Properties

Label 187.2.h.a.100.12
Level $187$
Weight $2$
Character 187.100
Analytic conductor $1.493$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [187,2,Mod(100,187)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(187, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("187.100");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 187 = 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 187.h (of order \(8\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.49320251780\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 100.12
Character \(\chi\) \(=\) 187.100
Dual form 187.2.h.a.144.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.12086 + 1.12086i) q^{2} +(-0.951848 - 2.29796i) q^{3} +0.512654i q^{4} +(0.910373 - 0.377089i) q^{5} +(1.50881 - 3.64258i) q^{6} +(-2.04824 - 0.848409i) q^{7} +(1.66711 - 1.66711i) q^{8} +(-2.25330 + 2.25330i) q^{9} +O(q^{10})\) \(q+(1.12086 + 1.12086i) q^{2} +(-0.951848 - 2.29796i) q^{3} +0.512654i q^{4} +(0.910373 - 0.377089i) q^{5} +(1.50881 - 3.64258i) q^{6} +(-2.04824 - 0.848409i) q^{7} +(1.66711 - 1.66711i) q^{8} +(-2.25330 + 2.25330i) q^{9} +(1.44307 + 0.597737i) q^{10} +(0.382683 - 0.923880i) q^{11} +(1.17806 - 0.487969i) q^{12} +0.304786i q^{13} +(-1.34484 - 3.24674i) q^{14} +(-1.73307 - 1.73307i) q^{15} +4.76249 q^{16} +(2.10233 + 3.54686i) q^{17} -5.05127 q^{18} +(5.08065 + 5.08065i) q^{19} +(0.193316 + 0.466707i) q^{20} +5.51434i q^{21} +(1.46447 - 0.606605i) q^{22} +(1.10308 - 2.66307i) q^{23} +(-5.41778 - 2.24412i) q^{24} +(-2.84895 + 2.84895i) q^{25} +(-0.341623 + 0.341623i) q^{26} +(0.428912 + 0.177661i) q^{27} +(0.434941 - 1.05004i) q^{28} +(-7.62083 + 3.15665i) q^{29} -3.88507i q^{30} +(-0.0844584 - 0.203900i) q^{31} +(2.00388 + 2.00388i) q^{32} -2.48730 q^{33} +(-1.61912 + 6.33195i) q^{34} -2.18459 q^{35} +(-1.15516 - 1.15516i) q^{36} +(0.566445 + 1.36752i) q^{37} +11.3894i q^{38} +(0.700388 - 0.290110i) q^{39} +(0.889042 - 2.14634i) q^{40} +(6.50940 + 2.69628i) q^{41} +(-6.18080 + 6.18080i) q^{42} +(4.67834 - 4.67834i) q^{43} +(0.473631 + 0.196184i) q^{44} +(-1.20165 + 2.90104i) q^{45} +(4.22133 - 1.74853i) q^{46} -3.08276i q^{47} +(-4.53317 - 10.9440i) q^{48} +(-1.47425 - 1.47425i) q^{49} -6.38655 q^{50} +(6.14946 - 8.20714i) q^{51} -0.156250 q^{52} +(3.08641 + 3.08641i) q^{53} +(0.281617 + 0.679884i) q^{54} -0.985381i q^{55} +(-4.82902 + 2.00025i) q^{56} +(6.83914 - 16.5111i) q^{57} +(-12.0800 - 5.00372i) q^{58} +(-8.22327 + 8.22327i) q^{59} +(0.888468 - 0.888468i) q^{60} +(6.37840 + 2.64202i) q^{61} +(0.133878 - 0.323210i) q^{62} +(6.52703 - 2.70358i) q^{63} -5.03286i q^{64} +(0.114932 + 0.277469i) q^{65} +(-2.78791 - 2.78791i) q^{66} -0.0723373 q^{67} +(-1.81831 + 1.07777i) q^{68} -7.16960 q^{69} +(-2.44862 - 2.44862i) q^{70} +(-1.32006 - 3.18690i) q^{71} +7.51298i q^{72} +(-3.02287 + 1.25211i) q^{73} +(-0.897893 + 2.16771i) q^{74} +(9.25855 + 3.83502i) q^{75} +(-2.60462 + 2.60462i) q^{76} +(-1.56766 + 1.56766i) q^{77} +(1.11021 + 0.459864i) q^{78} +(5.35739 - 12.9339i) q^{79} +(4.33565 - 1.79588i) q^{80} +8.40522i q^{81} +(4.27397 + 10.3183i) q^{82} +(-3.57107 - 3.57107i) q^{83} -2.82695 q^{84} +(3.25138 + 2.43620i) q^{85} +10.4875 q^{86} +(14.5077 + 14.5077i) q^{87} +(-0.902231 - 2.17818i) q^{88} +11.3144i q^{89} +(-4.59854 + 1.90478i) q^{90} +(0.258584 - 0.624276i) q^{91} +(1.36523 + 0.565499i) q^{92} +(-0.388164 + 0.388164i) q^{93} +(3.45534 - 3.45534i) q^{94} +(6.54114 + 2.70943i) q^{95} +(2.69745 - 6.51222i) q^{96} +(-0.163202 + 0.0676007i) q^{97} -3.30486i q^{98} +(1.21948 + 2.94408i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q - 16 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 56 q - 16 q^{6} - 16 q^{10} - 16 q^{14} + 24 q^{15} - 32 q^{16} + 8 q^{17} - 24 q^{19} + 16 q^{20} - 24 q^{24} - 8 q^{25} - 48 q^{27} - 40 q^{32} + 16 q^{33} + 64 q^{34} + 32 q^{35} + 64 q^{36} + 8 q^{37} - 32 q^{39} + 96 q^{40} - 24 q^{41} - 8 q^{42} - 32 q^{43} + 16 q^{44} - 32 q^{45} - 16 q^{46} - 24 q^{48} - 112 q^{50} - 48 q^{51} + 8 q^{53} - 72 q^{54} + 64 q^{56} + 40 q^{57} + 16 q^{58} + 16 q^{59} - 8 q^{60} - 64 q^{61} + 56 q^{62} + 16 q^{63} + 56 q^{65} + 24 q^{67} - 88 q^{68} - 64 q^{69} - 96 q^{70} - 16 q^{71} + 8 q^{73} - 48 q^{74} + 40 q^{75} + 88 q^{76} + 136 q^{78} - 32 q^{80} + 104 q^{82} - 56 q^{83} + 80 q^{84} - 8 q^{85} - 32 q^{86} + 56 q^{87} - 32 q^{91} + 40 q^{92} + 8 q^{93} + 16 q^{94} + 48 q^{95} + 64 q^{96} - 16 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/187\mathbb{Z}\right)^\times\).

\(n\) \(35\) \(122\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{8}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.12086 + 1.12086i 0.792568 + 0.792568i 0.981911 0.189343i \(-0.0606359\pi\)
−0.189343 + 0.981911i \(0.560636\pi\)
\(3\) −0.951848 2.29796i −0.549549 1.32673i −0.917815 0.397009i \(-0.870048\pi\)
0.368265 0.929721i \(-0.379952\pi\)
\(4\) 0.512654i 0.256327i
\(5\) 0.910373 0.377089i 0.407131 0.168639i −0.169713 0.985494i \(-0.554284\pi\)
0.576844 + 0.816854i \(0.304284\pi\)
\(6\) 1.50881 3.64258i 0.615968 1.48708i
\(7\) −2.04824 0.848409i −0.774162 0.320669i −0.0396053 0.999215i \(-0.512610\pi\)
−0.734557 + 0.678547i \(0.762610\pi\)
\(8\) 1.66711 1.66711i 0.589411 0.589411i
\(9\) −2.25330 + 2.25330i −0.751100 + 0.751100i
\(10\) 1.44307 + 0.597737i 0.456337 + 0.189021i
\(11\) 0.382683 0.923880i 0.115383 0.278560i
\(12\) 1.17806 0.487969i 0.340077 0.140864i
\(13\) 0.304786i 0.0845326i 0.999106 + 0.0422663i \(0.0134578\pi\)
−0.999106 + 0.0422663i \(0.986542\pi\)
\(14\) −1.34484 3.24674i −0.359425 0.867728i
\(15\) −1.73307 1.73307i −0.447478 0.447478i
\(16\) 4.76249 1.19062
\(17\) 2.10233 + 3.54686i 0.509889 + 0.860240i
\(18\) −5.05127 −1.19060
\(19\) 5.08065 + 5.08065i 1.16558 + 1.16558i 0.983234 + 0.182346i \(0.0583692\pi\)
0.182346 + 0.983234i \(0.441631\pi\)
\(20\) 0.193316 + 0.466707i 0.0432268 + 0.104359i
\(21\) 5.51434i 1.20333i
\(22\) 1.46447 0.606605i 0.312227 0.129329i
\(23\) 1.10308 2.66307i 0.230008 0.555288i −0.766170 0.642638i \(-0.777840\pi\)
0.996178 + 0.0873499i \(0.0278398\pi\)
\(24\) −5.41778 2.24412i −1.10590 0.458079i
\(25\) −2.84895 + 2.84895i −0.569790 + 0.569790i
\(26\) −0.341623 + 0.341623i −0.0669978 + 0.0669978i
\(27\) 0.428912 + 0.177661i 0.0825442 + 0.0341909i
\(28\) 0.434941 1.05004i 0.0821961 0.198439i
\(29\) −7.62083 + 3.15665i −1.41515 + 0.586175i −0.953638 0.300957i \(-0.902694\pi\)
−0.461515 + 0.887132i \(0.652694\pi\)
\(30\) 3.88507i 0.709313i
\(31\) −0.0844584 0.203900i −0.0151692 0.0366216i 0.916113 0.400919i \(-0.131309\pi\)
−0.931283 + 0.364297i \(0.881309\pi\)
\(32\) 2.00388 + 2.00388i 0.354239 + 0.354239i
\(33\) −2.48730 −0.432983
\(34\) −1.61912 + 6.33195i −0.277677 + 1.08592i
\(35\) −2.18459 −0.369263
\(36\) −1.15516 1.15516i −0.192527 0.192527i
\(37\) 0.566445 + 1.36752i 0.0931231 + 0.224819i 0.963577 0.267431i \(-0.0861747\pi\)
−0.870454 + 0.492250i \(0.836175\pi\)
\(38\) 11.3894i 1.84760i
\(39\) 0.700388 0.290110i 0.112152 0.0464548i
\(40\) 0.889042 2.14634i 0.140570 0.339366i
\(41\) 6.50940 + 2.69628i 1.01660 + 0.421089i 0.827857 0.560939i \(-0.189560\pi\)
0.188740 + 0.982027i \(0.439560\pi\)
\(42\) −6.18080 + 6.18080i −0.953719 + 0.953719i
\(43\) 4.67834 4.67834i 0.713441 0.713441i −0.253813 0.967253i \(-0.581685\pi\)
0.967253 + 0.253813i \(0.0816847\pi\)
\(44\) 0.473631 + 0.196184i 0.0714025 + 0.0295759i
\(45\) −1.20165 + 2.90104i −0.179131 + 0.432462i
\(46\) 4.22133 1.74853i 0.622400 0.257807i
\(47\) 3.08276i 0.449666i −0.974397 0.224833i \(-0.927816\pi\)
0.974397 0.224833i \(-0.0721837\pi\)
\(48\) −4.53317 10.9440i −0.654307 1.57964i
\(49\) −1.47425 1.47425i −0.210608 0.210608i
\(50\) −6.38655 −0.903194
\(51\) 6.14946 8.20714i 0.861097 1.14923i
\(52\) −0.156250 −0.0216680
\(53\) 3.08641 + 3.08641i 0.423952 + 0.423952i 0.886562 0.462610i \(-0.153087\pi\)
−0.462610 + 0.886562i \(0.653087\pi\)
\(54\) 0.281617 + 0.679884i 0.0383232 + 0.0925204i
\(55\) 0.985381i 0.132869i
\(56\) −4.82902 + 2.00025i −0.645306 + 0.267294i
\(57\) 6.83914 16.5111i 0.905866 2.18695i
\(58\) −12.0800 5.00372i −1.58619 0.657021i
\(59\) −8.22327 + 8.22327i −1.07058 + 1.07058i −0.0732660 + 0.997312i \(0.523342\pi\)
−0.997312 + 0.0732660i \(0.976658\pi\)
\(60\) 0.888468 0.888468i 0.114701 0.114701i
\(61\) 6.37840 + 2.64202i 0.816671 + 0.338276i 0.751612 0.659605i \(-0.229277\pi\)
0.0650586 + 0.997881i \(0.479277\pi\)
\(62\) 0.133878 0.323210i 0.0170025 0.0410477i
\(63\) 6.52703 2.70358i 0.822328 0.340619i
\(64\) 5.03286i 0.629107i
\(65\) 0.114932 + 0.277469i 0.0142555 + 0.0344159i
\(66\) −2.78791 2.78791i −0.343168 0.343168i
\(67\) −0.0723373 −0.00883741 −0.00441871 0.999990i \(-0.501407\pi\)
−0.00441871 + 0.999990i \(0.501407\pi\)
\(68\) −1.81831 + 1.07777i −0.220503 + 0.130698i
\(69\) −7.16960 −0.863118
\(70\) −2.44862 2.44862i −0.292666 0.292666i
\(71\) −1.32006 3.18690i −0.156662 0.378215i 0.825987 0.563689i \(-0.190618\pi\)
−0.982649 + 0.185473i \(0.940618\pi\)
\(72\) 7.51298i 0.885414i
\(73\) −3.02287 + 1.25211i −0.353800 + 0.146549i −0.552503 0.833511i \(-0.686327\pi\)
0.198703 + 0.980060i \(0.436327\pi\)
\(74\) −0.897893 + 2.16771i −0.104378 + 0.251991i
\(75\) 9.25855 + 3.83502i 1.06909 + 0.442830i
\(76\) −2.60462 + 2.60462i −0.298770 + 0.298770i
\(77\) −1.56766 + 1.56766i −0.178651 + 0.178651i
\(78\) 1.11021 + 0.459864i 0.125707 + 0.0520693i
\(79\) 5.35739 12.9339i 0.602753 1.45518i −0.267982 0.963424i \(-0.586357\pi\)
0.870735 0.491752i \(-0.163643\pi\)
\(80\) 4.33565 1.79588i 0.484740 0.200786i
\(81\) 8.40522i 0.933913i
\(82\) 4.27397 + 10.3183i 0.471981 + 1.13946i
\(83\) −3.57107 3.57107i −0.391976 0.391976i 0.483415 0.875391i \(-0.339396\pi\)
−0.875391 + 0.483415i \(0.839396\pi\)
\(84\) −2.82695 −0.308446
\(85\) 3.25138 + 2.43620i 0.352662 + 0.264244i
\(86\) 10.4875 1.13090
\(87\) 14.5077 + 14.5077i 1.55539 + 1.55539i
\(88\) −0.902231 2.17818i −0.0961782 0.232195i
\(89\) 11.3144i 1.19933i 0.800252 + 0.599664i \(0.204699\pi\)
−0.800252 + 0.599664i \(0.795301\pi\)
\(90\) −4.59854 + 1.90478i −0.484729 + 0.200781i
\(91\) 0.258584 0.624276i 0.0271069 0.0654419i
\(92\) 1.36523 + 0.565499i 0.142336 + 0.0589573i
\(93\) −0.388164 + 0.388164i −0.0402508 + 0.0402508i
\(94\) 3.45534 3.45534i 0.356391 0.356391i
\(95\) 6.54114 + 2.70943i 0.671107 + 0.277982i
\(96\) 2.69745 6.51222i 0.275307 0.664651i
\(97\) −0.163202 + 0.0676007i −0.0165707 + 0.00686381i −0.390953 0.920410i \(-0.627855\pi\)
0.374383 + 0.927274i \(0.377855\pi\)
\(98\) 3.30486i 0.333842i
\(99\) 1.21948 + 2.94408i 0.122562 + 0.295891i
\(100\) −1.46053 1.46053i −0.146053 0.146053i
\(101\) −6.94906 −0.691457 −0.345729 0.938335i \(-0.612368\pi\)
−0.345729 + 0.938335i \(0.612368\pi\)
\(102\) 16.0917 2.30636i 1.59332 0.228364i
\(103\) −10.8498 −1.06907 −0.534533 0.845148i \(-0.679512\pi\)
−0.534533 + 0.845148i \(0.679512\pi\)
\(104\) 0.508111 + 0.508111i 0.0498244 + 0.0498244i
\(105\) 2.07940 + 5.02011i 0.202928 + 0.489912i
\(106\) 6.91888i 0.672021i
\(107\) −11.0331 + 4.57004i −1.06661 + 0.441802i −0.845792 0.533514i \(-0.820871\pi\)
−0.220814 + 0.975316i \(0.570871\pi\)
\(108\) −0.0910788 + 0.219884i −0.00876406 + 0.0211583i
\(109\) 7.29615 + 3.02216i 0.698844 + 0.289471i 0.703679 0.710518i \(-0.251539\pi\)
−0.00483526 + 0.999988i \(0.501539\pi\)
\(110\) 1.10447 1.10447i 0.105307 0.105307i
\(111\) 2.60334 2.60334i 0.247098 0.247098i
\(112\) −9.75474 4.04054i −0.921736 0.381796i
\(113\) 5.70321 13.7688i 0.536512 1.29526i −0.390630 0.920548i \(-0.627743\pi\)
0.927143 0.374708i \(-0.122257\pi\)
\(114\) 26.1724 10.8410i 2.45127 1.01535i
\(115\) 2.84035i 0.264864i
\(116\) −1.61827 3.90685i −0.150253 0.362742i
\(117\) −0.686776 0.686776i −0.0634924 0.0634924i
\(118\) −18.4343 −1.69701
\(119\) −1.29688 9.04846i −0.118885 0.829471i
\(120\) −5.77844 −0.527497
\(121\) −0.707107 0.707107i −0.0642824 0.0642824i
\(122\) 4.18796 + 10.1106i 0.379160 + 0.915374i
\(123\) 17.5248i 1.58016i
\(124\) 0.104530 0.0432979i 0.00938711 0.00388827i
\(125\) −3.40475 + 8.21978i −0.304530 + 0.735200i
\(126\) 10.3462 + 4.28554i 0.921715 + 0.381787i
\(127\) 11.5480 11.5480i 1.02472 1.02472i 0.0250315 0.999687i \(-0.492031\pi\)
0.999687 0.0250315i \(-0.00796861\pi\)
\(128\) 9.64888 9.64888i 0.852849 0.852849i
\(129\) −15.2037 6.29759i −1.33861 0.554472i
\(130\) −0.182182 + 0.439827i −0.0159784 + 0.0385754i
\(131\) −15.9803 + 6.61928i −1.39621 + 0.578329i −0.948765 0.315983i \(-0.897666\pi\)
−0.447445 + 0.894312i \(0.647666\pi\)
\(132\) 1.27512i 0.110985i
\(133\) −6.09592 14.7169i −0.528584 1.27611i
\(134\) −0.0810800 0.0810800i −0.00700425 0.00700425i
\(135\) 0.457464 0.0393722
\(136\) 9.41780 + 2.40820i 0.807569 + 0.206501i
\(137\) −10.6544 −0.910270 −0.455135 0.890422i \(-0.650409\pi\)
−0.455135 + 0.890422i \(0.650409\pi\)
\(138\) −8.03612 8.03612i −0.684080 0.684080i
\(139\) 4.63793 + 11.1969i 0.393384 + 0.949712i 0.989197 + 0.146590i \(0.0468297\pi\)
−0.595814 + 0.803123i \(0.703170\pi\)
\(140\) 1.11994i 0.0946522i
\(141\) −7.08406 + 2.93431i −0.596585 + 0.247114i
\(142\) 2.09247 5.05167i 0.175596 0.423926i
\(143\) 0.281586 + 0.116637i 0.0235474 + 0.00975365i
\(144\) −10.7313 + 10.7313i −0.894278 + 0.894278i
\(145\) −5.74746 + 5.74746i −0.477301 + 0.477301i
\(146\) −4.79166 1.98477i −0.396560 0.164261i
\(147\) −1.98452 + 4.79104i −0.163680 + 0.395159i
\(148\) −0.701065 + 0.290391i −0.0576272 + 0.0238700i
\(149\) 13.6059i 1.11464i −0.830298 0.557320i \(-0.811830\pi\)
0.830298 0.557320i \(-0.188170\pi\)
\(150\) 6.07902 + 14.6761i 0.496350 + 1.19829i
\(151\) −4.25390 4.25390i −0.346177 0.346177i 0.512506 0.858684i \(-0.328717\pi\)
−0.858684 + 0.512506i \(0.828717\pi\)
\(152\) 16.9400 1.37401
\(153\) −12.7293 3.25498i −1.02910 0.263149i
\(154\) −3.51425 −0.283186
\(155\) −0.153777 0.153777i −0.0123517 0.0123517i
\(156\) 0.148726 + 0.359057i 0.0119076 + 0.0287476i
\(157\) 22.6873i 1.81064i −0.424727 0.905321i \(-0.639630\pi\)
0.424727 0.905321i \(-0.360370\pi\)
\(158\) 20.5020 8.49219i 1.63105 0.675602i
\(159\) 4.15467 10.0303i 0.329487 0.795451i
\(160\) 2.57992 + 1.06864i 0.203960 + 0.0844831i
\(161\) −4.51875 + 4.51875i −0.356127 + 0.356127i
\(162\) −9.42107 + 9.42107i −0.740189 + 0.740189i
\(163\) −11.1691 4.62639i −0.874830 0.362366i −0.100341 0.994953i \(-0.531993\pi\)
−0.774490 + 0.632587i \(0.781993\pi\)
\(164\) −1.38226 + 3.33707i −0.107936 + 0.260582i
\(165\) −2.26437 + 0.937933i −0.176281 + 0.0730180i
\(166\) 8.00534i 0.621335i
\(167\) 8.95471 + 21.6186i 0.692936 + 1.67290i 0.738780 + 0.673947i \(0.235402\pi\)
−0.0458434 + 0.998949i \(0.514598\pi\)
\(168\) 9.19299 + 9.19299i 0.709255 + 0.709255i
\(169\) 12.9071 0.992854
\(170\) 0.913702 + 6.37499i 0.0700777 + 0.488939i
\(171\) −22.8965 −1.75094
\(172\) 2.39837 + 2.39837i 0.182874 + 0.182874i
\(173\) 0.467353 + 1.12829i 0.0355322 + 0.0857822i 0.940649 0.339380i \(-0.110217\pi\)
−0.905117 + 0.425162i \(0.860217\pi\)
\(174\) 32.5223i 2.46551i
\(175\) 8.25241 3.41826i 0.623824 0.258396i
\(176\) 1.82253 4.39997i 0.137378 0.331660i
\(177\) 26.7241 + 11.0695i 2.00870 + 0.832032i
\(178\) −12.6819 + 12.6819i −0.950549 + 0.950549i
\(179\) −15.4138 + 15.4138i −1.15208 + 1.15208i −0.165947 + 0.986135i \(0.553068\pi\)
−0.986135 + 0.165947i \(0.946932\pi\)
\(180\) −1.48723 0.616031i −0.110852 0.0459163i
\(181\) −6.03596 + 14.5721i −0.448650 + 1.08314i 0.524179 + 0.851608i \(0.324372\pi\)
−0.972828 + 0.231528i \(0.925628\pi\)
\(182\) 0.989562 0.409890i 0.0733512 0.0303831i
\(183\) 17.1721i 1.26940i
\(184\) −2.60067 6.27857i −0.191724 0.462862i
\(185\) 1.03135 + 1.03135i 0.0758266 + 0.0758266i
\(186\) −0.870156 −0.0638029
\(187\) 4.08140 0.584970i 0.298461 0.0427773i
\(188\) 1.58039 0.115262
\(189\) −0.727786 0.727786i −0.0529386 0.0529386i
\(190\) 4.29481 + 10.3686i 0.311579 + 0.752217i
\(191\) 8.56666i 0.619861i 0.950759 + 0.309931i \(0.100306\pi\)
−0.950759 + 0.309931i \(0.899694\pi\)
\(192\) −11.5653 + 4.79051i −0.834655 + 0.345725i
\(193\) −4.58804 + 11.0765i −0.330254 + 0.797304i 0.668318 + 0.743876i \(0.267015\pi\)
−0.998572 + 0.0534279i \(0.982985\pi\)
\(194\) −0.258698 0.107156i −0.0185734 0.00769337i
\(195\) 0.528217 0.528217i 0.0378264 0.0378264i
\(196\) 0.755782 0.755782i 0.0539845 0.0539845i
\(197\) −17.6970 7.33033i −1.26086 0.522264i −0.350685 0.936494i \(-0.614051\pi\)
−0.910172 + 0.414230i \(0.864051\pi\)
\(198\) −1.93304 + 4.66676i −0.137375 + 0.331653i
\(199\) −10.5096 + 4.35321i −0.745005 + 0.308591i −0.722702 0.691160i \(-0.757100\pi\)
−0.0223031 + 0.999751i \(0.507100\pi\)
\(200\) 9.49901i 0.671681i
\(201\) 0.0688541 + 0.166229i 0.00485659 + 0.0117249i
\(202\) −7.78892 7.78892i −0.548027 0.548027i
\(203\) 18.2874 1.28353
\(204\) 4.20743 + 3.15255i 0.294579 + 0.220723i
\(205\) 6.94272 0.484901
\(206\) −12.1611 12.1611i −0.847307 0.847307i
\(207\) 3.51513 + 8.48627i 0.244318 + 0.589836i
\(208\) 1.45154i 0.100646i
\(209\) 6.63819 2.74963i 0.459173 0.190196i
\(210\) −3.29613 + 7.95755i −0.227454 + 0.549123i
\(211\) −22.4480 9.29828i −1.54539 0.640120i −0.562912 0.826517i \(-0.690319\pi\)
−0.982475 + 0.186397i \(0.940319\pi\)
\(212\) −1.58226 + 1.58226i −0.108670 + 0.108670i
\(213\) −6.06688 + 6.06688i −0.415696 + 0.415696i
\(214\) −17.4889 7.24413i −1.19552 0.495199i
\(215\) 2.49489 6.02319i 0.170150 0.410778i
\(216\) 1.01122 0.418862i 0.0688049 0.0284999i
\(217\) 0.489293i 0.0332154i
\(218\) 4.79054 + 11.5654i 0.324456 + 0.783307i
\(219\) 5.75462 + 5.75462i 0.388861 + 0.388861i
\(220\) 0.505160 0.0340579
\(221\) −1.08104 + 0.640760i −0.0727183 + 0.0431022i
\(222\) 5.83596 0.391684
\(223\) 10.1047 + 10.1047i 0.676659 + 0.676659i 0.959243 0.282584i \(-0.0911916\pi\)
−0.282584 + 0.959243i \(0.591192\pi\)
\(224\) −2.40432 5.80453i −0.160645 0.387832i
\(225\) 12.8391i 0.855939i
\(226\) 21.8253 9.04035i 1.45180 0.601355i
\(227\) −0.972198 + 2.34709i −0.0645271 + 0.155782i −0.952854 0.303430i \(-0.901868\pi\)
0.888327 + 0.459212i \(0.151868\pi\)
\(228\) 8.46451 + 3.50612i 0.560576 + 0.232198i
\(229\) 3.66555 3.66555i 0.242226 0.242226i −0.575544 0.817771i \(-0.695210\pi\)
0.817771 + 0.575544i \(0.195210\pi\)
\(230\) 3.18363 3.18363i 0.209922 0.209922i
\(231\) 5.09459 + 2.11025i 0.335199 + 0.138844i
\(232\) −7.44226 + 17.9672i −0.488608 + 1.17960i
\(233\) 1.98856 0.823689i 0.130275 0.0539617i −0.316594 0.948561i \(-0.602539\pi\)
0.446869 + 0.894600i \(0.352539\pi\)
\(234\) 1.53956i 0.100644i
\(235\) −1.16247 2.80646i −0.0758314 0.183073i
\(236\) −4.21570 4.21570i −0.274418 0.274418i
\(237\) −34.8210 −2.26187
\(238\) 8.68844 11.5957i 0.563188 0.751636i
\(239\) 25.1415 1.62627 0.813136 0.582074i \(-0.197759\pi\)
0.813136 + 0.582074i \(0.197759\pi\)
\(240\) −8.25375 8.25375i −0.532777 0.532777i
\(241\) −4.30712 10.3983i −0.277446 0.669813i 0.722318 0.691561i \(-0.243077\pi\)
−0.999763 + 0.0217480i \(0.993077\pi\)
\(242\) 1.58514i 0.101896i
\(243\) 20.6016 8.53347i 1.32159 0.547422i
\(244\) −1.35444 + 3.26992i −0.0867094 + 0.209335i
\(245\) −1.89805 0.786196i −0.121262 0.0502282i
\(246\) 19.6429 19.6429i 1.25238 1.25238i
\(247\) −1.54851 + 1.54851i −0.0985295 + 0.0985295i
\(248\) −0.480725 0.199123i −0.0305261 0.0126443i
\(249\) −4.80708 + 11.6053i −0.304636 + 0.735456i
\(250\) −13.0295 + 5.39698i −0.824056 + 0.341335i
\(251\) 18.5842i 1.17302i −0.809941 0.586511i \(-0.800501\pi\)
0.809941 0.586511i \(-0.199499\pi\)
\(252\) 1.38600 + 3.34611i 0.0873100 + 0.210785i
\(253\) −2.03823 2.03823i −0.128142 0.128142i
\(254\) 25.8874 1.62432
\(255\) 2.50349 9.79046i 0.156774 0.613102i
\(256\) 11.5644 0.722774
\(257\) −4.97755 4.97755i −0.310491 0.310491i 0.534609 0.845100i \(-0.320459\pi\)
−0.845100 + 0.534609i \(0.820459\pi\)
\(258\) −9.98254 24.1000i −0.621486 1.50040i
\(259\) 3.28159i 0.203908i
\(260\) −0.142246 + 0.0589202i −0.00882172 + 0.00365408i
\(261\) 10.0591 24.2849i 0.622645 1.50320i
\(262\) −25.3310 10.4924i −1.56496 0.648226i
\(263\) −9.07526 + 9.07526i −0.559605 + 0.559605i −0.929195 0.369590i \(-0.879498\pi\)
0.369590 + 0.929195i \(0.379498\pi\)
\(264\) −4.14659 + 4.14659i −0.255205 + 0.255205i
\(265\) 3.97364 + 1.64594i 0.244099 + 0.101109i
\(266\) 9.66287 23.3282i 0.592468 1.43035i
\(267\) 26.0002 10.7696i 1.59118 0.659090i
\(268\) 0.0370840i 0.00226527i
\(269\) −2.92664 7.06553i −0.178440 0.430793i 0.809199 0.587534i \(-0.199901\pi\)
−0.987640 + 0.156741i \(0.949901\pi\)
\(270\) 0.512753 + 0.512753i 0.0312052 + 0.0312052i
\(271\) 14.2400 0.865016 0.432508 0.901630i \(-0.357629\pi\)
0.432508 + 0.901630i \(0.357629\pi\)
\(272\) 10.0123 + 16.8919i 0.607086 + 1.02422i
\(273\) −1.68070 −0.101720
\(274\) −11.9421 11.9421i −0.721451 0.721451i
\(275\) 1.54184 + 3.72233i 0.0929765 + 0.224465i
\(276\) 3.67553i 0.221241i
\(277\) 29.3900 12.1738i 1.76588 0.731450i 0.770281 0.637705i \(-0.220116\pi\)
0.995596 0.0937450i \(-0.0298838\pi\)
\(278\) −7.35174 + 17.7487i −0.440928 + 1.06449i
\(279\) 0.649759 + 0.269139i 0.0389001 + 0.0161129i
\(280\) −3.64194 + 3.64194i −0.217648 + 0.217648i
\(281\) −22.5205 + 22.5205i −1.34346 + 1.34346i −0.450869 + 0.892590i \(0.648886\pi\)
−0.892590 + 0.450869i \(0.851114\pi\)
\(282\) −11.2292 4.65128i −0.668689 0.276980i
\(283\) −3.81994 + 9.22216i −0.227072 + 0.548200i −0.995819 0.0913533i \(-0.970881\pi\)
0.768747 + 0.639554i \(0.220881\pi\)
\(284\) 1.63378 0.676733i 0.0969469 0.0401567i
\(285\) 17.6103i 1.04314i
\(286\) 0.184885 + 0.446352i 0.0109325 + 0.0263933i
\(287\) −11.0453 11.0453i −0.651982 0.651982i
\(288\) −9.03068 −0.532138
\(289\) −8.16046 + 14.9133i −0.480027 + 0.877254i
\(290\) −12.8842 −0.756586
\(291\) 0.310688 + 0.310688i 0.0182128 + 0.0182128i
\(292\) −0.641902 1.54969i −0.0375645 0.0906886i
\(293\) 4.02872i 0.235360i −0.993052 0.117680i \(-0.962454\pi\)
0.993052 0.117680i \(-0.0375458\pi\)
\(294\) −7.59445 + 3.14573i −0.442918 + 0.183462i
\(295\) −4.38534 + 10.5872i −0.255324 + 0.616408i
\(296\) 3.22413 + 1.33548i 0.187399 + 0.0776230i
\(297\) 0.328275 0.328275i 0.0190484 0.0190484i
\(298\) 15.2503 15.2503i 0.883428 0.883428i
\(299\) 0.811667 + 0.336204i 0.0469399 + 0.0194432i
\(300\) −1.96604 + 4.74644i −0.113509 + 0.274036i
\(301\) −13.5515 + 5.61323i −0.781097 + 0.323541i
\(302\) 9.53605i 0.548738i
\(303\) 6.61444 + 15.9687i 0.379990 + 0.917377i
\(304\) 24.1966 + 24.1966i 1.38777 + 1.38777i
\(305\) 6.80301 0.389539
\(306\) −10.6194 17.9162i −0.607071 1.02420i
\(307\) 28.5771 1.63098 0.815490 0.578771i \(-0.196468\pi\)
0.815490 + 0.578771i \(0.196468\pi\)
\(308\) −0.803666 0.803666i −0.0457931 0.0457931i
\(309\) 10.3274 + 24.9325i 0.587504 + 1.41836i
\(310\) 0.344726i 0.0195791i
\(311\) −2.09621 + 0.868278i −0.118865 + 0.0492355i −0.441323 0.897348i \(-0.645491\pi\)
0.322458 + 0.946584i \(0.395491\pi\)
\(312\) 0.683977 1.65127i 0.0387226 0.0934845i
\(313\) 24.9867 + 10.3498i 1.41233 + 0.585008i 0.952922 0.303215i \(-0.0980601\pi\)
0.459412 + 0.888223i \(0.348060\pi\)
\(314\) 25.4293 25.4293i 1.43506 1.43506i
\(315\) 4.92254 4.92254i 0.277354 0.277354i
\(316\) 6.63061 + 2.74649i 0.373001 + 0.154502i
\(317\) 12.6558 30.5537i 0.710818 1.71607i 0.0128714 0.999917i \(-0.495903\pi\)
0.697947 0.716150i \(-0.254097\pi\)
\(318\) 15.8993 6.58571i 0.891590 0.369309i
\(319\) 8.24873i 0.461840i
\(320\) −1.89784 4.58178i −0.106092 0.256129i
\(321\) 21.0036 + 21.0036i 1.17230 + 1.17230i
\(322\) −10.1298 −0.564510
\(323\) −7.33918 + 28.7015i −0.408363 + 1.59700i
\(324\) −4.30897 −0.239387
\(325\) −0.868321 0.868321i −0.0481658 0.0481658i
\(326\) −7.33345 17.7045i −0.406162 0.980562i
\(327\) 19.6429i 1.08626i
\(328\) 15.3469 6.35687i 0.847388 0.351000i
\(329\) −2.61544 + 6.31423i −0.144194 + 0.348115i
\(330\) −3.58933 1.48675i −0.197586 0.0818429i
\(331\) 0.663758 0.663758i 0.0364835 0.0364835i −0.688630 0.725113i \(-0.741787\pi\)
0.725113 + 0.688630i \(0.241787\pi\)
\(332\) 1.83073 1.83073i 0.100474 0.100474i
\(333\) −4.35781 1.80506i −0.238806 0.0989168i
\(334\) −14.1944 + 34.2684i −0.776684 + 1.87508i
\(335\) −0.0658540 + 0.0272776i −0.00359799 + 0.00149034i
\(336\) 26.2620i 1.43271i
\(337\) 0.248898 + 0.600893i 0.0135583 + 0.0327327i 0.930514 0.366257i \(-0.119361\pi\)
−0.916955 + 0.398990i \(0.869361\pi\)
\(338\) 14.4671 + 14.4671i 0.786904 + 0.786904i
\(339\) −37.0687 −2.01329
\(340\) −1.24893 + 1.66684i −0.0677328 + 0.0903969i
\(341\) −0.220700 −0.0119516
\(342\) −25.6637 25.6637i −1.38774 1.38774i
\(343\) 7.70772 + 18.6081i 0.416178 + 1.00474i
\(344\) 15.5986i 0.841020i
\(345\) −6.52701 + 2.70358i −0.351403 + 0.145556i
\(346\) −0.740817 + 1.78849i −0.0398266 + 0.0961499i
\(347\) −1.27141 0.526636i −0.0682529 0.0282713i 0.348296 0.937385i \(-0.386760\pi\)
−0.416549 + 0.909113i \(0.636760\pi\)
\(348\) −7.43745 + 7.43745i −0.398689 + 0.398689i
\(349\) 7.13077 7.13077i 0.381701 0.381701i −0.490014 0.871715i \(-0.663008\pi\)
0.871715 + 0.490014i \(0.163008\pi\)
\(350\) 13.0812 + 5.41841i 0.699219 + 0.289626i
\(351\) −0.0541487 + 0.130727i −0.00289024 + 0.00697767i
\(352\) 2.61819 1.08449i 0.139550 0.0578035i
\(353\) 29.7786i 1.58495i −0.609902 0.792477i \(-0.708791\pi\)
0.609902 0.792477i \(-0.291209\pi\)
\(354\) 17.5466 + 42.3613i 0.932592 + 2.25148i
\(355\) −2.40349 2.40349i −0.127564 0.127564i
\(356\) −5.80040 −0.307420
\(357\) −19.5586 + 11.5929i −1.03515 + 0.613563i
\(358\) −34.5534 −1.82621
\(359\) −3.99870 3.99870i −0.211044 0.211044i 0.593667 0.804711i \(-0.297680\pi\)
−0.804711 + 0.593667i \(0.797680\pi\)
\(360\) 2.83306 + 6.83962i 0.149316 + 0.360480i
\(361\) 32.6260i 1.71716i
\(362\) −23.0988 + 9.56782i −1.21404 + 0.502874i
\(363\) −0.951848 + 2.29796i −0.0499590 + 0.120612i
\(364\) 0.320038 + 0.132564i 0.0167745 + 0.00694824i
\(365\) −2.27978 + 2.27978i −0.119329 + 0.119329i
\(366\) 19.2476 19.2476i 1.00609 1.00609i
\(367\) −28.2228 11.6903i −1.47322 0.610228i −0.505629 0.862751i \(-0.668740\pi\)
−0.967591 + 0.252523i \(0.918740\pi\)
\(368\) 5.25341 12.6829i 0.273853 0.661139i
\(369\) −20.7432 + 8.59210i −1.07985 + 0.447287i
\(370\) 2.31201i 0.120196i
\(371\) −3.70318 8.94026i −0.192259 0.464155i
\(372\) −0.198994 0.198994i −0.0103174 0.0103174i
\(373\) 0.755973 0.0391428 0.0195714 0.999808i \(-0.493770\pi\)
0.0195714 + 0.999808i \(0.493770\pi\)
\(374\) 5.23035 + 3.91901i 0.270455 + 0.202647i
\(375\) 22.1296 1.14277
\(376\) −5.13928 5.13928i −0.265038 0.265038i
\(377\) −0.962104 2.32273i −0.0495509 0.119626i
\(378\) 1.63149i 0.0839149i
\(379\) 10.0781 4.17447i 0.517675 0.214428i −0.108520 0.994094i \(-0.534611\pi\)
0.626195 + 0.779666i \(0.284611\pi\)
\(380\) −1.38900 + 3.35335i −0.0712543 + 0.172023i
\(381\) −37.5288 15.5449i −1.92266 0.796391i
\(382\) −9.60202 + 9.60202i −0.491282 + 0.491282i
\(383\) 24.0793 24.0793i 1.23039 1.23039i 0.266582 0.963812i \(-0.414106\pi\)
0.963812 0.266582i \(-0.0858944\pi\)
\(384\) −31.3570 12.9885i −1.60018 0.662817i
\(385\) −0.836007 + 2.01830i −0.0426068 + 0.102862i
\(386\) −17.5578 + 7.27266i −0.893666 + 0.370169i
\(387\) 21.0834i 1.07173i
\(388\) −0.0346558 0.0836664i −0.00175938 0.00424752i
\(389\) −7.33123 7.33123i −0.371708 0.371708i 0.496391 0.868099i \(-0.334658\pi\)
−0.868099 + 0.496391i \(0.834658\pi\)
\(390\) 1.18412 0.0599600
\(391\) 11.7646 1.68617i 0.594960 0.0852732i
\(392\) −4.91547 −0.248269
\(393\) 30.4217 + 30.4217i 1.53457 + 1.53457i
\(394\) −11.6196 28.0521i −0.585385 1.41324i
\(395\) 13.7949i 0.694096i
\(396\) −1.50930 + 0.625171i −0.0758449 + 0.0314160i
\(397\) −1.21286 + 2.92811i −0.0608719 + 0.146958i −0.951389 0.307992i \(-0.900343\pi\)
0.890517 + 0.454950i \(0.150343\pi\)
\(398\) −16.6591 6.90043i −0.835046 0.345887i
\(399\) −28.0164 + 28.0164i −1.40258 + 1.40258i
\(400\) −13.5681 + 13.5681i −0.678405 + 0.678405i
\(401\) −11.5944 4.80255i −0.578995 0.239828i 0.0739129 0.997265i \(-0.476451\pi\)
−0.652908 + 0.757437i \(0.726451\pi\)
\(402\) −0.109143 + 0.263495i −0.00544356 + 0.0131419i
\(403\) 0.0621461 0.0257418i 0.00309572 0.00128229i
\(404\) 3.56246i 0.177239i
\(405\) 3.16951 + 7.65189i 0.157494 + 0.380225i
\(406\) 20.4977 + 20.4977i 1.01728 + 1.01728i
\(407\) 1.48019 0.0733705
\(408\) −3.43036 23.9340i −0.169828 1.18491i
\(409\) 40.3629 1.99582 0.997909 0.0646276i \(-0.0205859\pi\)
0.997909 + 0.0646276i \(0.0205859\pi\)
\(410\) 7.78182 + 7.78182i 0.384317 + 0.384317i
\(411\) 10.1414 + 24.4835i 0.500238 + 1.20768i
\(412\) 5.56221i 0.274030i
\(413\) 23.8199 9.86654i 1.17210 0.485501i
\(414\) −5.57195 + 13.4519i −0.273846 + 0.661124i
\(415\) −4.59762 1.90440i −0.225688 0.0934832i
\(416\) −0.610755 + 0.610755i −0.0299447 + 0.0299447i
\(417\) 21.3156 21.3156i 1.04383 1.04383i
\(418\) 10.5224 + 4.35853i 0.514669 + 0.213183i
\(419\) −12.0348 + 29.0546i −0.587940 + 1.41941i 0.297529 + 0.954713i \(0.403838\pi\)
−0.885469 + 0.464699i \(0.846162\pi\)
\(420\) −2.57358 + 1.06601i −0.125578 + 0.0520161i
\(421\) 33.3000i 1.62294i 0.584394 + 0.811470i \(0.301332\pi\)
−0.584394 + 0.811470i \(0.698668\pi\)
\(422\) −14.7390 35.5832i −0.717485 1.73216i
\(423\) 6.94638 + 6.94638i 0.337744 + 0.337744i
\(424\) 10.2908 0.499763
\(425\) −16.0943 4.11541i −0.780686 0.199627i
\(426\) −13.6003 −0.658934
\(427\) −10.8230 10.8230i −0.523761 0.523761i
\(428\) −2.34285 5.65614i −0.113246 0.273400i
\(429\) 0.758095i 0.0366012i
\(430\) 9.54757 3.95473i 0.460425 0.190714i
\(431\) 5.16813 12.4770i 0.248940 0.600994i −0.749175 0.662373i \(-0.769550\pi\)
0.998115 + 0.0613782i \(0.0195496\pi\)
\(432\) 2.04269 + 0.846110i 0.0982790 + 0.0407085i
\(433\) 26.6016 26.6016i 1.27839 1.27839i 0.336825 0.941567i \(-0.390647\pi\)
0.941567 0.336825i \(-0.109353\pi\)
\(434\) −0.548429 + 0.548429i −0.0263254 + 0.0263254i
\(435\) 18.6782 + 7.73675i 0.895550 + 0.370949i
\(436\) −1.54933 + 3.74040i −0.0741992 + 0.179133i
\(437\) 19.1345 7.92576i 0.915326 0.379141i
\(438\) 12.9003i 0.616398i
\(439\) −0.0710817 0.171606i −0.00339254 0.00819033i 0.922174 0.386775i \(-0.126411\pi\)
−0.925567 + 0.378585i \(0.876411\pi\)
\(440\) −1.64274 1.64274i −0.0783143 0.0783143i
\(441\) 6.64387 0.316375
\(442\) −1.92989 0.493487i −0.0917956 0.0234728i
\(443\) −20.3984 −0.969159 −0.484580 0.874747i \(-0.661027\pi\)
−0.484580 + 0.874747i \(0.661027\pi\)
\(444\) 1.33461 + 1.33461i 0.0633380 + 0.0633380i
\(445\) 4.26655 + 10.3004i 0.202254 + 0.488284i
\(446\) 22.6518i 1.07260i
\(447\) −31.2659 + 12.9508i −1.47883 + 0.612550i
\(448\) −4.26992 + 10.3085i −0.201735 + 0.487031i
\(449\) 24.9357 + 10.3287i 1.17679 + 0.487441i 0.883431 0.468562i \(-0.155228\pi\)
0.293356 + 0.956003i \(0.405228\pi\)
\(450\) 14.3908 14.3908i 0.678390 0.678390i
\(451\) 4.98208 4.98208i 0.234597 0.234597i
\(452\) 7.05861 + 2.92377i 0.332009 + 0.137523i
\(453\) −5.72624 + 13.8244i −0.269042 + 0.649525i
\(454\) −3.72046 + 1.54107i −0.174610 + 0.0723258i
\(455\) 0.665834i 0.0312148i
\(456\) −16.1243 38.9274i −0.755088 1.82294i
\(457\) 7.23033 + 7.23033i 0.338221 + 0.338221i 0.855697 0.517477i \(-0.173129\pi\)
−0.517477 + 0.855697i \(0.673129\pi\)
\(458\) 8.21713 0.383961
\(459\) 0.271573 + 1.89479i 0.0126759 + 0.0884414i
\(460\) 1.45612 0.0678918
\(461\) −14.1356 14.1356i −0.658360 0.658360i 0.296632 0.954992i \(-0.404137\pi\)
−0.954992 + 0.296632i \(0.904137\pi\)
\(462\) 3.34503 + 8.07561i 0.155625 + 0.375711i
\(463\) 27.8496i 1.29428i −0.762371 0.647140i \(-0.775965\pi\)
0.762371 0.647140i \(-0.224035\pi\)
\(464\) −36.2942 + 15.0335i −1.68491 + 0.697914i
\(465\) −0.207002 + 0.499747i −0.00959949 + 0.0231752i
\(466\) 3.15214 + 1.30566i 0.146020 + 0.0604835i
\(467\) −6.53346 + 6.53346i −0.302333 + 0.302333i −0.841926 0.539593i \(-0.818578\pi\)
0.539593 + 0.841926i \(0.318578\pi\)
\(468\) 0.352079 0.352079i 0.0162748 0.0162748i
\(469\) 0.148164 + 0.0613717i 0.00684159 + 0.00283388i
\(470\) 1.84268 4.44862i 0.0849964 0.205199i
\(471\) −52.1346 + 21.5948i −2.40223 + 0.995038i
\(472\) 27.4181i 1.26202i
\(473\) −2.53190 6.11255i −0.116417 0.281055i
\(474\) −39.0295 39.0295i −1.79268 1.79268i
\(475\) −28.9490 −1.32827
\(476\) 4.63873 0.664851i 0.212616 0.0304734i
\(477\) −13.9092 −0.636860
\(478\) 28.1801 + 28.1801i 1.28893 + 1.28893i
\(479\) 4.94552 + 11.9395i 0.225967 + 0.545532i 0.995679 0.0928587i \(-0.0296005\pi\)
−0.769713 + 0.638391i \(0.779601\pi\)
\(480\) 6.94573i 0.317028i
\(481\) −0.416802 + 0.172645i −0.0190045 + 0.00787193i
\(482\) 6.82736 16.4827i 0.310978 0.750767i
\(483\) 14.6851 + 6.08275i 0.668194 + 0.276775i
\(484\) 0.362501 0.362501i 0.0164773 0.0164773i
\(485\) −0.123084 + 0.123084i −0.00558894 + 0.00558894i
\(486\) 32.6563 + 13.5267i 1.48132 + 0.613584i
\(487\) −0.795130 + 1.91961i −0.0360308 + 0.0869860i −0.940871 0.338766i \(-0.889990\pi\)
0.904840 + 0.425752i \(0.139990\pi\)
\(488\) 15.0380 6.22895i 0.680738 0.281971i
\(489\) 30.0698i 1.35980i
\(490\) −1.24623 3.00866i −0.0562988 0.135917i
\(491\) −9.21640 9.21640i −0.415930 0.415930i 0.467868 0.883798i \(-0.345022\pi\)
−0.883798 + 0.467868i \(0.845022\pi\)
\(492\) 8.98417 0.405038
\(493\) −27.2177 20.3937i −1.22582 0.918487i
\(494\) −3.47133 −0.156183
\(495\) 2.22036 + 2.22036i 0.0997978 + 0.0997978i
\(496\) −0.402232 0.971075i −0.0180608 0.0436026i
\(497\) 7.64749i 0.343037i
\(498\) −18.3960 + 7.61987i −0.824344 + 0.341454i
\(499\) 4.94409 11.9361i 0.221328 0.534333i −0.773743 0.633500i \(-0.781618\pi\)
0.995071 + 0.0991670i \(0.0316178\pi\)
\(500\) −4.21391 1.74546i −0.188452 0.0780593i
\(501\) 41.1552 41.1552i 1.83868 1.83868i
\(502\) 20.8302 20.8302i 0.929699 0.929699i
\(503\) 13.6361 + 5.64827i 0.608006 + 0.251844i 0.665375 0.746509i \(-0.268271\pi\)
−0.0573700 + 0.998353i \(0.518271\pi\)
\(504\) 6.37409 15.3884i 0.283924 0.685454i
\(505\) −6.32624 + 2.62041i −0.281514 + 0.116607i
\(506\) 4.56913i 0.203123i
\(507\) −12.2856 29.6601i −0.545622 1.31725i
\(508\) 5.92013 + 5.92013i 0.262663 + 0.262663i
\(509\) 11.9929 0.531577 0.265789 0.964031i \(-0.414368\pi\)
0.265789 + 0.964031i \(0.414368\pi\)
\(510\) 13.7798 8.16767i 0.610179 0.361671i
\(511\) 7.25387 0.320892
\(512\) −6.33572 6.33572i −0.280002 0.280002i
\(513\) 1.27652 + 3.08178i 0.0563596 + 0.136064i
\(514\) 11.1583i 0.492170i
\(515\) −9.87739 + 4.09135i −0.435250 + 0.180286i
\(516\) 3.22849 7.79426i 0.142126 0.343123i
\(517\) −2.84810 1.17972i −0.125259 0.0518840i
\(518\) 3.67820 3.67820i 0.161611 0.161611i
\(519\) 2.14792 2.14792i 0.0942831 0.0942831i
\(520\) 0.654174 + 0.270968i 0.0286874 + 0.0118827i
\(521\) 5.57772 13.4658i 0.244364 0.589948i −0.753343 0.657628i \(-0.771560\pi\)
0.997707 + 0.0676804i \(0.0215598\pi\)
\(522\) 38.4949 15.9451i 1.68487 0.697898i
\(523\) 15.2307i 0.665993i 0.942928 + 0.332997i \(0.108060\pi\)
−0.942928 + 0.332997i \(0.891940\pi\)
\(524\) −3.39340 8.19240i −0.148241 0.357886i
\(525\) −15.7101 15.7101i −0.685644 0.685644i
\(526\) −20.3442 −0.887049
\(527\) 0.545648 0.728227i 0.0237688 0.0317221i
\(528\) −11.8457 −0.515520
\(529\) 10.3883 + 10.3883i 0.451665 + 0.451665i
\(530\) 2.60903 + 6.29876i 0.113329 + 0.273601i
\(531\) 37.0590i 1.60822i
\(532\) 7.54466 3.12510i 0.327103 0.135490i
\(533\) −0.821790 + 1.98398i −0.0355957 + 0.0859356i
\(534\) 41.2138 + 17.0713i 1.78350 + 0.738748i
\(535\) −8.32089 + 8.32089i −0.359743 + 0.359743i
\(536\) −0.120594 + 0.120594i −0.00520887 + 0.00520887i
\(537\) 50.0919 + 20.7488i 2.16163 + 0.895375i
\(538\) 4.63912 11.1998i 0.200007 0.482859i
\(539\) −1.92620 + 0.797860i −0.0829675 + 0.0343663i
\(540\) 0.234521i 0.0100922i
\(541\) 7.71994 + 18.6376i 0.331906 + 0.801293i 0.998441 + 0.0558186i \(0.0177768\pi\)
−0.666535 + 0.745474i \(0.732223\pi\)
\(542\) 15.9610 + 15.9610i 0.685584 + 0.685584i
\(543\) 39.2315 1.68358
\(544\) −2.89467 + 11.3203i −0.124108 + 0.485353i
\(545\) 7.78184 0.333338
\(546\) −1.88382 1.88382i −0.0806203 0.0806203i
\(547\) −3.95124 9.53913i −0.168943 0.407864i 0.816620 0.577176i \(-0.195845\pi\)
−0.985562 + 0.169312i \(0.945845\pi\)
\(548\) 5.46204i 0.233327i
\(549\) −20.3257 + 8.41919i −0.867481 + 0.359322i
\(550\) −2.44403 + 5.90040i −0.104214 + 0.251594i
\(551\) −54.7566 22.6809i −2.33271 0.966240i
\(552\) −11.9525 + 11.9525i −0.508731 + 0.508731i
\(553\) −21.9465 + 21.9465i −0.933258 + 0.933258i
\(554\) 46.5872 + 19.2971i 1.97930 + 0.819853i
\(555\) 1.38832 3.35170i 0.0589310 0.142272i
\(556\) −5.74016 + 2.37765i −0.243437 + 0.100835i
\(557\) 4.27787i 0.181259i −0.995885 0.0906297i \(-0.971112\pi\)
0.995885 0.0906297i \(-0.0288880\pi\)
\(558\) 0.426622 + 1.02996i 0.0180603 + 0.0436015i
\(559\) 1.42590 + 1.42590i 0.0603090 + 0.0603090i
\(560\) −10.4041 −0.439653
\(561\) −5.22911 8.82210i −0.220773 0.372469i
\(562\) −50.4846 −2.12956
\(563\) −3.93666 3.93666i −0.165910 0.165910i 0.619269 0.785179i \(-0.287429\pi\)
−0.785179 + 0.619269i \(0.787429\pi\)
\(564\) −1.50429 3.63167i −0.0633420 0.152921i
\(565\) 14.6853i 0.617816i
\(566\) −14.6184 + 6.05513i −0.614456 + 0.254516i
\(567\) 7.13106 17.2159i 0.299477 0.723000i
\(568\) −7.51357 3.11222i −0.315262 0.130586i
\(569\) 7.02098 7.02098i 0.294335 0.294335i −0.544455 0.838790i \(-0.683264\pi\)
0.838790 + 0.544455i \(0.183264\pi\)
\(570\) 19.7387 19.7387i 0.826761 0.826761i
\(571\) 10.6172 + 4.39779i 0.444317 + 0.184042i 0.593613 0.804750i \(-0.297701\pi\)
−0.149297 + 0.988792i \(0.547701\pi\)
\(572\) −0.0597943 + 0.144356i −0.00250013 + 0.00603584i
\(573\) 19.6859 8.15415i 0.822389 0.340644i
\(574\) 24.7604i 1.03348i
\(575\) 4.44433 + 10.7296i 0.185342 + 0.447454i
\(576\) 11.3405 + 11.3405i 0.472523 + 0.472523i
\(577\) −3.16478 −0.131751 −0.0658757 0.997828i \(-0.520984\pi\)
−0.0658757 + 0.997828i \(0.520984\pi\)
\(578\) −25.8625 + 7.56901i −1.07574 + 0.314829i
\(579\) 29.8205 1.23930
\(580\) −2.94646 2.94646i −0.122345 0.122345i
\(581\) 4.28469 + 10.3441i 0.177759 + 0.429148i
\(582\) 0.696475i 0.0288698i
\(583\) 4.03259 1.67036i 0.167013 0.0691790i
\(584\) −2.95204 + 7.12685i −0.122156 + 0.294911i
\(585\) −0.884198 0.366247i −0.0365571 0.0151424i
\(586\) 4.51563 4.51563i 0.186539 0.186539i
\(587\) −16.5085 + 16.5085i −0.681378 + 0.681378i −0.960311 0.278933i \(-0.910019\pi\)
0.278933 + 0.960311i \(0.410019\pi\)
\(588\) −2.45615 1.01737i −0.101290 0.0419557i
\(589\) 0.606844 1.46505i 0.0250046 0.0603663i
\(590\) −16.7821 + 6.95136i −0.690907 + 0.286183i
\(591\) 47.6443i 1.95983i
\(592\) 2.69769 + 6.51281i 0.110875 + 0.267675i
\(593\) −4.00981 4.00981i −0.164663 0.164663i 0.619966 0.784629i \(-0.287146\pi\)
−0.784629 + 0.619966i \(0.787146\pi\)
\(594\) 0.735901 0.0301944
\(595\) −4.59272 7.74844i −0.188283 0.317655i
\(596\) 6.97514 0.285713
\(597\) 20.0070 + 20.0070i 0.818834 + 0.818834i
\(598\) 0.532928 + 1.28660i 0.0217931 + 0.0526131i
\(599\) 34.0787i 1.39242i −0.717839 0.696209i \(-0.754869\pi\)
0.717839 0.696209i \(-0.245131\pi\)
\(600\) 21.8284 9.04160i 0.891139 0.369122i
\(601\) 4.41452 10.6576i 0.180072 0.434732i −0.807909 0.589307i \(-0.799401\pi\)
0.987981 + 0.154575i \(0.0494008\pi\)
\(602\) −21.4810 8.89772i −0.875500 0.362644i
\(603\) 0.162998 0.162998i 0.00663778 0.00663778i
\(604\) 2.18078 2.18078i 0.0887347 0.0887347i
\(605\) −0.910373 0.377089i −0.0370119 0.0153308i
\(606\) −10.4848 + 25.3125i −0.425915 + 1.02825i
\(607\) −12.8938 + 5.34079i −0.523343 + 0.216776i −0.628685 0.777660i \(-0.716406\pi\)
0.105341 + 0.994436i \(0.466406\pi\)
\(608\) 20.3620i 0.825788i
\(609\) −17.4068 42.0238i −0.705361 1.70289i
\(610\) 7.62522 + 7.62522i 0.308736 + 0.308736i
\(611\) 0.939582 0.0380114
\(612\) 1.66868 6.52574i 0.0674523 0.263787i
\(613\) −7.57108 −0.305793 −0.152896 0.988242i \(-0.548860\pi\)
−0.152896 + 0.988242i \(0.548860\pi\)
\(614\) 32.0309 + 32.0309i 1.29266 + 1.29266i
\(615\) −6.60842 15.9541i −0.266477 0.643332i
\(616\) 5.22690i 0.210598i
\(617\) −13.1801 + 5.45939i −0.530612 + 0.219787i −0.631871 0.775073i \(-0.717713\pi\)
0.101259 + 0.994860i \(0.467713\pi\)
\(618\) −16.3703 + 39.5214i −0.658510 + 1.58978i
\(619\) −11.2081 4.64255i −0.450492 0.186600i 0.145890 0.989301i \(-0.453396\pi\)
−0.596382 + 0.802701i \(0.703396\pi\)
\(620\) 0.0788346 0.0788346i 0.00316607 0.00316607i
\(621\) 0.946248 0.946248i 0.0379716 0.0379716i
\(622\) −3.32277 1.37634i −0.133231 0.0551861i
\(623\) 9.59928 23.1747i 0.384587 0.928475i
\(624\) 3.33559 1.38165i 0.133531 0.0553102i
\(625\) 11.3782i 0.455126i
\(626\) 16.4059 + 39.6074i 0.655712 + 1.58303i
\(627\) −12.6371 12.6371i −0.504677 0.504677i
\(628\) 11.6307 0.464117
\(629\) −3.65955 + 4.88408i −0.145916 + 0.194741i
\(630\) 11.0350 0.439643
\(631\) −23.8985 23.8985i −0.951386 0.951386i 0.0474859 0.998872i \(-0.484879\pi\)
−0.998872 + 0.0474859i \(0.984879\pi\)
\(632\) −12.6308 30.4935i −0.502427 1.21297i
\(633\) 60.4353i 2.40209i
\(634\) 48.4318 20.0611i 1.92347 0.796728i
\(635\) 6.15836 14.8676i 0.244387 0.590003i
\(636\) 5.14206 + 2.12991i 0.203896 + 0.0844564i
\(637\) 0.449332 0.449332i 0.0178032 0.0178032i
\(638\) −9.24567 + 9.24567i −0.366039 + 0.366039i
\(639\) 10.1555 + 4.20656i 0.401746 + 0.166409i
\(640\) 5.14560 12.4226i 0.203398 0.491045i
\(641\) 33.8610 14.0257i 1.33743 0.553982i 0.404665 0.914465i \(-0.367388\pi\)
0.932766 + 0.360483i \(0.117388\pi\)
\(642\) 47.0841i 1.85826i
\(643\) −12.4766 30.1211i −0.492029 1.18786i −0.953686 0.300804i \(-0.902745\pi\)
0.461657 0.887058i \(-0.347255\pi\)
\(644\) −2.31655 2.31655i −0.0912850 0.0912850i
\(645\) −16.2158 −0.638498
\(646\) −40.3966 + 23.9442i −1.58938 + 0.942072i
\(647\) −14.3019 −0.562267 −0.281133 0.959669i \(-0.590710\pi\)
−0.281133 + 0.959669i \(0.590710\pi\)
\(648\) 14.0124 + 14.0124i 0.550459 + 0.550459i
\(649\) 4.45040 + 10.7442i 0.174694 + 0.421747i
\(650\) 1.94653i 0.0763493i
\(651\) 1.12438 0.465732i 0.0440678 0.0182535i
\(652\) 2.37174 5.72588i 0.0928844 0.224243i
\(653\) 18.7089 + 7.74946i 0.732134 + 0.303260i 0.717429 0.696632i \(-0.245319\pi\)
0.0147056 + 0.999892i \(0.495319\pi\)
\(654\) 22.0170 22.0170i 0.860931 0.860931i
\(655\) −12.0520 + 12.0520i −0.470912 + 0.470912i
\(656\) 31.0010 + 12.8410i 1.21039 + 0.501358i
\(657\) 3.99005 9.63283i 0.155667 0.375812i
\(658\) −10.0089 + 4.14583i −0.390188 + 0.161621i
\(659\) 9.12180i 0.355335i −0.984091 0.177667i \(-0.943145\pi\)
0.984091 0.177667i \(-0.0568551\pi\)
\(660\) −0.480835 1.16084i −0.0187165 0.0451856i
\(661\) −9.08758 9.08758i −0.353466 0.353466i 0.507932 0.861397i \(-0.330410\pi\)
−0.861397 + 0.507932i \(0.830410\pi\)
\(662\) 1.48796 0.0578312
\(663\) 2.50142 + 1.87427i 0.0971473 + 0.0727907i
\(664\) −11.9067 −0.462070
\(665\) −11.0991 11.0991i −0.430406 0.430406i
\(666\) −2.86127 6.90771i −0.110872 0.267669i
\(667\) 23.7768i 0.920643i
\(668\) −11.0829 + 4.59067i −0.428809 + 0.177618i
\(669\) 13.6021 32.8383i 0.525886 1.26960i
\(670\) −0.104387 0.0432387i −0.00403284 0.00167046i
\(671\) 4.88182 4.88182i 0.188460 0.188460i
\(672\) −11.0501 + 11.0501i −0.426265 + 0.426265i
\(673\) −23.2066 9.61249i −0.894549 0.370534i −0.112427 0.993660i \(-0.535863\pi\)
−0.782122 + 0.623125i \(0.785863\pi\)
\(674\) −0.394537 + 0.952496i −0.0151970 + 0.0366888i
\(675\) −1.72810 + 0.715801i −0.0665145 + 0.0275512i
\(676\) 6.61688i 0.254496i
\(677\) 0.102880 + 0.248374i 0.00395400 + 0.00954579i 0.925844 0.377905i \(-0.123356\pi\)
−0.921890 + 0.387451i \(0.873356\pi\)
\(678\) −41.5488 41.5488i −1.59567 1.59567i
\(679\) 0.391631 0.0150294
\(680\) 9.48181 1.35899i 0.363611 0.0521149i
\(681\) 6.31892 0.242142
\(682\) −0.247374 0.247374i −0.00947245 0.00947245i
\(683\) 0.549145 + 1.32575i 0.0210125 + 0.0507286i 0.934038 0.357175i \(-0.116260\pi\)
−0.913025 + 0.407903i \(0.866260\pi\)
\(684\) 11.7380i 0.448813i
\(685\) −9.69952 + 4.01767i −0.370600 + 0.153507i
\(686\) −12.2178 + 29.4963i −0.466477 + 1.12618i
\(687\) −11.9123 4.93425i −0.454484 0.188253i
\(688\) 22.2806 22.2806i 0.849439 0.849439i
\(689\) −0.940697 + 0.940697i −0.0358377 + 0.0358377i
\(690\) −10.3462 4.28554i −0.393873 0.163148i
\(691\) −5.55056 + 13.4002i −0.211153 + 0.509769i −0.993601 0.112947i \(-0.963971\pi\)
0.782448 + 0.622716i \(0.213971\pi\)
\(692\) −0.578422 + 0.239590i −0.0219883 + 0.00910786i
\(693\) 7.06480i 0.268370i
\(694\) −0.834789 2.01536i −0.0316881 0.0765020i
\(695\) 8.44449 + 8.44449i 0.320318 + 0.320318i
\(696\) 48.3719 1.83353
\(697\) 4.12154 + 28.7564i 0.156114 + 1.08923i
\(698\) 15.9852 0.605048
\(699\) −3.78562 3.78562i −0.143185 0.143185i
\(700\) 1.75239 + 4.23064i 0.0662340 + 0.159903i
\(701\) 35.8282i 1.35321i 0.736346 + 0.676606i \(0.236550\pi\)
−0.736346 + 0.676606i \(0.763450\pi\)
\(702\) −0.207219 + 0.0858330i −0.00782099 + 0.00323956i
\(703\) −4.06998 + 9.82580i −0.153502 + 0.370587i
\(704\) −4.64975 1.92599i −0.175244 0.0725885i
\(705\) −5.34264 + 5.34264i −0.201216 + 0.201216i
\(706\) 33.3776 33.3776i 1.25618 1.25618i
\(707\) 14.2333 + 5.89565i 0.535300 + 0.221729i
\(708\) −5.67481 + 13.7002i −0.213273 + 0.514885i
\(709\) −22.4913 + 9.31622i −0.844680 + 0.349878i −0.762697 0.646756i \(-0.776125\pi\)
−0.0819829 + 0.996634i \(0.526125\pi\)
\(710\) 5.38795i 0.202206i
\(711\) 17.0721 + 41.2157i 0.640255 + 1.54571i
\(712\) 18.8624 + 18.8624i 0.706897 + 0.706897i
\(713\) −0.636165 −0.0238246
\(714\) −34.9165 8.92839i −1.30672 0.334137i
\(715\) 0.300331 0.0112317
\(716\) −7.90195 7.90195i −0.295310 0.295310i
\(717\) −23.9309 57.7743i −0.893716 2.15762i
\(718\) 8.96397i 0.334533i
\(719\) 5.13640 2.12757i 0.191555 0.0793449i −0.284844 0.958574i \(-0.591942\pi\)
0.476399 + 0.879229i \(0.341942\pi\)
\(720\) −5.72285 + 13.8162i −0.213278 + 0.514899i
\(721\) 22.2231 + 9.20509i 0.827630 + 0.342816i
\(722\) −36.5691 + 36.5691i −1.36096 + 1.36096i
\(723\) −19.7952 + 19.7952i −0.736191 + 0.736191i
\(724\) −7.47046 3.09436i −0.277637 0.115001i
\(725\) 12.7182 30.7045i 0.472343 1.14034i
\(726\) −3.64258 + 1.50881i −0.135189 + 0.0559971i
\(727\) 2.96865i 0.110101i 0.998484 + 0.0550506i \(0.0175320\pi\)
−0.998484 + 0.0550506i \(0.982468\pi\)
\(728\) −0.609648 1.47182i −0.0225951 0.0545493i
\(729\) −21.3890 21.3890i −0.792186 0.792186i
\(730\) −5.11063 −0.189153
\(731\) 26.4288 + 6.75804i 0.977506 + 0.249955i
\(732\) 8.80337 0.325382
\(733\) −19.7202 19.7202i −0.728384 0.728384i 0.241914 0.970298i \(-0.422225\pi\)
−0.970298 + 0.241914i \(0.922225\pi\)
\(734\) −18.5307 44.7370i −0.683980 1.65127i
\(735\) 5.10998i 0.188484i
\(736\) 7.54690 3.12603i 0.278182 0.115227i
\(737\) −0.0276823 + 0.0668310i −0.00101969 + 0.00246175i
\(738\) −32.8807 13.6196i −1.21036 0.501346i
\(739\) −10.2158 + 10.2158i −0.375795 + 0.375795i −0.869582 0.493788i \(-0.835612\pi\)
0.493788 + 0.869582i \(0.335612\pi\)
\(740\) −0.528728 + 0.528728i −0.0194364 + 0.0194364i
\(741\) 5.03237 + 2.08448i 0.184869 + 0.0765752i
\(742\) 5.87004 14.1715i 0.215496 0.520253i
\(743\) −49.9110 + 20.6738i −1.83106 + 0.758449i −0.864193 + 0.503161i \(0.832170\pi\)
−0.966865 + 0.255288i \(0.917830\pi\)
\(744\) 1.29422i 0.0474485i
\(745\) −5.13064 12.3865i −0.187972 0.453805i
\(746\) 0.847340 + 0.847340i 0.0310233 + 0.0310233i
\(747\) 16.0934 0.588827
\(748\) 0.299888 + 2.09235i 0.0109650 + 0.0765038i
\(749\) 26.4756 0.967398
\(750\) 24.8041 + 24.8041i 0.905719 + 0.905719i
\(751\) −2.87153 6.93249i −0.104784 0.252970i 0.862788 0.505565i \(-0.168716\pi\)
−0.967572 + 0.252595i \(0.918716\pi\)
\(752\) 14.6816i 0.535383i
\(753\) −42.7057 + 17.6893i −1.55628 + 0.644633i
\(754\) 1.52507 3.68183i 0.0555396 0.134085i
\(755\) −5.47673 2.26854i −0.199319 0.0825605i
\(756\) 0.373103 0.373103i 0.0135696 0.0135696i
\(757\) −1.93330 + 1.93330i −0.0702670 + 0.0702670i −0.741367 0.671100i \(-0.765822\pi\)
0.671100 + 0.741367i \(0.265822\pi\)
\(758\) 15.9751 + 6.61710i 0.580241 + 0.240344i
\(759\) −2.74369 + 6.62385i −0.0995895 + 0.240430i
\(760\) 15.4217 6.38787i 0.559404 0.231713i
\(761\) 19.9761i 0.724132i −0.932152 0.362066i \(-0.882071\pi\)
0.932152 0.362066i \(-0.117929\pi\)
\(762\) −24.6408 59.4882i −0.892643 2.15503i
\(763\) −12.3802 12.3802i −0.448195 0.448195i
\(764\) −4.39173 −0.158887
\(765\) −12.8158 + 1.83684i −0.463358 + 0.0664112i
\(766\) 53.9790 1.95034
\(767\) −2.50634 2.50634i −0.0904987 0.0904987i
\(768\) −11.0075 26.5745i −0.397200 0.958925i
\(769\) 14.6466i 0.528171i −0.964499 0.264085i \(-0.914930\pi\)
0.964499 0.264085i \(-0.0850701\pi\)
\(770\) −3.19928 + 1.32518i −0.115294 + 0.0477563i
\(771\) −6.70035 + 16.1761i −0.241307 + 0.582567i
\(772\) −5.67842 2.35208i −0.204371 0.0846531i
\(773\) −32.3353 + 32.3353i −1.16302 + 1.16302i −0.179210 + 0.983811i \(0.557354\pi\)
−0.983811 + 0.179210i \(0.942646\pi\)
\(774\) −23.6316 + 23.6316i −0.849419 + 0.849419i
\(775\) 0.821520 + 0.340285i 0.0295099 + 0.0122234i
\(776\) −0.159378 + 0.384773i −0.00572135 + 0.0138126i
\(777\) −7.54097 + 3.12357i −0.270531 + 0.112058i
\(778\) 16.4346i 0.589208i
\(779\) 19.3731 + 46.7708i 0.694114 + 1.67574i
\(780\) 0.270793 + 0.270793i 0.00969594 + 0.00969594i
\(781\) −3.44947 −0.123432
\(782\) 15.0764 + 11.2965i 0.539131 + 0.403961i
\(783\) −3.82948 −0.136854
\(784\) −7.02112 7.02112i −0.250754 0.250754i
\(785\) −8.55513 20.6539i −0.305346 0.737170i
\(786\) 68.1970i 2.43250i
\(787\) 7.09216 2.93767i 0.252808 0.104717i −0.252681 0.967550i \(-0.581312\pi\)
0.505489 + 0.862833i \(0.331312\pi\)
\(788\) 3.75792 9.07243i 0.133870 0.323192i
\(789\) 29.4929 + 12.2164i 1.04997 + 0.434914i
\(790\) 15.4621 15.4621i 0.550118 0.550118i
\(791\) −23.3631 + 23.3631i −0.830696 + 0.830696i
\(792\) 6.94109 + 2.87509i 0.246641 + 0.102162i
\(793\) −0.805252 + 1.94405i −0.0285953 + 0.0690353i
\(794\) −4.64146 + 1.92256i −0.164719 + 0.0682289i
\(795\) 10.6980i 0.379418i
\(796\) −2.23169 5.38779i −0.0791003 0.190965i
\(797\) 35.3095 + 35.3095i 1.25073 + 1.25073i 0.955395 + 0.295330i \(0.0954295\pi\)
0.295330 + 0.955395i \(0.404570\pi\)
\(798\) −62.8050 −2.22327
\(799\) 10.9341 6.48096i 0.386821 0.229280i
\(800\) −11.4179 −0.403683
\(801\) −25.4948 25.4948i −0.900816 0.900816i
\(802\) −7.61269 18.3787i −0.268813 0.648973i
\(803\) 3.27193i 0.115464i
\(804\) −0.0852178 + 0.0352984i −0.00300540 + 0.00124488i
\(805\) −2.40978 + 5.81772i −0.0849335 + 0.205048i
\(806\) 0.0985100 + 0.0408042i 0.00346987 + 0.00143727i
\(807\) −13.4506 + 13.4506i −0.473484 + 0.473484i
\(808\) −11.5848 + 11.5848i −0.407552 + 0.407552i
\(809\) 33.8746 + 14.0313i 1.19097 + 0.493314i 0.888070 0.459709i \(-0.152046\pi\)
0.302897 + 0.953023i \(0.402046\pi\)
\(810\) −5.02411 + 12.1293i −0.176529 + 0.426179i
\(811\) 32.7313 13.5577i 1.14935 0.476076i 0.275035 0.961434i \(-0.411311\pi\)
0.874316 + 0.485358i \(0.161311\pi\)
\(812\) 9.37513i 0.329003i
\(813\) −13.5543 32.7229i −0.475369 1.14764i
\(814\) 1.65909 + 1.65909i 0.0581511 + 0.0581511i
\(815\) −11.9126 −0.417280
\(816\) 29.2868 39.0864i 1.02524 1.36830i
\(817\) 47.5380 1.66315
\(818\) 45.2412 + 45.2412i 1.58182 + 1.58182i
\(819\) 0.824015 + 1.98935i 0.0287934 + 0.0695135i
\(820\) 3.55922i 0.124293i
\(821\) −24.2758 + 10.0554i −0.847231 + 0.350935i −0.763701 0.645570i \(-0.776620\pi\)
−0.0835307 + 0.996505i \(0.526620\pi\)
\(822\) −16.0755 + 38.8097i −0.560697 + 1.35364i
\(823\) −44.8293 18.5689i −1.56265 0.647272i −0.577104 0.816671i \(-0.695817\pi\)
−0.985548 + 0.169399i \(0.945817\pi\)
\(824\) −18.0878 + 18.0878i −0.630119 + 0.630119i
\(825\) 7.08619 7.08619i 0.246709 0.246709i
\(826\) 37.7578 + 15.6398i 1.31376 + 0.544178i
\(827\) −11.2669 + 27.2007i −0.391788 + 0.945861i 0.597762 + 0.801674i \(0.296057\pi\)
−0.989550 + 0.144187i \(0.953943\pi\)
\(828\) −4.35052 + 1.80205i −0.151191 + 0.0626254i
\(829\) 40.5713i 1.40910i −0.709654 0.704550i \(-0.751149\pi\)
0.709654 0.704550i \(-0.248851\pi\)
\(830\) −3.01873 7.28785i −0.104782 0.252965i
\(831\) −55.9497 55.9497i −1.94087 1.94087i
\(832\) 1.53395 0.0531800
\(833\) 2.12961 8.32833i 0.0737867 0.288560i
\(834\) 47.7835 1.65461
\(835\) 16.3043 + 16.3043i 0.564232 + 0.564232i
\(836\) 1.40961 + 3.40310i 0.0487523 + 0.117699i
\(837\) 0.102460i 0.00354155i
\(838\) −46.0555 + 19.0768i −1.59096 + 0.658998i
\(839\) 0.759740 1.83418i 0.0262291 0.0633228i −0.910222 0.414120i \(-0.864089\pi\)
0.936451 + 0.350797i \(0.114089\pi\)
\(840\) 11.8356 + 4.90248i 0.408368 + 0.169152i
\(841\) 27.6065 27.6065i 0.951948 0.951948i
\(842\) −37.3246 + 37.3246i −1.28629 + 1.28629i
\(843\) 73.1873 + 30.3152i 2.52070 + 1.04411i
\(844\) 4.76680 11.5081i 0.164080 0.396125i
\(845\) 11.7503 4.86713i 0.404222 0.167434i
\(846\) 15.5718i 0.535371i
\(847\) 0.848409 + 2.04824i 0.0291517 + 0.0703784i
\(848\) 14.6990 + 14.6990i 0.504767 + 0.504767i
\(849\) 24.8282 0.852101
\(850\) −13.4266 22.6522i −0.460529 0.776964i
\(851\) 4.26664 0.146258
\(852\) −3.11021 3.11021i −0.106554 0.106554i
\(853\) −9.61832 23.2207i −0.329325 0.795061i −0.998643 0.0520844i \(-0.983414\pi\)
0.669318 0.742976i \(-0.266586\pi\)
\(854\) 24.2621i 0.830233i
\(855\) −20.8443 + 8.63400i −0.712861 + 0.295277i
\(856\) −10.7745 + 26.0120i −0.368266 + 0.889072i
\(857\) 18.2056 + 7.54102i 0.621893 + 0.257596i 0.671304 0.741182i \(-0.265734\pi\)
−0.0494112 + 0.998779i \(0.515734\pi\)
\(858\) 0.849718 0.849718i 0.0290089 0.0290089i
\(859\) −9.65385 + 9.65385i −0.329385 + 0.329385i −0.852353 0.522968i \(-0.824825\pi\)
0.522968 + 0.852353i \(0.324825\pi\)
\(860\) 3.08782 + 1.27902i 0.105294 + 0.0436141i
\(861\) −14.8682 + 35.8950i −0.506707 + 1.22330i
\(862\) 19.7777 8.19219i 0.673631 0.279027i
\(863\) 15.9712i 0.543667i 0.962344 + 0.271833i \(0.0876300\pi\)
−0.962344 + 0.271833i \(0.912370\pi\)
\(864\) 0.503476 + 1.21550i 0.0171286 + 0.0413521i
\(865\) 0.850931 + 0.850931i 0.0289325 + 0.0289325i
\(866\) 59.6334 2.02643
\(867\) 42.0378 + 4.55723i 1.42768 + 0.154771i
\(868\) −0.250838 −0.00851400
\(869\) −9.89917 9.89917i −0.335806 0.335806i
\(870\) 12.2638 + 29.6074i 0.415782 + 1.00379i
\(871\) 0.0220474i 0.000747049i
\(872\) 17.2017 7.12519i 0.582524 0.241289i
\(873\) 0.215420 0.520069i 0.00729085 0.0176017i
\(874\) 30.3307 + 12.5634i 1.02595 + 0.424963i
\(875\) 13.9475 13.9475i 0.471511 0.471511i
\(876\) −2.95013 + 2.95013i −0.0996757 + 0.0996757i
\(877\) −52.7803 21.8623i −1.78226 0.738238i −0.992116 0.125322i \(-0.960004\pi\)
−0.790148 0.612916i \(-0.789996\pi\)
\(878\) 0.112674 0.272019i 0.00380257 0.00918021i
\(879\) −9.25785 + 3.83473i −0.312260 + 0.129342i
\(880\) 4.69287i 0.158197i
\(881\) 12.5161 + 30.2165i 0.421678 + 1.01802i 0.981853 + 0.189646i \(0.0607340\pi\)
−0.560175 + 0.828375i \(0.689266\pi\)
\(882\) 7.44685 + 7.44685i 0.250749 + 0.250749i
\(883\) 41.5063 1.39680 0.698399 0.715709i \(-0.253896\pi\)
0.698399 + 0.715709i \(0.253896\pi\)
\(884\) −0.328489 0.554198i −0.0110483 0.0186397i
\(885\) 28.5031 0.958120
\(886\) −22.8638 22.8638i −0.768124 0.768124i
\(887\) 16.0381 + 38.7193i 0.538505 + 1.30007i 0.925766 + 0.378096i \(0.123421\pi\)
−0.387261 + 0.921970i \(0.626579\pi\)
\(888\) 8.68009i 0.291285i
\(889\) −33.4505 + 13.8556i −1.12189 + 0.464703i
\(890\) −6.76306 + 16.3275i −0.226698 + 0.547298i
\(891\) 7.76541 + 3.21654i 0.260151 + 0.107758i
\(892\) −5.18020 + 5.18020i −0.173446 + 0.173446i
\(893\) 15.6624 15.6624i 0.524122 0.524122i
\(894\) −49.5607 20.5287i −1.65756 0.686583i
\(895\) −8.21994 + 19.8447i −0.274762 + 0.663335i
\(896\) −27.9494 + 11.5770i −0.933725 + 0.386762i
\(897\) 2.18520i 0.0729616i
\(898\) 16.3724 + 39.5264i 0.546353 + 1.31901i
\(899\) 1.28729 + 1.28729i 0.0429334 + 0.0429334i
\(900\) 6.58201 0.219400
\(901\) −4.45844 + 17.4357i −0.148532 + 0.580868i
\(902\) 11.1684 0.371868
\(903\) 25.7980 + 25.7980i 0.858503 + 0.858503i
\(904\) −13.4461 32.4618i −0.447212 1.07966i
\(905\) 15.5422i 0.516639i
\(906\) −21.9135 + 9.07686i −0.728027 + 0.301559i
\(907\) 0.00921302 0.0222422i 0.000305913 0.000738540i −0.923727 0.383053i \(-0.874873\pi\)
0.924032 + 0.382314i \(0.124873\pi\)
\(908\) −1.20325 0.498402i −0.0399312 0.0165400i
\(909\) 15.6583 15.6583i 0.519354 0.519354i
\(910\) 0.746306 0.746306i 0.0247398 0.0247398i
\(911\) 11.1580 + 4.62179i 0.369681 + 0.153127i 0.559787 0.828637i \(-0.310883\pi\)
−0.190106 + 0.981764i \(0.560883\pi\)
\(912\) 32.5714 78.6342i 1.07855 2.60384i
\(913\) −4.66583 + 1.93265i −0.154416 + 0.0639614i
\(914\) 16.2084i 0.536125i
\(915\) −6.47542 15.6331i −0.214071 0.516813i
\(916\) 1.87916 + 1.87916i 0.0620892 + 0.0620892i
\(917\) 38.3475 1.26634
\(918\) −1.81940 + 2.42819i −0.0600492 + 0.0801423i
\(919\) 7.31860 0.241418 0.120709 0.992688i \(-0.461483\pi\)
0.120709 + 0.992688i \(0.461483\pi\)
\(920\) −4.73516 4.73516i −0.156114 0.156114i
\(921\) −27.2010 65.6691i −0.896304 2.16387i
\(922\) 31.6880i 1.04359i
\(923\) 0.971323 0.402335i 0.0319715 0.0132430i
\(924\) −1.08183 + 2.61176i −0.0355895 + 0.0859207i
\(925\) −5.50977 2.28222i −0.181160 0.0750390i
\(926\) 31.2155 31.2155i 1.02580 1.02580i
\(927\) 24.4479 24.4479i 0.802975 0.802975i
\(928\) −21.5967 8.94566i −0.708948 0.293656i
\(929\) −0.291137 + 0.702868i −0.00955191 + 0.0230603i −0.928584 0.371123i \(-0.878973\pi\)
0.919032 + 0.394184i \(0.128973\pi\)
\(930\) −0.792167 + 0.328126i −0.0259762 + 0.0107597i
\(931\) 14.9803i 0.490960i
\(932\) 0.422268 + 1.01945i 0.0138318 + 0.0333930i
\(933\) 3.99054 + 3.99054i 0.130644 + 0.130644i
\(934\) −14.6462 −0.479238
\(935\) 3.49501 2.07159i 0.114299 0.0677483i
\(936\) −2.28986 −0.0748463
\(937\) 10.8080 + 10.8080i 0.353081 + 0.353081i 0.861254 0.508174i \(-0.169679\pi\)
−0.508174 + 0.861254i \(0.669679\pi\)
\(938\) 0.0972824 + 0.234860i 0.00317638 + 0.00766847i
\(939\) 67.2701i 2.19528i
\(940\) 1.43874 0.595947i 0.0469266 0.0194377i
\(941\) 19.6363 47.4063i 0.640126 1.54540i −0.186383 0.982477i \(-0.559676\pi\)
0.826509 0.562924i \(-0.190324\pi\)
\(942\) −82.6403 34.2307i −2.69257 1.11530i
\(943\) 14.3608 14.3608i 0.467651 0.467651i
\(944\) −39.1633 + 39.1633i −1.27466 + 1.27466i
\(945\) −0.936997 0.388117i −0.0304805 0.0126254i
\(946\) 4.01341 9.68922i 0.130487 0.315024i
\(947\) 24.1279 9.99411i 0.784052 0.324765i 0.0455026 0.998964i \(-0.485511\pi\)
0.738550 + 0.674199i \(0.235511\pi\)
\(948\) 17.8511i 0.579778i
\(949\) −0.381627 0.921330i −0.0123881 0.0299076i
\(950\) −32.4478 32.4478i −1.05275 1.05275i
\(951\) −82.2576 −2.66739
\(952\) −17.2468 12.9227i −0.558971 0.418827i
\(953\) −16.9120 −0.547835 −0.273917 0.961753i \(-0.588319\pi\)
−0.273917 + 0.961753i \(0.588319\pi\)
\(954\) −15.5903 15.5903i −0.504755 0.504755i
\(955\) 3.23039 + 7.79886i 0.104533 + 0.252365i
\(956\) 12.8889i 0.416858i
\(957\) 18.9553 7.85153i 0.612737 0.253804i
\(958\) −7.83932 + 18.9258i −0.253277 + 0.611465i
\(959\) 21.8229 + 9.03933i 0.704697 + 0.291895i
\(960\) −8.72231 + 8.72231i −0.281511 + 0.281511i
\(961\) 21.8859 21.8859i 0.705996 0.705996i
\(962\) −0.660687 0.273666i −0.0213014 0.00882333i
\(963\) 14.5631 35.1585i 0.469290 1.13297i
\(964\) 5.33073 2.20806i 0.171691 0.0711169i
\(965\) 11.8139i 0.380301i
\(966\) 9.64199 + 23.2778i 0.310226 + 0.748952i
\(967\) 26.1949 + 26.1949i 0.842372 + 0.842372i 0.989167 0.146795i \(-0.0468959\pi\)
−0.146795 + 0.989167i \(0.546896\pi\)
\(968\) −2.35764 −0.0757776
\(969\) 72.9408 10.4543i 2.34320 0.335841i
\(970\) −0.275919 −0.00885923
\(971\) −34.7881 34.7881i −1.11640 1.11640i −0.992265 0.124137i \(-0.960384\pi\)
−0.124137 0.992265i \(-0.539616\pi\)
\(972\) 4.37472 + 10.5615i 0.140319 + 0.338761i
\(973\) 26.8689i 0.861377i
\(974\) −3.04285 + 1.26039i −0.0974991 + 0.0403855i
\(975\) −1.16886 + 2.82188i −0.0374335 + 0.0903725i
\(976\) 30.3771 + 12.5826i 0.972347 + 0.402759i
\(977\) 1.86938 1.86938i 0.0598069 0.0598069i −0.676571 0.736378i \(-0.736535\pi\)
0.736378 + 0.676571i \(0.236535\pi\)
\(978\) −33.7040 + 33.7040i −1.07773 + 1.07773i
\(979\) 10.4532 + 4.32985i 0.334085 + 0.138383i
\(980\) 0.403047 0.973041i 0.0128749 0.0310827i
\(981\) −23.2503 + 9.63057i −0.742324 + 0.307481i
\(982\) 20.6606i 0.659306i
\(983\) −4.20395 10.1492i −0.134085 0.323710i 0.842549 0.538620i \(-0.181054\pi\)
−0.976634 + 0.214910i \(0.931054\pi\)
\(984\) −29.2157 29.2157i −0.931363 0.931363i
\(985\) −18.8750 −0.601409
\(986\) −7.64869 53.3657i −0.243584 1.69951i
\(987\) 16.9994 0.541096
\(988\) −0.793852 0.793852i −0.0252558 0.0252558i
\(989\) −7.29817 17.6193i −0.232068 0.560262i
\(990\) 4.97743i 0.158193i
\(991\) 36.4187 15.0851i 1.15688 0.479195i 0.280044 0.959987i \(-0.409651\pi\)
0.876835 + 0.480792i \(0.159651\pi\)
\(992\) 0.239347 0.577836i 0.00759929 0.0183463i
\(993\) −2.15709 0.893496i −0.0684532 0.0283542i
\(994\) −8.57176 + 8.57176i −0.271880 + 0.271880i
\(995\) −7.92610 + 7.92610i −0.251274 + 0.251274i
\(996\) −5.94951 2.46437i −0.188517 0.0780865i
\(997\) −11.3308 + 27.3550i −0.358850 + 0.866340i 0.636612 + 0.771184i \(0.280335\pi\)
−0.995462 + 0.0951564i \(0.969665\pi\)
\(998\) 18.9203 7.83705i 0.598912 0.248078i
\(999\) 0.687181i 0.0217415i
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 187.2.h.a.100.12 56
17.5 odd 16 3179.2.a.bh.1.7 28
17.8 even 8 inner 187.2.h.a.144.12 yes 56
17.12 odd 16 3179.2.a.bi.1.7 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
187.2.h.a.100.12 56 1.1 even 1 trivial
187.2.h.a.144.12 yes 56 17.8 even 8 inner
3179.2.a.bh.1.7 28 17.5 odd 16
3179.2.a.bi.1.7 28 17.12 odd 16