Properties

Label 105.3.r.a.19.2
Level $105$
Weight $3$
Character 105.19
Analytic conductor $2.861$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [105,3,Mod(19,105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 5]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.19");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.r (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 19.2
Character \(\chi\) \(=\) 105.19
Dual form 105.3.r.a.94.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.95153 - 1.70407i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(3.80769 + 6.59511i) q^{4} +(-3.57204 - 3.49865i) q^{5} +5.90306i q^{6} +(-5.14807 + 4.74314i) q^{7} -12.3217i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-2.95153 - 1.70407i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(3.80769 + 6.59511i) q^{4} +(-3.57204 - 3.49865i) q^{5} +5.90306i q^{6} +(-5.14807 + 4.74314i) q^{7} -12.3217i q^{8} +(-1.50000 + 2.59808i) q^{9} +(4.58104 + 16.4134i) q^{10} +(0.694658 + 1.20318i) q^{11} +(6.59511 - 11.4231i) q^{12} +3.78639 q^{13} +(23.2773 - 5.22688i) q^{14} +(-2.15450 + 8.38798i) q^{15} +(-5.76621 + 9.98737i) q^{16} +(15.8536 + 27.4592i) q^{17} +(8.85459 - 5.11220i) q^{18} +(12.8335 + 7.40942i) q^{19} +(9.47278 - 36.8797i) q^{20} +(11.5731 + 3.61442i) q^{21} -4.73498i q^{22} +(-19.5874 - 11.3088i) q^{23} +(-18.4825 + 10.6709i) q^{24} +(0.518893 + 24.9946i) q^{25} +(-11.1756 - 6.45226i) q^{26} +5.19615 q^{27} +(-50.8838 - 15.8916i) q^{28} -42.9485 q^{29} +(20.6527 - 21.0859i) q^{30} +(-28.0131 + 16.1734i) q^{31} +(-8.64524 + 4.99133i) q^{32} +(1.20318 - 2.08398i) q^{33} -108.062i q^{34} +(34.9837 + 1.06860i) q^{35} -22.8461 q^{36} +(-7.29321 - 4.21074i) q^{37} +(-25.2523 - 43.7383i) q^{38} +(-3.27911 - 5.67959i) q^{39} +(-43.1092 + 44.0135i) q^{40} +46.3613i q^{41} +(-27.9991 - 30.3893i) q^{42} +9.92743i q^{43} +(-5.29008 + 9.16269i) q^{44} +(14.4478 - 4.03245i) q^{45} +(38.5418 + 66.7564i) q^{46} +(-27.2811 + 47.2522i) q^{47} +19.9747 q^{48} +(4.00517 - 48.8360i) q^{49} +(41.0610 - 74.6566i) q^{50} +(27.4592 - 47.5607i) q^{51} +(14.4174 + 24.9717i) q^{52} +(74.4321 - 42.9734i) q^{53} +(-15.3366 - 8.85459i) q^{54} +(1.72817 - 6.72818i) q^{55} +(58.4435 + 63.4328i) q^{56} -25.6670i q^{57} +(126.764 + 73.1872i) q^{58} +(-80.4509 + 46.4483i) q^{59} +(-63.5233 + 17.7296i) q^{60} +(1.41863 + 0.819048i) q^{61} +110.242 q^{62} +(-4.60095 - 20.4898i) q^{63} +80.1519 q^{64} +(-13.5251 - 13.2473i) q^{65} +(-7.10247 + 4.10061i) q^{66} +(-37.9034 + 21.8835i) q^{67} +(-120.731 + 209.112i) q^{68} +39.1748i q^{69} +(-101.434 - 62.7685i) q^{70} -60.9268 q^{71} +(32.0127 + 18.4825i) q^{72} +(-32.3243 - 55.9872i) q^{73} +(14.3508 + 24.8563i) q^{74} +(37.0425 - 22.4243i) q^{75} +112.851i q^{76} +(-9.28302 - 2.89920i) q^{77} +22.3513i q^{78} +(0.744936 - 1.29027i) q^{79} +(55.5395 - 15.5013i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(79.0028 - 136.837i) q^{82} +13.6731 q^{83} +(20.2292 + 90.0882i) q^{84} +(39.4406 - 153.551i) q^{85} +(16.9170 - 29.3011i) q^{86} +(37.1945 + 64.4228i) q^{87} +(14.8252 - 8.55936i) q^{88} +(110.062 + 63.5444i) q^{89} +(-49.5147 - 12.7181i) q^{90} +(-19.4926 + 17.9594i) q^{91} -172.241i q^{92} +(48.5201 + 28.0131i) q^{93} +(161.042 - 92.9775i) q^{94} +(-19.9187 - 71.3666i) q^{95} +(14.9740 + 8.64524i) q^{96} -119.276 q^{97} +(-95.0412 + 137.316i) q^{98} -4.16795 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 32 q^{4} - 6 q^{5} - 48 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 32 q^{4} - 6 q^{5} - 48 q^{9} + 78 q^{10} - 28 q^{11} + 60 q^{14} - 24 q^{15} - 40 q^{16} - 60 q^{19} + 12 q^{21} - 34 q^{25} - 96 q^{26} - 88 q^{29} + 84 q^{31} - 170 q^{35} - 192 q^{36} + 36 q^{39} + 330 q^{40} + 320 q^{44} + 18 q^{45} - 60 q^{46} + 356 q^{49} + 12 q^{51} - 468 q^{56} - 804 q^{59} - 198 q^{60} + 336 q^{61} - 400 q^{64} - 46 q^{65} - 108 q^{66} - 438 q^{70} + 344 q^{71} + 900 q^{74} + 144 q^{75} - 20 q^{79} + 1140 q^{80} - 144 q^{81} + 780 q^{84} + 304 q^{85} + 144 q^{86} + 24 q^{89} - 224 q^{91} - 924 q^{94} - 342 q^{95} + 900 q^{96} + 168 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.95153 1.70407i −1.47577 0.852033i −0.476139 0.879370i \(-0.657964\pi\)
−0.999626 + 0.0273367i \(0.991297\pi\)
\(3\) −0.866025 1.50000i −0.288675 0.500000i
\(4\) 3.80769 + 6.59511i 0.951922 + 1.64878i
\(5\) −3.57204 3.49865i −0.714407 0.699730i
\(6\) 5.90306i 0.983843i
\(7\) −5.14807 + 4.74314i −0.735438 + 0.677592i
\(8\) 12.3217i 1.54021i
\(9\) −1.50000 + 2.59808i −0.166667 + 0.288675i
\(10\) 4.58104 + 16.4134i 0.458104 + 1.64134i
\(11\) 0.694658 + 1.20318i 0.0631508 + 0.109380i 0.895872 0.444312i \(-0.146552\pi\)
−0.832721 + 0.553692i \(0.813218\pi\)
\(12\) 6.59511 11.4231i 0.549592 0.951922i
\(13\) 3.78639 0.291261 0.145630 0.989339i \(-0.453479\pi\)
0.145630 + 0.989339i \(0.453479\pi\)
\(14\) 23.2773 5.22688i 1.66266 0.373349i
\(15\) −2.15450 + 8.38798i −0.143633 + 0.559198i
\(16\) −5.76621 + 9.98737i −0.360388 + 0.624211i
\(17\) 15.8536 + 27.4592i 0.932563 + 1.61525i 0.778922 + 0.627121i \(0.215767\pi\)
0.153641 + 0.988127i \(0.450900\pi\)
\(18\) 8.85459 5.11220i 0.491922 0.284011i
\(19\) 12.8335 + 7.40942i 0.675447 + 0.389970i 0.798137 0.602475i \(-0.205819\pi\)
−0.122690 + 0.992445i \(0.539152\pi\)
\(20\) 9.47278 36.8797i 0.473639 1.84399i
\(21\) 11.5731 + 3.61442i 0.551099 + 0.172115i
\(22\) 4.73498i 0.215226i
\(23\) −19.5874 11.3088i −0.851625 0.491686i 0.00957359 0.999954i \(-0.496953\pi\)
−0.861199 + 0.508268i \(0.830286\pi\)
\(24\) −18.4825 + 10.6709i −0.770105 + 0.444620i
\(25\) 0.518893 + 24.9946i 0.0207557 + 0.999785i
\(26\) −11.1756 6.45226i −0.429833 0.248164i
\(27\) 5.19615 0.192450
\(28\) −50.8838 15.8916i −1.81728 0.567559i
\(29\) −42.9485 −1.48098 −0.740492 0.672065i \(-0.765407\pi\)
−0.740492 + 0.672065i \(0.765407\pi\)
\(30\) 20.6527 21.0859i 0.688425 0.702865i
\(31\) −28.0131 + 16.1734i −0.903649 + 0.521722i −0.878382 0.477959i \(-0.841377\pi\)
−0.0252666 + 0.999681i \(0.508043\pi\)
\(32\) −8.64524 + 4.99133i −0.270164 + 0.155979i
\(33\) 1.20318 2.08398i 0.0364601 0.0631508i
\(34\) 108.062i 3.17830i
\(35\) 34.9837 + 1.06860i 0.999534 + 0.0305314i
\(36\) −22.8461 −0.634615
\(37\) −7.29321 4.21074i −0.197114 0.113804i 0.398195 0.917301i \(-0.369637\pi\)
−0.595309 + 0.803497i \(0.702970\pi\)
\(38\) −25.2523 43.7383i −0.664534 1.15101i
\(39\) −3.27911 5.67959i −0.0840798 0.145630i
\(40\) −43.1092 + 44.0135i −1.07773 + 1.10034i
\(41\) 46.3613i 1.13076i 0.824829 + 0.565382i \(0.191271\pi\)
−0.824829 + 0.565382i \(0.808729\pi\)
\(42\) −27.9991 30.3893i −0.666644 0.723556i
\(43\) 9.92743i 0.230871i 0.993315 + 0.115435i \(0.0368263\pi\)
−0.993315 + 0.115435i \(0.963174\pi\)
\(44\) −5.29008 + 9.16269i −0.120229 + 0.208243i
\(45\) 14.4478 4.03245i 0.321063 0.0896100i
\(46\) 38.5418 + 66.7564i 0.837866 + 1.45123i
\(47\) −27.2811 + 47.2522i −0.580448 + 1.00537i 0.414978 + 0.909832i \(0.363789\pi\)
−0.995426 + 0.0955345i \(0.969544\pi\)
\(48\) 19.9747 0.416141
\(49\) 4.00517 48.8360i 0.0817381 0.996654i
\(50\) 41.0610 74.6566i 0.821219 1.49313i
\(51\) 27.4592 47.5607i 0.538416 0.932563i
\(52\) 14.4174 + 24.9717i 0.277258 + 0.480224i
\(53\) 74.4321 42.9734i 1.40438 0.810819i 0.409542 0.912291i \(-0.365689\pi\)
0.994838 + 0.101472i \(0.0323553\pi\)
\(54\) −15.3366 8.85459i −0.284011 0.163974i
\(55\) 1.72817 6.72818i 0.0314213 0.122331i
\(56\) 58.4435 + 63.4328i 1.04363 + 1.13273i
\(57\) 25.6670i 0.450298i
\(58\) 126.764 + 73.1872i 2.18558 + 1.26185i
\(59\) −80.4509 + 46.4483i −1.36357 + 0.787260i −0.990098 0.140380i \(-0.955168\pi\)
−0.373477 + 0.927640i \(0.621834\pi\)
\(60\) −63.5233 + 17.7296i −1.05872 + 0.295494i
\(61\) 1.41863 + 0.819048i 0.0232563 + 0.0134270i 0.511583 0.859234i \(-0.329059\pi\)
−0.488327 + 0.872661i \(0.662393\pi\)
\(62\) 110.242 1.77810
\(63\) −4.60095 20.4898i −0.0730310 0.325235i
\(64\) 80.1519 1.25237
\(65\) −13.5251 13.2473i −0.208079 0.203804i
\(66\) −7.10247 + 4.10061i −0.107613 + 0.0621305i
\(67\) −37.9034 + 21.8835i −0.565722 + 0.326620i −0.755439 0.655219i \(-0.772576\pi\)
0.189717 + 0.981839i \(0.439243\pi\)
\(68\) −120.731 + 209.112i −1.77545 + 3.07518i
\(69\) 39.1748i 0.567750i
\(70\) −101.434 62.7685i −1.44906 0.896693i
\(71\) −60.9268 −0.858124 −0.429062 0.903275i \(-0.641156\pi\)
−0.429062 + 0.903275i \(0.641156\pi\)
\(72\) 32.0127 + 18.4825i 0.444620 + 0.256702i
\(73\) −32.3243 55.9872i −0.442798 0.766949i 0.555098 0.831785i \(-0.312681\pi\)
−0.997896 + 0.0648364i \(0.979347\pi\)
\(74\) 14.3508 + 24.8563i 0.193929 + 0.335895i
\(75\) 37.0425 22.4243i 0.493901 0.298991i
\(76\) 112.851i 1.48488i
\(77\) −9.28302 2.89920i −0.120559 0.0376520i
\(78\) 22.3513i 0.286555i
\(79\) 0.744936 1.29027i 0.00942957 0.0163325i −0.861272 0.508144i \(-0.830332\pi\)
0.870702 + 0.491812i \(0.163665\pi\)
\(80\) 55.5395 15.5013i 0.694243 0.193766i
\(81\) −4.50000 7.79423i −0.0555556 0.0962250i
\(82\) 79.0028 136.837i 0.963449 1.66874i
\(83\) 13.6731 0.164736 0.0823681 0.996602i \(-0.473752\pi\)
0.0823681 + 0.996602i \(0.473752\pi\)
\(84\) 20.2292 + 90.0882i 0.240824 + 1.07248i
\(85\) 39.4406 153.551i 0.464007 1.80649i
\(86\) 16.9170 29.3011i 0.196709 0.340711i
\(87\) 37.1945 + 64.4228i 0.427523 + 0.740492i
\(88\) 14.8252 8.55936i 0.168469 0.0972654i
\(89\) 110.062 + 63.5444i 1.23665 + 0.713982i 0.968409 0.249369i \(-0.0802232\pi\)
0.268244 + 0.963351i \(0.413557\pi\)
\(90\) −49.5147 12.7181i −0.550164 0.141313i
\(91\) −19.4926 + 17.9594i −0.214204 + 0.197356i
\(92\) 172.241i 1.87219i
\(93\) 48.5201 + 28.0131i 0.521722 + 0.301216i
\(94\) 161.042 92.9775i 1.71321 0.989123i
\(95\) −19.9187 71.3666i −0.209671 0.751228i
\(96\) 14.9740 + 8.64524i 0.155979 + 0.0900546i
\(97\) −119.276 −1.22965 −0.614824 0.788664i \(-0.710773\pi\)
−0.614824 + 0.788664i \(0.710773\pi\)
\(98\) −95.0412 + 137.316i −0.969809 + 1.40118i
\(99\) −4.16795 −0.0421005
\(100\) −162.866 + 98.5938i −1.62866 + 0.985938i
\(101\) 103.691 59.8659i 1.02664 0.592732i 0.110621 0.993863i \(-0.464716\pi\)
0.916021 + 0.401131i \(0.131383\pi\)
\(102\) −162.093 + 93.5846i −1.58915 + 0.917496i
\(103\) 31.1886 54.0203i 0.302802 0.524469i −0.673967 0.738761i \(-0.735411\pi\)
0.976770 + 0.214292i \(0.0687445\pi\)
\(104\) 46.6547i 0.448603i
\(105\) −28.6939 53.4010i −0.273275 0.508581i
\(106\) −292.918 −2.76338
\(107\) −104.206 60.1634i −0.973888 0.562275i −0.0734689 0.997298i \(-0.523407\pi\)
−0.900419 + 0.435023i \(0.856740\pi\)
\(108\) 19.7853 + 34.2692i 0.183197 + 0.317307i
\(109\) 32.5298 + 56.3433i 0.298439 + 0.516911i 0.975779 0.218759i \(-0.0702009\pi\)
−0.677340 + 0.735670i \(0.736868\pi\)
\(110\) −16.5660 + 16.9135i −0.150600 + 0.153759i
\(111\) 14.5864i 0.131409i
\(112\) −17.6867 78.7656i −0.157917 0.703265i
\(113\) 133.463i 1.18109i 0.807005 + 0.590545i \(0.201087\pi\)
−0.807005 + 0.590545i \(0.798913\pi\)
\(114\) −43.7383 + 75.7569i −0.383669 + 0.664534i
\(115\) 30.4014 + 108.925i 0.264360 + 0.947172i
\(116\) −163.535 283.250i −1.40978 2.44181i
\(117\) −5.67959 + 9.83733i −0.0485435 + 0.0840798i
\(118\) 316.604 2.68309
\(119\) −211.858 66.1660i −1.78032 0.556017i
\(120\) 103.354 + 26.5471i 0.861283 + 0.221226i
\(121\) 59.5349 103.117i 0.492024 0.852211i
\(122\) −2.79143 4.83489i −0.0228805 0.0396303i
\(123\) 69.5420 40.1501i 0.565382 0.326424i
\(124\) −213.330 123.166i −1.72041 0.993277i
\(125\) 85.5939 91.0971i 0.684751 0.728777i
\(126\) −21.3361 + 68.3165i −0.169334 + 0.542195i
\(127\) 187.969i 1.48007i 0.672570 + 0.740034i \(0.265191\pi\)
−0.672570 + 0.740034i \(0.734809\pi\)
\(128\) −201.990 116.619i −1.57805 0.911086i
\(129\) 14.8912 8.59741i 0.115435 0.0666466i
\(130\) 17.3456 + 62.1474i 0.133428 + 0.478057i
\(131\) 61.6992 + 35.6220i 0.470986 + 0.271924i 0.716652 0.697431i \(-0.245673\pi\)
−0.245666 + 0.969354i \(0.579007\pi\)
\(132\) 18.3254 0.138829
\(133\) −101.212 + 22.7269i −0.760990 + 0.170879i
\(134\) 149.164 1.11316
\(135\) −18.5608 18.1795i −0.137488 0.134663i
\(136\) 338.343 195.343i 2.48782 1.43634i
\(137\) 32.8928 18.9907i 0.240093 0.138618i −0.375126 0.926974i \(-0.622401\pi\)
0.615220 + 0.788356i \(0.289067\pi\)
\(138\) 66.7564 115.626i 0.483742 0.837866i
\(139\) 98.4179i 0.708042i 0.935237 + 0.354021i \(0.115186\pi\)
−0.935237 + 0.354021i \(0.884814\pi\)
\(140\) 126.159 + 234.790i 0.901139 + 1.67707i
\(141\) 94.5044 0.670244
\(142\) 179.827 + 103.823i 1.26639 + 0.731150i
\(143\) 2.63025 + 4.55572i 0.0183933 + 0.0318582i
\(144\) −17.2986 29.9621i −0.120129 0.208070i
\(145\) 153.414 + 150.262i 1.05803 + 1.03629i
\(146\) 220.331i 1.50911i
\(147\) −76.7226 + 36.2855i −0.521923 + 0.246840i
\(148\) 64.1327i 0.433329i
\(149\) 89.3441 154.748i 0.599625 1.03858i −0.393252 0.919431i \(-0.628650\pi\)
0.992876 0.119149i \(-0.0380167\pi\)
\(150\) −147.545 + 3.06306i −0.983631 + 0.0204204i
\(151\) −120.777 209.191i −0.799846 1.38537i −0.919716 0.392584i \(-0.871581\pi\)
0.119870 0.992790i \(-0.461752\pi\)
\(152\) 91.2965 158.130i 0.600635 1.04033i
\(153\) −95.1215 −0.621709
\(154\) 22.4587 + 24.3760i 0.145836 + 0.158286i
\(155\) 156.649 + 40.2362i 1.01064 + 0.259588i
\(156\) 24.9717 43.2522i 0.160075 0.277258i
\(157\) 20.6624 + 35.7883i 0.131607 + 0.227951i 0.924296 0.381676i \(-0.124653\pi\)
−0.792689 + 0.609626i \(0.791320\pi\)
\(158\) −4.39740 + 2.53884i −0.0278317 + 0.0160686i
\(159\) −128.920 74.4321i −0.810819 0.468127i
\(160\) 48.3440 + 12.4174i 0.302150 + 0.0776090i
\(161\) 154.476 34.6874i 0.959480 0.215450i
\(162\) 30.6732i 0.189341i
\(163\) −60.5120 34.9366i −0.371239 0.214335i 0.302760 0.953067i \(-0.402092\pi\)
−0.674000 + 0.738732i \(0.735425\pi\)
\(164\) −305.758 + 176.529i −1.86438 + 1.07640i
\(165\) −11.5889 + 3.23452i −0.0702359 + 0.0196031i
\(166\) −40.3566 23.2999i −0.243112 0.140361i
\(167\) 32.7058 0.195843 0.0979217 0.995194i \(-0.468781\pi\)
0.0979217 + 0.995194i \(0.468781\pi\)
\(168\) 44.5357 142.600i 0.265093 0.848808i
\(169\) −154.663 −0.915167
\(170\) −378.072 + 386.002i −2.22395 + 2.27060i
\(171\) −38.5005 + 22.2283i −0.225149 + 0.129990i
\(172\) −65.4725 + 37.8006i −0.380654 + 0.219771i
\(173\) −12.4244 + 21.5197i −0.0718173 + 0.124391i −0.899698 0.436513i \(-0.856213\pi\)
0.827881 + 0.560904i \(0.189547\pi\)
\(174\) 253.528i 1.45706i
\(175\) −121.224 126.213i −0.692711 0.721216i
\(176\) −16.0222 −0.0910352
\(177\) 139.345 + 80.4509i 0.787260 + 0.454525i
\(178\) −216.568 375.106i −1.21667 2.10734i
\(179\) 70.0625 + 121.352i 0.391411 + 0.677943i 0.992636 0.121136i \(-0.0386539\pi\)
−0.601225 + 0.799080i \(0.705321\pi\)
\(180\) 81.6072 + 79.9306i 0.453373 + 0.444059i
\(181\) 281.086i 1.55296i 0.630142 + 0.776480i \(0.282997\pi\)
−0.630142 + 0.776480i \(0.717003\pi\)
\(182\) 88.1370 19.7910i 0.484269 0.108742i
\(183\) 2.83727i 0.0155042i
\(184\) −139.343 + 241.349i −0.757300 + 1.31168i
\(185\) 11.3197 + 40.5573i 0.0611877 + 0.219229i
\(186\) −95.4724 165.363i −0.513293 0.889049i
\(187\) −22.0256 + 38.1495i −0.117784 + 0.204008i
\(188\) −415.511 −2.21017
\(189\) −26.7501 + 24.6461i −0.141535 + 0.130403i
\(190\) −62.8227 + 244.584i −0.330646 + 1.28728i
\(191\) 51.1878 88.6599i 0.267999 0.464188i −0.700346 0.713804i \(-0.746971\pi\)
0.968345 + 0.249616i \(0.0803043\pi\)
\(192\) −69.4136 120.228i −0.361529 0.626187i
\(193\) −2.32270 + 1.34101i −0.0120347 + 0.00694825i −0.506005 0.862530i \(-0.668878\pi\)
0.493971 + 0.869479i \(0.335545\pi\)
\(194\) 352.047 + 203.254i 1.81467 + 1.04770i
\(195\) −8.15778 + 31.7602i −0.0418348 + 0.162873i
\(196\) 337.329 159.538i 1.72107 0.813969i
\(197\) 32.0387i 0.162633i 0.996688 + 0.0813164i \(0.0259124\pi\)
−0.996688 + 0.0813164i \(0.974088\pi\)
\(198\) 12.3018 + 7.10247i 0.0621305 + 0.0358710i
\(199\) 14.1309 8.15845i 0.0710093 0.0409973i −0.464075 0.885796i \(-0.653613\pi\)
0.535084 + 0.844799i \(0.320280\pi\)
\(200\) 307.976 6.39363i 1.53988 0.0319682i
\(201\) 65.6506 + 37.9034i 0.326620 + 0.188574i
\(202\) −408.062 −2.02011
\(203\) 221.102 203.711i 1.08917 1.00350i
\(204\) 418.224 2.05012
\(205\) 162.202 165.604i 0.791230 0.807826i
\(206\) −184.108 + 106.295i −0.893730 + 0.515995i
\(207\) 58.7621 33.9263i 0.283875 0.163895i
\(208\) −21.8331 + 37.8161i −0.104967 + 0.181808i
\(209\) 20.5881i 0.0985075i
\(210\) −6.30799 + 206.511i −0.0300381 + 0.983385i
\(211\) −311.474 −1.47618 −0.738091 0.674701i \(-0.764272\pi\)
−0.738091 + 0.674701i \(0.764272\pi\)
\(212\) 566.829 + 327.259i 2.67372 + 1.54367i
\(213\) 52.7642 + 91.3902i 0.247719 + 0.429062i
\(214\) 205.045 + 355.148i 0.958154 + 1.65957i
\(215\) 34.7326 35.4612i 0.161547 0.164936i
\(216\) 64.0253i 0.296414i
\(217\) 67.5007 216.132i 0.311063 0.995999i
\(218\) 221.732i 1.01712i
\(219\) −55.9872 + 96.9728i −0.255650 + 0.442798i
\(220\) 50.9534 14.2213i 0.231606 0.0646424i
\(221\) 60.0278 + 103.971i 0.271619 + 0.470458i
\(222\) 24.8563 43.0523i 0.111965 0.193929i
\(223\) −111.515 −0.500068 −0.250034 0.968237i \(-0.580442\pi\)
−0.250034 + 0.968237i \(0.580442\pi\)
\(224\) 20.8317 66.7013i 0.0929985 0.297774i
\(225\) −65.7163 36.1438i −0.292072 0.160639i
\(226\) 227.430 393.920i 1.00633 1.74301i
\(227\) −42.6365 73.8486i −0.187826 0.325324i 0.756699 0.653763i \(-0.226811\pi\)
−0.944525 + 0.328439i \(0.893477\pi\)
\(228\) 169.277 97.7319i 0.742441 0.428649i
\(229\) −60.4219 34.8846i −0.263851 0.152334i 0.362239 0.932085i \(-0.382012\pi\)
−0.626090 + 0.779751i \(0.715346\pi\)
\(230\) 95.8845 373.301i 0.416889 1.62305i
\(231\) 3.69053 + 16.4353i 0.0159763 + 0.0711485i
\(232\) 529.198i 2.28103i
\(233\) −150.319 86.7866i −0.645145 0.372475i 0.141449 0.989946i \(-0.454824\pi\)
−0.786594 + 0.617471i \(0.788157\pi\)
\(234\) 33.5269 19.3568i 0.143278 0.0827213i
\(235\) 262.768 73.3397i 1.11816 0.312084i
\(236\) −612.664 353.722i −2.59603 1.49882i
\(237\) −2.58053 −0.0108883
\(238\) 512.555 + 556.311i 2.15359 + 2.33744i
\(239\) −108.916 −0.455717 −0.227858 0.973694i \(-0.573172\pi\)
−0.227858 + 0.973694i \(0.573172\pi\)
\(240\) −71.3505 69.8847i −0.297294 0.291186i
\(241\) −89.8157 + 51.8551i −0.372679 + 0.215167i −0.674628 0.738158i \(-0.735696\pi\)
0.301949 + 0.953324i \(0.402363\pi\)
\(242\) −351.438 + 202.903i −1.45222 + 0.838442i
\(243\) −7.79423 + 13.5000i −0.0320750 + 0.0555556i
\(244\) 12.4747i 0.0511259i
\(245\) −185.167 + 160.431i −0.755783 + 0.654822i
\(246\) −273.674 −1.11249
\(247\) 48.5926 + 28.0550i 0.196731 + 0.113583i
\(248\) 199.283 + 345.169i 0.803561 + 1.39181i
\(249\) −11.8413 20.5097i −0.0475553 0.0823681i
\(250\) −407.869 + 123.018i −1.63147 + 0.492073i
\(251\) 231.368i 0.921787i −0.887456 0.460893i \(-0.847529\pi\)
0.887456 0.460893i \(-0.152471\pi\)
\(252\) 117.613 108.362i 0.466720 0.430010i
\(253\) 31.4230i 0.124201i
\(254\) 320.311 554.795i 1.26107 2.18423i
\(255\) −264.484 + 73.8185i −1.03719 + 0.289485i
\(256\) 237.149 + 410.754i 0.926364 + 1.60451i
\(257\) 46.1522 79.9380i 0.179581 0.311043i −0.762156 0.647393i \(-0.775859\pi\)
0.941737 + 0.336350i \(0.109193\pi\)
\(258\) −58.6022 −0.227140
\(259\) 57.5181 12.9156i 0.222078 0.0498672i
\(260\) 35.8676 139.641i 0.137952 0.537081i
\(261\) 64.4228 111.584i 0.246831 0.427523i
\(262\) −121.405 210.279i −0.463377 0.802592i
\(263\) −130.580 + 75.3906i −0.496503 + 0.286656i −0.727268 0.686353i \(-0.759210\pi\)
0.230765 + 0.973009i \(0.425877\pi\)
\(264\) −25.6781 14.8252i −0.0972654 0.0561562i
\(265\) −416.223 106.909i −1.57065 0.403432i
\(266\) 337.457 + 105.392i 1.26864 + 0.396211i
\(267\) 220.124i 0.824435i
\(268\) −288.649 166.651i −1.07705 0.621833i
\(269\) −95.5538 + 55.1680i −0.355219 + 0.205086i −0.666981 0.745074i \(-0.732414\pi\)
0.311763 + 0.950160i \(0.399081\pi\)
\(270\) 23.8038 + 85.2863i 0.0881622 + 0.315875i
\(271\) −85.9659 49.6324i −0.317217 0.183145i 0.332934 0.942950i \(-0.391961\pi\)
−0.650152 + 0.759805i \(0.725295\pi\)
\(272\) −365.660 −1.34434
\(273\) 43.8202 + 13.6856i 0.160513 + 0.0501304i
\(274\) −129.445 −0.472428
\(275\) −29.7127 + 17.9870i −0.108046 + 0.0654074i
\(276\) −258.362 + 149.165i −0.936093 + 0.540454i
\(277\) 337.139 194.648i 1.21711 0.702699i 0.252811 0.967516i \(-0.418645\pi\)
0.964299 + 0.264817i \(0.0853115\pi\)
\(278\) 167.711 290.483i 0.603276 1.04490i
\(279\) 97.0403i 0.347815i
\(280\) 13.1669 431.058i 0.0470247 1.53949i
\(281\) 307.374 1.09386 0.546928 0.837180i \(-0.315797\pi\)
0.546928 + 0.837180i \(0.315797\pi\)
\(282\) −278.933 161.042i −0.989123 0.571070i
\(283\) 224.540 + 388.915i 0.793428 + 1.37426i 0.923833 + 0.382796i \(0.125039\pi\)
−0.130405 + 0.991461i \(0.541628\pi\)
\(284\) −231.990 401.819i −0.816867 1.41486i
\(285\) −89.7998 + 91.6834i −0.315087 + 0.321696i
\(286\) 17.9285i 0.0626870i
\(287\) −219.898 238.671i −0.766197 0.831607i
\(288\) 29.9480i 0.103986i
\(289\) −358.172 + 620.372i −1.23935 + 2.14662i
\(290\) −196.749 704.930i −0.678445 2.43079i
\(291\) 103.296 + 178.914i 0.354969 + 0.614824i
\(292\) 246.161 426.364i 0.843018 1.46015i
\(293\) −73.8439 −0.252027 −0.126013 0.992029i \(-0.540218\pi\)
−0.126013 + 0.992029i \(0.540218\pi\)
\(294\) 288.282 + 23.6427i 0.980551 + 0.0804175i
\(295\) 449.880 + 115.554i 1.52502 + 0.391710i
\(296\) −51.8834 + 89.8646i −0.175282 + 0.303597i
\(297\) 3.60955 + 6.25193i 0.0121534 + 0.0210503i
\(298\) −527.403 + 304.496i −1.76981 + 1.02180i
\(299\) −74.1655 42.8195i −0.248045 0.143209i
\(300\) 288.937 + 158.915i 0.963124 + 0.529716i
\(301\) −47.0873 51.1071i −0.156436 0.169791i
\(302\) 823.246i 2.72598i
\(303\) −179.598 103.691i −0.592732 0.342214i
\(304\) −148.001 + 85.4486i −0.486847 + 0.281081i
\(305\) −2.20185 7.88897i −0.00721917 0.0258655i
\(306\) 280.754 + 162.093i 0.917496 + 0.529717i
\(307\) 162.912 0.530659 0.265330 0.964158i \(-0.414519\pi\)
0.265330 + 0.964158i \(0.414519\pi\)
\(308\) −16.2263 72.2618i −0.0526827 0.234616i
\(309\) −108.041 −0.349646
\(310\) −393.789 385.698i −1.27029 1.24419i
\(311\) 34.3514 19.8328i 0.110455 0.0637711i −0.443755 0.896148i \(-0.646354\pi\)
0.554210 + 0.832377i \(0.313021\pi\)
\(312\) −69.9820 + 40.4041i −0.224301 + 0.129500i
\(313\) 74.1316 128.400i 0.236842 0.410222i −0.722964 0.690885i \(-0.757221\pi\)
0.959806 + 0.280663i \(0.0905543\pi\)
\(314\) 140.840i 0.448536i
\(315\) −55.2518 + 89.2874i −0.175403 + 0.283452i
\(316\) 11.3459 0.0359049
\(317\) −44.9762 25.9670i −0.141881 0.0819149i 0.427379 0.904072i \(-0.359437\pi\)
−0.569260 + 0.822158i \(0.692770\pi\)
\(318\) 253.675 + 439.377i 0.797719 + 1.38169i
\(319\) −29.8346 51.6750i −0.0935253 0.161991i
\(320\) −286.306 280.424i −0.894705 0.876324i
\(321\) 208.412i 0.649259i
\(322\) −515.051 160.857i −1.59954 0.499556i
\(323\) 469.863i 1.45469i
\(324\) 34.2692 59.3560i 0.105769 0.183197i
\(325\) 1.96473 + 94.6394i 0.00604533 + 0.291198i
\(326\) 119.069 + 206.233i 0.365241 + 0.632617i
\(327\) 56.3433 97.5894i 0.172304 0.298439i
\(328\) 571.249 1.74161
\(329\) −83.6792 372.656i −0.254344 1.13269i
\(330\) 39.7169 + 10.2015i 0.120354 + 0.0309137i
\(331\) −193.516 + 335.179i −0.584639 + 1.01262i 0.410281 + 0.911959i \(0.365431\pi\)
−0.994920 + 0.100666i \(0.967903\pi\)
\(332\) 52.0629 + 90.1756i 0.156816 + 0.271613i
\(333\) 21.8796 12.6322i 0.0657046 0.0379346i
\(334\) −96.5323 55.7329i −0.289019 0.166865i
\(335\) 211.955 + 54.4419i 0.632702 + 0.162513i
\(336\) −102.831 + 94.7431i −0.306046 + 0.281974i
\(337\) 574.984i 1.70618i −0.521761 0.853092i \(-0.674725\pi\)
0.521761 0.853092i \(-0.325275\pi\)
\(338\) 456.493 + 263.556i 1.35057 + 0.779753i
\(339\) 200.195 115.582i 0.590545 0.340951i
\(340\) 1162.87 324.561i 3.42019 0.954591i
\(341\) −38.9191 22.4699i −0.114132 0.0658943i
\(342\) 151.514 0.443023
\(343\) 211.017 + 270.408i 0.615211 + 0.788362i
\(344\) 122.323 0.355589
\(345\) 137.059 139.934i 0.397272 0.405605i
\(346\) 73.3419 42.3440i 0.211971 0.122381i
\(347\) −21.1805 + 12.2286i −0.0610389 + 0.0352408i −0.530209 0.847867i \(-0.677886\pi\)
0.469170 + 0.883108i \(0.344553\pi\)
\(348\) −283.250 + 490.604i −0.813937 + 1.40978i
\(349\) 162.352i 0.465193i −0.972573 0.232597i \(-0.925278\pi\)
0.972573 0.232597i \(-0.0747222\pi\)
\(350\) 142.722 + 579.095i 0.407778 + 1.65456i
\(351\) 19.6747 0.0560532
\(352\) −12.0110 6.93454i −0.0341221 0.0197004i
\(353\) 195.326 + 338.314i 0.553331 + 0.958397i 0.998031 + 0.0627175i \(0.0199767\pi\)
−0.444701 + 0.895679i \(0.646690\pi\)
\(354\) −274.187 474.906i −0.774541 1.34154i
\(355\) 217.633 + 213.162i 0.613050 + 0.600455i
\(356\) 967.828i 2.71862i
\(357\) 84.2256 + 375.089i 0.235926 + 1.05067i
\(358\) 477.565i 1.33398i
\(359\) −168.035 + 291.044i −0.468063 + 0.810709i −0.999334 0.0364931i \(-0.988381\pi\)
0.531271 + 0.847202i \(0.321715\pi\)
\(360\) −49.6865 178.021i −0.138018 0.494504i
\(361\) −70.7009 122.458i −0.195847 0.339218i
\(362\) 478.989 829.633i 1.32317 2.29180i
\(363\) −206.235 −0.568140
\(364\) −192.666 60.1720i −0.529302 0.165308i
\(365\) −80.4164 + 313.080i −0.220319 + 0.857753i
\(366\) −4.83489 + 8.37428i −0.0132101 + 0.0228805i
\(367\) 174.508 + 302.258i 0.475500 + 0.823590i 0.999606 0.0280628i \(-0.00893385\pi\)
−0.524106 + 0.851653i \(0.675601\pi\)
\(368\) 225.890 130.418i 0.613832 0.354396i
\(369\) −120.450 69.5420i −0.326424 0.188461i
\(370\) 35.7019 138.996i 0.0964916 0.375664i
\(371\) −179.352 + 574.272i −0.483430 + 1.54790i
\(372\) 426.661i 1.14694i
\(373\) 142.361 + 82.1924i 0.381666 + 0.220355i 0.678543 0.734561i \(-0.262612\pi\)
−0.296877 + 0.954916i \(0.595945\pi\)
\(374\) 130.019 75.0663i 0.347644 0.200712i
\(375\) −210.772 49.4985i −0.562059 0.131996i
\(376\) 582.226 + 336.149i 1.54847 + 0.894012i
\(377\) −162.620 −0.431353
\(378\) 120.952 27.1597i 0.319980 0.0718510i
\(379\) 172.731 0.455755 0.227878 0.973690i \(-0.426821\pi\)
0.227878 + 0.973690i \(0.426821\pi\)
\(380\) 394.826 403.108i 1.03902 1.06081i
\(381\) 281.953 162.786i 0.740034 0.427259i
\(382\) −302.165 + 174.455i −0.791007 + 0.456688i
\(383\) −111.180 + 192.569i −0.290287 + 0.502791i −0.973877 0.227074i \(-0.927084\pi\)
0.683591 + 0.729866i \(0.260417\pi\)
\(384\) 403.980i 1.05203i
\(385\) 23.0160 + 42.8341i 0.0597818 + 0.111257i
\(386\) 9.14070 0.0236806
\(387\) −25.7922 14.8912i −0.0666466 0.0384784i
\(388\) −454.165 786.638i −1.17053 2.02742i
\(389\) 242.996 + 420.881i 0.624668 + 1.08196i 0.988605 + 0.150533i \(0.0480991\pi\)
−0.363937 + 0.931424i \(0.618568\pi\)
\(390\) 78.1994 79.8396i 0.200511 0.204717i
\(391\) 717.139i 1.83411i
\(392\) −601.742 49.3504i −1.53506 0.125894i
\(393\) 123.398i 0.313991i
\(394\) 54.5960 94.5631i 0.138569 0.240008i
\(395\) −7.17513 + 2.00261i −0.0181649 + 0.00506990i
\(396\) −15.8702 27.4881i −0.0400764 0.0694143i
\(397\) −197.795 + 342.591i −0.498224 + 0.862949i −0.999998 0.00204967i \(-0.999348\pi\)
0.501774 + 0.864999i \(0.332681\pi\)
\(398\) −55.6102 −0.139724
\(399\) 121.742 + 132.135i 0.305118 + 0.331166i
\(400\) −252.623 138.942i −0.631557 0.347355i
\(401\) −189.425 + 328.093i −0.472380 + 0.818187i −0.999500 0.0316039i \(-0.989939\pi\)
0.527120 + 0.849791i \(0.323272\pi\)
\(402\) −129.180 223.746i −0.321343 0.556582i
\(403\) −106.069 + 61.2387i −0.263198 + 0.151957i
\(404\) 789.644 + 455.901i 1.95456 + 1.12847i
\(405\) −11.1951 + 43.5852i −0.0276423 + 0.107618i
\(406\) −999.726 + 224.487i −2.46238 + 0.552924i
\(407\) 11.7001i 0.0287472i
\(408\) −586.028 338.343i −1.43634 0.829273i
\(409\) 674.493 389.419i 1.64913 0.952124i 0.671707 0.740817i \(-0.265562\pi\)
0.977420 0.211306i \(-0.0677718\pi\)
\(410\) −760.945 + 212.383i −1.85596 + 0.518008i
\(411\) −56.9720 32.8928i −0.138618 0.0800311i
\(412\) 475.026 1.15298
\(413\) 193.855 620.709i 0.469383 1.50293i
\(414\) −231.251 −0.558577
\(415\) −48.8408 47.8374i −0.117689 0.115271i
\(416\) −32.7342 + 18.8991i −0.0786881 + 0.0454306i
\(417\) 147.627 85.2324i 0.354021 0.204394i
\(418\) 35.0834 60.7663i 0.0839317 0.145374i
\(419\) 350.942i 0.837571i 0.908085 + 0.418785i \(0.137544\pi\)
−0.908085 + 0.418785i \(0.862456\pi\)
\(420\) 242.928 392.573i 0.578400 0.934698i
\(421\) 175.760 0.417482 0.208741 0.977971i \(-0.433063\pi\)
0.208741 + 0.977971i \(0.433063\pi\)
\(422\) 919.326 + 530.773i 2.17850 + 1.25776i
\(423\) −81.8432 141.757i −0.193483 0.335122i
\(424\) −529.505 917.129i −1.24883 2.16304i
\(425\) −678.106 + 410.502i −1.59554 + 0.965888i
\(426\) 359.655i 0.844260i
\(427\) −11.1881 + 2.51227i −0.0262016 + 0.00588353i
\(428\) 916.334i 2.14097i
\(429\) 4.55572 7.89074i 0.0106194 0.0183933i
\(430\) −162.943 + 45.4780i −0.378936 + 0.105763i
\(431\) −427.661 740.730i −0.992252 1.71863i −0.603720 0.797196i \(-0.706316\pi\)
−0.388532 0.921435i \(-0.627018\pi\)
\(432\) −29.9621 + 51.8959i −0.0693568 + 0.120129i
\(433\) −67.4511 −0.155776 −0.0778881 0.996962i \(-0.524818\pi\)
−0.0778881 + 0.996962i \(0.524818\pi\)
\(434\) −567.533 + 522.894i −1.30768 + 1.20482i
\(435\) 92.5327 360.251i 0.212719 0.828164i
\(436\) −247.727 + 429.075i −0.568180 + 0.984117i
\(437\) −167.583 290.262i −0.383485 0.664216i
\(438\) 330.496 190.812i 0.754557 0.435644i
\(439\) 242.742 + 140.147i 0.552944 + 0.319242i 0.750308 0.661088i \(-0.229905\pi\)
−0.197365 + 0.980330i \(0.563238\pi\)
\(440\) −82.9025 21.2940i −0.188415 0.0483954i
\(441\) 120.872 + 83.6598i 0.274086 + 0.189705i
\(442\) 409.166i 0.925715i
\(443\) −400.585 231.278i −0.904256 0.522072i −0.0256772 0.999670i \(-0.508174\pi\)
−0.878578 + 0.477598i \(0.841508\pi\)
\(444\) −96.1991 + 55.5406i −0.216665 + 0.125091i
\(445\) −170.826 612.052i −0.383879 1.37540i
\(446\) 329.140 + 190.029i 0.737983 + 0.426074i
\(447\) −309.497 −0.692387
\(448\) −412.628 + 380.172i −0.921044 + 0.848599i
\(449\) −502.561 −1.11929 −0.559644 0.828733i \(-0.689062\pi\)
−0.559644 + 0.828733i \(0.689062\pi\)
\(450\) 132.372 + 218.664i 0.294160 + 0.485921i
\(451\) −55.7812 + 32.2053i −0.123683 + 0.0714086i
\(452\) −880.203 + 508.186i −1.94735 + 1.12430i
\(453\) −209.191 + 362.330i −0.461791 + 0.799846i
\(454\) 290.622i 0.640136i
\(455\) 132.462 + 4.04613i 0.291125 + 0.00889259i
\(456\) −316.260 −0.693553
\(457\) 540.918 + 312.299i 1.18363 + 0.683368i 0.956851 0.290579i \(-0.0938479\pi\)
0.226777 + 0.973947i \(0.427181\pi\)
\(458\) 118.891 + 205.926i 0.259588 + 0.449620i
\(459\) 82.3776 + 142.682i 0.179472 + 0.310854i
\(460\) −602.612 + 615.252i −1.31003 + 1.33750i
\(461\) 68.1722i 0.147879i 0.997263 + 0.0739395i \(0.0235572\pi\)
−0.997263 + 0.0739395i \(0.976443\pi\)
\(462\) 17.1142 54.7982i 0.0370437 0.118611i
\(463\) 231.353i 0.499682i −0.968287 0.249841i \(-0.919622\pi\)
0.968287 0.249841i \(-0.0803784\pi\)
\(464\) 247.650 428.943i 0.533729 0.924446i
\(465\) −75.3076 269.819i −0.161952 0.580256i
\(466\) 295.780 + 512.306i 0.634721 + 1.09937i
\(467\) 246.131 426.312i 0.527048 0.912873i −0.472456 0.881355i \(-0.656632\pi\)
0.999503 0.0315188i \(-0.0100344\pi\)
\(468\) −86.5044 −0.184838
\(469\) 91.3324 292.439i 0.194739 0.623538i
\(470\) −900.543 231.310i −1.91605 0.492149i
\(471\) 35.7883 61.9871i 0.0759836 0.131607i
\(472\) 572.322 + 991.290i 1.21255 + 2.10019i
\(473\) −11.9445 + 6.89618i −0.0252527 + 0.0145797i
\(474\) 7.61653 + 4.39740i 0.0160686 + 0.00927722i
\(475\) −178.536 + 324.613i −0.375866 + 0.683396i
\(476\) −370.318 1649.17i −0.777979 3.46464i
\(477\) 257.841i 0.540546i
\(478\) 321.470 + 185.601i 0.672531 + 0.388286i
\(479\) 621.354 358.739i 1.29719 0.748933i 0.317272 0.948335i \(-0.397233\pi\)
0.979918 + 0.199401i \(0.0638998\pi\)
\(480\) −23.2410 83.2699i −0.0484187 0.173479i
\(481\) −27.6150 15.9435i −0.0574116 0.0331466i
\(482\) 353.458 0.733316
\(483\) −185.812 201.674i −0.384703 0.417545i
\(484\) 906.761 1.87347
\(485\) 426.058 + 417.305i 0.878470 + 0.860422i
\(486\) 46.0098 26.5638i 0.0946704 0.0546580i
\(487\) 347.225 200.471i 0.712988 0.411644i −0.0991784 0.995070i \(-0.531621\pi\)
0.812166 + 0.583426i \(0.198288\pi\)
\(488\) 10.0921 17.4799i 0.0206804 0.0358196i
\(489\) 121.024i 0.247493i
\(490\) 819.911 157.982i 1.67329 0.322411i
\(491\) 894.115 1.82101 0.910505 0.413499i \(-0.135693\pi\)
0.910505 + 0.413499i \(0.135693\pi\)
\(492\) 529.588 + 305.758i 1.07640 + 0.621459i
\(493\) −680.888 1179.33i −1.38111 2.39216i
\(494\) −95.6151 165.610i −0.193553 0.335243i
\(495\) 14.8881 + 14.5822i 0.0300769 + 0.0294590i
\(496\) 373.037i 0.752090i
\(497\) 313.655 288.985i 0.631097 0.581458i
\(498\) 80.7132i 0.162075i
\(499\) 261.273 452.538i 0.523593 0.906890i −0.476030 0.879429i \(-0.657925\pi\)
0.999623 0.0274608i \(-0.00874213\pi\)
\(500\) 926.710 + 217.632i 1.85342 + 0.435263i
\(501\) −28.3241 49.0588i −0.0565351 0.0979217i
\(502\) −394.267 + 682.891i −0.785393 + 1.36034i
\(503\) 849.283 1.68844 0.844218 0.536000i \(-0.180065\pi\)
0.844218 + 0.536000i \(0.180065\pi\)
\(504\) −252.469 + 56.6914i −0.500930 + 0.112483i
\(505\) −579.837 148.935i −1.14819 0.294920i
\(506\) −53.5468 + 92.7458i −0.105824 + 0.183292i
\(507\) 133.942 + 231.995i 0.264186 + 0.457584i
\(508\) −1239.67 + 715.726i −2.44030 + 1.40891i
\(509\) −589.645 340.432i −1.15844 0.668824i −0.207509 0.978233i \(-0.566536\pi\)
−0.950929 + 0.309409i \(0.899869\pi\)
\(510\) 906.423 + 232.820i 1.77730 + 0.456510i
\(511\) 431.963 + 134.907i 0.845329 + 0.264007i
\(512\) 683.520i 1.33500i
\(513\) 66.6848 + 38.5005i 0.129990 + 0.0750497i
\(514\) −272.439 + 157.293i −0.530037 + 0.306017i
\(515\) −300.405 + 83.8444i −0.583311 + 0.162805i
\(516\) 113.402 + 65.4725i 0.219771 + 0.126885i
\(517\) −75.8041 −0.146623
\(518\) −191.775 59.8939i −0.370223 0.115625i
\(519\) 43.0393 0.0829274
\(520\) −163.228 + 166.652i −0.313901 + 0.320485i
\(521\) −65.5525 + 37.8468i −0.125821 + 0.0726425i −0.561589 0.827416i \(-0.689810\pi\)
0.435769 + 0.900059i \(0.356477\pi\)
\(522\) −380.292 + 219.562i −0.728528 + 0.420616i
\(523\) 89.4351 154.906i 0.171004 0.296188i −0.767767 0.640729i \(-0.778632\pi\)
0.938771 + 0.344541i \(0.111966\pi\)
\(524\) 542.550i 1.03540i
\(525\) −84.3357 + 291.140i −0.160640 + 0.554552i
\(526\) 513.882 0.976963
\(527\) −888.216 512.812i −1.68542 0.973078i
\(528\) 13.8756 + 24.0333i 0.0262796 + 0.0455176i
\(529\) −8.72296 15.1086i −0.0164895 0.0285607i
\(530\) 1046.31 + 1024.82i 1.97418 + 1.93362i
\(531\) 278.690i 0.524840i
\(532\) −535.269 580.965i −1.00614 1.09204i
\(533\) 175.542i 0.329347i
\(534\) −375.106 + 649.703i −0.702446 + 1.21667i
\(535\) 161.737 + 579.486i 0.302313 + 1.08315i
\(536\) 269.642 + 467.033i 0.503063 + 0.871331i
\(537\) 121.352 210.188i 0.225981 0.391411i
\(538\) 376.040 0.698959
\(539\) 61.5409 29.1054i 0.114176 0.0539989i
\(540\) 49.2220 191.633i 0.0911518 0.354875i
\(541\) −357.392 + 619.020i −0.660613 + 1.14422i 0.319842 + 0.947471i \(0.396370\pi\)
−0.980455 + 0.196744i \(0.936963\pi\)
\(542\) 169.154 + 292.983i 0.312092 + 0.540559i
\(543\) 421.629 243.427i 0.776480 0.448301i
\(544\) −274.116 158.261i −0.503890 0.290921i
\(545\) 80.9278 315.071i 0.148491 0.578111i
\(546\) −106.015 115.066i −0.194167 0.210743i
\(547\) 422.685i 0.772734i 0.922345 + 0.386367i \(0.126270\pi\)
−0.922345 + 0.386367i \(0.873730\pi\)
\(548\) 250.491 + 144.621i 0.457100 + 0.263907i
\(549\) −4.25590 + 2.45715i −0.00775210 + 0.00447567i
\(550\) 118.349 2.45695i 0.215180 0.00446718i
\(551\) −551.180 318.224i −1.00033 0.577539i
\(552\) 482.699 0.874454
\(553\) 2.28494 + 10.1757i 0.00413190 + 0.0184009i
\(554\) −1326.77 −2.39489
\(555\) 51.0328 52.1033i 0.0919510 0.0938798i
\(556\) −649.077 + 374.745i −1.16740 + 0.674001i
\(557\) −427.861 + 247.026i −0.768152 + 0.443493i −0.832215 0.554453i \(-0.812928\pi\)
0.0640629 + 0.997946i \(0.479594\pi\)
\(558\) −165.363 + 286.417i −0.296350 + 0.513293i
\(559\) 37.5891i 0.0672436i
\(560\) −212.396 + 343.233i −0.379278 + 0.612917i
\(561\) 76.2991 0.136005
\(562\) −907.222 523.785i −1.61427 0.932002i
\(563\) −121.401 210.272i −0.215632 0.373485i 0.737836 0.674980i \(-0.235848\pi\)
−0.953468 + 0.301495i \(0.902514\pi\)
\(564\) 359.843 + 623.267i 0.638020 + 1.10508i
\(565\) 466.941 476.735i 0.826444 0.843779i
\(566\) 1530.52i 2.70411i
\(567\) 60.1354 + 18.7811i 0.106059 + 0.0331236i
\(568\) 750.721i 1.32169i
\(569\) 239.174 414.262i 0.420342 0.728053i −0.575631 0.817710i \(-0.695244\pi\)
0.995973 + 0.0896563i \(0.0285769\pi\)
\(570\) 421.282 117.582i 0.739090 0.206283i
\(571\) −54.1383 93.7703i −0.0948131 0.164221i 0.814717 0.579858i \(-0.196892\pi\)
−0.909531 + 0.415637i \(0.863559\pi\)
\(572\) −20.0303 + 34.6935i −0.0350180 + 0.0606530i
\(573\) −177.320 −0.309459
\(574\) 242.325 + 1079.17i 0.422170 + 1.88008i
\(575\) 272.495 495.447i 0.473904 0.861647i
\(576\) −120.228 + 208.241i −0.208729 + 0.361529i
\(577\) 49.6800 + 86.0482i 0.0861004 + 0.149130i 0.905860 0.423578i \(-0.139226\pi\)
−0.819759 + 0.572708i \(0.805893\pi\)
\(578\) 2114.31 1220.70i 3.65798 2.11193i
\(579\) 4.02304 + 2.32270i 0.00694825 + 0.00401157i
\(580\) −406.842 + 1583.93i −0.701452 + 2.73091i
\(581\) −70.3901 + 64.8535i −0.121153 + 0.111624i
\(582\) 704.093i 1.20978i
\(583\) 103.410 + 59.7037i 0.177375 + 0.102408i
\(584\) −689.857 + 398.289i −1.18126 + 0.682002i
\(585\) 54.7051 15.2684i 0.0935129 0.0260999i
\(586\) 217.952 + 125.835i 0.371932 + 0.214735i
\(587\) 3.32500 0.00566440 0.00283220 0.999996i \(-0.499098\pi\)
0.00283220 + 0.999996i \(0.499098\pi\)
\(588\) −531.443 367.830i −0.903814 0.625562i
\(589\) −479.342 −0.813823
\(590\) −1130.92 1107.69i −1.91682 1.87744i
\(591\) 48.0580 27.7463i 0.0813164 0.0469481i
\(592\) 84.1085 48.5600i 0.142075 0.0820271i
\(593\) −233.891 + 405.112i −0.394421 + 0.683157i −0.993027 0.117887i \(-0.962388\pi\)
0.598606 + 0.801043i \(0.295721\pi\)
\(594\) 24.6037i 0.0414203i
\(595\) 525.274 + 977.565i 0.882813 + 1.64297i
\(596\) 1360.78 2.28318
\(597\) −24.4754 14.1309i −0.0409973 0.0236698i
\(598\) 145.934 + 252.766i 0.244038 + 0.422685i
\(599\) 264.452 + 458.045i 0.441490 + 0.764683i 0.997800 0.0662916i \(-0.0211167\pi\)
−0.556310 + 0.830975i \(0.687783\pi\)
\(600\) −276.305 456.426i −0.460509 0.760711i
\(601\) 490.357i 0.815901i −0.913004 0.407951i \(-0.866244\pi\)
0.913004 0.407951i \(-0.133756\pi\)
\(602\) 51.8896 + 231.084i 0.0861953 + 0.383860i
\(603\) 131.301i 0.217747i
\(604\) 919.760 1593.07i 1.52278 2.63753i
\(605\) −573.433 + 160.048i −0.947823 + 0.264541i
\(606\) 353.392 + 612.093i 0.583155 + 1.01005i
\(607\) 49.6685 86.0283i 0.0818261 0.141727i −0.822208 0.569187i \(-0.807258\pi\)
0.904034 + 0.427460i \(0.140591\pi\)
\(608\) −147.931 −0.243308
\(609\) −497.047 155.234i −0.816168 0.254900i
\(610\) −6.94452 + 27.0366i −0.0113845 + 0.0443224i
\(611\) −103.297 + 178.915i −0.169062 + 0.292824i
\(612\) −362.193 627.336i −0.591818 1.02506i
\(613\) −248.004 + 143.185i −0.404573 + 0.233581i −0.688455 0.725279i \(-0.741711\pi\)
0.283882 + 0.958859i \(0.408378\pi\)
\(614\) −480.841 277.614i −0.783128 0.452139i
\(615\) −388.878 99.8855i −0.632321 0.162415i
\(616\) −35.7231 + 114.382i −0.0579920 + 0.185686i
\(617\) 335.855i 0.544336i 0.962250 + 0.272168i \(0.0877406\pi\)
−0.962250 + 0.272168i \(0.912259\pi\)
\(618\) 318.885 + 184.108i 0.515995 + 0.297910i
\(619\) 539.249 311.336i 0.871162 0.502966i 0.00342798 0.999994i \(-0.498909\pi\)
0.867734 + 0.497028i \(0.165576\pi\)
\(620\) 331.108 + 1186.32i 0.534045 + 1.91342i
\(621\) −101.779 58.7621i −0.163895 0.0946250i
\(622\) −135.186 −0.217340
\(623\) −868.007 + 194.910i −1.39327 + 0.312857i
\(624\) 75.6322 0.121205
\(625\) −624.461 + 25.9391i −0.999138 + 0.0415025i
\(626\) −437.603 + 252.650i −0.699046 + 0.403595i
\(627\) 30.8821 17.8298i 0.0492537 0.0284367i
\(628\) −157.352 + 272.541i −0.250560 + 0.433983i
\(629\) 267.021i 0.424517i
\(630\) 315.229 169.382i 0.500364 0.268860i
\(631\) −342.555 −0.542876 −0.271438 0.962456i \(-0.587499\pi\)
−0.271438 + 0.962456i \(0.587499\pi\)
\(632\) −15.8983 9.17886i −0.0251555 0.0145235i
\(633\) 269.745 + 467.212i 0.426137 + 0.738091i
\(634\) 88.4991 + 153.285i 0.139588 + 0.241774i
\(635\) 657.636 671.431i 1.03565 1.05737i
\(636\) 1133.66i 1.78248i
\(637\) 15.1651 184.912i 0.0238071 0.290286i
\(638\) 203.360i 0.318747i
\(639\) 91.3902 158.293i 0.143021 0.247719i
\(640\) 313.507 + 1123.26i 0.489854 + 1.75509i
\(641\) 486.307 + 842.309i 0.758670 + 1.31405i 0.943529 + 0.331289i \(0.107484\pi\)
−0.184859 + 0.982765i \(0.559183\pi\)
\(642\) 355.148 615.135i 0.553190 0.958154i
\(643\) 986.446 1.53413 0.767065 0.641569i \(-0.221716\pi\)
0.767065 + 0.641569i \(0.221716\pi\)
\(644\) 816.965 + 886.709i 1.26858 + 1.37688i
\(645\) −83.2711 21.3887i −0.129102 0.0331607i
\(646\) 800.679 1386.82i 1.23944 2.14677i
\(647\) −40.4977 70.1440i −0.0625930 0.108414i 0.833031 0.553227i \(-0.186604\pi\)
−0.895624 + 0.444812i \(0.853270\pi\)
\(648\) −96.0380 + 55.4476i −0.148207 + 0.0855672i
\(649\) −111.772 64.5315i −0.172222 0.0994321i
\(650\) 155.473 282.679i 0.239189 0.434891i
\(651\) −382.655 + 85.9246i −0.587796 + 0.131989i
\(652\) 532.111i 0.816121i
\(653\) 329.060 + 189.983i 0.503920 + 0.290938i 0.730331 0.683093i \(-0.239366\pi\)
−0.226411 + 0.974032i \(0.572699\pi\)
\(654\) −332.598 + 192.025i −0.508559 + 0.293617i
\(655\) −95.7627 343.107i −0.146203 0.523828i
\(656\) −463.028 267.329i −0.705835 0.407514i
\(657\) 193.946 0.295199
\(658\) −388.048 + 1242.50i −0.589739 + 1.88830i
\(659\) 409.417 0.621269 0.310635 0.950529i \(-0.399458\pi\)
0.310635 + 0.950529i \(0.399458\pi\)
\(660\) −65.4590 64.1141i −0.0991802 0.0971426i
\(661\) −392.365 + 226.532i −0.593592 + 0.342711i −0.766517 0.642224i \(-0.778012\pi\)
0.172924 + 0.984935i \(0.444678\pi\)
\(662\) 1142.33 659.527i 1.72558 0.996264i
\(663\) 103.971 180.084i 0.156819 0.271619i
\(664\) 168.476i 0.253728i
\(665\) 441.045 + 272.923i 0.663226 + 0.410410i
\(666\) −86.1046 −0.129286
\(667\) 841.249 + 485.696i 1.26124 + 0.728179i
\(668\) 124.534 + 215.699i 0.186428 + 0.322902i
\(669\) 96.5749 + 167.273i 0.144357 + 0.250034i
\(670\) −532.819 521.873i −0.795253 0.778915i
\(671\) 2.27584i 0.00339171i
\(672\) −118.093 + 26.5175i −0.175733 + 0.0394606i
\(673\) 1044.13i 1.55145i 0.631071 + 0.775725i \(0.282616\pi\)
−0.631071 + 0.775725i \(0.717384\pi\)
\(674\) −979.811 + 1697.08i −1.45372 + 2.51793i
\(675\) 2.69625 + 129.876i 0.00399444 + 0.192409i
\(676\) −588.909 1020.02i −0.871168 1.50891i
\(677\) −661.013 + 1144.91i −0.976386 + 1.69115i −0.301102 + 0.953592i \(0.597354\pi\)
−0.675284 + 0.737558i \(0.735979\pi\)
\(678\) −787.841 −1.16201
\(679\) 614.040 565.743i 0.904330 0.833200i
\(680\) −1892.01 485.974i −2.78237 0.714668i
\(681\) −73.8486 + 127.909i −0.108441 + 0.187826i
\(682\) 76.5806 + 132.641i 0.112288 + 0.194489i
\(683\) 715.045 412.831i 1.04692 0.604438i 0.125133 0.992140i \(-0.460064\pi\)
0.921785 + 0.387702i \(0.126731\pi\)
\(684\) −293.196 169.277i −0.428649 0.247480i
\(685\) −183.936 47.2450i −0.268520 0.0689708i
\(686\) −162.031 1157.71i −0.236197 1.68762i
\(687\) 120.844i 0.175901i
\(688\) −99.1490 57.2437i −0.144112 0.0832031i
\(689\) 281.829 162.714i 0.409041 0.236160i
\(690\) −642.990 + 179.461i −0.931869 + 0.260089i
\(691\) −219.857 126.935i −0.318173 0.183697i 0.332405 0.943137i \(-0.392140\pi\)
−0.650578 + 0.759440i \(0.725473\pi\)
\(692\) −189.233 −0.273458
\(693\) 21.4569 19.7692i 0.0309623 0.0285270i
\(694\) 83.3531 0.120105
\(695\) 344.330 351.552i 0.495439 0.505831i
\(696\) 793.797 458.299i 1.14051 0.658476i
\(697\) −1273.05 + 734.993i −1.82646 + 1.05451i
\(698\) −276.659 + 479.188i −0.396360 + 0.686516i
\(699\) 300.637i 0.430097i
\(700\) 370.802 1280.07i 0.529717 1.82867i
\(701\) 304.585 0.434500 0.217250 0.976116i \(-0.430291\pi\)
0.217250 + 0.976116i \(0.430291\pi\)
\(702\) −58.0704 33.5269i −0.0827213 0.0477592i
\(703\) −62.3983 108.077i −0.0887600 0.153737i
\(704\) 55.6782 + 96.4375i 0.0790884 + 0.136985i
\(705\) −337.573 330.638i −0.478827 0.468990i
\(706\) 1331.39i 1.88582i
\(707\) −249.854 + 800.014i −0.353401 + 1.13156i
\(708\) 1225.33i 1.73069i
\(709\) −23.4875 + 40.6815i −0.0331276 + 0.0573787i −0.882114 0.471036i \(-0.843880\pi\)
0.848986 + 0.528415i \(0.177213\pi\)
\(710\) −279.108 1000.01i −0.393110 1.40847i
\(711\) 2.23481 + 3.87080i 0.00314319 + 0.00544417i
\(712\) 782.973 1356.15i 1.09968 1.90470i
\(713\) 731.605 1.02609
\(714\) 390.582 1250.61i 0.547033 1.75156i
\(715\) 6.54354 25.4755i 0.00915180 0.0356301i
\(716\) −533.552 + 924.140i −0.745185 + 1.29070i
\(717\) 94.3243 + 163.374i 0.131554 + 0.227858i
\(718\) 991.918 572.684i 1.38150 0.797611i
\(719\) 276.768 + 159.792i 0.384934 + 0.222242i 0.679963 0.733247i \(-0.261996\pi\)
−0.295029 + 0.955488i \(0.595329\pi\)
\(720\) −43.0356 + 167.548i −0.0597717 + 0.232705i
\(721\) 95.6649 + 426.032i 0.132684 + 0.590891i
\(722\) 481.916i 0.667474i
\(723\) 155.565 + 89.8157i 0.215167 + 0.124226i
\(724\) −1853.79 + 1070.29i −2.56048 + 1.47830i
\(725\) −22.2857 1073.48i −0.0307389 1.48067i
\(726\) 608.709 + 351.438i 0.838442 + 0.484075i
\(727\) −1192.80 −1.64071 −0.820354 0.571855i \(-0.806224\pi\)
−0.820354 + 0.571855i \(0.806224\pi\)
\(728\) 221.290 + 240.181i 0.303970 + 0.329920i
\(729\) 27.0000 0.0370370
\(730\) 770.860 787.029i 1.05597 1.07812i
\(731\) −272.599 + 157.385i −0.372913 + 0.215301i
\(732\) 18.7121 10.8034i 0.0255630 0.0147588i
\(733\) −17.6644 + 30.5956i −0.0240988 + 0.0417403i −0.877823 0.478985i \(-0.841005\pi\)
0.853725 + 0.520725i \(0.174338\pi\)
\(734\) 1189.50i 1.62057i
\(735\) 401.006 + 138.813i 0.545587 + 0.188861i
\(736\) 225.783 0.306771
\(737\) −52.6598 30.4032i −0.0714516 0.0412526i
\(738\) 237.008 + 410.511i 0.321150 + 0.556247i
\(739\) 392.667 + 680.119i 0.531349 + 0.920324i 0.999331 + 0.0365854i \(0.0116481\pi\)
−0.467981 + 0.883738i \(0.655019\pi\)
\(740\) −224.378 + 229.084i −0.303213 + 0.309574i
\(741\) 97.1853i 0.131154i
\(742\) 1507.96 1389.35i 2.03229 1.87244i
\(743\) 419.098i 0.564062i 0.959405 + 0.282031i \(0.0910082\pi\)
−0.959405 + 0.282031i \(0.908992\pi\)
\(744\) 345.169 597.849i 0.463936 0.803561i
\(745\) −860.551 + 240.184i −1.15510 + 0.322394i
\(746\) −280.123 485.187i −0.375500 0.650384i
\(747\) −20.5097 + 35.5238i −0.0274560 + 0.0475553i
\(748\) −335.467 −0.448485
\(749\) 821.823 184.539i 1.09723 0.246381i
\(750\) 537.752 + 505.266i 0.717002 + 0.673688i
\(751\) 59.8519 103.667i 0.0796963 0.138038i −0.823423 0.567429i \(-0.807938\pi\)
0.903119 + 0.429391i \(0.141272\pi\)
\(752\) −314.617 544.933i −0.418374 0.724644i
\(753\) −347.053 + 200.371i −0.460893 + 0.266097i
\(754\) 479.978 + 277.115i 0.636575 + 0.367527i
\(755\) −300.469 + 1169.79i −0.397972 + 1.54940i
\(756\) −264.400 82.5754i −0.349735 0.109227i
\(757\) 995.970i 1.31568i −0.753157 0.657840i \(-0.771470\pi\)
0.753157 0.657840i \(-0.228530\pi\)
\(758\) −509.821 294.346i −0.672588 0.388319i
\(759\) −47.1344 + 27.2131i −0.0621007 + 0.0358539i
\(760\) −879.357 + 245.432i −1.15705 + 0.322937i
\(761\) 237.050 + 136.861i 0.311498 + 0.179843i 0.647596 0.761983i \(-0.275774\pi\)
−0.336099 + 0.941827i \(0.609108\pi\)
\(762\) −1109.59 −1.45615
\(763\) −434.710 135.765i −0.569738 0.177936i
\(764\) 779.629 1.02046
\(765\) 339.777 + 332.797i 0.444153 + 0.435028i
\(766\) 656.301 378.916i 0.856790 0.494668i
\(767\) −304.619 + 175.872i −0.397156 + 0.229298i
\(768\) 410.754 711.447i 0.534836 0.926364i
\(769\) 694.742i 0.903435i 0.892161 + 0.451718i \(0.149189\pi\)
−0.892161 + 0.451718i \(0.850811\pi\)
\(770\) 5.05978 165.647i 0.00657115 0.215126i
\(771\) −159.876 −0.207362
\(772\) −17.6882 10.2123i −0.0229122 0.0132284i
\(773\) −310.846 538.402i −0.402130 0.696510i 0.591853 0.806046i \(-0.298397\pi\)
−0.993983 + 0.109537i \(0.965063\pi\)
\(774\) 50.7510 + 87.9034i 0.0655698 + 0.113570i
\(775\) −418.783 691.785i −0.540365 0.892625i
\(776\) 1469.68i 1.89392i
\(777\) −69.1855 75.0919i −0.0890419 0.0966434i
\(778\) 1656.32i 2.12895i
\(779\) −343.511 + 594.978i −0.440964 + 0.763771i
\(780\) −240.524 + 67.1313i −0.308364 + 0.0860657i
\(781\) −42.3233 73.3061i −0.0541912 0.0938619i
\(782\) −1222.05 + 2116.66i −1.56273 + 2.70672i
\(783\) −223.167 −0.285016
\(784\) 464.649 + 321.600i 0.592665 + 0.410204i
\(785\) 51.4039 200.127i 0.0654827 0.254939i
\(786\) −210.279 + 364.214i −0.267531 + 0.463377i
\(787\) −11.6617 20.1986i −0.0148179 0.0256653i 0.858521 0.512778i \(-0.171384\pi\)
−0.873339 + 0.487112i \(0.838050\pi\)
\(788\) −211.299 + 121.993i −0.268145 + 0.154814i
\(789\) 226.172 + 130.580i 0.286656 + 0.165501i
\(790\) 24.5902 + 6.31614i 0.0311268 + 0.00799511i
\(791\) −633.035 687.077i −0.800297 0.868618i
\(792\) 51.3561i 0.0648436i
\(793\) 5.37150 + 3.10124i 0.00677365 + 0.00391077i
\(794\) 1167.60 674.111i 1.47052 0.849007i
\(795\) 200.096 + 716.921i 0.251693 + 0.901788i
\(796\) 107.612 + 62.1297i 0.135191 + 0.0780524i
\(797\) 140.581 0.176388 0.0881941 0.996103i \(-0.471890\pi\)
0.0881941 + 0.996103i \(0.471890\pi\)
\(798\) −134.158 597.458i −0.168118 0.748695i
\(799\) −1730.01 −2.16522
\(800\) −129.242 213.494i −0.161553 0.266868i
\(801\) −330.186 + 190.633i −0.412218 + 0.237994i
\(802\) 1118.18 645.584i 1.39425 0.804968i
\(803\) 44.9086 77.7840i 0.0559261 0.0968668i
\(804\) 577.297i 0.718031i
\(805\) −673.154 416.554i −0.836216 0.517458i
\(806\) 417.420 0.517890
\(807\) 165.504 + 95.5538i 0.205086 + 0.118406i
\(808\) −737.648 1277.64i −0.912931 1.58124i
\(809\) 92.8993 + 160.906i 0.114832 + 0.198895i 0.917713 0.397245i \(-0.130034\pi\)
−0.802880 + 0.596140i \(0.796700\pi\)
\(810\) 107.315 109.566i 0.132487 0.135266i
\(811\) 683.280i 0.842516i 0.906941 + 0.421258i \(0.138411\pi\)
−0.906941 + 0.421258i \(0.861589\pi\)
\(812\) 2185.38 + 682.523i 2.69136 + 0.840545i
\(813\) 171.932i 0.211478i
\(814\) −19.9378 + 34.5332i −0.0244936 + 0.0424241i
\(815\) 93.9201 + 336.505i 0.115239 + 0.412890i
\(816\) 316.671 + 548.491i 0.388078 + 0.672170i
\(817\) −73.5566 + 127.404i −0.0900325 + 0.155941i
\(818\) −2654.38 −3.24496
\(819\) −17.4210 77.5823i −0.0212711 0.0947281i
\(820\) 1709.79 + 439.171i 2.08511 + 0.535574i
\(821\) 382.762 662.963i 0.466214 0.807507i −0.533041 0.846089i \(-0.678951\pi\)
0.999255 + 0.0385823i \(0.0122842\pi\)
\(822\) 112.103 + 194.168i 0.136378 + 0.236214i
\(823\) −1336.87 + 771.839i −1.62438 + 0.937836i −0.638651 + 0.769496i \(0.720507\pi\)
−0.985729 + 0.168340i \(0.946159\pi\)
\(824\) −665.621 384.296i −0.807792 0.466379i
\(825\) 52.7125 + 28.9917i 0.0638939 + 0.0351415i
\(826\) −1629.90 + 1501.70i −1.97324 + 1.81804i
\(827\) 794.814i 0.961081i −0.876973 0.480540i \(-0.840441\pi\)
0.876973 0.480540i \(-0.159559\pi\)
\(828\) 447.496 + 258.362i 0.540454 + 0.312031i
\(829\) −686.072 + 396.104i −0.827590 + 0.477809i −0.853027 0.521867i \(-0.825236\pi\)
0.0254368 + 0.999676i \(0.491902\pi\)
\(830\) 62.6371 + 224.422i 0.0754663 + 0.270388i
\(831\) −583.943 337.139i −0.702699 0.405703i
\(832\) 303.487 0.364768
\(833\) 1404.49 664.247i 1.68607 0.797416i
\(834\) −580.967 −0.696603
\(835\) −116.826 114.426i −0.139912 0.137038i
\(836\) −135.781 + 78.3929i −0.162417 + 0.0937714i
\(837\) −145.560 + 84.0393i −0.173907 + 0.100405i
\(838\) 598.029 1035.82i 0.713638 1.23606i
\(839\) 1167.54i 1.39159i −0.718241 0.695795i \(-0.755052\pi\)
0.718241 0.695795i \(-0.244948\pi\)
\(840\) −657.989 + 353.557i −0.783321 + 0.420901i
\(841\) 1003.58 1.19331
\(842\) −518.761 299.507i −0.616105 0.355709i
\(843\) −266.193 461.060i −0.315769 0.546928i
\(844\) −1186.00 2054.21i −1.40521 2.43389i
\(845\) 552.463 + 541.113i 0.653802 + 0.640370i
\(846\) 557.865i 0.659415i
\(847\) 182.611 + 813.238i 0.215598 + 0.960140i
\(848\) 991.176i 1.16884i
\(849\) 388.915 673.620i 0.458086 0.793428i
\(850\) 2700.97 56.0728i 3.17762 0.0659679i
\(851\) 95.2367 + 164.955i 0.111911 + 0.193836i
\(852\) −401.819 + 695.971i −0.471618 + 0.816867i
\(853\) 1146.86 1.34450 0.672251 0.740324i \(-0.265328\pi\)
0.672251 + 0.740324i \(0.265328\pi\)
\(854\) 37.3030 + 11.6502i 0.0436804 + 0.0136419i
\(855\) 215.294 + 55.2995i 0.251806 + 0.0646778i
\(856\) −741.314 + 1283.99i −0.866021 + 1.49999i
\(857\) −107.457 186.121i −0.125387 0.217177i 0.796497 0.604643i \(-0.206684\pi\)
−0.921884 + 0.387465i \(0.873351\pi\)
\(858\) −26.8927 + 15.5265i −0.0313435 + 0.0180962i
\(859\) 986.635 + 569.634i 1.14859 + 0.663136i 0.948542 0.316651i \(-0.102558\pi\)
0.200044 + 0.979787i \(0.435892\pi\)
\(860\) 366.121 + 94.0404i 0.425722 + 0.109349i
\(861\) −167.569 + 536.543i −0.194622 + 0.623163i
\(862\) 2915.05i 3.38173i
\(863\) −471.152 272.020i −0.545947 0.315203i 0.201539 0.979481i \(-0.435406\pi\)
−0.747486 + 0.664278i \(0.768739\pi\)
\(864\) −44.9220 + 25.9357i −0.0519930 + 0.0300182i
\(865\) 119.670 33.4005i 0.138347 0.0386133i
\(866\) 199.084 + 114.941i 0.229889 + 0.132726i
\(867\) 1240.74 1.43108
\(868\) 1682.43 377.788i 1.93829 0.435240i
\(869\) 2.06990 0.00238194
\(870\) −887.005 + 905.611i −1.01955 + 1.04093i
\(871\) −143.517 + 82.8596i −0.164773 + 0.0951316i
\(872\) 694.244 400.822i 0.796151 0.459658i
\(873\) 178.914 309.888i 0.204941 0.354969i
\(874\) 1142.29i 1.30697i
\(875\) −8.55638 + 874.958i −0.00977872 + 0.999952i
\(876\) −852.728 −0.973433
\(877\) 456.068 + 263.311i 0.520032 + 0.300241i 0.736948 0.675950i \(-0.236266\pi\)
−0.216916 + 0.976190i \(0.569600\pi\)
\(878\) −477.641 827.298i −0.544010 0.942253i
\(879\) 63.9507 + 110.766i 0.0727539 + 0.126013i
\(880\) 57.2319 + 56.0560i 0.0650362 + 0.0637001i
\(881\) 121.399i 0.137797i 0.997624 + 0.0688983i \(0.0219484\pi\)
−0.997624 + 0.0688983i \(0.978052\pi\)
\(882\) −214.195 452.898i −0.242852 0.513490i
\(883\) 243.586i 0.275862i −0.990442 0.137931i \(-0.955955\pi\)
0.990442 0.137931i \(-0.0440453\pi\)
\(884\) −457.135 + 791.780i −0.517120 + 0.895679i
\(885\) −216.276 774.893i −0.244380 0.875585i
\(886\) 788.226 + 1365.25i 0.889646 + 1.54091i
\(887\) 636.947 1103.23i 0.718092 1.24377i −0.243663 0.969860i \(-0.578349\pi\)
0.961755 0.273911i \(-0.0883175\pi\)
\(888\) 179.729 0.202398
\(889\) −891.562 967.675i −1.00288 1.08850i
\(890\) −538.778 + 2097.59i −0.605368 + 2.35684i
\(891\) 6.25193 10.8287i 0.00701675 0.0121534i
\(892\) −424.615 735.454i −0.476025 0.824500i
\(893\) −700.223 + 404.274i −0.784124 + 0.452714i
\(894\) 913.489 + 527.403i 1.02180 + 0.589937i
\(895\) 174.302 678.597i 0.194751 0.758209i
\(896\) 1593.00 357.705i 1.77790 0.399225i
\(897\) 148.331i 0.165363i
\(898\) 1483.32 + 856.397i 1.65181 + 0.953671i
\(899\) 1203.12 694.623i 1.33829 0.772662i
\(900\) −11.8547 571.030i −0.0131719 0.634478i
\(901\) 2360.03 + 1362.57i 2.61935 + 1.51228i
\(902\) 219.520 0.243370
\(903\) −35.8819 + 114.891i −0.0397363 + 0.127232i
\(904\) 1644.49 1.81913
\(905\) 983.421 1004.05i 1.08665 1.10945i
\(906\) 1234.87 712.952i 1.36299 0.786923i
\(907\) 490.555 283.222i 0.540854 0.312262i −0.204571 0.978852i \(-0.565580\pi\)
0.745425 + 0.666589i \(0.232247\pi\)
\(908\) 324.693 562.384i 0.357591 0.619366i
\(909\) 359.195i 0.395154i
\(910\) −384.070 237.666i −0.422055 0.261172i
\(911\) −1468.26 −1.61170 −0.805850 0.592120i \(-0.798291\pi\)
−0.805850 + 0.592120i \(0.798291\pi\)
\(912\) 256.346 + 148.001i 0.281081 + 0.162282i
\(913\) 9.49814 + 16.4513i 0.0104032 + 0.0180189i
\(914\) −1064.36 1843.52i −1.16450 2.01698i
\(915\) −9.92660 + 10.1348i −0.0108487 + 0.0110763i
\(916\) 531.318i 0.580042i
\(917\) −486.592 + 109.263i −0.530635 + 0.119153i
\(918\) 561.508i 0.611664i
\(919\) −514.213 + 890.643i −0.559535 + 0.969143i 0.438000 + 0.898975i \(0.355687\pi\)
−0.997535 + 0.0701683i \(0.977646\pi\)
\(920\) 1342.14 374.596i 1.45884 0.407170i
\(921\) −141.086 244.369i −0.153188 0.265330i
\(922\) 116.170 201.212i 0.125998 0.218235i
\(923\) −230.693 −0.249938
\(924\) −94.3403 + 86.9199i −0.102100 + 0.0940692i
\(925\) 101.461 184.476i 0.109688 0.199434i
\(926\) −394.241 + 682.845i −0.425746 + 0.737414i
\(927\) 93.5659 + 162.061i 0.100934 + 0.174823i
\(928\) 371.300 214.370i 0.400108 0.231003i
\(929\) −551.039 318.143i −0.593153 0.342457i 0.173190 0.984888i \(-0.444593\pi\)
−0.766343 + 0.642431i \(0.777926\pi\)
\(930\) −237.517 + 924.708i −0.255394 + 0.994309i
\(931\) 413.247 597.061i 0.443874 0.641312i
\(932\) 1321.82i 1.41827i
\(933\) −59.4984 34.3514i −0.0637711 0.0368183i
\(934\) −1452.93 + 838.848i −1.55560 + 0.898124i
\(935\) 212.148 59.2115i 0.226897 0.0633278i
\(936\) 121.212 + 69.9820i 0.129500 + 0.0747671i
\(937\) −1396.05 −1.48991 −0.744956 0.667113i \(-0.767530\pi\)
−0.744956 + 0.667113i \(0.767530\pi\)
\(938\) −767.906 + 707.506i −0.818663 + 0.754271i
\(939\) −256.799 −0.273482
\(940\) 1484.22 + 1453.73i 1.57896 + 1.54652i
\(941\) −334.880 + 193.343i −0.355877 + 0.205466i −0.667271 0.744815i \(-0.732538\pi\)
0.311394 + 0.950281i \(0.399204\pi\)
\(942\) −211.260 + 121.971i −0.224268 + 0.129481i
\(943\) 524.290 908.097i 0.555981 0.962987i
\(944\) 1071.32i 1.13488i
\(945\) 181.781 + 5.55259i 0.192360 + 0.00587576i
\(946\) 47.0062 0.0496894
\(947\) −499.180 288.202i −0.527117 0.304331i 0.212725 0.977112i \(-0.431766\pi\)
−0.739842 + 0.672781i \(0.765100\pi\)
\(948\) −9.82587 17.0189i −0.0103648 0.0179524i
\(949\) −122.392 211.990i −0.128970 0.223382i
\(950\) 1080.12 653.867i 1.13697 0.688281i
\(951\) 89.9524i 0.0945872i
\(952\) −815.276 + 2610.45i −0.856382 + 2.74207i
\(953\) 1080.91i 1.13421i −0.823644 0.567107i \(-0.808063\pi\)
0.823644 0.567107i \(-0.191937\pi\)
\(954\) 439.377 761.024i 0.460563 0.797719i
\(955\) −493.035 + 137.608i −0.516267 + 0.144092i
\(956\) −414.719 718.315i −0.433807 0.751375i
\(957\) −51.6750 + 89.5037i −0.0539968 + 0.0935253i
\(958\) −2445.26 −2.55246
\(959\) −79.2588 + 253.780i −0.0826473 + 0.264630i
\(960\) −172.687 + 672.313i −0.179883 + 0.700326i
\(961\) 42.6564 73.8830i 0.0443875 0.0768814i
\(962\) 54.3376 + 94.1155i 0.0564840 + 0.0978331i
\(963\) 312.618 180.490i 0.324629 0.187425i
\(964\) −683.980 394.896i −0.709523 0.409643i
\(965\) 12.9885 + 3.33617i 0.0134596 + 0.00345718i
\(966\) 204.762 + 911.883i 0.211969 + 0.943978i
\(967\) 785.695i 0.812508i 0.913760 + 0.406254i \(0.133165\pi\)
−0.913760 + 0.406254i \(0.866835\pi\)
\(968\) −1270.58 733.570i −1.31258 0.757820i
\(969\) 704.795 406.914i 0.727343 0.419932i
\(970\) −546.408 1957.72i −0.563307 2.01827i
\(971\) −801.304 462.633i −0.825236 0.476450i 0.0269825 0.999636i \(-0.491410\pi\)
−0.852219 + 0.523186i \(0.824743\pi\)
\(972\) −118.712 −0.122132
\(973\) −466.810 506.662i −0.479764 0.520721i
\(974\) −1366.46 −1.40294
\(975\) 140.258 84.9072i 0.143854 0.0870843i
\(976\) −16.3603 + 9.44562i −0.0167626 + 0.00967789i
\(977\) 278.572 160.834i 0.285130 0.164620i −0.350614 0.936520i \(-0.614027\pi\)
0.635743 + 0.771900i \(0.280694\pi\)
\(978\) 206.233 357.206i 0.210872 0.365241i
\(979\) 176.567i 0.180354i
\(980\) −1763.12 610.322i −1.79910 0.622778i
\(981\) −195.179 −0.198959
\(982\) −2639.01 1523.63i −2.68738 1.55156i
\(983\) 713.047 + 1235.03i 0.725379 + 1.25639i 0.958818 + 0.284021i \(0.0916687\pi\)
−0.233439 + 0.972371i \(0.574998\pi\)
\(984\) −494.716 856.874i −0.502761 0.870807i
\(985\) 112.092 114.443i 0.113799 0.116186i
\(986\) 4641.11i 4.70701i
\(987\) −486.515 + 448.248i −0.492923 + 0.454152i
\(988\) 427.298i 0.432488i
\(989\) 112.267 194.452i 0.113516 0.196615i
\(990\) −19.0935 68.4101i −0.0192864 0.0691011i
\(991\) −854.919 1480.76i −0.862683 1.49421i −0.869329 0.494234i \(-0.835449\pi\)
0.00664562 0.999978i \(-0.497885\pi\)
\(992\) 161.453 279.645i 0.162755 0.281901i
\(993\) 670.358 0.675083
\(994\) −1418.21 + 318.457i −1.42677 + 0.320380i
\(995\) −79.0195 20.2966i −0.0794166 0.0203986i
\(996\) 90.1756 156.189i 0.0905378 0.156816i
\(997\) −687.055 1190.01i −0.689122 1.19359i −0.972122 0.234475i \(-0.924663\pi\)
0.283000 0.959120i \(-0.408670\pi\)
\(998\) −1542.31 + 890.453i −1.54540 + 0.892238i
\(999\) −37.8967 21.8796i −0.0379346 0.0219015i
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 105.3.r.a.19.2 32
3.2 odd 2 315.3.bi.e.19.15 32
5.2 odd 4 525.3.o.p.376.8 16
5.3 odd 4 525.3.o.q.376.1 16
5.4 even 2 inner 105.3.r.a.19.15 yes 32
7.2 even 3 735.3.e.a.244.6 32
7.3 odd 6 inner 105.3.r.a.94.15 yes 32
7.5 odd 6 735.3.e.a.244.14 32
15.14 odd 2 315.3.bi.e.19.2 32
21.17 even 6 315.3.bi.e.199.2 32
35.3 even 12 525.3.o.q.451.1 16
35.9 even 6 735.3.e.a.244.13 32
35.17 even 12 525.3.o.p.451.8 16
35.19 odd 6 735.3.e.a.244.5 32
35.24 odd 6 inner 105.3.r.a.94.2 yes 32
105.59 even 6 315.3.bi.e.199.15 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.3.r.a.19.2 32 1.1 even 1 trivial
105.3.r.a.19.15 yes 32 5.4 even 2 inner
105.3.r.a.94.2 yes 32 35.24 odd 6 inner
105.3.r.a.94.15 yes 32 7.3 odd 6 inner
315.3.bi.e.19.2 32 15.14 odd 2
315.3.bi.e.19.15 32 3.2 odd 2
315.3.bi.e.199.2 32 21.17 even 6
315.3.bi.e.199.15 32 105.59 even 6
525.3.o.p.376.8 16 5.2 odd 4
525.3.o.p.451.8 16 35.17 even 12
525.3.o.q.376.1 16 5.3 odd 4
525.3.o.q.451.1 16 35.3 even 12
735.3.e.a.244.5 32 35.19 odd 6
735.3.e.a.244.6 32 7.2 even 3
735.3.e.a.244.13 32 35.9 even 6
735.3.e.a.244.14 32 7.5 odd 6