LMFDB - Embedded newform 2541.2.a.bg.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2541,2,Mod(1,2541)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2541, 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("2541.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2541 = 3 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2541.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:	$20.2899871536$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.229.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 4x - 1 $ x^3 - 4*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 231)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.254102$ of defining polynomial
Character	$\chi$	$=$	2541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.93543 q^{2} +1.00000 q^{3} +1.74590 q^{4} +4.18953 q^{5} +1.93543 q^{6} +1.00000 q^{7} -0.491797 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.93543 q^{2} +1.00000 q^{3} +1.74590 q^{4} +4.18953 q^{5} +1.93543 q^{6} +1.00000 q^{7} -0.491797 q^{8} +1.00000 q^{9} +8.10856 q^{10} +1.74590 q^{12} +3.17313 q^{13} +1.93543 q^{14} +4.18953 q^{15} -4.44364 q^{16} -6.85446 q^{17} +1.93543 q^{18} +0.318669 q^{19} +7.31450 q^{20} +1.00000 q^{21} -1.87086 q^{23} -0.491797 q^{24} +12.5522 q^{25} +6.14137 q^{26} +1.00000 q^{27} +1.74590 q^{28} +3.17313 q^{29} +8.10856 q^{30} +9.23353 q^{31} -7.61676 q^{32} -13.2663 q^{34} +4.18953 q^{35} +1.74590 q^{36} -7.55220 q^{37} +0.616763 q^{38} +3.17313 q^{39} -2.06040 q^{40} -9.36266 q^{41} +1.93543 q^{42} +10.8873 q^{43} +4.18953 q^{45} -3.62093 q^{46} -8.06040 q^{47} -4.44364 q^{48} +1.00000 q^{49} +24.2939 q^{50} -6.85446 q^{51} +5.53996 q^{52} +0.508203 q^{53} +1.93543 q^{54} -0.491797 q^{56} +0.318669 q^{57} +6.14137 q^{58} -7.04399 q^{59} +7.31450 q^{60} +2.00000 q^{61} +17.8709 q^{62} +1.00000 q^{63} -5.85446 q^{64} +13.2939 q^{65} -2.66492 q^{67} -11.9672 q^{68} -1.87086 q^{69} +8.10856 q^{70} -5.01641 q^{71} -0.491797 q^{72} +4.82687 q^{73} -14.6168 q^{74} +12.5522 q^{75} +0.556364 q^{76} +6.14137 q^{78} -5.01641 q^{79} -18.6168 q^{80} +1.00000 q^{81} -18.1208 q^{82} -3.52461 q^{83} +1.74590 q^{84} -28.7170 q^{85} +21.0716 q^{86} +3.17313 q^{87} -1.74173 q^{89} +8.10856 q^{90} +3.17313 q^{91} -3.26634 q^{92} +9.23353 q^{93} -15.6004 q^{94} +1.33508 q^{95} -7.61676 q^{96} -12.2499 q^{97} +1.93543 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 2 q^{2} + 3 q^{3} + 6 q^{4} + 4 q^{5} - 2 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 2 * q^2 + 3 * q^3 + 6 * q^4 + 4 * q^5 - 2 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	$ 3 q - 2 q^{2} + 3 q^{3} + 6 q^{4} + 4 q^{5} - 2 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} + 11 q^{10} + 6 q^{12} + 4 q^{13} - 2 q^{14} + 4 q^{15} - 4 q^{16} - 8 q^{17} - 2 q^{18} + 8 q^{19} - 3 q^{20} + 3 q^{21} + 10 q^{23} - 3 q^{24} + 15 q^{25} - q^{26} + 3 q^{27} + 6 q^{28} + 4 q^{29} + 11 q^{30} - 2 q^{31} - 8 q^{32} - 4 q^{34} + 4 q^{35} + 6 q^{36} - 13 q^{38} + 4 q^{39} + 18 q^{40} - 14 q^{41} - 2 q^{42} + 14 q^{43} + 4 q^{45} - 28 q^{46} - 4 q^{48} + 3 q^{49} + 19 q^{50} - 8 q^{51} + 29 q^{52} - 2 q^{54} - 3 q^{56} + 8 q^{57} - q^{58} - 3 q^{60} + 6 q^{61} + 38 q^{62} + 3 q^{63} - 5 q^{64} - 14 q^{65} - 4 q^{67} - 42 q^{68} + 10 q^{69} + 11 q^{70} - 12 q^{71} - 3 q^{72} + 20 q^{73} - 29 q^{74} + 15 q^{75} + 11 q^{76} - q^{78} - 12 q^{79} - 41 q^{80} + 3 q^{81} - 6 q^{82} - 6 q^{83} + 6 q^{84} + 6 q^{85} + 24 q^{86} + 4 q^{87} + 26 q^{89} + 11 q^{90} + 4 q^{91} + 26 q^{92} - 2 q^{93} - 35 q^{94} + 8 q^{95} - 8 q^{96} - 4 q^{97} - 2 q^{98}+O(q^{100}) $ 3 * q - 2 * q^2 + 3 * q^3 + 6 * q^4 + 4 * q^5 - 2 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 + 11 * q^10 + 6 * q^12 + 4 * q^13 - 2 * q^14 + 4 * q^15 - 4 * q^16 - 8 * q^17 - 2 * q^18 + 8 * q^19 - 3 * q^20 + 3 * q^21 + 10 * q^23 - 3 * q^24 + 15 * q^25 - q^26 + 3 * q^27 + 6 * q^28 + 4 * q^29 + 11 * q^30 - 2 * q^31 - 8 * q^32 - 4 * q^34 + 4 * q^35 + 6 * q^36 - 13 * q^38 + 4 * q^39 + 18 * q^40 - 14 * q^41 - 2 * q^42 + 14 * q^43 + 4 * q^45 - 28 * q^46 - 4 * q^48 + 3 * q^49 + 19 * q^50 - 8 * q^51 + 29 * q^52 - 2 * q^54 - 3 * q^56 + 8 * q^57 - q^58 - 3 * q^60 + 6 * q^61 + 38 * q^62 + 3 * q^63 - 5 * q^64 - 14 * q^65 - 4 * q^67 - 42 * q^68 + 10 * q^69 + 11 * q^70 - 12 * q^71 - 3 * q^72 + 20 * q^73 - 29 * q^74 + 15 * q^75 + 11 * q^76 - q^78 - 12 * q^79 - 41 * q^80 + 3 * q^81 - 6 * q^82 - 6 * q^83 + 6 * q^84 + 6 * q^85 + 24 * q^86 + 4 * q^87 + 26 * q^89 + 11 * q^90 + 4 * q^91 + 26 * q^92 - 2 * q^93 - 35 * q^94 + 8 * q^95 - 8 * q^96 - 4 * q^97 - 2 * q^98

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 $

$2$	1.93543	1.36856	0.684279	−	0.729221i	$-0.260117\pi$
$2$	1.93543	1.36856	0.684279	+	0.729221i	$0.260117\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.74590	0.872949
$5$	4.18953	1.87362	0.936808	−	0.349843i	$-0.113765\pi$
$5$	4.18953	1.87362	0.936808	+	0.349843i	$0.113765\pi$
$6$	1.93543	0.790137
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−0.491797	−0.173876
$9$	1.00000	0.333333
$10$	8.10856	2.56415
$11$	0	0
$11$	0	0
$12$	1.74590	0.503997
$13$	3.17313	0.880067	0.440034	−	0.897981i	$-0.354967\pi$
$13$	3.17313	0.880067	0.440034	+	0.897981i	$0.354967\pi$
$14$	1.93543	0.517266
$15$	4.18953	1.08173
$16$	−4.44364	−1.11091
$17$	−6.85446	−1.66245	−0.831225	−	0.555936i	$-0.812360\pi$
$17$	−6.85446	−1.66245	−0.831225	+	0.555936i	$0.812360\pi$
$18$	1.93543	0.456186
$19$	0.318669	0.0731078	0.0365539	−	0.999332i	$-0.488362\pi$
$19$	0.318669	0.0731078	0.0365539	+	0.999332i	$0.488362\pi$
$20$	7.31450	1.63557
$21$	1.00000	0.218218
$22$	0	0
$23$	−1.87086	−0.390102	−0.195051	−	0.980793i	$-0.562487\pi$
$23$	−1.87086	−0.390102	−0.195051	+	0.980793i	$0.562487\pi$
$24$	−0.491797	−0.100388
$25$	12.5522	2.51044
$26$	6.14137	1.20442
$27$	1.00000	0.192450
$28$	1.74590	0.329944
$29$	3.17313	0.589235	0.294617	−	0.955615i	$-0.404808\pi$
$29$	3.17313	0.589235	0.294617	+	0.955615i	$0.404808\pi$
$30$	8.10856	1.48041
$31$	9.23353	1.65839	0.829195	−	0.558959i	$-0.188799\pi$
$31$	9.23353	1.65839	0.829195	+	0.558959i	$0.188799\pi$
$32$	−7.61676	−1.34647
$33$	0	0
$34$	−13.2663	−2.27516
$35$	4.18953	0.708161
$36$	1.74590	0.290983
$37$	−7.55220	−1.24157	−0.620787	−	0.783980i	$-0.713187\pi$
$37$	−7.55220	−1.24157	−0.620787	+	0.783980i	$0.713187\pi$
$38$	0.616763	0.100052
$39$	3.17313	0.508107
$40$	−2.06040	−0.325778
$41$	−9.36266	−1.46220	−0.731101	−	0.682269i	$-0.760993\pi$
$41$	−9.36266	−1.46220	−0.731101	+	0.682269i	$0.760993\pi$
$42$	1.93543	0.298644
$43$	10.8873	1.66029	0.830147	−	0.557545i	$-0.188257\pi$
$43$	10.8873	1.66029	0.830147	+	0.557545i	$0.188257\pi$
$44$	0	0
$45$	4.18953	0.624539
$46$	−3.62093	−0.533877
$47$	−8.06040	−1.17573	−0.587865	−	0.808959i	$-0.700031\pi$
$47$	−8.06040	−1.17573	−0.587865	+	0.808959i	$0.700031\pi$
$48$	−4.44364	−0.641384
$49$	1.00000	0.142857
$50$	24.2939	3.43568
$51$	−6.85446	−0.959816
$52$	5.53996	0.768254
$53$	0.508203	0.0698071	0.0349036	−	0.999391i	$-0.488888\pi$
$53$	0.508203	0.0698071	0.0349036	+	0.999391i	$0.488888\pi$
$54$	1.93543	0.263379
$55$	0	0
$56$	−0.491797	−0.0657191
$57$	0.318669	0.0422088
$58$	6.14137	0.806402
$59$	−7.04399	−0.917050	−0.458525	−	0.888682i	$-0.651622\pi$
$59$	−7.04399	−0.917050	−0.458525	+	0.888682i	$0.651622\pi$
$60$	7.31450	0.944298
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	17.8709	2.26960
$63$	1.00000	0.125988
$64$	−5.85446	−0.731807
$65$	13.2939	1.64891
$66$	0	0
$67$	−2.66492	−0.325572	−0.162786	−	0.986661i	$-0.552048\pi$
$67$	−2.66492	−0.325572	−0.162786	+	0.986661i	$0.552048\pi$
$68$	−11.9672	−1.45123
$69$	−1.87086	−0.225226
$70$	8.10856	0.969158
$71$	−5.01641	−0.595338	−0.297669	−	0.954669i	$-0.596209\pi$
$71$	−5.01641	−0.595338	−0.297669	+	0.954669i	$0.596209\pi$
$72$	−0.491797	−0.0579588
$73$	4.82687	0.564943	0.282471	−	0.959276i	$-0.408846\pi$
$73$	4.82687	0.564943	0.282471	+	0.959276i	$0.408846\pi$
$74$	−14.6168	−1.69916
$75$	12.5522	1.44940
$76$	0.556364	0.0638194
$77$	0	0
$78$	6.14137	0.695374
$79$	−5.01641	−0.564390	−0.282195	−	0.959357i	$-0.591062\pi$
$79$	−5.01641	−0.564390	−0.282195	+	0.959357i	$0.591062\pi$
$80$	−18.6168	−2.08142
$81$	1.00000	0.111111
$82$	−18.1208	−2.00111
$83$	−3.52461	−0.386876	−0.193438	−	0.981112i	$-0.561964\pi$
$83$	−3.52461	−0.386876	−0.193438	+	0.981112i	$0.561964\pi$
$84$	1.74590	0.190493
$85$	−28.7170	−3.11479
$86$	21.0716	2.27221
$87$	3.17313	0.340195
$88$	0	0
$89$	−1.74173	−0.184623	−0.0923115	−	0.995730i	$-0.529426\pi$
$89$	−1.74173	−0.184623	−0.0923115	+	0.995730i	$0.529426\pi$
$90$	8.10856	0.854717
$91$	3.17313	0.332634
$92$	−3.26634	−0.340539
$93$	9.23353	0.957472
$94$	−15.6004	−1.60905
$95$	1.33508	0.136976
$96$	−7.61676	−0.777383
$97$	−12.2499	−1.24379	−0.621896	−	0.783100i	$-0.713637\pi$
$97$	−12.2499	−1.24379	−0.621896	+	0.783100i	$0.713637\pi$
$98$	1.93543	0.195508
$99$	0	0
$100$	21.9149	2.19149
$101$	−4.88727	−0.486302	−0.243151	−	0.969988i	$-0.578181\pi$
$101$	−4.88727	−0.486302	−0.243151	+	0.969988i	$0.578181\pi$
$102$	−13.2663	−1.31356
$103$	−0.637339	−0.0627988	−0.0313994	−	0.999507i	$-0.509996\pi$
$103$	−0.637339	−0.0627988	−0.0313994	+	0.999507i	$0.509996\pi$
$104$	−1.56053	−0.153023
$105$	4.18953	0.408857
$106$	0.983593	0.0955350
$107$	−0.956008	−0.0924208	−0.0462104	−	0.998932i	$-0.514714\pi$
$107$	−0.956008	−0.0924208	−0.0462104	+	0.998932i	$0.514714\pi$
$108$	1.74590	0.167999
$109$	7.61259	0.729154	0.364577	−	0.931173i	$-0.381214\pi$
$109$	7.61259	0.729154	0.364577	+	0.931173i	$0.381214\pi$
$110$	0	0
$111$	−7.55220	−0.716823
$112$	−4.44364	−0.419884
$113$	−7.70892	−0.725194	−0.362597	−	0.931946i	$-0.618110\pi$
$113$	−7.70892	−0.725194	−0.362597	+	0.931946i	$0.618110\pi$
$114$	0.616763	0.0577651
$115$	−7.83805	−0.730902
$116$	5.53996	0.514372
$117$	3.17313	0.293356
$118$	−13.6332	−1.25504
$119$	−6.85446	−0.628347
$120$	−2.06040	−0.188088
$121$	0	0
$122$	3.87086	0.350452
$123$	−9.36266	−0.844203
$124$	16.1208	1.44769
$125$	31.6402	2.82998
$126$	1.93543	0.172422
$127$	5.49180	0.487318	0.243659	−	0.969861i	$-0.421652\pi$
$127$	5.49180	0.487318	0.243659	+	0.969861i	$0.421652\pi$
$128$	3.90262	0.344946
$129$	10.8873	0.958571
$130$	25.7295	2.25663
$131$	−4.00000	−0.349482	−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000	−0.349482	−0.174741	+	0.984614i	$0.555909\pi$
$132$	0	0
$133$	0.318669	0.0276321
$134$	−5.15778	−0.445564
$135$	4.18953	0.360578
$136$	3.37100	0.289061
$137$	15.6126	1.33387	0.666937	−	0.745114i	$-0.267605\pi$
$137$	15.6126	1.33387	0.666937	+	0.745114i	$0.267605\pi$
$138$	−3.62093	−0.308234
$139$	9.01641	0.764762	0.382381	−	0.924005i	$-0.375104\pi$
$139$	9.01641	0.764762	0.382381	+	0.924005i	$0.375104\pi$
$140$	7.31450	0.618188
$141$	−8.06040	−0.678808
$142$	−9.70892	−0.814754
$143$	0	0
$144$	−4.44364	−0.370303
$145$	13.2939	1.10400
$146$	9.34209	0.773157
$147$	1.00000	0.0824786
$148$	−13.1854	−1.08383
$149$	5.20594	0.426487	0.213244	−	0.976999i	$-0.431597\pi$
$149$	5.20594	0.426487	0.213244	+	0.976999i	$0.431597\pi$
$150$	24.2939	1.98359
$151$	−6.24993	−0.508612	−0.254306	−	0.967124i	$-0.581847\pi$
$151$	−6.24993	−0.508612	−0.254306	+	0.967124i	$0.581847\pi$
$152$	−0.156721	−0.0127117
$153$	−6.85446	−0.554150
$154$	0	0
$155$	38.6842	3.10719
$156$	5.53996	0.443552
$157$	−18.1208	−1.44620	−0.723099	−	0.690745i	$-0.757283\pi$
$157$	−18.1208	−1.44620	−0.723099	+	0.690745i	$0.757283\pi$
$158$	−9.70892	−0.772400
$159$	0.508203	0.0403031
$160$	−31.9107	−2.52276
$161$	−1.87086	−0.147445
$162$	1.93543	0.152062
$163$	−2.66492	−0.208733	−0.104366	−	0.994539i	$-0.533281\pi$
$163$	−2.66492	−0.208733	−0.104366	+	0.994539i	$0.533281\pi$
$164$	−16.3463	−1.27643
$165$	0	0
$166$	−6.82164	−0.529462
$167$	11.1455	0.862468	0.431234	−	0.902240i	$-0.358078\pi$
$167$	11.1455	0.862468	0.431234	+	0.902240i	$0.358078\pi$
$168$	−0.491797	−0.0379429
$169$	−2.93126	−0.225482
$170$	−55.5798	−4.26277
$171$	0.318669	0.0243693
$172$	19.0081	1.44935
$173$	24.8461	1.88902	0.944508	−	0.328489i	$-0.106539\pi$
$173$	24.8461	1.88902	0.944508	+	0.328489i	$0.106539\pi$
$174$	6.14137	0.465576
$175$	12.5522	0.948857
$176$	0	0
$177$	−7.04399	−0.529459
$178$	−3.37100	−0.252667
$179$	−12.7581	−0.953588	−0.476794	−	0.879015i	$-0.658201\pi$
$179$	−12.7581	−0.953588	−0.476794	+	0.879015i	$0.658201\pi$
$180$	7.31450	0.545191
$181$	−3.23353	−0.240346	−0.120173	−	0.992753i	$-0.538345\pi$
$181$	−3.23353	−0.240346	−0.120173	+	0.992753i	$0.538345\pi$
$182$	6.14137	0.455229
$183$	2.00000	0.147844
$184$	0.920085	0.0678296
$185$	−31.6402	−2.32623
$186$	17.8709	1.31036
$187$	0	0
$188$	−14.0726	−1.02635
$189$	1.00000	0.0727393
$190$	2.58395	0.187459
$191$	20.9753	1.51772	0.758858	−	0.651256i	$-0.225758\pi$
$191$	20.9753	1.51772	0.758858	+	0.651256i	$0.225758\pi$
$192$	−5.85446	−0.422509
$193$	−0.249933	−0.0179905	−0.00899527	−	0.999960i	$-0.502863\pi$
$193$	−0.249933	−0.0179905	−0.00899527	+	0.999960i	$0.502863\pi$
$194$	−23.7089	−1.70220
$195$	13.2939	0.951998
$196$	1.74590	0.124707
$197$	−18.4999	−1.31806	−0.659030	−	0.752116i	$-0.729033\pi$
$197$	−18.4999	−1.31806	−0.659030	+	0.752116i	$0.729033\pi$
$198$	0	0
$199$	9.87086	0.699727	0.349864	−	0.936801i	$-0.386228\pi$
$199$	9.87086	0.699727	0.349864	+	0.936801i	$0.386228\pi$
$200$	−6.17313	−0.436506
$201$	−2.66492	−0.187969
$202$	−9.45898	−0.665532
$203$	3.17313	0.222710
$204$	−11.9672	−0.837871
$205$	−39.2252	−2.73961
$206$	−1.23353	−0.0859438
$207$	−1.87086	−0.130034
$208$	−14.1002	−0.977674
$209$	0	0
$210$	8.10856	0.559544
$211$	4.63734	0.319248	0.159624	−	0.987178i	$-0.448972\pi$
$211$	4.63734	0.319248	0.159624	+	0.987178i	$0.448972\pi$
$212$	0.887271	0.0609381
$213$	−5.01641	−0.343719
$214$	−1.85029	−0.126483
$215$	45.6126	3.11075
$216$	−0.491797	−0.0334625
$217$	9.23353	0.626813
$218$	14.7337	0.997889
$219$	4.82687	0.326170
$220$	0	0
$221$	−21.7501	−1.46307
$222$	−14.6168	−0.981013
$223$	−18.3463	−1.22856	−0.614278	−	0.789090i	$-0.710553\pi$
$223$	−18.3463	−1.22856	−0.614278	+	0.789090i	$0.710553\pi$
$224$	−7.61676	−0.508916
$225$	12.5522	0.836813
$226$	−14.9201	−0.992469
$227$	−0.379068	−0.0251596	−0.0125798	−	0.999921i	$-0.504004\pi$
$227$	−0.379068	−0.0251596	−0.0125798	+	0.999921i	$0.504004\pi$
$228$	0.556364	0.0368461
$229$	24.9424	1.64824	0.824121	−	0.566413i	$-0.191669\pi$
$229$	24.9424	1.64824	0.824121	+	0.566413i	$0.191669\pi$
$230$	−15.1700	−1.00028
$231$	0	0
$232$	−1.56053	−0.102454
$233$	−23.4506	−1.53630	−0.768151	−	0.640268i	$-0.778823\pi$
$233$	−23.4506	−1.53630	−0.768151	+	0.640268i	$0.778823\pi$
$234$	6.14137	0.401474
$235$	−33.7693	−2.20287
$236$	−12.2981	−0.800538
$237$	−5.01641	−0.325851
$238$	−13.2663	−0.859929
$239$	−5.07681	−0.328391	−0.164196	−	0.986428i	$-0.552503\pi$
$239$	−5.07681	−0.328391	−0.164196	+	0.986428i	$0.552503\pi$
$240$	−18.6168	−1.20171
$241$	−19.2939	−1.24283	−0.621415	−	0.783481i	$-0.713442\pi$
$241$	−19.2939	−1.24283	−0.621415	+	0.783481i	$0.713442\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	3.49180	0.223539
$245$	4.18953	0.267660
$246$	−18.1208	−1.15534
$247$	1.01118	0.0643397
$248$	−4.54102	−0.288355
$249$	−3.52461	−0.223363
$250$	61.2374	3.87299
$251$	23.8021	1.50238	0.751188	−	0.660088i	$-0.229481\pi$
$251$	23.8021	1.50238	0.751188	+	0.660088i	$0.229481\pi$
$252$	1.74590	0.109981
$253$	0	0
$254$	10.6290	0.666923
$255$	−28.7170	−1.79833
$256$	19.2622	1.20389
$257$	14.9149	0.930363	0.465182	−	0.885215i	$-0.345989\pi$
$257$	14.9149	0.930363	0.465182	+	0.885215i	$0.345989\pi$
$258$	21.0716	1.31186
$259$	−7.55220	−0.469271
$260$	23.2098	1.43941
$261$	3.17313	0.196412
$262$	−7.74173	−0.478286
$263$	−2.92319	−0.180252	−0.0901259	−	0.995930i	$-0.528727\pi$
$263$	−2.92319	−0.180252	−0.0901259	+	0.995930i	$0.528727\pi$
$264$	0	0
$265$	2.12914	0.130792
$266$	0.616763	0.0378162
$267$	−1.74173	−0.106592
$268$	−4.65269	−0.284208
$269$	11.9672	0.729652	0.364826	−	0.931076i	$-0.381128\pi$
$269$	11.9672	0.729652	0.364826	+	0.931076i	$0.381128\pi$
$270$	8.10856	0.493471
$271$	20.3187	1.23427	0.617136	−	0.786857i	$-0.288293\pi$
$271$	20.3187	1.23427	0.617136	+	0.786857i	$0.288293\pi$
$272$	30.4587	1.84683
$273$	3.17313	0.192046
$274$	30.2171	1.82548
$275$	0	0
$276$	−3.26634	−0.196611
$277$	−18.0552	−1.08483	−0.542415	−	0.840111i	$-0.682490\pi$
$277$	−18.0552	−1.08483	−0.542415	+	0.840111i	$0.682490\pi$
$278$	17.4506	1.04662
$279$	9.23353	0.552797
$280$	−2.06040	−0.123132
$281$	−27.2939	−1.62822	−0.814110	−	0.580711i	$-0.802774\pi$
$281$	−27.2939	−1.62822	−0.814110	+	0.580711i	$0.802774\pi$
$282$	−15.6004	−0.928988
$283$	−29.8901	−1.77678	−0.888391	−	0.459087i	$-0.848177\pi$
$283$	−29.8901	−1.77678	−0.888391	+	0.459087i	$0.848177\pi$
$284$	−8.75814	−0.519700
$285$	1.33508	0.0790831
$286$	0	0
$287$	−9.36266	−0.552660
$288$	−7.61676	−0.448822
$289$	29.9836	1.76374
$290$	25.7295	1.51089
$291$	−12.2499	−0.718104
$292$	8.42723	0.493166
$293$	4.34625	0.253911	0.126955	−	0.991908i	$-0.459479\pi$
$293$	4.34625	0.253911	0.126955	+	0.991908i	$0.459479\pi$
$294$	1.93543	0.112877
$295$	−29.5110	−1.71820
$296$	3.71414	0.215880
$297$	0	0
$298$	10.0757	0.583672
$299$	−5.93649	−0.343316
$300$	21.9149	1.26525
$301$	10.8873	0.627532
$302$	−12.0963	−0.696065
$303$	−4.88727	−0.280766
$304$	−1.41605	−0.0812161
$305$	8.37907	0.479784
$306$	−13.2663	−0.758386
$307$	20.7581	1.18473	0.592365	−	0.805670i	$-0.298194\pi$
$307$	20.7581	1.18473	0.592365	+	0.805670i	$0.298194\pi$
$308$	0	0
$309$	−0.637339	−0.0362569
$310$	74.8706	4.25236
$311$	8.00000	0.453638	0.226819	−	0.973937i	$-0.427167\pi$
$311$	8.00000	0.453638	0.226819	+	0.973937i	$0.427167\pi$
$312$	−1.56053	−0.0883478
$313$	8.12914	0.459486	0.229743	−	0.973251i	$-0.426211\pi$
$313$	8.12914	0.459486	0.229743	+	0.973251i	$0.426211\pi$
$314$	−35.0716	−1.97920
$315$	4.18953	0.236054
$316$	−8.75814	−0.492684
$317$	−19.9917	−1.12284	−0.561422	−	0.827530i	$-0.689745\pi$
$317$	−19.9917	−1.12284	−0.561422	+	0.827530i	$0.689745\pi$
$318$	0.983593	0.0551572
$319$	0	0
$320$	−24.5275	−1.37113
$321$	−0.956008	−0.0533592
$322$	−3.62093	−0.201787
$323$	−2.18431	−0.121538
$324$	1.74590	0.0969944
$325$	39.8297	2.20935
$326$	−5.15778	−0.285663
$327$	7.61259	0.420977
$328$	4.60453	0.254242
$329$	−8.06040	−0.444384
$330$	0	0
$331$	17.0164	0.935306	0.467653	−	0.883912i	$-0.345100\pi$
$331$	17.0164	0.935306	0.467653	+	0.883912i	$0.345100\pi$
$332$	−6.15361	−0.337723
$333$	−7.55220	−0.413858
$334$	21.5714	1.18034
$335$	−11.1648	−0.609998
$336$	−4.44364	−0.242420
$337$	−1.52461	−0.0830508	−0.0415254	−	0.999137i	$-0.513222\pi$
$337$	−1.52461	−0.0830508	−0.0415254	+	0.999137i	$0.513222\pi$
$338$	−5.67326	−0.308585
$339$	−7.70892	−0.418691
$340$	−50.1369	−2.71906
$341$	0	0
$342$	0.616763	0.0333507
$343$	1.00000	0.0539949
$344$	−5.35432	−0.288686
$345$	−7.83805	−0.421986
$346$	48.0880	2.58523
$347$	−17.4506	−0.936800	−0.468400	−	0.883517i	$-0.655169\pi$
$347$	−17.4506	−0.936800	−0.468400	+	0.883517i	$0.655169\pi$
$348$	5.53996	0.296973
$349$	−6.85969	−0.367191	−0.183595	−	0.983002i	$-0.558774\pi$
$349$	−6.85969	−0.367191	−0.183595	+	0.983002i	$0.558774\pi$
$350$	24.2939	1.29856
$351$	3.17313	0.169369
$352$	0	0
$353$	−31.9313	−1.69953	−0.849765	−	0.527162i	$-0.823256\pi$
$353$	−31.9313	−1.69953	−0.849765	+	0.527162i	$0.823256\pi$
$354$	−13.6332	−0.724595
$355$	−21.0164	−1.11544
$356$	−3.04088	−0.161166
$357$	−6.85446	−0.362776
$358$	−24.6925	−1.30504
$359$	24.4342	1.28959	0.644795	−	0.764356i	$-0.276943\pi$
$359$	24.4342	1.28959	0.644795	+	0.764356i	$0.276943\pi$
$360$	−2.06040	−0.108593
$361$	−18.8984	−0.994655
$362$	−6.25827	−0.328927
$363$	0	0
$364$	5.53996	0.290373
$365$	20.2223	1.05849
$366$	3.87086	0.202333
$367$	17.0716	0.891129	0.445565	−	0.895250i	$-0.353003\pi$
$367$	17.0716	0.891129	0.445565	+	0.895250i	$0.353003\pi$
$368$	8.31344	0.433368
$369$	−9.36266	−0.487401
$370$	−61.2374	−3.18358
$371$	0.508203	0.0263846
$372$	16.1208	0.835824
$373$	−3.17836	−0.164569	−0.0822845	−	0.996609i	$-0.526222\pi$
$373$	−3.17836	−0.164569	−0.0822845	+	0.996609i	$0.526222\pi$
$374$	0	0
$375$	31.6402	1.63389
$376$	3.96408	0.204432
$377$	10.0687	0.518566
$378$	1.93543	0.0995479
$379$	3.93960	0.202364	0.101182	−	0.994868i	$-0.467738\pi$
$379$	3.93960	0.202364	0.101182	+	0.994868i	$0.467738\pi$
$380$	2.33091	0.119573
$381$	5.49180	0.281353
$382$	40.5962	2.07708
$383$	−24.7581	−1.26508	−0.632541	−	0.774527i	$-0.717988\pi$
$383$	−24.7581	−1.26508	−0.632541	+	0.774527i	$0.717988\pi$
$384$	3.90262	0.199155
$385$	0	0
$386$	−0.483728	−0.0246211
$387$	10.8873	0.553431
$388$	−21.3871	−1.08577
$389$	3.65375	0.185252	0.0926261	−	0.995701i	$-0.470474\pi$
$389$	3.65375	0.185252	0.0926261	+	0.995701i	$0.470474\pi$
$390$	25.7295	1.30286
$391$	12.8238	0.648526
$392$	−0.491797	−0.0248395
$393$	−4.00000	−0.201773
$394$	−35.8052	−1.80384
$395$	−21.0164	−1.05745
$396$	0	0
$397$	4.56337	0.229029	0.114515	−	0.993422i	$-0.463469\pi$
$397$	4.56337	0.229029	0.114515	+	0.993422i	$0.463469\pi$
$398$	19.1044	0.957617
$399$	0.318669	0.0159534
$400$	−55.7774	−2.78887
$401$	−7.23353	−0.361225	−0.180613	−	0.983554i	$-0.557808\pi$
$401$	−7.23353	−0.361225	−0.180613	+	0.983554i	$0.557808\pi$
$402$	−5.15778	−0.257247
$403$	29.2992	1.45949
$404$	−8.53268	−0.424517
$405$	4.18953	0.208180
$406$	6.14137	0.304791
$407$	0	0
$408$	3.37100	0.166889
$409$	−5.30749	−0.262439	−0.131219	−	0.991353i	$-0.541889\pi$
$409$	−5.30749	−0.262439	−0.131219	+	0.991353i	$0.541889\pi$
$410$	−75.9177	−3.74931
$411$	15.6126	0.770112
$412$	−1.11273	−0.0548202
$413$	−7.04399	−0.346612
$414$	−3.62093	−0.177959
$415$	−14.7665	−0.724858
$416$	−24.1690	−1.18498
$417$	9.01641	0.441535
$418$	0	0
$419$	−11.4231	−0.558053	−0.279026	−	0.960283i	$-0.590012\pi$
$419$	−11.4231	−0.558053	−0.279026	+	0.960283i	$0.590012\pi$
$420$	7.31450	0.356911
$421$	−27.4147	−1.33611	−0.668056	−	0.744111i	$-0.732873\pi$
$421$	−27.4147	−1.33611	−0.668056	+	0.744111i	$0.732873\pi$
$422$	8.97526	0.436909
$423$	−8.06040	−0.391910
$424$	−0.249933	−0.0121378
$425$	−86.0385	−4.17348
$426$	−9.70892	−0.470399
$427$	2.00000	0.0967868
$428$	−1.66909	−0.0806786
$429$	0	0
$430$	88.2801	4.25724
$431$	2.28586	0.110106	0.0550529	−	0.998483i	$-0.482467\pi$
$431$	2.28586	0.110106	0.0550529	+	0.998483i	$0.482467\pi$
$432$	−4.44364	−0.213795
$433$	31.5714	1.51723	0.758613	−	0.651541i	$-0.225877\pi$
$433$	31.5714	1.51723	0.758613	+	0.651541i	$0.225877\pi$
$434$	17.8709	0.857829
$435$	13.2939	0.637395
$436$	13.2908	0.636515
$437$	−0.596187	−0.0285195
$438$	9.34209	0.446382
$439$	18.5275	0.884267	0.442133	−	0.896949i	$-0.354222\pi$
$439$	18.5275	0.884267	0.442133	+	0.896949i	$0.354222\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	−42.0958	−2.00229
$443$	28.4342	1.35095	0.675476	−	0.737382i	$-0.263938\pi$
$443$	28.4342	1.35095	0.675476	+	0.737382i	$0.263938\pi$
$444$	−13.1854	−0.625750
$445$	−7.29703	−0.345913
$446$	−35.5079	−1.68135
$447$	5.20594	0.246233
$448$	−5.85446	−0.276597
$449$	−5.68656	−0.268365	−0.134183	−	0.990957i	$-0.542841\pi$
$449$	−5.68656	−0.268365	−0.134183	+	0.990957i	$0.542841\pi$
$450$	24.2939	1.14523
$451$	0	0
$452$	−13.4590	−0.633057
$453$	−6.24993	−0.293647
$454$	−0.733661	−0.0344324
$455$	13.2939	0.623229
$456$	−0.156721	−0.00733911
$457$	13.0081	0.608492	0.304246	−	0.952594i	$-0.401596\pi$
$457$	13.0081	0.608492	0.304246	+	0.952594i	$0.401596\pi$
$458$	48.2744	2.25571
$459$	−6.85446	−0.319939
$460$	−13.6844	−0.638040
$461$	6.37907	0.297103	0.148551	−	0.988905i	$-0.452539\pi$
$461$	6.37907	0.297103	0.148551	+	0.988905i	$0.452539\pi$
$462$	0	0
$463$	34.0932	1.58445	0.792223	−	0.610232i	$-0.208924\pi$
$463$	34.0932	1.58445	0.792223	+	0.610232i	$0.208924\pi$
$464$	−14.1002	−0.654586
$465$	38.6842	1.79394
$466$	−45.3871	−2.10252
$467$	18.1484	0.839807	0.419903	−	0.907569i	$-0.362064\pi$
$467$	18.1484	0.839807	0.419903	+	0.907569i	$0.362064\pi$
$468$	5.53996	0.256085
$469$	−2.66492	−0.123055
$470$	−65.3582	−3.01475
$471$	−18.1208	−0.834962
$472$	3.46421	0.159453
$473$	0	0
$474$	−9.70892	−0.445945
$475$	4.00000	0.183533
$476$	−11.9672	−0.548515
$477$	0.508203	0.0232690
$478$	−9.82581	−0.449422
$479$	42.7498	1.95329	0.976644	−	0.214864i	$-0.0689307\pi$
$479$	42.7498	1.95329	0.976644	+	0.214864i	$0.0689307\pi$
$480$	−31.9107	−1.45652
$481$	−23.9641	−1.09267
$482$	−37.3421	−1.70089
$483$	−1.87086	−0.0851273
$484$	0	0
$485$	−51.3215	−2.33039
$486$	1.93543	0.0877930
$487$	26.7909	1.21401	0.607007	−	0.794697i	$-0.292370\pi$
$487$	26.7909	1.21401	0.607007	+	0.794697i	$0.292370\pi$
$488$	−0.983593	−0.0445252
$489$	−2.66492	−0.120512
$490$	8.10856	0.366307
$491$	−31.6813	−1.42976	−0.714879	−	0.699248i	$-0.753518\pi$
$491$	−31.6813	−1.42976	−0.714879	+	0.699248i	$0.753518\pi$
$492$	−16.3463	−0.736946
$493$	−21.7501	−0.979574
$494$	1.95707	0.0880526
$495$	0	0
$496$	−41.0304	−1.84232
$497$	−5.01641	−0.225017
$498$	−6.82164	−0.305685
$499$	−24.1260	−1.08003	−0.540015	−	0.841656i	$-0.681581\pi$
$499$	−24.1260	−1.08003	−0.540015	+	0.841656i	$0.681581\pi$
$500$	55.2405	2.47043
$501$	11.1455	0.497946
$502$	46.0674	2.05609
$503$	−30.8873	−1.37720	−0.688598	−	0.725144i	$-0.741773\pi$
$503$	−30.8873	−1.37720	−0.688598	+	0.725144i	$0.741773\pi$
$504$	−0.491797	−0.0219064
$505$	−20.4754	−0.911143
$506$	0	0
$507$	−2.93126	−0.130182
$508$	9.58812	0.425404
$509$	28.2088	1.25033	0.625166	−	0.780492i	$-0.285031\pi$
$509$	28.2088	1.25033	0.625166	+	0.780492i	$0.285031\pi$
$510$	−55.5798	−2.46111
$511$	4.82687	0.213528
$512$	29.4754	1.30264
$513$	0.318669	0.0140696
$514$	28.8667	1.27326
$515$	−2.67015	−0.117661
$516$	19.0081	0.836784
$517$	0	0
$518$	−14.6168	−0.642224
$519$	24.8461	1.09062
$520$	−6.53791	−0.286706
$521$	−33.7610	−1.47910	−0.739548	−	0.673104i	$-0.764961\pi$
$521$	−33.7610	−1.47910	−0.739548	+	0.673104i	$0.764961\pi$
$522$	6.14137	0.268801
$523$	−12.8185	−0.560515	−0.280258	−	0.959925i	$-0.590420\pi$
$523$	−12.8185	−0.560515	−0.280258	+	0.959925i	$0.590420\pi$
$524$	−6.98359	−0.305080
$525$	12.5522	0.547823
$526$	−5.65765	−0.246685
$527$	−63.2908	−2.75699
$528$	0	0
$529$	−19.4999	−0.847820
$530$	4.12080	0.178996
$531$	−7.04399	−0.305683
$532$	0.556364	0.0241215
$533$	−29.7089	−1.28684
$534$	−3.37100	−0.145877
$535$	−4.00523	−0.173161
$536$	1.31060	0.0566093
$537$	−12.7581	−0.550554
$538$	23.1617	0.998571
$539$	0	0
$540$	7.31450	0.314766
$541$	21.8625	0.939943	0.469972	−	0.882681i	$-0.344264\pi$
$541$	21.8625	0.939943	0.469972	+	0.882681i	$0.344264\pi$
$542$	39.3254	1.68917
$543$	−3.23353	−0.138764
$544$	52.2088	2.23843
$545$	31.8932	1.36616
$546$	6.14137	0.262827
$547$	−23.4178	−1.00127	−0.500637	−	0.865657i	$-0.666901\pi$
$547$	−23.4178	−1.00127	−0.500637	+	0.865657i	$0.666901\pi$
$548$	27.2580	1.16440
$549$	2.00000	0.0853579
$550$	0	0
$551$	1.01118	0.0430776
$552$	0.920085	0.0391614
$553$	−5.01641	−0.213319
$554$	−34.9446	−1.48465
$555$	−31.6402	−1.34305
$556$	15.7417	0.667598
$557$	6.91486	0.292992	0.146496	−	0.989211i	$-0.453200\pi$
$557$	6.91486	0.292992	0.146496	+	0.989211i	$0.453200\pi$
$558$	17.8709	0.756534
$559$	34.5467	1.46117
$560$	−18.6168	−0.786702
$561$	0	0
$562$	−52.8255	−2.22831
$563$	−11.8381	−0.498914	−0.249457	−	0.968386i	$-0.580252\pi$
$563$	−11.8381	−0.498914	−0.249457	+	0.968386i	$0.580252\pi$
$564$	−14.0726	−0.592565
$565$	−32.2968	−1.35874
$566$	−57.8503	−2.43163
$567$	1.00000	0.0419961
$568$	2.46705	0.103515
$569$	−10.0000	−0.419222	−0.209611	−	0.977785i	$-0.567220\pi$
$569$	−10.0000	−0.419222	−0.209611	+	0.977785i	$0.567220\pi$
$570$	2.58395	0.108230
$571$	15.2252	0.637154	0.318577	−	0.947897i	$-0.396795\pi$
$571$	15.2252	0.637154	0.318577	+	0.947897i	$0.396795\pi$
$572$	0	0
$573$	20.9753	0.876254
$574$	−18.1208	−0.756347
$575$	−23.4835	−0.979328
$576$	−5.85446	−0.243936
$577$	17.3215	0.721104	0.360552	−	0.932739i	$-0.382588\pi$
$577$	17.3215	0.721104	0.360552	+	0.932739i	$0.382588\pi$
$578$	58.0312	2.41378
$579$	−0.249933	−0.0103868
$580$	23.2098	0.963736
$581$	−3.52461	−0.146225
$582$	−23.7089	−0.982766
$583$	0	0
$584$	−2.37384	−0.0982302
$585$	13.2939	0.549636
$586$	8.41188	0.347492
$587$	27.8678	1.15023	0.575113	−	0.818074i	$-0.304958\pi$
$587$	27.8678	1.15023	0.575113	+	0.818074i	$0.304958\pi$
$588$	1.74590	0.0719996
$589$	2.94244	0.121241
$590$	−57.1166	−2.35145
$591$	−18.4999	−0.760983
$592$	33.5592	1.37927
$593$	24.3463	0.999781	0.499890	−	0.866089i	$-0.333374\pi$
$593$	24.3463	0.999781	0.499890	+	0.866089i	$0.333374\pi$
$594$	0	0
$595$	−28.7170	−1.17728
$596$	9.08904	0.372302
$597$	9.87086	0.403988
$598$	−11.4897	−0.469848
$599$	21.0164	0.858707	0.429354	−	0.903136i	$-0.358741\pi$
$599$	21.0164	0.858707	0.429354	+	0.903136i	$0.358741\pi$
$600$	−6.17313	−0.252017
$601$	−40.9477	−1.67029	−0.835145	−	0.550030i	$-0.814616\pi$
$601$	−40.9477	−1.67029	−0.835145	+	0.550030i	$0.814616\pi$
$602$	21.0716	0.858813
$603$	−2.66492	−0.108524
$604$	−10.9117	−0.443993
$605$	0	0
$606$	−9.45898	−0.384245
$607$	14.0276	0.569362	0.284681	−	0.958622i	$-0.408112\pi$
$607$	14.0276	0.569362	0.284681	+	0.958622i	$0.408112\pi$
$608$	−2.42723	−0.0984371
$609$	3.17313	0.128582
$610$	16.2171	0.656612
$611$	−25.5767	−1.03472
$612$	−11.9672	−0.483745
$613$	−18.5306	−0.748442	−0.374221	−	0.927339i	$-0.622090\pi$
$613$	−18.5306	−0.748442	−0.374221	+	0.927339i	$0.622090\pi$
$614$	40.1760	1.62137
$615$	−39.2252	−1.58171
$616$	0	0
$617$	2.43424	0.0979987	0.0489994	−	0.998799i	$-0.484397\pi$
$617$	2.43424	0.0979987	0.0489994	+	0.998799i	$0.484397\pi$
$618$	−1.23353	−0.0496197
$619$	−30.4259	−1.22292	−0.611460	−	0.791275i	$-0.709418\pi$
$619$	−30.4259	−1.22292	−0.611460	+	0.791275i	$0.709418\pi$
$620$	67.5386	2.71242
$621$	−1.87086	−0.0750752
$622$	15.4835	0.620830
$623$	−1.74173	−0.0697809
$624$	−14.1002	−0.564461
$625$	69.7966	2.79187
$626$	15.7334	0.628833
$627$	0	0
$628$	−31.6371	−1.26246
$629$	51.7662	2.06405
$630$	8.10856	0.323053
$631$	34.9836	1.39267	0.696337	−	0.717715i	$-0.254812\pi$
$631$	34.9836	1.39267	0.696337	+	0.717715i	$0.254812\pi$
$632$	2.46705	0.0981341
$633$	4.63734	0.184318
$634$	−38.6925	−1.53668
$635$	23.0081	0.913047
$636$	0.887271	0.0351826
$637$	3.17313	0.125724
$638$	0	0
$639$	−5.01641	−0.198446
$640$	16.3502	0.646297
$641$	8.56337	0.338233	0.169116	−	0.985596i	$-0.445909\pi$
$641$	8.56337	0.338233	0.169116	+	0.985596i	$0.445909\pi$
$642$	−1.85029	−0.0730251
$643$	−5.11273	−0.201626	−0.100813	−	0.994905i	$-0.532144\pi$
$643$	−5.11273	−0.201626	−0.100813	+	0.994905i	$0.532144\pi$
$644$	−3.26634	−0.128712
$645$	45.6126	1.79599
$646$	−4.22758	−0.166332
$647$	25.7693	1.01310	0.506548	−	0.862212i	$-0.330921\pi$
$647$	25.7693	1.01310	0.506548	+	0.862212i	$0.330921\pi$
$648$	−0.491797	−0.0193196
$649$	0	0
$650$	77.0877	3.02363
$651$	9.23353	0.361890
$652$	−4.65269	−0.182213
$653$	−47.8953	−1.87429	−0.937145	−	0.348941i	$-0.886541\pi$
$653$	−47.8953	−1.87429	−0.937145	+	0.348941i	$0.886541\pi$
$654$	14.7337	0.576132
$655$	−16.7581	−0.654795
$656$	41.6043	1.62437
$657$	4.82687	0.188314
$658$	−15.6004	−0.608165
$659$	−8.95601	−0.348877	−0.174438	−	0.984668i	$-0.555811\pi$
$659$	−8.95601	−0.348877	−0.174438	+	0.984668i	$0.555811\pi$
$660$	0	0
$661$	−10.7993	−0.420044	−0.210022	−	0.977697i	$-0.567353\pi$
$661$	−10.7993	−0.420044	−0.210022	+	0.977697i	$0.567353\pi$
$662$	32.9341	1.28002
$663$	−21.7501	−0.844703
$664$	1.73339	0.0672686
$665$	1.33508	0.0517720
$666$	−14.6168	−0.566388
$667$	−5.93649	−0.229862
$668$	19.4590	0.752891
$669$	−18.3463	−0.709307
$670$	−21.6087	−0.834817
$671$	0	0
$672$	−7.61676	−0.293823
$673$	−32.2499	−1.24314	−0.621572	−	0.783357i	$-0.713506\pi$
$673$	−32.2499	−1.24314	−0.621572	+	0.783357i	$0.713506\pi$
$674$	−2.95078	−0.113660
$675$	12.5522	0.483134
$676$	−5.11769	−0.196834
$677$	27.7089	1.06494	0.532470	−	0.846449i	$-0.321264\pi$
$677$	27.7089	1.06494	0.532470	+	0.846449i	$0.321264\pi$
$678$	−14.9201	−0.573002
$679$	−12.2499	−0.470109
$680$	14.1229	0.541589
$681$	−0.379068	−0.0145259
$682$	0	0
$683$	22.3156	0.853881	0.426941	−	0.904280i	$-0.359591\pi$
$683$	22.3156	0.853881	0.426941	+	0.904280i	$0.359591\pi$
$684$	0.556364	0.0212731
$685$	65.4095	2.49917
$686$	1.93543	0.0738951
$687$	24.9424	0.951614
$688$	−48.3791	−1.84443
$689$	1.61259	0.0614349
$690$	−15.1700	−0.577513
$691$	25.1372	0.956264	0.478132	−	0.878288i	$-0.341314\pi$
$691$	25.1372	0.956264	0.478132	+	0.878288i	$0.341314\pi$
$692$	43.3788	1.64901
$693$	0	0
$694$	−33.7745	−1.28206
$695$	37.7745	1.43287
$696$	−1.56053	−0.0591519
$697$	64.1760	2.43084
$698$	−13.2765	−0.502521
$699$	−23.4506	−0.886985
$700$	21.9149	0.828304
$701$	19.2747	0.727995	0.363997	−	0.931400i	$-0.381412\pi$
$701$	19.2747	0.727995	0.363997	+	0.931400i	$0.381412\pi$
$702$	6.14137	0.231791
$703$	−2.40665	−0.0907686
$704$	0	0
$705$	−33.7693	−1.27183
$706$	−61.8008	−2.32590
$707$	−4.88727	−0.183805
$708$	−12.2981	−0.462191
$709$	9.76098	0.366581	0.183291	−	0.983059i	$-0.441325\pi$
$709$	9.76098	0.366581	0.183291	+	0.983059i	$0.441325\pi$
$710$	−40.6758	−1.52654
$711$	−5.01641	−0.188130
$712$	0.856577	0.0321016
$713$	−17.2747	−0.646942
$714$	−13.2663	−0.496480
$715$	0	0
$716$	−22.2744	−0.832434
$717$	−5.07681	−0.189597
$718$	47.2908	1.76488
$719$	14.0276	0.523141	0.261570	−	0.965184i	$-0.415760\pi$
$719$	14.0276	0.523141	0.261570	+	0.965184i	$0.415760\pi$
$720$	−18.6168	−0.693806
$721$	−0.637339	−0.0237357
$722$	−36.5767	−1.36124
$723$	−19.2939	−0.717549
$724$	−5.64541	−0.209810
$725$	39.8297	1.47924
$726$	0	0
$727$	−34.3051	−1.27231	−0.636153	−	0.771563i	$-0.719475\pi$
$727$	−34.3051	−1.27231	−0.636153	+	0.771563i	$0.719475\pi$
$728$	−1.56053	−0.0578372
$729$	1.00000	0.0370370
$730$	39.1390	1.44860
$731$	−74.6263	−2.76016
$732$	3.49180	0.129061
$733$	10.7581	0.397361	0.198680	−	0.980064i	$-0.436334\pi$
$733$	10.7581	0.397361	0.198680	+	0.980064i	$0.436334\pi$
$734$	33.0409	1.21956
$735$	4.18953	0.154533
$736$	14.2499	0.525259
$737$	0	0
$738$	−18.1208	−0.667036
$739$	6.38741	0.234965	0.117482	−	0.993075i	$-0.462518\pi$
$739$	6.38741	0.234965	0.117482	+	0.993075i	$0.462518\pi$
$740$	−55.2405	−2.03068
$741$	1.01118	0.0371466
$742$	0.983593	0.0361088
$743$	23.1096	0.847810	0.423905	−	0.905707i	$-0.360659\pi$
$743$	23.1096	0.847810	0.423905	+	0.905707i	$0.360659\pi$
$744$	−4.54102	−0.166482
$745$	21.8105	0.799074
$746$	−6.15149	−0.225222
$747$	−3.52461	−0.128959
$748$	0	0
$749$	−0.956008	−0.0349318
$750$	61.2374	2.23607
$751$	31.8678	1.16287	0.581435	−	0.813593i	$-0.302491\pi$
$751$	31.8678	1.16287	0.581435	+	0.813593i	$0.302491\pi$
$752$	35.8175	1.30613
$753$	23.8021	0.867398
$754$	19.4874	0.709688
$755$	−26.1843	−0.952944
$756$	1.74590	0.0634977
$757$	−48.3103	−1.75587	−0.877934	−	0.478781i	$-0.841079\pi$
$757$	−48.3103	−1.75587	−0.877934	+	0.478781i	$0.841079\pi$
$758$	7.62483	0.276946
$759$	0	0
$760$	−0.656586	−0.0238169
$761$	17.8625	0.647516	0.323758	−	0.946140i	$-0.395054\pi$
$761$	17.8625	0.647516	0.323758	+	0.946140i	$0.395054\pi$
$762$	10.6290	0.385048
$763$	7.61259	0.275594
$764$	36.6207	1.32489
$765$	−28.7170	−1.03826
$766$	−47.9177	−1.73134
$767$	−22.3515	−0.807065
$768$	19.2622	0.695064
$769$	24.8820	0.897269	0.448635	−	0.893715i	$-0.351910\pi$
$769$	24.8820	0.897269	0.448635	+	0.893715i	$0.351910\pi$
$770$	0	0
$771$	14.9149	0.537145
$772$	−0.436357	−0.0157048
$773$	−34.9700	−1.25778	−0.628892	−	0.777492i	$-0.716491\pi$
$773$	−34.9700	−1.25778	−0.628892	+	0.777492i	$0.716491\pi$
$774$	21.0716	0.757402
$775$	115.901	4.16329
$776$	6.02448	0.216266
$777$	−7.55220	−0.270933
$778$	7.07158	0.253528
$779$	−2.98359	−0.106898
$780$	23.2098	0.831046
$781$	0	0
$782$	24.8195	0.887544
$783$	3.17313	0.113398
$784$	−4.44364	−0.158701
$785$	−75.9177	−2.70962
$786$	−7.74173	−0.276138
$787$	15.1648	0.540566	0.270283	−	0.962781i	$-0.412883\pi$
$787$	15.1648	0.540566	0.270283	+	0.962781i	$0.412883\pi$
$788$	−32.2989	−1.15060
$789$	−2.92319	−0.104068
$790$	−40.6758	−1.44718
$791$	−7.70892	−0.274097
$792$	0	0
$793$	6.34625	0.225362
$794$	8.83210	0.313440
$795$	2.12914	0.0755126
$796$	17.2335	0.610826
$797$	8.24470	0.292042	0.146021	−	0.989281i	$-0.453353\pi$
$797$	8.24470	0.292042	0.146021	+	0.989281i	$0.453353\pi$
$798$	0.616763	0.0218332
$799$	55.2497	1.95459
$800$	−95.6071	−3.38022
$801$	−1.74173	−0.0615410
$802$	−14.0000	−0.494357
$803$	0	0
$804$	−4.65269	−0.164088
$805$	−7.83805	−0.276255
$806$	56.7065	1.99740
$807$	11.9672	0.421265
$808$	2.40354	0.0845564
$809$	−29.8433	−1.04923	−0.524617	−	0.851338i	$-0.675791\pi$
$809$	−29.8433	−1.04923	−0.524617	+	0.851338i	$0.675791\pi$
$810$	8.10856	0.284906
$811$	16.6321	0.584032	0.292016	−	0.956413i	$-0.405674\pi$
$811$	16.6321	0.584032	0.292016	+	0.956413i	$0.405674\pi$
$812$	5.53996	0.194414
$813$	20.3187	0.712607
$814$	0	0
$815$	−11.1648	−0.391086
$816$	30.4587	1.06627
$817$	3.46944	0.121380
$818$	−10.2723	−0.359162
$819$	3.17313	0.110878
$820$	−68.4832	−2.39154
$821$	−30.3327	−1.05862	−0.529309	−	0.848429i	$-0.677549\pi$
$821$	−30.3327	−1.05862	−0.529309	+	0.848429i	$0.677549\pi$
$822$	30.2171	1.05394
$823$	−18.4067	−0.641616	−0.320808	−	0.947144i	$-0.603954\pi$
$823$	−18.4067	−0.641616	−0.320808	+	0.947144i	$0.603954\pi$
$824$	0.313441	0.0109192
$825$	0	0
$826$	−13.6332	−0.474359
$827$	−45.4559	−1.58066	−0.790328	−	0.612684i	$-0.790090\pi$
$827$	−45.4559	−1.58066	−0.790328	+	0.612684i	$0.790090\pi$
$828$	−3.26634	−0.113513
$829$	−20.3463	−0.706655	−0.353327	−	0.935500i	$-0.614950\pi$
$829$	−20.3463	−0.706655	−0.353327	+	0.935500i	$0.614950\pi$
$830$	−28.5795	−0.992009
$831$	−18.0552	−0.626327
$832$	−18.5769	−0.644040
$833$	−6.85446	−0.237493
$834$	17.4506	0.604266
$835$	46.6946	1.61593
$836$	0	0
$837$	9.23353	0.319157
$838$	−22.1086	−0.763728
$839$	16.1812	0.558637	0.279318	−	0.960199i	$-0.409891\pi$
$839$	16.1812	0.558637	0.279318	+	0.960199i	$0.409891\pi$
$840$	−2.06040	−0.0710905
$841$	−18.9313	−0.652802
$842$	−53.0593	−1.82855
$843$	−27.2939	−0.940053
$844$	8.09632	0.278687
$845$	−12.2806	−0.422466
$846$	−15.6004	−0.536351
$847$	0	0
$848$	−2.25827	−0.0775493
$849$	−29.8901	−1.02583
$850$	−166.522	−5.71165
$851$	14.1291	0.484341
$852$	−8.75814	−0.300049
$853$	20.9836	0.718465	0.359232	−	0.933248i	$-0.383039\pi$
$853$	20.9836	0.718465	0.359232	+	0.933248i	$0.383039\pi$
$854$	3.87086	0.132458
$855$	1.33508	0.0456586
$856$	0.470162	0.0160698
$857$	−4.79095	−0.163656	−0.0818279	−	0.996646i	$-0.526076\pi$
$857$	−4.79095	−0.163656	−0.0818279	+	0.996646i	$0.526076\pi$
$858$	0	0
$859$	−9.96719	−0.340076	−0.170038	−	0.985438i	$-0.554389\pi$
$859$	−9.96719	−0.340076	−0.170038	+	0.985438i	$0.554389\pi$
$860$	79.6350	2.71553
$861$	−9.36266	−0.319079
$862$	4.42412	0.150686
$863$	25.5470	0.869629	0.434814	−	0.900520i	$-0.356814\pi$
$863$	25.5470	0.869629	0.434814	+	0.900520i	$0.356814\pi$
$864$	−7.61676	−0.259128
$865$	104.094	3.53929
$866$	61.1044	2.07641
$867$	29.9836	1.01830
$868$	16.1208	0.547176
$869$	0	0
$870$	25.7295	0.872311
$871$	−8.45614	−0.286525
$872$	−3.74385	−0.126783
$873$	−12.2499	−0.414597
$874$	−1.15388	−0.0390306
$875$	31.6402	1.06963
$876$	8.42723	0.284730
$877$	50.9893	1.72179	0.860893	−	0.508787i	$-0.169906\pi$
$877$	50.9893	1.72179	0.860893	+	0.508787i	$0.169906\pi$
$878$	35.8586	1.21017
$879$	4.34625	0.146596
$880$	0	0
$881$	32.1895	1.08449	0.542246	−	0.840219i	$-0.317574\pi$
$881$	32.1895	1.08449	0.542246	+	0.840219i	$0.317574\pi$
$882$	1.93543	0.0651694
$883$	36.6154	1.23221	0.616104	−	0.787665i	$-0.288710\pi$
$883$	36.6154	1.23221	0.616104	+	0.787665i	$0.288710\pi$
$884$	−37.9734	−1.27718
$885$	−29.5110	−0.992003
$886$	55.0325	1.84885
$887$	48.2004	1.61841	0.809206	−	0.587525i	$-0.199897\pi$
$887$	48.2004	1.61841	0.809206	+	0.587525i	$0.199897\pi$
$888$	3.71414	0.124639
$889$	5.49180	0.184189
$890$	−14.1229	−0.473401
$891$	0	0
$892$	−32.0307	−1.07247
$893$	−2.56860	−0.0859550
$894$	10.0757	0.336983
$895$	−53.4506	−1.78666
$896$	3.90262	0.130377
$897$	−5.93649	−0.198214
$898$	−11.0060	−0.367273
$899$	29.2992	0.977181
$900$	21.9149	0.730495
$901$	−3.48346	−0.116051
$902$	0	0
$903$	10.8873	0.362306
$904$	3.79122	0.126094
$905$	−13.5470	−0.450316
$906$	−12.0963	−0.401873
$907$	22.9013	0.760425	0.380212	−	0.924899i	$-0.375851\pi$
$907$	22.9013	0.760425	0.380212	+	0.924899i	$0.375851\pi$
$908$	−0.661814	−0.0219631
$909$	−4.88727	−0.162101
$910$	25.7295	0.852924
$911$	−36.0552	−1.19456	−0.597281	−	0.802032i	$-0.703752\pi$
$911$	−36.0552	−1.19456	−0.597281	+	0.802032i	$0.703752\pi$
$912$	−1.41605	−0.0468901
$913$	0	0
$914$	25.1762	0.832756
$915$	8.37907	0.277003
$916$	43.5470	1.43883
$917$	−4.00000	−0.132092
$918$	−13.2663	−0.437854
$919$	28.3379	0.934782	0.467391	−	0.884051i	$-0.345194\pi$
$919$	28.3379	0.934782	0.467391	+	0.884051i	$0.345194\pi$
$920$	3.85473	0.127087
$921$	20.7581	0.684004
$922$	12.3463	0.406602
$923$	−15.9177	−0.523937
$924$	0	0
$925$	−94.7966	−3.11689
$926$	65.9851	2.16841
$927$	−0.637339	−0.0209329
$928$	−24.1690	−0.793385
$929$	5.08514	0.166838	0.0834191	−	0.996515i	$-0.473416\pi$
$929$	5.08514	0.166838	0.0834191	+	0.996515i	$0.473416\pi$
$930$	74.8706	2.45510
$931$	0.318669	0.0104440
$932$	−40.9424	−1.34111
$933$	8.00000	0.261908
$934$	35.1250	1.14932
$935$	0	0
$936$	−1.56053	−0.0510076
$937$	−32.2088	−1.05222	−0.526108	−	0.850418i	$-0.676349\pi$
$937$	−32.2088	−1.05222	−0.526108	+	0.850418i	$0.676349\pi$
$938$	−5.15778	−0.168407
$939$	8.12914	0.265284
$940$	−58.9578	−1.92299
$941$	−32.7805	−1.06861	−0.534307	−	0.845291i	$-0.679427\pi$
$941$	−32.7805	−1.06861	−0.534307	+	0.845291i	$0.679427\pi$
$942$	−35.0716	−1.14269
$943$	17.5163	0.570408
$944$	31.3009	1.01876
$945$	4.18953	0.136286
$946$	0	0
$947$	−27.3627	−0.889167	−0.444584	−	0.895737i	$-0.646648\pi$
$947$	−27.3627	−0.889167	−0.444584	+	0.895737i	$0.646648\pi$
$948$	−8.75814	−0.284451
$949$	15.3163	0.497188
$950$	7.74173	0.251175
$951$	−19.9917	−0.648274
$952$	3.37100	0.109255
$953$	24.6894	0.799768	0.399884	−	0.916566i	$-0.369050\pi$
$953$	24.6894	0.799768	0.399884	+	0.916566i	$0.369050\pi$
$954$	0.983593	0.0318450
$955$	87.8765	2.84362
$956$	−8.86359	−0.286669
$957$	0	0
$958$	82.7393	2.67319
$959$	15.6126	0.504157
$960$	−24.5275	−0.791620
$961$	54.2580	1.75026
$962$	−46.3808	−1.49538
$963$	−0.956008	−0.0308069
$964$	−33.6852	−1.08493
$965$	−1.04710	−0.0337074
$966$	−3.62093	−0.116502
$967$	−21.3298	−0.685922	−0.342961	−	0.939350i	$-0.611430\pi$
$967$	−21.3298	−0.685922	−0.342961	+	0.939350i	$0.611430\pi$
$968$	0	0
$969$	−2.18431	−0.0701700
$970$	−99.3293	−3.18927
$971$	28.4946	0.914436	0.457218	−	0.889355i	$-0.348846\pi$
$971$	28.4946	0.914436	0.457218	+	0.889355i	$0.348846\pi$
$972$	1.74590	0.0559997
$973$	9.01641	0.289053
$974$	51.8521	1.66145
$975$	39.8297	1.27557
$976$	−8.88727	−0.284475
$977$	−19.8157	−0.633960	−0.316980	−	0.948432i	$-0.602669\pi$
$977$	−19.8157	−0.633960	−0.316980	+	0.948432i	$0.602669\pi$
$978$	−5.15778	−0.164928
$979$	0	0
$980$	7.31450	0.233653
$981$	7.61259	0.243051
$982$	−61.3171	−1.95671
$983$	−53.7745	−1.71514	−0.857571	−	0.514366i	$-0.828027\pi$
$983$	−53.7745	−1.71514	−0.857571	+	0.514366i	$0.828027\pi$
$984$	4.60453	0.146787
$985$	−77.5058	−2.46954
$986$	−42.0958	−1.34060
$987$	−8.06040	−0.256565
$988$	1.76541	0.0561653
$989$	−20.3686	−0.647684
$990$	0	0
$991$	49.7693	1.58097	0.790487	−	0.612479i	$-0.209827\pi$
$991$	49.7693	1.58097	0.790487	+	0.612479i	$0.209827\pi$
$992$	−70.3296	−2.23297
$993$	17.0164	0.539999
$994$	−9.70892	−0.307948
$995$	41.3543	1.31102
$996$	−6.15361	−0.194985
$997$	−0.659696	−0.0208928	−0.0104464	−	0.999945i	$-0.503325\pi$
$997$	−0.659696	−0.0208928	−0.0104464	+	0.999945i	$0.503325\pi$
$998$	−46.6943	−1.47808
$999$	−7.55220	−0.238941

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2541.2.a.bg.1.3		3
3.2	odd	2		7623.2.a.cd.1.1		3
11.10	odd	2		231.2.a.e.1.1	✓	3
33.32	even	2		693.2.a.l.1.3		3
44.43	even	2		3696.2.a.bo.1.3		3
55.54	odd	2		5775.2.a.bp.1.3		3
77.76	even	2		1617.2.a.t.1.1		3
231.230	odd	2		4851.2.a.bi.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.a.e.1.1	✓	3	11.10	odd	2
693.2.a.l.1.3		3	33.32	even	2
1617.2.a.t.1.1		3	77.76	even	2
2541.2.a.bg.1.3		3	1.1	even	1	trivial
3696.2.a.bo.1.3		3	44.43	even	2
4851.2.a.bi.1.3		3	231.230	odd	2
5775.2.a.bp.1.3		3	55.54	odd	2
7623.2.a.cd.1.1		3	3.2	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:	\( N \)	\(=\)	\( 2541 = 3 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2541.a (trivial)

\(f(q)\)	\(=\)	\(q+1.93543 q^{2} +1.00000 q^{3} +1.74590 q^{4} +4.18953 q^{5} +1.93543 q^{6} +1.00000 q^{7} -0.491797 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.93543 q^{2} +1.00000 q^{3} +1.74590 q^{4} +4.18953 q^{5} +1.93543 q^{6} +1.00000 q^{7} -0.491797 q^{8} +1.00000 q^{9} +8.10856 q^{10} +1.74590 q^{12} +3.17313 q^{13} +1.93543 q^{14} +4.18953 q^{15} -4.44364 q^{16} -6.85446 q^{17} +1.93543 q^{18} +0.318669 q^{19} +7.31450 q^{20} +1.00000 q^{21} -1.87086 q^{23} -0.491797 q^{24} +12.5522 q^{25} +6.14137 q^{26} +1.00000 q^{27} +1.74590 q^{28} +3.17313 q^{29} +8.10856 q^{30} +9.23353 q^{31} -7.61676 q^{32} -13.2663 q^{34} +4.18953 q^{35} +1.74590 q^{36} -7.55220 q^{37} +0.616763 q^{38} +3.17313 q^{39} -2.06040 q^{40} -9.36266 q^{41} +1.93543 q^{42} +10.8873 q^{43} +4.18953 q^{45} -3.62093 q^{46} -8.06040 q^{47} -4.44364 q^{48} +1.00000 q^{49} +24.2939 q^{50} -6.85446 q^{51} +5.53996 q^{52} +0.508203 q^{53} +1.93543 q^{54} -0.491797 q^{56} +0.318669 q^{57} +6.14137 q^{58} -7.04399 q^{59} +7.31450 q^{60} +2.00000 q^{61} +17.8709 q^{62} +1.00000 q^{63} -5.85446 q^{64} +13.2939 q^{65} -2.66492 q^{67} -11.9672 q^{68} -1.87086 q^{69} +8.10856 q^{70} -5.01641 q^{71} -0.491797 q^{72} +4.82687 q^{73} -14.6168 q^{74} +12.5522 q^{75} +0.556364 q^{76} +6.14137 q^{78} -5.01641 q^{79} -18.6168 q^{80} +1.00000 q^{81} -18.1208 q^{82} -3.52461 q^{83} +1.74590 q^{84} -28.7170 q^{85} +21.0716 q^{86} +3.17313 q^{87} -1.74173 q^{89} +8.10856 q^{90} +3.17313 q^{91} -3.26634 q^{92} +9.23353 q^{93} -15.6004 q^{94} +1.33508 q^{95} -7.61676 q^{96} -12.2499 q^{97} +1.93543 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 2 q^{2} + 3 q^{3} + 6 q^{4} + 4 q^{5} - 2 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 2 * q^2 + 3 * q^3 + 6 * q^4 + 4 * q^5 - 2 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 2 q^{2} + 3 q^{3} + 6 q^{4} + 4 q^{5} - 2 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} + 11 q^{10} + 6 q^{12} + 4 q^{13} - 2 q^{14} + 4 q^{15} - 4 q^{16} - 8 q^{17} - 2 q^{18} + 8 q^{19} - 3 q^{20} + 3 q^{21} + 10 q^{23} - 3 q^{24} + 15 q^{25} - q^{26} + 3 q^{27} + 6 q^{28} + 4 q^{29} + 11 q^{30} - 2 q^{31} - 8 q^{32} - 4 q^{34} + 4 q^{35} + 6 q^{36} - 13 q^{38} + 4 q^{39} + 18 q^{40} - 14 q^{41} - 2 q^{42} + 14 q^{43} + 4 q^{45} - 28 q^{46} - 4 q^{48} + 3 q^{49} + 19 q^{50} - 8 q^{51} + 29 q^{52} - 2 q^{54} - 3 q^{56} + 8 q^{57} - q^{58} - 3 q^{60} + 6 q^{61} + 38 q^{62} + 3 q^{63} - 5 q^{64} - 14 q^{65} - 4 q^{67} - 42 q^{68} + 10 q^{69} + 11 q^{70} - 12 q^{71} - 3 q^{72} + 20 q^{73} - 29 q^{74} + 15 q^{75} + 11 q^{76} - q^{78} - 12 q^{79} - 41 q^{80} + 3 q^{81} - 6 q^{82} - 6 q^{83} + 6 q^{84} + 6 q^{85} + 24 q^{86} + 4 q^{87} + 26 q^{89} + 11 q^{90} + 4 q^{91} + 26 q^{92} - 2 q^{93} - 35 q^{94} + 8 q^{95} - 8 q^{96} - 4 q^{97} - 2 q^{98}+O(q^{100}) \) 3 * q - 2 * q^2 + 3 * q^3 + 6 * q^4 + 4 * q^5 - 2 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 + 11 * q^10 + 6 * q^12 + 4 * q^13 - 2 * q^14 + 4 * q^15 - 4 * q^16 - 8 * q^17 - 2 * q^18 + 8 * q^19 - 3 * q^20 + 3 * q^21 + 10 * q^23 - 3 * q^24 + 15 * q^25 - q^26 + 3 * q^27 + 6 * q^28 + 4 * q^29 + 11 * q^30 - 2 * q^31 - 8 * q^32 - 4 * q^34 + 4 * q^35 + 6 * q^36 - 13 * q^38 + 4 * q^39 + 18 * q^40 - 14 * q^41 - 2 * q^42 + 14 * q^43 + 4 * q^45 - 28 * q^46 - 4 * q^48 + 3 * q^49 + 19 * q^50 - 8 * q^51 + 29 * q^52 - 2 * q^54 - 3 * q^56 + 8 * q^57 - q^58 - 3 * q^60 + 6 * q^61 + 38 * q^62 + 3 * q^63 - 5 * q^64 - 14 * q^65 - 4 * q^67 - 42 * q^68 + 10 * q^69 + 11 * q^70 - 12 * q^71 - 3 * q^72 + 20 * q^73 - 29 * q^74 + 15 * q^75 + 11 * q^76 - q^78 - 12 * q^79 - 41 * q^80 + 3 * q^81 - 6 * q^82 - 6 * q^83 + 6 * q^84 + 6 * q^85 + 24 * q^86 + 4 * q^87 + 26 * q^89 + 11 * q^90 + 4 * q^91 + 26 * q^92 - 2 * q^93 - 35 * q^94 + 8 * q^95 - 8 * q^96 - 4 * q^97 - 2 * q^98

Introduction

L-functions

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Database

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