LMFDB - Embedded newform 2166.2.a.u.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2166,2,Mod(1,2166)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2166, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2166.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2166 = 2 \cdot 3 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2166.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$17.2955970778$
Analytic rank:	$0$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.87939$ of defining polynomial
Character	$\chi$	$=$	2166.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.41147 q^{5} +1.00000 q^{6} -2.87939 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.41147 q^{5} +1.00000 q^{6} -2.87939 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.41147 q^{10} -0.347296 q^{11} +1.00000 q^{12} +1.65270 q^{13} -2.87939 q^{14} -3.41147 q^{15} +1.00000 q^{16} +6.94356 q^{17} +1.00000 q^{18} -3.41147 q^{20} -2.87939 q^{21} -0.347296 q^{22} +6.80066 q^{23} +1.00000 q^{24} +6.63816 q^{25} +1.65270 q^{26} +1.00000 q^{27} -2.87939 q^{28} -6.35504 q^{29} -3.41147 q^{30} -1.59627 q^{31} +1.00000 q^{32} -0.347296 q^{33} +6.94356 q^{34} +9.82295 q^{35} +1.00000 q^{36} +11.2121 q^{37} +1.65270 q^{39} -3.41147 q^{40} +3.49020 q^{41} -2.87939 q^{42} +2.28312 q^{43} -0.347296 q^{44} -3.41147 q^{45} +6.80066 q^{46} +5.59627 q^{47} +1.00000 q^{48} +1.29086 q^{49} +6.63816 q^{50} +6.94356 q^{51} +1.65270 q^{52} -1.98040 q^{53} +1.00000 q^{54} +1.18479 q^{55} -2.87939 q^{56} -6.35504 q^{58} -0.445622 q^{59} -3.41147 q^{60} -12.5321 q^{61} -1.59627 q^{62} -2.87939 q^{63} +1.00000 q^{64} -5.63816 q^{65} -0.347296 q^{66} +1.07873 q^{67} +6.94356 q^{68} +6.80066 q^{69} +9.82295 q^{70} +16.6236 q^{71} +1.00000 q^{72} +12.4192 q^{73} +11.2121 q^{74} +6.63816 q^{75} +1.00000 q^{77} +1.65270 q^{78} +10.9240 q^{79} -3.41147 q^{80} +1.00000 q^{81} +3.49020 q^{82} +11.7169 q^{83} -2.87939 q^{84} -23.6878 q^{85} +2.28312 q^{86} -6.35504 q^{87} -0.347296 q^{88} -1.79292 q^{89} -3.41147 q^{90} -4.75877 q^{91} +6.80066 q^{92} -1.59627 q^{93} +5.59627 q^{94} +1.00000 q^{96} -3.65270 q^{97} +1.29086 q^{98} -0.347296 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9} + 3 q^{12} + 6 q^{13} - 3 q^{14} + 3 q^{16} + 6 q^{17} + 3 q^{18} - 3 q^{21} + 6 q^{23} + 3 q^{24} + 3 q^{25} + 6 q^{26} + 3 q^{27} - 3 q^{28} + 6 q^{29} + 9 q^{31} + 3 q^{32} + 6 q^{34} + 9 q^{35} + 3 q^{36} + 9 q^{37} + 6 q^{39} + 9 q^{41} - 3 q^{42} + 15 q^{43} + 6 q^{46} + 3 q^{47} + 3 q^{48} - 12 q^{49} + 3 q^{50} + 6 q^{51} + 6 q^{52} - 3 q^{53} + 3 q^{54} - 3 q^{56} + 6 q^{58} - 12 q^{59} - 33 q^{61} + 9 q^{62} - 3 q^{63} + 3 q^{64} + 12 q^{67} + 6 q^{68} + 6 q^{69} + 9 q^{70} + 15 q^{71} + 3 q^{72} + 3 q^{73} + 9 q^{74} + 3 q^{75} + 3 q^{77} + 6 q^{78} + 15 q^{79} + 3 q^{81} + 9 q^{82} + 27 q^{83} - 3 q^{84} - 27 q^{85} + 15 q^{86} + 6 q^{87} - 15 q^{89} - 3 q^{91} + 6 q^{92} + 9 q^{93} + 3 q^{94} + 3 q^{96} - 12 q^{97} - 12 q^{98}+O(q^{100}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9 + 3 * q^12 + 6 * q^13 - 3 * q^14 + 3 * q^16 + 6 * q^17 + 3 * q^18 - 3 * q^21 + 6 * q^23 + 3 * q^24 + 3 * q^25 + 6 * q^26 + 3 * q^27 - 3 * q^28 + 6 * q^29 + 9 * q^31 + 3 * q^32 + 6 * q^34 + 9 * q^35 + 3 * q^36 + 9 * q^37 + 6 * q^39 + 9 * q^41 - 3 * q^42 + 15 * q^43 + 6 * q^46 + 3 * q^47 + 3 * q^48 - 12 * q^49 + 3 * q^50 + 6 * q^51 + 6 * q^52 - 3 * q^53 + 3 * q^54 - 3 * q^56 + 6 * q^58 - 12 * q^59 - 33 * q^61 + 9 * q^62 - 3 * q^63 + 3 * q^64 + 12 * q^67 + 6 * q^68 + 6 * q^69 + 9 * q^70 + 15 * q^71 + 3 * q^72 + 3 * q^73 + 9 * q^74 + 3 * q^75 + 3 * q^77 + 6 * q^78 + 15 * q^79 + 3 * q^81 + 9 * q^82 + 27 * q^83 - 3 * q^84 - 27 * q^85 + 15 * q^86 + 6 * q^87 - 15 * q^89 - 3 * q^91 + 6 * q^92 + 9 * q^93 + 3 * q^94 + 3 * q^96 - 12 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−3.41147	−1.52566	−0.762829	−	0.646601i	$-0.776190\pi$
$5$	−3.41147	−1.52566	−0.762829	+	0.646601i	$0.776190\pi$
$6$	1.00000	0.408248
$7$	−2.87939	−1.08831	−0.544153	−	0.838986i	$-0.683149\pi$
$7$	−2.87939	−1.08831	−0.544153	+	0.838986i	$0.683149\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.41147	−1.07880
$11$	−0.347296	−0.104714	−0.0523569	−	0.998628i	$-0.516673\pi$
$11$	−0.347296	−0.104714	−0.0523569	+	0.998628i	$0.516673\pi$
$12$	1.00000	0.288675
$13$	1.65270	0.458378	0.229189	−	0.973382i	$-0.426393\pi$
$13$	1.65270	0.458378	0.229189	+	0.973382i	$0.426393\pi$
$14$	−2.87939	−0.769548
$15$	−3.41147	−0.880839
$16$	1.00000	0.250000
$17$	6.94356	1.68406	0.842031	−	0.539430i	$-0.181360\pi$
$17$	6.94356	1.68406	0.842031	+	0.539430i	$0.181360\pi$
$18$	1.00000	0.235702
$19$	0	0
$19$	0	0
$20$	−3.41147	−0.762829
$21$	−2.87939	−0.628333
$22$	−0.347296	−0.0740438
$23$	6.80066	1.41804	0.709018	−	0.705191i	$-0.249139\pi$
$23$	6.80066	1.41804	0.709018	+	0.705191i	$0.249139\pi$
$24$	1.00000	0.204124
$25$	6.63816	1.32763
$26$	1.65270	0.324122
$27$	1.00000	0.192450
$28$	−2.87939	−0.544153
$29$	−6.35504	−1.18010	−0.590050	−	0.807366i	$-0.700892\pi$
$29$	−6.35504	−1.18010	−0.590050	+	0.807366i	$0.700892\pi$
$30$	−3.41147	−0.622847
$31$	−1.59627	−0.286698	−0.143349	−	0.989672i	$-0.545787\pi$
$31$	−1.59627	−0.286698	−0.143349	+	0.989672i	$0.545787\pi$
$32$	1.00000	0.176777
$33$	−0.347296	−0.0604565
$34$	6.94356	1.19081
$35$	9.82295	1.66038
$36$	1.00000	0.166667
$37$	11.2121	1.84326	0.921632	−	0.388066i	$-0.126857\pi$
$37$	11.2121	1.84326	0.921632	+	0.388066i	$0.126857\pi$
$38$	0	0
$39$	1.65270	0.264644
$40$	−3.41147	−0.539401
$41$	3.49020	0.545078	0.272539	−	0.962145i	$-0.412137\pi$
$41$	3.49020	0.545078	0.272539	+	0.962145i	$0.412137\pi$
$42$	−2.87939	−0.444299
$43$	2.28312	0.348172	0.174086	−	0.984730i	$-0.444303\pi$
$43$	2.28312	0.348172	0.174086	+	0.984730i	$0.444303\pi$
$44$	−0.347296	−0.0523569
$45$	−3.41147	−0.508553
$46$	6.80066	1.00270
$47$	5.59627	0.816299	0.408150	−	0.912915i	$-0.366174\pi$
$47$	5.59627	0.816299	0.408150	+	0.912915i	$0.366174\pi$
$48$	1.00000	0.144338
$49$	1.29086	0.184408
$50$	6.63816	0.938777
$51$	6.94356	0.972293
$52$	1.65270	0.229189
$53$	−1.98040	−0.272029	−0.136014	−	0.990707i	$-0.543429\pi$
$53$	−1.98040	−0.272029	−0.136014	+	0.990707i	$0.543429\pi$
$54$	1.00000	0.136083
$55$	1.18479	0.159757
$56$	−2.87939	−0.384774
$57$	0	0
$58$	−6.35504	−0.834457
$59$	−0.445622	−0.0580151	−0.0290075	−	0.999579i	$-0.509235\pi$
$59$	−0.445622	−0.0580151	−0.0290075	+	0.999579i	$0.509235\pi$
$60$	−3.41147	−0.440419
$61$	−12.5321	−1.60457	−0.802285	−	0.596941i	$-0.796382\pi$
$61$	−12.5321	−1.60457	−0.802285	+	0.596941i	$0.796382\pi$
$62$	−1.59627	−0.202726
$63$	−2.87939	−0.362768
$64$	1.00000	0.125000
$65$	−5.63816	−0.699327
$66$	−0.347296	−0.0427492
$67$	1.07873	0.131787	0.0658937	−	0.997827i	$-0.479010\pi$
$67$	1.07873	0.131787	0.0658937	+	0.997827i	$0.479010\pi$
$68$	6.94356	0.842031
$69$	6.80066	0.818703
$70$	9.82295	1.17407
$71$	16.6236	1.97286	0.986430	−	0.164185i	$-0.0524993\pi$
$71$	16.6236	1.97286	0.986430	+	0.164185i	$0.0524993\pi$
$72$	1.00000	0.117851
$73$	12.4192	1.45356	0.726780	−	0.686871i	$-0.241016\pi$
$73$	12.4192	1.45356	0.726780	+	0.686871i	$0.241016\pi$
$74$	11.2121	1.30338
$75$	6.63816	0.766508
$76$	0	0
$77$	1.00000	0.113961
$78$	1.65270	0.187132
$79$	10.9240	1.22904	0.614521	−	0.788901i	$-0.289349\pi$
$79$	10.9240	1.22904	0.614521	+	0.788901i	$0.289349\pi$
$80$	−3.41147	−0.381414
$81$	1.00000	0.111111
$82$	3.49020	0.385428
$83$	11.7169	1.28609	0.643047	−	0.765826i	$-0.277670\pi$
$83$	11.7169	1.28609	0.643047	+	0.765826i	$0.277670\pi$
$84$	−2.87939	−0.314167
$85$	−23.6878	−2.56930
$86$	2.28312	0.246195
$87$	−6.35504	−0.681331
$88$	−0.347296	−0.0370219
$89$	−1.79292	−0.190049	−0.0950245	−	0.995475i	$-0.530293\pi$
$89$	−1.79292	−0.190049	−0.0950245	+	0.995475i	$0.530293\pi$
$90$	−3.41147	−0.359601
$91$	−4.75877	−0.498855
$92$	6.80066	0.709018
$93$	−1.59627	−0.165525
$94$	5.59627	0.577211
$95$	0	0
$96$	1.00000	0.102062
$97$	−3.65270	−0.370876	−0.185438	−	0.982656i	$-0.559370\pi$
$97$	−3.65270	−0.370876	−0.185438	+	0.982656i	$0.559370\pi$
$98$	1.29086	0.130396
$99$	−0.347296	−0.0349046
$100$	6.63816	0.663816
$101$	−9.90673	−0.985756	−0.492878	−	0.870098i	$-0.664055\pi$
$101$	−9.90673	−0.985756	−0.492878	+	0.870098i	$0.664055\pi$
$102$	6.94356	0.687515
$103$	−7.84524	−0.773014	−0.386507	−	0.922286i	$-0.626319\pi$
$103$	−7.84524	−0.773014	−0.386507	+	0.922286i	$0.626319\pi$
$104$	1.65270	0.162061
$105$	9.82295	0.958622
$106$	−1.98040	−0.192353
$107$	0.0273411	0.00264317	0.00132158	−	0.999999i	$-0.499579\pi$
$107$	0.0273411	0.00264317	0.00132158	+	0.999999i	$0.499579\pi$
$108$	1.00000	0.0962250
$109$	10.7733	1.03190	0.515948	−	0.856620i	$-0.327440\pi$
$109$	10.7733	1.03190	0.515948	+	0.856620i	$0.327440\pi$
$110$	1.18479	0.112966
$111$	11.2121	1.06421
$112$	−2.87939	−0.272076
$113$	11.6604	1.09692	0.548461	−	0.836176i	$-0.315214\pi$
$113$	11.6604	1.09692	0.548461	+	0.836176i	$0.315214\pi$
$114$	0	0
$115$	−23.2003	−2.16344
$116$	−6.35504	−0.590050
$117$	1.65270	0.152793
$118$	−0.445622	−0.0410229
$119$	−19.9932	−1.83277
$120$	−3.41147	−0.311424
$121$	−10.8794	−0.989035
$122$	−12.5321	−1.13460
$123$	3.49020	0.314701
$124$	−1.59627	−0.143349
$125$	−5.58853	−0.499853
$126$	−2.87939	−0.256516
$127$	−16.2121	−1.43859	−0.719297	−	0.694703i	$-0.755536\pi$
$127$	−16.2121	−1.43859	−0.719297	+	0.694703i	$0.755536\pi$
$128$	1.00000	0.0883883
$129$	2.28312	0.201017
$130$	−5.63816	−0.494499
$131$	−2.80066	−0.244695	−0.122347	−	0.992487i	$-0.539042\pi$
$131$	−2.80066	−0.244695	−0.122347	+	0.992487i	$0.539042\pi$
$132$	−0.347296	−0.0302283
$133$	0	0
$134$	1.07873	0.0931877
$135$	−3.41147	−0.293613
$136$	6.94356	0.595406
$137$	16.0351	1.36997	0.684985	−	0.728557i	$-0.259809\pi$
$137$	16.0351	1.36997	0.684985	+	0.728557i	$0.259809\pi$
$138$	6.80066	0.578911
$139$	−2.07873	−0.176315	−0.0881576	−	0.996107i	$-0.528098\pi$
$139$	−2.07873	−0.176315	−0.0881576	+	0.996107i	$0.528098\pi$
$140$	9.82295	0.830191
$141$	5.59627	0.471291
$142$	16.6236	1.39502
$143$	−0.573978	−0.0479984
$144$	1.00000	0.0833333
$145$	21.6800	1.80043
$146$	12.4192	1.02782
$147$	1.29086	0.106468
$148$	11.2121	0.921632
$149$	−1.66725	−0.136587	−0.0682933	−	0.997665i	$-0.521755\pi$
$149$	−1.66725	−0.136587	−0.0682933	+	0.997665i	$0.521755\pi$
$150$	6.63816	0.542003
$151$	−20.0523	−1.63183	−0.815917	−	0.578169i	$-0.803768\pi$
$151$	−20.0523	−1.63183	−0.815917	+	0.578169i	$0.803768\pi$
$152$	0	0
$153$	6.94356	0.561354
$154$	1.00000	0.0805823
$155$	5.44562	0.437403
$156$	1.65270	0.132322
$157$	−4.09833	−0.327082	−0.163541	−	0.986537i	$-0.552292\pi$
$157$	−4.09833	−0.327082	−0.163541	+	0.986537i	$0.552292\pi$
$158$	10.9240	0.869064
$159$	−1.98040	−0.157056
$160$	−3.41147	−0.269701
$161$	−19.5817	−1.54326
$162$	1.00000	0.0785674
$163$	−8.13516	−0.637195	−0.318598	−	0.947890i	$-0.603212\pi$
$163$	−8.13516	−0.637195	−0.318598	+	0.947890i	$0.603212\pi$
$164$	3.49020	0.272539
$165$	1.18479	0.0922360
$166$	11.7169	0.909406
$167$	13.3969	1.03669	0.518343	−	0.855173i	$-0.326549\pi$
$167$	13.3969	1.03669	0.518343	+	0.855173i	$0.326549\pi$
$168$	−2.87939	−0.222149
$169$	−10.2686	−0.789890
$170$	−23.6878	−1.81677
$171$	0	0
$172$	2.28312	0.174086
$173$	1.02229	0.0777232	0.0388616	−	0.999245i	$-0.487627\pi$
$173$	1.02229	0.0777232	0.0388616	+	0.999245i	$0.487627\pi$
$174$	−6.35504	−0.481774
$175$	−19.1138	−1.44487
$176$	−0.347296	−0.0261784
$177$	−0.445622	−0.0334950
$178$	−1.79292	−0.134385
$179$	−2.03508	−0.152109	−0.0760546	−	0.997104i	$-0.524232\pi$
$179$	−2.03508	−0.152109	−0.0760546	+	0.997104i	$0.524232\pi$
$180$	−3.41147	−0.254276
$181$	−22.3037	−1.65782	−0.828909	−	0.559384i	$-0.811038\pi$
$181$	−22.3037	−1.65782	−0.828909	+	0.559384i	$0.811038\pi$
$182$	−4.75877	−0.352744
$183$	−12.5321	−0.926399
$184$	6.80066	0.501351
$185$	−38.2499	−2.81219
$186$	−1.59627	−0.117044
$187$	−2.41147	−0.176344
$188$	5.59627	0.408150
$189$	−2.87939	−0.209444
$190$	0	0
$191$	10.7861	0.780456	0.390228	−	0.920718i	$-0.372396\pi$
$191$	10.7861	0.780456	0.390228	+	0.920718i	$0.372396\pi$
$192$	1.00000	0.0721688
$193$	2.86484	0.206216	0.103108	−	0.994670i	$-0.467121\pi$
$193$	2.86484	0.206216	0.103108	+	0.994670i	$0.467121\pi$
$194$	−3.65270	−0.262249
$195$	−5.63816	−0.403757
$196$	1.29086	0.0922042
$197$	−8.33544	−0.593875	−0.296938	−	0.954897i	$-0.595965\pi$
$197$	−8.33544	−0.593875	−0.296938	+	0.954897i	$0.595965\pi$
$198$	−0.347296	−0.0246813
$199$	−3.03415	−0.215085	−0.107543	−	0.994200i	$-0.534298\pi$
$199$	−3.03415	−0.215085	−0.107543	+	0.994200i	$0.534298\pi$
$200$	6.63816	0.469388
$201$	1.07873	0.0760874
$202$	−9.90673	−0.697035
$203$	18.2986	1.28431
$204$	6.94356	0.486147
$205$	−11.9067	−0.831602
$206$	−7.84524	−0.546604
$207$	6.80066	0.472679
$208$	1.65270	0.114594
$209$	0	0
$210$	9.82295	0.677848
$211$	16.6382	1.14542	0.572709	−	0.819759i	$-0.305893\pi$
$211$	16.6382	1.14542	0.572709	+	0.819759i	$0.305893\pi$
$212$	−1.98040	−0.136014
$213$	16.6236	1.13903
$214$	0.0273411	0.00186900
$215$	−7.78880	−0.531192
$216$	1.00000	0.0680414
$217$	4.59627	0.312015
$218$	10.7733	0.729661
$219$	12.4192	0.839213
$220$	1.18479	0.0798787
$221$	11.4757	0.771936
$222$	11.2121	0.752509
$223$	8.17024	0.547120	0.273560	−	0.961855i	$-0.411799\pi$
$223$	8.17024	0.547120	0.273560	+	0.961855i	$0.411799\pi$
$224$	−2.87939	−0.192387
$225$	6.63816	0.442544
$226$	11.6604	0.775641
$227$	−1.80066	−0.119514	−0.0597570	−	0.998213i	$-0.519033\pi$
$227$	−1.80066	−0.119514	−0.0597570	+	0.998213i	$0.519033\pi$
$228$	0	0
$229$	−18.7392	−1.23832	−0.619160	−	0.785265i	$-0.712527\pi$
$229$	−18.7392	−1.23832	−0.619160	+	0.785265i	$0.712527\pi$
$230$	−23.2003	−1.52978
$231$	1.00000	0.0657952
$232$	−6.35504	−0.417229
$233$	−4.09833	−0.268490	−0.134245	−	0.990948i	$-0.542861\pi$
$233$	−4.09833	−0.268490	−0.134245	+	0.990948i	$0.542861\pi$
$234$	1.65270	0.108041
$235$	−19.0915	−1.24539
$236$	−0.445622	−0.0290075
$237$	10.9240	0.709588
$238$	−19.9932	−1.29597
$239$	−28.2276	−1.82589	−0.912946	−	0.408080i	$-0.866199\pi$
$239$	−28.2276	−1.82589	−0.912946	+	0.408080i	$0.866199\pi$
$240$	−3.41147	−0.220210
$241$	−6.56212	−0.422703	−0.211352	−	0.977410i	$-0.567787\pi$
$241$	−6.56212	−0.422703	−0.211352	+	0.977410i	$0.567787\pi$
$242$	−10.8794	−0.699353
$243$	1.00000	0.0641500
$244$	−12.5321	−0.802285
$245$	−4.40373	−0.281344
$246$	3.49020	0.222527
$247$	0	0
$248$	−1.59627	−0.101363
$249$	11.7169	0.742527
$250$	−5.58853	−0.353449
$251$	8.89393	0.561380	0.280690	−	0.959798i	$-0.409437\pi$
$251$	8.89393	0.561380	0.280690	+	0.959798i	$0.409437\pi$
$252$	−2.87939	−0.181384
$253$	−2.36184	−0.148488
$254$	−16.2121	−1.01724
$255$	−23.6878	−1.48339
$256$	1.00000	0.0625000
$257$	13.4662	0.839996	0.419998	−	0.907525i	$-0.362031\pi$
$257$	13.4662	0.839996	0.419998	+	0.907525i	$0.362031\pi$
$258$	2.28312	0.142141
$259$	−32.2841	−2.00603
$260$	−5.63816	−0.349664
$261$	−6.35504	−0.393367
$262$	−2.80066	−0.173025
$263$	−16.7520	−1.03297	−0.516485	−	0.856296i	$-0.672760\pi$
$263$	−16.7520	−1.03297	−0.516485	+	0.856296i	$0.672760\pi$
$264$	−0.347296	−0.0213746
$265$	6.75608	0.415023
$266$	0	0
$267$	−1.79292	−0.109725
$268$	1.07873	0.0658937
$269$	−3.58946	−0.218853	−0.109427	−	0.993995i	$-0.534901\pi$
$269$	−3.58946	−0.218853	−0.109427	+	0.993995i	$0.534901\pi$
$270$	−3.41147	−0.207616
$271$	23.9590	1.45541	0.727704	−	0.685891i	$-0.240587\pi$
$271$	23.9590	1.45541	0.727704	+	0.685891i	$0.240587\pi$
$272$	6.94356	0.421015
$273$	−4.75877	−0.288014
$274$	16.0351	0.968715
$275$	−2.30541	−0.139021
$276$	6.80066	0.409352
$277$	−18.7219	−1.12489	−0.562446	−	0.826834i	$-0.690140\pi$
$277$	−18.7219	−1.12489	−0.562446	+	0.826834i	$0.690140\pi$
$278$	−2.07873	−0.124674
$279$	−1.59627	−0.0955660
$280$	9.82295	0.587033
$281$	10.6382	0.634619	0.317310	−	0.948322i	$-0.397221\pi$
$281$	10.6382	0.634619	0.317310	+	0.948322i	$0.397221\pi$
$282$	5.59627	0.333253
$283$	−14.0128	−0.832974	−0.416487	−	0.909142i	$-0.636739\pi$
$283$	−14.0128	−0.832974	−0.416487	+	0.909142i	$0.636739\pi$
$284$	16.6236	0.986430
$285$	0	0
$286$	−0.573978	−0.0339400
$287$	−10.0496	−0.593211
$288$	1.00000	0.0589256
$289$	31.2131	1.83606
$290$	21.6800	1.27310
$291$	−3.65270	−0.214125
$292$	12.4192	0.726780
$293$	11.5202	0.673019	0.336509	−	0.941680i	$-0.390754\pi$
$293$	11.5202	0.673019	0.336509	+	0.941680i	$0.390754\pi$
$294$	1.29086	0.0752844
$295$	1.52023	0.0885112
$296$	11.2121	0.651692
$297$	−0.347296	−0.0201522
$298$	−1.66725	−0.0965813
$299$	11.2395	0.649996
$300$	6.63816	0.383254
$301$	−6.57398	−0.378918
$302$	−20.0523	−1.15388
$303$	−9.90673	−0.569127
$304$	0	0
$305$	42.7529	2.44802
$306$	6.94356	0.396937
$307$	−4.29767	−0.245281	−0.122640	−	0.992451i	$-0.539136\pi$
$307$	−4.29767	−0.245281	−0.122640	+	0.992451i	$0.539136\pi$
$308$	1.00000	0.0569803
$309$	−7.84524	−0.446300
$310$	5.44562	0.309291
$311$	−22.9932	−1.30382	−0.651912	−	0.758294i	$-0.726033\pi$
$311$	−22.9932	−1.30382	−0.651912	+	0.758294i	$0.726033\pi$
$312$	1.65270	0.0935659
$313$	−9.20977	−0.520567	−0.260283	−	0.965532i	$-0.583816\pi$
$313$	−9.20977	−0.520567	−0.260283	+	0.965532i	$0.583816\pi$
$314$	−4.09833	−0.231282
$315$	9.82295	0.553460
$316$	10.9240	0.614521
$317$	−3.35504	−0.188438	−0.0942188	−	0.995552i	$-0.530035\pi$
$317$	−3.35504	−0.188438	−0.0942188	+	0.995552i	$0.530035\pi$
$318$	−1.98040	−0.111055
$319$	2.20708	0.123573
$320$	−3.41147	−0.190707
$321$	0.0273411	0.00152603
$322$	−19.5817	−1.09125
$323$	0	0
$324$	1.00000	0.0555556
$325$	10.9709	0.608556
$326$	−8.13516	−0.450565
$327$	10.7733	0.595766
$328$	3.49020	0.192714
$329$	−16.1138	−0.888383
$330$	1.18479	0.0652207
$331$	22.0743	1.21331	0.606656	−	0.794964i	$-0.292510\pi$
$331$	22.0743	1.21331	0.606656	+	0.794964i	$0.292510\pi$
$332$	11.7169	0.643047
$333$	11.2121	0.614421
$334$	13.3969	0.733047
$335$	−3.68004	−0.201062
$336$	−2.87939	−0.157083
$337$	13.1165	0.714501	0.357251	−	0.934009i	$-0.383714\pi$
$337$	13.1165	0.714501	0.357251	+	0.934009i	$0.383714\pi$
$338$	−10.2686	−0.558537
$339$	11.6604	0.633308
$340$	−23.6878	−1.28465
$341$	0.554378	0.0300212
$342$	0	0
$343$	16.4388	0.887613
$344$	2.28312	0.123098
$345$	−23.2003	−1.24906
$346$	1.02229	0.0549586
$347$	8.75877	0.470195	0.235098	−	0.971972i	$-0.424459\pi$
$347$	8.75877	0.470195	0.235098	+	0.971972i	$0.424459\pi$
$348$	−6.35504	−0.340666
$349$	3.26352	0.174692	0.0873461	−	0.996178i	$-0.472161\pi$
$349$	3.26352	0.174692	0.0873461	+	0.996178i	$0.472161\pi$
$350$	−19.1138	−1.02168
$351$	1.65270	0.0882148
$352$	−0.347296	−0.0185110
$353$	29.0838	1.54797	0.773987	−	0.633202i	$-0.218260\pi$
$353$	29.0838	1.54797	0.773987	+	0.633202i	$0.218260\pi$
$354$	−0.445622	−0.0236846
$355$	−56.7110	−3.00991
$356$	−1.79292	−0.0950245
$357$	−19.9932	−1.05815
$358$	−2.03508	−0.107557
$359$	6.61081	0.348905	0.174453	−	0.984666i	$-0.444184\pi$
$359$	6.61081	0.348905	0.174453	+	0.984666i	$0.444184\pi$
$360$	−3.41147	−0.179800
$361$	0	0
$362$	−22.3037	−1.17225
$363$	−10.8794	−0.571020
$364$	−4.75877	−0.249427
$365$	−42.3678	−2.21763
$366$	−12.5321	−0.655063
$367$	−5.79561	−0.302528	−0.151264	−	0.988493i	$-0.548334\pi$
$367$	−5.79561	−0.302528	−0.151264	+	0.988493i	$0.548334\pi$
$368$	6.80066	0.354509
$369$	3.49020	0.181693
$370$	−38.2499	−1.98852
$371$	5.70233	0.296050
$372$	−1.59627	−0.0827626
$373$	25.8898	1.34052	0.670262	−	0.742125i	$-0.266182\pi$
$373$	25.8898	1.34052	0.670262	+	0.742125i	$0.266182\pi$
$374$	−2.41147	−0.124694
$375$	−5.58853	−0.288590
$376$	5.59627	0.288605
$377$	−10.5030	−0.540932
$378$	−2.87939	−0.148100
$379$	19.1557	0.983962	0.491981	−	0.870606i	$-0.336273\pi$
$379$	19.1557	0.983962	0.491981	+	0.870606i	$0.336273\pi$
$380$	0	0
$381$	−16.2121	−0.830573
$382$	10.7861	0.551865
$383$	9.69459	0.495371	0.247685	−	0.968841i	$-0.420330\pi$
$383$	9.69459	0.495371	0.247685	+	0.968841i	$0.420330\pi$
$384$	1.00000	0.0510310
$385$	−3.41147	−0.173865
$386$	2.86484	0.145816
$387$	2.28312	0.116057
$388$	−3.65270	−0.185438
$389$	−0.817896	−0.0414690	−0.0207345	−	0.999785i	$-0.506600\pi$
$389$	−0.817896	−0.0414690	−0.0207345	+	0.999785i	$0.506600\pi$
$390$	−5.63816	−0.285499
$391$	47.2208	2.38806
$392$	1.29086	0.0651982
$393$	−2.80066	−0.141275
$394$	−8.33544	−0.419933
$395$	−37.2668	−1.87510
$396$	−0.347296	−0.0174523
$397$	−3.69728	−0.185561	−0.0927806	−	0.995687i	$-0.529576\pi$
$397$	−3.69728	−0.185561	−0.0927806	+	0.995687i	$0.529576\pi$
$398$	−3.03415	−0.152088
$399$	0	0
$400$	6.63816	0.331908
$401$	21.7401	1.08565	0.542824	−	0.839846i	$-0.317355\pi$
$401$	21.7401	1.08565	0.542824	+	0.839846i	$0.317355\pi$
$402$	1.07873	0.0538019
$403$	−2.63816	−0.131416
$404$	−9.90673	−0.492878
$405$	−3.41147	−0.169518
$406$	18.2986	0.908144
$407$	−3.89393	−0.193015
$408$	6.94356	0.343758
$409$	4.05468	0.200491	0.100246	−	0.994963i	$-0.468037\pi$
$409$	4.05468	0.200491	0.100246	+	0.994963i	$0.468037\pi$
$410$	−11.9067	−0.588031
$411$	16.0351	0.790952
$412$	−7.84524	−0.386507
$413$	1.28312	0.0631381
$414$	6.80066	0.334234
$415$	−39.9718	−1.96214
$416$	1.65270	0.0810305
$417$	−2.07873	−0.101796
$418$	0	0
$419$	23.4989	1.14800	0.573998	−	0.818857i	$-0.305392\pi$
$419$	23.4989	1.14800	0.573998	+	0.818857i	$0.305392\pi$
$420$	9.82295	0.479311
$421$	23.0729	1.12450	0.562251	−	0.826967i	$-0.309935\pi$
$421$	23.0729	1.12450	0.562251	+	0.826967i	$0.309935\pi$
$422$	16.6382	0.809933
$423$	5.59627	0.272100
$424$	−1.98040	−0.0961767
$425$	46.0925	2.23581
$426$	16.6236	0.805416
$427$	36.0847	1.74626
$428$	0.0273411	0.00132158
$429$	−0.573978	−0.0277119
$430$	−7.78880	−0.375609
$431$	3.51485	0.169304	0.0846522	−	0.996411i	$-0.473022\pi$
$431$	3.51485	0.169304	0.0846522	+	0.996411i	$0.473022\pi$
$432$	1.00000	0.0481125
$433$	34.1147	1.63945	0.819725	−	0.572757i	$-0.194126\pi$
$433$	34.1147	1.63945	0.819725	+	0.572757i	$0.194126\pi$
$434$	4.59627	0.220628
$435$	21.6800	1.03948
$436$	10.7733	0.515948
$437$	0	0
$438$	12.4192	0.593413
$439$	−9.70140	−0.463023	−0.231511	−	0.972832i	$-0.574367\pi$
$439$	−9.70140	−0.463023	−0.231511	+	0.972832i	$0.574367\pi$
$440$	1.18479	0.0564828
$441$	1.29086	0.0614695
$442$	11.4757	0.545841
$443$	15.1821	0.721324	0.360662	−	0.932697i	$-0.382551\pi$
$443$	15.1821	0.721324	0.360662	+	0.932697i	$0.382551\pi$
$444$	11.2121	0.532104
$445$	6.11650	0.289950
$446$	8.17024	0.386872
$447$	−1.66725	−0.0788583
$448$	−2.87939	−0.136038
$449$	−34.8384	−1.64413	−0.822064	−	0.569396i	$-0.807177\pi$
$449$	−34.8384	−1.64413	−0.822064	+	0.569396i	$0.807177\pi$
$450$	6.63816	0.312926
$451$	−1.21213	−0.0570771
$452$	11.6604	0.548461
$453$	−20.0523	−0.942140
$454$	−1.80066	−0.0845091
$455$	16.2344	0.761081
$456$	0	0
$457$	−31.8749	−1.49105	−0.745523	−	0.666479i	$-0.767800\pi$
$457$	−31.8749	−1.49105	−0.745523	+	0.666479i	$0.767800\pi$
$458$	−18.7392	−0.875624
$459$	6.94356	0.324098
$460$	−23.2003	−1.08172
$461$	−10.6895	−0.497862	−0.248931	−	0.968521i	$-0.580079\pi$
$461$	−10.6895	−0.497862	−0.248931	+	0.968521i	$0.580079\pi$
$462$	1.00000	0.0465242
$463$	15.3182	0.711897	0.355949	−	0.934506i	$-0.384158\pi$
$463$	15.3182	0.711897	0.355949	+	0.934506i	$0.384158\pi$
$464$	−6.35504	−0.295025
$465$	5.44562	0.252535
$466$	−4.09833	−0.189851
$467$	28.5125	1.31940	0.659700	−	0.751529i	$-0.270683\pi$
$467$	28.5125	1.31940	0.659700	+	0.751529i	$0.270683\pi$
$468$	1.65270	0.0763963
$469$	−3.10607	−0.143425
$470$	−19.0915	−0.880626
$471$	−4.09833	−0.188841
$472$	−0.445622	−0.0205114
$473$	−0.792919	−0.0364584
$474$	10.9240	0.501754
$475$	0	0
$476$	−19.9932	−0.916386
$477$	−1.98040	−0.0906763
$478$	−28.2276	−1.29110
$479$	8.05138	0.367877	0.183939	−	0.982938i	$-0.441115\pi$
$479$	8.05138	0.367877	0.183939	+	0.982938i	$0.441115\pi$
$480$	−3.41147	−0.155712
$481$	18.5303	0.844911
$482$	−6.56212	−0.298896
$483$	−19.5817	−0.890999
$484$	−10.8794	−0.494518
$485$	12.4611	0.565830
$486$	1.00000	0.0453609
$487$	−6.11556	−0.277123	−0.138561	−	0.990354i	$-0.544248\pi$
$487$	−6.11556	−0.277123	−0.138561	+	0.990354i	$0.544248\pi$
$488$	−12.5321	−0.567301
$489$	−8.13516	−0.367885
$490$	−4.40373	−0.198940
$491$	−22.6851	−1.02376	−0.511882	−	0.859056i	$-0.671052\pi$
$491$	−22.6851	−1.02376	−0.511882	+	0.859056i	$0.671052\pi$
$492$	3.49020	0.157350
$493$	−44.1266	−1.98736
$494$	0	0
$495$	1.18479	0.0532525
$496$	−1.59627	−0.0716745
$497$	−47.8658	−2.14707
$498$	11.7169	0.525046
$499$	24.8557	1.11269	0.556346	−	0.830951i	$-0.312203\pi$
$499$	24.8557	1.11269	0.556346	+	0.830951i	$0.312203\pi$
$500$	−5.58853	−0.249926
$501$	13.3969	0.598531
$502$	8.89393	0.396956
$503$	25.0232	1.11573	0.557865	−	0.829932i	$-0.311621\pi$
$503$	25.0232	1.11573	0.557865	+	0.829932i	$0.311621\pi$
$504$	−2.87939	−0.128258
$505$	33.7965	1.50393
$506$	−2.36184	−0.104997
$507$	−10.2686	−0.456043
$508$	−16.2121	−0.719297
$509$	−0.899310	−0.0398612	−0.0199306	−	0.999801i	$-0.506345\pi$
$509$	−0.899310	−0.0398612	−0.0199306	+	0.999801i	$0.506345\pi$
$510$	−23.6878	−1.04891
$511$	−35.7597	−1.58192
$512$	1.00000	0.0441942
$513$	0	0
$514$	13.4662	0.593967
$515$	26.7638	1.17935
$516$	2.28312	0.100509
$517$	−1.94356	−0.0854778
$518$	−32.2841	−1.41848
$519$	1.02229	0.0448735
$520$	−5.63816	−0.247249
$521$	6.63547	0.290705	0.145353	−	0.989380i	$-0.453568\pi$
$521$	6.63547	0.290705	0.145353	+	0.989380i	$0.453568\pi$
$522$	−6.35504	−0.278152
$523$	−37.9522	−1.65954	−0.829768	−	0.558109i	$-0.811527\pi$
$523$	−37.9522	−1.65954	−0.829768	+	0.558109i	$0.811527\pi$
$524$	−2.80066	−0.122347
$525$	−19.1138	−0.834195
$526$	−16.7520	−0.730420
$527$	−11.0838	−0.482817
$528$	−0.347296	−0.0151141
$529$	23.2490	1.01082
$530$	6.75608	0.293465
$531$	−0.445622	−0.0193384
$532$	0	0
$533$	5.76827	0.249851
$534$	−1.79292	−0.0775872
$535$	−0.0932736	−0.00403257
$536$	1.07873	0.0465939
$537$	−2.03508	−0.0878203
$538$	−3.58946	−0.154753
$539$	−0.448311	−0.0193101
$540$	−3.41147	−0.146806
$541$	15.1307	0.650520	0.325260	−	0.945625i	$-0.394548\pi$
$541$	15.1307	0.650520	0.325260	+	0.945625i	$0.394548\pi$
$542$	23.9590	1.02913
$543$	−22.3037	−0.957141
$544$	6.94356	0.297703
$545$	−36.7529	−1.57432
$546$	−4.75877	−0.203657
$547$	−32.5868	−1.39331	−0.696655	−	0.717406i	$-0.745329\pi$
$547$	−32.5868	−1.39331	−0.696655	+	0.717406i	$0.745329\pi$
$548$	16.0351	0.684985
$549$	−12.5321	−0.534857
$550$	−2.30541	−0.0983029
$551$	0	0
$552$	6.80066	0.289455
$553$	−31.4543	−1.33757
$554$	−18.7219	−0.795419
$555$	−38.2499	−1.62362
$556$	−2.07873	−0.0881576
$557$	−19.9436	−0.845036	−0.422518	−	0.906355i	$-0.638854\pi$
$557$	−19.9436	−0.845036	−0.422518	+	0.906355i	$0.638854\pi$
$558$	−1.59627	−0.0675754
$559$	3.77332	0.159594
$560$	9.82295	0.415095
$561$	−2.41147	−0.101813
$562$	10.6382	0.448744
$563$	−3.96822	−0.167240	−0.0836202	−	0.996498i	$-0.526648\pi$
$563$	−3.96822	−0.167240	−0.0836202	+	0.996498i	$0.526648\pi$
$564$	5.59627	0.235645
$565$	−39.7793	−1.67353
$566$	−14.0128	−0.589002
$567$	−2.87939	−0.120923
$568$	16.6236	0.697511
$569$	−14.8135	−0.621012	−0.310506	−	0.950571i	$-0.600499\pi$
$569$	−14.8135	−0.621012	−0.310506	+	0.950571i	$0.600499\pi$
$570$	0	0
$571$	21.0615	0.881396	0.440698	−	0.897655i	$-0.354731\pi$
$571$	21.0615	0.881396	0.440698	+	0.897655i	$0.354731\pi$
$572$	−0.573978	−0.0239992
$573$	10.7861	0.450596
$574$	−10.0496	−0.419463
$575$	45.1438	1.88263
$576$	1.00000	0.0416667
$577$	−44.2422	−1.84183	−0.920913	−	0.389769i	$-0.872555\pi$
$577$	−44.2422	−1.84183	−0.920913	+	0.389769i	$0.872555\pi$
$578$	31.2131	1.29829
$579$	2.86484	0.119059
$580$	21.6800	0.900215
$581$	−33.7374	−1.39966
$582$	−3.65270	−0.151409
$583$	0.687786	0.0284852
$584$	12.4192	0.513911
$585$	−5.63816	−0.233109
$586$	11.5202	0.475896
$587$	10.0024	0.412842	0.206421	−	0.978463i	$-0.433818\pi$
$587$	10.0024	0.412842	0.206421	+	0.978463i	$0.433818\pi$
$588$	1.29086	0.0532341
$589$	0	0
$590$	1.52023	0.0625869
$591$	−8.33544	−0.342874
$592$	11.2121	0.460816
$593$	−11.4911	−0.471884	−0.235942	−	0.971767i	$-0.575818\pi$
$593$	−11.4911	−0.471884	−0.235942	+	0.971767i	$0.575818\pi$
$594$	−0.347296	−0.0142497
$595$	68.2063	2.79618
$596$	−1.66725	−0.0682933
$597$	−3.03415	−0.124179
$598$	11.2395	0.459616
$599$	−6.41653	−0.262172	−0.131086	−	0.991371i	$-0.541846\pi$
$599$	−6.41653	−0.262172	−0.131086	+	0.991371i	$0.541846\pi$
$600$	6.63816	0.271002
$601$	−31.5158	−1.28556	−0.642778	−	0.766053i	$-0.722218\pi$
$601$	−31.5158	−1.28556	−0.642778	+	0.766053i	$0.722218\pi$
$602$	−6.57398	−0.267935
$603$	1.07873	0.0439291
$604$	−20.0523	−0.815917
$605$	37.1147	1.50893
$606$	−9.90673	−0.402433
$607$	−0.748341	−0.0303742	−0.0151871	−	0.999885i	$-0.504834\pi$
$607$	−0.748341	−0.0303742	−0.0151871	+	0.999885i	$0.504834\pi$
$608$	0	0
$609$	18.2986	0.741497
$610$	42.7529	1.73101
$611$	9.24897	0.374173
$612$	6.94356	0.280677
$613$	−30.6878	−1.23947	−0.619734	−	0.784812i	$-0.712760\pi$
$613$	−30.6878	−1.23947	−0.619734	+	0.784812i	$0.712760\pi$
$614$	−4.29767	−0.173440
$615$	−11.9067	−0.480126
$616$	1.00000	0.0402911
$617$	−27.2918	−1.09873	−0.549363	−	0.835584i	$-0.685130\pi$
$617$	−27.2918	−1.09873	−0.549363	+	0.835584i	$0.685130\pi$
$618$	−7.84524	−0.315582
$619$	−13.2371	−0.532044	−0.266022	−	0.963967i	$-0.585709\pi$
$619$	−13.2371	−0.532044	−0.266022	+	0.963967i	$0.585709\pi$
$620$	5.44562	0.218701
$621$	6.80066	0.272901
$622$	−22.9932	−0.921943
$623$	5.16250	0.206831
$624$	1.65270	0.0661611
$625$	−14.1257	−0.565027
$626$	−9.20977	−0.368096
$627$	0	0
$628$	−4.09833	−0.163541
$629$	77.8522	3.10417
$630$	9.82295	0.391356
$631$	−12.2395	−0.487246	−0.243623	−	0.969870i	$-0.578336\pi$
$631$	−12.2395	−0.487246	−0.243623	+	0.969870i	$0.578336\pi$
$632$	10.9240	0.434532
$633$	16.6382	0.661307
$634$	−3.35504	−0.133246
$635$	55.3073	2.19480
$636$	−1.98040	−0.0785280
$637$	2.13341	0.0845287
$638$	2.20708	0.0873792
$639$	16.6236	0.657620
$640$	−3.41147	−0.134850
$641$	−8.95367	−0.353649	−0.176824	−	0.984242i	$-0.556582\pi$
$641$	−8.95367	−0.353649	−0.176824	+	0.984242i	$0.556582\pi$
$642$	0.0273411	0.00107907
$643$	−31.3696	−1.23710	−0.618548	−	0.785747i	$-0.712279\pi$
$643$	−31.3696	−1.23710	−0.618548	+	0.785747i	$0.712279\pi$
$644$	−19.5817	−0.771628
$645$	−7.78880	−0.306684
$646$	0	0
$647$	−5.54933	−0.218166	−0.109083	−	0.994033i	$-0.534792\pi$
$647$	−5.54933	−0.218166	−0.109083	+	0.994033i	$0.534792\pi$
$648$	1.00000	0.0392837
$649$	0.154763	0.00607498
$650$	10.9709	0.430314
$651$	4.59627	0.180142
$652$	−8.13516	−0.318598
$653$	38.9103	1.52268	0.761340	−	0.648353i	$-0.224542\pi$
$653$	38.9103	1.52268	0.761340	+	0.648353i	$0.224542\pi$
$654$	10.7733	0.421270
$655$	9.55438	0.373320
$656$	3.49020	0.136269
$657$	12.4192	0.484520
$658$	−16.1138	−0.628182
$659$	39.5158	1.53932	0.769658	−	0.638456i	$-0.220427\pi$
$659$	39.5158	1.53932	0.769658	+	0.638456i	$0.220427\pi$
$660$	1.18479	0.0461180
$661$	0.0915189	0.00355967	0.00177984	−	0.999998i	$-0.499433\pi$
$661$	0.0915189	0.00355967	0.00177984	+	0.999998i	$0.499433\pi$
$662$	22.0743	0.857941
$663$	11.4757	0.445677
$664$	11.7169	0.454703
$665$	0	0
$666$	11.2121	0.434461
$667$	−43.2184	−1.67342
$668$	13.3969	0.518343
$669$	8.17024	0.315880
$670$	−3.68004	−0.142173
$671$	4.35235	0.168021
$672$	−2.87939	−0.111075
$673$	39.8563	1.53635	0.768173	−	0.640242i	$-0.221166\pi$
$673$	39.8563	1.53635	0.768173	+	0.640242i	$0.221166\pi$
$674$	13.1165	0.505229
$675$	6.63816	0.255503
$676$	−10.2686	−0.394945
$677$	−29.3824	−1.12926	−0.564628	−	0.825345i	$-0.690980\pi$
$677$	−29.3824	−1.12926	−0.564628	+	0.825345i	$0.690980\pi$
$678$	11.6604	0.447817
$679$	10.5175	0.403626
$680$	−23.6878	−0.908385
$681$	−1.80066	−0.0690014
$682$	0.554378	0.0212282
$683$	21.0933	0.807112	0.403556	−	0.914955i	$-0.367774\pi$
$683$	21.0933	0.807112	0.403556	+	0.914955i	$0.367774\pi$
$684$	0	0
$685$	−54.7033	−2.09010
$686$	16.4388	0.627637
$687$	−18.7392	−0.714944
$688$	2.28312	0.0870431
$689$	−3.27301	−0.124692
$690$	−23.2003	−0.883219
$691$	−16.1634	−0.614886	−0.307443	−	0.951566i	$-0.599473\pi$
$691$	−16.1634	−0.614886	−0.307443	+	0.951566i	$0.599473\pi$
$692$	1.02229	0.0388616
$693$	1.00000	0.0379869
$694$	8.75877	0.332478
$695$	7.09152	0.268997
$696$	−6.35504	−0.240887
$697$	24.2344	0.917944
$698$	3.26352	0.123526
$699$	−4.09833	−0.155013
$700$	−19.1138	−0.722434
$701$	−20.0729	−0.758141	−0.379071	−	0.925368i	$-0.623756\pi$
$701$	−20.0729	−0.758141	−0.379071	+	0.925368i	$0.623756\pi$
$702$	1.65270	0.0623773
$703$	0	0
$704$	−0.347296	−0.0130892
$705$	−19.0915	−0.719028
$706$	29.0838	1.09458
$707$	28.5253	1.07280
$708$	−0.445622	−0.0167475
$709$	−38.9009	−1.46095	−0.730476	−	0.682938i	$-0.760702\pi$
$709$	−38.9009	−1.46095	−0.730476	+	0.682938i	$0.760702\pi$
$710$	−56.7110	−2.12833
$711$	10.9240	0.409681
$712$	−1.79292	−0.0671925
$713$	−10.8557	−0.406548
$714$	−19.9932	−0.748226
$715$	1.95811	0.0732292
$716$	−2.03508	−0.0760546
$717$	−28.2276	−1.05418
$718$	6.61081	0.246713
$719$	3.06181	0.114186	0.0570932	−	0.998369i	$-0.481817\pi$
$719$	3.06181	0.114186	0.0570932	+	0.998369i	$0.481817\pi$
$720$	−3.41147	−0.127138
$721$	22.5895	0.841275
$722$	0	0
$723$	−6.56212	−0.244048
$724$	−22.3037	−0.828909
$725$	−42.1857	−1.56674
$726$	−10.8794	−0.403772
$727$	−17.4766	−0.648171	−0.324085	−	0.946028i	$-0.605056\pi$
$727$	−17.4766	−0.648171	−0.324085	+	0.946028i	$0.605056\pi$
$728$	−4.75877	−0.176372
$729$	1.00000	0.0370370
$730$	−42.3678	−1.56810
$731$	15.8530	0.586344
$732$	−12.5321	−0.463199
$733$	−41.4175	−1.52979	−0.764894	−	0.644156i	$-0.777209\pi$
$733$	−41.4175	−1.52979	−0.764894	+	0.644156i	$0.777209\pi$
$734$	−5.79561	−0.213920
$735$	−4.40373	−0.162434
$736$	6.80066	0.250676
$737$	−0.374638	−0.0137999
$738$	3.49020	0.128476
$739$	26.4534	0.973103	0.486551	−	0.873652i	$-0.338255\pi$
$739$	26.4534	0.973103	0.486551	+	0.873652i	$0.338255\pi$
$740$	−38.2499	−1.40609
$741$	0	0
$742$	5.70233	0.209339
$743$	15.0760	0.553086	0.276543	−	0.961002i	$-0.410811\pi$
$743$	15.0760	0.553086	0.276543	+	0.961002i	$0.410811\pi$
$744$	−1.59627	−0.0585220
$745$	5.68779	0.208384
$746$	25.8898	0.947893
$747$	11.7169	0.428698
$748$	−2.41147	−0.0881722
$749$	−0.0787257	−0.00287657
$750$	−5.58853	−0.204064
$751$	5.30541	0.193597	0.0967985	−	0.995304i	$-0.469140\pi$
$751$	5.30541	0.193597	0.0967985	+	0.995304i	$0.469140\pi$
$752$	5.59627	0.204075
$753$	8.89393	0.324113
$754$	−10.5030	−0.382496
$755$	68.4080	2.48962
$756$	−2.87939	−0.104722
$757$	8.13846	0.295797	0.147899	−	0.989003i	$-0.452749\pi$
$757$	8.13846	0.295797	0.147899	+	0.989003i	$0.452749\pi$
$758$	19.1557	0.695766
$759$	−2.36184	−0.0857295
$760$	0	0
$761$	−46.2113	−1.67516	−0.837579	−	0.546316i	$-0.816030\pi$
$761$	−46.2113	−1.67516	−0.837579	+	0.546316i	$0.816030\pi$
$762$	−16.2121	−0.587304
$763$	−31.0205	−1.12302
$764$	10.7861	0.390228
$765$	−23.6878	−0.856434
$766$	9.69459	0.350280
$767$	−0.736482	−0.0265928
$768$	1.00000	0.0360844
$769$	−26.8435	−0.968001	−0.484000	−	0.875068i	$-0.660817\pi$
$769$	−26.8435	−0.968001	−0.484000	+	0.875068i	$0.660817\pi$
$770$	−3.41147	−0.122941
$771$	13.4662	0.484972
$772$	2.86484	0.103108
$773$	21.0256	0.756238	0.378119	−	0.925757i	$-0.376571\pi$
$773$	21.0256	0.756238	0.378119	+	0.925757i	$0.376571\pi$
$774$	2.28312	0.0820650
$775$	−10.5963	−0.380629
$776$	−3.65270	−0.131124
$777$	−32.2841	−1.15818
$778$	−0.817896	−0.0293230
$779$	0	0
$780$	−5.63816	−0.201878
$781$	−5.77332	−0.206586
$782$	47.2208	1.68861
$783$	−6.35504	−0.227110
$784$	1.29086	0.0461021
$785$	13.9813	0.499015
$786$	−2.80066	−0.0998962
$787$	−45.5313	−1.62301	−0.811507	−	0.584342i	$-0.801353\pi$
$787$	−45.5313	−1.62301	−0.811507	+	0.584342i	$0.801353\pi$
$788$	−8.33544	−0.296938
$789$	−16.7520	−0.596386
$790$	−37.2668	−1.32589
$791$	−33.5749	−1.19379
$792$	−0.347296	−0.0123406
$793$	−20.7118	−0.735499
$794$	−3.69728	−0.131212
$795$	6.75608	0.239614
$796$	−3.03415	−0.107543
$797$	−36.1780	−1.28149	−0.640745	−	0.767754i	$-0.721374\pi$
$797$	−36.1780	−1.28149	−0.640745	+	0.767754i	$0.721374\pi$
$798$	0	0
$799$	38.8580	1.37470
$800$	6.63816	0.234694
$801$	−1.79292	−0.0633497
$802$	21.7401	0.767670
$803$	−4.31315	−0.152208
$804$	1.07873	0.0380437
$805$	66.8025	2.35448
$806$	−2.63816	−0.0929251
$807$	−3.58946	−0.126355
$808$	−9.90673	−0.348517
$809$	2.37876	0.0836326	0.0418163	−	0.999125i	$-0.486686\pi$
$809$	2.37876	0.0836326	0.0418163	+	0.999125i	$0.486686\pi$
$810$	−3.41147	−0.119867
$811$	37.0610	1.30139	0.650694	−	0.759340i	$-0.274478\pi$
$811$	37.0610	1.30139	0.650694	+	0.759340i	$0.274478\pi$
$812$	18.2986	0.642155
$813$	23.9590	0.840280
$814$	−3.89393	−0.136482
$815$	27.7529	0.972142
$816$	6.94356	0.243073
$817$	0	0
$818$	4.05468	0.141769
$819$	−4.75877	−0.166285
$820$	−11.9067	−0.415801
$821$	−25.9605	−0.906027	−0.453013	−	0.891504i	$-0.649651\pi$
$821$	−25.9605	−0.906027	−0.453013	+	0.891504i	$0.649651\pi$
$822$	16.0351	0.559288
$823$	−45.0110	−1.56899	−0.784493	−	0.620138i	$-0.787077\pi$
$823$	−45.0110	−1.56899	−0.784493	+	0.620138i	$0.787077\pi$
$824$	−7.84524	−0.273302
$825$	−2.30541	−0.0802640
$826$	1.28312	0.0446454
$827$	16.8429	0.585684	0.292842	−	0.956161i	$-0.405399\pi$
$827$	16.8429	0.585684	0.292842	+	0.956161i	$0.405399\pi$
$828$	6.80066	0.236339
$829$	13.0000	0.451509	0.225754	−	0.974184i	$-0.427515\pi$
$829$	13.0000	0.451509	0.225754	+	0.974184i	$0.427515\pi$
$830$	−39.9718	−1.38744
$831$	−18.7219	−0.649457
$832$	1.65270	0.0572972
$833$	8.96316	0.310555
$834$	−2.07873	−0.0719804
$835$	−45.7033	−1.58163
$836$	0	0
$837$	−1.59627	−0.0551750
$838$	23.4989	0.811755
$839$	−1.34049	−0.0462788	−0.0231394	−	0.999732i	$-0.507366\pi$
$839$	−1.34049	−0.0462788	−0.0231394	+	0.999732i	$0.507366\pi$
$840$	9.82295	0.338924
$841$	11.3865	0.392638
$842$	23.0729	0.795143
$843$	10.6382	0.366398
$844$	16.6382	0.572709
$845$	35.0310	1.20510
$846$	5.59627	0.192404
$847$	31.3259	1.07637
$848$	−1.98040	−0.0680072
$849$	−14.0128	−0.480918
$850$	46.0925	1.58096
$851$	76.2499	2.61381
$852$	16.6236	0.569515
$853$	−7.94532	−0.272042	−0.136021	−	0.990706i	$-0.543432\pi$
$853$	−7.94532	−0.272042	−0.136021	+	0.990706i	$0.543432\pi$
$854$	36.0847	1.23479
$855$	0	0
$856$	0.0273411	0.000934501 0
$857$	−47.8759	−1.63541	−0.817704	−	0.575638i	$-0.804754\pi$
$857$	−47.8759	−1.63541	−0.817704	+	0.575638i	$0.804754\pi$
$858$	−0.573978	−0.0195953
$859$	1.63722	0.0558613	0.0279306	−	0.999610i	$-0.491108\pi$
$859$	1.63722	0.0558613	0.0279306	+	0.999610i	$0.491108\pi$
$860$	−7.78880	−0.265596
$861$	−10.0496	−0.342490
$862$	3.51485	0.119716
$863$	−34.9231	−1.18880	−0.594399	−	0.804170i	$-0.702610\pi$
$863$	−34.9231	−1.18880	−0.594399	+	0.804170i	$0.702610\pi$
$864$	1.00000	0.0340207
$865$	−3.48751	−0.118579
$866$	34.1147	1.15927
$867$	31.2131	1.06005
$868$	4.59627	0.156007
$869$	−3.79385	−0.128698
$870$	21.6800	0.735022
$871$	1.78281	0.0604083
$872$	10.7733	0.364831
$873$	−3.65270	−0.123625
$874$	0	0
$875$	16.0915	0.543993
$876$	12.4192	0.419606
$877$	6.37195	0.215165	0.107583	−	0.994196i	$-0.465689\pi$
$877$	6.37195	0.215165	0.107583	+	0.994196i	$0.465689\pi$
$878$	−9.70140	−0.327406
$879$	11.5202	0.388568
$880$	1.18479	0.0399393
$881$	5.27395	0.177684	0.0888419	−	0.996046i	$-0.471683\pi$
$881$	5.27395	0.177684	0.0888419	+	0.996046i	$0.471683\pi$
$882$	1.29086	0.0434655
$883$	−3.25133	−0.109416	−0.0547081	−	0.998502i	$-0.517423\pi$
$883$	−3.25133	−0.109416	−0.0547081	+	0.998502i	$0.517423\pi$
$884$	11.4757	0.385968
$885$	1.52023	0.0511019
$886$	15.1821	0.510053
$887$	22.3705	0.751129	0.375564	−	0.926796i	$-0.377449\pi$
$887$	22.3705	0.751129	0.375564	+	0.926796i	$0.377449\pi$
$888$	11.2121	0.376255
$889$	46.6810	1.56563
$890$	6.11650	0.205025
$891$	−0.347296	−0.0116349
$892$	8.17024	0.273560
$893$	0	0
$894$	−1.66725	−0.0557612
$895$	6.94263	0.232067
$896$	−2.87939	−0.0961935
$897$	11.2395	0.375275
$898$	−34.8384	−1.16257
$899$	10.1443	0.338332
$900$	6.63816	0.221272
$901$	−13.7510	−0.458113
$902$	−1.21213	−0.0403596
$903$	−6.57398	−0.218768
$904$	11.6604	0.387821
$905$	76.0883	2.52926
$906$	−20.0523	−0.666194
$907$	−3.15745	−0.104841	−0.0524207	−	0.998625i	$-0.516694\pi$
$907$	−3.15745	−0.104841	−0.0524207	+	0.998625i	$0.516694\pi$
$908$	−1.80066	−0.0597570
$909$	−9.90673	−0.328585
$910$	16.2344	0.538166
$911$	44.3387	1.46901	0.734504	−	0.678604i	$-0.237415\pi$
$911$	44.3387	1.46901	0.734504	+	0.678604i	$0.237415\pi$
$912$	0	0
$913$	−4.06923	−0.134672
$914$	−31.8749	−1.05433
$915$	42.7529	1.41337
$916$	−18.7392	−0.619160
$917$	8.06418	0.266303
$918$	6.94356	0.229172
$919$	14.2044	0.468560	0.234280	−	0.972169i	$-0.424727\pi$
$919$	14.2044	0.468560	0.234280	+	0.972169i	$0.424727\pi$
$920$	−23.2003	−0.764890
$921$	−4.29767	−0.141613
$922$	−10.6895	−0.352041
$923$	27.4739	0.904314
$924$	1.00000	0.0328976
$925$	74.4279	2.44717
$926$	15.3182	0.503387
$927$	−7.84524	−0.257671
$928$	−6.35504	−0.208614
$929$	−15.4266	−0.506131	−0.253066	−	0.967449i	$-0.581439\pi$
$929$	−15.4266	−0.506131	−0.253066	+	0.967449i	$0.581439\pi$
$930$	5.44562	0.178569
$931$	0	0
$932$	−4.09833	−0.134245
$933$	−22.9932	−0.752763
$934$	28.5125	0.932957
$935$	8.22668	0.269041
$936$	1.65270	0.0540203
$937$	−9.69696	−0.316786	−0.158393	−	0.987376i	$-0.550631\pi$
$937$	−9.69696	−0.316786	−0.158393	+	0.987376i	$0.550631\pi$
$938$	−3.10607	−0.101417
$939$	−9.20977	−0.300549
$940$	−19.0915	−0.622697
$941$	17.9855	0.586309	0.293154	−	0.956065i	$-0.405295\pi$
$941$	17.9855	0.586309	0.293154	+	0.956065i	$0.405295\pi$
$942$	−4.09833	−0.133531
$943$	23.7357	0.772939
$944$	−0.445622	−0.0145038
$945$	9.82295	0.319541
$946$	−0.792919	−0.0257800
$947$	2.19396	0.0712942	0.0356471	−	0.999364i	$-0.488651\pi$
$947$	2.19396	0.0712942	0.0356471	+	0.999364i	$0.488651\pi$
$948$	10.9240	0.354794
$949$	20.5253	0.666279
$950$	0	0
$951$	−3.35504	−0.108795
$952$	−19.9932	−0.647983
$953$	11.3108	0.366392	0.183196	−	0.983076i	$-0.441356\pi$
$953$	11.3108	0.366392	0.183196	+	0.983076i	$0.441356\pi$
$954$	−1.98040	−0.0641178
$955$	−36.7965	−1.19071
$956$	−28.2276	−0.912946
$957$	2.20708	0.0713448
$958$	8.05138	0.260128
$959$	−46.1712	−1.49095
$960$	−3.41147	−0.110105
$961$	−28.4519	−0.917804
$962$	18.5303	0.597442
$963$	0.0273411	0.000881056 0
$964$	−6.56212	−0.211352
$965$	−9.77332	−0.314614
$966$	−19.5817	−0.630031
$967$	46.7844	1.50448	0.752242	−	0.658887i	$-0.228973\pi$
$967$	46.7844	1.50448	0.752242	+	0.658887i	$0.228973\pi$
$968$	−10.8794	−0.349677
$969$	0	0
$970$	12.4611	0.400102
$971$	−60.3715	−1.93741	−0.968706	−	0.248211i	$-0.920157\pi$
$971$	−60.3715	−1.93741	−0.968706	+	0.248211i	$0.920157\pi$
$972$	1.00000	0.0320750
$973$	5.98545	0.191885
$974$	−6.11556	−0.195955
$975$	10.9709	0.351350
$976$	−12.5321	−0.401142
$977$	−22.7956	−0.729296	−0.364648	−	0.931145i	$-0.618811\pi$
$977$	−22.7956	−0.729296	−0.364648	+	0.931145i	$0.618811\pi$
$978$	−8.13516	−0.260134
$979$	0.622674	0.0199008
$980$	−4.40373	−0.140672
$981$	10.7733	0.343966
$982$	−22.6851	−0.723911
$983$	30.7929	0.982142	0.491071	−	0.871120i	$-0.336606\pi$
$983$	30.7929	0.982142	0.491071	+	0.871120i	$0.336606\pi$
$984$	3.49020	0.111264
$985$	28.4361	0.906050
$986$	−44.1266	−1.40528
$987$	−16.1138	−0.512908
$988$	0	0
$989$	15.5267	0.493721
$990$	1.18479	0.0376552
$991$	38.1789	1.21279	0.606397	−	0.795162i	$-0.292614\pi$
$991$	38.1789	1.21279	0.606397	+	0.795162i	$0.292614\pi$
$992$	−1.59627	−0.0506815
$993$	22.0743	0.700506
$994$	−47.8658	−1.51821
$995$	10.3509	0.328146
$996$	11.7169	0.371264
$997$	30.9489	0.980163	0.490081	−	0.871677i	$-0.336967\pi$
$997$	30.9489	0.980163	0.490081	+	0.871677i	$0.336967\pi$
$998$	24.8557	0.786792
$999$	11.2121	0.354736

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2166.2.a.u.1.1		3
3.2	odd	2		6498.2.a.bn.1.3		3
19.3	odd	18		114.2.i.d.85.1	yes	6
19.13	odd	18		114.2.i.d.55.1	✓	6
19.18	odd	2		2166.2.a.o.1.1		3
57.32	even	18		342.2.u.a.55.1		6
57.41	even	18		342.2.u.a.199.1		6
57.56	even	2		6498.2.a.bs.1.3		3
76.3	even	18		912.2.bo.f.769.1		6
76.51	even	18		912.2.bo.f.625.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.d.55.1	✓	6	19.13	odd	18
114.2.i.d.85.1	yes	6	19.3	odd	18
342.2.u.a.55.1		6	57.32	even	18
342.2.u.a.199.1		6	57.41	even	18
912.2.bo.f.625.1		6	76.51	even	18
912.2.bo.f.769.1		6	76.3	even	18
2166.2.a.o.1.1		3	19.18	odd	2
2166.2.a.u.1.1		3	1.1	even	1	trivial
6498.2.a.bn.1.3		3	3.2	odd	2
6498.2.a.bs.1.3		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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 2166 = 2 \cdot 3 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2166.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.41147 q^{5} +1.00000 q^{6} -2.87939 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.41147 q^{5} +1.00000 q^{6} -2.87939 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.41147 q^{10} -0.347296 q^{11} +1.00000 q^{12} +1.65270 q^{13} -2.87939 q^{14} -3.41147 q^{15} +1.00000 q^{16} +6.94356 q^{17} +1.00000 q^{18} -3.41147 q^{20} -2.87939 q^{21} -0.347296 q^{22} +6.80066 q^{23} +1.00000 q^{24} +6.63816 q^{25} +1.65270 q^{26} +1.00000 q^{27} -2.87939 q^{28} -6.35504 q^{29} -3.41147 q^{30} -1.59627 q^{31} +1.00000 q^{32} -0.347296 q^{33} +6.94356 q^{34} +9.82295 q^{35} +1.00000 q^{36} +11.2121 q^{37} +1.65270 q^{39} -3.41147 q^{40} +3.49020 q^{41} -2.87939 q^{42} +2.28312 q^{43} -0.347296 q^{44} -3.41147 q^{45} +6.80066 q^{46} +5.59627 q^{47} +1.00000 q^{48} +1.29086 q^{49} +6.63816 q^{50} +6.94356 q^{51} +1.65270 q^{52} -1.98040 q^{53} +1.00000 q^{54} +1.18479 q^{55} -2.87939 q^{56} -6.35504 q^{58} -0.445622 q^{59} -3.41147 q^{60} -12.5321 q^{61} -1.59627 q^{62} -2.87939 q^{63} +1.00000 q^{64} -5.63816 q^{65} -0.347296 q^{66} +1.07873 q^{67} +6.94356 q^{68} +6.80066 q^{69} +9.82295 q^{70} +16.6236 q^{71} +1.00000 q^{72} +12.4192 q^{73} +11.2121 q^{74} +6.63816 q^{75} +1.00000 q^{77} +1.65270 q^{78} +10.9240 q^{79} -3.41147 q^{80} +1.00000 q^{81} +3.49020 q^{82} +11.7169 q^{83} -2.87939 q^{84} -23.6878 q^{85} +2.28312 q^{86} -6.35504 q^{87} -0.347296 q^{88} -1.79292 q^{89} -3.41147 q^{90} -4.75877 q^{91} +6.80066 q^{92} -1.59627 q^{93} +5.59627 q^{94} +1.00000 q^{96} -3.65270 q^{97} +1.29086 q^{98} -0.347296 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9} + 3 q^{12} + 6 q^{13} - 3 q^{14} + 3 q^{16} + 6 q^{17} + 3 q^{18} - 3 q^{21} + 6 q^{23} + 3 q^{24} + 3 q^{25} + 6 q^{26} + 3 q^{27} - 3 q^{28} + 6 q^{29} + 9 q^{31} + 3 q^{32} + 6 q^{34} + 9 q^{35} + 3 q^{36} + 9 q^{37} + 6 q^{39} + 9 q^{41} - 3 q^{42} + 15 q^{43} + 6 q^{46} + 3 q^{47} + 3 q^{48} - 12 q^{49} + 3 q^{50} + 6 q^{51} + 6 q^{52} - 3 q^{53} + 3 q^{54} - 3 q^{56} + 6 q^{58} - 12 q^{59} - 33 q^{61} + 9 q^{62} - 3 q^{63} + 3 q^{64} + 12 q^{67} + 6 q^{68} + 6 q^{69} + 9 q^{70} + 15 q^{71} + 3 q^{72} + 3 q^{73} + 9 q^{74} + 3 q^{75} + 3 q^{77} + 6 q^{78} + 15 q^{79} + 3 q^{81} + 9 q^{82} + 27 q^{83} - 3 q^{84} - 27 q^{85} + 15 q^{86} + 6 q^{87} - 15 q^{89} - 3 q^{91} + 6 q^{92} + 9 q^{93} + 3 q^{94} + 3 q^{96} - 12 q^{97} - 12 q^{98}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9 + 3 * q^12 + 6 * q^13 - 3 * q^14 + 3 * q^16 + 6 * q^17 + 3 * q^18 - 3 * q^21 + 6 * q^23 + 3 * q^24 + 3 * q^25 + 6 * q^26 + 3 * q^27 - 3 * q^28 + 6 * q^29 + 9 * q^31 + 3 * q^32 + 6 * q^34 + 9 * q^35 + 3 * q^36 + 9 * q^37 + 6 * q^39 + 9 * q^41 - 3 * q^42 + 15 * q^43 + 6 * q^46 + 3 * q^47 + 3 * q^48 - 12 * q^49 + 3 * q^50 + 6 * q^51 + 6 * q^52 - 3 * q^53 + 3 * q^54 - 3 * q^56 + 6 * q^58 - 12 * q^59 - 33 * q^61 + 9 * q^62 - 3 * q^63 + 3 * q^64 + 12 * q^67 + 6 * q^68 + 6 * q^69 + 9 * q^70 + 15 * q^71 + 3 * q^72 + 3 * q^73 + 9 * q^74 + 3 * q^75 + 3 * q^77 + 6 * q^78 + 15 * q^79 + 3 * q^81 + 9 * q^82 + 27 * q^83 - 3 * q^84 - 27 * q^85 + 15 * q^86 + 6 * q^87 - 15 * q^89 - 3 * q^91 + 6 * q^92 + 9 * q^93 + 3 * q^94 + 3 * q^96 - 12 * q^97 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

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