LMFDB - Embedded newform 6027.2.a.v.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6027,2,Mod(1,6027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6027 = 3 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6027.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:	$48.1258372982$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.981328.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 6x^{3} + 6x^{2} + 10x + 2 $ x^5 - 2x^4 - 6x^3 + 6x^2 + 10x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 861)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.74401$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.74401 q^{2} +1.00000 q^{3} +5.52961 q^{4} +0.811635 q^{5} -2.74401 q^{6} -9.68531 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.74401 q^{2} +1.00000 q^{3} +5.52961 q^{4} +0.811635 q^{5} -2.74401 q^{6} -9.68531 q^{8} +1.00000 q^{9} -2.22714 q^{10} -4.34125 q^{11} +5.52961 q^{12} +2.30248 q^{13} +0.811635 q^{15} +15.5174 q^{16} -0.928558 q^{17} -2.74401 q^{18} -4.60005 q^{19} +4.48803 q^{20} +11.9124 q^{22} +0.827185 q^{23} -9.68531 q^{24} -4.34125 q^{25} -6.31802 q^{26} +1.00000 q^{27} +3.78560 q^{29} -2.22714 q^{30} +5.65927 q^{31} -23.2093 q^{32} -4.34125 q^{33} +2.54797 q^{34} +5.52961 q^{36} -5.90634 q^{37} +12.6226 q^{38} +2.30248 q^{39} -7.86094 q^{40} -1.00000 q^{41} +10.2813 q^{43} -24.0054 q^{44} +0.811635 q^{45} -2.26981 q^{46} +1.48702 q^{47} +15.5174 q^{48} +11.9124 q^{50} -0.928558 q^{51} +12.7318 q^{52} -8.89199 q^{53} -2.74401 q^{54} -3.52351 q^{55} -4.60005 q^{57} -10.3877 q^{58} -13.6167 q^{59} +4.48803 q^{60} +2.35178 q^{61} -15.5291 q^{62} +32.6520 q^{64} +1.86877 q^{65} +11.9124 q^{66} +8.74120 q^{67} -5.13456 q^{68} +0.827185 q^{69} +5.74120 q^{71} -9.68531 q^{72} +10.4071 q^{73} +16.2071 q^{74} -4.34125 q^{75} -25.4365 q^{76} -6.31802 q^{78} +7.38163 q^{79} +12.5945 q^{80} +1.00000 q^{81} +2.74401 q^{82} +4.25932 q^{83} -0.753650 q^{85} -28.2122 q^{86} +3.78560 q^{87} +42.0463 q^{88} -11.3229 q^{89} -2.22714 q^{90} +4.57401 q^{92} +5.65927 q^{93} -4.08040 q^{94} -3.73356 q^{95} -23.2093 q^{96} -11.6504 q^{97} -4.34125 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 3 q^{2} + 5 q^{3} + 7 q^{4} - q^{5} - 3 q^{6} - 9 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q - 3 * q^2 + 5 * q^3 + 7 * q^4 - q^5 - 3 * q^6 - 9 * q^8 + 5 * q^9	$ 5 q - 3 q^{2} + 5 q^{3} + 7 q^{4} - q^{5} - 3 q^{6} - 9 q^{8} + 5 q^{9} - 5 q^{10} + 4 q^{11} + 7 q^{12} - 3 q^{13} - q^{15} + 3 q^{16} + 8 q^{17} - 3 q^{18} - 20 q^{19} + q^{20} + 14 q^{22} - 5 q^{23} - 9 q^{24} + 4 q^{25} - 13 q^{26} + 5 q^{27} + 9 q^{29} - 5 q^{30} - 16 q^{31} - 21 q^{32} + 4 q^{33} + 7 q^{36} - 19 q^{37} - 8 q^{38} - 3 q^{39} - 21 q^{40} - 5 q^{41} + 6 q^{43} - 24 q^{44} - q^{45} + 27 q^{46} - 9 q^{47} + 3 q^{48} + 14 q^{50} + 8 q^{51} - q^{52} - 29 q^{53} - 3 q^{54} - 32 q^{55} - 20 q^{57} - q^{58} - 28 q^{59} + q^{60} - 16 q^{61} + 8 q^{62} + 39 q^{64} + q^{65} + 14 q^{66} + 21 q^{67} + 24 q^{68} - 5 q^{69} + 6 q^{71} - 9 q^{72} + 4 q^{73} + 11 q^{74} + 4 q^{75} - 26 q^{76} - 13 q^{78} + 21 q^{79} + 25 q^{80} + 5 q^{81} + 3 q^{82} - 26 q^{83} - 20 q^{85} - 58 q^{86} + 9 q^{87} + 54 q^{88} - 12 q^{89} - 5 q^{90} + 15 q^{92} - 16 q^{93} + q^{94} + 18 q^{95} - 21 q^{96} - 37 q^{97} + 4 q^{99}+O(q^{100}) $ 5 * q - 3 * q^2 + 5 * q^3 + 7 * q^4 - q^5 - 3 * q^6 - 9 * q^8 + 5 * q^9 - 5 * q^10 + 4 * q^11 + 7 * q^12 - 3 * q^13 - q^15 + 3 * q^16 + 8 * q^17 - 3 * q^18 - 20 * q^19 + q^20 + 14 * q^22 - 5 * q^23 - 9 * q^24 + 4 * q^25 - 13 * q^26 + 5 * q^27 + 9 * q^29 - 5 * q^30 - 16 * q^31 - 21 * q^32 + 4 * q^33 + 7 * q^36 - 19 * q^37 - 8 * q^38 - 3 * q^39 - 21 * q^40 - 5 * q^41 + 6 * q^43 - 24 * q^44 - q^45 + 27 * q^46 - 9 * q^47 + 3 * q^48 + 14 * q^50 + 8 * q^51 - q^52 - 29 * q^53 - 3 * q^54 - 32 * q^55 - 20 * q^57 - q^58 - 28 * q^59 + q^60 - 16 * q^61 + 8 * q^62 + 39 * q^64 + q^65 + 14 * q^66 + 21 * q^67 + 24 * q^68 - 5 * q^69 + 6 * q^71 - 9 * q^72 + 4 * q^73 + 11 * q^74 + 4 * q^75 - 26 * q^76 - 13 * q^78 + 21 * q^79 + 25 * q^80 + 5 * q^81 + 3 * q^82 - 26 * q^83 - 20 * q^85 - 58 * q^86 + 9 * q^87 + 54 * q^88 - 12 * q^89 - 5 * q^90 + 15 * q^92 - 16 * q^93 + q^94 + 18 * q^95 - 21 * q^96 - 37 * q^97 + 4 * 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 $

$2$	−2.74401	−1.94031	−0.970155	−	0.242484i	$-0.922038\pi$
$2$	−2.74401	−1.94031	−0.970155	+	0.242484i	$0.922038\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.52961	2.76481
$5$	0.811635	0.362974	0.181487	−	0.983393i	$-0.441909\pi$
$5$	0.811635	0.362974	0.181487	+	0.983393i	$0.441909\pi$
$6$	−2.74401	−1.12024
$7$	0	0
$7$	0	0
$8$	−9.68531	−3.42427
$9$	1.00000	0.333333
$10$	−2.22714	−0.704283
$11$	−4.34125	−1.30894	−0.654468	−	0.756090i	$-0.727107\pi$
$11$	−4.34125	−1.30894	−0.654468	+	0.756090i	$0.727107\pi$
$12$	5.52961	1.59626
$13$	2.30248	0.638592	0.319296	−	0.947655i	$-0.396554\pi$
$13$	2.30248	0.638592	0.319296	+	0.947655i	$0.396554\pi$
$14$	0	0
$15$	0.811635	0.209563
$16$	15.5174	3.87935
$17$	−0.928558	−0.225208	−0.112604	−	0.993640i	$-0.535919\pi$
$17$	−0.928558	−0.225208	−0.112604	+	0.993640i	$0.535919\pi$
$18$	−2.74401	−0.646770
$19$	−4.60005	−1.05532	−0.527662	−	0.849455i	$-0.676931\pi$
$19$	−4.60005	−1.05532	−0.527662	+	0.849455i	$0.676931\pi$
$20$	4.48803	1.00355
$21$	0	0
$22$	11.9124	2.53974
$23$	0.827185	0.172480	0.0862399	−	0.996274i	$-0.472515\pi$
$23$	0.827185	0.172480	0.0862399	+	0.996274i	$0.472515\pi$
$24$	−9.68531	−1.97701
$25$	−4.34125	−0.868250
$26$	−6.31802	−1.23907
$27$	1.00000	0.192450
$28$	0	0
$29$	3.78560	0.702968	0.351484	−	0.936194i	$-0.385677\pi$
$29$	3.78560	0.702968	0.351484	+	0.936194i	$0.385677\pi$
$30$	−2.22714	−0.406618
$31$	5.65927	1.01644	0.508218	−	0.861229i	$-0.330305\pi$
$31$	5.65927	1.01644	0.508218	+	0.861229i	$0.330305\pi$
$32$	−23.2093	−4.10287
$33$	−4.34125	−0.755714
$34$	2.54797	0.436974
$35$	0	0
$36$	5.52961	0.921602
$37$	−5.90634	−0.970997	−0.485498	−	0.874238i	$-0.661362\pi$
$37$	−5.90634	−0.970997	−0.485498	+	0.874238i	$0.661362\pi$
$38$	12.6226	2.04765
$39$	2.30248	0.368691
$40$	−7.86094	−1.24292
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	10.2813	1.56789	0.783945	−	0.620830i	$-0.213204\pi$
$43$	10.2813	1.56789	0.783945	+	0.620830i	$0.213204\pi$
$44$	−24.0054	−3.61895
$45$	0.811635	0.120991
$46$	−2.26981	−0.334665
$47$	1.48702	0.216904	0.108452	−	0.994102i	$-0.465411\pi$
$47$	1.48702	0.216904	0.108452	+	0.994102i	$0.465411\pi$
$48$	15.5174	2.23974
$49$	0	0
$50$	11.9124	1.68467
$51$	−0.928558	−0.130024
$52$	12.7318	1.76558
$53$	−8.89199	−1.22141	−0.610705	−	0.791858i	$-0.709114\pi$
$53$	−8.89199	−1.22141	−0.610705	+	0.791858i	$0.709114\pi$
$54$	−2.74401	−0.373413
$55$	−3.52351	−0.475110
$56$	0	0
$57$	−4.60005	−0.609291
$58$	−10.3877	−1.36398
$59$	−13.6167	−1.77274	−0.886370	−	0.462977i	$-0.846781\pi$
$59$	−13.6167	−1.77274	−0.886370	+	0.462977i	$0.846781\pi$
$60$	4.48803	0.579402
$61$	2.35178	0.301114	0.150557	−	0.988601i	$-0.451893\pi$
$61$	2.35178	0.301114	0.150557	+	0.988601i	$0.451893\pi$
$62$	−15.5291	−1.97220
$63$	0	0
$64$	32.6520	4.08150
$65$	1.86877	0.231792
$66$	11.9124	1.46632
$67$	8.74120	1.06791	0.533954	−	0.845514i	$-0.320706\pi$
$67$	8.74120	1.06791	0.533954	+	0.845514i	$0.320706\pi$
$68$	−5.13456	−0.622657
$69$	0.827185	0.0995813
$70$	0	0
$71$	5.74120	0.681355	0.340678	−	0.940180i	$-0.389344\pi$
$71$	5.74120	0.681355	0.340678	+	0.940180i	$0.389344\pi$
$72$	−9.68531	−1.14142
$73$	10.4071	1.21806	0.609030	−	0.793147i	$-0.291559\pi$
$73$	10.4071	1.21806	0.609030	+	0.793147i	$0.291559\pi$
$74$	16.2071	1.88404
$75$	−4.34125	−0.501284
$76$	−25.4365	−2.91776
$77$	0	0
$78$	−6.31802	−0.715375
$79$	7.38163	0.830499	0.415249	−	0.909708i	$-0.363694\pi$
$79$	7.38163	0.830499	0.415249	+	0.909708i	$0.363694\pi$
$80$	12.5945	1.40810
$81$	1.00000	0.111111
$82$	2.74401	0.303026
$83$	4.25932	0.467521	0.233761	−	0.972294i	$-0.424897\pi$
$83$	4.25932	0.467521	0.233761	+	0.972294i	$0.424897\pi$
$84$	0	0
$85$	−0.753650	−0.0817448
$86$	−28.2122	−3.04219
$87$	3.78560	0.405859
$88$	42.0463	4.48215
$89$	−11.3229	−1.20023	−0.600114	−	0.799914i	$-0.704878\pi$
$89$	−11.3229	−1.20023	−0.600114	+	0.799914i	$0.704878\pi$
$90$	−2.22714	−0.234761
$91$	0	0
$92$	4.57401	0.476874
$93$	5.65927	0.586839
$94$	−4.08040	−0.420861
$95$	−3.73356	−0.383055
$96$	−23.2093	−2.36879
$97$	−11.6504	−1.18291	−0.591457	−	0.806336i	$-0.701447\pi$
$97$	−11.6504	−1.18291	−0.591457	+	0.806336i	$0.701447\pi$
$98$	0	0
$99$	−4.34125	−0.436312
$100$	−24.0054	−2.40054
$101$	3.91807	0.389863	0.194931	−	0.980817i	$-0.437552\pi$
$101$	3.91807	0.389863	0.194931	+	0.980817i	$0.437552\pi$
$102$	2.54797	0.252287
$103$	−11.6853	−1.15139	−0.575694	−	0.817665i	$-0.695268\pi$
$103$	−11.6853	−1.15139	−0.575694	+	0.817665i	$0.695268\pi$
$104$	−22.3002	−2.18671
$105$	0	0
$106$	24.3998	2.36991
$107$	6.08425	0.588187	0.294093	−	0.955777i	$-0.404982\pi$
$107$	6.08425	0.588187	0.294093	+	0.955777i	$0.404982\pi$
$108$	5.52961	0.532087
$109$	14.4643	1.38543	0.692713	−	0.721213i	$-0.256415\pi$
$109$	14.4643	1.38543	0.692713	+	0.721213i	$0.256415\pi$
$110$	9.66856	0.921861
$111$	−5.90634	−0.560605
$112$	0	0
$113$	16.2990	1.53328	0.766640	−	0.642077i	$-0.221927\pi$
$113$	16.2990	1.53328	0.766640	+	0.642077i	$0.221927\pi$
$114$	12.6226	1.18221
$115$	0.671372	0.0626058
$116$	20.9329	1.94357
$117$	2.30248	0.212864
$118$	37.3644	3.43967
$119$	0	0
$120$	−7.86094	−0.717602
$121$	7.84644	0.713313
$122$	−6.45331	−0.584255
$123$	−1.00000	−0.0901670
$124$	31.2936	2.81025
$125$	−7.58168	−0.678127
$126$	0	0
$127$	−8.58274	−0.761595	−0.380797	−	0.924659i	$-0.624350\pi$
$127$	−8.58274	−0.761595	−0.380797	+	0.924659i	$0.624350\pi$
$128$	−43.1788	−3.81650
$129$	10.2813	0.905222
$130$	−5.12793	−0.449749
$131$	−14.3056	−1.24988	−0.624942	−	0.780671i	$-0.714877\pi$
$131$	−14.3056	−1.24988	−0.624942	+	0.780671i	$0.714877\pi$
$132$	−24.0054	−2.08940
$133$	0	0
$134$	−23.9860	−2.07207
$135$	0.811635	0.0698544
$136$	8.99337	0.771175
$137$	−6.08040	−0.519484	−0.259742	−	0.965678i	$-0.583637\pi$
$137$	−6.08040	−0.519484	−0.259742	+	0.965678i	$0.583637\pi$
$138$	−2.26981	−0.193219
$139$	−17.3967	−1.47556	−0.737782	−	0.675039i	$-0.764127\pi$
$139$	−17.3967	−1.47556	−0.737782	+	0.675039i	$0.764127\pi$
$140$	0	0
$141$	1.48702	0.125230
$142$	−15.7539	−1.32204
$143$	−9.99562	−0.835876
$144$	15.5174	1.29312
$145$	3.07253	0.255159
$146$	−28.5573	−2.36342
$147$	0	0
$148$	−32.6598	−2.68462
$149$	1.79452	0.147012	0.0735062	−	0.997295i	$-0.476581\pi$
$149$	1.79452	0.147012	0.0735062	+	0.997295i	$0.476581\pi$
$150$	11.9124	0.972647
$151$	−21.0647	−1.71422	−0.857109	−	0.515136i	$-0.827741\pi$
$151$	−21.0647	−1.71422	−0.857109	+	0.515136i	$0.827741\pi$
$152$	44.5529	3.61372
$153$	−0.928558	−0.0750694
$154$	0	0
$155$	4.59326	0.368940
$156$	12.7318	1.01936
$157$	−16.4306	−1.31130	−0.655651	−	0.755064i	$-0.727606\pi$
$157$	−16.4306	−1.31130	−0.655651	+	0.755064i	$0.727606\pi$
$158$	−20.2553	−1.61143
$159$	−8.89199	−0.705181
$160$	−18.8375	−1.48924
$161$	0	0
$162$	−2.74401	−0.215590
$163$	−18.0431	−1.41325	−0.706623	−	0.707590i	$-0.749782\pi$
$163$	−18.0431	−1.41325	−0.706623	+	0.707590i	$0.749782\pi$
$164$	−5.52961	−0.431790
$165$	−3.52351	−0.274305
$166$	−11.6876	−0.907136
$167$	−19.0016	−1.47039	−0.735193	−	0.677858i	$-0.762908\pi$
$167$	−19.0016	−1.47039	−0.735193	+	0.677858i	$0.762908\pi$
$168$	0	0
$169$	−7.69861	−0.592201
$170$	2.06803	0.158610
$171$	−4.60005	−0.351774
$172$	56.8519	4.33491
$173$	−23.8308	−1.81182	−0.905911	−	0.423467i	$-0.860813\pi$
$173$	−23.8308	−1.81182	−0.905911	+	0.423467i	$0.860813\pi$
$174$	−10.3877	−0.787492
$175$	0	0
$176$	−67.3649	−5.07782
$177$	−13.6167	−1.02349
$178$	31.0703	2.32882
$179$	−14.7339	−1.10127	−0.550633	−	0.834748i	$-0.685614\pi$
$179$	−14.7339	−1.10127	−0.550633	+	0.834748i	$0.685614\pi$
$180$	4.48803	0.334518
$181$	20.1601	1.49849	0.749244	−	0.662295i	$-0.230417\pi$
$181$	20.1601	1.49849	0.749244	+	0.662295i	$0.230417\pi$
$182$	0	0
$183$	2.35178	0.173848
$184$	−8.01154	−0.590618
$185$	−4.79380	−0.352447
$186$	−15.5291	−1.13865
$187$	4.03110	0.294783
$188$	8.22264	0.599698
$189$	0	0
$190$	10.2449	0.743246
$191$	3.05432	0.221003	0.110502	−	0.993876i	$-0.464754\pi$
$191$	3.05432	0.221003	0.110502	+	0.993876i	$0.464754\pi$
$192$	32.6520	2.35645
$193$	−26.5605	−1.91187	−0.955934	−	0.293582i	$-0.905153\pi$
$193$	−26.5605	−1.91187	−0.955934	+	0.293582i	$0.905153\pi$
$194$	31.9687	2.29522
$195$	1.86877	0.133825
$196$	0	0
$197$	−11.5401	−0.822198	−0.411099	−	0.911591i	$-0.634855\pi$
$197$	−11.5401	−0.822198	−0.411099	+	0.911591i	$0.634855\pi$
$198$	11.9124	0.846581
$199$	−3.45327	−0.244796	−0.122398	−	0.992481i	$-0.539058\pi$
$199$	−3.45327	−0.244796	−0.122398	+	0.992481i	$0.539058\pi$
$200$	42.0463	2.97312
$201$	8.74120	0.616557
$202$	−10.7512	−0.756455
$203$	0	0
$204$	−5.13456	−0.359491
$205$	−0.811635	−0.0566871
$206$	32.0647	2.23405
$207$	0.827185	0.0574933
$208$	35.7284	2.47732
$209$	19.9699	1.38135
$210$	0	0
$211$	26.0952	1.79647	0.898235	−	0.439516i	$-0.144850\pi$
$211$	26.0952	1.79647	0.898235	+	0.439516i	$0.144850\pi$
$212$	−49.1693	−3.37696
$213$	5.74120	0.393381
$214$	−16.6953	−1.14127
$215$	8.34470	0.569104
$216$	−9.68531	−0.659002
$217$	0	0
$218$	−39.6902	−2.68816
$219$	10.4071	0.703247
$220$	−19.4836	−1.31359
$221$	−2.13798	−0.143816
$222$	16.2071	1.08775
$223$	0.0724832	0.00485383	0.00242692	−	0.999997i	$-0.499227\pi$
$223$	0.0724832	0.00485383	0.00242692	+	0.999997i	$0.499227\pi$
$224$	0	0
$225$	−4.34125	−0.289417
$226$	−44.7246	−2.97504
$227$	−12.9750	−0.861184	−0.430592	−	0.902547i	$-0.641695\pi$
$227$	−12.9750	−0.861184	−0.430592	+	0.902547i	$0.641695\pi$
$228$	−25.4365	−1.68457
$229$	−2.15907	−0.142675	−0.0713376	−	0.997452i	$-0.522727\pi$
$229$	−2.15907	−0.142675	−0.0713376	+	0.997452i	$0.522727\pi$
$230$	−1.84225	−0.121475
$231$	0	0
$232$	−36.6647	−2.40716
$233$	−2.86251	−0.187529	−0.0937645	−	0.995594i	$-0.529890\pi$
$233$	−2.86251	−0.187529	−0.0937645	+	0.995594i	$0.529890\pi$
$234$	−6.31802	−0.413022
$235$	1.20692	0.0787306
$236$	−75.2950	−4.90128
$237$	7.38163	0.479489
$238$	0	0
$239$	16.0421	1.03767	0.518837	−	0.854873i	$-0.326365\pi$
$239$	16.0421	1.03767	0.518837	+	0.854873i	$0.326365\pi$
$240$	12.5945	0.812969
$241$	−12.0986	−0.779340	−0.389670	−	0.920955i	$-0.627411\pi$
$241$	−12.0986	−0.779340	−0.389670	+	0.920955i	$0.627411\pi$
$242$	−21.5307	−1.38405
$243$	1.00000	0.0641500
$244$	13.0044	0.832522
$245$	0	0
$246$	2.74401	0.174952
$247$	−10.5915	−0.673921
$248$	−54.8118	−3.48055
$249$	4.25932	0.269923
$250$	20.8043	1.31578
$251$	5.17788	0.326825	0.163412	−	0.986558i	$-0.447750\pi$
$251$	5.17788	0.326825	0.163412	+	0.986558i	$0.447750\pi$
$252$	0	0
$253$	−3.59101	−0.225765
$254$	23.5511	1.47773
$255$	−0.753650	−0.0471954
$256$	53.1792	3.32370
$257$	0.436444	0.0272247	0.0136123	−	0.999907i	$-0.495667\pi$
$257$	0.436444	0.0272247	0.0136123	+	0.999907i	$0.495667\pi$
$258$	−28.2122	−1.75641
$259$	0	0
$260$	10.3336	0.640861
$261$	3.78560	0.234323
$262$	39.2547	2.42516
$263$	16.8574	1.03947	0.519736	−	0.854327i	$-0.326030\pi$
$263$	16.8574	1.03947	0.519736	+	0.854327i	$0.326030\pi$
$264$	42.0463	2.58777
$265$	−7.21705	−0.443340
$266$	0	0
$267$	−11.3229	−0.692952
$268$	48.3355	2.95256
$269$	−0.918849	−0.0560232	−0.0280116	−	0.999608i	$-0.508918\pi$
$269$	−0.918849	−0.0560232	−0.0280116	+	0.999608i	$0.508918\pi$
$270$	−2.22714	−0.135539
$271$	−3.93286	−0.238904	−0.119452	−	0.992840i	$-0.538114\pi$
$271$	−3.93286	−0.238904	−0.119452	+	0.992840i	$0.538114\pi$
$272$	−14.4088	−0.873662
$273$	0	0
$274$	16.6847	1.00796
$275$	18.8464	1.13648
$276$	4.57401	0.275323
$277$	22.9534	1.37913	0.689567	−	0.724222i	$-0.257801\pi$
$277$	22.9534	1.37913	0.689567	+	0.724222i	$0.257801\pi$
$278$	47.7367	2.86305
$279$	5.65927	0.338812
$280$	0	0
$281$	−13.2909	−0.792871	−0.396435	−	0.918063i	$-0.629753\pi$
$281$	−13.2909	−0.792871	−0.396435	+	0.918063i	$0.629753\pi$
$282$	−4.08040	−0.242984
$283$	−31.4345	−1.86858	−0.934292	−	0.356508i	$-0.883967\pi$
$283$	−31.4345	−1.86858	−0.934292	+	0.356508i	$0.883967\pi$
$284$	31.7466	1.88382
$285$	−3.73356	−0.221157
$286$	27.4281	1.62186
$287$	0	0
$288$	−23.2093	−1.36762
$289$	−16.1378	−0.949281
$290$	−8.43105	−0.495088
$291$	−11.6504	−0.682956
$292$	57.5473	3.36770
$293$	−18.8419	−1.10075	−0.550377	−	0.834916i	$-0.685516\pi$
$293$	−18.8419	−1.10075	−0.550377	+	0.834916i	$0.685516\pi$
$294$	0	0
$295$	−11.0518	−0.643459
$296$	57.2048	3.32496
$297$	−4.34125	−0.251905
$298$	−4.92418	−0.285250
$299$	1.90457	0.110144
$300$	−24.0054	−1.38595
$301$	0	0
$302$	57.8017	3.32611
$303$	3.91807	0.225087
$304$	−71.3808	−4.09397
$305$	1.90878	0.109297
$306$	2.54797	0.145658
$307$	1.31498	0.0750499	0.0375250	−	0.999296i	$-0.488053\pi$
$307$	1.31498	0.0750499	0.0375250	+	0.999296i	$0.488053\pi$
$308$	0	0
$309$	−11.6853	−0.664754
$310$	−12.6040	−0.715858
$311$	31.5532	1.78922	0.894609	−	0.446850i	$-0.147454\pi$
$311$	31.5532	1.78922	0.894609	+	0.446850i	$0.147454\pi$
$312$	−22.3002	−1.26250
$313$	−22.6616	−1.28091	−0.640453	−	0.767997i	$-0.721254\pi$
$313$	−22.6616	−1.28091	−0.640453	+	0.767997i	$0.721254\pi$
$314$	45.0857	2.54433
$315$	0	0
$316$	40.8176	2.29617
$317$	−6.11392	−0.343392	−0.171696	−	0.985150i	$-0.554925\pi$
$317$	−6.11392	−0.343392	−0.171696	+	0.985150i	$0.554925\pi$
$318$	24.3998	1.36827
$319$	−16.4342	−0.920140
$320$	26.5015	1.48148
$321$	6.08425	0.339590
$322$	0	0
$323$	4.27141	0.237667
$324$	5.52961	0.307201
$325$	−9.99562	−0.554457
$326$	49.5106	2.74214
$327$	14.4643	0.799876
$328$	9.68531	0.534782
$329$	0	0
$330$	9.66856	0.532237
$331$	−4.65182	−0.255687	−0.127844	−	0.991794i	$-0.540806\pi$
$331$	−4.65182	−0.255687	−0.127844	+	0.991794i	$0.540806\pi$
$332$	23.5524	1.29261
$333$	−5.90634	−0.323666
$334$	52.1406	2.85301
$335$	7.09467	0.387623
$336$	0	0
$337$	−10.5259	−0.573380	−0.286690	−	0.958023i	$-0.592555\pi$
$337$	−10.5259	−0.573380	−0.286690	+	0.958023i	$0.592555\pi$
$338$	21.1251	1.14905
$339$	16.2990	0.885239
$340$	−4.16739	−0.226009
$341$	−24.5683	−1.33045
$342$	12.6226	0.682552
$343$	0	0
$344$	−99.5780	−5.36889
$345$	0.671372	0.0361455
$346$	65.3921	3.51550
$347$	−11.5164	−0.618232	−0.309116	−	0.951024i	$-0.600033\pi$
$347$	−11.5164	−0.618232	−0.309116	+	0.951024i	$0.600033\pi$
$348$	20.9329	1.12212
$349$	23.1050	1.23678	0.618392	−	0.785870i	$-0.287784\pi$
$349$	23.1050	1.23678	0.618392	+	0.785870i	$0.287784\pi$
$350$	0	0
$351$	2.30248	0.122897
$352$	100.758	5.37039
$353$	20.7823	1.10613	0.553066	−	0.833137i	$-0.313458\pi$
$353$	20.7823	1.10613	0.553066	+	0.833137i	$0.313458\pi$
$354$	37.3644	1.98589
$355$	4.65976	0.247314
$356$	−62.6114	−3.31840
$357$	0	0
$358$	40.4301	2.13680
$359$	5.08036	0.268131	0.134066	−	0.990972i	$-0.457197\pi$
$359$	5.08036	0.268131	0.134066	+	0.990972i	$0.457197\pi$
$360$	−7.86094	−0.414308
$361$	2.16043	0.113707
$362$	−55.3195	−2.90753
$363$	7.84644	0.411831
$364$	0	0
$365$	8.44677	0.442124
$366$	−6.45331	−0.337320
$367$	26.8734	1.40278	0.701389	−	0.712778i	$-0.252563\pi$
$367$	26.8734	1.40278	0.701389	+	0.712778i	$0.252563\pi$
$368$	12.8358	0.669110
$369$	−1.00000	−0.0520579
$370$	13.1542	0.683856
$371$	0	0
$372$	31.2936	1.62250
$373$	8.45274	0.437666	0.218833	−	0.975762i	$-0.429775\pi$
$373$	8.45274	0.437666	0.218833	+	0.975762i	$0.429775\pi$
$374$	−11.0614	−0.571971
$375$	−7.58168	−0.391517
$376$	−14.4022	−0.742739
$377$	8.71625	0.448910
$378$	0	0
$379$	8.76462	0.450208	0.225104	−	0.974335i	$-0.427728\pi$
$379$	8.76462	0.450208	0.225104	+	0.974335i	$0.427728\pi$
$380$	−20.6451	−1.05907
$381$	−8.58274	−0.439707
$382$	−8.38110	−0.428815
$383$	14.3136	0.731393	0.365696	−	0.930734i	$-0.380831\pi$
$383$	14.3136	0.731393	0.365696	+	0.930734i	$0.380831\pi$
$384$	−43.1788	−2.20346
$385$	0	0
$386$	72.8824	3.70962
$387$	10.2813	0.522630
$388$	−64.4220	−3.27053
$389$	−22.7706	−1.15451	−0.577257	−	0.816563i	$-0.695877\pi$
$389$	−22.7706	−1.15451	−0.577257	+	0.816563i	$0.695877\pi$
$390$	−5.12793	−0.259663
$391$	−0.768088	−0.0388439
$392$	0	0
$393$	−14.3056	−0.721621
$394$	31.6662	1.59532
$395$	5.99119	0.301450
$396$	−24.0054	−1.20632
$397$	−32.4249	−1.62736	−0.813681	−	0.581312i	$-0.802539\pi$
$397$	−32.4249	−1.62736	−0.813681	+	0.581312i	$0.802539\pi$
$398$	9.47581	0.474980
$399$	0	0
$400$	−67.3649	−3.36824
$401$	−8.50519	−0.424729	−0.212364	−	0.977191i	$-0.568116\pi$
$401$	−8.50519	−0.424729	−0.212364	+	0.977191i	$0.568116\pi$
$402$	−23.9860	−1.19631
$403$	13.0303	0.649087
$404$	21.6654	1.07789
$405$	0.811635	0.0403305
$406$	0	0
$407$	25.6409	1.27097
$408$	8.99337	0.445238
$409$	21.6287	1.06947	0.534735	−	0.845020i	$-0.320411\pi$
$409$	21.6287	1.06947	0.534735	+	0.845020i	$0.320411\pi$
$410$	2.22714	0.109991
$411$	−6.08040	−0.299924
$412$	−64.6152	−3.18336
$413$	0	0
$414$	−2.26981	−0.111555
$415$	3.45701	0.169698
$416$	−53.4389	−2.62006
$417$	−17.3967	−0.851918
$418$	−54.7978	−2.68025
$419$	−12.1076	−0.591495	−0.295747	−	0.955266i	$-0.595569\pi$
$419$	−12.1076	−0.591495	−0.295747	+	0.955266i	$0.595569\pi$
$420$	0	0
$421$	−3.41183	−0.166282	−0.0831412	−	0.996538i	$-0.526495\pi$
$421$	−3.41183	−0.166282	−0.0831412	+	0.996538i	$0.526495\pi$
$422$	−71.6057	−3.48571
$423$	1.48702	0.0723013
$424$	86.1217	4.18244
$425$	4.03110	0.195537
$426$	−15.7539	−0.763281
$427$	0	0
$428$	33.6436	1.62622
$429$	−9.99562	−0.482593
$430$	−22.8980	−1.10424
$431$	34.1622	1.64554	0.822769	−	0.568376i	$-0.192428\pi$
$431$	34.1622	1.64554	0.822769	+	0.568376i	$0.192428\pi$
$432$	15.5174	0.746581
$433$	−25.7903	−1.23940	−0.619701	−	0.784838i	$-0.712746\pi$
$433$	−25.7903	−1.23940	−0.619701	+	0.784838i	$0.712746\pi$
$434$	0	0
$435$	3.07253	0.147316
$436$	79.9818	3.83044
$437$	−3.80509	−0.182022
$438$	−28.5573	−1.36452
$439$	33.3102	1.58981	0.794904	−	0.606735i	$-0.207521\pi$
$439$	33.3102	1.58981	0.794904	+	0.606735i	$0.207521\pi$
$440$	34.1263	1.62691
$441$	0	0
$442$	5.86665	0.279048
$443$	−33.8064	−1.60619	−0.803096	−	0.595850i	$-0.796815\pi$
$443$	−33.8064	−1.60619	−0.803096	+	0.595850i	$0.796815\pi$
$444$	−32.6598	−1.54997
$445$	−9.19009	−0.435652
$446$	−0.198895	−0.00941795
$447$	1.79452	0.0848777
$448$	0	0
$449$	−32.1965	−1.51945	−0.759724	−	0.650246i	$-0.774666\pi$
$449$	−32.1965	−1.51945	−0.759724	+	0.650246i	$0.774666\pi$
$450$	11.9124	0.561558
$451$	4.34125	0.204421
$452$	90.1271	4.23922
$453$	−21.0647	−0.989704
$454$	35.6037	1.67096
$455$	0	0
$456$	44.5529	2.08638
$457$	19.0072	0.889117	0.444559	−	0.895750i	$-0.353361\pi$
$457$	19.0072	0.889117	0.444559	+	0.895750i	$0.353361\pi$
$458$	5.92451	0.276834
$459$	−0.928558	−0.0433414
$460$	3.71243	0.173093
$461$	40.6207	1.89190	0.945948	−	0.324320i	$-0.105135\pi$
$461$	40.6207	1.89190	0.945948	+	0.324320i	$0.105135\pi$
$462$	0	0
$463$	−17.2395	−0.801189	−0.400594	−	0.916256i	$-0.631196\pi$
$463$	−17.2395	−0.801189	−0.400594	+	0.916256i	$0.631196\pi$
$464$	58.7427	2.72706
$465$	4.59326	0.213008
$466$	7.85476	0.363865
$467$	9.90129	0.458177	0.229089	−	0.973406i	$-0.426425\pi$
$467$	9.90129	0.458177	0.229089	+	0.973406i	$0.426425\pi$
$468$	12.7318	0.588528
$469$	0	0
$470$	−3.31180	−0.152762
$471$	−16.4306	−0.757080
$472$	131.882	6.07035
$473$	−44.6339	−2.05227
$474$	−20.2553	−0.930357
$475$	19.9699	0.916284
$476$	0	0
$477$	−8.89199	−0.407136
$478$	−44.0197	−2.01341
$479$	−29.3404	−1.34060	−0.670298	−	0.742092i	$-0.733834\pi$
$479$	−29.3404	−1.34060	−0.670298	+	0.742092i	$0.733834\pi$
$480$	−18.8375	−0.859811
$481$	−13.5992	−0.620071
$482$	33.1987	1.51216
$483$	0	0
$484$	43.3878	1.97217
$485$	−9.45584	−0.429368
$486$	−2.74401	−0.124471
$487$	−18.9402	−0.858262	−0.429131	−	0.903242i	$-0.641180\pi$
$487$	−18.9402	−0.858262	−0.429131	+	0.903242i	$0.641180\pi$
$488$	−22.7777	−1.03110
$489$	−18.0431	−0.815938
$490$	0	0
$491$	3.16173	0.142687	0.0713434	−	0.997452i	$-0.477271\pi$
$491$	3.16173	0.142687	0.0713434	+	0.997452i	$0.477271\pi$
$492$	−5.52961	−0.249294
$493$	−3.51515	−0.158314
$494$	29.0632	1.30762
$495$	−3.52351	−0.158370
$496$	87.8172	3.94311
$497$	0	0
$498$	−11.6876	−0.523735
$499$	−18.8619	−0.844375	−0.422187	−	0.906509i	$-0.638738\pi$
$499$	−18.8619	−0.844375	−0.422187	+	0.906509i	$0.638738\pi$
$500$	−41.9238	−1.87489
$501$	−19.0016	−0.848928
$502$	−14.2082	−0.634142
$503$	16.0684	0.716453	0.358226	−	0.933635i	$-0.383382\pi$
$503$	16.0684	0.716453	0.358226	+	0.933635i	$0.383382\pi$
$504$	0	0
$505$	3.18004	0.141510
$506$	9.85379	0.438054
$507$	−7.69861	−0.341907
$508$	−47.4592	−2.10566
$509$	1.96467	0.0870826	0.0435413	−	0.999052i	$-0.486136\pi$
$509$	1.96467	0.0870826	0.0435413	+	0.999052i	$0.486136\pi$
$510$	2.06803	0.0915737
$511$	0	0
$512$	−59.5670	−2.63251
$513$	−4.60005	−0.203097
$514$	−1.19761	−0.0528243
$515$	−9.48421	−0.417924
$516$	56.8519	2.50276
$517$	−6.45552	−0.283913
$518$	0	0
$519$	−23.8308	−1.04606
$520$	−18.0996	−0.793721
$521$	−31.2408	−1.36868	−0.684342	−	0.729161i	$-0.739911\pi$
$521$	−31.2408	−1.36868	−0.684342	+	0.729161i	$0.739911\pi$
$522$	−10.3877	−0.454659
$523$	−18.6684	−0.816314	−0.408157	−	0.912912i	$-0.633828\pi$
$523$	−18.6684	−0.816314	−0.408157	+	0.912912i	$0.633828\pi$
$524$	−79.1043	−3.45569
$525$	0	0
$526$	−46.2570	−2.01690
$527$	−5.25496	−0.228910
$528$	−67.3649	−2.93168
$529$	−22.3158	−0.970251
$530$	19.8037	0.860218
$531$	−13.6167	−0.590914
$532$	0	0
$533$	−2.30248	−0.0997313
$534$	31.0703	1.34454
$535$	4.93819	0.213497
$536$	−84.6612	−3.65681
$537$	−14.7339	−0.635816
$538$	2.52133	0.108702
$539$	0	0
$540$	4.48803	0.193134
$541$	43.5671	1.87309	0.936547	−	0.350542i	$-0.114002\pi$
$541$	43.5671	1.87309	0.936547	+	0.350542i	$0.114002\pi$
$542$	10.7918	0.463548
$543$	20.1601	0.865152
$544$	21.5512	0.924000
$545$	11.7397	0.502874
$546$	0	0
$547$	32.9640	1.40944	0.704719	−	0.709486i	$-0.251073\pi$
$547$	32.9640	1.40944	0.704719	+	0.709486i	$0.251073\pi$
$548$	−33.6223	−1.43627
$549$	2.35178	0.100371
$550$	−51.7149	−2.20513
$551$	−17.4139	−0.741858
$552$	−8.01154	−0.340994
$553$	0	0
$554$	−62.9843	−2.67595
$555$	−4.79380	−0.203485
$556$	−96.1968	−4.07965
$557$	13.9863	0.592620	0.296310	−	0.955092i	$-0.404244\pi$
$557$	13.9863	0.592620	0.296310	+	0.955092i	$0.404244\pi$
$558$	−15.5291	−0.657400
$559$	23.6725	1.00124
$560$	0	0
$561$	4.03110	0.170193
$562$	36.4705	1.53842
$563$	−17.3906	−0.732927	−0.366464	−	0.930432i	$-0.619432\pi$
$563$	−17.3906	−0.732927	−0.366464	+	0.930432i	$0.619432\pi$
$564$	8.22264	0.346236
$565$	13.2288	0.556541
$566$	86.2566	3.62564
$567$	0	0
$568$	−55.6053	−2.33315
$569$	−46.7570	−1.96016	−0.980079	−	0.198610i	$-0.936357\pi$
$569$	−46.7570	−1.96016	−0.980079	+	0.198610i	$0.936357\pi$
$570$	10.2449	0.429113
$571$	7.58178	0.317288	0.158644	−	0.987336i	$-0.449288\pi$
$571$	7.58178	0.317288	0.158644	+	0.987336i	$0.449288\pi$
$572$	−55.2719	−2.31103
$573$	3.05432	0.127596
$574$	0	0
$575$	−3.59101	−0.149756
$576$	32.6520	1.36050
$577$	−0.511336	−0.0212872	−0.0106436	−	0.999943i	$-0.503388\pi$
$577$	−0.511336	−0.0212872	−0.0106436	+	0.999943i	$0.503388\pi$
$578$	44.2823	1.84190
$579$	−26.5605	−1.10382
$580$	16.9899	0.705466
$581$	0	0
$582$	31.9687	1.32515
$583$	38.6024	1.59875
$584$	−100.796	−4.17097
$585$	1.86877	0.0772641
$586$	51.7023	2.13580
$587$	9.19657	0.379583	0.189792	−	0.981824i	$-0.439219\pi$
$587$	9.19657	0.379583	0.189792	+	0.981824i	$0.439219\pi$
$588$	0	0
$589$	−26.0329	−1.07267
$590$	30.3262	1.24851
$591$	−11.5401	−0.474696
$592$	−91.6511	−3.76684
$593$	−16.7265	−0.686877	−0.343438	−	0.939175i	$-0.611592\pi$
$593$	−16.7265	−0.686877	−0.343438	+	0.939175i	$0.611592\pi$
$594$	11.9124	0.488774
$595$	0	0
$596$	9.92298	0.406461
$597$	−3.45327	−0.141333
$598$	−5.22617	−0.213714
$599$	25.3269	1.03483	0.517415	−	0.855734i	$-0.326894\pi$
$599$	25.3269	1.03483	0.517415	+	0.855734i	$0.326894\pi$
$600$	42.0463	1.71653
$601$	−44.2100	−1.80336	−0.901681	−	0.432402i	$-0.857666\pi$
$601$	−44.2100	−1.80336	−0.901681	+	0.432402i	$0.857666\pi$
$602$	0	0
$603$	8.74120	0.355969
$604$	−116.479	−4.73948
$605$	6.36844	0.258914
$606$	−10.7512	−0.436739
$607$	6.92679	0.281150	0.140575	−	0.990070i	$-0.455105\pi$
$607$	6.92679	0.281150	0.140575	+	0.990070i	$0.455105\pi$
$608$	106.764	4.32985
$609$	0	0
$610$	−5.23773	−0.212070
$611$	3.42382	0.138513
$612$	−5.13456	−0.207552
$613$	−20.7708	−0.838925	−0.419462	−	0.907773i	$-0.637781\pi$
$613$	−20.7708	−0.838925	−0.419462	+	0.907773i	$0.637781\pi$
$614$	−3.60833	−0.145620
$615$	−0.811635	−0.0327283
$616$	0	0
$617$	−5.59015	−0.225051	−0.112526	−	0.993649i	$-0.535894\pi$
$617$	−5.59015	−0.225051	−0.112526	+	0.993649i	$0.535894\pi$
$618$	32.0647	1.28983
$619$	1.33263	0.0535629	0.0267815	−	0.999641i	$-0.491474\pi$
$619$	1.33263	0.0535629	0.0267815	+	0.999641i	$0.491474\pi$
$620$	25.3990	1.02005
$621$	0.827185	0.0331938
$622$	−86.5824	−3.47164
$623$	0	0
$624$	35.7284	1.43028
$625$	15.5527	0.622107
$626$	62.1836	2.48536
$627$	19.9699	0.797523
$628$	−90.8547	−3.62550
$629$	5.48438	0.218677
$630$	0	0
$631$	1.59667	0.0635626	0.0317813	−	0.999495i	$-0.489882\pi$
$631$	1.59667	0.0635626	0.0317813	+	0.999495i	$0.489882\pi$
$632$	−71.4934	−2.84386
$633$	26.0952	1.03719
$634$	16.7767	0.666287
$635$	−6.96605	−0.276439
$636$	−49.1693	−1.94969
$637$	0	0
$638$	45.0958	1.78536
$639$	5.74120	0.227118
$640$	−35.0454	−1.38529
$641$	47.2029	1.86440	0.932201	−	0.361940i	$-0.117886\pi$
$641$	47.2029	1.86440	0.932201	+	0.361940i	$0.117886\pi$
$642$	−16.6953	−0.658910
$643$	−42.1500	−1.66223	−0.831117	−	0.556098i	$-0.812298\pi$
$643$	−42.1500	−1.66223	−0.831117	+	0.556098i	$0.812298\pi$
$644$	0	0
$645$	8.34470	0.328572
$646$	−11.7208	−0.461149
$647$	26.2980	1.03388	0.516941	−	0.856021i	$-0.327071\pi$
$647$	26.2980	1.03388	0.516941	+	0.856021i	$0.327071\pi$
$648$	−9.68531	−0.380475
$649$	59.1134	2.32040
$650$	27.4281	1.07582
$651$	0	0
$652$	−99.7715	−3.90735
$653$	−36.0260	−1.40981	−0.704903	−	0.709304i	$-0.749010\pi$
$653$	−36.0260	−1.40981	−0.704903	+	0.709304i	$0.749010\pi$
$654$	−39.6902	−1.55201
$655$	−11.6109	−0.453676
$656$	−15.5174	−0.605853
$657$	10.4071	0.406020
$658$	0	0
$659$	27.6675	1.07777	0.538886	−	0.842378i	$-0.318845\pi$
$659$	27.6675	1.07777	0.538886	+	0.842378i	$0.318845\pi$
$660$	−19.4836	−0.758400
$661$	24.2040	0.941426	0.470713	−	0.882286i	$-0.343997\pi$
$661$	24.2040	0.941426	0.470713	+	0.882286i	$0.343997\pi$
$662$	12.7647	0.496113
$663$	−2.13798	−0.0830323
$664$	−41.2528	−1.60092
$665$	0	0
$666$	16.2071	0.628012
$667$	3.13139	0.121248
$668$	−105.071	−4.06533
$669$	0.0724832	0.00280236
$670$	−19.4679	−0.752109
$671$	−10.2096	−0.394139
$672$	0	0
$673$	28.3365	1.09229	0.546145	−	0.837690i	$-0.316095\pi$
$673$	28.3365	1.09229	0.546145	+	0.837690i	$0.316095\pi$
$674$	28.8831	1.11254
$675$	−4.34125	−0.167095
$676$	−42.5703	−1.63732
$677$	0.866634	0.0333074	0.0166537	−	0.999861i	$-0.494699\pi$
$677$	0.866634	0.0333074	0.0166537	+	0.999861i	$0.494699\pi$
$678$	−44.7246	−1.71764
$679$	0	0
$680$	7.29933	0.279917
$681$	−12.9750	−0.497205
$682$	67.4158	2.58148
$683$	7.98197	0.305422	0.152711	−	0.988271i	$-0.451200\pi$
$683$	7.98197	0.305422	0.152711	+	0.988271i	$0.451200\pi$
$684$	−25.4365	−0.972588
$685$	−4.93507	−0.188559
$686$	0	0
$687$	−2.15907	−0.0823736
$688$	159.540	6.08239
$689$	−20.4736	−0.779982
$690$	−1.84225	−0.0701334
$691$	−31.3602	−1.19300	−0.596500	−	0.802613i	$-0.703442\pi$
$691$	−31.3602	−1.19300	−0.596500	+	0.802613i	$0.703442\pi$
$692$	−131.775	−5.00934
$693$	0	0
$694$	31.6011	1.19956
$695$	−14.1197	−0.535592
$696$	−36.6647	−1.38977
$697$	0.928558	0.0351716
$698$	−63.4006	−2.39975
$699$	−2.86251	−0.108270
$700$	0	0
$701$	4.02784	0.152129	0.0760647	−	0.997103i	$-0.475764\pi$
$701$	4.02784	0.152129	0.0760647	+	0.997103i	$0.475764\pi$
$702$	−6.31802	−0.238458
$703$	27.1695	1.02472
$704$	−141.750	−5.34241
$705$	1.20692	0.0454551
$706$	−57.0270	−2.14624
$707$	0	0
$708$	−75.2950	−2.82976
$709$	−9.82890	−0.369132	−0.184566	−	0.982820i	$-0.559088\pi$
$709$	−9.82890	−0.369132	−0.184566	+	0.982820i	$0.559088\pi$
$710$	−12.7864	−0.479867
$711$	7.38163	0.276833
$712$	109.666	4.10991
$713$	4.68126	0.175315
$714$	0	0
$715$	−8.11279	−0.303401
$716$	−81.4730	−3.04479
$717$	16.0421	0.599102
$718$	−13.9406	−0.520258
$719$	−5.83288	−0.217530	−0.108765	−	0.994068i	$-0.534690\pi$
$719$	−5.83288	−0.217530	−0.108765	+	0.994068i	$0.534690\pi$
$720$	12.5945	0.469368
$721$	0	0
$722$	−5.92824	−0.220626
$723$	−12.0986	−0.449952
$724$	111.477	4.14303
$725$	−16.4342	−0.610352
$726$	−21.5307	−0.799081
$727$	−3.58617	−0.133004	−0.0665018	−	0.997786i	$-0.521184\pi$
$727$	−3.58617	−0.133004	−0.0665018	+	0.997786i	$0.521184\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−23.1781	−0.857859
$731$	−9.54682	−0.353102
$732$	13.0044	0.480657
$733$	−13.7872	−0.509242	−0.254621	−	0.967041i	$-0.581951\pi$
$733$	−13.7872	−0.509242	−0.254621	+	0.967041i	$0.581951\pi$
$734$	−73.7409	−2.72183
$735$	0	0
$736$	−19.1984	−0.707663
$737$	−37.9477	−1.39782
$738$	2.74401	0.101009
$739$	−23.3594	−0.859289	−0.429644	−	0.902998i	$-0.641361\pi$
$739$	−23.3594	−0.859289	−0.429644	+	0.902998i	$0.641361\pi$
$740$	−26.5078	−0.974447
$741$	−10.5915	−0.389088
$742$	0	0
$743$	1.64399	0.0603120	0.0301560	−	0.999545i	$-0.490400\pi$
$743$	1.64399	0.0603120	0.0301560	+	0.999545i	$0.490400\pi$
$744$	−54.8118	−2.00950
$745$	1.45649	0.0533617
$746$	−23.1944	−0.849208
$747$	4.25932	0.155840
$748$	22.2904	0.815018
$749$	0	0
$750$	20.8043	0.759664
$751$	25.2153	0.920120	0.460060	−	0.887888i	$-0.347828\pi$
$751$	25.2153	0.920120	0.460060	+	0.887888i	$0.347828\pi$
$752$	23.0747	0.841446
$753$	5.17788	0.188692
$754$	−23.9175	−0.871024
$755$	−17.0968	−0.622217
$756$	0	0
$757$	3.28211	0.119290	0.0596451	−	0.998220i	$-0.481003\pi$
$757$	3.28211	0.119290	0.0596451	+	0.998220i	$0.481003\pi$
$758$	−24.0502	−0.873544
$759$	−3.59101	−0.130346
$760$	36.1607	1.31169
$761$	29.3924	1.06547	0.532736	−	0.846282i	$-0.321164\pi$
$761$	29.3924	1.06547	0.532736	+	0.846282i	$0.321164\pi$
$762$	23.5511	0.853168
$763$	0	0
$764$	16.8892	0.611031
$765$	−0.753650	−0.0272483
$766$	−39.2768	−1.41913
$767$	−31.3521	−1.13206
$768$	53.1792	1.91894
$769$	14.2182	0.512721	0.256360	−	0.966581i	$-0.417477\pi$
$769$	14.2182	0.512721	0.256360	+	0.966581i	$0.417477\pi$
$770$	0	0
$771$	0.436444	0.0157182
$772$	−146.869	−5.28594
$773$	1.99553	0.0717744	0.0358872	−	0.999356i	$-0.488574\pi$
$773$	1.99553	0.0717744	0.0358872	+	0.999356i	$0.488574\pi$
$774$	−28.2122	−1.01406
$775$	−24.5683	−0.882520
$776$	112.837	4.05062
$777$	0	0
$778$	62.4828	2.24012
$779$	4.60005	0.164814
$780$	10.3336	0.370001
$781$	−24.9240	−0.891850
$782$	2.10765	0.0753692
$783$	3.78560	0.135286
$784$	0	0
$785$	−13.3356	−0.475969
$786$	39.2547	1.40017
$787$	8.15136	0.290564	0.145282	−	0.989390i	$-0.453591\pi$
$787$	8.15136	0.290564	0.145282	+	0.989390i	$0.453591\pi$
$788$	−63.8123	−2.27322
$789$	16.8574	0.600139
$790$	−16.4399	−0.584906
$791$	0	0
$792$	42.0463	1.49405
$793$	5.41491	0.192289
$794$	88.9745	3.15759
$795$	−7.21705	−0.255963
$796$	−19.0952	−0.676812
$797$	6.99495	0.247774	0.123887	−	0.992296i	$-0.460464\pi$
$797$	6.99495	0.247774	0.123887	+	0.992296i	$0.460464\pi$
$798$	0	0
$799$	−1.38078	−0.0488486
$800$	100.758	3.56232
$801$	−11.3229	−0.400076
$802$	23.3384	0.824106
$803$	−45.1798	−1.59436
$804$	48.3355	1.70466
$805$	0	0
$806$	−35.7554	−1.25943
$807$	−0.918849	−0.0323450
$808$	−37.9477	−1.33500
$809$	16.4662	0.578921	0.289461	−	0.957190i	$-0.406524\pi$
$809$	16.4662	0.578921	0.289461	+	0.957190i	$0.406524\pi$
$810$	−2.22714	−0.0782537
$811$	−22.4961	−0.789946	−0.394973	−	0.918693i	$-0.629246\pi$
$811$	−22.4961	−0.789946	−0.394973	+	0.918693i	$0.629246\pi$
$812$	0	0
$813$	−3.93286	−0.137931
$814$	−70.3590	−2.46608
$815$	−14.6444	−0.512972
$816$	−14.4088	−0.504409
$817$	−47.2947	−1.65463
$818$	−59.3494	−2.07510
$819$	0	0
$820$	−4.48803	−0.156729
$821$	−5.59832	−0.195383	−0.0976913	−	0.995217i	$-0.531146\pi$
$821$	−5.59832	−0.195383	−0.0976913	+	0.995217i	$0.531146\pi$
$822$	16.6847	0.581946
$823$	−3.64995	−0.127229	−0.0636146	−	0.997975i	$-0.520263\pi$
$823$	−3.64995	−0.127229	−0.0636146	+	0.997975i	$0.520263\pi$
$824$	113.176	3.94267
$825$	18.8464	0.656149
$826$	0	0
$827$	13.4612	0.468092	0.234046	−	0.972226i	$-0.424803\pi$
$827$	13.4612	0.468092	0.234046	+	0.972226i	$0.424803\pi$
$828$	4.57401	0.158958
$829$	−4.40869	−0.153120	−0.0765601	−	0.997065i	$-0.524394\pi$
$829$	−4.40869	−0.153120	−0.0765601	+	0.997065i	$0.524394\pi$
$830$	−9.48609	−0.329267
$831$	22.9534	0.796243
$832$	75.1803	2.60641
$833$	0	0
$834$	47.7367	1.65299
$835$	−15.4223	−0.533712
$836$	110.426	3.81917
$837$	5.65927	0.195613
$838$	33.2234	1.14768
$839$	−13.4240	−0.463447	−0.231724	−	0.972782i	$-0.574436\pi$
$839$	−13.4240	−0.463447	−0.231724	+	0.972782i	$0.574436\pi$
$840$	0	0
$841$	−14.6692	−0.505836
$842$	9.36211	0.322640
$843$	−13.2909	−0.457764
$844$	144.297	4.96689
$845$	−6.24846	−0.214954
$846$	−4.08040	−0.140287
$847$	0	0
$848$	−137.981	−4.73827
$849$	−31.4345	−1.07883
$850$	−11.0614	−0.379403
$851$	−4.88564	−0.167477
$852$	31.7466	1.08762
$853$	−38.1049	−1.30469	−0.652344	−	0.757923i	$-0.726214\pi$
$853$	−38.1049	−1.30469	−0.652344	+	0.757923i	$0.726214\pi$
$854$	0	0
$855$	−3.73356	−0.127685
$856$	−58.9279	−2.01411
$857$	0.247790	0.00846434	0.00423217	−	0.999991i	$-0.498653\pi$
$857$	0.247790	0.00846434	0.00423217	+	0.999991i	$0.498653\pi$
$858$	27.4281	0.936380
$859$	−47.9533	−1.63615	−0.818073	−	0.575114i	$-0.804958\pi$
$859$	−47.9533	−1.63615	−0.818073	+	0.575114i	$0.804958\pi$
$860$	46.1430	1.57346
$861$	0	0
$862$	−93.7417	−3.19285
$863$	49.7357	1.69302	0.846511	−	0.532371i	$-0.178699\pi$
$863$	49.7357	1.69302	0.846511	+	0.532371i	$0.178699\pi$
$864$	−23.2093	−0.789598
$865$	−19.3419	−0.657645
$866$	70.7689	2.40482
$867$	−16.1378	−0.548068
$868$	0	0
$869$	−32.0455	−1.08707
$870$	−8.43105	−0.285839
$871$	20.1264	0.681957
$872$	−140.091	−4.74408
$873$	−11.6504	−0.394305
$874$	10.4412	0.353179
$875$	0	0
$876$	57.5473	1.94434
$877$	33.1664	1.11995	0.559975	−	0.828509i	$-0.310811\pi$
$877$	33.1664	1.11995	0.559975	+	0.828509i	$0.310811\pi$
$878$	−91.4036	−3.08472
$879$	−18.8419	−0.635520
$880$	−54.6757	−1.84312
$881$	50.2317	1.69235	0.846175	−	0.532905i	$-0.178900\pi$
$881$	50.2317	1.69235	0.846175	+	0.532905i	$0.178900\pi$
$882$	0	0
$883$	16.4058	0.552098	0.276049	−	0.961144i	$-0.410975\pi$
$883$	16.4058	0.552098	0.276049	+	0.961144i	$0.410975\pi$
$884$	−11.8222	−0.397624
$885$	−11.0518	−0.371501
$886$	92.7653	3.11651
$887$	37.0206	1.24303	0.621514	−	0.783403i	$-0.286518\pi$
$887$	37.0206	1.24303	0.621514	+	0.783403i	$0.286518\pi$
$888$	57.2048	1.91967
$889$	0	0
$890$	25.2177	0.845300
$891$	−4.34125	−0.145437
$892$	0.400804	0.0134199
$893$	−6.84036	−0.228904
$894$	−4.92418	−0.164689
$895$	−11.9586	−0.399731
$896$	0	0
$897$	1.90457	0.0635918
$898$	88.3477	2.94820
$899$	21.4237	0.714522
$900$	−24.0054	−0.800181
$901$	8.25673	0.275071
$902$	−11.9124	−0.396641
$903$	0	0
$904$	−157.861	−5.25037
$905$	16.3626	0.543912
$906$	57.8017	1.92033
$907$	−18.0706	−0.600023	−0.300012	−	0.953936i	$-0.596991\pi$
$907$	−18.0706	−0.600023	−0.300012	+	0.953936i	$0.596991\pi$
$908$	−71.7470	−2.38101
$909$	3.91807	0.129954
$910$	0	0
$911$	−5.53854	−0.183500	−0.0917500	−	0.995782i	$-0.529246\pi$
$911$	−5.53854	−0.183500	−0.0917500	+	0.995782i	$0.529246\pi$
$912$	−71.3808	−2.36365
$913$	−18.4908	−0.611955
$914$	−52.1559	−1.72516
$915$	1.90878	0.0631025
$916$	−11.9388	−0.394470
$917$	0	0
$918$	2.54797	0.0840957
$919$	8.17855	0.269786	0.134893	−	0.990860i	$-0.456931\pi$
$919$	8.17855	0.269786	0.134893	+	0.990860i	$0.456931\pi$
$920$	−6.50245	−0.214379
$921$	1.31498	0.0433301
$922$	−111.464	−3.67086
$923$	13.2190	0.435108
$924$	0	0
$925$	25.6409	0.843068
$926$	47.3055	1.55456
$927$	−11.6853	−0.383796
$928$	−87.8613	−2.88419
$929$	−19.4793	−0.639096	−0.319548	−	0.947570i	$-0.603531\pi$
$929$	−19.4793	−0.639096	−0.319548	+	0.947570i	$0.603531\pi$
$930$	−12.6040	−0.413301
$931$	0	0
$932$	−15.8286	−0.518482
$933$	31.5532	1.03301
$934$	−27.1693	−0.889006
$935$	3.27178	0.106999
$936$	−22.3002	−0.728904
$937$	−38.9274	−1.27170	−0.635852	−	0.771811i	$-0.719351\pi$
$937$	−38.9274	−1.27170	−0.635852	+	0.771811i	$0.719351\pi$
$938$	0	0
$939$	−22.6616	−0.739532
$940$	6.67378	0.217675
$941$	−42.4334	−1.38329	−0.691644	−	0.722239i	$-0.743113\pi$
$941$	−42.4334	−1.38329	−0.691644	+	0.722239i	$0.743113\pi$
$942$	45.0857	1.46897
$943$	−0.827185	−0.0269368
$944$	−211.295	−6.87708
$945$	0	0
$946$	122.476	3.98204
$947$	49.8415	1.61963	0.809816	−	0.586684i	$-0.199567\pi$
$947$	49.8415	1.61963	0.809816	+	0.586684i	$0.199567\pi$
$948$	40.8176	1.32569
$949$	23.9621	0.777843
$950$	−54.7978	−1.77788
$951$	−6.11392	−0.198257
$952$	0	0
$953$	0.542351	0.0175685	0.00878423	−	0.999961i	$-0.497204\pi$
$953$	0.542351	0.0175685	0.00878423	+	0.999961i	$0.497204\pi$
$954$	24.3998	0.789971
$955$	2.47900	0.0802184
$956$	88.7064	2.86897
$957$	−16.4342	−0.531243
$958$	80.5104	2.60117
$959$	0	0
$960$	26.5015	0.855332
$961$	1.02737	0.0331411
$962$	37.3164	1.20313
$963$	6.08425	0.196062
$964$	−66.9006	−2.15472
$965$	−21.5574	−0.693959
$966$	0	0
$967$	−27.8705	−0.896256	−0.448128	−	0.893970i	$-0.647909\pi$
$967$	−27.8705	−0.896256	−0.448128	+	0.893970i	$0.647909\pi$
$968$	−75.9952	−2.44258
$969$	4.27141	0.137217
$970$	25.9470	0.833107
$971$	23.6249	0.758160	0.379080	−	0.925364i	$-0.376240\pi$
$971$	23.6249	0.758160	0.379080	+	0.925364i	$0.376240\pi$
$972$	5.52961	0.177362
$973$	0	0
$974$	51.9722	1.66530
$975$	−9.99562	−0.320116
$976$	36.4935	1.16813
$977$	−51.4143	−1.64489	−0.822445	−	0.568845i	$-0.807391\pi$
$977$	−51.4143	−1.64489	−0.822445	+	0.568845i	$0.807391\pi$
$978$	49.5106	1.58317
$979$	49.1556	1.57102
$980$	0	0
$981$	14.4643	0.461809
$982$	−8.67582	−0.276857
$983$	−50.4853	−1.61023	−0.805116	−	0.593117i	$-0.797897\pi$
$983$	−50.4853	−1.61023	−0.805116	+	0.593117i	$0.797897\pi$
$984$	9.68531	0.308756
$985$	−9.36635	−0.298437
$986$	9.64561	0.307179
$987$	0	0
$988$	−58.5669	−1.86326
$989$	8.50457	0.270430
$990$	9.66856	0.307287
$991$	61.6011	1.95682	0.978411	−	0.206667i	$-0.0662615\pi$
$991$	61.6011	1.95682	0.978411	+	0.206667i	$0.0662615\pi$
$992$	−131.348	−4.17030
$993$	−4.65182	−0.147621
$994$	0	0
$995$	−2.80279	−0.0888545
$996$	23.5524	0.746286
$997$	−17.5143	−0.554682	−0.277341	−	0.960772i	$-0.589453\pi$
$997$	−17.5143	−0.554682	−0.277341	+	0.960772i	$0.589453\pi$
$998$	51.7573	1.63835
$999$	−5.90634	−0.186868

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.v.1.1		5
7.6	odd	2		861.2.a.j.1.1	✓	5
21.20	even	2		2583.2.a.s.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.a.j.1.1	✓	5	7.6	odd	2
2583.2.a.s.1.5		5	21.20	even	2
6027.2.a.v.1.1		5	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:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.74401 q^{2} +1.00000 q^{3} +5.52961 q^{4} +0.811635 q^{5} -2.74401 q^{6} -9.68531 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.74401 q^{2} +1.00000 q^{3} +5.52961 q^{4} +0.811635 q^{5} -2.74401 q^{6} -9.68531 q^{8} +1.00000 q^{9} -2.22714 q^{10} -4.34125 q^{11} +5.52961 q^{12} +2.30248 q^{13} +0.811635 q^{15} +15.5174 q^{16} -0.928558 q^{17} -2.74401 q^{18} -4.60005 q^{19} +4.48803 q^{20} +11.9124 q^{22} +0.827185 q^{23} -9.68531 q^{24} -4.34125 q^{25} -6.31802 q^{26} +1.00000 q^{27} +3.78560 q^{29} -2.22714 q^{30} +5.65927 q^{31} -23.2093 q^{32} -4.34125 q^{33} +2.54797 q^{34} +5.52961 q^{36} -5.90634 q^{37} +12.6226 q^{38} +2.30248 q^{39} -7.86094 q^{40} -1.00000 q^{41} +10.2813 q^{43} -24.0054 q^{44} +0.811635 q^{45} -2.26981 q^{46} +1.48702 q^{47} +15.5174 q^{48} +11.9124 q^{50} -0.928558 q^{51} +12.7318 q^{52} -8.89199 q^{53} -2.74401 q^{54} -3.52351 q^{55} -4.60005 q^{57} -10.3877 q^{58} -13.6167 q^{59} +4.48803 q^{60} +2.35178 q^{61} -15.5291 q^{62} +32.6520 q^{64} +1.86877 q^{65} +11.9124 q^{66} +8.74120 q^{67} -5.13456 q^{68} +0.827185 q^{69} +5.74120 q^{71} -9.68531 q^{72} +10.4071 q^{73} +16.2071 q^{74} -4.34125 q^{75} -25.4365 q^{76} -6.31802 q^{78} +7.38163 q^{79} +12.5945 q^{80} +1.00000 q^{81} +2.74401 q^{82} +4.25932 q^{83} -0.753650 q^{85} -28.2122 q^{86} +3.78560 q^{87} +42.0463 q^{88} -11.3229 q^{89} -2.22714 q^{90} +4.57401 q^{92} +5.65927 q^{93} -4.08040 q^{94} -3.73356 q^{95} -23.2093 q^{96} -11.6504 q^{97} -4.34125 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 3 q^{2} + 5 q^{3} + 7 q^{4} - q^{5} - 3 q^{6} - 9 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q - 3 * q^2 + 5 * q^3 + 7 * q^4 - q^5 - 3 * q^6 - 9 * q^8 + 5 * q^9	\( 5 q - 3 q^{2} + 5 q^{3} + 7 q^{4} - q^{5} - 3 q^{6} - 9 q^{8} + 5 q^{9} - 5 q^{10} + 4 q^{11} + 7 q^{12} - 3 q^{13} - q^{15} + 3 q^{16} + 8 q^{17} - 3 q^{18} - 20 q^{19} + q^{20} + 14 q^{22} - 5 q^{23} - 9 q^{24} + 4 q^{25} - 13 q^{26} + 5 q^{27} + 9 q^{29} - 5 q^{30} - 16 q^{31} - 21 q^{32} + 4 q^{33} + 7 q^{36} - 19 q^{37} - 8 q^{38} - 3 q^{39} - 21 q^{40} - 5 q^{41} + 6 q^{43} - 24 q^{44} - q^{45} + 27 q^{46} - 9 q^{47} + 3 q^{48} + 14 q^{50} + 8 q^{51} - q^{52} - 29 q^{53} - 3 q^{54} - 32 q^{55} - 20 q^{57} - q^{58} - 28 q^{59} + q^{60} - 16 q^{61} + 8 q^{62} + 39 q^{64} + q^{65} + 14 q^{66} + 21 q^{67} + 24 q^{68} - 5 q^{69} + 6 q^{71} - 9 q^{72} + 4 q^{73} + 11 q^{74} + 4 q^{75} - 26 q^{76} - 13 q^{78} + 21 q^{79} + 25 q^{80} + 5 q^{81} + 3 q^{82} - 26 q^{83} - 20 q^{85} - 58 q^{86} + 9 q^{87} + 54 q^{88} - 12 q^{89} - 5 q^{90} + 15 q^{92} - 16 q^{93} + q^{94} + 18 q^{95} - 21 q^{96} - 37 q^{97} + 4 q^{99}+O(q^{100}) \) 5 * q - 3 * q^2 + 5 * q^3 + 7 * q^4 - q^5 - 3 * q^6 - 9 * q^8 + 5 * q^9 - 5 * q^10 + 4 * q^11 + 7 * q^12 - 3 * q^13 - q^15 + 3 * q^16 + 8 * q^17 - 3 * q^18 - 20 * q^19 + q^20 + 14 * q^22 - 5 * q^23 - 9 * q^24 + 4 * q^25 - 13 * q^26 + 5 * q^27 + 9 * q^29 - 5 * q^30 - 16 * q^31 - 21 * q^32 + 4 * q^33 + 7 * q^36 - 19 * q^37 - 8 * q^38 - 3 * q^39 - 21 * q^40 - 5 * q^41 + 6 * q^43 - 24 * q^44 - q^45 + 27 * q^46 - 9 * q^47 + 3 * q^48 + 14 * q^50 + 8 * q^51 - q^52 - 29 * q^53 - 3 * q^54 - 32 * q^55 - 20 * q^57 - q^58 - 28 * q^59 + q^60 - 16 * q^61 + 8 * q^62 + 39 * q^64 + q^65 + 14 * q^66 + 21 * q^67 + 24 * q^68 - 5 * q^69 + 6 * q^71 - 9 * q^72 + 4 * q^73 + 11 * q^74 + 4 * q^75 - 26 * q^76 - 13 * q^78 + 21 * q^79 + 25 * q^80 + 5 * q^81 + 3 * q^82 - 26 * q^83 - 20 * q^85 - 58 * q^86 + 9 * q^87 + 54 * q^88 - 12 * q^89 - 5 * q^90 + 15 * q^92 - 16 * q^93 + q^94 + 18 * q^95 - 21 * q^96 - 37 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more