LMFDB - Embedded newform 1083.2.a.m.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1083,2,Mod(1,1083)] 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("1083.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1083, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1083 = 3 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1083.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$8.64779853890$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 57)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.53209$ of defining polynomial
Character	$\chi$	$=$	1083.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.53209 q^{2} -1.00000 q^{3} +0.347296 q^{4} -2.53209 q^{5} +1.53209 q^{6} +0.532089 q^{7} +2.53209 q^{8} +1.00000 q^{9} +3.87939 q^{10} -5.10607 q^{11} -0.347296 q^{12} +4.06418 q^{13} -0.815207 q^{14} +2.53209 q^{15} -4.57398 q^{16} +1.94356 q^{17} -1.53209 q^{18} -0.879385 q^{20} -0.532089 q^{21} +7.82295 q^{22} +3.04189 q^{23} -2.53209 q^{24} +1.41147 q^{25} -6.22668 q^{26} -1.00000 q^{27} +0.184793 q^{28} +1.61081 q^{29} -3.87939 q^{30} +9.87939 q^{31} +1.94356 q^{32} +5.10607 q^{33} -2.97771 q^{34} -1.34730 q^{35} +0.347296 q^{36} +6.10607 q^{37} -4.06418 q^{39} -6.41147 q^{40} -8.47565 q^{41} +0.815207 q^{42} -0.177052 q^{43} -1.77332 q^{44} -2.53209 q^{45} -4.66044 q^{46} +7.55943 q^{47} +4.57398 q^{48} -6.71688 q^{49} -2.16250 q^{50} -1.94356 q^{51} +1.41147 q^{52} -9.90167 q^{53} +1.53209 q^{54} +12.9290 q^{55} +1.34730 q^{56} -2.46791 q^{58} -3.81521 q^{59} +0.879385 q^{60} -13.9290 q^{61} -15.1361 q^{62} +0.532089 q^{63} +6.17024 q^{64} -10.2909 q^{65} -7.82295 q^{66} -10.2121 q^{67} +0.674992 q^{68} -3.04189 q^{69} +2.06418 q^{70} +3.82295 q^{71} +2.53209 q^{72} -1.85710 q^{73} -9.35504 q^{74} -1.41147 q^{75} -2.71688 q^{77} +6.22668 q^{78} +10.5175 q^{79} +11.5817 q^{80} +1.00000 q^{81} +12.9855 q^{82} -11.4757 q^{83} -0.184793 q^{84} -4.92127 q^{85} +0.271259 q^{86} -1.61081 q^{87} -12.9290 q^{88} -5.92396 q^{89} +3.87939 q^{90} +2.16250 q^{91} +1.05644 q^{92} -9.87939 q^{93} -11.5817 q^{94} -1.94356 q^{96} -6.80066 q^{97} +10.2909 q^{98} -5.10607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{3} - 3 q^{5} - 3 q^{7} + 3 q^{8} + 3 q^{9} + 6 q^{10} - 3 q^{11} + 3 q^{13} - 6 q^{14} + 3 q^{15} - 6 q^{16} - 9 q^{17} + 3 q^{20} + 3 q^{21} + 3 q^{22} + 6 q^{23} - 3 q^{24} - 6 q^{25} - 12 q^{26}+ \cdots - 3 q^{99}+O(q^{100}) $ 3 * q - 3 * q^3 - 3 * q^5 - 3 * q^7 + 3 * q^8 + 3 * q^9 + 6 * q^10 - 3 * q^11 + 3 * q^13 - 6 * q^14 + 3 * q^15 - 6 * q^16 - 9 * q^17 + 3 * q^20 + 3 * q^21 + 3 * q^22 + 6 * q^23 - 3 * q^24 - 6 * q^25 - 12 * q^26 - 3 * q^27 - 3 * q^28 + 9 * q^29 - 6 * q^30 + 24 * q^31 - 9 * q^32 + 3 * q^33 - 15 * q^34 - 3 * q^35 + 6 * q^37 - 3 * q^39 - 9 * q^40 - 6 * q^41 + 6 * q^42 - 21 * q^43 - 12 * q^44 - 3 * q^45 + 9 * q^46 - 3 * q^47 + 6 * q^48 - 12 * q^49 - 9 * q^50 + 9 * q^51 - 6 * q^52 - 18 * q^53 + 6 * q^55 + 3 * q^56 - 12 * q^58 - 15 * q^59 - 3 * q^60 - 9 * q^61 - 3 * q^62 - 3 * q^63 - 3 * q^64 - 15 * q^65 - 3 * q^66 - 6 * q^67 - 3 * q^68 - 6 * q^69 - 3 * q^70 - 9 * q^71 + 3 * q^72 - 6 * q^73 - 3 * q^74 + 6 * q^75 + 12 * q^78 + 9 * q^79 + 3 * q^80 + 3 * q^81 + 21 * q^82 - 15 * q^83 + 3 * q^84 - 6 * q^85 - 18 * q^86 - 9 * q^87 - 6 * q^88 + 6 * q^90 + 9 * q^91 + 18 * q^92 - 24 * q^93 - 3 * q^94 + 9 * q^96 - 6 * q^97 + 15 * q^98 - 3 * 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 $

$2$	−1.53209	−1.08335	−0.541675	−	0.840588i	$-0.682210\pi$
$2$	−1.53209	−1.08335	−0.541675	+	0.840588i	$0.682210\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.347296	0.173648
$5$	−2.53209	−1.13238	−0.566192	−	0.824273i	$-0.691584\pi$
$5$	−2.53209	−1.13238	−0.566192	+	0.824273i	$0.691584\pi$
$6$	1.53209	0.625473
$7$	0.532089	0.201111	0.100555	−	0.994931i	$-0.467938\pi$
$7$	0.532089	0.201111	0.100555	+	0.994931i	$0.467938\pi$
$8$	2.53209	0.895229
$9$	1.00000	0.333333
$10$	3.87939	1.22677
$11$	−5.10607	−1.53954	−0.769769	−	0.638323i	$-0.779628\pi$
$11$	−5.10607	−1.53954	−0.769769	+	0.638323i	$0.779628\pi$
$12$	−0.347296	−0.100256
$13$	4.06418	1.12720	0.563600	−	0.826048i	$-0.309416\pi$
$13$	4.06418	1.12720	0.563600	+	0.826048i	$0.309416\pi$
$14$	−0.815207	−0.217873
$15$	2.53209	0.653783
$16$	−4.57398	−1.14349
$17$	1.94356	0.471383	0.235692	−	0.971828i	$-0.424264\pi$
$17$	1.94356	0.471383	0.235692	+	0.971828i	$0.424264\pi$
$18$	−1.53209	−0.361117
$19$	0	0
$19$	0	0
$20$	−0.879385	−0.196637
$21$	−0.532089	−0.116111
$22$	7.82295	1.66786
$23$	3.04189	0.634278	0.317139	−	0.948379i	$-0.397278\pi$
$23$	3.04189	0.634278	0.317139	+	0.948379i	$0.397278\pi$
$24$	−2.53209	−0.516860
$25$	1.41147	0.282295
$26$	−6.22668	−1.22115
$27$	−1.00000	−0.192450
$28$	0.184793	0.0349225
$29$	1.61081	0.299121	0.149560	−	0.988753i	$-0.452214\pi$
$29$	1.61081	0.299121	0.149560	+	0.988753i	$0.452214\pi$
$30$	−3.87939	−0.708276
$31$	9.87939	1.77439	0.887195	−	0.461395i	$-0.152651\pi$
$31$	9.87939	1.77439	0.887195	+	0.461395i	$0.152651\pi$
$32$	1.94356	0.343577
$33$	5.10607	0.888852
$34$	−2.97771	−0.510673
$35$	−1.34730	−0.227735
$36$	0.347296	0.0578827
$37$	6.10607	1.00383	0.501916	−	0.864917i	$-0.332629\pi$
$37$	6.10607	1.00383	0.501916	+	0.864917i	$0.332629\pi$
$38$	0	0
$39$	−4.06418	−0.650789
$40$	−6.41147	−1.01374
$41$	−8.47565	−1.32367	−0.661837	−	0.749648i	$-0.730223\pi$
$41$	−8.47565	−1.32367	−0.661837	+	0.749648i	$0.730223\pi$
$42$	0.815207	0.125789
$43$	−0.177052	−0.0270001	−0.0135001	−	0.999909i	$-0.504297\pi$
$43$	−0.177052	−0.0270001	−0.0135001	+	0.999909i	$0.504297\pi$
$44$	−1.77332	−0.267338
$45$	−2.53209	−0.377462
$46$	−4.66044	−0.687145
$47$	7.55943	1.10266	0.551328	−	0.834289i	$-0.314121\pi$
$47$	7.55943	1.10266	0.551328	+	0.834289i	$0.314121\pi$
$48$	4.57398	0.660197
$49$	−6.71688	−0.959554
$50$	−2.16250	−0.305824
$51$	−1.94356	−0.272153
$52$	1.41147	0.195736
$53$	−9.90167	−1.36010	−0.680050	−	0.733166i	$-0.738042\pi$
$53$	−9.90167	−1.36010	−0.680050	+	0.733166i	$0.738042\pi$
$54$	1.53209	0.208491
$55$	12.9290	1.74335
$56$	1.34730	0.180040
$57$	0	0
$58$	−2.46791	−0.324053
$59$	−3.81521	−0.496698	−0.248349	−	0.968671i	$-0.579888\pi$
$59$	−3.81521	−0.496698	−0.248349	+	0.968671i	$0.579888\pi$
$60$	0.879385	0.113528
$61$	−13.9290	−1.78343	−0.891714	−	0.452600i	$-0.850497\pi$
$61$	−13.9290	−1.78343	−0.891714	+	0.452600i	$0.850497\pi$
$62$	−15.1361	−1.92229
$63$	0.532089	0.0670369
$64$	6.17024	0.771281
$65$	−10.2909	−1.27642
$66$	−7.82295	−0.962938
$67$	−10.2121	−1.24761	−0.623805	−	0.781580i	$-0.714414\pi$
$67$	−10.2121	−1.24761	−0.623805	+	0.781580i	$0.714414\pi$
$68$	0.674992	0.0818548
$69$	−3.04189	−0.366200
$70$	2.06418	0.246716
$71$	3.82295	0.453700	0.226850	−	0.973930i	$-0.427157\pi$
$71$	3.82295	0.453700	0.226850	+	0.973930i	$0.427157\pi$
$72$	2.53209	0.298410
$73$	−1.85710	−0.217357	−0.108678	−	0.994077i	$-0.534662\pi$
$73$	−1.85710	−0.217357	−0.108678	+	0.994077i	$0.534662\pi$
$74$	−9.35504	−1.08750
$75$	−1.41147	−0.162983
$76$	0	0
$77$	−2.71688	−0.309617
$78$	6.22668	0.705033
$79$	10.5175	1.18332	0.591658	−	0.806189i	$-0.298474\pi$
$79$	10.5175	1.18332	0.591658	+	0.806189i	$0.298474\pi$
$80$	11.5817	1.29488
$81$	1.00000	0.111111
$82$	12.9855	1.43400
$83$	−11.4757	−1.25962	−0.629808	−	0.776751i	$-0.716867\pi$
$83$	−11.4757	−1.25962	−0.629808	+	0.776751i	$0.716867\pi$
$84$	−0.184793	−0.0201625
$85$	−4.92127	−0.533787
$86$	0.271259	0.0292506
$87$	−1.61081	−0.172697
$88$	−12.9290	−1.37824
$89$	−5.92396	−0.627939	−0.313969	−	0.949433i	$-0.601659\pi$
$89$	−5.92396	−0.627939	−0.313969	+	0.949433i	$0.601659\pi$
$90$	3.87939	0.408923
$91$	2.16250	0.226692
$92$	1.05644	0.110141
$93$	−9.87939	−1.02444
$94$	−11.5817	−1.19456
$95$	0	0
$96$	−1.94356	−0.198364
$97$	−6.80066	−0.690502	−0.345251	−	0.938510i	$-0.612206\pi$
$97$	−6.80066	−0.690502	−0.345251	+	0.938510i	$0.612206\pi$
$98$	10.2909	1.03953
$99$	−5.10607	−0.513179
$100$	0.490200	0.0490200
$101$	−8.75877	−0.871530	−0.435765	−	0.900060i	$-0.643522\pi$
$101$	−8.75877	−0.871530	−0.435765	+	0.900060i	$0.643522\pi$
$102$	2.97771	0.294837
$103$	−3.84524	−0.378882	−0.189441	−	0.981892i	$-0.560668\pi$
$103$	−3.84524	−0.378882	−0.189441	+	0.981892i	$0.560668\pi$
$104$	10.2909	1.00910
$105$	1.34730	0.131483
$106$	15.1702	1.47346
$107$	−5.67499	−0.548622	−0.274311	−	0.961641i	$-0.588450\pi$
$107$	−5.67499	−0.548622	−0.274311	+	0.961641i	$0.588450\pi$
$108$	−0.347296	−0.0334186
$109$	−2.08647	−0.199847	−0.0999236	−	0.994995i	$-0.531860\pi$
$109$	−2.08647	−0.199847	−0.0999236	+	0.994995i	$0.531860\pi$
$110$	−19.8084	−1.88866
$111$	−6.10607	−0.579562
$112$	−2.43376	−0.229969
$113$	7.27631	0.684498	0.342249	−	0.939609i	$-0.388811\pi$
$113$	7.27631	0.684498	0.342249	+	0.939609i	$0.388811\pi$
$114$	0	0
$115$	−7.70233	−0.718246
$116$	0.559430	0.0519418
$117$	4.06418	0.375733
$118$	5.84524	0.538098
$119$	1.03415	0.0948002
$120$	6.41147	0.585285
$121$	15.0719	1.37017
$122$	21.3405	1.93208
$123$	8.47565	0.764224
$124$	3.43107	0.308120
$125$	9.08647	0.812718
$126$	−0.815207	−0.0726245
$127$	1.82976	0.162365	0.0811823	−	0.996699i	$-0.474130\pi$
$127$	1.82976	0.162365	0.0811823	+	0.996699i	$0.474130\pi$
$128$	−13.3405	−1.17914
$129$	0.177052	0.0155885
$130$	15.7665	1.38281
$131$	−8.78611	−0.767646	−0.383823	−	0.923407i	$-0.625393\pi$
$131$	−8.78611	−0.767646	−0.383823	+	0.923407i	$0.625393\pi$
$132$	1.77332	0.154348
$133$	0	0
$134$	15.6459	1.35160
$135$	2.53209	0.217928
$136$	4.92127	0.421996
$137$	−12.6304	−1.07909	−0.539545	−	0.841957i	$-0.681404\pi$
$137$	−12.6304	−1.07909	−0.539545	+	0.841957i	$0.681404\pi$
$138$	4.66044	0.396723
$139$	−4.04963	−0.343485	−0.171743	−	0.985142i	$-0.554940\pi$
$139$	−4.04963	−0.343485	−0.171743	+	0.985142i	$0.554940\pi$
$140$	−0.467911	−0.0395457
$141$	−7.55943	−0.636619
$142$	−5.85710	−0.491517
$143$	−20.7520	−1.73537
$144$	−4.57398	−0.381165
$145$	−4.07873	−0.338720
$146$	2.84524	0.235473
$147$	6.71688	0.553999
$148$	2.12061	0.174313
$149$	6.06923	0.497211	0.248605	−	0.968605i	$-0.420028\pi$
$149$	6.06923	0.497211	0.248605	+	0.968605i	$0.420028\pi$
$150$	2.16250	0.176568
$151$	−0.162504	−0.0132244	−0.00661219	−	0.999978i	$-0.502105\pi$
$151$	−0.162504	−0.0132244	−0.00661219	+	0.999978i	$0.502105\pi$
$152$	0	0
$153$	1.94356	0.157128
$154$	4.16250	0.335424
$155$	−25.0155	−2.00929
$156$	−1.41147	−0.113008
$157$	6.66044	0.531561	0.265781	−	0.964034i	$-0.414370\pi$
$157$	6.66044	0.531561	0.265781	+	0.964034i	$0.414370\pi$
$158$	−16.1138	−1.28195
$159$	9.90167	0.785254
$160$	−4.92127	−0.389061
$161$	1.61856	0.127560
$162$	−1.53209	−0.120372
$163$	−0.448311	−0.0351144	−0.0175572	−	0.999846i	$-0.505589\pi$
$163$	−0.448311	−0.0351144	−0.0175572	+	0.999846i	$0.505589\pi$
$164$	−2.94356	−0.229854
$165$	−12.9290	−1.00652
$166$	17.5817	1.36461
$167$	3.38919	0.262263	0.131132	−	0.991365i	$-0.458139\pi$
$167$	3.38919	0.262263	0.131132	+	0.991365i	$0.458139\pi$
$168$	−1.34730	−0.103946
$169$	3.51754	0.270580
$170$	7.53983	0.578279
$171$	0	0
$172$	−0.0614894	−0.00468852
$173$	−1.61587	−0.122852	−0.0614260	−	0.998112i	$-0.519565\pi$
$173$	−1.61587	−0.122852	−0.0614260	+	0.998112i	$0.519565\pi$
$174$	2.46791	0.187092
$175$	0.751030	0.0567725
$176$	23.3550	1.76045
$177$	3.81521	0.286769
$178$	9.07604	0.680278
$179$	2.11381	0.157993	0.0789967	−	0.996875i	$-0.474828\pi$
$179$	2.11381	0.157993	0.0789967	+	0.996875i	$0.474828\pi$
$180$	−0.879385	−0.0655455
$181$	8.75196	0.650528	0.325264	−	0.945623i	$-0.394547\pi$
$181$	8.75196	0.650528	0.325264	+	0.945623i	$0.394547\pi$
$182$	−3.31315	−0.245587
$183$	13.9290	1.02966
$184$	7.70233	0.567824
$185$	−15.4611	−1.13672
$186$	15.1361	1.10983
$187$	−9.92396	−0.725712
$188$	2.62536	0.191474
$189$	−0.532089	−0.0387038
$190$	0	0
$191$	−19.0719	−1.38000	−0.689998	−	0.723811i	$-0.742389\pi$
$191$	−19.0719	−1.38000	−0.689998	+	0.723811i	$0.742389\pi$
$192$	−6.17024	−0.445299
$193$	−23.8357	−1.71573	−0.857867	−	0.513872i	$-0.828211\pi$
$193$	−23.8357	−1.71573	−0.857867	+	0.513872i	$0.828211\pi$
$194$	10.4192	0.748056
$195$	10.2909	0.736944
$196$	−2.33275	−0.166625
$197$	−4.38919	−0.312717	−0.156358	−	0.987700i	$-0.549975\pi$
$197$	−4.38919	−0.312717	−0.156358	+	0.987700i	$0.549975\pi$
$198$	7.82295	0.555953
$199$	−20.0378	−1.42044	−0.710220	−	0.703980i	$-0.751405\pi$
$199$	−20.0378	−1.42044	−0.710220	+	0.703980i	$0.751405\pi$
$200$	3.57398	0.252718
$201$	10.2121	0.720308
$202$	13.4192	0.944173
$203$	0.857097	0.0601564
$204$	−0.674992	−0.0472589
$205$	21.4611	1.49891
$206$	5.89124	0.410462
$207$	3.04189	0.211426
$208$	−18.5895	−1.28895
$209$	0	0
$210$	−2.06418	−0.142442
$211$	27.1925	1.87201	0.936006	−	0.351985i	$-0.114493\pi$
$211$	27.1925	1.87201	0.936006	+	0.351985i	$0.114493\pi$
$212$	−3.43882	−0.236179
$213$	−3.82295	−0.261944
$214$	8.69459	0.594350
$215$	0.448311	0.0305745
$216$	−2.53209	−0.172287
$217$	5.25671	0.356849
$218$	3.19665	0.216505
$219$	1.85710	0.125491
$220$	4.49020	0.302729
$221$	7.89899	0.531343
$222$	9.35504	0.627869
$223$	−12.0128	−0.804436	−0.402218	−	0.915544i	$-0.631761\pi$
$223$	−12.0128	−0.804436	−0.402218	+	0.915544i	$0.631761\pi$
$224$	1.03415	0.0690969
$225$	1.41147	0.0940983
$226$	−11.1480	−0.741551
$227$	4.34049	0.288088	0.144044	−	0.989571i	$-0.453989\pi$
$227$	4.34049	0.288088	0.144044	+	0.989571i	$0.453989\pi$
$228$	0	0
$229$	3.29591	0.217800	0.108900	−	0.994053i	$-0.465267\pi$
$229$	3.29591	0.217800	0.108900	+	0.994053i	$0.465267\pi$
$230$	11.8007	0.778112
$231$	2.71688	0.178758
$232$	4.07873	0.267781
$233$	−15.4311	−1.01092	−0.505462	−	0.862849i	$-0.668678\pi$
$233$	−15.4311	−1.01092	−0.505462	+	0.862849i	$0.668678\pi$
$234$	−6.22668	−0.407051
$235$	−19.1411	−1.24863
$236$	−1.32501	−0.0862507
$237$	−10.5175	−0.683188
$238$	−1.58441	−0.102702
$239$	15.8229	1.02350	0.511751	−	0.859134i	$-0.328997\pi$
$239$	15.8229	1.02350	0.511751	+	0.859134i	$0.328997\pi$
$240$	−11.5817	−0.747597
$241$	−23.6459	−1.52317	−0.761583	−	0.648067i	$-0.775578\pi$
$241$	−23.6459	−1.52317	−0.761583	+	0.648067i	$0.775578\pi$
$242$	−23.0915	−1.48438
$243$	−1.00000	−0.0641500
$244$	−4.83750	−0.309689
$245$	17.0077	1.08658
$246$	−12.9855	−0.827922
$247$	0	0
$248$	25.0155	1.58848
$249$	11.4757	0.727240
$250$	−13.9213	−0.880459
$251$	19.4115	1.22524	0.612621	−	0.790377i	$-0.290115\pi$
$251$	19.4115	1.22524	0.612621	+	0.790377i	$0.290115\pi$
$252$	0.184793	0.0116408
$253$	−15.5321	−0.976494
$254$	−2.80335	−0.175898
$255$	4.92127	0.308182
$256$	8.09833	0.506145
$257$	12.2959	0.766998	0.383499	−	0.923541i	$-0.374719\pi$
$257$	12.2959	0.766998	0.383499	+	0.923541i	$0.374719\pi$
$258$	−0.271259	−0.0168878
$259$	3.24897	0.201881
$260$	−3.57398	−0.221649
$261$	1.61081	0.0997069
$262$	13.4611	0.831630
$263$	6.34049	0.390971	0.195486	−	0.980707i	$-0.437372\pi$
$263$	6.34049	0.390971	0.195486	+	0.980707i	$0.437372\pi$
$264$	12.9290	0.795726
$265$	25.0719	1.54016
$266$	0	0
$267$	5.92396	0.362541
$268$	−3.54664	−0.216645
$269$	−2.32501	−0.141758	−0.0708791	−	0.997485i	$-0.522580\pi$
$269$	−2.32501	−0.141758	−0.0708791	+	0.997485i	$0.522580\pi$
$270$	−3.87939	−0.236092
$271$	14.9436	0.907757	0.453878	−	0.891064i	$-0.350040\pi$
$271$	14.9436	0.907757	0.453878	+	0.891064i	$0.350040\pi$
$272$	−8.88981	−0.539024
$273$	−2.16250	−0.130881
$274$	19.3509	1.16903
$275$	−7.20708	−0.434603
$276$	−1.05644	−0.0635900
$277$	−23.9659	−1.43997	−0.719984	−	0.693990i	$-0.755851\pi$
$277$	−23.9659	−1.43997	−0.719984	+	0.693990i	$0.755851\pi$
$278$	6.20439	0.372115
$279$	9.87939	0.591463
$280$	−3.41147	−0.203875
$281$	25.5604	1.52480	0.762402	−	0.647104i	$-0.224020\pi$
$281$	25.5604	1.52480	0.762402	+	0.647104i	$0.224020\pi$
$282$	11.5817	0.689681
$283$	−7.51073	−0.446467	−0.223233	−	0.974765i	$-0.571661\pi$
$283$	−7.51073	−0.446467	−0.223233	+	0.974765i	$0.571661\pi$
$284$	1.32770	0.0787843
$285$	0	0
$286$	31.7939	1.88001
$287$	−4.50980	−0.266205
$288$	1.94356	0.114526
$289$	−13.2226	−0.777798
$290$	6.24897	0.366952
$291$	6.80066	0.398662
$292$	−0.644963	−0.0377436
$293$	14.7665	0.862669	0.431334	−	0.902192i	$-0.358043\pi$
$293$	14.7665	0.862669	0.431334	+	0.902192i	$0.358043\pi$
$294$	−10.2909	−0.600175
$295$	9.66044	0.562453
$296$	15.4611	0.898658
$297$	5.10607	0.296284
$298$	−9.29860	−0.538653
$299$	12.3628	0.714958
$300$	−0.490200	−0.0283017
$301$	−0.0942073	−0.00543002
$302$	0.248970	0.0143266
$303$	8.75877	0.503178
$304$	0	0
$305$	35.2695	2.01953
$306$	−2.97771	−0.170224
$307$	5.51249	0.314614	0.157307	−	0.987550i	$-0.449719\pi$
$307$	5.51249	0.314614	0.157307	+	0.987550i	$0.449719\pi$
$308$	−0.943563	−0.0537645
$309$	3.84524	0.218748
$310$	38.3259	2.17677
$311$	17.3996	0.986642	0.493321	−	0.869847i	$-0.335783\pi$
$311$	17.3996	0.986642	0.493321	+	0.869847i	$0.335783\pi$
$312$	−10.2909	−0.582605
$313$	15.9436	0.901183	0.450592	−	0.892730i	$-0.351213\pi$
$313$	15.9436	0.901183	0.450592	+	0.892730i	$0.351213\pi$
$314$	−10.2044	−0.575867
$315$	−1.34730	−0.0759115
$316$	3.65270	0.205481
$317$	1.97359	0.110848	0.0554240	−	0.998463i	$-0.482349\pi$
$317$	1.97359	0.110848	0.0554240	+	0.998463i	$0.482349\pi$
$318$	−15.1702	−0.850705
$319$	−8.22493	−0.460507
$320$	−15.6236	−0.873386
$321$	5.67499	0.316747
$322$	−2.47977	−0.138192
$323$	0	0
$324$	0.347296	0.0192942
$325$	5.73648	0.318203
$326$	0.686852	0.0380412
$327$	2.08647	0.115382
$328$	−21.4611	−1.18499
$329$	4.02229	0.221756
$330$	19.8084	1.09042
$331$	−0.837496	−0.0460330	−0.0230165	−	0.999735i	$-0.507327\pi$
$331$	−0.837496	−0.0460330	−0.0230165	+	0.999735i	$0.507327\pi$
$332$	−3.98545	−0.218730
$333$	6.10607	0.334610
$334$	−5.19253	−0.284123
$335$	25.8580	1.41278
$336$	2.43376	0.132773
$337$	−3.32770	−0.181271	−0.0906356	−	0.995884i	$-0.528890\pi$
$337$	−3.32770	−0.181271	−0.0906356	+	0.995884i	$0.528890\pi$
$338$	−5.38919	−0.293133
$339$	−7.27631	−0.395195
$340$	−1.70914	−0.0926912
$341$	−50.4448	−2.73174
$342$	0	0
$343$	−7.29860	−0.394087
$344$	−0.448311	−0.0241713
$345$	7.70233	0.414680
$346$	2.47565	0.133092
$347$	4.00774	0.215147	0.107573	−	0.994197i	$-0.465692\pi$
$347$	4.00774	0.215147	0.107573	+	0.994197i	$0.465692\pi$
$348$	−0.559430	−0.0299886
$349$	−27.9026	−1.49359	−0.746796	−	0.665053i	$-0.768409\pi$
$349$	−27.9026	−1.49359	−0.746796	+	0.665053i	$0.768409\pi$
$350$	−1.15064	−0.0615045
$351$	−4.06418	−0.216930
$352$	−9.92396	−0.528949
$353$	12.9436	0.688916	0.344458	−	0.938802i	$-0.388063\pi$
$353$	12.9436	0.688916	0.344458	+	0.938802i	$0.388063\pi$
$354$	−5.84524	−0.310671
$355$	−9.68004	−0.513763
$356$	−2.05737	−0.109040
$357$	−1.03415	−0.0547329
$358$	−3.23854	−0.171162
$359$	11.4466	0.604126	0.302063	−	0.953288i	$-0.402325\pi$
$359$	11.4466	0.604126	0.302063	+	0.953288i	$0.402325\pi$
$360$	−6.41147	−0.337914
$361$	0	0
$362$	−13.4088	−0.704750
$363$	−15.0719	−0.791071
$364$	0.751030	0.0393647
$365$	4.70233	0.246131
$366$	−21.3405	−1.11549
$367$	−28.6013	−1.49298	−0.746488	−	0.665398i	$-0.768262\pi$
$367$	−28.6013	−1.49298	−0.746488	+	0.665398i	$0.768262\pi$
$368$	−13.9135	−0.725293
$369$	−8.47565	−0.441225
$370$	23.6878	1.23147
$371$	−5.26857	−0.273531
$372$	−3.43107	−0.177893
$373$	−12.5662	−0.650655	−0.325328	−	0.945601i	$-0.605475\pi$
$373$	−12.5662	−0.650655	−0.325328	+	0.945601i	$0.605475\pi$
$374$	15.2044	0.786200
$375$	−9.08647	−0.469223
$376$	19.1411	0.987129
$377$	6.54664	0.337169
$378$	0.815207	0.0419297
$379$	−2.19934	−0.112973	−0.0564863	−	0.998403i	$-0.517990\pi$
$379$	−2.19934	−0.112973	−0.0564863	+	0.998403i	$0.517990\pi$
$380$	0	0
$381$	−1.82976	−0.0937412
$382$	29.2199	1.49502
$383$	−5.92808	−0.302911	−0.151455	−	0.988464i	$-0.548396\pi$
$383$	−5.92808	−0.302911	−0.151455	+	0.988464i	$0.548396\pi$
$384$	13.3405	0.680779
$385$	6.87939	0.350606
$386$	36.5185	1.85874
$387$	−0.177052	−0.00900005
$388$	−2.36184	−0.119904
$389$	−33.1189	−1.67919	−0.839596	−	0.543211i	$-0.817208\pi$
$389$	−33.1189	−1.67919	−0.839596	+	0.543211i	$0.817208\pi$
$390$	−15.7665	−0.798368
$391$	5.91210	0.298988
$392$	−17.0077	−0.859021
$393$	8.78611	0.443201
$394$	6.72462	0.338782
$395$	−26.6313	−1.33997
$396$	−1.77332	−0.0891126
$397$	−26.0496	−1.30739	−0.653697	−	0.756757i	$-0.726783\pi$
$397$	−26.0496	−1.30739	−0.653697	+	0.756757i	$0.726783\pi$
$398$	30.6996	1.53883
$399$	0	0
$400$	−6.45605	−0.322803
$401$	−15.9682	−0.797415	−0.398707	−	0.917078i	$-0.630541\pi$
$401$	−15.9682	−0.797415	−0.398707	+	0.917078i	$0.630541\pi$
$402$	−15.6459	−0.780346
$403$	40.1516	2.00009
$404$	−3.04189	−0.151340
$405$	−2.53209	−0.125821
$406$	−1.31315	−0.0651704
$407$	−31.1780	−1.54544
$408$	−4.92127	−0.243639
$409$	−2.94862	−0.145800	−0.0728998	−	0.997339i	$-0.523225\pi$
$409$	−2.94862	−0.145800	−0.0728998	+	0.997339i	$0.523225\pi$
$410$	−32.8803	−1.62384
$411$	12.6304	0.623012
$412$	−1.33544	−0.0657922
$413$	−2.03003	−0.0998912
$414$	−4.66044	−0.229048
$415$	29.0574	1.42637
$416$	7.89899	0.387280
$417$	4.04963	0.198311
$418$	0	0
$419$	−33.4962	−1.63640	−0.818198	−	0.574937i	$-0.805027\pi$
$419$	−33.4962	−1.63640	−0.818198	+	0.574937i	$0.805027\pi$
$420$	0.467911	0.0228317
$421$	18.0178	0.878136	0.439068	−	0.898454i	$-0.355309\pi$
$421$	18.0178	0.878136	0.439068	+	0.898454i	$0.355309\pi$
$422$	−41.6614	−2.02804
$423$	7.55943	0.367552
$424$	−25.0719	−1.21760
$425$	2.74329	0.133069
$426$	5.85710	0.283777
$427$	−7.41147	−0.358666
$428$	−1.97090	−0.0952672
$429$	20.7520	1.00191
$430$	−0.686852	−0.0331229
$431$	21.3209	1.02699	0.513496	−	0.858092i	$-0.328350\pi$
$431$	21.3209	1.02699	0.513496	+	0.858092i	$0.328350\pi$
$432$	4.57398	0.220066
$433$	−22.0523	−1.05977	−0.529883	−	0.848071i	$-0.677764\pi$
$433$	−22.0523	−1.05977	−0.529883	+	0.848071i	$0.677764\pi$
$434$	−8.05375	−0.386592
$435$	4.07873	0.195560
$436$	−0.724622	−0.0347031
$437$	0	0
$438$	−2.84524	−0.135951
$439$	−3.38682	−0.161644	−0.0808221	−	0.996729i	$-0.525755\pi$
$439$	−3.38682	−0.161644	−0.0808221	+	0.996729i	$0.525755\pi$
$440$	32.7374	1.56070
$441$	−6.71688	−0.319851
$442$	−12.1019	−0.575631
$443$	−30.1644	−1.43315	−0.716576	−	0.697509i	$-0.754292\pi$
$443$	−30.1644	−1.43315	−0.716576	+	0.697509i	$0.754292\pi$
$444$	−2.12061	−0.100640
$445$	15.0000	0.711068
$446$	18.4047	0.871486
$447$	−6.06923	−0.287065
$448$	3.28312	0.155113
$449$	−30.9118	−1.45882	−0.729409	−	0.684078i	$-0.760205\pi$
$449$	−30.9118	−1.45882	−0.729409	+	0.684078i	$0.760205\pi$
$450$	−2.16250	−0.101941
$451$	43.2772	2.03785
$452$	2.52704	0.118862
$453$	0.162504	0.00763510
$454$	−6.65002	−0.312101
$455$	−5.47565	−0.256703
$456$	0	0
$457$	−39.0479	−1.82658	−0.913291	−	0.407307i	$-0.866468\pi$
$457$	−39.0479	−1.82658	−0.913291	+	0.407307i	$0.866468\pi$
$458$	−5.04963	−0.235954
$459$	−1.94356	−0.0907178
$460$	−2.67499	−0.124722
$461$	−1.50744	−0.0702083	−0.0351041	−	0.999384i	$-0.511176\pi$
$461$	−1.50744	−0.0702083	−0.0351041	+	0.999384i	$0.511176\pi$
$462$	−4.16250	−0.193657
$463$	−3.28312	−0.152579	−0.0762897	−	0.997086i	$-0.524307\pi$
$463$	−3.28312	−0.152579	−0.0762897	+	0.997086i	$0.524307\pi$
$464$	−7.36783	−0.342043
$465$	25.0155	1.16007
$466$	23.6418	1.09518
$467$	−22.8871	−1.05909	−0.529545	−	0.848282i	$-0.677637\pi$
$467$	−22.8871	−1.05909	−0.529545	+	0.848282i	$0.677637\pi$
$468$	1.41147	0.0652454
$469$	−5.43376	−0.250908
$470$	29.3259	1.35270
$471$	−6.66044	−0.306897
$472$	−9.66044	−0.444658
$473$	0.904038	0.0415677
$474$	16.1138	0.740132
$475$	0	0
$476$	0.359156	0.0164619
$477$	−9.90167	−0.453367
$478$	−24.2422	−1.10881
$479$	−9.65776	−0.441274	−0.220637	−	0.975356i	$-0.570814\pi$
$479$	−9.65776	−0.441274	−0.220637	+	0.975356i	$0.570814\pi$
$480$	4.92127	0.224624
$481$	24.8161	1.13152
$482$	36.2276	1.65012
$483$	−1.61856	−0.0736468
$484$	5.23442	0.237928
$485$	17.2199	0.781914
$486$	1.53209	0.0694970
$487$	−22.5107	−1.02006	−0.510029	−	0.860157i	$-0.670365\pi$
$487$	−22.5107	−1.02006	−0.510029	+	0.860157i	$0.670365\pi$
$488$	−35.2695	−1.59658
$489$	0.448311	0.0202733
$490$	−26.0574	−1.17715
$491$	7.27126	0.328147	0.164074	−	0.986448i	$-0.447537\pi$
$491$	7.27126	0.328147	0.164074	+	0.986448i	$0.447537\pi$
$492$	2.94356	0.132706
$493$	3.13072	0.141001
$494$	0	0
$495$	12.9290	0.581116
$496$	−45.1881	−2.02901
$497$	2.03415	0.0912440
$498$	−17.5817	−0.787856
$499$	−12.8111	−0.573503	−0.286752	−	0.958005i	$-0.592575\pi$
$499$	−12.8111	−0.573503	−0.286752	+	0.958005i	$0.592575\pi$
$500$	3.15570	0.141127
$501$	−3.38919	−0.151418
$502$	−29.7401	−1.32737
$503$	8.37052	0.373223	0.186611	−	0.982434i	$-0.440249\pi$
$503$	8.37052	0.373223	0.186611	+	0.982434i	$0.440249\pi$
$504$	1.34730	0.0600133
$505$	22.1780	0.986907
$506$	23.7965	1.05789
$507$	−3.51754	−0.156219
$508$	0.635467	0.0281943
$509$	13.6827	0.606476	0.303238	−	0.952915i	$-0.401932\pi$
$509$	13.6827	0.606476	0.303238	+	0.952915i	$0.401932\pi$
$510$	−7.53983	−0.333869
$511$	−0.988140	−0.0437128
$512$	14.2736	0.630811
$513$	0	0
$514$	−18.8384	−0.830928
$515$	9.73648	0.429041
$516$	0.0614894	0.00270692
$517$	−38.5990	−1.69758
$518$	−4.97771	−0.218708
$519$	1.61587	0.0709287
$520$	−26.0574	−1.14269
$521$	−16.9641	−0.743211	−0.371605	−	0.928391i	$-0.621193\pi$
$521$	−16.9641	−0.743211	−0.371605	+	0.928391i	$0.621193\pi$
$522$	−2.46791	−0.108018
$523$	−3.90673	−0.170829	−0.0854146	−	0.996345i	$-0.527221\pi$
$523$	−3.90673	−0.170829	−0.0854146	+	0.996345i	$0.527221\pi$
$524$	−3.05138	−0.133300
$525$	−0.751030	−0.0327776
$526$	−9.71419	−0.423559
$527$	19.2012	0.836418
$528$	−23.3550	−1.01640
$529$	−13.7469	−0.597692
$530$	−38.4124	−1.66853
$531$	−3.81521	−0.165566
$532$	0	0
$533$	−34.4466	−1.49205
$534$	−9.07604	−0.392759
$535$	14.3696	0.621251
$536$	−25.8580	−1.11690
$537$	−2.11381	−0.0912175
$538$	3.56212	0.153574
$539$	34.2968	1.47727
$540$	0.879385	0.0378427
$541$	13.1976	0.567409	0.283704	−	0.958912i	$-0.408437\pi$
$541$	13.1976	0.567409	0.283704	+	0.958912i	$0.408437\pi$
$542$	−22.8949	−0.983419
$543$	−8.75196	−0.375583
$544$	3.77744	0.161956
$545$	5.28312	0.226304
$546$	3.31315	0.141790
$547$	−31.5749	−1.35005	−0.675023	−	0.737797i	$-0.735866\pi$
$547$	−31.5749	−1.35005	−0.675023	+	0.737797i	$0.735866\pi$
$548$	−4.38650	−0.187382
$549$	−13.9290	−0.594476
$550$	11.0419	0.470828
$551$	0	0
$552$	−7.70233	−0.327833
$553$	5.59627	0.237977
$554$	36.7178	1.55999
$555$	15.4611	0.656287
$556$	−1.40642	−0.0596456
$557$	35.6323	1.50979	0.754894	−	0.655847i	$-0.227688\pi$
$557$	35.6323	1.50979	0.754894	+	0.655847i	$0.227688\pi$
$558$	−15.1361	−0.640762
$559$	−0.719570	−0.0304346
$560$	6.16250	0.260413
$561$	9.92396	0.418990
$562$	−39.1607	−1.65190
$563$	−21.9914	−0.926829	−0.463414	−	0.886142i	$-0.653376\pi$
$563$	−21.9914	−0.926829	−0.463414	+	0.886142i	$0.653376\pi$
$564$	−2.62536	−0.110548
$565$	−18.4243	−0.775115
$566$	11.5071	0.483680
$567$	0.532089	0.0223456
$568$	9.68004	0.406166
$569$	28.7588	1.20563	0.602815	−	0.797881i	$-0.294046\pi$
$569$	28.7588	1.20563	0.602815	+	0.797881i	$0.294046\pi$
$570$	0	0
$571$	7.30365	0.305648	0.152824	−	0.988253i	$-0.451163\pi$
$571$	7.30365	0.305648	0.152824	+	0.988253i	$0.451163\pi$
$572$	−7.20708	−0.301343
$573$	19.0719	0.796741
$574$	6.90941	0.288393
$575$	4.29355	0.179053
$576$	6.17024	0.257094
$577$	31.5090	1.31174	0.655868	−	0.754876i	$-0.272303\pi$
$577$	31.5090	1.31174	0.655868	+	0.754876i	$0.272303\pi$
$578$	20.2581	0.842628
$579$	23.8357	0.990580
$580$	−1.41653	−0.0588181
$581$	−6.10607	−0.253322
$582$	−10.4192	−0.431890
$583$	50.5586	2.09392
$584$	−4.70233	−0.194584
$585$	−10.2909	−0.425475
$586$	−22.6236	−0.934573
$587$	27.2891	1.12634	0.563171	−	0.826340i	$-0.309581\pi$
$587$	27.2891	1.12634	0.563171	+	0.826340i	$0.309581\pi$
$588$	2.33275	0.0962009
$589$	0	0
$590$	−14.8007	−0.609334
$591$	4.38919	0.180547
$592$	−27.9290	−1.14788
$593$	34.7716	1.42790	0.713948	−	0.700198i	$-0.246905\pi$
$593$	34.7716	1.42790	0.713948	+	0.700198i	$0.246905\pi$
$594$	−7.82295	−0.320979
$595$	−2.61856	−0.107350
$596$	2.10782	0.0863397
$597$	20.0378	0.820091
$598$	−18.9409	−0.774550
$599$	15.8990	0.649615	0.324807	−	0.945780i	$-0.394700\pi$
$599$	15.8990	0.649615	0.324807	+	0.945780i	$0.394700\pi$
$600$	−3.57398	−0.145907
$601$	−24.6928	−1.00724	−0.503621	−	0.863925i	$-0.667999\pi$
$601$	−24.6928	−1.00724	−0.503621	+	0.863925i	$0.667999\pi$
$602$	0.144334	0.00588261
$603$	−10.2121	−0.415870
$604$	−0.0564370	−0.00229639
$605$	−38.1634	−1.55156
$606$	−13.4192	−0.545118
$607$	4.01455	0.162945	0.0814727	−	0.996676i	$-0.474038\pi$
$607$	4.01455	0.162945	0.0814727	+	0.996676i	$0.474038\pi$
$608$	0	0
$609$	−0.857097	−0.0347313
$610$	−54.0360	−2.18785
$611$	30.7229	1.24291
$612$	0.674992	0.0272849
$613$	−40.2172	−1.62436	−0.812178	−	0.583409i	$-0.801718\pi$
$613$	−40.2172	−1.62436	−0.812178	+	0.583409i	$0.801718\pi$
$614$	−8.44562	−0.340838
$615$	−21.4611	−0.865395
$616$	−6.87939	−0.277178
$617$	−22.1803	−0.892947	−0.446474	−	0.894797i	$-0.647320\pi$
$617$	−22.1803	−0.892947	−0.446474	+	0.894797i	$0.647320\pi$
$618$	−5.89124	−0.236981
$619$	−23.2354	−0.933908	−0.466954	−	0.884282i	$-0.654649\pi$
$619$	−23.2354	−0.933908	−0.466954	+	0.884282i	$0.654649\pi$
$620$	−8.68779	−0.348910
$621$	−3.04189	−0.122067
$622$	−26.6578	−1.06888
$623$	−3.15207	−0.126285
$624$	18.5895	0.744174
$625$	−30.0651	−1.20260
$626$	−24.4270	−0.976298
$627$	0	0
$628$	2.31315	0.0923047
$629$	11.8675	0.473189
$630$	2.06418	0.0822388
$631$	28.0523	1.11675	0.558373	−	0.829590i	$-0.311426\pi$
$631$	28.0523	1.11675	0.558373	+	0.829590i	$0.311426\pi$
$632$	26.6313	1.05934
$633$	−27.1925	−1.08081
$634$	−3.02372	−0.120087
$635$	−4.63310	−0.183859
$636$	3.43882	0.136358
$637$	−27.2986	−1.08161
$638$	12.6013	0.498891
$639$	3.82295	0.151233
$640$	33.7793	1.33524
$641$	43.4789	1.71732	0.858658	−	0.512550i	$-0.171299\pi$
$641$	43.4789	1.71732	0.858658	+	0.512550i	$0.171299\pi$
$642$	−8.69459	−0.343148
$643$	39.3509	1.55185	0.775924	−	0.630826i	$-0.217284\pi$
$643$	39.3509	1.55185	0.775924	+	0.630826i	$0.217284\pi$
$644$	0.562118	0.0221506
$645$	−0.448311	−0.0176522
$646$	0	0
$647$	18.8862	0.742493	0.371246	−	0.928534i	$-0.378931\pi$
$647$	18.8862	0.742493	0.371246	+	0.928534i	$0.378931\pi$
$648$	2.53209	0.0994698
$649$	19.4807	0.764685
$650$	−8.78880	−0.344725
$651$	−5.25671	−0.206027
$652$	−0.155697	−0.00609755
$653$	−46.7428	−1.82919	−0.914593	−	0.404375i	$-0.867489\pi$
$653$	−46.7428	−1.82919	−0.914593	+	0.404375i	$0.867489\pi$
$654$	−3.19665	−0.124999
$655$	22.2472	0.869271
$656$	38.7674	1.51361
$657$	−1.85710	−0.0724522
$658$	−6.16250	−0.240239
$659$	2.08915	0.0813819	0.0406910	−	0.999172i	$-0.487044\pi$
$659$	2.08915	0.0813819	0.0406910	+	0.999172i	$0.487044\pi$
$660$	−4.49020	−0.174781
$661$	−12.4483	−0.484183	−0.242092	−	0.970253i	$-0.577833\pi$
$661$	−12.4483	−0.484183	−0.242092	+	0.970253i	$0.577833\pi$
$662$	1.28312	0.0498698
$663$	−7.89899	−0.306771
$664$	−29.0574	−1.12764
$665$	0	0
$666$	−9.35504	−0.362500
$667$	4.89992	0.189726
$668$	1.17705	0.0455415
$669$	12.0128	0.464441
$670$	−39.6168	−1.53053
$671$	71.1225	2.74565
$672$	−1.03415	−0.0398931
$673$	−10.8212	−0.417126	−0.208563	−	0.978009i	$-0.566879\pi$
$673$	−10.8212	−0.417126	−0.208563	+	0.978009i	$0.566879\pi$
$674$	5.09833	0.196380
$675$	−1.41147	−0.0543277
$676$	1.22163	0.0469857
$677$	4.36184	0.167639	0.0838196	−	0.996481i	$-0.473288\pi$
$677$	4.36184	0.167639	0.0838196	+	0.996481i	$0.473288\pi$
$678$	11.1480	0.428135
$679$	−3.61856	−0.138867
$680$	−12.4611	−0.477862
$681$	−4.34049	−0.166328
$682$	77.2859	2.95943
$683$	−44.6441	−1.70826	−0.854130	−	0.520059i	$-0.825910\pi$
$683$	−44.6441	−1.70826	−0.854130	+	0.520059i	$0.825910\pi$
$684$	0	0
$685$	31.9813	1.22194
$686$	11.1821	0.426935
$687$	−3.29591	−0.125747
$688$	0.809831	0.0308745
$689$	−40.2422	−1.53310
$690$	−11.8007	−0.449243
$691$	24.3209	0.925210	0.462605	−	0.886564i	$-0.346915\pi$
$691$	24.3209	0.925210	0.462605	+	0.886564i	$0.346915\pi$
$692$	−0.561185	−0.0213330
$693$	−2.71688	−0.103206
$694$	−6.14022	−0.233079
$695$	10.2540	0.388957
$696$	−4.07873	−0.154604
$697$	−16.4730	−0.623958
$698$	42.7493	1.61808
$699$	15.4311	0.583657
$700$	0.260830	0.00985844
$701$	−23.5594	−0.889827	−0.444914	−	0.895573i	$-0.646766\pi$
$701$	−23.5594	−0.889827	−0.444914	+	0.895573i	$0.646766\pi$
$702$	6.22668	0.235011
$703$	0	0
$704$	−31.5057	−1.18742
$705$	19.1411	0.720897
$706$	−19.8307	−0.746338
$707$	−4.66044	−0.175274
$708$	1.32501	0.0497968
$709$	−6.15333	−0.231093	−0.115547	−	0.993302i	$-0.536862\pi$
$709$	−6.15333	−0.231093	−0.115547	+	0.993302i	$0.536862\pi$
$710$	14.8307	0.556586
$711$	10.5175	0.394439
$712$	−15.0000	−0.562149
$713$	30.0520	1.12546
$714$	1.58441	0.0592949
$715$	52.5458	1.96510
$716$	0.734118	0.0274353
$717$	−15.8229	−0.590919
$718$	−17.5371	−0.654480
$719$	32.5749	1.21484	0.607420	−	0.794381i	$-0.292205\pi$
$719$	32.5749	1.21484	0.607420	+	0.794381i	$0.292205\pi$
$720$	11.5817	0.431625
$721$	−2.04601	−0.0761973
$722$	0	0
$723$	23.6459	0.879400
$724$	3.03952	0.112963
$725$	2.27362	0.0844402
$726$	23.0915	0.857007
$727$	32.2300	1.19534	0.597672	−	0.801741i	$-0.296093\pi$
$727$	32.2300	1.19534	0.597672	+	0.801741i	$0.296093\pi$
$728$	5.47565	0.202941
$729$	1.00000	0.0370370
$730$	−7.20439	−0.266647
$731$	−0.344111	−0.0127274
$732$	4.83750	0.178799
$733$	9.78106	0.361272	0.180636	−	0.983550i	$-0.442184\pi$
$733$	9.78106	0.361272	0.180636	+	0.983550i	$0.442184\pi$
$734$	43.8198	1.61742
$735$	−17.0077	−0.627340
$736$	5.91210	0.217923
$737$	52.1438	1.92074
$738$	12.9855	0.478001
$739$	27.7743	1.02169	0.510846	−	0.859672i	$-0.329332\pi$
$739$	27.7743	1.02169	0.510846	+	0.859672i	$0.329332\pi$
$740$	−5.36959	−0.197390
$741$	0	0
$742$	8.07192	0.296329
$743$	−32.3022	−1.18505	−0.592527	−	0.805551i	$-0.701870\pi$
$743$	−32.3022	−1.18505	−0.592527	+	0.805551i	$0.701870\pi$
$744$	−25.0155	−0.917112
$745$	−15.3678	−0.563034
$746$	19.2526	0.704887
$747$	−11.4757	−0.419872
$748$	−3.44656	−0.126019
$749$	−3.01960	−0.110334
$750$	13.9213	0.508333
$751$	3.48515	0.127175	0.0635874	−	0.997976i	$-0.479746\pi$
$751$	3.48515	0.127175	0.0635874	+	0.997976i	$0.479746\pi$
$752$	−34.5767	−1.26088
$753$	−19.4115	−0.707393
$754$	−10.0300	−0.365272
$755$	0.411474	0.0149751
$756$	−0.184793	−0.00672084
$757$	−36.9341	−1.34239	−0.671196	−	0.741280i	$-0.734219\pi$
$757$	−36.9341	−1.34239	−0.671196	+	0.741280i	$0.734219\pi$
$758$	3.36959	0.122389
$759$	15.5321	0.563779
$760$	0	0
$761$	31.3429	1.13618	0.568089	−	0.822967i	$-0.307683\pi$
$761$	31.3429	1.13618	0.568089	+	0.822967i	$0.307683\pi$
$762$	2.80335	0.101555
$763$	−1.11019	−0.0401914
$764$	−6.62361	−0.239634
$765$	−4.92127	−0.177929
$766$	9.08235	0.328159
$767$	−15.5057	−0.559878
$768$	−8.09833	−0.292223
$769$	−31.7425	−1.14466	−0.572331	−	0.820022i	$-0.693961\pi$
$769$	−31.7425	−1.14466	−0.572331	+	0.820022i	$0.693961\pi$
$770$	−10.5398	−0.379829
$771$	−12.2959	−0.442826
$772$	−8.27807	−0.297934
$773$	10.9572	0.394102	0.197051	−	0.980393i	$-0.436863\pi$
$773$	10.9572	0.394102	0.197051	+	0.980393i	$0.436863\pi$
$774$	0.271259	0.00975020
$775$	13.9445	0.500901
$776$	−17.2199	−0.618157
$777$	−3.24897	−0.116556
$778$	50.7410	1.81915
$779$	0	0
$780$	3.57398	0.127969
$781$	−19.5202	−0.698489
$782$	−9.05787	−0.323909
$783$	−1.61081	−0.0575658
$784$	30.7229	1.09725
$785$	−16.8648	−0.601932
$786$	−13.4611	−0.480142
$787$	46.3542	1.65235	0.826175	−	0.563414i	$-0.190512\pi$
$787$	46.3542	1.65235	0.826175	+	0.563414i	$0.190512\pi$
$788$	−1.52435	−0.0543027
$789$	−6.34049	−0.225727
$790$	40.8016	1.45166
$791$	3.87164	0.137660
$792$	−12.9290	−0.459413
$793$	−56.6100	−2.01028
$794$	39.9103	1.41637
$795$	−25.0719	−0.889209
$796$	−6.95904	−0.246657
$797$	−3.47296	−0.123019	−0.0615093	−	0.998107i	$-0.519591\pi$
$797$	−3.47296	−0.123019	−0.0615093	+	0.998107i	$0.519591\pi$
$798$	0	0
$799$	14.6922	0.519774
$800$	2.74329	0.0969899
$801$	−5.92396	−0.209313
$802$	24.4647	0.863880
$803$	9.48246	0.334629
$804$	3.54664	0.125080
$805$	−4.09833	−0.144447
$806$	−61.5158	−2.16680
$807$	2.32501	0.0818441
$808$	−22.1780	−0.780219
$809$	−51.9495	−1.82645	−0.913224	−	0.407457i	$-0.866416\pi$
$809$	−51.9495	−1.82645	−0.913224	+	0.407457i	$0.866416\pi$
$810$	3.87939	0.136308
$811$	16.7769	0.589118	0.294559	−	0.955633i	$-0.404827\pi$
$811$	16.7769	0.589118	0.294559	+	0.955633i	$0.404827\pi$
$812$	0.297667	0.0104460
$813$	−14.9436	−0.524094
$814$	47.7674	1.67425
$815$	1.13516	0.0397630
$816$	8.88981	0.311206
$817$	0	0
$818$	4.51754	0.157952
$819$	2.16250	0.0755640
$820$	7.45336	0.260283
$821$	−37.2472	−1.29994	−0.649968	−	0.759961i	$-0.725218\pi$
$821$	−37.2472	−1.29994	−0.649968	+	0.759961i	$0.725218\pi$
$822$	−19.3509	−0.674941
$823$	−4.39961	−0.153361	−0.0766805	−	0.997056i	$-0.524432\pi$
$823$	−4.39961	−0.153361	−0.0766805	+	0.997056i	$0.524432\pi$
$824$	−9.73648	−0.339186
$825$	7.20708	0.250918
$826$	3.11019	0.108217
$827$	−13.8625	−0.482045	−0.241023	−	0.970519i	$-0.577483\pi$
$827$	−13.8625	−0.482045	−0.241023	+	0.970519i	$0.577483\pi$
$828$	1.05644	0.0367137
$829$	16.3770	0.568797	0.284398	−	0.958706i	$-0.408206\pi$
$829$	16.3770	0.568797	0.284398	+	0.958706i	$0.408206\pi$
$830$	−44.5185	−1.54526
$831$	23.9659	0.831366
$832$	25.0770	0.869388
$833$	−13.0547	−0.452318
$834$	−6.20439	−0.214841
$835$	−8.58172	−0.296983
$836$	0	0
$837$	−9.87939	−0.341482
$838$	51.3191	1.77279
$839$	−38.2891	−1.32189	−0.660943	−	0.750436i	$-0.729844\pi$
$839$	−38.2891	−1.32189	−0.660943	+	0.750436i	$0.729844\pi$
$840$	3.41147	0.117707
$841$	−26.4053	−0.910527
$842$	−27.6049	−0.951329
$843$	−25.5604	−0.880346
$844$	9.44387	0.325071
$845$	−8.90673	−0.306401
$846$	−11.5817	−0.398188
$847$	8.01960	0.275557
$848$	45.2900	1.55527
$849$	7.51073	0.257768
$850$	−4.20296	−0.144160
$851$	18.5740	0.636708
$852$	−1.32770	−0.0454861
$853$	22.0901	0.756350	0.378175	−	0.925734i	$-0.376552\pi$
$853$	22.0901	0.756350	0.378175	+	0.925734i	$0.376552\pi$
$854$	11.3550	0.388561
$855$	0	0
$856$	−14.3696	−0.491142
$857$	45.0077	1.53744	0.768718	−	0.639588i	$-0.220895\pi$
$857$	45.0077	1.53744	0.768718	+	0.639588i	$0.220895\pi$
$858$	−31.7939	−1.08542
$859$	−15.9727	−0.544980	−0.272490	−	0.962159i	$-0.587847\pi$
$859$	−15.9727	−0.544980	−0.272490	+	0.962159i	$0.587847\pi$
$860$	0.155697	0.00530921
$861$	4.50980	0.153694
$862$	−32.6655	−1.11259
$863$	41.2576	1.40443	0.702213	−	0.711967i	$-0.252195\pi$
$863$	41.2576	1.40443	0.702213	+	0.711967i	$0.252195\pi$
$864$	−1.94356	−0.0661214
$865$	4.09152	0.139116
$866$	33.7861	1.14810
$867$	13.2226	0.449062
$868$	1.82564	0.0619661
$869$	−53.7033	−1.82176
$870$	−6.24897	−0.211860
$871$	−41.5039	−1.40631
$872$	−5.28312	−0.178909
$873$	−6.80066	−0.230167
$874$	0	0
$875$	4.83481	0.163446
$876$	0.644963	0.0217913
$877$	46.1652	1.55889	0.779444	−	0.626472i	$-0.215502\pi$
$877$	46.1652	1.55889	0.779444	+	0.626472i	$0.215502\pi$
$878$	5.18891	0.175117
$879$	−14.7665	−0.498062
$880$	−59.1370	−1.99351
$881$	18.9581	0.638715	0.319357	−	0.947634i	$-0.396533\pi$
$881$	18.9581	0.638715	0.319357	+	0.947634i	$0.396533\pi$
$882$	10.2909	0.346511
$883$	35.0496	1.17951	0.589757	−	0.807581i	$-0.299224\pi$
$883$	35.0496	1.17951	0.589757	+	0.807581i	$0.299224\pi$
$884$	2.74329	0.0922668
$885$	−9.66044	−0.324732
$886$	46.2145	1.55261
$887$	−17.8375	−0.598925	−0.299462	−	0.954108i	$-0.596807\pi$
$887$	−17.8375	−0.598925	−0.299462	+	0.954108i	$0.596807\pi$
$888$	−15.4611	−0.518841
$889$	0.973593	0.0326532
$890$	−22.9813	−0.770336
$891$	−5.10607	−0.171060
$892$	−4.17200	−0.139689
$893$	0	0
$894$	9.29860	0.310992
$895$	−5.35235	−0.178909
$896$	−7.09833	−0.237138
$897$	−12.3628	−0.412781
$898$	47.3596	1.58041
$899$	15.9139	0.530757
$900$	0.490200	0.0163400
$901$	−19.2445	−0.641128
$902$	−66.3046	−2.20770
$903$	0.0942073	0.00313502
$904$	18.4243	0.612782
$905$	−22.1607	−0.736648
$906$	−0.248970	−0.00827148
$907$	−14.2513	−0.473208	−0.236604	−	0.971606i	$-0.576034\pi$
$907$	−14.2513	−0.473208	−0.236604	+	0.971606i	$0.576034\pi$
$908$	1.50744	0.0500260
$909$	−8.75877	−0.290510
$910$	8.38919	0.278099
$911$	−16.4466	−0.544899	−0.272449	−	0.962170i	$-0.587834\pi$
$911$	−16.4466	−0.544899	−0.272449	+	0.962170i	$0.587834\pi$
$912$	0	0
$913$	58.5954	1.93923
$914$	59.8248	1.97883
$915$	−35.2695	−1.16597
$916$	1.14466	0.0378206
$917$	−4.67499	−0.154382
$918$	2.97771	0.0982791
$919$	−33.8999	−1.11826	−0.559128	−	0.829082i	$-0.688864\pi$
$919$	−33.8999	−1.11826	−0.559128	+	0.829082i	$0.688864\pi$
$920$	−19.5030	−0.642995
$921$	−5.51249	−0.181643
$922$	2.30953	0.0760602
$923$	15.5371	0.511411
$924$	0.943563	0.0310409
$925$	8.61856	0.283376
$926$	5.03003	0.165297
$927$	−3.84524	−0.126294
$928$	3.13072	0.102771
$929$	21.5345	0.706522	0.353261	−	0.935525i	$-0.385073\pi$
$929$	21.5345	0.706522	0.353261	+	0.935525i	$0.385073\pi$
$930$	−38.3259	−1.25676
$931$	0	0
$932$	−5.35916	−0.175545
$933$	−17.3996	−0.569638
$934$	35.0651	1.14737
$935$	25.1284	0.821785
$936$	10.2909	0.336367
$937$	7.56624	0.247178	0.123589	−	0.992333i	$-0.460560\pi$
$937$	7.56624	0.247178	0.123589	+	0.992333i	$0.460560\pi$
$938$	8.32501	0.271821
$939$	−15.9436	−0.520299
$940$	−6.64765	−0.216822
$941$	19.1275	0.623540	0.311770	−	0.950158i	$-0.399078\pi$
$941$	19.1275	0.623540	0.311770	+	0.950158i	$0.399078\pi$
$942$	10.2044	0.332477
$943$	−25.7820	−0.839577
$944$	17.4507	0.567971
$945$	1.34730	0.0438276
$946$	−1.38507	−0.0450324
$947$	60.2072	1.95647	0.978235	−	0.207498i	$-0.0665320\pi$
$947$	60.2072	1.95647	0.978235	+	0.207498i	$0.0665320\pi$
$948$	−3.65270	−0.118634
$949$	−7.54757	−0.245005
$950$	0	0
$951$	−1.97359	−0.0639981
$952$	2.61856	0.0848679
$953$	−19.7478	−0.639695	−0.319848	−	0.947469i	$-0.603632\pi$
$953$	−19.7478	−0.639695	−0.319848	+	0.947469i	$0.603632\pi$
$954$	15.1702	0.491155
$955$	48.2918	1.56269
$956$	5.49525	0.177729
$957$	8.22493	0.265874
$958$	14.7965	0.478055
$959$	−6.72050	−0.217016
$960$	15.6236	0.504250
$961$	66.6023	2.14846
$962$	−38.0205	−1.22583
$963$	−5.67499	−0.182874
$964$	−8.21213	−0.264495
$965$	60.3542	1.94287
$966$	2.47977	0.0797853
$967$	−5.16849	−0.166207	−0.0831037	−	0.996541i	$-0.526483\pi$
$967$	−5.16849	−0.166207	−0.0831037	+	0.996541i	$0.526483\pi$
$968$	38.1634	1.22662
$969$	0	0
$970$	−26.3824	−0.847087
$971$	−8.75784	−0.281052	−0.140526	−	0.990077i	$-0.544879\pi$
$971$	−8.75784	−0.281052	−0.140526	+	0.990077i	$0.544879\pi$
$972$	−0.347296	−0.0111395
$973$	−2.15476	−0.0690785
$974$	34.4884	1.10508
$975$	−5.73648	−0.183714
$976$	63.7110	2.03934
$977$	40.7279	1.30300	0.651501	−	0.758648i	$-0.274140\pi$
$977$	40.7279	1.30300	0.651501	+	0.758648i	$0.274140\pi$
$978$	−0.686852	−0.0219631
$979$	30.2481	0.966735
$980$	5.90673	0.188683
$981$	−2.08647	−0.0666157
$982$	−11.1402	−0.355499
$983$	3.95037	0.125997	0.0629986	−	0.998014i	$-0.479934\pi$
$983$	3.95037	0.125997	0.0629986	+	0.998014i	$0.479934\pi$
$984$	21.4611	0.684155
$985$	11.1138	0.354115
$986$	−4.79654	−0.152753
$987$	−4.02229	−0.128031
$988$	0	0
$989$	−0.538572	−0.0171256
$990$	−19.8084	−0.629552
$991$	−18.5621	−0.589645	−0.294823	−	0.955552i	$-0.595261\pi$
$991$	−18.5621	−0.589645	−0.294823	+	0.955552i	$0.595261\pi$
$992$	19.2012	0.609639
$993$	0.837496	0.0265771
$994$	−3.11650	−0.0988492
$995$	50.7374	1.60848
$996$	3.98545	0.126284
$997$	2.73917	0.0867504	0.0433752	−	0.999059i	$-0.486189\pi$
$997$	2.73917	0.0867504	0.0433752	+	0.999059i	$0.486189\pi$
$998$	19.6277	0.621305
$999$	−6.10607	−0.193187

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1083.2.a.m.1.1		3
3.2	odd	2		3249.2.a.w.1.3		3
19.9	even	9		57.2.i.a.43.1	yes	6
19.17	even	9		57.2.i.a.4.1	✓	6
19.18	odd	2		1083.2.a.n.1.3		3
57.17	odd	18		171.2.u.a.118.1		6
57.47	odd	18		171.2.u.a.100.1		6
57.56	even	2		3249.2.a.x.1.1		3
76.47	odd	18		912.2.bo.b.385.1		6
76.55	odd	18		912.2.bo.b.289.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.i.a.4.1	✓	6	19.17	even	9
57.2.i.a.43.1	yes	6	19.9	even	9
171.2.u.a.100.1		6	57.47	odd	18
171.2.u.a.118.1		6	57.17	odd	18
912.2.bo.b.289.1		6	76.55	odd	18
912.2.bo.b.385.1		6	76.47	odd	18
1083.2.a.m.1.1		3	1.1	even	1	trivial
1083.2.a.n.1.3		3	19.18	odd	2
3249.2.a.w.1.3		3	3.2	odd	2
3249.2.a.x.1.1		3	57.56	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1083 = 3 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1083.a (trivial)

\(f(q)\)	\(=\)	\(q-1.53209 q^{2} -1.00000 q^{3} +0.347296 q^{4} -2.53209 q^{5} +1.53209 q^{6} +0.532089 q^{7} +2.53209 q^{8} +1.00000 q^{9} +3.87939 q^{10} -5.10607 q^{11} -0.347296 q^{12} +4.06418 q^{13} -0.815207 q^{14} +2.53209 q^{15} -4.57398 q^{16} +1.94356 q^{17} -1.53209 q^{18} -0.879385 q^{20} -0.532089 q^{21} +7.82295 q^{22} +3.04189 q^{23} -2.53209 q^{24} +1.41147 q^{25} -6.22668 q^{26} -1.00000 q^{27} +0.184793 q^{28} +1.61081 q^{29} -3.87939 q^{30} +9.87939 q^{31} +1.94356 q^{32} +5.10607 q^{33} -2.97771 q^{34} -1.34730 q^{35} +0.347296 q^{36} +6.10607 q^{37} -4.06418 q^{39} -6.41147 q^{40} -8.47565 q^{41} +0.815207 q^{42} -0.177052 q^{43} -1.77332 q^{44} -2.53209 q^{45} -4.66044 q^{46} +7.55943 q^{47} +4.57398 q^{48} -6.71688 q^{49} -2.16250 q^{50} -1.94356 q^{51} +1.41147 q^{52} -9.90167 q^{53} +1.53209 q^{54} +12.9290 q^{55} +1.34730 q^{56} -2.46791 q^{58} -3.81521 q^{59} +0.879385 q^{60} -13.9290 q^{61} -15.1361 q^{62} +0.532089 q^{63} +6.17024 q^{64} -10.2909 q^{65} -7.82295 q^{66} -10.2121 q^{67} +0.674992 q^{68} -3.04189 q^{69} +2.06418 q^{70} +3.82295 q^{71} +2.53209 q^{72} -1.85710 q^{73} -9.35504 q^{74} -1.41147 q^{75} -2.71688 q^{77} +6.22668 q^{78} +10.5175 q^{79} +11.5817 q^{80} +1.00000 q^{81} +12.9855 q^{82} -11.4757 q^{83} -0.184793 q^{84} -4.92127 q^{85} +0.271259 q^{86} -1.61081 q^{87} -12.9290 q^{88} -5.92396 q^{89} +3.87939 q^{90} +2.16250 q^{91} +1.05644 q^{92} -9.87939 q^{93} -11.5817 q^{94} -1.94356 q^{96} -6.80066 q^{97} +10.2909 q^{98} -5.10607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{3} - 3 q^{5} - 3 q^{7} + 3 q^{8} + 3 q^{9} + 6 q^{10} - 3 q^{11} + 3 q^{13} - 6 q^{14} + 3 q^{15} - 6 q^{16} - 9 q^{17} + 3 q^{20} + 3 q^{21} + 3 q^{22} + 6 q^{23} - 3 q^{24} - 6 q^{25} - 12 q^{26}+ \cdots - 3 q^{99}+O(q^{100}) \) 3 * q - 3 * q^3 - 3 * q^5 - 3 * q^7 + 3 * q^8 + 3 * q^9 + 6 * q^10 - 3 * q^11 + 3 * q^13 - 6 * q^14 + 3 * q^15 - 6 * q^16 - 9 * q^17 + 3 * q^20 + 3 * q^21 + 3 * q^22 + 6 * q^23 - 3 * q^24 - 6 * q^25 - 12 * q^26 - 3 * q^27 - 3 * q^28 + 9 * q^29 - 6 * q^30 + 24 * q^31 - 9 * q^32 + 3 * q^33 - 15 * q^34 - 3 * q^35 + 6 * q^37 - 3 * q^39 - 9 * q^40 - 6 * q^41 + 6 * q^42 - 21 * q^43 - 12 * q^44 - 3 * q^45 + 9 * q^46 - 3 * q^47 + 6 * q^48 - 12 * q^49 - 9 * q^50 + 9 * q^51 - 6 * q^52 - 18 * q^53 + 6 * q^55 + 3 * q^56 - 12 * q^58 - 15 * q^59 - 3 * q^60 - 9 * q^61 - 3 * q^62 - 3 * q^63 - 3 * q^64 - 15 * q^65 - 3 * q^66 - 6 * q^67 - 3 * q^68 - 6 * q^69 - 3 * q^70 - 9 * q^71 + 3 * q^72 - 6 * q^73 - 3 * q^74 + 6 * q^75 + 12 * q^78 + 9 * q^79 + 3 * q^80 + 3 * q^81 + 21 * q^82 - 15 * q^83 + 3 * q^84 - 6 * q^85 - 18 * q^86 - 9 * q^87 - 6 * q^88 + 6 * q^90 + 9 * q^91 + 18 * q^92 - 24 * q^93 - 3 * q^94 + 9 * q^96 - 6 * q^97 + 15 * q^98 - 3 * q^99

Introduction

L-functions

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Database

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