LMFDB - Embedded newform 3381.2.a.bl.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3381,2,Mod(1,3381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3381, 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("3381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3381 = 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3381.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:	$26.9974209234$
Analytic rank:	$0$
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} - 4x^{9} - 6x^{8} + 36x^{7} + x^{6} - 100x^{5} + 26x^{4} + 108x^{3} - 33x^{2} - 36x + 14 $ x^10 - 4x^9 - 6x^8 + 36x^7 + x^6 - 100x^5 + 26x^4 + 108x^3 - 33x^2 - 36x + 14
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			1.4
Root			$-0.881528$ of defining polynomial
Character	$\chi$	$=$	3381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.881528 q^{2} +1.00000 q^{3} -1.22291 q^{4} -2.92694 q^{5} -0.881528 q^{6} +2.84108 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.881528 q^{2} +1.00000 q^{3} -1.22291 q^{4} -2.92694 q^{5} -0.881528 q^{6} +2.84108 q^{8} +1.00000 q^{9} +2.58018 q^{10} +3.24789 q^{11} -1.22291 q^{12} +1.62727 q^{13} -2.92694 q^{15} -0.0586778 q^{16} +4.45527 q^{17} -0.881528 q^{18} -1.70177 q^{19} +3.57938 q^{20} -2.86311 q^{22} -1.00000 q^{23} +2.84108 q^{24} +3.56697 q^{25} -1.43449 q^{26} +1.00000 q^{27} -8.39756 q^{29} +2.58018 q^{30} +3.59820 q^{31} -5.63044 q^{32} +3.24789 q^{33} -3.92745 q^{34} -1.22291 q^{36} -1.06269 q^{37} +1.50016 q^{38} +1.62727 q^{39} -8.31568 q^{40} +6.59494 q^{41} -6.47859 q^{43} -3.97188 q^{44} -2.92694 q^{45} +0.881528 q^{46} -5.36000 q^{47} -0.0586778 q^{48} -3.14438 q^{50} +4.45527 q^{51} -1.99001 q^{52} -0.262277 q^{53} -0.881528 q^{54} -9.50639 q^{55} -1.70177 q^{57} +7.40268 q^{58} +4.00977 q^{59} +3.57938 q^{60} +3.00348 q^{61} -3.17191 q^{62} +5.08075 q^{64} -4.76293 q^{65} -2.86311 q^{66} +3.32578 q^{67} -5.44839 q^{68} -1.00000 q^{69} +1.66025 q^{71} +2.84108 q^{72} +0.422209 q^{73} +0.936788 q^{74} +3.56697 q^{75} +2.08111 q^{76} -1.43449 q^{78} +0.231138 q^{79} +0.171746 q^{80} +1.00000 q^{81} -5.81362 q^{82} +17.3276 q^{83} -13.0403 q^{85} +5.71106 q^{86} -8.39756 q^{87} +9.22754 q^{88} +0.971997 q^{89} +2.58018 q^{90} +1.22291 q^{92} +3.59820 q^{93} +4.72499 q^{94} +4.98097 q^{95} -5.63044 q^{96} -19.0945 q^{97} +3.24789 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} + 10 q^{3} + 8 q^{4} + 4 q^{5} + 4 q^{6} + 12 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 4 * q^2 + 10 * q^3 + 8 * q^4 + 4 * q^5 + 4 * q^6 + 12 * q^8 + 10 * q^9	$ 10 q + 4 q^{2} + 10 q^{3} + 8 q^{4} + 4 q^{5} + 4 q^{6} + 12 q^{8} + 10 q^{9} + 8 q^{10} + 2 q^{11} + 8 q^{12} + 4 q^{15} + 4 q^{16} + 12 q^{17} + 4 q^{18} + 26 q^{19} + 24 q^{20} - 8 q^{22} - 10 q^{23} + 12 q^{24} - 2 q^{25} + 4 q^{26} + 10 q^{27} + 16 q^{29} + 8 q^{30} + 12 q^{31} + 8 q^{32} + 2 q^{33} + 28 q^{34} + 8 q^{36} - 8 q^{37} + 32 q^{38} + 4 q^{40} + 10 q^{41} - 4 q^{43} - 16 q^{44} + 4 q^{45} - 4 q^{46} + 2 q^{47} + 4 q^{48} - 8 q^{50} + 12 q^{51} + 24 q^{52} + 14 q^{53} + 4 q^{54} + 16 q^{55} + 26 q^{57} - 8 q^{58} + 38 q^{59} + 24 q^{60} + 14 q^{61} - 8 q^{62} + 8 q^{64} + 12 q^{65} - 8 q^{66} + 8 q^{68} - 10 q^{69} + 24 q^{71} + 12 q^{72} + 8 q^{73} - 8 q^{74} - 2 q^{75} + 64 q^{76} + 4 q^{78} - 16 q^{79} + 28 q^{80} + 10 q^{81} - 40 q^{82} + 28 q^{83} - 4 q^{85} + 20 q^{86} + 16 q^{87} - 68 q^{88} + 32 q^{89} + 8 q^{90} - 8 q^{92} + 12 q^{93} + 56 q^{94} + 8 q^{95} + 8 q^{96} + 4 q^{97} + 2 q^{99}+O(q^{100}) $ 10 * q + 4 * q^2 + 10 * q^3 + 8 * q^4 + 4 * q^5 + 4 * q^6 + 12 * q^8 + 10 * q^9 + 8 * q^10 + 2 * q^11 + 8 * q^12 + 4 * q^15 + 4 * q^16 + 12 * q^17 + 4 * q^18 + 26 * q^19 + 24 * q^20 - 8 * q^22 - 10 * q^23 + 12 * q^24 - 2 * q^25 + 4 * q^26 + 10 * q^27 + 16 * q^29 + 8 * q^30 + 12 * q^31 + 8 * q^32 + 2 * q^33 + 28 * q^34 + 8 * q^36 - 8 * q^37 + 32 * q^38 + 4 * q^40 + 10 * q^41 - 4 * q^43 - 16 * q^44 + 4 * q^45 - 4 * q^46 + 2 * q^47 + 4 * q^48 - 8 * q^50 + 12 * q^51 + 24 * q^52 + 14 * q^53 + 4 * q^54 + 16 * q^55 + 26 * q^57 - 8 * q^58 + 38 * q^59 + 24 * q^60 + 14 * q^61 - 8 * q^62 + 8 * q^64 + 12 * q^65 - 8 * q^66 + 8 * q^68 - 10 * q^69 + 24 * q^71 + 12 * q^72 + 8 * q^73 - 8 * q^74 - 2 * q^75 + 64 * q^76 + 4 * q^78 - 16 * q^79 + 28 * q^80 + 10 * q^81 - 40 * q^82 + 28 * q^83 - 4 * q^85 + 20 * q^86 + 16 * q^87 - 68 * q^88 + 32 * q^89 + 8 * q^90 - 8 * q^92 + 12 * q^93 + 56 * q^94 + 8 * q^95 + 8 * q^96 + 4 * 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 $

$2$	−0.881528	−0.623334	−0.311667	−	0.950191i	$-0.600887\pi$
$2$	−0.881528	−0.623334	−0.311667	+	0.950191i	$0.600887\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.22291	−0.611454
$5$	−2.92694	−1.30897	−0.654483	−	0.756076i	$-0.727114\pi$
$5$	−2.92694	−1.30897	−0.654483	+	0.756076i	$0.727114\pi$
$6$	−0.881528	−0.359882
$7$	0	0
$7$	0	0
$8$	2.84108	1.00447
$9$	1.00000	0.333333
$10$	2.58018	0.815924
$11$	3.24789	0.979277	0.489639	−	0.871925i	$-0.337129\pi$
$11$	3.24789	0.979277	0.489639	+	0.871925i	$0.337129\pi$
$12$	−1.22291	−0.353023
$13$	1.62727	0.451324	0.225662	−	0.974206i	$-0.427545\pi$
$13$	1.62727	0.451324	0.225662	+	0.974206i	$0.427545\pi$
$14$	0	0
$15$	−2.92694	−0.755732
$16$	−0.0586778	−0.0146695
$17$	4.45527	1.08056	0.540281	−	0.841484i	$-0.318318\pi$
$17$	4.45527	1.08056	0.540281	+	0.841484i	$0.318318\pi$
$18$	−0.881528	−0.207778
$19$	−1.70177	−0.390413	−0.195206	−	0.980762i	$-0.562538\pi$
$19$	−1.70177	−0.390413	−0.195206	+	0.980762i	$0.562538\pi$
$20$	3.57938	0.800373
$21$	0	0
$22$	−2.86311	−0.610417
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.84108	0.579934
$25$	3.56697	0.713394
$26$	−1.43449	−0.281326
$27$	1.00000	0.192450
$28$	0	0
$29$	−8.39756	−1.55939	−0.779694	−	0.626161i	$-0.784625\pi$
$29$	−8.39756	−1.55939	−0.779694	+	0.626161i	$0.784625\pi$
$30$	2.58018	0.471074
$31$	3.59820	0.646255	0.323128	−	0.946355i	$-0.395266\pi$
$31$	3.59820	0.646255	0.323128	+	0.946355i	$0.395266\pi$
$32$	−5.63044	−0.995331
$33$	3.24789	0.565386
$34$	−3.92745	−0.673552
$35$	0	0
$36$	−1.22291	−0.203818
$37$	−1.06269	−0.174705	−0.0873523	−	0.996177i	$-0.527841\pi$
$37$	−1.06269	−0.174705	−0.0873523	+	0.996177i	$0.527841\pi$
$38$	1.50016	0.243358
$39$	1.62727	0.260572
$40$	−8.31568	−1.31482
$41$	6.59494	1.02996	0.514978	−	0.857203i	$-0.327800\pi$
$41$	6.59494	1.02996	0.514978	+	0.857203i	$0.327800\pi$
$42$	0	0
$43$	−6.47859	−0.987975	−0.493988	−	0.869469i	$-0.664461\pi$
$43$	−6.47859	−0.987975	−0.493988	+	0.869469i	$0.664461\pi$
$44$	−3.97188	−0.598783
$45$	−2.92694	−0.436322
$46$	0.881528	0.129974
$47$	−5.36000	−0.781837	−0.390918	−	0.920425i	$-0.627843\pi$
$47$	−5.36000	−0.781837	−0.390918	+	0.920425i	$0.627843\pi$
$48$	−0.0586778	−0.00846941
$49$	0	0
$50$	−3.14438	−0.444683
$51$	4.45527	0.623863
$52$	−1.99001	−0.275964
$53$	−0.262277	−0.0360265	−0.0180133	−	0.999838i	$-0.505734\pi$
$53$	−0.262277	−0.0360265	−0.0180133	+	0.999838i	$0.505734\pi$
$54$	−0.881528	−0.119961
$55$	−9.50639	−1.28184
$56$	0	0
$57$	−1.70177	−0.225405
$58$	7.40268	0.972020
$59$	4.00977	0.522028	0.261014	−	0.965335i	$-0.415943\pi$
$59$	4.00977	0.522028	0.261014	+	0.965335i	$0.415943\pi$
$60$	3.57938	0.462096
$61$	3.00348	0.384556	0.192278	−	0.981340i	$-0.438412\pi$
$61$	3.00348	0.384556	0.192278	+	0.981340i	$0.438412\pi$
$62$	−3.17191	−0.402833
$63$	0	0
$64$	5.08075	0.635093
$65$	−4.76293	−0.590768
$66$	−2.86311	−0.352424
$67$	3.32578	0.406309	0.203155	−	0.979147i	$-0.434881\pi$
$67$	3.32578	0.406309	0.203155	+	0.979147i	$0.434881\pi$
$68$	−5.44839	−0.660715
$69$	−1.00000	−0.120386
$70$	0	0
$71$	1.66025	0.197036	0.0985178	−	0.995135i	$-0.468590\pi$
$71$	1.66025	0.197036	0.0985178	+	0.995135i	$0.468590\pi$
$72$	2.84108	0.334825
$73$	0.422209	0.0494159	0.0247079	−	0.999695i	$-0.492134\pi$
$73$	0.422209	0.0494159	0.0247079	+	0.999695i	$0.492134\pi$
$74$	0.936788	0.108899
$75$	3.56697	0.411878
$76$	2.08111	0.238719
$77$	0	0
$78$	−1.43449	−0.162424
$79$	0.231138	0.0260050	0.0130025	−	0.999915i	$-0.495861\pi$
$79$	0.231138	0.0260050	0.0130025	+	0.999915i	$0.495861\pi$
$80$	0.171746	0.0192018
$81$	1.00000	0.111111
$82$	−5.81362	−0.642007
$83$	17.3276	1.90195	0.950976	−	0.309263i	$-0.100082\pi$
$83$	17.3276	1.90195	0.950976	+	0.309263i	$0.100082\pi$
$84$	0	0
$85$	−13.0403	−1.41442
$86$	5.71106	0.615839
$87$	−8.39756	−0.900313
$88$	9.22754	0.983659
$89$	0.971997	0.103032	0.0515158	−	0.998672i	$-0.483595\pi$
$89$	0.971997	0.103032	0.0515158	+	0.998672i	$0.483595\pi$
$90$	2.58018	0.271975
$91$	0	0
$92$	1.22291	0.127497
$93$	3.59820	0.373116
$94$	4.72499	0.487346
$95$	4.98097	0.511037
$96$	−5.63044	−0.574655
$97$	−19.0945	−1.93875	−0.969377	−	0.245576i	$-0.921023\pi$
$97$	−19.0945	−1.93875	−0.969377	+	0.245576i	$0.921023\pi$
$98$	0	0
$99$	3.24789	0.326426
$100$	−4.36208	−0.436208
$101$	6.15472	0.612417	0.306209	−	0.951964i	$-0.400940\pi$
$101$	6.15472	0.612417	0.306209	+	0.951964i	$0.400940\pi$
$102$	−3.92745	−0.388875
$103$	2.54714	0.250977	0.125488	−	0.992095i	$-0.459950\pi$
$103$	2.54714	0.250977	0.125488	+	0.992095i	$0.459950\pi$
$104$	4.62322	0.453344
$105$	0	0
$106$	0.231205	0.0224566
$107$	−7.64216	−0.738796	−0.369398	−	0.929271i	$-0.620436\pi$
$107$	−7.64216	−0.738796	−0.369398	+	0.929271i	$0.620436\pi$
$108$	−1.22291	−0.117674
$109$	0.290264	0.0278023	0.0139011	−	0.999903i	$-0.495575\pi$
$109$	0.290264	0.0278023	0.0139011	+	0.999903i	$0.495575\pi$
$110$	8.38015	0.799016
$111$	−1.06269	−0.100866
$112$	0	0
$113$	9.02604	0.849098	0.424549	−	0.905405i	$-0.360433\pi$
$113$	9.02604	0.849098	0.424549	+	0.905405i	$0.360433\pi$
$114$	1.50016	0.140503
$115$	2.92694	0.272938
$116$	10.2694	0.953494
$117$	1.62727	0.150441
$118$	−3.53472	−0.325398
$119$	0	0
$120$	−8.31568	−0.759114
$121$	−0.451179	−0.0410162
$122$	−2.64765	−0.239707
$123$	6.59494	0.594645
$124$	−4.40026	−0.395155
$125$	4.19439	0.375158
$126$	0	0
$127$	5.04761	0.447903	0.223952	−	0.974600i	$-0.428104\pi$
$127$	5.04761	0.447903	0.223952	+	0.974600i	$0.428104\pi$
$128$	6.78206	0.599455
$129$	−6.47859	−0.570408
$130$	4.19865	0.368246
$131$	−0.519029	−0.0453478	−0.0226739	−	0.999743i	$-0.507218\pi$
$131$	−0.519029	−0.0453478	−0.0226739	+	0.999743i	$0.507218\pi$
$132$	−3.97188	−0.345708
$133$	0	0
$134$	−2.93177	−0.253266
$135$	−2.92694	−0.251911
$136$	12.6578	1.08540
$137$	21.6200	1.84712	0.923559	−	0.383456i	$-0.125266\pi$
$137$	21.6200	1.84712	0.923559	+	0.383456i	$0.125266\pi$
$138$	0.881528	0.0750406
$139$	12.4631	1.05710	0.528552	−	0.848901i	$-0.322735\pi$
$139$	12.4631	1.05710	0.528552	+	0.848901i	$0.322735\pi$
$140$	0	0
$141$	−5.36000	−0.451394
$142$	−1.46356	−0.122819
$143$	5.28521	0.441971
$144$	−0.0586778	−0.00488982
$145$	24.5791	2.04119
$146$	−0.372189	−0.0308026
$147$	0	0
$148$	1.29957	0.106824
$149$	11.8851	0.973662	0.486831	−	0.873496i	$-0.338153\pi$
$149$	11.8851	0.973662	0.486831	+	0.873496i	$0.338153\pi$
$150$	−3.14438	−0.256738
$151$	−7.09280	−0.577204	−0.288602	−	0.957449i	$-0.593190\pi$
$151$	−7.09280	−0.577204	−0.288602	+	0.957449i	$0.593190\pi$
$152$	−4.83487	−0.392160
$153$	4.45527	0.360188
$154$	0	0
$155$	−10.5317	−0.845926
$156$	−1.99001	−0.159328
$157$	−1.20726	−0.0963496	−0.0481748	−	0.998839i	$-0.515340\pi$
$157$	−1.20726	−0.0963496	−0.0481748	+	0.998839i	$0.515340\pi$
$158$	−0.203754	−0.0162098
$159$	−0.262277	−0.0207999
$160$	16.4800	1.30286
$161$	0	0
$162$	−0.881528	−0.0692594
$163$	7.61049	0.596099	0.298050	−	0.954550i	$-0.403664\pi$
$163$	7.61049	0.596099	0.298050	+	0.954550i	$0.403664\pi$
$164$	−8.06500	−0.629771
$165$	−9.50639	−0.740071
$166$	−15.2748	−1.18555
$167$	20.5372	1.58922	0.794610	−	0.607120i	$-0.207675\pi$
$167$	20.5372	1.58922	0.794610	+	0.607120i	$0.207675\pi$
$168$	0	0
$169$	−10.3520	−0.796306
$170$	11.4954	0.881657
$171$	−1.70177	−0.130138
$172$	7.92272	0.604102
$173$	13.1601	1.00054	0.500271	−	0.865869i	$-0.333234\pi$
$173$	13.1601	1.00054	0.500271	+	0.865869i	$0.333234\pi$
$174$	7.40268	0.561196
$175$	0	0
$176$	−0.190579	−0.0143655
$177$	4.00977	0.301393
$178$	−0.856843	−0.0642231
$179$	17.9134	1.33891	0.669454	−	0.742853i	$-0.266528\pi$
$179$	17.9134	1.33891	0.669454	+	0.742853i	$0.266528\pi$
$180$	3.57938	0.266791
$181$	10.0629	0.747972	0.373986	−	0.927434i	$-0.377991\pi$
$181$	10.0629	0.747972	0.373986	+	0.927434i	$0.377991\pi$
$182$	0	0
$183$	3.00348	0.222024
$184$	−2.84108	−0.209447
$185$	3.11042	0.228683
$186$	−3.17191	−0.232576
$187$	14.4703	1.05817
$188$	6.55479	0.478057
$189$	0	0
$190$	−4.39087	−0.318547
$191$	−5.15442	−0.372961	−0.186480	−	0.982459i	$-0.559708\pi$
$191$	−5.15442	−0.372961	−0.186480	+	0.982459i	$0.559708\pi$
$192$	5.08075	0.366671
$193$	−22.6017	−1.62690	−0.813452	−	0.581632i	$-0.802414\pi$
$193$	−22.6017	−1.62690	−0.813452	+	0.581632i	$0.802414\pi$
$194$	16.8324	1.20849
$195$	−4.76293	−0.341080
$196$	0	0
$197$	18.5839	1.32405	0.662023	−	0.749484i	$-0.269698\pi$
$197$	18.5839	1.32405	0.662023	+	0.749484i	$0.269698\pi$
$198$	−2.86311	−0.203472
$199$	19.3545	1.37201	0.686003	−	0.727599i	$-0.259364\pi$
$199$	19.3545	1.37201	0.686003	+	0.727599i	$0.259364\pi$
$200$	10.1341	0.716586
$201$	3.32578	0.234583
$202$	−5.42555	−0.381741
$203$	0	0
$204$	−5.44839	−0.381464
$205$	−19.3030	−1.34818
$206$	−2.24537	−0.156442
$207$	−1.00000	−0.0695048
$208$	−0.0954848	−0.00662068
$209$	−5.52717	−0.382322
$210$	0	0
$211$	−15.2356	−1.04886	−0.524430	−	0.851454i	$-0.675721\pi$
$211$	−15.2356	−1.04886	−0.524430	+	0.851454i	$0.675721\pi$
$212$	0.320741	0.0220286
$213$	1.66025	0.113759
$214$	6.73678	0.460517
$215$	18.9624	1.29323
$216$	2.84108	0.193311
$217$	0	0
$218$	−0.255876	−0.0173301
$219$	0.422209	0.0285303
$220$	11.6254	0.783787
$221$	7.24994	0.487684
$222$	0.936788	0.0628731
$223$	−8.81267	−0.590140	−0.295070	−	0.955476i	$-0.595343\pi$
$223$	−8.81267	−0.590140	−0.295070	+	0.955476i	$0.595343\pi$
$224$	0	0
$225$	3.56697	0.237798
$226$	−7.95670	−0.529272
$227$	−2.78738	−0.185005	−0.0925024	−	0.995712i	$-0.529487\pi$
$227$	−2.78738	−0.185005	−0.0925024	+	0.995712i	$0.529487\pi$
$228$	2.08111	0.137825
$229$	−14.0945	−0.931388	−0.465694	−	0.884946i	$-0.654195\pi$
$229$	−14.0945	−0.931388	−0.465694	+	0.884946i	$0.654195\pi$
$230$	−2.58018	−0.170132
$231$	0	0
$232$	−23.8582	−1.56637
$233$	26.1134	1.71075	0.855373	−	0.518013i	$-0.173328\pi$
$233$	26.1134	1.71075	0.855373	+	0.518013i	$0.173328\pi$
$234$	−1.43449	−0.0937753
$235$	15.6884	1.02340
$236$	−4.90358	−0.319196
$237$	0.231138	0.0150140
$238$	0	0
$239$	−17.4241	−1.12707	−0.563536	−	0.826091i	$-0.690559\pi$
$239$	−17.4241	−1.12707	−0.563536	+	0.826091i	$0.690559\pi$
$240$	0.171746	0.0110862
$241$	21.4631	1.38256	0.691279	−	0.722588i	$-0.257047\pi$
$241$	21.4631	1.38256	0.691279	+	0.722588i	$0.257047\pi$
$242$	0.397727	0.0255668
$243$	1.00000	0.0641500
$244$	−3.67298	−0.235139
$245$	0	0
$246$	−5.81362	−0.370663
$247$	−2.76924	−0.176203
$248$	10.2228	0.649147
$249$	17.3276	1.09809
$250$	−3.69747	−0.233849
$251$	23.9859	1.51397	0.756987	−	0.653430i	$-0.226671\pi$
$251$	23.9859	1.51397	0.756987	+	0.653430i	$0.226671\pi$
$252$	0	0
$253$	−3.24789	−0.204193
$254$	−4.44961	−0.279193
$255$	−13.0403	−0.816616
$256$	−16.1401	−1.00875
$257$	−14.4595	−0.901961	−0.450980	−	0.892534i	$-0.648926\pi$
$257$	−14.4595	−0.901961	−0.450980	+	0.892534i	$0.648926\pi$
$258$	5.71106	0.355555
$259$	0	0
$260$	5.82462	0.361228
$261$	−8.39756	−0.519796
$262$	0.457539	0.0282668
$263$	−18.8577	−1.16281	−0.581407	−	0.813613i	$-0.697498\pi$
$263$	−18.8577	−1.16281	−0.581407	+	0.813613i	$0.697498\pi$
$264$	9.22754	0.567916
$265$	0.767669	0.0471575
$266$	0	0
$267$	0.971997	0.0594853
$268$	−4.06713	−0.248439
$269$	10.9129	0.665371	0.332686	−	0.943038i	$-0.392045\pi$
$269$	10.9129	0.665371	0.332686	+	0.943038i	$0.392045\pi$
$270$	2.58018	0.157025
$271$	20.5899	1.25075	0.625374	−	0.780326i	$-0.284947\pi$
$271$	20.5899	1.25075	0.625374	+	0.780326i	$0.284947\pi$
$272$	−0.261426	−0.0158513
$273$	0	0
$274$	−19.0586	−1.15137
$275$	11.5851	0.698611
$276$	1.22291	0.0736104
$277$	−6.91541	−0.415506	−0.207753	−	0.978181i	$-0.566615\pi$
$277$	−6.91541	−0.415506	−0.207753	+	0.978181i	$0.566615\pi$
$278$	−10.9865	−0.658929
$279$	3.59820	0.215418
$280$	0	0
$281$	8.93818	0.533207	0.266604	−	0.963806i	$-0.414099\pi$
$281$	8.93818	0.533207	0.266604	+	0.963806i	$0.414099\pi$
$282$	4.72499	0.281369
$283$	26.5221	1.57658	0.788288	−	0.615307i	$-0.210968\pi$
$283$	26.5221	1.57658	0.788288	+	0.615307i	$0.210968\pi$
$284$	−2.03034	−0.120478
$285$	4.98097	0.295047
$286$	−4.65906	−0.275496
$287$	0	0
$288$	−5.63044	−0.331777
$289$	2.84946	0.167615
$290$	−21.6672	−1.27234
$291$	−19.0945	−1.11934
$292$	−0.516324	−0.0302155
$293$	−33.1128	−1.93447	−0.967235	−	0.253885i	$-0.918292\pi$
$293$	−33.1128	−1.93447	−0.967235	+	0.253885i	$0.918292\pi$
$294$	0	0
$295$	−11.7364	−0.683317
$296$	−3.01918	−0.175486
$297$	3.24789	0.188462
$298$	−10.4770	−0.606917
$299$	−1.62727	−0.0941076
$300$	−4.36208	−0.251845
$301$	0	0
$302$	6.25250	0.359791
$303$	6.15472	0.353579
$304$	0.0998561	0.00572714
$305$	−8.79101	−0.503372
$306$	−3.92745	−0.224517
$307$	3.58909	0.204840	0.102420	−	0.994741i	$-0.467341\pi$
$307$	3.58909	0.204840	0.102420	+	0.994741i	$0.467341\pi$
$308$	0	0
$309$	2.54714	0.144902
$310$	9.28399	0.527295
$311$	−24.6438	−1.39742	−0.698711	−	0.715404i	$-0.746243\pi$
$311$	−24.6438	−1.39742	−0.698711	+	0.715404i	$0.746243\pi$
$312$	4.62322	0.261738
$313$	13.2168	0.747058	0.373529	−	0.927618i	$-0.378148\pi$
$313$	13.2168	0.747058	0.373529	+	0.927618i	$0.378148\pi$
$314$	1.06423	0.0600580
$315$	0	0
$316$	−0.282660	−0.0159009
$317$	26.5348	1.49034	0.745172	−	0.666872i	$-0.232367\pi$
$317$	26.5348	1.49034	0.745172	+	0.666872i	$0.232367\pi$
$318$	0.231205	0.0129653
$319$	−27.2744	−1.52707
$320$	−14.8710	−0.831316
$321$	−7.64216	−0.426544
$322$	0	0
$323$	−7.58185	−0.421865
$324$	−1.22291	−0.0679394
$325$	5.80443	0.321972
$326$	−6.70886	−0.371569
$327$	0.290264	0.0160517
$328$	18.7368	1.03456
$329$	0	0
$330$	8.38015	0.461312
$331$	−9.61324	−0.528391	−0.264196	−	0.964469i	$-0.585106\pi$
$331$	−9.61324	−0.528391	−0.264196	+	0.964469i	$0.585106\pi$
$332$	−21.1901	−1.16296
$333$	−1.06269	−0.0582349
$334$	−18.1042	−0.990615
$335$	−9.73437	−0.531845
$336$	0	0
$337$	30.5517	1.66426	0.832130	−	0.554581i	$-0.187121\pi$
$337$	30.5517	1.66426	0.832130	+	0.554581i	$0.187121\pi$
$338$	9.12556	0.496365
$339$	9.02604	0.490227
$340$	15.9471	0.864853
$341$	11.6866	0.632863
$342$	1.50016	0.0811192
$343$	0	0
$344$	−18.4062	−0.992396
$345$	2.92694	0.157581
$346$	−11.6010	−0.623672
$347$	−22.1351	−1.18827	−0.594136	−	0.804364i	$-0.702506\pi$
$347$	−22.1351	−1.18827	−0.594136	+	0.804364i	$0.702506\pi$
$348$	10.2694	0.550500
$349$	−30.7222	−1.64452	−0.822262	−	0.569110i	$-0.807288\pi$
$349$	−30.7222	−1.64452	−0.822262	+	0.569110i	$0.807288\pi$
$350$	0	0
$351$	1.62727	0.0868574
$352$	−18.2871	−0.974705
$353$	36.5187	1.94370	0.971848	−	0.235609i	$-0.0757084\pi$
$353$	36.5187	1.94370	0.971848	+	0.235609i	$0.0757084\pi$
$354$	−3.53472	−0.187868
$355$	−4.85945	−0.257913
$356$	−1.18866	−0.0629991
$357$	0	0
$358$	−15.7911	−0.834588
$359$	−33.3957	−1.76256	−0.881278	−	0.472597i	$-0.843317\pi$
$359$	−33.3957	−1.76256	−0.881278	+	0.472597i	$0.843317\pi$
$360$	−8.31568	−0.438275
$361$	−16.1040	−0.847578
$362$	−8.87076	−0.466237
$363$	−0.451179	−0.0236807
$364$	0	0
$365$	−1.23578	−0.0646837
$366$	−2.64765	−0.138395
$367$	−6.34000	−0.330945	−0.165473	−	0.986214i	$-0.552915\pi$
$367$	−6.34000	−0.330945	−0.165473	+	0.986214i	$0.552915\pi$
$368$	0.0586778	0.00305879
$369$	6.59494	0.343319
$370$	−2.74192	−0.142546
$371$	0	0
$372$	−4.40026	−0.228143
$373$	−16.3697	−0.847590	−0.423795	−	0.905758i	$-0.639302\pi$
$373$	−16.3697	−0.847590	−0.423795	+	0.905758i	$0.639302\pi$
$374$	−12.7559	−0.659594
$375$	4.19439	0.216597
$376$	−15.2282	−0.785335
$377$	−13.6651	−0.703789
$378$	0	0
$379$	25.4173	1.30560	0.652799	−	0.757531i	$-0.273595\pi$
$379$	25.4173	1.30560	0.652799	+	0.757531i	$0.273595\pi$
$380$	−6.09127	−0.312476
$381$	5.04761	0.258597
$382$	4.54377	0.232479
$383$	−12.8881	−0.658549	−0.329274	−	0.944234i	$-0.606804\pi$
$383$	−12.8881	−0.658549	−0.329274	+	0.944234i	$0.606804\pi$
$384$	6.78206	0.346096
$385$	0	0
$386$	19.9240	1.01410
$387$	−6.47859	−0.329325
$388$	23.3509	1.18546
$389$	−31.0378	−1.57368	−0.786841	−	0.617156i	$-0.788285\pi$
$389$	−31.0378	−1.57368	−0.786841	+	0.617156i	$0.788285\pi$
$390$	4.19865	0.212607
$391$	−4.45527	−0.225313
$392$	0	0
$393$	−0.519029	−0.0261816
$394$	−16.3822	−0.825323
$395$	−0.676526	−0.0340397
$396$	−3.97188	−0.199594
$397$	21.6702	1.08759	0.543797	−	0.839216i	$-0.316986\pi$
$397$	21.6702	1.08759	0.543797	+	0.839216i	$0.316986\pi$
$398$	−17.0616	−0.855219
$399$	0	0
$400$	−0.209302	−0.0104651
$401$	9.45045	0.471933	0.235966	−	0.971761i	$-0.424174\pi$
$401$	9.45045	0.471933	0.235966	+	0.971761i	$0.424174\pi$
$402$	−2.93177	−0.146223
$403$	5.85525	0.291671
$404$	−7.52665	−0.374465
$405$	−2.92694	−0.145441
$406$	0	0
$407$	−3.45149	−0.171084
$408$	12.6578	0.626655
$409$	17.7125	0.875827	0.437914	−	0.899017i	$-0.355718\pi$
$409$	17.7125	0.875827	0.437914	+	0.899017i	$0.355718\pi$
$410$	17.0161	0.840366
$411$	21.6200	1.06643
$412$	−3.11491	−0.153461
$413$	0	0
$414$	0.881528	0.0433247
$415$	−50.7169	−2.48959
$416$	−9.16226	−0.449217
$417$	12.4631	0.610319
$418$	4.87235	0.238315
$419$	16.2508	0.793905	0.396953	−	0.917839i	$-0.370068\pi$
$419$	16.2508	0.793905	0.396953	+	0.917839i	$0.370068\pi$
$420$	0	0
$421$	28.5097	1.38948	0.694739	−	0.719262i	$-0.255520\pi$
$421$	28.5097	1.38948	0.694739	+	0.719262i	$0.255520\pi$
$422$	13.4306	0.653790
$423$	−5.36000	−0.260612
$424$	−0.745151	−0.0361877
$425$	15.8918	0.770867
$426$	−1.46356	−0.0709096
$427$	0	0
$428$	9.34567	0.451740
$429$	5.28521	0.255172
$430$	−16.7159	−0.806113
$431$	17.9299	0.863653	0.431827	−	0.901957i	$-0.357869\pi$
$431$	17.9299	0.863653	0.431827	+	0.901957i	$0.357869\pi$
$432$	−0.0586778	−0.00282314
$433$	−3.90105	−0.187472	−0.0937362	−	0.995597i	$-0.529881\pi$
$433$	−3.90105	−0.187472	−0.0937362	+	0.995597i	$0.529881\pi$
$434$	0	0
$435$	24.5791	1.17848
$436$	−0.354967	−0.0169998
$437$	1.70177	0.0814066
$438$	−0.372189	−0.0177839
$439$	−36.5472	−1.74430	−0.872151	−	0.489238i	$-0.837275\pi$
$439$	−36.5472	−1.74430	−0.872151	+	0.489238i	$0.837275\pi$
$440$	−27.0085	−1.28758
$441$	0	0
$442$	−6.39103	−0.303990
$443$	23.9266	1.13679	0.568393	−	0.822757i	$-0.307565\pi$
$443$	23.9266	1.13679	0.568393	+	0.822757i	$0.307565\pi$
$444$	1.29957	0.0616748
$445$	−2.84498	−0.134865
$446$	7.76862	0.367855
$447$	11.8851	0.562144
$448$	0	0
$449$	1.06561	0.0502893	0.0251446	−	0.999684i	$-0.491995\pi$
$449$	1.06561	0.0502893	0.0251446	+	0.999684i	$0.491995\pi$
$450$	−3.14438	−0.148228
$451$	21.4197	1.00861
$452$	−11.0380	−0.519185
$453$	−7.09280	−0.333249
$454$	2.45715	0.115320
$455$	0	0
$456$	−4.83487	−0.226413
$457$	−19.4729	−0.910903	−0.455452	−	0.890261i	$-0.650522\pi$
$457$	−19.4729	−0.910903	−0.455452	+	0.890261i	$0.650522\pi$
$458$	12.4247	0.580566
$459$	4.45527	0.207954
$460$	−3.57938	−0.166889
$461$	33.3763	1.55449	0.777245	−	0.629198i	$-0.216617\pi$
$461$	33.3763	1.55449	0.777245	+	0.629198i	$0.216617\pi$
$462$	0	0
$463$	4.43220	0.205982	0.102991	−	0.994682i	$-0.467159\pi$
$463$	4.43220	0.205982	0.102991	+	0.994682i	$0.467159\pi$
$464$	0.492750	0.0228754
$465$	−10.5317	−0.488396
$466$	−23.0197	−1.06637
$467$	−7.94219	−0.367521	−0.183760	−	0.982971i	$-0.558827\pi$
$467$	−7.94219	−0.367521	−0.183760	+	0.982971i	$0.558827\pi$
$468$	−1.99001	−0.0919880
$469$	0	0
$470$	−13.8298	−0.637919
$471$	−1.20726	−0.0556275
$472$	11.3921	0.524364
$473$	−21.0418	−0.967502
$474$	−0.203754	−0.00935875
$475$	−6.07016	−0.278518
$476$	0	0
$477$	−0.262277	−0.0120088
$478$	15.3598	0.702543
$479$	7.85795	0.359039	0.179519	−	0.983754i	$-0.442546\pi$
$479$	7.85795	0.359039	0.179519	+	0.983754i	$0.442546\pi$
$480$	16.4800	0.752204
$481$	−1.72928	−0.0788484
$482$	−18.9203	−0.861796
$483$	0	0
$484$	0.551750	0.0250796
$485$	55.8885	2.53777
$486$	−0.881528	−0.0399869
$487$	−35.6958	−1.61753	−0.808766	−	0.588131i	$-0.799864\pi$
$487$	−35.6958	−1.61753	−0.808766	+	0.588131i	$0.799864\pi$
$488$	8.53314	0.386277
$489$	7.61049	0.344158
$490$	0	0
$491$	22.5466	1.01751	0.508756	−	0.860911i	$-0.330106\pi$
$491$	22.5466	1.01751	0.508756	+	0.860911i	$0.330106\pi$
$492$	−8.06500	−0.363598
$493$	−37.4134	−1.68502
$494$	2.44116	0.109833
$495$	−9.50639	−0.427280
$496$	−0.211134	−0.00948021
$497$	0	0
$498$	−15.2748	−0.684479
$499$	6.24228	0.279443	0.139721	−	0.990191i	$-0.455379\pi$
$499$	6.24228	0.279443	0.139721	+	0.990191i	$0.455379\pi$
$500$	−5.12935	−0.229392
$501$	20.5372	0.917536
$502$	−21.1442	−0.943712
$503$	31.3858	1.39942	0.699712	−	0.714425i	$-0.253312\pi$
$503$	31.3858	1.39942	0.699712	+	0.714425i	$0.253312\pi$
$504$	0	0
$505$	−18.0145	−0.801634
$506$	2.86311	0.127281
$507$	−10.3520	−0.459748
$508$	−6.17277	−0.273872
$509$	7.40247	0.328109	0.164054	−	0.986451i	$-0.447543\pi$
$509$	7.40247	0.328109	0.164054	+	0.986451i	$0.447543\pi$
$510$	11.4954	0.509025
$511$	0	0
$512$	0.663799	0.0293361
$513$	−1.70177	−0.0751349
$514$	12.7465	0.562223
$515$	−7.45531	−0.328520
$516$	7.92272	0.348778
$517$	−17.4087	−0.765635
$518$	0	0
$519$	13.1601	0.577663
$520$	−13.5319	−0.593412
$521$	−17.8171	−0.780583	−0.390291	−	0.920691i	$-0.627626\pi$
$521$	−17.8171	−0.780583	−0.390291	+	0.920691i	$0.627626\pi$
$522$	7.40268	0.324007
$523$	12.9558	0.566516	0.283258	−	0.959044i	$-0.408585\pi$
$523$	12.9558	0.566516	0.283258	+	0.959044i	$0.408585\pi$
$524$	0.634725	0.0277281
$525$	0	0
$526$	16.6236	0.724822
$527$	16.0309	0.698319
$528$	−0.190579	−0.00829390
$529$	1.00000	0.0434783
$530$	−0.676722	−0.0293949
$531$	4.00977	0.174009
$532$	0	0
$533$	10.7318	0.464844
$534$	−0.856843	−0.0370792
$535$	22.3681	0.967059
$536$	9.44883	0.408127
$537$	17.9134	0.773019
$538$	−9.62002	−0.414749
$539$	0	0
$540$	3.57938	0.154032
$541$	40.7729	1.75296	0.876482	−	0.481435i	$-0.159884\pi$
$541$	40.7729	1.75296	0.876482	+	0.481435i	$0.159884\pi$
$542$	−18.1506	−0.779634
$543$	10.0629	0.431842
$544$	−25.0852	−1.07552
$545$	−0.849586	−0.0363923
$546$	0	0
$547$	38.8540	1.66128	0.830638	−	0.556813i	$-0.187976\pi$
$547$	38.8540	1.66128	0.830638	+	0.556813i	$0.187976\pi$
$548$	−26.4392	−1.12943
$549$	3.00348	0.128185
$550$	−10.2126	−0.435468
$551$	14.2907	0.608804
$552$	−2.84108	−0.120925
$553$	0	0
$554$	6.09612	0.258999
$555$	3.11042	0.132030
$556$	−15.2412	−0.646371
$557$	30.9222	1.31022	0.655108	−	0.755536i	$-0.272623\pi$
$557$	30.9222	1.31022	0.655108	+	0.755536i	$0.272623\pi$
$558$	−3.17191	−0.134278
$559$	−10.5424	−0.445897
$560$	0	0
$561$	14.4703	0.610935
$562$	−7.87926	−0.332366
$563$	6.07498	0.256030	0.128015	−	0.991772i	$-0.459139\pi$
$563$	6.07498	0.256030	0.128015	+	0.991772i	$0.459139\pi$
$564$	6.55479	0.276007
$565$	−26.4187	−1.11144
$566$	−23.3800	−0.982734
$567$	0	0
$568$	4.71691	0.197917
$569$	30.0816	1.26108	0.630542	−	0.776155i	$-0.282833\pi$
$569$	30.0816	1.26108	0.630542	+	0.776155i	$0.282833\pi$
$570$	−4.39087	−0.183913
$571$	−16.5970	−0.694565	−0.347282	−	0.937761i	$-0.612895\pi$
$571$	−16.5970	−0.694565	−0.347282	+	0.937761i	$0.612895\pi$
$572$	−6.46333	−0.270245
$573$	−5.15442	−0.215329
$574$	0	0
$575$	−3.56697	−0.148753
$576$	5.08075	0.211698
$577$	−26.8976	−1.11976	−0.559880	−	0.828574i	$-0.689153\pi$
$577$	−26.8976	−1.11976	−0.559880	+	0.828574i	$0.689153\pi$
$578$	−2.51188	−0.104480
$579$	−22.6017	−0.939293
$580$	−30.0580	−1.24809
$581$	0	0
$582$	16.8324	0.697723
$583$	−0.851848	−0.0352800
$584$	1.19953	0.0496370
$585$	−4.76293	−0.196923
$586$	29.1898	1.20582
$587$	6.11998	0.252599	0.126299	−	0.991992i	$-0.459690\pi$
$587$	6.11998	0.252599	0.126299	+	0.991992i	$0.459690\pi$
$588$	0	0
$589$	−6.12330	−0.252306
$590$	10.3459	0.425935
$591$	18.5839	0.764438
$592$	0.0623561	0.00256282
$593$	−12.8690	−0.528467	−0.264234	−	0.964459i	$-0.585119\pi$
$593$	−12.8690	−0.528467	−0.264234	+	0.964459i	$0.585119\pi$
$594$	−2.86311	−0.117475
$595$	0	0
$596$	−14.5343	−0.595350
$597$	19.3545	0.792128
$598$	1.43449	0.0586605
$599$	−8.31916	−0.339912	−0.169956	−	0.985452i	$-0.554362\pi$
$599$	−8.31916	−0.339912	−0.169956	+	0.985452i	$0.554362\pi$
$600$	10.1341	0.413721
$601$	40.7843	1.66363	0.831813	−	0.555056i	$-0.187303\pi$
$601$	40.7843	1.66363	0.831813	+	0.555056i	$0.187303\pi$
$602$	0	0
$603$	3.32578	0.135436
$604$	8.67385	0.352934
$605$	1.32057	0.0536889
$606$	−5.42555	−0.220398
$607$	−16.9510	−0.688020	−0.344010	−	0.938966i	$-0.611785\pi$
$607$	−16.9510	−0.688020	−0.344010	+	0.938966i	$0.611785\pi$
$608$	9.58171	0.388590
$609$	0	0
$610$	7.74952	0.313769
$611$	−8.72218	−0.352862
$612$	−5.44839	−0.220238
$613$	21.4550	0.866559	0.433279	−	0.901260i	$-0.357356\pi$
$613$	21.4550	0.866559	0.433279	+	0.901260i	$0.357356\pi$
$614$	−3.16388	−0.127684
$615$	−19.3030	−0.778371
$616$	0	0
$617$	−4.48266	−0.180465	−0.0902325	−	0.995921i	$-0.528761\pi$
$617$	−4.48266	−0.180465	−0.0902325	+	0.995921i	$0.528761\pi$
$618$	−2.24537	−0.0903221
$619$	−26.0213	−1.04588	−0.522942	−	0.852368i	$-0.675166\pi$
$619$	−26.0213	−1.04588	−0.522942	+	0.852368i	$0.675166\pi$
$620$	12.8793	0.517245
$621$	−1.00000	−0.0401286
$622$	21.7242	0.871061
$623$	0	0
$624$	−0.0954848	−0.00382245
$625$	−30.1116	−1.20446
$626$	−11.6510	−0.465667
$627$	−5.52717	−0.220734
$628$	1.47637	0.0589134
$629$	−4.73456	−0.188779
$630$	0	0
$631$	46.0572	1.83351	0.916754	−	0.399452i	$-0.130800\pi$
$631$	46.0572	1.83351	0.916754	+	0.399452i	$0.130800\pi$
$632$	0.656681	0.0261214
$633$	−15.2356	−0.605559
$634$	−23.3912	−0.928983
$635$	−14.7740	−0.586290
$636$	0.320741	0.0127182
$637$	0	0
$638$	24.0431	0.951877
$639$	1.66025	0.0656785
$640$	−19.8507	−0.784667
$641$	−19.5294	−0.771364	−0.385682	−	0.922632i	$-0.626034\pi$
$641$	−19.5294	−0.771364	−0.385682	+	0.922632i	$0.626034\pi$
$642$	6.73678	0.265880
$643$	42.9414	1.69345	0.846723	−	0.532035i	$-0.178572\pi$
$643$	42.9414	1.69345	0.846723	+	0.532035i	$0.178572\pi$
$644$	0	0
$645$	18.9624	0.746645
$646$	6.68361	0.262963
$647$	24.7999	0.974985	0.487493	−	0.873127i	$-0.337912\pi$
$647$	24.7999	0.974985	0.487493	+	0.873127i	$0.337912\pi$
$648$	2.84108	0.111608
$649$	13.0233	0.511210
$650$	−5.11677	−0.200696
$651$	0	0
$652$	−9.30693	−0.364487
$653$	9.56627	0.374357	0.187178	−	0.982326i	$-0.440066\pi$
$653$	9.56627	0.374357	0.187178	+	0.982326i	$0.440066\pi$
$654$	−0.255876	−0.0100056
$655$	1.51917	0.0593588
$656$	−0.386976	−0.0151089
$657$	0.422209	0.0164720
$658$	0	0
$659$	−1.53146	−0.0596574	−0.0298287	−	0.999555i	$-0.509496\pi$
$659$	−1.53146	−0.0596574	−0.0298287	+	0.999555i	$0.509496\pi$
$660$	11.6254	0.452520
$661$	6.17167	0.240050	0.120025	−	0.992771i	$-0.461703\pi$
$661$	6.17167	0.240050	0.120025	+	0.992771i	$0.461703\pi$
$662$	8.47434	0.329365
$663$	7.24994	0.281565
$664$	49.2292	1.91046
$665$	0	0
$666$	0.936788	0.0362998
$667$	8.39756	0.325155
$668$	−25.1152	−0.971735
$669$	−8.81267	−0.340718
$670$	8.58112	0.331517
$671$	9.75499	0.376587
$672$	0	0
$673$	−34.6630	−1.33616	−0.668081	−	0.744089i	$-0.732884\pi$
$673$	−34.6630	−1.33616	−0.668081	+	0.744089i	$0.732884\pi$
$674$	−26.9322	−1.03739
$675$	3.56697	0.137293
$676$	12.6595	0.486905
$677$	−8.20603	−0.315383	−0.157692	−	0.987488i	$-0.550405\pi$
$677$	−8.20603	−0.315383	−0.157692	+	0.987488i	$0.550405\pi$
$678$	−7.95670	−0.305575
$679$	0	0
$680$	−37.0486	−1.42075
$681$	−2.78738	−0.106813
$682$	−10.3020	−0.394485
$683$	13.4899	0.516176	0.258088	−	0.966121i	$-0.416908\pi$
$683$	13.4899	0.516176	0.258088	+	0.966121i	$0.416908\pi$
$684$	2.08111	0.0795731
$685$	−63.2803	−2.41782
$686$	0	0
$687$	−14.0945	−0.537737
$688$	0.380149	0.0144931
$689$	−0.426796	−0.0162596
$690$	−2.58018	−0.0982257
$691$	−23.6232	−0.898668	−0.449334	−	0.893364i	$-0.648339\pi$
$691$	−23.6232	−0.898668	−0.449334	+	0.893364i	$0.648339\pi$
$692$	−16.0936	−0.611785
$693$	0	0
$694$	19.5127	0.740691
$695$	−36.4786	−1.38371
$696$	−23.8582	−0.904341
$697$	29.3822	1.11293
$698$	27.0825	1.02509
$699$	26.1134	0.987699
$700$	0	0
$701$	30.7625	1.16188	0.580941	−	0.813946i	$-0.302685\pi$
$701$	30.7625	1.16188	0.580941	+	0.813946i	$0.302685\pi$
$702$	−1.43449	−0.0541412
$703$	1.80845	0.0682069
$704$	16.5017	0.621932
$705$	15.6884	0.590859
$706$	−32.1923	−1.21157
$707$	0	0
$708$	−4.90358	−0.184288
$709$	4.14309	0.155597	0.0777985	−	0.996969i	$-0.475211\pi$
$709$	4.14309	0.155597	0.0777985	+	0.996969i	$0.475211\pi$
$710$	4.28374	0.160766
$711$	0.231138	0.00866834
$712$	2.76153	0.103493
$713$	−3.59820	−0.134753
$714$	0	0
$715$	−15.4695	−0.578526
$716$	−21.9064	−0.818681
$717$	−17.4241	−0.650716
$718$	29.4392	1.09866
$719$	−15.8185	−0.589930	−0.294965	−	0.955508i	$-0.595308\pi$
$719$	−15.8185	−0.589930	−0.294965	+	0.955508i	$0.595308\pi$
$720$	0.171746	0.00640061
$721$	0	0
$722$	14.1961	0.528325
$723$	21.4631	0.798220
$724$	−12.3060	−0.457351
$725$	−29.9538	−1.11246
$726$	0.397727	0.0147610
$727$	4.56329	0.169243	0.0846216	−	0.996413i	$-0.473032\pi$
$727$	4.56329	0.169243	0.0846216	+	0.996413i	$0.473032\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	1.08938	0.0403196
$731$	−28.8639	−1.06757
$732$	−3.67298	−0.135757
$733$	−1.94942	−0.0720033	−0.0360017	−	0.999352i	$-0.511462\pi$
$733$	−1.94942	−0.0720033	−0.0360017	+	0.999352i	$0.511462\pi$
$734$	5.58889	0.206290
$735$	0	0
$736$	5.63044	0.207541
$737$	10.8018	0.397889
$738$	−5.81362	−0.214002
$739$	−50.7480	−1.86679	−0.933397	−	0.358845i	$-0.883171\pi$
$739$	−50.7480	−1.86679	−0.933397	+	0.358845i	$0.883171\pi$
$740$	−3.80376	−0.139829
$741$	−2.76924	−0.101731
$742$	0	0
$743$	−5.91601	−0.217037	−0.108519	−	0.994094i	$-0.534611\pi$
$743$	−5.91601	−0.217037	−0.108519	+	0.994094i	$0.534611\pi$
$744$	10.2228	0.374785
$745$	−34.7869	−1.27449
$746$	14.4303	0.528332
$747$	17.3276	0.633984
$748$	−17.6958	−0.647023
$749$	0	0
$750$	−3.69747	−0.135013
$751$	−31.7467	−1.15845	−0.579227	−	0.815166i	$-0.696646\pi$
$751$	−31.7467	−1.15845	−0.579227	+	0.815166i	$0.696646\pi$
$752$	0.314513	0.0114691
$753$	23.9859	0.874093
$754$	12.0462	0.438696
$755$	20.7602	0.755541
$756$	0	0
$757$	−16.9244	−0.615128	−0.307564	−	0.951527i	$-0.599514\pi$
$757$	−16.9244	−0.615128	−0.307564	+	0.951527i	$0.599514\pi$
$758$	−22.4060	−0.813824
$759$	−3.24789	−0.117891
$760$	14.1514	0.513324
$761$	−19.3099	−0.699985	−0.349992	−	0.936753i	$-0.613816\pi$
$761$	−19.3099	−0.699985	−0.349992	+	0.936753i	$0.613816\pi$
$762$	−4.44961	−0.161192
$763$	0	0
$764$	6.30339	0.228049
$765$	−13.0403	−0.471474
$766$	11.3612	0.410496
$767$	6.52499	0.235604
$768$	−16.1401	−0.582405
$769$	33.9309	1.22358	0.611790	−	0.791020i	$-0.290450\pi$
$769$	33.9309	1.22358	0.611790	+	0.791020i	$0.290450\pi$
$770$	0	0
$771$	−14.4595	−0.520747
$772$	27.6398	0.994777
$773$	−27.4843	−0.988541	−0.494271	−	0.869308i	$-0.664565\pi$
$773$	−27.4843	−0.988541	−0.494271	+	0.869308i	$0.664565\pi$
$774$	5.71106	0.205280
$775$	12.8347	0.461035
$776$	−54.2491	−1.94743
$777$	0	0
$778$	27.3607	0.980930
$779$	−11.2231	−0.402108
$780$	5.82462	0.208555
$781$	5.39232	0.192952
$782$	3.92745	0.140445
$783$	−8.39756	−0.300104
$784$	0	0
$785$	3.53357	0.126118
$786$	0.457539	0.0163199
$787$	−11.5331	−0.411109	−0.205555	−	0.978646i	$-0.565900\pi$
$787$	−11.5331	−0.411109	−0.205555	+	0.978646i	$0.565900\pi$
$788$	−22.7264	−0.809593
$789$	−18.8577	−0.671351
$790$	0.596376	0.0212181
$791$	0	0
$792$	9.22754	0.327886
$793$	4.88748	0.173560
$794$	−19.1029	−0.677935
$795$	0.767669	0.0272264
$796$	−23.6688	−0.838919
$797$	2.01548	0.0713921	0.0356961	−	0.999363i	$-0.488635\pi$
$797$	2.01548	0.0713921	0.0356961	+	0.999363i	$0.488635\pi$
$798$	0	0
$799$	−23.8803	−0.844823
$800$	−20.0836	−0.710063
$801$	0.971997	0.0343438
$802$	−8.33083	−0.294172
$803$	1.37129	0.0483918
$804$	−4.06713	−0.143437
$805$	0	0
$806$	−5.16156	−0.181808
$807$	10.9129	0.384152
$808$	17.4861	0.615158
$809$	−18.7273	−0.658416	−0.329208	−	0.944257i	$-0.606782\pi$
$809$	−18.7273	−0.658416	−0.329208	+	0.944257i	$0.606782\pi$
$810$	2.58018	0.0906582
$811$	17.3014	0.607535	0.303767	−	0.952746i	$-0.401755\pi$
$811$	17.3014	0.607535	0.303767	+	0.952746i	$0.401755\pi$
$812$	0	0
$813$	20.5899	0.722119
$814$	3.04259	0.106643
$815$	−22.2754	−0.780274
$816$	−0.261426	−0.00915173
$817$	11.0251	0.385718
$818$	−15.6141	−0.545933
$819$	0	0
$820$	23.6058	0.824349
$821$	−6.03221	−0.210526	−0.105263	−	0.994444i	$-0.533568\pi$
$821$	−6.03221	−0.210526	−0.105263	+	0.994444i	$0.533568\pi$
$822$	−19.0586	−0.664745
$823$	−29.5945	−1.03160	−0.515799	−	0.856710i	$-0.672505\pi$
$823$	−29.5945	−1.03160	−0.515799	+	0.856710i	$0.672505\pi$
$824$	7.23663	0.252100
$825$	11.5851	0.403343
$826$	0	0
$827$	27.9760	0.972820	0.486410	−	0.873731i	$-0.338306\pi$
$827$	27.9760	0.972820	0.486410	+	0.873731i	$0.338306\pi$
$828$	1.22291	0.0424990
$829$	12.3224	0.427976	0.213988	−	0.976836i	$-0.431355\pi$
$829$	12.3224	0.427976	0.213988	+	0.976836i	$0.431355\pi$
$830$	44.7083	1.55185
$831$	−6.91541	−0.239893
$832$	8.26776	0.286633
$833$	0	0
$834$	−10.9865	−0.380433
$835$	−60.1113	−2.08024
$836$	6.75922	0.233772
$837$	3.59820	0.124372
$838$	−14.3256	−0.494868
$839$	−47.7881	−1.64983	−0.824915	−	0.565257i	$-0.808777\pi$
$839$	−47.7881	−1.64983	−0.824915	+	0.565257i	$0.808777\pi$
$840$	0	0
$841$	41.5190	1.43169
$842$	−25.1321	−0.866110
$843$	8.93818	0.307847
$844$	18.6317	0.641329
$845$	30.2996	1.04234
$846$	4.72499	0.162449
$847$	0	0
$848$	0.0153898	0.000528490 0
$849$	26.5221	0.910236
$850$	−14.0091	−0.480508
$851$	1.06269	0.0364284
$852$	−2.03034	−0.0695582
$853$	−14.5802	−0.499217	−0.249608	−	0.968347i	$-0.580302\pi$
$853$	−14.5802	−0.499217	−0.249608	+	0.968347i	$0.580302\pi$
$854$	0	0
$855$	4.98097	0.170346
$856$	−21.7120	−0.742102
$857$	−7.01275	−0.239551	−0.119776	−	0.992801i	$-0.538217\pi$
$857$	−7.01275	−0.239551	−0.119776	+	0.992801i	$0.538217\pi$
$858$	−4.65906	−0.159058
$859$	31.6430	1.07965	0.539823	−	0.841779i	$-0.318491\pi$
$859$	31.6430	1.07965	0.539823	+	0.841779i	$0.318491\pi$
$860$	−23.1893	−0.790749
$861$	0	0
$862$	−15.8057	−0.538345
$863$	−40.1440	−1.36652	−0.683258	−	0.730177i	$-0.739438\pi$
$863$	−40.1440	−1.36652	−0.683258	+	0.730177i	$0.739438\pi$
$864$	−5.63044	−0.191552
$865$	−38.5187	−1.30968
$866$	3.43888	0.116858
$867$	2.84946	0.0967728
$868$	0	0
$869$	0.750711	0.0254661
$870$	−21.6672	−0.734587
$871$	5.41196	0.183377
$872$	0.824666	0.0279267
$873$	−19.0945	−0.646252
$874$	−1.50016	−0.0507436
$875$	0	0
$876$	−0.516324	−0.0174450
$877$	−18.9048	−0.638371	−0.319185	−	0.947692i	$-0.603409\pi$
$877$	−18.9048	−0.638371	−0.319185	+	0.947692i	$0.603409\pi$
$878$	32.2173	1.08728
$879$	−33.1128	−1.11687
$880$	0.557814	0.0188039
$881$	−7.94150	−0.267556	−0.133778	−	0.991011i	$-0.542711\pi$
$881$	−7.94150	−0.267556	−0.133778	+	0.991011i	$0.542711\pi$
$882$	0	0
$883$	−24.9266	−0.838847	−0.419424	−	0.907791i	$-0.637768\pi$
$883$	−24.9266	−0.838847	−0.419424	+	0.907791i	$0.637768\pi$
$884$	−8.86602	−0.298196
$885$	−11.7364	−0.394513
$886$	−21.0920	−0.708598
$887$	−20.6403	−0.693034	−0.346517	−	0.938044i	$-0.612636\pi$
$887$	−20.6403	−0.693034	−0.346517	+	0.938044i	$0.612636\pi$
$888$	−3.01918	−0.101317
$889$	0	0
$890$	2.50793	0.0840659
$891$	3.24789	0.108809
$892$	10.7771	0.360844
$893$	9.12148	0.305239
$894$	−10.4770	−0.350404
$895$	−52.4314	−1.75259
$896$	0	0
$897$	−1.62727	−0.0543330
$898$	−0.939366	−0.0313470
$899$	−30.2161	−1.00776
$900$	−4.36208	−0.145403
$901$	−1.16852	−0.0389289
$902$	−18.8820	−0.628703
$903$	0	0
$904$	25.6437	0.852898
$905$	−29.4536	−0.979070
$906$	6.25250	0.207726
$907$	23.9708	0.795936	0.397968	−	0.917399i	$-0.369715\pi$
$907$	23.9708	0.795936	0.397968	+	0.917399i	$0.369715\pi$
$908$	3.40871	0.113122
$909$	6.15472	0.204139
$910$	0	0
$911$	41.1592	1.36367	0.681833	−	0.731508i	$-0.261183\pi$
$911$	41.1592	1.36367	0.681833	+	0.731508i	$0.261183\pi$
$912$	0.0998561	0.00330656
$913$	56.2783	1.86254
$914$	17.1659	0.567797
$915$	−8.79101	−0.290622
$916$	17.2362	0.569501
$917$	0	0
$918$	−3.92745	−0.129625
$919$	25.8534	0.852826	0.426413	−	0.904529i	$-0.359777\pi$
$919$	25.8534	0.852826	0.426413	+	0.904529i	$0.359777\pi$
$920$	8.31568	0.274160
$921$	3.58909	0.118265
$922$	−29.4221	−0.968967
$923$	2.70168	0.0889269
$924$	0	0
$925$	−3.79057	−0.124633
$926$	−3.90710	−0.128395
$927$	2.54714	0.0836589
$928$	47.2820	1.55211
$929$	1.02275	0.0335553	0.0167777	−	0.999859i	$-0.494659\pi$
$929$	1.02275	0.0335553	0.0167777	+	0.999859i	$0.494659\pi$
$930$	9.28399	0.304434
$931$	0	0
$932$	−31.9343	−1.04604
$933$	−24.6438	−0.806802
$934$	7.00126	0.229088
$935$	−42.3536	−1.38511
$936$	4.62322	0.151115
$937$	−4.00181	−0.130733	−0.0653667	−	0.997861i	$-0.520822\pi$
$937$	−4.00181	−0.130733	−0.0653667	+	0.997861i	$0.520822\pi$
$938$	0	0
$939$	13.2168	0.431314
$940$	−19.1855	−0.625761
$941$	−20.8860	−0.680864	−0.340432	−	0.940269i	$-0.610573\pi$
$941$	−20.8860	−0.680864	−0.340432	+	0.940269i	$0.610573\pi$
$942$	1.06423	0.0346745
$943$	−6.59494	−0.214761
$944$	−0.235285	−0.00765786
$945$	0	0
$946$	18.5489	0.603077
$947$	−44.3717	−1.44189	−0.720943	−	0.692994i	$-0.756291\pi$
$947$	−44.3717	−1.44189	−0.720943	+	0.692994i	$0.756291\pi$
$948$	−0.282660	−0.00918038
$949$	0.687050	0.0223026
$950$	5.35101	0.173610
$951$	26.5348	0.860450
$952$	0	0
$953$	48.8326	1.58184	0.790921	−	0.611918i	$-0.209602\pi$
$953$	48.8326	1.58184	0.790921	+	0.611918i	$0.209602\pi$
$954$	0.231205	0.00748553
$955$	15.0867	0.488194
$956$	21.3081	0.689153
$957$	−27.2744	−0.881656
$958$	−6.92700	−0.223801
$959$	0	0
$960$	−14.8710	−0.479961
$961$	−18.0530	−0.582354
$962$	1.52441	0.0491489
$963$	−7.64216	−0.246265
$964$	−26.2474	−0.845371
$965$	66.1537	2.12956
$966$	0	0
$967$	−43.2342	−1.39032	−0.695159	−	0.718856i	$-0.744666\pi$
$967$	−43.2342	−1.39032	−0.695159	+	0.718856i	$0.744666\pi$
$968$	−1.28184	−0.0411998
$969$	−7.58185	−0.243564
$970$	−49.2673	−1.58188
$971$	42.2271	1.35513	0.677567	−	0.735461i	$-0.263034\pi$
$971$	42.2271	1.35513	0.677567	+	0.735461i	$0.263034\pi$
$972$	−1.22291	−0.0392248
$973$	0	0
$974$	31.4668	1.00826
$975$	5.80443	0.185891
$976$	−0.176238	−0.00564123
$977$	12.7643	0.408367	0.204183	−	0.978933i	$-0.434546\pi$
$977$	12.7643	0.408367	0.204183	+	0.978933i	$0.434546\pi$
$978$	−6.70886	−0.214526
$979$	3.15695	0.100896
$980$	0	0
$981$	0.290264	0.00926743
$982$	−19.8754	−0.634250
$983$	−1.44112	−0.0459647	−0.0229823	−	0.999736i	$-0.507316\pi$
$983$	−1.44112	−0.0459647	−0.0229823	+	0.999736i	$0.507316\pi$
$984$	18.7368	0.597306
$985$	−54.3938	−1.73313
$986$	32.9810	1.05033
$987$	0	0
$988$	3.38653	0.107740
$989$	6.47859	0.206007
$990$	8.38015	0.266339
$991$	−15.4317	−0.490205	−0.245102	−	0.969497i	$-0.578822\pi$
$991$	−15.4317	−0.490205	−0.245102	+	0.969497i	$0.578822\pi$
$992$	−20.2594	−0.643238
$993$	−9.61324	−0.305067
$994$	0	0
$995$	−56.6495	−1.79591
$996$	−21.1901	−0.671434
$997$	−7.50199	−0.237590	−0.118795	−	0.992919i	$-0.537903\pi$
$997$	−7.50199	−0.237590	−0.118795	+	0.992919i	$0.537903\pi$
$998$	−5.50274	−0.174186
$999$	−1.06269	−0.0336219

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.bl.1.4	yes	10
7.6	odd	2		3381.2.a.bk.1.4	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3381.2.a.bk.1.4	✓	10	7.6	odd	2
3381.2.a.bl.1.4	yes	10	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:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3381.a (trivial)

\(f(q)\)	\(=\)	\(q-0.881528 q^{2} +1.00000 q^{3} -1.22291 q^{4} -2.92694 q^{5} -0.881528 q^{6} +2.84108 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.881528 q^{2} +1.00000 q^{3} -1.22291 q^{4} -2.92694 q^{5} -0.881528 q^{6} +2.84108 q^{8} +1.00000 q^{9} +2.58018 q^{10} +3.24789 q^{11} -1.22291 q^{12} +1.62727 q^{13} -2.92694 q^{15} -0.0586778 q^{16} +4.45527 q^{17} -0.881528 q^{18} -1.70177 q^{19} +3.57938 q^{20} -2.86311 q^{22} -1.00000 q^{23} +2.84108 q^{24} +3.56697 q^{25} -1.43449 q^{26} +1.00000 q^{27} -8.39756 q^{29} +2.58018 q^{30} +3.59820 q^{31} -5.63044 q^{32} +3.24789 q^{33} -3.92745 q^{34} -1.22291 q^{36} -1.06269 q^{37} +1.50016 q^{38} +1.62727 q^{39} -8.31568 q^{40} +6.59494 q^{41} -6.47859 q^{43} -3.97188 q^{44} -2.92694 q^{45} +0.881528 q^{46} -5.36000 q^{47} -0.0586778 q^{48} -3.14438 q^{50} +4.45527 q^{51} -1.99001 q^{52} -0.262277 q^{53} -0.881528 q^{54} -9.50639 q^{55} -1.70177 q^{57} +7.40268 q^{58} +4.00977 q^{59} +3.57938 q^{60} +3.00348 q^{61} -3.17191 q^{62} +5.08075 q^{64} -4.76293 q^{65} -2.86311 q^{66} +3.32578 q^{67} -5.44839 q^{68} -1.00000 q^{69} +1.66025 q^{71} +2.84108 q^{72} +0.422209 q^{73} +0.936788 q^{74} +3.56697 q^{75} +2.08111 q^{76} -1.43449 q^{78} +0.231138 q^{79} +0.171746 q^{80} +1.00000 q^{81} -5.81362 q^{82} +17.3276 q^{83} -13.0403 q^{85} +5.71106 q^{86} -8.39756 q^{87} +9.22754 q^{88} +0.971997 q^{89} +2.58018 q^{90} +1.22291 q^{92} +3.59820 q^{93} +4.72499 q^{94} +4.98097 q^{95} -5.63044 q^{96} -19.0945 q^{97} +3.24789 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + 10 q^{3} + 8 q^{4} + 4 q^{5} + 4 q^{6} + 12 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 + 10 * q^3 + 8 * q^4 + 4 * q^5 + 4 * q^6 + 12 * q^8 + 10 * q^9	\( 10 q + 4 q^{2} + 10 q^{3} + 8 q^{4} + 4 q^{5} + 4 q^{6} + 12 q^{8} + 10 q^{9} + 8 q^{10} + 2 q^{11} + 8 q^{12} + 4 q^{15} + 4 q^{16} + 12 q^{17} + 4 q^{18} + 26 q^{19} + 24 q^{20} - 8 q^{22} - 10 q^{23} + 12 q^{24} - 2 q^{25} + 4 q^{26} + 10 q^{27} + 16 q^{29} + 8 q^{30} + 12 q^{31} + 8 q^{32} + 2 q^{33} + 28 q^{34} + 8 q^{36} - 8 q^{37} + 32 q^{38} + 4 q^{40} + 10 q^{41} - 4 q^{43} - 16 q^{44} + 4 q^{45} - 4 q^{46} + 2 q^{47} + 4 q^{48} - 8 q^{50} + 12 q^{51} + 24 q^{52} + 14 q^{53} + 4 q^{54} + 16 q^{55} + 26 q^{57} - 8 q^{58} + 38 q^{59} + 24 q^{60} + 14 q^{61} - 8 q^{62} + 8 q^{64} + 12 q^{65} - 8 q^{66} + 8 q^{68} - 10 q^{69} + 24 q^{71} + 12 q^{72} + 8 q^{73} - 8 q^{74} - 2 q^{75} + 64 q^{76} + 4 q^{78} - 16 q^{79} + 28 q^{80} + 10 q^{81} - 40 q^{82} + 28 q^{83} - 4 q^{85} + 20 q^{86} + 16 q^{87} - 68 q^{88} + 32 q^{89} + 8 q^{90} - 8 q^{92} + 12 q^{93} + 56 q^{94} + 8 q^{95} + 8 q^{96} + 4 q^{97} + 2 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 + 10 * q^3 + 8 * q^4 + 4 * q^5 + 4 * q^6 + 12 * q^8 + 10 * q^9 + 8 * q^10 + 2 * q^11 + 8 * q^12 + 4 * q^15 + 4 * q^16 + 12 * q^17 + 4 * q^18 + 26 * q^19 + 24 * q^20 - 8 * q^22 - 10 * q^23 + 12 * q^24 - 2 * q^25 + 4 * q^26 + 10 * q^27 + 16 * q^29 + 8 * q^30 + 12 * q^31 + 8 * q^32 + 2 * q^33 + 28 * q^34 + 8 * q^36 - 8 * q^37 + 32 * q^38 + 4 * q^40 + 10 * q^41 - 4 * q^43 - 16 * q^44 + 4 * q^45 - 4 * q^46 + 2 * q^47 + 4 * q^48 - 8 * q^50 + 12 * q^51 + 24 * q^52 + 14 * q^53 + 4 * q^54 + 16 * q^55 + 26 * q^57 - 8 * q^58 + 38 * q^59 + 24 * q^60 + 14 * q^61 - 8 * q^62 + 8 * q^64 + 12 * q^65 - 8 * q^66 + 8 * q^68 - 10 * q^69 + 24 * q^71 + 12 * q^72 + 8 * q^73 - 8 * q^74 - 2 * q^75 + 64 * q^76 + 4 * q^78 - 16 * q^79 + 28 * q^80 + 10 * q^81 - 40 * q^82 + 28 * q^83 - 4 * q^85 + 20 * q^86 + 16 * q^87 - 68 * q^88 + 32 * q^89 + 8 * q^90 - 8 * q^92 + 12 * q^93 + 56 * q^94 + 8 * q^95 + 8 * q^96 + 4 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

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Database

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