LMFDB - Embedded newform 7098.2.a.ck.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:	$3$
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			1.3
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.04892 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.04892 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +4.04892 q^{10} -5.74094 q^{11} -1.00000 q^{12} -1.00000 q^{14} -4.04892 q^{15} +1.00000 q^{16} +1.40581 q^{17} +1.00000 q^{18} +6.26875 q^{19} +4.04892 q^{20} +1.00000 q^{21} -5.74094 q^{22} +1.86294 q^{23} -1.00000 q^{24} +11.3937 q^{25} -1.00000 q^{27} -1.00000 q^{28} -3.20775 q^{29} -4.04892 q^{30} +8.63102 q^{31} +1.00000 q^{32} +5.74094 q^{33} +1.40581 q^{34} -4.04892 q^{35} +1.00000 q^{36} +3.36227 q^{37} +6.26875 q^{38} +4.04892 q^{40} -2.59419 q^{41} +1.00000 q^{42} -5.70171 q^{43} -5.74094 q^{44} +4.04892 q^{45} +1.86294 q^{46} -8.27413 q^{47} -1.00000 q^{48} +1.00000 q^{49} +11.3937 q^{50} -1.40581 q^{51} -3.16421 q^{53} -1.00000 q^{54} -23.2446 q^{55} -1.00000 q^{56} -6.26875 q^{57} -3.20775 q^{58} +7.50604 q^{59} -4.04892 q^{60} +13.5797 q^{61} +8.63102 q^{62} -1.00000 q^{63} +1.00000 q^{64} +5.74094 q^{66} +9.20775 q^{67} +1.40581 q^{68} -1.86294 q^{69} -4.04892 q^{70} -16.8334 q^{71} +1.00000 q^{72} -0.317667 q^{73} +3.36227 q^{74} -11.3937 q^{75} +6.26875 q^{76} +5.74094 q^{77} +1.10992 q^{79} +4.04892 q^{80} +1.00000 q^{81} -2.59419 q^{82} +7.10992 q^{83} +1.00000 q^{84} +5.69202 q^{85} -5.70171 q^{86} +3.20775 q^{87} -5.74094 q^{88} -8.02177 q^{89} +4.04892 q^{90} +1.86294 q^{92} -8.63102 q^{93} -8.27413 q^{94} +25.3817 q^{95} -1.00000 q^{96} +18.0978 q^{97} +1.00000 q^{98} -5.74094 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 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 + 3 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9} + 3 q^{10} - 3 q^{11} - 3 q^{12} - 3 q^{14} - 3 q^{15} + 3 q^{16} - 9 q^{17} + 3 q^{18} + 11 q^{19} + 3 q^{20} + 3 q^{21} - 3 q^{22} + 11 q^{23} - 3 q^{24} + 2 q^{25} - 3 q^{27} - 3 q^{28} + 8 q^{29} - 3 q^{30} + 11 q^{31} + 3 q^{32} + 3 q^{33} - 9 q^{34} - 3 q^{35} + 3 q^{36} + 3 q^{37} + 11 q^{38} + 3 q^{40} - 21 q^{41} + 3 q^{42} + 10 q^{43} - 3 q^{44} + 3 q^{45} + 11 q^{46} - 14 q^{47} - 3 q^{48} + 3 q^{49} + 2 q^{50} + 9 q^{51} + 2 q^{53} - 3 q^{54} - 24 q^{55} - 3 q^{56} - 11 q^{57} + 8 q^{58} + 32 q^{59} - 3 q^{60} - 6 q^{61} + 11 q^{62} - 3 q^{63} + 3 q^{64} + 3 q^{66} + 10 q^{67} - 9 q^{68} - 11 q^{69} - 3 q^{70} - 21 q^{71} + 3 q^{72} + 16 q^{73} + 3 q^{74} - 2 q^{75} + 11 q^{76} + 3 q^{77} + 4 q^{79} + 3 q^{80} + 3 q^{81} - 21 q^{82} + 22 q^{83} + 3 q^{84} + 12 q^{85} + 10 q^{86} - 8 q^{87} - 3 q^{88} - 21 q^{89} + 3 q^{90} + 11 q^{92} - 11 q^{93} - 14 q^{94} + 25 q^{95} - 3 q^{96} + 36 q^{97} + 3 q^{98} - 3 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9 + 3 * q^10 - 3 * q^11 - 3 * q^12 - 3 * q^14 - 3 * q^15 + 3 * q^16 - 9 * q^17 + 3 * q^18 + 11 * q^19 + 3 * q^20 + 3 * q^21 - 3 * q^22 + 11 * q^23 - 3 * q^24 + 2 * q^25 - 3 * q^27 - 3 * q^28 + 8 * q^29 - 3 * q^30 + 11 * q^31 + 3 * q^32 + 3 * q^33 - 9 * q^34 - 3 * q^35 + 3 * q^36 + 3 * q^37 + 11 * q^38 + 3 * q^40 - 21 * q^41 + 3 * q^42 + 10 * q^43 - 3 * q^44 + 3 * q^45 + 11 * q^46 - 14 * q^47 - 3 * q^48 + 3 * q^49 + 2 * q^50 + 9 * q^51 + 2 * q^53 - 3 * q^54 - 24 * q^55 - 3 * q^56 - 11 * q^57 + 8 * q^58 + 32 * q^59 - 3 * q^60 - 6 * q^61 + 11 * q^62 - 3 * q^63 + 3 * q^64 + 3 * q^66 + 10 * q^67 - 9 * q^68 - 11 * q^69 - 3 * q^70 - 21 * q^71 + 3 * q^72 + 16 * q^73 + 3 * q^74 - 2 * q^75 + 11 * q^76 + 3 * q^77 + 4 * q^79 + 3 * q^80 + 3 * q^81 - 21 * q^82 + 22 * q^83 + 3 * q^84 + 12 * q^85 + 10 * q^86 - 8 * q^87 - 3 * q^88 - 21 * q^89 + 3 * q^90 + 11 * q^92 - 11 * q^93 - 14 * q^94 + 25 * q^95 - 3 * q^96 + 36 * 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
$5$	4.04892	1.81073	0.905365	−	0.424633i	$-0.139597\pi$
$5$	4.04892	1.81073	0.905365	+	0.424633i	$0.139597\pi$
$6$	−1.00000	−0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	4.04892	1.28038
$11$	−5.74094	−1.73096	−0.865479	−	0.500945i	$-0.832986\pi$
$11$	−5.74094	−1.73096	−0.865479	+	0.500945i	$0.832986\pi$
$12$	−1.00000	−0.288675
$13$	0	0
$13$	0	0
$14$	−1.00000	−0.267261
$15$	−4.04892	−1.04543
$16$	1.00000	0.250000
$17$	1.40581	0.340960	0.170480	−	0.985361i	$-0.445468\pi$
$17$	1.40581	0.340960	0.170480	+	0.985361i	$0.445468\pi$
$18$	1.00000	0.235702
$19$	6.26875	1.43815	0.719075	−	0.694933i	$-0.244566\pi$
$19$	6.26875	1.43815	0.719075	+	0.694933i	$0.244566\pi$
$20$	4.04892	0.905365
$21$	1.00000	0.218218
$22$	−5.74094	−1.22397
$23$	1.86294	0.388449	0.194225	−	0.980957i	$-0.437781\pi$
$23$	1.86294	0.388449	0.194225	+	0.980957i	$0.437781\pi$
$24$	−1.00000	−0.204124
$25$	11.3937	2.27875
$26$	0	0
$27$	−1.00000	−0.192450
$28$	−1.00000	−0.188982
$29$	−3.20775	−0.595664	−0.297832	−	0.954618i	$-0.596264\pi$
$29$	−3.20775	−0.595664	−0.297832	+	0.954618i	$0.596264\pi$
$30$	−4.04892	−0.739228
$31$	8.63102	1.55018	0.775089	−	0.631852i	$-0.217705\pi$
$31$	8.63102	1.55018	0.775089	+	0.631852i	$0.217705\pi$
$32$	1.00000	0.176777
$33$	5.74094	0.999369
$34$	1.40581	0.241095
$35$	−4.04892	−0.684392
$36$	1.00000	0.166667
$37$	3.36227	0.552754	0.276377	−	0.961049i	$-0.410866\pi$
$37$	3.36227	0.552754	0.276377	+	0.961049i	$0.410866\pi$
$38$	6.26875	1.01693
$39$	0	0
$40$	4.04892	0.640190
$41$	−2.59419	−0.405144	−0.202572	−	0.979267i	$-0.564930\pi$
$41$	−2.59419	−0.405144	−0.202572	+	0.979267i	$0.564930\pi$
$42$	1.00000	0.154303
$43$	−5.70171	−0.869503	−0.434751	−	0.900551i	$-0.643164\pi$
$43$	−5.70171	−0.869503	−0.434751	+	0.900551i	$0.643164\pi$
$44$	−5.74094	−0.865479
$45$	4.04892	0.603577
$46$	1.86294	0.274675
$47$	−8.27413	−1.20691	−0.603453	−	0.797399i	$-0.706209\pi$
$47$	−8.27413	−1.20691	−0.603453	+	0.797399i	$0.706209\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	11.3937	1.61132
$51$	−1.40581	−0.196853
$52$	0	0
$53$	−3.16421	−0.434638	−0.217319	−	0.976101i	$-0.569731\pi$
$53$	−3.16421	−0.434638	−0.217319	+	0.976101i	$0.569731\pi$
$54$	−1.00000	−0.136083
$55$	−23.2446	−3.13430
$56$	−1.00000	−0.133631
$57$	−6.26875	−0.830316
$58$	−3.20775	−0.421198
$59$	7.50604	0.977203	0.488602	−	0.872507i	$-0.337507\pi$
$59$	7.50604	0.977203	0.488602	+	0.872507i	$0.337507\pi$
$60$	−4.04892	−0.522713
$61$	13.5797	1.73870	0.869352	−	0.494193i	$-0.164537\pi$
$61$	13.5797	1.73870	0.869352	+	0.494193i	$0.164537\pi$
$62$	8.63102	1.09614
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	5.74094	0.706661
$67$	9.20775	1.12491	0.562453	−	0.826829i	$-0.309858\pi$
$67$	9.20775	1.12491	0.562453	+	0.826829i	$0.309858\pi$
$68$	1.40581	0.170480
$69$	−1.86294	−0.224271
$70$	−4.04892	−0.483938
$71$	−16.8334	−1.99776	−0.998878	−	0.0473508i	$-0.984922\pi$
$71$	−16.8334	−1.99776	−0.998878	+	0.0473508i	$0.984922\pi$
$72$	1.00000	0.117851
$73$	−0.317667	−0.0371801	−0.0185901	−	0.999827i	$-0.505918\pi$
$73$	−0.317667	−0.0371801	−0.0185901	+	0.999827i	$0.505918\pi$
$74$	3.36227	0.390856
$75$	−11.3937	−1.31563
$76$	6.26875	0.719075
$77$	5.74094	0.654241
$78$	0	0
$79$	1.10992	0.124875	0.0624377	−	0.998049i	$-0.480113\pi$
$79$	1.10992	0.124875	0.0624377	+	0.998049i	$0.480113\pi$
$80$	4.04892	0.452683
$81$	1.00000	0.111111
$82$	−2.59419	−0.286480
$83$	7.10992	0.780415	0.390207	−	0.920727i	$-0.372403\pi$
$83$	7.10992	0.780415	0.390207	+	0.920727i	$0.372403\pi$
$84$	1.00000	0.109109
$85$	5.69202	0.617386
$86$	−5.70171	−0.614831
$87$	3.20775	0.343907
$88$	−5.74094	−0.611986
$89$	−8.02177	−0.850306	−0.425153	−	0.905122i	$-0.639780\pi$
$89$	−8.02177	−0.850306	−0.425153	+	0.905122i	$0.639780\pi$
$90$	4.04892	0.426793
$91$	0	0
$92$	1.86294	0.194225
$93$	−8.63102	−0.894995
$94$	−8.27413	−0.853411
$95$	25.3817	2.60410
$96$	−1.00000	−0.102062
$97$	18.0978	1.83756	0.918778	−	0.394774i	$-0.129177\pi$
$97$	18.0978	1.83756	0.918778	+	0.394774i	$0.129177\pi$
$98$	1.00000	0.101015
$99$	−5.74094	−0.576986
$100$	11.3937	1.13937
$101$	11.6093	1.15516	0.577582	−	0.816333i	$-0.303996\pi$
$101$	11.6093	1.15516	0.577582	+	0.816333i	$0.303996\pi$
$102$	−1.40581	−0.139196
$103$	17.5405	1.72832	0.864158	−	0.503221i	$-0.167852\pi$
$103$	17.5405	1.72832	0.864158	+	0.503221i	$0.167852\pi$
$104$	0	0
$105$	4.04892	0.395134
$106$	−3.16421	−0.307335
$107$	4.04892	0.391424	0.195712	−	0.980661i	$-0.437298\pi$
$107$	4.04892	0.391424	0.195712	+	0.980661i	$0.437298\pi$
$108$	−1.00000	−0.0962250
$109$	10.4179	0.997853	0.498927	−	0.866644i	$-0.333728\pi$
$109$	10.4179	0.997853	0.498927	+	0.866644i	$0.333728\pi$
$110$	−23.2446	−2.21628
$111$	−3.36227	−0.319133
$112$	−1.00000	−0.0944911
$113$	−2.31767	−0.218028	−0.109014	−	0.994040i	$-0.534769\pi$
$113$	−2.31767	−0.218028	−0.109014	+	0.994040i	$0.534769\pi$
$114$	−6.26875	−0.587122
$115$	7.54288	0.703377
$116$	−3.20775	−0.297832
$117$	0	0
$118$	7.50604	0.690987
$119$	−1.40581	−0.128871
$120$	−4.04892	−0.369614
$121$	21.9584	1.99622
$122$	13.5797	1.22945
$123$	2.59419	0.233910
$124$	8.63102	0.775089
$125$	25.8877	2.31547
$126$	−1.00000	−0.0890871
$127$	−12.1957	−1.08219	−0.541095	−	0.840961i	$-0.681990\pi$
$127$	−12.1957	−1.08219	−0.541095	+	0.840961i	$0.681990\pi$
$128$	1.00000	0.0883883
$129$	5.70171	0.502008
$130$	0	0
$131$	−11.2078	−0.979226	−0.489613	−	0.871940i	$-0.662862\pi$
$131$	−11.2078	−0.979226	−0.489613	+	0.871940i	$0.662862\pi$
$132$	5.74094	0.499685
$133$	−6.26875	−0.543570
$134$	9.20775	0.795429
$135$	−4.04892	−0.348475
$136$	1.40581	0.120547
$137$	0.768086	0.0656220	0.0328110	−	0.999462i	$-0.489554\pi$
$137$	0.768086	0.0656220	0.0328110	+	0.999462i	$0.489554\pi$
$138$	−1.86294	−0.158584
$139$	13.0271	1.10495	0.552474	−	0.833530i	$-0.313684\pi$
$139$	13.0271	1.10495	0.552474	+	0.833530i	$0.313684\pi$
$140$	−4.04892	−0.342196
$141$	8.27413	0.696807
$142$	−16.8334	−1.41263
$143$	0	0
$144$	1.00000	0.0833333
$145$	−12.9879	−1.07859
$146$	−0.317667	−0.0262903
$147$	−1.00000	−0.0824786
$148$	3.36227	0.276377
$149$	1.54958	0.126947	0.0634733	−	0.997984i	$-0.479782\pi$
$149$	1.54958	0.126947	0.0634733	+	0.997984i	$0.479782\pi$
$150$	−11.3937	−0.930294
$151$	−15.9323	−1.29655	−0.648276	−	0.761405i	$-0.724510\pi$
$151$	−15.9323	−1.29655	−0.648276	+	0.761405i	$0.724510\pi$
$152$	6.26875	0.508463
$153$	1.40581	0.113653
$154$	5.74094	0.462618
$155$	34.9463	2.80695
$156$	0	0
$157$	15.4276	1.23126	0.615628	−	0.788037i	$-0.288903\pi$
$157$	15.4276	1.23126	0.615628	+	0.788037i	$0.288903\pi$
$158$	1.10992	0.0883002
$159$	3.16421	0.250938
$160$	4.04892	0.320095
$161$	−1.86294	−0.146820
$162$	1.00000	0.0785674
$163$	−14.5133	−1.13677	−0.568386	−	0.822762i	$-0.692432\pi$
$163$	−14.5133	−1.13677	−0.568386	+	0.822762i	$0.692432\pi$
$164$	−2.59419	−0.202572
$165$	23.2446	1.80959
$166$	7.10992	0.551837
$167$	0.846543	0.0655075	0.0327537	−	0.999463i	$-0.489572\pi$
$167$	0.846543	0.0655075	0.0327537	+	0.999463i	$0.489572\pi$
$168$	1.00000	0.0771517
$169$	0	0
$170$	5.69202	0.436558
$171$	6.26875	0.479383
$172$	−5.70171	−0.434751
$173$	7.06100	0.536838	0.268419	−	0.963302i	$-0.413499\pi$
$173$	7.06100	0.536838	0.268419	+	0.963302i	$0.413499\pi$
$174$	3.20775	0.243179
$175$	−11.3937	−0.861285
$176$	−5.74094	−0.432740
$177$	−7.50604	−0.564189
$178$	−8.02177	−0.601257
$179$	−3.20775	−0.239759	−0.119879	−	0.992788i	$-0.538251\pi$
$179$	−3.20775	−0.239759	−0.119879	+	0.992788i	$0.538251\pi$
$180$	4.04892	0.301788
$181$	−25.4577	−1.89226	−0.946129	−	0.323791i	$-0.895042\pi$
$181$	−25.4577	−1.89226	−0.946129	+	0.323791i	$0.895042\pi$
$182$	0	0
$183$	−13.5797	−1.00384
$184$	1.86294	0.137338
$185$	13.6136	1.00089
$186$	−8.63102	−0.632857
$187$	−8.07069	−0.590187
$188$	−8.27413	−0.603453
$189$	1.00000	0.0727393
$190$	25.3817	1.84138
$191$	21.1782	1.53240	0.766201	−	0.642601i	$-0.222145\pi$
$191$	21.1782	1.53240	0.766201	+	0.642601i	$0.222145\pi$
$192$	−1.00000	−0.0721688
$193$	−10.4306	−0.750809	−0.375404	−	0.926861i	$-0.622496\pi$
$193$	−10.4306	−0.750809	−0.375404	+	0.926861i	$0.622496\pi$
$194$	18.0978	1.29935
$195$	0	0
$196$	1.00000	0.0714286
$197$	12.0435	0.858067	0.429033	−	0.903289i	$-0.358854\pi$
$197$	12.0435	0.858067	0.429033	+	0.903289i	$0.358854\pi$
$198$	−5.74094	−0.407991
$199$	−24.7899	−1.75731	−0.878653	−	0.477461i	$-0.841557\pi$
$199$	−24.7899	−1.75731	−0.878653	+	0.477461i	$0.841557\pi$
$200$	11.3937	0.805658
$201$	−9.20775	−0.649465
$202$	11.6093	0.816824
$203$	3.20775	0.225140
$204$	−1.40581	−0.0984266
$205$	−10.5036	−0.733607
$206$	17.5405	1.22210
$207$	1.86294	0.129483
$208$	0	0
$209$	−35.9885	−2.48938
$210$	4.04892	0.279402
$211$	5.20775	0.358516	0.179258	−	0.983802i	$-0.442630\pi$
$211$	5.20775	0.358516	0.179258	+	0.983802i	$0.442630\pi$
$212$	−3.16421	−0.217319
$213$	16.8334	1.15341
$214$	4.04892	0.276778
$215$	−23.0858	−1.57444
$216$	−1.00000	−0.0680414
$217$	−8.63102	−0.585912
$218$	10.4179	0.705589
$219$	0.317667	0.0214660
$220$	−23.2446	−1.56715
$221$	0	0
$222$	−3.36227	−0.225661
$223$	24.2784	1.62580	0.812902	−	0.582400i	$-0.197886\pi$
$223$	24.2784	1.62580	0.812902	+	0.582400i	$0.197886\pi$
$224$	−1.00000	−0.0668153
$225$	11.3937	0.759582
$226$	−2.31767	−0.154169
$227$	−19.7995	−1.31414	−0.657071	−	0.753829i	$-0.728205\pi$
$227$	−19.7995	−1.31414	−0.657071	+	0.753829i	$0.728205\pi$
$228$	−6.26875	−0.415158
$229$	18.3177	1.21047	0.605233	−	0.796049i	$-0.293080\pi$
$229$	18.3177	1.21047	0.605233	+	0.796049i	$0.293080\pi$
$230$	7.54288	0.497363
$231$	−5.74094	−0.377726
$232$	−3.20775	−0.210599
$233$	12.2392	0.801817	0.400909	−	0.916118i	$-0.368694\pi$
$233$	12.2392	0.801817	0.400909	+	0.916118i	$0.368694\pi$
$234$	0	0
$235$	−33.5013	−2.18538
$236$	7.50604	0.488602
$237$	−1.10992	−0.0720968
$238$	−1.40581	−0.0911253
$239$	−18.8713	−1.22068	−0.610341	−	0.792139i	$-0.708968\pi$
$239$	−18.8713	−1.22068	−0.610341	+	0.792139i	$0.708968\pi$
$240$	−4.04892	−0.261356
$241$	10.8659	0.699935	0.349968	−	0.936762i	$-0.386193\pi$
$241$	10.8659	0.699935	0.349968	+	0.936762i	$0.386193\pi$
$242$	21.9584	1.41154
$243$	−1.00000	−0.0641500
$244$	13.5797	0.869352
$245$	4.04892	0.258676
$246$	2.59419	0.165399
$247$	0	0
$248$	8.63102	0.548070
$249$	−7.10992	−0.450573
$250$	25.8877	1.63728
$251$	−13.0664	−0.824742	−0.412371	−	0.911016i	$-0.635299\pi$
$251$	−13.0664	−0.824742	−0.412371	+	0.911016i	$0.635299\pi$
$252$	−1.00000	−0.0629941
$253$	−10.6950	−0.672389
$254$	−12.1957	−0.765224
$255$	−5.69202	−0.356448
$256$	1.00000	0.0625000
$257$	−16.4155	−1.02397	−0.511985	−	0.858994i	$-0.671090\pi$
$257$	−16.4155	−1.02397	−0.511985	+	0.858994i	$0.671090\pi$
$258$	5.70171	0.354973
$259$	−3.36227	−0.208921
$260$	0	0
$261$	−3.20775	−0.198555
$262$	−11.2078	−0.692417
$263$	15.1250	0.932646	0.466323	−	0.884614i	$-0.345578\pi$
$263$	15.1250	0.932646	0.466323	+	0.884614i	$0.345578\pi$
$264$	5.74094	0.353330
$265$	−12.8116	−0.787012
$266$	−6.26875	−0.384362
$267$	8.02177	0.490924
$268$	9.20775	0.562453
$269$	5.58211	0.340347	0.170173	−	0.985414i	$-0.445567\pi$
$269$	5.58211	0.340347	0.170173	+	0.985414i	$0.445567\pi$
$270$	−4.04892	−0.246409
$271$	25.5308	1.55089	0.775443	−	0.631418i	$-0.217527\pi$
$271$	25.5308	1.55089	0.775443	+	0.631418i	$0.217527\pi$
$272$	1.40581	0.0852399
$273$	0	0
$274$	0.768086	0.0464018
$275$	−65.4107	−3.94441
$276$	−1.86294	−0.112136
$277$	−23.0019	−1.38205	−0.691026	−	0.722830i	$-0.742841\pi$
$277$	−23.0019	−1.38205	−0.691026	+	0.722830i	$0.742841\pi$
$278$	13.0271	0.781316
$279$	8.63102	0.516726
$280$	−4.04892	−0.241969
$281$	2.89008	0.172408	0.0862040	−	0.996278i	$-0.472526\pi$
$281$	2.89008	0.172408	0.0862040	+	0.996278i	$0.472526\pi$
$282$	8.27413	0.492717
$283$	−6.25906	−0.372063	−0.186031	−	0.982544i	$-0.559563\pi$
$283$	−6.25906	−0.372063	−0.186031	+	0.982544i	$0.559563\pi$
$284$	−16.8334	−0.998878
$285$	−25.3817	−1.50348
$286$	0	0
$287$	2.59419	0.153130
$288$	1.00000	0.0589256
$289$	−15.0237	−0.883746
$290$	−12.9879	−0.762677
$291$	−18.0978	−1.06091
$292$	−0.317667	−0.0185901
$293$	23.8019	1.39052	0.695262	−	0.718756i	$-0.255288\pi$
$293$	23.8019	1.39052	0.695262	+	0.718756i	$0.255288\pi$
$294$	−1.00000	−0.0583212
$295$	30.3913	1.76945
$296$	3.36227	0.195428
$297$	5.74094	0.333123
$298$	1.54958	0.0897648
$299$	0	0
$300$	−11.3937	−0.657817
$301$	5.70171	0.328641
$302$	−15.9323	−0.916801
$303$	−11.6093	−0.666934
$304$	6.26875	0.359537
$305$	54.9831	3.14833
$306$	1.40581	0.0803650
$307$	8.13036	0.464024	0.232012	−	0.972713i	$-0.425469\pi$
$307$	8.13036	0.464024	0.232012	+	0.972713i	$0.425469\pi$
$308$	5.74094	0.327120
$309$	−17.5405	−0.997843
$310$	34.9463	1.98482
$311$	−5.87800	−0.333311	−0.166655	−	0.986015i	$-0.553297\pi$
$311$	−5.87800	−0.333311	−0.166655	+	0.986015i	$0.553297\pi$
$312$	0	0
$313$	6.13275	0.346644	0.173322	−	0.984865i	$-0.444550\pi$
$313$	6.13275	0.346644	0.173322	+	0.984865i	$0.444550\pi$
$314$	15.4276	0.870629
$315$	−4.04892	−0.228131
$316$	1.10992	0.0624377
$317$	1.60388	0.0900826	0.0450413	−	0.998985i	$-0.485658\pi$
$317$	1.60388	0.0900826	0.0450413	+	0.998985i	$0.485658\pi$
$318$	3.16421	0.177440
$319$	18.4155	1.03107
$320$	4.04892	0.226341
$321$	−4.04892	−0.225989
$322$	−1.86294	−0.103817
$323$	8.81269	0.490351
$324$	1.00000	0.0555556
$325$	0	0
$326$	−14.5133	−0.803819
$327$	−10.4179	−0.576111
$328$	−2.59419	−0.143240
$329$	8.27413	0.456167
$330$	23.2446	1.27957
$331$	−20.2500	−1.11304	−0.556519	−	0.830835i	$-0.687863\pi$
$331$	−20.2500	−1.11304	−0.556519	+	0.830835i	$0.687863\pi$
$332$	7.10992	0.390207
$333$	3.36227	0.184251
$334$	0.846543	0.0463208
$335$	37.2814	2.03690
$336$	1.00000	0.0545545
$337$	3.11529	0.169701	0.0848504	−	0.996394i	$-0.472959\pi$
$337$	3.11529	0.169701	0.0848504	+	0.996394i	$0.472959\pi$
$338$	0	0
$339$	2.31767	0.125878
$340$	5.69202	0.308693
$341$	−49.5502	−2.68329
$342$	6.26875	0.338975
$343$	−1.00000	−0.0539949
$344$	−5.70171	−0.307416
$345$	−7.54288	−0.406095
$346$	7.06100	0.379602
$347$	−3.64742	−0.195804	−0.0979018	−	0.995196i	$-0.531213\pi$
$347$	−3.64742	−0.195804	−0.0979018	+	0.995196i	$0.531213\pi$
$348$	3.20775	0.171953
$349$	−10.4397	−0.558822	−0.279411	−	0.960172i	$-0.590139\pi$
$349$	−10.4397	−0.558822	−0.279411	+	0.960172i	$0.590139\pi$
$350$	−11.3937	−0.609021
$351$	0	0
$352$	−5.74094	−0.305993
$353$	14.7530	0.785224	0.392612	−	0.919704i	$-0.371572\pi$
$353$	14.7530	0.785224	0.392612	+	0.919704i	$0.371572\pi$
$354$	−7.50604	−0.398942
$355$	−68.1570	−3.61740
$356$	−8.02177	−0.425153
$357$	1.40581	0.0744035
$358$	−3.20775	−0.169535
$359$	31.3207	1.65304	0.826520	−	0.562907i	$-0.190317\pi$
$359$	31.3207	1.65304	0.826520	+	0.562907i	$0.190317\pi$
$360$	4.04892	0.213397
$361$	20.2972	1.06827
$362$	−25.4577	−1.33803
$363$	−21.9584	−1.15252
$364$	0	0
$365$	−1.28621	−0.0673232
$366$	−13.5797	−0.709823
$367$	−30.5080	−1.59250	−0.796251	−	0.604966i	$-0.793187\pi$
$367$	−30.5080	−1.59250	−0.796251	+	0.604966i	$0.793187\pi$
$368$	1.86294	0.0971123
$369$	−2.59419	−0.135048
$370$	13.6136	0.707735
$371$	3.16421	0.164278
$372$	−8.63102	−0.447498
$373$	2.57002	0.133071	0.0665354	−	0.997784i	$-0.478805\pi$
$373$	2.57002	0.133071	0.0665354	+	0.997784i	$0.478805\pi$
$374$	−8.07069	−0.417325
$375$	−25.8877	−1.33683
$376$	−8.27413	−0.426706
$377$	0	0
$378$	1.00000	0.0514344
$379$	30.3913	1.56110	0.780549	−	0.625094i	$-0.214940\pi$
$379$	30.3913	1.56110	0.780549	+	0.625094i	$0.214940\pi$
$380$	25.3817	1.30205
$381$	12.1957	0.624803
$382$	21.1782	1.08357
$383$	−2.98792	−0.152675	−0.0763377	−	0.997082i	$-0.524323\pi$
$383$	−2.98792	−0.152675	−0.0763377	+	0.997082i	$0.524323\pi$
$384$	−1.00000	−0.0510310
$385$	23.2446	1.18465
$386$	−10.4306	−0.530902
$387$	−5.70171	−0.289834
$388$	18.0978	0.918778
$389$	17.2078	0.872468	0.436234	−	0.899833i	$-0.356312\pi$
$389$	17.2078	0.872468	0.436234	+	0.899833i	$0.356312\pi$
$390$	0	0
$391$	2.61894	0.132446
$392$	1.00000	0.0505076
$393$	11.2078	0.565356
$394$	12.0435	0.606745
$395$	4.49396	0.226116
$396$	−5.74094	−0.288493
$397$	−28.0737	−1.40898	−0.704489	−	0.709715i	$-0.748824\pi$
$397$	−28.0737	−1.40898	−0.704489	+	0.709715i	$0.748824\pi$
$398$	−24.7899	−1.24260
$399$	6.26875	0.313830
$400$	11.3937	0.569687
$401$	27.9866	1.39758	0.698792	−	0.715325i	$-0.253721\pi$
$401$	27.9866	1.39758	0.698792	+	0.715325i	$0.253721\pi$
$402$	−9.20775	−0.459241
$403$	0	0
$404$	11.6093	0.577582
$405$	4.04892	0.201192
$406$	3.20775	0.159198
$407$	−19.3026	−0.956794
$408$	−1.40581	−0.0695981
$409$	−1.89738	−0.0938194	−0.0469097	−	0.998899i	$-0.514937\pi$
$409$	−1.89738	−0.0938194	−0.0469097	+	0.998899i	$0.514937\pi$
$410$	−10.5036	−0.518738
$411$	−0.768086	−0.0378869
$412$	17.5405	0.864158
$413$	−7.50604	−0.369348
$414$	1.86294	0.0915583
$415$	28.7875	1.41312
$416$	0	0
$417$	−13.0271	−0.637942
$418$	−35.9885	−1.76026
$419$	−4.48321	−0.219019	−0.109509	−	0.993986i	$-0.534928\pi$
$419$	−4.48321	−0.219019	−0.109509	+	0.993986i	$0.534928\pi$
$420$	4.04892	0.197567
$421$	−24.4403	−1.19115	−0.595573	−	0.803301i	$-0.703075\pi$
$421$	−24.4403	−1.19115	−0.595573	+	0.803301i	$0.703075\pi$
$422$	5.20775	0.253509
$423$	−8.27413	−0.402302
$424$	−3.16421	−0.153668
$425$	16.0175	0.776961
$426$	16.8334	0.815581
$427$	−13.5797	−0.657168
$428$	4.04892	0.195712
$429$	0	0
$430$	−23.0858	−1.11329
$431$	−9.43296	−0.454370	−0.227185	−	0.973852i	$-0.572952\pi$
$431$	−9.43296	−0.454370	−0.227185	+	0.973852i	$0.572952\pi$
$432$	−1.00000	−0.0481125
$433$	0.781495	0.0375563	0.0187781	−	0.999824i	$-0.494022\pi$
$433$	0.781495	0.0375563	0.0187781	+	0.999824i	$0.494022\pi$
$434$	−8.63102	−0.414302
$435$	12.9879	0.622723
$436$	10.4179	0.498927
$437$	11.6783	0.558648
$438$	0.317667	0.0151787
$439$	−26.7735	−1.27783	−0.638914	−	0.769278i	$-0.720616\pi$
$439$	−26.7735	−1.27783	−0.638914	+	0.769278i	$0.720616\pi$
$440$	−23.2446	−1.10814
$441$	1.00000	0.0476190
$442$	0	0
$443$	4.50498	0.214038	0.107019	−	0.994257i	$-0.465869\pi$
$443$	4.50498	0.214038	0.107019	+	0.994257i	$0.465869\pi$
$444$	−3.36227	−0.159566
$445$	−32.4795	−1.53968
$446$	24.2784	1.14962
$447$	−1.54958	−0.0732927
$448$	−1.00000	−0.0472456
$449$	5.87800	0.277400	0.138700	−	0.990334i	$-0.455708\pi$
$449$	5.87800	0.277400	0.138700	+	0.990334i	$0.455708\pi$
$450$	11.3937	0.537106
$451$	14.8931	0.701287
$452$	−2.31767	−0.109014
$453$	15.9323	0.748565
$454$	−19.7995	−0.929239
$455$	0	0
$456$	−6.26875	−0.293561
$457$	39.5066	1.84804	0.924021	−	0.382341i	$-0.124882\pi$
$457$	39.5066	1.84804	0.924021	+	0.382341i	$0.124882\pi$
$458$	18.3177	0.855928
$459$	−1.40581	−0.0656177
$460$	7.54288	0.351688
$461$	7.34481	0.342082	0.171041	−	0.985264i	$-0.445287\pi$
$461$	7.34481	0.342082	0.171041	+	0.985264i	$0.445287\pi$
$462$	−5.74094	−0.267093
$463$	2.87071	0.133413	0.0667065	−	0.997773i	$-0.478751\pi$
$463$	2.87071	0.133413	0.0667065	+	0.997773i	$0.478751\pi$
$464$	−3.20775	−0.148916
$465$	−34.9463	−1.62060
$466$	12.2392	0.566970
$467$	−33.5905	−1.55438	−0.777191	−	0.629265i	$-0.783356\pi$
$467$	−33.5905	−1.55438	−0.777191	+	0.629265i	$0.783356\pi$
$468$	0	0
$469$	−9.20775	−0.425174
$470$	−33.5013	−1.54530
$471$	−15.4276	−0.710866
$472$	7.50604	0.345494
$473$	32.7332	1.50507
$474$	−1.10992	−0.0509801
$475$	71.4245	3.27718
$476$	−1.40581	−0.0644353
$477$	−3.16421	−0.144879
$478$	−18.8713	−0.863153
$479$	−22.5133	−1.02866	−0.514330	−	0.857592i	$-0.671959\pi$
$479$	−22.5133	−1.02866	−0.514330	+	0.857592i	$0.671959\pi$
$480$	−4.04892	−0.184807
$481$	0	0
$482$	10.8659	0.494929
$483$	1.86294	0.0847666
$484$	21.9584	0.998108
$485$	73.2766	3.32732
$486$	−1.00000	−0.0453609
$487$	−5.22713	−0.236864	−0.118432	−	0.992962i	$-0.537787\pi$
$487$	−5.22713	−0.236864	−0.118432	+	0.992962i	$0.537787\pi$
$488$	13.5797	0.614725
$489$	14.5133	0.656316
$490$	4.04892	0.182911
$491$	−42.7375	−1.92872	−0.964358	−	0.264602i	$-0.914759\pi$
$491$	−42.7375	−1.92872	−0.964358	+	0.264602i	$0.914759\pi$
$492$	2.59419	0.116955
$493$	−4.50950	−0.203098
$494$	0	0
$495$	−23.2446	−1.04477
$496$	8.63102	0.387544
$497$	16.8334	0.755081
$498$	−7.10992	−0.318603
$499$	−20.5870	−0.921601	−0.460801	−	0.887504i	$-0.652438\pi$
$499$	−20.5870	−0.921601	−0.460801	+	0.887504i	$0.652438\pi$
$500$	25.8877	1.15773
$501$	−0.846543	−0.0378208
$502$	−13.0664	−0.583181
$503$	31.1051	1.38691	0.693455	−	0.720500i	$-0.256088\pi$
$503$	31.1051	1.38691	0.693455	+	0.720500i	$0.256088\pi$
$504$	−1.00000	−0.0445435
$505$	47.0049	2.09169
$506$	−10.6950	−0.475451
$507$	0	0
$508$	−12.1957	−0.541095
$509$	−16.7724	−0.743423	−0.371712	−	0.928348i	$-0.621229\pi$
$509$	−16.7724	−0.743423	−0.371712	+	0.928348i	$0.621229\pi$
$510$	−5.69202	−0.252047
$511$	0.317667	0.0140528
$512$	1.00000	0.0441942
$513$	−6.26875	−0.276772
$514$	−16.4155	−0.724057
$515$	71.0200	3.12951
$516$	5.70171	0.251004
$517$	47.5013	2.08910
$518$	−3.36227	−0.147730
$519$	−7.06100	−0.309943
$520$	0	0
$521$	−0.777184	−0.0340490	−0.0170245	−	0.999855i	$-0.505419\pi$
$521$	−0.777184	−0.0340490	−0.0170245	+	0.999855i	$0.505419\pi$
$522$	−3.20775	−0.140399
$523$	21.1347	0.924155	0.462077	−	0.886840i	$-0.347104\pi$
$523$	21.1347	0.924155	0.462077	+	0.886840i	$0.347104\pi$
$524$	−11.2078	−0.489613
$525$	11.3937	0.497263
$526$	15.1250	0.659481
$527$	12.1336	0.528548
$528$	5.74094	0.249842
$529$	−19.5295	−0.849107
$530$	−12.8116	−0.556501
$531$	7.50604	0.325734
$532$	−6.26875	−0.271785
$533$	0	0
$534$	8.02177	0.347136
$535$	16.3937	0.708763
$536$	9.20775	0.397714
$537$	3.20775	0.138425
$538$	5.58211	0.240662
$539$	−5.74094	−0.247280
$540$	−4.04892	−0.174238
$541$	1.57434	0.0676860	0.0338430	−	0.999427i	$-0.489225\pi$
$541$	1.57434	0.0676860	0.0338430	+	0.999427i	$0.489225\pi$
$542$	25.5308	1.09664
$543$	25.4577	1.09250
$544$	1.40581	0.0602737
$545$	42.1812	1.80684
$546$	0	0
$547$	11.8043	0.504717	0.252358	−	0.967634i	$-0.418794\pi$
$547$	11.8043	0.504717	0.252358	+	0.967634i	$0.418794\pi$
$548$	0.768086	0.0328110
$549$	13.5797	0.579568
$550$	−65.4107	−2.78912
$551$	−20.1086	−0.856655
$552$	−1.86294	−0.0792918
$553$	−1.10992	−0.0471984
$554$	−23.0019	−0.977258
$555$	−13.6136	−0.577864
$556$	13.0271	0.552474
$557$	−17.2078	−0.729116	−0.364558	−	0.931181i	$-0.618780\pi$
$557$	−17.2078	−0.729116	−0.364558	+	0.931181i	$0.618780\pi$
$558$	8.63102	0.365380
$559$	0	0
$560$	−4.04892	−0.171098
$561$	8.07069	0.340745
$562$	2.89008	0.121911
$563$	−24.0629	−1.01413	−0.507066	−	0.861908i	$-0.669270\pi$
$563$	−24.0629	−1.01413	−0.507066	+	0.861908i	$0.669270\pi$
$564$	8.27413	0.348404
$565$	−9.38404	−0.394790
$566$	−6.25906	−0.263088
$567$	−1.00000	−0.0419961
$568$	−16.8334	−0.706314
$569$	−16.8009	−0.704329	−0.352165	−	0.935938i	$-0.614554\pi$
$569$	−16.8009	−0.704329	−0.352165	+	0.935938i	$0.614554\pi$
$570$	−25.3817	−1.06312
$571$	25.3793	1.06209	0.531044	−	0.847344i	$-0.321800\pi$
$571$	25.3793	1.06209	0.531044	+	0.847344i	$0.321800\pi$
$572$	0	0
$573$	−21.1782	−0.884732
$574$	2.59419	0.108279
$575$	21.2258	0.885177
$576$	1.00000	0.0416667
$577$	11.0121	0.458439	0.229219	−	0.973375i	$-0.426383\pi$
$577$	11.0121	0.458439	0.229219	+	0.973375i	$0.426383\pi$
$578$	−15.0237	−0.624903
$579$	10.4306	0.433480
$580$	−12.9879	−0.539294
$581$	−7.10992	−0.294969
$582$	−18.0978	−0.750179
$583$	18.1655	0.752340
$584$	−0.317667	−0.0131452
$585$	0	0
$586$	23.8019	0.983249
$587$	3.17762	0.131154	0.0655772	−	0.997847i	$-0.479111\pi$
$587$	3.17762	0.131154	0.0655772	+	0.997847i	$0.479111\pi$
$588$	−1.00000	−0.0412393
$589$	54.1057	2.22939
$590$	30.3913	1.25119
$591$	−12.0435	−0.495405
$592$	3.36227	0.138189
$593$	−3.58450	−0.147198	−0.0735988	−	0.997288i	$-0.523448\pi$
$593$	−3.58450	−0.147198	−0.0735988	+	0.997288i	$0.523448\pi$
$594$	5.74094	0.235554
$595$	−5.69202	−0.233350
$596$	1.54958	0.0634733
$597$	24.7899	1.01458
$598$	0	0
$599$	28.3913	1.16004	0.580019	−	0.814603i	$-0.303045\pi$
$599$	28.3913	1.16004	0.580019	+	0.814603i	$0.303045\pi$
$600$	−11.3937	−0.465147
$601$	17.1642	0.700143	0.350071	−	0.936723i	$-0.386157\pi$
$601$	17.1642	0.700143	0.350071	+	0.936723i	$0.386157\pi$
$602$	5.70171	0.232384
$603$	9.20775	0.374969
$604$	−15.9323	−0.648276
$605$	88.9077	3.61461
$606$	−11.6093	−0.471594
$607$	−31.7584	−1.28903	−0.644517	−	0.764590i	$-0.722941\pi$
$607$	−31.7584	−1.28903	−0.644517	+	0.764590i	$0.722941\pi$
$608$	6.26875	0.254231
$609$	−3.20775	−0.129985
$610$	54.9831	2.22620
$611$	0	0
$612$	1.40581	0.0568266
$613$	2.95348	0.119290	0.0596449	−	0.998220i	$-0.481003\pi$
$613$	2.95348	0.119290	0.0596449	+	0.998220i	$0.481003\pi$
$614$	8.13036	0.328115
$615$	10.5036	0.423548
$616$	5.74094	0.231309
$617$	−14.3526	−0.577813	−0.288907	−	0.957357i	$-0.593292\pi$
$617$	−14.3526	−0.577813	−0.288907	+	0.957357i	$0.593292\pi$
$618$	−17.5405	−0.705582
$619$	−12.0000	−0.482321	−0.241160	−	0.970485i	$-0.577528\pi$
$619$	−12.0000	−0.482321	−0.241160	+	0.970485i	$0.577528\pi$
$620$	34.9463	1.40348
$621$	−1.86294	−0.0747571
$622$	−5.87800	−0.235686
$623$	8.02177	0.321385
$624$	0	0
$625$	47.8485	1.91394
$626$	6.13275	0.245114
$627$	35.9885	1.43724
$628$	15.4276	0.615628
$629$	4.72673	0.188467
$630$	−4.04892	−0.161313
$631$	−27.3793	−1.08995	−0.544976	−	0.838452i	$-0.683461\pi$
$631$	−27.3793	−1.08995	−0.544976	+	0.838452i	$0.683461\pi$
$632$	1.10992	0.0441501
$633$	−5.20775	−0.206990
$634$	1.60388	0.0636980
$635$	−49.3793	−1.95956
$636$	3.16421	0.125469
$637$	0	0
$638$	18.4155	0.729077
$639$	−16.8334	−0.665919
$640$	4.04892	0.160048
$641$	6.51334	0.257261	0.128631	−	0.991693i	$-0.458942\pi$
$641$	6.51334	0.257261	0.128631	+	0.991693i	$0.458942\pi$
$642$	−4.04892	−0.159798
$643$	−35.0331	−1.38157	−0.690786	−	0.723060i	$-0.742735\pi$
$643$	−35.0331	−1.38157	−0.690786	+	0.723060i	$0.742735\pi$
$644$	−1.86294	−0.0734100
$645$	23.0858	0.909001
$646$	8.81269	0.346731
$647$	−39.6340	−1.55817	−0.779087	−	0.626916i	$-0.784317\pi$
$647$	−39.6340	−1.55817	−0.779087	+	0.626916i	$0.784317\pi$
$648$	1.00000	0.0392837
$649$	−43.0917	−1.69150
$650$	0	0
$651$	8.63102	0.338276
$652$	−14.5133	−0.568386
$653$	−50.2103	−1.96488	−0.982440	−	0.186581i	$-0.940259\pi$
$653$	−50.2103	−1.96488	−0.982440	+	0.186581i	$0.940259\pi$
$654$	−10.4179	−0.407372
$655$	−45.3793	−1.77311
$656$	−2.59419	−0.101286
$657$	−0.317667	−0.0123934
$658$	8.27413	0.322559
$659$	−49.9667	−1.94643	−0.973214	−	0.229901i	$-0.926160\pi$
$659$	−49.9667	−1.94643	−0.973214	+	0.229901i	$0.926160\pi$
$660$	23.2446	0.904794
$661$	−8.73795	−0.339867	−0.169934	−	0.985456i	$-0.554355\pi$
$661$	−8.73795	−0.339867	−0.169934	+	0.985456i	$0.554355\pi$
$662$	−20.2500	−0.787037
$663$	0	0
$664$	7.10992	0.275918
$665$	−25.3817	−0.984258
$666$	3.36227	0.130285
$667$	−5.97584	−0.231385
$668$	0.846543	0.0327537
$669$	−24.2784	−0.938659
$670$	37.2814	1.44031
$671$	−77.9603	−3.00962
$672$	1.00000	0.0385758
$673$	−30.0790	−1.15946	−0.579731	−	0.814808i	$-0.696842\pi$
$673$	−30.0790	−1.15946	−0.579731	+	0.814808i	$0.696842\pi$
$674$	3.11529	0.119997
$675$	−11.3937	−0.438545
$676$	0	0
$677$	29.5991	1.13759	0.568793	−	0.822481i	$-0.307411\pi$
$677$	29.5991	1.13759	0.568793	+	0.822481i	$0.307411\pi$
$678$	2.31767	0.0890095
$679$	−18.0978	−0.694531
$680$	5.69202	0.218279
$681$	19.7995	0.758720
$682$	−49.5502	−1.89737
$683$	47.7294	1.82632	0.913158	−	0.407605i	$-0.133636\pi$
$683$	47.7294	1.82632	0.913158	+	0.407605i	$0.133636\pi$
$684$	6.26875	0.239692
$685$	3.10992	0.118824
$686$	−1.00000	−0.0381802
$687$	−18.3177	−0.698863
$688$	−5.70171	−0.217376
$689$	0	0
$690$	−7.54288	−0.287152
$691$	3.15990	0.120208	0.0601041	−	0.998192i	$-0.480857\pi$
$691$	3.15990	0.120208	0.0601041	+	0.998192i	$0.480857\pi$
$692$	7.06100	0.268419
$693$	5.74094	0.218080
$694$	−3.64742	−0.138454
$695$	52.7458	2.00076
$696$	3.20775	0.121589
$697$	−3.64694	−0.138138
$698$	−10.4397	−0.395147
$699$	−12.2392	−0.462929
$700$	−11.3937	−0.430643
$701$	46.2452	1.74666	0.873328	−	0.487132i	$-0.161957\pi$
$701$	46.2452	1.74666	0.873328	+	0.487132i	$0.161957\pi$
$702$	0	0
$703$	21.0772	0.794943
$704$	−5.74094	−0.216370
$705$	33.5013	1.26173
$706$	14.7530	0.555237
$707$	−11.6093	−0.436611
$708$	−7.50604	−0.282094
$709$	18.7084	0.702609	0.351305	−	0.936261i	$-0.385738\pi$
$709$	18.7084	0.702609	0.351305	+	0.936261i	$0.385738\pi$
$710$	−68.1570	−2.55789
$711$	1.10992	0.0416251
$712$	−8.02177	−0.300629
$713$	16.0790	0.602165
$714$	1.40581	0.0526112
$715$	0	0
$716$	−3.20775	−0.119879
$717$	18.8713	0.704762
$718$	31.3207	1.16888
$719$	−11.2078	−0.417979	−0.208989	−	0.977918i	$-0.567017\pi$
$719$	−11.2078	−0.417979	−0.208989	+	0.977918i	$0.567017\pi$
$720$	4.04892	0.150894
$721$	−17.5405	−0.653242
$722$	20.2972	0.755384
$723$	−10.8659	−0.404108
$724$	−25.4577	−0.946129
$725$	−36.5483	−1.35737
$726$	−21.9584	−0.814952
$727$	−12.3472	−0.457933	−0.228966	−	0.973434i	$-0.573535\pi$
$727$	−12.3472	−0.457933	−0.228966	+	0.973434i	$0.573535\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−1.28621	−0.0476047
$731$	−8.01554	−0.296465
$732$	−13.5797	−0.501921
$733$	−37.1487	−1.37212	−0.686059	−	0.727546i	$-0.740661\pi$
$733$	−37.1487	−1.37212	−0.686059	+	0.727546i	$0.740661\pi$
$734$	−30.5080	−1.12607
$735$	−4.04892	−0.149347
$736$	1.86294	0.0686688
$737$	−52.8611	−1.94716
$738$	−2.59419	−0.0954933
$739$	15.9323	0.586079	0.293039	−	0.956100i	$-0.405333\pi$
$739$	15.9323	0.586079	0.293039	+	0.956100i	$0.405333\pi$
$740$	13.6136	0.500445
$741$	0	0
$742$	3.16421	0.116162
$743$	10.8595	0.398396	0.199198	−	0.979959i	$-0.436166\pi$
$743$	10.8595	0.398396	0.199198	+	0.979959i	$0.436166\pi$
$744$	−8.63102	−0.316429
$745$	6.27413	0.229866
$746$	2.57002	0.0940953
$747$	7.10992	0.260138
$748$	−8.07069	−0.295094
$749$	−4.04892	−0.147944
$750$	−25.8877	−0.945285
$751$	0.0435405	0.00158882	0.000794408	−	1.00000i	$-0.499747\pi$
$751$	0.0435405	0.00158882	0.000794408		1.00000i	$0.499747\pi$
$752$	−8.27413	−0.301726
$753$	13.0664	0.476165
$754$	0	0
$755$	−64.5086	−2.34771
$756$	1.00000	0.0363696
$757$	−24.5023	−0.890552	−0.445276	−	0.895393i	$-0.646894\pi$
$757$	−24.5023	−0.890552	−0.445276	+	0.895393i	$0.646894\pi$
$758$	30.3913	1.10386
$759$	10.6950	0.388204
$760$	25.3817	0.920689
$761$	−25.8726	−0.937882	−0.468941	−	0.883230i	$-0.655364\pi$
$761$	−25.8726	−0.937882	−0.468941	+	0.883230i	$0.655364\pi$
$762$	12.1957	0.441802
$763$	−10.4179	−0.377153
$764$	21.1782	0.766201
$765$	5.69202	0.205795
$766$	−2.98792	−0.107958
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	−13.8237	−0.498496	−0.249248	−	0.968440i	$-0.580183\pi$
$769$	−13.8237	−0.498496	−0.249248	+	0.968440i	$0.580183\pi$
$770$	23.2446	0.837677
$771$	16.4155	0.591190
$772$	−10.4306	−0.375404
$773$	14.3043	0.514488	0.257244	−	0.966346i	$-0.417186\pi$
$773$	14.3043	0.514488	0.257244	+	0.966346i	$0.417186\pi$
$774$	−5.70171	−0.204944
$775$	98.3396	3.53246
$776$	18.0978	0.649674
$777$	3.36227	0.120621
$778$	17.2078	0.616928
$779$	−16.2623	−0.582658
$780$	0	0
$781$	96.6395	3.45803
$782$	2.61894	0.0936531
$783$	3.20775	0.114636
$784$	1.00000	0.0357143
$785$	62.4650	2.22947
$786$	11.2078	0.399767
$787$	33.7496	1.20304	0.601521	−	0.798857i	$-0.294562\pi$
$787$	33.7496	1.20304	0.601521	+	0.798857i	$0.294562\pi$
$788$	12.0435	0.429033
$789$	−15.1250	−0.538464
$790$	4.49396	0.159888
$791$	2.31767	0.0824068
$792$	−5.74094	−0.203995
$793$	0	0
$794$	−28.0737	−0.996297
$795$	12.8116	0.454382
$796$	−24.7899	−0.878653
$797$	−28.5459	−1.01115	−0.505573	−	0.862784i	$-0.668719\pi$
$797$	−28.5459	−1.01115	−0.505573	+	0.862784i	$0.668719\pi$
$798$	6.26875	0.221911
$799$	−11.6319	−0.411506
$800$	11.3937	0.402829
$801$	−8.02177	−0.283435
$802$	27.9866	0.988241
$803$	1.82371	0.0643573
$804$	−9.20775	−0.324732
$805$	−7.54288	−0.265851
$806$	0	0
$807$	−5.58211	−0.196499
$808$	11.6093	0.408412
$809$	−42.8659	−1.50709	−0.753543	−	0.657399i	$-0.771657\pi$
$809$	−42.8659	−1.50709	−0.753543	+	0.657399i	$0.771657\pi$
$810$	4.04892	0.142264
$811$	20.4131	0.716801	0.358401	−	0.933568i	$-0.383322\pi$
$811$	20.4131	0.716801	0.358401	+	0.933568i	$0.383322\pi$
$812$	3.20775	0.112570
$813$	−25.5308	−0.895404
$814$	−19.3026	−0.676556
$815$	−58.7633	−2.05839
$816$	−1.40581	−0.0492133
$817$	−35.7426	−1.25048
$818$	−1.89738	−0.0663403
$819$	0	0
$820$	−10.5036	−0.366803
$821$	−14.8465	−0.518148	−0.259074	−	0.965857i	$-0.583417\pi$
$821$	−14.8465	−0.518148	−0.259074	+	0.965857i	$0.583417\pi$
$822$	−0.768086	−0.0267901
$823$	0.328421	0.0114480	0.00572402	−	0.999984i	$-0.498178\pi$
$823$	0.328421	0.0114480	0.00572402	+	0.999984i	$0.498178\pi$
$824$	17.5405	0.611052
$825$	65.4107	2.27731
$826$	−7.50604	−0.261169
$827$	−18.5894	−0.646417	−0.323208	−	0.946328i	$-0.604761\pi$
$827$	−18.5894	−0.646417	−0.323208	+	0.946328i	$0.604761\pi$
$828$	1.86294	0.0647415
$829$	−21.2814	−0.739134	−0.369567	−	0.929204i	$-0.620494\pi$
$829$	−21.2814	−0.739134	−0.369567	+	0.929204i	$0.620494\pi$
$830$	28.7875	0.999227
$831$	23.0019	0.797928
$832$	0	0
$833$	1.40581	0.0487085
$834$	−13.0271	−0.451093
$835$	3.42758	0.118616
$836$	−35.9885	−1.24469
$837$	−8.63102	−0.298332
$838$	−4.48321	−0.154870
$839$	−0.396125	−0.0136757	−0.00683787	−	0.999977i	$-0.502177\pi$
$839$	−0.396125	−0.0136757	−0.00683787	+	0.999977i	$0.502177\pi$
$840$	4.04892	0.139701
$841$	−18.7103	−0.645184
$842$	−24.4403	−0.842267
$843$	−2.89008	−0.0995398
$844$	5.20775	0.179258
$845$	0	0
$846$	−8.27413	−0.284470
$847$	−21.9584	−0.754499
$848$	−3.16421	−0.108659
$849$	6.25906	0.214810
$850$	16.0175	0.549394
$851$	6.26370	0.214717
$852$	16.8334	0.576703
$853$	48.4940	1.66040	0.830201	−	0.557465i	$-0.188226\pi$
$853$	48.4940	1.66040	0.830201	+	0.557465i	$0.188226\pi$
$854$	−13.5797	−0.464688
$855$	25.3817	0.868034
$856$	4.04892	0.138389
$857$	−43.9463	−1.50118	−0.750588	−	0.660770i	$-0.770230\pi$
$857$	−43.9463	−1.50118	−0.750588	+	0.660770i	$0.770230\pi$
$858$	0	0
$859$	−9.87741	−0.337013	−0.168506	−	0.985701i	$-0.553894\pi$
$859$	−9.87741	−0.337013	−0.168506	+	0.985701i	$0.553894\pi$
$860$	−23.0858	−0.787218
$861$	−2.59419	−0.0884096
$862$	−9.43296	−0.321288
$863$	13.7342	0.467519	0.233759	−	0.972294i	$-0.424897\pi$
$863$	13.7342	0.467519	0.233759	+	0.972294i	$0.424897\pi$
$864$	−1.00000	−0.0340207
$865$	28.5894	0.972069
$866$	0.781495	0.0265563
$867$	15.0237	0.510231
$868$	−8.63102	−0.292956
$869$	−6.37196	−0.216154
$870$	12.9879	0.440332
$871$	0	0
$872$	10.4179	0.352794
$873$	18.0978	0.612519
$874$	11.6783	0.395024
$875$	−25.8877	−0.875164
$876$	0.317667	0.0107330
$877$	2.70543	0.0913559	0.0456780	−	0.998956i	$-0.485455\pi$
$877$	2.70543	0.0913559	0.0456780	+	0.998956i	$0.485455\pi$
$878$	−26.7735	−0.903561
$879$	−23.8019	−0.802819
$880$	−23.2446	−0.783575
$881$	15.3110	0.515839	0.257920	−	0.966166i	$-0.416963\pi$
$881$	15.3110	0.515839	0.257920	+	0.966166i	$0.416963\pi$
$882$	1.00000	0.0336718
$883$	−43.0858	−1.44995	−0.724976	−	0.688775i	$-0.758149\pi$
$883$	−43.0858	−1.44995	−0.724976	+	0.688775i	$0.758149\pi$
$884$	0	0
$885$	−30.3913	−1.02159
$886$	4.50498	0.151348
$887$	−17.5845	−0.590430	−0.295215	−	0.955431i	$-0.595391\pi$
$887$	−17.5845	−0.590430	−0.295215	+	0.955431i	$0.595391\pi$
$888$	−3.36227	−0.112830
$889$	12.1957	0.409030
$890$	−32.4795	−1.08871
$891$	−5.74094	−0.192329
$892$	24.2784	0.812902
$893$	−51.8684	−1.73571
$894$	−1.54958	−0.0518258
$895$	−12.9879	−0.434138
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	5.87800	0.196151
$899$	−27.6862	−0.923385
$900$	11.3937	0.379791
$901$	−4.44829	−0.148194
$902$	14.8931	0.495885
$903$	−5.70171	−0.189741
$904$	−2.31767	−0.0770845
$905$	−103.076	−3.42637
$906$	15.9323	0.529315
$907$	22.5870	0.749989	0.374995	−	0.927027i	$-0.377645\pi$
$907$	22.5870	0.749989	0.374995	+	0.927027i	$0.377645\pi$
$908$	−19.7995	−0.657071
$909$	11.6093	0.385055
$910$	0	0
$911$	−24.5429	−0.813142	−0.406571	−	0.913619i	$-0.633276\pi$
$911$	−24.5429	−0.813142	−0.406571	+	0.913619i	$0.633276\pi$
$912$	−6.26875	−0.207579
$913$	−40.8176	−1.35087
$914$	39.5066	1.30676
$915$	−54.9831	−1.81769
$916$	18.3177	0.605233
$917$	11.2078	0.370113
$918$	−1.40581	−0.0463987
$919$	60.0340	1.98034	0.990169	−	0.139877i	$-0.0446706\pi$
$919$	60.0340	1.98034	0.990169	+	0.139877i	$0.0446706\pi$
$920$	7.54288	0.248681
$921$	−8.13036	−0.267904
$922$	7.34481	0.241889
$923$	0	0
$924$	−5.74094	−0.188863
$925$	38.3088	1.25959
$926$	2.87071	0.0943373
$927$	17.5405	0.576105
$928$	−3.20775	−0.105300
$929$	−15.2319	−0.499743	−0.249871	−	0.968279i	$-0.580388\pi$
$929$	−15.2319	−0.499743	−0.249871	+	0.968279i	$0.580388\pi$
$930$	−34.9463	−1.14593
$931$	6.26875	0.205450
$932$	12.2392	0.400909
$933$	5.87800	0.192437
$934$	−33.5905	−1.09911
$935$	−32.6775	−1.06867
$936$	0	0
$937$	−13.1487	−0.429548	−0.214774	−	0.976664i	$-0.568902\pi$
$937$	−13.1487	−0.429548	−0.214774	+	0.976664i	$0.568902\pi$
$938$	−9.20775	−0.300644
$939$	−6.13275	−0.200135
$940$	−33.5013	−1.09269
$941$	14.1817	0.462309	0.231155	−	0.972917i	$-0.425750\pi$
$941$	14.1817	0.462309	0.231155	+	0.972917i	$0.425750\pi$
$942$	−15.4276	−0.502658
$943$	−4.83281	−0.157378
$944$	7.50604	0.244301
$945$	4.04892	0.131711
$946$	32.7332	1.06425
$947$	28.4510	0.924534	0.462267	−	0.886741i	$-0.347036\pi$
$947$	28.4510	0.924534	0.462267	+	0.886741i	$0.347036\pi$
$948$	−1.10992	−0.0360484
$949$	0	0
$950$	71.4245	2.31732
$951$	−1.60388	−0.0520092
$952$	−1.40581	−0.0455627
$953$	−35.0702	−1.13604	−0.568018	−	0.823016i	$-0.692290\pi$
$953$	−35.0702	−1.13604	−0.568018	+	0.823016i	$0.692290\pi$
$954$	−3.16421	−0.102445
$955$	85.7488	2.77477
$956$	−18.8713	−0.610341
$957$	−18.4155	−0.595289
$958$	−22.5133	−0.727373
$959$	−0.768086	−0.0248028
$960$	−4.04892	−0.130678
$961$	43.4946	1.40305
$962$	0	0
$963$	4.04892	0.130475
$964$	10.8659	0.349968
$965$	−42.2325	−1.35951
$966$	1.86294	0.0599390
$967$	60.1581	1.93455	0.967277	−	0.253723i	$-0.0816551\pi$
$967$	60.1581	1.93455	0.967277	+	0.253723i	$0.0816551\pi$
$968$	21.9584	0.705769
$969$	−8.81269	−0.283104
$970$	73.2766	2.35277
$971$	−6.42626	−0.206228	−0.103114	−	0.994670i	$-0.532881\pi$
$971$	−6.42626	−0.206228	−0.103114	+	0.994670i	$0.532881\pi$
$972$	−1.00000	−0.0320750
$973$	−13.0271	−0.417631
$974$	−5.22713	−0.167488
$975$	0	0
$976$	13.5797	0.434676
$977$	55.1896	1.76567	0.882835	−	0.469683i	$-0.155632\pi$
$977$	55.1896	1.76567	0.882835	+	0.469683i	$0.155632\pi$
$978$	14.5133	0.464085
$979$	46.0525	1.47184
$980$	4.04892	0.129338
$981$	10.4179	0.332618
$982$	−42.7375	−1.36381
$983$	−38.2452	−1.21983	−0.609916	−	0.792466i	$-0.708797\pi$
$983$	−38.2452	−1.21983	−0.609916	+	0.792466i	$0.708797\pi$
$984$	2.59419	0.0826997
$985$	48.7633	1.55373
$986$	−4.50950	−0.143612
$987$	−8.27413	−0.263368
$988$	0	0
$989$	−10.6219	−0.337758
$990$	−23.2446	−0.738761
$991$	54.9396	1.74521	0.872607	−	0.488423i	$-0.162428\pi$
$991$	54.9396	1.74521	0.872607	+	0.488423i	$0.162428\pi$
$992$	8.63102	0.274035
$993$	20.2500	0.642613
$994$	16.8334	0.533923
$995$	−100.372	−3.18201
$996$	−7.10992	−0.225286
$997$	−60.8745	−1.92792	−0.963958	−	0.266054i	$-0.914280\pi$
$997$	−60.8745	−1.92792	−0.963958	+	0.266054i	$0.914280\pi$
$998$	−20.5870	−0.651670
$999$	−3.36227	−0.106378

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7098.2.a.cb.1.1	✓	3	13.12	even	2
7098.2.a.ck.1.3	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.04892 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.04892 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +4.04892 q^{10} -5.74094 q^{11} -1.00000 q^{12} -1.00000 q^{14} -4.04892 q^{15} +1.00000 q^{16} +1.40581 q^{17} +1.00000 q^{18} +6.26875 q^{19} +4.04892 q^{20} +1.00000 q^{21} -5.74094 q^{22} +1.86294 q^{23} -1.00000 q^{24} +11.3937 q^{25} -1.00000 q^{27} -1.00000 q^{28} -3.20775 q^{29} -4.04892 q^{30} +8.63102 q^{31} +1.00000 q^{32} +5.74094 q^{33} +1.40581 q^{34} -4.04892 q^{35} +1.00000 q^{36} +3.36227 q^{37} +6.26875 q^{38} +4.04892 q^{40} -2.59419 q^{41} +1.00000 q^{42} -5.70171 q^{43} -5.74094 q^{44} +4.04892 q^{45} +1.86294 q^{46} -8.27413 q^{47} -1.00000 q^{48} +1.00000 q^{49} +11.3937 q^{50} -1.40581 q^{51} -3.16421 q^{53} -1.00000 q^{54} -23.2446 q^{55} -1.00000 q^{56} -6.26875 q^{57} -3.20775 q^{58} +7.50604 q^{59} -4.04892 q^{60} +13.5797 q^{61} +8.63102 q^{62} -1.00000 q^{63} +1.00000 q^{64} +5.74094 q^{66} +9.20775 q^{67} +1.40581 q^{68} -1.86294 q^{69} -4.04892 q^{70} -16.8334 q^{71} +1.00000 q^{72} -0.317667 q^{73} +3.36227 q^{74} -11.3937 q^{75} +6.26875 q^{76} +5.74094 q^{77} +1.10992 q^{79} +4.04892 q^{80} +1.00000 q^{81} -2.59419 q^{82} +7.10992 q^{83} +1.00000 q^{84} +5.69202 q^{85} -5.70171 q^{86} +3.20775 q^{87} -5.74094 q^{88} -8.02177 q^{89} +4.04892 q^{90} +1.86294 q^{92} -8.63102 q^{93} -8.27413 q^{94} +25.3817 q^{95} -1.00000 q^{96} +18.0978 q^{97} +1.00000 q^{98} -5.74094 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9} + 3 q^{10} - 3 q^{11} - 3 q^{12} - 3 q^{14} - 3 q^{15} + 3 q^{16} - 9 q^{17} + 3 q^{18} + 11 q^{19} + 3 q^{20} + 3 q^{21} - 3 q^{22} + 11 q^{23} - 3 q^{24} + 2 q^{25} - 3 q^{27} - 3 q^{28} + 8 q^{29} - 3 q^{30} + 11 q^{31} + 3 q^{32} + 3 q^{33} - 9 q^{34} - 3 q^{35} + 3 q^{36} + 3 q^{37} + 11 q^{38} + 3 q^{40} - 21 q^{41} + 3 q^{42} + 10 q^{43} - 3 q^{44} + 3 q^{45} + 11 q^{46} - 14 q^{47} - 3 q^{48} + 3 q^{49} + 2 q^{50} + 9 q^{51} + 2 q^{53} - 3 q^{54} - 24 q^{55} - 3 q^{56} - 11 q^{57} + 8 q^{58} + 32 q^{59} - 3 q^{60} - 6 q^{61} + 11 q^{62} - 3 q^{63} + 3 q^{64} + 3 q^{66} + 10 q^{67} - 9 q^{68} - 11 q^{69} - 3 q^{70} - 21 q^{71} + 3 q^{72} + 16 q^{73} + 3 q^{74} - 2 q^{75} + 11 q^{76} + 3 q^{77} + 4 q^{79} + 3 q^{80} + 3 q^{81} - 21 q^{82} + 22 q^{83} + 3 q^{84} + 12 q^{85} + 10 q^{86} - 8 q^{87} - 3 q^{88} - 21 q^{89} + 3 q^{90} + 11 q^{92} - 11 q^{93} - 14 q^{94} + 25 q^{95} - 3 q^{96} + 36 q^{97} + 3 q^{98} - 3 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9 + 3 * q^10 - 3 * q^11 - 3 * q^12 - 3 * q^14 - 3 * q^15 + 3 * q^16 - 9 * q^17 + 3 * q^18 + 11 * q^19 + 3 * q^20 + 3 * q^21 - 3 * q^22 + 11 * q^23 - 3 * q^24 + 2 * q^25 - 3 * q^27 - 3 * q^28 + 8 * q^29 - 3 * q^30 + 11 * q^31 + 3 * q^32 + 3 * q^33 - 9 * q^34 - 3 * q^35 + 3 * q^36 + 3 * q^37 + 11 * q^38 + 3 * q^40 - 21 * q^41 + 3 * q^42 + 10 * q^43 - 3 * q^44 + 3 * q^45 + 11 * q^46 - 14 * q^47 - 3 * q^48 + 3 * q^49 + 2 * q^50 + 9 * q^51 + 2 * q^53 - 3 * q^54 - 24 * q^55 - 3 * q^56 - 11 * q^57 + 8 * q^58 + 32 * q^59 - 3 * q^60 - 6 * q^61 + 11 * q^62 - 3 * q^63 + 3 * q^64 + 3 * q^66 + 10 * q^67 - 9 * q^68 - 11 * q^69 - 3 * q^70 - 21 * q^71 + 3 * q^72 + 16 * q^73 + 3 * q^74 - 2 * q^75 + 11 * q^76 + 3 * q^77 + 4 * q^79 + 3 * q^80 + 3 * q^81 - 21 * q^82 + 22 * q^83 + 3 * q^84 + 12 * q^85 + 10 * q^86 - 8 * q^87 - 3 * q^88 - 21 * q^89 + 3 * q^90 + 11 * q^92 - 11 * q^93 - 14 * q^94 + 25 * q^95 - 3 * q^96 + 36 * q^97 + 3 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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