Properties

Label 287.3.g.a.132.18
Level $287$
Weight $3$
Character 287.132
Analytic conductor $7.820$
Analytic rank $0$
Dimension $108$
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] = [287,3,Mod(132,287)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(287, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("287.132");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 287 = 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 287.g (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: \(7.82018358714\)
Analytic rank: \(0\)
Dimension: \(108\)
Relative dimension: \(54\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 132.18
Character \(\chi\) \(=\) 287.132
Dual form 287.3.g.a.237.38

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.66337i q^{2} +(2.23909 - 2.23909i) q^{3} +1.23319 q^{4} +6.64247 q^{5} +(-3.72444 - 3.72444i) q^{6} +(-0.102623 + 6.99925i) q^{7} -8.70475i q^{8} -1.02704i q^{9} +O(q^{10})\) \(q-1.66337i q^{2} +(2.23909 - 2.23909i) q^{3} +1.23319 q^{4} +6.64247 q^{5} +(-3.72444 - 3.72444i) q^{6} +(-0.102623 + 6.99925i) q^{7} -8.70475i q^{8} -1.02704i q^{9} -11.0489i q^{10} +(-3.18102 - 3.18102i) q^{11} +(2.76121 - 2.76121i) q^{12} +(2.77474 - 2.77474i) q^{13} +(11.6424 + 0.170701i) q^{14} +(14.8731 - 14.8731i) q^{15} -9.54651 q^{16} +(4.86501 + 4.86501i) q^{17} -1.70835 q^{18} +(13.5114 + 13.5114i) q^{19} +8.19139 q^{20} +(15.4422 + 15.9017i) q^{21} +(-5.29123 + 5.29123i) q^{22} -39.7354 q^{23} +(-19.4907 - 19.4907i) q^{24} +19.1224 q^{25} +(-4.61543 - 4.61543i) q^{26} +(17.8522 + 17.8522i) q^{27} +(-0.126554 + 8.63137i) q^{28} +(-31.5812 - 31.5812i) q^{29} +(-24.7395 - 24.7395i) q^{30} +10.8067i q^{31} -18.9396i q^{32} -14.2452 q^{33} +(8.09233 - 8.09233i) q^{34} +(-0.681672 + 46.4923i) q^{35} -1.26653i q^{36} -12.6510 q^{37} +(22.4745 - 22.4745i) q^{38} -12.4258i q^{39} -57.8210i q^{40} +(-39.6234 - 10.5350i) q^{41} +(26.4505 - 25.6861i) q^{42} +13.8876i q^{43} +(-3.92279 - 3.92279i) q^{44} -6.82205i q^{45} +66.0949i q^{46} +(-20.5919 - 20.5919i) q^{47} +(-21.3755 + 21.3755i) q^{48} +(-48.9789 - 1.43657i) q^{49} -31.8076i q^{50} +21.7864 q^{51} +(3.42176 - 3.42176i) q^{52} +(-6.26284 - 6.26284i) q^{53} +(29.6948 - 29.6948i) q^{54} +(-21.1298 - 21.1298i) q^{55} +(60.9267 + 0.893310i) q^{56} +60.5065 q^{57} +(-52.5313 + 52.5313i) q^{58} +16.2701i q^{59} +(18.3413 - 18.3413i) q^{60} +41.0771 q^{61} +17.9755 q^{62} +(7.18848 + 0.105398i) q^{63} -69.6896 q^{64} +(18.4311 - 18.4311i) q^{65} +23.6951i q^{66} +(-24.3946 + 24.3946i) q^{67} +(5.99946 + 5.99946i) q^{68} +(-88.9712 + 88.9712i) q^{69} +(77.3340 + 1.13388i) q^{70} +(13.8364 + 13.8364i) q^{71} -8.94009 q^{72} -51.0950 q^{73} +21.0434i q^{74} +(42.8166 - 42.8166i) q^{75} +(16.6621 + 16.6621i) q^{76} +(22.5912 - 21.9383i) q^{77} -20.6687 q^{78} +(18.2038 + 18.2038i) q^{79} -63.4124 q^{80} +89.1885 q^{81} +(-17.5236 + 65.9086i) q^{82} +46.2697i q^{83} +(19.0430 + 19.6098i) q^{84} +(32.3157 + 32.3157i) q^{85} +23.1003 q^{86} -141.426 q^{87} +(-27.6900 + 27.6900i) q^{88} +(71.9192 - 71.9192i) q^{89} -11.3476 q^{90} +(19.1363 + 19.7058i) q^{91} -49.0012 q^{92} +(24.1971 + 24.1971i) q^{93} +(-34.2520 + 34.2520i) q^{94} +(89.7491 + 89.7491i) q^{95} +(-42.4074 - 42.4074i) q^{96} +(46.8338 + 46.8338i) q^{97} +(-2.38956 + 81.4703i) q^{98} +(-3.26702 + 3.26702i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 108 q - 216 q^{4} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 108 q - 216 q^{4} - 2 q^{7} - 20 q^{11} - 4 q^{14} - 28 q^{15} + 408 q^{16} + 24 q^{18} + 20 q^{22} - 8 q^{23} + 452 q^{25} - 62 q^{28} + 168 q^{29} - 64 q^{30} - 10 q^{35} - 208 q^{37} - 44 q^{42} + 44 q^{44} + 272 q^{51} - 92 q^{53} + 24 q^{56} - 256 q^{57} + 248 q^{58} - 440 q^{60} - 252 q^{63} - 1104 q^{64} - 644 q^{65} - 348 q^{67} - 30 q^{70} - 564 q^{71} + 796 q^{72} + 1924 q^{78} + 196 q^{79} - 468 q^{81} + 32 q^{85} + 152 q^{86} + 840 q^{88} - 428 q^{92} + 32 q^{93} + 4 q^{95} + 108 q^{98} - 484 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).

\(n\) \(206\) \(211\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.66337i 0.831687i −0.909436 0.415844i \(-0.863486\pi\)
0.909436 0.415844i \(-0.136514\pi\)
\(3\) 2.23909 2.23909i 0.746363 0.746363i −0.227431 0.973794i \(-0.573033\pi\)
0.973794 + 0.227431i \(0.0730327\pi\)
\(4\) 1.23319 0.308296
\(5\) 6.64247 1.32849 0.664247 0.747514i \(-0.268752\pi\)
0.664247 + 0.747514i \(0.268752\pi\)
\(6\) −3.72444 3.72444i −0.620741 0.620741i
\(7\) −0.102623 + 6.99925i −0.0146605 + 0.999893i
\(8\) 8.70475i 1.08809i
\(9\) 1.02704i 0.114115i
\(10\) 11.0489i 1.10489i
\(11\) −3.18102 3.18102i −0.289184 0.289184i 0.547574 0.836757i \(-0.315552\pi\)
−0.836757 + 0.547574i \(0.815552\pi\)
\(12\) 2.76121 2.76121i 0.230101 0.230101i
\(13\) 2.77474 2.77474i 0.213441 0.213441i −0.592286 0.805728i \(-0.701775\pi\)
0.805728 + 0.592286i \(0.201775\pi\)
\(14\) 11.6424 + 0.170701i 0.831598 + 0.0121929i
\(15\) 14.8731 14.8731i 0.991538 0.991538i
\(16\) −9.54651 −0.596657
\(17\) 4.86501 + 4.86501i 0.286177 + 0.286177i 0.835566 0.549389i \(-0.185140\pi\)
−0.549389 + 0.835566i \(0.685140\pi\)
\(18\) −1.70835 −0.0949081
\(19\) 13.5114 + 13.5114i 0.711127 + 0.711127i 0.966771 0.255644i \(-0.0822875\pi\)
−0.255644 + 0.966771i \(0.582288\pi\)
\(20\) 8.19139 0.409570
\(21\) 15.4422 + 15.9017i 0.735341 + 0.757225i
\(22\) −5.29123 + 5.29123i −0.240510 + 0.240510i
\(23\) −39.7354 −1.72763 −0.863814 0.503811i \(-0.831931\pi\)
−0.863814 + 0.503811i \(0.831931\pi\)
\(24\) −19.4907 19.4907i −0.812113 0.812113i
\(25\) 19.1224 0.764894
\(26\) −4.61543 4.61543i −0.177516 0.177516i
\(27\) 17.8522 + 17.8522i 0.661192 + 0.661192i
\(28\) −0.126554 + 8.63137i −0.00451977 + 0.308263i
\(29\) −31.5812 31.5812i −1.08901 1.08901i −0.995631 0.0933745i \(-0.970235\pi\)
−0.0933745 0.995631i \(-0.529765\pi\)
\(30\) −24.7395 24.7395i −0.824650 0.824650i
\(31\) 10.8067i 0.348602i 0.984692 + 0.174301i \(0.0557666\pi\)
−0.984692 + 0.174301i \(0.944233\pi\)
\(32\) 18.9396i 0.591861i
\(33\) −14.2452 −0.431672
\(34\) 8.09233 8.09233i 0.238010 0.238010i
\(35\) −0.681672 + 46.4923i −0.0194763 + 1.32835i
\(36\) 1.26653i 0.0351813i
\(37\) −12.6510 −0.341920 −0.170960 0.985278i \(-0.554687\pi\)
−0.170960 + 0.985278i \(0.554687\pi\)
\(38\) 22.4745 22.4745i 0.591435 0.591435i
\(39\) 12.4258i 0.318609i
\(40\) 57.8210i 1.44552i
\(41\) −39.6234 10.5350i −0.966424 0.256951i
\(42\) 26.4505 25.6861i 0.629774 0.611573i
\(43\) 13.8876i 0.322968i 0.986875 + 0.161484i \(0.0516280\pi\)
−0.986875 + 0.161484i \(0.948372\pi\)
\(44\) −3.92279 3.92279i −0.0891543 0.0891543i
\(45\) 6.82205i 0.151601i
\(46\) 66.0949i 1.43685i
\(47\) −20.5919 20.5919i −0.438125 0.438125i 0.453255 0.891381i \(-0.350263\pi\)
−0.891381 + 0.453255i \(0.850263\pi\)
\(48\) −21.3755 + 21.3755i −0.445323 + 0.445323i
\(49\) −48.9789 1.43657i −0.999570 0.0293178i
\(50\) 31.8076i 0.636153i
\(51\) 21.7864 0.427184
\(52\) 3.42176 3.42176i 0.0658032 0.0658032i
\(53\) −6.26284 6.26284i −0.118167 0.118167i 0.645551 0.763717i \(-0.276628\pi\)
−0.763717 + 0.645551i \(0.776628\pi\)
\(54\) 29.6948 29.6948i 0.549905 0.549905i
\(55\) −21.1298 21.1298i −0.384179 0.384179i
\(56\) 60.9267 + 0.893310i 1.08798 + 0.0159520i
\(57\) 60.5065 1.06152
\(58\) −52.5313 + 52.5313i −0.905712 + 0.905712i
\(59\) 16.2701i 0.275765i 0.990449 + 0.137882i \(0.0440296\pi\)
−0.990449 + 0.137882i \(0.955970\pi\)
\(60\) 18.3413 18.3413i 0.305688 0.305688i
\(61\) 41.0771 0.673395 0.336697 0.941613i \(-0.390690\pi\)
0.336697 + 0.941613i \(0.390690\pi\)
\(62\) 17.9755 0.289928
\(63\) 7.18848 + 0.105398i 0.114103 + 0.00167298i
\(64\) −69.6896 −1.08890
\(65\) 18.4311 18.4311i 0.283555 0.283555i
\(66\) 23.6951i 0.359016i
\(67\) −24.3946 + 24.3946i −0.364098 + 0.364098i −0.865319 0.501221i \(-0.832884\pi\)
0.501221 + 0.865319i \(0.332884\pi\)
\(68\) 5.99946 + 5.99946i 0.0882273 + 0.0882273i
\(69\) −88.9712 + 88.9712i −1.28944 + 1.28944i
\(70\) 77.3340 + 1.13388i 1.10477 + 0.0161982i
\(71\) 13.8364 + 13.8364i 0.194879 + 0.194879i 0.797801 0.602921i \(-0.205997\pi\)
−0.602921 + 0.797801i \(0.705997\pi\)
\(72\) −8.94009 −0.124168
\(73\) −51.0950 −0.699932 −0.349966 0.936762i \(-0.613807\pi\)
−0.349966 + 0.936762i \(0.613807\pi\)
\(74\) 21.0434i 0.284371i
\(75\) 42.8166 42.8166i 0.570889 0.570889i
\(76\) 16.6621 + 16.6621i 0.219238 + 0.219238i
\(77\) 22.5912 21.9383i 0.293392 0.284913i
\(78\) −20.6687 −0.264983
\(79\) 18.2038 + 18.2038i 0.230428 + 0.230428i 0.812871 0.582444i \(-0.197903\pi\)
−0.582444 + 0.812871i \(0.697903\pi\)
\(80\) −63.4124 −0.792655
\(81\) 89.1885 1.10109
\(82\) −17.5236 + 65.9086i −0.213703 + 0.803763i
\(83\) 46.2697i 0.557467i 0.960369 + 0.278733i \(0.0899146\pi\)
−0.960369 + 0.278733i \(0.910085\pi\)
\(84\) 19.0430 + 19.6098i 0.226703 + 0.233450i
\(85\) 32.3157 + 32.3157i 0.380184 + 0.380184i
\(86\) 23.1003 0.268608
\(87\) −141.426 −1.62559
\(88\) −27.6900 + 27.6900i −0.314659 + 0.314659i
\(89\) 71.9192 71.9192i 0.808081 0.808081i −0.176262 0.984343i \(-0.556401\pi\)
0.984343 + 0.176262i \(0.0564006\pi\)
\(90\) −11.3476 −0.126085
\(91\) 19.1363 + 19.7058i 0.210289 + 0.216548i
\(92\) −49.0012 −0.532621
\(93\) 24.1971 + 24.1971i 0.260184 + 0.260184i
\(94\) −34.2520 + 34.2520i −0.364383 + 0.364383i
\(95\) 89.7491 + 89.7491i 0.944727 + 0.944727i
\(96\) −42.4074 42.4074i −0.441743 0.441743i
\(97\) 46.8338 + 46.8338i 0.482822 + 0.482822i 0.906032 0.423209i \(-0.139097\pi\)
−0.423209 + 0.906032i \(0.639097\pi\)
\(98\) −2.38956 + 81.4703i −0.0243833 + 0.831330i
\(99\) −3.26702 + 3.26702i −0.0330002 + 0.0330002i
\(100\) 23.5814 0.235814
\(101\) 29.3393 + 29.3393i 0.290489 + 0.290489i 0.837273 0.546785i \(-0.184148\pi\)
−0.546785 + 0.837273i \(0.684148\pi\)
\(102\) 36.2389i 0.355283i
\(103\) 75.6033 0.734012 0.367006 0.930219i \(-0.380383\pi\)
0.367006 + 0.930219i \(0.380383\pi\)
\(104\) −24.1534 24.1534i −0.232244 0.232244i
\(105\) 102.574 + 105.627i 0.976895 + 1.00597i
\(106\) −10.4174 + 10.4174i −0.0982778 + 0.0982778i
\(107\) 195.729 1.82924 0.914621 0.404312i \(-0.132489\pi\)
0.914621 + 0.404312i \(0.132489\pi\)
\(108\) 22.0150 + 22.0150i 0.203843 + 0.203843i
\(109\) 70.6126 70.6126i 0.647822 0.647822i −0.304644 0.952466i \(-0.598537\pi\)
0.952466 + 0.304644i \(0.0985375\pi\)
\(110\) −35.1468 + 35.1468i −0.319516 + 0.319516i
\(111\) −28.3268 + 28.3268i −0.255197 + 0.255197i
\(112\) 0.979695 66.8184i 0.00874728 0.596593i
\(113\) −57.0334 −0.504721 −0.252360 0.967633i \(-0.581207\pi\)
−0.252360 + 0.967633i \(0.581207\pi\)
\(114\) 100.645i 0.882851i
\(115\) −263.941 −2.29514
\(116\) −38.9454 38.9454i −0.335736 0.335736i
\(117\) −2.84976 2.84976i −0.0243569 0.0243569i
\(118\) 27.0633 0.229350
\(119\) −34.5507 + 33.5521i −0.290342 + 0.281951i
\(120\) −129.466 129.466i −1.07889 1.07889i
\(121\) 100.762i 0.832746i
\(122\) 68.3265i 0.560054i
\(123\) −112.309 + 65.1315i −0.913082 + 0.529525i
\(124\) 13.3266i 0.107473i
\(125\) −39.0421 −0.312337
\(126\) 0.175316 11.9571i 0.00139140 0.0948979i
\(127\) 107.101 0.843312 0.421656 0.906756i \(-0.361449\pi\)
0.421656 + 0.906756i \(0.361449\pi\)
\(128\) 40.1617i 0.313763i
\(129\) 31.0956 + 31.0956i 0.241051 + 0.241051i
\(130\) −30.6578 30.6578i −0.235829 0.235829i
\(131\) 101.394 0.774001 0.387000 0.922080i \(-0.373511\pi\)
0.387000 + 0.922080i \(0.373511\pi\)
\(132\) −17.5669 −0.133083
\(133\) −95.9563 + 93.1831i −0.721476 + 0.700625i
\(134\) 40.5773 + 40.5773i 0.302816 + 0.302816i
\(135\) 118.582 + 118.582i 0.878389 + 0.878389i
\(136\) 42.3487 42.3487i 0.311387 0.311387i
\(137\) −192.256 + 192.256i −1.40333 + 1.40333i −0.614089 + 0.789236i \(0.710477\pi\)
−0.789236 + 0.614089i \(0.789523\pi\)
\(138\) 147.992 + 147.992i 1.07241 + 1.07241i
\(139\) 84.5393i 0.608196i 0.952641 + 0.304098i \(0.0983551\pi\)
−0.952641 + 0.304098i \(0.901645\pi\)
\(140\) −0.840628 + 57.3336i −0.00600449 + 0.409526i
\(141\) −92.2141 −0.654001
\(142\) 23.0151 23.0151i 0.162078 0.162078i
\(143\) −17.6530 −0.123448
\(144\) 9.80461i 0.0680876i
\(145\) −209.777 209.777i −1.44674 1.44674i
\(146\) 84.9902i 0.582124i
\(147\) −112.885 + 106.452i −0.767924 + 0.724160i
\(148\) −15.6011 −0.105413
\(149\) 83.5605 83.5605i 0.560809 0.560809i −0.368728 0.929537i \(-0.620207\pi\)
0.929537 + 0.368728i \(0.120207\pi\)
\(150\) −71.2201 71.2201i −0.474801 0.474801i
\(151\) 110.409 + 110.409i 0.731183 + 0.731183i 0.970854 0.239671i \(-0.0770397\pi\)
−0.239671 + 0.970854i \(0.577040\pi\)
\(152\) 117.613 117.613i 0.773772 0.773772i
\(153\) 4.99654 4.99654i 0.0326571 0.0326571i
\(154\) −36.4916 37.5776i −0.236959 0.244011i
\(155\) 71.7829i 0.463115i
\(156\) 15.3233i 0.0982261i
\(157\) 47.6824 47.6824i 0.303710 0.303710i −0.538754 0.842463i \(-0.681105\pi\)
0.842463 + 0.538754i \(0.181105\pi\)
\(158\) 30.2797 30.2797i 0.191644 0.191644i
\(159\) −28.0461 −0.176391
\(160\) 125.805i 0.786284i
\(161\) 4.07779 278.118i 0.0253279 1.72744i
\(162\) 148.354i 0.915765i
\(163\) −249.804 −1.53254 −0.766270 0.642518i \(-0.777890\pi\)
−0.766270 + 0.642518i \(0.777890\pi\)
\(164\) −48.8630 12.9916i −0.297945 0.0792171i
\(165\) −94.6231 −0.573473
\(166\) 76.9639 0.463638
\(167\) 188.326 188.326i 1.12770 1.12770i 0.137147 0.990551i \(-0.456207\pi\)
0.990551 0.137147i \(-0.0437933\pi\)
\(168\) 138.420 134.420i 0.823931 0.800119i
\(169\) 153.602i 0.908886i
\(170\) 53.7530 53.7530i 0.316194 0.316194i
\(171\) 13.8767 13.8767i 0.0811503 0.0811503i
\(172\) 17.1260i 0.0995697i
\(173\) 212.654 1.22921 0.614606 0.788835i \(-0.289315\pi\)
0.614606 + 0.788835i \(0.289315\pi\)
\(174\) 235.244i 1.35198i
\(175\) −1.96240 + 133.842i −0.0112137 + 0.764812i
\(176\) 30.3677 + 30.3677i 0.172544 + 0.172544i
\(177\) 36.4303 + 36.4303i 0.205821 + 0.205821i
\(178\) −119.629 119.629i −0.672071 0.672071i
\(179\) 183.808 183.808i 1.02686 1.02686i 0.0272338 0.999629i \(-0.491330\pi\)
0.999629 0.0272338i \(-0.00866987\pi\)
\(180\) 8.41285i 0.0467381i
\(181\) −234.711 234.711i −1.29674 1.29674i −0.930531 0.366212i \(-0.880654\pi\)
−0.366212 0.930531i \(-0.619346\pi\)
\(182\) 32.7782 31.8309i 0.180100 0.174895i
\(183\) 91.9752 91.9752i 0.502597 0.502597i
\(184\) 345.887i 1.87982i
\(185\) −84.0341 −0.454239
\(186\) 40.2488 40.2488i 0.216391 0.216391i
\(187\) 30.9514i 0.165515i
\(188\) −25.3936 25.3936i −0.135072 0.135072i
\(189\) −126.784 + 123.120i −0.670814 + 0.651427i
\(190\) 149.286 149.286i 0.785718 0.785718i
\(191\) 106.658 106.658i 0.558417 0.558417i −0.370440 0.928857i \(-0.620793\pi\)
0.928857 + 0.370440i \(0.120793\pi\)
\(192\) −156.041 + 156.041i −0.812715 + 0.812715i
\(193\) −191.406 191.406i −0.991740 0.991740i 0.00822612 0.999966i \(-0.497382\pi\)
−0.999966 + 0.00822612i \(0.997382\pi\)
\(194\) 77.9021 77.9021i 0.401557 0.401557i
\(195\) 82.5377i 0.423270i
\(196\) −60.4001 1.77156i −0.308164 0.00903857i
\(197\) 262.352i 1.33174i 0.746069 + 0.665868i \(0.231939\pi\)
−0.746069 + 0.665868i \(0.768061\pi\)
\(198\) 5.43428 + 5.43428i 0.0274459 + 0.0274459i
\(199\) −157.423 157.423i −0.791070 0.791070i 0.190598 0.981668i \(-0.438957\pi\)
−0.981668 + 0.190598i \(0.938957\pi\)
\(200\) 166.455i 0.832276i
\(201\) 109.243i 0.543499i
\(202\) 48.8023 48.8023i 0.241596 0.241596i
\(203\) 224.285 217.803i 1.10485 1.07292i
\(204\) 26.8666 0.131699
\(205\) −263.197 69.9783i −1.28389 0.341358i
\(206\) 125.757i 0.610469i
\(207\) 40.8097i 0.197148i
\(208\) −26.4891 + 26.4891i −0.127351 + 0.127351i
\(209\) 85.9602i 0.411293i
\(210\) 175.697 170.619i 0.836651 0.812471i
\(211\) −4.35136 + 4.35136i −0.0206226 + 0.0206226i −0.717343 0.696720i \(-0.754642\pi\)
0.696720 + 0.717343i \(0.254642\pi\)
\(212\) −7.72324 7.72324i −0.0364304 0.0364304i
\(213\) 61.9619 0.290901
\(214\) 325.571i 1.52136i
\(215\) 92.2480i 0.429060i
\(216\) 155.399 155.399i 0.719438 0.719438i
\(217\) −75.6385 1.10902i −0.348564 0.00511067i
\(218\) −117.455 117.455i −0.538786 0.538786i
\(219\) −114.406 + 114.406i −0.522403 + 0.522403i
\(220\) −26.0570 26.0570i −0.118441 0.118441i
\(221\) 26.9982 0.122164
\(222\) 47.1181 + 47.1181i 0.212244 + 0.212244i
\(223\) 67.0770i 0.300794i 0.988626 + 0.150397i \(0.0480551\pi\)
−0.988626 + 0.150397i \(0.951945\pi\)
\(224\) 132.563 + 1.94364i 0.591798 + 0.00867697i
\(225\) 19.6393i 0.0872860i
\(226\) 94.8680i 0.419770i
\(227\) −169.622 169.622i −0.747236 0.747236i 0.226724 0.973959i \(-0.427199\pi\)
−0.973959 + 0.226724i \(0.927199\pi\)
\(228\) 74.6157 0.327262
\(229\) 246.442 + 246.442i 1.07616 + 1.07616i 0.996850 + 0.0793154i \(0.0252734\pi\)
0.0793154 + 0.996850i \(0.474727\pi\)
\(230\) 439.033i 1.90884i
\(231\) 1.46189 99.7055i 0.00632852 0.431626i
\(232\) −274.906 + 274.906i −1.18494 + 1.18494i
\(233\) −196.386 196.386i −0.842858 0.842858i 0.146372 0.989230i \(-0.453240\pi\)
−0.989230 + 0.146372i \(0.953240\pi\)
\(234\) −4.74021 + 4.74021i −0.0202573 + 0.0202573i
\(235\) −136.781 136.781i −0.582046 0.582046i
\(236\) 20.0641i 0.0850173i
\(237\) 81.5198 0.343965
\(238\) 55.8098 + 57.4707i 0.234495 + 0.241474i
\(239\) 239.529 + 239.529i 1.00221 + 1.00221i 0.999998 + 0.00221493i \(0.000705035\pi\)
0.00221493 + 0.999998i \(0.499295\pi\)
\(240\) −141.986 + 141.986i −0.591608 + 0.591608i
\(241\) −17.8130 −0.0739127 −0.0369563 0.999317i \(-0.511766\pi\)
−0.0369563 + 0.999317i \(0.511766\pi\)
\(242\) −167.605 −0.692584
\(243\) 39.0315 39.0315i 0.160623 0.160623i
\(244\) 50.6556 0.207605
\(245\) −325.341 9.54239i −1.32792 0.0389485i
\(246\) 108.338 + 186.812i 0.440399 + 0.759399i
\(247\) 74.9812 0.303568
\(248\) 94.0692 0.379311
\(249\) 103.602 + 103.602i 0.416072 + 0.416072i
\(250\) 64.9416i 0.259766i
\(251\) −252.831 −1.00730 −0.503648 0.863909i \(-0.668009\pi\)
−0.503648 + 0.863909i \(0.668009\pi\)
\(252\) 8.86473 + 0.129975i 0.0351775 + 0.000515774i
\(253\) 126.399 + 126.399i 0.499602 + 0.499602i
\(254\) 178.148i 0.701371i
\(255\) 144.715 0.567511
\(256\) −211.955 −0.827948
\(257\) 16.9557 16.9557i 0.0659757 0.0659757i −0.673349 0.739325i \(-0.735145\pi\)
0.739325 + 0.673349i \(0.235145\pi\)
\(258\) 51.7236 51.7236i 0.200479 0.200479i
\(259\) 1.29829 88.5478i 0.00501271 0.341883i
\(260\) 22.7290 22.7290i 0.0874191 0.0874191i
\(261\) −32.4350 + 32.4350i −0.124272 + 0.124272i
\(262\) 168.656i 0.643726i
\(263\) −17.1502 + 17.1502i −0.0652100 + 0.0652100i −0.738960 0.673750i \(-0.764683\pi\)
0.673750 + 0.738960i \(0.264683\pi\)
\(264\) 124.001i 0.469699i
\(265\) −41.6007 41.6007i −0.156984 0.156984i
\(266\) 154.998 + 159.611i 0.582701 + 0.600042i
\(267\) 322.067i 1.20624i
\(268\) −30.0830 + 30.0830i −0.112250 + 0.112250i
\(269\) 501.585i 1.86463i 0.361651 + 0.932314i \(0.382213\pi\)
−0.361651 + 0.932314i \(0.617787\pi\)
\(270\) 197.247 197.247i 0.730545 0.730545i
\(271\) 248.468i 0.916857i 0.888731 + 0.458428i \(0.151587\pi\)
−0.888731 + 0.458428i \(0.848413\pi\)
\(272\) −46.4439 46.4439i −0.170750 0.170750i
\(273\) 86.9710 + 1.27517i 0.318575 + 0.00467097i
\(274\) 319.793 + 319.793i 1.16713 + 1.16713i
\(275\) −60.8286 60.8286i −0.221195 0.221195i
\(276\) −109.718 + 109.718i −0.397529 + 0.397529i
\(277\) −89.7821 −0.324123 −0.162062 0.986781i \(-0.551814\pi\)
−0.162062 + 0.986781i \(0.551814\pi\)
\(278\) 140.621 0.505829
\(279\) 11.0988 0.0397808
\(280\) 404.703 + 5.93378i 1.44537 + 0.0211921i
\(281\) 239.382 239.382i 0.851895 0.851895i −0.138472 0.990366i \(-0.544219\pi\)
0.990366 + 0.138472i \(0.0442189\pi\)
\(282\) 153.387i 0.543924i
\(283\) 470.578i 1.66282i 0.555659 + 0.831410i \(0.312466\pi\)
−0.555659 + 0.831410i \(0.687534\pi\)
\(284\) 17.0629 + 17.0629i 0.0600805 + 0.0600805i
\(285\) 401.912 1.41022
\(286\) 29.3635i 0.102670i
\(287\) 77.8033 276.253i 0.271092 0.962554i
\(288\) −19.4516 −0.0675403
\(289\) 241.663i 0.836205i
\(290\) −348.937 + 348.937i −1.20323 + 1.20323i
\(291\) 209.730 0.720722
\(292\) −63.0096 −0.215786
\(293\) −266.815 266.815i −0.910633 0.910633i 0.0856893 0.996322i \(-0.472691\pi\)
−0.996322 + 0.0856893i \(0.972691\pi\)
\(294\) 177.069 + 187.770i 0.602275 + 0.638672i
\(295\) 108.074i 0.366352i
\(296\) 110.124i 0.372041i
\(297\) 113.576i 0.382412i
\(298\) −138.992 138.992i −0.466418 0.466418i
\(299\) −110.255 + 110.255i −0.368747 + 0.368747i
\(300\) 52.8009 52.8009i 0.176003 0.176003i
\(301\) −97.2028 1.42519i −0.322933 0.00473486i
\(302\) 183.651 183.651i 0.608115 0.608115i
\(303\) 131.387 0.433620
\(304\) −128.987 128.987i −0.424299 0.424299i
\(305\) 272.853 0.894600
\(306\) −8.31112 8.31112i −0.0271605 0.0271605i
\(307\) −393.282 −1.28105 −0.640524 0.767938i \(-0.721283\pi\)
−0.640524 + 0.767938i \(0.721283\pi\)
\(308\) 27.8591 27.0540i 0.0904517 0.0878376i
\(309\) 169.282 169.282i 0.547840 0.547840i
\(310\) 119.402 0.385167
\(311\) −65.0289 65.0289i −0.209096 0.209096i 0.594787 0.803883i \(-0.297236\pi\)
−0.803883 + 0.594787i \(0.797236\pi\)
\(312\) −108.163 −0.346677
\(313\) 2.22225 + 2.22225i 0.00709984 + 0.00709984i 0.710648 0.703548i \(-0.248402\pi\)
−0.703548 + 0.710648i \(0.748402\pi\)
\(314\) −79.3137 79.3137i −0.252591 0.252591i
\(315\) 47.7492 + 0.700102i 0.151585 + 0.00222255i
\(316\) 22.4486 + 22.4486i 0.0710400 + 0.0710400i
\(317\) −377.460 377.460i −1.19072 1.19072i −0.976864 0.213860i \(-0.931396\pi\)
−0.213860 0.976864i \(-0.568604\pi\)
\(318\) 46.6512i 0.146702i
\(319\) 200.921i 0.629845i
\(320\) −462.911 −1.44660
\(321\) 438.255 438.255i 1.36528 1.36528i
\(322\) −462.615 6.78288i −1.43669 0.0210649i
\(323\) 131.466i 0.407016i
\(324\) 109.986 0.339463
\(325\) 53.0595 53.0595i 0.163260 0.163260i
\(326\) 415.518i 1.27459i
\(327\) 316.216i 0.967021i
\(328\) −91.7045 + 344.912i −0.279587 + 1.05156i
\(329\) 146.241 142.015i 0.444501 0.431655i
\(330\) 157.394i 0.476950i
\(331\) 337.252 + 337.252i 1.01889 + 1.01889i 0.999818 + 0.0190686i \(0.00607008\pi\)
0.0190686 + 0.999818i \(0.493930\pi\)
\(332\) 57.0592i 0.171865i
\(333\) 12.9931i 0.0390183i
\(334\) −313.256 313.256i −0.937892 0.937892i
\(335\) −162.040 + 162.040i −0.483702 + 0.483702i
\(336\) −147.419 151.806i −0.438746 0.451803i
\(337\) 82.3054i 0.244230i −0.992516 0.122115i \(-0.961032\pi\)
0.992516 0.122115i \(-0.0389676\pi\)
\(338\) 255.497 0.755909
\(339\) −127.703 + 127.703i −0.376705 + 0.376705i
\(340\) 39.8512 + 39.8512i 0.117209 + 0.117209i
\(341\) 34.3762 34.3762i 0.100810 0.100810i
\(342\) −23.0822 23.0822i −0.0674917 0.0674917i
\(343\) 15.0813 342.668i 0.0439688 0.999033i
\(344\) 120.888 0.351419
\(345\) −590.988 + 590.988i −1.71301 + 1.71301i
\(346\) 353.722i 1.02232i
\(347\) −435.309 + 435.309i −1.25449 + 1.25449i −0.300809 + 0.953684i \(0.597257\pi\)
−0.953684 + 0.300809i \(0.902743\pi\)
\(348\) −174.405 −0.501162
\(349\) 448.942 1.28637 0.643183 0.765712i \(-0.277613\pi\)
0.643183 + 0.765712i \(0.277613\pi\)
\(350\) 222.630 + 3.26421i 0.636084 + 0.00932630i
\(351\) 99.0702 0.282251
\(352\) −60.2471 + 60.2471i −0.171157 + 0.171157i
\(353\) 524.419i 1.48561i 0.669510 + 0.742803i \(0.266504\pi\)
−0.669510 + 0.742803i \(0.733496\pi\)
\(354\) 60.5972 60.5972i 0.171179 0.171179i
\(355\) 91.9079 + 91.9079i 0.258896 + 0.258896i
\(356\) 88.6897 88.6897i 0.249129 0.249129i
\(357\) −2.23579 + 152.488i −0.00626272 + 0.427138i
\(358\) −305.742 305.742i −0.854029 0.854029i
\(359\) 315.335 0.878369 0.439185 0.898397i \(-0.355267\pi\)
0.439185 + 0.898397i \(0.355267\pi\)
\(360\) −59.3842 −0.164956
\(361\) 4.11649i 0.0114030i
\(362\) −390.412 + 390.412i −1.07849 + 1.07849i
\(363\) −225.616 225.616i −0.621530 0.621530i
\(364\) 23.5986 + 24.3009i 0.0648314 + 0.0667608i
\(365\) −339.397 −0.929855
\(366\) −152.989 152.989i −0.418003 0.418003i
\(367\) 221.393 0.603251 0.301626 0.953426i \(-0.402471\pi\)
0.301626 + 0.953426i \(0.402471\pi\)
\(368\) 379.335 1.03080
\(369\) −10.8198 + 40.6947i −0.0293220 + 0.110284i
\(370\) 139.780i 0.377784i
\(371\) 44.4779 43.1925i 0.119886 0.116422i
\(372\) 29.8395 + 29.8395i 0.0802136 + 0.0802136i
\(373\) −280.655 −0.752427 −0.376213 0.926533i \(-0.622774\pi\)
−0.376213 + 0.926533i \(0.622774\pi\)
\(374\) −51.4838 −0.137657
\(375\) −87.4186 + 87.4186i −0.233116 + 0.233116i
\(376\) −179.247 + 179.247i −0.476721 + 0.476721i
\(377\) −175.259 −0.464878
\(378\) 204.794 + 210.889i 0.541784 + 0.557907i
\(379\) −371.393 −0.979927 −0.489964 0.871743i \(-0.662990\pi\)
−0.489964 + 0.871743i \(0.662990\pi\)
\(380\) 110.677 + 110.677i 0.291256 + 0.291256i
\(381\) 239.808 239.808i 0.629416 0.629416i
\(382\) −177.412 177.412i −0.464428 0.464428i
\(383\) 322.678 + 322.678i 0.842501 + 0.842501i 0.989184 0.146683i \(-0.0468596\pi\)
−0.146683 + 0.989184i \(0.546860\pi\)
\(384\) 89.9257 + 89.9257i 0.234181 + 0.234181i
\(385\) 150.061 145.724i 0.389770 0.378505i
\(386\) −318.380 + 318.380i −0.824818 + 0.824818i
\(387\) 14.2631 0.0368555
\(388\) 57.7547 + 57.7547i 0.148852 + 0.148852i
\(389\) 491.989i 1.26475i 0.774661 + 0.632377i \(0.217921\pi\)
−0.774661 + 0.632377i \(0.782079\pi\)
\(390\) −137.291 −0.352029
\(391\) −193.313 193.313i −0.494407 0.494407i
\(392\) −12.5050 + 426.349i −0.0319005 + 1.08763i
\(393\) 227.030 227.030i 0.577685 0.577685i
\(394\) 436.390 1.10759
\(395\) 120.918 + 120.918i 0.306122 + 0.306122i
\(396\) −4.02884 + 4.02884i −0.0101739 + 0.0101739i
\(397\) 392.372 392.372i 0.988344 0.988344i −0.0115891 0.999933i \(-0.503689\pi\)
0.999933 + 0.0115891i \(0.00368902\pi\)
\(398\) −261.853 + 261.853i −0.657923 + 0.657923i
\(399\) −6.20938 + 423.500i −0.0155624 + 1.06140i
\(400\) −182.552 −0.456380
\(401\) 708.930i 1.76790i −0.467577 0.883952i \(-0.654873\pi\)
0.467577 0.883952i \(-0.345127\pi\)
\(402\) 181.712 0.452021
\(403\) 29.9856 + 29.9856i 0.0744061 + 0.0744061i
\(404\) 36.1809 + 36.1809i 0.0895566 + 0.0895566i
\(405\) 592.432 1.46279
\(406\) −362.289 373.071i −0.892337 0.918893i
\(407\) 40.2432 + 40.2432i 0.0988777 + 0.0988777i
\(408\) 189.645i 0.464816i
\(409\) 210.195i 0.513925i −0.966421 0.256962i \(-0.917278\pi\)
0.966421 0.256962i \(-0.0827217\pi\)
\(410\) −116.400 + 437.795i −0.283903 + 1.06779i
\(411\) 860.955i 2.09478i
\(412\) 93.2328 0.226293
\(413\) −113.879 1.66970i −0.275735 0.00404285i
\(414\) 67.8819 0.163966
\(415\) 307.345i 0.740591i
\(416\) −52.5523 52.5523i −0.126328 0.126328i
\(417\) 189.291 + 189.291i 0.453935 + 0.453935i
\(418\) −142.984 −0.342067
\(419\) −59.4123 −0.141795 −0.0708977 0.997484i \(-0.522586\pi\)
−0.0708977 + 0.997484i \(0.522586\pi\)
\(420\) 126.493 + 130.257i 0.301173 + 0.310136i
\(421\) −156.713 156.713i −0.372240 0.372240i 0.496052 0.868293i \(-0.334782\pi\)
−0.868293 + 0.496052i \(0.834782\pi\)
\(422\) 7.23794 + 7.23794i 0.0171515 + 0.0171515i
\(423\) −21.1486 + 21.1486i −0.0499967 + 0.0499967i
\(424\) −54.5164 + 54.5164i −0.128577 + 0.128577i
\(425\) 93.0304 + 93.0304i 0.218895 + 0.218895i
\(426\) 103.066i 0.241939i
\(427\) −4.21547 + 287.509i −0.00987229 + 0.673322i
\(428\) 241.370 0.563949
\(429\) −39.5266 + 39.5266i −0.0921366 + 0.0921366i
\(430\) 153.443 0.356844
\(431\) 235.492i 0.546384i −0.961959 0.273192i \(-0.911921\pi\)
0.961959 0.273192i \(-0.0880795\pi\)
\(432\) −170.426 170.426i −0.394505 0.394505i
\(433\) 334.485i 0.772484i −0.922398 0.386242i \(-0.873773\pi\)
0.922398 0.386242i \(-0.126227\pi\)
\(434\) −1.84471 + 125.815i −0.00425048 + 0.289897i
\(435\) −939.418 −2.15958
\(436\) 87.0785 87.0785i 0.199721 0.199721i
\(437\) −536.882 536.882i −1.22856 1.22856i
\(438\) 190.300 + 190.300i 0.434476 + 0.434476i
\(439\) −314.621 + 314.621i −0.716677 + 0.716677i −0.967923 0.251246i \(-0.919160\pi\)
0.251246 + 0.967923i \(0.419160\pi\)
\(440\) −183.930 + 183.930i −0.418022 + 0.418022i
\(441\) −1.47541 + 50.3031i −0.00334561 + 0.114066i
\(442\) 44.9082i 0.101602i
\(443\) 384.808i 0.868642i −0.900758 0.434321i \(-0.856988\pi\)
0.900758 0.434321i \(-0.143012\pi\)
\(444\) −34.9322 + 34.9322i −0.0786761 + 0.0786761i
\(445\) 477.721 477.721i 1.07353 1.07353i
\(446\) 111.574 0.250166
\(447\) 374.199i 0.837134i
\(448\) 7.15179 487.775i 0.0159638 1.08878i
\(449\) 271.399i 0.604451i −0.953236 0.302226i \(-0.902270\pi\)
0.953236 0.302226i \(-0.0977296\pi\)
\(450\) −32.6676 −0.0725946
\(451\) 92.5308 + 159.555i 0.205168 + 0.353780i
\(452\) −70.3328 −0.155604
\(453\) 494.429 1.09146
\(454\) −282.146 + 282.146i −0.621466 + 0.621466i
\(455\) 127.112 + 130.895i 0.279368 + 0.287682i
\(456\) 526.694i 1.15503i
\(457\) 350.559 350.559i 0.767089 0.767089i −0.210504 0.977593i \(-0.567511\pi\)
0.977593 + 0.210504i \(0.0675106\pi\)
\(458\) 409.925 409.925i 0.895033 0.895033i
\(459\) 173.702i 0.378436i
\(460\) −325.489 −0.707584
\(461\) 375.893i 0.815387i −0.913119 0.407693i \(-0.866333\pi\)
0.913119 0.407693i \(-0.133667\pi\)
\(462\) −165.848 2.43167i −0.358977 0.00526335i
\(463\) −586.857 586.857i −1.26751 1.26751i −0.947370 0.320140i \(-0.896270\pi\)
−0.320140 0.947370i \(-0.603730\pi\)
\(464\) 301.490 + 301.490i 0.649763 + 0.649763i
\(465\) 160.728 + 160.728i 0.345652 + 0.345652i
\(466\) −326.663 + 326.663i −0.700994 + 0.700994i
\(467\) 143.060i 0.306338i −0.988200 0.153169i \(-0.951052\pi\)
0.988200 0.153169i \(-0.0489479\pi\)
\(468\) −3.51428 3.51428i −0.00750914 0.00750914i
\(469\) −168.240 173.247i −0.358721 0.369397i
\(470\) −227.518 + 227.518i −0.484081 + 0.484081i
\(471\) 213.530i 0.453355i
\(472\) 141.627 0.300058
\(473\) 44.1768 44.1768i 0.0933970 0.0933970i
\(474\) 135.598i 0.286072i
\(475\) 258.370 + 258.370i 0.543937 + 0.543937i
\(476\) −42.6074 + 41.3760i −0.0895113 + 0.0869244i
\(477\) −6.43216 + 6.43216i −0.0134846 + 0.0134846i
\(478\) 398.426 398.426i 0.833527 0.833527i
\(479\) 527.110 527.110i 1.10044 1.10044i 0.106082 0.994357i \(-0.466169\pi\)
0.994357 0.106082i \(-0.0338305\pi\)
\(480\) −281.689 281.689i −0.586853 0.586853i
\(481\) −35.1033 + 35.1033i −0.0729799 + 0.0729799i
\(482\) 29.6296i 0.0614722i
\(483\) −613.601 631.862i −1.27040 1.30820i
\(484\) 124.258i 0.256732i
\(485\) 311.092 + 311.092i 0.641426 + 0.641426i
\(486\) −64.9239 64.9239i −0.133588 0.133588i
\(487\) 244.973i 0.503024i −0.967854 0.251512i \(-0.919072\pi\)
0.967854 0.251512i \(-0.0809278\pi\)
\(488\) 357.565i 0.732716i
\(489\) −559.334 + 559.334i −1.14383 + 1.14383i
\(490\) −15.8726 + 541.164i −0.0323930 + 1.10442i
\(491\) −244.999 −0.498981 −0.249490 0.968377i \(-0.580263\pi\)
−0.249490 + 0.968377i \(0.580263\pi\)
\(492\) −138.498 + 80.3192i −0.281500 + 0.163250i
\(493\) 307.285i 0.623297i
\(494\) 124.722i 0.252473i
\(495\) −21.7011 + 21.7011i −0.0438406 + 0.0438406i
\(496\) 103.166i 0.207996i
\(497\) −98.2644 + 95.4246i −0.197715 + 0.192001i
\(498\) 172.329 172.329i 0.346042 0.346042i
\(499\) 398.812 + 398.812i 0.799223 + 0.799223i 0.982973 0.183750i \(-0.0588237\pi\)
−0.183750 + 0.982973i \(0.558824\pi\)
\(500\) −48.1461 −0.0962922
\(501\) 843.355i 1.68334i
\(502\) 420.553i 0.837756i
\(503\) 315.401 315.401i 0.627039 0.627039i −0.320283 0.947322i \(-0.603778\pi\)
0.947322 + 0.320283i \(0.103778\pi\)
\(504\) 0.917462 62.5739i 0.00182036 0.124155i
\(505\) 194.886 + 194.886i 0.385912 + 0.385912i
\(506\) 210.249 210.249i 0.415513 0.415513i
\(507\) 343.928 + 343.928i 0.678358 + 0.678358i
\(508\) 132.075 0.259990
\(509\) 608.632 + 608.632i 1.19574 + 1.19574i 0.975430 + 0.220310i \(0.0707070\pi\)
0.220310 + 0.975430i \(0.429293\pi\)
\(510\) 240.716i 0.471991i
\(511\) 5.24354 357.627i 0.0102613 0.699857i
\(512\) 513.207i 1.00236i
\(513\) 482.416i 0.940382i
\(514\) −28.2038 28.2038i −0.0548711 0.0548711i
\(515\) 502.192 0.975130
\(516\) 38.3466 + 38.3466i 0.0743152 + 0.0743152i
\(517\) 131.006i 0.253397i
\(518\) −147.288 2.15955i −0.284340 0.00416901i
\(519\) 476.150 476.150i 0.917438 0.917438i
\(520\) −160.438 160.438i −0.308535 0.308535i
\(521\) −450.426 + 450.426i −0.864541 + 0.864541i −0.991862 0.127321i \(-0.959362\pi\)
0.127321 + 0.991862i \(0.459362\pi\)
\(522\) 53.9515 + 53.9515i 0.103355 + 0.103355i
\(523\) 720.116i 1.37689i −0.725286 0.688447i \(-0.758293\pi\)
0.725286 0.688447i \(-0.241707\pi\)
\(524\) 125.038 0.238622
\(525\) 295.290 + 304.078i 0.562458 + 0.579197i
\(526\) 28.5273 + 28.5273i 0.0542344 + 0.0542344i
\(527\) −52.5745 + 52.5745i −0.0997619 + 0.0997619i
\(528\) 135.992 0.257560
\(529\) 1049.91 1.98470
\(530\) −69.1975 + 69.1975i −0.130561 + 0.130561i
\(531\) 16.7100 0.0314690
\(532\) −118.332 + 114.912i −0.222428 + 0.216000i
\(533\) −139.176 + 80.7127i −0.261119 + 0.151431i
\(534\) −535.718 −1.00322
\(535\) 1300.12 2.43014
\(536\) 212.349 + 212.349i 0.396173 + 0.396173i
\(537\) 823.127i 1.53282i
\(538\) 834.323 1.55079
\(539\) 151.233 + 160.373i 0.280581 + 0.297538i
\(540\) 146.234 + 146.234i 0.270804 + 0.270804i
\(541\) 625.679i 1.15652i −0.815851 0.578262i \(-0.803731\pi\)
0.815851 0.578262i \(-0.196269\pi\)
\(542\) 413.296 0.762538
\(543\) −1051.08 −1.93568
\(544\) 92.1411 92.1411i 0.169377 0.169377i
\(545\) 469.042 469.042i 0.860628 0.860628i
\(546\) 2.12109 144.665i 0.00388478 0.264955i
\(547\) −332.460 + 332.460i −0.607788 + 0.607788i −0.942368 0.334579i \(-0.891406\pi\)
0.334579 + 0.942368i \(0.391406\pi\)
\(548\) −237.087 + 237.087i −0.432640 + 0.432640i
\(549\) 42.1876i 0.0768445i
\(550\) −101.181 + 101.181i −0.183965 + 0.183965i
\(551\) 853.412i 1.54884i
\(552\) 774.472 + 774.472i 1.40303 + 1.40303i
\(553\) −129.281 + 125.545i −0.233781 + 0.227025i
\(554\) 149.341i 0.269569i
\(555\) −188.160 + 188.160i −0.339027 + 0.339027i
\(556\) 104.253i 0.187505i
\(557\) 684.259 684.259i 1.22847 1.22847i 0.263930 0.964542i \(-0.414981\pi\)
0.964542 0.263930i \(-0.0850186\pi\)
\(558\) 18.4615i 0.0330851i
\(559\) 38.5345 + 38.5345i 0.0689346 + 0.0689346i
\(560\) 6.50759 443.839i 0.0116207 0.792570i
\(561\) −69.3029 69.3029i −0.123535 0.123535i
\(562\) −398.183 398.183i −0.708510 0.708510i
\(563\) −168.561 + 168.561i −0.299397 + 0.299397i −0.840778 0.541381i \(-0.817902\pi\)
0.541381 + 0.840778i \(0.317902\pi\)
\(564\) −113.717 −0.201626
\(565\) −378.843 −0.670518
\(566\) 782.748 1.38295
\(567\) −9.15283 + 624.253i −0.0161426 + 1.10097i
\(568\) 120.443 120.443i 0.212047 0.212047i
\(569\) 496.683i 0.872904i 0.899727 + 0.436452i \(0.143765\pi\)
−0.899727 + 0.436452i \(0.856235\pi\)
\(570\) 668.531i 1.17286i
\(571\) 286.208 + 286.208i 0.501240 + 0.501240i 0.911823 0.410583i \(-0.134675\pi\)
−0.410583 + 0.911823i \(0.634675\pi\)
\(572\) −21.7694 −0.0380584
\(573\) 477.632i 0.833563i
\(574\) −459.512 129.416i −0.800543 0.225464i
\(575\) −759.835 −1.32145
\(576\) 71.5738i 0.124260i
\(577\) 275.423 275.423i 0.477337 0.477337i −0.426942 0.904279i \(-0.640409\pi\)
0.904279 + 0.426942i \(0.140409\pi\)
\(578\) −401.977 −0.695461
\(579\) −857.149 −1.48040
\(580\) −258.694 258.694i −0.446024 0.446024i
\(581\) −323.853 4.74836i −0.557407 0.00817273i
\(582\) 348.859i 0.599415i
\(583\) 39.8444i 0.0683438i
\(584\) 444.769i 0.761591i
\(585\) −18.9294 18.9294i −0.0323580 0.0323580i
\(586\) −443.814 + 443.814i −0.757362 + 0.757362i
\(587\) −516.506 + 516.506i −0.879908 + 0.879908i −0.993525 0.113616i \(-0.963757\pi\)
0.113616 + 0.993525i \(0.463757\pi\)
\(588\) −139.208 + 131.275i −0.236748 + 0.223256i
\(589\) −146.013 + 146.013i −0.247900 + 0.247900i
\(590\) 179.767 0.304690
\(591\) 587.430 + 587.430i 0.993959 + 0.993959i
\(592\) 120.773 0.204009
\(593\) −743.392 743.392i −1.25361 1.25361i −0.954089 0.299524i \(-0.903172\pi\)
−0.299524 0.954089i \(-0.596828\pi\)
\(594\) −188.920 −0.318047
\(595\) −229.502 + 222.869i −0.385717 + 0.374570i
\(596\) 103.046 103.046i 0.172895 0.172895i
\(597\) −704.968 −1.18085
\(598\) 183.396 + 183.396i 0.306682 + 0.306682i
\(599\) −873.768 −1.45871 −0.729355 0.684135i \(-0.760180\pi\)
−0.729355 + 0.684135i \(0.760180\pi\)
\(600\) −372.708 372.708i −0.621180 0.621180i
\(601\) 515.697 + 515.697i 0.858065 + 0.858065i 0.991110 0.133045i \(-0.0424754\pi\)
−0.133045 + 0.991110i \(0.542475\pi\)
\(602\) −2.37063 + 161.685i −0.00393792 + 0.268579i
\(603\) 25.0541 + 25.0541i 0.0415491 + 0.0415491i
\(604\) 136.154 + 136.154i 0.225421 + 0.225421i
\(605\) 669.310i 1.10630i
\(606\) 218.545i 0.360636i
\(607\) −263.884 −0.434735 −0.217368 0.976090i \(-0.569747\pi\)
−0.217368 + 0.976090i \(0.569747\pi\)
\(608\) 255.900 255.900i 0.420888 0.420888i
\(609\) 14.5136 989.876i 0.0238319 1.62541i
\(610\) 453.857i 0.744027i
\(611\) −114.274 −0.187028
\(612\) 6.16166 6.16166i 0.0100681 0.0100681i
\(613\) 397.780i 0.648908i 0.945902 + 0.324454i \(0.105180\pi\)
−0.945902 + 0.324454i \(0.894820\pi\)
\(614\) 654.175i 1.06543i
\(615\) −746.009 + 432.634i −1.21302 + 0.703470i
\(616\) −190.967 196.651i −0.310012 0.319238i
\(617\) 19.4730i 0.0315607i 0.999875 + 0.0157804i \(0.00502325\pi\)
−0.999875 + 0.0157804i \(0.994977\pi\)
\(618\) −281.580 281.580i −0.455631 0.455631i
\(619\) 897.516i 1.44994i 0.688778 + 0.724972i \(0.258148\pi\)
−0.688778 + 0.724972i \(0.741852\pi\)
\(620\) 88.5216i 0.142777i
\(621\) −709.364 709.364i −1.14229 1.14229i
\(622\) −108.167 + 108.167i −0.173903 + 0.173903i
\(623\) 496.000 + 510.761i 0.796148 + 0.819841i
\(624\) 118.623i 0.190101i
\(625\) −737.394 −1.17983
\(626\) 3.69643 3.69643i 0.00590484 0.00590484i
\(627\) −192.472 192.472i −0.306974 0.306974i
\(628\) 58.8012 58.8012i 0.0936326 0.0936326i
\(629\) −61.5475 61.5475i −0.0978497 0.0978497i
\(630\) 1.16453 79.4249i 0.00184846 0.126071i
\(631\) 105.852 0.167753 0.0838763 0.996476i \(-0.473270\pi\)
0.0838763 + 0.996476i \(0.473270\pi\)
\(632\) 158.459 158.459i 0.250727 0.250727i
\(633\) 19.4862i 0.0307838i
\(634\) −627.857 + 627.857i −0.990310 + 0.990310i
\(635\) 711.412 1.12033
\(636\) −34.5860 −0.0543806
\(637\) −139.890 + 131.918i −0.219607 + 0.207092i
\(638\) 334.206 0.523834
\(639\) 14.2105 14.2105i 0.0222387 0.0222387i
\(640\) 266.773i 0.416833i
\(641\) −145.539 + 145.539i −0.227049 + 0.227049i −0.811459 0.584410i \(-0.801326\pi\)
0.584410 + 0.811459i \(0.301326\pi\)
\(642\) −728.981 728.981i −1.13548 1.13548i
\(643\) −108.037 + 108.037i −0.168020 + 0.168020i −0.786108 0.618089i \(-0.787907\pi\)
0.618089 + 0.786108i \(0.287907\pi\)
\(644\) 5.02866 342.971i 0.00780849 0.532564i
\(645\) 206.551 + 206.551i 0.320235 + 0.320235i
\(646\) 218.678 0.338510
\(647\) −878.729 −1.35816 −0.679080 0.734065i \(-0.737621\pi\)
−0.679080 + 0.734065i \(0.737621\pi\)
\(648\) 776.364i 1.19809i
\(649\) 51.7556 51.7556i 0.0797467 0.0797467i
\(650\) −88.2578 88.2578i −0.135781 0.135781i
\(651\) −171.844 + 166.878i −0.263970 + 0.256341i
\(652\) −308.055 −0.472477
\(653\) −290.301 290.301i −0.444564 0.444564i 0.448978 0.893543i \(-0.351788\pi\)
−0.893543 + 0.448978i \(0.851788\pi\)
\(654\) −525.986 −0.804259
\(655\) 673.507 1.02825
\(656\) 378.265 + 100.572i 0.576624 + 0.153312i
\(657\) 52.4764i 0.0798728i
\(658\) −236.223 243.253i −0.359002 0.369686i
\(659\) 346.814 + 346.814i 0.526274 + 0.526274i 0.919459 0.393186i \(-0.128627\pi\)
−0.393186 + 0.919459i \(0.628627\pi\)
\(660\) −116.688 −0.176800
\(661\) 476.749 0.721254 0.360627 0.932710i \(-0.382563\pi\)
0.360627 + 0.932710i \(0.382563\pi\)
\(662\) 560.976 560.976i 0.847395 0.847395i
\(663\) 60.4515 60.4515i 0.0911787 0.0911787i
\(664\) 402.766 0.606576
\(665\) −637.386 + 618.966i −0.958476 + 0.930776i
\(666\) 21.6124 0.0324510
\(667\) 1254.89 + 1254.89i 1.88140 + 1.88140i
\(668\) 232.240 232.240i 0.347665 0.347665i
\(669\) 150.191 + 150.191i 0.224501 + 0.224501i
\(670\) 269.534 + 269.534i 0.402289 + 0.402289i
\(671\) −130.667 130.667i −0.194735 0.194735i
\(672\) 301.172 292.468i 0.448172 0.435220i
\(673\) 620.343 620.343i 0.921758 0.921758i −0.0753960 0.997154i \(-0.524022\pi\)
0.997154 + 0.0753960i \(0.0240221\pi\)
\(674\) −136.905 −0.203123
\(675\) 341.376 + 341.376i 0.505742 + 0.505742i
\(676\) 189.419i 0.280206i
\(677\) 1027.38 1.51754 0.758772 0.651356i \(-0.225799\pi\)
0.758772 + 0.651356i \(0.225799\pi\)
\(678\) 212.418 + 212.418i 0.313301 + 0.313301i
\(679\) −332.607 + 322.995i −0.489849 + 0.475692i
\(680\) 281.300 281.300i 0.413676 0.413676i
\(681\) −759.600 −1.11542
\(682\) −57.1805 57.1805i −0.0838424 0.0838424i
\(683\) −624.740 + 624.740i −0.914699 + 0.914699i −0.996637 0.0819380i \(-0.973889\pi\)
0.0819380 + 0.996637i \(0.473889\pi\)
\(684\) 17.1126 17.1126i 0.0250183 0.0250183i
\(685\) −1277.05 + 1277.05i −1.86431 + 1.86431i
\(686\) −569.986 25.0859i −0.830883 0.0365683i
\(687\) 1103.61 1.60642
\(688\) 132.578i 0.192701i
\(689\) −34.7555 −0.0504434
\(690\) 983.034 + 983.034i 1.42469 + 1.42469i
\(691\) 559.233 + 559.233i 0.809309 + 0.809309i 0.984529 0.175220i \(-0.0560636\pi\)
−0.175220 + 0.984529i \(0.556064\pi\)
\(692\) 262.241 0.378961
\(693\) −22.5314 23.2020i −0.0325129 0.0334805i
\(694\) 724.082 + 724.082i 1.04335 + 1.04335i
\(695\) 561.549i 0.807985i
\(696\) 1231.08i 1.76879i
\(697\) −141.515 244.021i −0.203035 0.350102i
\(698\) 746.759i 1.06985i
\(699\) −879.451 −1.25816
\(700\) −2.42000 + 165.052i −0.00345715 + 0.235789i
\(701\) −195.759 −0.279256 −0.139628 0.990204i \(-0.544591\pi\)
−0.139628 + 0.990204i \(0.544591\pi\)
\(702\) 164.791i 0.234745i
\(703\) −170.933 170.933i −0.243149 0.243149i
\(704\) 221.684 + 221.684i 0.314892 + 0.314892i
\(705\) −612.529 −0.868836
\(706\) 872.305 1.23556
\(707\) −208.364 + 202.342i −0.294716 + 0.286199i
\(708\) 44.9253 + 44.9253i 0.0634538 + 0.0634538i
\(709\) −390.072 390.072i −0.550173 0.550173i 0.376318 0.926491i \(-0.377190\pi\)
−0.926491 + 0.376318i \(0.877190\pi\)
\(710\) 152.877 152.877i 0.215320 0.215320i
\(711\) 18.6959 18.6959i 0.0262953 0.0262953i
\(712\) −626.039 626.039i −0.879268 0.879268i
\(713\) 429.407i 0.602254i
\(714\) 253.645 + 3.71896i 0.355245 + 0.00520862i
\(715\) −117.259 −0.163999
\(716\) 226.670 226.670i 0.316578 0.316578i
\(717\) 1072.65 1.49603
\(718\) 524.519i 0.730528i
\(719\) −390.459 390.459i −0.543059 0.543059i 0.381365 0.924424i \(-0.375454\pi\)
−0.924424 + 0.381365i \(0.875454\pi\)
\(720\) 65.1268i 0.0904539i
\(721\) −7.75866 + 529.166i −0.0107610 + 0.733933i
\(722\) 6.84727 0.00948375
\(723\) −39.8848 + 39.8848i −0.0551657 + 0.0551657i
\(724\) −289.442 289.442i −0.399781 0.399781i
\(725\) −603.906 603.906i −0.832974 0.832974i
\(726\) −375.283 + 375.283i −0.516919 + 0.516919i
\(727\) −588.279 + 588.279i −0.809187 + 0.809187i −0.984511 0.175324i \(-0.943903\pi\)
0.175324 + 0.984511i \(0.443903\pi\)
\(728\) 171.534 166.577i 0.235624 0.228814i
\(729\) 627.907i 0.861326i
\(730\) 564.544i 0.773348i
\(731\) −67.5633 + 67.5633i −0.0924259 + 0.0924259i
\(732\) 113.422 113.422i 0.154949 0.154949i
\(733\) 642.566 0.876624 0.438312 0.898823i \(-0.355576\pi\)
0.438312 + 0.898823i \(0.355576\pi\)
\(734\) 368.260i 0.501716i
\(735\) −749.833 + 707.101i −1.02018 + 0.962042i
\(736\) 752.572i 1.02252i
\(737\) 155.199 0.210583
\(738\) 67.6905 + 17.9974i 0.0917215 + 0.0243867i
\(739\) −327.099 −0.442624 −0.221312 0.975203i \(-0.571034\pi\)
−0.221312 + 0.975203i \(0.571034\pi\)
\(740\) −103.630 −0.140040
\(741\) 167.890 167.890i 0.226572 0.226572i
\(742\) −71.8452 73.9834i −0.0968265 0.0997081i
\(743\) 585.868i 0.788516i 0.919000 + 0.394258i \(0.128998\pi\)
−0.919000 + 0.394258i \(0.871002\pi\)
\(744\) 210.629 210.629i 0.283104 0.283104i
\(745\) 555.048 555.048i 0.745031 0.745031i
\(746\) 466.835i 0.625784i
\(747\) 47.5207 0.0636154
\(748\) 38.1688i 0.0510278i
\(749\) −20.0864 + 1369.96i −0.0268176 + 1.82905i
\(750\) 145.410 + 145.410i 0.193880 + 0.193880i
\(751\) −20.5349 20.5349i −0.0273434 0.0273434i 0.693303 0.720646i \(-0.256155\pi\)
−0.720646 + 0.693303i \(0.756155\pi\)
\(752\) 196.581 + 196.581i 0.261411 + 0.261411i
\(753\) −566.112 + 566.112i −0.751809 + 0.751809i
\(754\) 291.521i 0.386633i
\(755\) 733.385 + 733.385i 0.971371 + 0.971371i
\(756\) −156.348 + 151.829i −0.206809 + 0.200833i
\(757\) −78.8076 + 78.8076i −0.104105 + 0.104105i −0.757241 0.653136i \(-0.773453\pi\)
0.653136 + 0.757241i \(0.273453\pi\)
\(758\) 617.765i 0.814993i
\(759\) 566.038 0.745769
\(760\) 781.243 781.243i 1.02795 1.02795i
\(761\) 26.8137i 0.0352348i −0.999845 0.0176174i \(-0.994392\pi\)
0.999845 0.0176174i \(-0.00560808\pi\)
\(762\) −398.890 398.890i −0.523478 0.523478i
\(763\) 486.989 + 501.482i 0.638255 + 0.657250i
\(764\) 131.529 131.529i 0.172158 0.172158i
\(765\) 33.1893 33.1893i 0.0433848 0.0433848i
\(766\) 536.734 536.734i 0.700697 0.700697i
\(767\) 45.1453 + 45.1453i 0.0588596 + 0.0588596i
\(768\) −474.585 + 474.585i −0.617949 + 0.617949i
\(769\) 1492.47i 1.94079i 0.241528 + 0.970394i \(0.422351\pi\)
−0.241528 + 0.970394i \(0.577649\pi\)
\(770\) −242.394 249.608i −0.314798 0.324166i
\(771\) 75.9308i 0.0984836i
\(772\) −236.039 236.039i −0.305750 0.305750i
\(773\) −531.207 531.207i −0.687202 0.687202i 0.274411 0.961613i \(-0.411517\pi\)
−0.961613 + 0.274411i \(0.911517\pi\)
\(774\) 23.7248i 0.0306522i
\(775\) 206.649i 0.266644i
\(776\) 407.676 407.676i 0.525356 0.525356i
\(777\) −195.359 201.173i −0.251428 0.258910i
\(778\) 818.362 1.05188
\(779\) −393.025 677.711i −0.504526 0.869975i
\(780\) 101.784i 0.130493i
\(781\) 88.0279i 0.112712i
\(782\) −321.552 + 321.552i −0.411192 + 0.411192i
\(783\) 1127.58i 1.44008i
\(784\) 467.578 + 13.7143i 0.596401 + 0.0174927i
\(785\) 316.729 316.729i 0.403476 0.403476i
\(786\) −377.636 377.636i −0.480454 0.480454i
\(787\) 808.732 1.02761 0.513807 0.857906i \(-0.328235\pi\)
0.513807 + 0.857906i \(0.328235\pi\)
\(788\) 323.529i 0.410570i
\(789\) 76.8018i 0.0973407i
\(790\) 201.132 201.132i 0.254597 0.254597i
\(791\) 5.85296 399.191i 0.00739945 0.504667i
\(792\) 28.4386 + 28.4386i 0.0359073 + 0.0359073i
\(793\) 113.978 113.978i 0.143730 0.143730i
\(794\) −652.662 652.662i −0.821993 0.821993i
\(795\) −186.295 −0.234334
\(796\) −194.132 194.132i −0.243884 0.243884i
\(797\) 603.159i 0.756787i 0.925645 + 0.378394i \(0.123523\pi\)
−0.925645 + 0.378394i \(0.876477\pi\)
\(798\) 704.439 + 10.3285i 0.882756 + 0.0129430i
\(799\) 200.359i 0.250763i
\(800\) 362.169i 0.452711i
\(801\) −73.8637 73.8637i −0.0922143 0.0922143i
\(802\) −1179.22 −1.47034
\(803\) 162.534 + 162.534i 0.202409 + 0.202409i
\(804\) 134.717i 0.167559i
\(805\) 27.0865 1847.39i 0.0336479 2.29490i
\(806\) 49.8774 49.8774i 0.0618826 0.0618826i
\(807\) 1123.09 + 1123.09i 1.39169 + 1.39169i
\(808\) 255.392 255.392i 0.316079 0.316079i
\(809\) −750.564 750.564i −0.927768 0.927768i 0.0697935 0.997561i \(-0.477766\pi\)
−0.997561 + 0.0697935i \(0.977766\pi\)
\(810\) 985.436i 1.21659i
\(811\) 169.224 0.208661 0.104330 0.994543i \(-0.466730\pi\)
0.104330 + 0.994543i \(0.466730\pi\)
\(812\) 276.585 268.592i 0.340622 0.330778i
\(813\) 556.342 + 556.342i 0.684308 + 0.684308i
\(814\) 66.9396 66.9396i 0.0822354 0.0822354i
\(815\) −1659.32 −2.03597
\(816\) −207.984 −0.254882
\(817\) −187.641 + 187.641i −0.229671 + 0.229671i
\(818\) −349.634 −0.427425
\(819\) 20.2386 19.6537i 0.0247113 0.0239972i
\(820\) −324.571 86.2963i −0.395818 0.105239i
\(821\) −258.388 −0.314724 −0.157362 0.987541i \(-0.550299\pi\)
−0.157362 + 0.987541i \(0.550299\pi\)
\(822\) 1432.09 1.74220
\(823\) 112.888 + 112.888i 0.137167 + 0.137167i 0.772356 0.635189i \(-0.219078\pi\)
−0.635189 + 0.772356i \(0.719078\pi\)
\(824\) 658.107i 0.798674i
\(825\) −272.401 −0.330183
\(826\) −2.77733 + 189.423i −0.00336238 + 0.229326i
\(827\) 81.2789 + 81.2789i 0.0982816 + 0.0982816i 0.754538 0.656256i \(-0.227861\pi\)
−0.656256 + 0.754538i \(0.727861\pi\)
\(828\) 50.3260i 0.0607802i
\(829\) −99.9547 −0.120573 −0.0602863 0.998181i \(-0.519201\pi\)
−0.0602863 + 0.998181i \(0.519201\pi\)
\(830\) 511.230 0.615940
\(831\) −201.030 + 201.030i −0.241913 + 0.241913i
\(832\) −193.370 + 193.370i −0.232416 + 0.232416i
\(833\) −231.294 245.272i −0.277664 0.294444i
\(834\) 314.862 314.862i 0.377532 0.377532i
\(835\) 1250.95 1250.95i 1.49814 1.49814i
\(836\) 106.005i 0.126800i
\(837\) −192.922 + 192.922i −0.230493 + 0.230493i
\(838\) 98.8249i 0.117929i
\(839\) 116.188 + 116.188i 0.138484 + 0.138484i 0.772950 0.634467i \(-0.218780\pi\)
−0.634467 + 0.772950i \(0.718780\pi\)
\(840\) 919.453 892.881i 1.09459 1.06295i
\(841\) 1153.74i 1.37187i
\(842\) −260.673 + 260.673i −0.309587 + 0.309587i
\(843\) 1072.00i 1.27165i
\(844\) −5.36603 + 5.36603i −0.00635786 + 0.00635786i
\(845\) 1020.29i 1.20745i
\(846\) 35.1781 + 35.1781i 0.0415816 + 0.0415816i
\(847\) 705.260 + 10.3406i 0.832656 + 0.0122085i
\(848\) 59.7883 + 59.7883i 0.0705051 + 0.0705051i
\(849\) 1053.67 + 1053.67i 1.24107 + 1.24107i
\(850\) 154.744 154.744i 0.182052 0.182052i
\(851\) 502.695 0.590711
\(852\) 76.4105 0.0896837
\(853\) 307.409 0.360386 0.180193 0.983631i \(-0.442328\pi\)
0.180193 + 0.983631i \(0.442328\pi\)
\(854\) 478.234 + 7.01190i 0.559993 + 0.00821066i
\(855\) 92.1756 92.1756i 0.107808 0.107808i
\(856\) 1703.77i 1.99039i
\(857\) 1460.96i 1.70474i 0.522943 + 0.852368i \(0.324834\pi\)
−0.522943 + 0.852368i \(0.675166\pi\)
\(858\) 65.7476 + 65.7476i 0.0766289 + 0.0766289i
\(859\) −1286.91 −1.49815 −0.749076 0.662485i \(-0.769502\pi\)
−0.749076 + 0.662485i \(0.769502\pi\)
\(860\) 113.759i 0.132278i
\(861\) −444.346 792.763i −0.516081 0.920747i
\(862\) −391.711 −0.454421
\(863\) 1236.40i 1.43268i 0.697753 + 0.716339i \(0.254184\pi\)
−0.697753 + 0.716339i \(0.745816\pi\)
\(864\) 338.112 338.112i 0.391334 0.391334i
\(865\) 1412.54 1.63300
\(866\) −556.375 −0.642465
\(867\) −541.106 541.106i −0.624113 0.624113i
\(868\) −93.2763 1.36762i −0.107461 0.00157560i
\(869\) 115.813i 0.133272i
\(870\) 1562.60i 1.79610i
\(871\) 135.377i 0.155427i
\(872\) −614.665 614.665i −0.704891 0.704891i
\(873\) 48.1000 48.1000i 0.0550973 0.0550973i
\(874\) −893.036 + 893.036i −1.02178 + 1.02178i
\(875\) 4.00663 273.265i 0.00457900 0.312303i
\(876\) −141.084 + 141.084i −0.161055 + 0.161055i
\(877\) 739.991 0.843775 0.421887 0.906648i \(-0.361368\pi\)
0.421887 + 0.906648i \(0.361368\pi\)
\(878\) 523.333 + 523.333i 0.596051 + 0.596051i
\(879\) −1194.85 −1.35932
\(880\) 201.716 + 201.716i 0.229223 + 0.229223i
\(881\) 1054.54 1.19698 0.598489 0.801131i \(-0.295768\pi\)
0.598489 + 0.801131i \(0.295768\pi\)
\(882\) 83.6730 + 2.45416i 0.0948673 + 0.00278250i
\(883\) 375.264 375.264i 0.424987 0.424987i −0.461930 0.886917i \(-0.652843\pi\)
0.886917 + 0.461930i \(0.152843\pi\)
\(884\) 33.2938 0.0376627
\(885\) 241.987 + 241.987i 0.273431 + 0.273431i
\(886\) −640.080 −0.722438
\(887\) −361.346 361.346i −0.407380 0.407380i 0.473444 0.880824i \(-0.343011\pi\)
−0.880824 + 0.473444i \(0.843011\pi\)
\(888\) 246.578 + 246.578i 0.277678 + 0.277678i
\(889\) −10.9910 + 749.623i −0.0123634 + 0.843221i
\(890\) −794.629 794.629i −0.892842 0.892842i
\(891\) −283.711 283.711i −0.318418 0.318418i
\(892\) 82.7184i 0.0927336i
\(893\) 556.451i 0.623125i
\(894\) −622.433 −0.696234
\(895\) 1220.94 1220.94i 1.36418 1.36418i
\(896\) −281.102 4.12153i −0.313730 0.00459992i
\(897\) 493.743i 0.550438i
\(898\) −451.438 −0.502715
\(899\) 341.287 341.287i 0.379629 0.379629i
\(900\) 24.2190i 0.0269099i
\(901\) 60.9375i 0.0676332i
\(902\) 265.400 153.913i 0.294235 0.170636i
\(903\) −220.837 + 214.455i −0.244559 + 0.237491i
\(904\) 496.462i 0.549183i
\(905\) −1559.06 1559.06i −1.72271 1.72271i
\(906\) 822.421i 0.907750i
\(907\) 1291.18i 1.42357i −0.702397 0.711786i \(-0.747887\pi\)
0.702397 0.711786i \(-0.252113\pi\)
\(908\) −209.176 209.176i −0.230370 0.230370i
\(909\) 30.1326 30.1326i 0.0331491 0.0331491i
\(910\) 217.728 211.435i 0.239261 0.232347i
\(911\) 1218.98i 1.33807i 0.743230 + 0.669037i \(0.233293\pi\)
−0.743230 + 0.669037i \(0.766707\pi\)
\(912\) −577.626 −0.633362
\(913\) 147.185 147.185i 0.161210 0.161210i
\(914\) −583.112 583.112i −0.637978 0.637978i
\(915\) 610.942 610.942i 0.667696 0.667696i
\(916\) 303.908 + 303.908i 0.331778 + 0.331778i
\(917\) −10.4054 + 709.682i −0.0113472 + 0.773917i
\(918\) 288.931 0.314740
\(919\) 381.625 381.625i 0.415261 0.415261i −0.468306 0.883567i \(-0.655135\pi\)
0.883567 + 0.468306i \(0.155135\pi\)
\(920\) 2297.54i 2.49733i
\(921\) −880.593 + 880.593i −0.956127 + 0.956127i
\(922\) −625.251 −0.678147
\(923\) 76.7848 0.0831905
\(924\) 1.80278 122.955i 0.00195106 0.133069i
\(925\) −241.918 −0.261533
\(926\) −976.163 + 976.163i −1.05417 + 1.05417i
\(927\) 77.6473i 0.0837619i
\(928\) −598.133 + 598.133i −0.644540 + 0.644540i
\(929\) −138.548 138.548i −0.149136 0.149136i 0.628596 0.777732i \(-0.283630\pi\)
−0.777732 + 0.628596i \(0.783630\pi\)
\(930\) 267.351 267.351i 0.287474 0.287474i
\(931\) −642.364 681.185i −0.689973 0.731670i
\(932\) −242.180 242.180i −0.259850 0.259850i
\(933\) −291.211 −0.312123
\(934\) −237.962 −0.254777
\(935\) 205.594i 0.219886i
\(936\) −24.8064 + 24.8064i −0.0265026 + 0.0265026i
\(937\) 136.385 + 136.385i 0.145555 + 0.145555i 0.776129 0.630574i \(-0.217181\pi\)
−0.630574 + 0.776129i \(0.717181\pi\)
\(938\) −288.175 + 279.847i −0.307223 + 0.298344i
\(939\) 9.95162 0.0105981
\(940\) −168.676 168.676i −0.179443 0.179443i
\(941\) −631.698 −0.671305 −0.335652 0.941986i \(-0.608957\pi\)
−0.335652 + 0.941986i \(0.608957\pi\)
\(942\) −355.181 −0.377050
\(943\) 1574.45 + 418.613i 1.66962 + 0.443916i
\(944\) 155.323i 0.164537i
\(945\) −842.157 + 817.819i −0.891172 + 0.865417i
\(946\) −73.4825 73.4825i −0.0776771 0.0776771i
\(947\) 1678.47 1.77240 0.886202 0.463299i \(-0.153334\pi\)
0.886202 + 0.463299i \(0.153334\pi\)
\(948\) 100.529 0.106043
\(949\) −141.775 + 141.775i −0.149394 + 0.149394i
\(950\) 429.766 429.766i 0.452385 0.452385i
\(951\) −1690.33 −1.77743
\(952\) 292.063 + 300.755i 0.306789 + 0.315919i
\(953\) −758.655 −0.796071 −0.398035 0.917370i \(-0.630308\pi\)
−0.398035 + 0.917370i \(0.630308\pi\)
\(954\) 10.6991 + 10.6991i 0.0112150 + 0.0112150i
\(955\) 708.470 708.470i 0.741853 0.741853i
\(956\) 295.383 + 295.383i 0.308978 + 0.308978i
\(957\) 449.879 + 449.879i 0.470093 + 0.470093i
\(958\) −876.782 876.782i −0.915221 0.915221i
\(959\) −1325.91 1365.37i −1.38260 1.42375i
\(960\) −1036.50 + 1036.50i −1.07969 + 1.07969i
\(961\) 844.216 0.878477
\(962\) 58.3900 + 58.3900i 0.0606964 + 0.0606964i
\(963\) 201.021i 0.208744i
\(964\) −21.9667 −0.0227870
\(965\) −1271.41 1271.41i −1.31752 1.31752i
\(966\) −1051.02 + 1020.65i −1.08802 + 1.05657i
\(967\) −33.5592 + 33.5592i −0.0347045 + 0.0347045i −0.724246 0.689542i \(-0.757812\pi\)
0.689542 + 0.724246i \(0.257812\pi\)
\(968\) −877.110 −0.906105
\(969\) 294.365 + 294.365i 0.303782 + 0.303782i
\(970\) 517.462 517.462i 0.533466 0.533466i
\(971\) 1153.07 1153.07i 1.18751 1.18751i 0.209754 0.977754i \(-0.432734\pi\)
0.977754 0.209754i \(-0.0672662\pi\)
\(972\) 48.1330 48.1330i 0.0495196 0.0495196i
\(973\) −591.711 8.67571i −0.608131 0.00891645i
\(974\) −407.481 −0.418359
\(975\) 237.610i 0.243702i
\(976\) −392.143 −0.401786
\(977\) 414.202 + 414.202i 0.423953 + 0.423953i 0.886562 0.462609i \(-0.153087\pi\)
−0.462609 + 0.886562i \(0.653087\pi\)
\(978\) 930.381 + 930.381i 0.951310 + 0.951310i
\(979\) −457.553 −0.467368
\(980\) −401.206 11.7675i −0.409393 0.0120077i
\(981\) −72.5217 72.5217i −0.0739263 0.0739263i
\(982\) 407.526i 0.414996i
\(983\) 323.740i 0.329339i 0.986349 + 0.164670i \(0.0526558\pi\)
−0.986349 + 0.164670i \(0.947344\pi\)
\(984\) 566.953 + 977.622i 0.576172 + 0.993519i
\(985\) 1742.67i 1.76920i
\(986\) −511.130 −0.518388
\(987\) 9.46332 645.430i 0.00958797 0.653931i
\(988\) 92.4657 0.0935888
\(989\) 551.830i 0.557968i
\(990\) 36.0970 + 36.0970i 0.0364617 + 0.0364617i
\(991\) 397.828 + 397.828i 0.401441 + 0.401441i 0.878741 0.477299i \(-0.158384\pi\)
−0.477299 + 0.878741i \(0.658384\pi\)
\(992\) 204.673 0.206324
\(993\) 1510.27 1.52092
\(994\) 158.727 + 163.451i 0.159685 + 0.164437i
\(995\) −1045.68 1045.68i −1.05093 1.05093i
\(996\) 127.761 + 127.761i 0.128274 + 0.128274i
\(997\) 442.253 442.253i 0.443584 0.443584i −0.449631 0.893215i \(-0.648444\pi\)
0.893215 + 0.449631i \(0.148444\pi\)
\(998\) 663.374 663.374i 0.664703 0.664703i
\(999\) −225.849 225.849i −0.226075 0.226075i
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 287.3.g.a.132.18 yes 108
7.6 odd 2 inner 287.3.g.a.132.17 108
41.32 even 4 inner 287.3.g.a.237.37 yes 108
287.237 odd 4 inner 287.3.g.a.237.38 yes 108
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
287.3.g.a.132.17 108 7.6 odd 2 inner
287.3.g.a.132.18 yes 108 1.1 even 1 trivial
287.3.g.a.237.37 yes 108 41.32 even 4 inner
287.3.g.a.237.38 yes 108 287.237 odd 4 inner