LMFDB - Embedded newform 6027.2.a.bk.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6027 = 3 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6027.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1258372982$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} - 19 x^{12} + 36 x^{11} + 134 x^{10} - 237 x^{9} - 438 x^{8} + 716 x^{7} + 662 x^{6} + \cdots + 16 $ x^14 - 2x^13 - 19x^12 + 36x^11 + 134x^10 - 237x^9 - 438x^8 + 716x^7 + 662x^6 - 1007x^5 - 384x^4 + 579x^3 + 44x^2 - 112*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 861)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.13215$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.13215 q^{2} +1.00000 q^{3} +2.54608 q^{4} +2.91322 q^{5} -2.13215 q^{6} -1.16433 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.13215 q^{2} +1.00000 q^{3} +2.54608 q^{4} +2.91322 q^{5} -2.13215 q^{6} -1.16433 q^{8} +1.00000 q^{9} -6.21144 q^{10} -1.50055 q^{11} +2.54608 q^{12} -2.14723 q^{13} +2.91322 q^{15} -2.60963 q^{16} +2.46605 q^{17} -2.13215 q^{18} -7.23455 q^{19} +7.41731 q^{20} +3.19941 q^{22} +4.49416 q^{23} -1.16433 q^{24} +3.48687 q^{25} +4.57823 q^{26} +1.00000 q^{27} -9.11879 q^{29} -6.21144 q^{30} -7.76497 q^{31} +7.89280 q^{32} -1.50055 q^{33} -5.25800 q^{34} +2.54608 q^{36} +1.76746 q^{37} +15.4252 q^{38} -2.14723 q^{39} -3.39196 q^{40} -1.00000 q^{41} +6.47180 q^{43} -3.82053 q^{44} +2.91322 q^{45} -9.58224 q^{46} -1.43939 q^{47} -2.60963 q^{48} -7.43455 q^{50} +2.46605 q^{51} -5.46703 q^{52} +3.74917 q^{53} -2.13215 q^{54} -4.37145 q^{55} -7.23455 q^{57} +19.4427 q^{58} -7.69935 q^{59} +7.41731 q^{60} +5.74045 q^{61} +16.5561 q^{62} -11.6094 q^{64} -6.25537 q^{65} +3.19941 q^{66} -13.0781 q^{67} +6.27877 q^{68} +4.49416 q^{69} -4.11377 q^{71} -1.16433 q^{72} +2.78408 q^{73} -3.76851 q^{74} +3.48687 q^{75} -18.4198 q^{76} +4.57823 q^{78} +15.6156 q^{79} -7.60243 q^{80} +1.00000 q^{81} +2.13215 q^{82} -1.23966 q^{83} +7.18416 q^{85} -13.7989 q^{86} -9.11879 q^{87} +1.74714 q^{88} -10.2933 q^{89} -6.21144 q^{90} +11.4425 q^{92} -7.76497 q^{93} +3.06901 q^{94} -21.0759 q^{95} +7.89280 q^{96} +2.93804 q^{97} -1.50055 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} + 14 q^{3} + 14 q^{4} - 10 q^{5} - 2 q^{6} - 6 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 2 * q^2 + 14 * q^3 + 14 * q^4 - 10 * q^5 - 2 * q^6 - 6 * q^8 + 14 * q^9	$ 14 q - 2 q^{2} + 14 q^{3} + 14 q^{4} - 10 q^{5} - 2 q^{6} - 6 q^{8} + 14 q^{9} - 3 q^{10} - 16 q^{11} + 14 q^{12} - 21 q^{13} - 10 q^{15} + 22 q^{16} - 12 q^{17} - 2 q^{18} - 2 q^{19} - 40 q^{20} + q^{22} - 7 q^{23} - 6 q^{24} + 22 q^{25} - 2 q^{26} + 14 q^{27} - 16 q^{29} - 3 q^{30} - 8 q^{31} - 19 q^{32} - 16 q^{33} - 33 q^{34} + 14 q^{36} + q^{37} - 32 q^{38} - 21 q^{39} + 13 q^{40} - 14 q^{41} + 14 q^{43} - 36 q^{44} - 10 q^{45} - 12 q^{46} - 12 q^{47} + 22 q^{48} - q^{50} - 12 q^{51} - 60 q^{52} - 20 q^{53} - 2 q^{54} + 11 q^{55} - 2 q^{57} + 21 q^{58} - 25 q^{59} - 40 q^{60} - 26 q^{61} + 33 q^{62} + 42 q^{64} - 8 q^{65} + q^{66} - 22 q^{67} - 15 q^{68} - 7 q^{69} - 36 q^{71} - 6 q^{72} - 31 q^{73} - 65 q^{74} + 22 q^{75} + 2 q^{76} - 2 q^{78} + 12 q^{79} - 112 q^{80} + 14 q^{81} + 2 q^{82} - 20 q^{83} + 40 q^{85} - 9 q^{86} - 16 q^{87} - 54 q^{88} - 39 q^{89} - 3 q^{90} + 63 q^{92} - 8 q^{93} - 14 q^{94} - 55 q^{95} - 19 q^{96} - 18 q^{97} - 16 q^{99}+O(q^{100}) $ 14 * q - 2 * q^2 + 14 * q^3 + 14 * q^4 - 10 * q^5 - 2 * q^6 - 6 * q^8 + 14 * q^9 - 3 * q^10 - 16 * q^11 + 14 * q^12 - 21 * q^13 - 10 * q^15 + 22 * q^16 - 12 * q^17 - 2 * q^18 - 2 * q^19 - 40 * q^20 + q^22 - 7 * q^23 - 6 * q^24 + 22 * q^25 - 2 * q^26 + 14 * q^27 - 16 * q^29 - 3 * q^30 - 8 * q^31 - 19 * q^32 - 16 * q^33 - 33 * q^34 + 14 * q^36 + q^37 - 32 * q^38 - 21 * q^39 + 13 * q^40 - 14 * q^41 + 14 * q^43 - 36 * q^44 - 10 * q^45 - 12 * q^46 - 12 * q^47 + 22 * q^48 - q^50 - 12 * q^51 - 60 * q^52 - 20 * q^53 - 2 * q^54 + 11 * q^55 - 2 * q^57 + 21 * q^58 - 25 * q^59 - 40 * q^60 - 26 * q^61 + 33 * q^62 + 42 * q^64 - 8 * q^65 + q^66 - 22 * q^67 - 15 * q^68 - 7 * q^69 - 36 * q^71 - 6 * q^72 - 31 * q^73 - 65 * q^74 + 22 * q^75 + 2 * q^76 - 2 * q^78 + 12 * q^79 - 112 * q^80 + 14 * q^81 + 2 * q^82 - 20 * q^83 + 40 * q^85 - 9 * q^86 - 16 * q^87 - 54 * q^88 - 39 * q^89 - 3 * q^90 + 63 * q^92 - 8 * q^93 - 14 * q^94 - 55 * q^95 - 19 * q^96 - 18 * q^97 - 16 * 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 $

$2$	−2.13215	−1.50766	−0.753830	−	0.657069i	$-0.771796\pi$
$2$	−2.13215	−1.50766	−0.753830	+	0.657069i	$0.771796\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.54608	1.27304
$5$	2.91322	1.30283	0.651417	−	0.758720i	$-0.274175\pi$
$5$	2.91322	1.30283	0.651417	+	0.758720i	$0.274175\pi$
$6$	−2.13215	−0.870448
$7$	0	0
$7$	0	0
$8$	−1.16433	−0.411654
$9$	1.00000	0.333333
$10$	−6.21144	−1.96423
$11$	−1.50055	−0.452434	−0.226217	−	0.974077i	$-0.572636\pi$
$11$	−1.50055	−0.452434	−0.226217	+	0.974077i	$0.572636\pi$
$12$	2.54608	0.734991
$13$	−2.14723	−0.595535	−0.297768	−	0.954638i	$-0.596242\pi$
$13$	−2.14723	−0.595535	−0.297768	+	0.954638i	$0.596242\pi$
$14$	0	0
$15$	2.91322	0.752191
$16$	−2.60963	−0.652407
$17$	2.46605	0.598105	0.299053	−	0.954237i	$-0.403329\pi$
$17$	2.46605	0.598105	0.299053	+	0.954237i	$0.403329\pi$
$18$	−2.13215	−0.502554
$19$	−7.23455	−1.65972	−0.829860	−	0.557972i	$-0.811580\pi$
$19$	−7.23455	−1.65972	−0.829860	+	0.557972i	$0.811580\pi$
$20$	7.41731	1.65856
$21$	0	0
$22$	3.19941	0.682117
$23$	4.49416	0.937097	0.468548	−	0.883438i	$-0.344777\pi$
$23$	4.49416	0.937097	0.468548	+	0.883438i	$0.344777\pi$
$24$	−1.16433	−0.237668
$25$	3.48687	0.697374
$26$	4.57823	0.897866
$27$	1.00000	0.192450
$28$	0	0
$29$	−9.11879	−1.69332	−0.846659	−	0.532136i	$-0.821389\pi$
$29$	−9.11879	−1.69332	−0.846659	+	0.532136i	$0.821389\pi$
$30$	−6.21144	−1.13405
$31$	−7.76497	−1.39463	−0.697315	−	0.716765i	$-0.745622\pi$
$31$	−7.76497	−1.39463	−0.697315	+	0.716765i	$0.745622\pi$
$32$	7.89280	1.39526
$33$	−1.50055	−0.261213
$34$	−5.25800	−0.901740
$35$	0	0
$36$	2.54608	0.424347
$37$	1.76746	0.290569	0.145285	−	0.989390i	$-0.453590\pi$
$37$	1.76746	0.290569	0.145285	+	0.989390i	$0.453590\pi$
$38$	15.4252	2.50229
$39$	−2.14723	−0.343833
$40$	−3.39196	−0.536316
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	6.47180	0.986941	0.493470	−	0.869763i	$-0.335728\pi$
$43$	6.47180	0.986941	0.493470	+	0.869763i	$0.335728\pi$
$44$	−3.82053	−0.575967
$45$	2.91322	0.434278
$46$	−9.58224	−1.41282
$47$	−1.43939	−0.209957	−0.104979	−	0.994474i	$-0.533477\pi$
$47$	−1.43939	−0.209957	−0.104979	+	0.994474i	$0.533477\pi$
$48$	−2.60963	−0.376667
$49$	0	0
$50$	−7.43455	−1.05140
$51$	2.46605	0.345316
$52$	−5.46703	−0.758141
$53$	3.74917	0.514988	0.257494	−	0.966280i	$-0.417103\pi$
$53$	3.74917	0.514988	0.257494	+	0.966280i	$0.417103\pi$
$54$	−2.13215	−0.290149
$55$	−4.37145	−0.589446
$56$	0	0
$57$	−7.23455	−0.958240
$58$	19.4427	2.55295
$59$	−7.69935	−1.00237	−0.501185	−	0.865340i	$-0.667102\pi$
$59$	−7.69935	−1.00237	−0.501185	+	0.865340i	$0.667102\pi$
$60$	7.41731	0.957570
$61$	5.74045	0.734990	0.367495	−	0.930026i	$-0.380216\pi$
$61$	5.74045	0.734990	0.367495	+	0.930026i	$0.380216\pi$
$62$	16.5561	2.10263
$63$	0	0
$64$	−11.6094	−1.45118
$65$	−6.25537	−0.775883
$66$	3.19941	0.393821
$67$	−13.0781	−1.59775	−0.798874	−	0.601499i	$-0.794571\pi$
$67$	−13.0781	−1.59775	−0.798874	+	0.601499i	$0.794571\pi$
$68$	6.27877	0.761413
$69$	4.49416	0.541033
$70$	0	0
$71$	−4.11377	−0.488215	−0.244107	−	0.969748i	$-0.578495\pi$
$71$	−4.11377	−0.488215	−0.244107	+	0.969748i	$0.578495\pi$
$72$	−1.16433	−0.137218
$73$	2.78408	0.325852	0.162926	−	0.986638i	$-0.447907\pi$
$73$	2.78408	0.325852	0.162926	+	0.986638i	$0.447907\pi$
$74$	−3.76851	−0.438080
$75$	3.48687	0.402629
$76$	−18.4198	−2.11289
$77$	0	0
$78$	4.57823	0.518383
$79$	15.6156	1.75690	0.878448	−	0.477838i	$-0.158580\pi$
$79$	15.6156	1.75690	0.878448	+	0.477838i	$0.158580\pi$
$80$	−7.60243	−0.849977
$81$	1.00000	0.111111
$82$	2.13215	0.235457
$83$	−1.23966	−0.136071	−0.0680353	−	0.997683i	$-0.521673\pi$
$83$	−1.23966	−0.136071	−0.0680353	+	0.997683i	$0.521673\pi$
$84$	0	0
$85$	7.18416	0.779232
$86$	−13.7989	−1.48797
$87$	−9.11879	−0.977637
$88$	1.74714	0.186246
$89$	−10.2933	−1.09109	−0.545546	−	0.838081i	$-0.683678\pi$
$89$	−10.2933	−1.09109	−0.545546	+	0.838081i	$0.683678\pi$
$90$	−6.21144	−0.654744
$91$	0	0
$92$	11.4425	1.19296
$93$	−7.76497	−0.805190
$94$	3.06901	0.316544
$95$	−21.0759	−2.16234
$96$	7.89280	0.805555
$97$	2.93804	0.298312	0.149156	−	0.988814i	$-0.452344\pi$
$97$	2.93804	0.298312	0.149156	+	0.988814i	$0.452344\pi$
$98$	0	0
$99$	−1.50055	−0.150811
$100$	8.87786	0.887786
$101$	−9.85932	−0.981039	−0.490520	−	0.871430i	$-0.663193\pi$
$101$	−9.85932	−0.981039	−0.490520	+	0.871430i	$0.663193\pi$
$102$	−5.25800	−0.520620
$103$	5.59038	0.550836	0.275418	−	0.961325i	$-0.411184\pi$
$103$	5.59038	0.550836	0.275418	+	0.961325i	$0.411184\pi$
$104$	2.50010	0.245155
$105$	0	0
$106$	−7.99380	−0.776427
$107$	13.7382	1.32812	0.664062	−	0.747678i	$-0.268831\pi$
$107$	13.7382	1.32812	0.664062	+	0.747678i	$0.268831\pi$
$108$	2.54608	0.244997
$109$	−16.8992	−1.61865	−0.809323	−	0.587364i	$-0.800166\pi$
$109$	−16.8992	−1.61865	−0.809323	+	0.587364i	$0.800166\pi$
$110$	9.32061	0.888685
$111$	1.76746	0.167760
$112$	0	0
$113$	−12.2739	−1.15463	−0.577315	−	0.816522i	$-0.695899\pi$
$113$	−12.2739	−1.15463	−0.577315	+	0.816522i	$0.695899\pi$
$114$	15.4252	1.44470
$115$	13.0925	1.22088
$116$	−23.2172	−2.15566
$117$	−2.14723	−0.198512
$118$	16.4162	1.51123
$119$	0	0
$120$	−3.39196	−0.309642
$121$	−8.74834	−0.795303
$122$	−12.2395	−1.10811
$123$	−1.00000	−0.0901670
$124$	−19.7703	−1.77542
$125$	−4.40808	−0.394271
$126$	0	0
$127$	9.83504	0.872719	0.436359	−	0.899773i	$-0.356268\pi$
$127$	9.83504	0.872719	0.436359	+	0.899773i	$0.356268\pi$
$128$	8.96745	0.792618
$129$	6.47180	0.569811
$130$	13.3374	1.16977
$131$	−1.68941	−0.147605	−0.0738024	−	0.997273i	$-0.523513\pi$
$131$	−1.68941	−0.147605	−0.0738024	+	0.997273i	$0.523513\pi$
$132$	−3.82053	−0.332535
$133$	0	0
$134$	27.8846	2.40886
$135$	2.91322	0.250730
$136$	−2.87131	−0.246212
$137$	−18.7959	−1.60584	−0.802921	−	0.596085i	$-0.796722\pi$
$137$	−18.7959	−1.60584	−0.802921	+	0.596085i	$0.796722\pi$
$138$	−9.58224	−0.815695
$139$	3.46444	0.293850	0.146925	−	0.989148i	$-0.453062\pi$
$139$	3.46444	0.293850	0.146925	+	0.989148i	$0.453062\pi$
$140$	0	0
$141$	−1.43939	−0.121219
$142$	8.77120	0.736062
$143$	3.22204	0.269441
$144$	−2.60963	−0.217469
$145$	−26.5651	−2.20611
$146$	−5.93610	−0.491275
$147$	0	0
$148$	4.50011	0.369907
$149$	−22.5119	−1.84424	−0.922121	−	0.386901i	$-0.873546\pi$
$149$	−22.5119	−1.84424	−0.922121	+	0.386901i	$0.873546\pi$
$150$	−7.43455	−0.607028
$151$	−15.5398	−1.26461	−0.632307	−	0.774718i	$-0.717892\pi$
$151$	−15.5398	−1.26461	−0.632307	+	0.774718i	$0.717892\pi$
$152$	8.42343	0.683230
$153$	2.46605	0.199368
$154$	0	0
$155$	−22.6211	−1.81697
$156$	−5.46703	−0.437713
$157$	−20.4910	−1.63536	−0.817680	−	0.575674i	$-0.804740\pi$
$157$	−20.4910	−1.63536	−0.817680	+	0.575674i	$0.804740\pi$
$158$	−33.2949	−2.64880
$159$	3.74917	0.297328
$160$	22.9935	1.81779
$161$	0	0
$162$	−2.13215	−0.167518
$163$	11.4712	0.898495	0.449247	−	0.893407i	$-0.351692\pi$
$163$	11.4712	0.898495	0.449247	+	0.893407i	$0.351692\pi$
$164$	−2.54608	−0.198816
$165$	−4.37145	−0.340317
$166$	2.64315	0.205148
$167$	1.21433	0.0939673	0.0469837	−	0.998896i	$-0.485039\pi$
$167$	1.21433	0.0939673	0.0469837	+	0.998896i	$0.485039\pi$
$168$	0	0
$169$	−8.38939	−0.645338
$170$	−15.3177	−1.17482
$171$	−7.23455	−0.553240
$172$	16.4778	1.25642
$173$	18.3164	1.39257	0.696285	−	0.717765i	$-0.254835\pi$
$173$	18.3164	1.39257	0.696285	+	0.717765i	$0.254835\pi$
$174$	19.4427	1.47395
$175$	0	0
$176$	3.91589	0.295171
$177$	−7.69935	−0.578719
$178$	21.9470	1.64500
$179$	7.80070	0.583052	0.291526	−	0.956563i	$-0.405837\pi$
$179$	7.80070	0.583052	0.291526	+	0.956563i	$0.405837\pi$
$180$	7.41731	0.552854
$181$	2.11732	0.157379	0.0786894	−	0.996899i	$-0.474926\pi$
$181$	2.11732	0.157379	0.0786894	+	0.996899i	$0.474926\pi$
$182$	0	0
$183$	5.74045	0.424346
$184$	−5.23270	−0.385760
$185$	5.14902	0.378563
$186$	16.5561	1.21395
$187$	−3.70044	−0.270603
$188$	−3.66481	−0.267284
$189$	0	0
$190$	44.9370	3.26007
$191$	−20.0465	−1.45051	−0.725256	−	0.688479i	$-0.758279\pi$
$191$	−20.0465	−1.45051	−0.725256	+	0.688479i	$0.758279\pi$
$192$	−11.6094	−0.837837
$193$	−8.66357	−0.623618	−0.311809	−	0.950145i	$-0.600935\pi$
$193$	−8.66357	−0.623618	−0.311809	+	0.950145i	$0.600935\pi$
$194$	−6.26435	−0.449754
$195$	−6.25537	−0.447956
$196$	0	0
$197$	10.9064	0.777051	0.388525	−	0.921438i	$-0.372985\pi$
$197$	10.9064	0.777051	0.388525	+	0.921438i	$0.372985\pi$
$198$	3.19941	0.227372
$199$	−18.3904	−1.30366	−0.651829	−	0.758366i	$-0.725998\pi$
$199$	−18.3904	−1.30366	−0.651829	+	0.758366i	$0.725998\pi$
$200$	−4.05988	−0.287077
$201$	−13.0781	−0.922460
$202$	21.0216	1.47907
$203$	0	0
$204$	6.27877	0.439602
$205$	−2.91322	−0.203468
$206$	−11.9195	−0.830474
$207$	4.49416	0.312366
$208$	5.60348	0.388531
$209$	10.8558	0.750914
$210$	0	0
$211$	24.2561	1.66986	0.834928	−	0.550358i	$-0.185509\pi$
$211$	24.2561	1.66986	0.834928	+	0.550358i	$0.185509\pi$
$212$	9.54569	0.655601
$213$	−4.11377	−0.281871
$214$	−29.2920	−2.00236
$215$	18.8538	1.28582
$216$	−1.16433	−0.0792228
$217$	0	0
$218$	36.0316	2.44037
$219$	2.78408	0.188131
$220$	−11.1301	−0.750389
$221$	−5.29519	−0.356193
$222$	−3.76851	−0.252926
$223$	−10.0523	−0.673149	−0.336574	−	0.941657i	$-0.609268\pi$
$223$	−10.0523	−0.673149	−0.336574	+	0.941657i	$0.609268\pi$
$224$	0	0
$225$	3.48687	0.232458
$226$	26.1698	1.74079
$227$	−3.70831	−0.246129	−0.123065	−	0.992399i	$-0.539272\pi$
$227$	−3.70831	−0.246129	−0.123065	+	0.992399i	$0.539272\pi$
$228$	−18.4198	−1.21988
$229$	−0.627708	−0.0414801	−0.0207401	−	0.999785i	$-0.506602\pi$
$229$	−0.627708	−0.0414801	−0.0207401	+	0.999785i	$0.506602\pi$
$230$	−27.9152	−1.84067
$231$	0	0
$232$	10.6173	0.697061
$233$	−5.69247	−0.372926	−0.186463	−	0.982462i	$-0.559702\pi$
$233$	−5.69247	−0.372926	−0.186463	+	0.982462i	$0.559702\pi$
$234$	4.57823	0.299289
$235$	−4.19327	−0.273539
$236$	−19.6032	−1.27606
$237$	15.6156	1.01434
$238$	0	0
$239$	−2.28786	−0.147989	−0.0739947	−	0.997259i	$-0.523575\pi$
$239$	−2.28786	−0.147989	−0.0739947	+	0.997259i	$0.523575\pi$
$240$	−7.60243	−0.490735
$241$	9.22536	0.594258	0.297129	−	0.954837i	$-0.403971\pi$
$241$	9.22536	0.594258	0.297129	+	0.954837i	$0.403971\pi$
$242$	18.6528	1.19905
$243$	1.00000	0.0641500
$244$	14.6157	0.935672
$245$	0	0
$246$	2.13215	0.135941
$247$	15.5343	0.988422
$248$	9.04101	0.574105
$249$	−1.23966	−0.0785604
$250$	9.39871	0.594427
$251$	−3.04049	−0.191914	−0.0959569	−	0.995385i	$-0.530591\pi$
$251$	−3.04049	−0.191914	−0.0959569	+	0.995385i	$0.530591\pi$
$252$	0	0
$253$	−6.74373	−0.423975
$254$	−20.9698	−1.31576
$255$	7.18416	0.449890
$256$	4.09881	0.256176
$257$	21.7197	1.35484	0.677418	−	0.735599i	$-0.263099\pi$
$257$	21.7197	1.35484	0.677418	+	0.735599i	$0.263099\pi$
$258$	−13.7989	−0.859081
$259$	0	0
$260$	−15.9267	−0.987732
$261$	−9.11879	−0.564439
$262$	3.60209	0.222538
$263$	−0.758785	−0.0467887	−0.0233944	−	0.999726i	$-0.507447\pi$
$263$	−0.758785	−0.0467887	−0.0233944	+	0.999726i	$0.507447\pi$
$264$	1.74714	0.107529
$265$	10.9222	0.670943
$266$	0	0
$267$	−10.2933	−0.629942
$268$	−33.2980	−2.03400
$269$	−9.21857	−0.562066	−0.281033	−	0.959698i	$-0.590677\pi$
$269$	−9.21857	−0.562066	−0.281033	+	0.959698i	$0.590677\pi$
$270$	−6.21144	−0.378016
$271$	21.9651	1.33429	0.667143	−	0.744930i	$-0.267517\pi$
$271$	21.9651	1.33429	0.667143	+	0.744930i	$0.267517\pi$
$272$	−6.43548	−0.390208
$273$	0	0
$274$	40.0758	2.42107
$275$	−5.23224	−0.315516
$276$	11.4425	0.688758
$277$	17.9529	1.07869	0.539343	−	0.842086i	$-0.318673\pi$
$277$	17.9529	1.07869	0.539343	+	0.842086i	$0.318673\pi$
$278$	−7.38672	−0.443026
$279$	−7.76497	−0.464877
$280$	0	0
$281$	−22.5886	−1.34752	−0.673761	−	0.738949i	$-0.735322\pi$
$281$	−22.5886	−1.34752	−0.673761	+	0.738949i	$0.735322\pi$
$282$	3.06901	0.182757
$283$	13.7918	0.819835	0.409917	−	0.912123i	$-0.365558\pi$
$283$	13.7918	0.819835	0.409917	+	0.912123i	$0.365558\pi$
$284$	−10.4740	−0.621518
$285$	−21.0759	−1.24843
$286$	−6.86989	−0.406225
$287$	0	0
$288$	7.89280	0.465087
$289$	−10.9186	−0.642270
$290$	56.6409	3.32607
$291$	2.93804	0.172231
$292$	7.08851	0.414824
$293$	−7.85590	−0.458947	−0.229473	−	0.973315i	$-0.573700\pi$
$293$	−7.85590	−0.458947	−0.229473	+	0.973315i	$0.573700\pi$
$294$	0	0
$295$	−22.4299	−1.30592
$296$	−2.05792	−0.119614
$297$	−1.50055	−0.0870710
$298$	47.9988	2.78049
$299$	−9.65001	−0.558074
$300$	8.87786	0.512564
$301$	0	0
$302$	33.1333	1.90661
$303$	−9.85932	−0.566403
$304$	18.8795	1.08281
$305$	16.7232	0.957569
$306$	−5.25800	−0.300580
$307$	−12.8613	−0.734035	−0.367018	−	0.930214i	$-0.619621\pi$
$307$	−12.8613	−0.734035	−0.367018	+	0.930214i	$0.619621\pi$
$308$	0	0
$309$	5.59038	0.318025
$310$	48.2317	2.73937
$311$	15.5497	0.881742	0.440871	−	0.897570i	$-0.354670\pi$
$311$	15.5497	0.881742	0.440871	+	0.897570i	$0.354670\pi$
$312$	2.50010	0.141540
$313$	−27.1677	−1.53561	−0.767804	−	0.640685i	$-0.778651\pi$
$313$	−27.1677	−1.53561	−0.767804	+	0.640685i	$0.778651\pi$
$314$	43.6900	2.46557
$315$	0	0
$316$	39.7587	2.23660
$317$	2.98972	0.167920	0.0839598	−	0.996469i	$-0.473243\pi$
$317$	2.98972	0.167920	0.0839598	+	0.996469i	$0.473243\pi$
$318$	−7.99380	−0.448270
$319$	13.6832	0.766114
$320$	−33.8208	−1.89064
$321$	13.7382	0.766792
$322$	0	0
$323$	−17.8408	−0.992687
$324$	2.54608	0.141449
$325$	−7.48713	−0.415311
$326$	−24.4584	−1.35463
$327$	−16.8992	−0.934526
$328$	1.16433	0.0642895
$329$	0	0
$330$	9.32061	0.513082
$331$	11.4220	0.627809	0.313904	−	0.949455i	$-0.398363\pi$
$331$	11.4220	0.627809	0.313904	+	0.949455i	$0.398363\pi$
$332$	−3.15628	−0.173224
$333$	1.76746	0.0968564
$334$	−2.58913	−0.141671
$335$	−38.0995	−2.08160
$336$	0	0
$337$	5.89417	0.321076	0.160538	−	0.987030i	$-0.448677\pi$
$337$	5.89417	0.321076	0.160538	+	0.987030i	$0.448677\pi$
$338$	17.8875	0.972950
$339$	−12.2739	−0.666626
$340$	18.2915	0.991994
$341$	11.6518	0.630978
$342$	15.4252	0.834098
$343$	0	0
$344$	−7.53534	−0.406278
$345$	13.0925	0.704876
$346$	−39.0534	−2.09952
$347$	−4.45569	−0.239194	−0.119597	−	0.992823i	$-0.538160\pi$
$347$	−4.45569	−0.239194	−0.119597	+	0.992823i	$0.538160\pi$
$348$	−23.2172	−1.24457
$349$	12.0671	0.645940	0.322970	−	0.946409i	$-0.395319\pi$
$349$	12.0671	0.645940	0.322970	+	0.946409i	$0.395319\pi$
$350$	0	0
$351$	−2.14723	−0.114611
$352$	−11.8436	−0.631264
$353$	−28.3315	−1.50793	−0.753966	−	0.656913i	$-0.771862\pi$
$353$	−28.3315	−1.50793	−0.753966	+	0.656913i	$0.771862\pi$
$354$	16.4162	0.872512
$355$	−11.9843	−0.636063
$356$	−26.2077	−1.38901
$357$	0	0
$358$	−16.6323	−0.879044
$359$	15.1427	0.799203	0.399601	−	0.916689i	$-0.369149\pi$
$359$	15.1427	0.799203	0.399601	+	0.916689i	$0.369149\pi$
$360$	−3.39196	−0.178772
$361$	33.3387	1.75467
$362$	−4.51444	−0.237274
$363$	−8.74834	−0.459169
$364$	0	0
$365$	8.11066	0.424531
$366$	−12.2395	−0.639770
$367$	15.8017	0.824844	0.412422	−	0.910993i	$-0.364683\pi$
$367$	15.8017	0.824844	0.412422	+	0.910993i	$0.364683\pi$
$368$	−11.7281	−0.611369
$369$	−1.00000	−0.0520579
$370$	−10.9785	−0.570745
$371$	0	0
$372$	−19.7703	−1.02504
$373$	12.4879	0.646601	0.323301	−	0.946296i	$-0.395207\pi$
$373$	12.4879	0.646601	0.323301	+	0.946296i	$0.395207\pi$
$374$	7.88992	0.407978
$375$	−4.40808	−0.227632
$376$	1.67593	0.0864296
$377$	19.5802	1.00843
$378$	0	0
$379$	3.92589	0.201659	0.100830	−	0.994904i	$-0.467850\pi$
$379$	3.92589	0.201659	0.100830	+	0.994904i	$0.467850\pi$
$380$	−53.6609	−2.75275
$381$	9.83504	0.503864
$382$	42.7422	2.18688
$383$	−12.8664	−0.657443	−0.328721	−	0.944427i	$-0.606618\pi$
$383$	−12.8664	−0.657443	−0.328721	+	0.944427i	$0.606618\pi$
$384$	8.96745	0.457618
$385$	0	0
$386$	18.4721	0.940204
$387$	6.47180	0.328980
$388$	7.48049	0.379764
$389$	24.1359	1.22374	0.611868	−	0.790960i	$-0.290418\pi$
$389$	24.1359	1.22374	0.611868	+	0.790960i	$0.290418\pi$
$390$	13.3374	0.675366
$391$	11.0828	0.560483
$392$	0	0
$393$	−1.68941	−0.0852197
$394$	−23.2542	−1.17153
$395$	45.4918	2.28894
$396$	−3.82053	−0.191989
$397$	16.9939	0.852902	0.426451	−	0.904511i	$-0.359764\pi$
$397$	16.9939	0.852902	0.426451	+	0.904511i	$0.359764\pi$
$398$	39.2111	1.96547
$399$	0	0
$400$	−9.09944	−0.454972
$401$	16.8777	0.842830	0.421415	−	0.906868i	$-0.361534\pi$
$401$	16.8777	0.842830	0.421415	+	0.906868i	$0.361534\pi$
$402$	27.8846	1.39076
$403$	16.6732	0.830551
$404$	−25.1026	−1.24890
$405$	2.91322	0.144759
$406$	0	0
$407$	−2.65217	−0.131463
$408$	−2.87131	−0.142151
$409$	−23.3733	−1.15573	−0.577867	−	0.816131i	$-0.696115\pi$
$409$	−23.3733	−1.15573	−0.577867	+	0.816131i	$0.696115\pi$
$410$	6.21144	0.306761
$411$	−18.7959	−0.927133
$412$	14.2336	0.701237
$413$	0	0
$414$	−9.58224	−0.470941
$415$	−3.61141	−0.177277
$416$	−16.9477	−0.830928
$417$	3.46444	0.169654
$418$	−23.1463	−1.13212
$419$	0.638417	0.0311887	0.0155944	−	0.999878i	$-0.495036\pi$
$419$	0.638417	0.0311887	0.0155944	+	0.999878i	$0.495036\pi$
$420$	0	0
$421$	−34.1543	−1.66458	−0.832290	−	0.554340i	$-0.812971\pi$
$421$	−34.1543	−1.66458	−0.832290	+	0.554340i	$0.812971\pi$
$422$	−51.7177	−2.51758
$423$	−1.43939	−0.0699857
$424$	−4.36528	−0.211997
$425$	8.59881	0.417103
$426$	8.77120	0.424966
$427$	0	0
$428$	34.9786	1.69076
$429$	3.22204	0.155562
$430$	−40.1992	−1.93858
$431$	−17.8141	−0.858073	−0.429036	−	0.903287i	$-0.641147\pi$
$431$	−17.8141	−0.858073	−0.429036	+	0.903287i	$0.641147\pi$
$432$	−2.60963	−0.125556
$433$	−18.6108	−0.894379	−0.447189	−	0.894439i	$-0.647575\pi$
$433$	−18.6108	−0.894379	−0.447189	+	0.894439i	$0.647575\pi$
$434$	0	0
$435$	−26.5651	−1.27370
$436$	−43.0267	−2.06060
$437$	−32.5132	−1.55532
$438$	−5.93610	−0.283638
$439$	30.0312	1.43331	0.716654	−	0.697428i	$-0.245673\pi$
$439$	30.0312	1.43331	0.716654	+	0.697428i	$0.245673\pi$
$440$	5.08982	0.242648
$441$	0	0
$442$	11.2902	0.537018
$443$	10.6865	0.507730	0.253865	−	0.967240i	$-0.418298\pi$
$443$	10.6865	0.507730	0.253865	+	0.967240i	$0.418298\pi$
$444$	4.50011	0.213566
$445$	−29.9868	−1.42151
$446$	21.4330	1.01488
$447$	−22.5119	−1.06477
$448$	0	0
$449$	−10.0579	−0.474660	−0.237330	−	0.971429i	$-0.576272\pi$
$449$	−10.0579	−0.474660	−0.237330	+	0.971429i	$0.576272\pi$
$450$	−7.43455	−0.350468
$451$	1.50055	0.0706583
$452$	−31.2503	−1.46989
$453$	−15.5398	−0.730125
$454$	7.90670	0.371080
$455$	0	0
$456$	8.42343	0.394463
$457$	28.5745	1.33666	0.668330	−	0.743865i	$-0.267010\pi$
$457$	28.5745	1.33666	0.668330	+	0.743865i	$0.267010\pi$
$458$	1.33837	0.0625380
$459$	2.46605	0.115105
$460$	33.3346	1.55423
$461$	−9.51845	−0.443318	−0.221659	−	0.975124i	$-0.571147\pi$
$461$	−9.51845	−0.443318	−0.221659	+	0.975124i	$0.571147\pi$
$462$	0	0
$463$	31.0602	1.44349	0.721745	−	0.692159i	$-0.243340\pi$
$463$	31.0602	1.44349	0.721745	+	0.692159i	$0.243340\pi$
$464$	23.7967	1.10473
$465$	−22.6211	−1.04903
$466$	12.1372	0.562246
$467$	−22.7912	−1.05465	−0.527325	−	0.849663i	$-0.676805\pi$
$467$	−22.7912	−1.05465	−0.527325	+	0.849663i	$0.676805\pi$
$468$	−5.46703	−0.252714
$469$	0	0
$470$	8.94071	0.412404
$471$	−20.4910	−0.944175
$472$	8.96461	0.412630
$473$	−9.71129	−0.446526
$474$	−33.2949	−1.52929
$475$	−25.2260	−1.15745
$476$	0	0
$477$	3.74917	0.171663
$478$	4.87807	0.223118
$479$	−34.2503	−1.56493	−0.782467	−	0.622692i	$-0.786039\pi$
$479$	−34.2503	−1.56493	−0.782467	+	0.622692i	$0.786039\pi$
$480$	22.9935	1.04950
$481$	−3.79516	−0.173044
$482$	−19.6699	−0.895939
$483$	0	0
$484$	−22.2740	−1.01245
$485$	8.55916	0.388651
$486$	−2.13215	−0.0967165
$487$	−9.18232	−0.416091	−0.208045	−	0.978119i	$-0.566710\pi$
$487$	−9.18232	−0.416091	−0.208045	+	0.978119i	$0.566710\pi$
$488$	−6.68380	−0.302561
$489$	11.4712	0.518746
$490$	0	0
$491$	−17.8804	−0.806931	−0.403465	−	0.914995i	$-0.632194\pi$
$491$	−17.8804	−0.806931	−0.403465	+	0.914995i	$0.632194\pi$
$492$	−2.54608	−0.114786
$493$	−22.4874	−1.01278
$494$	−33.1215	−1.49021
$495$	−4.37145	−0.196482
$496$	20.2637	0.909866
$497$	0	0
$498$	2.64315	0.118442
$499$	−23.6303	−1.05784	−0.528919	−	0.848672i	$-0.677402\pi$
$499$	−23.6303	−1.05784	−0.528919	+	0.848672i	$0.677402\pi$
$500$	−11.2233	−0.501923
$501$	1.21433	0.0542521
$502$	6.48278	0.289341
$503$	37.0939	1.65394	0.826968	−	0.562249i	$-0.190064\pi$
$503$	37.0939	1.65394	0.826968	+	0.562249i	$0.190064\pi$
$504$	0	0
$505$	−28.7224	−1.27813
$506$	14.3787	0.639210
$507$	−8.38939	−0.372586
$508$	25.0408	1.11101
$509$	−35.2024	−1.56032	−0.780158	−	0.625582i	$-0.784862\pi$
$509$	−35.2024	−1.56032	−0.780158	+	0.625582i	$0.784862\pi$
$510$	−15.3177	−0.678281
$511$	0	0
$512$	−26.6742	−1.17884
$513$	−7.23455	−0.319413
$514$	−46.3097	−2.04263
$515$	16.2860	0.717648
$516$	16.4778	0.725393
$517$	2.15989	0.0949917
$518$	0	0
$519$	18.3164	0.804001
$520$	7.28334	0.319395
$521$	24.0907	1.05543	0.527715	−	0.849421i	$-0.323049\pi$
$521$	24.0907	1.05543	0.527715	+	0.849421i	$0.323049\pi$
$522$	19.4427	0.850983
$523$	10.2611	0.448687	0.224343	−	0.974510i	$-0.427976\pi$
$523$	10.2611	0.448687	0.224343	+	0.974510i	$0.427976\pi$
$524$	−4.30139	−0.187907
$525$	0	0
$526$	1.61785	0.0705415
$527$	−19.1488	−0.834136
$528$	3.91589	0.170417
$529$	−2.80253	−0.121849
$530$	−23.2877	−1.01155
$531$	−7.69935	−0.334123
$532$	0	0
$533$	2.14723	0.0930070
$534$	21.9470	0.949739
$535$	40.0225	1.73032
$536$	15.2273	0.657719
$537$	7.80070	0.336625
$538$	19.6554	0.847406
$539$	0	0
$540$	7.41731	0.319190
$541$	34.4179	1.47974	0.739870	−	0.672750i	$-0.234887\pi$
$541$	34.4179	1.47974	0.739870	+	0.672750i	$0.234887\pi$
$542$	−46.8330	−2.01165
$543$	2.11732	0.0908627
$544$	19.4640	0.834514
$545$	−49.2310	−2.10883
$546$	0	0
$547$	29.2749	1.25171	0.625853	−	0.779941i	$-0.284751\pi$
$547$	29.2749	1.25171	0.625853	+	0.779941i	$0.284751\pi$
$548$	−47.8559	−2.04430
$549$	5.74045	0.244997
$550$	11.1559	0.475691
$551$	65.9704	2.81043
$552$	−5.23270	−0.222718
$553$	0	0
$554$	−38.2784	−1.62629
$555$	5.14902	0.218564
$556$	8.82075	0.374083
$557$	33.6058	1.42392	0.711961	−	0.702219i	$-0.247807\pi$
$557$	33.6058	1.42392	0.711961	+	0.702219i	$0.247807\pi$
$558$	16.5561	0.700876
$559$	−13.8965	−0.587758
$560$	0	0
$561$	−3.70044	−0.156233
$562$	48.1623	2.03161
$563$	−37.6392	−1.58630	−0.793152	−	0.609024i	$-0.791561\pi$
$563$	−37.6392	−1.58630	−0.793152	+	0.609024i	$0.791561\pi$
$564$	−3.66481	−0.154316
$565$	−35.7566	−1.50429
$566$	−29.4062	−1.23603
$567$	0	0
$568$	4.78980	0.200976
$569$	16.5430	0.693520	0.346760	−	0.937954i	$-0.387282\pi$
$569$	16.5430	0.693520	0.346760	+	0.937954i	$0.387282\pi$
$570$	44.9370	1.88220
$571$	−8.67402	−0.362997	−0.181498	−	0.983391i	$-0.558095\pi$
$571$	−8.67402	−0.362997	−0.181498	+	0.983391i	$0.558095\pi$
$572$	8.20358	0.343009
$573$	−20.0465	−0.837454
$574$	0	0
$575$	15.6706	0.653507
$576$	−11.6094	−0.483725
$577$	13.6404	0.567857	0.283929	−	0.958845i	$-0.408362\pi$
$577$	13.6404	0.567857	0.283929	+	0.958845i	$0.408362\pi$
$578$	23.2801	0.968325
$579$	−8.66357	−0.360046
$580$	−67.6369	−2.80847
$581$	0	0
$582$	−6.26435	−0.259666
$583$	−5.62583	−0.232998
$584$	−3.24160	−0.134138
$585$	−6.25537	−0.258628
$586$	16.7500	0.691936
$587$	−8.81891	−0.363996	−0.181998	−	0.983299i	$-0.558256\pi$
$587$	−8.81891	−0.363996	−0.181998	+	0.983299i	$0.558256\pi$
$588$	0	0
$589$	56.1761	2.31469
$590$	47.8241	1.96889
$591$	10.9064	0.448631
$592$	−4.61242	−0.189569
$593$	39.9050	1.63870	0.819351	−	0.573292i	$-0.194334\pi$
$593$	39.9050	1.63870	0.819351	+	0.573292i	$0.194334\pi$
$594$	3.19941	0.131274
$595$	0	0
$596$	−57.3170	−2.34780
$597$	−18.3904	−0.752667
$598$	20.5753	0.841387
$599$	10.0955	0.412493	0.206246	−	0.978500i	$-0.433875\pi$
$599$	10.0955	0.412493	0.206246	+	0.978500i	$0.433875\pi$
$600$	−4.05988	−0.165744
$601$	9.21459	0.375871	0.187935	−	0.982181i	$-0.439820\pi$
$601$	9.21459	0.375871	0.187935	+	0.982181i	$0.439820\pi$
$602$	0	0
$603$	−13.0781	−0.532583
$604$	−39.5657	−1.60991
$605$	−25.4859	−1.03615
$606$	21.0216	0.853944
$607$	−39.5129	−1.60378	−0.801890	−	0.597471i	$-0.796172\pi$
$607$	−39.5129	−1.60378	−0.801890	+	0.597471i	$0.796172\pi$
$608$	−57.1008	−2.31574
$609$	0	0
$610$	−35.6565	−1.44369
$611$	3.09071	0.125037
$612$	6.27877	0.253804
$613$	−19.9530	−0.805895	−0.402947	−	0.915223i	$-0.632014\pi$
$613$	−19.9530	−0.805895	−0.402947	+	0.915223i	$0.632014\pi$
$614$	27.4224	1.10668
$615$	−2.91322	−0.117473
$616$	0	0
$617$	5.18441	0.208716	0.104358	−	0.994540i	$-0.466721\pi$
$617$	5.18441	0.208716	0.104358	+	0.994540i	$0.466721\pi$
$618$	−11.9195	−0.479475
$619$	13.6896	0.550233	0.275117	−	0.961411i	$-0.411284\pi$
$619$	13.6896	0.550233	0.275117	+	0.961411i	$0.411284\pi$
$620$	−57.5952	−2.31308
$621$	4.49416	0.180344
$622$	−33.1543	−1.32937
$623$	0	0
$624$	5.60348	0.224319
$625$	−30.2761	−1.21104
$626$	57.9257	2.31518
$627$	10.8558	0.433540
$628$	−52.1718	−2.08188
$629$	4.35866	0.173791
$630$	0	0
$631$	42.1111	1.67642	0.838209	−	0.545350i	$-0.183603\pi$
$631$	42.1111	1.67642	0.838209	+	0.545350i	$0.183603\pi$
$632$	−18.1818	−0.723233
$633$	24.2561	0.964092
$634$	−6.37455	−0.253166
$635$	28.6517	1.13701
$636$	9.54569	0.378511
$637$	0	0
$638$	−29.1748	−1.15504
$639$	−4.11377	−0.162738
$640$	26.1242	1.03265
$641$	−3.51098	−0.138676	−0.0693378	−	0.997593i	$-0.522089\pi$
$641$	−3.51098	−0.138676	−0.0693378	+	0.997593i	$0.522089\pi$
$642$	−29.2920	−1.15606
$643$	−36.4566	−1.43771	−0.718854	−	0.695161i	$-0.755333\pi$
$643$	−36.4566	−1.43771	−0.718854	+	0.695161i	$0.755333\pi$
$644$	0	0
$645$	18.8538	0.742368
$646$	38.0393	1.49664
$647$	−14.4875	−0.569564	−0.284782	−	0.958592i	$-0.591921\pi$
$647$	−14.4875	−0.569564	−0.284782	+	0.958592i	$0.591921\pi$
$648$	−1.16433	−0.0457393
$649$	11.5533	0.453507
$650$	15.9637	0.626148
$651$	0	0
$652$	29.2067	1.14382
$653$	26.6506	1.04292	0.521458	−	0.853277i	$-0.325388\pi$
$653$	26.6506	1.04292	0.521458	+	0.853277i	$0.325388\pi$
$654$	36.0316	1.40895
$655$	−4.92164	−0.192304
$656$	2.60963	0.101889
$657$	2.78408	0.108617
$658$	0	0
$659$	−36.9262	−1.43844	−0.719220	−	0.694782i	$-0.755501\pi$
$659$	−36.9262	−1.43844	−0.719220	+	0.694782i	$0.755501\pi$
$660$	−11.1301	−0.433237
$661$	−22.7844	−0.886210	−0.443105	−	0.896470i	$-0.646123\pi$
$661$	−22.7844	−0.886210	−0.443105	+	0.896470i	$0.646123\pi$
$662$	−24.3534	−0.946523
$663$	−5.29519	−0.205648
$664$	1.44338	0.0560140
$665$	0	0
$666$	−3.76851	−0.146027
$667$	−40.9813	−1.58680
$668$	3.09177	0.119624
$669$	−10.0523	−0.388642
$670$	81.2340	3.13834
$671$	−8.61386	−0.332534
$672$	0	0
$673$	−22.6835	−0.874384	−0.437192	−	0.899368i	$-0.644027\pi$
$673$	−22.6835	−0.874384	−0.437192	+	0.899368i	$0.644027\pi$
$674$	−12.5673	−0.484074
$675$	3.48687	0.134210
$676$	−21.3601	−0.821541
$677$	−47.1910	−1.81370	−0.906848	−	0.421457i	$-0.861519\pi$
$677$	−47.1910	−1.81370	−0.906848	+	0.421457i	$0.861519\pi$
$678$	26.1698	1.00505
$679$	0	0
$680$	−8.36476	−0.320774
$681$	−3.70831	−0.142103
$682$	−24.8433	−0.951301
$683$	45.3118	1.73381	0.866904	−	0.498476i	$-0.166107\pi$
$683$	45.3118	1.73381	0.866904	+	0.498476i	$0.166107\pi$
$684$	−18.4198	−0.704297
$685$	−54.7567	−2.09214
$686$	0	0
$687$	−0.627708	−0.0239486
$688$	−16.8890	−0.643887
$689$	−8.05034	−0.306693
$690$	−27.9152	−1.06271
$691$	23.4256	0.891151	0.445576	−	0.895244i	$-0.352999\pi$
$691$	23.4256	0.891151	0.445576	+	0.895244i	$0.352999\pi$
$692$	46.6351	1.77280
$693$	0	0
$694$	9.50022	0.360623
$695$	10.0927	0.382838
$696$	10.6173	0.402448
$697$	−2.46605	−0.0934084
$698$	−25.7290	−0.973858
$699$	−5.69247	−0.215309
$700$	0	0
$701$	3.95291	0.149299	0.0746496	−	0.997210i	$-0.476216\pi$
$701$	3.95291	0.149299	0.0746496	+	0.997210i	$0.476216\pi$
$702$	4.57823	0.172794
$703$	−12.7868	−0.482264
$704$	17.4205	0.656561
$705$	−4.19327	−0.157928
$706$	60.4071	2.27345
$707$	0	0
$708$	−19.6032	−0.736733
$709$	−43.7509	−1.64310	−0.821549	−	0.570137i	$-0.806890\pi$
$709$	−43.7509	−1.64310	−0.821549	+	0.570137i	$0.806890\pi$
$710$	25.5525	0.958967
$711$	15.6156	0.585632
$712$	11.9849	0.449152
$713$	−34.8970	−1.30690
$714$	0	0
$715$	9.38652	0.351036
$716$	19.8612	0.742249
$717$	−2.28786	−0.0854417
$718$	−32.2867	−1.20493
$719$	−39.2991	−1.46561	−0.732805	−	0.680439i	$-0.761789\pi$
$719$	−39.2991	−1.46561	−0.732805	+	0.680439i	$0.761789\pi$
$720$	−7.60243	−0.283326
$721$	0	0
$722$	−71.0833	−2.64545
$723$	9.22536	0.343095
$724$	5.39086	0.200350
$725$	−31.7961	−1.18088
$726$	18.6528	0.692271
$727$	6.63007	0.245896	0.122948	−	0.992413i	$-0.460765\pi$
$727$	6.63007	0.245896	0.122948	+	0.992413i	$0.460765\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−17.2932	−0.640049
$731$	15.9598	0.590295
$732$	14.6157	0.540211
$733$	−18.4143	−0.680149	−0.340074	−	0.940399i	$-0.610452\pi$
$733$	−18.4143	−0.680149	−0.340074	+	0.940399i	$0.610452\pi$
$734$	−33.6918	−1.24359
$735$	0	0
$736$	35.4715	1.30750
$737$	19.6244	0.722875
$738$	2.13215	0.0784857
$739$	45.5824	1.67678	0.838388	−	0.545073i	$-0.183498\pi$
$739$	45.5824	1.67678	0.838388	+	0.545073i	$0.183498\pi$
$740$	13.1098	0.481927
$741$	15.5343	0.570666
$742$	0	0
$743$	3.83501	0.140693	0.0703465	−	0.997523i	$-0.477590\pi$
$743$	3.83501	0.140693	0.0703465	+	0.997523i	$0.477590\pi$
$744$	9.04101	0.331460
$745$	−65.5821	−2.40274
$746$	−26.6262	−0.974855
$747$	−1.23966	−0.0453569
$748$	−9.42164	−0.344489
$749$	0	0
$750$	9.39871	0.343192
$751$	−15.3335	−0.559528	−0.279764	−	0.960069i	$-0.590256\pi$
$751$	−15.3335	−0.559528	−0.279764	+	0.960069i	$0.590256\pi$
$752$	3.75628	0.136977
$753$	−3.04049	−0.110801
$754$	−41.7480	−1.52037
$755$	−45.2710	−1.64758
$756$	0	0
$757$	−40.5275	−1.47300	−0.736499	−	0.676439i	$-0.763522\pi$
$757$	−40.5275	−1.47300	−0.736499	+	0.676439i	$0.763522\pi$
$758$	−8.37060	−0.304034
$759$	−6.74373	−0.244782
$760$	24.5393	0.890135
$761$	−49.4612	−1.79297	−0.896483	−	0.443077i	$-0.853887\pi$
$761$	−49.4612	−1.79297	−0.896483	+	0.443077i	$0.853887\pi$
$762$	−20.9698	−0.759656
$763$	0	0
$764$	−51.0400	−1.84656
$765$	7.18416	0.259744
$766$	27.4332	0.991201
$767$	16.5323	0.596947
$768$	4.09881	0.147903
$769$	−30.7710	−1.10963	−0.554815	−	0.831974i	$-0.687211\pi$
$769$	−30.7710	−1.10963	−0.554815	+	0.831974i	$0.687211\pi$
$770$	0	0
$771$	21.7197	0.782215
$772$	−22.0582	−0.793891
$773$	−31.6733	−1.13921	−0.569605	−	0.821919i	$-0.692904\pi$
$773$	−31.6733	−1.13921	−0.569605	+	0.821919i	$0.692904\pi$
$774$	−13.7989	−0.495991
$775$	−27.0755	−0.972579
$776$	−3.42085	−0.122801
$777$	0	0
$778$	−51.4614	−1.84498
$779$	7.23455	0.259205
$780$	−15.9267	−0.570267
$781$	6.17294	0.220885
$782$	−23.6303	−0.845018
$783$	−9.11879	−0.325879
$784$	0	0
$785$	−59.6948	−2.13060
$786$	3.60209	0.128482
$787$	−21.1978	−0.755621	−0.377810	−	0.925883i	$-0.623323\pi$
$787$	−21.1978	−0.755621	−0.377810	+	0.925883i	$0.623323\pi$
$788$	27.7687	0.989218
$789$	−0.758785	−0.0270135
$790$	−96.9956	−3.45095
$791$	0	0
$792$	1.74714	0.0620821
$793$	−12.3261	−0.437712
$794$	−36.2337	−1.28589
$795$	10.9222	0.387369
$796$	−46.8234	−1.65961
$797$	−39.5421	−1.40065	−0.700326	−	0.713823i	$-0.746962\pi$
$797$	−39.5421	−1.40065	−0.700326	+	0.713823i	$0.746962\pi$
$798$	0	0
$799$	−3.54962	−0.125576
$800$	27.5212	0.973020
$801$	−10.2933	−0.363697
$802$	−35.9858	−1.27070
$803$	−4.17767	−0.147427
$804$	−33.2980	−1.17433
$805$	0	0
$806$	−35.5498	−1.25219
$807$	−9.21857	−0.324509
$808$	11.4795	0.403849
$809$	19.2888	0.678159	0.339080	−	0.940758i	$-0.389884\pi$
$809$	19.2888	0.678159	0.339080	+	0.940758i	$0.389884\pi$
$810$	−6.21144	−0.218248
$811$	29.6499	1.04115	0.520574	−	0.853817i	$-0.325718\pi$
$811$	29.6499	1.04115	0.520574	+	0.853817i	$0.325718\pi$
$812$	0	0
$813$	21.9651	0.770350
$814$	5.65485	0.198202
$815$	33.4182	1.17059
$816$	−6.43548	−0.225287
$817$	−46.8206	−1.63805
$818$	49.8354	1.74245
$819$	0	0
$820$	−7.41731	−0.259024
$821$	8.05452	0.281105	0.140552	−	0.990073i	$-0.455112\pi$
$821$	8.05452	0.281105	0.140552	+	0.990073i	$0.455112\pi$
$822$	40.0758	1.39780
$823$	−5.13488	−0.178991	−0.0894953	−	0.995987i	$-0.528525\pi$
$823$	−5.13488	−0.178991	−0.0894953	+	0.995987i	$0.528525\pi$
$824$	−6.50906	−0.226754
$825$	−5.23224	−0.182163
$826$	0	0
$827$	38.1238	1.32570	0.662848	−	0.748754i	$-0.269348\pi$
$827$	38.1238	1.32570	0.662848	+	0.748754i	$0.269348\pi$
$828$	11.4425	0.397654
$829$	1.89733	0.0658970	0.0329485	−	0.999457i	$-0.489510\pi$
$829$	1.89733	0.0658970	0.0329485	+	0.999457i	$0.489510\pi$
$830$	7.70009	0.267274
$831$	17.9529	0.622779
$832$	24.9281	0.864227
$833$	0	0
$834$	−7.38672	−0.255781
$835$	3.53760	0.122424
$836$	27.6399	0.955944
$837$	−7.76497	−0.268397
$838$	−1.36120	−0.0470220
$839$	−42.5450	−1.46882	−0.734408	−	0.678708i	$-0.762540\pi$
$839$	−42.5450	−1.46882	−0.734408	+	0.678708i	$0.762540\pi$
$840$	0	0
$841$	54.1524	1.86732
$842$	72.8223	2.50962
$843$	−22.5886	−0.777992
$844$	61.7580	2.12580
$845$	−24.4402	−0.840767
$846$	3.06901	0.105515
$847$	0	0
$848$	−9.78393	−0.335981
$849$	13.7918	0.473332
$850$	−18.3340	−0.628850
$851$	7.94326	0.272292
$852$	−10.4740	−0.358833
$853$	17.4335	0.596913	0.298457	−	0.954423i	$-0.403528\pi$
$853$	17.4335	0.596913	0.298457	+	0.954423i	$0.403528\pi$
$854$	0	0
$855$	−21.0759	−0.720779
$856$	−15.9959	−0.546727
$857$	−26.1027	−0.891653	−0.445826	−	0.895119i	$-0.647090\pi$
$857$	−26.1027	−0.891653	−0.445826	+	0.895119i	$0.647090\pi$
$858$	−6.86989	−0.234534
$859$	−36.5305	−1.24641	−0.623203	−	0.782060i	$-0.714169\pi$
$859$	−36.5305	−1.24641	−0.623203	+	0.782060i	$0.714169\pi$
$860$	48.0034	1.63690
$861$	0	0
$862$	37.9823	1.29368
$863$	−9.24397	−0.314669	−0.157334	−	0.987545i	$-0.550290\pi$
$863$	−9.24397	−0.314669	−0.157334	+	0.987545i	$0.550290\pi$
$864$	7.89280	0.268518
$865$	53.3598	1.81429
$866$	39.6811	1.34842
$867$	−10.9186	−0.370815
$868$	0	0
$869$	−23.4321	−0.794879
$870$	56.6409	1.92031
$871$	28.0818	0.951515
$872$	19.6763	0.666322
$873$	2.93804	0.0994375
$874$	69.3232	2.34489
$875$	0	0
$876$	7.08851	0.239499
$877$	−46.5927	−1.57332	−0.786662	−	0.617384i	$-0.788193\pi$
$877$	−46.5927	−1.57332	−0.786662	+	0.617384i	$0.788193\pi$
$878$	−64.0311	−2.16094
$879$	−7.85590	−0.264973
$880$	11.4079	0.384559
$881$	−17.0942	−0.575918	−0.287959	−	0.957643i	$-0.592977\pi$
$881$	−17.0942	−0.575918	−0.287959	+	0.957643i	$0.592977\pi$
$882$	0	0
$883$	−7.33116	−0.246713	−0.123357	−	0.992362i	$-0.539366\pi$
$883$	−7.33116	−0.246713	−0.123357	+	0.992362i	$0.539366\pi$
$884$	−13.4820	−0.453448
$885$	−22.4299	−0.753974
$886$	−22.7852	−0.765485
$887$	9.21041	0.309255	0.154628	−	0.987973i	$-0.450582\pi$
$887$	9.21041	0.309255	0.154628	+	0.987973i	$0.450582\pi$
$888$	−2.05792	−0.0690592
$889$	0	0
$890$	63.9365	2.14316
$891$	−1.50055	−0.0502704
$892$	−25.5939	−0.856946
$893$	10.4134	0.348470
$894$	47.9988	1.60532
$895$	22.7252	0.759619
$896$	0	0
$897$	−9.65001	−0.322204
$898$	21.4449	0.715626
$899$	70.8071	2.36155
$900$	8.87786	0.295929
$901$	9.24564	0.308017
$902$	−3.19941	−0.106529
$903$	0	0
$904$	14.2909	0.475308
$905$	6.16821	0.205038
$906$	33.1333	1.10078
$907$	−1.42495	−0.0473147	−0.0236574	−	0.999720i	$-0.507531\pi$
$907$	−1.42495	−0.0473147	−0.0236574	+	0.999720i	$0.507531\pi$
$908$	−9.44167	−0.313333
$909$	−9.85932	−0.327013
$910$	0	0
$911$	0.0834139	0.00276362	0.00138181	−	0.999999i	$-0.499560\pi$
$911$	0.0834139	0.00276362	0.00138181	+	0.999999i	$0.499560\pi$
$912$	18.8795	0.625162
$913$	1.86018	0.0615630
$914$	−60.9253	−2.01523
$915$	16.7232	0.552853
$916$	−1.59820	−0.0528059
$917$	0	0
$918$	−5.25800	−0.173540
$919$	17.4891	0.576911	0.288456	−	0.957493i	$-0.406858\pi$
$919$	17.4891	0.576911	0.288456	+	0.957493i	$0.406858\pi$
$920$	−15.2440	−0.502580
$921$	−12.8613	−0.423795
$922$	20.2948	0.668374
$923$	8.83323	0.290749
$924$	0	0
$925$	6.16292	0.202636
$926$	−66.2252	−2.17629
$927$	5.59038	0.183612
$928$	−71.9728	−2.36262
$929$	37.0853	1.21673	0.608364	−	0.793658i	$-0.291826\pi$
$929$	37.0853	1.21673	0.608364	+	0.793658i	$0.291826\pi$
$930$	48.2317	1.58158
$931$	0	0
$932$	−14.4935	−0.474751
$933$	15.5497	0.509074
$934$	48.5944	1.59006
$935$	−10.7802	−0.352551
$936$	2.50010	0.0817182
$937$	51.2474	1.67418	0.837090	−	0.547065i	$-0.184255\pi$
$937$	51.2474	1.67418	0.837090	+	0.547065i	$0.184255\pi$
$938$	0	0
$939$	−27.1677	−0.886584
$940$	−10.6764	−0.348226
$941$	9.65205	0.314648	0.157324	−	0.987547i	$-0.449713\pi$
$941$	9.65205	0.314648	0.157324	+	0.987547i	$0.449713\pi$
$942$	43.6900	1.42350
$943$	−4.49416	−0.146350
$944$	20.0924	0.653953
$945$	0	0
$946$	20.7060	0.673209
$947$	−16.2966	−0.529570	−0.264785	−	0.964307i	$-0.585301\pi$
$947$	−16.2966	−0.529570	−0.264785	+	0.964307i	$0.585301\pi$
$948$	39.7587	1.29130
$949$	−5.97808	−0.194057
$950$	53.7856	1.74504
$951$	2.98972	0.0969484
$952$	0	0
$953$	13.4806	0.436680	0.218340	−	0.975873i	$-0.429936\pi$
$953$	13.4806	0.436680	0.218340	+	0.975873i	$0.429936\pi$
$954$	−7.99380	−0.258809
$955$	−58.3999	−1.88978
$956$	−5.82508	−0.188397
$957$	13.6832	0.442316
$958$	73.0268	2.35939
$959$	0	0
$960$	−33.8208	−1.09156
$961$	29.2947	0.944992
$962$	8.09186	0.260892
$963$	13.7382	0.442708
$964$	23.4885	0.756515
$965$	−25.2389	−0.812470
$966$	0	0
$967$	48.2230	1.55075	0.775373	−	0.631503i	$-0.217562\pi$
$967$	48.2230	1.55075	0.775373	+	0.631503i	$0.217562\pi$
$968$	10.1860	0.327390
$969$	−17.8408	−0.573128
$970$	−18.2494	−0.585954
$971$	0.494306	0.0158630	0.00793152	−	0.999969i	$-0.497475\pi$
$971$	0.494306	0.0158630	0.00793152	+	0.999969i	$0.497475\pi$
$972$	2.54608	0.0816656
$973$	0	0
$974$	19.5781	0.627324
$975$	−7.48713	−0.239780
$976$	−14.9804	−0.479512
$977$	4.09452	0.130995	0.0654976	−	0.997853i	$-0.479137\pi$
$977$	4.09452	0.130995	0.0654976	+	0.997853i	$0.479137\pi$
$978$	−24.4584	−0.782093
$979$	15.4457	0.493647
$980$	0	0
$981$	−16.8992	−0.539549
$982$	38.1238	1.21658
$983$	−20.4954	−0.653703	−0.326851	−	0.945076i	$-0.605988\pi$
$983$	−20.4954	−0.653703	−0.326851	+	0.945076i	$0.605988\pi$
$984$	1.16433	0.0371176
$985$	31.7729	1.01237
$986$	47.9466	1.52693
$987$	0	0
$988$	39.5515	1.25830
$989$	29.0853	0.924859
$990$	9.32061	0.296228
$991$	0.869374	0.0276166	0.0138083	−	0.999905i	$-0.495605\pi$
$991$	0.869374	0.0276166	0.0138083	+	0.999905i	$0.495605\pi$
$992$	−61.2873	−1.94587
$993$	11.4220	0.362466
$994$	0	0
$995$	−53.5752	−1.69845
$996$	−3.15628	−0.100011
$997$	−36.6918	−1.16204	−0.581020	−	0.813889i	$-0.697346\pi$
$997$	−36.6918	−1.16204	−0.581020	+	0.813889i	$0.697346\pi$
$998$	50.3835	1.59486
$999$	1.76746	0.0559201

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bk.1.3		14
7.3	odd	6		861.2.i.g.247.12	✓	28
7.5	odd	6		861.2.i.g.739.12	yes	28
7.6	odd	2		6027.2.a.bj.1.3		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.g.247.12	✓	28	7.3	odd	6
861.2.i.g.739.12	yes	28	7.5	odd	6
6027.2.a.bj.1.3		14	7.6	odd	2
6027.2.a.bk.1.3		14	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.13215 q^{2} +1.00000 q^{3} +2.54608 q^{4} +2.91322 q^{5} -2.13215 q^{6} -1.16433 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.13215 q^{2} +1.00000 q^{3} +2.54608 q^{4} +2.91322 q^{5} -2.13215 q^{6} -1.16433 q^{8} +1.00000 q^{9} -6.21144 q^{10} -1.50055 q^{11} +2.54608 q^{12} -2.14723 q^{13} +2.91322 q^{15} -2.60963 q^{16} +2.46605 q^{17} -2.13215 q^{18} -7.23455 q^{19} +7.41731 q^{20} +3.19941 q^{22} +4.49416 q^{23} -1.16433 q^{24} +3.48687 q^{25} +4.57823 q^{26} +1.00000 q^{27} -9.11879 q^{29} -6.21144 q^{30} -7.76497 q^{31} +7.89280 q^{32} -1.50055 q^{33} -5.25800 q^{34} +2.54608 q^{36} +1.76746 q^{37} +15.4252 q^{38} -2.14723 q^{39} -3.39196 q^{40} -1.00000 q^{41} +6.47180 q^{43} -3.82053 q^{44} +2.91322 q^{45} -9.58224 q^{46} -1.43939 q^{47} -2.60963 q^{48} -7.43455 q^{50} +2.46605 q^{51} -5.46703 q^{52} +3.74917 q^{53} -2.13215 q^{54} -4.37145 q^{55} -7.23455 q^{57} +19.4427 q^{58} -7.69935 q^{59} +7.41731 q^{60} +5.74045 q^{61} +16.5561 q^{62} -11.6094 q^{64} -6.25537 q^{65} +3.19941 q^{66} -13.0781 q^{67} +6.27877 q^{68} +4.49416 q^{69} -4.11377 q^{71} -1.16433 q^{72} +2.78408 q^{73} -3.76851 q^{74} +3.48687 q^{75} -18.4198 q^{76} +4.57823 q^{78} +15.6156 q^{79} -7.60243 q^{80} +1.00000 q^{81} +2.13215 q^{82} -1.23966 q^{83} +7.18416 q^{85} -13.7989 q^{86} -9.11879 q^{87} +1.74714 q^{88} -10.2933 q^{89} -6.21144 q^{90} +11.4425 q^{92} -7.76497 q^{93} +3.06901 q^{94} -21.0759 q^{95} +7.89280 q^{96} +2.93804 q^{97} -1.50055 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} + 14 q^{3} + 14 q^{4} - 10 q^{5} - 2 q^{6} - 6 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 2 * q^2 + 14 * q^3 + 14 * q^4 - 10 * q^5 - 2 * q^6 - 6 * q^8 + 14 * q^9	\( 14 q - 2 q^{2} + 14 q^{3} + 14 q^{4} - 10 q^{5} - 2 q^{6} - 6 q^{8} + 14 q^{9} - 3 q^{10} - 16 q^{11} + 14 q^{12} - 21 q^{13} - 10 q^{15} + 22 q^{16} - 12 q^{17} - 2 q^{18} - 2 q^{19} - 40 q^{20} + q^{22} - 7 q^{23} - 6 q^{24} + 22 q^{25} - 2 q^{26} + 14 q^{27} - 16 q^{29} - 3 q^{30} - 8 q^{31} - 19 q^{32} - 16 q^{33} - 33 q^{34} + 14 q^{36} + q^{37} - 32 q^{38} - 21 q^{39} + 13 q^{40} - 14 q^{41} + 14 q^{43} - 36 q^{44} - 10 q^{45} - 12 q^{46} - 12 q^{47} + 22 q^{48} - q^{50} - 12 q^{51} - 60 q^{52} - 20 q^{53} - 2 q^{54} + 11 q^{55} - 2 q^{57} + 21 q^{58} - 25 q^{59} - 40 q^{60} - 26 q^{61} + 33 q^{62} + 42 q^{64} - 8 q^{65} + q^{66} - 22 q^{67} - 15 q^{68} - 7 q^{69} - 36 q^{71} - 6 q^{72} - 31 q^{73} - 65 q^{74} + 22 q^{75} + 2 q^{76} - 2 q^{78} + 12 q^{79} - 112 q^{80} + 14 q^{81} + 2 q^{82} - 20 q^{83} + 40 q^{85} - 9 q^{86} - 16 q^{87} - 54 q^{88} - 39 q^{89} - 3 q^{90} + 63 q^{92} - 8 q^{93} - 14 q^{94} - 55 q^{95} - 19 q^{96} - 18 q^{97} - 16 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 + 14 * q^3 + 14 * q^4 - 10 * q^5 - 2 * q^6 - 6 * q^8 + 14 * q^9 - 3 * q^10 - 16 * q^11 + 14 * q^12 - 21 * q^13 - 10 * q^15 + 22 * q^16 - 12 * q^17 - 2 * q^18 - 2 * q^19 - 40 * q^20 + q^22 - 7 * q^23 - 6 * q^24 + 22 * q^25 - 2 * q^26 + 14 * q^27 - 16 * q^29 - 3 * q^30 - 8 * q^31 - 19 * q^32 - 16 * q^33 - 33 * q^34 + 14 * q^36 + q^37 - 32 * q^38 - 21 * q^39 + 13 * q^40 - 14 * q^41 + 14 * q^43 - 36 * q^44 - 10 * q^45 - 12 * q^46 - 12 * q^47 + 22 * q^48 - q^50 - 12 * q^51 - 60 * q^52 - 20 * q^53 - 2 * q^54 + 11 * q^55 - 2 * q^57 + 21 * q^58 - 25 * q^59 - 40 * q^60 - 26 * q^61 + 33 * q^62 + 42 * q^64 - 8 * q^65 + q^66 - 22 * q^67 - 15 * q^68 - 7 * q^69 - 36 * q^71 - 6 * q^72 - 31 * q^73 - 65 * q^74 + 22 * q^75 + 2 * q^76 - 2 * q^78 + 12 * q^79 - 112 * q^80 + 14 * q^81 + 2 * q^82 - 20 * q^83 + 40 * q^85 - 9 * q^86 - 16 * q^87 - 54 * q^88 - 39 * q^89 - 3 * q^90 + 63 * q^92 - 8 * q^93 - 14 * q^94 - 55 * q^95 - 19 * q^96 - 18 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

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