LMFDB - Embedded newform 1805.2.a.l.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1805.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.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:	$14.4129975648$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{20})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 5 $ x^4 - 5*x^2 + 5
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.90211$ of defining polynomial
Character	$\chi$	$=$	1805.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.90211 q^{2} +1.90211 q^{3} +1.61803 q^{4} -1.00000 q^{5} +3.61803 q^{6} -4.23607 q^{7} -0.726543 q^{8} +0.618034 q^{9} +O(q^{10})$	\(q+1.90211 q^{2} +1.90211 q^{3} +1.61803 q^{4} -1.00000 q^{5} +3.61803 q^{6} -4.23607 q^{7} -0.726543 q^{8} +0.618034 q^{9} -1.90211 q^{10} -5.85410 q^{11} +3.07768 q^{12} -3.07768 q^{13} -8.05748 q^{14} -1.90211 q^{15} -4.61803 q^{16} +5.23607 q^{17} +1.17557 q^{18} -1.61803 q^{20} -8.05748 q^{21} -11.1352 q^{22} +4.09017 q^{23} -1.38197 q^{24} +1.00000 q^{25} -5.85410 q^{26} -4.53077 q^{27} -6.85410 q^{28} +2.80017 q^{29} -3.61803 q^{30} -1.90211 q^{31} -7.33094 q^{32} -11.1352 q^{33} +9.95959 q^{34} +4.23607 q^{35} +1.00000 q^{36} +2.80017 q^{37} -5.85410 q^{39} +0.726543 q^{40} +6.88191 q^{41} -15.3262 q^{42} +0.381966 q^{43} -9.47214 q^{44} -0.618034 q^{45} +7.77997 q^{46} -1.47214 q^{47} -8.78402 q^{48} +10.9443 q^{49} +1.90211 q^{50} +9.95959 q^{51} -4.97980 q^{52} -11.1352 q^{53} -8.61803 q^{54} +5.85410 q^{55} +3.07768 q^{56} +5.32624 q^{58} -14.0413 q^{59} -3.07768 q^{60} +3.94427 q^{61} -3.61803 q^{62} -2.61803 q^{63} -4.70820 q^{64} +3.07768 q^{65} -21.1803 q^{66} -5.98385 q^{67} +8.47214 q^{68} +7.77997 q^{69} +8.05748 q^{70} -0.171513 q^{71} -0.449028 q^{72} -1.00000 q^{73} +5.32624 q^{74} +1.90211 q^{75} +24.7984 q^{77} -11.1352 q^{78} +5.25731 q^{79} +4.61803 q^{80} -10.4721 q^{81} +13.0902 q^{82} -8.76393 q^{83} -13.0373 q^{84} -5.23607 q^{85} +0.726543 q^{86} +5.32624 q^{87} +4.25325 q^{88} -7.77997 q^{89} -1.17557 q^{90} +13.0373 q^{91} +6.61803 q^{92} -3.61803 q^{93} -2.80017 q^{94} -13.9443 q^{96} +2.62866 q^{97} +20.8172 q^{98} -3.61803 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 4 q^{5} + 10 q^{6} - 8 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 - 4 * q^5 + 10 * q^6 - 8 * q^7 - 2 * q^9	$ 4 q + 2 q^{4} - 4 q^{5} + 10 q^{6} - 8 q^{7} - 2 q^{9} - 10 q^{11} - 14 q^{16} + 12 q^{17} - 2 q^{20} - 6 q^{23} - 10 q^{24} + 4 q^{25} - 10 q^{26} - 14 q^{28} - 10 q^{30} + 8 q^{35} + 4 q^{36} - 10 q^{39} - 30 q^{42} + 6 q^{43} - 20 q^{44} + 2 q^{45} + 12 q^{47} + 8 q^{49} - 30 q^{54} + 10 q^{55} - 10 q^{58} - 20 q^{61} - 10 q^{62} - 6 q^{63} + 8 q^{64} - 40 q^{66} + 16 q^{68} - 4 q^{73} - 10 q^{74} + 50 q^{77} + 14 q^{80} - 24 q^{81} + 30 q^{82} - 44 q^{83} - 12 q^{85} - 10 q^{87} + 22 q^{92} - 10 q^{93} - 20 q^{96} - 10 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 - 4 * q^5 + 10 * q^6 - 8 * q^7 - 2 * q^9 - 10 * q^11 - 14 * q^16 + 12 * q^17 - 2 * q^20 - 6 * q^23 - 10 * q^24 + 4 * q^25 - 10 * q^26 - 14 * q^28 - 10 * q^30 + 8 * q^35 + 4 * q^36 - 10 * q^39 - 30 * q^42 + 6 * q^43 - 20 * q^44 + 2 * q^45 + 12 * q^47 + 8 * q^49 - 30 * q^54 + 10 * q^55 - 10 * q^58 - 20 * q^61 - 10 * q^62 - 6 * q^63 + 8 * q^64 - 40 * q^66 + 16 * q^68 - 4 * q^73 - 10 * q^74 + 50 * q^77 + 14 * q^80 - 24 * q^81 + 30 * q^82 - 44 * q^83 - 12 * q^85 - 10 * q^87 + 22 * q^92 - 10 * q^93 - 20 * q^96 - 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.90211	1.34500	0.672499	−	0.740098i	$-0.265221\pi$
$2$	1.90211	1.34500	0.672499	+	0.740098i	$0.265221\pi$
$3$	1.90211	1.09819	0.549093	−	0.835761i	$-0.314973\pi$
$3$	1.90211	1.09819	0.549093	+	0.835761i	$0.314973\pi$
$4$	1.61803	0.809017
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	3.61803	1.47706
$7$	−4.23607	−1.60108	−0.800542	−	0.599277i	$-0.795455\pi$
$7$	−4.23607	−1.60108	−0.800542	+	0.599277i	$0.795455\pi$
$8$	−0.726543	−0.256872
$9$	0.618034	0.206011
$10$	−1.90211	−0.601501
$11$	−5.85410	−1.76508	−0.882539	−	0.470239i	$-0.844168\pi$
$11$	−5.85410	−1.76508	−0.882539	+	0.470239i	$0.844168\pi$
$12$	3.07768	0.888451
$13$	−3.07768	−0.853596	−0.426798	−	0.904347i	$-0.640358\pi$
$13$	−3.07768	−0.853596	−0.426798	+	0.904347i	$0.640358\pi$
$14$	−8.05748	−2.15345
$15$	−1.90211	−0.491123
$16$	−4.61803	−1.15451
$17$	5.23607	1.26993	0.634967	−	0.772540i	$-0.281014\pi$
$17$	5.23607	1.26993	0.634967	+	0.772540i	$0.281014\pi$
$18$	1.17557	0.277085
$19$	0	0
$19$	0	0
$20$	−1.61803	−0.361803
$21$	−8.05748	−1.75829
$22$	−11.1352	−2.37402
$23$	4.09017	0.852859	0.426430	−	0.904521i	$-0.359771\pi$
$23$	4.09017	0.852859	0.426430	+	0.904521i	$0.359771\pi$
$24$	−1.38197	−0.282093
$25$	1.00000	0.200000
$26$	−5.85410	−1.14808
$27$	−4.53077	−0.871947
$28$	−6.85410	−1.29530
$29$	2.80017	0.519978	0.259989	−	0.965612i	$-0.416281\pi$
$29$	2.80017	0.519978	0.259989	+	0.965612i	$0.416281\pi$
$30$	−3.61803	−0.660560
$31$	−1.90211	−0.341630	−0.170815	−	0.985303i	$-0.554640\pi$
$31$	−1.90211	−0.341630	−0.170815	+	0.985303i	$0.554640\pi$
$32$	−7.33094	−1.29594
$33$	−11.1352	−1.93838
$34$	9.95959	1.70806
$35$	4.23607	0.716026
$36$	1.00000	0.166667
$37$	2.80017	0.460345	0.230172	−	0.973150i	$-0.426071\pi$
$37$	2.80017	0.460345	0.230172	+	0.973150i	$0.426071\pi$
$38$	0	0
$39$	−5.85410	−0.937407
$40$	0.726543	0.114876
$41$	6.88191	1.07477	0.537387	−	0.843336i	$-0.319412\pi$
$41$	6.88191	1.07477	0.537387	+	0.843336i	$0.319412\pi$
$42$	−15.3262	−2.36489
$43$	0.381966	0.0582493	0.0291246	−	0.999576i	$-0.490728\pi$
$43$	0.381966	0.0582493	0.0291246	+	0.999576i	$0.490728\pi$
$44$	−9.47214	−1.42798
$45$	−0.618034	−0.0921311
$46$	7.77997	1.14709
$47$	−1.47214	−0.214733	−0.107367	−	0.994220i	$-0.534242\pi$
$47$	−1.47214	−0.214733	−0.107367	+	0.994220i	$0.534242\pi$
$48$	−8.78402	−1.26786
$49$	10.9443	1.56347
$50$	1.90211	0.268999
$51$	9.95959	1.39462
$52$	−4.97980	−0.690574
$53$	−11.1352	−1.52953	−0.764766	−	0.644308i	$-0.777146\pi$
$53$	−11.1352	−1.52953	−0.764766	+	0.644308i	$0.777146\pi$
$54$	−8.61803	−1.17277
$55$	5.85410	0.789367
$56$	3.07768	0.411273
$57$	0	0
$58$	5.32624	0.699369
$59$	−14.0413	−1.82803	−0.914013	−	0.405685i	$-0.867033\pi$
$59$	−14.0413	−1.82803	−0.914013	+	0.405685i	$0.867033\pi$
$60$	−3.07768	−0.397327
$61$	3.94427	0.505012	0.252506	−	0.967595i	$-0.418745\pi$
$61$	3.94427	0.505012	0.252506	+	0.967595i	$0.418745\pi$
$62$	−3.61803	−0.459491
$63$	−2.61803	−0.329841
$64$	−4.70820	−0.588525
$65$	3.07768	0.381740
$66$	−21.1803	−2.60712
$67$	−5.98385	−0.731044	−0.365522	−	0.930803i	$-0.619110\pi$
$67$	−5.98385	−0.731044	−0.365522	+	0.930803i	$0.619110\pi$
$68$	8.47214	1.02740
$69$	7.77997	0.936598
$70$	8.05748	0.963053
$71$	−0.171513	−0.0203549	−0.0101774	−	0.999948i	$-0.503240\pi$
$71$	−0.171513	−0.0203549	−0.0101774	+	0.999948i	$0.503240\pi$
$72$	−0.449028	−0.0529185
$73$	−1.00000	−0.117041	−0.0585206	−	0.998286i	$-0.518638\pi$
$73$	−1.00000	−0.117041	−0.0585206	+	0.998286i	$0.518638\pi$
$74$	5.32624	0.619163
$75$	1.90211	0.219637
$76$	0	0
$77$	24.7984	2.82604
$78$	−11.1352	−1.26081
$79$	5.25731	0.591494	0.295747	−	0.955266i	$-0.404432\pi$
$79$	5.25731	0.591494	0.295747	+	0.955266i	$0.404432\pi$
$80$	4.61803	0.516312
$81$	−10.4721	−1.16357
$82$	13.0902	1.44557
$83$	−8.76393	−0.961967	−0.480983	−	0.876730i	$-0.659720\pi$
$83$	−8.76393	−0.961967	−0.480983	+	0.876730i	$0.659720\pi$
$84$	−13.0373	−1.42248
$85$	−5.23607	−0.567931
$86$	0.726543	0.0783451
$87$	5.32624	0.571033
$88$	4.25325	0.453398
$89$	−7.77997	−0.824675	−0.412337	−	0.911031i	$-0.635287\pi$
$89$	−7.77997	−0.824675	−0.412337	+	0.911031i	$0.635287\pi$
$90$	−1.17557	−0.123916
$91$	13.0373	1.36668
$92$	6.61803	0.689978
$93$	−3.61803	−0.375173
$94$	−2.80017	−0.288815
$95$	0	0
$96$	−13.9443	−1.42318
$97$	2.62866	0.266900	0.133450	−	0.991056i	$-0.457395\pi$
$97$	2.62866	0.266900	0.133450	+	0.991056i	$0.457395\pi$
$98$	20.8172	2.10286
$99$	−3.61803	−0.363626
$100$	1.61803	0.161803
$101$	3.29180	0.327546	0.163773	−	0.986498i	$-0.447634\pi$
$101$	3.29180	0.327546	0.163773	+	0.986498i	$0.447634\pi$
$102$	18.9443	1.87576
$103$	14.9394	1.47202	0.736011	−	0.676970i	$-0.236707\pi$
$103$	14.9394	1.47202	0.736011	+	0.676970i	$0.236707\pi$
$104$	2.23607	0.219265
$105$	8.05748	0.786330
$106$	−21.1803	−2.05722
$107$	8.33499	0.805774	0.402887	−	0.915250i	$-0.368007\pi$
$107$	8.33499	0.805774	0.402887	+	0.915250i	$0.368007\pi$
$108$	−7.33094	−0.705420
$109$	2.17963	0.208770	0.104385	−	0.994537i	$-0.466713\pi$
$109$	2.17963	0.208770	0.104385	+	0.994537i	$0.466713\pi$
$110$	11.1352	1.06170
$111$	5.32624	0.505544
$112$	19.5623	1.84846
$113$	−18.4661	−1.73714	−0.868572	−	0.495562i	$-0.834962\pi$
$113$	−18.4661	−1.73714	−0.868572	+	0.495562i	$0.834962\pi$
$114$	0	0
$115$	−4.09017	−0.381410
$116$	4.53077	0.420671
$117$	−1.90211	−0.175850
$118$	−26.7082	−2.45869
$119$	−22.1803	−2.03327
$120$	1.38197	0.126156
$121$	23.2705	2.11550
$122$	7.50245	0.679240
$123$	13.0902	1.18030
$124$	−3.07768	−0.276384
$125$	−1.00000	−0.0894427
$126$	−4.97980	−0.443636
$127$	−9.23305	−0.819301	−0.409650	−	0.912243i	$-0.634349\pi$
$127$	−9.23305	−0.819301	−0.409650	+	0.912243i	$0.634349\pi$
$128$	5.70634	0.504374
$129$	0.726543	0.0639685
$130$	5.85410	0.513439
$131$	−15.6180	−1.36455	−0.682277	−	0.731094i	$-0.739010\pi$
$131$	−15.6180	−1.36455	−0.682277	+	0.731094i	$0.739010\pi$
$132$	−18.0171	−1.56818
$133$	0	0
$134$	−11.3820	−0.983252
$135$	4.53077	0.389946
$136$	−3.80423	−0.326210
$137$	9.76393	0.834189	0.417095	−	0.908863i	$-0.363048\pi$
$137$	9.76393	0.834189	0.417095	+	0.908863i	$0.363048\pi$
$138$	14.7984	1.25972
$139$	−22.0902	−1.87366	−0.936832	−	0.349780i	$-0.886256\pi$
$139$	−22.0902	−1.87366	−0.936832	+	0.349780i	$0.886256\pi$
$140$	6.85410	0.579277
$141$	−2.80017	−0.235817
$142$	−0.326238	−0.0273773
$143$	18.0171	1.50666
$144$	−2.85410	−0.237842
$145$	−2.80017	−0.232541
$146$	−1.90211	−0.157420
$147$	20.8172	1.71698
$148$	4.53077	0.372427
$149$	7.09017	0.580849	0.290425	−	0.956898i	$-0.406203\pi$
$149$	7.09017	0.580849	0.290425	+	0.956898i	$0.406203\pi$
$150$	3.61803	0.295411
$151$	−0.620541	−0.0504989	−0.0252495	−	0.999681i	$-0.508038\pi$
$151$	−0.620541	−0.0504989	−0.0252495	+	0.999681i	$0.508038\pi$
$152$	0	0
$153$	3.23607	0.261621
$154$	47.1693	3.80101
$155$	1.90211	0.152781
$156$	−9.47214	−0.758378
$157$	−16.2705	−1.29853	−0.649264	−	0.760563i	$-0.724923\pi$
$157$	−16.2705	−1.29853	−0.649264	+	0.760563i	$0.724923\pi$
$158$	10.0000	0.795557
$159$	−21.1803	−1.67971
$160$	7.33094	0.579562
$161$	−17.3262	−1.36550
$162$	−19.9192	−1.56500
$163$	−25.1803	−1.97228	−0.986138	−	0.165926i	$-0.946939\pi$
$163$	−25.1803	−1.97228	−0.986138	+	0.165926i	$0.946939\pi$
$164$	11.1352	0.869510
$165$	11.1352	0.866871
$166$	−16.6700	−1.29384
$167$	−0.171513	−0.0132721	−0.00663605	−	0.999978i	$-0.502112\pi$
$167$	−0.171513	−0.0132721	−0.00663605	+	0.999978i	$0.502112\pi$
$168$	5.85410	0.451654
$169$	−3.52786	−0.271374
$170$	−9.95959	−0.763866
$171$	0	0
$172$	0.618034	0.0471246
$173$	13.2088	1.00425	0.502123	−	0.864796i	$-0.332553\pi$
$173$	13.2088	1.00425	0.502123	+	0.864796i	$0.332553\pi$
$174$	10.1311	0.768037
$175$	−4.23607	−0.320217
$176$	27.0344	2.03780
$177$	−26.7082	−2.00751
$178$	−14.7984	−1.10919
$179$	−10.1311	−0.757234	−0.378617	−	0.925553i	$-0.623600\pi$
$179$	−10.1311	−0.757234	−0.378617	+	0.925553i	$0.623600\pi$
$180$	−1.00000	−0.0745356
$181$	6.71040	0.498780	0.249390	−	0.968403i	$-0.419770\pi$
$181$	6.71040	0.498780	0.249390	+	0.968403i	$0.419770\pi$
$182$	24.7984	1.83818
$183$	7.50245	0.554597
$184$	−2.97168	−0.219075
$185$	−2.80017	−0.205873
$186$	−6.88191	−0.504606
$187$	−30.6525	−2.24153
$188$	−2.38197	−0.173723
$189$	19.1926	1.39606
$190$	0	0
$191$	13.0000	0.940647	0.470323	−	0.882494i	$-0.344137\pi$
$191$	13.0000	0.940647	0.470323	+	0.882494i	$0.344137\pi$
$192$	−8.95554	−0.646310
$193$	−1.45309	−0.104595	−0.0522977	−	0.998632i	$-0.516654\pi$
$193$	−1.45309	−0.104595	−0.0522977	+	0.998632i	$0.516654\pi$
$194$	5.00000	0.358979
$195$	5.85410	0.419221
$196$	17.7082	1.26487
$197$	14.8885	1.06076	0.530382	−	0.847759i	$-0.322048\pi$
$197$	14.8885	1.06076	0.530382	+	0.847759i	$0.322048\pi$
$198$	−6.88191	−0.489076
$199$	13.4164	0.951064	0.475532	−	0.879698i	$-0.342256\pi$
$199$	13.4164	0.951064	0.475532	+	0.879698i	$0.342256\pi$
$200$	−0.726543	−0.0513743
$201$	−11.3820	−0.802822
$202$	6.26137	0.440548
$203$	−11.8617	−0.832529
$204$	16.1150	1.12827
$205$	−6.88191	−0.480653
$206$	28.4164	1.97986
$207$	2.52786	0.175699
$208$	14.2128	0.985484
$209$	0	0
$210$	15.3262	1.05761
$211$	1.73060	0.119139	0.0595697	−	0.998224i	$-0.481027\pi$
$211$	1.73060	0.119139	0.0595697	+	0.998224i	$0.481027\pi$
$212$	−18.0171	−1.23742
$213$	−0.326238	−0.0223535
$214$	15.8541	1.08376
$215$	−0.381966	−0.0260499
$216$	3.29180	0.223978
$217$	8.05748	0.546977
$218$	4.14590	0.280796
$219$	−1.90211	−0.128533
$220$	9.47214	0.638611
$221$	−16.1150	−1.08401
$222$	10.1311	0.679955
$223$	14.8334	0.993317	0.496659	−	0.867946i	$-0.334560\pi$
$223$	14.8334	0.993317	0.496659	+	0.867946i	$0.334560\pi$
$224$	31.0543	2.07491
$225$	0.618034	0.0412023
$226$	−35.1246	−2.33645
$227$	−17.3965	−1.15465	−0.577324	−	0.816515i	$-0.695903\pi$
$227$	−17.3965	−1.15465	−0.577324	+	0.816515i	$0.695903\pi$
$228$	0	0
$229$	−18.1459	−1.19911	−0.599557	−	0.800332i	$-0.704657\pi$
$229$	−18.1459	−1.19911	−0.599557	+	0.800332i	$0.704657\pi$
$230$	−7.77997	−0.512996
$231$	47.1693	3.10351
$232$	−2.03444	−0.133568
$233$	1.76393	0.115559	0.0577795	−	0.998329i	$-0.481598\pi$
$233$	1.76393	0.115559	0.0577795	+	0.998329i	$0.481598\pi$
$234$	−3.61803	−0.236518
$235$	1.47214	0.0960316
$236$	−22.7194	−1.47890
$237$	10.0000	0.649570
$238$	−42.1895	−2.73474
$239$	−23.2148	−1.50164	−0.750820	−	0.660507i	$-0.770341\pi$
$239$	−23.2148	−1.50164	−0.750820	+	0.660507i	$0.770341\pi$
$240$	8.78402	0.567006
$241$	6.32688	0.407550	0.203775	−	0.979018i	$-0.434679\pi$
$241$	6.32688	0.407550	0.203775	+	0.979018i	$0.434679\pi$
$242$	44.2631	2.84534
$243$	−6.32688	−0.405870
$244$	6.38197	0.408564
$245$	−10.9443	−0.699204
$246$	24.8990	1.58750
$247$	0	0
$248$	1.38197	0.0877549
$249$	−16.6700	−1.05642
$250$	−1.90211	−0.120300
$251$	−3.00000	−0.189358	−0.0946792	−	0.995508i	$-0.530183\pi$
$251$	−3.00000	−0.189358	−0.0946792	+	0.995508i	$0.530183\pi$
$252$	−4.23607	−0.266847
$253$	−23.9443	−1.50536
$254$	−17.5623	−1.10196
$255$	−9.95959	−0.623694
$256$	20.2705	1.26691
$257$	3.24920	0.202679	0.101340	−	0.994852i	$-0.467687\pi$
$257$	3.24920	0.202679	0.101340	+	0.994852i	$0.467687\pi$
$258$	1.38197	0.0860374
$259$	−11.8617	−0.737051
$260$	4.97980	0.308834
$261$	1.73060	0.107121
$262$	−29.7073	−1.83532
$263$	−6.00000	−0.369976	−0.184988	−	0.982741i	$-0.559225\pi$
$263$	−6.00000	−0.369976	−0.184988	+	0.982741i	$0.559225\pi$
$264$	8.09017	0.497916
$265$	11.1352	0.684028
$266$	0	0
$267$	−14.7984	−0.905646
$268$	−9.68208	−0.591427
$269$	−19.6417	−1.19757	−0.598787	−	0.800908i	$-0.704350\pi$
$269$	−19.6417	−1.19757	−0.598787	+	0.800908i	$0.704350\pi$
$270$	8.61803	0.524477
$271$	8.61803	0.523508	0.261754	−	0.965135i	$-0.415699\pi$
$271$	8.61803	0.523508	0.261754	+	0.965135i	$0.415699\pi$
$272$	−24.1803	−1.46615
$273$	24.7984	1.50087
$274$	18.5721	1.12198
$275$	−5.85410	−0.353016
$276$	12.5882	0.757724
$277$	24.8328	1.49206	0.746030	−	0.665913i	$-0.231958\pi$
$277$	24.8328	1.49206	0.746030	+	0.665913i	$0.231958\pi$
$278$	−42.0180	−2.52007
$279$	−1.17557	−0.0703796
$280$	−3.07768	−0.183927
$281$	25.0705	1.49558	0.747790	−	0.663935i	$-0.231115\pi$
$281$	25.0705	1.49558	0.747790	+	0.663935i	$0.231115\pi$
$282$	−5.32624	−0.317173
$283$	−28.2705	−1.68051	−0.840254	−	0.542193i	$-0.817594\pi$
$283$	−28.2705	−1.68051	−0.840254	+	0.542193i	$0.817594\pi$
$284$	−0.277515	−0.0164675
$285$	0	0
$286$	34.2705	2.02646
$287$	−29.1522	−1.72080
$288$	−4.53077	−0.266978
$289$	10.4164	0.612730
$290$	−5.32624	−0.312767
$291$	5.00000	0.293105
$292$	−1.61803	−0.0946883
$293$	−13.8293	−0.807918	−0.403959	−	0.914777i	$-0.632366\pi$
$293$	−13.8293	−0.807918	−0.403959	+	0.914777i	$0.632366\pi$
$294$	39.5967	2.30933
$295$	14.0413	0.817518
$296$	−2.03444	−0.118250
$297$	26.5236	1.53905
$298$	13.4863	0.781241
$299$	−12.5882	−0.727997
$300$	3.07768	0.177690
$301$	−1.61803	−0.0932619
$302$	−1.18034	−0.0679209
$303$	6.26137	0.359706
$304$	0	0
$305$	−3.94427	−0.225848
$306$	6.15537	0.351879
$307$	−18.3601	−1.04787	−0.523933	−	0.851759i	$-0.675536\pi$
$307$	−18.3601	−1.04787	−0.523933	+	0.851759i	$0.675536\pi$
$308$	40.1246	2.28631
$309$	28.4164	1.61655
$310$	3.61803	0.205491
$311$	−2.76393	−0.156728	−0.0783641	−	0.996925i	$-0.524970\pi$
$311$	−2.76393	−0.156728	−0.0783641	+	0.996925i	$0.524970\pi$
$312$	4.25325	0.240793
$313$	3.27051	0.184860	0.0924301	−	0.995719i	$-0.470537\pi$
$313$	3.27051	0.184860	0.0924301	+	0.995719i	$0.470537\pi$
$314$	−30.9483	−1.74652
$315$	2.61803	0.147510
$316$	8.50651	0.478528
$317$	16.4580	0.924373	0.462186	−	0.886783i	$-0.347065\pi$
$317$	16.4580	0.924373	0.462186	+	0.886783i	$0.347065\pi$
$318$	−40.2874	−2.25921
$319$	−16.3925	−0.917802
$320$	4.70820	0.263197
$321$	15.8541	0.884890
$322$	−32.9565	−1.83659
$323$	0	0
$324$	−16.9443	−0.941348
$325$	−3.07768	−0.170719
$326$	−47.8959	−2.65271
$327$	4.14590	0.229269
$328$	−5.00000	−0.276079
$329$	6.23607	0.343806
$330$	21.1803	1.16594
$331$	19.9192	1.09486	0.547429	−	0.836852i	$-0.315607\pi$
$331$	19.9192	1.09486	0.547429	+	0.836852i	$0.315607\pi$
$332$	−14.1803	−0.778247
$333$	1.73060	0.0948363
$334$	−0.326238	−0.0178509
$335$	5.98385	0.326933
$336$	37.2097	2.02996
$337$	−28.4257	−1.54845	−0.774223	−	0.632913i	$-0.781859\pi$
$337$	−28.4257	−1.54845	−0.774223	+	0.632913i	$0.781859\pi$
$338$	−6.71040	−0.364997
$339$	−35.1246	−1.90771
$340$	−8.47214	−0.459466
$341$	11.1352	0.603003
$342$	0	0
$343$	−16.7082	−0.902158
$344$	−0.277515	−0.0149626
$345$	−7.77997	−0.418859
$346$	25.1246	1.35071
$347$	16.4721	0.884271	0.442135	−	0.896948i	$-0.354221\pi$
$347$	16.4721	0.884271	0.442135	+	0.896948i	$0.354221\pi$
$348$	8.61803	0.461975
$349$	−2.56231	−0.137157	−0.0685785	−	0.997646i	$-0.521846\pi$
$349$	−2.56231	−0.137157	−0.0685785	+	0.997646i	$0.521846\pi$
$350$	−8.05748	−0.430690
$351$	13.9443	0.744290
$352$	42.9161	2.28743
$353$	3.67376	0.195535	0.0977673	−	0.995209i	$-0.468830\pi$
$353$	3.67376	0.195535	0.0977673	+	0.995209i	$0.468830\pi$
$354$	−50.8020	−2.70010
$355$	0.171513	0.00910299
$356$	−12.5882	−0.667176
$357$	−42.1895	−2.23291
$358$	−19.2705	−1.01848
$359$	7.38197	0.389605	0.194803	−	0.980842i	$-0.437593\pi$
$359$	7.38197	0.389605	0.194803	+	0.980842i	$0.437593\pi$
$360$	0.449028	0.0236659
$361$	0	0
$362$	12.7639	0.670857
$363$	44.2631	2.32321
$364$	21.0948	1.10567
$365$	1.00000	0.0523424
$366$	14.2705	0.745931
$367$	31.0689	1.62178	0.810891	−	0.585197i	$-0.198983\pi$
$367$	31.0689	1.62178	0.810891	+	0.585197i	$0.198983\pi$
$368$	−18.8885	−0.984633
$369$	4.25325	0.221416
$370$	−5.32624	−0.276898
$371$	47.1693	2.44891
$372$	−5.85410	−0.303521
$373$	−5.42882	−0.281094	−0.140547	−	0.990074i	$-0.544886\pi$
$373$	−5.42882	−0.281094	−0.140547	+	0.990074i	$0.544886\pi$
$374$	−58.3045	−3.01485
$375$	−1.90211	−0.0982247
$376$	1.06957	0.0551588
$377$	−8.61803	−0.443851
$378$	36.5066	1.87770
$379$	12.8658	0.660870	0.330435	−	0.943829i	$-0.392805\pi$
$379$	12.8658	0.660870	0.330435	+	0.943829i	$0.392805\pi$
$380$	0	0
$381$	−17.5623	−0.899744
$382$	24.7275	1.26517
$383$	4.25325	0.217331	0.108666	−	0.994078i	$-0.465342\pi$
$383$	4.25325	0.217331	0.108666	+	0.994078i	$0.465342\pi$
$384$	10.8541	0.553896
$385$	−24.7984	−1.26384
$386$	−2.76393	−0.140680
$387$	0.236068	0.0120000
$388$	4.25325	0.215926
$389$	−20.8541	−1.05734	−0.528672	−	0.848826i	$-0.677310\pi$
$389$	−20.8541	−1.05734	−0.528672	+	0.848826i	$0.677310\pi$
$390$	11.1352	0.563851
$391$	21.4164	1.08307
$392$	−7.95148	−0.401610
$393$	−29.7073	−1.49853
$394$	28.3197	1.42673
$395$	−5.25731	−0.264524
$396$	−5.85410	−0.294180
$397$	−23.8328	−1.19613	−0.598067	−	0.801446i	$-0.704064\pi$
$397$	−23.8328	−1.19613	−0.598067	+	0.801446i	$0.704064\pi$
$398$	25.5195	1.27918
$399$	0	0
$400$	−4.61803	−0.230902
$401$	−9.06154	−0.452512	−0.226256	−	0.974068i	$-0.572649\pi$
$401$	−9.06154	−0.452512	−0.226256	+	0.974068i	$0.572649\pi$
$402$	−21.6498	−1.07979
$403$	5.85410	0.291614
$404$	5.32624	0.264990
$405$	10.4721	0.520365
$406$	−22.5623	−1.11975
$407$	−16.3925	−0.812545
$408$	−7.23607	−0.358239
$409$	−21.7153	−1.07375	−0.536876	−	0.843661i	$-0.680396\pi$
$409$	−21.7153	−1.07375	−0.536876	+	0.843661i	$0.680396\pi$
$410$	−13.0902	−0.646477
$411$	18.5721	0.916094
$412$	24.1724	1.19089
$413$	59.4800	2.92682
$414$	4.80828	0.236314
$415$	8.76393	0.430205
$416$	22.5623	1.10621
$417$	−42.0180	−2.05763
$418$	0	0
$419$	26.1803	1.27899	0.639497	−	0.768794i	$-0.279143\pi$
$419$	26.1803	1.27899	0.639497	+	0.768794i	$0.279143\pi$
$420$	13.0373	0.636154
$421$	11.5842	0.564579	0.282289	−	0.959329i	$-0.408906\pi$
$421$	11.5842	0.564579	0.282289	+	0.959329i	$0.408906\pi$
$422$	3.29180	0.160242
$423$	−0.909830	−0.0442375
$424$	8.09017	0.392893
$425$	5.23607	0.253987
$426$	−0.620541	−0.0300653
$427$	−16.7082	−0.808567
$428$	13.4863	0.651885
$429$	34.2705	1.65460
$430$	−0.726543	−0.0350370
$431$	−6.88191	−0.331490	−0.165745	−	0.986169i	$-0.553003\pi$
$431$	−6.88191	−0.331490	−0.165745	+	0.986169i	$0.553003\pi$
$432$	20.9232	1.00667
$433$	6.04937	0.290714	0.145357	−	0.989379i	$-0.453567\pi$
$433$	6.04937	0.290714	0.145357	+	0.989379i	$0.453567\pi$
$434$	15.3262	0.735683
$435$	−5.32624	−0.255374
$436$	3.52671	0.168899
$437$	0	0
$438$	−3.61803	−0.172876
$439$	−5.64083	−0.269222	−0.134611	−	0.990899i	$-0.542978\pi$
$439$	−5.64083	−0.269222	−0.134611	+	0.990899i	$0.542978\pi$
$440$	−4.25325	−0.202766
$441$	6.76393	0.322092
$442$	−30.6525	−1.45799
$443$	34.7771	1.65231	0.826155	−	0.563443i	$-0.190524\pi$
$443$	34.7771	1.65231	0.826155	+	0.563443i	$0.190524\pi$
$444$	8.61803	0.408994
$445$	7.77997	0.368806
$446$	28.2148	1.33601
$447$	13.4863	0.637880
$448$	19.9443	0.942278
$449$	−5.64083	−0.266207	−0.133104	−	0.991102i	$-0.542494\pi$
$449$	−5.64083	−0.266207	−0.133104	+	0.991102i	$0.542494\pi$
$450$	1.17557	0.0554169
$451$	−40.2874	−1.89706
$452$	−29.8788	−1.40538
$453$	−1.18034	−0.0554572
$454$	−33.0902	−1.55300
$455$	−13.0373	−0.611197
$456$	0	0
$457$	5.23607	0.244933	0.122466	−	0.992473i	$-0.460920\pi$
$457$	5.23607	0.244933	0.122466	+	0.992473i	$0.460920\pi$
$458$	−34.5155	−1.61281
$459$	−23.7234	−1.10731
$460$	−6.61803	−0.308567
$461$	−8.00000	−0.372597	−0.186299	−	0.982493i	$-0.559649\pi$
$461$	−8.00000	−0.372597	−0.186299	+	0.982493i	$0.559649\pi$
$462$	89.7214	4.17422
$463$	0.145898	0.00678046	0.00339023	−	0.999994i	$-0.498921\pi$
$463$	0.145898	0.00678046	0.00339023	+	0.999994i	$0.498921\pi$
$464$	−12.9313	−0.600319
$465$	3.61803	0.167782
$466$	3.35520	0.155427
$467$	−9.18034	−0.424815	−0.212408	−	0.977181i	$-0.568130\pi$
$467$	−9.18034	−0.424815	−0.212408	+	0.977181i	$0.568130\pi$
$468$	−3.07768	−0.142266
$469$	25.3480	1.17046
$470$	2.80017	0.129162
$471$	−30.9483	−1.42602
$472$	10.2016	0.469568
$473$	−2.23607	−0.102815
$474$	19.0211	0.873669
$475$	0	0
$476$	−35.8885	−1.64495
$477$	−6.88191	−0.315101
$478$	−44.1571	−2.01970
$479$	−11.4377	−0.522602	−0.261301	−	0.965257i	$-0.584151\pi$
$479$	−11.4377	−0.522602	−0.261301	+	0.965257i	$0.584151\pi$
$480$	13.9443	0.636466
$481$	−8.61803	−0.392949
$482$	12.0344	0.548154
$483$	−32.9565	−1.49957
$484$	37.6525	1.71148
$485$	−2.62866	−0.119361
$486$	−12.0344	−0.545893
$487$	21.0292	0.952926	0.476463	−	0.879195i	$-0.341919\pi$
$487$	21.0292	0.952926	0.476463	+	0.879195i	$0.341919\pi$
$488$	−2.86568	−0.129723
$489$	−47.8959	−2.16593
$490$	−20.8172	−0.940427
$491$	37.2705	1.68199	0.840997	−	0.541039i	$-0.181969\pi$
$491$	37.2705	1.68199	0.840997	+	0.541039i	$0.181969\pi$
$492$	21.1803	0.954883
$493$	14.6619	0.660338
$494$	0	0
$495$	3.61803	0.162619
$496$	8.78402	0.394414
$497$	0.726543	0.0325899
$498$	−31.7082	−1.42088
$499$	−29.5279	−1.32185	−0.660924	−	0.750453i	$-0.729836\pi$
$499$	−29.5279	−1.32185	−0.660924	+	0.750453i	$0.729836\pi$
$500$	−1.61803	−0.0723607
$501$	−0.326238	−0.0145752
$502$	−5.70634	−0.254686
$503$	31.6525	1.41131	0.705657	−	0.708554i	$-0.250652\pi$
$503$	31.6525	1.41131	0.705657	+	0.708554i	$0.250652\pi$
$504$	1.90211	0.0847268
$505$	−3.29180	−0.146483
$506$	−45.5447	−2.02471
$507$	−6.71040	−0.298019
$508$	−14.9394	−0.662828
$509$	−30.1563	−1.33665	−0.668327	−	0.743868i	$-0.732989\pi$
$509$	−30.1563	−1.33665	−0.668327	+	0.743868i	$0.732989\pi$
$510$	−18.9443	−0.838866
$511$	4.23607	0.187393
$512$	27.1441	1.19961
$513$	0	0
$514$	6.18034	0.272603
$515$	−14.9394	−0.658308
$516$	1.17557	0.0517516
$517$	8.61803	0.379021
$518$	−22.5623	−0.991331
$519$	25.1246	1.10285
$520$	−2.23607	−0.0980581
$521$	32.6789	1.43169	0.715845	−	0.698259i	$-0.246042\pi$
$521$	32.6789	1.43169	0.715845	+	0.698259i	$0.246042\pi$
$522$	3.29180	0.144078
$523$	6.53888	0.285925	0.142963	−	0.989728i	$-0.454337\pi$
$523$	6.53888	0.285925	0.142963	+	0.989728i	$0.454337\pi$
$524$	−25.2705	−1.10395
$525$	−8.05748	−0.351657
$526$	−11.4127	−0.497616
$527$	−9.95959	−0.433847
$528$	51.4226	2.23788
$529$	−6.27051	−0.272631
$530$	21.1803	0.920015
$531$	−8.67802	−0.376594
$532$	0	0
$533$	−21.1803	−0.917422
$534$	−28.1482	−1.21809
$535$	−8.33499	−0.360353
$536$	4.34752	0.187784
$537$	−19.2705	−0.831584
$538$	−37.3607	−1.61073
$539$	−64.0689	−2.75964
$540$	7.33094	0.315473
$541$	−24.5967	−1.05750	−0.528748	−	0.848779i	$-0.677338\pi$
$541$	−24.5967	−1.05750	−0.528748	+	0.848779i	$0.677338\pi$
$542$	16.3925	0.704117
$543$	12.7639	0.547753
$544$	−38.3853	−1.64576
$545$	−2.17963	−0.0933650
$546$	47.1693	2.01866
$547$	21.2663	0.909280	0.454640	−	0.890675i	$-0.349768\pi$
$547$	21.2663	0.909280	0.454640	+	0.890675i	$0.349768\pi$
$548$	15.7984	0.674873
$549$	2.43769	0.104038
$550$	−11.1352	−0.474805
$551$	0	0
$552$	−5.65248	−0.240585
$553$	−22.2703	−0.947031
$554$	47.2348	2.00682
$555$	−5.32624	−0.226086
$556$	−35.7426	−1.51583
$557$	−31.0689	−1.31643	−0.658215	−	0.752830i	$-0.728688\pi$
$557$	−31.0689	−1.31643	−0.658215	+	0.752830i	$0.728688\pi$
$558$	−2.23607	−0.0946603
$559$	−1.17557	−0.0497213
$560$	−19.5623	−0.826658
$561$	−58.3045	−2.46162
$562$	47.6869	2.01155
$563$	4.35926	0.183721	0.0918604	−	0.995772i	$-0.470719\pi$
$563$	4.35926	0.183721	0.0918604	+	0.995772i	$0.470719\pi$
$564$	−4.53077	−0.190780
$565$	18.4661	0.776875
$566$	−53.7737	−2.26028
$567$	44.3607	1.86297
$568$	0.124612	0.00522859
$569$	25.7970	1.08147	0.540734	−	0.841194i	$-0.318147\pi$
$569$	25.7970	1.08147	0.540734	+	0.841194i	$0.318147\pi$
$570$	0	0
$571$	−25.8541	−1.08196	−0.540980	−	0.841035i	$-0.681947\pi$
$571$	−25.8541	−1.08196	−0.540980	+	0.841035i	$0.681947\pi$
$572$	29.1522	1.21892
$573$	24.7275	1.03300
$574$	−55.4508	−2.31447
$575$	4.09017	0.170572
$576$	−2.90983	−0.121243
$577$	8.52786	0.355020	0.177510	−	0.984119i	$-0.443196\pi$
$577$	8.52786	0.355020	0.177510	+	0.984119i	$0.443196\pi$
$578$	19.8132	0.824120
$579$	−2.76393	−0.114865
$580$	−4.53077	−0.188130
$581$	37.1246	1.54019
$582$	9.51057	0.394226
$583$	65.1864	2.69974
$584$	0.726543	0.0300645
$585$	1.90211	0.0786427
$586$	−26.3050	−1.08665
$587$	36.4164	1.50307	0.751533	−	0.659695i	$-0.229315\pi$
$587$	36.4164	1.50307	0.751533	+	0.659695i	$0.229315\pi$
$588$	33.6830	1.38906
$589$	0	0
$590$	26.7082	1.09956
$591$	28.3197	1.16492
$592$	−12.9313	−0.531472
$593$	20.7082	0.850384	0.425192	−	0.905103i	$-0.360207\pi$
$593$	20.7082	0.850384	0.425192	+	0.905103i	$0.360207\pi$
$594$	50.4508	2.07002
$595$	22.1803	0.909305
$596$	11.4721	0.469917
$597$	25.5195	1.04444
$598$	−23.9443	−0.979154
$599$	30.0503	1.22782	0.613911	−	0.789375i	$-0.289595\pi$
$599$	30.0503	1.22782	0.613911	+	0.789375i	$0.289595\pi$
$600$	−1.38197	−0.0564185
$601$	−10.5146	−0.428900	−0.214450	−	0.976735i	$-0.568796\pi$
$601$	−10.5146	−0.428900	−0.214450	+	0.976735i	$0.568796\pi$
$602$	−3.07768	−0.125437
$603$	−3.69822	−0.150603
$604$	−1.00406	−0.0408545
$605$	−23.2705	−0.946081
$606$	11.9098	0.483804
$607$	16.2210	0.658389	0.329194	−	0.944262i	$-0.393223\pi$
$607$	16.2210	0.658389	0.329194	+	0.944262i	$0.393223\pi$
$608$	0	0
$609$	−22.5623	−0.914271
$610$	−7.50245	−0.303765
$611$	4.53077	0.183295
$612$	5.23607	0.211656
$613$	26.5279	1.07145	0.535725	−	0.844392i	$-0.320038\pi$
$613$	26.5279	1.07145	0.535725	+	0.844392i	$0.320038\pi$
$614$	−34.9230	−1.40938
$615$	−13.0902	−0.527847
$616$	−18.0171	−0.725929
$617$	21.6180	0.870309	0.435155	−	0.900356i	$-0.356694\pi$
$617$	21.6180	0.870309	0.435155	+	0.900356i	$0.356694\pi$
$618$	54.0512	2.17426
$619$	39.5410	1.58929	0.794644	−	0.607076i	$-0.207658\pi$
$619$	39.5410	1.58929	0.794644	+	0.607076i	$0.207658\pi$
$620$	3.07768	0.123603
$621$	−18.5316	−0.743648
$622$	−5.25731	−0.210799
$623$	32.9565	1.32037
$624$	27.0344	1.08224
$625$	1.00000	0.0400000
$626$	6.22088	0.248636
$627$	0	0
$628$	−26.3262	−1.05053
$629$	14.6619	0.584607
$630$	4.97980	0.198400
$631$	−41.1803	−1.63936	−0.819682	−	0.572819i	$-0.805850\pi$
$631$	−41.1803	−1.63936	−0.819682	+	0.572819i	$0.805850\pi$
$632$	−3.81966	−0.151938
$633$	3.29180	0.130837
$634$	31.3050	1.24328
$635$	9.23305	0.366402
$636$	−34.2705	−1.35891
$637$	−33.6830	−1.33457
$638$	−31.1803	−1.23444
$639$	−0.106001	−0.00419334
$640$	−5.70634	−0.225563
$641$	36.6952	1.44937	0.724686	−	0.689079i	$-0.241985\pi$
$641$	36.6952	1.44937	0.724686	+	0.689079i	$0.241985\pi$
$642$	30.1563	1.19017
$643$	−38.4721	−1.51719	−0.758596	−	0.651561i	$-0.774115\pi$
$643$	−38.4721	−1.51719	−0.758596	+	0.651561i	$0.774115\pi$
$644$	−28.0344	−1.10471
$645$	−0.726543	−0.0286076
$646$	0	0
$647$	8.52786	0.335265	0.167632	−	0.985850i	$-0.446388\pi$
$647$	8.52786	0.335265	0.167632	+	0.985850i	$0.446388\pi$
$648$	7.60845	0.298888
$649$	82.1994	3.22661
$650$	−5.85410	−0.229617
$651$	15.3262	0.600683
$652$	−40.7426	−1.59561
$653$	−13.7984	−0.539972	−0.269986	−	0.962864i	$-0.587019\pi$
$653$	−13.7984	−0.539972	−0.269986	+	0.962864i	$0.587019\pi$
$654$	7.88597	0.308366
$655$	15.6180	0.610247
$656$	−31.7809	−1.24084
$657$	−0.618034	−0.0241118
$658$	11.8617	0.462417
$659$	−7.26543	−0.283021	−0.141510	−	0.989937i	$-0.545196\pi$
$659$	−7.26543	−0.283021	−0.141510	+	0.989937i	$0.545196\pi$
$660$	18.0171	0.701314
$661$	29.3238	1.14056	0.570281	−	0.821450i	$-0.306834\pi$
$661$	29.3238	1.14056	0.570281	+	0.821450i	$0.306834\pi$
$662$	37.8885	1.47258
$663$	−30.6525	−1.19044
$664$	6.36737	0.247102
$665$	0	0
$666$	3.29180	0.127555
$667$	11.4532	0.443468
$668$	−0.277515	−0.0107374
$669$	28.2148	1.09085
$670$	11.3820	0.439724
$671$	−23.0902	−0.891386
$672$	59.0689	2.27863
$673$	−24.2380	−0.934304	−0.467152	−	0.884177i	$-0.654720\pi$
$673$	−24.2380	−0.934304	−0.467152	+	0.884177i	$0.654720\pi$
$674$	−54.0689	−2.08266
$675$	−4.53077	−0.174389
$676$	−5.70820	−0.219546
$677$	−33.5770	−1.29047	−0.645235	−	0.763985i	$-0.723240\pi$
$677$	−33.5770	−1.29047	−0.645235	+	0.763985i	$0.723240\pi$
$678$	−66.8110	−2.56586
$679$	−11.1352	−0.427328
$680$	3.80423	0.145885
$681$	−33.0902	−1.26802
$682$	21.1803	0.811037
$683$	−28.0422	−1.07300	−0.536502	−	0.843899i	$-0.680255\pi$
$683$	−28.0422	−1.07300	−0.536502	+	0.843899i	$0.680255\pi$
$684$	0	0
$685$	−9.76393	−0.373061
$686$	−31.7809	−1.21340
$687$	−34.5155	−1.31685
$688$	−1.76393	−0.0672493
$689$	34.2705	1.30560
$690$	−14.7984	−0.563364
$691$	−12.2361	−0.465482	−0.232741	−	0.972539i	$-0.574769\pi$
$691$	−12.2361	−0.465482	−0.232741	+	0.972539i	$0.574769\pi$
$692$	21.3723	0.812452
$693$	15.3262	0.582196
$694$	31.3319	1.18934
$695$	22.0902	0.837928
$696$	−3.86974	−0.146682
$697$	36.0341	1.36489
$698$	−4.87380	−0.184476
$699$	3.35520	0.126905
$700$	−6.85410	−0.259061
$701$	−31.9098	−1.20522	−0.602609	−	0.798037i	$-0.705872\pi$
$701$	−31.9098	−1.20522	−0.602609	+	0.798037i	$0.705872\pi$
$702$	26.5236	1.00107
$703$	0	0
$704$	27.5623	1.03879
$705$	2.80017	0.105460
$706$	6.98791	0.262993
$707$	−13.9443	−0.524428
$708$	−43.2148	−1.62411
$709$	36.1803	1.35878	0.679391	−	0.733777i	$-0.262244\pi$
$709$	36.1803	1.35878	0.679391	+	0.733777i	$0.262244\pi$
$710$	0.326238	0.0122435
$711$	3.24920	0.121854
$712$	5.65248	0.211835
$713$	−7.77997	−0.291362
$714$	−80.2492	−3.00325
$715$	−18.0171	−0.673800
$716$	−16.3925	−0.612616
$717$	−44.1571	−1.64908
$718$	14.0413	0.524018
$719$	−30.9098	−1.15274	−0.576371	−	0.817188i	$-0.695532\pi$
$719$	−30.9098	−1.15274	−0.576371	+	0.817188i	$0.695532\pi$
$720$	2.85410	0.106366
$721$	−63.2843	−2.35683
$722$	0	0
$723$	12.0344	0.447566
$724$	10.8576	0.403521
$725$	2.80017	0.103996
$726$	84.1935	3.12471
$727$	34.3607	1.27437	0.637184	−	0.770712i	$-0.280099\pi$
$727$	34.3607	1.27437	0.637184	+	0.770712i	$0.280099\pi$
$728$	−9.47214	−0.351061
$729$	19.3820	0.717851
$730$	1.90211	0.0704004
$731$	2.00000	0.0739727
$732$	12.1392	0.448679
$733$	−11.0000	−0.406294	−0.203147	−	0.979148i	$-0.565117\pi$
$733$	−11.0000	−0.406294	−0.203147	+	0.979148i	$0.565117\pi$
$734$	59.0965	2.18129
$735$	−20.8172	−0.767856
$736$	−29.9848	−1.10525
$737$	35.0301	1.29035
$738$	8.09017	0.297803
$739$	−27.7639	−1.02131	−0.510656	−	0.859785i	$-0.670598\pi$
$739$	−27.7639	−1.02131	−0.510656	+	0.859785i	$0.670598\pi$
$740$	−4.53077	−0.166554
$741$	0	0
$742$	89.7214	3.29377
$743$	5.98385	0.219526	0.109763	−	0.993958i	$-0.464991\pi$
$743$	5.98385	0.219526	0.109763	+	0.993958i	$0.464991\pi$
$744$	2.62866	0.0963712
$745$	−7.09017	−0.259764
$746$	−10.3262	−0.378070
$747$	−5.41641	−0.198176
$748$	−49.5967	−1.81344
$749$	−35.3076	−1.29011
$750$	−3.61803	−0.132112
$751$	−50.4590	−1.84127	−0.920637	−	0.390419i	$-0.872330\pi$
$751$	−50.4590	−1.84127	−0.920637	+	0.390419i	$0.872330\pi$
$752$	6.79837	0.247911
$753$	−5.70634	−0.207951
$754$	−16.3925	−0.596979
$755$	0.620541	0.0225838
$756$	31.0543	1.12944
$757$	2.97871	0.108263	0.0541316	−	0.998534i	$-0.482761\pi$
$757$	2.97871	0.108263	0.0541316	+	0.998534i	$0.482761\pi$
$758$	24.4721	0.888868
$759$	−45.5447	−1.65317
$760$	0	0
$761$	−18.8197	−0.682212	−0.341106	−	0.940025i	$-0.610802\pi$
$761$	−18.8197	−0.682212	−0.341106	+	0.940025i	$0.610802\pi$
$762$	−33.4055	−1.21015
$763$	−9.23305	−0.334259
$764$	21.0344	0.760999
$765$	−3.23607	−0.117000
$766$	8.09017	0.292310
$767$	43.2148	1.56040
$768$	38.5568	1.39130
$769$	−13.2705	−0.478547	−0.239273	−	0.970952i	$-0.576909\pi$
$769$	−13.2705	−0.478547	−0.239273	+	0.970952i	$0.576909\pi$
$770$	−47.1693	−1.69986
$771$	6.18034	0.222580
$772$	−2.35114	−0.0846194
$773$	32.5074	1.16921	0.584606	−	0.811318i	$-0.301249\pi$
$773$	32.5074	1.16921	0.584606	+	0.811318i	$0.301249\pi$
$774$	0.449028	0.0161400
$775$	−1.90211	−0.0683259
$776$	−1.90983	−0.0685589
$777$	−22.5623	−0.809418
$778$	−39.6669	−1.42213
$779$	0	0
$780$	9.47214	0.339157
$781$	1.00406	0.0359280
$782$	40.7364	1.45673
$783$	−12.6869	−0.453393
$784$	−50.5410	−1.80504
$785$	16.2705	0.580719
$786$	−56.5066	−2.01552
$787$	−20.1312	−0.717599	−0.358800	−	0.933415i	$-0.616814\pi$
$787$	−20.1312	−0.717599	−0.358800	+	0.933415i	$0.616814\pi$
$788$	24.0902	0.858177
$789$	−11.4127	−0.406302
$790$	−10.0000	−0.355784
$791$	78.2237	2.78131
$792$	2.62866	0.0934052
$793$	−12.1392	−0.431076
$794$	−45.3327	−1.60880
$795$	21.1803	0.751189
$796$	21.7082	0.769427
$797$	23.7234	0.840326	0.420163	−	0.907449i	$-0.361973\pi$
$797$	23.7234	0.840326	0.420163	+	0.907449i	$0.361973\pi$
$798$	0	0
$799$	−7.70820	−0.272697
$800$	−7.33094	−0.259188
$801$	−4.80828	−0.169892
$802$	−17.2361	−0.608627
$803$	5.85410	0.206587
$804$	−18.4164	−0.649497
$805$	17.3262	0.610670
$806$	11.1352	0.392219
$807$	−37.3607	−1.31516
$808$	−2.39163	−0.0841372
$809$	−53.2148	−1.87093	−0.935466	−	0.353417i	$-0.885020\pi$
$809$	−53.2148	−1.87093	−0.935466	+	0.353417i	$0.885020\pi$
$810$	19.9192	0.699889
$811$	13.1433	0.461523	0.230761	−	0.973010i	$-0.425878\pi$
$811$	13.1433	0.461523	0.230761	+	0.973010i	$0.425878\pi$
$812$	−19.1926	−0.673530
$813$	16.3925	0.574909
$814$	−31.1803	−1.09287
$815$	25.1803	0.882029
$816$	−45.9937	−1.61010
$817$	0	0
$818$	−41.3050	−1.44419
$819$	8.05748	0.281551
$820$	−11.1352	−0.388857
$821$	−27.4508	−0.958041	−0.479021	−	0.877804i	$-0.659008\pi$
$821$	−27.4508	−0.958041	−0.479021	+	0.877804i	$0.659008\pi$
$822$	35.3262	1.23214
$823$	−16.7639	−0.584354	−0.292177	−	0.956364i	$-0.594380\pi$
$823$	−16.7639	−0.584354	−0.292177	+	0.956364i	$0.594380\pi$
$824$	−10.8541	−0.378121
$825$	−11.1352	−0.387677
$826$	113.138	3.93657
$827$	9.23305	0.321065	0.160532	−	0.987031i	$-0.448679\pi$
$827$	9.23305	0.321065	0.160532	+	0.987031i	$0.448679\pi$
$828$	4.09017	0.142143
$829$	−25.9686	−0.901925	−0.450963	−	0.892543i	$-0.648919\pi$
$829$	−25.9686	−0.901925	−0.450963	+	0.892543i	$0.648919\pi$
$830$	16.6700	0.578624
$831$	47.2348	1.63856
$832$	14.4904	0.502363
$833$	57.3050	1.98550
$834$	−79.9230	−2.76751
$835$	0.171513	0.00593547
$836$	0	0
$837$	8.61803	0.297883
$838$	49.7980	1.72024
$839$	4.08174	0.140917	0.0704587	−	0.997515i	$-0.477554\pi$
$839$	4.08174	0.140917	0.0704587	+	0.997515i	$0.477554\pi$
$840$	−5.85410	−0.201986
$841$	−21.1591	−0.729623
$842$	22.0344	0.759357
$843$	47.6869	1.64242
$844$	2.80017	0.0963858
$845$	3.52786	0.121362
$846$	−1.73060	−0.0594992
$847$	−98.5755	−3.38709
$848$	51.4226	1.76586
$849$	−53.7737	−1.84551
$850$	9.95959	0.341611
$851$	11.4532	0.392610
$852$	−0.527864	−0.0180843
$853$	−15.4721	−0.529756	−0.264878	−	0.964282i	$-0.585332\pi$
$853$	−15.4721	−0.529756	−0.264878	+	0.964282i	$0.585332\pi$
$854$	−31.7809	−1.08752
$855$	0	0
$856$	−6.05573	−0.206981
$857$	−6.22088	−0.212501	−0.106251	−	0.994339i	$-0.533885\pi$
$857$	−6.22088	−0.212501	−0.106251	+	0.994339i	$0.533885\pi$
$858$	65.1864	2.22543
$859$	−22.7639	−0.776695	−0.388348	−	0.921513i	$-0.626954\pi$
$859$	−22.7639	−0.776695	−0.388348	+	0.921513i	$0.626954\pi$
$860$	−0.618034	−0.0210748
$861$	−55.4508	−1.88976
$862$	−13.0902	−0.445853
$863$	−36.3772	−1.23829	−0.619147	−	0.785275i	$-0.712521\pi$
$863$	−36.3772	−1.23829	−0.619147	+	0.785275i	$0.712521\pi$
$864$	33.2148	1.12999
$865$	−13.2088	−0.449112
$866$	11.5066	0.391009
$867$	19.8132	0.672891
$868$	13.0373	0.442514
$869$	−30.7768	−1.04403
$870$	−10.1311	−0.343477
$871$	18.4164	0.624016
$872$	−1.58359	−0.0536272
$873$	1.62460	0.0549843
$874$	0	0
$875$	4.23607	0.143205
$876$	−3.07768	−0.103985
$877$	11.9677	0.404121	0.202060	−	0.979373i	$-0.435236\pi$
$877$	11.9677	0.404121	0.202060	+	0.979373i	$0.435236\pi$
$878$	−10.7295	−0.362103
$879$	−26.3050	−0.887244
$880$	−27.0344	−0.911331
$881$	10.3262	0.347900	0.173950	−	0.984755i	$-0.444347\pi$
$881$	10.3262	0.347900	0.173950	+	0.984755i	$0.444347\pi$
$882$	12.8658	0.433213
$883$	−5.78522	−0.194688	−0.0973440	−	0.995251i	$-0.531035\pi$
$883$	−5.78522	−0.194688	−0.0973440	+	0.995251i	$0.531035\pi$
$884$	−26.0746	−0.876982
$885$	26.7082	0.897786
$886$	66.1500	2.22235
$887$	14.3188	0.480780	0.240390	−	0.970676i	$-0.422725\pi$
$887$	14.3188	0.480780	0.240390	+	0.970676i	$0.422725\pi$
$888$	−3.86974	−0.129860
$889$	39.1118	1.31177
$890$	14.7984	0.496043
$891$	61.3050	2.05379
$892$	24.0009	0.803610
$893$	0	0
$894$	25.6525	0.857947
$895$	10.1311	0.338646
$896$	−24.1724	−0.807545
$897$	−23.9443	−0.799476
$898$	−10.7295	−0.358048
$899$	−5.32624	−0.177640
$900$	1.00000	0.0333333
$901$	−58.3045	−1.94240
$902$	−76.6312	−2.55154
$903$	−3.07768	−0.102419
$904$	13.4164	0.446223
$905$	−6.71040	−0.223061
$906$	−2.24514	−0.0745898
$907$	51.9371	1.72454	0.862272	−	0.506446i	$-0.169041\pi$
$907$	51.9371	1.72454	0.862272	+	0.506446i	$0.169041\pi$
$908$	−28.1482	−0.934130
$909$	2.03444	0.0674782
$910$	−24.7984	−0.822058
$911$	−34.3035	−1.13653	−0.568264	−	0.822847i	$-0.692385\pi$
$911$	−34.3035	−1.13653	−0.568264	+	0.822847i	$0.692385\pi$
$912$	0	0
$913$	51.3050	1.69795
$914$	9.95959	0.329434
$915$	−7.50245	−0.248023
$916$	−29.3607	−0.970104
$917$	66.1591	2.18476
$918$	−45.1246	−1.48933
$919$	7.36068	0.242806	0.121403	−	0.992603i	$-0.461261\pi$
$919$	7.36068	0.242806	0.121403	+	0.992603i	$0.461261\pi$
$920$	2.97168	0.0979735
$921$	−34.9230	−1.15075
$922$	−15.2169	−0.501142
$923$	0.527864	0.0173749
$924$	76.3215	2.51079
$925$	2.80017	0.0920690
$926$	0.277515	0.00911969
$927$	9.23305	0.303253
$928$	−20.5279	−0.673860
$929$	37.5623	1.23238	0.616190	−	0.787598i	$-0.288675\pi$
$929$	37.5623	1.23238	0.616190	+	0.787598i	$0.288675\pi$
$930$	6.88191	0.225667
$931$	0	0
$932$	2.85410	0.0934892
$933$	−5.25731	−0.172117
$934$	−17.4620	−0.571376
$935$	30.6525	1.00244
$936$	1.38197	0.0451710
$937$	23.2016	0.757964	0.378982	−	0.925404i	$-0.376274\pi$
$937$	23.2016	0.757964	0.378982	+	0.925404i	$0.376274\pi$
$938$	48.2148	1.57427
$939$	6.22088	0.203011
$940$	2.38197	0.0776912
$941$	50.7615	1.65478	0.827389	−	0.561629i	$-0.189825\pi$
$941$	50.7615	1.65478	0.827389	+	0.561629i	$0.189825\pi$
$942$	−58.8673	−1.91800
$943$	28.1482	0.916631
$944$	64.8434	2.11047
$945$	−19.1926	−0.624337
$946$	−4.25325	−0.138285
$947$	1.41641	0.0460271	0.0230135	−	0.999735i	$-0.492674\pi$
$947$	1.41641	0.0460271	0.0230135	+	0.999735i	$0.492674\pi$
$948$	16.1803	0.525513
$949$	3.07768	0.0999058
$950$	0	0
$951$	31.3050	1.01513
$952$	16.1150	0.522289
$953$	−42.2300	−1.36796	−0.683982	−	0.729499i	$-0.739753\pi$
$953$	−42.2300	−1.36796	−0.683982	+	0.729499i	$0.739753\pi$
$954$	−13.0902	−0.423810
$955$	−13.0000	−0.420670
$956$	−37.5623	−1.21485
$957$	−31.1803	−1.00792
$958$	−21.7558	−0.702898
$959$	−41.3607	−1.33561
$960$	8.95554	0.289039
$961$	−27.3820	−0.883289
$962$	−16.3925	−0.528515
$963$	5.15131	0.165999
$964$	10.2371	0.329715
$965$	1.45309	0.0467765
$966$	−62.6869	−2.01692
$967$	−29.0557	−0.934369	−0.467185	−	0.884160i	$-0.654732\pi$
$967$	−29.0557	−0.934369	−0.467185	+	0.884160i	$0.654732\pi$
$968$	−16.9070	−0.543412
$969$	0	0
$970$	−5.00000	−0.160540
$971$	27.4216	0.880002	0.440001	−	0.897997i	$-0.354978\pi$
$971$	27.4216	0.880002	0.440001	+	0.897997i	$0.354978\pi$
$972$	−10.2371	−0.328355
$973$	93.5755	2.99989
$974$	40.0000	1.28168
$975$	−5.85410	−0.187481
$976$	−18.2148	−0.583041
$977$	36.7607	1.17608	0.588039	−	0.808832i	$-0.299900\pi$
$977$	36.7607	1.17608	0.588039	+	0.808832i	$0.299900\pi$
$978$	−91.1033	−2.91316
$979$	45.5447	1.45562
$980$	−17.7082	−0.565668
$981$	1.34708	0.0430091
$982$	70.8927	2.26228
$983$	19.6417	0.626472	0.313236	−	0.949675i	$-0.398587\pi$
$983$	19.6417	0.626472	0.313236	+	0.949675i	$0.398587\pi$
$984$	−9.51057	−0.303186
$985$	−14.8885	−0.474388
$986$	27.8885	0.888152
$987$	11.8617	0.377562
$988$	0	0
$989$	1.56231	0.0496784
$990$	6.88191	0.218721
$991$	−57.6839	−1.83239	−0.916195	−	0.400732i	$-0.868756\pi$
$991$	−57.6839	−1.83239	−0.916195	+	0.400732i	$0.868756\pi$
$992$	13.9443	0.442731
$993$	37.8885	1.20236
$994$	1.38197	0.0438333
$995$	−13.4164	−0.425329
$996$	−26.9726	−0.854660
$997$	−36.9443	−1.17004	−0.585018	−	0.811020i	$-0.698913\pi$
$997$	−36.9443	−1.17004	−0.585018	+	0.811020i	$0.698913\pi$
$998$	−56.1653	−1.77788
$999$	−12.6869	−0.401396

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.l.1.4	yes	4
5.4	even	2		9025.2.a.bl.1.1		4
19.18	odd	2	inner	1805.2.a.l.1.1	✓	4
95.94	odd	2		9025.2.a.bl.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1805.2.a.l.1.1	✓	4	19.18	odd	2	inner
1805.2.a.l.1.4	yes	4	1.1	even	1	trivial
9025.2.a.bl.1.1		4	5.4	even	2
9025.2.a.bl.1.4		4	95.94	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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.a (trivial)

\(f(q)\)	\(=\)	\(q+1.90211 q^{2} +1.90211 q^{3} +1.61803 q^{4} -1.00000 q^{5} +3.61803 q^{6} -4.23607 q^{7} -0.726543 q^{8} +0.618034 q^{9} +O(q^{10})\)	\(q+1.90211 q^{2} +1.90211 q^{3} +1.61803 q^{4} -1.00000 q^{5} +3.61803 q^{6} -4.23607 q^{7} -0.726543 q^{8} +0.618034 q^{9} -1.90211 q^{10} -5.85410 q^{11} +3.07768 q^{12} -3.07768 q^{13} -8.05748 q^{14} -1.90211 q^{15} -4.61803 q^{16} +5.23607 q^{17} +1.17557 q^{18} -1.61803 q^{20} -8.05748 q^{21} -11.1352 q^{22} +4.09017 q^{23} -1.38197 q^{24} +1.00000 q^{25} -5.85410 q^{26} -4.53077 q^{27} -6.85410 q^{28} +2.80017 q^{29} -3.61803 q^{30} -1.90211 q^{31} -7.33094 q^{32} -11.1352 q^{33} +9.95959 q^{34} +4.23607 q^{35} +1.00000 q^{36} +2.80017 q^{37} -5.85410 q^{39} +0.726543 q^{40} +6.88191 q^{41} -15.3262 q^{42} +0.381966 q^{43} -9.47214 q^{44} -0.618034 q^{45} +7.77997 q^{46} -1.47214 q^{47} -8.78402 q^{48} +10.9443 q^{49} +1.90211 q^{50} +9.95959 q^{51} -4.97980 q^{52} -11.1352 q^{53} -8.61803 q^{54} +5.85410 q^{55} +3.07768 q^{56} +5.32624 q^{58} -14.0413 q^{59} -3.07768 q^{60} +3.94427 q^{61} -3.61803 q^{62} -2.61803 q^{63} -4.70820 q^{64} +3.07768 q^{65} -21.1803 q^{66} -5.98385 q^{67} +8.47214 q^{68} +7.77997 q^{69} +8.05748 q^{70} -0.171513 q^{71} -0.449028 q^{72} -1.00000 q^{73} +5.32624 q^{74} +1.90211 q^{75} +24.7984 q^{77} -11.1352 q^{78} +5.25731 q^{79} +4.61803 q^{80} -10.4721 q^{81} +13.0902 q^{82} -8.76393 q^{83} -13.0373 q^{84} -5.23607 q^{85} +0.726543 q^{86} +5.32624 q^{87} +4.25325 q^{88} -7.77997 q^{89} -1.17557 q^{90} +13.0373 q^{91} +6.61803 q^{92} -3.61803 q^{93} -2.80017 q^{94} -13.9443 q^{96} +2.62866 q^{97} +20.8172 q^{98} -3.61803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 4 q^{5} + 10 q^{6} - 8 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 - 4 * q^5 + 10 * q^6 - 8 * q^7 - 2 * q^9	\( 4 q + 2 q^{4} - 4 q^{5} + 10 q^{6} - 8 q^{7} - 2 q^{9} - 10 q^{11} - 14 q^{16} + 12 q^{17} - 2 q^{20} - 6 q^{23} - 10 q^{24} + 4 q^{25} - 10 q^{26} - 14 q^{28} - 10 q^{30} + 8 q^{35} + 4 q^{36} - 10 q^{39} - 30 q^{42} + 6 q^{43} - 20 q^{44} + 2 q^{45} + 12 q^{47} + 8 q^{49} - 30 q^{54} + 10 q^{55} - 10 q^{58} - 20 q^{61} - 10 q^{62} - 6 q^{63} + 8 q^{64} - 40 q^{66} + 16 q^{68} - 4 q^{73} - 10 q^{74} + 50 q^{77} + 14 q^{80} - 24 q^{81} + 30 q^{82} - 44 q^{83} - 12 q^{85} - 10 q^{87} + 22 q^{92} - 10 q^{93} - 20 q^{96} - 10 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 - 4 * q^5 + 10 * q^6 - 8 * q^7 - 2 * q^9 - 10 * q^11 - 14 * q^16 + 12 * q^17 - 2 * q^20 - 6 * q^23 - 10 * q^24 + 4 * q^25 - 10 * q^26 - 14 * q^28 - 10 * q^30 + 8 * q^35 + 4 * q^36 - 10 * q^39 - 30 * q^42 + 6 * q^43 - 20 * q^44 + 2 * q^45 + 12 * q^47 + 8 * q^49 - 30 * q^54 + 10 * q^55 - 10 * q^58 - 20 * q^61 - 10 * q^62 - 6 * q^63 + 8 * q^64 - 40 * q^66 + 16 * q^68 - 4 * q^73 - 10 * q^74 + 50 * q^77 + 14 * q^80 - 24 * q^81 + 30 * q^82 - 44 * q^83 - 12 * q^85 - 10 * q^87 + 22 * q^92 - 10 * q^93 - 20 * q^96 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more