LMFDB - Embedded newform 7098.2.a.bi.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:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.56155$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.56155 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.56155 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.56155 q^{10} -1.56155 q^{11} -1.00000 q^{12} +1.00000 q^{14} -2.56155 q^{15} +1.00000 q^{16} -8.12311 q^{17} -1.00000 q^{18} -1.56155 q^{19} +2.56155 q^{20} +1.00000 q^{21} +1.56155 q^{22} +7.12311 q^{23} +1.00000 q^{24} +1.56155 q^{25} -1.00000 q^{27} -1.00000 q^{28} +2.12311 q^{29} +2.56155 q^{30} -1.00000 q^{32} +1.56155 q^{33} +8.12311 q^{34} -2.56155 q^{35} +1.00000 q^{36} +6.56155 q^{37} +1.56155 q^{38} -2.56155 q^{40} -5.24621 q^{41} -1.00000 q^{42} -8.00000 q^{43} -1.56155 q^{44} +2.56155 q^{45} -7.12311 q^{46} +12.6847 q^{47} -1.00000 q^{48} +1.00000 q^{49} -1.56155 q^{50} +8.12311 q^{51} +7.00000 q^{53} +1.00000 q^{54} -4.00000 q^{55} +1.00000 q^{56} +1.56155 q^{57} -2.12311 q^{58} +3.12311 q^{59} -2.56155 q^{60} +5.24621 q^{61} -1.00000 q^{63} +1.00000 q^{64} -1.56155 q^{66} -0.876894 q^{67} -8.12311 q^{68} -7.12311 q^{69} +2.56155 q^{70} -13.3693 q^{71} -1.00000 q^{72} +6.56155 q^{73} -6.56155 q^{74} -1.56155 q^{75} -1.56155 q^{76} +1.56155 q^{77} -2.43845 q^{79} +2.56155 q^{80} +1.00000 q^{81} +5.24621 q^{82} -3.12311 q^{83} +1.00000 q^{84} -20.8078 q^{85} +8.00000 q^{86} -2.12311 q^{87} +1.56155 q^{88} -7.56155 q^{89} -2.56155 q^{90} +7.12311 q^{92} -12.6847 q^{94} -4.00000 q^{95} +1.00000 q^{96} +9.12311 q^{97} -1.00000 q^{98} -1.56155 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} - q^{10} + q^{11} - 2 q^{12} + 2 q^{14} - q^{15} + 2 q^{16} - 8 q^{17} - 2 q^{18} + q^{19} + q^{20} + 2 q^{21} - q^{22} + 6 q^{23} + 2 q^{24} - q^{25} - 2 q^{27} - 2 q^{28} - 4 q^{29} + q^{30} - 2 q^{32} - q^{33} + 8 q^{34} - q^{35} + 2 q^{36} + 9 q^{37} - q^{38} - q^{40} + 6 q^{41} - 2 q^{42} - 16 q^{43} + q^{44} + q^{45} - 6 q^{46} + 13 q^{47} - 2 q^{48} + 2 q^{49} + q^{50} + 8 q^{51} + 14 q^{53} + 2 q^{54} - 8 q^{55} + 2 q^{56} - q^{57} + 4 q^{58} - 2 q^{59} - q^{60} - 6 q^{61} - 2 q^{63} + 2 q^{64} + q^{66} - 10 q^{67} - 8 q^{68} - 6 q^{69} + q^{70} - 2 q^{71} - 2 q^{72} + 9 q^{73} - 9 q^{74} + q^{75} + q^{76} - q^{77} - 9 q^{79} + q^{80} + 2 q^{81} - 6 q^{82} + 2 q^{83} + 2 q^{84} - 21 q^{85} + 16 q^{86} + 4 q^{87} - q^{88} - 11 q^{89} - q^{90} + 6 q^{92} - 13 q^{94} - 8 q^{95} + 2 q^{96} + 10 q^{97} - 2 q^{98} + q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9 - q^10 + q^11 - 2 * q^12 + 2 * q^14 - q^15 + 2 * q^16 - 8 * q^17 - 2 * q^18 + q^19 + q^20 + 2 * q^21 - q^22 + 6 * q^23 + 2 * q^24 - q^25 - 2 * q^27 - 2 * q^28 - 4 * q^29 + q^30 - 2 * q^32 - q^33 + 8 * q^34 - q^35 + 2 * q^36 + 9 * q^37 - q^38 - q^40 + 6 * q^41 - 2 * q^42 - 16 * q^43 + q^44 + q^45 - 6 * q^46 + 13 * q^47 - 2 * q^48 + 2 * q^49 + q^50 + 8 * q^51 + 14 * q^53 + 2 * q^54 - 8 * q^55 + 2 * q^56 - q^57 + 4 * q^58 - 2 * q^59 - q^60 - 6 * q^61 - 2 * q^63 + 2 * q^64 + q^66 - 10 * q^67 - 8 * q^68 - 6 * q^69 + q^70 - 2 * q^71 - 2 * q^72 + 9 * q^73 - 9 * q^74 + q^75 + q^76 - q^77 - 9 * q^79 + q^80 + 2 * q^81 - 6 * q^82 + 2 * q^83 + 2 * q^84 - 21 * q^85 + 16 * q^86 + 4 * q^87 - q^88 - 11 * q^89 - q^90 + 6 * q^92 - 13 * q^94 - 8 * q^95 + 2 * q^96 + 10 * q^97 - 2 * q^98 + 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
$5$	2.56155	1.14556	0.572781	−	0.819709i	$-0.305865\pi$
$5$	2.56155	1.14556	0.572781	+	0.819709i	$0.305865\pi$
$6$	1.00000	0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−2.56155	−0.810034
$11$	−1.56155	−0.470826	−0.235413	−	0.971895i	$-0.575644\pi$
$11$	−1.56155	−0.470826	−0.235413	+	0.971895i	$0.575644\pi$
$12$	−1.00000	−0.288675
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	−2.56155	−0.661390
$16$	1.00000	0.250000
$17$	−8.12311	−1.97014	−0.985071	−	0.172147i	$-0.944930\pi$
$17$	−8.12311	−1.97014	−0.985071	+	0.172147i	$0.944930\pi$
$18$	−1.00000	−0.235702
$19$	−1.56155	−0.358245	−0.179122	−	0.983827i	$-0.557326\pi$
$19$	−1.56155	−0.358245	−0.179122	+	0.983827i	$0.557326\pi$
$20$	2.56155	0.572781
$21$	1.00000	0.218218
$22$	1.56155	0.332924
$23$	7.12311	1.48527	0.742635	−	0.669696i	$-0.233576\pi$
$23$	7.12311	1.48527	0.742635	+	0.669696i	$0.233576\pi$
$24$	1.00000	0.204124
$25$	1.56155	0.312311
$26$	0	0
$27$	−1.00000	−0.192450
$28$	−1.00000	−0.188982
$29$	2.12311	0.394251	0.197125	−	0.980378i	$-0.436839\pi$
$29$	2.12311	0.394251	0.197125	+	0.980378i	$0.436839\pi$
$30$	2.56155	0.467673
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	−1.00000	−0.176777
$33$	1.56155	0.271831
$34$	8.12311	1.39310
$35$	−2.56155	−0.432981
$36$	1.00000	0.166667
$37$	6.56155	1.07871	0.539356	−	0.842078i	$-0.318668\pi$
$37$	6.56155	1.07871	0.539356	+	0.842078i	$0.318668\pi$
$38$	1.56155	0.253317
$39$	0	0
$40$	−2.56155	−0.405017
$41$	−5.24621	−0.819321	−0.409660	−	0.912238i	$-0.634353\pi$
$41$	−5.24621	−0.819321	−0.409660	+	0.912238i	$0.634353\pi$
$42$	−1.00000	−0.154303
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	−1.56155	−0.235413
$45$	2.56155	0.381854
$46$	−7.12311	−1.05024
$47$	12.6847	1.85025	0.925124	−	0.379666i	$-0.123961\pi$
$47$	12.6847	1.85025	0.925124	+	0.379666i	$0.123961\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−1.56155	−0.220837
$51$	8.12311	1.13746
$52$	0	0
$53$	7.00000	0.961524	0.480762	−	0.876851i	$-0.340360\pi$
$53$	7.00000	0.961524	0.480762	+	0.876851i	$0.340360\pi$
$54$	1.00000	0.136083
$55$	−4.00000	−0.539360
$56$	1.00000	0.133631
$57$	1.56155	0.206833
$58$	−2.12311	−0.278777
$59$	3.12311	0.406594	0.203297	−	0.979117i	$-0.434834\pi$
$59$	3.12311	0.406594	0.203297	+	0.979117i	$0.434834\pi$
$60$	−2.56155	−0.330695
$61$	5.24621	0.671709	0.335854	−	0.941914i	$-0.390975\pi$
$61$	5.24621	0.671709	0.335854	+	0.941914i	$0.390975\pi$
$62$	0	0
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	−1.56155	−0.192214
$67$	−0.876894	−0.107130	−0.0535648	−	0.998564i	$-0.517058\pi$
$67$	−0.876894	−0.107130	−0.0535648	+	0.998564i	$0.517058\pi$
$68$	−8.12311	−0.985071
$69$	−7.12311	−0.857521
$70$	2.56155	0.306164
$71$	−13.3693	−1.58665	−0.793323	−	0.608801i	$-0.791651\pi$
$71$	−13.3693	−1.58665	−0.793323	+	0.608801i	$0.791651\pi$
$72$	−1.00000	−0.117851
$73$	6.56155	0.767972	0.383986	−	0.923339i	$-0.374551\pi$
$73$	6.56155	0.767972	0.383986	+	0.923339i	$0.374551\pi$
$74$	−6.56155	−0.762765
$75$	−1.56155	−0.180313
$76$	−1.56155	−0.179122
$77$	1.56155	0.177955
$78$	0	0
$79$	−2.43845	−0.274347	−0.137173	−	0.990547i	$-0.543802\pi$
$79$	−2.43845	−0.274347	−0.137173	+	0.990547i	$0.543802\pi$
$80$	2.56155	0.286390
$81$	1.00000	0.111111
$82$	5.24621	0.579347
$83$	−3.12311	−0.342805	−0.171403	−	0.985201i	$-0.554830\pi$
$83$	−3.12311	−0.342805	−0.171403	+	0.985201i	$0.554830\pi$
$84$	1.00000	0.109109
$85$	−20.8078	−2.25692
$86$	8.00000	0.862662
$87$	−2.12311	−0.227621
$88$	1.56155	0.166462
$89$	−7.56155	−0.801523	−0.400761	−	0.916182i	$-0.631254\pi$
$89$	−7.56155	−0.801523	−0.400761	+	0.916182i	$0.631254\pi$
$90$	−2.56155	−0.270011
$91$	0	0
$92$	7.12311	0.742635
$93$	0	0
$94$	−12.6847	−1.30832
$95$	−4.00000	−0.410391
$96$	1.00000	0.102062
$97$	9.12311	0.926311	0.463156	−	0.886277i	$-0.346717\pi$
$97$	9.12311	0.926311	0.463156	+	0.886277i	$0.346717\pi$
$98$	−1.00000	−0.101015
$99$	−1.56155	−0.156942
$100$	1.56155	0.156155
$101$	14.8078	1.47343	0.736714	−	0.676205i	$-0.236377\pi$
$101$	14.8078	1.47343	0.736714	+	0.676205i	$0.236377\pi$
$102$	−8.12311	−0.804307
$103$	−10.2462	−1.00959	−0.504795	−	0.863239i	$-0.668432\pi$
$103$	−10.2462	−1.00959	−0.504795	+	0.863239i	$0.668432\pi$
$104$	0	0
$105$	2.56155	0.249982
$106$	−7.00000	−0.679900
$107$	−14.9309	−1.44342	−0.721711	−	0.692195i	$-0.756644\pi$
$107$	−14.9309	−1.44342	−0.721711	+	0.692195i	$0.756644\pi$
$108$	−1.00000	−0.0962250
$109$	−4.24621	−0.406713	−0.203357	−	0.979105i	$-0.565185\pi$
$109$	−4.24621	−0.406713	−0.203357	+	0.979105i	$0.565185\pi$
$110$	4.00000	0.381385
$111$	−6.56155	−0.622795
$112$	−1.00000	−0.0944911
$113$	−2.56155	−0.240971	−0.120485	−	0.992715i	$-0.538445\pi$
$113$	−2.56155	−0.240971	−0.120485	+	0.992715i	$0.538445\pi$
$114$	−1.56155	−0.146253
$115$	18.2462	1.70147
$116$	2.12311	0.197125
$117$	0	0
$118$	−3.12311	−0.287505
$119$	8.12311	0.744644
$120$	2.56155	0.233837
$121$	−8.56155	−0.778323
$122$	−5.24621	−0.474970
$123$	5.24621	0.473035
$124$	0	0
$125$	−8.80776	−0.787790
$126$	1.00000	0.0890871
$127$	−20.4924	−1.81841	−0.909204	−	0.416350i	$-0.863309\pi$
$127$	−20.4924	−1.81841	−0.909204	+	0.416350i	$0.863309\pi$
$128$	−1.00000	−0.0883883
$129$	8.00000	0.704361
$130$	0	0
$131$	−2.24621	−0.196252	−0.0981262	−	0.995174i	$-0.531285\pi$
$131$	−2.24621	−0.196252	−0.0981262	+	0.995174i	$0.531285\pi$
$132$	1.56155	0.135916
$133$	1.56155	0.135404
$134$	0.876894	0.0757521
$135$	−2.56155	−0.220463
$136$	8.12311	0.696551
$137$	−16.5616	−1.41495	−0.707474	−	0.706739i	$-0.750166\pi$
$137$	−16.5616	−1.41495	−0.707474	+	0.706739i	$0.750166\pi$
$138$	7.12311	0.606359
$139$	−9.56155	−0.811000	−0.405500	−	0.914095i	$-0.632903\pi$
$139$	−9.56155	−0.811000	−0.405500	+	0.914095i	$0.632903\pi$
$140$	−2.56155	−0.216491
$141$	−12.6847	−1.06824
$142$	13.3693	1.12193
$143$	0	0
$144$	1.00000	0.0833333
$145$	5.43845	0.451638
$146$	−6.56155	−0.543038
$147$	−1.00000	−0.0824786
$148$	6.56155	0.539356
$149$	11.4384	0.937074	0.468537	−	0.883444i	$-0.344781\pi$
$149$	11.4384	0.937074	0.468537	+	0.883444i	$0.344781\pi$
$150$	1.56155	0.127500
$151$	−6.93087	−0.564026	−0.282013	−	0.959411i	$-0.591002\pi$
$151$	−6.93087	−0.564026	−0.282013	+	0.959411i	$0.591002\pi$
$152$	1.56155	0.126659
$153$	−8.12311	−0.656714
$154$	−1.56155	−0.125834
$155$	0	0
$156$	0	0
$157$	−13.6847	−1.09215	−0.546077	−	0.837735i	$-0.683880\pi$
$157$	−13.6847	−1.09215	−0.546077	+	0.837735i	$0.683880\pi$
$158$	2.43845	0.193992
$159$	−7.00000	−0.555136
$160$	−2.56155	−0.202509
$161$	−7.12311	−0.561379
$162$	−1.00000	−0.0785674
$163$	8.49242	0.665178	0.332589	−	0.943072i	$-0.392078\pi$
$163$	8.49242	0.665178	0.332589	+	0.943072i	$0.392078\pi$
$164$	−5.24621	−0.409660
$165$	4.00000	0.311400
$166$	3.12311	0.242400
$167$	20.4924	1.58575	0.792876	−	0.609383i	$-0.208583\pi$
$167$	20.4924	1.58575	0.792876	+	0.609383i	$0.208583\pi$
$168$	−1.00000	−0.0771517
$169$	0	0
$170$	20.8078	1.59588
$171$	−1.56155	−0.119415
$172$	−8.00000	−0.609994
$173$	−18.0000	−1.36851	−0.684257	−	0.729241i	$-0.739873\pi$
$173$	−18.0000	−1.36851	−0.684257	+	0.729241i	$0.739873\pi$
$174$	2.12311	0.160952
$175$	−1.56155	−0.118042
$176$	−1.56155	−0.117706
$177$	−3.12311	−0.234747
$178$	7.56155	0.566762
$179$	−18.2462	−1.36379	−0.681893	−	0.731452i	$-0.738843\pi$
$179$	−18.2462	−1.36379	−0.681893	+	0.731452i	$0.738843\pi$
$180$	2.56155	0.190927
$181$	−3.24621	−0.241289	−0.120644	−	0.992696i	$-0.538496\pi$
$181$	−3.24621	−0.241289	−0.120644	+	0.992696i	$0.538496\pi$
$182$	0	0
$183$	−5.24621	−0.387811
$184$	−7.12311	−0.525122
$185$	16.8078	1.23573
$186$	0	0
$187$	12.6847	0.927594
$188$	12.6847	0.925124
$189$	1.00000	0.0727393
$190$	4.00000	0.290191
$191$	3.12311	0.225980	0.112990	−	0.993596i	$-0.463957\pi$
$191$	3.12311	0.225980	0.112990	+	0.993596i	$0.463957\pi$
$192$	−1.00000	−0.0721688
$193$	8.12311	0.584714	0.292357	−	0.956309i	$-0.405560\pi$
$193$	8.12311	0.584714	0.292357	+	0.956309i	$0.405560\pi$
$194$	−9.12311	−0.655001
$195$	0	0
$196$	1.00000	0.0714286
$197$	−8.43845	−0.601214	−0.300607	−	0.953748i	$-0.597189\pi$
$197$	−8.43845	−0.601214	−0.300607	+	0.953748i	$0.597189\pi$
$198$	1.56155	0.110975
$199$	−16.0000	−1.13421	−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000	−1.13421	−0.567105	+	0.823646i	$0.691937\pi$
$200$	−1.56155	−0.110418
$201$	0.876894	0.0618514
$202$	−14.8078	−1.04187
$203$	−2.12311	−0.149013
$204$	8.12311	0.568731
$205$	−13.4384	−0.938582
$206$	10.2462	0.713887
$207$	7.12311	0.495090
$208$	0	0
$209$	2.43845	0.168671
$210$	−2.56155	−0.176764
$211$	−3.12311	−0.215003	−0.107502	−	0.994205i	$-0.534285\pi$
$211$	−3.12311	−0.215003	−0.107502	+	0.994205i	$0.534285\pi$
$212$	7.00000	0.480762
$213$	13.3693	0.916050
$214$	14.9309	1.02065
$215$	−20.4924	−1.39757
$216$	1.00000	0.0680414
$217$	0	0
$218$	4.24621	0.287590
$219$	−6.56155	−0.443389
$220$	−4.00000	−0.269680
$221$	0	0
$222$	6.56155	0.440383
$223$	−26.2462	−1.75758	−0.878788	−	0.477212i	$-0.841647\pi$
$223$	−26.2462	−1.75758	−0.878788	+	0.477212i	$0.841647\pi$
$224$	1.00000	0.0668153
$225$	1.56155	0.104104
$226$	2.56155	0.170392
$227$	19.1231	1.26925	0.634623	−	0.772822i	$-0.281156\pi$
$227$	19.1231	1.26925	0.634623	+	0.772822i	$0.281156\pi$
$228$	1.56155	0.103416
$229$	20.0540	1.32520	0.662602	−	0.748972i	$-0.269452\pi$
$229$	20.0540	1.32520	0.662602	+	0.748972i	$0.269452\pi$
$230$	−18.2462	−1.20312
$231$	−1.56155	−0.102743
$232$	−2.12311	−0.139389
$233$	−23.3693	−1.53097	−0.765487	−	0.643451i	$-0.777502\pi$
$233$	−23.3693	−1.53097	−0.765487	+	0.643451i	$0.777502\pi$
$234$	0	0
$235$	32.4924	2.11957
$236$	3.12311	0.203297
$237$	2.43845	0.158394
$238$	−8.12311	−0.526543
$239$	5.36932	0.347312	0.173656	−	0.984806i	$-0.444442\pi$
$239$	5.36932	0.347312	0.173656	+	0.984806i	$0.444442\pi$
$240$	−2.56155	−0.165348
$241$	20.8078	1.34035	0.670173	−	0.742205i	$-0.266220\pi$
$241$	20.8078	1.34035	0.670173	+	0.742205i	$0.266220\pi$
$242$	8.56155	0.550357
$243$	−1.00000	−0.0641500
$244$	5.24621	0.335854
$245$	2.56155	0.163652
$246$	−5.24621	−0.334486
$247$	0	0
$248$	0	0
$249$	3.12311	0.197919
$250$	8.80776	0.557052
$251$	27.6155	1.74308	0.871538	−	0.490327i	$-0.163123\pi$
$251$	27.6155	1.74308	0.871538	+	0.490327i	$0.163123\pi$
$252$	−1.00000	−0.0629941
$253$	−11.1231	−0.699304
$254$	20.4924	1.28581
$255$	20.8078	1.30303
$256$	1.00000	0.0625000
$257$	0.369317	0.0230374	0.0115187	−	0.999934i	$-0.496333\pi$
$257$	0.369317	0.0230374	0.0115187	+	0.999934i	$0.496333\pi$
$258$	−8.00000	−0.498058
$259$	−6.56155	−0.407715
$260$	0	0
$261$	2.12311	0.131417
$262$	2.24621	0.138771
$263$	−3.12311	−0.192579	−0.0962895	−	0.995353i	$-0.530697\pi$
$263$	−3.12311	−0.192579	−0.0962895	+	0.995353i	$0.530697\pi$
$264$	−1.56155	−0.0961069
$265$	17.9309	1.10148
$266$	−1.56155	−0.0957449
$267$	7.56155	0.462760
$268$	−0.876894	−0.0535648
$269$	18.8769	1.15094	0.575472	−	0.817821i	$-0.304818\pi$
$269$	18.8769	1.15094	0.575472	+	0.817821i	$0.304818\pi$
$270$	2.56155	0.155891
$271$	−26.7386	−1.62426	−0.812128	−	0.583479i	$-0.801691\pi$
$271$	−26.7386	−1.62426	−0.812128	+	0.583479i	$0.801691\pi$
$272$	−8.12311	−0.492536
$273$	0	0
$274$	16.5616	1.00052
$275$	−2.43845	−0.147044
$276$	−7.12311	−0.428761
$277$	−15.4384	−0.927606	−0.463803	−	0.885938i	$-0.653516\pi$
$277$	−15.4384	−0.927606	−0.463803	+	0.885938i	$0.653516\pi$
$278$	9.56155	0.573464
$279$	0	0
$280$	2.56155	0.153082
$281$	15.9309	0.950356	0.475178	−	0.879890i	$-0.342384\pi$
$281$	15.9309	0.950356	0.475178	+	0.879890i	$0.342384\pi$
$282$	12.6847	0.755360
$283$	−20.0000	−1.18888	−0.594438	−	0.804141i	$-0.702626\pi$
$283$	−20.0000	−1.18888	−0.594438	+	0.804141i	$0.702626\pi$
$284$	−13.3693	−0.793323
$285$	4.00000	0.236940
$286$	0	0
$287$	5.24621	0.309674
$288$	−1.00000	−0.0589256
$289$	48.9848	2.88146
$290$	−5.43845	−0.319357
$291$	−9.12311	−0.534806
$292$	6.56155	0.383986
$293$	−21.9309	−1.28122	−0.640608	−	0.767868i	$-0.721317\pi$
$293$	−21.9309	−1.28122	−0.640608	+	0.767868i	$0.721317\pi$
$294$	1.00000	0.0583212
$295$	8.00000	0.465778
$296$	−6.56155	−0.381383
$297$	1.56155	0.0906105
$298$	−11.4384	−0.662611
$299$	0	0
$300$	−1.56155	−0.0901563
$301$	8.00000	0.461112
$302$	6.93087	0.398827
$303$	−14.8078	−0.850684
$304$	−1.56155	−0.0895612
$305$	13.4384	0.769483
$306$	8.12311	0.464367
$307$	−18.9309	−1.08044	−0.540221	−	0.841523i	$-0.681659\pi$
$307$	−18.9309	−1.08044	−0.540221	+	0.841523i	$0.681659\pi$
$308$	1.56155	0.0889777
$309$	10.2462	0.582887
$310$	0	0
$311$	−6.93087	−0.393014	−0.196507	−	0.980502i	$-0.562960\pi$
$311$	−6.93087	−0.393014	−0.196507	+	0.980502i	$0.562960\pi$
$312$	0	0
$313$	−6.00000	−0.339140	−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000	−0.339140	−0.169570	+	0.985518i	$0.554238\pi$
$314$	13.6847	0.772270
$315$	−2.56155	−0.144327
$316$	−2.43845	−0.137173
$317$	−16.5616	−0.930189	−0.465095	−	0.885261i	$-0.653980\pi$
$317$	−16.5616	−0.930189	−0.465095	+	0.885261i	$0.653980\pi$
$318$	7.00000	0.392541
$319$	−3.31534	−0.185623
$320$	2.56155	0.143195
$321$	14.9309	0.833360
$322$	7.12311	0.396955
$323$	12.6847	0.705793
$324$	1.00000	0.0555556
$325$	0	0
$326$	−8.49242	−0.470352
$327$	4.24621	0.234816
$328$	5.24621	0.289674
$329$	−12.6847	−0.699328
$330$	−4.00000	−0.220193
$331$	5.36932	0.295124	0.147562	−	0.989053i	$-0.452857\pi$
$331$	5.36932	0.295124	0.147562	+	0.989053i	$0.452857\pi$
$332$	−3.12311	−0.171403
$333$	6.56155	0.359571
$334$	−20.4924	−1.12130
$335$	−2.24621	−0.122724
$336$	1.00000	0.0545545
$337$	19.4924	1.06182	0.530910	−	0.847428i	$-0.321850\pi$
$337$	19.4924	1.06182	0.530910	+	0.847428i	$0.321850\pi$
$338$	0	0
$339$	2.56155	0.139124
$340$	−20.8078	−1.12846
$341$	0	0
$342$	1.56155	0.0844391
$343$	−1.00000	−0.0539949
$344$	8.00000	0.431331
$345$	−18.2462	−0.982343
$346$	18.0000	0.967686
$347$	−22.0540	−1.18392	−0.591960	−	0.805968i	$-0.701646\pi$
$347$	−22.0540	−1.18392	−0.591960	+	0.805968i	$0.701646\pi$
$348$	−2.12311	−0.113810
$349$	18.0000	0.963518	0.481759	−	0.876304i	$-0.339998\pi$
$349$	18.0000	0.963518	0.481759	+	0.876304i	$0.339998\pi$
$350$	1.56155	0.0834685
$351$	0	0
$352$	1.56155	0.0832310
$353$	13.1922	0.702152	0.351076	−	0.936347i	$-0.385816\pi$
$353$	13.1922	0.702152	0.351076	+	0.936347i	$0.385816\pi$
$354$	3.12311	0.165991
$355$	−34.2462	−1.81760
$356$	−7.56155	−0.400761
$357$	−8.12311	−0.429920
$358$	18.2462	0.964342
$359$	18.2462	0.962998	0.481499	−	0.876447i	$-0.340092\pi$
$359$	18.2462	0.962998	0.481499	+	0.876447i	$0.340092\pi$
$360$	−2.56155	−0.135006
$361$	−16.5616	−0.871661
$362$	3.24621	0.170617
$363$	8.56155	0.449365
$364$	0	0
$365$	16.8078	0.879759
$366$	5.24621	0.274224
$367$	−27.6155	−1.44152	−0.720759	−	0.693185i	$-0.756207\pi$
$367$	−27.6155	−1.44152	−0.720759	+	0.693185i	$0.756207\pi$
$368$	7.12311	0.371318
$369$	−5.24621	−0.273107
$370$	−16.8078	−0.873794
$371$	−7.00000	−0.363422
$372$	0	0
$373$	−31.9309	−1.65332	−0.826659	−	0.562703i	$-0.809761\pi$
$373$	−31.9309	−1.65332	−0.826659	+	0.562703i	$0.809761\pi$
$374$	−12.6847	−0.655908
$375$	8.80776	0.454831
$376$	−12.6847	−0.654161
$377$	0	0
$378$	−1.00000	−0.0514344
$379$	3.61553	0.185717	0.0928586	−	0.995679i	$-0.470400\pi$
$379$	3.61553	0.185717	0.0928586	+	0.995679i	$0.470400\pi$
$380$	−4.00000	−0.205196
$381$	20.4924	1.04986
$382$	−3.12311	−0.159792
$383$	−7.80776	−0.398958	−0.199479	−	0.979902i	$-0.563925\pi$
$383$	−7.80776	−0.398958	−0.199479	+	0.979902i	$0.563925\pi$
$384$	1.00000	0.0510310
$385$	4.00000	0.203859
$386$	−8.12311	−0.413455
$387$	−8.00000	−0.406663
$388$	9.12311	0.463156
$389$	−17.6847	−0.896648	−0.448324	−	0.893871i	$-0.647979\pi$
$389$	−17.6847	−0.896648	−0.448324	+	0.893871i	$0.647979\pi$
$390$	0	0
$391$	−57.8617	−2.92619
$392$	−1.00000	−0.0505076
$393$	2.24621	0.113306
$394$	8.43845	0.425123
$395$	−6.24621	−0.314281
$396$	−1.56155	−0.0784710
$397$	0.930870	0.0467190	0.0233595	−	0.999727i	$-0.492564\pi$
$397$	0.930870	0.0467190	0.0233595	+	0.999727i	$0.492564\pi$
$398$	16.0000	0.802008
$399$	−1.56155	−0.0781754
$400$	1.56155	0.0780776
$401$	−18.8078	−0.939215	−0.469607	−	0.882875i	$-0.655605\pi$
$401$	−18.8078	−0.939215	−0.469607	+	0.882875i	$0.655605\pi$
$402$	−0.876894	−0.0437355
$403$	0	0
$404$	14.8078	0.736714
$405$	2.56155	0.127285
$406$	2.12311	0.105368
$407$	−10.2462	−0.507886
$408$	−8.12311	−0.402154
$409$	7.43845	0.367808	0.183904	−	0.982944i	$-0.441127\pi$
$409$	7.43845	0.367808	0.183904	+	0.982944i	$0.441127\pi$
$410$	13.4384	0.663678
$411$	16.5616	0.816921
$412$	−10.2462	−0.504795
$413$	−3.12311	−0.153678
$414$	−7.12311	−0.350082
$415$	−8.00000	−0.392705
$416$	0	0
$417$	9.56155	0.468231
$418$	−2.43845	−0.119268
$419$	−1.36932	−0.0668955	−0.0334478	−	0.999440i	$-0.510649\pi$
$419$	−1.36932	−0.0668955	−0.0334478	+	0.999440i	$0.510649\pi$
$420$	2.56155	0.124991
$421$	−31.3002	−1.52548	−0.762739	−	0.646707i	$-0.776146\pi$
$421$	−31.3002	−1.52548	−0.762739	+	0.646707i	$0.776146\pi$
$422$	3.12311	0.152030
$423$	12.6847	0.616749
$424$	−7.00000	−0.339950
$425$	−12.6847	−0.615296
$426$	−13.3693	−0.647746
$427$	−5.24621	−0.253882
$428$	−14.9309	−0.721711
$429$	0	0
$430$	20.4924	0.988232
$431$	5.36932	0.258631	0.129315	−	0.991604i	$-0.458722\pi$
$431$	5.36932	0.258631	0.129315	+	0.991604i	$0.458722\pi$
$432$	−1.00000	−0.0481125
$433$	−33.6847	−1.61878	−0.809391	−	0.587271i	$-0.800202\pi$
$433$	−33.6847	−1.61878	−0.809391	+	0.587271i	$0.800202\pi$
$434$	0	0
$435$	−5.43845	−0.260754
$436$	−4.24621	−0.203357
$437$	−11.1231	−0.532090
$438$	6.56155	0.313523
$439$	−9.75379	−0.465523	−0.232761	−	0.972534i	$-0.574776\pi$
$439$	−9.75379	−0.465523	−0.232761	+	0.972534i	$0.574776\pi$
$440$	4.00000	0.190693
$441$	1.00000	0.0476190
$442$	0	0
$443$	10.0540	0.477679	0.238839	−	0.971059i	$-0.423233\pi$
$443$	10.0540	0.477679	0.238839	+	0.971059i	$0.423233\pi$
$444$	−6.56155	−0.311398
$445$	−19.3693	−0.918194
$446$	26.2462	1.24279
$447$	−11.4384	−0.541020
$448$	−1.00000	−0.0472456
$449$	31.3693	1.48041	0.740205	−	0.672381i	$-0.234729\pi$
$449$	31.3693	1.48041	0.740205	+	0.672381i	$0.234729\pi$
$450$	−1.56155	−0.0736123
$451$	8.19224	0.385757
$452$	−2.56155	−0.120485
$453$	6.93087	0.325641
$454$	−19.1231	−0.897492
$455$	0	0
$456$	−1.56155	−0.0731264
$457$	−0.0691303	−0.00323378	−0.00161689	−	0.999999i	$-0.500515\pi$
$457$	−0.0691303	−0.00323378	−0.00161689	+	0.999999i	$0.500515\pi$
$458$	−20.0540	−0.937061
$459$	8.12311	0.379154
$460$	18.2462	0.850734
$461$	31.0540	1.44633	0.723164	−	0.690676i	$-0.242687\pi$
$461$	31.0540	1.44633	0.723164	+	0.690676i	$0.242687\pi$
$462$	1.56155	0.0726500
$463$	−24.6847	−1.14719	−0.573597	−	0.819138i	$-0.694452\pi$
$463$	−24.6847	−1.14719	−0.573597	+	0.819138i	$0.694452\pi$
$464$	2.12311	0.0985627
$465$	0	0
$466$	23.3693	1.08256
$467$	28.9848	1.34126	0.670629	−	0.741793i	$-0.266024\pi$
$467$	28.9848	1.34126	0.670629	+	0.741793i	$0.266024\pi$
$468$	0	0
$469$	0.876894	0.0404912
$470$	−32.4924	−1.49876
$471$	13.6847	0.630556
$472$	−3.12311	−0.143753
$473$	12.4924	0.574402
$474$	−2.43845	−0.112002
$475$	−2.43845	−0.111884
$476$	8.12311	0.372322
$477$	7.00000	0.320508
$478$	−5.36932	−0.245587
$479$	−26.9309	−1.23050	−0.615251	−	0.788331i	$-0.710946\pi$
$479$	−26.9309	−1.23050	−0.615251	+	0.788331i	$0.710946\pi$
$480$	2.56155	0.116918
$481$	0	0
$482$	−20.8078	−0.947768
$483$	7.12311	0.324113
$484$	−8.56155	−0.389161
$485$	23.3693	1.06115
$486$	1.00000	0.0453609
$487$	−11.3153	−0.512747	−0.256374	−	0.966578i	$-0.582528\pi$
$487$	−11.3153	−0.512747	−0.256374	+	0.966578i	$0.582528\pi$
$488$	−5.24621	−0.237485
$489$	−8.49242	−0.384041
$490$	−2.56155	−0.115719
$491$	16.4924	0.744293	0.372146	−	0.928174i	$-0.378622\pi$
$491$	16.4924	0.744293	0.372146	+	0.928174i	$0.378622\pi$
$492$	5.24621	0.236517
$493$	−17.2462	−0.776730
$494$	0	0
$495$	−4.00000	−0.179787
$496$	0	0
$497$	13.3693	0.599696
$498$	−3.12311	−0.139950
$499$	−13.7538	−0.615704	−0.307852	−	0.951434i	$-0.599610\pi$
$499$	−13.7538	−0.615704	−0.307852	+	0.951434i	$0.599610\pi$
$500$	−8.80776	−0.393895
$501$	−20.4924	−0.915534
$502$	−27.6155	−1.23254
$503$	4.49242	0.200307	0.100154	−	0.994972i	$-0.468067\pi$
$503$	4.49242	0.200307	0.100154	+	0.994972i	$0.468067\pi$
$504$	1.00000	0.0445435
$505$	37.9309	1.68790
$506$	11.1231	0.494482
$507$	0	0
$508$	−20.4924	−0.909204
$509$	21.1922	0.939329	0.469665	−	0.882845i	$-0.344375\pi$
$509$	21.1922	0.939329	0.469665	+	0.882845i	$0.344375\pi$
$510$	−20.8078	−0.921383
$511$	−6.56155	−0.290266
$512$	−1.00000	−0.0441942
$513$	1.56155	0.0689442
$514$	−0.369317	−0.0162899
$515$	−26.2462	−1.15655
$516$	8.00000	0.352180
$517$	−19.8078	−0.871144
$518$	6.56155	0.288298
$519$	18.0000	0.790112
$520$	0	0
$521$	34.1231	1.49496	0.747480	−	0.664284i	$-0.231263\pi$
$521$	34.1231	1.49496	0.747480	+	0.664284i	$0.231263\pi$
$522$	−2.12311	−0.0929258
$523$	3.80776	0.166502	0.0832509	−	0.996529i	$-0.473470\pi$
$523$	3.80776	0.166502	0.0832509	+	0.996529i	$0.473470\pi$
$524$	−2.24621	−0.0981262
$525$	1.56155	0.0681518
$526$	3.12311	0.136174
$527$	0	0
$528$	1.56155	0.0679579
$529$	27.7386	1.20603
$530$	−17.9309	−0.778867
$531$	3.12311	0.135531
$532$	1.56155	0.0677019
$533$	0	0
$534$	−7.56155	−0.327220
$535$	−38.2462	−1.65353
$536$	0.876894	0.0378761
$537$	18.2462	0.787382
$538$	−18.8769	−0.813841
$539$	−1.56155	−0.0672608
$540$	−2.56155	−0.110232
$541$	26.1771	1.12544	0.562720	−	0.826647i	$-0.309755\pi$
$541$	26.1771	1.12544	0.562720	+	0.826647i	$0.309755\pi$
$542$	26.7386	1.14852
$543$	3.24621	0.139308
$544$	8.12311	0.348275
$545$	−10.8769	−0.465915
$546$	0	0
$547$	7.61553	0.325616	0.162808	−	0.986658i	$-0.447945\pi$
$547$	7.61553	0.325616	0.162808	+	0.986658i	$0.447945\pi$
$548$	−16.5616	−0.707474
$549$	5.24621	0.223903
$550$	2.43845	0.103976
$551$	−3.31534	−0.141238
$552$	7.12311	0.303180
$553$	2.43845	0.103693
$554$	15.4384	0.655917
$555$	−16.8078	−0.713450
$556$	−9.56155	−0.405500
$557$	−3.87689	−0.164269	−0.0821346	−	0.996621i	$-0.526174\pi$
$557$	−3.87689	−0.164269	−0.0821346	+	0.996621i	$0.526174\pi$
$558$	0	0
$559$	0	0
$560$	−2.56155	−0.108245
$561$	−12.6847	−0.535547
$562$	−15.9309	−0.672003
$563$	−22.2462	−0.937566	−0.468783	−	0.883313i	$-0.655307\pi$
$563$	−22.2462	−0.937566	−0.468783	+	0.883313i	$0.655307\pi$
$564$	−12.6847	−0.534120
$565$	−6.56155	−0.276047
$566$	20.0000	0.840663
$567$	−1.00000	−0.0419961
$568$	13.3693	0.560964
$569$	−22.0000	−0.922288	−0.461144	−	0.887325i	$-0.652561\pi$
$569$	−22.0000	−0.922288	−0.461144	+	0.887325i	$0.652561\pi$
$570$	−4.00000	−0.167542
$571$	−12.8769	−0.538881	−0.269441	−	0.963017i	$-0.586839\pi$
$571$	−12.8769	−0.538881	−0.269441	+	0.963017i	$0.586839\pi$
$572$	0	0
$573$	−3.12311	−0.130470
$574$	−5.24621	−0.218973
$575$	11.1231	0.463866
$576$	1.00000	0.0416667
$577$	31.4384	1.30880	0.654400	−	0.756149i	$-0.272921\pi$
$577$	31.4384	1.30880	0.654400	+	0.756149i	$0.272921\pi$
$578$	−48.9848	−2.03750
$579$	−8.12311	−0.337585
$580$	5.43845	0.225819
$581$	3.12311	0.129568
$582$	9.12311	0.378165
$583$	−10.9309	−0.452710
$584$	−6.56155	−0.271519
$585$	0	0
$586$	21.9309	0.905956
$587$	14.2462	0.588004	0.294002	−	0.955805i	$-0.405013\pi$
$587$	14.2462	0.588004	0.294002	+	0.955805i	$0.405013\pi$
$588$	−1.00000	−0.0412393
$589$	0	0
$590$	−8.00000	−0.329355
$591$	8.43845	0.347111
$592$	6.56155	0.269678
$593$	−31.9848	−1.31346	−0.656730	−	0.754126i	$-0.728061\pi$
$593$	−31.9848	−1.31346	−0.656730	+	0.754126i	$0.728061\pi$
$594$	−1.56155	−0.0640713
$595$	20.8078	0.853035
$596$	11.4384	0.468537
$597$	16.0000	0.654836
$598$	0	0
$599$	−33.8617	−1.38355	−0.691777	−	0.722112i	$-0.743172\pi$
$599$	−33.8617	−1.38355	−0.691777	+	0.722112i	$0.743172\pi$
$600$	1.56155	0.0637501
$601$	−25.3002	−1.03202	−0.516008	−	0.856584i	$-0.672583\pi$
$601$	−25.3002	−1.03202	−0.516008	+	0.856584i	$0.672583\pi$
$602$	−8.00000	−0.326056
$603$	−0.876894	−0.0357099
$604$	−6.93087	−0.282013
$605$	−21.9309	−0.891617
$606$	14.8078	0.601524
$607$	16.9848	0.689394	0.344697	−	0.938714i	$-0.387982\pi$
$607$	16.9848	0.689394	0.344697	+	0.938714i	$0.387982\pi$
$608$	1.56155	0.0633293
$609$	2.12311	0.0860326
$610$	−13.4384	−0.544107
$611$	0	0
$612$	−8.12311	−0.328357
$613$	−17.4384	−0.704332	−0.352166	−	0.935938i	$-0.614555\pi$
$613$	−17.4384	−0.704332	−0.352166	+	0.935938i	$0.614555\pi$
$614$	18.9309	0.763988
$615$	13.4384	0.541890
$616$	−1.56155	−0.0629168
$617$	22.1771	0.892816	0.446408	−	0.894830i	$-0.352703\pi$
$617$	22.1771	0.892816	0.446408	+	0.894830i	$0.352703\pi$
$618$	−10.2462	−0.412163
$619$	−30.9309	−1.24322	−0.621608	−	0.783328i	$-0.713520\pi$
$619$	−30.9309	−1.24322	−0.621608	+	0.783328i	$0.713520\pi$
$620$	0	0
$621$	−7.12311	−0.285840
$622$	6.93087	0.277903
$623$	7.56155	0.302947
$624$	0	0
$625$	−30.3693	−1.21477
$626$	6.00000	0.239808
$627$	−2.43845	−0.0973822
$628$	−13.6847	−0.546077
$629$	−53.3002	−2.12522
$630$	2.56155	0.102055
$631$	38.9309	1.54981	0.774907	−	0.632076i	$-0.217797\pi$
$631$	38.9309	1.54981	0.774907	+	0.632076i	$0.217797\pi$
$632$	2.43845	0.0969962
$633$	3.12311	0.124132
$634$	16.5616	0.657743
$635$	−52.4924	−2.08310
$636$	−7.00000	−0.277568
$637$	0	0
$638$	3.31534	0.131256
$639$	−13.3693	−0.528882
$640$	−2.56155	−0.101254
$641$	12.5616	0.496152	0.248076	−	0.968741i	$-0.420202\pi$
$641$	12.5616	0.496152	0.248076	+	0.968741i	$0.420202\pi$
$642$	−14.9309	−0.589274
$643$	−35.3153	−1.39270	−0.696351	−	0.717702i	$-0.745194\pi$
$643$	−35.3153	−1.39270	−0.696351	+	0.717702i	$0.745194\pi$
$644$	−7.12311	−0.280690
$645$	20.4924	0.806888
$646$	−12.6847	−0.499071
$647$	−46.0540	−1.81057	−0.905284	−	0.424806i	$-0.860342\pi$
$647$	−46.0540	−1.81057	−0.905284	+	0.424806i	$0.860342\pi$
$648$	−1.00000	−0.0392837
$649$	−4.87689	−0.191435
$650$	0	0
$651$	0	0
$652$	8.49242	0.332589
$653$	16.4384	0.643286	0.321643	−	0.946861i	$-0.395765\pi$
$653$	16.4384	0.643286	0.321643	+	0.946861i	$0.395765\pi$
$654$	−4.24621	−0.166040
$655$	−5.75379	−0.224819
$656$	−5.24621	−0.204830
$657$	6.56155	0.255991
$658$	12.6847	0.494499
$659$	30.9309	1.20490	0.602448	−	0.798158i	$-0.294192\pi$
$659$	30.9309	1.20490	0.602448	+	0.798158i	$0.294192\pi$
$660$	4.00000	0.155700
$661$	−17.0540	−0.663323	−0.331661	−	0.943398i	$-0.607609\pi$
$661$	−17.0540	−0.663323	−0.331661	+	0.943398i	$0.607609\pi$
$662$	−5.36932	−0.208684
$663$	0	0
$664$	3.12311	0.121200
$665$	4.00000	0.155113
$666$	−6.56155	−0.254255
$667$	15.1231	0.585569
$668$	20.4924	0.792876
$669$	26.2462	1.01474
$670$	2.24621	0.0867787
$671$	−8.19224	−0.316258
$672$	−1.00000	−0.0385758
$673$	−19.2462	−0.741887	−0.370943	−	0.928655i	$-0.620966\pi$
$673$	−19.2462	−0.741887	−0.370943	+	0.928655i	$0.620966\pi$
$674$	−19.4924	−0.750820
$675$	−1.56155	−0.0601042
$676$	0	0
$677$	24.7386	0.950783	0.475391	−	0.879774i	$-0.342306\pi$
$677$	24.7386	0.950783	0.475391	+	0.879774i	$0.342306\pi$
$678$	−2.56155	−0.0983758
$679$	−9.12311	−0.350113
$680$	20.8078	0.797941
$681$	−19.1231	−0.732799
$682$	0	0
$683$	−7.50758	−0.287269	−0.143635	−	0.989631i	$-0.545879\pi$
$683$	−7.50758	−0.287269	−0.143635	+	0.989631i	$0.545879\pi$
$684$	−1.56155	−0.0597075
$685$	−42.4233	−1.62091
$686$	1.00000	0.0381802
$687$	−20.0540	−0.765107
$688$	−8.00000	−0.304997
$689$	0	0
$690$	18.2462	0.694621
$691$	−32.9848	−1.25480	−0.627401	−	0.778696i	$-0.715881\pi$
$691$	−32.9848	−1.25480	−0.627401	+	0.778696i	$0.715881\pi$
$692$	−18.0000	−0.684257
$693$	1.56155	0.0593185
$694$	22.0540	0.837157
$695$	−24.4924	−0.929051
$696$	2.12311	0.0804761
$697$	42.6155	1.61418
$698$	−18.0000	−0.681310
$699$	23.3693	0.883909
$700$	−1.56155	−0.0590211
$701$	14.3002	0.540111	0.270055	−	0.962845i	$-0.412958\pi$
$701$	14.3002	0.540111	0.270055	+	0.962845i	$0.412958\pi$
$702$	0	0
$703$	−10.2462	−0.386443
$704$	−1.56155	−0.0588532
$705$	−32.4924	−1.22374
$706$	−13.1922	−0.496496
$707$	−14.8078	−0.556903
$708$	−3.12311	−0.117373
$709$	−15.3002	−0.574611	−0.287305	−	0.957839i	$-0.592759\pi$
$709$	−15.3002	−0.574611	−0.287305	+	0.957839i	$0.592759\pi$
$710$	34.2462	1.28524
$711$	−2.43845	−0.0914489
$712$	7.56155	0.283381
$713$	0	0
$714$	8.12311	0.304000
$715$	0	0
$716$	−18.2462	−0.681893
$717$	−5.36932	−0.200521
$718$	−18.2462	−0.680943
$719$	−19.8078	−0.738705	−0.369352	−	0.929289i	$-0.620420\pi$
$719$	−19.8078	−0.738705	−0.369352	+	0.929289i	$0.620420\pi$
$720$	2.56155	0.0954634
$721$	10.2462	0.381589
$722$	16.5616	0.616357
$723$	−20.8078	−0.773849
$724$	−3.24621	−0.120644
$725$	3.31534	0.123129
$726$	−8.56155	−0.317749
$727$	40.0000	1.48352	0.741759	−	0.670667i	$-0.233992\pi$
$727$	40.0000	1.48352	0.741759	+	0.670667i	$0.233992\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−16.8078	−0.622083
$731$	64.9848	2.40355
$732$	−5.24621	−0.193906
$733$	−28.8617	−1.06603	−0.533016	−	0.846105i	$-0.678942\pi$
$733$	−28.8617	−1.06603	−0.533016	+	0.846105i	$0.678942\pi$
$734$	27.6155	1.01931
$735$	−2.56155	−0.0944843
$736$	−7.12311	−0.262561
$737$	1.36932	0.0504394
$738$	5.24621	0.193116
$739$	9.36932	0.344656	0.172328	−	0.985040i	$-0.444871\pi$
$739$	9.36932	0.344656	0.172328	+	0.985040i	$0.444871\pi$
$740$	16.8078	0.617866
$741$	0	0
$742$	7.00000	0.256978
$743$	−28.4924	−1.04529	−0.522643	−	0.852552i	$-0.675054\pi$
$743$	−28.4924	−1.04529	−0.522643	+	0.852552i	$0.675054\pi$
$744$	0	0
$745$	29.3002	1.07348
$746$	31.9309	1.16907
$747$	−3.12311	−0.114268
$748$	12.6847	0.463797
$749$	14.9309	0.545562
$750$	−8.80776	−0.321614
$751$	−20.1922	−0.736825	−0.368413	−	0.929662i	$-0.620099\pi$
$751$	−20.1922	−0.736825	−0.368413	+	0.929662i	$0.620099\pi$
$752$	12.6847	0.462562
$753$	−27.6155	−1.00637
$754$	0	0
$755$	−17.7538	−0.646127
$756$	1.00000	0.0363696
$757$	3.26137	0.118536	0.0592682	−	0.998242i	$-0.481123\pi$
$757$	3.26137	0.118536	0.0592682	+	0.998242i	$0.481123\pi$
$758$	−3.61553	−0.131322
$759$	11.1231	0.403743
$760$	4.00000	0.145095
$761$	14.9848	0.543200	0.271600	−	0.962410i	$-0.412447\pi$
$761$	14.9848	0.543200	0.271600	+	0.962410i	$0.412447\pi$
$762$	−20.4924	−0.742362
$763$	4.24621	0.153723
$764$	3.12311	0.112990
$765$	−20.8078	−0.752306
$766$	7.80776	0.282106
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	−13.1231	−0.473231	−0.236616	−	0.971603i	$-0.576038\pi$
$769$	−13.1231	−0.473231	−0.236616	+	0.971603i	$0.576038\pi$
$770$	−4.00000	−0.144150
$771$	−0.369317	−0.0133006
$772$	8.12311	0.292357
$773$	28.7386	1.03366	0.516828	−	0.856089i	$-0.327113\pi$
$773$	28.7386	1.03366	0.516828	+	0.856089i	$0.327113\pi$
$774$	8.00000	0.287554
$775$	0	0
$776$	−9.12311	−0.327500
$777$	6.56155	0.235394
$778$	17.6847	0.634026
$779$	8.19224	0.293517
$780$	0	0
$781$	20.8769	0.747034
$782$	57.8617	2.06913
$783$	−2.12311	−0.0758736
$784$	1.00000	0.0357143
$785$	−35.0540	−1.25113
$786$	−2.24621	−0.0801197
$787$	−45.1771	−1.61039	−0.805195	−	0.593011i	$-0.797939\pi$
$787$	−45.1771	−1.61039	−0.805195	+	0.593011i	$0.797939\pi$
$788$	−8.43845	−0.300607
$789$	3.12311	0.111186
$790$	6.24621	0.222230
$791$	2.56155	0.0910783
$792$	1.56155	0.0554874
$793$	0	0
$794$	−0.930870	−0.0330353
$795$	−17.9309	−0.635942
$796$	−16.0000	−0.567105
$797$	17.5076	0.620150	0.310075	−	0.950712i	$-0.399646\pi$
$797$	17.5076	0.620150	0.310075	+	0.950712i	$0.399646\pi$
$798$	1.56155	0.0552784
$799$	−103.039	−3.64525
$800$	−1.56155	−0.0552092
$801$	−7.56155	−0.267174
$802$	18.8078	0.664125
$803$	−10.2462	−0.361581
$804$	0.876894	0.0309257
$805$	−18.2462	−0.643094
$806$	0	0
$807$	−18.8769	−0.664498
$808$	−14.8078	−0.520935
$809$	−19.9309	−0.700732	−0.350366	−	0.936613i	$-0.613943\pi$
$809$	−19.9309	−0.700732	−0.350366	+	0.936613i	$0.613943\pi$
$810$	−2.56155	−0.0900038
$811$	−24.0000	−0.842754	−0.421377	−	0.906886i	$-0.638453\pi$
$811$	−24.0000	−0.842754	−0.421377	+	0.906886i	$0.638453\pi$
$812$	−2.12311	−0.0745064
$813$	26.7386	0.937765
$814$	10.2462	0.359130
$815$	21.7538	0.762002
$816$	8.12311	0.284366
$817$	12.4924	0.437055
$818$	−7.43845	−0.260079
$819$	0	0
$820$	−13.4384	−0.469291
$821$	26.3002	0.917883	0.458941	−	0.888467i	$-0.348229\pi$
$821$	26.3002	0.917883	0.458941	+	0.888467i	$0.348229\pi$
$822$	−16.5616	−0.577650
$823$	−21.7538	−0.758289	−0.379145	−	0.925337i	$-0.623782\pi$
$823$	−21.7538	−0.758289	−0.379145	+	0.925337i	$0.623782\pi$
$824$	10.2462	0.356944
$825$	2.43845	0.0848958
$826$	3.12311	0.108667
$827$	−17.7538	−0.617360	−0.308680	−	0.951166i	$-0.599887\pi$
$827$	−17.7538	−0.617360	−0.308680	+	0.951166i	$0.599887\pi$
$828$	7.12311	0.247545
$829$	24.3693	0.846381	0.423191	−	0.906041i	$-0.360910\pi$
$829$	24.3693	0.846381	0.423191	+	0.906041i	$0.360910\pi$
$830$	8.00000	0.277684
$831$	15.4384	0.535554
$832$	0	0
$833$	−8.12311	−0.281449
$834$	−9.56155	−0.331089
$835$	52.4924	1.81658
$836$	2.43845	0.0843355
$837$	0	0
$838$	1.36932	0.0473023
$839$	−1.75379	−0.0605475	−0.0302738	−	0.999542i	$-0.509638\pi$
$839$	−1.75379	−0.0605475	−0.0302738	+	0.999542i	$0.509638\pi$
$840$	−2.56155	−0.0883820
$841$	−24.4924	−0.844566
$842$	31.3002	1.07868
$843$	−15.9309	−0.548688
$844$	−3.12311	−0.107502
$845$	0	0
$846$	−12.6847	−0.436108
$847$	8.56155	0.294178
$848$	7.00000	0.240381
$849$	20.0000	0.686398
$850$	12.6847	0.435080
$851$	46.7386	1.60218
$852$	13.3693	0.458025
$853$	−5.63068	−0.192791	−0.0963955	−	0.995343i	$-0.530731\pi$
$853$	−5.63068	−0.192791	−0.0963955	+	0.995343i	$0.530731\pi$
$854$	5.24621	0.179522
$855$	−4.00000	−0.136797
$856$	14.9309	0.510327
$857$	20.5616	0.702369	0.351185	−	0.936306i	$-0.385779\pi$
$857$	20.5616	0.702369	0.351185	+	0.936306i	$0.385779\pi$
$858$	0	0
$859$	−10.9309	−0.372956	−0.186478	−	0.982459i	$-0.559707\pi$
$859$	−10.9309	−0.372956	−0.186478	+	0.982459i	$0.559707\pi$
$860$	−20.4924	−0.698786
$861$	−5.24621	−0.178790
$862$	−5.36932	−0.182880
$863$	−32.8769	−1.11914	−0.559571	−	0.828782i	$-0.689034\pi$
$863$	−32.8769	−1.11914	−0.559571	+	0.828782i	$0.689034\pi$
$864$	1.00000	0.0340207
$865$	−46.1080	−1.56772
$866$	33.6847	1.14465
$867$	−48.9848	−1.66361
$868$	0	0
$869$	3.80776	0.129170
$870$	5.43845	0.184381
$871$	0	0
$872$	4.24621	0.143795
$873$	9.12311	0.308770
$874$	11.1231	0.376245
$875$	8.80776	0.297757
$876$	−6.56155	−0.221694
$877$	−41.5464	−1.40292	−0.701461	−	0.712708i	$-0.747469\pi$
$877$	−41.5464	−1.40292	−0.701461	+	0.712708i	$0.747469\pi$
$878$	9.75379	0.329174
$879$	21.9309	0.739710
$880$	−4.00000	−0.134840
$881$	57.0540	1.92220	0.961099	−	0.276205i	$-0.0890770\pi$
$881$	57.0540	1.92220	0.961099	+	0.276205i	$0.0890770\pi$
$882$	−1.00000	−0.0336718
$883$	−20.0000	−0.673054	−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000	−0.673054	−0.336527	+	0.941674i	$0.609252\pi$
$884$	0	0
$885$	−8.00000	−0.268917
$886$	−10.0540	−0.337770
$887$	−46.0540	−1.54634	−0.773171	−	0.634198i	$-0.781330\pi$
$887$	−46.0540	−1.54634	−0.773171	+	0.634198i	$0.781330\pi$
$888$	6.56155	0.220191
$889$	20.4924	0.687294
$890$	19.3693	0.649261
$891$	−1.56155	−0.0523140
$892$	−26.2462	−0.878788
$893$	−19.8078	−0.662842
$894$	11.4384	0.382559
$895$	−46.7386	−1.56230
$896$	1.00000	0.0334077
$897$	0	0
$898$	−31.3693	−1.04681
$899$	0	0
$900$	1.56155	0.0520518
$901$	−56.8617	−1.89434
$902$	−8.19224	−0.272772
$903$	−8.00000	−0.266223
$904$	2.56155	0.0851960
$905$	−8.31534	−0.276411
$906$	−6.93087	−0.230263
$907$	7.12311	0.236519	0.118259	−	0.992983i	$-0.462269\pi$
$907$	7.12311	0.236519	0.118259	+	0.992983i	$0.462269\pi$
$908$	19.1231	0.634623
$909$	14.8078	0.491143
$910$	0	0
$911$	−27.6155	−0.914943	−0.457472	−	0.889224i	$-0.651245\pi$
$911$	−27.6155	−0.914943	−0.457472	+	0.889224i	$0.651245\pi$
$912$	1.56155	0.0517082
$913$	4.87689	0.161402
$914$	0.0691303	0.00228663
$915$	−13.4384	−0.444261
$916$	20.0540	0.662602
$917$	2.24621	0.0741764
$918$	−8.12311	−0.268102
$919$	−17.0691	−0.563059	−0.281529	−	0.959553i	$-0.590842\pi$
$919$	−17.0691	−0.563059	−0.281529	+	0.959553i	$0.590842\pi$
$920$	−18.2462	−0.601560
$921$	18.9309	0.623793
$922$	−31.0540	−1.02271
$923$	0	0
$924$	−1.56155	−0.0513713
$925$	10.2462	0.336893
$926$	24.6847	0.811188
$927$	−10.2462	−0.336530
$928$	−2.12311	−0.0696944
$929$	19.2462	0.631448	0.315724	−	0.948851i	$-0.397753\pi$
$929$	19.2462	0.631448	0.315724	+	0.948851i	$0.397753\pi$
$930$	0	0
$931$	−1.56155	−0.0511778
$932$	−23.3693	−0.765487
$933$	6.93087	0.226906
$934$	−28.9848	−0.948413
$935$	32.4924	1.06262
$936$	0	0
$937$	−38.5616	−1.25975	−0.629876	−	0.776696i	$-0.716894\pi$
$937$	−38.5616	−1.25975	−0.629876	+	0.776696i	$0.716894\pi$
$938$	−0.876894	−0.0286316
$939$	6.00000	0.195803
$940$	32.4924	1.05979
$941$	35.3693	1.15301	0.576503	−	0.817095i	$-0.304417\pi$
$941$	35.3693	1.15301	0.576503	+	0.817095i	$0.304417\pi$
$942$	−13.6847	−0.445870
$943$	−37.3693	−1.21691
$944$	3.12311	0.101648
$945$	2.56155	0.0833273
$946$	−12.4924	−0.406164
$947$	−54.4384	−1.76901	−0.884506	−	0.466529i	$-0.845504\pi$
$947$	−54.4384	−1.76901	−0.884506	+	0.466529i	$0.845504\pi$
$948$	2.43845	0.0791971
$949$	0	0
$950$	2.43845	0.0791137
$951$	16.5616	0.537045
$952$	−8.12311	−0.263271
$953$	21.1231	0.684245	0.342122	−	0.939655i	$-0.388854\pi$
$953$	21.1231	0.684245	0.342122	+	0.939655i	$0.388854\pi$
$954$	−7.00000	−0.226633
$955$	8.00000	0.258874
$956$	5.36932	0.173656
$957$	3.31534	0.107170
$958$	26.9309	0.870097
$959$	16.5616	0.534800
$960$	−2.56155	−0.0826738
$961$	−31.0000	−1.00000
$962$	0	0
$963$	−14.9309	−0.481141
$964$	20.8078	0.670173
$965$	20.8078	0.669826
$966$	−7.12311	−0.229182
$967$	−4.49242	−0.144467	−0.0722333	−	0.997388i	$-0.523013\pi$
$967$	−4.49242	−0.144467	−0.0722333	+	0.997388i	$0.523013\pi$
$968$	8.56155	0.275179
$969$	−12.6847	−0.407490
$970$	−23.3693	−0.750344
$971$	0.384472	0.0123383	0.00616914	−	0.999981i	$-0.498036\pi$
$971$	0.384472	0.0123383	0.00616914	+	0.999981i	$0.498036\pi$
$972$	−1.00000	−0.0320750
$973$	9.56155	0.306529
$974$	11.3153	0.362567
$975$	0	0
$976$	5.24621	0.167927
$977$	−4.17708	−0.133637	−0.0668183	−	0.997765i	$-0.521285\pi$
$977$	−4.17708	−0.133637	−0.0668183	+	0.997765i	$0.521285\pi$
$978$	8.49242	0.271558
$979$	11.8078	0.377378
$980$	2.56155	0.0818258
$981$	−4.24621	−0.135571
$982$	−16.4924	−0.526294
$983$	30.7386	0.980410	0.490205	−	0.871607i	$-0.336922\pi$
$983$	30.7386	0.980410	0.490205	+	0.871607i	$0.336922\pi$
$984$	−5.24621	−0.167243
$985$	−21.6155	−0.688728
$986$	17.2462	0.549231
$987$	12.6847	0.403757
$988$	0	0
$989$	−56.9848	−1.81201
$990$	4.00000	0.127128
$991$	49.6695	1.57780	0.788902	−	0.614519i	$-0.210650\pi$
$991$	49.6695	1.57780	0.788902	+	0.614519i	$0.210650\pi$
$992$	0	0
$993$	−5.36932	−0.170390
$994$	−13.3693	−0.424049
$995$	−40.9848	−1.29931
$996$	3.12311	0.0989594
$997$	23.9848	0.759608	0.379804	−	0.925067i	$-0.375991\pi$
$997$	23.9848	0.759608	0.379804	+	0.925067i	$0.375991\pi$
$998$	13.7538	0.435369
$999$	−6.56155	−0.207598

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.bi.1.2		2
13.4	even	6		546.2.l.l.211.1	✓	4
13.10	even	6		546.2.l.l.295.1	yes	4
13.12	even	2		7098.2.a.bt.1.1		2
39.17	odd	6		1638.2.r.y.757.2		4
39.23	odd	6		1638.2.r.y.1387.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.l.l.211.1	✓	4	13.4	even	6
546.2.l.l.295.1	yes	4	13.10	even	6
1638.2.r.y.757.2		4	39.17	odd	6
1638.2.r.y.1387.2		4	39.23	odd	6
7098.2.a.bi.1.2		2	1.1	even	1	trivial
7098.2.a.bt.1.1		2	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.56155 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.56155 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.56155 q^{10} -1.56155 q^{11} -1.00000 q^{12} +1.00000 q^{14} -2.56155 q^{15} +1.00000 q^{16} -8.12311 q^{17} -1.00000 q^{18} -1.56155 q^{19} +2.56155 q^{20} +1.00000 q^{21} +1.56155 q^{22} +7.12311 q^{23} +1.00000 q^{24} +1.56155 q^{25} -1.00000 q^{27} -1.00000 q^{28} +2.12311 q^{29} +2.56155 q^{30} -1.00000 q^{32} +1.56155 q^{33} +8.12311 q^{34} -2.56155 q^{35} +1.00000 q^{36} +6.56155 q^{37} +1.56155 q^{38} -2.56155 q^{40} -5.24621 q^{41} -1.00000 q^{42} -8.00000 q^{43} -1.56155 q^{44} +2.56155 q^{45} -7.12311 q^{46} +12.6847 q^{47} -1.00000 q^{48} +1.00000 q^{49} -1.56155 q^{50} +8.12311 q^{51} +7.00000 q^{53} +1.00000 q^{54} -4.00000 q^{55} +1.00000 q^{56} +1.56155 q^{57} -2.12311 q^{58} +3.12311 q^{59} -2.56155 q^{60} +5.24621 q^{61} -1.00000 q^{63} +1.00000 q^{64} -1.56155 q^{66} -0.876894 q^{67} -8.12311 q^{68} -7.12311 q^{69} +2.56155 q^{70} -13.3693 q^{71} -1.00000 q^{72} +6.56155 q^{73} -6.56155 q^{74} -1.56155 q^{75} -1.56155 q^{76} +1.56155 q^{77} -2.43845 q^{79} +2.56155 q^{80} +1.00000 q^{81} +5.24621 q^{82} -3.12311 q^{83} +1.00000 q^{84} -20.8078 q^{85} +8.00000 q^{86} -2.12311 q^{87} +1.56155 q^{88} -7.56155 q^{89} -2.56155 q^{90} +7.12311 q^{92} -12.6847 q^{94} -4.00000 q^{95} +1.00000 q^{96} +9.12311 q^{97} -1.00000 q^{98} -1.56155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} - q^{10} + q^{11} - 2 q^{12} + 2 q^{14} - q^{15} + 2 q^{16} - 8 q^{17} - 2 q^{18} + q^{19} + q^{20} + 2 q^{21} - q^{22} + 6 q^{23} + 2 q^{24} - q^{25} - 2 q^{27} - 2 q^{28} - 4 q^{29} + q^{30} - 2 q^{32} - q^{33} + 8 q^{34} - q^{35} + 2 q^{36} + 9 q^{37} - q^{38} - q^{40} + 6 q^{41} - 2 q^{42} - 16 q^{43} + q^{44} + q^{45} - 6 q^{46} + 13 q^{47} - 2 q^{48} + 2 q^{49} + q^{50} + 8 q^{51} + 14 q^{53} + 2 q^{54} - 8 q^{55} + 2 q^{56} - q^{57} + 4 q^{58} - 2 q^{59} - q^{60} - 6 q^{61} - 2 q^{63} + 2 q^{64} + q^{66} - 10 q^{67} - 8 q^{68} - 6 q^{69} + q^{70} - 2 q^{71} - 2 q^{72} + 9 q^{73} - 9 q^{74} + q^{75} + q^{76} - q^{77} - 9 q^{79} + q^{80} + 2 q^{81} - 6 q^{82} + 2 q^{83} + 2 q^{84} - 21 q^{85} + 16 q^{86} + 4 q^{87} - q^{88} - 11 q^{89} - q^{90} + 6 q^{92} - 13 q^{94} - 8 q^{95} + 2 q^{96} + 10 q^{97} - 2 q^{98} + q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9 - q^10 + q^11 - 2 * q^12 + 2 * q^14 - q^15 + 2 * q^16 - 8 * q^17 - 2 * q^18 + q^19 + q^20 + 2 * q^21 - q^22 + 6 * q^23 + 2 * q^24 - q^25 - 2 * q^27 - 2 * q^28 - 4 * q^29 + q^30 - 2 * q^32 - q^33 + 8 * q^34 - q^35 + 2 * q^36 + 9 * q^37 - q^38 - q^40 + 6 * q^41 - 2 * q^42 - 16 * q^43 + q^44 + q^45 - 6 * q^46 + 13 * q^47 - 2 * q^48 + 2 * q^49 + q^50 + 8 * q^51 + 14 * q^53 + 2 * q^54 - 8 * q^55 + 2 * q^56 - q^57 + 4 * q^58 - 2 * q^59 - q^60 - 6 * q^61 - 2 * q^63 + 2 * q^64 + q^66 - 10 * q^67 - 8 * q^68 - 6 * q^69 + q^70 - 2 * q^71 - 2 * q^72 + 9 * q^73 - 9 * q^74 + q^75 + q^76 - q^77 - 9 * q^79 + q^80 + 2 * q^81 - 6 * q^82 + 2 * q^83 + 2 * q^84 - 21 * q^85 + 16 * q^86 + 4 * q^87 - q^88 - 11 * q^89 - q^90 + 6 * q^92 - 13 * q^94 - 8 * q^95 + 2 * q^96 + 10 * q^97 - 2 * q^98 + q^99

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