Properties

Label 105.3.k.d.83.8
Level $105$
Weight $3$
Character 105.83
Analytic conductor $2.861$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [105,3,Mod(62,105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 2]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.62");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.k (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: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 83.8
Character \(\chi\) \(=\) 105.83
Dual form 105.3.k.d.62.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.67168 - 1.67168i) q^{2} +(2.55943 + 1.56503i) q^{3} +1.58906i q^{4} +(-0.529219 + 4.97191i) q^{5} +(-1.66231 - 6.89480i) q^{6} +(6.78135 + 1.73590i) q^{7} +(-4.03033 + 4.03033i) q^{8} +(4.10134 + 8.01118i) q^{9} +O(q^{10})\) \(q+(-1.67168 - 1.67168i) q^{2} +(2.55943 + 1.56503i) q^{3} +1.58906i q^{4} +(-0.529219 + 4.97191i) q^{5} +(-1.66231 - 6.89480i) q^{6} +(6.78135 + 1.73590i) q^{7} +(-4.03033 + 4.03033i) q^{8} +(4.10134 + 8.01118i) q^{9} +(9.19616 - 7.42678i) q^{10} +4.41779i q^{11} +(-2.48693 + 4.06708i) q^{12} +(1.62244 - 1.62244i) q^{13} +(-8.43440 - 14.2381i) q^{14} +(-9.13571 + 11.8970i) q^{15} +19.8311 q^{16} +(13.9255 - 13.9255i) q^{17} +(6.53602 - 20.2483i) q^{18} -0.694013 q^{19} +(-7.90067 - 0.840961i) q^{20} +(14.6396 + 15.0559i) q^{21} +(7.38515 - 7.38515i) q^{22} +(23.1818 - 23.1818i) q^{23} +(-16.6229 + 4.00774i) q^{24} +(-24.4399 - 5.26247i) q^{25} -5.42443 q^{26} +(-2.04067 + 26.9228i) q^{27} +(-2.75844 + 10.7760i) q^{28} -49.1234 q^{29} +(35.1601 - 4.61602i) q^{30} +33.8768i q^{31} +(-17.0301 - 17.0301i) q^{32} +(-6.91399 + 11.3070i) q^{33} -46.5580 q^{34} +(-12.2195 + 32.7976i) q^{35} +(-12.7302 + 6.51728i) q^{36} +(2.02579 - 2.02579i) q^{37} +(1.16017 + 1.16017i) q^{38} +(6.69171 - 1.61335i) q^{39} +(-17.9055 - 22.1714i) q^{40} -32.5085 q^{41} +(0.695926 - 49.6416i) q^{42} +(-30.4591 - 30.4591i) q^{43} -7.02014 q^{44} +(-42.0014 + 16.1518i) q^{45} -77.5053 q^{46} +(18.7790 - 18.7790i) q^{47} +(50.7563 + 31.0364i) q^{48} +(42.9733 + 23.5434i) q^{49} +(32.0585 + 49.6529i) q^{50} +(57.4350 - 13.8474i) q^{51} +(2.57816 + 2.57816i) q^{52} +(33.8448 - 33.8448i) q^{53} +(48.4178 - 41.5950i) q^{54} +(-21.9649 - 2.33798i) q^{55} +(-34.3273 + 20.3348i) q^{56} +(-1.77628 - 1.08615i) q^{57} +(82.1189 + 82.1189i) q^{58} -23.1041i q^{59} +(-18.9051 - 14.5172i) q^{60} -12.9880i q^{61} +(56.6314 - 56.6314i) q^{62} +(13.9060 + 61.4461i) q^{63} -22.3867i q^{64} +(7.20802 + 8.92528i) q^{65} +(30.4598 - 7.34376i) q^{66} +(-56.3395 + 56.3395i) q^{67} +(22.1284 + 22.1284i) q^{68} +(95.6125 - 23.0519i) q^{69} +(75.2545 - 34.4000i) q^{70} -92.7547i q^{71} +(-48.8175 - 15.7579i) q^{72} +(95.4460 - 95.4460i) q^{73} -6.77295 q^{74} +(-54.3161 - 51.7181i) q^{75} -1.10283i q^{76} +(-7.66883 + 29.9586i) q^{77} +(-13.8834 - 8.48941i) q^{78} -100.280i q^{79} +(-10.4950 + 98.5987i) q^{80} +(-47.3580 + 65.7132i) q^{81} +(54.3440 + 54.3440i) q^{82} +(-5.62594 - 5.62594i) q^{83} +(-23.9248 + 23.2633i) q^{84} +(61.8666 + 76.6059i) q^{85} +101.836i q^{86} +(-125.728 - 76.8798i) q^{87} +(-17.8052 - 17.8052i) q^{88} +158.669i q^{89} +(97.2139 + 43.2123i) q^{90} +(13.8188 - 8.18596i) q^{91} +(36.8373 + 36.8373i) q^{92} +(-53.0184 + 86.7053i) q^{93} -62.7852 q^{94} +(0.367285 - 3.45057i) q^{95} +(-16.9346 - 70.2399i) q^{96} +(-37.1038 - 37.1038i) q^{97} +(-32.4807 - 111.195i) q^{98} +(-35.3917 + 18.1189i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 48 q^{15} - 24 q^{16} - 92 q^{18} - 60 q^{21} + 112 q^{22} - 72 q^{25} + 88 q^{28} - 108 q^{30} + 416 q^{36} + 72 q^{37} + 300 q^{42} - 328 q^{43} + 32 q^{46} + 148 q^{51} - 748 q^{57} - 392 q^{58} + 544 q^{60} - 220 q^{63} - 648 q^{67} - 8 q^{70} - 8 q^{72} + 500 q^{78} - 948 q^{81} + 672 q^{85} + 1288 q^{88} + 808 q^{91} + 292 q^{93}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.67168 1.67168i −0.835842 0.835842i 0.152466 0.988309i \(-0.451278\pi\)
−0.988309 + 0.152466i \(0.951278\pi\)
\(3\) 2.55943 + 1.56503i 0.853143 + 0.521678i
\(4\) 1.58906i 0.397265i
\(5\) −0.529219 + 4.97191i −0.105844 + 0.994383i
\(6\) −1.66231 6.89480i −0.277052 1.14913i
\(7\) 6.78135 + 1.73590i 0.968764 + 0.247985i
\(8\) −4.03033 + 4.03033i −0.503791 + 0.503791i
\(9\) 4.10134 + 8.01118i 0.455705 + 0.890131i
\(10\) 9.19616 7.42678i 0.919616 0.742678i
\(11\) 4.41779i 0.401617i 0.979630 + 0.200809i \(0.0643570\pi\)
−0.979630 + 0.200809i \(0.935643\pi\)
\(12\) −2.48693 + 4.06708i −0.207244 + 0.338924i
\(13\) 1.62244 1.62244i 0.124803 0.124803i −0.641946 0.766750i \(-0.721873\pi\)
0.766750 + 0.641946i \(0.221873\pi\)
\(14\) −8.43440 14.2381i −0.602457 1.01701i
\(15\) −9.13571 + 11.8970i −0.609047 + 0.793134i
\(16\) 19.8311 1.23945
\(17\) 13.9255 13.9255i 0.819145 0.819145i −0.166839 0.985984i \(-0.553356\pi\)
0.985984 + 0.166839i \(0.0533560\pi\)
\(18\) 6.53602 20.2483i 0.363112 1.12491i
\(19\) −0.694013 −0.0365270 −0.0182635 0.999833i \(-0.505814\pi\)
−0.0182635 + 0.999833i \(0.505814\pi\)
\(20\) −7.90067 0.840961i −0.395034 0.0420481i
\(21\) 14.6396 + 15.0559i 0.697125 + 0.716949i
\(22\) 7.38515 7.38515i 0.335689 0.335689i
\(23\) 23.1818 23.1818i 1.00790 1.00790i 0.00793606 0.999969i \(-0.497474\pi\)
0.999969 0.00793606i \(-0.00252615\pi\)
\(24\) −16.6229 + 4.00774i −0.692623 + 0.166989i
\(25\) −24.4399 5.26247i −0.977594 0.210499i
\(26\) −5.42443 −0.208632
\(27\) −2.04067 + 26.9228i −0.0755805 + 0.997140i
\(28\) −2.75844 + 10.7760i −0.0985158 + 0.384856i
\(29\) −49.1234 −1.69391 −0.846956 0.531663i \(-0.821567\pi\)
−0.846956 + 0.531663i \(0.821567\pi\)
\(30\) 35.1601 4.61602i 1.17200 0.153867i
\(31\) 33.8768i 1.09280i 0.837524 + 0.546401i \(0.184002\pi\)
−0.837524 + 0.546401i \(0.815998\pi\)
\(32\) −17.0301 17.0301i −0.532190 0.532190i
\(33\) −6.91399 + 11.3070i −0.209515 + 0.342637i
\(34\) −46.5580 −1.36935
\(35\) −12.2195 + 32.7976i −0.349130 + 0.937074i
\(36\) −12.7302 + 6.51728i −0.353618 + 0.181036i
\(37\) 2.02579 2.02579i 0.0547510 0.0547510i −0.679201 0.733952i \(-0.737674\pi\)
0.733952 + 0.679201i \(0.237674\pi\)
\(38\) 1.16017 + 1.16017i 0.0305308 + 0.0305308i
\(39\) 6.69171 1.61335i 0.171582 0.0413679i
\(40\) −17.9055 22.1714i −0.447638 0.554285i
\(41\) −32.5085 −0.792891 −0.396446 0.918058i \(-0.629756\pi\)
−0.396446 + 0.918058i \(0.629756\pi\)
\(42\) 0.695926 49.6416i 0.0165697 1.18194i
\(43\) −30.4591 30.4591i −0.708351 0.708351i 0.257838 0.966188i \(-0.416990\pi\)
−0.966188 + 0.257838i \(0.916990\pi\)
\(44\) −7.02014 −0.159549
\(45\) −42.0014 + 16.1518i −0.933365 + 0.358930i
\(46\) −77.5053 −1.68490
\(47\) 18.7790 18.7790i 0.399554 0.399554i −0.478522 0.878076i \(-0.658827\pi\)
0.878076 + 0.478522i \(0.158827\pi\)
\(48\) 50.7563 + 31.0364i 1.05742 + 0.646591i
\(49\) 42.9733 + 23.5434i 0.877007 + 0.480478i
\(50\) 32.0585 + 49.6529i 0.641171 + 0.993058i
\(51\) 57.4350 13.8474i 1.12618 0.271518i
\(52\) 2.57816 + 2.57816i 0.0495800 + 0.0495800i
\(53\) 33.8448 33.8448i 0.638581 0.638581i −0.311624 0.950205i \(-0.600873\pi\)
0.950205 + 0.311624i \(0.100873\pi\)
\(54\) 48.4178 41.5950i 0.896625 0.770278i
\(55\) −21.9649 2.33798i −0.399361 0.0425087i
\(56\) −34.3273 + 20.3348i −0.612988 + 0.363122i
\(57\) −1.77628 1.08615i −0.0311627 0.0190553i
\(58\) 82.1189 + 82.1189i 1.41584 + 1.41584i
\(59\) 23.1041i 0.391596i −0.980644 0.195798i \(-0.937270\pi\)
0.980644 0.195798i \(-0.0627296\pi\)
\(60\) −18.9051 14.5172i −0.315084 0.241953i
\(61\) 12.9880i 0.212919i −0.994317 0.106459i \(-0.966049\pi\)
0.994317 0.106459i \(-0.0339514\pi\)
\(62\) 56.6314 56.6314i 0.913410 0.913410i
\(63\) 13.9060 + 61.4461i 0.220731 + 0.975335i
\(64\) 22.3867i 0.349792i
\(65\) 7.20802 + 8.92528i 0.110893 + 0.137312i
\(66\) 30.4598 7.34376i 0.461512 0.111269i
\(67\) −56.3395 + 56.3395i −0.840888 + 0.840888i −0.988974 0.148086i \(-0.952689\pi\)
0.148086 + 0.988974i \(0.452689\pi\)
\(68\) 22.1284 + 22.1284i 0.325418 + 0.325418i
\(69\) 95.6125 23.0519i 1.38569 0.334085i
\(70\) 75.2545 34.4000i 1.07506 0.491429i
\(71\) 92.7547i 1.30640i −0.757184 0.653202i \(-0.773425\pi\)
0.757184 0.653202i \(-0.226575\pi\)
\(72\) −48.8175 15.7579i −0.678020 0.218860i
\(73\) 95.4460 95.4460i 1.30748 1.30748i 0.384251 0.923229i \(-0.374460\pi\)
0.923229 0.384251i \(-0.125540\pi\)
\(74\) −6.77295 −0.0915263
\(75\) −54.3161 51.7181i −0.724215 0.689574i
\(76\) 1.10283i 0.0145109i
\(77\) −7.66883 + 29.9586i −0.0995952 + 0.389072i
\(78\) −13.8834 8.48941i −0.177993 0.108839i
\(79\) 100.280i 1.26937i −0.772770 0.634687i \(-0.781129\pi\)
0.772770 0.634687i \(-0.218871\pi\)
\(80\) −10.4950 + 98.5987i −0.131188 + 1.23248i
\(81\) −47.3580 + 65.7132i −0.584667 + 0.811274i
\(82\) 54.3440 + 54.3440i 0.662732 + 0.662732i
\(83\) −5.62594 5.62594i −0.0677824 0.0677824i 0.672403 0.740185i \(-0.265262\pi\)
−0.740185 + 0.672403i \(0.765262\pi\)
\(84\) −23.9248 + 23.2633i −0.284819 + 0.276944i
\(85\) 61.8666 + 76.6059i 0.727842 + 0.901245i
\(86\) 101.836i 1.18414i
\(87\) −125.728 76.8798i −1.44515 0.883676i
\(88\) −17.8052 17.8052i −0.202331 0.202331i
\(89\) 158.669i 1.78280i 0.453220 + 0.891399i \(0.350275\pi\)
−0.453220 + 0.891399i \(0.649725\pi\)
\(90\) 97.2139 + 43.2123i 1.08015 + 0.480137i
\(91\) 13.8188 8.18596i 0.151854 0.0899556i
\(92\) 36.8373 + 36.8373i 0.400405 + 0.400405i
\(93\) −53.0184 + 86.7053i −0.570090 + 0.932315i
\(94\) −62.7852 −0.667928
\(95\) 0.367285 3.45057i 0.00386616 0.0363218i
\(96\) −16.9346 70.2399i −0.176402 0.731665i
\(97\) −37.1038 37.1038i −0.382514 0.382514i 0.489493 0.872007i \(-0.337182\pi\)
−0.872007 + 0.489493i \(0.837182\pi\)
\(98\) −32.4807 111.195i −0.331435 1.13464i
\(99\) −35.3917 + 18.1189i −0.357492 + 0.183019i
\(100\) 8.36238 38.8364i 0.0836238 0.388364i
\(101\) 17.6626 0.174877 0.0874384 0.996170i \(-0.472132\pi\)
0.0874384 + 0.996170i \(0.472132\pi\)
\(102\) −119.162 72.8648i −1.16825 0.714361i
\(103\) −96.5666 + 96.5666i −0.937540 + 0.937540i −0.998161 0.0606213i \(-0.980692\pi\)
0.0606213 + 0.998161i \(0.480692\pi\)
\(104\) 13.0780i 0.125750i
\(105\) −82.6044 + 64.8191i −0.786708 + 0.617325i
\(106\) −113.156 −1.06751
\(107\) −7.22790 7.22790i −0.0675504 0.0675504i 0.672524 0.740075i \(-0.265210\pi\)
−0.740075 + 0.672524i \(0.765210\pi\)
\(108\) −42.7819 3.24275i −0.396129 0.0300255i
\(109\) 125.106i 1.14776i −0.818940 0.573880i \(-0.805438\pi\)
0.818940 0.573880i \(-0.194562\pi\)
\(110\) 32.8100 + 40.6267i 0.298273 + 0.369334i
\(111\) 8.35527 2.01443i 0.0752727 0.0181480i
\(112\) 134.482 + 34.4248i 1.20073 + 0.307364i
\(113\) 71.6887 71.6887i 0.634414 0.634414i −0.314758 0.949172i \(-0.601923\pi\)
0.949172 + 0.314758i \(0.101923\pi\)
\(114\) 1.15367 + 4.78508i 0.0101199 + 0.0419744i
\(115\) 102.990 + 127.526i 0.895562 + 1.10892i
\(116\) 78.0601i 0.672932i
\(117\) 19.6519 + 6.34349i 0.167965 + 0.0542179i
\(118\) −38.6228 + 38.6228i −0.327312 + 0.327312i
\(119\) 118.607 70.2603i 0.996694 0.590422i
\(120\) −11.1290 84.7688i −0.0927413 0.706407i
\(121\) 101.483 0.838703
\(122\) −21.7119 + 21.7119i −0.177966 + 0.177966i
\(123\) −83.2032 50.8769i −0.676449 0.413634i
\(124\) −53.8323 −0.434132
\(125\) 39.0986 118.728i 0.312789 0.949823i
\(126\) 79.4720 125.965i 0.630730 0.999722i
\(127\) 4.25412 4.25412i 0.0334970 0.0334970i −0.690160 0.723657i \(-0.742460\pi\)
0.723657 + 0.690160i \(0.242460\pi\)
\(128\) −105.544 + 105.544i −0.824561 + 0.824561i
\(129\) −30.2883 125.627i −0.234793 0.973855i
\(130\) 2.87071 26.9698i 0.0220824 0.207460i
\(131\) 115.412 0.881007 0.440504 0.897751i \(-0.354800\pi\)
0.440504 + 0.897751i \(0.354800\pi\)
\(132\) −17.9675 10.9867i −0.136118 0.0832329i
\(133\) −4.70634 1.20473i −0.0353860 0.00905815i
\(134\) 188.364 1.40570
\(135\) −132.778 24.3941i −0.983539 0.180697i
\(136\) 112.249i 0.825357i
\(137\) 134.388 + 134.388i 0.980935 + 0.980935i 0.999822 0.0188868i \(-0.00601221\pi\)
−0.0188868 + 0.999822i \(0.506012\pi\)
\(138\) −198.369 121.298i −1.43746 0.878974i
\(139\) −228.384 −1.64305 −0.821524 0.570174i \(-0.806876\pi\)
−0.821524 + 0.570174i \(0.806876\pi\)
\(140\) −52.1174 19.4176i −0.372267 0.138697i
\(141\) 77.4534 18.6738i 0.549315 0.132438i
\(142\) −155.057 + 155.057i −1.09195 + 1.09195i
\(143\) 7.16762 + 7.16762i 0.0501232 + 0.0501232i
\(144\) 81.3342 + 158.871i 0.564821 + 1.10327i
\(145\) 25.9971 244.237i 0.179290 1.68440i
\(146\) −319.111 −2.18569
\(147\) 73.1409 + 127.512i 0.497557 + 0.867431i
\(148\) 3.21909 + 3.21909i 0.0217506 + 0.0217506i
\(149\) −67.7175 −0.454480 −0.227240 0.973839i \(-0.572970\pi\)
−0.227240 + 0.973839i \(0.572970\pi\)
\(150\) 4.34307 + 177.256i 0.0289538 + 1.18171i
\(151\) 108.833 0.720749 0.360375 0.932808i \(-0.382649\pi\)
0.360375 + 0.932808i \(0.382649\pi\)
\(152\) 2.79710 2.79710i 0.0184020 0.0184020i
\(153\) 168.673 + 54.4463i 1.10243 + 0.355858i
\(154\) 62.9012 37.2614i 0.408449 0.241957i
\(155\) −168.433 17.9283i −1.08666 0.115666i
\(156\) 2.56371 + 10.6335i 0.0164340 + 0.0681636i
\(157\) −12.8504 12.8504i −0.0818495 0.0818495i 0.664997 0.746846i \(-0.268433\pi\)
−0.746846 + 0.664997i \(0.768433\pi\)
\(158\) −167.637 + 167.637i −1.06100 + 1.06100i
\(159\) 139.592 33.6551i 0.877935 0.211667i
\(160\) 93.6847 75.6594i 0.585529 0.472871i
\(161\) 197.445 116.963i 1.22637 0.726476i
\(162\) 189.019 30.6841i 1.16679 0.189408i
\(163\) −140.352 140.352i −0.861054 0.861054i 0.130407 0.991461i \(-0.458372\pi\)
−0.991461 + 0.130407i \(0.958372\pi\)
\(164\) 51.6580i 0.314988i
\(165\) −52.5585 40.3597i −0.318536 0.244604i
\(166\) 18.8096i 0.113311i
\(167\) −70.3795 + 70.3795i −0.421434 + 0.421434i −0.885697 0.464263i \(-0.846319\pi\)
0.464263 + 0.885697i \(0.346319\pi\)
\(168\) −119.683 1.67784i −0.712399 0.00998712i
\(169\) 163.735i 0.968848i
\(170\) 24.6394 231.482i 0.144938 1.36166i
\(171\) −2.84638 5.55986i −0.0166455 0.0325138i
\(172\) 48.4013 48.4013i 0.281403 0.281403i
\(173\) 74.9815 + 74.9815i 0.433419 + 0.433419i 0.889790 0.456371i \(-0.150851\pi\)
−0.456371 + 0.889790i \(0.650851\pi\)
\(174\) 81.6586 + 338.696i 0.469302 + 1.94653i
\(175\) −156.600 78.1117i −0.894857 0.446352i
\(176\) 87.6098i 0.497783i
\(177\) 36.1587 59.1334i 0.204287 0.334087i
\(178\) 265.245 265.245i 1.49014 1.49014i
\(179\) −110.262 −0.615991 −0.307996 0.951388i \(-0.599658\pi\)
−0.307996 + 0.951388i \(0.599658\pi\)
\(180\) −25.6663 66.7428i −0.142590 0.370793i
\(181\) 58.1797i 0.321435i 0.987000 + 0.160717i \(0.0513808\pi\)
−0.987000 + 0.160717i \(0.948619\pi\)
\(182\) −36.7849 9.41625i −0.202115 0.0517376i
\(183\) 20.3267 33.2420i 0.111075 0.181650i
\(184\) 186.861i 1.01555i
\(185\) 8.99995 + 11.1441i 0.0486484 + 0.0602385i
\(186\) 233.574 56.3140i 1.25577 0.302763i
\(187\) 61.5198 + 61.5198i 0.328983 + 0.328983i
\(188\) 29.8410 + 29.8410i 0.158729 + 0.158729i
\(189\) −60.5737 + 179.030i −0.320496 + 0.947250i
\(190\) −6.38225 + 5.15428i −0.0335908 + 0.0271278i
\(191\) 12.6214i 0.0660807i 0.999454 + 0.0330403i \(0.0105190\pi\)
−0.999454 + 0.0330403i \(0.989481\pi\)
\(192\) 35.0359 57.2971i 0.182479 0.298423i
\(193\) 211.567 + 211.567i 1.09620 + 1.09620i 0.994851 + 0.101353i \(0.0323171\pi\)
0.101353 + 0.994851i \(0.467683\pi\)
\(194\) 124.052i 0.639442i
\(195\) 4.48005 + 34.1244i 0.0229746 + 0.174997i
\(196\) −37.4119 + 68.2872i −0.190877 + 0.348404i
\(197\) −102.520 102.520i −0.520407 0.520407i 0.397288 0.917694i \(-0.369952\pi\)
−0.917694 + 0.397288i \(0.869952\pi\)
\(198\) 89.4528 + 28.8748i 0.451782 + 0.145832i
\(199\) −235.953 −1.18570 −0.592848 0.805314i \(-0.701996\pi\)
−0.592848 + 0.805314i \(0.701996\pi\)
\(200\) 119.710 77.2912i 0.598551 0.386456i
\(201\) −232.370 + 56.0237i −1.15607 + 0.278725i
\(202\) −29.5262 29.5262i −0.146169 0.146169i
\(203\) −333.123 85.2732i −1.64100 0.420065i
\(204\) 22.0044 + 91.2677i 0.107865 + 0.447391i
\(205\) 17.2041 161.630i 0.0839227 0.788437i
\(206\) 322.858 1.56727
\(207\) 280.790 + 90.6371i 1.35647 + 0.437860i
\(208\) 32.1749 32.1749i 0.154687 0.154687i
\(209\) 3.06600i 0.0146699i
\(210\) 246.446 + 29.7314i 1.17355 + 0.141578i
\(211\) −89.6482 −0.424873 −0.212437 0.977175i \(-0.568140\pi\)
−0.212437 + 0.977175i \(0.568140\pi\)
\(212\) 53.7814 + 53.7814i 0.253686 + 0.253686i
\(213\) 145.164 237.399i 0.681522 1.11455i
\(214\) 24.1655i 0.112923i
\(215\) 167.559 135.320i 0.779346 0.629397i
\(216\) −100.283 116.732i −0.464274 0.540427i
\(217\) −58.8067 + 229.731i −0.270999 + 1.05867i
\(218\) −209.137 + 209.137i −0.959346 + 0.959346i
\(219\) 393.663 94.9110i 1.79755 0.433384i
\(220\) 3.71519 34.9035i 0.0168872 0.158652i
\(221\) 45.1866i 0.204464i
\(222\) −17.3349 10.5999i −0.0780850 0.0477473i
\(223\) 85.1659 85.1659i 0.381910 0.381910i −0.489880 0.871790i \(-0.662959\pi\)
0.871790 + 0.489880i \(0.162959\pi\)
\(224\) −85.9244 145.049i −0.383591 0.647541i
\(225\) −58.0776 217.375i −0.258123 0.966112i
\(226\) −239.682 −1.06054
\(227\) −129.989 + 129.989i −0.572639 + 0.572639i −0.932865 0.360226i \(-0.882700\pi\)
0.360226 + 0.932865i \(0.382700\pi\)
\(228\) 1.72596 2.82261i 0.00757001 0.0123799i
\(229\) 109.923 0.480011 0.240006 0.970771i \(-0.422851\pi\)
0.240006 + 0.970771i \(0.422851\pi\)
\(230\) 41.0173 385.350i 0.178336 1.67543i
\(231\) −66.5140 + 64.6748i −0.287939 + 0.279978i
\(232\) 197.984 197.984i 0.853378 0.853378i
\(233\) 218.319 218.319i 0.936990 0.936990i −0.0611395 0.998129i \(-0.519473\pi\)
0.998129 + 0.0611395i \(0.0194735\pi\)
\(234\) −22.2474 43.4561i −0.0950745 0.185710i
\(235\) 83.4295 + 103.306i 0.355019 + 0.439600i
\(236\) 36.7139 0.155567
\(237\) 156.942 256.661i 0.662204 1.08296i
\(238\) −315.726 80.8198i −1.32658 0.339579i
\(239\) −20.1742 −0.0844109 −0.0422054 0.999109i \(-0.513438\pi\)
−0.0422054 + 0.999109i \(0.513438\pi\)
\(240\) −181.171 + 235.931i −0.754881 + 0.983046i
\(241\) 257.604i 1.06890i 0.845201 + 0.534449i \(0.179481\pi\)
−0.845201 + 0.534449i \(0.820519\pi\)
\(242\) −169.648 169.648i −0.701024 0.701024i
\(243\) −224.053 + 94.0713i −0.922027 + 0.387125i
\(244\) 20.6388 0.0845852
\(245\) −139.798 + 201.200i −0.570605 + 0.821225i
\(246\) 54.0394 + 224.140i 0.219672 + 0.911137i
\(247\) −1.12600 + 1.12600i −0.00455869 + 0.00455869i
\(248\) −136.535 136.535i −0.550544 0.550544i
\(249\) −5.59441 23.2040i −0.0224675 0.0931887i
\(250\) −263.836 + 133.115i −1.05534 + 0.532460i
\(251\) −191.569 −0.763223 −0.381612 0.924323i \(-0.624631\pi\)
−0.381612 + 0.924323i \(0.624631\pi\)
\(252\) −97.6415 + 22.0975i −0.387466 + 0.0876887i
\(253\) 102.412 + 102.412i 0.404792 + 0.404792i
\(254\) −14.2231 −0.0559964
\(255\) 38.4524 + 292.890i 0.150794 + 1.14859i
\(256\) 263.325 1.02861
\(257\) −205.696 + 205.696i −0.800374 + 0.800374i −0.983154 0.182779i \(-0.941491\pi\)
0.182779 + 0.983154i \(0.441491\pi\)
\(258\) −159.377 + 260.642i −0.617739 + 1.01024i
\(259\) 17.2541 10.2210i 0.0666182 0.0394633i
\(260\) −14.1828 + 11.4540i −0.0545493 + 0.0440538i
\(261\) −201.472 393.537i −0.771923 1.50780i
\(262\) −192.932 192.932i −0.736383 0.736383i
\(263\) 4.82449 4.82449i 0.0183441 0.0183441i −0.697875 0.716219i \(-0.745871\pi\)
0.716219 + 0.697875i \(0.245871\pi\)
\(264\) −17.7054 73.4367i −0.0670657 0.278169i
\(265\) 150.362 + 186.185i 0.567404 + 0.702584i
\(266\) 5.85358 + 9.88145i 0.0220059 + 0.0371483i
\(267\) −248.322 + 406.102i −0.930046 + 1.52098i
\(268\) −89.5269 89.5269i −0.334056 0.334056i
\(269\) 106.984i 0.397708i −0.980029 0.198854i \(-0.936278\pi\)
0.980029 0.198854i \(-0.0637220\pi\)
\(270\) 181.183 + 262.742i 0.671049 + 0.973118i
\(271\) 187.036i 0.690171i −0.938571 0.345085i \(-0.887850\pi\)
0.938571 0.345085i \(-0.112150\pi\)
\(272\) 276.158 276.158i 1.01529 1.01529i
\(273\) 48.1794 + 0.675427i 0.176481 + 0.00247409i
\(274\) 449.309i 1.63981i
\(275\) 23.2485 107.970i 0.0845399 0.392619i
\(276\) 36.6308 + 151.934i 0.132720 + 0.550485i
\(277\) 95.7717 95.7717i 0.345746 0.345746i −0.512776 0.858522i \(-0.671383\pi\)
0.858522 + 0.512776i \(0.171383\pi\)
\(278\) 381.786 + 381.786i 1.37333 + 1.37333i
\(279\) −271.393 + 138.941i −0.972736 + 0.497995i
\(280\) −82.9364 181.434i −0.296201 0.647979i
\(281\) 140.834i 0.501189i 0.968092 + 0.250594i \(0.0806261\pi\)
−0.968092 + 0.250594i \(0.919374\pi\)
\(282\) −160.694 98.2610i −0.569838 0.348443i
\(283\) −204.752 + 204.752i −0.723504 + 0.723504i −0.969317 0.245813i \(-0.920945\pi\)
0.245813 + 0.969317i \(0.420945\pi\)
\(284\) 147.393 0.518989
\(285\) 6.34030 8.25667i 0.0222467 0.0289708i
\(286\) 23.9640i 0.0837902i
\(287\) −220.452 56.4314i −0.768124 0.196625i
\(288\) 66.5848 206.277i 0.231197 0.716240i
\(289\) 98.8373i 0.341998i
\(290\) −451.747 + 364.829i −1.55775 + 1.25803i
\(291\) −36.8958 153.033i −0.126790 0.525888i
\(292\) 151.669 + 151.669i 0.519416 + 0.519416i
\(293\) 158.208 + 158.208i 0.539959 + 0.539959i 0.923517 0.383558i \(-0.125301\pi\)
−0.383558 + 0.923517i \(0.625301\pi\)
\(294\) 90.8920 335.429i 0.309157 1.14092i
\(295\) 114.872 + 12.2272i 0.389396 + 0.0414480i
\(296\) 16.3292i 0.0551661i
\(297\) −118.939 9.01527i −0.400469 0.0303544i
\(298\) 113.202 + 113.202i 0.379873 + 0.379873i
\(299\) 75.2224i 0.251580i
\(300\) 82.1832 86.3116i 0.273944 0.287705i
\(301\) −153.680 259.427i −0.510564 0.861885i
\(302\) −181.935 181.935i −0.602433 0.602433i
\(303\) 45.2060 + 27.6425i 0.149195 + 0.0912293i
\(304\) −13.7631 −0.0452732
\(305\) 64.5754 + 6.87352i 0.211723 + 0.0225361i
\(306\) −190.950 372.984i −0.624020 1.21890i
\(307\) 390.484 + 390.484i 1.27194 + 1.27194i 0.945071 + 0.326865i \(0.105992\pi\)
0.326865 + 0.945071i \(0.394008\pi\)
\(308\) −47.6060 12.1862i −0.154565 0.0395657i
\(309\) −398.285 + 96.0253i −1.28895 + 0.310761i
\(310\) 251.596 + 311.537i 0.811600 + 1.00496i
\(311\) 314.164 1.01017 0.505087 0.863068i \(-0.331460\pi\)
0.505087 + 0.863068i \(0.331460\pi\)
\(312\) −20.4675 + 33.4721i −0.0656009 + 0.107282i
\(313\) −138.521 + 138.521i −0.442558 + 0.442558i −0.892871 0.450313i \(-0.851312\pi\)
0.450313 + 0.892871i \(0.351312\pi\)
\(314\) 42.9635i 0.136827i
\(315\) −312.864 + 36.6212i −0.993219 + 0.116258i
\(316\) 159.352 0.504278
\(317\) 171.788 + 171.788i 0.541917 + 0.541917i 0.924090 0.382174i \(-0.124824\pi\)
−0.382174 + 0.924090i \(0.624824\pi\)
\(318\) −289.614 177.092i −0.910736 0.556895i
\(319\) 217.017i 0.680304i
\(320\) 111.305 + 11.8475i 0.347827 + 0.0370234i
\(321\) −7.18738 29.8112i −0.0223906 0.0928697i
\(322\) −525.591 134.541i −1.63227 0.417830i
\(323\) −9.66445 + 9.66445i −0.0299209 + 0.0299209i
\(324\) −104.422 75.2547i −0.322291 0.232268i
\(325\) −48.1904 + 31.1142i −0.148278 + 0.0957361i
\(326\) 469.248i 1.43941i
\(327\) 195.795 320.199i 0.598761 0.979203i
\(328\) 131.020 131.020i 0.399452 0.399452i
\(329\) 159.946 94.7486i 0.486157 0.287990i
\(330\) 20.3926 + 155.330i 0.0617958 + 0.470697i
\(331\) −97.1798 −0.293595 −0.146797 0.989167i \(-0.546897\pi\)
−0.146797 + 0.989167i \(0.546897\pi\)
\(332\) 8.93996 8.93996i 0.0269276 0.0269276i
\(333\) 24.5374 + 7.92049i 0.0736858 + 0.0237853i
\(334\) 235.305 0.704505
\(335\) −250.299 309.931i −0.747162 0.925168i
\(336\) 290.320 + 298.576i 0.864049 + 0.888620i
\(337\) −142.405 + 142.405i −0.422566 + 0.422566i −0.886086 0.463520i \(-0.846586\pi\)
0.463520 + 0.886086i \(0.346586\pi\)
\(338\) 273.714 273.714i 0.809804 0.809804i
\(339\) 295.677 71.2869i 0.872205 0.210286i
\(340\) −121.731 + 98.3097i −0.358033 + 0.289146i
\(341\) −149.661 −0.438888
\(342\) −4.53608 + 14.0526i −0.0132634 + 0.0410894i
\(343\) 250.548 + 234.253i 0.730461 + 0.682955i
\(344\) 245.520 0.713722
\(345\) 64.0119 + 487.576i 0.185542 + 1.41326i
\(346\) 250.691i 0.724540i
\(347\) 42.5261 + 42.5261i 0.122554 + 0.122554i 0.765723 0.643170i \(-0.222381\pi\)
−0.643170 + 0.765723i \(0.722381\pi\)
\(348\) 122.167 199.789i 0.351054 0.574107i
\(349\) 323.576 0.927152 0.463576 0.886057i \(-0.346566\pi\)
0.463576 + 0.886057i \(0.346566\pi\)
\(350\) 131.208 + 392.364i 0.374879 + 1.12104i
\(351\) 40.3698 + 46.9916i 0.115014 + 0.133879i
\(352\) 75.2353 75.2353i 0.213737 0.213737i
\(353\) 121.979 + 121.979i 0.345550 + 0.345550i 0.858449 0.512899i \(-0.171428\pi\)
−0.512899 + 0.858449i \(0.671428\pi\)
\(354\) −159.298 + 38.4063i −0.449995 + 0.108492i
\(355\) 461.168 + 49.0876i 1.29907 + 0.138275i
\(356\) −252.135 −0.708243
\(357\) 413.525 + 5.79721i 1.15833 + 0.0162387i
\(358\) 184.324 + 184.324i 0.514872 + 0.514872i
\(359\) −456.029 −1.27028 −0.635138 0.772399i \(-0.719057\pi\)
−0.635138 + 0.772399i \(0.719057\pi\)
\(360\) 104.182 234.377i 0.289395 0.651047i
\(361\) −360.518 −0.998666
\(362\) 97.2581 97.2581i 0.268669 0.268669i
\(363\) 259.739 + 158.824i 0.715534 + 0.437533i
\(364\) 13.0080 + 21.9588i 0.0357362 + 0.0603264i
\(365\) 424.037 + 525.061i 1.16175 + 1.43852i
\(366\) −89.5499 + 21.5902i −0.244672 + 0.0589896i
\(367\) −52.7521 52.7521i −0.143739 0.143739i 0.631576 0.775314i \(-0.282409\pi\)
−0.775314 + 0.631576i \(0.782409\pi\)
\(368\) 459.721 459.721i 1.24924 1.24924i
\(369\) −133.329 260.432i −0.361324 0.705777i
\(370\) 3.58438 33.6745i 0.00968750 0.0910122i
\(371\) 288.264 170.762i 0.776993 0.460276i
\(372\) −137.780 84.2494i −0.370376 0.226477i
\(373\) −269.362 269.362i −0.722150 0.722150i 0.246893 0.969043i \(-0.420591\pi\)
−0.969043 + 0.246893i \(0.920591\pi\)
\(374\) 205.683i 0.549956i
\(375\) 285.883 242.685i 0.762355 0.647159i
\(376\) 151.371i 0.402583i
\(377\) −79.7000 + 79.7000i −0.211406 + 0.211406i
\(378\) 400.542 198.022i 1.05964 0.523868i
\(379\) 253.497i 0.668856i 0.942421 + 0.334428i \(0.108543\pi\)
−0.942421 + 0.334428i \(0.891457\pi\)
\(380\) 5.48317 + 0.583638i 0.0144294 + 0.00153589i
\(381\) 17.5459 4.23027i 0.0460523 0.0111031i
\(382\) 21.0990 21.0990i 0.0552330 0.0552330i
\(383\) −162.755 162.755i −0.424948 0.424948i 0.461955 0.886903i \(-0.347148\pi\)
−0.886903 + 0.461955i \(0.847148\pi\)
\(384\) −435.311 + 104.952i −1.13362 + 0.273313i
\(385\) −144.893 53.9834i −0.376345 0.140217i
\(386\) 707.348i 1.83251i
\(387\) 119.090 368.936i 0.307726 0.953324i
\(388\) 58.9602 58.9602i 0.151959 0.151959i
\(389\) −309.463 −0.795534 −0.397767 0.917486i \(-0.630215\pi\)
−0.397767 + 0.917486i \(0.630215\pi\)
\(390\) 49.5560 64.5345i 0.127067 0.165473i
\(391\) 645.635i 1.65124i
\(392\) −268.085 + 78.3089i −0.683889 + 0.199768i
\(393\) 295.389 + 180.624i 0.751625 + 0.459602i
\(394\) 342.763i 0.869956i
\(395\) 498.586 + 53.0704i 1.26224 + 0.134355i
\(396\) −28.7920 56.2396i −0.0727070 0.142019i
\(397\) −463.385 463.385i −1.16722 1.16722i −0.982859 0.184357i \(-0.940980\pi\)
−0.184357 0.982859i \(-0.559020\pi\)
\(398\) 394.440 + 394.440i 0.991055 + 0.991055i
\(399\) −10.1601 10.4490i −0.0254639 0.0261880i
\(400\) −484.670 104.361i −1.21167 0.260902i
\(401\) 516.485i 1.28799i 0.765028 + 0.643997i \(0.222725\pi\)
−0.765028 + 0.643997i \(0.777275\pi\)
\(402\) 482.104 + 294.796i 1.19926 + 0.733323i
\(403\) 54.9633 + 54.9633i 0.136385 + 0.136385i
\(404\) 28.0669i 0.0694724i
\(405\) −301.657 270.237i −0.744833 0.667251i
\(406\) 414.327 + 699.427i 1.02051 + 1.72273i
\(407\) 8.94950 + 8.94950i 0.0219889 + 0.0219889i
\(408\) −175.673 + 287.292i −0.430570 + 0.704147i
\(409\) 119.076 0.291139 0.145570 0.989348i \(-0.453499\pi\)
0.145570 + 0.989348i \(0.453499\pi\)
\(410\) −298.954 + 241.434i −0.729155 + 0.588863i
\(411\) 133.635 + 554.278i 0.325145 + 1.34861i
\(412\) −153.450 153.450i −0.372452 0.372452i
\(413\) 40.1064 156.677i 0.0971099 0.379364i
\(414\) −317.876 620.909i −0.767816 1.49978i
\(415\) 30.9491 24.9943i 0.0745760 0.0602273i
\(416\) −55.2607 −0.132838
\(417\) −584.532 357.428i −1.40175 0.857142i
\(418\) −5.12539 + 5.12539i −0.0122617 + 0.0122617i
\(419\) 732.322i 1.74778i 0.486120 + 0.873892i \(0.338412\pi\)
−0.486120 + 0.873892i \(0.661588\pi\)
\(420\) −103.001 131.263i −0.245242 0.312532i
\(421\) 307.320 0.729976 0.364988 0.931012i \(-0.381073\pi\)
0.364988 + 0.931012i \(0.381073\pi\)
\(422\) 149.864 + 149.864i 0.355127 + 0.355127i
\(423\) 227.461 + 73.4229i 0.537734 + 0.173577i
\(424\) 272.812i 0.643424i
\(425\) −413.619 + 267.054i −0.973220 + 0.628363i
\(426\) −639.525 + 154.187i −1.50123 + 0.361942i
\(427\) 22.5459 88.0764i 0.0528007 0.206268i
\(428\) 11.4856 11.4856i 0.0268354 0.0268354i
\(429\) 7.12744 + 29.5626i 0.0166141 + 0.0689104i
\(430\) −506.320 53.8936i −1.17749 0.125334i
\(431\) 205.822i 0.477546i 0.971075 + 0.238773i \(0.0767452\pi\)
−0.971075 + 0.238773i \(0.923255\pi\)
\(432\) −40.4689 + 533.909i −0.0936779 + 1.23590i
\(433\) −291.861 + 291.861i −0.674043 + 0.674043i −0.958646 0.284603i \(-0.908138\pi\)
0.284603 + 0.958646i \(0.408138\pi\)
\(434\) 482.343 285.731i 1.11139 0.658366i
\(435\) 448.777 584.422i 1.03167 1.34350i
\(436\) 198.801 0.455965
\(437\) −16.0885 + 16.0885i −0.0368157 + 0.0368157i
\(438\) −816.742 499.420i −1.86471 1.14023i
\(439\) −116.671 −0.265765 −0.132882 0.991132i \(-0.542423\pi\)
−0.132882 + 0.991132i \(0.542423\pi\)
\(440\) 97.9486 79.1029i 0.222610 0.179779i
\(441\) −12.3623 + 440.827i −0.0280325 + 0.999607i
\(442\) −75.5377 + 75.5377i −0.170900 + 0.170900i
\(443\) −282.021 + 282.021i −0.636617 + 0.636617i −0.949719 0.313102i \(-0.898632\pi\)
0.313102 + 0.949719i \(0.398632\pi\)
\(444\) 3.20105 + 13.2770i 0.00720957 + 0.0299032i
\(445\) −788.888 83.9707i −1.77278 0.188698i
\(446\) −284.741 −0.638433
\(447\) −173.318 105.980i −0.387736 0.237092i
\(448\) 38.8610 151.812i 0.0867433 0.338866i
\(449\) 407.834 0.908317 0.454158 0.890921i \(-0.349940\pi\)
0.454158 + 0.890921i \(0.349940\pi\)
\(450\) −266.295 + 460.470i −0.591767 + 1.02327i
\(451\) 143.616i 0.318439i
\(452\) 113.918 + 113.918i 0.252030 + 0.252030i
\(453\) 278.550 + 170.327i 0.614902 + 0.375999i
\(454\) 434.602 0.957272
\(455\) 33.3867 + 73.0378i 0.0733775 + 0.160523i
\(456\) 11.5365 2.78142i 0.0252994 0.00609961i
\(457\) 461.473 461.473i 1.00979 1.00979i 0.00983627 0.999952i \(-0.496869\pi\)
0.999952 0.00983627i \(-0.00313103\pi\)
\(458\) −183.756 183.756i −0.401214 0.401214i
\(459\) 346.495 + 403.330i 0.754891 + 0.878714i
\(460\) −202.647 + 163.657i −0.440537 + 0.355776i
\(461\) −788.797 −1.71106 −0.855528 0.517757i \(-0.826767\pi\)
−0.855528 + 0.517757i \(0.826767\pi\)
\(462\) 219.306 + 3.07446i 0.474689 + 0.00665467i
\(463\) −548.664 548.664i −1.18502 1.18502i −0.978427 0.206592i \(-0.933763\pi\)
−0.206592 0.978427i \(-0.566237\pi\)
\(464\) −974.173 −2.09951
\(465\) −403.033 309.489i −0.866738 0.665568i
\(466\) −729.920 −1.56635
\(467\) 299.104 299.104i 0.640480 0.640480i −0.310194 0.950673i \(-0.600394\pi\)
0.950673 + 0.310194i \(0.100394\pi\)
\(468\) −10.0802 + 31.2280i −0.0215389 + 0.0667266i
\(469\) −479.857 + 284.258i −1.02315 + 0.606094i
\(470\) 33.2272 312.163i 0.0706961 0.664176i
\(471\) −12.7783 53.0009i −0.0271302 0.112528i
\(472\) 93.1173 + 93.1173i 0.197283 + 0.197283i
\(473\) 134.562 134.562i 0.284486 0.284486i
\(474\) −691.414 + 166.698i −1.45868 + 0.351683i
\(475\) 16.9616 + 3.65222i 0.0357086 + 0.00768888i
\(476\) 111.648 + 188.473i 0.234554 + 0.395952i
\(477\) 409.946 + 132.328i 0.859426 + 0.277417i
\(478\) 33.7249 + 33.7249i 0.0705542 + 0.0705542i
\(479\) 568.767i 1.18740i −0.804685 0.593702i \(-0.797666\pi\)
0.804685 0.593702i \(-0.202334\pi\)
\(480\) 358.189 47.0251i 0.746226 0.0979690i
\(481\) 6.57345i 0.0136662i
\(482\) 430.633 430.633i 0.893430 0.893430i
\(483\) 688.397 + 9.65064i 1.42525 + 0.0199806i
\(484\) 161.263i 0.333188i
\(485\) 204.113 164.841i 0.420852 0.339878i
\(486\) 531.803 + 217.288i 1.09424 + 0.447094i
\(487\) 382.818 382.818i 0.786073 0.786073i −0.194775 0.980848i \(-0.562398\pi\)
0.980848 + 0.194775i \(0.0623976\pi\)
\(488\) 52.3461 + 52.3461i 0.107267 + 0.107267i
\(489\) −139.565 578.875i −0.285409 1.18379i
\(490\) 570.042 102.644i 1.16335 0.209479i
\(491\) 1.38553i 0.00282185i 0.999999 + 0.00141093i \(0.000449112\pi\)
−0.999999 + 0.00141093i \(0.999551\pi\)
\(492\) 80.8465 132.215i 0.164322 0.268730i
\(493\) −684.067 + 684.067i −1.38756 + 1.38756i
\(494\) 3.76462 0.00762070
\(495\) −71.3555 185.553i −0.144152 0.374855i
\(496\) 671.816i 1.35447i
\(497\) 161.012 629.002i 0.323969 1.26560i
\(498\) −29.4377 + 48.1418i −0.0591118 + 0.0966703i
\(499\) 356.741i 0.714913i 0.933930 + 0.357456i \(0.116356\pi\)
−0.933930 + 0.357456i \(0.883644\pi\)
\(500\) 188.666 + 62.1300i 0.377331 + 0.124260i
\(501\) −290.277 + 69.9849i −0.579396 + 0.139691i
\(502\) 320.243 + 320.243i 0.637934 + 0.637934i
\(503\) −279.707 279.707i −0.556078 0.556078i 0.372111 0.928188i \(-0.378634\pi\)
−0.928188 + 0.372111i \(0.878634\pi\)
\(504\) −303.694 191.602i −0.602568 0.380163i
\(505\) −9.34737 + 87.8167i −0.0185096 + 0.173894i
\(506\) 342.402i 0.676685i
\(507\) −256.251 + 419.069i −0.505427 + 0.826566i
\(508\) 6.76005 + 6.76005i 0.0133072 + 0.0133072i
\(509\) 493.836i 0.970208i 0.874457 + 0.485104i \(0.161218\pi\)
−0.874457 + 0.485104i \(0.838782\pi\)
\(510\) 425.340 553.901i 0.834000 1.08608i
\(511\) 812.937 481.568i 1.59087 0.942403i
\(512\) −18.0214 18.0214i −0.0351981 0.0351981i
\(513\) 1.41625 18.6847i 0.00276073 0.0364225i
\(514\) 687.719 1.33797
\(515\) −429.016 531.226i −0.833040 1.03151i
\(516\) 199.629 48.1300i 0.386879 0.0932752i
\(517\) 82.9618 + 82.9618i 0.160468 + 0.160468i
\(518\) −45.9297 11.7571i −0.0886674 0.0226972i
\(519\) 74.5612 + 309.258i 0.143663 + 0.595873i
\(520\) −65.0226 6.92112i −0.125043 0.0133098i
\(521\) 16.2593 0.0312079 0.0156039 0.999878i \(-0.495033\pi\)
0.0156039 + 0.999878i \(0.495033\pi\)
\(522\) −321.072 + 994.667i −0.615080 + 1.90549i
\(523\) 629.367 629.367i 1.20338 1.20338i 0.230246 0.973132i \(-0.426047\pi\)
0.973132 0.230246i \(-0.0739530\pi\)
\(524\) 183.397i 0.349993i
\(525\) −278.559 445.005i −0.530589 0.847629i
\(526\) −16.1301 −0.0306655
\(527\) 471.751 + 471.751i 0.895163 + 0.895163i
\(528\) −137.112 + 224.231i −0.259682 + 0.424680i
\(529\) 545.792i 1.03174i
\(530\) 59.8842 562.600i 0.112989 1.06151i
\(531\) 185.091 94.7580i 0.348571 0.178452i
\(532\) 1.91439 7.47866i 0.00359849 0.0140576i
\(533\) −52.7433 + 52.7433i −0.0989555 + 0.0989555i
\(534\) 1093.99 263.758i 2.04867 0.493928i
\(535\) 39.7616 32.1113i 0.0743208 0.0600212i
\(536\) 454.134i 0.847265i
\(537\) −282.209 172.564i −0.525528 0.321349i
\(538\) −178.843 + 178.843i −0.332421 + 0.332421i
\(539\) −104.010 + 189.847i −0.192968 + 0.352221i
\(540\) 38.7637 210.992i 0.0717846 0.390726i
\(541\) 577.099 1.06673 0.533364 0.845886i \(-0.320928\pi\)
0.533364 + 0.845886i \(0.320928\pi\)
\(542\) −312.666 + 312.666i −0.576874 + 0.576874i
\(543\) −91.0532 + 148.907i −0.167685 + 0.274230i
\(544\) −474.303 −0.871881
\(545\) 622.015 + 66.2084i 1.14131 + 0.121483i
\(546\) −79.4117 81.6699i −0.145443 0.149579i
\(547\) −289.511 + 289.511i −0.529270 + 0.529270i −0.920355 0.391084i \(-0.872100\pi\)
0.391084 + 0.920355i \(0.372100\pi\)
\(548\) −213.551 + 213.551i −0.389691 + 0.389691i
\(549\) 104.050 53.2684i 0.189526 0.0970280i
\(550\) −219.356 + 141.628i −0.398829 + 0.257505i
\(551\) 34.0923 0.0618735
\(552\) −292.443 + 478.257i −0.529788 + 0.866407i
\(553\) 174.077 680.037i 0.314786 1.22972i
\(554\) −320.200 −0.577979
\(555\) 5.59380 + 42.6078i 0.0100789 + 0.0767708i
\(556\) 362.915i 0.652726i
\(557\) −12.4652 12.4652i −0.0223792 0.0223792i 0.695829 0.718208i \(-0.255037\pi\)
−0.718208 + 0.695829i \(0.755037\pi\)
\(558\) 685.949 + 221.420i 1.22930 + 0.396809i
\(559\) −98.8363 −0.176809
\(560\) −242.327 + 650.413i −0.432728 + 1.16145i
\(561\) 61.1750 + 253.736i 0.109046 + 0.452292i
\(562\) 235.430 235.430i 0.418915 0.418915i
\(563\) −689.690 689.690i −1.22503 1.22503i −0.965823 0.259204i \(-0.916540\pi\)
−0.259204 0.965823i \(-0.583460\pi\)
\(564\) 29.6737 + 123.078i 0.0526130 + 0.218223i
\(565\) 318.491 + 394.369i 0.563701 + 0.697999i
\(566\) 684.560 1.20947
\(567\) −435.222 + 363.415i −0.767588 + 0.640944i
\(568\) 373.832 + 373.832i 0.658155 + 0.658155i
\(569\) −44.3368 −0.0779205 −0.0389602 0.999241i \(-0.512405\pi\)
−0.0389602 + 0.999241i \(0.512405\pi\)
\(570\) −24.4015 + 3.20358i −0.0428097 + 0.00562031i
\(571\) 89.1696 0.156164 0.0780819 0.996947i \(-0.475120\pi\)
0.0780819 + 0.996947i \(0.475120\pi\)
\(572\) −11.3898 + 11.3898i −0.0199122 + 0.0199122i
\(573\) −19.7529 + 32.3036i −0.0344728 + 0.0563762i
\(574\) 274.190 + 462.861i 0.477683 + 0.806378i
\(575\) −688.553 + 444.566i −1.19748 + 0.773159i
\(576\) 179.344 91.8155i 0.311361 0.159402i
\(577\) 146.556 + 146.556i 0.253997 + 0.253997i 0.822607 0.568610i \(-0.192519\pi\)
−0.568610 + 0.822607i \(0.692519\pi\)
\(578\) −165.225 + 165.225i −0.285856 + 0.285856i
\(579\) 210.381 + 872.601i 0.363353 + 1.50708i
\(580\) 388.108 + 41.3109i 0.669152 + 0.0712257i
\(581\) −28.3854 47.9175i −0.0488561 0.0824742i
\(582\) −194.145 + 317.502i −0.333583 + 0.545535i
\(583\) 149.519 + 149.519i 0.256465 + 0.256465i
\(584\) 769.358i 1.31739i
\(585\) −41.9395 + 94.3504i −0.0716914 + 0.161283i
\(586\) 528.948i 0.902642i
\(587\) −85.7254 + 85.7254i −0.146040 + 0.146040i −0.776346 0.630307i \(-0.782929\pi\)
0.630307 + 0.776346i \(0.282929\pi\)
\(588\) −202.625 + 116.225i −0.344600 + 0.197662i
\(589\) 23.5110i 0.0399167i
\(590\) −171.589 212.469i −0.290830 0.360118i
\(591\) −101.945 422.840i −0.172496 0.715465i
\(592\) 40.1736 40.1736i 0.0678608 0.0678608i
\(593\) −607.214 607.214i −1.02397 1.02397i −0.999706 0.0242632i \(-0.992276\pi\)
−0.0242632 0.999706i \(-0.507724\pi\)
\(594\) 183.758 + 213.900i 0.309357 + 0.360100i
\(595\) 286.559 + 626.885i 0.481612 + 1.05359i
\(596\) 107.607i 0.180549i
\(597\) −603.906 369.275i −1.01157 0.618551i
\(598\) −125.748 + 125.748i −0.210281 + 0.210281i
\(599\) 214.278 0.357726 0.178863 0.983874i \(-0.442758\pi\)
0.178863 + 0.983874i \(0.442758\pi\)
\(600\) 427.353 10.4709i 0.712255 0.0174515i
\(601\) 674.896i 1.12296i −0.827492 0.561478i \(-0.810233\pi\)
0.827492 0.561478i \(-0.189767\pi\)
\(602\) −176.777 + 690.585i −0.293649 + 1.14715i
\(603\) −682.414 220.278i −1.13170 0.365304i
\(604\) 172.942i 0.286328i
\(605\) −53.7068 + 504.565i −0.0887716 + 0.833992i
\(606\) −29.3607 121.780i −0.0484500 0.200957i
\(607\) −428.929 428.929i −0.706638 0.706638i 0.259189 0.965827i \(-0.416545\pi\)
−0.965827 + 0.259189i \(0.916545\pi\)
\(608\) 11.8191 + 11.8191i 0.0194393 + 0.0194393i
\(609\) −719.149 739.599i −1.18087 1.21445i
\(610\) −96.4594 119.440i −0.158130 0.195803i
\(611\) 60.9358i 0.0997313i
\(612\) −86.5185 + 268.031i −0.141370 + 0.437959i
\(613\) −134.802 134.802i −0.219905 0.219905i 0.588553 0.808458i \(-0.299698\pi\)
−0.808458 + 0.588553i \(0.799698\pi\)
\(614\) 1305.53i 2.12628i
\(615\) 296.989 386.754i 0.482908 0.628869i
\(616\) −89.8351 151.651i −0.145836 0.246187i
\(617\) −525.987 525.987i −0.852491 0.852491i 0.137948 0.990439i \(-0.455949\pi\)
−0.990439 + 0.137948i \(0.955949\pi\)
\(618\) 826.331 + 505.283i 1.33711 + 0.817610i
\(619\) 957.834 1.54739 0.773695 0.633558i \(-0.218406\pi\)
0.773695 + 0.633558i \(0.218406\pi\)
\(620\) 28.4891 267.650i 0.0459502 0.431693i
\(621\) 576.812 + 671.425i 0.928844 + 1.08120i
\(622\) −525.184 525.184i −0.844347 0.844347i
\(623\) −275.433 + 1075.99i −0.442107 + 1.72711i
\(624\) 132.704 31.9945i 0.212667 0.0512733i
\(625\) 569.613 + 257.228i 0.911381 + 0.411564i
\(626\) 463.126 0.739817
\(627\) 4.79840 7.84721i 0.00765295 0.0125155i
\(628\) 20.4200 20.4200i 0.0325159 0.0325159i
\(629\) 56.4200i 0.0896980i
\(630\) 584.229 + 461.791i 0.927348 + 0.733001i
\(631\) −482.882 −0.765265 −0.382633 0.923901i \(-0.624983\pi\)
−0.382633 + 0.923901i \(0.624983\pi\)
\(632\) 404.164 + 404.164i 0.639499 + 0.639499i
\(633\) −229.448 140.302i −0.362477 0.221647i
\(634\) 574.349i 0.905914i
\(635\) 18.8997 + 23.4025i 0.0297634 + 0.0368543i
\(636\) 53.4800 + 221.819i 0.0840880 + 0.348773i
\(637\) 107.920 31.5239i 0.169419 0.0494881i
\(638\) −362.784 + 362.784i −0.568627 + 0.568627i
\(639\) 743.074 380.419i 1.16287 0.595334i
\(640\) −468.899 580.610i −0.732654 0.907204i
\(641\) 618.098i 0.964272i −0.876096 0.482136i \(-0.839861\pi\)
0.876096 0.482136i \(-0.160139\pi\)
\(642\) −37.8199 + 61.8499i −0.0589094 + 0.0963395i
\(643\) −235.650 + 235.650i −0.366485 + 0.366485i −0.866193 0.499709i \(-0.833440\pi\)
0.499709 + 0.866193i \(0.333440\pi\)
\(644\) 185.861 + 313.752i 0.288604 + 0.487193i
\(645\) 640.637 84.1067i 0.993236 0.130398i
\(646\) 32.3118 0.0500183
\(647\) 129.060 129.060i 0.199474 0.199474i −0.600300 0.799775i \(-0.704952\pi\)
0.799775 + 0.600300i \(0.204952\pi\)
\(648\) −73.9775 455.714i −0.114163 0.703263i
\(649\) 102.069 0.157272
\(650\) 132.572 + 28.5459i 0.203957 + 0.0439167i
\(651\) −510.048 + 495.945i −0.783483 + 0.761820i
\(652\) 223.027 223.027i 0.342066 0.342066i
\(653\) 607.844 607.844i 0.930849 0.930849i −0.0669099 0.997759i \(-0.521314\pi\)
0.997759 + 0.0669099i \(0.0213140\pi\)
\(654\) −862.579 + 207.965i −1.31893 + 0.317990i
\(655\) −61.0782 + 573.818i −0.0932492 + 0.876059i
\(656\) −644.681 −0.982745
\(657\) 1156.09 + 373.178i 1.75965 + 0.568004i
\(658\) −425.768 108.989i −0.647064 0.165636i
\(659\) 795.993 1.20788 0.603940 0.797030i \(-0.293597\pi\)
0.603940 + 0.797030i \(0.293597\pi\)
\(660\) 64.1339 83.5186i 0.0971726 0.126543i
\(661\) 353.138i 0.534248i −0.963662 0.267124i \(-0.913927\pi\)
0.963662 0.267124i \(-0.0860734\pi\)
\(662\) 162.454 + 162.454i 0.245399 + 0.245399i
\(663\) 70.7185 115.652i 0.106664 0.174437i
\(664\) 45.3488 0.0682964
\(665\) 8.48052 22.7620i 0.0127527 0.0342285i
\(666\) −27.7782 54.2593i −0.0417090 0.0814704i
\(667\) −1138.77 + 1138.77i −1.70730 + 1.70730i
\(668\) −111.837 111.837i −0.167421 0.167421i
\(669\) 351.263 84.6885i 0.525058 0.126590i
\(670\) −99.6858 + 936.529i −0.148785 + 1.39780i
\(671\) 57.3785 0.0855119
\(672\) 7.08966 505.718i 0.0105501 0.752556i
\(673\) 45.1352 + 45.1352i 0.0670657 + 0.0670657i 0.739844 0.672778i \(-0.234899\pi\)
−0.672778 + 0.739844i \(0.734899\pi\)
\(674\) 476.112 0.706398
\(675\) 191.554 647.250i 0.283784 0.958888i
\(676\) −260.185 −0.384890
\(677\) 812.127 812.127i 1.19960 1.19960i 0.225309 0.974287i \(-0.427661\pi\)
0.974287 0.225309i \(-0.0723392\pi\)
\(678\) −613.449 375.110i −0.904791 0.553260i
\(679\) −187.206 316.022i −0.275708 0.465423i
\(680\) −558.090 59.4041i −0.820720 0.0873589i
\(681\) −536.135 + 129.260i −0.787276 + 0.189810i
\(682\) 250.186 + 250.186i 0.366841 + 0.366841i
\(683\) −654.128 + 654.128i −0.957728 + 0.957728i −0.999142 0.0414145i \(-0.986814\pi\)
0.0414145 + 0.999142i \(0.486814\pi\)
\(684\) 8.83495 4.52307i 0.0129166 0.00661268i
\(685\) −739.287 + 597.045i −1.07925 + 0.871599i
\(686\) −27.2396 810.435i −0.0397078 1.18139i
\(687\) 281.339 + 172.033i 0.409518 + 0.250411i
\(688\) −604.038 604.038i −0.877962 0.877962i
\(689\) 109.823i 0.159394i
\(690\) 708.066 922.082i 1.02618 1.33635i
\(691\) 1308.29i 1.89333i 0.322219 + 0.946665i \(0.395571\pi\)
−0.322219 + 0.946665i \(0.604429\pi\)
\(692\) −119.150 + 119.150i −0.172182 + 0.172182i
\(693\) −271.456 + 61.4340i −0.391711 + 0.0886493i
\(694\) 142.180i 0.204871i
\(695\) 120.865 1135.50i 0.173907 1.63382i
\(696\) 816.576 196.874i 1.17324 0.282865i
\(697\) −452.697 + 452.697i −0.649493 + 0.649493i
\(698\) −540.917 540.917i −0.774953 0.774953i
\(699\) 900.447 217.095i 1.28819 0.310579i
\(700\) 124.124 248.847i 0.177320 0.355496i
\(701\) 793.166i 1.13148i 0.824584 + 0.565739i \(0.191409\pi\)
−0.824584 + 0.565739i \(0.808591\pi\)
\(702\) 11.0695 146.041i 0.0157685 0.208035i
\(703\) −1.40592 + 1.40592i −0.00199989 + 0.00199989i
\(704\) 98.8997 0.140483
\(705\) 51.8545 + 394.974i 0.0735525 + 0.560247i
\(706\) 407.822i 0.577651i
\(707\) 119.776 + 30.6604i 0.169414 + 0.0433669i
\(708\) 93.9665 + 57.4584i 0.132721 + 0.0811560i
\(709\) 283.272i 0.399538i 0.979843 + 0.199769i \(0.0640192\pi\)
−0.979843 + 0.199769i \(0.935981\pi\)
\(710\) −688.869 852.987i −0.970238 1.20139i
\(711\) 803.365 411.285i 1.12991 0.578459i
\(712\) −639.489 639.489i −0.898158 0.898158i
\(713\) 785.326 + 785.326i 1.10144 + 1.10144i
\(714\) −681.592 700.974i −0.954610 0.981756i
\(715\) −39.4300 + 31.8435i −0.0551469 + 0.0445364i
\(716\) 175.214i 0.244712i
\(717\) −51.6344 31.5733i −0.0720145 0.0440353i
\(718\) 762.337 + 762.337i 1.06175 + 1.06175i
\(719\) 639.857i 0.889927i 0.895549 + 0.444963i \(0.146783\pi\)
−0.895549 + 0.444963i \(0.853217\pi\)
\(720\) −832.935 + 320.309i −1.15685 + 0.444874i
\(721\) −822.481 + 487.222i −1.14075 + 0.675758i
\(722\) 602.673 + 602.673i 0.834727 + 0.834727i
\(723\) −403.159 + 659.320i −0.557620 + 0.911922i
\(724\) −92.4510 −0.127695
\(725\) 1200.57 + 258.510i 1.65596 + 0.356566i
\(726\) −168.697 699.706i −0.232365 0.963782i
\(727\) −65.1910 65.1910i −0.0896713 0.0896713i 0.660848 0.750520i \(-0.270197\pi\)
−0.750520 + 0.660848i \(0.770197\pi\)
\(728\) −22.7020 + 88.6863i −0.0311841 + 0.121822i
\(729\) −720.671 109.881i −0.988575 0.150729i
\(730\) 168.880 1586.59i 0.231342 2.17342i
\(731\) −848.314 −1.16048
\(732\) 52.8235 + 32.3004i 0.0721632 + 0.0441262i
\(733\) −631.927 + 631.927i −0.862110 + 0.862110i −0.991583 0.129473i \(-0.958671\pi\)
0.129473 + 0.991583i \(0.458671\pi\)
\(734\) 176.370i 0.240286i
\(735\) −672.688 + 296.168i −0.915222 + 0.402950i
\(736\) −789.576 −1.07279
\(737\) −248.896 248.896i −0.337715 0.337715i
\(738\) −212.476 + 658.243i −0.287908 + 0.891928i
\(739\) 235.665i 0.318898i 0.987206 + 0.159449i \(0.0509717\pi\)
−0.987206 + 0.159449i \(0.949028\pi\)
\(740\) −17.7087 + 14.3015i −0.0239306 + 0.0193263i
\(741\) −4.64413 + 1.11969i −0.00626738 + 0.00151105i
\(742\) −767.348 196.427i −1.03416 0.264726i
\(743\) 122.316 122.316i 0.164625 0.164625i −0.619987 0.784612i \(-0.712862\pi\)
0.784612 + 0.619987i \(0.212862\pi\)
\(744\) −135.770 563.133i −0.182486 0.756899i
\(745\) 35.8374 336.685i 0.0481039 0.451927i
\(746\) 900.577i 1.20721i
\(747\) 21.9965 68.1443i 0.0294465 0.0912240i
\(748\) −97.7587 + 97.7587i −0.130693 + 0.130693i
\(749\) −36.4680 61.5618i −0.0486889 0.0821919i
\(750\) −883.599 72.2138i −1.17813 0.0962851i
\(751\) 314.517 0.418797 0.209399 0.977830i \(-0.432849\pi\)
0.209399 + 0.977830i \(0.432849\pi\)
\(752\) 372.409 372.409i 0.495225 0.495225i
\(753\) −490.307 299.812i −0.651138 0.398157i
\(754\) 266.467 0.353404
\(755\) −57.5966 + 541.109i −0.0762869 + 0.716700i
\(756\) −284.490 96.2552i −0.376309 0.127322i
\(757\) 782.579 782.579i 1.03379 1.03379i 0.0343817 0.999409i \(-0.489054\pi\)
0.999409 0.0343817i \(-0.0109462\pi\)
\(758\) 423.766 423.766i 0.559058 0.559058i
\(759\) 101.838 + 422.396i 0.134174 + 0.556516i
\(760\) 12.4267 + 15.3872i 0.0163509 + 0.0202463i
\(761\) −78.7855 −0.103529 −0.0517644 0.998659i \(-0.516485\pi\)
−0.0517644 + 0.998659i \(0.516485\pi\)
\(762\) −36.4029 22.2596i −0.0477729 0.0292121i
\(763\) 217.171 848.386i 0.284627 1.11191i
\(764\) −20.0562 −0.0262515
\(765\) −359.967 + 809.811i −0.470545 + 1.05858i
\(766\) 544.150i 0.710379i
\(767\) −37.4852 37.4852i −0.0488725 0.0488725i
\(768\) 673.962 + 412.113i 0.877554 + 0.536605i
\(769\) −959.073 −1.24717 −0.623584 0.781756i \(-0.714324\pi\)
−0.623584 + 0.781756i \(0.714324\pi\)
\(770\) 151.972 + 332.459i 0.197366 + 0.431764i
\(771\) −848.386 + 204.543i −1.10037 + 0.265296i
\(772\) −336.193 + 336.193i −0.435483 + 0.435483i
\(773\) 313.143 + 313.143i 0.405100 + 0.405100i 0.880026 0.474926i \(-0.157525\pi\)
−0.474926 + 0.880026i \(0.657525\pi\)
\(774\) −815.826 + 417.664i −1.05404 + 0.539618i
\(775\) 178.276 827.945i 0.230033 1.06832i
\(776\) 299.081 0.385414
\(777\) 60.1568 + 0.843339i 0.0774219 + 0.00108538i
\(778\) 517.324 + 517.324i 0.664941 + 0.664941i
\(779\) 22.5613 0.0289619
\(780\) −54.2257 + 7.11908i −0.0695202 + 0.00912702i
\(781\) 409.771 0.524674
\(782\) −1079.30 + 1079.30i −1.38018 + 1.38018i
\(783\) 100.245 1322.54i 0.128027 1.68907i
\(784\) 852.210 + 466.893i 1.08700 + 0.595527i
\(785\) 70.6916 57.0903i 0.0900530 0.0727265i
\(786\) −191.851 795.742i −0.244085 1.01239i
\(787\) 617.290 + 617.290i 0.784358 + 0.784358i 0.980563 0.196205i \(-0.0628617\pi\)
−0.196205 + 0.980563i \(0.562862\pi\)
\(788\) 162.911 162.911i 0.206739 0.206739i
\(789\) 19.8984 4.79745i 0.0252198 0.00608042i
\(790\) −744.762 922.195i −0.942736 1.16734i
\(791\) 610.590 361.702i 0.771922 0.457272i
\(792\) 69.6153 215.665i 0.0878981 0.272305i
\(793\) −21.0724 21.0724i −0.0265730 0.0265730i
\(794\) 1549.27i 1.95122i
\(795\) 93.4557 + 711.848i 0.117554 + 0.895407i
\(796\) 374.944i 0.471035i
\(797\) −843.997 + 843.997i −1.05897 + 1.05897i −0.0608184 + 0.998149i \(0.519371\pi\)
−0.998149 + 0.0608184i \(0.980629\pi\)
\(798\) −0.482982 + 34.4519i −0.000605240 + 0.0431728i
\(799\) 523.013i 0.654585i
\(800\) 326.592 + 505.833i 0.408240 + 0.632291i
\(801\) −1271.13 + 650.756i −1.58692 + 0.812429i
\(802\) 863.401 863.401i 1.07656 1.07656i
\(803\) 421.661 + 421.661i 0.525107 + 0.525107i
\(804\) −89.0251 369.250i −0.110728 0.459266i
\(805\) 477.036 + 1043.58i 0.592592 + 1.29637i
\(806\) 183.763i 0.227993i
\(807\) 167.433 273.817i 0.207476 0.339302i
\(808\) −71.1860 + 71.1860i −0.0881014 + 0.0881014i
\(809\) −56.0803 −0.0693205 −0.0346602 0.999399i \(-0.511035\pi\)
−0.0346602 + 0.999399i \(0.511035\pi\)
\(810\) 52.5259 + 956.026i 0.0648467 + 1.18028i
\(811\) 882.859i 1.08861i 0.838889 + 0.544303i \(0.183206\pi\)
−0.838889 + 0.544303i \(0.816794\pi\)
\(812\) 135.504 529.353i 0.166877 0.651912i
\(813\) 292.718 478.706i 0.360047 0.588814i
\(814\) 29.9215i 0.0367586i
\(815\) 772.094 623.540i 0.947354 0.765080i
\(816\) 1139.00 274.610i 1.39584 0.336532i
\(817\) 21.1390 + 21.1390i 0.0258739 + 0.0258739i
\(818\) −199.057 199.057i −0.243346 0.243346i
\(819\) 122.255 + 77.1311i 0.149273 + 0.0941771i
\(820\) 256.839 + 27.3384i 0.313219 + 0.0333395i
\(821\) 1159.68i 1.41253i 0.707949 + 0.706264i \(0.249621\pi\)
−0.707949 + 0.706264i \(0.750379\pi\)
\(822\) 703.184 1149.97i 0.855454 1.39900i
\(823\) 704.019 + 704.019i 0.855430 + 0.855430i 0.990796 0.135366i \(-0.0432210\pi\)
−0.135366 + 0.990796i \(0.543221\pi\)
\(824\) 778.391i 0.944649i
\(825\) 228.480 239.957i 0.276945 0.290857i
\(826\) −328.960 + 194.870i −0.398257 + 0.235920i
\(827\) −572.404 572.404i −0.692145 0.692145i 0.270558 0.962704i \(-0.412792\pi\)
−0.962704 + 0.270558i \(0.912792\pi\)
\(828\) −144.028 + 446.192i −0.173947 + 0.538880i
\(829\) 463.044 0.558557 0.279279 0.960210i \(-0.409905\pi\)
0.279279 + 0.960210i \(0.409905\pi\)
\(830\) −93.5197 9.95441i −0.112674 0.0119933i
\(831\) 395.007 95.2349i 0.475339 0.114603i
\(832\) −36.3212 36.3212i −0.0436552 0.0436552i
\(833\) 926.277 270.570i 1.11198 0.324814i
\(834\) 379.646 + 1574.66i 0.455210 + 1.88808i
\(835\) −312.674 387.167i −0.374460 0.463673i
\(836\) 4.87206 0.00582783
\(837\) −912.059 69.1316i −1.08968 0.0825945i
\(838\) 1224.21 1224.21i 1.46087 1.46087i
\(839\) 401.831i 0.478940i −0.970904 0.239470i \(-0.923026\pi\)
0.970904 0.239470i \(-0.0769737\pi\)
\(840\) 71.6806 594.166i 0.0853341 0.707340i
\(841\) 1572.11 1.86934
\(842\) −513.742 513.742i −0.610145 0.610145i
\(843\) −220.410 + 360.455i −0.261459 + 0.427586i
\(844\) 142.456i 0.168787i
\(845\) −814.078 86.6519i −0.963406 0.102547i
\(846\) −257.504 502.984i −0.304378 0.594543i
\(847\) 688.192 + 176.164i 0.812506 + 0.207986i
\(848\) 671.181 671.181i 0.791487 0.791487i
\(849\) −844.490 + 203.604i −0.994688 + 0.239816i
\(850\) 1137.87 + 245.010i 1.33867 + 0.288247i
\(851\) 93.9227i 0.110367i
\(852\) 377.241 + 230.675i 0.442771 + 0.270745i
\(853\) 615.673 615.673i 0.721774 0.721774i −0.247192 0.968966i \(-0.579508\pi\)
0.968966 + 0.247192i \(0.0795080\pi\)
\(854\) −184.926 + 109.546i −0.216541 + 0.128274i
\(855\) 29.1495 11.2096i 0.0340930 0.0131106i
\(856\) 58.2616 0.0680627
\(857\) −90.9145 + 90.9145i −0.106085 + 0.106085i −0.758157 0.652072i \(-0.773900\pi\)
0.652072 + 0.758157i \(0.273900\pi\)
\(858\) 37.5045 61.3341i 0.0437115 0.0714850i
\(859\) −974.498 −1.13446 −0.567228 0.823561i \(-0.691984\pi\)
−0.567228 + 0.823561i \(0.691984\pi\)
\(860\) 215.032 + 266.262i 0.250038 + 0.309607i
\(861\) −475.913 489.446i −0.552744 0.568463i
\(862\) 344.070 344.070i 0.399153 0.399153i
\(863\) −341.306 + 341.306i −0.395488 + 0.395488i −0.876638 0.481150i \(-0.840219\pi\)
0.481150 + 0.876638i \(0.340219\pi\)
\(864\) 493.250 423.744i 0.570891 0.490444i
\(865\) −412.483 + 333.120i −0.476859 + 0.385110i
\(866\) 975.798 1.12679
\(867\) 154.684 252.967i 0.178413 0.291773i
\(868\) −365.056 93.4474i −0.420571 0.107658i
\(869\) 443.018 0.509802
\(870\) −1727.18 + 226.755i −1.98527 + 0.260638i
\(871\) 182.815i 0.209891i
\(872\) 504.218 + 504.218i 0.578232 + 0.578232i
\(873\) 145.070 449.421i 0.166174 0.514801i
\(874\) 53.7897 0.0615443
\(875\) 471.240 737.264i 0.538560 0.842587i
\(876\) 150.819 + 625.555i 0.172168 + 0.714104i
\(877\) −798.731 + 798.731i −0.910754 + 0.910754i −0.996331 0.0855778i \(-0.972726\pi\)
0.0855778 + 0.996331i \(0.472726\pi\)
\(878\) 195.037 + 195.037i 0.222138 + 0.222138i
\(879\) 157.321 + 652.523i 0.178978 + 0.742347i
\(880\) −435.588 46.3648i −0.494987 0.0526873i
\(881\) 90.0599 0.102225 0.0511123 0.998693i \(-0.483723\pi\)
0.0511123 + 0.998693i \(0.483723\pi\)
\(882\) 757.589 716.257i 0.858945 0.812083i
\(883\) −149.663 149.663i −0.169494 0.169494i 0.617263 0.786757i \(-0.288241\pi\)
−0.786757 + 0.617263i \(0.788241\pi\)
\(884\) 71.8042 0.0812265
\(885\) 274.870 + 211.073i 0.310588 + 0.238500i
\(886\) 942.902 1.06422
\(887\) −449.819 + 449.819i −0.507124 + 0.507124i −0.913643 0.406518i \(-0.866743\pi\)
0.406518 + 0.913643i \(0.366743\pi\)
\(888\) −25.5557 + 41.7933i −0.0287789 + 0.0470646i
\(889\) 36.2333 21.4639i 0.0407574 0.0241439i
\(890\) 1178.40 + 1459.15i 1.32405 + 1.63949i
\(891\) −290.307 209.218i −0.325822 0.234812i
\(892\) 135.334 + 135.334i 0.151719 + 0.151719i
\(893\) −13.0329 + 13.0329i −0.0145945 + 0.0145945i
\(894\) 112.568 + 466.898i 0.125915 + 0.522258i
\(895\) 58.3530 548.215i 0.0651989 0.612531i
\(896\) −898.942 + 532.516i −1.00328 + 0.594326i
\(897\) 117.726 192.526i 0.131244 0.214633i
\(898\) −681.770 681.770i −0.759210 0.759210i
\(899\) 1664.15i 1.85111i
\(900\) 345.422 92.2889i 0.383803 0.102543i
\(901\) 942.610i 1.04618i
\(902\) −240.081 + 240.081i −0.266165 + 0.266165i
\(903\) 12.6802 904.500i 0.0140423 1.00166i
\(904\) 577.859i 0.639224i
\(905\) −289.264 30.7898i −0.319629 0.0340219i
\(906\) −180.915 750.382i −0.199685 0.828237i
\(907\) 1098.67 1098.67i 1.21133 1.21133i 0.240735 0.970591i \(-0.422611\pi\)
0.970591 0.240735i \(-0.0773886\pi\)
\(908\) −206.561 206.561i −0.227490 0.227490i
\(909\) 72.4402 + 141.498i 0.0796922 + 0.155663i
\(910\) 66.2841 177.908i 0.0728397 0.195504i
\(911\) 1217.82i 1.33680i −0.743804 0.668398i \(-0.766980\pi\)
0.743804 0.668398i \(-0.233020\pi\)
\(912\) −35.2255 21.5396i −0.0386245 0.0236180i
\(913\) 24.8542 24.8542i 0.0272226 0.0272226i
\(914\) −1542.88 −1.68805
\(915\) 154.519 + 118.655i 0.168873 + 0.129678i
\(916\) 174.674i 0.190692i
\(917\) 782.649 + 200.343i 0.853488 + 0.218477i
\(918\) 95.0097 1253.47i 0.103496 1.36544i
\(919\) 80.9089i 0.0880401i 0.999031 + 0.0440201i \(0.0140166\pi\)
−0.999031 + 0.0440201i \(0.985983\pi\)
\(920\) −929.055 98.8903i −1.00984 0.107489i
\(921\) 388.295 + 1610.54i 0.421602 + 1.74868i
\(922\) 1318.62 + 1318.62i 1.43017 + 1.43017i
\(923\) −150.489 150.489i −0.163044 0.163044i
\(924\) −102.772 105.695i −0.111225 0.114388i
\(925\) −60.1705 + 38.8493i −0.0650492 + 0.0419992i
\(926\) 1834.39i 1.98098i
\(927\) −1169.66 377.560i −1.26177 0.407292i
\(928\) 836.576 + 836.576i 0.901482 + 0.901482i
\(929\) 1204.04i 1.29607i −0.761612 0.648033i \(-0.775592\pi\)
0.761612 0.648033i \(-0.224408\pi\)
\(930\) 156.376 + 1191.11i 0.168147 + 1.28077i
\(931\) −29.8240 16.3394i −0.0320344 0.0175504i
\(932\) 346.921 + 346.921i 0.372233 + 0.372233i
\(933\) 804.081 + 491.678i 0.861823 + 0.526986i
\(934\) −1000.02 −1.07068
\(935\) −338.429 + 273.314i −0.361956 + 0.292314i
\(936\) −104.770 + 53.6372i −0.111934 + 0.0573048i
\(937\) 498.626 + 498.626i 0.532152 + 0.532152i 0.921212 0.389061i \(-0.127200\pi\)
−0.389061 + 0.921212i \(0.627200\pi\)
\(938\) 1277.36 + 326.980i 1.36179 + 0.348593i
\(939\) −571.323 + 137.744i −0.608438 + 0.146692i
\(940\) −164.159 + 132.574i −0.174638 + 0.141037i
\(941\) 759.571 0.807195 0.403598 0.914937i \(-0.367760\pi\)
0.403598 + 0.914937i \(0.367760\pi\)
\(942\) −67.2394 + 109.962i −0.0713794 + 0.116733i
\(943\) −753.607 + 753.607i −0.799159 + 0.799159i
\(944\) 458.181i 0.485361i
\(945\) −858.066 395.913i −0.908007 0.418956i
\(946\) −449.890 −0.475571
\(947\) −911.272 911.272i −0.962273 0.962273i 0.0370409 0.999314i \(-0.488207\pi\)
−0.999314 + 0.0370409i \(0.988207\pi\)
\(948\) 407.849 + 249.391i 0.430221 + 0.263070i
\(949\) 309.712i 0.326356i
\(950\) −22.2490 34.4598i −0.0234200 0.0362734i
\(951\) 170.825 + 708.531i 0.179626 + 0.745038i
\(952\) −194.852 + 761.196i −0.204676 + 0.799576i
\(953\) 335.606 335.606i 0.352158 0.352158i −0.508754 0.860912i \(-0.669894\pi\)
0.860912 + 0.508754i \(0.169894\pi\)
\(954\) −464.090 906.511i −0.486468 0.950221i
\(955\) −62.7525 6.67949i −0.0657095 0.00699423i
\(956\) 32.0580i 0.0335335i
\(957\) 339.639 555.440i 0.354900 0.580397i
\(958\) −950.798 + 950.798i −0.992483 + 0.992483i
\(959\) 678.048 + 1144.62i 0.707037 + 1.19355i
\(960\) 266.335 + 204.518i 0.277432 + 0.213040i
\(961\) −186.641 −0.194215
\(962\) −10.9887 + 10.9887i −0.0114228 + 0.0114228i
\(963\) 28.2599 87.5481i 0.0293457 0.0909118i
\(964\) −409.349 −0.424636
\(965\) −1163.86 + 939.929i −1.20607 + 0.974019i
\(966\) −1134.65 1166.92i −1.17459 1.20799i
\(967\) −44.4403 + 44.4403i −0.0459568 + 0.0459568i −0.729712 0.683755i \(-0.760346\pi\)
0.683755 + 0.729712i \(0.260346\pi\)
\(968\) −409.011 + 409.011i −0.422532 + 0.422532i
\(969\) −39.8607 + 9.61028i −0.0411359 + 0.00991773i
\(970\) −616.775 65.6506i −0.635850 0.0676810i
\(971\) −1113.37 −1.14663 −0.573313 0.819337i \(-0.694342\pi\)
−0.573313 + 0.819337i \(0.694342\pi\)
\(972\) −149.485 356.033i −0.153791 0.366289i
\(973\) −1548.75 396.450i −1.59173 0.407452i
\(974\) −1279.90 −1.31407
\(975\) −172.035 + 4.21514i −0.176446 + 0.00432322i
\(976\) 257.567i 0.263901i
\(977\) −537.682 537.682i −0.550340 0.550340i 0.376199 0.926539i \(-0.377231\pi\)
−0.926539 + 0.376199i \(0.877231\pi\)
\(978\) −734.388 + 1201.01i −0.750908 + 1.22802i
\(979\) −700.966 −0.716002
\(980\) −319.719 222.148i −0.326244 0.226681i
\(981\) 1002.25 513.102i 1.02166 0.523039i
\(982\) 2.31617 2.31617i 0.00235862 0.00235862i
\(983\) 994.643 + 994.643i 1.01184 + 1.01184i 0.999929 + 0.0119152i \(0.00379282\pi\)
0.0119152 + 0.999929i \(0.496207\pi\)
\(984\) 540.388 130.286i 0.549174 0.132404i
\(985\) 563.977 455.465i 0.572565 0.462401i
\(986\) 2287.09 2.31956
\(987\) 557.654 + 7.81775i 0.564999 + 0.00792072i
\(988\) −1.78928 1.78928i −0.00181101 0.00181101i
\(989\) −1412.19 −1.42790
\(990\) −190.903 + 429.471i −0.192831 + 0.433809i
\(991\) −717.169 −0.723682 −0.361841 0.932240i \(-0.617852\pi\)
−0.361841 + 0.932240i \(0.617852\pi\)
\(992\) 576.925 576.925i 0.581578 0.581578i
\(993\) −248.725 152.090i −0.250478 0.153162i
\(994\) −1320.65 + 782.330i −1.32863 + 0.787052i
\(995\) 124.871 1173.14i 0.125499 1.17904i
\(996\) 36.8725 8.88985i 0.0370206 0.00892555i
\(997\) −572.089 572.089i −0.573810 0.573810i 0.359381 0.933191i \(-0.382988\pi\)
−0.933191 + 0.359381i \(0.882988\pi\)
\(998\) 596.359 596.359i 0.597554 0.597554i
\(999\) 50.4058 + 58.6737i 0.0504562 + 0.0587325i
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.k.d.83.8 yes 32
3.2 odd 2 inner 105.3.k.d.83.9 yes 32
5.2 odd 4 inner 105.3.k.d.62.10 yes 32
7.6 odd 2 inner 105.3.k.d.83.7 yes 32
15.2 even 4 inner 105.3.k.d.62.7 32
21.20 even 2 inner 105.3.k.d.83.10 yes 32
35.27 even 4 inner 105.3.k.d.62.9 yes 32
105.62 odd 4 inner 105.3.k.d.62.8 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.3.k.d.62.7 32 15.2 even 4 inner
105.3.k.d.62.8 yes 32 105.62 odd 4 inner
105.3.k.d.62.9 yes 32 35.27 even 4 inner
105.3.k.d.62.10 yes 32 5.2 odd 4 inner
105.3.k.d.83.7 yes 32 7.6 odd 2 inner
105.3.k.d.83.8 yes 32 1.1 even 1 trivial
105.3.k.d.83.9 yes 32 3.2 odd 2 inner
105.3.k.d.83.10 yes 32 21.20 even 2 inner