LMFDB - Embedded newform 7098.2.a.cr.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("7098.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$56.6778153547$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.48406561.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 17x^{4} + 39x^{3} + 111x^{2} - 131x - 281 $ x^6 - 3x^5 - 17x^4 + 39x^3 + 111x^2 - 131*x - 281
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.83411$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.83411 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.83411 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.83411 q^{10} -0.198062 q^{11} +1.00000 q^{12} +1.00000 q^{14} +1.83411 q^{15} +1.00000 q^{16} +0.445042 q^{17} -1.00000 q^{18} -1.57281 q^{19} +1.83411 q^{20} -1.00000 q^{21} +0.198062 q^{22} +9.19592 q^{23} -1.00000 q^{24} -1.63605 q^{25} +1.00000 q^{27} -1.00000 q^{28} -9.88794 q^{29} -1.83411 q^{30} -6.88303 q^{31} -1.00000 q^{32} -0.198062 q^{33} -0.445042 q^{34} -1.83411 q^{35} +1.00000 q^{36} -5.13552 q^{37} +1.57281 q^{38} -1.83411 q^{40} -12.1234 q^{41} +1.00000 q^{42} -7.51027 q^{43} -0.198062 q^{44} +1.83411 q^{45} -9.19592 q^{46} +8.51673 q^{47} +1.00000 q^{48} +1.00000 q^{49} +1.63605 q^{50} +0.445042 q^{51} -1.38956 q^{53} -1.00000 q^{54} -0.363268 q^{55} +1.00000 q^{56} -1.57281 q^{57} +9.88794 q^{58} -11.7846 q^{59} +1.83411 q^{60} -10.1849 q^{61} +6.88303 q^{62} -1.00000 q^{63} +1.00000 q^{64} +0.198062 q^{66} -0.307727 q^{67} +0.445042 q^{68} +9.19592 q^{69} +1.83411 q^{70} -13.0597 q^{71} -1.00000 q^{72} +7.90088 q^{73} +5.13552 q^{74} -1.63605 q^{75} -1.57281 q^{76} +0.198062 q^{77} +6.98527 q^{79} +1.83411 q^{80} +1.00000 q^{81} +12.1234 q^{82} -3.19757 q^{83} -1.00000 q^{84} +0.816255 q^{85} +7.51027 q^{86} -9.88794 q^{87} +0.198062 q^{88} +5.55962 q^{89} -1.83411 q^{90} +9.19592 q^{92} -6.88303 q^{93} -8.51673 q^{94} -2.88471 q^{95} -1.00000 q^{96} -4.95178 q^{97} -1.00000 q^{98} -0.198062 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 10 q^{11} + 6 q^{12} + 6 q^{14} - 3 q^{15} + 6 q^{16} + 2 q^{17} - 6 q^{18} - 2 q^{19} - 3 q^{20} - 6 q^{21} + 10 q^{22} + 4 q^{23} - 6 q^{24} + 13 q^{25} + 6 q^{27} - 6 q^{28} + 2 q^{29} + 3 q^{30} - 9 q^{31} - 6 q^{32} - 10 q^{33} - 2 q^{34} + 3 q^{35} + 6 q^{36} - 7 q^{37} + 2 q^{38} + 3 q^{40} - 11 q^{41} + 6 q^{42} - 5 q^{43} - 10 q^{44} - 3 q^{45} - 4 q^{46} - 5 q^{47} + 6 q^{48} + 6 q^{49} - 13 q^{50} + 2 q^{51} - 6 q^{53} - 6 q^{54} + 5 q^{55} + 6 q^{56} - 2 q^{57} - 2 q^{58} - 28 q^{59} - 3 q^{60} + 23 q^{61} + 9 q^{62} - 6 q^{63} + 6 q^{64} + 10 q^{66} + 10 q^{67} + 2 q^{68} + 4 q^{69} - 3 q^{70} - 21 q^{71} - 6 q^{72} + 7 q^{73} + 7 q^{74} + 13 q^{75} - 2 q^{76} + 10 q^{77} - 14 q^{79} - 3 q^{80} + 6 q^{81} + 11 q^{82} - 17 q^{83} - 6 q^{84} - q^{85} + 5 q^{86} + 2 q^{87} + 10 q^{88} - 17 q^{89} + 3 q^{90} + 4 q^{92} - 9 q^{93} + 5 q^{94} - 22 q^{95} - 6 q^{96} - 6 q^{98} - 10 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 - 10 * q^11 + 6 * q^12 + 6 * q^14 - 3 * q^15 + 6 * q^16 + 2 * q^17 - 6 * q^18 - 2 * q^19 - 3 * q^20 - 6 * q^21 + 10 * q^22 + 4 * q^23 - 6 * q^24 + 13 * q^25 + 6 * q^27 - 6 * q^28 + 2 * q^29 + 3 * q^30 - 9 * q^31 - 6 * q^32 - 10 * q^33 - 2 * q^34 + 3 * q^35 + 6 * q^36 - 7 * q^37 + 2 * q^38 + 3 * q^40 - 11 * q^41 + 6 * q^42 - 5 * q^43 - 10 * q^44 - 3 * q^45 - 4 * q^46 - 5 * q^47 + 6 * q^48 + 6 * q^49 - 13 * q^50 + 2 * q^51 - 6 * q^53 - 6 * q^54 + 5 * q^55 + 6 * q^56 - 2 * q^57 - 2 * q^58 - 28 * q^59 - 3 * q^60 + 23 * q^61 + 9 * q^62 - 6 * q^63 + 6 * q^64 + 10 * q^66 + 10 * q^67 + 2 * q^68 + 4 * q^69 - 3 * q^70 - 21 * q^71 - 6 * q^72 + 7 * q^73 + 7 * q^74 + 13 * q^75 - 2 * q^76 + 10 * q^77 - 14 * q^79 - 3 * q^80 + 6 * q^81 + 11 * q^82 - 17 * q^83 - 6 * q^84 - q^85 + 5 * q^86 + 2 * q^87 + 10 * q^88 - 17 * q^89 + 3 * q^90 + 4 * q^92 - 9 * q^93 + 5 * q^94 - 22 * q^95 - 6 * q^96 - 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
$5$	1.83411	0.820238	0.410119	−	0.912032i	$-0.365487\pi$
$5$	1.83411	0.820238	0.410119	+	0.912032i	$0.365487\pi$
$6$	−1.00000	−0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.83411	−0.579996
$11$	−0.198062	−0.0597180	−0.0298590	−	0.999554i	$-0.509506\pi$
$11$	−0.198062	−0.0597180	−0.0298590	+	0.999554i	$0.509506\pi$
$12$	1.00000	0.288675
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	1.83411	0.473565
$16$	1.00000	0.250000
$17$	0.445042	0.107939	0.0539693	−	0.998543i	$-0.482813\pi$
$17$	0.445042	0.107939	0.0539693	+	0.998543i	$0.482813\pi$
$18$	−1.00000	−0.235702
$19$	−1.57281	−0.360828	−0.180414	−	0.983591i	$-0.557744\pi$
$19$	−1.57281	−0.360828	−0.180414	+	0.983591i	$0.557744\pi$
$20$	1.83411	0.410119
$21$	−1.00000	−0.218218
$22$	0.198062	0.0422270
$23$	9.19592	1.91748	0.958741	−	0.284281i	$-0.0917549\pi$
$23$	9.19592	1.91748	0.958741	+	0.284281i	$0.0917549\pi$
$24$	−1.00000	−0.204124
$25$	−1.63605	−0.327209
$26$	0	0
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	−9.88794	−1.83614	−0.918072	−	0.396413i	$-0.870255\pi$
$29$	−9.88794	−1.83614	−0.918072	+	0.396413i	$0.870255\pi$
$30$	−1.83411	−0.334861
$31$	−6.88303	−1.23623	−0.618114	−	0.786088i	$-0.712103\pi$
$31$	−6.88303	−1.23623	−0.618114	+	0.786088i	$0.712103\pi$
$32$	−1.00000	−0.176777
$33$	−0.198062	−0.0344782
$34$	−0.445042	−0.0763241
$35$	−1.83411	−0.310021
$36$	1.00000	0.166667
$37$	−5.13552	−0.844275	−0.422137	−	0.906532i	$-0.638720\pi$
$37$	−5.13552	−0.844275	−0.422137	+	0.906532i	$0.638720\pi$
$38$	1.57281	0.255144
$39$	0	0
$40$	−1.83411	−0.289998
$41$	−12.1234	−1.89336	−0.946682	−	0.322171i	$-0.895588\pi$
$41$	−12.1234	−1.89336	−0.946682	+	0.322171i	$0.895588\pi$
$42$	1.00000	0.154303
$43$	−7.51027	−1.14531	−0.572653	−	0.819798i	$-0.694086\pi$
$43$	−7.51027	−1.14531	−0.572653	+	0.819798i	$0.694086\pi$
$44$	−0.198062	−0.0298590
$45$	1.83411	0.273413
$46$	−9.19592	−1.35586
$47$	8.51673	1.24229	0.621146	−	0.783695i	$-0.286667\pi$
$47$	8.51673	1.24229	0.621146	+	0.783695i	$0.286667\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	1.63605	0.231372
$51$	0.445042	0.0623183
$52$	0	0
$53$	−1.38956	−0.190871	−0.0954353	−	0.995436i	$-0.530424\pi$
$53$	−1.38956	−0.190871	−0.0954353	+	0.995436i	$0.530424\pi$
$54$	−1.00000	−0.136083
$55$	−0.363268	−0.0489830
$56$	1.00000	0.133631
$57$	−1.57281	−0.208324
$58$	9.88794	1.29835
$59$	−11.7846	−1.53422	−0.767112	−	0.641514i	$-0.778307\pi$
$59$	−11.7846	−1.53422	−0.767112	+	0.641514i	$0.778307\pi$
$60$	1.83411	0.236782
$61$	−10.1849	−1.30405	−0.652024	−	0.758198i	$-0.726080\pi$
$61$	−10.1849	−1.30405	−0.652024	+	0.758198i	$0.726080\pi$
$62$	6.88303	0.874145
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	0.198062	0.0243798
$67$	−0.307727	−0.0375949	−0.0187974	−	0.999823i	$-0.505984\pi$
$67$	−0.307727	−0.0375949	−0.0187974	+	0.999823i	$0.505984\pi$
$68$	0.445042	0.0539693
$69$	9.19592	1.10706
$70$	1.83411	0.219218
$71$	−13.0597	−1.54990	−0.774951	−	0.632021i	$-0.782226\pi$
$71$	−13.0597	−1.54990	−0.774951	+	0.632021i	$0.782226\pi$
$72$	−1.00000	−0.117851
$73$	7.90088	0.924728	0.462364	−	0.886690i	$-0.347001\pi$
$73$	7.90088	0.924728	0.462364	+	0.886690i	$0.347001\pi$
$74$	5.13552	0.596992
$75$	−1.63605	−0.188914
$76$	−1.57281	−0.180414
$77$	0.198062	0.0225713
$78$	0	0
$79$	6.98527	0.785904	0.392952	−	0.919559i	$-0.371454\pi$
$79$	6.98527	0.785904	0.392952	+	0.919559i	$0.371454\pi$
$80$	1.83411	0.205060
$81$	1.00000	0.111111
$82$	12.1234	1.33881
$83$	−3.19757	−0.350979	−0.175489	−	0.984481i	$-0.556151\pi$
$83$	−3.19757	−0.350979	−0.175489	+	0.984481i	$0.556151\pi$
$84$	−1.00000	−0.109109
$85$	0.816255	0.0885353
$86$	7.51027	0.809853
$87$	−9.88794	−1.06010
$88$	0.198062	0.0211135
$89$	5.55962	0.589319	0.294659	−	0.955602i	$-0.404794\pi$
$89$	5.55962	0.589319	0.294659	+	0.955602i	$0.404794\pi$
$90$	−1.83411	−0.193332
$91$	0	0
$92$	9.19592	0.958741
$93$	−6.88303	−0.713737
$94$	−8.51673	−0.878434
$95$	−2.88471	−0.295965
$96$	−1.00000	−0.102062
$97$	−4.95178	−0.502777	−0.251388	−	0.967886i	$-0.580887\pi$
$97$	−4.95178	−0.502777	−0.251388	+	0.967886i	$0.580887\pi$
$98$	−1.00000	−0.101015
$99$	−0.198062	−0.0199060
$100$	−1.63605	−0.163605
$101$	−0.0853103	−0.00848869	−0.00424435	−	0.999991i	$-0.501351\pi$
$101$	−0.0853103	−0.00848869	−0.00424435	+	0.999991i	$0.501351\pi$
$102$	−0.445042	−0.0440657
$103$	7.20409	0.709840	0.354920	−	0.934897i	$-0.384508\pi$
$103$	7.20409	0.709840	0.354920	+	0.934897i	$0.384508\pi$
$104$	0	0
$105$	−1.83411	−0.178991
$106$	1.38956	0.134966
$107$	8.94825	0.865060	0.432530	−	0.901619i	$-0.357621\pi$
$107$	8.94825	0.865060	0.432530	+	0.901619i	$0.357621\pi$
$108$	1.00000	0.0962250
$109$	−0.615818	−0.0589846	−0.0294923	−	0.999565i	$-0.509389\pi$
$109$	−0.615818	−0.0589846	−0.0294923	+	0.999565i	$0.509389\pi$
$110$	0.363268	0.0346362
$111$	−5.13552	−0.487442
$112$	−1.00000	−0.0944911
$113$	8.18052	0.769559	0.384779	−	0.923009i	$-0.374278\pi$
$113$	8.18052	0.769559	0.384779	+	0.923009i	$0.374278\pi$
$114$	1.57281	0.147307
$115$	16.8663	1.57279
$116$	−9.88794	−0.918072
$117$	0	0
$118$	11.7846	1.08486
$119$	−0.445042	−0.0407969
$120$	−1.83411	−0.167430
$121$	−10.9608	−0.996434
$122$	10.1849	0.922102
$123$	−12.1234	−1.09313
$124$	−6.88303	−0.618114
$125$	−12.1712	−1.08863
$126$	1.00000	0.0890871
$127$	5.91677	0.525028	0.262514	−	0.964928i	$-0.415448\pi$
$127$	5.91677	0.525028	0.262514	+	0.964928i	$0.415448\pi$
$128$	−1.00000	−0.0883883
$129$	−7.51027	−0.661242
$130$	0	0
$131$	4.83450	0.422393	0.211196	−	0.977444i	$-0.432264\pi$
$131$	4.83450	0.422393	0.211196	+	0.977444i	$0.432264\pi$
$132$	−0.198062	−0.0172391
$133$	1.57281	0.136380
$134$	0.307727	0.0265836
$135$	1.83411	0.157855
$136$	−0.445042	−0.0381620
$137$	6.26783	0.535497	0.267748	−	0.963489i	$-0.413720\pi$
$137$	6.26783	0.535497	0.267748	+	0.963489i	$0.413720\pi$
$138$	−9.19592	−0.782809
$139$	13.6770	1.16007	0.580036	−	0.814591i	$-0.303038\pi$
$139$	13.6770	1.16007	0.580036	+	0.814591i	$0.303038\pi$
$140$	−1.83411	−0.155010
$141$	8.51673	0.717238
$142$	13.0597	1.09595
$143$	0	0
$144$	1.00000	0.0833333
$145$	−18.1356	−1.50608
$146$	−7.90088	−0.653881
$147$	1.00000	0.0824786
$148$	−5.13552	−0.422137
$149$	−13.3470	−1.09343	−0.546715	−	0.837319i	$-0.684122\pi$
$149$	−13.3470	−1.09343	−0.546715	+	0.837319i	$0.684122\pi$
$150$	1.63605	0.133583
$151$	−1.21548	−0.0989144	−0.0494572	−	0.998776i	$-0.515749\pi$
$151$	−1.21548	−0.0989144	−0.0494572	+	0.998776i	$0.515749\pi$
$152$	1.57281	0.127572
$153$	0.445042	0.0359795
$154$	−0.198062	−0.0159603
$155$	−12.6242	−1.01400
$156$	0	0
$157$	7.68582	0.613395	0.306698	−	0.951807i	$-0.400776\pi$
$157$	7.68582	0.613395	0.306698	+	0.951807i	$0.400776\pi$
$158$	−6.98527	−0.555718
$159$	−1.38956	−0.110199
$160$	−1.83411	−0.144999
$161$	−9.19592	−0.724740
$162$	−1.00000	−0.0785674
$163$	−12.1104	−0.948562	−0.474281	−	0.880374i	$-0.657292\pi$
$163$	−12.1104	−0.948562	−0.474281	+	0.880374i	$0.657292\pi$
$164$	−12.1234	−0.946682
$165$	−0.363268	−0.0282803
$166$	3.19757	0.248180
$167$	−14.8734	−1.15094	−0.575469	−	0.817823i	$-0.695181\pi$
$167$	−14.8734	−1.15094	−0.575469	+	0.817823i	$0.695181\pi$
$168$	1.00000	0.0771517
$169$	0	0
$170$	−0.816255	−0.0626039
$171$	−1.57281	−0.120276
$172$	−7.51027	−0.572653
$173$	−1.87323	−0.142419	−0.0712093	−	0.997461i	$-0.522686\pi$
$173$	−1.87323	−0.142419	−0.0712093	+	0.997461i	$0.522686\pi$
$174$	9.88794	0.749603
$175$	1.63605	0.123673
$176$	−0.198062	−0.0149295
$177$	−11.7846	−0.885784
$178$	−5.55962	−0.416711
$179$	−8.91285	−0.666178	−0.333089	−	0.942895i	$-0.608091\pi$
$179$	−8.91285	−0.666178	−0.333089	+	0.942895i	$0.608091\pi$
$180$	1.83411	0.136706
$181$	−13.2448	−0.984478	−0.492239	−	0.870460i	$-0.663821\pi$
$181$	−13.2448	−0.984478	−0.492239	+	0.870460i	$0.663821\pi$
$182$	0	0
$183$	−10.1849	−0.752893
$184$	−9.19592	−0.677932
$185$	−9.41910	−0.692506
$186$	6.88303	0.504688
$187$	−0.0881460	−0.00644587
$188$	8.51673	0.621146
$189$	−1.00000	−0.0727393
$190$	2.88471	0.209279
$191$	−6.56414	−0.474965	−0.237482	−	0.971392i	$-0.576322\pi$
$191$	−6.56414	−0.474965	−0.237482	+	0.971392i	$0.576322\pi$
$192$	1.00000	0.0721688
$193$	21.6428	1.55788	0.778940	−	0.627099i	$-0.215758\pi$
$193$	21.6428	1.55788	0.778940	+	0.627099i	$0.215758\pi$
$194$	4.95178	0.355517
$195$	0	0
$196$	1.00000	0.0714286
$197$	−0.437589	−0.0311769	−0.0155885	−	0.999878i	$-0.504962\pi$
$197$	−0.437589	−0.0311769	−0.0155885	+	0.999878i	$0.504962\pi$
$198$	0.198062	0.0140757
$199$	24.1946	1.71511	0.857553	−	0.514395i	$-0.171984\pi$
$199$	24.1946	1.71511	0.857553	+	0.514395i	$0.171984\pi$
$200$	1.63605	0.115686
$201$	−0.307727	−0.0217054
$202$	0.0853103	0.00600241
$203$	9.88794	0.693997
$204$	0.445042	0.0311592
$205$	−22.2357	−1.55301
$206$	−7.20409	−0.501932
$207$	9.19592	0.639161
$208$	0	0
$209$	0.311515	0.0215479
$210$	1.83411	0.126566
$211$	−11.6272	−0.800452	−0.400226	−	0.916416i	$-0.631068\pi$
$211$	−11.6272	−0.800452	−0.400226	+	0.916416i	$0.631068\pi$
$212$	−1.38956	−0.0954353
$213$	−13.0597	−0.894837
$214$	−8.94825	−0.611690
$215$	−13.7747	−0.939423
$216$	−1.00000	−0.0680414
$217$	6.88303	0.467250
$218$	0.615818	0.0417084
$219$	7.90088	0.533892
$220$	−0.363268	−0.0244915
$221$	0	0
$222$	5.13552	0.344674
$223$	−4.17401	−0.279512	−0.139756	−	0.990186i	$-0.544632\pi$
$223$	−4.17401	−0.279512	−0.139756	+	0.990186i	$0.544632\pi$
$224$	1.00000	0.0668153
$225$	−1.63605	−0.109070
$226$	−8.18052	−0.544160
$227$	−26.8243	−1.78039	−0.890194	−	0.455581i	$-0.849432\pi$
$227$	−26.8243	−1.78039	−0.890194	+	0.455581i	$0.849432\pi$
$228$	−1.57281	−0.104162
$229$	0.0599178	0.00395948	0.00197974	−	0.999998i	$-0.499370\pi$
$229$	0.0599178	0.00395948	0.00197974	+	0.999998i	$0.499370\pi$
$230$	−16.8663	−1.11213
$231$	0.198062	0.0130315
$232$	9.88794	0.649175
$233$	14.7018	0.963149	0.481574	−	0.876405i	$-0.340065\pi$
$233$	14.7018	0.963149	0.481574	+	0.876405i	$0.340065\pi$
$234$	0	0
$235$	15.6206	1.01898
$236$	−11.7846	−0.767112
$237$	6.98527	0.453742
$238$	0.445042	0.0288478
$239$	−8.06112	−0.521431	−0.260715	−	0.965416i	$-0.583958\pi$
$239$	−8.06112	−0.521431	−0.260715	+	0.965416i	$0.583958\pi$
$240$	1.83411	0.118391
$241$	1.03927	0.0669456	0.0334728	−	0.999440i	$-0.489343\pi$
$241$	1.03927	0.0669456	0.0334728	+	0.999440i	$0.489343\pi$
$242$	10.9608	0.704585
$243$	1.00000	0.0641500
$244$	−10.1849	−0.652024
$245$	1.83411	0.117177
$246$	12.1234	0.772962
$247$	0	0
$248$	6.88303	0.437073
$249$	−3.19757	−0.202638
$250$	12.1712	0.769776
$251$	−18.6029	−1.17421	−0.587103	−	0.809512i	$-0.699732\pi$
$251$	−18.6029	−1.17421	−0.587103	+	0.809512i	$0.699732\pi$
$252$	−1.00000	−0.0629941
$253$	−1.82136	−0.114508
$254$	−5.91677	−0.371251
$255$	0.816255	0.0511159
$256$	1.00000	0.0625000
$257$	22.7150	1.41692	0.708462	−	0.705749i	$-0.249389\pi$
$257$	22.7150	1.41692	0.708462	+	0.705749i	$0.249389\pi$
$258$	7.51027	0.467569
$259$	5.13552	0.319106
$260$	0	0
$261$	−9.88794	−0.612048
$262$	−4.83450	−0.298677
$263$	−16.2280	−1.00066	−0.500329	−	0.865835i	$-0.666788\pi$
$263$	−16.2280	−1.00066	−0.500329	+	0.865835i	$0.666788\pi$
$264$	0.198062	0.0121899
$265$	−2.54860	−0.156559
$266$	−1.57281	−0.0964353
$267$	5.55962	0.340243
$268$	−0.307727	−0.0187974
$269$	3.99465	0.243558	0.121779	−	0.992557i	$-0.461140\pi$
$269$	3.99465	0.243558	0.121779	+	0.992557i	$0.461140\pi$
$270$	−1.83411	−0.111620
$271$	25.3380	1.53917	0.769587	−	0.638542i	$-0.220462\pi$
$271$	25.3380	1.53917	0.769587	+	0.638542i	$0.220462\pi$
$272$	0.445042	0.0269846
$273$	0	0
$274$	−6.26783	−0.378653
$275$	0.324039	0.0195403
$276$	9.19592	0.553529
$277$	−18.8962	−1.13536	−0.567680	−	0.823249i	$-0.692159\pi$
$277$	−18.8962	−1.13536	−0.567680	+	0.823249i	$0.692159\pi$
$278$	−13.6770	−0.820295
$279$	−6.88303	−0.412076
$280$	1.83411	0.109609
$281$	15.7447	0.939251	0.469625	−	0.882866i	$-0.344389\pi$
$281$	15.7447	0.939251	0.469625	+	0.882866i	$0.344389\pi$
$282$	−8.51673	−0.507164
$283$	−6.46520	−0.384316	−0.192158	−	0.981364i	$-0.561549\pi$
$283$	−6.46520	−0.384316	−0.192158	+	0.981364i	$0.561549\pi$
$284$	−13.0597	−0.774951
$285$	−2.88471	−0.170875
$286$	0	0
$287$	12.1234	0.715624
$288$	−1.00000	−0.0589256
$289$	−16.8019	−0.988349
$290$	18.1356	1.06496
$291$	−4.95178	−0.290278
$292$	7.90088	0.462364
$293$	5.37856	0.314219	0.157109	−	0.987581i	$-0.449782\pi$
$293$	5.37856	0.314219	0.157109	+	0.987581i	$0.449782\pi$
$294$	−1.00000	−0.0583212
$295$	−21.6142	−1.25843
$296$	5.13552	0.298496
$297$	−0.198062	−0.0114927
$298$	13.3470	0.773171
$299$	0	0
$300$	−1.63605	−0.0944572
$301$	7.51027	0.432885
$302$	1.21548	0.0699431
$303$	−0.0853103	−0.00490095
$304$	−1.57281	−0.0902069
$305$	−18.6803	−1.06963
$306$	−0.445042	−0.0254414
$307$	−26.8264	−1.53106	−0.765532	−	0.643398i	$-0.777524\pi$
$307$	−26.8264	−1.53106	−0.765532	+	0.643398i	$0.777524\pi$
$308$	0.198062	0.0112856
$309$	7.20409	0.409826
$310$	12.6242	0.717007
$311$	22.2579	1.26213	0.631066	−	0.775729i	$-0.282618\pi$
$311$	22.2579	1.26213	0.631066	+	0.775729i	$0.282618\pi$
$312$	0	0
$313$	8.24762	0.466183	0.233091	−	0.972455i	$-0.425116\pi$
$313$	8.24762	0.466183	0.233091	+	0.972455i	$0.425116\pi$
$314$	−7.68582	−0.433736
$315$	−1.83411	−0.103340
$316$	6.98527	0.392952
$317$	13.7293	0.771112	0.385556	−	0.922685i	$-0.374010\pi$
$317$	13.7293	0.771112	0.385556	+	0.922685i	$0.374010\pi$
$318$	1.38956	0.0779226
$319$	1.95843	0.109651
$320$	1.83411	0.102530
$321$	8.94825	0.499443
$322$	9.19592	0.512469
$323$	−0.699967	−0.0389472
$324$	1.00000	0.0555556
$325$	0	0
$326$	12.1104	0.670734
$327$	−0.615818	−0.0340548
$328$	12.1234	0.669405
$329$	−8.51673	−0.469542
$330$	0.363268	0.0199972
$331$	17.9130	0.984586	0.492293	−	0.870430i	$-0.336159\pi$
$331$	17.9130	0.984586	0.492293	+	0.870430i	$0.336159\pi$
$332$	−3.19757	−0.175489
$333$	−5.13552	−0.281425
$334$	14.8734	0.813837
$335$	−0.564405	−0.0308368
$336$	−1.00000	−0.0545545
$337$	35.7827	1.94921	0.974604	−	0.223936i	$-0.0718906\pi$
$337$	35.7827	1.94921	0.974604	+	0.223936i	$0.0718906\pi$
$338$	0	0
$339$	8.18052	0.444305
$340$	0.816255	0.0442676
$341$	1.36327	0.0738251
$342$	1.57281	0.0850479
$343$	−1.00000	−0.0539949
$344$	7.51027	0.404927
$345$	16.8663	0.908052
$346$	1.87323	0.100705
$347$	−20.8470	−1.11913	−0.559563	−	0.828788i	$-0.689031\pi$
$347$	−20.8470	−1.11913	−0.559563	+	0.828788i	$0.689031\pi$
$348$	−9.88794	−0.530049
$349$	31.6493	1.69415	0.847073	−	0.531476i	$-0.178362\pi$
$349$	31.6493	1.69415	0.847073	+	0.531476i	$0.178362\pi$
$350$	−1.63605	−0.0874503
$351$	0	0
$352$	0.198062	0.0105568
$353$	6.19014	0.329468	0.164734	−	0.986338i	$-0.447323\pi$
$353$	6.19014	0.329468	0.164734	+	0.986338i	$0.447323\pi$
$354$	11.7846	0.626344
$355$	−23.9529	−1.27129
$356$	5.55962	0.294659
$357$	−0.445042	−0.0235541
$358$	8.91285	0.471059
$359$	−27.9172	−1.47341	−0.736706	−	0.676213i	$-0.763620\pi$
$359$	−27.9172	−1.47341	−0.736706	+	0.676213i	$0.763620\pi$
$360$	−1.83411	−0.0966660
$361$	−16.5263	−0.869803
$362$	13.2448	0.696131
$363$	−10.9608	−0.575291
$364$	0	0
$365$	14.4911	0.758497
$366$	10.1849	0.532376
$367$	2.49317	0.130142	0.0650712	−	0.997881i	$-0.479273\pi$
$367$	2.49317	0.130142	0.0650712	+	0.997881i	$0.479273\pi$
$368$	9.19592	0.479370
$369$	−12.1234	−0.631121
$370$	9.41910	0.489676
$371$	1.38956	0.0721423
$372$	−6.88303	−0.356868
$373$	−31.8691	−1.65012	−0.825061	−	0.565044i	$-0.808859\pi$
$373$	−31.8691	−1.65012	−0.825061	+	0.565044i	$0.808859\pi$
$374$	0.0881460	0.00455792
$375$	−12.1712	−0.628520
$376$	−8.51673	−0.439217
$377$	0	0
$378$	1.00000	0.0514344
$379$	−0.810157	−0.0416149	−0.0208075	−	0.999784i	$-0.506624\pi$
$379$	−0.810157	−0.0416149	−0.0208075	+	0.999784i	$0.506624\pi$
$380$	−2.88471	−0.147982
$381$	5.91677	0.303125
$382$	6.56414	0.335851
$383$	−25.2437	−1.28989	−0.644946	−	0.764228i	$-0.723120\pi$
$383$	−25.2437	−1.28989	−0.644946	+	0.764228i	$0.723120\pi$
$384$	−1.00000	−0.0510310
$385$	0.363268	0.0185138
$386$	−21.6428	−1.10159
$387$	−7.51027	−0.381769
$388$	−4.95178	−0.251388
$389$	3.03323	0.153791	0.0768954	−	0.997039i	$-0.475499\pi$
$389$	3.03323	0.153791	0.0768954	+	0.997039i	$0.475499\pi$
$390$	0	0
$391$	4.09257	0.206970
$392$	−1.00000	−0.0505076
$393$	4.83450	0.243868
$394$	0.437589	0.0220454
$395$	12.8117	0.644629
$396$	−0.198062	−0.00995300
$397$	−14.1365	−0.709490	−0.354745	−	0.934963i	$-0.615432\pi$
$397$	−14.1365	−0.709490	−0.354745	+	0.934963i	$0.615432\pi$
$398$	−24.1946	−1.21276
$399$	1.57281	0.0787391
$400$	−1.63605	−0.0818023
$401$	17.6596	0.881878	0.440939	−	0.897537i	$-0.354645\pi$
$401$	17.6596	0.881878	0.440939	+	0.897537i	$0.354645\pi$
$402$	0.307727	0.0153480
$403$	0	0
$404$	−0.0853103	−0.00424435
$405$	1.83411	0.0911376
$406$	−9.88794	−0.490730
$407$	1.01715	0.0504184
$408$	−0.445042	−0.0220329
$409$	11.6727	0.577180	0.288590	−	0.957453i	$-0.406814\pi$
$409$	11.6727	0.577180	0.288590	+	0.957453i	$0.406814\pi$
$410$	22.2357	1.09814
$411$	6.26783	0.309169
$412$	7.20409	0.354920
$413$	11.7846	0.579882
$414$	−9.19592	−0.451955
$415$	−5.86469	−0.287886
$416$	0	0
$417$	13.6770	0.669768
$418$	−0.311515	−0.0152367
$419$	−31.2971	−1.52896	−0.764482	−	0.644645i	$-0.777005\pi$
$419$	−31.2971	−1.52896	−0.764482	+	0.644645i	$0.777005\pi$
$420$	−1.83411	−0.0894953
$421$	32.8881	1.60287	0.801433	−	0.598085i	$-0.204071\pi$
$421$	32.8881	1.60287	0.801433	+	0.598085i	$0.204071\pi$
$422$	11.6272	0.566005
$423$	8.51673	0.414098
$424$	1.38956	0.0674830
$425$	−0.728109	−0.0353185
$426$	13.0597	0.632745
$427$	10.1849	0.492884
$428$	8.94825	0.432530
$429$	0	0
$430$	13.7747	0.664273
$431$	−37.9406	−1.82754	−0.913768	−	0.406237i	$-0.866841\pi$
$431$	−37.9406	−1.82754	−0.913768	+	0.406237i	$0.866841\pi$
$432$	1.00000	0.0481125
$433$	11.0673	0.531861	0.265931	−	0.963992i	$-0.414321\pi$
$433$	11.0673	0.531861	0.265931	+	0.963992i	$0.414321\pi$
$434$	−6.88303	−0.330396
$435$	−18.1356	−0.869533
$436$	−0.615818	−0.0294923
$437$	−14.4634	−0.691881
$438$	−7.90088	−0.377519
$439$	0.955444	0.0456009	0.0228004	−	0.999740i	$-0.492742\pi$
$439$	0.955444	0.0456009	0.0228004	+	0.999740i	$0.492742\pi$
$440$	0.363268	0.0173181
$441$	1.00000	0.0476190
$442$	0	0
$443$	−26.1946	−1.24454	−0.622272	−	0.782801i	$-0.713790\pi$
$443$	−26.1946	−1.24454	−0.622272	+	0.782801i	$0.713790\pi$
$444$	−5.13552	−0.243721
$445$	10.1970	0.483382
$446$	4.17401	0.197645
$447$	−13.3470	−0.631292
$448$	−1.00000	−0.0472456
$449$	24.1431	1.13938	0.569691	−	0.821859i	$-0.307063\pi$
$449$	24.1431	1.13938	0.569691	+	0.821859i	$0.307063\pi$
$450$	1.63605	0.0771240
$451$	2.40120	0.113068
$452$	8.18052	0.384779
$453$	−1.21548	−0.0571083
$454$	26.8243	1.25893
$455$	0	0
$456$	1.57281	0.0736536
$457$	10.6583	0.498574	0.249287	−	0.968430i	$-0.419804\pi$
$457$	10.6583	0.498574	0.249287	+	0.968430i	$0.419804\pi$
$458$	−0.0599178	−0.00279977
$459$	0.445042	0.0207728
$460$	16.8663	0.786396
$461$	−26.8656	−1.25126	−0.625628	−	0.780122i	$-0.715157\pi$
$461$	−26.8656	−1.25126	−0.625628	+	0.780122i	$0.715157\pi$
$462$	−0.198062	−0.00921469
$463$	17.0698	0.793301	0.396650	−	0.917970i	$-0.370173\pi$
$463$	17.0698	0.793301	0.396650	+	0.917970i	$0.370173\pi$
$464$	−9.88794	−0.459036
$465$	−12.6242	−0.585434
$466$	−14.7018	−0.681049
$467$	−32.1453	−1.48751	−0.743754	−	0.668454i	$-0.766956\pi$
$467$	−32.1453	−1.48751	−0.743754	+	0.668454i	$0.766956\pi$
$468$	0	0
$469$	0.307727	0.0142095
$470$	−15.6206	−0.720525
$471$	7.68582	0.354144
$472$	11.7846	0.542430
$473$	1.48750	0.0683954
$474$	−6.98527	−0.320844
$475$	2.57319	0.118066
$476$	−0.445042	−0.0203985
$477$	−1.38956	−0.0636235
$478$	8.06112	0.368707
$479$	−22.1790	−1.01338	−0.506692	−	0.862127i	$-0.669132\pi$
$479$	−22.1790	−1.01338	−0.506692	+	0.862127i	$0.669132\pi$
$480$	−1.83411	−0.0837152
$481$	0	0
$482$	−1.03927	−0.0473377
$483$	−9.19592	−0.418429
$484$	−10.9608	−0.498217
$485$	−9.08210	−0.412397
$486$	−1.00000	−0.0453609
$487$	−13.8814	−0.629024	−0.314512	−	0.949253i	$-0.601841\pi$
$487$	−13.8814	−0.629024	−0.314512	+	0.949253i	$0.601841\pi$
$488$	10.1849	0.461051
$489$	−12.1104	−0.547652
$490$	−1.83411	−0.0828566
$491$	12.7715	0.576369	0.288185	−	0.957575i	$-0.406948\pi$
$491$	12.7715	0.576369	0.288185	+	0.957575i	$0.406948\pi$
$492$	−12.1234	−0.546567
$493$	−4.40055	−0.198191
$494$	0	0
$495$	−0.363268	−0.0163277
$496$	−6.88303	−0.309057
$497$	13.0597	0.585808
$498$	3.19757	0.143287
$499$	−17.0569	−0.763573	−0.381787	−	0.924251i	$-0.624691\pi$
$499$	−17.0569	−0.763573	−0.381787	+	0.924251i	$0.624691\pi$
$500$	−12.1712	−0.544314
$501$	−14.8734	−0.664495
$502$	18.6029	0.830289
$503$	14.4879	0.645985	0.322992	−	0.946402i	$-0.395311\pi$
$503$	14.4879	0.645985	0.322992	+	0.946402i	$0.395311\pi$
$504$	1.00000	0.0445435
$505$	−0.156468	−0.00696275
$506$	1.82136	0.0809695
$507$	0	0
$508$	5.91677	0.262514
$509$	3.77985	0.167539	0.0837695	−	0.996485i	$-0.473304\pi$
$509$	3.77985	0.167539	0.0837695	+	0.996485i	$0.473304\pi$
$510$	−0.816255	−0.0361444
$511$	−7.90088	−0.349514
$512$	−1.00000	−0.0441942
$513$	−1.57281	−0.0694413
$514$	−22.7150	−1.00192
$515$	13.2131	0.582238
$516$	−7.51027	−0.330621
$517$	−1.68684	−0.0741873
$518$	−5.13552	−0.225642
$519$	−1.87323	−0.0822255
$520$	0	0
$521$	6.59714	0.289026	0.144513	−	0.989503i	$-0.453838\pi$
$521$	6.59714	0.289026	0.144513	+	0.989503i	$0.453838\pi$
$522$	9.88794	0.432783
$523$	−24.8111	−1.08491	−0.542456	−	0.840084i	$-0.682505\pi$
$523$	−24.8111	−1.08491	−0.542456	+	0.840084i	$0.682505\pi$
$524$	4.83450	0.211196
$525$	1.63605	0.0714029
$526$	16.2280	0.707572
$527$	−3.06323	−0.133437
$528$	−0.198062	−0.00861955
$529$	61.5650	2.67674
$530$	2.54860	0.110704
$531$	−11.7846	−0.511408
$532$	1.57281	0.0681900
$533$	0	0
$534$	−5.55962	−0.240588
$535$	16.4121	0.709556
$536$	0.307727	0.0132918
$537$	−8.91285	−0.384618
$538$	−3.99465	−0.172222
$539$	−0.198062	−0.00853115
$540$	1.83411	0.0789275
$541$	−30.4570	−1.30945	−0.654724	−	0.755868i	$-0.727215\pi$
$541$	−30.4570	−1.30945	−0.654724	+	0.755868i	$0.727215\pi$
$542$	−25.3380	−1.08836
$543$	−13.2448	−0.568389
$544$	−0.445042	−0.0190810
$545$	−1.12948	−0.0483815
$546$	0	0
$547$	32.5691	1.39255	0.696277	−	0.717773i	$-0.254838\pi$
$547$	32.5691	1.39255	0.696277	+	0.717773i	$0.254838\pi$
$548$	6.26783	0.267748
$549$	−10.1849	−0.434683
$550$	−0.324039	−0.0138171
$551$	15.5519	0.662532
$552$	−9.19592	−0.391404
$553$	−6.98527	−0.297044
$554$	18.8962	0.802821
$555$	−9.41910	−0.399819
$556$	13.6770	0.580036
$557$	20.8644	0.884052	0.442026	−	0.897002i	$-0.354260\pi$
$557$	20.8644	0.884052	0.442026	+	0.897002i	$0.354260\pi$
$558$	6.88303	0.291382
$559$	0	0
$560$	−1.83411	−0.0775052
$561$	−0.0881460	−0.00372153
$562$	−15.7447	−0.664150
$563$	11.9854	0.505124	0.252562	−	0.967581i	$-0.418727\pi$
$563$	11.9854	0.505124	0.252562	+	0.967581i	$0.418727\pi$
$564$	8.51673	0.358619
$565$	15.0040	0.631222
$566$	6.46520	0.271753
$567$	−1.00000	−0.0419961
$568$	13.0597	0.547973
$569$	5.07479	0.212746	0.106373	−	0.994326i	$-0.466076\pi$
$569$	5.07479	0.212746	0.106373	+	0.994326i	$0.466076\pi$
$570$	2.88471	0.120827
$571$	5.93197	0.248245	0.124123	−	0.992267i	$-0.460388\pi$
$571$	5.93197	0.248245	0.124123	+	0.992267i	$0.460388\pi$
$572$	0	0
$573$	−6.56414	−0.274221
$574$	−12.1234	−0.506023
$575$	−15.0450	−0.627418
$576$	1.00000	0.0416667
$577$	10.1542	0.422724	0.211362	−	0.977408i	$-0.432210\pi$
$577$	10.1542	0.422724	0.211362	+	0.977408i	$0.432210\pi$
$578$	16.8019	0.698868
$579$	21.6428	0.899442
$580$	−18.1356	−0.753038
$581$	3.19757	0.132658
$582$	4.95178	0.205258
$583$	0.275219	0.0113984
$584$	−7.90088	−0.326941
$585$	0	0
$586$	−5.37856	−0.222186
$587$	20.6043	0.850432	0.425216	−	0.905092i	$-0.360198\pi$
$587$	20.6043	0.850432	0.425216	+	0.905092i	$0.360198\pi$
$588$	1.00000	0.0412393
$589$	10.8257	0.446065
$590$	21.6142	0.889843
$591$	−0.437589	−0.0180000
$592$	−5.13552	−0.211069
$593$	−14.2590	−0.585548	−0.292774	−	0.956182i	$-0.594578\pi$
$593$	−14.2590	−0.585548	−0.292774	+	0.956182i	$0.594578\pi$
$594$	0.198062	0.00812659
$595$	−0.816255	−0.0334632
$596$	−13.3470	−0.546715
$597$	24.1946	0.990217
$598$	0	0
$599$	−5.47672	−0.223773	−0.111886	−	0.993721i	$-0.535689\pi$
$599$	−5.47672	−0.223773	−0.111886	+	0.993721i	$0.535689\pi$
$600$	1.63605	0.0667913
$601$	−30.9403	−1.26208	−0.631041	−	0.775750i	$-0.717372\pi$
$601$	−30.9403	−1.26208	−0.631041	+	0.775750i	$0.717372\pi$
$602$	−7.51027	−0.306096
$603$	−0.307727	−0.0125316
$604$	−1.21548	−0.0494572
$605$	−20.1032	−0.817313
$606$	0.0853103	0.00346549
$607$	6.80757	0.276311	0.138155	−	0.990411i	$-0.455883\pi$
$607$	6.80757	0.276311	0.138155	+	0.990411i	$0.455883\pi$
$608$	1.57281	0.0637859
$609$	9.88794	0.400680
$610$	18.6803	0.756343
$611$	0	0
$612$	0.445042	0.0179898
$613$	−24.2320	−0.978720	−0.489360	−	0.872082i	$-0.662770\pi$
$613$	−24.2320	−0.978720	−0.489360	+	0.872082i	$0.662770\pi$
$614$	26.8264	1.08263
$615$	−22.2357	−0.896630
$616$	−0.198062	−0.00798016
$617$	34.1377	1.37433	0.687165	−	0.726501i	$-0.258855\pi$
$617$	34.1377	1.37433	0.687165	+	0.726501i	$0.258855\pi$
$618$	−7.20409	−0.289791
$619$	−12.5873	−0.505925	−0.252963	−	0.967476i	$-0.581405\pi$
$619$	−12.5873	−0.505925	−0.252963	+	0.967476i	$0.581405\pi$
$620$	−12.6242	−0.507001
$621$	9.19592	0.369020
$622$	−22.2579	−0.892462
$623$	−5.55962	−0.222742
$624$	0	0
$625$	−14.1431	−0.565725
$626$	−8.24762	−0.329641
$627$	0.311515	0.0124407
$628$	7.68582	0.306698
$629$	−2.28552	−0.0911297
$630$	1.83411	0.0730726
$631$	39.8142	1.58498	0.792489	−	0.609887i	$-0.208785\pi$
$631$	39.8142	1.58498	0.792489	+	0.609887i	$0.208785\pi$
$632$	−6.98527	−0.277859
$633$	−11.6272	−0.462141
$634$	−13.7293	−0.545258
$635$	10.8520	0.430648
$636$	−1.38956	−0.0550996
$637$	0	0
$638$	−1.95843	−0.0775349
$639$	−13.0597	−0.516634
$640$	−1.83411	−0.0724995
$641$	−4.70878	−0.185986	−0.0929928	−	0.995667i	$-0.529643\pi$
$641$	−4.70878	−0.185986	−0.0929928	+	0.995667i	$0.529643\pi$
$642$	−8.94825	−0.353159
$643$	36.1977	1.42750	0.713749	−	0.700402i	$-0.246996\pi$
$643$	36.1977	1.42750	0.713749	+	0.700402i	$0.246996\pi$
$644$	−9.19592	−0.362370
$645$	−13.7747	−0.542376
$646$	0.699967	0.0275398
$647$	0.587951	0.0231147	0.0115574	−	0.999933i	$-0.496321\pi$
$647$	0.587951	0.0231147	0.0115574	+	0.999933i	$0.496321\pi$
$648$	−1.00000	−0.0392837
$649$	2.33408	0.0916208
$650$	0	0
$651$	6.88303	0.269767
$652$	−12.1104	−0.474281
$653$	−15.0839	−0.590279	−0.295139	−	0.955454i	$-0.595366\pi$
$653$	−15.0839	−0.590279	−0.295139	+	0.955454i	$0.595366\pi$
$654$	0.615818	0.0240804
$655$	8.86700	0.346463
$656$	−12.1234	−0.473341
$657$	7.90088	0.308243
$658$	8.51673	0.332017
$659$	−26.3996	−1.02838	−0.514191	−	0.857676i	$-0.671908\pi$
$659$	−26.3996	−1.02838	−0.514191	+	0.857676i	$0.671908\pi$
$660$	−0.363268	−0.0141402
$661$	49.5192	1.92607	0.963037	−	0.269369i	$-0.0868151\pi$
$661$	49.5192	1.92607	0.963037	+	0.269369i	$0.0868151\pi$
$662$	−17.9130	−0.696207
$663$	0	0
$664$	3.19757	0.124090
$665$	2.88471	0.111864
$666$	5.13552	0.198997
$667$	−90.9287	−3.52077
$668$	−14.8734	−0.575469
$669$	−4.17401	−0.161376
$670$	0.564405	0.0218049
$671$	2.01725	0.0778752
$672$	1.00000	0.0385758
$673$	−20.4206	−0.787156	−0.393578	−	0.919291i	$-0.628763\pi$
$673$	−20.4206	−0.787156	−0.393578	+	0.919291i	$0.628763\pi$
$674$	−35.7827	−1.37830
$675$	−1.63605	−0.0629714
$676$	0	0
$677$	−35.0603	−1.34748	−0.673738	−	0.738970i	$-0.735312\pi$
$677$	−35.0603	−1.34748	−0.673738	+	0.738970i	$0.735312\pi$
$678$	−8.18052	−0.314171
$679$	4.95178	0.190032
$680$	−0.816255	−0.0313020
$681$	−26.8243	−1.02791
$682$	−1.36327	−0.0522022
$683$	−24.0064	−0.918579	−0.459289	−	0.888287i	$-0.651896\pi$
$683$	−24.0064	−0.918579	−0.459289	+	0.888287i	$0.651896\pi$
$684$	−1.57281	−0.0601380
$685$	11.4959	0.439235
$686$	1.00000	0.0381802
$687$	0.0599178	0.00228601
$688$	−7.51027	−0.286326
$689$	0	0
$690$	−16.8663	−0.642090
$691$	5.29898	0.201583	0.100791	−	0.994908i	$-0.467863\pi$
$691$	5.29898	0.201583	0.100791	+	0.994908i	$0.467863\pi$
$692$	−1.87323	−0.0712093
$693$	0.198062	0.00752376
$694$	20.8470	0.791341
$695$	25.0852	0.951536
$696$	9.88794	0.374801
$697$	−5.39544	−0.204367
$698$	−31.6493	−1.19794
$699$	14.7018	0.556074
$700$	1.63605	0.0618367
$701$	47.1066	1.77919	0.889596	−	0.456749i	$-0.150986\pi$
$701$	47.1066	1.77919	0.889596	+	0.456749i	$0.150986\pi$
$702$	0	0
$703$	8.07721	0.304638
$704$	−0.198062	−0.00746475
$705$	15.6206	0.588306
$706$	−6.19014	−0.232969
$707$	0.0853103	0.00320842
$708$	−11.7846	−0.442892
$709$	48.5978	1.82513	0.912565	−	0.408932i	$-0.134099\pi$
$709$	48.5978	1.82513	0.912565	+	0.408932i	$0.134099\pi$
$710$	23.9529	0.898937
$711$	6.98527	0.261968
$712$	−5.55962	−0.208356
$713$	−63.2958	−2.37044
$714$	0.445042	0.0166553
$715$	0	0
$716$	−8.91285	−0.333089
$717$	−8.06112	−0.301048
$718$	27.9172	1.04186
$719$	1.43382	0.0534725	0.0267363	−	0.999643i	$-0.491489\pi$
$719$	1.43382	0.0534725	0.0267363	+	0.999643i	$0.491489\pi$
$720$	1.83411	0.0683532
$721$	−7.20409	−0.268294
$722$	16.5263	0.615044
$723$	1.03927	0.0386510
$724$	−13.2448	−0.492239
$725$	16.1771	0.600804
$726$	10.9608	0.406792
$727$	−10.0393	−0.372338	−0.186169	−	0.982518i	$-0.559607\pi$
$727$	−10.0393	−0.372338	−0.186169	+	0.982518i	$0.559607\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−14.4911	−0.536339
$731$	−3.34238	−0.123623
$732$	−10.1849	−0.376446
$733$	11.2968	0.417257	0.208628	−	0.977995i	$-0.433100\pi$
$733$	11.2968	0.417257	0.208628	+	0.977995i	$0.433100\pi$
$734$	−2.49317	−0.0920246
$735$	1.83411	0.0676521
$736$	−9.19592	−0.338966
$737$	0.0609492	0.00224509
$738$	12.1234	0.446270
$739$	−22.9571	−0.844489	−0.422245	−	0.906482i	$-0.638758\pi$
$739$	−22.9571	−0.844489	−0.422245	+	0.906482i	$0.638758\pi$
$740$	−9.41910	−0.346253
$741$	0	0
$742$	−1.38956	−0.0510123
$743$	47.1372	1.72930	0.864649	−	0.502377i	$-0.167541\pi$
$743$	47.1372	1.72930	0.864649	+	0.502377i	$0.167541\pi$
$744$	6.88303	0.252344
$745$	−24.4798	−0.896872
$746$	31.8691	1.16681
$747$	−3.19757	−0.116993
$748$	−0.0881460	−0.00322294
$749$	−8.94825	−0.326962
$750$	12.1712	0.444430
$751$	4.33483	0.158180	0.0790901	−	0.996867i	$-0.474799\pi$
$751$	4.33483	0.158180	0.0790901	+	0.996867i	$0.474799\pi$
$752$	8.51673	0.310573
$753$	−18.6029	−0.677928
$754$	0	0
$755$	−2.22932	−0.0811334
$756$	−1.00000	−0.0363696
$757$	−51.5048	−1.87197	−0.935987	−	0.352034i	$-0.885490\pi$
$757$	−51.5048	−1.87197	−0.935987	+	0.352034i	$0.885490\pi$
$758$	0.810157	0.0294262
$759$	−1.82136	−0.0661114
$760$	2.88471	0.104639
$761$	−15.3697	−0.557153	−0.278576	−	0.960414i	$-0.589863\pi$
$761$	−15.3697	−0.557153	−0.278576	+	0.960414i	$0.589863\pi$
$762$	−5.91677	−0.214342
$763$	0.615818	0.0222941
$764$	−6.56414	−0.237482
$765$	0.816255	0.0295118
$766$	25.2437	0.912092
$767$	0	0
$768$	1.00000	0.0360844
$769$	−22.3499	−0.805958	−0.402979	−	0.915209i	$-0.632025\pi$
$769$	−22.3499	−0.805958	−0.402979	+	0.915209i	$0.632025\pi$
$770$	−0.363268	−0.0130913
$771$	22.7150	0.818062
$772$	21.6428	0.778940
$773$	−4.13659	−0.148783	−0.0743913	−	0.997229i	$-0.523701\pi$
$773$	−4.13659	−0.148783	−0.0743913	+	0.997229i	$0.523701\pi$
$774$	7.51027	0.269951
$775$	11.2609	0.404505
$776$	4.95178	0.177758
$777$	5.13552	0.184236
$778$	−3.03323	−0.108746
$779$	19.0679	0.683178
$780$	0	0
$781$	2.58664	0.0925571
$782$	−4.09257	−0.146350
$783$	−9.88794	−0.353366
$784$	1.00000	0.0357143
$785$	14.0966	0.503130
$786$	−4.83450	−0.172441
$787$	−18.9440	−0.675279	−0.337640	−	0.941275i	$-0.609628\pi$
$787$	−18.9440	−0.675279	−0.337640	+	0.941275i	$0.609628\pi$
$788$	−0.437589	−0.0155885
$789$	−16.2280	−0.577730
$790$	−12.8117	−0.455821
$791$	−8.18052	−0.290866
$792$	0.198062	0.00703784
$793$	0	0
$794$	14.1365	0.501685
$795$	−2.54860	−0.0903896
$796$	24.1946	0.857553
$797$	−16.7957	−0.594934	−0.297467	−	0.954732i	$-0.596142\pi$
$797$	−16.7957	−0.594934	−0.297467	+	0.954732i	$0.596142\pi$
$798$	−1.57281	−0.0556769
$799$	3.79030	0.134091
$800$	1.63605	0.0578430
$801$	5.55962	0.196440
$802$	−17.6596	−0.623582
$803$	−1.56487	−0.0552229
$804$	−0.307727	−0.0108527
$805$	−16.8663	−0.594460
$806$	0	0
$807$	3.99465	0.140618
$808$	0.0853103	0.00300121
$809$	−14.9738	−0.526450	−0.263225	−	0.964734i	$-0.584786\pi$
$809$	−14.9738	−0.526450	−0.263225	+	0.964734i	$0.584786\pi$
$810$	−1.83411	−0.0644440
$811$	41.5904	1.46044	0.730218	−	0.683214i	$-0.239418\pi$
$811$	41.5904	1.46044	0.730218	+	0.683214i	$0.239418\pi$
$812$	9.88794	0.346999
$813$	25.3380	0.888643
$814$	−1.01715	−0.0356512
$815$	−22.2118	−0.778046
$816$	0.445042	0.0155796
$817$	11.8122	0.413258
$818$	−11.6727	−0.408128
$819$	0	0
$820$	−22.2357	−0.776504
$821$	−12.6711	−0.442225	−0.221112	−	0.975248i	$-0.570969\pi$
$821$	−12.6711	−0.442225	−0.221112	+	0.975248i	$0.570969\pi$
$822$	−6.26783	−0.218616
$823$	19.9118	0.694082	0.347041	−	0.937850i	$-0.387186\pi$
$823$	19.9118	0.694082	0.347041	+	0.937850i	$0.387186\pi$
$824$	−7.20409	−0.250966
$825$	0.324039	0.0112816
$826$	−11.7846	−0.410038
$827$	23.9099	0.831430	0.415715	−	0.909495i	$-0.363531\pi$
$827$	23.9099	0.831430	0.415715	+	0.909495i	$0.363531\pi$
$828$	9.19592	0.319580
$829$	−23.7810	−0.825949	−0.412975	−	0.910743i	$-0.635510\pi$
$829$	−23.7810	−0.825949	−0.412975	+	0.910743i	$0.635510\pi$
$830$	5.86469	0.203566
$831$	−18.8962	−0.655501
$832$	0	0
$833$	0.445042	0.0154198
$834$	−13.6770	−0.473598
$835$	−27.2794	−0.944044
$836$	0.311515	0.0107740
$837$	−6.88303	−0.237912
$838$	31.2971	1.08114
$839$	−52.1839	−1.80159	−0.900794	−	0.434247i	$-0.857015\pi$
$839$	−52.1839	−1.80159	−0.900794	+	0.434247i	$0.857015\pi$
$840$	1.83411	0.0632828
$841$	68.7714	2.37143
$842$	−32.8881	−1.13340
$843$	15.7447	0.542277
$844$	−11.6272	−0.400226
$845$	0	0
$846$	−8.51673	−0.292811
$847$	10.9608	0.376617
$848$	−1.38956	−0.0477177
$849$	−6.46520	−0.221885
$850$	0.728109	0.0249739
$851$	−47.2258	−1.61888
$852$	−13.0597	−0.447418
$853$	−8.03941	−0.275264	−0.137632	−	0.990483i	$-0.543949\pi$
$853$	−8.03941	−0.275264	−0.137632	+	0.990483i	$0.543949\pi$
$854$	−10.1849	−0.348522
$855$	−2.88471	−0.0986549
$856$	−8.94825	−0.305845
$857$	−46.1043	−1.57489	−0.787447	−	0.616382i	$-0.788598\pi$
$857$	−46.1043	−1.57489	−0.787447	+	0.616382i	$0.788598\pi$
$858$	0	0
$859$	52.6147	1.79519	0.897595	−	0.440821i	$-0.145313\pi$
$859$	52.6147	1.79519	0.897595	+	0.440821i	$0.145313\pi$
$860$	−13.7747	−0.469712
$861$	12.1234	0.413166
$862$	37.9406	1.29226
$863$	−12.4191	−0.422752	−0.211376	−	0.977405i	$-0.567794\pi$
$863$	−12.4191	−0.422752	−0.211376	+	0.977405i	$0.567794\pi$
$864$	−1.00000	−0.0340207
$865$	−3.43570	−0.116817
$866$	−11.0673	−0.376083
$867$	−16.8019	−0.570624
$868$	6.88303	0.233625
$869$	−1.38352	−0.0469326
$870$	18.1356	0.614853
$871$	0	0
$872$	0.615818	0.0208542
$873$	−4.95178	−0.167592
$874$	14.4634	0.489233
$875$	12.1712	0.411463
$876$	7.90088	0.266946
$877$	40.2554	1.35933	0.679665	−	0.733523i	$-0.262125\pi$
$877$	40.2554	1.35933	0.679665	+	0.733523i	$0.262125\pi$
$878$	−0.955444	−0.0322447
$879$	5.37856	0.181414
$880$	−0.363268	−0.0122458
$881$	19.3338	0.651372	0.325686	−	0.945478i	$-0.394405\pi$
$881$	19.3338	0.651372	0.325686	+	0.945478i	$0.394405\pi$
$882$	−1.00000	−0.0336718
$883$	−47.3204	−1.59246	−0.796230	−	0.604994i	$-0.793175\pi$
$883$	−47.3204	−1.59246	−0.796230	+	0.604994i	$0.793175\pi$
$884$	0	0
$885$	−21.6142	−0.726554
$886$	26.1946	0.880025
$887$	−30.3048	−1.01754	−0.508768	−	0.860904i	$-0.669899\pi$
$887$	−30.3048	−1.01754	−0.508768	+	0.860904i	$0.669899\pi$
$888$	5.13552	0.172337
$889$	−5.91677	−0.198442
$890$	−10.1970	−0.341803
$891$	−0.198062	−0.00663534
$892$	−4.17401	−0.139756
$893$	−13.3952	−0.448254
$894$	13.3470	0.446391
$895$	−16.3471	−0.546425
$896$	1.00000	0.0334077
$897$	0	0
$898$	−24.1431	−0.805665
$899$	68.0590	2.26989
$900$	−1.63605	−0.0545349
$901$	−0.618412	−0.0206023
$902$	−2.40120	−0.0799511
$903$	7.51027	0.249926
$904$	−8.18052	−0.272080
$905$	−24.2924	−0.807507
$906$	1.21548	0.0403816
$907$	−23.5100	−0.780636	−0.390318	−	0.920680i	$-0.627635\pi$
$907$	−23.5100	−0.780636	−0.390318	+	0.920680i	$0.627635\pi$
$908$	−26.8243	−0.890194
$909$	−0.0853103	−0.00282956
$910$	0	0
$911$	−51.9982	−1.72278	−0.861389	−	0.507946i	$-0.830405\pi$
$911$	−51.9982	−1.72278	−0.861389	+	0.507946i	$0.830405\pi$
$912$	−1.57281	−0.0520810
$913$	0.633318	0.0209598
$914$	−10.6583	−0.352545
$915$	−18.6803	−0.617552
$916$	0.0599178	0.00197974
$917$	−4.83450	−0.159649
$918$	−0.445042	−0.0146886
$919$	23.4363	0.773091	0.386546	−	0.922270i	$-0.373668\pi$
$919$	23.4363	0.773091	0.386546	+	0.922270i	$0.373668\pi$
$920$	−16.8663	−0.556066
$921$	−26.8264	−0.883960
$922$	26.8656	0.884771
$923$	0	0
$924$	0.198062	0.00651577
$925$	8.40195	0.276254
$926$	−17.0698	−0.560948
$927$	7.20409	0.236613
$928$	9.88794	0.324588
$929$	0.112654	0.00369607	0.00184804	−	0.999998i	$-0.499412\pi$
$929$	0.112654	0.00369607	0.00184804	+	0.999998i	$0.499412\pi$
$930$	12.6242	0.413964
$931$	−1.57281	−0.0515468
$932$	14.7018	0.481574
$933$	22.2579	0.728692
$934$	32.1453	1.05183
$935$	−0.161669	−0.00528715
$936$	0	0
$937$	−48.1961	−1.57450	−0.787249	−	0.616636i	$-0.788495\pi$
$937$	−48.1961	−1.57450	−0.787249	+	0.616636i	$0.788495\pi$
$938$	−0.307727	−0.0100477
$939$	8.24762	0.269151
$940$	15.6206	0.509488
$941$	−49.5239	−1.61443	−0.807217	−	0.590255i	$-0.799027\pi$
$941$	−49.5239	−1.61443	−0.807217	+	0.590255i	$0.799027\pi$
$942$	−7.68582	−0.250418
$943$	−111.486	−3.63049
$944$	−11.7846	−0.383556
$945$	−1.83411	−0.0596636
$946$	−1.48750	−0.0483628
$947$	−28.1767	−0.915620	−0.457810	−	0.889050i	$-0.651366\pi$
$947$	−28.1767	−0.915620	−0.457810	+	0.889050i	$0.651366\pi$
$948$	6.98527	0.226871
$949$	0	0
$950$	−2.57319	−0.0834854
$951$	13.7293	0.445202
$952$	0.445042	0.0144239
$953$	−55.7822	−1.80696	−0.903481	−	0.428627i	$-0.858997\pi$
$953$	−55.7822	−1.80696	−0.903481	+	0.428627i	$0.858997\pi$
$954$	1.38956	0.0449886
$955$	−12.0393	−0.389584
$956$	−8.06112	−0.260715
$957$	1.95843	0.0633070
$958$	22.1790	0.716571
$959$	−6.26783	−0.202399
$960$	1.83411	0.0591956
$961$	16.3760	0.528259
$962$	0	0
$963$	8.94825	0.288353
$964$	1.03927	0.0334728
$965$	39.6952	1.27783
$966$	9.19592	0.295874
$967$	−19.7898	−0.636396	−0.318198	−	0.948024i	$-0.603078\pi$
$967$	−19.7898	−0.636396	−0.318198	+	0.948024i	$0.603078\pi$
$968$	10.9608	0.352293
$969$	−0.699967	−0.0224862
$970$	9.08210	0.291609
$971$	1.89350	0.0607653	0.0303826	−	0.999538i	$-0.490327\pi$
$971$	1.89350	0.0607653	0.0303826	+	0.999538i	$0.490327\pi$
$972$	1.00000	0.0320750
$973$	−13.6770	−0.438466
$974$	13.8814	0.444787
$975$	0	0
$976$	−10.1849	−0.326012
$977$	−3.77878	−0.120894	−0.0604470	−	0.998171i	$-0.519253\pi$
$977$	−3.77878	−0.120894	−0.0604470	+	0.998171i	$0.519253\pi$
$978$	12.1104	0.387249
$979$	−1.10115	−0.0351930
$980$	1.83411	0.0585884
$981$	−0.615818	−0.0196615
$982$	−12.7715	−0.407555
$983$	−6.78621	−0.216447	−0.108223	−	0.994127i	$-0.534516\pi$
$983$	−6.78621	−0.216447	−0.108223	+	0.994127i	$0.534516\pi$
$984$	12.1234	0.386481
$985$	−0.802586	−0.0255725
$986$	4.40055	0.140142
$987$	−8.51673	−0.271090
$988$	0	0
$989$	−69.0639	−2.19610
$990$	0.363268	0.0115454
$991$	−22.6239	−0.718672	−0.359336	−	0.933208i	$-0.616997\pi$
$991$	−22.6239	−0.718672	−0.359336	+	0.933208i	$0.616997\pi$
$992$	6.88303	0.218536
$993$	17.9130	0.568451
$994$	−13.0597	−0.414229
$995$	44.3754	1.40680
$996$	−3.19757	−0.101319
$997$	37.3318	1.18231	0.591155	−	0.806558i	$-0.298672\pi$
$997$	37.3318	1.18231	0.591155	+	0.806558i	$0.298672\pi$
$998$	17.0569	0.539928
$999$	−5.13552	−0.162481

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7098.2.a.cr.1.4	✓	6	1.1	even	1	trivial
7098.2.a.ct.1.3	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.83411 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.83411 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.83411 q^{10} -0.198062 q^{11} +1.00000 q^{12} +1.00000 q^{14} +1.83411 q^{15} +1.00000 q^{16} +0.445042 q^{17} -1.00000 q^{18} -1.57281 q^{19} +1.83411 q^{20} -1.00000 q^{21} +0.198062 q^{22} +9.19592 q^{23} -1.00000 q^{24} -1.63605 q^{25} +1.00000 q^{27} -1.00000 q^{28} -9.88794 q^{29} -1.83411 q^{30} -6.88303 q^{31} -1.00000 q^{32} -0.198062 q^{33} -0.445042 q^{34} -1.83411 q^{35} +1.00000 q^{36} -5.13552 q^{37} +1.57281 q^{38} -1.83411 q^{40} -12.1234 q^{41} +1.00000 q^{42} -7.51027 q^{43} -0.198062 q^{44} +1.83411 q^{45} -9.19592 q^{46} +8.51673 q^{47} +1.00000 q^{48} +1.00000 q^{49} +1.63605 q^{50} +0.445042 q^{51} -1.38956 q^{53} -1.00000 q^{54} -0.363268 q^{55} +1.00000 q^{56} -1.57281 q^{57} +9.88794 q^{58} -11.7846 q^{59} +1.83411 q^{60} -10.1849 q^{61} +6.88303 q^{62} -1.00000 q^{63} +1.00000 q^{64} +0.198062 q^{66} -0.307727 q^{67} +0.445042 q^{68} +9.19592 q^{69} +1.83411 q^{70} -13.0597 q^{71} -1.00000 q^{72} +7.90088 q^{73} +5.13552 q^{74} -1.63605 q^{75} -1.57281 q^{76} +0.198062 q^{77} +6.98527 q^{79} +1.83411 q^{80} +1.00000 q^{81} +12.1234 q^{82} -3.19757 q^{83} -1.00000 q^{84} +0.816255 q^{85} +7.51027 q^{86} -9.88794 q^{87} +0.198062 q^{88} +5.55962 q^{89} -1.83411 q^{90} +9.19592 q^{92} -6.88303 q^{93} -8.51673 q^{94} -2.88471 q^{95} -1.00000 q^{96} -4.95178 q^{97} -1.00000 q^{98} -0.198062 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} - 3 q^{5} - 6 q^{6} - 6 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 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	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} - 3 q^{5} - 6 q^{6} - 6 q^{7} - 6 q^{8} + 6 q^{9} + 3 q^{10} - 10 q^{11} + 6 q^{12} + 6 q^{14} - 3 q^{15} + 6 q^{16} + 2 q^{17} - 6 q^{18} - 2 q^{19} - 3 q^{20} - 6 q^{21} + 10 q^{22} + 4 q^{23} - 6 q^{24} + 13 q^{25} + 6 q^{27} - 6 q^{28} + 2 q^{29} + 3 q^{30} - 9 q^{31} - 6 q^{32} - 10 q^{33} - 2 q^{34} + 3 q^{35} + 6 q^{36} - 7 q^{37} + 2 q^{38} + 3 q^{40} - 11 q^{41} + 6 q^{42} - 5 q^{43} - 10 q^{44} - 3 q^{45} - 4 q^{46} - 5 q^{47} + 6 q^{48} + 6 q^{49} - 13 q^{50} + 2 q^{51} - 6 q^{53} - 6 q^{54} + 5 q^{55} + 6 q^{56} - 2 q^{57} - 2 q^{58} - 28 q^{59} - 3 q^{60} + 23 q^{61} + 9 q^{62} - 6 q^{63} + 6 q^{64} + 10 q^{66} + 10 q^{67} + 2 q^{68} + 4 q^{69} - 3 q^{70} - 21 q^{71} - 6 q^{72} + 7 q^{73} + 7 q^{74} + 13 q^{75} - 2 q^{76} + 10 q^{77} - 14 q^{79} - 3 q^{80} + 6 q^{81} + 11 q^{82} - 17 q^{83} - 6 q^{84} - q^{85} + 5 q^{86} + 2 q^{87} + 10 q^{88} - 17 q^{89} + 3 q^{90} + 4 q^{92} - 9 q^{93} + 5 q^{94} - 22 q^{95} - 6 q^{96} - 6 q^{98} - 10 q^{99}+O(q^{100}) \) 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 - 10 * q^11 + 6 * q^12 + 6 * q^14 - 3 * q^15 + 6 * q^16 + 2 * q^17 - 6 * q^18 - 2 * q^19 - 3 * q^20 - 6 * q^21 + 10 * q^22 + 4 * q^23 - 6 * q^24 + 13 * q^25 + 6 * q^27 - 6 * q^28 + 2 * q^29 + 3 * q^30 - 9 * q^31 - 6 * q^32 - 10 * q^33 - 2 * q^34 + 3 * q^35 + 6 * q^36 - 7 * q^37 + 2 * q^38 + 3 * q^40 - 11 * q^41 + 6 * q^42 - 5 * q^43 - 10 * q^44 - 3 * q^45 - 4 * q^46 - 5 * q^47 + 6 * q^48 + 6 * q^49 - 13 * q^50 + 2 * q^51 - 6 * q^53 - 6 * q^54 + 5 * q^55 + 6 * q^56 - 2 * q^57 - 2 * q^58 - 28 * q^59 - 3 * q^60 + 23 * q^61 + 9 * q^62 - 6 * q^63 + 6 * q^64 + 10 * q^66 + 10 * q^67 + 2 * q^68 + 4 * q^69 - 3 * q^70 - 21 * q^71 - 6 * q^72 + 7 * q^73 + 7 * q^74 + 13 * q^75 - 2 * q^76 + 10 * q^77 - 14 * q^79 - 3 * q^80 + 6 * q^81 + 11 * q^82 - 17 * q^83 - 6 * q^84 - q^85 + 5 * q^86 + 2 * q^87 + 10 * q^88 - 17 * q^89 + 3 * q^90 + 4 * q^92 - 9 * q^93 + 5 * q^94 - 22 * q^95 - 6 * q^96 - 6 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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