Properties

Label 405.3.l.h.352.1
Level $405$
Weight $3$
Character 405.352
Analytic conductor $11.035$
Analytic rank $0$
Dimension $8$
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] = [405,3,Mod(28,405)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(405, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([4, 9]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("405.28");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 405.l (of order \(12\), degree \(4\), not 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: \(11.0354507066\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 15)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 352.1
Root \(0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 405.352
Dual form 405.3.l.h.298.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.814313 + 3.03906i) q^{2} +(-5.10867 - 2.94949i) q^{4} +(-4.99585 + 0.203583i) q^{5} +(-0.530550 + 1.98004i) q^{7} +(4.22474 - 4.22474i) q^{8} +O(q^{10})\) \(q+(-0.814313 + 3.03906i) q^{2} +(-5.10867 - 2.94949i) q^{4} +(-4.99585 + 0.203583i) q^{5} +(-0.530550 + 1.98004i) q^{7} +(4.22474 - 4.22474i) q^{8} +(3.44949 - 15.3485i) q^{10} +(1.67423 + 2.89986i) q^{11} +(-3.82478 - 14.2743i) q^{13} +(-5.58542 - 3.22474i) q^{14} +(-2.39898 - 4.15515i) q^{16} +(-2.65153 - 2.65153i) q^{17} -20.6969i q^{19} +(26.1226 + 13.6952i) q^{20} +(-10.1762 + 2.72670i) q^{22} +(6.02093 + 22.4704i) q^{23} +(24.9171 - 2.03414i) q^{25} +46.4949 q^{26} +(8.55051 - 8.55051i) q^{28} +(0.739215 - 0.426786i) q^{29} +(9.34847 - 16.1920i) q^{31} +(37.6657 - 10.0925i) q^{32} +(10.2173 - 5.89898i) q^{34} +(2.24745 - 10.0000i) q^{35} +(38.0454 + 38.0454i) q^{37} +(62.8992 + 16.8538i) q^{38} +(-20.2461 + 21.9663i) q^{40} +(14.3485 - 24.8523i) q^{41} +(-30.7286 - 8.23370i) q^{43} -19.7526i q^{44} -73.1918 q^{46} +(7.22994 - 26.9825i) q^{47} +(38.7962 + 22.3990i) q^{49} +(-14.1085 + 77.3810i) q^{50} +(-22.5623 + 84.2036i) q^{52} +(28.6969 - 28.6969i) q^{53} +(-8.95459 - 14.1464i) q^{55} +(6.12372 + 10.6066i) q^{56} +(0.695075 + 2.59405i) q^{58} +(-96.9378 - 55.9671i) q^{59} +(-47.0454 - 81.4850i) q^{61} +(41.5959 + 41.5959i) q^{62} +103.495i q^{64} +(22.0140 + 70.5335i) q^{65} +(74.9934 - 20.0944i) q^{67} +(5.72512 + 21.3664i) q^{68} +(28.5605 + 14.9733i) q^{70} -68.0000 q^{71} +(-39.7878 + 39.7878i) q^{73} +(-146.603 + 84.6413i) q^{74} +(-61.0454 + 105.734i) q^{76} +(-6.63010 + 1.77653i) q^{77} +(21.2132 - 12.2474i) q^{79} +(12.8309 + 20.2702i) q^{80} +(63.8434 + 63.8434i) q^{82} +(28.8866 + 7.74013i) q^{83} +(13.7865 + 12.7069i) q^{85} +(50.0454 - 86.6812i) q^{86} +(19.3244 + 5.17795i) q^{88} -94.1816i q^{89} +30.2929 q^{91} +(35.5173 - 132.553i) q^{92} +(76.1139 + 43.9444i) q^{94} +(4.21354 + 103.399i) q^{95} +(5.34248 - 19.9384i) q^{97} +(-99.6640 + 99.6640i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{2} + 4 q^{5} - 4 q^{7} + 24 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{2} + 4 q^{5} - 4 q^{7} + 24 q^{8} + 8 q^{10} - 16 q^{11} + 32 q^{13} + 20 q^{16} - 80 q^{17} + 36 q^{20} - 20 q^{22} - 56 q^{23} - 16 q^{25} + 176 q^{26} + 88 q^{28} + 16 q^{31} + 76 q^{32} - 80 q^{35} + 128 q^{37} + 96 q^{38} - 48 q^{40} + 56 q^{41} + 8 q^{43} - 272 q^{46} - 128 q^{47} - 164 q^{50} + 80 q^{52} + 112 q^{53} - 248 q^{55} + 12 q^{58} - 200 q^{61} + 176 q^{62} + 112 q^{65} + 200 q^{67} + 104 q^{68} + 60 q^{70} - 544 q^{71} + 152 q^{73} - 312 q^{76} - 88 q^{77} + 328 q^{80} + 256 q^{82} + 16 q^{83} - 232 q^{85} + 224 q^{86} - 12 q^{88} - 32 q^{91} - 104 q^{92} - 144 q^{95} + 20 q^{97} - 376 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.814313 + 3.03906i −0.407157 + 1.51953i 0.392887 + 0.919587i \(0.371476\pi\)
−0.800043 + 0.599942i \(0.795190\pi\)
\(3\) 0 0
\(4\) −5.10867 2.94949i −1.27717 0.737372i
\(5\) −4.99585 + 0.203583i −0.999171 + 0.0407165i
\(6\) 0 0
\(7\) −0.530550 + 1.98004i −0.0757929 + 0.282863i −0.993412 0.114598i \(-0.963442\pi\)
0.917619 + 0.397461i \(0.130109\pi\)
\(8\) 4.22474 4.22474i 0.528093 0.528093i
\(9\) 0 0
\(10\) 3.44949 15.3485i 0.344949 1.53485i
\(11\) 1.67423 + 2.89986i 0.152203 + 0.263624i 0.932037 0.362363i \(-0.118030\pi\)
−0.779834 + 0.625986i \(0.784697\pi\)
\(12\) 0 0
\(13\) −3.82478 14.2743i −0.294214 1.09802i −0.941840 0.336062i \(-0.890905\pi\)
0.647626 0.761958i \(-0.275762\pi\)
\(14\) −5.58542 3.22474i −0.398959 0.230339i
\(15\) 0 0
\(16\) −2.39898 4.15515i −0.149936 0.259697i
\(17\) −2.65153 2.65153i −0.155972 0.155972i 0.624807 0.780779i \(-0.285178\pi\)
−0.780779 + 0.624807i \(0.785178\pi\)
\(18\) 0 0
\(19\) 20.6969i 1.08931i −0.838659 0.544656i \(-0.816660\pi\)
0.838659 0.544656i \(-0.183340\pi\)
\(20\) 26.1226 + 13.6952i 1.30613 + 0.684759i
\(21\) 0 0
\(22\) −10.1762 + 2.72670i −0.462554 + 0.123941i
\(23\) 6.02093 + 22.4704i 0.261780 + 0.976975i 0.964192 + 0.265205i \(0.0854395\pi\)
−0.702413 + 0.711770i \(0.747894\pi\)
\(24\) 0 0
\(25\) 24.9171 2.03414i 0.996684 0.0813655i
\(26\) 46.4949 1.78827
\(27\) 0 0
\(28\) 8.55051 8.55051i 0.305375 0.305375i
\(29\) 0.739215 0.426786i 0.0254902 0.0147168i −0.487201 0.873290i \(-0.661982\pi\)
0.512691 + 0.858573i \(0.328649\pi\)
\(30\) 0 0
\(31\) 9.34847 16.1920i 0.301564 0.522323i −0.674927 0.737885i \(-0.735825\pi\)
0.976490 + 0.215561i \(0.0691581\pi\)
\(32\) 37.6657 10.0925i 1.17705 0.315391i
\(33\) 0 0
\(34\) 10.2173 5.89898i 0.300510 0.173499i
\(35\) 2.24745 10.0000i 0.0642128 0.285714i
\(36\) 0 0
\(37\) 38.0454 + 38.0454i 1.02825 + 1.02825i 0.999589 + 0.0286652i \(0.00912566\pi\)
0.0286652 + 0.999589i \(0.490874\pi\)
\(38\) 62.8992 + 16.8538i 1.65524 + 0.443521i
\(39\) 0 0
\(40\) −20.2461 + 21.9663i −0.506153 + 0.549157i
\(41\) 14.3485 24.8523i 0.349963 0.606153i −0.636280 0.771458i \(-0.719528\pi\)
0.986242 + 0.165305i \(0.0528609\pi\)
\(42\) 0 0
\(43\) −30.7286 8.23370i −0.714619 0.191481i −0.116849 0.993150i \(-0.537279\pi\)
−0.597769 + 0.801668i \(0.703946\pi\)
\(44\) 19.7526i 0.448922i
\(45\) 0 0
\(46\) −73.1918 −1.59113
\(47\) 7.22994 26.9825i 0.153828 0.574095i −0.845374 0.534174i \(-0.820623\pi\)
0.999203 0.0399212i \(-0.0127107\pi\)
\(48\) 0 0
\(49\) 38.7962 + 22.3990i 0.791759 + 0.457122i
\(50\) −14.1085 + 77.3810i −0.282169 + 1.54762i
\(51\) 0 0
\(52\) −22.5623 + 84.2036i −0.433890 + 1.61930i
\(53\) 28.6969 28.6969i 0.541452 0.541452i −0.382503 0.923954i \(-0.624938\pi\)
0.923954 + 0.382503i \(0.124938\pi\)
\(54\) 0 0
\(55\) −8.95459 14.1464i −0.162811 0.257208i
\(56\) 6.12372 + 10.6066i 0.109352 + 0.189404i
\(57\) 0 0
\(58\) 0.695075 + 2.59405i 0.0119840 + 0.0447251i
\(59\) −96.9378 55.9671i −1.64301 0.948595i −0.979754 0.200206i \(-0.935839\pi\)
−0.663261 0.748389i \(-0.730828\pi\)
\(60\) 0 0
\(61\) −47.0454 81.4850i −0.771236 1.33582i −0.936886 0.349636i \(-0.886305\pi\)
0.165650 0.986185i \(-0.447028\pi\)
\(62\) 41.5959 + 41.5959i 0.670902 + 0.670902i
\(63\) 0 0
\(64\) 103.495i 1.61711i
\(65\) 22.0140 + 70.5335i 0.338677 + 1.08513i
\(66\) 0 0
\(67\) 74.9934 20.0944i 1.11930 0.299917i 0.348703 0.937233i \(-0.386622\pi\)
0.770602 + 0.637317i \(0.219956\pi\)
\(68\) 5.72512 + 21.3664i 0.0841930 + 0.314212i
\(69\) 0 0
\(70\) 28.5605 + 14.9733i 0.408006 + 0.213904i
\(71\) −68.0000 −0.957746 −0.478873 0.877884i \(-0.658955\pi\)
−0.478873 + 0.877884i \(0.658955\pi\)
\(72\) 0 0
\(73\) −39.7878 + 39.7878i −0.545038 + 0.545038i −0.925001 0.379964i \(-0.875936\pi\)
0.379964 + 0.925001i \(0.375936\pi\)
\(74\) −146.603 + 84.6413i −1.98112 + 1.14380i
\(75\) 0 0
\(76\) −61.0454 + 105.734i −0.803229 + 1.39123i
\(77\) −6.63010 + 1.77653i −0.0861052 + 0.0230718i
\(78\) 0 0
\(79\) 21.2132 12.2474i 0.268522 0.155031i −0.359694 0.933070i \(-0.617119\pi\)
0.628216 + 0.778039i \(0.283786\pi\)
\(80\) 12.8309 + 20.2702i 0.160386 + 0.253377i
\(81\) 0 0
\(82\) 63.8434 + 63.8434i 0.778578 + 0.778578i
\(83\) 28.8866 + 7.74013i 0.348031 + 0.0932546i 0.428600 0.903494i \(-0.359007\pi\)
−0.0805689 + 0.996749i \(0.525674\pi\)
\(84\) 0 0
\(85\) 13.7865 + 12.7069i 0.162194 + 0.149492i
\(86\) 50.0454 86.6812i 0.581923 1.00792i
\(87\) 0 0
\(88\) 19.3244 + 5.17795i 0.219595 + 0.0588404i
\(89\) 94.1816i 1.05822i −0.848553 0.529110i \(-0.822526\pi\)
0.848553 0.529110i \(-0.177474\pi\)
\(90\) 0 0
\(91\) 30.2929 0.332889
\(92\) 35.5173 132.553i 0.386058 1.44079i
\(93\) 0 0
\(94\) 76.1139 + 43.9444i 0.809722 + 0.467493i
\(95\) 4.21354 + 103.399i 0.0443530 + 1.08841i
\(96\) 0 0
\(97\) 5.34248 19.9384i 0.0550771 0.205550i −0.932904 0.360125i \(-0.882734\pi\)
0.987981 + 0.154575i \(0.0494007\pi\)
\(98\) −99.6640 + 99.6640i −1.01698 + 1.01698i
\(99\) 0 0
\(100\) −133.293 63.1010i −1.33293 0.631010i
\(101\) −86.8105 150.360i −0.859509 1.48871i −0.872397 0.488797i \(-0.837436\pi\)
0.0128880 0.999917i \(-0.495898\pi\)
\(102\) 0 0
\(103\) −23.7011 88.4536i −0.230108 0.858773i −0.980294 0.197546i \(-0.936703\pi\)
0.750186 0.661227i \(-0.229964\pi\)
\(104\) −76.4639 44.1464i −0.735229 0.424485i
\(105\) 0 0
\(106\) 63.8434 + 110.580i 0.602296 + 1.04321i
\(107\) −4.74235 4.74235i −0.0443210 0.0443210i 0.684599 0.728920i \(-0.259977\pi\)
−0.728920 + 0.684599i \(0.759977\pi\)
\(108\) 0 0
\(109\) 39.3031i 0.360579i 0.983614 + 0.180289i \(0.0577034\pi\)
−0.983614 + 0.180289i \(0.942297\pi\)
\(110\) 50.2837 15.6939i 0.457124 0.142672i
\(111\) 0 0
\(112\) 9.50015 2.54556i 0.0848228 0.0227282i
\(113\) 5.25564 + 19.6143i 0.0465101 + 0.173578i 0.985274 0.170983i \(-0.0546944\pi\)
−0.938764 + 0.344561i \(0.888028\pi\)
\(114\) 0 0
\(115\) −34.6543 111.033i −0.301342 0.965506i
\(116\) −5.03520 −0.0434069
\(117\) 0 0
\(118\) 249.025 249.025i 2.11038 2.11038i
\(119\) 6.65691 3.84337i 0.0559404 0.0322972i
\(120\) 0 0
\(121\) 54.8939 95.0790i 0.453668 0.785777i
\(122\) 285.947 76.6194i 2.34383 0.628028i
\(123\) 0 0
\(124\) −95.5164 + 55.1464i −0.770294 + 0.444729i
\(125\) −124.068 + 15.2350i −0.992545 + 0.121880i
\(126\) 0 0
\(127\) −114.621 114.621i −0.902527 0.902527i 0.0931273 0.995654i \(-0.470314\pi\)
−0.995654 + 0.0931273i \(0.970314\pi\)
\(128\) −163.864 43.9073i −1.28019 0.343026i
\(129\) 0 0
\(130\) −232.282 + 9.46556i −1.78678 + 0.0728120i
\(131\) 13.0681 22.6346i 0.0997566 0.172783i −0.811827 0.583898i \(-0.801527\pi\)
0.911584 + 0.411114i \(0.134860\pi\)
\(132\) 0 0
\(133\) 40.9808 + 10.9808i 0.308126 + 0.0825621i
\(134\) 244.272i 1.82293i
\(135\) 0 0
\(136\) −22.4041 −0.164736
\(137\) 5.35536 19.9865i 0.0390902 0.145887i −0.943623 0.331023i \(-0.892606\pi\)
0.982713 + 0.185137i \(0.0592728\pi\)
\(138\) 0 0
\(139\) −72.0286 41.5857i −0.518191 0.299178i 0.218003 0.975948i \(-0.430046\pi\)
−0.736194 + 0.676770i \(0.763379\pi\)
\(140\) −40.9764 + 44.4578i −0.292688 + 0.317556i
\(141\) 0 0
\(142\) 55.3733 206.656i 0.389953 1.45532i
\(143\) 34.9898 34.9898i 0.244684 0.244684i
\(144\) 0 0
\(145\) −3.60612 + 2.28265i −0.0248698 + 0.0157424i
\(146\) −88.5176 153.317i −0.606285 1.05012i
\(147\) 0 0
\(148\) −82.1467 306.576i −0.555046 2.07146i
\(149\) −103.184 59.5732i −0.692509 0.399820i 0.112042 0.993703i \(-0.464261\pi\)
−0.804551 + 0.593883i \(0.797594\pi\)
\(150\) 0 0
\(151\) 72.4847 + 125.547i 0.480031 + 0.831438i 0.999738 0.0229066i \(-0.00729205\pi\)
−0.519707 + 0.854345i \(0.673959\pi\)
\(152\) −87.4393 87.4393i −0.575258 0.575258i
\(153\) 0 0
\(154\) 21.5959i 0.140233i
\(155\) −43.4072 + 82.7962i −0.280046 + 0.534169i
\(156\) 0 0
\(157\) −69.8673 + 18.7209i −0.445015 + 0.119241i −0.474366 0.880328i \(-0.657323\pi\)
0.0293510 + 0.999569i \(0.490656\pi\)
\(158\) 19.9465 + 74.4414i 0.126244 + 0.471148i
\(159\) 0 0
\(160\) −186.118 + 58.0887i −1.16324 + 0.363055i
\(161\) −47.6867 −0.296191
\(162\) 0 0
\(163\) 189.394 189.394i 1.16193 1.16193i 0.177872 0.984054i \(-0.443079\pi\)
0.984054 0.177872i \(-0.0569213\pi\)
\(164\) −146.603 + 84.6413i −0.893921 + 0.516106i
\(165\) 0 0
\(166\) −47.0454 + 81.4850i −0.283406 + 0.490874i
\(167\) −132.553 + 35.5173i −0.793728 + 0.212679i −0.632828 0.774292i \(-0.718106\pi\)
−0.160899 + 0.986971i \(0.551439\pi\)
\(168\) 0 0
\(169\) −42.7675 + 24.6918i −0.253062 + 0.146106i
\(170\) −49.8434 + 31.5505i −0.293196 + 0.185591i
\(171\) 0 0
\(172\) 132.697 + 132.697i 0.771494 + 0.771494i
\(173\) 47.3070 + 12.6759i 0.273451 + 0.0732709i 0.392938 0.919565i \(-0.371459\pi\)
−0.119488 + 0.992836i \(0.538125\pi\)
\(174\) 0 0
\(175\) −9.19210 + 50.4161i −0.0525263 + 0.288092i
\(176\) 8.03291 13.9134i 0.0456415 0.0790534i
\(177\) 0 0
\(178\) 286.223 + 76.6933i 1.60800 + 0.430861i
\(179\) 183.712i 1.02632i −0.858292 0.513161i \(-0.828474\pi\)
0.858292 0.513161i \(-0.171526\pi\)
\(180\) 0 0
\(181\) −21.7276 −0.120042 −0.0600209 0.998197i \(-0.519117\pi\)
−0.0600209 + 0.998197i \(0.519117\pi\)
\(182\) −24.6679 + 92.0617i −0.135538 + 0.505834i
\(183\) 0 0
\(184\) 120.369 + 69.4949i 0.654178 + 0.377690i
\(185\) −197.815 182.324i −1.06927 0.985535i
\(186\) 0 0
\(187\) 3.24978 12.1284i 0.0173785 0.0648575i
\(188\) −116.520 + 116.520i −0.619787 + 0.619787i
\(189\) 0 0
\(190\) −317.666 71.3939i −1.67193 0.375757i
\(191\) 20.0454 + 34.7197i 0.104950 + 0.181778i 0.913718 0.406350i \(-0.133198\pi\)
−0.808768 + 0.588128i \(0.799865\pi\)
\(192\) 0 0
\(193\) 28.3909 + 105.956i 0.147103 + 0.548996i 0.999653 + 0.0263498i \(0.00838836\pi\)
−0.852550 + 0.522646i \(0.824945\pi\)
\(194\) 56.2435 + 32.4722i 0.289915 + 0.167382i
\(195\) 0 0
\(196\) −132.131 228.858i −0.674138 1.16764i
\(197\) −67.3031 67.3031i −0.341640 0.341640i 0.515344 0.856984i \(-0.327664\pi\)
−0.856984 + 0.515344i \(0.827664\pi\)
\(198\) 0 0
\(199\) 251.394i 1.26329i 0.775259 + 0.631643i \(0.217619\pi\)
−0.775259 + 0.631643i \(0.782381\pi\)
\(200\) 96.6747 113.862i 0.483374 0.569311i
\(201\) 0 0
\(202\) 527.644 141.382i 2.61210 0.699910i
\(203\) 0.452863 + 1.69011i 0.00223085 + 0.00832565i
\(204\) 0 0
\(205\) −66.6234 + 127.079i −0.324992 + 0.619900i
\(206\) 288.116 1.39862
\(207\) 0 0
\(208\) −50.1362 + 50.1362i −0.241040 + 0.241040i
\(209\) 60.0182 34.6515i 0.287168 0.165797i
\(210\) 0 0
\(211\) −132.394 + 229.313i −0.627459 + 1.08679i 0.360601 + 0.932720i \(0.382572\pi\)
−0.988060 + 0.154071i \(0.950762\pi\)
\(212\) −231.244 + 61.9618i −1.09078 + 0.292272i
\(213\) 0 0
\(214\) 18.2740 10.5505i 0.0853926 0.0493014i
\(215\) 155.192 + 34.8786i 0.721822 + 0.162226i
\(216\) 0 0
\(217\) 27.1010 + 27.1010i 0.124889 + 0.124889i
\(218\) −119.444 32.0050i −0.547910 0.146812i
\(219\) 0 0
\(220\) 4.02128 + 98.6809i 0.0182785 + 0.448549i
\(221\) −27.7071 + 47.9902i −0.125372 + 0.217150i
\(222\) 0 0
\(223\) 45.6650 + 12.2359i 0.204776 + 0.0548695i 0.359749 0.933049i \(-0.382862\pi\)
−0.154973 + 0.987919i \(0.549529\pi\)
\(224\) 79.9342i 0.356849i
\(225\) 0 0
\(226\) −63.8888 −0.282694
\(227\) −7.74928 + 28.9207i −0.0341378 + 0.127404i −0.980892 0.194554i \(-0.937674\pi\)
0.946754 + 0.321958i \(0.104341\pi\)
\(228\) 0 0
\(229\) 211.135 + 121.899i 0.921988 + 0.532310i 0.884269 0.466978i \(-0.154657\pi\)
0.0377192 + 0.999288i \(0.487991\pi\)
\(230\) 365.656 14.9006i 1.58981 0.0647852i
\(231\) 0 0
\(232\) 1.31993 4.92606i 0.00568936 0.0212330i
\(233\) 161.712 161.712i 0.694042 0.694042i −0.269077 0.963119i \(-0.586719\pi\)
0.963119 + 0.269077i \(0.0867186\pi\)
\(234\) 0 0
\(235\) −30.6265 + 136.272i −0.130326 + 0.579883i
\(236\) 330.149 + 571.834i 1.39894 + 2.42303i
\(237\) 0 0
\(238\) 6.25941 + 23.3604i 0.0263000 + 0.0981531i
\(239\) 282.499 + 163.101i 1.18201 + 0.682431i 0.956478 0.291806i \(-0.0942561\pi\)
0.225528 + 0.974237i \(0.427589\pi\)
\(240\) 0 0
\(241\) 66.7878 + 115.680i 0.277128 + 0.479999i 0.970670 0.240417i \(-0.0772842\pi\)
−0.693542 + 0.720416i \(0.743951\pi\)
\(242\) 244.250 + 244.250i 1.00930 + 1.00930i
\(243\) 0 0
\(244\) 555.040i 2.27475i
\(245\) −198.380 104.004i −0.809714 0.424505i
\(246\) 0 0
\(247\) −295.434 + 79.1612i −1.19609 + 0.320491i
\(248\) −28.9123 107.902i −0.116582 0.435089i
\(249\) 0 0
\(250\) 54.7304 389.456i 0.218922 1.55782i
\(251\) −404.742 −1.61252 −0.806260 0.591562i \(-0.798512\pi\)
−0.806260 + 0.591562i \(0.798512\pi\)
\(252\) 0 0
\(253\) −55.0806 + 55.0806i −0.217710 + 0.217710i
\(254\) 441.677 255.002i 1.73889 1.00395i
\(255\) 0 0
\(256\) 59.8837 103.722i 0.233921 0.405162i
\(257\) 121.900 32.6631i 0.474320 0.127094i −0.0137364 0.999906i \(-0.504373\pi\)
0.488057 + 0.872812i \(0.337706\pi\)
\(258\) 0 0
\(259\) −95.5164 + 55.1464i −0.368789 + 0.212921i
\(260\) 95.5755 425.262i 0.367598 1.63562i
\(261\) 0 0
\(262\) 58.1464 + 58.1464i 0.221933 + 0.221933i
\(263\) 466.967 + 125.123i 1.77554 + 0.475754i 0.989759 0.142751i \(-0.0455950\pi\)
0.785780 + 0.618506i \(0.212262\pi\)
\(264\) 0 0
\(265\) −137.524 + 149.208i −0.518957 + 0.563049i
\(266\) −66.7423 + 115.601i −0.250911 + 0.434591i
\(267\) 0 0
\(268\) −442.385 118.537i −1.65069 0.442301i
\(269\) 3.50052i 0.0130131i −0.999979 0.00650653i \(-0.997929\pi\)
0.999979 0.00650653i \(-0.00207111\pi\)
\(270\) 0 0
\(271\) −103.576 −0.382197 −0.191099 0.981571i \(-0.561205\pi\)
−0.191099 + 0.981571i \(0.561205\pi\)
\(272\) −4.65655 + 17.3785i −0.0171197 + 0.0638915i
\(273\) 0 0
\(274\) 56.3791 + 32.5505i 0.205763 + 0.118797i
\(275\) 47.6158 + 68.8505i 0.173148 + 0.250365i
\(276\) 0 0
\(277\) −104.504 + 390.013i −0.377270 + 1.40799i 0.472730 + 0.881208i \(0.343269\pi\)
−0.850000 + 0.526783i \(0.823398\pi\)
\(278\) 185.035 185.035i 0.665594 0.665594i
\(279\) 0 0
\(280\) −32.7526 51.7423i −0.116973 0.184794i
\(281\) −186.348 322.765i −0.663162 1.14863i −0.979780 0.200077i \(-0.935881\pi\)
0.316618 0.948553i \(-0.397453\pi\)
\(282\) 0 0
\(283\) −28.2542 105.446i −0.0998381 0.372601i 0.897870 0.440260i \(-0.145114\pi\)
−0.997709 + 0.0676591i \(0.978447\pi\)
\(284\) 347.389 + 200.565i 1.22320 + 0.706216i
\(285\) 0 0
\(286\) 77.8434 + 134.829i 0.272180 + 0.471429i
\(287\) 41.5959 + 41.5959i 0.144934 + 0.144934i
\(288\) 0 0
\(289\) 274.939i 0.951345i
\(290\) −4.00060 12.8180i −0.0137952 0.0442000i
\(291\) 0 0
\(292\) 320.616 85.9088i 1.09800 0.294208i
\(293\) −86.5889 323.154i −0.295525 1.10292i −0.940799 0.338964i \(-0.889923\pi\)
0.645274 0.763951i \(-0.276743\pi\)
\(294\) 0 0
\(295\) 495.681 + 259.869i 1.68028 + 0.880910i
\(296\) 321.464 1.08603
\(297\) 0 0
\(298\) 265.070 265.070i 0.889498 0.889498i
\(299\) 297.720 171.889i 0.995719 0.574879i
\(300\) 0 0
\(301\) 32.6061 56.4755i 0.108326 0.187626i
\(302\) −440.570 + 118.050i −1.45884 + 0.390896i
\(303\) 0 0
\(304\) −85.9990 + 49.6515i −0.282891 + 0.163327i
\(305\) 251.621 + 397.510i 0.824987 + 1.30331i
\(306\) 0 0
\(307\) 168.969 + 168.969i 0.550389 + 0.550389i 0.926553 0.376164i \(-0.122757\pi\)
−0.376164 + 0.926553i \(0.622757\pi\)
\(308\) 39.1108 + 10.4797i 0.126983 + 0.0340251i
\(309\) 0 0
\(310\) −216.275 199.339i −0.697662 0.643029i
\(311\) −177.151 + 306.835i −0.569617 + 0.986606i 0.426986 + 0.904258i \(0.359575\pi\)
−0.996604 + 0.0823482i \(0.973758\pi\)
\(312\) 0 0
\(313\) −208.146 55.7726i −0.665003 0.178187i −0.0895003 0.995987i \(-0.528527\pi\)
−0.575503 + 0.817800i \(0.695194\pi\)
\(314\) 227.576i 0.724763i
\(315\) 0 0
\(316\) −144.495 −0.457262
\(317\) −156.372 + 583.589i −0.493288 + 1.84097i 0.0461283 + 0.998936i \(0.485312\pi\)
−0.539416 + 0.842039i \(0.681355\pi\)
\(318\) 0 0
\(319\) 2.47524 + 1.42908i 0.00775937 + 0.00447987i
\(320\) −21.0698 517.045i −0.0658430 1.61577i
\(321\) 0 0
\(322\) 38.8319 144.923i 0.120596 0.450071i
\(323\) −54.8786 + 54.8786i −0.169903 + 0.169903i
\(324\) 0 0
\(325\) −124.338 347.893i −0.382579 1.07044i
\(326\) 421.353 + 729.805i 1.29249 + 2.23867i
\(327\) 0 0
\(328\) −44.3759 165.613i −0.135292 0.504918i
\(329\) 49.5906 + 28.6311i 0.150731 + 0.0870247i
\(330\) 0 0
\(331\) −244.712 423.853i −0.739310 1.28052i −0.952806 0.303579i \(-0.901818\pi\)
0.213496 0.976944i \(-0.431515\pi\)
\(332\) −124.742 124.742i −0.375730 0.375730i
\(333\) 0 0
\(334\) 431.757i 1.29269i
\(335\) −370.565 + 115.656i −1.10616 + 0.345242i
\(336\) 0 0
\(337\) −399.141 + 106.950i −1.18440 + 0.317358i −0.796669 0.604416i \(-0.793406\pi\)
−0.387727 + 0.921774i \(0.626740\pi\)
\(338\) −40.2138 150.080i −0.118976 0.444023i
\(339\) 0 0
\(340\) −32.9517 105.578i −0.0969168 0.310524i
\(341\) 62.6061 0.183596
\(342\) 0 0
\(343\) −135.959 + 135.959i −0.396382 + 0.396382i
\(344\) −164.606 + 95.0352i −0.478505 + 0.276265i
\(345\) 0 0
\(346\) −77.0454 + 133.447i −0.222675 + 0.385684i
\(347\) −437.196 + 117.146i −1.25993 + 0.337598i −0.826166 0.563428i \(-0.809482\pi\)
−0.433767 + 0.901025i \(0.642816\pi\)
\(348\) 0 0
\(349\) 497.107 287.005i 1.42437 0.822363i 0.427705 0.903918i \(-0.359322\pi\)
0.996669 + 0.0815556i \(0.0259888\pi\)
\(350\) −145.732 68.9898i −0.416378 0.197114i
\(351\) 0 0
\(352\) 92.3281 + 92.3281i 0.262296 + 0.262296i
\(353\) −364.073 97.5531i −1.03137 0.276354i −0.296836 0.954928i \(-0.595932\pi\)
−0.734532 + 0.678574i \(0.762598\pi\)
\(354\) 0 0
\(355\) 339.718 13.8436i 0.956952 0.0389961i
\(356\) −277.788 + 481.143i −0.780303 + 1.35152i
\(357\) 0 0
\(358\) 558.311 + 149.599i 1.55953 + 0.417874i
\(359\) 216.272i 0.602430i −0.953556 0.301215i \(-0.902608\pi\)
0.953556 0.301215i \(-0.0973922\pi\)
\(360\) 0 0
\(361\) −67.3633 −0.186602
\(362\) 17.6930 66.0313i 0.0488758 0.182407i
\(363\) 0 0
\(364\) −154.756 89.3485i −0.425154 0.245463i
\(365\) 190.674 206.874i 0.522394 0.566778i
\(366\) 0 0
\(367\) −88.0327 + 328.542i −0.239871 + 0.895211i 0.736021 + 0.676958i \(0.236702\pi\)
−0.975892 + 0.218252i \(0.929964\pi\)
\(368\) 78.9240 78.9240i 0.214467 0.214467i
\(369\) 0 0
\(370\) 715.176 452.702i 1.93291 1.22352i
\(371\) 41.5959 + 72.0462i 0.112118 + 0.194195i
\(372\) 0 0
\(373\) −120.864 451.071i −0.324032 1.20930i −0.915281 0.402816i \(-0.868032\pi\)
0.591249 0.806489i \(-0.298635\pi\)
\(374\) 34.2124 + 19.7526i 0.0914771 + 0.0528143i
\(375\) 0 0
\(376\) −83.4495 144.539i −0.221940 0.384412i
\(377\) −8.91939 8.91939i −0.0236589 0.0236589i
\(378\) 0 0
\(379\) 210.000i 0.554090i −0.960857 0.277045i \(-0.910645\pi\)
0.960857 0.277045i \(-0.0893551\pi\)
\(380\) 283.448 540.658i 0.745917 1.42278i
\(381\) 0 0
\(382\) −121.838 + 32.6465i −0.318948 + 0.0854620i
\(383\) 62.4553 + 233.086i 0.163069 + 0.608581i 0.998279 + 0.0586495i \(0.0186794\pi\)
−0.835210 + 0.549931i \(0.814654\pi\)
\(384\) 0 0
\(385\) 32.7614 10.2251i 0.0850944 0.0265586i
\(386\) −345.126 −0.894109
\(387\) 0 0
\(388\) −86.1010 + 86.1010i −0.221910 + 0.221910i
\(389\) 474.008 273.669i 1.21853 0.703518i 0.253926 0.967224i \(-0.418278\pi\)
0.964603 + 0.263705i \(0.0849446\pi\)
\(390\) 0 0
\(391\) 43.6163 75.5457i 0.111551 0.193212i
\(392\) 258.534 69.2739i 0.659525 0.176719i
\(393\) 0 0
\(394\) 259.344 149.732i 0.658233 0.380031i
\(395\) −103.485 + 65.5051i −0.261987 + 0.165836i
\(396\) 0 0
\(397\) 45.2577 + 45.2577i 0.113999 + 0.113999i 0.761805 0.647806i \(-0.224313\pi\)
−0.647806 + 0.761805i \(0.724313\pi\)
\(398\) −764.001 204.713i −1.91960 0.514355i
\(399\) 0 0
\(400\) −68.2278 98.6546i −0.170569 0.246636i
\(401\) 260.151 450.595i 0.648756 1.12368i −0.334665 0.942337i \(-0.608623\pi\)
0.983420 0.181340i \(-0.0580436\pi\)
\(402\) 0 0
\(403\) −266.885 71.5117i −0.662246 0.177448i
\(404\) 1024.19i 2.53511i
\(405\) 0 0
\(406\) −5.50510 −0.0135594
\(407\) −46.6294 + 174.023i −0.114569 + 0.427576i
\(408\) 0 0
\(409\) −300.606 173.555i −0.734979 0.424340i 0.0852621 0.996359i \(-0.472827\pi\)
−0.820241 + 0.572018i \(0.806161\pi\)
\(410\) −331.950 305.955i −0.809633 0.746231i
\(411\) 0 0
\(412\) −139.812 + 521.786i −0.339350 + 1.26647i
\(413\) 162.247 162.247i 0.392851 0.392851i
\(414\) 0 0
\(415\) −145.889 32.7878i −0.351539 0.0790066i
\(416\) −288.126 499.049i −0.692611 1.19964i
\(417\) 0 0
\(418\) 56.4344 + 210.616i 0.135011 + 0.503866i
\(419\) 505.238 + 291.699i 1.20582 + 0.696180i 0.961843 0.273602i \(-0.0882151\pi\)
0.243975 + 0.969781i \(0.421548\pi\)
\(420\) 0 0
\(421\) −106.576 184.594i −0.253148 0.438466i 0.711243 0.702947i \(-0.248133\pi\)
−0.964391 + 0.264481i \(0.914799\pi\)
\(422\) −589.085 589.085i −1.39594 1.39594i
\(423\) 0 0
\(424\) 242.474i 0.571874i
\(425\) −71.4621 60.6749i −0.168146 0.142764i
\(426\) 0 0
\(427\) 186.304 49.9199i 0.436308 0.116908i
\(428\) 10.2396 + 38.2146i 0.0239242 + 0.0892864i
\(429\) 0 0
\(430\) −232.373 + 443.235i −0.540402 + 1.03078i
\(431\) 187.364 0.434720 0.217360 0.976092i \(-0.430255\pi\)
0.217360 + 0.976092i \(0.430255\pi\)
\(432\) 0 0
\(433\) 154.848 154.848i 0.357617 0.357617i −0.505317 0.862934i \(-0.668624\pi\)
0.862934 + 0.505317i \(0.168624\pi\)
\(434\) −104.430 + 60.2929i −0.240623 + 0.138924i
\(435\) 0 0
\(436\) 115.924 200.786i 0.265881 0.460519i
\(437\) 465.069 124.615i 1.06423 0.285160i
\(438\) 0 0
\(439\) −219.043 + 126.464i −0.498958 + 0.288074i −0.728283 0.685276i \(-0.759681\pi\)
0.229325 + 0.973350i \(0.426348\pi\)
\(440\) −97.5959 21.9342i −0.221809 0.0498504i
\(441\) 0 0
\(442\) −123.283 123.283i −0.278920 0.278920i
\(443\) 575.275 + 154.144i 1.29859 + 0.347956i 0.840917 0.541165i \(-0.182016\pi\)
0.457673 + 0.889121i \(0.348683\pi\)
\(444\) 0 0
\(445\) 19.1737 + 470.518i 0.0430871 + 1.05734i
\(446\) −74.3712 + 128.815i −0.166752 + 0.288822i
\(447\) 0 0
\(448\) −204.924 54.9092i −0.457420 0.122565i
\(449\) 297.909i 0.663495i 0.943368 + 0.331747i \(0.107638\pi\)
−0.943368 + 0.331747i \(0.892362\pi\)
\(450\) 0 0
\(451\) 96.0908 0.213062
\(452\) 31.0029 115.704i 0.0685905 0.255983i
\(453\) 0 0
\(454\) −81.5814 47.1010i −0.179695 0.103747i
\(455\) −151.339 + 6.16710i −0.332612 + 0.0135541i
\(456\) 0 0
\(457\) 104.591 390.338i 0.228864 0.854130i −0.751956 0.659213i \(-0.770890\pi\)
0.980820 0.194917i \(-0.0624438\pi\)
\(458\) −542.388 + 542.388i −1.18425 + 1.18425i
\(459\) 0 0
\(460\) −150.454 + 669.444i −0.327074 + 1.45531i
\(461\) −263.310 456.066i −0.571171 0.989298i −0.996446 0.0842333i \(-0.973156\pi\)
0.425275 0.905064i \(-0.360177\pi\)
\(462\) 0 0
\(463\) 122.875 + 458.577i 0.265389 + 0.990447i 0.962012 + 0.273009i \(0.0880187\pi\)
−0.696622 + 0.717438i \(0.745315\pi\)
\(464\) −3.54672 2.04770i −0.00764380 0.00441315i
\(465\) 0 0
\(466\) 359.767 + 623.135i 0.772033 + 1.33720i
\(467\) 488.742 + 488.742i 1.04656 + 1.04656i 0.998862 + 0.0476956i \(0.0151877\pi\)
0.0476956 + 0.998862i \(0.484812\pi\)
\(468\) 0 0
\(469\) 159.151i 0.339341i
\(470\) −389.200 204.044i −0.828086 0.434137i
\(471\) 0 0
\(472\) −645.984 + 173.091i −1.36861 + 0.366718i
\(473\) −27.5703 102.894i −0.0582882 0.217534i
\(474\) 0 0
\(475\) −42.1004 515.708i −0.0886325 1.08570i
\(476\) −45.3439 −0.0952603
\(477\) 0 0
\(478\) −725.716 + 725.716i −1.51823 + 1.51823i
\(479\) −160.171 + 92.4745i −0.334385 + 0.193057i −0.657786 0.753205i \(-0.728507\pi\)
0.323401 + 0.946262i \(0.395174\pi\)
\(480\) 0 0
\(481\) 397.555 688.586i 0.826518 1.43157i
\(482\) −405.944 + 108.772i −0.842207 + 0.225669i
\(483\) 0 0
\(484\) −560.869 + 323.818i −1.15882 + 0.669045i
\(485\) −22.6311 + 100.697i −0.0466621 + 0.207623i
\(486\) 0 0
\(487\) −120.682 120.682i −0.247807 0.247807i 0.572263 0.820070i \(-0.306066\pi\)
−0.820070 + 0.572263i \(0.806066\pi\)
\(488\) −543.008 145.499i −1.11272 0.298153i
\(489\) 0 0
\(490\) 477.617 518.197i 0.974729 1.05754i
\(491\) 52.8411 91.5234i 0.107619 0.186402i −0.807186 0.590297i \(-0.799011\pi\)
0.914805 + 0.403895i \(0.132344\pi\)
\(492\) 0 0
\(493\) −3.09169 0.828415i −0.00627117 0.00168035i
\(494\) 962.302i 1.94798i
\(495\) 0 0
\(496\) −89.7071 −0.180861
\(497\) 36.0774 134.643i 0.0725904 0.270911i
\(498\) 0 0
\(499\) 640.499 + 369.792i 1.28357 + 0.741067i 0.977498 0.210943i \(-0.0676535\pi\)
0.306067 + 0.952010i \(0.400987\pi\)
\(500\) 678.758 + 288.107i 1.35752 + 0.576215i
\(501\) 0 0
\(502\) 329.587 1230.04i 0.656548 2.45027i
\(503\) −406.409 + 406.409i −0.807970 + 0.807970i −0.984326 0.176357i \(-0.943569\pi\)
0.176357 + 0.984326i \(0.443569\pi\)
\(504\) 0 0
\(505\) 464.303 + 733.504i 0.919412 + 1.45248i
\(506\) −122.540 212.246i −0.242175 0.419459i
\(507\) 0 0
\(508\) 247.487 + 923.633i 0.487179 + 1.81818i
\(509\) −168.451 97.2554i −0.330945 0.191071i 0.325315 0.945606i \(-0.394530\pi\)
−0.656261 + 0.754534i \(0.727863\pi\)
\(510\) 0 0
\(511\) −57.6719 99.8907i −0.112861 0.195481i
\(512\) −213.376 213.376i −0.416750 0.416750i
\(513\) 0 0
\(514\) 397.060i 0.772491i
\(515\) 136.415 + 437.076i 0.264883 + 0.848692i
\(516\) 0 0
\(517\) 90.3500 24.2092i 0.174758 0.0468263i
\(518\) −89.8129 335.186i −0.173384 0.647078i
\(519\) 0 0
\(520\) 390.990 + 204.982i 0.751903 + 0.394197i
\(521\) −589.605 −1.13168 −0.565840 0.824515i \(-0.691448\pi\)
−0.565840 + 0.824515i \(0.691448\pi\)
\(522\) 0 0
\(523\) −141.546 + 141.546i −0.270642 + 0.270642i −0.829359 0.558716i \(-0.811294\pi\)
0.558716 + 0.829359i \(0.311294\pi\)
\(524\) −133.521 + 77.0885i −0.254812 + 0.147115i
\(525\) 0 0
\(526\) −760.514 + 1317.25i −1.44584 + 2.50428i
\(527\) −67.7214 + 18.1459i −0.128504 + 0.0344324i
\(528\) 0 0
\(529\) −10.5408 + 6.08571i −0.0199258 + 0.0115042i
\(530\) −341.464 539.444i −0.644272 1.01782i
\(531\) 0 0
\(532\) −176.969 176.969i −0.332649 0.332649i
\(533\) −409.628 109.759i −0.768532 0.205928i
\(534\) 0 0
\(535\) 24.6575 + 22.7266i 0.0460888 + 0.0424796i
\(536\) 231.934 401.722i 0.432713 0.749481i
\(537\) 0 0
\(538\) 10.6383 + 2.85052i 0.0197737 + 0.00529836i
\(539\) 150.005i 0.278302i
\(540\) 0 0
\(541\) 431.303 0.797233 0.398617 0.917118i \(-0.369490\pi\)
0.398617 + 0.917118i \(0.369490\pi\)
\(542\) 84.3429 314.772i 0.155614 0.580760i
\(543\) 0 0
\(544\) −126.632 73.1112i −0.232780 0.134396i
\(545\) −8.00142 196.352i −0.0146815 0.360280i
\(546\) 0 0
\(547\) −163.329 + 609.551i −0.298590 + 1.11435i 0.639734 + 0.768596i \(0.279044\pi\)
−0.938324 + 0.345757i \(0.887622\pi\)
\(548\) −86.3087 + 86.3087i −0.157498 + 0.157498i
\(549\) 0 0
\(550\) −248.015 + 88.6413i −0.450936 + 0.161166i
\(551\) −8.83316 15.2995i −0.0160311 0.0277668i
\(552\) 0 0
\(553\) 12.9958 + 48.5009i 0.0235005 + 0.0877050i
\(554\) −1100.17 635.186i −1.98588 1.14655i
\(555\) 0 0
\(556\) 245.313 + 424.895i 0.441211 + 0.764200i
\(557\) 214.091 + 214.091i 0.384364 + 0.384364i 0.872672 0.488308i \(-0.162386\pi\)
−0.488308 + 0.872672i \(0.662386\pi\)
\(558\) 0 0
\(559\) 470.120i 0.841003i
\(560\) −46.9431 + 14.6513i −0.0838270 + 0.0261630i
\(561\) 0 0
\(562\) 1132.65 303.492i 2.01539 0.540021i
\(563\) 245.972 + 917.982i 0.436896 + 1.63052i 0.736488 + 0.676451i \(0.236483\pi\)
−0.299592 + 0.954067i \(0.596851\pi\)
\(564\) 0 0
\(565\) −30.2495 96.9203i −0.0535390 0.171540i
\(566\) 343.464 0.606827
\(567\) 0 0
\(568\) −287.283 + 287.283i −0.505779 + 0.505779i
\(569\) −841.916 + 486.081i −1.47964 + 0.854272i −0.999734 0.0230473i \(-0.992663\pi\)
−0.479908 + 0.877319i \(0.659330\pi\)
\(570\) 0 0
\(571\) 462.015 800.233i 0.809133 1.40146i −0.104333 0.994542i \(-0.533271\pi\)
0.913465 0.406917i \(-0.133396\pi\)
\(572\) −281.953 + 75.5491i −0.492925 + 0.132079i
\(573\) 0 0
\(574\) −160.285 + 92.5403i −0.279241 + 0.161220i
\(575\) 195.732 + 547.650i 0.340404 + 0.952436i
\(576\) 0 0
\(577\) −497.879 497.879i −0.862874 0.862874i 0.128797 0.991671i \(-0.458889\pi\)
−0.991671 + 0.128797i \(0.958889\pi\)
\(578\) 835.555 + 223.886i 1.44560 + 0.387346i
\(579\) 0 0
\(580\) 25.1551 1.02508i 0.0433709 0.00176738i
\(581\) −30.6515 + 53.0900i −0.0527565 + 0.0913770i
\(582\) 0 0
\(583\) 131.262 + 35.1717i 0.225150 + 0.0603288i
\(584\) 336.186i 0.575661i
\(585\) 0 0
\(586\) 1052.59 1.79624
\(587\) 107.166 399.949i 0.182566 0.681345i −0.812573 0.582860i \(-0.801934\pi\)
0.995139 0.0984849i \(-0.0313996\pi\)
\(588\) 0 0
\(589\) −335.125 193.485i −0.568973 0.328497i
\(590\) −1193.40 + 1294.79i −2.02270 + 2.19456i
\(591\) 0 0
\(592\) 66.8144 249.355i 0.112862 0.421207i
\(593\) 451.258 451.258i 0.760974 0.760974i −0.215524 0.976498i \(-0.569146\pi\)
0.976498 + 0.215524i \(0.0691461\pi\)
\(594\) 0 0
\(595\) −32.4745 + 20.5561i −0.0545790 + 0.0345481i
\(596\) 351.421 + 608.679i 0.589633 + 1.02127i
\(597\) 0 0
\(598\) 279.943 + 1044.76i 0.468131 + 1.74709i
\(599\) −28.4560 16.4291i −0.0475058 0.0274275i 0.476059 0.879413i \(-0.342065\pi\)
−0.523565 + 0.851986i \(0.675398\pi\)
\(600\) 0 0
\(601\) 92.2418 + 159.768i 0.153481 + 0.265836i 0.932505 0.361158i \(-0.117618\pi\)
−0.779024 + 0.626994i \(0.784285\pi\)
\(602\) 145.081 + 145.081i 0.240998 + 0.240998i
\(603\) 0 0
\(604\) 855.171i 1.41585i
\(605\) −254.885 + 486.176i −0.421298 + 0.803597i
\(606\) 0 0
\(607\) −186.311 + 49.9219i −0.306938 + 0.0822437i −0.409000 0.912534i \(-0.634122\pi\)
0.102062 + 0.994778i \(0.467456\pi\)
\(608\) −208.884 779.565i −0.343559 1.28218i
\(609\) 0 0
\(610\) −1412.95 + 440.993i −2.31632 + 0.722940i
\(611\) −412.808 −0.675627
\(612\) 0 0
\(613\) −12.7128 + 12.7128i −0.0207386 + 0.0207386i −0.717400 0.696661i \(-0.754668\pi\)
0.696661 + 0.717400i \(0.254668\pi\)
\(614\) −651.102 + 375.914i −1.06043 + 0.612237i
\(615\) 0 0
\(616\) −20.5051 + 35.5159i −0.0332875 + 0.0576556i
\(617\) 544.705 145.953i 0.882828 0.236553i 0.211201 0.977443i \(-0.432263\pi\)
0.671627 + 0.740890i \(0.265596\pi\)
\(618\) 0 0
\(619\) 709.388 409.565i 1.14602 0.661656i 0.198108 0.980180i \(-0.436520\pi\)
0.947915 + 0.318524i \(0.103187\pi\)
\(620\) 465.959 294.949i 0.751547 0.475724i
\(621\) 0 0
\(622\) −788.232 788.232i −1.26725 1.26725i
\(623\) 186.483 + 49.9681i 0.299331 + 0.0802056i
\(624\) 0 0
\(625\) 616.725 101.370i 0.986759 0.162192i
\(626\) 338.992 587.152i 0.541521 0.937942i
\(627\) 0 0
\(628\) 412.146 + 110.434i 0.656283 + 0.175851i
\(629\) 201.757i 0.320759i
\(630\) 0 0
\(631\) 105.485 0.167171 0.0835853 0.996501i \(-0.473363\pi\)
0.0835853 + 0.996501i \(0.473363\pi\)
\(632\) 37.8780 141.363i 0.0599336 0.223675i
\(633\) 0 0
\(634\) −1646.23 950.448i −2.59657 1.49913i
\(635\) 595.964 + 549.294i 0.938526 + 0.865031i
\(636\) 0 0
\(637\) 171.342 639.458i 0.268983 1.00386i
\(638\) −6.35867 + 6.35867i −0.00996657 + 0.00996657i
\(639\) 0 0
\(640\) 827.580 + 185.994i 1.29309 + 0.290616i
\(641\) −82.3939 142.710i −0.128540 0.222637i 0.794571 0.607171i \(-0.207696\pi\)
−0.923111 + 0.384534i \(0.874362\pi\)
\(642\) 0 0
\(643\) −279.780 1044.15i −0.435116 1.62388i −0.740788 0.671739i \(-0.765548\pi\)
0.305672 0.952137i \(-0.401119\pi\)
\(644\) 243.616 + 140.652i 0.378285 + 0.218403i
\(645\) 0 0
\(646\) −122.091 211.467i −0.188995 0.327349i
\(647\) 321.287 + 321.287i 0.496580 + 0.496580i 0.910372 0.413792i \(-0.135796\pi\)
−0.413792 + 0.910372i \(0.635796\pi\)
\(648\) 0 0
\(649\) 374.808i 0.577516i
\(650\) 1158.52 94.5771i 1.78234 0.145503i
\(651\) 0 0
\(652\) −1526.17 + 408.935i −2.34074 + 0.627201i
\(653\) −62.1595 231.982i −0.0951907 0.355256i 0.901858 0.432033i \(-0.142204\pi\)
−0.997048 + 0.0767769i \(0.975537\pi\)
\(654\) 0 0
\(655\) −60.6784 + 115.740i −0.0926387 + 0.176702i
\(656\) −137.687 −0.209888
\(657\) 0 0
\(658\) −127.394 + 127.394i −0.193608 + 0.193608i
\(659\) 830.313 479.381i 1.25996 0.727438i 0.286893 0.957963i \(-0.407378\pi\)
0.973066 + 0.230525i \(0.0740444\pi\)
\(660\) 0 0
\(661\) −198.196 + 343.286i −0.299843 + 0.519344i −0.976100 0.217322i \(-0.930268\pi\)
0.676257 + 0.736666i \(0.263601\pi\)
\(662\) 1487.39 398.544i 2.24681 0.602030i
\(663\) 0 0
\(664\) 154.738 89.3383i 0.233040 0.134546i
\(665\) −206.969 46.5153i −0.311232 0.0699478i
\(666\) 0 0
\(667\) 14.0408 + 14.0408i 0.0210507 + 0.0210507i
\(668\) 781.925 + 209.516i 1.17055 + 0.313647i
\(669\) 0 0
\(670\) −49.7296 1220.35i −0.0742233 1.82142i
\(671\) 157.530 272.850i 0.234769 0.406632i
\(672\) 0 0
\(673\) −224.994 60.2870i −0.334315 0.0895795i 0.0877564 0.996142i \(-0.472030\pi\)
−0.422072 + 0.906562i \(0.638697\pi\)
\(674\) 1300.10i 1.92894i
\(675\) 0 0
\(676\) 291.313 0.430937
\(677\) 199.260 743.648i 0.294328 1.09845i −0.647422 0.762132i \(-0.724153\pi\)
0.941750 0.336315i \(-0.109181\pi\)
\(678\) 0 0
\(679\) 36.6444 + 21.1566i 0.0539681 + 0.0311585i
\(680\) 111.928 4.56108i 0.164599 0.00670747i
\(681\) 0 0
\(682\) −50.9810 + 190.264i −0.0747522 + 0.278979i
\(683\) 786.590 786.590i 1.15167 1.15167i 0.165452 0.986218i \(-0.447092\pi\)
0.986218 0.165452i \(-0.0529082\pi\)
\(684\) 0 0
\(685\) −22.6857 + 100.940i −0.0331178 + 0.147357i
\(686\) −302.474 523.901i −0.440925 0.763704i
\(687\) 0 0
\(688\) 39.5050 + 147.435i 0.0574200 + 0.214294i
\(689\) −519.387 299.868i −0.753828 0.435223i
\(690\) 0 0
\(691\) −178.439 309.066i −0.258233 0.447273i 0.707535 0.706678i \(-0.249807\pi\)
−0.965769 + 0.259405i \(0.916474\pi\)
\(692\) −204.288 204.288i −0.295214 0.295214i
\(693\) 0 0
\(694\) 1424.06i 2.05196i
\(695\) 368.310 + 193.092i 0.529943 + 0.277831i
\(696\) 0 0
\(697\) −103.942 + 27.8512i −0.149128 + 0.0399586i
\(698\) 467.423 + 1744.45i 0.669661 + 2.49921i
\(699\) 0 0
\(700\) 195.661 230.447i 0.279516 0.329210i
\(701\) 885.680 1.26345 0.631726 0.775192i \(-0.282347\pi\)
0.631726 + 0.775192i \(0.282347\pi\)
\(702\) 0 0
\(703\) 787.423 787.423i 1.12009 1.12009i
\(704\) −300.121 + 173.275i −0.426308 + 0.246129i
\(705\) 0 0
\(706\) 592.939 1027.00i 0.839857 1.45467i
\(707\) 343.776 92.1146i 0.486247 0.130289i
\(708\) 0 0
\(709\) −633.107 + 365.524i −0.892958 + 0.515549i −0.874909 0.484288i \(-0.839079\pi\)
−0.0180489 + 0.999837i \(0.505745\pi\)
\(710\) −234.565 + 1043.70i −0.330374 + 1.46999i
\(711\) 0 0
\(712\) −397.893 397.893i −0.558839 0.558839i
\(713\) 420.128 + 112.573i 0.589240 + 0.157886i
\(714\) 0 0
\(715\) −167.681 + 181.927i −0.234518 + 0.254444i
\(716\) −541.856 + 938.522i −0.756782 + 1.31078i
\(717\) 0 0
\(718\) 657.265 + 176.113i 0.915410 + 0.245283i
\(719\) 629.271i 0.875204i 0.899169 + 0.437602i \(0.144172\pi\)
−0.899169 + 0.437602i \(0.855828\pi\)
\(720\) 0 0
\(721\) 187.716 0.260356
\(722\) 54.8548 204.721i 0.0759762 0.283547i
\(723\) 0 0
\(724\) 110.999 + 64.0852i 0.153313 + 0.0885155i
\(725\) 17.5510 12.1379i 0.0242082 0.0167420i
\(726\) 0 0
\(727\) −5.81028 + 21.6843i −0.00799213 + 0.0298270i −0.969807 0.243875i \(-0.921581\pi\)
0.961815 + 0.273702i \(0.0882481\pi\)
\(728\) 127.980 127.980i 0.175796 0.175796i
\(729\) 0 0
\(730\) 473.434 + 747.929i 0.648539 + 1.02456i
\(731\) 59.6459 + 103.310i 0.0815950 + 0.141327i
\(732\) 0 0
\(733\) −143.935 537.172i −0.196364 0.732840i −0.991910 0.126947i \(-0.959482\pi\)
0.795546 0.605894i \(-0.207184\pi\)
\(734\) −926.773 535.073i −1.26263 0.728982i
\(735\) 0 0
\(736\) 453.565 + 785.598i 0.616257 + 1.06739i
\(737\) 183.828 + 183.828i 0.249427 + 0.249427i
\(738\) 0 0
\(739\) 192.334i 0.260262i −0.991497 0.130131i \(-0.958460\pi\)
0.991497 0.130131i \(-0.0415398\pi\)
\(740\) 472.807 + 1514.88i 0.638928 + 2.04714i
\(741\) 0 0
\(742\) −252.825 + 67.7442i −0.340734 + 0.0912995i
\(743\) −16.3619 61.0634i −0.0220214 0.0821850i 0.954041 0.299677i \(-0.0968790\pi\)
−0.976062 + 0.217492i \(0.930212\pi\)
\(744\) 0 0
\(745\) 527.619 + 276.613i 0.708214 + 0.371292i
\(746\) 1469.25 1.96951
\(747\) 0 0
\(748\) −52.3745 + 52.3745i −0.0700194 + 0.0700194i
\(749\) 11.9061 6.87398i 0.0158960 0.00917755i
\(750\) 0 0
\(751\) −113.893 + 197.269i −0.151656 + 0.262675i −0.931836 0.362879i \(-0.881794\pi\)
0.780181 + 0.625554i \(0.215127\pi\)
\(752\) −129.461 + 34.6889i −0.172155 + 0.0461289i
\(753\) 0 0
\(754\) 34.3697 19.8434i 0.0455832 0.0263175i
\(755\) −387.682 612.459i −0.513486 0.811204i
\(756\) 0 0
\(757\) −235.925 235.925i −0.311658 0.311658i 0.533894 0.845552i \(-0.320728\pi\)
−0.845552 + 0.533894i \(0.820728\pi\)
\(758\) 638.202 + 171.006i 0.841955 + 0.225601i
\(759\) 0 0
\(760\) 454.635 + 419.033i 0.598204 + 0.551359i
\(761\) 440.621 763.178i 0.579003 1.00286i −0.416592 0.909094i \(-0.636775\pi\)
0.995594 0.0937680i \(-0.0298912\pi\)
\(762\) 0 0
\(763\) −77.8216 20.8522i −0.101994 0.0273293i
\(764\) 236.495i 0.309548i
\(765\) 0 0
\(766\) −759.221 −0.991151
\(767\) −428.123 + 1597.78i −0.558179 + 2.08315i
\(768\) 0 0
\(769\) 1046.51 + 604.201i 1.36087 + 0.785697i 0.989739 0.142885i \(-0.0456378\pi\)
0.371128 + 0.928582i \(0.378971\pi\)
\(770\) 4.39655 + 107.890i 0.00570981 + 0.140117i
\(771\) 0 0
\(772\) 167.477 625.033i 0.216939 0.809629i
\(773\) −815.226 + 815.226i −1.05463 + 1.05463i −0.0562070 + 0.998419i \(0.517901\pi\)
−0.998419 + 0.0562070i \(0.982099\pi\)
\(774\) 0 0
\(775\) 200.000 422.474i 0.258065 0.545128i
\(776\) −61.6640 106.805i −0.0794640 0.137636i
\(777\) 0 0
\(778\) 445.704 + 1663.39i 0.572884 + 2.13803i
\(779\) −514.366 296.969i −0.660290 0.381219i
\(780\) 0 0
\(781\) −113.848 197.190i −0.145772 0.252485i
\(782\) 194.070 + 194.070i 0.248172 + 0.248172i
\(783\) 0 0
\(784\) 214.939i 0.274157i
\(785\) 345.236 107.751i 0.439791 0.137262i
\(786\) 0 0
\(787\) −1110.59 + 297.582i −1.41117 + 0.378122i −0.882343 0.470606i \(-0.844035\pi\)
−0.528829 + 0.848728i \(0.677369\pi\)
\(788\) 145.319 + 542.339i 0.184415 + 0.688247i
\(789\) 0 0
\(790\) −114.805 367.838i −0.145323 0.465617i
\(791\) −41.6255 −0.0526239
\(792\) 0 0
\(793\) −983.201 + 983.201i −1.23985 + 1.23985i
\(794\) −174.395 + 100.687i −0.219640 + 0.126809i
\(795\) 0 0
\(796\) 741.484 1284.29i 0.931512 1.61343i
\(797\) −425.130 + 113.913i −0.533413 + 0.142928i −0.515464 0.856911i \(-0.672380\pi\)
−0.0179491 + 0.999839i \(0.505714\pi\)
\(798\) 0 0
\(799\) −90.7153 + 52.3745i −0.113536 + 0.0655501i
\(800\) 917.991 328.093i 1.14749 0.410116i
\(801\) 0 0
\(802\) 1157.54 + 1157.54i 1.44332 + 1.44332i
\(803\) −181.993 48.7649i −0.226641 0.0607283i
\(804\) 0 0
\(805\) 238.236 9.70819i 0.295945 0.0120599i
\(806\) 434.656 752.846i 0.539276 0.934053i
\(807\) 0 0
\(808\) −1001.99 268.481i −1.24008 0.332279i
\(809\) 150.000i 0.185414i −0.995693 0.0927070i \(-0.970448\pi\)
0.995693 0.0927070i \(-0.0295520\pi\)
\(810\) 0 0
\(811\) −132.847 −0.163806 −0.0819032 0.996640i \(-0.526100\pi\)
−0.0819032 + 0.996640i \(0.526100\pi\)
\(812\) 2.67143 9.96990i 0.00328993 0.0122782i
\(813\) 0 0
\(814\) −490.896 283.419i −0.603066 0.348180i
\(815\) −907.627 + 984.741i −1.11365 + 1.20827i
\(816\) 0 0
\(817\) −170.412 + 635.988i −0.208583 + 0.778443i
\(818\) 772.232 772.232i 0.944048 0.944048i
\(819\) 0 0
\(820\) 715.176 452.702i 0.872166 0.552075i
\(821\) −254.947 441.581i −0.310532 0.537857i 0.667946 0.744210i \(-0.267174\pi\)
−0.978478 + 0.206353i \(0.933840\pi\)
\(822\) 0 0
\(823\) 109.943 + 410.312i 0.133588 + 0.498556i 1.00000 0.000773801i \(-0.000246309\pi\)
−0.866412 + 0.499330i \(0.833580\pi\)
\(824\) −473.825 273.563i −0.575030 0.331994i
\(825\) 0 0
\(826\) 360.959 + 625.200i 0.436997 + 0.756900i
\(827\) −1030.76 1030.76i −1.24638 1.24638i −0.957307 0.289073i \(-0.906653\pi\)
−0.289073 0.957307i \(-0.593347\pi\)
\(828\) 0 0
\(829\) 37.4235i 0.0451429i 0.999745 + 0.0225714i \(0.00718533\pi\)
−0.999745 + 0.0225714i \(0.992815\pi\)
\(830\) 218.443 416.665i 0.263184 0.502006i
\(831\) 0 0
\(832\) 1477.31 395.845i 1.77562 0.475775i
\(833\) −43.4777 162.261i −0.0521941 0.194791i
\(834\) 0 0
\(835\) 654.982 204.425i 0.784410 0.244820i
\(836\) −408.817 −0.489016
\(837\) 0 0
\(838\) −1297.91 + 1297.91i −1.54882 + 1.54882i
\(839\) −997.984 + 576.186i −1.18949 + 0.686754i −0.958191 0.286129i \(-0.907631\pi\)
−0.231301 + 0.972882i \(0.574298\pi\)
\(840\) 0 0
\(841\) −420.136 + 727.696i −0.499567 + 0.865275i
\(842\) 647.778 173.572i 0.769333 0.206142i
\(843\) 0 0
\(844\) 1352.71 780.989i 1.60274 0.925342i
\(845\) 208.633 132.064i 0.246903 0.156288i
\(846\) 0 0
\(847\) 159.136 + 159.136i 0.187882 + 0.187882i
\(848\) −188.084 50.3968i −0.221797 0.0594302i
\(849\) 0 0
\(850\) 242.587 167.769i 0.285397 0.197375i
\(851\) −625.828 + 1083.97i −0.735403 + 1.27375i
\(852\) 0 0
\(853\) −948.800 254.230i −1.11231 0.298042i −0.344542 0.938771i \(-0.611966\pi\)
−0.767768 + 0.640728i \(0.778632\pi\)
\(854\) 606.838i 0.710583i
\(855\) 0 0
\(856\) −40.0704 −0.0468112
\(857\) 152.697 569.873i 0.178176 0.664963i −0.817813 0.575485i \(-0.804813\pi\)
0.995989 0.0894780i \(-0.0285199\pi\)
\(858\) 0 0
\(859\) −421.639 243.434i −0.490849 0.283392i 0.234077 0.972218i \(-0.424793\pi\)
−0.724927 + 0.688826i \(0.758126\pi\)
\(860\) −689.949 635.920i −0.802267 0.739442i
\(861\) 0 0
\(862\) −152.573 + 569.411i −0.176999 + 0.660570i
\(863\) −411.319 + 411.319i −0.476615 + 0.476615i −0.904047 0.427432i \(-0.859418\pi\)
0.427432 + 0.904047i \(0.359418\pi\)
\(864\) 0 0
\(865\) −238.919 53.6959i −0.276207 0.0620762i
\(866\) 344.497 + 596.687i 0.397803 + 0.689015i
\(867\) 0 0
\(868\) −58.5159 218.384i −0.0674146 0.251595i
\(869\) 71.0318 + 41.0102i 0.0817397 + 0.0471924i
\(870\) 0 0
\(871\) −573.666 993.619i −0.658630 1.14078i
\(872\) 166.045 + 166.045i 0.190419 + 0.190419i
\(873\) 0 0
\(874\) 1514.85i 1.73323i
\(875\) 35.6585 253.743i 0.0407526 0.289992i
\(876\) 0 0
\(877\) −454.259 + 121.718i −0.517969 + 0.138789i −0.508327 0.861164i \(-0.669736\pi\)
−0.00964182 + 0.999954i \(0.503069\pi\)
\(878\) −205.963 768.665i −0.234582 0.875472i
\(879\) 0 0
\(880\) −37.2987 + 71.1447i −0.0423849 + 0.0808463i
\(881\) 533.151 0.605166 0.302583 0.953123i \(-0.402151\pi\)
0.302583 + 0.953123i \(0.402151\pi\)
\(882\) 0 0
\(883\) −745.939 + 745.939i −0.844778 + 0.844778i −0.989476 0.144698i \(-0.953779\pi\)
0.144698 + 0.989476i \(0.453779\pi\)
\(884\) 283.093 163.444i 0.320241 0.184891i
\(885\) 0 0
\(886\) −936.908 + 1622.77i −1.05746 + 1.83157i
\(887\) 527.568 141.361i 0.594778 0.159370i 0.0511420 0.998691i \(-0.483714\pi\)
0.543636 + 0.839321i \(0.317047\pi\)
\(888\) 0 0
\(889\) 287.766 166.142i 0.323696 0.186886i
\(890\) −1445.54 324.879i −1.62421 0.365032i
\(891\) 0 0
\(892\) −197.197 197.197i −0.221073 0.221073i
\(893\) −558.455 149.638i −0.625369 0.167567i
\(894\) 0 0
\(895\) 37.4005 + 917.797i 0.0417883 + 1.02547i
\(896\) 173.876 301.163i 0.194058 0.336119i
\(897\) 0 0
\(898\) −905.363 242.591i −1.00820 0.270146i
\(899\) 15.9592i 0.0177521i
\(900\) 0 0
\(901\) −152.182 −0.168903
\(902\) −78.2480 + 292.026i −0.0867495 + 0.323753i
\(903\) 0 0
\(904\) 105.069 + 60.6617i 0.116227 + 0.0671037i
\(905\) 108.548 4.42335i 0.119942 0.00488768i
\(906\) 0 0
\(907\) −346.751 + 1294.09i −0.382306 + 1.42678i 0.460065 + 0.887885i \(0.347826\pi\)
−0.842371 + 0.538899i \(0.818841\pi\)
\(908\) 124.890 124.890i 0.137544 0.137544i
\(909\) 0 0
\(910\) 104.495 464.949i 0.114830 0.510933i
\(911\) 574.681 + 995.377i 0.630824 + 1.09262i 0.987383 + 0.158347i \(0.0506165\pi\)
−0.356559 + 0.934273i \(0.616050\pi\)
\(912\) 0 0
\(913\) 25.9176 + 96.7258i 0.0283873 + 0.105943i
\(914\) 1101.09 + 635.714i 1.20469 + 0.695530i
\(915\) 0 0
\(916\) −719.080 1245.48i −0.785021 1.35970i
\(917\) 37.8842 + 37.8842i 0.0413132 + 0.0413132i
\(918\) 0 0
\(919\) 412.577i 0.448941i 0.974481 + 0.224470i \(0.0720652\pi\)
−0.974481 + 0.224470i \(0.927935\pi\)
\(920\) −615.492 322.681i −0.669013 0.350741i
\(921\) 0 0
\(922\) 1600.43 428.833i 1.73582 0.465112i
\(923\) 260.085 + 970.650i 0.281782 + 1.05163i
\(924\) 0 0
\(925\) 1025.37 + 870.592i 1.10851 + 0.941180i
\(926\) −1493.70 −1.61307
\(927\) 0 0
\(928\) 23.5357 23.5357i 0.0253618 0.0253618i
\(929\) −131.382 + 75.8536i −0.141423 + 0.0816508i −0.569042 0.822308i \(-0.692686\pi\)
0.427619 + 0.903959i \(0.359353\pi\)
\(930\) 0 0
\(931\) 463.590 802.962i 0.497949 0.862473i
\(932\) −1303.10 + 349.164i −1.39817 + 0.374640i
\(933\) 0 0
\(934\) −1883.31 + 1087.33i −2.01639 + 1.16416i
\(935\) −13.7663 + 61.2531i −0.0147233 + 0.0655113i
\(936\) 0 0
\(937\) 662.090 + 662.090i 0.706606 + 0.706606i 0.965820 0.259214i \(-0.0834635\pi\)
−0.259214 + 0.965820i \(0.583463\pi\)
\(938\) −483.669 129.599i −0.515639 0.138165i
\(939\) 0 0
\(940\) 558.395 605.838i 0.594037 0.644508i
\(941\) 766.885 1328.28i 0.814969 1.41157i −0.0943819 0.995536i \(-0.530087\pi\)
0.909350 0.416031i \(-0.136579\pi\)
\(942\) 0 0
\(943\) 644.832 + 172.782i 0.683809 + 0.183226i
\(944\) 537.056i 0.568915i
\(945\) 0 0
\(946\) 335.151 0.354282
\(947\) 429.417 1602.61i 0.453450 1.69230i −0.239155 0.970982i \(-0.576870\pi\)
0.692605 0.721317i \(-0.256463\pi\)
\(948\) 0 0
\(949\) 720.120 + 415.762i 0.758820 + 0.438105i
\(950\) 1601.55 + 292.002i 1.68584 + 0.307371i
\(951\) 0 0
\(952\) 11.8865 44.3610i 0.0124858 0.0465977i
\(953\) −145.501 + 145.501i −0.152676 + 0.152676i −0.779312 0.626636i \(-0.784431\pi\)
0.626636 + 0.779312i \(0.284431\pi\)
\(954\) 0 0
\(955\) −107.212 169.373i −0.112264 0.177354i
\(956\) −962.130 1666.46i −1.00641 1.74316i
\(957\) 0 0
\(958\) −150.606 562.071i −0.157209 0.586713i
\(959\) 36.7327 + 21.2077i 0.0383032 + 0.0221143i
\(960\) 0 0
\(961\) 305.712 + 529.509i 0.318119 + 0.550998i
\(962\) 1768.92 + 1768.92i 1.83879 + 1.83879i
\(963\) 0 0
\(964\) 787.959i 0.817385i
\(965\) −163.407 523.562i −0.169334 0.542551i
\(966\) 0 0
\(967\) −1573.24 + 421.548i −1.62693 + 0.435934i −0.953026 0.302888i \(-0.902049\pi\)
−0.673901 + 0.738822i \(0.735382\pi\)
\(968\) −169.772 633.597i −0.175384 0.654542i
\(969\) 0 0
\(970\) −287.595 150.776i −0.296490 0.155439i
\(971\) 72.4383 0.0746017 0.0373009 0.999304i \(-0.488124\pi\)
0.0373009 + 0.999304i \(0.488124\pi\)
\(972\) 0 0
\(973\) 120.556 120.556i 0.123901 0.123901i
\(974\) 465.033 268.487i 0.477447 0.275654i
\(975\) 0 0
\(976\) −225.722 + 390.962i −0.231272 + 0.400576i
\(977\) −964.876 + 258.538i −0.987591 + 0.264624i −0.716238 0.697856i \(-0.754138\pi\)
−0.271352 + 0.962480i \(0.587471\pi\)
\(978\) 0 0
\(979\) 273.113 157.682i 0.278972 0.161065i
\(980\) 706.699 + 1116.44i 0.721122 + 1.13923i
\(981\) 0 0
\(982\) 235.116 + 235.116i 0.239425 + 0.239425i
\(983\) 183.953 + 49.2900i 0.187134 + 0.0501424i 0.351169 0.936312i \(-0.385784\pi\)
−0.164035 + 0.986455i \(0.552451\pi\)
\(984\) 0 0
\(985\) 349.938 + 322.535i 0.355267 + 0.327446i
\(986\) 5.03520 8.72123i 0.00510670 0.00884506i
\(987\) 0 0
\(988\) 1742.76 + 466.970i 1.76392 + 0.472642i
\(989\) 740.059i 0.748290i
\(990\) 0 0
\(991\) −1131.94 −1.14222 −0.571109 0.820874i \(-0.693487\pi\)
−0.571109 + 0.820874i \(0.693487\pi\)
\(992\) 188.699 704.233i 0.190221 0.709913i
\(993\) 0 0
\(994\) 379.809 + 219.283i 0.382101 + 0.220606i
\(995\) −51.1794 1255.93i −0.0514366 1.26224i
\(996\) 0 0
\(997\) −408.216 + 1523.48i −0.409444 + 1.52807i 0.386265 + 0.922388i \(0.373765\pi\)
−0.795709 + 0.605679i \(0.792902\pi\)
\(998\) −1645.39 + 1645.39i −1.64868 + 1.64868i
\(999\) 0 0
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 405.3.l.h.352.1 8
3.2 odd 2 405.3.l.f.352.2 8
5.3 odd 4 inner 405.3.l.h.28.2 8
9.2 odd 6 405.3.l.f.217.1 8
9.4 even 3 15.3.f.a.7.1 4
9.5 odd 6 45.3.g.b.37.2 4
9.7 even 3 inner 405.3.l.h.217.2 8
15.8 even 4 405.3.l.f.28.1 8
36.23 even 6 720.3.bh.k.577.1 4
36.31 odd 6 240.3.bg.a.97.1 4
45.4 even 6 75.3.f.c.7.2 4
45.13 odd 12 15.3.f.a.13.1 yes 4
45.14 odd 6 225.3.g.a.82.1 4
45.22 odd 12 75.3.f.c.43.2 4
45.23 even 12 45.3.g.b.28.2 4
45.32 even 12 225.3.g.a.118.1 4
45.38 even 12 405.3.l.f.298.2 8
45.43 odd 12 inner 405.3.l.h.298.1 8
72.13 even 6 960.3.bg.i.577.1 4
72.67 odd 6 960.3.bg.h.577.2 4
180.23 odd 12 720.3.bh.k.433.1 4
180.67 even 12 1200.3.bg.k.193.2 4
180.103 even 12 240.3.bg.a.193.1 4
180.139 odd 6 1200.3.bg.k.1057.2 4
360.13 odd 12 960.3.bg.i.193.1 4
360.283 even 12 960.3.bg.h.193.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
15.3.f.a.7.1 4 9.4 even 3
15.3.f.a.13.1 yes 4 45.13 odd 12
45.3.g.b.28.2 4 45.23 even 12
45.3.g.b.37.2 4 9.5 odd 6
75.3.f.c.7.2 4 45.4 even 6
75.3.f.c.43.2 4 45.22 odd 12
225.3.g.a.82.1 4 45.14 odd 6
225.3.g.a.118.1 4 45.32 even 12
240.3.bg.a.97.1 4 36.31 odd 6
240.3.bg.a.193.1 4 180.103 even 12
405.3.l.f.28.1 8 15.8 even 4
405.3.l.f.217.1 8 9.2 odd 6
405.3.l.f.298.2 8 45.38 even 12
405.3.l.f.352.2 8 3.2 odd 2
405.3.l.h.28.2 8 5.3 odd 4 inner
405.3.l.h.217.2 8 9.7 even 3 inner
405.3.l.h.298.1 8 45.43 odd 12 inner
405.3.l.h.352.1 8 1.1 even 1 trivial
720.3.bh.k.433.1 4 180.23 odd 12
720.3.bh.k.577.1 4 36.23 even 6
960.3.bg.h.193.2 4 360.283 even 12
960.3.bg.h.577.2 4 72.67 odd 6
960.3.bg.i.193.1 4 360.13 odd 12
960.3.bg.i.577.1 4 72.13 even 6
1200.3.bg.k.193.2 4 180.67 even 12
1200.3.bg.k.1057.2 4 180.139 odd 6