LMFDB - Embedded newform 1547.2.a.i.1.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1547,2,Mod(1,1547)] 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("1547.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1547, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1547 = 7 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1547.a (trivial)

Newform invariants

comment:select newform

sage:traces = [14,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$12.3528571927$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 20 x^{12} + 19 x^{11} + 151 x^{10} - 133 x^{9} - 536 x^{8} + 404 x^{7} + 924 x^{6} + \cdots + 4 $ x^14 - x^13 - 20x^12 + 19x^11 + 151x^10 - 133x^9 - 536x^8 + 404x^7 + 924x^6 - 467x^5 - 778x^4 + 97x^3 + 278x^2 + 73x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.650788$ of defining polynomial
Character	$\chi$	$=$	1547.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.650788 q^{2} -1.79830 q^{3} -1.57647 q^{4} +0.841445 q^{5} +1.17031 q^{6} -1.00000 q^{7} +2.32753 q^{8} +0.233881 q^{9} -0.547603 q^{10} +0.796743 q^{11} +2.83497 q^{12} -1.00000 q^{13} +0.650788 q^{14} -1.51317 q^{15} +1.63822 q^{16} -1.00000 q^{17} -0.152207 q^{18} +1.25187 q^{19} -1.32652 q^{20} +1.79830 q^{21} -0.518511 q^{22} +1.21539 q^{23} -4.18559 q^{24} -4.29197 q^{25} +0.650788 q^{26} +4.97431 q^{27} +1.57647 q^{28} +4.84305 q^{29} +0.984753 q^{30} +0.804541 q^{31} -5.72119 q^{32} -1.43278 q^{33} +0.650788 q^{34} -0.841445 q^{35} -0.368707 q^{36} +9.74778 q^{37} -0.814703 q^{38} +1.79830 q^{39} +1.95849 q^{40} +4.04778 q^{41} -1.17031 q^{42} +7.06833 q^{43} -1.25605 q^{44} +0.196798 q^{45} -0.790959 q^{46} -11.0202 q^{47} -2.94601 q^{48} +1.00000 q^{49} +2.79316 q^{50} +1.79830 q^{51} +1.57647 q^{52} -12.8275 q^{53} -3.23722 q^{54} +0.670416 q^{55} -2.32753 q^{56} -2.25124 q^{57} -3.15180 q^{58} +9.70104 q^{59} +2.38548 q^{60} -9.69375 q^{61} -0.523586 q^{62} -0.233881 q^{63} +0.446837 q^{64} -0.841445 q^{65} +0.932438 q^{66} -3.42264 q^{67} +1.57647 q^{68} -2.18563 q^{69} +0.547603 q^{70} -11.9104 q^{71} +0.544363 q^{72} -4.98034 q^{73} -6.34374 q^{74} +7.71825 q^{75} -1.97354 q^{76} -0.796743 q^{77} -1.17031 q^{78} -0.581764 q^{79} +1.37847 q^{80} -9.64694 q^{81} -2.63425 q^{82} -4.45101 q^{83} -2.83497 q^{84} -0.841445 q^{85} -4.59999 q^{86} -8.70925 q^{87} +1.85444 q^{88} +5.54143 q^{89} -0.128074 q^{90} +1.00000 q^{91} -1.91603 q^{92} -1.44681 q^{93} +7.17183 q^{94} +1.05338 q^{95} +10.2884 q^{96} -6.10176 q^{97} -0.650788 q^{98} +0.186343 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + q^{2} - 4 q^{3} + 13 q^{4} - 9 q^{5} - 10 q^{6} - 14 q^{7} + 18 q^{9} - 9 q^{10} + 3 q^{11} - 16 q^{12} - 14 q^{13} - q^{14} - q^{15} + 11 q^{16} - 14 q^{17} + 5 q^{18} - 17 q^{19} - 24 q^{20}+ \cdots + 33 q^{99}+O(q^{100}) $ 14 * q + q^2 - 4 * q^3 + 13 * q^4 - 9 * q^5 - 10 * q^6 - 14 * q^7 + 18 * q^9 - 9 * q^10 + 3 * q^11 - 16 * q^12 - 14 * q^13 - q^14 - q^15 + 11 * q^16 - 14 * q^17 + 5 * q^18 - 17 * q^19 - 24 * q^20 + 4 * q^21 - 22 * q^22 - 6 * q^23 - 18 * q^24 + 11 * q^25 - q^26 - 19 * q^27 - 13 * q^28 + 3 * q^29 + 8 * q^30 - 19 * q^31 - 4 * q^32 - 34 * q^33 - q^34 + 9 * q^35 + 25 * q^36 - 45 * q^37 - 7 * q^38 + 4 * q^39 - 24 * q^40 - 29 * q^41 + 10 * q^42 + 7 * q^43 + 10 * q^44 - 48 * q^45 + q^46 - 10 * q^47 - 38 * q^48 + 14 * q^49 + 12 * q^50 + 4 * q^51 - 13 * q^52 - 15 * q^53 - 44 * q^54 - 2 * q^55 - 21 * q^57 - 42 * q^58 + 3 * q^59 + 8 * q^60 - 34 * q^61 - 16 * q^62 - 18 * q^63 - 20 * q^64 + 9 * q^65 - 16 * q^66 - 14 * q^67 - 13 * q^68 + 4 * q^69 + 9 * q^70 + 4 * q^71 - 6 * q^72 - 45 * q^73 - 22 * q^74 - 3 * q^75 - 29 * q^76 - 3 * q^77 + 10 * q^78 + 23 * q^79 - 37 * q^80 + 6 * q^81 + 15 * q^82 - 25 * q^83 + 16 * q^84 + 9 * q^85 + 40 * q^86 - 7 * q^87 - 36 * q^88 + 9 * q^89 - 57 * q^90 + 14 * q^91 - 38 * q^92 - 27 * q^93 + 13 * q^94 + 13 * q^95 + 3 * q^96 - 76 * q^97 + q^98 + 33 * 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 $

$2$	−0.650788	−0.460177	−0.230088	−	0.973170i	$-0.573902\pi$
$2$	−0.650788	−0.460177	−0.230088	+	0.973170i	$0.573902\pi$
$3$	−1.79830	−1.03825	−0.519124	−	0.854699i	$-0.673742\pi$
$3$	−1.79830	−1.03825	−0.519124	+	0.854699i	$0.673742\pi$
$4$	−1.57647	−0.788237
$5$	0.841445	0.376306	0.188153	−	0.982140i	$-0.439750\pi$
$5$	0.841445	0.376306	0.188153	+	0.982140i	$0.439750\pi$
$6$	1.17031	0.477778
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.32753	0.822905
$9$	0.233881	0.0779602
$10$	−0.547603	−0.173167
$11$	0.796743	0.240227	0.120114	−	0.992760i	$-0.461674\pi$
$11$	0.796743	0.240227	0.120114	+	0.992760i	$0.461674\pi$
$12$	2.83497	0.818386
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0.650788	0.173930
$15$	−1.51317	−0.390699
$16$	1.63822	0.409556
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−0.152207	−0.0358755
$19$	1.25187	0.287199	0.143600	−	0.989636i	$-0.454132\pi$
$19$	1.25187	0.287199	0.143600	+	0.989636i	$0.454132\pi$
$20$	−1.32652	−0.296618
$21$	1.79830	0.392421
$22$	−0.518511	−0.110547
$23$	1.21539	0.253426	0.126713	−	0.991939i	$-0.459557\pi$
$23$	1.21539	0.253426	0.126713	+	0.991939i	$0.459557\pi$
$24$	−4.18559	−0.854380
$25$	−4.29197	−0.858394
$26$	0.650788	0.127630
$27$	4.97431	0.957307
$28$	1.57647	0.297926
$29$	4.84305	0.899331	0.449666	−	0.893197i	$-0.351543\pi$
$29$	4.84305	0.899331	0.449666	+	0.893197i	$0.351543\pi$
$30$	0.984753	0.179791
$31$	0.804541	0.144500	0.0722499	−	0.997387i	$-0.476982\pi$
$31$	0.804541	0.144500	0.0722499	+	0.997387i	$0.476982\pi$
$32$	−5.72119	−1.01137
$33$	−1.43278	−0.249416
$34$	0.650788	0.111609
$35$	−0.841445	−0.142230
$36$	−0.368707	−0.0614511
$37$	9.74778	1.60253	0.801263	−	0.598313i	$-0.204162\pi$
$37$	9.74778	1.60253	0.801263	+	0.598313i	$0.204162\pi$
$38$	−0.814703	−0.132162
$39$	1.79830	0.287958
$40$	1.95849	0.309664
$41$	4.04778	0.632157	0.316078	−	0.948733i	$-0.397634\pi$
$41$	4.04778	0.632157	0.316078	+	0.948733i	$0.397634\pi$
$42$	−1.17031	−0.180583
$43$	7.06833	1.07791	0.538955	−	0.842334i	$-0.318819\pi$
$43$	7.06833	1.07791	0.538955	+	0.842334i	$0.318819\pi$
$44$	−1.25605	−0.189356
$45$	0.196798	0.0293369
$46$	−0.790959	−0.116621
$47$	−11.0202	−1.60746	−0.803732	−	0.594991i	$-0.797156\pi$
$47$	−11.0202	−1.60746	−0.803732	+	0.594991i	$0.797156\pi$
$48$	−2.94601	−0.425221
$49$	1.00000	0.142857
$50$	2.79316	0.395013
$51$	1.79830	0.251812
$52$	1.57647	0.218618
$53$	−12.8275	−1.76199	−0.880994	−	0.473127i	$-0.843125\pi$
$53$	−12.8275	−1.76199	−0.880994	+	0.473127i	$0.843125\pi$
$54$	−3.23722	−0.440530
$55$	0.670416	0.0903989
$56$	−2.32753	−0.311029
$57$	−2.25124	−0.298184
$58$	−3.15180	−0.413851
$59$	9.70104	1.26297	0.631484	−	0.775389i	$-0.282446\pi$
$59$	9.70104	1.26297	0.631484	+	0.775389i	$0.282446\pi$
$60$	2.38548	0.307964
$61$	−9.69375	−1.24116	−0.620579	−	0.784144i	$-0.713102\pi$
$61$	−9.69375	−1.24116	−0.620579	+	0.784144i	$0.713102\pi$
$62$	−0.523586	−0.0664955
$63$	−0.233881	−0.0294662
$64$	0.446837	0.0558546
$65$	−0.841445	−0.104368
$66$	0.932438	0.114775
$67$	−3.42264	−0.418141	−0.209071	−	0.977901i	$-0.567044\pi$
$67$	−3.42264	−0.418141	−0.209071	+	0.977901i	$0.567044\pi$
$68$	1.57647	0.191176
$69$	−2.18563	−0.263119
$70$	0.547603	0.0654510
$71$	−11.9104	−1.41351	−0.706753	−	0.707461i	$-0.749841\pi$
$71$	−11.9104	−1.41351	−0.706753	+	0.707461i	$0.749841\pi$
$72$	0.544363	0.0641538
$73$	−4.98034	−0.582905	−0.291452	−	0.956585i	$-0.594139\pi$
$73$	−4.98034	−0.582905	−0.291452	+	0.956585i	$0.594139\pi$
$74$	−6.34374	−0.737445
$75$	7.71825	0.891226
$76$	−1.97354	−0.226381
$77$	−0.796743	−0.0907973
$78$	−1.17031	−0.132512
$79$	−0.581764	−0.0654535	−0.0327268	−	0.999464i	$-0.510419\pi$
$79$	−0.581764	−0.0654535	−0.0327268	+	0.999464i	$0.510419\pi$
$80$	1.37847	0.154118
$81$	−9.64694	−1.07188
$82$	−2.63425	−0.290904
$83$	−4.45101	−0.488562	−0.244281	−	0.969704i	$-0.578552\pi$
$83$	−4.45101	−0.488562	−0.244281	+	0.969704i	$0.578552\pi$
$84$	−2.83497	−0.309321
$85$	−0.841445	−0.0912676
$86$	−4.59999	−0.496029
$87$	−8.70925	−0.933729
$88$	1.85444	0.197684
$89$	5.54143	0.587390	0.293695	−	0.955899i	$-0.405115\pi$
$89$	5.54143	0.587390	0.293695	+	0.955899i	$0.405115\pi$
$90$	−0.128074	−0.0135001
$91$	1.00000	0.104828
$92$	−1.91603	−0.199760
$93$	−1.44681	−0.150027
$94$	7.17183	0.739718
$95$	1.05338	0.108075
$96$	10.2884	1.05006
$97$	−6.10176	−0.619540	−0.309770	−	0.950812i	$-0.600252\pi$
$97$	−6.10176	−0.619540	−0.309770	+	0.950812i	$0.600252\pi$
$98$	−0.650788	−0.0657395
$99$	0.186343	0.0187282
$100$	6.76618	0.676618
$101$	−13.4688	−1.34020	−0.670098	−	0.742273i	$-0.733748\pi$
$101$	−13.4688	−1.34020	−0.670098	+	0.742273i	$0.733748\pi$
$102$	−1.17031	−0.115878
$103$	−1.82315	−0.179640	−0.0898199	−	0.995958i	$-0.528629\pi$
$103$	−1.82315	−0.179640	−0.0898199	+	0.995958i	$0.528629\pi$
$104$	−2.32753	−0.228233
$105$	1.51317	0.147670
$106$	8.34796	0.810826
$107$	4.47257	0.432380	0.216190	−	0.976351i	$-0.430637\pi$
$107$	4.47257	0.432380	0.216190	+	0.976351i	$0.430637\pi$
$108$	−7.84188	−0.754585
$109$	0.232041	0.0222255	0.0111127	−	0.999938i	$-0.496463\pi$
$109$	0.232041	0.0222255	0.0111127	+	0.999938i	$0.496463\pi$
$110$	−0.436299	−0.0415995
$111$	−17.5294	−1.66382
$112$	−1.63822	−0.154797
$113$	−16.3538	−1.53843	−0.769216	−	0.638989i	$-0.779353\pi$
$113$	−16.3538	−1.53843	−0.769216	+	0.638989i	$0.779353\pi$
$114$	1.46508	0.137217
$115$	1.02268	0.0953655
$116$	−7.63494	−0.708886
$117$	−0.233881	−0.0216223
$118$	−6.31332	−0.581188
$119$	1.00000	0.0916698
$120$	−3.52195	−0.321508
$121$	−10.3652	−0.942291
$122$	6.30858	0.571152
$123$	−7.27912	−0.656336
$124$	−1.26834	−0.113900
$125$	−7.81868	−0.699324
$126$	0.152207	0.0135596
$127$	2.10756	0.187016	0.0935078	−	0.995619i	$-0.470192\pi$
$127$	2.10756	0.187016	0.0935078	+	0.995619i	$0.470192\pi$
$128$	11.1516	0.985670
$129$	−12.7110	−1.11914
$130$	0.547603	0.0480279
$131$	−3.28052	−0.286621	−0.143310	−	0.989678i	$-0.545775\pi$
$131$	−3.28052	−0.286621	−0.143310	+	0.989678i	$0.545775\pi$
$132$	2.25875	0.196599
$133$	−1.25187	−0.108551
$134$	2.22741	0.192419
$135$	4.18561	0.360240
$136$	−2.32753	−0.199584
$137$	12.2625	1.04766	0.523828	−	0.851824i	$-0.324503\pi$
$137$	12.2625	1.04766	0.523828	+	0.851824i	$0.324503\pi$
$138$	1.42238	0.121081
$139$	−1.49602	−0.126891	−0.0634453	−	0.997985i	$-0.520209\pi$
$139$	−1.49602	−0.126891	−0.0634453	+	0.997985i	$0.520209\pi$
$140$	1.32652	0.112111
$141$	19.8177	1.66895
$142$	7.75115	0.650462
$143$	−0.796743	−0.0666270
$144$	0.383148	0.0319290
$145$	4.07516	0.338423
$146$	3.24115	0.268239
$147$	−1.79830	−0.148321
$148$	−15.3671	−1.26317
$149$	−1.19794	−0.0981390	−0.0490695	−	0.998795i	$-0.515626\pi$
$149$	−1.19794	−0.0981390	−0.0490695	+	0.998795i	$0.515626\pi$
$150$	−5.02294	−0.410122
$151$	−20.7021	−1.68472	−0.842358	−	0.538918i	$-0.818833\pi$
$151$	−20.7021	−1.68472	−0.842358	+	0.538918i	$0.818833\pi$
$152$	2.91377	0.236338
$153$	−0.233881	−0.0189081
$154$	0.518511	0.0417828
$155$	0.676977	0.0543761
$156$	−2.83497	−0.226980
$157$	−8.38163	−0.668927	−0.334463	−	0.942409i	$-0.608555\pi$
$157$	−8.38163	−0.668927	−0.334463	+	0.942409i	$0.608555\pi$
$158$	0.378605	0.0301202
$159$	23.0676	1.82938
$160$	−4.81407	−0.380586
$161$	−1.21539	−0.0957859
$162$	6.27811	0.493255
$163$	19.7842	1.54962	0.774808	−	0.632197i	$-0.217847\pi$
$163$	19.7842	1.54962	0.774808	+	0.632197i	$0.217847\pi$
$164$	−6.38122	−0.498290
$165$	−1.20561	−0.0938565
$166$	2.89667	0.224825
$167$	−8.47065	−0.655479	−0.327739	−	0.944768i	$-0.606287\pi$
$167$	−8.47065	−0.655479	−0.327739	+	0.944768i	$0.606287\pi$
$168$	4.18559	0.322925
$169$	1.00000	0.0769231
$170$	0.547603	0.0419992
$171$	0.292788	0.0223901
$172$	−11.1431	−0.849650
$173$	−21.4553	−1.63122	−0.815609	−	0.578603i	$-0.803598\pi$
$173$	−21.4553	−1.63122	−0.815609	+	0.578603i	$0.803598\pi$
$174$	5.66787	0.429680
$175$	4.29197	0.324442
$176$	1.30524	0.0983864
$177$	−17.4454	−1.31127
$178$	−3.60629	−0.270303
$179$	−0.851148	−0.0636178	−0.0318089	−	0.999494i	$-0.510127\pi$
$179$	−0.851148	−0.0636178	−0.0318089	+	0.999494i	$0.510127\pi$
$180$	−0.310247	−0.0231244
$181$	0.187920	0.0139680	0.00698401	−	0.999976i	$-0.497777\pi$
$181$	0.187920	0.0139680	0.00698401	+	0.999976i	$0.497777\pi$
$182$	−0.650788	−0.0482396
$183$	17.4323	1.28863
$184$	2.82885	0.208545
$185$	8.20222	0.603040
$186$	0.941564	0.0690388
$187$	−0.796743	−0.0582637
$188$	17.3731	1.26706
$189$	−4.97431	−0.361828
$190$	−0.685528	−0.0497335
$191$	22.5362	1.63066	0.815331	−	0.578995i	$-0.196555\pi$
$191$	22.5362	1.63066	0.815331	+	0.578995i	$0.196555\pi$
$192$	−0.803547	−0.0579910
$193$	−11.4897	−0.827047	−0.413524	−	0.910493i	$-0.635702\pi$
$193$	−11.4897	−0.827047	−0.413524	+	0.910493i	$0.635702\pi$
$194$	3.97095	0.285098
$195$	1.51317	0.108360
$196$	−1.57647	−0.112605
$197$	3.11017	0.221590	0.110795	−	0.993843i	$-0.464660\pi$
$197$	3.11017	0.221590	0.110795	+	0.993843i	$0.464660\pi$
$198$	−0.121270	−0.00861826
$199$	−17.0428	−1.20813	−0.604065	−	0.796935i	$-0.706453\pi$
$199$	−17.0428	−1.20813	−0.604065	+	0.796935i	$0.706453\pi$
$200$	−9.98968	−0.706377
$201$	6.15492	0.434135
$202$	8.76534	0.616727
$203$	−4.84305	−0.339915
$204$	−2.83497	−0.198488
$205$	3.40598	0.237884
$206$	1.18648	0.0826661
$207$	0.284255	0.0197571
$208$	−1.63822	−0.113590
$209$	0.997421	0.0689930
$210$	−0.984753	−0.0679544
$211$	−21.0782	−1.45108	−0.725541	−	0.688179i	$-0.758410\pi$
$211$	−21.0782	−1.45108	−0.725541	+	0.688179i	$0.758410\pi$
$212$	20.2222	1.38886
$213$	21.4185	1.46757
$214$	−2.91070	−0.198971
$215$	5.94762	0.405624
$216$	11.5778	0.787773
$217$	−0.804541	−0.0546158
$218$	−0.151009	−0.0102277
$219$	8.95614	0.605200
$220$	−1.05689	−0.0712558
$221$	1.00000	0.0672673
$222$	11.4079	0.765651
$223$	−21.8499	−1.46318	−0.731589	−	0.681746i	$-0.761221\pi$
$223$	−21.8499	−1.46318	−0.731589	+	0.681746i	$0.761221\pi$
$224$	5.72119	0.382263
$225$	−1.00381	−0.0669205
$226$	10.6428	0.707951
$227$	13.9686	0.927131	0.463565	−	0.886063i	$-0.346570\pi$
$227$	13.9686	0.927131	0.463565	+	0.886063i	$0.346570\pi$
$228$	3.54902	0.235040
$229$	23.6910	1.56555	0.782774	−	0.622307i	$-0.213804\pi$
$229$	23.6910	1.56555	0.782774	+	0.622307i	$0.213804\pi$
$230$	−0.665549	−0.0438850
$231$	1.43278	0.0942702
$232$	11.2723	0.740064
$233$	−19.3772	−1.26944	−0.634721	−	0.772742i	$-0.718885\pi$
$233$	−19.3772	−1.26944	−0.634721	+	0.772742i	$0.718885\pi$
$234$	0.152207	0.00995006
$235$	−9.27292	−0.604898
$236$	−15.2934	−0.995518
$237$	1.04618	0.0679570
$238$	−0.650788	−0.0421843
$239$	29.3048	1.89557	0.947785	−	0.318911i	$-0.103317\pi$
$239$	29.3048	1.89557	0.947785	+	0.318911i	$0.103317\pi$
$240$	−2.47891	−0.160013
$241$	1.44990	0.0933960	0.0466980	−	0.998909i	$-0.485130\pi$
$241$	1.44990	0.0933960	0.0466980	+	0.998909i	$0.485130\pi$
$242$	6.74555	0.433620
$243$	2.42516	0.155574
$244$	15.2820	0.978327
$245$	0.841445	0.0537580
$246$	4.73716	0.302031
$247$	−1.25187	−0.0796547
$248$	1.87259	0.118910
$249$	8.00425	0.507249
$250$	5.08831	0.321813
$251$	3.35421	0.211716	0.105858	−	0.994381i	$-0.466241\pi$
$251$	3.35421	0.211716	0.105858	+	0.994381i	$0.466241\pi$
$252$	0.368707	0.0232263
$253$	0.968351	0.0608797
$254$	−1.37157	−0.0860602
$255$	1.51317	0.0947584
$256$	−8.15099	−0.509437
$257$	−7.42625	−0.463237	−0.231618	−	0.972807i	$-0.574402\pi$
$257$	−7.42625	−0.463237	−0.231618	+	0.972807i	$0.574402\pi$
$258$	8.27215	0.515002
$259$	−9.74778	−0.605698
$260$	1.32652	0.0822671
$261$	1.13269	0.0701120
$262$	2.13493	0.131896
$263$	22.0319	1.35855	0.679273	−	0.733886i	$-0.262295\pi$
$263$	22.0319	1.35855	0.679273	+	0.733886i	$0.262295\pi$
$264$	−3.33484	−0.205245
$265$	−10.7936	−0.663046
$266$	0.814703	0.0499527
$267$	−9.96514	−0.609857
$268$	5.39570	0.329595
$269$	−20.5754	−1.25450	−0.627252	−	0.778816i	$-0.715820\pi$
$269$	−20.5754	−1.25450	−0.627252	+	0.778816i	$0.715820\pi$
$270$	−2.72395	−0.165774
$271$	19.1736	1.16471	0.582357	−	0.812933i	$-0.302131\pi$
$271$	19.1736	1.16471	0.582357	+	0.812933i	$0.302131\pi$
$272$	−1.63822	−0.0993318
$273$	−1.79830	−0.108838
$274$	−7.98029	−0.482107
$275$	−3.41960	−0.206210
$276$	3.44559	0.207400
$277$	3.69170	0.221813	0.110906	−	0.993831i	$-0.464625\pi$
$277$	3.69170	0.221813	0.110906	+	0.993831i	$0.464625\pi$
$278$	0.973591	0.0583921
$279$	0.188167	0.0112652
$280$	−1.95849	−0.117042
$281$	−7.88435	−0.470341	−0.235171	−	0.971954i	$-0.575565\pi$
$281$	−7.88435	−0.470341	−0.235171	+	0.971954i	$0.575565\pi$
$282$	−12.8971	−0.768011
$283$	20.4732	1.21701	0.608504	−	0.793551i	$-0.291770\pi$
$283$	20.4732	1.21701	0.608504	+	0.793551i	$0.291770\pi$
$284$	18.7765	1.11418
$285$	−1.89430	−0.112208
$286$	0.518511	0.0306602
$287$	−4.04778	−0.238933
$288$	−1.33807	−0.0788468
$289$	1.00000	0.0588235
$290$	−2.65206	−0.155735
$291$	10.9728	0.643236
$292$	7.85138	0.459467
$293$	−6.16643	−0.360247	−0.180123	−	0.983644i	$-0.557650\pi$
$293$	−6.16643	−0.360247	−0.180123	+	0.983644i	$0.557650\pi$
$294$	1.17031	0.0682540
$295$	8.16289	0.475262
$296$	22.6882	1.31873
$297$	3.96325	0.229971
$298$	0.779604	0.0451613
$299$	−1.21539	−0.0702876
$300$	−12.1676	−0.702498
$301$	−7.06833	−0.407412
$302$	13.4727	0.775267
$303$	24.2209	1.39146
$304$	2.05085	0.117624
$305$	−8.15676	−0.467055
$306$	0.152207	0.00870108
$307$	−20.9086	−1.19332	−0.596659	−	0.802495i	$-0.703505\pi$
$307$	−20.9086	−1.19332	−0.596659	+	0.802495i	$0.703505\pi$
$308$	1.25605	0.0715699
$309$	3.27856	0.186511
$310$	−0.440569	−0.0250226
$311$	20.4924	1.16202	0.581009	−	0.813897i	$-0.302658\pi$
$311$	20.4924	1.16202	0.581009	+	0.813897i	$0.302658\pi$
$312$	4.18559	0.236962
$313$	−11.6416	−0.658020	−0.329010	−	0.944326i	$-0.606715\pi$
$313$	−11.6416	−0.658020	−0.329010	+	0.944326i	$0.606715\pi$
$314$	5.45466	0.307824
$315$	−0.196798	−0.0110883
$316$	0.917136	0.0515929
$317$	−4.38727	−0.246414	−0.123207	−	0.992381i	$-0.539318\pi$
$317$	−4.38727	−0.246414	−0.123207	+	0.992381i	$0.539318\pi$
$318$	−15.0121	−0.841839
$319$	3.85867	0.216044
$320$	0.375989	0.0210184
$321$	−8.04303	−0.448918
$322$	0.790959	0.0440784
$323$	−1.25187	−0.0696560
$324$	15.2082	0.844898
$325$	4.29197	0.238076
$326$	−12.8753	−0.713097
$327$	−0.417279	−0.0230756
$328$	9.42132	0.520205
$329$	11.0202	0.607565
$330$	0.784596	0.0431906
$331$	27.1698	1.49339	0.746693	−	0.665168i	$-0.231640\pi$
$331$	27.1698	1.49339	0.746693	+	0.665168i	$0.231640\pi$
$332$	7.01691	0.385103
$333$	2.27982	0.124933
$334$	5.51260	0.301636
$335$	−2.87996	−0.157349
$336$	2.94601	0.160718
$337$	29.2310	1.59231	0.796156	−	0.605091i	$-0.206863\pi$
$337$	29.2310	1.59231	0.796156	+	0.605091i	$0.206863\pi$
$338$	−0.650788	−0.0353982
$339$	29.4089	1.59727
$340$	1.32652	0.0719405
$341$	0.641013	0.0347128
$342$	−0.190543	−0.0103034
$343$	−1.00000	−0.0539949
$344$	16.4517	0.887018
$345$	−1.83909	−0.0990131
$346$	13.9629	0.750648
$347$	−9.33094	−0.500911	−0.250455	−	0.968128i	$-0.580580\pi$
$347$	−9.33094	−0.500911	−0.250455	+	0.968128i	$0.580580\pi$
$348$	13.7299	0.736000
$349$	−2.54583	−0.136275	−0.0681377	−	0.997676i	$-0.521706\pi$
$349$	−2.54583	−0.136275	−0.0681377	+	0.997676i	$0.521706\pi$
$350$	−2.79316	−0.149301
$351$	−4.97431	−0.265509
$352$	−4.55832	−0.242959
$353$	−35.3313	−1.88050	−0.940249	−	0.340488i	$-0.889408\pi$
$353$	−35.3313	−1.88050	−0.940249	+	0.340488i	$0.889408\pi$
$354$	11.3532	0.603418
$355$	−10.0220	−0.531910
$356$	−8.73592	−0.463003
$357$	−1.79830	−0.0951761
$358$	0.553917	0.0292754
$359$	1.27201	0.0671342	0.0335671	−	0.999436i	$-0.489313\pi$
$359$	1.27201	0.0671342	0.0335671	+	0.999436i	$0.489313\pi$
$360$	0.458052	0.0241415
$361$	−17.4328	−0.917517
$362$	−0.122296	−0.00642775
$363$	18.6397	0.978332
$364$	−1.57647	−0.0826297
$365$	−4.19068	−0.219350
$366$	−11.3447	−0.592998
$367$	−2.48879	−0.129914	−0.0649569	−	0.997888i	$-0.520691\pi$
$367$	−2.48879	−0.129914	−0.0649569	+	0.997888i	$0.520691\pi$
$368$	1.99107	0.103792
$369$	0.946697	0.0492831
$370$	−5.33791	−0.277505
$371$	12.8275	0.665969
$372$	2.28085	0.118257
$373$	−24.0285	−1.24415	−0.622075	−	0.782958i	$-0.713710\pi$
$373$	−24.0285	−1.24415	−0.622075	+	0.782958i	$0.713710\pi$
$374$	0.518511	0.0268116
$375$	14.0603	0.726073
$376$	−25.6499	−1.32279
$377$	−4.84305	−0.249430
$378$	3.23722	0.166505
$379$	−4.69341	−0.241084	−0.120542	−	0.992708i	$-0.538463\pi$
$379$	−4.69341	−0.241084	−0.120542	+	0.992708i	$0.538463\pi$
$380$	−1.66063	−0.0851885
$381$	−3.79002	−0.194169
$382$	−14.6663	−0.750392
$383$	−13.4814	−0.688870	−0.344435	−	0.938810i	$-0.611929\pi$
$383$	−13.4814	−0.688870	−0.344435	+	0.938810i	$0.611929\pi$
$384$	−20.0539	−1.02337
$385$	−0.670416	−0.0341676
$386$	7.47737	0.380588
$387$	1.65315	0.0840341
$388$	9.61927	0.488345
$389$	31.8250	1.61359	0.806796	−	0.590830i	$-0.201200\pi$
$389$	31.8250	1.61359	0.806796	+	0.590830i	$0.201200\pi$
$390$	−0.984753	−0.0498649
$391$	−1.21539	−0.0614647
$392$	2.32753	0.117558
$393$	5.89936	0.297583
$394$	−2.02406	−0.101971
$395$	−0.489522	−0.0246305
$396$	−0.293765	−0.0147622
$397$	−32.9159	−1.65200	−0.826001	−	0.563668i	$-0.809390\pi$
$397$	−32.9159	−1.65200	−0.826001	+	0.563668i	$0.809390\pi$
$398$	11.0912	0.555953
$399$	2.25124	0.112703
$400$	−7.03120	−0.351560
$401$	34.4247	1.71909	0.859545	−	0.511060i	$-0.170747\pi$
$401$	34.4247	1.71909	0.859545	+	0.511060i	$0.170747\pi$
$402$	−4.00555	−0.199779
$403$	−0.804541	−0.0400771
$404$	21.2332	1.05639
$405$	−8.11737	−0.403356
$406$	3.15180	0.156421
$407$	7.76648	0.384970
$408$	4.18559	0.207218
$409$	−11.1450	−0.551083	−0.275541	−	0.961289i	$-0.588857\pi$
$409$	−11.1450	−0.551083	−0.275541	+	0.961289i	$0.588857\pi$
$410$	−2.21657	−0.109469
$411$	−22.0517	−1.08773
$412$	2.87414	0.141599
$413$	−9.70104	−0.477357
$414$	−0.184990	−0.00909176
$415$	−3.74528	−0.183849
$416$	5.72119	0.280504
$417$	2.69029	0.131744
$418$	−0.649110	−0.0317490
$419$	15.9203	0.777758	0.388879	−	0.921289i	$-0.372862\pi$
$419$	15.9203	0.777758	0.388879	+	0.921289i	$0.372862\pi$
$420$	−2.38548	−0.116399
$421$	−35.3186	−1.72132	−0.860662	−	0.509176i	$-0.829950\pi$
$421$	−35.3186	−1.72132	−0.860662	+	0.509176i	$0.829950\pi$
$422$	13.7174	0.667754
$423$	−2.57742	−0.125318
$424$	−29.8563	−1.44995
$425$	4.29197	0.208191
$426$	−13.9389	−0.675341
$427$	9.69375	0.469114
$428$	−7.05090	−0.340818
$429$	1.43278	0.0691754
$430$	−3.87064	−0.186659
$431$	−13.6960	−0.659713	−0.329856	−	0.944031i	$-0.607000\pi$
$431$	−13.6960	−0.659713	−0.329856	+	0.944031i	$0.607000\pi$
$432$	8.14903	0.392070
$433$	−31.6379	−1.52042	−0.760211	−	0.649676i	$-0.774904\pi$
$433$	−31.6379	−1.52042	−0.760211	+	0.649676i	$0.774904\pi$
$434$	0.523586	0.0251329
$435$	−7.32835	−0.351368
$436$	−0.365807	−0.0175190
$437$	1.52151	0.0727836
$438$	−5.82855	−0.278499
$439$	−24.4352	−1.16623	−0.583113	−	0.812391i	$-0.698166\pi$
$439$	−24.4352	−1.16623	−0.583113	+	0.812391i	$0.698166\pi$
$440$	1.56041	0.0743897
$441$	0.233881	0.0111372
$442$	−0.650788	−0.0309548
$443$	−28.2072	−1.34016	−0.670082	−	0.742287i	$-0.733741\pi$
$443$	−28.2072	−1.34016	−0.670082	+	0.742287i	$0.733741\pi$
$444$	27.6347	1.31149
$445$	4.66281	0.221038
$446$	14.2197	0.673320
$447$	2.15425	0.101893
$448$	−0.446837	−0.0211111
$449$	13.9665	0.659122	0.329561	−	0.944134i	$-0.393099\pi$
$449$	13.9665	0.659122	0.329561	+	0.944134i	$0.393099\pi$
$450$	0.653266	0.0307953
$451$	3.22504	0.151861
$452$	25.7813	1.21265
$453$	37.2286	1.74915
$454$	−9.09062	−0.426644
$455$	0.841445	0.0394476
$456$	−5.23982	−0.245377
$457$	−7.80505	−0.365105	−0.182552	−	0.983196i	$-0.558436\pi$
$457$	−7.80505	−0.365105	−0.182552	+	0.983196i	$0.558436\pi$
$458$	−15.4178	−0.720428
$459$	−4.97431	−0.232181
$460$	−1.61223	−0.0751707
$461$	12.0651	0.561927	0.280963	−	0.959718i	$-0.409346\pi$
$461$	12.0651	0.561927	0.280963	+	0.959718i	$0.409346\pi$
$462$	−0.932438	−0.0433810
$463$	35.1413	1.63316	0.816578	−	0.577236i	$-0.195869\pi$
$463$	35.1413	1.63316	0.816578	+	0.577236i	$0.195869\pi$
$464$	7.93399	0.368326
$465$	−1.21741	−0.0564560
$466$	12.6104	0.584167
$467$	13.9755	0.646711	0.323356	−	0.946278i	$-0.395189\pi$
$467$	13.9755	0.646711	0.323356	+	0.946278i	$0.395189\pi$
$468$	0.368707	0.0170435
$469$	3.42264	0.158043
$470$	6.03470	0.278360
$471$	15.0727	0.694512
$472$	22.5794	1.03930
$473$	5.63165	0.258943
$474$	−0.680845	−0.0312722
$475$	−5.37300	−0.246530
$476$	−1.57647	−0.0722576
$477$	−3.00009	−0.137365
$478$	−19.0712	−0.872297
$479$	−13.4273	−0.613510	−0.306755	−	0.951788i	$-0.599243\pi$
$479$	−13.4273	−0.613510	−0.306755	+	0.951788i	$0.599243\pi$
$480$	8.65714	0.395142
$481$	−9.74778	−0.444461
$482$	−0.943575	−0.0429787
$483$	2.18563	0.0994496
$484$	16.3405	0.742749
$485$	−5.13430	−0.233136
$486$	−1.57826	−0.0715914
$487$	0.927028	0.0420077	0.0210038	−	0.999779i	$-0.493314\pi$
$487$	0.927028	0.0420077	0.0210038	+	0.999779i	$0.493314\pi$
$488$	−22.5625	−1.02136
$489$	−35.5778	−1.60889
$490$	−0.547603	−0.0247382
$491$	19.0059	0.857724	0.428862	−	0.903370i	$-0.358915\pi$
$491$	19.0059	0.857724	0.428862	+	0.903370i	$0.358915\pi$
$492$	11.4753	0.517349
$493$	−4.84305	−0.218120
$494$	0.814703	0.0366552
$495$	0.156797	0.00704751
$496$	1.31802	0.0591807
$497$	11.9104	0.534255
$498$	−5.20907	−0.233424
$499$	8.63038	0.386349	0.193174	−	0.981164i	$-0.438122\pi$
$499$	8.63038	0.386349	0.193174	+	0.981164i	$0.438122\pi$
$500$	12.3260	0.551234
$501$	15.2328	0.680550
$502$	−2.18288	−0.0974268
$503$	−1.30100	−0.0580087	−0.0290044	−	0.999579i	$-0.509234\pi$
$503$	−1.30100	−0.0580087	−0.0290044	+	0.999579i	$0.509234\pi$
$504$	−0.544363	−0.0242479
$505$	−11.3333	−0.504324
$506$	−0.630191	−0.0280154
$507$	−1.79830	−0.0798653
$508$	−3.32251	−0.147413
$509$	−8.33492	−0.369439	−0.184719	−	0.982791i	$-0.559138\pi$
$509$	−8.33492	−0.369439	−0.184719	+	0.982791i	$0.559138\pi$
$510$	−0.984753	−0.0436056
$511$	4.98034	0.220317
$512$	−16.9986	−0.751239
$513$	6.22720	0.274938
$514$	4.83292	0.213171
$515$	−1.53408	−0.0675995
$516$	20.0385	0.882148
$517$	−8.78029	−0.386157
$518$	6.34374	0.278728
$519$	38.5831	1.69361
$520$	−1.95849	−0.0858853
$521$	27.3339	1.19752	0.598760	−	0.800929i	$-0.295660\pi$
$521$	27.3339	1.19752	0.598760	+	0.800929i	$0.295660\pi$
$522$	−0.737144	−0.0322639
$523$	−26.8415	−1.17370	−0.586848	−	0.809697i	$-0.699631\pi$
$523$	−26.8415	−1.17370	−0.586848	+	0.809697i	$0.699631\pi$
$524$	5.17166	0.225925
$525$	−7.71825	−0.336852
$526$	−14.3381	−0.625171
$527$	−0.804541	−0.0350464
$528$	−2.34722	−0.102150
$529$	−21.5228	−0.935775
$530$	7.02435	0.305118
$531$	2.26888	0.0984612
$532$	1.97354	0.0855640
$533$	−4.04778	−0.175329
$534$	6.48520	0.280642
$535$	3.76343	0.162707
$536$	−7.96628	−0.344091
$537$	1.53062	0.0660511
$538$	13.3902	0.577294
$539$	0.796743	0.0343182
$540$	−6.59851	−0.283955
$541$	−32.0934	−1.37980	−0.689902	−	0.723903i	$-0.742346\pi$
$541$	−32.0934	−1.37980	−0.689902	+	0.723903i	$0.742346\pi$
$542$	−12.4780	−0.535974
$543$	−0.337937	−0.0145023
$544$	5.72119	0.245294
$545$	0.195250	0.00836358
$546$	1.17031	0.0500847
$547$	−12.8588	−0.549801	−0.274901	−	0.961473i	$-0.588645\pi$
$547$	−12.8588	−0.549801	−0.274901	+	0.961473i	$0.588645\pi$
$548$	−19.3315	−0.825802
$549$	−2.26718	−0.0967609
$550$	2.22543	0.0948928
$551$	6.06287	0.258287
$552$	−5.08711	−0.216522
$553$	0.581764	0.0247391
$554$	−2.40251	−0.102073
$555$	−14.7501	−0.626105
$556$	2.35844	0.100020
$557$	−7.12653	−0.301961	−0.150980	−	0.988537i	$-0.548243\pi$
$557$	−7.12653	−0.301961	−0.150980	+	0.988537i	$0.548243\pi$
$558$	−0.122457	−0.00518400
$559$	−7.06833	−0.298959
$560$	−1.37847	−0.0582512
$561$	1.43278	0.0604922
$562$	5.13104	0.216440
$563$	−2.56748	−0.108206	−0.0541032	−	0.998535i	$-0.517230\pi$
$563$	−2.56748	−0.108206	−0.0541032	+	0.998535i	$0.517230\pi$
$564$	−31.2420	−1.31553
$565$	−13.7608	−0.578921
$566$	−13.3237	−0.560039
$567$	9.64694	0.405133
$568$	−27.7218	−1.16318
$569$	39.5766	1.65914	0.829570	−	0.558403i	$-0.188586\pi$
$569$	39.5766	1.65914	0.829570	+	0.558403i	$0.188586\pi$
$570$	1.23279	0.0516357
$571$	−15.3442	−0.642137	−0.321068	−	0.947056i	$-0.604042\pi$
$571$	−15.3442	−0.642137	−0.321068	+	0.947056i	$0.604042\pi$
$572$	1.25605	0.0525179
$573$	−40.5268	−1.69303
$574$	2.63425	0.109951
$575$	−5.21640	−0.217539
$576$	0.104507	0.00435444
$577$	−37.9635	−1.58044	−0.790221	−	0.612822i	$-0.790034\pi$
$577$	−37.9635	−1.58044	−0.790221	+	0.612822i	$0.790034\pi$
$578$	−0.650788	−0.0270692
$579$	20.6619	0.858681
$580$	−6.42438	−0.266758
$581$	4.45101	0.184659
$582$	−7.14096	−0.296002
$583$	−10.2202	−0.423277
$584$	−11.5919	−0.479675
$585$	−0.196798	−0.00813658
$586$	4.01304	0.165777
$587$	−1.14473	−0.0472481	−0.0236240	−	0.999721i	$-0.507520\pi$
$587$	−1.14473	−0.0472481	−0.0236240	+	0.999721i	$0.507520\pi$
$588$	2.83497	0.116912
$589$	1.00718	0.0415002
$590$	−5.31231	−0.218704
$591$	−5.59301	−0.230066
$592$	15.9690	0.656323
$593$	24.2168	0.994463	0.497231	−	0.867618i	$-0.334350\pi$
$593$	24.2168	0.994463	0.497231	+	0.867618i	$0.334350\pi$
$594$	−2.57924	−0.105827
$595$	0.841445	0.0344959
$596$	1.88852	0.0773568
$597$	30.6480	1.25434
$598$	0.790959	0.0323447
$599$	41.3412	1.68916	0.844578	−	0.535432i	$-0.179851\pi$
$599$	41.3412	1.68916	0.844578	+	0.535432i	$0.179851\pi$
$600$	17.9644	0.733395
$601$	−28.9763	−1.18197	−0.590984	−	0.806683i	$-0.701260\pi$
$601$	−28.9763	−1.18197	−0.590984	+	0.806683i	$0.701260\pi$
$602$	4.59999	0.187481
$603$	−0.800488	−0.0325984
$604$	32.6364	1.32796
$605$	−8.72175	−0.354590
$606$	−15.7627	−0.640316
$607$	0.748031	0.0303617	0.0151808	−	0.999885i	$-0.495168\pi$
$607$	0.748031	0.0303617	0.0151808	+	0.999885i	$0.495168\pi$
$608$	−7.16220	−0.290465
$609$	8.70925	0.352916
$610$	5.30832	0.214928
$611$	11.0202	0.445831
$612$	0.368707	0.0149041
$613$	16.1811	0.653549	0.326774	−	0.945102i	$-0.394038\pi$
$613$	16.1811	0.653549	0.326774	+	0.945102i	$0.394038\pi$
$614$	13.6071	0.549137
$615$	−6.12498	−0.246983
$616$	−1.85444	−0.0747176
$617$	8.80303	0.354397	0.177198	−	0.984175i	$-0.443297\pi$
$617$	8.80303	0.354397	0.177198	+	0.984175i	$0.443297\pi$
$618$	−2.13365	−0.0858279
$619$	−21.9572	−0.882533	−0.441266	−	0.897376i	$-0.645471\pi$
$619$	−21.9572	−0.882533	−0.441266	+	0.897376i	$0.645471\pi$
$620$	−1.06724	−0.0428613
$621$	6.04571	0.242606
$622$	−13.3362	−0.534734
$623$	−5.54143	−0.222013
$624$	2.94601	0.117935
$625$	14.8809	0.595234
$626$	7.57619	0.302805
$627$	−1.79366	−0.0716319
$628$	13.2134	0.527273
$629$	−9.74778	−0.388670
$630$	0.128074	0.00510257
$631$	14.0046	0.557515	0.278758	−	0.960361i	$-0.410077\pi$
$631$	14.0046	0.557515	0.278758	+	0.960361i	$0.410077\pi$
$632$	−1.35407	−0.0538620
$633$	37.9049	1.50658
$634$	2.85518	0.113394
$635$	1.77340	0.0703750
$636$	−36.3655	−1.44199
$637$	−1.00000	−0.0396214
$638$	−2.51117	−0.0994183
$639$	−2.78561	−0.110197
$640$	9.38345	0.370913
$641$	−31.4262	−1.24126	−0.620631	−	0.784103i	$-0.713123\pi$
$641$	−31.4262	−1.24126	−0.620631	+	0.784103i	$0.713123\pi$
$642$	5.23431	0.206582
$643$	−27.6464	−1.09027	−0.545133	−	0.838349i	$-0.683521\pi$
$643$	−27.6464	−1.09027	−0.545133	+	0.838349i	$0.683521\pi$
$644$	1.91603	0.0755020
$645$	−10.6956	−0.421139
$646$	0.814703	0.0320541
$647$	−6.84656	−0.269166	−0.134583	−	0.990902i	$-0.542969\pi$
$647$	−6.84656	−0.269166	−0.134583	+	0.990902i	$0.542969\pi$
$648$	−22.4535	−0.882058
$649$	7.72924	0.303399
$650$	−2.79316	−0.109557
$651$	1.44681	0.0567048
$652$	−31.1892	−1.22146
$653$	−0.945871	−0.0370148	−0.0185074	−	0.999829i	$-0.505891\pi$
$653$	−0.945871	−0.0370148	−0.0185074	+	0.999829i	$0.505891\pi$
$654$	0.271560	0.0106188
$655$	−2.76038	−0.107857
$656$	6.63116	0.258903
$657$	−1.16480	−0.0454434
$658$	−7.17183	−0.279587
$659$	20.9859	0.817493	0.408746	−	0.912648i	$-0.365966\pi$
$659$	20.9859	0.817493	0.408746	+	0.912648i	$0.365966\pi$
$660$	1.90061	0.0739812
$661$	46.2126	1.79746	0.898731	−	0.438500i	$-0.144490\pi$
$661$	46.2126	1.79746	0.898731	+	0.438500i	$0.144490\pi$
$662$	−17.6818	−0.687222
$663$	−1.79830	−0.0698402
$664$	−10.3598	−0.402040
$665$	−1.05338	−0.0408484
$666$	−1.48368	−0.0574913
$667$	5.88617	0.227914
$668$	13.3538	0.516673
$669$	39.2927	1.51914
$670$	1.87424	0.0724084
$671$	−7.72343	−0.298160
$672$	−10.2884	−0.396884
$673$	46.9851	1.81114	0.905572	−	0.424193i	$-0.139442\pi$
$673$	46.9851	1.81114	0.905572	+	0.424193i	$0.139442\pi$
$674$	−19.0232	−0.732745
$675$	−21.3496	−0.821746
$676$	−1.57647	−0.0606336
$677$	18.9931	0.729963	0.364981	−	0.931015i	$-0.381075\pi$
$677$	18.9931	0.729963	0.364981	+	0.931015i	$0.381075\pi$
$678$	−19.1390	−0.735029
$679$	6.10176	0.234164
$680$	−1.95849	−0.0751045
$681$	−25.1198	−0.962592
$682$	−0.417164	−0.0159740
$683$	−0.369431	−0.0141359	−0.00706795	−	0.999975i	$-0.502250\pi$
$683$	−0.369431	−0.0141359	−0.00706795	+	0.999975i	$0.502250\pi$
$684$	−0.461574	−0.0176487
$685$	10.3182	0.394239
$686$	0.650788	0.0248472
$687$	−42.6036	−1.62543
$688$	11.5795	0.441464
$689$	12.8275	0.488688
$690$	1.19686	0.0455635
$691$	−35.5005	−1.35050	−0.675252	−	0.737587i	$-0.735965\pi$
$691$	−35.5005	−1.35050	−0.675252	+	0.737587i	$0.735965\pi$
$692$	33.8238	1.28579
$693$	−0.186343	−0.00707858
$694$	6.07246	0.230508
$695$	−1.25882	−0.0477497
$696$	−20.2710	−0.768371
$697$	−4.04778	−0.153321
$698$	1.65680	0.0627107
$699$	34.8460	1.31800
$700$	−6.76618	−0.255738
$701$	4.30274	0.162512	0.0812561	−	0.996693i	$-0.474107\pi$
$701$	4.30274	0.162512	0.0812561	+	0.996693i	$0.474107\pi$
$702$	3.23722	0.122181
$703$	12.2030	0.460244
$704$	0.356015	0.0134178
$705$	16.6755	0.628035
$706$	22.9932	0.865361
$707$	13.4688	0.506547
$708$	27.5022	1.03360
$709$	−18.3577	−0.689437	−0.344719	−	0.938706i	$-0.612026\pi$
$709$	−18.3577	−0.689437	−0.344719	+	0.938706i	$0.612026\pi$
$710$	6.52217	0.244773
$711$	−0.136063	−0.00510277
$712$	12.8978	0.483366
$713$	0.977829	0.0366200
$714$	1.17031	0.0437978
$715$	−0.670416	−0.0250721
$716$	1.34181	0.0501459
$717$	−52.6988	−1.96807
$718$	−0.827810	−0.0308936
$719$	−42.4380	−1.58267	−0.791336	−	0.611382i	$-0.790614\pi$
$719$	−42.4380	−1.58267	−0.791336	+	0.611382i	$0.790614\pi$
$720$	0.322398	0.0120151
$721$	1.82315	0.0678975
$722$	11.3451	0.422220
$723$	−2.60735	−0.0969683
$724$	−0.296252	−0.0110101
$725$	−20.7862	−0.771980
$726$	−12.1305	−0.450206
$727$	−24.5006	−0.908679	−0.454339	−	0.890829i	$-0.650125\pi$
$727$	−24.5006	−0.908679	−0.454339	+	0.890829i	$0.650125\pi$
$728$	2.32753	0.0862639
$729$	24.5797	0.910358
$730$	2.72725	0.100940
$731$	−7.06833	−0.261432
$732$	−27.4815	−1.01575
$733$	−13.2573	−0.489668	−0.244834	−	0.969565i	$-0.578733\pi$
$733$	−13.2573	−0.489668	−0.244834	+	0.969565i	$0.578733\pi$
$734$	1.61967	0.0597833
$735$	−1.51317	−0.0558141
$736$	−6.95346	−0.256308
$737$	−2.72696	−0.100449
$738$	−0.616099	−0.0226789
$739$	36.9781	1.36026	0.680131	−	0.733091i	$-0.261923\pi$
$739$	36.9781	1.36026	0.680131	+	0.733091i	$0.261923\pi$
$740$	−12.9306	−0.475338
$741$	2.25124	0.0827014
$742$	−8.34796	−0.306463
$743$	−32.9774	−1.20982	−0.604911	−	0.796293i	$-0.706791\pi$
$743$	−32.9774	−1.20982	−0.604911	+	0.796293i	$0.706791\pi$
$744$	−3.36748	−0.123458
$745$	−1.00800	−0.0369303
$746$	15.6375	0.572528
$747$	−1.04100	−0.0380884
$748$	1.25605	0.0459256
$749$	−4.47257	−0.163424
$750$	−9.15030	−0.334122
$751$	−10.5985	−0.386744	−0.193372	−	0.981126i	$-0.561942\pi$
$751$	−10.5985	−0.386744	−0.193372	+	0.981126i	$0.561942\pi$
$752$	−18.0536	−0.658346
$753$	−6.03188	−0.219814
$754$	3.15180	0.114782
$755$	−17.4197	−0.633968
$756$	7.84188	0.285206
$757$	25.0113	0.909051	0.454525	−	0.890734i	$-0.349809\pi$
$757$	25.0113	0.909051	0.454525	+	0.890734i	$0.349809\pi$
$758$	3.05442	0.110941
$759$	−1.74139	−0.0632083
$760$	2.45177	0.0889352
$761$	−2.31376	−0.0838737	−0.0419369	−	0.999120i	$-0.513353\pi$
$761$	−2.31376	−0.0838737	−0.0419369	+	0.999120i	$0.513353\pi$
$762$	2.46650	0.0893519
$763$	−0.232041	−0.00840044
$764$	−35.5277	−1.28535
$765$	−0.196798	−0.00711523
$766$	8.77356	0.317002
$767$	−9.70104	−0.350284
$768$	14.6579	0.528922
$769$	−20.1751	−0.727533	−0.363766	−	0.931490i	$-0.618509\pi$
$769$	−20.1751	−0.727533	−0.363766	+	0.931490i	$0.618509\pi$
$770$	0.436299	0.0157231
$771$	13.3546	0.480955
$772$	18.1132	0.651910
$773$	−32.3032	−1.16186	−0.580932	−	0.813952i	$-0.697312\pi$
$773$	−32.3032	−1.16186	−0.580932	+	0.813952i	$0.697312\pi$
$774$	−1.07585	−0.0386705
$775$	−3.45307	−0.124038
$776$	−14.2020	−0.509823
$777$	17.5294	0.628865
$778$	−20.7113	−0.742537
$779$	5.06730	0.181555
$780$	−2.38548	−0.0854137
$781$	−9.48954	−0.339562
$782$	0.790959	0.0282846
$783$	24.0908	0.860936
$784$	1.63822	0.0585080
$785$	−7.05268	−0.251721
$786$	−3.83923	−0.136941
$787$	−19.0892	−0.680456	−0.340228	−	0.940343i	$-0.610504\pi$
$787$	−19.0892	−0.680456	−0.340228	+	0.940343i	$0.610504\pi$
$788$	−4.90310	−0.174666
$789$	−39.6200	−1.41051
$790$	0.318575	0.0113344
$791$	16.3538	0.581473
$792$	0.433718	0.0154115
$793$	9.69375	0.344235
$794$	21.4213	0.760213
$795$	19.4101	0.688407
$796$	26.8675	0.952293
$797$	−46.5232	−1.64793	−0.823967	−	0.566637i	$-0.808244\pi$
$797$	−46.5232	−1.64793	−0.823967	+	0.566637i	$0.808244\pi$
$798$	−1.46508	−0.0518633
$799$	11.0202	0.389867
$800$	24.5552	0.868157
$801$	1.29603	0.0457930
$802$	−22.4032	−0.791085
$803$	−3.96805	−0.140030
$804$	−9.70308	−0.342201
$805$	−1.02268	−0.0360448
$806$	0.523586	0.0184425
$807$	37.0007	1.30249
$808$	−31.3490	−1.10285
$809$	−20.2391	−0.711569	−0.355784	−	0.934568i	$-0.615786\pi$
$809$	−20.2391	−0.711569	−0.355784	+	0.934568i	$0.615786\pi$
$810$	5.28269	0.185615
$811$	−33.6678	−1.18224	−0.591118	−	0.806585i	$-0.701313\pi$
$811$	−33.6678	−1.18224	−0.591118	+	0.806585i	$0.701313\pi$
$812$	7.63494	0.267934
$813$	−34.4799	−1.20926
$814$	−5.05433	−0.177154
$815$	16.6473	0.583129
$816$	2.94601	0.103131
$817$	8.84865	0.309575
$818$	7.25301	0.253595
$819$	0.233881	0.00817245
$820$	−5.36945	−0.187509
$821$	−29.2842	−1.02203	−0.511013	−	0.859573i	$-0.670730\pi$
$821$	−29.2842	−1.02203	−0.511013	+	0.859573i	$0.670730\pi$
$822$	14.3510	0.500547
$823$	33.1953	1.15711	0.578557	−	0.815642i	$-0.303616\pi$
$823$	33.1953	1.15711	0.578557	+	0.815642i	$0.303616\pi$
$824$	−4.24342	−0.147827
$825$	6.14946	0.214097
$826$	6.31332	0.219668
$827$	42.1806	1.46676	0.733382	−	0.679817i	$-0.237941\pi$
$827$	42.1806	1.46676	0.733382	+	0.679817i	$0.237941\pi$
$828$	−0.448121	−0.0155733
$829$	−3.37249	−0.117131	−0.0585656	−	0.998284i	$-0.518653\pi$
$829$	−3.37249	−0.117131	−0.0585656	+	0.998284i	$0.518653\pi$
$830$	2.43739	0.0846029
$831$	−6.63878	−0.230297
$832$	−0.446837	−0.0154913
$833$	−1.00000	−0.0346479
$834$	−1.75081	−0.0606255
$835$	−7.12759	−0.246660
$836$	−1.57241	−0.0543829
$837$	4.00204	0.138331
$838$	−10.3608	−0.357906
$839$	16.0546	0.554267	0.277133	−	0.960831i	$-0.410616\pi$
$839$	16.0546	0.554267	0.277133	+	0.960831i	$0.410616\pi$
$840$	3.52195	0.121519
$841$	−5.54490	−0.191204
$842$	22.9849	0.792113
$843$	14.1784	0.488331
$844$	33.2292	1.14380
$845$	0.841445	0.0289466
$846$	1.67735	0.0576685
$847$	10.3652	0.356152
$848$	−21.0142	−0.721632
$849$	−36.8170	−1.26356
$850$	−2.79316	−0.0958047
$851$	11.8473	0.406121
$852$	−33.7657	−1.15679
$853$	−39.5050	−1.35263	−0.676313	−	0.736615i	$-0.736423\pi$
$853$	−39.5050	−1.35263	−0.676313	+	0.736615i	$0.736423\pi$
$854$	−6.30858	−0.215875
$855$	0.246365	0.00842552
$856$	10.4100	0.355808
$857$	13.8888	0.474434	0.237217	−	0.971457i	$-0.423765\pi$
$857$	13.8888	0.474434	0.237217	+	0.971457i	$0.423765\pi$
$858$	−0.932438	−0.0318329
$859$	−21.7866	−0.743350	−0.371675	−	0.928363i	$-0.621216\pi$
$859$	−21.7866	−0.743350	−0.371675	+	0.928363i	$0.621216\pi$
$860$	−9.37627	−0.319728
$861$	7.27912	0.248072
$862$	8.91319	0.303584
$863$	−39.9175	−1.35881	−0.679404	−	0.733765i	$-0.737761\pi$
$863$	−39.9175	−1.35881	−0.679404	+	0.733765i	$0.737761\pi$
$864$	−28.4590	−0.968194
$865$	−18.0535	−0.613837
$866$	20.5896	0.699663
$867$	−1.79830	−0.0610734
$868$	1.26834	0.0430502
$869$	−0.463516	−0.0157237
$870$	4.76921	0.161691
$871$	3.42264	0.115972
$872$	0.540081	0.0182895
$873$	−1.42708	−0.0482994
$874$	−0.990180	−0.0334933
$875$	7.81868	0.264320
$876$	−14.1191	−0.477041
$877$	−23.8123	−0.804083	−0.402042	−	0.915621i	$-0.631699\pi$
$877$	−23.8123	−0.804083	−0.402042	+	0.915621i	$0.631699\pi$
$878$	15.9021	0.536670
$879$	11.0891	0.374026
$880$	1.09829	0.0370234
$881$	53.9231	1.81672	0.908358	−	0.418194i	$-0.137337\pi$
$881$	53.9231	1.81672	0.908358	+	0.418194i	$0.137337\pi$
$882$	−0.152207	−0.00512506
$883$	7.00832	0.235849	0.117924	−	0.993023i	$-0.462376\pi$
$883$	7.00832	0.235849	0.117924	+	0.993023i	$0.462376\pi$
$884$	−1.57647	−0.0530226
$885$	−14.6793	−0.493440
$886$	18.3569	0.616712
$887$	35.3058	1.18545	0.592726	−	0.805404i	$-0.298052\pi$
$887$	35.3058	1.18545	0.592726	+	0.805404i	$0.298052\pi$
$888$	−40.8002	−1.36917
$889$	−2.10756	−0.0706853
$890$	−3.03450	−0.101717
$891$	−7.68614	−0.257495
$892$	34.4458	1.15333
$893$	−13.7959	−0.461663
$894$	−1.40196	−0.0468886
$895$	−0.716195	−0.0239398
$896$	−11.1516	−0.372548
$897$	2.18563	0.0729760
$898$	−9.08926	−0.303312
$899$	3.89643	0.129953
$900$	1.58248	0.0527493
$901$	12.8275	0.427345
$902$	−2.09882	−0.0698830
$903$	12.7110	0.422995
$904$	−38.0638	−1.26598
$905$	0.158125	0.00525624
$906$	−24.2280	−0.804920
$907$	10.2502	0.340354	0.170177	−	0.985414i	$-0.445566\pi$
$907$	10.2502	0.340354	0.170177	+	0.985414i	$0.445566\pi$
$908$	−22.0212	−0.730799
$909$	−3.15009	−0.104482
$910$	−0.547603	−0.0181528
$911$	17.1842	0.569338	0.284669	−	0.958626i	$-0.408116\pi$
$911$	17.1842	0.569338	0.284669	+	0.958626i	$0.408116\pi$
$912$	−3.68803	−0.122123
$913$	−3.54631	−0.117366
$914$	5.07943	0.168013
$915$	14.6683	0.484919
$916$	−37.3483	−1.23402
$917$	3.28052	0.108332
$918$	3.23722	0.106844
$919$	−6.19440	−0.204334	−0.102167	−	0.994767i	$-0.532578\pi$
$919$	−6.19440	−0.204334	−0.102167	+	0.994767i	$0.532578\pi$
$920$	2.38032	0.0784768
$921$	37.6000	1.23896
$922$	−7.85181	−0.258586
$923$	11.9104	0.392036
$924$	−2.25875	−0.0743073
$925$	−41.8372	−1.37560
$926$	−22.8695	−0.751540
$927$	−0.426398	−0.0140048
$928$	−27.7080	−0.909559
$929$	−25.5573	−0.838507	−0.419253	−	0.907869i	$-0.637708\pi$
$929$	−25.5573	−0.838507	−0.419253	+	0.907869i	$0.637708\pi$
$930$	0.792275	0.0259797
$931$	1.25187	0.0410284
$932$	30.5476	1.00062
$933$	−36.8515	−1.20646
$934$	−9.09512	−0.297601
$935$	−0.670416	−0.0219249
$936$	−0.544363	−0.0177931
$937$	51.3148	1.67638	0.838190	−	0.545378i	$-0.183614\pi$
$937$	51.3148	1.67638	0.838190	+	0.545378i	$0.183614\pi$
$938$	−2.22741	−0.0727275
$939$	20.9350	0.683188
$940$	14.6185	0.476803
$941$	−20.3997	−0.665010	−0.332505	−	0.943101i	$-0.607894\pi$
$941$	−20.3997	−0.665010	−0.332505	+	0.943101i	$0.607894\pi$
$942$	−9.80912	−0.319598
$943$	4.91962	0.160205
$944$	15.8925	0.517256
$945$	−4.18561	−0.136158
$946$	−3.66501	−0.119160
$947$	−36.6968	−1.19249	−0.596243	−	0.802804i	$-0.703341\pi$
$947$	−36.6968	−1.19249	−0.596243	+	0.802804i	$0.703341\pi$
$948$	−1.64928	−0.0535663
$949$	4.98034	0.161669
$950$	3.49668	0.113447
$951$	7.88963	0.255839
$952$	2.32753	0.0754356
$953$	−14.5923	−0.472690	−0.236345	−	0.971669i	$-0.575950\pi$
$953$	−14.5923	−0.472690	−0.236345	+	0.971669i	$0.575950\pi$
$954$	1.95243	0.0632121
$955$	18.9630	0.613627
$956$	−46.1983	−1.49416
$957$	−6.93904	−0.224307
$958$	8.73835	0.282323
$959$	−12.2625	−0.395977
$960$	−0.676141	−0.0218224
$961$	−30.3527	−0.979120
$962$	6.34374	0.204530
$963$	1.04605	0.0337084
$964$	−2.28572	−0.0736182
$965$	−9.66796	−0.311223
$966$	−1.42238	−0.0457644
$967$	−24.3658	−0.783550	−0.391775	−	0.920061i	$-0.628139\pi$
$967$	−24.3658	−0.783550	−0.391775	+	0.920061i	$0.628139\pi$
$968$	−24.1253	−0.775416
$969$	2.25124	0.0723203
$970$	3.34134	0.107284
$971$	24.2576	0.778463	0.389232	−	0.921140i	$-0.372741\pi$
$971$	24.2576	0.778463	0.389232	+	0.921140i	$0.372741\pi$
$972$	−3.82320	−0.122629
$973$	1.49602	0.0479602
$974$	−0.603299	−0.0193309
$975$	−7.71825	−0.247182
$976$	−15.8805	−0.508323
$977$	30.5053	0.975951	0.487975	−	0.872857i	$-0.337736\pi$
$977$	30.5053	0.975951	0.487975	+	0.872857i	$0.337736\pi$
$978$	23.1536	0.740372
$979$	4.41509	0.141107
$980$	−1.32652	−0.0423740
$981$	0.0542698	0.00173270
$982$	−12.3688	−0.394705
$983$	12.0725	0.385052	0.192526	−	0.981292i	$-0.438332\pi$
$983$	12.0725	0.385052	0.192526	+	0.981292i	$0.438332\pi$
$984$	−16.9423	−0.540102
$985$	2.61704	0.0833857
$986$	3.15180	0.100374
$987$	−19.8177	−0.630803
$988$	1.97354	0.0627868
$989$	8.59076	0.273170
$990$	−0.102042	−0.00324310
$991$	−19.7636	−0.627812	−0.313906	−	0.949454i	$-0.601638\pi$
$991$	−19.7636	−0.627812	−0.313906	+	0.949454i	$0.601638\pi$
$992$	−4.60293	−0.146143
$993$	−48.8594	−1.55051
$994$	−7.75115	−0.245852
$995$	−14.3406	−0.454626
$996$	−12.6185	−0.399832
$997$	−30.8553	−0.977197	−0.488598	−	0.872509i	$-0.662492\pi$
$997$	−30.8553	−0.977197	−0.488598	+	0.872509i	$0.662492\pi$
$998$	−5.61655	−0.177789
$999$	48.4885	1.53411

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1547.2.a.i.1.5	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1547.2.a.i.1.5	✓	14	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1547 = 7 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1547.a (trivial)

\(f(q)\)	\(=\)	\(q-0.650788 q^{2} -1.79830 q^{3} -1.57647 q^{4} +0.841445 q^{5} +1.17031 q^{6} -1.00000 q^{7} +2.32753 q^{8} +0.233881 q^{9} -0.547603 q^{10} +0.796743 q^{11} +2.83497 q^{12} -1.00000 q^{13} +0.650788 q^{14} -1.51317 q^{15} +1.63822 q^{16} -1.00000 q^{17} -0.152207 q^{18} +1.25187 q^{19} -1.32652 q^{20} +1.79830 q^{21} -0.518511 q^{22} +1.21539 q^{23} -4.18559 q^{24} -4.29197 q^{25} +0.650788 q^{26} +4.97431 q^{27} +1.57647 q^{28} +4.84305 q^{29} +0.984753 q^{30} +0.804541 q^{31} -5.72119 q^{32} -1.43278 q^{33} +0.650788 q^{34} -0.841445 q^{35} -0.368707 q^{36} +9.74778 q^{37} -0.814703 q^{38} +1.79830 q^{39} +1.95849 q^{40} +4.04778 q^{41} -1.17031 q^{42} +7.06833 q^{43} -1.25605 q^{44} +0.196798 q^{45} -0.790959 q^{46} -11.0202 q^{47} -2.94601 q^{48} +1.00000 q^{49} +2.79316 q^{50} +1.79830 q^{51} +1.57647 q^{52} -12.8275 q^{53} -3.23722 q^{54} +0.670416 q^{55} -2.32753 q^{56} -2.25124 q^{57} -3.15180 q^{58} +9.70104 q^{59} +2.38548 q^{60} -9.69375 q^{61} -0.523586 q^{62} -0.233881 q^{63} +0.446837 q^{64} -0.841445 q^{65} +0.932438 q^{66} -3.42264 q^{67} +1.57647 q^{68} -2.18563 q^{69} +0.547603 q^{70} -11.9104 q^{71} +0.544363 q^{72} -4.98034 q^{73} -6.34374 q^{74} +7.71825 q^{75} -1.97354 q^{76} -0.796743 q^{77} -1.17031 q^{78} -0.581764 q^{79} +1.37847 q^{80} -9.64694 q^{81} -2.63425 q^{82} -4.45101 q^{83} -2.83497 q^{84} -0.841445 q^{85} -4.59999 q^{86} -8.70925 q^{87} +1.85444 q^{88} +5.54143 q^{89} -0.128074 q^{90} +1.00000 q^{91} -1.91603 q^{92} -1.44681 q^{93} +7.17183 q^{94} +1.05338 q^{95} +10.2884 q^{96} -6.10176 q^{97} -0.650788 q^{98} +0.186343 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + q^{2} - 4 q^{3} + 13 q^{4} - 9 q^{5} - 10 q^{6} - 14 q^{7} + 18 q^{9} - 9 q^{10} + 3 q^{11} - 16 q^{12} - 14 q^{13} - q^{14} - q^{15} + 11 q^{16} - 14 q^{17} + 5 q^{18} - 17 q^{19} - 24 q^{20}+ \cdots + 33 q^{99}+O(q^{100}) \) 14 * q + q^2 - 4 * q^3 + 13 * q^4 - 9 * q^5 - 10 * q^6 - 14 * q^7 + 18 * q^9 - 9 * q^10 + 3 * q^11 - 16 * q^12 - 14 * q^13 - q^14 - q^15 + 11 * q^16 - 14 * q^17 + 5 * q^18 - 17 * q^19 - 24 * q^20 + 4 * q^21 - 22 * q^22 - 6 * q^23 - 18 * q^24 + 11 * q^25 - q^26 - 19 * q^27 - 13 * q^28 + 3 * q^29 + 8 * q^30 - 19 * q^31 - 4 * q^32 - 34 * q^33 - q^34 + 9 * q^35 + 25 * q^36 - 45 * q^37 - 7 * q^38 + 4 * q^39 - 24 * q^40 - 29 * q^41 + 10 * q^42 + 7 * q^43 + 10 * q^44 - 48 * q^45 + q^46 - 10 * q^47 - 38 * q^48 + 14 * q^49 + 12 * q^50 + 4 * q^51 - 13 * q^52 - 15 * q^53 - 44 * q^54 - 2 * q^55 - 21 * q^57 - 42 * q^58 + 3 * q^59 + 8 * q^60 - 34 * q^61 - 16 * q^62 - 18 * q^63 - 20 * q^64 + 9 * q^65 - 16 * q^66 - 14 * q^67 - 13 * q^68 + 4 * q^69 + 9 * q^70 + 4 * q^71 - 6 * q^72 - 45 * q^73 - 22 * q^74 - 3 * q^75 - 29 * q^76 - 3 * q^77 + 10 * q^78 + 23 * q^79 - 37 * q^80 + 6 * q^81 + 15 * q^82 - 25 * q^83 + 16 * q^84 + 9 * q^85 + 40 * q^86 - 7 * q^87 - 36 * q^88 + 9 * q^89 - 57 * q^90 + 14 * q^91 - 38 * q^92 - 27 * q^93 + 13 * q^94 + 13 * q^95 + 3 * q^96 - 76 * q^97 + q^98 + 33 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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