LMFDB - Embedded newform 3630.2.a.br.1.1

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			1.1
Root			$4.07314$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -4.07314 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -4.07314 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{12} -4.13537 q^{13} +4.07314 q^{14} +1.00000 q^{15} +1.00000 q^{16} +5.97245 q^{17} -1.00000 q^{18} -5.35441 q^{19} +1.00000 q^{20} -4.07314 q^{21} +3.33676 q^{23} -1.00000 q^{24} +1.00000 q^{25} +4.13537 q^{26} +1.00000 q^{27} -4.07314 q^{28} +2.45511 q^{29} -1.00000 q^{30} -4.92724 q^{31} -1.00000 q^{32} -5.97245 q^{34} -4.07314 q^{35} +1.00000 q^{36} +2.14590 q^{37} +5.35441 q^{38} -4.13537 q^{39} -1.00000 q^{40} +7.10782 q^{41} +4.07314 q^{42} +11.6807 q^{43} +1.00000 q^{45} -3.33676 q^{46} -4.01091 q^{47} +1.00000 q^{48} +9.59048 q^{49} -1.00000 q^{50} +5.97245 q^{51} -4.13537 q^{52} -1.63506 q^{53} -1.00000 q^{54} +4.07314 q^{56} -5.35441 q^{57} -2.45511 q^{58} -6.56293 q^{59} +1.00000 q^{60} -4.14628 q^{61} +4.92724 q^{62} -4.07314 q^{63} +1.00000 q^{64} -4.13537 q^{65} +13.0517 q^{67} +5.97245 q^{68} +3.33676 q^{69} +4.07314 q^{70} -13.1810 q^{71} -1.00000 q^{72} +6.00000 q^{73} -2.14590 q^{74} +1.00000 q^{75} -5.35441 q^{76} +4.13537 q^{78} -4.97182 q^{79} +1.00000 q^{80} +1.00000 q^{81} -7.10782 q^{82} +10.4721 q^{83} -4.07314 q^{84} +5.97245 q^{85} -11.6807 q^{86} +2.45511 q^{87} +13.5800 q^{89} -1.00000 q^{90} +16.8440 q^{91} +3.33676 q^{92} -4.92724 q^{93} +4.01091 q^{94} -5.35441 q^{95} -1.00000 q^{96} +8.43808 q^{97} -9.59048 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	−4.07314	−1.53950	−0.769751	−	0.638344i	$-0.779620\pi$
$7$	−4.07314	−1.53950	−0.769751	+	0.638344i	$0.779620\pi$
$8$	−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
$13$	−4.13537	−1.14695	−0.573473	−	0.819224i	$-0.694404\pi$
$13$	−4.13537	−1.14695	−0.573473	+	0.819224i	$0.694404\pi$
$14$	4.07314	1.08859
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	5.97245	1.44853	0.724266	−	0.689521i	$-0.242179\pi$
$17$	5.97245	1.44853	0.724266	+	0.689521i	$0.242179\pi$
$18$	−1.00000	−0.235702
$19$	−5.35441	−1.22839	−0.614193	−	0.789156i	$-0.710518\pi$
$19$	−5.35441	−1.22839	−0.614193	+	0.789156i	$0.710518\pi$
$20$	1.00000	0.223607
$21$	−4.07314	−0.888832
$22$	0	0
$23$	3.33676	0.695763	0.347881	−	0.937539i	$-0.386901\pi$
$23$	3.33676	0.695763	0.347881	+	0.937539i	$0.386901\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	4.13537	0.811014
$27$	1.00000	0.192450
$28$	−4.07314	−0.769751
$29$	2.45511	0.455902	0.227951	−	0.973673i	$-0.426797\pi$
$29$	2.45511	0.455902	0.227951	+	0.973673i	$0.426797\pi$
$30$	−1.00000	−0.182574
$31$	−4.92724	−0.884959	−0.442480	−	0.896779i	$-0.645901\pi$
$31$	−4.92724	−0.884959	−0.442480	+	0.896779i	$0.645901\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−5.97245	−1.02427
$35$	−4.07314	−0.688487
$36$	1.00000	0.166667
$37$	2.14590	0.352783	0.176392	−	0.984320i	$-0.443557\pi$
$37$	2.14590	0.352783	0.176392	+	0.984320i	$0.443557\pi$
$38$	5.35441	0.868601
$39$	−4.13537	−0.662190
$40$	−1.00000	−0.158114
$41$	7.10782	1.11006	0.555028	−	0.831832i	$-0.312708\pi$
$41$	7.10782	1.11006	0.555028	+	0.831832i	$0.312708\pi$
$42$	4.07314	0.628499
$43$	11.6807	1.78128	0.890641	−	0.454707i	$-0.150256\pi$
$43$	11.6807	1.78128	0.890641	+	0.454707i	$0.150256\pi$
$44$	0	0
$45$	1.00000	0.149071
$46$	−3.33676	−0.491979
$47$	−4.01091	−0.585051	−0.292526	−	0.956258i	$-0.594496\pi$
$47$	−4.01091	−0.585051	−0.292526	+	0.956258i	$0.594496\pi$
$48$	1.00000	0.144338
$49$	9.59048	1.37007
$50$	−1.00000	−0.141421
$51$	5.97245	0.836310
$52$	−4.13537	−0.573473
$53$	−1.63506	−0.224593	−0.112297	−	0.993675i	$-0.535821\pi$
$53$	−1.63506	−0.224593	−0.112297	+	0.993675i	$0.535821\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	4.07314	0.544296
$57$	−5.35441	−0.709209
$58$	−2.45511	−0.322371
$59$	−6.56293	−0.854421	−0.427210	−	0.904152i	$-0.640504\pi$
$59$	−6.56293	−0.854421	−0.427210	+	0.904152i	$0.640504\pi$
$60$	1.00000	0.129099
$61$	−4.14628	−0.530877	−0.265439	−	0.964128i	$-0.585517\pi$
$61$	−4.14628	−0.530877	−0.265439	+	0.964128i	$0.585517\pi$
$62$	4.92724	0.625761
$63$	−4.07314	−0.513168
$64$	1.00000	0.125000
$65$	−4.13537	−0.512930
$66$	0	0
$67$	13.0517	1.59452	0.797260	−	0.603636i	$-0.206282\pi$
$67$	13.0517	1.59452	0.797260	+	0.603636i	$0.206282\pi$
$68$	5.97245	0.724266
$69$	3.33676	0.401699
$70$	4.07314	0.486834
$71$	−13.1810	−1.56429	−0.782146	−	0.623095i	$-0.785875\pi$
$71$	−13.1810	−1.56429	−0.782146	+	0.623095i	$0.785875\pi$
$72$	−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	$0.385800\pi$
$74$	−2.14590	−0.249456
$75$	1.00000	0.115470
$76$	−5.35441	−0.614193
$77$	0	0
$78$	4.13537	0.468239
$79$	−4.97182	−0.559374	−0.279687	−	0.960091i	$-0.590231\pi$
$79$	−4.97182	−0.559374	−0.279687	+	0.960091i	$0.590231\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−7.10782	−0.784928
$83$	10.4721	1.14947	0.574733	−	0.818341i	$-0.305106\pi$
$83$	10.4721	1.14947	0.574733	+	0.818341i	$0.305106\pi$
$84$	−4.07314	−0.444416
$85$	5.97245	0.647803
$86$	−11.6807	−1.25956
$87$	2.45511	0.263215
$88$	0	0
$89$	13.5800	1.43947	0.719736	−	0.694248i	$-0.244263\pi$
$89$	13.5800	1.43947	0.719736	+	0.694248i	$0.244263\pi$
$90$	−1.00000	−0.105409
$91$	16.8440	1.76573
$92$	3.33676	0.347881
$93$	−4.92724	−0.510931
$94$	4.01091	0.413694
$95$	−5.35441	−0.549351
$96$	−1.00000	−0.102062
$97$	8.43808	0.856757	0.428379	−	0.903599i	$-0.359085\pi$
$97$	8.43808	0.856757	0.428379	+	0.903599i	$0.359085\pi$
$98$	−9.59048	−0.968785
$99$	0	0
$100$	1.00000	0.100000
$101$	1.97245	0.196266	0.0981329	−	0.995173i	$-0.468713\pi$
$101$	1.97245	0.196266	0.0981329	+	0.995173i	$0.468713\pi$
$102$	−5.97245	−0.591360
$103$	9.35441	0.921718	0.460859	−	0.887473i	$-0.347541\pi$
$103$	9.35441	0.921718	0.460859	+	0.887473i	$0.347541\pi$
$104$	4.13537	0.405507
$105$	−4.07314	−0.397498
$106$	1.63506	0.158811
$107$	8.34767	0.807000	0.403500	−	0.914980i	$-0.367794\pi$
$107$	8.34767	0.807000	0.403500	+	0.914980i	$0.367794\pi$
$108$	1.00000	0.0962250
$109$	14.4721	1.38618	0.693090	−	0.720851i	$-0.256249\pi$
$109$	14.4721	1.38618	0.693090	+	0.720851i	$0.256249\pi$
$110$	0	0
$111$	2.14590	0.203680
$112$	−4.07314	−0.384876
$113$	13.0735	1.22985	0.614927	−	0.788584i	$-0.289185\pi$
$113$	13.0735	1.22985	0.614927	+	0.788584i	$0.289185\pi$
$114$	5.35441	0.501487
$115$	3.33676	0.311155
$116$	2.45511	0.227951
$117$	−4.13537	−0.382315
$118$	6.56293	0.604167
$119$	−24.3266	−2.23002
$120$	−1.00000	−0.0912871
$121$	0	0
$122$	4.14628	0.375387
$123$	7.10782	0.640891
$124$	−4.92724	−0.442480
$125$	1.00000	0.0894427
$126$	4.07314	0.362864
$127$	19.5007	1.73041	0.865203	−	0.501421i	$-0.167189\pi$
$127$	19.5007	1.73041	0.865203	+	0.501421i	$0.167189\pi$
$128$	−1.00000	−0.0883883
$129$	11.6807	1.02842
$130$	4.13537	0.362696
$131$	−15.7252	−1.37392	−0.686960	−	0.726695i	$-0.741055\pi$
$131$	−15.7252	−1.37392	−0.686960	+	0.726695i	$0.741055\pi$
$132$	0	0
$133$	21.8093	1.89110
$134$	−13.0517	−1.12750
$135$	1.00000	0.0860663
$136$	−5.97245	−0.512133
$137$	−3.74628	−0.320066	−0.160033	−	0.987112i	$-0.551160\pi$
$137$	−3.74628	−0.320066	−0.160033	+	0.987112i	$0.551160\pi$
$138$	−3.33676	−0.284044
$139$	13.7473	1.16603	0.583015	−	0.812461i	$-0.301873\pi$
$139$	13.7473	1.16603	0.583015	+	0.812461i	$0.301873\pi$
$140$	−4.07314	−0.344243
$141$	−4.01091	−0.337779
$142$	13.1810	1.10612
$143$	0	0
$144$	1.00000	0.0833333
$145$	2.45511	0.203886
$146$	−6.00000	−0.496564
$147$	9.59048	0.791010
$148$	2.14590	0.176392
$149$	6.02755	0.493796	0.246898	−	0.969041i	$-0.420589\pi$
$149$	6.02755	0.493796	0.246898	+	0.969041i	$0.420589\pi$
$150$	−1.00000	−0.0816497
$151$	−14.8551	−1.20889	−0.604446	−	0.796646i	$-0.706605\pi$
$151$	−14.8551	−1.20889	−0.604446	+	0.796646i	$0.706605\pi$
$152$	5.35441	0.434300
$153$	5.97245	0.482844
$154$	0	0
$155$	−4.92724	−0.395766
$156$	−4.13537	−0.331095
$157$	−4.45133	−0.355254	−0.177627	−	0.984098i	$-0.556842\pi$
$157$	−4.45133	−0.355254	−0.177627	+	0.984098i	$0.556842\pi$
$158$	4.97182	0.395537
$159$	−1.63506	−0.129669
$160$	−1.00000	−0.0790569
$161$	−13.5911	−1.07113
$162$	−1.00000	−0.0785674
$163$	−18.2991	−1.43329	−0.716647	−	0.697436i	$-0.754324\pi$
$163$	−18.2991	−1.43329	−0.716647	+	0.697436i	$0.754324\pi$
$164$	7.10782	0.555028
$165$	0	0
$166$	−10.4721	−0.812795
$167$	12.9552	1.00250	0.501251	−	0.865302i	$-0.332873\pi$
$167$	12.9552	1.00250	0.501251	+	0.865302i	$0.332873\pi$
$168$	4.07314	0.314250
$169$	4.10132	0.315486
$170$	−5.97245	−0.458066
$171$	−5.35441	−0.409462
$172$	11.6807	0.890641
$173$	−10.3439	−0.786431	−0.393216	−	0.919446i	$-0.628637\pi$
$173$	−10.3439	−0.786431	−0.393216	+	0.919446i	$0.628637\pi$
$174$	−2.45511	−0.186121
$175$	−4.07314	−0.307901
$176$	0	0
$177$	−6.56293	−0.493300
$178$	−13.5800	−1.01786
$179$	4.88816	0.365358	0.182679	−	0.983173i	$-0.441523\pi$
$179$	4.88816	0.365358	0.182679	+	0.983173i	$0.441523\pi$
$180$	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	$0.596092\pi$
$182$	−16.8440	−1.24856
$183$	−4.14628	−0.306502
$184$	−3.33676	−0.245989
$185$	2.14590	0.157770
$186$	4.92724	0.361283
$187$	0	0
$188$	−4.01091	−0.292526
$189$	−4.07314	−0.296277
$190$	5.35441	0.388450
$191$	24.0701	1.74165	0.870827	−	0.491590i	$-0.163584\pi$
$191$	24.0701	1.74165	0.870827	+	0.491590i	$0.163584\pi$
$192$	1.00000	0.0721688
$193$	15.1116	1.08776	0.543878	−	0.839164i	$-0.316955\pi$
$193$	15.1116	1.08776	0.543878	+	0.839164i	$0.316955\pi$
$194$	−8.43808	−0.605819
$195$	−4.13537	−0.296140
$196$	9.59048	0.685034
$197$	−17.0515	−1.21487	−0.607433	−	0.794371i	$-0.707801\pi$
$197$	−17.0515	−1.21487	−0.607433	+	0.794371i	$0.707801\pi$
$198$	0	0
$199$	5.40990	0.383498	0.191749	−	0.981444i	$-0.438584\pi$
$199$	5.40990	0.383498	0.191749	+	0.981444i	$0.438584\pi$
$200$	−1.00000	−0.0707107
$201$	13.0517	0.920597
$202$	−1.97245	−0.138781
$203$	−10.0000	−0.701862
$204$	5.97245	0.418155
$205$	7.10782	0.496432
$206$	−9.35441	−0.651753
$207$	3.33676	0.231921
$208$	−4.13537	−0.286737
$209$	0	0
$210$	4.07314	0.281073
$211$	−25.8545	−1.77990	−0.889948	−	0.456062i	$-0.849260\pi$
$211$	−25.8545	−1.77990	−0.889948	+	0.456062i	$0.849260\pi$
$212$	−1.63506	−0.112297
$213$	−13.1810	−0.903145
$214$	−8.34767	−0.570635
$215$	11.6807	0.796614
$216$	−1.00000	−0.0680414
$217$	20.0694	1.36240
$218$	−14.4721	−0.980177
$219$	6.00000	0.405442
$220$	0	0
$221$	−24.6983	−1.66139
$222$	−2.14590	−0.144023
$223$	−9.74729	−0.652727	−0.326363	−	0.945244i	$-0.605823\pi$
$223$	−9.74729	−0.652727	−0.326363	+	0.945244i	$0.605823\pi$
$224$	4.07314	0.272148
$225$	1.00000	0.0666667
$226$	−13.0735	−0.869638
$227$	19.1599	1.27169	0.635844	−	0.771818i	$-0.280652\pi$
$227$	19.1599	1.27169	0.635844	+	0.771818i	$0.280652\pi$
$228$	−5.35441	−0.354605
$229$	19.2028	1.26896	0.634478	−	0.772941i	$-0.281215\pi$
$229$	19.2028	1.26896	0.634478	+	0.772941i	$0.281215\pi$
$230$	−3.33676	−0.220020
$231$	0	0
$232$	−2.45511	−0.161186
$233$	−5.83746	−0.382425	−0.191212	−	0.981549i	$-0.561242\pi$
$233$	−5.83746	−0.382425	−0.191212	+	0.981549i	$0.561242\pi$
$234$	4.13537	0.270338
$235$	−4.01091	−0.261643
$236$	−6.56293	−0.427210
$237$	−4.97182	−0.322955
$238$	24.3266	1.57686
$239$	15.1246	0.978330	0.489165	−	0.872191i	$-0.337302\pi$
$239$	15.1246	0.978330	0.489165	+	0.872191i	$0.337302\pi$
$240$	1.00000	0.0645497
$241$	−20.4902	−1.31989	−0.659944	−	0.751315i	$-0.729420\pi$
$241$	−20.4902	−1.31989	−0.659944	+	0.751315i	$0.729420\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	−4.14628	−0.265439
$245$	9.59048	0.612713
$246$	−7.10782	−0.453178
$247$	22.1425	1.40889
$248$	4.92724	0.312880
$249$	10.4721	0.663645
$250$	−1.00000	−0.0632456
$251$	14.6300	0.923434	0.461717	−	0.887027i	$-0.347234\pi$
$251$	14.6300	0.923434	0.461717	+	0.887027i	$0.347234\pi$
$252$	−4.07314	−0.256584
$253$	0	0
$254$	−19.5007	−1.22358
$255$	5.97245	0.374009
$256$	1.00000	0.0625000
$257$	21.4164	1.33592	0.667959	−	0.744198i	$-0.267168\pi$
$257$	21.4164	1.33592	0.667959	+	0.744198i	$0.267168\pi$
$258$	−11.6807	−0.727206
$259$	−8.74055	−0.543111
$260$	−4.13537	−0.256465
$261$	2.45511	0.151967
$262$	15.7252	0.971508
$263$	−30.3270	−1.87004	−0.935022	−	0.354590i	$-0.884620\pi$
$263$	−30.3270	−1.87004	−0.935022	+	0.354590i	$0.884620\pi$
$264$	0	0
$265$	−1.63506	−0.100441
$266$	−21.8093	−1.33721
$267$	13.5800	0.831080
$268$	13.0517	0.797260
$269$	−10.5796	−0.645048	−0.322524	−	0.946561i	$-0.604531\pi$
$269$	−10.5796	−0.645048	−0.322524	+	0.946561i	$0.604531\pi$
$270$	−1.00000	−0.0608581
$271$	0.825542	0.0501481	0.0250740	−	0.999686i	$-0.492018\pi$
$271$	0.825542	0.0501481	0.0250740	+	0.999686i	$0.492018\pi$
$272$	5.97245	0.362133
$273$	16.8440	1.01944
$274$	3.74628	0.226321
$275$	0	0
$276$	3.33676	0.200849
$277$	26.7321	1.60618	0.803089	−	0.595859i	$-0.203188\pi$
$277$	26.7321	1.60618	0.803089	+	0.595859i	$0.203188\pi$
$278$	−13.7473	−0.824508
$279$	−4.92724	−0.294986
$280$	4.07314	0.243417
$281$	6.94427	0.414261	0.207130	−	0.978313i	$-0.433588\pi$
$281$	6.94427	0.414261	0.207130	+	0.978313i	$0.433588\pi$
$282$	4.01091	0.238846
$283$	−5.57895	−0.331634	−0.165817	−	0.986157i	$-0.553026\pi$
$283$	−5.57895	−0.331634	−0.165817	+	0.986157i	$0.553026\pi$
$284$	−13.1810	−0.782146
$285$	−5.35441	−0.317168
$286$	0	0
$287$	−28.9512	−1.70893
$288$	−1.00000	−0.0589256
$289$	18.6701	1.09824
$290$	−2.45511	−0.144169
$291$	8.43808	0.494649
$292$	6.00000	0.351123
$293$	7.87175	0.459873	0.229936	−	0.973206i	$-0.426148\pi$
$293$	7.87175	0.459873	0.229936	+	0.973206i	$0.426148\pi$
$294$	−9.59048	−0.559328
$295$	−6.56293	−0.382108
$296$	−2.14590	−0.124728
$297$	0	0
$298$	−6.02755	−0.349167
$299$	−13.7988	−0.798003
$300$	1.00000	0.0577350
$301$	−47.5769	−2.74229
$302$	14.8551	0.854816
$303$	1.97245	0.113314
$304$	−5.35441	−0.307097
$305$	−4.14628	−0.237415
$306$	−5.97245	−0.341422
$307$	−20.5463	−1.17264	−0.586319	−	0.810080i	$-0.699424\pi$
$307$	−20.5463	−1.17264	−0.586319	+	0.810080i	$0.699424\pi$
$308$	0	0
$309$	9.35441	0.532154
$310$	4.92724	0.279849
$311$	12.8198	0.726945	0.363472	−	0.931605i	$-0.381591\pi$
$311$	12.8198	0.726945	0.363472	+	0.931605i	$0.381591\pi$
$312$	4.13537	0.234119
$313$	−1.36053	−0.0769019	−0.0384509	−	0.999260i	$-0.512242\pi$
$313$	−1.36053	−0.0769019	−0.0384509	+	0.999260i	$0.512242\pi$
$314$	4.45133	0.251203
$315$	−4.07314	−0.229496
$316$	−4.97182	−0.279687
$317$	−25.1197	−1.41087	−0.705433	−	0.708777i	$-0.749247\pi$
$317$	−25.1197	−1.41087	−0.705433	+	0.708777i	$0.749247\pi$
$318$	1.63506	0.0916898
$319$	0	0
$320$	1.00000	0.0559017
$321$	8.34767	0.465922
$322$	13.5911	0.757403
$323$	−31.9790	−1.77936
$324$	1.00000	0.0555556
$325$	−4.13537	−0.229389
$326$	18.2991	1.01349
$327$	14.4721	0.800311
$328$	−7.10782	−0.392464
$329$	16.3370	0.900688
$330$	0	0
$331$	4.64683	0.255413	0.127706	−	0.991812i	$-0.459238\pi$
$331$	4.64683	0.255413	0.127706	+	0.991812i	$0.459238\pi$
$332$	10.4721	0.574733
$333$	2.14590	0.117594
$334$	−12.9552	−0.708876
$335$	13.0517	0.713091
$336$	−4.07314	−0.222208
$337$	−19.3613	−1.05468	−0.527339	−	0.849655i	$-0.676810\pi$
$337$	−19.3613	−1.05468	−0.527339	+	0.849655i	$0.676810\pi$
$338$	−4.10132	−0.223082
$339$	13.0735	0.710056
$340$	5.97245	0.323901
$341$	0	0
$342$	5.35441	0.289534
$343$	−10.5514	−0.569722
$344$	−11.6807	−0.629779
$345$	3.33676	0.179645
$346$	10.3439	0.556091
$347$	−28.0150	−1.50393	−0.751963	−	0.659206i	$-0.770893\pi$
$347$	−28.0150	−1.50393	−0.751963	+	0.659206i	$0.770893\pi$
$348$	2.45511	0.131608
$349$	25.7300	1.37730	0.688648	−	0.725096i	$-0.258204\pi$
$349$	25.7300	1.37730	0.688648	+	0.725096i	$0.258204\pi$
$350$	4.07314	0.217719
$351$	−4.13537	−0.220730
$352$	0	0
$353$	−6.66702	−0.354850	−0.177425	−	0.984134i	$-0.556777\pi$
$353$	−6.66702	−0.354850	−0.177425	+	0.984134i	$0.556777\pi$
$354$	6.56293	0.348816
$355$	−13.1810	−0.699573
$356$	13.5800	0.719736
$357$	−24.3266	−1.28750
$358$	−4.88816	−0.258347
$359$	8.83329	0.466203	0.233102	−	0.972452i	$-0.425113\pi$
$359$	8.83329	0.466203	0.233102	+	0.972452i	$0.425113\pi$
$360$	−1.00000	−0.0527046
$361$	9.66974	0.508934
$362$	8.00000	0.420471
$363$	0	0
$364$	16.8440	0.882864
$365$	6.00000	0.314054
$366$	4.14628	0.216730
$367$	12.0341	0.628173	0.314086	−	0.949394i	$-0.398302\pi$
$367$	12.0341	0.628173	0.314086	+	0.949394i	$0.398302\pi$
$368$	3.33676	0.173941
$369$	7.10782	0.370018
$370$	−2.14590	−0.111560
$371$	6.65984	0.345762
$372$	−4.92724	−0.255466
$373$	31.8273	1.64796	0.823978	−	0.566622i	$-0.191750\pi$
$373$	31.8273	1.64796	0.823978	+	0.566622i	$0.191750\pi$
$374$	0	0
$375$	1.00000	0.0516398
$376$	4.01091	0.206847
$377$	−10.1528	−0.522895
$378$	4.07314	0.209500
$379$	−15.6153	−0.802102	−0.401051	−	0.916056i	$-0.631355\pi$
$379$	−15.6153	−0.802102	−0.401051	+	0.916056i	$0.631355\pi$
$380$	−5.35441	−0.274676
$381$	19.5007	0.999051
$382$	−24.0701	−1.23153
$383$	−0.346664	−0.0177137	−0.00885684	−	0.999961i	$-0.502819\pi$
$383$	−0.346664	−0.0177137	−0.00885684	+	0.999961i	$0.502819\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−15.1116	−0.769160
$387$	11.6807	0.593761
$388$	8.43808	0.428379
$389$	−1.93714	−0.0982171	−0.0491086	−	0.998793i	$-0.515638\pi$
$389$	−1.93714	−0.0982171	−0.0491086	+	0.998793i	$0.515638\pi$
$390$	4.13537	0.209403
$391$	19.9286	1.00783
$392$	−9.59048	−0.484392
$393$	−15.7252	−0.793233
$394$	17.0515	0.859041
$395$	−4.97182	−0.250160
$396$	0	0
$397$	30.9205	1.55186	0.775928	−	0.630822i	$-0.217282\pi$
$397$	30.9205	1.55186	0.775928	+	0.630822i	$0.217282\pi$
$398$	−5.40990	−0.271174
$399$	21.8093	1.09183
$400$	1.00000	0.0500000
$401$	32.1885	1.60742	0.803708	−	0.595024i	$-0.202858\pi$
$401$	32.1885	1.60742	0.803708	+	0.595024i	$0.202858\pi$
$402$	−13.0517	−0.650960
$403$	20.3760	1.01500
$404$	1.97245	0.0981329
$405$	1.00000	0.0496904
$406$	10.0000	0.496292
$407$	0	0
$408$	−5.97245	−0.295680
$409$	5.39249	0.266641	0.133321	−	0.991073i	$-0.457436\pi$
$409$	5.39249	0.266641	0.133321	+	0.991073i	$0.457436\pi$
$410$	−7.10782	−0.351030
$411$	−3.74628	−0.184790
$412$	9.35441	0.460859
$413$	26.7317	1.31538
$414$	−3.33676	−0.163993
$415$	10.4721	0.514057
$416$	4.13537	0.202753
$417$	13.7473	0.673208
$418$	0	0
$419$	5.67453	0.277219	0.138610	−	0.990347i	$-0.455737\pi$
$419$	5.67453	0.277219	0.138610	+	0.990347i	$0.455737\pi$
$420$	−4.07314	−0.198749
$421$	−7.43870	−0.362540	−0.181270	−	0.983433i	$-0.558021\pi$
$421$	−7.43870	−0.362540	−0.181270	+	0.983433i	$0.558021\pi$
$422$	25.8545	1.25858
$423$	−4.01091	−0.195017
$424$	1.63506	0.0794057
$425$	5.97245	0.289706
$426$	13.1810	0.638620
$427$	16.8884	0.817287
$428$	8.34767	0.403500
$429$	0	0
$430$	−11.6807	−0.563291
$431$	−29.1599	−1.40458	−0.702292	−	0.711889i	$-0.747840\pi$
$431$	−29.1599	−1.40458	−0.702292	+	0.711889i	$0.747840\pi$
$432$	1.00000	0.0481125
$433$	23.0918	1.10972	0.554861	−	0.831943i	$-0.312772\pi$
$433$	23.0918	1.10972	0.554861	+	0.831943i	$0.312772\pi$
$434$	−20.0694	−0.963360
$435$	2.45511	0.117713
$436$	14.4721	0.693090
$437$	−17.8664	−0.854666
$438$	−6.00000	−0.286691
$439$	37.6709	1.79793	0.898967	−	0.438017i	$-0.144319\pi$
$439$	37.6709	1.79793	0.898967	+	0.438017i	$0.144319\pi$
$440$	0	0
$441$	9.59048	0.456690
$442$	24.6983	1.17478
$443$	−16.9796	−0.806724	−0.403362	−	0.915041i	$-0.632158\pi$
$443$	−16.9796	−0.806724	−0.403362	+	0.915041i	$0.632158\pi$
$444$	2.14590	0.101840
$445$	13.5800	0.643752
$446$	9.74729	0.461547
$447$	6.02755	0.285093
$448$	−4.07314	−0.192438
$449$	−7.13877	−0.336899	−0.168450	−	0.985710i	$-0.553876\pi$
$449$	−7.13877	−0.336899	−0.168450	+	0.985710i	$0.553876\pi$
$450$	−1.00000	−0.0471405
$451$	0	0
$452$	13.0735	0.614927
$453$	−14.8551	−0.697954
$454$	−19.1599	−0.899219
$455$	16.8440	0.789657
$456$	5.35441	0.250743
$457$	−16.3266	−0.763727	−0.381864	−	0.924219i	$-0.624718\pi$
$457$	−16.3266	−0.763727	−0.381864	+	0.924219i	$0.624718\pi$
$458$	−19.2028	−0.897287
$459$	5.97245	0.278770
$460$	3.33676	0.155577
$461$	22.0636	1.02761	0.513803	−	0.857908i	$-0.328236\pi$
$461$	22.0636	1.02761	0.513803	+	0.857908i	$0.328236\pi$
$462$	0	0
$463$	−23.7592	−1.10418	−0.552092	−	0.833783i	$-0.686170\pi$
$463$	−23.7592	−1.10418	−0.552092	+	0.833783i	$0.686170\pi$
$464$	2.45511	0.113976
$465$	−4.92724	−0.228495
$466$	5.83746	0.270415
$467$	−2.59785	−0.120214	−0.0601070	−	0.998192i	$-0.519144\pi$
$467$	−2.59785	−0.120214	−0.0601070	+	0.998192i	$0.519144\pi$
$468$	−4.13537	−0.191158
$469$	−53.1615	−2.45477
$470$	4.01091	0.185009
$471$	−4.45133	−0.205106
$472$	6.56293	0.302083
$473$	0	0
$474$	4.97182	0.228363
$475$	−5.35441	−0.245677
$476$	−24.3266	−1.11501
$477$	−1.63506	−0.0748644
$478$	−15.1246	−0.691784
$479$	17.4382	0.796773	0.398386	−	0.917218i	$-0.369570\pi$
$479$	17.4382	0.796773	0.398386	+	0.917218i	$0.369570\pi$
$480$	−1.00000	−0.0456435
$481$	−8.87409	−0.404624
$482$	20.4902	0.933302
$483$	−13.5911	−0.618417
$484$	0	0
$485$	8.43808	0.383153
$486$	−1.00000	−0.0453609
$487$	20.4734	0.927737	0.463869	−	0.885904i	$-0.346461\pi$
$487$	20.4734	0.927737	0.463869	+	0.885904i	$0.346461\pi$
$488$	4.14628	0.187693
$489$	−18.2991	−0.827513
$490$	−9.59048	−0.433254
$491$	4.92112	0.222087	0.111044	−	0.993816i	$-0.464581\pi$
$491$	4.92112	0.222087	0.111044	+	0.993816i	$0.464581\pi$
$492$	7.10782	0.320445
$493$	14.6630	0.660388
$494$	−22.1425	−0.996238
$495$	0	0
$496$	−4.92724	−0.221240
$497$	53.6879	2.40823
$498$	−10.4721	−0.469268
$499$	−26.1766	−1.17182	−0.585912	−	0.810375i	$-0.699264\pi$
$499$	−26.1766	−1.17182	−0.585912	+	0.810375i	$0.699264\pi$
$500$	1.00000	0.0447214
$501$	12.9552	0.578795
$502$	−14.6300	−0.652967
$503$	8.89931	0.396800	0.198400	−	0.980121i	$-0.436425\pi$
$503$	8.89931	0.396800	0.198400	+	0.980121i	$0.436425\pi$
$504$	4.07314	0.181432
$505$	1.97245	0.0877728
$506$	0	0
$507$	4.10132	0.182146
$508$	19.5007	0.865203
$509$	15.7605	0.698573	0.349287	−	0.937016i	$-0.386424\pi$
$509$	15.7605	0.698573	0.349287	+	0.937016i	$0.386424\pi$
$510$	−5.97245	−0.264464
$511$	−24.4388	−1.08111
$512$	−1.00000	−0.0441942
$513$	−5.35441	−0.236403
$514$	−21.4164	−0.944637
$515$	9.35441	0.412205
$516$	11.6807	0.514212
$517$	0	0
$518$	8.74055	0.384038
$519$	−10.3439	−0.454046
$520$	4.13537	0.181348
$521$	−32.7269	−1.43379	−0.716895	−	0.697181i	$-0.754437\pi$
$521$	−32.7269	−1.43379	−0.716895	+	0.697181i	$0.754437\pi$
$522$	−2.45511	−0.107457
$523$	−17.0224	−0.744339	−0.372170	−	0.928165i	$-0.621386\pi$
$523$	−17.0224	−0.744339	−0.372170	+	0.928165i	$0.621386\pi$
$524$	−15.7252	−0.686960
$525$	−4.07314	−0.177766
$526$	30.3270	1.32232
$527$	−29.4277	−1.28189
$528$	0	0
$529$	−11.8660	−0.515914
$530$	1.63506	0.0710226
$531$	−6.56293	−0.284807
$532$	21.8093	0.945552
$533$	−29.3935	−1.27317
$534$	−13.5800	−0.587662
$535$	8.34767	0.360901
$536$	−13.0517	−0.563748
$537$	4.88816	0.210940
$538$	10.5796	0.456118
$539$	0	0
$540$	1.00000	0.0430331
$541$	16.4864	0.708805	0.354403	−	0.935093i	$-0.384684\pi$
$541$	16.4864	0.708805	0.354403	+	0.935093i	$0.384684\pi$
$542$	−0.825542	−0.0354601
$543$	−8.00000	−0.343313
$544$	−5.97245	−0.256067
$545$	14.4721	0.619918
$546$	−16.8440	−0.720855
$547$	9.60124	0.410520	0.205260	−	0.978708i	$-0.434196\pi$
$547$	9.60124	0.410520	0.205260	+	0.978708i	$0.434196\pi$
$548$	−3.74628	−0.160033
$549$	−4.14628	−0.176959
$550$	0	0
$551$	−13.1457	−0.560024
$552$	−3.33676	−0.142022
$553$	20.2509	0.861158
$554$	−26.7321	−1.13574
$555$	2.14590	0.0910883
$556$	13.7473	0.583015
$557$	−26.3891	−1.11814	−0.559071	−	0.829120i	$-0.688842\pi$
$557$	−26.3891	−1.11814	−0.559071	+	0.829120i	$0.688842\pi$
$558$	4.92724	0.208587
$559$	−48.3039	−2.04304
$560$	−4.07314	−0.172122
$561$	0	0
$562$	−6.94427	−0.292926
$563$	37.7994	1.59305	0.796527	−	0.604603i	$-0.206668\pi$
$563$	37.7994	1.59305	0.796527	+	0.604603i	$0.206668\pi$
$564$	−4.01091	−0.168890
$565$	13.0735	0.550007
$566$	5.57895	0.234501
$567$	−4.07314	−0.171056
$568$	13.1810	0.553061
$569$	2.43305	0.101999	0.0509994	−	0.998699i	$-0.483759\pi$
$569$	2.43305	0.101999	0.0509994	+	0.998699i	$0.483759\pi$
$570$	5.35441	0.224272
$571$	24.7058	1.03391	0.516953	−	0.856014i	$-0.327066\pi$
$571$	24.7058	1.03391	0.516953	+	0.856014i	$0.327066\pi$
$572$	0	0
$573$	24.0701	1.00554
$574$	28.9512	1.20840
$575$	3.33676	0.139153
$576$	1.00000	0.0416667
$577$	−24.5082	−1.02029	−0.510145	−	0.860088i	$-0.670408\pi$
$577$	−24.5082	−1.02029	−0.510145	+	0.860088i	$0.670408\pi$
$578$	−18.6701	−0.776575
$579$	15.1116	0.628017
$580$	2.45511	0.101943
$581$	−42.6545	−1.76961
$582$	−8.43808	−0.349770
$583$	0	0
$584$	−6.00000	−0.248282
$585$	−4.13537	−0.170977
$586$	−7.87175	−0.325179
$587$	−11.8768	−0.490207	−0.245104	−	0.969497i	$-0.578822\pi$
$587$	−11.8768	−0.490207	−0.245104	+	0.969497i	$0.578822\pi$
$588$	9.59048	0.395505
$589$	26.3825	1.08707
$590$	6.56293	0.270191
$591$	−17.0515	−0.701404
$592$	2.14590	0.0881959
$593$	11.2190	0.460711	0.230355	−	0.973107i	$-0.426011\pi$
$593$	11.2190	0.460711	0.230355	+	0.973107i	$0.426011\pi$
$594$	0	0
$595$	−24.3266	−0.997294
$596$	6.02755	0.246898
$597$	5.40990	0.221413
$598$	13.7988	0.564273
$599$	6.34011	0.259050	0.129525	−	0.991576i	$-0.458655\pi$
$599$	6.34011	0.259050	0.129525	+	0.991576i	$0.458655\pi$
$600$	−1.00000	−0.0408248
$601$	23.6054	0.962883	0.481441	−	0.876478i	$-0.340113\pi$
$601$	23.6054	0.962883	0.481441	+	0.876478i	$0.340113\pi$
$602$	47.5769	1.93909
$603$	13.0517	0.531507
$604$	−14.8551	−0.604446
$605$	0	0
$606$	−1.97245	−0.0801252
$607$	8.08916	0.328329	0.164164	−	0.986433i	$-0.447507\pi$
$607$	8.08916	0.328329	0.164164	+	0.986433i	$0.447507\pi$
$608$	5.35441	0.217150
$609$	−10.0000	−0.405220
$610$	4.14628	0.167878
$611$	16.5866	0.671022
$612$	5.97245	0.241422
$613$	−21.1675	−0.854946	−0.427473	−	0.904028i	$-0.640596\pi$
$613$	−21.1675	−0.854946	−0.427473	+	0.904028i	$0.640596\pi$
$614$	20.5463	0.829181
$615$	7.10782	0.286615
$616$	0	0
$617$	−13.2579	−0.533742	−0.266871	−	0.963732i	$-0.585990\pi$
$617$	−13.2579	−0.533742	−0.266871	+	0.963732i	$0.585990\pi$
$618$	−9.35441	−0.376290
$619$	−9.73537	−0.391298	−0.195649	−	0.980674i	$-0.562681\pi$
$619$	−9.73537	−0.391298	−0.195649	+	0.980674i	$0.562681\pi$
$620$	−4.92724	−0.197883
$621$	3.33676	0.133900
$622$	−12.8198	−0.514027
$623$	−55.3131	−2.21607
$624$	−4.13537	−0.165547
$625$	1.00000	0.0400000
$626$	1.36053	0.0543778
$627$	0	0
$628$	−4.45133	−0.177627
$629$	12.8163	0.511018
$630$	4.07314	0.162278
$631$	−21.4545	−0.854090	−0.427045	−	0.904230i	$-0.640445\pi$
$631$	−21.4545	−0.854090	−0.427045	+	0.904230i	$0.640445\pi$
$632$	4.97182	0.197769
$633$	−25.8545	−1.02762
$634$	25.1197	0.997632
$635$	19.5007	0.773862
$636$	−1.63506	−0.0648344
$637$	−39.6602	−1.57140
$638$	0	0
$639$	−13.1810	−0.521431
$640$	−1.00000	−0.0395285
$641$	−39.1315	−1.54560	−0.772801	−	0.634649i	$-0.781145\pi$
$641$	−39.1315	−1.54560	−0.772801	+	0.634649i	$0.781145\pi$
$642$	−8.34767	−0.329456
$643$	44.8729	1.76961	0.884807	−	0.465957i	$-0.154290\pi$
$643$	44.8729	1.76961	0.884807	+	0.465957i	$0.154290\pi$
$644$	−13.5911	−0.535565
$645$	11.6807	0.459925
$646$	31.9790	1.25820
$647$	10.3752	0.407892	0.203946	−	0.978982i	$-0.434623\pi$
$647$	10.3752	0.407892	0.203946	+	0.978982i	$0.434623\pi$
$648$	−1.00000	−0.0392837
$649$	0	0
$650$	4.13537	0.162203
$651$	20.0694	0.786580
$652$	−18.2991	−0.716647
$653$	−37.2988	−1.45962	−0.729808	−	0.683652i	$-0.760391\pi$
$653$	−37.2988	−1.45962	−0.729808	+	0.683652i	$0.760391\pi$
$654$	−14.4721	−0.565905
$655$	−15.7252	−0.614436
$656$	7.10782	0.277514
$657$	6.00000	0.234082
$658$	−16.3370	−0.636883
$659$	−2.58058	−0.100525	−0.0502626	−	0.998736i	$-0.516006\pi$
$659$	−2.58058	−0.100525	−0.0502626	+	0.998736i	$0.516006\pi$
$660$	0	0
$661$	−0.146283	−0.00568975	−0.00284487	−	0.999996i	$-0.500906\pi$
$661$	−0.146283	−0.00568975	−0.00284487	+	0.999996i	$0.500906\pi$
$662$	−4.64683	−0.180604
$663$	−24.6983	−0.959203
$664$	−10.4721	−0.406398
$665$	21.8093	0.845728
$666$	−2.14590	−0.0831519
$667$	8.19211	0.317200
$668$	12.9552	0.501251
$669$	−9.74729	−0.376852
$670$	−13.0517	−0.504231
$671$	0	0
$672$	4.07314	0.157125
$673$	5.21502	0.201024	0.100512	−	0.994936i	$-0.467952\pi$
$673$	5.21502	0.201024	0.100512	+	0.994936i	$0.467952\pi$
$674$	19.3613	0.745770
$675$	1.00000	0.0384900
$676$	4.10132	0.157743
$677$	28.8694	1.10954	0.554770	−	0.832004i	$-0.312806\pi$
$677$	28.8694	1.10954	0.554770	+	0.832004i	$0.312806\pi$
$678$	−13.0735	−0.502086
$679$	−34.3695	−1.31898
$680$	−5.97245	−0.229033
$681$	19.1599	0.734210
$682$	0	0
$683$	6.40479	0.245073	0.122536	−	0.992464i	$-0.460897\pi$
$683$	6.40479	0.245073	0.122536	+	0.992464i	$0.460897\pi$
$684$	−5.35441	−0.204731
$685$	−3.74628	−0.143138
$686$	10.5514	0.402854
$687$	19.2028	0.732632
$688$	11.6807	0.445321
$689$	6.76159	0.257596
$690$	−3.33676	−0.127028
$691$	19.1515	0.728556	0.364278	−	0.931290i	$-0.381316\pi$
$691$	19.1515	0.728556	0.364278	+	0.931290i	$0.381316\pi$
$692$	−10.3439	−0.393216
$693$	0	0
$694$	28.0150	1.06344
$695$	13.7473	0.521464
$696$	−2.45511	−0.0930606
$697$	42.4511	1.60795
$698$	−25.7300	−0.973896
$699$	−5.83746	−0.220793
$700$	−4.07314	−0.153950
$701$	−39.8810	−1.50628	−0.753142	−	0.657858i	$-0.771463\pi$
$701$	−39.8810	−1.50628	−0.753142	+	0.657858i	$0.771463\pi$
$702$	4.13537	0.156080
$703$	−11.4900	−0.433355
$704$	0	0
$705$	−4.01091	−0.151060
$706$	6.66702	0.250917
$707$	−8.03406	−0.302152
$708$	−6.56293	−0.246650
$709$	18.0361	0.677359	0.338679	−	0.940902i	$-0.390020\pi$
$709$	18.0361	0.677359	0.338679	+	0.940902i	$0.390020\pi$
$710$	13.1810	0.494673
$711$	−4.97182	−0.186458
$712$	−13.5800	−0.508930
$713$	−16.4410	−0.615722
$714$	24.3266	0.910401
$715$	0	0
$716$	4.88816	0.182679
$717$	15.1246	0.564839
$718$	−8.83329	−0.329656
$719$	−7.58297	−0.282797	−0.141399	−	0.989953i	$-0.545160\pi$
$719$	−7.58297	−0.282797	−0.141399	+	0.989953i	$0.545160\pi$
$720$	1.00000	0.0372678
$721$	−38.1018	−1.41899
$722$	−9.66974	−0.359871
$723$	−20.4902	−0.762038
$724$	−8.00000	−0.297318
$725$	2.45511	0.0911804
$726$	0	0
$727$	27.9840	1.03787	0.518934	−	0.854814i	$-0.326329\pi$
$727$	27.9840	1.03787	0.518934	+	0.854814i	$0.326329\pi$
$728$	−16.8440	−0.624279
$729$	1.00000	0.0370370
$730$	−6.00000	−0.222070
$731$	69.7621	2.58024
$732$	−4.14628	−0.153251
$733$	−13.7223	−0.506844	−0.253422	−	0.967356i	$-0.581556\pi$
$733$	−13.7223	−0.506844	−0.253422	+	0.967356i	$0.581556\pi$
$734$	−12.0341	−0.444185
$735$	9.59048	0.353750
$736$	−3.33676	−0.122995
$737$	0	0
$738$	−7.10782	−0.261643
$739$	−46.6495	−1.71603	−0.858014	−	0.513626i	$-0.828302\pi$
$739$	−46.6495	−1.71603	−0.858014	+	0.513626i	$0.828302\pi$
$740$	2.14590	0.0788848
$741$	22.1425	0.813425
$742$	−6.65984	−0.244490
$743$	26.3399	0.966316	0.483158	−	0.875533i	$-0.339490\pi$
$743$	26.3399	0.966316	0.483158	+	0.875533i	$0.339490\pi$
$744$	4.92724	0.180642
$745$	6.02755	0.220832
$746$	−31.8273	−1.16528
$747$	10.4721	0.383155
$748$	0	0
$749$	−34.0012	−1.24238
$750$	−1.00000	−0.0365148
$751$	4.47864	0.163428	0.0817140	−	0.996656i	$-0.473961\pi$
$751$	4.47864	0.163428	0.0817140	+	0.996656i	$0.473961\pi$
$752$	−4.01091	−0.146263
$753$	14.6300	0.533145
$754$	10.1528	0.369743
$755$	−14.8551	−0.540633
$756$	−4.07314	−0.148139
$757$	19.1027	0.694300	0.347150	−	0.937810i	$-0.387150\pi$
$757$	19.1027	0.694300	0.347150	+	0.937810i	$0.387150\pi$
$758$	15.6153	0.567172
$759$	0	0
$760$	5.35441	0.194225
$761$	2.98637	0.108256	0.0541279	−	0.998534i	$-0.482762\pi$
$761$	2.98637	0.108256	0.0541279	+	0.998534i	$0.482762\pi$
$762$	−19.5007	−0.706436
$763$	−58.9471	−2.13403
$764$	24.0701	0.870827
$765$	5.97245	0.215934
$766$	0.346664	0.0125255
$767$	27.1402	0.979975
$768$	1.00000	0.0360844
$769$	13.9222	0.502048	0.251024	−	0.967981i	$-0.419233\pi$
$769$	13.9222	0.502048	0.251024	+	0.967981i	$0.419233\pi$
$770$	0	0
$771$	21.4164	0.771293
$772$	15.1116	0.543878
$773$	−6.00378	−0.215941	−0.107971	−	0.994154i	$-0.534435\pi$
$773$	−6.00378	−0.215941	−0.107971	+	0.994154i	$0.534435\pi$
$774$	−11.6807	−0.419852
$775$	−4.92724	−0.176992
$776$	−8.43808	−0.302909
$777$	−8.74055	−0.313565
$778$	1.93714	0.0694500
$779$	−38.0582	−1.36358
$780$	−4.13537	−0.148070
$781$	0	0
$782$	−19.9286	−0.712647
$783$	2.45511	0.0877384
$784$	9.59048	0.342517
$785$	−4.45133	−0.158875
$786$	15.7252	0.560900
$787$	−37.5915	−1.33999	−0.669996	−	0.742365i	$-0.733704\pi$
$787$	−37.5915	−1.33999	−0.669996	+	0.742365i	$0.733704\pi$
$788$	−17.0515	−0.607433
$789$	−30.3270	−1.07967
$790$	4.97182	0.176890
$791$	−53.2503	−1.89336
$792$	0	0
$793$	17.1464	0.608888
$794$	−30.9205	−1.09733
$795$	−1.63506	−0.0579897
$796$	5.40990	0.191749
$797$	−23.2442	−0.823352	−0.411676	−	0.911330i	$-0.635056\pi$
$797$	−23.2442	−0.823352	−0.411676	+	0.911330i	$0.635056\pi$
$798$	−21.8093	−0.772040
$799$	−23.9549	−0.847465
$800$	−1.00000	−0.0353553
$801$	13.5800	0.479824
$802$	−32.1885	−1.13661
$803$	0	0
$804$	13.0517	0.460298
$805$	−13.5911	−0.479023
$806$	−20.3760	−0.717714
$807$	−10.5796	−0.372419
$808$	−1.97245	−0.0693905
$809$	−18.4239	−0.647751	−0.323875	−	0.946100i	$-0.604986\pi$
$809$	−18.4239	−0.647751	−0.323875	+	0.946100i	$0.604986\pi$
$810$	−1.00000	−0.0351364
$811$	7.93987	0.278806	0.139403	−	0.990236i	$-0.455482\pi$
$811$	7.93987	0.278806	0.139403	+	0.990236i	$0.455482\pi$
$812$	−10.0000	−0.350931
$813$	0.825542	0.0289530
$814$	0	0
$815$	−18.2991	−0.640988
$816$	5.97245	0.209077
$817$	−62.5430	−2.18810
$818$	−5.39249	−0.188544
$819$	16.8440	0.588576
$820$	7.10782	0.248216
$821$	−44.5280	−1.55404	−0.777019	−	0.629477i	$-0.783269\pi$
$821$	−44.5280	−1.55404	−0.777019	+	0.629477i	$0.783269\pi$
$822$	3.74628	0.130667
$823$	5.97283	0.208200	0.104100	−	0.994567i	$-0.466804\pi$
$823$	5.97283	0.208200	0.104100	+	0.994567i	$0.466804\pi$
$824$	−9.35441	−0.325876
$825$	0	0
$826$	−26.7317	−0.930116
$827$	−20.7865	−0.722818	−0.361409	−	0.932407i	$-0.617704\pi$
$827$	−20.7865	−0.722818	−0.361409	+	0.932407i	$0.617704\pi$
$828$	3.33676	0.115960
$829$	−32.2573	−1.12034	−0.560171	−	0.828377i	$-0.689264\pi$
$829$	−32.2573	−1.12034	−0.560171	+	0.828377i	$0.689264\pi$
$830$	−10.4721	−0.363493
$831$	26.7321	0.927327
$832$	−4.13537	−0.143368
$833$	57.2786	1.98459
$834$	−13.7473	−0.476030
$835$	12.9552	0.448333
$836$	0	0
$837$	−4.92724	−0.170310
$838$	−5.67453	−0.196023
$839$	−42.2497	−1.45862	−0.729311	−	0.684183i	$-0.760159\pi$
$839$	−42.2497	−1.45862	−0.729311	+	0.684183i	$0.760159\pi$
$840$	4.07314	0.140537
$841$	−22.9724	−0.792153
$842$	7.43870	0.256355
$843$	6.94427	0.239173
$844$	−25.8545	−0.889948
$845$	4.10132	0.141090
$846$	4.01091	0.137898
$847$	0	0
$848$	−1.63506	−0.0561483
$849$	−5.57895	−0.191469
$850$	−5.97245	−0.204853
$851$	7.16035	0.245454
$852$	−13.1810	−0.451572
$853$	−27.3214	−0.935469	−0.467734	−	0.883869i	$-0.654930\pi$
$853$	−27.3214	−0.935469	−0.467734	+	0.883869i	$0.654930\pi$
$854$	−16.8884	−0.577909
$855$	−5.35441	−0.183117
$856$	−8.34767	−0.285318
$857$	−32.2432	−1.10141	−0.550703	−	0.834701i	$-0.685640\pi$
$857$	−32.2432	−1.10141	−0.550703	+	0.834701i	$0.685640\pi$
$858$	0	0
$859$	23.6148	0.805726	0.402863	−	0.915260i	$-0.368015\pi$
$859$	23.6148	0.805726	0.402863	+	0.915260i	$0.368015\pi$
$860$	11.6807	0.398307
$861$	−28.9512	−0.986653
$862$	29.1599	0.993191
$863$	9.45085	0.321711	0.160855	−	0.986978i	$-0.448575\pi$
$863$	9.45085	0.321711	0.160855	+	0.986978i	$0.448575\pi$
$864$	−1.00000	−0.0340207
$865$	−10.3439	−0.351703
$866$	−23.0918	−0.784691
$867$	18.6701	0.634071
$868$	20.0694	0.681198
$869$	0	0
$870$	−2.45511	−0.0832359
$871$	−53.9737	−1.82883
$872$	−14.4721	−0.490088
$873$	8.43808	0.285586
$874$	17.8664	0.604340
$875$	−4.07314	−0.137697
$876$	6.00000	0.202721
$877$	7.78551	0.262898	0.131449	−	0.991323i	$-0.458037\pi$
$877$	7.78551	0.262898	0.131449	+	0.991323i	$0.458037\pi$
$878$	−37.6709	−1.27133
$879$	7.87175	0.265508
$880$	0	0
$881$	−1.10705	−0.0372975	−0.0186488	−	0.999826i	$-0.505936\pi$
$881$	−1.10705	−0.0372975	−0.0186488	+	0.999826i	$0.505936\pi$
$882$	−9.59048	−0.322928
$883$	−16.6595	−0.560635	−0.280318	−	0.959907i	$-0.590440\pi$
$883$	−16.6595	−0.560635	−0.280318	+	0.959907i	$0.590440\pi$
$884$	−24.6983	−0.830694
$885$	−6.56293	−0.220610
$886$	16.9796	0.570440
$887$	7.34977	0.246781	0.123391	−	0.992358i	$-0.460623\pi$
$887$	7.34977	0.246781	0.123391	+	0.992358i	$0.460623\pi$
$888$	−2.14590	−0.0720116
$889$	−79.4291	−2.66397
$890$	−13.5800	−0.455201
$891$	0	0
$892$	−9.74729	−0.326363
$893$	21.4761	0.718669
$894$	−6.02755	−0.201592
$895$	4.88816	0.163393
$896$	4.07314	0.136074
$897$	−13.7988	−0.460727
$898$	7.13877	0.238224
$899$	−12.0969	−0.403455
$900$	1.00000	0.0333333
$901$	−9.76532	−0.325330
$902$	0	0
$903$	−47.5769	−1.58326
$904$	−13.0735	−0.434819
$905$	−8.00000	−0.265929
$906$	14.8551	0.493528
$907$	57.3678	1.90487	0.952433	−	0.304747i	$-0.0985719\pi$
$907$	57.3678	1.90487	0.952433	+	0.304747i	$0.0985719\pi$
$908$	19.1599	0.635844
$909$	1.97245	0.0654219
$910$	−16.8440	−0.558372
$911$	16.1252	0.534253	0.267126	−	0.963661i	$-0.413926\pi$
$911$	16.1252	0.534253	0.267126	+	0.963661i	$0.413926\pi$
$912$	−5.35441	−0.177302
$913$	0	0
$914$	16.3266	0.540037
$915$	−4.14628	−0.137072
$916$	19.2028	0.634478
$917$	64.0511	2.11515
$918$	−5.97245	−0.197120
$919$	−40.7506	−1.34424	−0.672120	−	0.740443i	$-0.734616\pi$
$919$	−40.7506	−1.34424	−0.672120	+	0.740443i	$0.734616\pi$
$920$	−3.33676	−0.110010
$921$	−20.5463	−0.677023
$922$	−22.0636	−0.726627
$923$	54.5082	1.79416
$924$	0	0
$925$	2.14590	0.0705567
$926$	23.7592	0.780776
$927$	9.35441	0.307239
$928$	−2.45511	−0.0805929
$929$	−58.3454	−1.91425	−0.957126	−	0.289673i	$-0.906453\pi$
$929$	−58.3454	−1.91425	−0.957126	+	0.289673i	$0.906453\pi$
$930$	4.92724	0.161571
$931$	−51.3514	−1.68297
$932$	−5.83746	−0.191212
$933$	12.8198	0.419702
$934$	2.59785	0.0850041
$935$	0	0
$936$	4.13537	0.135169
$937$	28.0130	0.915145	0.457573	−	0.889172i	$-0.348719\pi$
$937$	28.0130	0.915145	0.457573	+	0.889172i	$0.348719\pi$
$938$	53.1615	1.73578
$939$	−1.36053	−0.0443993
$940$	−4.01091	−0.130821
$941$	−13.4906	−0.439780	−0.219890	−	0.975525i	$-0.570570\pi$
$941$	−13.4906	−0.439780	−0.219890	+	0.975525i	$0.570570\pi$
$942$	4.45133	0.145032
$943$	23.7171	0.772335
$944$	−6.56293	−0.213605
$945$	−4.07314	−0.132499
$946$	0	0
$947$	−36.5192	−1.18671	−0.593357	−	0.804939i	$-0.702198\pi$
$947$	−36.5192	−1.18671	−0.593357	+	0.804939i	$0.702198\pi$
$948$	−4.97182	−0.161477
$949$	−24.8122	−0.805439
$950$	5.35441	0.173720
$951$	−25.1197	−0.814563
$952$	24.3266	0.788430
$953$	30.9398	1.00224	0.501119	−	0.865378i	$-0.332922\pi$
$953$	30.9398	1.00224	0.501119	+	0.865378i	$0.332922\pi$
$954$	1.63506	0.0529371
$955$	24.0701	0.778891
$956$	15.1246	0.489165
$957$	0	0
$958$	−17.4382	−0.563404
$959$	15.2591	0.492743
$960$	1.00000	0.0322749
$961$	−6.72227	−0.216847
$962$	8.87409	0.286112
$963$	8.34767	0.269000
$964$	−20.4902	−0.659944
$965$	15.1116	0.486460
$966$	13.5911	0.437287
$967$	31.3913	1.00947	0.504737	−	0.863273i	$-0.331589\pi$
$967$	31.3913	1.00947	0.504737	+	0.863273i	$0.331589\pi$
$968$	0	0
$969$	−31.9790	−1.02731
$970$	−8.43808	−0.270930
$971$	35.9982	1.15524	0.577619	−	0.816306i	$-0.303982\pi$
$971$	35.9982	1.15524	0.577619	+	0.816306i	$0.303982\pi$
$972$	1.00000	0.0320750
$973$	−55.9947	−1.79511
$974$	−20.4734	−0.656009
$975$	−4.13537	−0.132438
$976$	−4.14628	−0.132719
$977$	58.7239	1.87874	0.939371	−	0.342902i	$-0.111410\pi$
$977$	58.7239	1.87874	0.939371	+	0.342902i	$0.111410\pi$
$978$	18.2991	0.585140
$979$	0	0
$980$	9.59048	0.306357
$981$	14.4721	0.462060
$982$	−4.92112	−0.157039
$983$	−43.9957	−1.40325	−0.701623	−	0.712548i	$-0.747541\pi$
$983$	−43.9957	−1.40325	−0.701623	+	0.712548i	$0.747541\pi$
$984$	−7.10782	−0.226589
$985$	−17.0515	−0.543305
$986$	−14.6630	−0.466965
$987$	16.3370	0.520012
$988$	22.1425	0.704447
$989$	38.9756	1.23935
$990$	0	0
$991$	−40.8969	−1.29913	−0.649567	−	0.760305i	$-0.725050\pi$
$991$	−40.8969	−1.29913	−0.649567	+	0.760305i	$0.725050\pi$
$992$	4.92724	0.156440
$993$	4.64683	0.147463
$994$	−53.6879	−1.70288
$995$	5.40990	0.171505
$996$	10.4721	0.331822
$997$	−30.7616	−0.974230	−0.487115	−	0.873338i	$-0.661951\pi$
$997$	−30.7616	−0.974230	−0.487115	+	0.873338i	$0.661951\pi$
$998$	26.1766	0.828604
$999$	2.14590	0.0678932

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3630.2.a.br.1.1		4
11.7	odd	10		330.2.m.e.181.1	yes	8
11.8	odd	10		330.2.m.e.31.1	✓	8
11.10	odd	2		3630.2.a.bt.1.4		4
33.8	even	10		990.2.n.k.361.1		8
33.29	even	10		990.2.n.k.181.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.m.e.31.1	✓	8	11.8	odd	10
330.2.m.e.181.1	yes	8	11.7	odd	10
990.2.n.k.181.1		8	33.29	even	10
990.2.n.k.361.1		8	33.8	even	10
3630.2.a.br.1.1		4	1.1	even	1	trivial
3630.2.a.bt.1.4		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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -4.07314 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -4.07314 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{12} -4.13537 q^{13} +4.07314 q^{14} +1.00000 q^{15} +1.00000 q^{16} +5.97245 q^{17} -1.00000 q^{18} -5.35441 q^{19} +1.00000 q^{20} -4.07314 q^{21} +3.33676 q^{23} -1.00000 q^{24} +1.00000 q^{25} +4.13537 q^{26} +1.00000 q^{27} -4.07314 q^{28} +2.45511 q^{29} -1.00000 q^{30} -4.92724 q^{31} -1.00000 q^{32} -5.97245 q^{34} -4.07314 q^{35} +1.00000 q^{36} +2.14590 q^{37} +5.35441 q^{38} -4.13537 q^{39} -1.00000 q^{40} +7.10782 q^{41} +4.07314 q^{42} +11.6807 q^{43} +1.00000 q^{45} -3.33676 q^{46} -4.01091 q^{47} +1.00000 q^{48} +9.59048 q^{49} -1.00000 q^{50} +5.97245 q^{51} -4.13537 q^{52} -1.63506 q^{53} -1.00000 q^{54} +4.07314 q^{56} -5.35441 q^{57} -2.45511 q^{58} -6.56293 q^{59} +1.00000 q^{60} -4.14628 q^{61} +4.92724 q^{62} -4.07314 q^{63} +1.00000 q^{64} -4.13537 q^{65} +13.0517 q^{67} +5.97245 q^{68} +3.33676 q^{69} +4.07314 q^{70} -13.1810 q^{71} -1.00000 q^{72} +6.00000 q^{73} -2.14590 q^{74} +1.00000 q^{75} -5.35441 q^{76} +4.13537 q^{78} -4.97182 q^{79} +1.00000 q^{80} +1.00000 q^{81} -7.10782 q^{82} +10.4721 q^{83} -4.07314 q^{84} +5.97245 q^{85} -11.6807 q^{86} +2.45511 q^{87} +13.5800 q^{89} -1.00000 q^{90} +16.8440 q^{91} +3.33676 q^{92} -4.92724 q^{93} +4.01091 q^{94} -5.35441 q^{95} -1.00000 q^{96} +8.43808 q^{97} -9.59048 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} - 4 q^{6} - q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 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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