LMFDB - Embedded newform 7098.2.a.cg.1.2

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			1.2
Root			$0.445042$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.55496 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.55496 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.55496 q^{10} +3.24698 q^{11} +1.00000 q^{12} +1.00000 q^{14} +2.55496 q^{15} +1.00000 q^{16} +3.40581 q^{17} -1.00000 q^{18} -2.85086 q^{19} +2.55496 q^{20} -1.00000 q^{21} -3.24698 q^{22} -8.54288 q^{23} -1.00000 q^{24} +1.52781 q^{25} +1.00000 q^{27} -1.00000 q^{28} -6.18598 q^{29} -2.55496 q^{30} -0.423272 q^{31} -1.00000 q^{32} +3.24698 q^{33} -3.40581 q^{34} -2.55496 q^{35} +1.00000 q^{36} +5.54288 q^{37} +2.85086 q^{38} -2.55496 q^{40} -3.14675 q^{41} +1.00000 q^{42} +4.93900 q^{43} +3.24698 q^{44} +2.55496 q^{45} +8.54288 q^{46} +4.50604 q^{47} +1.00000 q^{48} +1.00000 q^{49} -1.52781 q^{50} +3.40581 q^{51} +4.12498 q^{53} -1.00000 q^{54} +8.29590 q^{55} +1.00000 q^{56} -2.85086 q^{57} +6.18598 q^{58} +14.9269 q^{59} +2.55496 q^{60} +3.17629 q^{61} +0.423272 q^{62} -1.00000 q^{63} +1.00000 q^{64} -3.24698 q^{66} +5.47219 q^{67} +3.40581 q^{68} -8.54288 q^{69} +2.55496 q^{70} -4.21983 q^{71} -1.00000 q^{72} +12.2959 q^{73} -5.54288 q^{74} +1.52781 q^{75} -2.85086 q^{76} -3.24698 q^{77} +10.2567 q^{79} +2.55496 q^{80} +1.00000 q^{81} +3.14675 q^{82} +16.8509 q^{83} -1.00000 q^{84} +8.70171 q^{85} -4.93900 q^{86} -6.18598 q^{87} -3.24698 q^{88} +1.96615 q^{89} -2.55496 q^{90} -8.54288 q^{92} -0.423272 q^{93} -4.50604 q^{94} -7.28382 q^{95} -1.00000 q^{96} +1.12737 q^{97} -1.00000 q^{98} +3.24698 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 8 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 + 8 * q^5 - 3 * q^6 - 3 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 8 q^{5} - 3 q^{6} - 3 q^{7} - 3 q^{8} + 3 q^{9} - 8 q^{10} + 5 q^{11} + 3 q^{12} + 3 q^{14} + 8 q^{15} + 3 q^{16} - 3 q^{17} - 3 q^{18} + 5 q^{19} + 8 q^{20} - 3 q^{21} - 5 q^{22} - 7 q^{23} - 3 q^{24} + 11 q^{25} + 3 q^{27} - 3 q^{28} - 4 q^{29} - 8 q^{30} - 4 q^{31} - 3 q^{32} + 5 q^{33} + 3 q^{34} - 8 q^{35} + 3 q^{36} - 2 q^{37} - 5 q^{38} - 8 q^{40} + 18 q^{41} + 3 q^{42} + 5 q^{43} + 5 q^{44} + 8 q^{45} + 7 q^{46} + 23 q^{47} + 3 q^{48} + 3 q^{49} - 11 q^{50} - 3 q^{51} - 12 q^{53} - 3 q^{54} + 11 q^{55} + 3 q^{56} + 5 q^{57} + 4 q^{58} + 16 q^{59} + 8 q^{60} + 17 q^{61} + 4 q^{62} - 3 q^{63} + 3 q^{64} - 5 q^{66} + 10 q^{67} - 3 q^{68} - 7 q^{69} + 8 q^{70} - 14 q^{71} - 3 q^{72} + 23 q^{73} + 2 q^{74} + 11 q^{75} + 5 q^{76} - 5 q^{77} + 4 q^{79} + 8 q^{80} + 3 q^{81} - 18 q^{82} + 37 q^{83} - 3 q^{84} - q^{85} - 5 q^{86} - 4 q^{87} - 5 q^{88} - 10 q^{89} - 8 q^{90} - 7 q^{92} - 4 q^{93} - 23 q^{94} + 11 q^{95} - 3 q^{96} + 20 q^{97} - 3 q^{98} + 5 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 8 * q^5 - 3 * q^6 - 3 * q^7 - 3 * q^8 + 3 * q^9 - 8 * q^10 + 5 * q^11 + 3 * q^12 + 3 * q^14 + 8 * q^15 + 3 * q^16 - 3 * q^17 - 3 * q^18 + 5 * q^19 + 8 * q^20 - 3 * q^21 - 5 * q^22 - 7 * q^23 - 3 * q^24 + 11 * q^25 + 3 * q^27 - 3 * q^28 - 4 * q^29 - 8 * q^30 - 4 * q^31 - 3 * q^32 + 5 * q^33 + 3 * q^34 - 8 * q^35 + 3 * q^36 - 2 * q^37 - 5 * q^38 - 8 * q^40 + 18 * q^41 + 3 * q^42 + 5 * q^43 + 5 * q^44 + 8 * q^45 + 7 * q^46 + 23 * q^47 + 3 * q^48 + 3 * q^49 - 11 * q^50 - 3 * q^51 - 12 * q^53 - 3 * q^54 + 11 * q^55 + 3 * q^56 + 5 * q^57 + 4 * q^58 + 16 * q^59 + 8 * q^60 + 17 * q^61 + 4 * q^62 - 3 * q^63 + 3 * q^64 - 5 * q^66 + 10 * q^67 - 3 * q^68 - 7 * q^69 + 8 * q^70 - 14 * q^71 - 3 * q^72 + 23 * q^73 + 2 * q^74 + 11 * q^75 + 5 * q^76 - 5 * q^77 + 4 * q^79 + 8 * q^80 + 3 * q^81 - 18 * q^82 + 37 * q^83 - 3 * q^84 - q^85 - 5 * q^86 - 4 * q^87 - 5 * q^88 - 10 * q^89 - 8 * q^90 - 7 * q^92 - 4 * q^93 - 23 * q^94 + 11 * q^95 - 3 * q^96 + 20 * q^97 - 3 * q^98 + 5 * 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
$5$	2.55496	1.14261	0.571306	−	0.820737i	$-0.306437\pi$
$5$	2.55496	1.14261	0.571306	+	0.820737i	$0.306437\pi$
$6$	−1.00000	−0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−2.55496	−0.807949
$11$	3.24698	0.979001	0.489501	−	0.872003i	$-0.337179\pi$
$11$	3.24698	0.979001	0.489501	+	0.872003i	$0.337179\pi$
$12$	1.00000	0.288675
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	2.55496	0.659687
$16$	1.00000	0.250000
$17$	3.40581	0.826031	0.413016	−	0.910724i	$-0.364476\pi$
$17$	3.40581	0.826031	0.413016	+	0.910724i	$0.364476\pi$
$18$	−1.00000	−0.235702
$19$	−2.85086	−0.654031	−0.327016	−	0.945019i	$-0.606043\pi$
$19$	−2.85086	−0.654031	−0.327016	+	0.945019i	$0.606043\pi$
$20$	2.55496	0.571306
$21$	−1.00000	−0.218218
$22$	−3.24698	−0.692258
$23$	−8.54288	−1.78131	−0.890656	−	0.454677i	$-0.849755\pi$
$23$	−8.54288	−1.78131	−0.890656	+	0.454677i	$0.849755\pi$
$24$	−1.00000	−0.204124
$25$	1.52781	0.305562
$26$	0	0
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	−6.18598	−1.14871	−0.574354	−	0.818607i	$-0.694747\pi$
$29$	−6.18598	−1.14871	−0.574354	+	0.818607i	$0.694747\pi$
$30$	−2.55496	−0.466469
$31$	−0.423272	−0.0760218	−0.0380109	−	0.999277i	$-0.512102\pi$
$31$	−0.423272	−0.0760218	−0.0380109	+	0.999277i	$0.512102\pi$
$32$	−1.00000	−0.176777
$33$	3.24698	0.565227
$34$	−3.40581	−0.584092
$35$	−2.55496	−0.431867
$36$	1.00000	0.166667
$37$	5.54288	0.911243	0.455622	−	0.890174i	$-0.349417\pi$
$37$	5.54288	0.911243	0.455622	+	0.890174i	$0.349417\pi$
$38$	2.85086	0.462470
$39$	0	0
$40$	−2.55496	−0.403974
$41$	−3.14675	−0.491440	−0.245720	−	0.969341i	$-0.579024\pi$
$41$	−3.14675	−0.491440	−0.245720	+	0.969341i	$0.579024\pi$
$42$	1.00000	0.154303
$43$	4.93900	0.753191	0.376595	−	0.926378i	$-0.377095\pi$
$43$	4.93900	0.753191	0.376595	+	0.926378i	$0.377095\pi$
$44$	3.24698	0.489501
$45$	2.55496	0.380871
$46$	8.54288	1.25958
$47$	4.50604	0.657274	0.328637	−	0.944456i	$-0.393411\pi$
$47$	4.50604	0.657274	0.328637	+	0.944456i	$0.393411\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	−1.52781	−0.216065
$51$	3.40581	0.476909
$52$	0	0
$53$	4.12498	0.566610	0.283305	−	0.959030i	$-0.408569\pi$
$53$	4.12498	0.566610	0.283305	+	0.959030i	$0.408569\pi$
$54$	−1.00000	−0.136083
$55$	8.29590	1.11862
$56$	1.00000	0.133631
$57$	−2.85086	−0.377605
$58$	6.18598	0.812259
$59$	14.9269	1.94332	0.971660	−	0.236384i	$-0.0759624\pi$
$59$	14.9269	1.94332	0.971660	+	0.236384i	$0.0759624\pi$
$60$	2.55496	0.329844
$61$	3.17629	0.406683	0.203341	−	0.979108i	$-0.434820\pi$
$61$	3.17629	0.406683	0.203341	+	0.979108i	$0.434820\pi$
$62$	0.423272	0.0537555
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	−3.24698	−0.399676
$67$	5.47219	0.668534	0.334267	−	0.942478i	$-0.391511\pi$
$67$	5.47219	0.668534	0.334267	+	0.942478i	$0.391511\pi$
$68$	3.40581	0.413016
$69$	−8.54288	−1.02844
$70$	2.55496	0.305376
$71$	−4.21983	−0.500802	−0.250401	−	0.968142i	$-0.580562\pi$
$71$	−4.21983	−0.500802	−0.250401	+	0.968142i	$0.580562\pi$
$72$	−1.00000	−0.117851
$73$	12.2959	1.43913	0.719563	−	0.694427i	$-0.244342\pi$
$73$	12.2959	1.43913	0.719563	+	0.694427i	$0.244342\pi$
$74$	−5.54288	−0.644346
$75$	1.52781	0.176416
$76$	−2.85086	−0.327016
$77$	−3.24698	−0.370028
$78$	0	0
$79$	10.2567	1.15397	0.576983	−	0.816756i	$-0.304230\pi$
$79$	10.2567	1.15397	0.576983	+	0.816756i	$0.304230\pi$
$80$	2.55496	0.285653
$81$	1.00000	0.111111
$82$	3.14675	0.347501
$83$	16.8509	1.84962	0.924811	−	0.380427i	$-0.124223\pi$
$83$	16.8509	1.84962	0.924811	+	0.380427i	$0.124223\pi$
$84$	−1.00000	−0.109109
$85$	8.70171	0.943833
$86$	−4.93900	−0.532586
$87$	−6.18598	−0.663207
$88$	−3.24698	−0.346129
$89$	1.96615	0.208411	0.104206	−	0.994556i	$-0.466770\pi$
$89$	1.96615	0.208411	0.104206	+	0.994556i	$0.466770\pi$
$90$	−2.55496	−0.269316
$91$	0	0
$92$	−8.54288	−0.890656
$93$	−0.423272	−0.0438912
$94$	−4.50604	−0.464763
$95$	−7.28382	−0.747304
$96$	−1.00000	−0.102062
$97$	1.12737	0.114468	0.0572338	−	0.998361i	$-0.481772\pi$
$97$	1.12737	0.114468	0.0572338	+	0.998361i	$0.481772\pi$
$98$	−1.00000	−0.101015
$99$	3.24698	0.326334
$100$	1.52781	0.152781
$101$	−1.03385	−0.102872	−0.0514361	−	0.998676i	$-0.516380\pi$
$101$	−1.03385	−0.102872	−0.0514361	+	0.998676i	$0.516380\pi$
$102$	−3.40581	−0.337226
$103$	8.18060	0.806059	0.403029	−	0.915187i	$-0.367957\pi$
$103$	8.18060	0.806059	0.403029	+	0.915187i	$0.367957\pi$
$104$	0	0
$105$	−2.55496	−0.249338
$106$	−4.12498	−0.400654
$107$	−0.780167	−0.0754216	−0.0377108	−	0.999289i	$-0.512007\pi$
$107$	−0.780167	−0.0754216	−0.0377108	+	0.999289i	$0.512007\pi$
$108$	1.00000	0.0962250
$109$	6.93900	0.664636	0.332318	−	0.943167i	$-0.392169\pi$
$109$	6.93900	0.664636	0.332318	+	0.943167i	$0.392169\pi$
$110$	−8.29590	−0.790983
$111$	5.54288	0.526107
$112$	−1.00000	−0.0944911
$113$	−5.20237	−0.489398	−0.244699	−	0.969599i	$-0.578689\pi$
$113$	−5.20237	−0.489398	−0.244699	+	0.969599i	$0.578689\pi$
$114$	2.85086	0.267007
$115$	−21.8267	−2.03535
$116$	−6.18598	−0.574354
$117$	0	0
$118$	−14.9269	−1.37413
$119$	−3.40581	−0.312210
$120$	−2.55496	−0.233235
$121$	−0.457123	−0.0415567
$122$	−3.17629	−0.287568
$123$	−3.14675	−0.283733
$124$	−0.423272	−0.0380109
$125$	−8.87130	−0.793473
$126$	1.00000	0.0890871
$127$	−14.6136	−1.29674	−0.648372	−	0.761324i	$-0.724550\pi$
$127$	−14.6136	−1.29674	−0.648372	+	0.761324i	$0.724550\pi$
$128$	−1.00000	−0.0883883
$129$	4.93900	0.434855
$130$	0	0
$131$	19.7778	1.72799	0.863996	−	0.503499i	$-0.167954\pi$
$131$	19.7778	1.72799	0.863996	+	0.503499i	$0.167954\pi$
$132$	3.24698	0.282613
$133$	2.85086	0.247200
$134$	−5.47219	−0.472725
$135$	2.55496	0.219896
$136$	−3.40581	−0.292046
$137$	16.7627	1.43213	0.716067	−	0.698031i	$-0.245940\pi$
$137$	16.7627	1.43213	0.716067	+	0.698031i	$0.245940\pi$
$138$	8.54288	0.727218
$139$	12.1685	1.03212	0.516060	−	0.856552i	$-0.327398\pi$
$139$	12.1685	1.03212	0.516060	+	0.856552i	$0.327398\pi$
$140$	−2.55496	−0.215933
$141$	4.50604	0.379477
$142$	4.21983	0.354120
$143$	0	0
$144$	1.00000	0.0833333
$145$	−15.8049	−1.31253
$146$	−12.2959	−1.01762
$147$	1.00000	0.0824786
$148$	5.54288	0.455622
$149$	0.753020	0.0616898	0.0308449	−	0.999524i	$-0.490180\pi$
$149$	0.753020	0.0616898	0.0308449	+	0.999524i	$0.490180\pi$
$150$	−1.52781	−0.124745
$151$	15.1021	1.22900	0.614498	−	0.788919i	$-0.289359\pi$
$151$	15.1021	1.22900	0.614498	+	0.788919i	$0.289359\pi$
$152$	2.85086	0.231235
$153$	3.40581	0.275344
$154$	3.24698	0.261649
$155$	−1.08144	−0.0868634
$156$	0	0
$157$	−18.5133	−1.47753	−0.738763	−	0.673966i	$-0.764590\pi$
$157$	−18.5133	−1.47753	−0.738763	+	0.673966i	$0.764590\pi$
$158$	−10.2567	−0.815977
$159$	4.12498	0.327132
$160$	−2.55496	−0.201987
$161$	8.54288	0.673273
$162$	−1.00000	−0.0785674
$163$	−20.1444	−1.57783	−0.788914	−	0.614504i	$-0.789356\pi$
$163$	−20.1444	−1.57783	−0.788914	+	0.614504i	$0.789356\pi$
$164$	−3.14675	−0.245720
$165$	8.29590	0.645835
$166$	−16.8509	−1.30788
$167$	18.5157	1.43279	0.716395	−	0.697695i	$-0.245791\pi$
$167$	18.5157	1.43279	0.716395	+	0.697695i	$0.245791\pi$
$168$	1.00000	0.0771517
$169$	0	0
$170$	−8.70171	−0.667391
$171$	−2.85086	−0.218010
$172$	4.93900	0.376595
$173$	−22.5676	−1.71579	−0.857893	−	0.513829i	$-0.828227\pi$
$173$	−22.5676	−1.71579	−0.857893	+	0.513829i	$0.828227\pi$
$174$	6.18598	0.468958
$175$	−1.52781	−0.115492
$176$	3.24698	0.244750
$177$	14.9269	1.12198
$178$	−1.96615	−0.147369
$179$	11.8116	0.882842	0.441421	−	0.897300i	$-0.354474\pi$
$179$	11.8116	0.882842	0.441421	+	0.897300i	$0.354474\pi$
$180$	2.55496	0.190435
$181$	−5.48858	−0.407963	−0.203982	−	0.978975i	$-0.565388\pi$
$181$	−5.48858	−0.407963	−0.203982	+	0.978975i	$0.565388\pi$
$182$	0	0
$183$	3.17629	0.234798
$184$	8.54288	0.629789
$185$	14.1618	1.04120
$186$	0.423272	0.0310358
$187$	11.0586	0.808685
$188$	4.50604	0.328637
$189$	−1.00000	−0.0727393
$190$	7.28382	0.528424
$191$	−5.17523	−0.374466	−0.187233	−	0.982316i	$-0.559952\pi$
$191$	−5.17523	−0.374466	−0.187233	+	0.982316i	$0.559952\pi$
$192$	1.00000	0.0721688
$193$	1.67696	0.120710	0.0603550	−	0.998177i	$-0.480777\pi$
$193$	1.67696	0.120710	0.0603550	+	0.998177i	$0.480777\pi$
$194$	−1.12737	−0.0809408
$195$	0	0
$196$	1.00000	0.0714286
$197$	−20.4916	−1.45996	−0.729982	−	0.683467i	$-0.760472\pi$
$197$	−20.4916	−1.45996	−0.729982	+	0.683467i	$0.760472\pi$
$198$	−3.24698	−0.230753
$199$	−5.36898	−0.380597	−0.190298	−	0.981726i	$-0.560946\pi$
$199$	−5.36898	−0.380597	−0.190298	+	0.981726i	$0.560946\pi$
$200$	−1.52781	−0.108033
$201$	5.47219	0.385978
$202$	1.03385	0.0727416
$203$	6.18598	0.434171
$204$	3.40581	0.238455
$205$	−8.03982	−0.561525
$206$	−8.18060	−0.569970
$207$	−8.54288	−0.593771
$208$	0	0
$209$	−9.25667	−0.640297
$210$	2.55496	0.176309
$211$	6.69202	0.460698	0.230349	−	0.973108i	$-0.426013\pi$
$211$	6.69202	0.460698	0.230349	+	0.973108i	$0.426013\pi$
$212$	4.12498	0.283305
$213$	−4.21983	−0.289138
$214$	0.780167	0.0533312
$215$	12.6189	0.860605
$216$	−1.00000	−0.0680414
$217$	0.423272	0.0287335
$218$	−6.93900	−0.469968
$219$	12.2959	0.830880
$220$	8.29590	0.559309
$221$	0	0
$222$	−5.54288	−0.372014
$223$	18.5864	1.24464	0.622319	−	0.782764i	$-0.286191\pi$
$223$	18.5864	1.24464	0.622319	+	0.782764i	$0.286191\pi$
$224$	1.00000	0.0668153
$225$	1.52781	0.101854
$226$	5.20237	0.346057
$227$	6.92394	0.459558	0.229779	−	0.973243i	$-0.426200\pi$
$227$	6.92394	0.459558	0.229779	+	0.973243i	$0.426200\pi$
$228$	−2.85086	−0.188802
$229$	5.73855	0.379214	0.189607	−	0.981860i	$-0.439279\pi$
$229$	5.73855	0.379214	0.189607	+	0.981860i	$0.439279\pi$
$230$	21.8267	1.43921
$231$	−3.24698	−0.213636
$232$	6.18598	0.406130
$233$	11.2892	0.739580	0.369790	−	0.929115i	$-0.379430\pi$
$233$	11.2892	0.739580	0.369790	+	0.929115i	$0.379430\pi$
$234$	0	0
$235$	11.5127	0.751009
$236$	14.9269	0.971660
$237$	10.2567	0.666242
$238$	3.40581	0.220766
$239$	19.3491	1.25159	0.625795	−	0.779987i	$-0.284774\pi$
$239$	19.3491	1.25159	0.625795	+	0.779987i	$0.284774\pi$
$240$	2.55496	0.164922
$241$	−5.95108	−0.383343	−0.191671	−	0.981459i	$-0.561391\pi$
$241$	−5.95108	−0.383343	−0.191671	+	0.981459i	$0.561391\pi$
$242$	0.457123	0.0293850
$243$	1.00000	0.0641500
$244$	3.17629	0.203341
$245$	2.55496	0.163230
$246$	3.14675	0.200630
$247$	0	0
$248$	0.423272	0.0268778
$249$	16.8509	1.06788
$250$	8.87130	0.561070
$251$	−8.84415	−0.558238	−0.279119	−	0.960257i	$-0.590042\pi$
$251$	−8.84415	−0.558238	−0.279119	+	0.960257i	$0.590042\pi$
$252$	−1.00000	−0.0629941
$253$	−27.7385	−1.74391
$254$	14.6136	0.916937
$255$	8.70171	0.544922
$256$	1.00000	0.0625000
$257$	−5.50902	−0.343644	−0.171822	−	0.985128i	$-0.554965\pi$
$257$	−5.50902	−0.343644	−0.171822	+	0.985128i	$0.554965\pi$
$258$	−4.93900	−0.307489
$259$	−5.54288	−0.344418
$260$	0	0
$261$	−6.18598	−0.382903
$262$	−19.7778	−1.22187
$263$	−2.84548	−0.175460	−0.0877299	−	0.996144i	$-0.527961\pi$
$263$	−2.84548	−0.175460	−0.0877299	+	0.996144i	$0.527961\pi$
$264$	−3.24698	−0.199838
$265$	10.5392	0.647415
$266$	−2.85086	−0.174797
$267$	1.96615	0.120326
$268$	5.47219	0.334267
$269$	26.0291	1.58702	0.793510	−	0.608557i	$-0.208251\pi$
$269$	26.0291	1.58702	0.793510	+	0.608557i	$0.208251\pi$
$270$	−2.55496	−0.155490
$271$	2.45042	0.148852	0.0744262	−	0.997227i	$-0.476287\pi$
$271$	2.45042	0.148852	0.0744262	+	0.997227i	$0.476287\pi$
$272$	3.40581	0.206508
$273$	0	0
$274$	−16.7627	−1.01267
$275$	4.96077	0.299146
$276$	−8.54288	−0.514221
$277$	−11.9812	−0.719881	−0.359941	−	0.932975i	$-0.617203\pi$
$277$	−11.9812	−0.719881	−0.359941	+	0.932975i	$0.617203\pi$
$278$	−12.1685	−0.729819
$279$	−0.423272	−0.0253406
$280$	2.55496	0.152688
$281$	2.88231	0.171944	0.0859722	−	0.996298i	$-0.472600\pi$
$281$	2.88231	0.171944	0.0859722	+	0.996298i	$0.472600\pi$
$282$	−4.50604	−0.268331
$283$	−3.71917	−0.221082	−0.110541	−	0.993872i	$-0.535258\pi$
$283$	−3.71917	−0.221082	−0.110541	+	0.993872i	$0.535258\pi$
$284$	−4.21983	−0.250401
$285$	−7.28382	−0.431456
$286$	0	0
$287$	3.14675	0.185747
$288$	−1.00000	−0.0589256
$289$	−5.40044	−0.317673
$290$	15.8049	0.928097
$291$	1.12737	0.0660879
$292$	12.2959	0.719563
$293$	16.2862	0.951450	0.475725	−	0.879594i	$-0.342186\pi$
$293$	16.2862	0.951450	0.475725	+	0.879594i	$0.342186\pi$
$294$	−1.00000	−0.0583212
$295$	38.1377	2.22046
$296$	−5.54288	−0.322173
$297$	3.24698	0.188409
$298$	−0.753020	−0.0436213
$299$	0	0
$300$	1.52781	0.0882082
$301$	−4.93900	−0.284679
$302$	−15.1021	−0.869031
$303$	−1.03385	−0.0593932
$304$	−2.85086	−0.163508
$305$	8.11529	0.464680
$306$	−3.40581	−0.194697
$307$	−1.91723	−0.109422	−0.0547111	−	0.998502i	$-0.517424\pi$
$307$	−1.91723	−0.109422	−0.0547111	+	0.998502i	$0.517424\pi$
$308$	−3.24698	−0.185014
$309$	8.18060	0.465378
$310$	1.08144	0.0614217
$311$	−16.2064	−0.918982	−0.459491	−	0.888182i	$-0.651968\pi$
$311$	−16.2064	−0.918982	−0.459491	+	0.888182i	$0.651968\pi$
$312$	0	0
$313$	−24.2543	−1.37093	−0.685466	−	0.728104i	$-0.740402\pi$
$313$	−24.2543	−1.37093	−0.685466	+	0.728104i	$0.740402\pi$
$314$	18.5133	1.04477
$315$	−2.55496	−0.143956
$316$	10.2567	0.576983
$317$	−23.2911	−1.30816	−0.654080	−	0.756426i	$-0.726944\pi$
$317$	−23.2911	−1.30816	−0.654080	+	0.756426i	$0.726944\pi$
$318$	−4.12498	−0.231317
$319$	−20.0858	−1.12459
$320$	2.55496	0.142827
$321$	−0.780167	−0.0435447
$322$	−8.54288	−0.476076
$323$	−9.70948	−0.540250
$324$	1.00000	0.0555556
$325$	0	0
$326$	20.1444	1.11569
$327$	6.93900	0.383728
$328$	3.14675	0.173750
$329$	−4.50604	−0.248426
$330$	−8.29590	−0.456674
$331$	−34.3957	−1.89056	−0.945278	−	0.326266i	$-0.894209\pi$
$331$	−34.3957	−1.89056	−0.945278	+	0.326266i	$0.894209\pi$
$332$	16.8509	0.924811
$333$	5.54288	0.303748
$334$	−18.5157	−1.01314
$335$	13.9812	0.763875
$336$	−1.00000	−0.0545545
$337$	−14.8049	−0.806475	−0.403238	−	0.915095i	$-0.632115\pi$
$337$	−14.8049	−0.806475	−0.403238	+	0.915095i	$0.632115\pi$
$338$	0	0
$339$	−5.20237	−0.282554
$340$	8.70171	0.471916
$341$	−1.37435	−0.0744255
$342$	2.85086	0.154157
$343$	−1.00000	−0.0539949
$344$	−4.93900	−0.266293
$345$	−21.8267	−1.17511
$346$	22.5676	1.21324
$347$	26.6122	1.42862	0.714310	−	0.699830i	$-0.246741\pi$
$347$	26.6122	1.42862	0.714310	+	0.699830i	$0.246741\pi$
$348$	−6.18598	−0.331603
$349$	−13.2567	−0.709613	−0.354807	−	0.934940i	$-0.615453\pi$
$349$	−13.2567	−0.709613	−0.354807	+	0.934940i	$0.615453\pi$
$350$	1.52781	0.0816649
$351$	0	0
$352$	−3.24698	−0.173065
$353$	22.5483	1.20012	0.600061	−	0.799954i	$-0.295143\pi$
$353$	22.5483	1.20012	0.600061	+	0.799954i	$0.295143\pi$
$354$	−14.9269	−0.793357
$355$	−10.7815	−0.572222
$356$	1.96615	0.104206
$357$	−3.40581	−0.180255
$358$	−11.8116	−0.624264
$359$	31.8025	1.67847	0.839237	−	0.543766i	$-0.183002\pi$
$359$	31.8025	1.67847	0.839237	+	0.543766i	$0.183002\pi$
$360$	−2.55496	−0.134658
$361$	−10.8726	−0.572243
$362$	5.48858	0.288473
$363$	−0.457123	−0.0239928
$364$	0	0
$365$	31.4155	1.64436
$366$	−3.17629	−0.166027
$367$	−3.31037	−0.172800	−0.0864000	−	0.996261i	$-0.527536\pi$
$367$	−3.31037	−0.172800	−0.0864000	+	0.996261i	$0.527536\pi$
$368$	−8.54288	−0.445328
$369$	−3.14675	−0.163813
$370$	−14.1618	−0.736238
$371$	−4.12498	−0.214158
$372$	−0.423272	−0.0219456
$373$	34.8950	1.80679	0.903397	−	0.428805i	$-0.141065\pi$
$373$	34.8950	1.80679	0.903397	+	0.428805i	$0.141065\pi$
$374$	−11.0586	−0.571827
$375$	−8.87130	−0.458112
$376$	−4.50604	−0.232381
$377$	0	0
$378$	1.00000	0.0514344
$379$	−33.3545	−1.71331	−0.856653	−	0.515893i	$-0.827460\pi$
$379$	−33.3545	−1.71331	−0.856653	+	0.515893i	$0.827460\pi$
$380$	−7.28382	−0.373652
$381$	−14.6136	−0.748676
$382$	5.17523	0.264788
$383$	−23.3980	−1.19558	−0.597792	−	0.801651i	$-0.703955\pi$
$383$	−23.3980	−1.19558	−0.597792	+	0.801651i	$0.703955\pi$
$384$	−1.00000	−0.0510310
$385$	−8.29590	−0.422798
$386$	−1.67696	−0.0853548
$387$	4.93900	0.251064
$388$	1.12737	0.0572338
$389$	−9.38644	−0.475911	−0.237956	−	0.971276i	$-0.576477\pi$
$389$	−9.38644	−0.475911	−0.237956	+	0.971276i	$0.576477\pi$
$390$	0	0
$391$	−29.0954	−1.47142
$392$	−1.00000	−0.0505076
$393$	19.7778	0.997657
$394$	20.4916	1.03235
$395$	26.2054	1.31853
$396$	3.24698	0.163167
$397$	7.96376	0.399689	0.199845	−	0.979828i	$-0.435956\pi$
$397$	7.96376	0.399689	0.199845	+	0.979828i	$0.435956\pi$
$398$	5.36898	0.269123
$399$	2.85086	0.142721
$400$	1.52781	0.0763906
$401$	25.4359	1.27021	0.635105	−	0.772426i	$-0.280957\pi$
$401$	25.4359	1.27021	0.635105	+	0.772426i	$0.280957\pi$
$402$	−5.47219	−0.272928
$403$	0	0
$404$	−1.03385	−0.0514361
$405$	2.55496	0.126957
$406$	−6.18598	−0.307005
$407$	17.9976	0.892108
$408$	−3.40581	−0.168613
$409$	−26.9801	−1.33408	−0.667041	−	0.745021i	$-0.732440\pi$
$409$	−26.9801	−1.33408	−0.667041	+	0.745021i	$0.732440\pi$
$410$	8.03982	0.397058
$411$	16.7627	0.826843
$412$	8.18060	0.403029
$413$	−14.9269	−0.734506
$414$	8.54288	0.419859
$415$	43.0532	2.11340
$416$	0	0
$417$	12.1685	0.595895
$418$	9.25667	0.452758
$419$	−38.1594	−1.86421	−0.932105	−	0.362188i	$-0.882030\pi$
$419$	−38.1594	−1.86421	−0.932105	+	0.362188i	$0.882030\pi$
$420$	−2.55496	−0.124669
$421$	−12.0828	−0.588878	−0.294439	−	0.955670i	$-0.595133\pi$
$421$	−12.0828	−0.588878	−0.294439	+	0.955670i	$0.595133\pi$
$422$	−6.69202	−0.325763
$423$	4.50604	0.219091
$424$	−4.12498	−0.200327
$425$	5.20344	0.252404
$426$	4.21983	0.204452
$427$	−3.17629	−0.153712
$428$	−0.780167	−0.0377108
$429$	0	0
$430$	−12.6189	−0.608539
$431$	−28.7023	−1.38254	−0.691271	−	0.722596i	$-0.742949\pi$
$431$	−28.7023	−1.38254	−0.691271	+	0.722596i	$0.742949\pi$
$432$	1.00000	0.0481125
$433$	9.33406	0.448566	0.224283	−	0.974524i	$-0.427996\pi$
$433$	9.33406	0.448566	0.224283	+	0.974524i	$0.427996\pi$
$434$	−0.423272	−0.0203177
$435$	−15.8049	−0.757788
$436$	6.93900	0.332318
$437$	24.3545	1.16503
$438$	−12.2959	−0.587521
$439$	−15.3123	−0.730816	−0.365408	−	0.930848i	$-0.619070\pi$
$439$	−15.3123	−0.730816	−0.365408	+	0.930848i	$0.619070\pi$
$440$	−8.29590	−0.395491
$441$	1.00000	0.0476190
$442$	0	0
$443$	9.89679	0.470211	0.235105	−	0.971970i	$-0.424456\pi$
$443$	9.89679	0.470211	0.235105	+	0.971970i	$0.424456\pi$
$444$	5.54288	0.263053
$445$	5.02343	0.238133
$446$	−18.5864	−0.880092
$447$	0.753020	0.0356166
$448$	−1.00000	−0.0472456
$449$	−26.9288	−1.27085	−0.635425	−	0.772162i	$-0.719175\pi$
$449$	−26.9288	−1.27085	−0.635425	+	0.772162i	$0.719175\pi$
$450$	−1.52781	−0.0720217
$451$	−10.2174	−0.481120
$452$	−5.20237	−0.244699
$453$	15.1021	0.709561
$454$	−6.92394	−0.324956
$455$	0	0
$456$	2.85086	0.133504
$457$	−21.3351	−0.998015	−0.499008	−	0.866598i	$-0.666302\pi$
$457$	−21.3351	−0.998015	−0.499008	+	0.866598i	$0.666302\pi$
$458$	−5.73855	−0.268145
$459$	3.40581	0.158970
$460$	−21.8267	−1.01767
$461$	24.3045	1.13197	0.565987	−	0.824414i	$-0.308495\pi$
$461$	24.3045	1.13197	0.565987	+	0.824414i	$0.308495\pi$
$462$	3.24698	0.151063
$463$	−37.0465	−1.72170	−0.860849	−	0.508860i	$-0.830067\pi$
$463$	−37.0465	−1.72170	−0.860849	+	0.508860i	$0.830067\pi$
$464$	−6.18598	−0.287177
$465$	−1.08144	−0.0501506
$466$	−11.2892	−0.522962
$467$	32.8582	1.52049	0.760247	−	0.649634i	$-0.225078\pi$
$467$	32.8582	1.52049	0.760247	+	0.649634i	$0.225078\pi$
$468$	0	0
$469$	−5.47219	−0.252682
$470$	−11.5127	−0.531043
$471$	−18.5133	−0.853050
$472$	−14.9269	−0.687067
$473$	16.0368	0.737374
$474$	−10.2567	−0.471104
$475$	−4.35557	−0.199847
$476$	−3.40581	−0.156105
$477$	4.12498	0.188870
$478$	−19.3491	−0.885008
$479$	−20.8829	−0.954164	−0.477082	−	0.878859i	$-0.658306\pi$
$479$	−20.8829	−0.954164	−0.477082	+	0.878859i	$0.658306\pi$
$480$	−2.55496	−0.116617
$481$	0	0
$482$	5.95108	0.271064
$483$	8.54288	0.388714
$484$	−0.457123	−0.0207783
$485$	2.88040	0.130792
$486$	−1.00000	−0.0453609
$487$	33.0224	1.49639	0.748193	−	0.663481i	$-0.230922\pi$
$487$	33.0224	1.49639	0.748193	+	0.663481i	$0.230922\pi$
$488$	−3.17629	−0.143784
$489$	−20.1444	−0.910959
$490$	−2.55496	−0.115421
$491$	1.14244	0.0515576	0.0257788	−	0.999668i	$-0.491793\pi$
$491$	1.14244	0.0515576	0.0257788	+	0.999668i	$0.491793\pi$
$492$	−3.14675	−0.141867
$493$	−21.0683	−0.948868
$494$	0	0
$495$	8.29590	0.372873
$496$	−0.423272	−0.0190055
$497$	4.21983	0.189285
$498$	−16.8509	−0.755105
$499$	16.4239	0.735233	0.367617	−	0.929977i	$-0.380174\pi$
$499$	16.4239	0.735233	0.367617	+	0.929977i	$0.380174\pi$
$500$	−8.87130	−0.396736
$501$	18.5157	0.827222
$502$	8.84415	0.394734
$503$	−27.7797	−1.23864	−0.619318	−	0.785141i	$-0.712591\pi$
$503$	−27.7797	−1.23864	−0.619318	+	0.785141i	$0.712591\pi$
$504$	1.00000	0.0445435
$505$	−2.64145	−0.117543
$506$	27.7385	1.23313
$507$	0	0
$508$	−14.6136	−0.648372
$509$	−16.3827	−0.726151	−0.363076	−	0.931760i	$-0.618273\pi$
$509$	−16.3827	−0.726151	−0.363076	+	0.931760i	$0.618273\pi$
$510$	−8.70171	−0.385318
$511$	−12.2959	−0.543938
$512$	−1.00000	−0.0441942
$513$	−2.85086	−0.125868
$514$	5.50902	0.242993
$515$	20.9011	0.921013
$516$	4.93900	0.217427
$517$	14.6310	0.643472
$518$	5.54288	0.243540
$519$	−22.5676	−0.990609
$520$	0	0
$521$	3.65519	0.160137	0.0800683	−	0.996789i	$-0.474486\pi$
$521$	3.65519	0.160137	0.0800683	+	0.996789i	$0.474486\pi$
$522$	6.18598	0.270753
$523$	−4.77884	−0.208964	−0.104482	−	0.994527i	$-0.533318\pi$
$523$	−4.77884	−0.208964	−0.104482	+	0.994527i	$0.533318\pi$
$524$	19.7778	0.863996
$525$	−1.52781	−0.0666791
$526$	2.84548	0.124069
$527$	−1.44158	−0.0627964
$528$	3.24698	0.141307
$529$	49.9807	2.17308
$530$	−10.5392	−0.457792
$531$	14.9269	0.647773
$532$	2.85086	0.123600
$533$	0	0
$534$	−1.96615	−0.0850836
$535$	−1.99330	−0.0861777
$536$	−5.47219	−0.236363
$537$	11.8116	0.509709
$538$	−26.0291	−1.12219
$539$	3.24698	0.139857
$540$	2.55496	0.109948
$541$	−26.4450	−1.13696	−0.568481	−	0.822697i	$-0.692469\pi$
$541$	−26.4450	−1.13696	−0.568481	+	0.822697i	$0.692469\pi$
$542$	−2.45042	−0.105254
$543$	−5.48858	−0.235538
$544$	−3.40581	−0.146023
$545$	17.7289	0.759421
$546$	0	0
$547$	26.0073	1.11199	0.555996	−	0.831185i	$-0.312337\pi$
$547$	26.0073	1.11199	0.555996	+	0.831185i	$0.312337\pi$
$548$	16.7627	0.716067
$549$	3.17629	0.135561
$550$	−4.96077	−0.211528
$551$	17.6353	0.751291
$552$	8.54288	0.363609
$553$	−10.2567	−0.436158
$554$	11.9812	0.509033
$555$	14.1618	0.601136
$556$	12.1685	0.516060
$557$	27.9135	1.18273	0.591367	−	0.806403i	$-0.298589\pi$
$557$	27.9135	1.18273	0.591367	+	0.806403i	$0.298589\pi$
$558$	0.423272	0.0179185
$559$	0	0
$560$	−2.55496	−0.107967
$561$	11.0586	0.466895
$562$	−2.88231	−0.121583
$563$	35.9323	1.51437	0.757183	−	0.653203i	$-0.226575\pi$
$563$	35.9323	1.51437	0.757183	+	0.653203i	$0.226575\pi$
$564$	4.50604	0.189739
$565$	−13.2918	−0.559192
$566$	3.71917	0.156328
$567$	−1.00000	−0.0419961
$568$	4.21983	0.177060
$569$	37.1226	1.55626	0.778130	−	0.628103i	$-0.216168\pi$
$569$	37.1226	1.55626	0.778130	+	0.628103i	$0.216168\pi$
$570$	7.28382	0.305085
$571$	−14.8280	−0.620533	−0.310267	−	0.950650i	$-0.600418\pi$
$571$	−14.8280	−0.620533	−0.310267	+	0.950650i	$0.600418\pi$
$572$	0	0
$573$	−5.17523	−0.216198
$574$	−3.14675	−0.131343
$575$	−13.0519	−0.544302
$576$	1.00000	0.0416667
$577$	27.4161	1.14135	0.570673	−	0.821177i	$-0.306682\pi$
$577$	27.4161	1.14135	0.570673	+	0.821177i	$0.306682\pi$
$578$	5.40044	0.224629
$579$	1.67696	0.0696919
$580$	−15.8049	−0.656264
$581$	−16.8509	−0.699091
$582$	−1.12737	−0.0467312
$583$	13.3937	0.554712
$584$	−12.2959	−0.508808
$585$	0	0
$586$	−16.2862	−0.672777
$587$	−1.54288	−0.0636813	−0.0318407	−	0.999493i	$-0.510137\pi$
$587$	−1.54288	−0.0636813	−0.0318407	+	0.999493i	$0.510137\pi$
$588$	1.00000	0.0412393
$589$	1.20669	0.0497206
$590$	−38.1377	−1.57010
$591$	−20.4916	−0.842910
$592$	5.54288	0.227811
$593$	−35.9124	−1.47475	−0.737374	−	0.675485i	$-0.763934\pi$
$593$	−35.9124	−1.47475	−0.737374	+	0.675485i	$0.763934\pi$
$594$	−3.24698	−0.133225
$595$	−8.70171	−0.356735
$596$	0.753020	0.0308449
$597$	−5.36898	−0.219738
$598$	0	0
$599$	−25.6209	−1.04684	−0.523420	−	0.852075i	$-0.675344\pi$
$599$	−25.6209	−1.04684	−0.523420	+	0.852075i	$0.675344\pi$
$600$	−1.52781	−0.0623726
$601$	9.42519	0.384462	0.192231	−	0.981350i	$-0.438428\pi$
$601$	9.42519	0.384462	0.192231	+	0.981350i	$0.438428\pi$
$602$	4.93900	0.201299
$603$	5.47219	0.222845
$604$	15.1021	0.614498
$605$	−1.16793	−0.0474832
$606$	1.03385	0.0419974
$607$	−29.0495	−1.17908	−0.589542	−	0.807738i	$-0.700692\pi$
$607$	−29.0495	−1.17908	−0.589542	+	0.807738i	$0.700692\pi$
$608$	2.85086	0.115617
$609$	6.18598	0.250669
$610$	−8.11529	−0.328579
$611$	0	0
$612$	3.40581	0.137672
$613$	−16.3763	−0.661431	−0.330716	−	0.943730i	$-0.607290\pi$
$613$	−16.3763	−0.661431	−0.330716	+	0.943730i	$0.607290\pi$
$614$	1.91723	0.0773731
$615$	−8.03982	−0.324197
$616$	3.24698	0.130825
$617$	−21.7313	−0.874867	−0.437434	−	0.899251i	$-0.644112\pi$
$617$	−21.7313	−0.874867	−0.437434	+	0.899251i	$0.644112\pi$
$618$	−8.18060	−0.329072
$619$	−29.4437	−1.18344	−0.591721	−	0.806143i	$-0.701551\pi$
$619$	−29.4437	−1.18344	−0.591721	+	0.806143i	$0.701551\pi$
$620$	−1.08144	−0.0434317
$621$	−8.54288	−0.342814
$622$	16.2064	0.649818
$623$	−1.96615	−0.0787721
$624$	0	0
$625$	−30.3048	−1.21219
$626$	24.2543	0.969396
$627$	−9.25667	−0.369676
$628$	−18.5133	−0.738763
$629$	18.8780	0.752715
$630$	2.55496	0.101792
$631$	31.9855	1.27332	0.636662	−	0.771143i	$-0.280315\pi$
$631$	31.9855	1.27332	0.636662	+	0.771143i	$0.280315\pi$
$632$	−10.2567	−0.407988
$633$	6.69202	0.265984
$634$	23.2911	0.925008
$635$	−37.3370	−1.48168
$636$	4.12498	0.163566
$637$	0	0
$638$	20.0858	0.795203
$639$	−4.21983	−0.166934
$640$	−2.55496	−0.100994
$641$	−38.9353	−1.53785	−0.768926	−	0.639338i	$-0.779208\pi$
$641$	−38.9353	−1.53785	−0.768926	+	0.639338i	$0.779208\pi$
$642$	0.780167	0.0307908
$643$	43.4010	1.71157	0.855785	−	0.517332i	$-0.173075\pi$
$643$	43.4010	1.71157	0.855785	+	0.517332i	$0.173075\pi$
$644$	8.54288	0.336636
$645$	12.6189	0.496870
$646$	9.70948	0.382014
$647$	29.4825	1.15908	0.579538	−	0.814945i	$-0.303233\pi$
$647$	29.4825	1.15908	0.579538	+	0.814945i	$0.303233\pi$
$648$	−1.00000	−0.0392837
$649$	48.4674	1.90251
$650$	0	0
$651$	0.423272	0.0165893
$652$	−20.1444	−0.788914
$653$	−36.3715	−1.42333	−0.711663	−	0.702521i	$-0.752058\pi$
$653$	−36.3715	−1.42333	−0.711663	+	0.702521i	$0.752058\pi$
$654$	−6.93900	−0.271336
$655$	50.5314	1.97442
$656$	−3.14675	−0.122860
$657$	12.2959	0.479709
$658$	4.50604	0.175664
$659$	5.29483	0.206257	0.103129	−	0.994668i	$-0.467115\pi$
$659$	5.29483	0.206257	0.103129	+	0.994668i	$0.467115\pi$
$660$	8.29590	0.322917
$661$	4.78209	0.186002	0.0930008	−	0.995666i	$-0.470354\pi$
$661$	4.78209	0.186002	0.0930008	+	0.995666i	$0.470354\pi$
$662$	34.3957	1.33682
$663$	0	0
$664$	−16.8509	−0.653940
$665$	7.28382	0.282454
$666$	−5.54288	−0.214782
$667$	52.8461	2.04621
$668$	18.5157	0.716395
$669$	18.5864	0.718592
$670$	−13.9812	−0.540141
$671$	10.3134	0.398143
$672$	1.00000	0.0385758
$673$	27.5687	1.06270	0.531348	−	0.847154i	$-0.321686\pi$
$673$	27.5687	1.06270	0.531348	+	0.847154i	$0.321686\pi$
$674$	14.8049	0.570264
$675$	1.52781	0.0588055
$676$	0	0
$677$	6.08038	0.233688	0.116844	−	0.993150i	$-0.462722\pi$
$677$	6.08038	0.233688	0.116844	+	0.993150i	$0.462722\pi$
$678$	5.20237	0.199796
$679$	−1.12737	−0.0432647
$680$	−8.70171	−0.333695
$681$	6.92394	0.265326
$682$	1.37435	0.0526267
$683$	50.2941	1.92445	0.962225	−	0.272255i	$-0.0877695\pi$
$683$	50.2941	1.92445	0.962225	+	0.272255i	$0.0877695\pi$
$684$	−2.85086	−0.109005
$685$	42.8280	1.63637
$686$	1.00000	0.0381802
$687$	5.73855	0.218939
$688$	4.93900	0.188298
$689$	0	0
$690$	21.8267	0.830928
$691$	−1.83340	−0.0697457	−0.0348728	−	0.999392i	$-0.511103\pi$
$691$	−1.83340	−0.0697457	−0.0348728	+	0.999392i	$0.511103\pi$
$692$	−22.5676	−0.857893
$693$	−3.24698	−0.123343
$694$	−26.6122	−1.01019
$695$	31.0901	1.17931
$696$	6.18598	0.234479
$697$	−10.7172	−0.405945
$698$	13.2567	0.501772
$699$	11.2892	0.426996
$700$	−1.52781	−0.0577458
$701$	2.42327	0.0915257	0.0457629	−	0.998952i	$-0.485428\pi$
$701$	2.42327	0.0915257	0.0457629	+	0.998952i	$0.485428\pi$
$702$	0	0
$703$	−15.8019	−0.595981
$704$	3.24698	0.122375
$705$	11.5127	0.433595
$706$	−22.5483	−0.848615
$707$	1.03385	0.0388820
$708$	14.9269	0.560988
$709$	−21.0355	−0.790005	−0.395003	−	0.918680i	$-0.629256\pi$
$709$	−21.0355	−0.790005	−0.395003	+	0.918680i	$0.629256\pi$
$710$	10.7815	0.404622
$711$	10.2567	0.384655
$712$	−1.96615	−0.0736845
$713$	3.61596	0.135419
$714$	3.40581	0.127459
$715$	0	0
$716$	11.8116	0.441421
$717$	19.3491	0.722606
$718$	−31.8025	−1.18686
$719$	10.7584	0.401221	0.200610	−	0.979671i	$-0.435708\pi$
$719$	10.7584	0.401221	0.200610	+	0.979671i	$0.435708\pi$
$720$	2.55496	0.0952177
$721$	−8.18060	−0.304662
$722$	10.8726	0.404637
$723$	−5.95108	−0.221323
$724$	−5.48858	−0.203982
$725$	−9.45101	−0.351002
$726$	0.457123	0.0169654
$727$	−8.15777	−0.302555	−0.151277	−	0.988491i	$-0.548339\pi$
$727$	−8.15777	−0.302555	−0.151277	+	0.988491i	$0.548339\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−31.4155	−1.16274
$731$	16.8213	0.622159
$732$	3.17629	0.117399
$733$	19.3884	0.716125	0.358063	−	0.933698i	$-0.383437\pi$
$733$	19.3884	0.716125	0.358063	+	0.933698i	$0.383437\pi$
$734$	3.31037	0.122188
$735$	2.55496	0.0942411
$736$	8.54288	0.314895
$737$	17.7681	0.654496
$738$	3.14675	0.115834
$739$	−35.7579	−1.31538	−0.657688	−	0.753290i	$-0.728466\pi$
$739$	−35.7579	−1.31538	−0.657688	+	0.753290i	$0.728466\pi$
$740$	14.1618	0.520599
$741$	0	0
$742$	4.12498	0.151433
$743$	−27.8799	−1.02282	−0.511408	−	0.859338i	$-0.670876\pi$
$743$	−27.8799	−1.02282	−0.511408	+	0.859338i	$0.670876\pi$
$744$	0.423272	0.0155179
$745$	1.92394	0.0704875
$746$	−34.8950	−1.27760
$747$	16.8509	0.616541
$748$	11.0586	0.404343
$749$	0.780167	0.0285067
$750$	8.87130	0.323934
$751$	20.3526	0.742676	0.371338	−	0.928498i	$-0.378899\pi$
$751$	20.3526	0.742676	0.371338	+	0.928498i	$0.378899\pi$
$752$	4.50604	0.164318
$753$	−8.84415	−0.322299
$754$	0	0
$755$	38.5854	1.40426
$756$	−1.00000	−0.0363696
$757$	−53.9023	−1.95911	−0.979556	−	0.201172i	$-0.935525\pi$
$757$	−53.9023	−1.95911	−0.979556	+	0.201172i	$0.935525\pi$
$758$	33.3545	1.21149
$759$	−27.7385	−1.00685
$760$	7.28382	0.264212
$761$	−20.2446	−0.733866	−0.366933	−	0.930247i	$-0.619592\pi$
$761$	−20.2446	−0.733866	−0.366933	+	0.930247i	$0.619592\pi$
$762$	14.6136	0.529394
$763$	−6.93900	−0.251209
$764$	−5.17523	−0.187233
$765$	8.70171	0.314611
$766$	23.3980	0.845406
$767$	0	0
$768$	1.00000	0.0360844
$769$	10.5351	0.379906	0.189953	−	0.981793i	$-0.439166\pi$
$769$	10.5351	0.379906	0.189953	+	0.981793i	$0.439166\pi$
$770$	8.29590	0.298963
$771$	−5.50902	−0.198403
$772$	1.67696	0.0603550
$773$	−24.5526	−0.883094	−0.441547	−	0.897238i	$-0.645570\pi$
$773$	−24.5526	−0.883094	−0.441547	+	0.897238i	$0.645570\pi$
$774$	−4.93900	−0.177529
$775$	−0.646679	−0.0232294
$776$	−1.12737	−0.0404704
$777$	−5.54288	−0.198850
$778$	9.38644	0.336520
$779$	8.97093	0.321417
$780$	0	0
$781$	−13.7017	−0.490286
$782$	29.0954	1.04045
$783$	−6.18598	−0.221069
$784$	1.00000	0.0357143
$785$	−47.3008	−1.68824
$786$	−19.7778	−0.705450
$787$	−37.2301	−1.32711	−0.663555	−	0.748127i	$-0.730953\pi$
$787$	−37.2301	−1.32711	−0.663555	+	0.748127i	$0.730953\pi$
$788$	−20.4916	−0.729982
$789$	−2.84548	−0.101302
$790$	−26.2054	−0.932345
$791$	5.20237	0.184975
$792$	−3.24698	−0.115376
$793$	0	0
$794$	−7.96376	−0.282623
$795$	10.5392	0.373785
$796$	−5.36898	−0.190298
$797$	23.5163	0.832991	0.416495	−	0.909138i	$-0.363258\pi$
$797$	23.5163	0.832991	0.416495	+	0.909138i	$0.363258\pi$
$798$	−2.85086	−0.100919
$799$	15.3467	0.542928
$800$	−1.52781	−0.0540163
$801$	1.96615	0.0694704
$802$	−25.4359	−0.898174
$803$	39.9245	1.40891
$804$	5.47219	0.192989
$805$	21.8267	0.769290
$806$	0	0
$807$	26.0291	0.916267
$808$	1.03385	0.0363708
$809$	45.8437	1.61178	0.805889	−	0.592067i	$-0.201688\pi$
$809$	45.8437	1.61178	0.805889	+	0.592067i	$0.201688\pi$
$810$	−2.55496	−0.0897721
$811$	39.7192	1.39473	0.697364	−	0.716717i	$-0.254356\pi$
$811$	39.7192	1.39473	0.697364	+	0.716717i	$0.254356\pi$
$812$	6.18598	0.217085
$813$	2.45042	0.0859399
$814$	−17.9976	−0.630816
$815$	−51.4680	−1.80285
$816$	3.40581	0.119227
$817$	−14.0804	−0.492610
$818$	26.9801	0.943339
$819$	0	0
$820$	−8.03982	−0.280763
$821$	−21.5319	−0.751467	−0.375734	−	0.926728i	$-0.622609\pi$
$821$	−21.5319	−0.751467	−0.375734	+	0.926728i	$0.622609\pi$
$822$	−16.7627	−0.584667
$823$	22.2107	0.774218	0.387109	−	0.922034i	$-0.373474\pi$
$823$	22.2107	0.774218	0.387109	+	0.922034i	$0.373474\pi$
$824$	−8.18060	−0.284985
$825$	4.96077	0.172712
$826$	14.9269	0.519374
$827$	−15.8793	−0.552178	−0.276089	−	0.961132i	$-0.589039\pi$
$827$	−15.8793	−0.552178	−0.276089	+	0.961132i	$0.589039\pi$
$828$	−8.54288	−0.296885
$829$	11.5948	0.402703	0.201352	−	0.979519i	$-0.435467\pi$
$829$	11.5948	0.402703	0.201352	+	0.979519i	$0.435467\pi$
$830$	−43.0532	−1.49440
$831$	−11.9812	−0.415624
$832$	0	0
$833$	3.40581	0.118004
$834$	−12.1685	−0.421361
$835$	47.3069	1.63712
$836$	−9.25667	−0.320149
$837$	−0.423272	−0.0146304
$838$	38.1594	1.31820
$839$	16.7759	0.579167	0.289583	−	0.957153i	$-0.406483\pi$
$839$	16.7759	0.579167	0.289583	+	0.957153i	$0.406483\pi$
$840$	2.55496	0.0881544
$841$	9.26636	0.319530
$842$	12.0828	0.416400
$843$	2.88231	0.0992722
$844$	6.69202	0.230349
$845$	0	0
$846$	−4.50604	−0.154921
$847$	0.457123	0.0157069
$848$	4.12498	0.141652
$849$	−3.71917	−0.127642
$850$	−5.20344	−0.178476
$851$	−47.3521	−1.62321
$852$	−4.21983	−0.144569
$853$	−25.7864	−0.882909	−0.441455	−	0.897284i	$-0.645537\pi$
$853$	−25.7864	−0.882909	−0.441455	+	0.897284i	$0.645537\pi$
$854$	3.17629	0.108690
$855$	−7.28382	−0.249101
$856$	0.780167	0.0266656
$857$	−7.85517	−0.268327	−0.134164	−	0.990959i	$-0.542835\pi$
$857$	−7.85517	−0.268327	−0.134164	+	0.990959i	$0.542835\pi$
$858$	0	0
$859$	7.97179	0.271994	0.135997	−	0.990709i	$-0.456576\pi$
$859$	7.97179	0.271994	0.135997	+	0.990709i	$0.456576\pi$
$860$	12.6189	0.430302
$861$	3.14675	0.107241
$862$	28.7023	0.977604
$863$	5.64310	0.192093	0.0960467	−	0.995377i	$-0.469380\pi$
$863$	5.64310	0.192093	0.0960467	+	0.995377i	$0.469380\pi$
$864$	−1.00000	−0.0340207
$865$	−57.6594	−1.96048
$866$	−9.33406	−0.317184
$867$	−5.40044	−0.183408
$868$	0.423272	0.0143668
$869$	33.3032	1.12973
$870$	15.8049	0.535837
$871$	0	0
$872$	−6.93900	−0.234984
$873$	1.12737	0.0381559
$874$	−24.3545	−0.823803
$875$	8.87130	0.299905
$876$	12.2959	0.415440
$877$	4.71273	0.159137	0.0795687	−	0.996829i	$-0.474646\pi$
$877$	4.71273	0.159137	0.0795687	+	0.996829i	$0.474646\pi$
$878$	15.3123	0.516765
$879$	16.2862	0.549320
$880$	8.29590	0.279655
$881$	24.1400	0.813299	0.406649	−	0.913584i	$-0.366697\pi$
$881$	24.1400	0.813299	0.406649	+	0.913584i	$0.366697\pi$
$882$	−1.00000	−0.0336718
$883$	9.48858	0.319316	0.159658	−	0.987172i	$-0.448961\pi$
$883$	9.48858	0.319316	0.159658	+	0.987172i	$0.448961\pi$
$884$	0	0
$885$	38.1377	1.28198
$886$	−9.89679	−0.332489
$887$	37.4319	1.25684	0.628420	−	0.777874i	$-0.283702\pi$
$887$	37.4319	1.25684	0.628420	+	0.777874i	$0.283702\pi$
$888$	−5.54288	−0.186007
$889$	14.6136	0.490123
$890$	−5.02343	−0.168386
$891$	3.24698	0.108778
$892$	18.5864	0.622319
$893$	−12.8461	−0.429877
$894$	−0.753020	−0.0251848
$895$	30.1782	1.00875
$896$	1.00000	0.0334077
$897$	0	0
$898$	26.9288	0.898627
$899$	2.61835	0.0873269
$900$	1.52781	0.0509270
$901$	14.0489	0.468037
$902$	10.2174	0.340204
$903$	−4.93900	−0.164360
$904$	5.20237	0.173028
$905$	−14.0231	−0.466144
$906$	−15.1021	−0.501735
$907$	−53.1041	−1.76329	−0.881646	−	0.471912i	$-0.843564\pi$
$907$	−53.1041	−1.76329	−0.881646	+	0.471912i	$0.843564\pi$
$908$	6.92394	0.229779
$909$	−1.03385	−0.0342907
$910$	0	0
$911$	−4.68127	−0.155097	−0.0775487	−	0.996989i	$-0.524709\pi$
$911$	−4.68127	−0.155097	−0.0775487	+	0.996989i	$0.524709\pi$
$912$	−2.85086	−0.0944012
$913$	54.7144	1.81078
$914$	21.3351	0.705703
$915$	8.11529	0.268283
$916$	5.73855	0.189607
$917$	−19.7778	−0.653120
$918$	−3.40581	−0.112409
$919$	17.1515	0.565777	0.282889	−	0.959153i	$-0.408707\pi$
$919$	17.1515	0.565777	0.282889	+	0.959153i	$0.408707\pi$
$920$	21.8267	0.719605
$921$	−1.91723	−0.0631749
$922$	−24.3045	−0.800427
$923$	0	0
$924$	−3.24698	−0.106818
$925$	8.46847	0.278442
$926$	37.0465	1.21742
$927$	8.18060	0.268686
$928$	6.18598	0.203065
$929$	−27.7235	−0.909578	−0.454789	−	0.890599i	$-0.650285\pi$
$929$	−27.7235	−0.909578	−0.454789	+	0.890599i	$0.650285\pi$
$930$	1.08144	0.0354619
$931$	−2.85086	−0.0934330
$932$	11.2892	0.369790
$933$	−16.2064	−0.530574
$934$	−32.8582	−1.07515
$935$	28.2543	0.924014
$936$	0	0
$937$	−6.49396	−0.212148	−0.106074	−	0.994358i	$-0.533828\pi$
$937$	−6.49396	−0.212148	−0.106074	+	0.994358i	$0.533828\pi$
$938$	5.47219	0.178673
$939$	−24.2543	−0.791508
$940$	11.5127	0.375504
$941$	−7.95779	−0.259416	−0.129708	−	0.991552i	$-0.541404\pi$
$941$	−7.95779	−0.259416	−0.129708	+	0.991552i	$0.541404\pi$
$942$	18.5133	0.603197
$943$	26.8823	0.875409
$944$	14.9269	0.485830
$945$	−2.55496	−0.0831128
$946$	−16.0368	−0.521403
$947$	56.4717	1.83508	0.917542	−	0.397639i	$-0.130170\pi$
$947$	56.4717	1.83508	0.917542	+	0.397639i	$0.130170\pi$
$948$	10.2567	0.333121
$949$	0	0
$950$	4.35557	0.141313
$951$	−23.2911	−0.755266
$952$	3.40581	0.110383
$953$	37.2204	1.20569	0.602844	−	0.797859i	$-0.294034\pi$
$953$	37.2204	1.20569	0.602844	+	0.797859i	$0.294034\pi$
$954$	−4.12498	−0.133551
$955$	−13.2225	−0.427870
$956$	19.3491	0.625795
$957$	−20.0858	−0.649280
$958$	20.8829	0.674696
$959$	−16.7627	−0.541296
$960$	2.55496	0.0824609
$961$	−30.8208	−0.994221
$962$	0	0
$963$	−0.780167	−0.0251405
$964$	−5.95108	−0.191671
$965$	4.28455	0.137925
$966$	−8.54288	−0.274863
$967$	−24.0790	−0.774330	−0.387165	−	0.922010i	$-0.626546\pi$
$967$	−24.0790	−0.774330	−0.387165	+	0.922010i	$0.626546\pi$
$968$	0.457123	0.0146925
$969$	−9.70948	−0.311913
$970$	−2.88040	−0.0924839
$971$	−28.4204	−0.912054	−0.456027	−	0.889966i	$-0.650728\pi$
$971$	−28.4204	−0.912054	−0.456027	+	0.889966i	$0.650728\pi$
$972$	1.00000	0.0320750
$973$	−12.1685	−0.390105
$974$	−33.0224	−1.05810
$975$	0	0
$976$	3.17629	0.101671
$977$	−20.6297	−0.660002	−0.330001	−	0.943981i	$-0.607049\pi$
$977$	−20.6297	−0.660002	−0.330001	+	0.943981i	$0.607049\pi$
$978$	20.1444	0.644146
$979$	6.38404	0.204035
$980$	2.55496	0.0816151
$981$	6.93900	0.221545
$982$	−1.14244	−0.0364567
$983$	48.3749	1.54292	0.771461	−	0.636277i	$-0.219527\pi$
$983$	48.3749	1.54292	0.771461	+	0.636277i	$0.219527\pi$
$984$	3.14675	0.100315
$985$	−52.3551	−1.66817
$986$	21.0683	0.670951
$987$	−4.50604	−0.143429
$988$	0	0
$989$	−42.1933	−1.34167
$990$	−8.29590	−0.263661
$991$	12.6276	0.401128	0.200564	−	0.979681i	$-0.435723\pi$
$991$	12.6276	0.401128	0.200564	+	0.979681i	$0.435723\pi$
$992$	0.423272	0.0134389
$993$	−34.3957	−1.09151
$994$	−4.21983	−0.133845
$995$	−13.7175	−0.434874
$996$	16.8509	0.533940
$997$	−11.1733	−0.353862	−0.176931	−	0.984223i	$-0.556617\pi$
$997$	−11.1733	−0.353862	−0.176931	+	0.984223i	$0.556617\pi$
$998$	−16.4239	−0.519888
$999$	5.54288	0.175369

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.cg.1.2	✓	3
13.12	even	2		7098.2.a.cl.1.2	yes	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7098.2.a.cg.1.2	✓	3	1.1	even	1	trivial
7098.2.a.cl.1.2	yes	3	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.55496 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.55496 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.55496 q^{10} +3.24698 q^{11} +1.00000 q^{12} +1.00000 q^{14} +2.55496 q^{15} +1.00000 q^{16} +3.40581 q^{17} -1.00000 q^{18} -2.85086 q^{19} +2.55496 q^{20} -1.00000 q^{21} -3.24698 q^{22} -8.54288 q^{23} -1.00000 q^{24} +1.52781 q^{25} +1.00000 q^{27} -1.00000 q^{28} -6.18598 q^{29} -2.55496 q^{30} -0.423272 q^{31} -1.00000 q^{32} +3.24698 q^{33} -3.40581 q^{34} -2.55496 q^{35} +1.00000 q^{36} +5.54288 q^{37} +2.85086 q^{38} -2.55496 q^{40} -3.14675 q^{41} +1.00000 q^{42} +4.93900 q^{43} +3.24698 q^{44} +2.55496 q^{45} +8.54288 q^{46} +4.50604 q^{47} +1.00000 q^{48} +1.00000 q^{49} -1.52781 q^{50} +3.40581 q^{51} +4.12498 q^{53} -1.00000 q^{54} +8.29590 q^{55} +1.00000 q^{56} -2.85086 q^{57} +6.18598 q^{58} +14.9269 q^{59} +2.55496 q^{60} +3.17629 q^{61} +0.423272 q^{62} -1.00000 q^{63} +1.00000 q^{64} -3.24698 q^{66} +5.47219 q^{67} +3.40581 q^{68} -8.54288 q^{69} +2.55496 q^{70} -4.21983 q^{71} -1.00000 q^{72} +12.2959 q^{73} -5.54288 q^{74} +1.52781 q^{75} -2.85086 q^{76} -3.24698 q^{77} +10.2567 q^{79} +2.55496 q^{80} +1.00000 q^{81} +3.14675 q^{82} +16.8509 q^{83} -1.00000 q^{84} +8.70171 q^{85} -4.93900 q^{86} -6.18598 q^{87} -3.24698 q^{88} +1.96615 q^{89} -2.55496 q^{90} -8.54288 q^{92} -0.423272 q^{93} -4.50604 q^{94} -7.28382 q^{95} -1.00000 q^{96} +1.12737 q^{97} -1.00000 q^{98} +3.24698 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 8 q^{5} - 3 q^{6} - 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 8 * q^5 - 3 * q^6 - 3 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 8 q^{5} - 3 q^{6} - 3 q^{7} - 3 q^{8} + 3 q^{9} - 8 q^{10} + 5 q^{11} + 3 q^{12} + 3 q^{14} + 8 q^{15} + 3 q^{16} - 3 q^{17} - 3 q^{18} + 5 q^{19} + 8 q^{20} - 3 q^{21} - 5 q^{22} - 7 q^{23} - 3 q^{24} + 11 q^{25} + 3 q^{27} - 3 q^{28} - 4 q^{29} - 8 q^{30} - 4 q^{31} - 3 q^{32} + 5 q^{33} + 3 q^{34} - 8 q^{35} + 3 q^{36} - 2 q^{37} - 5 q^{38} - 8 q^{40} + 18 q^{41} + 3 q^{42} + 5 q^{43} + 5 q^{44} + 8 q^{45} + 7 q^{46} + 23 q^{47} + 3 q^{48} + 3 q^{49} - 11 q^{50} - 3 q^{51} - 12 q^{53} - 3 q^{54} + 11 q^{55} + 3 q^{56} + 5 q^{57} + 4 q^{58} + 16 q^{59} + 8 q^{60} + 17 q^{61} + 4 q^{62} - 3 q^{63} + 3 q^{64} - 5 q^{66} + 10 q^{67} - 3 q^{68} - 7 q^{69} + 8 q^{70} - 14 q^{71} - 3 q^{72} + 23 q^{73} + 2 q^{74} + 11 q^{75} + 5 q^{76} - 5 q^{77} + 4 q^{79} + 8 q^{80} + 3 q^{81} - 18 q^{82} + 37 q^{83} - 3 q^{84} - q^{85} - 5 q^{86} - 4 q^{87} - 5 q^{88} - 10 q^{89} - 8 q^{90} - 7 q^{92} - 4 q^{93} - 23 q^{94} + 11 q^{95} - 3 q^{96} + 20 q^{97} - 3 q^{98} + 5 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 8 * q^5 - 3 * q^6 - 3 * q^7 - 3 * q^8 + 3 * q^9 - 8 * q^10 + 5 * q^11 + 3 * q^12 + 3 * q^14 + 8 * q^15 + 3 * q^16 - 3 * q^17 - 3 * q^18 + 5 * q^19 + 8 * q^20 - 3 * q^21 - 5 * q^22 - 7 * q^23 - 3 * q^24 + 11 * q^25 + 3 * q^27 - 3 * q^28 - 4 * q^29 - 8 * q^30 - 4 * q^31 - 3 * q^32 + 5 * q^33 + 3 * q^34 - 8 * q^35 + 3 * q^36 - 2 * q^37 - 5 * q^38 - 8 * q^40 + 18 * q^41 + 3 * q^42 + 5 * q^43 + 5 * q^44 + 8 * q^45 + 7 * q^46 + 23 * q^47 + 3 * q^48 + 3 * q^49 - 11 * q^50 - 3 * q^51 - 12 * q^53 - 3 * q^54 + 11 * q^55 + 3 * q^56 + 5 * q^57 + 4 * q^58 + 16 * q^59 + 8 * q^60 + 17 * q^61 + 4 * q^62 - 3 * q^63 + 3 * q^64 - 5 * q^66 + 10 * q^67 - 3 * q^68 - 7 * q^69 + 8 * q^70 - 14 * q^71 - 3 * q^72 + 23 * q^73 + 2 * q^74 + 11 * q^75 + 5 * q^76 - 5 * q^77 + 4 * q^79 + 8 * q^80 + 3 * q^81 - 18 * q^82 + 37 * q^83 - 3 * q^84 - q^85 - 5 * q^86 - 4 * q^87 - 5 * q^88 - 10 * q^89 - 8 * q^90 - 7 * q^92 - 4 * q^93 - 23 * q^94 + 11 * q^95 - 3 * q^96 + 20 * q^97 - 3 * q^98 + 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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