LMFDB - Embedded newform 3630.2.a.br.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3630,2,Mod(1,3630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3630, 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("3630.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3630.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:	$28.9856959337$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.43025.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 21x^{2} + 10x + 100 $ x^4 - x^3 - 21x^2 + 10x + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 330)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.86832$ of defining polynomial
Character	$\chi$	$=$	3630.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -2.86832 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -2.86832 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{12} +5.25908 q^{13} +2.86832 q^{14} +1.00000 q^{15} +1.00000 q^{16} -0.154687 q^{17} -1.00000 q^{18} -1.46335 q^{19} +1.00000 q^{20} -2.86832 q^{21} +3.78694 q^{23} -1.00000 q^{24} +1.00000 q^{25} -5.25908 q^{26} +1.00000 q^{27} -2.86832 q^{28} +3.48636 q^{29} -1.00000 q^{30} +2.98578 q^{31} -1.00000 q^{32} +0.154687 q^{34} -2.86832 q^{35} +1.00000 q^{36} +8.85410 q^{37} +1.46335 q^{38} +5.25908 q^{39} -1.00000 q^{40} -8.41377 q^{41} +2.86832 q^{42} -7.86289 q^{43} +1.00000 q^{45} -3.78694 q^{46} -10.9957 q^{47} +1.00000 q^{48} +1.22728 q^{49} -1.00000 q^{50} -0.154687 q^{51} +5.25908 q^{52} +10.5765 q^{53} -1.00000 q^{54} +2.86832 q^{56} -1.46335 q^{57} -3.48636 q^{58} +7.92741 q^{59} +1.00000 q^{60} -1.73665 q^{61} -2.98578 q^{62} -2.86832 q^{63} +1.00000 q^{64} +5.25908 q^{65} -11.2406 q^{67} -0.154687 q^{68} +3.78694 q^{69} +2.86832 q^{70} +3.54544 q^{71} -1.00000 q^{72} +6.00000 q^{73} -8.85410 q^{74} +1.00000 q^{75} -1.46335 q^{76} -5.25908 q^{78} +6.78958 q^{79} +1.00000 q^{80} +1.00000 q^{81} +8.41377 q^{82} +1.52786 q^{83} -2.86832 q^{84} -0.154687 q^{85} +7.86289 q^{86} +3.48636 q^{87} -10.8859 q^{89} -1.00000 q^{90} -15.0847 q^{91} +3.78694 q^{92} +2.98578 q^{93} +10.9957 q^{94} -1.46335 q^{95} -1.00000 q^{96} +19.4449 q^{97} -1.22728 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} - 4 q^{6} - q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^5 - 4 * q^6 - q^7 - 4 * q^8 + 4 * q^9	$ 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} - 4 q^{6} - q^{7} - 4 q^{8} + 4 q^{9} - 4 q^{10} + 4 q^{12} - 4 q^{13} + q^{14} + 4 q^{15} + 4 q^{16} + 5 q^{17} - 4 q^{18} - 7 q^{19} + 4 q^{20} - q^{21} + 8 q^{23} - 4 q^{24} + 4 q^{25} + 4 q^{26} + 4 q^{27} - q^{28} - q^{29} - 4 q^{30} + 9 q^{31} - 4 q^{32} - 5 q^{34} - q^{35} + 4 q^{36} + 22 q^{37} + 7 q^{38} - 4 q^{39} - 4 q^{40} - 3 q^{41} + q^{42} + q^{43} + 4 q^{45} - 8 q^{46} + 2 q^{47} + 4 q^{48} + 15 q^{49} - 4 q^{50} + 5 q^{51} - 4 q^{52} + 5 q^{53} - 4 q^{54} + q^{56} - 7 q^{57} + q^{58} + 16 q^{59} + 4 q^{60} + 14 q^{61} - 9 q^{62} - q^{63} + 4 q^{64} - 4 q^{65} + 29 q^{67} + 5 q^{68} + 8 q^{69} + q^{70} - 6 q^{71} - 4 q^{72} + 24 q^{73} - 22 q^{74} + 4 q^{75} - 7 q^{76} + 4 q^{78} - 3 q^{79} + 4 q^{80} + 4 q^{81} + 3 q^{82} + 24 q^{83} - q^{84} + 5 q^{85} - q^{86} - q^{87} + 5 q^{89} - 4 q^{90} - 16 q^{91} + 8 q^{92} + 9 q^{93} - 2 q^{94} - 7 q^{95} - 4 q^{96} + 30 q^{97} - 15 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^5 - 4 * q^6 - q^7 - 4 * q^8 + 4 * q^9 - 4 * q^10 + 4 * q^12 - 4 * q^13 + q^14 + 4 * q^15 + 4 * q^16 + 5 * q^17 - 4 * q^18 - 7 * q^19 + 4 * q^20 - q^21 + 8 * q^23 - 4 * q^24 + 4 * q^25 + 4 * q^26 + 4 * q^27 - q^28 - q^29 - 4 * q^30 + 9 * q^31 - 4 * q^32 - 5 * q^34 - q^35 + 4 * q^36 + 22 * q^37 + 7 * q^38 - 4 * q^39 - 4 * q^40 - 3 * q^41 + q^42 + q^43 + 4 * q^45 - 8 * q^46 + 2 * q^47 + 4 * q^48 + 15 * q^49 - 4 * q^50 + 5 * q^51 - 4 * q^52 + 5 * q^53 - 4 * q^54 + q^56 - 7 * q^57 + q^58 + 16 * q^59 + 4 * q^60 + 14 * q^61 - 9 * q^62 - q^63 + 4 * q^64 - 4 * q^65 + 29 * q^67 + 5 * q^68 + 8 * q^69 + q^70 - 6 * q^71 - 4 * q^72 + 24 * q^73 - 22 * q^74 + 4 * q^75 - 7 * q^76 + 4 * q^78 - 3 * q^79 + 4 * q^80 + 4 * q^81 + 3 * q^82 + 24 * q^83 - q^84 + 5 * q^85 - q^86 - q^87 + 5 * q^89 - 4 * q^90 - 16 * q^91 + 8 * q^92 + 9 * q^93 - 2 * q^94 - 7 * q^95 - 4 * q^96 + 30 * q^97 - 15 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.00000	−0.408248
$7$	−2.86832	−1.08412	−0.542062	−	0.840338i	$-0.682356\pi$
$7$	−2.86832	−1.08412	−0.542062	+	0.840338i	$0.682356\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	0	0
$11$	0	0
$12$	1.00000	0.288675
$13$	5.25908	1.45861	0.729303	−	0.684191i	$-0.239844\pi$
$13$	5.25908	1.45861	0.729303	+	0.684191i	$0.239844\pi$
$14$	2.86832	0.766592
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−0.154687	−0.0375172	−0.0187586	−	0.999824i	$-0.505971\pi$
$17$	−0.154687	−0.0375172	−0.0187586	+	0.999824i	$0.505971\pi$
$18$	−1.00000	−0.235702
$19$	−1.46335	−0.335715	−0.167857	−	0.985811i	$-0.553685\pi$
$19$	−1.46335	−0.335715	−0.167857	+	0.985811i	$0.553685\pi$
$20$	1.00000	0.223607
$21$	−2.86832	−0.625919
$22$	0	0
$23$	3.78694	0.789632	0.394816	−	0.918760i	$-0.370808\pi$
$23$	3.78694	0.789632	0.394816	+	0.918760i	$0.370808\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−5.25908	−1.03139
$27$	1.00000	0.192450
$28$	−2.86832	−0.542062
$29$	3.48636	0.647400	0.323700	−	0.946160i	$-0.395073\pi$
$29$	3.48636	0.647400	0.323700	+	0.946160i	$0.395073\pi$
$30$	−1.00000	−0.182574
$31$	2.98578	0.536262	0.268131	−	0.963383i	$-0.413594\pi$
$31$	2.98578	0.536262	0.268131	+	0.963383i	$0.413594\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	0.154687	0.0265287
$35$	−2.86832	−0.484835
$36$	1.00000	0.166667
$37$	8.85410	1.45561	0.727803	−	0.685787i	$-0.240542\pi$
$37$	8.85410	1.45561	0.727803	+	0.685787i	$0.240542\pi$
$38$	1.46335	0.237386
$39$	5.25908	0.842127
$40$	−1.00000	−0.158114
$41$	−8.41377	−1.31401	−0.657005	−	0.753886i	$-0.728177\pi$
$41$	−8.41377	−1.31401	−0.657005	+	0.753886i	$0.728177\pi$
$42$	2.86832	0.442592
$43$	−7.86289	−1.19908	−0.599540	−	0.800345i	$-0.704650\pi$
$43$	−7.86289	−1.19908	−0.599540	+	0.800345i	$0.704650\pi$
$44$	0	0
$45$	1.00000	0.149071
$46$	−3.78694	−0.558354
$47$	−10.9957	−1.60389	−0.801946	−	0.597397i	$-0.796202\pi$
$47$	−10.9957	−1.60389	−0.801946	+	0.597397i	$0.796202\pi$
$48$	1.00000	0.144338
$49$	1.22728	0.175326
$50$	−1.00000	−0.141421
$51$	−0.154687	−0.0216606
$52$	5.25908	0.729303
$53$	10.5765	1.45280	0.726399	−	0.687273i	$-0.241193\pi$
$53$	10.5765	1.45280	0.726399	+	0.687273i	$0.241193\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	2.86832	0.383296
$57$	−1.46335	−0.193825
$58$	−3.48636	−0.457781
$59$	7.92741	1.03206	0.516030	−	0.856570i	$-0.327409\pi$
$59$	7.92741	1.03206	0.516030	+	0.856570i	$0.327409\pi$
$60$	1.00000	0.129099
$61$	−1.73665	−0.222355	−0.111177	−	0.993801i	$-0.535462\pi$
$61$	−1.73665	−0.222355	−0.111177	+	0.993801i	$0.535462\pi$
$62$	−2.98578	−0.379194
$63$	−2.86832	−0.361375
$64$	1.00000	0.125000
$65$	5.25908	0.652308
$66$	0	0
$67$	−11.2406	−1.37326	−0.686628	−	0.727009i	$-0.740910\pi$
$67$	−11.2406	−1.37326	−0.686628	+	0.727009i	$0.740910\pi$
$68$	−0.154687	−0.0187586
$69$	3.78694	0.455894
$70$	2.86832	0.342830
$71$	3.54544	0.420767	0.210383	−	0.977619i	$-0.432529\pi$
$71$	3.54544	0.420767	0.210383	+	0.977619i	$0.432529\pi$
$72$	−1.00000	−0.117851
$73$	6.00000	0.702247	0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000	0.702247	0.351123	+	0.936329i	$0.385800\pi$
$74$	−8.85410	−1.02927
$75$	1.00000	0.115470
$76$	−1.46335	−0.167857
$77$	0	0
$78$	−5.25908	−0.595473
$79$	6.78958	0.763888	0.381944	−	0.924185i	$-0.375255\pi$
$79$	6.78958	0.763888	0.381944	+	0.924185i	$0.375255\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	8.41377	0.929145
$83$	1.52786	0.167705	0.0838524	−	0.996478i	$-0.473278\pi$
$83$	1.52786	0.167705	0.0838524	+	0.996478i	$0.473278\pi$
$84$	−2.86832	−0.312960
$85$	−0.154687	−0.0167782
$86$	7.86289	0.847877
$87$	3.48636	0.373777
$88$	0	0
$89$	−10.8859	−1.15390	−0.576952	−	0.816778i	$-0.695758\pi$
$89$	−10.8859	−1.15390	−0.576952	+	0.816778i	$0.695758\pi$
$90$	−1.00000	−0.105409
$91$	−15.0847	−1.58131
$92$	3.78694	0.394816
$93$	2.98578	0.309611
$94$	10.9957	1.13412
$95$	−1.46335	−0.150136
$96$	−1.00000	−0.102062
$97$	19.4449	1.97433	0.987163	−	0.159718i	$-0.0510584\pi$
$97$	19.4449	1.97433	0.987163	+	0.159718i	$0.0510584\pi$
$98$	−1.22728	−0.123974
$99$	0	0
$100$	1.00000	0.100000
$101$	−4.15469	−0.413407	−0.206703	−	0.978404i	$-0.566274\pi$
$101$	−4.15469	−0.413407	−0.206703	+	0.978404i	$0.566274\pi$
$102$	0.154687	0.0153163
$103$	5.46335	0.538320	0.269160	−	0.963096i	$-0.413254\pi$
$103$	5.46335	0.538320	0.269160	+	0.963096i	$0.413254\pi$
$104$	−5.25908	−0.515695
$105$	−2.86832	−0.279920
$106$	−10.5765	−1.02728
$107$	15.7827	1.52577	0.762884	−	0.646535i	$-0.223783\pi$
$107$	15.7827	1.52577	0.762884	+	0.646535i	$0.223783\pi$
$108$	1.00000	0.0962250
$109$	5.52786	0.529473	0.264737	−	0.964321i	$-0.414715\pi$
$109$	5.52786	0.529473	0.264737	+	0.964321i	$0.414715\pi$
$110$	0	0
$111$	8.85410	0.840394
$112$	−2.86832	−0.271031
$113$	2.75087	0.258780	0.129390	−	0.991594i	$-0.458698\pi$
$113$	2.75087	0.258780	0.129390	+	0.991594i	$0.458698\pi$
$114$	1.46335	0.137055
$115$	3.78694	0.353134
$116$	3.48636	0.323700
$117$	5.25908	0.486202
$118$	−7.92741	−0.729777
$119$	0.443693	0.0406733
$120$	−1.00000	−0.0912871
$121$	0	0
$122$	1.73665	0.157229
$123$	−8.41377	−0.758644
$124$	2.98578	0.268131
$125$	1.00000	0.0894427
$126$	2.86832	0.255531
$127$	13.2000	1.17131	0.585655	−	0.810560i	$-0.300837\pi$
$127$	13.2000	1.17131	0.585655	+	0.810560i	$0.300837\pi$
$128$	−1.00000	−0.0883883
$129$	−7.86289	−0.692289
$130$	−5.25908	−0.461252
$131$	7.66670	0.669842	0.334921	−	0.942246i	$-0.391290\pi$
$131$	7.66670	0.669842	0.334921	+	0.942246i	$0.391290\pi$
$132$	0	0
$133$	4.19735	0.363957
$134$	11.2406	0.971038
$135$	1.00000	0.0860663
$136$	0.154687	0.0132643
$137$	−12.5597	−1.07304	−0.536522	−	0.843886i	$-0.680262\pi$
$137$	−12.5597	−1.07304	−0.536522	+	0.843886i	$0.680262\pi$
$138$	−3.78694	−0.322366
$139$	19.0771	1.61810	0.809050	−	0.587741i	$-0.199982\pi$
$139$	19.0771	1.61810	0.809050	+	0.587741i	$0.199982\pi$
$140$	−2.86832	−0.242418
$141$	−10.9957	−0.926007
$142$	−3.54544	−0.297527
$143$	0	0
$144$	1.00000	0.0833333
$145$	3.48636	0.289526
$146$	−6.00000	−0.496564
$147$	1.22728	0.101224
$148$	8.85410	0.727803
$149$	12.1547	0.995751	0.497875	−	0.867249i	$-0.334114\pi$
$149$	12.1547	0.995751	0.497875	+	0.867249i	$0.334114\pi$
$150$	−1.00000	−0.0816497
$151$	−4.66334	−0.379497	−0.189749	−	0.981833i	$-0.560767\pi$
$151$	−4.66334	−0.379497	−0.189749	+	0.981833i	$0.560767\pi$
$152$	1.46335	0.118693
$153$	−0.154687	−0.0125057
$154$	0	0
$155$	2.98578	0.239824
$156$	5.25908	0.421063
$157$	21.9461	1.75149	0.875747	−	0.482771i	$-0.160370\pi$
$157$	21.9461	1.75149	0.875747	+	0.482771i	$0.160370\pi$
$158$	−6.78958	−0.540150
$159$	10.5765	0.838773
$160$	−1.00000	−0.0790569
$161$	−10.8622	−0.856059
$162$	−1.00000	−0.0785674
$163$	12.5984	0.986781	0.493391	−	0.869808i	$-0.335757\pi$
$163$	12.5984	0.986781	0.493391	+	0.869808i	$0.335757\pi$
$164$	−8.41377	−0.657005
$165$	0	0
$166$	−1.52786	−0.118585
$167$	2.05145	0.158746	0.0793731	−	0.996845i	$-0.474708\pi$
$167$	2.05145	0.158746	0.0793731	+	0.996845i	$0.474708\pi$
$168$	2.86832	0.221296
$169$	14.6579	1.12753
$170$	0.154687	0.0118640
$171$	−1.46335	−0.111905
$172$	−7.86289	−0.599540
$173$	9.64983	0.733663	0.366832	−	0.930287i	$-0.380443\pi$
$173$	9.64983	0.733663	0.366832	+	0.930287i	$0.380443\pi$
$174$	−3.48636	−0.264300
$175$	−2.86832	−0.216825
$176$	0	0
$177$	7.92741	0.595861
$178$	10.8859	0.815933
$179$	−21.7711	−1.62725	−0.813624	−	0.581392i	$-0.802508\pi$
$179$	−21.7711	−1.62725	−0.813624	+	0.581392i	$0.802508\pi$
$180$	1.00000	0.0745356
$181$	−8.00000	−0.594635	−0.297318	−	0.954779i	$-0.596092\pi$
$181$	−8.00000	−0.594635	−0.297318	+	0.954779i	$0.596092\pi$
$182$	15.0847	1.11816
$183$	−1.73665	−0.128377
$184$	−3.78694	−0.279177
$185$	8.85410	0.650967
$186$	−2.98578	−0.218928
$187$	0	0
$188$	−10.9957	−0.801946
$189$	−2.86832	−0.208640
$190$	1.46335	0.106162
$191$	−22.7991	−1.64968	−0.824842	−	0.565363i	$-0.808736\pi$
$191$	−22.7991	−1.64968	−0.824842	+	0.565363i	$0.808736\pi$
$192$	1.00000	0.0721688
$193$	27.0187	1.94485	0.972426	−	0.233213i	$-0.0749241\pi$
$193$	27.0187	1.94485	0.972426	+	0.233213i	$0.0749241\pi$
$194$	−19.4449	−1.39606
$195$	5.25908	0.376610
$196$	1.22728	0.0876628
$197$	21.9929	1.56693	0.783466	−	0.621435i	$-0.213450\pi$
$197$	21.9929	1.56693	0.783466	+	0.621435i	$0.213450\pi$
$198$	0	0
$199$	4.65527	0.330003	0.165002	−	0.986293i	$-0.447237\pi$
$199$	4.65527	0.330003	0.165002	+	0.986293i	$0.447237\pi$
$200$	−1.00000	−0.0707107
$201$	−11.2406	−0.792850
$202$	4.15469	0.292323
$203$	−10.0000	−0.701862
$204$	−0.154687	−0.0108303
$205$	−8.41377	−0.587643
$206$	−5.46335	−0.380649
$207$	3.78694	0.263211
$208$	5.25908	0.364651
$209$	0	0
$210$	2.86832	0.197933
$211$	−10.0284	−0.690386	−0.345193	−	0.938532i	$-0.612187\pi$
$211$	−10.0284	−0.690386	−0.345193	+	0.938532i	$0.612187\pi$
$212$	10.5765	0.726399
$213$	3.54544	0.242930
$214$	−15.7827	−1.07888
$215$	−7.86289	−0.536245
$216$	−1.00000	−0.0680414
$217$	−8.56418	−0.581374
$218$	−5.52786	−0.374394
$219$	6.00000	0.405442
$220$	0	0
$221$	−0.813513	−0.0547228
$222$	−8.85410	−0.594248
$223$	−15.0771	−1.00964	−0.504819	−	0.863225i	$-0.668441\pi$
$223$	−15.0771	−1.00964	−0.504819	+	0.863225i	$0.668441\pi$
$224$	2.86832	0.191648
$225$	1.00000	0.0666667
$226$	−2.75087	−0.182985
$227$	−29.7718	−1.97602	−0.988012	−	0.154377i	$-0.950663\pi$
$227$	−29.7718	−1.97602	−0.988012	+	0.154377i	$0.950663\pi$
$228$	−1.46335	−0.0969125
$229$	16.4460	1.08678	0.543391	−	0.839479i	$-0.317140\pi$
$229$	16.4460	1.08678	0.543391	+	0.839479i	$0.317140\pi$
$230$	−3.78694	−0.249704
$231$	0	0
$232$	−3.48636	−0.228891
$233$	0.0130640	0.000855852 0	0.000427926	−	1.00000i	$-0.499864\pi$
$233$	0.0130640	0.000855852 0	0.000427926		1.00000i	$0.499864\pi$
$234$	−5.25908	−0.343797
$235$	−10.9957	−0.717282
$236$	7.92741	0.516030
$237$	6.78958	0.441031
$238$	−0.443693	−0.0287604
$239$	−25.1246	−1.62518	−0.812588	−	0.582838i	$-0.801942\pi$
$239$	−25.1246	−1.62518	−0.812588	+	0.582838i	$0.801942\pi$
$240$	1.00000	0.0645497
$241$	1.91319	0.123239	0.0616196	−	0.998100i	$-0.480373\pi$
$241$	1.91319	0.123239	0.0616196	+	0.998100i	$0.480373\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	−1.73665	−0.111177
$245$	1.22728	0.0784080
$246$	8.41377	0.536442
$247$	−7.69586	−0.489676
$248$	−2.98578	−0.189597
$249$	1.52786	0.0968244
$250$	−1.00000	−0.0632456
$251$	15.8951	1.00329	0.501646	−	0.865073i	$-0.332728\pi$
$251$	15.8951	1.00329	0.501646	+	0.865073i	$0.332728\pi$
$252$	−2.86832	−0.180687
$253$	0	0
$254$	−13.2000	−0.828241
$255$	−0.154687	−0.00968690
$256$	1.00000	0.0625000
$257$	−5.41641	−0.337866	−0.168933	−	0.985628i	$-0.554032\pi$
$257$	−5.41641	−0.337866	−0.168933	+	0.985628i	$0.554032\pi$
$258$	7.86289	0.489522
$259$	−25.3964	−1.57806
$260$	5.25908	0.326154
$261$	3.48636	0.215800
$262$	−7.66670	−0.473650
$263$	3.56115	0.219590	0.109795	−	0.993954i	$-0.464981\pi$
$263$	3.56115	0.219590	0.109795	+	0.993954i	$0.464981\pi$
$264$	0	0
$265$	10.5765	0.649711
$266$	−4.19735	−0.257356
$267$	−10.8859	−0.666206
$268$	−11.2406	−0.686628
$269$	4.76845	0.290737	0.145369	−	0.989378i	$-0.453563\pi$
$269$	4.76845	0.290737	0.145369	+	0.989378i	$0.453563\pi$
$270$	−1.00000	−0.0608581
$271$	−8.52623	−0.517932	−0.258966	−	0.965886i	$-0.583382\pi$
$271$	−8.52623	−0.517932	−0.258966	+	0.965886i	$0.583382\pi$
$272$	−0.154687	−0.00937930
$273$	−15.0847	−0.912970
$274$	12.5597	0.758757
$275$	0	0
$276$	3.78694	0.227947
$277$	−31.8558	−1.91403	−0.957016	−	0.290037i	$-0.906333\pi$
$277$	−31.8558	−1.91403	−0.957016	+	0.290037i	$0.906333\pi$
$278$	−19.0771	−1.14417
$279$	2.98578	0.178754
$280$	2.86832	0.171415
$281$	−10.9443	−0.652881	−0.326440	−	0.945218i	$-0.605849\pi$
$281$	−10.9443	−0.652881	−0.326440	+	0.945218i	$0.605849\pi$
$282$	10.9957	0.654786
$283$	15.4033	0.915634	0.457817	−	0.889047i	$-0.348632\pi$
$283$	15.4033	0.915634	0.457817	+	0.889047i	$0.348632\pi$
$284$	3.54544	0.210383
$285$	−1.46335	−0.0866812
$286$	0	0
$287$	24.1334	1.42455
$288$	−1.00000	−0.0589256
$289$	−16.9761	−0.998592
$290$	−3.48636	−0.204726
$291$	19.4449	1.13988
$292$	6.00000	0.351123
$293$	−3.17770	−0.185643	−0.0928215	−	0.995683i	$-0.529589\pi$
$293$	−3.17770	−0.185643	−0.0928215	+	0.995683i	$0.529589\pi$
$294$	−1.22728	−0.0715763
$295$	7.92741	0.461552
$296$	−8.85410	−0.514634
$297$	0	0
$298$	−12.1547	−0.704102
$299$	19.9158	1.15176
$300$	1.00000	0.0577350
$301$	22.5533	1.29995
$302$	4.66334	0.268345
$303$	−4.15469	−0.238681
$304$	−1.46335	−0.0839287
$305$	−1.73665	−0.0994401
$306$	0.154687	0.00884289
$307$	−6.91363	−0.394582	−0.197291	−	0.980345i	$-0.563214\pi$
$307$	−6.91363	−0.394582	−0.197291	+	0.980345i	$0.563214\pi$
$308$	0	0
$309$	5.46335	0.310799
$310$	−2.98578	−0.169581
$311$	11.3105	0.641361	0.320681	−	0.947187i	$-0.396088\pi$
$311$	11.3105	0.641361	0.320681	+	0.947187i	$0.396088\pi$
$312$	−5.25908	−0.297737
$313$	19.4909	1.10169	0.550845	−	0.834608i	$-0.314306\pi$
$313$	19.4909	1.10169	0.550845	+	0.834608i	$0.314306\pi$
$314$	−21.9461	−1.23849
$315$	−2.86832	−0.161612
$316$	6.78958	0.381944
$317$	−13.0994	−0.735736	−0.367868	−	0.929878i	$-0.619912\pi$
$317$	−13.0994	−0.735736	−0.367868	+	0.929878i	$0.619912\pi$
$318$	−10.5765	−0.593102
$319$	0	0
$320$	1.00000	0.0559017
$321$	15.7827	0.880903
$322$	10.8622	0.605325
$323$	0.226361	0.0125951
$324$	1.00000	0.0555556
$325$	5.25908	0.291721
$326$	−12.5984	−0.697760
$327$	5.52786	0.305692
$328$	8.41377	0.464573
$329$	31.5393	1.73882
$330$	0	0
$331$	19.8064	1.08866	0.544330	−	0.838871i	$-0.316784\pi$
$331$	19.8064	1.08866	0.544330	+	0.838871i	$0.316784\pi$
$332$	1.52786	0.0838524
$333$	8.85410	0.485202
$334$	−2.05145	−0.112251
$335$	−11.2406	−0.614139
$336$	−2.86832	−0.156480
$337$	19.7258	1.07453	0.537266	−	0.843413i	$-0.319457\pi$
$337$	19.7258	1.07453	0.537266	+	0.843413i	$0.319457\pi$
$338$	−14.6579	−0.797285
$339$	2.75087	0.149407
$340$	−0.154687	−0.00838910
$341$	0	0
$342$	1.46335	0.0791287
$343$	16.5580	0.894050
$344$	7.86289	0.423939
$345$	3.78694	0.203882
$346$	−9.64983	−0.518778
$347$	31.1085	1.66999	0.834995	−	0.550258i	$-0.185471\pi$
$347$	31.1085	1.66999	0.834995	+	0.550258i	$0.185471\pi$
$348$	3.48636	0.186888
$349$	26.2832	1.40691	0.703455	−	0.710740i	$-0.251640\pi$
$349$	26.2832	1.40691	0.703455	+	0.710740i	$0.251640\pi$
$350$	2.86832	0.153318
$351$	5.25908	0.280709
$352$	0	0
$353$	−33.6456	−1.79077	−0.895386	−	0.445290i	$-0.853100\pi$
$353$	−33.6456	−1.79077	−0.895386	+	0.445290i	$0.853100\pi$
$354$	−7.92741	−0.421337
$355$	3.54544	0.188173
$356$	−10.8859	−0.576952
$357$	0.443693	0.0234827
$358$	21.7711	1.15064
$359$	−15.3281	−0.808987	−0.404493	−	0.914541i	$-0.632552\pi$
$359$	−15.3281	−0.808987	−0.404493	+	0.914541i	$0.632552\pi$
$360$	−1.00000	−0.0527046
$361$	−16.8586	−0.887296
$362$	8.00000	0.420471
$363$	0	0
$364$	−15.0847	−0.790655
$365$	6.00000	0.314054
$366$	1.73665	0.0907760
$367$	−7.91699	−0.413263	−0.206632	−	0.978419i	$-0.566250\pi$
$367$	−7.91699	−0.413263	−0.206632	+	0.978419i	$0.566250\pi$
$368$	3.78694	0.197408
$369$	−8.41377	−0.438003
$370$	−8.85410	−0.460303
$371$	−30.3369	−1.57501
$372$	2.98578	0.154805
$373$	0.756300	0.0391597	0.0195799	−	0.999808i	$-0.493767\pi$
$373$	0.756300	0.0391597	0.0195799	+	0.999808i	$0.493767\pi$
$374$	0	0
$375$	1.00000	0.0516398
$376$	10.9957	0.567061
$377$	18.3350	0.944302
$378$	2.86832	0.147531
$379$	17.5331	0.900615	0.450307	−	0.892874i	$-0.351314\pi$
$379$	17.5331	0.900615	0.450307	+	0.892874i	$0.351314\pi$
$380$	−1.46335	−0.0750681
$381$	13.2000	0.676256
$382$	22.7991	1.16650
$383$	−11.2652	−0.575626	−0.287813	−	0.957687i	$-0.592928\pi$
$383$	−11.2652	−0.575626	−0.287813	+	0.957687i	$0.592928\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−27.0187	−1.37522
$387$	−7.86289	−0.399693
$388$	19.4449	0.987163
$389$	−4.49250	−0.227779	−0.113890	−	0.993493i	$-0.536331\pi$
$389$	−4.49250	−0.227779	−0.113890	+	0.993493i	$0.536331\pi$
$390$	−5.25908	−0.266304
$391$	−0.585792	−0.0296248
$392$	−1.22728	−0.0619869
$393$	7.66670	0.386734
$394$	−21.9929	−1.10799
$395$	6.78958	0.341621
$396$	0	0
$397$	34.3335	1.72315	0.861576	−	0.507629i	$-0.169478\pi$
$397$	34.3335	1.72315	0.861576	+	0.507629i	$0.169478\pi$
$398$	−4.65527	−0.233347
$399$	4.19735	0.210130
$400$	1.00000	0.0500000
$401$	−14.0997	−0.704104	−0.352052	−	0.935980i	$-0.614516\pi$
$401$	−14.0997	−0.704104	−0.352052	+	0.935980i	$0.614516\pi$
$402$	11.2406	0.560629
$403$	15.7024	0.782194
$404$	−4.15469	−0.206703
$405$	1.00000	0.0496904
$406$	10.0000	0.496292
$407$	0	0
$408$	0.154687	0.00765816
$409$	23.7312	1.17343	0.586717	−	0.809792i	$-0.300420\pi$
$409$	23.7312	1.17343	0.586717	+	0.809792i	$0.300420\pi$
$410$	8.41377	0.415526
$411$	−12.5597	−0.619523
$412$	5.46335	0.269160
$413$	−22.7384	−1.11888
$414$	−3.78694	−0.186118
$415$	1.52786	0.0749999
$416$	−5.25908	−0.257848
$417$	19.0771	0.934210
$418$	0	0
$419$	3.09133	0.151021	0.0755106	−	0.997145i	$-0.475941\pi$
$419$	3.09133	0.151021	0.0755106	+	0.997145i	$0.475941\pi$
$420$	−2.86832	−0.139960
$421$	−24.0797	−1.17358	−0.586788	−	0.809741i	$-0.699608\pi$
$421$	−24.0797	−1.17358	−0.586788	+	0.809741i	$0.699608\pi$
$422$	10.0284	0.488177
$423$	−10.9957	−0.534630
$424$	−10.5765	−0.513642
$425$	−0.154687	−0.00750344
$426$	−3.54544	−0.171777
$427$	4.98126	0.241060
$428$	15.7827	0.762884
$429$	0	0
$430$	7.86289	0.379182
$431$	19.7718	0.952374	0.476187	−	0.879344i	$-0.342018\pi$
$431$	19.7718	0.952374	0.476187	+	0.879344i	$0.342018\pi$
$432$	1.00000	0.0481125
$433$	14.0622	0.675785	0.337892	−	0.941185i	$-0.390286\pi$
$433$	14.0622	0.675785	0.337892	+	0.941185i	$0.390286\pi$
$434$	8.56418	0.411094
$435$	3.48636	0.167158
$436$	5.52786	0.264737
$437$	−5.54161	−0.265091
$438$	−6.00000	−0.286691
$439$	−16.2110	−0.773708	−0.386854	−	0.922141i	$-0.626438\pi$
$439$	−16.2110	−0.773708	−0.386854	+	0.922141i	$0.626438\pi$
$440$	0	0
$441$	1.22728	0.0584418
$442$	0.813513	0.0386949
$443$	9.59146	0.455704	0.227852	−	0.973696i	$-0.426830\pi$
$443$	9.59146	0.455704	0.227852	+	0.973696i	$0.426830\pi$
$444$	8.85410	0.420197
$445$	−10.8859	−0.516041
$446$	15.0771	0.713922
$447$	12.1547	0.574897
$448$	−2.86832	−0.135516
$449$	−34.2909	−1.61829	−0.809143	−	0.587611i	$-0.800068\pi$
$449$	−34.2909	−1.61829	−0.809143	+	0.587611i	$0.800068\pi$
$450$	−1.00000	−0.0471405
$451$	0	0
$452$	2.75087	0.129390
$453$	−4.66334	−0.219103
$454$	29.7718	1.39726
$455$	−15.0847	−0.707183
$456$	1.46335	0.0685275
$457$	8.44369	0.394979	0.197490	−	0.980305i	$-0.436721\pi$
$457$	8.44369	0.394979	0.197490	+	0.980305i	$0.436721\pi$
$458$	−16.4460	−0.768471
$459$	−0.154687	−0.00722019
$460$	3.78694	0.176567
$461$	1.27258	0.0592702	0.0296351	−	0.999561i	$-0.490565\pi$
$461$	1.27258	0.0592702	0.0296351	+	0.999561i	$0.490565\pi$
$462$	0	0
$463$	−32.5903	−1.51460	−0.757299	−	0.653068i	$-0.773482\pi$
$463$	−32.5903	−1.51460	−0.757299	+	0.653068i	$0.773482\pi$
$464$	3.48636	0.161850
$465$	2.98578	0.138462
$466$	−0.0130640	−0.000605179 0
$467$	11.4571	0.530173	0.265087	−	0.964225i	$-0.414599\pi$
$467$	11.4571	0.530173	0.265087	+	0.964225i	$0.414599\pi$
$468$	5.25908	0.243101
$469$	32.2416	1.48878
$470$	10.9957	0.507195
$471$	21.9461	1.01122
$472$	−7.92741	−0.364889
$473$	0	0
$474$	−6.78958	−0.311856
$475$	−1.46335	−0.0671430
$476$	0.443693	0.0203366
$477$	10.5765	0.484266
$478$	25.1246	1.14917
$479$	4.57504	0.209039	0.104520	−	0.994523i	$-0.466670\pi$
$479$	4.57504	0.209039	0.104520	+	0.994523i	$0.466670\pi$
$480$	−1.00000	−0.0456435
$481$	46.5644	2.12315
$482$	−1.91319	−0.0871433
$483$	−10.8622	−0.494246
$484$	0	0
$485$	19.4449	0.882945
$486$	−1.00000	−0.0453609
$487$	22.7977	1.03306	0.516530	−	0.856269i	$-0.327223\pi$
$487$	22.7977	1.03306	0.516530	+	0.856269i	$0.327223\pi$
$488$	1.73665	0.0786143
$489$	12.5984	0.569718
$490$	−1.22728	−0.0554428
$491$	13.9684	0.630387	0.315193	−	0.949027i	$-0.397931\pi$
$491$	13.9684	0.630387	0.315193	+	0.949027i	$0.397931\pi$
$492$	−8.41377	−0.379322
$493$	−0.539295	−0.0242886
$494$	7.69586	0.346253
$495$	0	0
$496$	2.98578	0.134065
$497$	−10.1695	−0.456163
$498$	−1.52786	−0.0684652
$499$	23.6128	1.05706	0.528528	−	0.848916i	$-0.322744\pi$
$499$	23.6128	1.05706	0.528528	+	0.848916i	$0.322744\pi$
$500$	1.00000	0.0447214
$501$	2.05145	0.0916522
$502$	−15.8951	−0.709435
$503$	3.97699	0.177325	0.0886626	−	0.996062i	$-0.471741\pi$
$503$	3.97699	0.177325	0.0886626	+	0.996062i	$0.471741\pi$
$504$	2.86832	0.127765
$505$	−4.15469	−0.184881
$506$	0	0
$507$	14.6579	0.650981
$508$	13.2000	0.585655
$509$	−16.3139	−0.723100	−0.361550	−	0.932353i	$-0.617752\pi$
$509$	−16.3139	−0.723100	−0.361550	+	0.932353i	$0.617752\pi$
$510$	0.154687	0.00684967
$511$	−17.2099	−0.761323
$512$	−1.00000	−0.0441942
$513$	−1.46335	−0.0646083
$514$	5.41641	0.238908
$515$	5.46335	0.240744
$516$	−7.86289	−0.346144
$517$	0	0
$518$	25.3964	1.11585
$519$	9.64983	0.423581
$520$	−5.25908	−0.230626
$521$	−11.4856	−0.503195	−0.251598	−	0.967832i	$-0.580956\pi$
$521$	−11.4856	−0.503195	−0.251598	+	0.967832i	$0.580956\pi$
$522$	−3.48636	−0.152594
$523$	−36.6263	−1.60156	−0.800779	−	0.598960i	$-0.795581\pi$
$523$	−36.6263	−1.60156	−0.800779	+	0.598960i	$0.795581\pi$
$524$	7.66670	0.334921
$525$	−2.86832	−0.125184
$526$	−3.56115	−0.155273
$527$	−0.461862	−0.0201190
$528$	0	0
$529$	−8.65907	−0.376481
$530$	−10.5765	−0.459415
$531$	7.92741	0.344020
$532$	4.19735	0.181978
$533$	−44.2487	−1.91662
$534$	10.8859	0.471079
$535$	15.7827	0.682344
$536$	11.2406	0.485519
$537$	−21.7711	−0.939492
$538$	−4.76845	−0.205582
$539$	0	0
$540$	1.00000	0.0430331
$541$	−33.3457	−1.43364	−0.716822	−	0.697257i	$-0.754404\pi$
$541$	−33.3457	−1.43364	−0.716822	+	0.697257i	$0.754404\pi$
$542$	8.52623	0.366233
$543$	−8.00000	−0.343313
$544$	0.154687	0.00663216
$545$	5.52786	0.236788
$546$	15.0847	0.645567
$547$	32.0928	1.37219	0.686095	−	0.727512i	$-0.259324\pi$
$547$	32.0928	1.37219	0.686095	+	0.727512i	$0.259324\pi$
$548$	−12.5597	−0.536522
$549$	−1.73665	−0.0741183
$550$	0	0
$551$	−5.10175	−0.217342
$552$	−3.78694	−0.161183
$553$	−19.4747	−0.828149
$554$	31.8558	1.35342
$555$	8.85410	0.375836
$556$	19.0771	0.809050
$557$	−8.18126	−0.346651	−0.173326	−	0.984865i	$-0.555451\pi$
$557$	−8.18126	−0.346651	−0.173326	+	0.984865i	$0.555451\pi$
$558$	−2.98578	−0.126398
$559$	−41.3516	−1.74898
$560$	−2.86832	−0.121209
$561$	0	0
$562$	10.9443	0.461656
$563$	9.71907	0.409610	0.204805	−	0.978803i	$-0.434344\pi$
$563$	9.71907	0.409610	0.204805	+	0.978803i	$0.434344\pi$
$564$	−10.9957	−0.463004
$565$	2.75087	0.115730
$566$	−15.4033	−0.647451
$567$	−2.86832	−0.120458
$568$	−3.54544	−0.148763
$569$	−25.2574	−1.05885	−0.529424	−	0.848358i	$-0.677592\pi$
$569$	−25.2574	−1.05885	−0.529424	+	0.848358i	$0.677592\pi$
$570$	1.46335	0.0612928
$571$	−28.7407	−1.20276	−0.601381	−	0.798963i	$-0.705383\pi$
$571$	−28.7407	−1.20276	−0.601381	+	0.798963i	$0.705383\pi$
$572$	0	0
$573$	−22.7991	−0.952446
$574$	−24.1334	−1.00731
$575$	3.78694	0.157926
$576$	1.00000	0.0416667
$577$	11.3542	0.472683	0.236342	−	0.971670i	$-0.424052\pi$
$577$	11.3542	0.472683	0.236342	+	0.971670i	$0.424052\pi$
$578$	16.9761	0.706112
$579$	27.0187	1.12286
$580$	3.48636	0.144763
$581$	−4.38241	−0.181813
$582$	−19.4449	−0.806015
$583$	0	0
$584$	−6.00000	−0.248282
$585$	5.25908	0.217436
$586$	3.17770	0.131269
$587$	−39.5246	−1.63135	−0.815677	−	0.578507i	$-0.803636\pi$
$587$	−39.5246	−1.63135	−0.815677	+	0.578507i	$0.803636\pi$
$588$	1.22728	0.0506121
$589$	−4.36923	−0.180031
$590$	−7.92741	−0.326366
$591$	21.9929	0.904668
$592$	8.85410	0.363901
$593$	16.7224	0.686708	0.343354	−	0.939206i	$-0.388437\pi$
$593$	16.7224	0.686708	0.343354	+	0.939206i	$0.388437\pi$
$594$	0	0
$595$	0.443693	0.0181896
$596$	12.1547	0.497875
$597$	4.65527	0.190527
$598$	−19.9158	−0.814419
$599$	−41.0823	−1.67858	−0.839289	−	0.543685i	$-0.817029\pi$
$599$	−41.0823	−1.67858	−0.839289	+	0.543685i	$0.817029\pi$
$600$	−1.00000	−0.0408248
$601$	−20.0114	−0.816281	−0.408141	−	0.912919i	$-0.633823\pi$
$601$	−20.0114	−0.816281	−0.408141	+	0.912919i	$0.633823\pi$
$602$	−22.5533	−0.919204
$603$	−11.2406	−0.457752
$604$	−4.66334	−0.189749
$605$	0	0
$606$	4.15469	0.168773
$607$	0.392388	0.0159265	0.00796327	−	0.999968i	$-0.497465\pi$
$607$	0.392388	0.0159265	0.00796327	+	0.999968i	$0.497465\pi$
$608$	1.46335	0.0593465
$609$	−10.0000	−0.405220
$610$	1.73665	0.0703148
$611$	−57.8274	−2.33945
$612$	−0.154687	−0.00625286
$613$	−27.0932	−1.09428	−0.547142	−	0.837040i	$-0.684284\pi$
$613$	−27.0932	−1.09428	−0.547142	+	0.837040i	$0.684284\pi$
$614$	6.91363	0.279011
$615$	−8.41377	−0.339276
$616$	0	0
$617$	−22.7554	−0.916097	−0.458049	−	0.888927i	$-0.651451\pi$
$617$	−22.7554	−0.916097	−0.458049	+	0.888927i	$0.651451\pi$
$618$	−5.46335	−0.219768
$619$	−11.5639	−0.464794	−0.232397	−	0.972621i	$-0.574657\pi$
$619$	−11.5639	−0.464794	−0.232397	+	0.972621i	$0.574657\pi$
$620$	2.98578	0.119912
$621$	3.78694	0.151965
$622$	−11.3105	−0.453511
$623$	31.2243	1.25097
$624$	5.25908	0.210532
$625$	1.00000	0.0400000
$626$	−19.4909	−0.779012
$627$	0	0
$628$	21.9461	0.875747
$629$	−1.36962	−0.0546102
$630$	2.86832	0.114277
$631$	−16.8515	−0.670846	−0.335423	−	0.942068i	$-0.608879\pi$
$631$	−16.8515	−0.670846	−0.335423	+	0.942068i	$0.608879\pi$
$632$	−6.78958	−0.270075
$633$	−10.0284	−0.398595
$634$	13.0994	0.520244
$635$	13.2000	0.523826
$636$	10.5765	0.419387
$637$	6.45436	0.255731
$638$	0	0
$639$	3.54544	0.140256
$640$	−1.00000	−0.0395285
$641$	36.3137	1.43431	0.717153	−	0.696915i	$-0.245445\pi$
$641$	36.3137	1.43431	0.717153	+	0.696915i	$0.245445\pi$
$642$	−15.7827	−0.622892
$643$	6.46994	0.255149	0.127575	−	0.991829i	$-0.459281\pi$
$643$	6.46994	0.255149	0.127575	+	0.991829i	$0.459281\pi$
$644$	−10.8622	−0.428030
$645$	−7.86289	−0.309601
$646$	−0.226361	−0.00890606
$647$	23.9374	0.941075	0.470537	−	0.882380i	$-0.344060\pi$
$647$	23.9374	0.941075	0.470537	+	0.882380i	$0.344060\pi$
$648$	−1.00000	−0.0392837
$649$	0	0
$650$	−5.25908	−0.206278
$651$	−8.56418	−0.335657
$652$	12.5984	0.493391
$653$	8.35073	0.326789	0.163395	−	0.986561i	$-0.447756\pi$
$653$	8.35073	0.326789	0.163395	+	0.986561i	$0.447756\pi$
$654$	−5.52786	−0.216157
$655$	7.66670	0.299563
$656$	−8.41377	−0.328502
$657$	6.00000	0.234082
$658$	−31.5393	−1.22953
$659$	16.2510	0.633049	0.316525	−	0.948584i	$-0.397484\pi$
$659$	16.2510	0.633049	0.316525	+	0.948584i	$0.397484\pi$
$660$	0	0
$661$	2.26335	0.0880342	0.0440171	−	0.999031i	$-0.485984\pi$
$661$	2.26335	0.0880342	0.0440171	+	0.999031i	$0.485984\pi$
$662$	−19.8064	−0.769799
$663$	−0.813513	−0.0315942
$664$	−1.52786	−0.0592926
$665$	4.19735	0.162766
$666$	−8.85410	−0.343089
$667$	13.2026	0.511208
$668$	2.05145	0.0793731
$669$	−15.0771	−0.582915
$670$	11.2406	0.434262
$671$	0	0
$672$	2.86832	0.110648
$673$	−31.4624	−1.21279	−0.606394	−	0.795165i	$-0.707384\pi$
$673$	−31.4624	−1.21279	−0.606394	+	0.795165i	$0.707384\pi$
$674$	−19.7258	−0.759809
$675$	1.00000	0.0384900
$676$	14.6579	0.563766
$677$	−22.2102	−0.853608	−0.426804	−	0.904344i	$-0.640361\pi$
$677$	−22.2102	−0.853608	−0.426804	+	0.904344i	$0.640361\pi$
$678$	−2.75087	−0.105646
$679$	−55.7741	−2.14041
$680$	0.154687	0.00593199
$681$	−29.7718	−1.14086
$682$	0	0
$683$	19.1269	0.731872	0.365936	−	0.930640i	$-0.380749\pi$
$683$	19.1269	0.731872	0.365936	+	0.930640i	$0.380749\pi$
$684$	−1.46335	−0.0559525
$685$	−12.5597	−0.479880
$686$	−16.5580	−0.632189
$687$	16.4460	0.627454
$688$	−7.86289	−0.299770
$689$	55.6228	2.11906
$690$	−3.78694	−0.144166
$691$	31.5691	1.20095	0.600473	−	0.799645i	$-0.294979\pi$
$691$	31.5691	1.20095	0.600473	+	0.799645i	$0.294979\pi$
$692$	9.64983	0.366832
$693$	0	0
$694$	−31.1085	−1.18086
$695$	19.0771	0.723636
$696$	−3.48636	−0.132150
$697$	1.30150	0.0492979
$698$	−26.2832	−0.994836
$699$	0.0130640	0.000494126 0
$700$	−2.86832	−0.108412
$701$	50.7535	1.91694	0.958468	−	0.285202i	$-0.0920606\pi$
$701$	50.7535	1.91694	0.958468	+	0.285202i	$0.0920606\pi$
$702$	−5.25908	−0.198491
$703$	−12.9566	−0.488668
$704$	0	0
$705$	−10.9957	−0.414123
$706$	33.6456	1.26627
$707$	11.9170	0.448184
$708$	7.92741	0.297930
$709$	−8.88210	−0.333574	−0.166787	−	0.985993i	$-0.553339\pi$
$709$	−8.88210	−0.333574	−0.166787	+	0.985993i	$0.553339\pi$
$710$	−3.54544	−0.133058
$711$	6.78958	0.254629
$712$	10.8859	0.407966
$713$	11.3070	0.423449
$714$	−0.443693	−0.0166048
$715$	0	0
$716$	−21.7711	−0.813624
$717$	−25.1246	−0.938296
$718$	15.3281	0.572040
$719$	−28.7815	−1.07337	−0.536685	−	0.843783i	$-0.680323\pi$
$719$	−28.7815	−1.07337	−0.536685	+	0.843783i	$0.680323\pi$
$720$	1.00000	0.0372678
$721$	−15.6706	−0.583605
$722$	16.8586	0.627413
$723$	1.91319	0.0711522
$724$	−8.00000	−0.297318
$725$	3.48636	0.129480
$726$	0	0
$727$	34.4759	1.27864	0.639321	−	0.768940i	$-0.279216\pi$
$727$	34.4759	1.27864	0.639321	+	0.768940i	$0.279216\pi$
$728$	15.0847	0.559078
$729$	1.00000	0.0370370
$730$	−6.00000	−0.222070
$731$	1.21629	0.0449861
$732$	−1.73665	−0.0641883
$733$	−29.0851	−1.07428	−0.537142	−	0.843492i	$-0.680496\pi$
$733$	−29.0851	−1.07428	−0.537142	+	0.843492i	$0.680496\pi$
$734$	7.91699	0.292221
$735$	1.22728	0.0452689
$736$	−3.78694	−0.139589
$737$	0	0
$738$	8.41377	0.309715
$739$	30.3199	1.11534	0.557668	−	0.830064i	$-0.311696\pi$
$739$	30.3199	1.11534	0.557668	+	0.830064i	$0.311696\pi$
$740$	8.85410	0.325483
$741$	−7.69586	−0.282714
$742$	30.3369	1.11370
$743$	−35.8347	−1.31465	−0.657324	−	0.753608i	$-0.728312\pi$
$743$	−35.8347	−1.31465	−0.657324	+	0.753608i	$0.728312\pi$
$744$	−2.98578	−0.109464
$745$	12.1547	0.445313
$746$	−0.756300	−0.0276901
$747$	1.52786	0.0559016
$748$	0	0
$749$	−45.2698	−1.65412
$750$	−1.00000	−0.0365148
$751$	−30.5438	−1.11456	−0.557280	−	0.830325i	$-0.688155\pi$
$751$	−30.5438	−1.11456	−0.557280	+	0.830325i	$0.688155\pi$
$752$	−10.9957	−0.400973
$753$	15.8951	0.579251
$754$	−18.3350	−0.667722
$755$	−4.66334	−0.169716
$756$	−2.86832	−0.104320
$757$	17.0579	0.619980	0.309990	−	0.950740i	$-0.399674\pi$
$757$	17.0579	0.619980	0.309990	+	0.950740i	$0.399674\pi$
$758$	−17.5331	−0.636831
$759$	0	0
$760$	1.46335	0.0530812
$761$	49.5085	1.79468	0.897340	−	0.441340i	$-0.145497\pi$
$761$	49.5085	1.79468	0.897340	+	0.441340i	$0.145497\pi$
$762$	−13.2000	−0.478185
$763$	−15.8557	−0.574015
$764$	−22.7991	−0.824842
$765$	−0.154687	−0.00559273
$766$	11.2652	0.407029
$767$	41.6909	1.50537
$768$	1.00000	0.0360844
$769$	−32.6881	−1.17876	−0.589381	−	0.807855i	$-0.700628\pi$
$769$	−32.6881	−1.17876	−0.589381	+	0.807855i	$0.700628\pi$
$770$	0	0
$771$	−5.41641	−0.195067
$772$	27.0187	0.972426
$773$	−33.4325	−1.20248	−0.601242	−	0.799067i	$-0.705327\pi$
$773$	−33.4325	−1.20248	−0.601242	+	0.799067i	$0.705327\pi$
$774$	7.86289	0.282626
$775$	2.98578	0.107252
$776$	−19.4449	−0.698029
$777$	−25.3964	−0.911092
$778$	4.49250	0.161064
$779$	12.3123	0.441132
$780$	5.25908	0.188305
$781$	0	0
$782$	0.585792	0.0209479
$783$	3.48636	0.124592
$784$	1.22728	0.0438314
$785$	21.9461	0.783291
$786$	−7.66670	−0.273462
$787$	−25.7447	−0.917700	−0.458850	−	0.888514i	$-0.651739\pi$
$787$	−25.7447	−0.917700	−0.458850	+	0.888514i	$0.651739\pi$
$788$	21.9929	0.783466
$789$	3.56115	0.126780
$790$	−6.78958	−0.241563
$791$	−7.89038	−0.280550
$792$	0	0
$793$	−9.13316	−0.324328
$794$	−34.3335	−1.21845
$795$	10.5765	0.375111
$796$	4.65527	0.165002
$797$	5.15540	0.182614	0.0913069	−	0.995823i	$-0.470896\pi$
$797$	5.15540	0.182614	0.0913069	+	0.995823i	$0.470896\pi$
$798$	−4.19735	−0.148585
$799$	1.70090	0.0601735
$800$	−1.00000	−0.0353553
$801$	−10.8859	−0.384634
$802$	14.0997	0.497877
$803$	0	0
$804$	−11.2406	−0.396425
$805$	−10.8622	−0.382841
$806$	−15.7024	−0.553095
$807$	4.76845	0.167857
$808$	4.15469	0.146161
$809$	37.9706	1.33498	0.667488	−	0.744620i	$-0.267369\pi$
$809$	37.9706	1.33498	0.667488	+	0.744620i	$0.267369\pi$
$810$	−1.00000	−0.0351364
$811$	−43.0117	−1.51034	−0.755172	−	0.655527i	$-0.772447\pi$
$811$	−43.0117	−1.51034	−0.755172	+	0.655527i	$0.772447\pi$
$812$	−10.0000	−0.350931
$813$	−8.52623	−0.299028
$814$	0	0
$815$	12.5984	0.441302
$816$	−0.154687	−0.00541514
$817$	11.5061	0.402549
$818$	−23.7312	−0.829742
$819$	−15.0847	−0.527103
$820$	−8.41377	−0.293821
$821$	−29.6023	−1.03313	−0.516564	−	0.856248i	$-0.672789\pi$
$821$	−29.6023	−1.03313	−0.516564	+	0.856248i	$0.672789\pi$
$822$	12.5597	0.438069
$823$	−9.27214	−0.323207	−0.161603	−	0.986856i	$-0.551666\pi$
$823$	−9.27214	−0.323207	−0.161603	+	0.986856i	$0.551666\pi$
$824$	−5.46335	−0.190325
$825$	0	0
$826$	22.7384	0.791169
$827$	−20.9926	−0.729985	−0.364992	−	0.931011i	$-0.618928\pi$
$827$	−20.9926	−0.729985	−0.364992	+	0.931011i	$0.618928\pi$
$828$	3.78694	0.131605
$829$	−36.1205	−1.25452	−0.627258	−	0.778811i	$-0.715823\pi$
$829$	−36.1205	−1.25452	−0.627258	+	0.778811i	$0.715823\pi$
$830$	−1.52786	−0.0530329
$831$	−31.8558	−1.10507
$832$	5.25908	0.182326
$833$	−0.189844	−0.00657772
$834$	−19.0771	−0.660586
$835$	2.05145	0.0709935
$836$	0	0
$837$	2.98578	0.103204
$838$	−3.09133	−0.106788
$839$	8.74452	0.301894	0.150947	−	0.988542i	$-0.451768\pi$
$839$	8.74452	0.301894	0.150947	+	0.988542i	$0.451768\pi$
$840$	2.86832	0.0989666
$841$	−16.8453	−0.580873
$842$	24.0797	0.829843
$843$	−10.9443	−0.376941
$844$	−10.0284	−0.345193
$845$	14.6579	0.504247
$846$	10.9957	0.378041
$847$	0	0
$848$	10.5765	0.363199
$849$	15.4033	0.528641
$850$	0.154687	0.00530573
$851$	33.5300	1.14939
$852$	3.54544	0.121465
$853$	12.2762	0.420328	0.210164	−	0.977666i	$-0.432600\pi$
$853$	12.2762	0.420328	0.210164	+	0.977666i	$0.432600\pi$
$854$	−4.98126	−0.170455
$855$	−1.46335	−0.0500454
$856$	−15.7827	−0.539440
$857$	−7.32716	−0.250291	−0.125145	−	0.992138i	$-0.539940\pi$
$857$	−7.32716	−0.250291	−0.125145	+	0.992138i	$0.539940\pi$
$858$	0	0
$859$	−39.0378	−1.33195	−0.665976	−	0.745973i	$-0.731985\pi$
$859$	−39.0378	−1.33195	−0.665976	+	0.745973i	$0.731985\pi$
$860$	−7.86289	−0.268122
$861$	24.1334	0.822464
$862$	−19.7718	−0.673430
$863$	−46.4508	−1.58121	−0.790603	−	0.612330i	$-0.790233\pi$
$863$	−46.4508	−1.58121	−0.790603	+	0.612330i	$0.790233\pi$
$864$	−1.00000	−0.0340207
$865$	9.64983	0.328104
$866$	−14.0622	−0.477852
$867$	−16.9761	−0.576538
$868$	−8.56418	−0.290687
$869$	0	0
$870$	−3.48636	−0.118199
$871$	−59.1151	−2.00304
$872$	−5.52786	−0.187197
$873$	19.4449	0.658108
$874$	5.54161	0.187448
$875$	−2.86832	−0.0969670
$876$	6.00000	0.202721
$877$	11.4752	0.387489	0.193744	−	0.981052i	$-0.437937\pi$
$877$	11.4752	0.387489	0.193744	+	0.981052i	$0.437937\pi$
$878$	16.2110	0.547094
$879$	−3.17770	−0.107181
$880$	0	0
$881$	−3.82114	−0.128738	−0.0643688	−	0.997926i	$-0.520503\pi$
$881$	−3.82114	−0.128738	−0.0643688	+	0.997926i	$0.520503\pi$
$882$	−1.22728	−0.0413246
$883$	11.2194	0.377564	0.188782	−	0.982019i	$-0.439546\pi$
$883$	11.2194	0.377564	0.188782	+	0.982019i	$0.439546\pi$
$884$	−0.813513	−0.0273614
$885$	7.92741	0.266477
$886$	−9.59146	−0.322232
$887$	−44.3564	−1.48934	−0.744671	−	0.667432i	$-0.767394\pi$
$887$	−44.3564	−1.48934	−0.744671	+	0.667432i	$0.767394\pi$
$888$	−8.85410	−0.297124
$889$	−37.8618	−1.26985
$890$	10.8859	0.364896
$891$	0	0
$892$	−15.0771	−0.504819
$893$	16.0906	0.538450
$894$	−12.1547	−0.406514
$895$	−21.7711	−0.727727
$896$	2.86832	0.0958240
$897$	19.9158	0.664970
$898$	34.2909	1.14430
$899$	10.4095	0.347176
$900$	1.00000	0.0333333
$901$	−1.63605	−0.0545049
$902$	0	0
$903$	22.5533	0.750527
$904$	−2.75087	−0.0914925
$905$	−8.00000	−0.265929
$906$	4.66334	0.154929
$907$	−7.79746	−0.258910	−0.129455	−	0.991585i	$-0.541323\pi$
$907$	−7.79746	−0.258910	−0.129455	+	0.991585i	$0.541323\pi$
$908$	−29.7718	−0.988012
$909$	−4.15469	−0.137802
$910$	15.0847	0.500054
$911$	−18.4897	−0.612592	−0.306296	−	0.951936i	$-0.599090\pi$
$911$	−18.4897	−0.612592	−0.306296	+	0.951936i	$0.599090\pi$
$912$	−1.46335	−0.0484563
$913$	0	0
$914$	−8.44369	−0.279293
$915$	−1.73665	−0.0574118
$916$	16.4460	0.543391
$917$	−21.9906	−0.726192
$918$	0.154687	0.00510544
$919$	1.79217	0.0591183	0.0295592	−	0.999563i	$-0.490590\pi$
$919$	1.79217	0.0591183	0.0295592	+	0.999563i	$0.490590\pi$
$920$	−3.78694	−0.124852
$921$	−6.91363	−0.227812
$922$	−1.27258	−0.0419103
$923$	18.6458	0.613733
$924$	0	0
$925$	8.85410	0.291121
$926$	32.5903	1.07098
$927$	5.46335	0.179440
$928$	−3.48636	−0.114445
$929$	−1.88034	−0.0616921	−0.0308461	−	0.999524i	$-0.509820\pi$
$929$	−1.88034	−0.0616921	−0.0308461	+	0.999524i	$0.509820\pi$
$930$	−2.98578	−0.0979075
$931$	−1.79593	−0.0588594
$932$	0.0130640	0.000427926 0
$933$	11.3105	0.370290
$934$	−11.4571	−0.374889
$935$	0	0
$936$	−5.25908	−0.171898
$937$	−24.1433	−0.788729	−0.394364	−	0.918954i	$-0.629035\pi$
$937$	−24.1433	−0.788729	−0.394364	+	0.918954i	$0.629035\pi$
$938$	−32.2416	−1.05273
$939$	19.4909	0.636061
$940$	−10.9957	−0.358641
$941$	18.0306	0.587782	0.293891	−	0.955839i	$-0.405050\pi$
$941$	18.0306	0.587782	0.293891	+	0.955839i	$0.405050\pi$
$942$	−21.9461	−0.715044
$943$	−31.8624	−1.03758
$944$	7.92741	0.258015
$945$	−2.86832	−0.0933066
$946$	0	0
$947$	44.5325	1.44711	0.723555	−	0.690266i	$-0.242507\pi$
$947$	44.5325	1.44711	0.723555	+	0.690266i	$0.242507\pi$
$948$	6.78958	0.220515
$949$	31.5545	1.02430
$950$	1.46335	0.0474772
$951$	−13.0994	−0.424777
$952$	−0.443693	−0.0143802
$953$	32.1623	1.04184	0.520919	−	0.853606i	$-0.325589\pi$
$953$	32.1623	1.04184	0.520919	+	0.853606i	$0.325589\pi$
$954$	−10.5765	−0.342428
$955$	−22.7991	−0.737761
$956$	−25.1246	−0.812588
$957$	0	0
$958$	−4.57504	−0.147813
$959$	36.0252	1.16331
$960$	1.00000	0.0322749
$961$	−22.0851	−0.712423
$962$	−46.5644	−1.50130
$963$	15.7827	0.508589
$964$	1.91319	0.0616196
$965$	27.0187	0.869764
$966$	10.8622	0.349485
$967$	−17.6537	−0.567704	−0.283852	−	0.958868i	$-0.591612\pi$
$967$	−17.6537	−0.567704	−0.283852	+	0.958868i	$0.591612\pi$
$968$	0	0
$969$	0.226361	0.00727177
$970$	−19.4449	−0.624337
$971$	1.60238	0.0514229	0.0257114	−	0.999669i	$-0.491815\pi$
$971$	1.60238	0.0514229	0.0257114	+	0.999669i	$0.491815\pi$
$972$	1.00000	0.0320750
$973$	−54.7193	−1.75422
$974$	−22.7977	−0.730484
$975$	5.25908	0.168425
$976$	−1.73665	−0.0555887
$977$	−8.18177	−0.261758	−0.130879	−	0.991398i	$-0.541780\pi$
$977$	−8.18177	−0.261758	−0.130879	+	0.991398i	$0.541780\pi$
$978$	−12.5984	−0.402852
$979$	0	0
$980$	1.22728	0.0392040
$981$	5.52786	0.176491
$982$	−13.9684	−0.445751
$983$	12.9372	0.412633	0.206316	−	0.978485i	$-0.433852\pi$
$983$	12.9372	0.412633	0.206316	+	0.978485i	$0.433852\pi$
$984$	8.41377	0.268221
$985$	21.9929	0.700753
$986$	0.539295	0.0171747
$987$	31.5393	1.00391
$988$	−7.69586	−0.244838
$989$	−29.7763	−0.946832
$990$	0	0
$991$	4.05553	0.128828	0.0644140	−	0.997923i	$-0.479482\pi$
$991$	4.05553	0.128828	0.0644140	+	0.997923i	$0.479482\pi$
$992$	−2.98578	−0.0947986
$993$	19.8064	0.628539
$994$	10.1695	0.322556
$995$	4.65527	0.147582
$996$	1.52786	0.0484122
$997$	56.9704	1.80427	0.902135	−	0.431453i	$-0.141999\pi$
$997$	56.9704	1.80427	0.902135	+	0.431453i	$0.141999\pi$
$998$	−23.6128	−0.747451
$999$	8.85410	0.280131

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3630.2.a.br.1.2		4
11.2	odd	10		330.2.m.e.301.2	yes	8
11.6	odd	10		330.2.m.e.91.2	✓	8
11.10	odd	2		3630.2.a.bt.1.3		4
33.2	even	10		990.2.n.k.631.2		8
33.17	even	10		990.2.n.k.91.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.m.e.91.2	✓	8	11.6	odd	10
330.2.m.e.301.2	yes	8	11.2	odd	10
990.2.n.k.91.2		8	33.17	even	10
990.2.n.k.631.2		8	33.2	even	10
3630.2.a.br.1.2		4	1.1	even	1	trivial
3630.2.a.bt.1.3		4	11.10	odd	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:	\( N \)	\(=\)	\( 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3630.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -2.86832 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -2.86832 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{12} +5.25908 q^{13} +2.86832 q^{14} +1.00000 q^{15} +1.00000 q^{16} -0.154687 q^{17} -1.00000 q^{18} -1.46335 q^{19} +1.00000 q^{20} -2.86832 q^{21} +3.78694 q^{23} -1.00000 q^{24} +1.00000 q^{25} -5.25908 q^{26} +1.00000 q^{27} -2.86832 q^{28} +3.48636 q^{29} -1.00000 q^{30} +2.98578 q^{31} -1.00000 q^{32} +0.154687 q^{34} -2.86832 q^{35} +1.00000 q^{36} +8.85410 q^{37} +1.46335 q^{38} +5.25908 q^{39} -1.00000 q^{40} -8.41377 q^{41} +2.86832 q^{42} -7.86289 q^{43} +1.00000 q^{45} -3.78694 q^{46} -10.9957 q^{47} +1.00000 q^{48} +1.22728 q^{49} -1.00000 q^{50} -0.154687 q^{51} +5.25908 q^{52} +10.5765 q^{53} -1.00000 q^{54} +2.86832 q^{56} -1.46335 q^{57} -3.48636 q^{58} +7.92741 q^{59} +1.00000 q^{60} -1.73665 q^{61} -2.98578 q^{62} -2.86832 q^{63} +1.00000 q^{64} +5.25908 q^{65} -11.2406 q^{67} -0.154687 q^{68} +3.78694 q^{69} +2.86832 q^{70} +3.54544 q^{71} -1.00000 q^{72} +6.00000 q^{73} -8.85410 q^{74} +1.00000 q^{75} -1.46335 q^{76} -5.25908 q^{78} +6.78958 q^{79} +1.00000 q^{80} +1.00000 q^{81} +8.41377 q^{82} +1.52786 q^{83} -2.86832 q^{84} -0.154687 q^{85} +7.86289 q^{86} +3.48636 q^{87} -10.8859 q^{89} -1.00000 q^{90} -15.0847 q^{91} +3.78694 q^{92} +2.98578 q^{93} +10.9957 q^{94} -1.46335 q^{95} -1.00000 q^{96} +19.4449 q^{97} -1.22728 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} - 4 q^{6} - q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^5 - 4 * q^6 - q^7 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} - 4 q^{6} - q^{7} - 4 q^{8} + 4 q^{9} - 4 q^{10} + 4 q^{12} - 4 q^{13} + q^{14} + 4 q^{15} + 4 q^{16} + 5 q^{17} - 4 q^{18} - 7 q^{19} + 4 q^{20} - q^{21} + 8 q^{23} - 4 q^{24} + 4 q^{25} + 4 q^{26} + 4 q^{27} - q^{28} - q^{29} - 4 q^{30} + 9 q^{31} - 4 q^{32} - 5 q^{34} - q^{35} + 4 q^{36} + 22 q^{37} + 7 q^{38} - 4 q^{39} - 4 q^{40} - 3 q^{41} + q^{42} + q^{43} + 4 q^{45} - 8 q^{46} + 2 q^{47} + 4 q^{48} + 15 q^{49} - 4 q^{50} + 5 q^{51} - 4 q^{52} + 5 q^{53} - 4 q^{54} + q^{56} - 7 q^{57} + q^{58} + 16 q^{59} + 4 q^{60} + 14 q^{61} - 9 q^{62} - q^{63} + 4 q^{64} - 4 q^{65} + 29 q^{67} + 5 q^{68} + 8 q^{69} + q^{70} - 6 q^{71} - 4 q^{72} + 24 q^{73} - 22 q^{74} + 4 q^{75} - 7 q^{76} + 4 q^{78} - 3 q^{79} + 4 q^{80} + 4 q^{81} + 3 q^{82} + 24 q^{83} - q^{84} + 5 q^{85} - q^{86} - q^{87} + 5 q^{89} - 4 q^{90} - 16 q^{91} + 8 q^{92} + 9 q^{93} - 2 q^{94} - 7 q^{95} - 4 q^{96} + 30 q^{97} - 15 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^5 - 4 * q^6 - q^7 - 4 * q^8 + 4 * q^9 - 4 * q^10 + 4 * q^12 - 4 * q^13 + q^14 + 4 * q^15 + 4 * q^16 + 5 * q^17 - 4 * q^18 - 7 * q^19 + 4 * q^20 - q^21 + 8 * q^23 - 4 * q^24 + 4 * q^25 + 4 * q^26 + 4 * q^27 - q^28 - q^29 - 4 * q^30 + 9 * q^31 - 4 * q^32 - 5 * q^34 - q^35 + 4 * q^36 + 22 * q^37 + 7 * q^38 - 4 * q^39 - 4 * q^40 - 3 * q^41 + q^42 + q^43 + 4 * q^45 - 8 * q^46 + 2 * q^47 + 4 * q^48 + 15 * q^49 - 4 * q^50 + 5 * q^51 - 4 * q^52 + 5 * q^53 - 4 * q^54 + q^56 - 7 * q^57 + q^58 + 16 * q^59 + 4 * q^60 + 14 * q^61 - 9 * q^62 - q^63 + 4 * q^64 - 4 * q^65 + 29 * q^67 + 5 * q^68 + 8 * q^69 + q^70 - 6 * q^71 - 4 * q^72 + 24 * q^73 - 22 * q^74 + 4 * q^75 - 7 * q^76 + 4 * q^78 - 3 * q^79 + 4 * q^80 + 4 * q^81 + 3 * q^82 + 24 * q^83 - q^84 + 5 * q^85 - q^86 - q^87 + 5 * q^89 - 4 * q^90 - 16 * q^91 + 8 * q^92 + 9 * q^93 - 2 * q^94 - 7 * q^95 - 4 * q^96 + 30 * q^97 - 15 * q^98

Introduction

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