LMFDB - Embedded newform 6027.2.a.ba.1.3

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:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 8x^{6} + 14x^{5} + 18x^{4} - 24x^{3} - 10x^{2} + 10x - 1 $ x^8 - 2x^7 - 8x^6 + 14x^5 + 18x^4 - 24x^3 - 10x^2 + 10*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.17091$ 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)

$f(q)$	$=$	$q-1.17091 q^{2} +1.00000 q^{3} -0.628975 q^{4} -2.94759 q^{5} -1.17091 q^{6} +3.07829 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.17091 q^{2} +1.00000 q^{3} -0.628975 q^{4} -2.94759 q^{5} -1.17091 q^{6} +3.07829 q^{8} +1.00000 q^{9} +3.45135 q^{10} +0.735179 q^{11} -0.628975 q^{12} -4.56463 q^{13} -2.94759 q^{15} -2.34644 q^{16} +1.29990 q^{17} -1.17091 q^{18} +0.205172 q^{19} +1.85396 q^{20} -0.860827 q^{22} +7.81932 q^{23} +3.07829 q^{24} +3.68826 q^{25} +5.34477 q^{26} +1.00000 q^{27} -10.2205 q^{29} +3.45135 q^{30} +6.98437 q^{31} -3.40911 q^{32} +0.735179 q^{33} -1.52206 q^{34} -0.628975 q^{36} -5.74813 q^{37} -0.240237 q^{38} -4.56463 q^{39} -9.07351 q^{40} -1.00000 q^{41} -2.33978 q^{43} -0.462409 q^{44} -2.94759 q^{45} -9.15571 q^{46} +3.34825 q^{47} -2.34644 q^{48} -4.31861 q^{50} +1.29990 q^{51} +2.87104 q^{52} -5.83919 q^{53} -1.17091 q^{54} -2.16700 q^{55} +0.205172 q^{57} +11.9673 q^{58} +12.6741 q^{59} +1.85396 q^{60} +12.0452 q^{61} -8.17806 q^{62} +8.68463 q^{64} +13.4546 q^{65} -0.860827 q^{66} -0.636074 q^{67} -0.817601 q^{68} +7.81932 q^{69} -13.2397 q^{71} +3.07829 q^{72} +2.69801 q^{73} +6.73054 q^{74} +3.68826 q^{75} -0.129048 q^{76} +5.34477 q^{78} +10.7810 q^{79} +6.91634 q^{80} +1.00000 q^{81} +1.17091 q^{82} +2.11698 q^{83} -3.83155 q^{85} +2.73966 q^{86} -10.2205 q^{87} +2.26309 q^{88} +9.36156 q^{89} +3.45135 q^{90} -4.91815 q^{92} +6.98437 q^{93} -3.92049 q^{94} -0.604761 q^{95} -3.40911 q^{96} -0.379314 q^{97} +0.735179 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 8 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} - 6 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 8 * q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 - 6 * q^8 + 8 * q^9	$ 8 q - 2 q^{2} + 8 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} - 6 q^{8} + 8 q^{9} + 2 q^{10} - 2 q^{11} + 4 q^{12} - 4 q^{13} - 2 q^{15} - 8 q^{17} - 2 q^{18} - 6 q^{19} - 4 q^{20} - 14 q^{22} - 12 q^{23} - 6 q^{24} - 4 q^{25} - 4 q^{26} + 8 q^{27} - 4 q^{29} + 2 q^{30} + 10 q^{31} - 4 q^{32} - 2 q^{33} - 4 q^{34} + 4 q^{36} - 20 q^{37} + 18 q^{38} - 4 q^{39} - 12 q^{40} - 8 q^{41} - 8 q^{43} + 20 q^{44} - 2 q^{45} - 12 q^{46} - 24 q^{47} - 22 q^{50} - 8 q^{51} + 30 q^{52} - 36 q^{53} - 2 q^{54} - 4 q^{55} - 6 q^{57} + 14 q^{58} - 10 q^{59} - 4 q^{60} + 22 q^{61} - 30 q^{62} - 24 q^{64} + 8 q^{65} - 14 q^{66} - 14 q^{67} - 38 q^{68} - 12 q^{69} - 10 q^{71} - 6 q^{72} + 12 q^{73} - 2 q^{74} - 4 q^{75} - 32 q^{76} - 4 q^{78} + 16 q^{79} + 14 q^{80} + 8 q^{81} + 2 q^{82} - 24 q^{83} - 44 q^{85} + 36 q^{86} - 4 q^{87} - 34 q^{88} - 2 q^{89} + 2 q^{90} - 48 q^{92} + 10 q^{93} + 34 q^{94} - 24 q^{95} - 4 q^{96} - 16 q^{97} - 2 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 + 8 * q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 - 6 * q^8 + 8 * q^9 + 2 * q^10 - 2 * q^11 + 4 * q^12 - 4 * q^13 - 2 * q^15 - 8 * q^17 - 2 * q^18 - 6 * q^19 - 4 * q^20 - 14 * q^22 - 12 * q^23 - 6 * q^24 - 4 * q^25 - 4 * q^26 + 8 * q^27 - 4 * q^29 + 2 * q^30 + 10 * q^31 - 4 * q^32 - 2 * q^33 - 4 * q^34 + 4 * q^36 - 20 * q^37 + 18 * q^38 - 4 * q^39 - 12 * q^40 - 8 * q^41 - 8 * q^43 + 20 * q^44 - 2 * q^45 - 12 * q^46 - 24 * q^47 - 22 * q^50 - 8 * q^51 + 30 * q^52 - 36 * q^53 - 2 * q^54 - 4 * q^55 - 6 * q^57 + 14 * q^58 - 10 * q^59 - 4 * q^60 + 22 * q^61 - 30 * q^62 - 24 * q^64 + 8 * q^65 - 14 * q^66 - 14 * q^67 - 38 * q^68 - 12 * q^69 - 10 * q^71 - 6 * q^72 + 12 * q^73 - 2 * q^74 - 4 * q^75 - 32 * q^76 - 4 * q^78 + 16 * q^79 + 14 * q^80 + 8 * q^81 + 2 * q^82 - 24 * q^83 - 44 * q^85 + 36 * q^86 - 4 * q^87 - 34 * q^88 - 2 * q^89 + 2 * q^90 - 48 * q^92 + 10 * q^93 + 34 * q^94 - 24 * q^95 - 4 * q^96 - 16 * q^97 - 2 * 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 $

$2$	−1.17091	−0.827957	−0.413978	−	0.910287i	$-0.635861\pi$
$2$	−1.17091	−0.827957	−0.413978	+	0.910287i	$0.635861\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.628975	−0.314487
$5$	−2.94759	−1.31820	−0.659100	−	0.752055i	$-0.729063\pi$
$5$	−2.94759	−1.31820	−0.659100	+	0.752055i	$0.729063\pi$
$6$	−1.17091	−0.478021
$7$	0	0
$7$	0	0
$8$	3.07829	1.08834
$9$	1.00000	0.333333
$10$	3.45135	1.09141
$11$	0.735179	0.221665	0.110832	−	0.993839i	$-0.464648\pi$
$11$	0.735179	0.221665	0.110832	+	0.993839i	$0.464648\pi$
$12$	−0.628975	−0.181569
$13$	−4.56463	−1.26600	−0.633001	−	0.774151i	$-0.718177\pi$
$13$	−4.56463	−1.26600	−0.633001	+	0.774151i	$0.718177\pi$
$14$	0	0
$15$	−2.94759	−0.761063
$16$	−2.34644	−0.586610
$17$	1.29990	0.315271	0.157635	−	0.987497i	$-0.449613\pi$
$17$	1.29990	0.315271	0.157635	+	0.987497i	$0.449613\pi$
$18$	−1.17091	−0.275986
$19$	0.205172	0.0470696	0.0235348	−	0.999723i	$-0.492508\pi$
$19$	0.205172	0.0470696	0.0235348	+	0.999723i	$0.492508\pi$
$20$	1.85396	0.414557
$21$	0	0
$22$	−0.860827	−0.183529
$23$	7.81932	1.63044	0.815221	−	0.579150i	$-0.196616\pi$
$23$	7.81932	1.63044	0.815221	+	0.579150i	$0.196616\pi$
$24$	3.07829	0.628353
$25$	3.68826	0.737652
$26$	5.34477	1.04819
$27$	1.00000	0.192450
$28$	0	0
$29$	−10.2205	−1.89791	−0.948954	−	0.315414i	$-0.897857\pi$
$29$	−10.2205	−1.89791	−0.948954	+	0.315414i	$0.897857\pi$
$30$	3.45135	0.630128
$31$	6.98437	1.25443	0.627215	−	0.778846i	$-0.284195\pi$
$31$	6.98437	1.25443	0.627215	+	0.778846i	$0.284195\pi$
$32$	−3.40911	−0.602651
$33$	0.735179	0.127978
$34$	−1.52206	−0.261031
$35$	0	0
$36$	−0.628975	−0.104829
$37$	−5.74813	−0.944987	−0.472494	−	0.881334i	$-0.656646\pi$
$37$	−5.74813	−0.944987	−0.472494	+	0.881334i	$0.656646\pi$
$38$	−0.240237	−0.0389716
$39$	−4.56463	−0.730926
$40$	−9.07351	−1.43465
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−2.33978	−0.356813	−0.178406	−	0.983957i	$-0.557094\pi$
$43$	−2.33978	−0.356813	−0.178406	+	0.983957i	$0.557094\pi$
$44$	−0.462409	−0.0697108
$45$	−2.94759	−0.439400
$46$	−9.15571	−1.34994
$47$	3.34825	0.488392	0.244196	−	0.969726i	$-0.421476\pi$
$47$	3.34825	0.488392	0.244196	+	0.969726i	$0.421476\pi$
$48$	−2.34644	−0.338680
$49$	0	0
$50$	−4.31861	−0.610744
$51$	1.29990	0.182022
$52$	2.87104	0.398141
$53$	−5.83919	−0.802075	−0.401038	−	0.916062i	$-0.631350\pi$
$53$	−5.83919	−0.802075	−0.401038	+	0.916062i	$0.631350\pi$
$54$	−1.17091	−0.159340
$55$	−2.16700	−0.292199
$56$	0	0
$57$	0.205172	0.0271756
$58$	11.9673	1.57139
$59$	12.6741	1.65003	0.825016	−	0.565109i	$-0.191166\pi$
$59$	12.6741	1.65003	0.825016	+	0.565109i	$0.191166\pi$
$60$	1.85396	0.239345
$61$	12.0452	1.54224	0.771118	−	0.636693i	$-0.219698\pi$
$61$	12.0452	1.54224	0.771118	+	0.636693i	$0.219698\pi$
$62$	−8.17806	−1.03861
$63$	0	0
$64$	8.68463	1.08558
$65$	13.4546	1.66884
$66$	−0.860827	−0.105961
$67$	−0.636074	−0.0777088	−0.0388544	−	0.999245i	$-0.512371\pi$
$67$	−0.636074	−0.0777088	−0.0388544	+	0.999245i	$0.512371\pi$
$68$	−0.817601	−0.0991487
$69$	7.81932	0.941336
$70$	0	0
$71$	−13.2397	−1.57127	−0.785634	−	0.618691i	$-0.787663\pi$
$71$	−13.2397	−1.57127	−0.785634	+	0.618691i	$0.787663\pi$
$72$	3.07829	0.362780
$73$	2.69801	0.315779	0.157889	−	0.987457i	$-0.449531\pi$
$73$	2.69801	0.315779	0.157889	+	0.987457i	$0.449531\pi$
$74$	6.73054	0.782409
$75$	3.68826	0.425883
$76$	−0.129048	−0.0148028
$77$	0	0
$78$	5.34477	0.605176
$79$	10.7810	1.21296	0.606479	−	0.795099i	$-0.292581\pi$
$79$	10.7810	1.21296	0.606479	+	0.795099i	$0.292581\pi$
$80$	6.91634	0.773270
$81$	1.00000	0.111111
$82$	1.17091	0.129305
$83$	2.11698	0.232369	0.116185	−	0.993228i	$-0.462934\pi$
$83$	2.11698	0.232369	0.116185	+	0.993228i	$0.462934\pi$
$84$	0	0
$85$	−3.83155	−0.415590
$86$	2.73966	0.295426
$87$	−10.2205	−1.09576
$88$	2.26309	0.241247
$89$	9.36156	0.992323	0.496162	−	0.868230i	$-0.334742\pi$
$89$	9.36156	0.992323	0.496162	+	0.868230i	$0.334742\pi$
$90$	3.45135	0.363804
$91$	0	0
$92$	−4.91815	−0.512753
$93$	6.98437	0.724246
$94$	−3.92049	−0.404368
$95$	−0.604761	−0.0620471
$96$	−3.40911	−0.347941
$97$	−0.379314	−0.0385135	−0.0192567	−	0.999815i	$-0.506130\pi$
$97$	−0.379314	−0.0385135	−0.0192567	+	0.999815i	$0.506130\pi$
$98$	0	0
$99$	0.735179	0.0738883
$100$	−2.31982	−0.231982
$101$	11.1148	1.10597	0.552984	−	0.833192i	$-0.313489\pi$
$101$	11.1148	1.10597	0.552984	+	0.833192i	$0.313489\pi$
$102$	−1.52206	−0.150706
$103$	−1.83093	−0.180407	−0.0902035	−	0.995923i	$-0.528752\pi$
$103$	−1.83093	−0.180407	−0.0902035	+	0.995923i	$0.528752\pi$
$104$	−14.0513	−1.37784
$105$	0	0
$106$	6.83716	0.664084
$107$	−12.0728	−1.16713	−0.583563	−	0.812068i	$-0.698342\pi$
$107$	−12.0728	−1.16713	−0.583563	+	0.812068i	$0.698342\pi$
$108$	−0.628975	−0.0605231
$109$	−4.72109	−0.452198	−0.226099	−	0.974104i	$-0.572597\pi$
$109$	−4.72109	−0.452198	−0.226099	+	0.974104i	$0.572597\pi$
$110$	2.53736	0.241928
$111$	−5.74813	−0.545589
$112$	0	0
$113$	0.290899	0.0273654	0.0136827	−	0.999906i	$-0.495645\pi$
$113$	0.290899	0.0273654	0.0136827	+	0.999906i	$0.495645\pi$
$114$	−0.240237	−0.0225003
$115$	−23.0481	−2.14925
$116$	6.42847	0.596868
$117$	−4.56463	−0.422001
$118$	−14.8403	−1.36616
$119$	0	0
$120$	−9.07351	−0.828295
$121$	−10.4595	−0.950865
$122$	−14.1039	−1.27690
$123$	−1.00000	−0.0901670
$124$	−4.39299	−0.394502
$125$	3.86647	0.345828
$126$	0	0
$127$	−7.01519	−0.622497	−0.311249	−	0.950328i	$-0.600747\pi$
$127$	−7.01519	−0.622497	−0.311249	+	0.950328i	$0.600747\pi$
$128$	−3.35069	−0.296162
$129$	−2.33978	−0.206006
$130$	−15.7542	−1.38173
$131$	−20.5015	−1.79123	−0.895613	−	0.444835i	$-0.853262\pi$
$131$	−20.5015	−1.79123	−0.895613	+	0.444835i	$0.853262\pi$
$132$	−0.462409	−0.0402475
$133$	0	0
$134$	0.744784	0.0643395
$135$	−2.94759	−0.253688
$136$	4.00145	0.343122
$137$	16.3722	1.39877	0.699387	−	0.714743i	$-0.253456\pi$
$137$	16.3722	1.39877	0.699387	+	0.714743i	$0.253456\pi$
$138$	−9.15571	−0.779386
$139$	16.6768	1.41451	0.707253	−	0.706960i	$-0.249934\pi$
$139$	16.6768	1.41451	0.707253	+	0.706960i	$0.249934\pi$
$140$	0	0
$141$	3.34825	0.281973
$142$	15.5025	1.30094
$143$	−3.35583	−0.280628
$144$	−2.34644	−0.195537
$145$	30.1259	2.50182
$146$	−3.15913	−0.261451
$147$	0	0
$148$	3.61543	0.297187
$149$	−18.7722	−1.53788	−0.768941	−	0.639319i	$-0.779216\pi$
$149$	−18.7722	−1.53788	−0.768941	+	0.639319i	$0.779216\pi$
$150$	−4.31861	−0.352613
$151$	7.05428	0.574069	0.287034	−	0.957920i	$-0.407331\pi$
$151$	7.05428	0.574069	0.287034	+	0.957920i	$0.407331\pi$
$152$	0.631577	0.0512277
$153$	1.29990	0.105090
$154$	0	0
$155$	−20.5870	−1.65359
$156$	2.87104	0.229867
$157$	9.41375	0.751299	0.375649	−	0.926762i	$-0.377420\pi$
$157$	9.41375	0.751299	0.375649	+	0.926762i	$0.377420\pi$
$158$	−12.6236	−1.00428
$159$	−5.83919	−0.463078
$160$	10.0486	0.794414
$161$	0	0
$162$	−1.17091	−0.0919952
$163$	13.1149	1.02724	0.513620	−	0.858018i	$-0.328304\pi$
$163$	13.1149	1.02724	0.513620	+	0.858018i	$0.328304\pi$
$164$	0.628975	0.0491147
$165$	−2.16700	−0.168701
$166$	−2.47879	−0.192392
$167$	−17.8255	−1.37938	−0.689689	−	0.724105i	$-0.742253\pi$
$167$	−17.8255	−1.37938	−0.689689	+	0.724105i	$0.742253\pi$
$168$	0	0
$169$	7.83588	0.602760
$170$	4.48640	0.344091
$171$	0.205172	0.0156899
$172$	1.47166	0.112213
$173$	−19.7655	−1.50274	−0.751371	−	0.659880i	$-0.770607\pi$
$173$	−19.7655	−1.50274	−0.751371	+	0.659880i	$0.770607\pi$
$174$	11.9673	0.907240
$175$	0	0
$176$	−1.72506	−0.130031
$177$	12.6741	0.952647
$178$	−10.9615	−0.821601
$179$	−13.4411	−1.00463	−0.502316	−	0.864684i	$-0.667519\pi$
$179$	−13.4411	−1.00463	−0.502316	+	0.864684i	$0.667519\pi$
$180$	1.85396	0.138186
$181$	8.21899	0.610912	0.305456	−	0.952206i	$-0.401191\pi$
$181$	8.21899	0.610912	0.305456	+	0.952206i	$0.401191\pi$
$182$	0	0
$183$	12.0452	0.890410
$184$	24.0701	1.77447
$185$	16.9431	1.24568
$186$	−8.17806	−0.599644
$187$	0.955657	0.0698845
$188$	−2.10596	−0.153593
$189$	0	0
$190$	0.708119	0.0513724
$191$	3.28155	0.237445	0.118722	−	0.992927i	$-0.462120\pi$
$191$	3.28155	0.237445	0.118722	+	0.992927i	$0.462120\pi$
$192$	8.68463	0.626759
$193$	13.7930	0.992841	0.496420	−	0.868082i	$-0.334648\pi$
$193$	13.7930	0.992841	0.496420	+	0.868082i	$0.334648\pi$
$194$	0.444142	0.0318875
$195$	13.4546	0.963507
$196$	0	0
$197$	−23.8854	−1.70177	−0.850883	−	0.525355i	$-0.823933\pi$
$197$	−23.8854	−1.70177	−0.850883	+	0.525355i	$0.823933\pi$
$198$	−0.860827	−0.0611763
$199$	−25.3686	−1.79833	−0.899166	−	0.437608i	$-0.855826\pi$
$199$	−25.3686	−1.79833	−0.899166	+	0.437608i	$0.855826\pi$
$200$	11.3535	0.802815
$201$	−0.636074	−0.0448652
$202$	−13.0144	−0.915693
$203$	0	0
$204$	−0.817601	−0.0572435
$205$	2.94759	0.205868
$206$	2.14385	0.149369
$207$	7.81932	0.543480
$208$	10.7106	0.742650
$209$	0.150838	0.0104337
$210$	0	0
$211$	−2.29547	−0.158027	−0.0790134	−	0.996874i	$-0.525177\pi$
$211$	−2.29547	−0.158027	−0.0790134	+	0.996874i	$0.525177\pi$
$212$	3.67270	0.252242
$213$	−13.2397	−0.907172
$214$	14.1362	0.966330
$215$	6.89669	0.470351
$216$	3.07829	0.209451
$217$	0	0
$218$	5.52796	0.374401
$219$	2.69801	0.182315
$220$	1.36299	0.0918928
$221$	−5.93355	−0.399134
$222$	6.73054	0.451724
$223$	−9.29813	−0.622649	−0.311325	−	0.950304i	$-0.600773\pi$
$223$	−9.29813	−0.622649	−0.311325	+	0.950304i	$0.600773\pi$
$224$	0	0
$225$	3.68826	0.245884
$226$	−0.340616	−0.0226574
$227$	−6.59863	−0.437966	−0.218983	−	0.975729i	$-0.570274\pi$
$227$	−6.59863	−0.437966	−0.218983	+	0.975729i	$0.570274\pi$
$228$	−0.129048	−0.00854639
$229$	9.69155	0.640436	0.320218	−	0.947344i	$-0.396244\pi$
$229$	9.69155	0.640436	0.320218	+	0.947344i	$0.396244\pi$
$230$	26.9872	1.77948
$231$	0	0
$232$	−31.4618	−2.06557
$233$	24.0753	1.57723	0.788613	−	0.614890i	$-0.210799\pi$
$233$	24.0753	1.57723	0.788613	+	0.614890i	$0.210799\pi$
$234$	5.34477	0.349398
$235$	−9.86925	−0.643799
$236$	−7.97171	−0.518914
$237$	10.7810	0.700302
$238$	0	0
$239$	−5.05867	−0.327218	−0.163609	−	0.986525i	$-0.552314\pi$
$239$	−5.05867	−0.327218	−0.163609	+	0.986525i	$0.552314\pi$
$240$	6.91634	0.446448
$241$	3.21287	0.206959	0.103480	−	0.994632i	$-0.467002\pi$
$241$	3.21287	0.206959	0.103480	+	0.994632i	$0.467002\pi$
$242$	12.2471	0.787275
$243$	1.00000	0.0641500
$244$	−7.57615	−0.485013
$245$	0	0
$246$	1.17091	0.0746544
$247$	−0.936533	−0.0595902
$248$	21.4999	1.36525
$249$	2.11698	0.134158
$250$	−4.52728	−0.286330
$251$	−28.9183	−1.82531	−0.912653	−	0.408736i	$-0.865970\pi$
$251$	−28.9183	−1.82531	−0.912653	+	0.408736i	$0.865970\pi$
$252$	0	0
$253$	5.74861	0.361412
$254$	8.21414	0.515401
$255$	−3.83155	−0.239941
$256$	−13.4459	−0.840370
$257$	−7.74014	−0.482816	−0.241408	−	0.970424i	$-0.577609\pi$
$257$	−7.74014	−0.482816	−0.241408	+	0.970424i	$0.577609\pi$
$258$	2.73966	0.170564
$259$	0	0
$260$	−8.46263	−0.524830
$261$	−10.2205	−0.632636
$262$	24.0054	1.48306
$263$	−13.8041	−0.851199	−0.425599	−	0.904912i	$-0.639937\pi$
$263$	−13.8041	−0.851199	−0.425599	+	0.904912i	$0.639937\pi$
$264$	2.26309	0.139284
$265$	17.2115	1.05730
$266$	0	0
$267$	9.36156	0.572918
$268$	0.400074	0.0244384
$269$	−9.88416	−0.602648	−0.301324	−	0.953522i	$-0.597429\pi$
$269$	−9.88416	−0.602648	−0.301324	+	0.953522i	$0.597429\pi$
$270$	3.45135	0.210043
$271$	−9.17765	−0.557502	−0.278751	−	0.960363i	$-0.589920\pi$
$271$	−9.17765	−0.557502	−0.278751	+	0.960363i	$0.589920\pi$
$272$	−3.05013	−0.184941
$273$	0	0
$274$	−19.1704	−1.15813
$275$	2.71153	0.163511
$276$	−4.91815	−0.296038
$277$	−13.6038	−0.817373	−0.408687	−	0.912675i	$-0.634013\pi$
$277$	−13.6038	−0.817373	−0.408687	+	0.912675i	$0.634013\pi$
$278$	−19.5270	−1.17115
$279$	6.98437	0.418144
$280$	0	0
$281$	15.9950	0.954181	0.477090	−	0.878854i	$-0.341691\pi$
$281$	15.9950	0.954181	0.477090	+	0.878854i	$0.341691\pi$
$282$	−3.92049	−0.233462
$283$	19.9521	1.18603	0.593014	−	0.805192i	$-0.297938\pi$
$283$	19.9521	1.18603	0.593014	+	0.805192i	$0.297938\pi$
$284$	8.32746	0.494144
$285$	−0.604761	−0.0358229
$286$	3.92936	0.232348
$287$	0	0
$288$	−3.40911	−0.200884
$289$	−15.3103	−0.900604
$290$	−35.2747	−2.07140
$291$	−0.379314	−0.0222358
$292$	−1.69698	−0.0993084
$293$	5.62507	0.328620	0.164310	−	0.986409i	$-0.447460\pi$
$293$	5.62507	0.328620	0.164310	+	0.986409i	$0.447460\pi$
$294$	0	0
$295$	−37.3581	−2.17507
$296$	−17.6944	−1.02847
$297$	0.735179	0.0426594
$298$	21.9806	1.27330
$299$	−35.6923	−2.06414
$300$	−2.31982	−0.133935
$301$	0	0
$302$	−8.25991	−0.475304
$303$	11.1148	0.638530
$304$	−0.481423	−0.0276115
$305$	−35.5044	−2.03297
$306$	−1.52206	−0.0870103
$307$	−1.07877	−0.0615685	−0.0307842	−	0.999526i	$-0.509800\pi$
$307$	−1.07877	−0.0615685	−0.0307842	+	0.999526i	$0.509800\pi$
$308$	0	0
$309$	−1.83093	−0.104158
$310$	24.1055	1.36910
$311$	−9.73481	−0.552010	−0.276005	−	0.961156i	$-0.589011\pi$
$311$	−9.73481	−0.552010	−0.276005	+	0.961156i	$0.589011\pi$
$312$	−14.0513	−0.795496
$313$	−30.4329	−1.72017	−0.860084	−	0.510152i	$-0.829589\pi$
$313$	−30.4329	−1.72017	−0.860084	+	0.510152i	$0.829589\pi$
$314$	−11.0226	−0.622043
$315$	0	0
$316$	−6.78098	−0.381460
$317$	−21.8406	−1.22669	−0.613345	−	0.789815i	$-0.710177\pi$
$317$	−21.8406	−1.22669	−0.613345	+	0.789815i	$0.710177\pi$
$318$	6.83716	0.383409
$319$	−7.51394	−0.420700
$320$	−25.5987	−1.43101
$321$	−12.0728	−0.673840
$322$	0	0
$323$	0.266702	0.0148397
$324$	−0.628975	−0.0349430
$325$	−16.8355	−0.933868
$326$	−15.3564	−0.850510
$327$	−4.72109	−0.261077
$328$	−3.07829	−0.169970
$329$	0	0
$330$	2.53736	0.139677
$331$	−20.4051	−1.12157	−0.560783	−	0.827963i	$-0.689500\pi$
$331$	−20.4051	−1.12157	−0.560783	+	0.827963i	$0.689500\pi$
$332$	−1.33153	−0.0730772
$333$	−5.74813	−0.314996
$334$	20.8720	1.14207
$335$	1.87488	0.102436
$336$	0	0
$337$	15.1472	0.825119	0.412559	−	0.910931i	$-0.364635\pi$
$337$	15.1472	0.825119	0.412559	+	0.910931i	$0.364635\pi$
$338$	−9.17510	−0.499060
$339$	0.290899	0.0157994
$340$	2.40995	0.130698
$341$	5.13477	0.278063
$342$	−0.240237	−0.0129905
$343$	0	0
$344$	−7.20251	−0.388333
$345$	−23.0481	−1.24087
$346$	23.1436	1.24421
$347$	−10.2650	−0.551054	−0.275527	−	0.961293i	$-0.588852\pi$
$347$	−10.2650	−0.551054	−0.275527	+	0.961293i	$0.588852\pi$
$348$	6.42847	0.344602
$349$	11.4058	0.610540	0.305270	−	0.952266i	$-0.401253\pi$
$349$	11.4058	0.610540	0.305270	+	0.952266i	$0.401253\pi$
$350$	0	0
$351$	−4.56463	−0.243642
$352$	−2.50631	−0.133587
$353$	−29.5367	−1.57208	−0.786041	−	0.618175i	$-0.787872\pi$
$353$	−29.5367	−1.57208	−0.786041	+	0.618175i	$0.787872\pi$
$354$	−14.8403	−0.788750
$355$	39.0253	2.07125
$356$	−5.88818	−0.312073
$357$	0	0
$358$	15.7382	0.831792
$359$	7.96542	0.420399	0.210199	−	0.977659i	$-0.432589\pi$
$359$	7.96542	0.420399	0.210199	+	0.977659i	$0.432589\pi$
$360$	−9.07351	−0.478216
$361$	−18.9579	−0.997784
$362$	−9.62368	−0.505809
$363$	−10.4595	−0.548982
$364$	0	0
$365$	−7.95263	−0.416260
$366$	−14.1039	−0.737221
$367$	2.82624	0.147529	0.0737644	−	0.997276i	$-0.476499\pi$
$367$	2.82624	0.147529	0.0737644	+	0.997276i	$0.476499\pi$
$368$	−18.3476	−0.956434
$369$	−1.00000	−0.0520579
$370$	−19.8388	−1.03137
$371$	0	0
$372$	−4.39299	−0.227766
$373$	6.18083	0.320031	0.160016	−	0.987114i	$-0.448846\pi$
$373$	6.18083	0.320031	0.160016	+	0.987114i	$0.448846\pi$
$374$	−1.11899	−0.0578614
$375$	3.86647	0.199664
$376$	10.3069	0.531536
$377$	46.6531	2.40276
$378$	0	0
$379$	13.4202	0.689348	0.344674	−	0.938722i	$-0.387989\pi$
$379$	13.4202	0.689348	0.344674	+	0.938722i	$0.387989\pi$
$380$	0.380379	0.0195130
$381$	−7.01519	−0.359399
$382$	−3.84240	−0.196594
$383$	6.04337	0.308802	0.154401	−	0.988008i	$-0.450655\pi$
$383$	6.04337	0.308802	0.154401	+	0.988008i	$0.450655\pi$
$384$	−3.35069	−0.170989
$385$	0	0
$386$	−16.1503	−0.822029
$387$	−2.33978	−0.118938
$388$	0.238579	0.0121120
$389$	23.2716	1.17992	0.589959	−	0.807433i	$-0.299144\pi$
$389$	23.2716	1.17992	0.589959	+	0.807433i	$0.299144\pi$
$390$	−15.7542	−0.797743
$391$	10.1643	0.514031
$392$	0	0
$393$	−20.5015	−1.03416
$394$	27.9676	1.40899
$395$	−31.7779	−1.59892
$396$	−0.462409	−0.0232369
$397$	11.1219	0.558191	0.279095	−	0.960263i	$-0.409965\pi$
$397$	11.1219	0.558191	0.279095	+	0.960263i	$0.409965\pi$
$398$	29.7043	1.48894
$399$	0	0
$400$	−8.65428	−0.432714
$401$	−2.50482	−0.125085	−0.0625424	−	0.998042i	$-0.519921\pi$
$401$	−2.50482	−0.125085	−0.0625424	+	0.998042i	$0.519921\pi$
$402$	0.744784	0.0371464
$403$	−31.8811	−1.58811
$404$	−6.99095	−0.347813
$405$	−2.94759	−0.146467
$406$	0	0
$407$	−4.22591	−0.209471
$408$	4.00145	0.198101
$409$	9.26167	0.457960	0.228980	−	0.973431i	$-0.426461\pi$
$409$	9.26167	0.457960	0.228980	+	0.973431i	$0.426461\pi$
$410$	−3.45135	−0.170450
$411$	16.3722	0.807583
$412$	1.15161	0.0567357
$413$	0	0
$414$	−9.15571	−0.449978
$415$	−6.23999	−0.306309
$416$	15.5613	0.762957
$417$	16.6768	0.816666
$418$	−0.176617	−0.00863864
$419$	−26.5761	−1.29833	−0.649163	−	0.760649i	$-0.724881\pi$
$419$	−26.5761	−1.29833	−0.649163	+	0.760649i	$0.724881\pi$
$420$	0	0
$421$	−33.0969	−1.61304	−0.806521	−	0.591205i	$-0.798652\pi$
$421$	−33.0969	−1.61304	−0.806521	+	0.591205i	$0.798652\pi$
$422$	2.68779	0.130839
$423$	3.34825	0.162797
$424$	−17.9747	−0.872930
$425$	4.79435	0.232560
$426$	15.5025	0.751100
$427$	0	0
$428$	7.59351	0.367046
$429$	−3.35583	−0.162021
$430$	−8.07539	−0.389430
$431$	−22.0997	−1.06450	−0.532252	−	0.846586i	$-0.678654\pi$
$431$	−22.0997	−1.06450	−0.532252	+	0.846586i	$0.678654\pi$
$432$	−2.34644	−0.112893
$433$	−11.0547	−0.531253	−0.265626	−	0.964076i	$-0.585579\pi$
$433$	−11.0547	−0.531253	−0.265626	+	0.964076i	$0.585579\pi$
$434$	0	0
$435$	30.1259	1.44443
$436$	2.96945	0.142211
$437$	1.60430	0.0767442
$438$	−3.15913	−0.150949
$439$	21.1957	1.01161	0.505807	−	0.862647i	$-0.331195\pi$
$439$	21.1957	1.01161	0.505807	+	0.862647i	$0.331195\pi$
$440$	−6.67066	−0.318011
$441$	0	0
$442$	6.94764	0.330465
$443$	−15.7890	−0.750160	−0.375080	−	0.926992i	$-0.622385\pi$
$443$	−15.7890	−0.750160	−0.375080	+	0.926992i	$0.622385\pi$
$444$	3.61543	0.171581
$445$	−27.5940	−1.30808
$446$	10.8873	0.515527
$447$	−18.7722	−0.887897
$448$	0	0
$449$	−28.0956	−1.32592	−0.662958	−	0.748657i	$-0.730699\pi$
$449$	−28.0956	−1.32592	−0.662958	+	0.748657i	$0.730699\pi$
$450$	−4.31861	−0.203581
$451$	−0.735179	−0.0346182
$452$	−0.182968	−0.00860608
$453$	7.05428	0.331439
$454$	7.72638	0.362617
$455$	0	0
$456$	0.631577	0.0295763
$457$	3.55168	0.166140	0.0830702	−	0.996544i	$-0.473527\pi$
$457$	3.55168	0.166140	0.0830702	+	0.996544i	$0.473527\pi$
$458$	−11.3479	−0.530253
$459$	1.29990	0.0606739
$460$	14.4967	0.675911
$461$	−7.68730	−0.358033	−0.179017	−	0.983846i	$-0.557292\pi$
$461$	−7.68730	−0.358033	−0.179017	+	0.983846i	$0.557292\pi$
$462$	0	0
$463$	−25.3808	−1.17955	−0.589774	−	0.807568i	$-0.700783\pi$
$463$	−25.3808	−1.17955	−0.589774	+	0.807568i	$0.700783\pi$
$464$	23.9819	1.11333
$465$	−20.5870	−0.954701
$466$	−28.1900	−1.30588
$467$	−17.3365	−0.802237	−0.401118	−	0.916026i	$-0.631378\pi$
$467$	−17.3365	−0.802237	−0.401118	+	0.916026i	$0.631378\pi$
$468$	2.87104	0.132714
$469$	0	0
$470$	11.5560	0.533038
$471$	9.41375	0.433763
$472$	39.0146	1.79579
$473$	−1.72016	−0.0790929
$474$	−12.6236	−0.579820
$475$	0.756726	0.0347210
$476$	0	0
$477$	−5.83919	−0.267358
$478$	5.92323	0.270922
$479$	−2.91060	−0.132989	−0.0664944	−	0.997787i	$-0.521181\pi$
$479$	−2.91060	−0.132989	−0.0664944	+	0.997787i	$0.521181\pi$
$480$	10.0486	0.458655
$481$	26.2381	1.19636
$482$	−3.76198	−0.171353
$483$	0	0
$484$	6.57877	0.299035
$485$	1.11806	0.0507685
$486$	−1.17091	−0.0531135
$487$	−31.1136	−1.40989	−0.704946	−	0.709261i	$-0.749029\pi$
$487$	−31.1136	−1.40989	−0.704946	+	0.709261i	$0.749029\pi$
$488$	37.0787	1.67847
$489$	13.1149	0.593077
$490$	0	0
$491$	33.0456	1.49133	0.745663	−	0.666323i	$-0.232133\pi$
$491$	33.0456	1.49133	0.745663	+	0.666323i	$0.232133\pi$
$492$	0.628975	0.0283564
$493$	−13.2856	−0.598355
$494$	1.09659	0.0493381
$495$	−2.16700	−0.0973996
$496$	−16.3884	−0.735862
$497$	0	0
$498$	−2.47879	−0.111077
$499$	−17.9770	−0.804762	−0.402381	−	0.915472i	$-0.631817\pi$
$499$	−17.9770	−0.804762	−0.402381	+	0.915472i	$0.631817\pi$
$500$	−2.43191	−0.108758
$501$	−17.8255	−0.796385
$502$	33.8606	1.51127
$503$	11.7380	0.523373	0.261686	−	0.965153i	$-0.415721\pi$
$503$	11.7380	0.523373	0.261686	+	0.965153i	$0.415721\pi$
$504$	0	0
$505$	−32.7619	−1.45789
$506$	−6.73109	−0.299233
$507$	7.83588	0.348004
$508$	4.41238	0.195767
$509$	1.29563	0.0574278	0.0287139	−	0.999588i	$-0.490859\pi$
$509$	1.29563	0.0574278	0.0287139	+	0.999588i	$0.490859\pi$
$510$	4.48640	0.198661
$511$	0	0
$512$	22.4453	0.991952
$513$	0.205172	0.00905855
$514$	9.06299	0.399751
$515$	5.39682	0.237813
$516$	1.47166	0.0647862
$517$	2.46156	0.108259
$518$	0	0
$519$	−19.7655	−0.867609
$520$	41.4173	1.81627
$521$	20.7146	0.907524	0.453762	−	0.891123i	$-0.350082\pi$
$521$	20.7146	0.907524	0.453762	+	0.891123i	$0.350082\pi$
$522$	11.9673	0.523795
$523$	11.0745	0.484255	0.242128	−	0.970244i	$-0.422155\pi$
$523$	11.0745	0.484255	0.242128	+	0.970244i	$0.422155\pi$
$524$	12.8949	0.563318
$525$	0	0
$526$	16.1634	0.704756
$527$	9.07896	0.395486
$528$	−1.72506	−0.0750734
$529$	38.1418	1.65834
$530$	−20.1531	−0.875395
$531$	12.6741	0.550011
$532$	0	0
$533$	4.56463	0.197716
$534$	−10.9615	−0.474352
$535$	35.5857	1.53851
$536$	−1.95802	−0.0845735
$537$	−13.4411	−0.580024
$538$	11.5734	0.498967
$539$	0	0
$540$	1.85396	0.0797816
$541$	−10.7336	−0.461472	−0.230736	−	0.973016i	$-0.574113\pi$
$541$	−10.7336	−0.461472	−0.230736	+	0.973016i	$0.574113\pi$
$542$	10.7462	0.461588
$543$	8.21899	0.352710
$544$	−4.43148	−0.189998
$545$	13.9158	0.596088
$546$	0	0
$547$	26.2180	1.12100	0.560500	−	0.828155i	$-0.310609\pi$
$547$	26.2180	1.12100	0.560500	+	0.828155i	$0.310609\pi$
$548$	−10.2977	−0.439897
$549$	12.0452	0.514078
$550$	−3.17495	−0.135380
$551$	−2.09697	−0.0893338
$552$	24.0701	1.02449
$553$	0	0
$554$	15.9288	0.676750
$555$	16.9431	0.719195
$556$	−10.4893	−0.444844
$557$	3.82486	0.162064	0.0810322	−	0.996711i	$-0.474178\pi$
$557$	3.82486	0.162064	0.0810322	+	0.996711i	$0.474178\pi$
$558$	−8.17806	−0.346205
$559$	10.6802	0.451726
$560$	0	0
$561$	0.955657	0.0403478
$562$	−18.7286	−0.790020
$563$	−34.6211	−1.45910	−0.729552	−	0.683926i	$-0.760271\pi$
$563$	−34.6211	−1.45910	−0.729552	+	0.683926i	$0.760271\pi$
$564$	−2.10596	−0.0886770
$565$	−0.857449	−0.0360731
$566$	−23.3620	−0.981980
$567$	0	0
$568$	−40.7557	−1.71007
$569$	−11.6212	−0.487185	−0.243592	−	0.969878i	$-0.578326\pi$
$569$	−11.6212	−0.487185	−0.243592	+	0.969878i	$0.578326\pi$
$570$	0.708119	0.0296598
$571$	15.0096	0.628132	0.314066	−	0.949401i	$-0.398309\pi$
$571$	15.0096	0.628132	0.314066	+	0.949401i	$0.398309\pi$
$572$	2.11073	0.0882540
$573$	3.28155	0.137089
$574$	0	0
$575$	28.8397	1.20270
$576$	8.68463	0.361860
$577$	−23.3891	−0.973700	−0.486850	−	0.873486i	$-0.661854\pi$
$577$	−23.3891	−0.973700	−0.486850	+	0.873486i	$0.661854\pi$
$578$	17.9269	0.745662
$579$	13.7930	0.573217
$580$	−18.9484	−0.786791
$581$	0	0
$582$	0.444142	0.0184103
$583$	−4.29286	−0.177792
$584$	8.30526	0.343674
$585$	13.4546	0.556281
$586$	−6.58643	−0.272083
$587$	−38.5946	−1.59297	−0.796484	−	0.604660i	$-0.793309\pi$
$587$	−38.5946	−1.59297	−0.796484	+	0.604660i	$0.793309\pi$
$588$	0	0
$589$	1.43300	0.0590455
$590$	43.7429	1.80087
$591$	−23.8854	−0.982515
$592$	13.4877	0.554340
$593$	−27.6583	−1.13579	−0.567895	−	0.823101i	$-0.692242\pi$
$593$	−27.6583	−1.13579	−0.567895	+	0.823101i	$0.692242\pi$
$594$	−0.860827	−0.0353202
$595$	0	0
$596$	11.8073	0.483644
$597$	−25.3686	−1.03827
$598$	41.7925	1.70902
$599$	1.90407	0.0777980	0.0388990	−	0.999243i	$-0.487615\pi$
$599$	1.90407	0.0777980	0.0388990	+	0.999243i	$0.487615\pi$
$600$	11.3535	0.463505
$601$	7.15202	0.291737	0.145868	−	0.989304i	$-0.453402\pi$
$601$	7.15202	0.291737	0.145868	+	0.989304i	$0.453402\pi$
$602$	0	0
$603$	−0.636074	−0.0259029
$604$	−4.43696	−0.180537
$605$	30.8303	1.25343
$606$	−13.0144	−0.528676
$607$	27.1091	1.10033	0.550163	−	0.835057i	$-0.314566\pi$
$607$	27.1091	1.10033	0.550163	+	0.835057i	$0.314566\pi$
$608$	−0.699452	−0.0283665
$609$	0	0
$610$	41.5724	1.68322
$611$	−15.2835	−0.618305
$612$	−0.817601	−0.0330496
$613$	−44.8087	−1.80981	−0.904904	−	0.425616i	$-0.860057\pi$
$613$	−44.8087	−1.80981	−0.904904	+	0.425616i	$0.860057\pi$
$614$	1.26314	0.0509761
$615$	2.94759	0.118858
$616$	0	0
$617$	−19.2364	−0.774430	−0.387215	−	0.921989i	$-0.626563\pi$
$617$	−19.2364	−0.774430	−0.387215	+	0.921989i	$0.626563\pi$
$618$	2.14385	0.0862384
$619$	−17.4185	−0.700111	−0.350055	−	0.936729i	$-0.613837\pi$
$619$	−17.4185	−0.700111	−0.350055	+	0.936729i	$0.613837\pi$
$620$	12.9487	0.520033
$621$	7.81932	0.313779
$622$	11.3986	0.457041
$623$	0	0
$624$	10.7106	0.428769
$625$	−29.8380	−1.19352
$626$	35.6341	1.42423
$627$	0.150838	0.00602389
$628$	−5.92101	−0.236274
$629$	−7.47197	−0.297927
$630$	0	0
$631$	14.1325	0.562606	0.281303	−	0.959619i	$-0.409233\pi$
$631$	14.1325	0.562606	0.281303	+	0.959619i	$0.409233\pi$
$632$	33.1870	1.32011
$633$	−2.29547	−0.0912368
$634$	25.5733	1.01565
$635$	20.6779	0.820576
$636$	3.67270	0.145632
$637$	0	0
$638$	8.79813	0.348321
$639$	−13.2397	−0.523756
$640$	9.87646	0.390401
$641$	−18.2182	−0.719576	−0.359788	−	0.933034i	$-0.617151\pi$
$641$	−18.2182	−0.719576	−0.359788	+	0.933034i	$0.617151\pi$
$642$	14.1362	0.557911
$643$	7.78639	0.307065	0.153533	−	0.988144i	$-0.450935\pi$
$643$	7.78639	0.307065	0.153533	+	0.988144i	$0.450935\pi$
$644$	0	0
$645$	6.89669	0.271557
$646$	−0.312283	−0.0122866
$647$	15.2676	0.600233	0.300116	−	0.953903i	$-0.402974\pi$
$647$	15.2676	0.600233	0.300116	+	0.953903i	$0.402974\pi$
$648$	3.07829	0.120927
$649$	9.31777	0.365754
$650$	19.7129	0.773203
$651$	0	0
$652$	−8.24895	−0.323054
$653$	36.0434	1.41049	0.705244	−	0.708965i	$-0.250838\pi$
$653$	36.0434	1.41049	0.705244	+	0.708965i	$0.250838\pi$
$654$	5.52796	0.216160
$655$	60.4299	2.36119
$656$	2.34644	0.0916132
$657$	2.69801	0.105260
$658$	0	0
$659$	40.5528	1.57971	0.789857	−	0.613291i	$-0.210155\pi$
$659$	40.5528	1.57971	0.789857	+	0.613291i	$0.210155\pi$
$660$	1.36299	0.0530543
$661$	−1.83785	−0.0714842	−0.0357421	−	0.999361i	$-0.511379\pi$
$661$	−1.83785	−0.0714842	−0.0357421	+	0.999361i	$0.511379\pi$
$662$	23.8925	0.928608
$663$	−5.93355	−0.230440
$664$	6.51669	0.252896
$665$	0	0
$666$	6.73054	0.260803
$667$	−79.9178	−3.09443
$668$	11.2118	0.433797
$669$	−9.29813	−0.359487
$670$	−2.19531	−0.0848123
$671$	8.85541	0.341859
$672$	0	0
$673$	31.5015	1.21429	0.607146	−	0.794590i	$-0.292314\pi$
$673$	31.5015	1.21429	0.607146	+	0.794590i	$0.292314\pi$
$674$	−17.7359	−0.683163
$675$	3.68826	0.141961
$676$	−4.92857	−0.189560
$677$	5.03952	0.193684	0.0968422	−	0.995300i	$-0.469126\pi$
$677$	5.03952	0.193684	0.0968422	+	0.995300i	$0.469126\pi$
$678$	−0.340616	−0.0130813
$679$	0	0
$680$	−11.7946	−0.452303
$681$	−6.59863	−0.252860
$682$	−6.01234	−0.230224
$683$	9.21689	0.352675	0.176337	−	0.984330i	$-0.443575\pi$
$683$	9.21689	0.352675	0.176337	+	0.984330i	$0.443575\pi$
$684$	−0.129048	−0.00493426
$685$	−48.2586	−1.84386
$686$	0	0
$687$	9.69155	0.369756
$688$	5.49015	0.209310
$689$	26.6538	1.01543
$690$	26.9872	1.02739
$691$	31.7005	1.20595	0.602973	−	0.797762i	$-0.293983\pi$
$691$	31.7005	1.20595	0.602973	+	0.797762i	$0.293983\pi$
$692$	12.4320	0.472593
$693$	0	0
$694$	12.0194	0.456249
$695$	−49.1562	−1.86460
$696$	−31.4618	−1.19256
$697$	−1.29990	−0.0492371
$698$	−13.3552	−0.505501
$699$	24.0753	0.910612
$700$	0	0
$701$	−43.8376	−1.65572	−0.827861	−	0.560933i	$-0.810443\pi$
$701$	−43.8376	−1.65572	−0.827861	+	0.560933i	$0.810443\pi$
$702$	5.34477	0.201725
$703$	−1.17935	−0.0444802
$704$	6.38476	0.240635
$705$	−9.86925	−0.371697
$706$	34.5848	1.30162
$707$	0	0
$708$	−7.97171	−0.299595
$709$	−26.3574	−0.989874	−0.494937	−	0.868929i	$-0.664809\pi$
$709$	−26.3574	−0.989874	−0.494937	+	0.868929i	$0.664809\pi$
$710$	−45.6950	−1.71490
$711$	10.7810	0.404319
$712$	28.8176	1.07998
$713$	54.6131	2.04528
$714$	0	0
$715$	9.89158	0.369924
$716$	8.45408	0.315944
$717$	−5.05867	−0.188919
$718$	−9.32677	−0.348072
$719$	−38.6791	−1.44249	−0.721243	−	0.692682i	$-0.756429\pi$
$719$	−38.6791	−1.44249	−0.721243	+	0.692682i	$0.756429\pi$
$720$	6.91634	0.257757
$721$	0	0
$722$	22.1980	0.826123
$723$	3.21287	0.119488
$724$	−5.16953	−0.192124
$725$	−37.6960	−1.40000
$726$	12.2471	0.454533
$727$	−42.3237	−1.56970	−0.784849	−	0.619687i	$-0.787259\pi$
$727$	−42.3237	−1.56970	−0.784849	+	0.619687i	$0.787259\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	9.31180	0.344645
$731$	−3.04147	−0.112493
$732$	−7.57615	−0.280023
$733$	10.4618	0.386416	0.193208	−	0.981158i	$-0.438111\pi$
$733$	10.4618	0.386416	0.193208	+	0.981158i	$0.438111\pi$
$734$	−3.30927	−0.122147
$735$	0	0
$736$	−26.6569	−0.982587
$737$	−0.467628	−0.0172253
$738$	1.17091	0.0431017
$739$	−20.7922	−0.764854	−0.382427	−	0.923986i	$-0.624912\pi$
$739$	−20.7922	−0.764854	−0.382427	+	0.923986i	$0.624912\pi$
$740$	−10.6568	−0.391751
$741$	−0.936533	−0.0344044
$742$	0	0
$743$	41.0163	1.50474	0.752370	−	0.658740i	$-0.228910\pi$
$743$	41.0163	1.50474	0.752370	+	0.658740i	$0.228910\pi$
$744$	21.4999	0.788225
$745$	55.3328	2.02724
$746$	−7.23719	−0.264972
$747$	2.11698	0.0774564
$748$	−0.601084	−0.0219778
$749$	0	0
$750$	−4.52728	−0.165313
$751$	−25.9895	−0.948371	−0.474185	−	0.880425i	$-0.657257\pi$
$751$	−25.9895	−0.948371	−0.474185	+	0.880425i	$0.657257\pi$
$752$	−7.85647	−0.286496
$753$	−28.9183	−1.05384
$754$	−54.6264	−1.98938
$755$	−20.7931	−0.756738
$756$	0	0
$757$	−19.2370	−0.699182	−0.349591	−	0.936902i	$-0.613679\pi$
$757$	−19.2370	−0.699182	−0.349591	+	0.936902i	$0.613679\pi$
$758$	−15.7138	−0.570751
$759$	5.74861	0.208661
$760$	−1.86163	−0.0675283
$761$	13.8501	0.502066	0.251033	−	0.967978i	$-0.419230\pi$
$761$	13.8501	0.502066	0.251033	+	0.967978i	$0.419230\pi$
$762$	8.21414	0.297567
$763$	0	0
$764$	−2.06401	−0.0746734
$765$	−3.83155	−0.138530
$766$	−7.07623	−0.255674
$767$	−57.8528	−2.08894
$768$	−13.4459	−0.485188
$769$	−19.8296	−0.715074	−0.357537	−	0.933899i	$-0.616383\pi$
$769$	−19.8296	−0.715074	−0.357537	+	0.933899i	$0.616383\pi$
$770$	0	0
$771$	−7.74014	−0.278754
$772$	−8.67543	−0.312236
$773$	52.2103	1.87787	0.938936	−	0.344091i	$-0.111813\pi$
$773$	52.2103	1.87787	0.938936	+	0.344091i	$0.111813\pi$
$774$	2.73966	0.0984752
$775$	25.7602	0.925333
$776$	−1.16764	−0.0419157
$777$	0	0
$778$	−27.2489	−0.976921
$779$	−0.205172	−0.00735104
$780$	−8.46263	−0.303011
$781$	−9.73359	−0.348295
$782$	−11.9015	−0.425595
$783$	−10.2205	−0.365253
$784$	0	0
$785$	−27.7478	−0.990362
$786$	24.0054	0.856244
$787$	38.7058	1.37971	0.689857	−	0.723946i	$-0.257673\pi$
$787$	38.7058	1.37971	0.689857	+	0.723946i	$0.257673\pi$
$788$	15.0233	0.535184
$789$	−13.8041	−0.491440
$790$	37.2090	1.32384
$791$	0	0
$792$	2.26309	0.0804155
$793$	−54.9821	−1.95247
$794$	−13.0227	−0.462158
$795$	17.2115	0.610430
$796$	15.9562	0.565552
$797$	−37.4303	−1.32585	−0.662924	−	0.748687i	$-0.730685\pi$
$797$	−37.4303	−1.32585	−0.662924	+	0.748687i	$0.730685\pi$
$798$	0	0
$799$	4.35237	0.153976
$800$	−12.5737	−0.444546
$801$	9.36156	0.330774
$802$	2.93291	0.103565
$803$	1.98352	0.0699971
$804$	0.400074	0.0141095
$805$	0	0
$806$	37.3299	1.31489
$807$	−9.88416	−0.347939
$808$	34.2146	1.20367
$809$	38.5794	1.35638	0.678190	−	0.734886i	$-0.262765\pi$
$809$	38.5794	1.35638	0.678190	+	0.734886i	$0.262765\pi$
$810$	3.45135	0.121268
$811$	−43.7757	−1.53717	−0.768587	−	0.639745i	$-0.779040\pi$
$811$	−43.7757	−1.53717	−0.768587	+	0.639745i	$0.779040\pi$
$812$	0	0
$813$	−9.17765	−0.321874
$814$	4.94815	0.173433
$815$	−38.6573	−1.35411
$816$	−3.05013	−0.106776
$817$	−0.480056	−0.0167950
$818$	−10.8446	−0.379171
$819$	0	0
$820$	−1.85396	−0.0647430
$821$	−9.99336	−0.348771	−0.174385	−	0.984677i	$-0.555794\pi$
$821$	−9.99336	−0.348771	−0.174385	+	0.984677i	$0.555794\pi$
$822$	−19.1704	−0.668644
$823$	−14.6858	−0.511913	−0.255957	−	0.966688i	$-0.582390\pi$
$823$	−14.6858	−0.511913	−0.255957	+	0.966688i	$0.582390\pi$
$824$	−5.63613	−0.196344
$825$	2.71153	0.0944034
$826$	0	0
$827$	−33.2522	−1.15629	−0.578146	−	0.815933i	$-0.696224\pi$
$827$	−33.2522	−1.15629	−0.578146	+	0.815933i	$0.696224\pi$
$828$	−4.91815	−0.170918
$829$	29.7741	1.03410	0.517048	−	0.855956i	$-0.327031\pi$
$829$	29.7741	1.03410	0.517048	+	0.855956i	$0.327031\pi$
$830$	7.30646	0.253611
$831$	−13.6038	−0.471911
$832$	−39.6422	−1.37435
$833$	0	0
$834$	−19.5270	−0.676164
$835$	52.5422	1.81830
$836$	−0.0948732	−0.00328126
$837$	6.98437	0.241415
$838$	31.1181	1.07496
$839$	−41.2929	−1.42559	−0.712795	−	0.701372i	$-0.752571\pi$
$839$	−41.2929	−1.42559	−0.712795	+	0.701372i	$0.752571\pi$
$840$	0	0
$841$	75.4596	2.60206
$842$	38.7534	1.33553
$843$	15.9950	0.550896
$844$	1.44379	0.0496974
$845$	−23.0969	−0.794559
$846$	−3.92049	−0.134789
$847$	0	0
$848$	13.7013	0.470506
$849$	19.9521	0.684753
$850$	−5.61374	−0.192550
$851$	−44.9465	−1.54075
$852$	8.32746	0.285294
$853$	−4.00104	−0.136993	−0.0684964	−	0.997651i	$-0.521820\pi$
$853$	−4.00104	−0.136993	−0.0684964	+	0.997651i	$0.521820\pi$
$854$	0	0
$855$	−0.604761	−0.0206824
$856$	−37.1637	−1.27023
$857$	41.6354	1.42224	0.711119	−	0.703071i	$-0.248189\pi$
$857$	41.6354	1.42224	0.711119	+	0.703071i	$0.248189\pi$
$858$	3.92936	0.134146
$859$	6.29690	0.214848	0.107424	−	0.994213i	$-0.465740\pi$
$859$	6.29690	0.214848	0.107424	+	0.994213i	$0.465740\pi$
$860$	−4.33784	−0.147919
$861$	0	0
$862$	25.8767	0.881363
$863$	1.64503	0.0559976	0.0279988	−	0.999608i	$-0.491087\pi$
$863$	1.64503	0.0559976	0.0279988	+	0.999608i	$0.491087\pi$
$864$	−3.40911	−0.115980
$865$	58.2605	1.98092
$866$	12.9440	0.439855
$867$	−15.3103	−0.519964
$868$	0	0
$869$	7.92598	0.268870
$870$	−35.2747	−1.19592
$871$	2.90344	0.0983794
$872$	−14.5329	−0.492145
$873$	−0.379314	−0.0128378
$874$	−1.87849	−0.0635409
$875$	0	0
$876$	−1.69698	−0.0573357
$877$	−37.6279	−1.27060	−0.635302	−	0.772263i	$-0.719125\pi$
$877$	−37.6279	−1.27060	−0.635302	+	0.772263i	$0.719125\pi$
$878$	−24.8182	−0.837572
$879$	5.62507	0.189729
$880$	5.08475	0.171407
$881$	−34.9336	−1.17694	−0.588472	−	0.808518i	$-0.700270\pi$
$881$	−34.9336	−1.17694	−0.588472	+	0.808518i	$0.700270\pi$
$882$	0	0
$883$	58.1016	1.95527	0.977637	−	0.210301i	$-0.0674443\pi$
$883$	58.1016	1.95527	0.977637	+	0.210301i	$0.0674443\pi$
$884$	3.73205	0.125522
$885$	−37.3581	−1.25578
$886$	18.4875	0.621100
$887$	−45.9321	−1.54225	−0.771124	−	0.636685i	$-0.780305\pi$
$887$	−45.9321	−1.54225	−0.771124	+	0.636685i	$0.780305\pi$
$888$	−17.6944	−0.593785
$889$	0	0
$890$	32.3100	1.08303
$891$	0.735179	0.0246294
$892$	5.84829	0.195815
$893$	0.686965	0.0229884
$894$	21.9806	0.735140
$895$	39.6187	1.32431
$896$	0	0
$897$	−35.6923	−1.19173
$898$	32.8974	1.09780
$899$	−71.3841	−2.38079
$900$	−2.31982	−0.0773273
$901$	−7.59034	−0.252871
$902$	0.860827	0.0286624
$903$	0	0
$904$	0.895470	0.0297829
$905$	−24.2262	−0.805305
$906$	−8.25991	−0.274417
$907$	−5.87846	−0.195191	−0.0975955	−	0.995226i	$-0.531115\pi$
$907$	−5.87846	−0.195191	−0.0975955	+	0.995226i	$0.531115\pi$
$908$	4.15037	0.137735
$909$	11.1148	0.368656
$910$	0	0
$911$	59.8217	1.98198	0.990990	−	0.133935i	$-0.0427615\pi$
$911$	59.8217	1.98198	0.990990	+	0.133935i	$0.0427615\pi$
$912$	−0.481423	−0.0159415
$913$	1.55636	0.0515081
$914$	−4.15869	−0.137557
$915$	−35.5044	−1.17374
$916$	−6.09574	−0.201409
$917$	0	0
$918$	−1.52206	−0.0502354
$919$	36.5137	1.20448	0.602238	−	0.798317i	$-0.294276\pi$
$919$	36.5137	1.20448	0.602238	+	0.798317i	$0.294276\pi$
$920$	−70.9487	−2.33911
$921$	−1.07877	−0.0355466
$922$	9.00112	0.296436
$923$	60.4346	1.98923
$924$	0	0
$925$	−21.2006	−0.697072
$926$	29.7186	0.976615
$927$	−1.83093	−0.0601357
$928$	34.8429	1.14378
$929$	7.35496	0.241308	0.120654	−	0.992695i	$-0.461501\pi$
$929$	7.35496	0.241308	0.120654	+	0.992695i	$0.461501\pi$
$930$	24.1055	0.790451
$931$	0	0
$932$	−15.1428	−0.496018
$933$	−9.73481	−0.318703
$934$	20.2994	0.664218
$935$	−2.81688	−0.0921218
$936$	−14.0513	−0.459280
$937$	10.5834	0.345744	0.172872	−	0.984944i	$-0.444695\pi$
$937$	10.5834	0.345744	0.172872	+	0.984944i	$0.444695\pi$
$938$	0	0
$939$	−30.4329	−0.993140
$940$	6.20750	0.202466
$941$	12.9045	0.420675	0.210338	−	0.977629i	$-0.432544\pi$
$941$	12.9045	0.420675	0.210338	+	0.977629i	$0.432544\pi$
$942$	−11.0226	−0.359137
$943$	−7.81932	−0.254632
$944$	−29.7391	−0.967926
$945$	0	0
$946$	2.01414	0.0654855
$947$	−20.4076	−0.663157	−0.331579	−	0.943428i	$-0.607581\pi$
$947$	−20.4076	−0.663157	−0.331579	+	0.943428i	$0.607581\pi$
$948$	−6.78098	−0.220236
$949$	−12.3154	−0.399776
$950$	−0.886056	−0.0287475
$951$	−21.8406	−0.708230
$952$	0	0
$953$	−45.4473	−1.47218	−0.736092	−	0.676882i	$-0.763331\pi$
$953$	−45.4473	−1.47218	−0.736092	+	0.676882i	$0.763331\pi$
$954$	6.83716	0.221361
$955$	−9.67266	−0.313000
$956$	3.18177	0.102906
$957$	−7.51394	−0.242891
$958$	3.40805	0.110109
$959$	0	0
$960$	−25.5987	−0.826194
$961$	17.7815	0.573596
$962$	−30.7224	−0.990531
$963$	−12.0728	−0.389042
$964$	−2.02081	−0.0650861
$965$	−40.6560	−1.30876
$966$	0	0
$967$	16.9520	0.545141	0.272570	−	0.962136i	$-0.412126\pi$
$967$	16.9520	0.545141	0.272570	+	0.962136i	$0.412126\pi$
$968$	−32.1974	−1.03486
$969$	0.266702	0.00856769
$970$	−1.30915	−0.0420341
$971$	−42.3882	−1.36030	−0.680152	−	0.733071i	$-0.738086\pi$
$971$	−42.3882	−1.36030	−0.680152	+	0.733071i	$0.738086\pi$
$972$	−0.628975	−0.0201744
$973$	0	0
$974$	36.4312	1.16733
$975$	−16.8355	−0.539169
$976$	−28.2635	−0.904691
$977$	−4.20581	−0.134556	−0.0672780	−	0.997734i	$-0.521431\pi$
$977$	−4.20581	−0.134556	−0.0672780	+	0.997734i	$0.521431\pi$
$978$	−15.3564	−0.491042
$979$	6.88243	0.219963
$980$	0	0
$981$	−4.72109	−0.150733
$982$	−38.6934	−1.23475
$983$	37.1082	1.18357	0.591783	−	0.806097i	$-0.298424\pi$
$983$	37.1082	1.18357	0.591783	+	0.806097i	$0.298424\pi$
$984$	−3.07829	−0.0981322
$985$	70.4043	2.24327
$986$	15.5563	0.495413
$987$	0	0
$988$	0.589056	0.0187404
$989$	−18.2955	−0.581762
$990$	2.53736	0.0806427
$991$	−2.05021	−0.0651270	−0.0325635	−	0.999470i	$-0.510367\pi$
$991$	−2.05021	−0.0651270	−0.0325635	+	0.999470i	$0.510367\pi$
$992$	−23.8105	−0.755983
$993$	−20.4051	−0.647536
$994$	0	0
$995$	74.7761	2.37056
$996$	−1.33153	−0.0421911
$997$	−18.3658	−0.581651	−0.290826	−	0.956776i	$-0.593930\pi$
$997$	−18.3658	−0.581651	−0.290826	+	0.956776i	$0.593930\pi$
$998$	21.0494	0.666308
$999$	−5.74813	−0.181863

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.ba.1.3	yes	8
7.6	odd	2		6027.2.a.z.1.3	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.z.1.3	✓	8	7.6	odd	2
6027.2.a.ba.1.3	yes	8	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)

\(f(q)\)	\(=\)	\(q-1.17091 q^{2} +1.00000 q^{3} -0.628975 q^{4} -2.94759 q^{5} -1.17091 q^{6} +3.07829 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.17091 q^{2} +1.00000 q^{3} -0.628975 q^{4} -2.94759 q^{5} -1.17091 q^{6} +3.07829 q^{8} +1.00000 q^{9} +3.45135 q^{10} +0.735179 q^{11} -0.628975 q^{12} -4.56463 q^{13} -2.94759 q^{15} -2.34644 q^{16} +1.29990 q^{17} -1.17091 q^{18} +0.205172 q^{19} +1.85396 q^{20} -0.860827 q^{22} +7.81932 q^{23} +3.07829 q^{24} +3.68826 q^{25} +5.34477 q^{26} +1.00000 q^{27} -10.2205 q^{29} +3.45135 q^{30} +6.98437 q^{31} -3.40911 q^{32} +0.735179 q^{33} -1.52206 q^{34} -0.628975 q^{36} -5.74813 q^{37} -0.240237 q^{38} -4.56463 q^{39} -9.07351 q^{40} -1.00000 q^{41} -2.33978 q^{43} -0.462409 q^{44} -2.94759 q^{45} -9.15571 q^{46} +3.34825 q^{47} -2.34644 q^{48} -4.31861 q^{50} +1.29990 q^{51} +2.87104 q^{52} -5.83919 q^{53} -1.17091 q^{54} -2.16700 q^{55} +0.205172 q^{57} +11.9673 q^{58} +12.6741 q^{59} +1.85396 q^{60} +12.0452 q^{61} -8.17806 q^{62} +8.68463 q^{64} +13.4546 q^{65} -0.860827 q^{66} -0.636074 q^{67} -0.817601 q^{68} +7.81932 q^{69} -13.2397 q^{71} +3.07829 q^{72} +2.69801 q^{73} +6.73054 q^{74} +3.68826 q^{75} -0.129048 q^{76} +5.34477 q^{78} +10.7810 q^{79} +6.91634 q^{80} +1.00000 q^{81} +1.17091 q^{82} +2.11698 q^{83} -3.83155 q^{85} +2.73966 q^{86} -10.2205 q^{87} +2.26309 q^{88} +9.36156 q^{89} +3.45135 q^{90} -4.91815 q^{92} +6.98437 q^{93} -3.92049 q^{94} -0.604761 q^{95} -3.40911 q^{96} -0.379314 q^{97} +0.735179 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 8 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} - 6 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 8 * q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 - 6 * q^8 + 8 * q^9	\( 8 q - 2 q^{2} + 8 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} - 6 q^{8} + 8 q^{9} + 2 q^{10} - 2 q^{11} + 4 q^{12} - 4 q^{13} - 2 q^{15} - 8 q^{17} - 2 q^{18} - 6 q^{19} - 4 q^{20} - 14 q^{22} - 12 q^{23} - 6 q^{24} - 4 q^{25} - 4 q^{26} + 8 q^{27} - 4 q^{29} + 2 q^{30} + 10 q^{31} - 4 q^{32} - 2 q^{33} - 4 q^{34} + 4 q^{36} - 20 q^{37} + 18 q^{38} - 4 q^{39} - 12 q^{40} - 8 q^{41} - 8 q^{43} + 20 q^{44} - 2 q^{45} - 12 q^{46} - 24 q^{47} - 22 q^{50} - 8 q^{51} + 30 q^{52} - 36 q^{53} - 2 q^{54} - 4 q^{55} - 6 q^{57} + 14 q^{58} - 10 q^{59} - 4 q^{60} + 22 q^{61} - 30 q^{62} - 24 q^{64} + 8 q^{65} - 14 q^{66} - 14 q^{67} - 38 q^{68} - 12 q^{69} - 10 q^{71} - 6 q^{72} + 12 q^{73} - 2 q^{74} - 4 q^{75} - 32 q^{76} - 4 q^{78} + 16 q^{79} + 14 q^{80} + 8 q^{81} + 2 q^{82} - 24 q^{83} - 44 q^{85} + 36 q^{86} - 4 q^{87} - 34 q^{88} - 2 q^{89} + 2 q^{90} - 48 q^{92} + 10 q^{93} + 34 q^{94} - 24 q^{95} - 4 q^{96} - 16 q^{97} - 2 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 8 * q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 - 6 * q^8 + 8 * q^9 + 2 * q^10 - 2 * q^11 + 4 * q^12 - 4 * q^13 - 2 * q^15 - 8 * q^17 - 2 * q^18 - 6 * q^19 - 4 * q^20 - 14 * q^22 - 12 * q^23 - 6 * q^24 - 4 * q^25 - 4 * q^26 + 8 * q^27 - 4 * q^29 + 2 * q^30 + 10 * q^31 - 4 * q^32 - 2 * q^33 - 4 * q^34 + 4 * q^36 - 20 * q^37 + 18 * q^38 - 4 * q^39 - 12 * q^40 - 8 * q^41 - 8 * q^43 + 20 * q^44 - 2 * q^45 - 12 * q^46 - 24 * q^47 - 22 * q^50 - 8 * q^51 + 30 * q^52 - 36 * q^53 - 2 * q^54 - 4 * q^55 - 6 * q^57 + 14 * q^58 - 10 * q^59 - 4 * q^60 + 22 * q^61 - 30 * q^62 - 24 * q^64 + 8 * q^65 - 14 * q^66 - 14 * q^67 - 38 * q^68 - 12 * q^69 - 10 * q^71 - 6 * q^72 + 12 * q^73 - 2 * q^74 - 4 * q^75 - 32 * q^76 - 4 * q^78 + 16 * q^79 + 14 * q^80 + 8 * q^81 + 2 * q^82 - 24 * q^83 - 44 * q^85 + 36 * q^86 - 4 * q^87 - 34 * q^88 - 2 * q^89 + 2 * q^90 - 48 * q^92 + 10 * q^93 + 34 * q^94 - 24 * q^95 - 4 * q^96 - 16 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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