LMFDB - Embedded newform 1805.2.a.u.1.2

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:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 12x^{7} - 4x^{6} + 48x^{5} + 27x^{4} - 72x^{3} - 51x^{2} + 27x + 19 $ x^9 - 12x^7 - 4x^6 + 48x^5 + 27x^4 - 72x^3 - 51x^2 + 27*x + 19
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.81702$ 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)

$f(q)$	$=$	$q-1.81702 q^{2} -0.177104 q^{3} +1.30157 q^{4} -1.00000 q^{5} +0.321803 q^{6} +1.07346 q^{7} +1.26906 q^{8} -2.96863 q^{9} +O(q^{10})$	\(q-1.81702 q^{2} -0.177104 q^{3} +1.30157 q^{4} -1.00000 q^{5} +0.321803 q^{6} +1.07346 q^{7} +1.26906 q^{8} -2.96863 q^{9} +1.81702 q^{10} -3.31015 q^{11} -0.230514 q^{12} -2.65763 q^{13} -1.95051 q^{14} +0.177104 q^{15} -4.90905 q^{16} -3.99991 q^{17} +5.39408 q^{18} -1.30157 q^{20} -0.190115 q^{21} +6.01462 q^{22} +1.75378 q^{23} -0.224755 q^{24} +1.00000 q^{25} +4.82898 q^{26} +1.05707 q^{27} +1.39719 q^{28} -2.25251 q^{29} -0.321803 q^{30} +8.05272 q^{31} +6.38175 q^{32} +0.586242 q^{33} +7.26792 q^{34} -1.07346 q^{35} -3.86390 q^{36} +5.64805 q^{37} +0.470678 q^{39} -1.26906 q^{40} +0.896172 q^{41} +0.345443 q^{42} -8.51211 q^{43} -4.30841 q^{44} +2.96863 q^{45} -3.18666 q^{46} -6.29616 q^{47} +0.869414 q^{48} -5.84768 q^{49} -1.81702 q^{50} +0.708401 q^{51} -3.45911 q^{52} +3.39943 q^{53} -1.92072 q^{54} +3.31015 q^{55} +1.36228 q^{56} +4.09287 q^{58} +1.48676 q^{59} +0.230514 q^{60} +13.7298 q^{61} -14.6320 q^{62} -3.18672 q^{63} -1.77769 q^{64} +2.65763 q^{65} -1.06522 q^{66} -12.8597 q^{67} -5.20618 q^{68} -0.310602 q^{69} +1.95051 q^{70} -11.0262 q^{71} -3.76736 q^{72} -2.61065 q^{73} -10.2626 q^{74} -0.177104 q^{75} -3.55333 q^{77} -0.855233 q^{78} +6.57050 q^{79} +4.90905 q^{80} +8.71869 q^{81} -1.62837 q^{82} +2.69888 q^{83} -0.247449 q^{84} +3.99991 q^{85} +15.4667 q^{86} +0.398929 q^{87} -4.20077 q^{88} -0.789838 q^{89} -5.39408 q^{90} -2.85287 q^{91} +2.28268 q^{92} -1.42617 q^{93} +11.4403 q^{94} -1.13024 q^{96} +18.7179 q^{97} +10.6254 q^{98} +9.82663 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 3 q^{3} + 6 q^{4} - 9 q^{5} - 12 q^{6} - 12 q^{8} + 6 q^{9}+O(q^{10}) $ 9 * q + 3 * q^3 + 6 * q^4 - 9 * q^5 - 12 * q^6 - 12 * q^8 + 6 * q^9	$ 9 q + 3 q^{3} + 6 q^{4} - 9 q^{5} - 12 q^{6} - 12 q^{8} + 6 q^{9} + 6 q^{12} - 3 q^{13} + 12 q^{14} - 3 q^{15} - 12 q^{16} - 9 q^{17} + 6 q^{18} - 6 q^{20} + 12 q^{21} + 12 q^{22} + 15 q^{24} + 9 q^{25} + 21 q^{26} + 6 q^{27} - 15 q^{28} + 15 q^{29} + 12 q^{30} + 30 q^{31} - 9 q^{32} + 9 q^{33} - 6 q^{36} + 30 q^{37} + 6 q^{39} + 12 q^{40} + 18 q^{41} + 36 q^{42} - 6 q^{43} - 24 q^{44} - 6 q^{45} + 21 q^{46} + 21 q^{47} + 15 q^{48} + 3 q^{49} + 18 q^{51} - 3 q^{52} - 9 q^{53} - 9 q^{54} + 36 q^{56} + 18 q^{58} + 27 q^{59} - 6 q^{60} + 12 q^{61} - 6 q^{62} - 15 q^{63} + 24 q^{64} + 3 q^{65} + 3 q^{66} + 36 q^{67} + 3 q^{68} + 27 q^{69} - 12 q^{70} - 6 q^{71} + 12 q^{72} - 9 q^{73} - 9 q^{74} + 3 q^{75} + 12 q^{77} + 54 q^{78} + 45 q^{79} + 12 q^{80} - 15 q^{81} - 48 q^{82} - 12 q^{84} + 9 q^{85} - 9 q^{86} + 45 q^{87} + 39 q^{88} - 9 q^{89} - 6 q^{90} + 51 q^{91} - 54 q^{92} + 9 q^{93} + 33 q^{94} - 9 q^{96} + 45 q^{97} + 33 q^{98} + 12 q^{99}+O(q^{100}) $ 9 * q + 3 * q^3 + 6 * q^4 - 9 * q^5 - 12 * q^6 - 12 * q^8 + 6 * q^9 + 6 * q^12 - 3 * q^13 + 12 * q^14 - 3 * q^15 - 12 * q^16 - 9 * q^17 + 6 * q^18 - 6 * q^20 + 12 * q^21 + 12 * q^22 + 15 * q^24 + 9 * q^25 + 21 * q^26 + 6 * q^27 - 15 * q^28 + 15 * q^29 + 12 * q^30 + 30 * q^31 - 9 * q^32 + 9 * q^33 - 6 * q^36 + 30 * q^37 + 6 * q^39 + 12 * q^40 + 18 * q^41 + 36 * q^42 - 6 * q^43 - 24 * q^44 - 6 * q^45 + 21 * q^46 + 21 * q^47 + 15 * q^48 + 3 * q^49 + 18 * q^51 - 3 * q^52 - 9 * q^53 - 9 * q^54 + 36 * q^56 + 18 * q^58 + 27 * q^59 - 6 * q^60 + 12 * q^61 - 6 * q^62 - 15 * q^63 + 24 * q^64 + 3 * q^65 + 3 * q^66 + 36 * q^67 + 3 * q^68 + 27 * q^69 - 12 * q^70 - 6 * q^71 + 12 * q^72 - 9 * q^73 - 9 * q^74 + 3 * q^75 + 12 * q^77 + 54 * q^78 + 45 * q^79 + 12 * q^80 - 15 * q^81 - 48 * q^82 - 12 * q^84 + 9 * q^85 - 9 * q^86 + 45 * q^87 + 39 * q^88 - 9 * q^89 - 6 * q^90 + 51 * q^91 - 54 * q^92 + 9 * q^93 + 33 * q^94 - 9 * q^96 + 45 * q^97 + 33 * q^98 + 12 * 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 $

$2$	−1.81702	−1.28483	−0.642415	−	0.766357i	$-0.722067\pi$
$2$	−1.81702	−1.28483	−0.642415	+	0.766357i	$0.722067\pi$
$3$	−0.177104	−0.102251	−0.0511256	−	0.998692i	$-0.516281\pi$
$3$	−0.177104	−0.102251	−0.0511256	+	0.998692i	$0.516281\pi$
$4$	1.30157	0.650787
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.321803	0.131375
$7$	1.07346	0.405731	0.202865	−	0.979207i	$-0.434975\pi$
$7$	1.07346	0.405731	0.202865	+	0.979207i	$0.434975\pi$
$8$	1.26906	0.448679
$9$	−2.96863	−0.989545
$10$	1.81702	0.574593
$11$	−3.31015	−0.998048	−0.499024	−	0.866588i	$-0.666308\pi$
$11$	−3.31015	−0.998048	−0.499024	+	0.866588i	$0.666308\pi$
$12$	−0.230514	−0.0665438
$13$	−2.65763	−0.737094	−0.368547	−	0.929609i	$-0.620145\pi$
$13$	−2.65763	−0.737094	−0.368547	+	0.929609i	$0.620145\pi$
$14$	−1.95051	−0.521295
$15$	0.177104	0.0457281
$16$	−4.90905	−1.22726
$17$	−3.99991	−0.970120	−0.485060	−	0.874481i	$-0.661202\pi$
$17$	−3.99991	−0.970120	−0.485060	+	0.874481i	$0.661202\pi$
$18$	5.39408	1.27140
$19$	0	0
$19$	0	0
$20$	−1.30157	−0.291041
$21$	−0.190115	−0.0414865
$22$	6.01462	1.28232
$23$	1.75378	0.365689	0.182844	−	0.983142i	$-0.441470\pi$
$23$	1.75378	0.365689	0.182844	+	0.983142i	$0.441470\pi$
$24$	−0.224755	−0.0458780
$25$	1.00000	0.200000
$26$	4.82898	0.947041
$27$	1.05707	0.203433
$28$	1.39719	0.264044
$29$	−2.25251	−0.418281	−0.209140	−	0.977886i	$-0.567067\pi$
$29$	−2.25251	−0.418281	−0.209140	+	0.977886i	$0.567067\pi$
$30$	−0.321803	−0.0587529
$31$	8.05272	1.44631	0.723156	−	0.690685i	$-0.242691\pi$
$31$	8.05272	1.44631	0.723156	+	0.690685i	$0.242691\pi$
$32$	6.38175	1.12815
$33$	0.586242	0.102052
$34$	7.26792	1.24644
$35$	−1.07346	−0.181448
$36$	−3.86390	−0.643983
$37$	5.64805	0.928534	0.464267	−	0.885695i	$-0.346318\pi$
$37$	5.64805	0.928534	0.464267	+	0.885695i	$0.346318\pi$
$38$	0	0
$39$	0.470678	0.0753688
$40$	−1.26906	−0.200655
$41$	0.896172	0.139959	0.0699793	−	0.997548i	$-0.477707\pi$
$41$	0.896172	0.139959	0.0699793	+	0.997548i	$0.477707\pi$
$42$	0.345443	0.0533030
$43$	−8.51211	−1.29808	−0.649042	−	0.760752i	$-0.724830\pi$
$43$	−8.51211	−1.29808	−0.649042	+	0.760752i	$0.724830\pi$
$44$	−4.30841	−0.649517
$45$	2.96863	0.442538
$46$	−3.18666	−0.469848
$47$	−6.29616	−0.918389	−0.459194	−	0.888336i	$-0.651862\pi$
$47$	−6.29616	−0.918389	−0.459194	+	0.888336i	$0.651862\pi$
$48$	0.869414	0.125489
$49$	−5.84768	−0.835382
$50$	−1.81702	−0.256966
$51$	0.708401	0.0991959
$52$	−3.45911	−0.479692
$53$	3.39943	0.466947	0.233474	−	0.972363i	$-0.424991\pi$
$53$	3.39943	0.466947	0.233474	+	0.972363i	$0.424991\pi$
$54$	−1.92072	−0.261377
$55$	3.31015	0.446341
$56$	1.36228	0.182043
$57$	0	0
$58$	4.09287	0.537420
$59$	1.48676	0.193560	0.0967801	−	0.995306i	$-0.469146\pi$
$59$	1.48676	0.193560	0.0967801	+	0.995306i	$0.469146\pi$
$60$	0.230514	0.0297593
$61$	13.7298	1.75792	0.878962	−	0.476892i	$-0.158237\pi$
$61$	13.7298	1.75792	0.878962	+	0.476892i	$0.158237\pi$
$62$	−14.6320	−1.85826
$63$	−3.18672	−0.401489
$64$	−1.77769	−0.222211
$65$	2.65763	0.329639
$66$	−1.06522	−0.131119
$67$	−12.8597	−1.57106	−0.785531	−	0.618822i	$-0.787610\pi$
$67$	−12.8597	−1.57106	−0.785531	+	0.618822i	$0.787610\pi$
$68$	−5.20618	−0.631342
$69$	−0.310602	−0.0373921
$70$	1.95051	0.233130
$71$	−11.0262	−1.30857	−0.654287	−	0.756246i	$-0.727031\pi$
$71$	−11.0262	−1.30857	−0.654287	+	0.756246i	$0.727031\pi$
$72$	−3.76736	−0.443988
$73$	−2.61065	−0.305553	−0.152776	−	0.988261i	$-0.548821\pi$
$73$	−2.61065	−0.305553	−0.152776	+	0.988261i	$0.548821\pi$
$74$	−10.2626	−1.19301
$75$	−0.177104	−0.0204502
$76$	0	0
$77$	−3.55333	−0.404939
$78$	−0.855233	−0.0968360
$79$	6.57050	0.739239	0.369619	−	0.929183i	$-0.379488\pi$
$79$	6.57050	0.739239	0.369619	+	0.929183i	$0.379488\pi$
$80$	4.90905	0.548849
$81$	8.71869	0.968743
$82$	−1.62837	−0.179823
$83$	2.69888	0.296241	0.148120	−	0.988969i	$-0.452678\pi$
$83$	2.69888	0.296241	0.148120	+	0.988969i	$0.452678\pi$
$84$	−0.247449	−0.0269989
$85$	3.99991	0.433851
$86$	15.4667	1.66782
$87$	0.398929	0.0427697
$88$	−4.20077	−0.447803
$89$	−0.789838	−0.0837227	−0.0418613	−	0.999123i	$-0.513329\pi$
$89$	−0.789838	−0.0837227	−0.0418613	+	0.999123i	$0.513329\pi$
$90$	−5.39408	−0.568586
$91$	−2.85287	−0.299062
$92$	2.28268	0.237986
$93$	−1.42617	−0.147887
$94$	11.4403	1.17997
$95$	0	0
$96$	−1.13024	−0.115354
$97$	18.7179	1.90052	0.950259	−	0.311461i	$-0.100818\pi$
$97$	18.7179	1.90052	0.950259	+	0.311461i	$0.100818\pi$
$98$	10.6254	1.07332
$99$	9.82663	0.987613
$100$	1.30157	0.130157
$101$	18.9172	1.88233	0.941164	−	0.337951i	$-0.109734\pi$
$101$	18.9172	1.88233	0.941164	+	0.337951i	$0.109734\pi$
$102$	−1.28718	−0.127450
$103$	11.6438	1.14730	0.573650	−	0.819101i	$-0.305527\pi$
$103$	11.6438	1.14730	0.573650	+	0.819101i	$0.305527\pi$
$104$	−3.37268	−0.330719
$105$	0.190115	0.0185533
$106$	−6.17684	−0.599948
$107$	−11.3958	−1.10168	−0.550838	−	0.834612i	$-0.685692\pi$
$107$	−11.3958	−1.10168	−0.550838	+	0.834612i	$0.685692\pi$
$108$	1.37586	0.132392
$109$	12.7375	1.22003	0.610014	−	0.792390i	$-0.291164\pi$
$109$	12.7375	1.22003	0.610014	+	0.792390i	$0.291164\pi$
$110$	−6.01462	−0.573472
$111$	−1.00029	−0.0949438
$112$	−5.26969	−0.497939
$113$	−16.5894	−1.56060	−0.780300	−	0.625406i	$-0.784933\pi$
$113$	−16.5894	−1.56060	−0.780300	+	0.625406i	$0.784933\pi$
$114$	0	0
$115$	−1.75378	−0.163541
$116$	−2.93181	−0.272212
$117$	7.88954	0.729388
$118$	−2.70148	−0.248692
$119$	−4.29375	−0.393608
$120$	0.224755	0.0205172
$121$	−0.0428972	−0.00389975
$122$	−24.9474	−2.25863
$123$	−0.158716	−0.0143109
$124$	10.4812	0.941241
$125$	−1.00000	−0.0894427
$126$	5.79034	0.515845
$127$	9.72338	0.862811	0.431405	−	0.902158i	$-0.358018\pi$
$127$	9.72338	0.862811	0.431405	+	0.902158i	$0.358018\pi$
$128$	−9.53340	−0.842642
$129$	1.50753	0.132731
$130$	−4.82898	−0.423529
$131$	14.7903	1.29224	0.646118	−	0.763238i	$-0.276392\pi$
$131$	14.7903	1.29224	0.646118	+	0.763238i	$0.276392\pi$
$132$	0.763038	0.0664139
$133$	0	0
$134$	23.3664	2.01855
$135$	−1.05707	−0.0909782
$136$	−5.07610	−0.435272
$137$	3.59629	0.307252	0.153626	−	0.988129i	$-0.450905\pi$
$137$	3.59629	0.307252	0.153626	+	0.988129i	$0.450905\pi$
$138$	0.564372	0.0480425
$139$	−5.85467	−0.496587	−0.248293	−	0.968685i	$-0.579870\pi$
$139$	−5.85467	−0.496587	−0.248293	+	0.968685i	$0.579870\pi$
$140$	−1.39719	−0.118084
$141$	1.11508	0.0939063
$142$	20.0349	1.68129
$143$	8.79716	0.735656
$144$	14.5732	1.21443
$145$	2.25251	0.187061
$146$	4.74360	0.392584
$147$	1.03565	0.0854189
$148$	7.35136	0.604278
$149$	10.0667	0.824693	0.412347	−	0.911027i	$-0.364709\pi$
$149$	10.0667	0.824693	0.412347	+	0.911027i	$0.364709\pi$
$150$	0.321803	0.0262751
$151$	2.12653	0.173054	0.0865272	−	0.996249i	$-0.472423\pi$
$151$	2.12653	0.173054	0.0865272	+	0.996249i	$0.472423\pi$
$152$	0	0
$153$	11.8743	0.959977
$154$	6.45648	0.520278
$155$	−8.05272	−0.646810
$156$	0.612622	0.0490490
$157$	−11.5499	−0.921783	−0.460891	−	0.887457i	$-0.652470\pi$
$157$	−11.5499	−0.921783	−0.460891	+	0.887457i	$0.652470\pi$
$158$	−11.9388	−0.949796
$159$	−0.602053	−0.0477459
$160$	−6.38175	−0.504522
$161$	1.88262	0.148371
$162$	−15.8421	−1.24467
$163$	18.4313	1.44365	0.721827	−	0.692073i	$-0.243303\pi$
$163$	18.4313	1.44365	0.721827	+	0.692073i	$0.243303\pi$
$164$	1.16643	0.0910832
$165$	−0.586242	−0.0456389
$166$	−4.90393	−0.380619
$167$	−1.94262	−0.150324	−0.0751621	−	0.997171i	$-0.523947\pi$
$167$	−1.94262	−0.150324	−0.0751621	+	0.997171i	$0.523947\pi$
$168$	−0.241266	−0.0186141
$169$	−5.93699	−0.456692
$170$	−7.26792	−0.557424
$171$	0	0
$172$	−11.0791	−0.844777
$173$	12.0515	0.916255	0.458128	−	0.888886i	$-0.348520\pi$
$173$	12.0515	0.916255	0.458128	+	0.888886i	$0.348520\pi$
$174$	−0.724864	−0.0549518
$175$	1.07346	0.0811462
$176$	16.2497	1.22487
$177$	−0.263312	−0.0197918
$178$	1.43515	0.107569
$179$	18.3104	1.36858	0.684291	−	0.729209i	$-0.260112\pi$
$179$	18.3104	1.36858	0.684291	+	0.729209i	$0.260112\pi$
$180$	3.86390	0.287998
$181$	25.6514	1.90665	0.953327	−	0.301941i	$-0.0976346\pi$
$181$	25.6514	1.90665	0.953327	+	0.301941i	$0.0976346\pi$
$182$	5.18373	0.384244
$183$	−2.43161	−0.179750
$184$	2.22565	0.164077
$185$	−5.64805	−0.415253
$186$	2.59139	0.190010
$187$	13.2403	0.968226
$188$	−8.19492	−0.597676
$189$	1.13473	0.0825392
$190$	0	0
$191$	9.22171	0.667259	0.333630	−	0.942704i	$-0.391726\pi$
$191$	9.22171	0.667259	0.333630	+	0.942704i	$0.391726\pi$
$192$	0.314837	0.0227214
$193$	−12.0020	−0.863922	−0.431961	−	0.901892i	$-0.642178\pi$
$193$	−12.0020	−0.863922	−0.431961	+	0.901892i	$0.642178\pi$
$194$	−34.0109	−2.44184
$195$	−0.470678	−0.0337059
$196$	−7.61119	−0.543656
$197$	−26.8972	−1.91635	−0.958174	−	0.286186i	$-0.907613\pi$
$197$	−26.8972	−1.91635	−0.958174	+	0.286186i	$0.907613\pi$
$198$	−17.8552	−1.26891
$199$	−4.57394	−0.324238	−0.162119	−	0.986771i	$-0.551833\pi$
$199$	−4.57394	−0.324238	−0.162119	+	0.986771i	$0.551833\pi$
$200$	1.26906	0.0897358
$201$	2.27751	0.160643
$202$	−34.3729	−2.41847
$203$	−2.41799	−0.169709
$204$	0.922036	0.0645554
$205$	−0.896172	−0.0625914
$206$	−21.1571	−1.47408
$207$	−5.20634	−0.361865
$208$	13.0465	0.904609
$209$	0	0
$210$	−0.345443	−0.0238378
$211$	15.5626	1.07138	0.535688	−	0.844416i	$-0.320052\pi$
$211$	15.5626	1.07138	0.535688	+	0.844416i	$0.320052\pi$
$212$	4.42461	0.303883
$213$	1.95279	0.133803
$214$	20.7065	1.41547
$215$	8.51211	0.580521
$216$	1.34148	0.0912762
$217$	8.64430	0.586813
$218$	−23.1443	−1.56753
$219$	0.462357	0.0312432
$220$	4.30841	0.290473
$221$	10.6303	0.715070
$222$	1.81756	0.121987
$223$	20.1284	1.34790	0.673949	−	0.738778i	$-0.264597\pi$
$223$	20.1284	1.34790	0.673949	+	0.738778i	$0.264597\pi$
$224$	6.85058	0.457723
$225$	−2.96863	−0.197909
$226$	30.1433	2.00510
$227$	−13.8680	−0.920453	−0.460226	−	0.887802i	$-0.652232\pi$
$227$	−13.8680	−0.920453	−0.460226	+	0.887802i	$0.652232\pi$
$228$	0	0
$229$	8.70352	0.575145	0.287572	−	0.957759i	$-0.407152\pi$
$229$	8.70352	0.575145	0.287572	+	0.957759i	$0.407152\pi$
$230$	3.18666	0.210122
$231$	0.629309	0.0414055
$232$	−2.85856	−0.187674
$233$	15.7206	1.02989	0.514946	−	0.857223i	$-0.327812\pi$
$233$	15.7206	1.02989	0.514946	+	0.857223i	$0.327812\pi$
$234$	−14.3355	−0.937139
$235$	6.29616	0.410716
$236$	1.93513	0.125966
$237$	−1.16366	−0.0755881
$238$	7.80185	0.505719
$239$	−13.8346	−0.894887	−0.447443	−	0.894312i	$-0.647665\pi$
$239$	−13.8346	−0.894887	−0.447443	+	0.894312i	$0.647665\pi$
$240$	−0.869414	−0.0561204
$241$	−12.1767	−0.784373	−0.392187	−	0.919886i	$-0.628281\pi$
$241$	−12.1767	−0.784373	−0.392187	+	0.919886i	$0.628281\pi$
$242$	0.0779453	0.00501051
$243$	−4.71533	−0.302489
$244$	17.8704	1.14403
$245$	5.84768	0.373594
$246$	0.288390	0.0183871
$247$	0	0
$248$	10.2194	0.648929
$249$	−0.477983	−0.0302910
$250$	1.81702	0.114919
$251$	4.38309	0.276658	0.138329	−	0.990386i	$-0.455827\pi$
$251$	4.38309	0.276658	0.138329	+	0.990386i	$0.455827\pi$
$252$	−4.14775	−0.261284
$253$	−5.80528	−0.364975
$254$	−17.6676	−1.10856
$255$	−0.708401	−0.0443618
$256$	20.8778	1.30486
$257$	−23.1584	−1.44458	−0.722290	−	0.691590i	$-0.756910\pi$
$257$	−23.1584	−1.44458	−0.722290	+	0.691590i	$0.756910\pi$
$258$	−2.73922	−0.170536
$259$	6.06298	0.376735
$260$	3.45911	0.214525
$261$	6.68688	0.413908
$262$	−26.8743	−1.66030
$263$	32.0083	1.97371	0.986857	−	0.161595i	$-0.0516639\pi$
$263$	32.0083	1.97371	0.986857	+	0.161595i	$0.0516639\pi$
$264$	0.743974	0.0457884
$265$	−3.39943	−0.208825
$266$	0	0
$267$	0.139884	0.00856074
$268$	−16.7378	−1.02243
$269$	−3.78715	−0.230907	−0.115453	−	0.993313i	$-0.536832\pi$
$269$	−3.78715	−0.230907	−0.115453	+	0.993313i	$0.536832\pi$
$270$	1.92072	0.116891
$271$	16.7383	1.01678	0.508389	−	0.861128i	$-0.330241\pi$
$271$	16.7383	1.01678	0.508389	+	0.861128i	$0.330241\pi$
$272$	19.6358	1.19059
$273$	0.505255	0.0305794
$274$	−6.53455	−0.394767
$275$	−3.31015	−0.199610
$276$	−0.404272	−0.0243343
$277$	11.5892	0.696330	0.348165	−	0.937433i	$-0.386805\pi$
$277$	11.5892	0.696330	0.348165	+	0.937433i	$0.386805\pi$
$278$	10.6381	0.638030
$279$	−23.9056	−1.43119
$280$	−1.36228	−0.0814121
$281$	2.55105	0.152183	0.0760916	−	0.997101i	$-0.475756\pi$
$281$	2.55105	0.152183	0.0760916	+	0.997101i	$0.475756\pi$
$282$	−2.02612	−0.120654
$283$	−0.518893	−0.0308450	−0.0154225	−	0.999881i	$-0.504909\pi$
$283$	−0.518893	−0.0308450	−0.0154225	+	0.999881i	$0.504909\pi$
$284$	−14.3515	−0.851603
$285$	0	0
$286$	−15.9847	−0.945192
$287$	0.962007	0.0567855
$288$	−18.9451	−1.11635
$289$	−1.00075	−0.0588674
$290$	−4.09287	−0.240341
$291$	−3.31503	−0.194330
$292$	−3.39795	−0.198850
$293$	−1.16042	−0.0677925	−0.0338963	−	0.999425i	$-0.510792\pi$
$293$	−1.16042	−0.0677925	−0.0338963	+	0.999425i	$0.510792\pi$
$294$	−1.88180	−0.109749
$295$	−1.48676	−0.0865627
$296$	7.16769	0.416614
$297$	−3.49906	−0.203036
$298$	−18.2914	−1.05959
$299$	−4.66091	−0.269547
$300$	−0.230514	−0.0133088
$301$	−9.13743	−0.526673
$302$	−3.86395	−0.222345
$303$	−3.35031	−0.192470
$304$	0	0
$305$	−13.7298	−0.786168
$306$	−21.5758	−1.23341
$307$	14.9713	0.854456	0.427228	−	0.904144i	$-0.359490\pi$
$307$	14.9713	0.854456	0.427228	+	0.904144i	$0.359490\pi$
$308$	−4.62492	−0.263529
$309$	−2.06217	−0.117313
$310$	14.6320	0.831041
$311$	11.2063	0.635452	0.317726	−	0.948183i	$-0.397081\pi$
$311$	11.2063	0.635452	0.317726	+	0.948183i	$0.397081\pi$
$312$	0.597316	0.0338164
$313$	13.6242	0.770087	0.385044	−	0.922898i	$-0.374186\pi$
$313$	13.6242	0.770087	0.385044	+	0.922898i	$0.374186\pi$
$314$	20.9864	1.18433
$315$	3.18672	0.179551
$316$	8.55199	0.481087
$317$	8.68500	0.487798	0.243899	−	0.969801i	$-0.421573\pi$
$317$	8.68500	0.487798	0.243899	+	0.969801i	$0.421573\pi$
$318$	1.09394	0.0613454
$319$	7.45615	0.417464
$320$	1.77769	0.0993759
$321$	2.01825	0.112648
$322$	−3.42076	−0.190632
$323$	0	0
$324$	11.3480	0.630446
$325$	−2.65763	−0.147419
$326$	−33.4902	−1.85485
$327$	−2.25586	−0.124749
$328$	1.13729	0.0627964
$329$	−6.75869	−0.372619
$330$	1.06522	0.0586382
$331$	23.3399	1.28288	0.641439	−	0.767174i	$-0.278338\pi$
$331$	23.3399	1.28288	0.641439	+	0.767174i	$0.278338\pi$
$332$	3.51279	0.192790
$333$	−16.7670	−0.918826
$334$	3.52978	0.193141
$335$	12.8597	0.702600
$336$	0.933284	0.0509148
$337$	12.8541	0.700206	0.350103	−	0.936711i	$-0.386147\pi$
$337$	12.8541	0.700206	0.350103	+	0.936711i	$0.386147\pi$
$338$	10.7877	0.586771
$339$	2.93805	0.159573
$340$	5.20618	0.282345
$341$	−26.6557	−1.44349
$342$	0	0
$343$	−13.7915	−0.744671
$344$	−10.8023	−0.582423
$345$	0.310602	0.0167223
$346$	−21.8978	−1.17723
$347$	−32.4343	−1.74116	−0.870581	−	0.492025i	$-0.836257\pi$
$347$	−32.4343	−1.74116	−0.870581	+	0.492025i	$0.836257\pi$
$348$	0.519236	0.0278340
$349$	12.1085	0.648152	0.324076	−	0.946031i	$-0.394947\pi$
$349$	12.1085	0.648152	0.324076	+	0.946031i	$0.394947\pi$
$350$	−1.95051	−0.104259
$351$	−2.80930	−0.149950
$352$	−21.1246	−1.12594
$353$	−23.0962	−1.22929	−0.614643	−	0.788805i	$-0.710700\pi$
$353$	−23.0962	−1.22929	−0.614643	+	0.788805i	$0.710700\pi$
$354$	0.478444	0.0254290
$355$	11.0262	0.585212
$356$	−1.02803	−0.0544856
$357$	0.760442	0.0402469
$358$	−33.2704	−1.75839
$359$	−6.44613	−0.340214	−0.170107	−	0.985426i	$-0.554411\pi$
$359$	−6.44613	−0.340214	−0.170107	+	0.985426i	$0.554411\pi$
$360$	3.76736	0.198557
$361$	0	0
$362$	−46.6092	−2.44972
$363$	0.00759728	0.000398754 0
$364$	−3.71322	−0.194626
$365$	2.61065	0.136647
$366$	4.41829	0.230948
$367$	−8.61879	−0.449897	−0.224949	−	0.974371i	$-0.572221\pi$
$367$	−8.61879	−0.449897	−0.224949	+	0.974371i	$0.572221\pi$
$368$	−8.60941	−0.448796
$369$	−2.66041	−0.138495
$370$	10.2626	0.533530
$371$	3.64916	0.189455
$372$	−1.85627	−0.0962430
$373$	9.50581	0.492192	0.246096	−	0.969245i	$-0.420852\pi$
$373$	9.50581	0.492192	0.246096	+	0.969245i	$0.420852\pi$
$374$	−24.0579	−1.24401
$375$	0.177104	0.00914563
$376$	−7.99017	−0.412062
$377$	5.98634	0.308312
$378$	−2.06182	−0.106049
$379$	11.3635	0.583706	0.291853	−	0.956463i	$-0.405728\pi$
$379$	11.3635	0.583706	0.291853	+	0.956463i	$0.405728\pi$
$380$	0	0
$381$	−1.72205	−0.0882234
$382$	−16.7561	−0.857315
$383$	2.73290	0.139644	0.0698222	−	0.997559i	$-0.477757\pi$
$383$	2.73290	0.139644	0.0698222	+	0.997559i	$0.477757\pi$
$384$	1.68841	0.0861611
$385$	3.55333	0.181094
$386$	21.8079	1.10999
$387$	25.2693	1.28451
$388$	24.3628	1.23683
$389$	−22.1536	−1.12323	−0.561615	−	0.827398i	$-0.689820\pi$
$389$	−22.1536	−1.12323	−0.561615	+	0.827398i	$0.689820\pi$
$390$	0.855233	0.0433064
$391$	−7.01496	−0.354762
$392$	−7.42103	−0.374818
$393$	−2.61943	−0.132133
$394$	48.8729	2.46218
$395$	−6.57050	−0.330598
$396$	12.7901	0.642726
$397$	16.9608	0.851238	0.425619	−	0.904903i	$-0.360056\pi$
$397$	16.9608	0.851238	0.425619	+	0.904903i	$0.360056\pi$
$398$	8.31096	0.416591
$399$	0	0
$400$	−4.90905	−0.245453
$401$	−6.61906	−0.330540	−0.165270	−	0.986248i	$-0.552850\pi$
$401$	−6.61906	−0.330540	−0.165270	+	0.986248i	$0.552850\pi$
$402$	−4.13828	−0.206399
$403$	−21.4012	−1.06607
$404$	24.6221	1.22499
$405$	−8.71869	−0.433235
$406$	4.39354	0.218048
$407$	−18.6959	−0.926722
$408$	0.899000	0.0445071
$409$	−35.7642	−1.76842	−0.884212	−	0.467085i	$-0.845304\pi$
$409$	−35.7642	−1.76842	−0.884212	+	0.467085i	$0.845304\pi$
$410$	1.62837	0.0804192
$411$	−0.636919	−0.0314169
$412$	15.1553	0.746648
$413$	1.59599	0.0785333
$414$	9.46004	0.464935
$415$	−2.69888	−0.132483
$416$	−16.9603	−0.831549
$417$	1.03689	0.0507766
$418$	0	0
$419$	−29.6681	−1.44938	−0.724691	−	0.689074i	$-0.758018\pi$
$419$	−29.6681	−1.44938	−0.724691	+	0.689074i	$0.758018\pi$
$420$	0.247449	0.0120743
$421$	−12.3465	−0.601733	−0.300867	−	0.953666i	$-0.597276\pi$
$421$	−12.3465	−0.601733	−0.300867	+	0.953666i	$0.597276\pi$
$422$	−28.2777	−1.37654
$423$	18.6910	0.908787
$424$	4.31406	0.209509
$425$	−3.99991	−0.194024
$426$	−3.54827	−0.171914
$427$	14.7385	0.713244
$428$	−14.8325	−0.716957
$429$	−1.55802	−0.0752217
$430$	−15.4667	−0.745871
$431$	17.0666	0.822069	0.411035	−	0.911620i	$-0.365168\pi$
$431$	17.0666	0.822069	0.411035	+	0.911620i	$0.365168\pi$
$432$	−5.18922	−0.249666
$433$	2.80017	0.134568	0.0672839	−	0.997734i	$-0.478567\pi$
$433$	2.80017	0.134568	0.0672839	+	0.997734i	$0.478567\pi$
$434$	−15.7069	−0.753955
$435$	−0.398929	−0.0191272
$436$	16.5788	0.793979
$437$	0	0
$438$	−0.840113	−0.0401421
$439$	−21.2151	−1.01254	−0.506270	−	0.862375i	$-0.668976\pi$
$439$	−21.2151	−1.01254	−0.506270	+	0.862375i	$0.668976\pi$
$440$	4.20077	0.200264
$441$	17.3596	0.826648
$442$	−19.3155	−0.918743
$443$	22.7790	1.08226	0.541131	−	0.840939i	$-0.317996\pi$
$443$	22.7790	1.08226	0.541131	+	0.840939i	$0.317996\pi$
$444$	−1.30196	−0.0617882
$445$	0.789838	0.0374419
$446$	−36.5738	−1.73182
$447$	−1.78285	−0.0843259
$448$	−1.90828	−0.0901580
$449$	29.7698	1.40492	0.702461	−	0.711722i	$-0.252084\pi$
$449$	29.7698	1.40492	0.702461	+	0.711722i	$0.252084\pi$
$450$	5.39408	0.254279
$451$	−2.96646	−0.139685
$452$	−21.5923	−1.01562
$453$	−0.376617	−0.0176950
$454$	25.1985	1.18262
$455$	2.85287	0.133745
$456$	0	0
$457$	−36.7666	−1.71987	−0.859934	−	0.510406i	$-0.829495\pi$
$457$	−36.7666	−1.71987	−0.859934	+	0.510406i	$0.829495\pi$
$458$	−15.8145	−0.738963
$459$	−4.22818	−0.197355
$460$	−2.28268	−0.106430
$461$	−25.7299	−1.19836	−0.599181	−	0.800613i	$-0.704507\pi$
$461$	−25.7299	−1.19836	−0.599181	+	0.800613i	$0.704507\pi$
$462$	−1.14347	−0.0531990
$463$	−35.5688	−1.65302	−0.826511	−	0.562920i	$-0.809678\pi$
$463$	−35.5688	−1.65302	−0.826511	+	0.562920i	$0.809678\pi$
$464$	11.0577	0.513341
$465$	1.42617	0.0661371
$466$	−28.5647	−1.32324
$467$	−7.11571	−0.329276	−0.164638	−	0.986354i	$-0.552646\pi$
$467$	−7.11571	−0.329276	−0.164638	+	0.986354i	$0.552646\pi$
$468$	10.2688	0.474676
$469$	−13.8044	−0.637428
$470$	−11.4403	−0.527700
$471$	2.04554	0.0942534
$472$	1.88679	0.0868463
$473$	28.1764	1.29555
$474$	2.11440	0.0971178
$475$	0	0
$476$	−5.58864	−0.256155
$477$	−10.0917	−0.462065
$478$	25.1378	1.14978
$479$	−8.81275	−0.402665	−0.201332	−	0.979523i	$-0.564527\pi$
$479$	−8.81275	−0.402665	−0.201332	+	0.979523i	$0.564527\pi$
$480$	1.13024	0.0515880
$481$	−15.0104	−0.684417
$482$	22.1254	1.00779
$483$	−0.333420	−0.0151711
$484$	−0.0558339	−0.00253791
$485$	−18.7179	−0.849937
$486$	8.56786	0.388646
$487$	4.78306	0.216741	0.108370	−	0.994111i	$-0.465437\pi$
$487$	4.78306	0.216741	0.108370	+	0.994111i	$0.465437\pi$
$488$	17.4239	0.788744
$489$	−3.26427	−0.147615
$490$	−10.6254	−0.480005
$491$	10.0710	0.454497	0.227248	−	0.973837i	$-0.427027\pi$
$491$	10.0710	0.454497	0.227248	+	0.973837i	$0.427027\pi$
$492$	−0.206581	−0.00931337
$493$	9.00984	0.405783
$494$	0	0
$495$	−9.82663	−0.441674
$496$	−39.5312	−1.77500
$497$	−11.8363	−0.530929
$498$	0.868507	0.0389187
$499$	−1.92213	−0.0860462	−0.0430231	−	0.999074i	$-0.513699\pi$
$499$	−1.92213	−0.0860462	−0.0430231	+	0.999074i	$0.513699\pi$
$500$	−1.30157	−0.0582082
$501$	0.344046	0.0153708
$502$	−7.96418	−0.355459
$503$	−16.2293	−0.723629	−0.361814	−	0.932250i	$-0.617843\pi$
$503$	−16.2293	−0.723629	−0.361814	+	0.932250i	$0.617843\pi$
$504$	−4.04412	−0.180140
$505$	−18.9172	−0.841802
$506$	10.5483	0.468931
$507$	1.05147	0.0466973
$508$	12.6557	0.561506
$509$	33.8249	1.49926	0.749631	−	0.661856i	$-0.230231\pi$
$509$	33.8249	1.49926	0.749631	+	0.661856i	$0.230231\pi$
$510$	1.28718	0.0569973
$511$	−2.80243	−0.123972
$512$	−18.8686	−0.833884
$513$	0	0
$514$	42.0793	1.85604
$515$	−11.6438	−0.513088
$516$	1.96216	0.0863794
$517$	20.8412	0.916596
$518$	−11.0166	−0.484040
$519$	−2.13436	−0.0936882
$520$	3.37268	0.147902
$521$	−6.88838	−0.301785	−0.150893	−	0.988550i	$-0.548215\pi$
$521$	−6.88838	−0.301785	−0.150893	+	0.988550i	$0.548215\pi$
$522$	−12.1502	−0.531801
$523$	20.1891	0.882809	0.441405	−	0.897308i	$-0.354480\pi$
$523$	20.1891	0.882809	0.441405	+	0.897308i	$0.354480\pi$
$524$	19.2507	0.840970
$525$	−0.190115	−0.00829729
$526$	−58.1598	−2.53589
$527$	−32.2101	−1.40310
$528$	−2.87789	−0.125244
$529$	−19.9242	−0.866272
$530$	6.17684	0.268305
$531$	−4.41366	−0.191536
$532$	0	0
$533$	−2.38169	−0.103163
$534$	−0.254172	−0.0109991
$535$	11.3958	0.492684
$536$	−16.3197	−0.704902
$537$	−3.24285	−0.139939
$538$	6.88135	0.296676
$539$	19.3567	0.833752
$540$	−1.37586	−0.0592074
$541$	2.62143	0.112704	0.0563520	−	0.998411i	$-0.482053\pi$
$541$	2.62143	0.112704	0.0563520	+	0.998411i	$0.482053\pi$
$542$	−30.4138	−1.30639
$543$	−4.54297	−0.194958
$544$	−25.5264	−1.09444
$545$	−12.7375	−0.545613
$546$	−0.918061	−0.0392894
$547$	−26.5701	−1.13606	−0.568029	−	0.823009i	$-0.692294\pi$
$547$	−26.5701	−1.13606	−0.568029	+	0.823009i	$0.692294\pi$
$548$	4.68085	0.199956
$549$	−40.7588	−1.73954
$550$	6.01462	0.256464
$551$	0	0
$552$	−0.394172	−0.0167771
$553$	7.05319	0.299932
$554$	−21.0579	−0.894666
$555$	1.00029	0.0424601
$556$	−7.62029	−0.323172
$557$	17.4267	0.738394	0.369197	−	0.929351i	$-0.379633\pi$
$557$	17.4267	0.738394	0.369197	+	0.929351i	$0.379633\pi$
$558$	43.4370	1.83884
$559$	22.6220	0.956811
$560$	5.26969	0.222685
$561$	−2.34491	−0.0990023
$562$	−4.63533	−0.195529
$563$	2.25335	0.0949676	0.0474838	−	0.998872i	$-0.484880\pi$
$563$	2.25335	0.0949676	0.0474838	+	0.998872i	$0.484880\pi$
$564$	1.45135	0.0611131
$565$	16.5894	0.697921
$566$	0.942840	0.0396305
$567$	9.35919	0.393049
$568$	−13.9929	−0.587130
$569$	8.49148	0.355982	0.177991	−	0.984032i	$-0.443040\pi$
$569$	8.49148	0.355982	0.177991	+	0.984032i	$0.443040\pi$
$570$	0	0
$571$	−2.29006	−0.0958359	−0.0479179	−	0.998851i	$-0.515259\pi$
$571$	−2.29006	−0.0958359	−0.0479179	+	0.998851i	$0.515259\pi$
$572$	11.4502	0.478755
$573$	−1.63320	−0.0682281
$574$	−1.74799	−0.0729597
$575$	1.75378	0.0731378
$576$	5.27731	0.219888
$577$	−2.00916	−0.0836426	−0.0418213	−	0.999125i	$-0.513316\pi$
$577$	−2.00916	−0.0836426	−0.0418213	+	0.999125i	$0.513316\pi$
$578$	1.81838	0.0756346
$579$	2.12560	0.0883370
$580$	2.93181	0.121737
$581$	2.89715	0.120194
$582$	6.02348	0.249681
$583$	−11.2526	−0.466036
$584$	−3.31305	−0.137095
$585$	−7.88954	−0.326192
$586$	2.10851	0.0871018
$587$	−7.38929	−0.304989	−0.152494	−	0.988304i	$-0.548731\pi$
$587$	−7.38929	−0.304989	−0.152494	+	0.988304i	$0.548731\pi$
$588$	1.34797	0.0555895
$589$	0	0
$590$	2.70148	0.111218
$591$	4.76361	0.195949
$592$	−27.7266	−1.13956
$593$	−23.4755	−0.964022	−0.482011	−	0.876165i	$-0.660094\pi$
$593$	−23.4755	−0.964022	−0.482011	+	0.876165i	$0.660094\pi$
$594$	6.35788	0.260867
$595$	4.29375	0.176027
$596$	13.1025	0.536700
$597$	0.810065	0.0331538
$598$	8.46898	0.346322
$599$	32.2695	1.31850	0.659249	−	0.751925i	$-0.270874\pi$
$599$	32.2695	1.31850	0.659249	+	0.751925i	$0.270874\pi$
$600$	−0.224755	−0.00917559
$601$	−29.8357	−1.21703	−0.608513	−	0.793544i	$-0.708233\pi$
$601$	−29.8357	−1.21703	−0.608513	+	0.793544i	$0.708233\pi$
$602$	16.6029	0.676685
$603$	38.1757	1.55464
$604$	2.76784	0.112622
$605$	0.0428972	0.00174402
$606$	6.08759	0.247291
$607$	9.11607	0.370010	0.185005	−	0.982738i	$-0.440770\pi$
$607$	9.11607	0.370010	0.185005	+	0.982738i	$0.440770\pi$
$608$	0	0
$609$	0.428236	0.0173530
$610$	24.9474	1.01009
$611$	16.7329	0.676939
$612$	15.4552	0.624741
$613$	42.0516	1.69845	0.849224	−	0.528033i	$-0.177070\pi$
$613$	42.0516	1.69845	0.849224	+	0.528033i	$0.177070\pi$
$614$	−27.2032	−1.09783
$615$	0.158716	0.00640004
$616$	−4.50937	−0.181688
$617$	33.6832	1.35604	0.678018	−	0.735045i	$-0.262839\pi$
$617$	33.6832	1.35604	0.678018	+	0.735045i	$0.262839\pi$
$618$	3.74701	0.150727
$619$	−41.6917	−1.67573	−0.837865	−	0.545878i	$-0.816196\pi$
$619$	−41.6917	−1.67573	−0.837865	+	0.545878i	$0.816196\pi$
$620$	−10.4812	−0.420936
$621$	1.85387	0.0743933
$622$	−20.3621	−0.816447
$623$	−0.847862	−0.0339689
$624$	−2.31058	−0.0924973
$625$	1.00000	0.0400000
$626$	−24.7556	−0.989431
$627$	0	0
$628$	−15.0331	−0.599884
$629$	−22.5917	−0.900790
$630$	−5.79034	−0.230693
$631$	−8.32410	−0.331377	−0.165689	−	0.986178i	$-0.552985\pi$
$631$	−8.32410	−0.331377	−0.165689	+	0.986178i	$0.552985\pi$
$632$	8.33833	0.331681
$633$	−2.75621	−0.109549
$634$	−15.7808	−0.626737
$635$	−9.72338	−0.385861
$636$	−0.783617	−0.0310724
$637$	15.5410	0.615756
$638$	−13.5480	−0.536371
$639$	32.7329	1.29489
$640$	9.53340	0.376841
$641$	7.26032	0.286765	0.143383	−	0.989667i	$-0.454202\pi$
$641$	7.26032	0.286765	0.143383	+	0.989667i	$0.454202\pi$
$642$	−3.66721	−0.144733
$643$	3.57195	0.140864	0.0704320	−	0.997517i	$-0.477562\pi$
$643$	3.57195	0.140864	0.0704320	+	0.997517i	$0.477562\pi$
$644$	2.45037	0.0965581
$645$	−1.50753	−0.0593590
$646$	0	0
$647$	21.0229	0.826494	0.413247	−	0.910619i	$-0.364395\pi$
$647$	21.0229	0.826494	0.413247	+	0.910619i	$0.364395\pi$
$648$	11.0645	0.434655
$649$	−4.92141	−0.193182
$650$	4.82898	0.189408
$651$	−1.53094	−0.0600024
$652$	23.9898	0.939512
$653$	−23.2646	−0.910413	−0.455207	−	0.890386i	$-0.650435\pi$
$653$	−23.2646	−0.910413	−0.455207	+	0.890386i	$0.650435\pi$
$654$	4.09895	0.160282
$655$	−14.7903	−0.577905
$656$	−4.39936	−0.171766
$657$	7.75005	0.302358
$658$	12.2807	0.478752
$659$	23.5264	0.916457	0.458228	−	0.888834i	$-0.348484\pi$
$659$	23.5264	0.916457	0.458228	+	0.888834i	$0.348484\pi$
$660$	−0.763038	−0.0297012
$661$	21.3079	0.828781	0.414390	−	0.910099i	$-0.363995\pi$
$661$	21.3079	0.828781	0.414390	+	0.910099i	$0.363995\pi$
$662$	−42.4092	−1.64828
$663$	−1.88267	−0.0731168
$664$	3.42503	0.132917
$665$	0	0
$666$	30.4660	1.18054
$667$	−3.95041	−0.152961
$668$	−2.52846	−0.0978291
$669$	−3.56483	−0.137824
$670$	−23.3664	−0.902722
$671$	−45.4478	−1.75449
$672$	−1.21327	−0.0468028
$673$	−7.74601	−0.298587	−0.149293	−	0.988793i	$-0.547700\pi$
$673$	−7.74601	−0.298587	−0.149293	+	0.988793i	$0.547700\pi$
$674$	−23.3562	−0.899645
$675$	1.05707	0.0406867
$676$	−7.72744	−0.297209
$677$	3.31146	0.127270	0.0636348	−	0.997973i	$-0.479731\pi$
$677$	3.31146	0.127270	0.0636348	+	0.997973i	$0.479731\pi$
$678$	−5.33851	−0.205024
$679$	20.0930	0.771099
$680$	5.07610	0.194660
$681$	2.45608	0.0941174
$682$	48.4341	1.85464
$683$	4.09964	0.156868	0.0784342	−	0.996919i	$-0.475008\pi$
$683$	4.09964	0.156868	0.0784342	+	0.996919i	$0.475008\pi$
$684$	0	0
$685$	−3.59629	−0.137407
$686$	25.0595	0.956776
$687$	−1.54143	−0.0588092
$688$	41.7864	1.59309
$689$	−9.03443	−0.344184
$690$	−0.564372	−0.0214853
$691$	−22.8437	−0.869016	−0.434508	−	0.900668i	$-0.643078\pi$
$691$	−22.8437	−0.869016	−0.434508	+	0.900668i	$0.643078\pi$
$692$	15.6859	0.596287
$693$	10.5485	0.400705
$694$	58.9338	2.23710
$695$	5.85467	0.222080
$696$	0.506264	0.0191899
$697$	−3.58460	−0.135777
$698$	−22.0014	−0.832765
$699$	−2.78419	−0.105308
$700$	1.39719	0.0528089
$701$	−43.1824	−1.63098	−0.815488	−	0.578774i	$-0.803531\pi$
$701$	−43.1824	−1.63098	−0.815488	+	0.578774i	$0.803531\pi$
$702$	5.10457	0.192660
$703$	0	0
$704$	5.88442	0.221778
$705$	−1.11508	−0.0419962
$706$	41.9663	1.57942
$707$	20.3069	0.763718
$708$	−0.342720	−0.0128802
$709$	12.5505	0.471343	0.235671	−	0.971833i	$-0.424271\pi$
$709$	12.5505	0.471343	0.235671	+	0.971833i	$0.424271\pi$
$710$	−20.0349	−0.751898
$711$	−19.5054	−0.731510
$712$	−1.00235	−0.0375646
$713$	14.1227	0.528900
$714$	−1.38174	−0.0517103
$715$	−8.79716	−0.328995
$716$	23.8323	0.890656
$717$	2.45017	0.0915033
$718$	11.7128	0.437117
$719$	22.4682	0.837923	0.418961	−	0.908004i	$-0.362394\pi$
$719$	22.4682	0.837923	0.418961	+	0.908004i	$0.362394\pi$
$720$	−14.5732	−0.543110
$721$	12.4992	0.465495
$722$	0	0
$723$	2.15655	0.0802031
$724$	33.3872	1.24083
$725$	−2.25251	−0.0836562
$726$	−0.0138044	−0.000512331 0
$727$	29.5868	1.09731	0.548656	−	0.836048i	$-0.315140\pi$
$727$	29.5868	1.09731	0.548656	+	0.836048i	$0.315140\pi$
$728$	−3.62045	−0.134183
$729$	−25.3210	−0.937814
$730$	−4.74360	−0.175569
$731$	34.0476	1.25930
$732$	−3.16492	−0.116979
$733$	46.8312	1.72975	0.864876	−	0.501986i	$-0.167397\pi$
$733$	46.8312	1.72975	0.864876	+	0.501986i	$0.167397\pi$
$734$	15.6605	0.578041
$735$	−1.03565	−0.0382005
$736$	11.1922	0.412550
$737$	42.5675	1.56800
$738$	4.83402	0.177943
$739$	38.9919	1.43434	0.717170	−	0.696898i	$-0.245437\pi$
$739$	38.9919	1.43434	0.717170	+	0.696898i	$0.245437\pi$
$740$	−7.35136	−0.270241
$741$	0	0
$742$	−6.63061	−0.243417
$743$	−12.1347	−0.445177	−0.222589	−	0.974912i	$-0.571451\pi$
$743$	−12.1347	−0.445177	−0.222589	+	0.974912i	$0.571451\pi$
$744$	−1.80989	−0.0663538
$745$	−10.0667	−0.368814
$746$	−17.2723	−0.632383
$747$	−8.01199	−0.293143
$748$	17.2332	0.630109
$749$	−12.2330	−0.446984
$750$	−0.321803	−0.0117506
$751$	5.31316	0.193880	0.0969399	−	0.995290i	$-0.469095\pi$
$751$	5.31316	0.193880	0.0969399	+	0.995290i	$0.469095\pi$
$752$	30.9082	1.12710
$753$	−0.776265	−0.0282887
$754$	−10.8773	−0.396129
$755$	−2.12653	−0.0773923
$756$	1.47693	0.0537155
$757$	−21.2441	−0.772129	−0.386065	−	0.922472i	$-0.626166\pi$
$757$	−21.2441	−0.772129	−0.386065	+	0.922472i	$0.626166\pi$
$758$	−20.6478	−0.749963
$759$	1.02814	0.0373191
$760$	0	0
$761$	37.4718	1.35835	0.679176	−	0.733975i	$-0.262337\pi$
$761$	37.4718	1.35835	0.679176	+	0.733975i	$0.262337\pi$
$762$	3.12901	0.113352
$763$	13.6732	0.495003
$764$	12.0027	0.434244
$765$	−11.8743	−0.429315
$766$	−4.96574	−0.179419
$767$	−3.95127	−0.142672
$768$	−3.69755	−0.133424
$769$	−2.99630	−0.108049	−0.0540247	−	0.998540i	$-0.517205\pi$
$769$	−2.99630	−0.108049	−0.0540247	+	0.998540i	$0.517205\pi$
$770$	−6.45648	−0.232675
$771$	4.10145	0.147710
$772$	−15.6215	−0.562229
$773$	−15.8749	−0.570981	−0.285491	−	0.958382i	$-0.592157\pi$
$773$	−15.8749	−0.570981	−0.285491	+	0.958382i	$0.592157\pi$
$774$	−45.9150	−1.65038
$775$	8.05272	0.289262
$776$	23.7541	0.852722
$777$	−1.07378	−0.0385216
$778$	40.2536	1.44316
$779$	0	0
$780$	−0.612622	−0.0219354
$781$	36.4985	1.30602
$782$	12.7464	0.455809
$783$	−2.38106	−0.0850923
$784$	28.7066	1.02523
$785$	11.5499	0.412234
$786$	4.75956	0.169768
$787$	−4.85017	−0.172890	−0.0864449	−	0.996257i	$-0.527551\pi$
$787$	−4.85017	−0.172890	−0.0864449	+	0.996257i	$0.527551\pi$
$788$	−35.0087	−1.24713
$789$	−5.66880	−0.201815
$790$	11.9388	0.424762
$791$	−17.8081	−0.633183
$792$	12.4705	0.443121
$793$	−36.4888	−1.29576
$794$	−30.8182	−1.09370
$795$	0.602053	0.0213526
$796$	−5.95333	−0.211010
$797$	−42.7169	−1.51311	−0.756555	−	0.653930i	$-0.773119\pi$
$797$	−42.7169	−1.51311	−0.756555	+	0.653930i	$0.773119\pi$
$798$	0	0
$799$	25.1840	0.890947
$800$	6.38175	0.225629
$801$	2.34474	0.0828473
$802$	12.0270	0.424688
$803$	8.64163	0.304957
$804$	2.96434	0.104544
$805$	−1.88262	−0.0663536
$806$	38.8864	1.36972
$807$	0.670721	0.0236105
$808$	24.0069	0.844561
$809$	15.3572	0.539930	0.269965	−	0.962870i	$-0.412988\pi$
$809$	15.3572	0.539930	0.269965	+	0.962870i	$0.412988\pi$
$810$	15.8421	0.556633
$811$	28.5751	1.00341	0.501703	−	0.865040i	$-0.332707\pi$
$811$	28.5751	1.00341	0.501703	+	0.865040i	$0.332707\pi$
$812$	−3.14719	−0.110445
$813$	−2.96442	−0.103967
$814$	33.9709	1.19068
$815$	−18.4313	−0.645622
$816$	−3.47758	−0.121740
$817$	0	0
$818$	64.9843	2.27212
$819$	8.46912	0.295935
$820$	−1.16643	−0.0407337
$821$	−0.898646	−0.0313630	−0.0156815	−	0.999877i	$-0.504992\pi$
$821$	−0.898646	−0.0313630	−0.0156815	+	0.999877i	$0.504992\pi$
$822$	1.15730	0.0403654
$823$	−36.7102	−1.27964	−0.639818	−	0.768526i	$-0.720990\pi$
$823$	−36.7102	−1.27964	−0.639818	+	0.768526i	$0.720990\pi$
$824$	14.7767	0.514769
$825$	0.586242	0.0204103
$826$	−2.89994	−0.100902
$827$	42.3584	1.47295	0.736473	−	0.676467i	$-0.236490\pi$
$827$	42.3584	1.47295	0.736473	+	0.676467i	$0.236490\pi$
$828$	−6.77643	−0.235497
$829$	−24.3888	−0.847059	−0.423530	−	0.905882i	$-0.639209\pi$
$829$	−24.3888	−0.847059	−0.423530	+	0.905882i	$0.639209\pi$
$830$	4.90393	0.170218
$831$	−2.05251	−0.0712006
$832$	4.72445	0.163791
$833$	23.3902	0.810421
$834$	−1.88405	−0.0652393
$835$	1.94262	0.0672271
$836$	0	0
$837$	8.51230	0.294228
$838$	53.9077	1.86221
$839$	23.4810	0.810653	0.405327	−	0.914172i	$-0.367158\pi$
$839$	23.4810	0.810653	0.405327	+	0.914172i	$0.367158\pi$
$840$	0.241266	0.00832448
$841$	−23.9262	−0.825041
$842$	22.4339	0.773125
$843$	−0.451803	−0.0155609
$844$	20.2559	0.697238
$845$	5.93699	0.204239
$846$	−33.9620	−1.16764
$847$	−0.0460486	−0.00158225
$848$	−16.6880	−0.573067
$849$	0.0918981	0.00315394
$850$	7.26792	0.249288
$851$	9.90545	0.339555
$852$	2.54171	0.0870775
$853$	5.83975	0.199949	0.0999745	−	0.994990i	$-0.468124\pi$
$853$	5.83975	0.199949	0.0999745	+	0.994990i	$0.468124\pi$
$854$	−26.7801	−0.916397
$855$	0	0
$856$	−14.4619	−0.494299
$857$	27.0008	0.922330	0.461165	−	0.887314i	$-0.347432\pi$
$857$	27.0008	0.922330	0.461165	+	0.887314i	$0.347432\pi$
$858$	2.83095	0.0966470
$859$	−3.18654	−0.108723	−0.0543617	−	0.998521i	$-0.517312\pi$
$859$	−3.18654	−0.108723	−0.0543617	+	0.998521i	$0.517312\pi$
$860$	11.0791	0.377796
$861$	−0.170376	−0.00580639
$862$	−31.0104	−1.05622
$863$	−8.42174	−0.286679	−0.143340	−	0.989674i	$-0.545784\pi$
$863$	−8.42174	−0.286679	−0.143340	+	0.989674i	$0.545784\pi$
$864$	6.74596	0.229502
$865$	−12.0515	−0.409762
$866$	−5.08798	−0.172897
$867$	0.177236	0.00601926
$868$	11.2512	0.381891
$869$	−21.7493	−0.737796
$870$	0.724864	0.0245752
$871$	34.1763	1.15802
$872$	16.1646	0.547401
$873$	−55.5667	−1.88065
$874$	0	0
$875$	−1.07346	−0.0362897
$876$	0.601791	0.0203326
$877$	41.8102	1.41183	0.705915	−	0.708297i	$-0.250536\pi$
$877$	41.8102	1.41183	0.705915	+	0.708297i	$0.250536\pi$
$878$	38.5483	1.30094
$879$	0.205516	0.00693187
$880$	−16.2497	−0.547778
$881$	−27.8465	−0.938173	−0.469087	−	0.883152i	$-0.655417\pi$
$881$	−27.8465	−0.938173	−0.469087	+	0.883152i	$0.655417\pi$
$882$	−31.5428	−1.06210
$883$	28.0898	0.945296	0.472648	−	0.881251i	$-0.343298\pi$
$883$	28.0898	0.945296	0.472648	+	0.881251i	$0.343298\pi$
$884$	13.8361	0.465358
$885$	0.263312	0.00885114
$886$	−41.3899	−1.39052
$887$	−0.112362	−0.00377274	−0.00188637	−	0.999998i	$-0.500600\pi$
$887$	−0.112362	−0.00377274	−0.00188637	+	0.999998i	$0.500600\pi$
$888$	−1.26943	−0.0425993
$889$	10.4377	0.350069
$890$	−1.43515	−0.0481065
$891$	−28.8602	−0.966853
$892$	26.1986	0.877195
$893$	0	0
$894$	3.23948	0.108344
$895$	−18.3104	−0.612049
$896$	−10.2338	−0.341886
$897$	0.825466	0.0275615
$898$	−54.0924	−1.80509
$899$	−18.1388	−0.604964
$900$	−3.86390	−0.128797
$901$	−13.5974	−0.452995
$902$	5.39014	0.179472
$903$	1.61828	0.0538529
$904$	−21.0529	−0.700208
$905$	−25.6514	−0.852681
$906$	0.684322	0.0227351
$907$	−36.0731	−1.19779	−0.598894	−	0.800829i	$-0.704393\pi$
$907$	−36.0731	−1.19779	−0.598894	+	0.800829i	$0.704393\pi$
$908$	−18.0503	−0.599019
$909$	−56.1581	−1.86265
$910$	−5.18373	−0.171839
$911$	51.0528	1.69145	0.845727	−	0.533615i	$-0.179167\pi$
$911$	51.0528	1.69145	0.845727	+	0.533615i	$0.179167\pi$
$912$	0	0
$913$	−8.93370	−0.295662
$914$	66.8057	2.20974
$915$	2.43161	0.0803866
$916$	11.3283	0.374297
$917$	15.8769	0.524300
$918$	7.68271	0.253567
$919$	41.2224	1.35980	0.679900	−	0.733305i	$-0.262023\pi$
$919$	41.2224	1.35980	0.679900	+	0.733305i	$0.262023\pi$
$920$	−2.22565	−0.0733774
$921$	−2.65148	−0.0873692
$922$	46.7519	1.53969
$923$	29.3037	0.964543
$924$	0.819093	0.0269462
$925$	5.64805	0.185707
$926$	64.6294	2.12385
$927$	−34.5662	−1.13530
$928$	−14.3750	−0.471882
$929$	12.9464	0.424757	0.212378	−	0.977187i	$-0.431879\pi$
$929$	12.9464	0.424757	0.212378	+	0.977187i	$0.431879\pi$
$930$	−2.59139	−0.0849749
$931$	0	0
$932$	20.4616	0.670241
$933$	−1.98469	−0.0649757
$934$	12.9294	0.423063
$935$	−13.2403	−0.433004
$936$	10.0123	0.327261
$937$	31.0792	1.01531	0.507657	−	0.861560i	$-0.330512\pi$
$937$	31.0792	1.01531	0.507657	+	0.861560i	$0.330512\pi$
$938$	25.0829	0.818987
$939$	−2.41291	−0.0787424
$940$	8.19492	0.267289
$941$	−1.69686	−0.0553160	−0.0276580	−	0.999617i	$-0.508805\pi$
$941$	−1.69686	−0.0553160	−0.0276580	+	0.999617i	$0.508805\pi$
$942$	−3.71679	−0.121100
$943$	1.57169	0.0511813
$944$	−7.29860	−0.237549
$945$	−1.13473	−0.0369126
$946$	−51.1971	−1.66456
$947$	−47.1251	−1.53136	−0.765680	−	0.643222i	$-0.777597\pi$
$947$	−47.1251	−1.53136	−0.765680	+	0.643222i	$0.777597\pi$
$948$	−1.51459	−0.0491917
$949$	6.93813	0.225221
$950$	0	0
$951$	−1.53815	−0.0498779
$952$	−5.44901	−0.176603
$953$	−51.7089	−1.67502	−0.837508	−	0.546426i	$-0.815988\pi$
$953$	−51.7089	−1.67502	−0.837508	+	0.546426i	$0.815988\pi$
$954$	18.3368	0.593675
$955$	−9.22171	−0.298408
$956$	−18.0068	−0.582381
$957$	−1.32052	−0.0426862
$958$	16.0130	0.517356
$959$	3.86049	0.124662
$960$	−0.314837	−0.0101613
$961$	33.8463	1.09182
$962$	27.2743	0.879360
$963$	33.8300	1.09016
$964$	−15.8489	−0.510460
$965$	12.0020	0.386357
$966$	0.605832	0.0194923
$967$	−11.5790	−0.372356	−0.186178	−	0.982516i	$-0.559610\pi$
$967$	−11.5790	−0.372356	−0.186178	+	0.982516i	$0.559610\pi$
$968$	−0.0544390	−0.00174973
$969$	0	0
$970$	34.0109	1.09202
$971$	59.2842	1.90252	0.951260	−	0.308390i	$-0.0997901\pi$
$971$	59.2842	1.90252	0.951260	+	0.308390i	$0.0997901\pi$
$972$	−6.13735	−0.196856
$973$	−6.28478	−0.201481
$974$	−8.69093	−0.278475
$975$	0.470678	0.0150738
$976$	−67.4005	−2.15744
$977$	−21.9879	−0.703454	−0.351727	−	0.936103i	$-0.614405\pi$
$977$	−21.9879	−0.703454	−0.351727	+	0.936103i	$0.614405\pi$
$978$	5.93126	0.189661
$979$	2.61448	0.0835592
$980$	7.61119	0.243130
$981$	−37.8129	−1.20727
$982$	−18.2992	−0.583951
$983$	−19.7062	−0.628531	−0.314265	−	0.949335i	$-0.601758\pi$
$983$	−19.7062	−0.628531	−0.314265	+	0.949335i	$0.601758\pi$
$984$	−0.201419	−0.00642101
$985$	26.8972	0.857017
$986$	−16.3711	−0.521361
$987$	1.19699	0.0381007
$988$	0	0
$989$	−14.9284	−0.474695
$990$	17.8552	0.567476
$991$	46.7488	1.48503	0.742513	−	0.669832i	$-0.233634\pi$
$991$	46.7488	1.48503	0.742513	+	0.669832i	$0.233634\pi$
$992$	51.3905	1.63165
$993$	−4.13360	−0.131176
$994$	21.5068	0.682153
$995$	4.57394	0.145004
$996$	−0.622131	−0.0197130
$997$	11.6112	0.367729	0.183865	−	0.982952i	$-0.441139\pi$
$997$	11.6112	0.367729	0.183865	+	0.982952i	$0.441139\pi$
$998$	3.49255	0.110555
$999$	5.97039	0.188895

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.u.1.2		9
5.4	even	2		9025.2.a.cd.1.8		9
19.14	odd	18		95.2.k.b.6.3	✓	18
19.15	odd	18		95.2.k.b.16.3	yes	18
19.18	odd	2		1805.2.a.t.1.8		9
57.14	even	18		855.2.bs.b.766.1		18
57.53	even	18		855.2.bs.b.586.1		18
95.14	odd	18		475.2.l.b.101.1		18
95.33	even	36		475.2.u.c.424.1		36
95.34	odd	18		475.2.l.b.301.1		18
95.52	even	36		475.2.u.c.424.6		36
95.53	even	36		475.2.u.c.149.6		36
95.72	even	36		475.2.u.c.149.1		36
95.94	odd	2		9025.2.a.ce.1.2		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.b.6.3	✓	18	19.14	odd	18
95.2.k.b.16.3	yes	18	19.15	odd	18
475.2.l.b.101.1		18	95.14	odd	18
475.2.l.b.301.1		18	95.34	odd	18
475.2.u.c.149.1		36	95.72	even	36
475.2.u.c.149.6		36	95.53	even	36
475.2.u.c.424.1		36	95.33	even	36
475.2.u.c.424.6		36	95.52	even	36
855.2.bs.b.586.1		18	57.53	even	18
855.2.bs.b.766.1		18	57.14	even	18
1805.2.a.t.1.8		9	19.18	odd	2
1805.2.a.u.1.2		9	1.1	even	1	trivial
9025.2.a.cd.1.8		9	5.4	even	2
9025.2.a.ce.1.2		9	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)

\(f(q)\)	\(=\)	\(q-1.81702 q^{2} -0.177104 q^{3} +1.30157 q^{4} -1.00000 q^{5} +0.321803 q^{6} +1.07346 q^{7} +1.26906 q^{8} -2.96863 q^{9} +O(q^{10})\)	\(q-1.81702 q^{2} -0.177104 q^{3} +1.30157 q^{4} -1.00000 q^{5} +0.321803 q^{6} +1.07346 q^{7} +1.26906 q^{8} -2.96863 q^{9} +1.81702 q^{10} -3.31015 q^{11} -0.230514 q^{12} -2.65763 q^{13} -1.95051 q^{14} +0.177104 q^{15} -4.90905 q^{16} -3.99991 q^{17} +5.39408 q^{18} -1.30157 q^{20} -0.190115 q^{21} +6.01462 q^{22} +1.75378 q^{23} -0.224755 q^{24} +1.00000 q^{25} +4.82898 q^{26} +1.05707 q^{27} +1.39719 q^{28} -2.25251 q^{29} -0.321803 q^{30} +8.05272 q^{31} +6.38175 q^{32} +0.586242 q^{33} +7.26792 q^{34} -1.07346 q^{35} -3.86390 q^{36} +5.64805 q^{37} +0.470678 q^{39} -1.26906 q^{40} +0.896172 q^{41} +0.345443 q^{42} -8.51211 q^{43} -4.30841 q^{44} +2.96863 q^{45} -3.18666 q^{46} -6.29616 q^{47} +0.869414 q^{48} -5.84768 q^{49} -1.81702 q^{50} +0.708401 q^{51} -3.45911 q^{52} +3.39943 q^{53} -1.92072 q^{54} +3.31015 q^{55} +1.36228 q^{56} +4.09287 q^{58} +1.48676 q^{59} +0.230514 q^{60} +13.7298 q^{61} -14.6320 q^{62} -3.18672 q^{63} -1.77769 q^{64} +2.65763 q^{65} -1.06522 q^{66} -12.8597 q^{67} -5.20618 q^{68} -0.310602 q^{69} +1.95051 q^{70} -11.0262 q^{71} -3.76736 q^{72} -2.61065 q^{73} -10.2626 q^{74} -0.177104 q^{75} -3.55333 q^{77} -0.855233 q^{78} +6.57050 q^{79} +4.90905 q^{80} +8.71869 q^{81} -1.62837 q^{82} +2.69888 q^{83} -0.247449 q^{84} +3.99991 q^{85} +15.4667 q^{86} +0.398929 q^{87} -4.20077 q^{88} -0.789838 q^{89} -5.39408 q^{90} -2.85287 q^{91} +2.28268 q^{92} -1.42617 q^{93} +11.4403 q^{94} -1.13024 q^{96} +18.7179 q^{97} +10.6254 q^{98} +9.82663 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 3 q^{3} + 6 q^{4} - 9 q^{5} - 12 q^{6} - 12 q^{8} + 6 q^{9}+O(q^{10}) \) 9 * q + 3 * q^3 + 6 * q^4 - 9 * q^5 - 12 * q^6 - 12 * q^8 + 6 * q^9	\( 9 q + 3 q^{3} + 6 q^{4} - 9 q^{5} - 12 q^{6} - 12 q^{8} + 6 q^{9} + 6 q^{12} - 3 q^{13} + 12 q^{14} - 3 q^{15} - 12 q^{16} - 9 q^{17} + 6 q^{18} - 6 q^{20} + 12 q^{21} + 12 q^{22} + 15 q^{24} + 9 q^{25} + 21 q^{26} + 6 q^{27} - 15 q^{28} + 15 q^{29} + 12 q^{30} + 30 q^{31} - 9 q^{32} + 9 q^{33} - 6 q^{36} + 30 q^{37} + 6 q^{39} + 12 q^{40} + 18 q^{41} + 36 q^{42} - 6 q^{43} - 24 q^{44} - 6 q^{45} + 21 q^{46} + 21 q^{47} + 15 q^{48} + 3 q^{49} + 18 q^{51} - 3 q^{52} - 9 q^{53} - 9 q^{54} + 36 q^{56} + 18 q^{58} + 27 q^{59} - 6 q^{60} + 12 q^{61} - 6 q^{62} - 15 q^{63} + 24 q^{64} + 3 q^{65} + 3 q^{66} + 36 q^{67} + 3 q^{68} + 27 q^{69} - 12 q^{70} - 6 q^{71} + 12 q^{72} - 9 q^{73} - 9 q^{74} + 3 q^{75} + 12 q^{77} + 54 q^{78} + 45 q^{79} + 12 q^{80} - 15 q^{81} - 48 q^{82} - 12 q^{84} + 9 q^{85} - 9 q^{86} + 45 q^{87} + 39 q^{88} - 9 q^{89} - 6 q^{90} + 51 q^{91} - 54 q^{92} + 9 q^{93} + 33 q^{94} - 9 q^{96} + 45 q^{97} + 33 q^{98} + 12 q^{99}+O(q^{100}) \) 9 * q + 3 * q^3 + 6 * q^4 - 9 * q^5 - 12 * q^6 - 12 * q^8 + 6 * q^9 + 6 * q^12 - 3 * q^13 + 12 * q^14 - 3 * q^15 - 12 * q^16 - 9 * q^17 + 6 * q^18 - 6 * q^20 + 12 * q^21 + 12 * q^22 + 15 * q^24 + 9 * q^25 + 21 * q^26 + 6 * q^27 - 15 * q^28 + 15 * q^29 + 12 * q^30 + 30 * q^31 - 9 * q^32 + 9 * q^33 - 6 * q^36 + 30 * q^37 + 6 * q^39 + 12 * q^40 + 18 * q^41 + 36 * q^42 - 6 * q^43 - 24 * q^44 - 6 * q^45 + 21 * q^46 + 21 * q^47 + 15 * q^48 + 3 * q^49 + 18 * q^51 - 3 * q^52 - 9 * q^53 - 9 * q^54 + 36 * q^56 + 18 * q^58 + 27 * q^59 - 6 * q^60 + 12 * q^61 - 6 * q^62 - 15 * q^63 + 24 * q^64 + 3 * q^65 + 3 * q^66 + 36 * q^67 + 3 * q^68 + 27 * q^69 - 12 * q^70 - 6 * q^71 + 12 * q^72 - 9 * q^73 - 9 * q^74 + 3 * q^75 + 12 * q^77 + 54 * q^78 + 45 * q^79 + 12 * q^80 - 15 * q^81 - 48 * q^82 - 12 * q^84 + 9 * q^85 - 9 * q^86 + 45 * q^87 + 39 * q^88 - 9 * q^89 - 6 * q^90 + 51 * q^91 - 54 * q^92 + 9 * q^93 + 33 * q^94 - 9 * q^96 + 45 * q^97 + 33 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more