Properties

Label 930.2.j.h.497.7
Level $930$
Weight $2$
Character 930.497
Analytic conductor $7.426$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [930,2,Mod(497,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.497");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.j (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 497.7
Character \(\chi\) \(=\) 930.497
Dual form 930.2.j.h.683.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(0.0980849 + 1.72927i) q^{3} -1.00000i q^{4} +(-0.278761 + 2.21862i) q^{5} +(-1.29214 - 1.15342i) q^{6} +(-1.59354 - 1.59354i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.98076 + 0.339231i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(0.0980849 + 1.72927i) q^{3} -1.00000i q^{4} +(-0.278761 + 2.21862i) q^{5} +(-1.29214 - 1.15342i) q^{6} +(-1.59354 - 1.59354i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.98076 + 0.339231i) q^{9} +(-1.37169 - 1.76592i) q^{10} +3.70376i q^{11} +(1.72927 - 0.0980849i) q^{12} +(-1.02541 + 1.02541i) q^{13} +2.25360 q^{14} +(-3.86395 - 0.264439i) q^{15} -1.00000 q^{16} +(0.479745 - 0.479745i) q^{17} +(1.86784 - 2.34759i) q^{18} -0.296019i q^{19} +(2.21862 + 0.278761i) q^{20} +(2.59936 - 2.91196i) q^{21} +(-2.61895 - 2.61895i) q^{22} +(-1.49449 - 1.49449i) q^{23} +(-1.15342 + 1.29214i) q^{24} +(-4.84458 - 1.23693i) q^{25} -1.45015i q^{26} +(-0.878989 - 5.12127i) q^{27} +(-1.59354 + 1.59354i) q^{28} -1.30186 q^{29} +(2.91921 - 2.54523i) q^{30} -1.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +(-6.40480 + 0.363282i) q^{33} +0.678461i q^{34} +(3.97967 - 3.09124i) q^{35} +(0.339231 + 2.98076i) q^{36} +(-2.24098 - 2.24098i) q^{37} +(0.209317 + 0.209317i) q^{38} +(-1.87380 - 1.67264i) q^{39} +(-1.76592 + 1.37169i) q^{40} -5.01872i q^{41} +(0.221044 + 3.89709i) q^{42} +(-7.37080 + 7.37080i) q^{43} +3.70376 q^{44} +(0.0782930 - 6.70775i) q^{45} +2.11353 q^{46} +(-0.230740 + 0.230740i) q^{47} +(-0.0980849 - 1.72927i) q^{48} -1.92128i q^{49} +(4.30028 - 2.55100i) q^{50} +(0.876664 + 0.782553i) q^{51} +(1.02541 + 1.02541i) q^{52} +(-0.282801 - 0.282801i) q^{53} +(4.24282 + 2.99974i) q^{54} +(-8.21724 - 1.03246i) q^{55} -2.25360i q^{56} +(0.511898 - 0.0290350i) q^{57} +(0.920553 - 0.920553i) q^{58} +12.3141 q^{59} +(-0.264439 + 3.86395i) q^{60} +11.1031 q^{61} +(0.707107 - 0.707107i) q^{62} +(5.29053 + 4.20937i) q^{63} +1.00000i q^{64} +(-1.98916 - 2.56085i) q^{65} +(4.27200 - 4.78576i) q^{66} +(-9.42240 - 9.42240i) q^{67} +(-0.479745 - 0.479745i) q^{68} +(2.43779 - 2.73097i) q^{69} +(-0.628216 + 4.99989i) q^{70} +6.43406i q^{71} +(-2.34759 - 1.86784i) q^{72} +(-5.91592 + 5.91592i) q^{73} +3.16922 q^{74} +(1.66381 - 8.49893i) q^{75} -0.296019 q^{76} +(5.90207 - 5.90207i) q^{77} +(2.50771 - 0.142238i) q^{78} -3.56575i q^{79} +(0.278761 - 2.21862i) q^{80} +(8.76985 - 2.02233i) q^{81} +(3.54877 + 3.54877i) q^{82} +(-1.95472 - 1.95472i) q^{83} +(-2.91196 - 2.59936i) q^{84} +(0.930639 + 1.19811i) q^{85} -10.4239i q^{86} +(-0.127693 - 2.25127i) q^{87} +(-2.61895 + 2.61895i) q^{88} -10.7601 q^{89} +(4.68773 + 4.79845i) q^{90} +3.26807 q^{91} +(-1.49449 + 1.49449i) q^{92} +(-0.0980849 - 1.72927i) q^{93} -0.326316i q^{94} +(0.656756 + 0.0825186i) q^{95} +(1.29214 + 1.15342i) q^{96} +(5.06700 + 5.06700i) q^{97} +(1.35855 + 1.35855i) q^{98} +(-1.25643 - 11.0400i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 4 q^{3} + 8 q^{6} - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 4 q^{3} + 8 q^{6} - 8 q^{7} + 4 q^{12} + 24 q^{13} - 12 q^{15} - 40 q^{16} - 56 q^{21} + 16 q^{22} - 48 q^{25} + 8 q^{27} - 8 q^{28} + 4 q^{30} - 40 q^{31} - 20 q^{33} - 8 q^{37} - 8 q^{40} + 12 q^{42} - 16 q^{43} + 76 q^{45} - 8 q^{46} + 4 q^{48} + 16 q^{51} - 24 q^{52} - 48 q^{55} + 56 q^{57} - 56 q^{58} + 12 q^{60} + 128 q^{61} - 24 q^{63} + 16 q^{66} + 8 q^{67} + 32 q^{70} + 248 q^{73} - 8 q^{75} + 56 q^{76} + 8 q^{78} + 40 q^{81} - 8 q^{82} - 48 q^{85} + 12 q^{87} + 16 q^{88} + 16 q^{90} - 192 q^{91} + 4 q^{93} - 8 q^{96} + 24 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) 0.0980849 + 1.72927i 0.0566293 + 0.998395i
\(4\) 1.00000i 0.500000i
\(5\) −0.278761 + 2.21862i −0.124666 + 0.992199i
\(6\) −1.29214 1.15342i −0.527512 0.470883i
\(7\) −1.59354 1.59354i −0.602300 0.602300i 0.338622 0.940922i \(-0.390039\pi\)
−0.940922 + 0.338622i \(0.890039\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) −2.98076 + 0.339231i −0.993586 + 0.113077i
\(10\) −1.37169 1.76592i −0.433767 0.558432i
\(11\) 3.70376i 1.11672i 0.829597 + 0.558362i \(0.188570\pi\)
−0.829597 + 0.558362i \(0.811430\pi\)
\(12\) 1.72927 0.0980849i 0.499198 0.0283147i
\(13\) −1.02541 + 1.02541i −0.284399 + 0.284399i −0.834860 0.550462i \(-0.814452\pi\)
0.550462 + 0.834860i \(0.314452\pi\)
\(14\) 2.25360 0.602300
\(15\) −3.86395 0.264439i −0.997666 0.0682780i
\(16\) −1.00000 −0.250000
\(17\) 0.479745 0.479745i 0.116355 0.116355i −0.646532 0.762887i \(-0.723781\pi\)
0.762887 + 0.646532i \(0.223781\pi\)
\(18\) 1.86784 2.34759i 0.440255 0.553332i
\(19\) 0.296019i 0.0679115i −0.999423 0.0339558i \(-0.989189\pi\)
0.999423 0.0339558i \(-0.0108105\pi\)
\(20\) 2.21862 + 0.278761i 0.496099 + 0.0623328i
\(21\) 2.59936 2.91196i 0.567226 0.635442i
\(22\) −2.61895 2.61895i −0.558362 0.558362i
\(23\) −1.49449 1.49449i −0.311623 0.311623i 0.533915 0.845538i \(-0.320720\pi\)
−0.845538 + 0.533915i \(0.820720\pi\)
\(24\) −1.15342 + 1.29214i −0.235441 + 0.263756i
\(25\) −4.84458 1.23693i −0.968917 0.247386i
\(26\) 1.45015i 0.284399i
\(27\) −0.878989 5.12127i −0.169162 0.985588i
\(28\) −1.59354 + 1.59354i −0.301150 + 0.301150i
\(29\) −1.30186 −0.241749 −0.120875 0.992668i \(-0.538570\pi\)
−0.120875 + 0.992668i \(0.538570\pi\)
\(30\) 2.91921 2.54523i 0.532972 0.464694i
\(31\) −1.00000 −0.179605
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) −6.40480 + 0.363282i −1.11493 + 0.0632393i
\(34\) 0.678461i 0.116355i
\(35\) 3.97967 3.09124i 0.672688 0.522516i
\(36\) 0.339231 + 2.98076i 0.0565384 + 0.496793i
\(37\) −2.24098 2.24098i −0.368414 0.368414i 0.498484 0.866899i \(-0.333890\pi\)
−0.866899 + 0.498484i \(0.833890\pi\)
\(38\) 0.209317 + 0.209317i 0.0339558 + 0.0339558i
\(39\) −1.87380 1.67264i −0.300047 0.267837i
\(40\) −1.76592 + 1.37169i −0.279216 + 0.216883i
\(41\) 5.01872i 0.783792i −0.920010 0.391896i \(-0.871819\pi\)
0.920010 0.391896i \(-0.128181\pi\)
\(42\) 0.221044 + 3.89709i 0.0341079 + 0.601334i
\(43\) −7.37080 + 7.37080i −1.12404 + 1.12404i −0.132907 + 0.991128i \(0.542431\pi\)
−0.991128 + 0.132907i \(0.957569\pi\)
\(44\) 3.70376 0.558362
\(45\) 0.0782930 6.70775i 0.0116712 0.999932i
\(46\) 2.11353 0.311623
\(47\) −0.230740 + 0.230740i −0.0336569 + 0.0336569i −0.723735 0.690078i \(-0.757576\pi\)
0.690078 + 0.723735i \(0.257576\pi\)
\(48\) −0.0980849 1.72927i −0.0141573 0.249599i
\(49\) 1.92128i 0.274469i
\(50\) 4.30028 2.55100i 0.608152 0.360765i
\(51\) 0.876664 + 0.782553i 0.122758 + 0.109579i
\(52\) 1.02541 + 1.02541i 0.142199 + 0.142199i
\(53\) −0.282801 0.282801i −0.0388457 0.0388457i 0.687417 0.726263i \(-0.258744\pi\)
−0.726263 + 0.687417i \(0.758744\pi\)
\(54\) 4.24282 + 2.99974i 0.577375 + 0.408213i
\(55\) −8.21724 1.03246i −1.10801 0.139217i
\(56\) 2.25360i 0.301150i
\(57\) 0.511898 0.0290350i 0.0678025 0.00384578i
\(58\) 0.920553 0.920553i 0.120875 0.120875i
\(59\) 12.3141 1.60316 0.801581 0.597886i \(-0.203992\pi\)
0.801581 + 0.597886i \(0.203992\pi\)
\(60\) −0.264439 + 3.86395i −0.0341390 + 0.498833i
\(61\) 11.1031 1.42160 0.710801 0.703393i \(-0.248333\pi\)
0.710801 + 0.703393i \(0.248333\pi\)
\(62\) 0.707107 0.707107i 0.0898027 0.0898027i
\(63\) 5.29053 + 4.20937i 0.666544 + 0.530331i
\(64\) 1.00000i 0.125000i
\(65\) −1.98916 2.56085i −0.246725 0.317635i
\(66\) 4.27200 4.78576i 0.525846 0.589086i
\(67\) −9.42240 9.42240i −1.15113 1.15113i −0.986326 0.164803i \(-0.947301\pi\)
−0.164803 0.986326i \(-0.552699\pi\)
\(68\) −0.479745 0.479745i −0.0581776 0.0581776i
\(69\) 2.43779 2.73097i 0.293476 0.328770i
\(70\) −0.628216 + 4.99989i −0.0750861 + 0.597602i
\(71\) 6.43406i 0.763582i 0.924249 + 0.381791i \(0.124693\pi\)
−0.924249 + 0.381791i \(0.875307\pi\)
\(72\) −2.34759 1.86784i −0.276666 0.220127i
\(73\) −5.91592 + 5.91592i −0.692407 + 0.692407i −0.962761 0.270354i \(-0.912859\pi\)
0.270354 + 0.962761i \(0.412859\pi\)
\(74\) 3.16922 0.368414
\(75\) 1.66381 8.49893i 0.192120 0.981371i
\(76\) −0.296019 −0.0339558
\(77\) 5.90207 5.90207i 0.672603 0.672603i
\(78\) 2.50771 0.142238i 0.283942 0.0161053i
\(79\) 3.56575i 0.401178i −0.979675 0.200589i \(-0.935714\pi\)
0.979675 0.200589i \(-0.0642856\pi\)
\(80\) 0.278761 2.21862i 0.0311664 0.248050i
\(81\) 8.76985 2.02233i 0.974427 0.224703i
\(82\) 3.54877 + 3.54877i 0.391896 + 0.391896i
\(83\) −1.95472 1.95472i −0.214558 0.214558i 0.591642 0.806200i \(-0.298480\pi\)
−0.806200 + 0.591642i \(0.798480\pi\)
\(84\) −2.91196 2.59936i −0.317721 0.283613i
\(85\) 0.930639 + 1.19811i 0.100942 + 0.129953i
\(86\) 10.4239i 1.12404i
\(87\) −0.127693 2.25127i −0.0136901 0.241361i
\(88\) −2.61895 + 2.61895i −0.279181 + 0.279181i
\(89\) −10.7601 −1.14057 −0.570283 0.821448i \(-0.693166\pi\)
−0.570283 + 0.821448i \(0.693166\pi\)
\(90\) 4.68773 + 4.79845i 0.494130 + 0.505802i
\(91\) 3.26807 0.342587
\(92\) −1.49449 + 1.49449i −0.155811 + 0.155811i
\(93\) −0.0980849 1.72927i −0.0101709 0.179317i
\(94\) 0.326316i 0.0336569i
\(95\) 0.656756 + 0.0825186i 0.0673817 + 0.00846623i
\(96\) 1.29214 + 1.15342i 0.131878 + 0.117721i
\(97\) 5.06700 + 5.06700i 0.514476 + 0.514476i 0.915895 0.401419i \(-0.131483\pi\)
−0.401419 + 0.915895i \(0.631483\pi\)
\(98\) 1.35855 + 1.35855i 0.137234 + 0.137234i
\(99\) −1.25643 11.0400i −0.126276 1.10956i
\(100\) −1.23693 + 4.84458i −0.123693 + 0.484458i
\(101\) 2.21327i 0.220229i 0.993919 + 0.110115i \(0.0351218\pi\)
−0.993919 + 0.110115i \(0.964878\pi\)
\(102\) −1.17324 + 0.0665468i −0.116168 + 0.00658911i
\(103\) −4.54917 + 4.54917i −0.448243 + 0.448243i −0.894770 0.446527i \(-0.852661\pi\)
0.446527 + 0.894770i \(0.352661\pi\)
\(104\) −1.45015 −0.142199
\(105\) 5.73595 + 6.57873i 0.559771 + 0.642019i
\(106\) 0.399941 0.0388457
\(107\) −11.0754 + 11.0754i −1.07070 + 1.07070i −0.0733937 + 0.997303i \(0.523383\pi\)
−0.997303 + 0.0733937i \(0.976617\pi\)
\(108\) −5.12127 + 0.878989i −0.492794 + 0.0845808i
\(109\) 9.99461i 0.957310i −0.878003 0.478655i \(-0.841125\pi\)
0.878003 0.478655i \(-0.158875\pi\)
\(110\) 6.54053 5.08041i 0.623615 0.484398i
\(111\) 3.65545 4.09506i 0.346960 0.388686i
\(112\) 1.59354 + 1.59354i 0.150575 + 0.150575i
\(113\) −3.56657 3.56657i −0.335515 0.335515i 0.519161 0.854676i \(-0.326244\pi\)
−0.854676 + 0.519161i \(0.826244\pi\)
\(114\) −0.341436 + 0.382497i −0.0319784 + 0.0358242i
\(115\) 3.73232 2.89911i 0.348040 0.270343i
\(116\) 1.30186i 0.120875i
\(117\) 2.70866 3.40436i 0.250416 0.314733i
\(118\) −8.70740 + 8.70740i −0.801581 + 0.801581i
\(119\) −1.52898 −0.140162
\(120\) −2.54523 2.91921i −0.232347 0.266486i
\(121\) −2.71780 −0.247073
\(122\) −7.85106 + 7.85106i −0.710801 + 0.710801i
\(123\) 8.67872 0.492260i 0.782534 0.0443856i
\(124\) 1.00000i 0.0898027i
\(125\) 4.09476 10.4035i 0.366247 0.930518i
\(126\) −6.71744 + 0.764491i −0.598437 + 0.0681063i
\(127\) −6.47722 6.47722i −0.574760 0.574760i 0.358695 0.933455i \(-0.383222\pi\)
−0.933455 + 0.358695i \(0.883222\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) −13.4691 12.0231i −1.18589 1.05858i
\(130\) 3.21735 + 0.404246i 0.282180 + 0.0354547i
\(131\) 16.5912i 1.44958i 0.688970 + 0.724790i \(0.258063\pi\)
−0.688970 + 0.724790i \(0.741937\pi\)
\(132\) 0.363282 + 6.40480i 0.0316197 + 0.557466i
\(133\) −0.471718 + 0.471718i −0.0409031 + 0.0409031i
\(134\) 13.3253 1.15113
\(135\) 11.6072 0.522539i 0.998988 0.0449730i
\(136\) 0.678461 0.0581776
\(137\) −11.5131 + 11.5131i −0.983626 + 0.983626i −0.999868 0.0162416i \(-0.994830\pi\)
0.0162416 + 0.999868i \(0.494830\pi\)
\(138\) 0.207305 + 3.65486i 0.0176470 + 0.311123i
\(139\) 1.69987i 0.144181i −0.997398 0.0720907i \(-0.977033\pi\)
0.997398 0.0720907i \(-0.0229671\pi\)
\(140\) −3.09124 3.97967i −0.261258 0.336344i
\(141\) −0.421645 0.376380i −0.0355089 0.0316969i
\(142\) −4.54956 4.54956i −0.381791 0.381791i
\(143\) −3.79788 3.79788i −0.317595 0.317595i
\(144\) 2.98076 0.339231i 0.248397 0.0282692i
\(145\) 0.362907 2.88834i 0.0301378 0.239863i
\(146\) 8.36638i 0.692407i
\(147\) 3.32241 0.188449i 0.274028 0.0155430i
\(148\) −2.24098 + 2.24098i −0.184207 + 0.184207i
\(149\) 11.1620 0.914429 0.457214 0.889357i \(-0.348847\pi\)
0.457214 + 0.889357i \(0.348847\pi\)
\(150\) 4.83316 + 7.18614i 0.394626 + 0.586746i
\(151\) −2.13427 −0.173684 −0.0868422 0.996222i \(-0.527678\pi\)
−0.0868422 + 0.996222i \(0.527678\pi\)
\(152\) 0.209317 0.209317i 0.0169779 0.0169779i
\(153\) −1.26726 + 1.59275i −0.102452 + 0.128766i
\(154\) 8.34679i 0.672603i
\(155\) 0.278761 2.21862i 0.0223906 0.178204i
\(156\) −1.67264 + 1.87380i −0.133918 + 0.150024i
\(157\) −7.87504 7.87504i −0.628497 0.628497i 0.319193 0.947690i \(-0.396588\pi\)
−0.947690 + 0.319193i \(0.896588\pi\)
\(158\) 2.52136 + 2.52136i 0.200589 + 0.200589i
\(159\) 0.461301 0.516778i 0.0365835 0.0409831i
\(160\) 1.37169 + 1.76592i 0.108442 + 0.139608i
\(161\) 4.76305i 0.375381i
\(162\) −4.77121 + 7.63122i −0.374862 + 0.599565i
\(163\) 2.27337 2.27337i 0.178064 0.178064i −0.612447 0.790511i \(-0.709815\pi\)
0.790511 + 0.612447i \(0.209815\pi\)
\(164\) −5.01872 −0.391896
\(165\) 0.979419 14.3111i 0.0762477 1.11412i
\(166\) 2.76439 0.214558
\(167\) −8.76742 + 8.76742i −0.678444 + 0.678444i −0.959648 0.281204i \(-0.909266\pi\)
0.281204 + 0.959648i \(0.409266\pi\)
\(168\) 3.89709 0.221044i 0.300667 0.0170539i
\(169\) 10.8971i 0.838235i
\(170\) −1.50525 0.189128i −0.115447 0.0145055i
\(171\) 0.100419 + 0.882362i 0.00767922 + 0.0674759i
\(172\) 7.37080 + 7.37080i 0.562018 + 0.562018i
\(173\) 6.46161 + 6.46161i 0.491267 + 0.491267i 0.908705 0.417438i \(-0.137072\pi\)
−0.417438 + 0.908705i \(0.637072\pi\)
\(174\) 1.68218 + 1.50159i 0.127526 + 0.113836i
\(175\) 5.74893 + 9.69112i 0.434578 + 0.732580i
\(176\) 3.70376i 0.279181i
\(177\) 1.20783 + 21.2945i 0.0907860 + 1.60059i
\(178\) 7.60852 7.60852i 0.570283 0.570283i
\(179\) −18.6584 −1.39459 −0.697297 0.716782i \(-0.745614\pi\)
−0.697297 + 0.716782i \(0.745614\pi\)
\(180\) −6.70775 0.0782930i −0.499966 0.00583562i
\(181\) 20.5221 1.52539 0.762697 0.646756i \(-0.223875\pi\)
0.762697 + 0.646756i \(0.223875\pi\)
\(182\) −2.31087 + 2.31087i −0.171293 + 0.171293i
\(183\) 1.08904 + 19.2002i 0.0805044 + 1.41932i
\(184\) 2.11353i 0.155811i
\(185\) 5.59658 4.34719i 0.411469 0.319612i
\(186\) 1.29214 + 1.15342i 0.0947440 + 0.0845731i
\(187\) 1.77686 + 1.77686i 0.129937 + 0.129937i
\(188\) 0.230740 + 0.230740i 0.0168285 + 0.0168285i
\(189\) −6.76023 + 9.56163i −0.491734 + 0.695506i
\(190\) −0.522746 + 0.406047i −0.0379240 + 0.0294577i
\(191\) 22.5879i 1.63440i 0.576351 + 0.817202i \(0.304476\pi\)
−0.576351 + 0.817202i \(0.695524\pi\)
\(192\) −1.72927 + 0.0980849i −0.124799 + 0.00707867i
\(193\) 7.24548 7.24548i 0.521541 0.521541i −0.396496 0.918037i \(-0.629774\pi\)
0.918037 + 0.396496i \(0.129774\pi\)
\(194\) −7.16582 −0.514476
\(195\) 4.23330 3.69098i 0.303153 0.264317i
\(196\) −1.92128 −0.137234
\(197\) −3.23816 + 3.23816i −0.230709 + 0.230709i −0.812989 0.582279i \(-0.802161\pi\)
0.582279 + 0.812989i \(0.302161\pi\)
\(198\) 8.69489 + 6.91803i 0.617919 + 0.491643i
\(199\) 17.2659i 1.22394i 0.790879 + 0.611972i \(0.209623\pi\)
−0.790879 + 0.611972i \(0.790377\pi\)
\(200\) −2.55100 4.30028i −0.180383 0.304076i
\(201\) 15.3697 17.2181i 1.08409 1.21447i
\(202\) −1.56502 1.56502i −0.110115 0.110115i
\(203\) 2.07456 + 2.07456i 0.145606 + 0.145606i
\(204\) 0.782553 0.876664i 0.0547897 0.0613788i
\(205\) 11.1346 + 1.39902i 0.777677 + 0.0977119i
\(206\) 6.43350i 0.448243i
\(207\) 4.96169 + 3.94774i 0.344861 + 0.274387i
\(208\) 1.02541 1.02541i 0.0710996 0.0710996i
\(209\) 1.09638 0.0758384
\(210\) −8.70779 0.595941i −0.600895 0.0411238i
\(211\) −21.7612 −1.49810 −0.749050 0.662513i \(-0.769490\pi\)
−0.749050 + 0.662513i \(0.769490\pi\)
\(212\) −0.282801 + 0.282801i −0.0194228 + 0.0194228i
\(213\) −11.1262 + 0.631083i −0.762357 + 0.0432411i
\(214\) 15.6629i 1.07070i
\(215\) −14.2983 18.4077i −0.975138 1.25540i
\(216\) 2.99974 4.24282i 0.204107 0.288687i
\(217\) 1.59354 + 1.59354i 0.108176 + 0.108176i
\(218\) 7.06726 + 7.06726i 0.478655 + 0.478655i
\(219\) −10.8105 9.64998i −0.730506 0.652085i
\(220\) −1.03246 + 8.21724i −0.0696085 + 0.554006i
\(221\) 0.983873i 0.0661825i
\(222\) 0.310853 + 5.48044i 0.0208631 + 0.367823i
\(223\) −5.37150 + 5.37150i −0.359702 + 0.359702i −0.863703 0.504001i \(-0.831861\pi\)
0.504001 + 0.863703i \(0.331861\pi\)
\(224\) −2.25360 −0.150575
\(225\) 14.8601 + 2.04356i 0.990676 + 0.136237i
\(226\) 5.04389 0.335515
\(227\) −12.5296 + 12.5296i −0.831620 + 0.831620i −0.987738 0.156118i \(-0.950102\pi\)
0.156118 + 0.987738i \(0.450102\pi\)
\(228\) −0.0290350 0.511898i −0.00192289 0.0339013i
\(229\) 7.68865i 0.508081i 0.967194 + 0.254040i \(0.0817596\pi\)
−0.967194 + 0.254040i \(0.918240\pi\)
\(230\) −0.589168 + 4.68912i −0.0388486 + 0.309192i
\(231\) 10.7852 + 9.62738i 0.709613 + 0.633435i
\(232\) −0.920553 0.920553i −0.0604373 0.0604373i
\(233\) 6.41781 + 6.41781i 0.420445 + 0.420445i 0.885357 0.464912i \(-0.153914\pi\)
−0.464912 + 0.885357i \(0.653914\pi\)
\(234\) 0.491937 + 4.32256i 0.0321589 + 0.282575i
\(235\) −0.447604 0.576247i −0.0291985 0.0375902i
\(236\) 12.3141i 0.801581i
\(237\) 6.16614 0.349746i 0.400534 0.0227184i
\(238\) 1.08115 1.08115i 0.0700808 0.0700808i
\(239\) −23.1583 −1.49799 −0.748994 0.662577i \(-0.769463\pi\)
−0.748994 + 0.662577i \(0.769463\pi\)
\(240\) 3.86395 + 0.264439i 0.249417 + 0.0170695i
\(241\) −24.6719 −1.58926 −0.794628 0.607097i \(-0.792334\pi\)
−0.794628 + 0.607097i \(0.792334\pi\)
\(242\) 1.92178 1.92178i 0.123537 0.123537i
\(243\) 4.35735 + 14.9671i 0.279524 + 0.960139i
\(244\) 11.1031i 0.710801i
\(245\) 4.26260 + 0.535577i 0.272327 + 0.0342168i
\(246\) −5.78870 + 6.48486i −0.369074 + 0.413460i
\(247\) 0.303542 + 0.303542i 0.0193139 + 0.0193139i
\(248\) −0.707107 0.707107i −0.0449013 0.0449013i
\(249\) 3.18851 3.57196i 0.202063 0.226364i
\(250\) 4.46095 + 10.2518i 0.282136 + 0.648382i
\(251\) 18.6979i 1.18020i 0.807330 + 0.590100i \(0.200912\pi\)
−0.807330 + 0.590100i \(0.799088\pi\)
\(252\) 4.20937 5.29053i 0.265166 0.333272i
\(253\) 5.53522 5.53522i 0.347997 0.347997i
\(254\) 9.16017 0.574760
\(255\) −1.98057 + 1.72684i −0.124028 + 0.108139i
\(256\) 1.00000 0.0625000
\(257\) 7.29634 7.29634i 0.455133 0.455133i −0.441921 0.897054i \(-0.645703\pi\)
0.897054 + 0.441921i \(0.145703\pi\)
\(258\) 18.0257 1.02242i 1.12223 0.0636534i
\(259\) 7.14216i 0.443792i
\(260\) −2.56085 + 1.98916i −0.158817 + 0.123363i
\(261\) 3.88053 0.441631i 0.240199 0.0273362i
\(262\) −11.7317 11.7317i −0.724790 0.724790i
\(263\) 11.3678 + 11.3678i 0.700968 + 0.700968i 0.964618 0.263650i \(-0.0849264\pi\)
−0.263650 + 0.964618i \(0.584926\pi\)
\(264\) −4.78576 4.27200i −0.294543 0.262923i
\(265\) 0.706262 0.548595i 0.0433854 0.0336999i
\(266\) 0.667110i 0.0409031i
\(267\) −1.05540 18.6071i −0.0645894 1.13874i
\(268\) −9.42240 + 9.42240i −0.575565 + 0.575565i
\(269\) −5.71888 −0.348687 −0.174343 0.984685i \(-0.555780\pi\)
−0.174343 + 0.984685i \(0.555780\pi\)
\(270\) −7.83804 + 8.57702i −0.477008 + 0.521981i
\(271\) −14.6399 −0.889311 −0.444656 0.895702i \(-0.646674\pi\)
−0.444656 + 0.895702i \(0.646674\pi\)
\(272\) −0.479745 + 0.479745i −0.0290888 + 0.0290888i
\(273\) 0.320548 + 5.65138i 0.0194005 + 0.342037i
\(274\) 16.2819i 0.983626i
\(275\) 4.58129 17.9432i 0.276262 1.08201i
\(276\) −2.73097 2.43779i −0.164385 0.146738i
\(277\) −0.510362 0.510362i −0.0306647 0.0306647i 0.691608 0.722273i \(-0.256903\pi\)
−0.722273 + 0.691608i \(0.756903\pi\)
\(278\) 1.20199 + 1.20199i 0.0720907 + 0.0720907i
\(279\) 2.98076 0.339231i 0.178453 0.0203092i
\(280\) 4.99989 + 0.628216i 0.298801 + 0.0375431i
\(281\) 29.3698i 1.75206i 0.482260 + 0.876028i \(0.339816\pi\)
−0.482260 + 0.876028i \(0.660184\pi\)
\(282\) 0.564289 0.0320067i 0.0336029 0.00190597i
\(283\) −1.77470 + 1.77470i −0.105495 + 0.105495i −0.757884 0.652389i \(-0.773767\pi\)
0.652389 + 0.757884i \(0.273767\pi\)
\(284\) 6.43406 0.381791
\(285\) −0.0782792 + 1.14380i −0.00463686 + 0.0677530i
\(286\) 5.37102 0.317595
\(287\) −7.99751 + 7.99751i −0.472078 + 0.472078i
\(288\) −1.86784 + 2.34759i −0.110064 + 0.138333i
\(289\) 16.5397i 0.972923i
\(290\) 1.78575 + 2.29898i 0.104863 + 0.135001i
\(291\) −8.26522 + 9.25921i −0.484516 + 0.542785i
\(292\) 5.91592 + 5.91592i 0.346203 + 0.346203i
\(293\) 14.2801 + 14.2801i 0.834255 + 0.834255i 0.988096 0.153841i \(-0.0491644\pi\)
−0.153841 + 0.988096i \(0.549164\pi\)
\(294\) −2.21605 + 2.48256i −0.129243 + 0.144786i
\(295\) −3.43269 + 27.3204i −0.199859 + 1.59066i
\(296\) 3.16922i 0.184207i
\(297\) 18.9679 3.25556i 1.10063 0.188907i
\(298\) −7.89274 + 7.89274i −0.457214 + 0.457214i
\(299\) 3.06494 0.177250
\(300\) −8.49893 1.66381i −0.490686 0.0960600i
\(301\) 23.4913 1.35401
\(302\) 1.50916 1.50916i 0.0868422 0.0868422i
\(303\) −3.82735 + 0.217089i −0.219876 + 0.0124714i
\(304\) 0.296019i 0.0169779i
\(305\) −3.09510 + 24.6335i −0.177225 + 1.41051i
\(306\) −0.230155 2.02233i −0.0131571 0.115609i
\(307\) 0.577798 + 0.577798i 0.0329767 + 0.0329767i 0.723403 0.690426i \(-0.242577\pi\)
−0.690426 + 0.723403i \(0.742577\pi\)
\(308\) −5.90207 5.90207i −0.336302 0.336302i
\(309\) −8.31296 7.42055i −0.472908 0.422140i
\(310\) 1.37169 + 1.76592i 0.0779068 + 0.100297i
\(311\) 29.9949i 1.70086i −0.526091 0.850429i \(-0.676343\pi\)
0.526091 0.850429i \(-0.323657\pi\)
\(312\) −0.142238 2.50771i −0.00805265 0.141971i
\(313\) −6.71881 + 6.71881i −0.379769 + 0.379769i −0.871019 0.491250i \(-0.836540\pi\)
0.491250 + 0.871019i \(0.336540\pi\)
\(314\) 11.1370 0.628497
\(315\) −10.8138 + 10.5643i −0.609289 + 0.595230i
\(316\) −3.56575 −0.200589
\(317\) 17.6706 17.6706i 0.992478 0.992478i −0.00749364 0.999972i \(-0.502385\pi\)
0.999972 + 0.00749364i \(0.00238532\pi\)
\(318\) 0.0392281 + 0.691606i 0.00219980 + 0.0387833i
\(319\) 4.82177i 0.269967i
\(320\) −2.21862 0.278761i −0.124025 0.0155832i
\(321\) −20.2387 18.0660i −1.12961 1.00835i
\(322\) −3.36798 3.36798i −0.187690 0.187690i
\(323\) −0.142014 0.142014i −0.00790185 0.00790185i
\(324\) −2.02233 8.76985i −0.112352 0.487214i
\(325\) 6.23607 3.69934i 0.345915 0.205202i
\(326\) 3.21503i 0.178064i
\(327\) 17.2834 0.980320i 0.955774 0.0542118i
\(328\) 3.54877 3.54877i 0.195948 0.195948i
\(329\) 0.735386 0.0405431
\(330\) 9.42693 + 10.8120i 0.518935 + 0.595183i
\(331\) 15.4781 0.850755 0.425377 0.905016i \(-0.360141\pi\)
0.425377 + 0.905016i \(0.360141\pi\)
\(332\) −1.95472 + 1.95472i −0.107279 + 0.107279i
\(333\) 7.44002 + 5.91961i 0.407711 + 0.324392i
\(334\) 12.3990i 0.678444i
\(335\) 23.5314 18.2782i 1.28566 0.998643i
\(336\) −2.59936 + 2.91196i −0.141806 + 0.158860i
\(337\) −18.1620 18.1620i −0.989349 0.989349i 0.0105948 0.999944i \(-0.496627\pi\)
−0.999944 + 0.0105948i \(0.996627\pi\)
\(338\) −7.70538 7.70538i −0.419117 0.419117i
\(339\) 5.81774 6.51740i 0.315976 0.353976i
\(340\) 1.19811 0.930639i 0.0649765 0.0504710i
\(341\) 3.70376i 0.200570i
\(342\) −0.694931 0.552918i −0.0375776 0.0298984i
\(343\) −14.2164 + 14.2164i −0.767613 + 0.767613i
\(344\) −10.4239 −0.562018
\(345\) 5.37942 + 6.16983i 0.289618 + 0.332172i
\(346\) −9.13810 −0.491267
\(347\) 12.9136 12.9136i 0.693239 0.693239i −0.269704 0.962943i \(-0.586926\pi\)
0.962943 + 0.269704i \(0.0869260\pi\)
\(348\) −2.25127 + 0.127693i −0.120681 + 0.00684505i
\(349\) 30.6701i 1.64173i −0.571119 0.820867i \(-0.693490\pi\)
0.571119 0.820867i \(-0.306510\pi\)
\(350\) −10.9178 2.78755i −0.583579 0.149001i
\(351\) 6.15274 + 4.35009i 0.328409 + 0.232191i
\(352\) 2.61895 + 2.61895i 0.139591 + 0.139591i
\(353\) −11.6278 11.6278i −0.618886 0.618886i 0.326359 0.945246i \(-0.394178\pi\)
−0.945246 + 0.326359i \(0.894178\pi\)
\(354\) −15.9115 14.2034i −0.845688 0.754902i
\(355\) −14.2748 1.79356i −0.757625 0.0951924i
\(356\) 10.7601i 0.570283i
\(357\) −0.149970 2.64402i −0.00793725 0.139937i
\(358\) 13.1935 13.1935i 0.697297 0.697297i
\(359\) 14.2862 0.753998 0.376999 0.926214i \(-0.376956\pi\)
0.376999 + 0.926214i \(0.376956\pi\)
\(360\) 4.79845 4.68773i 0.252901 0.247065i
\(361\) 18.9124 0.995388
\(362\) −14.5113 + 14.5113i −0.762697 + 0.762697i
\(363\) −0.266575 4.69982i −0.0139916 0.246677i
\(364\) 3.26807i 0.171293i
\(365\) −11.4761 14.7743i −0.600686 0.773324i
\(366\) −14.3467 12.8065i −0.749913 0.669408i
\(367\) 4.98013 + 4.98013i 0.259961 + 0.259961i 0.825038 0.565077i \(-0.191154\pi\)
−0.565077 + 0.825038i \(0.691154\pi\)
\(368\) 1.49449 + 1.49449i 0.0779057 + 0.0779057i
\(369\) 1.70250 + 14.9596i 0.0886288 + 0.778765i
\(370\) −0.883454 + 7.03131i −0.0459286 + 0.365540i
\(371\) 0.901307i 0.0467935i
\(372\) −1.72927 + 0.0980849i −0.0896585 + 0.00508546i
\(373\) 16.3054 16.3054i 0.844264 0.844264i −0.145146 0.989410i \(-0.546365\pi\)
0.989410 + 0.145146i \(0.0463653\pi\)
\(374\) −2.51285 −0.129937
\(375\) 18.3921 + 6.06053i 0.949765 + 0.312964i
\(376\) −0.326316 −0.0168285
\(377\) 1.33494 1.33494i 0.0687531 0.0687531i
\(378\) −1.98089 11.5413i −0.101886 0.593620i
\(379\) 17.5558i 0.901780i −0.892579 0.450890i \(-0.851107\pi\)
0.892579 0.450890i \(-0.148893\pi\)
\(380\) 0.0825186 0.656756i 0.00423311 0.0336909i
\(381\) 10.5655 11.8362i 0.541289 0.606386i
\(382\) −15.9721 15.9721i −0.817202 0.817202i
\(383\) 6.79735 + 6.79735i 0.347328 + 0.347328i 0.859113 0.511785i \(-0.171016\pi\)
−0.511785 + 0.859113i \(0.671016\pi\)
\(384\) 1.15342 1.29214i 0.0588604 0.0659390i
\(385\) 11.4492 + 14.7397i 0.583506 + 0.751207i
\(386\) 10.2467i 0.521541i
\(387\) 19.4702 24.4710i 0.989724 1.24393i
\(388\) 5.06700 5.06700i 0.257238 0.257238i
\(389\) −9.51345 −0.482351 −0.241175 0.970482i \(-0.577533\pi\)
−0.241175 + 0.970482i \(0.577533\pi\)
\(390\) −0.383478 + 5.60331i −0.0194182 + 0.283735i
\(391\) −1.43395 −0.0725178
\(392\) 1.35855 1.35855i 0.0686172 0.0686172i
\(393\) −28.6907 + 1.62735i −1.44725 + 0.0820887i
\(394\) 4.57945i 0.230709i
\(395\) 7.91105 + 0.993990i 0.398048 + 0.0500131i
\(396\) −11.0400 + 1.25643i −0.554781 + 0.0631379i
\(397\) 10.8764 + 10.8764i 0.545869 + 0.545869i 0.925243 0.379374i \(-0.123861\pi\)
−0.379374 + 0.925243i \(0.623861\pi\)
\(398\) −12.2088 12.2088i −0.611972 0.611972i
\(399\) −0.861997 0.769460i −0.0431538 0.0385212i
\(400\) 4.84458 + 1.23693i 0.242229 + 0.0618465i
\(401\) 8.00715i 0.399858i 0.979810 + 0.199929i \(0.0640711\pi\)
−0.979810 + 0.199929i \(0.935929\pi\)
\(402\) 1.30701 + 23.0430i 0.0651877 + 1.14928i
\(403\) 1.02541 1.02541i 0.0510795 0.0510795i
\(404\) 2.21327 0.110115
\(405\) 2.04210 + 20.0207i 0.101473 + 0.994838i
\(406\) −2.93387 −0.145606
\(407\) 8.30003 8.30003i 0.411417 0.411417i
\(408\) 0.0665468 + 1.17324i 0.00329456 + 0.0580842i
\(409\) 4.41491i 0.218303i −0.994025 0.109152i \(-0.965187\pi\)
0.994025 0.109152i \(-0.0348134\pi\)
\(410\) −8.86264 + 6.88413i −0.437695 + 0.339983i
\(411\) −21.0384 18.7799i −1.03775 0.926346i
\(412\) 4.54917 + 4.54917i 0.224122 + 0.224122i
\(413\) −19.6230 19.6230i −0.965585 0.965585i
\(414\) −6.29992 + 0.716973i −0.309624 + 0.0352373i
\(415\) 4.88168 3.79188i 0.239632 0.186136i
\(416\) 1.45015i 0.0710996i
\(417\) 2.93954 0.166732i 0.143950 0.00816490i
\(418\) −0.775260 + 0.775260i −0.0379192 + 0.0379192i
\(419\) −2.07061 −0.101156 −0.0505780 0.998720i \(-0.516106\pi\)
−0.0505780 + 0.998720i \(0.516106\pi\)
\(420\) 6.57873 5.73595i 0.321009 0.279885i
\(421\) −28.7331 −1.40036 −0.700182 0.713964i \(-0.746898\pi\)
−0.700182 + 0.713964i \(0.746898\pi\)
\(422\) 15.3875 15.3875i 0.749050 0.749050i
\(423\) 0.609507 0.766055i 0.0296352 0.0372469i
\(424\) 0.399941i 0.0194228i
\(425\) −2.91757 + 1.73075i −0.141523 + 0.0839539i
\(426\) 7.42119 8.31367i 0.359558 0.402799i
\(427\) −17.6931 17.6931i −0.856232 0.856232i
\(428\) 11.0754 + 11.0754i 0.535348 + 0.535348i
\(429\) 6.19505 6.94008i 0.299100 0.335070i
\(430\) 23.1267 + 2.90577i 1.11527 + 0.140129i
\(431\) 20.1008i 0.968224i −0.875006 0.484112i \(-0.839143\pi\)
0.875006 0.484112i \(-0.160857\pi\)
\(432\) 0.878989 + 5.12127i 0.0422904 + 0.246397i
\(433\) 17.4620 17.4620i 0.839169 0.839169i −0.149581 0.988750i \(-0.547792\pi\)
0.988750 + 0.149581i \(0.0477924\pi\)
\(434\) −2.25360 −0.108176
\(435\) 5.03031 + 0.344263i 0.241185 + 0.0165061i
\(436\) −9.99461 −0.478655
\(437\) −0.442398 + 0.442398i −0.0211628 + 0.0211628i
\(438\) 14.4677 0.820615i 0.691295 0.0392105i
\(439\) 36.4397i 1.73917i 0.493781 + 0.869587i \(0.335615\pi\)
−0.493781 + 0.869587i \(0.664385\pi\)
\(440\) −5.08041 6.54053i −0.242199 0.311807i
\(441\) 0.651757 + 5.72687i 0.0310361 + 0.272708i
\(442\) −0.695704 0.695704i −0.0330912 0.0330912i
\(443\) 5.18559 + 5.18559i 0.246375 + 0.246375i 0.819481 0.573106i \(-0.194262\pi\)
−0.573106 + 0.819481i \(0.694262\pi\)
\(444\) −4.09506 3.65545i −0.194343 0.173480i
\(445\) 2.99949 23.8726i 0.142189 1.13167i
\(446\) 7.59645i 0.359702i
\(447\) 1.09483 + 19.3022i 0.0517835 + 0.912961i
\(448\) 1.59354 1.59354i 0.0752875 0.0752875i
\(449\) 38.7024 1.82648 0.913240 0.407423i \(-0.133573\pi\)
0.913240 + 0.407423i \(0.133573\pi\)
\(450\) −11.9527 + 9.06269i −0.563457 + 0.427219i
\(451\) 18.5881 0.875279
\(452\) −3.56657 + 3.56657i −0.167757 + 0.167757i
\(453\) −0.209340 3.69073i −0.00983563 0.173406i
\(454\) 17.7196i 0.831620i
\(455\) −0.911009 + 7.25062i −0.0427088 + 0.339914i
\(456\) 0.382497 + 0.341436i 0.0179121 + 0.0159892i
\(457\) −3.48182 3.48182i −0.162873 0.162873i 0.620965 0.783838i \(-0.286741\pi\)
−0.783838 + 0.620965i \(0.786741\pi\)
\(458\) −5.43670 5.43670i −0.254040 0.254040i
\(459\) −2.87859 2.03521i −0.134361 0.0949955i
\(460\) −2.89911 3.73232i −0.135172 0.174020i
\(461\) 13.8727i 0.646117i −0.946379 0.323059i \(-0.895289\pi\)
0.946379 0.323059i \(-0.104711\pi\)
\(462\) −14.4339 + 0.818694i −0.671524 + 0.0380891i
\(463\) −2.51704 + 2.51704i −0.116977 + 0.116977i −0.763172 0.646195i \(-0.776359\pi\)
0.646195 + 0.763172i \(0.276359\pi\)
\(464\) 1.30186 0.0604373
\(465\) 3.86395 + 0.264439i 0.179186 + 0.0122631i
\(466\) −9.07616 −0.420445
\(467\) −30.0390 + 30.0390i −1.39004 + 1.39004i −0.564836 + 0.825204i \(0.691060\pi\)
−0.825204 + 0.564836i \(0.808940\pi\)
\(468\) −3.40436 2.70866i −0.157367 0.125208i
\(469\) 30.0299i 1.38665i
\(470\) 0.723972 + 0.0909641i 0.0333944 + 0.00419586i
\(471\) 12.8457 14.3905i 0.591897 0.663079i
\(472\) 8.70740 + 8.70740i 0.400791 + 0.400791i
\(473\) −27.2996 27.2996i −1.25524 1.25524i
\(474\) −4.11281 + 4.60743i −0.188908 + 0.211626i
\(475\) −0.366155 + 1.43409i −0.0168004 + 0.0658006i
\(476\) 1.52898i 0.0700808i
\(477\) 0.938896 + 0.747026i 0.0429891 + 0.0342040i
\(478\) 16.3754 16.3754i 0.748994 0.748994i
\(479\) −24.4251 −1.11601 −0.558005 0.829837i \(-0.688433\pi\)
−0.558005 + 0.829837i \(0.688433\pi\)
\(480\) −2.91921 + 2.54523i −0.133243 + 0.116174i
\(481\) 4.59586 0.209553
\(482\) 17.4457 17.4457i 0.794628 0.794628i
\(483\) −8.23660 + 0.467183i −0.374778 + 0.0212576i
\(484\) 2.71780i 0.123537i
\(485\) −12.6542 + 9.82929i −0.574600 + 0.446325i
\(486\) −13.6644 7.50222i −0.619831 0.340307i
\(487\) 16.3280 + 16.3280i 0.739891 + 0.739891i 0.972557 0.232666i \(-0.0747448\pi\)
−0.232666 + 0.972557i \(0.574745\pi\)
\(488\) 7.85106 + 7.85106i 0.355401 + 0.355401i
\(489\) 4.15426 + 3.70829i 0.187862 + 0.167695i
\(490\) −3.39282 + 2.63540i −0.153272 + 0.119055i
\(491\) 12.7037i 0.573309i −0.958034 0.286655i \(-0.907457\pi\)
0.958034 0.286655i \(-0.0925432\pi\)
\(492\) −0.492260 8.67872i −0.0221928 0.391267i
\(493\) −0.624560 + 0.624560i −0.0281288 + 0.0281288i
\(494\) −0.429274 −0.0193139
\(495\) 24.8439 + 0.289978i 1.11665 + 0.0130336i
\(496\) 1.00000 0.0449013
\(497\) 10.2529 10.2529i 0.459906 0.459906i
\(498\) 0.271144 + 4.78037i 0.0121503 + 0.214214i
\(499\) 10.7503i 0.481248i 0.970618 + 0.240624i \(0.0773521\pi\)
−0.970618 + 0.240624i \(0.922648\pi\)
\(500\) −10.4035 4.09476i −0.465259 0.183123i
\(501\) −16.0212 14.3013i −0.715775 0.638935i
\(502\) −13.2214 13.2214i −0.590100 0.590100i
\(503\) −19.9599 19.9599i −0.889968 0.889968i 0.104551 0.994520i \(-0.466659\pi\)
−0.994520 + 0.104551i \(0.966659\pi\)
\(504\) 0.764491 + 6.71744i 0.0340531 + 0.299219i
\(505\) −4.91042 0.616974i −0.218511 0.0274550i
\(506\) 7.82799i 0.347997i
\(507\) −18.8440 + 1.06884i −0.836890 + 0.0474687i
\(508\) −6.47722 + 6.47722i −0.287380 + 0.287380i
\(509\) −13.5548 −0.600804 −0.300402 0.953813i \(-0.597121\pi\)
−0.300402 + 0.953813i \(0.597121\pi\)
\(510\) 0.179412 2.62154i 0.00794449 0.116084i
\(511\) 18.8545 0.834073
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −1.51599 + 0.260198i −0.0669328 + 0.0114880i
\(514\) 10.3186i 0.455133i
\(515\) −8.82478 11.3610i −0.388866 0.500627i
\(516\) −12.0231 + 13.4691i −0.529289 + 0.592943i
\(517\) −0.854605 0.854605i −0.0375855 0.0375855i
\(518\) −5.05027 5.05027i −0.221896 0.221896i
\(519\) −10.5401 + 11.8077i −0.462659 + 0.518299i
\(520\) 0.404246 3.21735i 0.0177274 0.141090i
\(521\) 25.4930i 1.11687i −0.829548 0.558435i \(-0.811402\pi\)
0.829548 0.558435i \(-0.188598\pi\)
\(522\) −2.43167 + 3.05623i −0.106431 + 0.133767i
\(523\) −11.2546 + 11.2546i −0.492128 + 0.492128i −0.908976 0.416848i \(-0.863135\pi\)
0.416848 + 0.908976i \(0.363135\pi\)
\(524\) 16.5912 0.724790
\(525\) −16.1947 + 10.8920i −0.706794 + 0.475366i
\(526\) −16.0765 −0.700968
\(527\) −0.479745 + 0.479745i −0.0208980 + 0.0208980i
\(528\) 6.40480 0.363282i 0.278733 0.0158098i
\(529\) 18.5330i 0.805783i
\(530\) −0.111488 + 0.887318i −0.00484272 + 0.0385426i
\(531\) −36.7054 + 4.17733i −1.59288 + 0.181281i
\(532\) 0.471718 + 0.471718i 0.0204516 + 0.0204516i
\(533\) 5.14626 + 5.14626i 0.222909 + 0.222909i
\(534\) 13.9035 + 12.4109i 0.601662 + 0.537073i
\(535\) −21.4847 27.6595i −0.928865 1.19582i
\(536\) 13.3253i 0.575565i
\(537\) −1.83011 32.2654i −0.0789749 1.39236i
\(538\) 4.04386 4.04386i 0.174343 0.174343i
\(539\) 7.11595 0.306506
\(540\) −0.522539 11.6072i −0.0224865 0.499494i
\(541\) 33.4322 1.43736 0.718681 0.695340i \(-0.244746\pi\)
0.718681 + 0.695340i \(0.244746\pi\)
\(542\) 10.3520 10.3520i 0.444656 0.444656i
\(543\) 2.01291 + 35.4883i 0.0863821 + 1.52295i
\(544\) 0.678461i 0.0290888i
\(545\) 22.1743 + 2.78610i 0.949842 + 0.119344i
\(546\) −4.22279 3.76947i −0.180719 0.161318i
\(547\) 10.5375 + 10.5375i 0.450553 + 0.450553i 0.895538 0.444985i \(-0.146791\pi\)
−0.444985 + 0.895538i \(0.646791\pi\)
\(548\) 11.5131 + 11.5131i 0.491813 + 0.491813i
\(549\) −33.0956 + 3.76650i −1.41248 + 0.160750i
\(550\) 9.44827 + 15.9272i 0.402876 + 0.679138i
\(551\) 0.385376i 0.0164176i
\(552\) 3.65486 0.207305i 0.155561 0.00882349i
\(553\) −5.68215 + 5.68215i −0.241630 + 0.241630i
\(554\) 0.721760 0.0306647
\(555\) 8.06641 + 9.25162i 0.342400 + 0.392709i
\(556\) −1.69987 −0.0720907
\(557\) 0.950084 0.950084i 0.0402563 0.0402563i −0.686692 0.726948i \(-0.740938\pi\)
0.726948 + 0.686692i \(0.240938\pi\)
\(558\) −1.86784 + 2.34759i −0.0790721 + 0.0993813i
\(559\) 15.1162i 0.639348i
\(560\) −3.97967 + 3.09124i −0.168172 + 0.130629i
\(561\) −2.89838 + 3.24695i −0.122370 + 0.137086i
\(562\) −20.7676 20.7676i −0.876028 0.876028i
\(563\) −1.08303 1.08303i −0.0456442 0.0456442i 0.683916 0.729560i \(-0.260275\pi\)
−0.729560 + 0.683916i \(0.760275\pi\)
\(564\) −0.376380 + 0.421645i −0.0158485 + 0.0177544i
\(565\) 8.90710 6.91866i 0.374725 0.291070i
\(566\) 2.50981i 0.105495i
\(567\) −17.1977 10.7524i −0.722237 0.451559i
\(568\) −4.54956 + 4.54956i −0.190895 + 0.190895i
\(569\) 22.3470 0.936835 0.468418 0.883507i \(-0.344824\pi\)
0.468418 + 0.883507i \(0.344824\pi\)
\(570\) −0.753439 0.864142i −0.0315581 0.0361949i
\(571\) −3.60507 −0.150867 −0.0754337 0.997151i \(-0.524034\pi\)
−0.0754337 + 0.997151i \(0.524034\pi\)
\(572\) −3.79788 + 3.79788i −0.158797 + 0.158797i
\(573\) −39.0606 + 2.21553i −1.63178 + 0.0925552i
\(574\) 11.3102i 0.472078i
\(575\) 5.39160 + 9.08876i 0.224845 + 0.379028i
\(576\) −0.339231 2.98076i −0.0141346 0.124198i
\(577\) −23.8009 23.8009i −0.990846 0.990846i 0.00911207 0.999958i \(-0.497099\pi\)
−0.999958 + 0.00911207i \(0.997099\pi\)
\(578\) −11.6953 11.6953i −0.486461 0.486461i
\(579\) 13.2401 + 11.8187i 0.550239 + 0.491170i
\(580\) −2.88834 0.362907i −0.119932 0.0150689i
\(581\) 6.22983i 0.258457i
\(582\) −0.702859 12.3916i −0.0291344 0.513650i
\(583\) 1.04743 1.04743i 0.0433799 0.0433799i
\(584\) −8.36638 −0.346203
\(585\) 6.79793 + 6.95850i 0.281060 + 0.287698i
\(586\) −20.1952 −0.834255
\(587\) −7.26273 + 7.26273i −0.299765 + 0.299765i −0.840922 0.541157i \(-0.817987\pi\)
0.541157 + 0.840922i \(0.317987\pi\)
\(588\) −0.188449 3.32241i −0.00777149 0.137014i
\(589\) 0.296019i 0.0121973i
\(590\) −16.8912 21.7457i −0.695399 0.895258i
\(591\) −5.91727 5.28204i −0.243404 0.217274i
\(592\) 2.24098 + 2.24098i 0.0921036 + 0.0921036i
\(593\) −17.6248 17.6248i −0.723763 0.723763i 0.245606 0.969370i \(-0.421013\pi\)
−0.969370 + 0.245606i \(0.921013\pi\)
\(594\) −11.1103 + 15.7144i −0.455862 + 0.644769i
\(595\) 0.426220 3.39224i 0.0174733 0.139068i
\(596\) 11.1620i 0.457214i
\(597\) −29.8573 + 1.69352i −1.22198 + 0.0693111i
\(598\) −2.16724 + 2.16724i −0.0886250 + 0.0886250i
\(599\) 34.3921 1.40522 0.702612 0.711573i \(-0.252017\pi\)
0.702612 + 0.711573i \(0.252017\pi\)
\(600\) 7.18614 4.83316i 0.293373 0.197313i
\(601\) −31.0073 −1.26482 −0.632408 0.774636i \(-0.717933\pi\)
−0.632408 + 0.774636i \(0.717933\pi\)
\(602\) −16.6108 + 16.6108i −0.677007 + 0.677007i
\(603\) 31.2823 + 24.8895i 1.27391 + 1.01358i
\(604\) 2.13427i 0.0868422i
\(605\) 0.757617 6.02978i 0.0308015 0.245146i
\(606\) 2.55284 2.85985i 0.103702 0.116174i
\(607\) 0.212009 + 0.212009i 0.00860518 + 0.00860518i 0.711396 0.702791i \(-0.248063\pi\)
−0.702791 + 0.711396i \(0.748063\pi\)
\(608\) −0.209317 0.209317i −0.00848894 0.00848894i
\(609\) −3.38400 + 3.79096i −0.137126 + 0.153617i
\(610\) −15.2300 19.6071i −0.616644 0.793868i
\(611\) 0.473208i 0.0191440i
\(612\) 1.59275 + 1.26726i 0.0643830 + 0.0512259i
\(613\) 23.9172 23.9172i 0.966008 0.966008i −0.0334327 0.999441i \(-0.510644\pi\)
0.999441 + 0.0334327i \(0.0106439\pi\)
\(614\) −0.817129 −0.0329767
\(615\) −1.32715 + 19.3920i −0.0535157 + 0.781963i
\(616\) 8.34679 0.336302
\(617\) −7.85266 + 7.85266i −0.316136 + 0.316136i −0.847281 0.531145i \(-0.821762\pi\)
0.531145 + 0.847281i \(0.321762\pi\)
\(618\) 11.1253 0.631029i 0.447524 0.0253837i
\(619\) 7.62713i 0.306560i −0.988183 0.153280i \(-0.951016\pi\)
0.988183 0.153280i \(-0.0489837\pi\)
\(620\) −2.21862 0.278761i −0.0891021 0.0111953i
\(621\) −6.34004 + 8.96732i −0.254417 + 0.359846i
\(622\) 21.2096 + 21.2096i 0.850429 + 0.850429i
\(623\) 17.1466 + 17.1466i 0.686963 + 0.686963i
\(624\) 1.87380 + 1.67264i 0.0750119 + 0.0669592i
\(625\) 21.9400 + 11.9848i 0.877600 + 0.479393i
\(626\) 9.50183i 0.379769i
\(627\) 0.107539 + 1.89594i 0.00429468 + 0.0757167i
\(628\) −7.87504 + 7.87504i −0.314248 + 0.314248i
\(629\) −2.15019 −0.0857338
\(630\) 0.176441 15.1166i 0.00702959 0.602259i
\(631\) 44.1114 1.75605 0.878024 0.478616i \(-0.158861\pi\)
0.878024 + 0.478616i \(0.158861\pi\)
\(632\) 2.52136 2.52136i 0.100294 0.100294i
\(633\) −2.13444 37.6310i −0.0848364 1.49570i
\(634\) 24.9900i 0.992478i
\(635\) 16.1761 12.5649i 0.641929 0.498623i
\(636\) −0.516778 0.461301i −0.0204916 0.0182918i
\(637\) 1.97011 + 1.97011i 0.0780585 + 0.0780585i
\(638\) 3.40950 + 3.40950i 0.134984 + 0.134984i
\(639\) −2.18263 19.1784i −0.0863435 0.758684i
\(640\) 1.76592 1.37169i 0.0698040 0.0542208i
\(641\) 34.4732i 1.36161i 0.732464 + 0.680805i \(0.238370\pi\)
−0.732464 + 0.680805i \(0.761630\pi\)
\(642\) 27.0855 1.53630i 1.06898 0.0606328i
\(643\) 25.0469 25.0469i 0.987752 0.987752i −0.0121735 0.999926i \(-0.503875\pi\)
0.999926 + 0.0121735i \(0.00387503\pi\)
\(644\) 4.76305 0.187690
\(645\) 30.4295 26.5312i 1.19816 1.04467i
\(646\) 0.200838 0.00790185
\(647\) 3.66605 3.66605i 0.144127 0.144127i −0.631361 0.775489i \(-0.717504\pi\)
0.775489 + 0.631361i \(0.217504\pi\)
\(648\) 7.63122 + 4.77121i 0.299783 + 0.187431i
\(649\) 45.6085i 1.79029i
\(650\) −1.79374 + 7.02539i −0.0703562 + 0.275559i
\(651\) −2.59936 + 2.91196i −0.101877 + 0.114129i
\(652\) −2.27337 2.27337i −0.0890320 0.0890320i
\(653\) 32.0216 + 32.0216i 1.25310 + 1.25310i 0.954322 + 0.298780i \(0.0965796\pi\)
0.298780 + 0.954322i \(0.403420\pi\)
\(654\) −11.5280 + 12.9144i −0.450781 + 0.504993i
\(655\) −36.8096 4.62497i −1.43827 0.180713i
\(656\) 5.01872i 0.195948i
\(657\) 15.6271 19.6408i 0.609670 0.766261i
\(658\) −0.519996 + 0.519996i −0.0202716 + 0.0202716i
\(659\) −6.39570 −0.249141 −0.124571 0.992211i \(-0.539755\pi\)
−0.124571 + 0.992211i \(0.539755\pi\)
\(660\) −14.3111 0.979419i −0.557059 0.0381238i
\(661\) −22.1241 −0.860528 −0.430264 0.902703i \(-0.641579\pi\)
−0.430264 + 0.902703i \(0.641579\pi\)
\(662\) −10.9447 + 10.9447i −0.425377 + 0.425377i
\(663\) −1.70138 + 0.0965031i −0.0660763 + 0.00374787i
\(664\) 2.76439i 0.107279i
\(665\) −0.915068 1.17806i −0.0354848 0.0456832i
\(666\) −9.44668 + 1.07510i −0.366052 + 0.0416592i
\(667\) 1.94562 + 1.94562i 0.0753345 + 0.0753345i
\(668\) 8.76742 + 8.76742i 0.339222 + 0.339222i
\(669\) −9.81565 8.76192i −0.379495 0.338755i
\(670\) −3.71457 + 29.5638i −0.143506 + 1.14215i
\(671\) 41.1230i 1.58754i
\(672\) −0.221044 3.89709i −0.00852697 0.150333i
\(673\) 27.8518 27.8518i 1.07361 1.07361i 0.0765405 0.997066i \(-0.475613\pi\)
0.997066 0.0765405i \(-0.0243874\pi\)
\(674\) 25.6850 0.989349
\(675\) −2.07631 + 25.8977i −0.0799173 + 0.996801i
\(676\) 10.8971 0.419117
\(677\) 0.671792 0.671792i 0.0258191 0.0258191i −0.694079 0.719898i \(-0.744188\pi\)
0.719898 + 0.694079i \(0.244188\pi\)
\(678\) 0.494730 + 8.72226i 0.0190000 + 0.334976i
\(679\) 16.1489i 0.619738i
\(680\) −0.189128 + 1.50525i −0.00725274 + 0.0577237i
\(681\) −22.8961 20.4382i −0.877380 0.783192i
\(682\) 2.61895 + 2.61895i 0.100285 + 0.100285i
\(683\) 5.91720 + 5.91720i 0.226415 + 0.226415i 0.811193 0.584778i \(-0.198818\pi\)
−0.584778 + 0.811193i \(0.698818\pi\)
\(684\) 0.882362 0.100419i 0.0337380 0.00383961i
\(685\) −22.3337 28.7525i −0.853329 1.09858i
\(686\) 20.1050i 0.767613i
\(687\) −13.2958 + 0.754141i −0.507265 + 0.0287723i
\(688\) 7.37080 7.37080i 0.281009 0.281009i
\(689\) 0.579976 0.0220953
\(690\) −8.16655 0.558900i −0.310895 0.0212770i
\(691\) 43.7242 1.66335 0.831673 0.555266i \(-0.187383\pi\)
0.831673 + 0.555266i \(0.187383\pi\)
\(692\) 6.46161 6.46161i 0.245634 0.245634i
\(693\) −15.5905 + 19.5948i −0.592234 + 0.744345i
\(694\) 18.2626i 0.693239i
\(695\) 3.77138 + 0.473858i 0.143057 + 0.0179745i
\(696\) 1.50159 1.68218i 0.0569178 0.0637628i
\(697\) −2.40770 2.40770i −0.0911982 0.0911982i
\(698\) 21.6871 + 21.6871i 0.820867 + 0.820867i
\(699\) −10.4687 + 11.7276i −0.395961 + 0.443580i
\(700\) 9.69112 5.74893i 0.366290 0.217289i
\(701\) 14.1168i 0.533184i −0.963809 0.266592i \(-0.914102\pi\)
0.963809 0.266592i \(-0.0858977\pi\)
\(702\) −7.42663 + 1.27467i −0.280300 + 0.0481093i
\(703\) −0.663373 + 0.663373i −0.0250196 + 0.0250196i
\(704\) −3.70376 −0.139591
\(705\) 0.952584 0.830551i 0.0358764 0.0312803i
\(706\) 16.4442 0.618886
\(707\) 3.52693 3.52693i 0.132644 0.132644i
\(708\) 21.2945 1.20783i 0.800295 0.0453930i
\(709\) 25.3893i 0.953514i 0.879035 + 0.476757i \(0.158188\pi\)
−0.879035 + 0.476757i \(0.841812\pi\)
\(710\) 11.3620 8.82553i 0.426409 0.331216i
\(711\) 1.20961 + 10.6286i 0.0453639 + 0.398605i
\(712\) −7.60852 7.60852i −0.285141 0.285141i
\(713\) 1.49449 + 1.49449i 0.0559691 + 0.0559691i
\(714\) 1.97565 + 1.76356i 0.0739369 + 0.0659997i
\(715\) 9.48477 7.36737i 0.354710 0.275524i
\(716\) 18.6584i 0.697297i
\(717\) −2.27148 40.0470i −0.0848300 1.49558i
\(718\) −10.1019 + 10.1019i −0.376999 + 0.376999i
\(719\) 43.5310 1.62343 0.811716 0.584052i \(-0.198534\pi\)
0.811716 + 0.584052i \(0.198534\pi\)
\(720\) −0.0782930 + 6.70775i −0.00291781 + 0.249983i
\(721\) 14.4986 0.539954
\(722\) −13.3731 + 13.3731i −0.497694 + 0.497694i
\(723\) −2.41994 42.6644i −0.0899985 1.58671i
\(724\) 20.5221i 0.762697i
\(725\) 6.30697 + 1.61031i 0.234235 + 0.0598054i
\(726\) 3.51177 + 3.13478i 0.130334 + 0.116343i
\(727\) 28.7629 + 28.7629i 1.06676 + 1.06676i 0.997606 + 0.0691526i \(0.0220295\pi\)
0.0691526 + 0.997606i \(0.477970\pi\)
\(728\) 2.31087 + 2.31087i 0.0856467 + 0.0856467i
\(729\) −25.4548 + 9.00308i −0.942769 + 0.333447i
\(730\) 18.5619 + 2.33222i 0.687005 + 0.0863193i
\(731\) 7.07220i 0.261575i
\(732\) 19.2002 1.08904i 0.709660 0.0402522i
\(733\) 5.04195 5.04195i 0.186229 0.186229i −0.607835 0.794063i \(-0.707962\pi\)
0.794063 + 0.607835i \(0.207962\pi\)
\(734\) −7.04297 −0.259961
\(735\) −0.508062 + 7.42372i −0.0187402 + 0.273828i
\(736\) −2.11353 −0.0779057
\(737\) 34.8983 34.8983i 1.28549 1.28549i
\(738\) −11.7819 9.37417i −0.433697 0.345068i
\(739\) 42.4476i 1.56146i 0.624869 + 0.780730i \(0.285152\pi\)
−0.624869 + 0.780730i \(0.714848\pi\)
\(740\) −4.34719 5.59658i −0.159806 0.205734i
\(741\) −0.495134 + 0.554680i −0.0181892 + 0.0203767i
\(742\) −0.637320 0.637320i −0.0233968 0.0233968i
\(743\) 2.91864 + 2.91864i 0.107074 + 0.107074i 0.758614 0.651540i \(-0.225877\pi\)
−0.651540 + 0.758614i \(0.725877\pi\)
\(744\) 1.15342 1.29214i 0.0422865 0.0473720i
\(745\) −3.11153 + 24.7643i −0.113998 + 0.907295i
\(746\) 23.0594i 0.844264i
\(747\) 6.48964 + 5.16344i 0.237443 + 0.188920i
\(748\) 1.77686 1.77686i 0.0649683 0.0649683i
\(749\) 35.2980 1.28976
\(750\) −17.2906 + 8.71975i −0.631365 + 0.318400i
\(751\) 47.4716 1.73226 0.866132 0.499815i \(-0.166599\pi\)
0.866132 + 0.499815i \(0.166599\pi\)
\(752\) 0.230740 0.230740i 0.00841423 0.00841423i
\(753\) −32.3337 + 1.83398i −1.17831 + 0.0668339i
\(754\) 1.88790i 0.0687531i
\(755\) 0.594950 4.73514i 0.0216525 0.172329i
\(756\) 9.56163 + 6.76023i 0.347753 + 0.245867i
\(757\) 27.8063 + 27.8063i 1.01064 + 1.01064i 0.999943 + 0.0106944i \(0.00340420\pi\)
0.0106944 + 0.999943i \(0.496596\pi\)
\(758\) 12.4138 + 12.4138i 0.450890 + 0.450890i
\(759\) 10.1148 + 9.02898i 0.367145 + 0.327731i
\(760\) 0.406047 + 0.522746i 0.0147289 + 0.0189620i
\(761\) 1.65428i 0.0599675i 0.999550 + 0.0299838i \(0.00954556\pi\)
−0.999550 + 0.0299838i \(0.990454\pi\)
\(762\) 0.898474 + 15.8404i 0.0325483 + 0.573838i
\(763\) −15.9268 + 15.9268i −0.576588 + 0.576588i
\(764\) 22.5879 0.817202
\(765\) −3.18045 3.25557i −0.114989 0.117705i
\(766\) −9.61290 −0.347328
\(767\) −12.6271 + 12.6271i −0.455937 + 0.455937i
\(768\) 0.0980849 + 1.72927i 0.00353933 + 0.0623997i
\(769\) 37.6670i 1.35831i −0.733997 0.679153i \(-0.762347\pi\)
0.733997 0.679153i \(-0.237653\pi\)
\(770\) −18.5184 2.32676i −0.667356 0.0838505i
\(771\) 13.3330 + 11.9017i 0.480177 + 0.428629i
\(772\) −7.24548 7.24548i −0.260771 0.260771i
\(773\) −3.59275 3.59275i −0.129222 0.129222i 0.639538 0.768760i \(-0.279126\pi\)
−0.768760 + 0.639538i \(0.779126\pi\)
\(774\) 3.53610 + 31.0711i 0.127102 + 1.11683i
\(775\) 4.84458 + 1.23693i 0.174023 + 0.0444318i
\(776\) 7.16582i 0.257238i
\(777\) −12.3507 + 0.700538i −0.443080 + 0.0251317i
\(778\) 6.72702 6.72702i 0.241175 0.241175i
\(779\) −1.48564 −0.0532285
\(780\) −3.69098 4.23330i −0.132158 0.151577i
\(781\) −23.8302 −0.852710
\(782\) 1.01395 1.01395i 0.0362589 0.0362589i
\(783\) 1.14432 + 6.66717i 0.0408947 + 0.238265i
\(784\) 1.92128i 0.0686172i
\(785\) 19.6670 15.2765i 0.701946 0.545242i
\(786\) 19.1367 21.4381i 0.682582 0.764671i
\(787\) −12.4252 12.4252i −0.442911 0.442911i 0.450078 0.892989i \(-0.351396\pi\)
−0.892989 + 0.450078i \(0.851396\pi\)
\(788\) 3.23816 + 3.23816i 0.115355 + 0.115355i
\(789\) −18.5430 + 20.7730i −0.660148 + 0.739539i
\(790\) −6.29682 + 4.89110i −0.224031 + 0.174018i
\(791\) 11.3669i 0.404161i
\(792\) 6.91803 8.69489i 0.245822 0.308959i
\(793\) −11.3852 + 11.3852i −0.404302 + 0.404302i
\(794\) −15.3815 −0.545869
\(795\) 1.01794 + 1.16751i 0.0361027 + 0.0414073i
\(796\) 17.2659 0.611972
\(797\) −10.3655 + 10.3655i −0.367165 + 0.367165i −0.866442 0.499277i \(-0.833599\pi\)
0.499277 + 0.866442i \(0.333599\pi\)
\(798\) 1.15361 0.0654334i 0.0408375 0.00231632i
\(799\) 0.221393i 0.00783231i
\(800\) −4.30028 + 2.55100i −0.152038 + 0.0901914i
\(801\) 32.0732 3.65015i 1.13325 0.128972i
\(802\) −5.66191 5.66191i −0.199929 0.199929i
\(803\) −21.9111 21.9111i −0.773227 0.773227i
\(804\) −17.2181 15.3697i −0.607235 0.542047i
\(805\) −10.5674 1.32775i −0.372452 0.0467971i
\(806\) 1.45015i 0.0510795i
\(807\) −0.560936 9.88950i −0.0197459 0.348127i
\(808\) −1.56502 + 1.56502i −0.0550573 + 0.0550573i
\(809\) −18.7297 −0.658500 −0.329250 0.944243i \(-0.606796\pi\)
−0.329250 + 0.944243i \(0.606796\pi\)
\(810\) −15.6008 12.7128i −0.548156 0.446683i
\(811\) −20.9677 −0.736276 −0.368138 0.929771i \(-0.620005\pi\)
−0.368138 + 0.929771i \(0.620005\pi\)
\(812\) 2.07456 2.07456i 0.0728028 0.0728028i
\(813\) −1.43595 25.3164i −0.0503611 0.887884i
\(814\) 11.7380i 0.411417i
\(815\) 4.41003 + 5.67748i 0.154476 + 0.198873i
\(816\) −0.876664 0.782553i −0.0306894 0.0273948i
\(817\) 2.18190 + 2.18190i 0.0763350 + 0.0763350i
\(818\) 3.12182 + 3.12182i 0.109152 + 0.109152i
\(819\) −9.74132 + 1.10863i −0.340389 + 0.0387386i
\(820\) 1.39902 11.1346i 0.0488559 0.388839i
\(821\) 47.8971i 1.67162i 0.549018 + 0.835811i \(0.315002\pi\)
−0.549018 + 0.835811i \(0.684998\pi\)
\(822\) 28.1558 1.59701i 0.982048 0.0557021i
\(823\) 7.06755 7.06755i 0.246359 0.246359i −0.573115 0.819475i \(-0.694265\pi\)
0.819475 + 0.573115i \(0.194265\pi\)
\(824\) −6.43350 −0.224122
\(825\) 31.4779 + 6.16234i 1.09592 + 0.214545i
\(826\) 27.7511 0.965585
\(827\) −31.7052 + 31.7052i −1.10250 + 1.10250i −0.108391 + 0.994108i \(0.534570\pi\)
−0.994108 + 0.108391i \(0.965430\pi\)
\(828\) 3.94774 4.96169i 0.137193 0.172431i
\(829\) 56.5372i 1.96362i 0.189867 + 0.981810i \(0.439194\pi\)
−0.189867 + 0.981810i \(0.560806\pi\)
\(830\) −0.770602 + 6.13313i −0.0267480 + 0.212884i
\(831\) 0.832495 0.932612i 0.0288789 0.0323520i
\(832\) −1.02541 1.02541i −0.0355498 0.0355498i
\(833\) −0.921724 0.921724i −0.0319358 0.0319358i
\(834\) −1.96067 + 2.19647i −0.0678926 + 0.0760575i
\(835\) −17.0076 21.8956i −0.588572 0.757730i
\(836\) 1.09638i 0.0379192i
\(837\) 0.878989 + 5.12127i 0.0303823 + 0.177017i
\(838\) 1.46414 1.46414i 0.0505780 0.0505780i
\(839\) −22.1729 −0.765492 −0.382746 0.923854i \(-0.625022\pi\)
−0.382746 + 0.923854i \(0.625022\pi\)
\(840\) −0.595941 + 8.70779i −0.0205619 + 0.300447i
\(841\) −27.3052 −0.941557
\(842\) 20.3173 20.3173i 0.700182 0.700182i
\(843\) −50.7884 + 2.88074i −1.74925 + 0.0992178i
\(844\) 21.7612i 0.749050i
\(845\) −24.1765 3.03767i −0.831696 0.104499i
\(846\) 0.110696 + 0.972669i 0.00380582 + 0.0334411i
\(847\) 4.33092 + 4.33092i 0.148812 + 0.148812i
\(848\) 0.282801 + 0.282801i 0.00971142 + 0.00971142i
\(849\) −3.24302 2.89487i −0.111300 0.0993518i
\(850\) 0.839209 3.28686i 0.0287846 0.112738i
\(851\) 6.69824i 0.229613i
\(852\) 0.631083 + 11.1262i 0.0216206 + 0.381178i
\(853\) 10.9476 10.9476i 0.374837 0.374837i −0.494398 0.869235i \(-0.664612\pi\)
0.869235 + 0.494398i \(0.164612\pi\)
\(854\) 25.0219 0.856232
\(855\) −1.98562 0.0231763i −0.0679069 0.000792611i
\(856\) −15.6629 −0.535348
\(857\) −27.1672 + 27.1672i −0.928013 + 0.928013i −0.997577 0.0695640i \(-0.977839\pi\)
0.0695640 + 0.997577i \(0.477839\pi\)
\(858\) 0.526815 + 9.28794i 0.0179852 + 0.317085i
\(859\) 27.0450i 0.922764i −0.887201 0.461382i \(-0.847354\pi\)
0.887201 0.461382i \(-0.152646\pi\)
\(860\) −18.4077 + 14.2983i −0.627698 + 0.487569i
\(861\) −14.6143 13.0454i −0.498054 0.444587i
\(862\) 14.2134 + 14.2134i 0.484112 + 0.484112i
\(863\) −37.2201 37.2201i −1.26699 1.26699i −0.947636 0.319352i \(-0.896535\pi\)
−0.319352 0.947636i \(-0.603465\pi\)
\(864\) −4.24282 2.99974i −0.144344 0.102053i
\(865\) −16.1371 + 12.5346i −0.548679 + 0.426191i
\(866\) 24.6950i 0.839169i
\(867\) −28.6016 + 1.62229i −0.971362 + 0.0550960i
\(868\) 1.59354 1.59354i 0.0540882 0.0540882i
\(869\) 13.2067 0.448005
\(870\) −3.80040 + 3.31354i −0.128846 + 0.112339i
\(871\) 19.3237 0.654759
\(872\) 7.06726 7.06726i 0.239327 0.239327i
\(873\) −16.8224 13.3846i −0.569352 0.453001i
\(874\) 0.625645i 0.0211628i
\(875\) −23.1035 + 10.0532i −0.781042 + 0.339861i
\(876\) −9.64998 + 10.8105i −0.326042 + 0.365253i
\(877\) −9.25658 9.25658i −0.312572 0.312572i 0.533333 0.845905i \(-0.320939\pi\)
−0.845905 + 0.533333i \(0.820939\pi\)
\(878\) −25.7668 25.7668i −0.869587 0.869587i
\(879\) −23.2936 + 26.0949i −0.785673 + 0.880159i
\(880\) 8.21724 + 1.03246i 0.277003 + 0.0348043i
\(881\) 4.80357i 0.161836i 0.996721 + 0.0809182i \(0.0257852\pi\)
−0.996721 + 0.0809182i \(0.974215\pi\)
\(882\) −4.51037 3.58865i −0.151872 0.120836i
\(883\) 20.8825 20.8825i 0.702751 0.702751i −0.262249 0.965000i \(-0.584464\pi\)
0.965000 + 0.262249i \(0.0844642\pi\)
\(884\) 0.983873 0.0330912
\(885\) −47.5811 3.25634i −1.59942 0.109461i
\(886\) −7.33353 −0.246375
\(887\) 12.2705 12.2705i 0.412003 0.412003i −0.470433 0.882436i \(-0.655902\pi\)
0.882436 + 0.470433i \(0.155902\pi\)
\(888\) 5.48044 0.310853i 0.183912 0.0104315i
\(889\) 20.6434i 0.692356i
\(890\) 14.7595 + 19.0014i 0.494739 + 0.636928i
\(891\) 7.49021 + 32.4814i 0.250932 + 1.08817i
\(892\) 5.37150 + 5.37150i 0.179851 + 0.179851i
\(893\) 0.0683036 + 0.0683036i 0.00228569 + 0.00228569i
\(894\) −14.4229 12.8745i −0.482372 0.430589i
\(895\) 5.20123 41.3960i 0.173858 1.38371i
\(896\) 2.25360i 0.0752875i
\(897\) 0.300624 + 5.30011i 0.0100376 + 0.176966i
\(898\) −27.3667 + 27.3667i −0.913240 + 0.913240i
\(899\) 1.30186 0.0434194
\(900\) 2.04356 14.8601i 0.0681186 0.495338i
\(901\) −0.271344 −0.00903979
\(902\) −13.1438 + 13.1438i −0.437640 + 0.437640i
\(903\) 2.30414 + 40.6228i 0.0766769 + 1.35184i
\(904\) 5.04389i 0.167757i
\(905\) −5.72075 + 45.5308i −0.190164 + 1.51349i
\(906\) 2.75777 + 2.46172i 0.0916207 + 0.0817850i
\(907\) 11.8612 + 11.8612i 0.393843 + 0.393843i 0.876055 0.482211i \(-0.160166\pi\)
−0.482211 + 0.876055i \(0.660166\pi\)
\(908\) 12.5296 + 12.5296i 0.415810 + 0.415810i
\(909\) −0.750811 6.59724i −0.0249028 0.218817i
\(910\) −4.48278 5.77114i −0.148603 0.191311i
\(911\) 33.8899i 1.12282i 0.827537 + 0.561411i \(0.189741\pi\)
−0.827537 + 0.561411i \(0.810259\pi\)
\(912\) −0.511898 + 0.0290350i −0.0169506 + 0.000961446i
\(913\) 7.23979 7.23979i 0.239602 0.239602i
\(914\) 4.92404 0.162873
\(915\) −42.9016 2.93609i −1.41828 0.0970641i
\(916\) 7.68865 0.254040
\(917\) 26.4387 26.4387i 0.873082 0.873082i
\(918\) 3.47458 0.596360i 0.114678 0.0196828i
\(919\) 57.2926i 1.88991i −0.327202 0.944954i \(-0.606106\pi\)
0.327202 0.944954i \(-0.393894\pi\)
\(920\) 4.68912 + 0.589168i 0.154596 + 0.0194243i
\(921\) −0.942496 + 1.05584i −0.0310563 + 0.0347912i
\(922\) 9.80950 + 9.80950i 0.323059 + 0.323059i
\(923\) −6.59757 6.59757i −0.217162 0.217162i
\(924\) 9.62738 10.7852i 0.316717 0.354807i
\(925\) 8.08467 + 13.6285i 0.265822 + 0.448104i
\(926\) 3.55963i 0.116977i
\(927\) 12.0168 15.1032i 0.394683 0.496055i
\(928\) −0.920553 + 0.920553i −0.0302186 + 0.0302186i
\(929\) −39.2239 −1.28689 −0.643447 0.765491i \(-0.722496\pi\)
−0.643447 + 0.765491i \(0.722496\pi\)
\(930\) −2.91921 + 2.54523i −0.0957246 + 0.0834615i
\(931\) −0.568736 −0.0186396
\(932\) 6.41781 6.41781i 0.210223 0.210223i
\(933\) 51.8694 2.94205i 1.69813 0.0963184i
\(934\) 42.4816i 1.39004i
\(935\) −4.43749 + 3.44686i −0.145122 + 0.112724i
\(936\) 4.32256 0.491937i 0.141287 0.0160795i
\(937\) 14.6953 + 14.6953i 0.480074 + 0.480074i 0.905155 0.425081i \(-0.139755\pi\)
−0.425081 + 0.905155i \(0.639755\pi\)
\(938\) −21.2343 21.2343i −0.693326 0.693326i
\(939\) −12.2777 10.9596i −0.400666 0.357654i
\(940\) −0.576247 + 0.447604i −0.0187951 + 0.0145992i
\(941\) 36.6501i 1.19476i −0.801959 0.597379i \(-0.796209\pi\)
0.801959 0.597379i \(-0.203791\pi\)
\(942\) 1.09237 + 19.2589i 0.0355913 + 0.627488i
\(943\) −7.50042 + 7.50042i −0.244247 + 0.244247i
\(944\) −12.3141 −0.400791
\(945\) −19.3292 17.6638i −0.628778 0.574604i
\(946\) 38.6075 1.25524
\(947\) −35.2800 + 35.2800i −1.14645 + 1.14645i −0.159200 + 0.987246i \(0.550891\pi\)
−0.987246 + 0.159200i \(0.949109\pi\)
\(948\) −0.349746 6.16614i −0.0113592 0.200267i
\(949\) 12.1325i 0.393839i
\(950\) −0.755145 1.27297i −0.0245001 0.0413005i
\(951\) 32.2904 + 28.8240i 1.04709 + 0.934682i
\(952\) −1.08115 1.08115i −0.0350404 0.0350404i
\(953\) 9.14374 + 9.14374i 0.296195 + 0.296195i 0.839521 0.543327i \(-0.182835\pi\)
−0.543327 + 0.839521i \(0.682835\pi\)
\(954\) −1.19213 + 0.135672i −0.0385965 + 0.00439255i
\(955\) −50.1141 6.29663i −1.62165 0.203754i
\(956\) 23.1583i 0.748994i
\(957\) 8.33814 0.472942i 0.269534 0.0152881i
\(958\) 17.2711 17.2711i 0.558005 0.558005i
\(959\) 36.6929 1.18488
\(960\) 0.264439 3.86395i 0.00853475 0.124708i
\(961\) 1.00000 0.0322581
\(962\) −3.24976 + 3.24976i −0.104777 + 0.104777i
\(963\) 29.2559 36.7701i 0.942758 1.18490i
\(964\) 24.6719i 0.794628i
\(965\) 14.0552 + 18.0948i 0.452454 + 0.582491i
\(966\) 5.49381 6.15451i 0.176760 0.198018i
\(967\) 22.9601 + 22.9601i 0.738346 + 0.738346i 0.972258 0.233912i \(-0.0751527\pi\)
−0.233912 + 0.972258i \(0.575153\pi\)
\(968\) −1.92178 1.92178i −0.0617683 0.0617683i
\(969\) 0.231651 0.259510i 0.00744170 0.00833665i
\(970\) 1.99755 15.8983i 0.0641374 0.510462i
\(971\) 0.280300i 0.00899525i 0.999990 + 0.00449762i \(0.00143164\pi\)
−0.999990 + 0.00449762i \(0.998568\pi\)
\(972\) 14.9671 4.35735i 0.480069 0.139762i
\(973\) −2.70881 + 2.70881i −0.0868405 + 0.0868405i
\(974\) −23.0912 −0.739891
\(975\) 7.00882 + 10.4210i 0.224462 + 0.333739i
\(976\) −11.1031 −0.355401
\(977\) −20.5957 + 20.5957i −0.658916 + 0.658916i −0.955124 0.296208i \(-0.904278\pi\)
0.296208 + 0.955124i \(0.404278\pi\)
\(978\) −5.55966 + 0.315346i −0.177778 + 0.0100836i
\(979\) 39.8527i 1.27370i
\(980\) 0.535577 4.26260i 0.0171084 0.136164i
\(981\) 3.39048 + 29.7915i 0.108250 + 0.951170i
\(982\) 8.98286 + 8.98286i 0.286655 + 0.286655i
\(983\) −10.1213 10.1213i −0.322820 0.322820i 0.527028 0.849848i \(-0.323306\pi\)
−0.849848 + 0.527028i \(0.823306\pi\)
\(984\) 6.48486 + 5.78870i 0.206730 + 0.184537i
\(985\) −6.28159 8.08693i −0.200148 0.257671i
\(986\) 0.883261i 0.0281288i
\(987\) 0.0721302 + 1.27168i 0.00229593 + 0.0404781i
\(988\) 0.303542 0.303542i 0.00965697 0.00965697i
\(989\) 22.0312 0.700550
\(990\) −17.7723 + 17.3622i −0.564841 + 0.551807i
\(991\) −16.7627 −0.532485 −0.266243 0.963906i \(-0.585782\pi\)
−0.266243 + 0.963906i \(0.585782\pi\)
\(992\) −0.707107 + 0.707107i −0.0224507 + 0.0224507i
\(993\) 1.51817 + 26.7659i 0.0481777 + 0.849389i
\(994\) 14.4998i 0.459906i
\(995\) −38.3064 4.81304i −1.21440 0.152584i
\(996\) −3.57196 3.18851i −0.113182 0.101032i
\(997\) −26.7133 26.7133i −0.846019 0.846019i 0.143615 0.989634i \(-0.454127\pi\)
−0.989634 + 0.143615i \(0.954127\pi\)
\(998\) −7.60159 7.60159i −0.240624 0.240624i
\(999\) −9.50685 + 13.4464i −0.300783 + 0.425427i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 930.2.j.h.497.7 40
3.2 odd 2 inner 930.2.j.h.497.11 yes 40
5.3 odd 4 inner 930.2.j.h.683.11 yes 40
15.8 even 4 inner 930.2.j.h.683.7 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.j.h.497.7 40 1.1 even 1 trivial
930.2.j.h.497.11 yes 40 3.2 odd 2 inner
930.2.j.h.683.7 yes 40 15.8 even 4 inner
930.2.j.h.683.11 yes 40 5.3 odd 4 inner