LMFDB - Embedded newform 5577.2.a.bg.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5577,2,Mod(1,5577)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5577, 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("5577.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5577 = 3 \cdot 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5577.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:	$44.5325692073$
Analytic rank:	$0$
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} - 6 x^{13} - 5 x^{12} + 90 x^{11} - 84 x^{10} - 450 x^{9} + 761 x^{8} + 782 x^{7} - 2061 x^{6} + \cdots + 64 $ x^14 - 6x^13 - 5x^12 + 90x^11 - 84x^10 - 450x^9 + 761x^8 + 782x^7 - 2061x^6 - 92x^5 + 1921x^4 - 400x^3 - 635x^2 + 112*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 429)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$2.08864$ of defining polynomial
Character	$\chi$	$=$	5577.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.08864 q^{2} +1.00000 q^{3} +2.36242 q^{4} -2.92121 q^{5} +2.08864 q^{6} +0.790904 q^{7} +0.756961 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.08864 q^{2} +1.00000 q^{3} +2.36242 q^{4} -2.92121 q^{5} +2.08864 q^{6} +0.790904 q^{7} +0.756961 q^{8} +1.00000 q^{9} -6.10137 q^{10} +1.00000 q^{11} +2.36242 q^{12} +1.65191 q^{14} -2.92121 q^{15} -3.14382 q^{16} +1.09987 q^{17} +2.08864 q^{18} +7.97576 q^{19} -6.90113 q^{20} +0.790904 q^{21} +2.08864 q^{22} +5.50513 q^{23} +0.756961 q^{24} +3.53350 q^{25} +1.00000 q^{27} +1.86845 q^{28} -8.51829 q^{29} -6.10137 q^{30} +2.39900 q^{31} -8.08022 q^{32} +1.00000 q^{33} +2.29722 q^{34} -2.31040 q^{35} +2.36242 q^{36} +0.852009 q^{37} +16.6585 q^{38} -2.21125 q^{40} +6.48992 q^{41} +1.65191 q^{42} +1.85866 q^{43} +2.36242 q^{44} -2.92121 q^{45} +11.4982 q^{46} +2.87688 q^{47} -3.14382 q^{48} -6.37447 q^{49} +7.38020 q^{50} +1.09987 q^{51} +12.8446 q^{53} +2.08864 q^{54} -2.92121 q^{55} +0.598683 q^{56} +7.97576 q^{57} -17.7916 q^{58} +5.46628 q^{59} -6.90113 q^{60} -1.14097 q^{61} +5.01065 q^{62} +0.790904 q^{63} -10.5890 q^{64} +2.08864 q^{66} -1.00054 q^{67} +2.59834 q^{68} +5.50513 q^{69} -4.82560 q^{70} +7.38994 q^{71} +0.756961 q^{72} -12.6053 q^{73} +1.77954 q^{74} +3.53350 q^{75} +18.8421 q^{76} +0.790904 q^{77} -1.98358 q^{79} +9.18377 q^{80} +1.00000 q^{81} +13.5551 q^{82} +17.9932 q^{83} +1.86845 q^{84} -3.21294 q^{85} +3.88208 q^{86} -8.51829 q^{87} +0.756961 q^{88} +10.7782 q^{89} -6.10137 q^{90} +13.0054 q^{92} +2.39900 q^{93} +6.00876 q^{94} -23.2989 q^{95} -8.08022 q^{96} +15.6202 q^{97} -13.3140 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 6 q^{2} + 14 q^{3} + 18 q^{4} + 12 q^{5} + 6 q^{6} + 12 q^{7} + 12 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q + 6 * q^2 + 14 * q^3 + 18 * q^4 + 12 * q^5 + 6 * q^6 + 12 * q^7 + 12 * q^8 + 14 * q^9	$ 14 q + 6 q^{2} + 14 q^{3} + 18 q^{4} + 12 q^{5} + 6 q^{6} + 12 q^{7} + 12 q^{8} + 14 q^{9} + 14 q^{11} + 18 q^{12} - 2 q^{14} + 12 q^{15} + 22 q^{16} + 2 q^{17} + 6 q^{18} - 2 q^{19} + 44 q^{20} + 12 q^{21} + 6 q^{22} + 2 q^{23} + 12 q^{24} + 20 q^{25} + 14 q^{27} + 24 q^{28} + 28 q^{31} + 30 q^{32} + 14 q^{33} - 16 q^{34} - 2 q^{35} + 18 q^{36} - 10 q^{38} + 10 q^{40} + 40 q^{41} - 2 q^{42} - 2 q^{43} + 18 q^{44} + 12 q^{45} + 32 q^{46} + 48 q^{47} + 22 q^{48} + 10 q^{49} + 2 q^{51} + 8 q^{53} + 6 q^{54} + 12 q^{55} - 10 q^{56} - 2 q^{57} - 16 q^{58} + 40 q^{59} + 44 q^{60} + 4 q^{61} - 6 q^{62} + 12 q^{63} + 16 q^{64} + 6 q^{66} + 40 q^{67} + 22 q^{68} + 2 q^{69} - 40 q^{70} + 36 q^{71} + 12 q^{72} + 10 q^{73} - 48 q^{74} + 20 q^{75} - 4 q^{76} + 12 q^{77} - 24 q^{79} + 68 q^{80} + 14 q^{81} + 46 q^{82} + 12 q^{83} + 24 q^{84} + 34 q^{85} + 48 q^{86} + 12 q^{88} + 20 q^{89} + 36 q^{92} + 28 q^{93} - 50 q^{94} - 60 q^{95} + 30 q^{96} - 16 q^{97} + 44 q^{98} + 14 q^{99}+O(q^{100}) $ 14 * q + 6 * q^2 + 14 * q^3 + 18 * q^4 + 12 * q^5 + 6 * q^6 + 12 * q^7 + 12 * q^8 + 14 * q^9 + 14 * q^11 + 18 * q^12 - 2 * q^14 + 12 * q^15 + 22 * q^16 + 2 * q^17 + 6 * q^18 - 2 * q^19 + 44 * q^20 + 12 * q^21 + 6 * q^22 + 2 * q^23 + 12 * q^24 + 20 * q^25 + 14 * q^27 + 24 * q^28 + 28 * q^31 + 30 * q^32 + 14 * q^33 - 16 * q^34 - 2 * q^35 + 18 * q^36 - 10 * q^38 + 10 * q^40 + 40 * q^41 - 2 * q^42 - 2 * q^43 + 18 * q^44 + 12 * q^45 + 32 * q^46 + 48 * q^47 + 22 * q^48 + 10 * q^49 + 2 * q^51 + 8 * q^53 + 6 * q^54 + 12 * q^55 - 10 * q^56 - 2 * q^57 - 16 * q^58 + 40 * q^59 + 44 * q^60 + 4 * q^61 - 6 * q^62 + 12 * q^63 + 16 * q^64 + 6 * q^66 + 40 * q^67 + 22 * q^68 + 2 * q^69 - 40 * q^70 + 36 * q^71 + 12 * q^72 + 10 * q^73 - 48 * q^74 + 20 * q^75 - 4 * q^76 + 12 * q^77 - 24 * q^79 + 68 * q^80 + 14 * q^81 + 46 * q^82 + 12 * q^83 + 24 * q^84 + 34 * q^85 + 48 * q^86 + 12 * q^88 + 20 * q^89 + 36 * q^92 + 28 * q^93 - 50 * q^94 - 60 * q^95 + 30 * q^96 - 16 * q^97 + 44 * q^98 + 14 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.08864	1.47689	0.738446	−	0.674313i	$-0.235560\pi$
$2$	2.08864	1.47689	0.738446	+	0.674313i	$0.235560\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.36242	1.18121
$5$	−2.92121	−1.30641	−0.653204	−	0.757182i	$-0.726575\pi$
$5$	−2.92121	−1.30641	−0.653204	+	0.757182i	$0.726575\pi$
$6$	2.08864	0.852684
$7$	0.790904	0.298934	0.149467	−	0.988767i	$-0.452244\pi$
$7$	0.790904	0.298934	0.149467	+	0.988767i	$0.452244\pi$
$8$	0.756961	0.267626
$9$	1.00000	0.333333
$10$	−6.10137	−1.92942
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.36242	0.681971
$13$	0	0
$13$	0	0
$14$	1.65191	0.441493
$15$	−2.92121	−0.754254
$16$	−3.14382	−0.785954
$17$	1.09987	0.266757	0.133378	−	0.991065i	$-0.457417\pi$
$17$	1.09987	0.266757	0.133378	+	0.991065i	$0.457417\pi$
$18$	2.08864	0.492297
$19$	7.97576	1.82976	0.914882	−	0.403720i	$-0.132283\pi$
$19$	7.97576	1.82976	0.914882	+	0.403720i	$0.132283\pi$
$20$	−6.90113	−1.54314
$21$	0.790904	0.172589
$22$	2.08864	0.445300
$23$	5.50513	1.14790	0.573950	−	0.818890i	$-0.305410\pi$
$23$	5.50513	1.14790	0.573950	+	0.818890i	$0.305410\pi$
$24$	0.756961	0.154514
$25$	3.53350	0.706699
$26$	0	0
$27$	1.00000	0.192450
$28$	1.86845	0.353103
$29$	−8.51829	−1.58181	−0.790903	−	0.611941i	$-0.790389\pi$
$29$	−8.51829	−1.58181	−0.790903	+	0.611941i	$0.790389\pi$
$30$	−6.10137	−1.11395
$31$	2.39900	0.430873	0.215437	−	0.976518i	$-0.430883\pi$
$31$	2.39900	0.430873	0.215437	+	0.976518i	$0.430883\pi$
$32$	−8.08022	−1.42840
$33$	1.00000	0.174078
$34$	2.29722	0.393971
$35$	−2.31040	−0.390529
$36$	2.36242	0.393736
$37$	0.852009	0.140069	0.0700347	−	0.997545i	$-0.477689\pi$
$37$	0.852009	0.140069	0.0700347	+	0.997545i	$0.477689\pi$
$38$	16.6585	2.70236
$39$	0	0
$40$	−2.21125	−0.349629
$41$	6.48992	1.01356	0.506778	−	0.862077i	$-0.330837\pi$
$41$	6.48992	1.01356	0.506778	+	0.862077i	$0.330837\pi$
$42$	1.65191	0.254896
$43$	1.85866	0.283444	0.141722	−	0.989907i	$-0.454736\pi$
$43$	1.85866	0.283444	0.141722	+	0.989907i	$0.454736\pi$
$44$	2.36242	0.356148
$45$	−2.92121	−0.435469
$46$	11.4982	1.69532
$47$	2.87688	0.419635	0.209818	−	0.977741i	$-0.432713\pi$
$47$	2.87688	0.419635	0.209818	+	0.977741i	$0.432713\pi$
$48$	−3.14382	−0.453771
$49$	−6.37447	−0.910639
$50$	7.38020	1.04372
$51$	1.09987	0.154012
$52$	0	0
$53$	12.8446	1.76434	0.882168	−	0.470935i	$-0.156083\pi$
$53$	12.8446	1.76434	0.882168	+	0.470935i	$0.156083\pi$
$54$	2.08864	0.284228
$55$	−2.92121	−0.393897
$56$	0.598683	0.0800024
$57$	7.97576	1.05642
$58$	−17.7916	−2.33616
$59$	5.46628	0.711650	0.355825	−	0.934553i	$-0.384200\pi$
$59$	5.46628	0.711650	0.355825	+	0.934553i	$0.384200\pi$
$60$	−6.90113	−0.890932
$61$	−1.14097	−0.146086	−0.0730432	−	0.997329i	$-0.523271\pi$
$61$	−1.14097	−0.146086	−0.0730432	+	0.997329i	$0.523271\pi$
$62$	5.01065	0.636353
$63$	0.790904	0.0996445
$64$	−10.5890	−1.32363
$65$	0	0
$66$	2.08864	0.257094
$67$	−1.00054	−0.122235	−0.0611175	−	0.998131i	$-0.519466\pi$
$67$	−1.00054	−0.122235	−0.0611175	+	0.998131i	$0.519466\pi$
$68$	2.59834	0.315095
$69$	5.50513	0.662740
$70$	−4.82560	−0.576769
$71$	7.38994	0.877025	0.438512	−	0.898725i	$-0.355505\pi$
$71$	7.38994	0.877025	0.438512	+	0.898725i	$0.355505\pi$
$72$	0.756961	0.0892087
$73$	−12.6053	−1.47534	−0.737672	−	0.675160i	$-0.764075\pi$
$73$	−12.6053	−1.47534	−0.737672	+	0.675160i	$0.764075\pi$
$74$	1.77954	0.206867
$75$	3.53350	0.408013
$76$	18.8421	2.16133
$77$	0.790904	0.0901319
$78$	0	0
$79$	−1.98358	−0.223170	−0.111585	−	0.993755i	$-0.535593\pi$
$79$	−1.98358	−0.223170	−0.111585	+	0.993755i	$0.535593\pi$
$80$	9.18377	1.02678
$81$	1.00000	0.111111
$82$	13.5551	1.49691
$83$	17.9932	1.97501	0.987505	−	0.157588i	$-0.0503718\pi$
$83$	17.9932	1.97501	0.987505	+	0.157588i	$0.0503718\pi$
$84$	1.86845	0.203864
$85$	−3.21294	−0.348493
$86$	3.88208	0.418615
$87$	−8.51829	−0.913256
$88$	0.756961	0.0806923
$89$	10.7782	1.14249	0.571244	−	0.820780i	$-0.306461\pi$
$89$	10.7782	1.14249	0.571244	+	0.820780i	$0.306461\pi$
$90$	−6.10137	−0.643141
$91$	0	0
$92$	13.0054	1.35591
$93$	2.39900	0.248765
$94$	6.00876	0.619756
$95$	−23.2989	−2.39042
$96$	−8.08022	−0.824684
$97$	15.6202	1.58599	0.792997	−	0.609226i	$-0.208520\pi$
$97$	15.6202	1.58599	0.792997	+	0.609226i	$0.208520\pi$
$98$	−13.3140	−1.34491
$99$	1.00000	0.100504
$100$	8.34760	0.834760
$101$	13.6066	1.35390	0.676951	−	0.736028i	$-0.263301\pi$
$101$	13.6066	1.35390	0.676951	+	0.736028i	$0.263301\pi$
$102$	2.29722	0.227459
$103$	9.43118	0.929281	0.464641	−	0.885499i	$-0.346184\pi$
$103$	9.43118	0.929281	0.464641	+	0.885499i	$0.346184\pi$
$104$	0	0
$105$	−2.31040	−0.225472
$106$	26.8277	2.60573
$107$	−3.32426	−0.321369	−0.160684	−	0.987006i	$-0.551370\pi$
$107$	−3.32426	−0.321369	−0.160684	+	0.987006i	$0.551370\pi$
$108$	2.36242	0.227324
$109$	2.53808	0.243104	0.121552	−	0.992585i	$-0.461213\pi$
$109$	2.53808	0.243104	0.121552	+	0.992585i	$0.461213\pi$
$110$	−6.10137	−0.581743
$111$	0.852009	0.0808691
$112$	−2.48646	−0.234948
$113$	−3.14040	−0.295424	−0.147712	−	0.989030i	$-0.547191\pi$
$113$	−3.14040	−0.295424	−0.147712	+	0.989030i	$0.547191\pi$
$114$	16.6585	1.56021
$115$	−16.0817	−1.49962
$116$	−20.1238	−1.86844
$117$	0	0
$118$	11.4171	1.05103
$119$	0.869888	0.0797425
$120$	−2.21125	−0.201858
$121$	1.00000	0.0909091
$122$	−2.38308	−0.215754
$123$	6.48992	0.585176
$124$	5.66744	0.508951
$125$	4.28397	0.383170
$126$	1.65191	0.147164
$127$	−1.94230	−0.172351	−0.0861755	−	0.996280i	$-0.527465\pi$
$127$	−1.94230	−0.172351	−0.0861755	+	0.996280i	$0.527465\pi$
$128$	−5.95626	−0.526464
$129$	1.85866	0.163646
$130$	0	0
$131$	−14.5999	−1.27560	−0.637800	−	0.770202i	$-0.720155\pi$
$131$	−14.5999	−1.27560	−0.637800	+	0.770202i	$0.720155\pi$
$132$	2.36242	0.205622
$133$	6.30806	0.546978
$134$	−2.08976	−0.180528
$135$	−2.92121	−0.251418
$136$	0.832555	0.0713910
$137$	−16.5069	−1.41028	−0.705141	−	0.709067i	$-0.749116\pi$
$137$	−16.5069	−1.41028	−0.705141	+	0.709067i	$0.749116\pi$
$138$	11.4982	0.978795
$139$	−21.4877	−1.82256	−0.911281	−	0.411786i	$-0.864905\pi$
$139$	−21.4877	−1.82256	−0.911281	+	0.411786i	$0.864905\pi$
$140$	−5.45813	−0.461296
$141$	2.87688	0.242277
$142$	15.4349	1.29527
$143$	0	0
$144$	−3.14382	−0.261985
$145$	24.8838	2.06648
$146$	−26.3280	−2.17892
$147$	−6.37447	−0.525758
$148$	2.01280	0.165451
$149$	23.5380	1.92830	0.964152	−	0.265349i	$-0.0854872\pi$
$149$	23.5380	1.92830	0.964152	+	0.265349i	$0.0854872\pi$
$150$	7.38020	0.602591
$151$	−8.97016	−0.729982	−0.364991	−	0.931011i	$-0.618928\pi$
$151$	−8.97016	−0.729982	−0.364991	+	0.931011i	$0.618928\pi$
$152$	6.03734	0.489693
$153$	1.09987	0.0889189
$154$	1.65191	0.133115
$155$	−7.00799	−0.562896
$156$	0	0
$157$	0.208325	0.0166261	0.00831306	−	0.999965i	$-0.497354\pi$
$157$	0.208325	0.0166261	0.00831306	+	0.999965i	$0.497354\pi$
$158$	−4.14298	−0.329598
$159$	12.8446	1.01864
$160$	23.6041	1.86607
$161$	4.35403	0.343146
$162$	2.08864	0.164099
$163$	0.970655	0.0760275	0.0380138	−	0.999277i	$-0.487897\pi$
$163$	0.970655	0.0760275	0.0380138	+	0.999277i	$0.487897\pi$
$164$	15.3319	1.19722
$165$	−2.92121	−0.227416
$166$	37.5813	2.91688
$167$	12.0169	0.929895	0.464947	−	0.885338i	$-0.346073\pi$
$167$	12.0169	0.929895	0.464947	+	0.885338i	$0.346073\pi$
$168$	0.598683	0.0461894
$169$	0	0
$170$	−6.71069	−0.514686
$171$	7.97576	0.609922
$172$	4.39094	0.334806
$173$	6.92374	0.526402	0.263201	−	0.964741i	$-0.415222\pi$
$173$	6.92374	0.526402	0.263201	+	0.964741i	$0.415222\pi$
$174$	−17.7916	−1.34878
$175$	2.79466	0.211256
$176$	−3.14382	−0.236974
$177$	5.46628	0.410871
$178$	22.5118	1.68733
$179$	−3.86609	−0.288965	−0.144483	−	0.989507i	$-0.546152\pi$
$179$	−3.86609	−0.288965	−0.144483	+	0.989507i	$0.546152\pi$
$180$	−6.90113	−0.514380
$181$	0.455152	0.0338312	0.0169156	−	0.999857i	$-0.494615\pi$
$181$	0.455152	0.0338312	0.0169156	+	0.999857i	$0.494615\pi$
$182$	0	0
$183$	−1.14097	−0.0843431
$184$	4.16717	0.307208
$185$	−2.48890	−0.182988
$186$	5.01065	0.367398
$187$	1.09987	0.0804302
$188$	6.79638	0.495677
$189$	0.790904	0.0575298
$190$	−48.6630	−3.53039
$191$	25.0910	1.81552	0.907762	−	0.419485i	$-0.137789\pi$
$191$	25.0910	1.81552	0.907762	+	0.419485i	$0.137789\pi$
$192$	−10.5890	−0.764199
$193$	−1.66965	−0.120184	−0.0600920	−	0.998193i	$-0.519139\pi$
$193$	−1.66965	−0.120184	−0.0600920	+	0.998193i	$0.519139\pi$
$194$	32.6250	2.34234
$195$	0	0
$196$	−15.0592	−1.07565
$197$	9.48397	0.675705	0.337853	−	0.941199i	$-0.390299\pi$
$197$	9.48397	0.675705	0.337853	+	0.941199i	$0.390299\pi$
$198$	2.08864	0.148433
$199$	−11.4889	−0.814429	−0.407214	−	0.913333i	$-0.633500\pi$
$199$	−11.4889	−0.814429	−0.407214	+	0.913333i	$0.633500\pi$
$200$	2.67472	0.189131
$201$	−1.00054	−0.0705724
$202$	28.4192	1.99957
$203$	−6.73715	−0.472855
$204$	2.59834	0.181920
$205$	−18.9585	−1.32412
$206$	19.6983	1.37245
$207$	5.50513	0.382633
$208$	0	0
$209$	7.97576	0.551695
$210$	−4.82560	−0.332998
$211$	−2.01150	−0.138477	−0.0692386	−	0.997600i	$-0.522057\pi$
$211$	−2.01150	−0.138477	−0.0692386	+	0.997600i	$0.522057\pi$
$212$	30.3442	2.08405
$213$	7.38994	0.506351
$214$	−6.94319	−0.474627
$215$	−5.42956	−0.370293
$216$	0.756961	0.0515047
$217$	1.89738	0.128802
$218$	5.30114	0.359039
$219$	−12.6053	−0.851790
$220$	−6.90113	−0.465274
$221$	0	0
$222$	1.77954	0.119435
$223$	−16.0883	−1.07735	−0.538676	−	0.842513i	$-0.681075\pi$
$223$	−16.0883	−1.07735	−0.538676	+	0.842513i	$0.681075\pi$
$224$	−6.39068	−0.426995
$225$	3.53350	0.235566
$226$	−6.55916	−0.436309
$227$	−17.1332	−1.13717	−0.568587	−	0.822623i	$-0.692510\pi$
$227$	−17.1332	−1.13717	−0.568587	+	0.822623i	$0.692510\pi$
$228$	18.8421	1.24785
$229$	−7.34582	−0.485425	−0.242713	−	0.970098i	$-0.578037\pi$
$229$	−7.34582	−0.485425	−0.242713	+	0.970098i	$0.578037\pi$
$230$	−33.5888	−2.21478
$231$	0.790904	0.0520377
$232$	−6.44801	−0.423333
$233$	−23.9636	−1.56991	−0.784954	−	0.619554i	$-0.787314\pi$
$233$	−23.9636	−1.56991	−0.784954	+	0.619554i	$0.787314\pi$
$234$	0	0
$235$	−8.40397	−0.548215
$236$	12.9136	0.840607
$237$	−1.98358	−0.128847
$238$	1.81688	0.117771
$239$	−1.31728	−0.0852079	−0.0426039	−	0.999092i	$-0.513565\pi$
$239$	−1.31728	−0.0852079	−0.0426039	+	0.999092i	$0.513565\pi$
$240$	9.18377	0.592810
$241$	−4.96510	−0.319830	−0.159915	−	0.987131i	$-0.551122\pi$
$241$	−4.96510	−0.319830	−0.159915	+	0.987131i	$0.551122\pi$
$242$	2.08864	0.134263
$243$	1.00000	0.0641500
$244$	−2.69545	−0.172559
$245$	18.6212	1.18966
$246$	13.5551	0.864242
$247$	0	0
$248$	1.81595	0.115313
$249$	17.9932	1.14027
$250$	8.94768	0.565901
$251$	4.47882	0.282701	0.141350	−	0.989960i	$-0.454856\pi$
$251$	4.47882	0.282701	0.141350	+	0.989960i	$0.454856\pi$
$252$	1.86845	0.117701
$253$	5.50513	0.346105
$254$	−4.05676	−0.254544
$255$	−3.21294	−0.201202
$256$	8.73761	0.546100
$257$	−7.80222	−0.486689	−0.243345	−	0.969940i	$-0.578245\pi$
$257$	−7.80222	−0.486689	−0.243345	+	0.969940i	$0.578245\pi$
$258$	3.88208	0.241688
$259$	0.673858	0.0418715
$260$	0	0
$261$	−8.51829	−0.527269
$262$	−30.4940	−1.88392
$263$	−10.6126	−0.654402	−0.327201	−	0.944955i	$-0.606105\pi$
$263$	−10.6126	−0.654402	−0.327201	+	0.944955i	$0.606105\pi$
$264$	0.756961	0.0465877
$265$	−37.5217	−2.30494
$266$	13.1753	0.807827
$267$	10.7782	0.659616
$268$	−2.36369	−0.144385
$269$	−15.5131	−0.945852	−0.472926	−	0.881102i	$-0.656802\pi$
$269$	−15.5131	−0.945852	−0.472926	+	0.881102i	$0.656802\pi$
$270$	−6.10137	−0.371317
$271$	−9.31583	−0.565896	−0.282948	−	0.959135i	$-0.591312\pi$
$271$	−9.31583	−0.565896	−0.282948	+	0.959135i	$0.591312\pi$
$272$	−3.45778	−0.209659
$273$	0	0
$274$	−34.4770	−2.08283
$275$	3.53350	0.213078
$276$	13.0054	0.782835
$277$	19.2586	1.15714	0.578569	−	0.815634i	$-0.303612\pi$
$277$	19.2586	1.15714	0.578569	+	0.815634i	$0.303612\pi$
$278$	−44.8800	−2.69173
$279$	2.39900	0.143624
$280$	−1.74888	−0.104516
$281$	−7.40534	−0.441766	−0.220883	−	0.975300i	$-0.570894\pi$
$281$	−7.40534	−0.441766	−0.220883	+	0.975300i	$0.570894\pi$
$282$	6.00876	0.357816
$283$	−15.5014	−0.921463	−0.460731	−	0.887540i	$-0.652413\pi$
$283$	−15.5014	−0.921463	−0.460731	+	0.887540i	$0.652413\pi$
$284$	17.4581	1.03595
$285$	−23.2989	−1.38011
$286$	0	0
$287$	5.13290	0.302986
$288$	−8.08022	−0.476132
$289$	−15.7903	−0.928841
$290$	51.9732	3.05197
$291$	15.6202	0.915674
$292$	−29.7791	−1.74269
$293$	−1.81629	−0.106109	−0.0530545	−	0.998592i	$-0.516896\pi$
$293$	−1.81629	−0.106109	−0.0530545	+	0.998592i	$0.516896\pi$
$294$	−13.3140	−0.776487
$295$	−15.9682	−0.929704
$296$	0.644938	0.0374862
$297$	1.00000	0.0580259
$298$	49.1623	2.84790
$299$	0	0
$300$	8.34760	0.481949
$301$	1.47002	0.0847308
$302$	−18.7354	−1.07810
$303$	13.6066	0.781676
$304$	−25.0743	−1.43811
$305$	3.33302	0.190848
$306$	2.29722	0.131324
$307$	−29.0363	−1.65719	−0.828595	−	0.559849i	$-0.810859\pi$
$307$	−29.0363	−1.65719	−0.828595	+	0.559849i	$0.810859\pi$
$308$	1.86845	0.106465
$309$	9.43118	0.536521
$310$	−14.6372	−0.831336
$311$	−15.7918	−0.895471	−0.447735	−	0.894166i	$-0.647769\pi$
$311$	−15.7918	−0.895471	−0.447735	+	0.894166i	$0.647769\pi$
$312$	0	0
$313$	−21.1348	−1.19461	−0.597306	−	0.802013i	$-0.703762\pi$
$313$	−21.1348	−1.19461	−0.597306	+	0.802013i	$0.703762\pi$
$314$	0.435115	0.0245550
$315$	−2.31040	−0.130176
$316$	−4.68604	−0.263610
$317$	−20.5708	−1.15537	−0.577686	−	0.816259i	$-0.696044\pi$
$317$	−20.5708	−1.15537	−0.577686	+	0.816259i	$0.696044\pi$
$318$	26.8277	1.50442
$319$	−8.51829	−0.476933
$320$	30.9329	1.72920
$321$	−3.32426	−0.185542
$322$	9.09401	0.506789
$323$	8.77227	0.488102
$324$	2.36242	0.131245
$325$	0	0
$326$	2.02735	0.112284
$327$	2.53808	0.140356
$328$	4.91262	0.271254
$329$	2.27533	0.125443
$330$	−6.10137	−0.335869
$331$	−16.0902	−0.884399	−0.442199	−	0.896917i	$-0.645802\pi$
$331$	−16.0902	−0.884399	−0.442199	+	0.896917i	$0.645802\pi$
$332$	42.5075	2.33290
$333$	0.852009	0.0466898
$334$	25.0990	1.37335
$335$	2.92278	0.159689
$336$	−2.48646	−0.135647
$337$	10.9426	0.596081	0.298041	−	0.954553i	$-0.403667\pi$
$337$	10.9426	0.596081	0.298041	+	0.954553i	$0.403667\pi$
$338$	0	0
$339$	−3.14040	−0.170563
$340$	−7.59032	−0.411643
$341$	2.39900	0.129913
$342$	16.6585	0.900788
$343$	−10.5779	−0.571154
$344$	1.40694	0.0758569
$345$	−16.0817	−0.865808
$346$	14.4612	0.777439
$347$	−5.97141	−0.320562	−0.160281	−	0.987071i	$-0.551240\pi$
$347$	−5.97141	−0.320562	−0.160281	+	0.987071i	$0.551240\pi$
$348$	−20.1238	−1.07875
$349$	−31.3931	−1.68043	−0.840217	−	0.542250i	$-0.817573\pi$
$349$	−31.3931	−1.68043	−0.840217	+	0.542250i	$0.817573\pi$
$350$	5.83703	0.312002
$351$	0	0
$352$	−8.08022	−0.430677
$353$	−2.18923	−0.116521	−0.0582606	−	0.998301i	$-0.518555\pi$
$353$	−2.18923	−0.116521	−0.0582606	+	0.998301i	$0.518555\pi$
$354$	11.4171	0.606812
$355$	−21.5876	−1.14575
$356$	25.4627	1.34952
$357$	0.869888	0.0460394
$358$	−8.07488	−0.426771
$359$	32.9795	1.74059	0.870296	−	0.492528i	$-0.163927\pi$
$359$	32.9795	1.74059	0.870296	+	0.492528i	$0.163927\pi$
$360$	−2.21125	−0.116543
$361$	44.6127	2.34804
$362$	0.950649	0.0499650
$363$	1.00000	0.0524864
$364$	0	0
$365$	36.8229	1.92740
$366$	−2.38308	−0.124566
$367$	6.63750	0.346475	0.173237	−	0.984880i	$-0.444577\pi$
$367$	6.63750	0.346475	0.173237	+	0.984880i	$0.444577\pi$
$368$	−17.3071	−0.902197
$369$	6.48992	0.337852
$370$	−5.19842	−0.270253
$371$	10.1588	0.527419
$372$	5.66744	0.293843
$373$	28.7363	1.48791	0.743954	−	0.668231i	$-0.232948\pi$
$373$	28.7363	1.48791	0.743954	+	0.668231i	$0.232948\pi$
$374$	2.29722	0.118787
$375$	4.28397	0.221223
$376$	2.17768	0.112305
$377$	0	0
$378$	1.65191	0.0849653
$379$	20.9574	1.07651	0.538256	−	0.842782i	$-0.319084\pi$
$379$	20.9574	1.07651	0.538256	+	0.842782i	$0.319084\pi$
$380$	−55.0418	−2.82358
$381$	−1.94230	−0.0995069
$382$	52.4062	2.68133
$383$	−2.90990	−0.148689	−0.0743445	−	0.997233i	$-0.523686\pi$
$383$	−2.90990	−0.148689	−0.0743445	+	0.997233i	$0.523686\pi$
$384$	−5.95626	−0.303954
$385$	−2.31040	−0.117749
$386$	−3.48730	−0.177499
$387$	1.85866	0.0944812
$388$	36.9015	1.87339
$389$	20.8262	1.05593	0.527965	−	0.849266i	$-0.322955\pi$
$389$	20.8262	1.05593	0.527965	+	0.849266i	$0.322955\pi$
$390$	0	0
$391$	6.05491	0.306210
$392$	−4.82522	−0.243711
$393$	−14.5999	−0.736468
$394$	19.8086	0.997943
$395$	5.79446	0.291551
$396$	2.36242	0.118716
$397$	−30.7766	−1.54463	−0.772317	−	0.635237i	$-0.780902\pi$
$397$	−30.7766	−1.54463	−0.772317	+	0.635237i	$0.780902\pi$
$398$	−23.9963	−1.20282
$399$	6.30806	0.315798
$400$	−11.1087	−0.555433
$401$	−22.9270	−1.14492	−0.572460	−	0.819933i	$-0.694011\pi$
$401$	−22.9270	−1.14492	−0.572460	+	0.819933i	$0.694011\pi$
$402$	−2.08976	−0.104228
$403$	0	0
$404$	32.1444	1.59924
$405$	−2.92121	−0.145156
$406$	−14.0715	−0.698356
$407$	0.852009	0.0422325
$408$	0.832555	0.0412176
$409$	10.6040	0.524333	0.262167	−	0.965023i	$-0.415563\pi$
$409$	10.6040	0.524333	0.262167	+	0.965023i	$0.415563\pi$
$410$	−39.5974	−1.95558
$411$	−16.5069	−0.814227
$412$	22.2804	1.09768
$413$	4.32331	0.212736
$414$	11.4982	0.565108
$415$	−52.5620	−2.58017
$416$	0	0
$417$	−21.4877	−1.05226
$418$	16.6585	0.814794
$419$	9.22572	0.450706	0.225353	−	0.974277i	$-0.427646\pi$
$419$	9.22572	0.450706	0.225353	+	0.974277i	$0.427646\pi$
$420$	−5.45813	−0.266330
$421$	5.70936	0.278257	0.139129	−	0.990274i	$-0.455570\pi$
$421$	5.70936	0.278257	0.139129	+	0.990274i	$0.455570\pi$
$422$	−4.20130	−0.204516
$423$	2.87688	0.139878
$424$	9.72283	0.472182
$425$	3.88637	0.188517
$426$	15.4349	0.747825
$427$	−0.902399	−0.0436702
$428$	−7.85330	−0.379603
$429$	0	0
$430$	−11.3404	−0.546882
$431$	−10.6304	−0.512047	−0.256024	−	0.966671i	$-0.582412\pi$
$431$	−10.6304	−0.512047	−0.256024	+	0.966671i	$0.582412\pi$
$432$	−3.14382	−0.151257
$433$	−17.1373	−0.823566	−0.411783	−	0.911282i	$-0.635094\pi$
$433$	−17.1373	−0.823566	−0.411783	+	0.911282i	$0.635094\pi$
$434$	3.96294	0.190227
$435$	24.8838	1.19308
$436$	5.99601	0.287157
$437$	43.9076	2.10039
$438$	−26.3280	−1.25800
$439$	29.5949	1.41249	0.706245	−	0.707968i	$-0.250388\pi$
$439$	29.5949	1.41249	0.706245	+	0.707968i	$0.250388\pi$
$440$	−2.21125	−0.105417
$441$	−6.37447	−0.303546
$442$	0	0
$443$	−29.3218	−1.39312	−0.696560	−	0.717499i	$-0.745287\pi$
$443$	−29.3218	−1.39312	−0.696560	+	0.717499i	$0.745287\pi$
$444$	2.01280	0.0955234
$445$	−31.4855	−1.49256
$446$	−33.6026	−1.59113
$447$	23.5380	1.11331
$448$	−8.37492	−0.395678
$449$	17.0682	0.805496	0.402748	−	0.915311i	$-0.368055\pi$
$449$	17.0682	0.805496	0.402748	+	0.915311i	$0.368055\pi$
$450$	7.38020	0.347906
$451$	6.48992	0.305598
$452$	−7.41893	−0.348957
$453$	−8.97016	−0.421455
$454$	−35.7852	−1.67948
$455$	0	0
$456$	6.03734	0.282724
$457$	−23.1149	−1.08127	−0.540635	−	0.841257i	$-0.681816\pi$
$457$	−23.1149	−1.08127	−0.540635	+	0.841257i	$0.681816\pi$
$458$	−15.3428	−0.716921
$459$	1.09987	0.0513373
$460$	−37.9916	−1.77137
$461$	−29.3753	−1.36814	−0.684072	−	0.729414i	$-0.739793\pi$
$461$	−29.3753	−1.36814	−0.684072	+	0.729414i	$0.739793\pi$
$462$	1.65191	0.0768540
$463$	39.9044	1.85451	0.927257	−	0.374425i	$-0.122160\pi$
$463$	39.9044	1.85451	0.927257	+	0.374425i	$0.122160\pi$
$464$	26.7799	1.24323
$465$	−7.00799	−0.324988
$466$	−50.0514	−2.31859
$467$	−26.0180	−1.20397	−0.601985	−	0.798507i	$-0.705623\pi$
$467$	−26.0180	−1.20397	−0.601985	+	0.798507i	$0.705623\pi$
$468$	0	0
$469$	−0.791329	−0.0365402
$470$	−17.5529	−0.809654
$471$	0.208325	0.00959909
$472$	4.13776	0.190456
$473$	1.85866	0.0854615
$474$	−4.14298	−0.190293
$475$	28.1823	1.29309
$476$	2.05504	0.0941926
$477$	12.8446	0.588112
$478$	−2.75133	−0.125843
$479$	19.9600	0.911997	0.455999	−	0.889981i	$-0.349282\pi$
$479$	19.9600	0.911997	0.455999	+	0.889981i	$0.349282\pi$
$480$	23.6041	1.07737
$481$	0	0
$482$	−10.3703	−0.472355
$483$	4.35403	0.198115
$484$	2.36242	0.107383
$485$	−45.6300	−2.07195
$486$	2.08864	0.0947426
$487$	19.3071	0.874888	0.437444	−	0.899246i	$-0.355884\pi$
$487$	19.3071	0.874888	0.437444	+	0.899246i	$0.355884\pi$
$488$	−0.863671	−0.0390966
$489$	0.970655	0.0438945
$490$	38.8930	1.75701
$491$	15.4052	0.695225	0.347613	−	0.937638i	$-0.386992\pi$
$491$	15.4052	0.695225	0.347613	+	0.937638i	$0.386992\pi$
$492$	15.3319	0.691216
$493$	−9.36898	−0.421957
$494$	0	0
$495$	−2.92121	−0.131299
$496$	−7.54202	−0.338647
$497$	5.84474	0.262172
$498$	37.5813	1.68406
$499$	−18.2944	−0.818971	−0.409485	−	0.912317i	$-0.634292\pi$
$499$	−18.2944	−0.818971	−0.409485	+	0.912317i	$0.634292\pi$
$500$	10.1205	0.452604
$501$	12.0169	0.536875
$502$	9.35465	0.417518
$503$	10.5443	0.470147	0.235074	−	0.971978i	$-0.424467\pi$
$503$	10.5443	0.470147	0.235074	+	0.971978i	$0.424467\pi$
$504$	0.598683	0.0266675
$505$	−39.7477	−1.76875
$506$	11.4982	0.511159
$507$	0	0
$508$	−4.58852	−0.203583
$509$	36.1867	1.60395	0.801974	−	0.597360i	$-0.203783\pi$
$509$	36.1867	1.60395	0.801974	+	0.597360i	$0.203783\pi$
$510$	−6.71069	−0.297154
$511$	−9.96961	−0.441030
$512$	30.1622	1.33300
$513$	7.97576	0.352138
$514$	−16.2960	−0.718787
$515$	−27.5505	−1.21402
$516$	4.39094	0.193300
$517$	2.87688	0.126525
$518$	1.40745	0.0618396
$519$	6.92374	0.303919
$520$	0	0
$521$	−4.68476	−0.205243	−0.102622	−	0.994720i	$-0.532723\pi$
$521$	−4.68476	−0.205243	−0.102622	+	0.994720i	$0.532723\pi$
$522$	−17.7916	−0.778719
$523$	−23.4675	−1.02616	−0.513082	−	0.858340i	$-0.671496\pi$
$523$	−23.4675	−1.02616	−0.513082	+	0.858340i	$0.671496\pi$
$524$	−34.4911	−1.50675
$525$	2.79466	0.121969
$526$	−22.1659	−0.966481
$527$	2.63858	0.114938
$528$	−3.14382	−0.136817
$529$	7.30649	0.317674
$530$	−78.3694	−3.40415
$531$	5.46628	0.237217
$532$	14.9023	0.646096
$533$	0	0
$534$	22.5118	0.974182
$535$	9.71088	0.419838
$536$	−0.757367	−0.0327133
$537$	−3.86609	−0.166834
$538$	−32.4013	−1.39692
$539$	−6.37447	−0.274568
$540$	−6.90113	−0.296977
$541$	6.52430	0.280502	0.140251	−	0.990116i	$-0.455209\pi$
$541$	6.52430	0.280502	0.140251	+	0.990116i	$0.455209\pi$
$542$	−19.4574	−0.835768
$543$	0.455152	0.0195324
$544$	−8.88716	−0.381034
$545$	−7.41429	−0.317593
$546$	0	0
$547$	−6.37525	−0.272586	−0.136293	−	0.990669i	$-0.543519\pi$
$547$	−6.37525	−0.272586	−0.136293	+	0.990669i	$0.543519\pi$
$548$	−38.9963	−1.66584
$549$	−1.14097	−0.0486955
$550$	7.38020	0.314693
$551$	−67.9398	−2.89433
$552$	4.16717	0.177367
$553$	−1.56882	−0.0667130
$554$	40.2243	1.70897
$555$	−2.48890	−0.105648
$556$	−50.7629	−2.15283
$557$	33.3684	1.41386	0.706932	−	0.707281i	$-0.250078\pi$
$557$	33.3684	1.41386	0.706932	+	0.707281i	$0.250078\pi$
$558$	5.01065	0.212118
$559$	0	0
$560$	7.26348	0.306938
$561$	1.09987	0.0464364
$562$	−15.4671	−0.652440
$563$	−10.4648	−0.441041	−0.220520	−	0.975382i	$-0.570776\pi$
$563$	−10.4648	−0.441041	−0.220520	+	0.975382i	$0.570776\pi$
$564$	6.79638	0.286179
$565$	9.17378	0.385944
$566$	−32.3769	−1.36090
$567$	0.790904	0.0332148
$568$	5.59390	0.234715
$569$	16.1139	0.675531	0.337765	−	0.941230i	$-0.390329\pi$
$569$	16.1139	0.675531	0.337765	+	0.941230i	$0.390329\pi$
$570$	−48.6630	−2.03827
$571$	−42.0710	−1.76062	−0.880309	−	0.474401i	$-0.842665\pi$
$571$	−42.0710	−1.76062	−0.880309	+	0.474401i	$0.842665\pi$
$572$	0	0
$573$	25.0910	1.04819
$574$	10.7208	0.447477
$575$	19.4524	0.811220
$576$	−10.5890	−0.441210
$577$	27.6103	1.14943	0.574716	−	0.818353i	$-0.305112\pi$
$577$	27.6103	1.14943	0.574716	+	0.818353i	$0.305112\pi$
$578$	−32.9802	−1.37180
$579$	−1.66965	−0.0693883
$580$	58.7858	2.44095
$581$	14.2309	0.590397
$582$	32.6250	1.35235
$583$	12.8446	0.531967
$584$	−9.54175	−0.394840
$585$	0	0
$586$	−3.79358	−0.156712
$587$	−35.8953	−1.48156	−0.740779	−	0.671749i	$-0.765544\pi$
$587$	−35.8953	−1.48156	−0.740779	+	0.671749i	$0.765544\pi$
$588$	−15.0592	−0.621029
$589$	19.1338	0.788396
$590$	−33.3518	−1.37307
$591$	9.48397	0.390118
$592$	−2.67856	−0.110088
$593$	29.4446	1.20915	0.604573	−	0.796550i	$-0.293344\pi$
$593$	29.4446	1.20915	0.604573	+	0.796550i	$0.293344\pi$
$594$	2.08864	0.0856979
$595$	−2.54113	−0.104176
$596$	55.6065	2.27773
$597$	−11.4889	−0.470211
$598$	0	0
$599$	−17.4165	−0.711620	−0.355810	−	0.934558i	$-0.615795\pi$
$599$	−17.4165	−0.711620	−0.355810	+	0.934558i	$0.615795\pi$
$600$	2.67472	0.109195
$601$	45.1984	1.84368	0.921841	−	0.387567i	$-0.126684\pi$
$601$	45.1984	1.84368	0.921841	+	0.387567i	$0.126684\pi$
$602$	3.07035	0.125138
$603$	−1.00054	−0.0407450
$604$	−21.1913	−0.862261
$605$	−2.92121	−0.118764
$606$	28.4192	1.15445
$607$	−14.9828	−0.608132	−0.304066	−	0.952651i	$-0.598344\pi$
$607$	−14.9828	−0.608132	−0.304066	+	0.952651i	$0.598344\pi$
$608$	−64.4459	−2.61363
$609$	−6.73715	−0.273003
$610$	6.96149	0.281862
$611$	0	0
$612$	2.59834	0.105032
$613$	39.9385	1.61310	0.806549	−	0.591167i	$-0.201332\pi$
$613$	39.9385	1.61310	0.806549	+	0.591167i	$0.201332\pi$
$614$	−60.6464	−2.44749
$615$	−18.9585	−0.764479
$616$	0.598683	0.0241216
$617$	1.00137	0.0403138	0.0201569	−	0.999797i	$-0.493583\pi$
$617$	1.00137	0.0403138	0.0201569	+	0.999797i	$0.493583\pi$
$618$	19.6983	0.792383
$619$	41.6163	1.67270	0.836351	−	0.548194i	$-0.184685\pi$
$619$	41.6163	1.67270	0.836351	+	0.548194i	$0.184685\pi$
$620$	−16.5558	−0.664897
$621$	5.50513	0.220913
$622$	−32.9834	−1.32251
$623$	8.52453	0.341528
$624$	0	0
$625$	−30.1819	−1.20728
$626$	−44.1431	−1.76431
$627$	7.97576	0.318521
$628$	0.492150	0.0196389
$629$	0.937096	0.0373645
$630$	−4.82560	−0.192256
$631$	1.08468	0.0431806	0.0215903	−	0.999767i	$-0.493127\pi$
$631$	1.08468	0.0431806	0.0215903	+	0.999767i	$0.493127\pi$
$632$	−1.50149	−0.0597261
$633$	−2.01150	−0.0799499
$634$	−42.9650	−1.70636
$635$	5.67387	0.225161
$636$	30.3442	1.20323
$637$	0	0
$638$	−17.7916	−0.704378
$639$	7.38994	0.292342
$640$	17.3995	0.687776
$641$	3.37408	0.133268	0.0666340	−	0.997777i	$-0.478774\pi$
$641$	3.37408	0.133268	0.0666340	+	0.997777i	$0.478774\pi$
$642$	−6.94319	−0.274026
$643$	3.26800	0.128877	0.0644387	−	0.997922i	$-0.479474\pi$
$643$	3.26800	0.128877	0.0644387	+	0.997922i	$0.479474\pi$
$644$	10.2860	0.405327
$645$	−5.42956	−0.213789
$646$	18.3221	0.720874
$647$	1.39918	0.0550076	0.0275038	−	0.999622i	$-0.491244\pi$
$647$	1.39918	0.0550076	0.0275038	+	0.999622i	$0.491244\pi$
$648$	0.756961	0.0297362
$649$	5.46628	0.214570
$650$	0	0
$651$	1.89738	0.0743641
$652$	2.29309	0.0898044
$653$	14.4639	0.566017	0.283008	−	0.959117i	$-0.408668\pi$
$653$	14.4639	0.566017	0.283008	+	0.959117i	$0.408668\pi$
$654$	5.30114	0.207291
$655$	42.6495	1.66645
$656$	−20.4031	−0.796608
$657$	−12.6053	−0.491781
$658$	4.75235	0.185266
$659$	−29.3539	−1.14347	−0.571733	−	0.820440i	$-0.693729\pi$
$659$	−29.3539	−1.14347	−0.571733	+	0.820440i	$0.693729\pi$
$660$	−6.90113	−0.268626
$661$	−26.6244	−1.03557	−0.517784	−	0.855511i	$-0.673243\pi$
$661$	−26.6244	−1.03557	−0.517784	+	0.855511i	$0.673243\pi$
$662$	−33.6067	−1.30616
$663$	0	0
$664$	13.6201	0.528564
$665$	−18.4272	−0.714576
$666$	1.77954	0.0689558
$667$	−46.8943	−1.81576
$668$	28.3889	1.09840
$669$	−16.0883	−0.622009
$670$	6.10464	0.235843
$671$	−1.14097	−0.0440467
$672$	−6.39068	−0.246526
$673$	−12.0316	−0.463784	−0.231892	−	0.972742i	$-0.574492\pi$
$673$	−12.0316	−0.463784	−0.231892	+	0.972742i	$0.574492\pi$
$674$	22.8552	0.880348
$675$	3.53350	0.136004
$676$	0	0
$677$	13.7989	0.530335	0.265168	−	0.964202i	$-0.414573\pi$
$677$	13.7989	0.530335	0.265168	+	0.964202i	$0.414573\pi$
$678$	−6.55916	−0.251903
$679$	12.3541	0.474107
$680$	−2.43207	−0.0932657
$681$	−17.1332	−0.656547
$682$	5.01065	0.191868
$683$	−15.3270	−0.586471	−0.293236	−	0.956040i	$-0.594732\pi$
$683$	−15.3270	−0.586471	−0.293236	+	0.956040i	$0.594732\pi$
$684$	18.8421	0.720445
$685$	48.2203	1.84240
$686$	−22.0935	−0.843533
$687$	−7.34582	−0.280260
$688$	−5.84330	−0.222774
$689$	0	0
$690$	−33.5888	−1.27871
$691$	20.2572	0.770621	0.385310	−	0.922787i	$-0.374094\pi$
$691$	20.2572	0.770621	0.385310	+	0.922787i	$0.374094\pi$
$692$	16.3568	0.621791
$693$	0.790904	0.0300440
$694$	−12.4721	−0.473436
$695$	62.7701	2.38101
$696$	−6.44801	−0.244411
$697$	7.13804	0.270373
$698$	−65.5689	−2.48182
$699$	−23.9636	−0.906387
$700$	6.60215	0.249538
$701$	−22.7355	−0.858710	−0.429355	−	0.903136i	$-0.641259\pi$
$701$	−22.7355	−0.858710	−0.429355	+	0.903136i	$0.641259\pi$
$702$	0	0
$703$	6.79542	0.256294
$704$	−10.5890	−0.399090
$705$	−8.40397	−0.316512
$706$	−4.57252	−0.172089
$707$	10.7615	0.404727
$708$	12.9136	0.485325
$709$	22.1284	0.831049	0.415524	−	0.909582i	$-0.363598\pi$
$709$	22.1284	0.831049	0.415524	+	0.909582i	$0.363598\pi$
$710$	−45.0888	−1.69215
$711$	−1.98358	−0.0743900
$712$	8.15869	0.305760
$713$	13.2068	0.494599
$714$	1.81688	0.0679952
$715$	0	0
$716$	−9.13333	−0.341329
$717$	−1.31728	−0.0491948
$718$	68.8824	2.57067
$719$	−27.6537	−1.03131	−0.515654	−	0.856797i	$-0.672451\pi$
$719$	−27.6537	−1.03131	−0.515654	+	0.856797i	$0.672451\pi$
$720$	9.18377	0.342259
$721$	7.45915	0.277793
$722$	93.1800	3.46780
$723$	−4.96510	−0.184654
$724$	1.07526	0.0399617
$725$	−30.0993	−1.11786
$726$	2.08864	0.0775167
$727$	−6.47028	−0.239970	−0.119985	−	0.992776i	$-0.538285\pi$
$727$	−6.47028	−0.239970	−0.119985	+	0.992776i	$0.538285\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	76.9098	2.84656
$731$	2.04428	0.0756105
$732$	−2.69545	−0.0996268
$733$	−26.2710	−0.970341	−0.485171	−	0.874419i	$-0.661243\pi$
$733$	−26.2710	−0.970341	−0.485171	+	0.874419i	$0.661243\pi$
$734$	13.8634	0.511706
$735$	18.6212	0.686853
$736$	−44.4827	−1.63965
$737$	−1.00054	−0.0368553
$738$	13.5551	0.498970
$739$	35.4995	1.30587	0.652935	−	0.757414i	$-0.273537\pi$
$739$	35.4995	1.30587	0.652935	+	0.757414i	$0.273537\pi$
$740$	−5.87983	−0.216147
$741$	0	0
$742$	21.2181	0.778941
$743$	22.3034	0.818233	0.409117	−	0.912482i	$-0.365837\pi$
$743$	22.3034	0.818233	0.409117	+	0.912482i	$0.365837\pi$
$744$	1.81595	0.0665759
$745$	−68.7594	−2.51915
$746$	60.0197	2.19748
$747$	17.9932	0.658337
$748$	2.59834	0.0950048
$749$	−2.62917	−0.0960679
$750$	8.94768	0.326723
$751$	−37.2489	−1.35923	−0.679615	−	0.733569i	$-0.737853\pi$
$751$	−37.2489	−1.35923	−0.679615	+	0.733569i	$0.737853\pi$
$752$	−9.04437	−0.329814
$753$	4.47882	0.163217
$754$	0	0
$755$	26.2038	0.953653
$756$	1.86845	0.0679547
$757$	36.6749	1.33297	0.666486	−	0.745517i	$-0.267798\pi$
$757$	36.6749	1.33297	0.666486	+	0.745517i	$0.267798\pi$
$758$	43.7725	1.58989
$759$	5.50513	0.199824
$760$	−17.6364	−0.639738
$761$	40.3013	1.46092	0.730461	−	0.682955i	$-0.239305\pi$
$761$	40.3013	1.46092	0.730461	+	0.682955i	$0.239305\pi$
$762$	−4.05676	−0.146961
$763$	2.00738	0.0726720
$764$	59.2755	2.14451
$765$	−3.21294	−0.116164
$766$	−6.07774	−0.219598
$767$	0	0
$768$	8.73761	0.315291
$769$	−36.6058	−1.32004	−0.660019	−	0.751249i	$-0.729452\pi$
$769$	−36.6058	−1.32004	−0.660019	+	0.751249i	$0.729452\pi$
$770$	−4.82560	−0.173902
$771$	−7.80222	−0.280990
$772$	−3.94441	−0.141963
$773$	−24.9995	−0.899171	−0.449585	−	0.893237i	$-0.648428\pi$
$773$	−24.9995	−0.899171	−0.449585	+	0.893237i	$0.648428\pi$
$774$	3.88208	0.139538
$775$	8.47686	0.304498
$776$	11.8239	0.424453
$777$	0.673858	0.0241745
$778$	43.4984	1.55949
$779$	51.7620	1.85457
$780$	0	0
$781$	7.38994	0.264433
$782$	12.6465	0.452239
$783$	−8.51829	−0.304419
$784$	20.0402	0.715720
$785$	−0.608561	−0.0217205
$786$	−30.4940	−1.08768
$787$	−44.1903	−1.57521	−0.787606	−	0.616179i	$-0.788680\pi$
$787$	−44.1903	−1.57521	−0.787606	+	0.616179i	$0.788680\pi$
$788$	22.4051	0.798149
$789$	−10.6126	−0.377819
$790$	12.1025	0.430589
$791$	−2.48375	−0.0883121
$792$	0.756961	0.0268974
$793$	0	0
$794$	−64.2813	−2.28126
$795$	−37.5217	−1.33076
$796$	−27.1417	−0.962011
$797$	−41.2725	−1.46195	−0.730974	−	0.682405i	$-0.760934\pi$
$797$	−41.2725	−1.46195	−0.730974	+	0.682405i	$0.760934\pi$
$798$	13.1753	0.466399
$799$	3.16418	0.111941
$800$	−28.5514	−1.00945
$801$	10.7782	0.380830
$802$	−47.8862	−1.69092
$803$	−12.6053	−0.444833
$804$	−2.36369	−0.0833608
$805$	−12.7191	−0.448288
$806$	0	0
$807$	−15.5131	−0.546088
$808$	10.2996	0.362340
$809$	−50.7139	−1.78301	−0.891504	−	0.453014i	$-0.850349\pi$
$809$	−50.7139	−1.78301	−0.891504	+	0.453014i	$0.850349\pi$
$810$	−6.10137	−0.214380
$811$	2.28942	0.0803923	0.0401961	−	0.999192i	$-0.487202\pi$
$811$	2.28942	0.0803923	0.0401961	+	0.999192i	$0.487202\pi$
$812$	−15.9160	−0.558541
$813$	−9.31583	−0.326720
$814$	1.77954	0.0623729
$815$	−2.83549	−0.0993229
$816$	−3.45778	−0.121046
$817$	14.8243	0.518635
$818$	22.1479	0.774384
$819$	0	0
$820$	−44.7878	−1.56406
$821$	−17.6203	−0.614952	−0.307476	−	0.951556i	$-0.599484\pi$
$821$	−17.6203	−0.614952	−0.307476	+	0.951556i	$0.599484\pi$
$822$	−34.4770	−1.20252
$823$	5.05289	0.176133	0.0880663	−	0.996115i	$-0.471931\pi$
$823$	5.05289	0.176133	0.0880663	+	0.996115i	$0.471931\pi$
$824$	7.13903	0.248700
$825$	3.53350	0.123021
$826$	9.02983	0.314188
$827$	−2.05631	−0.0715049	−0.0357525	−	0.999361i	$-0.511383\pi$
$827$	−2.05631	−0.0715049	−0.0357525	+	0.999361i	$0.511383\pi$
$828$	13.0054	0.451970
$829$	25.4921	0.885379	0.442689	−	0.896675i	$-0.354024\pi$
$829$	25.4921	0.885379	0.442689	+	0.896675i	$0.354024\pi$
$830$	−109.783	−3.81063
$831$	19.2586	0.668073
$832$	0	0
$833$	−7.01106	−0.242919
$834$	−44.8800	−1.55407
$835$	−35.1039	−1.21482
$836$	18.8421	0.651667
$837$	2.39900	0.0829216
$838$	19.2692	0.665644
$839$	6.47244	0.223454	0.111727	−	0.993739i	$-0.464362\pi$
$839$	6.47244	0.223454	0.111727	+	0.993739i	$0.464362\pi$
$840$	−1.74888	−0.0603422
$841$	43.5612	1.50211
$842$	11.9248	0.410956
$843$	−7.40534	−0.255054
$844$	−4.75200	−0.163571
$845$	0	0
$846$	6.00876	0.206585
$847$	0.790904	0.0271758
$848$	−40.3810	−1.38669
$849$	−15.5014	−0.532007
$850$	8.11723	0.278419
$851$	4.69042	0.160786
$852$	17.4581	0.598106
$853$	−17.7273	−0.606970	−0.303485	−	0.952836i	$-0.598150\pi$
$853$	−17.7273	−0.606970	−0.303485	+	0.952836i	$0.598150\pi$
$854$	−1.88479	−0.0644961
$855$	−23.2989	−0.796806
$856$	−2.51634	−0.0860066
$857$	−1.16474	−0.0397868	−0.0198934	−	0.999802i	$-0.506333\pi$
$857$	−1.16474	−0.0397868	−0.0198934	+	0.999802i	$0.506333\pi$
$858$	0	0
$859$	23.3570	0.796931	0.398465	−	0.917183i	$-0.369543\pi$
$859$	23.3570	0.796931	0.398465	+	0.917183i	$0.369543\pi$
$860$	−12.8269	−0.437393
$861$	5.13290	0.174929
$862$	−22.2030	−0.756238
$863$	−47.0994	−1.60328	−0.801641	−	0.597806i	$-0.796039\pi$
$863$	−47.0994	−1.60328	−0.801641	+	0.597806i	$0.796039\pi$
$864$	−8.08022	−0.274895
$865$	−20.2257	−0.687696
$866$	−35.7936	−1.21632
$867$	−15.7903	−0.536267
$868$	4.48240	0.152143
$869$	−1.98358	−0.0672883
$870$	51.9732	1.76206
$871$	0	0
$872$	1.92123	0.0650610
$873$	15.6202	0.528665
$874$	91.7072	3.10204
$875$	3.38821	0.114542
$876$	−29.7791	−1.00614
$877$	−0.336073	−0.0113484	−0.00567419	−	0.999984i	$-0.501806\pi$
$877$	−0.336073	−0.0113484	−0.00567419	+	0.999984i	$0.501806\pi$
$878$	61.8132	2.08609
$879$	−1.81629	−0.0612621
$880$	9.18377	0.309585
$881$	49.9123	1.68159	0.840793	−	0.541356i	$-0.182089\pi$
$881$	49.9123	1.68159	0.840793	+	0.541356i	$0.182089\pi$
$882$	−13.3140	−0.448305
$883$	40.7621	1.37175	0.685877	−	0.727718i	$-0.259419\pi$
$883$	40.7621	1.37175	0.685877	+	0.727718i	$0.259419\pi$
$884$	0	0
$885$	−15.9682	−0.536765
$886$	−61.2426	−2.05749
$887$	15.1667	0.509247	0.254623	−	0.967040i	$-0.418048\pi$
$887$	15.1667	0.509247	0.254623	+	0.967040i	$0.418048\pi$
$888$	0.644938	0.0216427
$889$	−1.53617	−0.0515215
$890$	−65.7619	−2.20434
$891$	1.00000	0.0335013
$892$	−38.0073	−1.27258
$893$	22.9453	0.767834
$894$	49.1623	1.64423
$895$	11.2937	0.377506
$896$	−4.71083	−0.157378
$897$	0	0
$898$	35.6492	1.18963
$899$	−20.4354	−0.681558
$900$	8.34760	0.278253
$901$	14.1273	0.470648
$902$	13.5551	0.451336
$903$	1.47002	0.0489194
$904$	−2.37716	−0.0790631
$905$	−1.32960	−0.0441973
$906$	−18.7354	−0.622443
$907$	30.9091	1.02632	0.513160	−	0.858293i	$-0.328475\pi$
$907$	30.9091	1.02632	0.513160	+	0.858293i	$0.328475\pi$
$908$	−40.4759	−1.34324
$909$	13.6066	0.451301
$910$	0	0
$911$	−34.7951	−1.15281	−0.576407	−	0.817163i	$-0.695546\pi$
$911$	−34.7951	−1.15281	−0.576407	+	0.817163i	$0.695546\pi$
$912$	−25.0743	−0.830294
$913$	17.9932	0.595488
$914$	−48.2787	−1.59692
$915$	3.33302	0.110186
$916$	−17.3539	−0.573389
$917$	−11.5471	−0.381320
$918$	2.29722	0.0758197
$919$	−35.3511	−1.16612	−0.583062	−	0.812427i	$-0.698146\pi$
$919$	−35.3511	−1.16612	−0.583062	+	0.812427i	$0.698146\pi$
$920$	−12.1732	−0.401338
$921$	−29.0363	−0.956779
$922$	−61.3544	−2.02060
$923$	0	0
$924$	1.86845	0.0614674
$925$	3.01057	0.0989870
$926$	83.3459	2.73892
$927$	9.43118	0.309760
$928$	68.8297	2.25945
$929$	33.8608	1.11094	0.555469	−	0.831538i	$-0.312539\pi$
$929$	33.8608	1.11094	0.555469	+	0.831538i	$0.312539\pi$
$930$	−14.6372	−0.479972
$931$	−50.8412	−1.66625
$932$	−56.6121	−1.85439
$933$	−15.7918	−0.517000
$934$	−54.3423	−1.77813
$935$	−3.21294	−0.105075
$936$	0	0
$937$	−0.726333	−0.0237283	−0.0118641	−	0.999930i	$-0.503777\pi$
$937$	−0.726333	−0.0237283	−0.0118641	+	0.999930i	$0.503777\pi$
$938$	−1.65280	−0.0539659
$939$	−21.1348	−0.689709
$940$	−19.8537	−0.647556
$941$	−22.1799	−0.723046	−0.361523	−	0.932363i	$-0.617743\pi$
$941$	−22.1799	−0.723046	−0.361523	+	0.932363i	$0.617743\pi$
$942$	0.435115	0.0141768
$943$	35.7279	1.16346
$944$	−17.1850	−0.559324
$945$	−2.31040	−0.0751573
$946$	3.88208	0.126217
$947$	−38.6041	−1.25447	−0.627233	−	0.778832i	$-0.715813\pi$
$947$	−38.6041	−1.25447	−0.627233	+	0.778832i	$0.715813\pi$
$948$	−4.68604	−0.152195
$949$	0	0
$950$	58.8627	1.90976
$951$	−20.5708	−0.667054
$952$	0.658471	0.0213412
$953$	13.3622	0.432845	0.216423	−	0.976300i	$-0.430561\pi$
$953$	13.3622	0.432845	0.216423	+	0.976300i	$0.430561\pi$
$954$	26.8277	0.868578
$955$	−73.2963	−2.37181
$956$	−3.11197	−0.100648
$957$	−8.51829	−0.275357
$958$	41.6893	1.34692
$959$	−13.0554	−0.421581
$960$	30.9329	0.998355
$961$	−25.2448	−0.814348
$962$	0	0
$963$	−3.32426	−0.107123
$964$	−11.7296	−0.377786
$965$	4.87741	0.157009
$966$	9.09401	0.292595
$967$	18.2080	0.585529	0.292765	−	0.956185i	$-0.405425\pi$
$967$	18.2080	0.585529	0.292765	+	0.956185i	$0.405425\pi$
$968$	0.756961	0.0243296
$969$	8.77227	0.281806
$970$	−95.3047	−3.06005
$971$	−26.5271	−0.851295	−0.425647	−	0.904889i	$-0.639954\pi$
$971$	−26.5271	−0.851295	−0.425647	+	0.904889i	$0.639954\pi$
$972$	2.36242	0.0757746
$973$	−16.9947	−0.544825
$974$	40.3256	1.29212
$975$	0	0
$976$	3.58701	0.114817
$977$	39.7013	1.27016	0.635079	−	0.772447i	$-0.280967\pi$
$977$	39.7013	1.27016	0.635079	+	0.772447i	$0.280967\pi$
$978$	2.02735	0.0648275
$979$	10.7782	0.344473
$980$	43.9911	1.40524
$981$	2.53808	0.0810347
$982$	32.1758	1.02677
$983$	12.6453	0.403322	0.201661	−	0.979455i	$-0.435366\pi$
$983$	12.6453	0.403322	0.201661	+	0.979455i	$0.435366\pi$
$984$	4.91262	0.156608
$985$	−27.7047	−0.882746
$986$	−19.5684	−0.623185
$987$	2.27533	0.0724246
$988$	0	0
$989$	10.2322	0.325365
$990$	−6.10137	−0.193914
$991$	41.6215	1.32215	0.661075	−	0.750320i	$-0.270100\pi$
$991$	41.6215	1.32215	0.661075	+	0.750320i	$0.270100\pi$
$992$	−19.3845	−0.615457
$993$	−16.0902	−0.510608
$994$	12.2076	0.387200
$995$	33.5616	1.06398
$996$	42.5075	1.34690
$997$	9.40365	0.297817	0.148908	−	0.988851i	$-0.452424\pi$
$997$	9.40365	0.297817	0.148908	+	0.988851i	$0.452424\pi$
$998$	−38.2105	−1.20953
$999$	0.852009	0.0269564

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5577.2.a.bg.1.11		14
13.2	odd	12		429.2.s.b.199.12	yes	28
13.7	odd	12		429.2.s.b.166.12	✓	28
13.12	even	2		5577.2.a.bf.1.4		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.s.b.166.12	✓	28	13.7	odd	12
429.2.s.b.199.12	yes	28	13.2	odd	12
5577.2.a.bf.1.4		14	13.12	even	2
5577.2.a.bg.1.11		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:	\( N \)	\(=\)	\( 5577 = 3 \cdot 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5577.a (trivial)

\(f(q)\)	\(=\)	\(q+2.08864 q^{2} +1.00000 q^{3} +2.36242 q^{4} -2.92121 q^{5} +2.08864 q^{6} +0.790904 q^{7} +0.756961 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.08864 q^{2} +1.00000 q^{3} +2.36242 q^{4} -2.92121 q^{5} +2.08864 q^{6} +0.790904 q^{7} +0.756961 q^{8} +1.00000 q^{9} -6.10137 q^{10} +1.00000 q^{11} +2.36242 q^{12} +1.65191 q^{14} -2.92121 q^{15} -3.14382 q^{16} +1.09987 q^{17} +2.08864 q^{18} +7.97576 q^{19} -6.90113 q^{20} +0.790904 q^{21} +2.08864 q^{22} +5.50513 q^{23} +0.756961 q^{24} +3.53350 q^{25} +1.00000 q^{27} +1.86845 q^{28} -8.51829 q^{29} -6.10137 q^{30} +2.39900 q^{31} -8.08022 q^{32} +1.00000 q^{33} +2.29722 q^{34} -2.31040 q^{35} +2.36242 q^{36} +0.852009 q^{37} +16.6585 q^{38} -2.21125 q^{40} +6.48992 q^{41} +1.65191 q^{42} +1.85866 q^{43} +2.36242 q^{44} -2.92121 q^{45} +11.4982 q^{46} +2.87688 q^{47} -3.14382 q^{48} -6.37447 q^{49} +7.38020 q^{50} +1.09987 q^{51} +12.8446 q^{53} +2.08864 q^{54} -2.92121 q^{55} +0.598683 q^{56} +7.97576 q^{57} -17.7916 q^{58} +5.46628 q^{59} -6.90113 q^{60} -1.14097 q^{61} +5.01065 q^{62} +0.790904 q^{63} -10.5890 q^{64} +2.08864 q^{66} -1.00054 q^{67} +2.59834 q^{68} +5.50513 q^{69} -4.82560 q^{70} +7.38994 q^{71} +0.756961 q^{72} -12.6053 q^{73} +1.77954 q^{74} +3.53350 q^{75} +18.8421 q^{76} +0.790904 q^{77} -1.98358 q^{79} +9.18377 q^{80} +1.00000 q^{81} +13.5551 q^{82} +17.9932 q^{83} +1.86845 q^{84} -3.21294 q^{85} +3.88208 q^{86} -8.51829 q^{87} +0.756961 q^{88} +10.7782 q^{89} -6.10137 q^{90} +13.0054 q^{92} +2.39900 q^{93} +6.00876 q^{94} -23.2989 q^{95} -8.08022 q^{96} +15.6202 q^{97} -13.3140 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 6 q^{2} + 14 q^{3} + 18 q^{4} + 12 q^{5} + 6 q^{6} + 12 q^{7} + 12 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q + 6 * q^2 + 14 * q^3 + 18 * q^4 + 12 * q^5 + 6 * q^6 + 12 * q^7 + 12 * q^8 + 14 * q^9	\( 14 q + 6 q^{2} + 14 q^{3} + 18 q^{4} + 12 q^{5} + 6 q^{6} + 12 q^{7} + 12 q^{8} + 14 q^{9} + 14 q^{11} + 18 q^{12} - 2 q^{14} + 12 q^{15} + 22 q^{16} + 2 q^{17} + 6 q^{18} - 2 q^{19} + 44 q^{20} + 12 q^{21} + 6 q^{22} + 2 q^{23} + 12 q^{24} + 20 q^{25} + 14 q^{27} + 24 q^{28} + 28 q^{31} + 30 q^{32} + 14 q^{33} - 16 q^{34} - 2 q^{35} + 18 q^{36} - 10 q^{38} + 10 q^{40} + 40 q^{41} - 2 q^{42} - 2 q^{43} + 18 q^{44} + 12 q^{45} + 32 q^{46} + 48 q^{47} + 22 q^{48} + 10 q^{49} + 2 q^{51} + 8 q^{53} + 6 q^{54} + 12 q^{55} - 10 q^{56} - 2 q^{57} - 16 q^{58} + 40 q^{59} + 44 q^{60} + 4 q^{61} - 6 q^{62} + 12 q^{63} + 16 q^{64} + 6 q^{66} + 40 q^{67} + 22 q^{68} + 2 q^{69} - 40 q^{70} + 36 q^{71} + 12 q^{72} + 10 q^{73} - 48 q^{74} + 20 q^{75} - 4 q^{76} + 12 q^{77} - 24 q^{79} + 68 q^{80} + 14 q^{81} + 46 q^{82} + 12 q^{83} + 24 q^{84} + 34 q^{85} + 48 q^{86} + 12 q^{88} + 20 q^{89} + 36 q^{92} + 28 q^{93} - 50 q^{94} - 60 q^{95} + 30 q^{96} - 16 q^{97} + 44 q^{98} + 14 q^{99}+O(q^{100}) \) 14 * q + 6 * q^2 + 14 * q^3 + 18 * q^4 + 12 * q^5 + 6 * q^6 + 12 * q^7 + 12 * q^8 + 14 * q^9 + 14 * q^11 + 18 * q^12 - 2 * q^14 + 12 * q^15 + 22 * q^16 + 2 * q^17 + 6 * q^18 - 2 * q^19 + 44 * q^20 + 12 * q^21 + 6 * q^22 + 2 * q^23 + 12 * q^24 + 20 * q^25 + 14 * q^27 + 24 * q^28 + 28 * q^31 + 30 * q^32 + 14 * q^33 - 16 * q^34 - 2 * q^35 + 18 * q^36 - 10 * q^38 + 10 * q^40 + 40 * q^41 - 2 * q^42 - 2 * q^43 + 18 * q^44 + 12 * q^45 + 32 * q^46 + 48 * q^47 + 22 * q^48 + 10 * q^49 + 2 * q^51 + 8 * q^53 + 6 * q^54 + 12 * q^55 - 10 * q^56 - 2 * q^57 - 16 * q^58 + 40 * q^59 + 44 * q^60 + 4 * q^61 - 6 * q^62 + 12 * q^63 + 16 * q^64 + 6 * q^66 + 40 * q^67 + 22 * q^68 + 2 * q^69 - 40 * q^70 + 36 * q^71 + 12 * q^72 + 10 * q^73 - 48 * q^74 + 20 * q^75 - 4 * q^76 + 12 * q^77 - 24 * q^79 + 68 * q^80 + 14 * q^81 + 46 * q^82 + 12 * q^83 + 24 * q^84 + 34 * q^85 + 48 * q^86 + 12 * q^88 + 20 * q^89 + 36 * q^92 + 28 * q^93 - 50 * q^94 - 60 * q^95 + 30 * q^96 - 16 * q^97 + 44 * q^98 + 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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