LMFDB - Embedded newform 3450.2.a.bq.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3450,2,Mod(1,3450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3450, 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("3450.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3450.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:	$27.5483886973$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.568.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 6x - 2 $ x^3 - x^2 - 6*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 690)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.363328$ of defining polynomial
Character	$\chi$	$=$	3450.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.50466 q^{11} +1.00000 q^{12} +2.72666 q^{13} -2.00000 q^{14} +1.00000 q^{16} -0.726656 q^{17} -1.00000 q^{18} -7.78734 q^{19} +2.00000 q^{21} -3.50466 q^{22} +1.00000 q^{23} -1.00000 q^{24} -2.72666 q^{26} +1.00000 q^{27} +2.00000 q^{28} -2.00000 q^{29} +8.28267 q^{31} -1.00000 q^{32} +3.50466 q^{33} +0.726656 q^{34} +1.00000 q^{36} +9.50466 q^{37} +7.78734 q^{38} +2.72666 q^{39} +0.726656 q^{41} -2.00000 q^{42} +5.50466 q^{43} +3.50466 q^{44} -1.00000 q^{46} +2.72666 q^{47} +1.00000 q^{48} -3.00000 q^{49} -0.726656 q^{51} +2.72666 q^{52} -0.231321 q^{53} -1.00000 q^{54} -2.00000 q^{56} -7.78734 q^{57} +2.00000 q^{58} +9.29200 q^{59} +4.05135 q^{61} -8.28267 q^{62} +2.00000 q^{63} +1.00000 q^{64} -3.50466 q^{66} +4.05135 q^{67} -0.726656 q^{68} +1.00000 q^{69} -11.7360 q^{71} -1.00000 q^{72} +3.71733 q^{73} -9.50466 q^{74} -7.78734 q^{76} +7.00933 q^{77} -2.72666 q^{78} -9.73599 q^{79} +1.00000 q^{81} -0.726656 q^{82} -13.5233 q^{83} +2.00000 q^{84} -5.50466 q^{86} -2.00000 q^{87} -3.50466 q^{88} -9.55602 q^{89} +5.45331 q^{91} +1.00000 q^{92} +8.28267 q^{93} -2.72666 q^{94} -1.00000 q^{96} +4.54669 q^{97} +3.00000 q^{98} +3.50466 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{6} + 6 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^6 + 6 * q^7 - 3 * q^8 + 3 * q^9	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{6} + 6 q^{7} - 3 q^{8} + 3 q^{9} + 3 q^{12} + 4 q^{13} - 6 q^{14} + 3 q^{16} + 2 q^{17} - 3 q^{18} + 4 q^{19} + 6 q^{21} + 3 q^{23} - 3 q^{24} - 4 q^{26} + 3 q^{27} + 6 q^{28} - 6 q^{29} + 8 q^{31} - 3 q^{32} - 2 q^{34} + 3 q^{36} + 18 q^{37} - 4 q^{38} + 4 q^{39} - 2 q^{41} - 6 q^{42} + 6 q^{43} - 3 q^{46} + 4 q^{47} + 3 q^{48} - 9 q^{49} + 2 q^{51} + 4 q^{52} + 14 q^{53} - 3 q^{54} - 6 q^{56} + 4 q^{57} + 6 q^{58} - 10 q^{59} + 10 q^{61} - 8 q^{62} + 6 q^{63} + 3 q^{64} + 10 q^{67} + 2 q^{68} + 3 q^{69} - 10 q^{71} - 3 q^{72} + 28 q^{73} - 18 q^{74} + 4 q^{76} - 4 q^{78} - 4 q^{79} + 3 q^{81} + 2 q^{82} + 12 q^{83} + 6 q^{84} - 6 q^{86} - 6 q^{87} - 16 q^{89} + 8 q^{91} + 3 q^{92} + 8 q^{93} - 4 q^{94} - 3 q^{96} + 22 q^{97} + 9 q^{98}+O(q^{100}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^6 + 6 * q^7 - 3 * q^8 + 3 * q^9 + 3 * q^12 + 4 * q^13 - 6 * q^14 + 3 * q^16 + 2 * q^17 - 3 * q^18 + 4 * q^19 + 6 * q^21 + 3 * q^23 - 3 * q^24 - 4 * q^26 + 3 * q^27 + 6 * q^28 - 6 * q^29 + 8 * q^31 - 3 * q^32 - 2 * q^34 + 3 * q^36 + 18 * q^37 - 4 * q^38 + 4 * q^39 - 2 * q^41 - 6 * q^42 + 6 * q^43 - 3 * q^46 + 4 * q^47 + 3 * q^48 - 9 * q^49 + 2 * q^51 + 4 * q^52 + 14 * q^53 - 3 * q^54 - 6 * q^56 + 4 * q^57 + 6 * q^58 - 10 * q^59 + 10 * q^61 - 8 * q^62 + 6 * q^63 + 3 * q^64 + 10 * q^67 + 2 * q^68 + 3 * q^69 - 10 * q^71 - 3 * q^72 + 28 * q^73 - 18 * q^74 + 4 * q^76 - 4 * q^78 - 4 * q^79 + 3 * q^81 + 2 * q^82 + 12 * q^83 + 6 * q^84 - 6 * q^86 - 6 * q^87 - 16 * q^89 + 8 * q^91 + 3 * q^92 + 8 * q^93 - 4 * q^94 - 3 * q^96 + 22 * q^97 + 9 * 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
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	2.00000	0.755929	0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000	0.755929	0.377964	+	0.925820i	$0.376624\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	3.50466	1.05670	0.528348	−	0.849028i	$-0.322812\pi$
$11$	3.50466	1.05670	0.528348	+	0.849028i	$0.322812\pi$
$12$	1.00000	0.288675
$13$	2.72666	0.756238	0.378119	−	0.925757i	$-0.376571\pi$
$13$	2.72666	0.756238	0.378119	+	0.925757i	$0.376571\pi$
$14$	−2.00000	−0.534522
$15$	0	0
$16$	1.00000	0.250000
$17$	−0.726656	−0.176240	−0.0881200	−	0.996110i	$-0.528086\pi$
$17$	−0.726656	−0.176240	−0.0881200	+	0.996110i	$0.528086\pi$
$18$	−1.00000	−0.235702
$19$	−7.78734	−1.78654	−0.893269	−	0.449523i	$-0.851594\pi$
$19$	−7.78734	−1.78654	−0.893269	+	0.449523i	$0.851594\pi$
$20$	0	0
$21$	2.00000	0.436436
$22$	−3.50466	−0.747197
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.00000	−0.204124
$25$	0	0
$26$	−2.72666	−0.534741
$27$	1.00000	0.192450
$28$	2.00000	0.377964
$29$	−2.00000	−0.371391	−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000	−0.371391	−0.185695	+	0.982607i	$0.559454\pi$
$30$	0	0
$31$	8.28267	1.48761	0.743806	−	0.668396i	$-0.233019\pi$
$31$	8.28267	1.48761	0.743806	+	0.668396i	$0.233019\pi$
$32$	−1.00000	−0.176777
$33$	3.50466	0.610084
$34$	0.726656	0.124621
$35$	0	0
$36$	1.00000	0.166667
$37$	9.50466	1.56256	0.781279	−	0.624182i	$-0.214568\pi$
$37$	9.50466	1.56256	0.781279	+	0.624182i	$0.214568\pi$
$38$	7.78734	1.26327
$39$	2.72666	0.436614
$40$	0	0
$41$	0.726656	0.113485	0.0567423	−	0.998389i	$-0.481929\pi$
$41$	0.726656	0.113485	0.0567423	+	0.998389i	$0.481929\pi$
$42$	−2.00000	−0.308607
$43$	5.50466	0.839453	0.419727	−	0.907651i	$-0.362126\pi$
$43$	5.50466	0.839453	0.419727	+	0.907651i	$0.362126\pi$
$44$	3.50466	0.528348
$45$	0	0
$46$	−1.00000	−0.147442
$47$	2.72666	0.397724	0.198862	−	0.980028i	$-0.436275\pi$
$47$	2.72666	0.397724	0.198862	+	0.980028i	$0.436275\pi$
$48$	1.00000	0.144338
$49$	−3.00000	−0.428571
$50$	0	0
$51$	−0.726656	−0.101752
$52$	2.72666	0.378119
$53$	−0.231321	−0.0317744	−0.0158872	−	0.999874i	$-0.505057\pi$
$53$	−0.231321	−0.0317744	−0.0158872	+	0.999874i	$0.505057\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	−2.00000	−0.267261
$57$	−7.78734	−1.03146
$58$	2.00000	0.262613
$59$	9.29200	1.20972	0.604858	−	0.796334i	$-0.293230\pi$
$59$	9.29200	1.20972	0.604858	+	0.796334i	$0.293230\pi$
$60$	0	0
$61$	4.05135	0.518722	0.259361	−	0.965780i	$-0.416488\pi$
$61$	4.05135	0.518722	0.259361	+	0.965780i	$0.416488\pi$
$62$	−8.28267	−1.05190
$63$	2.00000	0.251976
$64$	1.00000	0.125000
$65$	0	0
$66$	−3.50466	−0.431394
$67$	4.05135	0.494951	0.247476	−	0.968894i	$-0.420399\pi$
$67$	4.05135	0.494951	0.247476	+	0.968894i	$0.420399\pi$
$68$	−0.726656	−0.0881200
$69$	1.00000	0.120386
$70$	0	0
$71$	−11.7360	−1.39281	−0.696403	−	0.717651i	$-0.745217\pi$
$71$	−11.7360	−1.39281	−0.696403	+	0.717651i	$0.745217\pi$
$72$	−1.00000	−0.117851
$73$	3.71733	0.435080	0.217540	−	0.976051i	$-0.430197\pi$
$73$	3.71733	0.435080	0.217540	+	0.976051i	$0.430197\pi$
$74$	−9.50466	−1.10489
$75$	0	0
$76$	−7.78734	−0.893269
$77$	7.00933	0.798787
$78$	−2.72666	−0.308733
$79$	−9.73599	−1.09538	−0.547692	−	0.836680i	$-0.684493\pi$
$79$	−9.73599	−1.09538	−0.547692	+	0.836680i	$0.684493\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−0.726656	−0.0802458
$83$	−13.5233	−1.48438	−0.742189	−	0.670191i	$-0.766212\pi$
$83$	−13.5233	−1.48438	−0.742189	+	0.670191i	$0.766212\pi$
$84$	2.00000	0.218218
$85$	0	0
$86$	−5.50466	−0.593583
$87$	−2.00000	−0.214423
$88$	−3.50466	−0.373598
$89$	−9.55602	−1.01294	−0.506468	−	0.862259i	$-0.669049\pi$
$89$	−9.55602	−1.01294	−0.506468	+	0.862259i	$0.669049\pi$
$90$	0	0
$91$	5.45331	0.571663
$92$	1.00000	0.104257
$93$	8.28267	0.858873
$94$	−2.72666	−0.281233
$95$	0	0
$96$	−1.00000	−0.102062
$97$	4.54669	0.461646	0.230823	−	0.972996i	$-0.425858\pi$
$97$	4.54669	0.461646	0.230823	+	0.972996i	$0.425858\pi$
$98$	3.00000	0.303046
$99$	3.50466	0.352232
$100$	0	0
$101$	3.45331	0.343617	0.171809	−	0.985130i	$-0.445039\pi$
$101$	3.45331	0.343617	0.171809	+	0.985130i	$0.445039\pi$
$102$	0.726656	0.0719497
$103$	14.4626	1.42505	0.712523	−	0.701649i	$-0.247552\pi$
$103$	14.4626	1.42505	0.712523	+	0.701649i	$0.247552\pi$
$104$	−2.72666	−0.267371
$105$	0	0
$106$	0.231321	0.0224679
$107$	−13.0607	−1.26262	−0.631312	−	0.775529i	$-0.717483\pi$
$107$	−13.0607	−1.26262	−0.631312	+	0.775529i	$0.717483\pi$
$108$	1.00000	0.0962250
$109$	−10.9580	−1.04958	−0.524792	−	0.851231i	$-0.675857\pi$
$109$	−10.9580	−1.04958	−0.524792	+	0.851231i	$0.675857\pi$
$110$	0	0
$111$	9.50466	0.902143
$112$	2.00000	0.188982
$113$	11.7360	1.10403	0.552014	−	0.833835i	$-0.313859\pi$
$113$	11.7360	1.10403	0.552014	+	0.833835i	$0.313859\pi$
$114$	7.78734	0.729351
$115$	0	0
$116$	−2.00000	−0.185695
$117$	2.72666	0.252079
$118$	−9.29200	−0.855398
$119$	−1.45331	−0.133225
$120$	0	0
$121$	1.28267	0.116607
$122$	−4.05135	−0.366792
$123$	0.726656	0.0655204
$124$	8.28267	0.743806
$125$	0	0
$126$	−2.00000	−0.178174
$127$	12.2827	1.08991	0.544955	−	0.838465i	$-0.316547\pi$
$127$	12.2827	1.08991	0.544955	+	0.838465i	$0.316547\pi$
$128$	−1.00000	−0.0883883
$129$	5.50466	0.484659
$130$	0	0
$131$	−14.8480	−1.29728	−0.648639	−	0.761097i	$-0.724661\pi$
$131$	−14.8480	−1.29728	−0.648639	+	0.761097i	$0.724661\pi$
$132$	3.50466	0.305042
$133$	−15.5747	−1.35050
$134$	−4.05135	−0.349983
$135$	0	0
$136$	0.726656	0.0623103
$137$	3.27334	0.279661	0.139830	−	0.990175i	$-0.455344\pi$
$137$	3.27334	0.279661	0.139830	+	0.990175i	$0.455344\pi$
$138$	−1.00000	−0.0851257
$139$	14.0187	1.18905	0.594524	−	0.804078i	$-0.297341\pi$
$139$	14.0187	1.18905	0.594524	+	0.804078i	$0.297341\pi$
$140$	0	0
$141$	2.72666	0.229626
$142$	11.7360	0.984862
$143$	9.55602	0.799114
$144$	1.00000	0.0833333
$145$	0	0
$146$	−3.71733	−0.307648
$147$	−3.00000	−0.247436
$148$	9.50466	0.781279
$149$	−4.49534	−0.368272	−0.184136	−	0.982901i	$-0.558949\pi$
$149$	−4.49534	−0.368272	−0.184136	+	0.982901i	$0.558949\pi$
$150$	0	0
$151$	22.3013	1.81486	0.907428	−	0.420207i	$-0.138043\pi$
$151$	22.3013	1.81486	0.907428	+	0.420207i	$0.138043\pi$
$152$	7.78734	0.631636
$153$	−0.726656	−0.0587467
$154$	−7.00933	−0.564828
$155$	0	0
$156$	2.72666	0.218307
$157$	9.60737	0.766751	0.383376	−	0.923592i	$-0.374761\pi$
$157$	9.60737	0.766751	0.383376	+	0.923592i	$0.374761\pi$
$158$	9.73599	0.774553
$159$	−0.231321	−0.0183449
$160$	0	0
$161$	2.00000	0.157622
$162$	−1.00000	−0.0785674
$163$	14.1214	1.10607	0.553035	−	0.833158i	$-0.313470\pi$
$163$	14.1214	1.10607	0.553035	+	0.833158i	$0.313470\pi$
$164$	0.726656	0.0567423
$165$	0	0
$166$	13.5233	1.04961
$167$	8.74531	0.676733	0.338366	−	0.941014i	$-0.390126\pi$
$167$	8.74531	0.676733	0.338366	+	0.941014i	$0.390126\pi$
$168$	−2.00000	−0.154303
$169$	−5.56534	−0.428103
$170$	0	0
$171$	−7.78734	−0.595513
$172$	5.50466	0.419727
$173$	5.89730	0.448363	0.224182	−	0.974547i	$-0.428029\pi$
$173$	5.89730	0.448363	0.224182	+	0.974547i	$0.428029\pi$
$174$	2.00000	0.151620
$175$	0	0
$176$	3.50466	0.264174
$177$	9.29200	0.698430
$178$	9.55602	0.716254
$179$	−0.623954	−0.0466365	−0.0233182	−	0.999728i	$-0.507423\pi$
$179$	−0.623954	−0.0466365	−0.0233182	+	0.999728i	$0.507423\pi$
$180$	0	0
$181$	−14.0700	−1.04582	−0.522908	−	0.852389i	$-0.675153\pi$
$181$	−14.0700	−1.04582	−0.522908	+	0.852389i	$0.675153\pi$
$182$	−5.45331	−0.404226
$183$	4.05135	0.299485
$184$	−1.00000	−0.0737210
$185$	0	0
$186$	−8.28267	−0.607315
$187$	−2.54669	−0.186232
$188$	2.72666	0.198862
$189$	2.00000	0.145479
$190$	0	0
$191$	−19.5747	−1.41637	−0.708187	−	0.706025i	$-0.750487\pi$
$191$	−19.5747	−1.41637	−0.708187	+	0.706025i	$0.750487\pi$
$192$	1.00000	0.0721688
$193$	−10.0187	−0.721159	−0.360579	−	0.932729i	$-0.617421\pi$
$193$	−10.0187	−0.721159	−0.360579	+	0.932729i	$0.617421\pi$
$194$	−4.54669	−0.326433
$195$	0	0
$196$	−3.00000	−0.214286
$197$	2.00000	0.142494	0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000	0.142494	0.0712470	+	0.997459i	$0.477302\pi$
$198$	−3.50466	−0.249066
$199$	23.1893	1.64385	0.821923	−	0.569599i	$-0.192901\pi$
$199$	23.1893	1.64385	0.821923	+	0.569599i	$0.192901\pi$
$200$	0	0
$201$	4.05135	0.285760
$202$	−3.45331	−0.242974
$203$	−4.00000	−0.280745
$204$	−0.726656	−0.0508761
$205$	0	0
$206$	−14.4626	−1.00766
$207$	1.00000	0.0695048
$208$	2.72666	0.189060
$209$	−27.2920	−1.88783
$210$	0	0
$211$	−7.57467	−0.521462	−0.260731	−	0.965411i	$-0.583964\pi$
$211$	−7.57467	−0.521462	−0.260731	+	0.965411i	$0.583964\pi$
$212$	−0.231321	−0.0158872
$213$	−11.7360	−0.804136
$214$	13.0607	0.892810
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	16.5653	1.12453
$218$	10.9580	0.742168
$219$	3.71733	0.251194
$220$	0	0
$221$	−1.98134	−0.133280
$222$	−9.50466	−0.637911
$223$	−26.5840	−1.78020	−0.890098	−	0.455769i	$-0.849364\pi$
$223$	−26.5840	−1.78020	−0.890098	+	0.455769i	$0.849364\pi$
$224$	−2.00000	−0.133631
$225$	0	0
$226$	−11.7360	−0.780666
$227$	−11.9673	−0.794298	−0.397149	−	0.917754i	$-0.630000\pi$
$227$	−11.9673	−0.794298	−0.397149	+	0.917754i	$0.630000\pi$
$228$	−7.78734	−0.515729
$229$	26.5327	1.75333	0.876663	−	0.481104i	$-0.159764\pi$
$229$	26.5327	1.75333	0.876663	+	0.481104i	$0.159764\pi$
$230$	0	0
$231$	7.00933	0.461180
$232$	2.00000	0.131306
$233$	24.4040	1.59876	0.799381	−	0.600825i	$-0.205161\pi$
$233$	24.4040	1.59876	0.799381	+	0.600825i	$0.205161\pi$
$234$	−2.72666	−0.178247
$235$	0	0
$236$	9.29200	0.604858
$237$	−9.73599	−0.632420
$238$	1.45331	0.0942043
$239$	−3.55602	−0.230020	−0.115010	−	0.993364i	$-0.536690\pi$
$239$	−3.55602	−0.230020	−0.115010	+	0.993364i	$0.536690\pi$
$240$	0	0
$241$	3.55602	0.229063	0.114532	−	0.993420i	$-0.463463\pi$
$241$	3.55602	0.229063	0.114532	+	0.993420i	$0.463463\pi$
$242$	−1.28267	−0.0824533
$243$	1.00000	0.0641500
$244$	4.05135	0.259361
$245$	0	0
$246$	−0.726656	−0.0463299
$247$	−21.2334	−1.35105
$248$	−8.28267	−0.525950
$249$	−13.5233	−0.857006
$250$	0	0
$251$	6.05135	0.381958	0.190979	−	0.981594i	$-0.438834\pi$
$251$	6.05135	0.381958	0.190979	+	0.981594i	$0.438834\pi$
$252$	2.00000	0.125988
$253$	3.50466	0.220336
$254$	−12.2827	−0.770683
$255$	0	0
$256$	1.00000	0.0625000
$257$	16.9066	1.05461	0.527303	−	0.849677i	$-0.323203\pi$
$257$	16.9066	1.05461	0.527303	+	0.849677i	$0.323203\pi$
$258$	−5.50466	−0.342705
$259$	19.0093	1.18118
$260$	0	0
$261$	−2.00000	−0.123797
$262$	14.8480	0.917314
$263$	0.887968	0.0547545	0.0273772	−	0.999625i	$-0.491284\pi$
$263$	0.887968	0.0547545	0.0273772	+	0.999625i	$0.491284\pi$
$264$	−3.50466	−0.215697
$265$	0	0
$266$	15.5747	0.954944
$267$	−9.55602	−0.584819
$268$	4.05135	0.247476
$269$	20.1214	1.22682	0.613410	−	0.789764i	$-0.289797\pi$
$269$	20.1214	1.22682	0.613410	+	0.789764i	$0.289797\pi$
$270$	0	0
$271$	−30.5840	−1.85785	−0.928923	−	0.370273i	$-0.879264\pi$
$271$	−30.5840	−1.85785	−0.928923	+	0.370273i	$0.879264\pi$
$272$	−0.726656	−0.0440600
$273$	5.45331	0.330050
$274$	−3.27334	−0.197750
$275$	0	0
$276$	1.00000	0.0601929
$277$	−4.38538	−0.263492	−0.131746	−	0.991284i	$-0.542058\pi$
$277$	−4.38538	−0.263492	−0.131746	+	0.991284i	$0.542058\pi$
$278$	−14.0187	−0.840783
$279$	8.28267	0.495871
$280$	0	0
$281$	10.1214	0.603790	0.301895	−	0.953341i	$-0.402381\pi$
$281$	10.1214	0.603790	0.301895	+	0.953341i	$0.402381\pi$
$282$	−2.72666	−0.162370
$283$	25.1820	1.49692	0.748458	−	0.663182i	$-0.230794\pi$
$283$	25.1820	1.49692	0.748458	+	0.663182i	$0.230794\pi$
$284$	−11.7360	−0.696403
$285$	0	0
$286$	−9.55602	−0.565059
$287$	1.45331	0.0857864
$288$	−1.00000	−0.0589256
$289$	−16.4720	−0.968939
$290$	0	0
$291$	4.54669	0.266532
$292$	3.71733	0.217540
$293$	0.759350	0.0443617	0.0221809	−	0.999754i	$-0.492939\pi$
$293$	0.759350	0.0443617	0.0221809	+	0.999754i	$0.492939\pi$
$294$	3.00000	0.174964
$295$	0	0
$296$	−9.50466	−0.552447
$297$	3.50466	0.203361
$298$	4.49534	0.260408
$299$	2.72666	0.157687
$300$	0	0
$301$	11.0093	0.634567
$302$	−22.3013	−1.28330
$303$	3.45331	0.198388
$304$	−7.78734	−0.446634
$305$	0	0
$306$	0.726656	0.0415402
$307$	−27.5747	−1.57377	−0.786885	−	0.617100i	$-0.788307\pi$
$307$	−27.5747	−1.57377	−0.786885	+	0.617100i	$0.788307\pi$
$308$	7.00933	0.399394
$309$	14.4626	0.822751
$310$	0	0
$311$	24.1214	1.36780	0.683898	−	0.729577i	$-0.260283\pi$
$311$	24.1214	1.36780	0.683898	+	0.729577i	$0.260283\pi$
$312$	−2.72666	−0.154367
$313$	8.58400	0.485196	0.242598	−	0.970127i	$-0.422000\pi$
$313$	8.58400	0.485196	0.242598	+	0.970127i	$0.422000\pi$
$314$	−9.60737	−0.542175
$315$	0	0
$316$	−9.73599	−0.547692
$317$	24.1214	1.35479	0.677395	−	0.735619i	$-0.263109\pi$
$317$	24.1214	1.35479	0.677395	+	0.735619i	$0.263109\pi$
$318$	0.231321	0.0129718
$319$	−7.00933	−0.392447
$320$	0	0
$321$	−13.0607	−0.728976
$322$	−2.00000	−0.111456
$323$	5.65872	0.314860
$324$	1.00000	0.0555556
$325$	0	0
$326$	−14.1214	−0.782110
$327$	−10.9580	−0.605978
$328$	−0.726656	−0.0401229
$329$	5.45331	0.300651
$330$	0	0
$331$	8.10270	0.445365	0.222682	−	0.974891i	$-0.428519\pi$
$331$	8.10270	0.445365	0.222682	+	0.974891i	$0.428519\pi$
$332$	−13.5233	−0.742189
$333$	9.50466	0.520852
$334$	−8.74531	−0.478522
$335$	0	0
$336$	2.00000	0.109109
$337$	−24.1214	−1.31397	−0.656987	−	0.753902i	$-0.728169\pi$
$337$	−24.1214	−1.31397	−0.656987	+	0.753902i	$0.728169\pi$
$338$	5.56534	0.302715
$339$	11.7360	0.637411
$340$	0	0
$341$	29.0280	1.57195
$342$	7.78734	0.421091
$343$	−20.0000	−1.07990
$344$	−5.50466	−0.296792
$345$	0	0
$346$	−5.89730	−0.317041
$347$	−21.9160	−1.17651	−0.588255	−	0.808675i	$-0.700185\pi$
$347$	−21.9160	−1.17651	−0.588255	+	0.808675i	$0.700185\pi$
$348$	−2.00000	−0.107211
$349$	26.5653	1.42201	0.711005	−	0.703187i	$-0.248240\pi$
$349$	26.5653	1.42201	0.711005	+	0.703187i	$0.248240\pi$
$350$	0	0
$351$	2.72666	0.145538
$352$	−3.50466	−0.186799
$353$	−22.9507	−1.22154	−0.610772	−	0.791807i	$-0.709141\pi$
$353$	−22.9507	−1.22154	−0.610772	+	0.791807i	$0.709141\pi$
$354$	−9.29200	−0.493864
$355$	0	0
$356$	−9.55602	−0.506468
$357$	−1.45331	−0.0769175
$358$	0.623954	0.0329770
$359$	5.02799	0.265367	0.132683	−	0.991158i	$-0.457641\pi$
$359$	5.02799	0.265367	0.132683	+	0.991158i	$0.457641\pi$
$360$	0	0
$361$	41.6426	2.19172
$362$	14.0700	0.739503
$363$	1.28267	0.0673228
$364$	5.45331	0.285831
$365$	0	0
$366$	−4.05135	−0.211768
$367$	7.45331	0.389060	0.194530	−	0.980897i	$-0.437682\pi$
$367$	7.45331	0.389060	0.194530	+	0.980897i	$0.437682\pi$
$368$	1.00000	0.0521286
$369$	0.726656	0.0378282
$370$	0	0
$371$	−0.462642	−0.0240192
$372$	8.28267	0.429437
$373$	14.4953	0.750540	0.375270	−	0.926916i	$-0.377550\pi$
$373$	14.4953	0.750540	0.375270	+	0.926916i	$0.377550\pi$
$374$	2.54669	0.131686
$375$	0	0
$376$	−2.72666	−0.140617
$377$	−5.45331	−0.280860
$378$	−2.00000	−0.102869
$379$	17.1379	0.880317	0.440159	−	0.897920i	$-0.354922\pi$
$379$	17.1379	0.880317	0.440159	+	0.897920i	$0.354922\pi$
$380$	0	0
$381$	12.2827	0.629260
$382$	19.5747	1.00153
$383$	0.565344	0.0288878	0.0144439	−	0.999896i	$-0.495402\pi$
$383$	0.565344	0.0288878	0.0144439	+	0.999896i	$0.495402\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	10.0187	0.509936
$387$	5.50466	0.279818
$388$	4.54669	0.230823
$389$	−29.5233	−1.49689	−0.748446	−	0.663196i	$-0.769200\pi$
$389$	−29.5233	−1.49689	−0.748446	+	0.663196i	$0.769200\pi$
$390$	0	0
$391$	−0.726656	−0.0367486
$392$	3.00000	0.151523
$393$	−14.8480	−0.748983
$394$	−2.00000	−0.100759
$395$	0	0
$396$	3.50466	0.176116
$397$	−37.7360	−1.89391	−0.946957	−	0.321359i	$-0.895860\pi$
$397$	−37.7360	−1.89391	−0.946957	+	0.321359i	$0.895860\pi$
$398$	−23.1893	−1.16237
$399$	−15.5747	−0.779709
$400$	0	0
$401$	−6.90663	−0.344900	−0.172450	−	0.985018i	$-0.555168\pi$
$401$	−6.90663	−0.344900	−0.172450	+	0.985018i	$0.555168\pi$
$402$	−4.05135	−0.202063
$403$	22.5840	1.12499
$404$	3.45331	0.171809
$405$	0	0
$406$	4.00000	0.198517
$407$	33.3107	1.65115
$408$	0.726656	0.0359749
$409$	2.00000	0.0988936	0.0494468	−	0.998777i	$-0.484254\pi$
$409$	2.00000	0.0988936	0.0494468	+	0.998777i	$0.484254\pi$
$410$	0	0
$411$	3.27334	0.161462
$412$	14.4626	0.712523
$413$	18.5840	0.914459
$414$	−1.00000	−0.0491473
$415$	0	0
$416$	−2.72666	−0.133685
$417$	14.0187	0.686497
$418$	27.2920	1.33490
$419$	27.9673	1.36629	0.683146	−	0.730282i	$-0.260611\pi$
$419$	27.9673	1.36629	0.683146	+	0.730282i	$0.260611\pi$
$420$	0	0
$421$	2.59804	0.126621	0.0633103	−	0.997994i	$-0.479834\pi$
$421$	2.59804	0.126621	0.0633103	+	0.997994i	$0.479834\pi$
$422$	7.57467	0.368729
$423$	2.72666	0.132575
$424$	0.231321	0.0112339
$425$	0	0
$426$	11.7360	0.568610
$427$	8.10270	0.392117
$428$	−13.0607	−0.631312
$429$	9.55602	0.461369
$430$	0	0
$431$	−15.2147	−0.732868	−0.366434	−	0.930444i	$-0.619421\pi$
$431$	−15.2147	−0.732868	−0.366434	+	0.930444i	$0.619421\pi$
$432$	1.00000	0.0481125
$433$	−27.1307	−1.30382	−0.651909	−	0.758297i	$-0.726032\pi$
$433$	−27.1307	−1.30382	−0.651909	+	0.758297i	$0.726032\pi$
$434$	−16.5653	−0.795162
$435$	0	0
$436$	−10.9580	−0.524792
$437$	−7.78734	−0.372519
$438$	−3.71733	−0.177621
$439$	−1.65872	−0.0791663	−0.0395832	−	0.999216i	$-0.512603\pi$
$439$	−1.65872	−0.0791663	−0.0395832	+	0.999216i	$0.512603\pi$
$440$	0	0
$441$	−3.00000	−0.142857
$442$	1.98134	0.0942429
$443$	4.00000	0.190046	0.0950229	−	0.995475i	$-0.469708\pi$
$443$	4.00000	0.190046	0.0950229	+	0.995475i	$0.469708\pi$
$444$	9.50466	0.451071
$445$	0	0
$446$	26.5840	1.25879
$447$	−4.49534	−0.212622
$448$	2.00000	0.0944911
$449$	−14.9507	−0.705568	−0.352784	−	0.935705i	$-0.614765\pi$
$449$	−14.9507	−0.705568	−0.352784	+	0.935705i	$0.614765\pi$
$450$	0	0
$451$	2.54669	0.119919
$452$	11.7360	0.552014
$453$	22.3013	1.04781
$454$	11.9673	0.561654
$455$	0	0
$456$	7.78734	0.364675
$457$	1.43466	0.0671104	0.0335552	−	0.999437i	$-0.489317\pi$
$457$	1.43466	0.0671104	0.0335552	+	0.999437i	$0.489317\pi$
$458$	−26.5327	−1.23979
$459$	−0.726656	−0.0339174
$460$	0	0
$461$	−13.5747	−0.632236	−0.316118	−	0.948720i	$-0.602379\pi$
$461$	−13.5747	−0.632236	−0.316118	+	0.948720i	$0.602379\pi$
$462$	−7.00933	−0.326103
$463$	1.73599	0.0806781	0.0403390	−	0.999186i	$-0.487156\pi$
$463$	1.73599	0.0806781	0.0403390	+	0.999186i	$0.487156\pi$
$464$	−2.00000	−0.0928477
$465$	0	0
$466$	−24.4040	−1.13049
$467$	−28.1727	−1.30368	−0.651839	−	0.758358i	$-0.726002\pi$
$467$	−28.1727	−1.30368	−0.651839	+	0.758358i	$0.726002\pi$
$468$	2.72666	0.126040
$469$	8.10270	0.374148
$470$	0	0
$471$	9.60737	0.442684
$472$	−9.29200	−0.427699
$473$	19.2920	0.887047
$474$	9.73599	0.447189
$475$	0	0
$476$	−1.45331	−0.0666125
$477$	−0.231321	−0.0105915
$478$	3.55602	0.162648
$479$	−26.3786	−1.20527	−0.602634	−	0.798017i	$-0.705882\pi$
$479$	−26.3786	−1.20527	−0.602634	+	0.798017i	$0.705882\pi$
$480$	0	0
$481$	25.9160	1.18167
$482$	−3.55602	−0.161972
$483$	2.00000	0.0910032
$484$	1.28267	0.0583033
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	20.2827	0.919096	0.459548	−	0.888153i	$-0.348011\pi$
$487$	20.2827	0.919096	0.459548	+	0.888153i	$0.348011\pi$
$488$	−4.05135	−0.183396
$489$	14.1214	0.638590
$490$	0	0
$491$	18.6426	0.841329	0.420665	−	0.907216i	$-0.361797\pi$
$491$	18.6426	0.841329	0.420665	+	0.907216i	$0.361797\pi$
$492$	0.726656	0.0327602
$493$	1.45331	0.0654539
$494$	21.2334	0.955335
$495$	0	0
$496$	8.28267	0.371903
$497$	−23.4720	−1.05286
$498$	13.5233	0.605995
$499$	20.9907	0.939671	0.469836	−	0.882754i	$-0.344313\pi$
$499$	20.9907	0.939671	0.469836	+	0.882754i	$0.344313\pi$
$500$	0	0
$501$	8.74531	0.390712
$502$	−6.05135	−0.270085
$503$	−13.5560	−0.604433	−0.302216	−	0.953239i	$-0.597727\pi$
$503$	−13.5560	−0.604433	−0.302216	+	0.953239i	$0.597727\pi$
$504$	−2.00000	−0.0890871
$505$	0	0
$506$	−3.50466	−0.155801
$507$	−5.56534	−0.247166
$508$	12.2827	0.544955
$509$	−26.0000	−1.15243	−0.576215	−	0.817298i	$-0.695471\pi$
$509$	−26.0000	−1.15243	−0.576215	+	0.817298i	$0.695471\pi$
$510$	0	0
$511$	7.43466	0.328890
$512$	−1.00000	−0.0441942
$513$	−7.78734	−0.343819
$514$	−16.9066	−0.745719
$515$	0	0
$516$	5.50466	0.242329
$517$	9.55602	0.420273
$518$	−19.0093	−0.835222
$519$	5.89730	0.258863
$520$	0	0
$521$	−44.6027	−1.95408	−0.977039	−	0.213061i	$-0.931657\pi$
$521$	−44.6027	−1.95408	−0.977039	+	0.213061i	$0.931657\pi$
$522$	2.00000	0.0875376
$523$	19.7287	0.862677	0.431339	−	0.902190i	$-0.358041\pi$
$523$	19.7287	0.862677	0.431339	+	0.902190i	$0.358041\pi$
$524$	−14.8480	−0.648639
$525$	0	0
$526$	−0.887968	−0.0387173
$527$	−6.01866	−0.262177
$528$	3.50466	0.152521
$529$	1.00000	0.0434783
$530$	0	0
$531$	9.29200	0.403238
$532$	−15.5747	−0.675248
$533$	1.98134	0.0858215
$534$	9.55602	0.413529
$535$	0	0
$536$	−4.05135	−0.174992
$537$	−0.623954	−0.0269256
$538$	−20.1214	−0.867493
$539$	−10.5140	−0.452870
$540$	0	0
$541$	−13.4720	−0.579205	−0.289603	−	0.957147i	$-0.593523\pi$
$541$	−13.4720	−0.579205	−0.289603	+	0.957147i	$0.593523\pi$
$542$	30.5840	1.31370
$543$	−14.0700	−0.603802
$544$	0.726656	0.0311551
$545$	0	0
$546$	−5.45331	−0.233380
$547$	23.0466	0.985403	0.492702	−	0.870198i	$-0.336009\pi$
$547$	23.0466	0.985403	0.492702	+	0.870198i	$0.336009\pi$
$548$	3.27334	0.139830
$549$	4.05135	0.172907
$550$	0	0
$551$	15.5747	0.663503
$552$	−1.00000	−0.0425628
$553$	−19.4720	−0.828032
$554$	4.38538	0.186317
$555$	0	0
$556$	14.0187	0.594524
$557$	37.2593	1.57873	0.789364	−	0.613926i	$-0.210411\pi$
$557$	37.2593	1.57873	0.789364	+	0.613926i	$0.210411\pi$
$558$	−8.28267	−0.350633
$559$	15.0093	0.634827
$560$	0	0
$561$	−2.54669	−0.107521
$562$	−10.1214	−0.426944
$563$	−46.5513	−1.96190	−0.980952	−	0.194251i	$-0.937772\pi$
$563$	−46.5513	−1.96190	−0.980952	+	0.194251i	$0.937772\pi$
$564$	2.72666	0.114813
$565$	0	0
$566$	−25.1820	−1.05848
$567$	2.00000	0.0839921
$568$	11.7360	0.492431
$569$	−20.0000	−0.838444	−0.419222	−	0.907884i	$-0.637697\pi$
$569$	−20.0000	−0.838444	−0.419222	+	0.907884i	$0.637697\pi$
$570$	0	0
$571$	−13.6660	−0.571903	−0.285952	−	0.958244i	$-0.592310\pi$
$571$	−13.6660	−0.571903	−0.285952	+	0.958244i	$0.592310\pi$
$572$	9.55602	0.399557
$573$	−19.5747	−0.817744
$574$	−1.45331	−0.0606601
$575$	0	0
$576$	1.00000	0.0416667
$577$	6.30133	0.262328	0.131164	−	0.991361i	$-0.458129\pi$
$577$	6.30133	0.262328	0.131164	+	0.991361i	$0.458129\pi$
$578$	16.4720	0.685144
$579$	−10.0187	−0.416361
$580$	0	0
$581$	−27.0466	−1.12208
$582$	−4.54669	−0.188466
$583$	−0.810702	−0.0335758
$584$	−3.71733	−0.153824
$585$	0	0
$586$	−0.759350	−0.0313685
$587$	35.5747	1.46832	0.734162	−	0.678974i	$-0.237575\pi$
$587$	35.5747	1.46832	0.734162	+	0.678974i	$0.237575\pi$
$588$	−3.00000	−0.123718
$589$	−64.5000	−2.65767
$590$	0	0
$591$	2.00000	0.0822690
$592$	9.50466	0.390639
$593$	−4.54669	−0.186710	−0.0933550	−	0.995633i	$-0.529759\pi$
$593$	−4.54669	−0.186710	−0.0933550	+	0.995633i	$0.529759\pi$
$594$	−3.50466	−0.143798
$595$	0	0
$596$	−4.49534	−0.184136
$597$	23.1893	0.949075
$598$	−2.72666	−0.111501
$599$	16.1214	0.658701	0.329350	−	0.944208i	$-0.393170\pi$
$599$	16.1214	0.658701	0.329350	+	0.944208i	$0.393170\pi$
$600$	0	0
$601$	−9.39470	−0.383218	−0.191609	−	0.981471i	$-0.561371\pi$
$601$	−9.39470	−0.383218	−0.191609	+	0.981471i	$0.561371\pi$
$602$	−11.0093	−0.448707
$603$	4.05135	0.164984
$604$	22.3013	0.907428
$605$	0	0
$606$	−3.45331	−0.140281
$607$	−10.9066	−0.442686	−0.221343	−	0.975196i	$-0.571044\pi$
$607$	−10.9066	−0.442686	−0.221343	+	0.975196i	$0.571044\pi$
$608$	7.78734	0.315818
$609$	−4.00000	−0.162088
$610$	0	0
$611$	7.43466	0.300774
$612$	−0.726656	−0.0293733
$613$	−43.4206	−1.75374	−0.876871	−	0.480725i	$-0.840373\pi$
$613$	−43.4206	−1.75374	−0.876871	+	0.480725i	$0.840373\pi$
$614$	27.5747	1.11282
$615$	0	0
$616$	−7.00933	−0.282414
$617$	−20.0959	−0.809031	−0.404516	−	0.914531i	$-0.632560\pi$
$617$	−20.0959	−0.809031	−0.404516	+	0.914531i	$0.632560\pi$
$618$	−14.4626	−0.581773
$619$	27.3247	1.09827	0.549136	−	0.835733i	$-0.314957\pi$
$619$	27.3247	1.09827	0.549136	+	0.835733i	$0.314957\pi$
$620$	0	0
$621$	1.00000	0.0401286
$622$	−24.1214	−0.967178
$623$	−19.1120	−0.765707
$624$	2.72666	0.109154
$625$	0	0
$626$	−8.58400	−0.343086
$627$	−27.2920	−1.08994
$628$	9.60737	0.383376
$629$	−6.90663	−0.275385
$630$	0	0
$631$	39.8947	1.58818	0.794091	−	0.607799i	$-0.207947\pi$
$631$	39.8947	1.58818	0.794091	+	0.607799i	$0.207947\pi$
$632$	9.73599	0.387277
$633$	−7.57467	−0.301066
$634$	−24.1214	−0.957982
$635$	0	0
$636$	−0.231321	−0.00917247
$637$	−8.17997	−0.324102
$638$	7.00933	0.277502
$639$	−11.7360	−0.464268
$640$	0	0
$641$	49.1680	1.94202	0.971010	−	0.239040i	$-0.0768327\pi$
$641$	49.1680	1.94202	0.971010	+	0.239040i	$0.0768327\pi$
$642$	13.0607	0.515464
$643$	−20.9766	−0.827238	−0.413619	−	0.910450i	$-0.635735\pi$
$643$	−20.9766	−0.827238	−0.413619	+	0.910450i	$0.635735\pi$
$644$	2.00000	0.0788110
$645$	0	0
$646$	−5.65872	−0.222639
$647$	−25.9813	−1.02143	−0.510716	−	0.859749i	$-0.670620\pi$
$647$	−25.9813	−1.02143	−0.510716	+	0.859749i	$0.670620\pi$
$648$	−1.00000	−0.0392837
$649$	32.5653	1.27830
$650$	0	0
$651$	16.5653	0.649247
$652$	14.1214	0.553035
$653$	−0.0840454	−0.00328895	−0.00164448	−	0.999999i	$-0.500523\pi$
$653$	−0.0840454	−0.00328895	−0.00164448	+	0.999999i	$0.500523\pi$
$654$	10.9580	0.428491
$655$	0	0
$656$	0.726656	0.0283712
$657$	3.71733	0.145027
$658$	−5.45331	−0.212592
$659$	10.6167	0.413568	0.206784	−	0.978387i	$-0.433700\pi$
$659$	10.6167	0.413568	0.206784	+	0.978387i	$0.433700\pi$
$660$	0	0
$661$	−39.9860	−1.55527	−0.777637	−	0.628714i	$-0.783582\pi$
$661$	−39.9860	−1.55527	−0.777637	+	0.628714i	$0.783582\pi$
$662$	−8.10270	−0.314920
$663$	−1.98134	−0.0769490
$664$	13.5233	0.524807
$665$	0	0
$666$	−9.50466	−0.368298
$667$	−2.00000	−0.0774403
$668$	8.74531	0.338366
$669$	−26.5840	−1.02780
$670$	0	0
$671$	14.1986	0.548132
$672$	−2.00000	−0.0771517
$673$	2.86667	0.110502	0.0552511	−	0.998472i	$-0.482404\pi$
$673$	2.86667	0.110502	0.0552511	+	0.998472i	$0.482404\pi$
$674$	24.1214	0.929120
$675$	0	0
$676$	−5.56534	−0.214052
$677$	−3.76868	−0.144842	−0.0724211	−	0.997374i	$-0.523073\pi$
$677$	−3.76868	−0.144842	−0.0724211	+	0.997374i	$0.523073\pi$
$678$	−11.7360	−0.450718
$679$	9.09337	0.348972
$680$	0	0
$681$	−11.9673	−0.458588
$682$	−29.0280	−1.11154
$683$	−39.6120	−1.51571	−0.757855	−	0.652423i	$-0.773753\pi$
$683$	−39.6120	−1.51571	−0.757855	+	0.652423i	$0.773753\pi$
$684$	−7.78734	−0.297756
$685$	0	0
$686$	20.0000	0.763604
$687$	26.5327	1.01228
$688$	5.50466	0.209863
$689$	−0.630732	−0.0240290
$690$	0	0
$691$	−49.0653	−1.86653	−0.933266	−	0.359186i	$-0.883054\pi$
$691$	−49.0653	−1.86653	−0.933266	+	0.359186i	$0.883054\pi$
$692$	5.89730	0.224182
$693$	7.00933	0.266262
$694$	21.9160	0.831918
$695$	0	0
$696$	2.00000	0.0758098
$697$	−0.528030	−0.0200005
$698$	−26.5653	−1.00551
$699$	24.4040	0.923045
$700$	0	0
$701$	−10.5140	−0.397108	−0.198554	−	0.980090i	$-0.563625\pi$
$701$	−10.5140	−0.397108	−0.198554	+	0.980090i	$0.563625\pi$
$702$	−2.72666	−0.102911
$703$	−74.0160	−2.79157
$704$	3.50466	0.132087
$705$	0	0
$706$	22.9507	0.863762
$707$	6.90663	0.259750
$708$	9.29200	0.349215
$709$	−17.1447	−0.643884	−0.321942	−	0.946759i	$-0.604336\pi$
$709$	−17.1447	−0.643884	−0.321942	+	0.946759i	$0.604336\pi$
$710$	0	0
$711$	−9.73599	−0.365128
$712$	9.55602	0.358127
$713$	8.28267	0.310189
$714$	1.45331	0.0543889
$715$	0	0
$716$	−0.623954	−0.0233182
$717$	−3.55602	−0.132802
$718$	−5.02799	−0.187643
$719$	29.0093	1.08187	0.540933	−	0.841066i	$-0.318071\pi$
$719$	29.0093	1.08187	0.540933	+	0.841066i	$0.318071\pi$
$720$	0	0
$721$	28.9253	1.07723
$722$	−41.6426	−1.54978
$723$	3.55602	0.132250
$724$	−14.0700	−0.522908
$725$	0	0
$726$	−1.28267	−0.0476044
$727$	−38.9253	−1.44366	−0.721829	−	0.692071i	$-0.756698\pi$
$727$	−38.9253	−1.44366	−0.721829	+	0.692071i	$0.756698\pi$
$728$	−5.45331	−0.202113
$729$	1.00000	0.0370370
$730$	0	0
$731$	−4.00000	−0.147945
$732$	4.05135	0.149742
$733$	−5.50466	−0.203319	−0.101660	−	0.994819i	$-0.532415\pi$
$733$	−5.50466	−0.203319	−0.101660	+	0.994819i	$0.532415\pi$
$734$	−7.45331	−0.275107
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	14.1986	0.523013
$738$	−0.726656	−0.0267486
$739$	28.6027	1.05217	0.526083	−	0.850433i	$-0.323660\pi$
$739$	28.6027	1.05217	0.526083	+	0.850433i	$0.323660\pi$
$740$	0	0
$741$	−21.2334	−0.780028
$742$	0.462642	0.0169841
$743$	−9.98134	−0.366180	−0.183090	−	0.983096i	$-0.558610\pi$
$743$	−9.98134	−0.366180	−0.183090	+	0.983096i	$0.558610\pi$
$744$	−8.28267	−0.303657
$745$	0	0
$746$	−14.4953	−0.530712
$747$	−13.5233	−0.494792
$748$	−2.54669	−0.0931161
$749$	−26.1214	−0.954454
$750$	0	0
$751$	−21.8387	−0.796905	−0.398453	−	0.917189i	$-0.630453\pi$
$751$	−21.8387	−0.796905	−0.398453	+	0.917189i	$0.630453\pi$
$752$	2.72666	0.0994309
$753$	6.05135	0.220524
$754$	5.45331	0.198598
$755$	0	0
$756$	2.00000	0.0727393
$757$	16.5513	0.601568	0.300784	−	0.953692i	$-0.402752\pi$
$757$	16.5513	0.601568	0.300784	+	0.953692i	$0.402752\pi$
$758$	−17.1379	−0.622478
$759$	3.50466	0.127211
$760$	0	0
$761$	20.5840	0.746169	0.373085	−	0.927797i	$-0.378300\pi$
$761$	20.5840	0.746169	0.373085	+	0.927797i	$0.378300\pi$
$762$	−12.2827	−0.444954
$763$	−21.9160	−0.793411
$764$	−19.5747	−0.708187
$765$	0	0
$766$	−0.565344	−0.0204267
$767$	25.3361	0.914833
$768$	1.00000	0.0360844
$769$	7.76142	0.279884	0.139942	−	0.990160i	$-0.455308\pi$
$769$	7.76142	0.279884	0.139942	+	0.990160i	$0.455308\pi$
$770$	0	0
$771$	16.9066	0.608877
$772$	−10.0187	−0.360579
$773$	21.8247	0.784978	0.392489	−	0.919757i	$-0.371614\pi$
$773$	21.8247	0.784978	0.392489	+	0.919757i	$0.371614\pi$
$774$	−5.50466	−0.197861
$775$	0	0
$776$	−4.54669	−0.163217
$777$	19.0093	0.681956
$778$	29.5233	1.05846
$779$	−5.65872	−0.202745
$780$	0	0
$781$	−41.1307	−1.47177
$782$	0.726656	0.0259852
$783$	−2.00000	−0.0714742
$784$	−3.00000	−0.107143
$785$	0	0
$786$	14.8480	0.529611
$787$	46.4299	1.65505	0.827524	−	0.561430i	$-0.189748\pi$
$787$	46.4299	1.65505	0.827524	+	0.561430i	$0.189748\pi$
$788$	2.00000	0.0712470
$789$	0.887968	0.0316125
$790$	0	0
$791$	23.4720	0.834567
$792$	−3.50466	−0.124533
$793$	11.0466	0.392278
$794$	37.7360	1.33920
$795$	0	0
$796$	23.1893	0.821923
$797$	−44.3340	−1.57039	−0.785196	−	0.619248i	$-0.787438\pi$
$797$	−44.3340	−1.57039	−0.785196	+	0.619248i	$0.787438\pi$
$798$	15.5747	0.551337
$799$	−1.98134	−0.0700949
$800$	0	0
$801$	−9.55602	−0.337645
$802$	6.90663	0.243881
$803$	13.0280	0.459748
$804$	4.05135	0.142880
$805$	0	0
$806$	−22.5840	−0.795488
$807$	20.1214	0.708305
$808$	−3.45331	−0.121487
$809$	−1.96269	−0.0690043	−0.0345022	−	0.999405i	$-0.510985\pi$
$809$	−1.96269	−0.0690043	−0.0345022	+	0.999405i	$0.510985\pi$
$810$	0	0
$811$	31.8973	1.12007	0.560033	−	0.828470i	$-0.310789\pi$
$811$	31.8973	1.12007	0.560033	+	0.828470i	$0.310789\pi$
$812$	−4.00000	−0.140372
$813$	−30.5840	−1.07263
$814$	−33.3107	−1.16754
$815$	0	0
$816$	−0.726656	−0.0254381
$817$	−42.8667	−1.49972
$818$	−2.00000	−0.0699284
$819$	5.45331	0.190554
$820$	0	0
$821$	11.4906	0.401026	0.200513	−	0.979691i	$-0.435739\pi$
$821$	11.4906	0.401026	0.200513	+	0.979691i	$0.435739\pi$
$822$	−3.27334	−0.114171
$823$	−37.1307	−1.29429	−0.647147	−	0.762365i	$-0.724038\pi$
$823$	−37.1307	−1.29429	−0.647147	+	0.762365i	$0.724038\pi$
$824$	−14.4626	−0.503830
$825$	0	0
$826$	−18.5840	−0.646620
$827$	−40.2100	−1.39824	−0.699120	−	0.715005i	$-0.746425\pi$
$827$	−40.2100	−1.39824	−0.699120	+	0.715005i	$0.746425\pi$
$828$	1.00000	0.0347524
$829$	−6.88797	−0.239229	−0.119615	−	0.992820i	$-0.538166\pi$
$829$	−6.88797	−0.239229	−0.119615	+	0.992820i	$0.538166\pi$
$830$	0	0
$831$	−4.38538	−0.152127
$832$	2.72666	0.0945298
$833$	2.17997	0.0755315
$834$	−14.0187	−0.485426
$835$	0	0
$836$	−27.2920	−0.943914
$837$	8.28267	0.286291
$838$	−27.9673	−0.966115
$839$	−26.3786	−0.910690	−0.455345	−	0.890315i	$-0.650484\pi$
$839$	−26.3786	−0.910690	−0.455345	+	0.890315i	$0.650484\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	−2.59804	−0.0895343
$843$	10.1214	0.348598
$844$	−7.57467	−0.260731
$845$	0	0
$846$	−2.72666	−0.0937444
$847$	2.56534	0.0881463
$848$	−0.231321	−0.00794359
$849$	25.1820	0.864245
$850$	0	0
$851$	9.50466	0.325816
$852$	−11.7360	−0.402068
$853$	11.7546	0.402471	0.201236	−	0.979543i	$-0.435504\pi$
$853$	11.7546	0.402471	0.201236	+	0.979543i	$0.435504\pi$
$854$	−8.10270	−0.277269
$855$	0	0
$856$	13.0607	0.446405
$857$	−53.5347	−1.82871	−0.914356	−	0.404912i	$-0.867302\pi$
$857$	−53.5347	−1.82871	−0.914356	+	0.404912i	$0.867302\pi$
$858$	−9.55602	−0.326237
$859$	−7.11203	−0.242659	−0.121330	−	0.992612i	$-0.538716\pi$
$859$	−7.11203	−0.242659	−0.121330	+	0.992612i	$0.538716\pi$
$860$	0	0
$861$	1.45331	0.0495288
$862$	15.2147	0.518216
$863$	28.0373	0.954401	0.477201	−	0.878794i	$-0.341651\pi$
$863$	28.0373	0.954401	0.477201	+	0.878794i	$0.341651\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	27.1307	0.921938
$867$	−16.4720	−0.559417
$868$	16.5653	0.562264
$869$	−34.1214	−1.15749
$870$	0	0
$871$	11.0466	0.374301
$872$	10.9580	0.371084
$873$	4.54669	0.153882
$874$	7.78734	0.263411
$875$	0	0
$876$	3.71733	0.125597
$877$	−46.4040	−1.56695	−0.783476	−	0.621422i	$-0.786555\pi$
$877$	−46.4040	−1.56695	−0.783476	+	0.621422i	$0.786555\pi$
$878$	1.65872	0.0559790
$879$	0.759350	0.0256123
$880$	0	0
$881$	14.6494	0.493550	0.246775	−	0.969073i	$-0.420629\pi$
$881$	14.6494	0.493550	0.246775	+	0.969073i	$0.420629\pi$
$882$	3.00000	0.101015
$883$	−13.7614	−0.463109	−0.231554	−	0.972822i	$-0.574381\pi$
$883$	−13.7614	−0.463109	−0.231554	+	0.972822i	$0.574381\pi$
$884$	−1.98134	−0.0666398
$885$	0	0
$886$	−4.00000	−0.134383
$887$	35.8573	1.20397	0.601986	−	0.798507i	$-0.294376\pi$
$887$	35.8573	1.20397	0.601986	+	0.798507i	$0.294376\pi$
$888$	−9.50466	−0.318956
$889$	24.5653	0.823895
$890$	0	0
$891$	3.50466	0.117411
$892$	−26.5840	−0.890098
$893$	−21.2334	−0.710548
$894$	4.49534	0.150347
$895$	0	0
$896$	−2.00000	−0.0668153
$897$	2.72666	0.0910404
$898$	14.9507	0.498912
$899$	−16.5653	−0.552485
$900$	0	0
$901$	0.168091	0.00559992
$902$	−2.54669	−0.0847954
$903$	11.0093	0.366368
$904$	−11.7360	−0.390333
$905$	0	0
$906$	−22.3013	−0.740912
$907$	1.60737	0.0533718	0.0266859	−	0.999644i	$-0.491505\pi$
$907$	1.60737	0.0533718	0.0266859	+	0.999644i	$0.491505\pi$
$908$	−11.9673	−0.397149
$909$	3.45331	0.114539
$910$	0	0
$911$	−15.8973	−0.526701	−0.263350	−	0.964700i	$-0.584828\pi$
$911$	−15.8973	−0.526701	−0.263350	+	0.964700i	$0.584828\pi$
$912$	−7.78734	−0.257864
$913$	−47.3947	−1.56854
$914$	−1.43466	−0.0474542
$915$	0	0
$916$	26.5327	0.876663
$917$	−29.6960	−0.980649
$918$	0.726656	0.0239832
$919$	−42.3013	−1.39539	−0.697696	−	0.716394i	$-0.745791\pi$
$919$	−42.3013	−1.39539	−0.697696	+	0.716394i	$0.745791\pi$
$920$	0	0
$921$	−27.5747	−0.908616
$922$	13.5747	0.447058
$923$	−32.0000	−1.05329
$924$	7.00933	0.230590
$925$	0	0
$926$	−1.73599	−0.0570480
$927$	14.4626	0.475015
$928$	2.00000	0.0656532
$929$	−42.0628	−1.38003	−0.690017	−	0.723793i	$-0.742397\pi$
$929$	−42.0628	−1.38003	−0.690017	+	0.723793i	$0.742397\pi$
$930$	0	0
$931$	23.3620	0.765659
$932$	24.4040	0.799381
$933$	24.1214	0.789698
$934$	28.1727	0.921839
$935$	0	0
$936$	−2.72666	−0.0891236
$937$	8.44398	0.275853	0.137926	−	0.990442i	$-0.455956\pi$
$937$	8.44398	0.275853	0.137926	+	0.990442i	$0.455956\pi$
$938$	−8.10270	−0.264563
$939$	8.58400	0.280128
$940$	0	0
$941$	−19.2993	−0.629138	−0.314569	−	0.949235i	$-0.601860\pi$
$941$	−19.2993	−0.629138	−0.314569	+	0.949235i	$0.601860\pi$
$942$	−9.60737	−0.313025
$943$	0.726656	0.0236632
$944$	9.29200	0.302429
$945$	0	0
$946$	−19.2920	−0.627237
$947$	−3.36927	−0.109486	−0.0547432	−	0.998500i	$-0.517434\pi$
$947$	−3.36927	−0.109486	−0.0547432	+	0.998500i	$0.517434\pi$
$948$	−9.73599	−0.316210
$949$	10.1359	0.329024
$950$	0	0
$951$	24.1214	0.782189
$952$	1.45331	0.0471021
$953$	24.0441	0.778865	0.389432	−	0.921055i	$-0.372671\pi$
$953$	24.0441	0.778865	0.389432	+	0.921055i	$0.372671\pi$
$954$	0.231321	0.00748929
$955$	0	0
$956$	−3.55602	−0.115010
$957$	−7.00933	−0.226579
$958$	26.3786	0.852254
$959$	6.54669	0.211404
$960$	0	0
$961$	37.6027	1.21299
$962$	−25.9160	−0.835564
$963$	−13.0607	−0.420875
$964$	3.55602	0.114532
$965$	0	0
$966$	−2.00000	−0.0643489
$967$	−26.9439	−0.866459	−0.433229	−	0.901284i	$-0.642626\pi$
$967$	−26.9439	−0.866459	−0.433229	+	0.901284i	$0.642626\pi$
$968$	−1.28267	−0.0412266
$969$	5.65872	0.181784
$970$	0	0
$971$	−5.84595	−0.187605	−0.0938027	−	0.995591i	$-0.529902\pi$
$971$	−5.84595	−0.187605	−0.0938027	+	0.995591i	$0.529902\pi$
$972$	1.00000	0.0320750
$973$	28.0373	0.898835
$974$	−20.2827	−0.649899
$975$	0	0
$976$	4.05135	0.129681
$977$	23.8387	0.762667	0.381334	−	0.924437i	$-0.375465\pi$
$977$	23.8387	0.762667	0.381334	+	0.924437i	$0.375465\pi$
$978$	−14.1214	−0.451551
$979$	−33.4906	−1.07037
$980$	0	0
$981$	−10.9580	−0.349861
$982$	−18.6426	−0.594910
$983$	44.6680	1.42469	0.712345	−	0.701830i	$-0.247633\pi$
$983$	44.6680	1.42469	0.712345	+	0.701830i	$0.247633\pi$
$984$	−0.726656	−0.0231650
$985$	0	0
$986$	−1.45331	−0.0462829
$987$	5.45331	0.173581
$988$	−21.2334	−0.675524
$989$	5.50466	0.175038
$990$	0	0
$991$	−10.0586	−0.319522	−0.159761	−	0.987156i	$-0.551072\pi$
$991$	−10.0586	−0.319522	−0.159761	+	0.987156i	$0.551072\pi$
$992$	−8.28267	−0.262975
$993$	8.10270	0.257132
$994$	23.4720	0.744486
$995$	0	0
$996$	−13.5233	−0.428503
$997$	−38.2640	−1.21183	−0.605917	−	0.795528i	$-0.707194\pi$
$997$	−38.2640	−1.21183	−0.605917	+	0.795528i	$0.707194\pi$
$998$	−20.9907	−0.664448
$999$	9.50466	0.300714

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3450.2.a.bq.1.3		3
5.2	odd	4		690.2.d.d.139.1	✓	6
5.3	odd	4		690.2.d.d.139.4	yes	6
5.4	even	2		3450.2.a.br.1.3		3
15.2	even	4		2070.2.d.d.829.6		6
15.8	even	4		2070.2.d.d.829.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.d.d.139.1	✓	6	5.2	odd	4
690.2.d.d.139.4	yes	6	5.3	odd	4
2070.2.d.d.829.3		6	15.8	even	4
2070.2.d.d.829.6		6	15.2	even	4
3450.2.a.bq.1.3		3	1.1	even	1	trivial
3450.2.a.br.1.3		3	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3450.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.50466 q^{11} +1.00000 q^{12} +2.72666 q^{13} -2.00000 q^{14} +1.00000 q^{16} -0.726656 q^{17} -1.00000 q^{18} -7.78734 q^{19} +2.00000 q^{21} -3.50466 q^{22} +1.00000 q^{23} -1.00000 q^{24} -2.72666 q^{26} +1.00000 q^{27} +2.00000 q^{28} -2.00000 q^{29} +8.28267 q^{31} -1.00000 q^{32} +3.50466 q^{33} +0.726656 q^{34} +1.00000 q^{36} +9.50466 q^{37} +7.78734 q^{38} +2.72666 q^{39} +0.726656 q^{41} -2.00000 q^{42} +5.50466 q^{43} +3.50466 q^{44} -1.00000 q^{46} +2.72666 q^{47} +1.00000 q^{48} -3.00000 q^{49} -0.726656 q^{51} +2.72666 q^{52} -0.231321 q^{53} -1.00000 q^{54} -2.00000 q^{56} -7.78734 q^{57} +2.00000 q^{58} +9.29200 q^{59} +4.05135 q^{61} -8.28267 q^{62} +2.00000 q^{63} +1.00000 q^{64} -3.50466 q^{66} +4.05135 q^{67} -0.726656 q^{68} +1.00000 q^{69} -11.7360 q^{71} -1.00000 q^{72} +3.71733 q^{73} -9.50466 q^{74} -7.78734 q^{76} +7.00933 q^{77} -2.72666 q^{78} -9.73599 q^{79} +1.00000 q^{81} -0.726656 q^{82} -13.5233 q^{83} +2.00000 q^{84} -5.50466 q^{86} -2.00000 q^{87} -3.50466 q^{88} -9.55602 q^{89} +5.45331 q^{91} +1.00000 q^{92} +8.28267 q^{93} -2.72666 q^{94} -1.00000 q^{96} +4.54669 q^{97} +3.00000 q^{98} +3.50466 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{6} + 6 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^6 + 6 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{6} + 6 q^{7} - 3 q^{8} + 3 q^{9} + 3 q^{12} + 4 q^{13} - 6 q^{14} + 3 q^{16} + 2 q^{17} - 3 q^{18} + 4 q^{19} + 6 q^{21} + 3 q^{23} - 3 q^{24} - 4 q^{26} + 3 q^{27} + 6 q^{28} - 6 q^{29} + 8 q^{31} - 3 q^{32} - 2 q^{34} + 3 q^{36} + 18 q^{37} - 4 q^{38} + 4 q^{39} - 2 q^{41} - 6 q^{42} + 6 q^{43} - 3 q^{46} + 4 q^{47} + 3 q^{48} - 9 q^{49} + 2 q^{51} + 4 q^{52} + 14 q^{53} - 3 q^{54} - 6 q^{56} + 4 q^{57} + 6 q^{58} - 10 q^{59} + 10 q^{61} - 8 q^{62} + 6 q^{63} + 3 q^{64} + 10 q^{67} + 2 q^{68} + 3 q^{69} - 10 q^{71} - 3 q^{72} + 28 q^{73} - 18 q^{74} + 4 q^{76} - 4 q^{78} - 4 q^{79} + 3 q^{81} + 2 q^{82} + 12 q^{83} + 6 q^{84} - 6 q^{86} - 6 q^{87} - 16 q^{89} + 8 q^{91} + 3 q^{92} + 8 q^{93} - 4 q^{94} - 3 q^{96} + 22 q^{97} + 9 q^{98}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^6 + 6 * q^7 - 3 * q^8 + 3 * q^9 + 3 * q^12 + 4 * q^13 - 6 * q^14 + 3 * q^16 + 2 * q^17 - 3 * q^18 + 4 * q^19 + 6 * q^21 + 3 * q^23 - 3 * q^24 - 4 * q^26 + 3 * q^27 + 6 * q^28 - 6 * q^29 + 8 * q^31 - 3 * q^32 - 2 * q^34 + 3 * q^36 + 18 * q^37 - 4 * q^38 + 4 * q^39 - 2 * q^41 - 6 * q^42 + 6 * q^43 - 3 * q^46 + 4 * q^47 + 3 * q^48 - 9 * q^49 + 2 * q^51 + 4 * q^52 + 14 * q^53 - 3 * q^54 - 6 * q^56 + 4 * q^57 + 6 * q^58 - 10 * q^59 + 10 * q^61 - 8 * q^62 + 6 * q^63 + 3 * q^64 + 10 * q^67 + 2 * q^68 + 3 * q^69 - 10 * q^71 - 3 * q^72 + 28 * q^73 - 18 * q^74 + 4 * q^76 - 4 * q^78 - 4 * q^79 + 3 * q^81 + 2 * q^82 + 12 * q^83 + 6 * q^84 - 6 * q^86 - 6 * q^87 - 16 * q^89 + 8 * q^91 + 3 * q^92 + 8 * q^93 - 4 * q^94 - 3 * q^96 + 22 * q^97 + 9 * q^98

Introduction

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