LMFDB - Embedded newform 3381.2.a.x.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3381,2,Mod(1,3381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3381, 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("3381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3381 = 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3381.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:	$26.9974209234$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.15317.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 4x^{2} + 5x + 2 $ x^4 - 2x^3 - 4x^2 + 5*x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 483)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.69353$ of defining polynomial
Character	$\chi$	$=$	3381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.69353 q^{2} +1.00000 q^{3} +5.25508 q^{4} -1.04900 q^{5} +2.69353 q^{6} +8.76763 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.69353 q^{2} +1.00000 q^{3} +5.25508 q^{4} -1.04900 q^{5} +2.69353 q^{6} +8.76763 q^{8} +1.00000 q^{9} -2.82550 q^{10} +0.180969 q^{11} +5.25508 q^{12} +4.89961 q^{13} -1.04900 q^{15} +13.1057 q^{16} -2.82550 q^{17} +2.69353 q^{18} +0.180969 q^{19} -5.51256 q^{20} +0.487443 q^{22} +1.00000 q^{23} +8.76763 q^{24} -3.89961 q^{25} +13.1972 q^{26} +1.00000 q^{27} -5.68466 q^{29} -2.82550 q^{30} +0.825498 q^{31} +17.7652 q^{32} +0.180969 q^{33} -7.61055 q^{34} +5.25508 q^{36} +6.46356 q^{37} +0.487443 q^{38} +4.89961 q^{39} -9.19722 q^{40} +3.47003 q^{41} +0.125506 q^{43} +0.951004 q^{44} -1.04900 q^{45} +2.69353 q^{46} +12.0316 q^{47} +13.1057 q^{48} -10.5037 q^{50} -2.82550 q^{51} +25.7478 q^{52} +8.55269 q^{53} +2.69353 q^{54} -0.189835 q^{55} +0.180969 q^{57} -15.3118 q^{58} +4.30647 q^{59} -5.51256 q^{60} -9.01625 q^{61} +2.22350 q^{62} +21.6397 q^{64} -5.13967 q^{65} +0.487443 q^{66} -15.7074 q^{67} -14.8482 q^{68} +1.00000 q^{69} -2.22350 q^{71} +8.76763 q^{72} -13.0717 q^{73} +17.4098 q^{74} -3.89961 q^{75} +0.951004 q^{76} +13.1972 q^{78} -16.1948 q^{79} -13.7478 q^{80} +1.00000 q^{81} +9.34660 q^{82} -10.8757 q^{83} +2.96394 q^{85} +0.338054 q^{86} -5.68466 q^{87} +1.58667 q^{88} +14.7466 q^{89} -2.82550 q^{90} +5.25508 q^{92} +0.825498 q^{93} +32.4074 q^{94} -0.189835 q^{95} +17.7652 q^{96} -10.4636 q^{97} +0.180969 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 4 q^{3} + 4 q^{4} - 5 q^{5} + 2 q^{6} + 9 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 4 * q^3 + 4 * q^4 - 5 * q^5 + 2 * q^6 + 9 * q^8 + 4 * q^9	$ 4 q + 2 q^{2} + 4 q^{3} + 4 q^{4} - 5 q^{5} + 2 q^{6} + 9 q^{8} + 4 q^{9} - 2 q^{10} + q^{11} + 4 q^{12} - 7 q^{13} - 5 q^{15} + 8 q^{16} - 2 q^{17} + 2 q^{18} + q^{19} - 13 q^{20} + 11 q^{22} + 4 q^{23} + 9 q^{24} + 11 q^{25} + 19 q^{26} + 4 q^{27} + 2 q^{29} - 2 q^{30} - 6 q^{31} + 20 q^{32} + q^{33} - 23 q^{34} + 4 q^{36} + 16 q^{37} + 11 q^{38} - 7 q^{39} - 3 q^{40} - 5 q^{41} + 9 q^{43} + 3 q^{44} - 5 q^{45} + 2 q^{46} + 21 q^{47} + 8 q^{48} - 17 q^{50} - 2 q^{51} + 24 q^{52} + 10 q^{53} + 2 q^{54} - 17 q^{55} + q^{57} + q^{58} + 26 q^{59} - 13 q^{60} - 2 q^{61} + 19 q^{62} + 27 q^{64} + 26 q^{65} + 11 q^{66} + 5 q^{67} - 7 q^{68} + 4 q^{69} - 19 q^{71} + 9 q^{72} - 10 q^{73} + 9 q^{74} + 11 q^{75} + 3 q^{76} + 19 q^{78} - 6 q^{79} + 24 q^{80} + 4 q^{81} + 31 q^{82} + 2 q^{83} - 7 q^{85} - 17 q^{86} + 2 q^{87} - 20 q^{88} + 17 q^{89} - 2 q^{90} + 4 q^{92} - 6 q^{93} + 44 q^{94} - 17 q^{95} + 20 q^{96} - 32 q^{97} + q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 4 * q^3 + 4 * q^4 - 5 * q^5 + 2 * q^6 + 9 * q^8 + 4 * q^9 - 2 * q^10 + q^11 + 4 * q^12 - 7 * q^13 - 5 * q^15 + 8 * q^16 - 2 * q^17 + 2 * q^18 + q^19 - 13 * q^20 + 11 * q^22 + 4 * q^23 + 9 * q^24 + 11 * q^25 + 19 * q^26 + 4 * q^27 + 2 * q^29 - 2 * q^30 - 6 * q^31 + 20 * q^32 + q^33 - 23 * q^34 + 4 * q^36 + 16 * q^37 + 11 * q^38 - 7 * q^39 - 3 * q^40 - 5 * q^41 + 9 * q^43 + 3 * q^44 - 5 * q^45 + 2 * q^46 + 21 * q^47 + 8 * q^48 - 17 * q^50 - 2 * q^51 + 24 * q^52 + 10 * q^53 + 2 * q^54 - 17 * q^55 + q^57 + q^58 + 26 * q^59 - 13 * q^60 - 2 * q^61 + 19 * q^62 + 27 * q^64 + 26 * q^65 + 11 * q^66 + 5 * q^67 - 7 * q^68 + 4 * q^69 - 19 * q^71 + 9 * q^72 - 10 * q^73 + 9 * q^74 + 11 * q^75 + 3 * q^76 + 19 * q^78 - 6 * q^79 + 24 * q^80 + 4 * q^81 + 31 * q^82 + 2 * q^83 - 7 * q^85 - 17 * q^86 + 2 * q^87 - 20 * q^88 + 17 * q^89 - 2 * q^90 + 4 * q^92 - 6 * q^93 + 44 * q^94 - 17 * q^95 + 20 * q^96 - 32 * q^97 + 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 $

$2$	2.69353	1.90461	0.952305	−	0.305148i	$-0.0987059\pi$
$2$	2.69353	1.90461	0.952305	+	0.305148i	$0.0987059\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.25508	2.62754
$5$	−1.04900	−0.469125	−0.234563	−	0.972101i	$-0.575366\pi$
$5$	−1.04900	−0.469125	−0.234563	+	0.972101i	$0.575366\pi$
$6$	2.69353	1.09963
$7$	0	0
$7$	0	0
$8$	8.76763	3.09983
$9$	1.00000	0.333333
$10$	−2.82550	−0.893501
$11$	0.180969	0.0545641	0.0272820	−	0.999628i	$-0.491315\pi$
$11$	0.180969	0.0545641	0.0272820	+	0.999628i	$0.491315\pi$
$12$	5.25508	1.51701
$13$	4.89961	1.35891	0.679453	−	0.733719i	$-0.262217\pi$
$13$	4.89961	1.35891	0.679453	+	0.733719i	$0.262217\pi$
$14$	0	0
$15$	−1.04900	−0.270850
$16$	13.1057	3.27642
$17$	−2.82550	−0.685284	−0.342642	−	0.939466i	$-0.611322\pi$
$17$	−2.82550	−0.685284	−0.342642	+	0.939466i	$0.611322\pi$
$18$	2.69353	0.634870
$19$	0.180969	0.0415170	0.0207585	−	0.999785i	$-0.493392\pi$
$19$	0.180969	0.0415170	0.0207585	+	0.999785i	$0.493392\pi$
$20$	−5.51256	−1.23265
$21$	0	0
$22$	0.487443	0.103923
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	8.76763	1.78969
$25$	−3.89961	−0.779921
$26$	13.1972	2.58819
$27$	1.00000	0.192450
$28$	0	0
$29$	−5.68466	−1.05561	−0.527807	−	0.849364i	$-0.676986\pi$
$29$	−5.68466	−1.05561	−0.527807	+	0.849364i	$0.676986\pi$
$30$	−2.82550	−0.515863
$31$	0.825498	0.148264	0.0741319	−	0.997248i	$-0.476381\pi$
$31$	0.825498	0.148264	0.0741319	+	0.997248i	$0.476381\pi$
$32$	17.7652	3.14048
$33$	0.180969	0.0315026
$34$	−7.61055	−1.30520
$35$	0	0
$36$	5.25508	0.875846
$37$	6.46356	1.06260	0.531301	−	0.847183i	$-0.321703\pi$
$37$	6.46356	1.06260	0.531301	+	0.847183i	$0.321703\pi$
$38$	0.487443	0.0790738
$39$	4.89961	0.784565
$40$	−9.19722	−1.45421
$41$	3.47003	0.541927	0.270964	−	0.962590i	$-0.412658\pi$
$41$	3.47003	0.541927	0.270964	+	0.962590i	$0.412658\pi$
$42$	0	0
$43$	0.125506	0.0191395	0.00956976	−	0.999954i	$-0.496954\pi$
$43$	0.125506	0.0191395	0.00956976	+	0.999954i	$0.496954\pi$
$44$	0.951004	0.143369
$45$	−1.04900	−0.156375
$46$	2.69353	0.397139
$47$	12.0316	1.75499	0.877493	−	0.479589i	$-0.159214\pi$
$47$	12.0316	1.75499	0.877493	+	0.479589i	$0.159214\pi$
$48$	13.1057	1.89164
$49$	0	0
$50$	−10.5037	−1.48545
$51$	−2.82550	−0.395649
$52$	25.7478	3.57058
$53$	8.55269	1.17480	0.587401	−	0.809296i	$-0.300151\pi$
$53$	8.55269	1.17480	0.587401	+	0.809296i	$0.300151\pi$
$54$	2.69353	0.366542
$55$	−0.189835	−0.0255974
$56$	0	0
$57$	0.180969	0.0239699
$58$	−15.3118	−2.01053
$59$	4.30647	0.560655	0.280328	−	0.959904i	$-0.409557\pi$
$59$	4.30647	0.560655	0.280328	+	0.959904i	$0.409557\pi$
$60$	−5.51256	−0.711668
$61$	−9.01625	−1.15441	−0.577206	−	0.816599i	$-0.695857\pi$
$61$	−9.01625	−1.15441	−0.577206	+	0.816599i	$0.695857\pi$
$62$	2.22350	0.282385
$63$	0	0
$64$	21.6397	2.70497
$65$	−5.13967	−0.637497
$66$	0.487443	0.0600001
$67$	−15.7074	−1.91896	−0.959480	−	0.281775i	$-0.909077\pi$
$67$	−15.7074	−1.91896	−0.959480	+	0.281775i	$0.909077\pi$
$68$	−14.8482	−1.80061
$69$	1.00000	0.120386
$70$	0	0
$71$	−2.22350	−0.263881	−0.131940	−	0.991258i	$-0.542121\pi$
$71$	−2.22350	−0.263881	−0.131940	+	0.991258i	$0.542121\pi$
$72$	8.76763	1.03328
$73$	−13.0717	−1.52993	−0.764964	−	0.644073i	$-0.777243\pi$
$73$	−13.0717	−1.52993	−0.764964	+	0.644073i	$0.777243\pi$
$74$	17.4098	2.02384
$75$	−3.89961	−0.450288
$76$	0.951004	0.109088
$77$	0	0
$78$	13.1972	1.49429
$79$	−16.1948	−1.82206	−0.911029	−	0.412341i	$-0.864711\pi$
$79$	−16.1948	−1.82206	−0.911029	+	0.412341i	$0.864711\pi$
$80$	−13.7478	−1.53705
$81$	1.00000	0.111111
$82$	9.34660	1.03216
$83$	−10.8757	−1.19377	−0.596883	−	0.802328i	$-0.703594\pi$
$83$	−10.8757	−1.19377	−0.596883	+	0.802328i	$0.703594\pi$
$84$	0	0
$85$	2.96394	0.321484
$86$	0.338054	0.0364533
$87$	−5.68466	−0.609459
$88$	1.58667	0.169139
$89$	14.7466	1.56314	0.781568	−	0.623821i	$-0.214420\pi$
$89$	14.7466	1.56314	0.781568	+	0.623821i	$0.214420\pi$
$90$	−2.82550	−0.297834
$91$	0	0
$92$	5.25508	0.547880
$93$	0.825498	0.0856001
$94$	32.4074	3.34256
$95$	−0.189835	−0.0194767
$96$	17.7652	1.81316
$97$	−10.4636	−1.06241	−0.531207	−	0.847242i	$-0.678261\pi$
$97$	−10.4636	−1.06241	−0.531207	+	0.847242i	$0.678261\pi$
$98$	0	0
$99$	0.180969	0.0181880
$100$	−20.4927	−2.04927
$101$	−14.7316	−1.46585	−0.732923	−	0.680312i	$-0.761844\pi$
$101$	−14.7316	−1.46585	−0.732923	+	0.680312i	$0.761844\pi$
$102$	−7.61055	−0.753557
$103$	−5.96362	−0.587613	−0.293806	−	0.955865i	$-0.594922\pi$
$103$	−5.96362	−0.587613	−0.293806	+	0.955865i	$0.594922\pi$
$104$	42.9580	4.21238
$105$	0	0
$106$	23.0369	2.23754
$107$	−8.55060	−0.826618	−0.413309	−	0.910591i	$-0.635627\pi$
$107$	−8.55060	−0.826618	−0.413309	+	0.910591i	$0.635627\pi$
$108$	5.25508	0.505670
$109$	9.00123	0.862162	0.431081	−	0.902313i	$-0.358132\pi$
$109$	9.00123	0.862162	0.431081	+	0.902313i	$0.358132\pi$
$110$	−0.511326	−0.0487530
$111$	6.46356	0.613494
$112$	0	0
$113$	9.81016	0.922863	0.461431	−	0.887176i	$-0.347336\pi$
$113$	9.81016	0.922863	0.461431	+	0.887176i	$0.347336\pi$
$114$	0.487443	0.0456533
$115$	−1.04900	−0.0978194
$116$	−29.8733	−2.77367
$117$	4.89961	0.452969
$118$	11.5996	1.06783
$119$	0	0
$120$	−9.19722	−0.839587
$121$	−10.9673	−0.997023
$122$	−24.2855	−2.19870
$123$	3.47003	0.312882
$124$	4.33805	0.389569
$125$	9.33565	0.835006
$126$	0	0
$127$	13.6421	1.21054	0.605272	−	0.796019i	$-0.293065\pi$
$127$	13.6421	1.21054	0.605272	+	0.796019i	$0.293065\pi$
$128$	22.7567	2.01143
$129$	0.125506	0.0110502
$130$	−13.8438	−1.21418
$131$	9.72104	0.849331	0.424666	−	0.905350i	$-0.360392\pi$
$131$	9.72104	0.849331	0.424666	+	0.905350i	$0.360392\pi$
$132$	0.951004	0.0827743
$133$	0	0
$134$	−42.3082	−3.65487
$135$	−1.04900	−0.0902832
$136$	−24.7729	−2.12426
$137$	−5.96725	−0.509817	−0.254908	−	0.966965i	$-0.582045\pi$
$137$	−5.96725	−0.509817	−0.254908	+	0.966965i	$0.582045\pi$
$138$	2.69353	0.229288
$139$	−7.36317	−0.624536	−0.312268	−	0.949994i	$-0.601089\pi$
$139$	−7.36317	−0.624536	−0.312268	+	0.949994i	$0.601089\pi$
$140$	0	0
$141$	12.0316	1.01324
$142$	−5.98905	−0.502590
$143$	0.886675	0.0741475
$144$	13.1057	1.09214
$145$	5.96318	0.495216
$146$	−35.2090	−2.91392
$147$	0	0
$148$	33.9665	2.79203
$149$	21.9288	1.79648	0.898238	−	0.439509i	$-0.144848\pi$
$149$	21.9288	1.79648	0.898238	+	0.439509i	$0.144848\pi$
$150$	−10.5037	−0.857623
$151$	16.7927	1.36657	0.683287	−	0.730150i	$-0.260550\pi$
$151$	16.7927	1.36657	0.683287	+	0.730150i	$0.260550\pi$
$152$	1.58667	0.128696
$153$	−2.82550	−0.228428
$154$	0	0
$155$	−0.865944	−0.0695543
$156$	25.7478	2.06148
$157$	−16.7425	−1.33620	−0.668099	−	0.744072i	$-0.732892\pi$
$157$	−16.7425	−1.33620	−0.668099	+	0.744072i	$0.732892\pi$
$158$	−43.6211	−3.47031
$159$	8.55269	0.678272
$160$	−18.6357	−1.47328
$161$	0	0
$162$	2.69353	0.211623
$163$	25.1308	1.96840	0.984198	−	0.177070i	$-0.0566621\pi$
$163$	25.1308	1.96840	0.984198	+	0.177070i	$0.0566621\pi$
$164$	18.2353	1.42393
$165$	−0.189835	−0.0147787
$166$	−29.2940	−2.27366
$167$	−9.98018	−0.772290	−0.386145	−	0.922438i	$-0.626194\pi$
$167$	−9.98018	−0.772290	−0.386145	+	0.922438i	$0.626194\pi$
$168$	0	0
$169$	11.0061	0.846627
$170$	7.98344	0.612302
$171$	0.180969	0.0138390
$172$	0.659545	0.0502898
$173$	12.5065	0.950853	0.475427	−	0.879755i	$-0.342294\pi$
$173$	12.5065	0.950853	0.475427	+	0.879755i	$0.342294\pi$
$174$	−15.3118	−1.16078
$175$	0	0
$176$	2.37172	0.178775
$177$	4.30647	0.323694
$178$	39.7203	2.97716
$179$	−19.3081	−1.44316	−0.721579	−	0.692332i	$-0.756583\pi$
$179$	−19.3081	−1.44316	−0.721579	+	0.692332i	$0.756583\pi$
$180$	−5.51256	−0.410882
$181$	−17.7656	−1.32050	−0.660251	−	0.751045i	$-0.729550\pi$
$181$	−17.7656	−1.32050	−0.660251	+	0.751045i	$0.729550\pi$
$182$	0	0
$183$	−9.01625	−0.666500
$184$	8.76763	0.646359
$185$	−6.78025	−0.498494
$186$	2.22350	0.163035
$187$	−0.511326	−0.0373919
$188$	63.2269	4.61129
$189$	0	0
$190$	−0.511326	−0.0370955
$191$	−8.79275	−0.636221	−0.318110	−	0.948054i	$-0.603048\pi$
$191$	−8.79275	−0.636221	−0.318110	+	0.948054i	$0.603048\pi$
$192$	21.6397	1.56171
$193$	−6.79275	−0.488953	−0.244476	−	0.969655i	$-0.578616\pi$
$193$	−6.79275	−0.488953	−0.244476	+	0.969655i	$0.578616\pi$
$194$	−28.1839	−2.02348
$195$	−5.13967	−0.368059
$196$	0	0
$197$	14.6534	1.04401	0.522006	−	0.852942i	$-0.325184\pi$
$197$	14.6534	1.04401	0.522006	+	0.852942i	$0.325184\pi$
$198$	0.487443	0.0346411
$199$	4.45469	0.315785	0.157892	−	0.987456i	$-0.449530\pi$
$199$	4.45469	0.315785	0.157892	+	0.987456i	$0.449530\pi$
$200$	−34.1903	−2.41762
$201$	−15.7074	−1.10791
$202$	−39.6799	−2.79187
$203$	0	0
$204$	−14.8482	−1.03958
$205$	−3.64004	−0.254232
$206$	−16.0632	−1.11917
$207$	1.00000	0.0695048
$208$	64.2127	4.45235
$209$	0.0327496	0.00226534
$210$	0	0
$211$	−4.59793	−0.316535	−0.158267	−	0.987396i	$-0.550591\pi$
$211$	−4.59793	−0.316535	−0.158267	+	0.987396i	$0.550591\pi$
$212$	44.9450	3.08684
$213$	−2.22350	−0.152352
$214$	−23.0313	−1.57438
$215$	−0.131656	−0.00897884
$216$	8.76763	0.596562
$217$	0	0
$218$	24.2450	1.64208
$219$	−13.0717	−0.883304
$220$	−0.997599	−0.0672581
$221$	−13.8438	−0.931237
$222$	17.4098	1.16847
$223$	−13.0442	−0.873504	−0.436752	−	0.899582i	$-0.643871\pi$
$223$	−13.0442	−0.873504	−0.436752	+	0.899582i	$0.643871\pi$
$224$	0	0
$225$	−3.89961	−0.259974
$226$	26.4239	1.75769
$227$	0.320321	0.0212604	0.0106302	−	0.999943i	$-0.496616\pi$
$227$	0.320321	0.0212604	0.0106302	+	0.999943i	$0.496616\pi$
$228$	0.951004	0.0629818
$229$	−8.88459	−0.587110	−0.293555	−	0.955942i	$-0.594838\pi$
$229$	−8.88459	−0.587110	−0.293555	+	0.955942i	$0.594838\pi$
$230$	−2.82550	−0.186308
$231$	0	0
$232$	−49.8410	−3.27222
$233$	−0.418313	−0.0274046	−0.0137023	−	0.999906i	$-0.504362\pi$
$233$	−0.418313	−0.0274046	−0.0137023	+	0.999906i	$0.504362\pi$
$234$	13.1972	0.862729
$235$	−12.6211	−0.823309
$236$	22.6309	1.47314
$237$	−16.1948	−1.05197
$238$	0	0
$239$	−15.0571	−0.973965	−0.486982	−	0.873412i	$-0.661902\pi$
$239$	−15.0571	−0.973965	−0.486982	+	0.873412i	$0.661902\pi$
$240$	−13.7478	−0.887418
$241$	−5.31701	−0.342498	−0.171249	−	0.985228i	$-0.554780\pi$
$241$	−5.31701	−0.342498	−0.171249	+	0.985228i	$0.554780\pi$
$242$	−29.5406	−1.89894
$243$	1.00000	0.0641500
$244$	−47.3811	−3.03326
$245$	0	0
$246$	9.34660	0.595918
$247$	0.886675	0.0564178
$248$	7.23766	0.459592
$249$	−10.8757	−0.689221
$250$	25.1458	1.59036
$251$	7.19107	0.453896	0.226948	−	0.973907i	$-0.427125\pi$
$251$	7.19107	0.453896	0.226948	+	0.973907i	$0.427125\pi$
$252$	0	0
$253$	0.180969	0.0113774
$254$	36.7454	2.30561
$255$	2.96394	0.185609
$256$	18.0162	1.12602
$257$	8.77255	0.547217	0.273608	−	0.961841i	$-0.411783\pi$
$257$	8.77255	0.547217	0.273608	+	0.961841i	$0.411783\pi$
$258$	0.338054	0.0210463
$259$	0	0
$260$	−27.0094	−1.67505
$261$	−5.68466	−0.351872
$262$	26.1839	1.61764
$263$	16.0304	0.988477	0.494239	−	0.869326i	$-0.335447\pi$
$263$	16.0304	0.988477	0.494239	+	0.869326i	$0.335447\pi$
$264$	1.58667	0.0976525
$265$	−8.97173	−0.551129
$266$	0	0
$267$	14.7466	0.902476
$268$	−82.5435	−5.04214
$269$	−6.27373	−0.382516	−0.191258	−	0.981540i	$-0.561257\pi$
$269$	−6.27373	−0.382516	−0.191258	+	0.981540i	$0.561257\pi$
$270$	−2.82550	−0.171954
$271$	17.1397	1.04116	0.520580	−	0.853813i	$-0.325716\pi$
$271$	17.1397	1.04116	0.520580	+	0.853813i	$0.325716\pi$
$272$	−37.0301	−2.24528
$273$	0	0
$274$	−16.0729	−0.971002
$275$	−0.705706	−0.0425557
$276$	5.25508	0.316319
$277$	−23.9563	−1.43939	−0.719697	−	0.694288i	$-0.755719\pi$
$277$	−23.9563	−1.43939	−0.719697	+	0.694288i	$0.755719\pi$
$278$	−19.8329	−1.18950
$279$	0.825498	0.0494212
$280$	0	0
$281$	−7.27132	−0.433771	−0.216885	−	0.976197i	$-0.569590\pi$
$281$	−7.27132	−0.433771	−0.216885	+	0.976197i	$0.569590\pi$
$282$	32.4074	1.92983
$283$	−26.5365	−1.57743	−0.788716	−	0.614758i	$-0.789254\pi$
$283$	−26.5365	−1.57743	−0.788716	+	0.614758i	$0.789254\pi$
$284$	−11.6847	−0.693357
$285$	−0.189835	−0.0112449
$286$	2.38828	0.141222
$287$	0	0
$288$	17.7652	1.04683
$289$	−9.01656	−0.530386
$290$	16.0620	0.943192
$291$	−10.4636	−0.613385
$292$	−68.6928	−4.01994
$293$	32.7086	1.91086	0.955428	−	0.295223i	$-0.0953939\pi$
$293$	32.7086	1.91086	0.955428	+	0.295223i	$0.0953939\pi$
$294$	0	0
$295$	−4.51748	−0.263018
$296$	56.6701	3.29388
$297$	0.180969	0.0105009
$298$	59.0657	3.42159
$299$	4.89961	0.283352
$300$	−20.4927	−1.18315
$301$	0	0
$302$	45.2317	2.60279
$303$	−14.7316	−0.846307
$304$	2.37172	0.136027
$305$	9.45801	0.541564
$306$	−7.61055	−0.435066
$307$	20.4281	1.16589	0.582946	−	0.812511i	$-0.301900\pi$
$307$	20.4281	1.16589	0.582946	+	0.812511i	$0.301900\pi$
$308$	0	0
$309$	−5.96362	−0.339258
$310$	−2.33244	−0.132474
$311$	−15.9515	−0.904526	−0.452263	−	0.891884i	$-0.649383\pi$
$311$	−15.9515	−0.904526	−0.452263	+	0.891884i	$0.649383\pi$
$312$	42.9580	2.43202
$313$	2.91328	0.164668	0.0823340	−	0.996605i	$-0.473763\pi$
$313$	2.91328	0.164668	0.0823340	+	0.996605i	$0.473763\pi$
$314$	−45.0964	−2.54494
$315$	0	0
$316$	−85.1050	−4.78753
$317$	0.295090	0.0165739	0.00828695	−	0.999966i	$-0.497362\pi$
$317$	0.295090	0.0165739	0.00828695	+	0.999966i	$0.497362\pi$
$318$	23.0369	1.29184
$319$	−1.02874	−0.0575986
$320$	−22.7000	−1.26897
$321$	−8.55060	−0.477248
$322$	0	0
$323$	−0.511326	−0.0284510
$324$	5.25508	0.291949
$325$	−19.1065	−1.05984
$326$	67.6904	3.74903
$327$	9.00123	0.497769
$328$	30.4239	1.67988
$329$	0	0
$330$	−0.511326	−0.0281476
$331$	10.8907	0.598609	0.299305	−	0.954158i	$-0.403245\pi$
$331$	10.8907	0.598609	0.299305	+	0.954158i	$0.403245\pi$
$332$	−57.1528	−3.13667
$333$	6.46356	0.354201
$334$	−26.8819	−1.47091
$335$	16.4770	0.900233
$336$	0	0
$337$	1.29884	0.0707522	0.0353761	−	0.999374i	$-0.488737\pi$
$337$	1.29884	0.0707522	0.0353761	+	0.999374i	$0.488737\pi$
$338$	29.6453	1.61249
$339$	9.81016	0.532815
$340$	15.5757	0.844712
$341$	0.149389	0.00808987
$342$	0.487443	0.0263579
$343$	0	0
$344$	1.10039	0.0593292
$345$	−1.04900	−0.0564761
$346$	33.6866	1.81100
$347$	18.2928	0.982009	0.491005	−	0.871157i	$-0.336630\pi$
$347$	18.2928	0.982009	0.491005	+	0.871157i	$0.336630\pi$
$348$	−29.8733	−1.60138
$349$	22.9333	1.22759	0.613795	−	0.789466i	$-0.289642\pi$
$349$	22.9333	1.22759	0.613795	+	0.789466i	$0.289642\pi$
$350$	0	0
$351$	4.89961	0.261522
$352$	3.21495	0.171357
$353$	−15.5867	−0.829595	−0.414797	−	0.909914i	$-0.636147\pi$
$353$	−15.5867	−0.829595	−0.414797	+	0.909914i	$0.636147\pi$
$354$	11.5996	0.616512
$355$	2.33244	0.123793
$356$	77.4945	4.10720
$357$	0	0
$358$	−52.0070	−2.74865
$359$	−21.6094	−1.14050	−0.570250	−	0.821471i	$-0.693154\pi$
$359$	−21.6094	−1.14050	−0.570250	+	0.821471i	$0.693154\pi$
$360$	−9.19722	−0.484736
$361$	−18.9673	−0.998276
$362$	−47.8520	−2.51504
$363$	−10.9673	−0.575631
$364$	0	0
$365$	13.7122	0.717728
$366$	−24.2855	−1.26942
$367$	4.46399	0.233019	0.116509	−	0.993190i	$-0.462830\pi$
$367$	4.46399	0.233019	0.116509	+	0.993190i	$0.462830\pi$
$368$	13.1057	0.683181
$369$	3.47003	0.180642
$370$	−18.2628	−0.949436
$371$	0	0
$372$	4.33805	0.224918
$373$	−30.7527	−1.59232	−0.796158	−	0.605089i	$-0.793138\pi$
$373$	−30.7527	−1.59232	−0.796158	+	0.605089i	$0.793138\pi$
$374$	−1.37727	−0.0712169
$375$	9.33565	0.482091
$376$	105.488	5.44015
$377$	−27.8526	−1.43448
$378$	0	0
$379$	22.7013	1.16609	0.583045	−	0.812440i	$-0.301861\pi$
$379$	22.7013	1.16609	0.583045	+	0.812440i	$0.301861\pi$
$380$	−0.997599	−0.0511758
$381$	13.6421	0.698907
$382$	−23.6835	−1.21175
$383$	18.3478	0.937531	0.468765	−	0.883323i	$-0.344699\pi$
$383$	18.3478	0.937531	0.468765	+	0.883323i	$0.344699\pi$
$384$	22.7567	1.16130
$385$	0	0
$386$	−18.2964	−0.931264
$387$	0.125506	0.00637984
$388$	−54.9868	−2.79153
$389$	−22.0620	−1.11859	−0.559294	−	0.828970i	$-0.688928\pi$
$389$	−22.0620	−1.11859	−0.559294	+	0.828970i	$0.688928\pi$
$390$	−13.8438	−0.701009
$391$	−2.82550	−0.142892
$392$	0	0
$393$	9.72104	0.490362
$394$	39.4693	1.98843
$395$	16.9883	0.854774
$396$	0.951004	0.0477897
$397$	−23.3045	−1.16962	−0.584808	−	0.811171i	$-0.698830\pi$
$397$	−23.3045	−1.16962	−0.584808	+	0.811171i	$0.698830\pi$
$398$	11.9988	0.601447
$399$	0	0
$400$	−51.1070	−2.55535
$401$	14.2087	0.709547	0.354773	−	0.934952i	$-0.384558\pi$
$401$	14.2087	0.709547	0.354773	+	0.934952i	$0.384558\pi$
$402$	−42.3082	−2.11014
$403$	4.04461	0.201477
$404$	−77.4156	−3.85157
$405$	−1.04900	−0.0521250
$406$	0	0
$407$	1.16970	0.0579799
$408$	−24.7729	−1.22644
$409$	33.2758	1.64538	0.822692	−	0.568488i	$-0.192471\pi$
$409$	33.2758	1.64538	0.822692	+	0.568488i	$0.192471\pi$
$410$	−9.80455	−0.484212
$411$	−5.96725	−0.294343
$412$	−31.3393	−1.54398
$413$	0	0
$414$	2.69353	0.132380
$415$	11.4086	0.560026
$416$	87.0427	4.26762
$417$	−7.36317	−0.360576
$418$	0.0882119	0.00431459
$419$	−1.93819	−0.0946867	−0.0473434	−	0.998879i	$-0.515075\pi$
$419$	−1.93819	−0.0946867	−0.0473434	+	0.998879i	$0.515075\pi$
$420$	0	0
$421$	−3.10852	−0.151500	−0.0757501	−	0.997127i	$-0.524135\pi$
$421$	−3.10852	−0.151500	−0.0757501	+	0.997127i	$0.524135\pi$
$422$	−12.3846	−0.602875
$423$	12.0316	0.584995
$424$	74.9868	3.64168
$425$	11.0183	0.534468
$426$	−5.98905	−0.290170
$427$	0	0
$428$	−44.9341	−2.17197
$429$	0.886675	0.0428091
$430$	−0.354618	−0.0171012
$431$	−27.2204	−1.31116	−0.655579	−	0.755126i	$-0.727576\pi$
$431$	−27.2204	−1.31116	−0.655579	+	0.755126i	$0.727576\pi$
$432$	13.1057	0.630548
$433$	12.2146	0.586998	0.293499	−	0.955959i	$-0.405180\pi$
$433$	12.2146	0.586998	0.293499	+	0.955959i	$0.405180\pi$
$434$	0	0
$435$	5.96318	0.285913
$436$	47.3022	2.26536
$437$	0.180969	0.00865690
$438$	−35.2090	−1.68235
$439$	−28.7859	−1.37387	−0.686937	−	0.726717i	$-0.741045\pi$
$439$	−28.7859	−1.37387	−0.686937	+	0.726717i	$0.741045\pi$
$440$	−1.66441	−0.0793475
$441$	0	0
$442$	−37.2887	−1.77364
$443$	−32.1005	−1.52514	−0.762569	−	0.646907i	$-0.776062\pi$
$443$	−32.1005	−1.52514	−0.762569	+	0.646907i	$0.776062\pi$
$444$	33.9665	1.61198
$445$	−15.4691	−0.733306
$446$	−35.1349	−1.66368
$447$	21.9288	1.03720
$448$	0	0
$449$	−25.6596	−1.21095	−0.605476	−	0.795864i	$-0.707017\pi$
$449$	−25.6596	−1.21095	−0.605476	+	0.795864i	$0.707017\pi$
$450$	−10.5037	−0.495149
$451$	0.627966	0.0295697
$452$	51.5532	2.42486
$453$	16.7927	0.788992
$454$	0.862792	0.0404928
$455$	0	0
$456$	1.58667	0.0743024
$457$	16.8061	0.786157	0.393078	−	0.919505i	$-0.371410\pi$
$457$	16.8061	0.786157	0.393078	+	0.919505i	$0.371410\pi$
$458$	−23.9309	−1.11822
$459$	−2.82550	−0.131883
$460$	−5.51256	−0.257024
$461$	−8.73248	−0.406712	−0.203356	−	0.979105i	$-0.565185\pi$
$461$	−8.73248	−0.406712	−0.203356	+	0.979105i	$0.565185\pi$
$462$	0	0
$463$	18.2312	0.847275	0.423638	−	0.905832i	$-0.360753\pi$
$463$	18.2312	0.847275	0.423638	+	0.905832i	$0.360753\pi$
$464$	−74.5014	−3.45864
$465$	−0.865944	−0.0401572
$466$	−1.12674	−0.0521951
$467$	−13.8127	−0.639175	−0.319587	−	0.947557i	$-0.603544\pi$
$467$	−13.8127	−0.639175	−0.319587	+	0.947557i	$0.603544\pi$
$468$	25.7478	1.19019
$469$	0	0
$470$	−33.9952	−1.56808
$471$	−16.7425	−0.771455
$472$	37.7576	1.73793
$473$	0.0227127	0.00104433
$474$	−43.6211	−2.00359
$475$	−0.705706	−0.0323800
$476$	0	0
$477$	8.55269	0.391601
$478$	−40.5568	−1.85502
$479$	19.4814	0.890128	0.445064	−	0.895499i	$-0.353181\pi$
$479$	19.4814	0.890128	0.445064	+	0.895499i	$0.353181\pi$
$480$	−18.6357	−0.850598
$481$	31.6689	1.44398
$482$	−14.3215	−0.652326
$483$	0	0
$484$	−57.6338	−2.61972
$485$	10.9762	0.498405
$486$	2.69353	0.122181
$487$	27.5268	1.24736	0.623680	−	0.781680i	$-0.285637\pi$
$487$	27.5268	1.24736	0.623680	+	0.781680i	$0.285637\pi$
$488$	−79.0512	−3.57848
$489$	25.1308	1.13645
$490$	0	0
$491$	15.3547	0.692950	0.346475	−	0.938059i	$-0.387379\pi$
$491$	15.3547	0.692950	0.346475	+	0.938059i	$0.387379\pi$
$492$	18.2353	0.822109
$493$	16.0620	0.723396
$494$	2.38828	0.107454
$495$	−0.189835	−0.00853246
$496$	10.8187	0.485775
$497$	0	0
$498$	−29.2940	−1.31270
$499$	−8.11621	−0.363331	−0.181666	−	0.983360i	$-0.558149\pi$
$499$	−8.11621	−0.363331	−0.181666	+	0.983360i	$0.558149\pi$
$500$	49.0596	2.19401
$501$	−9.98018	−0.445882
$502$	19.3693	0.864495
$503$	19.1576	0.854194	0.427097	−	0.904206i	$-0.359536\pi$
$503$	19.1576	0.854194	0.427097	+	0.904206i	$0.359536\pi$
$504$	0	0
$505$	15.4534	0.687666
$506$	0.487443	0.0216695
$507$	11.0061	0.488800
$508$	71.6904	3.18075
$509$	3.87856	0.171914	0.0859571	−	0.996299i	$-0.472605\pi$
$509$	3.87856	0.171914	0.0859571	+	0.996299i	$0.472605\pi$
$510$	7.98344	0.353513
$511$	0	0
$512$	3.01385	0.133194
$513$	0.180969	0.00798996
$514$	23.6291	1.04223
$515$	6.25581	0.275664
$516$	0.659545	0.0290349
$517$	2.17734	0.0957592
$518$	0	0
$519$	12.5065	0.548976
$520$	−45.0627	−1.97613
$521$	−35.3522	−1.54881	−0.774404	−	0.632691i	$-0.781950\pi$
$521$	−35.3522	−1.54881	−0.774404	+	0.632691i	$0.781950\pi$
$522$	−15.3118	−0.670178
$523$	39.3231	1.71948	0.859740	−	0.510733i	$-0.170626\pi$
$523$	39.3231	1.71948	0.859740	+	0.510733i	$0.170626\pi$
$524$	51.0848	2.23165
$525$	0	0
$526$	43.1783	1.88266
$527$	−2.33244	−0.101603
$528$	2.37172	0.103216
$529$	1.00000	0.0434783
$530$	−24.1656	−1.04969
$531$	4.30647	0.186885
$532$	0	0
$533$	17.0018	0.736428
$534$	39.7203	1.71887
$535$	8.96955	0.387787
$536$	−137.716	−5.94845
$537$	−19.3081	−0.833208
$538$	−16.8984	−0.728543
$539$	0	0
$540$	−5.51256	−0.237223
$541$	−2.43081	−0.104509	−0.0522544	−	0.998634i	$-0.516641\pi$
$541$	−2.43081	−0.104509	−0.0522544	+	0.998634i	$0.516641\pi$
$542$	46.1661	1.98301
$543$	−17.7656	−0.762393
$544$	−50.1956	−2.15212
$545$	−9.44226	−0.404462
$546$	0	0
$547$	−20.0320	−0.856507	−0.428254	−	0.903659i	$-0.640871\pi$
$547$	−20.0320	−0.856507	−0.428254	+	0.903659i	$0.640871\pi$
$548$	−31.3584	−1.33956
$549$	−9.01625	−0.384804
$550$	−1.90084	−0.0810520
$551$	−1.02874	−0.0438260
$552$	8.76763	0.373175
$553$	0	0
$554$	−64.5269	−2.74149
$555$	−6.78025	−0.287806
$556$	−38.6940	−1.64099
$557$	34.5733	1.46492	0.732459	−	0.680811i	$-0.238372\pi$
$557$	34.5733	1.46492	0.732459	+	0.680811i	$0.238372\pi$
$558$	2.22350	0.0941282
$559$	0.614931	0.0260088
$560$	0	0
$561$	−0.511326	−0.0215882
$562$	−19.5855	−0.826164
$563$	−11.6307	−0.490177	−0.245089	−	0.969501i	$-0.578817\pi$
$563$	−11.6307	−0.490177	−0.245089	+	0.969501i	$0.578817\pi$
$564$	63.2269	2.66233
$565$	−10.2908	−0.432938
$566$	−71.4767	−3.00439
$567$	0	0
$568$	−19.4948	−0.817985
$569$	20.0340	0.839871	0.419935	−	0.907554i	$-0.362053\pi$
$569$	20.0340	0.839871	0.419935	+	0.907554i	$0.362053\pi$
$570$	−0.511326	−0.0214171
$571$	−30.6328	−1.28194	−0.640972	−	0.767564i	$-0.721469\pi$
$571$	−30.6328	−1.28194	−0.640972	+	0.767564i	$0.721469\pi$
$572$	4.65955	0.194825
$573$	−8.79275	−0.367322
$574$	0	0
$575$	−3.89961	−0.162625
$576$	21.6397	0.901655
$577$	−6.02586	−0.250860	−0.125430	−	0.992102i	$-0.540031\pi$
$577$	−6.02586	−0.250860	−0.125430	+	0.992102i	$0.540031\pi$
$578$	−24.2863	−1.01018
$579$	−6.79275	−0.282297
$580$	31.3370	1.30120
$581$	0	0
$582$	−28.1839	−1.16826
$583$	1.54777	0.0641020
$584$	−114.608	−4.74251
$585$	−5.13967	−0.212499
$586$	88.1014	3.63944
$587$	0.00886676	0.000365971 0	0.000182985	−	1.00000i	$-0.499942\pi$
$587$	0.00886676	0.000365971 0	0.000182985		1.00000i	$0.499942\pi$
$588$	0	0
$589$	0.149389	0.00615547
$590$	−12.1679	−0.500946
$591$	14.6534	0.602760
$592$	84.7094	3.48154
$593$	46.0454	1.89086	0.945429	−	0.325827i	$-0.105643\pi$
$593$	46.0454	1.89086	0.945429	+	0.325827i	$0.105643\pi$
$594$	0.487443	0.0200000
$595$	0	0
$596$	115.237	4.72031
$597$	4.45469	0.182318
$598$	13.1972	0.539674
$599$	−24.6357	−1.00659	−0.503293	−	0.864116i	$-0.667878\pi$
$599$	−24.6357	−1.00659	−0.503293	+	0.864116i	$0.667878\pi$
$600$	−34.1903	−1.39581
$601$	32.4037	1.32177	0.660887	−	0.750486i	$-0.270180\pi$
$601$	32.4037	1.32177	0.660887	+	0.750486i	$0.270180\pi$
$602$	0	0
$603$	−15.7074	−0.639654
$604$	88.2472	3.59073
$605$	11.5046	0.467729
$606$	−39.6799	−1.61188
$607$	−10.5554	−0.428431	−0.214215	−	0.976786i	$-0.568719\pi$
$607$	−10.5554	−0.428431	−0.214215	+	0.976786i	$0.568719\pi$
$608$	3.21495	0.130383
$609$	0	0
$610$	25.4754	1.03147
$611$	58.9500	2.38486
$612$	−14.8482	−0.600203
$613$	4.26511	0.172266	0.0861332	−	0.996284i	$-0.472549\pi$
$613$	4.26511	0.172266	0.0861332	+	0.996284i	$0.472549\pi$
$614$	55.0236	2.22057
$615$	−3.64004	−0.146781
$616$	0	0
$617$	−9.32470	−0.375398	−0.187699	−	0.982227i	$-0.560103\pi$
$617$	−9.32470	−0.375398	−0.187699	+	0.982227i	$0.560103\pi$
$618$	−16.0632	−0.646155
$619$	−3.64538	−0.146520	−0.0732601	−	0.997313i	$-0.523340\pi$
$619$	−3.64538	−0.146520	−0.0732601	+	0.997313i	$0.523340\pi$
$620$	−4.55060	−0.182757
$621$	1.00000	0.0401286
$622$	−42.9658	−1.72277
$623$	0	0
$624$	64.2127	2.57057
$625$	9.70497	0.388199
$626$	7.84698	0.313628
$627$	0.0327496	0.00130789
$628$	−87.9833	−3.51091
$629$	−18.2628	−0.728185
$630$	0	0
$631$	15.3155	0.609699	0.304849	−	0.952401i	$-0.401394\pi$
$631$	15.3155	0.609699	0.304849	+	0.952401i	$0.401394\pi$
$632$	−141.990	−5.64807
$633$	−4.59793	−0.182751
$634$	0.794832	0.0315668
$635$	−14.3105	−0.567896
$636$	44.9450	1.78219
$637$	0	0
$638$	−2.77095	−0.109703
$639$	−2.22350	−0.0879602
$640$	−23.8717	−0.943611
$641$	17.8252	0.704052	0.352026	−	0.935990i	$-0.385493\pi$
$641$	17.8252	0.704052	0.352026	+	0.935990i	$0.385493\pi$
$642$	−23.0313	−0.908971
$643$	10.2196	0.403022	0.201511	−	0.979486i	$-0.435415\pi$
$643$	10.2196	0.403022	0.201511	+	0.979486i	$0.435415\pi$
$644$	0	0
$645$	−0.131656	−0.00518393
$646$	−1.37727	−0.0541880
$647$	1.71217	0.0673124	0.0336562	−	0.999433i	$-0.489285\pi$
$647$	1.71217	0.0673124	0.0336562	+	0.999433i	$0.489285\pi$
$648$	8.76763	0.344425
$649$	0.779336	0.0305916
$650$	−51.4640	−2.01858
$651$	0	0
$652$	132.064	5.17204
$653$	−2.80044	−0.109590	−0.0547949	−	0.998498i	$-0.517451\pi$
$653$	−2.80044	−0.109590	−0.0547949	+	0.998498i	$0.517451\pi$
$654$	24.2450	0.948056
$655$	−10.1973	−0.398443
$656$	45.4771	1.77558
$657$	−13.0717	−0.509976
$658$	0	0
$659$	25.7153	1.00173	0.500863	−	0.865526i	$-0.333016\pi$
$659$	25.7153	1.00173	0.500863	+	0.865526i	$0.333016\pi$
$660$	−0.997599	−0.0388315
$661$	−10.5129	−0.408903	−0.204452	−	0.978877i	$-0.565541\pi$
$661$	−10.5129	−0.408903	−0.204452	+	0.978877i	$0.565541\pi$
$662$	29.3345	1.14012
$663$	−13.8438	−0.537650
$664$	−95.3544	−3.70047
$665$	0	0
$666$	17.4098	0.674615
$667$	−5.68466	−0.220111
$668$	−52.4466	−2.02922
$669$	−13.0442	−0.504318
$670$	44.3811	1.71459
$671$	−1.63166	−0.0629894
$672$	0	0
$673$	23.1235	0.891345	0.445672	−	0.895196i	$-0.352965\pi$
$673$	23.1235	0.891345	0.445672	+	0.895196i	$0.352965\pi$
$674$	3.49845	0.134755
$675$	−3.89961	−0.150096
$676$	57.8382	2.22455
$677$	44.2843	1.70198	0.850992	−	0.525178i	$-0.176001\pi$
$677$	44.2843	1.70198	0.850992	+	0.525178i	$0.176001\pi$
$678$	26.4239	1.01480
$679$	0	0
$680$	25.9867	0.996545
$681$	0.320321	0.0122747
$682$	0.402383	0.0154081
$683$	25.9663	0.993574	0.496787	−	0.867872i	$-0.334513\pi$
$683$	25.9663	0.993574	0.496787	+	0.867872i	$0.334513\pi$
$684$	0.951004	0.0363625
$685$	6.25962	0.239168
$686$	0	0
$687$	−8.88459	−0.338968
$688$	1.64485	0.0627092
$689$	41.9048	1.59645
$690$	−2.82550	−0.107565
$691$	11.2697	0.428719	0.214359	−	0.976755i	$-0.431234\pi$
$691$	11.2697	0.428719	0.214359	+	0.976755i	$0.431234\pi$
$692$	65.7228	2.49840
$693$	0	0
$694$	49.2721	1.87034
$695$	7.72393	0.292986
$696$	−49.8410	−1.88922
$697$	−9.80455	−0.371374
$698$	61.7713	2.33808
$699$	−0.418313	−0.0158221
$700$	0	0
$701$	41.4152	1.56423	0.782115	−	0.623134i	$-0.214141\pi$
$701$	41.4152	1.56423	0.782115	+	0.623134i	$0.214141\pi$
$702$	13.1972	0.498097
$703$	1.16970	0.0441161
$704$	3.91611	0.147594
$705$	−12.6211	−0.475337
$706$	−41.9831	−1.58005
$707$	0	0
$708$	22.6309	0.850520
$709$	27.9629	1.05017	0.525084	−	0.851050i	$-0.324034\pi$
$709$	27.9629	1.05017	0.525084	+	0.851050i	$0.324034\pi$
$710$	6.28249	0.235778
$711$	−16.1948	−0.607353
$712$	129.293	4.84545
$713$	0.825498	0.0309151
$714$	0	0
$715$	−0.930118	−0.0347845
$716$	−101.466	−3.79195
$717$	−15.0571	−0.562319
$718$	−58.2054	−2.17221
$719$	39.1607	1.46045	0.730224	−	0.683207i	$-0.239415\pi$
$719$	39.1607	1.46045	0.730224	+	0.683207i	$0.239415\pi$
$720$	−13.7478	−0.512351
$721$	0	0
$722$	−51.0888	−1.90133
$723$	−5.31701	−0.197742
$724$	−93.3594	−3.46967
$725$	22.1679	0.823296
$726$	−29.5406	−1.09635
$727$	39.7139	1.47291	0.736453	−	0.676488i	$-0.236499\pi$
$727$	39.7139	1.47291	0.736453	+	0.676488i	$0.236499\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	36.9341	1.36699
$731$	−0.354618	−0.0131160
$732$	−47.3811	−1.75126
$733$	19.6633	0.726280	0.363140	−	0.931735i	$-0.381705\pi$
$733$	19.6633	0.726280	0.363140	+	0.931735i	$0.381705\pi$
$734$	12.0239	0.443810
$735$	0	0
$736$	17.7652	0.654835
$737$	−2.84254	−0.104706
$738$	9.34660	0.344053
$739$	−7.05398	−0.259485	−0.129742	−	0.991548i	$-0.541415\pi$
$739$	−7.05398	−0.259485	−0.129742	+	0.991548i	$0.541415\pi$
$740$	−35.6307	−1.30981
$741$	0.886675	0.0325728
$742$	0	0
$743$	−33.3545	−1.22366	−0.611829	−	0.790990i	$-0.709566\pi$
$743$	−33.3545	−1.22366	−0.611829	+	0.790990i	$0.709566\pi$
$744$	7.23766	0.265346
$745$	−23.0032	−0.842772
$746$	−82.8333	−3.03274
$747$	−10.8757	−0.397922
$748$	−2.68706	−0.0982486
$749$	0	0
$750$	25.1458	0.918195
$751$	5.86039	0.213849	0.106924	−	0.994267i	$-0.465900\pi$
$751$	5.86039	0.213849	0.106924	+	0.994267i	$0.465900\pi$
$752$	157.682	5.75008
$753$	7.19107	0.262057
$754$	−75.0217	−2.73213
$755$	−17.6155	−0.641095
$756$	0	0
$757$	−4.25464	−0.154638	−0.0773188	−	0.997006i	$-0.524636\pi$
$757$	−4.25464	−0.154638	−0.0773188	+	0.997006i	$0.524636\pi$
$758$	61.1466	2.22095
$759$	0.180969	0.00656874
$760$	−1.66441	−0.0603744
$761$	−16.2300	−0.588338	−0.294169	−	0.955753i	$-0.595043\pi$
$761$	−16.2300	−0.588338	−0.294169	+	0.955753i	$0.595043\pi$
$762$	36.7454	1.33115
$763$	0	0
$764$	−46.2066	−1.67170
$765$	2.96394	0.107161
$766$	49.4204	1.78563
$767$	21.1000	0.761878
$768$	18.0162	0.650105
$769$	34.4633	1.24278	0.621388	−	0.783503i	$-0.286569\pi$
$769$	34.4633	1.24278	0.621388	+	0.783503i	$0.286569\pi$
$770$	0	0
$771$	8.77255	0.315936
$772$	−35.6964	−1.28474
$773$	−40.0968	−1.44218	−0.721091	−	0.692840i	$-0.756359\pi$
$773$	−40.0968	−1.44218	−0.721091	+	0.692840i	$0.756359\pi$
$774$	0.338054	0.0121511
$775$	−3.21912	−0.115634
$776$	−91.7407	−3.29330
$777$	0	0
$778$	−59.4245	−2.13047
$779$	0.627966	0.0224992
$780$	−27.0094	−0.967090
$781$	−0.402383	−0.0143984
$782$	−7.61055	−0.272153
$783$	−5.68466	−0.203153
$784$	0	0
$785$	17.5628	0.626845
$786$	26.1839	0.933947
$787$	10.7641	0.383697	0.191849	−	0.981425i	$-0.438552\pi$
$787$	10.7641	0.383697	0.191849	+	0.981425i	$0.438552\pi$
$788$	77.0047	2.74318
$789$	16.0304	0.570698
$790$	45.7584	1.62801
$791$	0	0
$792$	1.58667	0.0563797
$793$	−44.1761	−1.56874
$794$	−62.7711	−2.22766
$795$	−8.97173	−0.318195
$796$	23.4098	0.829737
$797$	−28.7263	−1.01754	−0.508769	−	0.860903i	$-0.669899\pi$
$797$	−28.7263	−1.01754	−0.508769	+	0.860903i	$0.669899\pi$
$798$	0	0
$799$	−33.9952	−1.20266
$800$	−69.2774	−2.44933
$801$	14.7466	0.521045
$802$	38.2714	1.35141
$803$	−2.36557	−0.0834791
$804$	−82.5435	−2.91108
$805$	0	0
$806$	10.8943	0.383734
$807$	−6.27373	−0.220846
$808$	−129.161	−4.54387
$809$	−7.02676	−0.247048	−0.123524	−	0.992342i	$-0.539420\pi$
$809$	−7.02676	−0.247048	−0.123524	+	0.992342i	$0.539420\pi$
$810$	−2.82550	−0.0992779
$811$	−29.3729	−1.03142	−0.515712	−	0.856762i	$-0.672472\pi$
$811$	−29.3729	−1.03142	−0.515712	+	0.856762i	$0.672472\pi$
$812$	0	0
$813$	17.1397	0.601114
$814$	3.15062	0.110429
$815$	−26.3621	−0.923425
$816$	−37.0301	−1.29631
$817$	0.0227127	0.000794616 0
$818$	89.6293	3.13381
$819$	0	0
$820$	−19.1287	−0.668004
$821$	−20.8592	−0.727990	−0.363995	−	0.931401i	$-0.618587\pi$
$821$	−20.8592	−0.727990	−0.363995	+	0.931401i	$0.618587\pi$
$822$	−16.0729	−0.560608
$823$	8.32421	0.290164	0.145082	−	0.989420i	$-0.453655\pi$
$823$	8.32421	0.290164	0.145082	+	0.989420i	$0.453655\pi$
$824$	−52.2868	−1.82150
$825$	−0.705706	−0.0245695
$826$	0	0
$827$	26.0102	0.904462	0.452231	−	0.891901i	$-0.350628\pi$
$827$	26.0102	0.904462	0.452231	+	0.891901i	$0.350628\pi$
$828$	5.25508	0.182627
$829$	−20.5616	−0.714132	−0.357066	−	0.934079i	$-0.616223\pi$
$829$	−20.5616	−0.714132	−0.357066	+	0.934079i	$0.616223\pi$
$830$	30.7293	1.06663
$831$	−23.9563	−0.831035
$832$	106.026	3.67580
$833$	0	0
$834$	−19.8329	−0.686756
$835$	10.4692	0.362301
$836$	0.172102	0.00595226
$837$	0.825498	0.0285334
$838$	−5.22056	−0.180341
$839$	−11.8568	−0.409341	−0.204670	−	0.978831i	$-0.565612\pi$
$839$	−11.8568	−0.409341	−0.204670	+	0.978831i	$0.565612\pi$
$840$	0	0
$841$	3.31534	0.114322
$842$	−8.37289	−0.288549
$843$	−7.27132	−0.250438
$844$	−24.1625	−0.831708
$845$	−11.5454	−0.397174
$846$	32.4074	1.11419
$847$	0	0
$848$	112.089	3.84915
$849$	−26.5365	−0.910730
$850$	29.6782	1.01795
$851$	6.46356	0.221568
$852$	−11.6847	−0.400310
$853$	−30.2041	−1.03417	−0.517085	−	0.855934i	$-0.672983\pi$
$853$	−30.2041	−1.03417	−0.517085	+	0.855934i	$0.672983\pi$
$854$	0	0
$855$	−0.189835	−0.00649223
$856$	−74.9686	−2.56237
$857$	50.5499	1.72675	0.863375	−	0.504562i	$-0.168346\pi$
$857$	50.5499	1.72675	0.863375	+	0.504562i	$0.168346\pi$
$858$	2.38828	0.0815346
$859$	−10.0834	−0.344040	−0.172020	−	0.985093i	$-0.555029\pi$
$859$	−10.0834	−0.344040	−0.172020	+	0.985093i	$0.555029\pi$
$860$	−0.691860	−0.0235922
$861$	0	0
$862$	−73.3187	−2.49725
$863$	39.8098	1.35514	0.677571	−	0.735458i	$-0.263033\pi$
$863$	39.8098	1.35514	0.677571	+	0.735458i	$0.263033\pi$
$864$	17.7652	0.604386
$865$	−13.1193	−0.446069
$866$	32.9004	1.11800
$867$	−9.01656	−0.306219
$868$	0	0
$869$	−2.93075	−0.0994190
$870$	16.0620	0.544552
$871$	−76.9599	−2.60769
$872$	78.9195	2.67255
$873$	−10.4636	−0.354138
$874$	0.487443	0.0164880
$875$	0	0
$876$	−68.6928	−2.32092
$877$	−30.8941	−1.04322	−0.521609	−	0.853184i	$-0.674668\pi$
$877$	−30.8941	−1.04322	−0.521609	+	0.853184i	$0.674668\pi$
$878$	−77.5354	−2.61669
$879$	32.7086	1.10323
$880$	−2.48792	−0.0838679
$881$	−15.2972	−0.515375	−0.257688	−	0.966228i	$-0.582961\pi$
$881$	−15.2972	−0.515375	−0.257688	+	0.966228i	$0.582961\pi$
$882$	0	0
$883$	3.35890	0.113036	0.0565180	−	0.998402i	$-0.482000\pi$
$883$	3.35890	0.113036	0.0565180	+	0.998402i	$0.482000\pi$
$884$	−72.7504	−2.44686
$885$	−4.51748	−0.151853
$886$	−86.4634	−2.90479
$887$	51.2123	1.71954	0.859770	−	0.510681i	$-0.170607\pi$
$887$	51.2123	1.71954	0.859770	+	0.510681i	$0.170607\pi$
$888$	56.6701	1.90173
$889$	0	0
$890$	−41.6664	−1.39666
$891$	0.180969	0.00606267
$892$	−68.5483	−2.29517
$893$	2.17734	0.0728618
$894$	59.0657	1.97545
$895$	20.2542	0.677022
$896$	0	0
$897$	4.89961	0.163593
$898$	−69.1148	−2.30639
$899$	−4.69267	−0.156509
$900$	−20.4927	−0.683091
$901$	−24.1656	−0.805073
$902$	1.69144	0.0563188
$903$	0	0
$904$	86.0119	2.86071
$905$	18.6360	0.619481
$906$	45.2317	1.50272
$907$	27.1380	0.901103	0.450552	−	0.892750i	$-0.351227\pi$
$907$	27.1380	0.901103	0.450552	+	0.892750i	$0.351227\pi$
$908$	1.68331	0.0558626
$909$	−14.7316	−0.488615
$910$	0	0
$911$	−0.642982	−0.0213029	−0.0106515	−	0.999943i	$-0.503391\pi$
$911$	−0.642982	−0.0213029	−0.0106515	+	0.999943i	$0.503391\pi$
$912$	2.37172	0.0785354
$913$	−1.96816	−0.0651367
$914$	45.2677	1.49732
$915$	9.45801	0.312672
$916$	−46.6892	−1.54266
$917$	0	0
$918$	−7.61055	−0.251186
$919$	51.8741	1.71117	0.855585	−	0.517662i	$-0.173198\pi$
$919$	51.8741	1.71117	0.855585	+	0.517662i	$0.173198\pi$
$920$	−9.19722	−0.303223
$921$	20.4281	0.673129
$922$	−23.5212	−0.774628
$923$	−10.8943	−0.358589
$924$	0	0
$925$	−25.2053	−0.828747
$926$	49.1062	1.61373
$927$	−5.96362	−0.195871
$928$	−100.989	−3.31514
$929$	2.08704	0.0684736	0.0342368	−	0.999414i	$-0.489100\pi$
$929$	2.08704	0.0684736	0.0342368	+	0.999414i	$0.489100\pi$
$930$	−2.33244	−0.0764838
$931$	0	0
$932$	−2.19827	−0.0720067
$933$	−15.9515	−0.522229
$934$	−37.2048	−1.21738
$935$	0.536379	0.0175415
$936$	42.9580	1.40413
$937$	35.6141	1.16346	0.581731	−	0.813382i	$-0.302376\pi$
$937$	35.6141	1.16346	0.581731	+	0.813382i	$0.302376\pi$
$938$	0	0
$939$	2.91328	0.0950711
$940$	−66.3248	−2.16328
$941$	19.5524	0.637389	0.318695	−	0.947857i	$-0.396756\pi$
$941$	19.5524	0.637389	0.318695	+	0.947857i	$0.396756\pi$
$942$	−45.0964	−1.46932
$943$	3.47003	0.113000
$944$	56.4393	1.83694
$945$	0	0
$946$	0.0611772	0.00198904
$947$	−14.2793	−0.464016	−0.232008	−	0.972714i	$-0.574530\pi$
$947$	−14.2793	−0.464016	−0.232008	+	0.972714i	$0.574530\pi$
$948$	−85.1050	−2.76408
$949$	−64.0462	−2.07903
$950$	−1.90084	−0.0616713
$951$	0.295090	0.00956894
$952$	0	0
$953$	36.6697	1.18785	0.593924	−	0.804521i	$-0.297578\pi$
$953$	36.6697	1.18785	0.593924	+	0.804521i	$0.297578\pi$
$954$	23.0369	0.745846
$955$	9.22356	0.298467
$956$	−79.1264	−2.55913
$957$	−1.02874	−0.0332546
$958$	52.4737	1.69535
$959$	0	0
$960$	−22.7000	−0.732639
$961$	−30.3186	−0.978018
$962$	85.3010	2.75021
$963$	−8.55060	−0.275539
$964$	−27.9413	−0.899928
$965$	7.12557	0.229380
$966$	0	0
$967$	3.23340	0.103979	0.0519895	−	0.998648i	$-0.483444\pi$
$967$	3.23340	0.103979	0.0519895	+	0.998648i	$0.483444\pi$
$968$	−96.1568	−3.09060
$969$	−0.511326	−0.0164262
$970$	29.5648	0.949267
$971$	−35.0009	−1.12323	−0.561617	−	0.827398i	$-0.689820\pi$
$971$	−35.0009	−1.12323	−0.561617	+	0.827398i	$0.689820\pi$
$972$	5.25508	0.168557
$973$	0	0
$974$	74.1442	2.37573
$975$	−19.1065	−0.611899
$976$	−118.164	−3.78234
$977$	11.1142	0.355576	0.177788	−	0.984069i	$-0.443106\pi$
$977$	11.1142	0.355576	0.177788	+	0.984069i	$0.443106\pi$
$978$	67.6904	2.16450
$979$	2.66867	0.0852910
$980$	0	0
$981$	9.00123	0.287387
$982$	41.3584	1.31980
$983$	−12.0343	−0.383834	−0.191917	−	0.981411i	$-0.561471\pi$
$983$	−12.0343	−0.383834	−0.191917	+	0.981411i	$0.561471\pi$
$984$	30.4239	0.969879
$985$	−15.3714	−0.489772
$986$	43.2634	1.37779
$987$	0	0
$988$	4.65955	0.148240
$989$	0.125506	0.00399087
$990$	−0.511326	−0.0162510
$991$	59.7732	1.89876	0.949380	−	0.314130i	$-0.101713\pi$
$991$	59.7732	1.89876	0.949380	+	0.314130i	$0.101713\pi$
$992$	14.6652	0.465619
$993$	10.8907	0.345607
$994$	0	0
$995$	−4.67296	−0.148143
$996$	−57.1528	−1.81096
$997$	−24.4287	−0.773666	−0.386833	−	0.922150i	$-0.626431\pi$
$997$	−24.4287	−0.773666	−0.386833	+	0.922150i	$0.626431\pi$
$998$	−21.8612	−0.692004
$999$	6.46356	0.204498

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.x.1.4		4
7.6	odd	2		483.2.a.j.1.4	✓	4
21.20	even	2		1449.2.a.o.1.1		4
28.27	even	2		7728.2.a.ce.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.a.j.1.4	✓	4	7.6	odd	2
1449.2.a.o.1.1		4	21.20	even	2
3381.2.a.x.1.4		4	1.1	even	1	trivial
7728.2.a.ce.1.2		4	28.27	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:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3381.a (trivial)

\(f(q)\)	\(=\)	\(q+2.69353 q^{2} +1.00000 q^{3} +5.25508 q^{4} -1.04900 q^{5} +2.69353 q^{6} +8.76763 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.69353 q^{2} +1.00000 q^{3} +5.25508 q^{4} -1.04900 q^{5} +2.69353 q^{6} +8.76763 q^{8} +1.00000 q^{9} -2.82550 q^{10} +0.180969 q^{11} +5.25508 q^{12} +4.89961 q^{13} -1.04900 q^{15} +13.1057 q^{16} -2.82550 q^{17} +2.69353 q^{18} +0.180969 q^{19} -5.51256 q^{20} +0.487443 q^{22} +1.00000 q^{23} +8.76763 q^{24} -3.89961 q^{25} +13.1972 q^{26} +1.00000 q^{27} -5.68466 q^{29} -2.82550 q^{30} +0.825498 q^{31} +17.7652 q^{32} +0.180969 q^{33} -7.61055 q^{34} +5.25508 q^{36} +6.46356 q^{37} +0.487443 q^{38} +4.89961 q^{39} -9.19722 q^{40} +3.47003 q^{41} +0.125506 q^{43} +0.951004 q^{44} -1.04900 q^{45} +2.69353 q^{46} +12.0316 q^{47} +13.1057 q^{48} -10.5037 q^{50} -2.82550 q^{51} +25.7478 q^{52} +8.55269 q^{53} +2.69353 q^{54} -0.189835 q^{55} +0.180969 q^{57} -15.3118 q^{58} +4.30647 q^{59} -5.51256 q^{60} -9.01625 q^{61} +2.22350 q^{62} +21.6397 q^{64} -5.13967 q^{65} +0.487443 q^{66} -15.7074 q^{67} -14.8482 q^{68} +1.00000 q^{69} -2.22350 q^{71} +8.76763 q^{72} -13.0717 q^{73} +17.4098 q^{74} -3.89961 q^{75} +0.951004 q^{76} +13.1972 q^{78} -16.1948 q^{79} -13.7478 q^{80} +1.00000 q^{81} +9.34660 q^{82} -10.8757 q^{83} +2.96394 q^{85} +0.338054 q^{86} -5.68466 q^{87} +1.58667 q^{88} +14.7466 q^{89} -2.82550 q^{90} +5.25508 q^{92} +0.825498 q^{93} +32.4074 q^{94} -0.189835 q^{95} +17.7652 q^{96} -10.4636 q^{97} +0.180969 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 4 q^{3} + 4 q^{4} - 5 q^{5} + 2 q^{6} + 9 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 4 * q^3 + 4 * q^4 - 5 * q^5 + 2 * q^6 + 9 * q^8 + 4 * q^9	\( 4 q + 2 q^{2} + 4 q^{3} + 4 q^{4} - 5 q^{5} + 2 q^{6} + 9 q^{8} + 4 q^{9} - 2 q^{10} + q^{11} + 4 q^{12} - 7 q^{13} - 5 q^{15} + 8 q^{16} - 2 q^{17} + 2 q^{18} + q^{19} - 13 q^{20} + 11 q^{22} + 4 q^{23} + 9 q^{24} + 11 q^{25} + 19 q^{26} + 4 q^{27} + 2 q^{29} - 2 q^{30} - 6 q^{31} + 20 q^{32} + q^{33} - 23 q^{34} + 4 q^{36} + 16 q^{37} + 11 q^{38} - 7 q^{39} - 3 q^{40} - 5 q^{41} + 9 q^{43} + 3 q^{44} - 5 q^{45} + 2 q^{46} + 21 q^{47} + 8 q^{48} - 17 q^{50} - 2 q^{51} + 24 q^{52} + 10 q^{53} + 2 q^{54} - 17 q^{55} + q^{57} + q^{58} + 26 q^{59} - 13 q^{60} - 2 q^{61} + 19 q^{62} + 27 q^{64} + 26 q^{65} + 11 q^{66} + 5 q^{67} - 7 q^{68} + 4 q^{69} - 19 q^{71} + 9 q^{72} - 10 q^{73} + 9 q^{74} + 11 q^{75} + 3 q^{76} + 19 q^{78} - 6 q^{79} + 24 q^{80} + 4 q^{81} + 31 q^{82} + 2 q^{83} - 7 q^{85} - 17 q^{86} + 2 q^{87} - 20 q^{88} + 17 q^{89} - 2 q^{90} + 4 q^{92} - 6 q^{93} + 44 q^{94} - 17 q^{95} + 20 q^{96} - 32 q^{97} + q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 4 * q^3 + 4 * q^4 - 5 * q^5 + 2 * q^6 + 9 * q^8 + 4 * q^9 - 2 * q^10 + q^11 + 4 * q^12 - 7 * q^13 - 5 * q^15 + 8 * q^16 - 2 * q^17 + 2 * q^18 + q^19 - 13 * q^20 + 11 * q^22 + 4 * q^23 + 9 * q^24 + 11 * q^25 + 19 * q^26 + 4 * q^27 + 2 * q^29 - 2 * q^30 - 6 * q^31 + 20 * q^32 + q^33 - 23 * q^34 + 4 * q^36 + 16 * q^37 + 11 * q^38 - 7 * q^39 - 3 * q^40 - 5 * q^41 + 9 * q^43 + 3 * q^44 - 5 * q^45 + 2 * q^46 + 21 * q^47 + 8 * q^48 - 17 * q^50 - 2 * q^51 + 24 * q^52 + 10 * q^53 + 2 * q^54 - 17 * q^55 + q^57 + q^58 + 26 * q^59 - 13 * q^60 - 2 * q^61 + 19 * q^62 + 27 * q^64 + 26 * q^65 + 11 * q^66 + 5 * q^67 - 7 * q^68 + 4 * q^69 - 19 * q^71 + 9 * q^72 - 10 * q^73 + 9 * q^74 + 11 * q^75 + 3 * q^76 + 19 * q^78 - 6 * q^79 + 24 * q^80 + 4 * q^81 + 31 * q^82 + 2 * q^83 - 7 * q^85 - 17 * q^86 + 2 * q^87 - 20 * q^88 + 17 * q^89 - 2 * q^90 + 4 * q^92 - 6 * q^93 + 44 * q^94 - 17 * q^95 + 20 * q^96 - 32 * q^97 + q^99

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