LMFDB - Embedded newform 8085.2.a.ck.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8085,2,Mod(1,8085)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8085, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8085.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8085 = 3 \cdot 5 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8085.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:	$64.5590500342$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 16x^{8} + 84x^{6} - 2x^{5} - 169x^{4} + 8x^{3} + 128x^{2} - 4x - 32 $ x^10 - 16x^8 + 84x^6 - 2x^5 - 169x^4 + 8x^3 + 128x^2 - 4*x - 32
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 1155)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.761016$ of defining polynomial
Character	$\chi$	$=$	8085.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.761016 q^{2} -1.00000 q^{3} -1.42085 q^{4} -1.00000 q^{5} +0.761016 q^{6} +2.60333 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.761016 q^{2} -1.00000 q^{3} -1.42085 q^{4} -1.00000 q^{5} +0.761016 q^{6} +2.60333 q^{8} +1.00000 q^{9} +0.761016 q^{10} +1.00000 q^{11} +1.42085 q^{12} -5.44119 q^{13} +1.00000 q^{15} +0.860535 q^{16} +5.24891 q^{17} -0.761016 q^{18} -4.98737 q^{19} +1.42085 q^{20} -0.761016 q^{22} -0.495809 q^{23} -2.60333 q^{24} +1.00000 q^{25} +4.14084 q^{26} -1.00000 q^{27} +5.87296 q^{29} -0.761016 q^{30} -6.63522 q^{31} -5.86153 q^{32} -1.00000 q^{33} -3.99451 q^{34} -1.42085 q^{36} +1.61660 q^{37} +3.79547 q^{38} +5.44119 q^{39} -2.60333 q^{40} -3.44957 q^{41} +9.38154 q^{43} -1.42085 q^{44} -1.00000 q^{45} +0.377319 q^{46} +7.81669 q^{47} -0.860535 q^{48} -0.761016 q^{50} -5.24891 q^{51} +7.73114 q^{52} -9.45077 q^{53} +0.761016 q^{54} -1.00000 q^{55} +4.98737 q^{57} -4.46942 q^{58} +2.56369 q^{59} -1.42085 q^{60} -9.40449 q^{61} +5.04951 q^{62} +2.73965 q^{64} +5.44119 q^{65} +0.761016 q^{66} -7.51426 q^{67} -7.45794 q^{68} +0.495809 q^{69} +14.5924 q^{71} +2.60333 q^{72} -3.46758 q^{73} -1.23026 q^{74} -1.00000 q^{75} +7.08633 q^{76} -4.14084 q^{78} -14.1438 q^{79} -0.860535 q^{80} +1.00000 q^{81} +2.62518 q^{82} +5.33707 q^{83} -5.24891 q^{85} -7.13951 q^{86} -5.87296 q^{87} +2.60333 q^{88} +9.79460 q^{89} +0.761016 q^{90} +0.704473 q^{92} +6.63522 q^{93} -5.94863 q^{94} +4.98737 q^{95} +5.86153 q^{96} +11.6638 q^{97} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{3} + 12 q^{4} - 10 q^{5} + 10 q^{9}+O(q^{10}) $ 10 * q - 10 * q^3 + 12 * q^4 - 10 * q^5 + 10 * q^9	$ 10 q - 10 q^{3} + 12 q^{4} - 10 q^{5} + 10 q^{9} + 10 q^{11} - 12 q^{12} - 4 q^{13} + 10 q^{15} + 24 q^{16} - 12 q^{17} - 9 q^{19} - 12 q^{20} - q^{23} + 10 q^{25} - 6 q^{26} - 10 q^{27} + 3 q^{29} - 9 q^{31} - 10 q^{32} - 10 q^{33} - 6 q^{34} + 12 q^{36} + 3 q^{37} - 42 q^{38} + 4 q^{39} - 3 q^{41} + 12 q^{44} - 10 q^{45} - 22 q^{46} - 21 q^{47} - 24 q^{48} + 12 q^{51} - 24 q^{52} - 5 q^{53} - 10 q^{55} + 9 q^{57} - 26 q^{58} - 16 q^{59} + 12 q^{60} - 20 q^{61} + 18 q^{62} + 70 q^{64} + 4 q^{65} - q^{67} - 30 q^{68} + q^{69} + 22 q^{71} + q^{73} - 34 q^{74} - 10 q^{75} + 28 q^{76} + 6 q^{78} + 19 q^{79} - 24 q^{80} + 10 q^{81} - 32 q^{82} - 20 q^{83} + 12 q^{85} - 3 q^{87} - 18 q^{89} - 8 q^{92} + 9 q^{93} + 6 q^{94} + 9 q^{95} + 10 q^{96} - 6 q^{97} + 10 q^{99}+O(q^{100}) $ 10 * q - 10 * q^3 + 12 * q^4 - 10 * q^5 + 10 * q^9 + 10 * q^11 - 12 * q^12 - 4 * q^13 + 10 * q^15 + 24 * q^16 - 12 * q^17 - 9 * q^19 - 12 * q^20 - q^23 + 10 * q^25 - 6 * q^26 - 10 * q^27 + 3 * q^29 - 9 * q^31 - 10 * q^32 - 10 * q^33 - 6 * q^34 + 12 * q^36 + 3 * q^37 - 42 * q^38 + 4 * q^39 - 3 * q^41 + 12 * q^44 - 10 * q^45 - 22 * q^46 - 21 * q^47 - 24 * q^48 + 12 * q^51 - 24 * q^52 - 5 * q^53 - 10 * q^55 + 9 * q^57 - 26 * q^58 - 16 * q^59 + 12 * q^60 - 20 * q^61 + 18 * q^62 + 70 * q^64 + 4 * q^65 - q^67 - 30 * q^68 + q^69 + 22 * q^71 + q^73 - 34 * q^74 - 10 * q^75 + 28 * q^76 + 6 * q^78 + 19 * q^79 - 24 * q^80 + 10 * q^81 - 32 * q^82 - 20 * q^83 + 12 * q^85 - 3 * q^87 - 18 * q^89 - 8 * q^92 + 9 * q^93 + 6 * q^94 + 9 * q^95 + 10 * q^96 - 6 * q^97 + 10 * 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 $

$2$	−0.761016	−0.538120	−0.269060	−	0.963123i	$-0.586713\pi$
$2$	−0.761016	−0.538120	−0.269060	+	0.963123i	$0.586713\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.42085	−0.710427
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.761016	0.310684
$7$	0	0
$7$	0	0
$8$	2.60333	0.920415
$9$	1.00000	0.333333
$10$	0.761016	0.240654
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.42085	0.410165
$13$	−5.44119	−1.50912	−0.754558	−	0.656234i	$-0.772148\pi$
$13$	−5.44119	−1.50912	−0.754558	+	0.656234i	$0.772148\pi$
$14$	0	0
$15$	1.00000	0.258199
$16$	0.860535	0.215134
$17$	5.24891	1.27305	0.636524	−	0.771257i	$-0.280371\pi$
$17$	5.24891	1.27305	0.636524	+	0.771257i	$0.280371\pi$
$18$	−0.761016	−0.179373
$19$	−4.98737	−1.14418	−0.572091	−	0.820190i	$-0.693867\pi$
$19$	−4.98737	−1.14418	−0.572091	+	0.820190i	$0.693867\pi$
$20$	1.42085	0.317713
$21$	0	0
$22$	−0.761016	−0.162249
$23$	−0.495809	−0.103383	−0.0516917	−	0.998663i	$-0.516461\pi$
$23$	−0.495809	−0.103383	−0.0516917	+	0.998663i	$0.516461\pi$
$24$	−2.60333	−0.531402
$25$	1.00000	0.200000
$26$	4.14084	0.812085
$27$	−1.00000	−0.192450
$28$	0	0
$29$	5.87296	1.09058	0.545291	−	0.838247i	$-0.316419\pi$
$29$	5.87296	1.09058	0.545291	+	0.838247i	$0.316419\pi$
$30$	−0.761016	−0.138942
$31$	−6.63522	−1.19172	−0.595860	−	0.803088i	$-0.703189\pi$
$31$	−6.63522	−1.19172	−0.595860	+	0.803088i	$0.703189\pi$
$32$	−5.86153	−1.03618
$33$	−1.00000	−0.174078
$34$	−3.99451	−0.685053
$35$	0	0
$36$	−1.42085	−0.236809
$37$	1.61660	0.265767	0.132883	−	0.991132i	$-0.457576\pi$
$37$	1.61660	0.265767	0.132883	+	0.991132i	$0.457576\pi$
$38$	3.79547	0.615707
$39$	5.44119	0.871288
$40$	−2.60333	−0.411622
$41$	−3.44957	−0.538733	−0.269366	−	0.963038i	$-0.586814\pi$
$41$	−3.44957	−0.538733	−0.269366	+	0.963038i	$0.586814\pi$
$42$	0	0
$43$	9.38154	1.43067	0.715336	−	0.698781i	$-0.246274\pi$
$43$	9.38154	1.43067	0.715336	+	0.698781i	$0.246274\pi$
$44$	−1.42085	−0.214202
$45$	−1.00000	−0.149071
$46$	0.377319	0.0556326
$47$	7.81669	1.14018	0.570091	−	0.821582i	$-0.306908\pi$
$47$	7.81669	1.14018	0.570091	+	0.821582i	$0.306908\pi$
$48$	−0.860535	−0.124208
$49$	0	0
$50$	−0.761016	−0.107624
$51$	−5.24891	−0.734995
$52$	7.73114	1.07212
$53$	−9.45077	−1.29816	−0.649082	−	0.760719i	$-0.724847\pi$
$53$	−9.45077	−1.29816	−0.649082	+	0.760719i	$0.724847\pi$
$54$	0.761016	0.103561
$55$	−1.00000	−0.134840
$56$	0	0
$57$	4.98737	0.660593
$58$	−4.46942	−0.586863
$59$	2.56369	0.333765	0.166882	−	0.985977i	$-0.446630\pi$
$59$	2.56369	0.333765	0.166882	+	0.985977i	$0.446630\pi$
$60$	−1.42085	−0.183431
$61$	−9.40449	−1.20412	−0.602061	−	0.798450i	$-0.705653\pi$
$61$	−9.40449	−1.20412	−0.602061	+	0.798450i	$0.705653\pi$
$62$	5.04951	0.641288
$63$	0	0
$64$	2.73965	0.342456
$65$	5.44119	0.674897
$66$	0.761016	0.0936746
$67$	−7.51426	−0.918013	−0.459007	−	0.888433i	$-0.651795\pi$
$67$	−7.51426	−0.918013	−0.459007	+	0.888433i	$0.651795\pi$
$68$	−7.45794	−0.904408
$69$	0.495809	0.0596884
$70$	0	0
$71$	14.5924	1.73180	0.865902	−	0.500213i	$-0.166745\pi$
$71$	14.5924	1.73180	0.865902	+	0.500213i	$0.166745\pi$
$72$	2.60333	0.306805
$73$	−3.46758	−0.405850	−0.202925	−	0.979194i	$-0.565045\pi$
$73$	−3.46758	−0.405850	−0.202925	+	0.979194i	$0.565045\pi$
$74$	−1.23026	−0.143014
$75$	−1.00000	−0.115470
$76$	7.08633	0.812858
$77$	0	0
$78$	−4.14084	−0.468857
$79$	−14.1438	−1.59130	−0.795651	−	0.605755i	$-0.792871\pi$
$79$	−14.1438	−1.59130	−0.795651	+	0.605755i	$0.792871\pi$
$80$	−0.860535	−0.0962108
$81$	1.00000	0.111111
$82$	2.62518	0.289903
$83$	5.33707	0.585819	0.292910	−	0.956140i	$-0.405376\pi$
$83$	5.33707	0.585819	0.292910	+	0.956140i	$0.405376\pi$
$84$	0	0
$85$	−5.24891	−0.569325
$86$	−7.13951	−0.769873
$87$	−5.87296	−0.629647
$88$	2.60333	0.277515
$89$	9.79460	1.03823	0.519113	−	0.854706i	$-0.326263\pi$
$89$	9.79460	1.03823	0.519113	+	0.854706i	$0.326263\pi$
$90$	0.761016	0.0802182
$91$	0	0
$92$	0.704473	0.0734464
$93$	6.63522	0.688040
$94$	−5.94863	−0.613554
$95$	4.98737	0.511693
$96$	5.86153	0.598240
$97$	11.6638	1.18427	0.592137	−	0.805837i	$-0.298284\pi$
$97$	11.6638	1.18427	0.592137	+	0.805837i	$0.298284\pi$
$98$	0	0
$99$	1.00000	0.100504
$100$	−1.42085	−0.142085
$101$	2.11253	0.210204	0.105102	−	0.994461i	$-0.466483\pi$
$101$	2.11253	0.210204	0.105102	+	0.994461i	$0.466483\pi$
$102$	3.99451	0.395515
$103$	−15.4957	−1.52684	−0.763419	−	0.645903i	$-0.776481\pi$
$103$	−15.4957	−1.52684	−0.763419	+	0.645903i	$0.776481\pi$
$104$	−14.1652	−1.38901
$105$	0	0
$106$	7.19219	0.698568
$107$	0.841709	0.0813710	0.0406855	−	0.999172i	$-0.487046\pi$
$107$	0.841709	0.0813710	0.0406855	+	0.999172i	$0.487046\pi$
$108$	1.42085	0.136722
$109$	19.0476	1.82443	0.912216	−	0.409709i	$-0.134370\pi$
$109$	19.0476	1.82443	0.912216	+	0.409709i	$0.134370\pi$
$110$	0.761016	0.0725601
$111$	−1.61660	−0.153441
$112$	0	0
$113$	8.16823	0.768403	0.384201	−	0.923249i	$-0.374477\pi$
$113$	8.16823	0.768403	0.384201	+	0.923249i	$0.374477\pi$
$114$	−3.79547	−0.355478
$115$	0.495809	0.0462345
$116$	−8.34462	−0.774779
$117$	−5.44119	−0.503038
$118$	−1.95101	−0.179605
$119$	0	0
$120$	2.60333	0.237650
$121$	1.00000	0.0909091
$122$	7.15697	0.647961
$123$	3.44957	0.311037
$124$	9.42768	0.846631
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−1.77751	−0.157728	−0.0788641	−	0.996885i	$-0.525129\pi$
$127$	−1.77751	−0.157728	−0.0788641	+	0.996885i	$0.525129\pi$
$128$	9.63815	0.851900
$129$	−9.38154	−0.825999
$130$	−4.14084	−0.363175
$131$	−20.7980	−1.81713	−0.908564	−	0.417746i	$-0.862820\pi$
$131$	−20.7980	−1.81713	−0.908564	+	0.417746i	$0.862820\pi$
$132$	1.42085	0.123669
$133$	0	0
$134$	5.71848	0.494001
$135$	1.00000	0.0860663
$136$	13.6646	1.17173
$137$	−14.2322	−1.21594	−0.607971	−	0.793959i	$-0.708016\pi$
$137$	−14.2322	−1.21594	−0.607971	+	0.793959i	$0.708016\pi$
$138$	−0.377319	−0.0321195
$139$	23.2315	1.97047	0.985235	−	0.171209i	$-0.0547674\pi$
$139$	23.2315	1.97047	0.985235	+	0.171209i	$0.0547674\pi$
$140$	0	0
$141$	−7.81669	−0.658284
$142$	−11.1051	−0.931918
$143$	−5.44119	−0.455015
$144$	0.860535	0.0717113
$145$	−5.87296	−0.487723
$146$	2.63889	0.218396
$147$	0	0
$148$	−2.29695	−0.188808
$149$	−0.530254	−0.0434401	−0.0217200	−	0.999764i	$-0.506914\pi$
$149$	−0.530254	−0.0434401	−0.0217200	+	0.999764i	$0.506914\pi$
$150$	0.761016	0.0621367
$151$	12.2433	0.996342	0.498171	−	0.867079i	$-0.334005\pi$
$151$	12.2433	0.996342	0.498171	+	0.867079i	$0.334005\pi$
$152$	−12.9838	−1.05312
$153$	5.24891	0.424350
$154$	0	0
$155$	6.63522	0.532954
$156$	−7.73114	−0.618987
$157$	−9.58316	−0.764819	−0.382410	−	0.923993i	$-0.624906\pi$
$157$	−9.58316	−0.764819	−0.382410	+	0.923993i	$0.624906\pi$
$158$	10.7637	0.856312
$159$	9.45077	0.749495
$160$	5.86153	0.463395
$161$	0	0
$162$	−0.761016	−0.0597911
$163$	−11.6703	−0.914088	−0.457044	−	0.889444i	$-0.651092\pi$
$163$	−11.6703	−0.914088	−0.457044	+	0.889444i	$0.651092\pi$
$164$	4.90134	0.382730
$165$	1.00000	0.0778499
$166$	−4.06160	−0.315241
$167$	24.1409	1.86808	0.934039	−	0.357170i	$-0.116258\pi$
$167$	24.1409	1.86808	0.934039	+	0.357170i	$0.116258\pi$
$168$	0	0
$169$	16.6066	1.27743
$170$	3.99451	0.306365
$171$	−4.98737	−0.381394
$172$	−13.3298	−1.01639
$173$	15.6559	1.19030	0.595150	−	0.803615i	$-0.297093\pi$
$173$	15.6559	1.19030	0.595150	+	0.803615i	$0.297093\pi$
$174$	4.46942	0.338826
$175$	0	0
$176$	0.860535	0.0648653
$177$	−2.56369	−0.192699
$178$	−7.45385	−0.558690
$179$	16.2748	1.21643	0.608216	−	0.793771i	$-0.291885\pi$
$179$	16.2748	1.21643	0.608216	+	0.793771i	$0.291885\pi$
$180$	1.42085	0.105904
$181$	18.4857	1.37403	0.687017	−	0.726641i	$-0.258920\pi$
$181$	18.4857	1.37403	0.687017	+	0.726641i	$0.258920\pi$
$182$	0	0
$183$	9.40449	0.695200
$184$	−1.29075	−0.0951556
$185$	−1.61660	−0.118855
$186$	−5.04951	−0.370248
$187$	5.24891	0.383839
$188$	−11.1064	−0.810016
$189$	0	0
$190$	−3.79547	−0.275352
$191$	7.44111	0.538420	0.269210	−	0.963082i	$-0.413237\pi$
$191$	7.44111	0.538420	0.269210	+	0.963082i	$0.413237\pi$
$192$	−2.73965	−0.197717
$193$	0.239671	0.0172519	0.00862596	−	0.999963i	$-0.497254\pi$
$193$	0.239671	0.0172519	0.00862596	+	0.999963i	$0.497254\pi$
$194$	−8.87631	−0.637282
$195$	−5.44119	−0.389652
$196$	0	0
$197$	12.5099	0.891292	0.445646	−	0.895209i	$-0.352974\pi$
$197$	12.5099	0.891292	0.445646	+	0.895209i	$0.352974\pi$
$198$	−0.761016	−0.0540831
$199$	7.47820	0.530116	0.265058	−	0.964233i	$-0.414609\pi$
$199$	7.47820	0.530116	0.265058	+	0.964233i	$0.414609\pi$
$200$	2.60333	0.184083
$201$	7.51426	0.530015
$202$	−1.60767	−0.113115
$203$	0	0
$204$	7.45794	0.522160
$205$	3.44957	0.240929
$206$	11.7925	0.821622
$207$	−0.495809	−0.0344611
$208$	−4.68234	−0.324662
$209$	−4.98737	−0.344984
$210$	0	0
$211$	−22.8991	−1.57644	−0.788218	−	0.615396i	$-0.788996\pi$
$211$	−22.8991	−1.57644	−0.788218	+	0.615396i	$0.788996\pi$
$212$	13.4282	0.922251
$213$	−14.5924	−0.999858
$214$	−0.640554	−0.0437874
$215$	−9.38154	−0.639816
$216$	−2.60333	−0.177134
$217$	0	0
$218$	−14.4956	−0.981763
$219$	3.46758	0.234318
$220$	1.42085	0.0957940
$221$	−28.5604	−1.92118
$222$	1.23026	0.0825694
$223$	−14.9187	−0.999032	−0.499516	−	0.866305i	$-0.666489\pi$
$223$	−14.9187	−0.999032	−0.499516	+	0.866305i	$0.666489\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	−6.21616	−0.413493
$227$	−10.3984	−0.690164	−0.345082	−	0.938573i	$-0.612149\pi$
$227$	−10.3984	−0.690164	−0.345082	+	0.938573i	$0.612149\pi$
$228$	−7.08633	−0.469304
$229$	−7.96263	−0.526185	−0.263093	−	0.964771i	$-0.584742\pi$
$229$	−7.96263	−0.526185	−0.263093	+	0.964771i	$0.584742\pi$
$230$	−0.377319	−0.0248797
$231$	0	0
$232$	15.2892	1.00379
$233$	−1.72761	−0.113180	−0.0565898	−	0.998398i	$-0.518023\pi$
$233$	−1.72761	−0.113180	−0.0565898	+	0.998398i	$0.518023\pi$
$234$	4.14084	0.270695
$235$	−7.81669	−0.509905
$236$	−3.64264	−0.237115
$237$	14.1438	0.918739
$238$	0	0
$239$	−16.1222	−1.04286	−0.521429	−	0.853294i	$-0.674601\pi$
$239$	−16.1222	−1.04286	−0.521429	+	0.853294i	$0.674601\pi$
$240$	0.860535	0.0555473
$241$	4.00135	0.257750	0.128875	−	0.991661i	$-0.458863\pi$
$241$	4.00135	0.257750	0.128875	+	0.991661i	$0.458863\pi$
$242$	−0.761016	−0.0489200
$243$	−1.00000	−0.0641500
$244$	13.3624	0.855440
$245$	0	0
$246$	−2.62518	−0.167375
$247$	27.1372	1.72670
$248$	−17.2736	−1.09688
$249$	−5.33707	−0.338223
$250$	0.761016	0.0481309
$251$	−13.7938	−0.870657	−0.435329	−	0.900272i	$-0.643368\pi$
$251$	−13.7938	−0.870657	−0.435329	+	0.900272i	$0.643368\pi$
$252$	0	0
$253$	−0.495809	−0.0311713
$254$	1.35271	0.0848766
$255$	5.24891	0.328700
$256$	−12.8141	−0.800880
$257$	−13.3372	−0.831954	−0.415977	−	0.909375i	$-0.636560\pi$
$257$	−13.3372	−0.831954	−0.415977	+	0.909375i	$0.636560\pi$
$258$	7.13951	0.444486
$259$	0	0
$260$	−7.73114	−0.479465
$261$	5.87296	0.363527
$262$	15.8276	0.977832
$263$	1.94343	0.119837	0.0599184	−	0.998203i	$-0.480916\pi$
$263$	1.94343	0.119837	0.0599184	+	0.998203i	$0.480916\pi$
$264$	−2.60333	−0.160224
$265$	9.45077	0.580556
$266$	0	0
$267$	−9.79460	−0.599420
$268$	10.6767	0.652182
$269$	5.63285	0.343441	0.171721	−	0.985146i	$-0.445067\pi$
$269$	5.63285	0.343441	0.171721	+	0.985146i	$0.445067\pi$
$270$	−0.761016	−0.0463140
$271$	27.1109	1.64687	0.823435	−	0.567411i	$-0.192055\pi$
$271$	27.1109	1.64687	0.823435	+	0.567411i	$0.192055\pi$
$272$	4.51688	0.273876
$273$	0	0
$274$	10.8310	0.654323
$275$	1.00000	0.0603023
$276$	−0.704473	−0.0424043
$277$	14.7014	0.883322	0.441661	−	0.897182i	$-0.354389\pi$
$277$	14.7014	0.883322	0.441661	+	0.897182i	$0.354389\pi$
$278$	−17.6795	−1.06035
$279$	−6.63522	−0.397240
$280$	0	0
$281$	−25.6499	−1.53014	−0.765071	−	0.643945i	$-0.777296\pi$
$281$	−25.6499	−1.53014	−0.765071	+	0.643945i	$0.777296\pi$
$282$	5.94863	0.354236
$283$	−1.37168	−0.0815380	−0.0407690	−	0.999169i	$-0.512981\pi$
$283$	−1.37168	−0.0815380	−0.0407690	+	0.999169i	$0.512981\pi$
$284$	−20.7337	−1.23032
$285$	−4.98737	−0.295426
$286$	4.14084	0.244853
$287$	0	0
$288$	−5.86153	−0.345394
$289$	10.5511	0.620653
$290$	4.46942	0.262453
$291$	−11.6638	−0.683741
$292$	4.92693	0.288327
$293$	−29.3300	−1.71348	−0.856738	−	0.515751i	$-0.827513\pi$
$293$	−29.3300	−1.71348	−0.856738	+	0.515751i	$0.827513\pi$
$294$	0	0
$295$	−2.56369	−0.149264
$296$	4.20853	0.244616
$297$	−1.00000	−0.0580259
$298$	0.403532	0.0233760
$299$	2.69779	0.156017
$300$	1.42085	0.0820331
$301$	0	0
$302$	−9.31732	−0.536151
$303$	−2.11253	−0.121362
$304$	−4.29181	−0.246152
$305$	9.40449	0.538499
$306$	−3.99451	−0.228351
$307$	−15.9425	−0.909885	−0.454942	−	0.890521i	$-0.650340\pi$
$307$	−15.9425	−0.909885	−0.454942	+	0.890521i	$0.650340\pi$
$308$	0	0
$309$	15.4957	0.881521
$310$	−5.04951	−0.286793
$311$	−7.12095	−0.403792	−0.201896	−	0.979407i	$-0.564710\pi$
$311$	−7.12095	−0.403792	−0.201896	+	0.979407i	$0.564710\pi$
$312$	14.1652	0.801946
$313$	13.6397	0.770964	0.385482	−	0.922715i	$-0.374035\pi$
$313$	13.6397	0.770964	0.385482	+	0.922715i	$0.374035\pi$
$314$	7.29294	0.411564
$315$	0	0
$316$	20.0963	1.13050
$317$	−2.18669	−0.122817	−0.0614083	−	0.998113i	$-0.519559\pi$
$317$	−2.18669	−0.122817	−0.0614083	+	0.998113i	$0.519559\pi$
$318$	−7.19219	−0.403318
$319$	5.87296	0.328823
$320$	−2.73965	−0.153151
$321$	−0.841709	−0.0469796
$322$	0	0
$323$	−26.1783	−1.45660
$324$	−1.42085	−0.0789363
$325$	−5.44119	−0.301823
$326$	8.88128	0.491889
$327$	−19.0476	−1.05334
$328$	−8.98036	−0.495857
$329$	0	0
$330$	−0.761016	−0.0418926
$331$	9.50240	0.522299	0.261150	−	0.965298i	$-0.415898\pi$
$331$	9.50240	0.522299	0.261150	+	0.965298i	$0.415898\pi$
$332$	−7.58320	−0.416182
$333$	1.61660	0.0885890
$334$	−18.3716	−1.00525
$335$	7.51426	0.410548
$336$	0	0
$337$	13.2924	0.724084	0.362042	−	0.932162i	$-0.382080\pi$
$337$	13.2924	0.724084	0.362042	+	0.932162i	$0.382080\pi$
$338$	−12.6379	−0.687410
$339$	−8.16823	−0.443637
$340$	7.45794	0.404464
$341$	−6.63522	−0.359317
$342$	3.79547	0.205236
$343$	0	0
$344$	24.4232	1.31681
$345$	−0.495809	−0.0266935
$346$	−11.9144	−0.640524
$347$	−29.9756	−1.60917	−0.804587	−	0.593835i	$-0.797613\pi$
$347$	−29.9756	−1.60917	−0.804587	+	0.593835i	$0.797613\pi$
$348$	8.34462	0.447319
$349$	−12.2813	−0.657403	−0.328701	−	0.944434i	$-0.606611\pi$
$349$	−12.2813	−0.657403	−0.328701	+	0.944434i	$0.606611\pi$
$350$	0	0
$351$	5.44119	0.290429
$352$	−5.86153	−0.312421
$353$	6.19302	0.329621	0.164811	−	0.986325i	$-0.447299\pi$
$353$	6.19302	0.329621	0.164811	+	0.986325i	$0.447299\pi$
$354$	1.95101	0.103695
$355$	−14.5924	−0.774487
$356$	−13.9167	−0.737583
$357$	0	0
$358$	−12.3854	−0.654587
$359$	8.63706	0.455847	0.227923	−	0.973679i	$-0.426806\pi$
$359$	8.63706	0.455847	0.227923	+	0.973679i	$0.426806\pi$
$360$	−2.60333	−0.137207
$361$	5.87387	0.309151
$362$	−14.0679	−0.739395
$363$	−1.00000	−0.0524864
$364$	0	0
$365$	3.46758	0.181502
$366$	−7.15697	−0.374101
$367$	−15.2709	−0.797135	−0.398568	−	0.917139i	$-0.630493\pi$
$367$	−15.2709	−0.797135	−0.398568	+	0.917139i	$0.630493\pi$
$368$	−0.426661	−0.0222413
$369$	−3.44957	−0.179578
$370$	1.23026	0.0639580
$371$	0	0
$372$	−9.42768	−0.488802
$373$	13.5497	0.701575	0.350787	−	0.936455i	$-0.385914\pi$
$373$	13.5497	0.701575	0.350787	+	0.936455i	$0.385914\pi$
$374$	−3.99451	−0.206551
$375$	1.00000	0.0516398
$376$	20.3494	1.04944
$377$	−31.9559	−1.64581
$378$	0	0
$379$	37.1859	1.91011	0.955056	−	0.296425i	$-0.0957945\pi$
$379$	37.1859	1.91011	0.955056	+	0.296425i	$0.0957945\pi$
$380$	−7.08633	−0.363521
$381$	1.77751	0.0910644
$382$	−5.66280	−0.289734
$383$	8.42335	0.430413	0.215207	−	0.976569i	$-0.430958\pi$
$383$	8.42335	0.430413	0.215207	+	0.976569i	$0.430958\pi$
$384$	−9.63815	−0.491845
$385$	0	0
$386$	−0.182394	−0.00928360
$387$	9.38154	0.476891
$388$	−16.5725	−0.841341
$389$	31.8152	1.61310	0.806548	−	0.591169i	$-0.201333\pi$
$389$	31.8152	1.61310	0.806548	+	0.591169i	$0.201333\pi$
$390$	4.14084	0.209679
$391$	−2.60246	−0.131612
$392$	0	0
$393$	20.7980	1.04912
$394$	−9.52022	−0.479622
$395$	14.1438	0.711652
$396$	−1.42085	−0.0714006
$397$	−20.8899	−1.04844	−0.524218	−	0.851584i	$-0.675642\pi$
$397$	−20.8899	−1.04844	−0.524218	+	0.851584i	$0.675642\pi$
$398$	−5.69103	−0.285266
$399$	0	0
$400$	0.860535	0.0430268
$401$	−4.14960	−0.207221	−0.103610	−	0.994618i	$-0.533040\pi$
$401$	−4.14960	−0.207221	−0.103610	+	0.994618i	$0.533040\pi$
$402$	−5.71848	−0.285212
$403$	36.1035	1.79844
$404$	−3.00160	−0.149335
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	1.61660	0.0801317
$408$	−13.6646	−0.676500
$409$	−30.0431	−1.48553	−0.742767	−	0.669550i	$-0.766487\pi$
$409$	−30.0431	−1.48553	−0.742767	+	0.669550i	$0.766487\pi$
$410$	−2.62518	−0.129648
$411$	14.2322	0.702025
$412$	22.0172	1.08471
$413$	0	0
$414$	0.377319	0.0185442
$415$	−5.33707	−0.261986
$416$	31.8937	1.56372
$417$	−23.2315	−1.13765
$418$	3.79547	0.185643
$419$	−24.8292	−1.21299	−0.606494	−	0.795088i	$-0.707424\pi$
$419$	−24.8292	−1.21299	−0.606494	+	0.795088i	$0.707424\pi$
$420$	0	0
$421$	−36.9496	−1.80081	−0.900406	−	0.435050i	$-0.856731\pi$
$421$	−36.9496	−1.80081	−0.900406	+	0.435050i	$0.856731\pi$
$422$	17.4266	0.848312
$423$	7.81669	0.380060
$424$	−24.6034	−1.19485
$425$	5.24891	0.254610
$426$	11.1051	0.538043
$427$	0	0
$428$	−1.19595	−0.0578082
$429$	5.44119	0.262703
$430$	7.13951	0.344298
$431$	−8.46281	−0.407639	−0.203820	−	0.979008i	$-0.565336\pi$
$431$	−8.46281	−0.407639	−0.203820	+	0.979008i	$0.565336\pi$
$432$	−0.860535	−0.0414025
$433$	−0.717685	−0.0344898	−0.0172449	−	0.999851i	$-0.505489\pi$
$433$	−0.717685	−0.0344898	−0.0172449	+	0.999851i	$0.505489\pi$
$434$	0	0
$435$	5.87296	0.281587
$436$	−27.0639	−1.29613
$437$	2.47279	0.118289
$438$	−2.63889	−0.126091
$439$	−28.6854	−1.36908	−0.684539	−	0.728977i	$-0.739996\pi$
$439$	−28.6854	−1.36908	−0.684539	+	0.728977i	$0.739996\pi$
$440$	−2.60333	−0.124109
$441$	0	0
$442$	21.7349	1.03382
$443$	−38.8664	−1.84660	−0.923300	−	0.384080i	$-0.874519\pi$
$443$	−38.8664	−1.84660	−0.923300	+	0.384080i	$0.874519\pi$
$444$	2.29695	0.109008
$445$	−9.79460	−0.464308
$446$	11.3534	0.537599
$447$	0.530254	0.0250801
$448$	0	0
$449$	−15.5954	−0.735993	−0.367997	−	0.929827i	$-0.619956\pi$
$449$	−15.5954	−0.735993	−0.367997	+	0.929827i	$0.619956\pi$
$450$	−0.761016	−0.0358746
$451$	−3.44957	−0.162434
$452$	−11.6059	−0.545894
$453$	−12.2433	−0.575238
$454$	7.91332	0.371391
$455$	0	0
$456$	12.9838	0.608020
$457$	−22.5616	−1.05539	−0.527695	−	0.849434i	$-0.676943\pi$
$457$	−22.5616	−1.05539	−0.527695	+	0.849434i	$0.676943\pi$
$458$	6.05969	0.283151
$459$	−5.24891	−0.244998
$460$	−0.704473	−0.0328462
$461$	−36.8884	−1.71806	−0.859032	−	0.511922i	$-0.828934\pi$
$461$	−36.8884	−1.71806	−0.859032	+	0.511922i	$0.828934\pi$
$462$	0	0
$463$	−4.09225	−0.190183	−0.0950916	−	0.995469i	$-0.530314\pi$
$463$	−4.09225	−0.190183	−0.0950916	+	0.995469i	$0.530314\pi$
$464$	5.05389	0.234621
$465$	−6.63522	−0.307701
$466$	1.31474	0.0609042
$467$	−17.7002	−0.819070	−0.409535	−	0.912294i	$-0.634309\pi$
$467$	−17.7002	−0.819070	−0.409535	+	0.912294i	$0.634309\pi$
$468$	7.73114	0.357372
$469$	0	0
$470$	5.94863	0.274390
$471$	9.58316	0.441569
$472$	6.67413	0.307202
$473$	9.38154	0.431364
$474$	−10.7637	−0.494392
$475$	−4.98737	−0.228836
$476$	0	0
$477$	−9.45077	−0.432721
$478$	12.2693	0.561183
$479$	8.26458	0.377618	0.188809	−	0.982014i	$-0.439537\pi$
$479$	8.26458	0.377618	0.188809	+	0.982014i	$0.439537\pi$
$480$	−5.86153	−0.267541
$481$	−8.79621	−0.401073
$482$	−3.04510	−0.138700
$483$	0	0
$484$	−1.42085	−0.0645843
$485$	−11.6638	−0.529624
$486$	0.761016	0.0345204
$487$	6.54861	0.296746	0.148373	−	0.988931i	$-0.452596\pi$
$487$	6.54861	0.296746	0.148373	+	0.988931i	$0.452596\pi$
$488$	−24.4829	−1.10829
$489$	11.6703	0.527749
$490$	0	0
$491$	8.44585	0.381156	0.190578	−	0.981672i	$-0.438964\pi$
$491$	8.44585	0.381156	0.190578	+	0.981672i	$0.438964\pi$
$492$	−4.90134	−0.220969
$493$	30.8267	1.38836
$494$	−20.6519	−0.929172
$495$	−1.00000	−0.0449467
$496$	−5.70984	−0.256379
$497$	0	0
$498$	4.06160	0.182004
$499$	−29.2340	−1.30870	−0.654348	−	0.756194i	$-0.727057\pi$
$499$	−29.2340	−1.30870	−0.654348	+	0.756194i	$0.727057\pi$
$500$	1.42085	0.0635425
$501$	−24.1409	−1.07854
$502$	10.4973	0.468518
$503$	12.1053	0.539748	0.269874	−	0.962896i	$-0.413018\pi$
$503$	12.1053	0.539748	0.269874	+	0.962896i	$0.413018\pi$
$504$	0	0
$505$	−2.11253	−0.0940063
$506$	0.377319	0.0167739
$507$	−16.6066	−0.737524
$508$	2.52558	0.112054
$509$	29.0040	1.28558	0.642790	−	0.766042i	$-0.277777\pi$
$509$	29.0040	1.28558	0.642790	+	0.766042i	$0.277777\pi$
$510$	−3.99451	−0.176880
$511$	0	0
$512$	−9.52456	−0.420930
$513$	4.98737	0.220198
$514$	10.1499	0.447691
$515$	15.4957	0.682823
$516$	13.3298	0.586812
$517$	7.81669	0.343778
$518$	0	0
$519$	−15.6559	−0.687220
$520$	14.1652	0.621185
$521$	−32.6854	−1.43197	−0.715987	−	0.698113i	$-0.754023\pi$
$521$	−32.6854	−1.43197	−0.715987	+	0.698113i	$0.754023\pi$
$522$	−4.46942	−0.195621
$523$	−10.7379	−0.469537	−0.234768	−	0.972051i	$-0.575433\pi$
$523$	−10.7379	−0.469537	−0.234768	+	0.972051i	$0.575433\pi$
$524$	29.5509	1.29094
$525$	0	0
$526$	−1.47898	−0.0644866
$527$	−34.8277	−1.51712
$528$	−0.860535	−0.0374500
$529$	−22.7542	−0.989312
$530$	−7.19219	−0.312409
$531$	2.56369	0.111255
$532$	0	0
$533$	18.7698	0.813009
$534$	7.45385	0.322560
$535$	−0.841709	−0.0363902
$536$	−19.5621	−0.844953
$537$	−16.2748	−0.702308
$538$	−4.28669	−0.184812
$539$	0	0
$540$	−1.42085	−0.0611438
$541$	31.3387	1.34735	0.673677	−	0.739026i	$-0.264714\pi$
$541$	31.3387	1.34735	0.673677	+	0.739026i	$0.264714\pi$
$542$	−20.6318	−0.886213
$543$	−18.4857	−0.793299
$544$	−30.7667	−1.31911
$545$	−19.0476	−0.815911
$546$	0	0
$547$	−17.5756	−0.751478	−0.375739	−	0.926725i	$-0.622611\pi$
$547$	−17.5756	−0.751478	−0.375739	+	0.926725i	$0.622611\pi$
$548$	20.2219	0.863838
$549$	−9.40449	−0.401374
$550$	−0.761016	−0.0324498
$551$	−29.2906	−1.24782
$552$	1.29075	0.0549381
$553$	0	0
$554$	−11.1880	−0.475333
$555$	1.61660	0.0686207
$556$	−33.0086	−1.39987
$557$	5.01093	0.212320	0.106160	−	0.994349i	$-0.466144\pi$
$557$	5.01093	0.212320	0.106160	+	0.994349i	$0.466144\pi$
$558$	5.04951	0.213763
$559$	−51.0468	−2.15905
$560$	0	0
$561$	−5.24891	−0.221609
$562$	19.5200	0.823400
$563$	−40.2625	−1.69686	−0.848431	−	0.529307i	$-0.822452\pi$
$563$	−40.2625	−1.69686	−0.848431	+	0.529307i	$0.822452\pi$
$564$	11.1064	0.467663
$565$	−8.16823	−0.343640
$566$	1.04387	0.0438772
$567$	0	0
$568$	37.9889	1.59398
$569$	15.3307	0.642695	0.321347	−	0.946961i	$-0.395864\pi$
$569$	15.3307	0.642695	0.321347	+	0.946961i	$0.395864\pi$
$570$	3.79547	0.158975
$571$	−16.5089	−0.690877	−0.345439	−	0.938441i	$-0.612270\pi$
$571$	−16.5089	−0.690877	−0.345439	+	0.938441i	$0.612270\pi$
$572$	7.73114	0.323255
$573$	−7.44111	−0.310857
$574$	0	0
$575$	−0.495809	−0.0206767
$576$	2.73965	0.114152
$577$	−31.2472	−1.30084	−0.650419	−	0.759576i	$-0.725407\pi$
$577$	−31.2472	−1.30084	−0.650419	+	0.759576i	$0.725407\pi$
$578$	−8.02956	−0.333986
$579$	−0.239671	−0.00996041
$580$	8.34462	0.346492
$581$	0	0
$582$	8.87631	0.367935
$583$	−9.45077	−0.391411
$584$	−9.02725	−0.373550
$585$	5.44119	0.224966
$586$	22.3206	0.922056
$587$	−7.70319	−0.317945	−0.158972	−	0.987283i	$-0.550818\pi$
$587$	−7.70319	−0.317945	−0.158972	+	0.987283i	$0.550818\pi$
$588$	0	0
$589$	33.0923	1.36354
$590$	1.95101	0.0803220
$591$	−12.5099	−0.514588
$592$	1.39114	0.0571755
$593$	1.40674	0.0577681	0.0288840	−	0.999583i	$-0.490805\pi$
$593$	1.40674	0.0577681	0.0288840	+	0.999583i	$0.490805\pi$
$594$	0.761016	0.0312249
$595$	0	0
$596$	0.753413	0.0308610
$597$	−7.47820	−0.306062
$598$	−2.05306	−0.0839561
$599$	34.9411	1.42765	0.713827	−	0.700322i	$-0.246960\pi$
$599$	34.9411	1.42765	0.713827	+	0.700322i	$0.246960\pi$
$600$	−2.60333	−0.106280
$601$	0.449631	0.0183408	0.00917042	−	0.999958i	$-0.497081\pi$
$601$	0.449631	0.0183408	0.00917042	+	0.999958i	$0.497081\pi$
$602$	0	0
$603$	−7.51426	−0.306004
$604$	−17.3959	−0.707828
$605$	−1.00000	−0.0406558
$606$	1.60767	0.0653071
$607$	−15.6878	−0.636746	−0.318373	−	0.947965i	$-0.603136\pi$
$607$	−15.6878	−0.636746	−0.318373	+	0.947965i	$0.603136\pi$
$608$	29.2336	1.18558
$609$	0	0
$610$	−7.15697	−0.289777
$611$	−42.5321	−1.72066
$612$	−7.45794	−0.301469
$613$	−42.6521	−1.72270	−0.861352	−	0.508009i	$-0.830382\pi$
$613$	−42.6521	−1.72270	−0.861352	+	0.508009i	$0.830382\pi$
$614$	12.1325	0.489627
$615$	−3.44957	−0.139100
$616$	0	0
$617$	−8.52651	−0.343265	−0.171632	−	0.985161i	$-0.554904\pi$
$617$	−8.52651	−0.343265	−0.171632	+	0.985161i	$0.554904\pi$
$618$	−11.7925	−0.474364
$619$	−1.98726	−0.0798748	−0.0399374	−	0.999202i	$-0.512716\pi$
$619$	−1.98726	−0.0798748	−0.0399374	+	0.999202i	$0.512716\pi$
$620$	−9.42768	−0.378625
$621$	0.495809	0.0198961
$622$	5.41916	0.217288
$623$	0	0
$624$	4.68234	0.187444
$625$	1.00000	0.0400000
$626$	−10.3801	−0.414871
$627$	4.98737	0.199176
$628$	13.6163	0.543348
$629$	8.48538	0.338334
$630$	0	0
$631$	28.9651	1.15308	0.576541	−	0.817068i	$-0.304402\pi$
$631$	28.9651	1.15308	0.576541	+	0.817068i	$0.304402\pi$
$632$	−36.8209	−1.46466
$633$	22.8991	0.910156
$634$	1.66410	0.0660900
$635$	1.77751	0.0705382
$636$	−13.4282	−0.532462
$637$	0	0
$638$	−4.46942	−0.176946
$639$	14.5924	0.577268
$640$	−9.63815	−0.380981
$641$	19.9348	0.787377	0.393689	−	0.919244i	$-0.371199\pi$
$641$	19.9348	0.787377	0.393689	+	0.919244i	$0.371199\pi$
$642$	0.640554	0.0252806
$643$	−32.3011	−1.27383	−0.636916	−	0.770933i	$-0.719790\pi$
$643$	−32.3011	−1.27383	−0.636916	+	0.770933i	$0.719790\pi$
$644$	0	0
$645$	9.38154	0.369398
$646$	19.9221	0.783825
$647$	−4.41025	−0.173385	−0.0866924	−	0.996235i	$-0.527630\pi$
$647$	−4.41025	−0.173385	−0.0866924	+	0.996235i	$0.527630\pi$
$648$	2.60333	0.102268
$649$	2.56369	0.100634
$650$	4.14084	0.162417
$651$	0	0
$652$	16.5818	0.649393
$653$	−15.1265	−0.591946	−0.295973	−	0.955196i	$-0.595644\pi$
$653$	−15.1265	−0.591946	−0.295973	+	0.955196i	$0.595644\pi$
$654$	14.4956	0.566821
$655$	20.7980	0.812644
$656$	−2.96848	−0.115900
$657$	−3.46758	−0.135283
$658$	0	0
$659$	−24.7745	−0.965079	−0.482539	−	0.875874i	$-0.660285\pi$
$659$	−24.7745	−0.965079	−0.482539	+	0.875874i	$0.660285\pi$
$660$	−1.42085	−0.0553067
$661$	−9.33162	−0.362958	−0.181479	−	0.983395i	$-0.558088\pi$
$661$	−9.33162	−0.362958	−0.181479	+	0.983395i	$0.558088\pi$
$662$	−7.23148	−0.281060
$663$	28.5604	1.10919
$664$	13.8941	0.539197
$665$	0	0
$666$	−1.23026	−0.0476715
$667$	−2.91187	−0.112748
$668$	−34.3007	−1.32713
$669$	14.9187	0.576792
$670$	−5.71848	−0.220924
$671$	−9.40449	−0.363056
$672$	0	0
$673$	23.8710	0.920160	0.460080	−	0.887877i	$-0.347821\pi$
$673$	23.8710	0.920160	0.460080	+	0.887877i	$0.347821\pi$
$674$	−10.1157	−0.389644
$675$	−1.00000	−0.0384900
$676$	−23.5955	−0.907520
$677$	9.68248	0.372128	0.186064	−	0.982538i	$-0.440427\pi$
$677$	9.68248	0.372128	0.186064	+	0.982538i	$0.440427\pi$
$678$	6.21616	0.238730
$679$	0	0
$680$	−13.6646	−0.524015
$681$	10.3984	0.398466
$682$	5.04951	0.193356
$683$	−25.4201	−0.972673	−0.486336	−	0.873772i	$-0.661667\pi$
$683$	−25.4201	−0.972673	−0.486336	+	0.873772i	$0.661667\pi$
$684$	7.08633	0.270953
$685$	14.2322	0.543786
$686$	0	0
$687$	7.96263	0.303793
$688$	8.07315	0.307786
$689$	51.4235	1.95908
$690$	0.377319	0.0143643
$691$	−16.8431	−0.640741	−0.320370	−	0.947292i	$-0.603807\pi$
$691$	−16.8431	−0.640741	−0.320370	+	0.947292i	$0.603807\pi$
$692$	−22.2448	−0.845621
$693$	0	0
$694$	22.8119	0.865928
$695$	−23.2315	−0.881221
$696$	−15.2892	−0.579537
$697$	−18.1065	−0.685833
$698$	9.34627	0.353761
$699$	1.72761	0.0653443
$700$	0	0
$701$	−26.0468	−0.983773	−0.491887	−	0.870659i	$-0.663693\pi$
$701$	−26.0468	−0.983773	−0.491887	+	0.870659i	$0.663693\pi$
$702$	−4.14084	−0.156286
$703$	−8.06257	−0.304086
$704$	2.73965	0.103254
$705$	7.81669	0.294394
$706$	−4.71299	−0.177376
$707$	0	0
$708$	3.64264	0.136899
$709$	20.4885	0.769463	0.384732	−	0.923028i	$-0.374294\pi$
$709$	20.4885	0.769463	0.384732	+	0.923028i	$0.374294\pi$
$710$	11.1051	0.416767
$711$	−14.1438	−0.530434
$712$	25.4985	0.955598
$713$	3.28980	0.123204
$714$	0	0
$715$	5.44119	0.203489
$716$	−23.1241	−0.864187
$717$	16.1222	0.602095
$718$	−6.57294	−0.245300
$719$	22.8857	0.853494	0.426747	−	0.904371i	$-0.359659\pi$
$719$	22.8857	0.853494	0.426747	+	0.904371i	$0.359659\pi$
$720$	−0.860535	−0.0320703
$721$	0	0
$722$	−4.47011	−0.166360
$723$	−4.00135	−0.148812
$724$	−26.2655	−0.976151
$725$	5.87296	0.218116
$726$	0.761016	0.0282440
$727$	−27.7988	−1.03100	−0.515500	−	0.856890i	$-0.672394\pi$
$727$	−27.7988	−1.03100	−0.515500	+	0.856890i	$0.672394\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−2.63889	−0.0976696
$731$	49.2429	1.82132
$732$	−13.3624	−0.493889
$733$	9.78815	0.361534	0.180767	−	0.983526i	$-0.442142\pi$
$733$	9.78815	0.361534	0.180767	+	0.983526i	$0.442142\pi$
$734$	11.6214	0.428954
$735$	0	0
$736$	2.90620	0.107124
$737$	−7.51426	−0.276791
$738$	2.62518	0.0966342
$739$	17.2732	0.635404	0.317702	−	0.948191i	$-0.397089\pi$
$739$	17.2732	0.635404	0.317702	+	0.948191i	$0.397089\pi$
$740$	2.29695	0.0844375
$741$	−27.1372	−0.996912
$742$	0	0
$743$	30.6410	1.12411	0.562055	−	0.827100i	$-0.310011\pi$
$743$	30.6410	1.12411	0.562055	+	0.827100i	$0.310011\pi$
$744$	17.2736	0.633282
$745$	0.530254	0.0194270
$746$	−10.3115	−0.377531
$747$	5.33707	0.195273
$748$	−7.45794	−0.272689
$749$	0	0
$750$	−0.761016	−0.0277884
$751$	27.0640	0.987580	0.493790	−	0.869581i	$-0.335611\pi$
$751$	27.0640	0.987580	0.493790	+	0.869581i	$0.335611\pi$
$752$	6.72654	0.245292
$753$	13.7938	0.502674
$754$	24.3190	0.885644
$755$	−12.2433	−0.445578
$756$	0	0
$757$	27.2762	0.991369	0.495684	−	0.868503i	$-0.334917\pi$
$757$	27.2762	0.991369	0.495684	+	0.868503i	$0.334917\pi$
$758$	−28.2991	−1.02787
$759$	0.495809	0.0179967
$760$	12.9838	0.470970
$761$	0.634367	0.0229958	0.0114979	−	0.999934i	$-0.496340\pi$
$761$	0.634367	0.0229958	0.0114979	+	0.999934i	$0.496340\pi$
$762$	−1.35271	−0.0490036
$763$	0	0
$764$	−10.5727	−0.382508
$765$	−5.24891	−0.189775
$766$	−6.41031	−0.231614
$767$	−13.9496	−0.503689
$768$	12.8141	0.462389
$769$	37.8412	1.36459	0.682294	−	0.731078i	$-0.260983\pi$
$769$	37.8412	1.36459	0.682294	+	0.731078i	$0.260983\pi$
$770$	0	0
$771$	13.3372	0.480329
$772$	−0.340538	−0.0122562
$773$	20.1963	0.726411	0.363206	−	0.931709i	$-0.381682\pi$
$773$	20.1963	0.726411	0.363206	+	0.931709i	$0.381682\pi$
$774$	−7.13951	−0.256624
$775$	−6.63522	−0.238344
$776$	30.3645	1.09002
$777$	0	0
$778$	−24.2119	−0.868038
$779$	17.2043	0.616408
$780$	7.73114	0.276819
$781$	14.5924	0.522159
$782$	1.98051	0.0708231
$783$	−5.87296	−0.209882
$784$	0	0
$785$	9.58316	0.342038
$786$	−15.8276	−0.564552
$787$	−34.5203	−1.23051	−0.615257	−	0.788327i	$-0.710948\pi$
$787$	−34.5203	−1.23051	−0.615257	+	0.788327i	$0.710948\pi$
$788$	−17.7747	−0.633198
$789$	−1.94343	−0.0691878
$790$	−10.7637	−0.382954
$791$	0	0
$792$	2.60333	0.0925051
$793$	51.1716	1.81716
$794$	15.8976	0.564184
$795$	−9.45077	−0.335184
$796$	−10.6254	−0.376608
$797$	32.2941	1.14392	0.571958	−	0.820283i	$-0.306184\pi$
$797$	32.2941	1.14392	0.571958	+	0.820283i	$0.306184\pi$
$798$	0	0
$799$	41.0291	1.45151
$800$	−5.86153	−0.207236
$801$	9.79460	0.346075
$802$	3.15791	0.111510
$803$	−3.46758	−0.122368
$804$	−10.6767	−0.376537
$805$	0	0
$806$	−27.4754	−0.967778
$807$	−5.63285	−0.198286
$808$	5.49960	0.193475
$809$	31.8545	1.11994	0.559972	−	0.828512i	$-0.310812\pi$
$809$	31.8545	1.11994	0.559972	+	0.828512i	$0.310812\pi$
$810$	0.761016	0.0267394
$811$	47.6606	1.67359	0.836795	−	0.547516i	$-0.184426\pi$
$811$	47.6606	1.67359	0.836795	+	0.547516i	$0.184426\pi$
$812$	0	0
$813$	−27.1109	−0.950821
$814$	−1.23026	−0.0431205
$815$	11.6703	0.408793
$816$	−4.51688	−0.158122
$817$	−46.7892	−1.63695
$818$	22.8633	0.799395
$819$	0	0
$820$	−4.90134	−0.171162
$821$	−24.1282	−0.842078	−0.421039	−	0.907042i	$-0.638335\pi$
$821$	−24.1282	−0.842078	−0.421039	+	0.907042i	$0.638335\pi$
$822$	−10.8310	−0.377773
$823$	−2.11771	−0.0738186	−0.0369093	−	0.999319i	$-0.511751\pi$
$823$	−2.11771	−0.0738186	−0.0369093	+	0.999319i	$0.511751\pi$
$824$	−40.3404	−1.40532
$825$	−1.00000	−0.0348155
$826$	0	0
$827$	−48.2089	−1.67639	−0.838193	−	0.545373i	$-0.816388\pi$
$827$	−48.2089	−1.67639	−0.838193	+	0.545373i	$0.816388\pi$
$828$	0.704473	0.0244821
$829$	6.75486	0.234606	0.117303	−	0.993096i	$-0.462575\pi$
$829$	6.75486	0.234606	0.117303	+	0.993096i	$0.462575\pi$
$830$	4.06160	0.140980
$831$	−14.7014	−0.509986
$832$	−14.9070	−0.516806
$833$	0	0
$834$	17.6795	0.612192
$835$	−24.1409	−0.835430
$836$	7.08633	0.245086
$837$	6.63522	0.229347
$838$	18.8954	0.652732
$839$	−19.4474	−0.671398	−0.335699	−	0.941969i	$-0.608973\pi$
$839$	−19.4474	−0.671398	−0.335699	+	0.941969i	$0.608973\pi$
$840$	0	0
$841$	5.49166	0.189368
$842$	28.1192	0.969053
$843$	25.6499	0.883428
$844$	32.5362	1.11994
$845$	−16.6066	−0.571283
$846$	−5.94863	−0.204518
$847$	0	0
$848$	−8.13273	−0.279279
$849$	1.37168	0.0470760
$850$	−3.99451	−0.137011
$851$	−0.801524	−0.0274759
$852$	20.7337	0.710326
$853$	−32.8859	−1.12599	−0.562995	−	0.826460i	$-0.690351\pi$
$853$	−32.8859	−1.12599	−0.562995	+	0.826460i	$0.690351\pi$
$854$	0	0
$855$	4.98737	0.170564
$856$	2.19124	0.0748951
$857$	−50.7238	−1.73269	−0.866346	−	0.499445i	$-0.833537\pi$
$857$	−50.7238	−1.73269	−0.866346	+	0.499445i	$0.833537\pi$
$858$	−4.14084	−0.141366
$859$	−1.16961	−0.0399065	−0.0199533	−	0.999801i	$-0.506352\pi$
$859$	−1.16961	−0.0399065	−0.0199533	+	0.999801i	$0.506352\pi$
$860$	13.3298	0.454543
$861$	0	0
$862$	6.44034	0.219359
$863$	−45.6972	−1.55555	−0.777775	−	0.628543i	$-0.783652\pi$
$863$	−45.6972	−1.55555	−0.777775	+	0.628543i	$0.783652\pi$
$864$	5.86153	0.199413
$865$	−15.6559	−0.532318
$866$	0.546170	0.0185596
$867$	−10.5511	−0.358334
$868$	0	0
$869$	−14.1438	−0.479796
$870$	−4.46942	−0.151527
$871$	40.8866	1.38539
$872$	49.5872	1.67923
$873$	11.6638	0.394758
$874$	−1.88183	−0.0636538
$875$	0	0
$876$	−4.92693	−0.166466
$877$	−36.0000	−1.21563	−0.607816	−	0.794078i	$-0.707954\pi$
$877$	−36.0000	−1.21563	−0.607816	+	0.794078i	$0.707954\pi$
$878$	21.8300	0.736727
$879$	29.3300	0.989276
$880$	−0.860535	−0.0290086
$881$	−22.9913	−0.774596	−0.387298	−	0.921955i	$-0.626592\pi$
$881$	−22.9913	−0.774596	−0.387298	+	0.921955i	$0.626592\pi$
$882$	0	0
$883$	−16.9023	−0.568808	−0.284404	−	0.958705i	$-0.591796\pi$
$883$	−16.9023	−0.568808	−0.284404	+	0.958705i	$0.591796\pi$
$884$	40.5801	1.36486
$885$	2.56369	0.0861777
$886$	29.5780	0.993692
$887$	−16.1421	−0.541998	−0.270999	−	0.962580i	$-0.587354\pi$
$887$	−16.1421	−0.541998	−0.270999	+	0.962580i	$0.587354\pi$
$888$	−4.20853	−0.141229
$889$	0	0
$890$	7.45385	0.249854
$891$	1.00000	0.0335013
$892$	21.1973	0.709740
$893$	−38.9847	−1.30457
$894$	−0.403532	−0.0134961
$895$	−16.2748	−0.544005
$896$	0	0
$897$	−2.69779	−0.0900767
$898$	11.8684	0.396052
$899$	−38.9684	−1.29967
$900$	−1.42085	−0.0473618
$901$	−49.6063	−1.65263
$902$	2.62518	0.0874089
$903$	0	0
$904$	21.2646	0.707249
$905$	−18.4857	−0.614487
$906$	9.31732	0.309547
$907$	23.8140	0.790730	0.395365	−	0.918524i	$-0.370618\pi$
$907$	23.8140	0.790730	0.395365	+	0.918524i	$0.370618\pi$
$908$	14.7746	0.490311
$909$	2.11253	0.0700681
$910$	0	0
$911$	16.8394	0.557914	0.278957	−	0.960304i	$-0.410011\pi$
$911$	16.8394	0.557914	0.278957	+	0.960304i	$0.410011\pi$
$912$	4.29181	0.142116
$913$	5.33707	0.176631
$914$	17.1698	0.567926
$915$	−9.40449	−0.310903
$916$	11.3137	0.373816
$917$	0	0
$918$	3.99451	0.131838
$919$	−17.0044	−0.560922	−0.280461	−	0.959865i	$-0.590487\pi$
$919$	−17.0044	−0.560922	−0.280461	+	0.959865i	$0.590487\pi$
$920$	1.29075	0.0425549
$921$	15.9425	0.525322
$922$	28.0727	0.924524
$923$	−79.4003	−2.61349
$924$	0	0
$925$	1.61660	0.0531534
$926$	3.11427	0.102341
$927$	−15.4957	−0.508946
$928$	−34.4245	−1.13004
$929$	−16.8409	−0.552531	−0.276265	−	0.961081i	$-0.589097\pi$
$929$	−16.8409	−0.552531	−0.276265	+	0.961081i	$0.589097\pi$
$930$	5.04951	0.165580
$931$	0	0
$932$	2.45469	0.0804059
$933$	7.12095	0.233129
$934$	13.4702	0.440758
$935$	−5.24891	−0.171658
$936$	−14.1652	−0.463004
$937$	16.5302	0.540019	0.270009	−	0.962858i	$-0.412973\pi$
$937$	16.5302	0.540019	0.270009	+	0.962858i	$0.412973\pi$
$938$	0	0
$939$	−13.6397	−0.445116
$940$	11.1064	0.362250
$941$	−2.57768	−0.0840300	−0.0420150	−	0.999117i	$-0.513378\pi$
$941$	−2.57768	−0.0840300	−0.0420150	+	0.999117i	$0.513378\pi$
$942$	−7.29294	−0.237617
$943$	1.71033	0.0556960
$944$	2.20615	0.0718041
$945$	0	0
$946$	−7.13951	−0.232125
$947$	33.6754	1.09430	0.547152	−	0.837033i	$-0.315712\pi$
$947$	33.6754	1.09430	0.547152	+	0.837033i	$0.315712\pi$
$948$	−20.0963	−0.652697
$949$	18.8678	0.612474
$950$	3.79547	0.123141
$951$	2.18669	0.0709082
$952$	0	0
$953$	−56.5989	−1.83342	−0.916709	−	0.399556i	$-0.869164\pi$
$953$	−56.5989	−1.83342	−0.916709	+	0.399556i	$0.869164\pi$
$954$	7.19219	0.232856
$955$	−7.44111	−0.240789
$956$	22.9073	0.740875
$957$	−5.87296	−0.189846
$958$	−6.28948	−0.203204
$959$	0	0
$960$	2.73965	0.0884218
$961$	13.0261	0.420198
$962$	6.69406	0.215825
$963$	0.841709	0.0271237
$964$	−5.68534	−0.183113
$965$	−0.239671	−0.00771530
$966$	0	0
$967$	27.2299	0.875656	0.437828	−	0.899059i	$-0.355748\pi$
$967$	27.2299	0.875656	0.437828	+	0.899059i	$0.355748\pi$
$968$	2.60333	0.0836741
$969$	26.1783	0.840968
$970$	8.87631	0.285001
$971$	41.4755	1.33101	0.665506	−	0.746393i	$-0.268216\pi$
$971$	41.4755	1.33101	0.665506	+	0.746393i	$0.268216\pi$
$972$	1.42085	0.0455739
$973$	0	0
$974$	−4.98360	−0.159685
$975$	5.44119	0.174258
$976$	−8.09290	−0.259047
$977$	−12.9587	−0.414586	−0.207293	−	0.978279i	$-0.566465\pi$
$977$	−12.9587	−0.414586	−0.207293	+	0.978279i	$0.566465\pi$
$978$	−8.88128	−0.283992
$979$	9.79460	0.313037
$980$	0	0
$981$	19.0476	0.608144
$982$	−6.42743	−0.205107
$983$	18.6194	0.593866	0.296933	−	0.954898i	$-0.404036\pi$
$983$	18.6194	0.593866	0.296933	+	0.954898i	$0.404036\pi$
$984$	8.98036	0.286283
$985$	−12.5099	−0.398598
$986$	−23.4596	−0.747106
$987$	0	0
$988$	−38.5581	−1.22670
$989$	−4.65146	−0.147908
$990$	0.761016	0.0241867
$991$	0.665486	0.0211399	0.0105699	−	0.999944i	$-0.496635\pi$
$991$	0.665486	0.0211399	0.0105699	+	0.999944i	$0.496635\pi$
$992$	38.8926	1.23484
$993$	−9.50240	−0.301550
$994$	0	0
$995$	−7.47820	−0.237075
$996$	7.58320	0.240283
$997$	37.9906	1.20317	0.601587	−	0.798807i	$-0.294535\pi$
$997$	37.9906	1.20317	0.601587	+	0.798807i	$0.294535\pi$
$998$	22.2476	0.704235
$999$	−1.61660	−0.0511469

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8085.2.a.ck.1.5		10
7.3	odd	6		1155.2.q.l.331.6	✓	20
7.5	odd	6		1155.2.q.l.991.6	yes	20
7.6	odd	2		8085.2.a.cn.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.q.l.331.6	✓	20	7.3	odd	6
1155.2.q.l.991.6	yes	20	7.5	odd	6
8085.2.a.ck.1.5		10	1.1	even	1	trivial
8085.2.a.cn.1.5		10	7.6	odd	2

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:	\( N \)	\(=\)	\( 8085 = 3 \cdot 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8085.a (trivial)

\(f(q)\)	\(=\)	\(q-0.761016 q^{2} -1.00000 q^{3} -1.42085 q^{4} -1.00000 q^{5} +0.761016 q^{6} +2.60333 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.761016 q^{2} -1.00000 q^{3} -1.42085 q^{4} -1.00000 q^{5} +0.761016 q^{6} +2.60333 q^{8} +1.00000 q^{9} +0.761016 q^{10} +1.00000 q^{11} +1.42085 q^{12} -5.44119 q^{13} +1.00000 q^{15} +0.860535 q^{16} +5.24891 q^{17} -0.761016 q^{18} -4.98737 q^{19} +1.42085 q^{20} -0.761016 q^{22} -0.495809 q^{23} -2.60333 q^{24} +1.00000 q^{25} +4.14084 q^{26} -1.00000 q^{27} +5.87296 q^{29} -0.761016 q^{30} -6.63522 q^{31} -5.86153 q^{32} -1.00000 q^{33} -3.99451 q^{34} -1.42085 q^{36} +1.61660 q^{37} +3.79547 q^{38} +5.44119 q^{39} -2.60333 q^{40} -3.44957 q^{41} +9.38154 q^{43} -1.42085 q^{44} -1.00000 q^{45} +0.377319 q^{46} +7.81669 q^{47} -0.860535 q^{48} -0.761016 q^{50} -5.24891 q^{51} +7.73114 q^{52} -9.45077 q^{53} +0.761016 q^{54} -1.00000 q^{55} +4.98737 q^{57} -4.46942 q^{58} +2.56369 q^{59} -1.42085 q^{60} -9.40449 q^{61} +5.04951 q^{62} +2.73965 q^{64} +5.44119 q^{65} +0.761016 q^{66} -7.51426 q^{67} -7.45794 q^{68} +0.495809 q^{69} +14.5924 q^{71} +2.60333 q^{72} -3.46758 q^{73} -1.23026 q^{74} -1.00000 q^{75} +7.08633 q^{76} -4.14084 q^{78} -14.1438 q^{79} -0.860535 q^{80} +1.00000 q^{81} +2.62518 q^{82} +5.33707 q^{83} -5.24891 q^{85} -7.13951 q^{86} -5.87296 q^{87} +2.60333 q^{88} +9.79460 q^{89} +0.761016 q^{90} +0.704473 q^{92} +6.63522 q^{93} -5.94863 q^{94} +4.98737 q^{95} +5.86153 q^{96} +11.6638 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{3} + 12 q^{4} - 10 q^{5} + 10 q^{9}+O(q^{10}) \) 10 * q - 10 * q^3 + 12 * q^4 - 10 * q^5 + 10 * q^9	\( 10 q - 10 q^{3} + 12 q^{4} - 10 q^{5} + 10 q^{9} + 10 q^{11} - 12 q^{12} - 4 q^{13} + 10 q^{15} + 24 q^{16} - 12 q^{17} - 9 q^{19} - 12 q^{20} - q^{23} + 10 q^{25} - 6 q^{26} - 10 q^{27} + 3 q^{29} - 9 q^{31} - 10 q^{32} - 10 q^{33} - 6 q^{34} + 12 q^{36} + 3 q^{37} - 42 q^{38} + 4 q^{39} - 3 q^{41} + 12 q^{44} - 10 q^{45} - 22 q^{46} - 21 q^{47} - 24 q^{48} + 12 q^{51} - 24 q^{52} - 5 q^{53} - 10 q^{55} + 9 q^{57} - 26 q^{58} - 16 q^{59} + 12 q^{60} - 20 q^{61} + 18 q^{62} + 70 q^{64} + 4 q^{65} - q^{67} - 30 q^{68} + q^{69} + 22 q^{71} + q^{73} - 34 q^{74} - 10 q^{75} + 28 q^{76} + 6 q^{78} + 19 q^{79} - 24 q^{80} + 10 q^{81} - 32 q^{82} - 20 q^{83} + 12 q^{85} - 3 q^{87} - 18 q^{89} - 8 q^{92} + 9 q^{93} + 6 q^{94} + 9 q^{95} + 10 q^{96} - 6 q^{97} + 10 q^{99}+O(q^{100}) \) 10 * q - 10 * q^3 + 12 * q^4 - 10 * q^5 + 10 * q^9 + 10 * q^11 - 12 * q^12 - 4 * q^13 + 10 * q^15 + 24 * q^16 - 12 * q^17 - 9 * q^19 - 12 * q^20 - q^23 + 10 * q^25 - 6 * q^26 - 10 * q^27 + 3 * q^29 - 9 * q^31 - 10 * q^32 - 10 * q^33 - 6 * q^34 + 12 * q^36 + 3 * q^37 - 42 * q^38 + 4 * q^39 - 3 * q^41 + 12 * q^44 - 10 * q^45 - 22 * q^46 - 21 * q^47 - 24 * q^48 + 12 * q^51 - 24 * q^52 - 5 * q^53 - 10 * q^55 + 9 * q^57 - 26 * q^58 - 16 * q^59 + 12 * q^60 - 20 * q^61 + 18 * q^62 + 70 * q^64 + 4 * q^65 - q^67 - 30 * q^68 + q^69 + 22 * q^71 + q^73 - 34 * q^74 - 10 * q^75 + 28 * q^76 + 6 * q^78 + 19 * q^79 - 24 * q^80 + 10 * q^81 - 32 * q^82 - 20 * q^83 + 12 * q^85 - 3 * q^87 - 18 * q^89 - 8 * q^92 + 9 * q^93 + 6 * q^94 + 9 * q^95 + 10 * q^96 - 6 * q^97 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more