LMFDB - Embedded newform 107.2.a.b.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [107,2,Mod(1,107)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("107.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(107, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 107 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	107.a (trivial)

Newform invariants

comment:select newform

sage:traces = [7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$0.854399301628$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 10x^{5} + 7x^{4} + 29x^{3} - 12x^{2} - 20x + 8 $ x^7 - x^6 - 10x^5 + 7x^4 + 29x^3 - 12x^2 - 20*x + 8
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.400681$ of defining polynomial
Character	$\chi$	$=$	107.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.400681 q^{2} +2.05242 q^{3} -1.83945 q^{4} +0.858034 q^{5} -0.822367 q^{6} +3.08104 q^{7} +1.53840 q^{8} +1.21244 q^{9} -0.343798 q^{10} -1.56312 q^{11} -3.77534 q^{12} -4.04020 q^{13} -1.23452 q^{14} +1.76105 q^{15} +3.06250 q^{16} -0.343798 q^{17} -0.485802 q^{18} +1.63409 q^{19} -1.57831 q^{20} +6.32361 q^{21} +0.626314 q^{22} -7.84845 q^{23} +3.15744 q^{24} -4.26378 q^{25} +1.61883 q^{26} -3.66883 q^{27} -5.66744 q^{28} -3.98461 q^{29} -0.705619 q^{30} +6.10060 q^{31} -4.30388 q^{32} -3.20819 q^{33} +0.137753 q^{34} +2.64364 q^{35} -2.23023 q^{36} +7.64770 q^{37} -0.654748 q^{38} -8.29220 q^{39} +1.32000 q^{40} +0.592274 q^{41} -2.53375 q^{42} +3.65195 q^{43} +2.87530 q^{44} +1.04031 q^{45} +3.14473 q^{46} -3.80419 q^{47} +6.28555 q^{48} +2.49283 q^{49} +1.70842 q^{50} -0.705619 q^{51} +7.43177 q^{52} +12.6409 q^{53} +1.47003 q^{54} -1.34121 q^{55} +4.73987 q^{56} +3.35384 q^{57} +1.59656 q^{58} -8.55816 q^{59} -3.23937 q^{60} +8.95223 q^{61} -2.44439 q^{62} +3.73558 q^{63} -4.40052 q^{64} -3.46663 q^{65} +1.28546 q^{66} +13.1646 q^{67} +0.632401 q^{68} -16.1083 q^{69} -1.05926 q^{70} +7.08789 q^{71} +1.86521 q^{72} +3.52777 q^{73} -3.06429 q^{74} -8.75108 q^{75} -3.00583 q^{76} -4.81605 q^{77} +3.32253 q^{78} +3.98353 q^{79} +2.62773 q^{80} -11.1673 q^{81} -0.237313 q^{82} -17.2874 q^{83} -11.6320 q^{84} -0.294990 q^{85} -1.46327 q^{86} -8.17811 q^{87} -2.40470 q^{88} +2.34142 q^{89} -0.416834 q^{90} -12.4480 q^{91} +14.4369 q^{92} +12.5210 q^{93} +1.52427 q^{94} +1.40210 q^{95} -8.83338 q^{96} +2.44185 q^{97} -0.998831 q^{98} -1.89519 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} + 3 q^{3} + 7 q^{4} + 5 q^{5} - 5 q^{6} + 4 q^{7} - 6 q^{8} + 6 q^{9} - q^{10} - 2 q^{11} + 6 q^{12} + 18 q^{13} - 9 q^{14} - 9 q^{15} - q^{16} - q^{17} - 17 q^{18} - 4 q^{19} - 10 q^{20}+ \cdots - 52 q^{99}+O(q^{100}) $ 7 * q - q^2 + 3 * q^3 + 7 * q^4 + 5 * q^5 - 5 * q^6 + 4 * q^7 - 6 * q^8 + 6 * q^9 - q^10 - 2 * q^11 + 6 * q^12 + 18 * q^13 - 9 * q^14 - 9 * q^15 - q^16 - q^17 - 17 * q^18 - 4 * q^19 - 10 * q^20 - 11 * q^21 - 5 * q^22 - 31 * q^24 + 8 * q^25 - 22 * q^26 + 3 * q^27 + 3 * q^28 - 3 * q^29 - 8 * q^30 + 4 * q^31 - 13 * q^32 - 6 * q^33 - 19 * q^35 + 14 * q^36 + 25 * q^37 + 18 * q^38 + 5 * q^39 + 13 * q^40 + 17 * q^42 + 11 * q^43 - 17 * q^44 + 25 * q^45 + q^46 - 9 * q^47 + 19 * q^48 + 13 * q^49 + 7 * q^50 - 8 * q^51 + 44 * q^52 + 8 * q^53 - 35 * q^54 - 13 * q^55 + 26 * q^56 - 3 * q^57 + 35 * q^58 - 19 * q^59 + 9 * q^60 + 25 * q^61 + 23 * q^62 - 11 * q^63 - 18 * q^64 + 8 * q^65 + 63 * q^66 - 24 * q^67 + 11 * q^68 - 5 * q^70 - 19 * q^71 - 15 * q^72 + 30 * q^73 - 17 * q^74 - 41 * q^75 + 4 * q^76 + 6 * q^77 - 18 * q^78 - 21 * q^79 + 19 * q^80 - 17 * q^81 + 6 * q^82 + 12 * q^83 - 36 * q^84 + 2 * q^85 + 31 * q^86 - 15 * q^87 - 8 * q^88 - 22 * q^89 - 36 * q^90 - 2 * q^91 - 7 * q^92 + 9 * q^93 + 16 * q^94 - 44 * q^95 + 2 * q^96 - 4 * q^97 - 22 * q^98 - 52 * q^99

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 $

$2$	−0.400681	−0.283324	−0.141662	−	0.989915i	$-0.545245\pi$
$2$	−0.400681	−0.283324	−0.141662	+	0.989915i	$0.545245\pi$
$3$	2.05242	1.18497	0.592483	−	0.805583i	$-0.298148\pi$
$3$	2.05242	1.18497	0.592483	+	0.805583i	$0.298148\pi$
$4$	−1.83945	−0.919727
$5$	0.858034	0.383724	0.191862	−	0.981422i	$-0.438547\pi$
$5$	0.858034	0.383724	0.191862	+	0.981422i	$0.438547\pi$
$6$	−0.822367	−0.335730
$7$	3.08104	1.16453	0.582263	−	0.813001i	$-0.302168\pi$
$7$	3.08104	1.16453	0.582263	+	0.813001i	$0.302168\pi$
$8$	1.53840	0.543905
$9$	1.21244	0.404147
$10$	−0.343798	−0.108718
$11$	−1.56312	−0.471300	−0.235650	−	0.971838i	$-0.575722\pi$
$11$	−1.56312	−0.471300	−0.235650	+	0.971838i	$0.575722\pi$
$12$	−3.77534	−1.08985
$13$	−4.04020	−1.12055	−0.560275	−	0.828307i	$-0.689305\pi$
$13$	−4.04020	−1.12055	−0.560275	+	0.828307i	$0.689305\pi$
$14$	−1.23452	−0.329938
$15$	1.76105	0.454701
$16$	3.06250	0.765626
$17$	−0.343798	−0.0833832	−0.0416916	−	0.999131i	$-0.513275\pi$
$17$	−0.343798	−0.0833832	−0.0416916	+	0.999131i	$0.513275\pi$
$18$	−0.485802	−0.114505
$19$	1.63409	0.374886	0.187443	−	0.982276i	$-0.439980\pi$
$19$	1.63409	0.374886	0.187443	+	0.982276i	$0.439980\pi$
$20$	−1.57831	−0.352922
$21$	6.32361	1.37992
$22$	0.626314	0.133531
$23$	−7.84845	−1.63651	−0.818257	−	0.574852i	$-0.805060\pi$
$23$	−7.84845	−1.63651	−0.818257	+	0.574852i	$0.805060\pi$
$24$	3.15744	0.644510
$25$	−4.26378	−0.852756
$26$	1.61883	0.317479
$27$	−3.66883	−0.706067
$28$	−5.66744	−1.07105
$29$	−3.98461	−0.739924	−0.369962	−	0.929047i	$-0.620629\pi$
$29$	−3.98461	−0.739924	−0.369962	+	0.929047i	$0.620629\pi$
$30$	−0.705619	−0.128828
$31$	6.10060	1.09570	0.547850	−	0.836577i	$-0.315447\pi$
$31$	6.10060	1.09570	0.547850	+	0.836577i	$0.315447\pi$
$32$	−4.30388	−0.760826
$33$	−3.20819	−0.558474
$34$	0.137753	0.0236245
$35$	2.64364	0.446857
$36$	−2.23023	−0.371705
$37$	7.64770	1.25727	0.628637	−	0.777699i	$-0.283613\pi$
$37$	7.64770	1.25727	0.628637	+	0.777699i	$0.283613\pi$
$38$	−0.654748	−0.106214
$39$	−8.29220	−1.32782
$40$	1.32000	0.208710
$41$	0.592274	0.0924976	0.0462488	−	0.998930i	$-0.485273\pi$
$41$	0.592274	0.0924976	0.0462488	+	0.998930i	$0.485273\pi$
$42$	−2.53375	−0.390966
$43$	3.65195	0.556917	0.278459	−	0.960448i	$-0.410176\pi$
$43$	3.65195	0.556917	0.278459	+	0.960448i	$0.410176\pi$
$44$	2.87530	0.433467
$45$	1.04031	0.155081
$46$	3.14473	0.463664
$47$	−3.80419	−0.554897	−0.277449	−	0.960740i	$-0.589489\pi$
$47$	−3.80419	−0.554897	−0.277449	+	0.960740i	$0.589489\pi$
$48$	6.28555	0.907241
$49$	2.49283	0.356119
$50$	1.70842	0.241606
$51$	−0.705619	−0.0988064
$52$	7.43177	1.03060
$53$	12.6409	1.73636	0.868180	−	0.496249i	$-0.165290\pi$
$53$	12.6409	1.73636	0.868180	+	0.496249i	$0.165290\pi$
$54$	1.47003	0.200046
$55$	−1.34121	−0.180849
$56$	4.73987	0.633392
$57$	3.35384	0.444227
$58$	1.59656	0.209639
$59$	−8.55816	−1.11418	−0.557089	−	0.830453i	$-0.688082\pi$
$59$	−8.55816	−1.11418	−0.557089	+	0.830453i	$0.688082\pi$
$60$	−3.23937	−0.418201
$61$	8.95223	1.14622	0.573108	−	0.819480i	$-0.305738\pi$
$61$	8.95223	1.14622	0.573108	+	0.819480i	$0.305738\pi$
$62$	−2.44439	−0.310438
$63$	3.73558	0.470639
$64$	−4.40052	−0.550065
$65$	−3.46663	−0.429982
$66$	1.28546	0.158229
$67$	13.1646	1.60832	0.804158	−	0.594415i	$-0.202616\pi$
$67$	13.1646	1.60832	0.804158	+	0.594415i	$0.202616\pi$
$68$	0.632401	0.0766898
$69$	−16.1083	−1.93922
$70$	−1.05926	−0.126605
$71$	7.08789	0.841177	0.420589	−	0.907251i	$-0.361824\pi$
$71$	7.08789	0.841177	0.420589	+	0.907251i	$0.361824\pi$
$72$	1.86521	0.219818
$73$	3.52777	0.412895	0.206447	−	0.978458i	$-0.433810\pi$
$73$	3.52777	0.412895	0.206447	+	0.978458i	$0.433810\pi$
$74$	−3.06429	−0.356216
$75$	−8.75108	−1.01049
$76$	−3.00583	−0.344792
$77$	−4.81605	−0.548840
$78$	3.32253	0.376202
$79$	3.98353	0.448182	0.224091	−	0.974568i	$-0.428059\pi$
$79$	3.98353	0.448182	0.224091	+	0.974568i	$0.428059\pi$
$80$	2.62773	0.293789
$81$	−11.1673	−1.24081
$82$	−0.237313	−0.0262068
$83$	−17.2874	−1.89754	−0.948770	−	0.315966i	$-0.897671\pi$
$83$	−17.2874	−1.89754	−0.948770	+	0.315966i	$0.897671\pi$
$84$	−11.6320	−1.26915
$85$	−0.294990	−0.0319962
$86$	−1.46327	−0.157788
$87$	−8.17811	−0.876786
$88$	−2.40470	−0.256342
$89$	2.34142	0.248190	0.124095	−	0.992270i	$-0.460397\pi$
$89$	2.34142	0.248190	0.124095	+	0.992270i	$0.460397\pi$
$90$	−0.416834	−0.0439382
$91$	−12.4480	−1.30491
$92$	14.4369	1.50515
$93$	12.5210	1.29837
$94$	1.52427	0.157216
$95$	1.40210	0.143853
$96$	−8.83338	−0.901553
$97$	2.44185	0.247932	0.123966	−	0.992286i	$-0.460439\pi$
$97$	2.44185	0.247932	0.123966	+	0.992286i	$0.460439\pi$
$98$	−0.998831	−0.100897
$99$	−1.89519	−0.190474
$100$	7.84303	0.784303
$101$	14.8606	1.47868	0.739340	−	0.673332i	$-0.235138\pi$
$101$	14.8606	1.47868	0.739340	+	0.673332i	$0.235138\pi$
$102$	0.282728	0.0279942
$103$	−14.0057	−1.38002	−0.690012	−	0.723798i	$-0.742395\pi$
$103$	−14.0057	−1.38002	−0.690012	+	0.723798i	$0.742395\pi$
$104$	−6.21543	−0.609473
$105$	5.42587	0.529510
$106$	−5.06497	−0.491953
$107$	1.00000	0.0966736
$107$	1.00000	0.0966736
$108$	6.74865	0.649389
$109$	−7.27844	−0.697148	−0.348574	−	0.937281i	$-0.613334\pi$
$109$	−7.27844	−0.697148	−0.348574	+	0.937281i	$0.613334\pi$
$110$	0.537399	0.0512390
$111$	15.6963	1.48983
$112$	9.43571	0.891590
$113$	9.98665	0.939465	0.469732	−	0.882809i	$-0.344350\pi$
$113$	9.98665	0.939465	0.469732	+	0.882809i	$0.344350\pi$
$114$	−1.34382	−0.125860
$115$	−6.73423	−0.627971
$116$	7.32952	0.680529
$117$	−4.89850	−0.452867
$118$	3.42909	0.315674
$119$	−1.05926	−0.0971019
$120$	2.70919	0.247314
$121$	−8.55664	−0.777877
$122$	−3.58699	−0.324751
$123$	1.21560	0.109607
$124$	−11.2218	−1.00774
$125$	−7.94863	−0.710947
$126$	−1.49678	−0.133343
$127$	−20.1182	−1.78520	−0.892601	−	0.450848i	$-0.851122\pi$
$127$	−20.1182	−1.78520	−0.892601	+	0.450848i	$0.851122\pi$
$128$	10.3710	0.916673
$129$	7.49535	0.659929
$130$	1.38901	0.121824
$131$	−19.0407	−1.66360	−0.831798	−	0.555078i	$-0.812688\pi$
$131$	−19.0407	−1.66360	−0.831798	+	0.555078i	$0.812688\pi$
$132$	5.90132	0.513644
$133$	5.03470	0.436564
$134$	−5.27482	−0.455675
$135$	−3.14798	−0.270935
$136$	−0.528898	−0.0453526
$137$	10.4337	0.891409	0.445705	−	0.895180i	$-0.352953\pi$
$137$	10.4337	0.891409	0.445705	+	0.895180i	$0.352953\pi$
$138$	6.45431	0.549427
$139$	−8.04313	−0.682209	−0.341105	−	0.940025i	$-0.610801\pi$
$139$	−8.04313	−0.682209	−0.341105	+	0.940025i	$0.610801\pi$
$140$	−4.86286	−0.410986
$141$	−7.80780	−0.657535
$142$	−2.83998	−0.238326
$143$	6.31534	0.528115
$144$	3.71310	0.309425
$145$	−3.41893	−0.283927
$146$	−1.41351	−0.116983
$147$	5.11635	0.421989
$148$	−14.0676	−1.15635
$149$	5.43794	0.445493	0.222747	−	0.974876i	$-0.428498\pi$
$149$	5.43794	0.445493	0.222747	+	0.974876i	$0.428498\pi$
$150$	3.50639	0.286296
$151$	2.26716	0.184499	0.0922494	−	0.995736i	$-0.470594\pi$
$151$	2.26716	0.184499	0.0922494	+	0.995736i	$0.470594\pi$
$152$	2.51388	0.203902
$153$	−0.416834	−0.0336990
$154$	1.92970	0.155500
$155$	5.23452	0.420446
$156$	15.2531	1.22123
$157$	23.6776	1.88968	0.944840	−	0.327531i	$-0.106217\pi$
$157$	23.6776	1.88968	0.944840	+	0.327531i	$0.106217\pi$
$158$	−1.59613	−0.126981
$159$	25.9445	2.05753
$160$	−3.69287	−0.291947
$161$	−24.1814	−1.90576
$162$	4.47453	0.351552
$163$	7.44006	0.582751	0.291375	−	0.956609i	$-0.405887\pi$
$163$	7.44006	0.582751	0.291375	+	0.956609i	$0.405887\pi$
$164$	−1.08946	−0.0850726
$165$	−2.75274	−0.214300
$166$	6.92674	0.537619
$167$	16.5490	1.28060	0.640299	−	0.768125i	$-0.278810\pi$
$167$	16.5490	1.28060	0.640299	+	0.768125i	$0.278810\pi$
$168$	9.72822	0.750548
$169$	3.32323	0.255633
$170$	0.118197	0.00906529
$171$	1.98123	0.151509
$172$	−6.71760	−0.512212
$173$	19.9068	1.51348	0.756742	−	0.653714i	$-0.226790\pi$
$173$	19.9068	1.51348	0.756742	+	0.653714i	$0.226790\pi$
$174$	3.27682	0.248415
$175$	−13.1369	−0.993056
$176$	−4.78707	−0.360839
$177$	−17.5650	−1.32026
$178$	−0.938162	−0.0703182
$179$	2.86289	0.213982	0.106991	−	0.994260i	$-0.465878\pi$
$179$	2.86289	0.213982	0.106991	+	0.994260i	$0.465878\pi$
$180$	−1.91361	−0.142632
$181$	−3.68801	−0.274128	−0.137064	−	0.990562i	$-0.543767\pi$
$181$	−3.68801	−0.274128	−0.137064	+	0.990562i	$0.543767\pi$
$182$	4.98769	0.369713
$183$	18.3738	1.35823
$184$	−12.0740	−0.890109
$185$	6.56199	0.482447
$186$	−5.01693	−0.367859
$187$	0.537399	0.0392985
$188$	6.99763	0.510354
$189$	−11.3038	−0.822232
$190$	−0.561796	−0.0407570
$191$	2.54895	0.184436	0.0922179	−	0.995739i	$-0.470604\pi$
$191$	2.54895	0.184436	0.0922179	+	0.995739i	$0.470604\pi$
$192$	−9.03173	−0.651809
$193$	−2.29500	−0.165198	−0.0825988	−	0.996583i	$-0.526322\pi$
$193$	−2.29500	−0.165198	−0.0825988	+	0.996583i	$0.526322\pi$
$194$	−0.978401	−0.0702451
$195$	−7.11499	−0.509515
$196$	−4.58545	−0.327532
$197$	−23.8635	−1.70021	−0.850103	−	0.526617i	$-0.823460\pi$
$197$	−23.8635	−1.70021	−0.850103	+	0.526617i	$0.823460\pi$
$198$	0.759368	0.0539660
$199$	19.9864	1.41680	0.708400	−	0.705811i	$-0.249417\pi$
$199$	19.9864	1.41680	0.708400	+	0.705811i	$0.249417\pi$
$200$	−6.55938	−0.463818
$201$	27.0194	1.90580
$202$	−5.95434	−0.418946
$203$	−12.2768	−0.861661
$204$	1.29795	0.0908749
$205$	0.508191	0.0354936
$206$	5.61182	0.390994
$207$	−9.51577	−0.661392
$208$	−12.3731	−0.857922
$209$	−2.55428	−0.176683
$210$	−2.17404	−0.150023
$211$	−13.9182	−0.958171	−0.479086	−	0.877768i	$-0.659032\pi$
$211$	−13.9182	−0.958171	−0.479086	+	0.877768i	$0.659032\pi$
$212$	−23.2523	−1.59698
$213$	14.5473	0.996767
$214$	−0.400681	−0.0273900
$215$	3.13350	0.213703
$216$	−5.64412	−0.384033
$217$	18.7962	1.27597
$218$	2.91633	0.197519
$219$	7.24048	0.489267
$220$	2.46710	0.166332
$221$	1.38901	0.0934351
$222$	−6.28922	−0.422105
$223$	−0.937849	−0.0628030	−0.0314015	−	0.999507i	$-0.509997\pi$
$223$	−0.937849	−0.0628030	−0.0314015	+	0.999507i	$0.509997\pi$
$224$	−13.2604	−0.886001
$225$	−5.16957	−0.344638
$226$	−4.00146	−0.266173
$227$	−13.5014	−0.896122	−0.448061	−	0.894003i	$-0.647885\pi$
$227$	−13.5014	−0.896122	−0.448061	+	0.894003i	$0.647885\pi$
$228$	−6.16924	−0.408568
$229$	22.1489	1.46364	0.731820	−	0.681498i	$-0.238671\pi$
$229$	22.1489	1.46364	0.731820	+	0.681498i	$0.238671\pi$
$230$	2.69828	0.177919
$231$	−9.88458	−0.650358
$232$	−6.12992	−0.402449
$233$	4.30702	0.282162	0.141081	−	0.989998i	$-0.454942\pi$
$233$	4.30702	0.282162	0.141081	+	0.989998i	$0.454942\pi$
$234$	1.96274	0.128308
$235$	−3.26412	−0.212928
$236$	15.7423	1.02474
$237$	8.17589	0.531081
$238$	0.424424	0.0275113
$239$	−12.2987	−0.795538	−0.397769	−	0.917486i	$-0.630215\pi$
$239$	−12.2987	−0.795538	−0.397769	+	0.917486i	$0.630215\pi$
$240$	5.39321	0.348130
$241$	−21.9315	−1.41274	−0.706368	−	0.707845i	$-0.749667\pi$
$241$	−21.9315	−1.41274	−0.706368	+	0.707845i	$0.749667\pi$
$242$	3.42849	0.220391
$243$	−11.9136	−0.764255
$244$	−16.4672	−1.05421
$245$	2.13894	0.136652
$246$	−0.487066	−0.0310542
$247$	−6.60205	−0.420078
$248$	9.38514	0.595957
$249$	−35.4811	−2.24852
$250$	3.18487	0.201429
$251$	15.5593	0.982092	0.491046	−	0.871134i	$-0.336615\pi$
$251$	15.5593	0.982092	0.491046	+	0.871134i	$0.336615\pi$
$252$	−6.87143	−0.432860
$253$	12.2681	0.771289
$254$	8.06098	0.505791
$255$	−0.605445	−0.0379144
$256$	4.64559	0.290350
$257$	−21.0087	−1.31049	−0.655243	−	0.755418i	$-0.727434\pi$
$257$	−21.0087	−1.31049	−0.655243	+	0.755418i	$0.727434\pi$
$258$	−3.00324	−0.186974
$259$	23.5629	1.46413
$260$	6.37671	0.395467
$261$	−4.83111	−0.299038
$262$	7.62926	0.471337
$263$	30.3403	1.87086	0.935432	−	0.353508i	$-0.115011\pi$
$263$	30.3403	1.87086	0.935432	+	0.353508i	$0.115011\pi$
$264$	−4.93547	−0.303757
$265$	10.8463	0.666284
$266$	−2.01731	−0.123689
$267$	4.80558	0.294097
$268$	−24.2158	−1.47921
$269$	4.44775	0.271184	0.135592	−	0.990765i	$-0.456706\pi$
$269$	4.44775	0.271184	0.135592	+	0.990765i	$0.456706\pi$
$270$	1.26134	0.0767624
$271$	−3.02256	−0.183608	−0.0918038	−	0.995777i	$-0.529263\pi$
$271$	−3.02256	−0.183608	−0.0918038	+	0.995777i	$0.529263\pi$
$272$	−1.05288	−0.0638403
$273$	−25.5486	−1.54627
$274$	−4.18058	−0.252558
$275$	6.66481	0.401903
$276$	29.6306	1.78355
$277$	15.5342	0.933360	0.466680	−	0.884426i	$-0.345450\pi$
$277$	15.5342	0.933360	0.466680	+	0.884426i	$0.345450\pi$
$278$	3.22273	0.193286
$279$	7.39660	0.442823
$280$	4.06697	0.243048
$281$	−23.9934	−1.43132	−0.715662	−	0.698447i	$-0.753875\pi$
$281$	−23.9934	−1.43132	−0.715662	+	0.698447i	$0.753875\pi$
$282$	3.12844	0.186296
$283$	−0.375834	−0.0223410	−0.0111705	−	0.999938i	$-0.503556\pi$
$283$	−0.375834	−0.0223410	−0.0111705	+	0.999938i	$0.503556\pi$
$284$	−13.0378	−0.773654
$285$	2.87771	0.170461
$286$	−2.53044	−0.149628
$287$	1.82482	0.107716
$288$	−5.21820	−0.307485
$289$	−16.8818	−0.993047
$290$	1.36990	0.0804434
$291$	5.01170	0.293791
$292$	−6.48918	−0.379751
$293$	−1.19887	−0.0700389	−0.0350194	−	0.999387i	$-0.511149\pi$
$293$	−1.19887	−0.0700389	−0.0350194	+	0.999387i	$0.511149\pi$
$294$	−2.05002	−0.119560
$295$	−7.34319	−0.427537
$296$	11.7652	0.683838
$297$	5.73483	0.332769
$298$	−2.17888	−0.126219
$299$	31.7093	1.83380
$300$	16.0972	0.929373
$301$	11.2518	0.648544
$302$	−0.908408	−0.0522730
$303$	30.5001	1.75219
$304$	5.00440	0.287022
$305$	7.68132	0.439831
$306$	0.167018	0.00954776
$307$	−3.53770	−0.201907	−0.100954	−	0.994891i	$-0.532189\pi$
$307$	−3.53770	−0.201907	−0.100954	+	0.994891i	$0.532189\pi$
$308$	8.85891	0.504783
$309$	−28.7456	−1.63528
$310$	−2.09737	−0.119123
$311$	−27.8999	−1.58206	−0.791030	−	0.611777i	$-0.790455\pi$
$311$	−27.8999	−1.58206	−0.791030	+	0.611777i	$0.790455\pi$
$312$	−12.7567	−0.722206
$313$	−4.32943	−0.244714	−0.122357	−	0.992486i	$-0.539045\pi$
$313$	−4.32943	−0.244714	−0.122357	+	0.992486i	$0.539045\pi$
$314$	−9.48718	−0.535392
$315$	3.20525	0.180596
$316$	−7.32752	−0.412205
$317$	1.93923	0.108918	0.0544589	−	0.998516i	$-0.482657\pi$
$317$	1.93923	0.108918	0.0544589	+	0.998516i	$0.482657\pi$
$318$	−10.3955	−0.582948
$319$	6.22845	0.348726
$320$	−3.77580	−0.211073
$321$	2.05242	0.114555
$322$	9.68904	0.539949
$323$	−0.561796	−0.0312592
$324$	20.5418	1.14121
$325$	17.2265	0.955556
$326$	−2.98109	−0.165107
$327$	−14.9384	−0.826097
$328$	0.911152	0.0503099
$329$	−11.7209	−0.646192
$330$	1.10297	0.0607165
$331$	24.7851	1.36231	0.681157	−	0.732138i	$-0.261477\pi$
$331$	24.7851	1.36231	0.681157	+	0.732138i	$0.261477\pi$
$332$	31.7994	1.74522
$333$	9.27238	0.508123
$334$	−6.63086	−0.362825
$335$	11.2957	0.617150
$336$	19.3661	1.05651
$337$	−26.2295	−1.42881	−0.714406	−	0.699731i	$-0.753303\pi$
$337$	−26.2295	−1.42881	−0.714406	+	0.699731i	$0.753303\pi$
$338$	−1.33156	−0.0724271
$339$	20.4968	1.11323
$340$	0.542621	0.0294278
$341$	−9.53599	−0.516403
$342$	−0.793843	−0.0429261
$343$	−13.8868	−0.749816
$344$	5.61815	0.302910
$345$	−13.8215	−0.744124
$346$	−7.97627	−0.428807
$347$	16.2012	0.869726	0.434863	−	0.900497i	$-0.356797\pi$
$347$	16.2012	0.869726	0.434863	+	0.900497i	$0.356797\pi$
$348$	15.0433	0.806404
$349$	−9.68150	−0.518239	−0.259119	−	0.965845i	$-0.583432\pi$
$349$	−9.68150	−0.518239	−0.259119	+	0.965845i	$0.583432\pi$
$350$	5.26370	0.281357
$351$	14.8228	0.791183
$352$	6.72750	0.358577
$353$	0.951831	0.0506609	0.0253304	−	0.999679i	$-0.491936\pi$
$353$	0.951831	0.0506609	0.0253304	+	0.999679i	$0.491936\pi$
$354$	7.03795	0.374063
$355$	6.08164	0.322780
$356$	−4.30693	−0.228267
$357$	−2.17404	−0.115063
$358$	−1.14710	−0.0606263
$359$	−15.4999	−0.818052	−0.409026	−	0.912523i	$-0.634131\pi$
$359$	−15.4999	−0.818052	−0.409026	+	0.912523i	$0.634131\pi$
$360$	1.60042	0.0843493
$361$	−16.3298	−0.859461
$362$	1.47772	0.0776671
$363$	−17.5619	−0.921758
$364$	22.8976	1.20016
$365$	3.02695	0.158438
$366$	−7.36202	−0.384819
$367$	−2.63718	−0.137660	−0.0688299	−	0.997628i	$-0.521927\pi$
$367$	−2.63718	−0.137660	−0.0688299	+	0.997628i	$0.521927\pi$
$368$	−24.0359	−1.25296
$369$	0.718096	0.0373826
$370$	−2.62926	−0.136689
$371$	38.9471	2.02204
$372$	−23.0318	−1.19414
$373$	8.98443	0.465196	0.232598	−	0.972573i	$-0.425277\pi$
$373$	8.98443	0.465196	0.232598	+	0.972573i	$0.425277\pi$
$374$	−0.215325	−0.0111342
$375$	−16.3140	−0.842449
$376$	−5.85235	−0.301812
$377$	16.0986	0.829123
$378$	4.52923	0.232958
$379$	1.01229	0.0519977	0.0259988	−	0.999662i	$-0.491723\pi$
$379$	1.01229	0.0519977	0.0259988	+	0.999662i	$0.491723\pi$
$380$	−2.57910	−0.132305
$381$	−41.2910	−2.11540
$382$	−1.02132	−0.0522551
$383$	4.16498	0.212821	0.106410	−	0.994322i	$-0.466064\pi$
$383$	4.16498	0.212821	0.106410	+	0.994322i	$0.466064\pi$
$384$	21.2856	1.08623
$385$	−4.13234	−0.210603
$386$	0.919562	0.0468045
$387$	4.42777	0.225076
$388$	−4.49166	−0.228030
$389$	2.14928	0.108973	0.0544865	−	0.998515i	$-0.482648\pi$
$389$	2.14928	0.108973	0.0544865	+	0.998515i	$0.482648\pi$
$390$	2.85084	0.144358
$391$	2.69828	0.136458
$392$	3.83497	0.193695
$393$	−39.0796	−1.97131
$394$	9.56166	0.481710
$395$	3.41800	0.171978
$396$	3.48612	0.175184
$397$	10.2162	0.512738	0.256369	−	0.966579i	$-0.417474\pi$
$397$	10.2162	0.512738	0.256369	+	0.966579i	$0.417474\pi$
$398$	−8.00818	−0.401414
$399$	10.3333	0.517314
$400$	−13.0578	−0.652892
$401$	8.64190	0.431556	0.215778	−	0.976442i	$-0.430771\pi$
$401$	8.64190	0.431556	0.215778	+	0.976442i	$0.430771\pi$
$402$	−10.8262	−0.539960
$403$	−24.6476	−1.22779
$404$	−27.3353	−1.35998
$405$	−9.58193	−0.476130
$406$	4.91907	0.244129
$407$	−11.9543	−0.592553
$408$	−1.08552	−0.0537413
$409$	−21.2166	−1.04909	−0.524546	−	0.851382i	$-0.675765\pi$
$409$	−21.2166	−1.04909	−0.524546	+	0.851382i	$0.675765\pi$
$410$	−0.203622	−0.0100562
$411$	21.4143	1.05629
$412$	25.7629	1.26925
$413$	−26.3681	−1.29749
$414$	3.81279	0.187388
$415$	−14.8332	−0.728133
$416$	17.3885	0.852544
$417$	−16.5079	−0.808396
$418$	1.02345	0.0500587
$419$	−16.5527	−0.808650	−0.404325	−	0.914615i	$-0.632494\pi$
$419$	−16.5527	−0.808650	−0.404325	+	0.914615i	$0.632494\pi$
$420$	−9.98064	−0.487005
$421$	8.84459	0.431059	0.215529	−	0.976497i	$-0.430852\pi$
$421$	8.84459	0.431059	0.215529	+	0.976497i	$0.430852\pi$
$422$	5.57678	0.271473
$423$	−4.61235	−0.224260
$424$	19.4467	0.944416
$425$	1.46588	0.0711055
$426$	−5.82884	−0.282408
$427$	27.5822	1.33480
$428$	−1.83945	−0.0889134
$429$	12.9617	0.625799
$430$	−1.25553	−0.0605472
$431$	−28.3430	−1.36523	−0.682616	−	0.730777i	$-0.739158\pi$
$431$	−28.3430	−1.36523	−0.682616	+	0.730777i	$0.739158\pi$
$432$	−11.2358	−0.540583
$433$	29.9692	1.44023	0.720114	−	0.693855i	$-0.244089\pi$
$433$	29.9692	1.44023	0.720114	+	0.693855i	$0.244089\pi$
$434$	−7.53128	−0.361513
$435$	−7.01710	−0.336444
$436$	13.3884	0.641186
$437$	−12.8251	−0.613506
$438$	−2.90113	−0.138621
$439$	13.6019	0.649183	0.324592	−	0.945854i	$-0.394773\pi$
$439$	13.6019	0.649183	0.324592	+	0.945854i	$0.394773\pi$
$440$	−2.06332	−0.0983648
$441$	3.02241	0.143924
$442$	−0.556551	−0.0264724
$443$	−30.1900	−1.43437	−0.717185	−	0.696883i	$-0.754570\pi$
$443$	−30.1900	−1.43437	−0.717185	+	0.696883i	$0.754570\pi$
$444$	−28.8727	−1.37024
$445$	2.00902	0.0952365
$446$	0.375779	0.0177936
$447$	11.1609	0.527895
$448$	−13.5582	−0.640565
$449$	−15.9602	−0.753207	−0.376603	−	0.926375i	$-0.622908\pi$
$449$	−15.9602	−0.753207	−0.376603	+	0.926375i	$0.622908\pi$
$450$	2.07135	0.0976444
$451$	−0.925797	−0.0435941
$452$	−18.3700	−0.864052
$453$	4.65317	0.218625
$454$	5.40977	0.253893
$455$	−10.6808	−0.500725
$456$	5.15954	0.241617
$457$	10.6928	0.500187	0.250093	−	0.968222i	$-0.419539\pi$
$457$	10.6928	0.500187	0.250093	+	0.968222i	$0.419539\pi$
$458$	−8.87464	−0.414685
$459$	1.26134	0.0588741
$460$	12.3873	0.577562
$461$	−30.1188	−1.40277	−0.701387	−	0.712781i	$-0.747435\pi$
$461$	−30.1188	−1.40277	−0.701387	+	0.712781i	$0.747435\pi$
$462$	3.96056	0.184262
$463$	−16.5292	−0.768176	−0.384088	−	0.923296i	$-0.625484\pi$
$463$	−16.5292	−0.768176	−0.384088	+	0.923296i	$0.625484\pi$
$464$	−12.2029	−0.566505
$465$	10.7434	0.498215
$466$	−1.72574	−0.0799434
$467$	39.1468	1.81150	0.905750	−	0.423813i	$-0.139308\pi$
$467$	39.1468	1.81150	0.905750	+	0.423813i	$0.139308\pi$
$468$	9.01057	0.416514
$469$	40.5608	1.87293
$470$	1.30787	0.0603276
$471$	48.5965	2.23921
$472$	−13.1658	−0.606007
$473$	−5.70845	−0.262475
$474$	−3.27592	−0.150468
$475$	−6.96739	−0.319686
$476$	1.94845	0.0893073
$477$	15.3263	0.701744
$478$	4.92786	0.225395
$479$	2.08979	0.0954849	0.0477425	−	0.998860i	$-0.484797\pi$
$479$	2.08979	0.0954849	0.0477425	+	0.998860i	$0.484797\pi$
$480$	−7.57934	−0.345948
$481$	−30.8983	−1.40884
$482$	8.78756	0.400262
$483$	−49.6305	−2.25827
$484$	15.7396	0.715434
$485$	2.09519	0.0951375
$486$	4.77354	0.216532
$487$	−33.4056	−1.51375	−0.756877	−	0.653557i	$-0.773276\pi$
$487$	−33.4056	−1.51375	−0.756877	+	0.653557i	$0.773276\pi$
$488$	13.7721	0.623433
$489$	15.2702	0.690540
$490$	−0.857031	−0.0387167
$491$	16.1338	0.728110	0.364055	−	0.931377i	$-0.381392\pi$
$491$	16.1338	0.728110	0.364055	+	0.931377i	$0.381392\pi$
$492$	−2.23603	−0.100808
$493$	1.36990	0.0616973
$494$	2.64532	0.119018
$495$	−1.62614	−0.0730896
$496$	18.6831	0.838896
$497$	21.8381	0.979572
$498$	14.2166	0.637061
$499$	−21.5343	−0.964007	−0.482003	−	0.876169i	$-0.660091\pi$
$499$	−21.5343	−0.964007	−0.482003	+	0.876169i	$0.660091\pi$
$500$	14.6212	0.653878
$501$	33.9655	1.51747
$502$	−6.23430	−0.278251
$503$	−19.6399	−0.875700	−0.437850	−	0.899048i	$-0.644260\pi$
$503$	−19.6399	−0.875700	−0.437850	+	0.899048i	$0.644260\pi$
$504$	5.74681	0.255983
$505$	12.7509	0.567406
$506$	−4.91560	−0.218525
$507$	6.82067	0.302917
$508$	37.0065	1.64190
$509$	33.7799	1.49727	0.748633	−	0.662984i	$-0.230710\pi$
$509$	33.7799	1.49727	0.748633	+	0.662984i	$0.230710\pi$
$510$	0.242590	0.0107421
$511$	10.8692	0.480826
$512$	−22.6033	−0.998936
$513$	−5.99519	−0.264694
$514$	8.41778	0.371292
$515$	−12.0174	−0.529549
$516$	−13.7874	−0.606954
$517$	5.94641	0.261523
$518$	−9.44121	−0.414823
$519$	40.8571	1.79343
$520$	−5.33305	−0.233870
$521$	27.3215	1.19698	0.598489	−	0.801131i	$-0.295768\pi$
$521$	27.3215	1.19698	0.598489	+	0.801131i	$0.295768\pi$
$522$	1.93573	0.0847247
$523$	−4.31540	−0.188699	−0.0943496	−	0.995539i	$-0.530077\pi$
$523$	−4.31540	−0.188699	−0.0943496	+	0.995539i	$0.530077\pi$
$524$	35.0246	1.53006
$525$	−26.9625	−1.17674
$526$	−12.1568	−0.530061
$527$	−2.09737	−0.0913629
$528$	−9.82509	−0.427582
$529$	38.5982	1.67818
$530$	−4.34591	−0.188774
$531$	−10.3763	−0.450291
$532$	−9.26110	−0.401520
$533$	−2.39291	−0.103648
$534$	−1.92551	−0.0833248
$535$	0.858034	0.0370960
$536$	20.2524	0.874772
$537$	5.87585	0.253562
$538$	−1.78213	−0.0768331
$539$	−3.89661	−0.167839
$540$	5.79057	0.249186
$541$	−38.0043	−1.63393	−0.816967	−	0.576685i	$-0.804346\pi$
$541$	−38.0043	−1.63393	−0.816967	+	0.576685i	$0.804346\pi$
$542$	1.21108	0.0520205
$543$	−7.56936	−0.324832
$544$	1.47966	0.0634401
$545$	−6.24515	−0.267513
$546$	10.2369	0.438097
$547$	2.79784	0.119627	0.0598135	−	0.998210i	$-0.480949\pi$
$547$	2.79784	0.119627	0.0598135	+	0.998210i	$0.480949\pi$
$548$	−19.1923	−0.819853
$549$	10.8540	0.463239
$550$	−2.67046	−0.113869
$551$	−6.51121	−0.277387
$552$	−24.7810	−1.05475
$553$	12.2734	0.521919
$554$	−6.22426	−0.264444
$555$	13.4680	0.571684
$556$	14.7950	0.627447
$557$	−41.9379	−1.77697	−0.888483	−	0.458910i	$-0.848240\pi$
$557$	−41.9379	−1.77697	−0.888483	+	0.458910i	$0.848240\pi$
$558$	−2.96368	−0.125463
$559$	−14.7546	−0.624054
$560$	8.09615	0.342125
$561$	1.10297	0.0465674
$562$	9.61368	0.405529
$563$	12.3159	0.519054	0.259527	−	0.965736i	$-0.416433\pi$
$563$	12.3159	0.519054	0.259527	+	0.965736i	$0.416433\pi$
$564$	14.3621	0.604753
$565$	8.56888	0.360496
$566$	0.150590	0.00632975
$567$	−34.4070	−1.44496
$568$	10.9040	0.457521
$569$	5.52854	0.231769	0.115884	−	0.993263i	$-0.463030\pi$
$569$	5.52854	0.231769	0.115884	+	0.993263i	$0.463030\pi$
$570$	−1.15304	−0.0482957
$571$	−28.7910	−1.20487	−0.602433	−	0.798169i	$-0.705802\pi$
$571$	−28.7910	−1.20487	−0.602433	+	0.798169i	$0.705802\pi$
$572$	−11.6168	−0.485722
$573$	5.23153	0.218550
$574$	−0.731171	−0.0305185
$575$	33.4641	1.39555
$576$	−5.33537	−0.222307
$577$	2.16381	0.0900807	0.0450404	−	0.998985i	$-0.485658\pi$
$577$	2.16381	0.0900807	0.0450404	+	0.998985i	$0.485658\pi$
$578$	6.76422	0.281354
$579$	−4.71031	−0.195754
$580$	6.28897	0.261135
$581$	−53.2633	−2.20973
$582$	−2.00809	−0.0832382
$583$	−19.7593	−0.818346
$584$	5.42712	0.224576
$585$	−4.20308	−0.173776
$586$	0.480366	0.0198437
$587$	34.4416	1.42156	0.710778	−	0.703416i	$-0.248343\pi$
$587$	34.4416	1.42156	0.710778	+	0.703416i	$0.248343\pi$
$588$	−9.41129	−0.388115
$589$	9.96891	0.410762
$590$	2.94228	0.121132
$591$	−48.9780	−2.01469
$592$	23.4211	0.962602
$593$	23.5676	0.967806	0.483903	−	0.875122i	$-0.339219\pi$
$593$	23.5676	0.967806	0.483903	+	0.875122i	$0.339219\pi$
$594$	−2.29784	−0.0942815
$595$	−0.908878	−0.0372604
$596$	−10.0028	−0.409732
$597$	41.0206	1.67886
$598$	−12.7053	−0.519559
$599$	−34.3462	−1.40335	−0.701675	−	0.712497i	$-0.747564\pi$
$599$	−34.3462	−1.40335	−0.701675	+	0.712497i	$0.747564\pi$
$600$	−13.4626	−0.549609
$601$	5.58348	0.227755	0.113878	−	0.993495i	$-0.463673\pi$
$601$	5.58348	0.227755	0.113878	+	0.993495i	$0.463673\pi$
$602$	−4.50839	−0.183748
$603$	15.9613	0.649996
$604$	−4.17034	−0.169689
$605$	−7.34189	−0.298490
$606$	−12.2208	−0.496437
$607$	6.51339	0.264370	0.132185	−	0.991225i	$-0.457801\pi$
$607$	6.51339	0.264370	0.132185	+	0.991225i	$0.457801\pi$
$608$	−7.03292	−0.285223
$609$	−25.1971	−1.02104
$610$	−3.07776	−0.124615
$611$	15.3697	0.621790
$612$	0.766748	0.0309939
$613$	31.5232	1.27321	0.636606	−	0.771189i	$-0.280338\pi$
$613$	31.5232	1.27321	0.636606	+	0.771189i	$0.280338\pi$
$614$	1.41749	0.0572052
$615$	1.04302	0.0420587
$616$	−7.40900	−0.298517
$617$	23.6858	0.953553	0.476776	−	0.879025i	$-0.341805\pi$
$617$	23.6858	0.953553	0.476776	+	0.879025i	$0.341805\pi$
$618$	11.5178	0.463315
$619$	25.6089	1.02931	0.514653	−	0.857398i	$-0.327921\pi$
$619$	25.6089	1.02931	0.514653	+	0.857398i	$0.327921\pi$
$620$	−9.62866	−0.386696
$621$	28.7946	1.15549
$622$	11.1790	0.448236
$623$	7.21401	0.289023
$624$	−25.3949	−1.01661
$625$	14.4987	0.579948
$626$	1.73472	0.0693334
$627$	−5.24247	−0.209364
$628$	−43.5539	−1.73799
$629$	−2.62926	−0.104836
$630$	−1.28428	−0.0511671
$631$	−18.7159	−0.745067	−0.372534	−	0.928019i	$-0.621511\pi$
$631$	−18.7159	−0.745067	−0.372534	+	0.928019i	$0.621511\pi$
$632$	6.12825	0.243769
$633$	−28.5661	−1.13540
$634$	−0.777011	−0.0308591
$635$	−17.2621	−0.685025
$636$	−47.7236	−1.89237
$637$	−10.0716	−0.399049
$638$	−2.49562	−0.0988026
$639$	8.59363	0.339959
$640$	8.89864	0.351750
$641$	11.5357	0.455632	0.227816	−	0.973704i	$-0.426841\pi$
$641$	11.5357	0.455632	0.227816	+	0.973704i	$0.426841\pi$
$642$	−0.822367	−0.0324562
$643$	12.5190	0.493701	0.246851	−	0.969054i	$-0.420604\pi$
$643$	12.5190	0.493701	0.246851	+	0.969054i	$0.420604\pi$
$644$	44.4806	1.75278
$645$	6.43126	0.253231
$646$	0.225101	0.00885648
$647$	−22.1925	−0.872478	−0.436239	−	0.899831i	$-0.643690\pi$
$647$	−22.1925	−0.872478	−0.436239	+	0.899831i	$0.643690\pi$
$648$	−17.1798	−0.674884
$649$	13.3775	0.525111
$650$	−6.90234	−0.270732
$651$	38.5778	1.51198
$652$	−13.6857	−0.535972
$653$	−0.545398	−0.0213431	−0.0106715	−	0.999943i	$-0.503397\pi$
$653$	−0.545398	−0.0213431	−0.0106715	+	0.999943i	$0.503397\pi$
$654$	5.98555	0.234053
$655$	−16.3376	−0.638363
$656$	1.81384	0.0708185
$657$	4.27721	0.166870
$658$	4.69633	0.183082
$659$	−0.416896	−0.0162400	−0.00811999	−	0.999967i	$-0.502585\pi$
$659$	−0.416896	−0.0162400	−0.00811999	+	0.999967i	$0.502585\pi$
$660$	5.06353	0.197098
$661$	28.6717	1.11520	0.557600	−	0.830110i	$-0.311722\pi$
$661$	28.6717	1.11520	0.557600	+	0.830110i	$0.311722\pi$
$662$	−9.93093	−0.385976
$663$	2.85084	0.110718
$664$	−26.5949	−1.03208
$665$	4.31994	0.167520
$666$	−3.71527	−0.143964
$667$	31.2730	1.21090
$668$	−30.4411	−1.17780
$669$	−1.92486	−0.0744195
$670$	−4.52598	−0.174854
$671$	−13.9935	−0.540211
$672$	−27.2160	−1.04988
$673$	6.25365	0.241060	0.120530	−	0.992710i	$-0.461541\pi$
$673$	6.25365	0.241060	0.120530	+	0.992710i	$0.461541\pi$
$674$	10.5097	0.404817
$675$	15.6431	0.602102
$676$	−6.11293	−0.235113
$677$	−9.78422	−0.376038	−0.188019	−	0.982165i	$-0.560207\pi$
$677$	−9.78422	−0.376038	−0.188019	+	0.982165i	$0.560207\pi$
$678$	−8.21269	−0.315406
$679$	7.52343	0.288723
$680$	−0.453812	−0.0174029
$681$	−27.7107	−1.06188
$682$	3.82089	0.146309
$683$	24.7545	0.947205	0.473602	−	0.880739i	$-0.342953\pi$
$683$	24.7545	0.947205	0.473602	+	0.880739i	$0.342953\pi$
$684$	−3.64439	−0.139347
$685$	8.95245	0.342055
$686$	5.56417	0.212441
$687$	45.4589	1.73436
$688$	11.1841	0.426390
$689$	−51.0718	−1.94568
$690$	5.53801	0.210829
$691$	−41.1103	−1.56391	−0.781955	−	0.623334i	$-0.785778\pi$
$691$	−41.1103	−1.56391	−0.781955	+	0.623334i	$0.785778\pi$
$692$	−36.6176	−1.39199
$693$	−5.83918	−0.221812
$694$	−6.49152	−0.246415
$695$	−6.90128	−0.261780
$696$	−12.5812	−0.476889
$697$	−0.203622	−0.00771275
$698$	3.87919	0.146830
$699$	8.83983	0.334353
$700$	24.1647	0.913340
$701$	20.9689	0.791986	0.395993	−	0.918254i	$-0.370400\pi$
$701$	20.9689	0.791986	0.395993	+	0.918254i	$0.370400\pi$
$702$	−5.93922	−0.224161
$703$	12.4970	0.471334
$704$	6.87856	0.259246
$705$	−6.69935	−0.252312
$706$	−0.381381	−0.0143535
$707$	45.7860	1.72196
$708$	32.3100	1.21428
$709$	−33.2811	−1.24990	−0.624948	−	0.780666i	$-0.714880\pi$
$709$	−33.2811	−1.24990	−0.624948	+	0.780666i	$0.714880\pi$
$710$	−2.43680	−0.0914515
$711$	4.82979	0.181131
$712$	3.60203	0.134992
$713$	−47.8802	−1.79313
$714$	0.871098	0.0326000
$715$	5.41877	0.202651
$716$	−5.26615	−0.196805
$717$	−25.2422	−0.942686
$718$	6.21050	0.231774
$719$	49.7380	1.85492	0.927458	−	0.373928i	$-0.121989\pi$
$719$	49.7380	1.85492	0.927458	+	0.373928i	$0.121989\pi$
$720$	3.18597	0.118734
$721$	−43.1522	−1.60707
$722$	6.54302	0.243506
$723$	−45.0128	−1.67404
$724$	6.78393	0.252123
$725$	16.9895	0.630975
$726$	7.03670	0.261157
$727$	−20.6762	−0.766838	−0.383419	−	0.923575i	$-0.625253\pi$
$727$	−20.6762	−0.766838	−0.383419	+	0.923575i	$0.625253\pi$
$728$	−19.1500	−0.709747
$729$	9.05028	0.335195
$730$	−1.21284	−0.0448893
$731$	−1.25553	−0.0464376
$732$	−33.7977	−1.24920
$733$	2.70726	0.0999949	0.0499975	−	0.998749i	$-0.484079\pi$
$733$	2.70726	0.0999949	0.0499975	+	0.998749i	$0.484079\pi$
$734$	1.05667	0.0390024
$735$	4.39000	0.161928
$736$	33.7788	1.24510
$737$	−20.5780	−0.757999
$738$	−0.287728	−0.0105914
$739$	−4.12593	−0.151775	−0.0758873	−	0.997116i	$-0.524179\pi$
$739$	−4.12593	−0.151775	−0.0758873	+	0.997116i	$0.524179\pi$
$740$	−12.0705	−0.443720
$741$	−13.5502	−0.497779
$742$	−15.6054	−0.572892
$743$	−31.7860	−1.16611	−0.583057	−	0.812431i	$-0.698143\pi$
$743$	−31.7860	−1.16611	−0.583057	+	0.812431i	$0.698143\pi$
$744$	19.2623	0.706189
$745$	4.66593	0.170947
$746$	−3.59989	−0.131801
$747$	−20.9600	−0.766885
$748$	−0.988520	−0.0361439
$749$	3.08104	0.112579
$750$	6.53669	0.238686
$751$	−46.7601	−1.70630	−0.853150	−	0.521666i	$-0.825311\pi$
$751$	−46.7601	−1.70630	−0.853150	+	0.521666i	$0.825311\pi$
$752$	−11.6503	−0.424844
$753$	31.9342	1.16375
$754$	−6.45042	−0.234911
$755$	1.94530	0.0707967
$756$	20.7929	0.756230
$757$	30.2678	1.10010	0.550051	−	0.835131i	$-0.314608\pi$
$757$	30.2678	1.10010	0.550051	+	0.835131i	$0.314608\pi$
$758$	−0.405604	−0.0147322
$759$	25.1793	0.913952
$760$	2.15699	0.0782423
$761$	9.68827	0.351200	0.175600	−	0.984462i	$-0.443814\pi$
$761$	9.68827	0.351200	0.175600	+	0.984462i	$0.443814\pi$
$762$	16.5445	0.599345
$763$	−22.4252	−0.811847
$764$	−4.68868	−0.169631
$765$	−0.357658	−0.0129311
$766$	−1.66883	−0.0602973
$767$	34.5767	1.24849
$768$	9.53472	0.344055
$769$	23.5689	0.849915	0.424958	−	0.905213i	$-0.360289\pi$
$769$	23.5689	0.849915	0.424958	+	0.905213i	$0.360289\pi$
$770$	1.65575	0.0596691
$771$	−43.1187	−1.55288
$772$	4.22154	0.151937
$773$	5.10704	0.183687	0.0918436	−	0.995773i	$-0.470724\pi$
$773$	5.10704	0.183687	0.0918436	+	0.995773i	$0.470724\pi$
$774$	−1.77412	−0.0637696
$775$	−26.0116	−0.934364
$776$	3.75653	0.134851
$777$	48.3611	1.73494
$778$	−0.861178	−0.0308747
$779$	0.967827	0.0346760
$780$	13.0877	0.468615
$781$	−11.0792	−0.396446
$782$	−1.08115	−0.0386618
$783$	14.6189	0.522436
$784$	7.63431	0.272654
$785$	20.3162	0.725116
$786$	15.6585	0.558519
$787$	40.3189	1.43721	0.718606	−	0.695417i	$-0.244781\pi$
$787$	40.3189	1.43721	0.718606	+	0.695417i	$0.244781\pi$
$788$	43.8959	1.56373
$789$	62.2711	2.21691
$790$	−1.36953	−0.0487257
$791$	30.7693	1.09403
$792$	−2.91556	−0.103600
$793$	−36.1688	−1.28439
$794$	−4.09345	−0.145271
$795$	22.2612	0.789524
$796$	−36.7641	−1.30307
$797$	32.5063	1.15143	0.575715	−	0.817650i	$-0.304724\pi$
$797$	32.5063	1.15143	0.575715	+	0.817650i	$0.304724\pi$
$798$	−4.14037	−0.146568
$799$	1.30787	0.0462691
$800$	18.3508	0.648799
$801$	2.83883	0.100305
$802$	−3.46265	−0.122270
$803$	−5.51435	−0.194597
$804$	−49.7010	−1.75282
$805$	−20.7485	−0.731288
$806$	9.87584	0.347862
$807$	9.12867	0.321345
$808$	22.8614	0.804262
$809$	40.5004	1.42392	0.711959	−	0.702221i	$-0.247808\pi$
$809$	40.5004	1.42392	0.711959	+	0.702221i	$0.247808\pi$
$810$	3.83930	0.134899
$811$	5.17273	0.181639	0.0908196	−	0.995867i	$-0.471051\pi$
$811$	5.17273	0.181639	0.0908196	+	0.995867i	$0.471051\pi$
$812$	22.5826	0.792493
$813$	−6.20358	−0.217569
$814$	4.78986	0.167885
$815$	6.38382	0.223616
$816$	−2.16096	−0.0756487
$817$	5.96761	0.208780
$818$	8.50107	0.297233
$819$	−15.0925	−0.527375
$820$	−0.934794	−0.0326444
$821$	6.50706	0.227098	0.113549	−	0.993532i	$-0.463778\pi$
$821$	6.50706	0.227098	0.113549	+	0.993532i	$0.463778\pi$
$822$	−8.58031	−0.299273
$823$	42.8219	1.49268	0.746339	−	0.665566i	$-0.231810\pi$
$823$	42.8219	1.49268	0.746339	+	0.665566i	$0.231810\pi$
$824$	−21.5463	−0.750602
$825$	13.6790	0.476242
$826$	10.5652	0.367610
$827$	27.2737	0.948401	0.474200	−	0.880417i	$-0.342737\pi$
$827$	27.2737	0.948401	0.474200	+	0.880417i	$0.342737\pi$
$828$	17.5038	0.608300
$829$	−45.7752	−1.58984	−0.794919	−	0.606715i	$-0.792487\pi$
$829$	−45.7752	−1.58984	−0.794919	+	0.606715i	$0.792487\pi$
$830$	5.94338	0.206298
$831$	31.8828	1.10600
$832$	17.7790	0.616376
$833$	−0.857031	−0.0296944
$834$	6.61440	0.229038
$835$	14.1996	0.491397
$836$	4.69849	0.162501
$837$	−22.3820	−0.773637
$838$	6.63234	0.229110
$839$	−50.1044	−1.72980	−0.864898	−	0.501948i	$-0.832617\pi$
$839$	−50.1044	−1.72980	−0.864898	+	0.501948i	$0.832617\pi$
$840$	8.34714	0.288004
$841$	−13.1228	−0.452512
$842$	−3.54386	−0.122129
$843$	−49.2445	−1.69607
$844$	25.6020	0.881256
$845$	2.85144	0.0980926
$846$	1.84808	0.0635383
$847$	−26.3634	−0.905857
$848$	38.7128	1.32940
$849$	−0.771370	−0.0264734
$850$	−0.587350	−0.0201459
$851$	−60.0226	−2.05755
$852$	−26.7592	−0.916754
$853$	31.6634	1.08413	0.542067	−	0.840335i	$-0.317642\pi$
$853$	31.6634	1.08413	0.542067	+	0.840335i	$0.317642\pi$
$854$	−11.0517	−0.378181
$855$	1.69997	0.0581376
$856$	1.53840	0.0525813
$857$	−33.3618	−1.13962	−0.569809	−	0.821777i	$-0.692983\pi$
$857$	−33.3618	−1.13962	−0.569809	+	0.821777i	$0.692983\pi$
$858$	−5.19352	−0.177304
$859$	−25.5566	−0.871981	−0.435990	−	0.899951i	$-0.643602\pi$
$859$	−25.5566	−0.871981	−0.435990	+	0.899951i	$0.643602\pi$
$860$	−5.76393	−0.196548
$861$	3.74531	0.127640
$862$	11.3565	0.386803
$863$	12.6757	0.431486	0.215743	−	0.976450i	$-0.430783\pi$
$863$	12.6757	0.431486	0.215743	+	0.976450i	$0.430783\pi$
$864$	15.7902	0.537194
$865$	17.0807	0.580761
$866$	−12.0081	−0.408052
$867$	−34.6486	−1.17673
$868$	−34.5748	−1.17354
$869$	−6.22675	−0.211228
$870$	2.81162	0.0953228
$871$	−53.1878	−1.80220
$872$	−11.1971	−0.379183
$873$	2.96059	0.100201
$874$	5.13876	0.173821
$875$	−24.4901	−0.827916
$876$	−13.3185	−0.449992
$877$	−51.9996	−1.75590	−0.877950	−	0.478752i	$-0.841089\pi$
$877$	−51.9996	−1.75590	−0.877950	+	0.478752i	$0.841089\pi$
$878$	−5.45002	−0.183929
$879$	−2.46059	−0.0829938
$880$	−4.10747	−0.138463
$881$	24.5788	0.828081	0.414040	−	0.910258i	$-0.364117\pi$
$881$	24.5788	0.828081	0.414040	+	0.910258i	$0.364117\pi$
$882$	−1.21102	−0.0407773
$883$	6.62659	0.223002	0.111501	−	0.993764i	$-0.464434\pi$
$883$	6.62659	0.223002	0.111501	+	0.993764i	$0.464434\pi$
$884$	−2.55503	−0.0859348
$885$	−15.0713	−0.506617
$886$	12.0966	0.406392
$887$	14.7796	0.496250	0.248125	−	0.968728i	$-0.420186\pi$
$887$	14.7796	0.496250	0.248125	+	0.968728i	$0.420186\pi$
$888$	24.1472	0.810326
$889$	−61.9851	−2.07891
$890$	−0.804975	−0.0269828
$891$	17.4559	0.584794
$892$	1.72513	0.0577617
$893$	−6.21637	−0.208023
$894$	−4.47198	−0.149565
$895$	2.45645	0.0821101
$896$	31.9534	1.06749
$897$	65.0809	2.17299
$898$	6.39494	0.213402
$899$	−24.3085	−0.810735
$900$	9.50920	0.316973
$901$	−4.34591	−0.144783
$902$	0.370949	0.0123513
$903$	23.0935	0.768504
$904$	15.3634	0.510980
$905$	−3.16444	−0.105189
$906$	−1.86444	−0.0619418
$907$	−21.5048	−0.714054	−0.357027	−	0.934094i	$-0.616210\pi$
$907$	−21.5048	−0.714054	−0.357027	+	0.934094i	$0.616210\pi$
$908$	24.8353	0.824188
$909$	18.0175	0.597604
$910$	4.27961	0.141868
$911$	25.4159	0.842065	0.421033	−	0.907045i	$-0.361668\pi$
$911$	25.4159	0.842065	0.421033	+	0.907045i	$0.361668\pi$
$912$	10.2711	0.340112
$913$	27.0224	0.894310
$914$	−4.28439	−0.141715
$915$	15.7653	0.521185
$916$	−40.7419	−1.34615
$917$	−58.6653	−1.93730
$918$	−0.505393	−0.0166805
$919$	−20.7751	−0.685306	−0.342653	−	0.939462i	$-0.611325\pi$
$919$	−20.7751	−0.685306	−0.342653	+	0.939462i	$0.611325\pi$
$920$	−10.3599	−0.341557
$921$	−7.26086	−0.239253
$922$	12.0680	0.397440
$923$	−28.6365	−0.942581
$924$	18.1822	0.598152
$925$	−32.6081	−1.07215
$926$	6.62293	0.217643
$927$	−16.9811	−0.557732
$928$	17.1493	0.562954
$929$	0.734942	0.0241127	0.0120563	−	0.999927i	$-0.496162\pi$
$929$	0.734942	0.0241127	0.0120563	+	0.999927i	$0.496162\pi$
$930$	−4.30469	−0.141156
$931$	4.07351	0.133504
$932$	−7.92257	−0.259512
$933$	−57.2625	−1.87469
$934$	−15.6854	−0.513242
$935$	0.461106	0.0150798
$936$	−7.53584	−0.246317
$937$	−18.0314	−0.589061	−0.294531	−	0.955642i	$-0.595163\pi$
$937$	−18.0314	−0.589061	−0.294531	+	0.955642i	$0.595163\pi$
$938$	−16.2520	−0.530645
$939$	−8.88583	−0.289978
$940$	6.00420	0.195835
$941$	31.5482	1.02844	0.514221	−	0.857658i	$-0.328081\pi$
$941$	31.5482	1.02844	0.514221	+	0.857658i	$0.328081\pi$
$942$	−19.4717	−0.634422
$943$	−4.64843	−0.151374
$944$	−26.2094	−0.853043
$945$	−9.69906	−0.315511
$946$	2.28727	0.0743655
$947$	−31.4358	−1.02153	−0.510764	−	0.859721i	$-0.670637\pi$
$947$	−31.4358	−1.02153	−0.510764	+	0.859721i	$0.670637\pi$
$948$	−15.0392	−0.488450
$949$	−14.2529	−0.462669
$950$	2.79170	0.0905748
$951$	3.98011	0.129064
$952$	−1.62956	−0.0528142
$953$	42.2834	1.36969	0.684847	−	0.728687i	$-0.259869\pi$
$953$	42.2834	1.36969	0.684847	+	0.728687i	$0.259869\pi$
$954$	−6.14097	−0.198821
$955$	2.18709	0.0707725
$956$	22.6229	0.731678
$957$	12.7834	0.413229
$958$	−0.837339	−0.0270532
$959$	32.1466	1.03807
$960$	−7.74953	−0.250115
$961$	6.21726	0.200557
$962$	12.3803	0.399158
$963$	1.21244	0.0390703
$964$	40.3421	1.29933
$965$	−1.96919	−0.0633903
$966$	19.8860	0.639822
$967$	30.8891	0.993328	0.496664	−	0.867943i	$-0.334558\pi$
$967$	30.8891	0.993328	0.496664	+	0.867943i	$0.334558\pi$
$968$	−13.1635	−0.423091
$969$	−1.15304	−0.0370411
$970$	−0.839501	−0.0269548
$971$	−24.5489	−0.787811	−0.393906	−	0.919151i	$-0.628876\pi$
$971$	−24.5489	−0.787811	−0.393906	+	0.919151i	$0.628876\pi$
$972$	21.9144	0.702906
$973$	−24.7812	−0.794450
$974$	13.3850	0.428883
$975$	35.3561	1.13230
$976$	27.4162	0.877572
$977$	−23.9232	−0.765373	−0.382686	−	0.923878i	$-0.625001\pi$
$977$	−23.9232	−0.765373	−0.382686	+	0.923878i	$0.625001\pi$
$978$	−6.11846	−0.195647
$979$	−3.65993	−0.116972
$980$	−3.93447	−0.125682
$981$	−8.82467	−0.281750
$982$	−6.46453	−0.206291
$983$	−3.26031	−0.103988	−0.0519939	−	0.998647i	$-0.516558\pi$
$983$	−3.26031	−0.103988	−0.0519939	+	0.998647i	$0.516558\pi$
$984$	1.87007	0.0596156
$985$	−20.4757	−0.652410
$986$	−0.548894	−0.0174803
$987$	−24.0562	−0.765716
$988$	12.1442	0.386357
$989$	−28.6622	−0.911404
$990$	0.651564	0.0207080
$991$	−7.31531	−0.232379	−0.116189	−	0.993227i	$-0.537068\pi$
$991$	−7.31531	−0.232379	−0.116189	+	0.993227i	$0.537068\pi$
$992$	−26.2562	−0.833636
$993$	50.8695	1.61430
$994$	−8.75011	−0.277537
$995$	17.1490	0.543661
$996$	65.2659	2.06803
$997$	28.0435	0.888146	0.444073	−	0.895991i	$-0.353533\pi$
$997$	28.0435	0.888146	0.444073	+	0.895991i	$0.353533\pi$
$998$	8.62838	0.273127
$999$	−28.0581	−0.887720

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	107.2.a.b.1.4	✓	7
3.2	odd	2		963.2.a.f.1.4		7
4.3	odd	2		1712.2.a.t.1.2		7
5.4	even	2		2675.2.a.g.1.4		7
7.6	odd	2		5243.2.a.g.1.4		7
8.3	odd	2		6848.2.a.bv.1.6		7
8.5	even	2		6848.2.a.bu.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
107.2.a.b.1.4	✓	7	1.1	even	1	trivial
963.2.a.f.1.4		7	3.2	odd	2
1712.2.a.t.1.2		7	4.3	odd	2
2675.2.a.g.1.4		7	5.4	even	2
5243.2.a.g.1.4		7	7.6	odd	2
6848.2.a.bu.1.2		7	8.5	even	2
6848.2.a.bv.1.6		7	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 107 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	107.a (trivial)

\(f(q)\)	\(=\)	\(q-0.400681 q^{2} +2.05242 q^{3} -1.83945 q^{4} +0.858034 q^{5} -0.822367 q^{6} +3.08104 q^{7} +1.53840 q^{8} +1.21244 q^{9} -0.343798 q^{10} -1.56312 q^{11} -3.77534 q^{12} -4.04020 q^{13} -1.23452 q^{14} +1.76105 q^{15} +3.06250 q^{16} -0.343798 q^{17} -0.485802 q^{18} +1.63409 q^{19} -1.57831 q^{20} +6.32361 q^{21} +0.626314 q^{22} -7.84845 q^{23} +3.15744 q^{24} -4.26378 q^{25} +1.61883 q^{26} -3.66883 q^{27} -5.66744 q^{28} -3.98461 q^{29} -0.705619 q^{30} +6.10060 q^{31} -4.30388 q^{32} -3.20819 q^{33} +0.137753 q^{34} +2.64364 q^{35} -2.23023 q^{36} +7.64770 q^{37} -0.654748 q^{38} -8.29220 q^{39} +1.32000 q^{40} +0.592274 q^{41} -2.53375 q^{42} +3.65195 q^{43} +2.87530 q^{44} +1.04031 q^{45} +3.14473 q^{46} -3.80419 q^{47} +6.28555 q^{48} +2.49283 q^{49} +1.70842 q^{50} -0.705619 q^{51} +7.43177 q^{52} +12.6409 q^{53} +1.47003 q^{54} -1.34121 q^{55} +4.73987 q^{56} +3.35384 q^{57} +1.59656 q^{58} -8.55816 q^{59} -3.23937 q^{60} +8.95223 q^{61} -2.44439 q^{62} +3.73558 q^{63} -4.40052 q^{64} -3.46663 q^{65} +1.28546 q^{66} +13.1646 q^{67} +0.632401 q^{68} -16.1083 q^{69} -1.05926 q^{70} +7.08789 q^{71} +1.86521 q^{72} +3.52777 q^{73} -3.06429 q^{74} -8.75108 q^{75} -3.00583 q^{76} -4.81605 q^{77} +3.32253 q^{78} +3.98353 q^{79} +2.62773 q^{80} -11.1673 q^{81} -0.237313 q^{82} -17.2874 q^{83} -11.6320 q^{84} -0.294990 q^{85} -1.46327 q^{86} -8.17811 q^{87} -2.40470 q^{88} +2.34142 q^{89} -0.416834 q^{90} -12.4480 q^{91} +14.4369 q^{92} +12.5210 q^{93} +1.52427 q^{94} +1.40210 q^{95} -8.83338 q^{96} +2.44185 q^{97} -0.998831 q^{98} -1.89519 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} + 3 q^{3} + 7 q^{4} + 5 q^{5} - 5 q^{6} + 4 q^{7} - 6 q^{8} + 6 q^{9} - q^{10} - 2 q^{11} + 6 q^{12} + 18 q^{13} - 9 q^{14} - 9 q^{15} - q^{16} - q^{17} - 17 q^{18} - 4 q^{19} - 10 q^{20}+ \cdots - 52 q^{99}+O(q^{100}) \) 7 * q - q^2 + 3 * q^3 + 7 * q^4 + 5 * q^5 - 5 * q^6 + 4 * q^7 - 6 * q^8 + 6 * q^9 - q^10 - 2 * q^11 + 6 * q^12 + 18 * q^13 - 9 * q^14 - 9 * q^15 - q^16 - q^17 - 17 * q^18 - 4 * q^19 - 10 * q^20 - 11 * q^21 - 5 * q^22 - 31 * q^24 + 8 * q^25 - 22 * q^26 + 3 * q^27 + 3 * q^28 - 3 * q^29 - 8 * q^30 + 4 * q^31 - 13 * q^32 - 6 * q^33 - 19 * q^35 + 14 * q^36 + 25 * q^37 + 18 * q^38 + 5 * q^39 + 13 * q^40 + 17 * q^42 + 11 * q^43 - 17 * q^44 + 25 * q^45 + q^46 - 9 * q^47 + 19 * q^48 + 13 * q^49 + 7 * q^50 - 8 * q^51 + 44 * q^52 + 8 * q^53 - 35 * q^54 - 13 * q^55 + 26 * q^56 - 3 * q^57 + 35 * q^58 - 19 * q^59 + 9 * q^60 + 25 * q^61 + 23 * q^62 - 11 * q^63 - 18 * q^64 + 8 * q^65 + 63 * q^66 - 24 * q^67 + 11 * q^68 - 5 * q^70 - 19 * q^71 - 15 * q^72 + 30 * q^73 - 17 * q^74 - 41 * q^75 + 4 * q^76 + 6 * q^77 - 18 * q^78 - 21 * q^79 + 19 * q^80 - 17 * q^81 + 6 * q^82 + 12 * q^83 - 36 * q^84 + 2 * q^85 + 31 * q^86 - 15 * q^87 - 8 * q^88 - 22 * q^89 - 36 * q^90 - 2 * q^91 - 7 * q^92 + 9 * q^93 + 16 * q^94 - 44 * q^95 + 2 * q^96 - 4 * q^97 - 22 * q^98 - 52 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more