LMFDB - Embedded newform 7098.2.a.cp.1.6

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:	$1$
Dimension:	$6$
Coefficient field:	6.6.8569169.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 12x^{4} + 11x^{3} + 44x^{2} - 9x - 41 $ x^6 - 2x^5 - 12x^4 + 11x^3 + 44x^2 - 9*x - 41
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$2.18325$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.93408 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.93408 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.93408 q^{10} +4.81154 q^{11} -1.00000 q^{12} +1.00000 q^{14} -3.93408 q^{15} +1.00000 q^{16} -3.61347 q^{17} -1.00000 q^{18} -7.71258 q^{19} +3.93408 q^{20} +1.00000 q^{21} -4.81154 q^{22} -3.86172 q^{23} +1.00000 q^{24} +10.4770 q^{25} -1.00000 q^{27} -1.00000 q^{28} -4.45147 q^{29} +3.93408 q^{30} +1.01880 q^{31} -1.00000 q^{32} -4.81154 q^{33} +3.61347 q^{34} -3.93408 q^{35} +1.00000 q^{36} +7.30140 q^{37} +7.71258 q^{38} -3.93408 q^{40} +7.28601 q^{41} -1.00000 q^{42} -4.73996 q^{43} +4.81154 q^{44} +3.93408 q^{45} +3.86172 q^{46} -10.4986 q^{47} -1.00000 q^{48} +1.00000 q^{49} -10.4770 q^{50} +3.61347 q^{51} -10.5944 q^{53} +1.00000 q^{54} +18.9289 q^{55} +1.00000 q^{56} +7.71258 q^{57} +4.45147 q^{58} -3.70984 q^{59} -3.93408 q^{60} -11.8947 q^{61} -1.01880 q^{62} -1.00000 q^{63} +1.00000 q^{64} +4.81154 q^{66} -3.12611 q^{67} -3.61347 q^{68} +3.86172 q^{69} +3.93408 q^{70} -8.73053 q^{71} -1.00000 q^{72} -15.7564 q^{73} -7.30140 q^{74} -10.4770 q^{75} -7.71258 q^{76} -4.81154 q^{77} -0.731774 q^{79} +3.93408 q^{80} +1.00000 q^{81} -7.28601 q^{82} -0.380858 q^{83} +1.00000 q^{84} -14.2157 q^{85} +4.73996 q^{86} +4.45147 q^{87} -4.81154 q^{88} +0.469836 q^{89} -3.93408 q^{90} -3.86172 q^{92} -1.01880 q^{93} +10.4986 q^{94} -30.3419 q^{95} +1.00000 q^{96} +11.3667 q^{97} -1.00000 q^{98} +4.81154 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} + 3 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 + 3 * q^5 + 6 * q^6 - 6 * q^7 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} + 3 q^{5} + 6 q^{6} - 6 q^{7} - 6 q^{8} + 6 q^{9} - 3 q^{10} + 6 q^{11} - 6 q^{12} + 6 q^{14} - 3 q^{15} + 6 q^{16} + 10 q^{17} - 6 q^{18} - 8 q^{19} + 3 q^{20} + 6 q^{21} - 6 q^{22} - 12 q^{23} + 6 q^{24} + 5 q^{25} - 6 q^{27} - 6 q^{28} + 4 q^{29} + 3 q^{30} - 7 q^{31} - 6 q^{32} - 6 q^{33} - 10 q^{34} - 3 q^{35} + 6 q^{36} - 3 q^{37} + 8 q^{38} - 3 q^{40} - 3 q^{41} - 6 q^{42} - 3 q^{43} + 6 q^{44} + 3 q^{45} + 12 q^{46} - 29 q^{47} - 6 q^{48} + 6 q^{49} - 5 q^{50} - 10 q^{51} - 12 q^{53} + 6 q^{54} + 29 q^{55} + 6 q^{56} + 8 q^{57} - 4 q^{58} - 2 q^{59} - 3 q^{60} + 13 q^{61} + 7 q^{62} - 6 q^{63} + 6 q^{64} + 6 q^{66} - 22 q^{67} + 10 q^{68} + 12 q^{69} + 3 q^{70} - q^{71} - 6 q^{72} - 29 q^{73} + 3 q^{74} - 5 q^{75} - 8 q^{76} - 6 q^{77} - 24 q^{79} + 3 q^{80} + 6 q^{81} + 3 q^{82} - 7 q^{83} + 6 q^{84} - 21 q^{85} + 3 q^{86} - 4 q^{87} - 6 q^{88} + 11 q^{89} - 3 q^{90} - 12 q^{92} + 7 q^{93} + 29 q^{94} + 8 q^{95} + 6 q^{96} + 4 q^{97} - 6 q^{98} + 6 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 + 3 * q^5 + 6 * q^6 - 6 * q^7 - 6 * q^8 + 6 * q^9 - 3 * q^10 + 6 * q^11 - 6 * q^12 + 6 * q^14 - 3 * q^15 + 6 * q^16 + 10 * q^17 - 6 * q^18 - 8 * q^19 + 3 * q^20 + 6 * q^21 - 6 * q^22 - 12 * q^23 + 6 * q^24 + 5 * q^25 - 6 * q^27 - 6 * q^28 + 4 * q^29 + 3 * q^30 - 7 * q^31 - 6 * q^32 - 6 * q^33 - 10 * q^34 - 3 * q^35 + 6 * q^36 - 3 * q^37 + 8 * q^38 - 3 * q^40 - 3 * q^41 - 6 * q^42 - 3 * q^43 + 6 * q^44 + 3 * q^45 + 12 * q^46 - 29 * q^47 - 6 * q^48 + 6 * q^49 - 5 * q^50 - 10 * q^51 - 12 * q^53 + 6 * q^54 + 29 * q^55 + 6 * q^56 + 8 * q^57 - 4 * q^58 - 2 * q^59 - 3 * q^60 + 13 * q^61 + 7 * q^62 - 6 * q^63 + 6 * q^64 + 6 * q^66 - 22 * q^67 + 10 * q^68 + 12 * q^69 + 3 * q^70 - q^71 - 6 * q^72 - 29 * q^73 + 3 * q^74 - 5 * q^75 - 8 * q^76 - 6 * q^77 - 24 * q^79 + 3 * q^80 + 6 * q^81 + 3 * q^82 - 7 * q^83 + 6 * q^84 - 21 * q^85 + 3 * q^86 - 4 * q^87 - 6 * q^88 + 11 * q^89 - 3 * q^90 - 12 * q^92 + 7 * q^93 + 29 * q^94 + 8 * q^95 + 6 * q^96 + 4 * q^97 - 6 * q^98 + 6 * 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
$5$	3.93408	1.75937	0.879686	−	0.475555i	$-0.157753\pi$
$5$	3.93408	1.75937	0.879686	+	0.475555i	$0.157753\pi$
$6$	1.00000	0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−3.93408	−1.24406
$11$	4.81154	1.45073	0.725366	−	0.688363i	$-0.241670\pi$
$11$	4.81154	1.45073	0.725366	+	0.688363i	$0.241670\pi$
$12$	−1.00000	−0.288675
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	−3.93408	−1.01577
$16$	1.00000	0.250000
$17$	−3.61347	−0.876396	−0.438198	−	0.898878i	$-0.644383\pi$
$17$	−3.61347	−0.876396	−0.438198	+	0.898878i	$0.644383\pi$
$18$	−1.00000	−0.235702
$19$	−7.71258	−1.76939	−0.884693	−	0.466174i	$-0.845632\pi$
$19$	−7.71258	−1.76939	−0.884693	+	0.466174i	$0.845632\pi$
$20$	3.93408	0.879686
$21$	1.00000	0.218218
$22$	−4.81154	−1.02582
$23$	−3.86172	−0.805224	−0.402612	−	0.915371i	$-0.631898\pi$
$23$	−3.86172	−0.805224	−0.402612	+	0.915371i	$0.631898\pi$
$24$	1.00000	0.204124
$25$	10.4770	2.09539
$26$	0	0
$27$	−1.00000	−0.192450
$28$	−1.00000	−0.188982
$29$	−4.45147	−0.826618	−0.413309	−	0.910591i	$-0.635627\pi$
$29$	−4.45147	−0.826618	−0.413309	+	0.910591i	$0.635627\pi$
$30$	3.93408	0.718261
$31$	1.01880	0.182981	0.0914906	−	0.995806i	$-0.470837\pi$
$31$	1.01880	0.182981	0.0914906	+	0.995806i	$0.470837\pi$
$32$	−1.00000	−0.176777
$33$	−4.81154	−0.837581
$34$	3.61347	0.619706
$35$	−3.93408	−0.664980
$36$	1.00000	0.166667
$37$	7.30140	1.20034	0.600172	−	0.799871i	$-0.295099\pi$
$37$	7.30140	1.20034	0.600172	+	0.799871i	$0.295099\pi$
$38$	7.71258	1.25114
$39$	0	0
$40$	−3.93408	−0.622032
$41$	7.28601	1.13788	0.568942	−	0.822378i	$-0.307353\pi$
$41$	7.28601	1.13788	0.568942	+	0.822378i	$0.307353\pi$
$42$	−1.00000	−0.154303
$43$	−4.73996	−0.722838	−0.361419	−	0.932404i	$-0.617708\pi$
$43$	−4.73996	−0.722838	−0.361419	+	0.932404i	$0.617708\pi$
$44$	4.81154	0.725366
$45$	3.93408	0.586457
$46$	3.86172	0.569380
$47$	−10.4986	−1.53138	−0.765691	−	0.643208i	$-0.777603\pi$
$47$	−10.4986	−1.53138	−0.765691	+	0.643208i	$0.777603\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−10.4770	−1.48166
$51$	3.61347	0.505988
$52$	0	0
$53$	−10.5944	−1.45525	−0.727626	−	0.685975i	$-0.759376\pi$
$53$	−10.5944	−1.45525	−0.727626	+	0.685975i	$0.759376\pi$
$54$	1.00000	0.136083
$55$	18.9289	2.55238
$56$	1.00000	0.133631
$57$	7.71258	1.02156
$58$	4.45147	0.584507
$59$	−3.70984	−0.482980	−0.241490	−	0.970403i	$-0.577636\pi$
$59$	−3.70984	−0.482980	−0.241490	+	0.970403i	$0.577636\pi$
$60$	−3.93408	−0.507887
$61$	−11.8947	−1.52296	−0.761482	−	0.648186i	$-0.775528\pi$
$61$	−11.8947	−1.52296	−0.761482	+	0.648186i	$0.775528\pi$
$62$	−1.01880	−0.129387
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	4.81154	0.592259
$67$	−3.12611	−0.381915	−0.190957	−	0.981598i	$-0.561159\pi$
$67$	−3.12611	−0.381915	−0.190957	+	0.981598i	$0.561159\pi$
$68$	−3.61347	−0.438198
$69$	3.86172	0.464896
$70$	3.93408	0.470212
$71$	−8.73053	−1.03612	−0.518061	−	0.855343i	$-0.673346\pi$
$71$	−8.73053	−1.03612	−0.518061	+	0.855343i	$0.673346\pi$
$72$	−1.00000	−0.117851
$73$	−15.7564	−1.84414	−0.922072	−	0.387019i	$-0.873505\pi$
$73$	−15.7564	−1.84414	−0.922072	+	0.387019i	$0.873505\pi$
$74$	−7.30140	−0.848771
$75$	−10.4770	−1.20977
$76$	−7.71258	−0.884693
$77$	−4.81154	−0.548325
$78$	0	0
$79$	−0.731774	−0.0823310	−0.0411655	−	0.999152i	$-0.513107\pi$
$79$	−0.731774	−0.0823310	−0.0411655	+	0.999152i	$0.513107\pi$
$80$	3.93408	0.439843
$81$	1.00000	0.111111
$82$	−7.28601	−0.804605
$83$	−0.380858	−0.0418046	−0.0209023	−	0.999782i	$-0.506654\pi$
$83$	−0.380858	−0.0418046	−0.0209023	+	0.999782i	$0.506654\pi$
$84$	1.00000	0.109109
$85$	−14.2157	−1.54191
$86$	4.73996	0.511123
$87$	4.45147	0.477248
$88$	−4.81154	−0.512912
$89$	0.469836	0.0498025	0.0249013	−	0.999690i	$-0.492073\pi$
$89$	0.469836	0.0498025	0.0249013	+	0.999690i	$0.492073\pi$
$90$	−3.93408	−0.414688
$91$	0	0
$92$	−3.86172	−0.402612
$93$	−1.01880	−0.105644
$94$	10.4986	1.08285
$95$	−30.3419	−3.11301
$96$	1.00000	0.102062
$97$	11.3667	1.15411	0.577057	−	0.816704i	$-0.304201\pi$
$97$	11.3667	1.15411	0.577057	+	0.816704i	$0.304201\pi$
$98$	−1.00000	−0.101015
$99$	4.81154	0.483578
$100$	10.4770	1.04770
$101$	2.43888	0.242678	0.121339	−	0.992611i	$-0.461281\pi$
$101$	2.43888	0.242678	0.121339	+	0.992611i	$0.461281\pi$
$102$	−3.61347	−0.357787
$103$	18.5174	1.82457	0.912287	−	0.409551i	$-0.134315\pi$
$103$	18.5174	1.82457	0.912287	+	0.409551i	$0.134315\pi$
$104$	0	0
$105$	3.93408	0.383926
$106$	10.5944	1.02902
$107$	−18.9523	−1.83219	−0.916095	−	0.400961i	$-0.868676\pi$
$107$	−18.9523	−1.83219	−0.916095	+	0.400961i	$0.868676\pi$
$108$	−1.00000	−0.0962250
$109$	−13.0695	−1.25184	−0.625918	−	0.779889i	$-0.715275\pi$
$109$	−13.0695	−1.25184	−0.625918	+	0.779889i	$0.715275\pi$
$110$	−18.9289	−1.80480
$111$	−7.30140	−0.693018
$112$	−1.00000	−0.0944911
$113$	0.383319	0.0360596	0.0180298	−	0.999837i	$-0.494261\pi$
$113$	0.383319	0.0360596	0.0180298	+	0.999837i	$0.494261\pi$
$114$	−7.71258	−0.722349
$115$	−15.1923	−1.41669
$116$	−4.45147	−0.413309
$117$	0	0
$118$	3.70984	0.341519
$119$	3.61347	0.331247
$120$	3.93408	0.359130
$121$	12.1509	1.10463
$122$	11.8947	1.07690
$123$	−7.28601	−0.656957
$124$	1.01880	0.0914906
$125$	21.5467	1.92720
$126$	1.00000	0.0890871
$127$	−8.48244	−0.752695	−0.376347	−	0.926479i	$-0.622820\pi$
$127$	−8.48244	−0.752695	−0.376347	+	0.926479i	$0.622820\pi$
$128$	−1.00000	−0.0883883
$129$	4.73996	0.417330
$130$	0	0
$131$	10.1450	0.886372	0.443186	−	0.896430i	$-0.353848\pi$
$131$	10.1450	0.886372	0.443186	+	0.896430i	$0.353848\pi$
$132$	−4.81154	−0.418791
$133$	7.71258	0.668765
$134$	3.12611	0.270055
$135$	−3.93408	−0.338591
$136$	3.61347	0.309853
$137$	−1.73976	−0.148638	−0.0743189	−	0.997235i	$-0.523678\pi$
$137$	−1.73976	−0.148638	−0.0743189	+	0.997235i	$0.523678\pi$
$138$	−3.86172	−0.328731
$139$	−6.78513	−0.575507	−0.287754	−	0.957704i	$-0.592908\pi$
$139$	−6.78513	−0.575507	−0.287754	+	0.957704i	$0.592908\pi$
$140$	−3.93408	−0.332490
$141$	10.4986	0.884144
$142$	8.73053	0.732649
$143$	0	0
$144$	1.00000	0.0833333
$145$	−17.5124	−1.45433
$146$	15.7564	1.30401
$147$	−1.00000	−0.0824786
$148$	7.30140	0.600172
$149$	−19.2424	−1.57640	−0.788199	−	0.615420i	$-0.788986\pi$
$149$	−19.2424	−1.57640	−0.788199	+	0.615420i	$0.788986\pi$
$150$	10.4770	0.855440
$151$	6.95569	0.566046	0.283023	−	0.959113i	$-0.408663\pi$
$151$	6.95569	0.566046	0.283023	+	0.959113i	$0.408663\pi$
$152$	7.71258	0.625572
$153$	−3.61347	−0.292132
$154$	4.81154	0.387725
$155$	4.00802	0.321932
$156$	0	0
$157$	1.09347	0.0872686	0.0436343	−	0.999048i	$-0.486106\pi$
$157$	1.09347	0.0872686	0.0436343	+	0.999048i	$0.486106\pi$
$158$	0.731774	0.0582168
$159$	10.5944	0.840190
$160$	−3.93408	−0.311016
$161$	3.86172	0.304346
$162$	−1.00000	−0.0785674
$163$	−17.2244	−1.34912	−0.674558	−	0.738222i	$-0.735666\pi$
$163$	−17.2244	−1.34912	−0.674558	+	0.738222i	$0.735666\pi$
$164$	7.28601	0.568942
$165$	−18.9289	−1.47362
$166$	0.380858	0.0295603
$167$	−21.5911	−1.67077	−0.835384	−	0.549667i	$-0.814755\pi$
$167$	−21.5911	−1.67077	−0.835384	+	0.549667i	$0.814755\pi$
$168$	−1.00000	−0.0771517
$169$	0	0
$170$	14.2157	1.09029
$171$	−7.71258	−0.589795
$172$	−4.73996	−0.361419
$173$	23.4276	1.78117	0.890584	−	0.454819i	$-0.150296\pi$
$173$	23.4276	1.78117	0.890584	+	0.454819i	$0.150296\pi$
$174$	−4.45147	−0.337465
$175$	−10.4770	−0.791983
$176$	4.81154	0.362683
$177$	3.70984	0.278849
$178$	−0.469836	−0.0352157
$179$	3.15190	0.235584	0.117792	−	0.993038i	$-0.462418\pi$
$179$	3.15190	0.235584	0.117792	+	0.993038i	$0.462418\pi$
$180$	3.93408	0.293229
$181$	1.49375	0.111029	0.0555147	−	0.998458i	$-0.482320\pi$
$181$	1.49375	0.111029	0.0555147	+	0.998458i	$0.482320\pi$
$182$	0	0
$183$	11.8947	0.879284
$184$	3.86172	0.284690
$185$	28.7243	2.11185
$186$	1.01880	0.0747017
$187$	−17.3864	−1.27142
$188$	−10.4986	−0.765691
$189$	1.00000	0.0727393
$190$	30.3419	2.20123
$191$	3.19802	0.231401	0.115700	−	0.993284i	$-0.463089\pi$
$191$	3.19802	0.231401	0.115700	+	0.993284i	$0.463089\pi$
$192$	−1.00000	−0.0721688
$193$	−3.88466	−0.279624	−0.139812	−	0.990178i	$-0.544650\pi$
$193$	−3.88466	−0.279624	−0.139812	+	0.990178i	$0.544650\pi$
$194$	−11.3667	−0.816082
$195$	0	0
$196$	1.00000	0.0714286
$197$	−11.9583	−0.851994	−0.425997	−	0.904725i	$-0.640077\pi$
$197$	−11.9583	−0.851994	−0.425997	+	0.904725i	$0.640077\pi$
$198$	−4.81154	−0.341941
$199$	25.6975	1.82165	0.910823	−	0.412797i	$-0.135448\pi$
$199$	25.6975	1.82165	0.910823	+	0.412797i	$0.135448\pi$
$200$	−10.4770	−0.740832
$201$	3.12611	0.220499
$202$	−2.43888	−0.171599
$203$	4.45147	0.312432
$204$	3.61347	0.252994
$205$	28.6637	2.00196
$206$	−18.5174	−1.29017
$207$	−3.86172	−0.268408
$208$	0	0
$209$	−37.1093	−2.56691
$210$	−3.93408	−0.271477
$211$	−18.5638	−1.27799	−0.638993	−	0.769212i	$-0.720649\pi$
$211$	−18.5638	−1.27799	−0.638993	+	0.769212i	$0.720649\pi$
$212$	−10.5944	−0.727626
$213$	8.73053	0.598206
$214$	18.9523	1.29555
$215$	−18.6474	−1.27174
$216$	1.00000	0.0680414
$217$	−1.01880	−0.0691604
$218$	13.0695	0.885181
$219$	15.7564	1.06472
$220$	18.9289	1.27619
$221$	0	0
$222$	7.30140	0.490038
$223$	−18.0768	−1.21051	−0.605255	−	0.796032i	$-0.706929\pi$
$223$	−18.0768	−1.21051	−0.605255	+	0.796032i	$0.706929\pi$
$224$	1.00000	0.0668153
$225$	10.4770	0.698463
$226$	−0.383319	−0.0254980
$227$	−4.25355	−0.282318	−0.141159	−	0.989987i	$-0.545083\pi$
$227$	−4.25355	−0.282318	−0.141159	+	0.989987i	$0.545083\pi$
$228$	7.71258	0.510778
$229$	16.2898	1.07646	0.538229	−	0.842799i	$-0.319094\pi$
$229$	16.2898	1.07646	0.538229	+	0.842799i	$0.319094\pi$
$230$	15.1923	1.00175
$231$	4.81154	0.316576
$232$	4.45147	0.292254
$233$	10.5462	0.690905	0.345452	−	0.938436i	$-0.387725\pi$
$233$	10.5462	0.690905	0.345452	+	0.938436i	$0.387725\pi$
$234$	0	0
$235$	−41.3024	−2.69427
$236$	−3.70984	−0.241490
$237$	0.731774	0.0475338
$238$	−3.61347	−0.234227
$239$	15.8572	1.02571	0.512857	−	0.858474i	$-0.328587\pi$
$239$	15.8572	1.02571	0.512857	+	0.858474i	$0.328587\pi$
$240$	−3.93408	−0.253944
$241$	15.5235	0.999957	0.499979	−	0.866038i	$-0.333341\pi$
$241$	15.5235	0.999957	0.499979	+	0.866038i	$0.333341\pi$
$242$	−12.1509	−0.781088
$243$	−1.00000	−0.0641500
$244$	−11.8947	−0.761482
$245$	3.93408	0.251339
$246$	7.28601	0.464539
$247$	0	0
$248$	−1.01880	−0.0646936
$249$	0.380858	0.0241359
$250$	−21.5467	−1.36274
$251$	7.93745	0.501007	0.250504	−	0.968116i	$-0.419404\pi$
$251$	7.93745	0.501007	0.250504	+	0.968116i	$0.419404\pi$
$252$	−1.00000	−0.0629941
$253$	−18.5808	−1.16817
$254$	8.48244	0.532236
$255$	14.2157	0.890221
$256$	1.00000	0.0625000
$257$	15.3365	0.956665	0.478332	−	0.878179i	$-0.341241\pi$
$257$	15.3365	0.956665	0.478332	+	0.878179i	$0.341241\pi$
$258$	−4.73996	−0.295097
$259$	−7.30140	−0.453687
$260$	0	0
$261$	−4.45147	−0.275539
$262$	−10.1450	−0.626760
$263$	14.6702	0.904604	0.452302	−	0.891865i	$-0.350603\pi$
$263$	14.6702	0.904604	0.452302	+	0.891865i	$0.350603\pi$
$264$	4.81154	0.296130
$265$	−41.6791	−2.56033
$266$	−7.71258	−0.472888
$267$	−0.469836	−0.0287535
$268$	−3.12611	−0.190957
$269$	13.0947	0.798395	0.399198	−	0.916865i	$-0.369289\pi$
$269$	13.0947	0.798395	0.399198	+	0.916865i	$0.369289\pi$
$270$	3.93408	0.239420
$271$	10.8665	0.660092	0.330046	−	0.943965i	$-0.392936\pi$
$271$	10.8665	0.660092	0.330046	+	0.943965i	$0.392936\pi$
$272$	−3.61347	−0.219099
$273$	0	0
$274$	1.73976	0.105103
$275$	50.4102	3.03985
$276$	3.86172	0.232448
$277$	22.9560	1.37929	0.689645	−	0.724147i	$-0.257766\pi$
$277$	22.9560	1.37929	0.689645	+	0.724147i	$0.257766\pi$
$278$	6.78513	0.406945
$279$	1.01880	0.0609937
$280$	3.93408	0.235106
$281$	9.42525	0.562263	0.281132	−	0.959669i	$-0.409290\pi$
$281$	9.42525	0.562263	0.281132	+	0.959669i	$0.409290\pi$
$282$	−10.4986	−0.625184
$283$	−19.1238	−1.13679	−0.568396	−	0.822755i	$-0.692436\pi$
$283$	−19.1238	−1.13679	−0.568396	+	0.822755i	$0.692436\pi$
$284$	−8.73053	−0.518061
$285$	30.3419	1.79730
$286$	0	0
$287$	−7.28601	−0.430079
$288$	−1.00000	−0.0589256
$289$	−3.94280	−0.231930
$290$	17.5124	1.02837
$291$	−11.3667	−0.666328
$292$	−15.7564	−0.922072
$293$	19.6143	1.14588	0.572940	−	0.819597i	$-0.305803\pi$
$293$	19.6143	1.14588	0.572940	+	0.819597i	$0.305803\pi$
$294$	1.00000	0.0583212
$295$	−14.5948	−0.849742
$296$	−7.30140	−0.424385
$297$	−4.81154	−0.279194
$298$	19.2424	1.11468
$299$	0	0
$300$	−10.4770	−0.604887
$301$	4.73996	0.273207
$302$	−6.95569	−0.400255
$303$	−2.43888	−0.140110
$304$	−7.71258	−0.442347
$305$	−46.7948	−2.67946
$306$	3.61347	0.206569
$307$	−6.84964	−0.390930	−0.195465	−	0.980711i	$-0.562622\pi$
$307$	−6.84964	−0.390930	−0.195465	+	0.980711i	$0.562622\pi$
$308$	−4.81154	−0.274163
$309$	−18.5174	−1.05342
$310$	−4.00802	−0.227640
$311$	11.1603	0.632843	0.316422	−	0.948619i	$-0.397519\pi$
$311$	11.1603	0.632843	0.316422	+	0.948619i	$0.397519\pi$
$312$	0	0
$313$	13.7636	0.777966	0.388983	−	0.921245i	$-0.372826\pi$
$313$	13.7636	0.777966	0.388983	+	0.921245i	$0.372826\pi$
$314$	−1.09347	−0.0617082
$315$	−3.93408	−0.221660
$316$	−0.731774	−0.0411655
$317$	−1.05913	−0.0594867	−0.0297434	−	0.999558i	$-0.509469\pi$
$317$	−1.05913	−0.0594867	−0.0297434	+	0.999558i	$0.509469\pi$
$318$	−10.5944	−0.594104
$319$	−21.4184	−1.19920
$320$	3.93408	0.219922
$321$	18.9523	1.05782
$322$	−3.86172	−0.215205
$323$	27.8692	1.55068
$324$	1.00000	0.0555556
$325$	0	0
$326$	17.2244	0.953969
$327$	13.0695	0.722747
$328$	−7.28601	−0.402302
$329$	10.4986	0.578808
$330$	18.9289	1.04200
$331$	2.59428	0.142594	0.0712972	−	0.997455i	$-0.477286\pi$
$331$	2.59428	0.142594	0.0712972	+	0.997455i	$0.477286\pi$
$332$	−0.380858	−0.0209023
$333$	7.30140	0.400114
$334$	21.5911	1.18141
$335$	−12.2983	−0.671930
$336$	1.00000	0.0545545
$337$	−18.0032	−0.980696	−0.490348	−	0.871527i	$-0.663130\pi$
$337$	−18.0032	−0.980696	−0.490348	+	0.871527i	$0.663130\pi$
$338$	0	0
$339$	−0.383319	−0.0208190
$340$	−14.2157	−0.770954
$341$	4.90197	0.265457
$342$	7.71258	0.417048
$343$	−1.00000	−0.0539949
$344$	4.73996	0.255562
$345$	15.1923	0.817926
$346$	−23.4276	−1.25948
$347$	32.2122	1.72924	0.864621	−	0.502424i	$-0.167558\pi$
$347$	32.2122	1.72924	0.864621	+	0.502424i	$0.167558\pi$
$348$	4.45147	0.238624
$349$	−26.9689	−1.44361	−0.721807	−	0.692095i	$-0.756688\pi$
$349$	−26.9689	−1.44361	−0.721807	+	0.692095i	$0.756688\pi$
$350$	10.4770	0.560017
$351$	0	0
$352$	−4.81154	−0.256456
$353$	15.0234	0.799614	0.399807	−	0.916599i	$-0.369077\pi$
$353$	15.0234	0.799614	0.399807	+	0.916599i	$0.369077\pi$
$354$	−3.70984	−0.197176
$355$	−34.3465	−1.82293
$356$	0.469836	0.0249013
$357$	−3.61347	−0.191245
$358$	−3.15190	−0.166583
$359$	0.187328	0.00988678	0.00494339	−	0.999988i	$-0.498426\pi$
$359$	0.187328	0.00988678	0.00494339	+	0.999988i	$0.498426\pi$
$360$	−3.93408	−0.207344
$361$	40.4838	2.13073
$362$	−1.49375	−0.0785097
$363$	−12.1509	−0.637756
$364$	0	0
$365$	−61.9867	−3.24453
$366$	−11.8947	−0.621748
$367$	−15.6194	−0.815323	−0.407662	−	0.913133i	$-0.633656\pi$
$367$	−15.6194	−0.815323	−0.407662	+	0.913133i	$0.633656\pi$
$368$	−3.86172	−0.201306
$369$	7.28601	0.379294
$370$	−28.7243	−1.49330
$371$	10.5944	0.550033
$372$	−1.01880	−0.0528221
$373$	−35.0244	−1.81350	−0.906748	−	0.421673i	$-0.861443\pi$
$373$	−35.0244	−1.81350	−0.906748	+	0.421673i	$0.861443\pi$
$374$	17.3864	0.899027
$375$	−21.5467	−1.11267
$376$	10.4986	0.541426
$377$	0	0
$378$	−1.00000	−0.0514344
$379$	−7.86687	−0.404094	−0.202047	−	0.979376i	$-0.564759\pi$
$379$	−7.86687	−0.404094	−0.202047	+	0.979376i	$0.564759\pi$
$380$	−30.3419	−1.55650
$381$	8.48244	0.434569
$382$	−3.19802	−0.163625
$383$	−25.0867	−1.28187	−0.640935	−	0.767595i	$-0.721453\pi$
$383$	−25.0867	−1.28187	−0.640935	+	0.767595i	$0.721453\pi$
$384$	1.00000	0.0510310
$385$	−18.9289	−0.964709
$386$	3.88466	0.197724
$387$	−4.73996	−0.240946
$388$	11.3667	0.577057
$389$	−10.1352	−0.513877	−0.256939	−	0.966428i	$-0.582714\pi$
$389$	−10.1352	−0.513877	−0.256939	+	0.966428i	$0.582714\pi$
$390$	0	0
$391$	13.9542	0.705696
$392$	−1.00000	−0.0505076
$393$	−10.1450	−0.511747
$394$	11.9583	0.602451
$395$	−2.87885	−0.144851
$396$	4.81154	0.241789
$397$	12.0921	0.606884	0.303442	−	0.952850i	$-0.401864\pi$
$397$	12.0921	0.606884	0.303442	+	0.952850i	$0.401864\pi$
$398$	−25.6975	−1.28810
$399$	−7.71258	−0.386112
$400$	10.4770	0.523848
$401$	−0.593140	−0.0296200	−0.0148100	−	0.999890i	$-0.504714\pi$
$401$	−0.593140	−0.0296200	−0.0148100	+	0.999890i	$0.504714\pi$
$402$	−3.12611	−0.155916
$403$	0	0
$404$	2.43888	0.121339
$405$	3.93408	0.195486
$406$	−4.45147	−0.220923
$407$	35.1310	1.74138
$408$	−3.61347	−0.178894
$409$	−12.2539	−0.605918	−0.302959	−	0.953004i	$-0.597975\pi$
$409$	−12.2539	−0.605918	−0.302959	+	0.953004i	$0.597975\pi$
$410$	−28.6637	−1.41560
$411$	1.73976	0.0858161
$412$	18.5174	0.912287
$413$	3.70984	0.182549
$414$	3.86172	0.189793
$415$	−1.49832	−0.0735499
$416$	0	0
$417$	6.78513	0.332269
$418$	37.1093	1.81508
$419$	15.8430	0.773980	0.386990	−	0.922084i	$-0.373515\pi$
$419$	15.8430	0.773980	0.386990	+	0.922084i	$0.373515\pi$
$420$	3.93408	0.191963
$421$	29.5123	1.43834	0.719170	−	0.694834i	$-0.244522\pi$
$421$	29.5123	1.43834	0.719170	+	0.694834i	$0.244522\pi$
$422$	18.5638	0.903673
$423$	−10.4986	−0.510461
$424$	10.5944	0.514509
$425$	−37.8582	−1.83639
$426$	−8.73053	−0.422995
$427$	11.8947	0.575627
$428$	−18.9523	−0.916095
$429$	0	0
$430$	18.6474	0.899256
$431$	−25.2998	−1.21865	−0.609324	−	0.792921i	$-0.708559\pi$
$431$	−25.2998	−1.21865	−0.609324	+	0.792921i	$0.708559\pi$
$432$	−1.00000	−0.0481125
$433$	−18.5267	−0.890334	−0.445167	−	0.895448i	$-0.646856\pi$
$433$	−18.5267	−0.890334	−0.445167	+	0.895448i	$0.646856\pi$
$434$	1.01880	0.0489038
$435$	17.5124	0.839657
$436$	−13.0695	−0.625918
$437$	29.7838	1.42475
$438$	−15.7564	−0.752868
$439$	9.04946	0.431907	0.215954	−	0.976404i	$-0.430714\pi$
$439$	9.04946	0.431907	0.215954	+	0.976404i	$0.430714\pi$
$440$	−18.9289	−0.902402
$441$	1.00000	0.0476190
$442$	0	0
$443$	19.9039	0.945662	0.472831	−	0.881153i	$-0.343232\pi$
$443$	19.9039	0.945662	0.472831	+	0.881153i	$0.343232\pi$
$444$	−7.30140	−0.346509
$445$	1.84837	0.0876212
$446$	18.0768	0.855960
$447$	19.2424	0.910134
$448$	−1.00000	−0.0472456
$449$	−2.84944	−0.134474	−0.0672368	−	0.997737i	$-0.521418\pi$
$449$	−2.84944	−0.134474	−0.0672368	+	0.997737i	$0.521418\pi$
$450$	−10.4770	−0.493888
$451$	35.0569	1.65076
$452$	0.383319	0.0180298
$453$	−6.95569	−0.326807
$454$	4.25355	0.199629
$455$	0	0
$456$	−7.71258	−0.361174
$457$	22.6889	1.06134	0.530671	−	0.847578i	$-0.321940\pi$
$457$	22.6889	1.06134	0.530671	+	0.847578i	$0.321940\pi$
$458$	−16.2898	−0.761170
$459$	3.61347	0.168663
$460$	−15.1923	−0.708345
$461$	9.94245	0.463066	0.231533	−	0.972827i	$-0.425626\pi$
$461$	9.94245	0.463066	0.231533	+	0.972827i	$0.425626\pi$
$462$	−4.81154	−0.223853
$463$	−22.5357	−1.04732	−0.523662	−	0.851926i	$-0.675435\pi$
$463$	−22.5357	−1.04732	−0.523662	+	0.851926i	$0.675435\pi$
$464$	−4.45147	−0.206654
$465$	−4.00802	−0.185868
$466$	−10.5462	−0.488543
$467$	−21.7935	−1.00849	−0.504243	−	0.863562i	$-0.668228\pi$
$467$	−21.7935	−1.00849	−0.504243	+	0.863562i	$0.668228\pi$
$468$	0	0
$469$	3.12611	0.144350
$470$	41.3024	1.90514
$471$	−1.09347	−0.0503846
$472$	3.70984	0.170759
$473$	−22.8065	−1.04864
$474$	−0.731774	−0.0336115
$475$	−80.8043	−3.70755
$476$	3.61347	0.165623
$477$	−10.5944	−0.485084
$478$	−15.8572	−0.725290
$479$	37.7401	1.72439	0.862195	−	0.506577i	$-0.169089\pi$
$479$	37.7401	1.72439	0.862195	+	0.506577i	$0.169089\pi$
$480$	3.93408	0.179565
$481$	0	0
$482$	−15.5235	−0.707076
$483$	−3.86172	−0.175714
$484$	12.1509	0.552313
$485$	44.7175	2.03052
$486$	1.00000	0.0453609
$487$	−2.57450	−0.116662	−0.0583308	−	0.998297i	$-0.518578\pi$
$487$	−2.57450	−0.116662	−0.0583308	+	0.998297i	$0.518578\pi$
$488$	11.8947	0.538449
$489$	17.2244	0.778912
$490$	−3.93408	−0.177723
$491$	−12.5532	−0.566519	−0.283259	−	0.959043i	$-0.591416\pi$
$491$	−12.5532	−0.566519	−0.283259	+	0.959043i	$0.591416\pi$
$492$	−7.28601	−0.328479
$493$	16.0853	0.724445
$494$	0	0
$495$	18.9289	0.850793
$496$	1.01880	0.0457453
$497$	8.73053	0.391618
$498$	−0.380858	−0.0170667
$499$	−3.79738	−0.169994	−0.0849970	−	0.996381i	$-0.527088\pi$
$499$	−3.79738	−0.169994	−0.0849970	+	0.996381i	$0.527088\pi$
$500$	21.5467	0.963600
$501$	21.5911	0.964619
$502$	−7.93745	−0.354266
$503$	34.5483	1.54043	0.770216	−	0.637784i	$-0.220149\pi$
$503$	34.5483	1.54043	0.770216	+	0.637784i	$0.220149\pi$
$504$	1.00000	0.0445435
$505$	9.59475	0.426961
$506$	18.5808	0.826018
$507$	0	0
$508$	−8.48244	−0.376347
$509$	−34.6920	−1.53770	−0.768849	−	0.639431i	$-0.779170\pi$
$509$	−34.6920	−1.53770	−0.768849	+	0.639431i	$0.779170\pi$
$510$	−14.2157	−0.629481
$511$	15.7564	0.697021
$512$	−1.00000	−0.0441942
$513$	7.71258	0.340519
$514$	−15.3365	−0.676464
$515$	72.8489	3.21011
$516$	4.73996	0.208665
$517$	−50.5146	−2.22163
$518$	7.30140	0.320805
$519$	−23.4276	−1.02836
$520$	0	0
$521$	−10.5590	−0.462599	−0.231300	−	0.972883i	$-0.574298\pi$
$521$	−10.5590	−0.462599	−0.231300	+	0.972883i	$0.574298\pi$
$522$	4.45147	0.194836
$523$	−22.6374	−0.989864	−0.494932	−	0.868932i	$-0.664807\pi$
$523$	−22.6374	−0.989864	−0.494932	+	0.868932i	$0.664807\pi$
$524$	10.1450	0.443186
$525$	10.4770	0.457252
$526$	−14.6702	−0.639652
$527$	−3.68139	−0.160364
$528$	−4.81154	−0.209395
$529$	−8.08712	−0.351614
$530$	41.6791	1.81043
$531$	−3.70984	−0.160993
$532$	7.71258	0.334383
$533$	0	0
$534$	0.469836	0.0203318
$535$	−74.5599	−3.22350
$536$	3.12611	0.135027
$537$	−3.15190	−0.136014
$538$	−13.0947	−0.564551
$539$	4.81154	0.207248
$540$	−3.93408	−0.169296
$541$	1.92266	0.0826618	0.0413309	−	0.999146i	$-0.486840\pi$
$541$	1.92266	0.0826618	0.0413309	+	0.999146i	$0.486840\pi$
$542$	−10.8665	−0.466755
$543$	−1.49375	−0.0641029
$544$	3.61347	0.154926
$545$	−51.4166	−2.20244
$546$	0	0
$547$	−23.5913	−1.00869	−0.504346	−	0.863502i	$-0.668266\pi$
$547$	−23.5913	−1.00869	−0.504346	+	0.863502i	$0.668266\pi$
$548$	−1.73976	−0.0743189
$549$	−11.8947	−0.507655
$550$	−50.4102	−2.14950
$551$	34.3323	1.46261
$552$	−3.86172	−0.164366
$553$	0.731774	0.0311182
$554$	−22.9560	−0.975306
$555$	−28.7243	−1.21928
$556$	−6.78513	−0.287754
$557$	−37.2227	−1.57718	−0.788589	−	0.614921i	$-0.789188\pi$
$557$	−37.2227	−1.57718	−0.788589	+	0.614921i	$0.789188\pi$
$558$	−1.01880	−0.0431291
$559$	0	0
$560$	−3.93408	−0.166245
$561$	17.3864	0.734053
$562$	−9.42525	−0.397580
$563$	35.3321	1.48907	0.744535	−	0.667583i	$-0.232671\pi$
$563$	35.3321	1.48907	0.744535	+	0.667583i	$0.232671\pi$
$564$	10.4986	0.442072
$565$	1.50801	0.0634423
$566$	19.1238	0.803833
$567$	−1.00000	−0.0419961
$568$	8.73053	0.366325
$569$	−42.5755	−1.78486	−0.892430	−	0.451186i	$-0.851001\pi$
$569$	−42.5755	−1.78486	−0.892430	+	0.451186i	$0.851001\pi$
$570$	−30.3419	−1.27088
$571$	31.7267	1.32772	0.663861	−	0.747856i	$-0.268917\pi$
$571$	31.7267	1.32772	0.663861	+	0.747856i	$0.268917\pi$
$572$	0	0
$573$	−3.19802	−0.133599
$574$	7.28601	0.304112
$575$	−40.4591	−1.68726
$576$	1.00000	0.0416667
$577$	−30.9593	−1.28885	−0.644427	−	0.764666i	$-0.722904\pi$
$577$	−30.9593	−1.28885	−0.644427	+	0.764666i	$0.722904\pi$
$578$	3.94280	0.163999
$579$	3.88466	0.161441
$580$	−17.5124	−0.727164
$581$	0.380858	0.0158007
$582$	11.3667	0.471165
$583$	−50.9753	−2.11118
$584$	15.7564	0.652003
$585$	0	0
$586$	−19.6143	−0.810259
$587$	−1.79841	−0.0742282	−0.0371141	−	0.999311i	$-0.511817\pi$
$587$	−1.79841	−0.0742282	−0.0371141	+	0.999311i	$0.511817\pi$
$588$	−1.00000	−0.0412393
$589$	−7.85754	−0.323764
$590$	14.5948	0.600858
$591$	11.9583	0.491899
$592$	7.30140	0.300086
$593$	−28.6678	−1.17725	−0.588624	−	0.808407i	$-0.700330\pi$
$593$	−28.6678	−1.17725	−0.588624	+	0.808407i	$0.700330\pi$
$594$	4.81154	0.197420
$595$	14.2157	0.582786
$596$	−19.2424	−0.788199
$597$	−25.6975	−1.05173
$598$	0	0
$599$	7.13836	0.291665	0.145833	−	0.989309i	$-0.453414\pi$
$599$	7.13836	0.291665	0.145833	+	0.989309i	$0.453414\pi$
$600$	10.4770	0.427720
$601$	26.6183	1.08579	0.542893	−	0.839802i	$-0.317329\pi$
$601$	26.6183	1.08579	0.542893	+	0.839802i	$0.317329\pi$
$602$	−4.73996	−0.193186
$603$	−3.12611	−0.127305
$604$	6.95569	0.283023
$605$	47.8025	1.94345
$606$	2.43888	0.0990728
$607$	−45.6948	−1.85470	−0.927348	−	0.374200i	$-0.877917\pi$
$607$	−45.6948	−1.85470	−0.927348	+	0.374200i	$0.877917\pi$
$608$	7.71258	0.312786
$609$	−4.45147	−0.180383
$610$	46.7948	1.89467
$611$	0	0
$612$	−3.61347	−0.146066
$613$	−11.7581	−0.474904	−0.237452	−	0.971399i	$-0.576312\pi$
$613$	−11.7581	−0.474904	−0.237452	+	0.971399i	$0.576312\pi$
$614$	6.84964	0.276429
$615$	−28.6637	−1.15583
$616$	4.81154	0.193862
$617$	45.6887	1.83936	0.919678	−	0.392672i	$-0.128449\pi$
$617$	45.6887	1.83936	0.919678	+	0.392672i	$0.128449\pi$
$618$	18.5174	0.744879
$619$	22.5395	0.905937	0.452969	−	0.891526i	$-0.350365\pi$
$619$	22.5395	0.905937	0.452969	+	0.891526i	$0.350365\pi$
$620$	4.00802	0.160966
$621$	3.86172	0.154965
$622$	−11.1603	−0.447488
$623$	−0.469836	−0.0188236
$624$	0	0
$625$	32.3818	1.29527
$626$	−13.7636	−0.550105
$627$	37.1093	1.48200
$628$	1.09347	0.0436343
$629$	−26.3834	−1.05198
$630$	3.93408	0.156737
$631$	−12.7494	−0.507544	−0.253772	−	0.967264i	$-0.581671\pi$
$631$	−12.7494	−0.507544	−0.253772	+	0.967264i	$0.581671\pi$
$632$	0.731774	0.0291084
$633$	18.5638	0.737846
$634$	1.05913	0.0420635
$635$	−33.3706	−1.32427
$636$	10.5944	0.420095
$637$	0	0
$638$	21.4184	0.847964
$639$	−8.73053	−0.345374
$640$	−3.93408	−0.155508
$641$	9.79264	0.386786	0.193393	−	0.981121i	$-0.438051\pi$
$641$	9.79264	0.386786	0.193393	+	0.981121i	$0.438051\pi$
$642$	−18.9523	−0.747989
$643$	31.5951	1.24599	0.622995	−	0.782226i	$-0.285916\pi$
$643$	31.5951	1.24599	0.622995	+	0.782226i	$0.285916\pi$
$644$	3.86172	0.152173
$645$	18.6474	0.734240
$646$	−27.8692	−1.09650
$647$	6.07753	0.238932	0.119466	−	0.992838i	$-0.461882\pi$
$647$	6.07753	0.238932	0.119466	+	0.992838i	$0.461882\pi$
$648$	−1.00000	−0.0392837
$649$	−17.8500	−0.700675
$650$	0	0
$651$	1.01880	0.0399298
$652$	−17.2244	−0.674558
$653$	10.6316	0.416048	0.208024	−	0.978124i	$-0.433297\pi$
$653$	10.6316	0.416048	0.208024	+	0.978124i	$0.433297\pi$
$654$	−13.0695	−0.511060
$655$	39.9112	1.55946
$656$	7.28601	0.284471
$657$	−15.7564	−0.614714
$658$	−10.4986	−0.409279
$659$	−34.0689	−1.32714	−0.663568	−	0.748116i	$-0.730959\pi$
$659$	−34.0689	−1.32714	−0.663568	+	0.748116i	$0.730959\pi$
$660$	−18.9289	−0.736808
$661$	10.8620	0.422484	0.211242	−	0.977434i	$-0.432249\pi$
$661$	10.8620	0.422484	0.211242	+	0.977434i	$0.432249\pi$
$662$	−2.59428	−0.100829
$663$	0	0
$664$	0.380858	0.0147802
$665$	30.3419	1.17661
$666$	−7.30140	−0.282924
$667$	17.1903	0.665613
$668$	−21.5911	−0.835384
$669$	18.0768	0.698888
$670$	12.2983	0.475127
$671$	−57.2320	−2.20942
$672$	−1.00000	−0.0385758
$673$	44.8669	1.72949	0.864747	−	0.502208i	$-0.167479\pi$
$673$	44.8669	1.72949	0.864747	+	0.502208i	$0.167479\pi$
$674$	18.0032	0.693457
$675$	−10.4770	−0.403258
$676$	0	0
$677$	39.6948	1.52560	0.762798	−	0.646637i	$-0.223825\pi$
$677$	39.6948	1.52560	0.762798	+	0.646637i	$0.223825\pi$
$678$	0.383319	0.0147213
$679$	−11.3667	−0.436214
$680$	14.2157	0.545147
$681$	4.25355	0.162996
$682$	−4.90197	−0.187706
$683$	−36.7583	−1.40652	−0.703258	−	0.710935i	$-0.748272\pi$
$683$	−36.7583	−1.40652	−0.703258	+	0.710935i	$0.748272\pi$
$684$	−7.71258	−0.294898
$685$	−6.84435	−0.261509
$686$	1.00000	0.0381802
$687$	−16.2898	−0.621493
$688$	−4.73996	−0.180709
$689$	0	0
$690$	−15.1923	−0.578361
$691$	−20.0634	−0.763250	−0.381625	−	0.924317i	$-0.624635\pi$
$691$	−20.0634	−0.763250	−0.381625	+	0.924317i	$0.624635\pi$
$692$	23.4276	0.890584
$693$	−4.81154	−0.182775
$694$	−32.2122	−1.22276
$695$	−26.6932	−1.01253
$696$	−4.45147	−0.168733
$697$	−26.3278	−0.997237
$698$	26.9689	1.02079
$699$	−10.5462	−0.398894
$700$	−10.4770	−0.395992
$701$	38.1795	1.44202	0.721010	−	0.692925i	$-0.243678\pi$
$701$	38.1795	1.44202	0.721010	+	0.692925i	$0.243678\pi$
$702$	0	0
$703$	−56.3126	−2.12387
$704$	4.81154	0.181342
$705$	41.3024	1.55554
$706$	−15.0234	−0.565412
$707$	−2.43888	−0.0917236
$708$	3.70984	0.139424
$709$	−28.4246	−1.06751	−0.533753	−	0.845640i	$-0.679219\pi$
$709$	−28.4246	−1.06751	−0.533753	+	0.845640i	$0.679219\pi$
$710$	34.3465	1.28900
$711$	−0.731774	−0.0274437
$712$	−0.469836	−0.0176079
$713$	−3.93431	−0.147341
$714$	3.61347	0.135231
$715$	0	0
$716$	3.15190	0.117792
$717$	−15.8572	−0.592196
$718$	−0.187328	−0.00699101
$719$	−2.84829	−0.106223	−0.0531116	−	0.998589i	$-0.516914\pi$
$719$	−2.84829	−0.106223	−0.0531116	+	0.998589i	$0.516914\pi$
$720$	3.93408	0.146614
$721$	−18.5174	−0.689624
$722$	−40.4838	−1.50665
$723$	−15.5235	−0.577325
$724$	1.49375	0.0555147
$725$	−46.6379	−1.73209
$726$	12.1509	0.450962
$727$	−21.5949	−0.800912	−0.400456	−	0.916316i	$-0.631148\pi$
$727$	−21.5949	−0.800912	−0.400456	+	0.916316i	$0.631148\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	61.9867	2.29423
$731$	17.1277	0.633492
$732$	11.8947	0.439642
$733$	25.3980	0.938097	0.469048	−	0.883173i	$-0.344597\pi$
$733$	25.3980	0.938097	0.469048	+	0.883173i	$0.344597\pi$
$734$	15.6194	0.576521
$735$	−3.93408	−0.145111
$736$	3.86172	0.142345
$737$	−15.0414	−0.554057
$738$	−7.28601	−0.268202
$739$	−23.4637	−0.863125	−0.431563	−	0.902083i	$-0.642038\pi$
$739$	−23.4637	−0.863125	−0.431563	+	0.902083i	$0.642038\pi$
$740$	28.7243	1.05593
$741$	0	0
$742$	−10.5944	−0.388932
$743$	−12.2641	−0.449928	−0.224964	−	0.974367i	$-0.572226\pi$
$743$	−12.2641	−0.449928	−0.224964	+	0.974367i	$0.572226\pi$
$744$	1.01880	0.0373509
$745$	−75.7010	−2.77347
$746$	35.0244	1.28234
$747$	−0.380858	−0.0139349
$748$	−17.3864	−0.635708
$749$	18.9523	0.692503
$750$	21.5467	0.786776
$751$	15.1978	0.554574	0.277287	−	0.960787i	$-0.410565\pi$
$751$	15.1978	0.554574	0.277287	+	0.960787i	$0.410565\pi$
$752$	−10.4986	−0.382846
$753$	−7.93745	−0.289257
$754$	0	0
$755$	27.3642	0.995886
$756$	1.00000	0.0363696
$757$	1.47834	0.0537311	0.0268655	−	0.999639i	$-0.491447\pi$
$757$	1.47834	0.0537311	0.0268655	+	0.999639i	$0.491447\pi$
$758$	7.86687	0.285738
$759$	18.5808	0.674441
$760$	30.3419	1.10061
$761$	7.59688	0.275387	0.137693	−	0.990475i	$-0.456031\pi$
$761$	7.59688	0.275387	0.137693	+	0.990475i	$0.456031\pi$
$762$	−8.48244	−0.307286
$763$	13.0695	0.473149
$764$	3.19802	0.115700
$765$	−14.2157	−0.513969
$766$	25.0867	0.906419
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	−10.2870	−0.370958	−0.185479	−	0.982648i	$-0.559384\pi$
$769$	−10.2870	−0.370958	−0.185479	+	0.982648i	$0.559384\pi$
$770$	18.9289	0.682152
$771$	−15.3365	−0.552331
$772$	−3.88466	−0.139812
$773$	−11.5082	−0.413922	−0.206961	−	0.978349i	$-0.566357\pi$
$773$	−11.5082	−0.413922	−0.206961	+	0.978349i	$0.566357\pi$
$774$	4.73996	0.170374
$775$	10.6739	0.383417
$776$	−11.3667	−0.408041
$777$	7.30140	0.261936
$778$	10.1352	0.363366
$779$	−56.1939	−2.01335
$780$	0	0
$781$	−42.0072	−1.50314
$782$	−13.9542	−0.499002
$783$	4.45147	0.159083
$784$	1.00000	0.0357143
$785$	4.30181	0.153538
$786$	10.1450	0.361860
$787$	−17.9919	−0.641341	−0.320670	−	0.947191i	$-0.603908\pi$
$787$	−17.9919	−0.641341	−0.320670	+	0.947191i	$0.603908\pi$
$788$	−11.9583	−0.425997
$789$	−14.6702	−0.522274
$790$	2.87885	0.102425
$791$	−0.383319	−0.0136293
$792$	−4.81154	−0.170971
$793$	0	0
$794$	−12.0921	−0.429132
$795$	41.6791	1.47821
$796$	25.6975	0.910823
$797$	−33.6262	−1.19110	−0.595551	−	0.803318i	$-0.703066\pi$
$797$	−33.6262	−1.19110	−0.595551	+	0.803318i	$0.703066\pi$
$798$	7.71258	0.273022
$799$	37.9365	1.34210
$800$	−10.4770	−0.370416
$801$	0.469836	0.0166008
$802$	0.593140	0.0209445
$803$	−75.8123	−2.67536
$804$	3.12611	0.110249
$805$	15.1923	0.535458
$806$	0	0
$807$	−13.0947	−0.460954
$808$	−2.43888	−0.0857996
$809$	−39.5694	−1.39119	−0.695594	−	0.718435i	$-0.744859\pi$
$809$	−39.5694	−1.39119	−0.695594	+	0.718435i	$0.744859\pi$
$810$	−3.93408	−0.138229
$811$	13.7186	0.481725	0.240863	−	0.970559i	$-0.422570\pi$
$811$	13.7186	0.481725	0.240863	+	0.970559i	$0.422570\pi$
$812$	4.45147	0.156216
$813$	−10.8665	−0.381104
$814$	−35.1310	−1.23134
$815$	−67.7619	−2.37360
$816$	3.61347	0.126497
$817$	36.5573	1.27898
$818$	12.2539	0.428449
$819$	0	0
$820$	28.6637	1.00098
$821$	5.77385	0.201509	0.100754	−	0.994911i	$-0.467874\pi$
$821$	5.77385	0.201509	0.100754	+	0.994911i	$0.467874\pi$
$822$	−1.73976	−0.0606811
$823$	−12.6373	−0.440507	−0.220253	−	0.975443i	$-0.570688\pi$
$823$	−12.6373	−0.440507	−0.220253	+	0.975443i	$0.570688\pi$
$824$	−18.5174	−0.645084
$825$	−50.4102	−1.75506
$826$	−3.70984	−0.129082
$827$	1.59504	0.0554649	0.0277325	−	0.999615i	$-0.491171\pi$
$827$	1.59504	0.0554649	0.0277325	+	0.999615i	$0.491171\pi$
$828$	−3.86172	−0.134204
$829$	22.1618	0.769713	0.384856	−	0.922976i	$-0.374251\pi$
$829$	22.1618	0.769713	0.384856	+	0.922976i	$0.374251\pi$
$830$	1.49832	0.0520076
$831$	−22.9560	−0.796334
$832$	0	0
$833$	−3.61347	−0.125199
$834$	−6.78513	−0.234950
$835$	−84.9410	−2.93950
$836$	−37.1093	−1.28345
$837$	−1.01880	−0.0352147
$838$	−15.8430	−0.547286
$839$	−4.11002	−0.141894	−0.0709468	−	0.997480i	$-0.522602\pi$
$839$	−4.11002	−0.141894	−0.0709468	+	0.997480i	$0.522602\pi$
$840$	−3.93408	−0.135739
$841$	−9.18439	−0.316703
$842$	−29.5123	−1.01706
$843$	−9.42525	−0.324623
$844$	−18.5638	−0.638993
$845$	0	0
$846$	10.4986	0.360950
$847$	−12.1509	−0.417509
$848$	−10.5944	−0.363813
$849$	19.1238	0.656327
$850$	37.8582	1.29853
$851$	−28.1960	−0.966546
$852$	8.73053	0.299103
$853$	−26.3560	−0.902412	−0.451206	−	0.892420i	$-0.649006\pi$
$853$	−26.3560	−0.902412	−0.451206	+	0.892420i	$0.649006\pi$
$854$	−11.8947	−0.407029
$855$	−30.3419	−1.03767
$856$	18.9523	0.647777
$857$	6.47039	0.221024	0.110512	−	0.993875i	$-0.464751\pi$
$857$	6.47039	0.221024	0.110512	+	0.993875i	$0.464751\pi$
$858$	0	0
$859$	−36.4673	−1.24425	−0.622125	−	0.782918i	$-0.713730\pi$
$859$	−36.4673	−1.24425	−0.622125	+	0.782918i	$0.713730\pi$
$860$	−18.6474	−0.635870
$861$	7.28601	0.248306
$862$	25.2998	0.861714
$863$	−50.9368	−1.73391	−0.866954	−	0.498389i	$-0.833925\pi$
$863$	−50.9368	−1.73391	−0.866954	+	0.498389i	$0.833925\pi$
$864$	1.00000	0.0340207
$865$	92.1660	3.13374
$866$	18.5267	0.629561
$867$	3.94280	0.133905
$868$	−1.01880	−0.0345802
$869$	−3.52096	−0.119440
$870$	−17.5124	−0.593727
$871$	0	0
$872$	13.0695	0.442591
$873$	11.3667	0.384705
$874$	−29.7838	−1.00745
$875$	−21.5467	−0.728413
$876$	15.7564	0.532358
$877$	33.5197	1.13188	0.565940	−	0.824446i	$-0.308513\pi$
$877$	33.5197	1.13188	0.565940	+	0.824446i	$0.308513\pi$
$878$	−9.04946	−0.305404
$879$	−19.6143	−0.661574
$880$	18.9289	0.638095
$881$	−21.3685	−0.719924	−0.359962	−	0.932967i	$-0.617210\pi$
$881$	−21.3685	−0.719924	−0.359962	+	0.932967i	$0.617210\pi$
$882$	−1.00000	−0.0336718
$883$	−27.9621	−0.941000	−0.470500	−	0.882400i	$-0.655926\pi$
$883$	−27.9621	−0.941000	−0.470500	+	0.882400i	$0.655926\pi$
$884$	0	0
$885$	14.5948	0.490599
$886$	−19.9039	−0.668684
$887$	−25.2726	−0.848572	−0.424286	−	0.905528i	$-0.639475\pi$
$887$	−25.2726	−0.848572	−0.424286	+	0.905528i	$0.639475\pi$
$888$	7.30140	0.245019
$889$	8.48244	0.284492
$890$	−1.84837	−0.0619576
$891$	4.81154	0.161193
$892$	−18.0768	−0.605255
$893$	80.9715	2.70961
$894$	−19.2424	−0.643562
$895$	12.3998	0.414479
$896$	1.00000	0.0334077
$897$	0	0
$898$	2.84944	0.0950871
$899$	−4.53514	−0.151255
$900$	10.4770	0.349232
$901$	38.2825	1.27538
$902$	−35.0569	−1.16727
$903$	−4.73996	−0.157736
$904$	−0.383319	−0.0127490
$905$	5.87652	0.195342
$906$	6.95569	0.231087
$907$	−45.8740	−1.52322	−0.761611	−	0.648034i	$-0.775591\pi$
$907$	−45.8740	−1.52322	−0.761611	+	0.648034i	$0.775591\pi$
$908$	−4.25355	−0.141159
$909$	2.43888	0.0808926
$910$	0	0
$911$	23.5865	0.781454	0.390727	−	0.920507i	$-0.372224\pi$
$911$	23.5865	0.781454	0.390727	+	0.920507i	$0.372224\pi$
$912$	7.71258	0.255389
$913$	−1.83251	−0.0606473
$914$	−22.6889	−0.750482
$915$	46.7948	1.54699
$916$	16.2898	0.538229
$917$	−10.1450	−0.335017
$918$	−3.61347	−0.119262
$919$	−17.3816	−0.573365	−0.286682	−	0.958026i	$-0.592552\pi$
$919$	−17.3816	−0.573365	−0.286682	+	0.958026i	$0.592552\pi$
$920$	15.1923	0.500875
$921$	6.84964	0.225703
$922$	−9.94245	−0.327437
$923$	0	0
$924$	4.81154	0.158288
$925$	76.4964	2.51519
$926$	22.5357	0.740570
$927$	18.5174	0.608191
$928$	4.45147	0.146127
$929$	−28.1143	−0.922401	−0.461200	−	0.887296i	$-0.652581\pi$
$929$	−28.1143	−0.922401	−0.461200	+	0.887296i	$0.652581\pi$
$930$	4.00802	0.131428
$931$	−7.71258	−0.252769
$932$	10.5462	0.345452
$933$	−11.1603	−0.365372
$934$	21.7935	0.713107
$935$	−68.3993	−2.23690
$936$	0	0
$937$	−4.39725	−0.143652	−0.0718260	−	0.997417i	$-0.522883\pi$
$937$	−4.39725	−0.143652	−0.0718260	+	0.997417i	$0.522883\pi$
$938$	−3.12611	−0.102071
$939$	−13.7636	−0.449159
$940$	−41.3024	−1.34714
$941$	−22.4304	−0.731209	−0.365604	−	0.930770i	$-0.619138\pi$
$941$	−22.4304	−0.731209	−0.365604	+	0.930770i	$0.619138\pi$
$942$	1.09347	0.0356273
$943$	−28.1365	−0.916251
$944$	−3.70984	−0.120745
$945$	3.93408	0.127975
$946$	22.8065	0.741503
$947$	57.2579	1.86063	0.930316	−	0.366759i	$-0.119533\pi$
$947$	57.2579	1.86063	0.930316	+	0.366759i	$0.119533\pi$
$948$	0.731774	0.0237669
$949$	0	0
$950$	80.8043	2.62164
$951$	1.05913	0.0343447
$952$	−3.61347	−0.117113
$953$	−12.2786	−0.397744	−0.198872	−	0.980025i	$-0.563728\pi$
$953$	−12.2786	−0.397744	−0.198872	+	0.980025i	$0.563728\pi$
$954$	10.5944	0.343006
$955$	12.5813	0.407120
$956$	15.8572	0.512857
$957$	21.4184	0.692359
$958$	−37.7401	−1.21933
$959$	1.73976	0.0561798
$960$	−3.93408	−0.126972
$961$	−29.9621	−0.966518
$962$	0	0
$963$	−18.9523	−0.610730
$964$	15.5235	0.499979
$965$	−15.2825	−0.491962
$966$	3.86172	0.124249
$967$	11.7694	0.378477	0.189238	−	0.981931i	$-0.439398\pi$
$967$	11.7694	0.378477	0.189238	+	0.981931i	$0.439398\pi$
$968$	−12.1509	−0.390544
$969$	−27.8692	−0.895287
$970$	−44.7175	−1.43579
$971$	−37.3432	−1.19840	−0.599200	−	0.800600i	$-0.704514\pi$
$971$	−37.3432	−1.19840	−0.599200	+	0.800600i	$0.704514\pi$
$972$	−1.00000	−0.0320750
$973$	6.78513	0.217521
$974$	2.57450	0.0824922
$975$	0	0
$976$	−11.8947	−0.380741
$977$	−47.1492	−1.50844	−0.754218	−	0.656625i	$-0.771984\pi$
$977$	−47.1492	−1.50844	−0.754218	+	0.656625i	$0.771984\pi$
$978$	−17.2244	−0.550774
$979$	2.26063	0.0722502
$980$	3.93408	0.125669
$981$	−13.0695	−0.417278
$982$	12.5532	0.400589
$983$	24.3817	0.777654	0.388827	−	0.921311i	$-0.372880\pi$
$983$	24.3817	0.777654	0.388827	+	0.921311i	$0.372880\pi$
$984$	7.28601	0.232269
$985$	−47.0449	−1.49897
$986$	−16.0853	−0.512260
$987$	−10.4986	−0.334175
$988$	0	0
$989$	18.3044	0.582046
$990$	−18.9289	−0.601602
$991$	−28.4168	−0.902688	−0.451344	−	0.892350i	$-0.649055\pi$
$991$	−28.4168	−0.902688	−0.451344	+	0.892350i	$0.649055\pi$
$992$	−1.01880	−0.0323468
$993$	−2.59428	−0.0823269
$994$	−8.73053	−0.276915
$995$	101.096	3.20495
$996$	0.380858	0.0120680
$997$	−9.94278	−0.314891	−0.157445	−	0.987528i	$-0.550326\pi$
$997$	−9.94278	−0.314891	−0.157445	+	0.987528i	$0.550326\pi$
$998$	3.79738	0.120204
$999$	−7.30140	−0.231006

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.cp.1.6	✓	6
13.12	even	2		7098.2.a.cs.1.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7098.2.a.cp.1.6	✓	6	1.1	even	1	trivial
7098.2.a.cs.1.1	yes	6	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.93408 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.93408 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.93408 q^{10} +4.81154 q^{11} -1.00000 q^{12} +1.00000 q^{14} -3.93408 q^{15} +1.00000 q^{16} -3.61347 q^{17} -1.00000 q^{18} -7.71258 q^{19} +3.93408 q^{20} +1.00000 q^{21} -4.81154 q^{22} -3.86172 q^{23} +1.00000 q^{24} +10.4770 q^{25} -1.00000 q^{27} -1.00000 q^{28} -4.45147 q^{29} +3.93408 q^{30} +1.01880 q^{31} -1.00000 q^{32} -4.81154 q^{33} +3.61347 q^{34} -3.93408 q^{35} +1.00000 q^{36} +7.30140 q^{37} +7.71258 q^{38} -3.93408 q^{40} +7.28601 q^{41} -1.00000 q^{42} -4.73996 q^{43} +4.81154 q^{44} +3.93408 q^{45} +3.86172 q^{46} -10.4986 q^{47} -1.00000 q^{48} +1.00000 q^{49} -10.4770 q^{50} +3.61347 q^{51} -10.5944 q^{53} +1.00000 q^{54} +18.9289 q^{55} +1.00000 q^{56} +7.71258 q^{57} +4.45147 q^{58} -3.70984 q^{59} -3.93408 q^{60} -11.8947 q^{61} -1.01880 q^{62} -1.00000 q^{63} +1.00000 q^{64} +4.81154 q^{66} -3.12611 q^{67} -3.61347 q^{68} +3.86172 q^{69} +3.93408 q^{70} -8.73053 q^{71} -1.00000 q^{72} -15.7564 q^{73} -7.30140 q^{74} -10.4770 q^{75} -7.71258 q^{76} -4.81154 q^{77} -0.731774 q^{79} +3.93408 q^{80} +1.00000 q^{81} -7.28601 q^{82} -0.380858 q^{83} +1.00000 q^{84} -14.2157 q^{85} +4.73996 q^{86} +4.45147 q^{87} -4.81154 q^{88} +0.469836 q^{89} -3.93408 q^{90} -3.86172 q^{92} -1.01880 q^{93} +10.4986 q^{94} -30.3419 q^{95} +1.00000 q^{96} +11.3667 q^{97} -1.00000 q^{98} +4.81154 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} + 3 q^{5} + 6 q^{6} - 6 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 + 3 * q^5 + 6 * q^6 - 6 * q^7 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} + 3 q^{5} + 6 q^{6} - 6 q^{7} - 6 q^{8} + 6 q^{9} - 3 q^{10} + 6 q^{11} - 6 q^{12} + 6 q^{14} - 3 q^{15} + 6 q^{16} + 10 q^{17} - 6 q^{18} - 8 q^{19} + 3 q^{20} + 6 q^{21} - 6 q^{22} - 12 q^{23} + 6 q^{24} + 5 q^{25} - 6 q^{27} - 6 q^{28} + 4 q^{29} + 3 q^{30} - 7 q^{31} - 6 q^{32} - 6 q^{33} - 10 q^{34} - 3 q^{35} + 6 q^{36} - 3 q^{37} + 8 q^{38} - 3 q^{40} - 3 q^{41} - 6 q^{42} - 3 q^{43} + 6 q^{44} + 3 q^{45} + 12 q^{46} - 29 q^{47} - 6 q^{48} + 6 q^{49} - 5 q^{50} - 10 q^{51} - 12 q^{53} + 6 q^{54} + 29 q^{55} + 6 q^{56} + 8 q^{57} - 4 q^{58} - 2 q^{59} - 3 q^{60} + 13 q^{61} + 7 q^{62} - 6 q^{63} + 6 q^{64} + 6 q^{66} - 22 q^{67} + 10 q^{68} + 12 q^{69} + 3 q^{70} - q^{71} - 6 q^{72} - 29 q^{73} + 3 q^{74} - 5 q^{75} - 8 q^{76} - 6 q^{77} - 24 q^{79} + 3 q^{80} + 6 q^{81} + 3 q^{82} - 7 q^{83} + 6 q^{84} - 21 q^{85} + 3 q^{86} - 4 q^{87} - 6 q^{88} + 11 q^{89} - 3 q^{90} - 12 q^{92} + 7 q^{93} + 29 q^{94} + 8 q^{95} + 6 q^{96} + 4 q^{97} - 6 q^{98} + 6 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 + 3 * q^5 + 6 * q^6 - 6 * q^7 - 6 * q^8 + 6 * q^9 - 3 * q^10 + 6 * q^11 - 6 * q^12 + 6 * q^14 - 3 * q^15 + 6 * q^16 + 10 * q^17 - 6 * q^18 - 8 * q^19 + 3 * q^20 + 6 * q^21 - 6 * q^22 - 12 * q^23 + 6 * q^24 + 5 * q^25 - 6 * q^27 - 6 * q^28 + 4 * q^29 + 3 * q^30 - 7 * q^31 - 6 * q^32 - 6 * q^33 - 10 * q^34 - 3 * q^35 + 6 * q^36 - 3 * q^37 + 8 * q^38 - 3 * q^40 - 3 * q^41 - 6 * q^42 - 3 * q^43 + 6 * q^44 + 3 * q^45 + 12 * q^46 - 29 * q^47 - 6 * q^48 + 6 * q^49 - 5 * q^50 - 10 * q^51 - 12 * q^53 + 6 * q^54 + 29 * q^55 + 6 * q^56 + 8 * q^57 - 4 * q^58 - 2 * q^59 - 3 * q^60 + 13 * q^61 + 7 * q^62 - 6 * q^63 + 6 * q^64 + 6 * q^66 - 22 * q^67 + 10 * q^68 + 12 * q^69 + 3 * q^70 - q^71 - 6 * q^72 - 29 * q^73 + 3 * q^74 - 5 * q^75 - 8 * q^76 - 6 * q^77 - 24 * q^79 + 3 * q^80 + 6 * q^81 + 3 * q^82 - 7 * q^83 + 6 * q^84 - 21 * q^85 + 3 * q^86 - 4 * q^87 - 6 * q^88 + 11 * q^89 - 3 * q^90 - 12 * q^92 + 7 * q^93 + 29 * q^94 + 8 * q^95 + 6 * q^96 + 4 * q^97 - 6 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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