LMFDB - Embedded newform 7098.2.a.cj.1.1

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:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
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			1.1
Root			$1.80194$ of defining polynomial
Character	$\chi$	$=$	7098.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.801938 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.801938 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.801938 q^{10} +4.04892 q^{11} -1.00000 q^{12} -1.00000 q^{14} +0.801938 q^{15} +1.00000 q^{16} -0.753020 q^{17} +1.00000 q^{18} +0.664874 q^{19} -0.801938 q^{20} +1.00000 q^{21} +4.04892 q^{22} -3.80194 q^{23} -1.00000 q^{24} -4.35690 q^{25} -1.00000 q^{27} -1.00000 q^{28} -8.74094 q^{29} +0.801938 q^{30} +0.335126 q^{31} +1.00000 q^{32} -4.04892 q^{33} -0.753020 q^{34} +0.801938 q^{35} +1.00000 q^{36} -4.58211 q^{37} +0.664874 q^{38} -0.801938 q^{40} +6.89977 q^{41} +1.00000 q^{42} -1.30798 q^{43} +4.04892 q^{44} -0.801938 q^{45} -3.80194 q^{46} -5.49396 q^{47} -1.00000 q^{48} +1.00000 q^{49} -4.35690 q^{50} +0.753020 q^{51} +3.04892 q^{53} -1.00000 q^{54} -3.24698 q^{55} -1.00000 q^{56} -0.664874 q^{57} -8.74094 q^{58} -2.58211 q^{59} +0.801938 q^{60} +3.71379 q^{61} +0.335126 q^{62} -1.00000 q^{63} +1.00000 q^{64} -4.04892 q^{66} -8.86294 q^{67} -0.753020 q^{68} +3.80194 q^{69} +0.801938 q^{70} -10.1957 q^{71} +1.00000 q^{72} +9.44265 q^{73} -4.58211 q^{74} +4.35690 q^{75} +0.664874 q^{76} -4.04892 q^{77} +11.7899 q^{79} -0.801938 q^{80} +1.00000 q^{81} +6.89977 q^{82} +9.21313 q^{83} +1.00000 q^{84} +0.603875 q^{85} -1.30798 q^{86} +8.74094 q^{87} +4.04892 q^{88} +1.75302 q^{89} -0.801938 q^{90} -3.80194 q^{92} -0.335126 q^{93} -5.49396 q^{94} -0.533188 q^{95} -1.00000 q^{96} -8.18598 q^{97} +1.00000 q^{98} +4.04892 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + 2 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 + 2 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + 2 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9} + 2 q^{10} + 3 q^{11} - 3 q^{12} - 3 q^{14} - 2 q^{15} + 3 q^{16} - 7 q^{17} + 3 q^{18} + 3 q^{19} + 2 q^{20} + 3 q^{21} + 3 q^{22} - 7 q^{23} - 3 q^{24} - 9 q^{25} - 3 q^{27} - 3 q^{28} - 12 q^{29} - 2 q^{30} + 3 q^{32} - 3 q^{33} - 7 q^{34} - 2 q^{35} + 3 q^{36} - 8 q^{37} + 3 q^{38} + 2 q^{40} - 2 q^{41} + 3 q^{42} - 9 q^{43} + 3 q^{44} + 2 q^{45} - 7 q^{46} - 7 q^{47} - 3 q^{48} + 3 q^{49} - 9 q^{50} + 7 q^{51} - 3 q^{54} - 5 q^{55} - 3 q^{56} - 3 q^{57} - 12 q^{58} - 2 q^{59} - 2 q^{60} + 3 q^{61} - 3 q^{63} + 3 q^{64} - 3 q^{66} - 32 q^{67} - 7 q^{68} + 7 q^{69} - 2 q^{70} + 6 q^{71} + 3 q^{72} - 13 q^{73} - 8 q^{74} + 9 q^{75} + 3 q^{76} - 3 q^{77} + 12 q^{79} + 2 q^{80} + 3 q^{81} - 2 q^{82} + 7 q^{83} + 3 q^{84} - 7 q^{85} - 9 q^{86} + 12 q^{87} + 3 q^{88} + 10 q^{89} + 2 q^{90} - 7 q^{92} - 7 q^{94} - 5 q^{95} - 3 q^{96} - 10 q^{97} + 3 q^{98} + 3 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 + 2 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9 + 2 * q^10 + 3 * q^11 - 3 * q^12 - 3 * q^14 - 2 * q^15 + 3 * q^16 - 7 * q^17 + 3 * q^18 + 3 * q^19 + 2 * q^20 + 3 * q^21 + 3 * q^22 - 7 * q^23 - 3 * q^24 - 9 * q^25 - 3 * q^27 - 3 * q^28 - 12 * q^29 - 2 * q^30 + 3 * q^32 - 3 * q^33 - 7 * q^34 - 2 * q^35 + 3 * q^36 - 8 * q^37 + 3 * q^38 + 2 * q^40 - 2 * q^41 + 3 * q^42 - 9 * q^43 + 3 * q^44 + 2 * q^45 - 7 * q^46 - 7 * q^47 - 3 * q^48 + 3 * q^49 - 9 * q^50 + 7 * q^51 - 3 * q^54 - 5 * q^55 - 3 * q^56 - 3 * q^57 - 12 * q^58 - 2 * q^59 - 2 * q^60 + 3 * q^61 - 3 * q^63 + 3 * q^64 - 3 * q^66 - 32 * q^67 - 7 * q^68 + 7 * q^69 - 2 * q^70 + 6 * q^71 + 3 * q^72 - 13 * q^73 - 8 * q^74 + 9 * q^75 + 3 * q^76 - 3 * q^77 + 12 * q^79 + 2 * q^80 + 3 * q^81 - 2 * q^82 + 7 * q^83 + 3 * q^84 - 7 * q^85 - 9 * q^86 + 12 * q^87 + 3 * q^88 + 10 * q^89 + 2 * q^90 - 7 * q^92 - 7 * q^94 - 5 * q^95 - 3 * q^96 - 10 * q^97 + 3 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−0.801938	−0.358637	−0.179319	−	0.983791i	$-0.557389\pi$
$5$	−0.801938	−0.358637	−0.179319	+	0.983791i	$0.557389\pi$
$6$	−1.00000	−0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.801938	−0.253595
$11$	4.04892	1.22079	0.610397	−	0.792095i	$-0.291010\pi$
$11$	4.04892	1.22079	0.610397	+	0.792095i	$0.291010\pi$
$12$	−1.00000	−0.288675
$13$	0	0
$13$	0	0
$14$	−1.00000	−0.267261
$15$	0.801938	0.207059
$16$	1.00000	0.250000
$17$	−0.753020	−0.182634	−0.0913171	−	0.995822i	$-0.529108\pi$
$17$	−0.753020	−0.182634	−0.0913171	+	0.995822i	$0.529108\pi$
$18$	1.00000	0.235702
$19$	0.664874	0.152533	0.0762663	−	0.997087i	$-0.475700\pi$
$19$	0.664874	0.152533	0.0762663	+	0.997087i	$0.475700\pi$
$20$	−0.801938	−0.179319
$21$	1.00000	0.218218
$22$	4.04892	0.863232
$23$	−3.80194	−0.792759	−0.396379	−	0.918087i	$-0.629734\pi$
$23$	−3.80194	−0.792759	−0.396379	+	0.918087i	$0.629734\pi$
$24$	−1.00000	−0.204124
$25$	−4.35690	−0.871379
$26$	0	0
$27$	−1.00000	−0.192450
$28$	−1.00000	−0.188982
$29$	−8.74094	−1.62315	−0.811576	−	0.584247i	$-0.801390\pi$
$29$	−8.74094	−1.62315	−0.811576	+	0.584247i	$0.801390\pi$
$30$	0.801938	0.146413
$31$	0.335126	0.0601903	0.0300952	−	0.999547i	$-0.490419\pi$
$31$	0.335126	0.0601903	0.0300952	+	0.999547i	$0.490419\pi$
$32$	1.00000	0.176777
$33$	−4.04892	−0.704826
$34$	−0.753020	−0.129142
$35$	0.801938	0.135552
$36$	1.00000	0.166667
$37$	−4.58211	−0.753293	−0.376647	−	0.926357i	$-0.622923\pi$
$37$	−4.58211	−0.753293	−0.376647	+	0.926357i	$0.622923\pi$
$38$	0.664874	0.107857
$39$	0	0
$40$	−0.801938	−0.126797
$41$	6.89977	1.07756	0.538782	−	0.842445i	$-0.318885\pi$
$41$	6.89977	1.07756	0.538782	+	0.842445i	$0.318885\pi$
$42$	1.00000	0.154303
$43$	−1.30798	−0.199465	−0.0997324	−	0.995014i	$-0.531799\pi$
$43$	−1.30798	−0.199465	−0.0997324	+	0.995014i	$0.531799\pi$
$44$	4.04892	0.610397
$45$	−0.801938	−0.119546
$46$	−3.80194	−0.560565
$47$	−5.49396	−0.801376	−0.400688	−	0.916214i	$-0.631229\pi$
$47$	−5.49396	−0.801376	−0.400688	+	0.916214i	$0.631229\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−4.35690	−0.616158
$51$	0.753020	0.105444
$52$	0	0
$53$	3.04892	0.418801	0.209401	−	0.977830i	$-0.432849\pi$
$53$	3.04892	0.418801	0.209401	+	0.977830i	$0.432849\pi$
$54$	−1.00000	−0.136083
$55$	−3.24698	−0.437823
$56$	−1.00000	−0.133631
$57$	−0.664874	−0.0880648
$58$	−8.74094	−1.14774
$59$	−2.58211	−0.336161	−0.168081	−	0.985773i	$-0.553757\pi$
$59$	−2.58211	−0.336161	−0.168081	+	0.985773i	$0.553757\pi$
$60$	0.801938	0.103530
$61$	3.71379	0.475502	0.237751	−	0.971326i	$-0.423590\pi$
$61$	3.71379	0.475502	0.237751	+	0.971326i	$0.423590\pi$
$62$	0.335126	0.0425610
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	−4.04892	−0.498387
$67$	−8.86294	−1.08278	−0.541390	−	0.840772i	$-0.682102\pi$
$67$	−8.86294	−1.08278	−0.541390	+	0.840772i	$0.682102\pi$
$68$	−0.753020	−0.0913171
$69$	3.80194	0.457700
$70$	0.801938	0.0958499
$71$	−10.1957	−1.21000	−0.605002	−	0.796224i	$-0.706828\pi$
$71$	−10.1957	−1.21000	−0.605002	+	0.796224i	$0.706828\pi$
$72$	1.00000	0.117851
$73$	9.44265	1.10518	0.552589	−	0.833454i	$-0.313640\pi$
$73$	9.44265	1.10518	0.552589	+	0.833454i	$0.313640\pi$
$74$	−4.58211	−0.532659
$75$	4.35690	0.503091
$76$	0.664874	0.0762663
$77$	−4.04892	−0.461417
$78$	0	0
$79$	11.7899	1.32646	0.663231	−	0.748415i	$-0.269185\pi$
$79$	11.7899	1.32646	0.663231	+	0.748415i	$0.269185\pi$
$80$	−0.801938	−0.0896594
$81$	1.00000	0.111111
$82$	6.89977	0.761952
$83$	9.21313	1.01127	0.505636	−	0.862747i	$-0.331258\pi$
$83$	9.21313	1.01127	0.505636	+	0.862747i	$0.331258\pi$
$84$	1.00000	0.109109
$85$	0.603875	0.0654995
$86$	−1.30798	−0.141043
$87$	8.74094	0.937127
$88$	4.04892	0.431616
$89$	1.75302	0.185820	0.0929099	−	0.995675i	$-0.470383\pi$
$89$	1.75302	0.185820	0.0929099	+	0.995675i	$0.470383\pi$
$90$	−0.801938	−0.0845317
$91$	0	0
$92$	−3.80194	−0.396379
$93$	−0.335126	−0.0347509
$94$	−5.49396	−0.566659
$95$	−0.533188	−0.0547039
$96$	−1.00000	−0.102062
$97$	−8.18598	−0.831160	−0.415580	−	0.909557i	$-0.636421\pi$
$97$	−8.18598	−0.831160	−0.415580	+	0.909557i	$0.636421\pi$
$98$	1.00000	0.101015
$99$	4.04892	0.406932
$100$	−4.35690	−0.435690
$101$	15.6189	1.55414	0.777071	−	0.629413i	$-0.216704\pi$
$101$	15.6189	1.55414	0.777071	+	0.629413i	$0.216704\pi$
$102$	0.753020	0.0745601
$103$	−13.1347	−1.29420	−0.647099	−	0.762406i	$-0.724018\pi$
$103$	−13.1347	−1.29420	−0.647099	+	0.762406i	$0.724018\pi$
$104$	0	0
$105$	−0.801938	−0.0782611
$106$	3.04892	0.296137
$107$	−10.1642	−0.982611	−0.491306	−	0.870987i	$-0.663480\pi$
$107$	−10.1642	−0.982611	−0.491306	+	0.870987i	$0.663480\pi$
$108$	−1.00000	−0.0962250
$109$	−13.4494	−1.28821	−0.644107	−	0.764935i	$-0.722771\pi$
$109$	−13.4494	−1.28821	−0.644107	+	0.764935i	$0.722771\pi$
$110$	−3.24698	−0.309587
$111$	4.58211	0.434914
$112$	−1.00000	−0.0944911
$113$	−3.26444	−0.307092	−0.153546	−	0.988141i	$-0.549069\pi$
$113$	−3.26444	−0.307092	−0.153546	+	0.988141i	$0.549069\pi$
$114$	−0.664874	−0.0622712
$115$	3.04892	0.284313
$116$	−8.74094	−0.811576
$117$	0	0
$118$	−2.58211	−0.237702
$119$	0.753020	0.0690293
$120$	0.801938	0.0732066
$121$	5.39373	0.490339
$122$	3.71379	0.336231
$123$	−6.89977	−0.622132
$124$	0.335126	0.0300952
$125$	7.50365	0.671147
$126$	−1.00000	−0.0890871
$127$	7.74094	0.686897	0.343449	−	0.939171i	$-0.388405\pi$
$127$	7.74094	0.686897	0.343449	+	0.939171i	$0.388405\pi$
$128$	1.00000	0.0883883
$129$	1.30798	0.115161
$130$	0	0
$131$	9.12498	0.797253	0.398627	−	0.917113i	$-0.369487\pi$
$131$	9.12498	0.797253	0.398627	+	0.917113i	$0.369487\pi$
$132$	−4.04892	−0.352413
$133$	−0.664874	−0.0576519
$134$	−8.86294	−0.765641
$135$	0.801938	0.0690198
$136$	−0.753020	−0.0645710
$137$	−10.4722	−0.894699	−0.447350	−	0.894359i	$-0.647632\pi$
$137$	−10.4722	−0.894699	−0.447350	+	0.894359i	$0.647632\pi$
$138$	3.80194	0.323642
$139$	3.66487	0.310851	0.155425	−	0.987848i	$-0.450325\pi$
$139$	3.66487	0.310851	0.155425	+	0.987848i	$0.450325\pi$
$140$	0.801938	0.0677761
$141$	5.49396	0.462675
$142$	−10.1957	−0.855602
$143$	0	0
$144$	1.00000	0.0833333
$145$	7.00969	0.582123
$146$	9.44265	0.781479
$147$	−1.00000	−0.0824786
$148$	−4.58211	−0.376647
$149$	−18.7385	−1.53512	−0.767561	−	0.640976i	$-0.778530\pi$
$149$	−18.7385	−1.53512	−0.767561	+	0.640976i	$0.778530\pi$
$150$	4.35690	0.355739
$151$	−17.4209	−1.41769	−0.708846	−	0.705364i	$-0.750784\pi$
$151$	−17.4209	−1.41769	−0.708846	+	0.705364i	$0.750784\pi$
$152$	0.664874	0.0539284
$153$	−0.753020	−0.0608781
$154$	−4.04892	−0.326271
$155$	−0.268750	−0.0215865
$156$	0	0
$157$	4.39612	0.350849	0.175424	−	0.984493i	$-0.443870\pi$
$157$	4.39612	0.350849	0.175424	+	0.984493i	$0.443870\pi$
$158$	11.7899	0.937951
$159$	−3.04892	−0.241795
$160$	−0.801938	−0.0633987
$161$	3.80194	0.299635
$162$	1.00000	0.0785674
$163$	−11.8062	−0.924737	−0.462368	−	0.886688i	$-0.653000\pi$
$163$	−11.8062	−0.924737	−0.462368	+	0.886688i	$0.653000\pi$
$164$	6.89977	0.538782
$165$	3.24698	0.252777
$166$	9.21313	0.715077
$167$	−8.05861	−0.623594	−0.311797	−	0.950149i	$-0.600931\pi$
$167$	−8.05861	−0.623594	−0.311797	+	0.950149i	$0.600931\pi$
$168$	1.00000	0.0771517
$169$	0	0
$170$	0.603875	0.0463151
$171$	0.664874	0.0508442
$172$	−1.30798	−0.0997324
$173$	−10.4940	−0.797841	−0.398920	−	0.916986i	$-0.630615\pi$
$173$	−10.4940	−0.797841	−0.398920	+	0.916986i	$0.630615\pi$
$174$	8.74094	0.662649
$175$	4.35690	0.329350
$176$	4.04892	0.305199
$177$	2.58211	0.194083
$178$	1.75302	0.131394
$179$	4.08575	0.305384	0.152692	−	0.988274i	$-0.451206\pi$
$179$	4.08575	0.305384	0.152692	+	0.988274i	$0.451206\pi$
$180$	−0.801938	−0.0597729
$181$	−13.1196	−0.975173	−0.487586	−	0.873075i	$-0.662123\pi$
$181$	−13.1196	−0.975173	−0.487586	+	0.873075i	$0.662123\pi$
$182$	0	0
$183$	−3.71379	−0.274531
$184$	−3.80194	−0.280283
$185$	3.67456	0.270159
$186$	−0.335126	−0.0245726
$187$	−3.04892	−0.222959
$188$	−5.49396	−0.400688
$189$	1.00000	0.0727393
$190$	−0.533188	−0.0386815
$191$	−5.74094	−0.415400	−0.207700	−	0.978193i	$-0.566598\pi$
$191$	−5.74094	−0.415400	−0.207700	+	0.978193i	$0.566598\pi$
$192$	−1.00000	−0.0721688
$193$	11.3817	0.819269	0.409635	−	0.912250i	$-0.365656\pi$
$193$	11.3817	0.819269	0.409635	+	0.912250i	$0.365656\pi$
$194$	−8.18598	−0.587719
$195$	0	0
$196$	1.00000	0.0714286
$197$	−8.63102	−0.614935	−0.307467	−	0.951559i	$-0.599482\pi$
$197$	−8.63102	−0.614935	−0.307467	+	0.951559i	$0.599482\pi$
$198$	4.04892	0.287744
$199$	3.87263	0.274523	0.137262	−	0.990535i	$-0.456170\pi$
$199$	3.87263	0.274523	0.137262	+	0.990535i	$0.456170\pi$
$200$	−4.35690	−0.308079
$201$	8.86294	0.625143
$202$	15.6189	1.09894
$203$	8.74094	0.613494
$204$	0.753020	0.0527220
$205$	−5.53319	−0.386455
$206$	−13.1347	−0.915136
$207$	−3.80194	−0.264253
$208$	0	0
$209$	2.69202	0.186211
$210$	−0.801938	−0.0553390
$211$	0.533188	0.0367062	0.0183531	−	0.999832i	$-0.494158\pi$
$211$	0.533188	0.0367062	0.0183531	+	0.999832i	$0.494158\pi$
$212$	3.04892	0.209401
$213$	10.1957	0.698596
$214$	−10.1642	−0.694811
$215$	1.04892	0.0715356
$216$	−1.00000	−0.0680414
$217$	−0.335126	−0.0227498
$218$	−13.4494	−0.910905
$219$	−9.44265	−0.638075
$220$	−3.24698	−0.218911
$221$	0	0
$222$	4.58211	0.307531
$223$	−23.0640	−1.54448	−0.772239	−	0.635332i	$-0.780863\pi$
$223$	−23.0640	−1.54448	−0.772239	+	0.635332i	$0.780863\pi$
$224$	−1.00000	−0.0668153
$225$	−4.35690	−0.290460
$226$	−3.26444	−0.217147
$227$	−28.8388	−1.91410	−0.957048	−	0.289928i	$-0.906368\pi$
$227$	−28.8388	−1.91410	−0.957048	+	0.289928i	$0.906368\pi$
$228$	−0.664874	−0.0440324
$229$	16.3817	1.08253	0.541265	−	0.840852i	$-0.317946\pi$
$229$	16.3817	1.08253	0.541265	+	0.840852i	$0.317946\pi$
$230$	3.04892	0.201040
$231$	4.04892	0.266399
$232$	−8.74094	−0.573871
$233$	−10.0261	−0.656830	−0.328415	−	0.944533i	$-0.606515\pi$
$233$	−10.0261	−0.656830	−0.328415	+	0.944533i	$0.606515\pi$
$234$	0	0
$235$	4.40581	0.287404
$236$	−2.58211	−0.168081
$237$	−11.7899	−0.765833
$238$	0.753020	0.0488111
$239$	−7.32975	−0.474122	−0.237061	−	0.971495i	$-0.576184\pi$
$239$	−7.32975	−0.474122	−0.237061	+	0.971495i	$0.576184\pi$
$240$	0.801938	0.0517649
$241$	−9.00969	−0.580365	−0.290183	−	0.956971i	$-0.593716\pi$
$241$	−9.00969	−0.580365	−0.290183	+	0.956971i	$0.593716\pi$
$242$	5.39373	0.346722
$243$	−1.00000	−0.0641500
$244$	3.71379	0.237751
$245$	−0.801938	−0.0512339
$246$	−6.89977	−0.439913
$247$	0	0
$248$	0.335126	0.0212805
$249$	−9.21313	−0.583858
$250$	7.50365	0.474572
$251$	−26.2978	−1.65990	−0.829952	−	0.557835i	$-0.811632\pi$
$251$	−26.2978	−1.65990	−0.829952	+	0.557835i	$0.811632\pi$
$252$	−1.00000	−0.0629941
$253$	−15.3937	−0.967796
$254$	7.74094	0.485710
$255$	−0.603875	−0.0378161
$256$	1.00000	0.0625000
$257$	−21.4209	−1.33620	−0.668099	−	0.744073i	$-0.732892\pi$
$257$	−21.4209	−1.33620	−0.668099	+	0.744073i	$0.732892\pi$
$258$	1.30798	0.0814312
$259$	4.58211	0.284718
$260$	0	0
$261$	−8.74094	−0.541051
$262$	9.12498	0.563743
$263$	7.50902	0.463026	0.231513	−	0.972832i	$-0.425632\pi$
$263$	7.50902	0.463026	0.231513	+	0.972832i	$0.425632\pi$
$264$	−4.04892	−0.249194
$265$	−2.44504	−0.150198
$266$	−0.664874	−0.0407661
$267$	−1.75302	−0.107283
$268$	−8.86294	−0.541390
$269$	−11.3870	−0.694279	−0.347140	−	0.937813i	$-0.612847\pi$
$269$	−11.3870	−0.694279	−0.347140	+	0.937813i	$0.612847\pi$
$270$	0.801938	0.0488044
$271$	−17.4470	−1.05983	−0.529914	−	0.848052i	$-0.677776\pi$
$271$	−17.4470	−1.05983	−0.529914	+	0.848052i	$0.677776\pi$
$272$	−0.753020	−0.0456586
$273$	0	0
$274$	−10.4722	−0.632648
$275$	−17.6407	−1.06377
$276$	3.80194	0.228850
$277$	−20.5351	−1.23383	−0.616917	−	0.787028i	$-0.711619\pi$
$277$	−20.5351	−1.23383	−0.616917	+	0.787028i	$0.711619\pi$
$278$	3.66487	0.219805
$279$	0.335126	0.0200634
$280$	0.801938	0.0479249
$281$	10.2567	0.611862	0.305931	−	0.952054i	$-0.401032\pi$
$281$	10.2567	0.611862	0.305931	+	0.952054i	$0.401032\pi$
$282$	5.49396	0.327161
$283$	−1.21744	−0.0723693	−0.0361846	−	0.999345i	$-0.511520\pi$
$283$	−1.21744	−0.0723693	−0.0361846	+	0.999345i	$0.511520\pi$
$284$	−10.1957	−0.605002
$285$	0.533188	0.0315833
$286$	0	0
$287$	−6.89977	−0.407281
$288$	1.00000	0.0589256
$289$	−16.4330	−0.966645
$290$	7.00969	0.411623
$291$	8.18598	0.479871
$292$	9.44265	0.552589
$293$	−0.408206	−0.0238477	−0.0119238	−	0.999929i	$-0.503796\pi$
$293$	−0.408206	−0.0238477	−0.0119238	+	0.999929i	$0.503796\pi$
$294$	−1.00000	−0.0583212
$295$	2.07069	0.120560
$296$	−4.58211	−0.266329
$297$	−4.04892	−0.234942
$298$	−18.7385	−1.08549
$299$	0	0
$300$	4.35690	0.251546
$301$	1.30798	0.0753906
$302$	−17.4209	−1.00246
$303$	−15.6189	−0.897285
$304$	0.664874	0.0381332
$305$	−2.97823	−0.170533
$306$	−0.753020	−0.0430473
$307$	19.1540	1.09318	0.546590	−	0.837401i	$-0.315926\pi$
$307$	19.1540	1.09318	0.546590	+	0.837401i	$0.315926\pi$
$308$	−4.04892	−0.230708
$309$	13.1347	0.747205
$310$	−0.268750	−0.0152640
$311$	19.2513	1.09164	0.545820	−	0.837902i	$-0.316218\pi$
$311$	19.2513	1.09164	0.545820	+	0.837902i	$0.316218\pi$
$312$	0	0
$313$	26.4644	1.49586	0.747929	−	0.663779i	$-0.231048\pi$
$313$	26.4644	1.49586	0.747929	+	0.663779i	$0.231048\pi$
$314$	4.39612	0.248088
$315$	0.801938	0.0451841
$316$	11.7899	0.663231
$317$	1.19136	0.0669133	0.0334567	−	0.999440i	$-0.489348\pi$
$317$	1.19136	0.0669133	0.0334567	+	0.999440i	$0.489348\pi$
$318$	−3.04892	−0.170975
$319$	−35.3913	−1.98153
$320$	−0.801938	−0.0448297
$321$	10.1642	0.567311
$322$	3.80194	0.211874
$323$	−0.500664	−0.0278577
$324$	1.00000	0.0555556
$325$	0	0
$326$	−11.8062	−0.653888
$327$	13.4494	0.743751
$328$	6.89977	0.380976
$329$	5.49396	0.302892
$330$	3.24698	0.178740
$331$	10.8847	0.598278	0.299139	−	0.954210i	$-0.403301\pi$
$331$	10.8847	0.598278	0.299139	+	0.954210i	$0.403301\pi$
$332$	9.21313	0.505636
$333$	−4.58211	−0.251098
$334$	−8.05861	−0.440947
$335$	7.10752	0.388325
$336$	1.00000	0.0545545
$337$	−21.2717	−1.15875	−0.579373	−	0.815063i	$-0.696702\pi$
$337$	−21.2717	−1.15875	−0.579373	+	0.815063i	$0.696702\pi$
$338$	0	0
$339$	3.26444	0.177300
$340$	0.603875	0.0327497
$341$	1.35690	0.0734800
$342$	0.664874	0.0359523
$343$	−1.00000	−0.0539949
$344$	−1.30798	−0.0705215
$345$	−3.04892	−0.164148
$346$	−10.4940	−0.564159
$347$	3.18060	0.170744	0.0853719	−	0.996349i	$-0.472792\pi$
$347$	3.18060	0.170744	0.0853719	+	0.996349i	$0.472792\pi$
$348$	8.74094	0.468564
$349$	3.32736	0.178109	0.0890546	−	0.996027i	$-0.471615\pi$
$349$	3.32736	0.178109	0.0890546	+	0.996027i	$0.471615\pi$
$350$	4.35690	0.232886
$351$	0	0
$352$	4.04892	0.215808
$353$	21.1594	1.12620	0.563101	−	0.826388i	$-0.309608\pi$
$353$	21.1594	1.12620	0.563101	+	0.826388i	$0.309608\pi$
$354$	2.58211	0.137237
$355$	8.17629	0.433953
$356$	1.75302	0.0929099
$357$	−0.753020	−0.0398541
$358$	4.08575	0.215939
$359$	26.4088	1.39380	0.696902	−	0.717167i	$-0.254561\pi$
$359$	26.4088	1.39380	0.696902	+	0.717167i	$0.254561\pi$
$360$	−0.801938	−0.0422658
$361$	−18.5579	−0.976734
$362$	−13.1196	−0.689551
$363$	−5.39373	−0.283097
$364$	0	0
$365$	−7.57242	−0.396358
$366$	−3.71379	−0.194123
$367$	14.4504	0.754306	0.377153	−	0.926151i	$-0.376903\pi$
$367$	14.4504	0.754306	0.377153	+	0.926151i	$0.376903\pi$
$368$	−3.80194	−0.198190
$369$	6.89977	0.359188
$370$	3.67456	0.191031
$371$	−3.04892	−0.158292
$372$	−0.335126	−0.0173755
$373$	21.5719	1.11695	0.558476	−	0.829520i	$-0.311386\pi$
$373$	21.5719	1.11695	0.558476	+	0.829520i	$0.311386\pi$
$374$	−3.04892	−0.157656
$375$	−7.50365	−0.387487
$376$	−5.49396	−0.283329
$377$	0	0
$378$	1.00000	0.0514344
$379$	−3.66056	−0.188030	−0.0940152	−	0.995571i	$-0.529970\pi$
$379$	−3.66056	−0.188030	−0.0940152	+	0.995571i	$0.529970\pi$
$380$	−0.533188	−0.0273520
$381$	−7.74094	−0.396580
$382$	−5.74094	−0.293732
$383$	4.53989	0.231978	0.115989	−	0.993251i	$-0.462996\pi$
$383$	4.53989	0.231978	0.115989	+	0.993251i	$0.462996\pi$
$384$	−1.00000	−0.0510310
$385$	3.24698	0.165481
$386$	11.3817	0.579311
$387$	−1.30798	−0.0664883
$388$	−8.18598	−0.415580
$389$	−5.90648	−0.299470	−0.149735	−	0.988726i	$-0.547842\pi$
$389$	−5.90648	−0.299470	−0.149735	+	0.988726i	$0.547842\pi$
$390$	0	0
$391$	2.86294	0.144785
$392$	1.00000	0.0505076
$393$	−9.12498	−0.460294
$394$	−8.63102	−0.434825
$395$	−9.45473	−0.475719
$396$	4.04892	0.203466
$397$	−35.4784	−1.78061	−0.890305	−	0.455364i	$-0.849509\pi$
$397$	−35.4784	−1.78061	−0.890305	+	0.455364i	$0.849509\pi$
$398$	3.87263	0.194117
$399$	0.664874	0.0332854
$400$	−4.35690	−0.217845
$401$	9.60819	0.479810	0.239905	−	0.970796i	$-0.422884\pi$
$401$	9.60819	0.479810	0.239905	+	0.970796i	$0.422884\pi$
$402$	8.86294	0.442043
$403$	0	0
$404$	15.6189	0.777071
$405$	−0.801938	−0.0398486
$406$	8.74094	0.433806
$407$	−18.5526	−0.919617
$408$	0.753020	0.0372801
$409$	−20.9812	−1.03745	−0.518727	−	0.854940i	$-0.673594\pi$
$409$	−20.9812	−1.03745	−0.518727	+	0.854940i	$0.673594\pi$
$410$	−5.53319	−0.273265
$411$	10.4722	0.516555
$412$	−13.1347	−0.647099
$413$	2.58211	0.127057
$414$	−3.80194	−0.186855
$415$	−7.38835	−0.362680
$416$	0	0
$417$	−3.66487	−0.179470
$418$	2.69202	0.131671
$419$	14.1970	0.693569	0.346784	−	0.937945i	$-0.387274\pi$
$419$	14.1970	0.693569	0.346784	+	0.937945i	$0.387274\pi$
$420$	−0.801938	−0.0391306
$421$	−27.9269	−1.36107	−0.680537	−	0.732713i	$-0.738254\pi$
$421$	−27.9269	−1.36107	−0.680537	+	0.732713i	$0.738254\pi$
$422$	0.533188	0.0259552
$423$	−5.49396	−0.267125
$424$	3.04892	0.148069
$425$	3.28083	0.159144
$426$	10.1957	0.493982
$427$	−3.71379	−0.179723
$428$	−10.1642	−0.491306
$429$	0	0
$430$	1.04892	0.0505833
$431$	31.7549	1.52958	0.764791	−	0.644279i	$-0.222842\pi$
$431$	31.7549	1.52958	0.764791	+	0.644279i	$0.222842\pi$
$432$	−1.00000	−0.0481125
$433$	−16.4101	−0.788620	−0.394310	−	0.918977i	$-0.629016\pi$
$433$	−16.4101	−0.788620	−0.394310	+	0.918977i	$0.629016\pi$
$434$	−0.335126	−0.0160865
$435$	−7.00969	−0.336089
$436$	−13.4494	−0.644107
$437$	−2.52781	−0.120922
$438$	−9.44265	−0.451187
$439$	−6.83207	−0.326077	−0.163038	−	0.986620i	$-0.552129\pi$
$439$	−6.83207	−0.326077	−0.163038	+	0.986620i	$0.552129\pi$
$440$	−3.24698	−0.154794
$441$	1.00000	0.0476190
$442$	0	0
$443$	16.7114	0.793983	0.396991	−	0.917822i	$-0.370054\pi$
$443$	16.7114	0.793983	0.396991	+	0.917822i	$0.370054\pi$
$444$	4.58211	0.217457
$445$	−1.40581	−0.0666419
$446$	−23.0640	−1.09211
$447$	18.7385	0.886303
$448$	−1.00000	−0.0472456
$449$	31.6668	1.49445	0.747224	−	0.664572i	$-0.231386\pi$
$449$	31.6668	1.49445	0.747224	+	0.664572i	$0.231386\pi$
$450$	−4.35690	−0.205386
$451$	27.9366	1.31548
$452$	−3.26444	−0.153546
$453$	17.4209	0.818504
$454$	−28.8388	−1.35347
$455$	0	0
$456$	−0.664874	−0.0311356
$457$	−40.3260	−1.88637	−0.943186	−	0.332265i	$-0.892187\pi$
$457$	−40.3260	−1.88637	−0.943186	+	0.332265i	$0.892187\pi$
$458$	16.3817	0.765464
$459$	0.753020	0.0351480
$460$	3.04892	0.142157
$461$	−25.1008	−1.16906	−0.584531	−	0.811371i	$-0.698721\pi$
$461$	−25.1008	−1.16906	−0.584531	+	0.811371i	$0.698721\pi$
$462$	4.04892	0.188373
$463$	−25.4330	−1.18197	−0.590985	−	0.806683i	$-0.701261\pi$
$463$	−25.4330	−1.18197	−0.590985	+	0.806683i	$0.701261\pi$
$464$	−8.74094	−0.405788
$465$	0.268750	0.0124630
$466$	−10.0261	−0.464449
$467$	32.6829	1.51239	0.756193	−	0.654349i	$-0.227057\pi$
$467$	32.6829	1.51239	0.756193	+	0.654349i	$0.227057\pi$
$468$	0	0
$469$	8.86294	0.409252
$470$	4.40581	0.203225
$471$	−4.39612	−0.202563
$472$	−2.58211	−0.118851
$473$	−5.29590	−0.243506
$474$	−11.7899	−0.541526
$475$	−2.89679	−0.132914
$476$	0.753020	0.0345146
$477$	3.04892	0.139600
$478$	−7.32975	−0.335255
$479$	−9.80864	−0.448168	−0.224084	−	0.974570i	$-0.571939\pi$
$479$	−9.80864	−0.448168	−0.224084	+	0.974570i	$0.571939\pi$
$480$	0.801938	0.0366033
$481$	0	0
$482$	−9.00969	−0.410380
$483$	−3.80194	−0.172994
$484$	5.39373	0.245170
$485$	6.56465	0.298085
$486$	−1.00000	−0.0453609
$487$	16.0683	0.728124	0.364062	−	0.931375i	$-0.381390\pi$
$487$	16.0683	0.728124	0.364062	+	0.931375i	$0.381390\pi$
$488$	3.71379	0.168115
$489$	11.8062	0.533897
$490$	−0.801938	−0.0362279
$491$	12.3676	0.558144	0.279072	−	0.960270i	$-0.409973\pi$
$491$	12.3676	0.558144	0.279072	+	0.960270i	$0.409973\pi$
$492$	−6.89977	−0.311066
$493$	6.58211	0.296443
$494$	0	0
$495$	−3.24698	−0.145941
$496$	0.335126	0.0150476
$497$	10.1957	0.457338
$498$	−9.21313	−0.412850
$499$	32.4064	1.45071	0.725355	−	0.688375i	$-0.241676\pi$
$499$	32.4064	1.45071	0.725355	+	0.688375i	$0.241676\pi$
$500$	7.50365	0.335573
$501$	8.05861	0.360032
$502$	−26.2978	−1.17373
$503$	31.9162	1.42307	0.711536	−	0.702650i	$-0.248000\pi$
$503$	31.9162	1.42307	0.711536	+	0.702650i	$0.248000\pi$
$504$	−1.00000	−0.0445435
$505$	−12.5254	−0.557374
$506$	−15.3937	−0.684335
$507$	0	0
$508$	7.74094	0.343449
$509$	−11.3056	−0.501111	−0.250556	−	0.968102i	$-0.580613\pi$
$509$	−11.3056	−0.501111	−0.250556	+	0.968102i	$0.580613\pi$
$510$	−0.603875	−0.0267401
$511$	−9.44265	−0.417718
$512$	1.00000	0.0441942
$513$	−0.664874	−0.0293549
$514$	−21.4209	−0.944834
$515$	10.5332	0.464148
$516$	1.30798	0.0575805
$517$	−22.2446	−0.978316
$518$	4.58211	0.201326
$519$	10.4940	0.460634
$520$	0	0
$521$	40.1213	1.75774	0.878872	−	0.477057i	$-0.158297\pi$
$521$	40.1213	1.75774	0.878872	+	0.477057i	$0.158297\pi$
$522$	−8.74094	−0.382580
$523$	9.51679	0.416140	0.208070	−	0.978114i	$-0.433282\pi$
$523$	9.51679	0.416140	0.208070	+	0.978114i	$0.433282\pi$
$524$	9.12498	0.398627
$525$	−4.35690	−0.190151
$526$	7.50902	0.327409
$527$	−0.252356	−0.0109928
$528$	−4.04892	−0.176207
$529$	−8.54527	−0.371533
$530$	−2.44504	−0.106206
$531$	−2.58211	−0.112054
$532$	−0.664874	−0.0288260
$533$	0	0
$534$	−1.75302	−0.0758606
$535$	8.15106	0.352401
$536$	−8.86294	−0.382821
$537$	−4.08575	−0.176313
$538$	−11.3870	−0.490930
$539$	4.04892	0.174399
$540$	0.801938	0.0345099
$541$	−13.9675	−0.600509	−0.300254	−	0.953859i	$-0.597072\pi$
$541$	−13.9675	−0.600509	−0.300254	+	0.953859i	$0.597072\pi$
$542$	−17.4470	−0.749411
$543$	13.1196	0.563016
$544$	−0.753020	−0.0322855
$545$	10.7855	0.462002
$546$	0	0
$547$	17.6160	0.753204	0.376602	−	0.926375i	$-0.377092\pi$
$547$	17.6160	0.753204	0.376602	+	0.926375i	$0.377092\pi$
$548$	−10.4722	−0.447350
$549$	3.71379	0.158501
$550$	−17.6407	−0.752202
$551$	−5.81163	−0.247584
$552$	3.80194	0.161821
$553$	−11.7899	−0.501356
$554$	−20.5351	−0.872453
$555$	−3.67456	−0.155977
$556$	3.66487	0.155425
$557$	15.8950	0.673492	0.336746	−	0.941595i	$-0.390674\pi$
$557$	15.8950	0.673492	0.336746	+	0.941595i	$0.390674\pi$
$558$	0.335126	0.0141870
$559$	0	0
$560$	0.801938	0.0338881
$561$	3.04892	0.128725
$562$	10.2567	0.432651
$563$	4.29829	0.181151	0.0905757	−	0.995890i	$-0.471129\pi$
$563$	4.29829	0.181151	0.0905757	+	0.995890i	$0.471129\pi$
$564$	5.49396	0.231337
$565$	2.61788	0.110135
$566$	−1.21744	−0.0511728
$567$	−1.00000	−0.0419961
$568$	−10.1957	−0.427801
$569$	3.03252	0.127130	0.0635650	−	0.997978i	$-0.479753\pi$
$569$	3.03252	0.127130	0.0635650	+	0.997978i	$0.479753\pi$
$570$	0.533188	0.0223328
$571$	38.1976	1.59852	0.799260	−	0.600986i	$-0.205225\pi$
$571$	38.1976	1.59852	0.799260	+	0.600986i	$0.205225\pi$
$572$	0	0
$573$	5.74094	0.239831
$574$	−6.89977	−0.287991
$575$	16.5646	0.690794
$576$	1.00000	0.0416667
$577$	−17.0761	−0.710886	−0.355443	−	0.934698i	$-0.615670\pi$
$577$	−17.0761	−0.710886	−0.355443	+	0.934698i	$0.615670\pi$
$578$	−16.4330	−0.683521
$579$	−11.3817	−0.473005
$580$	7.00969	0.291061
$581$	−9.21313	−0.382225
$582$	8.18598	0.339320
$583$	12.3448	0.511270
$584$	9.44265	0.390740
$585$	0	0
$586$	−0.408206	−0.0168628
$587$	−43.9721	−1.81492	−0.907462	−	0.420135i	$-0.861983\pi$
$587$	−43.9721	−1.81492	−0.907462	+	0.420135i	$0.861983\pi$
$588$	−1.00000	−0.0412393
$589$	0.222816	0.00918099
$590$	2.07069	0.0852489
$591$	8.63102	0.355033
$592$	−4.58211	−0.188323
$593$	16.5778	0.680768	0.340384	−	0.940286i	$-0.389443\pi$
$593$	16.5778	0.680768	0.340384	+	0.940286i	$0.389443\pi$
$594$	−4.04892	−0.166129
$595$	−0.603875	−0.0247565
$596$	−18.7385	−0.767561
$597$	−3.87263	−0.158496
$598$	0	0
$599$	−2.05861	−0.0841124	−0.0420562	−	0.999115i	$-0.513391\pi$
$599$	−2.05861	−0.0841124	−0.0420562	+	0.999115i	$0.513391\pi$
$600$	4.35690	0.177870
$601$	23.4620	0.957036	0.478518	−	0.878078i	$-0.341174\pi$
$601$	23.4620	0.957036	0.478518	+	0.878078i	$0.341174\pi$
$602$	1.30798	0.0533092
$603$	−8.86294	−0.360927
$604$	−17.4209	−0.708846
$605$	−4.32544	−0.175854
$606$	−15.6189	−0.634476
$607$	13.9095	0.564568	0.282284	−	0.959331i	$-0.408908\pi$
$607$	13.9095	0.564568	0.282284	+	0.959331i	$0.408908\pi$
$608$	0.664874	0.0269642
$609$	−8.74094	−0.354201
$610$	−2.97823	−0.120585
$611$	0	0
$612$	−0.753020	−0.0304390
$613$	−5.99462	−0.242121	−0.121060	−	0.992645i	$-0.538629\pi$
$613$	−5.99462	−0.242121	−0.121060	+	0.992645i	$0.538629\pi$
$614$	19.1540	0.772994
$615$	5.53319	0.223120
$616$	−4.04892	−0.163136
$617$	−39.4881	−1.58973	−0.794866	−	0.606785i	$-0.792459\pi$
$617$	−39.4881	−1.58973	−0.794866	+	0.606785i	$0.792459\pi$
$618$	13.1347	0.528354
$619$	−24.5786	−0.987899	−0.493950	−	0.869491i	$-0.664447\pi$
$619$	−24.5786	−0.987899	−0.493950	+	0.869491i	$0.664447\pi$
$620$	−0.268750	−0.0107933
$621$	3.80194	0.152567
$622$	19.2513	0.771906
$623$	−1.75302	−0.0702333
$624$	0	0
$625$	15.7670	0.630681
$626$	26.4644	1.05773
$627$	−2.69202	−0.107509
$628$	4.39612	0.175424
$629$	3.45042	0.137577
$630$	0.801938	0.0319500
$631$	−17.2241	−0.685682	−0.342841	−	0.939393i	$-0.611389\pi$
$631$	−17.2241	−0.685682	−0.342841	+	0.939393i	$0.611389\pi$
$632$	11.7899	0.468975
$633$	−0.533188	−0.0211923
$634$	1.19136	0.0473149
$635$	−6.20775	−0.246347
$636$	−3.04892	−0.120897
$637$	0	0
$638$	−35.3913	−1.40116
$639$	−10.1957	−0.403334
$640$	−0.801938	−0.0316994
$641$	−39.4631	−1.55870	−0.779349	−	0.626590i	$-0.784450\pi$
$641$	−39.4631	−1.55870	−0.779349	+	0.626590i	$0.784450\pi$
$642$	10.1642	0.401149
$643$	7.93661	0.312989	0.156495	−	0.987679i	$-0.449981\pi$
$643$	7.93661	0.312989	0.156495	+	0.987679i	$0.449981\pi$
$644$	3.80194	0.149817
$645$	−1.04892	−0.0413011
$646$	−0.500664	−0.0196984
$647$	34.9554	1.37424	0.687119	−	0.726545i	$-0.258875\pi$
$647$	34.9554	1.37424	0.687119	+	0.726545i	$0.258875\pi$
$648$	1.00000	0.0392837
$649$	−10.4547	−0.410384
$650$	0	0
$651$	0.335126	0.0131346
$652$	−11.8062	−0.462368
$653$	−25.5609	−1.00028	−0.500138	−	0.865946i	$-0.666717\pi$
$653$	−25.5609	−1.00028	−0.500138	+	0.865946i	$0.666717\pi$
$654$	13.4494	0.525911
$655$	−7.31767	−0.285925
$656$	6.89977	0.269391
$657$	9.44265	0.368393
$658$	5.49396	0.214177
$659$	18.4397	0.718307	0.359154	−	0.933278i	$-0.383065\pi$
$659$	18.4397	0.718307	0.359154	+	0.933278i	$0.383065\pi$
$660$	3.24698	0.126389
$661$	−26.3201	−1.02373	−0.511866	−	0.859065i	$-0.671046\pi$
$661$	−26.3201	−1.02373	−0.511866	+	0.859065i	$0.671046\pi$
$662$	10.8847	0.423046
$663$	0	0
$664$	9.21313	0.357539
$665$	0.533188	0.0206761
$666$	−4.58211	−0.177553
$667$	33.2325	1.28677
$668$	−8.05861	−0.311797
$669$	23.0640	0.891705
$670$	7.10752	0.274588
$671$	15.0368	0.580491
$672$	1.00000	0.0385758
$673$	31.6732	1.22091	0.610457	−	0.792050i	$-0.290986\pi$
$673$	31.6732	1.22091	0.610457	+	0.792050i	$0.290986\pi$
$674$	−21.2717	−0.819357
$675$	4.35690	0.167697
$676$	0	0
$677$	18.3187	0.704046	0.352023	−	0.935991i	$-0.385494\pi$
$677$	18.3187	0.704046	0.352023	+	0.935991i	$0.385494\pi$
$678$	3.26444	0.125370
$679$	8.18598	0.314149
$680$	0.603875	0.0231576
$681$	28.8388	1.10510
$682$	1.35690	0.0519582
$683$	9.86486	0.377468	0.188734	−	0.982028i	$-0.439562\pi$
$683$	9.86486	0.377468	0.188734	+	0.982028i	$0.439562\pi$
$684$	0.664874	0.0254221
$685$	8.39804	0.320873
$686$	−1.00000	−0.0381802
$687$	−16.3817	−0.624999
$688$	−1.30798	−0.0498662
$689$	0	0
$690$	−3.04892	−0.116070
$691$	45.5284	1.73198	0.865991	−	0.500060i	$-0.166689\pi$
$691$	45.5284	1.73198	0.865991	+	0.500060i	$0.166689\pi$
$692$	−10.4940	−0.398920
$693$	−4.04892	−0.153806
$694$	3.18060	0.120734
$695$	−2.93900	−0.111483
$696$	8.74094	0.331324
$697$	−5.19567	−0.196800
$698$	3.32736	0.125942
$699$	10.0261	0.379221
$700$	4.35690	0.164675
$701$	43.7821	1.65363	0.826813	−	0.562476i	$-0.190151\pi$
$701$	43.7821	1.65363	0.826813	+	0.562476i	$0.190151\pi$
$702$	0	0
$703$	−3.04652	−0.114902
$704$	4.04892	0.152599
$705$	−4.40581	−0.165933
$706$	21.1594	0.796345
$707$	−15.6189	−0.587411
$708$	2.58211	0.0970415
$709$	3.89248	0.146185	0.0730925	−	0.997325i	$-0.476713\pi$
$709$	3.89248	0.146185	0.0730925	+	0.997325i	$0.476713\pi$
$710$	8.17629	0.306851
$711$	11.7899	0.442154
$712$	1.75302	0.0656972
$713$	−1.27413	−0.0477164
$714$	−0.753020	−0.0281811
$715$	0	0
$716$	4.08575	0.152692
$717$	7.32975	0.273734
$718$	26.4088	0.985568
$719$	−40.9077	−1.52560	−0.762799	−	0.646636i	$-0.776175\pi$
$719$	−40.9077	−1.52560	−0.762799	+	0.646636i	$0.776175\pi$
$720$	−0.801938	−0.0298865
$721$	13.1347	0.489161
$722$	−18.5579	−0.690655
$723$	9.00969	0.335074
$724$	−13.1196	−0.487586
$725$	38.0834	1.41438
$726$	−5.39373	−0.200180
$727$	−9.91962	−0.367898	−0.183949	−	0.982936i	$-0.558888\pi$
$727$	−9.91962	−0.367898	−0.183949	+	0.982936i	$0.558888\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−7.57242	−0.280268
$731$	0.984935	0.0364291
$732$	−3.71379	−0.137266
$733$	−32.8471	−1.21324	−0.606618	−	0.794993i	$-0.707474\pi$
$733$	−32.8471	−1.21324	−0.606618	+	0.794993i	$0.707474\pi$
$734$	14.4504	0.533375
$735$	0.801938	0.0295799
$736$	−3.80194	−0.140141
$737$	−35.8853	−1.32185
$738$	6.89977	0.253984
$739$	18.5338	0.681776	0.340888	−	0.940104i	$-0.389272\pi$
$739$	18.5338	0.681776	0.340888	+	0.940104i	$0.389272\pi$
$740$	3.67456	0.135080
$741$	0	0
$742$	−3.04892	−0.111929
$743$	−10.8455	−0.397882	−0.198941	−	0.980011i	$-0.563750\pi$
$743$	−10.8455	−0.397882	−0.198941	+	0.980011i	$0.563750\pi$
$744$	−0.335126	−0.0122863
$745$	15.0271	0.550552
$746$	21.5719	0.789805
$747$	9.21313	0.337091
$748$	−3.04892	−0.111479
$749$	10.1642	0.371392
$750$	−7.50365	−0.273994
$751$	−16.3913	−0.598128	−0.299064	−	0.954233i	$-0.596674\pi$
$751$	−16.3913	−0.598128	−0.299064	+	0.954233i	$0.596674\pi$
$752$	−5.49396	−0.200344
$753$	26.2978	0.958346
$754$	0	0
$755$	13.9705	0.508437
$756$	1.00000	0.0363696
$757$	−39.2737	−1.42743	−0.713713	−	0.700439i	$-0.752988\pi$
$757$	−39.2737	−1.42743	−0.713713	+	0.700439i	$0.752988\pi$
$758$	−3.66056	−0.132958
$759$	15.3937	0.558757
$760$	−0.533188	−0.0193408
$761$	29.1752	1.05760	0.528801	−	0.848746i	$-0.322642\pi$
$761$	29.1752	1.05760	0.528801	+	0.848746i	$0.322642\pi$
$762$	−7.74094	−0.280425
$763$	13.4494	0.486899
$764$	−5.74094	−0.207700
$765$	0.603875	0.0218332
$766$	4.53989	0.164033
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	20.3134	0.732518	0.366259	−	0.930513i	$-0.380638\pi$
$769$	20.3134	0.732518	0.366259	+	0.930513i	$0.380638\pi$
$770$	3.24698	0.117013
$771$	21.4209	0.771454
$772$	11.3817	0.409635
$773$	7.57434	0.272430	0.136215	−	0.990679i	$-0.456506\pi$
$773$	7.57434	0.272430	0.136215	+	0.990679i	$0.456506\pi$
$774$	−1.30798	−0.0470143
$775$	−1.46011	−0.0524486
$776$	−8.18598	−0.293860
$777$	−4.58211	−0.164382
$778$	−5.90648	−0.211757
$779$	4.58748	0.164364
$780$	0	0
$781$	−41.2814	−1.47717
$782$	2.86294	0.102378
$783$	8.74094	0.312376
$784$	1.00000	0.0357143
$785$	−3.52542	−0.125828
$786$	−9.12498	−0.325477
$787$	−10.8398	−0.386399	−0.193199	−	0.981160i	$-0.561886\pi$
$787$	−10.8398	−0.386399	−0.193199	+	0.981160i	$0.561886\pi$
$788$	−8.63102	−0.307467
$789$	−7.50902	−0.267328
$790$	−9.45473	−0.336384
$791$	3.26444	0.116070
$792$	4.04892	0.143872
$793$	0	0
$794$	−35.4784	−1.25908
$795$	2.44504	0.0867167
$796$	3.87263	0.137262
$797$	4.71917	0.167162	0.0835808	−	0.996501i	$-0.473364\pi$
$797$	4.71917	0.167162	0.0835808	+	0.996501i	$0.473364\pi$
$798$	0.664874	0.0235363
$799$	4.13706	0.146359
$800$	−4.35690	−0.154040
$801$	1.75302	0.0619399
$802$	9.60819	0.339277
$803$	38.2325	1.34920
$804$	8.86294	0.312572
$805$	−3.04892	−0.107460
$806$	0	0
$807$	11.3870	0.400842
$808$	15.6189	0.549472
$809$	−3.73423	−0.131289	−0.0656443	−	0.997843i	$-0.520910\pi$
$809$	−3.73423	−0.131289	−0.0656443	+	0.997843i	$0.520910\pi$
$810$	−0.801938	−0.0281772
$811$	−31.1062	−1.09229	−0.546143	−	0.837692i	$-0.683905\pi$
$811$	−31.1062	−1.09229	−0.546143	+	0.837692i	$0.683905\pi$
$812$	8.74094	0.306747
$813$	17.4470	0.611892
$814$	−18.5526	−0.650267
$815$	9.46788	0.331645
$816$	0.753020	0.0263610
$817$	−0.869641	−0.0304249
$818$	−20.9812	−0.733591
$819$	0	0
$820$	−5.53319	−0.193227
$821$	37.8786	1.32197	0.660986	−	0.750398i	$-0.270138\pi$
$821$	37.8786	1.32197	0.660986	+	0.750398i	$0.270138\pi$
$822$	10.4722	0.365260
$823$	26.3773	0.919456	0.459728	−	0.888060i	$-0.347947\pi$
$823$	26.3773	0.919456	0.459728	+	0.888060i	$0.347947\pi$
$824$	−13.1347	−0.457568
$825$	17.6407	0.614171
$826$	2.58211	0.0898429
$827$	−2.49263	−0.0866773	−0.0433386	−	0.999060i	$-0.513799\pi$
$827$	−2.49263	−0.0866773	−0.0433386	+	0.999060i	$0.513799\pi$
$828$	−3.80194	−0.132126
$829$	−47.8437	−1.66168	−0.830840	−	0.556512i	$-0.812139\pi$
$829$	−47.8437	−1.66168	−0.830840	+	0.556512i	$0.812139\pi$
$830$	−7.38835	−0.256454
$831$	20.5351	0.712355
$832$	0	0
$833$	−0.753020	−0.0260906
$834$	−3.66487	−0.126904
$835$	6.46250	0.223644
$836$	2.69202	0.0931055
$837$	−0.335126	−0.0115836
$838$	14.1970	0.490427
$839$	11.3773	0.392789	0.196395	−	0.980525i	$-0.437077\pi$
$839$	11.3773	0.392789	0.196395	+	0.980525i	$0.437077\pi$
$840$	−0.801938	−0.0276695
$841$	47.4040	1.63462
$842$	−27.9269	−0.962425
$843$	−10.2567	−0.353258
$844$	0.533188	0.0183531
$845$	0	0
$846$	−5.49396	−0.188886
$847$	−5.39373	−0.185331
$848$	3.04892	0.104700
$849$	1.21744	0.0417824
$850$	3.28083	0.112532
$851$	17.4209	0.597180
$852$	10.1957	0.349298
$853$	−13.2905	−0.455059	−0.227529	−	0.973771i	$-0.573065\pi$
$853$	−13.2905	−0.455059	−0.227529	+	0.973771i	$0.573065\pi$
$854$	−3.71379	−0.127083
$855$	−0.533188	−0.0182346
$856$	−10.1642	−0.347406
$857$	21.5026	0.734514	0.367257	−	0.930119i	$-0.380297\pi$
$857$	21.5026	0.734514	0.367257	+	0.930119i	$0.380297\pi$
$858$	0	0
$859$	−26.0398	−0.888467	−0.444234	−	0.895911i	$-0.646524\pi$
$859$	−26.0398	−0.888467	−0.444234	+	0.895911i	$0.646524\pi$
$860$	1.04892	0.0357678
$861$	6.89977	0.235144
$862$	31.7549	1.08158
$863$	21.4679	0.730775	0.365388	−	0.930856i	$-0.380936\pi$
$863$	21.4679	0.730775	0.365388	+	0.930856i	$0.380936\pi$
$864$	−1.00000	−0.0340207
$865$	8.41550	0.286136
$866$	−16.4101	−0.557639
$867$	16.4330	0.558093
$868$	−0.335126	−0.0113749
$869$	47.7362	1.61934
$870$	−7.00969	−0.237651
$871$	0	0
$872$	−13.4494	−0.455453
$873$	−8.18598	−0.277053
$874$	−2.52781	−0.0855045
$875$	−7.50365	−0.253670
$876$	−9.44265	−0.319038
$877$	−40.5792	−1.37026	−0.685132	−	0.728419i	$-0.740255\pi$
$877$	−40.5792	−1.37026	−0.685132	+	0.728419i	$0.740255\pi$
$878$	−6.83207	−0.230571
$879$	0.408206	0.0137685
$880$	−3.24698	−0.109456
$881$	−56.1680	−1.89235	−0.946175	−	0.323656i	$-0.895088\pi$
$881$	−56.1680	−1.89235	−0.946175	+	0.323656i	$0.895088\pi$
$882$	1.00000	0.0336718
$883$	−45.7174	−1.53851	−0.769256	−	0.638941i	$-0.779373\pi$
$883$	−45.7174	−1.53851	−0.769256	+	0.638941i	$0.779373\pi$
$884$	0	0
$885$	−2.07069	−0.0696054
$886$	16.7114	0.561430
$887$	5.37004	0.180308	0.0901542	−	0.995928i	$-0.471264\pi$
$887$	5.37004	0.180308	0.0901542	+	0.995928i	$0.471264\pi$
$888$	4.58211	0.153765
$889$	−7.74094	−0.259623
$890$	−1.40581	−0.0471230
$891$	4.04892	0.135644
$892$	−23.0640	−0.772239
$893$	−3.65279	−0.122236
$894$	18.7385	0.626711
$895$	−3.27652	−0.109522
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	31.6668	1.05673
$899$	−2.92931	−0.0976980
$900$	−4.35690	−0.145230
$901$	−2.29590	−0.0764874
$902$	27.9366	0.930187
$903$	−1.30798	−0.0435268
$904$	−3.26444	−0.108574
$905$	10.5211	0.349733
$906$	17.4209	0.578770
$907$	30.9065	1.02623	0.513116	−	0.858319i	$-0.328491\pi$
$907$	30.9065	1.02623	0.513116	+	0.858319i	$0.328491\pi$
$908$	−28.8388	−0.957048
$909$	15.6189	0.518048
$910$	0	0
$911$	−20.8267	−0.690019	−0.345010	−	0.938599i	$-0.612124\pi$
$911$	−20.8267	−0.690019	−0.345010	+	0.938599i	$0.612124\pi$
$912$	−0.664874	−0.0220162
$913$	37.3032	1.23456
$914$	−40.3260	−1.33387
$915$	2.97823	0.0984572
$916$	16.3817	0.541265
$917$	−9.12498	−0.301333
$918$	0.753020	0.0248534
$919$	20.6316	0.680574	0.340287	−	0.940322i	$-0.389476\pi$
$919$	20.6316	0.680574	0.340287	+	0.940322i	$0.389476\pi$
$920$	3.04892	0.100520
$921$	−19.1540	−0.631147
$922$	−25.1008	−0.826651
$923$	0	0
$924$	4.04892	0.133200
$925$	19.9638	0.656404
$926$	−25.4330	−0.835779
$927$	−13.1347	−0.431399
$928$	−8.74094	−0.286935
$929$	40.9982	1.34511	0.672554	−	0.740048i	$-0.265197\pi$
$929$	40.9982	1.34511	0.672554	+	0.740048i	$0.265197\pi$
$930$	0.268750	0.00881266
$931$	0.664874	0.0217904
$932$	−10.0261	−0.328415
$933$	−19.2513	−0.630259
$934$	32.6829	1.06942
$935$	2.44504	0.0799614
$936$	0	0
$937$	−4.45042	−0.145389	−0.0726944	−	0.997354i	$-0.523160\pi$
$937$	−4.45042	−0.145389	−0.0726944	+	0.997354i	$0.523160\pi$
$938$	8.86294	0.289385
$939$	−26.4644	−0.863634
$940$	4.40581	0.143702
$941$	−21.8745	−0.713090	−0.356545	−	0.934278i	$-0.616045\pi$
$941$	−21.8745	−0.713090	−0.356545	+	0.934278i	$0.616045\pi$
$942$	−4.39612	−0.143233
$943$	−26.2325	−0.854248
$944$	−2.58211	−0.0840404
$945$	−0.801938	−0.0260870
$946$	−5.29590	−0.172184
$947$	11.0546	0.359225	0.179612	−	0.983737i	$-0.442516\pi$
$947$	11.0546	0.359225	0.179612	+	0.983737i	$0.442516\pi$
$948$	−11.7899	−0.382917
$949$	0	0
$950$	−2.89679	−0.0939842
$951$	−1.19136	−0.0386324
$952$	0.753020	0.0244055
$953$	−1.52052	−0.0492543	−0.0246272	−	0.999697i	$-0.507840\pi$
$953$	−1.52052	−0.0492543	−0.0246272	+	0.999697i	$0.507840\pi$
$954$	3.04892	0.0987123
$955$	4.60388	0.148978
$956$	−7.32975	−0.237061
$957$	35.3913	1.14404
$958$	−9.80864	−0.316903
$959$	10.4722	0.338165
$960$	0.801938	0.0258824
$961$	−30.8877	−0.996377
$962$	0	0
$963$	−10.1642	−0.327537
$964$	−9.00969	−0.290183
$965$	−9.12737	−0.293821
$966$	−3.80194	−0.122325
$967$	−33.7041	−1.08385	−0.541925	−	0.840427i	$-0.682304\pi$
$967$	−33.7041	−1.08385	−0.541925	+	0.840427i	$0.682304\pi$
$968$	5.39373	0.173361
$969$	0.500664	0.0160836
$970$	6.56465	0.210778
$971$	−36.5357	−1.17249	−0.586243	−	0.810135i	$-0.699394\pi$
$971$	−36.5357	−1.17249	−0.586243	+	0.810135i	$0.699394\pi$
$972$	−1.00000	−0.0320750
$973$	−3.66487	−0.117490
$974$	16.0683	0.514861
$975$	0	0
$976$	3.71379	0.118876
$977$	−11.8933	−0.380501	−0.190251	−	0.981736i	$-0.560930\pi$
$977$	−11.8933	−0.380501	−0.190251	+	0.981736i	$0.560930\pi$
$978$	11.8062	0.377522
$979$	7.09783	0.226848
$980$	−0.801938	−0.0256170
$981$	−13.4494	−0.429405
$982$	12.3676	0.394668
$983$	−47.0113	−1.49943	−0.749715	−	0.661761i	$-0.769809\pi$
$983$	−47.0113	−1.49943	−0.749715	+	0.661761i	$0.769809\pi$
$984$	−6.89977	−0.219957
$985$	6.92154	0.220539
$986$	6.58211	0.209617
$987$	−5.49396	−0.174875
$988$	0	0
$989$	4.97285	0.158128
$990$	−3.24698	−0.103196
$991$	−15.2097	−0.483151	−0.241576	−	0.970382i	$-0.577664\pi$
$991$	−15.2097	−0.483151	−0.241576	+	0.970382i	$0.577664\pi$
$992$	0.335126	0.0106402
$993$	−10.8847	−0.345416
$994$	10.1957	0.323387
$995$	−3.10560	−0.0984543
$996$	−9.21313	−0.291929
$997$	44.4295	1.40710	0.703548	−	0.710648i	$-0.251598\pi$
$997$	44.4295	1.40710	0.703548	+	0.710648i	$0.251598\pi$
$998$	32.4064	1.02581
$999$	4.58211	0.144971

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.cj.1.1	yes	3
13.12	even	2		7098.2.a.cc.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7098.2.a.cc.1.3	✓	3	13.12	even	2
7098.2.a.cj.1.1	yes	3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.801938 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.801938 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.801938 q^{10} +4.04892 q^{11} -1.00000 q^{12} -1.00000 q^{14} +0.801938 q^{15} +1.00000 q^{16} -0.753020 q^{17} +1.00000 q^{18} +0.664874 q^{19} -0.801938 q^{20} +1.00000 q^{21} +4.04892 q^{22} -3.80194 q^{23} -1.00000 q^{24} -4.35690 q^{25} -1.00000 q^{27} -1.00000 q^{28} -8.74094 q^{29} +0.801938 q^{30} +0.335126 q^{31} +1.00000 q^{32} -4.04892 q^{33} -0.753020 q^{34} +0.801938 q^{35} +1.00000 q^{36} -4.58211 q^{37} +0.664874 q^{38} -0.801938 q^{40} +6.89977 q^{41} +1.00000 q^{42} -1.30798 q^{43} +4.04892 q^{44} -0.801938 q^{45} -3.80194 q^{46} -5.49396 q^{47} -1.00000 q^{48} +1.00000 q^{49} -4.35690 q^{50} +0.753020 q^{51} +3.04892 q^{53} -1.00000 q^{54} -3.24698 q^{55} -1.00000 q^{56} -0.664874 q^{57} -8.74094 q^{58} -2.58211 q^{59} +0.801938 q^{60} +3.71379 q^{61} +0.335126 q^{62} -1.00000 q^{63} +1.00000 q^{64} -4.04892 q^{66} -8.86294 q^{67} -0.753020 q^{68} +3.80194 q^{69} +0.801938 q^{70} -10.1957 q^{71} +1.00000 q^{72} +9.44265 q^{73} -4.58211 q^{74} +4.35690 q^{75} +0.664874 q^{76} -4.04892 q^{77} +11.7899 q^{79} -0.801938 q^{80} +1.00000 q^{81} +6.89977 q^{82} +9.21313 q^{83} +1.00000 q^{84} +0.603875 q^{85} -1.30798 q^{86} +8.74094 q^{87} +4.04892 q^{88} +1.75302 q^{89} -0.801938 q^{90} -3.80194 q^{92} -0.335126 q^{93} -5.49396 q^{94} -0.533188 q^{95} -1.00000 q^{96} -8.18598 q^{97} +1.00000 q^{98} +4.04892 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + 2 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 + 2 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + 2 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9} + 2 q^{10} + 3 q^{11} - 3 q^{12} - 3 q^{14} - 2 q^{15} + 3 q^{16} - 7 q^{17} + 3 q^{18} + 3 q^{19} + 2 q^{20} + 3 q^{21} + 3 q^{22} - 7 q^{23} - 3 q^{24} - 9 q^{25} - 3 q^{27} - 3 q^{28} - 12 q^{29} - 2 q^{30} + 3 q^{32} - 3 q^{33} - 7 q^{34} - 2 q^{35} + 3 q^{36} - 8 q^{37} + 3 q^{38} + 2 q^{40} - 2 q^{41} + 3 q^{42} - 9 q^{43} + 3 q^{44} + 2 q^{45} - 7 q^{46} - 7 q^{47} - 3 q^{48} + 3 q^{49} - 9 q^{50} + 7 q^{51} - 3 q^{54} - 5 q^{55} - 3 q^{56} - 3 q^{57} - 12 q^{58} - 2 q^{59} - 2 q^{60} + 3 q^{61} - 3 q^{63} + 3 q^{64} - 3 q^{66} - 32 q^{67} - 7 q^{68} + 7 q^{69} - 2 q^{70} + 6 q^{71} + 3 q^{72} - 13 q^{73} - 8 q^{74} + 9 q^{75} + 3 q^{76} - 3 q^{77} + 12 q^{79} + 2 q^{80} + 3 q^{81} - 2 q^{82} + 7 q^{83} + 3 q^{84} - 7 q^{85} - 9 q^{86} + 12 q^{87} + 3 q^{88} + 10 q^{89} + 2 q^{90} - 7 q^{92} - 7 q^{94} - 5 q^{95} - 3 q^{96} - 10 q^{97} + 3 q^{98} + 3 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 + 2 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9 + 2 * q^10 + 3 * q^11 - 3 * q^12 - 3 * q^14 - 2 * q^15 + 3 * q^16 - 7 * q^17 + 3 * q^18 + 3 * q^19 + 2 * q^20 + 3 * q^21 + 3 * q^22 - 7 * q^23 - 3 * q^24 - 9 * q^25 - 3 * q^27 - 3 * q^28 - 12 * q^29 - 2 * q^30 + 3 * q^32 - 3 * q^33 - 7 * q^34 - 2 * q^35 + 3 * q^36 - 8 * q^37 + 3 * q^38 + 2 * q^40 - 2 * q^41 + 3 * q^42 - 9 * q^43 + 3 * q^44 + 2 * q^45 - 7 * q^46 - 7 * q^47 - 3 * q^48 + 3 * q^49 - 9 * q^50 + 7 * q^51 - 3 * q^54 - 5 * q^55 - 3 * q^56 - 3 * q^57 - 12 * q^58 - 2 * q^59 - 2 * q^60 + 3 * q^61 - 3 * q^63 + 3 * q^64 - 3 * q^66 - 32 * q^67 - 7 * q^68 + 7 * q^69 - 2 * q^70 + 6 * q^71 + 3 * q^72 - 13 * q^73 - 8 * q^74 + 9 * q^75 + 3 * q^76 - 3 * q^77 + 12 * q^79 + 2 * q^80 + 3 * q^81 - 2 * q^82 + 7 * q^83 + 3 * q^84 - 7 * q^85 - 9 * q^86 + 12 * q^87 + 3 * q^88 + 10 * q^89 + 2 * q^90 - 7 * q^92 - 7 * q^94 - 5 * q^95 - 3 * q^96 - 10 * q^97 + 3 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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