Properties

Label 930.2.r.b.119.10
Level $930$
Weight $2$
Character 930.119
Analytic conductor $7.426$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [930,2,Mod(119,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.119");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.r (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(32\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 119.10
Character \(\chi\) \(=\) 930.119
Dual form 930.2.r.b.719.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +(-1.12093 + 1.32043i) q^{3} +1.00000 q^{4} +(-2.03226 - 0.932700i) q^{5} +(-1.12093 + 1.32043i) q^{6} +(1.69016 + 0.975816i) q^{7} +1.00000 q^{8} +(-0.487050 - 2.96020i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(-1.12093 + 1.32043i) q^{3} +1.00000 q^{4} +(-2.03226 - 0.932700i) q^{5} +(-1.12093 + 1.32043i) q^{6} +(1.69016 + 0.975816i) q^{7} +1.00000 q^{8} +(-0.487050 - 2.96020i) q^{9} +(-2.03226 - 0.932700i) q^{10} +(-0.165181 - 0.286103i) q^{11} +(-1.12093 + 1.32043i) q^{12} +(2.28936 + 3.96529i) q^{13} +(1.69016 + 0.975816i) q^{14} +(3.50957 - 1.63796i) q^{15} +1.00000 q^{16} +(1.39586 + 0.805898i) q^{17} +(-0.487050 - 2.96020i) q^{18} +(-3.00716 + 5.20856i) q^{19} +(-2.03226 - 0.932700i) q^{20} +(-3.18304 + 1.13792i) q^{21} +(-0.165181 - 0.286103i) q^{22} +3.57984i q^{23} +(-1.12093 + 1.32043i) q^{24} +(3.26014 + 3.79097i) q^{25} +(2.28936 + 3.96529i) q^{26} +(4.45467 + 2.67505i) q^{27} +(1.69016 + 0.975816i) q^{28} -5.80181 q^{29} +(3.50957 - 1.63796i) q^{30} +(5.00448 - 2.44033i) q^{31} +1.00000 q^{32} +(0.562934 + 0.102590i) q^{33} +(1.39586 + 0.805898i) q^{34} +(-2.52470 - 3.55952i) q^{35} +(-0.487050 - 2.96020i) q^{36} +(-2.32112 + 4.02031i) q^{37} +(-3.00716 + 5.20856i) q^{38} +(-7.80208 - 1.42186i) q^{39} +(-2.03226 - 0.932700i) q^{40} +(-3.67894 + 2.12404i) q^{41} +(-3.18304 + 1.13792i) q^{42} +(-5.17982 + 8.97172i) q^{43} +(-0.165181 - 0.286103i) q^{44} +(-1.77117 + 6.47016i) q^{45} +3.57984i q^{46} +9.38539 q^{47} +(-1.12093 + 1.32043i) q^{48} +(-1.59557 - 2.76360i) q^{49} +(3.26014 + 3.79097i) q^{50} +(-2.62878 + 0.939773i) q^{51} +(2.28936 + 3.96529i) q^{52} +(-3.84607 + 2.22053i) q^{53} +(4.45467 + 2.67505i) q^{54} +(0.0688434 + 0.735499i) q^{55} +(1.69016 + 0.975816i) q^{56} +(-3.50671 - 9.80914i) q^{57} -5.80181 q^{58} +(1.42124 + 0.820553i) q^{59} +(3.50957 - 1.63796i) q^{60} +2.17067i q^{61} +(5.00448 - 2.44033i) q^{62} +(2.06542 - 5.47849i) q^{63} +1.00000 q^{64} +(-0.954147 - 10.1938i) q^{65} +(0.562934 + 0.102590i) q^{66} +(5.38440 - 3.10868i) q^{67} +(1.39586 + 0.805898i) q^{68} +(-4.72691 - 4.01273i) q^{69} +(-2.52470 - 3.55952i) q^{70} +(0.0180409 - 0.0104159i) q^{71} +(-0.487050 - 2.96020i) q^{72} +(1.98018 + 3.42977i) q^{73} +(-2.32112 + 4.02031i) q^{74} +(-8.66008 + 0.0553790i) q^{75} +(-3.00716 + 5.20856i) q^{76} -0.644747i q^{77} +(-7.80208 - 1.42186i) q^{78} +(-2.32185 - 1.34052i) q^{79} +(-2.03226 - 0.932700i) q^{80} +(-8.52556 + 2.88353i) q^{81} +(-3.67894 + 2.12404i) q^{82} +(12.7695 - 7.37245i) q^{83} +(-3.18304 + 1.13792i) q^{84} +(-2.08508 - 2.93971i) q^{85} +(-5.17982 + 8.97172i) q^{86} +(6.50340 - 7.66086i) q^{87} +(-0.165181 - 0.286103i) q^{88} +8.32490 q^{89} +(-1.77117 + 6.47016i) q^{90} +8.93598i q^{91} +3.57984i q^{92} +(-2.38737 + 9.34347i) q^{93} +9.38539 q^{94} +(10.9693 - 7.78035i) q^{95} +(-1.12093 + 1.32043i) q^{96} +1.82231i q^{97} +(-1.59557 - 2.76360i) q^{98} +(-0.766469 + 0.628317i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9} + 2 q^{10} + 64 q^{16} + 6 q^{17} - 4 q^{18} + 4 q^{19} + 2 q^{20} + 2 q^{25} + 18 q^{31} + 64 q^{32} - 8 q^{33} + 6 q^{34} + 16 q^{35} - 4 q^{36} + 4 q^{38} - 8 q^{39} + 2 q^{40} + 9 q^{45} - 4 q^{47} + 30 q^{49} + 2 q^{50} - 8 q^{51} - 6 q^{53} + 6 q^{57} + 18 q^{62} + 12 q^{63} + 64 q^{64} - 8 q^{66} + 6 q^{68} - 10 q^{69} + 16 q^{70} - 4 q^{72} - 63 q^{75} + 4 q^{76} - 8 q^{78} - 30 q^{79} + 2 q^{80} - 12 q^{81} - 54 q^{83} - 16 q^{87} + 9 q^{90} - 18 q^{93} - 4 q^{94} - 56 q^{95} + 30 q^{98} - 102 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.12093 + 1.32043i −0.647167 + 0.762348i
\(4\) 1.00000 0.500000
\(5\) −2.03226 0.932700i −0.908853 0.417116i
\(6\) −1.12093 + 1.32043i −0.457616 + 0.539062i
\(7\) 1.69016 + 0.975816i 0.638822 + 0.368824i 0.784160 0.620558i \(-0.213094\pi\)
−0.145339 + 0.989382i \(0.546427\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.487050 2.96020i −0.162350 0.986733i
\(10\) −2.03226 0.932700i −0.642656 0.294946i
\(11\) −0.165181 0.286103i −0.0498041 0.0862632i 0.840049 0.542511i \(-0.182526\pi\)
−0.889853 + 0.456248i \(0.849193\pi\)
\(12\) −1.12093 + 1.32043i −0.323583 + 0.381174i
\(13\) 2.28936 + 3.96529i 0.634954 + 1.09977i 0.986525 + 0.163612i \(0.0523145\pi\)
−0.351570 + 0.936161i \(0.614352\pi\)
\(14\) 1.69016 + 0.975816i 0.451715 + 0.260798i
\(15\) 3.50957 1.63796i 0.906167 0.422919i
\(16\) 1.00000 0.250000
\(17\) 1.39586 + 0.805898i 0.338545 + 0.195459i 0.659628 0.751592i \(-0.270714\pi\)
−0.321084 + 0.947051i \(0.604047\pi\)
\(18\) −0.487050 2.96020i −0.114799 0.697726i
\(19\) −3.00716 + 5.20856i −0.689890 + 1.19492i 0.281983 + 0.959419i \(0.409008\pi\)
−0.971873 + 0.235505i \(0.924325\pi\)
\(20\) −2.03226 0.932700i −0.454427 0.208558i
\(21\) −3.18304 + 1.13792i −0.694596 + 0.248314i
\(22\) −0.165181 0.286103i −0.0352168 0.0609973i
\(23\) 3.57984i 0.746448i 0.927741 + 0.373224i \(0.121748\pi\)
−0.927741 + 0.373224i \(0.878252\pi\)
\(24\) −1.12093 + 1.32043i −0.228808 + 0.269531i
\(25\) 3.26014 + 3.79097i 0.652029 + 0.758194i
\(26\) 2.28936 + 3.96529i 0.448981 + 0.777657i
\(27\) 4.45467 + 2.67505i 0.857302 + 0.514814i
\(28\) 1.69016 + 0.975816i 0.319411 + 0.184412i
\(29\) −5.80181 −1.07737 −0.538684 0.842508i \(-0.681078\pi\)
−0.538684 + 0.842508i \(0.681078\pi\)
\(30\) 3.50957 1.63796i 0.640757 0.299049i
\(31\) 5.00448 2.44033i 0.898830 0.438296i
\(32\) 1.00000 0.176777
\(33\) 0.562934 + 0.102590i 0.0979942 + 0.0178586i
\(34\) 1.39586 + 0.805898i 0.239387 + 0.138210i
\(35\) −2.52470 3.55952i −0.426753 0.601669i
\(36\) −0.487050 2.96020i −0.0811751 0.493367i
\(37\) −2.32112 + 4.02031i −0.381591 + 0.660934i −0.991290 0.131699i \(-0.957957\pi\)
0.609699 + 0.792633i \(0.291290\pi\)
\(38\) −3.00716 + 5.20856i −0.487826 + 0.844939i
\(39\) −7.80208 1.42186i −1.24933 0.227680i
\(40\) −2.03226 0.932700i −0.321328 0.147473i
\(41\) −3.67894 + 2.12404i −0.574554 + 0.331719i −0.758966 0.651130i \(-0.774295\pi\)
0.184412 + 0.982849i \(0.440962\pi\)
\(42\) −3.18304 + 1.13792i −0.491154 + 0.175585i
\(43\) −5.17982 + 8.97172i −0.789916 + 1.36817i 0.136102 + 0.990695i \(0.456542\pi\)
−0.926018 + 0.377479i \(0.876791\pi\)
\(44\) −0.165181 0.286103i −0.0249020 0.0431316i
\(45\) −1.77117 + 6.47016i −0.264030 + 0.964515i
\(46\) 3.57984i 0.527818i
\(47\) 9.38539 1.36900 0.684500 0.729013i \(-0.260021\pi\)
0.684500 + 0.729013i \(0.260021\pi\)
\(48\) −1.12093 + 1.32043i −0.161792 + 0.190587i
\(49\) −1.59557 2.76360i −0.227938 0.394800i
\(50\) 3.26014 + 3.79097i 0.461054 + 0.536124i
\(51\) −2.62878 + 0.939773i −0.368103 + 0.131595i
\(52\) 2.28936 + 3.96529i 0.317477 + 0.549887i
\(53\) −3.84607 + 2.22053i −0.528299 + 0.305013i −0.740323 0.672251i \(-0.765328\pi\)
0.212025 + 0.977264i \(0.431994\pi\)
\(54\) 4.45467 + 2.67505i 0.606204 + 0.364028i
\(55\) 0.0688434 + 0.735499i 0.00928285 + 0.0991747i
\(56\) 1.69016 + 0.975816i 0.225858 + 0.130399i
\(57\) −3.50671 9.80914i −0.464475 1.29925i
\(58\) −5.80181 −0.761815
\(59\) 1.42124 + 0.820553i 0.185030 + 0.106827i 0.589654 0.807656i \(-0.299264\pi\)
−0.404624 + 0.914483i \(0.632598\pi\)
\(60\) 3.50957 1.63796i 0.453084 0.211460i
\(61\) 2.17067i 0.277926i 0.990298 + 0.138963i \(0.0443768\pi\)
−0.990298 + 0.138963i \(0.955623\pi\)
\(62\) 5.00448 2.44033i 0.635569 0.309922i
\(63\) 2.06542 5.47849i 0.260218 0.690225i
\(64\) 1.00000 0.125000
\(65\) −0.954147 10.1938i −0.118347 1.26438i
\(66\) 0.562934 + 0.102590i 0.0692924 + 0.0126280i
\(67\) 5.38440 3.10868i 0.657809 0.379786i −0.133633 0.991031i \(-0.542664\pi\)
0.791442 + 0.611245i \(0.209331\pi\)
\(68\) 1.39586 + 0.805898i 0.169272 + 0.0977295i
\(69\) −4.72691 4.01273i −0.569053 0.483076i
\(70\) −2.52470 3.55952i −0.301760 0.425445i
\(71\) 0.0180409 0.0104159i 0.00214106 0.00123614i −0.498929 0.866643i \(-0.666273\pi\)
0.501070 + 0.865407i \(0.332940\pi\)
\(72\) −0.487050 2.96020i −0.0573994 0.348863i
\(73\) 1.98018 + 3.42977i 0.231762 + 0.401424i 0.958327 0.285674i \(-0.0922175\pi\)
−0.726564 + 0.687098i \(0.758884\pi\)
\(74\) −2.32112 + 4.02031i −0.269825 + 0.467351i
\(75\) −8.66008 + 0.0553790i −0.999980 + 0.00639461i
\(76\) −3.00716 + 5.20856i −0.344945 + 0.597462i
\(77\) 0.644747i 0.0734757i
\(78\) −7.80208 1.42186i −0.883411 0.160994i
\(79\) −2.32185 1.34052i −0.261228 0.150820i 0.363667 0.931529i \(-0.381525\pi\)
−0.624895 + 0.780709i \(0.714858\pi\)
\(80\) −2.03226 0.932700i −0.227213 0.104279i
\(81\) −8.52556 + 2.88353i −0.947285 + 0.320393i
\(82\) −3.67894 + 2.12404i −0.406271 + 0.234561i
\(83\) 12.7695 7.37245i 1.40163 0.809231i 0.407070 0.913397i \(-0.366551\pi\)
0.994560 + 0.104166i \(0.0332173\pi\)
\(84\) −3.18304 + 1.13792i −0.347298 + 0.124157i
\(85\) −2.08508 2.93971i −0.226158 0.318856i
\(86\) −5.17982 + 8.97172i −0.558555 + 0.967445i
\(87\) 6.50340 7.66086i 0.697237 0.821330i
\(88\) −0.165181 0.286103i −0.0176084 0.0304987i
\(89\) 8.32490 0.882437 0.441219 0.897400i \(-0.354546\pi\)
0.441219 + 0.897400i \(0.354546\pi\)
\(90\) −1.77117 + 6.47016i −0.186697 + 0.682015i
\(91\) 8.93598i 0.936745i
\(92\) 3.57984i 0.373224i
\(93\) −2.38737 + 9.34347i −0.247559 + 0.968873i
\(94\) 9.38539 0.968029
\(95\) 10.9693 7.78035i 1.12543 0.798247i
\(96\) −1.12093 + 1.32043i −0.114404 + 0.134765i
\(97\) 1.82231i 0.185027i 0.995711 + 0.0925137i \(0.0294902\pi\)
−0.995711 + 0.0925137i \(0.970510\pi\)
\(98\) −1.59557 2.76360i −0.161176 0.279166i
\(99\) −0.766469 + 0.628317i −0.0770331 + 0.0631482i
\(100\) 3.26014 + 3.79097i 0.326014 + 0.379097i
\(101\) 0.765602i 0.0761803i −0.999274 0.0380901i \(-0.987873\pi\)
0.999274 0.0380901i \(-0.0121274\pi\)
\(102\) −2.62878 + 0.939773i −0.260288 + 0.0930514i
\(103\) −8.27469 + 4.77739i −0.815329 + 0.470731i −0.848803 0.528709i \(-0.822676\pi\)
0.0334739 + 0.999440i \(0.489343\pi\)
\(104\) 2.28936 + 3.96529i 0.224490 + 0.388829i
\(105\) 7.53009 + 0.656278i 0.734862 + 0.0640462i
\(106\) −3.84607 + 2.22053i −0.373564 + 0.215677i
\(107\) 4.55170 7.88378i 0.440030 0.762154i −0.557661 0.830068i \(-0.688301\pi\)
0.997691 + 0.0679147i \(0.0216346\pi\)
\(108\) 4.45467 + 2.67505i 0.428651 + 0.257407i
\(109\) 7.60812 0.728726 0.364363 0.931257i \(-0.381287\pi\)
0.364363 + 0.931257i \(0.381287\pi\)
\(110\) 0.0688434 + 0.735499i 0.00656396 + 0.0701271i
\(111\) −2.70671 7.57134i −0.256909 0.718640i
\(112\) 1.69016 + 0.975816i 0.159705 + 0.0922060i
\(113\) −1.15680 2.00363i −0.108822 0.188486i 0.806471 0.591274i \(-0.201375\pi\)
−0.915293 + 0.402788i \(0.868041\pi\)
\(114\) −3.50671 9.80914i −0.328433 0.918710i
\(115\) 3.33891 7.27515i 0.311355 0.678411i
\(116\) −5.80181 −0.538684
\(117\) 10.6230 8.70826i 0.982098 0.805079i
\(118\) 1.42124 + 0.820553i 0.130836 + 0.0755380i
\(119\) 1.57282 + 2.72420i 0.144180 + 0.249727i
\(120\) 3.50957 1.63796i 0.320379 0.149525i
\(121\) 5.44543 9.43176i 0.495039 0.857433i
\(122\) 2.17067i 0.196523i
\(123\) 1.31919 7.23866i 0.118947 0.652688i
\(124\) 5.00448 2.44033i 0.449415 0.219148i
\(125\) −3.08961 10.7450i −0.276343 0.961059i
\(126\) 2.06542 5.47849i 0.184002 0.488063i
\(127\) 5.06743 8.77704i 0.449661 0.778836i −0.548702 0.836018i \(-0.684878\pi\)
0.998364 + 0.0571814i \(0.0182113\pi\)
\(128\) 1.00000 0.0883883
\(129\) −6.04029 16.8962i −0.531818 1.48763i
\(130\) −0.954147 10.1938i −0.0836842 0.894053i
\(131\) −7.99557 4.61625i −0.698577 0.403323i 0.108240 0.994125i \(-0.465478\pi\)
−0.806817 + 0.590801i \(0.798812\pi\)
\(132\) 0.562934 + 0.102590i 0.0489971 + 0.00892931i
\(133\) −10.1652 + 5.86887i −0.881433 + 0.508896i
\(134\) 5.38440 3.10868i 0.465141 0.268549i
\(135\) −6.55802 9.59126i −0.564425 0.825484i
\(136\) 1.39586 + 0.805898i 0.119694 + 0.0691052i
\(137\) −8.94523 + 5.16453i −0.764242 + 0.441235i −0.830817 0.556546i \(-0.812126\pi\)
0.0665746 + 0.997781i \(0.478793\pi\)
\(138\) −4.72691 4.01273i −0.402381 0.341586i
\(139\) 15.5578i 1.31959i 0.751445 + 0.659796i \(0.229357\pi\)
−0.751445 + 0.659796i \(0.770643\pi\)
\(140\) −2.52470 3.55952i −0.213376 0.300835i
\(141\) −10.5203 + 12.3927i −0.885971 + 1.04366i
\(142\) 0.0180409 0.0104159i 0.00151396 0.000874086i
\(143\) 0.756320 1.30998i 0.0632467 0.109546i
\(144\) −0.487050 2.96020i −0.0405875 0.246683i
\(145\) 11.7908 + 5.41134i 0.979170 + 0.449388i
\(146\) 1.98018 + 3.42977i 0.163881 + 0.283850i
\(147\) 5.43764 + 0.990965i 0.448489 + 0.0817334i
\(148\) −2.32112 + 4.02031i −0.190795 + 0.330467i
\(149\) 6.57925 + 3.79853i 0.538993 + 0.311188i 0.744671 0.667432i \(-0.232607\pi\)
−0.205678 + 0.978620i \(0.565940\pi\)
\(150\) −8.66008 + 0.0553790i −0.707092 + 0.00452168i
\(151\) 12.8565i 1.04625i −0.852257 0.523123i \(-0.824767\pi\)
0.852257 0.523123i \(-0.175233\pi\)
\(152\) −3.00716 + 5.20856i −0.243913 + 0.422470i
\(153\) 1.70577 4.52452i 0.137903 0.365786i
\(154\) 0.644747i 0.0519552i
\(155\) −12.4465 + 0.291708i −0.999725 + 0.0234306i
\(156\) −7.80208 1.42186i −0.624666 0.113840i
\(157\) 18.5672i 1.48182i −0.671602 0.740912i \(-0.734393\pi\)
0.671602 0.740912i \(-0.265607\pi\)
\(158\) −2.32185 1.34052i −0.184716 0.106646i
\(159\) 1.37912 7.56751i 0.109371 0.600142i
\(160\) −2.03226 0.932700i −0.160664 0.0737364i
\(161\) −3.49326 + 6.05051i −0.275308 + 0.476847i
\(162\) −8.52556 + 2.88353i −0.669832 + 0.226552i
\(163\) 10.2734i 0.804672i −0.915492 0.402336i \(-0.868198\pi\)
0.915492 0.402336i \(-0.131802\pi\)
\(164\) −3.67894 + 2.12404i −0.287277 + 0.165860i
\(165\) −1.04834 0.733537i −0.0816132 0.0571058i
\(166\) 12.7695 7.37245i 0.991102 0.572213i
\(167\) 13.1917 + 7.61625i 1.02081 + 0.589363i 0.914338 0.404953i \(-0.132712\pi\)
0.106469 + 0.994316i \(0.466045\pi\)
\(168\) −3.18304 + 1.13792i −0.245577 + 0.0877923i
\(169\) −3.98235 + 6.89762i −0.306334 + 0.530586i
\(170\) −2.08508 2.93971i −0.159918 0.225465i
\(171\) 16.8830 + 6.36497i 1.29108 + 0.486741i
\(172\) −5.17982 + 8.97172i −0.394958 + 0.684087i
\(173\) 8.51064 + 14.7409i 0.647052 + 1.12073i 0.983824 + 0.179140i \(0.0573316\pi\)
−0.336772 + 0.941586i \(0.609335\pi\)
\(174\) 6.50340 7.66086i 0.493021 0.580768i
\(175\) 1.81088 + 9.58866i 0.136890 + 0.724835i
\(176\) −0.165181 0.286103i −0.0124510 0.0215658i
\(177\) −2.67658 + 0.956862i −0.201184 + 0.0719222i
\(178\) 8.32490 0.623978
\(179\) 13.0503 22.6038i 0.975427 1.68949i 0.296909 0.954906i \(-0.404044\pi\)
0.678518 0.734584i \(-0.262623\pi\)
\(180\) −1.77117 + 6.47016i −0.132015 + 0.482257i
\(181\) 0.630738 0.364157i 0.0468824 0.0270676i −0.476376 0.879242i \(-0.658050\pi\)
0.523258 + 0.852174i \(0.324716\pi\)
\(182\) 8.93598i 0.662379i
\(183\) −2.86621 2.43316i −0.211876 0.179864i
\(184\) 3.57984i 0.263909i
\(185\) 8.46686 6.00539i 0.622496 0.441525i
\(186\) −2.38737 + 9.34347i −0.175050 + 0.685097i
\(187\) 0.532478i 0.0389386i
\(188\) 9.38539 0.684500
\(189\) 4.91877 + 8.86821i 0.357788 + 0.645068i
\(190\) 10.9693 7.78035i 0.795800 0.564446i
\(191\) −20.8724 + 12.0507i −1.51027 + 0.871955i −0.510342 + 0.859971i \(0.670481\pi\)
−0.999928 + 0.0119839i \(0.996185\pi\)
\(192\) −1.12093 + 1.32043i −0.0808959 + 0.0952935i
\(193\) −9.95662 5.74846i −0.716693 0.413783i 0.0968412 0.995300i \(-0.469126\pi\)
−0.813534 + 0.581517i \(0.802459\pi\)
\(194\) 1.82231i 0.130834i
\(195\) 14.5297 + 10.1666i 1.04049 + 0.728044i
\(196\) −1.59557 2.76360i −0.113969 0.197400i
\(197\) −23.3678 + 13.4914i −1.66489 + 0.961223i −0.694557 + 0.719438i \(0.744400\pi\)
−0.970330 + 0.241785i \(0.922267\pi\)
\(198\) −0.766469 + 0.628317i −0.0544706 + 0.0446525i
\(199\) 16.7830 9.68967i 1.18971 0.686882i 0.231473 0.972841i \(-0.425645\pi\)
0.958242 + 0.285959i \(0.0923121\pi\)
\(200\) 3.26014 + 3.79097i 0.230527 + 0.268062i
\(201\) −1.93072 + 10.5943i −0.136183 + 0.747264i
\(202\) 0.765602i 0.0538676i
\(203\) −9.80600 5.66150i −0.688246 0.397359i
\(204\) −2.62878 + 0.939773i −0.184051 + 0.0657973i
\(205\) 9.45765 0.885245i 0.660551 0.0618282i
\(206\) −8.27469 + 4.77739i −0.576525 + 0.332857i
\(207\) 10.5970 1.74356i 0.736545 0.121186i
\(208\) 2.28936 + 3.96529i 0.158739 + 0.274943i
\(209\) 1.98691 0.137437
\(210\) 7.53009 + 0.656278i 0.519626 + 0.0452875i
\(211\) −3.31031 + 5.73362i −0.227891 + 0.394719i −0.957183 0.289484i \(-0.906516\pi\)
0.729292 + 0.684203i \(0.239850\pi\)
\(212\) −3.84607 + 2.22053i −0.264149 + 0.152507i
\(213\) −0.00646907 + 0.0354972i −0.000443253 + 0.00243223i
\(214\) 4.55170 7.88378i 0.311148 0.538924i
\(215\) 18.8947 13.4016i 1.28860 0.913983i
\(216\) 4.45467 + 2.67505i 0.303102 + 0.182014i
\(217\) 10.8397 + 0.758891i 0.735846 + 0.0515169i
\(218\) 7.60812 0.515287
\(219\) −6.74839 1.22984i −0.456014 0.0831048i
\(220\) 0.0688434 + 0.735499i 0.00464142 + 0.0495873i
\(221\) 7.37996i 0.496430i
\(222\) −2.70671 7.57134i −0.181662 0.508155i
\(223\) 8.34451 14.4531i 0.558790 0.967853i −0.438808 0.898581i \(-0.644599\pi\)
0.997598 0.0692716i \(-0.0220675\pi\)
\(224\) 1.69016 + 0.975816i 0.112929 + 0.0651995i
\(225\) 9.63418 11.4971i 0.642279 0.766471i
\(226\) −1.15680 2.00363i −0.0769491 0.133280i
\(227\) −9.22552 15.9791i −0.612320 1.06057i −0.990848 0.134979i \(-0.956903\pi\)
0.378529 0.925589i \(-0.376430\pi\)
\(228\) −3.50671 9.80914i −0.232237 0.649626i
\(229\) 9.54074 + 5.50835i 0.630470 + 0.364002i 0.780934 0.624614i \(-0.214744\pi\)
−0.150464 + 0.988615i \(0.548077\pi\)
\(230\) 3.33891 7.27515i 0.220161 0.479709i
\(231\) 0.851341 + 0.722714i 0.0560141 + 0.0475511i
\(232\) −5.80181 −0.380907
\(233\) −19.4217 −1.27236 −0.636179 0.771542i \(-0.719486\pi\)
−0.636179 + 0.771542i \(0.719486\pi\)
\(234\) 10.6230 8.70826i 0.694448 0.569277i
\(235\) −19.0735 8.75375i −1.24422 0.571032i
\(236\) 1.42124 + 0.820553i 0.0925148 + 0.0534134i
\(237\) 4.37267 1.56320i 0.284036 0.101541i
\(238\) 1.57282 + 2.72420i 0.101951 + 0.176583i
\(239\) −7.58762 13.1421i −0.490802 0.850094i 0.509142 0.860683i \(-0.329963\pi\)
−0.999944 + 0.0105883i \(0.996630\pi\)
\(240\) 3.50957 1.63796i 0.226542 0.105730i
\(241\) 24.4006 + 14.0877i 1.57178 + 0.907469i 0.995951 + 0.0899015i \(0.0286552\pi\)
0.575832 + 0.817568i \(0.304678\pi\)
\(242\) 5.44543 9.43176i 0.350046 0.606297i
\(243\) 5.74903 14.4896i 0.368801 0.929509i
\(244\) 2.17067i 0.138963i
\(245\) 0.664991 + 7.10453i 0.0424847 + 0.453892i
\(246\) 1.31919 7.23866i 0.0841082 0.461520i
\(247\) −27.5379 −1.75220
\(248\) 5.00448 2.44033i 0.317785 0.154961i
\(249\) −4.57884 + 25.1251i −0.290172 + 1.59224i
\(250\) −3.08961 10.7450i −0.195404 0.679571i
\(251\) 0.116519 0.201816i 0.00735460 0.0127385i −0.862325 0.506356i \(-0.830992\pi\)
0.869679 + 0.493617i \(0.164326\pi\)
\(252\) 2.06542 5.47849i 0.130109 0.345113i
\(253\) 1.02420 0.591323i 0.0643910 0.0371762i
\(254\) 5.06743 8.77704i 0.317959 0.550720i
\(255\) 6.21888 + 0.542001i 0.389442 + 0.0339414i
\(256\) 1.00000 0.0625000
\(257\) −7.88542 13.6580i −0.491879 0.851960i 0.508077 0.861312i \(-0.330356\pi\)
−0.999956 + 0.00935193i \(0.997023\pi\)
\(258\) −6.04029 16.8962i −0.376052 1.05191i
\(259\) −7.84616 + 4.52998i −0.487537 + 0.281479i
\(260\) −0.954147 10.1938i −0.0591737 0.632191i
\(261\) 2.82577 + 17.1745i 0.174911 + 1.06308i
\(262\) −7.99557 4.61625i −0.493968 0.285193i
\(263\) 18.7956i 1.15899i 0.814977 + 0.579493i \(0.196749\pi\)
−0.814977 + 0.579493i \(0.803251\pi\)
\(264\) 0.562934 + 0.102590i 0.0346462 + 0.00631398i
\(265\) 9.88730 0.925461i 0.607372 0.0568506i
\(266\) −10.1652 + 5.86887i −0.623268 + 0.359844i
\(267\) −9.33159 + 10.9924i −0.571084 + 0.672725i
\(268\) 5.38440 3.10868i 0.328904 0.189893i
\(269\) −10.3372 17.9046i −0.630271 1.09166i −0.987496 0.157643i \(-0.949610\pi\)
0.357225 0.934018i \(-0.383723\pi\)
\(270\) −6.55802 9.59126i −0.399109 0.583706i
\(271\) 4.19858i 0.255046i −0.991836 0.127523i \(-0.959297\pi\)
0.991836 0.127523i \(-0.0407026\pi\)
\(272\) 1.39586 + 0.805898i 0.0846362 + 0.0488647i
\(273\) −11.7993 10.0166i −0.714126 0.606230i
\(274\) −8.94523 + 5.16453i −0.540401 + 0.312001i
\(275\) 0.546092 1.55893i 0.0329306 0.0940073i
\(276\) −4.72691 4.01273i −0.284527 0.241538i
\(277\) 17.0716 1.02573 0.512866 0.858469i \(-0.328584\pi\)
0.512866 + 0.858469i \(0.328584\pi\)
\(278\) 15.5578i 0.933093i
\(279\) −9.66130 13.6257i −0.578407 0.815748i
\(280\) −2.52470 3.55952i −0.150880 0.212722i
\(281\) 30.4242i 1.81495i 0.420102 + 0.907477i \(0.361994\pi\)
−0.420102 + 0.907477i \(0.638006\pi\)
\(282\) −10.5203 + 12.3927i −0.626476 + 0.737976i
\(283\) 3.94960i 0.234779i −0.993086 0.117390i \(-0.962547\pi\)
0.993086 0.117390i \(-0.0374526\pi\)
\(284\) 0.0180409 0.0104159i 0.00107053 0.000618072i
\(285\) −2.02245 + 23.2054i −0.119799 + 1.37457i
\(286\) 0.756320 1.30998i 0.0447221 0.0774610i
\(287\) −8.29068 −0.489384
\(288\) −0.487050 2.96020i −0.0286997 0.174431i
\(289\) −7.20106 12.4726i −0.423592 0.733682i
\(290\) 11.7908 + 5.41134i 0.692378 + 0.317765i
\(291\) −2.40622 2.04267i −0.141055 0.119744i
\(292\) 1.98018 + 3.42977i 0.115881 + 0.200712i
\(293\) −7.39011 + 12.8000i −0.431735 + 0.747786i −0.997023 0.0771072i \(-0.975432\pi\)
0.565288 + 0.824893i \(0.308765\pi\)
\(294\) 5.43764 + 0.990965i 0.317130 + 0.0577943i
\(295\) −2.12299 2.99316i −0.123606 0.174269i
\(296\) −2.32112 + 4.02031i −0.134913 + 0.233676i
\(297\) 0.0295098 1.71636i 0.00171233 0.0995935i
\(298\) 6.57925 + 3.79853i 0.381126 + 0.220043i
\(299\) −14.1951 + 8.19554i −0.820923 + 0.473960i
\(300\) −8.66008 + 0.0553790i −0.499990 + 0.00319731i
\(301\) −17.5095 + 10.1091i −1.00923 + 0.582679i
\(302\) 12.8565i 0.739808i
\(303\) 1.01092 + 0.858183i 0.0580759 + 0.0493013i
\(304\) −3.00716 + 5.20856i −0.172473 + 0.298731i
\(305\) 2.02458 4.41136i 0.115927 0.252594i
\(306\) 1.70577 4.52452i 0.0975122 0.258650i
\(307\) −11.2636 6.50301i −0.642845 0.371147i 0.142865 0.989742i \(-0.454369\pi\)
−0.785710 + 0.618596i \(0.787702\pi\)
\(308\) 0.644747i 0.0367379i
\(309\) 2.96712 16.2812i 0.168793 0.926206i
\(310\) −12.4465 + 0.291708i −0.706913 + 0.0165679i
\(311\) 24.9699i 1.41591i −0.706256 0.707956i \(-0.749617\pi\)
0.706256 0.707956i \(-0.250383\pi\)
\(312\) −7.80208 1.42186i −0.441706 0.0804972i
\(313\) −6.43179 + 11.1402i −0.363546 + 0.629680i −0.988542 0.150948i \(-0.951767\pi\)
0.624996 + 0.780628i \(0.285101\pi\)
\(314\) 18.5672i 1.04781i
\(315\) −9.30724 + 9.20729i −0.524404 + 0.518772i
\(316\) −2.32185 1.34052i −0.130614 0.0754101i
\(317\) −6.81198 + 11.7987i −0.382599 + 0.662681i −0.991433 0.130617i \(-0.958304\pi\)
0.608834 + 0.793298i \(0.291638\pi\)
\(318\) 1.37912 7.56751i 0.0773369 0.424365i
\(319\) 0.958351 + 1.65991i 0.0536574 + 0.0929373i
\(320\) −2.03226 0.932700i −0.113607 0.0521395i
\(321\) 5.30783 + 14.8473i 0.296254 + 0.828697i
\(322\) −3.49326 + 6.05051i −0.194672 + 0.337182i
\(323\) −8.39513 + 4.84693i −0.467117 + 0.269690i
\(324\) −8.52556 + 2.88353i −0.473642 + 0.160196i
\(325\) −7.56866 + 21.6063i −0.419834 + 1.19850i
\(326\) 10.2734i 0.568989i
\(327\) −8.52814 + 10.0460i −0.471607 + 0.555543i
\(328\) −3.67894 + 2.12404i −0.203136 + 0.117280i
\(329\) 15.8628 + 9.15842i 0.874547 + 0.504920i
\(330\) −1.04834 0.733537i −0.0577093 0.0403799i
\(331\) 13.3530 7.70937i 0.733949 0.423745i −0.0859163 0.996302i \(-0.527382\pi\)
0.819865 + 0.572557i \(0.194048\pi\)
\(332\) 12.7695 7.37245i 0.700815 0.404616i
\(333\) 13.0314 + 4.91290i 0.714117 + 0.269225i
\(334\) 13.1917 + 7.61625i 0.721819 + 0.416743i
\(335\) −13.8420 + 1.29562i −0.756267 + 0.0707873i
\(336\) −3.18304 + 1.13792i −0.173649 + 0.0620785i
\(337\) 8.19338 0.446322 0.223161 0.974782i \(-0.428362\pi\)
0.223161 + 0.974782i \(0.428362\pi\)
\(338\) −3.98235 + 6.89762i −0.216611 + 0.375181i
\(339\) 3.94234 + 0.718458i 0.214118 + 0.0390213i
\(340\) −2.08508 2.93971i −0.113079 0.159428i
\(341\) −1.52483 1.02870i −0.0825743 0.0557071i
\(342\) 16.8830 + 6.36497i 0.912928 + 0.344178i
\(343\) 19.8893i 1.07392i
\(344\) −5.17982 + 8.97172i −0.279277 + 0.483723i
\(345\) 5.86363 + 12.5637i 0.315687 + 0.676407i
\(346\) 8.51064 + 14.7409i 0.457535 + 0.792473i
\(347\) −22.4803 12.9790i −1.20681 0.696751i −0.244748 0.969587i \(-0.578705\pi\)
−0.962061 + 0.272836i \(0.912038\pi\)
\(348\) 6.50340 7.66086i 0.348619 0.410665i
\(349\) −11.9841 −0.641497 −0.320748 0.947164i \(-0.603934\pi\)
−0.320748 + 0.947164i \(0.603934\pi\)
\(350\) 1.81088 + 9.58866i 0.0967957 + 0.512535i
\(351\) −0.408995 + 23.7882i −0.0218306 + 1.26972i
\(352\) −0.165181 0.286103i −0.00880420 0.0152493i
\(353\) 13.6272 + 7.86764i 0.725300 + 0.418752i 0.816700 0.577062i \(-0.195801\pi\)
−0.0914002 + 0.995814i \(0.529134\pi\)
\(354\) −2.67658 + 0.956862i −0.142259 + 0.0508567i
\(355\) −0.0463788 + 0.00434110i −0.00246153 + 0.000230401i
\(356\) 8.32490 0.441219
\(357\) −5.36011 0.976836i −0.283687 0.0516996i
\(358\) 13.0503 22.6038i 0.689731 1.19465i
\(359\) 14.9659 8.64059i 0.789873 0.456033i −0.0500451 0.998747i \(-0.515937\pi\)
0.839918 + 0.542714i \(0.182603\pi\)
\(360\) −1.77117 + 6.47016i −0.0933486 + 0.341007i
\(361\) −8.58604 14.8715i −0.451897 0.782708i
\(362\) 0.630738 0.364157i 0.0331508 0.0191397i
\(363\) 6.35002 + 17.7626i 0.333290 + 0.932294i
\(364\) 8.93598i 0.468373i
\(365\) −0.825288 8.81709i −0.0431976 0.461508i
\(366\) −2.86621 2.43316i −0.149819 0.127183i
\(367\) 10.2023 + 17.6709i 0.532556 + 0.922415i 0.999277 + 0.0380101i \(0.0121019\pi\)
−0.466721 + 0.884405i \(0.654565\pi\)
\(368\) 3.57984i 0.186612i
\(369\) 8.07941 + 9.85589i 0.420597 + 0.513077i
\(370\) 8.46686 6.00539i 0.440171 0.312205i
\(371\) −8.66732 −0.449985
\(372\) −2.38737 + 9.34347i −0.123779 + 0.484436i
\(373\) 23.5595i 1.21986i 0.792453 + 0.609932i \(0.208803\pi\)
−0.792453 + 0.609932i \(0.791197\pi\)
\(374\) 0.532478i 0.0275338i
\(375\) 17.6512 + 7.96471i 0.911502 + 0.411296i
\(376\) 9.38539 0.484015
\(377\) −13.2824 23.0058i −0.684080 1.18486i
\(378\) 4.91877 + 8.86821i 0.252994 + 0.456132i
\(379\) −3.65423 + 6.32930i −0.187705 + 0.325115i −0.944485 0.328555i \(-0.893438\pi\)
0.756780 + 0.653670i \(0.226772\pi\)
\(380\) 10.9693 7.78035i 0.562716 0.399124i
\(381\) 5.90922 + 16.5296i 0.302739 + 0.846836i
\(382\) −20.8724 + 12.0507i −1.06792 + 0.616565i
\(383\) −11.0470 + 6.37801i −0.564477 + 0.325901i −0.754941 0.655793i \(-0.772334\pi\)
0.190463 + 0.981694i \(0.439001\pi\)
\(384\) −1.12093 + 1.32043i −0.0572020 + 0.0673827i
\(385\) −0.601355 + 1.31029i −0.0306479 + 0.0667787i
\(386\) −9.95662 5.74846i −0.506779 0.292589i
\(387\) 29.0809 + 10.9636i 1.47827 + 0.557313i
\(388\) 1.82231i 0.0925137i
\(389\) 12.1118 20.9783i 0.614093 1.06364i −0.376450 0.926437i \(-0.622855\pi\)
0.990543 0.137203i \(-0.0438112\pi\)
\(390\) 14.5297 + 10.1666i 0.735738 + 0.514805i
\(391\) −2.88498 + 4.99694i −0.145900 + 0.252706i
\(392\) −1.59557 2.76360i −0.0805882 0.139583i
\(393\) 15.0579 5.38310i 0.759569 0.271541i
\(394\) −23.3678 + 13.4914i −1.17725 + 0.679687i
\(395\) 3.46829 + 4.88986i 0.174509 + 0.246036i
\(396\) −0.766469 + 0.628317i −0.0385165 + 0.0315741i
\(397\) 8.87940 + 5.12652i 0.445644 + 0.257293i 0.705989 0.708223i \(-0.250503\pi\)
−0.260345 + 0.965516i \(0.583836\pi\)
\(398\) 16.7830 9.68967i 0.841255 0.485699i
\(399\) 3.64501 20.0010i 0.182479 1.00130i
\(400\) 3.26014 + 3.79097i 0.163007 + 0.189549i
\(401\) 1.23442 0.0616439 0.0308219 0.999525i \(-0.490188\pi\)
0.0308219 + 0.999525i \(0.490188\pi\)
\(402\) −1.93072 + 10.5943i −0.0962957 + 0.528396i
\(403\) 21.1337 + 14.2574i 1.05274 + 0.710212i
\(404\) 0.765602i 0.0380901i
\(405\) 20.0156 + 2.09171i 0.994584 + 0.103938i
\(406\) −9.80600 5.66150i −0.486664 0.280975i
\(407\) 1.53363 0.0760191
\(408\) −2.62878 + 0.939773i −0.130144 + 0.0465257i
\(409\) 15.8439 + 9.14748i 0.783431 + 0.452314i 0.837645 0.546215i \(-0.183932\pi\)
−0.0542140 + 0.998529i \(0.517265\pi\)
\(410\) 9.45765 0.885245i 0.467080 0.0437191i
\(411\) 3.20756 17.6006i 0.158217 0.868172i
\(412\) −8.27469 + 4.77739i −0.407665 + 0.235365i
\(413\) 1.60142 + 2.77374i 0.0788006 + 0.136487i
\(414\) 10.5970 1.74356i 0.520816 0.0856914i
\(415\) −32.8271 + 3.07265i −1.61142 + 0.150830i
\(416\) 2.28936 + 3.96529i 0.112245 + 0.194414i
\(417\) −20.5429 17.4391i −1.00599 0.853996i
\(418\) 1.98691 0.0971829
\(419\) 33.5368i 1.63838i 0.573522 + 0.819190i \(0.305577\pi\)
−0.573522 + 0.819190i \(0.694423\pi\)
\(420\) 7.53009 + 0.656278i 0.367431 + 0.0320231i
\(421\) −16.7516 29.0146i −0.816422 1.41408i −0.908302 0.418315i \(-0.862621\pi\)
0.0918798 0.995770i \(-0.470712\pi\)
\(422\) −3.31031 + 5.73362i −0.161143 + 0.279108i
\(423\) −4.57116 27.7826i −0.222257 1.35084i
\(424\) −3.84607 + 2.22053i −0.186782 + 0.107839i
\(425\) 1.49555 + 7.91899i 0.0725450 + 0.384128i
\(426\) −0.00646907 + 0.0354972i −0.000313427 + 0.00171985i
\(427\) −2.11817 + 3.66878i −0.102506 + 0.177545i
\(428\) 4.55170 7.88378i 0.220015 0.381077i
\(429\) 0.881959 + 2.46706i 0.0425814 + 0.119111i
\(430\) 18.8947 13.4016i 0.911181 0.646284i
\(431\) −1.74288 1.00625i −0.0839515 0.0484694i 0.457437 0.889242i \(-0.348768\pi\)
−0.541388 + 0.840773i \(0.682101\pi\)
\(432\) 4.45467 + 2.67505i 0.214326 + 0.128703i
\(433\) −29.3924 −1.41251 −0.706254 0.707959i \(-0.749616\pi\)
−0.706254 + 0.707959i \(0.749616\pi\)
\(434\) 10.8397 + 0.758891i 0.520322 + 0.0364279i
\(435\) −20.3619 + 9.50312i −0.976276 + 0.455640i
\(436\) 7.60812 0.364363
\(437\) −18.6458 10.7652i −0.891949 0.514967i
\(438\) −6.74839 1.22984i −0.322451 0.0587640i
\(439\) −7.51591 13.0179i −0.358715 0.621312i 0.629032 0.777380i \(-0.283452\pi\)
−0.987746 + 0.156067i \(0.950118\pi\)
\(440\) 0.0688434 + 0.735499i 0.00328198 + 0.0350635i
\(441\) −7.40369 + 6.06921i −0.352557 + 0.289010i
\(442\) 7.37996i 0.351029i
\(443\) 17.7288 + 30.7072i 0.842323 + 1.45895i 0.887926 + 0.459986i \(0.152145\pi\)
−0.0456038 + 0.998960i \(0.514521\pi\)
\(444\) −2.70671 7.57134i −0.128455 0.359320i
\(445\) −16.9183 7.76463i −0.802006 0.368079i
\(446\) 8.34451 14.4531i 0.395124 0.684375i
\(447\) −12.3905 + 4.42954i −0.586052 + 0.209510i
\(448\) 1.69016 + 0.975816i 0.0798527 + 0.0461030i
\(449\) −19.8626 −0.937376 −0.468688 0.883364i \(-0.655273\pi\)
−0.468688 + 0.883364i \(0.655273\pi\)
\(450\) 9.63418 11.4971i 0.454160 0.541977i
\(451\) 1.21539 + 0.701704i 0.0572303 + 0.0330419i
\(452\) −1.15680 2.00363i −0.0544112 0.0942430i
\(453\) 16.9761 + 14.4112i 0.797605 + 0.677096i
\(454\) −9.22552 15.9791i −0.432975 0.749935i
\(455\) 8.33459 18.1602i 0.390731 0.851364i
\(456\) −3.50671 9.80914i −0.164217 0.459355i
\(457\) 22.1897 1.03799 0.518996 0.854776i \(-0.326306\pi\)
0.518996 + 0.854776i \(0.326306\pi\)
\(458\) 9.54074 + 5.50835i 0.445809 + 0.257388i
\(459\) 4.06226 + 7.32400i 0.189610 + 0.341855i
\(460\) 3.33891 7.27515i 0.155678 0.339206i
\(461\) −13.2741 −0.618235 −0.309118 0.951024i \(-0.600034\pi\)
−0.309118 + 0.951024i \(0.600034\pi\)
\(462\) 0.851341 + 0.722714i 0.0396080 + 0.0336237i
\(463\) 22.6449 1.05240 0.526200 0.850361i \(-0.323616\pi\)
0.526200 + 0.850361i \(0.323616\pi\)
\(464\) −5.80181 −0.269342
\(465\) 13.5664 16.7616i 0.629127 0.777303i
\(466\) −19.4217 −0.899693
\(467\) 30.7257 1.42182 0.710908 0.703285i \(-0.248284\pi\)
0.710908 + 0.703285i \(0.248284\pi\)
\(468\) 10.6230 8.70826i 0.491049 0.402539i
\(469\) 12.1340 0.560297
\(470\) −19.0735 8.75375i −0.879797 0.403780i
\(471\) 24.5166 + 20.8125i 1.12967 + 0.958988i
\(472\) 1.42124 + 0.820553i 0.0654178 + 0.0377690i
\(473\) 3.42244 0.157364
\(474\) 4.37267 1.56320i 0.200844 0.0718004i
\(475\) −29.5493 + 5.58057i −1.35581 + 0.256054i
\(476\) 1.57282 + 2.72420i 0.0720899 + 0.124863i
\(477\) 8.44645 + 10.3036i 0.386736 + 0.471771i
\(478\) −7.58762 13.1421i −0.347050 0.601108i
\(479\) −24.5703 14.1856i −1.12264 0.648159i −0.180569 0.983562i \(-0.557794\pi\)
−0.942075 + 0.335404i \(0.891127\pi\)
\(480\) 3.50957 1.63796i 0.160189 0.0747623i
\(481\) −21.2556 −0.969170
\(482\) 24.4006 + 14.0877i 1.11142 + 0.641678i
\(483\) −4.07356 11.3948i −0.185353 0.518480i
\(484\) 5.44543 9.43176i 0.247520 0.428716i
\(485\) 1.69967 3.70340i 0.0771779 0.168163i
\(486\) 5.74903 14.4896i 0.260781 0.657262i
\(487\) −2.36161 4.09043i −0.107015 0.185355i 0.807545 0.589806i \(-0.200796\pi\)
−0.914560 + 0.404451i \(0.867463\pi\)
\(488\) 2.17067i 0.0982615i
\(489\) 13.5652 + 11.5157i 0.613440 + 0.520757i
\(490\) 0.664991 + 7.10453i 0.0300412 + 0.320950i
\(491\) 6.25568 + 10.8352i 0.282315 + 0.488984i 0.971954 0.235169i \(-0.0755644\pi\)
−0.689640 + 0.724153i \(0.742231\pi\)
\(492\) 1.31919 7.23866i 0.0594735 0.326344i
\(493\) −8.09849 4.67566i −0.364737 0.210581i
\(494\) −27.5379 −1.23899
\(495\) 2.14369 0.562015i 0.0963519 0.0252607i
\(496\) 5.00448 2.44033i 0.224708 0.109574i
\(497\) 0.0406561 0.00182368
\(498\) −4.57884 + 25.1251i −0.205183 + 1.12588i
\(499\) 19.3605 + 11.1778i 0.866693 + 0.500386i 0.866248 0.499614i \(-0.166525\pi\)
0.000445285 1.00000i \(0.499858\pi\)
\(500\) −3.08961 10.7450i −0.138172 0.480529i
\(501\) −24.8436 + 8.88146i −1.10993 + 0.396794i
\(502\) 0.116519 0.201816i 0.00520048 0.00900750i
\(503\) 20.5254 35.5510i 0.915180 1.58514i 0.108543 0.994092i \(-0.465381\pi\)
0.806637 0.591047i \(-0.201285\pi\)
\(504\) 2.06542 5.47849i 0.0920009 0.244031i
\(505\) −0.714077 + 1.55590i −0.0317760 + 0.0692367i
\(506\) 1.02420 0.591323i 0.0455313 0.0262875i
\(507\) −4.64389 12.9901i −0.206242 0.576911i
\(508\) 5.06743 8.77704i 0.224831 0.389418i
\(509\) 12.4960 + 21.6437i 0.553876 + 0.959341i 0.997990 + 0.0633709i \(0.0201851\pi\)
−0.444114 + 0.895970i \(0.646482\pi\)
\(510\) 6.21888 + 0.542001i 0.275377 + 0.0240002i
\(511\) 7.72916i 0.341918i
\(512\) 1.00000 0.0441942
\(513\) −27.3291 + 15.1581i −1.20661 + 0.669247i
\(514\) −7.88542 13.6580i −0.347811 0.602426i
\(515\) 21.2722 1.99110i 0.937364 0.0877382i
\(516\) −6.04029 16.8962i −0.265909 0.743814i
\(517\) −1.55029 2.68519i −0.0681818 0.118094i
\(518\) −7.84616 + 4.52998i −0.344740 + 0.199036i
\(519\) −29.0040 5.28574i −1.27313 0.232018i
\(520\) −0.954147 10.1938i −0.0418421 0.447027i
\(521\) 27.9613 + 16.1435i 1.22501 + 0.707259i 0.965982 0.258611i \(-0.0832648\pi\)
0.259027 + 0.965870i \(0.416598\pi\)
\(522\) 2.82577 + 17.1745i 0.123681 + 0.751708i
\(523\) 36.5284 1.59728 0.798638 0.601811i \(-0.205554\pi\)
0.798638 + 0.601811i \(0.205554\pi\)
\(524\) −7.99557 4.61625i −0.349288 0.201662i
\(525\) −14.6910 8.35704i −0.641167 0.364731i
\(526\) 18.7956i 0.819526i
\(527\) 8.95219 + 0.626746i 0.389963 + 0.0273015i
\(528\) 0.562934 + 0.102590i 0.0244985 + 0.00446466i
\(529\) 10.1848 0.442816
\(530\) 9.88730 0.925461i 0.429477 0.0401995i
\(531\) 1.73678 4.60680i 0.0753700 0.199918i
\(532\) −10.1652 + 5.86887i −0.440717 + 0.254448i
\(533\) −16.8449 9.72538i −0.729632 0.421253i
\(534\) −9.33159 + 10.9924i −0.403818 + 0.475688i
\(535\) −16.6034 + 11.7765i −0.717829 + 0.509143i
\(536\) 5.38440 3.10868i 0.232571 0.134275i
\(537\) 15.2182 + 42.5692i 0.656715 + 1.83700i
\(538\) −10.3372 17.9046i −0.445669 0.771921i
\(539\) −0.527116 + 0.912992i −0.0227045 + 0.0393253i
\(540\) −6.55802 9.59126i −0.282212 0.412742i
\(541\) 8.74210 15.1418i 0.375852 0.650995i −0.614602 0.788837i \(-0.710683\pi\)
0.990454 + 0.137842i \(0.0440167\pi\)
\(542\) 4.19858i 0.180344i
\(543\) −0.226168 + 1.24104i −0.00970582 + 0.0532579i
\(544\) 1.39586 + 0.805898i 0.0598468 + 0.0345526i
\(545\) −15.4617 7.09609i −0.662305 0.303963i
\(546\) −11.7993 10.0166i −0.504964 0.428670i
\(547\) 15.7800 9.11061i 0.674706 0.389542i −0.123152 0.992388i \(-0.539300\pi\)
0.797857 + 0.602846i \(0.205967\pi\)
\(548\) −8.94523 + 5.16453i −0.382121 + 0.220618i
\(549\) 6.42561 1.05722i 0.274238 0.0451213i
\(550\) 0.546092 1.55893i 0.0232855 0.0664732i
\(551\) 17.4470 30.2190i 0.743266 1.28737i
\(552\) −4.72691 4.01273i −0.201191 0.170793i
\(553\) −2.61620 4.53139i −0.111252 0.192694i
\(554\) 17.0716 0.725302
\(555\) −1.56106 + 17.9115i −0.0662631 + 0.760299i
\(556\) 15.5578i 0.659796i
\(557\) 29.3983i 1.24565i −0.782362 0.622824i \(-0.785985\pi\)
0.782362 0.622824i \(-0.214015\pi\)
\(558\) −9.66130 13.6257i −0.408995 0.576821i
\(559\) −47.4339 −2.00624
\(560\) −2.52470 3.55952i −0.106688 0.150417i
\(561\) 0.703097 + 0.596868i 0.0296848 + 0.0251998i
\(562\) 30.4242i 1.28337i
\(563\) 17.4816 + 30.2789i 0.736760 + 1.27611i 0.953947 + 0.299975i \(0.0969785\pi\)
−0.217187 + 0.976130i \(0.569688\pi\)
\(564\) −10.5203 + 12.3927i −0.442986 + 0.521828i
\(565\) 0.482124 + 5.15085i 0.0202831 + 0.216698i
\(566\) 3.94960i 0.166014i
\(567\) −17.2234 3.44574i −0.723314 0.144708i
\(568\) 0.0180409 0.0104159i 0.000756980 0.000437043i
\(569\) 6.11901 + 10.5984i 0.256522 + 0.444309i 0.965308 0.261114i \(-0.0840900\pi\)
−0.708786 + 0.705424i \(0.750757\pi\)
\(570\) −2.02245 + 23.2054i −0.0847109 + 0.971968i
\(571\) 1.55963 0.900452i 0.0652684 0.0376827i −0.467011 0.884252i \(-0.654669\pi\)
0.532279 + 0.846569i \(0.321336\pi\)
\(572\) 0.756320 1.30998i 0.0316233 0.0547732i
\(573\) 7.48436 41.0683i 0.312663 1.71565i
\(574\) −8.29068 −0.346046
\(575\) −13.5711 + 11.6708i −0.565953 + 0.486705i
\(576\) −0.487050 2.96020i −0.0202938 0.123342i
\(577\) 27.9526 + 16.1384i 1.16368 + 0.671851i 0.952183 0.305528i \(-0.0988329\pi\)
0.211497 + 0.977379i \(0.432166\pi\)
\(578\) −7.20106 12.4726i −0.299525 0.518792i
\(579\) 18.7510 6.70339i 0.779267 0.278583i
\(580\) 11.7908 + 5.41134i 0.489585 + 0.224694i
\(581\) 28.7766 1.19385
\(582\) −2.40622 2.04267i −0.0997412 0.0846715i
\(583\) 1.27060 + 0.733581i 0.0526229 + 0.0303818i
\(584\) 1.98018 + 3.42977i 0.0819404 + 0.141925i
\(585\) −29.7109 + 7.78935i −1.22839 + 0.322050i
\(586\) −7.39011 + 12.8000i −0.305282 + 0.528765i
\(587\) 35.8198i 1.47844i 0.673464 + 0.739220i \(0.264806\pi\)
−0.673464 + 0.739220i \(0.735194\pi\)
\(588\) 5.43764 + 0.990965i 0.224245 + 0.0408667i
\(589\) −2.33867 + 33.4046i −0.0963631 + 1.37641i
\(590\) −2.12299 2.99316i −0.0874023 0.123227i
\(591\) 8.37917 45.9783i 0.344673 1.89130i
\(592\) −2.32112 + 4.02031i −0.0953976 + 0.165234i
\(593\) 10.9478 0.449570 0.224785 0.974408i \(-0.427832\pi\)
0.224785 + 0.974408i \(0.427832\pi\)
\(594\) 0.0295098 1.71636i 0.00121080 0.0704232i
\(595\) −0.655510 7.00324i −0.0268733 0.287105i
\(596\) 6.57925 + 3.79853i 0.269497 + 0.155594i
\(597\) −6.01800 + 33.0221i −0.246300 + 1.35150i
\(598\) −14.1951 + 8.19554i −0.580480 + 0.335141i
\(599\) −3.30821 + 1.91000i −0.135170 + 0.0780403i −0.566060 0.824364i \(-0.691533\pi\)
0.430890 + 0.902404i \(0.358200\pi\)
\(600\) −8.66008 + 0.0553790i −0.353546 + 0.00226084i
\(601\) −38.3932 22.1663i −1.56609 0.904183i −0.996618 0.0821717i \(-0.973814\pi\)
−0.569472 0.822011i \(-0.692852\pi\)
\(602\) −17.5095 + 10.1091i −0.713634 + 0.412017i
\(603\) −11.8248 14.4248i −0.481543 0.587423i
\(604\) 12.8565i 0.523123i
\(605\) −19.8635 + 14.0888i −0.807567 + 0.572792i
\(606\) 1.01092 + 0.858183i 0.0410659 + 0.0348613i
\(607\) 17.8704 10.3175i 0.725337 0.418774i −0.0913767 0.995816i \(-0.529127\pi\)
0.816714 + 0.577043i \(0.195793\pi\)
\(608\) −3.00716 + 5.20856i −0.121957 + 0.211235i
\(609\) 18.4674 6.60198i 0.748336 0.267526i
\(610\) 2.02458 4.41136i 0.0819729 0.178611i
\(611\) 21.4865 + 37.2158i 0.869253 + 1.50559i
\(612\) 1.70577 4.52452i 0.0689515 0.182893i
\(613\) 13.7205 23.7646i 0.554165 0.959842i −0.443803 0.896124i \(-0.646371\pi\)
0.997968 0.0637178i \(-0.0202957\pi\)
\(614\) −11.2636 6.50301i −0.454560 0.262440i
\(615\) −9.43242 + 13.4804i −0.380352 + 0.543583i
\(616\) 0.644747i 0.0259776i
\(617\) 16.5097 28.5956i 0.664655 1.15122i −0.314724 0.949183i \(-0.601912\pi\)
0.979379 0.202033i \(-0.0647548\pi\)
\(618\) 2.96712 16.2812i 0.119355 0.654927i
\(619\) 44.0193i 1.76928i 0.466271 + 0.884642i \(0.345597\pi\)
−0.466271 + 0.884642i \(0.654403\pi\)
\(620\) −12.4465 + 0.291708i −0.499863 + 0.0117153i
\(621\) −9.57625 + 15.9470i −0.384281 + 0.639931i
\(622\) 24.9699i 1.00120i
\(623\) 14.0704 + 8.12357i 0.563720 + 0.325464i
\(624\) −7.80208 1.42186i −0.312333 0.0569201i
\(625\) −3.74294 + 24.7182i −0.149718 + 0.988729i
\(626\) −6.43179 + 11.1402i −0.257066 + 0.445251i
\(627\) −2.22718 + 2.62357i −0.0889449 + 0.104775i
\(628\) 18.5672i 0.740912i
\(629\) −6.47991 + 3.74118i −0.258371 + 0.149171i
\(630\) −9.30724 + 9.20729i −0.370809 + 0.366827i
\(631\) −4.56897 + 2.63789i −0.181888 + 0.105013i −0.588179 0.808731i \(-0.700155\pi\)
0.406292 + 0.913743i \(0.366822\pi\)
\(632\) −2.32185 1.34052i −0.0923581 0.0533230i
\(633\) −3.86021 10.7980i −0.153430 0.429181i
\(634\) −6.81198 + 11.7987i −0.270538 + 0.468586i
\(635\) −18.4847 + 13.1108i −0.733541 + 0.520287i
\(636\) 1.37912 7.56751i 0.0546855 0.300071i
\(637\) 7.30565 12.6538i 0.289460 0.501360i
\(638\) 0.958351 + 1.65991i 0.0379415 + 0.0657166i
\(639\) −0.0396201 0.0483317i −0.00156735 0.00191197i
\(640\) −2.03226 0.932700i −0.0803320 0.0368682i
\(641\) −8.67612 15.0275i −0.342686 0.593550i 0.642245 0.766500i \(-0.278003\pi\)
−0.984931 + 0.172950i \(0.944670\pi\)
\(642\) 5.30783 + 14.8473i 0.209483 + 0.585977i
\(643\) −3.50937 −0.138396 −0.0691980 0.997603i \(-0.522044\pi\)
−0.0691980 + 0.997603i \(0.522044\pi\)
\(644\) −3.49326 + 6.05051i −0.137654 + 0.238423i
\(645\) −3.48365 + 39.9712i −0.137169 + 1.57387i
\(646\) −8.39513 + 4.84693i −0.330302 + 0.190700i
\(647\) 16.2327i 0.638172i 0.947726 + 0.319086i \(0.103376\pi\)
−0.947726 + 0.319086i \(0.896624\pi\)
\(648\) −8.52556 + 2.88353i −0.334916 + 0.113276i
\(649\) 0.542161i 0.0212817i
\(650\) −7.56866 + 21.6063i −0.296867 + 0.847469i
\(651\) −13.1526 + 13.4624i −0.515489 + 0.527631i
\(652\) 10.2734i 0.402336i
\(653\) −8.99314 −0.351929 −0.175964 0.984397i \(-0.556304\pi\)
−0.175964 + 0.984397i \(0.556304\pi\)
\(654\) −8.52814 + 10.0460i −0.333477 + 0.392828i
\(655\) 11.9435 + 16.8389i 0.466671 + 0.657949i
\(656\) −3.67894 + 2.12404i −0.143639 + 0.0829298i
\(657\) 9.18836 7.53220i 0.358472 0.293859i
\(658\) 15.8628 + 9.15842i 0.618398 + 0.357032i
\(659\) 48.8063i 1.90122i 0.310382 + 0.950612i \(0.399543\pi\)
−0.310382 + 0.950612i \(0.600457\pi\)
\(660\) −1.04834 0.733537i −0.0408066 0.0285529i
\(661\) −12.1080 20.9716i −0.470946 0.815702i 0.528502 0.848932i \(-0.322754\pi\)
−0.999448 + 0.0332300i \(0.989421\pi\)
\(662\) 13.3530 7.70937i 0.518980 0.299633i
\(663\) −9.74470 8.27239i −0.378453 0.321273i
\(664\) 12.7695 7.37245i 0.495551 0.286106i
\(665\) 26.1322 2.44600i 1.01336 0.0948517i
\(666\) 13.0314 + 4.91290i 0.504957 + 0.190371i
\(667\) 20.7695i 0.804199i
\(668\) 13.1917 + 7.61625i 0.510403 + 0.294682i
\(669\) 9.73070 + 27.2192i 0.376211 + 1.05235i
\(670\) −13.8420 + 1.29562i −0.534761 + 0.0500542i
\(671\) 0.621034 0.358554i 0.0239748 0.0138418i
\(672\) −3.18304 + 1.13792i −0.122788 + 0.0438961i
\(673\) 5.78371 + 10.0177i 0.222945 + 0.386153i 0.955701 0.294339i \(-0.0950995\pi\)
−0.732756 + 0.680492i \(0.761766\pi\)
\(674\) 8.19338 0.315597
\(675\) 4.38183 + 25.6086i 0.168657 + 0.985675i
\(676\) −3.98235 + 6.89762i −0.153167 + 0.265293i
\(677\) −30.6277 + 17.6829i −1.17712 + 0.679609i −0.955346 0.295490i \(-0.904517\pi\)
−0.221771 + 0.975099i \(0.571184\pi\)
\(678\) 3.94234 + 0.718458i 0.151405 + 0.0275922i
\(679\) −1.77824 + 3.08000i −0.0682425 + 0.118199i
\(680\) −2.08508 2.93971i −0.0799591 0.112733i
\(681\) 31.4403 + 5.72974i 1.20480 + 0.219564i
\(682\) −1.52483 1.02870i −0.0583888 0.0393908i
\(683\) −9.10481 −0.348386 −0.174193 0.984712i \(-0.555732\pi\)
−0.174193 + 0.984712i \(0.555732\pi\)
\(684\) 16.8830 + 6.36497i 0.645538 + 0.243371i
\(685\) 22.9960 2.15244i 0.878630 0.0822406i
\(686\) 19.8893i 0.759379i
\(687\) −17.9678 + 6.42339i −0.685515 + 0.245068i
\(688\) −5.17982 + 8.97172i −0.197479 + 0.342043i
\(689\) −17.6101 10.1672i −0.670891 0.387339i
\(690\) 5.86363 + 12.5637i 0.223224 + 0.478292i
\(691\) −8.20590 14.2130i −0.312167 0.540690i 0.666664 0.745358i \(-0.267722\pi\)
−0.978831 + 0.204669i \(0.934388\pi\)
\(692\) 8.51064 + 14.7409i 0.323526 + 0.560363i
\(693\) −1.90858 + 0.314024i −0.0725010 + 0.0119288i
\(694\) −22.4803 12.9790i −0.853342 0.492677i
\(695\) 14.5107 31.6174i 0.550423 1.19932i
\(696\) 6.50340 7.66086i 0.246511 0.290384i
\(697\) −6.84703 −0.259350
\(698\) −11.9841 −0.453607
\(699\) 21.7703 25.6449i 0.823428 0.969980i
\(700\) 1.81088 + 9.58866i 0.0684449 + 0.362417i
\(701\) −6.93865 4.00603i −0.262069 0.151306i 0.363209 0.931708i \(-0.381681\pi\)
−0.625278 + 0.780402i \(0.715014\pi\)
\(702\) −0.408995 + 23.7882i −0.0154365 + 0.897828i
\(703\) −13.9600 24.1794i −0.526511 0.911944i
\(704\) −0.165181 0.286103i −0.00622551 0.0107829i
\(705\) 32.9387 15.3729i 1.24054 0.578976i
\(706\) 13.6272 + 7.86764i 0.512865 + 0.296103i
\(707\) 0.747087 1.29399i 0.0280971 0.0486656i
\(708\) −2.67658 + 0.956862i −0.100592 + 0.0359611i
\(709\) 25.3806i 0.953188i −0.879123 0.476594i \(-0.841871\pi\)
0.879123 0.476594i \(-0.158129\pi\)
\(710\) −0.0463788 + 0.00434110i −0.00174056 + 0.000162918i
\(711\) −2.83735 + 7.52603i −0.106409 + 0.282248i
\(712\) 8.32490 0.311989
\(713\) 8.73599 + 17.9152i 0.327165 + 0.670930i
\(714\) −5.36011 0.976836i −0.200597 0.0365572i
\(715\) −2.75886 + 1.95681i −0.103175 + 0.0731804i
\(716\) 13.0503 22.6038i 0.487714 0.844745i
\(717\) 25.8584 + 4.71248i 0.965699 + 0.175991i
\(718\) 14.9659 8.64059i 0.558524 0.322464i
\(719\) 4.34034 7.51769i 0.161867 0.280363i −0.773671 0.633588i \(-0.781582\pi\)
0.935538 + 0.353225i \(0.114915\pi\)
\(720\) −1.77117 + 6.47016i −0.0660074 + 0.241129i
\(721\) −18.6474 −0.694467
\(722\) −8.58604 14.8715i −0.319539 0.553458i
\(723\) −45.9531 + 16.4280i −1.70901 + 0.610962i
\(724\) 0.630738 0.364157i 0.0234412 0.0135338i
\(725\) −18.9147 21.9945i −0.702475 0.816855i
\(726\) 6.35002 + 17.7626i 0.235671 + 0.659232i
\(727\) −29.6131 17.0971i −1.09829 0.634098i −0.162519 0.986705i \(-0.551962\pi\)
−0.935771 + 0.352607i \(0.885295\pi\)
\(728\) 8.93598i 0.331189i
\(729\) 12.6882 + 23.8329i 0.469934 + 0.882702i
\(730\) −0.825288 8.81709i −0.0305453 0.326335i
\(731\) −14.4606 + 8.34882i −0.534844 + 0.308792i
\(732\) −2.86621 2.43316i −0.105938 0.0899321i
\(733\) −32.1527 + 18.5634i −1.18759 + 0.685654i −0.957758 0.287576i \(-0.907151\pi\)
−0.229831 + 0.973231i \(0.573817\pi\)
\(734\) 10.2023 + 17.6709i 0.376574 + 0.652246i
\(735\) −10.1264 7.08558i −0.373519 0.261356i
\(736\) 3.57984i 0.131955i
\(737\) −1.77881 1.02699i −0.0655231 0.0378298i
\(738\) 8.07941 + 9.85589i 0.297407 + 0.362800i
\(739\) 3.28215 1.89495i 0.120736 0.0697068i −0.438416 0.898772i \(-0.644460\pi\)
0.559152 + 0.829065i \(0.311127\pi\)
\(740\) 8.46686 6.00539i 0.311248 0.220762i
\(741\) 30.8680 36.3618i 1.13396 1.33578i
\(742\) −8.66732 −0.318187
\(743\) 20.1548i 0.739408i 0.929150 + 0.369704i \(0.120541\pi\)
−0.929150 + 0.369704i \(0.879459\pi\)
\(744\) −2.38737 + 9.34347i −0.0875252 + 0.342548i
\(745\) −9.82784 13.8561i −0.360064 0.507647i
\(746\) 23.5595i 0.862575i
\(747\) −28.0433 34.2094i −1.02605 1.25166i
\(748\) 0.532478i 0.0194693i
\(749\) 15.3862 8.88325i 0.562201 0.324587i
\(750\) 17.6512 + 7.96471i 0.644529 + 0.290830i
\(751\) −2.10830 + 3.65168i −0.0769329 + 0.133252i −0.901925 0.431892i \(-0.857846\pi\)
0.824992 + 0.565144i \(0.191179\pi\)
\(752\) 9.38539 0.342250
\(753\) 0.135875 + 0.380076i 0.00495155 + 0.0138507i
\(754\) −13.2824 23.0058i −0.483718 0.837823i
\(755\) −11.9913 + 26.1277i −0.436406 + 0.950885i
\(756\) 4.91877 + 8.86821i 0.178894 + 0.322534i
\(757\) −18.5401 32.1124i −0.673851 1.16714i −0.976803 0.214139i \(-0.931306\pi\)
0.302952 0.953006i \(-0.402028\pi\)
\(758\) −3.65423 + 6.32930i −0.132727 + 0.229891i
\(759\) −0.367256 + 2.01521i −0.0133305 + 0.0731475i
\(760\) 10.9693 7.78035i 0.397900 0.282223i
\(761\) 8.41569 14.5764i 0.305068 0.528394i −0.672208 0.740362i \(-0.734654\pi\)
0.977277 + 0.211968i \(0.0679873\pi\)
\(762\) 5.90922 + 16.5296i 0.214069 + 0.598803i
\(763\) 12.8590 + 7.42413i 0.465526 + 0.268772i
\(764\) −20.8724 + 12.0507i −0.755135 + 0.435978i
\(765\) −7.68658 + 7.60403i −0.277909 + 0.274924i
\(766\) −11.0470 + 6.37801i −0.399146 + 0.230447i
\(767\) 7.51417i 0.271321i
\(768\) −1.12093 + 1.32043i −0.0404479 + 0.0476468i
\(769\) 16.9466 29.3524i 0.611110 1.05847i −0.379944 0.925009i \(-0.624057\pi\)
0.991054 0.133464i \(-0.0426099\pi\)
\(770\) −0.601355 + 1.31029i −0.0216713 + 0.0472196i
\(771\) 26.8733 + 4.89743i 0.967818 + 0.176377i
\(772\) −9.95662 5.74846i −0.358347 0.206891i
\(773\) 9.88908i 0.355685i −0.984059 0.177843i \(-0.943088\pi\)
0.984059 0.177843i \(-0.0569118\pi\)
\(774\) 29.0809 + 10.9636i 1.04529 + 0.394080i
\(775\) 25.5665 + 11.0160i 0.918377 + 0.395706i
\(776\) 1.82231i 0.0654171i
\(777\) 2.81346 15.4380i 0.100932 0.553837i
\(778\) 12.1118 20.9783i 0.434229 0.752107i
\(779\) 25.5493i 0.915399i
\(780\) 14.5297 + 10.1666i 0.520245 + 0.364022i
\(781\) −0.00596005 0.00344104i −0.000213268 0.000123130i
\(782\) −2.88498 + 4.99694i −0.103167 + 0.178690i
\(783\) −25.8451 15.5201i −0.923630 0.554644i
\(784\) −1.59557 2.76360i −0.0569845 0.0987000i
\(785\) −17.3176 + 37.7334i −0.618093 + 1.34676i
\(786\) 15.0579 5.38310i 0.537096 0.192009i
\(787\) −14.5035 + 25.1208i −0.516993 + 0.895458i 0.482812 + 0.875724i \(0.339615\pi\)
−0.999805 + 0.0197342i \(0.993718\pi\)
\(788\) −23.3678 + 13.4914i −0.832443 + 0.480611i
\(789\) −24.8182 21.0685i −0.883551 0.750057i
\(790\) 3.46829 + 4.88986i 0.123396 + 0.173974i
\(791\) 4.51529i 0.160545i
\(792\) −0.766469 + 0.628317i −0.0272353 + 0.0223263i
\(793\) −8.60733 + 4.96944i −0.305655 + 0.176470i
\(794\) 8.87940 + 5.12652i 0.315118 + 0.181933i
\(795\) −9.86093 + 14.0928i −0.349731 + 0.499821i
\(796\) 16.7830 9.68967i 0.594857 0.343441i
\(797\) 37.6492 21.7368i 1.33360 0.769956i 0.347752 0.937586i \(-0.386945\pi\)
0.985850 + 0.167631i \(0.0536117\pi\)
\(798\) 3.64501 20.0010i 0.129032 0.708026i
\(799\) 13.1007 + 7.56367i 0.463468 + 0.267583i
\(800\) 3.26014 + 3.79097i 0.115263 + 0.134031i
\(801\) −4.05465 24.6434i −0.143264 0.870730i
\(802\) 1.23442 0.0435888
\(803\) 0.654178 1.13307i 0.0230854 0.0399851i
\(804\) −1.93072 + 10.5943i −0.0680914 + 0.373632i
\(805\) 12.7425 9.03803i 0.449115 0.318549i
\(806\) 21.1337 + 14.2574i 0.744402 + 0.502195i
\(807\) 35.2289 + 6.42018i 1.24012 + 0.226001i
\(808\) 0.765602i 0.0269338i
\(809\) 1.55700 2.69681i 0.0547413 0.0948146i −0.837356 0.546658i \(-0.815900\pi\)
0.892097 + 0.451843i \(0.149233\pi\)
\(810\) 20.0156 + 2.09171i 0.703277 + 0.0734951i
\(811\) −15.8602 27.4707i −0.556929 0.964628i −0.997751 0.0670340i \(-0.978646\pi\)
0.440822 0.897594i \(-0.354687\pi\)
\(812\) −9.80600 5.66150i −0.344123 0.198680i
\(813\) 5.54391 + 4.70630i 0.194434 + 0.165057i
\(814\) 1.53363 0.0537536
\(815\) −9.58196 + 20.8781i −0.335641 + 0.731329i
\(816\) −2.62878 + 0.939773i −0.0920257 + 0.0328986i
\(817\) −31.1531 53.9588i −1.08991 1.88778i
\(818\) 15.8439 + 9.14748i 0.553969 + 0.319834i
\(819\) 26.4523 4.35227i 0.924318 0.152081i
\(820\) 9.45765 0.885245i 0.330275 0.0309141i
\(821\) 1.35963 0.0474514 0.0237257 0.999719i \(-0.492447\pi\)
0.0237257 + 0.999719i \(0.492447\pi\)
\(822\) 3.20756 17.6006i 0.111876 0.613890i
\(823\) 4.14634 7.18168i 0.144532 0.250338i −0.784666 0.619919i \(-0.787166\pi\)
0.929198 + 0.369581i \(0.120499\pi\)
\(824\) −8.27469 + 4.77739i −0.288262 + 0.166428i
\(825\) 1.44633 + 2.46852i 0.0503547 + 0.0859430i
\(826\) 1.60142 + 2.77374i 0.0557204 + 0.0965106i
\(827\) 0.176663 0.101997i 0.00614319 0.00354677i −0.496925 0.867793i \(-0.665538\pi\)
0.503068 + 0.864247i \(0.332204\pi\)
\(828\) 10.5970 1.74356i 0.368272 0.0605929i
\(829\) 3.74903i 0.130209i −0.997878 0.0651046i \(-0.979262\pi\)
0.997878 0.0651046i \(-0.0207381\pi\)
\(830\) −32.8271 + 3.07265i −1.13945 + 0.106653i
\(831\) −19.1360 + 22.5417i −0.663819 + 0.781965i
\(832\) 2.28936 + 3.96529i 0.0793693 + 0.137472i
\(833\) 5.14345i 0.178210i
\(834\) −20.5429 17.4391i −0.711342 0.603867i
\(835\) −19.7053 27.7821i −0.681931 0.961439i
\(836\) 1.98691 0.0687187
\(837\) 28.8213 + 2.51635i 0.996210 + 0.0869778i
\(838\) 33.5368i 1.15851i
\(839\) 32.5879i 1.12506i −0.826777 0.562529i \(-0.809828\pi\)
0.826777 0.562529i \(-0.190172\pi\)
\(840\) 7.53009 + 0.656278i 0.259813 + 0.0226438i
\(841\) 4.66096 0.160723
\(842\) −16.7516 29.0146i −0.577298 0.999909i
\(843\) −40.1729 34.1032i −1.38363 1.17458i
\(844\) −3.31031 + 5.73362i −0.113945 + 0.197359i
\(845\) 14.5266 10.3034i 0.499729 0.354448i
\(846\) −4.57116 27.7826i −0.157160 0.955187i
\(847\) 18.4073 10.6275i 0.632483 0.365164i
\(848\) −3.84607 + 2.22053i −0.132075 + 0.0762534i
\(849\) 5.21515 + 4.42721i 0.178984 + 0.151941i
\(850\) 1.49555 + 7.91899i 0.0512971 + 0.271619i
\(851\) −14.3920 8.30925i −0.493353 0.284837i
\(852\) −0.00646907 + 0.0354972i −0.000221627 + 0.00121611i
\(853\) 25.4205i 0.870380i −0.900339 0.435190i \(-0.856681\pi\)
0.900339 0.435190i \(-0.143319\pi\)
\(854\) −2.11817 + 3.66878i −0.0724824 + 0.125543i
\(855\) −28.3740 28.6820i −0.970371 0.980905i
\(856\) 4.55170 7.88378i 0.155574 0.269462i
\(857\) 13.2267 + 22.9092i 0.451814 + 0.782565i 0.998499 0.0547736i \(-0.0174437\pi\)
−0.546685 + 0.837339i \(0.684110\pi\)
\(858\) 0.881959 + 2.46706i 0.0301096 + 0.0842241i
\(859\) −2.82489 + 1.63095i −0.0963839 + 0.0556473i −0.547417 0.836860i \(-0.684389\pi\)
0.451033 + 0.892507i \(0.351056\pi\)
\(860\) 18.8947 13.4016i 0.644302 0.456991i
\(861\) 9.29324 10.9472i 0.316713 0.373081i
\(862\) −1.74288 1.00625i −0.0593627 0.0342731i
\(863\) 22.5302 13.0078i 0.766937 0.442791i −0.0648441 0.997895i \(-0.520655\pi\)
0.831781 + 0.555104i \(0.187322\pi\)
\(864\) 4.45467 + 2.67505i 0.151551 + 0.0910071i
\(865\) −3.54702 37.8951i −0.120602 1.28847i
\(866\) −29.3924 −0.998794
\(867\) 24.5410 + 4.47239i 0.833456 + 0.151890i
\(868\) 10.8397 + 0.758891i 0.367923 + 0.0257584i
\(869\) 0.885715i 0.0300458i
\(870\) −20.3619 + 9.50312i −0.690332 + 0.322186i
\(871\) 24.6537 + 14.2338i 0.835357 + 0.482294i
\(872\) 7.60812 0.257644
\(873\) 5.39440 0.887556i 0.182573 0.0300392i
\(874\) −18.6458 10.7652i −0.630703 0.364137i
\(875\) 5.26316 21.1756i 0.177927 0.715867i
\(876\) −6.74839 1.22984i −0.228007 0.0415524i
\(877\) −2.37350 + 1.37034i −0.0801473 + 0.0462731i −0.539538 0.841961i \(-0.681401\pi\)
0.459391 + 0.888234i \(0.348068\pi\)
\(878\) −7.51591 13.0179i −0.253650 0.439334i
\(879\) −8.61775 24.1060i −0.290669 0.813075i
\(880\) 0.0688434 + 0.735499i 0.00232071 + 0.0247937i
\(881\) −8.45408 14.6429i −0.284825 0.493331i 0.687742 0.725955i \(-0.258602\pi\)
−0.972567 + 0.232624i \(0.925269\pi\)
\(882\) −7.40369 + 6.06921i −0.249295 + 0.204361i
\(883\) 25.2714 0.850451 0.425225 0.905087i \(-0.360195\pi\)
0.425225 + 0.905087i \(0.360195\pi\)
\(884\) 7.37996i 0.248215i
\(885\) 6.33197 + 0.551857i 0.212847 + 0.0185505i
\(886\) 17.7288 + 30.7072i 0.595612 + 1.03163i
\(887\) 17.0768 29.5779i 0.573383 0.993129i −0.422832 0.906208i \(-0.638964\pi\)
0.996215 0.0869208i \(-0.0277027\pi\)
\(888\) −2.70671 7.57134i −0.0908312 0.254077i
\(889\) 17.1296 9.88975i 0.574507 0.331692i
\(890\) −16.9183 7.76463i −0.567104 0.260271i
\(891\) 2.23325 + 1.96288i 0.0748168 + 0.0657590i
\(892\) 8.34451 14.4531i 0.279395 0.483926i
\(893\) −28.2234 + 48.8843i −0.944460 + 1.63585i
\(894\) −12.3905 + 4.42954i −0.414401 + 0.148146i
\(895\) −47.6042 + 33.7648i −1.59123 + 1.12863i
\(896\) 1.69016 + 0.975816i 0.0564644 + 0.0325997i
\(897\) 5.09004 27.9302i 0.169951 0.932561i
\(898\) −19.8626 −0.662825
\(899\) −29.0350 + 14.1583i −0.968372 + 0.472207i
\(900\) 9.63418 11.4971i 0.321139 0.383236i
\(901\) −7.15809 −0.238470
\(902\) 1.21539 + 0.701704i 0.0404679 + 0.0233642i
\(903\) 6.27851 34.4516i 0.208936 1.14648i
\(904\) −1.15680 2.00363i −0.0384746 0.0666399i
\(905\) −1.62147 + 0.151771i −0.0538995 + 0.00504505i
\(906\) 16.9761 + 14.4112i 0.563992 + 0.478779i
\(907\) 31.6455i 1.05077i −0.850864 0.525385i \(-0.823921\pi\)
0.850864 0.525385i \(-0.176079\pi\)
\(908\) −9.22552 15.9791i −0.306160 0.530284i
\(909\) −2.26634 + 0.372887i −0.0751696 + 0.0123679i
\(910\) 8.33459 18.1602i 0.276289 0.602005i
\(911\) 17.9166 31.0324i 0.593603 1.02815i −0.400140 0.916454i \(-0.631038\pi\)
0.993742 0.111696i \(-0.0356282\pi\)
\(912\) −3.50671 9.80914i −0.116119 0.324813i
\(913\) −4.21855 2.43558i −0.139614 0.0806060i
\(914\) 22.1897 0.733972
\(915\) 3.55547 + 7.61811i 0.117540 + 0.251847i
\(916\) 9.54074 + 5.50835i 0.315235 + 0.182001i
\(917\) −9.00922 15.6044i −0.297511 0.515303i
\(918\) 4.06226 + 7.32400i 0.134075 + 0.241728i
\(919\) 6.19060 + 10.7224i 0.204209 + 0.353701i 0.949880 0.312613i \(-0.101204\pi\)
−0.745671 + 0.666314i \(0.767871\pi\)
\(920\) 3.33891 7.27515i 0.110081 0.239855i
\(921\) 21.2124 7.58329i 0.698971 0.249878i
\(922\) −13.2741 −0.437158
\(923\) 0.0826044 + 0.0476917i 0.00271896 + 0.00156979i
\(924\) 0.851341 + 0.722714i 0.0280071 + 0.0237755i
\(925\) −22.8081 + 4.30745i −0.749925 + 0.141628i
\(926\) 22.6449 0.744159
\(927\) 18.1722 + 22.1679i 0.596854 + 0.728089i
\(928\) −5.80181 −0.190454
\(929\) −10.4584 −0.343128 −0.171564 0.985173i \(-0.554882\pi\)
−0.171564 + 0.985173i \(0.554882\pi\)
\(930\) 13.5664 16.7616i 0.444860 0.549636i
\(931\) 19.1925 0.629009
\(932\) −19.4217 −0.636179
\(933\) 32.9709 + 27.9894i 1.07942 + 0.916332i
\(934\) 30.7257 1.00538
\(935\) −0.496642 + 1.08213i −0.0162419 + 0.0353895i
\(936\) 10.6230 8.70826i 0.347224 0.284638i
\(937\) 44.0293 + 25.4203i 1.43837 + 0.830445i 0.997737 0.0672408i \(-0.0214196\pi\)
0.440636 + 0.897686i \(0.354753\pi\)
\(938\) 12.1340 0.396190
\(939\) −7.50023 20.9800i −0.244761 0.684657i
\(940\) −19.0735 8.75375i −0.622110 0.285516i
\(941\) −28.6468 49.6177i −0.933858 1.61749i −0.776657 0.629924i \(-0.783086\pi\)
−0.157201 0.987567i \(-0.550247\pi\)
\(942\) 24.5166 + 20.8125i 0.798795 + 0.678107i
\(943\) −7.60371 13.1700i −0.247611 0.428875i
\(944\) 1.42124 + 0.820553i 0.0462574 + 0.0267067i
\(945\) −1.72482 22.6102i −0.0561084 0.735511i
\(946\) 3.42244 0.111273
\(947\) 12.7816 + 7.37944i 0.415345 + 0.239799i 0.693084 0.720857i \(-0.256252\pi\)
−0.277739 + 0.960657i \(0.589585\pi\)
\(948\) 4.37267 1.56320i 0.142018 0.0507705i
\(949\) −9.06669 + 15.7040i −0.294317 + 0.509772i
\(950\) −29.5493 + 5.58057i −0.958705 + 0.181058i
\(951\) −7.94358 22.2202i −0.257588 0.720539i
\(952\) 1.57282 + 2.72420i 0.0509753 + 0.0882917i
\(953\) 31.5523i 1.02208i 0.859557 + 0.511039i \(0.170739\pi\)
−0.859557 + 0.511039i \(0.829261\pi\)
\(954\) 8.44645 + 10.3036i 0.273464 + 0.333592i
\(955\) 53.6577 5.02241i 1.73632 0.162521i
\(956\) −7.58762 13.1421i −0.245401 0.425047i
\(957\) −3.26603 0.595207i −0.105576 0.0192403i
\(958\) −24.5703 14.1856i −0.793829 0.458317i
\(959\) −20.1585 −0.650953
\(960\) 3.50957 1.63796i 0.113271 0.0528649i
\(961\) 19.0896 24.4252i 0.615793 0.787908i
\(962\) −21.2556 −0.685307
\(963\) −25.5545 9.63415i −0.823481 0.310456i
\(964\) 24.4006 + 14.0877i 0.785891 + 0.453735i
\(965\) 14.8728 + 20.9689i 0.478773 + 0.675012i
\(966\) −4.07356 11.3948i −0.131065 0.366621i
\(967\) −20.7858 + 36.0021i −0.668427 + 1.15775i 0.309917 + 0.950764i \(0.399699\pi\)
−0.978344 + 0.206986i \(0.933634\pi\)
\(968\) 5.44543 9.43176i 0.175023 0.303148i
\(969\) 3.01030 16.5182i 0.0967049 0.530641i
\(970\) 1.69967 3.70340i 0.0545730 0.118909i
\(971\) 46.6818 26.9517i 1.49809 0.864923i 0.498092 0.867124i \(-0.334034\pi\)
0.999998 + 0.00220154i \(0.000700772\pi\)
\(972\) 5.74903 14.4896i 0.184400 0.464754i
\(973\) −15.1815 + 26.2952i −0.486697 + 0.842984i
\(974\) −2.36161 4.09043i −0.0756709 0.131066i
\(975\) −20.0456 34.2129i −0.641974 1.09569i
\(976\) 2.17067i 0.0694814i
\(977\) 48.9259 1.56528 0.782639 0.622476i \(-0.213873\pi\)
0.782639 + 0.622476i \(0.213873\pi\)
\(978\) 13.5652 + 11.5157i 0.433768 + 0.368231i
\(979\) −1.37512 2.38178i −0.0439490 0.0761219i
\(980\) 0.664991 + 7.10453i 0.0212424 + 0.226946i
\(981\) −3.70554 22.5216i −0.118309 0.719058i
\(982\) 6.25568 + 10.8352i 0.199627 + 0.345764i
\(983\) 22.8627 13.1998i 0.729207 0.421008i −0.0889250 0.996038i \(-0.528343\pi\)
0.818132 + 0.575031i \(0.195010\pi\)
\(984\) 1.31919 7.23866i 0.0420541 0.230760i
\(985\) 60.0728 5.62287i 1.91408 0.179160i
\(986\) −8.09849 4.67566i −0.257908 0.148903i
\(987\) −29.8741 + 10.6798i −0.950903 + 0.339942i
\(988\) −27.5379 −0.876098
\(989\) −32.1173 18.5429i −1.02127 0.589631i
\(990\) 2.14369 0.562015i 0.0681311 0.0178620i
\(991\) 7.07855i 0.224857i −0.993660 0.112429i \(-0.964137\pi\)
0.993660 0.112429i \(-0.0358630\pi\)
\(992\) 5.00448 2.44033i 0.158892 0.0774806i
\(993\) −4.78809 + 26.2733i −0.151946 + 0.833759i
\(994\) 0.0406561 0.00128953
\(995\) −43.1449 + 4.03841i −1.36779 + 0.128026i
\(996\) −4.57884 + 25.1251i −0.145086 + 0.796119i
\(997\) −30.1116 + 17.3849i −0.953644 + 0.550587i −0.894211 0.447646i \(-0.852263\pi\)
−0.0594332 + 0.998232i \(0.518929\pi\)
\(998\) 19.3605 + 11.1778i 0.612845 + 0.353826i
\(999\) −21.0944 + 11.7000i −0.667396 + 0.370172i
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 930.2.r.b.119.10 yes 64
3.2 odd 2 930.2.r.a.119.11 64
5.4 even 2 930.2.r.a.119.23 yes 64
15.14 odd 2 inner 930.2.r.b.119.22 yes 64
31.6 odd 6 inner 930.2.r.b.719.22 yes 64
93.68 even 6 930.2.r.a.719.23 yes 64
155.99 odd 6 930.2.r.a.719.11 yes 64
465.254 even 6 inner 930.2.r.b.719.10 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.r.a.119.11 64 3.2 odd 2
930.2.r.a.119.23 yes 64 5.4 even 2
930.2.r.a.719.11 yes 64 155.99 odd 6
930.2.r.a.719.23 yes 64 93.68 even 6
930.2.r.b.119.10 yes 64 1.1 even 1 trivial
930.2.r.b.119.22 yes 64 15.14 odd 2 inner
930.2.r.b.719.10 yes 64 465.254 even 6 inner
930.2.r.b.719.22 yes 64 31.6 odd 6 inner