LMFDB - Embedded newform 7098.2.a.cu.1.2

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			1.2
Root			$1.49793$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.867888 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.867888 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.867888 q^{10} +5.35276 q^{11} +1.00000 q^{12} -1.00000 q^{14} -0.867888 q^{15} +1.00000 q^{16} +4.35460 q^{17} +1.00000 q^{18} -0.607847 q^{19} -0.867888 q^{20} -1.00000 q^{21} +5.35276 q^{22} +0.637291 q^{23} +1.00000 q^{24} -4.24677 q^{25} +1.00000 q^{27} -1.00000 q^{28} -2.55099 q^{29} -0.867888 q^{30} +10.2957 q^{31} +1.00000 q^{32} +5.35276 q^{33} +4.35460 q^{34} +0.867888 q^{35} +1.00000 q^{36} +1.33336 q^{37} -0.607847 q^{38} -0.867888 q^{40} -11.1587 q^{41} -1.00000 q^{42} +1.75311 q^{43} +5.35276 q^{44} -0.867888 q^{45} +0.637291 q^{46} +3.42699 q^{47} +1.00000 q^{48} +1.00000 q^{49} -4.24677 q^{50} +4.35460 q^{51} -9.33003 q^{53} +1.00000 q^{54} -4.64560 q^{55} -1.00000 q^{56} -0.607847 q^{57} -2.55099 q^{58} +12.7937 q^{59} -0.867888 q^{60} +1.59146 q^{61} +10.2957 q^{62} -1.00000 q^{63} +1.00000 q^{64} +5.35276 q^{66} +5.46332 q^{67} +4.35460 q^{68} +0.637291 q^{69} +0.867888 q^{70} +6.47595 q^{71} +1.00000 q^{72} -5.67666 q^{73} +1.33336 q^{74} -4.24677 q^{75} -0.607847 q^{76} -5.35276 q^{77} +7.81241 q^{79} -0.867888 q^{80} +1.00000 q^{81} -11.1587 q^{82} +5.90798 q^{83} -1.00000 q^{84} -3.77931 q^{85} +1.75311 q^{86} -2.55099 q^{87} +5.35276 q^{88} +0.515132 q^{89} -0.867888 q^{90} +0.637291 q^{92} +10.2957 q^{93} +3.42699 q^{94} +0.527543 q^{95} +1.00000 q^{96} -8.56664 q^{97} +1.00000 q^{98} +5.35276 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−0.867888	−0.388132	−0.194066	−	0.980989i	$-0.562168\pi$
$5$	−0.867888	−0.388132	−0.194066	+	0.980989i	$0.562168\pi$
$6$	1.00000	0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.867888	−0.274450
$11$	5.35276	1.61392	0.806958	−	0.590608i	$-0.201112\pi$
$11$	5.35276	1.61392	0.806958	+	0.590608i	$0.201112\pi$
$12$	1.00000	0.288675
$13$	0	0
$13$	0	0
$14$	−1.00000	−0.267261
$15$	−0.867888	−0.224088
$16$	1.00000	0.250000
$17$	4.35460	1.05615	0.528073	−	0.849199i	$-0.322915\pi$
$17$	4.35460	1.05615	0.528073	+	0.849199i	$0.322915\pi$
$18$	1.00000	0.235702
$19$	−0.607847	−0.139450	−0.0697248	−	0.997566i	$-0.522212\pi$
$19$	−0.607847	−0.139450	−0.0697248	+	0.997566i	$0.522212\pi$
$20$	−0.867888	−0.194066
$21$	−1.00000	−0.218218
$22$	5.35276	1.14121
$23$	0.637291	0.132884	0.0664422	−	0.997790i	$-0.478835\pi$
$23$	0.637291	0.132884	0.0664422	+	0.997790i	$0.478835\pi$
$24$	1.00000	0.204124
$25$	−4.24677	−0.849354
$26$	0	0
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	−2.55099	−0.473706	−0.236853	−	0.971545i	$-0.576116\pi$
$29$	−2.55099	−0.473706	−0.236853	+	0.971545i	$0.576116\pi$
$30$	−0.867888	−0.158454
$31$	10.2957	1.84916	0.924580	−	0.380988i	$-0.124416\pi$
$31$	10.2957	1.84916	0.924580	+	0.380988i	$0.124416\pi$
$32$	1.00000	0.176777
$33$	5.35276	0.931795
$34$	4.35460	0.746808
$35$	0.867888	0.146700
$36$	1.00000	0.166667
$37$	1.33336	0.219203	0.109601	−	0.993976i	$-0.465043\pi$
$37$	1.33336	0.219203	0.109601	+	0.993976i	$0.465043\pi$
$38$	−0.607847	−0.0986057
$39$	0	0
$40$	−0.867888	−0.137225
$41$	−11.1587	−1.74269	−0.871347	−	0.490667i	$-0.836753\pi$
$41$	−11.1587	−1.74269	−0.871347	+	0.490667i	$0.836753\pi$
$42$	−1.00000	−0.154303
$43$	1.75311	0.267347	0.133674	−	0.991025i	$-0.457323\pi$
$43$	1.75311	0.267347	0.133674	+	0.991025i	$0.457323\pi$
$44$	5.35276	0.806958
$45$	−0.867888	−0.129377
$46$	0.637291	0.0939634
$47$	3.42699	0.499877	0.249939	−	0.968262i	$-0.419590\pi$
$47$	3.42699	0.499877	0.249939	+	0.968262i	$0.419590\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	−4.24677	−0.600584
$51$	4.35460	0.609766
$52$	0	0
$53$	−9.33003	−1.28158	−0.640789	−	0.767717i	$-0.721393\pi$
$53$	−9.33003	−1.28158	−0.640789	+	0.767717i	$0.721393\pi$
$54$	1.00000	0.136083
$55$	−4.64560	−0.626412
$56$	−1.00000	−0.133631
$57$	−0.607847	−0.0805112
$58$	−2.55099	−0.334961
$59$	12.7937	1.66560	0.832798	−	0.553576i	$-0.186737\pi$
$59$	12.7937	1.66560	0.832798	+	0.553576i	$0.186737\pi$
$60$	−0.867888	−0.112044
$61$	1.59146	0.203766	0.101883	−	0.994796i	$-0.467513\pi$
$61$	1.59146	0.203766	0.101883	+	0.994796i	$0.467513\pi$
$62$	10.2957	1.30755
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	5.35276	0.658879
$67$	5.46332	0.667451	0.333726	−	0.942670i	$-0.391694\pi$
$67$	5.46332	0.667451	0.333726	+	0.942670i	$0.391694\pi$
$68$	4.35460	0.528073
$69$	0.637291	0.0767208
$70$	0.867888	0.103733
$71$	6.47595	0.768554	0.384277	−	0.923218i	$-0.374451\pi$
$71$	6.47595	0.768554	0.384277	+	0.923218i	$0.374451\pi$
$72$	1.00000	0.117851
$73$	−5.67666	−0.664403	−0.332202	−	0.943208i	$-0.607791\pi$
$73$	−5.67666	−0.664403	−0.332202	+	0.943208i	$0.607791\pi$
$74$	1.33336	0.155000
$75$	−4.24677	−0.490375
$76$	−0.607847	−0.0697248
$77$	−5.35276	−0.610003
$78$	0	0
$79$	7.81241	0.878965	0.439483	−	0.898251i	$-0.355162\pi$
$79$	7.81241	0.878965	0.439483	+	0.898251i	$0.355162\pi$
$80$	−0.867888	−0.0970329
$81$	1.00000	0.111111
$82$	−11.1587	−1.23227
$83$	5.90798	0.648485	0.324242	−	0.945974i	$-0.394891\pi$
$83$	5.90798	0.648485	0.324242	+	0.945974i	$0.394891\pi$
$84$	−1.00000	−0.109109
$85$	−3.77931	−0.409923
$86$	1.75311	0.189043
$87$	−2.55099	−0.273495
$88$	5.35276	0.570606
$89$	0.515132	0.0546039	0.0273019	−	0.999627i	$-0.491308\pi$
$89$	0.515132	0.0546039	0.0273019	+	0.999627i	$0.491308\pi$
$90$	−0.867888	−0.0914835
$91$	0	0
$92$	0.637291	0.0664422
$93$	10.2957	1.06761
$94$	3.42699	0.353467
$95$	0.527543	0.0541248
$96$	1.00000	0.102062
$97$	−8.56664	−0.869811	−0.434905	−	0.900476i	$-0.643218\pi$
$97$	−8.56664	−0.869811	−0.434905	+	0.900476i	$0.643218\pi$
$98$	1.00000	0.101015
$99$	5.35276	0.537972
$100$	−4.24677	−0.424677
$101$	1.20825	0.120225	0.0601127	−	0.998192i	$-0.480854\pi$
$101$	1.20825	0.120225	0.0601127	+	0.998192i	$0.480854\pi$
$102$	4.35460	0.431170
$103$	9.36266	0.922530	0.461265	−	0.887262i	$-0.347396\pi$
$103$	9.36266	0.922530	0.461265	+	0.887262i	$0.347396\pi$
$104$	0	0
$105$	0.867888	0.0846972
$106$	−9.33003	−0.906213
$107$	−11.7393	−1.13488	−0.567442	−	0.823413i	$-0.692067\pi$
$107$	−11.7393	−1.13488	−0.567442	+	0.823413i	$0.692067\pi$
$108$	1.00000	0.0962250
$109$	−1.94681	−0.186470	−0.0932352	−	0.995644i	$-0.529721\pi$
$109$	−1.94681	−0.186470	−0.0932352	+	0.995644i	$0.529721\pi$
$110$	−4.64560	−0.442940
$111$	1.33336	0.126557
$112$	−1.00000	−0.0944911
$113$	−16.2568	−1.52931	−0.764655	−	0.644440i	$-0.777091\pi$
$113$	−16.2568	−1.52931	−0.764655	+	0.644440i	$0.777091\pi$
$114$	−0.607847	−0.0569300
$115$	−0.553097	−0.0515766
$116$	−2.55099	−0.236853
$117$	0	0
$118$	12.7937	1.17775
$119$	−4.35460	−0.399185
$120$	−0.867888	−0.0792270
$121$	17.6520	1.60473
$122$	1.59146	0.144084
$123$	−11.1587	−1.00615
$124$	10.2957	0.924580
$125$	8.02516	0.717793
$126$	−1.00000	−0.0890871
$127$	20.0857	1.78232	0.891159	−	0.453690i	$-0.149893\pi$
$127$	20.0857	1.78232	0.891159	+	0.453690i	$0.149893\pi$
$128$	1.00000	0.0883883
$129$	1.75311	0.154353
$130$	0	0
$131$	−13.3617	−1.16742	−0.583708	−	0.811964i	$-0.698399\pi$
$131$	−13.3617	−1.16742	−0.583708	+	0.811964i	$0.698399\pi$
$132$	5.35276	0.465898
$133$	0.607847	0.0527070
$134$	5.46332	0.471959
$135$	−0.867888	−0.0746959
$136$	4.35460	0.373404
$137$	21.8669	1.86821	0.934107	−	0.356993i	$-0.116198\pi$
$137$	21.8669	1.86821	0.934107	+	0.356993i	$0.116198\pi$
$138$	0.637291	0.0542498
$139$	−6.75093	−0.572607	−0.286303	−	0.958139i	$-0.592427\pi$
$139$	−6.75093	−0.572607	−0.286303	+	0.958139i	$0.592427\pi$
$140$	0.867888	0.0733500
$141$	3.42699	0.288604
$142$	6.47595	0.543450
$143$	0	0
$144$	1.00000	0.0833333
$145$	2.21397	0.183860
$146$	−5.67666	−0.469804
$147$	1.00000	0.0824786
$148$	1.33336	0.109601
$149$	−4.40175	−0.360605	−0.180303	−	0.983611i	$-0.557708\pi$
$149$	−4.40175	−0.360605	−0.180303	+	0.983611i	$0.557708\pi$
$150$	−4.24677	−0.346747
$151$	17.6948	1.43998	0.719990	−	0.693984i	$-0.244146\pi$
$151$	17.6948	1.43998	0.719990	+	0.693984i	$0.244146\pi$
$152$	−0.607847	−0.0493029
$153$	4.35460	0.352048
$154$	−5.35276	−0.431337
$155$	−8.93551	−0.717717
$156$	0	0
$157$	5.09101	0.406307	0.203153	−	0.979147i	$-0.434881\pi$
$157$	5.09101	0.406307	0.203153	+	0.979147i	$0.434881\pi$
$158$	7.81241	0.621522
$159$	−9.33003	−0.739920
$160$	−0.867888	−0.0686126
$161$	−0.637291	−0.0502256
$162$	1.00000	0.0785674
$163$	17.0021	1.33171	0.665853	−	0.746083i	$-0.268068\pi$
$163$	17.0021	1.33171	0.665853	+	0.746083i	$0.268068\pi$
$164$	−11.1587	−0.871347
$165$	−4.64560	−0.361659
$166$	5.90798	0.458548
$167$	−13.2249	−1.02337	−0.511685	−	0.859173i	$-0.670979\pi$
$167$	−13.2249	−1.02337	−0.511685	+	0.859173i	$0.670979\pi$
$168$	−1.00000	−0.0771517
$169$	0	0
$170$	−3.77931	−0.289860
$171$	−0.607847	−0.0464832
$172$	1.75311	0.133674
$173$	9.63880	0.732825	0.366412	−	0.930453i	$-0.380586\pi$
$173$	9.63880	0.732825	0.366412	+	0.930453i	$0.380586\pi$
$174$	−2.55099	−0.193390
$175$	4.24677	0.321026
$176$	5.35276	0.403479
$177$	12.7937	0.961633
$178$	0.515132	0.0386108
$179$	−3.66877	−0.274217	−0.137108	−	0.990556i	$-0.543781\pi$
$179$	−3.66877	−0.274217	−0.137108	+	0.990556i	$0.543781\pi$
$180$	−0.867888	−0.0646886
$181$	−16.0972	−1.19649	−0.598246	−	0.801312i	$-0.704136\pi$
$181$	−16.0972	−1.19649	−0.598246	+	0.801312i	$0.704136\pi$
$182$	0	0
$183$	1.59146	0.117644
$184$	0.637291	0.0469817
$185$	−1.15721	−0.0850795
$186$	10.2957	0.754916
$187$	23.3091	1.70453
$188$	3.42699	0.249939
$189$	−1.00000	−0.0727393
$190$	0.527543	0.0382720
$191$	2.18895	0.158387	0.0791934	−	0.996859i	$-0.474766\pi$
$191$	2.18895	0.158387	0.0791934	+	0.996859i	$0.474766\pi$
$192$	1.00000	0.0721688
$193$	1.80959	0.130257	0.0651287	−	0.997877i	$-0.479254\pi$
$193$	1.80959	0.130257	0.0651287	+	0.997877i	$0.479254\pi$
$194$	−8.56664	−0.615049
$195$	0	0
$196$	1.00000	0.0714286
$197$	22.7743	1.62260	0.811302	−	0.584627i	$-0.198759\pi$
$197$	22.7743	1.62260	0.811302	+	0.584627i	$0.198759\pi$
$198$	5.35276	0.380404
$199$	−14.5430	−1.03092	−0.515462	−	0.856913i	$-0.672380\pi$
$199$	−14.5430	−1.03092	−0.515462	+	0.856913i	$0.672380\pi$
$200$	−4.24677	−0.300292
$201$	5.46332	0.385353
$202$	1.20825	0.0850122
$203$	2.55099	0.179044
$204$	4.35460	0.304883
$205$	9.68450	0.676395
$206$	9.36266	0.652327
$207$	0.637291	0.0442948
$208$	0	0
$209$	−3.25365	−0.225060
$210$	0.867888	0.0598900
$211$	−22.0616	−1.51879	−0.759393	−	0.650633i	$-0.774504\pi$
$211$	−22.0616	−1.51879	−0.759393	+	0.650633i	$0.774504\pi$
$212$	−9.33003	−0.640789
$213$	6.47595	0.443725
$214$	−11.7393	−0.802484
$215$	−1.52151	−0.103766
$216$	1.00000	0.0680414
$217$	−10.2957	−0.698917
$218$	−1.94681	−0.131854
$219$	−5.67666	−0.383593
$220$	−4.64560	−0.313206
$221$	0	0
$222$	1.33336	0.0894892
$223$	−28.6176	−1.91638	−0.958188	−	0.286140i	$-0.907628\pi$
$223$	−28.6176	−1.91638	−0.958188	+	0.286140i	$0.907628\pi$
$224$	−1.00000	−0.0668153
$225$	−4.24677	−0.283118
$226$	−16.2568	−1.08139
$227$	−6.01264	−0.399073	−0.199536	−	0.979890i	$-0.563944\pi$
$227$	−6.01264	−0.399073	−0.199536	+	0.979890i	$0.563944\pi$
$228$	−0.607847	−0.0402556
$229$	6.33101	0.418365	0.209182	−	0.977877i	$-0.432920\pi$
$229$	6.33101	0.418365	0.209182	+	0.977877i	$0.432920\pi$
$230$	−0.553097	−0.0364702
$231$	−5.35276	−0.352186
$232$	−2.55099	−0.167481
$233$	19.7278	1.29241	0.646205	−	0.763164i	$-0.276355\pi$
$233$	19.7278	1.29241	0.646205	+	0.763164i	$0.276355\pi$
$234$	0	0
$235$	−2.97424	−0.194018
$236$	12.7937	0.832798
$237$	7.81241	0.507471
$238$	−4.35460	−0.282267
$239$	27.9126	1.80552	0.902758	−	0.430149i	$-0.141539\pi$
$239$	27.9126	1.80552	0.902758	+	0.430149i	$0.141539\pi$
$240$	−0.867888	−0.0560220
$241$	−24.0821	−1.55127	−0.775633	−	0.631184i	$-0.782569\pi$
$241$	−24.0821	−1.55127	−0.775633	+	0.631184i	$0.782569\pi$
$242$	17.6520	1.13471
$243$	1.00000	0.0641500
$244$	1.59146	0.101883
$245$	−0.867888	−0.0554474
$246$	−11.1587	−0.711452
$247$	0	0
$248$	10.2957	0.653777
$249$	5.90798	0.374403
$250$	8.02516	0.507556
$251$	7.17410	0.452825	0.226413	−	0.974032i	$-0.427300\pi$
$251$	7.17410	0.452825	0.226413	+	0.974032i	$0.427300\pi$
$252$	−1.00000	−0.0629941
$253$	3.41126	0.214464
$254$	20.0857	1.26029
$255$	−3.77931	−0.236669
$256$	1.00000	0.0625000
$257$	−4.18796	−0.261238	−0.130619	−	0.991433i	$-0.541696\pi$
$257$	−4.18796	−0.261238	−0.130619	+	0.991433i	$0.541696\pi$
$258$	1.75311	0.109144
$259$	−1.33336	−0.0828509
$260$	0	0
$261$	−2.55099	−0.157902
$262$	−13.3617	−0.825487
$263$	5.46817	0.337182	0.168591	−	0.985686i	$-0.446078\pi$
$263$	5.46817	0.337182	0.168591	+	0.985686i	$0.446078\pi$
$264$	5.35276	0.329439
$265$	8.09743	0.497421
$266$	0.607847	0.0372695
$267$	0.515132	0.0315256
$268$	5.46332	0.333726
$269$	−10.7324	−0.654367	−0.327183	−	0.944961i	$-0.606100\pi$
$269$	−10.7324	−0.654367	−0.327183	+	0.944961i	$0.606100\pi$
$270$	−0.867888	−0.0528180
$271$	21.5276	1.30771	0.653855	−	0.756620i	$-0.273151\pi$
$271$	21.5276	1.30771	0.653855	+	0.756620i	$0.273151\pi$
$272$	4.35460	0.264036
$273$	0	0
$274$	21.8669	1.32103
$275$	−22.7319	−1.37079
$276$	0.637291	0.0383604
$277$	7.23334	0.434609	0.217305	−	0.976104i	$-0.430274\pi$
$277$	7.23334	0.434609	0.217305	+	0.976104i	$0.430274\pi$
$278$	−6.75093	−0.404894
$279$	10.2957	0.616387
$280$	0.867888	0.0518663
$281$	8.37168	0.499412	0.249706	−	0.968322i	$-0.419666\pi$
$281$	8.37168	0.499412	0.249706	+	0.968322i	$0.419666\pi$
$282$	3.42699	0.204074
$283$	25.5063	1.51619	0.758096	−	0.652143i	$-0.226130\pi$
$283$	25.5063	1.51619	0.758096	+	0.652143i	$0.226130\pi$
$284$	6.47595	0.384277
$285$	0.527543	0.0312490
$286$	0	0
$287$	11.1587	0.658677
$288$	1.00000	0.0589256
$289$	1.96253	0.115443
$290$	2.21397	0.130009
$291$	−8.56664	−0.502185
$292$	−5.67666	−0.332202
$293$	−4.43656	−0.259187	−0.129593	−	0.991567i	$-0.541367\pi$
$293$	−4.43656	−0.259187	−0.129593	+	0.991567i	$0.541367\pi$
$294$	1.00000	0.0583212
$295$	−11.1035	−0.646471
$296$	1.33336	0.0774999
$297$	5.35276	0.310598
$298$	−4.40175	−0.254986
$299$	0	0
$300$	−4.24677	−0.245187
$301$	−1.75311	−0.101048
$302$	17.6948	1.01822
$303$	1.20825	0.0694122
$304$	−0.607847	−0.0348624
$305$	−1.38121	−0.0790881
$306$	4.35460	0.248936
$307$	18.1029	1.03319	0.516593	−	0.856231i	$-0.327200\pi$
$307$	18.1029	1.03319	0.516593	+	0.856231i	$0.327200\pi$
$308$	−5.35276	−0.305002
$309$	9.36266	0.532623
$310$	−8.93551	−0.507503
$311$	−10.0829	−0.571747	−0.285873	−	0.958267i	$-0.592284\pi$
$311$	−10.0829	−0.571747	−0.285873	+	0.958267i	$0.592284\pi$
$312$	0	0
$313$	14.2531	0.805630	0.402815	−	0.915281i	$-0.368032\pi$
$313$	14.2531	0.805630	0.402815	+	0.915281i	$0.368032\pi$
$314$	5.09101	0.287302
$315$	0.867888	0.0489000
$316$	7.81241	0.439483
$317$	29.5478	1.65957	0.829784	−	0.558085i	$-0.188464\pi$
$317$	29.5478	1.65957	0.829784	+	0.558085i	$0.188464\pi$
$318$	−9.33003	−0.523202
$319$	−13.6548	−0.764523
$320$	−0.867888	−0.0485164
$321$	−11.7393	−0.655226
$322$	−0.637291	−0.0355148
$323$	−2.64693	−0.147279
$324$	1.00000	0.0555556
$325$	0	0
$326$	17.0021	0.941658
$327$	−1.94681	−0.107659
$328$	−11.1587	−0.616136
$329$	−3.42699	−0.188936
$330$	−4.64560	−0.255732
$331$	−11.0027	−0.604765	−0.302382	−	0.953187i	$-0.597782\pi$
$331$	−11.0027	−0.604765	−0.302382	+	0.953187i	$0.597782\pi$
$332$	5.90798	0.324242
$333$	1.33336	0.0730676
$334$	−13.2249	−0.723632
$335$	−4.74156	−0.259059
$336$	−1.00000	−0.0545545
$337$	−3.07513	−0.167513	−0.0837566	−	0.996486i	$-0.526692\pi$
$337$	−3.07513	−0.167513	−0.0837566	+	0.996486i	$0.526692\pi$
$338$	0	0
$339$	−16.2568	−0.882948
$340$	−3.77931	−0.204962
$341$	55.1103	2.98439
$342$	−0.607847	−0.0328686
$343$	−1.00000	−0.0539949
$344$	1.75311	0.0945216
$345$	−0.553097	−0.0297778
$346$	9.63880	0.518185
$347$	25.4335	1.36534	0.682670	−	0.730726i	$-0.260818\pi$
$347$	25.4335	1.36534	0.682670	+	0.730726i	$0.260818\pi$
$348$	−2.55099	−0.136747
$349$	−29.4043	−1.57397	−0.786987	−	0.616969i	$-0.788360\pi$
$349$	−29.4043	−1.57397	−0.786987	+	0.616969i	$0.788360\pi$
$350$	4.24677	0.226999
$351$	0	0
$352$	5.35276	0.285303
$353$	−22.5077	−1.19796	−0.598981	−	0.800763i	$-0.704428\pi$
$353$	−22.5077	−1.19796	−0.598981	+	0.800763i	$0.704428\pi$
$354$	12.7937	0.679977
$355$	−5.62040	−0.298300
$356$	0.515132	0.0273019
$357$	−4.35460	−0.230470
$358$	−3.66877	−0.193900
$359$	18.5835	0.980802	0.490401	−	0.871497i	$-0.336850\pi$
$359$	18.5835	0.980802	0.490401	+	0.871497i	$0.336850\pi$
$360$	−0.867888	−0.0457417
$361$	−18.6305	−0.980554
$362$	−16.0972	−0.846048
$363$	17.6520	0.926490
$364$	0	0
$365$	4.92671	0.257876
$366$	1.59146	0.0831872
$367$	3.38814	0.176860	0.0884298	−	0.996082i	$-0.471815\pi$
$367$	3.38814	0.176860	0.0884298	+	0.996082i	$0.471815\pi$
$368$	0.637291	0.0332211
$369$	−11.1587	−0.580898
$370$	−1.15721	−0.0601603
$371$	9.33003	0.484391
$372$	10.2957	0.533807
$373$	−2.72907	−0.141306	−0.0706529	−	0.997501i	$-0.522508\pi$
$373$	−2.72907	−0.141306	−0.0706529	+	0.997501i	$0.522508\pi$
$374$	23.3091	1.20529
$375$	8.02516	0.414418
$376$	3.42699	0.176733
$377$	0	0
$378$	−1.00000	−0.0514344
$379$	13.8794	0.712938	0.356469	−	0.934307i	$-0.383981\pi$
$379$	13.8794	0.712938	0.356469	+	0.934307i	$0.383981\pi$
$380$	0.527543	0.0270624
$381$	20.0857	1.02902
$382$	2.18895	0.111996
$383$	−22.2119	−1.13498	−0.567489	−	0.823381i	$-0.692085\pi$
$383$	−22.2119	−1.13498	−0.567489	+	0.823381i	$0.692085\pi$
$384$	1.00000	0.0510310
$385$	4.64560	0.236761
$386$	1.80959	0.0921059
$387$	1.75311	0.0891158
$388$	−8.56664	−0.434905
$389$	19.3237	0.979748	0.489874	−	0.871793i	$-0.337043\pi$
$389$	19.3237	0.979748	0.489874	+	0.871793i	$0.337043\pi$
$390$	0	0
$391$	2.77515	0.140345
$392$	1.00000	0.0505076
$393$	−13.3617	−0.674008
$394$	22.7743	1.14735
$395$	−6.78030	−0.341154
$396$	5.35276	0.268986
$397$	−18.3450	−0.920712	−0.460356	−	0.887735i	$-0.652278\pi$
$397$	−18.3450	−0.920712	−0.460356	+	0.887735i	$0.652278\pi$
$398$	−14.5430	−0.728973
$399$	0.607847	0.0304304
$400$	−4.24677	−0.212338
$401$	16.0696	0.802476	0.401238	−	0.915974i	$-0.368580\pi$
$401$	16.0696	0.802476	0.401238	+	0.915974i	$0.368580\pi$
$402$	5.46332	0.272486
$403$	0	0
$404$	1.20825	0.0601127
$405$	−0.867888	−0.0431257
$406$	2.55099	0.126603
$407$	7.13714	0.353775
$408$	4.35460	0.215585
$409$	−7.17158	−0.354612	−0.177306	−	0.984156i	$-0.556738\pi$
$409$	−7.17158	−0.354612	−0.177306	+	0.984156i	$0.556738\pi$
$410$	9.68450	0.478283
$411$	21.8669	1.07861
$412$	9.36266	0.461265
$413$	−12.7937	−0.629536
$414$	0.637291	0.0313211
$415$	−5.12746	−0.251697
$416$	0	0
$417$	−6.75093	−0.330595
$418$	−3.25365	−0.159141
$419$	7.55122	0.368901	0.184451	−	0.982842i	$-0.440949\pi$
$419$	7.55122	0.368901	0.184451	+	0.982842i	$0.440949\pi$
$420$	0.867888	0.0423486
$421$	13.5246	0.659149	0.329575	−	0.944130i	$-0.393095\pi$
$421$	13.5246	0.659149	0.329575	+	0.944130i	$0.393095\pi$
$422$	−22.0616	−1.07394
$423$	3.42699	0.166626
$424$	−9.33003	−0.453106
$425$	−18.4930	−0.897041
$426$	6.47595	0.313761
$427$	−1.59146	−0.0770164
$428$	−11.7393	−0.567442
$429$	0	0
$430$	−1.52151	−0.0733736
$431$	1.83515	0.0883960	0.0441980	−	0.999023i	$-0.485927\pi$
$431$	1.83515	0.0883960	0.0441980	+	0.999023i	$0.485927\pi$
$432$	1.00000	0.0481125
$433$	−16.7598	−0.805424	−0.402712	−	0.915327i	$-0.631932\pi$
$433$	−16.7598	−0.805424	−0.402712	+	0.915327i	$0.631932\pi$
$434$	−10.2957	−0.494209
$435$	2.21397	0.106152
$436$	−1.94681	−0.0932352
$437$	−0.387375	−0.0185307
$438$	−5.67666	−0.271241
$439$	−10.6616	−0.508853	−0.254426	−	0.967092i	$-0.581887\pi$
$439$	−10.6616	−0.508853	−0.254426	+	0.967092i	$0.581887\pi$
$440$	−4.64560	−0.221470
$441$	1.00000	0.0476190
$442$	0	0
$443$	−27.1443	−1.28966	−0.644831	−	0.764325i	$-0.723072\pi$
$443$	−27.1443	−1.28966	−0.644831	+	0.764325i	$0.723072\pi$
$444$	1.33336	0.0632784
$445$	−0.447077	−0.0211935
$446$	−28.6176	−1.35508
$447$	−4.40175	−0.208196
$448$	−1.00000	−0.0472456
$449$	14.2999	0.674855	0.337427	−	0.941352i	$-0.390443\pi$
$449$	14.2999	0.674855	0.337427	+	0.941352i	$0.390443\pi$
$450$	−4.24677	−0.200195
$451$	−59.7298	−2.81256
$452$	−16.2568	−0.764655
$453$	17.6948	0.831373
$454$	−6.01264	−0.282187
$455$	0	0
$456$	−0.607847	−0.0284650
$457$	−31.4356	−1.47050	−0.735248	−	0.677799i	$-0.762934\pi$
$457$	−31.4356	−1.47050	−0.735248	+	0.677799i	$0.762934\pi$
$458$	6.33101	0.295829
$459$	4.35460	0.203255
$460$	−0.553097	−0.0257883
$461$	−27.7744	−1.29358	−0.646791	−	0.762667i	$-0.723889\pi$
$461$	−27.7744	−1.29358	−0.646791	+	0.762667i	$0.723889\pi$
$462$	−5.35276	−0.249033
$463$	−9.28374	−0.431452	−0.215726	−	0.976454i	$-0.569212\pi$
$463$	−9.28374	−0.431452	−0.215726	+	0.976454i	$0.569212\pi$
$464$	−2.55099	−0.118427
$465$	−8.93551	−0.414374
$466$	19.7278	0.913872
$467$	−19.2484	−0.890709	−0.445354	−	0.895354i	$-0.646922\pi$
$467$	−19.2484	−0.890709	−0.445354	+	0.895354i	$0.646922\pi$
$468$	0	0
$469$	−5.46332	−0.252273
$470$	−2.97424	−0.137192
$471$	5.09101	0.234581
$472$	12.7937	0.588877
$473$	9.38399	0.431476
$474$	7.81241	0.358836
$475$	2.58138	0.118442
$476$	−4.35460	−0.199593
$477$	−9.33003	−0.427193
$478$	27.9126	1.27669
$479$	28.5633	1.30509	0.652544	−	0.757750i	$-0.273702\pi$
$479$	28.5633	1.30509	0.652544	+	0.757750i	$0.273702\pi$
$480$	−0.867888	−0.0396135
$481$	0	0
$482$	−24.0821	−1.09691
$483$	−0.637291	−0.0289977
$484$	17.6520	0.802364
$485$	7.43489	0.337601
$486$	1.00000	0.0453609
$487$	−26.3280	−1.19304	−0.596519	−	0.802599i	$-0.703450\pi$
$487$	−26.3280	−1.19304	−0.596519	+	0.802599i	$0.703450\pi$
$488$	1.59146	0.0720422
$489$	17.0021	0.768861
$490$	−0.867888	−0.0392072
$491$	−24.6042	−1.11037	−0.555187	−	0.831726i	$-0.687353\pi$
$491$	−24.6042	−1.11037	−0.555187	+	0.831726i	$0.687353\pi$
$492$	−11.1587	−0.503073
$493$	−11.1085	−0.500303
$494$	0	0
$495$	−4.64560	−0.208804
$496$	10.2957	0.462290
$497$	−6.47595	−0.290486
$498$	5.90798	0.264743
$499$	25.4842	1.14083	0.570415	−	0.821357i	$-0.306782\pi$
$499$	25.4842	1.14083	0.570415	+	0.821357i	$0.306782\pi$
$500$	8.02516	0.358896
$501$	−13.2249	−0.590843
$502$	7.17410	0.320196
$503$	−1.45005	−0.0646543	−0.0323272	−	0.999477i	$-0.510292\pi$
$503$	−1.45005	−0.0646543	−0.0323272	+	0.999477i	$0.510292\pi$
$504$	−1.00000	−0.0445435
$505$	−1.04863	−0.0466633
$506$	3.41126	0.151649
$507$	0	0
$508$	20.0857	0.891159
$509$	−11.5493	−0.511912	−0.255956	−	0.966688i	$-0.582390\pi$
$509$	−11.5493	−0.511912	−0.255956	+	0.966688i	$0.582390\pi$
$510$	−3.77931	−0.167350
$511$	5.67666	0.251121
$512$	1.00000	0.0441942
$513$	−0.607847	−0.0268371
$514$	−4.18796	−0.184723
$515$	−8.12574	−0.358063
$516$	1.75311	0.0771765
$517$	18.3438	0.806760
$518$	−1.33336	−0.0585844
$519$	9.63880	0.423097
$520$	0	0
$521$	−18.9865	−0.831812	−0.415906	−	0.909408i	$-0.636535\pi$
$521$	−18.9865	−0.831812	−0.415906	+	0.909408i	$0.636535\pi$
$522$	−2.55099	−0.111654
$523$	−10.3954	−0.454559	−0.227280	−	0.973830i	$-0.572983\pi$
$523$	−10.3954	−0.454559	−0.227280	+	0.973830i	$0.572983\pi$
$524$	−13.3617	−0.583708
$525$	4.24677	0.185344
$526$	5.46817	0.238424
$527$	44.8336	1.95298
$528$	5.35276	0.232949
$529$	−22.5939	−0.982342
$530$	8.09743	0.351730
$531$	12.7937	0.555199
$532$	0.607847	0.0263535
$533$	0	0
$534$	0.515132	0.0222919
$535$	10.1884	0.440484
$536$	5.46332	0.235980
$537$	−3.66877	−0.158319
$538$	−10.7324	−0.462707
$539$	5.35276	0.230560
$540$	−0.867888	−0.0373480
$541$	−37.5886	−1.61606	−0.808029	−	0.589143i	$-0.799466\pi$
$541$	−37.5886	−1.61606	−0.808029	+	0.589143i	$0.799466\pi$
$542$	21.5276	0.924690
$543$	−16.0972	−0.690796
$544$	4.35460	0.186702
$545$	1.68961	0.0723750
$546$	0	0
$547$	5.57237	0.238257	0.119129	−	0.992879i	$-0.461990\pi$
$547$	5.57237	0.238257	0.119129	+	0.992879i	$0.461990\pi$
$548$	21.8669	0.934107
$549$	1.59146	0.0679221
$550$	−22.7319	−0.969292
$551$	1.55061	0.0660581
$552$	0.637291	0.0271249
$553$	−7.81241	−0.332218
$554$	7.23334	0.307315
$555$	−1.15721	−0.0491207
$556$	−6.75093	−0.286303
$557$	41.8537	1.77340	0.886699	−	0.462348i	$-0.152993\pi$
$557$	41.8537	1.77340	0.886699	+	0.462348i	$0.152993\pi$
$558$	10.2957	0.435851
$559$	0	0
$560$	0.867888	0.0366750
$561$	23.3091	0.984111
$562$	8.37168	0.353138
$563$	−5.44338	−0.229411	−0.114706	−	0.993400i	$-0.536592\pi$
$563$	−5.44338	−0.229411	−0.114706	+	0.993400i	$0.536592\pi$
$564$	3.42699	0.144302
$565$	14.1091	0.593573
$566$	25.5063	1.07211
$567$	−1.00000	−0.0419961
$568$	6.47595	0.271725
$569$	−1.74702	−0.0732389	−0.0366194	−	0.999329i	$-0.511659\pi$
$569$	−1.74702	−0.0732389	−0.0366194	+	0.999329i	$0.511659\pi$
$570$	0.527543	0.0220963
$571$	−35.0720	−1.46772	−0.733859	−	0.679301i	$-0.762283\pi$
$571$	−35.0720	−1.46772	−0.733859	+	0.679301i	$0.762283\pi$
$572$	0	0
$573$	2.18895	0.0914447
$574$	11.1587	0.465755
$575$	−2.70643	−0.112866
$576$	1.00000	0.0416667
$577$	2.40386	0.100074	0.0500370	−	0.998747i	$-0.484066\pi$
$577$	2.40386	0.100074	0.0500370	+	0.998747i	$0.484066\pi$
$578$	1.96253	0.0816305
$579$	1.80959	0.0752041
$580$	2.21397	0.0919302
$581$	−5.90798	−0.245104
$582$	−8.56664	−0.355099
$583$	−49.9414	−2.06836
$584$	−5.67666	−0.234902
$585$	0	0
$586$	−4.43656	−0.183273
$587$	5.66913	0.233990	0.116995	−	0.993133i	$-0.462674\pi$
$587$	5.66913	0.233990	0.116995	+	0.993133i	$0.462674\pi$
$588$	1.00000	0.0412393
$589$	−6.25820	−0.257865
$590$	−11.1035	−0.457124
$591$	22.7743	0.936811
$592$	1.33336	0.0548007
$593$	−2.70333	−0.111012	−0.0555062	−	0.998458i	$-0.517677\pi$
$593$	−2.70333	−0.111012	−0.0555062	+	0.998458i	$0.517677\pi$
$594$	5.35276	0.219626
$595$	3.77931	0.154936
$596$	−4.40175	−0.180303
$597$	−14.5430	−0.595204
$598$	0	0
$599$	25.6833	1.04939	0.524696	−	0.851290i	$-0.324179\pi$
$599$	25.6833	1.04939	0.524696	+	0.851290i	$0.324179\pi$
$600$	−4.24677	−0.173374
$601$	−3.04950	−0.124392	−0.0621958	−	0.998064i	$-0.519810\pi$
$601$	−3.04950	−0.124392	−0.0621958	+	0.998064i	$0.519810\pi$
$602$	−1.75311	−0.0714516
$603$	5.46332	0.222484
$604$	17.6948	0.719990
$605$	−15.3200	−0.622845
$606$	1.20825	0.0490818
$607$	−34.8610	−1.41496	−0.707482	−	0.706731i	$-0.750169\pi$
$607$	−34.8610	−1.41496	−0.707482	+	0.706731i	$0.750169\pi$
$608$	−0.607847	−0.0246514
$609$	2.55099	0.103371
$610$	−1.38121	−0.0559237
$611$	0	0
$612$	4.35460	0.176024
$613$	7.87038	0.317882	0.158941	−	0.987288i	$-0.449192\pi$
$613$	7.87038	0.317882	0.158941	+	0.987288i	$0.449192\pi$
$614$	18.1029	0.730572
$615$	9.68450	0.390517
$616$	−5.35276	−0.215669
$617$	−35.6399	−1.43481	−0.717404	−	0.696658i	$-0.754670\pi$
$617$	−35.6399	−1.43481	−0.717404	+	0.696658i	$0.754670\pi$
$618$	9.36266	0.376621
$619$	−44.7915	−1.80032	−0.900161	−	0.435557i	$-0.856552\pi$
$619$	−44.7915	−1.80032	−0.900161	+	0.435557i	$0.856552\pi$
$620$	−8.93551	−0.358859
$621$	0.637291	0.0255736
$622$	−10.0829	−0.404286
$623$	−0.515132	−0.0206383
$624$	0	0
$625$	14.2689	0.570756
$626$	14.2531	0.569667
$627$	−3.25365	−0.129938
$628$	5.09101	0.203153
$629$	5.80624	0.231510
$630$	0.867888	0.0345775
$631$	−3.79899	−0.151235	−0.0756177	−	0.997137i	$-0.524093\pi$
$631$	−3.79899	−0.151235	−0.0756177	+	0.997137i	$0.524093\pi$
$632$	7.81241	0.310761
$633$	−22.0616	−0.876871
$634$	29.5478	1.17349
$635$	−17.4322	−0.691774
$636$	−9.33003	−0.369960
$637$	0	0
$638$	−13.6548	−0.540599
$639$	6.47595	0.256185
$640$	−0.867888	−0.0343063
$641$	−21.8263	−0.862089	−0.431044	−	0.902331i	$-0.641855\pi$
$641$	−21.8263	−0.862089	−0.431044	+	0.902331i	$0.641855\pi$
$642$	−11.7393	−0.463314
$643$	−23.6512	−0.932712	−0.466356	−	0.884597i	$-0.654433\pi$
$643$	−23.6512	−0.932712	−0.466356	+	0.884597i	$0.654433\pi$
$644$	−0.637291	−0.0251128
$645$	−1.52151	−0.0599093
$646$	−2.64693	−0.104142
$647$	6.13604	0.241233	0.120616	−	0.992699i	$-0.461513\pi$
$647$	6.13604	0.241233	0.120616	+	0.992699i	$0.461513\pi$
$648$	1.00000	0.0392837
$649$	68.4815	2.68813
$650$	0	0
$651$	−10.2957	−0.403520
$652$	17.0021	0.665853
$653$	−29.5698	−1.15716	−0.578579	−	0.815626i	$-0.696392\pi$
$653$	−29.5698	−1.15716	−0.578579	+	0.815626i	$0.696392\pi$
$654$	−1.94681	−0.0761262
$655$	11.5964	0.453111
$656$	−11.1587	−0.435674
$657$	−5.67666	−0.221468
$658$	−3.42699	−0.133598
$659$	31.3472	1.22111	0.610557	−	0.791972i	$-0.290946\pi$
$659$	31.3472	1.22111	0.610557	+	0.791972i	$0.290946\pi$
$660$	−4.64560	−0.180830
$661$	38.3524	1.49174	0.745868	−	0.666094i	$-0.232035\pi$
$661$	38.3524	1.49174	0.745868	+	0.666094i	$0.232035\pi$
$662$	−11.0027	−0.427633
$663$	0	0
$664$	5.90798	0.229274
$665$	−0.527543	−0.0204572
$666$	1.33336	0.0516666
$667$	−1.62572	−0.0629482
$668$	−13.2249	−0.511685
$669$	−28.6176	−1.10642
$670$	−4.74156	−0.183182
$671$	8.51872	0.328862
$672$	−1.00000	−0.0385758
$673$	7.38797	0.284785	0.142393	−	0.989810i	$-0.454520\pi$
$673$	7.38797	0.284785	0.142393	+	0.989810i	$0.454520\pi$
$674$	−3.07513	−0.118450
$675$	−4.24677	−0.163458
$676$	0	0
$677$	−5.09208	−0.195704	−0.0978522	−	0.995201i	$-0.531197\pi$
$677$	−5.09208	−0.195704	−0.0978522	+	0.995201i	$0.531197\pi$
$678$	−16.2568	−0.624338
$679$	8.56664	0.328757
$680$	−3.77931	−0.144930
$681$	−6.01264	−0.230405
$682$	55.1103	2.11028
$683$	−39.4052	−1.50780	−0.753900	−	0.656990i	$-0.771830\pi$
$683$	−39.4052	−1.50780	−0.753900	+	0.656990i	$0.771830\pi$
$684$	−0.607847	−0.0232416
$685$	−18.9780	−0.725113
$686$	−1.00000	−0.0381802
$687$	6.33101	0.241543
$688$	1.75311	0.0668368
$689$	0	0
$690$	−0.553097	−0.0210561
$691$	−45.1660	−1.71820	−0.859098	−	0.511811i	$-0.828975\pi$
$691$	−45.1660	−1.71820	−0.859098	+	0.511811i	$0.828975\pi$
$692$	9.63880	0.366412
$693$	−5.35276	−0.203334
$694$	25.4335	0.965442
$695$	5.85906	0.222247
$696$	−2.55099	−0.0966949
$697$	−48.5916	−1.84054
$698$	−29.4043	−1.11297
$699$	19.7278	0.746173
$700$	4.24677	0.160513
$701$	−48.3525	−1.82625	−0.913125	−	0.407679i	$-0.866338\pi$
$701$	−48.3525	−1.82625	−0.913125	+	0.407679i	$0.866338\pi$
$702$	0	0
$703$	−0.810477	−0.0305677
$704$	5.35276	0.201740
$705$	−2.97424	−0.112016
$706$	−22.5077	−0.847087
$707$	−1.20825	−0.0454410
$708$	12.7937	0.480816
$709$	−18.6069	−0.698797	−0.349398	−	0.936974i	$-0.613614\pi$
$709$	−18.6069	−0.698797	−0.349398	+	0.936974i	$0.613614\pi$
$710$	−5.62040	−0.210930
$711$	7.81241	0.292988
$712$	0.515132	0.0193054
$713$	6.56135	0.245724
$714$	−4.35460	−0.162967
$715$	0	0
$716$	−3.66877	−0.137108
$717$	27.9126	1.04242
$718$	18.5835	0.693532
$719$	−24.0858	−0.898250	−0.449125	−	0.893469i	$-0.648264\pi$
$719$	−24.0858	−0.898250	−0.449125	+	0.893469i	$0.648264\pi$
$720$	−0.867888	−0.0323443
$721$	−9.36266	−0.348684
$722$	−18.6305	−0.693356
$723$	−24.0821	−0.895624
$724$	−16.0972	−0.598246
$725$	10.8335	0.402344
$726$	17.6520	0.655127
$727$	12.2797	0.455429	0.227715	−	0.973728i	$-0.426875\pi$
$727$	12.2797	0.455429	0.227715	+	0.973728i	$0.426875\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	4.92671	0.182346
$731$	7.63411	0.282358
$732$	1.59146	0.0588222
$733$	−22.3496	−0.825500	−0.412750	−	0.910844i	$-0.635432\pi$
$733$	−22.3496	−0.825500	−0.412750	+	0.910844i	$0.635432\pi$
$734$	3.38814	0.125059
$735$	−0.867888	−0.0320125
$736$	0.637291	0.0234909
$737$	29.2438	1.07721
$738$	−11.1587	−0.410757
$739$	−46.9441	−1.72687	−0.863434	−	0.504462i	$-0.831691\pi$
$739$	−46.9441	−1.72687	−0.863434	+	0.504462i	$0.831691\pi$
$740$	−1.15721	−0.0425398
$741$	0	0
$742$	9.33003	0.342516
$743$	9.26395	0.339861	0.169931	−	0.985456i	$-0.445646\pi$
$743$	9.26395	0.339861	0.169931	+	0.985456i	$0.445646\pi$
$744$	10.2957	0.377458
$745$	3.82023	0.139962
$746$	−2.72907	−0.0999183
$747$	5.90798	0.216162
$748$	23.3091	0.852265
$749$	11.7393	0.428946
$750$	8.02516	0.293038
$751$	2.52263	0.0920522	0.0460261	−	0.998940i	$-0.485344\pi$
$751$	2.52263	0.0920522	0.0460261	+	0.998940i	$0.485344\pi$
$752$	3.42699	0.124969
$753$	7.17410	0.261439
$754$	0	0
$755$	−15.3571	−0.558902
$756$	−1.00000	−0.0363696
$757$	−47.3884	−1.72236	−0.861180	−	0.508300i	$-0.830274\pi$
$757$	−47.3884	−1.72236	−0.861180	+	0.508300i	$0.830274\pi$
$758$	13.8794	0.504123
$759$	3.41126	0.123821
$760$	0.527543	0.0191360
$761$	−8.04993	−0.291810	−0.145905	−	0.989299i	$-0.546609\pi$
$761$	−8.04993	−0.291810	−0.145905	+	0.989299i	$0.546609\pi$
$762$	20.0857	0.727629
$763$	1.94681	0.0704792
$764$	2.18895	0.0791934
$765$	−3.77931	−0.136641
$766$	−22.2119	−0.802550
$767$	0	0
$768$	1.00000	0.0360844
$769$	−19.4408	−0.701054	−0.350527	−	0.936553i	$-0.613998\pi$
$769$	−19.4408	−0.701054	−0.350527	+	0.936553i	$0.613998\pi$
$770$	4.64560	0.167416
$771$	−4.18796	−0.150826
$772$	1.80959	0.0651287
$773$	49.6532	1.78590	0.892951	−	0.450154i	$-0.148631\pi$
$773$	49.6532	1.78590	0.892951	+	0.450154i	$0.148631\pi$
$774$	1.75311	0.0630144
$775$	−43.7234	−1.57059
$776$	−8.56664	−0.307524
$777$	−1.33336	−0.0478340
$778$	19.3237	0.692787
$779$	6.78277	0.243018
$780$	0	0
$781$	34.6642	1.24038
$782$	2.77515	0.0992390
$783$	−2.55099	−0.0911648
$784$	1.00000	0.0357143
$785$	−4.41843	−0.157701
$786$	−13.3617	−0.476595
$787$	46.2080	1.64714	0.823568	−	0.567218i	$-0.191980\pi$
$787$	46.2080	1.64714	0.823568	+	0.567218i	$0.191980\pi$
$788$	22.7743	0.811302
$789$	5.46817	0.194672
$790$	−6.78030	−0.241232
$791$	16.2568	0.578025
$792$	5.35276	0.190202
$793$	0	0
$794$	−18.3450	−0.651041
$795$	8.09743	0.287186
$796$	−14.5430	−0.515462
$797$	46.1221	1.63373	0.816864	−	0.576831i	$-0.195711\pi$
$797$	46.1221	1.63373	0.816864	+	0.576831i	$0.195711\pi$
$798$	0.607847	0.0215175
$799$	14.9231	0.527943
$800$	−4.24677	−0.150146
$801$	0.515132	0.0182013
$802$	16.0696	0.567436
$803$	−30.3858	−1.07229
$804$	5.46332	0.192677
$805$	0.553097	0.0194941
$806$	0	0
$807$	−10.7324	−0.377799
$808$	1.20825	0.0425061
$809$	−14.0664	−0.494549	−0.247274	−	0.968946i	$-0.579535\pi$
$809$	−14.0664	−0.494549	−0.247274	+	0.968946i	$0.579535\pi$
$810$	−0.867888	−0.0304945
$811$	26.1250	0.917372	0.458686	−	0.888598i	$-0.348320\pi$
$811$	26.1250	0.917372	0.458686	+	0.888598i	$0.348320\pi$
$812$	2.55099	0.0895221
$813$	21.5276	0.755007
$814$	7.13714	0.250157
$815$	−14.7559	−0.516877
$816$	4.35460	0.152441
$817$	−1.06562	−0.0372815
$818$	−7.17158	−0.250749
$819$	0	0
$820$	9.68450	0.338197
$821$	−19.8433	−0.692537	−0.346269	−	0.938135i	$-0.612551\pi$
$821$	−19.8433	−0.692537	−0.346269	+	0.938135i	$0.612551\pi$
$822$	21.8669	0.762695
$823$	−41.5073	−1.44685	−0.723427	−	0.690401i	$-0.757434\pi$
$823$	−41.5073	−1.44685	−0.723427	+	0.690401i	$0.757434\pi$
$824$	9.36266	0.326164
$825$	−22.7319	−0.791424
$826$	−12.7937	−0.445149
$827$	−5.40873	−0.188080	−0.0940400	−	0.995568i	$-0.529978\pi$
$827$	−5.40873	−0.188080	−0.0940400	+	0.995568i	$0.529978\pi$
$828$	0.637291	0.0221474
$829$	−49.5627	−1.72138	−0.860691	−	0.509128i	$-0.829968\pi$
$829$	−49.5627	−1.72138	−0.860691	+	0.509128i	$0.829968\pi$
$830$	−5.12746	−0.177977
$831$	7.23334	0.250922
$832$	0	0
$833$	4.35460	0.150878
$834$	−6.75093	−0.233766
$835$	11.4777	0.397202
$836$	−3.25365	−0.112530
$837$	10.2957	0.355871
$838$	7.55122	0.260852
$839$	−20.0595	−0.692532	−0.346266	−	0.938136i	$-0.612551\pi$
$839$	−20.0595	−0.692532	−0.346266	+	0.938136i	$0.612551\pi$
$840$	0.867888	0.0299450
$841$	−22.4925	−0.775602
$842$	13.5246	0.466089
$843$	8.37168	0.288336
$844$	−22.0616	−0.759393
$845$	0	0
$846$	3.42699	0.117822
$847$	−17.6520	−0.606530
$848$	−9.33003	−0.320395
$849$	25.5063	0.875374
$850$	−18.4930	−0.634304
$851$	0.849737	0.0291286
$852$	6.47595	0.221862
$853$	22.6533	0.775633	0.387816	−	0.921737i	$-0.373229\pi$
$853$	22.6533	0.775633	0.387816	+	0.921737i	$0.373229\pi$
$854$	−1.59146	−0.0544588
$855$	0.527543	0.0180416
$856$	−11.7393	−0.401242
$857$	−32.5071	−1.11042	−0.555211	−	0.831709i	$-0.687363\pi$
$857$	−32.5071	−1.11042	−0.555211	+	0.831709i	$0.687363\pi$
$858$	0	0
$859$	30.4702	1.03963	0.519816	−	0.854278i	$-0.326001\pi$
$859$	30.4702	1.03963	0.519816	+	0.854278i	$0.326001\pi$
$860$	−1.52151	−0.0518830
$861$	11.1587	0.380287
$862$	1.83515	0.0625054
$863$	12.1092	0.412203	0.206101	−	0.978531i	$-0.433922\pi$
$863$	12.1092	0.412203	0.206101	+	0.978531i	$0.433922\pi$
$864$	1.00000	0.0340207
$865$	−8.36541	−0.284432
$866$	−16.7598	−0.569521
$867$	1.96253	0.0666510
$868$	−10.2957	−0.349458
$869$	41.8179	1.41858
$870$	2.21397	0.0750607
$871$	0	0
$872$	−1.94681	−0.0659272
$873$	−8.56664	−0.289937
$874$	−0.387375	−0.0131032
$875$	−8.02516	−0.271300
$876$	−5.67666	−0.191797
$877$	11.5262	0.389211	0.194605	−	0.980882i	$-0.437657\pi$
$877$	11.5262	0.389211	0.194605	+	0.980882i	$0.437657\pi$
$878$	−10.6616	−0.359813
$879$	−4.43656	−0.149642
$880$	−4.64560	−0.156603
$881$	−49.9398	−1.68251	−0.841257	−	0.540636i	$-0.818184\pi$
$881$	−49.9398	−1.68251	−0.841257	+	0.540636i	$0.818184\pi$
$882$	1.00000	0.0336718
$883$	−26.7012	−0.898569	−0.449284	−	0.893389i	$-0.648321\pi$
$883$	−26.7012	−0.898569	−0.449284	+	0.893389i	$0.648321\pi$
$884$	0	0
$885$	−11.1035	−0.373240
$886$	−27.1443	−0.911929
$887$	45.0050	1.51112	0.755559	−	0.655080i	$-0.227365\pi$
$887$	45.0050	1.51112	0.755559	+	0.655080i	$0.227365\pi$
$888$	1.33336	0.0447446
$889$	−20.0857	−0.673653
$890$	−0.447077	−0.0149861
$891$	5.35276	0.179324
$892$	−28.6176	−0.958188
$893$	−2.08308	−0.0697077
$894$	−4.40175	−0.147216
$895$	3.18408	0.106432
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	14.2999	0.477194
$899$	−26.2642	−0.875959
$900$	−4.24677	−0.141559
$901$	−40.6285	−1.35353
$902$	−59.7298	−1.98878
$903$	−1.75311	−0.0583400
$904$	−16.2568	−0.540693
$905$	13.9705	0.464397
$906$	17.6948	0.587869
$907$	−5.52935	−0.183599	−0.0917995	−	0.995778i	$-0.529262\pi$
$907$	−5.52935	−0.183599	−0.0917995	+	0.995778i	$0.529262\pi$
$908$	−6.01264	−0.199536
$909$	1.20825	0.0400752
$910$	0	0
$911$	−31.1422	−1.03179	−0.515893	−	0.856653i	$-0.672540\pi$
$911$	−31.1422	−1.03179	−0.515893	+	0.856653i	$0.672540\pi$
$912$	−0.607847	−0.0201278
$913$	31.6240	1.04660
$914$	−31.4356	−1.03980
$915$	−1.38121	−0.0456615
$916$	6.33101	0.209182
$917$	13.3617	0.441242
$918$	4.35460	0.143723
$919$	35.1608	1.15985	0.579924	−	0.814670i	$-0.303082\pi$
$919$	35.1608	1.15985	0.579924	+	0.814670i	$0.303082\pi$
$920$	−0.553097	−0.0182351
$921$	18.1029	0.596510
$922$	−27.7744	−0.914701
$923$	0	0
$924$	−5.35276	−0.176093
$925$	−5.66247	−0.186181
$926$	−9.28374	−0.305083
$927$	9.36266	0.307510
$928$	−2.55099	−0.0837403
$929$	47.0395	1.54332	0.771658	−	0.636038i	$-0.219428\pi$
$929$	47.0395	1.54332	0.771658	+	0.636038i	$0.219428\pi$
$930$	−8.93551	−0.293007
$931$	−0.607847	−0.0199214
$932$	19.7278	0.646205
$933$	−10.0829	−0.330098
$934$	−19.2484	−0.629826
$935$	−20.2297	−0.661582
$936$	0	0
$937$	−38.3293	−1.25217	−0.626083	−	0.779757i	$-0.715343\pi$
$937$	−38.3293	−1.25217	−0.626083	+	0.779757i	$0.715343\pi$
$938$	−5.46332	−0.178384
$939$	14.2531	0.465131
$940$	−2.97424	−0.0970091
$941$	−26.3515	−0.859035	−0.429518	−	0.903059i	$-0.641316\pi$
$941$	−26.3515	−0.859035	−0.429518	+	0.903059i	$0.641316\pi$
$942$	5.09101	0.165874
$943$	−7.11133	−0.231577
$944$	12.7937	0.416399
$945$	0.867888	0.0282324
$946$	9.38399	0.305100
$947$	−55.2714	−1.79608	−0.898040	−	0.439914i	$-0.855009\pi$
$947$	−55.2714	−1.79608	−0.898040	+	0.439914i	$0.855009\pi$
$948$	7.81241	0.253735
$949$	0	0
$950$	2.58138	0.0837512
$951$	29.5478	0.958152
$952$	−4.35460	−0.141133
$953$	33.8964	1.09801	0.549007	−	0.835818i	$-0.315006\pi$
$953$	33.8964	1.09801	0.549007	+	0.835818i	$0.315006\pi$
$954$	−9.33003	−0.302071
$955$	−1.89976	−0.0614749
$956$	27.9126	0.902758
$957$	−13.6548	−0.441397
$958$	28.5633	0.922837
$959$	−21.8669	−0.706119
$960$	−0.867888	−0.0280110
$961$	75.0012	2.41939
$962$	0	0
$963$	−11.7393	−0.378295
$964$	−24.0821	−0.775633
$965$	−1.57053	−0.0505570
$966$	−0.637291	−0.0205045
$967$	29.8259	0.959137	0.479569	−	0.877504i	$-0.340793\pi$
$967$	29.8259	0.959137	0.479569	+	0.877504i	$0.340793\pi$
$968$	17.6520	0.567357
$969$	−2.64693	−0.0850316
$970$	7.43489	0.238720
$971$	38.0973	1.22260	0.611301	−	0.791398i	$-0.290647\pi$
$971$	38.0973	1.22260	0.611301	+	0.791398i	$0.290647\pi$
$972$	1.00000	0.0320750
$973$	6.75093	0.216425
$974$	−26.3280	−0.843605
$975$	0	0
$976$	1.59146	0.0509415
$977$	−29.6916	−0.949918	−0.474959	−	0.880008i	$-0.657537\pi$
$977$	−29.6916	−0.949918	−0.474959	+	0.880008i	$0.657537\pi$
$978$	17.0021	0.543667
$979$	2.75738	0.0881261
$980$	−0.867888	−0.0277237
$981$	−1.94681	−0.0621568
$982$	−24.6042	−0.785153
$983$	11.0384	0.352071	0.176036	−	0.984384i	$-0.443673\pi$
$983$	11.0384	0.352071	0.176036	+	0.984384i	$0.443673\pi$
$984$	−11.1587	−0.355726
$985$	−19.7656	−0.629784
$986$	−11.1085	−0.353768
$987$	−3.42699	−0.109082
$988$	0	0
$989$	1.11724	0.0355263
$990$	−4.64560	−0.147647
$991$	−30.9435	−0.982951	−0.491476	−	0.870891i	$-0.663542\pi$
$991$	−30.9435	−0.982951	−0.491476	+	0.870891i	$0.663542\pi$
$992$	10.2957	0.326888
$993$	−11.0027	−0.349161
$994$	−6.47595	−0.205405
$995$	12.6217	0.400134
$996$	5.90798	0.187201
$997$	36.5937	1.15893	0.579467	−	0.814996i	$-0.303261\pi$
$997$	36.5937	1.15893	0.579467	+	0.814996i	$0.303261\pi$
$998$	25.4842	0.806688
$999$	1.33336	0.0421856

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.cu.1.2	yes	6
13.12	even	2		7098.2.a.cq.1.5	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7098.2.a.cq.1.5	✓	6	13.12	even	2
7098.2.a.cu.1.2	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.867888 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.867888 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.867888 q^{10} +5.35276 q^{11} +1.00000 q^{12} -1.00000 q^{14} -0.867888 q^{15} +1.00000 q^{16} +4.35460 q^{17} +1.00000 q^{18} -0.607847 q^{19} -0.867888 q^{20} -1.00000 q^{21} +5.35276 q^{22} +0.637291 q^{23} +1.00000 q^{24} -4.24677 q^{25} +1.00000 q^{27} -1.00000 q^{28} -2.55099 q^{29} -0.867888 q^{30} +10.2957 q^{31} +1.00000 q^{32} +5.35276 q^{33} +4.35460 q^{34} +0.867888 q^{35} +1.00000 q^{36} +1.33336 q^{37} -0.607847 q^{38} -0.867888 q^{40} -11.1587 q^{41} -1.00000 q^{42} +1.75311 q^{43} +5.35276 q^{44} -0.867888 q^{45} +0.637291 q^{46} +3.42699 q^{47} +1.00000 q^{48} +1.00000 q^{49} -4.24677 q^{50} +4.35460 q^{51} -9.33003 q^{53} +1.00000 q^{54} -4.64560 q^{55} -1.00000 q^{56} -0.607847 q^{57} -2.55099 q^{58} +12.7937 q^{59} -0.867888 q^{60} +1.59146 q^{61} +10.2957 q^{62} -1.00000 q^{63} +1.00000 q^{64} +5.35276 q^{66} +5.46332 q^{67} +4.35460 q^{68} +0.637291 q^{69} +0.867888 q^{70} +6.47595 q^{71} +1.00000 q^{72} -5.67666 q^{73} +1.33336 q^{74} -4.24677 q^{75} -0.607847 q^{76} -5.35276 q^{77} +7.81241 q^{79} -0.867888 q^{80} +1.00000 q^{81} -11.1587 q^{82} +5.90798 q^{83} -1.00000 q^{84} -3.77931 q^{85} +1.75311 q^{86} -2.55099 q^{87} +5.35276 q^{88} +0.515132 q^{89} -0.867888 q^{90} +0.637291 q^{92} +10.2957 q^{93} +3.42699 q^{94} +0.527543 q^{95} +1.00000 q^{96} -8.56664 q^{97} +1.00000 q^{98} +5.35276 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 9 q^{5} + 6 q^{6} - 6 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 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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Representations

Groups

Database

Properties

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