\)
\(542\) 8.07360 5.28870i 0.346791 0.227169i
\(543\) −0.717229 + 5.69019i −0.0307792 + 0.244189i
\(544\) 11.5105 + 39.7846i 0.493507 + 1.70575i
\(545\) 0.213135 0.585583i 0.00912969 0.0250836i
\(546\) 5.69138 8.59536i 0.243569 0.367847i
\(547\) 27.1086 + 4.77997i 1.15908 + 0.204377i 0.719936 0.694040i \(-0.244171\pi\)
0.439143 + 0.898417i \(0.355282\pi\)
\(548\) 19.2618 + 38.7102i 0.822824 + 1.65362i
\(549\) 6.90894 15.2532i 0.294867 0.650993i
\(550\) −2.87614 12.2363i −0.122639 0.521758i
\(551\) 7.99126 + 6.70546i 0.340439 + 0.285662i
\(552\) −7.87719 + 24.9797i −0.335276 + 1.06321i
\(553\) 23.2278 + 8.24985i 0.987748 + 0.350819i
\(554\) 24.4444 + 18.2686i 1.03854 + 0.776159i
\(555\) 0.243892 + 4.95844i 0.0103526 + 0.210474i
\(556\) −15.4595 + 4.56594i −0.655628 + 0.193639i
\(557\) 26.5015i 1.12291i 0.827508 + 0.561453i \(0.189758\pi\)
−0.827508 + 0.561453i \(0.810242\pi\)
\(558\) 3.50210 + 6.35476i 0.148256 + 0.269018i
\(559\) −12.9653 7.48553i −0.548374 0.316604i
\(560\) 8.17071 1.93982i 0.345276 0.0819722i
\(561\) 25.1477 5.72079i 1.06174 0.241532i
\(562\) −8.52191 19.8570i −0.359475 0.837618i
\(563\) 21.7410 + 7.91307i 0.916273 + 0.333496i 0.756755 0.653699i \(-0.226784\pi\)
0.159518 + 0.987195i \(0.449006\pi\)
\(564\) 24.8639 28.8768i 1.04696 1.21593i
\(565\) 0.443001 2.51239i 0.0186372 0.105697i
\(566\) 36.9645 8.68849i 1.55373 0.365204i
\(567\) 3.43316 23.5630i 0.144179 0.989552i
\(568\) −8.04504 9.69659i −0.337562 0.406860i
\(569\) 24.7233 + 4.35938i 1.03645 + 0.182755i 0.665888 0.746052i \(-0.268053\pi\)
0.370565 + 0.928806i \(0.379164\pi\)
\(570\) 2.02510 + 2.78290i 0.0848222 + 0.116563i
\(571\) −4.16942 + 11.4554i −0.174485 + 0.479393i −0.995850 0.0910094i \(-0.970991\pi\)
0.821365 + 0.570403i \(0.193213\pi\)
\(572\) −3.84445 5.20412i −0.160745 0.217595i
\(573\) −3.06231 13.4615i −0.127930 0.562361i
\(574\) 18.1643 + 27.2634i 0.758165 + 1.13795i
\(575\) 11.6829 20.2354i 0.487212 0.843875i
\(576\) 10.1446 21.7506i 0.422692 0.906273i
\(577\) −9.83529 −0.409449 −0.204724 0.978820i \(-0.565630\pi\)
−0.204724 + 0.978820i \(0.565630\pi\)
\(578\) 51.6828 2.91416i 2.14972 0.121213i
\(579\) −31.4585 + 1.54735i −1.30737 + 0.0643059i
\(580\) 3.73505 8.57140i 0.155090 0.355908i
\(581\) −7.02294 8.23839i −0.291361 0.341786i
\(582\) −10.4230 + 10.8096i −0.432046 + 0.448073i
\(583\) 19.0040 22.6481i 0.787066 0.937989i
\(584\) 6.49226 + 7.82505i 0.268652 + 0.323803i
\(585\) −0.371618 3.76845i −0.0153645 0.155806i
\(586\) −19.6768 + 4.62501i −0.812839 + 0.191057i
\(587\) −5.17871 + 29.3699i −0.213748 + 1.21223i 0.669317 + 0.742977i \(0.266587\pi\)
−0.883066 + 0.469250i \(0.844524\pi\)
\(588\) −23.8682 + 4.27879i −0.984309 + 0.176454i
\(589\) 2.84567 + 1.03574i 0.117254 + 0.0426768i
\(590\) −9.57007 + 12.8053i −0.393994 + 0.527184i
\(591\) 3.42535 + 0.431754i 0.140900 + 0.0177600i
\(592\) 4.24617 13.8101i 0.174517 0.567590i
\(593\) 13.9554 8.05717i 0.573081 0.330868i −0.185298 0.982682i \(-0.559325\pi\)
0.758379 + 0.651814i \(0.225992\pi\)
\(594\) −13.1556 7.09096i −0.539783 0.290946i
\(595\) −0.119768 15.3705i −0.00491001 0.630131i
\(596\) 3.76728 15.6371i 0.154314 0.640520i
\(597\) 12.9682 + 30.8262i 0.530754 + 1.26163i
\(598\) 1.41840 11.9434i 0.0580027 0.488400i
\(599\) −27.8463 + 23.3658i −1.13777 + 0.954701i −0.999363 0.0356744i \(-0.988642\pi\)
−0.138405 + 0.990376i \(0.544198\pi\)
\(600\) −13.0344 + 16.9853i −0.532126 + 0.693421i
\(601\) −2.55108 + 14.4679i −0.104061 + 0.590158i 0.887531 + 0.460749i \(0.152419\pi\)
−0.991591 + 0.129409i \(0.958692\pi\)
\(602\) 8.32461 + 34.2172i 0.339286 + 1.39459i
\(603\) 19.9082 29.1100i 0.810726 1.18545i
\(604\) −17.6071 1.09094i −0.716424 0.0443898i
\(605\) 5.36385 + 0.945791i 0.218071 + 0.0384519i
\(606\) −5.53462 + 22.2697i −0.224829 + 0.904643i
\(607\) −5.10561 + 14.0275i −0.207230 + 0.569361i −0.999148 0.0412670i \(-0.986861\pi\)
0.791918 + 0.610628i \(0.209083\pi\)
\(608\) −2.78382 9.62197i −0.112899 0.390222i
\(609\) −12.1464 + 24.1110i −0.492197 + 0.977026i
\(610\) −5.23968 + 3.43231i −0.212148 + 0.138970i
\(611\) −8.74902 + 15.1538i −0.353948 + 0.613055i
\(612\) −34.6569 26.9929i −1.40092 1.09112i
\(613\) −3.78715 6.55954i −0.152962 0.264937i 0.779353 0.626585i \(-0.215548\pi\)
−0.932315 + 0.361647i \(0.882214\pi\)
\(614\) 24.9661 16.3543i 1.00755 0.660006i
\(615\) 11.4966 + 3.55528i 0.463587 + 0.143363i
\(616\) −2.60926 + 14.9939i −0.105130 + 0.604121i
\(617\) −10.6833 + 1.88376i −0.430095 + 0.0758373i −0.384505 0.923123i \(-0.625628\pi\)
−0.0455899 + 0.998960i \(0.514517\pi\)
\(618\) 0.180618 0.131435i 0.00726554 0.00528709i
\(619\) −6.96809 19.1447i −0.280071 0.769490i −0.997353 0.0727067i \(-0.976836\pi\)
0.717282 0.696783i \(-0.245386\pi\)
\(620\) 0.167850 2.70900i 0.00674103 0.108796i
\(621\) −8.79109 26.3535i −0.352774 1.05753i
\(622\) 2.82967 + 12.0386i 0.113459 + 0.482704i
\(623\) 3.47302 20.6354i 0.139144 0.826742i
\(624\) −2.71744 + 10.6803i −0.108785 + 0.427555i
\(625\) 12.2195 10.2534i 0.488779 0.410134i
\(626\) 36.0281 + 26.9258i 1.43997 + 1.07617i
\(627\) −6.08202 + 1.38358i −0.242892 + 0.0552549i
\(628\) −9.83693 + 10.3495i −0.392536 + 0.412989i
\(629\) −22.9022 13.2226i −0.913171 0.527220i
\(630\) −5.80774 + 6.75345i −0.231386 + 0.269064i
\(631\) 1.15005 0.663979i 0.0457826 0.0264326i −0.476934 0.878939i \(-0.658252\pi\)
0.522717 + 0.852507i \(0.324919\pi\)
\(632\) −26.3509 0.146387i −1.04818 0.00582295i
\(633\) 0.960357 + 19.5245i 0.0381708 + 0.776030i
\(634\) −13.2436 30.8592i −0.525972 1.22558i
\(635\) −8.83296 3.21494i −0.350526 0.127581i
\(636\) −50.3541 0.641219i −1.99667 0.0254260i
\(637\) 10.4027 3.97092i 0.412169 0.157334i
\(638\) 11.6052 + 12.3465i 0.459455 + 0.488804i
\(639\) 12.9458 + 3.31622i 0.512126 + 0.131188i
\(640\) −7.56403 + 4.83566i −0.298995 + 0.191146i
\(641\) −26.6213 + 31.7260i −1.05148 + 1.25310i −0.0849909 + 0.996382i \(0.527086\pi\)
−0.966486 + 0.256720i \(0.917358\pi\)
\(642\) 4.38130 + 2.95042i 0.172916 + 0.116444i
\(643\) 8.96318 24.6261i 0.353473 0.971160i −0.627772 0.778397i \(-0.716033\pi\)
0.981245 0.192763i \(-0.0617448\pi\)
\(644\) −22.6235 + 16.9868i −0.891492 + 0.669373i
\(645\) 10.3058 + 7.81797i 0.405789 + 0.307832i
\(646\) −18.3049 + 1.03213i −0.720195 + 0.0406086i
\(647\) −12.2917 + 21.2898i −0.483235 + 0.836987i −0.999815 0.0192516i \(-0.993872\pi\)
0.516580 + 0.856239i \(0.327205\pi\)
\(648\) 4.83344 + 24.9928i 0.189875 + 0.981808i
\(649\) −14.4858 25.0902i −0.568619 0.984876i
\(650\) 4.42857 8.77744i 0.173703 0.344280i
\(651\) −0.919485 + 7.78311i −0.0360375 + 0.305044i
\(652\) 10.6356 7.85685i 0.416522 0.307698i
\(653\) 21.0649 3.71431i 0.824334 0.145352i 0.254459 0.967084i \(-0.418103\pi\)
0.569875 + 0.821731i \(0.306992\pi\)
\(654\) 0.132739 1.91904i 0.00519050 0.0750404i
\(655\) 3.87077 4.61300i 0.151243 0.180245i
\(656\) −27.9364 21.1213i −1.09073 0.824649i
\(657\) −10.4471 2.67616i −0.407580 0.104407i
\(658\) 39.9928 9.72974i 1.55908 0.379305i
\(659\) −0.281639 + 0.102508i −0.0109711 + 0.00399315i −0.347500 0.937680i \(-0.612969\pi\)
0.336529 + 0.941673i \(0.390747\pi\)
\(660\) 2.73335 + 4.87667i 0.106396 + 0.189824i
\(661\) 4.83767 + 27.4358i 0.188164 + 1.06713i 0.921823 + 0.387612i \(0.126700\pi\)
−0.733659 + 0.679518i \(0.762189\pi\)
\(662\) 11.2375 + 26.1848i 0.436760 + 1.01770i
\(663\) 17.9436 + 9.21542i 0.696870 + 0.357897i
\(664\) 9.99023 + 5.84210i 0.387696 + 0.226717i
\(665\) 0.0289661 + 3.71739i 0.00112326 + 0.144154i
\(666\) 4.95354 + 14.5019i 0.191946 + 0.561936i
\(667\) 31.4981i 1.21961i
\(668\) 32.1510 + 7.74579i 1.24396 + 0.299694i
\(669\) 23.8673 5.42951i 0.922763 0.209917i
\(670\) −12.1229 + 5.20269i −0.468347 + 0.200998i
\(671\) −1.97121 11.1793i −0.0760977 0.431572i
\(672\) 22.5848 12.7251i 0.871226 0.490882i
\(673\) 4.30481 + 3.61216i 0.165938 + 0.139239i 0.721975 0.691919i \(-0.243234\pi\)
−0.556037 + 0.831157i \(0.687679\pi\)
\(674\) −0.0524186 + 0.0492713i −0.00201909 + 0.00189786i
\(675\) 0.615110 22.7006i 0.0236756 0.873745i
\(676\) −1.29493 + 20.8993i −0.0498049 + 0.803821i
\(677\) −8.85711 1.56175i −0.340406 0.0600228i 0.000831985 1.00000i \(-0.499735\pi\)
−0.341238 + 0.939977i \(0.610846\pi\)
\(678\) −0.829069 7.83128i −0.0318402 0.300758i
\(679\) −15.9505 + 2.94083i −0.612124 + 0.112859i
\(680\) 5.53431 + 15.4723i 0.212231 + 0.593336i
\(681\) 0.580885 + 2.55348i 0.0222596 + 0.0978497i
\(682\) 4.39158 + 2.21573i 0.168162 + 0.0848447i
\(683\) 18.9460 + 32.8154i 0.724947 + 1.25565i 0.958996 + 0.283421i \(0.0914693\pi\)
−0.234048 + 0.972225i \(0.575197\pi\)
\(684\) 8.38183 + 6.52828i 0.320487 + 0.249615i
\(685\) 8.57749 + 14.8566i 0.327729 + 0.567643i
\(686\) −23.6532 11.2483i −0.903085 0.429462i
\(687\) −42.8023 + 2.10533i −1.63301 + 0.0803232i
\(688\) −20.4537 31.6058i −0.779790 1.20496i
\(689\) 22.7728 4.01545i 0.867573 0.152977i
\(690\) −2.50646 + 10.0852i −0.0954194 + 0.383939i
\(691\) −8.75744 + 10.4367i −0.333149 + 0.397031i −0.906450 0.422314i \(-0.861218\pi\)
0.573301 + 0.819345i \(0.305663\pi\)
\(692\) −18.8632 + 28.4501i −0.717072 + 1.08151i
\(693\) −7.09621 14.4990i −0.269563 0.550773i
\(694\) −15.2100 4.58428i −0.577364 0.174017i
\(695\) −6.00993 + 2.18743i −0.227969 + 0.0829741i
\(696\) 3.76838 28.6146i 0.142840 1.08464i
\(697\) −49.1059 + 41.2047i −1.86002 + 1.56074i
\(698\) −6.55923 4.90207i −0.248270 0.185546i
\(699\) −11.2148 1.41358i −0.424181 0.0534666i
\(700\) −22.1268 + 6.72301i −0.836313 + 0.254106i
\(701\) 44.6510i 1.68645i −0.537563 0.843223i \(-0.680655\pi\)
0.537563 0.843223i \(-0.319345\pi\)
\(702\) −4.31729 10.8626i −0.162946 0.409983i
\(703\) 5.53894 + 3.19791i 0.208905 + 0.120611i
\(704\) −2.64707 16.0533i −0.0997653 0.605030i
\(705\) 9.13758 12.0453i 0.344141 0.453652i
\(706\) 12.2866 + 28.6291i 0.462411 + 1.07747i
\(707\) −18.8622 + 16.0794i −0.709388 + 0.604728i
\(708\) −17.4669 + 46.1528i −0.656448 + 1.73453i
\(709\) −25.9051 + 9.42868i −0.972886 + 0.354101i −0.779070 0.626937i \(-0.784308\pi\)
−0.193815 + 0.981038i \(0.562086\pi\)
\(710\) −3.42376 3.64246i −0.128491 0.136699i
\(711\) 22.7169 16.2829i 0.851951 0.610655i
\(712\) 3.76215 + 22.0519i 0.140992 + 0.826429i
\(713\) 3.12732 + 8.59225i 0.117119 + 0.321782i
\(714\) −13.4678 45.4968i −0.504020 1.70267i
\(715\) −1.65009 1.96651i −0.0617100 0.0735431i
\(716\) 11.3937 1.28898i 0.425804 0.0481715i
\(717\) 5.70784 + 8.85143i 0.213163 + 0.330563i
\(718\) −34.0152 + 1.91797i −1.26944 + 0.0715778i
\(719\) −6.51896 + 11.2912i −0.243116 + 0.421089i −0.961600 0.274454i \(-0.911503\pi\)
0.718484 + 0.695543i \(0.244836\pi\)
\(720\) 3.48359 8.86214i 0.129826 0.330273i
\(721\) 0.241270 0.00187998i 0.00898535 7.00143e-5i
\(722\) −22.4004 + 1.26306i −0.833656 + 0.0470062i
\(723\) 5.32206 4.93103i 0.197929 0.183387i
\(724\) 2.64552 6.07109i 0.0983201 0.225630i
\(725\) −8.80607 + 24.1945i −0.327049 + 0.898560i
\(726\) 16.7195 1.77003i 0.620518 0.0656920i
\(727\) −20.8441 + 24.8410i −0.773065 + 0.921303i −0.998598 0.0529322i \(-0.983143\pi\)
0.225533 + 0.974236i \(0.427588\pi\)
\(728\) −9.10156 + 7.67187i −0.337326 + 0.284338i
\(729\) −19.7130 18.4499i −0.730111 0.683329i
\(730\) 2.76294 + 2.93943i 0.102261 + 0.108793i
\(731\) −64.7514 + 23.5676i −2.39492 + 0.871679i
\(732\) −12.6162 + 14.6524i −0.466308 + 0.541567i
\(733\) 36.1597 30.3416i 1.33559 1.12069i 0.352855 0.935678i \(-0.385211\pi\)
0.982736 0.185016i \(-0.0592337\pi\)
\(734\) 2.56964 + 0.305172i 0.0948471 + 0.0112641i
\(735\) −9.34684 + 2.28004i −0.344763 + 0.0841006i
\(736\) 16.8527 25.1137i 0.621200 0.925705i
\(737\) 23.9079i 0.880657i
\(738\) 37.1393 + 0.739608i 1.36712 + 0.0272253i
\(739\) 19.6789i 0.723899i 0.932198 + 0.361949i \(0.117889\pi\)
−0.932198 + 0.361949i \(0.882111\pi\)
\(740\) 1.34264 5.57298i 0.0493564 0.204867i
\(741\) −4.33968 2.22876i −0.159422 0.0818757i
\(742\) −43.8221 32.2215i −1.60876 1.18289i
\(743\) 21.0569 17.6688i 0.772503 0.648207i −0.168846 0.985643i \(-0.554004\pi\)
0.941349 + 0.337435i \(0.109559\pi\)
\(744\) −1.81307 8.17983i −0.0664705 0.299887i
\(745\) 1.10817 6.28473i 0.0406001 0.230255i
\(746\) −3.07286 13.0732i −0.112505 0.478645i
\(747\) −12.2158 + 1.20464i −0.446952 + 0.0440753i
\(748\) −29.7230 1.84164i −1.08678 0.0673371i
\(749\) 1.99306 + 5.34590i 0.0728247 + 0.195335i
\(750\) −10.1733 + 15.1072i −0.371478 + 0.551636i
\(751\) −23.5971 + 4.16081i −0.861070 + 0.151830i −0.586710 0.809797i \(-0.699577\pi\)
−0.274360 + 0.961627i \(0.588466\pi\)
\(752\) −36.9406 + 23.9061i −1.34708 + 0.871766i
\(753\) 3.19750 25.3676i 0.116523 0.924448i
\(754\) 0.746096 + 13.2320i 0.0271712 + 0.481883i
\(755\) −6.99920 −0.254727
\(756\) −11.4682 + 24.9896i −0.417094 + 0.908864i
\(757\) 33.0690 1.20191 0.600957 0.799281i \(-0.294786\pi\)
0.600957 + 0.799281i \(0.294786\pi\)
\(758\) 1.46974 + 26.0659i 0.0533834 + 0.946758i
\(759\) −15.0045 11.3824i −0.544628 0.413156i
\(760\) −1.33848 3.74200i −0.0485519 0.135737i
\(761\) −26.4161 + 4.65788i −0.957585 + 0.168848i −0.630536 0.776160i \(-0.717165\pi\)
−0.327048 + 0.945008i \(0.606054\pi\)
\(762\) −28.9469 2.00224i −1.04864 0.0725335i
\(763\) 1.32311 1.60201i 0.0478999 0.0579966i
\(764\) −0.985823 + 15.9106i −0.0356658 + 0.575624i
\(765\) −14.3865 9.83885i −0.520144 0.355724i
\(766\) 2.66975 + 11.3583i 0.0964620 + 0.410390i
\(767\) 3.93486 22.3157i 0.142080 0.805774i
\(768\) −18.3145 + 20.7985i −0.660869 + 0.750502i
\(769\) −28.4299 + 23.8555i −1.02521 + 0.860253i −0.990273 0.139137i \(-0.955567\pi\)
−0.0349363 + 0.999390i \(0.511123\pi\)
\(770\) −0.665375 + 6.00161i −0.0239784 + 0.216283i
\(771\) 0.266110 + 5.41015i 0.00958373 + 0.194842i
\(772\) 35.3574 + 8.51828i 1.27254 + 0.306580i
\(773\) 51.2688i 1.84401i −0.387175 0.922006i \(-0.626549\pi\)
0.387175 0.922006i \(-0.373451\pi\)
\(774\) 37.2430 + 14.4014i 1.33867 + 0.517647i
\(775\) 7.47424i 0.268483i
\(776\) 15.0641 8.58605i 0.540770 0.308221i
\(777\) −4.76691 + 15.8511i −0.171012 + 0.568656i
\(778\) 9.17978 + 1.09020i 0.329111 + 0.0390855i
\(779\) 11.8763 9.96542i 0.425514 0.357048i
\(780\) −0.814051 + 4.29609i −0.0291477 + 0.153825i
\(781\) 8.51318 3.09854i 0.304625 0.110875i
\(782\) −37.9142 40.3360i −1.35581 1.44241i
\(783\) 14.5825 + 26.9160i 0.521137 + 0.961901i
\(784\) 27.8363 + 3.02309i 0.994154 + 0.107968i
\(785\) −3.64149 + 4.33976i −0.129970 + 0.154893i
\(786\) 7.54787 16.9873i 0.269224 0.605915i
\(787\) 9.37260 25.7510i 0.334097 0.917924i −0.652937 0.757412i \(-0.726463\pi\)
0.987034 0.160512i \(-0.0513144\pi\)
\(788\) −3.65464 1.59254i −0.130191 0.0567318i
\(789\) 1.09945 + 0.340003i 0.0391416 + 0.0121044i
\(790\) −10.4386 + 0.588584i −0.371387 + 0.0209409i
\(791\) 4.19548 7.39934i 0.149174 0.263090i
\(792\) 12.2691 + 12.1356i 0.435965 + 0.431218i
\(793\) 4.43934 7.68917i 0.157646 0.273050i
\(794\) −22.0307 + 1.24222i −0.781842 + 0.0440846i
\(795\) −19.9560 + 0.981579i −0.707766 + 0.0348130i
\(796\) −4.34103 38.3718i −0.153864 1.36005i
\(797\) 9.62153 + 11.4665i 0.340812 + 0.406164i 0.909041 0.416706i \(-0.136816\pi\)
−0.568229 + 0.822870i \(0.692371\pi\)
\(798\) 3.25721 + 11.0035i 0.115304 + 0.389519i
\(799\) 27.5456 + 75.6809i 0.974493 + 2.67740i
\(800\) 19.9662 14.5789i 0.705911 0.515442i
\(801\) −16.9619 16.5918i −0.599318 0.586243i
\(802\) 26.6742 + 28.3781i 0.941900 + 1.00207i
\(803\) −6.87004 + 2.50049i −0.242439 + 0.0882404i
\(804\) −31.5259 + 25.7765i −1.11183 + 0.909066i
\(805\) −8.54213 + 7.28187i −0.301071 + 0.256652i
\(806\) 1.51728 + 3.53545i 0.0534440 + 0.124531i
\(807\) −45.2307 5.70118i −1.59220 0.200691i
\(808\) 13.3758 22.8732i 0.470559 0.804675i
\(809\) 5.63879 + 3.25556i 0.198249 + 0.114459i 0.595839 0.803104i \(-0.296820\pi\)
−0.397589 + 0.917563i \(0.630153\pi\)
\(810\) 2.52727 + 9.77855i 0.0887993 + 0.343583i
\(811\) 40.6079i 1.42594i 0.701196 + 0.712969i \(0.252650\pi\)
−0.701196 + 0.712969i \(0.747350\pi\)
\(812\) 21.3002 22.7626i 0.747489 0.798810i
\(813\) 7.14419 9.41756i 0.250558 0.330288i
\(814\) 8.32159 + 6.21917i 0.291671 + 0.217982i
\(815\) 4.01892 3.37228i 0.140777 0.118126i
\(816\) 29.6176 + 41.1795i 1.03682 + 1.44157i
\(817\) 15.6602 5.69986i 0.547882 0.199413i
\(818\) 13.7592 + 4.14702i 0.481080 + 0.144997i
\(819\) 3.03768 12.2548i 0.106145 0.428218i
\(820\) −11.5811 7.67859i −0.404429 0.268148i
\(821\) 9.81497 11.6970i 0.342545 0.408229i −0.567078 0.823664i \(-0.691926\pi\)
0.909623 + 0.415435i \(0.136371\pi\)
\(822\) 38.1204 + 36.7570i 1.32960 + 1.28205i
\(823\) 32.1857 5.67520i 1.12192 0.197825i 0.418237 0.908338i \(-0.362648\pi\)
0.703684 + 0.710513i \(0.251537\pi\)
\(824\) −0.242867 + 0.0868714i −0.00846066 + 0.00302631i
\(825\) −8.34308 12.9380i −0.290469 0.450444i
\(826\) −44.3579 + 29.5536i −1.54341 + 1.02830i
\(827\) −21.1490 36.6312i −0.735423 1.27379i −0.954537 0.298091i \(-0.903650\pi\)
0.219114 0.975699i \(-0.429683\pi\)
\(828\) 1.16786 + 32.0576i 0.0405861 + 1.11408i
\(829\) −3.76673 6.52417i −0.130824 0.226594i 0.793171 0.609000i \(-0.208429\pi\)
−0.923994 + 0.382406i \(0.875096\pi\)
\(830\) 4.09948 + 2.06835i 0.142295 + 0.0717935i
\(831\) 35.7068 + 11.0422i 1.23865 + 0.383050i
\(832\) 6.48480 10.9492i 0.224820 0.379596i
\(833\) 16.7759 48.4265i 0.581251 1.67788i
\(834\) −15.9632 + 11.6164i −0.552761 + 0.402242i
\(835\) 12.9219 + 2.27847i 0.447179 + 0.0788498i
\(836\) 7.18855 + 0.445404i 0.248621 + 0.0154046i
\(837\) 6.65030 + 5.89449i 0.229868 + 0.203743i
\(838\) 18.7712 17.6441i 0.648439 0.609505i
\(839\) −24.8238 20.8297i −0.857014 0.719120i 0.104308 0.994545i \(-0.466737\pi\)
−0.961323 + 0.275425i \(0.911182\pi\)
\(840\) 8.63135 5.59330i 0.297810 0.192987i
\(841\) −0.991232 5.62156i −0.0341804 0.193847i
\(842\) 38.5776 16.5561i 1.32947 0.570561i
\(843\) −17.9867 19.4130i −0.619495 0.668620i
\(844\) 5.28682 21.9444i 0.181980 0.755356i
\(845\) 8.30792i 0.285801i
\(846\) 16.8322 43.5293i 0.578704 1.49657i
\(847\) 15.7973 + 8.95719i 0.542802 + 0.307773i
\(848\) 55.5807 + 17.0894i 1.90865 + 0.586851i
\(849\) 39.0843 25.2035i 1.34137 0.864982i
\(850\) −17.8459 41.5830i −0.612109 1.42628i
\(851\) 3.35343 + 19.0182i 0.114954 + 0.651937i
\(852\) −13.2644 7.88510i −0.454432 0.270139i
\(853\) 30.6631 11.1605i 1.04989 0.382127i 0.241266 0.970459i \(-0.422437\pi\)
0.808619 + 0.588332i \(0.200215\pi\)
\(854\) −20.2928 + 4.93697i −0.694404 + 0.168940i
\(855\) 3.47939 + 2.37954i 0.118993 + 0.0813786i
\(856\) −3.89452 4.69402i −0.133112 0.160438i
\(857\) 0.736228 0.877402i 0.0251491 0.0299715i −0.753323 0.657650i \(-0.771550\pi\)
0.778472 + 0.627679i \(0.215995\pi\)
\(858\) −6.57285 4.42624i −0.224394 0.151109i
\(859\) 41.2185 7.26793i 1.40636 0.247979i 0.581604 0.813472i \(-0.302425\pi\)
0.824753 + 0.565493i \(0.191314\pi\)
\(860\) −8.87516 12.0140i −0.302640 0.409675i
\(861\) 32.1539 + 23.9996i 1.09580 + 0.817905i
\(862\) −4.80254 + 9.51866i −0.163575 + 0.324207i
\(863\) 4.98661 + 8.63707i 0.169746 + 0.294009i 0.938331 0.345739i \(-0.112372\pi\)
−0.768584 + 0.639748i \(0.779039\pi\)
\(864\) 2.77436 29.2627i 0.0943857 0.995536i
\(865\) −6.77179 + 11.7291i −0.230248 + 0.398801i
\(866\) −22.1873 + 1.25104i −0.753955 + 0.0425121i
\(867\) 58.4382 24.5843i 1.98466 0.834926i
\(868\) 3.55039 8.32413i 0.120508 0.282539i
\(869\) 6.48049 17.8050i 0.219835 0.603993i
\(870\) 0.790183 11.4239i 0.0267897 0.387306i
\(871\) 12.0197 14.3245i 0.407273 0.485369i
\(872\) −0.771283 + 2.08300i −0.0261189 + 0.0705394i
\(873\) −7.58808 + 16.7526i −0.256818 + 0.566990i
\(874\) 9.16960 + 9.75534i 0.310166 + 0.329979i
\(875\) −18.4332 + 6.87226i −0.623156 + 0.232325i
\(876\) 10.7042 + 6.36319i 0.361663 + 0.214992i
\(877\) −10.4009 3.78562i −0.351213 0.127831i 0.160388 0.987054i \(-0.448725\pi\)
−0.511602 + 0.859223i \(0.670948\pi\)
\(878\) −10.4092 24.2545i −0.351292 0.818550i
\(879\) −20.8051 + 13.4162i −0.701740 + 0.452517i
\(880\) −1.44213 6.29215i −0.0486141 0.212108i
\(881\) 27.6047 15.9376i 0.930025 0.536950i 0.0432056 0.999066i \(-0.486243\pi\)
0.886820 + 0.462116i \(0.152910\pi\)
\(882\) −25.7837 + 14.7378i −0.868181 + 0.496247i
\(883\) 0.372870 + 0.215276i 0.0125481 + 0.00724463i 0.506261 0.862380i \(-0.331027\pi\)
−0.493713 + 0.869625i \(0.664361\pi\)
\(884\) −16.8828 16.0467i −0.567831 0.539709i
\(885\) −5.78449 + 18.7051i −0.194444 + 0.628766i
\(886\) −1.67601 1.25258i −0.0563067 0.0420811i
\(887\) −24.2559 + 20.3531i −0.814435 + 0.683392i −0.951662 0.307148i \(-0.900625\pi\)
0.137227 + 0.990540i \(0.456181\pi\)
\(888\) −0.771134 17.6784i −0.0258776 0.593250i
\(889\) −24.1648 19.9579i −0.810461 0.669366i
\(890\) 2.03088 + 8.64024i 0.0680754 + 0.289621i
\(891\) −18.0914 2.78008i −0.606086 0.0931361i
\(892\) −28.2096 1.74787i −0.944527 0.0585231i
\(893\) −6.66195 18.3036i −0.222934 0.612505i
\(894\) −2.07392 19.5899i −0.0693621 0.655185i
\(895\) 4.48030 0.789998i 0.149760 0.0264067i
\(896\) −29.1617 + 6.75240i −0.974224 + 0.225582i
\(897\) −3.26749 14.3634i −0.109098 0.479579i
\(898\) 41.9918 27.5072i 1.40128 0.917926i
\(899\) −5.03779 8.72571i −0.168020 0.291019i
\(900\) −8.06543 + 24.9508i −0.268848 + 0.831692i
\(901\) 53.2164 92.1735i 1.77289 3.07074i
\(902\) 21.0652 13.7990i 0.701394 0.459456i
\(903\) 23.6556 + 36.0637i 0.787208 + 1.20013i
\(904\) −1.62876 + 8.94626i −0.0541718 + 0.297548i
\(905\) 0.898666 2.46906i 0.0298727 0.0820745i
\(906\) −20.7641 + 5.97096i −0.689842 + 0.198372i
\(907\) −29.7661 5.24856i −0.988366 0.174276i −0.343981 0.938977i \(-0.611776\pi\)
−0.644385 + 0.764701i \(0.722887\pi\)
\(908\) 0.186999 3.01805i 0.00620579 0.100158i
\(909\) 2.75808 + 27.9687i 0.0914796 + 0.927663i
\(910\) −3.41598 + 3.26138i −0.113239 + 0.108114i
\(911\) −4.29164 + 24.3391i −0.142188 + 0.806391i 0.827393 + 0.561623i \(0.189823\pi\)
−0.969582 + 0.244768i \(0.921288\pi\)
\(912\) −7.16307 9.95934i −0.237193 0.329787i
\(913\) −6.37462 + 5.34894i −0.210969 + 0.177024i
\(914\) 2.42368 20.4081i 0.0801682 0.675040i
\(915\) −4.63650 + 6.11190i −0.153278 + 0.202053i
\(916\) 48.1072 + 11.5899i 1.58951 + 0.382943i
\(917\) 17.3093 10.1742i 0.571604 0.335981i
\(918\) −51.0730 16.9154i −1.68566 0.558292i
\(919\) 9.69494 5.59737i 0.319806 0.184640i −0.331500 0.943455i \(-0.607555\pi\)
0.651306 + 0.758815i \(0.274221\pi\)
\(920\) 6.05749 10.3586i 0.199709 0.341511i
\(921\) 22.0921 29.1220i 0.727958 0.959604i
\(922\) −9.43084 + 12.6190i −0.310588 + 0.415583i
\(923\) 6.65852 + 2.42350i 0.219168 + 0.0797706i
\(924\) 3.14600 + 18.3723i 0.103496 + 0.604403i
\(925\) −2.74117 + 15.5459i −0.0901290 + 0.511147i
\(926\) 22.7488 5.34709i 0.747572 0.175716i
\(927\) 0.154439 0.225822i 0.00507245 0.00741698i
\(928\) −13.4828 + 30.4775i −0.442593 + 1.00047i
\(929\) −19.3022 + 23.0035i −0.633285 + 0.754719i −0.983294 0.182027i \(-0.941734\pi\)
0.350009 + 0.936746i \(0.386179\pi\)
\(930\) −0.918681 3.19473i −0.0301247 0.104759i
\(931\) −4.05728 + 11.7120i −0.132972 + 0.383846i
\(932\) 11.9655 + 5.21404i 0.391942 + 0.170792i
\(933\) 8.20828 + 12.7290i 0.268727 + 0.416728i
\(934\) 27.0498 1.52522i 0.885096 0.0499066i
\(935\) −11.8155 −0.386408
\(936\) 1.24996 + 13.4394i 0.0408562 + 0.439281i
\(937\) −8.39440 + 14.5395i −0.274233 + 0.474985i −0.969941 0.243339i \(-0.921757\pi\)
0.695708 + 0.718324i \(0.255091\pi\)
\(938\) −43.8948 + 2.81830i −1.43321 + 0.0920207i
\(939\) 52.6275 + 16.2749i 1.71743 + 0.531111i
\(940\) −14.0419 + 10.3732i −0.457997 + 0.338337i
\(941\) 4.19846 11.5352i 0.136866 0.376036i −0.852258 0.523122i \(-0.824767\pi\)
0.989124 + 0.147086i \(0.0469895\pi\)
\(942\) −7.10080 + 15.9811i −0.231356 + 0.520691i
\(943\) 46.1002 + 8.12871i 1.50123 + 0.264707i
\(944\) 34.3647 45.4530i 1.11847 1.47937i
\(945\) −3.92825 + 10.1773i −0.127786 + 0.331067i
\(946\) 26.3514 6.19389i 0.856759 0.201381i
\(947\) 0.918014 5.20632i 0.0298315 0.169183i −0.966252 0.257598i \(-0.917069\pi\)
0.996084 + 0.0884151i \(0.0281802\pi\)
\(948\) −30.4654 + 10.6512i −0.989470 + 0.345934i
\(949\) −5.37336 1.95574i −0.174426 0.0634860i
\(950\) 4.31606 + 10.0569i 0.140031 + 0.326289i
\(951\) −27.9526 30.1692i −0.906425 0.978303i
\(952\) 0.122544 + 54.7884i 0.00397167 + 1.77570i
\(953\) −9.94744 5.74316i −0.322229 0.186039i 0.330157 0.943926i \(-0.392898\pi\)
−0.652386 + 0.757887i \(0.726232\pi\)
\(954\) −58.3649 + 19.9363i −1.88963 + 0.645461i
\(955\) 6.32478i 0.204665i
\(956\) −3.44480 11.6635i −0.111413 0.377223i
\(957\) 18.4605 + 9.48090i 0.596743 + 0.306474i
\(958\) −2.53333 1.89329i −0.0818481 0.0611695i
\(959\) 10.3709 + 56.2500i 0.334895 + 1.81641i
\(960\) −6.74224 + 8.68559i −0.217605 + 0.280326i
\(961\) 21.5068 + 18.0463i 0.693768 + 0.582140i
\(962\) 1.85923 + 7.90995i 0.0599440 + 0.255027i
\(963\) 6.26690 + 1.60535i 0.201948 + 0.0517316i
\(964\) −7.50046 + 3.73215i −0.241574 + 0.120205i
\(965\) 14.2106 + 2.50570i 0.457454 + 0.0806614i
\(966\) −19.1294 + 28.8900i −0.615477 + 0.929519i
\(967\) 20.4496 56.1849i 0.657616 1.80679i 0.0701496 0.997536i \(-0.477652\pi\)
0.587466 0.809249i \(-0.300125\pi\)
\(968\) −19.0999 3.47734i −0.613894 0.111766i
\(969\) −20.6974 + 8.70719i −0.664898 + 0.279715i
\(970\) 5.75473 3.76970i 0.184773 0.121038i
\(971\) 7.40502 + 12.8259i 0.237638 + 0.411602i 0.960036 0.279876i \(-0.0902934\pi\)
−0.722398 + 0.691478i \(0.756960\pi\)
\(972\) 15.8395 + 26.8535i 0.508053 + 0.861326i
\(973\) −21.3236 + 0.166155i −0.683605 + 0.00532668i
\(974\) −52.8205 26.6501i −1.69248 0.853923i
\(975\) 1.50580 11.9464i 0.0482242 0.382590i
\(976\) 18.7440 12.1302i 0.599982 0.388278i
\(977\) −6.17928 7.36418i −0.197693 0.235601i 0.658086 0.752942i \(-0.271366\pi\)
−0.855779 + 0.517341i \(0.826922\pi\)
\(978\) 9.04585 13.4329i 0.289254 0.429535i
\(979\) −15.8409 2.79318i −0.506278 0.0892705i
\(980\) 11.0974 + 0.514146i 0.354493 + 0.0164238i
\(981\) −0.634825 2.26881i −0.0202684 0.0724375i
\(982\) −6.11621 1.84342i −0.195176 0.0588259i
\(983\) 6.19092 35.1105i 0.197460 1.11985i −0.711412 0.702775i \(-0.751944\pi\)
0.908872 0.417075i \(-0.136945\pi\)
\(984\) −40.9075 12.8999i −1.30408 0.411235i
\(985\) −1.48632 0.540975i −0.0473580 0.0172369i
\(986\) 48.8617 + 36.5170i 1.55607 + 1.16294i
\(987\) 42.1510 27.6484i 1.34168 0.880059i
\(988\) 4.08314 + 3.88092i 0.129902 + 0.123469i
\(989\) 43.5779 + 25.1597i 1.38570 + 0.800032i
\(990\) 5.15635 + 4.50465i 0.163879 + 0.143167i
\(991\) 44.2710 25.5599i 1.40631 0.811936i 0.411284 0.911507i \(-0.365080\pi\)
0.995030 + 0.0995709i \(0.0317470\pi\)
\(992\) −0.651918 + 9.65251i −0.0206984 + 0.306467i
\(993\) 23.7184 + 25.5993i 0.752682 + 0.812368i
\(994\) −6.69246 15.2649i −0.212272 0.484174i
\(995\) −2.66055 15.0887i −0.0843451 0.478345i
\(996\) 13.9262 + 2.63883i 0.441268 + 0.0836144i
\(997\) −44.0548 + 16.0346i −1.39523 + 0.507822i −0.926759 0.375657i \(-0.877417\pi\)
−0.468470 + 0.883479i \(0.655195\pi\)
\(998\) 15.6819 52.0302i 0.496400 1.64699i
\(999\) 11.6704 + 14.6991i 0.369235 + 0.465060i
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 756.2.bs.a.11.3 840
4.3 odd 2 inner 756.2.bs.a.11.17 yes 840
7.2 even 3 756.2.ci.a.443.95 yes 840
27.5 odd 18 756.2.ci.a.599.77 yes 840
28.23 odd 6 756.2.ci.a.443.77 yes 840
108.59 even 18 756.2.ci.a.599.95 yes 840
189.86 odd 18 inner 756.2.bs.a.275.17 yes 840
756.275 even 18 inner 756.2.bs.a.275.3 yes 840
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
756.2.bs.a.11.3 840 1.1 even 1 trivial
756.2.bs.a.11.17 yes 840 4.3 odd 2 inner
756.2.bs.a.275.3 yes 840 756.275 even 18 inner
756.2.bs.a.275.17 yes 840 189.86 odd 18 inner
756.2.ci.a.443.77 yes 840 28.23 odd 6
756.2.ci.a.443.95 yes 840 7.2 even 3
756.2.ci.a.599.77 yes 840 27.5 odd 18
756.2.ci.a.599.95 yes 840 108.59 even 18