LMFDB - Embedded newform 7942.2.a.bd.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7942,2,Mod(1,7942)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7942, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("7942.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7942 = 2 \cdot 11 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7942.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:	$63.4171892853$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.1940.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 8x - 2 $ x^3 - 8*x - 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 418)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.252000$ of defining polynomial
Character	$\chi$	$=$	7942.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.252000 q^{3} +1.00000 q^{4} +2.00000 q^{5} -0.252000 q^{6} +1.74800 q^{7} -1.00000 q^{8} -2.93650 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.252000 q^{3} +1.00000 q^{4} +2.00000 q^{5} -0.252000 q^{6} +1.74800 q^{7} -1.00000 q^{8} -2.93650 q^{9} -2.00000 q^{10} +1.00000 q^{11} +0.252000 q^{12} -2.93650 q^{13} -1.74800 q^{14} +0.504001 q^{15} +1.00000 q^{16} -1.68450 q^{17} +2.93650 q^{18} +2.00000 q^{20} +0.440497 q^{21} -1.00000 q^{22} +4.50400 q^{23} -0.252000 q^{24} -1.00000 q^{25} +2.93650 q^{26} -1.49600 q^{27} +1.74800 q^{28} -1.00000 q^{29} -0.504001 q^{30} +5.43250 q^{31} -1.00000 q^{32} +0.252000 q^{33} +1.68450 q^{34} +3.49600 q^{35} -2.93650 q^{36} -3.18049 q^{37} -0.739998 q^{39} -2.00000 q^{40} -2.18850 q^{41} -0.440497 q^{42} +7.18850 q^{43} +1.00000 q^{44} -5.87299 q^{45} -4.50400 q^{46} +6.62099 q^{47} +0.252000 q^{48} -3.94450 q^{49} +1.00000 q^{50} -0.424493 q^{51} -2.93650 q^{52} -1.00800 q^{53} +1.49600 q^{54} +2.00000 q^{55} -1.74800 q^{56} +1.00000 q^{58} +0.504001 q^{60} +9.44050 q^{61} -5.43250 q^{62} -5.13299 q^{63} +1.00000 q^{64} -5.87299 q^{65} -0.252000 q^{66} -0.756001 q^{67} -1.68450 q^{68} +1.13501 q^{69} -3.49600 q^{70} -7.18850 q^{71} +2.93650 q^{72} +8.18850 q^{73} +3.18049 q^{74} -0.252000 q^{75} +1.74800 q^{77} +0.739998 q^{78} +2.75600 q^{79} +2.00000 q^{80} +8.43250 q^{81} +2.18850 q^{82} -3.69250 q^{83} +0.440497 q^{84} -3.36899 q^{85} -7.18850 q^{86} -0.252000 q^{87} -1.00000 q^{88} +10.3690 q^{89} +5.87299 q^{90} -5.13299 q^{91} +4.50400 q^{92} +1.36899 q^{93} -6.62099 q^{94} -0.252000 q^{96} -12.3690 q^{97} +3.94450 q^{98} -2.93650 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{4} + 6 q^{5} + 6 q^{7} - 3 q^{8} + 7 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^4 + 6 * q^5 + 6 * q^7 - 3 * q^8 + 7 * q^9	$ 3 q - 3 q^{2} + 3 q^{4} + 6 q^{5} + 6 q^{7} - 3 q^{8} + 7 q^{9} - 6 q^{10} + 3 q^{11} + 7 q^{13} - 6 q^{14} + 3 q^{16} + 10 q^{17} - 7 q^{18} + 6 q^{20} - 16 q^{21} - 3 q^{22} + 12 q^{23} - 3 q^{25} - 7 q^{26} - 6 q^{27} + 6 q^{28} - 3 q^{29} + 2 q^{31} - 3 q^{32} - 10 q^{34} + 12 q^{35} + 7 q^{36} + 4 q^{37} - 6 q^{39} - 6 q^{40} + 10 q^{41} + 16 q^{42} + 5 q^{43} + 3 q^{44} + 14 q^{45} - 12 q^{46} - 11 q^{47} + 7 q^{49} + 3 q^{50} + 10 q^{51} + 7 q^{52} + 6 q^{54} + 6 q^{55} - 6 q^{56} + 3 q^{58} + 11 q^{61} - 2 q^{62} + 20 q^{63} + 3 q^{64} + 14 q^{65} + 10 q^{68} + 32 q^{69} - 12 q^{70} - 5 q^{71} - 7 q^{72} + 8 q^{73} - 4 q^{74} + 6 q^{77} + 6 q^{78} + 6 q^{79} + 6 q^{80} + 11 q^{81} - 10 q^{82} + 7 q^{83} - 16 q^{84} + 20 q^{85} - 5 q^{86} - 3 q^{88} + q^{89} - 14 q^{90} + 20 q^{91} + 12 q^{92} - 26 q^{93} + 11 q^{94} - 7 q^{97} - 7 q^{98} + 7 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + 3 * q^4 + 6 * q^5 + 6 * q^7 - 3 * q^8 + 7 * q^9 - 6 * q^10 + 3 * q^11 + 7 * q^13 - 6 * q^14 + 3 * q^16 + 10 * q^17 - 7 * q^18 + 6 * q^20 - 16 * q^21 - 3 * q^22 + 12 * q^23 - 3 * q^25 - 7 * q^26 - 6 * q^27 + 6 * q^28 - 3 * q^29 + 2 * q^31 - 3 * q^32 - 10 * q^34 + 12 * q^35 + 7 * q^36 + 4 * q^37 - 6 * q^39 - 6 * q^40 + 10 * q^41 + 16 * q^42 + 5 * q^43 + 3 * q^44 + 14 * q^45 - 12 * q^46 - 11 * q^47 + 7 * q^49 + 3 * q^50 + 10 * q^51 + 7 * q^52 + 6 * q^54 + 6 * q^55 - 6 * q^56 + 3 * q^58 + 11 * q^61 - 2 * q^62 + 20 * q^63 + 3 * q^64 + 14 * q^65 + 10 * q^68 + 32 * q^69 - 12 * q^70 - 5 * q^71 - 7 * q^72 + 8 * q^73 - 4 * q^74 + 6 * q^77 + 6 * q^78 + 6 * q^79 + 6 * q^80 + 11 * q^81 - 10 * q^82 + 7 * q^83 - 16 * q^84 + 20 * q^85 - 5 * q^86 - 3 * q^88 + q^89 - 14 * q^90 + 20 * q^91 + 12 * q^92 - 26 * q^93 + 11 * q^94 - 7 * q^97 - 7 * q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.252000	0.145492	0.0727462	−	0.997350i	$-0.476824\pi$
$3$	0.252000	0.145492	0.0727462	+	0.997350i	$0.476824\pi$
$4$	1.00000	0.500000
$5$	2.00000	0.894427	0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000	0.894427	0.447214	+	0.894427i	$0.352416\pi$
$6$	−0.252000	−0.102879
$7$	1.74800	0.660682	0.330341	−	0.943862i	$-0.392836\pi$
$7$	1.74800	0.660682	0.330341	+	0.943862i	$0.392836\pi$
$8$	−1.00000	−0.353553
$9$	−2.93650	−0.978832
$10$	−2.00000	−0.632456
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.252000	0.0727462
$13$	−2.93650	−0.814437	−0.407219	−	0.913331i	$-0.633501\pi$
$13$	−2.93650	−0.814437	−0.407219	+	0.913331i	$0.633501\pi$
$14$	−1.74800	−0.467173
$15$	0.504001	0.130132
$16$	1.00000	0.250000
$17$	−1.68450	−0.408550	−0.204275	−	0.978914i	$-0.565484\pi$
$17$	−1.68450	−0.408550	−0.204275	+	0.978914i	$0.565484\pi$
$18$	2.93650	0.692139
$19$	0	0
$19$	0	0
$20$	2.00000	0.447214
$21$	0.440497	0.0961242
$22$	−1.00000	−0.213201
$23$	4.50400	0.939149	0.469575	−	0.882893i	$-0.344407\pi$
$23$	4.50400	0.939149	0.469575	+	0.882893i	$0.344407\pi$
$24$	−0.252000	−0.0514394
$25$	−1.00000	−0.200000
$26$	2.93650	0.575894
$27$	−1.49600	−0.287905
$28$	1.74800	0.330341
$29$	−1.00000	−0.185695	−0.0928477	−	0.995680i	$-0.529597\pi$
$29$	−1.00000	−0.185695	−0.0928477	+	0.995680i	$0.529597\pi$
$30$	−0.504001	−0.0920175
$31$	5.43250	0.975705	0.487852	−	0.872926i	$-0.337780\pi$
$31$	5.43250	0.975705	0.487852	+	0.872926i	$0.337780\pi$
$32$	−1.00000	−0.176777
$33$	0.252000	0.0438676
$34$	1.68450	0.288889
$35$	3.49600	0.590932
$36$	−2.93650	−0.489416
$37$	−3.18049	−0.522870	−0.261435	−	0.965221i	$-0.584196\pi$
$37$	−3.18049	−0.522870	−0.261435	+	0.965221i	$0.584196\pi$
$38$	0	0
$39$	−0.739998	−0.118495
$40$	−2.00000	−0.316228
$41$	−2.18850	−0.341786	−0.170893	−	0.985290i	$-0.554665\pi$
$41$	−2.18850	−0.341786	−0.170893	+	0.985290i	$0.554665\pi$
$42$	−0.440497	−0.0679701
$43$	7.18850	1.09624	0.548118	−	0.836401i	$-0.315345\pi$
$43$	7.18850	1.09624	0.548118	+	0.836401i	$0.315345\pi$
$44$	1.00000	0.150756
$45$	−5.87299	−0.875494
$46$	−4.50400	−0.664079
$47$	6.62099	0.965771	0.482885	−	0.875684i	$-0.339589\pi$
$47$	6.62099	0.965771	0.482885	+	0.875684i	$0.339589\pi$
$48$	0.252000	0.0363731
$49$	−3.94450	−0.563500
$50$	1.00000	0.141421
$51$	−0.424493	−0.0594410
$52$	−2.93650	−0.407219
$53$	−1.00800	−0.138460	−0.0692298	−	0.997601i	$-0.522054\pi$
$53$	−1.00800	−0.138460	−0.0692298	+	0.997601i	$0.522054\pi$
$54$	1.49600	0.203580
$55$	2.00000	0.269680
$56$	−1.74800	−0.233586
$57$	0	0
$58$	1.00000	0.131306
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0.504001	0.0650662
$61$	9.44050	1.20873	0.604366	−	0.796707i	$-0.293427\pi$
$61$	9.44050	1.20873	0.604366	+	0.796707i	$0.293427\pi$
$62$	−5.43250	−0.689928
$63$	−5.13299	−0.646696
$64$	1.00000	0.125000
$65$	−5.87299	−0.728455
$66$	−0.252000	−0.0310191
$67$	−0.756001	−0.0923602	−0.0461801	−	0.998933i	$-0.514705\pi$
$67$	−0.756001	−0.0923602	−0.0461801	+	0.998933i	$0.514705\pi$
$68$	−1.68450	−0.204275
$69$	1.13501	0.136639
$70$	−3.49600	−0.417852
$71$	−7.18850	−0.853118	−0.426559	−	0.904460i	$-0.640274\pi$
$71$	−7.18850	−0.853118	−0.426559	+	0.904460i	$0.640274\pi$
$72$	2.93650	0.346069
$73$	8.18850	0.958391	0.479195	−	0.877708i	$-0.340928\pi$
$73$	8.18850	0.958391	0.479195	+	0.877708i	$0.340928\pi$
$74$	3.18049	0.369725
$75$	−0.252000	−0.0290985
$76$	0	0
$77$	1.74800	0.199203
$78$	0.739998	0.0837883
$79$	2.75600	0.310074	0.155037	−	0.987909i	$-0.450450\pi$
$79$	2.75600	0.310074	0.155037	+	0.987909i	$0.450450\pi$
$80$	2.00000	0.223607
$81$	8.43250	0.936944
$82$	2.18850	0.241679
$83$	−3.69250	−0.405304	−0.202652	−	0.979251i	$-0.564956\pi$
$83$	−3.69250	−0.405304	−0.202652	+	0.979251i	$0.564956\pi$
$84$	0.440497	0.0480621
$85$	−3.36899	−0.365418
$86$	−7.18850	−0.775155
$87$	−0.252000	−0.0270173
$88$	−1.00000	−0.106600
$89$	10.3690	1.09911	0.549555	−	0.835457i	$-0.314797\pi$
$89$	10.3690	1.09911	0.549555	+	0.835457i	$0.314797\pi$
$90$	5.87299	0.619068
$91$	−5.13299	−0.538084
$92$	4.50400	0.469575
$93$	1.36899	0.141958
$94$	−6.62099	−0.682903
$95$	0	0
$96$	−0.252000	−0.0257197
$97$	−12.3690	−1.25588	−0.627940	−	0.778261i	$-0.716102\pi$
$97$	−12.3690	−1.25588	−0.627940	+	0.778261i	$0.716102\pi$
$98$	3.94450	0.398454
$99$	−2.93650	−0.295129
$100$	−1.00000	−0.100000
$101$	6.93650	0.690207	0.345104	−	0.938565i	$-0.387844\pi$
$101$	6.93650	0.690207	0.345104	+	0.938565i	$0.387844\pi$
$102$	0.424493	0.0420311
$103$	6.62099	0.652386	0.326193	−	0.945303i	$-0.394234\pi$
$103$	6.62099	0.652386	0.326193	+	0.945303i	$0.394234\pi$
$104$	2.93650	0.287947
$105$	0.880993	0.0859761
$106$	1.00800	0.0979058
$107$	17.6130	1.70271	0.851356	−	0.524588i	$-0.175781\pi$
$107$	17.6130	1.70271	0.851356	+	0.524588i	$0.175781\pi$
$108$	−1.49600	−0.143953
$109$	−3.94450	−0.377814	−0.188907	−	0.981995i	$-0.560495\pi$
$109$	−3.94450	−0.377814	−0.188907	+	0.981995i	$0.560495\pi$
$110$	−2.00000	−0.190693
$111$	−0.801486	−0.0760737
$112$	1.74800	0.165170
$113$	−14.3690	−1.35172	−0.675860	−	0.737030i	$-0.736228\pi$
$113$	−14.3690	−1.35172	−0.675860	+	0.737030i	$0.736228\pi$
$114$	0	0
$115$	9.00800	0.840000
$116$	−1.00000	−0.0928477
$117$	8.62301	0.797197
$118$	0	0
$119$	−2.94450	−0.269922
$120$	−0.504001	−0.0460088
$121$	1.00000	0.0909091
$122$	−9.44050	−0.854702
$123$	−0.551502	−0.0497273
$124$	5.43250	0.487852
$125$	−12.0000	−1.07331
$126$	5.13299	0.457283
$127$	11.8730	1.05356	0.526779	−	0.850002i	$-0.323400\pi$
$127$	11.8730	1.05356	0.526779	+	0.850002i	$0.323400\pi$
$128$	−1.00000	−0.0883883
$129$	1.81150	0.159494
$130$	5.87299	0.515095
$131$	11.6130	1.01463	0.507316	−	0.861760i	$-0.330638\pi$
$131$	11.6130	1.01463	0.507316	+	0.861760i	$0.330638\pi$
$132$	0.252000	0.0219338
$133$	0	0
$134$	0.756001	0.0653086
$135$	−2.99200	−0.257510
$136$	1.68450	0.144444
$137$	9.92849	0.848249	0.424124	−	0.905604i	$-0.360582\pi$
$137$	9.92849	0.848249	0.424124	+	0.905604i	$0.360582\pi$
$138$	−1.13501	−0.0966185
$139$	5.51200	0.467522	0.233761	−	0.972294i	$-0.424897\pi$
$139$	5.51200	0.467522	0.233761	+	0.972294i	$0.424897\pi$
$140$	3.49600	0.295466
$141$	1.66849	0.140512
$142$	7.18850	0.603245
$143$	−2.93650	−0.245562
$144$	−2.93650	−0.244708
$145$	−2.00000	−0.166091
$146$	−8.18850	−0.677685
$147$	−0.994015	−0.0819850
$148$	−3.18049	−0.261435
$149$	8.42449	0.690161	0.345081	−	0.938573i	$-0.387852\pi$
$149$	8.42449	0.690161	0.345081	+	0.938573i	$0.387852\pi$
$150$	0.252000	0.0205757
$151$	13.9980	1.13914	0.569570	−	0.821943i	$-0.307110\pi$
$151$	13.9980	1.13914	0.569570	+	0.821943i	$0.307110\pi$
$152$	0	0
$153$	4.94651	0.399902
$154$	−1.74800	−0.140858
$155$	10.8650	0.872697
$156$	−0.739998	−0.0592473
$157$	1.00800	0.0804473	0.0402236	−	0.999191i	$-0.487193\pi$
$157$	1.00800	0.0804473	0.0402236	+	0.999191i	$0.487193\pi$
$158$	−2.75600	−0.219256
$159$	−0.254017	−0.0201448
$160$	−2.00000	−0.158114
$161$	7.87299	0.620479
$162$	−8.43250	−0.662519
$163$	17.2420	1.35050	0.675248	−	0.737591i	$-0.264037\pi$
$163$	17.2420	1.35050	0.675248	+	0.737591i	$0.264037\pi$
$164$	−2.18850	−0.170893
$165$	0.504001	0.0392364
$166$	3.69250	0.286593
$167$	22.4860	1.74002	0.870009	−	0.493036i	$-0.164113\pi$
$167$	22.4860	1.74002	0.870009	+	0.493036i	$0.164113\pi$
$168$	−0.440497	−0.0339850
$169$	−4.37699	−0.336692
$170$	3.36899	0.258390
$171$	0	0
$172$	7.18850	0.548118
$173$	−9.43250	−0.717139	−0.358570	−	0.933503i	$-0.616735\pi$
$173$	−9.43250	−0.717139	−0.358570	+	0.933503i	$0.616735\pi$
$174$	0.252000	0.0191041
$175$	−1.74800	−0.132136
$176$	1.00000	0.0753778
$177$	0	0
$178$	−10.3690	−0.777189
$179$	10.5040	0.785106	0.392553	−	0.919729i	$-0.371592\pi$
$179$	10.5040	0.785106	0.392553	+	0.919729i	$0.371592\pi$
$180$	−5.87299	−0.437747
$181$	−9.19650	−0.683570	−0.341785	−	0.939778i	$-0.611032\pi$
$181$	−9.19650	−0.683570	−0.341785	+	0.939778i	$0.611032\pi$
$182$	5.13299	0.380483
$183$	2.37901	0.175861
$184$	−4.50400	−0.332039
$185$	−6.36099	−0.467669
$186$	−1.36899	−0.100379
$187$	−1.68450	−0.123183
$188$	6.62099	0.482885
$189$	−2.61501	−0.190214
$190$	0	0
$191$	24.6210	1.78151	0.890756	−	0.454481i	$-0.150175\pi$
$191$	24.6210	1.78151	0.890756	+	0.454481i	$0.150175\pi$
$192$	0.252000	0.0181866
$193$	12.6925	0.913626	0.456813	−	0.889563i	$-0.348991\pi$
$193$	12.6925	0.913626	0.456813	+	0.889563i	$0.348991\pi$
$194$	12.3690	0.888042
$195$	−1.48000	−0.105985
$196$	−3.94450	−0.281750
$197$	−20.3690	−1.45123	−0.725615	−	0.688101i	$-0.758445\pi$
$197$	−20.3690	−1.45123	−0.725615	+	0.688101i	$0.758445\pi$
$198$	2.93650	0.208688
$199$	8.81150	0.624631	0.312315	−	0.949978i	$-0.398895\pi$
$199$	8.81150	0.624631	0.312315	+	0.949978i	$0.398895\pi$
$200$	1.00000	0.0707107
$201$	−0.190513	−0.0134377
$202$	−6.93650	−0.488050
$203$	−1.74800	−0.122686
$204$	−0.424493	−0.0297205
$205$	−4.37699	−0.305702
$206$	−6.62099	−0.461306
$207$	−13.2260	−0.919269
$208$	−2.93650	−0.203609
$209$	0	0
$210$	−0.880993	−0.0607943
$211$	−6.48800	−0.446652	−0.223326	−	0.974744i	$-0.571691\pi$
$211$	−6.48800	−0.446652	−0.223326	+	0.974744i	$0.571691\pi$
$212$	−1.00800	−0.0692298
$213$	−1.81150	−0.124122
$214$	−17.6130	−1.20400
$215$	14.3770	0.980503
$216$	1.49600	0.101790
$217$	9.49600	0.644630
$218$	3.94450	0.267155
$219$	2.06350	0.139439
$220$	2.00000	0.134840
$221$	4.94651	0.332739
$222$	0.801486	0.0537922
$223$	−19.1885	−1.28496	−0.642478	−	0.766304i	$-0.722094\pi$
$223$	−19.1885	−1.28496	−0.642478	+	0.766304i	$0.722094\pi$
$224$	−1.74800	−0.116793
$225$	2.93650	0.195766
$226$	14.3690	0.955811
$227$	−0.551502	−0.0366045	−0.0183022	−	0.999833i	$-0.505826\pi$
$227$	−0.551502	−0.0366045	−0.0183022	+	0.999833i	$0.505826\pi$
$228$	0	0
$229$	24.0615	1.59003	0.795014	−	0.606591i	$-0.207463\pi$
$229$	24.0615	1.59003	0.795014	+	0.606591i	$0.207463\pi$
$230$	−9.00800	−0.593970
$231$	0.440497	0.0289825
$232$	1.00000	0.0656532
$233$	−17.4305	−1.14191	−0.570954	−	0.820982i	$-0.693427\pi$
$233$	−17.4305	−1.14191	−0.570954	+	0.820982i	$0.693427\pi$
$234$	−8.62301	−0.563704
$235$	13.2420	0.863812
$236$	0	0
$237$	0.694513	0.0451135
$238$	2.94450	0.190863
$239$	−10.9920	−0.711013	−0.355507	−	0.934674i	$-0.615692\pi$
$239$	−10.9920	−0.711013	−0.355507	+	0.934674i	$0.615692\pi$
$240$	0.504001	0.0325331
$241$	8.88099	0.572075	0.286038	−	0.958218i	$-0.407662\pi$
$241$	8.88099	0.572075	0.286038	+	0.958218i	$0.407662\pi$
$242$	−1.00000	−0.0642824
$243$	6.61299	0.424223
$244$	9.44050	0.604366
$245$	−7.88899	−0.504009
$246$	0.551502	0.0351625
$247$	0	0
$248$	−5.43250	−0.344964
$249$	−0.930511	−0.0589687
$250$	12.0000	0.758947
$251$	−7.11699	−0.449220	−0.224610	−	0.974449i	$-0.572111\pi$
$251$	−7.11699	−0.449220	−0.224610	+	0.974449i	$0.572111\pi$
$252$	−5.13299	−0.323348
$253$	4.50400	0.283164
$254$	−11.8730	−0.744978
$255$	−0.848987	−0.0531656
$256$	1.00000	0.0625000
$257$	17.2420	1.07553	0.537763	−	0.843096i	$-0.319270\pi$
$257$	17.2420	1.07553	0.537763	+	0.843096i	$0.319270\pi$
$258$	−1.81150	−0.112779
$259$	−5.55950	−0.345451
$260$	−5.87299	−0.364227
$261$	2.93650	0.181765
$262$	−11.6130	−0.717453
$263$	23.3850	1.44198	0.720990	−	0.692945i	$-0.243687\pi$
$263$	23.3850	1.44198	0.720990	+	0.692945i	$0.243687\pi$
$264$	−0.252000	−0.0155096
$265$	−2.01600	−0.123842
$266$	0	0
$267$	2.61299	0.159912
$268$	−0.756001	−0.0461801
$269$	−0.315505	−0.0192367	−0.00961833	−	0.999954i	$-0.503062\pi$
$269$	−0.315505	−0.0192367	−0.00961833	+	0.999954i	$0.503062\pi$
$270$	2.99200	0.182087
$271$	−12.0000	−0.728948	−0.364474	−	0.931214i	$-0.618751\pi$
$271$	−12.0000	−0.728948	−0.364474	+	0.931214i	$0.618751\pi$
$272$	−1.68450	−0.102138
$273$	−1.29352	−0.0782872
$274$	−9.92849	−0.599802
$275$	−1.00000	−0.0603023
$276$	1.13501	0.0683196
$277$	−1.44050	−0.0865511	−0.0432755	−	0.999063i	$-0.513779\pi$
$277$	−1.44050	−0.0865511	−0.0432755	+	0.999063i	$0.513779\pi$
$278$	−5.51200	−0.330588
$279$	−15.9525	−0.955051
$280$	−3.49600	−0.208926
$281$	−15.0535	−0.898016	−0.449008	−	0.893528i	$-0.648222\pi$
$281$	−15.0535	−0.898016	−0.449008	+	0.893528i	$0.648222\pi$
$282$	−1.66849	−0.0993573
$283$	23.2420	1.38159	0.690796	−	0.723049i	$-0.257260\pi$
$283$	23.2420	1.38159	0.690796	+	0.723049i	$0.257260\pi$
$284$	−7.18850	−0.426559
$285$	0	0
$286$	2.93650	0.173639
$287$	−3.82549	−0.225812
$288$	2.93650	0.173035
$289$	−14.1625	−0.833087
$290$	2.00000	0.117444
$291$	−3.11699	−0.182721
$292$	8.18850	0.479195
$293$	14.0080	0.818356	0.409178	−	0.912455i	$-0.365815\pi$
$293$	14.0080	0.818356	0.409178	+	0.912455i	$0.365815\pi$
$294$	0.994015	0.0579721
$295$	0	0
$296$	3.18049	0.184862
$297$	−1.49600	−0.0868067
$298$	−8.42449	−0.488018
$299$	−13.2260	−0.764878
$300$	−0.252000	−0.0145492
$301$	12.5655	0.724263
$302$	−13.9980	−0.805493
$303$	1.74800	0.100420
$304$	0	0
$305$	18.8810	1.08112
$306$	−4.94651	−0.282773
$307$	14.1010	0.804786	0.402393	−	0.915467i	$-0.368179\pi$
$307$	14.1010	0.804786	0.402393	+	0.915467i	$0.368179\pi$
$308$	1.74800	0.0996015
$309$	1.66849	0.0949172
$310$	−10.8650	−0.617090
$311$	−19.6130	−1.11215	−0.556075	−	0.831132i	$-0.687693\pi$
$311$	−19.6130	−1.11215	−0.556075	+	0.831132i	$0.687693\pi$
$312$	0.739998	0.0418941
$313$	−18.3055	−1.03469	−0.517344	−	0.855778i	$-0.673079\pi$
$313$	−18.3055	−1.03469	−0.517344	+	0.855778i	$0.673079\pi$
$314$	−1.00800	−0.0568848
$315$	−10.2660	−0.578423
$316$	2.75600	0.155037
$317$	−15.4305	−0.866662	−0.433331	−	0.901235i	$-0.642662\pi$
$317$	−15.4305	−0.866662	−0.433331	+	0.901235i	$0.642662\pi$
$318$	0.254017	0.0142446
$319$	−1.00000	−0.0559893
$320$	2.00000	0.111803
$321$	4.43848	0.247732
$322$	−7.87299	−0.438745
$323$	0	0
$324$	8.43250	0.468472
$325$	2.93650	0.162887
$326$	−17.2420	−0.954945
$327$	−0.994015	−0.0549691
$328$	2.18850	0.120839
$329$	11.5735	0.638067
$330$	−0.504001	−0.0277443
$331$	14.1250	0.776380	0.388190	−	0.921579i	$-0.373100\pi$
$331$	14.1250	0.776380	0.388190	+	0.921579i	$0.373100\pi$
$332$	−3.69250	−0.202652
$333$	9.33951	0.511802
$334$	−22.4860	−1.23038
$335$	−1.51200	−0.0826095
$336$	0.440497	0.0240311
$337$	28.6110	1.55854	0.779270	−	0.626689i	$-0.215590\pi$
$337$	28.6110	1.55854	0.779270	+	0.626689i	$0.215590\pi$
$338$	4.37699	0.238077
$339$	−3.62099	−0.196665
$340$	−3.36899	−0.182709
$341$	5.43250	0.294186
$342$	0	0
$343$	−19.1310	−1.03298
$344$	−7.18850	−0.387578
$345$	2.27002	0.122214
$346$	9.43250	0.507094
$347$	7.62899	0.409546	0.204773	−	0.978810i	$-0.434354\pi$
$347$	7.62899	0.409546	0.204773	+	0.978810i	$0.434354\pi$
$348$	−0.252000	−0.0135086
$349$	−25.1230	−1.34480	−0.672401	−	0.740187i	$-0.734737\pi$
$349$	−25.1230	−1.34480	−0.672401	+	0.740187i	$0.734737\pi$
$350$	1.74800	0.0934345
$351$	4.39300	0.234481
$352$	−1.00000	−0.0533002
$353$	−26.7620	−1.42440	−0.712198	−	0.701978i	$-0.752300\pi$
$353$	−26.7620	−1.42440	−0.712198	+	0.701978i	$0.752300\pi$
$354$	0	0
$355$	−14.3770	−0.763052
$356$	10.3690	0.549555
$357$	−0.742014	−0.0392716
$358$	−10.5040	−0.555154
$359$	7.63901	0.403172	0.201586	−	0.979471i	$-0.435391\pi$
$359$	7.63901	0.403172	0.201586	+	0.979471i	$0.435391\pi$
$360$	5.87299	0.309534
$361$	0	0
$362$	9.19650	0.483357
$363$	0.252000	0.0132266
$364$	−5.13299	−0.269042
$365$	16.3770	0.857211
$366$	−2.37901	−0.124353
$367$	27.5495	1.43807	0.719036	−	0.694973i	$-0.244584\pi$
$367$	27.5495	1.43807	0.719036	+	0.694973i	$0.244584\pi$
$368$	4.50400	0.234787
$369$	6.42651	0.334551
$370$	6.36099	0.330692
$371$	−1.76199	−0.0914778
$372$	1.36899	0.0709789
$373$	−32.9285	−1.70497	−0.852486	−	0.522749i	$-0.824906\pi$
$373$	−32.9285	−1.70497	−0.852486	+	0.522749i	$0.824906\pi$
$374$	1.68450	0.0871032
$375$	−3.02400	−0.156159
$376$	−6.62099	−0.341452
$377$	2.93650	0.151237
$378$	2.61501	0.134501
$379$	−30.5020	−1.56678	−0.783391	−	0.621529i	$-0.786512\pi$
$379$	−30.5020	−1.56678	−0.783391	+	0.621529i	$0.786512\pi$
$380$	0	0
$381$	2.99200	0.153285
$382$	−24.6210	−1.25972
$383$	−9.51200	−0.486041	−0.243020	−	0.970021i	$-0.578138\pi$
$383$	−9.51200	−0.486041	−0.243020	+	0.970021i	$0.578138\pi$
$384$	−0.252000	−0.0128598
$385$	3.49600	0.178173
$386$	−12.6925	−0.646031
$387$	−21.1090	−1.07303
$388$	−12.3690	−0.627940
$389$	29.0535	1.47307	0.736535	−	0.676399i	$-0.236461\pi$
$389$	29.0535	1.47307	0.736535	+	0.676399i	$0.236461\pi$
$390$	1.48000	0.0749425
$391$	−7.58697	−0.383689
$392$	3.94450	0.199227
$393$	2.92648	0.147621
$394$	20.3690	1.02617
$395$	5.51200	0.277339
$396$	−2.93650	−0.147564
$397$	−17.1805	−0.862264	−0.431132	−	0.902289i	$-0.641886\pi$
$397$	−17.1805	−0.862264	−0.431132	+	0.902289i	$0.641886\pi$
$398$	−8.81150	−0.441681
$399$	0	0
$400$	−1.00000	−0.0500000
$401$	30.8175	1.53895	0.769476	−	0.638676i	$-0.220517\pi$
$401$	30.8175	1.53895	0.769476	+	0.638676i	$0.220517\pi$
$402$	0.190513	0.00950190
$403$	−15.9525	−0.794651
$404$	6.93650	0.345104
$405$	16.8650	0.838028
$406$	1.74800	0.0867518
$407$	−3.18049	−0.157651
$408$	0.424493	0.0210156
$409$	−28.9105	−1.42953	−0.714765	−	0.699364i	$-0.753467\pi$
$409$	−28.9105	−1.42953	−0.714765	+	0.699364i	$0.753467\pi$
$410$	4.37699	0.216164
$411$	2.50198	0.123414
$412$	6.62099	0.326193
$413$	0	0
$414$	13.2260	0.650021
$415$	−7.38499	−0.362515
$416$	2.93650	0.143974
$417$	1.38903	0.0680209
$418$	0	0
$419$	−14.2520	−0.696256	−0.348128	−	0.937447i	$-0.613183\pi$
$419$	−14.2520	−0.696256	−0.348128	+	0.937447i	$0.613183\pi$
$420$	0.880993	0.0429881
$421$	22.6925	1.10596	0.552982	−	0.833193i	$-0.313490\pi$
$421$	22.6925	1.10596	0.552982	+	0.833193i	$0.313490\pi$
$422$	6.48800	0.315831
$423$	−19.4425	−0.945327
$424$	1.00800	0.0489529
$425$	1.68450	0.0817100
$426$	1.81150	0.0877676
$427$	16.5020	0.798587
$428$	17.6130	0.851356
$429$	−0.739998	−0.0357274
$430$	−14.3770	−0.693320
$431$	−24.6290	−1.18634	−0.593168	−	0.805078i	$-0.702123\pi$
$431$	−24.6290	−1.18634	−0.593168	+	0.805078i	$0.702123\pi$
$432$	−1.49600	−0.0719763
$433$	22.0515	1.05973	0.529863	−	0.848083i	$-0.322243\pi$
$433$	22.0515	1.05973	0.529863	+	0.848083i	$0.322243\pi$
$434$	−9.49600	−0.455823
$435$	−0.504001	−0.0241650
$436$	−3.94450	−0.188907
$437$	0	0
$438$	−2.06350	−0.0985980
$439$	−27.8730	−1.33031	−0.665153	−	0.746707i	$-0.731634\pi$
$439$	−27.8730	−1.33031	−0.665153	+	0.746707i	$0.731634\pi$
$440$	−2.00000	−0.0953463
$441$	11.5830	0.551571
$442$	−4.94651	−0.235282
$443$	−19.0060	−0.903002	−0.451501	−	0.892271i	$-0.649111\pi$
$443$	−19.0060	−0.903002	−0.451501	+	0.892271i	$0.649111\pi$
$444$	−0.801486	−0.0380368
$445$	20.7380	0.983075
$446$	19.1885	0.908602
$447$	2.12298	0.100413
$448$	1.74800	0.0825852
$449$	33.3055	1.57178	0.785892	−	0.618364i	$-0.212204\pi$
$449$	33.3055	1.57178	0.785892	+	0.618364i	$0.212204\pi$
$450$	−2.93650	−0.138428
$451$	−2.18850	−0.103052
$452$	−14.3690	−0.675860
$453$	3.52750	0.165736
$454$	0.551502	0.0258833
$455$	−10.2660	−0.481277
$456$	0	0
$457$	−10.3155	−0.482539	−0.241269	−	0.970458i	$-0.577564\pi$
$457$	−10.3155	−0.482539	−0.241269	+	0.970458i	$0.577564\pi$
$458$	−24.0615	−1.12432
$459$	2.52000	0.117624
$460$	9.00800	0.420000
$461$	24.3215	1.13276	0.566382	−	0.824143i	$-0.308343\pi$
$461$	24.3215	1.13276	0.566382	+	0.824143i	$0.308343\pi$
$462$	−0.440497	−0.0204938
$463$	−15.6130	−0.725597	−0.362799	−	0.931868i	$-0.618179\pi$
$463$	−15.6130	−0.725597	−0.362799	+	0.931868i	$0.618179\pi$
$464$	−1.00000	−0.0464238
$465$	2.73798	0.126971
$466$	17.4305	0.807451
$467$	10.1250	0.468529	0.234264	−	0.972173i	$-0.424732\pi$
$467$	10.1250	0.468529	0.234264	+	0.972173i	$0.424732\pi$
$468$	8.62301	0.398599
$469$	−1.32149	−0.0610207
$470$	−13.2420	−0.610807
$471$	0.254017	0.0117045
$472$	0	0
$473$	7.18850	0.330527
$474$	−0.694513	−0.0319001
$475$	0	0
$476$	−2.94450	−0.134961
$477$	2.95999	0.135529
$478$	10.9920	0.502762
$479$	21.6210	0.987888	0.493944	−	0.869494i	$-0.335555\pi$
$479$	21.6210	0.987888	0.493944	+	0.869494i	$0.335555\pi$
$480$	−0.504001	−0.0230044
$481$	9.33951	0.425845
$482$	−8.88099	−0.404518
$483$	1.98400	0.0902750
$484$	1.00000	0.0454545
$485$	−24.7380	−1.12329
$486$	−6.61299	−0.299971
$487$	3.04548	0.138004	0.0690020	−	0.997617i	$-0.478019\pi$
$487$	3.04548	0.138004	0.0690020	+	0.997617i	$0.478019\pi$
$488$	−9.44050	−0.427351
$489$	4.34499	0.196487
$490$	7.88899	0.356388
$491$	27.2420	1.22941	0.614707	−	0.788756i	$-0.289274\pi$
$491$	27.2420	1.22941	0.614707	+	0.788756i	$0.289274\pi$
$492$	−0.551502	−0.0248636
$493$	1.68450	0.0758659
$494$	0	0
$495$	−5.87299	−0.263971
$496$	5.43250	0.243926
$497$	−12.5655	−0.563639
$498$	0.930511	0.0416972
$499$	−11.8730	−0.531508	−0.265754	−	0.964041i	$-0.585621\pi$
$499$	−11.8730	−0.531508	−0.265754	+	0.964041i	$0.585621\pi$
$500$	−12.0000	−0.536656
$501$	5.66648	0.253159
$502$	7.11699	0.317647
$503$	1.13501	0.0506076	0.0253038	−	0.999680i	$-0.491945\pi$
$503$	1.13501	0.0506076	0.0253038	+	0.999680i	$0.491945\pi$
$504$	5.13299	0.228642
$505$	13.8730	0.617340
$506$	−4.50400	−0.200227
$507$	−1.10300	−0.0489861
$508$	11.8730	0.526779
$509$	−22.8650	−1.01347	−0.506736	−	0.862101i	$-0.669148\pi$
$509$	−22.8650	−1.01347	−0.506736	+	0.862101i	$0.669148\pi$
$510$	0.848987	0.0375938
$511$	14.3135	0.633191
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−17.2420	−0.760511
$515$	13.2420	0.583511
$516$	1.81150	0.0797470
$517$	6.62099	0.291191
$518$	5.55950	0.244271
$519$	−2.37699	−0.104338
$520$	5.87299	0.257548
$521$	24.9525	1.09319	0.546594	−	0.837397i	$-0.315924\pi$
$521$	24.9525	1.09319	0.546594	+	0.837397i	$0.315924\pi$
$522$	−2.93650	−0.128527
$523$	−5.37901	−0.235208	−0.117604	−	0.993061i	$-0.537521\pi$
$523$	−5.37901	−0.235208	−0.117604	+	0.993061i	$0.537521\pi$
$524$	11.6130	0.507316
$525$	−0.440497	−0.0192248
$526$	−23.3850	−1.01963
$527$	−9.15101	−0.398624
$528$	0.252000	0.0109669
$529$	−2.71398	−0.117999
$530$	2.01600	0.0875696
$531$	0	0
$532$	0	0
$533$	6.42651	0.278363
$534$	−2.61299	−0.113075
$535$	35.2260	1.52295
$536$	0.756001	0.0326543
$537$	2.64701	0.114227
$538$	0.315505	0.0136024
$539$	−3.94450	−0.169902
$540$	−2.99200	−0.128755
$541$	−31.8255	−1.36828	−0.684142	−	0.729349i	$-0.739823\pi$
$541$	−31.8255	−1.36828	−0.684142	+	0.729349i	$0.739823\pi$
$542$	12.0000	0.515444
$543$	−2.31752	−0.0994543
$544$	1.68450	0.0722221
$545$	−7.88899	−0.337927
$546$	1.29352	0.0553574
$547$	7.18850	0.307358	0.153679	−	0.988121i	$-0.450888\pi$
$547$	7.18850	0.307358	0.153679	+	0.988121i	$0.450888\pi$
$548$	9.92849	0.424124
$549$	−27.7220	−1.18315
$550$	1.00000	0.0426401
$551$	0	0
$552$	−1.13501	−0.0483092
$553$	4.81749	0.204860
$554$	1.44050	0.0612008
$555$	−1.60297	−0.0680424
$556$	5.51200	0.233761
$557$	30.9365	1.31082	0.655411	−	0.755273i	$-0.272496\pi$
$557$	30.9365	1.31082	0.655411	+	0.755273i	$0.272496\pi$
$558$	15.9525	0.675323
$559$	−21.1090	−0.892815
$560$	3.49600	0.147733
$561$	−0.424493	−0.0179221
$562$	15.0535	0.634993
$563$	10.4880	0.442016	0.221008	−	0.975272i	$-0.429065\pi$
$563$	10.4880	0.442016	0.221008	+	0.975272i	$0.429065\pi$
$564$	1.66849	0.0702562
$565$	−28.7380	−1.20902
$566$	−23.2420	−0.976933
$567$	14.7400	0.619022
$568$	7.18850	0.301623
$569$	17.6190	0.738626	0.369313	−	0.929305i	$-0.379593\pi$
$569$	17.6190	0.738626	0.369313	+	0.929305i	$0.379593\pi$
$570$	0	0
$571$	17.6130	0.737081	0.368540	−	0.929612i	$-0.379858\pi$
$571$	17.6130	0.737081	0.368540	+	0.929612i	$0.379858\pi$
$572$	−2.93650	−0.122781
$573$	6.20450	0.259197
$574$	3.82549	0.159673
$575$	−4.50400	−0.187830
$576$	−2.93650	−0.122354
$577$	−26.1865	−1.09016	−0.545079	−	0.838385i	$-0.683500\pi$
$577$	−26.1865	−1.09016	−0.545079	+	0.838385i	$0.683500\pi$
$578$	14.1625	0.589081
$579$	3.19851	0.132926
$580$	−2.00000	−0.0830455
$581$	−6.45448	−0.267777
$582$	3.11699	0.129203
$583$	−1.00800	−0.0417472
$584$	−8.18850	−0.338842
$585$	17.2460	0.713035
$586$	−14.0080	−0.578665
$587$	22.2520	0.918438	0.459219	−	0.888323i	$-0.348129\pi$
$587$	22.2520	0.918438	0.459219	+	0.888323i	$0.348129\pi$
$588$	−0.994015	−0.0409925
$589$	0	0
$590$	0	0
$591$	−5.13299	−0.211143
$592$	−3.18049	−0.130718
$593$	−2.86499	−0.117651	−0.0588255	−	0.998268i	$-0.518736\pi$
$593$	−2.86499	−0.117651	−0.0588255	+	0.998268i	$0.518736\pi$
$594$	1.49600	0.0613816
$595$	−5.88899	−0.241425
$596$	8.42449	0.345081
$597$	2.22050	0.0908791
$598$	13.2260	0.540851
$599$	−17.3155	−0.707492	−0.353746	−	0.935341i	$-0.615092\pi$
$599$	−17.3155	−0.707492	−0.353746	+	0.935341i	$0.615092\pi$
$600$	0.252000	0.0102879
$601$	19.7300	0.804803	0.402401	−	0.915463i	$-0.368176\pi$
$601$	19.7300	0.804803	0.402401	+	0.915463i	$0.368176\pi$
$602$	−12.5655	−0.512131
$603$	2.21999	0.0904052
$604$	13.9980	0.569570
$605$	2.00000	0.0813116
$606$	−1.74800	−0.0710076
$607$	8.12499	0.329783	0.164892	−	0.986312i	$-0.447273\pi$
$607$	8.12499	0.329783	0.164892	+	0.986312i	$0.447273\pi$
$608$	0	0
$609$	−0.440497	−0.0178498
$610$	−18.8810	−0.764469
$611$	−19.4425	−0.786560
$612$	4.94651	0.199951
$613$	−1.96050	−0.0791839	−0.0395919	−	0.999216i	$-0.512606\pi$
$613$	−1.96050	−0.0791839	−0.0395919	+	0.999216i	$0.512606\pi$
$614$	−14.1010	−0.569070
$615$	−1.10300	−0.0444774
$616$	−1.74800	−0.0704289
$617$	0.0555027	0.00223445	0.00111723	−	0.999999i	$-0.499644\pi$
$617$	0.0555027	0.00223445	0.00111723	+	0.999999i	$0.499644\pi$
$618$	−1.66849	−0.0671166
$619$	43.3850	1.74379	0.871895	−	0.489693i	$-0.162891\pi$
$619$	43.3850	1.74379	0.871895	+	0.489693i	$0.162891\pi$
$620$	10.8650	0.436349
$621$	−6.73798	−0.270386
$622$	19.6130	0.786409
$623$	18.1250	0.726162
$624$	−0.739998	−0.0296236
$625$	−19.0000	−0.760000
$626$	18.3055	0.731634
$627$	0	0
$628$	1.00800	0.0402236
$629$	5.35753	0.213619
$630$	10.2660	0.409007
$631$	−15.8035	−0.629127	−0.314564	−	0.949236i	$-0.601858\pi$
$631$	−15.8035	−0.629127	−0.314564	+	0.949236i	$0.601858\pi$
$632$	−2.75600	−0.109628
$633$	−1.63498	−0.0649845
$634$	15.4305	0.612823
$635$	23.7460	0.942331
$636$	−0.254017	−0.0100724
$637$	11.5830	0.458935
$638$	1.00000	0.0395904
$639$	21.1090	0.835059
$640$	−2.00000	−0.0790569
$641$	−13.9920	−0.552651	−0.276325	−	0.961064i	$-0.589117\pi$
$641$	−13.9920	−0.552651	−0.276325	+	0.961064i	$0.589117\pi$
$642$	−4.43848	−0.175173
$643$	1.89101	0.0745742	0.0372871	−	0.999305i	$-0.488128\pi$
$643$	1.89101	0.0745742	0.0372871	+	0.999305i	$0.488128\pi$
$644$	7.87299	0.310239
$645$	3.62301	0.142656
$646$	0	0
$647$	−37.4225	−1.47123	−0.735615	−	0.677400i	$-0.763107\pi$
$647$	−37.4225	−1.47123	−0.735615	+	0.677400i	$0.763107\pi$
$648$	−8.43250	−0.331260
$649$	0	0
$650$	−2.93650	−0.115179
$651$	2.39300	0.0937889
$652$	17.2420	0.675248
$653$	20.0455	0.784440	0.392220	−	0.919871i	$-0.371707\pi$
$653$	20.0455	0.784440	0.392220	+	0.919871i	$0.371707\pi$
$654$	0.994015	0.0388691
$655$	23.2260	0.907514
$656$	−2.18850	−0.0854464
$657$	−24.0455	−0.938104
$658$	−11.5735	−0.451182
$659$	−19.3790	−0.754899	−0.377450	−	0.926030i	$-0.623199\pi$
$659$	−19.3790	−0.754899	−0.377450	+	0.926030i	$0.623199\pi$
$660$	0.504001	0.0196182
$661$	−15.6845	−0.610056	−0.305028	−	0.952343i	$-0.598666\pi$
$661$	−15.6845	−0.610056	−0.305028	+	0.952343i	$0.598666\pi$
$662$	−14.1250	−0.548983
$663$	1.24652	0.0484110
$664$	3.69250	0.143297
$665$	0	0
$666$	−9.33951	−0.361899
$667$	−4.50400	−0.174396
$668$	22.4860	0.870009
$669$	−4.83551	−0.186952
$670$	1.51200	0.0584137
$671$	9.44050	0.364446
$672$	−0.440497	−0.0169925
$673$	14.6605	0.565120	0.282560	−	0.959250i	$-0.408816\pi$
$673$	14.6605	0.565120	0.282560	+	0.959250i	$0.408816\pi$
$674$	−28.6110	−1.10205
$675$	1.49600	0.0575810
$676$	−4.37699	−0.168346
$677$	34.4485	1.32396	0.661982	−	0.749520i	$-0.269716\pi$
$677$	34.4485	1.32396	0.661982	+	0.749520i	$0.269716\pi$
$678$	3.62099	0.139063
$679$	−21.6210	−0.829737
$680$	3.36899	0.129195
$681$	−0.138979	−0.00532567
$682$	−5.43250	−0.208021
$683$	27.4780	1.05142	0.525708	−	0.850665i	$-0.323801\pi$
$683$	27.4780	1.05142	0.525708	+	0.850665i	$0.323801\pi$
$684$	0	0
$685$	19.8570	0.758697
$686$	19.1310	0.730424
$687$	6.06350	0.231337
$688$	7.18850	0.274059
$689$	2.95999	0.112767
$690$	−2.27002	−0.0864182
$691$	−29.2600	−1.11310	−0.556551	−	0.830813i	$-0.687876\pi$
$691$	−29.2600	−1.11310	−0.556551	+	0.830813i	$0.687876\pi$
$692$	−9.43250	−0.358570
$693$	−5.13299	−0.194986
$694$	−7.62899	−0.289593
$695$	11.0240	0.418164
$696$	0.252000	0.00955205
$697$	3.68651	0.139637
$698$	25.1230	0.950919
$699$	−4.39249	−0.166139
$700$	−1.74800	−0.0660682
$701$	14.6390	0.552908	0.276454	−	0.961027i	$-0.410841\pi$
$701$	14.6390	0.552908	0.276454	+	0.961027i	$0.410841\pi$
$702$	−4.39300	−0.165803
$703$	0	0
$704$	1.00000	0.0376889
$705$	3.33698	0.125678
$706$	26.7620	1.00720
$707$	12.1250	0.456007
$708$	0	0
$709$	11.9840	0.450068	0.225034	−	0.974351i	$-0.427751\pi$
$709$	11.9840	0.450068	0.225034	+	0.974351i	$0.427751\pi$
$710$	14.3770	0.539559
$711$	−8.09299	−0.303511
$712$	−10.3690	−0.388594
$713$	24.4680	0.916332
$714$	0.742014	0.0277692
$715$	−5.87299	−0.219637
$716$	10.5040	0.392553
$717$	−2.76999	−0.103447
$718$	−7.63901	−0.285085
$719$	10.8275	0.403798	0.201899	−	0.979406i	$-0.435289\pi$
$719$	10.8275	0.403798	0.201899	+	0.979406i	$0.435289\pi$
$720$	−5.87299	−0.218873
$721$	11.5735	0.431019
$722$	0	0
$723$	2.23801	0.0832326
$724$	−9.19650	−0.341785
$725$	1.00000	0.0371391
$726$	−0.252000	−0.00935261
$727$	−27.0775	−1.00425	−0.502124	−	0.864795i	$-0.667448\pi$
$727$	−27.0775	−1.00425	−0.502124	+	0.864795i	$0.667448\pi$
$728$	5.13299	0.190241
$729$	−23.6310	−0.875223
$730$	−16.3770	−0.606140
$731$	−12.1090	−0.447867
$732$	2.37901	0.0879307
$733$	44.2975	1.63616	0.818082	−	0.575101i	$-0.195037\pi$
$733$	44.2975	1.63616	0.818082	+	0.575101i	$0.195037\pi$
$734$	−27.5495	−1.01687
$735$	−1.98803	−0.0733296
$736$	−4.50400	−0.166020
$737$	−0.756001	−0.0278477
$738$	−6.42651	−0.236563
$739$	−21.6290	−0.795635	−0.397818	−	0.917464i	$-0.630232\pi$
$739$	−21.6290	−0.795635	−0.397818	+	0.917464i	$0.630232\pi$
$740$	−6.36099	−0.233835
$741$	0	0
$742$	1.76199	0.0646846
$743$	37.6370	1.38077	0.690384	−	0.723443i	$-0.257442\pi$
$743$	37.6370	1.38077	0.690384	+	0.723443i	$0.257442\pi$
$744$	−1.36899	−0.0501896
$745$	16.8490	0.617299
$746$	32.9285	1.20560
$747$	10.8430	0.396725
$748$	−1.68450	−0.0615913
$749$	30.7875	1.12495
$750$	3.02400	0.110421
$751$	42.9345	1.56670	0.783351	−	0.621580i	$-0.213509\pi$
$751$	42.9345	1.56670	0.783351	+	0.621580i	$0.213509\pi$
$752$	6.62099	0.241443
$753$	−1.79348	−0.0653582
$754$	−2.93650	−0.106941
$755$	27.9960	1.01888
$756$	−2.61501	−0.0951069
$757$	12.8970	0.468749	0.234375	−	0.972146i	$-0.424696\pi$
$757$	12.8970	0.468749	0.234375	+	0.972146i	$0.424696\pi$
$758$	30.5020	1.10788
$759$	1.13501	0.0411983
$760$	0	0
$761$	15.6030	0.565607	0.282804	−	0.959178i	$-0.408736\pi$
$761$	15.6030	0.565607	0.282804	+	0.959178i	$0.408736\pi$
$762$	−2.99200	−0.108389
$763$	−6.89498	−0.249615
$764$	24.6210	0.890756
$765$	9.89303	0.357683
$766$	9.51200	0.343683
$767$	0	0
$768$	0.252000	0.00909328
$769$	−45.8890	−1.65480	−0.827400	−	0.561613i	$-0.810181\pi$
$769$	−45.8890	−1.65480	−0.827400	+	0.561613i	$0.810181\pi$
$770$	−3.49600	−0.125987
$771$	4.34499	0.156481
$772$	12.6925	0.456813
$773$	38.9265	1.40009	0.700044	−	0.714100i	$-0.253164\pi$
$773$	38.9265	1.40009	0.700044	+	0.714100i	$0.253164\pi$
$774$	21.1090	0.758747
$775$	−5.43250	−0.195141
$776$	12.3690	0.444021
$777$	−1.40100	−0.0502605
$778$	−29.0535	−1.04162
$779$	0	0
$780$	−1.48000	−0.0529924
$781$	−7.18850	−0.257225
$782$	7.58697	0.271309
$783$	1.49600	0.0534627
$784$	−3.94450	−0.140875
$785$	2.01600	0.0719542
$786$	−2.92648	−0.104384
$787$	−24.9185	−0.888248	−0.444124	−	0.895965i	$-0.646485\pi$
$787$	−24.9185	−0.888248	−0.444124	+	0.895965i	$0.646485\pi$
$788$	−20.3690	−0.725615
$789$	5.89303	0.209797
$790$	−5.51200	−0.196108
$791$	−25.1170	−0.893057
$792$	2.93650	0.104344
$793$	−27.7220	−0.984436
$794$	17.1805	0.609713
$795$	−0.508034	−0.0180181
$796$	8.81150	0.312315
$797$	−34.9265	−1.23716	−0.618580	−	0.785722i	$-0.712292\pi$
$797$	−34.9265	−1.23716	−0.618580	+	0.785722i	$0.712292\pi$
$798$	0	0
$799$	−11.1530	−0.394566
$800$	1.00000	0.0353553
$801$	−30.4485	−1.07584
$802$	−30.8175	−1.08820
$803$	8.18850	0.288966
$804$	−0.190513	−0.00671886
$805$	15.7460	0.554973
$806$	15.9525	0.561903
$807$	−0.0795073	−0.00279879
$808$	−6.93650	−0.244025
$809$	50.0415	1.75936	0.879682	−	0.475563i	$-0.157755\pi$
$809$	50.0415	1.75936	0.879682	+	0.475563i	$0.157755\pi$
$810$	−16.8650	−0.592575
$811$	14.4305	0.506723	0.253361	−	0.967372i	$-0.418464\pi$
$811$	14.4305	0.506723	0.253361	+	0.967372i	$0.418464\pi$
$812$	−1.74800	−0.0613428
$813$	−3.02400	−0.106056
$814$	3.18049	0.111476
$815$	34.4840	1.20792
$816$	−0.424493	−0.0148602
$817$	0	0
$818$	28.9105	1.01083
$819$	15.0730	0.526694
$820$	−4.37699	−0.152851
$821$	9.17848	0.320331	0.160166	−	0.987090i	$-0.448797\pi$
$821$	9.17848	0.320331	0.160166	+	0.987090i	$0.448797\pi$
$822$	−2.50198	−0.0872667
$823$	46.8550	1.63326	0.816631	−	0.577160i	$-0.195839\pi$
$823$	46.8550	1.63326	0.816631	+	0.577160i	$0.195839\pi$
$824$	−6.62099	−0.230653
$825$	−0.252000	−0.00877353
$826$	0	0
$827$	19.4385	0.675942	0.337971	−	0.941156i	$-0.390259\pi$
$827$	19.4385	0.675942	0.337971	+	0.941156i	$0.390259\pi$
$828$	−13.2260	−0.459635
$829$	−25.3035	−0.878826	−0.439413	−	0.898285i	$-0.644813\pi$
$829$	−25.3035	−0.878826	−0.439413	+	0.898285i	$0.644813\pi$
$830$	7.38499	0.256337
$831$	−0.363006	−0.0125925
$832$	−2.93650	−0.101805
$833$	6.64449	0.230218
$834$	−1.38903	−0.0480981
$835$	44.9720	1.55632
$836$	0	0
$837$	−8.12701	−0.280911
$838$	14.2520	0.492327
$839$	−29.4225	−1.01578	−0.507888	−	0.861423i	$-0.669574\pi$
$839$	−29.4225	−1.01578	−0.507888	+	0.861423i	$0.669574\pi$
$840$	−0.880993	−0.0303972
$841$	−28.0000	−0.965517
$842$	−22.6925	−0.782035
$843$	−3.79348	−0.130655
$844$	−6.48800	−0.223326
$845$	−8.75398	−0.301146
$846$	19.4425	0.668447
$847$	1.74800	0.0600620
$848$	−1.00800	−0.0346149
$849$	5.85699	0.201011
$850$	−1.68450	−0.0577777
$851$	−14.3250	−0.491053
$852$	−1.81150	−0.0620611
$853$	−52.5475	−1.79919	−0.899596	−	0.436724i	$-0.856139\pi$
$853$	−52.5475	−1.79919	−0.899596	+	0.436724i	$0.856139\pi$
$854$	−16.5020	−0.564686
$855$	0	0
$856$	−17.6130	−0.602000
$857$	−21.7005	−0.741275	−0.370637	−	0.928778i	$-0.620861\pi$
$857$	−21.7005	−0.741275	−0.370637	+	0.928778i	$0.620861\pi$
$858$	0.739998	0.0252631
$859$	28.9880	0.989057	0.494528	−	0.869162i	$-0.335341\pi$
$859$	28.9880	0.989057	0.494528	+	0.869162i	$0.335341\pi$
$860$	14.3770	0.490251
$861$	−0.964025	−0.0328539
$862$	24.6290	0.838867
$863$	−6.14900	−0.209314	−0.104657	−	0.994508i	$-0.533375\pi$
$863$	−6.14900	−0.209314	−0.104657	+	0.994508i	$0.533375\pi$
$864$	1.49600	0.0508949
$865$	−18.8650	−0.641429
$866$	−22.0515	−0.749339
$867$	−3.56895	−0.121208
$868$	9.49600	0.322315
$869$	2.75600	0.0934909
$870$	0.504001	0.0170872
$871$	2.21999	0.0752216
$872$	3.94450	0.133578
$873$	36.3215	1.22930
$874$	0	0
$875$	−20.9760	−0.709118
$876$	2.06350	0.0697193
$877$	45.7460	1.54473	0.772366	−	0.635178i	$-0.219073\pi$
$877$	45.7460	1.54473	0.772366	+	0.635178i	$0.219073\pi$
$878$	27.8730	0.940668
$879$	3.53002	0.119065
$880$	2.00000	0.0674200
$881$	8.67448	0.292251	0.146125	−	0.989266i	$-0.453320\pi$
$881$	8.67448	0.292251	0.146125	+	0.989266i	$0.453320\pi$
$882$	−11.5830	−0.390020
$883$	−7.40301	−0.249131	−0.124566	−	0.992211i	$-0.539754\pi$
$883$	−7.40301	−0.249131	−0.124566	+	0.992211i	$0.539754\pi$
$884$	4.94651	0.166369
$885$	0	0
$886$	19.0060	0.638519
$887$	35.8870	1.20497	0.602483	−	0.798131i	$-0.294178\pi$
$887$	35.8870	1.20497	0.602483	+	0.798131i	$0.294178\pi$
$888$	0.801486	0.0268961
$889$	20.7540	0.696066
$890$	−20.7380	−0.695139
$891$	8.43250	0.282499
$892$	−19.1885	−0.642478
$893$	0	0
$894$	−2.12298	−0.0710029
$895$	21.0080	0.702220
$896$	−1.74800	−0.0583966
$897$	−3.33295	−0.111284
$898$	−33.3055	−1.11142
$899$	−5.43250	−0.181184
$900$	2.93650	0.0978832
$901$	1.69797	0.0565677
$902$	2.18850	0.0728690
$903$	3.16651	0.105375
$904$	14.3690	0.477906
$905$	−18.3930	−0.611404
$906$	−3.52750	−0.117193
$907$	−44.8610	−1.48958	−0.744792	−	0.667297i	$-0.767451\pi$
$907$	−44.8610	−1.48958	−0.744792	+	0.667297i	$0.767451\pi$
$908$	−0.551502	−0.0183022
$909$	−20.3690	−0.675597
$910$	10.2660	0.340314
$911$	−21.4760	−0.711530	−0.355765	−	0.934575i	$-0.615780\pi$
$911$	−21.4760	−0.711530	−0.355765	+	0.934575i	$0.615780\pi$
$912$	0	0
$913$	−3.69250	−0.122204
$914$	10.3155	0.341207
$915$	4.75802	0.157295
$916$	24.0615	0.795014
$917$	20.2995	0.670349
$918$	−2.52000	−0.0831725
$919$	−44.6090	−1.47151	−0.735757	−	0.677246i	$-0.763173\pi$
$919$	−44.6090	−1.47151	−0.735757	+	0.677246i	$0.763173\pi$
$920$	−9.00800	−0.296985
$921$	3.55345	0.117090
$922$	−24.3215	−0.800986
$923$	21.1090	0.694811
$924$	0.440497	0.0144913
$925$	3.18049	0.104574
$926$	15.6130	0.513075
$927$	−19.4425	−0.638576
$928$	1.00000	0.0328266
$929$	41.7380	1.36938	0.684689	−	0.728835i	$-0.259938\pi$
$929$	41.7380	1.36938	0.684689	+	0.728835i	$0.259938\pi$
$930$	−2.73798	−0.0897820
$931$	0	0
$932$	−17.4305	−0.570954
$933$	−4.94248	−0.161810
$934$	−10.1250	−0.331300
$935$	−3.36899	−0.110178
$936$	−8.62301	−0.281852
$937$	6.03201	0.197057	0.0985285	−	0.995134i	$-0.468586\pi$
$937$	6.03201	0.197057	0.0985285	+	0.995134i	$0.468586\pi$
$938$	1.32149	0.0431482
$939$	−4.61299	−0.150539
$940$	13.2420	0.431906
$941$	−49.9325	−1.62775	−0.813876	−	0.581039i	$-0.802646\pi$
$941$	−49.9325	−1.62775	−0.813876	+	0.581039i	$0.802646\pi$
$942$	−0.254017	−0.00827631
$943$	−9.85699	−0.320988
$944$	0	0
$945$	−5.23001	−0.170132
$946$	−7.18850	−0.233718
$947$	−3.60700	−0.117212	−0.0586059	−	0.998281i	$-0.518666\pi$
$947$	−3.60700	−0.117212	−0.0586059	+	0.998281i	$0.518666\pi$
$948$	0.694513	0.0225567
$949$	−24.0455	−0.780549
$950$	0	0
$951$	−3.88849	−0.126093
$952$	2.94450	0.0954317
$953$	21.7460	0.704421	0.352211	−	0.935921i	$-0.385430\pi$
$953$	21.7460	0.704421	0.352211	+	0.935921i	$0.385430\pi$
$954$	−2.95999	−0.0958333
$955$	49.2420	1.59343
$956$	−10.9920	−0.355507
$957$	−0.252000	−0.00814602
$958$	−21.6210	−0.698543
$959$	17.3550	0.560422
$960$	0.504001	0.0162666
$961$	−1.48800	−0.0479999
$962$	−9.33951	−0.301118
$963$	−51.7205	−1.66667
$964$	8.88099	0.286038
$965$	25.3850	0.817172
$966$	−1.98400	−0.0638341
$967$	1.36899	0.0440238	0.0220119	−	0.999758i	$-0.492993\pi$
$967$	1.36899	0.0440238	0.0220119	+	0.999758i	$0.492993\pi$
$968$	−1.00000	−0.0321412
$969$	0	0
$970$	24.7380	0.794289
$971$	40.5180	1.30028	0.650142	−	0.759813i	$-0.274709\pi$
$971$	40.5180	1.30028	0.650142	+	0.759813i	$0.274709\pi$
$972$	6.61299	0.212112
$973$	9.63498	0.308883
$974$	−3.04548	−0.0975836
$975$	0.739998	0.0236989
$976$	9.44050	0.302183
$977$	−25.3770	−0.811882	−0.405941	−	0.913899i	$-0.633056\pi$
$977$	−25.3770	−0.811882	−0.405941	+	0.913899i	$0.633056\pi$
$978$	−4.34499	−0.138937
$979$	10.3690	0.331394
$980$	−7.88899	−0.252005
$981$	11.5830	0.369817
$982$	−27.2420	−0.869327
$983$	−31.9105	−1.01779	−0.508893	−	0.860830i	$-0.669945\pi$
$983$	−31.9105	−1.01779	−0.508893	+	0.860830i	$0.669945\pi$
$984$	0.551502	0.0175812
$985$	−40.7380	−1.29802
$986$	−1.68450	−0.0536453
$987$	2.91652	0.0928340
$988$	0	0
$989$	32.3770	1.02953
$990$	5.87299	0.186656
$991$	−21.8790	−0.695009	−0.347504	−	0.937678i	$-0.612971\pi$
$991$	−21.8790	−0.695009	−0.347504	+	0.937678i	$0.612971\pi$
$992$	−5.43250	−0.172482
$993$	3.55950	0.112957
$994$	12.5655	0.398553
$995$	17.6230	0.558687
$996$	−0.930511	−0.0294844
$997$	−3.72998	−0.118130	−0.0590648	−	0.998254i	$-0.518812\pi$
$997$	−3.72998	−0.118130	−0.0590648	+	0.998254i	$0.518812\pi$
$998$	11.8730	0.375833
$999$	4.75802	0.150537

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7942.2.a.bd.1.2		3
19.7	even	3		418.2.e.i.353.2	yes	6
19.11	even	3		418.2.e.i.45.2	✓	6
19.18	odd	2		7942.2.a.bj.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.e.i.45.2	✓	6	19.11	even	3
418.2.e.i.353.2	yes	6	19.7	even	3
7942.2.a.bd.1.2		3	1.1	even	1	trivial
7942.2.a.bj.1.2		3	19.18	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:	\( N \)	\(=\)	\( 7942 = 2 \cdot 11 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7942.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.252000 q^{3} +1.00000 q^{4} +2.00000 q^{5} -0.252000 q^{6} +1.74800 q^{7} -1.00000 q^{8} -2.93650 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.252000 q^{3} +1.00000 q^{4} +2.00000 q^{5} -0.252000 q^{6} +1.74800 q^{7} -1.00000 q^{8} -2.93650 q^{9} -2.00000 q^{10} +1.00000 q^{11} +0.252000 q^{12} -2.93650 q^{13} -1.74800 q^{14} +0.504001 q^{15} +1.00000 q^{16} -1.68450 q^{17} +2.93650 q^{18} +2.00000 q^{20} +0.440497 q^{21} -1.00000 q^{22} +4.50400 q^{23} -0.252000 q^{24} -1.00000 q^{25} +2.93650 q^{26} -1.49600 q^{27} +1.74800 q^{28} -1.00000 q^{29} -0.504001 q^{30} +5.43250 q^{31} -1.00000 q^{32} +0.252000 q^{33} +1.68450 q^{34} +3.49600 q^{35} -2.93650 q^{36} -3.18049 q^{37} -0.739998 q^{39} -2.00000 q^{40} -2.18850 q^{41} -0.440497 q^{42} +7.18850 q^{43} +1.00000 q^{44} -5.87299 q^{45} -4.50400 q^{46} +6.62099 q^{47} +0.252000 q^{48} -3.94450 q^{49} +1.00000 q^{50} -0.424493 q^{51} -2.93650 q^{52} -1.00800 q^{53} +1.49600 q^{54} +2.00000 q^{55} -1.74800 q^{56} +1.00000 q^{58} +0.504001 q^{60} +9.44050 q^{61} -5.43250 q^{62} -5.13299 q^{63} +1.00000 q^{64} -5.87299 q^{65} -0.252000 q^{66} -0.756001 q^{67} -1.68450 q^{68} +1.13501 q^{69} -3.49600 q^{70} -7.18850 q^{71} +2.93650 q^{72} +8.18850 q^{73} +3.18049 q^{74} -0.252000 q^{75} +1.74800 q^{77} +0.739998 q^{78} +2.75600 q^{79} +2.00000 q^{80} +8.43250 q^{81} +2.18850 q^{82} -3.69250 q^{83} +0.440497 q^{84} -3.36899 q^{85} -7.18850 q^{86} -0.252000 q^{87} -1.00000 q^{88} +10.3690 q^{89} +5.87299 q^{90} -5.13299 q^{91} +4.50400 q^{92} +1.36899 q^{93} -6.62099 q^{94} -0.252000 q^{96} -12.3690 q^{97} +3.94450 q^{98} -2.93650 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{4} + 6 q^{5} + 6 q^{7} - 3 q^{8} + 7 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^4 + 6 * q^5 + 6 * q^7 - 3 * q^8 + 7 * q^9	\( 3 q - 3 q^{2} + 3 q^{4} + 6 q^{5} + 6 q^{7} - 3 q^{8} + 7 q^{9} - 6 q^{10} + 3 q^{11} + 7 q^{13} - 6 q^{14} + 3 q^{16} + 10 q^{17} - 7 q^{18} + 6 q^{20} - 16 q^{21} - 3 q^{22} + 12 q^{23} - 3 q^{25} - 7 q^{26} - 6 q^{27} + 6 q^{28} - 3 q^{29} + 2 q^{31} - 3 q^{32} - 10 q^{34} + 12 q^{35} + 7 q^{36} + 4 q^{37} - 6 q^{39} - 6 q^{40} + 10 q^{41} + 16 q^{42} + 5 q^{43} + 3 q^{44} + 14 q^{45} - 12 q^{46} - 11 q^{47} + 7 q^{49} + 3 q^{50} + 10 q^{51} + 7 q^{52} + 6 q^{54} + 6 q^{55} - 6 q^{56} + 3 q^{58} + 11 q^{61} - 2 q^{62} + 20 q^{63} + 3 q^{64} + 14 q^{65} + 10 q^{68} + 32 q^{69} - 12 q^{70} - 5 q^{71} - 7 q^{72} + 8 q^{73} - 4 q^{74} + 6 q^{77} + 6 q^{78} + 6 q^{79} + 6 q^{80} + 11 q^{81} - 10 q^{82} + 7 q^{83} - 16 q^{84} + 20 q^{85} - 5 q^{86} - 3 q^{88} + q^{89} - 14 q^{90} + 20 q^{91} + 12 q^{92} - 26 q^{93} + 11 q^{94} - 7 q^{97} - 7 q^{98} + 7 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^4 + 6 * q^5 + 6 * q^7 - 3 * q^8 + 7 * q^9 - 6 * q^10 + 3 * q^11 + 7 * q^13 - 6 * q^14 + 3 * q^16 + 10 * q^17 - 7 * q^18 + 6 * q^20 - 16 * q^21 - 3 * q^22 + 12 * q^23 - 3 * q^25 - 7 * q^26 - 6 * q^27 + 6 * q^28 - 3 * q^29 + 2 * q^31 - 3 * q^32 - 10 * q^34 + 12 * q^35 + 7 * q^36 + 4 * q^37 - 6 * q^39 - 6 * q^40 + 10 * q^41 + 16 * q^42 + 5 * q^43 + 3 * q^44 + 14 * q^45 - 12 * q^46 - 11 * q^47 + 7 * q^49 + 3 * q^50 + 10 * q^51 + 7 * q^52 + 6 * q^54 + 6 * q^55 - 6 * q^56 + 3 * q^58 + 11 * q^61 - 2 * q^62 + 20 * q^63 + 3 * q^64 + 14 * q^65 + 10 * q^68 + 32 * q^69 - 12 * q^70 - 5 * q^71 - 7 * q^72 + 8 * q^73 - 4 * q^74 + 6 * q^77 + 6 * q^78 + 6 * q^79 + 6 * q^80 + 11 * q^81 - 10 * q^82 + 7 * q^83 - 16 * q^84 + 20 * q^85 - 5 * q^86 - 3 * q^88 + q^89 - 14 * q^90 + 20 * q^91 + 12 * q^92 - 26 * q^93 + 11 * q^94 - 7 * q^97 - 7 * q^98 + 7 * q^99

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