LMFDB - Embedded newform 5577.2.a.bk.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:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{17} - 29 x^{16} + 26 x^{15} + 347 x^{14} - 277 x^{13} - 2215 x^{12} + 1560 x^{11} + \cdots - 71 $ x^18 - x^17 - 29x^16 + 26x^15 + 347x^14 - 277x^13 - 2215x^12 + 1560x^11 + 8156x^10 - 4977x^9 - 17520x^8 + 8853x^7 + 21169x^6 - 7818x^5 - 13097x^4 + 2237x^3 + 3379x^2 + 285x - 71
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$1.02759$ 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)

$f(q)$	$=$	$q+1.02759 q^{2} +1.00000 q^{3} -0.944062 q^{4} +4.21828 q^{5} +1.02759 q^{6} -0.280543 q^{7} -3.02528 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.02759 q^{2} +1.00000 q^{3} -0.944062 q^{4} +4.21828 q^{5} +1.02759 q^{6} -0.280543 q^{7} -3.02528 q^{8} +1.00000 q^{9} +4.33466 q^{10} -1.00000 q^{11} -0.944062 q^{12} -0.288282 q^{14} +4.21828 q^{15} -1.22062 q^{16} +3.03654 q^{17} +1.02759 q^{18} +6.29266 q^{19} -3.98232 q^{20} -0.280543 q^{21} -1.02759 q^{22} -4.59848 q^{23} -3.02528 q^{24} +12.7939 q^{25} +1.00000 q^{27} +0.264850 q^{28} +5.95426 q^{29} +4.33466 q^{30} +1.87066 q^{31} +4.79627 q^{32} -1.00000 q^{33} +3.12031 q^{34} -1.18341 q^{35} -0.944062 q^{36} -5.56531 q^{37} +6.46626 q^{38} -12.7615 q^{40} -4.85883 q^{41} -0.288282 q^{42} -3.56228 q^{43} +0.944062 q^{44} +4.21828 q^{45} -4.72535 q^{46} +10.4041 q^{47} -1.22062 q^{48} -6.92130 q^{49} +13.1469 q^{50} +3.03654 q^{51} +3.44121 q^{53} +1.02759 q^{54} -4.21828 q^{55} +0.848721 q^{56} +6.29266 q^{57} +6.11853 q^{58} +5.95837 q^{59} -3.98232 q^{60} -9.95328 q^{61} +1.92227 q^{62} -0.280543 q^{63} +7.36983 q^{64} -1.02759 q^{66} +8.39974 q^{67} -2.86668 q^{68} -4.59848 q^{69} -1.21606 q^{70} -14.1046 q^{71} -3.02528 q^{72} -0.579081 q^{73} -5.71885 q^{74} +12.7939 q^{75} -5.94066 q^{76} +0.280543 q^{77} +3.33443 q^{79} -5.14892 q^{80} +1.00000 q^{81} -4.99288 q^{82} +5.30236 q^{83} +0.264850 q^{84} +12.8090 q^{85} -3.66056 q^{86} +5.95426 q^{87} +3.02528 q^{88} +11.8659 q^{89} +4.33466 q^{90} +4.34125 q^{92} +1.87066 q^{93} +10.6912 q^{94} +26.5442 q^{95} +4.79627 q^{96} -2.52495 q^{97} -7.11224 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + q^{2} + 18 q^{3} + 23 q^{4} - 6 q^{5} + q^{6} + q^{7} + 6 q^{8} + 18 q^{9}+O(q^{10}) $ 18 * q + q^2 + 18 * q^3 + 23 * q^4 - 6 * q^5 + q^6 + q^7 + 6 * q^8 + 18 * q^9	$ 18 q + q^{2} + 18 q^{3} + 23 q^{4} - 6 q^{5} + q^{6} + q^{7} + 6 q^{8} + 18 q^{9} - 7 q^{10} - 18 q^{11} + 23 q^{12} + 7 q^{14} - 6 q^{15} + 25 q^{16} + 19 q^{17} + q^{18} - 2 q^{20} + q^{21} - q^{22} + 38 q^{23} + 6 q^{24} + 36 q^{25} + 18 q^{27} + 33 q^{28} + 47 q^{29} - 7 q^{30} - 22 q^{31} + 33 q^{32} - 18 q^{33} + 4 q^{34} + 20 q^{35} + 23 q^{36} - 41 q^{37} + 14 q^{38} - 28 q^{40} + 8 q^{41} + 7 q^{42} + 28 q^{43} - 23 q^{44} - 6 q^{45} + 6 q^{46} + 11 q^{47} + 25 q^{48} + 9 q^{49} - q^{50} + 19 q^{51} + 49 q^{53} + q^{54} + 6 q^{55} + 35 q^{56} - 27 q^{58} - 2 q^{59} - 2 q^{60} - 13 q^{61} + 46 q^{62} + q^{63} + 40 q^{64} - q^{66} + 4 q^{67} + 30 q^{68} + 38 q^{69} - 83 q^{70} + 2 q^{71} + 6 q^{72} + 39 q^{73} + 42 q^{74} + 36 q^{75} + 20 q^{76} - q^{77} + 18 q^{79} + 18 q^{80} + 18 q^{81} - 12 q^{82} + 5 q^{83} + 33 q^{84} + 2 q^{85} + 57 q^{86} + 47 q^{87} - 6 q^{88} - 9 q^{89} - 7 q^{90} + 86 q^{92} - 22 q^{93} - 27 q^{94} + 74 q^{95} + 33 q^{96} - 17 q^{97} + 4 q^{98} - 18 q^{99}+O(q^{100}) $ 18 * q + q^2 + 18 * q^3 + 23 * q^4 - 6 * q^5 + q^6 + q^7 + 6 * q^8 + 18 * q^9 - 7 * q^10 - 18 * q^11 + 23 * q^12 + 7 * q^14 - 6 * q^15 + 25 * q^16 + 19 * q^17 + q^18 - 2 * q^20 + q^21 - q^22 + 38 * q^23 + 6 * q^24 + 36 * q^25 + 18 * q^27 + 33 * q^28 + 47 * q^29 - 7 * q^30 - 22 * q^31 + 33 * q^32 - 18 * q^33 + 4 * q^34 + 20 * q^35 + 23 * q^36 - 41 * q^37 + 14 * q^38 - 28 * q^40 + 8 * q^41 + 7 * q^42 + 28 * q^43 - 23 * q^44 - 6 * q^45 + 6 * q^46 + 11 * q^47 + 25 * q^48 + 9 * q^49 - q^50 + 19 * q^51 + 49 * q^53 + q^54 + 6 * q^55 + 35 * q^56 - 27 * q^58 - 2 * q^59 - 2 * q^60 - 13 * q^61 + 46 * q^62 + q^63 + 40 * q^64 - q^66 + 4 * q^67 + 30 * q^68 + 38 * q^69 - 83 * q^70 + 2 * q^71 + 6 * q^72 + 39 * q^73 + 42 * q^74 + 36 * q^75 + 20 * q^76 - q^77 + 18 * q^79 + 18 * q^80 + 18 * q^81 - 12 * q^82 + 5 * q^83 + 33 * q^84 + 2 * q^85 + 57 * q^86 + 47 * q^87 - 6 * q^88 - 9 * q^89 - 7 * q^90 + 86 * q^92 - 22 * q^93 - 27 * q^94 + 74 * q^95 + 33 * q^96 - 17 * q^97 + 4 * q^98 - 18 * 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 $

$2$	1.02759	0.726615	0.363307	−	0.931669i	$-0.381648\pi$
$2$	1.02759	0.726615	0.363307	+	0.931669i	$0.381648\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.944062	−0.472031
$5$	4.21828	1.88647	0.943236	−	0.332122i	$-0.107765\pi$
$5$	4.21828	1.88647	0.943236	+	0.332122i	$0.107765\pi$
$6$	1.02759	0.419511
$7$	−0.280543	−0.106035	−0.0530176	−	0.998594i	$-0.516884\pi$
$7$	−0.280543	−0.106035	−0.0530176	+	0.998594i	$0.516884\pi$
$8$	−3.02528	−1.06960
$9$	1.00000	0.333333
$10$	4.33466	1.37074
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.944062	−0.272527
$13$	0	0
$13$	0	0
$14$	−0.288282	−0.0770467
$15$	4.21828	1.08916
$16$	−1.22062	−0.305155
$17$	3.03654	0.736469	0.368235	−	0.929733i	$-0.379962\pi$
$17$	3.03654	0.736469	0.368235	+	0.929733i	$0.379962\pi$
$18$	1.02759	0.242205
$19$	6.29266	1.44363	0.721817	−	0.692084i	$-0.243307\pi$
$19$	6.29266	1.44363	0.721817	+	0.692084i	$0.243307\pi$
$20$	−3.98232	−0.890474
$21$	−0.280543	−0.0612194
$22$	−1.02759	−0.219083
$23$	−4.59848	−0.958850	−0.479425	−	0.877583i	$-0.659155\pi$
$23$	−4.59848	−0.958850	−0.479425	+	0.877583i	$0.659155\pi$
$24$	−3.02528	−0.617533
$25$	12.7939	2.55878
$26$	0	0
$27$	1.00000	0.192450
$28$	0.264850	0.0500519
$29$	5.95426	1.10568	0.552839	−	0.833288i	$-0.313544\pi$
$29$	5.95426	1.10568	0.552839	+	0.833288i	$0.313544\pi$
$30$	4.33466	0.791396
$31$	1.87066	0.335980	0.167990	−	0.985789i	$-0.446272\pi$
$31$	1.87066	0.335980	0.167990	+	0.985789i	$0.446272\pi$
$32$	4.79627	0.847869
$33$	−1.00000	−0.174078
$34$	3.12031	0.535129
$35$	−1.18341	−0.200033
$36$	−0.944062	−0.157344
$37$	−5.56531	−0.914931	−0.457466	−	0.889227i	$-0.651243\pi$
$37$	−5.56531	−0.914931	−0.457466	+	0.889227i	$0.651243\pi$
$38$	6.46626	1.04897
$39$	0	0
$40$	−12.7615	−2.01777
$41$	−4.85883	−0.758822	−0.379411	−	0.925228i	$-0.623873\pi$
$41$	−4.85883	−0.758822	−0.379411	+	0.925228i	$0.623873\pi$
$42$	−0.288282	−0.0444829
$43$	−3.56228	−0.543243	−0.271621	−	0.962404i	$-0.587560\pi$
$43$	−3.56228	−0.543243	−0.271621	+	0.962404i	$0.587560\pi$
$44$	0.944062	0.142323
$45$	4.21828	0.628824
$46$	−4.72535	−0.696714
$47$	10.4041	1.51760	0.758800	−	0.651323i	$-0.225786\pi$
$47$	10.4041	1.51760	0.758800	+	0.651323i	$0.225786\pi$
$48$	−1.22062	−0.176181
$49$	−6.92130	−0.988757
$50$	13.1469	1.85925
$51$	3.03654	0.425201
$52$	0	0
$53$	3.44121	0.472686	0.236343	−	0.971670i	$-0.424051\pi$
$53$	3.44121	0.472686	0.236343	+	0.971670i	$0.424051\pi$
$54$	1.02759	0.139837
$55$	−4.21828	−0.568793
$56$	0.848721	0.113415
$57$	6.29266	0.833483
$58$	6.11853	0.803402
$59$	5.95837	0.775714	0.387857	−	0.921720i	$-0.373215\pi$
$59$	5.95837	0.775714	0.387857	+	0.921720i	$0.373215\pi$
$60$	−3.98232	−0.514115
$61$	−9.95328	−1.27439	−0.637194	−	0.770704i	$-0.719905\pi$
$61$	−9.95328	−1.27439	−0.637194	+	0.770704i	$0.719905\pi$
$62$	1.92227	0.244128
$63$	−0.280543	−0.0353451
$64$	7.36983	0.921229
$65$	0	0
$66$	−1.02759	−0.126487
$67$	8.39974	1.02619	0.513096	−	0.858331i	$-0.328498\pi$
$67$	8.39974	1.02619	0.513096	+	0.858331i	$0.328498\pi$
$68$	−2.86668	−0.347637
$69$	−4.59848	−0.553592
$70$	−1.21606	−0.145347
$71$	−14.1046	−1.67391	−0.836955	−	0.547272i	$-0.815666\pi$
$71$	−14.1046	−1.67391	−0.836955	+	0.547272i	$0.815666\pi$
$72$	−3.02528	−0.356533
$73$	−0.579081	−0.0677763	−0.0338881	−	0.999426i	$-0.510789\pi$
$73$	−0.579081	−0.0677763	−0.0338881	+	0.999426i	$0.510789\pi$
$74$	−5.71885	−0.664803
$75$	12.7939	1.47731
$76$	−5.94066	−0.681441
$77$	0.280543	0.0319708
$78$	0	0
$79$	3.33443	0.375152	0.187576	−	0.982250i	$-0.439937\pi$
$79$	3.33443	0.375152	0.187576	+	0.982250i	$0.439937\pi$
$80$	−5.14892	−0.575667
$81$	1.00000	0.111111
$82$	−4.99288	−0.551371
$83$	5.30236	0.582010	0.291005	−	0.956722i	$-0.406010\pi$
$83$	5.30236	0.582010	0.291005	+	0.956722i	$0.406010\pi$
$84$	0.264850	0.0288975
$85$	12.8090	1.38933
$86$	−3.66056	−0.394728
$87$	5.95426	0.638364
$88$	3.02528	0.322496
$89$	11.8659	1.25779	0.628894	−	0.777491i	$-0.283508\pi$
$89$	11.8659	1.25779	0.628894	+	0.777491i	$0.283508\pi$
$90$	4.33466	0.456913
$91$	0	0
$92$	4.34125	0.452607
$93$	1.87066	0.193978
$94$	10.6912	1.10271
$95$	26.5442	2.72338
$96$	4.79627	0.489517
$97$	−2.52495	−0.256370	−0.128185	−	0.991750i	$-0.540915\pi$
$97$	−2.52495	−0.256370	−0.128185	+	0.991750i	$0.540915\pi$
$98$	−7.11224	−0.718445
$99$	−1.00000	−0.100504
$100$	−12.0782	−1.20782
$101$	4.39218	0.437038	0.218519	−	0.975833i	$-0.429877\pi$
$101$	4.39218	0.437038	0.218519	+	0.975833i	$0.429877\pi$
$102$	3.12031	0.308957
$103$	3.84604	0.378962	0.189481	−	0.981884i	$-0.439320\pi$
$103$	3.84604	0.378962	0.189481	+	0.981884i	$0.439320\pi$
$104$	0	0
$105$	−1.18341	−0.115489
$106$	3.53615	0.343461
$107$	14.6964	1.42076	0.710379	−	0.703819i	$-0.248524\pi$
$107$	14.6964	1.42076	0.710379	+	0.703819i	$0.248524\pi$
$108$	−0.944062	−0.0908425
$109$	16.6950	1.59909	0.799547	−	0.600604i	$-0.205073\pi$
$109$	16.6950	1.59909	0.799547	+	0.600604i	$0.205073\pi$
$110$	−4.33466	−0.413293
$111$	−5.56531	−0.528236
$112$	0.342436	0.0323572
$113$	−11.1630	−1.05012	−0.525062	−	0.851064i	$-0.675958\pi$
$113$	−11.1630	−1.05012	−0.525062	+	0.851064i	$0.675958\pi$
$114$	6.46626	0.605621
$115$	−19.3977	−1.80884
$116$	−5.62119	−0.521915
$117$	0	0
$118$	6.12275	0.563645
$119$	−0.851879	−0.0780917
$120$	−12.7615	−1.16496
$121$	1.00000	0.0909091
$122$	−10.2279	−0.925989
$123$	−4.85883	−0.438106
$124$	−1.76602	−0.158593
$125$	32.8769	2.94060
$126$	−0.288282	−0.0256822
$127$	8.25937	0.732901	0.366450	−	0.930438i	$-0.380573\pi$
$127$	8.25937	0.732901	0.366450	+	0.930438i	$0.380573\pi$
$128$	−2.01939	−0.178490
$129$	−3.56228	−0.313641
$130$	0	0
$131$	−6.58492	−0.575328	−0.287664	−	0.957731i	$-0.592879\pi$
$131$	−6.58492	−0.575328	−0.287664	+	0.957731i	$0.592879\pi$
$132$	0.944062	0.0821701
$133$	−1.76536	−0.153076
$134$	8.63148	0.745646
$135$	4.21828	0.363052
$136$	−9.18640	−0.787727
$137$	−18.8364	−1.60931	−0.804653	−	0.593745i	$-0.797649\pi$
$137$	−18.8364	−1.60931	−0.804653	+	0.593745i	$0.797649\pi$
$138$	−4.72535	−0.402248
$139$	17.1960	1.45855	0.729274	−	0.684222i	$-0.239858\pi$
$139$	17.1960	1.45855	0.729274	+	0.684222i	$0.239858\pi$
$140$	1.11721	0.0944216
$141$	10.4041	0.876187
$142$	−14.4937	−1.21629
$143$	0	0
$144$	−1.22062	−0.101718
$145$	25.1167	2.08583
$146$	−0.595056	−0.0492472
$147$	−6.92130	−0.570859
$148$	5.25400	0.431876
$149$	−7.96434	−0.652464	−0.326232	−	0.945290i	$-0.605779\pi$
$149$	−7.96434	−0.652464	−0.326232	+	0.945290i	$0.605779\pi$
$150$	13.1469	1.07344
$151$	13.5866	1.10566	0.552829	−	0.833294i	$-0.313548\pi$
$151$	13.5866	1.10566	0.552829	+	0.833294i	$0.313548\pi$
$152$	−19.0371	−1.54411
$153$	3.03654	0.245490
$154$	0.288282	0.0232305
$155$	7.89096	0.633817
$156$	0	0
$157$	−10.4482	−0.833854	−0.416927	−	0.908940i	$-0.636893\pi$
$157$	−10.4482	−0.833854	−0.416927	+	0.908940i	$0.636893\pi$
$158$	3.42642	0.272591
$159$	3.44121	0.272906
$160$	20.2320	1.59948
$161$	1.29007	0.101672
$162$	1.02759	0.0807350
$163$	9.64228	0.755242	0.377621	−	0.925960i	$-0.376742\pi$
$163$	9.64228	0.755242	0.377621	+	0.925960i	$0.376742\pi$
$164$	4.58704	0.358188
$165$	−4.21828	−0.328393
$166$	5.44865	0.422897
$167$	−19.6568	−1.52109	−0.760546	−	0.649284i	$-0.775069\pi$
$167$	−19.6568	−1.52109	−0.760546	+	0.649284i	$0.775069\pi$
$168$	0.848721	0.0654803
$169$	0	0
$170$	13.1624	1.00951
$171$	6.29266	0.481211
$172$	3.36302	0.256428
$173$	4.53624	0.344884	0.172442	−	0.985020i	$-0.444834\pi$
$173$	4.53624	0.344884	0.172442	+	0.985020i	$0.444834\pi$
$174$	6.11853	0.463844
$175$	−3.58924	−0.271321
$176$	1.22062	0.0920078
$177$	5.95837	0.447859
$178$	12.1933	0.913927
$179$	−8.12881	−0.607576	−0.303788	−	0.952740i	$-0.598251\pi$
$179$	−8.12881	−0.607576	−0.303788	+	0.952740i	$0.598251\pi$
$180$	−3.98232	−0.296825
$181$	−7.33458	−0.545175	−0.272588	−	0.962131i	$-0.587879\pi$
$181$	−7.33458	−0.545175	−0.272588	+	0.962131i	$0.587879\pi$
$182$	0	0
$183$	−9.95328	−0.735768
$184$	13.9117	1.02559
$185$	−23.4760	−1.72599
$186$	1.92227	0.140947
$187$	−3.03654	−0.222054
$188$	−9.82217	−0.716355
$189$	−0.280543	−0.0204065
$190$	27.2765	1.97885
$191$	24.9404	1.80462	0.902311	−	0.431085i	$-0.141869\pi$
$191$	24.9404	1.80462	0.902311	+	0.431085i	$0.141869\pi$
$192$	7.36983	0.531872
$193$	11.4126	0.821499	0.410749	−	0.911748i	$-0.365267\pi$
$193$	11.4126	0.821499	0.410749	+	0.911748i	$0.365267\pi$
$194$	−2.59461	−0.186282
$195$	0	0
$196$	6.53414	0.466724
$197$	−26.0221	−1.85400	−0.926998	−	0.375066i	$-0.877620\pi$
$197$	−26.0221	−1.85400	−0.926998	+	0.375066i	$0.877620\pi$
$198$	−1.02759	−0.0730275
$199$	−0.0998653	−0.00707926	−0.00353963	−	0.999994i	$-0.501127\pi$
$199$	−0.0998653	−0.00707926	−0.00353963	+	0.999994i	$0.501127\pi$
$200$	−38.7052	−2.73687
$201$	8.39974	0.592472
$202$	4.51335	0.317558
$203$	−1.67042	−0.117241
$204$	−2.86668	−0.200708
$205$	−20.4959	−1.43150
$206$	3.95214	0.275359
$207$	−4.59848	−0.319617
$208$	0	0
$209$	−6.29266	−0.435272
$210$	−1.21606	−0.0839159
$211$	−11.4162	−0.785923	−0.392962	−	0.919555i	$-0.628550\pi$
$211$	−11.4162	−0.785923	−0.392962	+	0.919555i	$0.628550\pi$
$212$	−3.24872	−0.223123
$213$	−14.1046	−0.966432
$214$	15.1019	1.03234
$215$	−15.0267	−1.02481
$216$	−3.02528	−0.205844
$217$	−0.524799	−0.0356257
$218$	17.1556	1.16192
$219$	−0.579081	−0.0391306
$220$	3.98232	0.268488
$221$	0	0
$222$	−5.71885	−0.383824
$223$	−10.1288	−0.678271	−0.339136	−	0.940737i	$-0.610135\pi$
$223$	−10.1288	−0.678271	−0.339136	+	0.940737i	$0.610135\pi$
$224$	−1.34556	−0.0899040
$225$	12.7939	0.852927
$226$	−11.4709	−0.763036
$227$	6.34684	0.421254	0.210627	−	0.977566i	$-0.432449\pi$
$227$	6.34684	0.421254	0.210627	+	0.977566i	$0.432449\pi$
$228$	−5.94066	−0.393430
$229$	19.1631	1.26633	0.633167	−	0.774015i	$-0.281755\pi$
$229$	19.1631	1.26633	0.633167	+	0.774015i	$0.281755\pi$
$230$	−19.9328	−1.31433
$231$	0.280543	0.0184584
$232$	−18.0133	−1.18263
$233$	−2.32994	−0.152639	−0.0763196	−	0.997083i	$-0.524317\pi$
$233$	−2.32994	−0.152639	−0.0763196	+	0.997083i	$0.524317\pi$
$234$	0	0
$235$	43.8876	2.86291
$236$	−5.62507	−0.366161
$237$	3.33443	0.216594
$238$	−0.875381	−0.0567425
$239$	−26.5607	−1.71807	−0.859036	−	0.511916i	$-0.828936\pi$
$239$	−26.5607	−1.71807	−0.859036	+	0.511916i	$0.828936\pi$
$240$	−5.14892	−0.332362
$241$	−30.8932	−1.99001	−0.995005	−	0.0998299i	$-0.968170\pi$
$241$	−30.8932	−1.99001	−0.995005	+	0.0998299i	$0.968170\pi$
$242$	1.02759	0.0660559
$243$	1.00000	0.0641500
$244$	9.39652	0.601551
$245$	−29.1960	−1.86526
$246$	−4.99288	−0.318334
$247$	0	0
$248$	−5.65927	−0.359364
$249$	5.30236	0.336024
$250$	33.7839	2.13668
$251$	10.2050	0.644133	0.322066	−	0.946717i	$-0.395623\pi$
$251$	10.2050	0.644133	0.322066	+	0.946717i	$0.395623\pi$
$252$	0.264850	0.0166840
$253$	4.59848	0.289104
$254$	8.48723	0.532536
$255$	12.8090	0.802130
$256$	−16.8148	−1.05092
$257$	−31.0001	−1.93374	−0.966868	−	0.255279i	$-0.917833\pi$
$257$	−31.0001	−1.93374	−0.966868	+	0.255279i	$0.917833\pi$
$258$	−3.66056	−0.227896
$259$	1.56131	0.0970149
$260$	0	0
$261$	5.95426	0.368559
$262$	−6.76659	−0.418041
$263$	23.5474	1.45200	0.725998	−	0.687696i	$-0.241378\pi$
$263$	23.5474	1.45200	0.725998	+	0.687696i	$0.241378\pi$
$264$	3.02528	0.186193
$265$	14.5160	0.891710
$266$	−1.81406	−0.111227
$267$	11.8659	0.726184
$268$	−7.92988	−0.484395
$269$	29.5547	1.80198	0.900990	−	0.433840i	$-0.142842\pi$
$269$	29.5547	1.80198	0.900990	+	0.433840i	$0.142842\pi$
$270$	4.33466	0.263799
$271$	−22.7356	−1.38109	−0.690544	−	0.723290i	$-0.742629\pi$
$271$	−22.7356	−1.38109	−0.690544	+	0.723290i	$0.742629\pi$
$272$	−3.70647	−0.224737
$273$	0	0
$274$	−19.3561	−1.16935
$275$	−12.7939	−0.771501
$276$	4.34125	0.261313
$277$	11.1735	0.671349	0.335674	−	0.941978i	$-0.391036\pi$
$277$	11.1735	0.671349	0.335674	+	0.941978i	$0.391036\pi$
$278$	17.6704	1.05980
$279$	1.87066	0.111993
$280$	3.58015	0.213955
$281$	15.0197	0.896001	0.448000	−	0.894033i	$-0.352136\pi$
$281$	15.0197	0.896001	0.448000	+	0.894033i	$0.352136\pi$
$282$	10.6912	0.636650
$283$	8.74879	0.520062	0.260031	−	0.965600i	$-0.416267\pi$
$283$	8.74879	0.520062	0.260031	+	0.965600i	$0.416267\pi$
$284$	13.3156	0.790138
$285$	26.5442	1.57234
$286$	0	0
$287$	1.36311	0.0804618
$288$	4.79627	0.282623
$289$	−7.77942	−0.457613
$290$	25.8097	1.51560
$291$	−2.52495	−0.148015
$292$	0.546688	0.0319925
$293$	−0.698890	−0.0408296	−0.0204148	−	0.999792i	$-0.506499\pi$
$293$	−0.698890	−0.0408296	−0.0204148	+	0.999792i	$0.506499\pi$
$294$	−7.11224	−0.414794
$295$	25.1341	1.46336
$296$	16.8366	0.978610
$297$	−1.00000	−0.0580259
$298$	−8.18406	−0.474090
$299$	0	0
$300$	−12.0782	−0.697338
$301$	0.999373	0.0576029
$302$	13.9614	0.803388
$303$	4.39218	0.252324
$304$	−7.68095	−0.440533
$305$	−41.9858	−2.40410
$306$	3.12031	0.178376
$307$	11.1086	0.633999	0.316999	−	0.948426i	$-0.397325\pi$
$307$	11.1086	0.633999	0.316999	+	0.948426i	$0.397325\pi$
$308$	−0.264850	−0.0150912
$309$	3.84604	0.218794
$310$	8.10866	0.460541
$311$	5.99123	0.339732	0.169866	−	0.985467i	$-0.445667\pi$
$311$	5.99123	0.339732	0.169866	+	0.985467i	$0.445667\pi$
$312$	0	0
$313$	−16.1118	−0.910692	−0.455346	−	0.890314i	$-0.650485\pi$
$313$	−16.1118	−0.910692	−0.455346	+	0.890314i	$0.650485\pi$
$314$	−10.7364	−0.605890
$315$	−1.18341	−0.0666775
$316$	−3.14791	−0.177084
$317$	−20.8731	−1.17235	−0.586175	−	0.810185i	$-0.699367\pi$
$317$	−20.8731	−1.17235	−0.586175	+	0.810185i	$0.699367\pi$
$318$	3.53615	0.198297
$319$	−5.95426	−0.333374
$320$	31.0880	1.73787
$321$	14.6964	0.820275
$322$	1.32566	0.0738762
$323$	19.1079	1.06319
$324$	−0.944062	−0.0524479
$325$	0	0
$326$	9.90829	0.548770
$327$	16.6950	0.923237
$328$	14.6993	0.811635
$329$	−2.91881	−0.160919
$330$	−4.33466	−0.238615
$331$	−12.7876	−0.702868	−0.351434	−	0.936213i	$-0.614306\pi$
$331$	−12.7876	−0.702868	−0.351434	+	0.936213i	$0.614306\pi$
$332$	−5.00576	−0.274727
$333$	−5.56531	−0.304977
$334$	−20.1991	−1.10525
$335$	35.4325	1.93588
$336$	0.342436	0.0186814
$337$	14.7158	0.801619	0.400809	−	0.916161i	$-0.368729\pi$
$337$	14.7158	0.801619	0.400809	+	0.916161i	$0.368729\pi$
$338$	0	0
$339$	−11.1630	−0.606290
$340$	−12.0925	−0.655807
$341$	−1.87066	−0.101302
$342$	6.46626	0.349655
$343$	3.90552	0.210878
$344$	10.7769	0.581052
$345$	−19.3977	−1.04434
$346$	4.66139	0.250598
$347$	35.4358	1.90230	0.951148	−	0.308737i	$-0.0999062\pi$
$347$	35.4358	1.90230	0.951148	+	0.308737i	$0.0999062\pi$
$348$	−5.62119	−0.301328
$349$	−34.6911	−1.85697	−0.928486	−	0.371368i	$-0.878889\pi$
$349$	−34.6911	−1.85697	−0.928486	+	0.371368i	$0.878889\pi$
$350$	−3.68826	−0.197146
$351$	0	0
$352$	−4.79627	−0.255642
$353$	−2.00914	−0.106936	−0.0534679	−	0.998570i	$-0.517027\pi$
$353$	−2.00914	−0.106936	−0.0534679	+	0.998570i	$0.517027\pi$
$354$	6.12275	0.325421
$355$	−59.4972	−3.15779
$356$	−11.2022	−0.593715
$357$	−0.851879	−0.0450862
$358$	−8.35307	−0.441473
$359$	−34.6240	−1.82738	−0.913692	−	0.406406i	$-0.866782\pi$
$359$	−34.6240	−1.82738	−0.913692	+	0.406406i	$0.866782\pi$
$360$	−12.7615	−0.672590
$361$	20.5975	1.08408
$362$	−7.53693	−0.396132
$363$	1.00000	0.0524864
$364$	0	0
$365$	−2.44273	−0.127858
$366$	−10.2279	−0.534620
$367$	28.5642	1.49104	0.745520	−	0.666483i	$-0.232201\pi$
$367$	28.5642	1.49104	0.745520	+	0.666483i	$0.232201\pi$
$368$	5.61300	0.292598
$369$	−4.85883	−0.252941
$370$	−24.1237	−1.25413
$371$	−0.965406	−0.0501214
$372$	−1.76602	−0.0915637
$373$	−34.1618	−1.76883	−0.884415	−	0.466701i	$-0.845443\pi$
$373$	−34.1618	−1.76883	−0.884415	+	0.466701i	$0.845443\pi$
$374$	−3.12031	−0.161348
$375$	32.8769	1.69775
$376$	−31.4755	−1.62322
$377$	0	0
$378$	−0.288282	−0.0148276
$379$	−24.6549	−1.26644	−0.633220	−	0.773972i	$-0.718267\pi$
$379$	−24.6549	−1.26644	−0.633220	+	0.773972i	$0.718267\pi$
$380$	−25.0594	−1.28552
$381$	8.25937	0.423140
$382$	25.6284	1.31127
$383$	7.83905	0.400557	0.200278	−	0.979739i	$-0.435815\pi$
$383$	7.83905	0.400557	0.200278	+	0.979739i	$0.435815\pi$
$384$	−2.01939	−0.103052
$385$	1.18341	0.0603121
$386$	11.7275	0.596913
$387$	−3.56228	−0.181081
$388$	2.38371	0.121015
$389$	8.70245	0.441232	0.220616	−	0.975361i	$-0.429193\pi$
$389$	8.70245	0.441232	0.220616	+	0.975361i	$0.429193\pi$
$390$	0	0
$391$	−13.9635	−0.706163
$392$	20.9389	1.05757
$393$	−6.58492	−0.332166
$394$	−26.7400	−1.34714
$395$	14.0656	0.707715
$396$	0.944062	0.0474409
$397$	1.24810	0.0626405	0.0313202	−	0.999509i	$-0.490029\pi$
$397$	1.24810	0.0626405	0.0313202	+	0.999509i	$0.490029\pi$
$398$	−0.102620	−0.00514390
$399$	−1.76536	−0.0883785
$400$	−15.6165	−0.780825
$401$	−34.6525	−1.73046	−0.865232	−	0.501371i	$-0.832829\pi$
$401$	−34.6525	−1.73046	−0.865232	+	0.501371i	$0.832829\pi$
$402$	8.63148	0.430499
$403$	0	0
$404$	−4.14649	−0.206296
$405$	4.21828	0.209608
$406$	−1.71651	−0.0851889
$407$	5.56531	0.275862
$408$	−9.18640	−0.454794
$409$	−14.3374	−0.708941	−0.354470	−	0.935067i	$-0.615339\pi$
$409$	−14.3374	−0.708941	−0.354470	+	0.935067i	$0.615339\pi$
$410$	−21.0614	−1.04015
$411$	−18.8364	−0.929133
$412$	−3.63090	−0.178882
$413$	−1.67158	−0.0822530
$414$	−4.72535	−0.232238
$415$	22.3669	1.09795
$416$	0	0
$417$	17.1960	0.842093
$418$	−6.46626	−0.316275
$419$	−28.5933	−1.39688	−0.698438	−	0.715671i	$-0.746121\pi$
$419$	−28.5933	−1.39688	−0.698438	+	0.715671i	$0.746121\pi$
$420$	1.11721	0.0545143
$421$	−3.27579	−0.159652	−0.0798262	−	0.996809i	$-0.525437\pi$
$421$	−3.27579	−0.159652	−0.0798262	+	0.996809i	$0.525437\pi$
$422$	−11.7311	−0.571063
$423$	10.4041	0.505867
$424$	−10.4106	−0.505585
$425$	38.8492	1.88446
$426$	−14.4937	−0.702224
$427$	2.79232	0.135130
$428$	−13.8744	−0.670642
$429$	0	0
$430$	−15.4413	−0.744644
$431$	33.3192	1.60493	0.802464	−	0.596701i	$-0.203522\pi$
$431$	33.3192	1.60493	0.802464	+	0.596701i	$0.203522\pi$
$432$	−1.22062	−0.0587272
$433$	0.0576705	0.00277147	0.00138573	−	0.999999i	$-0.499559\pi$
$433$	0.0576705	0.00277147	0.00138573	+	0.999999i	$0.499559\pi$
$434$	−0.539278	−0.0258862
$435$	25.1167	1.20426
$436$	−15.7611	−0.754822
$437$	−28.9367	−1.38423
$438$	−0.595056	−0.0284329
$439$	15.6132	0.745178	0.372589	−	0.927996i	$-0.378470\pi$
$439$	15.6132	0.745178	0.372589	+	0.927996i	$0.378470\pi$
$440$	12.7615	0.608381
$441$	−6.92130	−0.329586
$442$	0	0
$443$	−19.6352	−0.932898	−0.466449	−	0.884548i	$-0.654467\pi$
$443$	−19.6352	−0.932898	−0.466449	+	0.884548i	$0.654467\pi$
$444$	5.25400	0.249344
$445$	50.0539	2.37278
$446$	−10.4082	−0.492842
$447$	−7.96434	−0.376700
$448$	−2.06755	−0.0976827
$449$	−19.1669	−0.904543	−0.452271	−	0.891880i	$-0.649386\pi$
$449$	−19.1669	−0.904543	−0.452271	+	0.891880i	$0.649386\pi$
$450$	13.1469	0.619749
$451$	4.85883	0.228793
$452$	10.5385	0.495691
$453$	13.5866	0.638352
$454$	6.52194	0.306090
$455$	0	0
$456$	−19.0371	−0.891493
$457$	21.5196	1.00664	0.503322	−	0.864099i	$-0.332111\pi$
$457$	21.5196	1.00664	0.503322	+	0.864099i	$0.332111\pi$
$458$	19.6918	0.920137
$459$	3.03654	0.141734
$460$	18.3126	0.853831
$461$	31.4756	1.46597	0.732983	−	0.680247i	$-0.238127\pi$
$461$	31.4756	1.46597	0.732983	+	0.680247i	$0.238127\pi$
$462$	0.288282	0.0134121
$463$	−19.0878	−0.887086	−0.443543	−	0.896253i	$-0.646279\pi$
$463$	−19.0878	−0.887086	−0.443543	+	0.896253i	$0.646279\pi$
$464$	−7.26789	−0.337403
$465$	7.89096	0.365935
$466$	−2.39422	−0.110910
$467$	−33.8103	−1.56455	−0.782277	−	0.622931i	$-0.785942\pi$
$467$	−33.8103	−1.56455	−0.782277	+	0.622931i	$0.785942\pi$
$468$	0	0
$469$	−2.35649	−0.108812
$470$	45.0984	2.08023
$471$	−10.4482	−0.481426
$472$	−18.0258	−0.829703
$473$	3.56228	0.163794
$474$	3.42642	0.157381
$475$	80.5076	3.69394
$476$	0.804227	0.0368617
$477$	3.44121	0.157562
$478$	−27.2935	−1.24838
$479$	−13.3355	−0.609315	−0.304658	−	0.952462i	$-0.598542\pi$
$479$	−13.3355	−0.609315	−0.304658	+	0.952462i	$0.598542\pi$
$480$	20.2320	0.923461
$481$	0	0
$482$	−31.7455	−1.44597
$483$	1.29007	0.0587003
$484$	−0.944062	−0.0429119
$485$	−10.6510	−0.483636
$486$	1.02759	0.0466123
$487$	5.04496	0.228609	0.114305	−	0.993446i	$-0.463536\pi$
$487$	5.04496	0.228609	0.114305	+	0.993446i	$0.463536\pi$
$488$	30.1115	1.36308
$489$	9.64228	0.436039
$490$	−30.0014	−1.35533
$491$	16.2893	0.735124	0.367562	−	0.929999i	$-0.380193\pi$
$491$	16.2893	0.735124	0.367562	+	0.929999i	$0.380193\pi$
$492$	4.58704	0.206800
$493$	18.0803	0.814298
$494$	0	0
$495$	−4.21828	−0.189598
$496$	−2.28336	−0.102526
$497$	3.95695	0.177493
$498$	5.44865	0.244160
$499$	−13.7989	−0.617723	−0.308861	−	0.951107i	$-0.599948\pi$
$499$	−13.7989	−0.617723	−0.308861	+	0.951107i	$0.599948\pi$
$500$	−31.0378	−1.38805
$501$	−19.6568	−0.878203
$502$	10.4865	0.468036
$503$	−2.13233	−0.0950759	−0.0475380	−	0.998869i	$-0.515138\pi$
$503$	−2.13233	−0.0950759	−0.0475380	+	0.998869i	$0.515138\pi$
$504$	0.848721	0.0378051
$505$	18.5274	0.824460
$506$	4.72535	0.210067
$507$	0	0
$508$	−7.79736	−0.345952
$509$	−16.5769	−0.734758	−0.367379	−	0.930071i	$-0.619745\pi$
$509$	−16.5769	−0.734758	−0.367379	+	0.930071i	$0.619745\pi$
$510$	13.1624	0.582839
$511$	0.162457	0.00718667
$512$	−13.2399	−0.585126
$513$	6.29266	0.277828
$514$	−31.8554	−1.40508
$515$	16.2237	0.714901
$516$	3.36302	0.148049
$517$	−10.4041	−0.457574
$518$	1.60438	0.0704925
$519$	4.53624	0.199119
$520$	0	0
$521$	−34.1395	−1.49568	−0.747839	−	0.663880i	$-0.768909\pi$
$521$	−34.1395	−1.49568	−0.747839	+	0.663880i	$0.768909\pi$
$522$	6.11853	0.267801
$523$	9.54246	0.417262	0.208631	−	0.977994i	$-0.433099\pi$
$523$	9.54246	0.417262	0.208631	+	0.977994i	$0.433099\pi$
$524$	6.21658	0.271573
$525$	−3.58924	−0.156647
$526$	24.1971	1.05504
$527$	5.68033	0.247439
$528$	1.22062	0.0531207
$529$	−1.85396	−0.0806071
$530$	14.9165	0.647930
$531$	5.95837	0.258571
$532$	1.66661	0.0722567
$533$	0	0
$534$	12.1933	0.527656
$535$	61.9937	2.68022
$536$	−25.4116	−1.09761
$537$	−8.12881	−0.350784
$538$	30.3700	1.30934
$539$	6.92130	0.298121
$540$	−3.98232	−0.171372
$541$	5.36984	0.230867	0.115434	−	0.993315i	$-0.463174\pi$
$541$	5.36984	0.230867	0.115434	+	0.993315i	$0.463174\pi$
$542$	−23.3628	−1.00352
$543$	−7.33458	−0.314757
$544$	14.5641	0.624430
$545$	70.4243	3.01665
$546$	0	0
$547$	9.25497	0.395714	0.197857	−	0.980231i	$-0.436602\pi$
$547$	9.25497	0.395714	0.197857	+	0.980231i	$0.436602\pi$
$548$	17.7828	0.759643
$549$	−9.95328	−0.424796
$550$	−13.1469	−0.560584
$551$	37.4681	1.59620
$552$	13.9117	0.592122
$553$	−0.935450	−0.0397794
$554$	11.4817	0.487812
$555$	−23.4760	−0.996503
$556$	−16.2341	−0.688480
$557$	4.49704	0.190546	0.0952729	−	0.995451i	$-0.469628\pi$
$557$	4.49704	0.190546	0.0952729	+	0.995451i	$0.469628\pi$
$558$	1.92227	0.0813760
$559$	0	0
$560$	1.44449	0.0610410
$561$	−3.03654	−0.128203
$562$	15.4341	0.651047
$563$	2.54267	0.107161	0.0535804	−	0.998564i	$-0.482937\pi$
$563$	2.54267	0.107161	0.0535804	+	0.998564i	$0.482937\pi$
$564$	−9.82217	−0.413588
$565$	−47.0886	−1.98103
$566$	8.99016	0.377884
$567$	−0.280543	−0.0117817
$568$	42.6705	1.79041
$569$	−24.2314	−1.01583	−0.507917	−	0.861406i	$-0.669584\pi$
$569$	−24.2314	−1.01583	−0.507917	+	0.861406i	$0.669584\pi$
$570$	27.2765	1.14249
$571$	20.0985	0.841096	0.420548	−	0.907270i	$-0.361838\pi$
$571$	20.0985	0.841096	0.420548	+	0.907270i	$0.361838\pi$
$572$	0	0
$573$	24.9404	1.04190
$574$	1.40072	0.0584647
$575$	−58.8325	−2.45349
$576$	7.36983	0.307076
$577$	−29.4598	−1.22643	−0.613214	−	0.789917i	$-0.710124\pi$
$577$	−29.4598	−1.22643	−0.613214	+	0.789917i	$0.710124\pi$
$578$	−7.99404	−0.332508
$579$	11.4126	0.474293
$580$	−23.7118	−0.984578
$581$	−1.48754	−0.0617136
$582$	−2.59461	−0.107550
$583$	−3.44121	−0.142520
$584$	1.75188	0.0724935
$585$	0	0
$586$	−0.718171	−0.0296674
$587$	3.15994	0.130425	0.0652123	−	0.997871i	$-0.479228\pi$
$587$	3.15994	0.130425	0.0652123	+	0.997871i	$0.479228\pi$
$588$	6.53414	0.269463
$589$	11.7714	0.485032
$590$	25.8275	1.06330
$591$	−26.0221	−1.07041
$592$	6.79314	0.279196
$593$	−4.18467	−0.171844	−0.0859218	−	0.996302i	$-0.527384\pi$
$593$	−4.18467	−0.171844	−0.0859218	+	0.996302i	$0.527384\pi$
$594$	−1.02759	−0.0421625
$595$	−3.59347	−0.147318
$596$	7.51883	0.307983
$597$	−0.0998653	−0.00408722
$598$	0	0
$599$	1.12652	0.0460284	0.0230142	−	0.999735i	$-0.492674\pi$
$599$	1.12652	0.0460284	0.0230142	+	0.999735i	$0.492674\pi$
$600$	−38.7052	−1.58013
$601$	36.3327	1.48204	0.741022	−	0.671481i	$-0.234342\pi$
$601$	36.3327	1.48204	0.741022	+	0.671481i	$0.234342\pi$
$602$	1.02694	0.0418551
$603$	8.39974	0.342064
$604$	−12.8266	−0.521906
$605$	4.21828	0.171498
$606$	4.51335	0.183342
$607$	−40.4178	−1.64051	−0.820253	−	0.572000i	$-0.806168\pi$
$607$	−40.4178	−1.64051	−0.820253	+	0.572000i	$0.806168\pi$
$608$	30.1813	1.22401
$609$	−1.67042	−0.0676890
$610$	−43.1441	−1.74685
$611$	0	0
$612$	−2.86668	−0.115879
$613$	29.9401	1.20927	0.604635	−	0.796502i	$-0.293319\pi$
$613$	29.9401	1.20927	0.604635	+	0.796502i	$0.293319\pi$
$614$	11.4150	0.460673
$615$	−20.4959	−0.826475
$616$	−0.848721	−0.0341960
$617$	−2.93101	−0.117998	−0.0589989	−	0.998258i	$-0.518791\pi$
$617$	−2.93101	−0.117998	−0.0589989	+	0.998258i	$0.518791\pi$
$618$	3.95214	0.158979
$619$	17.8597	0.717844	0.358922	−	0.933368i	$-0.383144\pi$
$619$	17.8597	0.717844	0.358922	+	0.933368i	$0.383144\pi$
$620$	−7.44956	−0.299182
$621$	−4.59848	−0.184531
$622$	6.15652	0.246854
$623$	−3.32891	−0.133370
$624$	0	0
$625$	74.7144	2.98858
$626$	−16.5563	−0.661722
$627$	−6.29266	−0.251305
$628$	9.86372	0.393605
$629$	−16.8993	−0.673819
$630$	−1.21606	−0.0484488
$631$	−19.9991	−0.796150	−0.398075	−	0.917353i	$-0.630322\pi$
$631$	−19.9991	−0.796150	−0.398075	+	0.917353i	$0.630322\pi$
$632$	−10.0876	−0.401263
$633$	−11.4162	−0.453753
$634$	−21.4489	−0.851846
$635$	34.8404	1.38260
$636$	−3.24872	−0.128820
$637$	0	0
$638$	−6.11853	−0.242235
$639$	−14.1046	−0.557970
$640$	−8.51835	−0.336717
$641$	−44.4545	−1.75585	−0.877925	−	0.478799i	$-0.841072\pi$
$641$	−44.4545	−1.75585	−0.877925	+	0.478799i	$0.841072\pi$
$642$	15.1019	0.596024
$643$	17.7248	0.698999	0.349500	−	0.936936i	$-0.386352\pi$
$643$	17.7248	0.698999	0.349500	+	0.936936i	$0.386352\pi$
$644$	−1.21791	−0.0479923
$645$	−15.0267	−0.591676
$646$	19.6351	0.772531
$647$	42.0987	1.65507	0.827536	−	0.561413i	$-0.189742\pi$
$647$	42.0987	1.65507	0.827536	+	0.561413i	$0.189742\pi$
$648$	−3.02528	−0.118844
$649$	−5.95837	−0.233887
$650$	0	0
$651$	−0.524799	−0.0205685
$652$	−9.10291	−0.356498
$653$	39.2544	1.53614	0.768071	−	0.640364i	$-0.221217\pi$
$653$	39.2544	1.53614	0.768071	+	0.640364i	$0.221217\pi$
$654$	17.1556	0.670837
$655$	−27.7771	−1.08534
$656$	5.93079	0.231558
$657$	−0.579081	−0.0225921
$658$	−2.99933	−0.116926
$659$	11.4640	0.446574	0.223287	−	0.974753i	$-0.428321\pi$
$659$	11.4640	0.446574	0.223287	+	0.974753i	$0.428321\pi$
$660$	3.98232	0.155012
$661$	33.9343	1.31989	0.659947	−	0.751313i	$-0.270579\pi$
$661$	33.9343	1.31989	0.659947	+	0.751313i	$0.270579\pi$
$662$	−13.1403	−0.510714
$663$	0	0
$664$	−16.0412	−0.622518
$665$	−7.44678	−0.288774
$666$	−5.71885	−0.221601
$667$	−27.3806	−1.06018
$668$	18.5573	0.718003
$669$	−10.1288	−0.391600
$670$	36.4100	1.40664
$671$	9.95328	0.384242
$672$	−1.34556	−0.0519061
$673$	−33.4005	−1.28749	−0.643747	−	0.765239i	$-0.722621\pi$
$673$	−33.4005	−1.28749	−0.643747	+	0.765239i	$0.722621\pi$
$674$	15.1217	0.582468
$675$	12.7939	0.492437
$676$	0	0
$677$	16.8129	0.646171	0.323086	−	0.946370i	$-0.395280\pi$
$677$	16.8129	0.646171	0.323086	+	0.946370i	$0.395280\pi$
$678$	−11.4709	−0.440539
$679$	0.708358	0.0271843
$680$	−38.7508	−1.48603
$681$	6.34684	0.243211
$682$	−1.92227	−0.0736074
$683$	−33.7542	−1.29157	−0.645783	−	0.763521i	$-0.723469\pi$
$683$	−33.7542	−1.29157	−0.645783	+	0.763521i	$0.723469\pi$
$684$	−5.94066	−0.227147
$685$	−79.4574	−3.03591
$686$	4.01326	0.153227
$687$	19.1631	0.731118
$688$	4.34820	0.165773
$689$	0	0
$690$	−19.9328	−0.758830
$691$	−45.5354	−1.73225	−0.866125	−	0.499828i	$-0.833397\pi$
$691$	−45.5354	−1.73225	−0.866125	+	0.499828i	$0.833397\pi$
$692$	−4.28249	−0.162796
$693$	0.280543	0.0106569
$694$	36.4134	1.38224
$695$	72.5377	2.75151
$696$	−18.0133	−0.682793
$697$	−14.7540	−0.558849
$698$	−35.6482	−1.34930
$699$	−2.32994	−0.0881263
$700$	3.38846	0.128072
$701$	−9.73968	−0.367863	−0.183931	−	0.982939i	$-0.558882\pi$
$701$	−9.73968	−0.367863	−0.183931	+	0.982939i	$0.558882\pi$
$702$	0	0
$703$	−35.0206	−1.32083
$704$	−7.36983	−0.277761
$705$	43.8876	1.65290
$706$	−2.06457	−0.0777012
$707$	−1.23219	−0.0463414
$708$	−5.62507	−0.211403
$709$	−14.7215	−0.552879	−0.276440	−	0.961031i	$-0.589155\pi$
$709$	−14.7215	−0.552879	−0.276440	+	0.961031i	$0.589155\pi$
$710$	−61.1387	−2.29449
$711$	3.33443	0.125051
$712$	−35.8979	−1.34533
$713$	−8.60218	−0.322154
$714$	−0.875381	−0.0327603
$715$	0	0
$716$	7.67410	0.286795
$717$	−26.5607	−0.991929
$718$	−35.5792	−1.32780
$719$	3.99205	0.148878	0.0744392	−	0.997226i	$-0.476283\pi$
$719$	3.99205	0.148878	0.0744392	+	0.997226i	$0.476283\pi$
$720$	−5.14892	−0.191889
$721$	−1.07898	−0.0401833
$722$	21.1658	0.787709
$723$	−30.8932	−1.14893
$724$	6.92430	0.257340
$725$	76.1782	2.82919
$726$	1.02759	0.0381374
$727$	6.29298	0.233394	0.116697	−	0.993168i	$-0.462769\pi$
$727$	6.29298	0.233394	0.116697	+	0.993168i	$0.462769\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−2.51012	−0.0929036
$731$	−10.8170	−0.400082
$732$	9.39652	0.347305
$733$	4.34691	0.160557	0.0802785	−	0.996772i	$-0.474419\pi$
$733$	4.34691	0.160557	0.0802785	+	0.996772i	$0.474419\pi$
$734$	29.3523	1.08341
$735$	−29.1960	−1.07691
$736$	−22.0556	−0.812979
$737$	−8.39974	−0.309409
$738$	−4.99288	−0.183790
$739$	−46.1177	−1.69647	−0.848233	−	0.529623i	$-0.822333\pi$
$739$	−46.1177	−1.69647	−0.848233	+	0.529623i	$0.822333\pi$
$740$	22.1629	0.814723
$741$	0	0
$742$	−0.992040	−0.0364189
$743$	−11.9544	−0.438565	−0.219282	−	0.975661i	$-0.570372\pi$
$743$	−11.9544	−0.438565	−0.219282	+	0.975661i	$0.570372\pi$
$744$	−5.65927	−0.207479
$745$	−33.5958	−1.23086
$746$	−35.1043	−1.28526
$747$	5.30236	0.194003
$748$	2.86668	0.104816
$749$	−4.12298	−0.150650
$750$	33.7839	1.23361
$751$	−0.608996	−0.0222226	−0.0111113	−	0.999938i	$-0.503537\pi$
$751$	−0.608996	−0.0222226	−0.0111113	+	0.999938i	$0.503537\pi$
$752$	−12.6995	−0.463104
$753$	10.2050	0.371890
$754$	0	0
$755$	57.3119	2.08580
$756$	0.264850	0.00963250
$757$	19.7702	0.718559	0.359279	−	0.933230i	$-0.383023\pi$
$757$	19.7702	0.718559	0.359279	+	0.933230i	$0.383023\pi$
$758$	−25.3351	−0.920213
$759$	4.59848	0.166914
$760$	−80.3037	−2.91292
$761$	38.0129	1.37797	0.688983	−	0.724778i	$-0.258058\pi$
$761$	38.0129	1.37797	0.688983	+	0.724778i	$0.258058\pi$
$762$	8.48723	0.307460
$763$	−4.68367	−0.169560
$764$	−23.5453	−0.851838
$765$	12.8090	0.463110
$766$	8.05531	0.291050
$767$	0	0
$768$	−16.8148	−0.606751
$769$	25.8637	0.932668	0.466334	−	0.884609i	$-0.345574\pi$
$769$	25.8637	0.932668	0.466334	+	0.884609i	$0.345574\pi$
$770$	1.21606	0.0438236
$771$	−31.0001	−1.11644
$772$	−10.7742	−0.387773
$773$	−0.420835	−0.0151364	−0.00756820	−	0.999971i	$-0.502409\pi$
$773$	−0.420835	−0.0151364	−0.00756820	+	0.999971i	$0.502409\pi$
$774$	−3.66056	−0.131576
$775$	23.9330	0.859699
$776$	7.63870	0.274214
$777$	1.56131	0.0560116
$778$	8.94254	0.320606
$779$	−30.5750	−1.09546
$780$	0	0
$781$	14.1046	0.504703
$782$	−14.3487	−0.513109
$783$	5.95426	0.212788
$784$	8.44828	0.301724
$785$	−44.0733	−1.57304
$786$	−6.76659	−0.241356
$787$	−15.9309	−0.567874	−0.283937	−	0.958843i	$-0.591641\pi$
$787$	−15.9309	−0.567874	−0.283937	+	0.958843i	$0.591641\pi$
$788$	24.5665	0.875144
$789$	23.5474	0.838311
$790$	14.4536	0.514236
$791$	3.13169	0.111350
$792$	3.02528	0.107499
$793$	0	0
$794$	1.28254	0.0455155
$795$	14.5160	0.514829
$796$	0.0942791	0.00334163
$797$	−4.59223	−0.162665	−0.0813326	−	0.996687i	$-0.525918\pi$
$797$	−4.59223	−0.162665	−0.0813326	+	0.996687i	$0.525918\pi$
$798$	−1.81406	−0.0642171
$799$	31.5926	1.11767
$800$	61.3630	2.16951
$801$	11.8659	0.419263
$802$	−35.6085	−1.25738
$803$	0.579081	0.0204353
$804$	−7.92988	−0.279665
$805$	5.44188	0.191801
$806$	0	0
$807$	29.5547	1.04037
$808$	−13.2876	−0.467456
$809$	−9.58323	−0.336928	−0.168464	−	0.985708i	$-0.553881\pi$
$809$	−9.58323	−0.336928	−0.168464	+	0.985708i	$0.553881\pi$
$810$	4.33466	0.152304
$811$	−41.6306	−1.46185	−0.730924	−	0.682459i	$-0.760911\pi$
$811$	−41.6306	−1.46185	−0.730924	+	0.682459i	$0.760911\pi$
$812$	1.57698	0.0553413
$813$	−22.7356	−0.797371
$814$	5.71885	0.200446
$815$	40.6738	1.42474
$816$	−3.70647	−0.129752
$817$	−22.4162	−0.784244
$818$	−14.7330	−0.515127
$819$	0	0
$820$	19.3494	0.675711
$821$	−6.78650	−0.236850	−0.118425	−	0.992963i	$-0.537785\pi$
$821$	−6.78650	−0.236850	−0.118425	+	0.992963i	$0.537785\pi$
$822$	−19.3561	−0.675122
$823$	−5.70451	−0.198847	−0.0994233	−	0.995045i	$-0.531700\pi$
$823$	−5.70451	−0.198847	−0.0994233	+	0.995045i	$0.531700\pi$
$824$	−11.6354	−0.405337
$825$	−12.7939	−0.445426
$826$	−1.71769	−0.0597662
$827$	−20.4785	−0.712106	−0.356053	−	0.934466i	$-0.615878\pi$
$827$	−20.4785	−0.712106	−0.356053	+	0.934466i	$0.615878\pi$
$828$	4.34125	0.150869
$829$	−40.8059	−1.41725	−0.708623	−	0.705587i	$-0.750683\pi$
$829$	−40.8059	−1.41725	−0.708623	+	0.705587i	$0.750683\pi$
$830$	22.9839	0.797784
$831$	11.1735	0.387603
$832$	0	0
$833$	−21.0168	−0.728189
$834$	17.6704	0.611877
$835$	−82.9181	−2.86950
$836$	5.94066	0.205462
$837$	1.87066	0.0646594
$838$	−29.3822	−1.01499
$839$	−5.02544	−0.173497	−0.0867487	−	0.996230i	$-0.527648\pi$
$839$	−5.02544	−0.173497	−0.0867487	+	0.996230i	$0.527648\pi$
$840$	3.58015	0.123527
$841$	6.45320	0.222524
$842$	−3.36617	−0.116006
$843$	15.0197	0.517306
$844$	10.7776	0.370980
$845$	0	0
$846$	10.6912	0.367570
$847$	−0.280543	−0.00963956
$848$	−4.20041	−0.144243
$849$	8.74879	0.300258
$850$	39.9210	1.36928
$851$	25.5920	0.877282
$852$	13.3156	0.456186
$853$	27.6640	0.947197	0.473599	−	0.880741i	$-0.342955\pi$
$853$	27.6640	0.947197	0.473599	+	0.880741i	$0.342955\pi$
$854$	2.86936	0.0981874
$855$	26.5442	0.907792
$856$	−44.4609	−1.51964
$857$	−2.49268	−0.0851483	−0.0425742	−	0.999093i	$-0.513556\pi$
$857$	−2.49268	−0.0851483	−0.0425742	+	0.999093i	$0.513556\pi$
$858$	0	0
$859$	3.04705	0.103964	0.0519819	−	0.998648i	$-0.483446\pi$
$859$	3.04705	0.103964	0.0519819	+	0.998648i	$0.483446\pi$
$860$	14.1862	0.483744
$861$	1.36311	0.0464547
$862$	34.2384	1.16616
$863$	1.94678	0.0662692	0.0331346	−	0.999451i	$-0.489451\pi$
$863$	1.94678	0.0662692	0.0331346	+	0.999451i	$0.489451\pi$
$864$	4.79627	0.163172
$865$	19.1351	0.650614
$866$	0.0592615	0.00201379
$867$	−7.77942	−0.264203
$868$	0.495443	0.0168164
$869$	−3.33443	−0.113113
$870$	25.8097	0.875030
$871$	0	0
$872$	−50.5072	−1.71039
$873$	−2.52495	−0.0854568
$874$	−29.7350	−1.00580
$875$	−9.22337	−0.311807
$876$	0.546688	0.0184709
$877$	14.2717	0.481921	0.240961	−	0.970535i	$-0.422538\pi$
$877$	14.2717	0.481921	0.240961	+	0.970535i	$0.422538\pi$
$878$	16.0440	0.541457
$879$	−0.698890	−0.0235730
$880$	5.14892	0.173570
$881$	−14.7510	−0.496974	−0.248487	−	0.968635i	$-0.579933\pi$
$881$	−14.7510	−0.496974	−0.248487	+	0.968635i	$0.579933\pi$
$882$	−7.11224	−0.239482
$883$	0.848647	0.0285593	0.0142796	−	0.999898i	$-0.495454\pi$
$883$	0.848647	0.0285593	0.0142796	+	0.999898i	$0.495454\pi$
$884$	0	0
$885$	25.1341	0.844873
$886$	−20.1769	−0.677857
$887$	13.3487	0.448204	0.224102	−	0.974566i	$-0.428055\pi$
$887$	13.3487	0.448204	0.224102	+	0.974566i	$0.428055\pi$
$888$	16.8366	0.565001
$889$	−2.31711	−0.0777133
$890$	51.4348	1.72410
$891$	−1.00000	−0.0335013
$892$	9.56217	0.320165
$893$	65.4697	2.19086
$894$	−8.18406	−0.273716
$895$	−34.2896	−1.14617
$896$	0.566525	0.0189263
$897$	0	0
$898$	−19.6957	−0.657254
$899$	11.1384	0.371486
$900$	−12.0782	−0.402608
$901$	10.4494	0.348119
$902$	4.99288	0.166245
$903$	0.999373	0.0332570
$904$	33.7712	1.12321
$905$	−30.9393	−1.02846
$906$	13.9614	0.463836
$907$	−11.5866	−0.384726	−0.192363	−	0.981324i	$-0.561615\pi$
$907$	−11.5866	−0.384726	−0.192363	+	0.981324i	$0.561615\pi$
$908$	−5.99181	−0.198845
$909$	4.39218	0.145679
$910$	0	0
$911$	−31.2395	−1.03501	−0.517505	−	0.855680i	$-0.673139\pi$
$911$	−31.2395	−1.03501	−0.517505	+	0.855680i	$0.673139\pi$
$912$	−7.68095	−0.254342
$913$	−5.30236	−0.175483
$914$	22.1133	0.731443
$915$	−41.9858	−1.38801
$916$	−18.0912	−0.597749
$917$	1.84735	0.0610050
$918$	3.12031	0.102986
$919$	−23.7104	−0.782135	−0.391068	−	0.920362i	$-0.627894\pi$
$919$	−23.7104	−0.782135	−0.391068	+	0.920362i	$0.627894\pi$
$920$	58.6835	1.93474
$921$	11.1086	0.366039
$922$	32.3440	1.06519
$923$	0	0
$924$	−0.264850	−0.00871292
$925$	−71.2020	−2.34111
$926$	−19.6144	−0.644569
$927$	3.84604	0.126321
$928$	28.5582	0.937470
$929$	−41.6068	−1.36507	−0.682537	−	0.730851i	$-0.739123\pi$
$929$	−41.6068	−1.36507	−0.682537	+	0.730851i	$0.739123\pi$
$930$	8.10866	0.265893
$931$	−43.5533	−1.42740
$932$	2.19961	0.0720505
$933$	5.99123	0.196144
$934$	−34.7431	−1.13683
$935$	−12.8090	−0.418899
$936$	0	0
$937$	−8.23603	−0.269060	−0.134530	−	0.990910i	$-0.542952\pi$
$937$	−8.23603	−0.269060	−0.134530	+	0.990910i	$0.542952\pi$
$938$	−2.42150	−0.0790647
$939$	−16.1118	−0.525788
$940$	−41.4327	−1.35138
$941$	−28.4544	−0.927588	−0.463794	−	0.885943i	$-0.653512\pi$
$941$	−28.4544	−0.927588	−0.463794	+	0.885943i	$0.653512\pi$
$942$	−10.7364	−0.349811
$943$	22.3432	0.727596
$944$	−7.27291	−0.236713
$945$	−1.18341	−0.0384963
$946$	3.66056	0.119015
$947$	−19.3316	−0.628191	−0.314096	−	0.949391i	$-0.601701\pi$
$947$	−19.3316	−0.628191	−0.314096	+	0.949391i	$0.601701\pi$
$948$	−3.14791	−0.102239
$949$	0	0
$950$	82.7287	2.68407
$951$	−20.8731	−0.676856
$952$	2.57718	0.0835268
$953$	−13.9502	−0.451890	−0.225945	−	0.974140i	$-0.572547\pi$
$953$	−13.9502	−0.451890	−0.225945	+	0.974140i	$0.572547\pi$
$954$	3.53615	0.114487
$955$	105.206	3.40437
$956$	25.0750	0.810983
$957$	−5.95426	−0.192474
$958$	−13.7034	−0.442737
$959$	5.28443	0.170643
$960$	31.0880	1.00336
$961$	−27.5006	−0.887117
$962$	0	0
$963$	14.6964	0.473586
$964$	29.1652	0.939346
$965$	48.1417	1.54974
$966$	1.32566	0.0426525
$967$	3.78243	0.121635	0.0608174	−	0.998149i	$-0.480629\pi$
$967$	3.78243	0.121635	0.0608174	+	0.998149i	$0.480629\pi$
$968$	−3.02528	−0.0972363
$969$	19.1079	0.613834
$970$	−10.9448	−0.351417
$971$	41.9445	1.34606	0.673031	−	0.739614i	$-0.264992\pi$
$971$	41.9445	1.34606	0.673031	+	0.739614i	$0.264992\pi$
$972$	−0.944062	−0.0302808
$973$	−4.82422	−0.154657
$974$	5.18414	0.166111
$975$	0	0
$976$	12.1492	0.388886
$977$	−43.5936	−1.39468	−0.697342	−	0.716739i	$-0.745634\pi$
$977$	−43.5936	−1.39468	−0.697342	+	0.716739i	$0.745634\pi$
$978$	9.90829	0.316832
$979$	−11.8659	−0.379237
$980$	27.5628	0.880462
$981$	16.6950	0.533031
$982$	16.7386	0.534152
$983$	−44.7656	−1.42780	−0.713900	−	0.700248i	$-0.753073\pi$
$983$	−44.7656	−1.42780	−0.713900	+	0.700248i	$0.753073\pi$
$984$	14.6993	0.468598
$985$	−109.768	−3.49751
$986$	18.5792	0.591681
$987$	−2.91881	−0.0929067
$988$	0	0
$989$	16.3811	0.520888
$990$	−4.33466	−0.137764
$991$	1.83664	0.0583428	0.0291714	−	0.999574i	$-0.490713\pi$
$991$	1.83664	0.0583428	0.0291714	+	0.999574i	$0.490713\pi$
$992$	8.97218	0.284867
$993$	−12.7876	−0.405801
$994$	4.06611	0.128969
$995$	−0.421260	−0.0133548
$996$	−5.00576	−0.158614
$997$	10.5133	0.332960	0.166480	−	0.986045i	$-0.446760\pi$
$997$	10.5133	0.332960	0.166480	+	0.986045i	$0.446760\pi$
$998$	−14.1796	−0.448846
$999$	−5.56531	−0.176079

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5577.2.a.bk.1.11	yes	18
13.12	even	2		5577.2.a.bi.1.8	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5577.2.a.bi.1.8	✓	18	13.12	even	2
5577.2.a.bk.1.11	yes	18	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)

\(f(q)\)	\(=\)	\(q+1.02759 q^{2} +1.00000 q^{3} -0.944062 q^{4} +4.21828 q^{5} +1.02759 q^{6} -0.280543 q^{7} -3.02528 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.02759 q^{2} +1.00000 q^{3} -0.944062 q^{4} +4.21828 q^{5} +1.02759 q^{6} -0.280543 q^{7} -3.02528 q^{8} +1.00000 q^{9} +4.33466 q^{10} -1.00000 q^{11} -0.944062 q^{12} -0.288282 q^{14} +4.21828 q^{15} -1.22062 q^{16} +3.03654 q^{17} +1.02759 q^{18} +6.29266 q^{19} -3.98232 q^{20} -0.280543 q^{21} -1.02759 q^{22} -4.59848 q^{23} -3.02528 q^{24} +12.7939 q^{25} +1.00000 q^{27} +0.264850 q^{28} +5.95426 q^{29} +4.33466 q^{30} +1.87066 q^{31} +4.79627 q^{32} -1.00000 q^{33} +3.12031 q^{34} -1.18341 q^{35} -0.944062 q^{36} -5.56531 q^{37} +6.46626 q^{38} -12.7615 q^{40} -4.85883 q^{41} -0.288282 q^{42} -3.56228 q^{43} +0.944062 q^{44} +4.21828 q^{45} -4.72535 q^{46} +10.4041 q^{47} -1.22062 q^{48} -6.92130 q^{49} +13.1469 q^{50} +3.03654 q^{51} +3.44121 q^{53} +1.02759 q^{54} -4.21828 q^{55} +0.848721 q^{56} +6.29266 q^{57} +6.11853 q^{58} +5.95837 q^{59} -3.98232 q^{60} -9.95328 q^{61} +1.92227 q^{62} -0.280543 q^{63} +7.36983 q^{64} -1.02759 q^{66} +8.39974 q^{67} -2.86668 q^{68} -4.59848 q^{69} -1.21606 q^{70} -14.1046 q^{71} -3.02528 q^{72} -0.579081 q^{73} -5.71885 q^{74} +12.7939 q^{75} -5.94066 q^{76} +0.280543 q^{77} +3.33443 q^{79} -5.14892 q^{80} +1.00000 q^{81} -4.99288 q^{82} +5.30236 q^{83} +0.264850 q^{84} +12.8090 q^{85} -3.66056 q^{86} +5.95426 q^{87} +3.02528 q^{88} +11.8659 q^{89} +4.33466 q^{90} +4.34125 q^{92} +1.87066 q^{93} +10.6912 q^{94} +26.5442 q^{95} +4.79627 q^{96} -2.52495 q^{97} -7.11224 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + q^{2} + 18 q^{3} + 23 q^{4} - 6 q^{5} + q^{6} + q^{7} + 6 q^{8} + 18 q^{9}+O(q^{10}) \) 18 * q + q^2 + 18 * q^3 + 23 * q^4 - 6 * q^5 + q^6 + q^7 + 6 * q^8 + 18 * q^9	\( 18 q + q^{2} + 18 q^{3} + 23 q^{4} - 6 q^{5} + q^{6} + q^{7} + 6 q^{8} + 18 q^{9} - 7 q^{10} - 18 q^{11} + 23 q^{12} + 7 q^{14} - 6 q^{15} + 25 q^{16} + 19 q^{17} + q^{18} - 2 q^{20} + q^{21} - q^{22} + 38 q^{23} + 6 q^{24} + 36 q^{25} + 18 q^{27} + 33 q^{28} + 47 q^{29} - 7 q^{30} - 22 q^{31} + 33 q^{32} - 18 q^{33} + 4 q^{34} + 20 q^{35} + 23 q^{36} - 41 q^{37} + 14 q^{38} - 28 q^{40} + 8 q^{41} + 7 q^{42} + 28 q^{43} - 23 q^{44} - 6 q^{45} + 6 q^{46} + 11 q^{47} + 25 q^{48} + 9 q^{49} - q^{50} + 19 q^{51} + 49 q^{53} + q^{54} + 6 q^{55} + 35 q^{56} - 27 q^{58} - 2 q^{59} - 2 q^{60} - 13 q^{61} + 46 q^{62} + q^{63} + 40 q^{64} - q^{66} + 4 q^{67} + 30 q^{68} + 38 q^{69} - 83 q^{70} + 2 q^{71} + 6 q^{72} + 39 q^{73} + 42 q^{74} + 36 q^{75} + 20 q^{76} - q^{77} + 18 q^{79} + 18 q^{80} + 18 q^{81} - 12 q^{82} + 5 q^{83} + 33 q^{84} + 2 q^{85} + 57 q^{86} + 47 q^{87} - 6 q^{88} - 9 q^{89} - 7 q^{90} + 86 q^{92} - 22 q^{93} - 27 q^{94} + 74 q^{95} + 33 q^{96} - 17 q^{97} + 4 q^{98} - 18 q^{99}+O(q^{100}) \) 18 * q + q^2 + 18 * q^3 + 23 * q^4 - 6 * q^5 + q^6 + q^7 + 6 * q^8 + 18 * q^9 - 7 * q^10 - 18 * q^11 + 23 * q^12 + 7 * q^14 - 6 * q^15 + 25 * q^16 + 19 * q^17 + q^18 - 2 * q^20 + q^21 - q^22 + 38 * q^23 + 6 * q^24 + 36 * q^25 + 18 * q^27 + 33 * q^28 + 47 * q^29 - 7 * q^30 - 22 * q^31 + 33 * q^32 - 18 * q^33 + 4 * q^34 + 20 * q^35 + 23 * q^36 - 41 * q^37 + 14 * q^38 - 28 * q^40 + 8 * q^41 + 7 * q^42 + 28 * q^43 - 23 * q^44 - 6 * q^45 + 6 * q^46 + 11 * q^47 + 25 * q^48 + 9 * q^49 - q^50 + 19 * q^51 + 49 * q^53 + q^54 + 6 * q^55 + 35 * q^56 - 27 * q^58 - 2 * q^59 - 2 * q^60 - 13 * q^61 + 46 * q^62 + q^63 + 40 * q^64 - q^66 + 4 * q^67 + 30 * q^68 + 38 * q^69 - 83 * q^70 + 2 * q^71 + 6 * q^72 + 39 * q^73 + 42 * q^74 + 36 * q^75 + 20 * q^76 - q^77 + 18 * q^79 + 18 * q^80 + 18 * q^81 - 12 * q^82 + 5 * q^83 + 33 * q^84 + 2 * q^85 + 57 * q^86 + 47 * q^87 - 6 * q^88 - 9 * q^89 - 7 * q^90 + 86 * q^92 - 22 * q^93 - 27 * q^94 + 74 * q^95 + 33 * q^96 - 17 * q^97 + 4 * q^98 - 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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