LMFDB - Embedded newform 1547.2.a.g.1.9

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 = [9,-3] 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:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 6x^{7} + 21x^{6} + 6x^{5} - 34x^{4} - 2x^{3} + 13x^{2} - 1 $ x^9 - 3x^8 - 6x^7 + 21x^6 + 6x^5 - 34x^4 - 2x^3 + 13*x^2 - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-2.20091$ 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)

$f(q)$	$=$	\(q+2.20091 q^{2} +0.186661 q^{3} +2.84398 q^{4} -2.74655 q^{5} +0.410824 q^{6} +1.00000 q^{7} +1.85753 q^{8} -2.96516 q^{9} -6.04489 q^{10} -4.50572 q^{11} +0.530861 q^{12} -1.00000 q^{13} +2.20091 q^{14} -0.512674 q^{15} -1.59973 q^{16} +1.00000 q^{17} -6.52603 q^{18} -4.55532 q^{19} -7.81113 q^{20} +0.186661 q^{21} -9.91666 q^{22} +0.0507068 q^{23} +0.346728 q^{24} +2.54352 q^{25} -2.20091 q^{26} -1.11346 q^{27} +2.84398 q^{28} +2.94234 q^{29} -1.12835 q^{30} +8.62083 q^{31} -7.23590 q^{32} -0.841043 q^{33} +2.20091 q^{34} -2.74655 q^{35} -8.43286 q^{36} -8.04437 q^{37} -10.0258 q^{38} -0.186661 q^{39} -5.10179 q^{40} -0.594226 q^{41} +0.410824 q^{42} -11.6328 q^{43} -12.8142 q^{44} +8.14394 q^{45} +0.111601 q^{46} +13.3003 q^{47} -0.298607 q^{48} +1.00000 q^{49} +5.59804 q^{50} +0.186661 q^{51} -2.84398 q^{52} +1.24248 q^{53} -2.45063 q^{54} +12.3752 q^{55} +1.85753 q^{56} -0.850302 q^{57} +6.47581 q^{58} -1.17250 q^{59} -1.45804 q^{60} -3.74391 q^{61} +18.9736 q^{62} -2.96516 q^{63} -12.7261 q^{64} +2.74655 q^{65} -1.85106 q^{66} -1.32325 q^{67} +2.84398 q^{68} +0.00946499 q^{69} -6.04489 q^{70} +7.60887 q^{71} -5.50786 q^{72} +10.5866 q^{73} -17.7049 q^{74} +0.474776 q^{75} -12.9553 q^{76} -4.50572 q^{77} -0.410824 q^{78} -3.16726 q^{79} +4.39372 q^{80} +8.68763 q^{81} -1.30784 q^{82} -10.3441 q^{83} +0.530861 q^{84} -2.74655 q^{85} -25.6026 q^{86} +0.549220 q^{87} -8.36950 q^{88} -15.0735 q^{89} +17.9240 q^{90} -1.00000 q^{91} +0.144209 q^{92} +1.60917 q^{93} +29.2727 q^{94} +12.5114 q^{95} -1.35066 q^{96} -8.06416 q^{97} +2.20091 q^{98} +13.3602 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 3 q^{2} - 4 q^{3} + 3 q^{4} - 6 q^{5} + 2 q^{6} + 9 q^{7} - 6 q^{8} + 5 q^{9} - 9 q^{10} - 7 q^{11} + 2 q^{12} - 9 q^{13} - 3 q^{14} - 5 q^{15} + 3 q^{16} + 9 q^{17} - 9 q^{18} - 6 q^{19} + 6 q^{20}+ \cdots - 25 q^{99}+O(q^{100}) $ 9 * q - 3 * q^2 - 4 * q^3 + 3 * q^4 - 6 * q^5 + 2 * q^6 + 9 * q^7 - 6 * q^8 + 5 * q^9 - 9 * q^10 - 7 * q^11 + 2 * q^12 - 9 * q^13 - 3 * q^14 - 5 * q^15 + 3 * q^16 + 9 * q^17 - 9 * q^18 - 6 * q^19 + 6 * q^20 - 4 * q^21 - 4 * q^22 - 3 * q^23 + 8 * q^24 - 13 * q^25 + 3 * q^26 - 13 * q^27 + 3 * q^28 - 4 * q^29 + 10 * q^32 - 12 * q^33 - 3 * q^34 - 6 * q^35 - 17 * q^36 - 31 * q^37 - 3 * q^38 + 4 * q^39 - 18 * q^40 + 3 * q^41 + 2 * q^42 - 24 * q^43 - 20 * q^44 + 3 * q^45 + 5 * q^46 + 7 * q^47 + 2 * q^48 + 9 * q^49 + 24 * q^50 - 4 * q^51 - 3 * q^52 - 18 * q^53 + 6 * q^55 - 6 * q^56 - 35 * q^57 + 2 * q^58 - 9 * q^59 + 2 * q^60 - 22 * q^61 + 30 * q^62 + 5 * q^63 - 36 * q^64 + 6 * q^65 + 22 * q^66 - 32 * q^67 + 3 * q^68 - 2 * q^69 - 9 * q^70 + 18 * q^71 - 10 * q^72 - 14 * q^73 + 12 * q^74 + 11 * q^75 - 27 * q^76 - 7 * q^77 - 2 * q^78 - 46 * q^79 - q^80 + 29 * q^81 + 3 * q^82 - 16 * q^83 + 2 * q^84 - 6 * q^85 - 34 * q^86 + 3 * q^87 - 10 * q^89 + 21 * q^90 - 9 * q^91 + 14 * q^92 - 83 * q^93 + q^94 - 55 * q^96 - 15 * q^97 - 3 * q^98 - 25 * 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 $

$2$	2.20091	1.55627	0.778137	−	0.628094i	$-0.216165\pi$
$2$	2.20091	1.55627	0.778137	+	0.628094i	$0.216165\pi$
$3$	0.186661	0.107769	0.0538844	−	0.998547i	$-0.482840\pi$
$3$	0.186661	0.107769	0.0538844	+	0.998547i	$0.482840\pi$
$4$	2.84398	1.42199
$5$	−2.74655	−1.22829	−0.614146	−	0.789192i	$-0.710500\pi$
$5$	−2.74655	−1.22829	−0.614146	+	0.789192i	$0.710500\pi$
$6$	0.410824	0.167718
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.85753	0.656735
$9$	−2.96516	−0.988386
$10$	−6.04489	−1.91156
$11$	−4.50572	−1.35853	−0.679263	−	0.733895i	$-0.737700\pi$
$11$	−4.50572	−1.35853	−0.679263	+	0.733895i	$0.737700\pi$
$12$	0.530861	0.153246
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	2.20091	0.588217
$15$	−0.512674	−0.132372
$16$	−1.59973	−0.399931
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−6.52603	−1.53820
$19$	−4.55532	−1.04506	−0.522531	−	0.852620i	$-0.675012\pi$
$19$	−4.55532	−1.04506	−0.522531	+	0.852620i	$0.675012\pi$
$20$	−7.81113	−1.74662
$21$	0.186661	0.0407328
$22$	−9.91666	−2.11424
$23$	0.0507068	0.0105731	0.00528655	−	0.999986i	$-0.498317\pi$
$23$	0.0507068	0.0105731	0.00528655	+	0.999986i	$0.498317\pi$
$24$	0.346728	0.0707756
$25$	2.54352	0.508704
$26$	−2.20091	−0.431633
$27$	−1.11346	−0.214286
$28$	2.84398	0.537462
$29$	2.94234	0.546379	0.273189	−	0.961960i	$-0.411921\pi$
$29$	2.94234	0.546379	0.273189	+	0.961960i	$0.411921\pi$
$30$	−1.12835	−0.206007
$31$	8.62083	1.54835	0.774173	−	0.632974i	$-0.218166\pi$
$31$	8.62083	1.54835	0.774173	+	0.632974i	$0.218166\pi$
$32$	−7.23590	−1.27914
$33$	−0.841043	−0.146407
$34$	2.20091	0.377452
$35$	−2.74655	−0.464251
$36$	−8.43286	−1.40548
$37$	−8.04437	−1.32249	−0.661243	−	0.750172i	$-0.729971\pi$
$37$	−8.04437	−1.32249	−0.661243	+	0.750172i	$0.729971\pi$
$38$	−10.0258	−1.62640
$39$	−0.186661	−0.0298897
$40$	−5.10179	−0.806663
$41$	−0.594226	−0.0928025	−0.0464013	−	0.998923i	$-0.514775\pi$
$41$	−0.594226	−0.0928025	−0.0464013	+	0.998923i	$0.514775\pi$
$42$	0.410824	0.0633915
$43$	−11.6328	−1.77398	−0.886990	−	0.461789i	$-0.847208\pi$
$43$	−11.6328	−1.77398	−0.886990	+	0.461789i	$0.847208\pi$
$44$	−12.8142	−1.93181
$45$	8.14394	1.21403
$46$	0.111601	0.0164546
$47$	13.3003	1.94005	0.970024	−	0.243008i	$-0.0781342\pi$
$47$	13.3003	1.94005	0.970024	+	0.243008i	$0.0781342\pi$
$48$	−0.298607	−0.0431002
$49$	1.00000	0.142857
$50$	5.59804	0.791683
$51$	0.186661	0.0261378
$52$	−2.84398	−0.394390
$53$	1.24248	0.170667	0.0853336	−	0.996352i	$-0.472804\pi$
$53$	1.24248	0.170667	0.0853336	+	0.996352i	$0.472804\pi$
$54$	−2.45063	−0.333488
$55$	12.3752	1.66867
$56$	1.85753	0.248223
$57$	−0.850302	−0.112625
$58$	6.47581	0.850315
$59$	−1.17250	−0.152647	−0.0763235	−	0.997083i	$-0.524318\pi$
$59$	−1.17250	−0.152647	−0.0763235	+	0.997083i	$0.524318\pi$
$60$	−1.45804	−0.188232
$61$	−3.74391	−0.479358	−0.239679	−	0.970852i	$-0.577042\pi$
$61$	−3.74391	−0.479358	−0.239679	+	0.970852i	$0.577042\pi$
$62$	18.9736	2.40965
$63$	−2.96516	−0.373575
$64$	−12.7261	−1.59076
$65$	2.74655	0.340667
$66$	−1.85106	−0.227849
$67$	−1.32325	−0.161661	−0.0808303	−	0.996728i	$-0.525757\pi$
$67$	−1.32325	−0.161661	−0.0808303	+	0.996728i	$0.525757\pi$
$68$	2.84398	0.344884
$69$	0.00946499	0.00113945
$70$	−6.04489	−0.722502
$71$	7.60887	0.903007	0.451504	−	0.892269i	$-0.350888\pi$
$71$	7.60887	0.903007	0.451504	+	0.892269i	$0.350888\pi$
$72$	−5.50786	−0.649108
$73$	10.5866	1.23907	0.619535	−	0.784969i	$-0.287321\pi$
$73$	10.5866	1.23907	0.619535	+	0.784969i	$0.287321\pi$
$74$	−17.7049	−2.05815
$75$	0.474776	0.0548224
$76$	−12.9553	−1.48607
$77$	−4.50572	−0.513474
$78$	−0.410824	−0.0465166
$79$	−3.16726	−0.356345	−0.178173	−	0.983999i	$-0.557019\pi$
$79$	−3.16726	−0.356345	−0.178173	+	0.983999i	$0.557019\pi$
$80$	4.39372	0.491233
$81$	8.68763	0.965292
$82$	−1.30784	−0.144426
$83$	−10.3441	−1.13542	−0.567708	−	0.823230i	$-0.692170\pi$
$83$	−10.3441	−1.13542	−0.567708	+	0.823230i	$0.692170\pi$
$84$	0.530861	0.0579217
$85$	−2.74655	−0.297905
$86$	−25.6026	−2.76080
$87$	0.549220	0.0588826
$88$	−8.36950	−0.892191
$89$	−15.0735	−1.59778	−0.798892	−	0.601474i	$-0.794580\pi$
$89$	−15.0735	−1.59778	−0.798892	+	0.601474i	$0.794580\pi$
$90$	17.9240	1.88936
$91$	−1.00000	−0.104828
$92$	0.144209	0.0150349
$93$	1.60917	0.166864
$94$	29.2727	3.01925
$95$	12.5114	1.28364
$96$	−1.35066	−0.137851
$97$	−8.06416	−0.818792	−0.409396	−	0.912357i	$-0.634260\pi$
$97$	−8.06416	−0.818792	−0.409396	+	0.912357i	$0.634260\pi$
$98$	2.20091	0.222325
$99$	13.3602	1.34275
$100$	7.23372	0.723372
$101$	10.8235	1.07698	0.538489	−	0.842632i	$-0.318995\pi$
$101$	10.8235	1.07698	0.538489	+	0.842632i	$0.318995\pi$
$102$	0.410824	0.0406776
$103$	−3.15503	−0.310874	−0.155437	−	0.987846i	$-0.549679\pi$
$103$	−3.15503	−0.310874	−0.155437	+	0.987846i	$0.549679\pi$
$104$	−1.85753	−0.182146
$105$	−0.512674	−0.0500318
$106$	2.73457	0.265605
$107$	−12.9240	−1.24941	−0.624705	−	0.780861i	$-0.714781\pi$
$107$	−12.9240	−1.24941	−0.624705	+	0.780861i	$0.714781\pi$
$108$	−3.16667	−0.304713
$109$	−0.942031	−0.0902302	−0.0451151	−	0.998982i	$-0.514365\pi$
$109$	−0.942031	−0.0902302	−0.0451151	+	0.998982i	$0.514365\pi$
$110$	27.2366	2.59690
$111$	−1.50157	−0.142523
$112$	−1.59973	−0.151160
$113$	17.6287	1.65837	0.829186	−	0.558973i	$-0.188804\pi$
$113$	17.6287	1.65837	0.829186	+	0.558973i	$0.188804\pi$
$114$	−1.87143	−0.175276
$115$	−0.139269	−0.0129869
$116$	8.36796	0.776946
$117$	2.96516	0.274129
$118$	−2.58057	−0.237561
$119$	1.00000	0.0916698
$120$	−0.952305	−0.0869332
$121$	9.30150	0.845591
$122$	−8.23999	−0.746013
$123$	−0.110919	−0.0100012
$124$	24.5175	2.20174
$125$	6.74684	0.603456
$126$	−6.52603	−0.581385
$127$	2.95001	0.261771	0.130886	−	0.991397i	$-0.458218\pi$
$127$	2.95001	0.261771	0.130886	+	0.991397i	$0.458218\pi$
$128$	−13.5371	−1.19652
$129$	−2.17139	−0.191180
$130$	6.04489	0.530172
$131$	10.2320	0.893971	0.446985	−	0.894541i	$-0.352498\pi$
$131$	10.2320	0.893971	0.446985	+	0.894541i	$0.352498\pi$
$132$	−2.39191	−0.208189
$133$	−4.55532	−0.394996
$134$	−2.91235	−0.251588
$135$	3.05818	0.263206
$136$	1.85753	0.159282
$137$	−18.5805	−1.58744	−0.793718	−	0.608286i	$-0.791857\pi$
$137$	−18.5805	−1.58744	−0.793718	+	0.608286i	$0.791857\pi$
$138$	0.0208315	0.00177330
$139$	−11.5357	−0.978447	−0.489223	−	0.872159i	$-0.662720\pi$
$139$	−11.5357	−0.978447	−0.489223	+	0.872159i	$0.662720\pi$
$140$	−7.81113	−0.660161
$141$	2.48265	0.209077
$142$	16.7464	1.40533
$143$	4.50572	0.376787
$144$	4.74344	0.395286
$145$	−8.08127	−0.671113
$146$	23.3001	1.92833
$147$	0.186661	0.0153956
$148$	−22.8780	−1.88056
$149$	−15.2190	−1.24679	−0.623395	−	0.781907i	$-0.714247\pi$
$149$	−15.2190	−1.24679	−0.623395	+	0.781907i	$0.714247\pi$
$150$	1.04494	0.0853188
$151$	−11.5463	−0.939623	−0.469811	−	0.882767i	$-0.655678\pi$
$151$	−11.5463	−0.939623	−0.469811	+	0.882767i	$0.655678\pi$
$152$	−8.46163	−0.686329
$153$	−2.96516	−0.239719
$154$	−9.91666	−0.799107
$155$	−23.6775	−1.90182
$156$	−0.530861	−0.0425029
$157$	−9.14426	−0.729791	−0.364896	−	0.931048i	$-0.618895\pi$
$157$	−9.14426	−0.729791	−0.364896	+	0.931048i	$0.618895\pi$
$158$	−6.97085	−0.554571
$159$	0.231922	0.0183926
$160$	19.8737	1.57116
$161$	0.0507068	0.00399626
$162$	19.1207	1.50226
$163$	−3.35459	−0.262752	−0.131376	−	0.991333i	$-0.541940\pi$
$163$	−3.35459	−0.262752	−0.131376	+	0.991333i	$0.541940\pi$
$164$	−1.68997	−0.131964
$165$	2.30996	0.179830
$166$	−22.7665	−1.76702
$167$	−4.35419	−0.336937	−0.168469	−	0.985707i	$-0.553882\pi$
$167$	−4.35419	−0.336937	−0.168469	+	0.985707i	$0.553882\pi$
$168$	0.346728	0.0267507
$169$	1.00000	0.0769231
$170$	−6.04489	−0.463622
$171$	13.5072	1.03292
$172$	−33.0834	−2.52258
$173$	14.6634	1.11484	0.557418	−	0.830232i	$-0.311792\pi$
$173$	14.6634	1.11484	0.557418	+	0.830232i	$0.311792\pi$
$174$	1.20878	0.0916375
$175$	2.54352	0.192272
$176$	7.20791	0.543317
$177$	−0.218861	−0.0164506
$178$	−33.1753	−2.48659
$179$	−10.4214	−0.778929	−0.389464	−	0.921042i	$-0.627340\pi$
$179$	−10.4214	−0.778929	−0.389464	+	0.921042i	$0.627340\pi$
$180$	23.1612	1.72634
$181$	−7.03669	−0.523033	−0.261517	−	0.965199i	$-0.584223\pi$
$181$	−7.03669	−0.523033	−0.261517	+	0.965199i	$0.584223\pi$
$182$	−2.20091	−0.163142
$183$	−0.698842	−0.0516599
$184$	0.0941893	0.00694372
$185$	22.0942	1.62440
$186$	3.54164	0.259686
$187$	−4.50572	−0.329491
$188$	37.8258	2.75873
$189$	−1.11346	−0.0809925
$190$	27.5364	1.99770
$191$	18.6773	1.35144	0.675721	−	0.737157i	$-0.263832\pi$
$191$	18.6773	1.35144	0.675721	+	0.737157i	$0.263832\pi$
$192$	−2.37546	−0.171434
$193$	6.11104	0.439882	0.219941	−	0.975513i	$-0.429413\pi$
$193$	6.11104	0.439882	0.219941	+	0.975513i	$0.429413\pi$
$194$	−17.7485	−1.27426
$195$	0.512674	0.0367133
$196$	2.84398	0.203142
$197$	3.15097	0.224497	0.112249	−	0.993680i	$-0.464195\pi$
$197$	3.15097	0.224497	0.112249	+	0.993680i	$0.464195\pi$
$198$	29.4045	2.08968
$199$	12.3313	0.874145	0.437072	−	0.899426i	$-0.356015\pi$
$199$	12.3313	0.874145	0.437072	+	0.899426i	$0.356015\pi$
$200$	4.72465	0.334084
$201$	−0.246999	−0.0174220
$202$	23.8215	1.67607
$203$	2.94234	0.206512
$204$	0.530861	0.0371677
$205$	1.63207	0.113989
$206$	−6.94391	−0.483805
$207$	−0.150354	−0.0104503
$208$	1.59973	0.110921
$209$	20.5250	1.41974
$210$	−1.12835	−0.0778633
$211$	−17.7378	−1.22112	−0.610559	−	0.791971i	$-0.709055\pi$
$211$	−17.7378	−1.22112	−0.610559	+	0.791971i	$0.709055\pi$
$212$	3.53358	0.242687
$213$	1.42028	0.0973161
$214$	−28.4445	−1.94442
$215$	31.9499	2.17897
$216$	−2.06829	−0.140729
$217$	8.62083	0.585220
$218$	−2.07332	−0.140423
$219$	1.97611	0.133533
$220$	35.1948	2.37283
$221$	−1.00000	−0.0672673
$222$	−3.30482	−0.221805
$223$	−23.9302	−1.60248	−0.801242	−	0.598341i	$-0.795827\pi$
$223$	−23.9302	−1.60248	−0.801242	+	0.598341i	$0.795827\pi$
$224$	−7.23590	−0.483469
$225$	−7.54193	−0.502795
$226$	38.7992	2.58088
$227$	15.5141	1.02971	0.514855	−	0.857277i	$-0.327846\pi$
$227$	15.5141	1.02971	0.514855	+	0.857277i	$0.327846\pi$
$228$	−2.41824	−0.160152
$229$	−1.24319	−0.0821526	−0.0410763	−	0.999156i	$-0.513079\pi$
$229$	−1.24319	−0.0821526	−0.0410763	+	0.999156i	$0.513079\pi$
$230$	−0.306517	−0.0202111
$231$	−0.841043	−0.0553366
$232$	5.46547	0.358826
$233$	18.3324	1.20100	0.600498	−	0.799626i	$-0.294969\pi$
$233$	18.3324	1.20100	0.600498	+	0.799626i	$0.294969\pi$
$234$	6.52603	0.426620
$235$	−36.5299	−2.38295
$236$	−3.33458	−0.217063
$237$	−0.591205	−0.0384029
$238$	2.20091	0.142663
$239$	−14.6029	−0.944585	−0.472292	−	0.881442i	$-0.656573\pi$
$239$	−14.6029	−0.944585	−0.472292	+	0.881442i	$0.656573\pi$
$240$	0.820137	0.0529396
$241$	−4.49374	−0.289467	−0.144734	−	0.989471i	$-0.546232\pi$
$241$	−4.49374	−0.289467	−0.144734	+	0.989471i	$0.546232\pi$
$242$	20.4717	1.31597
$243$	4.96203	0.318315
$244$	−10.6476	−0.681644
$245$	−2.74655	−0.175470
$246$	−0.244122	−0.0155647
$247$	4.55532	0.289848
$248$	16.0134	1.01685
$249$	−1.93085	−0.122363
$250$	14.8492	0.939143
$251$	−0.711416	−0.0449042	−0.0224521	−	0.999748i	$-0.507147\pi$
$251$	−0.711416	−0.0449042	−0.0224521	+	0.999748i	$0.507147\pi$
$252$	−8.43286	−0.531220
$253$	−0.228471	−0.0143638
$254$	6.49270	0.407388
$255$	−0.512674	−0.0321049
$256$	−4.34169	−0.271356
$257$	13.7105	0.855235	0.427618	−	0.903960i	$-0.359353\pi$
$257$	13.7105	0.855235	0.427618	+	0.903960i	$0.359353\pi$
$258$	−4.77901	−0.297528
$259$	−8.04437	−0.499853
$260$	7.81113	0.484426
$261$	−8.72450	−0.540033
$262$	22.5196	1.39126
$263$	20.0286	1.23501	0.617507	−	0.786566i	$-0.288143\pi$
$263$	20.0286	1.23501	0.617507	+	0.786566i	$0.288143\pi$
$264$	−1.56226	−0.0961505
$265$	−3.41252	−0.209629
$266$	−10.0258	−0.614723
$267$	−2.81363	−0.172191
$268$	−3.76330	−0.229880
$269$	4.82120	0.293954	0.146977	−	0.989140i	$-0.453046\pi$
$269$	4.82120	0.293954	0.146977	+	0.989140i	$0.453046\pi$
$270$	6.73076	0.409621
$271$	−5.25703	−0.319342	−0.159671	−	0.987170i	$-0.551043\pi$
$271$	−5.25703	−0.319342	−0.159671	+	0.987170i	$0.551043\pi$
$272$	−1.59973	−0.0969976
$273$	−0.186661	−0.0112972
$274$	−40.8938	−2.47049
$275$	−11.4604	−0.691087
$276$	0.0269183	0.00162029
$277$	−12.2316	−0.734925	−0.367463	−	0.930038i	$-0.619773\pi$
$277$	−12.2316	−0.734925	−0.367463	+	0.930038i	$0.619773\pi$
$278$	−25.3890	−1.52273
$279$	−25.5621	−1.53036
$280$	−5.10179	−0.304890
$281$	−27.3339	−1.63060	−0.815302	−	0.579036i	$-0.803429\pi$
$281$	−27.3339	−1.63060	−0.815302	+	0.579036i	$0.803429\pi$
$282$	5.46408	0.325381
$283$	12.6446	0.751645	0.375822	−	0.926692i	$-0.377360\pi$
$283$	12.6446	0.751645	0.375822	+	0.926692i	$0.377360\pi$
$284$	21.6395	1.28407
$285$	2.33539	0.138337
$286$	9.91666	0.586384
$287$	−0.594226	−0.0350761
$288$	21.4556	1.26428
$289$	1.00000	0.0588235
$290$	−17.7861	−1.04444
$291$	−1.50527	−0.0882403
$292$	30.1081	1.76195
$293$	21.6244	1.26331	0.631654	−	0.775250i	$-0.282376\pi$
$293$	21.6244	1.26331	0.631654	+	0.775250i	$0.282376\pi$
$294$	0.410824	0.0239597
$295$	3.22033	0.187495
$296$	−14.9426	−0.868523
$297$	5.01695	0.291113
$298$	−33.4956	−1.94035
$299$	−0.0507068	−0.00293245
$300$	1.35026	0.0779570
$301$	−11.6328	−0.670501
$302$	−25.4123	−1.46231
$303$	2.02033	0.116065
$304$	7.28726	0.417953
$305$	10.2828	0.588792
$306$	−6.52603	−0.373068
$307$	7.39812	0.422233	0.211117	−	0.977461i	$-0.432290\pi$
$307$	7.39812	0.422233	0.211117	+	0.977461i	$0.432290\pi$
$308$	−12.8142	−0.730156
$309$	−0.588921	−0.0335025
$310$	−52.1119	−2.95976
$311$	−11.6550	−0.660893	−0.330447	−	0.943825i	$-0.607199\pi$
$311$	−11.6550	−0.660893	−0.330447	+	0.943825i	$0.607199\pi$
$312$	−0.346728	−0.0196296
$313$	−27.2766	−1.54176	−0.770882	−	0.636978i	$-0.780184\pi$
$313$	−27.2766	−1.54176	−0.770882	+	0.636978i	$0.780184\pi$
$314$	−20.1256	−1.13576
$315$	8.14394	0.458859
$316$	−9.00765	−0.506720
$317$	31.9636	1.79525	0.897627	−	0.440755i	$-0.145289\pi$
$317$	31.9636	1.79525	0.897627	+	0.440755i	$0.145289\pi$
$318$	0.510438	0.0286240
$319$	−13.2573	−0.742269
$320$	34.9528	1.95392
$321$	−2.41241	−0.134647
$322$	0.111601	0.00621927
$323$	−4.55532	−0.253465
$324$	24.7075	1.37264
$325$	−2.54352	−0.141089
$326$	−7.38314	−0.408914
$327$	−0.175841	−0.00972401
$328$	−1.10379	−0.0609467
$329$	13.3003	0.733269
$330$	5.08401	0.279866
$331$	9.88534	0.543347	0.271674	−	0.962389i	$-0.412423\pi$
$331$	9.88534	0.543347	0.271674	+	0.962389i	$0.412423\pi$
$332$	−29.4186	−1.61455
$333$	23.8528	1.30713
$334$	−9.58316	−0.524367
$335$	3.63437	0.198567
$336$	−0.298607	−0.0162903
$337$	25.9902	1.41578	0.707888	−	0.706324i	$-0.249648\pi$
$337$	25.9902	1.41578	0.707888	+	0.706324i	$0.249648\pi$
$338$	2.20091	0.119713
$339$	3.29060	0.178721
$340$	−7.81113	−0.423618
$341$	−38.8430	−2.10347
$342$	29.7282	1.60752
$343$	1.00000	0.0539949
$344$	−21.6082	−1.16503
$345$	−0.0259960	−0.00139958
$346$	32.2727	1.73499
$347$	−26.2306	−1.40813	−0.704065	−	0.710135i	$-0.748634\pi$
$347$	−26.2306	−1.40813	−0.704065	+	0.710135i	$0.748634\pi$
$348$	1.56197	0.0837306
$349$	−16.0057	−0.856768	−0.428384	−	0.903597i	$-0.640917\pi$
$349$	−16.0057	−0.856768	−0.428384	+	0.903597i	$0.640917\pi$
$350$	5.59804	0.299228
$351$	1.11346	0.0594323
$352$	32.6029	1.73774
$353$	−27.8678	−1.48325	−0.741626	−	0.670814i	$-0.765945\pi$
$353$	−27.8678	−1.48325	−0.741626	+	0.670814i	$0.765945\pi$
$354$	−0.481692	−0.0256016
$355$	−20.8981	−1.10916
$356$	−42.8687	−2.27204
$357$	0.186661	0.00987916
$358$	−22.9364	−1.21223
$359$	−37.8621	−1.99829	−0.999143	−	0.0413995i	$-0.986818\pi$
$359$	−37.8621	−1.99829	−0.999143	+	0.0413995i	$0.986818\pi$
$360$	15.1276	0.797294
$361$	1.75095	0.0921555
$362$	−15.4871	−0.813983
$363$	1.73623	0.0911284
$364$	−2.84398	−0.149065
$365$	−29.0766	−1.52194
$366$	−1.53809	−0.0803970
$367$	−2.27783	−0.118902	−0.0594508	−	0.998231i	$-0.518935\pi$
$367$	−2.27783	−0.118902	−0.0594508	+	0.998231i	$0.518935\pi$
$368$	−0.0811169	−0.00422851
$369$	1.76197	0.0917247
$370$	48.6273	2.52801
$371$	1.24248	0.0645061
$372$	4.57646	0.237279
$373$	−12.5646	−0.650573	−0.325286	−	0.945616i	$-0.605461\pi$
$373$	−12.5646	−0.650573	−0.325286	+	0.945616i	$0.605461\pi$
$374$	−9.91666	−0.512778
$375$	1.25937	0.0650338
$376$	24.7057	1.27410
$377$	−2.94234	−0.151538
$378$	−2.45063	−0.126047
$379$	−4.50281	−0.231294	−0.115647	−	0.993290i	$-0.536894\pi$
$379$	−4.50281	−0.231294	−0.115647	+	0.993290i	$0.536894\pi$
$380$	35.5822	1.82533
$381$	0.550653	0.0282108
$382$	41.1070	2.10322
$383$	2.22158	0.113518	0.0567588	−	0.998388i	$-0.481923\pi$
$383$	2.22158	0.113518	0.0567588	+	0.998388i	$0.481923\pi$
$384$	−2.52685	−0.128948
$385$	12.3752	0.630697
$386$	13.4498	0.684578
$387$	34.4930	1.75338
$388$	−22.9343	−1.16431
$389$	25.6830	1.30218	0.651089	−	0.759002i	$-0.274313\pi$
$389$	25.6830	1.30218	0.651089	+	0.759002i	$0.274313\pi$
$390$	1.12835	0.0571360
$391$	0.0507068	0.00256435
$392$	1.85753	0.0938193
$393$	1.90991	0.0963422
$394$	6.93499	0.349380
$395$	8.69904	0.437696
$396$	37.9961	1.90938
$397$	−20.2669	−1.01717	−0.508584	−	0.861012i	$-0.669831\pi$
$397$	−20.2669	−1.01717	−0.508584	+	0.861012i	$0.669831\pi$
$398$	27.1401	1.36041
$399$	−0.850302	−0.0425683
$400$	−4.06893	−0.203447
$401$	−35.8745	−1.79149	−0.895744	−	0.444570i	$-0.853357\pi$
$401$	−35.8745	−1.79149	−0.895744	+	0.444570i	$0.853357\pi$
$402$	−0.543622	−0.0271134
$403$	−8.62083	−0.429434
$404$	30.7818	1.53145
$405$	−23.8610	−1.18566
$406$	6.47581	0.321389
$407$	36.2457	1.79663
$408$	0.346728	0.0171656
$409$	13.6731	0.676090	0.338045	−	0.941130i	$-0.390234\pi$
$409$	13.6731	0.676090	0.338045	+	0.941130i	$0.390234\pi$
$410$	3.59203	0.177398
$411$	−3.46825	−0.171076
$412$	−8.97284	−0.442060
$413$	−1.17250	−0.0576951
$414$	−0.330914	−0.0162635
$415$	28.4107	1.39462
$416$	7.23590	0.354769
$417$	−2.15327	−0.105446
$418$	45.1736	2.20951
$419$	−11.3633	−0.555131	−0.277566	−	0.960707i	$-0.589528\pi$
$419$	−11.3633	−0.555131	−0.277566	+	0.960707i	$0.589528\pi$
$420$	−1.45804	−0.0711448
$421$	10.1372	0.494059	0.247029	−	0.969008i	$-0.420546\pi$
$421$	10.1372	0.494059	0.247029	+	0.969008i	$0.420546\pi$
$422$	−39.0391	−1.90040
$423$	−39.4375	−1.91752
$424$	2.30793	0.112083
$425$	2.54352	0.123379
$426$	3.12590	0.151451
$427$	−3.74391	−0.181180
$428$	−36.7556	−1.77665
$429$	0.841043	0.0406059
$430$	70.3188	3.39107
$431$	12.7321	0.613284	0.306642	−	0.951825i	$-0.400795\pi$
$431$	12.7321	0.613284	0.306642	+	0.951825i	$0.400795\pi$
$432$	1.78124	0.0856997
$433$	−14.6700	−0.704997	−0.352499	−	0.935812i	$-0.614668\pi$
$433$	−14.6700	−0.704997	−0.352499	+	0.935812i	$0.614668\pi$
$434$	18.9736	0.910763
$435$	−1.50846	−0.0723251
$436$	−2.67912	−0.128307
$437$	−0.230986	−0.0110495
$438$	4.34923	0.207814
$439$	−30.1235	−1.43771	−0.718857	−	0.695158i	$-0.755334\pi$
$439$	−30.1235	−1.43771	−0.718857	+	0.695158i	$0.755334\pi$
$440$	22.9872	1.09587
$441$	−2.96516	−0.141198
$442$	−2.20091	−0.104686
$443$	16.6088	0.789109	0.394555	−	0.918873i	$-0.370899\pi$
$443$	16.6088	0.789109	0.394555	+	0.918873i	$0.370899\pi$
$444$	−4.27044	−0.202666
$445$	41.4000	1.96255
$446$	−52.6680	−2.49390
$447$	−2.84080	−0.134365
$448$	−12.7261	−0.601251
$449$	−30.0792	−1.41952	−0.709762	−	0.704441i	$-0.751198\pi$
$449$	−30.0792	−1.41952	−0.709762	+	0.704441i	$0.751198\pi$
$450$	−16.5991	−0.782488
$451$	2.67742	0.126075
$452$	50.1358	2.35819
$453$	−2.15524	−0.101262
$454$	34.1451	1.60251
$455$	2.74655	0.128760
$456$	−1.57946	−0.0739649
$457$	−3.02469	−0.141489	−0.0707445	−	0.997494i	$-0.522537\pi$
$457$	−3.02469	−0.141489	−0.0707445	+	0.997494i	$0.522537\pi$
$458$	−2.73615	−0.127852
$459$	−1.11346	−0.0519720
$460$	−0.396077	−0.0184672
$461$	20.7217	0.965108	0.482554	−	0.875866i	$-0.339709\pi$
$461$	20.7217	0.965108	0.482554	+	0.875866i	$0.339709\pi$
$462$	−1.85106	−0.0861189
$463$	−29.6231	−1.37670	−0.688350	−	0.725379i	$-0.741665\pi$
$463$	−29.6231	−1.37670	−0.688350	+	0.725379i	$0.741665\pi$
$464$	−4.70693	−0.218514
$465$	−4.41967	−0.204957
$466$	40.3479	1.86908
$467$	34.8500	1.61266	0.806332	−	0.591463i	$-0.201450\pi$
$467$	34.8500	1.61266	0.806332	+	0.591463i	$0.201450\pi$
$468$	8.43286	0.389809
$469$	−1.32325	−0.0611020
$470$	−80.3988	−3.70852
$471$	−1.70688	−0.0786488
$472$	−2.17796	−0.100249
$473$	52.4140	2.41000
$474$	−1.30119	−0.0597655
$475$	−11.5865	−0.531627
$476$	2.84398	0.130354
$477$	−3.68414	−0.168685
$478$	−32.1397	−1.47003
$479$	30.1404	1.37715	0.688576	−	0.725164i	$-0.258236\pi$
$479$	30.1404	1.37715	0.688576	+	0.725164i	$0.258236\pi$
$480$	3.70965	0.169322
$481$	8.04437	0.366792
$482$	−9.89029	−0.450490
$483$	0.00946499	0.000430672 0
$484$	26.4533	1.20242
$485$	22.1486	1.00572
$486$	10.9210	0.495385
$487$	−16.1115	−0.730082	−0.365041	−	0.930991i	$-0.618945\pi$
$487$	−16.1115	−0.730082	−0.365041	+	0.930991i	$0.618945\pi$
$488$	−6.95441	−0.314811
$489$	−0.626172	−0.0283165
$490$	−6.04489	−0.273080
$491$	24.1862	1.09151	0.545754	−	0.837945i	$-0.316243\pi$
$491$	24.1862	1.09151	0.545754	+	0.837945i	$0.316243\pi$
$492$	−0.315452	−0.0142217
$493$	2.94234	0.132516
$494$	10.0258	0.451083
$495$	−36.6943	−1.64929
$496$	−13.7910	−0.619232
$497$	7.60887	0.341305
$498$	−4.24962	−0.190430
$499$	−12.1212	−0.542617	−0.271309	−	0.962492i	$-0.587456\pi$
$499$	−12.1212	−0.542617	−0.271309	+	0.962492i	$0.587456\pi$
$500$	19.1879	0.858109
$501$	−0.812758	−0.0363114
$502$	−1.56576	−0.0698832
$503$	−34.7695	−1.55030	−0.775149	−	0.631779i	$-0.782325\pi$
$503$	−34.7695	−1.55030	−0.775149	+	0.631779i	$0.782325\pi$
$504$	−5.50786	−0.245340
$505$	−29.7272	−1.32284
$506$	−0.502842	−0.0223541
$507$	0.186661	0.00828991
$508$	8.38979	0.372237
$509$	−21.8609	−0.968968	−0.484484	−	0.874800i	$-0.660993\pi$
$509$	−21.8609	−0.968968	−0.484484	+	0.874800i	$0.660993\pi$
$510$	−1.12835	−0.0499640
$511$	10.5866	0.468324
$512$	17.5185	0.774216
$513$	5.07218	0.223942
$514$	30.1754	1.33098
$515$	8.66543	0.381844
$516$	−6.17538	−0.271856
$517$	−59.9274	−2.63561
$518$	−17.7049	−0.777908
$519$	2.73708	0.120145
$520$	5.10179	0.223728
$521$	−25.0681	−1.09825	−0.549126	−	0.835740i	$-0.685039\pi$
$521$	−25.0681	−1.09825	−0.549126	+	0.835740i	$0.685039\pi$
$522$	−19.2018	−0.840440
$523$	−1.42808	−0.0624457	−0.0312229	−	0.999512i	$-0.509940\pi$
$523$	−1.42808	−0.0624457	−0.0312229	+	0.999512i	$0.509940\pi$
$524$	29.0995	1.27122
$525$	0.474776	0.0207209
$526$	44.0810	1.92202
$527$	8.62083	0.375529
$528$	1.34544	0.0585527
$529$	−22.9974	−0.999888
$530$	−7.51063	−0.326241
$531$	3.47666	0.150874
$532$	−12.9553	−0.561682
$533$	0.594226	0.0257388
$534$	−6.19253	−0.267977
$535$	35.4963	1.53464
$536$	−2.45797	−0.106168
$537$	−1.94526	−0.0839443
$538$	10.6110	0.457473
$539$	−4.50572	−0.194075
$540$	8.69741	0.374277
$541$	−3.32635	−0.143011	−0.0715056	−	0.997440i	$-0.522780\pi$
$541$	−3.32635	−0.143011	−0.0715056	+	0.997440i	$0.522780\pi$
$542$	−11.5702	−0.496983
$543$	−1.31348	−0.0563667
$544$	−7.23590	−0.310237
$545$	2.58733	0.110829
$546$	−0.410824	−0.0175816
$547$	28.3280	1.21122	0.605608	−	0.795763i	$-0.292930\pi$
$547$	28.3280	1.21122	0.605608	+	0.795763i	$0.292930\pi$
$548$	−52.8425	−2.25732
$549$	11.1013	0.473791
$550$	−25.2232	−1.07552
$551$	−13.4033	−0.571000
$552$	0.0175815	0.000748317 0
$553$	−3.16726	−0.134686
$554$	−26.9206	−1.14375
$555$	4.12413	0.175060
$556$	−32.8074	−1.39134
$557$	−18.4078	−0.779963	−0.389981	−	0.920823i	$-0.627519\pi$
$557$	−18.4078	−0.779963	−0.389981	+	0.920823i	$0.627519\pi$
$558$	−56.2598	−2.38167
$559$	11.6328	0.492013
$560$	4.39372	0.185669
$561$	−0.841043	−0.0355089
$562$	−60.1593	−2.53767
$563$	32.5862	1.37335	0.686673	−	0.726966i	$-0.259070\pi$
$563$	32.5862	1.37335	0.686673	+	0.726966i	$0.259070\pi$
$564$	7.06062	0.297306
$565$	−48.4182	−2.03697
$566$	27.8296	1.16977
$567$	8.68763	0.364846
$568$	14.1337	0.593036
$569$	9.48520	0.397640	0.198820	−	0.980036i	$-0.436289\pi$
$569$	9.48520	0.397640	0.198820	+	0.980036i	$0.436289\pi$
$570$	5.13998	0.215290
$571$	24.2153	1.01338	0.506689	−	0.862129i	$-0.330869\pi$
$571$	24.2153	1.01338	0.506689	+	0.862129i	$0.330869\pi$
$572$	12.8142	0.535788
$573$	3.48633	0.145643
$574$	−1.30784	−0.0545880
$575$	0.128974	0.00537857
$576$	37.7348	1.57228
$577$	21.5349	0.896511	0.448256	−	0.893905i	$-0.352045\pi$
$577$	21.5349	0.896511	0.448256	+	0.893905i	$0.352045\pi$
$578$	2.20091	0.0915456
$579$	1.14069	0.0474056
$580$	−22.9830	−0.954317
$581$	−10.3441	−0.429147
$582$	−3.31295	−0.137326
$583$	−5.59824	−0.231856
$584$	19.6649	0.813740
$585$	−8.14394	−0.336711
$586$	47.5931	1.96605
$587$	−46.6382	−1.92497	−0.962483	−	0.271341i	$-0.912533\pi$
$587$	−46.6382	−1.92497	−0.962483	+	0.271341i	$0.912533\pi$
$588$	0.530861	0.0218924
$589$	−39.2706	−1.61812
$590$	7.08765	0.291794
$591$	0.588164	0.0241938
$592$	12.8688	0.528903
$593$	−9.70436	−0.398510	−0.199255	−	0.979948i	$-0.563852\pi$
$593$	−9.70436	−0.398510	−0.199255	+	0.979948i	$0.563852\pi$
$594$	11.0418	0.453052
$595$	−2.74655	−0.112597
$596$	−43.2826	−1.77293
$597$	2.30178	0.0942056
$598$	−0.111601	−0.00456370
$599$	9.12520	0.372846	0.186423	−	0.982470i	$-0.440311\pi$
$599$	9.12520	0.372846	0.186423	+	0.982470i	$0.440311\pi$
$600$	0.881910	0.0360038
$601$	46.8048	1.90921	0.954605	−	0.297875i	$-0.0962780\pi$
$601$	46.8048	1.90921	0.954605	+	0.297875i	$0.0962780\pi$
$602$	−25.6026	−1.04348
$603$	3.92364	0.159783
$604$	−32.8374	−1.33614
$605$	−25.5470	−1.03863
$606$	4.44655	0.180629
$607$	6.42403	0.260743	0.130372	−	0.991465i	$-0.458383\pi$
$607$	6.42403	0.260743	0.130372	+	0.991465i	$0.458383\pi$
$608$	32.9618	1.33678
$609$	0.549220	0.0222555
$610$	22.6315	0.916323
$611$	−13.3003	−0.538073
$612$	−8.43286	−0.340878
$613$	39.5294	1.59658	0.798289	−	0.602274i	$-0.205739\pi$
$613$	39.5294	1.59658	0.798289	+	0.602274i	$0.205739\pi$
$614$	16.2826	0.657111
$615$	0.304644	0.0122844
$616$	−8.36950	−0.337217
$617$	−35.5744	−1.43217	−0.716087	−	0.698011i	$-0.754068\pi$
$617$	−35.5744	−1.43217	−0.716087	+	0.698011i	$0.754068\pi$
$618$	−1.29616	−0.0521392
$619$	−21.6337	−0.869532	−0.434766	−	0.900543i	$-0.643169\pi$
$619$	−21.6337	−0.869532	−0.434766	+	0.900543i	$0.643169\pi$
$620$	−67.3384	−2.70438
$621$	−0.0564602	−0.00226567
$622$	−25.6515	−1.02853
$623$	−15.0735	−0.603906
$624$	0.298607	0.0119538
$625$	−31.2481	−1.24992
$626$	−60.0332	−2.39941
$627$	3.83122	0.153004
$628$	−26.0061	−1.03776
$629$	−8.04437	−0.320750
$630$	17.9240	0.714111
$631$	0.679694	0.0270582	0.0135291	−	0.999908i	$-0.495693\pi$
$631$	0.679694	0.0270582	0.0135291	+	0.999908i	$0.495693\pi$
$632$	−5.88328	−0.234024
$633$	−3.31095	−0.131599
$634$	70.3489	2.79391
$635$	−8.10235	−0.321532
$636$	0.659582	0.0261541
$637$	−1.00000	−0.0396214
$638$	−29.1782	−1.15517
$639$	−22.5615	−0.892519
$640$	37.1802	1.46968
$641$	22.3386	0.882320	0.441160	−	0.897428i	$-0.354567\pi$
$641$	22.3386	0.882320	0.441160	+	0.897428i	$0.354567\pi$
$642$	−5.30948	−0.209548
$643$	24.3692	0.961029	0.480515	−	0.876987i	$-0.340450\pi$
$643$	24.3692	0.961029	0.480515	+	0.876987i	$0.340450\pi$
$644$	0.144209	0.00568264
$645$	5.96381	0.234825
$646$	−10.0258	−0.394461
$647$	6.15979	0.242166	0.121083	−	0.992642i	$-0.461363\pi$
$647$	6.15979	0.242166	0.121083	+	0.992642i	$0.461363\pi$
$648$	16.1375	0.633941
$649$	5.28297	0.207375
$650$	−5.59804	−0.219573
$651$	1.60917	0.0630685
$652$	−9.54040	−0.373631
$653$	−46.4723	−1.81860	−0.909301	−	0.416139i	$-0.863383\pi$
$653$	−46.4723	−1.81860	−0.909301	+	0.416139i	$0.863383\pi$
$654$	−0.387009	−0.0151332
$655$	−28.1026	−1.09806
$656$	0.950599	0.0371146
$657$	−31.3910	−1.22468
$658$	29.2727	1.14117
$659$	−31.1607	−1.21385	−0.606924	−	0.794760i	$-0.707597\pi$
$659$	−31.1607	−1.21385	−0.606924	+	0.794760i	$0.707597\pi$
$660$	6.56950	0.255717
$661$	−20.3071	−0.789854	−0.394927	−	0.918713i	$-0.629230\pi$
$661$	−20.3071	−0.789854	−0.394927	+	0.918713i	$0.629230\pi$
$662$	21.7567	0.845598
$663$	−0.186661	−0.00724932
$664$	−19.2145	−0.745668
$665$	12.5114	0.485171
$666$	52.4978	2.03425
$667$	0.149197	0.00577691
$668$	−12.3832	−0.479122
$669$	−4.46683	−0.172698
$670$	7.99889	0.309024
$671$	16.8690	0.651220
$672$	−1.35066	−0.0521029
$673$	−5.66328	−0.218303	−0.109152	−	0.994025i	$-0.534813\pi$
$673$	−5.66328	−0.218303	−0.109152	+	0.994025i	$0.534813\pi$
$674$	57.2020	2.20334
$675$	−2.83211	−0.109008
$676$	2.84398	0.109384
$677$	−17.4253	−0.669707	−0.334854	−	0.942270i	$-0.608687\pi$
$677$	−17.4253	−0.669707	−0.334854	+	0.942270i	$0.608687\pi$
$678$	7.24230	0.278139
$679$	−8.06416	−0.309474
$680$	−5.10179	−0.195645
$681$	2.89589	0.110971
$682$	−85.4898	−3.27357
$683$	42.5457	1.62796	0.813982	−	0.580890i	$-0.197295\pi$
$683$	42.5457	1.62796	0.813982	+	0.580890i	$0.197295\pi$
$684$	38.4144	1.46881
$685$	51.0321	1.94984
$686$	2.20091	0.0840309
$687$	−0.232056	−0.00885349
$688$	18.6092	0.709470
$689$	−1.24248	−0.0473345
$690$	−0.0572148	−0.00217813
$691$	40.2907	1.53273	0.766366	−	0.642404i	$-0.222063\pi$
$691$	40.2907	1.53273	0.766366	+	0.642404i	$0.222063\pi$
$692$	41.7024	1.58529
$693$	13.3602	0.507511
$694$	−57.7310	−2.19144
$695$	31.6834	1.20182
$696$	1.02019	0.0386703
$697$	−0.594226	−0.0225079
$698$	−35.2271	−1.33337
$699$	3.42195	0.129430
$700$	7.23372	0.273409
$701$	5.24426	0.198073	0.0990364	−	0.995084i	$-0.468424\pi$
$701$	5.24426	0.198073	0.0990364	+	0.995084i	$0.468424\pi$
$702$	2.45063	0.0924930
$703$	36.6447	1.38208
$704$	57.3401	2.16109
$705$	−6.81871	−0.256808
$706$	−61.3343	−2.30835
$707$	10.8235	0.407059
$708$	−0.622437	−0.0233926
$709$	−9.31121	−0.349690	−0.174845	−	0.984596i	$-0.555942\pi$
$709$	−9.31121	−0.349690	−0.174845	+	0.984596i	$0.555942\pi$
$710$	−45.9948	−1.72615
$711$	9.39144	0.352206
$712$	−27.9994	−1.04932
$713$	0.437135	0.0163708
$714$	0.410824	0.0153747
$715$	−12.3752	−0.462805
$716$	−29.6382	−1.10763
$717$	−2.72580	−0.101797
$718$	−83.3309	−3.10988
$719$	22.5770	0.841981	0.420991	−	0.907065i	$-0.361683\pi$
$719$	22.5770	0.841981	0.420991	+	0.907065i	$0.361683\pi$
$720$	−13.0281	−0.485528
$721$	−3.15503	−0.117499
$722$	3.85369	0.143419
$723$	−0.838806	−0.0311955
$724$	−20.0122	−0.743749
$725$	7.48389	0.277945
$726$	3.82128	0.141821
$727$	45.9467	1.70407	0.852034	−	0.523486i	$-0.175369\pi$
$727$	45.9467	1.70407	0.852034	+	0.523486i	$0.175369\pi$
$728$	−1.85753	−0.0688445
$729$	−25.1367	−0.930988
$730$	−63.9949	−2.36856
$731$	−11.6328	−0.430253
$732$	−1.98750	−0.0734600
$733$	−26.7497	−0.988022	−0.494011	−	0.869456i	$-0.664470\pi$
$733$	−26.7497	−0.988022	−0.494011	+	0.869456i	$0.664470\pi$
$734$	−5.01328	−0.185044
$735$	−0.512674	−0.0189103
$736$	−0.366909	−0.0135245
$737$	5.96219	0.219620
$738$	3.87794	0.142749
$739$	−3.17357	−0.116742	−0.0583708	−	0.998295i	$-0.518591\pi$
$739$	−3.17357	−0.116742	−0.0583708	+	0.998295i	$0.518591\pi$
$740$	62.8356	2.30988
$741$	0.850302	0.0312366
$742$	2.73457	0.100389
$743$	−2.36723	−0.0868452	−0.0434226	−	0.999057i	$-0.513826\pi$
$743$	−2.36723	−0.0868452	−0.0434226	+	0.999057i	$0.513826\pi$
$744$	2.98908	0.109585
$745$	41.7997	1.53142
$746$	−27.6536	−1.01247
$747$	30.6720	1.12223
$748$	−12.8142	−0.468533
$749$	−12.9240	−0.472232
$750$	2.77176	0.101210
$751$	28.4447	1.03796	0.518981	−	0.854786i	$-0.326312\pi$
$751$	28.4447	1.03796	0.518981	+	0.854786i	$0.326312\pi$
$752$	−21.2768	−0.775886
$753$	−0.132794	−0.00483927
$754$	−6.47581	−0.235835
$755$	31.7124	1.15413
$756$	−3.16667	−0.115171
$757$	19.6201	0.713103	0.356551	−	0.934276i	$-0.383952\pi$
$757$	19.6201	0.713103	0.356551	+	0.934276i	$0.383952\pi$
$758$	−9.91025	−0.359957
$759$	−0.0426466	−0.00154797
$760$	23.2403	0.843013
$761$	−11.0348	−0.400012	−0.200006	−	0.979795i	$-0.564096\pi$
$761$	−11.0348	−0.400012	−0.200006	+	0.979795i	$0.564096\pi$
$762$	1.21194	0.0439038
$763$	−0.942031	−0.0341038
$764$	53.1180	1.92174
$765$	8.14394	0.294445
$766$	4.88950	0.176665
$767$	1.17250	0.0423366
$768$	−0.810426	−0.0292437
$769$	12.8991	0.465153	0.232577	−	0.972578i	$-0.425284\pi$
$769$	12.8991	0.465153	0.232577	+	0.972578i	$0.425284\pi$
$770$	27.2366	0.981538
$771$	2.55921	0.0921677
$772$	17.3797	0.625509
$773$	−11.0250	−0.396542	−0.198271	−	0.980147i	$-0.563533\pi$
$773$	−11.0250	−0.396542	−0.198271	+	0.980147i	$0.563533\pi$
$774$	75.9158	2.72874
$775$	21.9272	0.787649
$776$	−14.9794	−0.537729
$777$	−1.50157	−0.0538686
$778$	56.5258	2.02655
$779$	2.70689	0.0969844
$780$	1.45804	0.0522060
$781$	−34.2834	−1.22676
$782$	0.111601	0.00399084
$783$	−3.27619	−0.117081
$784$	−1.59973	−0.0571330
$785$	25.1151	0.896397
$786$	4.20353	0.149935
$787$	42.3482	1.50955	0.754775	−	0.655984i	$-0.227746\pi$
$787$	42.3482	1.50955	0.754775	+	0.655984i	$0.227746\pi$
$788$	8.96131	0.319233
$789$	3.73855	0.133096
$790$	19.1458	0.681175
$791$	17.6287	0.626806
$792$	24.8169	0.881829
$793$	3.74391	0.132950
$794$	−44.6056	−1.58299
$795$	−0.636984	−0.0225915
$796$	35.0701	1.24303
$797$	8.45957	0.299653	0.149827	−	0.988712i	$-0.452128\pi$
$797$	8.45957	0.299653	0.149827	+	0.988712i	$0.452128\pi$
$798$	−1.87143	−0.0662480
$799$	13.3003	0.470531
$800$	−18.4046	−0.650702
$801$	44.6952	1.57923
$802$	−78.9564	−2.78805
$803$	−47.7003	−1.68331
$804$	−0.702462	−0.0247739
$805$	−0.139269	−0.00490857
$806$	−18.9736	−0.668317
$807$	0.899931	0.0316791
$808$	20.1049	0.707289
$809$	21.1140	0.742330	0.371165	−	0.928567i	$-0.378958\pi$
$809$	21.1140	0.742330	0.371165	+	0.928567i	$0.378958\pi$
$810$	−52.5158	−1.84522
$811$	5.28391	0.185543	0.0927715	−	0.995687i	$-0.470427\pi$
$811$	5.28391	0.185543	0.0927715	+	0.995687i	$0.470427\pi$
$812$	8.36796	0.293658
$813$	−0.981283	−0.0344151
$814$	79.7732	2.79605
$815$	9.21354	0.322736
$816$	−0.298607	−0.0104533
$817$	52.9910	1.85392
$818$	30.0932	1.05218
$819$	2.96516	0.103611
$820$	4.64158	0.162091
$821$	−29.4908	−1.02924	−0.514618	−	0.857419i	$-0.672066\pi$
$821$	−29.4908	−1.02924	−0.514618	+	0.857419i	$0.672066\pi$
$822$	−7.63329	−0.266241
$823$	−14.9924	−0.522603	−0.261301	−	0.965257i	$-0.584152\pi$
$823$	−14.9924	−0.522603	−0.261301	+	0.965257i	$0.584152\pi$
$824$	−5.86055	−0.204162
$825$	−2.13921	−0.0744777
$826$	−2.58057	−0.0897895
$827$	−6.18931	−0.215223	−0.107612	−	0.994193i	$-0.534320\pi$
$827$	−6.18931	−0.215223	−0.107612	+	0.994193i	$0.534320\pi$
$828$	−0.427603	−0.0148602
$829$	−25.6717	−0.891616	−0.445808	−	0.895129i	$-0.647084\pi$
$829$	−25.6717	−0.891616	−0.445808	+	0.895129i	$0.647084\pi$
$830$	62.5292	2.17042
$831$	−2.28316	−0.0792021
$832$	12.7261	0.441197
$833$	1.00000	0.0346479
$834$	−4.73914	−0.164103
$835$	11.9590	0.413858
$836$	58.3728	2.01886
$837$	−9.59898	−0.331789
$838$	−25.0095	−0.863937
$839$	16.5823	0.572486	0.286243	−	0.958157i	$-0.407594\pi$
$839$	16.5823	0.572486	0.286243	+	0.958157i	$0.407594\pi$
$840$	−0.952305	−0.0328577
$841$	−20.3426	−0.701471
$842$	22.3111	0.768891
$843$	−5.10218	−0.175728
$844$	−50.4459	−1.73642
$845$	−2.74655	−0.0944841
$846$	−86.7982	−2.98418
$847$	9.30150	0.319603
$848$	−1.98762	−0.0682551
$849$	2.36026	0.0810039
$850$	5.59804	0.192011
$851$	−0.407904	−0.0139828
$852$	4.03926	0.138383
$853$	−27.8993	−0.955255	−0.477628	−	0.878562i	$-0.658503\pi$
$853$	−27.8993	−0.955255	−0.477628	+	0.878562i	$0.658503\pi$
$854$	−8.23999	−0.281967
$855$	−37.0983	−1.26873
$856$	−24.0067	−0.820531
$857$	−21.5364	−0.735669	−0.367835	−	0.929891i	$-0.619901\pi$
$857$	−21.5364	−0.735669	−0.367835	+	0.929891i	$0.619901\pi$
$858$	1.85106	0.0631940
$859$	−41.3404	−1.41052	−0.705259	−	0.708950i	$-0.749169\pi$
$859$	−41.3404	−1.41052	−0.705259	+	0.708950i	$0.749169\pi$
$860$	90.8651	3.09847
$861$	−0.110919	−0.00378011
$862$	28.0222	0.954439
$863$	31.2898	1.06512	0.532559	−	0.846393i	$-0.321230\pi$
$863$	31.2898	1.06512	0.532559	+	0.846393i	$0.321230\pi$
$864$	8.05691	0.274102
$865$	−40.2736	−1.36934
$866$	−32.2874	−1.09717
$867$	0.186661	0.00633935
$868$	24.5175	0.832178
$869$	14.2708	0.484104
$870$	−3.31998	−0.112558
$871$	1.32325	0.0448366
$872$	−1.74985	−0.0592574
$873$	23.9115	0.809282
$874$	−0.508378	−0.0171961
$875$	6.74684	0.228085
$876$	5.62002	0.189883
$877$	16.3642	0.552581	0.276291	−	0.961074i	$-0.410895\pi$
$877$	16.3642	0.552581	0.276291	+	0.961074i	$0.410895\pi$
$878$	−66.2989	−2.23748
$879$	4.03643	0.136145
$880$	−19.7969	−0.667352
$881$	3.23042	0.108836	0.0544178	−	0.998518i	$-0.482670\pi$
$881$	3.23042	0.108836	0.0544178	+	0.998518i	$0.482670\pi$
$882$	−6.52603	−0.219743
$883$	−11.1382	−0.374829	−0.187414	−	0.982281i	$-0.560011\pi$
$883$	−11.1382	−0.374829	−0.187414	+	0.982281i	$0.560011\pi$
$884$	−2.84398	−0.0956535
$885$	0.601112	0.0202061
$886$	36.5544	1.22807
$887$	−56.6958	−1.90366	−0.951830	−	0.306627i	$-0.900799\pi$
$887$	−56.6958	−1.90366	−0.951830	+	0.306627i	$0.900799\pi$
$888$	−2.78921	−0.0935997
$889$	2.95001	0.0989403
$890$	91.1174	3.05426
$891$	−39.1440	−1.31137
$892$	−68.0570	−2.27872
$893$	−60.5872	−2.02747
$894$	−6.25233	−0.209109
$895$	28.6227	0.956753
$896$	−13.5371	−0.452242
$897$	−0.00946499	−0.000316027 0
$898$	−66.2014	−2.20917
$899$	25.3654	0.845983
$900$	−21.4491	−0.714971
$901$	1.24248	0.0413929
$902$	5.89274	0.196207
$903$	−2.17139	−0.0722592
$904$	32.7459	1.08911
$905$	19.3266	0.642438
$906$	−4.74348	−0.157592
$907$	43.5503	1.44606	0.723032	−	0.690815i	$-0.242748\pi$
$907$	43.5503	1.44606	0.723032	+	0.690815i	$0.242748\pi$
$908$	44.1219	1.46424
$909$	−32.0934	−1.06447
$910$	6.04489	0.200386
$911$	−22.0647	−0.731035	−0.365518	−	0.930804i	$-0.619108\pi$
$911$	−22.0647	−0.731035	−0.365518	+	0.930804i	$0.619108\pi$
$912$	1.36025	0.0450424
$913$	46.6078	1.54249
$914$	−6.65705	−0.220196
$915$	1.91940	0.0634535
$916$	−3.53562	−0.116820
$917$	10.2320	0.337889
$918$	−2.45063	−0.0808828
$919$	23.4348	0.773041	0.386521	−	0.922281i	$-0.373677\pi$
$919$	23.4348	0.773041	0.386521	+	0.922281i	$0.373677\pi$
$920$	−0.258695	−0.00852893
$921$	1.38094	0.0455036
$922$	45.6066	1.50197
$923$	−7.60887	−0.250449
$924$	−2.39191	−0.0786881
$925$	−20.4610	−0.672753
$926$	−65.1975	−2.14252
$927$	9.35515	0.307263
$928$	−21.2905	−0.698894
$929$	−51.9337	−1.70389	−0.851945	−	0.523631i	$-0.824577\pi$
$929$	−51.9337	−1.70389	−0.851945	+	0.523631i	$0.824577\pi$
$930$	−9.72728	−0.318970
$931$	−4.55532	−0.149295
$932$	52.1371	1.70781
$933$	−2.17553	−0.0712237
$934$	76.7014	2.50975
$935$	12.3752	0.404711
$936$	5.50786	0.180030
$937$	−53.3075	−1.74148	−0.870741	−	0.491742i	$-0.836360\pi$
$937$	−53.3075	−1.74148	−0.870741	+	0.491742i	$0.836360\pi$
$938$	−2.91235	−0.0950915
$939$	−5.09148	−0.166154
$940$	−103.890	−3.38853
$941$	1.88634	0.0614928	0.0307464	−	0.999527i	$-0.490212\pi$
$941$	1.88634	0.0614928	0.0307464	+	0.999527i	$0.490212\pi$
$942$	−3.75668	−0.122399
$943$	−0.0301313	−0.000981210 0
$944$	1.87568	0.0610483
$945$	3.05818	0.0994826
$946$	115.358	3.75062
$947$	1.50318	0.0488469	0.0244234	−	0.999702i	$-0.492225\pi$
$947$	1.50318	0.0488469	0.0244234	+	0.999702i	$0.492225\pi$
$948$	−1.68138	−0.0546086
$949$	−10.5866	−0.343656
$950$	−25.5009	−0.827358
$951$	5.96636	0.193473
$952$	1.85753	0.0602028
$953$	−30.4687	−0.986976	−0.493488	−	0.869752i	$-0.664278\pi$
$953$	−30.4687	−0.986976	−0.493488	+	0.869752i	$0.664278\pi$
$954$	−8.10843	−0.262520
$955$	−51.2981	−1.65997
$956$	−41.5305	−1.34319
$957$	−2.47463	−0.0799935
$958$	66.3362	2.14323
$959$	−18.5805	−0.599994
$960$	6.52432	0.210572
$961$	43.3187	1.39738
$962$	17.7049	0.570828
$963$	38.3217	1.23490
$964$	−12.7801	−0.411620
$965$	−16.7843	−0.540304
$966$	0.0208315	0.000670244 0
$967$	4.33866	0.139522	0.0697609	−	0.997564i	$-0.477776\pi$
$967$	4.33866	0.139522	0.0697609	+	0.997564i	$0.477776\pi$
$968$	17.2778	0.555329
$969$	−0.850302	−0.0273156
$970$	48.7470	1.56517
$971$	23.9894	0.769857	0.384928	−	0.922946i	$-0.374226\pi$
$971$	23.9894	0.769857	0.384928	+	0.922946i	$0.374226\pi$
$972$	14.1119	0.452641
$973$	−11.5357	−0.369818
$974$	−35.4599	−1.13621
$975$	−0.474776	−0.0152050
$976$	5.98922	0.191710
$977$	−29.0268	−0.928649	−0.464325	−	0.885665i	$-0.653703\pi$
$977$	−29.0268	−0.928649	−0.464325	+	0.885665i	$0.653703\pi$
$978$	−1.37815	−0.0440682
$979$	67.9168	2.17063
$980$	−7.81113	−0.249517
$981$	2.79327	0.0891823
$982$	53.2316	1.69869
$983$	−7.88661	−0.251544	−0.125772	−	0.992059i	$-0.540141\pi$
$983$	−7.88661	−0.251544	−0.125772	+	0.992059i	$0.540141\pi$
$984$	−0.206035	−0.00656816
$985$	−8.65429	−0.275749
$986$	6.47581	0.206232
$987$	2.48265	0.0790236
$988$	12.9553	0.412162
$989$	−0.589860	−0.0187565
$990$	−80.7607	−2.56674
$991$	−39.5107	−1.25510	−0.627549	−	0.778577i	$-0.715942\pi$
$991$	−39.5107	−1.25510	−0.627549	+	0.778577i	$0.715942\pi$
$992$	−62.3794	−1.98055
$993$	1.84521	0.0585559
$994$	16.7464	0.531164
$995$	−33.8686	−1.07371
$996$	−5.49130	−0.173999
$997$	−6.45614	−0.204468	−0.102234	−	0.994760i	$-0.532599\pi$
$997$	−6.45614	−0.204468	−0.102234	+	0.994760i	$0.532599\pi$
$998$	−26.6775	−0.844462
$999$	8.95711	0.283390

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1547.2.a.g.1.9	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1547.2.a.g.1.9	✓	9	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)

\(f(q)\)	\(=\)	\(q+2.20091 q^{2} +0.186661 q^{3} +2.84398 q^{4} -2.74655 q^{5} +0.410824 q^{6} +1.00000 q^{7} +1.85753 q^{8} -2.96516 q^{9} -6.04489 q^{10} -4.50572 q^{11} +0.530861 q^{12} -1.00000 q^{13} +2.20091 q^{14} -0.512674 q^{15} -1.59973 q^{16} +1.00000 q^{17} -6.52603 q^{18} -4.55532 q^{19} -7.81113 q^{20} +0.186661 q^{21} -9.91666 q^{22} +0.0507068 q^{23} +0.346728 q^{24} +2.54352 q^{25} -2.20091 q^{26} -1.11346 q^{27} +2.84398 q^{28} +2.94234 q^{29} -1.12835 q^{30} +8.62083 q^{31} -7.23590 q^{32} -0.841043 q^{33} +2.20091 q^{34} -2.74655 q^{35} -8.43286 q^{36} -8.04437 q^{37} -10.0258 q^{38} -0.186661 q^{39} -5.10179 q^{40} -0.594226 q^{41} +0.410824 q^{42} -11.6328 q^{43} -12.8142 q^{44} +8.14394 q^{45} +0.111601 q^{46} +13.3003 q^{47} -0.298607 q^{48} +1.00000 q^{49} +5.59804 q^{50} +0.186661 q^{51} -2.84398 q^{52} +1.24248 q^{53} -2.45063 q^{54} +12.3752 q^{55} +1.85753 q^{56} -0.850302 q^{57} +6.47581 q^{58} -1.17250 q^{59} -1.45804 q^{60} -3.74391 q^{61} +18.9736 q^{62} -2.96516 q^{63} -12.7261 q^{64} +2.74655 q^{65} -1.85106 q^{66} -1.32325 q^{67} +2.84398 q^{68} +0.00946499 q^{69} -6.04489 q^{70} +7.60887 q^{71} -5.50786 q^{72} +10.5866 q^{73} -17.7049 q^{74} +0.474776 q^{75} -12.9553 q^{76} -4.50572 q^{77} -0.410824 q^{78} -3.16726 q^{79} +4.39372 q^{80} +8.68763 q^{81} -1.30784 q^{82} -10.3441 q^{83} +0.530861 q^{84} -2.74655 q^{85} -25.6026 q^{86} +0.549220 q^{87} -8.36950 q^{88} -15.0735 q^{89} +17.9240 q^{90} -1.00000 q^{91} +0.144209 q^{92} +1.60917 q^{93} +29.2727 q^{94} +12.5114 q^{95} -1.35066 q^{96} -8.06416 q^{97} +2.20091 q^{98} +13.3602 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 3 q^{2} - 4 q^{3} + 3 q^{4} - 6 q^{5} + 2 q^{6} + 9 q^{7} - 6 q^{8} + 5 q^{9} - 9 q^{10} - 7 q^{11} + 2 q^{12} - 9 q^{13} - 3 q^{14} - 5 q^{15} + 3 q^{16} + 9 q^{17} - 9 q^{18} - 6 q^{19} + 6 q^{20}+ \cdots - 25 q^{99}+O(q^{100}) \) 9 * q - 3 * q^2 - 4 * q^3 + 3 * q^4 - 6 * q^5 + 2 * q^6 + 9 * q^7 - 6 * q^8 + 5 * q^9 - 9 * q^10 - 7 * q^11 + 2 * q^12 - 9 * q^13 - 3 * q^14 - 5 * q^15 + 3 * q^16 + 9 * q^17 - 9 * q^18 - 6 * q^19 + 6 * q^20 - 4 * q^21 - 4 * q^22 - 3 * q^23 + 8 * q^24 - 13 * q^25 + 3 * q^26 - 13 * q^27 + 3 * q^28 - 4 * q^29 + 10 * q^32 - 12 * q^33 - 3 * q^34 - 6 * q^35 - 17 * q^36 - 31 * q^37 - 3 * q^38 + 4 * q^39 - 18 * q^40 + 3 * q^41 + 2 * q^42 - 24 * q^43 - 20 * q^44 + 3 * q^45 + 5 * q^46 + 7 * q^47 + 2 * q^48 + 9 * q^49 + 24 * q^50 - 4 * q^51 - 3 * q^52 - 18 * q^53 + 6 * q^55 - 6 * q^56 - 35 * q^57 + 2 * q^58 - 9 * q^59 + 2 * q^60 - 22 * q^61 + 30 * q^62 + 5 * q^63 - 36 * q^64 + 6 * q^65 + 22 * q^66 - 32 * q^67 + 3 * q^68 - 2 * q^69 - 9 * q^70 + 18 * q^71 - 10 * q^72 - 14 * q^73 + 12 * q^74 + 11 * q^75 - 27 * q^76 - 7 * q^77 - 2 * q^78 - 46 * q^79 - q^80 + 29 * q^81 + 3 * q^82 - 16 * q^83 + 2 * q^84 - 6 * q^85 - 34 * q^86 + 3 * q^87 - 10 * q^89 + 21 * q^90 - 9 * q^91 + 14 * q^92 - 83 * q^93 + q^94 - 55 * q^96 - 15 * q^97 - 3 * q^98 - 25 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more