Properties

 Label 637.4.a.a.1.1 Level $637$ Weight $4$ Character 637.1 Self dual yes Analytic conductor $37.584$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

Related objects

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,4,Mod(1,637)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("637.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$637 = 7^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 637.a (trivial)

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: yes Analytic conductor: $$37.5842166737$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 13) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 637.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-5.00000 q^{2} +7.00000 q^{3} +17.0000 q^{4} +7.00000 q^{5} -35.0000 q^{6} -45.0000 q^{8} +22.0000 q^{9} +O(q^{10})$$ $$q-5.00000 q^{2} +7.00000 q^{3} +17.0000 q^{4} +7.00000 q^{5} -35.0000 q^{6} -45.0000 q^{8} +22.0000 q^{9} -35.0000 q^{10} -26.0000 q^{11} +119.000 q^{12} -13.0000 q^{13} +49.0000 q^{15} +89.0000 q^{16} -77.0000 q^{17} -110.000 q^{18} +126.000 q^{19} +119.000 q^{20} +130.000 q^{22} -96.0000 q^{23} -315.000 q^{24} -76.0000 q^{25} +65.0000 q^{26} -35.0000 q^{27} -82.0000 q^{29} -245.000 q^{30} -196.000 q^{31} -85.0000 q^{32} -182.000 q^{33} +385.000 q^{34} +374.000 q^{36} -131.000 q^{37} -630.000 q^{38} -91.0000 q^{39} -315.000 q^{40} -336.000 q^{41} -201.000 q^{43} -442.000 q^{44} +154.000 q^{45} +480.000 q^{46} +105.000 q^{47} +623.000 q^{48} +380.000 q^{50} -539.000 q^{51} -221.000 q^{52} -432.000 q^{53} +175.000 q^{54} -182.000 q^{55} +882.000 q^{57} +410.000 q^{58} +294.000 q^{59} +833.000 q^{60} +56.0000 q^{61} +980.000 q^{62} -287.000 q^{64} -91.0000 q^{65} +910.000 q^{66} +478.000 q^{67} -1309.00 q^{68} -672.000 q^{69} +9.00000 q^{71} -990.000 q^{72} -98.0000 q^{73} +655.000 q^{74} -532.000 q^{75} +2142.00 q^{76} +455.000 q^{78} +1304.00 q^{79} +623.000 q^{80} -839.000 q^{81} +1680.00 q^{82} +308.000 q^{83} -539.000 q^{85} +1005.00 q^{86} -574.000 q^{87} +1170.00 q^{88} +1190.00 q^{89} -770.000 q^{90} -1632.00 q^{92} -1372.00 q^{93} -525.000 q^{94} +882.000 q^{95} -595.000 q^{96} -70.0000 q^{97} -572.000 q^{99} +O(q^{100})$$

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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −5.00000 −1.76777 −0.883883 0.467707i $$-0.845080\pi$$
−0.883883 + 0.467707i $$0.845080\pi$$
$$3$$ 7.00000 1.34715 0.673575 0.739119i $$-0.264758\pi$$
0.673575 + 0.739119i $$0.264758\pi$$
$$4$$ 17.0000 2.12500
$$5$$ 7.00000 0.626099 0.313050 0.949737i $$-0.398649\pi$$
0.313050 + 0.949737i $$0.398649\pi$$
$$6$$ −35.0000 −2.38145
$$7$$ 0 0
$$8$$ −45.0000 −1.98874
$$9$$ 22.0000 0.814815
$$10$$ −35.0000 −1.10680
$$11$$ −26.0000 −0.712663 −0.356332 0.934360i $$-0.615973\pi$$
−0.356332 + 0.934360i $$0.615973\pi$$
$$12$$ 119.000 2.86270
$$13$$ −13.0000 −0.277350
$$14$$ 0 0
$$15$$ 49.0000 0.843450
$$16$$ 89.0000 1.39062
$$17$$ −77.0000 −1.09854 −0.549272 0.835644i $$-0.685095\pi$$
−0.549272 + 0.835644i $$0.685095\pi$$
$$18$$ −110.000 −1.44040
$$19$$ 126.000 1.52139 0.760694 0.649110i $$-0.224859\pi$$
0.760694 + 0.649110i $$0.224859\pi$$
$$20$$ 119.000 1.33046
$$21$$ 0 0
$$22$$ 130.000 1.25982
$$23$$ −96.0000 −0.870321 −0.435161 0.900353i $$-0.643308\pi$$
−0.435161 + 0.900353i $$0.643308\pi$$
$$24$$ −315.000 −2.67913
$$25$$ −76.0000 −0.608000
$$26$$ 65.0000 0.490290
$$27$$ −35.0000 −0.249472
$$28$$ 0 0
$$29$$ −82.0000 −0.525070 −0.262535 0.964923i $$-0.584558\pi$$
−0.262535 + 0.964923i $$0.584558\pi$$
$$30$$ −245.000 −1.49102
$$31$$ −196.000 −1.13557 −0.567785 0.823177i $$-0.692199\pi$$
−0.567785 + 0.823177i $$0.692199\pi$$
$$32$$ −85.0000 −0.469563
$$33$$ −182.000 −0.960065
$$34$$ 385.000 1.94197
$$35$$ 0 0
$$36$$ 374.000 1.73148
$$37$$ −131.000 −0.582061 −0.291031 0.956714i $$-0.593998\pi$$
−0.291031 + 0.956714i $$0.593998\pi$$
$$38$$ −630.000 −2.68946
$$39$$ −91.0000 −0.373632
$$40$$ −315.000 −1.24515
$$41$$ −336.000 −1.27986 −0.639932 0.768432i $$-0.721037\pi$$
−0.639932 + 0.768432i $$0.721037\pi$$
$$42$$ 0 0
$$43$$ −201.000 −0.712842 −0.356421 0.934325i $$-0.616003\pi$$
−0.356421 + 0.934325i $$0.616003\pi$$
$$44$$ −442.000 −1.51441
$$45$$ 154.000 0.510155
$$46$$ 480.000 1.53852
$$47$$ 105.000 0.325869 0.162934 0.986637i $$-0.447904\pi$$
0.162934 + 0.986637i $$0.447904\pi$$
$$48$$ 623.000 1.87338
$$49$$ 0 0
$$50$$ 380.000 1.07480
$$51$$ −539.000 −1.47990
$$52$$ −221.000 −0.589369
$$53$$ −432.000 −1.11962 −0.559809 0.828622i $$-0.689126\pi$$
−0.559809 + 0.828622i $$0.689126\pi$$
$$54$$ 175.000 0.441009
$$55$$ −182.000 −0.446198
$$56$$ 0 0
$$57$$ 882.000 2.04954
$$58$$ 410.000 0.928201
$$59$$ 294.000 0.648738 0.324369 0.945931i $$-0.394848\pi$$
0.324369 + 0.945931i $$0.394848\pi$$
$$60$$ 833.000 1.79233
$$61$$ 56.0000 0.117542 0.0587710 0.998271i $$-0.481282\pi$$
0.0587710 + 0.998271i $$0.481282\pi$$
$$62$$ 980.000 2.00742
$$63$$ 0 0
$$64$$ −287.000 −0.560547
$$65$$ −91.0000 −0.173649
$$66$$ 910.000 1.69717
$$67$$ 478.000 0.871597 0.435798 0.900044i $$-0.356466\pi$$
0.435798 + 0.900044i $$0.356466\pi$$
$$68$$ −1309.00 −2.33441
$$69$$ −672.000 −1.17245
$$70$$ 0 0
$$71$$ 9.00000 0.0150437 0.00752186 0.999972i $$-0.497606\pi$$
0.00752186 + 0.999972i $$0.497606\pi$$
$$72$$ −990.000 −1.62045
$$73$$ −98.0000 −0.157124 −0.0785619 0.996909i $$-0.525033\pi$$
−0.0785619 + 0.996909i $$0.525033\pi$$
$$74$$ 655.000 1.02895
$$75$$ −532.000 −0.819068
$$76$$ 2142.00 3.23295
$$77$$ 0 0
$$78$$ 455.000 0.660495
$$79$$ 1304.00 1.85711 0.928554 0.371198i $$-0.121053\pi$$
0.928554 + 0.371198i $$0.121053\pi$$
$$80$$ 623.000 0.870669
$$81$$ −839.000 −1.15089
$$82$$ 1680.00 2.26250
$$83$$ 308.000 0.407318 0.203659 0.979042i $$-0.434717\pi$$
0.203659 + 0.979042i $$0.434717\pi$$
$$84$$ 0 0
$$85$$ −539.000 −0.687797
$$86$$ 1005.00 1.26014
$$87$$ −574.000 −0.707348
$$88$$ 1170.00 1.41730
$$89$$ 1190.00 1.41730 0.708650 0.705560i $$-0.249304\pi$$
0.708650 + 0.705560i $$0.249304\pi$$
$$90$$ −770.000 −0.901835
$$91$$ 0 0
$$92$$ −1632.00 −1.84943
$$93$$ −1372.00 −1.52978
$$94$$ −525.000 −0.576060
$$95$$ 882.000 0.952540
$$96$$ −595.000 −0.632572
$$97$$ −70.0000 −0.0732724 −0.0366362 0.999329i $$-0.511664\pi$$
−0.0366362 + 0.999329i $$0.511664\pi$$
$$98$$ 0 0
$$99$$ −572.000 −0.580689
$$100$$ −1292.00 −1.29200
$$101$$ −420.000 −0.413778 −0.206889 0.978364i $$-0.566334\pi$$
−0.206889 + 0.978364i $$0.566334\pi$$
$$102$$ 2695.00 2.61613
$$103$$ −588.000 −0.562499 −0.281249 0.959635i $$-0.590749\pi$$
−0.281249 + 0.959635i $$0.590749\pi$$
$$104$$ 585.000 0.551577
$$105$$ 0 0
$$106$$ 2160.00 1.97922
$$107$$ −684.000 −0.617989 −0.308994 0.951064i $$-0.599992\pi$$
−0.308994 + 0.951064i $$0.599992\pi$$
$$108$$ −595.000 −0.530129
$$109$$ 373.000 0.327770 0.163885 0.986479i $$-0.447597\pi$$
0.163885 + 0.986479i $$0.447597\pi$$
$$110$$ 910.000 0.788774
$$111$$ −917.000 −0.784124
$$112$$ 0 0
$$113$$ −1734.00 −1.44355 −0.721774 0.692128i $$-0.756673\pi$$
−0.721774 + 0.692128i $$0.756673\pi$$
$$114$$ −4410.00 −3.62311
$$115$$ −672.000 −0.544907
$$116$$ −1394.00 −1.11577
$$117$$ −286.000 −0.225989
$$118$$ −1470.00 −1.14682
$$119$$ 0 0
$$120$$ −2205.00 −1.67740
$$121$$ −655.000 −0.492111
$$122$$ −280.000 −0.207787
$$123$$ −2352.00 −1.72417
$$124$$ −3332.00 −2.41308
$$125$$ −1407.00 −1.00677
$$126$$ 0 0
$$127$$ 1892.00 1.32195 0.660976 0.750407i $$-0.270143\pi$$
0.660976 + 0.750407i $$0.270143\pi$$
$$128$$ 2115.00 1.46048
$$129$$ −1407.00 −0.960306
$$130$$ 455.000 0.306970
$$131$$ −1435.00 −0.957073 −0.478536 0.878068i $$-0.658833\pi$$
−0.478536 + 0.878068i $$0.658833\pi$$
$$132$$ −3094.00 −2.04014
$$133$$ 0 0
$$134$$ −2390.00 −1.54078
$$135$$ −245.000 −0.156194
$$136$$ 3465.00 2.18472
$$137$$ −1776.00 −1.10755 −0.553773 0.832667i $$-0.686813\pi$$
−0.553773 + 0.832667i $$0.686813\pi$$
$$138$$ 3360.00 2.07262
$$139$$ 1869.00 1.14048 0.570239 0.821479i $$-0.306850\pi$$
0.570239 + 0.821479i $$0.306850\pi$$
$$140$$ 0 0
$$141$$ 735.000 0.438994
$$142$$ −45.0000 −0.0265938
$$143$$ 338.000 0.197657
$$144$$ 1958.00 1.13310
$$145$$ −574.000 −0.328746
$$146$$ 490.000 0.277758
$$147$$ 0 0
$$148$$ −2227.00 −1.23688
$$149$$ 2466.00 1.35586 0.677928 0.735128i $$-0.262878\pi$$
0.677928 + 0.735128i $$0.262878\pi$$
$$150$$ 2660.00 1.44792
$$151$$ −3323.00 −1.79087 −0.895437 0.445189i $$-0.853137\pi$$
−0.895437 + 0.445189i $$0.853137\pi$$
$$152$$ −5670.00 −3.02564
$$153$$ −1694.00 −0.895110
$$154$$ 0 0
$$155$$ −1372.00 −0.710979
$$156$$ −1547.00 −0.793969
$$157$$ 2730.00 1.38776 0.693878 0.720092i $$-0.255901\pi$$
0.693878 + 0.720092i $$0.255901\pi$$
$$158$$ −6520.00 −3.28293
$$159$$ −3024.00 −1.50829
$$160$$ −595.000 −0.293993
$$161$$ 0 0
$$162$$ 4195.00 2.03451
$$163$$ −544.000 −0.261407 −0.130704 0.991421i $$-0.541724\pi$$
−0.130704 + 0.991421i $$0.541724\pi$$
$$164$$ −5712.00 −2.71971
$$165$$ −1274.00 −0.601096
$$166$$ −1540.00 −0.720043
$$167$$ −1624.00 −0.752508 −0.376254 0.926516i $$-0.622788\pi$$
−0.376254 + 0.926516i $$0.622788\pi$$
$$168$$ 0 0
$$169$$ 169.000 0.0769231
$$170$$ 2695.00 1.21587
$$171$$ 2772.00 1.23965
$$172$$ −3417.00 −1.51479
$$173$$ 336.000 0.147662 0.0738312 0.997271i $$-0.476477\pi$$
0.0738312 + 0.997271i $$0.476477\pi$$
$$174$$ 2870.00 1.25043
$$175$$ 0 0
$$176$$ −2314.00 −0.991047
$$177$$ 2058.00 0.873948
$$178$$ −5950.00 −2.50546
$$179$$ −3029.00 −1.26479 −0.632397 0.774645i $$-0.717929\pi$$
−0.632397 + 0.774645i $$0.717929\pi$$
$$180$$ 2618.00 1.08408
$$181$$ 28.0000 0.0114985 0.00574924 0.999983i $$-0.498170\pi$$
0.00574924 + 0.999983i $$0.498170\pi$$
$$182$$ 0 0
$$183$$ 392.000 0.158347
$$184$$ 4320.00 1.73084
$$185$$ −917.000 −0.364428
$$186$$ 6860.00 2.70430
$$187$$ 2002.00 0.782892
$$188$$ 1785.00 0.692471
$$189$$ 0 0
$$190$$ −4410.00 −1.68387
$$191$$ 422.000 0.159868 0.0799342 0.996800i $$-0.474529\pi$$
0.0799342 + 0.996800i $$0.474529\pi$$
$$192$$ −2009.00 −0.755141
$$193$$ 492.000 0.183497 0.0917485 0.995782i $$-0.470754\pi$$
0.0917485 + 0.995782i $$0.470754\pi$$
$$194$$ 350.000 0.129529
$$195$$ −637.000 −0.233931
$$196$$ 0 0
$$197$$ 2991.00 1.08173 0.540863 0.841111i $$-0.318098\pi$$
0.540863 + 0.841111i $$0.318098\pi$$
$$198$$ 2860.00 1.02652
$$199$$ 70.0000 0.0249355 0.0124678 0.999922i $$-0.496031\pi$$
0.0124678 + 0.999922i $$0.496031\pi$$
$$200$$ 3420.00 1.20915
$$201$$ 3346.00 1.17417
$$202$$ 2100.00 0.731463
$$203$$ 0 0
$$204$$ −9163.00 −3.14480
$$205$$ −2352.00 −0.801321
$$206$$ 2940.00 0.994367
$$207$$ −2112.00 −0.709150
$$208$$ −1157.00 −0.385690
$$209$$ −3276.00 −1.08424
$$210$$ 0 0
$$211$$ 2851.00 0.930194 0.465097 0.885260i $$-0.346019\pi$$
0.465097 + 0.885260i $$0.346019\pi$$
$$212$$ −7344.00 −2.37919
$$213$$ 63.0000 0.0202661
$$214$$ 3420.00 1.09246
$$215$$ −1407.00 −0.446310
$$216$$ 1575.00 0.496135
$$217$$ 0 0
$$218$$ −1865.00 −0.579421
$$219$$ −686.000 −0.211669
$$220$$ −3094.00 −0.948170
$$221$$ 1001.00 0.304681
$$222$$ 4585.00 1.38615
$$223$$ −217.000 −0.0651632 −0.0325816 0.999469i $$-0.510373\pi$$
−0.0325816 + 0.999469i $$0.510373\pi$$
$$224$$ 0 0
$$225$$ −1672.00 −0.495407
$$226$$ 8670.00 2.55186
$$227$$ 2576.00 0.753194 0.376597 0.926377i $$-0.377094\pi$$
0.376597 + 0.926377i $$0.377094\pi$$
$$228$$ 14994.0 4.35527
$$229$$ −455.000 −0.131298 −0.0656490 0.997843i $$-0.520912\pi$$
−0.0656490 + 0.997843i $$0.520912\pi$$
$$230$$ 3360.00 0.963269
$$231$$ 0 0
$$232$$ 3690.00 1.04423
$$233$$ 3061.00 0.860656 0.430328 0.902673i $$-0.358398\pi$$
0.430328 + 0.902673i $$0.358398\pi$$
$$234$$ 1430.00 0.399496
$$235$$ 735.000 0.204026
$$236$$ 4998.00 1.37857
$$237$$ 9128.00 2.50180
$$238$$ 0 0
$$239$$ −3477.00 −0.941039 −0.470520 0.882389i $$-0.655934\pi$$
−0.470520 + 0.882389i $$0.655934\pi$$
$$240$$ 4361.00 1.17292
$$241$$ 1610.00 0.430329 0.215164 0.976578i $$-0.430971\pi$$
0.215164 + 0.976578i $$0.430971\pi$$
$$242$$ 3275.00 0.869938
$$243$$ −4928.00 −1.30095
$$244$$ 952.000 0.249777
$$245$$ 0 0
$$246$$ 11760.0 3.04793
$$247$$ −1638.00 −0.421957
$$248$$ 8820.00 2.25835
$$249$$ 2156.00 0.548719
$$250$$ 7035.00 1.77973
$$251$$ −1008.00 −0.253484 −0.126742 0.991936i $$-0.540452\pi$$
−0.126742 + 0.991936i $$0.540452\pi$$
$$252$$ 0 0
$$253$$ 2496.00 0.620246
$$254$$ −9460.00 −2.33690
$$255$$ −3773.00 −0.926566
$$256$$ −8279.00 −2.02124
$$257$$ −6041.00 −1.46625 −0.733127 0.680092i $$-0.761940\pi$$
−0.733127 + 0.680092i $$0.761940\pi$$
$$258$$ 7035.00 1.69760
$$259$$ 0 0
$$260$$ −1547.00 −0.369003
$$261$$ −1804.00 −0.427834
$$262$$ 7175.00 1.69188
$$263$$ −3708.00 −0.869373 −0.434686 0.900582i $$-0.643141\pi$$
−0.434686 + 0.900582i $$0.643141\pi$$
$$264$$ 8190.00 1.90932
$$265$$ −3024.00 −0.700992
$$266$$ 0 0
$$267$$ 8330.00 1.90932
$$268$$ 8126.00 1.85214
$$269$$ −8344.00 −1.89124 −0.945618 0.325278i $$-0.894542\pi$$
−0.945618 + 0.325278i $$0.894542\pi$$
$$270$$ 1225.00 0.276115
$$271$$ 1617.00 0.362457 0.181228 0.983441i $$-0.441993\pi$$
0.181228 + 0.983441i $$0.441993\pi$$
$$272$$ −6853.00 −1.52766
$$273$$ 0 0
$$274$$ 8880.00 1.95788
$$275$$ 1976.00 0.433299
$$276$$ −11424.0 −2.49146
$$277$$ −3820.00 −0.828598 −0.414299 0.910141i $$-0.635973\pi$$
−0.414299 + 0.910141i $$0.635973\pi$$
$$278$$ −9345.00 −2.01610
$$279$$ −4312.00 −0.925278
$$280$$ 0 0
$$281$$ −6214.00 −1.31920 −0.659602 0.751615i $$-0.729275\pi$$
−0.659602 + 0.751615i $$0.729275\pi$$
$$282$$ −3675.00 −0.776039
$$283$$ 5292.00 1.11158 0.555789 0.831323i $$-0.312416\pi$$
0.555789 + 0.831323i $$0.312416\pi$$
$$284$$ 153.000 0.0319679
$$285$$ 6174.00 1.28321
$$286$$ −1690.00 −0.349412
$$287$$ 0 0
$$288$$ −1870.00 −0.382607
$$289$$ 1016.00 0.206798
$$290$$ 2870.00 0.581146
$$291$$ −490.000 −0.0987090
$$292$$ −1666.00 −0.333888
$$293$$ 903.000 0.180047 0.0900236 0.995940i $$-0.471306\pi$$
0.0900236 + 0.995940i $$0.471306\pi$$
$$294$$ 0 0
$$295$$ 2058.00 0.406174
$$296$$ 5895.00 1.15757
$$297$$ 910.000 0.177790
$$298$$ −12330.0 −2.39684
$$299$$ 1248.00 0.241384
$$300$$ −9044.00 −1.74052
$$301$$ 0 0
$$302$$ 16615.0 3.16585
$$303$$ −2940.00 −0.557421
$$304$$ 11214.0 2.11568
$$305$$ 392.000 0.0735930
$$306$$ 8470.00 1.58235
$$307$$ −2114.00 −0.393004 −0.196502 0.980503i $$-0.562958\pi$$
−0.196502 + 0.980503i $$0.562958\pi$$
$$308$$ 0 0
$$309$$ −4116.00 −0.757770
$$310$$ 6860.00 1.25684
$$311$$ −3402.00 −0.620288 −0.310144 0.950690i $$-0.600377\pi$$
−0.310144 + 0.950690i $$0.600377\pi$$
$$312$$ 4095.00 0.743057
$$313$$ 10689.0 1.93028 0.965141 0.261732i $$-0.0842937\pi$$
0.965141 + 0.261732i $$0.0842937\pi$$
$$314$$ −13650.0 −2.45323
$$315$$ 0 0
$$316$$ 22168.0 3.94635
$$317$$ −7054.00 −1.24982 −0.624909 0.780698i $$-0.714864\pi$$
−0.624909 + 0.780698i $$0.714864\pi$$
$$318$$ 15120.0 2.66631
$$319$$ 2132.00 0.374198
$$320$$ −2009.00 −0.350958
$$321$$ −4788.00 −0.832524
$$322$$ 0 0
$$323$$ −9702.00 −1.67131
$$324$$ −14263.0 −2.44564
$$325$$ 988.000 0.168629
$$326$$ 2720.00 0.462107
$$327$$ 2611.00 0.441555
$$328$$ 15120.0 2.54531
$$329$$ 0 0
$$330$$ 6370.00 1.06260
$$331$$ 9704.00 1.61142 0.805710 0.592310i $$-0.201784\pi$$
0.805710 + 0.592310i $$0.201784\pi$$
$$332$$ 5236.00 0.865551
$$333$$ −2882.00 −0.474272
$$334$$ 8120.00 1.33026
$$335$$ 3346.00 0.545706
$$336$$ 0 0
$$337$$ −10449.0 −1.68900 −0.844500 0.535555i $$-0.820103\pi$$
−0.844500 + 0.535555i $$0.820103\pi$$
$$338$$ −845.000 −0.135982
$$339$$ −12138.0 −1.94468
$$340$$ −9163.00 −1.46157
$$341$$ 5096.00 0.809278
$$342$$ −13860.0 −2.19141
$$343$$ 0 0
$$344$$ 9045.00 1.41766
$$345$$ −4704.00 −0.734072
$$346$$ −1680.00 −0.261033
$$347$$ −621.000 −0.0960721 −0.0480361 0.998846i $$-0.515296\pi$$
−0.0480361 + 0.998846i $$0.515296\pi$$
$$348$$ −9758.00 −1.50311
$$349$$ −12481.0 −1.91431 −0.957153 0.289584i $$-0.906483\pi$$
−0.957153 + 0.289584i $$0.906483\pi$$
$$350$$ 0 0
$$351$$ 455.000 0.0691912
$$352$$ 2210.00 0.334640
$$353$$ 1400.00 0.211089 0.105545 0.994415i $$-0.466341\pi$$
0.105545 + 0.994415i $$0.466341\pi$$
$$354$$ −10290.0 −1.54494
$$355$$ 63.0000 0.00941885
$$356$$ 20230.0 3.01176
$$357$$ 0 0
$$358$$ 15145.0 2.23586
$$359$$ −4968.00 −0.730365 −0.365182 0.930936i $$-0.618993\pi$$
−0.365182 + 0.930936i $$0.618993\pi$$
$$360$$ −6930.00 −1.01456
$$361$$ 9017.00 1.31462
$$362$$ −140.000 −0.0203266
$$363$$ −4585.00 −0.662948
$$364$$ 0 0
$$365$$ −686.000 −0.0983750
$$366$$ −1960.00 −0.279920
$$367$$ −8722.00 −1.24056 −0.620279 0.784381i $$-0.712981\pi$$
−0.620279 + 0.784381i $$0.712981\pi$$
$$368$$ −8544.00 −1.21029
$$369$$ −7392.00 −1.04285
$$370$$ 4585.00 0.644224
$$371$$ 0 0
$$372$$ −23324.0 −3.25079
$$373$$ 10012.0 1.38982 0.694908 0.719098i $$-0.255445\pi$$
0.694908 + 0.719098i $$0.255445\pi$$
$$374$$ −10010.0 −1.38397
$$375$$ −9849.00 −1.35627
$$376$$ −4725.00 −0.648067
$$377$$ 1066.00 0.145628
$$378$$ 0 0
$$379$$ −3372.00 −0.457013 −0.228507 0.973542i $$-0.573384\pi$$
−0.228507 + 0.973542i $$0.573384\pi$$
$$380$$ 14994.0 2.02415
$$381$$ 13244.0 1.78087
$$382$$ −2110.00 −0.282610
$$383$$ 847.000 0.113002 0.0565009 0.998403i $$-0.482006\pi$$
0.0565009 + 0.998403i $$0.482006\pi$$
$$384$$ 14805.0 1.96749
$$385$$ 0 0
$$386$$ −2460.00 −0.324380
$$387$$ −4422.00 −0.580834
$$388$$ −1190.00 −0.155704
$$389$$ 11314.0 1.47466 0.737330 0.675533i $$-0.236086\pi$$
0.737330 + 0.675533i $$0.236086\pi$$
$$390$$ 3185.00 0.413535
$$391$$ 7392.00 0.956086
$$392$$ 0 0
$$393$$ −10045.0 −1.28932
$$394$$ −14955.0 −1.91224
$$395$$ 9128.00 1.16273
$$396$$ −9724.00 −1.23396
$$397$$ −1862.00 −0.235393 −0.117697 0.993050i $$-0.537551\pi$$
−0.117697 + 0.993050i $$0.537551\pi$$
$$398$$ −350.000 −0.0440802
$$399$$ 0 0
$$400$$ −6764.00 −0.845500
$$401$$ 6820.00 0.849313 0.424657 0.905355i $$-0.360395\pi$$
0.424657 + 0.905355i $$0.360395\pi$$
$$402$$ −16730.0 −2.07566
$$403$$ 2548.00 0.314950
$$404$$ −7140.00 −0.879278
$$405$$ −5873.00 −0.720572
$$406$$ 0 0
$$407$$ 3406.00 0.414814
$$408$$ 24255.0 2.94314
$$409$$ 12992.0 1.57069 0.785346 0.619057i $$-0.212485\pi$$
0.785346 + 0.619057i $$0.212485\pi$$
$$410$$ 11760.0 1.41655
$$411$$ −12432.0 −1.49203
$$412$$ −9996.00 −1.19531
$$413$$ 0 0
$$414$$ 10560.0 1.25361
$$415$$ 2156.00 0.255021
$$416$$ 1105.00 0.130233
$$417$$ 13083.0 1.53640
$$418$$ 16380.0 1.91668
$$419$$ 7343.00 0.856155 0.428078 0.903742i $$-0.359191\pi$$
0.428078 + 0.903742i $$0.359191\pi$$
$$420$$ 0 0
$$421$$ −5059.00 −0.585655 −0.292827 0.956165i $$-0.594596\pi$$
−0.292827 + 0.956165i $$0.594596\pi$$
$$422$$ −14255.0 −1.64437
$$423$$ 2310.00 0.265523
$$424$$ 19440.0 2.22663
$$425$$ 5852.00 0.667915
$$426$$ −315.000 −0.0358258
$$427$$ 0 0
$$428$$ −11628.0 −1.31323
$$429$$ 2366.00 0.266274
$$430$$ 7035.00 0.788972
$$431$$ 3243.00 0.362436 0.181218 0.983443i $$-0.441996\pi$$
0.181218 + 0.983443i $$0.441996\pi$$
$$432$$ −3115.00 −0.346922
$$433$$ −11599.0 −1.28733 −0.643663 0.765309i $$-0.722586\pi$$
−0.643663 + 0.765309i $$0.722586\pi$$
$$434$$ 0 0
$$435$$ −4018.00 −0.442870
$$436$$ 6341.00 0.696511
$$437$$ −12096.0 −1.32410
$$438$$ 3430.00 0.374182
$$439$$ 17374.0 1.88887 0.944437 0.328692i $$-0.106608\pi$$
0.944437 + 0.328692i $$0.106608\pi$$
$$440$$ 8190.00 0.887370
$$441$$ 0 0
$$442$$ −5005.00 −0.538605
$$443$$ 989.000 0.106070 0.0530348 0.998593i $$-0.483111\pi$$
0.0530348 + 0.998593i $$0.483111\pi$$
$$444$$ −15589.0 −1.66626
$$445$$ 8330.00 0.887370
$$446$$ 1085.00 0.115193
$$447$$ 17262.0 1.82654
$$448$$ 0 0
$$449$$ −14474.0 −1.52131 −0.760657 0.649154i $$-0.775123\pi$$
−0.760657 + 0.649154i $$0.775123\pi$$
$$450$$ 8360.00 0.875765
$$451$$ 8736.00 0.912111
$$452$$ −29478.0 −3.06754
$$453$$ −23261.0 −2.41258
$$454$$ −12880.0 −1.33147
$$455$$ 0 0
$$456$$ −39690.0 −4.07600
$$457$$ −1594.00 −0.163160 −0.0815801 0.996667i $$-0.525997\pi$$
−0.0815801 + 0.996667i $$0.525997\pi$$
$$458$$ 2275.00 0.232104
$$459$$ 2695.00 0.274056
$$460$$ −11424.0 −1.15793
$$461$$ 5915.00 0.597590 0.298795 0.954317i $$-0.403415\pi$$
0.298795 + 0.954317i $$0.403415\pi$$
$$462$$ 0 0
$$463$$ −11072.0 −1.11136 −0.555680 0.831396i $$-0.687542\pi$$
−0.555680 + 0.831396i $$0.687542\pi$$
$$464$$ −7298.00 −0.730175
$$465$$ −9604.00 −0.957795
$$466$$ −15305.0 −1.52144
$$467$$ −1260.00 −0.124852 −0.0624260 0.998050i $$-0.519884\pi$$
−0.0624260 + 0.998050i $$0.519884\pi$$
$$468$$ −4862.00 −0.480227
$$469$$ 0 0
$$470$$ −3675.00 −0.360670
$$471$$ 19110.0 1.86952
$$472$$ −13230.0 −1.29017
$$473$$ 5226.00 0.508016
$$474$$ −45640.0 −4.42260
$$475$$ −9576.00 −0.925004
$$476$$ 0 0
$$477$$ −9504.00 −0.912281
$$478$$ 17385.0 1.66354
$$479$$ 12033.0 1.14781 0.573906 0.818921i $$-0.305428\pi$$
0.573906 + 0.818921i $$0.305428\pi$$
$$480$$ −4165.00 −0.396053
$$481$$ 1703.00 0.161435
$$482$$ −8050.00 −0.760721
$$483$$ 0 0
$$484$$ −11135.0 −1.04574
$$485$$ −490.000 −0.0458758
$$486$$ 24640.0 2.29978
$$487$$ −2280.00 −0.212149 −0.106075 0.994358i $$-0.533828\pi$$
−0.106075 + 0.994358i $$0.533828\pi$$
$$488$$ −2520.00 −0.233760
$$489$$ −3808.00 −0.352155
$$490$$ 0 0
$$491$$ 16767.0 1.54111 0.770554 0.637375i $$-0.219980\pi$$
0.770554 + 0.637375i $$0.219980\pi$$
$$492$$ −39984.0 −3.66386
$$493$$ 6314.00 0.576812
$$494$$ 8190.00 0.745922
$$495$$ −4004.00 −0.363569
$$496$$ −17444.0 −1.57915
$$497$$ 0 0
$$498$$ −10780.0 −0.970007
$$499$$ 12840.0 1.15190 0.575949 0.817485i $$-0.304633\pi$$
0.575949 + 0.817485i $$0.304633\pi$$
$$500$$ −23919.0 −2.13938
$$501$$ −11368.0 −1.01374
$$502$$ 5040.00 0.448100
$$503$$ 2198.00 0.194839 0.0974195 0.995243i $$-0.468941\pi$$
0.0974195 + 0.995243i $$0.468941\pi$$
$$504$$ 0 0
$$505$$ −2940.00 −0.259066
$$506$$ −12480.0 −1.09645
$$507$$ 1183.00 0.103627
$$508$$ 32164.0 2.80915
$$509$$ 17066.0 1.48612 0.743062 0.669223i $$-0.233373\pi$$
0.743062 + 0.669223i $$0.233373\pi$$
$$510$$ 18865.0 1.63795
$$511$$ 0 0
$$512$$ 24475.0 2.11260
$$513$$ −4410.00 −0.379544
$$514$$ 30205.0 2.59200
$$515$$ −4116.00 −0.352180
$$516$$ −23919.0 −2.04065
$$517$$ −2730.00 −0.232235
$$518$$ 0 0
$$519$$ 2352.00 0.198924
$$520$$ 4095.00 0.345342
$$521$$ −2583.00 −0.217204 −0.108602 0.994085i $$-0.534637\pi$$
−0.108602 + 0.994085i $$0.534637\pi$$
$$522$$ 9020.00 0.756312
$$523$$ −18620.0 −1.55678 −0.778390 0.627781i $$-0.783963\pi$$
−0.778390 + 0.627781i $$0.783963\pi$$
$$524$$ −24395.0 −2.03378
$$525$$ 0 0
$$526$$ 18540.0 1.53685
$$527$$ 15092.0 1.24747
$$528$$ −16198.0 −1.33509
$$529$$ −2951.00 −0.242541
$$530$$ 15120.0 1.23919
$$531$$ 6468.00 0.528601
$$532$$ 0 0
$$533$$ 4368.00 0.354970
$$534$$ −41650.0 −3.37523
$$535$$ −4788.00 −0.386922
$$536$$ −21510.0 −1.73338
$$537$$ −21203.0 −1.70387
$$538$$ 41720.0 3.34327
$$539$$ 0 0
$$540$$ −4165.00 −0.331913
$$541$$ −16833.0 −1.33772 −0.668861 0.743388i $$-0.733218\pi$$
−0.668861 + 0.743388i $$0.733218\pi$$
$$542$$ −8085.00 −0.640739
$$543$$ 196.000 0.0154902
$$544$$ 6545.00 0.515836
$$545$$ 2611.00 0.205216
$$546$$ 0 0
$$547$$ −8615.00 −0.673402 −0.336701 0.941612i $$-0.609311\pi$$
−0.336701 + 0.941612i $$0.609311\pi$$
$$548$$ −30192.0 −2.35354
$$549$$ 1232.00 0.0957750
$$550$$ −9880.00 −0.765972
$$551$$ −10332.0 −0.798835
$$552$$ 30240.0 2.33170
$$553$$ 0 0
$$554$$ 19100.0 1.46477
$$555$$ −6419.00 −0.490939
$$556$$ 31773.0 2.42352
$$557$$ 8535.00 0.649263 0.324632 0.945841i $$-0.394760\pi$$
0.324632 + 0.945841i $$0.394760\pi$$
$$558$$ 21560.0 1.63568
$$559$$ 2613.00 0.197707
$$560$$ 0 0
$$561$$ 14014.0 1.05467
$$562$$ 31070.0 2.33204
$$563$$ 4641.00 0.347415 0.173708 0.984797i $$-0.444425\pi$$
0.173708 + 0.984797i $$0.444425\pi$$
$$564$$ 12495.0 0.932862
$$565$$ −12138.0 −0.903804
$$566$$ −26460.0 −1.96501
$$567$$ 0 0
$$568$$ −405.000 −0.0299180
$$569$$ −4793.00 −0.353134 −0.176567 0.984289i $$-0.556499\pi$$
−0.176567 + 0.984289i $$0.556499\pi$$
$$570$$ −30870.0 −2.26842
$$571$$ −5563.00 −0.407713 −0.203857 0.979001i $$-0.565348\pi$$
−0.203857 + 0.979001i $$0.565348\pi$$
$$572$$ 5746.00 0.420022
$$573$$ 2954.00 0.215367
$$574$$ 0 0
$$575$$ 7296.00 0.529155
$$576$$ −6314.00 −0.456742
$$577$$ −24038.0 −1.73434 −0.867171 0.498011i $$-0.834064\pi$$
−0.867171 + 0.498011i $$0.834064\pi$$
$$578$$ −5080.00 −0.365571
$$579$$ 3444.00 0.247198
$$580$$ −9758.00 −0.698584
$$581$$ 0 0
$$582$$ 2450.00 0.174494
$$583$$ 11232.0 0.797911
$$584$$ 4410.00 0.312478
$$585$$ −2002.00 −0.141491
$$586$$ −4515.00 −0.318281
$$587$$ 21224.0 1.49235 0.746174 0.665751i $$-0.231889\pi$$
0.746174 + 0.665751i $$0.231889\pi$$
$$588$$ 0 0
$$589$$ −24696.0 −1.72764
$$590$$ −10290.0 −0.718021
$$591$$ 20937.0 1.45725
$$592$$ −11659.0 −0.809429
$$593$$ −4354.00 −0.301513 −0.150757 0.988571i $$-0.548171\pi$$
−0.150757 + 0.988571i $$0.548171\pi$$
$$594$$ −4550.00 −0.314291
$$595$$ 0 0
$$596$$ 41922.0 2.88119
$$597$$ 490.000 0.0335919
$$598$$ −6240.00 −0.426710
$$599$$ 7310.00 0.498629 0.249314 0.968423i $$-0.419795\pi$$
0.249314 + 0.968423i $$0.419795\pi$$
$$600$$ 23940.0 1.62891
$$601$$ 7595.00 0.515485 0.257743 0.966214i $$-0.417021\pi$$
0.257743 + 0.966214i $$0.417021\pi$$
$$602$$ 0 0
$$603$$ 10516.0 0.710190
$$604$$ −56491.0 −3.80561
$$605$$ −4585.00 −0.308110
$$606$$ 14700.0 0.985391
$$607$$ 826.000 0.0552328 0.0276164 0.999619i $$-0.491208\pi$$
0.0276164 + 0.999619i $$0.491208\pi$$
$$608$$ −10710.0 −0.714388
$$609$$ 0 0
$$610$$ −1960.00 −0.130095
$$611$$ −1365.00 −0.0903797
$$612$$ −28798.0 −1.90211
$$613$$ 14590.0 0.961312 0.480656 0.876909i $$-0.340398\pi$$
0.480656 + 0.876909i $$0.340398\pi$$
$$614$$ 10570.0 0.694740
$$615$$ −16464.0 −1.07950
$$616$$ 0 0
$$617$$ 4888.00 0.318936 0.159468 0.987203i $$-0.449022\pi$$
0.159468 + 0.987203i $$0.449022\pi$$
$$618$$ 20580.0 1.33956
$$619$$ 11004.0 0.714520 0.357260 0.934005i $$-0.383711\pi$$
0.357260 + 0.934005i $$0.383711\pi$$
$$620$$ −23324.0 −1.51083
$$621$$ 3360.00 0.217121
$$622$$ 17010.0 1.09653
$$623$$ 0 0
$$624$$ −8099.00 −0.519582
$$625$$ −349.000 −0.0223360
$$626$$ −53445.0 −3.41229
$$627$$ −22932.0 −1.46063
$$628$$ 46410.0 2.94898
$$629$$ 10087.0 0.639420
$$630$$ 0 0
$$631$$ −4975.00 −0.313869 −0.156935 0.987609i $$-0.550161\pi$$
−0.156935 + 0.987609i $$0.550161\pi$$
$$632$$ −58680.0 −3.69330
$$633$$ 19957.0 1.25311
$$634$$ 35270.0 2.20939
$$635$$ 13244.0 0.827673
$$636$$ −51408.0 −3.20513
$$637$$ 0 0
$$638$$ −10660.0 −0.661494
$$639$$ 198.000 0.0122578
$$640$$ 14805.0 0.914405
$$641$$ 3950.00 0.243394 0.121697 0.992567i $$-0.461166\pi$$
0.121697 + 0.992567i $$0.461166\pi$$
$$642$$ 23940.0 1.47171
$$643$$ 3682.00 0.225823 0.112911 0.993605i $$-0.463982\pi$$
0.112911 + 0.993605i $$0.463982\pi$$
$$644$$ 0 0
$$645$$ −9849.00 −0.601247
$$646$$ 48510.0 2.95449
$$647$$ −10402.0 −0.632063 −0.316032 0.948749i $$-0.602351\pi$$
−0.316032 + 0.948749i $$0.602351\pi$$
$$648$$ 37755.0 2.28882
$$649$$ −7644.00 −0.462332
$$650$$ −4940.00 −0.298097
$$651$$ 0 0
$$652$$ −9248.00 −0.555490
$$653$$ −31680.0 −1.89852 −0.949260 0.314491i $$-0.898166\pi$$
−0.949260 + 0.314491i $$0.898166\pi$$
$$654$$ −13055.0 −0.780567
$$655$$ −10045.0 −0.599222
$$656$$ −29904.0 −1.77981
$$657$$ −2156.00 −0.128027
$$658$$ 0 0
$$659$$ 21940.0 1.29691 0.648453 0.761255i $$-0.275416\pi$$
0.648453 + 0.761255i $$0.275416\pi$$
$$660$$ −21658.0 −1.27733
$$661$$ 31374.0 1.84615 0.923077 0.384616i $$-0.125666\pi$$
0.923077 + 0.384616i $$0.125666\pi$$
$$662$$ −48520.0 −2.84862
$$663$$ 7007.00 0.410451
$$664$$ −13860.0 −0.810049
$$665$$ 0 0
$$666$$ 14410.0 0.838403
$$667$$ 7872.00 0.456979
$$668$$ −27608.0 −1.59908
$$669$$ −1519.00 −0.0877847
$$670$$ −16730.0 −0.964681
$$671$$ −1456.00 −0.0837679
$$672$$ 0 0
$$673$$ 18013.0 1.03172 0.515862 0.856672i $$-0.327472\pi$$
0.515862 + 0.856672i $$0.327472\pi$$
$$674$$ 52245.0 2.98576
$$675$$ 2660.00 0.151679
$$676$$ 2873.00 0.163462
$$677$$ 10640.0 0.604030 0.302015 0.953303i $$-0.402341\pi$$
0.302015 + 0.953303i $$0.402341\pi$$
$$678$$ 60690.0 3.43774
$$679$$ 0 0
$$680$$ 24255.0 1.36785
$$681$$ 18032.0 1.01467
$$682$$ −25480.0 −1.43062
$$683$$ −9336.00 −0.523034 −0.261517 0.965199i $$-0.584223\pi$$
−0.261517 + 0.965199i $$0.584223\pi$$
$$684$$ 47124.0 2.63426
$$685$$ −12432.0 −0.693434
$$686$$ 0 0
$$687$$ −3185.00 −0.176878
$$688$$ −17889.0 −0.991296
$$689$$ 5616.00 0.310526
$$690$$ 23520.0 1.29767
$$691$$ −4200.00 −0.231224 −0.115612 0.993294i $$-0.536883\pi$$
−0.115612 + 0.993294i $$0.536883\pi$$
$$692$$ 5712.00 0.313783
$$693$$ 0 0
$$694$$ 3105.00 0.169833
$$695$$ 13083.0 0.714052
$$696$$ 25830.0 1.40673
$$697$$ 25872.0 1.40599
$$698$$ 62405.0 3.38405
$$699$$ 21427.0 1.15943
$$700$$ 0 0
$$701$$ 9872.00 0.531898 0.265949 0.963987i $$-0.414315\pi$$
0.265949 + 0.963987i $$0.414315\pi$$
$$702$$ −2275.00 −0.122314
$$703$$ −16506.0 −0.885541
$$704$$ 7462.00 0.399481
$$705$$ 5145.00 0.274854
$$706$$ −7000.00 −0.373156
$$707$$ 0 0
$$708$$ 34986.0 1.85714
$$709$$ 28450.0 1.50700 0.753499 0.657449i $$-0.228364\pi$$
0.753499 + 0.657449i $$0.228364\pi$$
$$710$$ −315.000 −0.0166503
$$711$$ 28688.0 1.51320
$$712$$ −53550.0 −2.81864
$$713$$ 18816.0 0.988310
$$714$$ 0 0
$$715$$ 2366.00 0.123753
$$716$$ −51493.0 −2.68769
$$717$$ −24339.0 −1.26772
$$718$$ 24840.0 1.29111
$$719$$ −32718.0 −1.69705 −0.848523 0.529159i $$-0.822507\pi$$
−0.848523 + 0.529159i $$0.822507\pi$$
$$720$$ 13706.0 0.709434
$$721$$ 0 0
$$722$$ −45085.0 −2.32395
$$723$$ 11270.0 0.579718
$$724$$ 476.000 0.0244343
$$725$$ 6232.00 0.319242
$$726$$ 22925.0 1.17194
$$727$$ 22834.0 1.16488 0.582439 0.812874i $$-0.302099\pi$$
0.582439 + 0.812874i $$0.302099\pi$$
$$728$$ 0 0
$$729$$ −11843.0 −0.601687
$$730$$ 3430.00 0.173904
$$731$$ 15477.0 0.783088
$$732$$ 6664.00 0.336487
$$733$$ −7875.00 −0.396821 −0.198410 0.980119i $$-0.563578\pi$$
−0.198410 + 0.980119i $$0.563578\pi$$
$$734$$ 43610.0 2.19302
$$735$$ 0 0
$$736$$ 8160.00 0.408671
$$737$$ −12428.0 −0.621155
$$738$$ 36960.0 1.84352
$$739$$ −2140.00 −0.106524 −0.0532620 0.998581i $$-0.516962\pi$$
−0.0532620 + 0.998581i $$0.516962\pi$$
$$740$$ −15589.0 −0.774410
$$741$$ −11466.0 −0.568440
$$742$$ 0 0
$$743$$ 31971.0 1.57860 0.789302 0.614006i $$-0.210443\pi$$
0.789302 + 0.614006i $$0.210443\pi$$
$$744$$ 61740.0 3.04234
$$745$$ 17262.0 0.848900
$$746$$ −50060.0 −2.45687
$$747$$ 6776.00 0.331889
$$748$$ 34034.0 1.66364
$$749$$ 0 0
$$750$$ 49245.0 2.39756
$$751$$ −7432.00 −0.361115 −0.180558 0.983564i $$-0.557790\pi$$
−0.180558 + 0.983564i $$0.557790\pi$$
$$752$$ 9345.00 0.453161
$$753$$ −7056.00 −0.341481
$$754$$ −5330.00 −0.257437
$$755$$ −23261.0 −1.12126
$$756$$ 0 0
$$757$$ 20176.0 0.968704 0.484352 0.874873i $$-0.339055\pi$$
0.484352 + 0.874873i $$0.339055\pi$$
$$758$$ 16860.0 0.807893
$$759$$ 17472.0 0.835564
$$760$$ −39690.0 −1.89435
$$761$$ 9478.00 0.451481 0.225741 0.974187i $$-0.427520\pi$$
0.225741 + 0.974187i $$0.427520\pi$$
$$762$$ −66220.0 −3.14816
$$763$$ 0 0
$$764$$ 7174.00 0.339720
$$765$$ −11858.0 −0.560427
$$766$$ −4235.00 −0.199761
$$767$$ −3822.00 −0.179928
$$768$$ −57953.0 −2.72292
$$769$$ 12096.0 0.567221 0.283610 0.958940i $$-0.408468\pi$$
0.283610 + 0.958940i $$0.408468\pi$$
$$770$$ 0 0
$$771$$ −42287.0 −1.97526
$$772$$ 8364.00 0.389931
$$773$$ −17941.0 −0.834790 −0.417395 0.908725i $$-0.637057\pi$$
−0.417395 + 0.908725i $$0.637057\pi$$
$$774$$ 22110.0 1.02678
$$775$$ 14896.0 0.690426
$$776$$ 3150.00 0.145720
$$777$$ 0 0
$$778$$ −56570.0 −2.60685
$$779$$ −42336.0 −1.94717
$$780$$ −10829.0 −0.497103
$$781$$ −234.000 −0.0107211
$$782$$ −36960.0 −1.69014
$$783$$ 2870.00 0.130990
$$784$$ 0 0
$$785$$ 19110.0 0.868873
$$786$$ 50225.0 2.27922
$$787$$ −6664.00 −0.301837 −0.150919 0.988546i $$-0.548223\pi$$
−0.150919 + 0.988546i $$0.548223\pi$$
$$788$$ 50847.0 2.29867
$$789$$ −25956.0 −1.17118
$$790$$ −45640.0 −2.05544
$$791$$ 0 0
$$792$$ 25740.0 1.15484
$$793$$ −728.000 −0.0326003
$$794$$ 9310.00 0.416120
$$795$$ −21168.0 −0.944342
$$796$$ 1190.00 0.0529880
$$797$$ 1442.00 0.0640882 0.0320441 0.999486i $$-0.489798\pi$$
0.0320441 + 0.999486i $$0.489798\pi$$
$$798$$ 0 0
$$799$$ −8085.00 −0.357981
$$800$$ 6460.00 0.285494
$$801$$ 26180.0 1.15484
$$802$$ −34100.0 −1.50139
$$803$$ 2548.00 0.111976
$$804$$ 56882.0 2.49512
$$805$$ 0 0
$$806$$ −12740.0 −0.556759
$$807$$ −58408.0 −2.54778
$$808$$ 18900.0 0.822896
$$809$$ 30207.0 1.31276 0.656379 0.754431i $$-0.272087\pi$$
0.656379 + 0.754431i $$0.272087\pi$$
$$810$$ 29365.0 1.27380
$$811$$ −21140.0 −0.915322 −0.457661 0.889127i $$-0.651313\pi$$
−0.457661 + 0.889127i $$0.651313\pi$$
$$812$$ 0 0
$$813$$ 11319.0 0.488284
$$814$$ −17030.0 −0.733294
$$815$$ −3808.00 −0.163667
$$816$$ −47971.0 −2.05799
$$817$$ −25326.0 −1.08451
$$818$$ −64960.0 −2.77662
$$819$$ 0 0
$$820$$ −39984.0 −1.70281
$$821$$ 569.000 0.0241879 0.0120939 0.999927i $$-0.496150\pi$$
0.0120939 + 0.999927i $$0.496150\pi$$
$$822$$ 62160.0 2.63757
$$823$$ −8538.00 −0.361623 −0.180812 0.983518i $$-0.557872\pi$$
−0.180812 + 0.983518i $$0.557872\pi$$
$$824$$ 26460.0 1.11866
$$825$$ 13832.0 0.583719
$$826$$ 0 0
$$827$$ −32702.0 −1.37504 −0.687521 0.726164i $$-0.741301\pi$$
−0.687521 + 0.726164i $$0.741301\pi$$
$$828$$ −35904.0 −1.50694
$$829$$ 21154.0 0.886259 0.443130 0.896458i $$-0.353868\pi$$
0.443130 + 0.896458i $$0.353868\pi$$
$$830$$ −10780.0 −0.450818
$$831$$ −26740.0 −1.11625
$$832$$ 3731.00 0.155468
$$833$$ 0 0
$$834$$ −65415.0 −2.71599
$$835$$ −11368.0 −0.471145
$$836$$ −55692.0 −2.30400
$$837$$ 6860.00 0.283293
$$838$$ −36715.0 −1.51348
$$839$$ 2184.00 0.0898690 0.0449345 0.998990i $$-0.485692\pi$$
0.0449345 + 0.998990i $$0.485692\pi$$
$$840$$ 0 0
$$841$$ −17665.0 −0.724302
$$842$$ 25295.0 1.03530
$$843$$ −43498.0 −1.77717
$$844$$ 48467.0 1.97666
$$845$$ 1183.00 0.0481615
$$846$$ −11550.0 −0.469382
$$847$$ 0 0
$$848$$ −38448.0 −1.55697
$$849$$ 37044.0 1.49746
$$850$$ −29260.0 −1.18072
$$851$$ 12576.0 0.506580
$$852$$ 1071.00 0.0430656
$$853$$ −36687.0 −1.47261 −0.736307 0.676648i $$-0.763432\pi$$
−0.736307 + 0.676648i $$0.763432\pi$$
$$854$$ 0 0
$$855$$ 19404.0 0.776144
$$856$$ 30780.0 1.22902
$$857$$ −36806.0 −1.46706 −0.733529 0.679658i $$-0.762128\pi$$
−0.733529 + 0.679658i $$0.762128\pi$$
$$858$$ −11830.0 −0.470710
$$859$$ −4900.00 −0.194628 −0.0973142 0.995254i $$-0.531025\pi$$
−0.0973142 + 0.995254i $$0.531025\pi$$
$$860$$ −23919.0 −0.948408
$$861$$ 0 0
$$862$$ −16215.0 −0.640702
$$863$$ −13697.0 −0.540268 −0.270134 0.962823i $$-0.587068\pi$$
−0.270134 + 0.962823i $$0.587068\pi$$
$$864$$ 2975.00 0.117143
$$865$$ 2352.00 0.0924513
$$866$$ 57995.0 2.27569
$$867$$ 7112.00 0.278588
$$868$$ 0 0
$$869$$ −33904.0 −1.32349
$$870$$ 20090.0 0.782891
$$871$$ −6214.00 −0.241737
$$872$$ −16785.0 −0.651848
$$873$$ −1540.00 −0.0597034
$$874$$ 60480.0 2.34069
$$875$$ 0 0
$$876$$ −11662.0 −0.449797
$$877$$ 6239.00 0.240224 0.120112 0.992760i $$-0.461675\pi$$
0.120112 + 0.992760i $$0.461675\pi$$
$$878$$ −86870.0 −3.33909
$$879$$ 6321.00 0.242551
$$880$$ −16198.0 −0.620494
$$881$$ −133.000 −0.00508613 −0.00254307 0.999997i $$-0.500809\pi$$
−0.00254307 + 0.999997i $$0.500809\pi$$
$$882$$ 0 0
$$883$$ −26003.0 −0.991020 −0.495510 0.868602i $$-0.665019\pi$$
−0.495510 + 0.868602i $$0.665019\pi$$
$$884$$ 17017.0 0.647448
$$885$$ 14406.0 0.547178
$$886$$ −4945.00 −0.187506
$$887$$ 31248.0 1.18287 0.591435 0.806353i $$-0.298562\pi$$
0.591435 + 0.806353i $$0.298562\pi$$
$$888$$ 41265.0 1.55942
$$889$$ 0 0
$$890$$ −41650.0 −1.56866
$$891$$ 21814.0 0.820198
$$892$$ −3689.00 −0.138472
$$893$$ 13230.0 0.495773
$$894$$ −86310.0 −3.22890
$$895$$ −21203.0 −0.791886
$$896$$ 0 0
$$897$$ 8736.00 0.325180
$$898$$ 72370.0 2.68933
$$899$$ 16072.0 0.596253
$$900$$ −28424.0 −1.05274
$$901$$ 33264.0 1.22995
$$902$$ −43680.0 −1.61240
$$903$$ 0 0
$$904$$ 78030.0 2.87084
$$905$$ 196.000 0.00719918
$$906$$ 116305. 4.26487
$$907$$ −38253.0 −1.40041 −0.700204 0.713943i $$-0.746908\pi$$
−0.700204 + 0.713943i $$0.746908\pi$$
$$908$$ 43792.0 1.60054
$$909$$ −9240.00 −0.337152
$$910$$ 0 0
$$911$$ 36374.0 1.32286 0.661429 0.750007i $$-0.269950\pi$$
0.661429 + 0.750007i $$0.269950\pi$$
$$912$$ 78498.0 2.85014
$$913$$ −8008.00 −0.290281
$$914$$ 7970.00 0.288429
$$915$$ 2744.00 0.0991408
$$916$$ −7735.00 −0.279008
$$917$$ 0 0
$$918$$ −13475.0 −0.484468
$$919$$ −27648.0 −0.992408 −0.496204 0.868206i $$-0.665273\pi$$
−0.496204 + 0.868206i $$0.665273\pi$$
$$920$$ 30240.0 1.08368
$$921$$ −14798.0 −0.529436
$$922$$ −29575.0 −1.05640
$$923$$ −117.000 −0.00417237
$$924$$ 0 0
$$925$$ 9956.00 0.353893
$$926$$ 55360.0 1.96462
$$927$$ −12936.0 −0.458332
$$928$$ 6970.00 0.246553
$$929$$ −756.000 −0.0266992 −0.0133496 0.999911i $$-0.504249\pi$$
−0.0133496 + 0.999911i $$0.504249\pi$$
$$930$$ 48020.0 1.69316
$$931$$ 0 0
$$932$$ 52037.0 1.82889
$$933$$ −23814.0 −0.835622
$$934$$ 6300.00 0.220709
$$935$$ 14014.0 0.490168
$$936$$ 12870.0 0.449433
$$937$$ −20846.0 −0.726797 −0.363399 0.931634i $$-0.618384\pi$$
−0.363399 + 0.931634i $$0.618384\pi$$
$$938$$ 0 0
$$939$$ 74823.0 2.60038
$$940$$ 12495.0 0.433555
$$941$$ 41321.0 1.43148 0.715742 0.698365i $$-0.246089\pi$$
0.715742 + 0.698365i $$0.246089\pi$$
$$942$$ −95550.0 −3.30487
$$943$$ 32256.0 1.11389
$$944$$ 26166.0 0.902151
$$945$$ 0 0
$$946$$ −26130.0 −0.898055
$$947$$ 54966.0 1.88612 0.943060 0.332624i $$-0.107934\pi$$
0.943060 + 0.332624i $$0.107934\pi$$
$$948$$ 155176. 5.31633
$$949$$ 1274.00 0.0435783
$$950$$ 47880.0 1.63519
$$951$$ −49378.0 −1.68369
$$952$$ 0 0
$$953$$ −44553.0 −1.51439 −0.757195 0.653189i $$-0.773431\pi$$
−0.757195 + 0.653189i $$0.773431\pi$$
$$954$$ 47520.0 1.61270
$$955$$ 2954.00 0.100093
$$956$$ −59109.0 −1.99971
$$957$$ 14924.0 0.504101
$$958$$ −60165.0 −2.02906
$$959$$ 0 0
$$960$$ −14063.0 −0.472793
$$961$$ 8625.00 0.289517
$$962$$ −8515.00 −0.285379
$$963$$ −15048.0 −0.503546
$$964$$ 27370.0 0.914448
$$965$$ 3444.00 0.114887
$$966$$ 0 0
$$967$$ −27907.0 −0.928054 −0.464027 0.885821i $$-0.653596\pi$$
−0.464027 + 0.885821i $$0.653596\pi$$
$$968$$ 29475.0 0.978680
$$969$$ −67914.0 −2.25151
$$970$$ 2450.00 0.0810977
$$971$$ 16443.0 0.543441 0.271720 0.962376i $$-0.412407\pi$$
0.271720 + 0.962376i $$0.412407\pi$$
$$972$$ −83776.0 −2.76452
$$973$$ 0 0
$$974$$ 11400.0 0.375030
$$975$$ 6916.00 0.227168
$$976$$ 4984.00 0.163457
$$977$$ −45414.0 −1.48713 −0.743563 0.668666i $$-0.766866\pi$$
−0.743563 + 0.668666i $$0.766866\pi$$
$$978$$ 19040.0 0.622528
$$979$$ −30940.0 −1.01006
$$980$$ 0 0
$$981$$ 8206.00 0.267072
$$982$$ −83835.0 −2.72432
$$983$$ 8981.00 0.291403 0.145702 0.989329i $$-0.453456\pi$$
0.145702 + 0.989329i $$0.453456\pi$$
$$984$$ 105840. 3.42892
$$985$$ 20937.0 0.677267
$$986$$ −31570.0 −1.01967
$$987$$ 0 0
$$988$$ −27846.0 −0.896659
$$989$$ 19296.0 0.620402
$$990$$ 20020.0 0.642704
$$991$$ −17414.0 −0.558198 −0.279099 0.960262i $$-0.590036\pi$$
−0.279099 + 0.960262i $$0.590036\pi$$
$$992$$ 16660.0 0.533221
$$993$$ 67928.0 2.17083
$$994$$ 0 0
$$995$$ 490.000 0.0156121
$$996$$ 36652.0 1.16603
$$997$$ 23702.0 0.752909 0.376454 0.926435i $$-0.377143\pi$$
0.376454 + 0.926435i $$0.377143\pi$$
$$998$$ −64200.0 −2.03629
$$999$$ 4585.00 0.145208
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 637.4.a.a.1.1 1
7.6 odd 2 13.4.a.a.1.1 1
21.20 even 2 117.4.a.b.1.1 1
28.27 even 2 208.4.a.g.1.1 1
35.13 even 4 325.4.b.b.274.2 2
35.27 even 4 325.4.b.b.274.1 2
35.34 odd 2 325.4.a.d.1.1 1
56.13 odd 2 832.4.a.r.1.1 1
56.27 even 2 832.4.a.a.1.1 1
77.76 even 2 1573.4.a.a.1.1 1
84.83 odd 2 1872.4.a.k.1.1 1
91.6 even 12 169.4.e.e.23.2 4
91.20 even 12 169.4.e.e.23.1 4
91.34 even 4 169.4.b.a.168.1 2
91.41 even 12 169.4.e.e.147.1 4
91.48 odd 6 169.4.c.e.146.1 2
91.55 odd 6 169.4.c.e.22.1 2
91.62 odd 6 169.4.c.a.22.1 2
91.69 odd 6 169.4.c.a.146.1 2
91.76 even 12 169.4.e.e.147.2 4
91.83 even 4 169.4.b.a.168.2 2
91.90 odd 2 169.4.a.e.1.1 1
273.272 even 2 1521.4.a.a.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
13.4.a.a.1.1 1 7.6 odd 2
117.4.a.b.1.1 1 21.20 even 2
169.4.a.e.1.1 1 91.90 odd 2
169.4.b.a.168.1 2 91.34 even 4
169.4.b.a.168.2 2 91.83 even 4
169.4.c.a.22.1 2 91.62 odd 6
169.4.c.a.146.1 2 91.69 odd 6
169.4.c.e.22.1 2 91.55 odd 6
169.4.c.e.146.1 2 91.48 odd 6
169.4.e.e.23.1 4 91.20 even 12
169.4.e.e.23.2 4 91.6 even 12
169.4.e.e.147.1 4 91.41 even 12
169.4.e.e.147.2 4 91.76 even 12
208.4.a.g.1.1 1 28.27 even 2
325.4.a.d.1.1 1 35.34 odd 2
325.4.b.b.274.1 2 35.27 even 4
325.4.b.b.274.2 2 35.13 even 4
637.4.a.a.1.1 1 1.1 even 1 trivial
832.4.a.a.1.1 1 56.27 even 2
832.4.a.r.1.1 1 56.13 odd 2
1521.4.a.a.1.1 1 273.272 even 2
1573.4.a.a.1.1 1 77.76 even 2
1872.4.a.k.1.1 1 84.83 odd 2