LMFDB - Embedded newform 6037.2.a.b.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6037,2,Mod(1,6037)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6037, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("6037.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6037 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6037.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:	$48.2056877002$
Analytic rank:	$0$
Dimension:	$259$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6037.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.42988 q^{2} +0.381455 q^{3} +3.90430 q^{4} -2.17078 q^{5} -0.926887 q^{6} -2.70764 q^{7} -4.62721 q^{8} -2.85449 q^{9} +O(q^{10})$	\(q-2.42988 q^{2} +0.381455 q^{3} +3.90430 q^{4} -2.17078 q^{5} -0.926887 q^{6} -2.70764 q^{7} -4.62721 q^{8} -2.85449 q^{9} +5.27472 q^{10} +5.11321 q^{11} +1.48931 q^{12} +6.54077 q^{13} +6.57923 q^{14} -0.828053 q^{15} +3.43495 q^{16} -0.0279003 q^{17} +6.93606 q^{18} +7.94119 q^{19} -8.47537 q^{20} -1.03284 q^{21} -12.4245 q^{22} +7.01359 q^{23} -1.76507 q^{24} -0.287719 q^{25} -15.8933 q^{26} -2.23322 q^{27} -10.5714 q^{28} +8.51367 q^{29} +2.01207 q^{30} +3.77239 q^{31} +0.907913 q^{32} +1.95046 q^{33} +0.0677944 q^{34} +5.87769 q^{35} -11.1448 q^{36} -0.838138 q^{37} -19.2961 q^{38} +2.49501 q^{39} +10.0447 q^{40} -8.68434 q^{41} +2.50968 q^{42} +3.58105 q^{43} +19.9635 q^{44} +6.19647 q^{45} -17.0422 q^{46} +7.68087 q^{47} +1.31028 q^{48} +0.331317 q^{49} +0.699122 q^{50} -0.0106427 q^{51} +25.5371 q^{52} +13.0055 q^{53} +5.42645 q^{54} -11.0996 q^{55} +12.5288 q^{56} +3.02920 q^{57} -20.6872 q^{58} +10.0502 q^{59} -3.23297 q^{60} +5.26980 q^{61} -9.16644 q^{62} +7.72894 q^{63} -9.07602 q^{64} -14.1986 q^{65} -4.73937 q^{66} -12.6218 q^{67} -0.108931 q^{68} +2.67537 q^{69} -14.2821 q^{70} -11.1737 q^{71} +13.2083 q^{72} +5.14509 q^{73} +2.03657 q^{74} -0.109752 q^{75} +31.0048 q^{76} -13.8447 q^{77} -6.06256 q^{78} -9.63964 q^{79} -7.45652 q^{80} +7.71160 q^{81} +21.1019 q^{82} +9.70275 q^{83} -4.03252 q^{84} +0.0605655 q^{85} -8.70150 q^{86} +3.24758 q^{87} -23.6599 q^{88} +0.517760 q^{89} -15.0567 q^{90} -17.7101 q^{91} +27.3832 q^{92} +1.43899 q^{93} -18.6636 q^{94} -17.2386 q^{95} +0.346327 q^{96} -6.38286 q^{97} -0.805060 q^{98} -14.5956 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9}+O(q^{10}) $ 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9	\( 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9} + 18 q^{10} + 108 q^{11} + 46 q^{12} + 33 q^{13} + 35 q^{14} + 40 q^{15} + 301 q^{16} + 67 q^{17} + 117 q^{18} + 69 q^{19} + 103 q^{20} + 24 q^{21} + 42 q^{22} + 162 q^{23} + 45 q^{24} + 291 q^{25} + 41 q^{26} + 101 q^{27} + 87 q^{28} + 78 q^{29} + 48 q^{30} + 25 q^{31} + 314 q^{32} + 67 q^{33} + 9 q^{34} + 252 q^{35} + 337 q^{36} + 49 q^{37} + 59 q^{38} + 93 q^{39} + 44 q^{40} + 60 q^{41} + 38 q^{42} + 178 q^{43} + 171 q^{44} + 67 q^{45} + 43 q^{46} + 185 q^{47} + 67 q^{48} + 273 q^{49} + 204 q^{50} + 145 q^{51} + 83 q^{52} + 112 q^{53} + 60 q^{54} + 57 q^{55} + 93 q^{56} + 109 q^{57} + 63 q^{58} + 228 q^{59} + 53 q^{60} + 20 q^{61} + 126 q^{62} + 153 q^{63} + 345 q^{64} + 113 q^{65} + 5 q^{66} + 208 q^{67} + 166 q^{68} + 10 q^{69} + 69 q^{70} + 150 q^{71} + 331 q^{72} + 75 q^{73} + 84 q^{74} + 72 q^{75} + 102 q^{76} + 166 q^{77} + 69 q^{78} + 52 q^{79} + 180 q^{80} + 327 q^{81} + 43 q^{82} + 434 q^{83} + 75 q^{85} + 133 q^{86} + 144 q^{87} + 111 q^{88} + 78 q^{89} - 8 q^{90} + 35 q^{91} + 372 q^{92} + 160 q^{93} + 36 q^{94} + 154 q^{95} + 60 q^{96} + 35 q^{97} + 254 q^{98} + 234 q^{99}+O(q^{100}) \) 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9 + 18 * q^10 + 108 * q^11 + 46 * q^12 + 33 * q^13 + 35 * q^14 + 40 * q^15 + 301 * q^16 + 67 * q^17 + 117 * q^18 + 69 * q^19 + 103 * q^20 + 24 * q^21 + 42 * q^22 + 162 * q^23 + 45 * q^24 + 291 * q^25 + 41 * q^26 + 101 * q^27 + 87 * q^28 + 78 * q^29 + 48 * q^30 + 25 * q^31 + 314 * q^32 + 67 * q^33 + 9 * q^34 + 252 * q^35 + 337 * q^36 + 49 * q^37 + 59 * q^38 + 93 * q^39 + 44 * q^40 + 60 * q^41 + 38 * q^42 + 178 * q^43 + 171 * q^44 + 67 * q^45 + 43 * q^46 + 185 * q^47 + 67 * q^48 + 273 * q^49 + 204 * q^50 + 145 * q^51 + 83 * q^52 + 112 * q^53 + 60 * q^54 + 57 * q^55 + 93 * q^56 + 109 * q^57 + 63 * q^58 + 228 * q^59 + 53 * q^60 + 20 * q^61 + 126 * q^62 + 153 * q^63 + 345 * q^64 + 113 * q^65 + 5 * q^66 + 208 * q^67 + 166 * q^68 + 10 * q^69 + 69 * q^70 + 150 * q^71 + 331 * q^72 + 75 * q^73 + 84 * q^74 + 72 * q^75 + 102 * q^76 + 166 * q^77 + 69 * q^78 + 52 * q^79 + 180 * q^80 + 327 * q^81 + 43 * q^82 + 434 * q^83 + 75 * q^85 + 133 * q^86 + 144 * q^87 + 111 * q^88 + 78 * q^89 - 8 * q^90 + 35 * q^91 + 372 * q^92 + 160 * q^93 + 36 * q^94 + 154 * q^95 + 60 * q^96 + 35 * q^97 + 254 * q^98 + 234 * q^99

Display 100 coefficients 10 coefficients

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 $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.42988	−1.71818	−0.859091	−	0.511823i	$-0.828970\pi$
$2$	−2.42988	−1.71818	−0.859091	+	0.511823i	$0.828970\pi$
$3$	0.381455	0.220233	0.110116	−	0.993919i	$-0.464878\pi$
$3$	0.381455	0.220233	0.110116	+	0.993919i	$0.464878\pi$
$4$	3.90430	1.95215
$5$	−2.17078	−0.970802	−0.485401	−	0.874292i	$-0.661326\pi$
$5$	−2.17078	−0.970802	−0.485401	+	0.874292i	$0.661326\pi$
$6$	−0.926887	−0.378400
$7$	−2.70764	−1.02339	−0.511696	−	0.859167i	$-0.670983\pi$
$7$	−2.70764	−1.02339	−0.511696	+	0.859167i	$0.670983\pi$
$8$	−4.62721	−1.63597
$9$	−2.85449	−0.951497
$10$	5.27472	1.66801
$11$	5.11321	1.54169	0.770845	−	0.637022i	$-0.219834\pi$
$11$	5.11321	1.54169	0.770845	+	0.637022i	$0.219834\pi$
$12$	1.48931	0.429927
$13$	6.54077	1.81408	0.907042	−	0.421040i	$-0.138335\pi$
$13$	6.54077	1.81408	0.907042	+	0.421040i	$0.138335\pi$
$14$	6.57923	1.75837
$15$	−0.828053	−0.213802
$16$	3.43495	0.858738
$17$	−0.0279003	−0.00676683	−0.00338341	−	0.999994i	$-0.501077\pi$
$17$	−0.0279003	−0.00676683	−0.00338341	+	0.999994i	$0.501077\pi$
$18$	6.93606	1.63485
$19$	7.94119	1.82183	0.910917	−	0.412590i	$-0.135376\pi$
$19$	7.94119	1.82183	0.910917	+	0.412590i	$0.135376\pi$
$20$	−8.47537	−1.89515
$21$	−1.03284	−0.225385
$22$	−12.4245	−2.64891
$23$	7.01359	1.46244	0.731218	−	0.682144i	$-0.238952\pi$
$23$	7.01359	1.46244	0.731218	+	0.682144i	$0.238952\pi$
$24$	−1.76507	−0.360294
$25$	−0.287719	−0.0575438
$26$	−15.8933	−3.11693
$27$	−2.23322	−0.429784
$28$	−10.5714	−1.99781
$29$	8.51367	1.58095	0.790474	−	0.612495i	$-0.209834\pi$
$29$	8.51367	1.58095	0.790474	+	0.612495i	$0.209834\pi$
$30$	2.01207	0.367352
$31$	3.77239	0.677541	0.338770	−	0.940869i	$-0.389989\pi$
$31$	3.77239	0.677541	0.338770	+	0.940869i	$0.389989\pi$
$32$	0.907913	0.160498
$33$	1.95046	0.339531
$34$	0.0677944	0.0116266
$35$	5.87769	0.993511
$36$	−11.1448	−1.85747
$37$	−0.838138	−0.137789	−0.0688946	−	0.997624i	$-0.521947\pi$
$37$	−0.838138	−0.137789	−0.0688946	+	0.997624i	$0.521947\pi$
$38$	−19.2961	−3.13024
$39$	2.49501	0.399521
$40$	10.0447	1.58820
$41$	−8.68434	−1.35627	−0.678133	−	0.734939i	$-0.737211\pi$
$41$	−8.68434	−1.35627	−0.678133	+	0.734939i	$0.737211\pi$
$42$	2.50968	0.387252
$43$	3.58105	0.546104	0.273052	−	0.961999i	$-0.411967\pi$
$43$	3.58105	0.546104	0.273052	+	0.961999i	$0.411967\pi$
$44$	19.9635	3.00961
$45$	6.19647	0.923715
$46$	−17.0422	−2.51273
$47$	7.68087	1.12037	0.560185	−	0.828368i	$-0.310730\pi$
$47$	7.68087	1.12037	0.560185	+	0.828368i	$0.310730\pi$
$48$	1.31028	0.189122
$49$	0.331317	0.0473311
$50$	0.699122	0.0988708
$51$	−0.0106427	−0.00149028
$52$	25.5371	3.54136
$53$	13.0055	1.78645	0.893223	−	0.449613i	$-0.148438\pi$
$53$	13.0055	1.78645	0.893223	+	0.449613i	$0.148438\pi$
$54$	5.42645	0.738447
$55$	−11.0996	−1.49668
$56$	12.5288	1.67423
$57$	3.02920	0.401228
$58$	−20.6872	−2.71636
$59$	10.0502	1.30843	0.654215	−	0.756309i	$-0.272999\pi$
$59$	10.0502	1.30843	0.654215	+	0.756309i	$0.272999\pi$
$60$	−3.23297	−0.417374
$61$	5.26980	0.674729	0.337364	−	0.941374i	$-0.390465\pi$
$61$	5.26980	0.674729	0.337364	+	0.941374i	$0.390465\pi$
$62$	−9.16644	−1.16414
$63$	7.72894	0.973755
$64$	−9.07602	−1.13450
$65$	−14.1986	−1.76112
$66$	−4.73937	−0.583376
$67$	−12.6218	−1.54200	−0.770999	−	0.636837i	$-0.780243\pi$
$67$	−12.6218	−1.54200	−0.770999	+	0.636837i	$0.780243\pi$
$68$	−0.108931	−0.0132099
$69$	2.67537	0.322076
$70$	−14.2821	−1.70703
$71$	−11.1737	−1.32607	−0.663036	−	0.748587i	$-0.730733\pi$
$71$	−11.1737	−1.32607	−0.663036	+	0.748587i	$0.730733\pi$
$72$	13.2083	1.55662
$73$	5.14509	0.602187	0.301094	−	0.953595i	$-0.402648\pi$
$73$	5.14509	0.602187	0.301094	+	0.953595i	$0.402648\pi$
$74$	2.03657	0.236747
$75$	−0.109752	−0.0126730
$76$	31.0048	3.55649
$77$	−13.8447	−1.57775
$78$	−6.06256	−0.686450
$79$	−9.63964	−1.08454	−0.542272	−	0.840203i	$-0.682436\pi$
$79$	−9.63964	−1.08454	−0.542272	+	0.840203i	$0.682436\pi$
$80$	−7.45652	−0.833664
$81$	7.71160	0.856845
$82$	21.1019	2.33031
$83$	9.70275	1.06502	0.532508	−	0.846425i	$-0.321250\pi$
$83$	9.70275	1.06502	0.532508	+	0.846425i	$0.321250\pi$
$84$	−4.03252	−0.439984
$85$	0.0605655	0.00656925
$86$	−8.70150	−0.938307
$87$	3.24758	0.348177
$88$	−23.6599	−2.52215
$89$	0.517760	0.0548824	0.0274412	−	0.999623i	$-0.491264\pi$
$89$	0.517760	0.0548824	0.0274412	+	0.999623i	$0.491264\pi$
$90$	−15.0567	−1.58711
$91$	−17.7101	−1.85652
$92$	27.3832	2.85489
$93$	1.43899	0.149217
$94$	−18.6636	−1.92500
$95$	−17.2386	−1.76864
$96$	0.346327	0.0353469
$97$	−6.38286	−0.648081	−0.324041	−	0.946043i	$-0.605041\pi$
$97$	−6.38286	−0.648081	−0.324041	+	0.946043i	$0.605041\pi$
$98$	−0.805060	−0.0813234
$99$	−14.5956	−1.46691
$100$	−1.12334	−0.112334
$101$	−3.42167	−0.340469	−0.170234	−	0.985404i	$-0.554453\pi$
$101$	−3.42167	−0.340469	−0.170234	+	0.985404i	$0.554453\pi$
$102$	0.0258605	0.00256057
$103$	10.9741	1.08131	0.540654	−	0.841245i	$-0.318177\pi$
$103$	10.9741	1.08131	0.540654	+	0.841245i	$0.318177\pi$
$104$	−30.2655	−2.96778
$105$	2.24207	0.218804
$106$	−31.6018	−3.06944
$107$	−1.70405	−0.164737	−0.0823684	−	0.996602i	$-0.526248\pi$
$107$	−1.70405	−0.164737	−0.0823684	+	0.996602i	$0.526248\pi$
$108$	−8.71917	−0.839002
$109$	−7.63030	−0.730850	−0.365425	−	0.930841i	$-0.619076\pi$
$109$	−7.63030	−0.730850	−0.365425	+	0.930841i	$0.619076\pi$
$110$	26.9708	2.57156
$111$	−0.319712	−0.0303457
$112$	−9.30062	−0.878826
$113$	−11.9116	−1.12055	−0.560274	−	0.828307i	$-0.689304\pi$
$113$	−11.9116	−1.12055	−0.560274	+	0.828307i	$0.689304\pi$
$114$	−7.36059	−0.689382
$115$	−15.2250	−1.41973
$116$	33.2399	3.08625
$117$	−18.6706	−1.72610
$118$	−24.4208	−2.24812
$119$	0.0755441	0.00692511
$120$	3.83158	0.349774
$121$	15.1449	1.37681
$122$	−12.8050	−1.15931
$123$	−3.31268	−0.298694
$124$	14.7285	1.32266
$125$	11.4785	1.02667
$126$	−18.7804	−1.67309
$127$	−19.0225	−1.68797	−0.843985	−	0.536366i	$-0.819797\pi$
$127$	−19.0225	−1.68797	−0.843985	+	0.536366i	$0.819797\pi$
$128$	20.2378	1.78878
$129$	1.36601	0.120270
$130$	34.5008	3.02592
$131$	−12.8748	−1.12488	−0.562439	−	0.826839i	$-0.690137\pi$
$131$	−12.8748	−1.12488	−0.562439	+	0.826839i	$0.690137\pi$
$132$	7.61517	0.662815
$133$	−21.5019	−1.86445
$134$	30.6694	2.64943
$135$	4.84783	0.417235
$136$	0.129101	0.0110703
$137$	7.15901	0.611636	0.305818	−	0.952090i	$-0.401070\pi$
$137$	7.15901	0.611636	0.305818	+	0.952090i	$0.401070\pi$
$138$	−6.50081	−0.553386
$139$	1.79961	0.152641	0.0763206	−	0.997083i	$-0.475683\pi$
$139$	1.79961	0.152641	0.0763206	+	0.997083i	$0.475683\pi$
$140$	22.9483	1.93948
$141$	2.92990	0.246742
$142$	27.1507	2.27843
$143$	33.4444	2.79676
$144$	−9.80505	−0.817087
$145$	−18.4813	−1.53479
$146$	−12.5019	−1.03467
$147$	0.126383	0.0104239
$148$	−3.27234	−0.268985
$149$	3.26256	0.267279	0.133640	−	0.991030i	$-0.457334\pi$
$149$	3.26256	0.267279	0.133640	+	0.991030i	$0.457334\pi$
$150$	0.266683	0.0217746
$151$	−7.50807	−0.610998	−0.305499	−	0.952192i	$-0.598823\pi$
$151$	−7.50807	−0.610998	−0.305499	+	0.952192i	$0.598823\pi$
$152$	−36.7455	−2.98046
$153$	0.0796413	0.00643862
$154$	33.6410	2.71087
$155$	−8.18902	−0.657758
$156$	9.74126	0.779925
$157$	17.4635	1.39374	0.696870	−	0.717198i	$-0.254576\pi$
$157$	17.4635	1.39374	0.696870	+	0.717198i	$0.254576\pi$
$158$	23.4231	1.86344
$159$	4.96102	0.393434
$160$	−1.97088	−0.155812
$161$	−18.9903	−1.49664
$162$	−18.7382	−1.47222
$163$	−4.63131	−0.362752	−0.181376	−	0.983414i	$-0.558055\pi$
$163$	−4.63131	−0.362752	−0.181376	+	0.983414i	$0.558055\pi$
$164$	−33.9063	−2.64763
$165$	−4.23401	−0.329617
$166$	−23.5765	−1.82989
$167$	−4.60701	−0.356501	−0.178251	−	0.983985i	$-0.557044\pi$
$167$	−4.60701	−0.356501	−0.178251	+	0.983985i	$0.557044\pi$
$168$	4.77918	0.368721
$169$	29.7817	2.29090
$170$	−0.147167	−0.0112872
$171$	−22.6681	−1.73347
$172$	13.9815	1.06608
$173$	−3.85338	−0.292967	−0.146483	−	0.989213i	$-0.546795\pi$
$173$	−3.85338	−0.292967	−0.146483	+	0.989213i	$0.546795\pi$
$174$	−7.89121	−0.598231
$175$	0.779040	0.0588899
$176$	17.5636	1.32391
$177$	3.83371	0.288159
$178$	−1.25809	−0.0942980
$179$	−10.1651	−0.759778	−0.379889	−	0.925032i	$-0.624038\pi$
$179$	−10.1651	−0.759778	−0.379889	+	0.925032i	$0.624038\pi$
$180$	24.1929	1.80323
$181$	3.73076	0.277305	0.138653	−	0.990341i	$-0.455723\pi$
$181$	3.73076	0.277305	0.138653	+	0.990341i	$0.455723\pi$
$182$	43.0333	3.18984
$183$	2.01019	0.148597
$184$	−32.4534	−2.39249
$185$	1.81941	0.133766
$186$	−3.49658	−0.256382
$187$	−0.142660	−0.0104324
$188$	29.9884	2.18713
$189$	6.04676	0.439837
$190$	41.8876	3.03884
$191$	24.5691	1.77776	0.888880	−	0.458140i	$-0.151484\pi$
$191$	24.5691	1.77776	0.888880	+	0.458140i	$0.151484\pi$
$192$	−3.46209	−0.249855
$193$	−1.32536	−0.0954014	−0.0477007	−	0.998862i	$-0.515189\pi$
$193$	−1.32536	−0.0954014	−0.0477007	+	0.998862i	$0.515189\pi$
$194$	15.5096	1.11352
$195$	−5.41611	−0.387856
$196$	1.29356	0.0923973
$197$	27.2035	1.93817	0.969086	−	0.246724i	$-0.0793541\pi$
$197$	27.2035	1.93817	0.969086	+	0.246724i	$0.0793541\pi$
$198$	35.4655	2.52043
$199$	10.4326	0.739547	0.369773	−	0.929122i	$-0.379435\pi$
$199$	10.4326	0.739547	0.369773	+	0.929122i	$0.379435\pi$
$200$	1.33134	0.0941398
$201$	−4.81464	−0.339599
$202$	8.31424	0.584988
$203$	−23.0520	−1.61793
$204$	−0.0415523	−0.00290924
$205$	18.8518	1.31667
$206$	−26.6656	−1.85788
$207$	−20.0202	−1.39150
$208$	22.4672	1.55782
$209$	40.6050	2.80870
$210$	−5.44796	−0.375945
$211$	−13.3026	−0.915790	−0.457895	−	0.889006i	$-0.651396\pi$
$211$	−13.3026	−0.915790	−0.457895	+	0.889006i	$0.651396\pi$
$212$	50.7775	3.48741
$213$	−4.26225	−0.292045
$214$	4.14063	0.283048
$215$	−7.77366	−0.530159
$216$	10.3336	0.703112
$217$	−10.2143	−0.693390
$218$	18.5407	1.25573
$219$	1.96262	0.132621
$220$	−43.3363	−2.92174
$221$	−0.182490	−0.0122756
$222$	0.776860	0.0521394
$223$	−16.7060	−1.11872	−0.559358	−	0.828926i	$-0.688952\pi$
$223$	−16.7060	−1.11872	−0.559358	+	0.828926i	$0.688952\pi$
$224$	−2.45830	−0.164252
$225$	0.821292	0.0547528
$226$	28.9437	1.92531
$227$	19.5423	1.29707	0.648533	−	0.761186i	$-0.275383\pi$
$227$	19.5423	1.29707	0.648533	+	0.761186i	$0.275383\pi$
$228$	11.8269	0.783256
$229$	10.7710	0.711769	0.355884	−	0.934530i	$-0.384180\pi$
$229$	10.7710	0.711769	0.355884	+	0.934530i	$0.384180\pi$
$230$	36.9948	2.43936
$231$	−5.28114	−0.347473
$232$	−39.3945	−2.58638
$233$	17.3009	1.13342	0.566710	−	0.823917i	$-0.308216\pi$
$233$	17.3009	1.13342	0.566710	+	0.823917i	$0.308216\pi$
$234$	45.3672	2.96575
$235$	−16.6735	−1.08766
$236$	39.2392	2.55425
$237$	−3.67708	−0.238852
$238$	−0.183563	−0.0118986
$239$	8.99359	0.581747	0.290874	−	0.956761i	$-0.406054\pi$
$239$	8.99359	0.581747	0.290874	+	0.956761i	$0.406054\pi$
$240$	−2.84432	−0.183600
$241$	−0.747944	−0.0481793	−0.0240896	−	0.999710i	$-0.507669\pi$
$241$	−0.747944	−0.0481793	−0.0240896	+	0.999710i	$0.507669\pi$
$242$	−36.8003	−2.36561
$243$	9.64129	0.618489
$244$	20.5749	1.31717
$245$	−0.719217	−0.0459491
$246$	8.04941	0.513211
$247$	51.9415	3.30496
$248$	−17.4556	−1.10843
$249$	3.70116	0.234551
$250$	−27.8913	−1.76400
$251$	3.19751	0.201825	0.100913	−	0.994895i	$-0.467824\pi$
$251$	3.19751	0.201825	0.100913	+	0.994895i	$0.467824\pi$
$252$	30.1761	1.90092
$253$	35.8620	2.25462
$254$	46.2222	2.90024
$255$	0.0231030	0.00144676
$256$	−31.0233	−1.93895
$257$	2.11386	0.131859	0.0659293	−	0.997824i	$-0.478999\pi$
$257$	2.11386	0.131859	0.0659293	+	0.997824i	$0.478999\pi$
$258$	−3.31923	−0.206646
$259$	2.26938	0.141012
$260$	−55.4355	−3.43796
$261$	−24.3022	−1.50427
$262$	31.2842	1.93275
$263$	−10.2742	−0.633534	−0.316767	−	0.948503i	$-0.602597\pi$
$263$	−10.2742	−0.633534	−0.316767	+	0.948503i	$0.602597\pi$
$264$	−9.02518	−0.555461
$265$	−28.2321	−1.73429
$266$	52.2469	3.20346
$267$	0.197502	0.0120869
$268$	−49.2793	−3.01021
$269$	−8.18748	−0.499199	−0.249600	−	0.968349i	$-0.580299\pi$
$269$	−8.18748	−0.499199	−0.249600	+	0.968349i	$0.580299\pi$
$270$	−11.7796	−0.716886
$271$	−8.44352	−0.512907	−0.256454	−	0.966557i	$-0.582554\pi$
$271$	−8.44352	−0.512907	−0.256454	+	0.966557i	$0.582554\pi$
$272$	−0.0958363	−0.00581093
$273$	−6.75558	−0.408867
$274$	−17.3955	−1.05090
$275$	−1.47117	−0.0887148
$276$	10.4454	0.628741
$277$	−8.86079	−0.532393	−0.266197	−	0.963919i	$-0.585767\pi$
$277$	−8.86079	−0.532393	−0.266197	+	0.963919i	$0.585767\pi$
$278$	−4.37284	−0.262265
$279$	−10.7683	−0.644678
$280$	−27.1973	−1.62535
$281$	−15.8292	−0.944291	−0.472146	−	0.881521i	$-0.656520\pi$
$281$	−15.8292	−0.944291	−0.472146	+	0.881521i	$0.656520\pi$
$282$	−7.11930	−0.423948
$283$	−2.83901	−0.168761	−0.0843807	−	0.996434i	$-0.526891\pi$
$283$	−2.83901	−0.168761	−0.0843807	+	0.996434i	$0.526891\pi$
$284$	−43.6254	−2.58869
$285$	−6.57573	−0.389512
$286$	−81.2656	−4.80534
$287$	23.5141	1.38799
$288$	−2.59163	−0.152713
$289$	−16.9992	−0.999954
$290$	44.9073	2.63704
$291$	−2.43477	−0.142729
$292$	20.0880	1.17556
$293$	−3.38920	−0.197999	−0.0989997	−	0.995087i	$-0.531564\pi$
$293$	−3.38920	−0.197999	−0.0989997	+	0.995087i	$0.531564\pi$
$294$	−0.307094	−0.0179101
$295$	−21.8169	−1.27023
$296$	3.87824	0.225418
$297$	−11.4189	−0.662594
$298$	−7.92761	−0.459234
$299$	45.8743	2.65298
$300$	−0.428504	−0.0247397
$301$	−9.69619	−0.558879
$302$	18.2437	1.04981
$303$	−1.30521	−0.0749825
$304$	27.2776	1.56448
$305$	−11.4396	−0.655028
$306$	−0.193518	−0.0110627
$307$	20.9825	1.19754	0.598768	−	0.800923i	$-0.295657\pi$
$307$	20.9825	1.19754	0.598768	+	0.800923i	$0.295657\pi$
$308$	−54.0540	−3.08001
$309$	4.18611	0.238139
$310$	19.8983	1.13015
$311$	−34.0275	−1.92952	−0.964761	−	0.263129i	$-0.915245\pi$
$311$	−34.0275	−1.92952	−0.964761	+	0.263129i	$0.915245\pi$
$312$	−11.5449	−0.653603
$313$	20.6352	1.16637	0.583186	−	0.812339i	$-0.301806\pi$
$313$	20.6352	1.16637	0.583186	+	0.812339i	$0.301806\pi$
$314$	−42.4342	−2.39470
$315$	−16.7778	−0.945323
$316$	−37.6360	−2.11719
$317$	−7.59523	−0.426591	−0.213295	−	0.976988i	$-0.568420\pi$
$317$	−7.59523	−0.426591	−0.213295	+	0.976988i	$0.568420\pi$
$318$	−12.0547	−0.675992
$319$	43.5322	2.43733
$320$	19.7020	1.10138
$321$	−0.650018	−0.0362805
$322$	46.1440	2.57151
$323$	−0.221562	−0.0123280
$324$	30.1084	1.67269
$325$	−1.88191	−0.104389
$326$	11.2535	0.623275
$327$	−2.91061	−0.160957
$328$	40.1843	2.21881
$329$	−20.7970	−1.14658
$330$	10.2881	0.566343
$331$	−6.91192	−0.379913	−0.189957	−	0.981792i	$-0.560835\pi$
$331$	−6.91192	−0.379913	−0.189957	+	0.981792i	$0.560835\pi$
$332$	37.8824	2.07907
$333$	2.39246	0.131106
$334$	11.1945	0.612534
$335$	27.3991	1.49697
$336$	−3.54776	−0.193546
$337$	−6.84462	−0.372850	−0.186425	−	0.982469i	$-0.559690\pi$
$337$	−6.84462	−0.372850	−0.186425	+	0.982469i	$0.559690\pi$
$338$	−72.3659	−3.93619
$339$	−4.54373	−0.246782
$340$	0.236466	0.0128242
$341$	19.2890	1.04456
$342$	55.0806	2.97842
$343$	18.0564	0.974954
$344$	−16.5703	−0.893408
$345$	−5.80763	−0.312672
$346$	9.36323	0.503370
$347$	10.6196	0.570091	0.285045	−	0.958514i	$-0.407991\pi$
$347$	10.6196	0.570091	0.285045	+	0.958514i	$0.407991\pi$
$348$	12.6795	0.679693
$349$	−0.592091	−0.0316939	−0.0158470	−	0.999874i	$-0.505044\pi$
$349$	−0.592091	−0.0316939	−0.0158470	+	0.999874i	$0.505044\pi$
$350$	−1.89297	−0.101184
$351$	−14.6070	−0.779664
$352$	4.64235	0.247438
$353$	−13.3053	−0.708169	−0.354084	−	0.935213i	$-0.615207\pi$
$353$	−13.3053	−0.708169	−0.354084	+	0.935213i	$0.615207\pi$
$354$	−9.31544	−0.495110
$355$	24.2556	1.28735
$356$	2.02149	0.107139
$357$	0.0288166	0.00152514
$358$	24.7000	1.30544
$359$	−7.21305	−0.380690	−0.190345	−	0.981717i	$-0.560961\pi$
$359$	−7.21305	−0.380690	−0.190345	+	0.981717i	$0.560961\pi$
$360$	−28.6724	−1.51117
$361$	44.0625	2.31908
$362$	−9.06529	−0.476461
$363$	5.77710	0.303219
$364$	−69.1454	−3.62420
$365$	−11.1688	−0.584604
$366$	−4.88451	−0.255317
$367$	−6.54698	−0.341749	−0.170875	−	0.985293i	$-0.554659\pi$
$367$	−6.54698	−0.341749	−0.170875	+	0.985293i	$0.554659\pi$
$368$	24.0914	1.25585
$369$	24.7894	1.29048
$370$	−4.42095	−0.229834
$371$	−35.2143	−1.82824
$372$	5.61826	0.291293
$373$	−21.7384	−1.12557	−0.562786	−	0.826602i	$-0.690271\pi$
$373$	−21.7384	−1.12557	−0.562786	+	0.826602i	$0.690271\pi$
$374$	0.346647	0.0179247
$375$	4.37851	0.226105
$376$	−35.5410	−1.83289
$377$	55.6860	2.86797
$378$	−14.6929	−0.755721
$379$	−31.4655	−1.61628	−0.808138	−	0.588994i	$-0.799524\pi$
$379$	−31.4655	−1.61628	−0.808138	+	0.588994i	$0.799524\pi$
$380$	−67.3045	−3.45265
$381$	−7.25620	−0.371747
$382$	−59.7000	−3.05452
$383$	27.5479	1.40763	0.703816	−	0.710382i	$-0.251478\pi$
$383$	27.5479	1.40763	0.703816	+	0.710382i	$0.251478\pi$
$384$	7.71979	0.393949
$385$	30.0539	1.53169
$386$	3.22046	0.163917
$387$	−10.2221	−0.519617
$388$	−24.9206	−1.26515
$389$	10.9966	0.557548	0.278774	−	0.960357i	$-0.410072\pi$
$389$	10.9966	0.557548	0.278774	+	0.960357i	$0.410072\pi$
$390$	13.1605	0.666407
$391$	−0.195682	−0.00989604
$392$	−1.53308	−0.0774320
$393$	−4.91116	−0.247735
$394$	−66.1012	−3.33013
$395$	20.9255	1.05288
$396$	−56.9857	−2.86364
$397$	−39.5138	−1.98314	−0.991571	−	0.129561i	$-0.958643\pi$
$397$	−39.5138	−1.98314	−0.991571	+	0.129561i	$0.958643\pi$
$398$	−25.3499	−1.27068
$399$	−8.20199	−0.410613
$400$	−0.988302	−0.0494151
$401$	33.7732	1.68656	0.843278	−	0.537478i	$-0.180623\pi$
$401$	33.7732	1.68656	0.843278	+	0.537478i	$0.180623\pi$
$402$	11.6990	0.583492
$403$	24.6743	1.22912
$404$	−13.3592	−0.664646
$405$	−16.7402	−0.831827
$406$	56.0134	2.77990
$407$	−4.28558	−0.212428
$408$	0.0492461	0.00243804
$409$	25.7484	1.27317	0.636587	−	0.771205i	$-0.280345\pi$
$409$	25.7484	1.27317	0.636587	+	0.771205i	$0.280345\pi$
$410$	−45.8075	−2.26227
$411$	2.73084	0.134702
$412$	42.8461	2.11087
$413$	−27.2124	−1.33904
$414$	48.6467	2.39086
$415$	−21.0625	−1.03392
$416$	5.93845	0.291157
$417$	0.686471	0.0336166
$418$	−98.6650	−4.82586
$419$	−29.0944	−1.42135	−0.710677	−	0.703518i	$-0.751611\pi$
$419$	−29.0944	−1.42135	−0.710677	+	0.703518i	$0.751611\pi$
$420$	8.75372	0.427138
$421$	−30.4606	−1.48456	−0.742278	−	0.670092i	$-0.766255\pi$
$421$	−30.4606	−1.48456	−0.742278	+	0.670092i	$0.766255\pi$
$422$	32.3237	1.57349
$423$	−21.9250	−1.06603
$424$	−60.1793	−2.92257
$425$	0.00802746	0.000389389 0
$426$	10.3567	0.501786
$427$	−14.2687	−0.690512
$428$	−6.65312	−0.321591
$429$	12.7575	0.615938
$430$	18.8890	0.910910
$431$	−35.1939	−1.69523	−0.847616	−	0.530610i	$-0.821963\pi$
$431$	−35.1939	−1.69523	−0.847616	+	0.530610i	$0.821963\pi$
$432$	−7.67101	−0.369072
$433$	37.1689	1.78622	0.893110	−	0.449837i	$-0.148518\pi$
$433$	37.1689	1.78622	0.893110	+	0.449837i	$0.148518\pi$
$434$	24.8194	1.19137
$435$	−7.04977	−0.338011
$436$	−29.7910	−1.42673
$437$	55.6962	2.66431
$438$	−4.76892	−0.227868
$439$	−33.8850	−1.61724	−0.808622	−	0.588329i	$-0.799786\pi$
$439$	−33.8850	−1.61724	−0.808622	+	0.588329i	$0.799786\pi$
$440$	51.3604	2.44851
$441$	−0.945743	−0.0450354
$442$	0.443428	0.0210917
$443$	24.6304	1.17022	0.585112	−	0.810952i	$-0.301050\pi$
$443$	24.6304	1.17022	0.585112	+	0.810952i	$0.301050\pi$
$444$	−1.24825	−0.0592393
$445$	−1.12394	−0.0532800
$446$	40.5935	1.92216
$447$	1.24452	0.0588637
$448$	24.5746	1.16104
$449$	−31.3391	−1.47898	−0.739491	−	0.673166i	$-0.764934\pi$
$449$	−31.3391	−1.47898	−0.739491	+	0.673166i	$0.764934\pi$
$450$	−1.99564	−0.0940753
$451$	−44.4049	−2.09094
$452$	−46.5064	−2.18748
$453$	−2.86399	−0.134562
$454$	−47.4853	−2.22860
$455$	38.4446	1.80231
$456$	−14.0168	−0.656395
$457$	−5.27861	−0.246923	−0.123461	−	0.992349i	$-0.539400\pi$
$457$	−5.27861	−0.246923	−0.123461	+	0.992349i	$0.539400\pi$
$458$	−26.1722	−1.22295
$459$	0.0623077	0.00290827
$460$	−59.4428	−2.77153
$461$	1.04519	0.0486793	0.0243397	−	0.999704i	$-0.492252\pi$
$461$	1.04519	0.0486793	0.0243397	+	0.999704i	$0.492252\pi$
$462$	12.8325	0.597022
$463$	12.7165	0.590985	0.295492	−	0.955345i	$-0.404516\pi$
$463$	12.7165	0.590985	0.295492	+	0.955345i	$0.404516\pi$
$464$	29.2440	1.35762
$465$	−3.12374	−0.144860
$466$	−42.0391	−1.94742
$467$	42.9765	1.98871	0.994357	−	0.106083i	$-0.0338309\pi$
$467$	42.9765	1.98871	0.994357	+	0.106083i	$0.0338309\pi$
$468$	−72.8956	−3.36960
$469$	34.1753	1.57807
$470$	40.5145	1.86879
$471$	6.66153	0.306947
$472$	−46.5046	−2.14055
$473$	18.3106	0.841924
$474$	8.93486	0.410392
$475$	−2.28483	−0.104835
$476$	0.294947	0.0135189
$477$	−37.1242	−1.69980
$478$	−21.8533	−0.999548
$479$	14.7895	0.675750	0.337875	−	0.941191i	$-0.390292\pi$
$479$	14.7895	0.675750	0.337875	+	0.941191i	$0.390292\pi$
$480$	−0.751800	−0.0343148
$481$	−5.48207	−0.249961
$482$	1.81741	0.0827808
$483$	−7.24393	−0.329610
$484$	59.1303	2.68774
$485$	13.8558	0.629158
$486$	−23.4272	−1.06268
$487$	7.61778	0.345195	0.172597	−	0.984992i	$-0.444784\pi$
$487$	7.61778	0.345195	0.172597	+	0.984992i	$0.444784\pi$
$488$	−24.3845	−1.10383
$489$	−1.76664	−0.0798900
$490$	1.74761	0.0789489
$491$	−3.95144	−0.178326	−0.0891630	−	0.996017i	$-0.528419\pi$
$491$	−3.95144	−0.178326	−0.0891630	+	0.996017i	$0.528419\pi$
$492$	−12.9337	−0.583096
$493$	−0.237534	−0.0106980
$494$	−126.211	−5.67852
$495$	31.6839	1.42408
$496$	12.9580	0.581830
$497$	30.2543	1.35709
$498$	−8.99336	−0.403002
$499$	9.77167	0.437440	0.218720	−	0.975788i	$-0.429812\pi$
$499$	9.77167	0.437440	0.218720	+	0.975788i	$0.429812\pi$
$500$	44.8154	2.00420
$501$	−1.75737	−0.0785133
$502$	−7.76955	−0.346772
$503$	11.9231	0.531625	0.265812	−	0.964025i	$-0.414360\pi$
$503$	11.9231	0.531625	0.265812	+	0.964025i	$0.414360\pi$
$504$	−35.7634	−1.59303
$505$	7.42769	0.330528
$506$	−87.1402	−3.87385
$507$	11.3604	0.504532
$508$	−74.2694	−3.29517
$509$	12.1535	0.538693	0.269346	−	0.963043i	$-0.413192\pi$
$509$	12.1535	0.538693	0.269346	+	0.963043i	$0.413192\pi$
$510$	−0.0561374	−0.00248580
$511$	−13.9311	−0.616273
$512$	34.9071	1.54269
$513$	−17.7344	−0.782995
$514$	−5.13641	−0.226557
$515$	−23.8223	−1.04974
$516$	5.33330	0.234785
$517$	39.2739	1.72726
$518$	−5.51431	−0.242285
$519$	−1.46989	−0.0645209
$520$	65.6998	2.88113
$521$	37.3354	1.63569	0.817847	−	0.575435i	$-0.195167\pi$
$521$	37.3354	1.63569	0.817847	+	0.575435i	$0.195167\pi$
$522$	59.0513	2.58461
$523$	11.8713	0.519095	0.259548	−	0.965730i	$-0.416427\pi$
$523$	11.8713	0.519095	0.259548	+	0.965730i	$0.416427\pi$
$524$	−50.2672	−2.19593
$525$	0.297168	0.0129695
$526$	24.9650	1.08853
$527$	−0.105251	−0.00458480
$528$	6.69973	0.291568
$529$	26.1905	1.13872
$530$	68.6006	2.97982
$531$	−28.6883	−1.24497
$532$	−83.9498	−3.63968
$533$	−56.8023	−2.46038
$534$	−0.479905	−0.0207675
$535$	3.69912	0.159927
$536$	58.4037	2.52266
$537$	−3.87754	−0.167328
$538$	19.8946	0.857715
$539$	1.69410	0.0729699
$540$	18.9274	0.814505
$541$	−1.58914	−0.0683225	−0.0341612	−	0.999416i	$-0.510876\pi$
$541$	−1.58914	−0.0683225	−0.0341612	+	0.999416i	$0.510876\pi$
$542$	20.5167	0.881268
$543$	1.42312	0.0610718
$544$	−0.0253311	−0.00108606
$545$	16.5637	0.709511
$546$	16.4152	0.702507
$547$	−40.2811	−1.72230	−0.861148	−	0.508354i	$-0.830254\pi$
$547$	−40.2811	−1.72230	−0.861148	+	0.508354i	$0.830254\pi$
$548$	27.9509	1.19400
$549$	−15.0426	−0.642003
$550$	3.57476	0.152428
$551$	67.6086	2.88022
$552$	−12.3795	−0.526906
$553$	26.1007	1.10991
$554$	21.5306	0.914749
$555$	0.694023	0.0294597
$556$	7.02623	0.297979
$557$	17.6685	0.748640	0.374320	−	0.927300i	$-0.377876\pi$
$557$	17.6685	0.748640	0.374320	+	0.927300i	$0.377876\pi$
$558$	26.1655	1.10767
$559$	23.4228	0.990680
$560$	20.1896	0.853166
$561$	−0.0544184	−0.00229755
$562$	38.4630	1.62246
$563$	−23.4192	−0.987001	−0.493500	−	0.869746i	$-0.664283\pi$
$563$	−23.4192	−0.987001	−0.493500	+	0.869746i	$0.664283\pi$
$564$	11.4392	0.481678
$565$	25.8574	1.08783
$566$	6.89843	0.289963
$567$	−20.8803	−0.876888
$568$	51.7030	2.16941
$569$	3.60300	0.151045	0.0755227	−	0.997144i	$-0.475937\pi$
$569$	3.60300	0.151045	0.0755227	+	0.997144i	$0.475937\pi$
$570$	15.9782	0.669253
$571$	7.82842	0.327609	0.163805	−	0.986493i	$-0.447623\pi$
$571$	7.82842	0.327609	0.163805	+	0.986493i	$0.447623\pi$
$572$	130.577	5.45969
$573$	9.37201	0.391521
$574$	−57.1363	−2.38482
$575$	−2.01794	−0.0841541
$576$	25.9074	1.07948
$577$	−8.78037	−0.365532	−0.182766	−	0.983156i	$-0.558505\pi$
$577$	−8.78037	−0.365532	−0.182766	+	0.983156i	$0.558505\pi$
$578$	41.3060	1.71810
$579$	−0.505564	−0.0210105
$580$	−72.1565	−2.99614
$581$	−26.2716	−1.08993
$582$	5.91619	0.245234
$583$	66.5000	2.75415
$584$	−23.8074	−0.985158
$585$	40.5297	1.67570
$586$	8.23534	0.340199
$587$	26.3610	1.08803	0.544017	−	0.839074i	$-0.316903\pi$
$587$	26.3610	1.08803	0.544017	+	0.839074i	$0.316903\pi$
$588$	0.493435	0.0203489
$589$	29.9572	1.23437
$590$	53.0123	2.18248
$591$	10.3769	0.426849
$592$	−2.87897	−0.118325
$593$	−22.3609	−0.918252	−0.459126	−	0.888371i	$-0.651837\pi$
$593$	−22.3609	−0.918252	−0.459126	+	0.888371i	$0.651837\pi$
$594$	27.7466	1.13846
$595$	−0.163989	−0.00672291
$596$	12.7380	0.521769
$597$	3.97956	0.162872
$598$	−111.469	−4.55830
$599$	−9.04870	−0.369720	−0.184860	−	0.982765i	$-0.559183\pi$
$599$	−9.04870	−0.369720	−0.184860	+	0.982765i	$0.559183\pi$
$600$	0.507845	0.0207327
$601$	16.9125	0.689876	0.344938	−	0.938625i	$-0.387900\pi$
$601$	16.9125	0.689876	0.344938	+	0.938625i	$0.387900\pi$
$602$	23.5605	0.960256
$603$	36.0288	1.46721
$604$	−29.3138	−1.19276
$605$	−32.8763	−1.33661
$606$	3.17150	0.128833
$607$	−33.3170	−1.35230	−0.676148	−	0.736766i	$-0.736352\pi$
$607$	−33.3170	−1.35230	−0.676148	+	0.736766i	$0.736352\pi$
$608$	7.20990	0.292400
$609$	−8.79327	−0.356321
$610$	27.7967	1.12546
$611$	50.2388	2.03245
$612$	0.310943	0.0125691
$613$	45.4364	1.83516	0.917580	−	0.397550i	$-0.130140\pi$
$613$	45.4364	1.83516	0.917580	+	0.397550i	$0.130140\pi$
$614$	−50.9849	−2.05758
$615$	7.19110	0.289973
$616$	64.0625	2.58115
$617$	−26.2290	−1.05594	−0.527970	−	0.849263i	$-0.677047\pi$
$617$	−26.2290	−1.05594	−0.527970	+	0.849263i	$0.677047\pi$
$618$	−10.1717	−0.409167
$619$	−27.5434	−1.10706	−0.553531	−	0.832828i	$-0.686720\pi$
$619$	−27.5434	−1.10706	−0.553531	+	0.832828i	$0.686720\pi$
$620$	−31.9724	−1.28404
$621$	−15.6629	−0.628531
$622$	82.6826	3.31527
$623$	−1.40191	−0.0561662
$624$	8.57023	0.343084
$625$	−23.4786	−0.939145
$626$	−50.1410	−2.00404
$627$	15.4889	0.618569
$628$	68.1828	2.72079
$629$	0.0233843	0.000932395 0
$630$	40.7680	1.62424
$631$	33.7132	1.34210	0.671050	−	0.741412i	$-0.265844\pi$
$631$	33.7132	1.34210	0.671050	+	0.741412i	$0.265844\pi$
$632$	44.6046	1.77428
$633$	−5.07435	−0.201687
$634$	18.4555	0.732960
$635$	41.2936	1.63868
$636$	19.3693	0.768043
$637$	2.16707	0.0858625
$638$	−105.778	−4.18778
$639$	31.8952	1.26175
$640$	−43.9317	−1.73655
$641$	−17.4400	−0.688838	−0.344419	−	0.938816i	$-0.611924\pi$
$641$	−17.4400	−0.688838	−0.344419	+	0.938816i	$0.611924\pi$
$642$	1.57946	0.0623364
$643$	−13.5358	−0.533798	−0.266899	−	0.963724i	$-0.585999\pi$
$643$	−13.5358	−0.533798	−0.266899	+	0.963724i	$0.585999\pi$
$644$	−74.1438	−2.92167
$645$	−2.96530	−0.116758
$646$	0.538368	0.0211818
$647$	−2.40965	−0.0947332	−0.0473666	−	0.998878i	$-0.515083\pi$
$647$	−2.40965	−0.0947332	−0.0473666	+	0.998878i	$0.515083\pi$
$648$	−35.6832	−1.40177
$649$	51.3890	2.01719
$650$	4.57280	0.179360
$651$	−3.89628	−0.152707
$652$	−18.0820	−0.708147
$653$	−44.3138	−1.73413	−0.867066	−	0.498193i	$-0.833997\pi$
$653$	−44.3138	−1.73413	−0.867066	+	0.498193i	$0.833997\pi$
$654$	7.07243	0.276554
$655$	27.9484	1.09203
$656$	−29.8303	−1.16468
$657$	−14.6866	−0.572979
$658$	50.5342	1.97003
$659$	16.6422	0.648290	0.324145	−	0.946007i	$-0.394923\pi$
$659$	16.6422	0.648290	0.324145	+	0.946007i	$0.394923\pi$
$660$	−16.5308	−0.643462
$661$	2.68299	0.104356	0.0521781	−	0.998638i	$-0.483384\pi$
$661$	2.68299	0.104356	0.0521781	+	0.998638i	$0.483384\pi$
$662$	16.7951	0.652760
$663$	−0.0696116	−0.00270349
$664$	−44.8967	−1.74233
$665$	46.6758	1.81001
$666$	−5.81338	−0.225264
$667$	59.7114	2.31203
$668$	−17.9872	−0.695944
$669$	−6.37258	−0.246378
$670$	−66.5765	−2.57207
$671$	26.9456	1.04022
$672$	−0.937730	−0.0361737
$673$	4.65760	0.179537	0.0897686	−	0.995963i	$-0.471387\pi$
$673$	4.65760	0.179537	0.0897686	+	0.995963i	$0.471387\pi$
$674$	16.6316	0.640625
$675$	0.642541	0.0247314
$676$	116.277	4.47218
$677$	−24.3519	−0.935919	−0.467959	−	0.883750i	$-0.655011\pi$
$677$	−24.3519	−0.935919	−0.467959	+	0.883750i	$0.655011\pi$
$678$	11.0407	0.424016
$679$	17.2825	0.663241
$680$	−0.280249	−0.0107471
$681$	7.45449	0.285657
$682$	−46.8699	−1.79474
$683$	48.2607	1.84665	0.923323	−	0.384024i	$-0.125462\pi$
$683$	48.2607	1.84665	0.923323	+	0.384024i	$0.125462\pi$
$684$	−88.5029	−3.38399
$685$	−15.5406	−0.593777
$686$	−43.8748	−1.67515
$687$	4.10865	0.156755
$688$	12.3007	0.468961
$689$	85.0662	3.24077
$690$	14.1118	0.537228
$691$	31.2586	1.18913	0.594566	−	0.804047i	$-0.297324\pi$
$691$	31.2586	1.18913	0.594566	+	0.804047i	$0.297324\pi$
$692$	−15.0447	−0.571915
$693$	39.5197	1.50123
$694$	−25.8043	−0.979520
$695$	−3.90656	−0.148184
$696$	−15.0272	−0.569606
$697$	0.242296	0.00917762
$698$	1.43871	0.0544559
$699$	6.59951	0.249617
$700$	3.04161	0.114962
$701$	−41.9224	−1.58339	−0.791693	−	0.610919i	$-0.790800\pi$
$701$	−41.9224	−1.58339	−0.791693	+	0.610919i	$0.790800\pi$
$702$	35.4932	1.33961
$703$	−6.65581	−0.251029
$704$	−46.4076	−1.74905
$705$	−6.36017	−0.239538
$706$	32.3302	1.21676
$707$	9.26465	0.348433
$708$	14.9680	0.562530
$709$	13.4696	0.505863	0.252931	−	0.967484i	$-0.418605\pi$
$709$	13.4696	0.505863	0.252931	+	0.967484i	$0.418605\pi$
$710$	−58.9381	−2.21191
$711$	27.5163	1.03194
$712$	−2.39578	−0.0897858
$713$	26.4580	0.990859
$714$	−0.0700208	−0.00262046
$715$	−72.6003	−2.71510
$716$	−39.6877	−1.48320
$717$	3.43065	0.128120
$718$	17.5268	0.654095
$719$	26.7882	0.999030	0.499515	−	0.866305i	$-0.333512\pi$
$719$	26.7882	0.999030	0.499515	+	0.866305i	$0.333512\pi$
$720$	21.2846	0.793230
$721$	−29.7138	−1.10660
$722$	−107.066	−3.98460
$723$	−0.285306	−0.0106107
$724$	14.5660	0.541342
$725$	−2.44955	−0.0909738
$726$	−14.0376	−0.520985
$727$	−16.9320	−0.627973	−0.313987	−	0.949427i	$-0.601665\pi$
$727$	−16.9320	−0.627973	−0.313987	+	0.949427i	$0.601665\pi$
$728$	81.9482	3.03720
$729$	−19.4571	−0.720633
$730$	27.1389	1.00446
$731$	−0.0999124	−0.00369539
$732$	7.84838	0.290084
$733$	−15.2462	−0.563130	−0.281565	−	0.959542i	$-0.590853\pi$
$733$	−15.2462	−0.563130	−0.281565	+	0.959542i	$0.590853\pi$
$734$	15.9083	0.587188
$735$	−0.274349	−0.0101195
$736$	6.36773	0.234718
$737$	−64.5379	−2.37728
$738$	−60.2352	−2.21729
$739$	−24.7430	−0.910184	−0.455092	−	0.890444i	$-0.650394\pi$
$739$	−24.7430	−0.910184	−0.455092	+	0.890444i	$0.650394\pi$
$740$	7.10353	0.261131
$741$	19.8133	0.727861
$742$	85.5664	3.14124
$743$	10.6923	0.392261	0.196131	−	0.980578i	$-0.437162\pi$
$743$	10.6923	0.392261	0.196131	+	0.980578i	$0.437162\pi$
$744$	−6.65853	−0.244114
$745$	−7.08229	−0.259475
$746$	52.8217	1.93394
$747$	−27.6964	−1.01336
$748$	−0.556988	−0.0203655
$749$	4.61396	0.168590
$750$	−10.6392	−0.388490
$751$	19.9609	0.728385	0.364192	−	0.931324i	$-0.381345\pi$
$751$	19.9609	0.728385	0.364192	+	0.931324i	$0.381345\pi$
$752$	26.3834	0.962104
$753$	1.21970	0.0444485
$754$	−135.310	−4.92770
$755$	16.2984	0.593158
$756$	23.6084	0.858628
$757$	5.54047	0.201372	0.100686	−	0.994918i	$-0.467896\pi$
$757$	5.54047	0.201372	0.100686	+	0.994918i	$0.467896\pi$
$758$	76.4573	2.77705
$759$	13.6797	0.496542
$760$	79.7665	2.89343
$761$	10.5736	0.383293	0.191646	−	0.981464i	$-0.438617\pi$
$761$	10.5736	0.383293	0.191646	+	0.981464i	$0.438617\pi$
$762$	17.6317	0.638728
$763$	20.6601	0.747946
$764$	95.9252	3.47045
$765$	−0.172884	−0.00625062
$766$	−66.9380	−2.41857
$767$	65.7364	2.37360
$768$	−11.8340	−0.427021
$769$	−5.21778	−0.188158	−0.0940789	−	0.995565i	$-0.529991\pi$
$769$	−5.21778	−0.188158	−0.0940789	+	0.995565i	$0.529991\pi$
$770$	−73.0272	−2.63172
$771$	0.806340	0.0290396
$772$	−5.17459	−0.186238
$773$	−18.8714	−0.678756	−0.339378	−	0.940650i	$-0.610217\pi$
$773$	−18.8714	−0.678756	−0.339378	+	0.940650i	$0.610217\pi$
$774$	24.8384	0.892797
$775$	−1.08539	−0.0389883
$776$	29.5348	1.06024
$777$	0.865664	0.0310555
$778$	−26.7203	−0.957969
$779$	−68.9640	−2.47089
$780$	−21.1461	−0.757152
$781$	−57.1334	−2.04439
$782$	0.475482	0.0170032
$783$	−19.0129	−0.679466
$784$	1.13806	0.0406450
$785$	−37.9094	−1.35305
$786$	11.9335	0.425654
$787$	−9.14067	−0.325830	−0.162915	−	0.986640i	$-0.552090\pi$
$787$	−9.14067	−0.325830	−0.162915	+	0.986640i	$0.552090\pi$
$788$	106.211	3.78360
$789$	−3.91914	−0.139525
$790$	−50.8464	−1.80903
$791$	32.2523	1.14676
$792$	67.5370	2.39982
$793$	34.4686	1.22401
$794$	96.0137	3.40740
$795$	−10.7693	−0.381947
$796$	40.7319	1.44371
$797$	−2.79399	−0.0989680	−0.0494840	−	0.998775i	$-0.515758\pi$
$797$	−2.79399	−0.0989680	−0.0494840	+	0.998775i	$0.515758\pi$
$798$	19.9298	0.705508
$799$	−0.214299	−0.00758135
$800$	−0.261224	−0.00923566
$801$	−1.47794	−0.0522205
$802$	−82.0648	−2.89781
$803$	26.3079	0.928386
$804$	−18.7978	−0.662947
$805$	41.2237	1.45294
$806$	−59.9556	−2.11185
$807$	−3.12315	−0.109940
$808$	15.8328	0.556996
$809$	−8.03597	−0.282530	−0.141265	−	0.989972i	$-0.545117\pi$
$809$	−8.03597	−0.282530	−0.141265	+	0.989972i	$0.545117\pi$
$810$	40.6766	1.42923
$811$	16.0818	0.564707	0.282354	−	0.959310i	$-0.408885\pi$
$811$	16.0818	0.564707	0.282354	+	0.959310i	$0.408885\pi$
$812$	−90.0017	−3.15844
$813$	−3.22082	−0.112959
$814$	10.4134	0.364990
$815$	10.0536	0.352161
$816$	−0.0365572	−0.00127976
$817$	28.4378	0.994911
$818$	−62.5653	−2.18755
$819$	50.5532	1.76647
$820$	73.6030	2.57033
$821$	22.7981	0.795659	0.397830	−	0.917459i	$-0.369764\pi$
$821$	22.7981	0.795659	0.397830	+	0.917459i	$0.369764\pi$
$822$	−6.63560	−0.231443
$823$	47.7720	1.66523	0.832613	−	0.553855i	$-0.186844\pi$
$823$	47.7720	1.66523	0.832613	+	0.553855i	$0.186844\pi$
$824$	−50.7794	−1.76898
$825$	−0.561184	−0.0195379
$826$	66.1229	2.30071
$827$	16.8441	0.585728	0.292864	−	0.956154i	$-0.405392\pi$
$827$	16.8441	0.585728	0.292864	+	0.956154i	$0.405392\pi$
$828$	−78.1650	−2.71642
$829$	−34.0417	−1.18232	−0.591159	−	0.806555i	$-0.701330\pi$
$829$	−34.0417	−1.18232	−0.591159	+	0.806555i	$0.701330\pi$
$830$	51.1793	1.77646
$831$	−3.37999	−0.117251
$832$	−59.3642	−2.05808
$833$	−0.00924387	−0.000320281 0
$834$	−1.66804	−0.0577595
$835$	10.0008	0.346092
$836$	158.534	5.48301
$837$	−8.42458	−0.291196
$838$	70.6958	2.44215
$839$	−25.2000	−0.870002	−0.435001	−	0.900430i	$-0.643252\pi$
$839$	−25.2000	−0.870002	−0.435001	+	0.900430i	$0.643252\pi$
$840$	−10.3745	−0.357955
$841$	43.4826	1.49940
$842$	74.0154	2.55074
$843$	−6.03812	−0.207964
$844$	−51.9374	−1.78776
$845$	−64.6495	−2.22401
$846$	53.2750	1.83163
$847$	−41.0070	−1.40902
$848$	44.6734	1.53409
$849$	−1.08295	−0.0371668
$850$	−0.0195057	−0.000669041 0
$851$	−5.87836	−0.201508
$852$	−16.6411	−0.570115
$853$	0.607629	0.0208048	0.0104024	−	0.999946i	$-0.496689\pi$
$853$	0.607629	0.0208048	0.0104024	+	0.999946i	$0.496689\pi$
$854$	34.6712	1.18643
$855$	49.2073	1.68286
$856$	7.88500	0.269504
$857$	2.78457	0.0951191	0.0475595	−	0.998868i	$-0.484856\pi$
$857$	2.78457	0.0951191	0.0475595	+	0.998868i	$0.484856\pi$
$858$	−30.9991	−1.05829
$859$	4.46737	0.152425	0.0762123	−	0.997092i	$-0.475717\pi$
$859$	4.46737	0.152425	0.0762123	+	0.997092i	$0.475717\pi$
$860$	−30.3507	−1.03495
$861$	8.96955	0.305682
$862$	85.5169	2.91272
$863$	47.2136	1.60717	0.803585	−	0.595190i	$-0.202923\pi$
$863$	47.2136	1.60717	0.803585	+	0.595190i	$0.202923\pi$
$864$	−2.02757	−0.0689794
$865$	8.36483	0.284413
$866$	−90.3157	−3.06905
$867$	−6.48443	−0.220223
$868$	−39.8796	−1.35360
$869$	−49.2895	−1.67203
$870$	17.1301	0.580764
$871$	−82.5563	−2.79731
$872$	35.3070	1.19565
$873$	18.2198	0.616647
$874$	−135.335	−4.57777
$875$	−31.0796	−1.05068
$876$	7.66264	0.258897
$877$	−54.6348	−1.84489	−0.922443	−	0.386134i	$-0.873810\pi$
$877$	−54.6348	−1.84489	−0.922443	+	0.386134i	$0.873810\pi$
$878$	82.3364	2.77872
$879$	−1.29283	−0.0436060
$880$	−38.1268	−1.28525
$881$	−10.3240	−0.347825	−0.173912	−	0.984761i	$-0.555641\pi$
$881$	−10.3240	−0.347825	−0.173912	+	0.984761i	$0.555641\pi$
$882$	2.29804	0.0773790
$883$	−3.12060	−0.105017	−0.0525083	−	0.998620i	$-0.516722\pi$
$883$	−3.12060	−0.105017	−0.0525083	+	0.998620i	$0.516722\pi$
$884$	−0.712495	−0.0239638
$885$	−8.32214	−0.279746
$886$	−59.8488	−2.01066
$887$	10.6041	0.356050	0.178025	−	0.984026i	$-0.443029\pi$
$887$	10.6041	0.356050	0.178025	+	0.984026i	$0.443029\pi$
$888$	1.47937	0.0496445
$889$	51.5060	1.72746
$890$	2.73104	0.0915447
$891$	39.4311	1.32099
$892$	−65.2252	−2.18390
$893$	60.9952	2.04113
$894$	−3.02402	−0.101139
$895$	22.0663	0.737594
$896$	−54.7966	−1.83063
$897$	17.4990	0.584274
$898$	76.1501	2.54116
$899$	32.1169	1.07116
$900$	3.20657	0.106886
$901$	−0.362859	−0.0120886
$902$	107.898	3.59262
$903$	−3.69865	−0.123084
$904$	55.1175	1.83318
$905$	−8.09866	−0.269209
$906$	6.95914	0.231202
$907$	−33.1586	−1.10101	−0.550506	−	0.834831i	$-0.685565\pi$
$907$	−33.1586	−1.10101	−0.550506	+	0.834831i	$0.685565\pi$
$908$	76.2989	2.53207
$909$	9.76713	0.323955
$910$	−93.4157	−3.09670
$911$	−11.7842	−0.390427	−0.195213	−	0.980761i	$-0.562540\pi$
$911$	−11.7842	−0.390427	−0.195213	+	0.980761i	$0.562540\pi$
$912$	10.4052	0.344549
$913$	49.6122	1.64192
$914$	12.8264	0.424259
$915$	−4.36368	−0.144259
$916$	42.0533	1.38948
$917$	34.8604	1.15119
$918$	−0.151400	−0.00499694
$919$	34.9680	1.15349	0.576744	−	0.816925i	$-0.304323\pi$
$919$	34.9680	1.15349	0.576744	+	0.816925i	$0.304323\pi$
$920$	70.4491	2.32264
$921$	8.00387	0.263737
$922$	−2.53968	−0.0836399
$923$	−73.0846	−2.40561
$924$	−20.6191	−0.678320
$925$	0.241148	0.00792891
$926$	−30.8995	−1.01542
$927$	−31.3254	−1.02886
$928$	7.72967	0.253739
$929$	−25.5273	−0.837523	−0.418762	−	0.908096i	$-0.637536\pi$
$929$	−25.5273	−0.837523	−0.418762	+	0.908096i	$0.637536\pi$
$930$	7.59030	0.248896
$931$	2.63105	0.0862293
$932$	67.5480	2.21261
$933$	−12.9799	−0.424944
$934$	−104.428	−3.41697
$935$	0.309684	0.0101277
$936$	86.3928	2.82384
$937$	52.7905	1.72459	0.862295	−	0.506407i	$-0.169027\pi$
$937$	52.7905	1.72459	0.862295	+	0.506407i	$0.169027\pi$
$938$	−83.0417	−2.71141
$939$	7.87140	0.256873
$940$	−65.0982	−2.12327
$941$	24.6981	0.805136	0.402568	−	0.915390i	$-0.368118\pi$
$941$	24.6981	0.805136	0.402568	+	0.915390i	$0.368118\pi$
$942$	−16.1867	−0.527391
$943$	−60.9084	−1.98345
$944$	34.5221	1.12360
$945$	−13.1262	−0.426995
$946$	−44.4926	−1.44658
$947$	−49.7029	−1.61513	−0.807563	−	0.589782i	$-0.799214\pi$
$947$	−49.7029	−1.61513	−0.807563	+	0.589782i	$0.799214\pi$
$948$	−14.3564	−0.466275
$949$	33.6529	1.09242
$950$	5.55186	0.180126
$951$	−2.89723	−0.0939493
$952$	−0.349558	−0.0113293
$953$	2.56181	0.0829853	0.0414926	−	0.999139i	$-0.486789\pi$
$953$	2.56181	0.0829853	0.0414926	+	0.999139i	$0.486789\pi$
$954$	90.2072	2.92057
$955$	−53.3342	−1.72585
$956$	35.1137	1.13566
$957$	16.6055	0.536781
$958$	−35.9367	−1.16106
$959$	−19.3840	−0.625943
$960$	7.51543	0.242559
$961$	−16.7691	−0.540938
$962$	13.3208	0.429479
$963$	4.86420	0.156747
$964$	−2.92020	−0.0940532
$965$	2.87706	0.0926158
$966$	17.6019	0.566330
$967$	5.97558	0.192162	0.0960808	−	0.995374i	$-0.469369\pi$
$967$	5.97558	0.192162	0.0960808	+	0.995374i	$0.469369\pi$
$968$	−70.0787	−2.25242
$969$	−0.0845157	−0.00271504
$970$	−33.6678	−1.08101
$971$	−38.4435	−1.23371	−0.616855	−	0.787076i	$-0.711594\pi$
$971$	−38.4435	−1.23371	−0.616855	+	0.787076i	$0.711594\pi$
$972$	37.6425	1.20738
$973$	−4.87271	−0.156212
$974$	−18.5103	−0.593107
$975$	−0.717862	−0.0229900
$976$	18.1015	0.579415
$977$	24.4448	0.782057	0.391029	−	0.920379i	$-0.372119\pi$
$977$	24.4448	0.782057	0.391029	+	0.920379i	$0.372119\pi$
$978$	4.29271	0.137266
$979$	2.64741	0.0846117
$980$	−2.80804	−0.0896995
$981$	21.7806	0.695402
$982$	9.60151	0.306396
$983$	−52.1539	−1.66345	−0.831725	−	0.555188i	$-0.812646\pi$
$983$	−52.1539	−1.66345	−0.831725	+	0.555188i	$0.812646\pi$
$984$	15.3285	0.488654
$985$	−59.0529	−1.88158
$986$	0.577179	0.0183811
$987$	−7.93312	−0.252514
$988$	202.795	6.45177
$989$	25.1160	0.798642
$990$	−76.9879	−2.44683
$991$	17.7836	0.564915	0.282458	−	0.959280i	$-0.408850\pi$
$991$	17.7836	0.564915	0.282458	+	0.959280i	$0.408850\pi$
$992$	3.42500	0.108744
$993$	−2.63658	−0.0836694
$994$	−73.5143	−2.33173
$995$	−22.6468	−0.717953
$996$	14.4504	0.457879
$997$	−41.2168	−1.30535	−0.652674	−	0.757639i	$-0.726353\pi$
$997$	−41.2168	−1.30535	−0.652674	+	0.757639i	$0.726353\pi$
$998$	−23.7439	−0.751601
$999$	1.87175	0.0592195

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6037.2.a.b.1.17	✓	259

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6037.2.a.b.1.17	✓	259	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6037 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6037.a (trivial)

\(f(q)\)	\(=\)	\(q-2.42988 q^{2} +0.381455 q^{3} +3.90430 q^{4} -2.17078 q^{5} -0.926887 q^{6} -2.70764 q^{7} -4.62721 q^{8} -2.85449 q^{9} +O(q^{10})\)	\(q-2.42988 q^{2} +0.381455 q^{3} +3.90430 q^{4} -2.17078 q^{5} -0.926887 q^{6} -2.70764 q^{7} -4.62721 q^{8} -2.85449 q^{9} +5.27472 q^{10} +5.11321 q^{11} +1.48931 q^{12} +6.54077 q^{13} +6.57923 q^{14} -0.828053 q^{15} +3.43495 q^{16} -0.0279003 q^{17} +6.93606 q^{18} +7.94119 q^{19} -8.47537 q^{20} -1.03284 q^{21} -12.4245 q^{22} +7.01359 q^{23} -1.76507 q^{24} -0.287719 q^{25} -15.8933 q^{26} -2.23322 q^{27} -10.5714 q^{28} +8.51367 q^{29} +2.01207 q^{30} +3.77239 q^{31} +0.907913 q^{32} +1.95046 q^{33} +0.0677944 q^{34} +5.87769 q^{35} -11.1448 q^{36} -0.838138 q^{37} -19.2961 q^{38} +2.49501 q^{39} +10.0447 q^{40} -8.68434 q^{41} +2.50968 q^{42} +3.58105 q^{43} +19.9635 q^{44} +6.19647 q^{45} -17.0422 q^{46} +7.68087 q^{47} +1.31028 q^{48} +0.331317 q^{49} +0.699122 q^{50} -0.0106427 q^{51} +25.5371 q^{52} +13.0055 q^{53} +5.42645 q^{54} -11.0996 q^{55} +12.5288 q^{56} +3.02920 q^{57} -20.6872 q^{58} +10.0502 q^{59} -3.23297 q^{60} +5.26980 q^{61} -9.16644 q^{62} +7.72894 q^{63} -9.07602 q^{64} -14.1986 q^{65} -4.73937 q^{66} -12.6218 q^{67} -0.108931 q^{68} +2.67537 q^{69} -14.2821 q^{70} -11.1737 q^{71} +13.2083 q^{72} +5.14509 q^{73} +2.03657 q^{74} -0.109752 q^{75} +31.0048 q^{76} -13.8447 q^{77} -6.06256 q^{78} -9.63964 q^{79} -7.45652 q^{80} +7.71160 q^{81} +21.1019 q^{82} +9.70275 q^{83} -4.03252 q^{84} +0.0605655 q^{85} -8.70150 q^{86} +3.24758 q^{87} -23.6599 q^{88} +0.517760 q^{89} -15.0567 q^{90} -17.7101 q^{91} +27.3832 q^{92} +1.43899 q^{93} -18.6636 q^{94} -17.2386 q^{95} +0.346327 q^{96} -6.38286 q^{97} -0.805060 q^{98} -14.5956 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9}+O(q^{10}) \) 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9	\( 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9} + 18 q^{10} + 108 q^{11} + 46 q^{12} + 33 q^{13} + 35 q^{14} + 40 q^{15} + 301 q^{16} + 67 q^{17} + 117 q^{18} + 69 q^{19} + 103 q^{20} + 24 q^{21} + 42 q^{22} + 162 q^{23} + 45 q^{24} + 291 q^{25} + 41 q^{26} + 101 q^{27} + 87 q^{28} + 78 q^{29} + 48 q^{30} + 25 q^{31} + 314 q^{32} + 67 q^{33} + 9 q^{34} + 252 q^{35} + 337 q^{36} + 49 q^{37} + 59 q^{38} + 93 q^{39} + 44 q^{40} + 60 q^{41} + 38 q^{42} + 178 q^{43} + 171 q^{44} + 67 q^{45} + 43 q^{46} + 185 q^{47} + 67 q^{48} + 273 q^{49} + 204 q^{50} + 145 q^{51} + 83 q^{52} + 112 q^{53} + 60 q^{54} + 57 q^{55} + 93 q^{56} + 109 q^{57} + 63 q^{58} + 228 q^{59} + 53 q^{60} + 20 q^{61} + 126 q^{62} + 153 q^{63} + 345 q^{64} + 113 q^{65} + 5 q^{66} + 208 q^{67} + 166 q^{68} + 10 q^{69} + 69 q^{70} + 150 q^{71} + 331 q^{72} + 75 q^{73} + 84 q^{74} + 72 q^{75} + 102 q^{76} + 166 q^{77} + 69 q^{78} + 52 q^{79} + 180 q^{80} + 327 q^{81} + 43 q^{82} + 434 q^{83} + 75 q^{85} + 133 q^{86} + 144 q^{87} + 111 q^{88} + 78 q^{89} - 8 q^{90} + 35 q^{91} + 372 q^{92} + 160 q^{93} + 36 q^{94} + 154 q^{95} + 60 q^{96} + 35 q^{97} + 254 q^{98} + 234 q^{99}+O(q^{100}) \) 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9 + 18 * q^10 + 108 * q^11 + 46 * q^12 + 33 * q^13 + 35 * q^14 + 40 * q^15 + 301 * q^16 + 67 * q^17 + 117 * q^18 + 69 * q^19 + 103 * q^20 + 24 * q^21 + 42 * q^22 + 162 * q^23 + 45 * q^24 + 291 * q^25 + 41 * q^26 + 101 * q^27 + 87 * q^28 + 78 * q^29 + 48 * q^30 + 25 * q^31 + 314 * q^32 + 67 * q^33 + 9 * q^34 + 252 * q^35 + 337 * q^36 + 49 * q^37 + 59 * q^38 + 93 * q^39 + 44 * q^40 + 60 * q^41 + 38 * q^42 + 178 * q^43 + 171 * q^44 + 67 * q^45 + 43 * q^46 + 185 * q^47 + 67 * q^48 + 273 * q^49 + 204 * q^50 + 145 * q^51 + 83 * q^52 + 112 * q^53 + 60 * q^54 + 57 * q^55 + 93 * q^56 + 109 * q^57 + 63 * q^58 + 228 * q^59 + 53 * q^60 + 20 * q^61 + 126 * q^62 + 153 * q^63 + 345 * q^64 + 113 * q^65 + 5 * q^66 + 208 * q^67 + 166 * q^68 + 10 * q^69 + 69 * q^70 + 150 * q^71 + 331 * q^72 + 75 * q^73 + 84 * q^74 + 72 * q^75 + 102 * q^76 + 166 * q^77 + 69 * q^78 + 52 * q^79 + 180 * q^80 + 327 * q^81 + 43 * q^82 + 434 * q^83 + 75 * q^85 + 133 * q^86 + 144 * q^87 + 111 * q^88 + 78 * q^89 - 8 * q^90 + 35 * q^91 + 372 * q^92 + 160 * q^93 + 36 * q^94 + 154 * q^95 + 60 * q^96 + 35 * q^97 + 254 * q^98 + 234 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more