Properties

Label 756.2.bs.a.11.12
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 11.12
Character \(\chi\) \(=\) 756.11
Dual form 756.2.bs.a.275.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.35727 + 0.397255i) q^{2} +(-1.72583 + 0.146654i) q^{3} +(1.68438 - 1.07837i) q^{4} +(3.07035 - 0.541386i) q^{5} +(2.28416 - 0.884644i) q^{6} +(-1.38755 - 2.25271i) q^{7} +(-1.85777 + 2.13276i) q^{8} +(2.95699 - 0.506199i) q^{9} +O(q^{10})\) \(q+(-1.35727 + 0.397255i) q^{2} +(-1.72583 + 0.146654i) q^{3} +(1.68438 - 1.07837i) q^{4} +(3.07035 - 0.541386i) q^{5} +(2.28416 - 0.884644i) q^{6} +(-1.38755 - 2.25271i) q^{7} +(-1.85777 + 2.13276i) q^{8} +(2.95699 - 0.506199i) q^{9} +(-3.95223 + 1.95452i) q^{10} +(-0.939330 + 5.32721i) q^{11} +(-2.74880 + 2.10810i) q^{12} +(-2.38539 + 2.00158i) q^{13} +(2.77819 + 2.50633i) q^{14} +(-5.21951 + 1.38462i) q^{15} +(1.67425 - 3.63275i) q^{16} -0.715891i q^{17} +(-3.81234 + 1.86173i) q^{18} +6.85106i q^{19} +(4.58781 - 4.22286i) q^{20} +(2.72505 + 3.68431i) q^{21} +(-0.841332 - 7.60362i) q^{22} +(5.34951 - 4.48877i) q^{23} +(2.89342 - 3.95324i) q^{24} +(4.43549 - 1.61439i) q^{25} +(2.44248 - 3.66429i) q^{26} +(-5.02902 + 1.30727i) q^{27} +(-4.76641 - 2.29812i) q^{28} +(0.764599 - 0.911214i) q^{29} +(6.53425 - 3.95278i) q^{30} +(0.532375 - 1.46269i) q^{31} +(-0.829287 + 5.59574i) q^{32} +(0.839871 - 9.33161i) q^{33} +(0.284391 + 0.971659i) q^{34} +(-5.47985 - 6.16541i) q^{35} +(4.43481 - 4.04134i) q^{36} +(-2.69638 + 4.67026i) q^{37} +(-2.72162 - 9.29875i) q^{38} +(3.82323 - 3.80421i) q^{39} +(-4.54936 + 7.55410i) q^{40} +(5.71892 + 6.81554i) q^{41} +(-5.16224 - 3.91807i) q^{42} +(0.211142 + 0.580109i) q^{43} +(4.16249 + 9.98596i) q^{44} +(8.80493 - 3.15508i) q^{45} +(-5.47755 + 8.21760i) q^{46} +(11.6206 - 4.22955i) q^{47} +(-2.35672 + 6.51505i) q^{48} +(-3.14940 + 6.25150i) q^{49} +(-5.37884 + 3.95318i) q^{50} +(0.104988 + 1.23551i) q^{51} +(-1.85946 + 5.94373i) q^{52} +(2.70339 + 1.56080i) q^{53} +(6.30643 - 3.77212i) q^{54} +16.8649i q^{55} +(7.38225 + 1.22570i) q^{56} +(-1.00473 - 11.8238i) q^{57} +(-0.675785 + 1.54051i) q^{58} +(-4.96290 + 4.16437i) q^{59} +(-7.29849 + 7.96076i) q^{60} +(-0.865832 + 0.315137i) q^{61} +(-0.141518 + 2.19676i) q^{62} +(-5.24329 - 5.95885i) q^{63} +(-1.09737 - 7.92438i) q^{64} +(-6.24035 + 7.43695i) q^{65} +(2.56710 + 12.9992i) q^{66} +(1.96505 - 0.346492i) q^{67} +(-0.771993 - 1.20583i) q^{68} +(-8.57405 + 8.53138i) q^{69} +(9.88689 + 6.19124i) q^{70} +(0.970934 + 1.68171i) q^{71} +(-4.41380 + 7.24695i) q^{72} +(2.59762 + 4.49921i) q^{73} +(1.80443 - 7.40997i) q^{74} +(-7.41815 + 3.43664i) q^{75} +(7.38795 + 11.5398i) q^{76} +(13.3040 - 5.27574i) q^{77} +(-3.67793 + 6.68215i) q^{78} +(7.51648 + 1.32536i) q^{79} +(3.17382 - 12.0602i) q^{80} +(8.48753 - 2.99365i) q^{81} +(-10.4696 - 6.97868i) q^{82} +(1.49245 + 1.25232i) q^{83} +(8.56304 + 3.26716i) q^{84} +(-0.387573 - 2.19804i) q^{85} +(-0.517029 - 0.703488i) q^{86} +(-1.18594 + 1.68473i) q^{87} +(-9.61661 - 11.9001i) q^{88} +14.7566i q^{89} +(-10.6973 + 7.78010i) q^{90} +(7.81882 + 2.59629i) q^{91} +(4.17005 - 13.3295i) q^{92} +(-0.704281 + 2.60243i) q^{93} +(-14.0921 + 10.3570i) q^{94} +(3.70906 + 21.0351i) q^{95} +(0.610574 - 9.77892i) q^{96} +(-8.96858 + 3.26430i) q^{97} +(1.79115 - 9.73611i) q^{98} +(-0.0809591 + 16.2280i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.35727 + 0.397255i −0.959737 + 0.280902i
\(3\) −1.72583 + 0.146654i −0.996409 + 0.0846706i
\(4\) 1.68438 1.07837i 0.842189 0.539183i
\(5\) 3.07035 0.541386i 1.37310 0.242115i 0.562057 0.827098i \(-0.310010\pi\)
0.811045 + 0.584984i \(0.198899\pi\)
\(6\) 2.28416 0.884644i 0.932506 0.361154i
\(7\) −1.38755 2.25271i −0.524445 0.851444i
\(8\) −1.85777 + 2.13276i −0.656822 + 0.754046i
\(9\) 2.95699 0.506199i 0.985662 0.168733i
\(10\) −3.95223 + 1.95452i −1.24981 + 0.618073i
\(11\) −0.939330 + 5.32721i −0.283219 + 1.60621i 0.428361 + 0.903608i \(0.359091\pi\)
−0.711580 + 0.702605i \(0.752020\pi\)
\(12\) −2.74880 + 2.10810i −0.793511 + 0.608556i
\(13\) −2.38539 + 2.00158i −0.661587 + 0.555137i −0.910562 0.413372i \(-0.864351\pi\)
0.248975 + 0.968510i \(0.419906\pi\)
\(14\) 2.77819 + 2.50633i 0.742501 + 0.669845i
\(15\) −5.21951 + 1.38462i −1.34767 + 0.357507i
\(16\) 1.67425 3.63275i 0.418563 0.908188i
\(17\) 0.715891i 0.173629i −0.996224 0.0868145i \(-0.972331\pi\)
0.996224 0.0868145i \(-0.0276687\pi\)
\(18\) −3.81234 + 1.86173i −0.898578 + 0.438813i
\(19\) 6.85106i 1.57174i 0.618392 + 0.785870i \(0.287785\pi\)
−0.618392 + 0.785870i \(0.712215\pi\)
\(20\) 4.58781 4.22286i 1.02587 0.944260i
\(21\) 2.72505 + 3.68431i 0.594654 + 0.803982i
\(22\) −0.841332 7.60362i −0.179373 1.62110i
\(23\) 5.34951 4.48877i 1.11545 0.935973i 0.117083 0.993122i \(-0.462646\pi\)
0.998366 + 0.0571492i \(0.0182011\pi\)
\(24\) 2.89342 3.95324i 0.590617 0.806952i
\(25\) 4.43549 1.61439i 0.887097 0.322877i
\(26\) 2.44248 3.66429i 0.479010 0.718627i
\(27\) −5.02902 + 1.30727i −0.967836 + 0.251584i
\(28\) −4.76641 2.29812i −0.900766 0.434304i
\(29\) 0.764599 0.911214i 0.141982 0.169208i −0.690367 0.723459i \(-0.742551\pi\)
0.832349 + 0.554251i \(0.186995\pi\)
\(30\) 6.53425 3.95278i 1.19299 0.721676i
\(31\) 0.532375 1.46269i 0.0956174 0.262707i −0.882658 0.470016i \(-0.844248\pi\)
0.978276 + 0.207309i \(0.0664705\pi\)
\(32\) −0.829287 + 5.59574i −0.146599 + 0.989196i
\(33\) 0.839871 9.33161i 0.146203 1.62443i
\(34\) 0.284391 + 0.971659i 0.0487727 + 0.166638i
\(35\) −5.47985 6.16541i −0.926264 1.04214i
\(36\) 4.43481 4.04134i 0.739135 0.673557i
\(37\) −2.69638 + 4.67026i −0.443282 + 0.767786i −0.997931 0.0642980i \(-0.979519\pi\)
0.554649 + 0.832084i \(0.312853\pi\)
\(38\) −2.72162 9.29875i −0.441504 1.50846i
\(39\) 3.82323 3.80421i 0.612208 0.609161i
\(40\) −4.54936 + 7.55410i −0.719317 + 1.19441i
\(41\) 5.71892 + 6.81554i 0.893145 + 1.06441i 0.997556 + 0.0698746i \(0.0222599\pi\)
−0.104411 + 0.994534i \(0.533296\pi\)
\(42\) −5.16224 3.91807i −0.796551 0.604571i
\(43\) 0.211142 + 0.580109i 0.0321989 + 0.0884657i 0.954750 0.297408i \(-0.0961222\pi\)
−0.922552 + 0.385874i \(0.873900\pi\)
\(44\) 4.16249 + 9.98596i 0.627519 + 1.50544i
\(45\) 8.80493 3.15508i 1.31256 0.470331i
\(46\) −5.47755 + 8.21760i −0.807621 + 1.21162i
\(47\) 11.6206 4.22955i 1.69504 0.616944i 0.699794 0.714345i \(-0.253275\pi\)
0.995245 + 0.0974011i \(0.0310530\pi\)
\(48\) −2.35672 + 6.51505i −0.340163 + 0.940366i
\(49\) −3.14940 + 6.25150i −0.449914 + 0.893072i
\(50\) −5.37884 + 3.95318i −0.760683 + 0.559064i
\(51\) 0.104988 + 1.23551i 0.0147013 + 0.173006i
\(52\) −1.85946 + 5.94373i −0.257860 + 0.824247i
\(53\) 2.70339 + 1.56080i 0.371339 + 0.214393i 0.674043 0.738692i \(-0.264556\pi\)
−0.302704 + 0.953084i \(0.597889\pi\)
\(54\) 6.30643 3.77212i 0.858197 0.513321i
\(55\) 16.8649i 2.27407i
\(56\) 7.38225 + 1.22570i 0.986495 + 0.163791i
\(57\) −1.00473 11.8238i −0.133080 1.56610i
\(58\) −0.675785 + 1.54051i −0.0887349 + 0.202278i
\(59\) −4.96290 + 4.16437i −0.646115 + 0.542154i −0.905889 0.423515i \(-0.860796\pi\)
0.259775 + 0.965669i \(0.416352\pi\)
\(60\) −7.29849 + 7.96076i −0.942232 + 1.02773i
\(61\) −0.865832 + 0.315137i −0.110858 + 0.0403492i −0.396854 0.917882i \(-0.629898\pi\)
0.285995 + 0.958231i \(0.407676\pi\)
\(62\) −0.141518 + 2.19676i −0.0179728 + 0.278988i
\(63\) −5.24329 5.95885i −0.660592 0.750745i
\(64\) −1.09737 7.92438i −0.137171 0.990547i
\(65\) −6.24035 + 7.43695i −0.774020 + 0.922441i
\(66\) 2.56710 + 12.9992i 0.315988 + 1.60009i
\(67\) 1.96505 0.346492i 0.240069 0.0423307i −0.0523188 0.998630i \(-0.516661\pi\)
0.292388 + 0.956300i \(0.405550\pi\)
\(68\) −0.771993 1.20583i −0.0936179 0.146228i
\(69\) −8.57405 + 8.53138i −1.03219 + 1.02706i
\(70\) 9.88689 + 6.19124i 1.18171 + 0.739994i
\(71\) 0.970934 + 1.68171i 0.115229 + 0.199582i 0.917871 0.396879i \(-0.129907\pi\)
−0.802642 + 0.596460i \(0.796573\pi\)
\(72\) −4.41380 + 7.24695i −0.520172 + 0.854062i
\(73\) 2.59762 + 4.49921i 0.304028 + 0.526593i 0.977045 0.213035i \(-0.0683349\pi\)
−0.673016 + 0.739628i \(0.735002\pi\)
\(74\) 1.80443 7.40997i 0.209761 0.861391i
\(75\) −7.41815 + 3.43664i −0.856574 + 0.396829i
\(76\) 7.38795 + 11.5398i 0.847456 + 1.32370i
\(77\) 13.3040 5.27574i 1.51613 0.601226i
\(78\) −3.67793 + 6.68215i −0.416444 + 0.756604i
\(79\) 7.51648 + 1.32536i 0.845670 + 0.149114i 0.579663 0.814857i \(-0.303184\pi\)
0.266007 + 0.963971i \(0.414295\pi\)
\(80\) 3.17382 12.0602i 0.354844 1.34838i
\(81\) 8.48753 2.99365i 0.943058 0.332627i
\(82\) −10.4696 6.97868i −1.15618 0.770666i
\(83\) 1.49245 + 1.25232i 0.163818 + 0.137460i 0.721012 0.692923i \(-0.243677\pi\)
−0.557194 + 0.830383i \(0.688122\pi\)
\(84\) 8.56304 + 3.26716i 0.934304 + 0.356476i
\(85\) −0.387573 2.19804i −0.0420382 0.238410i
\(86\) −0.517029 0.703488i −0.0557526 0.0758591i
\(87\) −1.18594 + 1.68473i −0.127146 + 0.180622i
\(88\) −9.61661 11.9001i −1.02513 1.26856i
\(89\) 14.7566i 1.56419i 0.623157 + 0.782097i \(0.285850\pi\)
−0.623157 + 0.782097i \(0.714150\pi\)
\(90\) −10.6973 + 7.78010i −1.12760 + 0.820095i
\(91\) 7.81882 + 2.59629i 0.819635 + 0.272165i
\(92\) 4.17005 13.3295i 0.434758 1.38970i
\(93\) −0.704281 + 2.60243i −0.0730305 + 0.269859i
\(94\) −14.0921 + 10.3570i −1.45349 + 1.06824i
\(95\) 3.70906 + 21.0351i 0.380542 + 2.15816i
\(96\) 0.610574 9.77892i 0.0623165 0.998056i
\(97\) −8.96858 + 3.26430i −0.910622 + 0.331439i −0.754501 0.656299i \(-0.772121\pi\)
−0.156121 + 0.987738i \(0.549899\pi\)
\(98\) 1.79115 9.73611i 0.180934 0.983495i
\(99\) −0.0809591 + 16.2280i −0.00813670 + 1.63097i
\(100\) 5.73013 7.50231i 0.573013 0.750231i
\(101\) 9.04832 10.7834i 0.900342 1.07299i −0.0966379 0.995320i \(-0.530809\pi\)
0.996979 0.0776656i \(-0.0247467\pi\)
\(102\) −0.633308 1.63521i −0.0627069 0.161910i
\(103\) −0.959551 + 0.169195i −0.0945474 + 0.0166713i −0.220722 0.975337i \(-0.570841\pi\)
0.126174 + 0.992008i \(0.459730\pi\)
\(104\) 0.162613 8.80594i 0.0159455 0.863493i
\(105\) 10.3615 + 9.83681i 1.01118 + 0.959974i
\(106\) −4.28927 1.04450i −0.416611 0.101451i
\(107\) 8.03908 + 13.9241i 0.777167 + 1.34609i 0.933568 + 0.358399i \(0.116677\pi\)
−0.156401 + 0.987694i \(0.549989\pi\)
\(108\) −7.06105 + 7.62506i −0.679450 + 0.733722i
\(109\) 1.84168 3.18989i 0.176401 0.305536i −0.764244 0.644927i \(-0.776888\pi\)
0.940645 + 0.339391i \(0.110221\pi\)
\(110\) −6.69967 22.8903i −0.638789 2.18250i
\(111\) 3.96858 8.45552i 0.376681 0.802562i
\(112\) −10.5066 + 1.26903i −0.992785 + 0.119912i
\(113\) 6.20667 17.0527i 0.583875 1.60418i −0.197625 0.980278i \(-0.563323\pi\)
0.781500 0.623905i \(-0.214455\pi\)
\(114\) 6.06075 + 15.6489i 0.567641 + 1.46566i
\(115\) 13.9947 16.6782i 1.30501 1.55525i
\(116\) 0.305251 2.35934i 0.0283418 0.219060i
\(117\) −6.04036 + 7.12611i −0.558431 + 0.658809i
\(118\) 5.08169 7.62372i 0.467808 0.701820i
\(119\) −1.61269 + 0.993336i −0.147835 + 0.0910589i
\(120\) 6.74359 13.7043i 0.615603 1.25102i
\(121\) −17.1602 6.24579i −1.56001 0.567799i
\(122\) 1.04998 0.771683i 0.0950607 0.0698649i
\(123\) −10.8694 10.9238i −0.980062 0.984964i
\(124\) −0.680594 3.03781i −0.0611191 0.272804i
\(125\) −0.755610 + 0.436252i −0.0675838 + 0.0390195i
\(126\) 9.48376 + 6.00486i 0.844880 + 0.534956i
\(127\) −13.8342 7.98721i −1.22759 0.708750i −0.261066 0.965321i \(-0.584074\pi\)
−0.966525 + 0.256571i \(0.917407\pi\)
\(128\) 4.63742 + 10.3196i 0.409894 + 0.912133i
\(129\) −0.449471 0.970205i −0.0395737 0.0854217i
\(130\) 5.51548 12.5730i 0.483740 1.10272i
\(131\) −5.74272 + 4.81871i −0.501744 + 0.421013i −0.858213 0.513294i \(-0.828425\pi\)
0.356469 + 0.934307i \(0.383981\pi\)
\(132\) −8.64824 16.6236i −0.752733 1.44690i
\(133\) 15.4334 9.50619i 1.33825 0.824292i
\(134\) −2.52947 + 1.25091i −0.218513 + 0.108062i
\(135\) −14.7331 + 6.73641i −1.26802 + 0.579777i
\(136\) 1.52683 + 1.32996i 0.130924 + 0.114043i
\(137\) 4.86558 + 13.3681i 0.415694 + 1.14211i 0.954116 + 0.299436i \(0.0967984\pi\)
−0.538422 + 0.842675i \(0.680979\pi\)
\(138\) 8.24819 14.9855i 0.702132 1.27565i
\(139\) −2.97104 + 0.523874i −0.252000 + 0.0444344i −0.298221 0.954497i \(-0.596393\pi\)
0.0462210 + 0.998931i \(0.485282\pi\)
\(140\) −15.8787 4.47558i −1.34200 0.378255i
\(141\) −19.4349 + 9.00370i −1.63672 + 0.758248i
\(142\) −1.98589 1.89683i −0.166652 0.159178i
\(143\) −8.42215 14.5876i −0.704295 1.21988i
\(144\) 3.11184 11.5895i 0.259320 0.965791i
\(145\) 1.85427 3.21169i 0.153989 0.266716i
\(146\) −5.31301 5.07474i −0.439708 0.419988i
\(147\) 4.51853 11.2509i 0.372682 0.927959i
\(148\) 0.494538 + 10.7742i 0.0406508 + 0.885631i
\(149\) 0.249928 0.686671i 0.0204749 0.0562543i −0.929034 0.369994i \(-0.879360\pi\)
0.949509 + 0.313740i \(0.101582\pi\)
\(150\) 8.70322 7.61135i 0.710615 0.621464i
\(151\) 6.45178 + 1.13762i 0.525038 + 0.0925784i 0.429884 0.902884i \(-0.358554\pi\)
0.0951542 + 0.995463i \(0.469666\pi\)
\(152\) −14.6117 12.7277i −1.18516 1.03235i
\(153\) −0.362383 2.11688i −0.0292969 0.171139i
\(154\) −15.9614 + 12.4457i −1.28620 + 1.00290i
\(155\) 0.842699 4.77919i 0.0676872 0.383873i
\(156\) 2.33744 10.5306i 0.187145 0.843120i
\(157\) −8.51234 + 7.14270i −0.679358 + 0.570049i −0.915819 0.401592i \(-0.868457\pi\)
0.236460 + 0.971641i \(0.424013\pi\)
\(158\) −10.7284 + 1.18709i −0.853507 + 0.0944396i
\(159\) −4.89449 2.29722i −0.388158 0.182181i
\(160\) 0.483249 + 17.6298i 0.0382042 + 1.39376i
\(161\) −17.5346 5.82248i −1.38192 0.458876i
\(162\) −10.3306 + 7.43490i −0.811652 + 0.584141i
\(163\) 12.3454 7.12759i 0.966962 0.558276i 0.0686536 0.997641i \(-0.478130\pi\)
0.898309 + 0.439365i \(0.144796\pi\)
\(164\) 16.9825 + 5.31285i 1.32611 + 0.414864i
\(165\) −2.47330 29.1060i −0.192546 2.26590i
\(166\) −2.52316 1.10685i −0.195835 0.0859083i
\(167\) −4.10845 1.49535i −0.317921 0.115714i 0.178130 0.984007i \(-0.442995\pi\)
−0.496052 + 0.868293i \(0.665217\pi\)
\(168\) −12.9203 1.03272i −0.996821 0.0796758i
\(169\) −0.573668 + 3.25343i −0.0441283 + 0.250264i
\(170\) 1.39922 + 2.82937i 0.107315 + 0.217003i
\(171\) 3.46800 + 20.2585i 0.265204 + 1.54920i
\(172\) 0.981213 + 0.749433i 0.0748168 + 0.0571437i
\(173\) −9.40966 + 11.2140i −0.715403 + 0.852584i −0.994176 0.107773i \(-0.965628\pi\)
0.278772 + 0.960357i \(0.410073\pi\)
\(174\) 0.940370 2.75776i 0.0712893 0.209065i
\(175\) −9.79121 7.75182i −0.740146 0.585983i
\(176\) 17.7797 + 12.3314i 1.34020 + 0.929517i
\(177\) 7.95441 7.91482i 0.597890 0.594914i
\(178\) −5.86212 20.0287i −0.439385 1.50121i
\(179\) 13.7190 1.02541 0.512705 0.858565i \(-0.328644\pi\)
0.512705 + 0.858565i \(0.328644\pi\)
\(180\) 11.4285 14.8093i 0.851830 1.10382i
\(181\) 8.59532 14.8875i 0.638885 1.10658i −0.346792 0.937942i \(-0.612729\pi\)
0.985678 0.168640i \(-0.0539375\pi\)
\(182\) −11.6437 0.417810i −0.863085 0.0309701i
\(183\) 1.44806 0.670851i 0.107044 0.0495907i
\(184\) −0.364679 + 19.7483i −0.0268845 + 1.45587i
\(185\) −5.75041 + 15.7991i −0.422778 + 1.16157i
\(186\) −0.0779266 3.81198i −0.00571385 0.279508i
\(187\) 3.81370 + 0.672458i 0.278885 + 0.0491750i
\(188\) 15.0125 19.6554i 1.09490 1.43352i
\(189\) 9.92292 + 9.51502i 0.721786 + 0.692116i
\(190\) −13.3905 27.0770i −0.971451 1.96437i
\(191\) 4.09607 23.2299i 0.296381 1.68086i −0.365155 0.930947i \(-0.618984\pi\)
0.661536 0.749913i \(-0.269905\pi\)
\(192\) 3.05601 + 13.5152i 0.220548 + 0.975376i
\(193\) 17.0947 + 6.22197i 1.23050 + 0.447867i 0.873770 0.486339i \(-0.161668\pi\)
0.356734 + 0.934206i \(0.383890\pi\)
\(194\) 10.8761 7.99335i 0.780855 0.573889i
\(195\) 9.67913 13.7501i 0.693137 0.984665i
\(196\) 1.43663 + 13.9261i 0.102617 + 0.994721i
\(197\) −4.93284 2.84797i −0.351450 0.202910i 0.313874 0.949465i \(-0.398373\pi\)
−0.665324 + 0.746555i \(0.731706\pi\)
\(198\) −6.33675 22.0579i −0.450333 1.56759i
\(199\) 18.7174i 1.32684i −0.748246 0.663421i \(-0.769104\pi\)
0.748246 0.663421i \(-0.230896\pi\)
\(200\) −4.79702 + 12.4590i −0.339201 + 0.880985i
\(201\) −3.34053 + 0.886168i −0.235623 + 0.0625055i
\(202\) −7.99729 + 18.2305i −0.562687 + 1.28269i
\(203\) −3.11362 0.458063i −0.218533 0.0321497i
\(204\) 1.50917 + 1.96784i 0.105663 + 0.137777i
\(205\) 21.2489 + 17.8300i 1.48409 + 1.24530i
\(206\) 1.23516 0.610830i 0.0860576 0.0425585i
\(207\) 13.5462 15.9811i 0.941526 1.11077i
\(208\) 3.27749 + 12.0167i 0.227253 + 0.833205i
\(209\) −36.4970 6.43540i −2.52455 0.445146i
\(210\) −17.9711 9.23508i −1.24012 0.637281i
\(211\) 2.32437 6.38615i 0.160016 0.439640i −0.833612 0.552351i \(-0.813731\pi\)
0.993628 + 0.112710i \(0.0359532\pi\)
\(212\) 6.23664 0.286264i 0.428334 0.0196607i
\(213\) −1.92230 2.75995i −0.131714 0.189109i
\(214\) −16.4426 15.7052i −1.12400 1.07359i
\(215\) 0.962343 + 1.66683i 0.0656312 + 0.113677i
\(216\) 6.55468 13.1543i 0.445990 0.895038i
\(217\) −4.03371 + 0.830270i −0.273826 + 0.0563624i
\(218\) −1.23247 + 5.06116i −0.0834731 + 0.342785i
\(219\) −5.14288 7.38393i −0.347524 0.498959i
\(220\) 18.1866 + 28.4069i 1.22614 + 1.91519i
\(221\) 1.43291 + 1.70768i 0.0963880 + 0.114871i
\(222\) −2.02745 + 13.0530i −0.136073 + 0.876058i
\(223\) 2.58077 + 0.455059i 0.172821 + 0.0304730i 0.259389 0.965773i \(-0.416479\pi\)
−0.0865679 + 0.996246i \(0.527590\pi\)
\(224\) 13.7563 5.89623i 0.919128 0.393959i
\(225\) 12.2985 7.01895i 0.819898 0.467930i
\(226\) −1.64988 + 25.6108i −0.109748 + 1.70360i
\(227\) −1.18640 + 6.72840i −0.0787440 + 0.446580i 0.919788 + 0.392416i \(0.128361\pi\)
−0.998532 + 0.0541641i \(0.982751\pi\)
\(228\) −14.4427 18.8322i −0.956491 1.24719i
\(229\) −1.89736 0.690584i −0.125381 0.0456351i 0.278567 0.960417i \(-0.410140\pi\)
−0.403949 + 0.914782i \(0.632363\pi\)
\(230\) −12.3691 + 28.1964i −0.815595 + 1.85921i
\(231\) −22.1868 + 11.0561i −1.45978 + 0.727439i
\(232\) 0.522953 + 3.32354i 0.0343335 + 0.218201i
\(233\) 8.01345 + 4.62657i 0.524978 + 0.303096i 0.738969 0.673739i \(-0.235313\pi\)
−0.213991 + 0.976836i \(0.568646\pi\)
\(234\) 5.36753 12.0716i 0.350886 0.789148i
\(235\) 33.3895 19.2774i 2.17809 1.25752i
\(236\) −3.86868 + 12.3662i −0.251830 + 0.804970i
\(237\) −13.1665 1.18502i −0.855259 0.0769756i
\(238\) 1.79426 1.98888i 0.116304 0.128920i
\(239\) 2.45174 + 13.9045i 0.158590 + 0.899407i 0.955430 + 0.295217i \(0.0953920\pi\)
−0.796840 + 0.604190i \(0.793497\pi\)
\(240\) −3.70880 + 21.2794i −0.239402 + 1.37358i
\(241\) −8.01379 + 2.91678i −0.516214 + 0.187886i −0.586972 0.809607i \(-0.699680\pi\)
0.0707586 + 0.997493i \(0.477458\pi\)
\(242\) 25.7722 + 1.66028i 1.65670 + 0.106727i
\(243\) −14.2090 + 6.41125i −0.911508 + 0.411282i
\(244\) −1.11855 + 1.46449i −0.0716081 + 0.0937546i
\(245\) −6.28529 + 20.8993i −0.401552 + 1.33521i
\(246\) 19.0923 + 10.5086i 1.21728 + 0.670004i
\(247\) −13.7129 16.3424i −0.872532 1.03984i
\(248\) 2.13054 + 3.85277i 0.135289 + 0.244651i
\(249\) −2.75938 1.94241i −0.174869 0.123095i
\(250\) 0.852266 0.892282i 0.0539020 0.0564329i
\(251\) −14.9245 + 25.8501i −0.942029 + 1.63164i −0.180435 + 0.983587i \(0.557750\pi\)
−0.761594 + 0.648055i \(0.775583\pi\)
\(252\) −15.2575 4.38277i −0.961132 0.276088i
\(253\) 18.8876 + 32.7144i 1.18746 + 2.05673i
\(254\) 21.9498 + 5.34509i 1.37725 + 0.335381i
\(255\) 0.991235 + 3.73660i 0.0620736 + 0.233995i
\(256\) −10.3938 12.1643i −0.649610 0.760268i
\(257\) 5.72786 15.7372i 0.357294 0.981658i −0.622670 0.782485i \(-0.713952\pi\)
0.979964 0.199173i \(-0.0638257\pi\)
\(258\) 0.995473 + 1.13828i 0.0619754 + 0.0708661i
\(259\) 14.2621 0.406076i 0.886204 0.0252323i
\(260\) −2.49133 + 19.2560i −0.154506 + 1.19421i
\(261\) 1.79965 3.08148i 0.111396 0.190739i
\(262\) 5.88018 8.82163i 0.363279 0.545002i
\(263\) −6.37251 5.34717i −0.392946 0.329721i 0.424814 0.905281i \(-0.360340\pi\)
−0.817759 + 0.575560i \(0.804784\pi\)
\(264\) 18.3418 + 19.1273i 1.12886 + 1.17720i
\(265\) 9.14534 + 3.32863i 0.561794 + 0.204476i
\(266\) −17.1710 + 19.0335i −1.05282 + 1.16702i
\(267\) −2.16411 25.4674i −0.132441 1.55858i
\(268\) 2.93624 2.70267i 0.179360 0.165092i
\(269\) −14.7828 8.53486i −0.901324 0.520380i −0.0236943 0.999719i \(-0.507543\pi\)
−0.877629 + 0.479340i \(0.840876\pi\)
\(270\) 17.3208 14.9959i 1.05411 0.912624i
\(271\) −6.29656 + 3.63532i −0.382489 + 0.220830i −0.678901 0.734230i \(-0.737543\pi\)
0.296412 + 0.955060i \(0.404210\pi\)
\(272\) −2.60065 1.19858i −0.157688 0.0726747i
\(273\) −13.8747 3.33410i −0.839736 0.201789i
\(274\) −11.9144 16.2112i −0.719778 0.979357i
\(275\) 4.43378 + 25.1452i 0.267367 + 1.51631i
\(276\) −5.24198 + 23.6160i −0.315530 + 1.42152i
\(277\) −18.2723 15.3323i −1.09787 0.921226i −0.100595 0.994927i \(-0.532075\pi\)
−0.997280 + 0.0737010i \(0.976519\pi\)
\(278\) 3.82439 1.89130i 0.229372 0.113433i
\(279\) 0.833814 4.59464i 0.0499191 0.275074i
\(280\) 23.3297 0.233316i 1.39421 0.0139433i
\(281\) −4.82539 13.2576i −0.287859 0.790885i −0.996365 0.0851810i \(-0.972853\pi\)
0.708507 0.705704i \(-0.249369\pi\)
\(282\) 22.8017 19.9411i 1.35782 1.18747i
\(283\) −19.5676 + 3.45030i −1.16317 + 0.205099i −0.721720 0.692185i \(-0.756648\pi\)
−0.441454 + 0.897284i \(0.645537\pi\)
\(284\) 3.44891 + 1.78561i 0.204655 + 0.105956i
\(285\) −9.48610 35.7591i −0.561908 2.11819i
\(286\) 17.2261 + 16.4536i 1.01860 + 0.972921i
\(287\) 7.41814 22.3400i 0.437879 1.31869i
\(288\) 0.380366 + 16.9663i 0.0224133 + 0.999749i
\(289\) 16.4875 0.969853
\(290\) −1.24089 + 5.09575i −0.0728675 + 0.299233i
\(291\) 14.9995 6.94890i 0.879288 0.407352i
\(292\) 9.22717 + 4.77718i 0.539979 + 0.279563i
\(293\) −14.1877 + 2.50168i −0.828857 + 0.146150i −0.571952 0.820287i \(-0.693814\pi\)
−0.256905 + 0.966437i \(0.582703\pi\)
\(294\) −1.66339 + 17.0656i −0.0970111 + 0.995283i
\(295\) −12.9833 + 15.4729i −0.755918 + 0.900868i
\(296\) −4.95131 14.4270i −0.287789 0.838553i
\(297\) −2.24017 28.0186i −0.129988 1.62580i
\(298\) −0.0664367 + 1.03128i −0.00384857 + 0.0597407i
\(299\) −3.77602 + 21.4149i −0.218373 + 1.23846i
\(300\) −8.78900 + 13.7881i −0.507433 + 0.796055i
\(301\) 1.01385 1.28057i 0.0584371 0.0738110i
\(302\) −9.20875 + 1.01894i −0.529904 + 0.0586332i
\(303\) −14.0345 + 19.9372i −0.806258 + 1.14536i
\(304\) 24.8882 + 11.4704i 1.42744 + 0.657872i
\(305\) −2.48780 + 1.43633i −0.142451 + 0.0822440i
\(306\) 1.33279 + 2.72922i 0.0761907 + 0.156019i
\(307\) 1.57170 0.907422i 0.0897017 0.0517893i −0.454478 0.890758i \(-0.650174\pi\)
0.544180 + 0.838969i \(0.316841\pi\)
\(308\) 16.7198 23.2329i 0.952699 1.32382i
\(309\) 1.63121 0.432723i 0.0927963 0.0246168i
\(310\) 0.754783 + 6.82142i 0.0428688 + 0.387431i
\(311\) 2.77568 + 15.7416i 0.157394 + 0.892627i 0.956564 + 0.291522i \(0.0941616\pi\)
−0.799170 + 0.601105i \(0.794727\pi\)
\(312\) 1.01078 + 15.2214i 0.0572242 + 0.861743i
\(313\) 1.02629 + 0.861158i 0.0580093 + 0.0486755i 0.671331 0.741157i \(-0.265723\pi\)
−0.613322 + 0.789833i \(0.710167\pi\)
\(314\) 8.71609 13.0762i 0.491877 0.737930i
\(315\) −19.3248 15.4571i −1.08883 0.870910i
\(316\) 14.0898 5.87312i 0.792614 0.330389i
\(317\) −7.08595 19.4685i −0.397986 1.09346i −0.963264 0.268558i \(-0.913453\pi\)
0.565277 0.824901i \(-0.308769\pi\)
\(318\) 7.55573 + 1.17359i 0.423704 + 0.0658117i
\(319\) 4.13601 + 4.92911i 0.231572 + 0.275977i
\(320\) −7.65944 23.7365i −0.428176 1.32691i
\(321\) −15.9161 22.8517i −0.888351 1.27546i
\(322\) 26.1123 + 0.936988i 1.45518 + 0.0522163i
\(323\) 4.90461 0.272900
\(324\) 11.0679 14.1951i 0.614886 0.788616i
\(325\) −7.34903 + 12.7289i −0.407651 + 0.706072i
\(326\) −13.9245 + 14.5783i −0.771209 + 0.807419i
\(327\) −2.71062 + 5.77530i −0.149898 + 0.319375i
\(328\) −25.1604 0.464619i −1.38925 0.0256543i
\(329\) −25.6521 20.3091i −1.41425 1.11968i
\(330\) 14.9195 + 38.5223i 0.821289 + 2.12058i
\(331\) −1.66308 4.56928i −0.0914113 0.251150i 0.885559 0.464528i \(-0.153776\pi\)
−0.976970 + 0.213377i \(0.931554\pi\)
\(332\) 3.86431 + 0.499963i 0.212082 + 0.0274390i
\(333\) −5.60907 + 15.1748i −0.307375 + 0.831574i
\(334\) 6.17032 + 0.397500i 0.337625 + 0.0217502i
\(335\) 5.84581 2.12770i 0.319391 0.116249i
\(336\) 17.9466 3.73097i 0.979066 0.203541i
\(337\) −10.1710 + 8.53448i −0.554049 + 0.464903i −0.876310 0.481748i \(-0.840002\pi\)
0.322260 + 0.946651i \(0.395557\pi\)
\(338\) −0.513819 4.64369i −0.0279481 0.252583i
\(339\) −8.21083 + 30.3403i −0.445951 + 1.64786i
\(340\) −3.02311 3.28437i −0.163951 0.178120i
\(341\) 7.29197 + 4.21002i 0.394882 + 0.227985i
\(342\) −12.7548 26.1186i −0.689700 1.41233i
\(343\) 18.4528 1.57960i 0.996356 0.0852903i
\(344\) −1.62949 0.627393i −0.0878562 0.0338268i
\(345\) −21.7066 + 30.8362i −1.16864 + 1.66016i
\(346\) 8.31666 18.9585i 0.447106 1.01921i
\(347\) −28.8618 10.5048i −1.54938 0.563929i −0.581109 0.813825i \(-0.697381\pi\)
−0.968273 + 0.249897i \(0.919603\pi\)
\(348\) −0.180805 + 4.11660i −0.00969215 + 0.220673i
\(349\) −11.8972 9.98290i −0.636840 0.534372i 0.266206 0.963916i \(-0.414230\pi\)
−0.903046 + 0.429544i \(0.858674\pi\)
\(350\) 16.3688 + 6.63173i 0.874948 + 0.354481i
\(351\) 9.37956 13.1843i 0.500644 0.703726i
\(352\) −29.0307 9.67403i −1.54734 0.515627i
\(353\) −2.14123 5.88299i −0.113966 0.313120i 0.869576 0.493800i \(-0.164392\pi\)
−0.983542 + 0.180680i \(0.942170\pi\)
\(354\) −7.65209 + 13.9025i −0.406704 + 0.738909i
\(355\) 3.89156 + 4.63778i 0.206542 + 0.246148i
\(356\) 15.9130 + 24.8556i 0.843387 + 1.31735i
\(357\) 2.63756 1.95084i 0.139595 0.103249i
\(358\) −18.6205 + 5.44996i −0.984123 + 0.288039i
\(359\) 16.6874 0.880727 0.440364 0.897820i \(-0.354850\pi\)
0.440364 + 0.897820i \(0.354850\pi\)
\(360\) −9.62852 + 24.6403i −0.507468 + 1.29866i
\(361\) −27.9370 −1.47037
\(362\) −5.75205 + 23.6210i −0.302321 + 1.24149i
\(363\) 30.5315 + 8.26257i 1.60249 + 0.433673i
\(364\) 15.9696 4.05842i 0.837034 0.212719i
\(365\) 10.4114 + 12.4078i 0.544958 + 0.649456i
\(366\) −1.69892 + 1.48578i −0.0888039 + 0.0776628i
\(367\) −11.4488 2.01874i −0.597623 0.105377i −0.133350 0.991069i \(-0.542573\pi\)
−0.464274 + 0.885692i \(0.653685\pi\)
\(368\) −7.35016 26.9488i −0.383154 1.40480i
\(369\) 20.3608 + 17.2585i 1.05994 + 0.898444i
\(370\) 1.52859 23.7281i 0.0794678 1.23356i
\(371\) −0.235058 8.25564i −0.0122036 0.428611i
\(372\) 1.62010 + 5.14294i 0.0839981 + 0.266649i
\(373\) −4.36056 24.7299i −0.225781 1.28047i −0.861186 0.508289i \(-0.830278\pi\)
0.635405 0.772179i \(-0.280833\pi\)
\(374\) −5.44336 + 0.602302i −0.281470 + 0.0311443i
\(375\) 1.24008 0.863710i 0.0640373 0.0446018i
\(376\) −12.5678 + 32.6416i −0.648134 + 1.68336i
\(377\) 3.70400i 0.190766i
\(378\) −17.2480 8.97255i −0.887141 0.461498i
\(379\) 26.9640i 1.38505i −0.721396 0.692523i \(-0.756499\pi\)
0.721396 0.692523i \(-0.243501\pi\)
\(380\) 28.9310 + 31.4314i 1.48413 + 1.61240i
\(381\) 25.0469 + 11.7557i 1.28319 + 0.602264i
\(382\) 3.66873 + 33.1565i 0.187709 + 1.69644i
\(383\) 3.00368 + 17.0347i 0.153481 + 0.870433i 0.960162 + 0.279445i \(0.0901506\pi\)
−0.806681 + 0.590987i \(0.798738\pi\)
\(384\) −9.51682 17.1298i −0.485653 0.874152i
\(385\) 37.9918 23.4010i 1.93624 1.19262i
\(386\) −25.6739 1.65394i −1.30677 0.0841836i
\(387\) 0.917995 + 1.60849i 0.0466643 + 0.0817643i
\(388\) −11.5864 + 15.1697i −0.588209 + 0.770126i
\(389\) 8.31568 + 1.46628i 0.421622 + 0.0743432i 0.380434 0.924808i \(-0.375775\pi\)
0.0411878 + 0.999151i \(0.486886\pi\)
\(390\) −7.67492 + 22.5077i −0.388634 + 1.13972i
\(391\) −3.21347 3.82966i −0.162512 0.193674i
\(392\) −7.48211 18.3308i −0.377904 0.925845i
\(393\) 9.20428 9.15848i 0.464295 0.461984i
\(394\) 7.82658 + 1.90588i 0.394297 + 0.0960170i
\(395\) 23.7958 1.19729
\(396\) 17.3633 + 27.4213i 0.872540 + 1.37797i
\(397\) 3.24955 0.163090 0.0815450 0.996670i \(-0.474015\pi\)
0.0815450 + 0.996670i \(0.474015\pi\)
\(398\) 7.43559 + 25.4046i 0.372712 + 1.27342i
\(399\) −25.2414 + 18.6695i −1.26365 + 0.934642i
\(400\) 1.56146 18.8159i 0.0780731 0.940795i
\(401\) 3.74963 + 4.46864i 0.187248 + 0.223153i 0.851499 0.524356i \(-0.175694\pi\)
−0.664251 + 0.747509i \(0.731250\pi\)
\(402\) 4.18198 2.52982i 0.208578 0.126176i
\(403\) 1.65776 + 4.55467i 0.0825791 + 0.226884i
\(404\) 3.61236 27.9207i 0.179722 1.38910i
\(405\) 24.4390 13.7866i 1.21438 0.685060i
\(406\) 4.40800 0.615184i 0.218765 0.0305311i
\(407\) −22.3467 18.7511i −1.10768 0.929456i
\(408\) −2.83009 2.07137i −0.140110 0.102548i
\(409\) −14.0893 5.12810i −0.696673 0.253568i −0.0306835 0.999529i \(-0.509768\pi\)
−0.665990 + 0.745961i \(0.731991\pi\)
\(410\) −35.9236 15.7589i −1.77414 0.778275i
\(411\) −10.3576 22.3575i −0.510905 1.10281i
\(412\) −1.43379 + 1.31974i −0.0706378 + 0.0650187i
\(413\) 16.2674 + 5.40170i 0.800466 + 0.265800i
\(414\) −12.0373 + 27.0721i −0.591601 + 1.33052i
\(415\) 5.26034 + 3.03706i 0.258220 + 0.149083i
\(416\) −9.22213 15.0079i −0.452152 0.735822i
\(417\) 5.05068 1.33983i 0.247333 0.0656118i
\(418\) 52.0928 5.76401i 2.54794 0.281927i
\(419\) 19.7309 16.5562i 0.963919 0.808824i −0.0176671 0.999844i \(-0.505624\pi\)
0.981586 + 0.191020i \(0.0611795\pi\)
\(420\) 28.0603 + 5.39542i 1.36920 + 0.263270i
\(421\) −3.36518 + 1.22482i −0.164009 + 0.0596943i −0.422720 0.906260i \(-0.638925\pi\)
0.258711 + 0.965955i \(0.416702\pi\)
\(422\) −0.617871 + 9.59111i −0.0300775 + 0.466888i
\(423\) 32.2210 18.3891i 1.56664 0.894107i
\(424\) −8.35110 + 2.86607i −0.405565 + 0.139189i
\(425\) −1.15572 3.17532i −0.0560608 0.154026i
\(426\) 3.70548 + 2.98236i 0.179531 + 0.144496i
\(427\) 1.91130 + 1.51320i 0.0924942 + 0.0732288i
\(428\) 28.5561 + 14.7843i 1.38031 + 0.714628i
\(429\) 16.6745 + 23.9406i 0.805054 + 1.15586i
\(430\) −1.96832 1.88004i −0.0949207 0.0906637i
\(431\) −10.6190 + 18.3926i −0.511498 + 0.885940i 0.488414 + 0.872612i \(0.337576\pi\)
−0.999911 + 0.0133275i \(0.995758\pi\)
\(432\) −3.67087 + 20.4579i −0.176615 + 0.984280i
\(433\) −15.6803 −0.753549 −0.376775 0.926305i \(-0.622967\pi\)
−0.376775 + 0.926305i \(0.622967\pi\)
\(434\) 5.14502 2.72931i 0.246969 0.131011i
\(435\) −2.72915 + 5.81476i −0.130853 + 0.278797i
\(436\) −0.337780 7.35898i −0.0161767 0.352431i
\(437\) 30.7528 + 36.6498i 1.47111 + 1.75320i
\(438\) 9.91359 + 7.97896i 0.473690 + 0.381250i
\(439\) 8.96431 + 24.6292i 0.427843 + 1.17549i 0.947119 + 0.320883i \(0.103980\pi\)
−0.519276 + 0.854607i \(0.673798\pi\)
\(440\) −35.9689 31.3312i −1.71475 1.49366i
\(441\) −6.14823 + 20.0798i −0.292773 + 0.956182i
\(442\) −2.62323 1.74855i −0.124774 0.0831701i
\(443\) 15.1516 + 12.7137i 0.719875 + 0.604047i 0.927351 0.374194i \(-0.122080\pi\)
−0.207476 + 0.978240i \(0.566525\pi\)
\(444\) −2.43356 18.5219i −0.115492 0.879009i
\(445\) 7.98900 + 45.3078i 0.378715 + 2.14780i
\(446\) −3.68358 + 0.407584i −0.174423 + 0.0192997i
\(447\) −0.330630 + 1.22173i −0.0156383 + 0.0577859i
\(448\) −16.3287 + 13.4675i −0.771457 + 0.636281i
\(449\) −4.11679 + 2.37683i −0.194283 + 0.112169i −0.593986 0.804475i \(-0.702447\pi\)
0.399703 + 0.916645i \(0.369113\pi\)
\(450\) −13.9041 + 14.4123i −0.655444 + 0.679400i
\(451\) −41.6797 + 24.0638i −1.96262 + 1.13312i
\(452\) −7.93468 35.4162i −0.373216 1.66584i
\(453\) −11.3015 1.01717i −0.530991 0.0477907i
\(454\) −1.06262 9.60358i −0.0498714 0.450718i
\(455\) 25.4121 + 3.73853i 1.19134 + 0.175265i
\(456\) 27.0839 + 19.8230i 1.26832 + 0.928297i
\(457\) −0.0503050 + 0.285294i −0.00235317 + 0.0133455i −0.985962 0.166971i \(-0.946601\pi\)
0.983609 + 0.180317i \(0.0577123\pi\)
\(458\) 2.84958 + 0.183573i 0.133152 + 0.00857782i
\(459\) 0.935860 + 3.60023i 0.0436822 + 0.168044i
\(460\) 5.58710 43.1838i 0.260500 2.01346i
\(461\) 20.4757 24.4020i 0.953647 1.13651i −0.0368973 0.999319i \(-0.511747\pi\)
0.990544 0.137193i \(-0.0438081\pi\)
\(462\) 25.7214 23.8200i 1.19667 1.10820i
\(463\) −14.0097 + 2.47028i −0.651084 + 0.114804i −0.489428 0.872043i \(-0.662795\pi\)
−0.161656 + 0.986847i \(0.551683\pi\)
\(464\) −2.03008 4.30320i −0.0942441 0.199771i
\(465\) −0.753471 + 8.37165i −0.0349414 + 0.388226i
\(466\) −12.7144 3.09613i −0.588981 0.143425i
\(467\) −28.2111 −1.30545 −0.652727 0.757593i \(-0.726375\pi\)
−0.652727 + 0.757593i \(0.726375\pi\)
\(468\) −2.48968 + 18.5168i −0.115085 + 0.855938i
\(469\) −3.50716 3.94592i −0.161945 0.182205i
\(470\) −37.6606 + 39.4289i −1.73715 + 1.81872i
\(471\) 13.6434 13.5755i 0.628652 0.625524i
\(472\) 0.338323 18.3211i 0.0155726 0.843299i
\(473\) −3.28869 + 0.579885i −0.151214 + 0.0266631i
\(474\) 18.3413 3.62207i 0.842446 0.166367i
\(475\) 11.0602 + 30.3878i 0.507479 + 1.39429i
\(476\) −1.64521 + 3.41223i −0.0754079 + 0.156399i
\(477\) 8.78395 + 3.24681i 0.402190 + 0.148661i
\(478\) −8.85131 17.8982i −0.404849 0.818646i
\(479\) −22.6593 19.0134i −1.03533 0.868746i −0.0438551 0.999038i \(-0.513964\pi\)
−0.991476 + 0.130292i \(0.958408\pi\)
\(480\) −3.41949 30.3552i −0.156078 1.38552i
\(481\) −2.91599 16.5374i −0.132958 0.754040i
\(482\) 9.71819 7.14238i 0.442651 0.325327i
\(483\) 31.1157 + 7.47711i 1.41581 + 0.340220i
\(484\) −35.6394 + 7.98468i −1.61997 + 0.362940i
\(485\) −25.7694 + 14.8780i −1.17013 + 0.675575i
\(486\) 16.7386 14.3464i 0.759278 0.650767i
\(487\) −21.6133 12.4785i −0.979393 0.565453i −0.0773062 0.997007i \(-0.524632\pi\)
−0.902087 + 0.431555i \(0.857965\pi\)
\(488\) 0.936405 2.43207i 0.0423891 0.110095i
\(489\) −20.2607 + 14.1115i −0.916221 + 0.638145i
\(490\) 0.228483 30.8630i 0.0103218 1.39425i
\(491\) −4.97347 1.81020i −0.224450 0.0816930i 0.227348 0.973814i \(-0.426995\pi\)
−0.451797 + 0.892121i \(0.649217\pi\)
\(492\) −30.0880 6.67854i −1.35647 0.301092i
\(493\) −0.652329 0.547369i −0.0293794 0.0246523i
\(494\) 25.1043 + 16.7336i 1.12949 + 0.752880i
\(495\) 8.53701 + 49.8693i 0.383710 + 2.24146i
\(496\) −4.42225 4.38290i −0.198565 0.196798i
\(497\) 2.44118 4.52069i 0.109502 0.202781i
\(498\) 4.51686 + 1.54021i 0.202405 + 0.0690184i
\(499\) 6.84315 18.8014i 0.306341 0.841666i −0.687021 0.726638i \(-0.741082\pi\)
0.993362 0.115028i \(-0.0366958\pi\)
\(500\) −0.802293 + 1.54964i −0.0358796 + 0.0693019i
\(501\) 7.30979 + 1.97821i 0.326577 + 0.0883798i
\(502\) 9.98760 41.0144i 0.445769 1.83056i
\(503\) 14.4425 + 25.0151i 0.643958 + 1.11537i 0.984541 + 0.175153i \(0.0560421\pi\)
−0.340583 + 0.940214i \(0.610625\pi\)
\(504\) 22.4497 0.112511i 0.999987 0.00501165i
\(505\) 21.9435 38.0073i 0.976475 1.69130i
\(506\) −38.6316 36.8991i −1.71738 1.64036i
\(507\) 0.512926 5.69901i 0.0227799 0.253102i
\(508\) −31.9152 + 1.46492i −1.41601 + 0.0649953i
\(509\) 2.65452 + 3.16353i 0.117659 + 0.140221i 0.821659 0.569979i \(-0.193049\pi\)
−0.704000 + 0.710200i \(0.748604\pi\)
\(510\) −2.82976 4.67781i −0.125304 0.207137i
\(511\) 6.53108 12.0946i 0.288918 0.535032i
\(512\) 18.9395 + 12.3813i 0.837015 + 0.547180i
\(513\) −8.95616 34.4541i −0.395424 1.52119i
\(514\) −1.52260 + 23.6351i −0.0671590 + 1.04250i
\(515\) −2.85456 + 1.03897i −0.125787 + 0.0457827i
\(516\) −1.80331 1.14950i −0.0793865 0.0506037i
\(517\) 11.6161 + 65.8783i 0.510876 + 2.89732i
\(518\) −19.1962 + 6.21685i −0.843435 + 0.273153i
\(519\) 14.5949 20.7334i 0.640645 0.910096i
\(520\) −4.26813 27.1254i −0.187170 1.18953i
\(521\) 37.1168 21.4294i 1.62612 0.938840i 0.640882 0.767639i \(-0.278569\pi\)
0.985236 0.171201i \(-0.0547647\pi\)
\(522\) −1.21848 + 4.89733i −0.0533316 + 0.214351i
\(523\) −9.20667 5.31547i −0.402579 0.232429i 0.285017 0.958522i \(-0.408001\pi\)
−0.687596 + 0.726093i \(0.741334\pi\)
\(524\) −4.47657 + 14.3093i −0.195560 + 0.625104i
\(525\) 18.0348 + 11.9424i 0.787103 + 0.521210i
\(526\) 10.7734 + 4.72605i 0.469743 + 0.206066i
\(527\) −1.04713 0.381122i −0.0456135 0.0166020i
\(528\) −32.4933 18.6745i −1.41409 0.812704i
\(529\) 4.47426 25.3748i 0.194533 1.10325i
\(530\) −13.7350 0.884828i −0.596612 0.0384345i
\(531\) −12.5672 + 14.8262i −0.545371 + 0.643402i
\(532\) 15.7446 32.6549i 0.682614 1.41577i
\(533\) −27.2837 4.81085i −1.18179 0.208381i
\(534\) 13.0543 + 33.7064i 0.564915 + 1.45862i
\(535\) 32.2211 + 38.3996i 1.39304 + 1.66016i
\(536\) −2.91163 + 4.83470i −0.125763 + 0.208827i
\(537\) −23.6767 + 2.01195i −1.02173 + 0.0868220i
\(538\) 23.4548 + 5.71158i 1.01121 + 0.246244i
\(539\) −30.3447 22.6497i −1.30704 0.975593i
\(540\) −17.5518 + 27.2343i −0.755310 + 1.17198i
\(541\) 13.9888 + 24.2293i 0.601425 + 1.04170i 0.992605 + 0.121385i \(0.0387336\pi\)
−0.391180 + 0.920314i \(0.627933\pi\)
\(542\) 7.10200 7.43546i 0.305057 0.319380i
\(543\) −12.6508 + 26.9539i −0.542896 + 1.15670i
\(544\) 4.00594 + 0.593679i 0.171753 + 0.0254538i
\(545\) 3.92765 10.7911i 0.168242 0.462241i
\(546\) 20.1563 0.986515i 0.862608 0.0422190i
\(547\) 31.5283 + 5.55929i 1.34805 + 0.237698i 0.800631 0.599158i \(-0.204498\pi\)
0.547422 + 0.836856i \(0.315609\pi\)
\(548\) 22.6111 + 17.2700i 0.965900 + 0.737737i
\(549\) −2.40073 + 1.37014i −0.102461 + 0.0584761i
\(550\) −16.0069 32.3675i −0.682536 1.38016i
\(551\) 6.24277 + 5.23831i 0.265951 + 0.223160i
\(552\) −2.26679 34.1358i −0.0964812 1.45292i
\(553\) −7.44386 18.7715i −0.316545 0.798243i
\(554\) 30.8913 + 13.5513i 1.31244 + 0.575740i
\(555\) 7.60723 28.1099i 0.322909 1.19320i
\(556\) −4.43942 + 4.08627i −0.188273 + 0.173296i
\(557\) 16.2977i 0.690554i 0.938501 + 0.345277i \(0.112215\pi\)
−0.938501 + 0.345277i \(0.887785\pi\)
\(558\) 0.693529 + 6.56741i 0.0293594 + 0.278021i
\(559\) −1.66479 0.961166i −0.0704130 0.0406530i
\(560\) −31.5720 + 9.58450i −1.33416 + 0.405019i
\(561\) −6.68042 0.601256i −0.282047 0.0253850i
\(562\) 11.8160 + 16.0773i 0.498429 + 0.678181i
\(563\) 29.1981 + 10.6272i 1.23055 + 0.447885i 0.873787 0.486309i \(-0.161657\pi\)
0.356766 + 0.934194i \(0.383879\pi\)
\(564\) −23.0264 + 36.1236i −0.969588 + 1.52108i
\(565\) 9.82458 55.7179i 0.413323 2.34407i
\(566\) 25.1879 12.4563i 1.05873 0.523579i
\(567\) −18.5207 14.9661i −0.777796 0.628517i
\(568\) −5.39046 1.05345i −0.226179 0.0442020i
\(569\) −31.7611 5.60033i −1.33149 0.234778i −0.537788 0.843080i \(-0.680740\pi\)
−0.793706 + 0.608302i \(0.791851\pi\)
\(570\) 27.0807 + 44.7665i 1.13429 + 1.87506i
\(571\) 14.7064 40.4055i 0.615443 1.69092i −0.102429 0.994740i \(-0.532661\pi\)
0.717872 0.696175i \(-0.245116\pi\)
\(572\) −29.9168 15.4888i −1.25089 0.647621i
\(573\) −3.66236 + 40.6917i −0.152997 + 1.69992i
\(574\) −1.19377 + 33.2683i −0.0498270 + 1.38859i
\(575\) 16.4811 28.5460i 0.687308 1.19045i
\(576\) −7.25621 22.8768i −0.302342 0.953200i
\(577\) −46.6619 −1.94256 −0.971280 0.237939i \(-0.923528\pi\)
−0.971280 + 0.237939i \(0.923528\pi\)
\(578\) −22.3780 + 6.54974i −0.930803 + 0.272433i
\(579\) −30.4151 8.23106i −1.26401 0.342071i
\(580\) −0.340088 7.40927i −0.0141214 0.307653i
\(581\) 0.750250 5.09972i 0.0311256 0.211572i
\(582\) −17.5980 + 15.3902i −0.729459 + 0.637944i
\(583\) −10.8541 + 12.9354i −0.449530 + 0.535729i
\(584\) −14.4215 2.81840i −0.596768 0.116626i
\(585\) −14.6880 + 25.1498i −0.607275 + 1.03982i
\(586\) 18.2628 9.03161i 0.754430 0.373093i
\(587\) 3.85725 21.8756i 0.159206 0.902902i −0.795633 0.605779i \(-0.792862\pi\)
0.954839 0.297123i \(-0.0960272\pi\)
\(588\) −4.52170 23.8234i −0.186472 0.982460i
\(589\) 10.0210 + 3.64733i 0.412907 + 0.150286i
\(590\) 11.4752 26.1586i 0.472427 1.07693i
\(591\) 8.93091 + 4.19170i 0.367369 + 0.172424i
\(592\) 12.4515 + 17.6145i 0.511753 + 0.723950i
\(593\) −10.6347 + 6.13996i −0.436716 + 0.252138i −0.702203 0.711976i \(-0.747800\pi\)
0.265488 + 0.964114i \(0.414467\pi\)
\(594\) 14.1710 + 37.1389i 0.581445 + 1.52383i
\(595\) −4.41376 + 3.92298i −0.180946 + 0.160826i
\(596\) −0.319510 1.42613i −0.0130877 0.0584164i
\(597\) 2.74498 + 32.3031i 0.112345 + 1.32208i
\(598\) −3.38208 30.5659i −0.138304 1.24993i
\(599\) 29.0570 24.3817i 1.18724 0.996209i 0.187332 0.982297i \(-0.440016\pi\)
0.999903 0.0139121i \(-0.00442851\pi\)
\(600\) 6.45169 22.2056i 0.263389 0.906542i
\(601\) 5.57129 31.5964i 0.227258 1.28884i −0.631064 0.775731i \(-0.717382\pi\)
0.858322 0.513112i \(-0.171507\pi\)
\(602\) −0.867350 + 2.14084i −0.0353506 + 0.0872542i
\(603\) 5.63524 2.01928i 0.229485 0.0822314i
\(604\) 12.0940 5.04120i 0.492098 0.205123i
\(605\) −56.0691 9.88649i −2.27953 0.401943i
\(606\) 11.1284 32.6355i 0.452061 1.32573i
\(607\) 9.99169 27.4519i 0.405550 1.11424i −0.553954 0.832547i \(-0.686882\pi\)
0.959505 0.281693i \(-0.0908959\pi\)
\(608\) −38.3367 5.68149i −1.55476 0.230415i
\(609\) 5.44076 + 0.333916i 0.220471 + 0.0135310i
\(610\) 2.80603 2.93778i 0.113613 0.118947i
\(611\) −19.2538 + 33.3486i −0.778927 + 1.34914i
\(612\) −2.89316 3.17484i −0.116949 0.128335i
\(613\) 14.0183 + 24.2804i 0.566193 + 0.980675i 0.996938 + 0.0782012i \(0.0249177\pi\)
−0.430745 + 0.902474i \(0.641749\pi\)
\(614\) −1.77275 + 1.85598i −0.0715423 + 0.0749015i
\(615\) −39.2869 27.6553i −1.58420 1.11517i
\(616\) −13.4639 + 38.1754i −0.542477 + 1.53813i
\(617\) −0.607922 + 0.107193i −0.0244740 + 0.00431543i −0.185872 0.982574i \(-0.559511\pi\)
0.161398 + 0.986889i \(0.448400\pi\)
\(618\) −2.04209 + 1.23533i −0.0821451 + 0.0496922i
\(619\) −0.280034 0.769388i −0.0112555 0.0309243i 0.933938 0.357436i \(-0.116349\pi\)
−0.945193 + 0.326512i \(0.894127\pi\)
\(620\) −3.73429 8.95869i −0.149973 0.359790i
\(621\) −21.0348 + 29.5673i −0.844096 + 1.18650i
\(622\) −10.0208 20.2631i −0.401797 0.812474i
\(623\) 33.2423 20.4755i 1.33182 0.820334i
\(624\) −7.41869 20.2581i −0.296985 0.810972i
\(625\) −20.1630 + 16.9188i −0.806521 + 0.676751i
\(626\) −1.73505 0.761128i −0.0693466 0.0304208i
\(627\) 63.9314 + 5.75400i 2.55317 + 0.229793i
\(628\) −6.63554 + 21.2104i −0.264787 + 0.846388i
\(629\) 3.34340 + 1.93031i 0.133310 + 0.0769666i
\(630\) 32.3694 + 13.3027i 1.28963 + 0.529991i
\(631\) −24.7439 + 14.2859i −0.985039 + 0.568713i −0.903788 0.427981i \(-0.859225\pi\)
−0.0812516 + 0.996694i \(0.525892\pi\)
\(632\) −16.7906 + 13.5687i −0.667894 + 0.539733i
\(633\) −3.07491 + 11.3623i −0.122217 + 0.451610i
\(634\) 17.3515 + 23.6091i 0.689116 + 0.937637i
\(635\) −46.8001 17.0339i −1.85721 0.675968i
\(636\) −10.7214 + 1.40867i −0.425131 + 0.0558574i
\(637\) −5.00032 21.2160i −0.198120 0.840609i
\(638\) −7.57181 5.04709i −0.299771 0.199816i
\(639\) 3.72232 + 4.48130i 0.147253 + 0.177277i
\(640\) 19.8254 + 29.1742i 0.783668 + 1.15321i
\(641\) 8.77587 10.4587i 0.346626 0.413093i −0.564361 0.825528i \(-0.690877\pi\)
0.910987 + 0.412435i \(0.135322\pi\)
\(642\) 30.6804 + 24.6932i 1.21086 + 0.974562i
\(643\) −9.79457 + 26.9104i −0.386260 + 1.06124i 0.582411 + 0.812894i \(0.302109\pi\)
−0.968671 + 0.248346i \(0.920113\pi\)
\(644\) −35.8137 + 9.10147i −1.41126 + 0.358648i
\(645\) −1.90529 2.73553i −0.0750206 0.107711i
\(646\) −6.65689 + 1.94838i −0.261912 + 0.0766580i
\(647\) −8.47527 + 14.6796i −0.333197 + 0.577115i −0.983137 0.182871i \(-0.941461\pi\)
0.649940 + 0.759986i \(0.274794\pi\)
\(648\) −9.38315 + 23.6634i −0.368605 + 0.929586i
\(649\) −17.5226 30.3501i −0.687824 1.19135i
\(650\) 4.91802 20.1960i 0.192901 0.792153i
\(651\) 6.83974 2.02446i 0.268071 0.0793450i
\(652\) 13.1081 25.3184i 0.513352 0.991544i
\(653\) 30.1973 5.32460i 1.18171 0.208368i 0.451934 0.892051i \(-0.350734\pi\)
0.729779 + 0.683683i \(0.239623\pi\)
\(654\) 1.38479 8.91546i 0.0541496 0.348622i
\(655\) −15.0234 + 17.9042i −0.587012 + 0.699574i
\(656\) 34.3341 9.36448i 1.34052 0.365621i
\(657\) 9.95862 + 11.9892i 0.388523 + 0.467743i
\(658\) 42.8848 + 17.3746i 1.67183 + 0.677331i
\(659\) 1.52432 0.554805i 0.0593789 0.0216121i −0.312160 0.950030i \(-0.601052\pi\)
0.371539 + 0.928417i \(0.378830\pi\)
\(660\) −35.5529 46.3584i −1.38390 1.80450i
\(661\) −5.40402 30.6477i −0.210192 1.19206i −0.889057 0.457796i \(-0.848639\pi\)
0.678865 0.734263i \(-0.262472\pi\)
\(662\) 4.07242 + 5.54109i 0.158279 + 0.215361i
\(663\) −2.72340 2.73702i −0.105768 0.106297i
\(664\) −5.44354 + 0.856531i −0.211250 + 0.0332399i
\(665\) 42.2395 37.5428i 1.63798 1.45585i
\(666\) 1.58477 22.8246i 0.0614084 0.884434i
\(667\) 8.30665i 0.321635i
\(668\) −8.53271 + 1.91167i −0.330141 + 0.0739649i
\(669\) −4.52071 0.406876i −0.174781 0.0157307i
\(670\) −7.08912 + 5.21015i −0.273877 + 0.201286i
\(671\) −0.865498 4.90848i −0.0334122 0.189490i
\(672\) −22.8763 + 12.1933i −0.882471 + 0.470367i
\(673\) 2.09886 + 1.76115i 0.0809050 + 0.0678873i 0.682343 0.731032i \(-0.260961\pi\)
−0.601438 + 0.798919i \(0.705405\pi\)
\(674\) 10.4144 15.6241i 0.401150 0.601818i
\(675\) −20.1957 + 13.9171i −0.777334 + 0.535671i
\(676\) 2.54212 + 6.09863i 0.0977739 + 0.234563i
\(677\) −6.54137 1.15342i −0.251405 0.0443295i 0.0465252 0.998917i \(-0.485185\pi\)
−0.297930 + 0.954588i \(0.596296\pi\)
\(678\) −0.908504 44.4419i −0.0348909 1.70678i
\(679\) 19.7979 + 15.6742i 0.759773 + 0.601522i
\(680\) 5.40791 + 3.25685i 0.207384 + 0.124894i
\(681\) 1.06078 11.7861i 0.0406491 0.451643i
\(682\) −11.5696 2.81737i −0.443024 0.107883i
\(683\) 6.18005 + 10.7042i 0.236473 + 0.409583i 0.959700 0.281028i \(-0.0906752\pi\)
−0.723227 + 0.690611i \(0.757342\pi\)
\(684\) 27.6875 + 30.3831i 1.05866 + 1.16173i
\(685\) 22.1763 + 38.4105i 0.847313 + 1.46759i
\(686\) −24.4179 + 9.47440i −0.932281 + 0.361734i
\(687\) 3.37581 + 0.913576i 0.128795 + 0.0348551i
\(688\) 2.46090 + 0.204221i 0.0938208 + 0.00778584i
\(689\) −9.57269 + 1.68792i −0.364690 + 0.0643047i
\(690\) 17.2119 50.4761i 0.655246 1.92159i
\(691\) 20.4228 24.3389i 0.776920 0.925897i −0.221870 0.975076i \(-0.571216\pi\)
0.998790 + 0.0491790i \(0.0156605\pi\)
\(692\) −3.75662 + 29.0357i −0.142805 + 1.10377i
\(693\) 36.6692 22.3348i 1.39295 0.848427i
\(694\) 43.3464 + 2.79243i 1.64541 + 0.105999i
\(695\) −8.83850 + 3.21695i −0.335264 + 0.122026i
\(696\) −1.38994 5.65917i −0.0526854 0.214510i
\(697\) 4.87918 4.09412i 0.184812 0.155076i
\(698\) 20.1134 + 8.82331i 0.761305 + 0.333967i
\(699\) −14.5084 6.80947i −0.548756 0.257558i
\(700\) −24.8514 2.49848i −0.939294 0.0944336i
\(701\) 21.9376i 0.828570i 0.910147 + 0.414285i \(0.135968\pi\)
−0.910147 + 0.414285i \(0.864032\pi\)
\(702\) −7.49309 + 21.6208i −0.282808 + 0.816024i
\(703\) −31.9962 18.4730i −1.20676 0.696723i
\(704\) 43.2456 + 1.59772i 1.62988 + 0.0602162i
\(705\) −54.7975 + 38.1663i −2.06379 + 1.43743i
\(706\) 5.24328 + 7.13420i 0.197334 + 0.268499i
\(707\) −36.8468 5.42076i −1.38577 0.203869i
\(708\) 4.86314 21.9093i 0.182768 0.823402i
\(709\) 22.8294 8.30922i 0.857376 0.312059i 0.124332 0.992241i \(-0.460321\pi\)
0.733044 + 0.680181i \(0.238099\pi\)
\(710\) −7.12429 4.74879i −0.267370 0.178219i
\(711\) 22.8970 + 0.114230i 0.858705 + 0.00428397i
\(712\) −31.4723 27.4144i −1.17947 1.02740i
\(713\) −3.71773 10.2144i −0.139230 0.382531i
\(714\) −2.80491 + 3.69560i −0.104971 + 0.138304i
\(715\) −33.7564 40.2294i −1.26242 1.50449i
\(716\) 23.1080 14.7942i 0.863588 0.552884i
\(717\) −6.27043 23.6373i −0.234174 0.882749i
\(718\) −22.6493 + 6.62915i −0.845266 + 0.247398i
\(719\) −1.98800 + 3.44331i −0.0741398 + 0.128414i −0.900712 0.434417i \(-0.856954\pi\)
0.826572 + 0.562831i \(0.190288\pi\)
\(720\) 3.28006 37.2685i 0.122241 1.38892i
\(721\) 1.71257 + 1.92682i 0.0637796 + 0.0717586i
\(722\) 37.9181 11.0981i 1.41116 0.413028i
\(723\) 13.4027 6.20912i 0.498451 0.230920i
\(724\) −1.57645 34.3451i −0.0585885 1.27643i
\(725\) 1.92032 5.27603i 0.0713189 0.195947i
\(726\) −44.7219 + 0.914229i −1.65979 + 0.0339302i
\(727\) 4.39404 5.23662i 0.162966 0.194215i −0.678382 0.734710i \(-0.737318\pi\)
0.841348 + 0.540494i \(0.181763\pi\)
\(728\) −20.0629 + 11.8524i −0.743579 + 0.439278i
\(729\) 23.5821 13.1485i 0.873411 0.486983i
\(730\) −19.0602 12.7048i −0.705449 0.470227i
\(731\) 0.415294 0.151155i 0.0153602 0.00559066i
\(732\) 1.71566 2.69151i 0.0634127 0.0994810i
\(733\) 1.85748 1.55861i 0.0686074 0.0575685i −0.607839 0.794060i \(-0.707963\pi\)
0.676447 + 0.736492i \(0.263519\pi\)
\(734\) 16.3411 1.80813i 0.603162 0.0667391i
\(735\) 7.78238 36.9905i 0.287057 1.36441i
\(736\) 20.6817 + 33.6569i 0.762337 + 1.24061i
\(737\) 10.7937i 0.397591i
\(738\) −34.4912 15.3361i −1.26964 0.564531i
\(739\) 11.4322i 0.420542i −0.977643 0.210271i \(-0.932565\pi\)
0.977643 0.210271i \(-0.0674346\pi\)
\(740\) 7.35138 + 32.8127i 0.270242 + 1.20622i
\(741\) 26.0628 + 26.1932i 0.957443 + 0.962231i
\(742\) 3.59863 + 11.1118i 0.132110 + 0.407926i
\(743\) −4.83557 + 4.05753i −0.177400 + 0.148856i −0.727164 0.686464i \(-0.759162\pi\)
0.549764 + 0.835320i \(0.314718\pi\)
\(744\) −4.24197 6.33678i −0.155518 0.232318i
\(745\) 0.395612 2.24363i 0.0144941 0.0822002i
\(746\) 15.7426 + 31.8330i 0.576376 + 1.16549i
\(747\) 5.04709 + 2.94761i 0.184663 + 0.107847i
\(748\) 7.14886 2.97989i 0.261388 0.108956i
\(749\) 20.2123 37.4301i 0.738541 1.36767i
\(750\) −1.34001 + 1.66492i −0.0489302 + 0.0607941i
\(751\) −26.4072 + 4.65629i −0.963611 + 0.169911i −0.633253 0.773945i \(-0.718281\pi\)
−0.330358 + 0.943856i \(0.607169\pi\)
\(752\) 4.09090 49.2961i 0.149180 1.79764i
\(753\) 21.9662 46.8016i 0.800494 1.70554i
\(754\) −1.47143 5.02734i −0.0535864 0.183085i
\(755\) 20.4251 0.743346
\(756\) 26.9746 + 5.32634i 0.981057 + 0.193717i
\(757\) 39.9285 1.45122 0.725612 0.688104i \(-0.241557\pi\)
0.725612 + 0.688104i \(0.241557\pi\)
\(758\) 10.7116 + 36.5975i 0.389062 + 1.32928i
\(759\) −37.3946 53.6895i −1.35734 1.94881i
\(760\) −51.7536 31.1679i −1.87730 1.13058i
\(761\) 37.4336 6.60055i 1.35697 0.239270i 0.552621 0.833433i \(-0.313628\pi\)
0.804345 + 0.594163i \(0.202517\pi\)
\(762\) −38.6655 6.00571i −1.40070 0.217564i
\(763\) −9.74132 + 0.277359i −0.352659 + 0.0100411i
\(764\) −18.1511 43.5450i −0.656683 1.57540i
\(765\) −2.25869 6.30337i −0.0816631 0.227899i
\(766\) −10.8439 21.9275i −0.391807 0.792273i
\(767\) 3.50313 19.8672i 0.126491 0.717365i
\(768\) 19.7218 + 19.4692i 0.711650 + 0.702535i
\(769\) 22.2817 18.6966i 0.803499 0.674216i −0.145548 0.989351i \(-0.546494\pi\)
0.949047 + 0.315135i \(0.102050\pi\)
\(770\) −42.2690 + 46.8539i −1.52327 + 1.68850i
\(771\) −7.57741 + 27.9997i −0.272894 + 1.00838i
\(772\) 35.5035 7.95423i 1.27780 0.286279i
\(773\) 9.83593i 0.353774i −0.984231 0.176887i \(-0.943397\pi\)
0.984231 0.176887i \(-0.0566027\pi\)
\(774\) −1.88495 1.81848i −0.0677532 0.0653641i
\(775\) 7.34719i 0.263919i
\(776\) 9.69961 25.1922i 0.348196 0.904347i
\(777\) −24.5544 + 2.79241i −0.880885 + 0.100177i
\(778\) −11.8691 + 1.31330i −0.425529 + 0.0470843i
\(779\) −46.6937 + 39.1806i −1.67297 + 1.40379i
\(780\) 1.47565 33.5980i 0.0528369 1.20300i
\(781\) −9.87082 + 3.59269i −0.353206 + 0.128556i
\(782\) 5.88290 + 3.92133i 0.210372 + 0.140226i
\(783\) −2.65399 + 5.58205i −0.0948457 + 0.199486i
\(784\) 17.4373 + 21.9076i 0.622759 + 0.782413i
\(785\) −22.2689 + 26.5390i −0.794811 + 0.947219i
\(786\) −8.85447 + 16.0870i −0.315828 + 0.573804i
\(787\) −2.90940 + 7.99350i −0.103709 + 0.284937i −0.980684 0.195598i \(-0.937335\pi\)
0.876975 + 0.480535i \(0.159558\pi\)
\(788\) −11.3799 + 0.522343i −0.405393 + 0.0186077i
\(789\) 11.7821 + 8.29376i 0.419452 + 0.295266i
\(790\) −32.2973 + 9.45298i −1.14909 + 0.336322i
\(791\) −47.0269 + 9.67967i −1.67208 + 0.344169i
\(792\) −34.4600 30.3205i −1.22448 1.07739i
\(793\) 1.43457 2.48475i 0.0509432 0.0882361i
\(794\) −4.41052 + 1.29090i −0.156524 + 0.0458123i
\(795\) −16.2715 4.40346i −0.577089 0.156175i
\(796\) −20.1842 31.5272i −0.715411 1.11745i
\(797\) 0.581477 + 0.692977i 0.0205970 + 0.0245465i 0.776245 0.630432i \(-0.217122\pi\)
−0.755648 + 0.654978i \(0.772678\pi\)
\(798\) 26.8429 35.3668i 0.950229 1.25197i
\(799\) −3.02790 8.31908i −0.107119 0.294308i
\(800\) 5.35538 + 26.1586i 0.189341 + 0.924847i
\(801\) 7.46976 + 43.6350i 0.263931 + 1.54177i
\(802\) −6.86446 4.57560i −0.242392 0.161570i
\(803\) −26.4082 + 9.61181i −0.931926 + 0.339194i
\(804\) −4.67110 + 5.09496i −0.164737 + 0.179685i
\(805\) −56.9896 8.38408i −2.00862 0.295500i
\(806\) −4.05940 5.52337i −0.142986 0.194552i
\(807\) 26.7643 + 12.5618i 0.942148 + 0.442195i
\(808\) 6.18866 + 39.3310i 0.217716 + 1.38366i
\(809\) 11.7351 + 6.77524i 0.412583 + 0.238205i 0.691899 0.721995i \(-0.256774\pi\)
−0.279316 + 0.960199i \(0.590108\pi\)
\(810\) −27.6935 + 28.4206i −0.973052 + 0.998599i
\(811\) 54.5756i 1.91641i 0.286083 + 0.958205i \(0.407647\pi\)
−0.286083 + 0.958205i \(0.592353\pi\)
\(812\) −5.73847 + 2.58607i −0.201381 + 0.0907533i
\(813\) 10.3337 7.19737i 0.362418 0.252423i
\(814\) 37.7795 + 16.5730i 1.32417 + 0.580883i
\(815\) 34.0458 28.5678i 1.19257 1.00069i
\(816\) 4.66406 + 1.68715i 0.163275 + 0.0590622i
\(817\) −3.97436 + 1.44655i −0.139045 + 0.0506083i
\(818\) 21.1602 + 1.36317i 0.739851 + 0.0476621i
\(819\) 24.4344 + 3.71932i 0.853806 + 0.129963i
\(820\) 55.0184 + 7.11825i 1.92133 + 0.248580i
\(821\) 29.1785 34.7735i 1.01834 1.21360i 0.0416048 0.999134i \(-0.486753\pi\)
0.976730 0.214471i \(-0.0688026\pi\)
\(822\) 22.9398 + 26.2306i 0.800116 + 0.914896i
\(823\) −0.221913 + 0.0391293i −0.00773540 + 0.00136396i −0.177515 0.984118i \(-0.556806\pi\)
0.169779 + 0.985482i \(0.445695\pi\)
\(824\) 1.42177 2.36082i 0.0495299 0.0822431i
\(825\) −11.3396 42.7461i −0.394794 1.48823i
\(826\) −24.2251 0.869272i −0.842900 0.0302458i
\(827\) −14.0407 24.3192i −0.488243 0.845662i 0.511665 0.859185i \(-0.329029\pi\)
−0.999909 + 0.0135228i \(0.995695\pi\)
\(828\) 5.58339 41.5260i 0.194036 1.44313i
\(829\) 10.7436 + 18.6084i 0.373140 + 0.646297i 0.990047 0.140739i \(-0.0449479\pi\)
−0.616907 + 0.787036i \(0.711615\pi\)
\(830\) −8.34620 2.03242i −0.289701 0.0705463i
\(831\) 33.7834 + 23.7812i 1.17193 + 0.824961i
\(832\) 18.4789 + 16.7062i 0.640640 + 0.579185i
\(833\) 4.47539 + 2.25463i 0.155063 + 0.0781182i
\(834\) −6.32289 + 3.82492i −0.218944 + 0.132446i
\(835\) −13.4239 2.36700i −0.464554 0.0819135i
\(836\) −68.4144 + 28.5175i −2.36616 + 0.986297i
\(837\) −0.765201 + 8.05185i −0.0264492 + 0.278313i
\(838\) −20.2032 + 30.3095i −0.697908 + 1.04702i
\(839\) 16.3635 + 13.7306i 0.564930 + 0.474032i 0.879959 0.475050i \(-0.157570\pi\)
−0.315029 + 0.949082i \(0.602014\pi\)
\(840\) −40.2289 + 3.82405i −1.38803 + 0.131942i
\(841\) 4.79010 + 27.1660i 0.165176 + 0.936759i
\(842\) 4.08089 2.99925i 0.140637 0.103361i
\(843\) 10.2721 + 22.1728i 0.353789 + 0.763672i
\(844\) −2.97149 13.2632i −0.102283 0.456538i
\(845\) 10.2998i 0.354322i
\(846\) −36.4275 + 37.7589i −1.25240 + 1.29818i
\(847\) 9.74066 + 47.3232i 0.334693 + 1.62604i
\(848\) 10.1962 7.20756i 0.350137 0.247509i
\(849\) 33.2644 8.82430i 1.14163 0.302849i
\(850\) 2.83005 + 3.85066i 0.0970697 + 0.132077i
\(851\) 6.53944 + 37.0870i 0.224169 + 1.27133i
\(852\) −6.21411 2.57586i −0.212892 0.0882474i
\(853\) 29.0878 10.5871i 0.995946 0.362495i 0.207926 0.978144i \(-0.433329\pi\)
0.788020 + 0.615650i \(0.211106\pi\)
\(854\) −3.19528 1.29455i −0.109340 0.0442986i
\(855\) 21.6156 + 60.3231i 0.739238 + 2.06301i
\(856\) −44.6316 8.72233i −1.52548 0.298123i
\(857\) 6.69969 7.98438i 0.228857 0.272741i −0.639380 0.768891i \(-0.720809\pi\)
0.868237 + 0.496150i \(0.165253\pi\)
\(858\) −32.1424 25.8698i −1.09732 0.883182i
\(859\) 11.0565 1.94957i 0.377244 0.0665184i 0.0181889 0.999835i \(-0.494210\pi\)
0.359056 + 0.933316i \(0.383099\pi\)
\(860\) 3.41840 + 1.76981i 0.116566 + 0.0603499i
\(861\) −9.52622 + 39.6429i −0.324653 + 1.35103i
\(862\) 7.10628 29.1822i 0.242041 0.993949i
\(863\) −17.9872 31.1547i −0.612291 1.06052i −0.990853 0.134944i \(-0.956915\pi\)
0.378562 0.925576i \(-0.376419\pi\)
\(864\) −3.14462 29.2252i −0.106982 0.994261i
\(865\) −22.8199 + 39.5251i −0.775898 + 1.34390i
\(866\) 21.2825 6.22909i 0.723209 0.211673i
\(867\) −28.4546 + 2.41795i −0.966370 + 0.0821180i
\(868\) −5.89895 + 5.74830i −0.200224 + 0.195110i
\(869\) −14.1209 + 38.7969i −0.479019 + 1.31609i
\(870\) 1.39425 8.97639i 0.0472696 0.304328i
\(871\) −3.99388 + 4.75972i −0.135327 + 0.161277i
\(872\) 3.38185 + 9.85396i 0.114524 + 0.333697i
\(873\) −24.8676 + 14.1924i −0.841640 + 0.480339i
\(874\) −56.2992 37.5270i −1.90435 1.26937i
\(875\) 2.03120 + 1.09685i 0.0686670 + 0.0370802i
\(876\) −16.6251 6.89141i −0.561711 0.232839i
\(877\) −21.9969 8.00622i −0.742783 0.270351i −0.0572174 0.998362i \(-0.518223\pi\)
−0.685566 + 0.728011i \(0.740445\pi\)
\(878\) −21.9511 29.8675i −0.740814 1.00798i
\(879\) 24.1188 6.39816i 0.813506 0.215805i
\(880\) 61.2661 + 28.2361i 2.06528 + 0.951840i
\(881\) −24.5640 + 14.1820i −0.827583 + 0.477805i −0.853024 0.521871i \(-0.825234\pi\)
0.0254414 + 0.999676i \(0.491901\pi\)
\(882\) 0.368009 29.6962i 0.0123915 0.999923i
\(883\) 28.8666 + 16.6661i 0.971437 + 0.560860i 0.899674 0.436562i \(-0.143804\pi\)
0.0717632 + 0.997422i \(0.477137\pi\)
\(884\) 4.25506 + 1.33117i 0.143113 + 0.0447720i
\(885\) 20.1378 28.6077i 0.676926 0.961636i
\(886\) −25.6154 11.2369i −0.860568 0.377512i
\(887\) 9.47973 7.95444i 0.318298 0.267084i −0.469613 0.882872i \(-0.655607\pi\)
0.787912 + 0.615788i \(0.211162\pi\)
\(888\) 10.6609 + 24.1725i 0.357757 + 0.811175i
\(889\) 1.20288 + 42.2472i 0.0403432 + 1.41693i
\(890\) −28.8420 58.3214i −0.966786 1.95494i
\(891\) 7.97518 + 48.0268i 0.267179 + 1.60896i
\(892\) 4.83771 2.01652i 0.161978 0.0675182i
\(893\) 28.9769 + 79.6134i 0.969675 + 2.66416i
\(894\) −0.0365833 1.78957i −0.00122353 0.0598521i
\(895\) 42.1223 7.42729i 1.40799 0.248267i
\(896\) 16.8124 24.7658i 0.561663 0.827366i
\(897\) 3.37620 37.5123i 0.112728 1.25250i
\(898\) 4.64340 4.86142i 0.154952 0.162228i
\(899\) −0.925768 1.60348i −0.0308761 0.0534790i
\(900\) 13.1463 25.0848i 0.438209 0.836161i
\(901\) 1.11736 1.93533i 0.0372248 0.0644752i
\(902\) 47.0113 49.2186i 1.56531 1.63880i
\(903\) −1.56192 + 2.35874i −0.0519776 + 0.0784938i
\(904\) 24.8388 + 44.9174i 0.826126 + 1.49393i
\(905\) 18.3308 50.3633i 0.609335 1.67413i
\(906\) 15.7433 3.10901i 0.523036 0.103290i
\(907\) −32.3116 5.69740i −1.07289 0.189179i −0.390819 0.920467i \(-0.627808\pi\)
−0.682068 + 0.731288i \(0.738919\pi\)
\(908\) 5.25734 + 12.6125i 0.174471 + 0.418562i
\(909\) 21.2972 36.4665i 0.706384 1.20952i
\(910\) −35.9763 + 5.02088i −1.19260 + 0.166441i
\(911\) −4.55525 + 25.8341i −0.150922 + 0.855922i 0.811497 + 0.584356i \(0.198653\pi\)
−0.962420 + 0.271566i \(0.912458\pi\)
\(912\) −44.6350 16.1460i −1.47801 0.534648i
\(913\) −8.07326 + 6.77427i −0.267186 + 0.224196i
\(914\) −0.0450568 0.407205i −0.00149035 0.0134692i
\(915\) 4.08287 2.84371i 0.134976 0.0940100i
\(916\) −3.94058 + 0.882850i −0.130200 + 0.0291702i
\(917\) 18.8235 + 6.25046i 0.621606 + 0.206409i
\(918\) −2.70043 4.51472i −0.0891274 0.149008i
\(919\) −18.9440 + 10.9373i −0.624904 + 0.360789i −0.778776 0.627302i \(-0.784159\pi\)
0.153872 + 0.988091i \(0.450826\pi\)
\(920\) 9.57178 + 60.8318i 0.315572 + 2.00556i
\(921\) −2.57941 + 1.79655i −0.0849946 + 0.0591984i
\(922\) −18.0973 + 41.2542i −0.596002 + 1.35863i
\(923\) −5.68212 2.06812i −0.187029 0.0680730i
\(924\) −25.4484 + 42.5481i −0.837189 + 1.39973i
\(925\) −4.42014 + 25.0679i −0.145333 + 0.824227i
\(926\) 18.0336 8.91825i 0.592621 0.293072i
\(927\) −2.75173 + 0.986030i −0.0903787 + 0.0323855i
\(928\) 4.46484 + 5.03415i 0.146566 + 0.165254i
\(929\) −16.8762 + 20.1123i −0.553691 + 0.659864i −0.968199 0.250182i \(-0.919509\pi\)
0.414507 + 0.910046i \(0.363954\pi\)
\(930\) −2.30301 11.6619i −0.0755188 0.382410i
\(931\) −42.8294 21.5767i −1.40368 0.707148i
\(932\) 18.4868 0.848551i 0.605555 0.0277952i
\(933\) −7.09892 26.7604i −0.232408 0.876095i
\(934\) 38.2902 11.2070i 1.25289 0.366704i
\(935\) 12.0734 0.394844
\(936\) −3.97671 26.1213i −0.129983 0.853803i
\(937\) −6.30311 + 10.9173i −0.205914 + 0.356653i −0.950423 0.310959i \(-0.899350\pi\)
0.744510 + 0.667611i \(0.232683\pi\)
\(938\) 6.32770 + 3.96245i 0.206607 + 0.129379i
\(939\) −1.89749 1.33570i −0.0619223 0.0435891i
\(940\) 35.4524 68.4766i 1.15633 2.23346i
\(941\) 10.3743 28.5031i 0.338192 0.929174i −0.647716 0.761882i \(-0.724275\pi\)
0.985907 0.167292i \(-0.0535023\pi\)
\(942\) −13.1248 + 23.8455i −0.427630 + 0.776928i
\(943\) 61.1868 + 10.7889i 1.99252 + 0.351334i
\(944\) 6.81897 + 25.0012i 0.221938 + 0.813719i
\(945\) 35.6181 + 23.8423i 1.15866 + 0.775591i
\(946\) 4.23329 2.09351i 0.137636 0.0680659i
\(947\) 8.00565 45.4023i 0.260149 1.47538i −0.522354 0.852729i \(-0.674946\pi\)
0.782503 0.622647i \(-0.213943\pi\)
\(948\) −23.4553 + 12.2023i −0.761793 + 0.396313i
\(949\) −15.2018 5.53302i −0.493473 0.179609i
\(950\) −27.0835 36.8507i −0.878703 1.19560i
\(951\) 15.0843 + 32.5601i 0.489141 + 1.05583i
\(952\) 0.877468 5.28489i 0.0284389 0.171284i
\(953\) 31.9739 + 18.4601i 1.03574 + 0.597983i 0.918623 0.395136i \(-0.129302\pi\)
0.117114 + 0.993118i \(0.462636\pi\)
\(954\) −13.2120 0.917344i −0.427755 0.0297001i
\(955\) 73.5416i 2.37975i
\(956\) 19.1238 + 20.7765i 0.618508 + 0.671961i
\(957\) −7.86093 7.90024i −0.254108 0.255379i
\(958\) 38.3080 + 16.8049i 1.23768 + 0.542941i
\(959\) 23.3631 29.5096i 0.754435 0.952915i
\(960\) 16.6999 + 39.8419i 0.538989 + 1.28589i
\(961\) 21.8913 + 18.3690i 0.706172 + 0.592549i
\(962\) 10.5273 + 21.2873i 0.339415 + 0.686332i
\(963\) 30.8198 + 37.1040i 0.993154 + 1.19566i
\(964\) −10.3529 + 13.5548i −0.333444 + 0.436569i
\(965\) 55.8552 + 9.84879i 1.79804 + 0.317044i
\(966\) −45.2027 + 2.21238i −1.45437 + 0.0711820i
\(967\) −17.5659 + 48.2620i −0.564882 + 1.55200i 0.247508 + 0.968886i \(0.420389\pi\)
−0.812390 + 0.583115i \(0.801834\pi\)
\(968\) 45.2005 24.9953i 1.45280 0.803380i
\(969\) −8.46452 + 0.719279i −0.271920 + 0.0231066i
\(970\) 29.0658 30.4305i 0.933247 0.977066i
\(971\) 8.12920 + 14.0802i 0.260878 + 0.451854i 0.966476 0.256759i \(-0.0826545\pi\)
−0.705597 + 0.708613i \(0.749321\pi\)
\(972\) −17.0196 + 26.1215i −0.545905 + 0.837847i
\(973\) 5.30260 + 5.96598i 0.169994 + 0.191261i
\(974\) 34.2923 + 8.35067i 1.09880 + 0.267573i
\(975\) 10.8164 23.0457i 0.346404 0.738053i
\(976\) −0.304806 + 3.67297i −0.00975661 + 0.117569i
\(977\) −7.30101 8.70101i −0.233580 0.278370i 0.636504 0.771274i \(-0.280380\pi\)
−0.870084 + 0.492904i \(0.835936\pi\)
\(978\) 21.8934 27.2018i 0.700074 0.869818i
\(979\) −78.6113 13.8613i −2.51243 0.443009i
\(980\) 11.9503 + 41.9802i 0.381740 + 1.34101i
\(981\) 3.83111 10.3647i 0.122318 0.330920i
\(982\) 7.46946 + 0.481192i 0.238360 + 0.0153555i
\(983\) −9.48731 + 53.8052i −0.302598 + 1.71612i 0.332001 + 0.943279i \(0.392276\pi\)
−0.634600 + 0.772841i \(0.718835\pi\)
\(984\) 43.4907 2.88801i 1.38643 0.0920664i
\(985\) −16.6874 6.07371i −0.531704 0.193525i
\(986\) 1.10283 + 0.483788i 0.0351214 + 0.0154070i
\(987\) 47.2497 + 31.2881i 1.50397 + 0.995912i
\(988\) −40.7208 12.7392i −1.29550 0.405289i
\(989\) 3.73348 + 2.15553i 0.118718 + 0.0685417i
\(990\) −31.3979 64.2949i −0.997890 2.04343i
\(991\) −40.4408 + 23.3485i −1.28464 + 0.741689i −0.977694 0.210037i \(-0.932642\pi\)
−0.306950 + 0.951726i \(0.599308\pi\)
\(992\) 7.74333 + 4.19202i 0.245851 + 0.133097i
\(993\) 3.54030 + 7.64191i 0.112348 + 0.242509i
\(994\) −1.51748 + 7.10557i −0.0481314 + 0.225375i
\(995\) −10.1333 57.4690i −0.321249 1.82189i
\(996\) −6.74247 0.296135i −0.213643 0.00938341i
\(997\) −24.1009 + 8.77202i −0.763284 + 0.277813i −0.694185 0.719797i \(-0.744235\pi\)
−0.0690996 + 0.997610i \(0.522013\pi\)
\(998\) −1.81907 + 28.2371i −0.0575816 + 0.893829i
\(999\) 7.45486 27.0117i 0.235861 0.854613i
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.11.12 840
4.3 odd 2 inner 756.2.bs.a.11.28 yes 840
7.2 even 3 756.2.ci.a.443.105 yes 840
27.5 odd 18 756.2.ci.a.599.65 yes 840
28.23 odd 6 756.2.ci.a.443.65 yes 840
108.59 even 18 756.2.ci.a.599.105 yes 840
189.86 odd 18 inner 756.2.bs.a.275.28 yes 840
756.275 even 18 inner 756.2.bs.a.275.12 yes 840
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
756.2.bs.a.11.12 840 1.1 even 1 trivial
756.2.bs.a.11.28 yes 840 4.3 odd 2 inner
756.2.bs.a.275.12 yes 840 756.275 even 18 inner
756.2.bs.a.275.28 yes 840 189.86 odd 18 inner
756.2.ci.a.443.65 yes 840 28.23 odd 6
756.2.ci.a.443.105 yes 840 7.2 even 3
756.2.ci.a.599.65 yes 840 27.5 odd 18
756.2.ci.a.599.105 yes 840 108.59 even 18