LMFDB - Embedded newform 7098.2.a.cs.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("7098.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$56.6778153547$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.8569169.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 12x^{4} + 11x^{3} + 44x^{2} - 9x - 41 $ x^6 - 2x^5 - 12x^4 + 11x^3 + 44x^2 - 9*x - 41
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$3.67480$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.63544 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.63544 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.63544 q^{10} -6.10263 q^{11} -1.00000 q^{12} +1.00000 q^{14} +1.63544 q^{15} +1.00000 q^{16} -3.54767 q^{17} +1.00000 q^{18} -6.98822 q^{19} -1.63544 q^{20} -1.00000 q^{21} -6.10263 q^{22} +5.07637 q^{23} -1.00000 q^{24} -2.32533 q^{25} -1.00000 q^{27} +1.00000 q^{28} -7.10027 q^{29} +1.63544 q^{30} +5.14267 q^{31} +1.00000 q^{32} +6.10263 q^{33} -3.54767 q^{34} -1.63544 q^{35} +1.00000 q^{36} +8.47498 q^{37} -6.98822 q^{38} -1.63544 q^{40} +5.52528 q^{41} -1.00000 q^{42} -4.12515 q^{43} -6.10263 q^{44} -1.63544 q^{45} +5.07637 q^{46} +12.5400 q^{47} -1.00000 q^{48} +1.00000 q^{49} -2.32533 q^{50} +3.54767 q^{51} -13.9815 q^{53} -1.00000 q^{54} +9.98050 q^{55} +1.00000 q^{56} +6.98822 q^{57} -7.10027 q^{58} +1.33938 q^{59} +1.63544 q^{60} +9.77901 q^{61} +5.14267 q^{62} +1.00000 q^{63} +1.00000 q^{64} +6.10263 q^{66} +9.30099 q^{67} -3.54767 q^{68} -5.07637 q^{69} -1.63544 q^{70} -6.97782 q^{71} +1.00000 q^{72} -5.42300 q^{73} +8.47498 q^{74} +2.32533 q^{75} -6.98822 q^{76} -6.10263 q^{77} +0.425466 q^{79} -1.63544 q^{80} +1.00000 q^{81} +5.52528 q^{82} +12.9663 q^{83} -1.00000 q^{84} +5.80201 q^{85} -4.12515 q^{86} +7.10027 q^{87} -6.10263 q^{88} +5.43276 q^{89} -1.63544 q^{90} +5.07637 q^{92} -5.14267 q^{93} +12.5400 q^{94} +11.4288 q^{95} -1.00000 q^{96} +9.00557 q^{97} +1.00000 q^{98} -6.10263 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 3 q^{5} - 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 3 * q^5 - 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 3 q^{5} - 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9} - 3 q^{10} - 6 q^{11} - 6 q^{12} + 6 q^{14} + 3 q^{15} + 6 q^{16} + 10 q^{17} + 6 q^{18} + 8 q^{19} - 3 q^{20} - 6 q^{21} - 6 q^{22} - 12 q^{23} - 6 q^{24} + 5 q^{25} - 6 q^{27} + 6 q^{28} + 4 q^{29} + 3 q^{30} + 7 q^{31} + 6 q^{32} + 6 q^{33} + 10 q^{34} - 3 q^{35} + 6 q^{36} + 3 q^{37} + 8 q^{38} - 3 q^{40} + 3 q^{41} - 6 q^{42} - 3 q^{43} - 6 q^{44} - 3 q^{45} - 12 q^{46} + 29 q^{47} - 6 q^{48} + 6 q^{49} + 5 q^{50} - 10 q^{51} - 12 q^{53} - 6 q^{54} + 29 q^{55} + 6 q^{56} - 8 q^{57} + 4 q^{58} + 2 q^{59} + 3 q^{60} + 13 q^{61} + 7 q^{62} + 6 q^{63} + 6 q^{64} + 6 q^{66} + 22 q^{67} + 10 q^{68} + 12 q^{69} - 3 q^{70} + q^{71} + 6 q^{72} + 29 q^{73} + 3 q^{74} - 5 q^{75} + 8 q^{76} - 6 q^{77} - 24 q^{79} - 3 q^{80} + 6 q^{81} + 3 q^{82} + 7 q^{83} - 6 q^{84} + 21 q^{85} - 3 q^{86} - 4 q^{87} - 6 q^{88} - 11 q^{89} - 3 q^{90} - 12 q^{92} - 7 q^{93} + 29 q^{94} + 8 q^{95} - 6 q^{96} - 4 q^{97} + 6 q^{98} - 6 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 3 * q^5 - 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9 - 3 * q^10 - 6 * q^11 - 6 * q^12 + 6 * q^14 + 3 * q^15 + 6 * q^16 + 10 * q^17 + 6 * q^18 + 8 * q^19 - 3 * q^20 - 6 * q^21 - 6 * q^22 - 12 * q^23 - 6 * q^24 + 5 * q^25 - 6 * q^27 + 6 * q^28 + 4 * q^29 + 3 * q^30 + 7 * q^31 + 6 * q^32 + 6 * q^33 + 10 * q^34 - 3 * q^35 + 6 * q^36 + 3 * q^37 + 8 * q^38 - 3 * q^40 + 3 * q^41 - 6 * q^42 - 3 * q^43 - 6 * q^44 - 3 * q^45 - 12 * q^46 + 29 * q^47 - 6 * q^48 + 6 * q^49 + 5 * q^50 - 10 * q^51 - 12 * q^53 - 6 * q^54 + 29 * q^55 + 6 * q^56 - 8 * q^57 + 4 * q^58 + 2 * q^59 + 3 * q^60 + 13 * q^61 + 7 * q^62 + 6 * q^63 + 6 * q^64 + 6 * q^66 + 22 * q^67 + 10 * q^68 + 12 * q^69 - 3 * q^70 + q^71 + 6 * q^72 + 29 * q^73 + 3 * q^74 - 5 * q^75 + 8 * q^76 - 6 * q^77 - 24 * q^79 - 3 * q^80 + 6 * q^81 + 3 * q^82 + 7 * q^83 - 6 * q^84 + 21 * q^85 - 3 * q^86 - 4 * q^87 - 6 * q^88 - 11 * q^89 - 3 * q^90 - 12 * q^92 - 7 * q^93 + 29 * q^94 + 8 * q^95 - 6 * q^96 - 4 * q^97 + 6 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−1.63544	−0.731392	−0.365696	−	0.930734i	$-0.619169\pi$
$5$	−1.63544	−0.731392	−0.365696	+	0.930734i	$0.619169\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.63544	−0.517172
$11$	−6.10263	−1.84001	−0.920006	−	0.391904i	$-0.871817\pi$
$11$	−6.10263	−1.84001	−0.920006	+	0.391904i	$0.871817\pi$
$12$	−1.00000	−0.288675
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	1.63544	0.422269
$16$	1.00000	0.250000
$17$	−3.54767	−0.860437	−0.430218	−	0.902725i	$-0.641563\pi$
$17$	−3.54767	−0.860437	−0.430218	+	0.902725i	$0.641563\pi$
$18$	1.00000	0.235702
$19$	−6.98822	−1.60321	−0.801604	−	0.597856i	$-0.796020\pi$
$19$	−6.98822	−1.60321	−0.801604	+	0.597856i	$0.796020\pi$
$20$	−1.63544	−0.365696
$21$	−1.00000	−0.218218
$22$	−6.10263	−1.30109
$23$	5.07637	1.05850	0.529248	−	0.848467i	$-0.322474\pi$
$23$	5.07637	1.05850	0.529248	+	0.848467i	$0.322474\pi$
$24$	−1.00000	−0.204124
$25$	−2.32533	−0.465066
$26$	0	0
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	−7.10027	−1.31849	−0.659244	−	0.751929i	$-0.729123\pi$
$29$	−7.10027	−1.31849	−0.659244	+	0.751929i	$0.729123\pi$
$30$	1.63544	0.298590
$31$	5.14267	0.923650	0.461825	−	0.886971i	$-0.347195\pi$
$31$	5.14267	0.923650	0.461825	+	0.886971i	$0.347195\pi$
$32$	1.00000	0.176777
$33$	6.10263	1.06233
$34$	−3.54767	−0.608421
$35$	−1.63544	−0.276440
$36$	1.00000	0.166667
$37$	8.47498	1.39328	0.696639	−	0.717421i	$-0.254678\pi$
$37$	8.47498	1.39328	0.696639	+	0.717421i	$0.254678\pi$
$38$	−6.98822	−1.13364
$39$	0	0
$40$	−1.63544	−0.258586
$41$	5.52528	0.862904	0.431452	−	0.902136i	$-0.358001\pi$
$41$	5.52528	0.862904	0.431452	+	0.902136i	$0.358001\pi$
$42$	−1.00000	−0.154303
$43$	−4.12515	−0.629079	−0.314540	−	0.949244i	$-0.601850\pi$
$43$	−4.12515	−0.629079	−0.314540	+	0.949244i	$0.601850\pi$
$44$	−6.10263	−0.920006
$45$	−1.63544	−0.243797
$46$	5.07637	0.748469
$47$	12.5400	1.82915	0.914574	−	0.404418i	$-0.132526\pi$
$47$	12.5400	1.82915	0.914574	+	0.404418i	$0.132526\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−2.32533	−0.328851
$51$	3.54767	0.496773
$52$	0	0
$53$	−13.9815	−1.92050	−0.960252	−	0.279135i	$-0.909952\pi$
$53$	−13.9815	−1.92050	−0.960252	+	0.279135i	$0.909952\pi$
$54$	−1.00000	−0.136083
$55$	9.98050	1.34577
$56$	1.00000	0.133631
$57$	6.98822	0.925612
$58$	−7.10027	−0.932311
$59$	1.33938	0.174372	0.0871861	−	0.996192i	$-0.472213\pi$
$59$	1.33938	0.174372	0.0871861	+	0.996192i	$0.472213\pi$
$60$	1.63544	0.211135
$61$	9.77901	1.25207	0.626037	−	0.779793i	$-0.284676\pi$
$61$	9.77901	1.25207	0.626037	+	0.779793i	$0.284676\pi$
$62$	5.14267	0.653119
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	6.10263	0.751182
$67$	9.30099	1.13630	0.568149	−	0.822926i	$-0.307660\pi$
$67$	9.30099	1.13630	0.568149	+	0.822926i	$0.307660\pi$
$68$	−3.54767	−0.430218
$69$	−5.07637	−0.611123
$70$	−1.63544	−0.195473
$71$	−6.97782	−0.828115	−0.414057	−	0.910251i	$-0.635889\pi$
$71$	−6.97782	−0.828115	−0.414057	+	0.910251i	$0.635889\pi$
$72$	1.00000	0.117851
$73$	−5.42300	−0.634714	−0.317357	−	0.948306i	$-0.602795\pi$
$73$	−5.42300	−0.634714	−0.317357	+	0.948306i	$0.602795\pi$
$74$	8.47498	0.985197
$75$	2.32533	0.268506
$76$	−6.98822	−0.801604
$77$	−6.10263	−0.695459
$78$	0	0
$79$	0.425466	0.0478686	0.0239343	−	0.999714i	$-0.492381\pi$
$79$	0.425466	0.0478686	0.0239343	+	0.999714i	$0.492381\pi$
$80$	−1.63544	−0.182848
$81$	1.00000	0.111111
$82$	5.52528	0.610166
$83$	12.9663	1.42323	0.711617	−	0.702567i	$-0.247963\pi$
$83$	12.9663	1.42323	0.711617	+	0.702567i	$0.247963\pi$
$84$	−1.00000	−0.109109
$85$	5.80201	0.629317
$86$	−4.12515	−0.444826
$87$	7.10027	0.761229
$88$	−6.10263	−0.650543
$89$	5.43276	0.575871	0.287935	−	0.957650i	$-0.407031\pi$
$89$	5.43276	0.575871	0.287935	+	0.957650i	$0.407031\pi$
$90$	−1.63544	−0.172391
$91$	0	0
$92$	5.07637	0.529248
$93$	−5.14267	−0.533270
$94$	12.5400	1.29340
$95$	11.4288	1.17257
$96$	−1.00000	−0.102062
$97$	9.00557	0.914377	0.457189	−	0.889370i	$-0.348856\pi$
$97$	9.00557	0.914377	0.457189	+	0.889370i	$0.348856\pi$
$98$	1.00000	0.101015
$99$	−6.10263	−0.613337
$100$	−2.32533	−0.232533
$101$	11.2415	1.11857	0.559286	−	0.828975i	$-0.311075\pi$
$101$	11.2415	1.11857	0.559286	+	0.828975i	$0.311075\pi$
$102$	3.54767	0.351272
$103$	−12.0316	−1.18551	−0.592754	−	0.805383i	$-0.701959\pi$
$103$	−12.0316	−1.18551	−0.592754	+	0.805383i	$0.701959\pi$
$104$	0	0
$105$	1.63544	0.159603
$106$	−13.9815	−1.35800
$107$	17.1417	1.65715	0.828576	−	0.559876i	$-0.189151\pi$
$107$	17.1417	1.65715	0.828576	+	0.559876i	$0.189151\pi$
$108$	−1.00000	−0.0962250
$109$	5.97536	0.572336	0.286168	−	0.958180i	$-0.407619\pi$
$109$	5.97536	0.572336	0.286168	+	0.958180i	$0.407619\pi$
$110$	9.98050	0.951603
$111$	−8.47498	−0.804410
$112$	1.00000	0.0944911
$113$	−14.1971	−1.33555	−0.667773	−	0.744365i	$-0.732752\pi$
$113$	−14.1971	−1.33555	−0.667773	+	0.744365i	$0.732752\pi$
$114$	6.98822	0.654507
$115$	−8.30210	−0.774175
$116$	−7.10027	−0.659244
$117$	0	0
$118$	1.33938	0.123300
$119$	−3.54767	−0.325215
$120$	1.63544	0.149295
$121$	26.2421	2.38565
$122$	9.77901	0.885350
$123$	−5.52528	−0.498198
$124$	5.14267	0.461825
$125$	11.9802	1.07154
$126$	1.00000	0.0890871
$127$	−7.73298	−0.686191	−0.343095	−	0.939301i	$-0.611475\pi$
$127$	−7.73298	−0.686191	−0.343095	+	0.939301i	$0.611475\pi$
$128$	1.00000	0.0883883
$129$	4.12515	0.363199
$130$	0	0
$131$	0.725948	0.0634264	0.0317132	−	0.999497i	$-0.489904\pi$
$131$	0.725948	0.0634264	0.0317132	+	0.999497i	$0.489904\pi$
$132$	6.10263	0.531166
$133$	−6.98822	−0.605956
$134$	9.30099	0.803484
$135$	1.63544	0.140756
$136$	−3.54767	−0.304210
$137$	−6.43903	−0.550124	−0.275062	−	0.961427i	$-0.588698\pi$
$137$	−6.43903	−0.550124	−0.275062	+	0.961427i	$0.588698\pi$
$138$	−5.07637	−0.432129
$139$	−6.28777	−0.533322	−0.266661	−	0.963790i	$-0.585920\pi$
$139$	−6.28777	−0.533322	−0.266661	+	0.963790i	$0.585920\pi$
$140$	−1.63544	−0.138220
$141$	−12.5400	−1.05606
$142$	−6.97782	−0.585566
$143$	0	0
$144$	1.00000	0.0833333
$145$	11.6121	0.964331
$146$	−5.42300	−0.448811
$147$	−1.00000	−0.0824786
$148$	8.47498	0.696639
$149$	−9.62578	−0.788575	−0.394287	−	0.918987i	$-0.629009\pi$
$149$	−9.62578	−0.788575	−0.394287	+	0.918987i	$0.629009\pi$
$150$	2.32533	0.189862
$151$	23.2672	1.89346	0.946729	−	0.322031i	$-0.104366\pi$
$151$	23.2672	1.89346	0.946729	+	0.322031i	$0.104366\pi$
$152$	−6.98822	−0.566819
$153$	−3.54767	−0.286812
$154$	−6.10263	−0.491764
$155$	−8.41053	−0.675550
$156$	0	0
$157$	5.03255	0.401641	0.200820	−	0.979628i	$-0.435639\pi$
$157$	5.03255	0.401641	0.200820	+	0.979628i	$0.435639\pi$
$158$	0.425466	0.0338482
$159$	13.9815	1.10880
$160$	−1.63544	−0.129293
$161$	5.07637	0.400074
$162$	1.00000	0.0785674
$163$	−1.20380	−0.0942889	−0.0471445	−	0.998888i	$-0.515012\pi$
$163$	−1.20380	−0.0942889	−0.0471445	+	0.998888i	$0.515012\pi$
$164$	5.52528	0.431452
$165$	−9.98050	−0.776981
$166$	12.9663	1.00638
$167$	−12.1773	−0.942308	−0.471154	−	0.882051i	$-0.656162\pi$
$167$	−12.1773	−0.942308	−0.471154	+	0.882051i	$0.656162\pi$
$168$	−1.00000	−0.0771517
$169$	0	0
$170$	5.80201	0.444994
$171$	−6.98822	−0.534403
$172$	−4.12515	−0.314540
$173$	4.39363	0.334042	0.167021	−	0.985953i	$-0.446585\pi$
$173$	4.39363	0.334042	0.167021	+	0.985953i	$0.446585\pi$
$174$	7.10027	0.538270
$175$	−2.32533	−0.175778
$176$	−6.10263	−0.460003
$177$	−1.33938	−0.100674
$178$	5.43276	0.407202
$179$	−13.5056	−1.00946	−0.504729	−	0.863278i	$-0.668408\pi$
$179$	−13.5056	−1.00946	−0.504729	+	0.863278i	$0.668408\pi$
$180$	−1.63544	−0.121899
$181$	18.7513	1.39377	0.696887	−	0.717181i	$-0.254568\pi$
$181$	18.7513	1.39377	0.696887	+	0.717181i	$0.254568\pi$
$182$	0	0
$183$	−9.77901	−0.722885
$184$	5.07637	0.374235
$185$	−13.8603	−1.01903
$186$	−5.14267	−0.377079
$187$	21.6501	1.58321
$188$	12.5400	0.914574
$189$	−1.00000	−0.0727393
$190$	11.4288	0.829134
$191$	−15.4546	−1.11826	−0.559128	−	0.829081i	$-0.688864\pi$
$191$	−15.4546	−1.11826	−0.559128	+	0.829081i	$0.688864\pi$
$192$	−1.00000	−0.0721688
$193$	26.6387	1.91749	0.958746	−	0.284263i	$-0.0917489\pi$
$193$	26.6387	1.91749	0.958746	+	0.284263i	$0.0917489\pi$
$194$	9.00557	0.646563
$195$	0	0
$196$	1.00000	0.0714286
$197$	−12.0949	−0.861728	−0.430864	−	0.902417i	$-0.641791\pi$
$197$	−12.0949	−0.861728	−0.430864	+	0.902417i	$0.641791\pi$
$198$	−6.10263	−0.433695
$199$	−1.66713	−0.118180	−0.0590898	−	0.998253i	$-0.518820\pi$
$199$	−1.66713	−0.118180	−0.0590898	+	0.998253i	$0.518820\pi$
$200$	−2.32533	−0.164426
$201$	−9.30099	−0.656042
$202$	11.2415	0.790950
$203$	−7.10027	−0.498341
$204$	3.54767	0.248387
$205$	−9.03628	−0.631121
$206$	−12.0316	−0.838281
$207$	5.07637	0.352832
$208$	0	0
$209$	42.6465	2.94992
$210$	1.63544	0.112856
$211$	−9.55777	−0.657984	−0.328992	−	0.944333i	$-0.606709\pi$
$211$	−9.55777	−0.657984	−0.328992	+	0.944333i	$0.606709\pi$
$212$	−13.9815	−0.960252
$213$	6.97782	0.478112
$214$	17.1417	1.17178
$215$	6.74644	0.460104
$216$	−1.00000	−0.0680414
$217$	5.14267	0.349107
$218$	5.97536	0.404702
$219$	5.42300	0.366452
$220$	9.98050	0.672885
$221$	0	0
$222$	−8.47498	−0.568804
$223$	−12.8994	−0.863808	−0.431904	−	0.901919i	$-0.642158\pi$
$223$	−12.8994	−0.863808	−0.431904	+	0.901919i	$0.642158\pi$
$224$	1.00000	0.0668153
$225$	−2.32533	−0.155022
$226$	−14.1971	−0.944374
$227$	−25.0814	−1.66471	−0.832356	−	0.554241i	$-0.813009\pi$
$227$	−25.0814	−1.66471	−0.832356	+	0.554241i	$0.813009\pi$
$228$	6.98822	0.462806
$229$	5.62186	0.371503	0.185751	−	0.982597i	$-0.440528\pi$
$229$	5.62186	0.371503	0.185751	+	0.982597i	$0.440528\pi$
$230$	−8.30210	−0.547424
$231$	6.10263	0.401524
$232$	−7.10027	−0.466156
$233$	−3.81125	−0.249683	−0.124842	−	0.992177i	$-0.539842\pi$
$233$	−3.81125	−0.249683	−0.124842	+	0.992177i	$0.539842\pi$
$234$	0	0
$235$	−20.5085	−1.33782
$236$	1.33938	0.0871861
$237$	−0.425466	−0.0276370
$238$	−3.54767	−0.229961
$239$	−7.52873	−0.486993	−0.243497	−	0.969902i	$-0.578294\pi$
$239$	−7.52873	−0.486993	−0.243497	+	0.969902i	$0.578294\pi$
$240$	1.63544	0.105567
$241$	25.1552	1.62039	0.810194	−	0.586162i	$-0.199362\pi$
$241$	25.1552	1.62039	0.810194	+	0.586162i	$0.199362\pi$
$242$	26.2421	1.68691
$243$	−1.00000	−0.0641500
$244$	9.77901	0.626037
$245$	−1.63544	−0.104485
$246$	−5.52528	−0.352279
$247$	0	0
$248$	5.14267	0.326560
$249$	−12.9663	−0.821705
$250$	11.9802	0.757691
$251$	11.5100	0.726502	0.363251	−	0.931691i	$-0.381667\pi$
$251$	11.5100	0.726502	0.363251	+	0.931691i	$0.381667\pi$
$252$	1.00000	0.0629941
$253$	−30.9792	−1.94764
$254$	−7.73298	−0.485210
$255$	−5.80201	−0.363336
$256$	1.00000	0.0625000
$257$	23.4705	1.46405	0.732025	−	0.681278i	$-0.238575\pi$
$257$	23.4705	1.46405	0.732025	+	0.681278i	$0.238575\pi$
$258$	4.12515	0.256821
$259$	8.47498	0.526610
$260$	0	0
$261$	−7.10027	−0.439496
$262$	0.725948	0.0448492
$263$	5.33803	0.329157	0.164579	−	0.986364i	$-0.447374\pi$
$263$	5.33803	0.329157	0.164579	+	0.986364i	$0.447374\pi$
$264$	6.10263	0.375591
$265$	22.8659	1.40464
$266$	−6.98822	−0.428475
$267$	−5.43276	−0.332479
$268$	9.30099	0.568149
$269$	−14.8536	−0.905640	−0.452820	−	0.891602i	$-0.649582\pi$
$269$	−14.8536	−0.905640	−0.452820	+	0.891602i	$0.649582\pi$
$270$	1.63544	0.0995298
$271$	7.61244	0.462423	0.231211	−	0.972904i	$-0.425731\pi$
$271$	7.61244	0.462423	0.231211	+	0.972904i	$0.425731\pi$
$272$	−3.54767	−0.215109
$273$	0	0
$274$	−6.43903	−0.388996
$275$	14.1906	0.855727
$276$	−5.07637	−0.305561
$277$	24.7275	1.48573	0.742865	−	0.669441i	$-0.233466\pi$
$277$	24.7275	1.48573	0.742865	+	0.669441i	$0.233466\pi$
$278$	−6.28777	−0.377115
$279$	5.14267	0.307883
$280$	−1.63544	−0.0977364
$281$	14.2868	0.852282	0.426141	−	0.904657i	$-0.359873\pi$
$281$	14.2868	0.852282	0.426141	+	0.904657i	$0.359873\pi$
$282$	−12.5400	−0.746747
$283$	13.6588	0.811933	0.405967	−	0.913888i	$-0.366935\pi$
$283$	13.6588	0.811933	0.405967	+	0.913888i	$0.366935\pi$
$284$	−6.97782	−0.414057
$285$	−11.4288	−0.676985
$286$	0	0
$287$	5.52528	0.326147
$288$	1.00000	0.0589256
$289$	−4.41402	−0.259648
$290$	11.6121	0.681885
$291$	−9.00557	−0.527916
$292$	−5.42300	−0.317357
$293$	−5.12462	−0.299383	−0.149692	−	0.988733i	$-0.547828\pi$
$293$	−5.12462	−0.299383	−0.149692	+	0.988733i	$0.547828\pi$
$294$	−1.00000	−0.0583212
$295$	−2.19047	−0.127534
$296$	8.47498	0.492598
$297$	6.10263	0.354111
$298$	−9.62578	−0.557606
$299$	0	0
$300$	2.32533	0.134253
$301$	−4.12515	−0.237770
$302$	23.2672	1.33888
$303$	−11.2415	−0.645808
$304$	−6.98822	−0.400802
$305$	−15.9930	−0.915757
$306$	−3.54767	−0.202807
$307$	−6.03654	−0.344523	−0.172262	−	0.985051i	$-0.555107\pi$
$307$	−6.03654	−0.344523	−0.172262	+	0.985051i	$0.555107\pi$
$308$	−6.10263	−0.347730
$309$	12.0316	0.684454
$310$	−8.41053	−0.477686
$311$	29.0381	1.64660	0.823300	−	0.567607i	$-0.192131\pi$
$311$	29.0381	1.64660	0.823300	+	0.567607i	$0.192131\pi$
$312$	0	0
$313$	−19.5358	−1.10423	−0.552114	−	0.833769i	$-0.686179\pi$
$313$	−19.5358	−1.10423	−0.552114	+	0.833769i	$0.686179\pi$
$314$	5.03255	0.284003
$315$	−1.63544	−0.0921467
$316$	0.425466	0.0239343
$317$	−0.678552	−0.0381113	−0.0190556	−	0.999818i	$-0.506066\pi$
$317$	−0.678552	−0.0381113	−0.0190556	+	0.999818i	$0.506066\pi$
$318$	13.9815	0.784042
$319$	43.3303	2.42603
$320$	−1.63544	−0.0914240
$321$	−17.1417	−0.956758
$322$	5.07637	0.282895
$323$	24.7919	1.37946
$324$	1.00000	0.0555556
$325$	0	0
$326$	−1.20380	−0.0666723
$327$	−5.97536	−0.330438
$328$	5.52528	0.305083
$329$	12.5400	0.691353
$330$	−9.98050	−0.549408
$331$	7.34456	0.403694	0.201847	−	0.979417i	$-0.435306\pi$
$331$	7.34456	0.403694	0.201847	+	0.979417i	$0.435306\pi$
$332$	12.9663	0.711617
$333$	8.47498	0.464426
$334$	−12.1773	−0.666312
$335$	−15.2112	−0.831079
$336$	−1.00000	−0.0545545
$337$	12.3117	0.670661	0.335330	−	0.942101i	$-0.391152\pi$
$337$	12.3117	0.670661	0.335330	+	0.942101i	$0.391152\pi$
$338$	0	0
$339$	14.1971	0.771078
$340$	5.80201	0.314658
$341$	−31.3838	−1.69953
$342$	−6.98822	−0.377880
$343$	1.00000	0.0539949
$344$	−4.12515	−0.222413
$345$	8.30210	0.446970
$346$	4.39363	0.236203
$347$	−27.6911	−1.48654	−0.743268	−	0.668994i	$-0.766725\pi$
$347$	−27.6911	−1.48654	−0.743268	+	0.668994i	$0.766725\pi$
$348$	7.10027	0.380614
$349$	15.4077	0.824756	0.412378	−	0.911013i	$-0.364698\pi$
$349$	15.4077	0.824756	0.412378	+	0.911013i	$0.364698\pi$
$350$	−2.32533	−0.124294
$351$	0	0
$352$	−6.10263	−0.325271
$353$	10.0852	0.536783	0.268391	−	0.963310i	$-0.413508\pi$
$353$	10.0852	0.536783	0.268391	+	0.963310i	$0.413508\pi$
$354$	−1.33938	−0.0711871
$355$	11.4118	0.605677
$356$	5.43276	0.287935
$357$	3.54767	0.187763
$358$	−13.5056	−0.713795
$359$	−9.58915	−0.506096	−0.253048	−	0.967454i	$-0.581433\pi$
$359$	−9.58915	−0.506096	−0.253048	+	0.967454i	$0.581433\pi$
$360$	−1.63544	−0.0861954
$361$	29.8352	1.57027
$362$	18.7513	0.985547
$363$	−26.2421	−1.37735
$364$	0	0
$365$	8.86900	0.464225
$366$	−9.77901	−0.511157
$367$	28.5690	1.49129	0.745646	−	0.666342i	$-0.232141\pi$
$367$	28.5690	1.49129	0.745646	+	0.666342i	$0.232141\pi$
$368$	5.07637	0.264624
$369$	5.52528	0.287635
$370$	−13.8603	−0.720565
$371$	−13.9815	−0.725882
$372$	−5.14267	−0.266635
$373$	−4.07830	−0.211166	−0.105583	−	0.994410i	$-0.533671\pi$
$373$	−4.07830	−0.211166	−0.105583	+	0.994410i	$0.533671\pi$
$374$	21.6501	1.11950
$375$	−11.9802	−0.618652
$376$	12.5400	0.646702
$377$	0	0
$378$	−1.00000	−0.0514344
$379$	19.1829	0.985358	0.492679	−	0.870211i	$-0.336018\pi$
$379$	19.1829	0.985358	0.492679	+	0.870211i	$0.336018\pi$
$380$	11.4288	0.586287
$381$	7.73298	0.396172
$382$	−15.4546	−0.790726
$383$	16.7419	0.855469	0.427735	−	0.903904i	$-0.359312\pi$
$383$	16.7419	0.855469	0.427735	+	0.903904i	$0.359312\pi$
$384$	−1.00000	−0.0510310
$385$	9.98050	0.508653
$386$	26.6387	1.35587
$387$	−4.12515	−0.209693
$388$	9.00557	0.457189
$389$	30.6902	1.55605	0.778027	−	0.628231i	$-0.216221\pi$
$389$	30.6902	1.55605	0.778027	+	0.628231i	$0.216221\pi$
$390$	0	0
$391$	−18.0093	−0.910769
$392$	1.00000	0.0505076
$393$	−0.725948	−0.0366192
$394$	−12.0949	−0.609334
$395$	−0.695824	−0.0350107
$396$	−6.10263	−0.306669
$397$	−16.9850	−0.852451	−0.426225	−	0.904617i	$-0.640157\pi$
$397$	−16.9850	−0.852451	−0.426225	+	0.904617i	$0.640157\pi$
$398$	−1.66713	−0.0835656
$399$	6.98822	0.349849
$400$	−2.32533	−0.116266
$401$	16.2088	0.809431	0.404715	−	0.914443i	$-0.367371\pi$
$401$	16.2088	0.809431	0.404715	+	0.914443i	$0.367371\pi$
$402$	−9.30099	−0.463891
$403$	0	0
$404$	11.2415	0.559286
$405$	−1.63544	−0.0812658
$406$	−7.10027	−0.352381
$407$	−51.7197	−2.56365
$408$	3.54767	0.175636
$409$	21.6253	1.06930	0.534650	−	0.845073i	$-0.320443\pi$
$409$	21.6253	1.06930	0.534650	+	0.845073i	$0.320443\pi$
$410$	−9.03628	−0.446270
$411$	6.43903	0.317614
$412$	−12.0316	−0.592754
$413$	1.33938	0.0659065
$414$	5.07637	0.249490
$415$	−21.2056	−1.04094
$416$	0	0
$417$	6.28777	0.307913
$418$	42.6465	2.08591
$419$	−14.3387	−0.700489	−0.350245	−	0.936658i	$-0.613902\pi$
$419$	−14.3387	−0.700489	−0.350245	+	0.936658i	$0.613902\pi$
$420$	1.63544	0.0798014
$421$	−9.01740	−0.439481	−0.219741	−	0.975558i	$-0.570521\pi$
$421$	−9.01740	−0.439481	−0.219741	+	0.975558i	$0.570521\pi$
$422$	−9.55777	−0.465265
$423$	12.5400	0.609716
$424$	−13.9815	−0.679001
$425$	8.24951	0.400160
$426$	6.97782	0.338077
$427$	9.77901	0.473240
$428$	17.1417	0.828576
$429$	0	0
$430$	6.74644	0.325342
$431$	13.0031	0.626340	0.313170	−	0.949697i	$-0.398609\pi$
$431$	13.0031	0.626340	0.313170	+	0.949697i	$0.398609\pi$
$432$	−1.00000	−0.0481125
$433$	−6.05210	−0.290845	−0.145423	−	0.989370i	$-0.546454\pi$
$433$	−6.05210	−0.290845	−0.145423	+	0.989370i	$0.546454\pi$
$434$	5.14267	0.246856
$435$	−11.6121	−0.556757
$436$	5.97536	0.286168
$437$	−35.4748	−1.69699
$438$	5.42300	0.259121
$439$	−14.5258	−0.693278	−0.346639	−	0.937999i	$-0.612677\pi$
$439$	−14.5258	−0.693278	−0.346639	+	0.937999i	$0.612677\pi$
$440$	9.98050	0.475802
$441$	1.00000	0.0476190
$442$	0	0
$443$	2.36752	0.112484	0.0562421	−	0.998417i	$-0.482088\pi$
$443$	2.36752	0.112484	0.0562421	+	0.998417i	$0.482088\pi$
$444$	−8.47498	−0.402205
$445$	−8.88496	−0.421187
$446$	−12.8994	−0.610805
$447$	9.62578	0.455284
$448$	1.00000	0.0472456
$449$	16.3780	0.772927	0.386464	−	0.922305i	$-0.373696\pi$
$449$	16.3780	0.772927	0.386464	+	0.922305i	$0.373696\pi$
$450$	−2.32533	−0.109617
$451$	−33.7188	−1.58775
$452$	−14.1971	−0.667773
$453$	−23.2672	−1.09319
$454$	−25.0814	−1.17713
$455$	0	0
$456$	6.98822	0.327253
$457$	−24.1776	−1.13098	−0.565489	−	0.824756i	$-0.691313\pi$
$457$	−24.1776	−1.13098	−0.565489	+	0.824756i	$0.691313\pi$
$458$	5.62186	0.262692
$459$	3.54767	0.165591
$460$	−8.30210	−0.387088
$461$	−32.4542	−1.51154	−0.755771	−	0.654836i	$-0.772738\pi$
$461$	−32.4542	−1.51154	−0.755771	+	0.654836i	$0.772738\pi$
$462$	6.10263	0.283920
$463$	33.0957	1.53809	0.769043	−	0.639197i	$-0.220733\pi$
$463$	33.0957	1.53809	0.769043	+	0.639197i	$0.220733\pi$
$464$	−7.10027	−0.329622
$465$	8.41053	0.390029
$466$	−3.81125	−0.176553
$467$	17.3142	0.801205	0.400603	−	0.916252i	$-0.368801\pi$
$467$	17.3142	0.801205	0.400603	+	0.916252i	$0.368801\pi$
$468$	0	0
$469$	9.30099	0.429480
$470$	−20.5085	−0.945985
$471$	−5.03255	−0.231887
$472$	1.33938	0.0616499
$473$	25.1743	1.15751
$474$	−0.425466	−0.0195423
$475$	16.2499	0.745597
$476$	−3.54767	−0.162607
$477$	−13.9815	−0.640168
$478$	−7.52873	−0.344356
$479$	1.74917	0.0799217	0.0399608	−	0.999201i	$-0.487277\pi$
$479$	1.74917	0.0799217	0.0399608	+	0.999201i	$0.487277\pi$
$480$	1.63544	0.0746474
$481$	0	0
$482$	25.1552	1.14579
$483$	−5.07637	−0.230983
$484$	26.2421	1.19282
$485$	−14.7281	−0.668768
$486$	−1.00000	−0.0453609
$487$	−8.92335	−0.404355	−0.202178	−	0.979349i	$-0.564802\pi$
$487$	−8.92335	−0.404355	−0.202178	+	0.979349i	$0.564802\pi$
$488$	9.77901	0.442675
$489$	1.20380	0.0544377
$490$	−1.63544	−0.0738817
$491$	−7.95372	−0.358946	−0.179473	−	0.983763i	$-0.557439\pi$
$491$	−7.95372	−0.358946	−0.179473	+	0.983763i	$0.557439\pi$
$492$	−5.52528	−0.249099
$493$	25.1894	1.13447
$494$	0	0
$495$	9.98050	0.448590
$496$	5.14267	0.230913
$497$	−6.97782	−0.312998
$498$	−12.9663	−0.581033
$499$	1.01316	0.0453550	0.0226775	−	0.999743i	$-0.492781\pi$
$499$	1.01316	0.0453550	0.0226775	+	0.999743i	$0.492781\pi$
$500$	11.9802	0.535769
$501$	12.1773	0.544042
$502$	11.5100	0.513715
$503$	7.29874	0.325435	0.162717	−	0.986673i	$-0.447974\pi$
$503$	7.29874	0.325435	0.162717	+	0.986673i	$0.447974\pi$
$504$	1.00000	0.0445435
$505$	−18.3848	−0.818115
$506$	−30.9792	−1.37719
$507$	0	0
$508$	−7.73298	−0.343095
$509$	−36.4647	−1.61627	−0.808135	−	0.588998i	$-0.799523\pi$
$509$	−36.4647	−1.61627	−0.808135	+	0.588998i	$0.799523\pi$
$510$	−5.80201	−0.256917
$511$	−5.42300	−0.239899
$512$	1.00000	0.0441942
$513$	6.98822	0.308537
$514$	23.4705	1.03524
$515$	19.6770	0.867071
$516$	4.12515	0.181600
$517$	−76.5270	−3.36566
$518$	8.47498	0.372369
$519$	−4.39363	−0.192859
$520$	0	0
$521$	11.4558	0.501888	0.250944	−	0.968002i	$-0.419259\pi$
$521$	11.4558	0.501888	0.250944	+	0.968002i	$0.419259\pi$
$522$	−7.10027	−0.310770
$523$	−13.7900	−0.602993	−0.301496	−	0.953467i	$-0.597486\pi$
$523$	−13.7900	−0.602993	−0.301496	+	0.953467i	$0.597486\pi$
$524$	0.725948	0.0317132
$525$	2.32533	0.101486
$526$	5.33803	0.232749
$527$	−18.2445	−0.794743
$528$	6.10263	0.265583
$529$	2.76949	0.120413
$530$	22.8659	0.993231
$531$	1.33938	0.0581240
$532$	−6.98822	−0.302978
$533$	0	0
$534$	−5.43276	−0.235098
$535$	−28.0343	−1.21203
$536$	9.30099	0.401742
$537$	13.5056	0.582811
$538$	−14.8536	−0.640384
$539$	−6.10263	−0.262859
$540$	1.63544	0.0703782
$541$	20.2575	0.870937	0.435469	−	0.900204i	$-0.356583\pi$
$541$	20.2575	0.870937	0.435469	+	0.900204i	$0.356583\pi$
$542$	7.61244	0.326982
$543$	−18.7513	−0.804696
$544$	−3.54767	−0.152105
$545$	−9.77236	−0.418602
$546$	0	0
$547$	−6.65687	−0.284627	−0.142314	−	0.989822i	$-0.545454\pi$
$547$	−6.65687	−0.284627	−0.142314	+	0.989822i	$0.545454\pi$
$548$	−6.43903	−0.275062
$549$	9.77901	0.417358
$550$	14.1906	0.605090
$551$	49.6183	2.11381
$552$	−5.07637	−0.216064
$553$	0.425466	0.0180926
$554$	24.7275	1.05057
$555$	13.8603	0.588339
$556$	−6.28777	−0.266661
$557$	−27.5885	−1.16896	−0.584480	−	0.811408i	$-0.698702\pi$
$557$	−27.5885	−1.16896	−0.584480	+	0.811408i	$0.698702\pi$
$558$	5.14267	0.217706
$559$	0	0
$560$	−1.63544	−0.0691100
$561$	−21.6501	−0.914069
$562$	14.2868	0.602654
$563$	27.0532	1.14015	0.570077	−	0.821591i	$-0.306913\pi$
$563$	27.0532	1.14015	0.570077	+	0.821591i	$0.306913\pi$
$564$	−12.5400	−0.528030
$565$	23.2185	0.976808
$566$	13.6588	0.574124
$567$	1.00000	0.0419961
$568$	−6.97782	−0.292783
$569$	21.5632	0.903976	0.451988	−	0.892024i	$-0.350715\pi$
$569$	21.5632	0.903976	0.451988	+	0.892024i	$0.350715\pi$
$570$	−11.4288	−0.478701
$571$	−30.4739	−1.27529	−0.637646	−	0.770330i	$-0.720092\pi$
$571$	−30.4739	−1.27529	−0.637646	+	0.770330i	$0.720092\pi$
$572$	0	0
$573$	15.4546	0.645625
$574$	5.52528	0.230621
$575$	−11.8042	−0.492270
$576$	1.00000	0.0416667
$577$	−9.47631	−0.394504	−0.197252	−	0.980353i	$-0.563202\pi$
$577$	−9.47631	−0.394504	−0.197252	+	0.980353i	$0.563202\pi$
$578$	−4.41402	−0.183599
$579$	−26.6387	−1.10706
$580$	11.6121	0.482165
$581$	12.9663	0.537932
$582$	−9.00557	−0.373293
$583$	85.3238	3.53375
$584$	−5.42300	−0.224405
$585$	0	0
$586$	−5.12462	−0.211696
$587$	7.01590	0.289577	0.144789	−	0.989463i	$-0.453750\pi$
$587$	7.01590	0.289577	0.144789	+	0.989463i	$0.453750\pi$
$588$	−1.00000	−0.0412393
$589$	−35.9381	−1.48080
$590$	−2.19047	−0.0901804
$591$	12.0949	0.497519
$592$	8.47498	0.348320
$593$	37.0690	1.52224	0.761120	−	0.648611i	$-0.224650\pi$
$593$	37.0690	1.52224	0.761120	+	0.648611i	$0.224650\pi$
$594$	6.10263	0.250394
$595$	5.80201	0.237859
$596$	−9.62578	−0.394287
$597$	1.66713	0.0682311
$598$	0	0
$599$	35.9298	1.46805	0.734026	−	0.679121i	$-0.237639\pi$
$599$	35.9298	1.46805	0.734026	+	0.679121i	$0.237639\pi$
$600$	2.32533	0.0949312
$601$	36.0451	1.47031	0.735156	−	0.677898i	$-0.237109\pi$
$601$	36.0451	1.47031	0.735156	+	0.677898i	$0.237109\pi$
$602$	−4.12515	−0.168129
$603$	9.30099	0.378766
$604$	23.2672	0.946729
$605$	−42.9174	−1.74484
$606$	−11.2415	−0.456655
$607$	−1.67354	−0.0679270	−0.0339635	−	0.999423i	$-0.510813\pi$
$607$	−1.67354	−0.0679270	−0.0339635	+	0.999423i	$0.510813\pi$
$608$	−6.98822	−0.283410
$609$	7.10027	0.287717
$610$	−15.9930	−0.647538
$611$	0	0
$612$	−3.54767	−0.143406
$613$	4.91534	0.198529	0.0992643	−	0.995061i	$-0.468351\pi$
$613$	4.91534	0.198529	0.0992643	+	0.995061i	$0.468351\pi$
$614$	−6.03654	−0.243615
$615$	9.03628	0.364378
$616$	−6.10263	−0.245882
$617$	33.6190	1.35345	0.676724	−	0.736237i	$-0.263399\pi$
$617$	33.6190	1.35345	0.676724	+	0.736237i	$0.263399\pi$
$618$	12.0316	0.483982
$619$	42.1161	1.69279	0.846395	−	0.532556i	$-0.178768\pi$
$619$	42.1161	1.69279	0.846395	+	0.532556i	$0.178768\pi$
$620$	−8.41053	−0.337775
$621$	−5.07637	−0.203708
$622$	29.0381	1.16432
$623$	5.43276	0.217659
$624$	0	0
$625$	−7.96620	−0.318648
$626$	−19.5358	−0.780807
$627$	−42.6465	−1.70314
$628$	5.03255	0.200820
$629$	−30.0665	−1.19883
$630$	−1.63544	−0.0651576
$631$	2.64150	0.105156	0.0525782	−	0.998617i	$-0.483256\pi$
$631$	2.64150	0.105156	0.0525782	+	0.998617i	$0.483256\pi$
$632$	0.425466	0.0169241
$633$	9.55777	0.379887
$634$	−0.678552	−0.0269487
$635$	12.6468	0.501874
$636$	13.9815	0.554402
$637$	0	0
$638$	43.3303	1.71546
$639$	−6.97782	−0.276038
$640$	−1.63544	−0.0646465
$641$	11.5557	0.456423	0.228212	−	0.973612i	$-0.426712\pi$
$641$	11.5557	0.456423	0.228212	+	0.973612i	$0.426712\pi$
$642$	−17.1417	−0.676530
$643$	−3.56186	−0.140466	−0.0702331	−	0.997531i	$-0.522374\pi$
$643$	−3.56186	−0.140466	−0.0702331	+	0.997531i	$0.522374\pi$
$644$	5.07637	0.200037
$645$	−6.74644	−0.265641
$646$	24.7919	0.975425
$647$	−1.82761	−0.0718508	−0.0359254	−	0.999354i	$-0.511438\pi$
$647$	−1.82761	−0.0718508	−0.0359254	+	0.999354i	$0.511438\pi$
$648$	1.00000	0.0392837
$649$	−8.17373	−0.320847
$650$	0	0
$651$	−5.14267	−0.201557
$652$	−1.20380	−0.0471445
$653$	8.87467	0.347293	0.173646	−	0.984808i	$-0.444445\pi$
$653$	8.87467	0.347293	0.173646	+	0.984808i	$0.444445\pi$
$654$	−5.97536	−0.233655
$655$	−1.18725	−0.0463895
$656$	5.52528	0.215726
$657$	−5.42300	−0.211571
$658$	12.5400	0.488860
$659$	−29.1477	−1.13543	−0.567717	−	0.823224i	$-0.692173\pi$
$659$	−29.1477	−1.13543	−0.567717	+	0.823224i	$0.692173\pi$
$660$	−9.98050	−0.388490
$661$	−28.7817	−1.11948	−0.559739	−	0.828669i	$-0.689099\pi$
$661$	−28.7817	−1.11948	−0.559739	+	0.828669i	$0.689099\pi$
$662$	7.34456	0.285455
$663$	0	0
$664$	12.9663	0.503189
$665$	11.4288	0.443191
$666$	8.47498	0.328399
$667$	−36.0436	−1.39561
$668$	−12.1773	−0.471154
$669$	12.8994	0.498720
$670$	−15.2112	−0.587661
$671$	−59.6777	−2.30383
$672$	−1.00000	−0.0385758
$673$	−15.1749	−0.584948	−0.292474	−	0.956273i	$-0.594478\pi$
$673$	−15.1749	−0.584948	−0.292474	+	0.956273i	$0.594478\pi$
$674$	12.3117	0.474229
$675$	2.32533	0.0895020
$676$	0	0
$677$	−4.78147	−0.183767	−0.0918835	−	0.995770i	$-0.529289\pi$
$677$	−4.78147	−0.183767	−0.0918835	+	0.995770i	$0.529289\pi$
$678$	14.1971	0.545235
$679$	9.00557	0.345602
$680$	5.80201	0.222497
$681$	25.0814	0.961122
$682$	−31.3838	−1.20175
$683$	−32.6068	−1.24766	−0.623832	−	0.781558i	$-0.714425\pi$
$683$	−32.6068	−1.24766	−0.623832	+	0.781558i	$0.714425\pi$
$684$	−6.98822	−0.267201
$685$	10.5307	0.402356
$686$	1.00000	0.0381802
$687$	−5.62186	−0.214487
$688$	−4.12515	−0.157270
$689$	0	0
$690$	8.30210	0.316056
$691$	−18.1050	−0.688745	−0.344373	−	0.938833i	$-0.611908\pi$
$691$	−18.1050	−0.688745	−0.344373	+	0.938833i	$0.611908\pi$
$692$	4.39363	0.167021
$693$	−6.10263	−0.231820
$694$	−27.6911	−1.05114
$695$	10.2833	0.390067
$696$	7.10027	0.269135
$697$	−19.6019	−0.742475
$698$	15.4077	0.583191
$699$	3.81125	0.144155
$700$	−2.32533	−0.0878892
$701$	21.1639	0.799350	0.399675	−	0.916657i	$-0.369123\pi$
$701$	21.1639	0.799350	0.399675	+	0.916657i	$0.369123\pi$
$702$	0	0
$703$	−59.2251	−2.23372
$704$	−6.10263	−0.230002
$705$	20.5085	0.772393
$706$	10.0852	0.379563
$707$	11.2415	0.422780
$708$	−1.33938	−0.0503369
$709$	−13.1241	−0.492885	−0.246442	−	0.969157i	$-0.579262\pi$
$709$	−13.1241	−0.492885	−0.246442	+	0.969157i	$0.579262\pi$
$710$	11.4118	0.428278
$711$	0.425466	0.0159562
$712$	5.43276	0.203601
$713$	26.1061	0.977680
$714$	3.54767	0.132768
$715$	0	0
$716$	−13.5056	−0.504729
$717$	7.52873	0.281166
$718$	−9.58915	−0.357864
$719$	−39.1967	−1.46179	−0.730895	−	0.682490i	$-0.760897\pi$
$719$	−39.1967	−1.46179	−0.730895	+	0.682490i	$0.760897\pi$
$720$	−1.63544	−0.0609493
$721$	−12.0316	−0.448080
$722$	29.8352	1.11035
$723$	−25.1552	−0.935532
$724$	18.7513	0.696887
$725$	16.5105	0.613183
$726$	−26.2421	−0.973936
$727$	−24.3447	−0.902896	−0.451448	−	0.892298i	$-0.649092\pi$
$727$	−24.3447	−0.902896	−0.451448	+	0.892298i	$0.649092\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	8.86900	0.328256
$731$	14.6347	0.541283
$732$	−9.77901	−0.361443
$733$	6.10468	0.225481	0.112741	−	0.993624i	$-0.464037\pi$
$733$	6.10468	0.225481	0.112741	+	0.993624i	$0.464037\pi$
$734$	28.5690	1.05450
$735$	1.63544	0.0603242
$736$	5.07637	0.187117
$737$	−56.7605	−2.09080
$738$	5.52528	0.203389
$739$	−26.9952	−0.993036	−0.496518	−	0.868026i	$-0.665388\pi$
$739$	−26.9952	−0.993036	−0.496518	+	0.868026i	$0.665388\pi$
$740$	−13.8603	−0.509516
$741$	0	0
$742$	−13.9815	−0.513276
$743$	5.51112	0.202183	0.101092	−	0.994877i	$-0.467766\pi$
$743$	5.51112	0.202183	0.101092	+	0.994877i	$0.467766\pi$
$744$	−5.14267	−0.188539
$745$	15.7424	0.576757
$746$	−4.07830	−0.149317
$747$	12.9663	0.474411
$748$	21.6501	0.791607
$749$	17.1417	0.626345
$750$	−11.9802	−0.437453
$751$	−10.2855	−0.375324	−0.187662	−	0.982234i	$-0.560091\pi$
$751$	−10.2855	−0.375324	−0.187662	+	0.982234i	$0.560091\pi$
$752$	12.5400	0.457287
$753$	−11.5100	−0.419446
$754$	0	0
$755$	−38.0522	−1.38486
$756$	−1.00000	−0.0363696
$757$	17.0081	0.618169	0.309085	−	0.951035i	$-0.399977\pi$
$757$	17.0081	0.618169	0.309085	+	0.951035i	$0.399977\pi$
$758$	19.1829	0.696754
$759$	30.9792	1.12447
$760$	11.4288	0.414567
$761$	45.2730	1.64115	0.820573	−	0.571542i	$-0.193655\pi$
$761$	45.2730	1.64115	0.820573	+	0.571542i	$0.193655\pi$
$762$	7.73298	0.280136
$763$	5.97536	0.216323
$764$	−15.4546	−0.559128
$765$	5.80201	0.209772
$766$	16.7419	0.604908
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	44.6585	1.61043	0.805214	−	0.592985i	$-0.202051\pi$
$769$	44.6585	1.61043	0.805214	+	0.592985i	$0.202051\pi$
$770$	9.98050	0.359672
$771$	−23.4705	−0.845270
$772$	26.6387	0.958746
$773$	−44.0942	−1.58596	−0.792980	−	0.609248i	$-0.791471\pi$
$773$	−44.0942	−1.58596	−0.792980	+	0.609248i	$0.791471\pi$
$774$	−4.12515	−0.148275
$775$	−11.9584	−0.429558
$776$	9.00557	0.323281
$777$	−8.47498	−0.304038
$778$	30.6902	1.10030
$779$	−38.6119	−1.38341
$780$	0	0
$781$	42.5831	1.52374
$782$	−18.0093	−0.644011
$783$	7.10027	0.253743
$784$	1.00000	0.0357143
$785$	−8.23044	−0.293757
$786$	−0.725948	−0.0258937
$787$	32.2708	1.15033	0.575164	−	0.818038i	$-0.304938\pi$
$787$	32.2708	1.15033	0.575164	+	0.818038i	$0.304938\pi$
$788$	−12.0949	−0.430864
$789$	−5.33803	−0.190039
$790$	−0.695824	−0.0247563
$791$	−14.1971	−0.504789
$792$	−6.10263	−0.216848
$793$	0	0
$794$	−16.9850	−0.602774
$795$	−22.8659	−0.810970
$796$	−1.66713	−0.0590898
$797$	3.22031	0.114069	0.0570346	−	0.998372i	$-0.481835\pi$
$797$	3.22031	0.114069	0.0570346	+	0.998372i	$0.481835\pi$
$798$	6.98822	0.247380
$799$	−44.4878	−1.57387
$800$	−2.32533	−0.0822128
$801$	5.43276	0.191957
$802$	16.2088	0.572354
$803$	33.0946	1.16788
$804$	−9.30099	−0.328021
$805$	−8.30210	−0.292611
$806$	0	0
$807$	14.8536	0.522871
$808$	11.2415	0.395475
$809$	12.4026	0.436053	0.218027	−	0.975943i	$-0.430038\pi$
$809$	12.4026	0.436053	0.218027	+	0.975943i	$0.430038\pi$
$810$	−1.63544	−0.0574636
$811$	23.2208	0.815392	0.407696	−	0.913118i	$-0.366332\pi$
$811$	23.2208	0.815392	0.407696	+	0.913118i	$0.366332\pi$
$812$	−7.10027	−0.249171
$813$	−7.61244	−0.266980
$814$	−51.7197	−1.81277
$815$	1.96875	0.0689622
$816$	3.54767	0.124193
$817$	28.8274	1.00854
$818$	21.6253	0.756110
$819$	0	0
$820$	−9.03628	−0.315561
$821$	−17.3689	−0.606179	−0.303089	−	0.952962i	$-0.598018\pi$
$821$	−17.3689	−0.606179	−0.303089	+	0.952962i	$0.598018\pi$
$822$	6.43903	0.224587
$823$	−38.3476	−1.33671	−0.668356	−	0.743841i	$-0.733002\pi$
$823$	−38.3476	−1.33671	−0.668356	+	0.743841i	$0.733002\pi$
$824$	−12.0316	−0.419141
$825$	−14.1906	−0.494054
$826$	1.33938	0.0466029
$827$	−42.7381	−1.48615	−0.743075	−	0.669208i	$-0.766634\pi$
$827$	−42.7381	−1.48615	−0.743075	+	0.669208i	$0.766634\pi$
$828$	5.07637	0.176416
$829$	−3.60364	−0.125160	−0.0625798	−	0.998040i	$-0.519933\pi$
$829$	−3.60364	−0.125160	−0.0625798	+	0.998040i	$0.519933\pi$
$830$	−21.2056	−0.736057
$831$	−24.7275	−0.857787
$832$	0	0
$833$	−3.54767	−0.122920
$834$	6.28777	0.217728
$835$	19.9153	0.689196
$836$	42.6465	1.47496
$837$	−5.14267	−0.177757
$838$	−14.3387	−0.495321
$839$	−11.2006	−0.386687	−0.193343	−	0.981131i	$-0.561933\pi$
$839$	−11.2006	−0.386687	−0.193343	+	0.981131i	$0.561933\pi$
$840$	1.63544	0.0564281
$841$	21.4138	0.738408
$842$	−9.01740	−0.310760
$843$	−14.2868	−0.492065
$844$	−9.55777	−0.328992
$845$	0	0
$846$	12.5400	0.431134
$847$	26.2421	0.901689
$848$	−13.9815	−0.480126
$849$	−13.6588	−0.468770
$850$	8.24951	0.282956
$851$	43.0221	1.47478
$852$	6.97782	0.239056
$853$	−2.01152	−0.0688731	−0.0344366	−	0.999407i	$-0.510964\pi$
$853$	−2.01152	−0.0688731	−0.0344366	+	0.999407i	$0.510964\pi$
$854$	9.77901	0.334631
$855$	11.4288	0.390858
$856$	17.1417	0.585892
$857$	2.98988	0.102132	0.0510661	−	0.998695i	$-0.483738\pi$
$857$	2.98988	0.102132	0.0510661	+	0.998695i	$0.483738\pi$
$858$	0	0
$859$	−39.7580	−1.35653	−0.678263	−	0.734819i	$-0.737267\pi$
$859$	−39.7580	−1.35653	−0.678263	+	0.734819i	$0.737267\pi$
$860$	6.74644	0.230052
$861$	−5.52528	−0.188301
$862$	13.0031	0.442889
$863$	2.45124	0.0834410	0.0417205	−	0.999129i	$-0.486716\pi$
$863$	2.45124	0.0834410	0.0417205	+	0.999129i	$0.486716\pi$
$864$	−1.00000	−0.0340207
$865$	−7.18553	−0.244315
$866$	−6.05210	−0.205659
$867$	4.41402	0.149908
$868$	5.14267	0.174554
$869$	−2.59646	−0.0880788
$870$	−11.6121	−0.393686
$871$	0	0
$872$	5.97536	0.202351
$873$	9.00557	0.304792
$874$	−35.4748	−1.19995
$875$	11.9802	0.405003
$876$	5.42300	0.183226
$877$	48.6192	1.64175	0.820876	−	0.571106i	$-0.193486\pi$
$877$	48.6192	1.64175	0.820876	+	0.571106i	$0.193486\pi$
$878$	−14.5258	−0.490222
$879$	5.12462	0.172849
$880$	9.98050	0.336443
$881$	−14.5592	−0.490513	−0.245257	−	0.969458i	$-0.578872\pi$
$881$	−14.5592	−0.490513	−0.245257	+	0.969458i	$0.578872\pi$
$882$	1.00000	0.0336718
$883$	57.3052	1.92847	0.964237	−	0.265040i	$-0.0853852\pi$
$883$	57.3052	1.92847	0.964237	+	0.265040i	$0.0853852\pi$
$884$	0	0
$885$	2.19047	0.0736320
$886$	2.36752	0.0795383
$887$	−37.9150	−1.27306	−0.636530	−	0.771252i	$-0.719631\pi$
$887$	−37.9150	−1.27306	−0.636530	+	0.771252i	$0.719631\pi$
$888$	−8.47498	−0.284402
$889$	−7.73298	−0.259356
$890$	−8.88496	−0.297824
$891$	−6.10263	−0.204446
$892$	−12.8994	−0.431904
$893$	−87.6323	−2.93250
$894$	9.62578	0.321934
$895$	22.0877	0.738310
$896$	1.00000	0.0334077
$897$	0	0
$898$	16.3780	0.546542
$899$	−36.5143	−1.21782
$900$	−2.32533	−0.0775110
$901$	49.6017	1.65247
$902$	−33.7188	−1.12271
$903$	4.12515	0.137276
$904$	−14.1971	−0.472187
$905$	−30.6667	−1.01939
$906$	−23.2672	−0.773001
$907$	−48.9030	−1.62380	−0.811899	−	0.583798i	$-0.801566\pi$
$907$	−48.9030	−1.62380	−0.811899	+	0.583798i	$0.801566\pi$
$908$	−25.0814	−0.832356
$909$	11.2415	0.372857
$910$	0	0
$911$	−37.4786	−1.24172	−0.620860	−	0.783921i	$-0.713217\pi$
$911$	−37.4786	−1.24172	−0.620860	+	0.783921i	$0.713217\pi$
$912$	6.98822	0.231403
$913$	−79.1284	−2.61877
$914$	−24.1776	−0.799723
$915$	15.9930	0.528713
$916$	5.62186	0.185751
$917$	0.725948	0.0239729
$918$	3.54767	0.117091
$919$	−32.3308	−1.06649	−0.533247	−	0.845960i	$-0.679028\pi$
$919$	−32.3308	−1.06649	−0.533247	+	0.845960i	$0.679028\pi$
$920$	−8.30210	−0.273712
$921$	6.03654	0.198911
$922$	−32.4542	−1.06882
$923$	0	0
$924$	6.10263	0.200762
$925$	−19.7071	−0.647966
$926$	33.0957	1.08759
$927$	−12.0316	−0.395169
$928$	−7.10027	−0.233078
$929$	7.40041	0.242799	0.121400	−	0.992604i	$-0.461262\pi$
$929$	7.40041	0.242799	0.121400	+	0.992604i	$0.461262\pi$
$930$	8.41053	0.275792
$931$	−6.98822	−0.229030
$932$	−3.81125	−0.124842
$933$	−29.0381	−0.950665
$934$	17.3142	0.566538
$935$	−35.4075	−1.15795
$936$	0	0
$937$	−42.1991	−1.37859	−0.689293	−	0.724483i	$-0.742079\pi$
$937$	−42.1991	−1.37859	−0.689293	+	0.724483i	$0.742079\pi$
$938$	9.30099	0.303688
$939$	19.5358	0.637526
$940$	−20.5085	−0.668912
$941$	−15.9645	−0.520427	−0.260213	−	0.965551i	$-0.583793\pi$
$941$	−15.9645	−0.520427	−0.260213	+	0.965551i	$0.583793\pi$
$942$	−5.03255	−0.163969
$943$	28.0484	0.913380
$944$	1.33938	0.0435930
$945$	1.63544	0.0532009
$946$	25.1743	0.818486
$947$	15.2780	0.496468	0.248234	−	0.968700i	$-0.420150\pi$
$947$	15.2780	0.496468	0.248234	+	0.968700i	$0.420150\pi$
$948$	−0.425466	−0.0138185
$949$	0	0
$950$	16.2499	0.527217
$951$	0.678552	0.0220036
$952$	−3.54767	−0.114981
$953$	18.5583	0.601164	0.300582	−	0.953756i	$-0.402819\pi$
$953$	18.5583	0.601164	0.300582	+	0.953756i	$0.402819\pi$
$954$	−13.9815	−0.452667
$955$	25.2751	0.817883
$956$	−7.52873	−0.243497
$957$	−43.3303	−1.40067
$958$	1.74917	0.0565131
$959$	−6.43903	−0.207927
$960$	1.63544	0.0527837
$961$	−4.55297	−0.146870
$962$	0	0
$963$	17.1417	0.552384
$964$	25.1552	0.810194
$965$	−43.5660	−1.40244
$966$	−5.07637	−0.163329
$967$	−27.5750	−0.886753	−0.443377	−	0.896335i	$-0.646220\pi$
$967$	−27.5750	−0.886753	−0.443377	+	0.896335i	$0.646220\pi$
$968$	26.2421	0.843453
$969$	−24.7919	−0.796431
$970$	−14.7281	−0.472891
$971$	22.8731	0.734032	0.367016	−	0.930215i	$-0.380379\pi$
$971$	22.8731	0.734032	0.367016	+	0.930215i	$0.380379\pi$
$972$	−1.00000	−0.0320750
$973$	−6.28777	−0.201577
$974$	−8.92335	−0.285922
$975$	0	0
$976$	9.77901	0.313019
$977$	6.62778	0.212041	0.106021	−	0.994364i	$-0.466189\pi$
$977$	6.62778	0.212041	0.106021	+	0.994364i	$0.466189\pi$
$978$	1.20380	0.0384933
$979$	−33.1541	−1.05961
$980$	−1.63544	−0.0522423
$981$	5.97536	0.190779
$982$	−7.95372	−0.253813
$983$	−38.4851	−1.22748	−0.613742	−	0.789507i	$-0.710337\pi$
$983$	−38.4851	−1.22748	−0.613742	+	0.789507i	$0.710337\pi$
$984$	−5.52528	−0.176140
$985$	19.7806	0.630261
$986$	25.1894	0.802195
$987$	−12.5400	−0.399153
$988$	0	0
$989$	−20.9408	−0.665878
$990$	9.98050	0.317201
$991$	−43.8888	−1.39417	−0.697087	−	0.716987i	$-0.745521\pi$
$991$	−43.8888	−1.39417	−0.697087	+	0.716987i	$0.745521\pi$
$992$	5.14267	0.163280
$993$	−7.34456	−0.233073
$994$	−6.97782	−0.221323
$995$	2.72649	0.0864357
$996$	−12.9663	−0.410852
$997$	52.5337	1.66376	0.831880	−	0.554955i	$-0.187265\pi$
$997$	52.5337	1.66376	0.831880	+	0.554955i	$0.187265\pi$
$998$	1.01316	0.0320709
$999$	−8.47498	−0.268137

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.63544 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.63544 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.63544 q^{10} -6.10263 q^{11} -1.00000 q^{12} +1.00000 q^{14} +1.63544 q^{15} +1.00000 q^{16} -3.54767 q^{17} +1.00000 q^{18} -6.98822 q^{19} -1.63544 q^{20} -1.00000 q^{21} -6.10263 q^{22} +5.07637 q^{23} -1.00000 q^{24} -2.32533 q^{25} -1.00000 q^{27} +1.00000 q^{28} -7.10027 q^{29} +1.63544 q^{30} +5.14267 q^{31} +1.00000 q^{32} +6.10263 q^{33} -3.54767 q^{34} -1.63544 q^{35} +1.00000 q^{36} +8.47498 q^{37} -6.98822 q^{38} -1.63544 q^{40} +5.52528 q^{41} -1.00000 q^{42} -4.12515 q^{43} -6.10263 q^{44} -1.63544 q^{45} +5.07637 q^{46} +12.5400 q^{47} -1.00000 q^{48} +1.00000 q^{49} -2.32533 q^{50} +3.54767 q^{51} -13.9815 q^{53} -1.00000 q^{54} +9.98050 q^{55} +1.00000 q^{56} +6.98822 q^{57} -7.10027 q^{58} +1.33938 q^{59} +1.63544 q^{60} +9.77901 q^{61} +5.14267 q^{62} +1.00000 q^{63} +1.00000 q^{64} +6.10263 q^{66} +9.30099 q^{67} -3.54767 q^{68} -5.07637 q^{69} -1.63544 q^{70} -6.97782 q^{71} +1.00000 q^{72} -5.42300 q^{73} +8.47498 q^{74} +2.32533 q^{75} -6.98822 q^{76} -6.10263 q^{77} +0.425466 q^{79} -1.63544 q^{80} +1.00000 q^{81} +5.52528 q^{82} +12.9663 q^{83} -1.00000 q^{84} +5.80201 q^{85} -4.12515 q^{86} +7.10027 q^{87} -6.10263 q^{88} +5.43276 q^{89} -1.63544 q^{90} +5.07637 q^{92} -5.14267 q^{93} +12.5400 q^{94} +11.4288 q^{95} -1.00000 q^{96} +9.00557 q^{97} +1.00000 q^{98} -6.10263 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 3 q^{5} - 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 3 * q^5 - 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 3 q^{5} - 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9} - 3 q^{10} - 6 q^{11} - 6 q^{12} + 6 q^{14} + 3 q^{15} + 6 q^{16} + 10 q^{17} + 6 q^{18} + 8 q^{19} - 3 q^{20} - 6 q^{21} - 6 q^{22} - 12 q^{23} - 6 q^{24} + 5 q^{25} - 6 q^{27} + 6 q^{28} + 4 q^{29} + 3 q^{30} + 7 q^{31} + 6 q^{32} + 6 q^{33} + 10 q^{34} - 3 q^{35} + 6 q^{36} + 3 q^{37} + 8 q^{38} - 3 q^{40} + 3 q^{41} - 6 q^{42} - 3 q^{43} - 6 q^{44} - 3 q^{45} - 12 q^{46} + 29 q^{47} - 6 q^{48} + 6 q^{49} + 5 q^{50} - 10 q^{51} - 12 q^{53} - 6 q^{54} + 29 q^{55} + 6 q^{56} - 8 q^{57} + 4 q^{58} + 2 q^{59} + 3 q^{60} + 13 q^{61} + 7 q^{62} + 6 q^{63} + 6 q^{64} + 6 q^{66} + 22 q^{67} + 10 q^{68} + 12 q^{69} - 3 q^{70} + q^{71} + 6 q^{72} + 29 q^{73} + 3 q^{74} - 5 q^{75} + 8 q^{76} - 6 q^{77} - 24 q^{79} - 3 q^{80} + 6 q^{81} + 3 q^{82} + 7 q^{83} - 6 q^{84} + 21 q^{85} - 3 q^{86} - 4 q^{87} - 6 q^{88} - 11 q^{89} - 3 q^{90} - 12 q^{92} - 7 q^{93} + 29 q^{94} + 8 q^{95} - 6 q^{96} - 4 q^{97} + 6 q^{98} - 6 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 3 * q^5 - 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9 - 3 * q^10 - 6 * q^11 - 6 * q^12 + 6 * q^14 + 3 * q^15 + 6 * q^16 + 10 * q^17 + 6 * q^18 + 8 * q^19 - 3 * q^20 - 6 * q^21 - 6 * q^22 - 12 * q^23 - 6 * q^24 + 5 * q^25 - 6 * q^27 + 6 * q^28 + 4 * q^29 + 3 * q^30 + 7 * q^31 + 6 * q^32 + 6 * q^33 + 10 * q^34 - 3 * q^35 + 6 * q^36 + 3 * q^37 + 8 * q^38 - 3 * q^40 + 3 * q^41 - 6 * q^42 - 3 * q^43 - 6 * q^44 - 3 * q^45 - 12 * q^46 + 29 * q^47 - 6 * q^48 + 6 * q^49 + 5 * q^50 - 10 * q^51 - 12 * q^53 - 6 * q^54 + 29 * q^55 + 6 * q^56 - 8 * q^57 + 4 * q^58 + 2 * q^59 + 3 * q^60 + 13 * q^61 + 7 * q^62 + 6 * q^63 + 6 * q^64 + 6 * q^66 + 22 * q^67 + 10 * q^68 + 12 * q^69 - 3 * q^70 + q^71 + 6 * q^72 + 29 * q^73 + 3 * q^74 - 5 * q^75 + 8 * q^76 - 6 * q^77 - 24 * q^79 - 3 * q^80 + 6 * q^81 + 3 * q^82 + 7 * q^83 - 6 * q^84 + 21 * q^85 - 3 * q^86 - 4 * q^87 - 6 * q^88 - 11 * q^89 - 3 * q^90 - 12 * q^92 - 7 * q^93 + 29 * q^94 + 8 * q^95 - 6 * q^96 - 4 * q^97 + 6 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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