LMFDB - Embedded newform 3381.2.a.bk.1.9

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:	$1$
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} - 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			1.9
Root			$2.42151$ 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)

$f(q)$	$=$	$q+2.42151 q^{2} -1.00000 q^{3} +3.86372 q^{4} -2.93909 q^{5} -2.42151 q^{6} +4.51302 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.42151 q^{2} -1.00000 q^{3} +3.86372 q^{4} -2.93909 q^{5} -2.42151 q^{6} +4.51302 q^{8} +1.00000 q^{9} -7.11705 q^{10} -1.07667 q^{11} -3.86372 q^{12} +2.25920 q^{13} +2.93909 q^{15} +3.20089 q^{16} +1.82520 q^{17} +2.42151 q^{18} -5.97996 q^{19} -11.3558 q^{20} -2.60718 q^{22} -1.00000 q^{23} -4.51302 q^{24} +3.63828 q^{25} +5.47067 q^{26} -1.00000 q^{27} +2.11716 q^{29} +7.11705 q^{30} -4.79531 q^{31} -1.27505 q^{32} +1.07667 q^{33} +4.41974 q^{34} +3.86372 q^{36} +0.784985 q^{37} -14.4805 q^{38} -2.25920 q^{39} -13.2642 q^{40} -0.651383 q^{41} -11.5144 q^{43} -4.15996 q^{44} -2.93909 q^{45} -2.42151 q^{46} -11.6887 q^{47} -3.20089 q^{48} +8.81013 q^{50} -1.82520 q^{51} +8.72890 q^{52} +5.13402 q^{53} -2.42151 q^{54} +3.16444 q^{55} +5.97996 q^{57} +5.12672 q^{58} +4.95423 q^{59} +11.3558 q^{60} -6.70542 q^{61} -11.6119 q^{62} -9.48932 q^{64} -6.63999 q^{65} +2.60718 q^{66} -4.90507 q^{67} +7.05206 q^{68} +1.00000 q^{69} -12.3101 q^{71} +4.51302 q^{72} +6.14919 q^{73} +1.90085 q^{74} -3.63828 q^{75} -23.1049 q^{76} -5.47067 q^{78} -4.65761 q^{79} -9.40772 q^{80} +1.00000 q^{81} -1.57733 q^{82} -11.6404 q^{83} -5.36444 q^{85} -27.8823 q^{86} -2.11716 q^{87} -4.85905 q^{88} +7.98858 q^{89} -7.11705 q^{90} -3.86372 q^{92} +4.79531 q^{93} -28.3043 q^{94} +17.5757 q^{95} +1.27505 q^{96} +12.4025 q^{97} -1.07667 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.42151	1.71227	0.856134	−	0.516754i	$-0.172860\pi$
$2$	2.42151	1.71227	0.856134	+	0.516754i	$0.172860\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.86372	1.93186
$5$	−2.93909	−1.31440	−0.657202	−	0.753715i	$-0.728260\pi$
$5$	−2.93909	−1.31440	−0.657202	+	0.753715i	$0.728260\pi$
$6$	−2.42151	−0.988578
$7$	0	0
$7$	0	0
$8$	4.51302	1.59559
$9$	1.00000	0.333333
$10$	−7.11705	−2.25061
$11$	−1.07667	−0.324629	−0.162315	−	0.986739i	$-0.551896\pi$
$11$	−1.07667	−0.324629	−0.162315	+	0.986739i	$0.551896\pi$
$12$	−3.86372	−1.11536
$13$	2.25920	0.626588	0.313294	−	0.949656i	$-0.398567\pi$
$13$	2.25920	0.626588	0.313294	+	0.949656i	$0.398567\pi$
$14$	0	0
$15$	2.93909	0.758871
$16$	3.20089	0.800222
$17$	1.82520	0.442676	0.221338	−	0.975197i	$-0.428958\pi$
$17$	1.82520	0.442676	0.221338	+	0.975197i	$0.428958\pi$
$18$	2.42151	0.570756
$19$	−5.97996	−1.37190	−0.685948	−	0.727651i	$-0.740612\pi$
$19$	−5.97996	−1.37190	−0.685948	+	0.727651i	$0.740612\pi$
$20$	−11.3558	−2.53924
$21$	0	0
$22$	−2.60718	−0.555852
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−4.51302	−0.921216
$25$	3.63828	0.727656
$26$	5.47067	1.07289
$27$	−1.00000	−0.192450
$28$	0	0
$29$	2.11716	0.393146	0.196573	−	0.980489i	$-0.437019\pi$
$29$	2.11716	0.393146	0.196573	+	0.980489i	$0.437019\pi$
$30$	7.11705	1.29939
$31$	−4.79531	−0.861262	−0.430631	−	0.902528i	$-0.641709\pi$
$31$	−4.79531	−0.861262	−0.430631	+	0.902528i	$0.641709\pi$
$32$	−1.27505	−0.225398
$33$	1.07667	0.187425
$34$	4.41974	0.757980
$35$	0	0
$36$	3.86372	0.643953
$37$	0.784985	0.129051	0.0645254	−	0.997916i	$-0.479447\pi$
$37$	0.784985	0.129051	0.0645254	+	0.997916i	$0.479447\pi$
$38$	−14.4805	−2.34905
$39$	−2.25920	−0.361761
$40$	−13.2642	−2.09725
$41$	−0.651383	−0.101729	−0.0508645	−	0.998706i	$-0.516198\pi$
$41$	−0.651383	−0.101729	−0.0508645	+	0.998706i	$0.516198\pi$
$42$	0	0
$43$	−11.5144	−1.75593	−0.877966	−	0.478724i	$-0.841100\pi$
$43$	−11.5144	−1.75593	−0.877966	+	0.478724i	$0.841100\pi$
$44$	−4.15996	−0.627138
$45$	−2.93909	−0.438134
$46$	−2.42151	−0.357032
$47$	−11.6887	−1.70497	−0.852484	−	0.522753i	$-0.824905\pi$
$47$	−11.6887	−1.70497	−0.852484	+	0.522753i	$0.824905\pi$
$48$	−3.20089	−0.462009
$49$	0	0
$50$	8.81013	1.24594
$51$	−1.82520	−0.255579
$52$	8.72890	1.21048
$53$	5.13402	0.705212	0.352606	−	0.935772i	$-0.385296\pi$
$53$	5.13402	0.705212	0.352606	+	0.935772i	$0.385296\pi$
$54$	−2.42151	−0.329526
$55$	3.16444	0.426694
$56$	0	0
$57$	5.97996	0.792064
$58$	5.12672	0.673172
$59$	4.95423	0.644986	0.322493	−	0.946572i	$-0.395479\pi$
$59$	4.95423	0.644986	0.322493	+	0.946572i	$0.395479\pi$
$60$	11.3558	1.46603
$61$	−6.70542	−0.858541	−0.429271	−	0.903176i	$-0.641229\pi$
$61$	−6.70542	−0.858541	−0.429271	+	0.903176i	$0.641229\pi$
$62$	−11.6119	−1.47471
$63$	0	0
$64$	−9.48932	−1.18616
$65$	−6.63999	−0.823589
$66$	2.60718	0.320921
$67$	−4.90507	−0.599250	−0.299625	−	0.954057i	$-0.596862\pi$
$67$	−4.90507	−0.599250	−0.299625	+	0.954057i	$0.596862\pi$
$68$	7.05206	0.855188
$69$	1.00000	0.120386
$70$	0	0
$71$	−12.3101	−1.46093	−0.730467	−	0.682948i	$-0.760698\pi$
$71$	−12.3101	−1.46093	−0.730467	+	0.682948i	$0.760698\pi$
$72$	4.51302	0.531864
$73$	6.14919	0.719708	0.359854	−	0.933009i	$-0.382826\pi$
$73$	6.14919	0.719708	0.359854	+	0.933009i	$0.382826\pi$
$74$	1.90085	0.220969
$75$	−3.63828	−0.420112
$76$	−23.1049	−2.65031
$77$	0	0
$78$	−5.47067	−0.619431
$79$	−4.65761	−0.524022	−0.262011	−	0.965065i	$-0.584386\pi$
$79$	−4.65761	−0.524022	−0.262011	+	0.965065i	$0.584386\pi$
$80$	−9.40772	−1.05181
$81$	1.00000	0.111111
$82$	−1.57733	−0.174187
$83$	−11.6404	−1.27770	−0.638850	−	0.769331i	$-0.720590\pi$
$83$	−11.6404	−1.27770	−0.638850	+	0.769331i	$0.720590\pi$
$84$	0	0
$85$	−5.36444	−0.581855
$86$	−27.8823	−3.00662
$87$	−2.11716	−0.226983
$88$	−4.85905	−0.517976
$89$	7.98858	0.846788	0.423394	−	0.905946i	$-0.360839\pi$
$89$	7.98858	0.846788	0.423394	+	0.905946i	$0.360839\pi$
$90$	−7.11705	−0.750203
$91$	0	0
$92$	−3.86372	−0.402821
$93$	4.79531	0.497250
$94$	−28.3043	−2.91936
$95$	17.5757	1.80322
$96$	1.27505	0.130134
$97$	12.4025	1.25928	0.629640	−	0.776887i	$-0.283203\pi$
$97$	12.4025	1.25928	0.629640	+	0.776887i	$0.283203\pi$
$98$	0	0
$99$	−1.07667	−0.108210
$100$	14.0573	1.40573
$101$	5.35438	0.532781	0.266391	−	0.963865i	$-0.414169\pi$
$101$	5.35438	0.532781	0.266391	+	0.963865i	$0.414169\pi$
$102$	−4.41974	−0.437620
$103$	−9.70318	−0.956083	−0.478042	−	0.878337i	$-0.658653\pi$
$103$	−9.70318	−0.956083	−0.478042	+	0.878337i	$0.658653\pi$
$104$	10.1958	0.999780
$105$	0	0
$106$	12.4321	1.20751
$107$	−9.43117	−0.911745	−0.455873	−	0.890045i	$-0.650673\pi$
$107$	−9.43117	−0.911745	−0.455873	+	0.890045i	$0.650673\pi$
$108$	−3.86372	−0.371787
$109$	−5.70465	−0.546406	−0.273203	−	0.961956i	$-0.588083\pi$
$109$	−5.70465	−0.546406	−0.273203	+	0.961956i	$0.588083\pi$
$110$	7.66274	0.730614
$111$	−0.784985	−0.0745075
$112$	0	0
$113$	−7.00751	−0.659211	−0.329606	−	0.944119i	$-0.606916\pi$
$113$	−7.00751	−0.659211	−0.329606	+	0.944119i	$0.606916\pi$
$114$	14.4805	1.35623
$115$	2.93909	0.274072
$116$	8.18010	0.759504
$117$	2.25920	0.208863
$118$	11.9967	1.10439
$119$	0	0
$120$	13.2642	1.21085
$121$	−9.84077	−0.894616
$122$	−16.2373	−1.47005
$123$	0.651383	0.0587332
$124$	−18.5277	−1.66384
$125$	4.00223	0.357970
$126$	0	0
$127$	14.0531	1.24701	0.623506	−	0.781819i	$-0.285708\pi$
$127$	14.0531	1.24701	0.623506	+	0.781819i	$0.285708\pi$
$128$	−20.4284	−1.80563
$129$	11.5144	1.01379
$130$	−16.0788	−1.41021
$131$	13.4789	1.17765	0.588827	−	0.808259i	$-0.299590\pi$
$131$	13.4789	1.17765	0.588827	+	0.808259i	$0.299590\pi$
$132$	4.15996	0.362078
$133$	0	0
$134$	−11.8777	−1.02608
$135$	2.93909	0.252957
$136$	8.23716	0.706331
$137$	10.7549	0.918853	0.459426	−	0.888216i	$-0.348055\pi$
$137$	10.7549	0.918853	0.459426	+	0.888216i	$0.348055\pi$
$138$	2.42151	0.206133
$139$	13.2698	1.12553	0.562765	−	0.826617i	$-0.309738\pi$
$139$	13.2698	1.12553	0.562765	+	0.826617i	$0.309738\pi$
$140$	0	0
$141$	11.6887	0.984364
$142$	−29.8089	−2.50151
$143$	−2.43242	−0.203409
$144$	3.20089	0.266741
$145$	−6.22253	−0.516753
$146$	14.8903	1.23233
$147$	0	0
$148$	3.03296	0.249308
$149$	0.675921	0.0553736	0.0276868	−	0.999617i	$-0.491186\pi$
$149$	0.675921	0.0553736	0.0276868	+	0.999617i	$0.491186\pi$
$150$	−8.81013	−0.719344
$151$	10.1121	0.822913	0.411456	−	0.911429i	$-0.365020\pi$
$151$	10.1121	0.822913	0.411456	+	0.911429i	$0.365020\pi$
$152$	−26.9877	−2.18899
$153$	1.82520	0.147559
$154$	0	0
$155$	14.0939	1.13205
$156$	−8.72890	−0.698871
$157$	−22.6777	−1.80988	−0.904938	−	0.425543i	$-0.860083\pi$
$157$	−22.6777	−1.80988	−0.904938	+	0.425543i	$0.860083\pi$
$158$	−11.2784	−0.897265
$159$	−5.13402	−0.407154
$160$	3.74748	0.296264
$161$	0	0
$162$	2.42151	0.190252
$163$	−18.5996	−1.45683	−0.728415	−	0.685137i	$-0.759742\pi$
$163$	−18.5996	−1.45683	−0.728415	+	0.685137i	$0.759742\pi$
$164$	−2.51676	−0.196526
$165$	−3.16444	−0.246352
$166$	−28.1874	−2.18777
$167$	13.3263	1.03122	0.515611	−	0.856823i	$-0.327565\pi$
$167$	13.3263	1.03122	0.515611	+	0.856823i	$0.327565\pi$
$168$	0	0
$169$	−7.89604	−0.607387
$170$	−12.9900	−0.996291
$171$	−5.97996	−0.457299
$172$	−44.4885	−3.39221
$173$	3.24652	0.246829	0.123414	−	0.992355i	$-0.460616\pi$
$173$	3.24652	0.246829	0.123414	+	0.992355i	$0.460616\pi$
$174$	−5.12672	−0.388656
$175$	0	0
$176$	−3.44631	−0.259776
$177$	−4.95423	−0.372383
$178$	19.3444	1.44993
$179$	−11.6213	−0.868617	−0.434309	−	0.900764i	$-0.643007\pi$
$179$	−11.6213	−0.868617	−0.434309	+	0.900764i	$0.643007\pi$
$180$	−11.3558	−0.846414
$181$	−0.109172	−0.00811472	−0.00405736	−	0.999992i	$-0.501292\pi$
$181$	−0.109172	−0.00811472	−0.00405736	+	0.999992i	$0.501292\pi$
$182$	0	0
$183$	6.70542	0.495679
$184$	−4.51302	−0.332704
$185$	−2.30715	−0.169625
$186$	11.6119	0.851425
$187$	−1.96514	−0.143706
$188$	−45.1618	−3.29376
$189$	0	0
$190$	42.5597	3.08760
$191$	−12.3274	−0.891981	−0.445990	−	0.895038i	$-0.647148\pi$
$191$	−12.3274	−0.891981	−0.445990	+	0.895038i	$0.647148\pi$
$192$	9.48932	0.684833
$193$	−5.94298	−0.427785	−0.213892	−	0.976857i	$-0.568614\pi$
$193$	−5.94298	−0.427785	−0.213892	+	0.976857i	$0.568614\pi$
$194$	30.0327	2.15622
$195$	6.63999	0.475500
$196$	0	0
$197$	18.0182	1.28375	0.641873	−	0.766811i	$-0.278158\pi$
$197$	18.0182	1.28375	0.641873	+	0.766811i	$0.278158\pi$
$198$	−2.60718	−0.185284
$199$	14.0168	0.993627	0.496814	−	0.867857i	$-0.334503\pi$
$199$	14.0168	0.993627	0.496814	+	0.867857i	$0.334503\pi$
$200$	16.4196	1.16104
$201$	4.90507	0.345977
$202$	12.9657	0.912264
$203$	0	0
$204$	−7.05206	−0.493743
$205$	1.91448	0.133713
$206$	−23.4964	−1.63707
$207$	−1.00000	−0.0695048
$208$	7.23143	0.501410
$209$	6.43846	0.445357
$210$	0	0
$211$	20.4176	1.40561	0.702803	−	0.711385i	$-0.251932\pi$
$211$	20.4176	1.40561	0.702803	+	0.711385i	$0.251932\pi$
$212$	19.8364	1.36237
$213$	12.3101	0.843471
$214$	−22.8377	−1.56115
$215$	33.8420	2.30800
$216$	−4.51302	−0.307072
$217$	0	0
$218$	−13.8139	−0.935593
$219$	−6.14919	−0.415524
$220$	12.2265	0.824312
$221$	4.12348	0.277375
$222$	−1.90085	−0.127577
$223$	−5.11396	−0.342456	−0.171228	−	0.985231i	$-0.554773\pi$
$223$	−5.11396	−0.342456	−0.171228	+	0.985231i	$0.554773\pi$
$224$	0	0
$225$	3.63828	0.242552
$226$	−16.9688	−1.12875
$227$	22.5199	1.49470	0.747351	−	0.664430i	$-0.231326\pi$
$227$	22.5199	1.49470	0.747351	+	0.664430i	$0.231326\pi$
$228$	23.1049	1.53016
$229$	−8.51930	−0.562971	−0.281486	−	0.959565i	$-0.590827\pi$
$229$	−8.51930	−0.562971	−0.281486	+	0.959565i	$0.590827\pi$
$230$	7.11705	0.469285
$231$	0	0
$232$	9.55477	0.627302
$233$	18.5322	1.21408	0.607041	−	0.794670i	$-0.292356\pi$
$233$	18.5322	1.21408	0.607041	+	0.794670i	$0.292356\pi$
$234$	5.47067	0.357629
$235$	34.3541	2.24102
$236$	19.1418	1.24602
$237$	4.65761	0.302544
$238$	0	0
$239$	22.4541	1.45243	0.726217	−	0.687465i	$-0.241277\pi$
$239$	22.4541	1.45243	0.726217	+	0.687465i	$0.241277\pi$
$240$	9.40772	0.607266
$241$	−23.0220	−1.48298	−0.741490	−	0.670964i	$-0.765880\pi$
$241$	−23.0220	−1.48298	−0.741490	+	0.670964i	$0.765880\pi$
$242$	−23.8296	−1.53182
$243$	−1.00000	−0.0641500
$244$	−25.9079	−1.65858
$245$	0	0
$246$	1.57733	0.100567
$247$	−13.5099	−0.859614
$248$	−21.6413	−1.37422
$249$	11.6404	0.737681
$250$	9.69144	0.612941
$251$	−28.5202	−1.80018	−0.900089	−	0.435706i	$-0.856499\pi$
$251$	−28.5202	−1.80018	−0.900089	+	0.435706i	$0.856499\pi$
$252$	0	0
$253$	1.07667	0.0676899
$254$	34.0298	2.13522
$255$	5.36444	0.335934
$256$	−30.4890	−1.90556
$257$	20.0084	1.24809	0.624044	−	0.781389i	$-0.285488\pi$
$257$	20.0084	1.24809	0.624044	+	0.781389i	$0.285488\pi$
$258$	27.8823	1.73588
$259$	0	0
$260$	−25.6551	−1.59106
$261$	2.11716	0.131049
$262$	32.6393	2.01646
$263$	12.6331	0.778990	0.389495	−	0.921029i	$-0.372650\pi$
$263$	12.6331	0.778990	0.389495	+	0.921029i	$0.372650\pi$
$264$	4.85905	0.299054
$265$	−15.0894	−0.926933
$266$	0	0
$267$	−7.98858	−0.488893
$268$	−18.9518	−1.15767
$269$	−9.30286	−0.567205	−0.283603	−	0.958942i	$-0.591530\pi$
$269$	−9.30286	−0.567205	−0.283603	+	0.958942i	$0.591530\pi$
$270$	7.11705	0.433130
$271$	9.34011	0.567372	0.283686	−	0.958917i	$-0.408443\pi$
$271$	9.34011	0.567372	0.283686	+	0.958917i	$0.408443\pi$
$272$	5.84226	0.354239
$273$	0	0
$274$	26.0431	1.57332
$275$	−3.91724	−0.236218
$276$	3.86372	0.232569
$277$	19.1201	1.14881	0.574407	−	0.818570i	$-0.305233\pi$
$277$	19.1201	1.14881	0.574407	+	0.818570i	$0.305233\pi$
$278$	32.1330	1.92721
$279$	−4.79531	−0.287087
$280$	0	0
$281$	12.5065	0.746073	0.373037	−	0.927817i	$-0.378317\pi$
$281$	12.5065	0.746073	0.373037	+	0.927817i	$0.378317\pi$
$282$	28.3043	1.68549
$283$	−14.4872	−0.861175	−0.430587	−	0.902549i	$-0.641694\pi$
$283$	−14.4872	−0.861175	−0.430587	+	0.902549i	$0.641694\pi$
$284$	−47.5626	−2.82232
$285$	−17.5757	−1.04109
$286$	−5.89012	−0.348290
$287$	0	0
$288$	−1.27505	−0.0751328
$289$	−13.6686	−0.804038
$290$	−15.0679	−0.884819
$291$	−12.4025	−0.727045
$292$	23.7587	1.39038
$293$	11.3599	0.663654	0.331827	−	0.943340i	$-0.392335\pi$
$293$	11.3599	0.663654	0.331827	+	0.943340i	$0.392335\pi$
$294$	0	0
$295$	−14.5610	−0.847771
$296$	3.54265	0.205912
$297$	1.07667	0.0624749
$298$	1.63675	0.0948144
$299$	−2.25920	−0.130653
$300$	−14.0573	−0.811598
$301$	0	0
$302$	24.4866	1.40905
$303$	−5.35438	−0.307601
$304$	−19.1412	−1.09782
$305$	19.7079	1.12847
$306$	4.41974	0.252660
$307$	−29.4003	−1.67796	−0.838982	−	0.544160i	$-0.816849\pi$
$307$	−29.4003	−1.67796	−0.838982	+	0.544160i	$0.816849\pi$
$308$	0	0
$309$	9.70318	0.551995
$310$	34.1284	1.93837
$311$	−8.02484	−0.455047	−0.227523	−	0.973773i	$-0.573063\pi$
$311$	−8.02484	−0.455047	−0.227523	+	0.973773i	$0.573063\pi$
$312$	−10.1958	−0.577223
$313$	−21.4133	−1.21035	−0.605177	−	0.796091i	$-0.706898\pi$
$313$	−21.4133	−1.21035	−0.605177	+	0.796091i	$0.706898\pi$
$314$	−54.9143	−3.09899
$315$	0	0
$316$	−17.9957	−1.01234
$317$	−16.9553	−0.952305	−0.476152	−	0.879363i	$-0.657969\pi$
$317$	−16.9553	−0.952305	−0.476152	+	0.879363i	$0.657969\pi$
$318$	−12.4321	−0.697157
$319$	−2.27949	−0.127627
$320$	27.8900	1.55910
$321$	9.43117	0.526396
$322$	0	0
$323$	−10.9146	−0.607305
$324$	3.86372	0.214651
$325$	8.21958	0.455940
$326$	−45.0390	−2.49448
$327$	5.70465	0.315468
$328$	−2.93970	−0.162318
$329$	0	0
$330$	−7.66274	−0.421820
$331$	−15.7475	−0.865560	−0.432780	−	0.901500i	$-0.642467\pi$
$331$	−15.7475	−0.865560	−0.432780	+	0.901500i	$0.642467\pi$
$332$	−44.9753	−2.46834
$333$	0.784985	0.0430169
$334$	32.2698	1.76573
$335$	14.4165	0.787656
$336$	0	0
$337$	−2.51396	−0.136944	−0.0684719	−	0.997653i	$-0.521812\pi$
$337$	−2.51396	−0.136944	−0.0684719	+	0.997653i	$0.521812\pi$
$338$	−19.1203	−1.04001
$339$	7.00751	0.380596
$340$	−20.7267	−1.12406
$341$	5.16298	0.279591
$342$	−14.4805	−0.783018
$343$	0	0
$344$	−51.9648	−2.80175
$345$	−2.93909	−0.158236
$346$	7.86149	0.422636
$347$	25.9171	1.39130	0.695650	−	0.718380i	$-0.255116\pi$
$347$	25.9171	1.39130	0.695650	+	0.718380i	$0.255116\pi$
$348$	−8.18010	−0.438500
$349$	20.4638	1.09540	0.547701	−	0.836674i	$-0.315503\pi$
$349$	20.4638	1.09540	0.547701	+	0.836674i	$0.315503\pi$
$350$	0	0
$351$	−2.25920	−0.120587
$352$	1.37281	0.0731709
$353$	31.2232	1.66184	0.830922	−	0.556388i	$-0.187813\pi$
$353$	31.2232	1.66184	0.830922	+	0.556388i	$0.187813\pi$
$354$	−11.9967	−0.637619
$355$	36.1804	1.92026
$356$	30.8656	1.63588
$357$	0	0
$358$	−28.1411	−1.48730
$359$	22.3343	1.17876	0.589379	−	0.807857i	$-0.299373\pi$
$359$	22.3343	1.17876	0.589379	+	0.807857i	$0.299373\pi$
$360$	−13.2642	−0.699084
$361$	16.7599	0.882098
$362$	−0.264362	−0.0138946
$363$	9.84077	0.516507
$364$	0	0
$365$	−18.0730	−0.945987
$366$	16.2373	0.848735
$367$	18.3272	0.956672	0.478336	−	0.878177i	$-0.341240\pi$
$367$	18.3272	0.956672	0.478336	+	0.878177i	$0.341240\pi$
$368$	−3.20089	−0.166858
$369$	−0.651383	−0.0339096
$370$	−5.58678	−0.290443
$371$	0	0
$372$	18.5277	0.960617
$373$	−15.9184	−0.824224	−0.412112	−	0.911133i	$-0.635209\pi$
$373$	−15.9184	−0.824224	−0.412112	+	0.911133i	$0.635209\pi$
$374$	−4.75862	−0.246062
$375$	−4.00223	−0.206674
$376$	−52.7512	−2.72044
$377$	4.78307	0.246341
$378$	0	0
$379$	36.2783	1.86349	0.931746	−	0.363110i	$-0.118285\pi$
$379$	36.2783	1.86349	0.931746	+	0.363110i	$0.118285\pi$
$380$	67.9074	3.48358
$381$	−14.0531	−0.719962
$382$	−29.8510	−1.52731
$383$	−7.59152	−0.387908	−0.193954	−	0.981011i	$-0.562131\pi$
$383$	−7.59152	−0.387908	−0.193954	+	0.981011i	$0.562131\pi$
$384$	20.4284	1.04248
$385$	0	0
$386$	−14.3910	−0.732482
$387$	−11.5144	−0.585310
$388$	47.9196	2.43275
$389$	−21.7588	−1.10322	−0.551608	−	0.834103i	$-0.685986\pi$
$389$	−21.7588	−1.10322	−0.551608	+	0.834103i	$0.685986\pi$
$390$	16.0788	0.814182
$391$	−1.82520	−0.0923043
$392$	0	0
$393$	−13.4789	−0.679919
$394$	43.6313	2.19812
$395$	13.6891	0.688776
$396$	−4.15996	−0.209046
$397$	6.76941	0.339747	0.169873	−	0.985466i	$-0.445664\pi$
$397$	6.76941	0.339747	0.169873	+	0.985466i	$0.445664\pi$
$398$	33.9419	1.70136
$399$	0	0
$400$	11.6457	0.582286
$401$	35.0129	1.74846	0.874229	−	0.485513i	$-0.161367\pi$
$401$	35.0129	1.74846	0.874229	+	0.485513i	$0.161367\pi$
$402$	11.8777	0.592406
$403$	−10.8335	−0.539657
$404$	20.6878	1.02926
$405$	−2.93909	−0.146045
$406$	0	0
$407$	−0.845172	−0.0418936
$408$	−8.23716	−0.407800
$409$	−15.3187	−0.757460	−0.378730	−	0.925507i	$-0.623639\pi$
$409$	−15.3187	−0.757460	−0.378730	+	0.925507i	$0.623639\pi$
$410$	4.63593	0.228952
$411$	−10.7549	−0.530500
$412$	−37.4904	−1.84702
$413$	0	0
$414$	−2.42151	−0.119011
$415$	34.2123	1.67941
$416$	−2.88058	−0.141232
$417$	−13.2698	−0.649825
$418$	15.5908	0.762571
$419$	−24.2879	−1.18654	−0.593271	−	0.805003i	$-0.702164\pi$
$419$	−24.2879	−1.18654	−0.593271	+	0.805003i	$0.702164\pi$
$420$	0	0
$421$	5.23153	0.254969	0.127485	−	0.991841i	$-0.459310\pi$
$421$	5.23153	0.254969	0.127485	+	0.991841i	$0.459310\pi$
$422$	49.4414	2.40677
$423$	−11.6887	−0.568323
$424$	23.1699	1.12523
$425$	6.64059	0.322116
$426$	29.8089	1.44425
$427$	0	0
$428$	−36.4394	−1.76136
$429$	2.43242	0.117438
$430$	81.9487	3.95192
$431$	27.7033	1.33442	0.667211	−	0.744869i	$-0.267488\pi$
$431$	27.7033	1.33442	0.667211	+	0.744869i	$0.267488\pi$
$432$	−3.20089	−0.154003
$433$	23.0451	1.10748	0.553739	−	0.832690i	$-0.313201\pi$
$433$	23.0451	1.10748	0.553739	+	0.832690i	$0.313201\pi$
$434$	0	0
$435$	6.22253	0.298347
$436$	−22.0412	−1.05558
$437$	5.97996	0.286060
$438$	−14.8903	−0.711488
$439$	3.59717	0.171683	0.0858417	−	0.996309i	$-0.472642\pi$
$439$	3.59717	0.171683	0.0858417	+	0.996309i	$0.472642\pi$
$440$	14.2812	0.680829
$441$	0	0
$442$	9.98506	0.474941
$443$	6.65686	0.316277	0.158138	−	0.987417i	$-0.449451\pi$
$443$	6.65686	0.316277	0.158138	+	0.987417i	$0.449451\pi$
$444$	−3.03296	−0.143938
$445$	−23.4792	−1.11302
$446$	−12.3835	−0.586376
$447$	−0.675921	−0.0319700
$448$	0	0
$449$	−19.8979	−0.939040	−0.469520	−	0.882922i	$-0.655573\pi$
$449$	−19.8979	−0.939040	−0.469520	+	0.882922i	$0.655573\pi$
$450$	8.81013	0.415314
$451$	0.701326	0.0330242
$452$	−27.0751	−1.27350
$453$	−10.1121	−0.475109
$454$	54.5323	2.55933
$455$	0	0
$456$	26.9877	1.26381
$457$	2.00055	0.0935819	0.0467910	−	0.998905i	$-0.485101\pi$
$457$	2.00055	0.0935819	0.0467910	+	0.998905i	$0.485101\pi$
$458$	−20.6296	−0.963957
$459$	−1.82520	−0.0851930
$460$	11.3558	0.529469
$461$	−12.4966	−0.582026	−0.291013	−	0.956719i	$-0.593992\pi$
$461$	−12.4966	−0.582026	−0.291013	+	0.956719i	$0.593992\pi$
$462$	0	0
$463$	−26.0821	−1.21214	−0.606069	−	0.795412i	$-0.707255\pi$
$463$	−26.0821	−1.21214	−0.606069	+	0.795412i	$0.707255\pi$
$464$	6.77679	0.314604
$465$	−14.0939	−0.653587
$466$	44.8758	2.07883
$467$	−40.5905	−1.87831	−0.939153	−	0.343499i	$-0.888388\pi$
$467$	−40.5905	−1.87831	−0.939153	+	0.343499i	$0.888388\pi$
$468$	8.72890	0.403493
$469$	0	0
$470$	83.1889	3.83722
$471$	22.6777	1.04493
$472$	22.3585	1.02913
$473$	12.3973	0.570027
$474$	11.2784	0.518036
$475$	−21.7567	−0.998268
$476$	0	0
$477$	5.13402	0.235071
$478$	54.3729	2.48696
$479$	−37.7659	−1.72557	−0.862783	−	0.505574i	$-0.831281\pi$
$479$	−37.7659	−1.72557	−0.862783	+	0.505574i	$0.831281\pi$
$480$	−3.74748	−0.171048
$481$	1.77343	0.0808617
$482$	−55.7481	−2.53926
$483$	0	0
$484$	−38.0220	−1.72827
$485$	−36.4520	−1.65520
$486$	−2.42151	−0.109842
$487$	−26.4843	−1.20012	−0.600058	−	0.799957i	$-0.704856\pi$
$487$	−26.4843	−1.20012	−0.600058	+	0.799957i	$0.704856\pi$
$488$	−30.2617	−1.36988
$489$	18.5996	0.841101
$490$	0	0
$491$	−14.0610	−0.634564	−0.317282	−	0.948331i	$-0.602770\pi$
$491$	−14.0610	−0.634564	−0.317282	+	0.948331i	$0.602770\pi$
$492$	2.51676	0.113464
$493$	3.86424	0.174036
$494$	−32.7144	−1.47189
$495$	3.16444	0.142231
$496$	−15.3492	−0.689201
$497$	0	0
$498$	28.1874	1.26311
$499$	43.4383	1.94457	0.972283	−	0.233807i	$-0.0751183\pi$
$499$	43.4383	1.94457	0.972283	+	0.233807i	$0.0751183\pi$
$500$	15.4635	0.691548
$501$	−13.3263	−0.595376
$502$	−69.0620	−3.08239
$503$	−0.421489	−0.0187933	−0.00939664	−	0.999956i	$-0.502991\pi$
$503$	−0.421489	−0.0187933	−0.00939664	+	0.999956i	$0.502991\pi$
$504$	0	0
$505$	−15.7370	−0.700289
$506$	2.60718	0.115903
$507$	7.89604	0.350675
$508$	54.2972	2.40905
$509$	34.5850	1.53295	0.766476	−	0.642273i	$-0.222008\pi$
$509$	34.5850	1.53295	0.766476	+	0.642273i	$0.222008\pi$
$510$	12.9900	0.575209
$511$	0	0
$512$	−32.9726	−1.45720
$513$	5.97996	0.264021
$514$	48.4505	2.13706
$515$	28.5186	1.25668
$516$	44.4885	1.95850
$517$	12.5849	0.553483
$518$	0	0
$519$	−3.24652	−0.142507
$520$	−29.9664	−1.31411
$521$	−19.1543	−0.839167	−0.419583	−	0.907717i	$-0.637824\pi$
$521$	−19.1543	−0.839167	−0.419583	+	0.907717i	$0.637824\pi$
$522$	5.12672	0.224391
$523$	−2.99887	−0.131132	−0.0655658	−	0.997848i	$-0.520885\pi$
$523$	−2.99887	−0.131132	−0.0655658	+	0.997848i	$0.520885\pi$
$524$	52.0786	2.27506
$525$	0	0
$526$	30.5912	1.33384
$527$	−8.75239	−0.381260
$528$	3.44631	0.149981
$529$	1.00000	0.0434783
$530$	−36.5391	−1.58716
$531$	4.95423	0.214995
$532$	0	0
$533$	−1.47160	−0.0637421
$534$	−19.3444	−0.837116
$535$	27.7191	1.19840
$536$	−22.1367	−0.956159
$537$	11.6213	0.501496
$538$	−22.5270	−0.971207
$539$	0	0
$540$	11.3558	0.488677
$541$	−36.8291	−1.58341	−0.791703	−	0.610906i	$-0.790805\pi$
$541$	−36.8291	−1.58341	−0.791703	+	0.610906i	$0.790805\pi$
$542$	22.6172	0.971492
$543$	0.109172	0.00468504
$544$	−2.32721	−0.0997785
$545$	16.7665	0.718198
$546$	0	0
$547$	−32.3949	−1.38511	−0.692553	−	0.721367i	$-0.743514\pi$
$547$	−32.3949	−1.38511	−0.692553	+	0.721367i	$0.743514\pi$
$548$	41.5539	1.77509
$549$	−6.70542	−0.286180
$550$	−9.48564	−0.404469
$551$	−12.6605	−0.539356
$552$	4.51302	0.192087
$553$	0	0
$554$	46.2995	1.96708
$555$	2.30715	0.0979329
$556$	51.2708	2.17436
$557$	−32.4351	−1.37432	−0.687160	−	0.726506i	$-0.741143\pi$
$557$	−32.4351	−1.37432	−0.687160	+	0.726506i	$0.741143\pi$
$558$	−11.6119	−0.491571
$559$	−26.0133	−1.10025
$560$	0	0
$561$	1.96514	0.0829684
$562$	30.2846	1.27748
$563$	16.2052	0.682967	0.341484	−	0.939888i	$-0.389071\pi$
$563$	16.2052	0.682967	0.341484	+	0.939888i	$0.389071\pi$
$564$	45.1618	1.90165
$565$	20.5957	0.866469
$566$	−35.0809	−1.47456
$567$	0	0
$568$	−55.5555	−2.33106
$569$	−8.75613	−0.367076	−0.183538	−	0.983013i	$-0.558755\pi$
$569$	−8.75613	−0.367076	−0.183538	+	0.983013i	$0.558755\pi$
$570$	−42.5597	−1.78263
$571$	33.0877	1.38468	0.692340	−	0.721572i	$-0.256580\pi$
$571$	33.0877	1.38468	0.692340	+	0.721572i	$0.256580\pi$
$572$	−9.39817	−0.392957
$573$	12.3274	0.514985
$574$	0	0
$575$	−3.63828	−0.151727
$576$	−9.48932	−0.395388
$577$	−42.8806	−1.78514	−0.892572	−	0.450906i	$-0.851101\pi$
$577$	−42.8806	−1.78514	−0.892572	+	0.450906i	$0.851101\pi$
$578$	−33.0988	−1.37673
$579$	5.94298	0.246982
$580$	−24.0421	−0.998294
$581$	0	0
$582$	−30.0327	−1.24490
$583$	−5.52766	−0.228932
$584$	27.7514	1.14836
$585$	−6.63999	−0.274530
$586$	27.5082	1.13635
$587$	−17.0711	−0.704601	−0.352300	−	0.935887i	$-0.614600\pi$
$587$	−17.0711	−0.704601	−0.352300	+	0.935887i	$0.614600\pi$
$588$	0	0
$589$	28.6757	1.18156
$590$	−35.2595	−1.45161
$591$	−18.0182	−0.741171
$592$	2.51265	0.103269
$593$	2.61697	0.107466	0.0537330	−	0.998555i	$-0.482888\pi$
$593$	2.61697	0.107466	0.0537330	+	0.998555i	$0.482888\pi$
$594$	2.60718	0.106974
$595$	0	0
$596$	2.61157	0.106974
$597$	−14.0168	−0.573671
$598$	−5.47067	−0.223712
$599$	20.5688	0.840418	0.420209	−	0.907427i	$-0.361957\pi$
$599$	20.5688	0.840418	0.420209	+	0.907427i	$0.361957\pi$
$600$	−16.4196	−0.670328
$601$	32.8336	1.33931	0.669656	−	0.742672i	$-0.266442\pi$
$601$	32.8336	1.33931	0.669656	+	0.742672i	$0.266442\pi$
$602$	0	0
$603$	−4.90507	−0.199750
$604$	39.0704	1.58975
$605$	28.9230	1.17589
$606$	−12.9657	−0.526696
$607$	−3.72500	−0.151193	−0.0755965	−	0.997138i	$-0.524086\pi$
$607$	−3.72500	−0.151193	−0.0755965	+	0.997138i	$0.524086\pi$
$608$	7.62472	0.309223
$609$	0	0
$610$	47.7228	1.93224
$611$	−26.4070	−1.06831
$612$	7.05206	0.285063
$613$	36.3283	1.46729	0.733643	−	0.679535i	$-0.237819\pi$
$613$	36.3283	1.46729	0.733643	+	0.679535i	$0.237819\pi$
$614$	−71.1932	−2.87312
$615$	−1.91448	−0.0771991
$616$	0	0
$617$	−31.9411	−1.28590	−0.642951	−	0.765907i	$-0.722290\pi$
$617$	−31.9411	−1.28590	−0.642951	+	0.765907i	$0.722290\pi$
$618$	23.4964	0.945163
$619$	−17.0999	−0.687303	−0.343651	−	0.939097i	$-0.611664\pi$
$619$	−17.0999	−0.687303	−0.343651	+	0.939097i	$0.611664\pi$
$620$	54.4547	2.18695
$621$	1.00000	0.0401286
$622$	−19.4322	−0.779162
$623$	0	0
$624$	−7.23143	−0.289489
$625$	−29.9543	−1.19817
$626$	−51.8527	−2.07245
$627$	−6.43846	−0.257127
$628$	−87.6202	−3.49643
$629$	1.43275	0.0571277
$630$	0	0
$631$	31.9847	1.27329	0.636645	−	0.771157i	$-0.280322\pi$
$631$	31.9847	1.27329	0.636645	+	0.771157i	$0.280322\pi$
$632$	−21.0199	−0.836125
$633$	−20.4176	−0.811526
$634$	−41.0575	−1.63060
$635$	−41.3034	−1.63908
$636$	−19.8364	−0.786565
$637$	0	0
$638$	−5.51980	−0.218531
$639$	−12.3101	−0.486978
$640$	60.0410	2.37333
$641$	−11.8264	−0.467114	−0.233557	−	0.972343i	$-0.575037\pi$
$641$	−11.8264	−0.467114	−0.233557	+	0.972343i	$0.575037\pi$
$642$	22.8377	0.901331
$643$	42.1730	1.66314	0.831570	−	0.555421i	$-0.187443\pi$
$643$	42.1730	1.66314	0.831570	+	0.555421i	$0.187443\pi$
$644$	0	0
$645$	−33.8420	−1.33253
$646$	−26.4299	−1.03987
$647$	−21.3626	−0.839851	−0.419925	−	0.907559i	$-0.637944\pi$
$647$	−21.3626	−0.839851	−0.419925	+	0.907559i	$0.637944\pi$
$648$	4.51302	0.177288
$649$	−5.33409	−0.209381
$650$	19.9038	0.780692
$651$	0	0
$652$	−71.8634	−2.81439
$653$	−21.7566	−0.851401	−0.425700	−	0.904864i	$-0.639972\pi$
$653$	−21.7566	−0.851401	−0.425700	+	0.904864i	$0.639972\pi$
$654$	13.8139	0.540165
$655$	−39.6157	−1.54791
$656$	−2.08500	−0.0814057
$657$	6.14919	0.239903
$658$	0	0
$659$	−11.5661	−0.450550	−0.225275	−	0.974295i	$-0.572328\pi$
$659$	−11.5661	−0.450550	−0.225275	+	0.974295i	$0.572328\pi$
$660$	−12.2265	−0.475917
$661$	−26.6669	−1.03722	−0.518612	−	0.855010i	$-0.673551\pi$
$661$	−26.6669	−1.03722	−0.518612	+	0.855010i	$0.673551\pi$
$662$	−38.1327	−1.48207
$663$	−4.12348	−0.160143
$664$	−52.5334	−2.03869
$665$	0	0
$666$	1.90085	0.0736565
$667$	−2.11716	−0.0819767
$668$	51.4892	1.99218
$669$	5.11396	0.197717
$670$	34.9097	1.34868
$671$	7.21955	0.278707
$672$	0	0
$673$	−0.166761	−0.00642815	−0.00321407	−	0.999995i	$-0.501023\pi$
$673$	−0.166761	−0.00642815	−0.00321407	+	0.999995i	$0.501023\pi$
$674$	−6.08757	−0.234485
$675$	−3.63828	−0.140037
$676$	−30.5081	−1.17339
$677$	−29.1157	−1.11901	−0.559503	−	0.828828i	$-0.689008\pi$
$677$	−29.1157	−1.11901	−0.559503	+	0.828828i	$0.689008\pi$
$678$	16.9688	0.651682
$679$	0	0
$680$	−24.2098	−0.928403
$681$	−22.5199	−0.862966
$682$	12.5022	0.478734
$683$	−0.923218	−0.0353260	−0.0176630	−	0.999844i	$-0.505623\pi$
$683$	−0.923218	−0.0353260	−0.0176630	+	0.999844i	$0.505623\pi$
$684$	−23.1049	−0.883437
$685$	−31.6097	−1.20774
$686$	0	0
$687$	8.51930	0.325032
$688$	−36.8564	−1.40514
$689$	11.5988	0.441878
$690$	−7.11705	−0.270942
$691$	26.0948	0.992692	0.496346	−	0.868125i	$-0.334675\pi$
$691$	26.0948	0.992692	0.496346	+	0.868125i	$0.334675\pi$
$692$	12.5437	0.476838
$693$	0	0
$694$	62.7585	2.38228
$695$	−39.0012	−1.47940
$696$	−9.55477	−0.362173
$697$	−1.18890	−0.0450329
$698$	49.5534	1.87562
$699$	−18.5322	−0.700951
$700$	0	0
$701$	−6.60088	−0.249312	−0.124656	−	0.992200i	$-0.539783\pi$
$701$	−6.60088	−0.249312	−0.124656	+	0.992200i	$0.539783\pi$
$702$	−5.47067	−0.206477
$703$	−4.69418	−0.177044
$704$	10.2169	0.385064
$705$	−34.3541	−1.29385
$706$	75.6074	2.84552
$707$	0	0
$708$	−19.1418	−0.719391
$709$	−30.7256	−1.15392	−0.576962	−	0.816771i	$-0.695762\pi$
$709$	−30.7256	−1.15392	−0.576962	+	0.816771i	$0.695762\pi$
$710$	87.6113	3.28799
$711$	−4.65761	−0.174674
$712$	36.0526	1.35113
$713$	4.79531	0.179586
$714$	0	0
$715$	7.14910	0.267361
$716$	−44.9015	−1.67805
$717$	−22.4541	−0.838564
$718$	54.0827	2.01835
$719$	39.6963	1.48042	0.740212	−	0.672374i	$-0.234725\pi$
$719$	39.6963	1.48042	0.740212	+	0.672374i	$0.234725\pi$
$720$	−9.40772	−0.350605
$721$	0	0
$722$	40.5842	1.51039
$723$	23.0220	0.856199
$724$	−0.421811	−0.0156765
$725$	7.70281	0.286075
$726$	23.8296	0.884398
$727$	−17.5715	−0.651691	−0.325846	−	0.945423i	$-0.605649\pi$
$727$	−17.5715	−0.651691	−0.325846	+	0.945423i	$0.605649\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−43.7641	−1.61978
$731$	−21.0161	−0.777309
$732$	25.9079	0.957582
$733$	−12.1904	−0.450262	−0.225131	−	0.974328i	$-0.572281\pi$
$733$	−12.1904	−0.450262	−0.225131	+	0.974328i	$0.572281\pi$
$734$	44.3795	1.63808
$735$	0	0
$736$	1.27505	0.0469988
$737$	5.28116	0.194534
$738$	−1.57733	−0.0580624
$739$	−21.9068	−0.805856	−0.402928	−	0.915232i	$-0.632008\pi$
$739$	−21.9068	−0.805856	−0.402928	+	0.915232i	$0.632008\pi$
$740$	−8.91416	−0.327691
$741$	13.5099	0.496298
$742$	0	0
$743$	7.30376	0.267949	0.133974	−	0.990985i	$-0.457226\pi$
$743$	7.30376	0.267949	0.133974	+	0.990985i	$0.457226\pi$
$744$	21.6413	0.793409
$745$	−1.98660	−0.0727832
$746$	−38.5466	−1.41129
$747$	−11.6404	−0.425900
$748$	−7.59276	−0.277619
$749$	0	0
$750$	−9.69144	−0.353881
$751$	11.7596	0.429114	0.214557	−	0.976711i	$-0.431169\pi$
$751$	11.7596	0.429114	0.214557	+	0.976711i	$0.431169\pi$
$752$	−37.4142	−1.36435
$753$	28.5202	1.03933
$754$	11.5823	0.421801
$755$	−29.7205	−1.08164
$756$	0	0
$757$	−28.2283	−1.02598	−0.512988	−	0.858396i	$-0.671462\pi$
$757$	−28.2283	−1.02598	−0.512988	+	0.858396i	$0.671462\pi$
$758$	87.8484	3.19080
$759$	−1.07667	−0.0390808
$760$	79.3193	2.87721
$761$	5.97649	0.216648	0.108324	−	0.994116i	$-0.465452\pi$
$761$	5.97649	0.216648	0.108324	+	0.994116i	$0.465452\pi$
$762$	−34.0298	−1.23277
$763$	0	0
$764$	−47.6297	−1.72318
$765$	−5.36444	−0.193952
$766$	−18.3829	−0.664203
$767$	11.1926	0.404140
$768$	30.4890	1.10018
$769$	23.5927	0.850773	0.425387	−	0.905012i	$-0.360138\pi$
$769$	23.5927	0.850773	0.425387	+	0.905012i	$0.360138\pi$
$770$	0	0
$771$	−20.0084	−0.720584
$772$	−22.9620	−0.826420
$773$	−13.9013	−0.499997	−0.249998	−	0.968246i	$-0.580430\pi$
$773$	−13.9013	−0.499997	−0.249998	+	0.968246i	$0.580430\pi$
$774$	−27.8823	−1.00221
$775$	−17.4467	−0.626703
$776$	55.9725	2.00930
$777$	0	0
$778$	−52.6893	−1.88900
$779$	3.89524	0.139561
$780$	25.6551	0.918598
$781$	13.2539	0.474262
$782$	−4.41974	−0.158050
$783$	−2.11716	−0.0756610
$784$	0	0
$785$	66.6519	2.37891
$786$	−32.6393	−1.16420
$787$	14.6994	0.523977	0.261989	−	0.965071i	$-0.415622\pi$
$787$	14.6994	0.523977	0.261989	+	0.965071i	$0.415622\pi$
$788$	69.6174	2.48002
$789$	−12.6331	−0.449750
$790$	33.1484	1.17937
$791$	0	0
$792$	−4.85905	−0.172659
$793$	−15.1489	−0.537952
$794$	16.3922	0.581737
$795$	15.0894	0.535165
$796$	54.1571	1.91955
$797$	6.45704	0.228720	0.114360	−	0.993439i	$-0.463518\pi$
$797$	6.45704	0.228720	0.114360	+	0.993439i	$0.463518\pi$
$798$	0	0
$799$	−21.3342	−0.754749
$800$	−4.63897	−0.164012
$801$	7.98858	0.282263
$802$	84.7840	2.99383
$803$	−6.62067	−0.233638
$804$	18.9518	0.668379
$805$	0	0
$806$	−26.2335	−0.924037
$807$	9.30286	0.327476
$808$	24.1644	0.850102
$809$	3.41261	0.119981	0.0599905	−	0.998199i	$-0.480893\pi$
$809$	3.41261	0.119981	0.0599905	+	0.998199i	$0.480893\pi$
$810$	−7.11705	−0.250068
$811$	−54.2761	−1.90589	−0.952945	−	0.303143i	$-0.901964\pi$
$811$	−54.2761	−1.90589	−0.952945	+	0.303143i	$0.901964\pi$
$812$	0	0
$813$	−9.34011	−0.327572
$814$	−2.04659	−0.0717331
$815$	54.6658	1.91486
$816$	−5.84226	−0.204520
$817$	68.8557	2.40896
$818$	−37.0944	−1.29697
$819$	0	0
$820$	7.39700	0.258314
$821$	33.5849	1.17212	0.586061	−	0.810267i	$-0.300678\pi$
$821$	33.5849	1.17212	0.586061	+	0.810267i	$0.300678\pi$
$822$	−26.0431	−0.908358
$823$	30.7044	1.07029	0.535144	−	0.844761i	$-0.320257\pi$
$823$	30.7044	1.07029	0.535144	+	0.844761i	$0.320257\pi$
$824$	−43.7907	−1.52552
$825$	3.91724	0.136381
$826$	0	0
$827$	−22.6890	−0.788974	−0.394487	−	0.918901i	$-0.629078\pi$
$827$	−22.6890	−0.788974	−0.394487	+	0.918901i	$0.629078\pi$
$828$	−3.86372	−0.134274
$829$	−48.2924	−1.67727	−0.838633	−	0.544697i	$-0.816645\pi$
$829$	−48.2924	−1.67727	−0.838633	+	0.544697i	$0.816645\pi$
$830$	82.8454	2.87561
$831$	−19.1201	−0.663268
$832$	−21.4382	−0.743237
$833$	0	0
$834$	−32.1330	−1.11267
$835$	−39.1673	−1.35544
$836$	24.8764	0.860368
$837$	4.79531	0.165750
$838$	−58.8135	−2.03168
$839$	13.4310	0.463688	0.231844	−	0.972753i	$-0.425524\pi$
$839$	13.4310	0.463688	0.231844	+	0.972753i	$0.425524\pi$
$840$	0	0
$841$	−24.5176	−0.845436
$842$	12.6682	0.436576
$843$	−12.5065	−0.430746
$844$	78.8879	2.71543
$845$	23.2072	0.798352
$846$	−28.3043	−0.973121
$847$	0	0
$848$	16.4334	0.564327
$849$	14.4872	0.497200
$850$	16.0803	0.551548
$851$	−0.784985	−0.0269089
$852$	47.5626	1.62947
$853$	−8.95120	−0.306483	−0.153242	−	0.988189i	$-0.548971\pi$
$853$	−8.95120	−0.306483	−0.153242	+	0.988189i	$0.548971\pi$
$854$	0	0
$855$	17.5757	0.601075
$856$	−42.5630	−1.45477
$857$	−6.13932	−0.209715	−0.104858	−	0.994487i	$-0.533439\pi$
$857$	−6.13932	−0.209715	−0.104858	+	0.994487i	$0.533439\pi$
$858$	5.89012	0.201085
$859$	41.0489	1.40057	0.700285	−	0.713863i	$-0.253056\pi$
$859$	41.0489	1.40057	0.700285	+	0.713863i	$0.253056\pi$
$860$	130.756	4.45874
$861$	0	0
$862$	67.0839	2.28489
$863$	14.0676	0.478866	0.239433	−	0.970913i	$-0.423038\pi$
$863$	14.0676	0.478866	0.239433	+	0.970913i	$0.423038\pi$
$864$	1.27505	0.0433779
$865$	−9.54184	−0.324432
$866$	55.8040	1.89630
$867$	13.6686	0.464212
$868$	0	0
$869$	5.01472	0.170113
$870$	15.0679	0.510850
$871$	−11.0815	−0.375483
$872$	−25.7452	−0.871842
$873$	12.4025	0.419760
$874$	14.4805	0.489811
$875$	0	0
$876$	−23.7587	−0.802733
$877$	14.6258	0.493879	0.246940	−	0.969031i	$-0.420575\pi$
$877$	14.6258	0.493879	0.246940	+	0.969031i	$0.420575\pi$
$878$	8.71058	0.293968
$879$	−11.3599	−0.383161
$880$	10.1290	0.341450
$881$	25.1548	0.847487	0.423743	−	0.905782i	$-0.360716\pi$
$881$	25.1548	0.847487	0.423743	+	0.905782i	$0.360716\pi$
$882$	0	0
$883$	−35.1135	−1.18166	−0.590832	−	0.806795i	$-0.701200\pi$
$883$	−35.1135	−1.18166	−0.590832	+	0.806795i	$0.701200\pi$
$884$	15.9320	0.535851
$885$	14.5610	0.489461
$886$	16.1197	0.541550
$887$	−35.0826	−1.17796	−0.588978	−	0.808149i	$-0.700470\pi$
$887$	−35.0826	−1.17796	−0.588978	+	0.808149i	$0.700470\pi$
$888$	−3.54265	−0.118884
$889$	0	0
$890$	−56.8552	−1.90579
$891$	−1.07667	−0.0360699
$892$	−19.7589	−0.661577
$893$	69.8978	2.33904
$894$	−1.63675	−0.0547411
$895$	34.1561	1.14171
$896$	0	0
$897$	2.25920	0.0754323
$898$	−48.1830	−1.60789
$899$	−10.1524	−0.338602
$900$	14.0573	0.468576
$901$	9.37062	0.312180
$902$	1.69827	0.0565462
$903$	0	0
$904$	−31.6250	−1.05183
$905$	0.320868	0.0106660
$906$	−24.4866	−0.813514
$907$	−54.2296	−1.80066	−0.900332	−	0.435204i	$-0.856676\pi$
$907$	−54.2296	−1.80066	−0.900332	+	0.435204i	$0.856676\pi$
$908$	87.0108	2.88755
$909$	5.35438	0.177594
$910$	0	0
$911$	47.7875	1.58327	0.791635	−	0.610994i	$-0.209230\pi$
$911$	47.7875	1.58327	0.791635	+	0.610994i	$0.209230\pi$
$912$	19.1412	0.633828
$913$	12.5329	0.414779
$914$	4.84436	0.160237
$915$	−19.7079	−0.651522
$916$	−32.9162	−1.08758
$917$	0	0
$918$	−4.41974	−0.145873
$919$	16.5558	0.546126	0.273063	−	0.961996i	$-0.411963\pi$
$919$	16.5558	0.546126	0.273063	+	0.961996i	$0.411963\pi$
$920$	13.2642	0.437307
$921$	29.4003	0.968773
$922$	−30.2607	−0.996584
$923$	−27.8108	−0.915404
$924$	0	0
$925$	2.85599	0.0939045
$926$	−63.1581	−2.07550
$927$	−9.70318	−0.318694
$928$	−2.69947	−0.0886146
$929$	−36.5762	−1.20003	−0.600013	−	0.799990i	$-0.704838\pi$
$929$	−36.5762	−1.20003	−0.600013	+	0.799990i	$0.704838\pi$
$930$	−34.1284	−1.11912
$931$	0	0
$932$	71.6031	2.34544
$933$	8.02484	0.262721
$934$	−98.2905	−3.21616
$935$	5.77574	0.188887
$936$	10.1958	0.333260
$937$	44.5852	1.45654	0.728268	−	0.685293i	$-0.240326\pi$
$937$	44.5852	1.45654	0.728268	+	0.685293i	$0.240326\pi$
$938$	0	0
$939$	21.4133	0.698798
$940$	132.735	4.32933
$941$	38.7461	1.26309	0.631544	−	0.775340i	$-0.282421\pi$
$941$	38.7461	1.26309	0.631544	+	0.775340i	$0.282421\pi$
$942$	54.9143	1.78920
$943$	0.651383	0.0212119
$944$	15.8579	0.516132
$945$	0	0
$946$	30.0201	0.976038
$947$	42.1257	1.36890	0.684451	−	0.729059i	$-0.260042\pi$
$947$	42.1257	1.36890	0.684451	+	0.729059i	$0.260042\pi$
$948$	17.9957	0.584473
$949$	13.8922	0.450960
$950$	−52.6842	−1.70930
$951$	16.9553	0.549813
$952$	0	0
$953$	60.2547	1.95184	0.975920	−	0.218127i	$-0.0699947\pi$
$953$	60.2547	1.95184	0.975920	+	0.218127i	$0.0699947\pi$
$954$	12.4321	0.402504
$955$	36.2315	1.17242
$956$	86.7563	2.80590
$957$	2.27949	0.0736853
$958$	−91.4505	−2.95463
$959$	0	0
$960$	−27.8900	−0.900146
$961$	−8.00504	−0.258227
$962$	4.29439	0.138457
$963$	−9.43117	−0.303915
$964$	−88.9507	−2.86491
$965$	17.4670	0.562282
$966$	0	0
$967$	−52.7272	−1.69559	−0.847796	−	0.530322i	$-0.822071\pi$
$967$	−52.7272	−1.69559	−0.847796	+	0.530322i	$0.822071\pi$
$968$	−44.4116	−1.42744
$969$	10.9146	0.350628
$970$	−88.2690	−2.83415
$971$	−51.4776	−1.65199	−0.825997	−	0.563675i	$-0.809387\pi$
$971$	−51.4776	−1.65199	−0.825997	+	0.563675i	$0.809387\pi$
$972$	−3.86372	−0.123929
$973$	0	0
$974$	−64.1319	−2.05492
$975$	−8.21958	−0.263237
$976$	−21.4633	−0.687024
$977$	3.78549	0.121109	0.0605543	−	0.998165i	$-0.480713\pi$
$977$	3.78549	0.121109	0.0605543	+	0.998165i	$0.480713\pi$
$978$	45.0390	1.44019
$979$	−8.60109	−0.274892
$980$	0	0
$981$	−5.70465	−0.182135
$982$	−34.0489	−1.08654
$983$	13.9635	0.445365	0.222682	−	0.974891i	$-0.428519\pi$
$983$	13.9635	0.445365	0.222682	+	0.974891i	$0.428519\pi$
$984$	2.93970	0.0937143
$985$	−52.9573	−1.68736
$986$	9.35729	0.297997
$987$	0	0
$988$	−52.1984	−1.66065
$989$	11.5144	0.366137
$990$	7.66274	0.243538
$991$	−34.5001	−1.09593	−0.547966	−	0.836500i	$-0.684598\pi$
$991$	−34.5001	−1.09593	−0.547966	+	0.836500i	$0.684598\pi$
$992$	6.11424	0.194127
$993$	15.7475	0.499731
$994$	0	0
$995$	−41.1968	−1.30603
$996$	44.9753	1.42510
$997$	1.41313	0.0447544	0.0223772	−	0.999750i	$-0.492877\pi$
$997$	1.41313	0.0447544	0.0223772	+	0.999750i	$0.492877\pi$
$998$	105.186	3.32962
$999$	−0.784985	−0.0248358

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.bk.1.9	✓	10
7.6	odd	2		3381.2.a.bl.1.9	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3381.2.a.bk.1.9	✓	10	1.1	even	1	trivial
3381.2.a.bl.1.9	yes	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:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3381.a (trivial)

\(f(q)\)	\(=\)	\(q+2.42151 q^{2} -1.00000 q^{3} +3.86372 q^{4} -2.93909 q^{5} -2.42151 q^{6} +4.51302 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.42151 q^{2} -1.00000 q^{3} +3.86372 q^{4} -2.93909 q^{5} -2.42151 q^{6} +4.51302 q^{8} +1.00000 q^{9} -7.11705 q^{10} -1.07667 q^{11} -3.86372 q^{12} +2.25920 q^{13} +2.93909 q^{15} +3.20089 q^{16} +1.82520 q^{17} +2.42151 q^{18} -5.97996 q^{19} -11.3558 q^{20} -2.60718 q^{22} -1.00000 q^{23} -4.51302 q^{24} +3.63828 q^{25} +5.47067 q^{26} -1.00000 q^{27} +2.11716 q^{29} +7.11705 q^{30} -4.79531 q^{31} -1.27505 q^{32} +1.07667 q^{33} +4.41974 q^{34} +3.86372 q^{36} +0.784985 q^{37} -14.4805 q^{38} -2.25920 q^{39} -13.2642 q^{40} -0.651383 q^{41} -11.5144 q^{43} -4.15996 q^{44} -2.93909 q^{45} -2.42151 q^{46} -11.6887 q^{47} -3.20089 q^{48} +8.81013 q^{50} -1.82520 q^{51} +8.72890 q^{52} +5.13402 q^{53} -2.42151 q^{54} +3.16444 q^{55} +5.97996 q^{57} +5.12672 q^{58} +4.95423 q^{59} +11.3558 q^{60} -6.70542 q^{61} -11.6119 q^{62} -9.48932 q^{64} -6.63999 q^{65} +2.60718 q^{66} -4.90507 q^{67} +7.05206 q^{68} +1.00000 q^{69} -12.3101 q^{71} +4.51302 q^{72} +6.14919 q^{73} +1.90085 q^{74} -3.63828 q^{75} -23.1049 q^{76} -5.47067 q^{78} -4.65761 q^{79} -9.40772 q^{80} +1.00000 q^{81} -1.57733 q^{82} -11.6404 q^{83} -5.36444 q^{85} -27.8823 q^{86} -2.11716 q^{87} -4.85905 q^{88} +7.98858 q^{89} -7.11705 q^{90} -3.86372 q^{92} +4.79531 q^{93} -28.3043 q^{94} +17.5757 q^{95} +1.27505 q^{96} +12.4025 q^{97} -1.07667 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} - 10 q^{3} + 8 q^{4} - 4 q^{5} - 4 q^{6} + 12 q^{8} + 10 q^{9}+O(q^{10}) \) 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

Varieties

Fields

Representations

Groups

Database

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