LMFDB - Embedded newform 7098.2.a.cq.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("7098.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$56.6778153547$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.6148961.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 11x^{4} + 12x^{3} + 32x^{2} - 16x - 29 $ x^6 - 2x^5 - 11x^4 + 12x^3 + 32x^2 - 16*x - 29
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			1.6
Root			$-1.07530$ of defining polynomial
Character	$\chi$	$=$	7098.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.937626 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.937626 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.937626 q^{10} -0.541419 q^{11} +1.00000 q^{12} -1.00000 q^{14} +0.937626 q^{15} +1.00000 q^{16} -6.88128 q^{17} -1.00000 q^{18} +1.41866 q^{19} +0.937626 q^{20} +1.00000 q^{21} +0.541419 q^{22} +3.20210 q^{23} -1.00000 q^{24} -4.12086 q^{25} +1.00000 q^{27} +1.00000 q^{28} -0.718406 q^{29} -0.937626 q^{30} -5.76396 q^{31} -1.00000 q^{32} -0.541419 q^{33} +6.88128 q^{34} +0.937626 q^{35} +1.00000 q^{36} -0.659121 q^{37} -1.41866 q^{38} -0.937626 q^{40} -8.48062 q^{41} -1.00000 q^{42} +8.44660 q^{43} -0.541419 q^{44} +0.937626 q^{45} -3.20210 q^{46} -10.3352 q^{47} +1.00000 q^{48} +1.00000 q^{49} +4.12086 q^{50} -6.88128 q^{51} +8.00036 q^{53} -1.00000 q^{54} -0.507648 q^{55} -1.00000 q^{56} +1.41866 q^{57} +0.718406 q^{58} -3.66602 q^{59} +0.937626 q^{60} +2.95612 q^{61} +5.76396 q^{62} +1.00000 q^{63} +1.00000 q^{64} +0.541419 q^{66} -10.4223 q^{67} -6.88128 q^{68} +3.20210 q^{69} -0.937626 q^{70} -1.41453 q^{71} -1.00000 q^{72} -12.9431 q^{73} +0.659121 q^{74} -4.12086 q^{75} +1.41866 q^{76} -0.541419 q^{77} +5.15704 q^{79} +0.937626 q^{80} +1.00000 q^{81} +8.48062 q^{82} -8.05509 q^{83} +1.00000 q^{84} -6.45207 q^{85} -8.44660 q^{86} -0.718406 q^{87} +0.541419 q^{88} -5.39621 q^{89} -0.937626 q^{90} +3.20210 q^{92} -5.76396 q^{93} +10.3352 q^{94} +1.33017 q^{95} -1.00000 q^{96} +14.3236 q^{97} -1.00000 q^{98} -0.541419 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} - 9 q^{5} - 6 q^{6} + 6 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 - 9 * q^5 - 6 * q^6 + 6 * q^7 - 6 * q^8 + 6 * q^9	$ 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} - 9 q^{5} - 6 q^{6} + 6 q^{7} - 6 q^{8} + 6 q^{9} + 9 q^{10} - 10 q^{11} + 6 q^{12} - 6 q^{14} - 9 q^{15} + 6 q^{16} + 4 q^{17} - 6 q^{18} - 2 q^{19} - 9 q^{20} + 6 q^{21} + 10 q^{22} - 6 q^{24} + 9 q^{25} + 6 q^{27} + 6 q^{28} - 4 q^{29} + 9 q^{30} - 9 q^{31} - 6 q^{32} - 10 q^{33} - 4 q^{34} - 9 q^{35} + 6 q^{36} - 9 q^{37} + 2 q^{38} + 9 q^{40} - 25 q^{41} - 6 q^{42} + 19 q^{43} - 10 q^{44} - 9 q^{45} - 21 q^{47} + 6 q^{48} + 6 q^{49} - 9 q^{50} + 4 q^{51} - 4 q^{53} - 6 q^{54} + 21 q^{55} - 6 q^{56} - 2 q^{57} + 4 q^{58} - 20 q^{59} - 9 q^{60} + 3 q^{61} + 9 q^{62} + 6 q^{63} + 6 q^{64} + 10 q^{66} - 24 q^{67} + 4 q^{68} + 9 q^{70} - 13 q^{71} - 6 q^{72} + 9 q^{73} + 9 q^{74} + 9 q^{75} - 2 q^{76} - 10 q^{77} + 28 q^{79} - 9 q^{80} + 6 q^{81} + 25 q^{82} - 15 q^{83} + 6 q^{84} - 17 q^{85} - 19 q^{86} - 4 q^{87} + 10 q^{88} - 11 q^{89} + 9 q^{90} - 9 q^{93} + 21 q^{94} - 6 q^{96} - 2 q^{97} - 6 q^{98} - 10 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 - 9 * q^5 - 6 * q^6 + 6 * q^7 - 6 * q^8 + 6 * q^9 + 9 * q^10 - 10 * q^11 + 6 * q^12 - 6 * q^14 - 9 * q^15 + 6 * q^16 + 4 * q^17 - 6 * q^18 - 2 * q^19 - 9 * q^20 + 6 * q^21 + 10 * q^22 - 6 * q^24 + 9 * q^25 + 6 * q^27 + 6 * q^28 - 4 * q^29 + 9 * q^30 - 9 * q^31 - 6 * q^32 - 10 * q^33 - 4 * q^34 - 9 * q^35 + 6 * q^36 - 9 * q^37 + 2 * q^38 + 9 * q^40 - 25 * q^41 - 6 * q^42 + 19 * q^43 - 10 * q^44 - 9 * q^45 - 21 * q^47 + 6 * q^48 + 6 * q^49 - 9 * q^50 + 4 * q^51 - 4 * q^53 - 6 * q^54 + 21 * q^55 - 6 * q^56 - 2 * q^57 + 4 * q^58 - 20 * q^59 - 9 * q^60 + 3 * q^61 + 9 * q^62 + 6 * q^63 + 6 * q^64 + 10 * q^66 - 24 * q^67 + 4 * q^68 + 9 * q^70 - 13 * q^71 - 6 * q^72 + 9 * q^73 + 9 * q^74 + 9 * q^75 - 2 * q^76 - 10 * q^77 + 28 * q^79 - 9 * q^80 + 6 * q^81 + 25 * q^82 - 15 * q^83 + 6 * q^84 - 17 * q^85 - 19 * q^86 - 4 * q^87 + 10 * q^88 - 11 * q^89 + 9 * q^90 - 9 * q^93 + 21 * q^94 - 6 * q^96 - 2 * q^97 - 6 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0.937626	0.419319	0.209660	−	0.977774i	$-0.432764\pi$
$5$	0.937626	0.419319	0.209660	+	0.977774i	$0.432764\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−0.937626	−0.296503
$11$	−0.541419	−0.163244	−0.0816219	−	0.996663i	$-0.526010\pi$
$11$	−0.541419	−0.163244	−0.0816219	+	0.996663i	$0.526010\pi$
$12$	1.00000	0.288675
$13$	0	0
$13$	0	0
$14$	−1.00000	−0.267261
$15$	0.937626	0.242094
$16$	1.00000	0.250000
$17$	−6.88128	−1.66896	−0.834478	−	0.551042i	$-0.814230\pi$
$17$	−6.88128	−1.66896	−0.834478	+	0.551042i	$0.814230\pi$
$18$	−1.00000	−0.235702
$19$	1.41866	0.325462	0.162731	−	0.986670i	$-0.447970\pi$
$19$	1.41866	0.325462	0.162731	+	0.986670i	$0.447970\pi$
$20$	0.937626	0.209660
$21$	1.00000	0.218218
$22$	0.541419	0.115431
$23$	3.20210	0.667684	0.333842	−	0.942629i	$-0.391655\pi$
$23$	3.20210	0.667684	0.333842	+	0.942629i	$0.391655\pi$
$24$	−1.00000	−0.204124
$25$	−4.12086	−0.824171
$26$	0	0
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	−0.718406	−0.133405	−0.0667023	−	0.997773i	$-0.521248\pi$
$29$	−0.718406	−0.133405	−0.0667023	+	0.997773i	$0.521248\pi$
$30$	−0.937626	−0.171186
$31$	−5.76396	−1.03524	−0.517619	−	0.855611i	$-0.673182\pi$
$31$	−5.76396	−1.03524	−0.517619	+	0.855611i	$0.673182\pi$
$32$	−1.00000	−0.176777
$33$	−0.541419	−0.0942489
$34$	6.88128	1.18013
$35$	0.937626	0.158488
$36$	1.00000	0.166667
$37$	−0.659121	−0.108359	−0.0541794	−	0.998531i	$-0.517254\pi$
$37$	−0.659121	−0.108359	−0.0541794	+	0.998531i	$0.517254\pi$
$38$	−1.41866	−0.230137
$39$	0	0
$40$	−0.937626	−0.148252
$41$	−8.48062	−1.32445	−0.662225	−	0.749305i	$-0.730388\pi$
$41$	−8.48062	−1.32445	−0.662225	+	0.749305i	$0.730388\pi$
$42$	−1.00000	−0.154303
$43$	8.44660	1.28809	0.644047	−	0.764986i	$-0.277254\pi$
$43$	8.44660	1.28809	0.644047	+	0.764986i	$0.277254\pi$
$44$	−0.541419	−0.0816219
$45$	0.937626	0.139773
$46$	−3.20210	−0.472124
$47$	−10.3352	−1.50755	−0.753773	−	0.657135i	$-0.771768\pi$
$47$	−10.3352	−1.50755	−0.753773	+	0.657135i	$0.771768\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	4.12086	0.582777
$51$	−6.88128	−0.963572
$52$	0	0
$53$	8.00036	1.09893	0.549467	−	0.835516i	$-0.314831\pi$
$53$	8.00036	1.09893	0.549467	+	0.835516i	$0.314831\pi$
$54$	−1.00000	−0.136083
$55$	−0.507648	−0.0684513
$56$	−1.00000	−0.133631
$57$	1.41866	0.187906
$58$	0.718406	0.0943313
$59$	−3.66602	−0.477276	−0.238638	−	0.971109i	$-0.576701\pi$
$59$	−3.66602	−0.477276	−0.238638	+	0.971109i	$0.576701\pi$
$60$	0.937626	0.121047
$61$	2.95612	0.378492	0.189246	−	0.981930i	$-0.439396\pi$
$61$	2.95612	0.378492	0.189246	+	0.981930i	$0.439396\pi$
$62$	5.76396	0.732024
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	0.541419	0.0666440
$67$	−10.4223	−1.27329	−0.636645	−	0.771157i	$-0.719678\pi$
$67$	−10.4223	−1.27329	−0.636645	+	0.771157i	$0.719678\pi$
$68$	−6.88128	−0.834478
$69$	3.20210	0.385488
$70$	−0.937626	−0.112068
$71$	−1.41453	−0.167874	−0.0839371	−	0.996471i	$-0.526749\pi$
$71$	−1.41453	−0.167874	−0.0839371	+	0.996471i	$0.526749\pi$
$72$	−1.00000	−0.117851
$73$	−12.9431	−1.51488	−0.757439	−	0.652906i	$-0.773550\pi$
$73$	−12.9431	−1.51488	−0.757439	+	0.652906i	$0.773550\pi$
$74$	0.659121	0.0766213
$75$	−4.12086	−0.475836
$76$	1.41866	0.162731
$77$	−0.541419	−0.0617004
$78$	0	0
$79$	5.15704	0.580212	0.290106	−	0.956995i	$-0.406309\pi$
$79$	5.15704	0.580212	0.290106	+	0.956995i	$0.406309\pi$
$80$	0.937626	0.104830
$81$	1.00000	0.111111
$82$	8.48062	0.936528
$83$	−8.05509	−0.884161	−0.442081	−	0.896975i	$-0.645759\pi$
$83$	−8.05509	−0.884161	−0.442081	+	0.896975i	$0.645759\pi$
$84$	1.00000	0.109109
$85$	−6.45207	−0.699825
$86$	−8.44660	−0.910821
$87$	−0.718406	−0.0770212
$88$	0.541419	0.0577154
$89$	−5.39621	−0.571997	−0.285998	−	0.958230i	$-0.592325\pi$
$89$	−5.39621	−0.571997	−0.285998	+	0.958230i	$0.592325\pi$
$90$	−0.937626	−0.0988345
$91$	0	0
$92$	3.20210	0.333842
$93$	−5.76396	−0.597695
$94$	10.3352	1.06600
$95$	1.33017	0.136473
$96$	−1.00000	−0.102062
$97$	14.3236	1.45434	0.727172	−	0.686456i	$-0.240834\pi$
$97$	14.3236	1.45434	0.727172	+	0.686456i	$0.240834\pi$
$98$	−1.00000	−0.101015
$99$	−0.541419	−0.0544146
$100$	−4.12086	−0.412086
$101$	−15.1070	−1.50320	−0.751602	−	0.659617i	$-0.770719\pi$
$101$	−15.1070	−1.50320	−0.751602	+	0.659617i	$0.770719\pi$
$102$	6.88128	0.681348
$103$	−8.17512	−0.805519	−0.402759	−	0.915306i	$-0.631949\pi$
$103$	−8.17512	−0.805519	−0.402759	+	0.915306i	$0.631949\pi$
$104$	0	0
$105$	0.937626	0.0915029
$106$	−8.00036	−0.777063
$107$	10.9016	1.05389	0.526947	−	0.849898i	$-0.323337\pi$
$107$	10.9016	1.05389	0.526947	+	0.849898i	$0.323337\pi$
$108$	1.00000	0.0962250
$109$	2.10645	0.201761	0.100881	−	0.994899i	$-0.467834\pi$
$109$	2.10645	0.201761	0.100881	+	0.994899i	$0.467834\pi$
$110$	0.507648	0.0484024
$111$	−0.659121	−0.0625610
$112$	1.00000	0.0944911
$113$	3.16314	0.297564	0.148782	−	0.988870i	$-0.452465\pi$
$113$	3.16314	0.297564	0.148782	+	0.988870i	$0.452465\pi$
$114$	−1.41866	−0.132869
$115$	3.00237	0.279973
$116$	−0.718406	−0.0667023
$117$	0	0
$118$	3.66602	0.337485
$119$	−6.88128	−0.630806
$120$	−0.937626	−0.0855932
$121$	−10.7069	−0.973351
$122$	−2.95612	−0.267635
$123$	−8.48062	−0.764672
$124$	−5.76396	−0.517619
$125$	−8.55195	−0.764910
$126$	−1.00000	−0.0890871
$127$	3.62328	0.321514	0.160757	−	0.986994i	$-0.448606\pi$
$127$	3.62328	0.321514	0.160757	+	0.986994i	$0.448606\pi$
$128$	−1.00000	−0.0883883
$129$	8.44660	0.743682
$130$	0	0
$131$	−5.71172	−0.499035	−0.249518	−	0.968370i	$-0.580272\pi$
$131$	−5.71172	−0.499035	−0.249518	+	0.968370i	$0.580272\pi$
$132$	−0.541419	−0.0471244
$133$	1.41866	0.123013
$134$	10.4223	0.900351
$135$	0.937626	0.0806980
$136$	6.88128	0.590065
$137$	0.144209	0.0123206	0.00616031	−	0.999981i	$-0.498039\pi$
$137$	0.144209	0.0123206	0.00616031	+	0.999981i	$0.498039\pi$
$138$	−3.20210	−0.272581
$139$	4.69416	0.398153	0.199077	−	0.979984i	$-0.436206\pi$
$139$	4.69416	0.398153	0.199077	+	0.979984i	$0.436206\pi$
$140$	0.937626	0.0792439
$141$	−10.3352	−0.870382
$142$	1.41453	0.118705
$143$	0	0
$144$	1.00000	0.0833333
$145$	−0.673596	−0.0559391
$146$	12.9431	1.07118
$147$	1.00000	0.0824786
$148$	−0.659121	−0.0541794
$149$	−6.83811	−0.560200	−0.280100	−	0.959971i	$-0.590368\pi$
$149$	−6.83811	−0.560200	−0.280100	+	0.959971i	$0.590368\pi$
$150$	4.12086	0.336467
$151$	−0.339572	−0.0276340	−0.0138170	−	0.999905i	$-0.504398\pi$
$151$	−0.339572	−0.0276340	−0.0138170	+	0.999905i	$0.504398\pi$
$152$	−1.41866	−0.115068
$153$	−6.88128	−0.556318
$154$	0.541419	0.0436288
$155$	−5.40444	−0.434095
$156$	0	0
$157$	−17.7934	−1.42007	−0.710033	−	0.704169i	$-0.751320\pi$
$157$	−17.7934	−1.42007	−0.710033	+	0.704169i	$0.751320\pi$
$158$	−5.15704	−0.410272
$159$	8.00036	0.634469
$160$	−0.937626	−0.0741259
$161$	3.20210	0.252361
$162$	−1.00000	−0.0785674
$163$	7.66576	0.600428	0.300214	−	0.953872i	$-0.402942\pi$
$163$	7.66576	0.600428	0.300214	+	0.953872i	$0.402942\pi$
$164$	−8.48062	−0.662225
$165$	−0.507648	−0.0395204
$166$	8.05509	0.625196
$167$	7.84243	0.606866	0.303433	−	0.952853i	$-0.401867\pi$
$167$	7.84243	0.606866	0.303433	+	0.952853i	$0.401867\pi$
$168$	−1.00000	−0.0771517
$169$	0	0
$170$	6.45207	0.494851
$171$	1.41866	0.108487
$172$	8.44660	0.644047
$173$	−20.1276	−1.53027	−0.765137	−	0.643867i	$-0.777329\pi$
$173$	−20.1276	−1.53027	−0.765137	+	0.643867i	$0.777329\pi$
$174$	0.718406	0.0544622
$175$	−4.12086	−0.311508
$176$	−0.541419	−0.0408110
$177$	−3.66602	−0.275555
$178$	5.39621	0.404463
$179$	7.02725	0.525241	0.262621	−	0.964899i	$-0.415413\pi$
$179$	7.02725	0.525241	0.262621	+	0.964899i	$0.415413\pi$
$180$	0.937626	0.0698865
$181$	−16.5514	−1.23025	−0.615127	−	0.788428i	$-0.710895\pi$
$181$	−16.5514	−1.23025	−0.615127	+	0.788428i	$0.710895\pi$
$182$	0	0
$183$	2.95612	0.218523
$184$	−3.20210	−0.236062
$185$	−0.618009	−0.0454369
$186$	5.76396	0.422634
$187$	3.72565	0.272447
$188$	−10.3352	−0.753773
$189$	1.00000	0.0727393
$190$	−1.33017	−0.0965007
$191$	−4.66925	−0.337855	−0.168928	−	0.985628i	$-0.554030\pi$
$191$	−4.66925	−0.337855	−0.168928	+	0.985628i	$0.554030\pi$
$192$	1.00000	0.0721688
$193$	8.87178	0.638605	0.319302	−	0.947653i	$-0.396551\pi$
$193$	8.87178	0.638605	0.319302	+	0.947653i	$0.396551\pi$
$194$	−14.3236	−1.02838
$195$	0	0
$196$	1.00000	0.0714286
$197$	−11.8953	−0.847508	−0.423754	−	0.905777i	$-0.639288\pi$
$197$	−11.8953	−0.847508	−0.423754	+	0.905777i	$0.639288\pi$
$198$	0.541419	0.0384769
$199$	−0.673030	−0.0477098	−0.0238549	−	0.999715i	$-0.507594\pi$
$199$	−0.673030	−0.0477098	−0.0238549	+	0.999715i	$0.507594\pi$
$200$	4.12086	0.291389
$201$	−10.4223	−0.735134
$202$	15.1070	1.06293
$203$	−0.718406	−0.0504222
$204$	−6.88128	−0.481786
$205$	−7.95166	−0.555368
$206$	8.17512	0.569588
$207$	3.20210	0.222561
$208$	0	0
$209$	−0.768088	−0.0531297
$210$	−0.937626	−0.0647024
$211$	27.8819	1.91947	0.959733	−	0.280912i	$-0.0906370\pi$
$211$	27.8819	1.91947	0.959733	+	0.280912i	$0.0906370\pi$
$212$	8.00036	0.549467
$213$	−1.41453	−0.0969222
$214$	−10.9016	−0.745216
$215$	7.91976	0.540123
$216$	−1.00000	−0.0680414
$217$	−5.76396	−0.391283
$218$	−2.10645	−0.142667
$219$	−12.9431	−0.874615
$220$	−0.507648	−0.0342256
$221$	0	0
$222$	0.659121	0.0442373
$223$	−11.3474	−0.759881	−0.379941	−	0.925011i	$-0.624056\pi$
$223$	−11.3474	−0.759881	−0.379941	+	0.925011i	$0.624056\pi$
$224$	−1.00000	−0.0668153
$225$	−4.12086	−0.274724
$226$	−3.16314	−0.210409
$227$	17.1855	1.14064	0.570319	−	0.821423i	$-0.306819\pi$
$227$	17.1855	1.14064	0.570319	+	0.821423i	$0.306819\pi$
$228$	1.41866	0.0939529
$229$	17.8682	1.18077	0.590383	−	0.807123i	$-0.298977\pi$
$229$	17.8682	1.18077	0.590383	+	0.807123i	$0.298977\pi$
$230$	−3.00237	−0.197971
$231$	−0.541419	−0.0356227
$232$	0.718406	0.0471656
$233$	−17.9082	−1.17320	−0.586602	−	0.809875i	$-0.699535\pi$
$233$	−17.9082	−1.17320	−0.586602	+	0.809875i	$0.699535\pi$
$234$	0	0
$235$	−9.69056	−0.632143
$236$	−3.66602	−0.238638
$237$	5.15704	0.334985
$238$	6.88128	0.446047
$239$	−13.5431	−0.876029	−0.438014	−	0.898968i	$-0.644318\pi$
$239$	−13.5431	−0.876029	−0.438014	+	0.898968i	$0.644318\pi$
$240$	0.937626	0.0605235
$241$	−14.3029	−0.921330	−0.460665	−	0.887574i	$-0.652389\pi$
$241$	−14.3029	−0.921330	−0.460665	+	0.887574i	$0.652389\pi$
$242$	10.7069	0.688263
$243$	1.00000	0.0641500
$244$	2.95612	0.189246
$245$	0.937626	0.0599027
$246$	8.48062	0.540705
$247$	0	0
$248$	5.76396	0.366012
$249$	−8.05509	−0.510471
$250$	8.55195	0.540873
$251$	12.6220	0.796695	0.398348	−	0.917235i	$-0.369584\pi$
$251$	12.6220	0.796695	0.398348	+	0.917235i	$0.369584\pi$
$252$	1.00000	0.0629941
$253$	−1.73368	−0.108995
$254$	−3.62328	−0.227345
$255$	−6.45207	−0.404044
$256$	1.00000	0.0625000
$257$	13.9756	0.871777	0.435888	−	0.900001i	$-0.356434\pi$
$257$	13.9756	0.871777	0.435888	+	0.900001i	$0.356434\pi$
$258$	−8.44660	−0.525863
$259$	−0.659121	−0.0409558
$260$	0	0
$261$	−0.718406	−0.0444682
$262$	5.71172	0.352871
$263$	−20.7739	−1.28097	−0.640485	−	0.767970i	$-0.721267\pi$
$263$	−20.7739	−1.28097	−0.640485	+	0.767970i	$0.721267\pi$
$264$	0.541419	0.0333220
$265$	7.50134	0.460804
$266$	−1.41866	−0.0869835
$267$	−5.39621	−0.330243
$268$	−10.4223	−0.636645
$269$	29.6258	1.80632	0.903159	−	0.429307i	$-0.141242\pi$
$269$	29.6258	1.80632	0.903159	+	0.429307i	$0.141242\pi$
$270$	−0.937626	−0.0570621
$271$	0.553873	0.0336454	0.0168227	−	0.999858i	$-0.494645\pi$
$271$	0.553873	0.0336454	0.0168227	+	0.999858i	$0.494645\pi$
$272$	−6.88128	−0.417239
$273$	0	0
$274$	−0.144209	−0.00871200
$275$	2.23111	0.134541
$276$	3.20210	0.192744
$277$	25.6186	1.53927	0.769635	−	0.638484i	$-0.220438\pi$
$277$	25.6186	1.53927	0.769635	+	0.638484i	$0.220438\pi$
$278$	−4.69416	−0.281537
$279$	−5.76396	−0.345079
$280$	−0.937626	−0.0560339
$281$	−14.1766	−0.845708	−0.422854	−	0.906198i	$-0.638972\pi$
$281$	−14.1766	−0.845708	−0.422854	+	0.906198i	$0.638972\pi$
$282$	10.3352	0.615453
$283$	−3.63484	−0.216069	−0.108034	−	0.994147i	$-0.534456\pi$
$283$	−3.63484	−0.216069	−0.108034	+	0.994147i	$0.534456\pi$
$284$	−1.41453	−0.0839371
$285$	1.33017	0.0787925
$286$	0	0
$287$	−8.48062	−0.500595
$288$	−1.00000	−0.0589256
$289$	30.3520	1.78541
$290$	0.673596	0.0395549
$291$	14.3236	0.839665
$292$	−12.9431	−0.757439
$293$	16.5678	0.967904	0.483952	−	0.875095i	$-0.339201\pi$
$293$	16.5678	0.967904	0.483952	+	0.875095i	$0.339201\pi$
$294$	−1.00000	−0.0583212
$295$	−3.43736	−0.200131
$296$	0.659121	0.0383106
$297$	−0.541419	−0.0314163
$298$	6.83811	0.396121
$299$	0	0
$300$	−4.12086	−0.237918
$301$	8.44660	0.486854
$302$	0.339572	0.0195402
$303$	−15.1070	−0.867875
$304$	1.41866	0.0813656
$305$	2.77174	0.158709
$306$	6.88128	0.393376
$307$	−2.58069	−0.147288	−0.0736440	−	0.997285i	$-0.523463\pi$
$307$	−2.58069	−0.147288	−0.0736440	+	0.997285i	$0.523463\pi$
$308$	−0.541419	−0.0308502
$309$	−8.17512	−0.465066
$310$	5.40444	0.306952
$311$	−23.1639	−1.31350	−0.656752	−	0.754106i	$-0.728070\pi$
$311$	−23.1639	−1.31350	−0.656752	+	0.754106i	$0.728070\pi$
$312$	0	0
$313$	−7.29077	−0.412099	−0.206049	−	0.978542i	$-0.566061\pi$
$313$	−7.29077	−0.412099	−0.206049	+	0.978542i	$0.566061\pi$
$314$	17.7934	1.00414
$315$	0.937626	0.0528293
$316$	5.15704	0.290106
$317$	−13.2339	−0.743288	−0.371644	−	0.928375i	$-0.621206\pi$
$317$	−13.2339	−0.743288	−0.371644	+	0.928375i	$0.621206\pi$
$318$	−8.00036	−0.448638
$319$	0.388958	0.0217775
$320$	0.937626	0.0524149
$321$	10.9016	0.608466
$322$	−3.20210	−0.178446
$323$	−9.76218	−0.543182
$324$	1.00000	0.0555556
$325$	0	0
$326$	−7.66576	−0.424567
$327$	2.10645	0.116487
$328$	8.48062	0.468264
$329$	−10.3352	−0.569798
$330$	0.507648	0.0279451
$331$	31.1374	1.71147	0.855734	−	0.517417i	$-0.173106\pi$
$331$	31.1374	1.71147	0.855734	+	0.517417i	$0.173106\pi$
$332$	−8.05509	−0.442081
$333$	−0.659121	−0.0361196
$334$	−7.84243	−0.429119
$335$	−9.77224	−0.533915
$336$	1.00000	0.0545545
$337$	−13.7131	−0.747001	−0.373500	−	0.927630i	$-0.621843\pi$
$337$	−13.7131	−0.747001	−0.373500	+	0.927630i	$0.621843\pi$
$338$	0	0
$339$	3.16314	0.171798
$340$	−6.45207	−0.349912
$341$	3.12072	0.168996
$342$	−1.41866	−0.0767122
$343$	1.00000	0.0539949
$344$	−8.44660	−0.455410
$345$	3.00237	0.161642
$346$	20.1276	1.08207
$347$	13.7242	0.736755	0.368378	−	0.929676i	$-0.379913\pi$
$347$	13.7242	0.736755	0.368378	+	0.929676i	$0.379913\pi$
$348$	−0.718406	−0.0385106
$349$	−2.63410	−0.141000	−0.0705001	−	0.997512i	$-0.522460\pi$
$349$	−2.63410	−0.141000	−0.0705001	+	0.997512i	$0.522460\pi$
$350$	4.12086	0.220269
$351$	0	0
$352$	0.541419	0.0288577
$353$	−17.0768	−0.908908	−0.454454	−	0.890770i	$-0.650166\pi$
$353$	−17.0768	−0.908908	−0.454454	+	0.890770i	$0.650166\pi$
$354$	3.66602	0.194847
$355$	−1.32630	−0.0703929
$356$	−5.39621	−0.285998
$357$	−6.88128	−0.364196
$358$	−7.02725	−0.371402
$359$	−20.2417	−1.06831	−0.534157	−	0.845385i	$-0.679371\pi$
$359$	−20.2417	−1.06831	−0.534157	+	0.845385i	$0.679371\pi$
$360$	−0.937626	−0.0494172
$361$	−16.9874	−0.894074
$362$	16.5514	0.869920
$363$	−10.7069	−0.561965
$364$	0	0
$365$	−12.1358	−0.635217
$366$	−2.95612	−0.154519
$367$	−0.450463	−0.0235140	−0.0117570	−	0.999931i	$-0.503742\pi$
$367$	−0.450463	−0.0235140	−0.0117570	+	0.999931i	$0.503742\pi$
$368$	3.20210	0.166921
$369$	−8.48062	−0.441484
$370$	0.618009	0.0321288
$371$	8.00036	0.415358
$372$	−5.76396	−0.298847
$373$	21.5364	1.11511	0.557555	−	0.830140i	$-0.311739\pi$
$373$	21.5364	1.11511	0.557555	+	0.830140i	$0.311739\pi$
$374$	−3.72565	−0.192649
$375$	−8.55195	−0.441621
$376$	10.3352	0.532998
$377$	0	0
$378$	−1.00000	−0.0514344
$379$	−22.0595	−1.13312	−0.566561	−	0.824020i	$-0.691727\pi$
$379$	−22.0595	−1.13312	−0.566561	+	0.824020i	$0.691727\pi$
$380$	1.33017	0.0682363
$381$	3.62328	0.185626
$382$	4.66925	0.238900
$383$	−20.8030	−1.06298	−0.531491	−	0.847064i	$-0.678368\pi$
$383$	−20.8030	−1.06298	−0.531491	+	0.847064i	$0.678368\pi$
$384$	−1.00000	−0.0510310
$385$	−0.507648	−0.0258722
$386$	−8.87178	−0.451562
$387$	8.44660	0.429365
$388$	14.3236	0.727172
$389$	14.6585	0.743214	0.371607	−	0.928390i	$-0.378807\pi$
$389$	14.6585	0.743214	0.371607	+	0.928390i	$0.378807\pi$
$390$	0	0
$391$	−22.0345	−1.11434
$392$	−1.00000	−0.0505076
$393$	−5.71172	−0.288118
$394$	11.8953	0.599279
$395$	4.83537	0.243294
$396$	−0.541419	−0.0272073
$397$	−17.1988	−0.863181	−0.431590	−	0.902070i	$-0.642047\pi$
$397$	−17.1988	−0.863181	−0.431590	+	0.902070i	$0.642047\pi$
$398$	0.673030	0.0337359
$399$	1.41866	0.0710217
$400$	−4.12086	−0.206043
$401$	26.8247	1.33956	0.669781	−	0.742558i	$-0.266388\pi$
$401$	26.8247	1.33956	0.669781	+	0.742558i	$0.266388\pi$
$402$	10.4223	0.519818
$403$	0	0
$404$	−15.1070	−0.751602
$405$	0.937626	0.0465910
$406$	0.718406	0.0356539
$407$	0.356860	0.0176889
$408$	6.88128	0.340674
$409$	−11.7817	−0.582570	−0.291285	−	0.956636i	$-0.594083\pi$
$409$	−11.7817	−0.582570	−0.291285	+	0.956636i	$0.594083\pi$
$410$	7.95166	0.392704
$411$	0.144209	0.00711332
$412$	−8.17512	−0.402759
$413$	−3.66602	−0.180393
$414$	−3.20210	−0.157375
$415$	−7.55267	−0.370746
$416$	0	0
$417$	4.69416	0.229874
$418$	0.768088	0.0375684
$419$	8.46291	0.413440	0.206720	−	0.978400i	$-0.433721\pi$
$419$	8.46291	0.413440	0.206720	+	0.978400i	$0.433721\pi$
$420$	0.937626	0.0457515
$421$	33.3600	1.62587	0.812935	−	0.582355i	$-0.197869\pi$
$421$	33.3600	1.62587	0.812935	+	0.582355i	$0.197869\pi$
$422$	−27.8819	−1.35727
$423$	−10.3352	−0.502515
$424$	−8.00036	−0.388532
$425$	28.3568	1.37551
$426$	1.41453	0.0685344
$427$	2.95612	0.143057
$428$	10.9016	0.526947
$429$	0	0
$430$	−7.91976	−0.381925
$431$	−32.8920	−1.58435	−0.792177	−	0.610291i	$-0.791052\pi$
$431$	−32.8920	−1.58435	−0.792177	+	0.610291i	$0.791052\pi$
$432$	1.00000	0.0481125
$433$	−6.17418	−0.296712	−0.148356	−	0.988934i	$-0.547398\pi$
$433$	−6.17418	−0.296712	−0.148356	+	0.988934i	$0.547398\pi$
$434$	5.76396	0.276679
$435$	−0.673596	−0.0322964
$436$	2.10645	0.100881
$437$	4.54269	0.217306
$438$	12.9431	0.618446
$439$	21.6122	1.03150	0.515748	−	0.856741i	$-0.327514\pi$
$439$	21.6122	1.03150	0.515748	+	0.856741i	$0.327514\pi$
$440$	0.507648	0.0242012
$441$	1.00000	0.0476190
$442$	0	0
$443$	29.8911	1.42017	0.710085	−	0.704116i	$-0.248656\pi$
$443$	29.8911	1.42017	0.710085	+	0.704116i	$0.248656\pi$
$444$	−0.659121	−0.0312805
$445$	−5.05963	−0.239849
$446$	11.3474	0.537317
$447$	−6.83811	−0.323432
$448$	1.00000	0.0472456
$449$	−2.80596	−0.132421	−0.0662107	−	0.997806i	$-0.521091\pi$
$449$	−2.80596	−0.132421	−0.0662107	+	0.997806i	$0.521091\pi$
$450$	4.12086	0.194259
$451$	4.59157	0.216208
$452$	3.16314	0.148782
$453$	−0.339572	−0.0159545
$454$	−17.1855	−0.806553
$455$	0	0
$456$	−1.41866	−0.0664347
$457$	−23.8961	−1.11781	−0.558905	−	0.829232i	$-0.688778\pi$
$457$	−23.8961	−1.11781	−0.558905	+	0.829232i	$0.688778\pi$
$458$	−17.8682	−0.834928
$459$	−6.88128	−0.321191
$460$	3.00237	0.139986
$461$	5.56698	0.259280	0.129640	−	0.991561i	$-0.458618\pi$
$461$	5.56698	0.259280	0.129640	+	0.991561i	$0.458618\pi$
$462$	0.541419	0.0251891
$463$	−8.34395	−0.387776	−0.193888	−	0.981024i	$-0.562110\pi$
$463$	−8.34395	−0.387776	−0.193888	+	0.981024i	$0.562110\pi$
$464$	−0.718406	−0.0333511
$465$	−5.40444	−0.250625
$466$	17.9082	0.829581
$467$	−9.20803	−0.426097	−0.213048	−	0.977042i	$-0.568339\pi$
$467$	−9.20803	−0.426097	−0.213048	+	0.977042i	$0.568339\pi$
$468$	0	0
$469$	−10.4223	−0.481258
$470$	9.69056	0.446992
$471$	−17.7934	−0.819875
$472$	3.66602	0.168742
$473$	−4.57315	−0.210274
$474$	−5.15704	−0.236871
$475$	−5.84609	−0.268237
$476$	−6.88128	−0.315403
$477$	8.00036	0.366311
$478$	13.5431	0.619446
$479$	18.6283	0.851148	0.425574	−	0.904924i	$-0.360072\pi$
$479$	18.6283	0.851148	0.425574	+	0.904924i	$0.360072\pi$
$480$	−0.937626	−0.0427966
$481$	0	0
$482$	14.3029	0.651479
$483$	3.20210	0.145701
$484$	−10.7069	−0.486676
$485$	13.4302	0.609834
$486$	−1.00000	−0.0453609
$487$	23.3895	1.05988	0.529940	−	0.848035i	$-0.322214\pi$
$487$	23.3895	1.05988	0.529940	+	0.848035i	$0.322214\pi$
$488$	−2.95612	−0.133817
$489$	7.66576	0.346657
$490$	−0.937626	−0.0423576
$491$	−16.7236	−0.754724	−0.377362	−	0.926066i	$-0.623169\pi$
$491$	−16.7236	−0.754724	−0.377362	+	0.926066i	$0.623169\pi$
$492$	−8.48062	−0.382336
$493$	4.94355	0.222646
$494$	0	0
$495$	−0.507648	−0.0228171
$496$	−5.76396	−0.258810
$497$	−1.41453	−0.0634505
$498$	8.05509	0.360957
$499$	40.4148	1.80921	0.904607	−	0.426246i	$-0.140164\pi$
$499$	40.4148	1.80921	0.904607	+	0.426246i	$0.140164\pi$
$500$	−8.55195	−0.382455
$501$	7.84243	0.350374
$502$	−12.6220	−0.563349
$503$	−1.58424	−0.0706377	−0.0353189	−	0.999376i	$-0.511245\pi$
$503$	−1.58424	−0.0706377	−0.0353189	+	0.999376i	$0.511245\pi$
$504$	−1.00000	−0.0445435
$505$	−14.1647	−0.630322
$506$	1.73368	0.0770714
$507$	0	0
$508$	3.62328	0.160757
$509$	−9.94420	−0.440769	−0.220385	−	0.975413i	$-0.570731\pi$
$509$	−9.94420	−0.440769	−0.220385	+	0.975413i	$0.570731\pi$
$510$	6.45207	0.285702
$511$	−12.9431	−0.572570
$512$	−1.00000	−0.0441942
$513$	1.41866	0.0626353
$514$	−13.9756	−0.616439
$515$	−7.66521	−0.337769
$516$	8.44660	0.371841
$517$	5.59567	0.246097
$518$	0.659121	0.0289601
$519$	−20.1276	−0.883504
$520$	0	0
$521$	−13.5896	−0.595370	−0.297685	−	0.954664i	$-0.596215\pi$
$521$	−13.5896	−0.595370	−0.297685	+	0.954664i	$0.596215\pi$
$522$	0.718406	0.0314438
$523$	−8.74561	−0.382419	−0.191209	−	0.981549i	$-0.561241\pi$
$523$	−8.74561	−0.382419	−0.191209	+	0.981549i	$0.561241\pi$
$524$	−5.71172	−0.249518
$525$	−4.12086	−0.179849
$526$	20.7739	0.905783
$527$	39.6634	1.72777
$528$	−0.541419	−0.0235622
$529$	−12.7465	−0.554198
$530$	−7.50134	−0.325838
$531$	−3.66602	−0.159092
$532$	1.41866	0.0615066
$533$	0	0
$534$	5.39621	0.233517
$535$	10.2216	0.441918
$536$	10.4223	0.450176
$537$	7.02725	0.303248
$538$	−29.6258	−1.27726
$539$	−0.541419	−0.0233206
$540$	0.937626	0.0403490
$541$	6.42123	0.276070	0.138035	−	0.990427i	$-0.455921\pi$
$541$	6.42123	0.276070	0.138035	+	0.990427i	$0.455921\pi$
$542$	−0.553873	−0.0237909
$543$	−16.5514	−0.710287
$544$	6.88128	0.295032
$545$	1.97506	0.0846024
$546$	0	0
$547$	−26.6205	−1.13821	−0.569106	−	0.822264i	$-0.692711\pi$
$547$	−26.6205	−1.13821	−0.569106	+	0.822264i	$0.692711\pi$
$548$	0.144209	0.00616031
$549$	2.95612	0.126164
$550$	−2.23111	−0.0951348
$551$	−1.01917	−0.0434182
$552$	−3.20210	−0.136290
$553$	5.15704	0.219299
$554$	−25.6186	−1.08843
$555$	−0.618009	−0.0262330
$556$	4.69416	0.199077
$557$	−14.6705	−0.621608	−0.310804	−	0.950474i	$-0.600598\pi$
$557$	−14.6705	−0.621608	−0.310804	+	0.950474i	$0.600598\pi$
$558$	5.76396	0.244008
$559$	0	0
$560$	0.937626	0.0396219
$561$	3.72565	0.157297
$562$	14.1766	0.598006
$563$	−29.9720	−1.26317	−0.631585	−	0.775306i	$-0.717595\pi$
$563$	−29.9720	−1.26317	−0.631585	+	0.775306i	$0.717595\pi$
$564$	−10.3352	−0.435191
$565$	2.96585	0.124774
$566$	3.63484	0.152784
$567$	1.00000	0.0419961
$568$	1.41453	0.0593525
$569$	41.7741	1.75126	0.875630	−	0.482982i	$-0.160446\pi$
$569$	41.7741	1.75126	0.875630	+	0.482982i	$0.160446\pi$
$570$	−1.33017	−0.0557147
$571$	−18.0037	−0.753433	−0.376717	−	0.926329i	$-0.622947\pi$
$571$	−18.0037	−0.753433	−0.376717	+	0.926329i	$0.622947\pi$
$572$	0	0
$573$	−4.66925	−0.195061
$574$	8.48062	0.353974
$575$	−13.1954	−0.550286
$576$	1.00000	0.0416667
$577$	21.7555	0.905692	0.452846	−	0.891589i	$-0.350409\pi$
$577$	21.7555	0.905692	0.452846	+	0.891589i	$0.350409\pi$
$578$	−30.3520	−1.26248
$579$	8.87178	0.368698
$580$	−0.673596	−0.0279695
$581$	−8.05509	−0.334182
$582$	−14.3236	−0.593733
$583$	−4.33154	−0.179394
$584$	12.9431	0.535590
$585$	0	0
$586$	−16.5678	−0.684412
$587$	13.2127	0.545347	0.272674	−	0.962107i	$-0.412092\pi$
$587$	13.2127	0.545347	0.272674	+	0.962107i	$0.412092\pi$
$588$	1.00000	0.0412393
$589$	−8.17709	−0.336931
$590$	3.43736	0.141514
$591$	−11.8953	−0.489309
$592$	−0.659121	−0.0270897
$593$	13.3583	0.548560	0.274280	−	0.961650i	$-0.411561\pi$
$593$	13.3583	0.548560	0.274280	+	0.961650i	$0.411561\pi$
$594$	0.541419	0.0222147
$595$	−6.45207	−0.264509
$596$	−6.83811	−0.280100
$597$	−0.673030	−0.0275453
$598$	0	0
$599$	−43.9858	−1.79721	−0.898605	−	0.438758i	$-0.855418\pi$
$599$	−43.9858	−1.79721	−0.898605	+	0.438758i	$0.855418\pi$
$600$	4.12086	0.168233
$601$	25.0983	1.02378	0.511891	−	0.859051i	$-0.328945\pi$
$601$	25.0983	1.02378	0.511891	+	0.859051i	$0.328945\pi$
$602$	−8.44660	−0.344258
$603$	−10.4223	−0.424430
$604$	−0.339572	−0.0138170
$605$	−10.0390	−0.408145
$606$	15.1070	0.613681
$607$	17.6247	0.715365	0.357683	−	0.933843i	$-0.383567\pi$
$607$	17.6247	0.715365	0.357683	+	0.933843i	$0.383567\pi$
$608$	−1.41866	−0.0575342
$609$	−0.718406	−0.0291113
$610$	−2.77174	−0.112224
$611$	0	0
$612$	−6.88128	−0.278159
$613$	28.0137	1.13146	0.565731	−	0.824590i	$-0.308594\pi$
$613$	28.0137	1.13146	0.565731	+	0.824590i	$0.308594\pi$
$614$	2.58069	0.104148
$615$	−7.95166	−0.320642
$616$	0.541419	0.0218144
$617$	−5.47793	−0.220533	−0.110267	−	0.993902i	$-0.535170\pi$
$617$	−5.47793	−0.220533	−0.110267	+	0.993902i	$0.535170\pi$
$618$	8.17512	0.328852
$619$	−8.77611	−0.352742	−0.176371	−	0.984324i	$-0.556436\pi$
$619$	−8.77611	−0.352742	−0.176371	+	0.984324i	$0.556436\pi$
$620$	−5.40444	−0.217048
$621$	3.20210	0.128496
$622$	23.1639	0.928788
$623$	−5.39621	−0.216194
$624$	0	0
$625$	12.5857	0.503430
$626$	7.29077	0.291398
$627$	−0.768088	−0.0306745
$628$	−17.7934	−0.710033
$629$	4.53560	0.180846
$630$	−0.937626	−0.0373559
$631$	−28.0222	−1.11555	−0.557773	−	0.829994i	$-0.688344\pi$
$631$	−28.0222	−1.11555	−0.557773	+	0.829994i	$0.688344\pi$
$632$	−5.15704	−0.205136
$633$	27.8819	1.10820
$634$	13.2339	0.525584
$635$	3.39728	0.134817
$636$	8.00036	0.317235
$637$	0	0
$638$	−0.388958	−0.0153990
$639$	−1.41453	−0.0559581
$640$	−0.937626	−0.0370629
$641$	−36.1055	−1.42608	−0.713041	−	0.701122i	$-0.752683\pi$
$641$	−36.1055	−1.42608	−0.713041	+	0.701122i	$0.752683\pi$
$642$	−10.9016	−0.430251
$643$	3.03743	0.119785	0.0598923	−	0.998205i	$-0.480924\pi$
$643$	3.03743	0.119785	0.0598923	+	0.998205i	$0.480924\pi$
$644$	3.20210	0.126180
$645$	7.91976	0.311840
$646$	9.76218	0.384088
$647$	10.3712	0.407734	0.203867	−	0.978999i	$-0.434649\pi$
$647$	10.3712	0.407734	0.203867	+	0.978999i	$0.434649\pi$
$648$	−1.00000	−0.0392837
$649$	1.98485	0.0779123
$650$	0	0
$651$	−5.76396	−0.225907
$652$	7.66576	0.300214
$653$	6.16705	0.241335	0.120668	−	0.992693i	$-0.461496\pi$
$653$	6.16705	0.241335	0.120668	+	0.992693i	$0.461496\pi$
$654$	−2.10645	−0.0823688
$655$	−5.35546	−0.209255
$656$	−8.48062	−0.331113
$657$	−12.9431	−0.504959
$658$	10.3352	0.402908
$659$	−21.4553	−0.835779	−0.417889	−	0.908498i	$-0.637230\pi$
$659$	−21.4553	−0.835779	−0.417889	+	0.908498i	$0.637230\pi$
$660$	−0.507648	−0.0197602
$661$	38.6428	1.50303	0.751516	−	0.659715i	$-0.229323\pi$
$661$	38.6428	1.50303	0.751516	+	0.659715i	$0.229323\pi$
$662$	−31.1374	−1.21019
$663$	0	0
$664$	8.05509	0.312598
$665$	1.33017	0.0515818
$666$	0.659121	0.0255404
$667$	−2.30041	−0.0890721
$668$	7.84243	0.303433
$669$	−11.3474	−0.438718
$670$	9.77224	0.377535
$671$	−1.60050	−0.0617866
$672$	−1.00000	−0.0385758
$673$	−45.6933	−1.76135	−0.880673	−	0.473725i	$-0.842909\pi$
$673$	−45.6933	−1.76135	−0.880673	+	0.473725i	$0.842909\pi$
$674$	13.7131	0.528209
$675$	−4.12086	−0.158612
$676$	0	0
$677$	−29.9066	−1.14940	−0.574702	−	0.818362i	$-0.694882\pi$
$677$	−29.9066	−1.14940	−0.574702	+	0.818362i	$0.694882\pi$
$678$	−3.16314	−0.121480
$679$	14.3236	0.549690
$680$	6.45207	0.247425
$681$	17.1855	0.658548
$682$	−3.12072	−0.119498
$683$	−13.4537	−0.514792	−0.257396	−	0.966306i	$-0.582864\pi$
$683$	−13.4537	−0.514792	−0.257396	+	0.966306i	$0.582864\pi$
$684$	1.41866	0.0542437
$685$	0.135214	0.00516627
$686$	−1.00000	−0.0381802
$687$	17.8682	0.681716
$688$	8.44660	0.322024
$689$	0	0
$690$	−3.00237	−0.114298
$691$	5.42935	0.206542	0.103271	−	0.994653i	$-0.467069\pi$
$691$	5.42935	0.206542	0.103271	+	0.994653i	$0.467069\pi$
$692$	−20.1276	−0.765137
$693$	−0.541419	−0.0205668
$694$	−13.7242	−0.520965
$695$	4.40136	0.166953
$696$	0.718406	0.0272311
$697$	58.3575	2.21045
$698$	2.63410	0.0997023
$699$	−17.9082	−0.677350
$700$	−4.12086	−0.155754
$701$	43.3374	1.63683	0.818415	−	0.574628i	$-0.194853\pi$
$701$	43.3374	1.63683	0.818415	+	0.574628i	$0.194853\pi$
$702$	0	0
$703$	−0.935067	−0.0352667
$704$	−0.541419	−0.0204055
$705$	−9.69056	−0.364968
$706$	17.0768	0.642695
$707$	−15.1070	−0.568158
$708$	−3.66602	−0.137778
$709$	−24.5355	−0.921450	−0.460725	−	0.887543i	$-0.652411\pi$
$709$	−24.5355	−0.921450	−0.460725	+	0.887543i	$0.652411\pi$
$710$	1.32630	0.0497753
$711$	5.15704	0.193404
$712$	5.39621	0.202231
$713$	−18.4568	−0.691212
$714$	6.88128	0.257525
$715$	0	0
$716$	7.02725	0.262621
$717$	−13.5431	−0.505775
$718$	20.2417	0.755412
$719$	−2.85737	−0.106562	−0.0532810	−	0.998580i	$-0.516968\pi$
$719$	−2.85737	−0.106562	−0.0532810	+	0.998580i	$0.516968\pi$
$720$	0.937626	0.0349433
$721$	−8.17512	−0.304457
$722$	16.9874	0.632206
$723$	−14.3029	−0.531930
$724$	−16.5514	−0.615127
$725$	2.96045	0.109948
$726$	10.7069	0.397369
$727$	−39.5988	−1.46864	−0.734319	−	0.678804i	$-0.762499\pi$
$727$	−39.5988	−1.46864	−0.734319	+	0.678804i	$0.762499\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	12.1358	0.449167
$731$	−58.1234	−2.14977
$732$	2.95612	0.109261
$733$	49.5614	1.83059	0.915297	−	0.402780i	$-0.131956\pi$
$733$	49.5614	1.83059	0.915297	+	0.402780i	$0.131956\pi$
$734$	0.450463	0.0166269
$735$	0.937626	0.0345849
$736$	−3.20210	−0.118031
$737$	5.64284	0.207857
$738$	8.48062	0.312176
$739$	38.7928	1.42702	0.713508	−	0.700647i	$-0.247105\pi$
$739$	38.7928	1.42702	0.713508	+	0.700647i	$0.247105\pi$
$740$	−0.618009	−0.0227185
$741$	0	0
$742$	−8.00036	−0.293702
$743$	−49.3413	−1.81016	−0.905078	−	0.425245i	$-0.860188\pi$
$743$	−49.3413	−1.81016	−0.905078	+	0.425245i	$0.860188\pi$
$744$	5.76396	0.211317
$745$	−6.41159	−0.234903
$746$	−21.5364	−0.788502
$747$	−8.05509	−0.294720
$748$	3.72565	0.136223
$749$	10.9016	0.398335
$750$	8.55195	0.312273
$751$	53.0479	1.93574	0.967872	−	0.251443i	$-0.0809050\pi$
$751$	53.0479	1.93574	0.967872	+	0.251443i	$0.0809050\pi$
$752$	−10.3352	−0.376886
$753$	12.6220	0.459972
$754$	0	0
$755$	−0.318392	−0.0115875
$756$	1.00000	0.0363696
$757$	−22.5710	−0.820357	−0.410178	−	0.912005i	$-0.634534\pi$
$757$	−22.5710	−0.820357	−0.410178	+	0.912005i	$0.634534\pi$
$758$	22.0595	0.801238
$759$	−1.73368	−0.0629285
$760$	−1.33017	−0.0482504
$761$	−14.7805	−0.535792	−0.267896	−	0.963448i	$-0.586328\pi$
$761$	−14.7805	−0.535792	−0.267896	+	0.963448i	$0.586328\pi$
$762$	−3.62328	−0.131258
$763$	2.10645	0.0762586
$764$	−4.66925	−0.168928
$765$	−6.45207	−0.233275
$766$	20.8030	0.751641
$767$	0	0
$768$	1.00000	0.0360844
$769$	20.3485	0.733786	0.366893	−	0.930263i	$-0.380422\pi$
$769$	20.3485	0.733786	0.366893	+	0.930263i	$0.380422\pi$
$770$	0.507648	0.0182944
$771$	13.9756	0.503321
$772$	8.87178	0.319302
$773$	−12.0616	−0.433826	−0.216913	−	0.976191i	$-0.569599\pi$
$773$	−12.0616	−0.433826	−0.216913	+	0.976191i	$0.569599\pi$
$774$	−8.44660	−0.303607
$775$	23.7525	0.853214
$776$	−14.3236	−0.514188
$777$	−0.659121	−0.0236458
$778$	−14.6585	−0.525532
$779$	−12.0311	−0.431059
$780$	0	0
$781$	0.765855	0.0274044
$782$	22.0345	0.787954
$783$	−0.718406	−0.0256737
$784$	1.00000	0.0357143
$785$	−16.6835	−0.595461
$786$	5.71172	0.203730
$787$	−48.4013	−1.72532	−0.862661	−	0.505783i	$-0.831204\pi$
$787$	−48.4013	−1.72532	−0.862661	+	0.505783i	$0.831204\pi$
$788$	−11.8953	−0.423754
$789$	−20.7739	−0.739569
$790$	−4.83537	−0.172035
$791$	3.16314	0.112468
$792$	0.541419	0.0192385
$793$	0	0
$794$	17.1988	0.610361
$795$	7.50134	0.266045
$796$	−0.673030	−0.0238549
$797$	3.70387	0.131198	0.0655989	−	0.997846i	$-0.479104\pi$
$797$	3.70387	0.131198	0.0655989	+	0.997846i	$0.479104\pi$
$798$	−1.41866	−0.0502199
$799$	71.1194	2.51603
$800$	4.12086	0.145694
$801$	−5.39621	−0.190666
$802$	−26.8247	−0.947214
$803$	7.00765	0.247295
$804$	−10.4223	−0.367567
$805$	3.00237	0.105820
$806$	0	0
$807$	29.6258	1.04288
$808$	15.1070	0.531463
$809$	−39.2120	−1.37862	−0.689311	−	0.724466i	$-0.742087\pi$
$809$	−39.2120	−1.37862	−0.689311	+	0.724466i	$0.742087\pi$
$810$	−0.937626	−0.0329448
$811$	17.1296	0.601503	0.300751	−	0.953703i	$-0.402763\pi$
$811$	17.1296	0.601503	0.300751	+	0.953703i	$0.402763\pi$
$812$	−0.718406	−0.0252111
$813$	0.553873	0.0194252
$814$	−0.356860	−0.0125080
$815$	7.18761	0.251771
$816$	−6.88128	−0.240893
$817$	11.9828	0.419226
$818$	11.7817	0.411939
$819$	0	0
$820$	−7.95166	−0.277684
$821$	−21.4776	−0.749572	−0.374786	−	0.927111i	$-0.622284\pi$
$821$	−21.4776	−0.749572	−0.374786	+	0.927111i	$0.622284\pi$
$822$	−0.144209	−0.00502987
$823$	16.1927	0.564443	0.282222	−	0.959349i	$-0.408929\pi$
$823$	16.1927	0.564443	0.282222	+	0.959349i	$0.408929\pi$
$824$	8.17512	0.284794
$825$	2.23111	0.0776772
$826$	3.66602	0.127557
$827$	−51.8352	−1.80249	−0.901243	−	0.433315i	$-0.857344\pi$
$827$	−51.8352	−1.80249	−0.901243	+	0.433315i	$0.857344\pi$
$828$	3.20210	0.111281
$829$	27.3323	0.949289	0.474645	−	0.880178i	$-0.342577\pi$
$829$	27.3323	0.949289	0.474645	+	0.880178i	$0.342577\pi$
$830$	7.55267	0.262157
$831$	25.6186	0.888698
$832$	0	0
$833$	−6.88128	−0.238422
$834$	−4.69416	−0.162545
$835$	7.35327	0.254470
$836$	−0.768088	−0.0265649
$837$	−5.76396	−0.199232
$838$	−8.46291	−0.292346
$839$	41.7152	1.44017	0.720084	−	0.693887i	$-0.244103\pi$
$839$	41.7152	1.44017	0.720084	+	0.693887i	$0.244103\pi$
$840$	−0.937626	−0.0323512
$841$	−28.4839	−0.982203
$842$	−33.3600	−1.14966
$843$	−14.1766	−0.488270
$844$	27.8819	0.959733
$845$	0	0
$846$	10.3352	0.355332
$847$	−10.7069	−0.367892
$848$	8.00036	0.274733
$849$	−3.63484	−0.124747
$850$	−28.3568	−0.972629
$851$	−2.11057	−0.0723495
$852$	−1.41453	−0.0484611
$853$	−32.1856	−1.10201	−0.551007	−	0.834500i	$-0.685756\pi$
$853$	−32.1856	−1.10201	−0.551007	+	0.834500i	$0.685756\pi$
$854$	−2.95612	−0.101156
$855$	1.33017	0.0454909
$856$	−10.9016	−0.372608
$857$	38.8035	1.32550	0.662750	−	0.748840i	$-0.269389\pi$
$857$	38.8035	1.32550	0.662750	+	0.748840i	$0.269389\pi$
$858$	0	0
$859$	−17.1372	−0.584713	−0.292356	−	0.956309i	$-0.594439\pi$
$859$	−17.1372	−0.584713	−0.292356	+	0.956309i	$0.594439\pi$
$860$	7.91976	0.270061
$861$	−8.48062	−0.289019
$862$	32.8920	1.12031
$863$	−37.9902	−1.29320	−0.646601	−	0.762829i	$-0.723810\pi$
$863$	−37.9902	−1.29320	−0.646601	+	0.762829i	$0.723810\pi$
$864$	−1.00000	−0.0340207
$865$	−18.8722	−0.641673
$866$	6.17418	0.209807
$867$	30.3520	1.03081
$868$	−5.76396	−0.195642
$869$	−2.79212	−0.0947160
$870$	0.673596	0.0228370
$871$	0	0
$872$	−2.10645	−0.0713334
$873$	14.3236	0.484781
$874$	−4.54269	−0.153659
$875$	−8.55195	−0.289109
$876$	−12.9431	−0.437308
$877$	3.34276	0.112877	0.0564385	−	0.998406i	$-0.482026\pi$
$877$	3.34276	0.112877	0.0564385	+	0.998406i	$0.482026\pi$
$878$	−21.6122	−0.729377
$879$	16.5678	0.558820
$880$	−0.507648	−0.0171128
$881$	−26.0850	−0.878828	−0.439414	−	0.898285i	$-0.644814\pi$
$881$	−26.0850	−0.878828	−0.439414	+	0.898285i	$0.644814\pi$
$882$	−1.00000	−0.0336718
$883$	18.5730	0.625030	0.312515	−	0.949913i	$-0.398828\pi$
$883$	18.5730	0.625030	0.312515	+	0.949913i	$0.398828\pi$
$884$	0	0
$885$	−3.43736	−0.115546
$886$	−29.8911	−1.00421
$887$	−40.7982	−1.36987	−0.684935	−	0.728604i	$-0.740169\pi$
$887$	−40.7982	−1.36987	−0.684935	+	0.728604i	$0.740169\pi$
$888$	0.659121	0.0221187
$889$	3.62328	0.121521
$890$	5.05963	0.169599
$891$	−0.541419	−0.0181382
$892$	−11.3474	−0.379941
$893$	−14.6621	−0.490649
$894$	6.83811	0.228701
$895$	6.58893	0.220244
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	2.80596	0.0936361
$899$	4.14086	0.138105
$900$	−4.12086	−0.137362
$901$	−55.0527	−1.83407
$902$	−4.59157	−0.152882
$903$	8.44660	0.281085
$904$	−3.16314	−0.105205
$905$	−15.5190	−0.515869
$906$	0.339572	0.0112815
$907$	−1.43334	−0.0475933	−0.0237967	−	0.999717i	$-0.507575\pi$
$907$	−1.43334	−0.0475933	−0.0237967	+	0.999717i	$0.507575\pi$
$908$	17.1855	0.570319
$909$	−15.1070	−0.501068
$910$	0	0
$911$	1.01971	0.0337844	0.0168922	−	0.999857i	$-0.494623\pi$
$911$	1.01971	0.0337844	0.0168922	+	0.999857i	$0.494623\pi$
$912$	1.41866	0.0469765
$913$	4.36118	0.144334
$914$	23.8961	0.790411
$915$	2.77174	0.0916308
$916$	17.8682	0.590383
$917$	−5.71172	−0.188618
$918$	6.88128	0.227116
$919$	−37.1578	−1.22572	−0.612861	−	0.790191i	$-0.709981\pi$
$919$	−37.1578	−1.22572	−0.612861	+	0.790191i	$0.709981\pi$
$920$	−3.00237	−0.0989853
$921$	−2.58069	−0.0850368
$922$	−5.56698	−0.183339
$923$	0	0
$924$	−0.541419	−0.0178114
$925$	2.71614	0.0893063
$926$	8.34395	0.274199
$927$	−8.17512	−0.268506
$928$	0.718406	0.0235828
$929$	−19.1570	−0.628521	−0.314260	−	0.949337i	$-0.601757\pi$
$929$	−19.1570	−0.628521	−0.314260	+	0.949337i	$0.601757\pi$
$930$	5.40444	0.177219
$931$	1.41866	0.0464946
$932$	−17.9082	−0.586602
$933$	−23.1639	−0.758352
$934$	9.20803	0.301296
$935$	3.49327	0.114242
$936$	0	0
$937$	−39.1334	−1.27843	−0.639216	−	0.769028i	$-0.720741\pi$
$937$	−39.1334	−1.27843	−0.639216	+	0.769028i	$0.720741\pi$
$938$	10.4223	0.340301
$939$	−7.29077	−0.237925
$940$	−9.69056	−0.316071
$941$	−49.2303	−1.60486	−0.802431	−	0.596745i	$-0.796460\pi$
$941$	−49.2303	−1.60486	−0.802431	+	0.596745i	$0.796460\pi$
$942$	17.7934	0.579739
$943$	−27.1558	−0.884315
$944$	−3.66602	−0.119319
$945$	0.937626	0.0305010
$946$	4.57315	0.148686
$947$	−40.6703	−1.32161	−0.660803	−	0.750560i	$-0.729784\pi$
$947$	−40.6703	−1.32161	−0.660803	+	0.750560i	$0.729784\pi$
$948$	5.15704	0.167493
$949$	0	0
$950$	5.84609	0.189672
$951$	−13.2339	−0.429138
$952$	6.88128	0.223024
$953$	15.8142	0.512271	0.256136	−	0.966641i	$-0.417551\pi$
$953$	15.8142	0.512271	0.256136	+	0.966641i	$0.417551\pi$
$954$	−8.00036	−0.259021
$955$	−4.37801	−0.141669
$956$	−13.5431	−0.438014
$957$	0.388958	0.0125732
$958$	−18.6283	−0.601852
$959$	0.144209	0.00465676
$960$	0.937626	0.0302618
$961$	2.22325	0.0717177
$962$	0	0
$963$	10.9016	0.351298
$964$	−14.3029	−0.460665
$965$	8.31841	0.267779
$966$	−3.20210	−0.103026
$967$	−21.0464	−0.676807	−0.338403	−	0.941001i	$-0.609887\pi$
$967$	−21.0464	−0.676807	−0.338403	+	0.941001i	$0.609887\pi$
$968$	10.7069	0.344132
$969$	−9.76218	−0.313606
$970$	−13.4302	−0.431218
$971$	1.29502	0.0415591	0.0207796	−	0.999784i	$-0.493385\pi$
$971$	1.29502	0.0415591	0.0207796	+	0.999784i	$0.493385\pi$
$972$	1.00000	0.0320750
$973$	4.69416	0.150488
$974$	−23.3895	−0.749448
$975$	0	0
$976$	2.95612	0.0946231
$977$	18.3458	0.586935	0.293468	−	0.955969i	$-0.405191\pi$
$977$	18.3458	0.586935	0.293468	+	0.955969i	$0.405191\pi$
$978$	−7.66576	−0.245124
$979$	2.92161	0.0933750
$980$	0.937626	0.0299514
$981$	2.10645	0.0672538
$982$	16.7236	0.533671
$983$	50.0030	1.59485	0.797423	−	0.603420i	$-0.206196\pi$
$983$	50.0030	1.59485	0.797423	+	0.603420i	$0.206196\pi$
$984$	8.48062	0.270352
$985$	−11.1534	−0.355376
$986$	−4.94355	−0.157435
$987$	−10.3352	−0.328973
$988$	0	0
$989$	27.0469	0.860041
$990$	0.507648	0.0161341
$991$	−57.7399	−1.83417	−0.917084	−	0.398695i	$-0.869463\pi$
$991$	−57.7399	−1.83417	−0.917084	+	0.398695i	$0.869463\pi$
$992$	5.76396	0.183006
$993$	31.1374	0.988116
$994$	1.41453	0.0448663
$995$	−0.631051	−0.0200056
$996$	−8.05509	−0.255235
$997$	−35.8285	−1.13470	−0.567350	−	0.823477i	$-0.692031\pi$
$997$	−35.8285	−1.13470	−0.567350	+	0.823477i	$0.692031\pi$
$998$	−40.4148	−1.27931
$999$	−0.659121	−0.0208537

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.cq.1.6	✓	6
13.12	even	2		7098.2.a.cu.1.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7098.2.a.cq.1.6	✓	6	1.1	even	1	trivial
7098.2.a.cu.1.1	yes	6	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.937626 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.937626 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.937626 q^{10} -0.541419 q^{11} +1.00000 q^{12} -1.00000 q^{14} +0.937626 q^{15} +1.00000 q^{16} -6.88128 q^{17} -1.00000 q^{18} +1.41866 q^{19} +0.937626 q^{20} +1.00000 q^{21} +0.541419 q^{22} +3.20210 q^{23} -1.00000 q^{24} -4.12086 q^{25} +1.00000 q^{27} +1.00000 q^{28} -0.718406 q^{29} -0.937626 q^{30} -5.76396 q^{31} -1.00000 q^{32} -0.541419 q^{33} +6.88128 q^{34} +0.937626 q^{35} +1.00000 q^{36} -0.659121 q^{37} -1.41866 q^{38} -0.937626 q^{40} -8.48062 q^{41} -1.00000 q^{42} +8.44660 q^{43} -0.541419 q^{44} +0.937626 q^{45} -3.20210 q^{46} -10.3352 q^{47} +1.00000 q^{48} +1.00000 q^{49} +4.12086 q^{50} -6.88128 q^{51} +8.00036 q^{53} -1.00000 q^{54} -0.507648 q^{55} -1.00000 q^{56} +1.41866 q^{57} +0.718406 q^{58} -3.66602 q^{59} +0.937626 q^{60} +2.95612 q^{61} +5.76396 q^{62} +1.00000 q^{63} +1.00000 q^{64} +0.541419 q^{66} -10.4223 q^{67} -6.88128 q^{68} +3.20210 q^{69} -0.937626 q^{70} -1.41453 q^{71} -1.00000 q^{72} -12.9431 q^{73} +0.659121 q^{74} -4.12086 q^{75} +1.41866 q^{76} -0.541419 q^{77} +5.15704 q^{79} +0.937626 q^{80} +1.00000 q^{81} +8.48062 q^{82} -8.05509 q^{83} +1.00000 q^{84} -6.45207 q^{85} -8.44660 q^{86} -0.718406 q^{87} +0.541419 q^{88} -5.39621 q^{89} -0.937626 q^{90} +3.20210 q^{92} -5.76396 q^{93} +10.3352 q^{94} +1.33017 q^{95} -1.00000 q^{96} +14.3236 q^{97} -1.00000 q^{98} -0.541419 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} - 9 q^{5} - 6 q^{6} + 6 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 - 9 * q^5 - 6 * q^6 + 6 * q^7 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} - 9 q^{5} - 6 q^{6} + 6 q^{7} - 6 q^{8} + 6 q^{9} + 9 q^{10} - 10 q^{11} + 6 q^{12} - 6 q^{14} - 9 q^{15} + 6 q^{16} + 4 q^{17} - 6 q^{18} - 2 q^{19} - 9 q^{20} + 6 q^{21} + 10 q^{22} - 6 q^{24} + 9 q^{25} + 6 q^{27} + 6 q^{28} - 4 q^{29} + 9 q^{30} - 9 q^{31} - 6 q^{32} - 10 q^{33} - 4 q^{34} - 9 q^{35} + 6 q^{36} - 9 q^{37} + 2 q^{38} + 9 q^{40} - 25 q^{41} - 6 q^{42} + 19 q^{43} - 10 q^{44} - 9 q^{45} - 21 q^{47} + 6 q^{48} + 6 q^{49} - 9 q^{50} + 4 q^{51} - 4 q^{53} - 6 q^{54} + 21 q^{55} - 6 q^{56} - 2 q^{57} + 4 q^{58} - 20 q^{59} - 9 q^{60} + 3 q^{61} + 9 q^{62} + 6 q^{63} + 6 q^{64} + 10 q^{66} - 24 q^{67} + 4 q^{68} + 9 q^{70} - 13 q^{71} - 6 q^{72} + 9 q^{73} + 9 q^{74} + 9 q^{75} - 2 q^{76} - 10 q^{77} + 28 q^{79} - 9 q^{80} + 6 q^{81} + 25 q^{82} - 15 q^{83} + 6 q^{84} - 17 q^{85} - 19 q^{86} - 4 q^{87} + 10 q^{88} - 11 q^{89} + 9 q^{90} - 9 q^{93} + 21 q^{94} - 6 q^{96} - 2 q^{97} - 6 q^{98} - 10 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 - 9 * q^5 - 6 * q^6 + 6 * q^7 - 6 * q^8 + 6 * q^9 + 9 * q^10 - 10 * q^11 + 6 * q^12 - 6 * q^14 - 9 * q^15 + 6 * q^16 + 4 * q^17 - 6 * q^18 - 2 * q^19 - 9 * q^20 + 6 * q^21 + 10 * q^22 - 6 * q^24 + 9 * q^25 + 6 * q^27 + 6 * q^28 - 4 * q^29 + 9 * q^30 - 9 * q^31 - 6 * q^32 - 10 * q^33 - 4 * q^34 - 9 * q^35 + 6 * q^36 - 9 * q^37 + 2 * q^38 + 9 * q^40 - 25 * q^41 - 6 * q^42 + 19 * q^43 - 10 * q^44 - 9 * q^45 - 21 * q^47 + 6 * q^48 + 6 * q^49 - 9 * q^50 + 4 * q^51 - 4 * q^53 - 6 * q^54 + 21 * q^55 - 6 * q^56 - 2 * q^57 + 4 * q^58 - 20 * q^59 - 9 * q^60 + 3 * q^61 + 9 * q^62 + 6 * q^63 + 6 * q^64 + 10 * q^66 - 24 * q^67 + 4 * q^68 + 9 * q^70 - 13 * q^71 - 6 * q^72 + 9 * q^73 + 9 * q^74 + 9 * q^75 - 2 * q^76 - 10 * q^77 + 28 * q^79 - 9 * q^80 + 6 * q^81 + 25 * q^82 - 15 * q^83 + 6 * q^84 - 17 * q^85 - 19 * q^86 - 4 * q^87 + 10 * q^88 - 11 * q^89 + 9 * q^90 - 9 * q^93 + 21 * q^94 - 6 * q^96 - 2 * q^97 - 6 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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