LMFDB - Embedded newform 6027.2.a.bl.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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 14 x^{14} + 68 x^{13} + 64 x^{12} - 456 x^{11} - 54 x^{10} + 1532 x^{9} - 400 x^{8} + \cdots - 49 $ x^16 - 4x^15 - 14x^14 + 68x^13 + 64x^12 - 456x^11 - 54x^10 + 1532x^9 - 400x^8 - 2708x^7 + 1218x^6 + 2424x^5 - 1276x^4 - 960x^3 + 500x^2 + 112*x - 49
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.83908$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.83908 q^{2} -1.00000 q^{3} +1.38223 q^{4} +2.07594 q^{5} +1.83908 q^{6} +1.13613 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.83908 q^{2} -1.00000 q^{3} +1.38223 q^{4} +2.07594 q^{5} +1.83908 q^{6} +1.13613 q^{8} +1.00000 q^{9} -3.81783 q^{10} -6.44723 q^{11} -1.38223 q^{12} +0.865716 q^{13} -2.07594 q^{15} -4.85390 q^{16} -2.06756 q^{17} -1.83908 q^{18} -3.75357 q^{19} +2.86943 q^{20} +11.8570 q^{22} +5.10432 q^{23} -1.13613 q^{24} -0.690475 q^{25} -1.59212 q^{26} -1.00000 q^{27} +1.38301 q^{29} +3.81783 q^{30} +3.75086 q^{31} +6.65447 q^{32} +6.44723 q^{33} +3.80241 q^{34} +1.38223 q^{36} -0.654747 q^{37} +6.90313 q^{38} -0.865716 q^{39} +2.35854 q^{40} -1.00000 q^{41} +11.2846 q^{43} -8.91156 q^{44} +2.07594 q^{45} -9.38727 q^{46} +13.3268 q^{47} +4.85390 q^{48} +1.26984 q^{50} +2.06756 q^{51} +1.19662 q^{52} -0.611905 q^{53} +1.83908 q^{54} -13.3841 q^{55} +3.75357 q^{57} -2.54346 q^{58} -3.36226 q^{59} -2.86943 q^{60} -12.3530 q^{61} -6.89814 q^{62} -2.53033 q^{64} +1.79717 q^{65} -11.8570 q^{66} +12.3187 q^{67} -2.85784 q^{68} -5.10432 q^{69} -3.50868 q^{71} +1.13613 q^{72} +0.660309 q^{73} +1.20413 q^{74} +0.690475 q^{75} -5.18830 q^{76} +1.59212 q^{78} -3.56152 q^{79} -10.0764 q^{80} +1.00000 q^{81} +1.83908 q^{82} -7.34512 q^{83} -4.29213 q^{85} -20.7534 q^{86} -1.38301 q^{87} -7.32489 q^{88} +11.2002 q^{89} -3.81783 q^{90} +7.05534 q^{92} -3.75086 q^{93} -24.5091 q^{94} -7.79218 q^{95} -6.65447 q^{96} -16.7499 q^{97} -6.44723 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 16 q^{3} + 12 q^{4} + 12 q^{5} + 4 q^{6} - 12 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 16 * q^3 + 12 * q^4 + 12 * q^5 + 4 * q^6 - 12 * q^8 + 16 * q^9	$ 16 q - 4 q^{2} - 16 q^{3} + 12 q^{4} + 12 q^{5} + 4 q^{6} - 12 q^{8} + 16 q^{9} + 4 q^{10} - 4 q^{11} - 12 q^{12} - 12 q^{15} + 8 q^{17} - 4 q^{18} - 4 q^{19} + 20 q^{20} - 16 q^{22} - 12 q^{23} + 12 q^{24} - 8 q^{25} + 8 q^{26} - 16 q^{27} - 16 q^{29} - 4 q^{30} + 4 q^{31} - 48 q^{32} + 4 q^{33} - 16 q^{34} + 12 q^{36} - 48 q^{37} + 4 q^{38} - 56 q^{40} - 16 q^{41} - 16 q^{43} + 12 q^{45} - 4 q^{46} + 36 q^{47} - 8 q^{50} - 8 q^{51} - 60 q^{53} + 4 q^{54} - 8 q^{55} + 4 q^{57} - 36 q^{58} + 36 q^{59} - 20 q^{60} + 4 q^{61} + 12 q^{62} + 52 q^{64} - 36 q^{65} + 16 q^{66} - 52 q^{67} + 8 q^{68} + 12 q^{69} - 12 q^{71} - 12 q^{72} + 16 q^{73} + 4 q^{74} + 8 q^{75} - 16 q^{76} - 8 q^{78} - 36 q^{79} + 68 q^{80} + 16 q^{81} + 4 q^{82} + 32 q^{83} - 28 q^{85} - 8 q^{86} + 16 q^{87} - 36 q^{88} + 12 q^{89} + 4 q^{90} - 36 q^{92} - 4 q^{93} - 24 q^{94} - 20 q^{95} + 48 q^{96} - 48 q^{97} - 4 q^{99}+O(q^{100}) $ 16 * q - 4 * q^2 - 16 * q^3 + 12 * q^4 + 12 * q^5 + 4 * q^6 - 12 * q^8 + 16 * q^9 + 4 * q^10 - 4 * q^11 - 12 * q^12 - 12 * q^15 + 8 * q^17 - 4 * q^18 - 4 * q^19 + 20 * q^20 - 16 * q^22 - 12 * q^23 + 12 * q^24 - 8 * q^25 + 8 * q^26 - 16 * q^27 - 16 * q^29 - 4 * q^30 + 4 * q^31 - 48 * q^32 + 4 * q^33 - 16 * q^34 + 12 * q^36 - 48 * q^37 + 4 * q^38 - 56 * q^40 - 16 * q^41 - 16 * q^43 + 12 * q^45 - 4 * q^46 + 36 * q^47 - 8 * q^50 - 8 * q^51 - 60 * q^53 + 4 * q^54 - 8 * q^55 + 4 * q^57 - 36 * q^58 + 36 * q^59 - 20 * q^60 + 4 * q^61 + 12 * q^62 + 52 * q^64 - 36 * q^65 + 16 * q^66 - 52 * q^67 + 8 * q^68 + 12 * q^69 - 12 * q^71 - 12 * q^72 + 16 * q^73 + 4 * q^74 + 8 * q^75 - 16 * q^76 - 8 * q^78 - 36 * q^79 + 68 * q^80 + 16 * q^81 + 4 * q^82 + 32 * q^83 - 28 * q^85 - 8 * q^86 + 16 * q^87 - 36 * q^88 + 12 * q^89 + 4 * q^90 - 36 * q^92 - 4 * q^93 - 24 * q^94 - 20 * q^95 + 48 * q^96 - 48 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.83908	−1.30043	−0.650214	−	0.759751i	$-0.725321\pi$
$2$	−1.83908	−1.30043	−0.650214	+	0.759751i	$0.725321\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.38223	0.691115
$5$	2.07594	0.928388	0.464194	−	0.885733i	$-0.346344\pi$
$5$	2.07594	0.928388	0.464194	+	0.885733i	$0.346344\pi$
$6$	1.83908	0.750803
$7$	0	0
$7$	0	0
$8$	1.13613	0.401683
$9$	1.00000	0.333333
$10$	−3.81783	−1.20730
$11$	−6.44723	−1.94391	−0.971957	−	0.235159i	$-0.924439\pi$
$11$	−6.44723	−1.94391	−0.971957	+	0.235159i	$0.924439\pi$
$12$	−1.38223	−0.399016
$13$	0.865716	0.240106	0.120053	−	0.992767i	$-0.461693\pi$
$13$	0.865716	0.240106	0.120053	+	0.992767i	$0.461693\pi$
$14$	0	0
$15$	−2.07594	−0.536005
$16$	−4.85390	−1.21347
$17$	−2.06756	−0.501456	−0.250728	−	0.968058i	$-0.580670\pi$
$17$	−2.06756	−0.501456	−0.250728	+	0.968058i	$0.580670\pi$
$18$	−1.83908	−0.433476
$19$	−3.75357	−0.861127	−0.430564	−	0.902560i	$-0.641685\pi$
$19$	−3.75357	−0.861127	−0.430564	+	0.902560i	$0.641685\pi$
$20$	2.86943	0.641623
$21$	0	0
$22$	11.8570	2.52792
$23$	5.10432	1.06432	0.532162	−	0.846643i	$-0.321380\pi$
$23$	5.10432	1.06432	0.532162	+	0.846643i	$0.321380\pi$
$24$	−1.13613	−0.231912
$25$	−0.690475	−0.138095
$26$	−1.59212	−0.312241
$27$	−1.00000	−0.192450
$28$	0	0
$29$	1.38301	0.256818	0.128409	−	0.991721i	$-0.459013\pi$
$29$	1.38301	0.256818	0.128409	+	0.991721i	$0.459013\pi$
$30$	3.81783	0.697037
$31$	3.75086	0.673674	0.336837	−	0.941563i	$-0.390643\pi$
$31$	3.75086	0.673674	0.336837	+	0.941563i	$0.390643\pi$
$32$	6.65447	1.17636
$33$	6.44723	1.12232
$34$	3.80241	0.652109
$35$	0	0
$36$	1.38223	0.230372
$37$	−0.654747	−0.107640	−0.0538199	−	0.998551i	$-0.517140\pi$
$37$	−0.654747	−0.107640	−0.0538199	+	0.998551i	$0.517140\pi$
$38$	6.90313	1.11983
$39$	−0.865716	−0.138625
$40$	2.35854	0.372917
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	11.2846	1.72089	0.860446	−	0.509542i	$-0.170185\pi$
$43$	11.2846	1.72089	0.860446	+	0.509542i	$0.170185\pi$
$44$	−8.91156	−1.34347
$45$	2.07594	0.309463
$46$	−9.38727	−1.38408
$47$	13.3268	1.94392	0.971958	−	0.235156i	$-0.0755601\pi$
$47$	13.3268	1.94392	0.971958	+	0.235156i	$0.0755601\pi$
$48$	4.85390	0.700600
$49$	0	0
$50$	1.26984	0.179583
$51$	2.06756	0.289516
$52$	1.19662	0.165941
$53$	−0.611905	−0.0840516	−0.0420258	−	0.999117i	$-0.513381\pi$
$53$	−0.611905	−0.0840516	−0.0420258	+	0.999117i	$0.513381\pi$
$54$	1.83908	0.250268
$55$	−13.3841	−1.80471
$56$	0	0
$57$	3.75357	0.497172
$58$	−2.54346	−0.333973
$59$	−3.36226	−0.437729	−0.218864	−	0.975755i	$-0.570235\pi$
$59$	−3.36226	−0.437729	−0.218864	+	0.975755i	$0.570235\pi$
$60$	−2.86943	−0.370441
$61$	−12.3530	−1.58164	−0.790818	−	0.612051i	$-0.790345\pi$
$61$	−12.3530	−1.58164	−0.790818	+	0.612051i	$0.790345\pi$
$62$	−6.89814	−0.876065
$63$	0	0
$64$	−2.53033	−0.316292
$65$	1.79717	0.222912
$66$	−11.8570	−1.45950
$67$	12.3187	1.50497	0.752487	−	0.658607i	$-0.228854\pi$
$67$	12.3187	1.50497	0.752487	+	0.658607i	$0.228854\pi$
$68$	−2.85784	−0.346564
$69$	−5.10432	−0.614488
$70$	0	0
$71$	−3.50868	−0.416403	−0.208202	−	0.978086i	$-0.566761\pi$
$71$	−3.50868	−0.416403	−0.208202	+	0.978086i	$0.566761\pi$
$72$	1.13613	0.133894
$73$	0.660309	0.0772833	0.0386416	−	0.999253i	$-0.487697\pi$
$73$	0.660309	0.0772833	0.0386416	+	0.999253i	$0.487697\pi$
$74$	1.20413	0.139978
$75$	0.690475	0.0797292
$76$	−5.18830	−0.595138
$77$	0	0
$78$	1.59212	0.180273
$79$	−3.56152	−0.400702	−0.200351	−	0.979724i	$-0.564208\pi$
$79$	−3.56152	−0.400702	−0.200351	+	0.979724i	$0.564208\pi$
$80$	−10.0764	−1.12658
$81$	1.00000	0.111111
$82$	1.83908	0.203093
$83$	−7.34512	−0.806232	−0.403116	−	0.915149i	$-0.632073\pi$
$83$	−7.34512	−0.806232	−0.403116	+	0.915149i	$0.632073\pi$
$84$	0	0
$85$	−4.29213	−0.465546
$86$	−20.7534	−2.23790
$87$	−1.38301	−0.148274
$88$	−7.32489	−0.780836
$89$	11.2002	1.18722	0.593611	−	0.804752i	$-0.297702\pi$
$89$	11.2002	1.18722	0.593611	+	0.804752i	$0.297702\pi$
$90$	−3.81783	−0.402434
$91$	0	0
$92$	7.05534	0.735571
$93$	−3.75086	−0.388946
$94$	−24.5091	−2.52792
$95$	−7.79218	−0.799461
$96$	−6.65447	−0.679169
$97$	−16.7499	−1.70069	−0.850347	−	0.526223i	$-0.823608\pi$
$97$	−16.7499	−1.70069	−0.850347	+	0.526223i	$0.823608\pi$
$98$	0	0
$99$	−6.44723	−0.647971
$100$	−0.954396	−0.0954396
$101$	10.6527	1.05998	0.529992	−	0.848002i	$-0.322195\pi$
$101$	10.6527	1.05998	0.529992	+	0.848002i	$0.322195\pi$
$102$	−3.80241	−0.376495
$103$	3.13032	0.308439	0.154220	−	0.988037i	$-0.450714\pi$
$103$	3.13032	0.308439	0.154220	+	0.988037i	$0.450714\pi$
$104$	0.983566	0.0964466
$105$	0	0
$106$	1.12534	0.109303
$107$	−2.90836	−0.281162	−0.140581	−	0.990069i	$-0.544897\pi$
$107$	−2.90836	−0.281162	−0.140581	+	0.990069i	$0.544897\pi$
$108$	−1.38223	−0.133005
$109$	−18.0354	−1.72748	−0.863741	−	0.503937i	$-0.831885\pi$
$109$	−18.0354	−1.72748	−0.863741	+	0.503937i	$0.831885\pi$
$110$	24.6144	2.34689
$111$	0.654747	0.0621458
$112$	0	0
$113$	0.882599	0.0830279	0.0415140	−	0.999138i	$-0.486782\pi$
$113$	0.882599	0.0830279	0.0415140	+	0.999138i	$0.486782\pi$
$114$	−6.90313	−0.646537
$115$	10.5963	0.988106
$116$	1.91163	0.177491
$117$	0.865716	0.0800355
$118$	6.18348	0.569235
$119$	0	0
$120$	−2.35854	−0.215304
$121$	30.5668	2.77880
$122$	22.7182	2.05681
$123$	1.00000	0.0901670
$124$	5.18455	0.465586
$125$	−11.8131	−1.05659
$126$	0	0
$127$	10.0367	0.890612	0.445306	−	0.895379i	$-0.353095\pi$
$127$	10.0367	0.890612	0.445306	+	0.895379i	$0.353095\pi$
$128$	−8.65545	−0.765041
$129$	−11.2846	−0.993557
$130$	−3.30515	−0.289881
$131$	8.63702	0.754620	0.377310	−	0.926087i	$-0.376849\pi$
$131$	8.63702	0.754620	0.377310	+	0.926087i	$0.376849\pi$
$132$	8.91156	0.775652
$133$	0	0
$134$	−22.6552	−1.95711
$135$	−2.07594	−0.178668
$136$	−2.34901	−0.201426
$137$	−9.78840	−0.836279	−0.418140	−	0.908383i	$-0.637318\pi$
$137$	−9.78840	−0.836279	−0.418140	+	0.908383i	$0.637318\pi$
$138$	9.38727	0.799097
$139$	7.41419	0.628863	0.314432	−	0.949280i	$-0.398186\pi$
$139$	7.41419	0.628863	0.314432	+	0.949280i	$0.398186\pi$
$140$	0	0
$141$	−13.3268	−1.12232
$142$	6.45275	0.541503
$143$	−5.58147	−0.466746
$144$	−4.85390	−0.404492
$145$	2.87104	0.238427
$146$	−1.21436	−0.100501
$147$	0	0
$148$	−0.905011	−0.0743915
$149$	−14.5604	−1.19284	−0.596418	−	0.802674i	$-0.703410\pi$
$149$	−14.5604	−1.19284	−0.596418	+	0.802674i	$0.703410\pi$
$150$	−1.26984	−0.103682
$151$	−15.7382	−1.28076	−0.640380	−	0.768058i	$-0.721223\pi$
$151$	−15.7382	−1.28076	−0.640380	+	0.768058i	$0.721223\pi$
$152$	−4.26454	−0.345900
$153$	−2.06756	−0.167152
$154$	0	0
$155$	7.78655	0.625431
$156$	−1.19662	−0.0958062
$157$	−11.2615	−0.898765	−0.449383	−	0.893339i	$-0.648356\pi$
$157$	−11.2615	−0.898765	−0.449383	+	0.893339i	$0.648356\pi$
$158$	6.54993	0.521084
$159$	0.611905	0.0485272
$160$	13.8143	1.09211
$161$	0	0
$162$	−1.83908	−0.144492
$163$	−13.3329	−1.04431	−0.522157	−	0.852850i	$-0.674872\pi$
$163$	−13.3329	−1.04431	−0.522157	+	0.852850i	$0.674872\pi$
$164$	−1.38223	−0.107934
$165$	13.3841	1.04195
$166$	13.5083	1.04845
$167$	7.46545	0.577694	0.288847	−	0.957375i	$-0.406728\pi$
$167$	7.46545	0.577694	0.288847	+	0.957375i	$0.406728\pi$
$168$	0	0
$169$	−12.2505	−0.942349
$170$	7.89358	0.605410
$171$	−3.75357	−0.287042
$172$	15.5980	1.18933
$173$	10.5624	0.803042	0.401521	−	0.915850i	$-0.368482\pi$
$173$	10.5624	0.803042	0.401521	+	0.915850i	$0.368482\pi$
$174$	2.54346	0.192820
$175$	0	0
$176$	31.2942	2.35889
$177$	3.36226	0.252723
$178$	−20.5982	−1.54390
$179$	−14.1339	−1.05642	−0.528208	−	0.849115i	$-0.677136\pi$
$179$	−14.1339	−1.05642	−0.528208	+	0.849115i	$0.677136\pi$
$180$	2.86943	0.213874
$181$	−7.95632	−0.591389	−0.295694	−	0.955283i	$-0.595551\pi$
$181$	−7.95632	−0.591389	−0.295694	+	0.955283i	$0.595551\pi$
$182$	0	0
$183$	12.3530	0.913158
$184$	5.79917	0.427520
$185$	−1.35921	−0.0999315
$186$	6.89814	0.505796
$187$	13.3300	0.974788
$188$	18.4207	1.34347
$189$	0	0
$190$	14.3305	1.03964
$191$	14.3584	1.03894	0.519468	−	0.854490i	$-0.326130\pi$
$191$	14.3584	1.03894	0.519468	+	0.854490i	$0.326130\pi$
$192$	2.53033	0.182611
$193$	14.1983	1.02202	0.511008	−	0.859576i	$-0.329272\pi$
$193$	14.1983	1.02202	0.511008	+	0.859576i	$0.329272\pi$
$194$	30.8044	2.21163
$195$	−1.79717	−0.128698
$196$	0	0
$197$	16.6739	1.18796	0.593982	−	0.804478i	$-0.297555\pi$
$197$	16.6739	1.18796	0.593982	+	0.804478i	$0.297555\pi$
$198$	11.8570	0.842641
$199$	−15.7283	−1.11495	−0.557474	−	0.830194i	$-0.688230\pi$
$199$	−15.7283	−1.11495	−0.557474	+	0.830194i	$0.688230\pi$
$200$	−0.784469	−0.0554703
$201$	−12.3187	−0.868897
$202$	−19.5912	−1.37843
$203$	0	0
$204$	2.85784	0.200089
$205$	−2.07594	−0.144990
$206$	−5.75692	−0.401104
$207$	5.10432	0.354775
$208$	−4.20210	−0.291363
$209$	24.2001	1.67396
$210$	0	0
$211$	−5.52824	−0.380580	−0.190290	−	0.981728i	$-0.560943\pi$
$211$	−5.52824	−0.380580	−0.190290	+	0.981728i	$0.560943\pi$
$212$	−0.845794	−0.0580894
$213$	3.50868	0.240410
$214$	5.34873	0.365631
$215$	23.4262	1.59766
$216$	−1.13613	−0.0773038
$217$	0	0
$218$	33.1687	2.24647
$219$	−0.660309	−0.0446195
$220$	−18.4999	−1.24726
$221$	−1.78992	−0.120403
$222$	−1.20413	−0.0808162
$223$	12.9221	0.865327	0.432664	−	0.901555i	$-0.357574\pi$
$223$	12.9221	0.865327	0.432664	+	0.901555i	$0.357574\pi$
$224$	0	0
$225$	−0.690475	−0.0460317
$226$	−1.62317	−0.107972
$227$	−3.64390	−0.241854	−0.120927	−	0.992661i	$-0.538587\pi$
$227$	−3.64390	−0.241854	−0.120927	+	0.992661i	$0.538587\pi$
$228$	5.18830	0.343603
$229$	−23.0808	−1.52522	−0.762611	−	0.646858i	$-0.776083\pi$
$229$	−23.0808	−1.52522	−0.762611	+	0.646858i	$0.776083\pi$
$230$	−19.4874	−1.28496
$231$	0	0
$232$	1.57127	0.103159
$233$	5.78012	0.378668	0.189334	−	0.981913i	$-0.439367\pi$
$233$	5.78012	0.378668	0.189334	+	0.981913i	$0.439367\pi$
$234$	−1.59212	−0.104080
$235$	27.6657	1.80471
$236$	−4.64742	−0.302521
$237$	3.56152	0.231345
$238$	0	0
$239$	−13.9510	−0.902417	−0.451209	−	0.892419i	$-0.649007\pi$
$239$	−13.9510	−0.902417	−0.451209	+	0.892419i	$0.649007\pi$
$240$	10.0764	0.650429
$241$	13.2115	0.851029	0.425514	−	0.904952i	$-0.360093\pi$
$241$	13.2115	0.851029	0.425514	+	0.904952i	$0.360093\pi$
$242$	−56.2149	−3.61363
$243$	−1.00000	−0.0641500
$244$	−17.0747	−1.09309
$245$	0	0
$246$	−1.83908	−0.117256
$247$	−3.24952	−0.206762
$248$	4.26146	0.270603
$249$	7.34512	0.465478
$250$	21.7253	1.37403
$251$	−9.07327	−0.572700	−0.286350	−	0.958125i	$-0.592442\pi$
$251$	−9.07327	−0.572700	−0.286350	+	0.958125i	$0.592442\pi$
$252$	0	0
$253$	−32.9087	−2.06895
$254$	−18.4583	−1.15818
$255$	4.29213	0.268783
$256$	20.9788	1.31117
$257$	−17.3028	−1.07932	−0.539660	−	0.841883i	$-0.681447\pi$
$257$	−17.3028	−1.07932	−0.539660	+	0.841883i	$0.681447\pi$
$258$	20.7534	1.29205
$259$	0	0
$260$	2.48411	0.154058
$261$	1.38301	0.0856059
$262$	−15.8842	−0.981330
$263$	15.5407	0.958279	0.479140	−	0.877739i	$-0.340949\pi$
$263$	15.5407	0.958279	0.479140	+	0.877739i	$0.340949\pi$
$264$	7.32489	0.450816
$265$	−1.27028	−0.0780325
$266$	0	0
$267$	−11.2002	−0.685443
$268$	17.0273	1.04011
$269$	11.0657	0.674690	0.337345	−	0.941381i	$-0.390471\pi$
$269$	11.0657	0.674690	0.337345	+	0.941381i	$0.390471\pi$
$270$	3.81783	0.232346
$271$	7.28543	0.442558	0.221279	−	0.975210i	$-0.428977\pi$
$271$	7.28543	0.442558	0.221279	+	0.975210i	$0.428977\pi$
$272$	10.0357	0.608505
$273$	0	0
$274$	18.0017	1.08752
$275$	4.45165	0.268445
$276$	−7.05534	−0.424682
$277$	−31.1322	−1.87055	−0.935277	−	0.353917i	$-0.884849\pi$
$277$	−31.1322	−1.87055	−0.935277	+	0.353917i	$0.884849\pi$
$278$	−13.6353	−0.817792
$279$	3.75086	0.224558
$280$	0	0
$281$	−24.9110	−1.48606	−0.743032	−	0.669256i	$-0.766613\pi$
$281$	−24.9110	−1.48606	−0.743032	+	0.669256i	$0.766613\pi$
$282$	24.5091	1.45950
$283$	5.35887	0.318551	0.159276	−	0.987234i	$-0.449084\pi$
$283$	5.35887	0.318551	0.159276	+	0.987234i	$0.449084\pi$
$284$	−4.84980	−0.287783
$285$	7.79218	0.461569
$286$	10.2648	0.606970
$287$	0	0
$288$	6.65447	0.392118
$289$	−12.7252	−0.748541
$290$	−5.28008	−0.310057
$291$	16.7499	0.981896
$292$	0.912699	0.0534116
$293$	28.4083	1.65963	0.829814	−	0.558040i	$-0.188446\pi$
$293$	28.4083	1.65963	0.829814	+	0.558040i	$0.188446\pi$
$294$	0	0
$295$	−6.97985	−0.406382
$296$	−0.743877	−0.0432370
$297$	6.44723	0.374106
$298$	26.7778	1.55120
$299$	4.41889	0.255551
$300$	0.954396	0.0551021
$301$	0	0
$302$	28.9440	1.66554
$303$	−10.6527	−0.611982
$304$	18.2194	1.04496
$305$	−25.6440	−1.46837
$306$	3.80241	0.217370
$307$	5.25225	0.299762	0.149881	−	0.988704i	$-0.452111\pi$
$307$	5.25225	0.299762	0.149881	+	0.988704i	$0.452111\pi$
$308$	0	0
$309$	−3.13032	−0.178078
$310$	−14.3201	−0.813328
$311$	6.91252	0.391973	0.195987	−	0.980607i	$-0.437209\pi$
$311$	6.91252	0.391973	0.195987	+	0.980607i	$0.437209\pi$
$312$	−0.983566	−0.0556834
$313$	−2.28563	−0.129192	−0.0645958	−	0.997912i	$-0.520576\pi$
$313$	−2.28563	−0.129192	−0.0645958	+	0.997912i	$0.520576\pi$
$314$	20.7108	1.16878
$315$	0	0
$316$	−4.92284	−0.276931
$317$	−13.1138	−0.736544	−0.368272	−	0.929718i	$-0.620051\pi$
$317$	−13.1138	−0.736544	−0.368272	+	0.929718i	$0.620051\pi$
$318$	−1.12534	−0.0631062
$319$	−8.91656	−0.499232
$320$	−5.25282	−0.293641
$321$	2.90836	0.162329
$322$	0	0
$323$	7.76072	0.431818
$324$	1.38223	0.0767906
$325$	−0.597755	−0.0331575
$326$	24.5203	1.35805
$327$	18.0354	0.997362
$328$	−1.13613	−0.0627323
$329$	0	0
$330$	−24.6144	−1.35498
$331$	−12.1363	−0.667069	−0.333534	−	0.942738i	$-0.608241\pi$
$331$	−12.1363	−0.667069	−0.333534	+	0.942738i	$0.608241\pi$
$332$	−10.1527	−0.557199
$333$	−0.654747	−0.0358799
$334$	−13.7296	−0.751250
$335$	25.5730	1.39720
$336$	0	0
$337$	−22.1981	−1.20921	−0.604604	−	0.796526i	$-0.706669\pi$
$337$	−22.1981	−1.20921	−0.604604	+	0.796526i	$0.706669\pi$
$338$	22.5298	1.22546
$339$	−0.882599	−0.0479362
$340$	−5.93271	−0.321746
$341$	−24.1826	−1.30956
$342$	6.90313	0.373278
$343$	0	0
$344$	12.8208	0.691252
$345$	−10.5963	−0.570483
$346$	−19.4251	−1.04430
$347$	31.0327	1.66592	0.832962	−	0.553331i	$-0.186643\pi$
$347$	31.0327	1.66592	0.832962	+	0.553331i	$0.186643\pi$
$348$	−1.91163	−0.102474
$349$	18.6506	0.998342	0.499171	−	0.866503i	$-0.333638\pi$
$349$	18.6506	0.998342	0.499171	+	0.866503i	$0.333638\pi$
$350$	0	0
$351$	−0.865716	−0.0462085
$352$	−42.9029	−2.28673
$353$	0.397213	0.0211415	0.0105708	−	0.999944i	$-0.496635\pi$
$353$	0.397213	0.0211415	0.0105708	+	0.999944i	$0.496635\pi$
$354$	−6.18348	−0.328648
$355$	−7.28380	−0.386584
$356$	15.4813	0.820508
$357$	0	0
$358$	25.9934	1.37379
$359$	3.07007	0.162032	0.0810159	−	0.996713i	$-0.474184\pi$
$359$	3.07007	0.162032	0.0810159	+	0.996713i	$0.474184\pi$
$360$	2.35854	0.124306
$361$	−4.91074	−0.258460
$362$	14.6323	0.769059
$363$	−30.5668	−1.60434
$364$	0	0
$365$	1.37076	0.0717489
$366$	−22.7182	−1.18750
$367$	−35.8228	−1.86994	−0.934968	−	0.354733i	$-0.884572\pi$
$367$	−35.8228	−1.86994	−0.934968	+	0.354733i	$0.884572\pi$
$368$	−24.7758	−1.29153
$369$	−1.00000	−0.0520579
$370$	2.49971	0.129954
$371$	0	0
$372$	−5.18455	−0.268806
$373$	−19.2853	−0.998556	−0.499278	−	0.866442i	$-0.666401\pi$
$373$	−19.2853	−0.998556	−0.499278	+	0.866442i	$0.666401\pi$
$374$	−24.5150	−1.26764
$375$	11.8131	0.610025
$376$	15.1410	0.780837
$377$	1.19729	0.0616636
$378$	0	0
$379$	−23.8292	−1.22403	−0.612013	−	0.790848i	$-0.709640\pi$
$379$	−23.8292	−1.22403	−0.612013	+	0.790848i	$0.709640\pi$
$380$	−10.7706	−0.552519
$381$	−10.0367	−0.514195
$382$	−26.4063	−1.35106
$383$	−19.8612	−1.01486	−0.507429	−	0.861693i	$-0.669404\pi$
$383$	−19.8612	−1.01486	−0.507429	+	0.861693i	$0.669404\pi$
$384$	8.65545	0.441696
$385$	0	0
$386$	−26.1119	−1.32906
$387$	11.2846	0.573630
$388$	−23.1522	−1.17538
$389$	−22.4236	−1.13692	−0.568462	−	0.822710i	$-0.692461\pi$
$389$	−22.4236	−1.13692	−0.568462	+	0.822710i	$0.692461\pi$
$390$	3.30515	0.167363
$391$	−10.5535	−0.533712
$392$	0	0
$393$	−8.63702	−0.435680
$394$	−30.6647	−1.54486
$395$	−7.39349	−0.372007
$396$	−8.91156	−0.447823
$397$	−35.9949	−1.80653	−0.903267	−	0.429079i	$-0.858838\pi$
$397$	−35.9949	−1.80653	−0.903267	+	0.429079i	$0.858838\pi$
$398$	28.9256	1.44991
$399$	0	0
$400$	3.35150	0.167575
$401$	29.2996	1.46315	0.731576	−	0.681760i	$-0.238785\pi$
$401$	29.2996	1.46315	0.731576	+	0.681760i	$0.238785\pi$
$402$	22.6552	1.12994
$403$	3.24718	0.161753
$404$	14.7245	0.732572
$405$	2.07594	0.103154
$406$	0	0
$407$	4.22130	0.209242
$408$	2.34901	0.116294
$409$	−29.1416	−1.44096	−0.720479	−	0.693477i	$-0.756078\pi$
$409$	−29.1416	−1.44096	−0.720479	+	0.693477i	$0.756078\pi$
$410$	3.81783	0.188549
$411$	9.78840	0.482826
$412$	4.32682	0.213167
$413$	0	0
$414$	−9.38727	−0.461359
$415$	−15.2480	−0.748496
$416$	5.76088	0.282450
$417$	−7.41419	−0.363074
$418$	−44.5061	−2.17686
$419$	−1.13374	−0.0553866	−0.0276933	−	0.999616i	$-0.508816\pi$
$419$	−1.13374	−0.0553866	−0.0276933	+	0.999616i	$0.508816\pi$
$420$	0	0
$421$	17.9733	0.875967	0.437984	−	0.898983i	$-0.355693\pi$
$421$	17.9733	0.875967	0.437984	+	0.898983i	$0.355693\pi$
$422$	10.1669	0.494917
$423$	13.3268	0.647972
$424$	−0.695203	−0.0337621
$425$	1.42760	0.0692486
$426$	−6.45275	−0.312637
$427$	0	0
$428$	−4.02003	−0.194315
$429$	5.58147	0.269476
$430$	−43.0828	−2.07764
$431$	−5.91704	−0.285014	−0.142507	−	0.989794i	$-0.545516\pi$
$431$	−5.91704	−0.285014	−0.142507	+	0.989794i	$0.545516\pi$
$432$	4.85390	0.233533
$433$	0.775364	0.0372616	0.0186308	−	0.999826i	$-0.494069\pi$
$433$	0.775364	0.0372616	0.0186308	+	0.999826i	$0.494069\pi$
$434$	0	0
$435$	−2.87104	−0.137656
$436$	−24.9291	−1.19389
$437$	−19.1594	−0.916518
$438$	1.21436	0.0580245
$439$	32.3419	1.54359	0.771797	−	0.635869i	$-0.219358\pi$
$439$	32.3419	1.54359	0.771797	+	0.635869i	$0.219358\pi$
$440$	−15.2060	−0.724919
$441$	0	0
$442$	3.29181	0.156575
$443$	−4.81006	−0.228533	−0.114266	−	0.993450i	$-0.536452\pi$
$443$	−4.81006	−0.228533	−0.114266	+	0.993450i	$0.536452\pi$
$444$	0.905011	0.0429499
$445$	23.2510	1.10220
$446$	−23.7648	−1.12530
$447$	14.5604	0.688684
$448$	0	0
$449$	−8.91035	−0.420505	−0.210253	−	0.977647i	$-0.567429\pi$
$449$	−8.91035	−0.420505	−0.210253	+	0.977647i	$0.567429\pi$
$450$	1.26984	0.0598609
$451$	6.44723	0.303588
$452$	1.21996	0.0573819
$453$	15.7382	0.739447
$454$	6.70144	0.314514
$455$	0	0
$456$	4.26454	0.199705
$457$	−4.42700	−0.207086	−0.103543	−	0.994625i	$-0.533018\pi$
$457$	−4.42700	−0.207086	−0.103543	+	0.994625i	$0.533018\pi$
$458$	42.4475	1.98344
$459$	2.06756	0.0965053
$460$	14.6465	0.682895
$461$	19.0939	0.889289	0.444645	−	0.895707i	$-0.353330\pi$
$461$	19.0939	0.889289	0.444645	+	0.895707i	$0.353330\pi$
$462$	0	0
$463$	−15.4688	−0.718897	−0.359449	−	0.933165i	$-0.617035\pi$
$463$	−15.4688	−0.718897	−0.359449	+	0.933165i	$0.617035\pi$
$464$	−6.71297	−0.311642
$465$	−7.78655	−0.361093
$466$	−10.6301	−0.492431
$467$	2.45321	0.113521	0.0567605	−	0.998388i	$-0.481923\pi$
$467$	2.45321	0.113521	0.0567605	+	0.998388i	$0.481923\pi$
$468$	1.19662	0.0553137
$469$	0	0
$470$	−50.8795	−2.34690
$471$	11.2615	0.518902
$472$	−3.81996	−0.175828
$473$	−72.7547	−3.34526
$474$	−6.54993	−0.300848
$475$	2.59174	0.118917
$476$	0	0
$477$	−0.611905	−0.0280172
$478$	25.6571	1.17353
$479$	2.25840	0.103189	0.0515944	−	0.998668i	$-0.483570\pi$
$479$	2.25840	0.103189	0.0515944	+	0.998668i	$0.483570\pi$
$480$	−13.8143	−0.630533
$481$	−0.566825	−0.0258450
$482$	−24.2971	−1.10670
$483$	0	0
$484$	42.2504	1.92047
$485$	−34.7717	−1.57890
$486$	1.83908	0.0834226
$487$	−1.19918	−0.0543401	−0.0271701	−	0.999631i	$-0.508650\pi$
$487$	−1.19918	−0.0543401	−0.0271701	+	0.999631i	$0.508650\pi$
$488$	−14.0346	−0.635316
$489$	13.3329	0.602934
$490$	0	0
$491$	−15.1114	−0.681967	−0.340983	−	0.940069i	$-0.610760\pi$
$491$	−15.1114	−0.681967	−0.340983	+	0.940069i	$0.610760\pi$
$492$	1.38223	0.0623158
$493$	−2.85945	−0.128783
$494$	5.97615	0.268880
$495$	−13.3841	−0.601569
$496$	−18.2063	−0.817486
$497$	0	0
$498$	−13.5083	−0.605321
$499$	−25.5628	−1.14435	−0.572175	−	0.820131i	$-0.693900\pi$
$499$	−25.5628	−1.14435	−0.572175	+	0.820131i	$0.693900\pi$
$500$	−16.3284	−0.730228
$501$	−7.46545	−0.333532
$502$	16.6865	0.744755
$503$	7.64100	0.340695	0.170348	−	0.985384i	$-0.445511\pi$
$503$	7.64100	0.340695	0.170348	+	0.985384i	$0.445511\pi$
$504$	0	0
$505$	22.1144	0.984077
$506$	60.5219	2.69053
$507$	12.2505	0.544065
$508$	13.8730	0.615515
$509$	18.7058	0.829119	0.414559	−	0.910022i	$-0.363936\pi$
$509$	18.7058	0.829119	0.414559	+	0.910022i	$0.363936\pi$
$510$	−7.89358	−0.349534
$511$	0	0
$512$	−21.2708	−0.940046
$513$	3.75357	0.165724
$514$	31.8213	1.40358
$515$	6.49835	0.286352
$516$	−15.5980	−0.686663
$517$	−85.9211	−3.77880
$518$	0	0
$519$	−10.5624	−0.463636
$520$	2.04182	0.0895399
$521$	27.6080	1.20953	0.604764	−	0.796404i	$-0.293267\pi$
$521$	27.6080	1.20953	0.604764	+	0.796404i	$0.293267\pi$
$522$	−2.54346	−0.111324
$523$	−13.6462	−0.596708	−0.298354	−	0.954455i	$-0.596438\pi$
$523$	−13.6462	−0.596708	−0.298354	+	0.954455i	$0.596438\pi$
$524$	11.9384	0.521530
$525$	0	0
$526$	−28.5806	−1.24617
$527$	−7.75511	−0.337818
$528$	−31.2942	−1.36191
$529$	3.05406	0.132785
$530$	2.33615	0.101476
$531$	−3.36226	−0.145910
$532$	0	0
$533$	−0.865716	−0.0374983
$534$	20.5982	0.891370
$535$	−6.03759	−0.261028
$536$	13.9957	0.604522
$537$	14.1339	0.609922
$538$	−20.3508	−0.877387
$539$	0	0
$540$	−2.86943	−0.123480
$541$	−35.7636	−1.53760	−0.768798	−	0.639491i	$-0.779145\pi$
$541$	−35.7636	−1.53760	−0.768798	+	0.639491i	$0.779145\pi$
$542$	−13.3985	−0.575516
$543$	7.95632	0.341438
$544$	−13.7585	−0.589891
$545$	−37.4405	−1.60377
$546$	0	0
$547$	−19.8289	−0.847821	−0.423910	−	0.905704i	$-0.639343\pi$
$547$	−19.8289	−0.847821	−0.423910	+	0.905704i	$0.639343\pi$
$548$	−13.5298	−0.577966
$549$	−12.3530	−0.527212
$550$	−8.18696	−0.349093
$551$	−5.19121	−0.221153
$552$	−5.79917	−0.246829
$553$	0	0
$554$	57.2548	2.43252
$555$	1.35921	0.0576955
$556$	10.2481	0.434617
$557$	1.39060	0.0589218	0.0294609	−	0.999566i	$-0.490621\pi$
$557$	1.39060	0.0589218	0.0294609	+	0.999566i	$0.490621\pi$
$558$	−6.89814	−0.292022
$559$	9.76929	0.413197
$560$	0	0
$561$	−13.3300	−0.562794
$562$	45.8134	1.93252
$563$	5.72970	0.241478	0.120739	−	0.992684i	$-0.461474\pi$
$563$	5.72970	0.241478	0.120739	+	0.992684i	$0.461474\pi$
$564$	−18.4207	−0.775653
$565$	1.83222	0.0770821
$566$	−9.85540	−0.414254
$567$	0	0
$568$	−3.98631	−0.167262
$569$	−32.0783	−1.34479	−0.672397	−	0.740191i	$-0.734735\pi$
$569$	−32.0783	−1.34479	−0.672397	+	0.740191i	$0.734735\pi$
$570$	−14.3305	−0.600237
$571$	41.0648	1.71851	0.859255	−	0.511547i	$-0.170927\pi$
$571$	41.0648	1.71851	0.859255	+	0.511547i	$0.170927\pi$
$572$	−7.71488	−0.322575
$573$	−14.3584	−0.599830
$574$	0	0
$575$	−3.52440	−0.146978
$576$	−2.53033	−0.105431
$577$	16.1354	0.671727	0.335864	−	0.941911i	$-0.390972\pi$
$577$	16.1354	0.671727	0.335864	+	0.941911i	$0.390972\pi$
$578$	23.4027	0.973425
$579$	−14.1983	−0.590061
$580$	3.96844	0.164780
$581$	0	0
$582$	−30.8044	−1.27689
$583$	3.94509	0.163389
$584$	0.750196	0.0310433
$585$	1.79717	0.0743040
$586$	−52.2452	−2.15823
$587$	0.183806	0.00758650	0.00379325	−	0.999993i	$-0.498793\pi$
$587$	0.183806	0.00758650	0.00379325	+	0.999993i	$0.498793\pi$
$588$	0	0
$589$	−14.0791	−0.580119
$590$	12.8365	0.528472
$591$	−16.6739	−0.685871
$592$	3.17808	0.130618
$593$	−46.8319	−1.92315	−0.961577	−	0.274536i	$-0.911476\pi$
$593$	−46.8319	−1.92315	−0.961577	+	0.274536i	$0.911476\pi$
$594$	−11.8570	−0.486499
$595$	0	0
$596$	−20.1258	−0.824387
$597$	15.7283	0.643716
$598$	−8.12671	−0.332326
$599$	−36.8518	−1.50572	−0.752862	−	0.658178i	$-0.771327\pi$
$599$	−36.8518	−1.50572	−0.752862	+	0.658178i	$0.771327\pi$
$600$	0.784469	0.0320258
$601$	−9.16452	−0.373829	−0.186914	−	0.982376i	$-0.559849\pi$
$601$	−9.16452	−0.373829	−0.186914	+	0.982376i	$0.559849\pi$
$602$	0	0
$603$	12.3187	0.501658
$604$	−21.7539	−0.885153
$605$	63.4548	2.57981
$606$	19.5912	0.795840
$607$	5.11896	0.207772	0.103886	−	0.994589i	$-0.466872\pi$
$607$	5.11896	0.207772	0.103886	+	0.994589i	$0.466872\pi$
$608$	−24.9780	−1.01299
$609$	0	0
$610$	47.1615	1.90952
$611$	11.5372	0.466747
$612$	−2.85784	−0.115521
$613$	−2.09194	−0.0844926	−0.0422463	−	0.999107i	$-0.513451\pi$
$613$	−2.09194	−0.0844926	−0.0422463	+	0.999107i	$0.513451\pi$
$614$	−9.65934	−0.389819
$615$	2.07594	0.0837100
$616$	0	0
$617$	0.384624	0.0154844	0.00774220	−	0.999970i	$-0.497536\pi$
$617$	0.384624	0.0154844	0.00774220	+	0.999970i	$0.497536\pi$
$618$	5.75692	0.231577
$619$	45.9882	1.84842	0.924211	−	0.381882i	$-0.124724\pi$
$619$	45.9882	1.84842	0.924211	+	0.381882i	$0.124724\pi$
$620$	10.7628	0.432245
$621$	−5.10432	−0.204829
$622$	−12.7127	−0.509733
$623$	0	0
$624$	4.20210	0.168219
$625$	−21.0709	−0.842835
$626$	4.20347	0.168005
$627$	−24.2001	−0.966460
$628$	−15.5660	−0.621150
$629$	1.35373	0.0539766
$630$	0	0
$631$	17.7279	0.705735	0.352868	−	0.935673i	$-0.385207\pi$
$631$	17.7279	0.705735	0.352868	+	0.935673i	$0.385207\pi$
$632$	−4.04634	−0.160955
$633$	5.52824	0.219728
$634$	24.1174	0.957824
$635$	20.8355	0.826834
$636$	0.845794	0.0335379
$637$	0	0
$638$	16.3983	0.649215
$639$	−3.50868	−0.138801
$640$	−17.9682	−0.710255
$641$	−30.3759	−1.19978	−0.599888	−	0.800084i	$-0.704788\pi$
$641$	−30.3759	−1.19978	−0.599888	+	0.800084i	$0.704788\pi$
$642$	−5.34873	−0.211097
$643$	−48.8439	−1.92621	−0.963107	−	0.269118i	$-0.913268\pi$
$643$	−48.8439	−1.92621	−0.963107	+	0.269118i	$0.913268\pi$
$644$	0	0
$645$	−23.4262	−0.922407
$646$	−14.2726	−0.561548
$647$	21.6126	0.849681	0.424840	−	0.905268i	$-0.360330\pi$
$647$	21.6126	0.849681	0.424840	+	0.905268i	$0.360330\pi$
$648$	1.13613	0.0446314
$649$	21.6773	0.850907
$650$	1.09932	0.0431190
$651$	0	0
$652$	−18.4291	−0.721741
$653$	−19.4895	−0.762682	−0.381341	−	0.924434i	$-0.624538\pi$
$653$	−19.4895	−0.762682	−0.381341	+	0.924434i	$0.624538\pi$
$654$	−33.1687	−1.29700
$655$	17.9299	0.700581
$656$	4.85390	0.189513
$657$	0.660309	0.0257611
$658$	0	0
$659$	7.29506	0.284175	0.142088	−	0.989854i	$-0.454619\pi$
$659$	7.29506	0.284175	0.142088	+	0.989854i	$0.454619\pi$
$660$	18.4999	0.720106
$661$	−12.7921	−0.497555	−0.248778	−	0.968561i	$-0.580029\pi$
$661$	−12.7921	−0.497555	−0.248778	+	0.968561i	$0.580029\pi$
$662$	22.3196	0.867476
$663$	1.78992	0.0695147
$664$	−8.34501	−0.323849
$665$	0	0
$666$	1.20413	0.0466593
$667$	7.05930	0.273337
$668$	10.3190	0.399253
$669$	−12.9221	−0.499597
$670$	−47.0308	−1.81696
$671$	79.6425	3.07457
$672$	0	0
$673$	−39.9104	−1.53843	−0.769217	−	0.638987i	$-0.779354\pi$
$673$	−39.9104	−1.53843	−0.769217	+	0.638987i	$0.779354\pi$
$674$	40.8242	1.57249
$675$	0.690475	0.0265764
$676$	−16.9331	−0.651272
$677$	50.3513	1.93516	0.967578	−	0.252572i	$-0.0812763\pi$
$677$	50.3513	1.93516	0.967578	+	0.252572i	$0.0812763\pi$
$678$	1.62317	0.0623376
$679$	0	0
$680$	−4.87641	−0.187002
$681$	3.64390	0.139635
$682$	44.4739	1.70299
$683$	−15.2281	−0.582686	−0.291343	−	0.956619i	$-0.594102\pi$
$683$	−15.2281	−0.582686	−0.291343	+	0.956619i	$0.594102\pi$
$684$	−5.18830	−0.198379
$685$	−20.3201	−0.776392
$686$	0	0
$687$	23.0808	0.880587
$688$	−54.7745	−2.08826
$689$	−0.529736	−0.0201813
$690$	19.4874	0.741873
$691$	−27.8658	−1.06007	−0.530033	−	0.847977i	$-0.677820\pi$
$691$	−27.8658	−1.06007	−0.530033	+	0.847977i	$0.677820\pi$
$692$	14.5996	0.554994
$693$	0	0
$694$	−57.0718	−2.16641
$695$	15.3914	0.583829
$696$	−1.57127	−0.0595590
$697$	2.06756	0.0783143
$698$	−34.3000	−1.29827
$699$	−5.78012	−0.218624
$700$	0	0
$701$	14.4947	0.547457	0.273728	−	0.961807i	$-0.411743\pi$
$701$	14.4947	0.547457	0.273728	+	0.961807i	$0.411743\pi$
$702$	1.59212	0.0600909
$703$	2.45764	0.0926915
$704$	16.3136	0.614843
$705$	−27.6657	−1.04195
$706$	−0.730509	−0.0274931
$707$	0	0
$708$	4.64742	0.174661
$709$	26.2940	0.987493	0.493747	−	0.869606i	$-0.335627\pi$
$709$	26.2940	0.987493	0.493747	+	0.869606i	$0.335627\pi$
$710$	13.3955	0.502725
$711$	−3.56152	−0.133567
$712$	12.7249	0.476887
$713$	19.1456	0.717007
$714$	0	0
$715$	−11.5868	−0.433322
$716$	−19.5363	−0.730105
$717$	13.9510	0.521011
$718$	−5.64611	−0.210711
$719$	21.2151	0.791191	0.395596	−	0.918425i	$-0.370538\pi$
$719$	21.2151	0.791191	0.395596	+	0.918425i	$0.370538\pi$
$720$	−10.0764	−0.375525
$721$	0	0
$722$	9.03126	0.336109
$723$	−13.2115	−0.491342
$724$	−10.9975	−0.408718
$725$	−0.954931	−0.0354653
$726$	56.2149	2.08633
$727$	41.5862	1.54235	0.771174	−	0.636625i	$-0.219670\pi$
$727$	41.5862	1.54235	0.771174	+	0.636625i	$0.219670\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−2.52094	−0.0933043
$731$	−23.3316	−0.862952
$732$	17.0747	0.631098
$733$	−2.38818	−0.0882094	−0.0441047	−	0.999027i	$-0.514044\pi$
$733$	−2.38818	−0.0882094	−0.0441047	+	0.999027i	$0.514044\pi$
$734$	65.8812	2.43172
$735$	0	0
$736$	33.9665	1.25202
$737$	−79.4218	−2.92554
$738$	1.83908	0.0676976
$739$	−33.2178	−1.22193	−0.610967	−	0.791656i	$-0.709219\pi$
$739$	−33.2178	−1.22193	−0.610967	+	0.791656i	$0.709219\pi$
$740$	−1.87875	−0.0690642
$741$	3.24952	0.119374
$742$	0	0
$743$	21.7022	0.796177	0.398088	−	0.917347i	$-0.369674\pi$
$743$	21.7022	0.796177	0.398088	+	0.917347i	$0.369674\pi$
$744$	−4.26146	−0.156233
$745$	−30.2265	−1.10741
$746$	35.4673	1.29855
$747$	−7.34512	−0.268744
$748$	18.4252	0.673691
$749$	0	0
$750$	−21.7253	−0.793294
$751$	−3.99626	−0.145826	−0.0729129	−	0.997338i	$-0.523230\pi$
$751$	−3.99626	−0.145826	−0.0729129	+	0.997338i	$0.523230\pi$
$752$	−64.6870	−2.35889
$753$	9.07327	0.330648
$754$	−2.20192	−0.0801891
$755$	−32.6717	−1.18904
$756$	0	0
$757$	−42.1854	−1.53326	−0.766628	−	0.642092i	$-0.778067\pi$
$757$	−42.1854	−1.53326	−0.766628	+	0.642092i	$0.778067\pi$
$758$	43.8240	1.59176
$759$	32.9087	1.19451
$760$	−8.85293	−0.321129
$761$	−11.5094	−0.417214	−0.208607	−	0.978000i	$-0.566893\pi$
$761$	−11.5094	−0.417214	−0.208607	+	0.978000i	$0.566893\pi$
$762$	18.4583	0.668674
$763$	0	0
$764$	19.8466	0.718025
$765$	−4.29213	−0.155182
$766$	36.5264	1.31975
$767$	−2.91076	−0.105102
$768$	−20.9788	−0.757006
$769$	−10.6229	−0.383072	−0.191536	−	0.981486i	$-0.561347\pi$
$769$	−10.6229	−0.383072	−0.191536	+	0.981486i	$0.561347\pi$
$770$	0	0
$771$	17.3028	0.623145
$772$	19.6253	0.706331
$773$	−14.0372	−0.504884	−0.252442	−	0.967612i	$-0.581234\pi$
$773$	−14.0372	−0.504884	−0.252442	+	0.967612i	$0.581234\pi$
$774$	−20.7534	−0.745966
$775$	−2.58987	−0.0930310
$776$	−19.0300	−0.683139
$777$	0	0
$778$	41.2389	1.47849
$779$	3.75357	0.134485
$780$	−2.48411	−0.0889454
$781$	22.6212	0.809452
$782$	19.4087	0.694055
$783$	−1.38301	−0.0494246
$784$	0	0
$785$	−23.3782	−0.834403
$786$	15.8842	0.566571
$787$	−11.2653	−0.401565	−0.200783	−	0.979636i	$-0.564348\pi$
$787$	−11.2653	−0.401565	−0.200783	+	0.979636i	$0.564348\pi$
$788$	23.0471	0.821020
$789$	−15.5407	−0.553263
$790$	13.5973	0.483769
$791$	0	0
$792$	−7.32489	−0.260279
$793$	−10.6942	−0.379761
$794$	66.1977	2.34927
$795$	1.27028	0.0450521
$796$	−21.7401	−0.770558
$797$	−21.5388	−0.762944	−0.381472	−	0.924380i	$-0.624583\pi$
$797$	−21.5388	−0.762944	−0.381472	+	0.924380i	$0.624583\pi$
$798$	0	0
$799$	−27.5540	−0.974789
$800$	−4.59475	−0.162449
$801$	11.2002	0.395741
$802$	−53.8844	−1.90273
$803$	−4.25716	−0.150232
$804$	−17.0273	−0.600508
$805$	0	0
$806$	−5.97183	−0.210349
$807$	−11.0657	−0.389533
$808$	12.1029	0.425777
$809$	44.1772	1.55319	0.776593	−	0.630002i	$-0.216946\pi$
$809$	44.1772	1.55319	0.776593	+	0.630002i	$0.216946\pi$
$810$	−3.81783	−0.134145
$811$	26.6265	0.934983	0.467491	−	0.883998i	$-0.345158\pi$
$811$	26.6265	0.934983	0.467491	+	0.883998i	$0.345158\pi$
$812$	0	0
$813$	−7.28543	−0.255511
$814$	−7.76333	−0.272105
$815$	−27.6783	−0.969528
$816$	−10.0357	−0.351320
$817$	−42.3576	−1.48191
$818$	53.5938	1.87386
$819$	0	0
$820$	−2.86943	−0.100205
$821$	−12.4085	−0.433060	−0.216530	−	0.976276i	$-0.569474\pi$
$821$	−12.4085	−0.433060	−0.216530	+	0.976276i	$0.569474\pi$
$822$	−18.0017	−0.627881
$823$	−4.97202	−0.173314	−0.0866568	−	0.996238i	$-0.527618\pi$
$823$	−4.97202	−0.173314	−0.0866568	+	0.996238i	$0.527618\pi$
$824$	3.55645	0.123895
$825$	−4.45165	−0.154987
$826$	0	0
$827$	−35.1605	−1.22265	−0.611326	−	0.791379i	$-0.709364\pi$
$827$	−35.1605	−1.22265	−0.611326	+	0.791379i	$0.709364\pi$
$828$	7.05534	0.245190
$829$	50.8093	1.76468	0.882340	−	0.470613i	$-0.155967\pi$
$829$	50.8093	1.76468	0.882340	+	0.470613i	$0.155967\pi$
$830$	28.0424	0.973366
$831$	31.1322	1.07996
$832$	−2.19055	−0.0759436
$833$	0	0
$834$	13.6353	0.472152
$835$	15.4978	0.536324
$836$	33.4501	1.15690
$837$	−3.75086	−0.129649
$838$	2.08503	0.0720263
$839$	23.4219	0.808614	0.404307	−	0.914623i	$-0.367513\pi$
$839$	23.4219	0.808614	0.404307	+	0.914623i	$0.367513\pi$
$840$	0	0
$841$	−27.0873	−0.934045
$842$	−33.0545	−1.13913
$843$	24.9110	0.857979
$844$	−7.64131	−0.263025
$845$	−25.4314	−0.874866
$846$	−24.5091	−0.842641
$847$	0	0
$848$	2.97013	0.101995
$849$	−5.35887	−0.183916
$850$	−2.62547	−0.0900529
$851$	−3.34204	−0.114564
$852$	4.84980	0.166151
$853$	36.3233	1.24369	0.621843	−	0.783142i	$-0.286384\pi$
$853$	36.3233	1.24369	0.621843	+	0.783142i	$0.286384\pi$
$854$	0	0
$855$	−7.79218	−0.266487
$856$	−3.30428	−0.112938
$857$	15.8461	0.541293	0.270647	−	0.962679i	$-0.412762\pi$
$857$	15.8461	0.541293	0.270647	+	0.962679i	$0.412762\pi$
$858$	−10.2648	−0.350434
$859$	−32.0788	−1.09451	−0.547257	−	0.836965i	$-0.684328\pi$
$859$	−32.0788	−1.09451	−0.547257	+	0.836965i	$0.684328\pi$
$860$	32.3805	1.10416
$861$	0	0
$862$	10.8819	0.370640
$863$	−14.5432	−0.495057	−0.247528	−	0.968881i	$-0.579618\pi$
$863$	−14.5432	−0.495057	−0.247528	+	0.968881i	$0.579618\pi$
$864$	−6.65447	−0.226390
$865$	21.9268	0.745534
$866$	−1.42596	−0.0484561
$867$	12.7252	0.432171
$868$	0	0
$869$	22.9619	0.778930
$870$	5.28008	0.179011
$871$	10.6645	0.361354
$872$	−20.4906	−0.693899
$873$	−16.7499	−0.566898
$874$	35.2357	1.19187
$875$	0	0
$876$	−0.912699	−0.0308372
$877$	−43.2112	−1.45914	−0.729569	−	0.683907i	$-0.760279\pi$
$877$	−43.2112	−1.45914	−0.729569	+	0.683907i	$0.760279\pi$
$878$	−59.4794	−2.00733
$879$	−28.4083	−0.958187
$880$	64.9649	2.18997
$881$	−30.7546	−1.03615	−0.518074	−	0.855336i	$-0.673351\pi$
$881$	−30.7546	−1.03615	−0.518074	+	0.855336i	$0.673351\pi$
$882$	0	0
$883$	−43.1740	−1.45292	−0.726461	−	0.687208i	$-0.758836\pi$
$883$	−43.1740	−1.45292	−0.726461	+	0.687208i	$0.758836\pi$
$884$	−2.47408	−0.0832123
$885$	6.97985	0.234625
$886$	8.84610	0.297191
$887$	−21.6010	−0.725291	−0.362646	−	0.931927i	$-0.618126\pi$
$887$	−21.6010	−0.725291	−0.362646	+	0.931927i	$0.618126\pi$
$888$	0.743877	0.0249629
$889$	0	0
$890$	−42.7606	−1.43334
$891$	−6.44723	−0.215990
$892$	17.8613	0.598041
$893$	−50.0231	−1.67396
$894$	−26.7778	−0.895584
$895$	−29.3411	−0.980765
$896$	0	0
$897$	−4.41889	−0.147542
$898$	16.3869	0.546837
$899$	5.18746	0.173011
$900$	−0.954396	−0.0318132
$901$	1.26515	0.0421482
$902$	−11.8570	−0.394795
$903$	0	0
$904$	1.00275	0.0333509
$905$	−16.5168	−0.549038
$906$	−28.9440	−0.961599
$907$	−23.2280	−0.771273	−0.385636	−	0.922651i	$-0.626018\pi$
$907$	−23.2280	−0.771273	−0.385636	+	0.922651i	$0.626018\pi$
$908$	−5.03671	−0.167149
$909$	10.6527	0.353328
$910$	0	0
$911$	30.9148	1.02425	0.512126	−	0.858910i	$-0.328858\pi$
$911$	30.9148	1.02425	0.512126	+	0.858910i	$0.328858\pi$
$912$	−18.2194	−0.603306
$913$	47.3557	1.56725
$914$	8.14162	0.269301
$915$	25.6440	0.847766
$916$	−31.9030	−1.05410
$917$	0	0
$918$	−3.80241	−0.125498
$919$	21.2573	0.701214	0.350607	−	0.936523i	$-0.385975\pi$
$919$	21.2573	0.701214	0.350607	+	0.936523i	$0.385975\pi$
$920$	12.0387	0.396905
$921$	−5.25225	−0.173068
$922$	−35.1152	−1.15646
$923$	−3.03752	−0.0999811
$924$	0	0
$925$	0.452086	0.0148645
$926$	28.4485	0.934875
$927$	3.13032	0.102813
$928$	9.20317	0.302109
$929$	−17.1140	−0.561493	−0.280746	−	0.959782i	$-0.590582\pi$
$929$	−17.1140	−0.561493	−0.280746	+	0.959782i	$0.590582\pi$
$930$	14.3201	0.469575
$931$	0	0
$932$	7.98945	0.261703
$933$	−6.91252	−0.226306
$934$	−4.51166	−0.147626
$935$	27.6723	0.904982
$936$	0.983566	0.0321489
$937$	−8.28226	−0.270570	−0.135285	−	0.990807i	$-0.543195\pi$
$937$	−8.28226	−0.270570	−0.135285	+	0.990807i	$0.543195\pi$
$938$	0	0
$939$	2.28563	0.0745888
$940$	38.2403	1.24726
$941$	12.6922	0.413754	0.206877	−	0.978367i	$-0.433670\pi$
$941$	12.6922	0.413754	0.206877	+	0.978367i	$0.433670\pi$
$942$	−20.7108	−0.674796
$943$	−5.10432	−0.166219
$944$	16.3201	0.531173
$945$	0	0
$946$	133.802	4.35028
$947$	−33.1557	−1.07741	−0.538707	−	0.842493i	$-0.681087\pi$
$947$	−33.1557	−1.07741	−0.538707	+	0.842493i	$0.681087\pi$
$948$	4.92284	0.159886
$949$	0.571640	0.0185562
$950$	−4.76644	−0.154644
$951$	13.1138	0.425244
$952$	0	0
$953$	43.5808	1.41172	0.705860	−	0.708352i	$-0.250561\pi$
$953$	43.5808	1.41172	0.705860	+	0.708352i	$0.250561\pi$
$954$	1.12534	0.0364344
$955$	29.8072	0.964537
$956$	−19.2835	−0.623674
$957$	8.91656	0.288232
$958$	−4.15338	−0.134190
$959$	0	0
$960$	5.25282	0.169534
$961$	−16.9311	−0.546164
$962$	1.04244	0.0336096
$963$	−2.90836	−0.0937207
$964$	18.2614	0.588159
$965$	29.4748	0.948828
$966$	0	0
$967$	3.95999	0.127345	0.0636723	−	0.997971i	$-0.479719\pi$
$967$	3.95999	0.127345	0.0636723	+	0.997971i	$0.479719\pi$
$968$	34.7279	1.11620
$969$	−7.76072	−0.249310
$970$	63.9482	2.05325
$971$	−50.7607	−1.62899	−0.814494	−	0.580171i	$-0.802986\pi$
$971$	−50.7607	−1.62899	−0.814494	+	0.580171i	$0.802986\pi$
$972$	−1.38223	−0.0443351
$973$	0	0
$974$	2.20540	0.0706654
$975$	0.597755	0.0191435
$976$	59.9601	1.91928
$977$	16.7125	0.534681	0.267340	−	0.963602i	$-0.413855\pi$
$977$	16.7125	0.534681	0.267340	+	0.963602i	$0.413855\pi$
$978$	−24.5203	−0.784073
$979$	−72.2105	−2.30786
$980$	0	0
$981$	−18.0354	−0.575827
$982$	27.7911	0.886849
$983$	48.6655	1.55219	0.776095	−	0.630616i	$-0.217198\pi$
$983$	48.6655	1.55219	0.776095	+	0.630616i	$0.217198\pi$
$984$	1.13613	0.0362185
$985$	34.6140	1.10289
$986$	5.25876	0.167473
$987$	0	0
$988$	−4.49159	−0.142897
$989$	57.6004	1.83159
$990$	24.6144	0.782298
$991$	45.1326	1.43369	0.716843	−	0.697235i	$-0.245587\pi$
$991$	45.1326	1.43369	0.716843	+	0.697235i	$0.245587\pi$
$992$	24.9600	0.792480
$993$	12.1363	0.385132
$994$	0	0
$995$	−32.6510	−1.03511
$996$	10.1527	0.321699
$997$	−45.8173	−1.45105	−0.725525	−	0.688196i	$-0.758403\pi$
$997$	−45.8173	−1.45105	−0.725525	+	0.688196i	$0.758403\pi$
$998$	47.0122	1.48815
$999$	0.654747	0.0207153

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bl.1.3	✓	16
7.6	odd	2		6027.2.a.bm.1.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.bl.1.3	✓	16	1.1	even	1	trivial
6027.2.a.bm.1.3	yes	16	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:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q-1.83908 q^{2} -1.00000 q^{3} +1.38223 q^{4} +2.07594 q^{5} +1.83908 q^{6} +1.13613 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.83908 q^{2} -1.00000 q^{3} +1.38223 q^{4} +2.07594 q^{5} +1.83908 q^{6} +1.13613 q^{8} +1.00000 q^{9} -3.81783 q^{10} -6.44723 q^{11} -1.38223 q^{12} +0.865716 q^{13} -2.07594 q^{15} -4.85390 q^{16} -2.06756 q^{17} -1.83908 q^{18} -3.75357 q^{19} +2.86943 q^{20} +11.8570 q^{22} +5.10432 q^{23} -1.13613 q^{24} -0.690475 q^{25} -1.59212 q^{26} -1.00000 q^{27} +1.38301 q^{29} +3.81783 q^{30} +3.75086 q^{31} +6.65447 q^{32} +6.44723 q^{33} +3.80241 q^{34} +1.38223 q^{36} -0.654747 q^{37} +6.90313 q^{38} -0.865716 q^{39} +2.35854 q^{40} -1.00000 q^{41} +11.2846 q^{43} -8.91156 q^{44} +2.07594 q^{45} -9.38727 q^{46} +13.3268 q^{47} +4.85390 q^{48} +1.26984 q^{50} +2.06756 q^{51} +1.19662 q^{52} -0.611905 q^{53} +1.83908 q^{54} -13.3841 q^{55} +3.75357 q^{57} -2.54346 q^{58} -3.36226 q^{59} -2.86943 q^{60} -12.3530 q^{61} -6.89814 q^{62} -2.53033 q^{64} +1.79717 q^{65} -11.8570 q^{66} +12.3187 q^{67} -2.85784 q^{68} -5.10432 q^{69} -3.50868 q^{71} +1.13613 q^{72} +0.660309 q^{73} +1.20413 q^{74} +0.690475 q^{75} -5.18830 q^{76} +1.59212 q^{78} -3.56152 q^{79} -10.0764 q^{80} +1.00000 q^{81} +1.83908 q^{82} -7.34512 q^{83} -4.29213 q^{85} -20.7534 q^{86} -1.38301 q^{87} -7.32489 q^{88} +11.2002 q^{89} -3.81783 q^{90} +7.05534 q^{92} -3.75086 q^{93} -24.5091 q^{94} -7.79218 q^{95} -6.65447 q^{96} -16.7499 q^{97} -6.44723 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 16 q^{3} + 12 q^{4} + 12 q^{5} + 4 q^{6} - 12 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 16 * q^3 + 12 * q^4 + 12 * q^5 + 4 * q^6 - 12 * q^8 + 16 * q^9	\( 16 q - 4 q^{2} - 16 q^{3} + 12 q^{4} + 12 q^{5} + 4 q^{6} - 12 q^{8} + 16 q^{9} + 4 q^{10} - 4 q^{11} - 12 q^{12} - 12 q^{15} + 8 q^{17} - 4 q^{18} - 4 q^{19} + 20 q^{20} - 16 q^{22} - 12 q^{23} + 12 q^{24} - 8 q^{25} + 8 q^{26} - 16 q^{27} - 16 q^{29} - 4 q^{30} + 4 q^{31} - 48 q^{32} + 4 q^{33} - 16 q^{34} + 12 q^{36} - 48 q^{37} + 4 q^{38} - 56 q^{40} - 16 q^{41} - 16 q^{43} + 12 q^{45} - 4 q^{46} + 36 q^{47} - 8 q^{50} - 8 q^{51} - 60 q^{53} + 4 q^{54} - 8 q^{55} + 4 q^{57} - 36 q^{58} + 36 q^{59} - 20 q^{60} + 4 q^{61} + 12 q^{62} + 52 q^{64} - 36 q^{65} + 16 q^{66} - 52 q^{67} + 8 q^{68} + 12 q^{69} - 12 q^{71} - 12 q^{72} + 16 q^{73} + 4 q^{74} + 8 q^{75} - 16 q^{76} - 8 q^{78} - 36 q^{79} + 68 q^{80} + 16 q^{81} + 4 q^{82} + 32 q^{83} - 28 q^{85} - 8 q^{86} + 16 q^{87} - 36 q^{88} + 12 q^{89} + 4 q^{90} - 36 q^{92} - 4 q^{93} - 24 q^{94} - 20 q^{95} + 48 q^{96} - 48 q^{97} - 4 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 16 * q^3 + 12 * q^4 + 12 * q^5 + 4 * q^6 - 12 * q^8 + 16 * q^9 + 4 * q^10 - 4 * q^11 - 12 * q^12 - 12 * q^15 + 8 * q^17 - 4 * q^18 - 4 * q^19 + 20 * q^20 - 16 * q^22 - 12 * q^23 + 12 * q^24 - 8 * q^25 + 8 * q^26 - 16 * q^27 - 16 * q^29 - 4 * q^30 + 4 * q^31 - 48 * q^32 + 4 * q^33 - 16 * q^34 + 12 * q^36 - 48 * q^37 + 4 * q^38 - 56 * q^40 - 16 * q^41 - 16 * q^43 + 12 * q^45 - 4 * q^46 + 36 * q^47 - 8 * q^50 - 8 * q^51 - 60 * q^53 + 4 * q^54 - 8 * q^55 + 4 * q^57 - 36 * q^58 + 36 * q^59 - 20 * q^60 + 4 * q^61 + 12 * q^62 + 52 * q^64 - 36 * q^65 + 16 * q^66 - 52 * q^67 + 8 * q^68 + 12 * q^69 - 12 * q^71 - 12 * q^72 + 16 * q^73 + 4 * q^74 + 8 * q^75 - 16 * q^76 - 8 * q^78 - 36 * q^79 + 68 * q^80 + 16 * q^81 + 4 * q^82 + 32 * q^83 - 28 * q^85 - 8 * q^86 + 16 * q^87 - 36 * q^88 + 12 * q^89 + 4 * q^90 - 36 * q^92 - 4 * q^93 - 24 * q^94 - 20 * q^95 + 48 * q^96 - 48 * q^97 - 4 * q^99

Introduction

L-functions

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Database

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