LMFDB - Embedded newform 1805.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, 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("1805.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.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:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	1805.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.381966 q^{2} +0.381966 q^{3} -1.85410 q^{4} -1.00000 q^{5} +0.145898 q^{6} -4.23607 q^{7} -1.47214 q^{8} -2.85410 q^{9} +O(q^{10})$	\(q+0.381966 q^{2} +0.381966 q^{3} -1.85410 q^{4} -1.00000 q^{5} +0.145898 q^{6} -4.23607 q^{7} -1.47214 q^{8} -2.85410 q^{9} -0.381966 q^{10} -2.38197 q^{11} -0.708204 q^{12} +5.00000 q^{13} -1.61803 q^{14} -0.381966 q^{15} +3.14590 q^{16} -6.00000 q^{17} -1.09017 q^{18} +1.85410 q^{20} -1.61803 q^{21} -0.909830 q^{22} +0.618034 q^{23} -0.562306 q^{24} +1.00000 q^{25} +1.90983 q^{26} -2.23607 q^{27} +7.85410 q^{28} +4.85410 q^{29} -0.145898 q^{30} +10.8541 q^{31} +4.14590 q^{32} -0.909830 q^{33} -2.29180 q^{34} +4.23607 q^{35} +5.29180 q^{36} +4.85410 q^{37} +1.90983 q^{39} +1.47214 q^{40} -11.1803 q^{41} -0.618034 q^{42} +3.85410 q^{43} +4.41641 q^{44} +2.85410 q^{45} +0.236068 q^{46} -5.76393 q^{47} +1.20163 q^{48} +10.9443 q^{49} +0.381966 q^{50} -2.29180 q^{51} -9.27051 q^{52} +3.38197 q^{53} -0.854102 q^{54} +2.38197 q^{55} +6.23607 q^{56} +1.85410 q^{58} -11.0902 q^{59} +0.708204 q^{60} -3.00000 q^{61} +4.14590 q^{62} +12.0902 q^{63} -4.70820 q^{64} -5.00000 q^{65} -0.347524 q^{66} +8.70820 q^{67} +11.1246 q^{68} +0.236068 q^{69} +1.61803 q^{70} +8.23607 q^{71} +4.20163 q^{72} -1.00000 q^{73} +1.85410 q^{74} +0.381966 q^{75} +10.0902 q^{77} +0.729490 q^{78} +8.00000 q^{79} -3.14590 q^{80} +7.70820 q^{81} -4.27051 q^{82} -4.47214 q^{83} +3.00000 q^{84} +6.00000 q^{85} +1.47214 q^{86} +1.85410 q^{87} +3.50658 q^{88} +6.70820 q^{89} +1.09017 q^{90} -21.1803 q^{91} -1.14590 q^{92} +4.14590 q^{93} -2.20163 q^{94} +1.58359 q^{96} -5.09017 q^{97} +4.18034 q^{98} +6.79837 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 2 q^{5} + 7 q^{6} - 4 q^{7} + 6 q^{8} + q^{9}+O(q^{10}) $ 2 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 2 * q^5 + 7 * q^6 - 4 * q^7 + 6 * q^8 + q^9	$ 2 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 2 q^{5} + 7 q^{6} - 4 q^{7} + 6 q^{8} + q^{9} - 3 q^{10} - 7 q^{11} + 12 q^{12} + 10 q^{13} - q^{14} - 3 q^{15} + 13 q^{16} - 12 q^{17} + 9 q^{18} - 3 q^{20} - q^{21} - 13 q^{22} - q^{23} + 19 q^{24} + 2 q^{25} + 15 q^{26} + 9 q^{28} + 3 q^{29} - 7 q^{30} + 15 q^{31} + 15 q^{32} - 13 q^{33} - 18 q^{34} + 4 q^{35} + 24 q^{36} + 3 q^{37} + 15 q^{39} - 6 q^{40} + q^{42} + q^{43} - 18 q^{44} - q^{45} - 4 q^{46} - 16 q^{47} + 27 q^{48} + 4 q^{49} + 3 q^{50} - 18 q^{51} + 15 q^{52} + 9 q^{53} + 5 q^{54} + 7 q^{55} + 8 q^{56} - 3 q^{58} - 11 q^{59} - 12 q^{60} - 6 q^{61} + 15 q^{62} + 13 q^{63} + 4 q^{64} - 10 q^{65} - 32 q^{66} + 4 q^{67} - 18 q^{68} - 4 q^{69} + q^{70} + 12 q^{71} + 33 q^{72} - 2 q^{73} - 3 q^{74} + 3 q^{75} + 9 q^{77} + 35 q^{78} + 16 q^{79} - 13 q^{80} + 2 q^{81} + 25 q^{82} + 6 q^{84} + 12 q^{85} - 6 q^{86} - 3 q^{87} - 31 q^{88} - 9 q^{90} - 20 q^{91} - 9 q^{92} + 15 q^{93} - 29 q^{94} + 30 q^{96} + q^{97} - 14 q^{98} - 11 q^{99}+O(q^{100}) $ 2 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 2 * q^5 + 7 * q^6 - 4 * q^7 + 6 * q^8 + q^9 - 3 * q^10 - 7 * q^11 + 12 * q^12 + 10 * q^13 - q^14 - 3 * q^15 + 13 * q^16 - 12 * q^17 + 9 * q^18 - 3 * q^20 - q^21 - 13 * q^22 - q^23 + 19 * q^24 + 2 * q^25 + 15 * q^26 + 9 * q^28 + 3 * q^29 - 7 * q^30 + 15 * q^31 + 15 * q^32 - 13 * q^33 - 18 * q^34 + 4 * q^35 + 24 * q^36 + 3 * q^37 + 15 * q^39 - 6 * q^40 + q^42 + q^43 - 18 * q^44 - q^45 - 4 * q^46 - 16 * q^47 + 27 * q^48 + 4 * q^49 + 3 * q^50 - 18 * q^51 + 15 * q^52 + 9 * q^53 + 5 * q^54 + 7 * q^55 + 8 * q^56 - 3 * q^58 - 11 * q^59 - 12 * q^60 - 6 * q^61 + 15 * q^62 + 13 * q^63 + 4 * q^64 - 10 * q^65 - 32 * q^66 + 4 * q^67 - 18 * q^68 - 4 * q^69 + q^70 + 12 * q^71 + 33 * q^72 - 2 * q^73 - 3 * q^74 + 3 * q^75 + 9 * q^77 + 35 * q^78 + 16 * q^79 - 13 * q^80 + 2 * q^81 + 25 * q^82 + 6 * q^84 + 12 * q^85 - 6 * q^86 - 3 * q^87 - 31 * q^88 - 9 * q^90 - 20 * q^91 - 9 * q^92 + 15 * q^93 - 29 * q^94 + 30 * q^96 + q^97 - 14 * q^98 - 11 * q^99

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 $

$2$	0.381966	0.270091	0.135045	−	0.990839i	$-0.456882\pi$
$2$	0.381966	0.270091	0.135045	+	0.990839i	$0.456882\pi$
$3$	0.381966	0.220528	0.110264	−	0.993902i	$-0.464830\pi$
$3$	0.381966	0.220528	0.110264	+	0.993902i	$0.464830\pi$
$4$	−1.85410	−0.927051
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.145898	0.0595626
$7$	−4.23607	−1.60108	−0.800542	−	0.599277i	$-0.795455\pi$
$7$	−4.23607	−1.60108	−0.800542	+	0.599277i	$0.795455\pi$
$8$	−1.47214	−0.520479
$9$	−2.85410	−0.951367
$10$	−0.381966	−0.120788
$11$	−2.38197	−0.718190	−0.359095	−	0.933301i	$-0.616915\pi$
$11$	−2.38197	−0.718190	−0.359095	+	0.933301i	$0.616915\pi$
$12$	−0.708204	−0.204441
$13$	5.00000	1.38675	0.693375	−	0.720577i	$-0.256123\pi$
$13$	5.00000	1.38675	0.693375	+	0.720577i	$0.256123\pi$
$14$	−1.61803	−0.432438
$15$	−0.381966	−0.0986232
$16$	3.14590	0.786475
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	−1.09017	−0.256956
$19$	0	0
$19$	0	0
$20$	1.85410	0.414590
$21$	−1.61803	−0.353084
$22$	−0.909830	−0.193976
$23$	0.618034	0.128869	0.0644345	−	0.997922i	$-0.479476\pi$
$23$	0.618034	0.128869	0.0644345	+	0.997922i	$0.479476\pi$
$24$	−0.562306	−0.114780
$25$	1.00000	0.200000
$26$	1.90983	0.374548
$27$	−2.23607	−0.430331
$28$	7.85410	1.48429
$29$	4.85410	0.901384	0.450692	−	0.892679i	$-0.351177\pi$
$29$	4.85410	0.901384	0.450692	+	0.892679i	$0.351177\pi$
$30$	−0.145898	−0.0266372
$31$	10.8541	1.94945	0.974727	−	0.223399i	$-0.0717152\pi$
$31$	10.8541	1.94945	0.974727	+	0.223399i	$0.0717152\pi$
$32$	4.14590	0.732898
$33$	−0.909830	−0.158381
$34$	−2.29180	−0.393040
$35$	4.23607	0.716026
$36$	5.29180	0.881966
$37$	4.85410	0.798009	0.399005	−	0.916949i	$-0.369356\pi$
$37$	4.85410	0.798009	0.399005	+	0.916949i	$0.369356\pi$
$38$	0	0
$39$	1.90983	0.305818
$40$	1.47214	0.232765
$41$	−11.1803	−1.74608	−0.873038	−	0.487652i	$-0.837853\pi$
$41$	−11.1803	−1.74608	−0.873038	+	0.487652i	$0.837853\pi$
$42$	−0.618034	−0.0953647
$43$	3.85410	0.587745	0.293873	−	0.955845i	$-0.405056\pi$
$43$	3.85410	0.587745	0.293873	+	0.955845i	$0.405056\pi$
$44$	4.41641	0.665799
$45$	2.85410	0.425464
$46$	0.236068	0.0348063
$47$	−5.76393	−0.840756	−0.420378	−	0.907349i	$-0.638103\pi$
$47$	−5.76393	−0.840756	−0.420378	+	0.907349i	$0.638103\pi$
$48$	1.20163	0.173440
$49$	10.9443	1.56347
$50$	0.381966	0.0540182
$51$	−2.29180	−0.320916
$52$	−9.27051	−1.28559
$53$	3.38197	0.464549	0.232274	−	0.972650i	$-0.425383\pi$
$53$	3.38197	0.464549	0.232274	+	0.972650i	$0.425383\pi$
$54$	−0.854102	−0.116229
$55$	2.38197	0.321184
$56$	6.23607	0.833330
$57$	0	0
$58$	1.85410	0.243456
$59$	−11.0902	−1.44382	−0.721909	−	0.691988i	$-0.756735\pi$
$59$	−11.0902	−1.44382	−0.721909	+	0.691988i	$0.756735\pi$
$60$	0.708204	0.0914287
$61$	−3.00000	−0.384111	−0.192055	−	0.981384i	$-0.561515\pi$
$61$	−3.00000	−0.384111	−0.192055	+	0.981384i	$0.561515\pi$
$62$	4.14590	0.526530
$63$	12.0902	1.52322
$64$	−4.70820	−0.588525
$65$	−5.00000	−0.620174
$66$	−0.347524	−0.0427773
$67$	8.70820	1.06388	0.531938	−	0.846783i	$-0.321464\pi$
$67$	8.70820	1.06388	0.531938	+	0.846783i	$0.321464\pi$
$68$	11.1246	1.34906
$69$	0.236068	0.0284192
$70$	1.61803	0.193392
$71$	8.23607	0.977441	0.488721	−	0.872440i	$-0.337464\pi$
$71$	8.23607	0.977441	0.488721	+	0.872440i	$0.337464\pi$
$72$	4.20163	0.495166
$73$	−1.00000	−0.117041	−0.0585206	−	0.998286i	$-0.518638\pi$
$73$	−1.00000	−0.117041	−0.0585206	+	0.998286i	$0.518638\pi$
$74$	1.85410	0.215535
$75$	0.381966	0.0441056
$76$	0	0
$77$	10.0902	1.14988
$78$	0.729490	0.0825985
$79$	8.00000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	−3.14590	−0.351722
$81$	7.70820	0.856467
$82$	−4.27051	−0.471599
$83$	−4.47214	−0.490881	−0.245440	−	0.969412i	$-0.578933\pi$
$83$	−4.47214	−0.490881	−0.245440	+	0.969412i	$0.578933\pi$
$84$	3.00000	0.327327
$85$	6.00000	0.650791
$86$	1.47214	0.158745
$87$	1.85410	0.198781
$88$	3.50658	0.373802
$89$	6.70820	0.711068	0.355534	−	0.934663i	$-0.384299\pi$
$89$	6.70820	0.711068	0.355534	+	0.934663i	$0.384299\pi$
$90$	1.09017	0.114914
$91$	−21.1803	−2.22030
$92$	−1.14590	−0.119468
$93$	4.14590	0.429910
$94$	−2.20163	−0.227080
$95$	0	0
$96$	1.58359	0.161625
$97$	−5.09017	−0.516828	−0.258414	−	0.966034i	$-0.583200\pi$
$97$	−5.09017	−0.516828	−0.258414	+	0.966034i	$0.583200\pi$
$98$	4.18034	0.422278
$99$	6.79837	0.683262
$100$	−1.85410	−0.185410
$101$	5.94427	0.591477	0.295739	−	0.955269i	$-0.404434\pi$
$101$	5.94427	0.591477	0.295739	+	0.955269i	$0.404434\pi$
$102$	−0.875388	−0.0866763
$103$	1.67376	0.164921	0.0824603	−	0.996594i	$-0.473722\pi$
$103$	1.67376	0.164921	0.0824603	+	0.996594i	$0.473722\pi$
$104$	−7.36068	−0.721774
$105$	1.61803	0.157904
$106$	1.29180	0.125470
$107$	3.00000	0.290021	0.145010	−	0.989430i	$-0.453678\pi$
$107$	3.00000	0.290021	0.145010	+	0.989430i	$0.453678\pi$
$108$	4.14590	0.398939
$109$	1.76393	0.168954	0.0844770	−	0.996425i	$-0.473078\pi$
$109$	1.76393	0.168954	0.0844770	+	0.996425i	$0.473078\pi$
$110$	0.909830	0.0867489
$111$	1.85410	0.175984
$112$	−13.3262	−1.25921
$113$	−14.9443	−1.40584	−0.702919	−	0.711269i	$-0.748121\pi$
$113$	−14.9443	−1.40584	−0.702919	+	0.711269i	$0.748121\pi$
$114$	0	0
$115$	−0.618034	−0.0576320
$116$	−9.00000	−0.835629
$117$	−14.2705	−1.31931
$118$	−4.23607	−0.389962
$119$	25.4164	2.32992
$120$	0.562306	0.0513313
$121$	−5.32624	−0.484203
$122$	−1.14590	−0.103745
$123$	−4.27051	−0.385059
$124$	−20.1246	−1.80724
$125$	−1.00000	−0.0894427
$126$	4.61803	0.411407
$127$	10.7082	0.950199	0.475100	−	0.879932i	$-0.342412\pi$
$127$	10.7082	0.950199	0.475100	+	0.879932i	$0.342412\pi$
$128$	−10.0902	−0.891853
$129$	1.47214	0.129614
$130$	−1.90983	−0.167503
$131$	−7.85410	−0.686216	−0.343108	−	0.939296i	$-0.611480\pi$
$131$	−7.85410	−0.686216	−0.343108	+	0.939296i	$0.611480\pi$
$132$	1.68692	0.146827
$133$	0	0
$134$	3.32624	0.287343
$135$	2.23607	0.192450
$136$	8.83282	0.757408
$137$	1.18034	0.100843	0.0504216	−	0.998728i	$-0.483943\pi$
$137$	1.18034	0.100843	0.0504216	+	0.998728i	$0.483943\pi$
$138$	0.0901699	0.00767578
$139$	8.14590	0.690926	0.345463	−	0.938432i	$-0.387722\pi$
$139$	8.14590	0.690926	0.345463	+	0.938432i	$0.387722\pi$
$140$	−7.85410	−0.663793
$141$	−2.20163	−0.185410
$142$	3.14590	0.263998
$143$	−11.9098	−0.995950
$144$	−8.97871	−0.748226
$145$	−4.85410	−0.403111
$146$	−0.381966	−0.0316117
$147$	4.18034	0.344789
$148$	−9.00000	−0.739795
$149$	−7.61803	−0.624094	−0.312047	−	0.950067i	$-0.601015\pi$
$149$	−7.61803	−0.624094	−0.312047	+	0.950067i	$0.601015\pi$
$150$	0.145898	0.0119125
$151$	−7.38197	−0.600736	−0.300368	−	0.953823i	$-0.597109\pi$
$151$	−7.38197	−0.600736	−0.300368	+	0.953823i	$0.597109\pi$
$152$	0	0
$153$	17.1246	1.38444
$154$	3.85410	0.310572
$155$	−10.8541	−0.871822
$156$	−3.54102	−0.283508
$157$	−24.0344	−1.91816	−0.959079	−	0.283140i	$-0.908624\pi$
$157$	−24.0344	−1.91816	−0.959079	+	0.283140i	$0.908624\pi$
$158$	3.05573	0.243101
$159$	1.29180	0.102446
$160$	−4.14590	−0.327762
$161$	−2.61803	−0.206330
$162$	2.94427	0.231324
$163$	8.52786	0.667954	0.333977	−	0.942581i	$-0.391609\pi$
$163$	8.52786	0.667954	0.333977	+	0.942581i	$0.391609\pi$
$164$	20.7295	1.61870
$165$	0.909830	0.0708302
$166$	−1.70820	−0.132582
$167$	8.23607	0.637326	0.318663	−	0.947868i	$-0.396766\pi$
$167$	8.23607	0.637326	0.318663	+	0.947868i	$0.396766\pi$
$168$	2.38197	0.183773
$169$	12.0000	0.923077
$170$	2.29180	0.175773
$171$	0	0
$172$	−7.14590	−0.544870
$173$	13.8885	1.05593	0.527963	−	0.849267i	$-0.322956\pi$
$173$	13.8885	1.05593	0.527963	+	0.849267i	$0.322956\pi$
$174$	0.708204	0.0536888
$175$	−4.23607	−0.320217
$176$	−7.49342	−0.564838
$177$	−4.23607	−0.318402
$178$	2.56231	0.192053
$179$	10.5279	0.786890	0.393445	−	0.919348i	$-0.371283\pi$
$179$	10.5279	0.786890	0.393445	+	0.919348i	$0.371283\pi$
$180$	−5.29180	−0.394427
$181$	8.29180	0.616324	0.308162	−	0.951334i	$-0.400286\pi$
$181$	8.29180	0.616324	0.308162	+	0.951334i	$0.400286\pi$
$182$	−8.09017	−0.599683
$183$	−1.14590	−0.0847072
$184$	−0.909830	−0.0670736
$185$	−4.85410	−0.356881
$186$	1.58359	0.116115
$187$	14.2918	1.04512
$188$	10.6869	0.779424
$189$	9.47214	0.688997
$190$	0	0
$191$	6.05573	0.438177	0.219089	−	0.975705i	$-0.429692\pi$
$191$	6.05573	0.438177	0.219089	+	0.975705i	$0.429692\pi$
$192$	−1.79837	−0.129786
$193$	4.00000	0.287926	0.143963	−	0.989583i	$-0.454015\pi$
$193$	4.00000	0.287926	0.143963	+	0.989583i	$0.454015\pi$
$194$	−1.94427	−0.139591
$195$	−1.90983	−0.136766
$196$	−20.2918	−1.44941
$197$	16.5279	1.17756	0.588781	−	0.808293i	$-0.299608\pi$
$197$	16.5279	1.17756	0.588781	+	0.808293i	$0.299608\pi$
$198$	2.59675	0.184543
$199$	13.4164	0.951064	0.475532	−	0.879698i	$-0.342256\pi$
$199$	13.4164	0.951064	0.475532	+	0.879698i	$0.342256\pi$
$200$	−1.47214	−0.104096
$201$	3.32624	0.234615
$202$	2.27051	0.159753
$203$	−20.5623	−1.44319
$204$	4.24922	0.297505
$205$	11.1803	0.780869
$206$	0.639320	0.0445436
$207$	−1.76393	−0.122602
$208$	15.7295	1.09064
$209$	0	0
$210$	0.618034	0.0426484
$211$	−6.90983	−0.475692	−0.237846	−	0.971303i	$-0.576441\pi$
$211$	−6.90983	−0.475692	−0.237846	+	0.971303i	$0.576441\pi$
$212$	−6.27051	−0.430660
$213$	3.14590	0.215553
$214$	1.14590	0.0783320
$215$	−3.85410	−0.262848
$216$	3.29180	0.223978
$217$	−45.9787	−3.12124
$218$	0.673762	0.0456329
$219$	−0.381966	−0.0258109
$220$	−4.41641	−0.297754
$221$	−30.0000	−2.01802
$222$	0.708204	0.0475315
$223$	10.2361	0.685458	0.342729	−	0.939434i	$-0.388649\pi$
$223$	10.2361	0.685458	0.342729	+	0.939434i	$0.388649\pi$
$224$	−17.5623	−1.17343
$225$	−2.85410	−0.190273
$226$	−5.70820	−0.379704
$227$	17.6525	1.17164	0.585818	−	0.810443i	$-0.300773\pi$
$227$	17.6525	1.17164	0.585818	+	0.810443i	$0.300773\pi$
$228$	0	0
$229$	−21.6180	−1.42856	−0.714280	−	0.699860i	$-0.753246\pi$
$229$	−21.6180	−1.42856	−0.714280	+	0.699860i	$0.753246\pi$
$230$	−0.236068	−0.0155659
$231$	3.85410	0.253581
$232$	−7.14590	−0.469151
$233$	−6.81966	−0.446771	−0.223385	−	0.974730i	$-0.571711\pi$
$233$	−6.81966	−0.446771	−0.223385	+	0.974730i	$0.571711\pi$
$234$	−5.45085	−0.356333
$235$	5.76393	0.375997
$236$	20.5623	1.33849
$237$	3.05573	0.198491
$238$	9.70820	0.629289
$239$	23.5623	1.52412	0.762059	−	0.647507i	$-0.224188\pi$
$239$	23.5623	1.52412	0.762059	+	0.647507i	$0.224188\pi$
$240$	−1.20163	−0.0775646
$241$	18.1246	1.16751	0.583754	−	0.811930i	$-0.301583\pi$
$241$	18.1246	1.16751	0.583754	+	0.811930i	$0.301583\pi$
$242$	−2.03444	−0.130779
$243$	9.65248	0.619207
$244$	5.56231	0.356090
$245$	−10.9443	−0.699204
$246$	−1.63119	−0.104001
$247$	0	0
$248$	−15.9787	−1.01465
$249$	−1.70820	−0.108253
$250$	−0.381966	−0.0241577
$251$	15.1803	0.958175	0.479087	−	0.877767i	$-0.340968\pi$
$251$	15.1803	0.958175	0.479087	+	0.877767i	$0.340968\pi$
$252$	−22.4164	−1.41210
$253$	−1.47214	−0.0925524
$254$	4.09017	0.256640
$255$	2.29180	0.143518
$256$	5.56231	0.347644
$257$	13.5279	0.843845	0.421922	−	0.906632i	$-0.361355\pi$
$257$	13.5279	0.843845	0.421922	+	0.906632i	$0.361355\pi$
$258$	0.562306	0.0350076
$259$	−20.5623	−1.27768
$260$	9.27051	0.574933
$261$	−13.8541	−0.857547
$262$	−3.00000	−0.185341
$263$	−19.8885	−1.22638	−0.613190	−	0.789935i	$-0.710114\pi$
$263$	−19.8885	−1.22638	−0.613190	+	0.789935i	$0.710114\pi$
$264$	1.33939	0.0824340
$265$	−3.38197	−0.207753
$266$	0	0
$267$	2.56231	0.156811
$268$	−16.1459	−0.986268
$269$	1.67376	0.102051	0.0510255	−	0.998697i	$-0.483751\pi$
$269$	1.67376	0.102051	0.0510255	+	0.998697i	$0.483751\pi$
$270$	0.854102	0.0519790
$271$	16.3820	0.995134	0.497567	−	0.867426i	$-0.334227\pi$
$271$	16.3820	0.995134	0.497567	+	0.867426i	$0.334227\pi$
$272$	−18.8754	−1.14449
$273$	−8.09017	−0.489639
$274$	0.450850	0.0272368
$275$	−2.38197	−0.143638
$276$	−0.437694	−0.0263461
$277$	−25.4164	−1.52712	−0.763562	−	0.645735i	$-0.776551\pi$
$277$	−25.4164	−1.52712	−0.763562	+	0.645735i	$0.776551\pi$
$278$	3.11146	0.186613
$279$	−30.9787	−1.85465
$280$	−6.23607	−0.372676
$281$	27.5066	1.64090	0.820452	−	0.571715i	$-0.193722\pi$
$281$	27.5066	1.64090	0.820452	+	0.571715i	$0.193722\pi$
$282$	−0.840946	−0.0500776
$283$	4.61803	0.274514	0.137257	−	0.990535i	$-0.456171\pi$
$283$	4.61803	0.274514	0.137257	+	0.990535i	$0.456171\pi$
$284$	−15.2705	−0.906138
$285$	0	0
$286$	−4.54915	−0.268997
$287$	47.3607	2.79561
$288$	−11.8328	−0.697255
$289$	19.0000	1.11765
$290$	−1.85410	−0.108877
$291$	−1.94427	−0.113975
$292$	1.85410	0.108503
$293$	22.0344	1.28727	0.643633	−	0.765334i	$-0.277426\pi$
$293$	22.0344	1.28727	0.643633	+	0.765334i	$0.277426\pi$
$294$	1.59675	0.0931242
$295$	11.0902	0.645695
$296$	−7.14590	−0.415347
$297$	5.32624	0.309060
$298$	−2.90983	−0.168562
$299$	3.09017	0.178709
$300$	−0.708204	−0.0408882
$301$	−16.3262	−0.941029
$302$	−2.81966	−0.162253
$303$	2.27051	0.130437
$304$	0	0
$305$	3.00000	0.171780
$306$	6.54102	0.373925
$307$	−12.2705	−0.700315	−0.350157	−	0.936691i	$-0.613872\pi$
$307$	−12.2705	−0.700315	−0.350157	+	0.936691i	$0.613872\pi$
$308$	−18.7082	−1.06600
$309$	0.639320	0.0363697
$310$	−4.14590	−0.235471
$311$	−7.05573	−0.400094	−0.200047	−	0.979786i	$-0.564109\pi$
$311$	−7.05573	−0.400094	−0.200047	+	0.979786i	$0.564109\pi$
$312$	−2.81153	−0.159172
$313$	−9.79837	−0.553837	−0.276918	−	0.960893i	$-0.589313\pi$
$313$	−9.79837	−0.553837	−0.276918	+	0.960893i	$0.589313\pi$
$314$	−9.18034	−0.518077
$315$	−12.0902	−0.681204
$316$	−14.8328	−0.834411
$317$	−13.2361	−0.743412	−0.371706	−	0.928351i	$-0.621227\pi$
$317$	−13.2361	−0.743412	−0.371706	+	0.928351i	$0.621227\pi$
$318$	0.493422	0.0276697
$319$	−11.5623	−0.647365
$320$	4.70820	0.263197
$321$	1.14590	0.0639578
$322$	−1.00000	−0.0557278
$323$	0	0
$324$	−14.2918	−0.793989
$325$	5.00000	0.277350
$326$	3.25735	0.180408
$327$	0.673762	0.0372591
$328$	16.4590	0.908795
$329$	24.4164	1.34612
$330$	0.347524	0.0191306
$331$	−0.291796	−0.0160386	−0.00801928	−	0.999968i	$-0.502553\pi$
$331$	−0.291796	−0.0160386	−0.00801928	+	0.999968i	$0.502553\pi$
$332$	8.29180	0.455071
$333$	−13.8541	−0.759200
$334$	3.14590	0.172136
$335$	−8.70820	−0.475780
$336$	−5.09017	−0.277692
$337$	28.0000	1.52526	0.762629	−	0.646837i	$-0.223908\pi$
$337$	28.0000	1.52526	0.762629	+	0.646837i	$0.223908\pi$
$338$	4.58359	0.249315
$339$	−5.70820	−0.310027
$340$	−11.1246	−0.603317
$341$	−25.8541	−1.40008
$342$	0	0
$343$	−16.7082	−0.902158
$344$	−5.67376	−0.305909
$345$	−0.236068	−0.0127095
$346$	5.30495	0.285196
$347$	−19.8885	−1.06767	−0.533836	−	0.845588i	$-0.679250\pi$
$347$	−19.8885	−1.06767	−0.533836	+	0.845588i	$0.679250\pi$
$348$	−3.43769	−0.184280
$349$	21.7426	1.16386	0.581929	−	0.813240i	$-0.302298\pi$
$349$	21.7426	1.16386	0.581929	+	0.813240i	$0.302298\pi$
$350$	−1.61803	−0.0864876
$351$	−11.1803	−0.596762
$352$	−9.87539	−0.526360
$353$	−36.1591	−1.92455	−0.962276	−	0.272075i	$-0.912290\pi$
$353$	−36.1591	−1.92455	−0.962276	+	0.272075i	$0.912290\pi$
$354$	−1.61803	−0.0859975
$355$	−8.23607	−0.437125
$356$	−12.4377	−0.659196
$357$	9.70820	0.513813
$358$	4.02129	0.212532
$359$	26.3820	1.39239	0.696193	−	0.717854i	$-0.254876\pi$
$359$	26.3820	1.39239	0.696193	+	0.717854i	$0.254876\pi$
$360$	−4.20163	−0.221445
$361$	0	0
$362$	3.16718	0.166464
$363$	−2.03444	−0.106781
$364$	39.2705	2.05833
$365$	1.00000	0.0523424
$366$	−0.437694	−0.0228786
$367$	1.65248	0.0862585	0.0431293	−	0.999070i	$-0.486267\pi$
$367$	1.65248	0.0862585	0.0431293	+	0.999070i	$0.486267\pi$
$368$	1.94427	0.101352
$369$	31.9098	1.66116
$370$	−1.85410	−0.0963902
$371$	−14.3262	−0.743781
$372$	−7.68692	−0.398548
$373$	−6.70820	−0.347338	−0.173669	−	0.984804i	$-0.555562\pi$
$373$	−6.70820	−0.347338	−0.173669	+	0.984804i	$0.555562\pi$
$374$	5.45898	0.282277
$375$	−0.381966	−0.0197246
$376$	8.48529	0.437596
$377$	24.2705	1.24999
$378$	3.61803	0.186092
$379$	−26.8328	−1.37831	−0.689155	−	0.724614i	$-0.742018\pi$
$379$	−26.8328	−1.37831	−0.689155	+	0.724614i	$0.742018\pi$
$380$	0	0
$381$	4.09017	0.209546
$382$	2.31308	0.118348
$383$	32.9230	1.68229	0.841143	−	0.540813i	$-0.181883\pi$
$383$	32.9230	1.68229	0.841143	+	0.540813i	$0.181883\pi$
$384$	−3.85410	−0.196679
$385$	−10.0902	−0.514243
$386$	1.52786	0.0777662
$387$	−11.0000	−0.559161
$388$	9.43769	0.479126
$389$	−24.3262	−1.23339	−0.616695	−	0.787202i	$-0.711529\pi$
$389$	−24.3262	−1.23339	−0.616695	+	0.787202i	$0.711529\pi$
$390$	−0.729490	−0.0369392
$391$	−3.70820	−0.187532
$392$	−16.1115	−0.813751
$393$	−3.00000	−0.151330
$394$	6.31308	0.318048
$395$	−8.00000	−0.402524
$396$	−12.6049	−0.633419
$397$	−16.8885	−0.847612	−0.423806	−	0.905753i	$-0.639306\pi$
$397$	−16.8885	−0.847612	−0.423806	+	0.905753i	$0.639306\pi$
$398$	5.12461	0.256874
$399$	0	0
$400$	3.14590	0.157295
$401$	6.76393	0.337775	0.168887	−	0.985635i	$-0.445983\pi$
$401$	6.76393	0.337775	0.168887	+	0.985635i	$0.445983\pi$
$402$	1.27051	0.0633673
$403$	54.2705	2.70341
$404$	−11.0213	−0.548329
$405$	−7.70820	−0.383024
$406$	−7.85410	−0.389793
$407$	−11.5623	−0.573122
$408$	3.37384	0.167030
$409$	−1.70820	−0.0844652	−0.0422326	−	0.999108i	$-0.513447\pi$
$409$	−1.70820	−0.0844652	−0.0422326	+	0.999108i	$0.513447\pi$
$410$	4.27051	0.210905
$411$	0.450850	0.0222388
$412$	−3.10333	−0.152890
$413$	46.9787	2.31167
$414$	−0.673762	−0.0331136
$415$	4.47214	0.219529
$416$	20.7295	1.01635
$417$	3.11146	0.152369
$418$	0	0
$419$	1.05573	0.0515757	0.0257878	−	0.999667i	$-0.491791\pi$
$419$	1.05573	0.0515757	0.0257878	+	0.999667i	$0.491791\pi$
$420$	−3.00000	−0.146385
$421$	26.1246	1.27324	0.636618	−	0.771179i	$-0.280333\pi$
$421$	26.1246	1.27324	0.636618	+	0.771179i	$0.280333\pi$
$422$	−2.63932	−0.128480
$423$	16.4508	0.799868
$424$	−4.97871	−0.241788
$425$	−6.00000	−0.291043
$426$	1.20163	0.0582190
$427$	12.7082	0.614993
$428$	−5.56231	−0.268864
$429$	−4.54915	−0.219635
$430$	−1.47214	−0.0709927
$431$	−25.1803	−1.21289	−0.606447	−	0.795124i	$-0.707406\pi$
$431$	−25.1803	−1.21289	−0.606447	+	0.795124i	$0.707406\pi$
$432$	−7.03444	−0.338445
$433$	−29.2148	−1.40397	−0.701986	−	0.712190i	$-0.747703\pi$
$433$	−29.2148	−1.40397	−0.701986	+	0.712190i	$0.747703\pi$
$434$	−17.5623	−0.843018
$435$	−1.85410	−0.0888974
$436$	−3.27051	−0.156629
$437$	0	0
$438$	−0.145898	−0.00697128
$439$	3.47214	0.165716	0.0828580	−	0.996561i	$-0.473595\pi$
$439$	3.47214	0.165716	0.0828580	+	0.996561i	$0.473595\pi$
$440$	−3.50658	−0.167170
$441$	−31.2361	−1.48743
$442$	−11.4590	−0.545048
$443$	−29.3607	−1.39497	−0.697484	−	0.716600i	$-0.745697\pi$
$443$	−29.3607	−1.39497	−0.697484	+	0.716600i	$0.745697\pi$
$444$	−3.43769	−0.163146
$445$	−6.70820	−0.317999
$446$	3.90983	0.185136
$447$	−2.90983	−0.137630
$448$	19.9443	0.942278
$449$	41.4721	1.95719	0.978596	−	0.205793i	$-0.0659773\pi$
$449$	41.4721	1.95719	0.978596	+	0.205793i	$0.0659773\pi$
$450$	−1.09017	−0.0513911
$451$	26.6312	1.25401
$452$	27.7082	1.30328
$453$	−2.81966	−0.132479
$454$	6.74265	0.316448
$455$	21.1803	0.992950
$456$	0	0
$457$	−6.00000	−0.280668	−0.140334	−	0.990104i	$-0.544818\pi$
$457$	−6.00000	−0.280668	−0.140334	+	0.990104i	$0.544818\pi$
$458$	−8.25735	−0.385841
$459$	13.4164	0.626224
$460$	1.14590	0.0534278
$461$	−1.05573	−0.0491702	−0.0245851	−	0.999698i	$-0.507826\pi$
$461$	−1.05573	−0.0491702	−0.0245851	+	0.999698i	$0.507826\pi$
$462$	1.47214	0.0684900
$463$	33.0344	1.53524	0.767620	−	0.640905i	$-0.221441\pi$
$463$	33.0344	1.53524	0.767620	+	0.640905i	$0.221441\pi$
$464$	15.2705	0.708916
$465$	−4.14590	−0.192261
$466$	−2.60488	−0.120669
$467$	−24.7082	−1.14336	−0.571680	−	0.820477i	$-0.693708\pi$
$467$	−24.7082	−1.14336	−0.571680	+	0.820477i	$0.693708\pi$
$468$	26.4590	1.22307
$469$	−36.8885	−1.70335
$470$	2.20163	0.101553
$471$	−9.18034	−0.423008
$472$	16.3262	0.751476
$473$	−9.18034	−0.422112
$474$	1.16718	0.0536105
$475$	0	0
$476$	−47.1246	−2.15995
$477$	−9.65248	−0.441957
$478$	9.00000	0.411650
$479$	−10.6180	−0.485150	−0.242575	−	0.970133i	$-0.577992\pi$
$479$	−10.6180	−0.485150	−0.242575	+	0.970133i	$0.577992\pi$
$480$	−1.58359	−0.0722808
$481$	24.2705	1.10664
$482$	6.92299	0.315333
$483$	−1.00000	−0.0455016
$484$	9.87539	0.448881
$485$	5.09017	0.231133
$486$	3.68692	0.167242
$487$	−35.4164	−1.60487	−0.802435	−	0.596739i	$-0.796463\pi$
$487$	−35.4164	−1.60487	−0.802435	+	0.596739i	$0.796463\pi$
$488$	4.41641	0.199921
$489$	3.25735	0.147303
$490$	−4.18034	−0.188849
$491$	8.67376	0.391441	0.195721	−	0.980660i	$-0.437295\pi$
$491$	8.67376	0.391441	0.195721	+	0.980660i	$0.437295\pi$
$492$	7.91796	0.356969
$493$	−29.1246	−1.31171
$494$	0	0
$495$	−6.79837	−0.305564
$496$	34.1459	1.53320
$497$	−34.8885	−1.56497
$498$	−0.652476	−0.0292381
$499$	26.6525	1.19313	0.596564	−	0.802565i	$-0.296532\pi$
$499$	26.6525	1.19313	0.596564	+	0.802565i	$0.296532\pi$
$500$	1.85410	0.0829180
$501$	3.14590	0.140548
$502$	5.79837	0.258794
$503$	−2.05573	−0.0916604	−0.0458302	−	0.998949i	$-0.514593\pi$
$503$	−2.05573	−0.0916604	−0.0458302	+	0.998949i	$0.514593\pi$
$504$	−17.7984	−0.792803
$505$	−5.94427	−0.264517
$506$	−0.562306	−0.0249975
$507$	4.58359	0.203564
$508$	−19.8541	−0.880883
$509$	10.7984	0.478630	0.239315	−	0.970942i	$-0.423077\pi$
$509$	10.7984	0.478630	0.239315	+	0.970942i	$0.423077\pi$
$510$	0.875388	0.0387628
$511$	4.23607	0.187393
$512$	22.3050	0.985749
$513$	0	0
$514$	5.16718	0.227915
$515$	−1.67376	−0.0737548
$516$	−2.72949	−0.120159
$517$	13.7295	0.603822
$518$	−7.85410	−0.345089
$519$	5.30495	0.232862
$520$	7.36068	0.322787
$521$	−0.381966	−0.0167342	−0.00836712	−	0.999965i	$-0.502663\pi$
$521$	−0.381966	−0.0167342	−0.00836712	+	0.999965i	$0.502663\pi$
$522$	−5.29180	−0.231616
$523$	10.5967	0.463363	0.231682	−	0.972792i	$-0.425577\pi$
$523$	10.5967	0.463363	0.231682	+	0.972792i	$0.425577\pi$
$524$	14.5623	0.636157
$525$	−1.61803	−0.0706168
$526$	−7.59675	−0.331234
$527$	−65.1246	−2.83687
$528$	−2.86223	−0.124563
$529$	−22.6180	−0.983393
$530$	−1.29180	−0.0561120
$531$	31.6525	1.37360
$532$	0	0
$533$	−55.9017	−2.42137
$534$	0.978714	0.0423531
$535$	−3.00000	−0.129701
$536$	−12.8197	−0.553725
$537$	4.02129	0.173531
$538$	0.639320	0.0275631
$539$	−26.0689	−1.12287
$540$	−4.14590	−0.178411
$541$	32.5967	1.40144	0.700722	−	0.713435i	$-0.252861\pi$
$541$	32.5967	1.40144	0.700722	+	0.713435i	$0.252861\pi$
$542$	6.25735	0.268776
$543$	3.16718	0.135917
$544$	−24.8754	−1.06652
$545$	−1.76393	−0.0755585
$546$	−3.09017	−0.132247
$547$	37.9787	1.62385	0.811926	−	0.583760i	$-0.198419\pi$
$547$	37.9787	1.62385	0.811926	+	0.583760i	$0.198419\pi$
$548$	−2.18847	−0.0934868
$549$	8.56231	0.365430
$550$	−0.909830	−0.0387953
$551$	0	0
$552$	−0.347524	−0.0147916
$553$	−33.8885	−1.44109
$554$	−9.70820	−0.412462
$555$	−1.85410	−0.0787022
$556$	−15.1033	−0.640524
$557$	−21.4721	−0.909804	−0.454902	−	0.890542i	$-0.650326\pi$
$557$	−21.4721	−0.909804	−0.454902	+	0.890542i	$0.650326\pi$
$558$	−11.8328	−0.500923
$559$	19.2705	0.815056
$560$	13.3262	0.563136
$561$	5.45898	0.230478
$562$	10.5066	0.443193
$563$	−30.1803	−1.27195	−0.635975	−	0.771710i	$-0.719402\pi$
$563$	−30.1803	−1.27195	−0.635975	+	0.771710i	$0.719402\pi$
$564$	4.08204	0.171885
$565$	14.9443	0.628710
$566$	1.76393	0.0741436
$567$	−32.6525	−1.37128
$568$	−12.1246	−0.508737
$569$	−0.437694	−0.0183491	−0.00917455	−	0.999958i	$-0.502920\pi$
$569$	−0.437694	−0.0183491	−0.00917455	+	0.999958i	$0.502920\pi$
$570$	0	0
$571$	26.8541	1.12381	0.561905	−	0.827202i	$-0.310069\pi$
$571$	26.8541	1.12381	0.561905	+	0.827202i	$0.310069\pi$
$572$	22.0820	0.923296
$573$	2.31308	0.0966304
$574$	18.0902	0.755069
$575$	0.618034	0.0257738
$576$	13.4377	0.559904
$577$	19.7639	0.822783	0.411392	−	0.911459i	$-0.365043\pi$
$577$	19.7639	0.822783	0.411392	+	0.911459i	$0.365043\pi$
$578$	7.25735	0.301866
$579$	1.52786	0.0634959
$580$	9.00000	0.373705
$581$	18.9443	0.785941
$582$	−0.742646	−0.0307837
$583$	−8.05573	−0.333634
$584$	1.47214	0.0609174
$585$	14.2705	0.590013
$586$	8.41641	0.347679
$587$	−42.2361	−1.74327	−0.871635	−	0.490156i	$-0.836940\pi$
$587$	−42.2361	−1.74327	−0.871635	+	0.490156i	$0.836940\pi$
$588$	−7.75078	−0.319637
$589$	0	0
$590$	4.23607	0.174396
$591$	6.31308	0.259686
$592$	15.2705	0.627614
$593$	−15.6525	−0.642770	−0.321385	−	0.946949i	$-0.604148\pi$
$593$	−15.6525	−0.642770	−0.321385	+	0.946949i	$0.604148\pi$
$594$	2.03444	0.0834742
$595$	−25.4164	−1.04197
$596$	14.1246	0.578567
$597$	5.12461	0.209736
$598$	1.18034	0.0482677
$599$	7.36068	0.300749	0.150375	−	0.988629i	$-0.451952\pi$
$599$	7.36068	0.300749	0.150375	+	0.988629i	$0.451952\pi$
$600$	−0.562306	−0.0229560
$601$	22.0000	0.897399	0.448699	−	0.893683i	$-0.351887\pi$
$601$	22.0000	0.897399	0.448699	+	0.893683i	$0.351887\pi$
$602$	−6.23607	−0.254163
$603$	−24.8541	−1.01214
$604$	13.6869	0.556913
$605$	5.32624	0.216542
$606$	0.867258	0.0352299
$607$	−16.5623	−0.672243	−0.336122	−	0.941819i	$-0.609115\pi$
$607$	−16.5623	−0.672243	−0.336122	+	0.941819i	$0.609115\pi$
$608$	0	0
$609$	−7.85410	−0.318264
$610$	1.14590	0.0463961
$611$	−28.8197	−1.16592
$612$	−31.7508	−1.28345
$613$	4.05573	0.163809	0.0819047	−	0.996640i	$-0.473900\pi$
$613$	4.05573	0.163809	0.0819047	+	0.996640i	$0.473900\pi$
$614$	−4.68692	−0.189149
$615$	4.27051	0.172204
$616$	−14.8541	−0.598489
$617$	−12.9098	−0.519730	−0.259865	−	0.965645i	$-0.583678\pi$
$617$	−12.9098	−0.519730	−0.259865	+	0.965645i	$0.583678\pi$
$618$	0.244199	0.00982311
$619$	−8.05573	−0.323787	−0.161894	−	0.986808i	$-0.551760\pi$
$619$	−8.05573	−0.323787	−0.161894	+	0.986808i	$0.551760\pi$
$620$	20.1246	0.808224
$621$	−1.38197	−0.0554564
$622$	−2.69505	−0.108062
$623$	−28.4164	−1.13848
$624$	6.00813	0.240518
$625$	1.00000	0.0400000
$626$	−3.74265	−0.149586
$627$	0	0
$628$	44.5623	1.77823
$629$	−29.1246	−1.16127
$630$	−4.61803	−0.183987
$631$	15.0000	0.597141	0.298570	−	0.954388i	$-0.403490\pi$
$631$	15.0000	0.597141	0.298570	+	0.954388i	$0.403490\pi$
$632$	−11.7771	−0.468467
$633$	−2.63932	−0.104904
$634$	−5.05573	−0.200789
$635$	−10.7082	−0.424942
$636$	−2.39512	−0.0949728
$637$	54.7214	2.16814
$638$	−4.41641	−0.174847
$639$	−23.5066	−0.929906
$640$	10.0902	0.398849
$641$	5.72949	0.226301	0.113151	−	0.993578i	$-0.463906\pi$
$641$	5.72949	0.226301	0.113151	+	0.993578i	$0.463906\pi$
$642$	0.437694	0.0172744
$643$	31.5967	1.24605	0.623027	−	0.782200i	$-0.285903\pi$
$643$	31.5967	1.24605	0.623027	+	0.782200i	$0.285903\pi$
$644$	4.85410	0.191278
$645$	−1.47214	−0.0579653
$646$	0	0
$647$	36.3050	1.42729	0.713647	−	0.700505i	$-0.247042\pi$
$647$	36.3050	1.42729	0.713647	+	0.700505i	$0.247042\pi$
$648$	−11.3475	−0.445773
$649$	26.4164	1.03693
$650$	1.90983	0.0749097
$651$	−17.5623	−0.688321
$652$	−15.8115	−0.619227
$653$	7.85410	0.307355	0.153677	−	0.988121i	$-0.450888\pi$
$653$	7.85410	0.307355	0.153677	+	0.988121i	$0.450888\pi$
$654$	0.257354	0.0100633
$655$	7.85410	0.306885
$656$	−35.1722	−1.37324
$657$	2.85410	0.111349
$658$	9.32624	0.363575
$659$	42.4721	1.65448	0.827240	−	0.561849i	$-0.189910\pi$
$659$	42.4721	1.65448	0.827240	+	0.561849i	$0.189910\pi$
$660$	−1.68692	−0.0656632
$661$	−3.70820	−0.144232	−0.0721162	−	0.997396i	$-0.522975\pi$
$661$	−3.70820	−0.144232	−0.0721162	+	0.997396i	$0.522975\pi$
$662$	−0.111456	−0.00433187
$663$	−11.4590	−0.445030
$664$	6.58359	0.255493
$665$	0	0
$666$	−5.29180	−0.205053
$667$	3.00000	0.116160
$668$	−15.2705	−0.590834
$669$	3.90983	0.151163
$670$	−3.32624	−0.128504
$671$	7.14590	0.275864
$672$	−6.70820	−0.258775
$673$	−11.1115	−0.428315	−0.214158	−	0.976799i	$-0.568701\pi$
$673$	−11.1115	−0.428315	−0.214158	+	0.976799i	$0.568701\pi$
$674$	10.6950	0.411958
$675$	−2.23607	−0.0860663
$676$	−22.2492	−0.855739
$677$	−8.38197	−0.322145	−0.161073	−	0.986943i	$-0.551495\pi$
$677$	−8.38197	−0.322145	−0.161073	+	0.986943i	$0.551495\pi$
$678$	−2.18034	−0.0837354
$679$	21.5623	0.827485
$680$	−8.83282	−0.338723
$681$	6.74265	0.258379
$682$	−9.87539	−0.378148
$683$	23.4721	0.898136	0.449068	−	0.893498i	$-0.351756\pi$
$683$	23.4721	0.898136	0.449068	+	0.893498i	$0.351756\pi$
$684$	0	0
$685$	−1.18034	−0.0450985
$686$	−6.38197	−0.243665
$687$	−8.25735	−0.315038
$688$	12.1246	0.462246
$689$	16.9098	0.644213
$690$	−0.0901699	−0.00343271
$691$	21.4721	0.816839	0.408419	−	0.912794i	$-0.366080\pi$
$691$	21.4721	0.816839	0.408419	+	0.912794i	$0.366080\pi$
$692$	−25.7508	−0.978898
$693$	−28.7984	−1.09396
$694$	−7.59675	−0.288369
$695$	−8.14590	−0.308992
$696$	−2.72949	−0.103461
$697$	67.0820	2.54091
$698$	8.30495	0.314347
$699$	−2.60488	−0.0985255
$700$	7.85410	0.296857
$701$	48.5755	1.83467	0.917335	−	0.398116i	$-0.130336\pi$
$701$	48.5755	1.83467	0.917335	+	0.398116i	$0.130336\pi$
$702$	−4.27051	−0.161180
$703$	0	0
$704$	11.2148	0.422673
$705$	2.20163	0.0829180
$706$	−13.8115	−0.519804
$707$	−25.1803	−0.947004
$708$	7.85410	0.295175
$709$	−15.7082	−0.589934	−0.294967	−	0.955507i	$-0.595309\pi$
$709$	−15.7082	−0.589934	−0.294967	+	0.955507i	$0.595309\pi$
$710$	−3.14590	−0.118063
$711$	−22.8328	−0.856297
$712$	−9.87539	−0.370096
$713$	6.70820	0.251224
$714$	3.70820	0.138776
$715$	11.9098	0.445402
$716$	−19.5197	−0.729487
$717$	9.00000	0.336111
$718$	10.0770	0.376071
$719$	12.2016	0.455044	0.227522	−	0.973773i	$-0.426938\pi$
$719$	12.2016	0.455044	0.227522	+	0.973773i	$0.426938\pi$
$720$	8.97871	0.334617
$721$	−7.09017	−0.264052
$722$	0	0
$723$	6.92299	0.257469
$724$	−15.3738	−0.571364
$725$	4.85410	0.180277
$726$	−0.777088	−0.0288404
$727$	−10.5836	−0.392524	−0.196262	−	0.980552i	$-0.562880\pi$
$727$	−10.5836	−0.392524	−0.196262	+	0.980552i	$0.562880\pi$
$728$	31.1803	1.15562
$729$	−19.4377	−0.719915
$730$	0.381966	0.0141372
$731$	−23.1246	−0.855295
$732$	2.12461	0.0785279
$733$	0.236068	0.00871937	0.00435968	−	0.999990i	$-0.498612\pi$
$733$	0.236068	0.00871937	0.00435968	+	0.999990i	$0.498612\pi$
$734$	0.631190	0.0232976
$735$	−4.18034	−0.154194
$736$	2.56231	0.0944478
$737$	−20.7426	−0.764065
$738$	12.1885	0.448664
$739$	−21.8328	−0.803133	−0.401567	−	0.915830i	$-0.631534\pi$
$739$	−21.8328	−0.803133	−0.401567	+	0.915830i	$0.631534\pi$
$740$	9.00000	0.330847
$741$	0	0
$742$	−5.47214	−0.200888
$743$	36.2361	1.32937	0.664686	−	0.747123i	$-0.268565\pi$
$743$	36.2361	1.32937	0.664686	+	0.747123i	$0.268565\pi$
$744$	−6.10333	−0.223759
$745$	7.61803	0.279103
$746$	−2.56231	−0.0938127
$747$	12.7639	0.467008
$748$	−26.4984	−0.968879
$749$	−12.7082	−0.464348
$750$	−0.145898	−0.00532744
$751$	−2.56231	−0.0934999	−0.0467499	−	0.998907i	$-0.514886\pi$
$751$	−2.56231	−0.0934999	−0.0467499	+	0.998907i	$0.514886\pi$
$752$	−18.1327	−0.661233
$753$	5.79837	0.211304
$754$	9.27051	0.337612
$755$	7.38197	0.268657
$756$	−17.5623	−0.638735
$757$	−14.3820	−0.522721	−0.261361	−	0.965241i	$-0.584171\pi$
$757$	−14.3820	−0.522721	−0.261361	+	0.965241i	$0.584171\pi$
$758$	−10.2492	−0.372269
$759$	−0.562306	−0.0204104
$760$	0	0
$761$	37.3607	1.35432	0.677162	−	0.735834i	$-0.263210\pi$
$761$	37.3607	1.35432	0.677162	+	0.735834i	$0.263210\pi$
$762$	1.56231	0.0565964
$763$	−7.47214	−0.270509
$764$	−11.2279	−0.406213
$765$	−17.1246	−0.619142
$766$	12.5755	0.454370
$767$	−55.4508	−2.00221
$768$	2.12461	0.0766653
$769$	13.6869	0.493563	0.246781	−	0.969071i	$-0.420627\pi$
$769$	13.6869	0.493563	0.246781	+	0.969071i	$0.420627\pi$
$770$	−3.85410	−0.138892
$771$	5.16718	0.186092
$772$	−7.41641	−0.266922
$773$	−39.7426	−1.42944	−0.714722	−	0.699409i	$-0.753447\pi$
$773$	−39.7426	−1.42944	−0.714722	+	0.699409i	$0.753447\pi$
$774$	−4.20163	−0.151024
$775$	10.8541	0.389891
$776$	7.49342	0.268998
$777$	−7.85410	−0.281764
$778$	−9.29180	−0.333127
$779$	0	0
$780$	3.54102	0.126789
$781$	−19.6180	−0.701988
$782$	−1.41641	−0.0506506
$783$	−10.8541	−0.387894
$784$	34.4296	1.22963
$785$	24.0344	0.857826
$786$	−1.14590	−0.0408728
$787$	−35.4853	−1.26491	−0.632457	−	0.774595i	$-0.717954\pi$
$787$	−35.4853	−1.26491	−0.632457	+	0.774595i	$0.717954\pi$
$788$	−30.6443	−1.09166
$789$	−7.59675	−0.270451
$790$	−3.05573	−0.108718
$791$	63.3050	2.25086
$792$	−10.0081	−0.355623
$793$	−15.0000	−0.532666
$794$	−6.45085	−0.228932
$795$	−1.29180	−0.0458153
$796$	−24.8754	−0.881685
$797$	−2.18034	−0.0772316	−0.0386158	−	0.999254i	$-0.512295\pi$
$797$	−2.18034	−0.0772316	−0.0386158	+	0.999254i	$0.512295\pi$
$798$	0	0
$799$	34.5836	1.22348
$800$	4.14590	0.146580
$801$	−19.1459	−0.676487
$802$	2.58359	0.0912298
$803$	2.38197	0.0840578
$804$	−6.16718	−0.217500
$805$	2.61803	0.0922736
$806$	20.7295	0.730165
$807$	0.639320	0.0225051
$808$	−8.75078	−0.307851
$809$	28.9098	1.01642	0.508208	−	0.861235i	$-0.330308\pi$
$809$	28.9098	1.01642	0.508208	+	0.861235i	$0.330308\pi$
$810$	−2.94427	−0.103451
$811$	40.3262	1.41605	0.708023	−	0.706190i	$-0.249587\pi$
$811$	40.3262	1.41605	0.708023	+	0.706190i	$0.249587\pi$
$812$	38.1246	1.33791
$813$	6.25735	0.219455
$814$	−4.41641	−0.154795
$815$	−8.52786	−0.298718
$816$	−7.20976	−0.252392
$817$	0	0
$818$	−0.652476	−0.0228133
$819$	60.4508	2.11232
$820$	−20.7295	−0.723905
$821$	12.3820	0.432134	0.216067	−	0.976379i	$-0.430677\pi$
$821$	12.3820	0.432134	0.216067	+	0.976379i	$0.430677\pi$
$822$	0.172209	0.00600649
$823$	8.36068	0.291435	0.145717	−	0.989326i	$-0.453451\pi$
$823$	8.36068	0.291435	0.145717	+	0.989326i	$0.453451\pi$
$824$	−2.46401	−0.0858377
$825$	−0.909830	−0.0316762
$826$	17.9443	0.624361
$827$	−35.8328	−1.24603	−0.623015	−	0.782210i	$-0.714092\pi$
$827$	−35.8328	−1.24603	−0.623015	+	0.782210i	$0.714092\pi$
$828$	3.27051	0.113658
$829$	43.3951	1.50717	0.753587	−	0.657348i	$-0.228322\pi$
$829$	43.3951	1.50717	0.753587	+	0.657348i	$0.228322\pi$
$830$	1.70820	0.0592926
$831$	−9.70820	−0.336774
$832$	−23.5410	−0.816138
$833$	−65.6656	−2.27518
$834$	1.18847	0.0411534
$835$	−8.23607	−0.285021
$836$	0	0
$837$	−24.2705	−0.838912
$838$	0.403252	0.0139301
$839$	−13.3820	−0.461997	−0.230998	−	0.972954i	$-0.574199\pi$
$839$	−13.3820	−0.461997	−0.230998	+	0.972954i	$0.574199\pi$
$840$	−2.38197	−0.0821856
$841$	−5.43769	−0.187507
$842$	9.97871	0.343889
$843$	10.5066	0.361866
$844$	12.8115	0.440991
$845$	−12.0000	−0.412813
$846$	6.28367	0.216037
$847$	22.5623	0.775250
$848$	10.6393	0.365356
$849$	1.76393	0.0605380
$850$	−2.29180	−0.0786080
$851$	3.00000	0.102839
$852$	−5.83282	−0.199829
$853$	52.9574	1.81323	0.906614	−	0.421961i	$-0.138658\pi$
$853$	52.9574	1.81323	0.906614	+	0.421961i	$0.138658\pi$
$854$	4.85410	0.166104
$855$	0	0
$856$	−4.41641	−0.150950
$857$	−32.6180	−1.11421	−0.557105	−	0.830442i	$-0.688088\pi$
$857$	−32.6180	−1.11421	−0.557105	+	0.830442i	$0.688088\pi$
$858$	−1.73762	−0.0593214
$859$	13.5967	0.463915	0.231958	−	0.972726i	$-0.425487\pi$
$859$	13.5967	0.463915	0.231958	+	0.972726i	$0.425487\pi$
$860$	7.14590	0.243673
$861$	18.0902	0.616511
$862$	−9.61803	−0.327592
$863$	−4.65248	−0.158372	−0.0791861	−	0.996860i	$-0.525232\pi$
$863$	−4.65248	−0.158372	−0.0791861	+	0.996860i	$0.525232\pi$
$864$	−9.27051	−0.315389
$865$	−13.8885	−0.472225
$866$	−11.1591	−0.379200
$867$	7.25735	0.246473
$868$	85.2492	2.89355
$869$	−19.0557	−0.646421
$870$	−0.708204	−0.0240104
$871$	43.5410	1.47533
$872$	−2.59675	−0.0879370
$873$	14.5279	0.491694
$874$	0	0
$875$	4.23607	0.143205
$876$	0.708204	0.0239280
$877$	−7.81966	−0.264051	−0.132026	−	0.991246i	$-0.542148\pi$
$877$	−7.81966	−0.264051	−0.132026	+	0.991246i	$0.542148\pi$
$878$	1.32624	0.0447584
$879$	8.41641	0.283878
$880$	7.49342	0.252603
$881$	25.0344	0.843432	0.421716	−	0.906728i	$-0.361428\pi$
$881$	25.0344	0.843432	0.421716	+	0.906728i	$0.361428\pi$
$882$	−11.9311	−0.401742
$883$	46.9230	1.57908	0.789542	−	0.613696i	$-0.210318\pi$
$883$	46.9230	1.57908	0.789542	+	0.613696i	$0.210318\pi$
$884$	55.6231	1.87081
$885$	4.23607	0.142394
$886$	−11.2148	−0.376768
$887$	12.4721	0.418773	0.209387	−	0.977833i	$-0.432853\pi$
$887$	12.4721	0.418773	0.209387	+	0.977833i	$0.432853\pi$
$888$	−2.72949	−0.0915957
$889$	−45.3607	−1.52135
$890$	−2.56231	−0.0858887
$891$	−18.3607	−0.615106
$892$	−18.9787	−0.635454
$893$	0	0
$894$	−1.11146	−0.0371727
$895$	−10.5279	−0.351908
$896$	42.7426	1.42793
$897$	1.18034	0.0394104
$898$	15.8409	0.528619
$899$	52.6869	1.75721
$900$	5.29180	0.176393
$901$	−20.2918	−0.676018
$902$	10.1722	0.338698
$903$	−6.23607	−0.207523
$904$	22.0000	0.731709
$905$	−8.29180	−0.275629
$906$	−1.07701	−0.0357814
$907$	−32.2492	−1.07082	−0.535409	−	0.844593i	$-0.679842\pi$
$907$	−32.2492	−1.07082	−0.535409	+	0.844593i	$0.679842\pi$
$908$	−32.7295	−1.08617
$909$	−16.9656	−0.562712
$910$	8.09017	0.268187
$911$	36.1033	1.19616	0.598078	−	0.801438i	$-0.295931\pi$
$911$	36.1033	1.19616	0.598078	+	0.801438i	$0.295931\pi$
$912$	0	0
$913$	10.6525	0.352545
$914$	−2.29180	−0.0758059
$915$	1.14590	0.0378822
$916$	40.0820	1.32435
$917$	33.2705	1.09869
$918$	5.12461	0.169137
$919$	22.8885	0.755023	0.377512	−	0.926005i	$-0.376780\pi$
$919$	22.8885	0.755023	0.377512	+	0.926005i	$0.376780\pi$
$920$	0.909830	0.0299962
$921$	−4.68692	−0.154439
$922$	−0.403252	−0.0132804
$923$	41.1803	1.35547
$924$	−7.14590	−0.235083
$925$	4.85410	0.159602
$926$	12.6180	0.414654
$927$	−4.77709	−0.156900
$928$	20.1246	0.660623
$929$	11.6180	0.381175	0.190588	−	0.981670i	$-0.438961\pi$
$929$	11.6180	0.381175	0.190588	+	0.981670i	$0.438961\pi$
$930$	−1.58359	−0.0519280
$931$	0	0
$932$	12.6443	0.414179
$933$	−2.69505	−0.0882319
$934$	−9.43769	−0.308811
$935$	−14.2918	−0.467392
$936$	21.0081	0.686672
$937$	2.56231	0.0837069	0.0418534	−	0.999124i	$-0.486674\pi$
$937$	2.56231	0.0837069	0.0418534	+	0.999124i	$0.486674\pi$
$938$	−14.0902	−0.460060
$939$	−3.74265	−0.122137
$940$	−10.6869	−0.348569
$941$	10.5066	0.342505	0.171252	−	0.985227i	$-0.445219\pi$
$941$	10.5066	0.342505	0.171252	+	0.985227i	$0.445219\pi$
$942$	−3.50658	−0.114250
$943$	−6.90983	−0.225015
$944$	−34.8885	−1.13553
$945$	−9.47214	−0.308129
$946$	−3.50658	−0.114009
$947$	48.0000	1.55979	0.779895	−	0.625910i	$-0.215272\pi$
$947$	48.0000	1.55979	0.779895	+	0.625910i	$0.215272\pi$
$948$	−5.66563	−0.184011
$949$	−5.00000	−0.162307
$950$	0	0
$951$	−5.05573	−0.163943
$952$	−37.4164	−1.21267
$953$	−11.8328	−0.383302	−0.191651	−	0.981463i	$-0.561384\pi$
$953$	−11.8328	−0.383302	−0.191651	+	0.981463i	$0.561384\pi$
$954$	−3.68692	−0.119368
$955$	−6.05573	−0.195959
$956$	−43.6869	−1.41294
$957$	−4.41641	−0.142762
$958$	−4.05573	−0.131035
$959$	−5.00000	−0.161458
$960$	1.79837	0.0580423
$961$	86.8115	2.80037
$962$	9.27051	0.298893
$963$	−8.56231	−0.275916
$964$	−33.6049	−1.08234
$965$	−4.00000	−0.128765
$966$	−0.381966	−0.0122896
$967$	28.7639	0.924986	0.462493	−	0.886623i	$-0.346955\pi$
$967$	28.7639	0.924986	0.462493	+	0.886623i	$0.346955\pi$
$968$	7.84095	0.252018
$969$	0	0
$970$	1.94427	0.0624268
$971$	−37.7984	−1.21301	−0.606504	−	0.795081i	$-0.707428\pi$
$971$	−37.7984	−1.21301	−0.606504	+	0.795081i	$0.707428\pi$
$972$	−17.8967	−0.574036
$973$	−34.5066	−1.10623
$974$	−13.5279	−0.433461
$975$	1.90983	0.0611635
$976$	−9.43769	−0.302093
$977$	53.6525	1.71649	0.858247	−	0.513236i	$-0.171554\pi$
$977$	53.6525	1.71649	0.858247	+	0.513236i	$0.171554\pi$
$978$	1.24420	0.0397851
$979$	−15.9787	−0.510682
$980$	20.2918	0.648198
$981$	−5.03444	−0.160737
$982$	3.31308	0.105725
$983$	13.8541	0.441877	0.220939	−	0.975288i	$-0.429088\pi$
$983$	13.8541	0.441877	0.220939	+	0.975288i	$0.429088\pi$
$984$	6.28677	0.200415
$985$	−16.5279	−0.526622
$986$	−11.1246	−0.354280
$987$	9.32624	0.296857
$988$	0	0
$989$	2.38197	0.0757421
$990$	−2.59675	−0.0825301
$991$	18.1459	0.576423	0.288212	−	0.957567i	$-0.406939\pi$
$991$	18.1459	0.576423	0.288212	+	0.957567i	$0.406939\pi$
$992$	45.0000	1.42875
$993$	−0.111456	−0.00353695
$994$	−13.3262	−0.422683
$995$	−13.4164	−0.425329
$996$	3.16718	0.100356
$997$	−3.23607	−0.102487	−0.0512437	−	0.998686i	$-0.516319\pi$
$997$	−3.23607	−0.102487	−0.0512437	+	0.998686i	$0.516319\pi$
$998$	10.1803	0.322253
$999$	−10.8541	−0.343409

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.e.1.1	yes	2
5.4	even	2		9025.2.a.k.1.2		2
19.18	odd	2		1805.2.a.c.1.2	✓	2
95.94	odd	2		9025.2.a.v.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1805.2.a.c.1.2	✓	2	19.18	odd	2
1805.2.a.e.1.1	yes	2	1.1	even	1	trivial
9025.2.a.k.1.2		2	5.4	even	2
9025.2.a.v.1.1		2	95.94	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.a (trivial)

\(f(q)\)	\(=\)	\(q+0.381966 q^{2} +0.381966 q^{3} -1.85410 q^{4} -1.00000 q^{5} +0.145898 q^{6} -4.23607 q^{7} -1.47214 q^{8} -2.85410 q^{9} +O(q^{10})\)	\(q+0.381966 q^{2} +0.381966 q^{3} -1.85410 q^{4} -1.00000 q^{5} +0.145898 q^{6} -4.23607 q^{7} -1.47214 q^{8} -2.85410 q^{9} -0.381966 q^{10} -2.38197 q^{11} -0.708204 q^{12} +5.00000 q^{13} -1.61803 q^{14} -0.381966 q^{15} +3.14590 q^{16} -6.00000 q^{17} -1.09017 q^{18} +1.85410 q^{20} -1.61803 q^{21} -0.909830 q^{22} +0.618034 q^{23} -0.562306 q^{24} +1.00000 q^{25} +1.90983 q^{26} -2.23607 q^{27} +7.85410 q^{28} +4.85410 q^{29} -0.145898 q^{30} +10.8541 q^{31} +4.14590 q^{32} -0.909830 q^{33} -2.29180 q^{34} +4.23607 q^{35} +5.29180 q^{36} +4.85410 q^{37} +1.90983 q^{39} +1.47214 q^{40} -11.1803 q^{41} -0.618034 q^{42} +3.85410 q^{43} +4.41641 q^{44} +2.85410 q^{45} +0.236068 q^{46} -5.76393 q^{47} +1.20163 q^{48} +10.9443 q^{49} +0.381966 q^{50} -2.29180 q^{51} -9.27051 q^{52} +3.38197 q^{53} -0.854102 q^{54} +2.38197 q^{55} +6.23607 q^{56} +1.85410 q^{58} -11.0902 q^{59} +0.708204 q^{60} -3.00000 q^{61} +4.14590 q^{62} +12.0902 q^{63} -4.70820 q^{64} -5.00000 q^{65} -0.347524 q^{66} +8.70820 q^{67} +11.1246 q^{68} +0.236068 q^{69} +1.61803 q^{70} +8.23607 q^{71} +4.20163 q^{72} -1.00000 q^{73} +1.85410 q^{74} +0.381966 q^{75} +10.0902 q^{77} +0.729490 q^{78} +8.00000 q^{79} -3.14590 q^{80} +7.70820 q^{81} -4.27051 q^{82} -4.47214 q^{83} +3.00000 q^{84} +6.00000 q^{85} +1.47214 q^{86} +1.85410 q^{87} +3.50658 q^{88} +6.70820 q^{89} +1.09017 q^{90} -21.1803 q^{91} -1.14590 q^{92} +4.14590 q^{93} -2.20163 q^{94} +1.58359 q^{96} -5.09017 q^{97} +4.18034 q^{98} +6.79837 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 2 q^{5} + 7 q^{6} - 4 q^{7} + 6 q^{8} + q^{9}+O(q^{10}) \) 2 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 2 * q^5 + 7 * q^6 - 4 * q^7 + 6 * q^8 + q^9	\( 2 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 2 q^{5} + 7 q^{6} - 4 q^{7} + 6 q^{8} + q^{9} - 3 q^{10} - 7 q^{11} + 12 q^{12} + 10 q^{13} - q^{14} - 3 q^{15} + 13 q^{16} - 12 q^{17} + 9 q^{18} - 3 q^{20} - q^{21} - 13 q^{22} - q^{23} + 19 q^{24} + 2 q^{25} + 15 q^{26} + 9 q^{28} + 3 q^{29} - 7 q^{30} + 15 q^{31} + 15 q^{32} - 13 q^{33} - 18 q^{34} + 4 q^{35} + 24 q^{36} + 3 q^{37} + 15 q^{39} - 6 q^{40} + q^{42} + q^{43} - 18 q^{44} - q^{45} - 4 q^{46} - 16 q^{47} + 27 q^{48} + 4 q^{49} + 3 q^{50} - 18 q^{51} + 15 q^{52} + 9 q^{53} + 5 q^{54} + 7 q^{55} + 8 q^{56} - 3 q^{58} - 11 q^{59} - 12 q^{60} - 6 q^{61} + 15 q^{62} + 13 q^{63} + 4 q^{64} - 10 q^{65} - 32 q^{66} + 4 q^{67} - 18 q^{68} - 4 q^{69} + q^{70} + 12 q^{71} + 33 q^{72} - 2 q^{73} - 3 q^{74} + 3 q^{75} + 9 q^{77} + 35 q^{78} + 16 q^{79} - 13 q^{80} + 2 q^{81} + 25 q^{82} + 6 q^{84} + 12 q^{85} - 6 q^{86} - 3 q^{87} - 31 q^{88} - 9 q^{90} - 20 q^{91} - 9 q^{92} + 15 q^{93} - 29 q^{94} + 30 q^{96} + q^{97} - 14 q^{98} - 11 q^{99}+O(q^{100}) \) 2 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 2 * q^5 + 7 * q^6 - 4 * q^7 + 6 * q^8 + q^9 - 3 * q^10 - 7 * q^11 + 12 * q^12 + 10 * q^13 - q^14 - 3 * q^15 + 13 * q^16 - 12 * q^17 + 9 * q^18 - 3 * q^20 - q^21 - 13 * q^22 - q^23 + 19 * q^24 + 2 * q^25 + 15 * q^26 + 9 * q^28 + 3 * q^29 - 7 * q^30 + 15 * q^31 + 15 * q^32 - 13 * q^33 - 18 * q^34 + 4 * q^35 + 24 * q^36 + 3 * q^37 + 15 * q^39 - 6 * q^40 + q^42 + q^43 - 18 * q^44 - q^45 - 4 * q^46 - 16 * q^47 + 27 * q^48 + 4 * q^49 + 3 * q^50 - 18 * q^51 + 15 * q^52 + 9 * q^53 + 5 * q^54 + 7 * q^55 + 8 * q^56 - 3 * q^58 - 11 * q^59 - 12 * q^60 - 6 * q^61 + 15 * q^62 + 13 * q^63 + 4 * q^64 - 10 * q^65 - 32 * q^66 + 4 * q^67 - 18 * q^68 - 4 * q^69 + q^70 + 12 * q^71 + 33 * q^72 - 2 * q^73 - 3 * q^74 + 3 * q^75 + 9 * q^77 + 35 * q^78 + 16 * q^79 - 13 * q^80 + 2 * q^81 + 25 * q^82 + 6 * q^84 + 12 * q^85 - 6 * q^86 - 3 * q^87 - 31 * q^88 - 9 * q^90 - 20 * q^91 - 9 * q^92 + 15 * q^93 - 29 * q^94 + 30 * q^96 + q^97 - 14 * q^98 - 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more