LMFDB - Embedded newform 7098.2.a.cu.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7098,2,Mod(1,7098)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7098, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("7098.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7098.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:	$56.6778153547$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.6148961.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 11x^{4} + 12x^{3} + 32x^{2} - 16x - 29 $ x^6 - 2x^5 - 11x^4 + 12x^3 + 32x^2 - 16*x - 29
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$3.58604$ of defining polynomial
Character	$\chi$	$=$	7098.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.59594 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.59594 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.59594 q^{10} +5.12317 q^{11} +1.00000 q^{12} -1.00000 q^{14} +2.59594 q^{15} +1.00000 q^{16} -3.39467 q^{17} +1.00000 q^{18} +0.0178327 q^{19} +2.59594 q^{20} -1.00000 q^{21} +5.12317 q^{22} +7.09063 q^{23} +1.00000 q^{24} +1.73890 q^{25} +1.00000 q^{27} -1.00000 q^{28} +4.27806 q^{29} +2.59594 q^{30} -0.430922 q^{31} +1.00000 q^{32} +5.12317 q^{33} -3.39467 q^{34} -2.59594 q^{35} +1.00000 q^{36} -4.46183 q^{37} +0.0178327 q^{38} +2.59594 q^{40} +2.69358 q^{41} -1.00000 q^{42} +11.1823 q^{43} +5.12317 q^{44} +2.59594 q^{45} +7.09063 q^{46} -5.56996 q^{47} +1.00000 q^{48} +1.00000 q^{49} +1.73890 q^{50} -3.39467 q^{51} -9.44524 q^{53} +1.00000 q^{54} +13.2994 q^{55} -1.00000 q^{56} +0.0178327 q^{57} +4.27806 q^{58} -13.2304 q^{59} +2.59594 q^{60} -7.25936 q^{61} -0.430922 q^{62} -1.00000 q^{63} +1.00000 q^{64} +5.12317 q^{66} -1.37917 q^{67} -3.39467 q^{68} +7.09063 q^{69} -2.59594 q^{70} +12.7469 q^{71} +1.00000 q^{72} -3.14421 q^{73} -4.46183 q^{74} +1.73890 q^{75} +0.0178327 q^{76} -5.12317 q^{77} +7.29899 q^{79} +2.59594 q^{80} +1.00000 q^{81} +2.69358 q^{82} +2.41028 q^{83} -1.00000 q^{84} -8.81236 q^{85} +11.1823 q^{86} +4.27806 q^{87} +5.12317 q^{88} -2.71911 q^{89} +2.59594 q^{90} +7.09063 q^{92} -0.430922 q^{93} -5.56996 q^{94} +0.0462926 q^{95} +1.00000 q^{96} +16.7222 q^{97} +1.00000 q^{98} +5.12317 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 9 q^{5} + 6 q^{6} - 6 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 9 * q^5 + 6 * q^6 - 6 * q^7 + 6 * q^8 + 6 * q^9	$ 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 9 q^{5} + 6 q^{6} - 6 q^{7} + 6 q^{8} + 6 q^{9} + 9 q^{10} + 10 q^{11} + 6 q^{12} - 6 q^{14} + 9 q^{15} + 6 q^{16} + 4 q^{17} + 6 q^{18} + 2 q^{19} + 9 q^{20} - 6 q^{21} + 10 q^{22} + 6 q^{24} + 9 q^{25} + 6 q^{27} - 6 q^{28} - 4 q^{29} + 9 q^{30} + 9 q^{31} + 6 q^{32} + 10 q^{33} + 4 q^{34} - 9 q^{35} + 6 q^{36} + 9 q^{37} + 2 q^{38} + 9 q^{40} + 25 q^{41} - 6 q^{42} + 19 q^{43} + 10 q^{44} + 9 q^{45} + 21 q^{47} + 6 q^{48} + 6 q^{49} + 9 q^{50} + 4 q^{51} - 4 q^{53} + 6 q^{54} + 21 q^{55} - 6 q^{56} + 2 q^{57} - 4 q^{58} + 20 q^{59} + 9 q^{60} + 3 q^{61} + 9 q^{62} - 6 q^{63} + 6 q^{64} + 10 q^{66} + 24 q^{67} + 4 q^{68} - 9 q^{70} + 13 q^{71} + 6 q^{72} - 9 q^{73} + 9 q^{74} + 9 q^{75} + 2 q^{76} - 10 q^{77} + 28 q^{79} + 9 q^{80} + 6 q^{81} + 25 q^{82} + 15 q^{83} - 6 q^{84} + 17 q^{85} + 19 q^{86} - 4 q^{87} + 10 q^{88} + 11 q^{89} + 9 q^{90} + 9 q^{93} + 21 q^{94} + 6 q^{96} + 2 q^{97} + 6 q^{98} + 10 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 9 * q^5 + 6 * q^6 - 6 * q^7 + 6 * q^8 + 6 * q^9 + 9 * q^10 + 10 * q^11 + 6 * q^12 - 6 * q^14 + 9 * q^15 + 6 * q^16 + 4 * q^17 + 6 * q^18 + 2 * q^19 + 9 * q^20 - 6 * q^21 + 10 * q^22 + 6 * q^24 + 9 * q^25 + 6 * q^27 - 6 * q^28 - 4 * q^29 + 9 * q^30 + 9 * q^31 + 6 * q^32 + 10 * q^33 + 4 * q^34 - 9 * q^35 + 6 * q^36 + 9 * q^37 + 2 * q^38 + 9 * q^40 + 25 * q^41 - 6 * q^42 + 19 * q^43 + 10 * q^44 + 9 * q^45 + 21 * q^47 + 6 * q^48 + 6 * q^49 + 9 * q^50 + 4 * q^51 - 4 * q^53 + 6 * q^54 + 21 * q^55 - 6 * q^56 + 2 * q^57 - 4 * q^58 + 20 * q^59 + 9 * q^60 + 3 * q^61 + 9 * q^62 - 6 * q^63 + 6 * q^64 + 10 * q^66 + 24 * q^67 + 4 * q^68 - 9 * q^70 + 13 * q^71 + 6 * q^72 - 9 * q^73 + 9 * q^74 + 9 * q^75 + 2 * q^76 - 10 * q^77 + 28 * q^79 + 9 * q^80 + 6 * q^81 + 25 * q^82 + 15 * q^83 - 6 * q^84 + 17 * q^85 + 19 * q^86 - 4 * q^87 + 10 * q^88 + 11 * q^89 + 9 * q^90 + 9 * q^93 + 21 * q^94 + 6 * q^96 + 2 * q^97 + 6 * q^98 + 10 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	2.59594	1.16094	0.580470	−	0.814282i	$-0.302869\pi$
$5$	2.59594	1.16094	0.580470	+	0.814282i	$0.302869\pi$
$6$	1.00000	0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.59594	0.820908
$11$	5.12317	1.54469	0.772347	−	0.635201i	$-0.219083\pi$
$11$	5.12317	1.54469	0.772347	+	0.635201i	$0.219083\pi$
$12$	1.00000	0.288675
$13$	0	0
$13$	0	0
$14$	−1.00000	−0.267261
$15$	2.59594	0.670269
$16$	1.00000	0.250000
$17$	−3.39467	−0.823328	−0.411664	−	0.911336i	$-0.635052\pi$
$17$	−3.39467	−0.823328	−0.411664	+	0.911336i	$0.635052\pi$
$18$	1.00000	0.235702
$19$	0.0178327	0.00409110	0.00204555	−	0.999998i	$-0.499349\pi$
$19$	0.0178327	0.00409110	0.00204555	+	0.999998i	$0.499349\pi$
$20$	2.59594	0.580470
$21$	−1.00000	−0.218218
$22$	5.12317	1.09226
$23$	7.09063	1.47850	0.739249	−	0.673432i	$-0.235181\pi$
$23$	7.09063	1.47850	0.739249	+	0.673432i	$0.235181\pi$
$24$	1.00000	0.204124
$25$	1.73890	0.347780
$26$	0	0
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	4.27806	0.794417	0.397208	−	0.917728i	$-0.369979\pi$
$29$	4.27806	0.794417	0.397208	+	0.917728i	$0.369979\pi$
$30$	2.59594	0.473951
$31$	−0.430922	−0.0773958	−0.0386979	−	0.999251i	$-0.512321\pi$
$31$	−0.430922	−0.0773958	−0.0386979	+	0.999251i	$0.512321\pi$
$32$	1.00000	0.176777
$33$	5.12317	0.891829
$34$	−3.39467	−0.582181
$35$	−2.59594	−0.438794
$36$	1.00000	0.166667
$37$	−4.46183	−0.733520	−0.366760	−	0.930316i	$-0.619533\pi$
$37$	−4.46183	−0.733520	−0.366760	+	0.930316i	$0.619533\pi$
$38$	0.0178327	0.00289285
$39$	0	0
$40$	2.59594	0.410454
$41$	2.69358	0.420666	0.210333	−	0.977630i	$-0.432545\pi$
$41$	2.69358	0.420666	0.210333	+	0.977630i	$0.432545\pi$
$42$	−1.00000	−0.154303
$43$	11.1823	1.70529	0.852643	−	0.522494i	$-0.174998\pi$
$43$	11.1823	1.70529	0.852643	+	0.522494i	$0.174998\pi$
$44$	5.12317	0.772347
$45$	2.59594	0.386980
$46$	7.09063	1.04546
$47$	−5.56996	−0.812463	−0.406231	−	0.913770i	$-0.633157\pi$
$47$	−5.56996	−0.812463	−0.406231	+	0.913770i	$0.633157\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	1.73890	0.245918
$51$	−3.39467	−0.475349
$52$	0	0
$53$	−9.44524	−1.29740	−0.648702	−	0.761043i	$-0.724688\pi$
$53$	−9.44524	−1.29740	−0.648702	+	0.761043i	$0.724688\pi$
$54$	1.00000	0.136083
$55$	13.2994	1.79330
$56$	−1.00000	−0.133631
$57$	0.0178327	0.00236200
$58$	4.27806	0.561737
$59$	−13.2304	−1.72245	−0.861223	−	0.508228i	$-0.830301\pi$
$59$	−13.2304	−1.72245	−0.861223	+	0.508228i	$0.830301\pi$
$60$	2.59594	0.335134
$61$	−7.25936	−0.929466	−0.464733	−	0.885451i	$-0.653850\pi$
$61$	−7.25936	−0.929466	−0.464733	+	0.885451i	$0.653850\pi$
$62$	−0.430922	−0.0547271
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	5.12317	0.630618
$67$	−1.37917	−0.168493	−0.0842463	−	0.996445i	$-0.526848\pi$
$67$	−1.37917	−0.168493	−0.0842463	+	0.996445i	$0.526848\pi$
$68$	−3.39467	−0.411664
$69$	7.09063	0.853611
$70$	−2.59594	−0.310274
$71$	12.7469	1.51278	0.756390	−	0.654121i	$-0.226961\pi$
$71$	12.7469	1.51278	0.756390	+	0.654121i	$0.226961\pi$
$72$	1.00000	0.117851
$73$	−3.14421	−0.368002	−0.184001	−	0.982926i	$-0.558905\pi$
$73$	−3.14421	−0.368002	−0.184001	+	0.982926i	$0.558905\pi$
$74$	−4.46183	−0.518677
$75$	1.73890	0.200791
$76$	0.0178327	0.00204555
$77$	−5.12317	−0.583839
$78$	0	0
$79$	7.29899	0.821201	0.410600	−	0.911815i	$-0.365319\pi$
$79$	7.29899	0.821201	0.410600	+	0.911815i	$0.365319\pi$
$80$	2.59594	0.290235
$81$	1.00000	0.111111
$82$	2.69358	0.297456
$83$	2.41028	0.264563	0.132282	−	0.991212i	$-0.457770\pi$
$83$	2.41028	0.264563	0.132282	+	0.991212i	$0.457770\pi$
$84$	−1.00000	−0.109109
$85$	−8.81236	−0.955834
$86$	11.1823	1.20582
$87$	4.27806	0.458657
$88$	5.12317	0.546132
$89$	−2.71911	−0.288225	−0.144112	−	0.989561i	$-0.546033\pi$
$89$	−2.71911	−0.288225	−0.144112	+	0.989561i	$0.546033\pi$
$90$	2.59594	0.273636
$91$	0	0
$92$	7.09063	0.739249
$93$	−0.430922	−0.0446845
$94$	−5.56996	−0.574498
$95$	0.0462926	0.00474952
$96$	1.00000	0.102062
$97$	16.7222	1.69788	0.848941	−	0.528487i	$-0.177240\pi$
$97$	16.7222	1.69788	0.848941	+	0.528487i	$0.177240\pi$
$98$	1.00000	0.101015
$99$	5.12317	0.514898
$100$	1.73890	0.173890
$101$	−13.7189	−1.36508	−0.682538	−	0.730850i	$-0.739124\pi$
$101$	−13.7189	−1.36508	−0.682538	+	0.730850i	$0.739124\pi$
$102$	−3.39467	−0.336122
$103$	4.24896	0.418662	0.209331	−	0.977845i	$-0.432871\pi$
$103$	4.24896	0.418662	0.209331	+	0.977845i	$0.432871\pi$
$104$	0	0
$105$	−2.59594	−0.253338
$106$	−9.44524	−0.917403
$107$	−2.43068	−0.234983	−0.117491	−	0.993074i	$-0.537485\pi$
$107$	−2.43068	−0.234983	−0.117491	+	0.993074i	$0.537485\pi$
$108$	1.00000	0.0962250
$109$	10.8152	1.03591	0.517956	−	0.855408i	$-0.326693\pi$
$109$	10.8152	1.03591	0.517956	+	0.855408i	$0.326693\pi$
$110$	13.2994	1.26805
$111$	−4.46183	−0.423498
$112$	−1.00000	−0.0944911
$113$	−1.94348	−0.182827	−0.0914137	−	0.995813i	$-0.529139\pi$
$113$	−1.94348	−0.182827	−0.0914137	+	0.995813i	$0.529139\pi$
$114$	0.0178327	0.00167019
$115$	18.4068	1.71645
$116$	4.27806	0.397208
$117$	0	0
$118$	−13.2304	−1.21795
$119$	3.39467	0.311189
$120$	2.59594	0.236976
$121$	15.2469	1.38608
$122$	−7.25936	−0.657232
$123$	2.69358	0.242872
$124$	−0.430922	−0.0386979
$125$	−8.46562	−0.757188
$126$	−1.00000	−0.0890871
$127$	−10.1063	−0.896787	−0.448394	−	0.893836i	$-0.648004\pi$
$127$	−10.1063	−0.896787	−0.448394	+	0.893836i	$0.648004\pi$
$128$	1.00000	0.0883883
$129$	11.1823	0.984547
$130$	0	0
$131$	−16.1622	−1.41210	−0.706049	−	0.708163i	$-0.749524\pi$
$131$	−16.1622	−1.41210	−0.706049	+	0.708163i	$0.749524\pi$
$132$	5.12317	0.445915
$133$	−0.0178327	−0.00154629
$134$	−1.37917	−0.119142
$135$	2.59594	0.223423
$136$	−3.39467	−0.291091
$137$	11.6110	0.991994	0.495997	−	0.868324i	$-0.334803\pi$
$137$	11.6110	0.991994	0.495997	+	0.868324i	$0.334803\pi$
$138$	7.09063	0.603594
$139$	−9.39315	−0.796716	−0.398358	−	0.917230i	$-0.630420\pi$
$139$	−9.39315	−0.796716	−0.398358	+	0.917230i	$0.630420\pi$
$140$	−2.59594	−0.219397
$141$	−5.56996	−0.469075
$142$	12.7469	1.06970
$143$	0	0
$144$	1.00000	0.0833333
$145$	11.1056	0.922269
$146$	−3.14421	−0.260216
$147$	1.00000	0.0824786
$148$	−4.46183	−0.366760
$149$	17.9543	1.47088	0.735438	−	0.677592i	$-0.236976\pi$
$149$	17.9543	1.47088	0.735438	+	0.677592i	$0.236976\pi$
$150$	1.73890	0.141981
$151$	5.67926	0.462172	0.231086	−	0.972933i	$-0.425772\pi$
$151$	5.67926	0.462172	0.231086	+	0.972933i	$0.425772\pi$
$152$	0.0178327	0.00144642
$153$	−3.39467	−0.274443
$154$	−5.12317	−0.412837
$155$	−1.11865	−0.0898518
$156$	0	0
$157$	9.36185	0.747157	0.373579	−	0.927598i	$-0.378131\pi$
$157$	9.36185	0.747157	0.373579	+	0.927598i	$0.378131\pi$
$158$	7.29899	0.580677
$159$	−9.44524	−0.749056
$160$	2.59594	0.205227
$161$	−7.09063	−0.558820
$162$	1.00000	0.0785674
$163$	−15.9019	−1.24553	−0.622767	−	0.782407i	$-0.713992\pi$
$163$	−15.9019	−1.24553	−0.622767	+	0.782407i	$0.713992\pi$
$164$	2.69358	0.210333
$165$	13.2994	1.03536
$166$	2.41028	0.187074
$167$	22.9624	1.77688	0.888441	−	0.458990i	$-0.151789\pi$
$167$	22.9624	1.77688	0.888441	+	0.458990i	$0.151789\pi$
$168$	−1.00000	−0.0771517
$169$	0	0
$170$	−8.81236	−0.675877
$171$	0.0178327	0.00136370
$172$	11.1823	0.852643
$173$	−13.2994	−1.01114	−0.505568	−	0.862787i	$-0.668717\pi$
$173$	−13.2994	−1.01114	−0.505568	+	0.862787i	$0.668717\pi$
$174$	4.27806	0.324319
$175$	−1.73890	−0.131448
$176$	5.12317	0.386173
$177$	−13.2304	−0.994454
$178$	−2.71911	−0.203806
$179$	11.1476	0.833213	0.416607	−	0.909087i	$-0.363219\pi$
$179$	11.1476	0.833213	0.416607	+	0.909087i	$0.363219\pi$
$180$	2.59594	0.193490
$181$	−18.9951	−1.41189	−0.705947	−	0.708264i	$-0.749479\pi$
$181$	−18.9951	−1.41189	−0.705947	+	0.708264i	$0.749479\pi$
$182$	0	0
$183$	−7.25936	−0.536627
$184$	7.09063	0.522728
$185$	−11.5826	−0.851572
$186$	−0.430922	−0.0315967
$187$	−17.3915	−1.27179
$188$	−5.56996	−0.406231
$189$	−1.00000	−0.0727393
$190$	0.0462926	0.00335842
$191$	−24.1986	−1.75095	−0.875475	−	0.483263i	$-0.839452\pi$
$191$	−24.1986	−1.75095	−0.875475	+	0.483263i	$0.839452\pi$
$192$	1.00000	0.0721688
$193$	−10.8065	−0.777871	−0.388936	−	0.921265i	$-0.627157\pi$
$193$	−10.8065	−0.777871	−0.388936	+	0.921265i	$0.627157\pi$
$194$	16.7222	1.20058
$195$	0	0
$196$	1.00000	0.0714286
$197$	−2.43849	−0.173735	−0.0868677	−	0.996220i	$-0.527686\pi$
$197$	−2.43849	−0.173735	−0.0868677	+	0.996220i	$0.527686\pi$
$198$	5.12317	0.364088
$199$	18.5328	1.31375	0.656877	−	0.753997i	$-0.271877\pi$
$199$	18.5328	1.31375	0.656877	+	0.753997i	$0.271877\pi$
$200$	1.73890	0.122959
$201$	−1.37917	−0.0972793
$202$	−13.7189	−0.965255
$203$	−4.27806	−0.300261
$204$	−3.39467	−0.237674
$205$	6.99236	0.488368
$206$	4.24896	0.296039
$207$	7.09063	0.492833
$208$	0	0
$209$	0.0913600	0.00631950
$210$	−2.59594	−0.179137
$211$	−6.21752	−0.428032	−0.214016	−	0.976830i	$-0.568654\pi$
$211$	−6.21752	−0.428032	−0.214016	+	0.976830i	$0.568654\pi$
$212$	−9.44524	−0.648702
$213$	12.7469	0.873404
$214$	−2.43068	−0.166158
$215$	29.0286	1.97973
$216$	1.00000	0.0680414
$217$	0.430922	0.0292529
$218$	10.8152	0.732500
$219$	−3.14421	−0.212466
$220$	13.2994	0.896648
$221$	0	0
$222$	−4.46183	−0.299458
$223$	19.3445	1.29540	0.647702	−	0.761894i	$-0.275730\pi$
$223$	19.3445	1.29540	0.647702	+	0.761894i	$0.275730\pi$
$224$	−1.00000	−0.0668153
$225$	1.73890	0.115927
$226$	−1.94348	−0.129278
$227$	9.78761	0.649626	0.324813	−	0.945778i	$-0.394699\pi$
$227$	9.78761	0.649626	0.324813	+	0.945778i	$0.394699\pi$
$228$	0.0178327	0.00118100
$229$	−7.53482	−0.497915	−0.248957	−	0.968514i	$-0.580088\pi$
$229$	−7.53482	−0.497915	−0.248957	+	0.968514i	$0.580088\pi$
$230$	18.4068	1.21371
$231$	−5.12317	−0.337080
$232$	4.27806	0.280869
$233$	29.4092	1.92666	0.963329	−	0.268323i	$-0.0864694\pi$
$233$	29.4092	1.92666	0.963329	+	0.268323i	$0.0864694\pi$
$234$	0	0
$235$	−14.4593	−0.943220
$236$	−13.2304	−0.861223
$237$	7.29899	0.474121
$238$	3.39467	0.220044
$239$	−26.1127	−1.68909	−0.844546	−	0.535483i	$-0.820130\pi$
$239$	−26.1127	−1.68909	−0.844546	+	0.535483i	$0.820130\pi$
$240$	2.59594	0.167567
$241$	−1.71173	−0.110262	−0.0551312	−	0.998479i	$-0.517558\pi$
$241$	−1.71173	−0.110262	−0.0551312	+	0.998479i	$0.517558\pi$
$242$	15.2469	0.980105
$243$	1.00000	0.0641500
$244$	−7.25936	−0.464733
$245$	2.59594	0.165848
$246$	2.69358	0.171736
$247$	0	0
$248$	−0.430922	−0.0273636
$249$	2.41028	0.152746
$250$	−8.46562	−0.535413
$251$	−16.7525	−1.05741	−0.528705	−	0.848806i	$-0.677322\pi$
$251$	−16.7525	−1.05741	−0.528705	+	0.848806i	$0.677322\pi$
$252$	−1.00000	−0.0629941
$253$	36.3265	2.28383
$254$	−10.1063	−0.634124
$255$	−8.81236	−0.551851
$256$	1.00000	0.0625000
$257$	−14.6283	−0.912489	−0.456244	−	0.889854i	$-0.650806\pi$
$257$	−14.6283	−0.912489	−0.456244	+	0.889854i	$0.650806\pi$
$258$	11.1823	0.696180
$259$	4.46183	0.277244
$260$	0	0
$261$	4.27806	0.264806
$262$	−16.1622	−0.998503
$263$	17.3602	1.07047	0.535236	−	0.844702i	$-0.320223\pi$
$263$	17.3602	1.07047	0.535236	+	0.844702i	$0.320223\pi$
$264$	5.12317	0.315309
$265$	−24.5193	−1.50621
$266$	−0.0178327	−0.00109339
$267$	−2.71911	−0.166407
$268$	−1.37917	−0.0842463
$269$	−7.43931	−0.453583	−0.226791	−	0.973943i	$-0.572824\pi$
$269$	−7.43931	−0.453583	−0.226791	+	0.973943i	$0.572824\pi$
$270$	2.59594	0.157984
$271$	11.3773	0.691119	0.345560	−	0.938397i	$-0.387689\pi$
$271$	11.3773	0.691119	0.345560	+	0.938397i	$0.387689\pi$
$272$	−3.39467	−0.205832
$273$	0	0
$274$	11.6110	0.701445
$275$	8.90868	0.537213
$276$	7.09063	0.426806
$277$	−7.53314	−0.452622	−0.226311	−	0.974055i	$-0.572667\pi$
$277$	−7.53314	−0.452622	−0.226311	+	0.974055i	$0.572667\pi$
$278$	−9.39315	−0.563364
$279$	−0.430922	−0.0257986
$280$	−2.59594	−0.155137
$281$	−7.32324	−0.436868	−0.218434	−	0.975852i	$-0.570095\pi$
$281$	−7.32324	−0.436868	−0.218434	+	0.975852i	$0.570095\pi$
$282$	−5.56996	−0.331686
$283$	−12.5399	−0.745419	−0.372709	−	0.927948i	$-0.621571\pi$
$283$	−12.5399	−0.745419	−0.372709	+	0.927948i	$0.621571\pi$
$284$	12.7469	0.756390
$285$	0.0462926	0.00274214
$286$	0	0
$287$	−2.69358	−0.158997
$288$	1.00000	0.0589256
$289$	−5.47621	−0.322130
$290$	11.1056	0.652143
$291$	16.7222	0.980273
$292$	−3.14421	−0.184001
$293$	19.0614	1.11358	0.556791	−	0.830653i	$-0.312033\pi$
$293$	19.0614	1.11358	0.556791	+	0.830653i	$0.312033\pi$
$294$	1.00000	0.0583212
$295$	−34.3452	−1.99965
$296$	−4.46183	−0.259338
$297$	5.12317	0.297276
$298$	17.9543	1.04007
$299$	0	0
$300$	1.73890	0.100395
$301$	−11.1823	−0.644537
$302$	5.67926	0.326805
$303$	−13.7189	−0.788127
$304$	0.0178327	0.00102278
$305$	−18.8449	−1.07905
$306$	−3.39467	−0.194060
$307$	−24.8387	−1.41762	−0.708809	−	0.705401i	$-0.750767\pi$
$307$	−24.8387	−1.41762	−0.708809	+	0.705401i	$0.750767\pi$
$308$	−5.12317	−0.291920
$309$	4.24896	0.241715
$310$	−1.11865	−0.0635348
$311$	−0.438633	−0.0248726	−0.0124363	−	0.999923i	$-0.503959\pi$
$311$	−0.438633	−0.0248726	−0.0124363	+	0.999923i	$0.503959\pi$
$312$	0	0
$313$	16.3187	0.922390	0.461195	−	0.887299i	$-0.347421\pi$
$313$	16.3187	0.922390	0.461195	+	0.887299i	$0.347421\pi$
$314$	9.36185	0.528320
$315$	−2.59594	−0.146265
$316$	7.29899	0.410600
$317$	−33.7161	−1.89368	−0.946841	−	0.321701i	$-0.895746\pi$
$317$	−33.7161	−1.89368	−0.946841	+	0.321701i	$0.895746\pi$
$318$	−9.44524	−0.529663
$319$	21.9172	1.22713
$320$	2.59594	0.145117
$321$	−2.43068	−0.135667
$322$	−7.09063	−0.395145
$323$	−0.0605362	−0.00336832
$324$	1.00000	0.0555556
$325$	0	0
$326$	−15.9019	−0.880725
$327$	10.8152	0.598084
$328$	2.69358	0.148728
$329$	5.56996	0.307082
$330$	13.2994	0.732110
$331$	10.8454	0.596120	0.298060	−	0.954547i	$-0.403661\pi$
$331$	10.8454	0.596120	0.298060	+	0.954547i	$0.403661\pi$
$332$	2.41028	0.132282
$333$	−4.46183	−0.244507
$334$	22.9624	1.25645
$335$	−3.58025	−0.195610
$336$	−1.00000	−0.0545545
$337$	−8.64433	−0.470887	−0.235443	−	0.971888i	$-0.575654\pi$
$337$	−8.64433	−0.470887	−0.235443	+	0.971888i	$0.575654\pi$
$338$	0	0
$339$	−1.94348	−0.105555
$340$	−8.81236	−0.477917
$341$	−2.20768	−0.119553
$342$	0.0178327	0.000964283 0
$343$	−1.00000	−0.0539949
$344$	11.1823	0.602910
$345$	18.4068	0.990991
$346$	−13.2994	−0.714981
$347$	−24.0533	−1.29125	−0.645624	−	0.763655i	$-0.723403\pi$
$347$	−24.0533	−1.29125	−0.645624	+	0.763655i	$0.723403\pi$
$348$	4.27806	0.229328
$349$	31.3486	1.67805	0.839025	−	0.544092i	$-0.183126\pi$
$349$	31.3486	1.67805	0.839025	+	0.544092i	$0.183126\pi$
$350$	−1.73890	−0.0929481
$351$	0	0
$352$	5.12317	0.273066
$353$	11.8086	0.628508	0.314254	−	0.949339i	$-0.398246\pi$
$353$	11.8086	0.628508	0.314254	+	0.949339i	$0.398246\pi$
$354$	−13.2304	−0.703185
$355$	33.0902	1.75625
$356$	−2.71911	−0.144112
$357$	3.39467	0.179665
$358$	11.1476	0.589171
$359$	10.2791	0.542510	0.271255	−	0.962508i	$-0.412561\pi$
$359$	10.2791	0.542510	0.271255	+	0.962508i	$0.412561\pi$
$360$	2.59594	0.136818
$361$	−18.9997	−0.999983
$362$	−18.9951	−0.998360
$363$	15.2469	0.800252
$364$	0	0
$365$	−8.16217	−0.427228
$366$	−7.25936	−0.379453
$367$	23.8024	1.24248	0.621238	−	0.783622i	$-0.286630\pi$
$367$	23.8024	1.24248	0.621238	+	0.783622i	$0.286630\pi$
$368$	7.09063	0.369625
$369$	2.69358	0.140222
$370$	−11.5826	−0.602152
$371$	9.44524	0.490372
$372$	−0.430922	−0.0223422
$373$	4.82143	0.249644	0.124822	−	0.992179i	$-0.460164\pi$
$373$	4.82143	0.249644	0.124822	+	0.992179i	$0.460164\pi$
$374$	−17.3915	−0.899291
$375$	−8.46562	−0.437163
$376$	−5.56996	−0.287249
$377$	0	0
$378$	−1.00000	−0.0514344
$379$	21.2547	1.09178	0.545892	−	0.837856i	$-0.316191\pi$
$379$	21.2547	1.09178	0.545892	+	0.837856i	$0.316191\pi$
$380$	0.0462926	0.00237476
$381$	−10.1063	−0.517760
$382$	−24.1986	−1.23811
$383$	−32.6499	−1.66833	−0.834165	−	0.551515i	$-0.814050\pi$
$383$	−32.6499	−1.66833	−0.834165	+	0.551515i	$0.814050\pi$
$384$	1.00000	0.0510310
$385$	−13.2994	−0.677802
$386$	−10.8065	−0.550038
$387$	11.1823	0.568429
$388$	16.7222	0.848941
$389$	−14.8469	−0.752769	−0.376385	−	0.926464i	$-0.622833\pi$
$389$	−14.8469	−0.752769	−0.376385	+	0.926464i	$0.622833\pi$
$390$	0	0
$391$	−24.0703	−1.21729
$392$	1.00000	0.0505076
$393$	−16.1622	−0.815275
$394$	−2.43849	−0.122849
$395$	18.9477	0.953364
$396$	5.12317	0.257449
$397$	15.5132	0.778583	0.389292	−	0.921115i	$-0.372720\pi$
$397$	15.5132	0.778583	0.389292	+	0.921115i	$0.372720\pi$
$398$	18.5328	0.928965
$399$	−0.0178327	−0.000892752 0
$400$	1.73890	0.0869450
$401$	11.1698	0.557792	0.278896	−	0.960321i	$-0.410032\pi$
$401$	11.1698	0.557792	0.278896	+	0.960321i	$0.410032\pi$
$402$	−1.37917	−0.0687868
$403$	0	0
$404$	−13.7189	−0.682538
$405$	2.59594	0.128993
$406$	−4.27806	−0.212317
$407$	−22.8587	−1.13306
$408$	−3.39467	−0.168061
$409$	−1.82157	−0.0900709	−0.0450355	−	0.998985i	$-0.514340\pi$
$409$	−1.82157	−0.0900709	−0.0450355	+	0.998985i	$0.514340\pi$
$410$	6.99236	0.345328
$411$	11.6110	0.572728
$412$	4.24896	0.209331
$413$	13.2304	0.651023
$414$	7.09063	0.348485
$415$	6.25695	0.307142
$416$	0	0
$417$	−9.39315	−0.459984
$418$	0.0913600	0.00446856
$419$	30.1385	1.47236	0.736182	−	0.676784i	$-0.236627\pi$
$419$	30.1385	1.47236	0.736182	+	0.676784i	$0.236627\pi$
$420$	−2.59594	−0.126669
$421$	17.7000	0.862645	0.431322	−	0.902198i	$-0.358047\pi$
$421$	17.7000	0.862645	0.431322	+	0.902198i	$0.358047\pi$
$422$	−6.21752	−0.302664
$423$	−5.56996	−0.270821
$424$	−9.44524	−0.458701
$425$	−5.90299	−0.286337
$426$	12.7469	0.617590
$427$	7.25936	0.351305
$428$	−2.43068	−0.117491
$429$	0	0
$430$	29.0286	1.39988
$431$	−27.9368	−1.34567	−0.672834	−	0.739794i	$-0.734923\pi$
$431$	−27.9368	−1.34567	−0.672834	+	0.739794i	$0.734923\pi$
$432$	1.00000	0.0481125
$433$	−26.1856	−1.25840	−0.629200	−	0.777243i	$-0.716617\pi$
$433$	−26.1856	−1.25840	−0.629200	+	0.777243i	$0.716617\pi$
$434$	0.430922	0.0206849
$435$	11.1056	0.532473
$436$	10.8152	0.517956
$437$	0.126445	0.00604869
$438$	−3.14421	−0.150236
$439$	7.29808	0.348318	0.174159	−	0.984718i	$-0.444279\pi$
$439$	7.29808	0.348318	0.174159	+	0.984718i	$0.444279\pi$
$440$	13.2994	0.634026
$441$	1.00000	0.0476190
$442$	0	0
$443$	−12.0853	−0.574190	−0.287095	−	0.957902i	$-0.592690\pi$
$443$	−12.0853	−0.574190	−0.287095	+	0.957902i	$0.592690\pi$
$444$	−4.46183	−0.211749
$445$	−7.05864	−0.334611
$446$	19.3445	0.915989
$447$	17.9543	0.849211
$448$	−1.00000	−0.0472456
$449$	33.3480	1.57379	0.786894	−	0.617088i	$-0.211688\pi$
$449$	33.3480	1.57379	0.786894	+	0.617088i	$0.211688\pi$
$450$	1.73890	0.0819725
$451$	13.7996	0.649800
$452$	−1.94348	−0.0914137
$453$	5.67926	0.266835
$454$	9.78761	0.459355
$455$	0	0
$456$	0.0178327	0.000835093 0
$457$	3.23421	0.151290	0.0756451	−	0.997135i	$-0.475898\pi$
$457$	3.23421	0.151290	0.0756451	+	0.997135i	$0.475898\pi$
$458$	−7.53482	−0.352079
$459$	−3.39467	−0.158450
$460$	18.4068	0.858223
$461$	−11.6384	−0.542052	−0.271026	−	0.962572i	$-0.587363\pi$
$461$	−11.6384	−0.542052	−0.271026	+	0.962572i	$0.587363\pi$
$462$	−5.12317	−0.238351
$463$	−13.4682	−0.625922	−0.312961	−	0.949766i	$-0.601321\pi$
$463$	−13.4682	−0.625922	−0.312961	+	0.949766i	$0.601321\pi$
$464$	4.27806	0.198604
$465$	−1.11865	−0.0518760
$466$	29.4092	1.36235
$467$	40.6722	1.88209	0.941043	−	0.338287i	$-0.109848\pi$
$467$	40.6722	1.88209	0.941043	+	0.338287i	$0.109848\pi$
$468$	0	0
$469$	1.37917	0.0636842
$470$	−14.4593	−0.666957
$471$	9.36185	0.431372
$472$	−13.2304	−0.608977
$473$	57.2888	2.63414
$474$	7.29899	0.335254
$475$	0.0310093	0.00142280
$476$	3.39467	0.155594
$477$	−9.44524	−0.432468
$478$	−26.1127	−1.19437
$479$	−23.0790	−1.05451	−0.527253	−	0.849709i	$-0.676778\pi$
$479$	−23.0790	−1.05451	−0.527253	+	0.849709i	$0.676778\pi$
$480$	2.59594	0.118488
$481$	0	0
$482$	−1.71173	−0.0779672
$483$	−7.09063	−0.322635
$484$	15.2469	0.693039
$485$	43.4098	1.97114
$486$	1.00000	0.0453609
$487$	32.9859	1.49473	0.747366	−	0.664412i	$-0.231318\pi$
$487$	32.9859	1.49473	0.747366	+	0.664412i	$0.231318\pi$
$488$	−7.25936	−0.328616
$489$	−15.9019	−0.719109
$490$	2.59594	0.117273
$491$	−36.9140	−1.66591	−0.832953	−	0.553343i	$-0.813352\pi$
$491$	−36.9140	−1.66591	−0.832953	+	0.553343i	$0.813352\pi$
$492$	2.69358	0.121436
$493$	−14.5226	−0.654066
$494$	0	0
$495$	13.2994	0.597765
$496$	−0.430922	−0.0193490
$497$	−12.7469	−0.571777
$498$	2.41028	0.108007
$499$	−23.2574	−1.04114	−0.520571	−	0.853818i	$-0.674281\pi$
$499$	−23.2574	−1.04114	−0.520571	+	0.853818i	$0.674281\pi$
$500$	−8.46562	−0.378594
$501$	22.9624	1.02588
$502$	−16.7525	−0.747702
$503$	5.83997	0.260392	0.130196	−	0.991488i	$-0.458439\pi$
$503$	5.83997	0.260392	0.130196	+	0.991488i	$0.458439\pi$
$504$	−1.00000	−0.0445435
$505$	−35.6133	−1.58477
$506$	36.3265	1.61491
$507$	0	0
$508$	−10.1063	−0.448394
$509$	−24.0780	−1.06724	−0.533620	−	0.845724i	$-0.679169\pi$
$509$	−24.0780	−1.06724	−0.533620	+	0.845724i	$0.679169\pi$
$510$	−8.81236	−0.390218
$511$	3.14421	0.139092
$512$	1.00000	0.0441942
$513$	0.0178327	0.000787333 0
$514$	−14.6283	−0.645227
$515$	11.0300	0.486041
$516$	11.1823	0.492274
$517$	−28.5359	−1.25501
$518$	4.46183	0.196041
$519$	−13.2994	−0.583780
$520$	0	0
$521$	−0.751277	−0.0329140	−0.0164570	−	0.999865i	$-0.505239\pi$
$521$	−0.751277	−0.0329140	−0.0164570	+	0.999865i	$0.505239\pi$
$522$	4.27806	0.187246
$523$	−37.7779	−1.65191	−0.825956	−	0.563734i	$-0.809364\pi$
$523$	−37.7779	−1.65191	−0.825956	+	0.563734i	$0.809364\pi$
$524$	−16.1622	−0.706049
$525$	−1.73890	−0.0758918
$526$	17.3602	0.756939
$527$	1.46284	0.0637222
$528$	5.12317	0.222957
$529$	27.2770	1.18596
$530$	−24.5193	−1.06505
$531$	−13.2304	−0.574149
$532$	−0.0178327	−0.000773146 0
$533$	0	0
$534$	−2.71911	−0.117667
$535$	−6.30990	−0.272801
$536$	−1.37917	−0.0595712
$537$	11.1476	0.481056
$538$	−7.43931	−0.320732
$539$	5.12317	0.220670
$540$	2.59594	0.111711
$541$	−16.6143	−0.714304	−0.357152	−	0.934046i	$-0.616252\pi$
$541$	−16.6143	−0.714304	−0.357152	+	0.934046i	$0.616252\pi$
$542$	11.3773	0.488695
$543$	−18.9951	−0.815158
$544$	−3.39467	−0.145545
$545$	28.0757	1.20263
$546$	0	0
$547$	−11.7682	−0.503170	−0.251585	−	0.967835i	$-0.580952\pi$
$547$	−11.7682	−0.503170	−0.251585	+	0.967835i	$0.580952\pi$
$548$	11.6110	0.495997
$549$	−7.25936	−0.309822
$550$	8.90868	0.379867
$551$	0.0762895	0.00325004
$552$	7.09063	0.301797
$553$	−7.29899	−0.310385
$554$	−7.53314	−0.320052
$555$	−11.5826	−0.491655
$556$	−9.39315	−0.398358
$557$	0.132670	0.00562139	0.00281070	−	0.999996i	$-0.499105\pi$
$557$	0.132670	0.00562139	0.00281070	+	0.999996i	$0.499105\pi$
$558$	−0.430922	−0.0182424
$559$	0	0
$560$	−2.59594	−0.109698
$561$	−17.3915	−0.734268
$562$	−7.32324	−0.308912
$563$	18.1753	0.765998	0.382999	−	0.923749i	$-0.374891\pi$
$563$	18.1753	0.765998	0.382999	+	0.923749i	$0.374891\pi$
$564$	−5.56996	−0.234538
$565$	−5.04516	−0.212251
$566$	−12.5399	−0.527090
$567$	−1.00000	−0.0419961
$568$	12.7469	0.534849
$569$	35.8748	1.50395	0.751974	−	0.659193i	$-0.229102\pi$
$569$	35.8748	1.50395	0.751974	+	0.659193i	$0.229102\pi$
$570$	0.0462926	0.00193899
$571$	−38.4148	−1.60761	−0.803805	−	0.594893i	$-0.797195\pi$
$571$	−38.4148	−1.60761	−0.803805	+	0.594893i	$0.797195\pi$
$572$	0	0
$573$	−24.1986	−1.01091
$574$	−2.69358	−0.112428
$575$	12.3299	0.514192
$576$	1.00000	0.0416667
$577$	35.5854	1.48144	0.740719	−	0.671815i	$-0.234485\pi$
$577$	35.5854	1.48144	0.740719	+	0.671815i	$0.234485\pi$
$578$	−5.47621	−0.227780
$579$	−10.8065	−0.449104
$580$	11.1056	0.461135
$581$	−2.41028	−0.0999954
$582$	16.7222	0.693158
$583$	−48.3896	−2.00409
$584$	−3.14421	−0.130108
$585$	0	0
$586$	19.0614	0.787421
$587$	15.3272	0.632620	0.316310	−	0.948656i	$-0.397556\pi$
$587$	15.3272	0.632620	0.316310	+	0.948656i	$0.397556\pi$
$588$	1.00000	0.0412393
$589$	−0.00768450	−0.000316634 0
$590$	−34.3452	−1.41397
$591$	−2.43849	−0.100306
$592$	−4.46183	−0.183380
$593$	−10.4121	−0.427574	−0.213787	−	0.976880i	$-0.568580\pi$
$593$	−10.4121	−0.427574	−0.213787	+	0.976880i	$0.568580\pi$
$594$	5.12317	0.210206
$595$	8.81236	0.361271
$596$	17.9543	0.735438
$597$	18.5328	0.758497
$598$	0	0
$599$	−40.4439	−1.65249	−0.826246	−	0.563309i	$-0.809528\pi$
$599$	−40.4439	−1.65249	−0.826246	+	0.563309i	$0.809528\pi$
$600$	1.73890	0.0709903
$601$	−12.5291	−0.511074	−0.255537	−	0.966799i	$-0.582252\pi$
$601$	−12.5291	−0.511074	−0.255537	+	0.966799i	$0.582252\pi$
$602$	−11.1823	−0.455757
$603$	−1.37917	−0.0561642
$604$	5.67926	0.231086
$605$	39.5799	1.60915
$606$	−13.7189	−0.557290
$607$	−23.0164	−0.934208	−0.467104	−	0.884202i	$-0.654703\pi$
$607$	−23.0164	−0.934208	−0.467104	+	0.884202i	$0.654703\pi$
$608$	0.0178327	0.000723212 0
$609$	−4.27806	−0.173356
$610$	−18.8449	−0.763006
$611$	0	0
$612$	−3.39467	−0.137221
$613$	−17.2101	−0.695111	−0.347556	−	0.937659i	$-0.612988\pi$
$613$	−17.2101	−0.695111	−0.347556	+	0.937659i	$0.612988\pi$
$614$	−24.8387	−1.00241
$615$	6.99236	0.281959
$616$	−5.12317	−0.206418
$617$	5.97264	0.240450	0.120225	−	0.992747i	$-0.461638\pi$
$617$	5.97264	0.240450	0.120225	+	0.992747i	$0.461638\pi$
$618$	4.24896	0.170918
$619$	−22.3969	−0.900208	−0.450104	−	0.892976i	$-0.648613\pi$
$619$	−22.3969	−0.900208	−0.450104	+	0.892976i	$0.648613\pi$
$620$	−1.11865	−0.0449259
$621$	7.09063	0.284537
$622$	−0.438633	−0.0175876
$623$	2.71911	0.108939
$624$	0	0
$625$	−30.6707	−1.22683
$626$	16.3187	0.652228
$627$	0.0913600	0.00364857
$628$	9.36185	0.373579
$629$	15.1464	0.603928
$630$	−2.59594	−0.103425
$631$	−49.2753	−1.96162	−0.980810	−	0.194965i	$-0.937541\pi$
$631$	−49.2753	−1.96162	−0.980810	+	0.194965i	$0.937541\pi$
$632$	7.29899	0.290338
$633$	−6.21752	−0.247124
$634$	−33.7161	−1.33904
$635$	−26.2353	−1.04112
$636$	−9.44524	−0.374528
$637$	0	0
$638$	21.9172	0.867712
$639$	12.7469	0.504260
$640$	2.59594	0.102614
$641$	34.9735	1.38137	0.690685	−	0.723156i	$-0.257309\pi$
$641$	34.9735	1.38137	0.690685	+	0.723156i	$0.257309\pi$
$642$	−2.43068	−0.0959313
$643$	−8.57982	−0.338355	−0.169178	−	0.985586i	$-0.554111\pi$
$643$	−8.57982	−0.338355	−0.169178	+	0.985586i	$0.554111\pi$
$644$	−7.09063	−0.279410
$645$	29.0286	1.14300
$646$	−0.0605362	−0.00238176
$647$	−9.80205	−0.385358	−0.192679	−	0.981262i	$-0.561718\pi$
$647$	−9.80205	−0.385358	−0.192679	+	0.981262i	$0.561718\pi$
$648$	1.00000	0.0392837
$649$	−67.7813	−2.66065
$650$	0	0
$651$	0.430922	0.0168892
$652$	−15.9019	−0.622767
$653$	2.72436	0.106612	0.0533062	−	0.998578i	$-0.483024\pi$
$653$	2.72436	0.106612	0.0533062	+	0.998578i	$0.483024\pi$
$654$	10.8152	0.422909
$655$	−41.9561	−1.63936
$656$	2.69358	0.105166
$657$	−3.14421	−0.122667
$658$	5.56996	0.217140
$659$	−16.7458	−0.652322	−0.326161	−	0.945314i	$-0.605755\pi$
$659$	−16.7458	−0.652322	−0.326161	+	0.945314i	$0.605755\pi$
$660$	13.2994	0.517680
$661$	0.629186	0.0244725	0.0122362	−	0.999925i	$-0.496105\pi$
$661$	0.629186	0.0244725	0.0122362	+	0.999925i	$0.496105\pi$
$662$	10.8454	0.421520
$663$	0	0
$664$	2.41028	0.0935371
$665$	−0.0462926	−0.00179515
$666$	−4.46183	−0.172892
$667$	30.3342	1.17454
$668$	22.9624	0.888441
$669$	19.3445	0.747902
$670$	−3.58025	−0.138317
$671$	−37.1909	−1.43574
$672$	−1.00000	−0.0385758
$673$	14.2637	0.549823	0.274912	−	0.961469i	$-0.411351\pi$
$673$	14.2637	0.549823	0.274912	+	0.961469i	$0.411351\pi$
$674$	−8.64433	−0.332967
$675$	1.73890	0.0669303
$676$	0	0
$677$	29.8956	1.14898	0.574491	−	0.818511i	$-0.305200\pi$
$677$	29.8956	1.14898	0.574491	+	0.818511i	$0.305200\pi$
$678$	−1.94348	−0.0746390
$679$	−16.7222	−0.641739
$680$	−8.81236	−0.337938
$681$	9.78761	0.375062
$682$	−2.20768	−0.0845366
$683$	−39.7702	−1.52176	−0.760881	−	0.648891i	$-0.775233\pi$
$683$	−39.7702	−1.52176	−0.760881	+	0.648891i	$0.775233\pi$
$684$	0.0178327	0.000681851 0
$685$	30.1414	1.15164
$686$	−1.00000	−0.0381802
$687$	−7.53482	−0.287471
$688$	11.1823	0.426321
$689$	0	0
$690$	18.4068	0.700736
$691$	−19.1792	−0.729611	−0.364806	−	0.931084i	$-0.618865\pi$
$691$	−19.1792	−0.729611	−0.364806	+	0.931084i	$0.618865\pi$
$692$	−13.2994	−0.505568
$693$	−5.12317	−0.194613
$694$	−24.0533	−0.913050
$695$	−24.3840	−0.924939
$696$	4.27806	0.162160
$697$	−9.14380	−0.346346
$698$	31.3486	1.18656
$699$	29.4092	1.11236
$700$	−1.73890	−0.0657242
$701$	5.24465	0.198088	0.0990439	−	0.995083i	$-0.468422\pi$
$701$	5.24465	0.198088	0.0990439	+	0.995083i	$0.468422\pi$
$702$	0	0
$703$	−0.0795665	−0.00300091
$704$	5.12317	0.193087
$705$	−14.4593	−0.544568
$706$	11.8086	0.444422
$707$	13.7189	0.515950
$708$	−13.2304	−0.497227
$709$	−30.2825	−1.13728	−0.568642	−	0.822585i	$-0.692531\pi$
$709$	−30.2825	−1.13728	−0.568642	+	0.822585i	$0.692531\pi$
$710$	33.0902	1.24185
$711$	7.29899	0.273734
$712$	−2.71911	−0.101903
$713$	−3.05551	−0.114430
$714$	3.39467	0.127042
$715$	0	0
$716$	11.1476	0.416607
$717$	−26.1127	−0.975198
$718$	10.2791	0.383612
$719$	−39.3354	−1.46696	−0.733481	−	0.679710i	$-0.762106\pi$
$719$	−39.3354	−1.46696	−0.733481	+	0.679710i	$0.762106\pi$
$720$	2.59594	0.0967449
$721$	−4.24896	−0.158239
$722$	−18.9997	−0.707095
$723$	−1.71173	−0.0636600
$724$	−18.9951	−0.705947
$725$	7.43913	0.276282
$726$	15.2469	0.565864
$727$	38.5454	1.42957	0.714785	−	0.699344i	$-0.246525\pi$
$727$	38.5454	1.42957	0.714785	+	0.699344i	$0.246525\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−8.16217	−0.302096
$731$	−37.9602	−1.40401
$732$	−7.25936	−0.268314
$733$	−9.12968	−0.337212	−0.168606	−	0.985684i	$-0.553927\pi$
$733$	−9.12968	−0.337212	−0.168606	+	0.985684i	$0.553927\pi$
$734$	23.8024	0.878564
$735$	2.59594	0.0957527
$736$	7.09063	0.261364
$737$	−7.06573	−0.260269
$738$	2.69358	0.0991519
$739$	27.5735	1.01431	0.507154	−	0.861856i	$-0.330698\pi$
$739$	27.5735	1.01431	0.507154	+	0.861856i	$0.330698\pi$
$740$	−11.5826	−0.425786
$741$	0	0
$742$	9.44524	0.346746
$743$	−12.2119	−0.448010	−0.224005	−	0.974588i	$-0.571913\pi$
$743$	−12.2119	−0.448010	−0.224005	+	0.974588i	$0.571913\pi$
$744$	−0.430922	−0.0157984
$745$	46.6084	1.70760
$746$	4.82143	0.176525
$747$	2.41028	0.0881877
$748$	−17.3915	−0.635895
$749$	2.43068	0.0888151
$750$	−8.46562	−0.309121
$751$	−8.52238	−0.310986	−0.155493	−	0.987837i	$-0.549697\pi$
$751$	−8.52238	−0.310986	−0.155493	+	0.987837i	$0.549697\pi$
$752$	−5.56996	−0.203116
$753$	−16.7525	−0.610496
$754$	0	0
$755$	14.7430	0.536553
$756$	−1.00000	−0.0363696
$757$	1.64966	0.0599578	0.0299789	−	0.999551i	$-0.490456\pi$
$757$	1.64966	0.0599578	0.0299789	+	0.999551i	$0.490456\pi$
$758$	21.2547	0.772007
$759$	36.3265	1.31857
$760$	0.0462926	0.00167921
$761$	29.4180	1.06640	0.533200	−	0.845989i	$-0.320989\pi$
$761$	29.4180	1.06640	0.533200	+	0.845989i	$0.320989\pi$
$762$	−10.1063	−0.366112
$763$	−10.8152	−0.391538
$764$	−24.1986	−0.875475
$765$	−8.81236	−0.318611
$766$	−32.6499	−1.17969
$767$	0	0
$768$	1.00000	0.0360844
$769$	10.4753	0.377750	0.188875	−	0.982001i	$-0.439516\pi$
$769$	10.4753	0.377750	0.188875	+	0.982001i	$0.439516\pi$
$770$	−13.2994	−0.479278
$771$	−14.6283	−0.526826
$772$	−10.8065	−0.388936
$773$	44.1861	1.58926	0.794632	−	0.607091i	$-0.207664\pi$
$773$	44.1861	1.58926	0.794632	+	0.607091i	$0.207664\pi$
$774$	11.1823	0.401940
$775$	−0.749330	−0.0269167
$776$	16.7222	0.600292
$777$	4.46183	0.160067
$778$	−14.8469	−0.532288
$779$	0.0480338	0.00172099
$780$	0	0
$781$	65.3046	2.33678
$782$	−24.0703	−0.860754
$783$	4.27806	0.152886
$784$	1.00000	0.0357143
$785$	24.3028	0.867404
$786$	−16.1622	−0.576486
$787$	28.2894	1.00841	0.504203	−	0.863585i	$-0.331786\pi$
$787$	28.2894	1.00841	0.504203	+	0.863585i	$0.331786\pi$
$788$	−2.43849	−0.0868677
$789$	17.3602	0.618038
$790$	18.9477	0.674130
$791$	1.94348	0.0691023
$792$	5.12317	0.182044
$793$	0	0
$794$	15.5132	0.550542
$795$	−24.5193	−0.869609
$796$	18.5328	0.656877
$797$	−30.6493	−1.08566	−0.542828	−	0.839844i	$-0.682646\pi$
$797$	−30.6493	−1.08566	−0.542828	+	0.839844i	$0.682646\pi$
$798$	−0.0178327	−0.000631271 0
$799$	18.9082	0.668924
$800$	1.73890	0.0614794
$801$	−2.71911	−0.0960749
$802$	11.1698	0.394419
$803$	−16.1083	−0.568450
$804$	−1.37917	−0.0486396
$805$	−18.4068	−0.648756
$806$	0	0
$807$	−7.43931	−0.261876
$808$	−13.7189	−0.482627
$809$	28.3202	0.995685	0.497843	−	0.867267i	$-0.334126\pi$
$809$	28.3202	0.995685	0.497843	+	0.867267i	$0.334126\pi$
$810$	2.59594	0.0912120
$811$	17.1631	0.602677	0.301338	−	0.953517i	$-0.402567\pi$
$811$	17.1631	0.602677	0.301338	+	0.953517i	$0.402567\pi$
$812$	−4.27806	−0.150131
$813$	11.3773	0.399018
$814$	−22.8587	−0.801196
$815$	−41.2804	−1.44599
$816$	−3.39467	−0.118837
$817$	0.199411	0.00697650
$818$	−1.82157	−0.0636898
$819$	0	0
$820$	6.99236	0.244184
$821$	31.4722	1.09839	0.549193	−	0.835695i	$-0.314935\pi$
$821$	31.4722	1.09839	0.549193	+	0.835695i	$0.314935\pi$
$822$	11.6110	0.404980
$823$	6.86696	0.239367	0.119684	−	0.992812i	$-0.461812\pi$
$823$	6.86696	0.239367	0.119684	+	0.992812i	$0.461812\pi$
$824$	4.24896	0.148019
$825$	8.90868	0.310160
$826$	13.2304	0.460343
$827$	50.9538	1.77184	0.885918	−	0.463842i	$-0.153529\pi$
$827$	50.9538	1.77184	0.885918	+	0.463842i	$0.153529\pi$
$828$	7.09063	0.246416
$829$	−48.0421	−1.66857	−0.834285	−	0.551333i	$-0.814119\pi$
$829$	−48.0421	−1.66857	−0.834285	+	0.551333i	$0.814119\pi$
$830$	6.25695	0.217182
$831$	−7.53314	−0.261322
$832$	0	0
$833$	−3.39467	−0.117618
$834$	−9.39315	−0.325258
$835$	59.6089	2.06285
$836$	0.0913600	0.00315975
$837$	−0.430922	−0.0148948
$838$	30.1385	1.04112
$839$	34.6500	1.19625	0.598126	−	0.801402i	$-0.295912\pi$
$839$	34.6500	1.19625	0.598126	+	0.801402i	$0.295912\pi$
$840$	−2.59594	−0.0895684
$841$	−10.6982	−0.368902
$842$	17.7000	0.609982
$843$	−7.32324	−0.252226
$844$	−6.21752	−0.214016
$845$	0	0
$846$	−5.56996	−0.191499
$847$	−15.2469	−0.523888
$848$	−9.44524	−0.324351
$849$	−12.5399	−0.430368
$850$	−5.90299	−0.202471
$851$	−31.6372	−1.08451
$852$	12.7469	0.436702
$853$	15.1124	0.517439	0.258719	−	0.965953i	$-0.416700\pi$
$853$	15.1124	0.517439	0.258719	+	0.965953i	$0.416700\pi$
$854$	7.25936	0.248410
$855$	0.0462926	0.00158317
$856$	−2.43068	−0.0830789
$857$	−30.9270	−1.05645	−0.528223	−	0.849106i	$-0.677142\pi$
$857$	−30.9270	−1.05645	−0.528223	+	0.849106i	$0.677142\pi$
$858$	0	0
$859$	−46.7434	−1.59486	−0.797432	−	0.603408i	$-0.793809\pi$
$859$	−46.7434	−1.59486	−0.797432	+	0.603408i	$0.793809\pi$
$860$	29.0286	0.989867
$861$	−2.69358	−0.0917968
$862$	−27.9368	−0.951530
$863$	26.8891	0.915316	0.457658	−	0.889128i	$-0.348688\pi$
$863$	26.8891	0.915316	0.457658	+	0.889128i	$0.348688\pi$
$864$	1.00000	0.0340207
$865$	−34.5245	−1.17387
$866$	−26.1856	−0.889823
$867$	−5.47621	−0.185982
$868$	0.430922	0.0146264
$869$	37.3940	1.26850
$870$	11.1056	0.376515
$871$	0	0
$872$	10.8152	0.366250
$873$	16.7222	0.565961
$874$	0.126445	0.00427707
$875$	8.46562	0.286190
$876$	−3.14421	−0.106233
$877$	28.1048	0.949033	0.474516	−	0.880247i	$-0.342623\pi$
$877$	28.1048	0.949033	0.474516	+	0.880247i	$0.342623\pi$
$878$	7.29808	0.246298
$879$	19.0614	0.642927
$880$	13.2994	0.448324
$881$	21.5473	0.725946	0.362973	−	0.931800i	$-0.381762\pi$
$881$	21.5473	0.725946	0.362973	+	0.931800i	$0.381762\pi$
$882$	1.00000	0.0336718
$883$	−26.4721	−0.890857	−0.445429	−	0.895317i	$-0.646949\pi$
$883$	−26.4721	−0.890857	−0.445429	+	0.895317i	$0.646949\pi$
$884$	0	0
$885$	−34.3452	−1.15450
$886$	−12.0853	−0.406014
$887$	−1.08719	−0.0365044	−0.0182522	−	0.999833i	$-0.505810\pi$
$887$	−1.08719	−0.0365044	−0.0182522	+	0.999833i	$0.505810\pi$
$888$	−4.46183	−0.149729
$889$	10.1063	0.338954
$890$	−7.05864	−0.236606
$891$	5.12317	0.171633
$892$	19.3445	0.647702
$893$	−0.0993275	−0.00332387
$894$	17.9543	0.600483
$895$	28.9386	0.967310
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	33.3480	1.11284
$899$	−1.84351	−0.0614845
$900$	1.73890	0.0579633
$901$	32.0635	1.06819
$902$	13.7996	0.459478
$903$	−11.1823	−0.372124
$904$	−1.94348	−0.0646392
$905$	−49.3101	−1.63912
$906$	5.67926	0.188681
$907$	10.3468	0.343559	0.171780	−	0.985135i	$-0.445048\pi$
$907$	10.3468	0.343559	0.171780	+	0.985135i	$0.445048\pi$
$908$	9.78761	0.324813
$909$	−13.7189	−0.455026
$910$	0	0
$911$	34.7272	1.15056	0.575281	−	0.817956i	$-0.304893\pi$
$911$	34.7272	1.15056	0.575281	+	0.817956i	$0.304893\pi$
$912$	0.0178327	0.000590500 0
$913$	12.3483	0.408669
$914$	3.23421	0.106978
$915$	−18.8449	−0.622992
$916$	−7.53482	−0.248957
$917$	16.1622	0.533723
$918$	−3.39467	−0.112041
$919$	54.3260	1.79205	0.896024	−	0.444005i	$-0.146443\pi$
$919$	54.3260	1.79205	0.896024	+	0.444005i	$0.146443\pi$
$920$	18.4068	0.606856
$921$	−24.8387	−0.818462
$922$	−11.6384	−0.383289
$923$	0	0
$924$	−5.12317	−0.168540
$925$	−7.75867	−0.255103
$926$	−13.4682	−0.442594
$927$	4.24896	0.139554
$928$	4.27806	0.140434
$929$	−53.7208	−1.76252	−0.881261	−	0.472630i	$-0.843305\pi$
$929$	−53.7208	−1.76252	−0.881261	+	0.472630i	$0.843305\pi$
$930$	−1.11865	−0.0366819
$931$	0.0178327	0.000584444 0
$932$	29.4092	0.963329
$933$	−0.438633	−0.0143602
$934$	40.6722	1.33084
$935$	−45.1472	−1.47647
$936$	0	0
$937$	−54.4398	−1.77847	−0.889236	−	0.457449i	$-0.848763\pi$
$937$	−54.4398	−1.77847	−0.889236	+	0.457449i	$0.848763\pi$
$938$	1.37917	0.0450316
$939$	16.3187	0.532542
$940$	−14.4593	−0.471610
$941$	46.9055	1.52908	0.764538	−	0.644578i	$-0.222967\pi$
$941$	46.9055	1.52908	0.764538	+	0.644578i	$0.222967\pi$
$942$	9.36185	0.305026
$943$	19.0991	0.621954
$944$	−13.2304	−0.430611
$945$	−2.59594	−0.0844459
$946$	57.2888	1.86262
$947$	−26.2982	−0.854577	−0.427288	−	0.904115i	$-0.640531\pi$
$947$	−26.2982	−0.854577	−0.427288	+	0.904115i	$0.640531\pi$
$948$	7.29899	0.237060
$949$	0	0
$950$	0.0310093	0.00100607
$951$	−33.7161	−1.09332
$952$	3.39467	0.110022
$953$	−31.6256	−1.02445	−0.512227	−	0.858850i	$-0.671179\pi$
$953$	−31.6256	−1.02445	−0.512227	+	0.858850i	$0.671179\pi$
$954$	−9.44524	−0.305801
$955$	−62.8181	−2.03275
$956$	−26.1127	−0.844546
$957$	21.9172	0.708484
$958$	−23.0790	−0.745648
$959$	−11.6110	−0.374938
$960$	2.59594	0.0837836
$961$	−30.8143	−0.994010
$962$	0	0
$963$	−2.43068	−0.0783276
$964$	−1.71173	−0.0551312
$965$	−28.0531	−0.903061
$966$	−7.09063	−0.228137
$967$	−13.0712	−0.420340	−0.210170	−	0.977665i	$-0.567402\pi$
$967$	−13.0712	−0.420340	−0.210170	+	0.977665i	$0.567402\pi$
$968$	15.2469	0.490052
$969$	−0.0605362	−0.00194470
$970$	43.4098	1.39381
$971$	−50.7418	−1.62838	−0.814190	−	0.580598i	$-0.802819\pi$
$971$	−50.7418	−1.62838	−0.814190	+	0.580598i	$0.802819\pi$
$972$	1.00000	0.0320750
$973$	9.39315	0.301130
$974$	32.9859	1.05694
$975$	0	0
$976$	−7.25936	−0.232366
$977$	9.21878	0.294935	0.147467	−	0.989067i	$-0.452888\pi$
$977$	9.21878	0.294935	0.147467	+	0.989067i	$0.452888\pi$
$978$	−15.9019	−0.508487
$979$	−13.9304	−0.445219
$980$	2.59594	0.0829242
$981$	10.8152	0.345304
$982$	−36.9140	−1.17797
$983$	4.08873	0.130410	0.0652052	−	0.997872i	$-0.479230\pi$
$983$	4.08873	0.130410	0.0652052	+	0.997872i	$0.479230\pi$
$984$	2.69358	0.0858681
$985$	−6.33018	−0.201696
$986$	−14.5226	−0.462494
$987$	5.56996	0.177294
$988$	0	0
$989$	79.2896	2.52126
$990$	13.2994	0.422684
$991$	−3.90744	−0.124124	−0.0620620	−	0.998072i	$-0.519768\pi$
$991$	−3.90744	−0.124124	−0.0620620	+	0.998072i	$0.519768\pi$
$992$	−0.430922	−0.0136818
$993$	10.8454	0.344170
$994$	−12.7469	−0.404308
$995$	48.1100	1.52519
$996$	2.41028	0.0763728
$997$	2.76475	0.0875604	0.0437802	−	0.999041i	$-0.486060\pi$
$997$	2.76475	0.0875604	0.0437802	+	0.999041i	$0.486060\pi$
$998$	−23.2574	−0.736199
$999$	−4.46183	−0.141166

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.cu.1.4	yes	6
13.12	even	2		7098.2.a.cq.1.3	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7098.2.a.cq.1.3	✓	6	13.12	even	2
7098.2.a.cu.1.4	yes	6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7098.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.59594 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.59594 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.59594 q^{10} +5.12317 q^{11} +1.00000 q^{12} -1.00000 q^{14} +2.59594 q^{15} +1.00000 q^{16} -3.39467 q^{17} +1.00000 q^{18} +0.0178327 q^{19} +2.59594 q^{20} -1.00000 q^{21} +5.12317 q^{22} +7.09063 q^{23} +1.00000 q^{24} +1.73890 q^{25} +1.00000 q^{27} -1.00000 q^{28} +4.27806 q^{29} +2.59594 q^{30} -0.430922 q^{31} +1.00000 q^{32} +5.12317 q^{33} -3.39467 q^{34} -2.59594 q^{35} +1.00000 q^{36} -4.46183 q^{37} +0.0178327 q^{38} +2.59594 q^{40} +2.69358 q^{41} -1.00000 q^{42} +11.1823 q^{43} +5.12317 q^{44} +2.59594 q^{45} +7.09063 q^{46} -5.56996 q^{47} +1.00000 q^{48} +1.00000 q^{49} +1.73890 q^{50} -3.39467 q^{51} -9.44524 q^{53} +1.00000 q^{54} +13.2994 q^{55} -1.00000 q^{56} +0.0178327 q^{57} +4.27806 q^{58} -13.2304 q^{59} +2.59594 q^{60} -7.25936 q^{61} -0.430922 q^{62} -1.00000 q^{63} +1.00000 q^{64} +5.12317 q^{66} -1.37917 q^{67} -3.39467 q^{68} +7.09063 q^{69} -2.59594 q^{70} +12.7469 q^{71} +1.00000 q^{72} -3.14421 q^{73} -4.46183 q^{74} +1.73890 q^{75} +0.0178327 q^{76} -5.12317 q^{77} +7.29899 q^{79} +2.59594 q^{80} +1.00000 q^{81} +2.69358 q^{82} +2.41028 q^{83} -1.00000 q^{84} -8.81236 q^{85} +11.1823 q^{86} +4.27806 q^{87} +5.12317 q^{88} -2.71911 q^{89} +2.59594 q^{90} +7.09063 q^{92} -0.430922 q^{93} -5.56996 q^{94} +0.0462926 q^{95} +1.00000 q^{96} +16.7222 q^{97} +1.00000 q^{98} +5.12317 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 9 q^{5} + 6 q^{6} - 6 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 9 * q^5 + 6 * q^6 - 6 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 9 q^{5} + 6 q^{6} - 6 q^{7} + 6 q^{8} + 6 q^{9} + 9 q^{10} + 10 q^{11} + 6 q^{12} - 6 q^{14} + 9 q^{15} + 6 q^{16} + 4 q^{17} + 6 q^{18} + 2 q^{19} + 9 q^{20} - 6 q^{21} + 10 q^{22} + 6 q^{24} + 9 q^{25} + 6 q^{27} - 6 q^{28} - 4 q^{29} + 9 q^{30} + 9 q^{31} + 6 q^{32} + 10 q^{33} + 4 q^{34} - 9 q^{35} + 6 q^{36} + 9 q^{37} + 2 q^{38} + 9 q^{40} + 25 q^{41} - 6 q^{42} + 19 q^{43} + 10 q^{44} + 9 q^{45} + 21 q^{47} + 6 q^{48} + 6 q^{49} + 9 q^{50} + 4 q^{51} - 4 q^{53} + 6 q^{54} + 21 q^{55} - 6 q^{56} + 2 q^{57} - 4 q^{58} + 20 q^{59} + 9 q^{60} + 3 q^{61} + 9 q^{62} - 6 q^{63} + 6 q^{64} + 10 q^{66} + 24 q^{67} + 4 q^{68} - 9 q^{70} + 13 q^{71} + 6 q^{72} - 9 q^{73} + 9 q^{74} + 9 q^{75} + 2 q^{76} - 10 q^{77} + 28 q^{79} + 9 q^{80} + 6 q^{81} + 25 q^{82} + 15 q^{83} - 6 q^{84} + 17 q^{85} + 19 q^{86} - 4 q^{87} + 10 q^{88} + 11 q^{89} + 9 q^{90} + 9 q^{93} + 21 q^{94} + 6 q^{96} + 2 q^{97} + 6 q^{98} + 10 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 9 * q^5 + 6 * q^6 - 6 * q^7 + 6 * q^8 + 6 * q^9 + 9 * q^10 + 10 * q^11 + 6 * q^12 - 6 * q^14 + 9 * q^15 + 6 * q^16 + 4 * q^17 + 6 * q^18 + 2 * q^19 + 9 * q^20 - 6 * q^21 + 10 * q^22 + 6 * q^24 + 9 * q^25 + 6 * q^27 - 6 * q^28 - 4 * q^29 + 9 * q^30 + 9 * q^31 + 6 * q^32 + 10 * q^33 + 4 * q^34 - 9 * q^35 + 6 * q^36 + 9 * q^37 + 2 * q^38 + 9 * q^40 + 25 * q^41 - 6 * q^42 + 19 * q^43 + 10 * q^44 + 9 * q^45 + 21 * q^47 + 6 * q^48 + 6 * q^49 + 9 * q^50 + 4 * q^51 - 4 * q^53 + 6 * q^54 + 21 * q^55 - 6 * q^56 + 2 * q^57 - 4 * q^58 + 20 * q^59 + 9 * q^60 + 3 * q^61 + 9 * q^62 - 6 * q^63 + 6 * q^64 + 10 * q^66 + 24 * q^67 + 4 * q^68 - 9 * q^70 + 13 * q^71 + 6 * q^72 - 9 * q^73 + 9 * q^74 + 9 * q^75 + 2 * q^76 - 10 * q^77 + 28 * q^79 + 9 * q^80 + 6 * q^81 + 25 * q^82 + 15 * q^83 - 6 * q^84 + 17 * q^85 + 19 * q^86 - 4 * q^87 + 10 * q^88 + 11 * q^89 + 9 * q^90 + 9 * q^93 + 21 * q^94 + 6 * q^96 + 2 * q^97 + 6 * q^98 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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