LMFDB - Embedded newform 6171.2.a.bo.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6171,2,Mod(1,6171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6171, 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("6171.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6171 = 3 \cdot 11^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6171.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:	$49.2756830873$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} - 19 x^{12} + 36 x^{11} + 136 x^{10} - 244 x^{9} - 449 x^{8} + 778 x^{7} + 638 x^{6} + \cdots + 4 $ x^14 - 2x^13 - 19x^12 + 36x^11 + 136x^10 - 244x^9 - 449x^8 + 778x^7 + 638x^6 - 1160x^5 - 195x^4 + 644x^3 - 151x^2 - 16*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$2.66608$ of defining polynomial
Character	$\chi$	$=$	6171.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.66608 q^{2} -1.00000 q^{3} +5.10797 q^{4} -4.17179 q^{5} -2.66608 q^{6} +3.51874 q^{7} +8.28610 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.66608 q^{2} -1.00000 q^{3} +5.10797 q^{4} -4.17179 q^{5} -2.66608 q^{6} +3.51874 q^{7} +8.28610 q^{8} +1.00000 q^{9} -11.1223 q^{10} -5.10797 q^{12} -5.16899 q^{13} +9.38123 q^{14} +4.17179 q^{15} +11.8754 q^{16} -1.00000 q^{17} +2.66608 q^{18} -7.53163 q^{19} -21.3094 q^{20} -3.51874 q^{21} +0.563727 q^{23} -8.28610 q^{24} +12.4038 q^{25} -13.7809 q^{26} -1.00000 q^{27} +17.9736 q^{28} -5.70584 q^{29} +11.1223 q^{30} -0.406317 q^{31} +15.0887 q^{32} -2.66608 q^{34} -14.6794 q^{35} +5.10797 q^{36} +0.528706 q^{37} -20.0799 q^{38} +5.16899 q^{39} -34.5678 q^{40} -9.32300 q^{41} -9.38123 q^{42} -6.15515 q^{43} -4.17179 q^{45} +1.50294 q^{46} +8.42670 q^{47} -11.8754 q^{48} +5.38153 q^{49} +33.0695 q^{50} +1.00000 q^{51} -26.4030 q^{52} +0.938674 q^{53} -2.66608 q^{54} +29.1566 q^{56} +7.53163 q^{57} -15.2122 q^{58} +6.67287 q^{59} +21.3094 q^{60} -10.0416 q^{61} -1.08327 q^{62} +3.51874 q^{63} +16.4767 q^{64} +21.5639 q^{65} -4.33448 q^{67} -5.10797 q^{68} -0.563727 q^{69} -39.1365 q^{70} -4.57303 q^{71} +8.28610 q^{72} +0.251474 q^{73} +1.40957 q^{74} -12.4038 q^{75} -38.4714 q^{76} +13.7809 q^{78} -13.1459 q^{79} -49.5418 q^{80} +1.00000 q^{81} -24.8558 q^{82} +4.79179 q^{83} -17.9736 q^{84} +4.17179 q^{85} -16.4101 q^{86} +5.70584 q^{87} +5.88541 q^{89} -11.1223 q^{90} -18.1883 q^{91} +2.87950 q^{92} +0.406317 q^{93} +22.4662 q^{94} +31.4204 q^{95} -15.0887 q^{96} -15.6397 q^{97} +14.3476 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{2} - 14 q^{3} + 14 q^{4} - 2 q^{6} - 6 q^{7} + 6 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q + 2 * q^2 - 14 * q^3 + 14 * q^4 - 2 * q^6 - 6 * q^7 + 6 * q^8 + 14 * q^9	$ 14 q + 2 q^{2} - 14 q^{3} + 14 q^{4} - 2 q^{6} - 6 q^{7} + 6 q^{8} + 14 q^{9} - 8 q^{10} - 14 q^{12} - 20 q^{13} + 4 q^{14} + 14 q^{16} - 14 q^{17} + 2 q^{18} - 16 q^{19} - 16 q^{20} + 6 q^{21} - 2 q^{23} - 6 q^{24} + 22 q^{25} - 4 q^{26} - 14 q^{27} + 30 q^{28} - 22 q^{29} + 8 q^{30} + 34 q^{32} - 2 q^{34} - 2 q^{35} + 14 q^{36} + 8 q^{37} - 16 q^{38} + 20 q^{39} - 74 q^{40} - 24 q^{41} - 4 q^{42} - 12 q^{43} - 26 q^{46} + 28 q^{47} - 14 q^{48} + 28 q^{49} + 50 q^{50} + 14 q^{51} - 48 q^{52} + 18 q^{53} - 2 q^{54} + 6 q^{56} + 16 q^{57} + 20 q^{59} + 16 q^{60} - 64 q^{61} - 62 q^{62} - 6 q^{63} - 4 q^{64} + 30 q^{65} + 10 q^{67} - 14 q^{68} + 2 q^{69} - 44 q^{70} - 8 q^{71} + 6 q^{72} - 44 q^{73} - 50 q^{74} - 22 q^{75} - 24 q^{76} + 4 q^{78} - 8 q^{79} - 102 q^{80} + 14 q^{81} - 46 q^{82} - 12 q^{83} - 30 q^{84} + 12 q^{86} + 22 q^{87} - 8 q^{89} - 8 q^{90} - 20 q^{91} - 20 q^{92} + 16 q^{94} + 30 q^{95} - 34 q^{96} - 14 q^{97} + 90 q^{98}+O(q^{100}) $ 14 * q + 2 * q^2 - 14 * q^3 + 14 * q^4 - 2 * q^6 - 6 * q^7 + 6 * q^8 + 14 * q^9 - 8 * q^10 - 14 * q^12 - 20 * q^13 + 4 * q^14 + 14 * q^16 - 14 * q^17 + 2 * q^18 - 16 * q^19 - 16 * q^20 + 6 * q^21 - 2 * q^23 - 6 * q^24 + 22 * q^25 - 4 * q^26 - 14 * q^27 + 30 * q^28 - 22 * q^29 + 8 * q^30 + 34 * q^32 - 2 * q^34 - 2 * q^35 + 14 * q^36 + 8 * q^37 - 16 * q^38 + 20 * q^39 - 74 * q^40 - 24 * q^41 - 4 * q^42 - 12 * q^43 - 26 * q^46 + 28 * q^47 - 14 * q^48 + 28 * q^49 + 50 * q^50 + 14 * q^51 - 48 * q^52 + 18 * q^53 - 2 * q^54 + 6 * q^56 + 16 * q^57 + 20 * q^59 + 16 * q^60 - 64 * q^61 - 62 * q^62 - 6 * q^63 - 4 * q^64 + 30 * q^65 + 10 * q^67 - 14 * q^68 + 2 * q^69 - 44 * q^70 - 8 * q^71 + 6 * q^72 - 44 * q^73 - 50 * q^74 - 22 * q^75 - 24 * q^76 + 4 * q^78 - 8 * q^79 - 102 * q^80 + 14 * q^81 - 46 * q^82 - 12 * q^83 - 30 * q^84 + 12 * q^86 + 22 * q^87 - 8 * q^89 - 8 * q^90 - 20 * q^91 - 20 * q^92 + 16 * q^94 + 30 * q^95 - 34 * q^96 - 14 * q^97 + 90 * 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 $

$2$	2.66608	1.88520	0.942601	−	0.333921i	$-0.108372\pi$
$2$	2.66608	1.88520	0.942601	+	0.333921i	$0.108372\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.10797	2.55399
$5$	−4.17179	−1.86568	−0.932840	−	0.360291i	$-0.882677\pi$
$5$	−4.17179	−1.86568	−0.932840	+	0.360291i	$0.882677\pi$
$6$	−2.66608	−1.08842
$7$	3.51874	1.32996	0.664979	−	0.746862i	$-0.268440\pi$
$7$	3.51874	1.32996	0.664979	+	0.746862i	$0.268440\pi$
$8$	8.28610	2.92958
$9$	1.00000	0.333333
$10$	−11.1223	−3.51718
$11$	0	0
$11$	0	0
$12$	−5.10797	−1.47454
$13$	−5.16899	−1.43362	−0.716810	−	0.697269i	$-0.754398\pi$
$13$	−5.16899	−1.43362	−0.716810	+	0.697269i	$0.754398\pi$
$14$	9.38123	2.50724
$15$	4.17179	1.07715
$16$	11.8754	2.96886
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	2.66608	0.628401
$19$	−7.53163	−1.72787	−0.863937	−	0.503599i	$-0.832009\pi$
$19$	−7.53163	−1.72787	−0.863937	+	0.503599i	$0.832009\pi$
$20$	−21.3094	−4.76492
$21$	−3.51874	−0.767852
$22$	0	0
$23$	0.563727	0.117545	0.0587726	−	0.998271i	$-0.481281\pi$
$23$	0.563727	0.117545	0.0587726	+	0.998271i	$0.481281\pi$
$24$	−8.28610	−1.69139
$25$	12.4038	2.48076
$26$	−13.7809	−2.70266
$27$	−1.00000	−0.192450
$28$	17.9736	3.39670
$29$	−5.70584	−1.05955	−0.529774	−	0.848139i	$-0.677723\pi$
$29$	−5.70584	−1.05955	−0.529774	+	0.848139i	$0.677723\pi$
$30$	11.1223	2.03065
$31$	−0.406317	−0.0729766	−0.0364883	−	0.999334i	$-0.511617\pi$
$31$	−0.406317	−0.0729766	−0.0364883	+	0.999334i	$0.511617\pi$
$32$	15.0887	2.66732
$33$	0	0
$34$	−2.66608	−0.457229
$35$	−14.6794	−2.48128
$36$	5.10797	0.851329
$37$	0.528706	0.0869187	0.0434594	−	0.999055i	$-0.486162\pi$
$37$	0.528706	0.0869187	0.0434594	+	0.999055i	$0.486162\pi$
$38$	−20.0799	−3.25739
$39$	5.16899	0.827700
$40$	−34.5678	−5.46566
$41$	−9.32300	−1.45601	−0.728004	−	0.685573i	$-0.759552\pi$
$41$	−9.32300	−1.45601	−0.728004	+	0.685573i	$0.759552\pi$
$42$	−9.38123	−1.44756
$43$	−6.15515	−0.938652	−0.469326	−	0.883025i	$-0.655503\pi$
$43$	−6.15515	−0.938652	−0.469326	+	0.883025i	$0.655503\pi$
$44$	0	0
$45$	−4.17179	−0.621893
$46$	1.50294	0.221596
$47$	8.42670	1.22916	0.614580	−	0.788854i	$-0.289325\pi$
$47$	8.42670	1.22916	0.614580	+	0.788854i	$0.289325\pi$
$48$	−11.8754	−1.71407
$49$	5.38153	0.768789
$50$	33.0695	4.67674
$51$	1.00000	0.140028
$52$	−26.4030	−3.66144
$53$	0.938674	0.128937	0.0644684	−	0.997920i	$-0.479465\pi$
$53$	0.938674	0.128937	0.0644684	+	0.997920i	$0.479465\pi$
$54$	−2.66608	−0.362807
$55$	0	0
$56$	29.1566	3.89622
$57$	7.53163	0.997589
$58$	−15.2122	−1.99746
$59$	6.67287	0.868734	0.434367	−	0.900736i	$-0.356972\pi$
$59$	6.67287	0.868734	0.434367	+	0.900736i	$0.356972\pi$
$60$	21.3094	2.75103
$61$	−10.0416	−1.28569	−0.642846	−	0.765995i	$-0.722247\pi$
$61$	−10.0416	−1.28569	−0.642846	+	0.765995i	$0.722247\pi$
$62$	−1.08327	−0.137576
$63$	3.51874	0.443319
$64$	16.4767	2.05958
$65$	21.5639	2.67467
$66$	0	0
$67$	−4.33448	−0.529541	−0.264771	−	0.964311i	$-0.585296\pi$
$67$	−4.33448	−0.529541	−0.264771	+	0.964311i	$0.585296\pi$
$68$	−5.10797	−0.619433
$69$	−0.563727	−0.0678648
$70$	−39.1365	−4.67771
$71$	−4.57303	−0.542718	−0.271359	−	0.962478i	$-0.587473\pi$
$71$	−4.57303	−0.542718	−0.271359	+	0.962478i	$0.587473\pi$
$72$	8.28610	0.976526
$73$	0.251474	0.0294328	0.0147164	−	0.999892i	$-0.495315\pi$
$73$	0.251474	0.0294328	0.0147164	+	0.999892i	$0.495315\pi$
$74$	1.40957	0.163859
$75$	−12.4038	−1.43227
$76$	−38.4714	−4.41297
$77$	0	0
$78$	13.7809	1.56038
$79$	−13.1459	−1.47903	−0.739517	−	0.673138i	$-0.764946\pi$
$79$	−13.1459	−1.47903	−0.739517	+	0.673138i	$0.764946\pi$
$80$	−49.5418	−5.53894
$81$	1.00000	0.111111
$82$	−24.8558	−2.74487
$83$	4.79179	0.525967	0.262983	−	0.964800i	$-0.415294\pi$
$83$	4.79179	0.525967	0.262983	+	0.964800i	$0.415294\pi$
$84$	−17.9736	−1.96108
$85$	4.17179	0.452494
$86$	−16.4101	−1.76955
$87$	5.70584	0.611730
$88$	0	0
$89$	5.88541	0.623852	0.311926	−	0.950106i	$-0.399026\pi$
$89$	5.88541	0.623852	0.311926	+	0.950106i	$0.399026\pi$
$90$	−11.1223	−1.17239
$91$	−18.1883	−1.90665
$92$	2.87950	0.300209
$93$	0.406317	0.0421331
$94$	22.4662	2.31722
$95$	31.4204	3.22366
$96$	−15.0887	−1.53998
$97$	−15.6397	−1.58797	−0.793986	−	0.607936i	$-0.791998\pi$
$97$	−15.6397	−1.58797	−0.793986	+	0.607936i	$0.791998\pi$
$98$	14.3476	1.44932
$99$	0	0
$100$	63.3583	6.33583
$101$	−0.390059	−0.0388123	−0.0194062	−	0.999812i	$-0.506178\pi$
$101$	−0.390059	−0.0388123	−0.0194062	+	0.999812i	$0.506178\pi$
$102$	2.66608	0.263981
$103$	8.64999	0.852309	0.426155	−	0.904650i	$-0.359868\pi$
$103$	8.64999	0.852309	0.426155	+	0.904650i	$0.359868\pi$
$104$	−42.8307	−4.19990
$105$	14.6794	1.43257
$106$	2.50258	0.243072
$107$	9.95073	0.961974	0.480987	−	0.876728i	$-0.340278\pi$
$107$	9.95073	0.961974	0.480987	+	0.876728i	$0.340278\pi$
$108$	−5.10797	−0.491515
$109$	−1.00632	−0.0963878	−0.0481939	−	0.998838i	$-0.515347\pi$
$109$	−1.00632	−0.0963878	−0.0481939	+	0.998838i	$0.515347\pi$
$110$	0	0
$111$	−0.528706	−0.0501826
$112$	41.7866	3.94846
$113$	6.12058	0.575775	0.287888	−	0.957664i	$-0.407047\pi$
$113$	6.12058	0.575775	0.287888	+	0.957664i	$0.407047\pi$
$114$	20.0799	1.88066
$115$	−2.35175	−0.219302
$116$	−29.1453	−2.70607
$117$	−5.16899	−0.477873
$118$	17.7904	1.63774
$119$	−3.51874	−0.322562
$120$	34.5678	3.15560
$121$	0	0
$122$	−26.7716	−2.42379
$123$	9.32300	0.840626
$124$	−2.07545	−0.186381
$125$	−30.8871	−2.76263
$126$	9.38123	0.835747
$127$	−17.0666	−1.51442	−0.757209	−	0.653173i	$-0.773437\pi$
$127$	−17.0666	−1.51442	−0.757209	+	0.653173i	$0.773437\pi$
$128$	13.7508	1.21541
$129$	6.15515	0.541931
$130$	57.4911	5.04230
$131$	6.35270	0.555038	0.277519	−	0.960720i	$-0.410488\pi$
$131$	6.35270	0.555038	0.277519	+	0.960720i	$0.410488\pi$
$132$	0	0
$133$	−26.5018	−2.29800
$134$	−11.5561	−0.998292
$135$	4.17179	0.359050
$136$	−8.28610	−0.710527
$137$	4.98821	0.426172	0.213086	−	0.977033i	$-0.431649\pi$
$137$	4.98821	0.426172	0.213086	+	0.977033i	$0.431649\pi$
$138$	−1.50294	−0.127939
$139$	2.20794	0.187275	0.0936376	−	0.995606i	$-0.470150\pi$
$139$	2.20794	0.187275	0.0936376	+	0.995606i	$0.470150\pi$
$140$	−74.9821	−6.33715
$141$	−8.42670	−0.709656
$142$	−12.1920	−1.02313
$143$	0	0
$144$	11.8754	0.989620
$145$	23.8035	1.97678
$146$	0.670450	0.0554868
$147$	−5.38153	−0.443861
$148$	2.70062	0.221989
$149$	−3.24706	−0.266010	−0.133005	−	0.991115i	$-0.542463\pi$
$149$	−3.24706	−0.266010	−0.133005	+	0.991115i	$0.542463\pi$
$150$	−33.0695	−2.70012
$151$	−13.9507	−1.13529	−0.567644	−	0.823274i	$-0.692145\pi$
$151$	−13.9507	−1.13529	−0.567644	+	0.823274i	$0.692145\pi$
$152$	−62.4078	−5.06194
$153$	−1.00000	−0.0808452
$154$	0	0
$155$	1.69507	0.136151
$156$	26.4030	2.11394
$157$	2.96168	0.236367	0.118184	−	0.992992i	$-0.462293\pi$
$157$	2.96168	0.236367	0.118184	+	0.992992i	$0.462293\pi$
$158$	−35.0481	−2.78828
$159$	−0.938674	−0.0744417
$160$	−62.9467	−4.97637
$161$	1.98361	0.156330
$162$	2.66608	0.209467
$163$	−24.6003	−1.92685	−0.963423	−	0.267984i	$-0.913643\pi$
$163$	−24.6003	−1.92685	−0.963423	+	0.267984i	$0.913643\pi$
$164$	−47.6216	−3.71862
$165$	0	0
$166$	12.7753	0.991554
$167$	5.11332	0.395680	0.197840	−	0.980234i	$-0.436607\pi$
$167$	5.11332	0.395680	0.197840	+	0.980234i	$0.436607\pi$
$168$	−29.1566	−2.24948
$169$	13.7184	1.05526
$170$	11.1223	0.853042
$171$	−7.53163	−0.575958
$172$	−31.4403	−2.39730
$173$	−18.0595	−1.37304	−0.686521	−	0.727110i	$-0.740863\pi$
$173$	−18.0595	−1.37304	−0.686521	+	0.727110i	$0.740863\pi$
$174$	15.2122	1.15323
$175$	43.6458	3.29931
$176$	0	0
$177$	−6.67287	−0.501564
$178$	15.6910	1.17609
$179$	6.57850	0.491700	0.245850	−	0.969308i	$-0.420933\pi$
$179$	6.57850	0.491700	0.245850	+	0.969308i	$0.420933\pi$
$180$	−21.3094	−1.58831
$181$	−11.1953	−0.832143	−0.416072	−	0.909332i	$-0.636593\pi$
$181$	−11.1953	−0.832143	−0.416072	+	0.909332i	$0.636593\pi$
$182$	−48.4915	−3.59443
$183$	10.0416	0.742295
$184$	4.67110	0.344358
$185$	−2.20565	−0.162163
$186$	1.08327	0.0794294
$187$	0	0
$188$	43.0434	3.13926
$189$	−3.51874	−0.255951
$190$	83.7692	6.07725
$191$	15.8029	1.14346	0.571730	−	0.820442i	$-0.306272\pi$
$191$	15.8029	1.14346	0.571730	+	0.820442i	$0.306272\pi$
$192$	−16.4767	−1.18910
$193$	−16.0396	−1.15456	−0.577278	−	0.816548i	$-0.695885\pi$
$193$	−16.0396	−1.15456	−0.577278	+	0.816548i	$0.695885\pi$
$194$	−41.6967	−2.99365
$195$	−21.5639	−1.54422
$196$	27.4887	1.96348
$197$	−25.9318	−1.84756	−0.923782	−	0.382919i	$-0.874919\pi$
$197$	−25.9318	−1.84756	−0.923782	+	0.382919i	$0.874919\pi$
$198$	0	0
$199$	−2.37520	−0.168373	−0.0841866	−	0.996450i	$-0.526829\pi$
$199$	−2.37520	−0.168373	−0.0841866	+	0.996450i	$0.526829\pi$
$200$	102.779	7.26759
$201$	4.33448	0.305731
$202$	−1.03993	−0.0731691
$203$	−20.0774	−1.40915
$204$	5.10797	0.357630
$205$	38.8936	2.71644
$206$	23.0616	1.60677
$207$	0.563727	0.0391817
$208$	−61.3840	−4.25622
$209$	0	0
$210$	39.1365	2.70068
$211$	10.2951	0.708742	0.354371	−	0.935105i	$-0.384695\pi$
$211$	10.2951	0.708742	0.354371	+	0.935105i	$0.384695\pi$
$212$	4.79472	0.329303
$213$	4.57303	0.313339
$214$	26.5294	1.81351
$215$	25.6780	1.75122
$216$	−8.28610	−0.563798
$217$	−1.42972	−0.0970559
$218$	−2.68292	−0.181710
$219$	−0.251474	−0.0169931
$220$	0	0
$221$	5.16899	0.347704
$222$	−1.40957	−0.0946042
$223$	−14.1459	−0.947282	−0.473641	−	0.880718i	$-0.657061\pi$
$223$	−14.1459	−0.947282	−0.473641	+	0.880718i	$0.657061\pi$
$224$	53.0931	3.54743
$225$	12.4038	0.826921
$226$	16.3179	1.08545
$227$	−4.04383	−0.268398	−0.134199	−	0.990954i	$-0.542846\pi$
$227$	−4.04383	−0.268398	−0.134199	+	0.990954i	$0.542846\pi$
$228$	38.4714	2.54783
$229$	15.3325	1.01320	0.506601	−	0.862181i	$-0.330902\pi$
$229$	15.3325	1.01320	0.506601	+	0.862181i	$0.330902\pi$
$230$	−6.26995	−0.413428
$231$	0	0
$232$	−47.2791	−3.10403
$233$	−13.6672	−0.895371	−0.447686	−	0.894191i	$-0.647752\pi$
$233$	−13.6672	−0.895371	−0.447686	+	0.894191i	$0.647752\pi$
$234$	−13.7809	−0.900887
$235$	−35.1544	−2.29322
$236$	34.0849	2.21874
$237$	13.1459	0.853921
$238$	−9.38123	−0.608095
$239$	8.52593	0.551497	0.275748	−	0.961230i	$-0.411074\pi$
$239$	8.52593	0.551497	0.275748	+	0.961230i	$0.411074\pi$
$240$	49.5418	3.19791
$241$	15.3391	0.988081	0.494041	−	0.869439i	$-0.335519\pi$
$241$	15.3391	0.988081	0.494041	+	0.869439i	$0.335519\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	−51.2921	−3.28364
$245$	−22.4506	−1.43432
$246$	24.8558	1.58475
$247$	38.9309	2.47711
$248$	−3.36678	−0.213791
$249$	−4.79179	−0.303667
$250$	−82.3475	−5.20811
$251$	−7.85051	−0.495520	−0.247760	−	0.968821i	$-0.579694\pi$
$251$	−7.85051	−0.495520	−0.247760	+	0.968821i	$0.579694\pi$
$252$	17.9736	1.13223
$253$	0	0
$254$	−45.5009	−2.85498
$255$	−4.17179	−0.261247
$256$	3.70725	0.231703
$257$	9.61307	0.599647	0.299824	−	0.953995i	$-0.403072\pi$
$257$	9.61307	0.599647	0.299824	+	0.953995i	$0.403072\pi$
$258$	16.4101	1.02165
$259$	1.86038	0.115598
$260$	110.148	6.83108
$261$	−5.70584	−0.353183
$262$	16.9368	1.04636
$263$	−6.00512	−0.370291	−0.185146	−	0.982711i	$-0.559276\pi$
$263$	−6.00512	−0.370291	−0.185146	+	0.982711i	$0.559276\pi$
$264$	0	0
$265$	−3.91595	−0.240555
$266$	−70.6560	−4.33220
$267$	−5.88541	−0.360181
$268$	−22.1404	−1.35244
$269$	30.1929	1.84089	0.920445	−	0.390871i	$-0.127826\pi$
$269$	30.1929	1.84089	0.920445	+	0.390871i	$0.127826\pi$
$270$	11.1223	0.676882
$271$	0.164811	0.0100116	0.00500579	−	0.999987i	$-0.498407\pi$
$271$	0.164811	0.0100116	0.00500579	+	0.999987i	$0.498407\pi$
$272$	−11.8754	−0.720054
$273$	18.1883	1.10081
$274$	13.2990	0.803419
$275$	0	0
$276$	−2.87950	−0.173326
$277$	7.84422	0.471313	0.235657	−	0.971836i	$-0.424276\pi$
$277$	7.84422	0.471313	0.235657	+	0.971836i	$0.424276\pi$
$278$	5.88655	0.353052
$279$	−0.406317	−0.0243255
$280$	−121.635	−7.26910
$281$	31.4671	1.87717	0.938584	−	0.345052i	$-0.112139\pi$
$281$	31.4671	1.87717	0.938584	+	0.345052i	$0.112139\pi$
$282$	−22.4662	−1.33785
$283$	−22.0192	−1.30890	−0.654452	−	0.756104i	$-0.727100\pi$
$283$	−22.0192	−1.30890	−0.654452	+	0.756104i	$0.727100\pi$
$284$	−23.3589	−1.38610
$285$	−31.4204	−1.86118
$286$	0	0
$287$	−32.8052	−1.93643
$288$	15.0887	0.889108
$289$	1.00000	0.0588235
$290$	63.4621	3.72662
$291$	15.6397	0.916816
$292$	1.28452	0.0751710
$293$	13.1462	0.768010	0.384005	−	0.923331i	$-0.374545\pi$
$293$	13.1462	0.768010	0.384005	+	0.923331i	$0.374545\pi$
$294$	−14.3476	−0.836767
$295$	−27.8378	−1.62078
$296$	4.38091	0.254635
$297$	0	0
$298$	−8.65692	−0.501482
$299$	−2.91390	−0.168515
$300$	−63.3583	−3.65800
$301$	−21.6584	−1.24837
$302$	−37.1935	−2.14025
$303$	0.390059	0.0224083
$304$	−89.4414	−5.12982
$305$	41.8914	2.39869
$306$	−2.66608	−0.152410
$307$	−7.84384	−0.447672	−0.223836	−	0.974627i	$-0.571858\pi$
$307$	−7.84384	−0.447672	−0.223836	+	0.974627i	$0.571858\pi$
$308$	0	0
$309$	−8.64999	−0.492081
$310$	4.51918	0.256672
$311$	−21.2725	−1.20625	−0.603125	−	0.797646i	$-0.706078\pi$
$311$	−21.2725	−1.20625	−0.603125	+	0.797646i	$0.706078\pi$
$312$	42.8307	2.42481
$313$	16.1103	0.910609	0.455304	−	0.890336i	$-0.349530\pi$
$313$	16.1103	0.910609	0.455304	+	0.890336i	$0.349530\pi$
$314$	7.89606	0.445600
$315$	−14.6794	−0.827092
$316$	−67.1491	−3.77743
$317$	21.4298	1.20362	0.601808	−	0.798641i	$-0.294447\pi$
$317$	21.4298	1.20362	0.601808	+	0.798641i	$0.294447\pi$
$318$	−2.50258	−0.140338
$319$	0	0
$320$	−68.7371	−3.84252
$321$	−9.95073	−0.555396
$322$	5.28845	0.294714
$323$	7.53163	0.419071
$324$	5.10797	0.283776
$325$	−64.1152	−3.55647
$326$	−65.5864	−3.63250
$327$	1.00632	0.0556495
$328$	−77.2513	−4.26549
$329$	29.6514	1.63473
$330$	0	0
$331$	10.9872	0.603911	0.301955	−	0.953322i	$-0.402361\pi$
$331$	10.9872	0.603911	0.301955	+	0.953322i	$0.402361\pi$
$332$	24.4763	1.34331
$333$	0.528706	0.0289729
$334$	13.6325	0.745937
$335$	18.0825	0.987955
$336$	−41.7866	−2.27965
$337$	17.9683	0.978794	0.489397	−	0.872061i	$-0.337217\pi$
$337$	17.9683	0.978794	0.489397	+	0.872061i	$0.337217\pi$
$338$	36.5744	1.98939
$339$	−6.12058	−0.332424
$340$	21.3094	1.15566
$341$	0	0
$342$	−20.0799	−1.08580
$343$	−5.69499	−0.307501
$344$	−51.0022	−2.74985
$345$	2.35175	0.126614
$346$	−48.1481	−2.58846
$347$	19.8011	1.06298	0.531489	−	0.847065i	$-0.321633\pi$
$347$	19.8011	1.06298	0.531489	+	0.847065i	$0.321633\pi$
$348$	29.1453	1.56235
$349$	27.0158	1.44612	0.723062	−	0.690783i	$-0.242734\pi$
$349$	27.0158	1.44612	0.723062	+	0.690783i	$0.242734\pi$
$350$	116.363	6.21987
$351$	5.16899	0.275900
$352$	0	0
$353$	−11.5050	−0.612349	−0.306174	−	0.951975i	$-0.599049\pi$
$353$	−11.5050	−0.612349	−0.306174	+	0.951975i	$0.599049\pi$
$354$	−17.7904	−0.945549
$355$	19.0777	1.01254
$356$	30.0625	1.59331
$357$	3.51874	0.186231
$358$	17.5388	0.926954
$359$	−23.8366	−1.25805	−0.629025	−	0.777385i	$-0.716546\pi$
$359$	−23.8366	−1.25805	−0.629025	+	0.777385i	$0.716546\pi$
$360$	−34.5678	−1.82189
$361$	37.7255	1.98555
$362$	−29.8477	−1.56876
$363$	0	0
$364$	−92.9054	−4.86957
$365$	−1.04910	−0.0549122
$366$	26.7716	1.39938
$367$	15.5228	0.810282	0.405141	−	0.914254i	$-0.367222\pi$
$367$	15.5228	0.810282	0.405141	+	0.914254i	$0.367222\pi$
$368$	6.69451	0.348975
$369$	−9.32300	−0.485336
$370$	−5.88043	−0.305709
$371$	3.30295	0.171481
$372$	2.07545	0.107607
$373$	32.2761	1.67119	0.835596	−	0.549344i	$-0.185123\pi$
$373$	32.2761	1.67119	0.835596	+	0.549344i	$0.185123\pi$
$374$	0	0
$375$	30.8871	1.59500
$376$	69.8245	3.60092
$377$	29.4934	1.51899
$378$	−9.38123	−0.482519
$379$	10.5630	0.542584	0.271292	−	0.962497i	$-0.412549\pi$
$379$	10.5630	0.542584	0.271292	+	0.962497i	$0.412549\pi$
$380$	160.494	8.23319
$381$	17.0666	0.874349
$382$	42.1319	2.15565
$383$	−30.7030	−1.56885	−0.784425	−	0.620224i	$-0.787042\pi$
$383$	−30.7030	−1.56885	−0.784425	+	0.620224i	$0.787042\pi$
$384$	−13.7508	−0.701715
$385$	0	0
$386$	−42.7628	−2.17657
$387$	−6.15515	−0.312884
$388$	−79.8872	−4.05566
$389$	4.93999	0.250468	0.125234	−	0.992127i	$-0.460032\pi$
$389$	4.93999	0.250468	0.125234	+	0.992127i	$0.460032\pi$
$390$	−57.4911	−2.91117
$391$	−0.563727	−0.0285089
$392$	44.5919	2.25223
$393$	−6.35270	−0.320451
$394$	−69.1362	−3.48303
$395$	54.8421	2.75940
$396$	0	0
$397$	11.1873	0.561474	0.280737	−	0.959785i	$-0.409421\pi$
$397$	11.1873	0.561474	0.280737	+	0.959785i	$0.409421\pi$
$398$	−6.33246	−0.317417
$399$	26.5018	1.32675
$400$	147.301	7.36504
$401$	6.35392	0.317300	0.158650	−	0.987335i	$-0.449286\pi$
$401$	6.35392	0.317300	0.158650	+	0.987335i	$0.449286\pi$
$402$	11.5561	0.576364
$403$	2.10025	0.104621
$404$	−1.99241	−0.0991262
$405$	−4.17179	−0.207298
$406$	−53.5278	−2.65654
$407$	0	0
$408$	8.28610	0.410223
$409$	28.9965	1.43378	0.716892	−	0.697185i	$-0.245564\pi$
$409$	28.9965	1.43378	0.716892	+	0.697185i	$0.245564\pi$
$410$	103.693	5.12105
$411$	−4.98821	−0.246050
$412$	44.1839	2.17679
$413$	23.4801	1.15538
$414$	1.50294	0.0738655
$415$	−19.9903	−0.981286
$416$	−77.9931	−3.82393
$417$	−2.20794	−0.108123
$418$	0	0
$419$	0.229095	0.0111920	0.00559602	−	0.999984i	$-0.498219\pi$
$419$	0.229095	0.0111920	0.00559602	+	0.999984i	$0.498219\pi$
$420$	74.9821	3.65875
$421$	3.96020	0.193008	0.0965041	−	0.995333i	$-0.469234\pi$
$421$	3.96020	0.193008	0.0965041	+	0.995333i	$0.469234\pi$
$422$	27.4475	1.33612
$423$	8.42670	0.409720
$424$	7.77795	0.377730
$425$	−12.4038	−0.601673
$426$	12.1920	0.590706
$427$	−35.3337	−1.70992
$428$	50.8281	2.45687
$429$	0	0
$430$	68.4595	3.30141
$431$	2.80476	0.135101	0.0675503	−	0.997716i	$-0.478482\pi$
$431$	2.80476	0.135101	0.0675503	+	0.997716i	$0.478482\pi$
$432$	−11.8754	−0.571357
$433$	−10.1738	−0.488920	−0.244460	−	0.969659i	$-0.578611\pi$
$433$	−10.1738	−0.488920	−0.244460	+	0.969659i	$0.578611\pi$
$434$	−3.81175	−0.182970
$435$	−23.8035	−1.14129
$436$	−5.14024	−0.246173
$437$	−4.24578	−0.203103
$438$	−0.670450	−0.0320353
$439$	−0.477530	−0.0227913	−0.0113956	−	0.999935i	$-0.503627\pi$
$439$	−0.477530	−0.0227913	−0.0113956	+	0.999935i	$0.503627\pi$
$440$	0	0
$441$	5.38153	0.256263
$442$	13.7809	0.655492
$443$	−8.99638	−0.427431	−0.213715	−	0.976896i	$-0.568557\pi$
$443$	−8.99638	−0.427431	−0.213715	+	0.976896i	$0.568557\pi$
$444$	−2.70062	−0.128166
$445$	−24.5527	−1.16391
$446$	−37.7142	−1.78582
$447$	3.24706	0.153581
$448$	57.9771	2.73916
$449$	30.4591	1.43745	0.718726	−	0.695293i	$-0.244726\pi$
$449$	30.4591	1.43745	0.718726	+	0.695293i	$0.244726\pi$
$450$	33.0695	1.55891
$451$	0	0
$452$	31.2637	1.47052
$453$	13.9507	0.655459
$454$	−10.7812	−0.505985
$455$	75.8778	3.55721
$456$	62.4078	2.92251
$457$	−33.0076	−1.54403	−0.772015	−	0.635605i	$-0.780751\pi$
$457$	−33.0076	−1.54403	−0.772015	+	0.635605i	$0.780751\pi$
$458$	40.8777	1.91009
$459$	1.00000	0.0466760
$460$	−12.0127	−0.560094
$461$	−34.9632	−1.62840	−0.814200	−	0.580584i	$-0.802824\pi$
$461$	−34.9632	−1.62840	−0.814200	+	0.580584i	$0.802824\pi$
$462$	0	0
$463$	−27.9307	−1.29805	−0.649025	−	0.760767i	$-0.724823\pi$
$463$	−27.9307	−1.29805	−0.649025	+	0.760767i	$0.724823\pi$
$464$	−67.7593	−3.14565
$465$	−1.69507	−0.0786068
$466$	−36.4379	−1.68796
$467$	−20.0256	−0.926673	−0.463337	−	0.886182i	$-0.653348\pi$
$467$	−20.0256	−0.926673	−0.463337	+	0.886182i	$0.653348\pi$
$468$	−26.4030	−1.22048
$469$	−15.2519	−0.704268
$470$	−93.7244	−4.32318
$471$	−2.96168	−0.136467
$472$	55.2921	2.54502
$473$	0	0
$474$	35.0481	1.60981
$475$	−93.4209	−4.28645
$476$	−17.9736	−0.823820
$477$	0.938674	0.0429789
$478$	22.7308	1.03968
$479$	23.5825	1.07751	0.538755	−	0.842462i	$-0.318895\pi$
$479$	23.5825	1.07751	0.538755	+	0.842462i	$0.318895\pi$
$480$	62.9467	2.87311
$481$	−2.73287	−0.124608
$482$	40.8954	1.86273
$483$	−1.98361	−0.0902573
$484$	0	0
$485$	65.2455	2.96265
$486$	−2.66608	−0.120936
$487$	14.6912	0.665723	0.332862	−	0.942976i	$-0.391986\pi$
$487$	14.6912	0.665723	0.332862	+	0.942976i	$0.391986\pi$
$488$	−83.2056	−3.76654
$489$	24.6003	1.11247
$490$	−59.8550	−2.70397
$491$	−28.6709	−1.29390	−0.646951	−	0.762532i	$-0.723956\pi$
$491$	−28.6709	−1.29390	−0.646951	+	0.762532i	$0.723956\pi$
$492$	47.6216	2.14695
$493$	5.70584	0.256978
$494$	103.793	4.66986
$495$	0	0
$496$	−4.82519	−0.216657
$497$	−16.0913	−0.721793
$498$	−12.7753	−0.572474
$499$	6.60326	0.295602	0.147801	−	0.989017i	$-0.452780\pi$
$499$	6.60326	0.295602	0.147801	+	0.989017i	$0.452780\pi$
$500$	−157.771	−7.05572
$501$	−5.11332	−0.228446
$502$	−20.9301	−0.934155
$503$	2.65507	0.118384	0.0591919	−	0.998247i	$-0.481148\pi$
$503$	2.65507	0.118384	0.0591919	+	0.998247i	$0.481148\pi$
$504$	29.1566	1.29874
$505$	1.62724	0.0724114
$506$	0	0
$507$	−13.7184	−0.609257
$508$	−87.1758	−3.86780
$509$	−10.4510	−0.463234	−0.231617	−	0.972807i	$-0.574402\pi$
$509$	−10.4510	−0.463234	−0.231617	+	0.972807i	$0.574402\pi$
$510$	−11.1223	−0.492504
$511$	0.884872	0.0391444
$512$	−17.6177	−0.778599
$513$	7.53163	0.332530
$514$	25.6292	1.13046
$515$	−36.0859	−1.59014
$516$	31.4403	1.38408
$517$	0	0
$518$	4.95991	0.217926
$519$	18.0595	0.792726
$520$	178.681	7.83567
$521$	−1.89695	−0.0831067	−0.0415534	−	0.999136i	$-0.513231\pi$
$521$	−1.89695	−0.0831067	−0.0415534	+	0.999136i	$0.513231\pi$
$522$	−15.2122	−0.665820
$523$	−6.02871	−0.263617	−0.131809	−	0.991275i	$-0.542078\pi$
$523$	−6.02871	−0.263617	−0.131809	+	0.991275i	$0.542078\pi$
$524$	32.4494	1.41756
$525$	−43.6458	−1.90486
$526$	−16.0101	−0.698074
$527$	0.406317	0.0176994
$528$	0	0
$529$	−22.6822	−0.986183
$530$	−10.4402	−0.453494
$531$	6.67287	0.289578
$532$	−135.371	−5.86906
$533$	48.1905	2.08736
$534$	−15.6910	−0.679014
$535$	−41.5123	−1.79474
$536$	−35.9160	−1.55133
$537$	−6.57850	−0.283883
$538$	80.4965	3.47045
$539$	0	0
$540$	21.3094	0.917010
$541$	−3.39873	−0.146123	−0.0730615	−	0.997327i	$-0.523277\pi$
$541$	−3.39873	−0.146123	−0.0730615	+	0.997327i	$0.523277\pi$
$542$	0.439400	0.0188738
$543$	11.1953	0.480438
$544$	−15.0887	−0.646921
$545$	4.19814	0.179829
$546$	48.4915	2.07524
$547$	−41.5388	−1.77607	−0.888035	−	0.459775i	$-0.847930\pi$
$547$	−41.5388	−1.77607	−0.888035	+	0.459775i	$0.847930\pi$
$548$	25.4796	1.08844
$549$	−10.0416	−0.428564
$550$	0	0
$551$	42.9743	1.83077
$552$	−4.67110	−0.198815
$553$	−46.2571	−1.96705
$554$	20.9133	0.888521
$555$	2.20565	0.0936246
$556$	11.2781	0.478298
$557$	27.2135	1.15307	0.576537	−	0.817071i	$-0.304404\pi$
$557$	27.2135	1.15307	0.576537	+	0.817071i	$0.304404\pi$
$558$	−1.08327	−0.0458586
$559$	31.8159	1.34567
$560$	−174.325	−7.36657
$561$	0	0
$562$	83.8936	3.53884
$563$	40.9541	1.72601	0.863005	−	0.505195i	$-0.168579\pi$
$563$	40.9541	1.72601	0.863005	+	0.505195i	$0.168579\pi$
$564$	−43.0434	−1.81245
$565$	−25.5337	−1.07421
$566$	−58.7048	−2.46755
$567$	3.51874	0.147773
$568$	−37.8925	−1.58994
$569$	−14.2457	−0.597211	−0.298605	−	0.954377i	$-0.596521\pi$
$569$	−14.2457	−0.597211	−0.298605	+	0.954377i	$0.596521\pi$
$570$	−83.7692	−3.50870
$571$	42.2025	1.76612	0.883060	−	0.469260i	$-0.155479\pi$
$571$	42.2025	1.76612	0.883060	+	0.469260i	$0.155479\pi$
$572$	0	0
$573$	−15.8029	−0.660177
$574$	−87.4612	−3.65056
$575$	6.99236	0.291602
$576$	16.4767	0.686528
$577$	0.641818	0.0267193	0.0133596	−	0.999911i	$-0.495747\pi$
$577$	0.641818	0.0267193	0.0133596	+	0.999911i	$0.495747\pi$
$578$	2.66608	0.110894
$579$	16.0396	0.666583
$580$	121.588	5.04866
$581$	16.8610	0.699514
$582$	41.6967	1.72838
$583$	0	0
$584$	2.08374	0.0862258
$585$	21.5639	0.891558
$586$	35.0488	1.44785
$587$	7.16340	0.295665	0.147833	−	0.989012i	$-0.452770\pi$
$587$	7.16340	0.295665	0.147833	+	0.989012i	$0.452770\pi$
$588$	−27.4887	−1.13361
$589$	3.06023	0.126094
$590$	−74.2178	−3.05550
$591$	25.9318	1.06669
$592$	6.27862	0.258050
$593$	32.2685	1.32511	0.662554	−	0.749014i	$-0.269472\pi$
$593$	32.2685	1.32511	0.662554	+	0.749014i	$0.269472\pi$
$594$	0	0
$595$	14.6794	0.601798
$596$	−16.5859	−0.679385
$597$	2.37520	0.0972103
$598$	−7.76868	−0.317685
$599$	−21.9953	−0.898705	−0.449353	−	0.893355i	$-0.648345\pi$
$599$	−21.9953	−0.898705	−0.449353	+	0.893355i	$0.648345\pi$
$600$	−102.779	−4.19594
$601$	−35.1752	−1.43483	−0.717413	−	0.696648i	$-0.754674\pi$
$601$	−35.1752	−1.43483	−0.717413	+	0.696648i	$0.754674\pi$
$602$	−57.7429	−2.35343
$603$	−4.33448	−0.176514
$604$	−71.2596	−2.89951
$605$	0	0
$606$	1.03993	0.0422442
$607$	12.4637	0.505885	0.252942	−	0.967481i	$-0.418602\pi$
$607$	12.4637	0.505885	0.252942	+	0.967481i	$0.418602\pi$
$608$	−113.642	−4.60880
$609$	20.0774	0.813576
$610$	111.686	4.52202
$611$	−43.5575	−1.76215
$612$	−5.10797	−0.206478
$613$	26.0173	1.05083	0.525414	−	0.850847i	$-0.323911\pi$
$613$	26.0173	1.05083	0.525414	+	0.850847i	$0.323911\pi$
$614$	−20.9123	−0.843951
$615$	−38.8936	−1.56834
$616$	0	0
$617$	−29.6897	−1.19526	−0.597630	−	0.801772i	$-0.703891\pi$
$617$	−29.6897	−1.19526	−0.597630	+	0.801772i	$0.703891\pi$
$618$	−23.0616	−0.927672
$619$	8.32516	0.334616	0.167308	−	0.985905i	$-0.446492\pi$
$619$	8.32516	0.334616	0.167308	+	0.985905i	$0.446492\pi$
$620$	8.65835	0.347728
$621$	−0.563727	−0.0226216
$622$	−56.7141	−2.27403
$623$	20.7092	0.829697
$624$	61.3840	2.45733
$625$	66.8355	2.67342
$626$	42.9514	1.71668
$627$	0	0
$628$	15.1282	0.603679
$629$	−0.528706	−0.0210809
$630$	−39.1365	−1.55924
$631$	18.2484	0.726458	0.363229	−	0.931700i	$-0.381674\pi$
$631$	18.2484	0.726458	0.363229	+	0.931700i	$0.381674\pi$
$632$	−108.929	−4.33295
$633$	−10.2951	−0.409193
$634$	57.1334	2.26906
$635$	71.1983	2.82542
$636$	−4.79472	−0.190123
$637$	−27.8170	−1.10215
$638$	0	0
$639$	−4.57303	−0.180906
$640$	−57.3652	−2.26756
$641$	9.63004	0.380364	0.190182	−	0.981749i	$-0.439092\pi$
$641$	9.63004	0.380364	0.190182	+	0.981749i	$0.439092\pi$
$642$	−26.5294	−1.04703
$643$	7.65093	0.301723	0.150862	−	0.988555i	$-0.451795\pi$
$643$	7.65093	0.301723	0.150862	+	0.988555i	$0.451795\pi$
$644$	10.1322	0.399265
$645$	−25.6780	−1.01107
$646$	20.0799	0.790034
$647$	−9.36227	−0.368069	−0.184034	−	0.982920i	$-0.558916\pi$
$647$	−9.36227	−0.368069	−0.184034	+	0.982920i	$0.558916\pi$
$648$	8.28610	0.325509
$649$	0	0
$650$	−170.936	−6.70466
$651$	1.42972	0.0560352
$652$	−125.658	−4.92114
$653$	15.7020	0.614465	0.307232	−	0.951634i	$-0.400597\pi$
$653$	15.7020	0.614465	0.307232	+	0.951634i	$0.400597\pi$
$654$	2.68292	0.104911
$655$	−26.5021	−1.03552
$656$	−110.715	−4.32268
$657$	0.251474	0.00981094
$658$	79.0529	3.08180
$659$	−16.1936	−0.630811	−0.315406	−	0.948957i	$-0.602141\pi$
$659$	−16.1936	−0.630811	−0.315406	+	0.948957i	$0.602141\pi$
$660$	0	0
$661$	26.5815	1.03390	0.516951	−	0.856015i	$-0.327067\pi$
$661$	26.5815	1.03390	0.516951	+	0.856015i	$0.327067\pi$
$662$	29.2927	1.13849
$663$	−5.16899	−0.200747
$664$	39.7052	1.54086
$665$	110.560	4.28734
$666$	1.40957	0.0546198
$667$	−3.21653	−0.124545
$668$	26.1187	1.01056
$669$	14.1459	0.546914
$670$	48.2095	1.86249
$671$	0	0
$672$	−53.0931	−2.04811
$673$	−22.3065	−0.859854	−0.429927	−	0.902864i	$-0.641461\pi$
$673$	−22.3065	−0.859854	−0.429927	+	0.902864i	$0.641461\pi$
$674$	47.9048	1.84522
$675$	−12.4038	−0.477423
$676$	70.0734	2.69513
$677$	−29.3846	−1.12934	−0.564671	−	0.825316i	$-0.690997\pi$
$677$	−29.3846	−1.12934	−0.564671	+	0.825316i	$0.690997\pi$
$678$	−16.3179	−0.626687
$679$	−55.0320	−2.11194
$680$	34.5678	1.32562
$681$	4.04383	0.154960
$682$	0	0
$683$	−23.5020	−0.899281	−0.449640	−	0.893210i	$-0.648448\pi$
$683$	−23.5020	−0.899281	−0.449640	+	0.893210i	$0.648448\pi$
$684$	−38.4714	−1.47099
$685$	−20.8098	−0.795100
$686$	−15.1833	−0.579701
$687$	−15.3325	−0.584972
$688$	−73.0951	−2.78673
$689$	−4.85199	−0.184846
$690$	6.26995	0.238693
$691$	−38.1301	−1.45054	−0.725269	−	0.688465i	$-0.758285\pi$
$691$	−38.1301	−1.45054	−0.725269	+	0.688465i	$0.758285\pi$
$692$	−92.2476	−3.50673
$693$	0	0
$694$	52.7912	2.00393
$695$	−9.21107	−0.349396
$696$	47.2791	1.79211
$697$	9.32300	0.353134
$698$	72.0263	2.72623
$699$	13.6672	0.516943
$700$	222.941	8.42640
$701$	−11.1032	−0.419361	−0.209681	−	0.977770i	$-0.567242\pi$
$701$	−11.1032	−0.419361	−0.209681	+	0.977770i	$0.567242\pi$
$702$	13.7809	0.520127
$703$	−3.98202	−0.150185
$704$	0	0
$705$	35.1544	1.32399
$706$	−30.6732	−1.15440
$707$	−1.37252	−0.0516188
$708$	−34.0849	−1.28099
$709$	24.6181	0.924552	0.462276	−	0.886736i	$-0.347033\pi$
$709$	24.6181	0.924552	0.462276	+	0.886736i	$0.347033\pi$
$710$	50.8626	1.90884
$711$	−13.1459	−0.493011
$712$	48.7671	1.82762
$713$	−0.229052	−0.00857805
$714$	9.38123	0.351084
$715$	0	0
$716$	33.6028	1.25579
$717$	−8.52593	−0.318407
$718$	−63.5504	−2.37168
$719$	27.0467	1.00867	0.504336	−	0.863507i	$-0.331737\pi$
$719$	27.0467	1.00867	0.504336	+	0.863507i	$0.331737\pi$
$720$	−49.5418	−1.84631
$721$	30.4371	1.13354
$722$	100.579	3.74316
$723$	−15.3391	−0.570469
$724$	−57.1855	−2.12528
$725$	−70.7741	−2.62849
$726$	0	0
$727$	29.6171	1.09844	0.549219	−	0.835679i	$-0.314925\pi$
$727$	29.6171	1.09844	0.549219	+	0.835679i	$0.314925\pi$
$728$	−150.710	−5.58569
$729$	1.00000	0.0370370
$730$	−2.79697	−0.103521
$731$	6.15515	0.227656
$732$	51.2921	1.89581
$733$	26.6251	0.983420	0.491710	−	0.870759i	$-0.336372\pi$
$733$	26.6251	0.983420	0.491710	+	0.870759i	$0.336372\pi$
$734$	41.3849	1.52754
$735$	22.4506	0.828102
$736$	8.50588	0.313531
$737$	0	0
$738$	−24.8558	−0.914956
$739$	42.0539	1.54698	0.773488	−	0.633811i	$-0.218510\pi$
$739$	42.0539	1.54698	0.773488	+	0.633811i	$0.218510\pi$
$740$	−11.2664	−0.414161
$741$	−38.9309	−1.43016
$742$	8.80592	0.323276
$743$	−34.8937	−1.28012	−0.640062	−	0.768323i	$-0.721091\pi$
$743$	−34.8937	−1.28012	−0.640062	+	0.768323i	$0.721091\pi$
$744$	3.36678	0.123432
$745$	13.5461	0.496289
$746$	86.0505	3.15053
$747$	4.79179	0.175322
$748$	0	0
$749$	35.0140	1.27938
$750$	82.3475	3.00691
$751$	31.7538	1.15871	0.579356	−	0.815075i	$-0.303304\pi$
$751$	31.7538	1.15871	0.579356	+	0.815075i	$0.303304\pi$
$752$	100.071	3.64921
$753$	7.85051	0.286089
$754$	78.6317	2.86360
$755$	58.1992	2.11809
$756$	−17.9736	−0.653694
$757$	−38.2620	−1.39066	−0.695329	−	0.718692i	$-0.744741\pi$
$757$	−38.2620	−1.39066	−0.695329	+	0.718692i	$0.744741\pi$
$758$	28.1618	1.02288
$759$	0	0
$760$	260.352	9.44397
$761$	−9.31453	−0.337652	−0.168826	−	0.985646i	$-0.553998\pi$
$761$	−9.31453	−0.337652	−0.168826	+	0.985646i	$0.553998\pi$
$762$	45.5009	1.64832
$763$	−3.54097	−0.128192
$764$	80.7209	2.92038
$765$	4.17179	0.150831
$766$	−81.8566	−2.95760
$767$	−34.4920	−1.24543
$768$	−3.70725	−0.133774
$769$	−51.8211	−1.86872	−0.934359	−	0.356333i	$-0.884027\pi$
$769$	−51.8211	−1.86872	−0.934359	+	0.356333i	$0.884027\pi$
$770$	0	0
$771$	−9.61307	−0.346206
$772$	−81.9299	−2.94872
$773$	53.8829	1.93803	0.969016	−	0.246997i	$-0.0794439\pi$
$773$	53.8829	1.93803	0.969016	+	0.246997i	$0.0794439\pi$
$774$	−16.4101	−0.589849
$775$	−5.03988	−0.181038
$776$	−129.592	−4.65209
$777$	−1.86038	−0.0667407
$778$	13.1704	0.472182
$779$	70.2174	2.51580
$780$	−110.148	−3.94393
$781$	0	0
$782$	−1.50294	−0.0537450
$783$	5.70584	0.203910
$784$	63.9080	2.28243
$785$	−12.3555	−0.440986
$786$	−16.9368	−0.604115
$787$	10.1769	0.362766	0.181383	−	0.983413i	$-0.441943\pi$
$787$	10.1769	0.362766	0.181383	+	0.983413i	$0.441943\pi$
$788$	−132.459	−4.71865
$789$	6.00512	0.213788
$790$	146.213	5.20203
$791$	21.5367	0.765757
$792$	0	0
$793$	51.9048	1.84319
$794$	29.8262	1.05849
$795$	3.91595	0.138884
$796$	−12.1324	−0.430023
$797$	−5.37582	−0.190421	−0.0952107	−	0.995457i	$-0.530352\pi$
$797$	−5.37582	−0.190421	−0.0952107	+	0.995457i	$0.530352\pi$
$798$	70.6560	2.50120
$799$	−8.42670	−0.298115
$800$	187.157	6.61700
$801$	5.88541	0.207951
$802$	16.9401	0.598174
$803$	0	0
$804$	22.1404	0.780832
$805$	−8.27519	−0.291662
$806$	5.59942	0.197231
$807$	−30.1929	−1.06284
$808$	−3.23207	−0.113704
$809$	42.6918	1.50096	0.750482	−	0.660891i	$-0.229821\pi$
$809$	42.6918	1.50096	0.750482	+	0.660891i	$0.229821\pi$
$810$	−11.1223	−0.390798
$811$	34.2832	1.20384	0.601922	−	0.798555i	$-0.294402\pi$
$811$	34.2832	1.20384	0.601922	+	0.798555i	$0.294402\pi$
$812$	−102.555	−3.59896
$813$	−0.164811	−0.00578019
$814$	0	0
$815$	102.627	3.59488
$816$	11.8754	0.415724
$817$	46.3583	1.62187
$818$	77.3069	2.70297
$819$	−18.1883	−0.635551
$820$	198.667	6.93776
$821$	−13.3621	−0.466341	−0.233171	−	0.972436i	$-0.574910\pi$
$821$	−13.3621	−0.466341	−0.233171	+	0.972436i	$0.574910\pi$
$822$	−13.2990	−0.463854
$823$	6.62755	0.231022	0.115511	−	0.993306i	$-0.463149\pi$
$823$	6.62755	0.231022	0.115511	+	0.993306i	$0.463149\pi$
$824$	71.6747	2.49691
$825$	0	0
$826$	62.5998	2.17813
$827$	−36.5151	−1.26975	−0.634877	−	0.772613i	$-0.718949\pi$
$827$	−36.5151	−1.26975	−0.634877	+	0.772613i	$0.718949\pi$
$828$	2.87950	0.100070
$829$	1.90205	0.0660608	0.0330304	−	0.999454i	$-0.489484\pi$
$829$	1.90205	0.0660608	0.0330304	+	0.999454i	$0.489484\pi$
$830$	−53.2957	−1.84992
$831$	−7.84422	−0.272113
$832$	−85.1677	−2.95266
$833$	−5.38153	−0.186459
$834$	−5.88655	−0.203834
$835$	−21.3317	−0.738213
$836$	0	0
$837$	0.406317	0.0140444
$838$	0.610786	0.0210992
$839$	53.8101	1.85773	0.928866	−	0.370415i	$-0.120785\pi$
$839$	53.8101	1.85773	0.928866	+	0.370415i	$0.120785\pi$
$840$	121.635	4.19681
$841$	3.55659	0.122641
$842$	10.5582	0.363859
$843$	−31.4671	−1.08378
$844$	52.5870	1.81012
$845$	−57.2304	−1.96879
$846$	22.4662	0.772405
$847$	0	0
$848$	11.1472	0.382795
$849$	22.0192	0.755696
$850$	−33.0695	−1.13428
$851$	0.298046	0.0102169
$852$	23.3589	0.800262
$853$	24.3795	0.834737	0.417368	−	0.908737i	$-0.362953\pi$
$853$	24.3795	0.834737	0.417368	+	0.908737i	$0.362953\pi$
$854$	−94.2024	−3.22354
$855$	31.4204	1.07455
$856$	82.4528	2.81818
$857$	19.7428	0.674402	0.337201	−	0.941433i	$-0.390520\pi$
$857$	19.7428	0.674402	0.337201	+	0.941433i	$0.390520\pi$
$858$	0	0
$859$	7.55659	0.257827	0.128914	−	0.991656i	$-0.458851\pi$
$859$	7.55659	0.257827	0.128914	+	0.991656i	$0.458851\pi$
$860$	131.162	4.47260
$861$	32.8052	1.11800
$862$	7.47771	0.254692
$863$	10.6953	0.364071	0.182035	−	0.983292i	$-0.441731\pi$
$863$	10.6953	0.364071	0.182035	+	0.983292i	$0.441731\pi$
$864$	−15.0887	−0.513327
$865$	75.3406	2.56166
$866$	−27.1240	−0.921712
$867$	−1.00000	−0.0339618
$868$	−7.30298	−0.247879
$869$	0	0
$870$	−63.4621	−2.15157
$871$	22.4049	0.759161
$872$	−8.33845	−0.282376
$873$	−15.6397	−0.529324
$874$	−11.3196	−0.382891
$875$	−108.684	−3.67418
$876$	−1.28452	−0.0434000
$877$	27.1987	0.918435	0.459217	−	0.888324i	$-0.348130\pi$
$877$	27.1987	0.918435	0.459217	+	0.888324i	$0.348130\pi$
$878$	−1.27313	−0.0429662
$879$	−13.1462	−0.443411
$880$	0	0
$881$	−3.88340	−0.130835	−0.0654175	−	0.997858i	$-0.520838\pi$
$881$	−3.88340	−0.130835	−0.0654175	+	0.997858i	$0.520838\pi$
$882$	14.3476	0.483108
$883$	−23.7755	−0.800110	−0.400055	−	0.916491i	$-0.631009\pi$
$883$	−23.7755	−0.800110	−0.400055	+	0.916491i	$0.631009\pi$
$884$	26.4030	0.888031
$885$	27.8378	0.935758
$886$	−23.9850	−0.805793
$887$	33.0417	1.10943	0.554716	−	0.832040i	$-0.312827\pi$
$887$	33.0417	1.10943	0.554716	+	0.832040i	$0.312827\pi$
$888$	−4.38091	−0.147014
$889$	−60.0530	−2.01411
$890$	−65.4594	−2.19420
$891$	0	0
$892$	−72.2571	−2.41935
$893$	−63.4668	−2.12384
$894$	8.65692	0.289531
$895$	−27.4441	−0.917355
$896$	48.3853	1.61644
$897$	2.91390	0.0972922
$898$	81.2062	2.70989
$899$	2.31838	0.0773222
$900$	63.3583	2.11194
$901$	−0.938674	−0.0312718
$902$	0	0
$903$	21.6584	0.720745
$904$	50.7157	1.68678
$905$	46.7046	1.55251
$906$	37.1935	1.23567
$907$	−8.10167	−0.269012	−0.134506	−	0.990913i	$-0.542945\pi$
$907$	−8.10167	−0.269012	−0.134506	+	0.990913i	$0.542945\pi$
$908$	−20.6557	−0.685485
$909$	−0.390059	−0.0129374
$910$	202.296	6.70605
$911$	−29.2790	−0.970056	−0.485028	−	0.874499i	$-0.661191\pi$
$911$	−29.2790	−0.970056	−0.485028	+	0.874499i	$0.661191\pi$
$912$	89.4414	2.96170
$913$	0	0
$914$	−88.0008	−2.91081
$915$	−41.8914	−1.38489
$916$	78.3181	2.58770
$917$	22.3535	0.738177
$918$	2.66608	0.0879937
$919$	8.51053	0.280736	0.140368	−	0.990099i	$-0.455171\pi$
$919$	8.51053	0.280736	0.140368	+	0.990099i	$0.455171\pi$
$920$	−19.4868	−0.642462
$921$	7.84384	0.258463
$922$	−93.2148	−3.06986
$923$	23.6379	0.778051
$924$	0	0
$925$	6.55797	0.215625
$926$	−74.4655	−2.44709
$927$	8.64999	0.284103
$928$	−86.0934	−2.82616
$929$	−33.4347	−1.09696	−0.548478	−	0.836165i	$-0.684792\pi$
$929$	−33.4347	−1.09696	−0.548478	+	0.836165i	$0.684792\pi$
$930$	−4.51918	−0.148190
$931$	−40.5317	−1.32837
$932$	−69.8119	−2.28677
$933$	21.2725	0.696429
$934$	−53.3898	−1.74697
$935$	0	0
$936$	−42.8307	−1.39997
$937$	34.5969	1.13023	0.565115	−	0.825012i	$-0.308832\pi$
$937$	34.5969	1.13023	0.565115	+	0.825012i	$0.308832\pi$
$938$	−40.6628	−1.32769
$939$	−16.1103	−0.525740
$940$	−179.568	−5.85686
$941$	−35.3897	−1.15367	−0.576836	−	0.816860i	$-0.695713\pi$
$941$	−35.3897	−1.15367	−0.576836	+	0.816860i	$0.695713\pi$
$942$	−7.89606	−0.257267
$943$	−5.25563	−0.171147
$944$	79.2433	2.57915
$945$	14.6794	0.477522
$946$	0	0
$947$	−28.4833	−0.925582	−0.462791	−	0.886468i	$-0.653152\pi$
$947$	−28.4833	−0.925582	−0.462791	+	0.886468i	$0.653152\pi$
$948$	67.1491	2.18090
$949$	−1.29987	−0.0421955
$950$	−249.068	−8.08082
$951$	−21.4298	−0.694908
$952$	−29.1566	−0.944972
$953$	9.95577	0.322499	0.161250	−	0.986914i	$-0.448448\pi$
$953$	9.95577	0.322499	0.161250	+	0.986914i	$0.448448\pi$
$954$	2.50258	0.0810240
$955$	−65.9265	−2.13333
$956$	43.5502	1.40852
$957$	0	0
$958$	62.8727	2.03133
$959$	17.5522	0.566790
$960$	68.7371	2.21848
$961$	−30.8349	−0.994674
$962$	−7.28606	−0.234912
$963$	9.95073	0.320658
$964$	78.3519	2.52355
$965$	66.9138	2.15403
$966$	−5.28845	−0.170153
$967$	−26.8081	−0.862092	−0.431046	−	0.902330i	$-0.641855\pi$
$967$	−26.8081	−0.862092	−0.431046	+	0.902330i	$0.641855\pi$
$968$	0	0
$969$	−7.53163	−0.241951
$970$	173.950	5.58519
$971$	39.5245	1.26840	0.634201	−	0.773168i	$-0.281329\pi$
$971$	39.5245	1.26840	0.634201	+	0.773168i	$0.281329\pi$
$972$	−5.10797	−0.163838
$973$	7.76917	0.249068
$974$	39.1680	1.25502
$975$	64.1152	2.05333
$976$	−119.248	−3.81704
$977$	−58.6742	−1.87715	−0.938577	−	0.345070i	$-0.887855\pi$
$977$	−58.6742	−1.87715	−0.938577	+	0.345070i	$0.887855\pi$
$978$	65.5864	2.09722
$979$	0	0
$980$	−114.677	−3.66322
$981$	−1.00632	−0.0321293
$982$	−76.4390	−2.43927
$983$	26.3697	0.841064	0.420532	−	0.907278i	$-0.361843\pi$
$983$	26.3697	0.841064	0.420532	+	0.907278i	$0.361843\pi$
$984$	77.2513	2.46268
$985$	108.182	3.44696
$986$	15.2122	0.484455
$987$	−29.6514	−0.943813
$988$	198.858	6.32652
$989$	−3.46982	−0.110334
$990$	0	0
$991$	−21.0543	−0.668813	−0.334406	−	0.942429i	$-0.608536\pi$
$991$	−21.0543	−0.668813	−0.334406	+	0.942429i	$0.608536\pi$
$992$	−6.13077	−0.194652
$993$	−10.9872	−0.348668
$994$	−42.9006	−1.36073
$995$	9.90881	0.314131
$996$	−24.4763	−0.775562
$997$	−51.1146	−1.61881	−0.809407	−	0.587248i	$-0.800211\pi$
$997$	−51.1146	−1.61881	−0.809407	+	0.587248i	$0.800211\pi$
$998$	17.6048	0.557270
$999$	−0.528706	−0.0167275

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6171.2.a.bo.1.14	yes	14
11.10	odd	2		6171.2.a.bn.1.1	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6171.2.a.bn.1.1	✓	14	11.10	odd	2
6171.2.a.bo.1.14	yes	14	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6171 = 3 \cdot 11^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6171.a (trivial)

\(f(q)\)	\(=\)	\(q+2.66608 q^{2} -1.00000 q^{3} +5.10797 q^{4} -4.17179 q^{5} -2.66608 q^{6} +3.51874 q^{7} +8.28610 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.66608 q^{2} -1.00000 q^{3} +5.10797 q^{4} -4.17179 q^{5} -2.66608 q^{6} +3.51874 q^{7} +8.28610 q^{8} +1.00000 q^{9} -11.1223 q^{10} -5.10797 q^{12} -5.16899 q^{13} +9.38123 q^{14} +4.17179 q^{15} +11.8754 q^{16} -1.00000 q^{17} +2.66608 q^{18} -7.53163 q^{19} -21.3094 q^{20} -3.51874 q^{21} +0.563727 q^{23} -8.28610 q^{24} +12.4038 q^{25} -13.7809 q^{26} -1.00000 q^{27} +17.9736 q^{28} -5.70584 q^{29} +11.1223 q^{30} -0.406317 q^{31} +15.0887 q^{32} -2.66608 q^{34} -14.6794 q^{35} +5.10797 q^{36} +0.528706 q^{37} -20.0799 q^{38} +5.16899 q^{39} -34.5678 q^{40} -9.32300 q^{41} -9.38123 q^{42} -6.15515 q^{43} -4.17179 q^{45} +1.50294 q^{46} +8.42670 q^{47} -11.8754 q^{48} +5.38153 q^{49} +33.0695 q^{50} +1.00000 q^{51} -26.4030 q^{52} +0.938674 q^{53} -2.66608 q^{54} +29.1566 q^{56} +7.53163 q^{57} -15.2122 q^{58} +6.67287 q^{59} +21.3094 q^{60} -10.0416 q^{61} -1.08327 q^{62} +3.51874 q^{63} +16.4767 q^{64} +21.5639 q^{65} -4.33448 q^{67} -5.10797 q^{68} -0.563727 q^{69} -39.1365 q^{70} -4.57303 q^{71} +8.28610 q^{72} +0.251474 q^{73} +1.40957 q^{74} -12.4038 q^{75} -38.4714 q^{76} +13.7809 q^{78} -13.1459 q^{79} -49.5418 q^{80} +1.00000 q^{81} -24.8558 q^{82} +4.79179 q^{83} -17.9736 q^{84} +4.17179 q^{85} -16.4101 q^{86} +5.70584 q^{87} +5.88541 q^{89} -11.1223 q^{90} -18.1883 q^{91} +2.87950 q^{92} +0.406317 q^{93} +22.4662 q^{94} +31.4204 q^{95} -15.0887 q^{96} -15.6397 q^{97} +14.3476 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{2} - 14 q^{3} + 14 q^{4} - 2 q^{6} - 6 q^{7} + 6 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q + 2 * q^2 - 14 * q^3 + 14 * q^4 - 2 * q^6 - 6 * q^7 + 6 * q^8 + 14 * q^9	\( 14 q + 2 q^{2} - 14 q^{3} + 14 q^{4} - 2 q^{6} - 6 q^{7} + 6 q^{8} + 14 q^{9} - 8 q^{10} - 14 q^{12} - 20 q^{13} + 4 q^{14} + 14 q^{16} - 14 q^{17} + 2 q^{18} - 16 q^{19} - 16 q^{20} + 6 q^{21} - 2 q^{23} - 6 q^{24} + 22 q^{25} - 4 q^{26} - 14 q^{27} + 30 q^{28} - 22 q^{29} + 8 q^{30} + 34 q^{32} - 2 q^{34} - 2 q^{35} + 14 q^{36} + 8 q^{37} - 16 q^{38} + 20 q^{39} - 74 q^{40} - 24 q^{41} - 4 q^{42} - 12 q^{43} - 26 q^{46} + 28 q^{47} - 14 q^{48} + 28 q^{49} + 50 q^{50} + 14 q^{51} - 48 q^{52} + 18 q^{53} - 2 q^{54} + 6 q^{56} + 16 q^{57} + 20 q^{59} + 16 q^{60} - 64 q^{61} - 62 q^{62} - 6 q^{63} - 4 q^{64} + 30 q^{65} + 10 q^{67} - 14 q^{68} + 2 q^{69} - 44 q^{70} - 8 q^{71} + 6 q^{72} - 44 q^{73} - 50 q^{74} - 22 q^{75} - 24 q^{76} + 4 q^{78} - 8 q^{79} - 102 q^{80} + 14 q^{81} - 46 q^{82} - 12 q^{83} - 30 q^{84} + 12 q^{86} + 22 q^{87} - 8 q^{89} - 8 q^{90} - 20 q^{91} - 20 q^{92} + 16 q^{94} + 30 q^{95} - 34 q^{96} - 14 q^{97} + 90 q^{98}+O(q^{100}) \) 14 * q + 2 * q^2 - 14 * q^3 + 14 * q^4 - 2 * q^6 - 6 * q^7 + 6 * q^8 + 14 * q^9 - 8 * q^10 - 14 * q^12 - 20 * q^13 + 4 * q^14 + 14 * q^16 - 14 * q^17 + 2 * q^18 - 16 * q^19 - 16 * q^20 + 6 * q^21 - 2 * q^23 - 6 * q^24 + 22 * q^25 - 4 * q^26 - 14 * q^27 + 30 * q^28 - 22 * q^29 + 8 * q^30 + 34 * q^32 - 2 * q^34 - 2 * q^35 + 14 * q^36 + 8 * q^37 - 16 * q^38 + 20 * q^39 - 74 * q^40 - 24 * q^41 - 4 * q^42 - 12 * q^43 - 26 * q^46 + 28 * q^47 - 14 * q^48 + 28 * q^49 + 50 * q^50 + 14 * q^51 - 48 * q^52 + 18 * q^53 - 2 * q^54 + 6 * q^56 + 16 * q^57 + 20 * q^59 + 16 * q^60 - 64 * q^61 - 62 * q^62 - 6 * q^63 - 4 * q^64 + 30 * q^65 + 10 * q^67 - 14 * q^68 + 2 * q^69 - 44 * q^70 - 8 * q^71 + 6 * q^72 - 44 * q^73 - 50 * q^74 - 22 * q^75 - 24 * q^76 + 4 * q^78 - 8 * q^79 - 102 * q^80 + 14 * q^81 - 46 * q^82 - 12 * q^83 - 30 * q^84 + 12 * q^86 + 22 * q^87 - 8 * q^89 - 8 * q^90 - 20 * q^91 - 20 * q^92 + 16 * q^94 + 30 * q^95 - 34 * q^96 - 14 * q^97 + 90 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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