LMFDB - Embedded newform 6027.2.a.be.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6027,2,Mod(1,6027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, 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("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6027 = 3 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6027.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:	$48.1258372982$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} - 11x^{8} + 56x^{7} + 26x^{6} - 266x^{5} + 52x^{4} + 526x^{3} - 255x^{2} - 372x + 239 $ x^10 - 4x^9 - 11x^8 + 56x^7 + 26x^6 - 266x^5 + 52x^4 + 526x^3 - 255x^2 - 372*x + 239
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.69562$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.69562 q^{2} +1.00000 q^{3} +0.875138 q^{4} -0.871357 q^{5} -1.69562 q^{6} +1.90734 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.69562 q^{2} +1.00000 q^{3} +0.875138 q^{4} -0.871357 q^{5} -1.69562 q^{6} +1.90734 q^{8} +1.00000 q^{9} +1.47749 q^{10} -0.879188 q^{11} +0.875138 q^{12} -6.61203 q^{13} -0.871357 q^{15} -4.98441 q^{16} -5.48590 q^{17} -1.69562 q^{18} +3.14642 q^{19} -0.762557 q^{20} +1.49077 q^{22} -8.57933 q^{23} +1.90734 q^{24} -4.24074 q^{25} +11.2115 q^{26} +1.00000 q^{27} +0.898544 q^{29} +1.47749 q^{30} -9.92346 q^{31} +4.63700 q^{32} -0.879188 q^{33} +9.30202 q^{34} +0.875138 q^{36} +5.47498 q^{37} -5.33515 q^{38} -6.61203 q^{39} -1.66198 q^{40} +1.00000 q^{41} +1.22541 q^{43} -0.769411 q^{44} -0.871357 q^{45} +14.5473 q^{46} -4.45708 q^{47} -4.98441 q^{48} +7.19069 q^{50} -5.48590 q^{51} -5.78644 q^{52} +9.34659 q^{53} -1.69562 q^{54} +0.766086 q^{55} +3.14642 q^{57} -1.52359 q^{58} -6.59869 q^{59} -0.762557 q^{60} -4.63726 q^{61} +16.8264 q^{62} +2.10622 q^{64} +5.76143 q^{65} +1.49077 q^{66} -8.87174 q^{67} -4.80092 q^{68} -8.57933 q^{69} +11.3486 q^{71} +1.90734 q^{72} +0.181676 q^{73} -9.28350 q^{74} -4.24074 q^{75} +2.75356 q^{76} +11.2115 q^{78} +10.9094 q^{79} +4.34320 q^{80} +1.00000 q^{81} -1.69562 q^{82} +11.9985 q^{83} +4.78018 q^{85} -2.07784 q^{86} +0.898544 q^{87} -1.67691 q^{88} +6.65352 q^{89} +1.47749 q^{90} -7.50810 q^{92} -9.92346 q^{93} +7.55754 q^{94} -2.74166 q^{95} +4.63700 q^{96} +2.66425 q^{97} -0.879188 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} + 10 q^{3} + 18 q^{4} + 6 q^{5} + 4 q^{6} + 12 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 4 * q^2 + 10 * q^3 + 18 * q^4 + 6 * q^5 + 4 * q^6 + 12 * q^8 + 10 * q^9	$ 10 q + 4 q^{2} + 10 q^{3} + 18 q^{4} + 6 q^{5} + 4 q^{6} + 12 q^{8} + 10 q^{9} + 2 q^{10} - 2 q^{11} + 18 q^{12} + 6 q^{15} + 14 q^{16} + 8 q^{17} + 4 q^{18} + 6 q^{19} + 20 q^{20} + 2 q^{22} + 12 q^{24} + 10 q^{25} + 16 q^{26} + 10 q^{27} + 16 q^{29} + 2 q^{30} + 2 q^{31} + 38 q^{32} - 2 q^{33} - 4 q^{34} + 18 q^{36} + 24 q^{37} - 26 q^{38} + 40 q^{40} + 10 q^{41} + 8 q^{43} - 8 q^{44} + 6 q^{45} + 4 q^{46} - 8 q^{47} + 14 q^{48} + 44 q^{50} + 8 q^{51} - 30 q^{52} + 24 q^{53} + 4 q^{54} + 6 q^{57} - 14 q^{58} + 6 q^{59} + 20 q^{60} - 14 q^{61} - 2 q^{62} + 86 q^{64} + 28 q^{65} + 2 q^{66} + 26 q^{67} - 6 q^{68} + 14 q^{71} + 12 q^{72} - 36 q^{73} + 18 q^{74} + 10 q^{75} - 32 q^{76} + 16 q^{78} + 20 q^{79} + 70 q^{80} + 10 q^{81} + 4 q^{82} + 40 q^{83} + 24 q^{85} - 36 q^{86} + 16 q^{87} + 14 q^{88} + 2 q^{89} + 2 q^{90} + 8 q^{92} + 2 q^{93} - 54 q^{94} - 24 q^{95} + 38 q^{96} + 16 q^{97} - 2 q^{99}+O(q^{100}) $ 10 * q + 4 * q^2 + 10 * q^3 + 18 * q^4 + 6 * q^5 + 4 * q^6 + 12 * q^8 + 10 * q^9 + 2 * q^10 - 2 * q^11 + 18 * q^12 + 6 * q^15 + 14 * q^16 + 8 * q^17 + 4 * q^18 + 6 * q^19 + 20 * q^20 + 2 * q^22 + 12 * q^24 + 10 * q^25 + 16 * q^26 + 10 * q^27 + 16 * q^29 + 2 * q^30 + 2 * q^31 + 38 * q^32 - 2 * q^33 - 4 * q^34 + 18 * q^36 + 24 * q^37 - 26 * q^38 + 40 * q^40 + 10 * q^41 + 8 * q^43 - 8 * q^44 + 6 * q^45 + 4 * q^46 - 8 * q^47 + 14 * q^48 + 44 * q^50 + 8 * q^51 - 30 * q^52 + 24 * q^53 + 4 * q^54 + 6 * q^57 - 14 * q^58 + 6 * q^59 + 20 * q^60 - 14 * q^61 - 2 * q^62 + 86 * q^64 + 28 * q^65 + 2 * q^66 + 26 * q^67 - 6 * q^68 + 14 * q^71 + 12 * q^72 - 36 * q^73 + 18 * q^74 + 10 * q^75 - 32 * q^76 + 16 * q^78 + 20 * q^79 + 70 * q^80 + 10 * q^81 + 4 * q^82 + 40 * q^83 + 24 * q^85 - 36 * q^86 + 16 * q^87 + 14 * q^88 + 2 * q^89 + 2 * q^90 + 8 * q^92 + 2 * q^93 - 54 * q^94 - 24 * q^95 + 38 * q^96 + 16 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.69562	−1.19899	−0.599493	−	0.800380i	$-0.704631\pi$
$2$	−1.69562	−1.19899	−0.599493	+	0.800380i	$0.704631\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.875138	0.437569
$5$	−0.871357	−0.389682	−0.194841	−	0.980835i	$-0.562419\pi$
$5$	−0.871357	−0.389682	−0.194841	+	0.980835i	$0.562419\pi$
$6$	−1.69562	−0.692235
$7$	0	0
$7$	0	0
$8$	1.90734	0.674347
$9$	1.00000	0.333333
$10$	1.47749	0.467224
$11$	−0.879188	−0.265085	−0.132543	−	0.991177i	$-0.542314\pi$
$11$	−0.879188	−0.265085	−0.132543	+	0.991177i	$0.542314\pi$
$12$	0.875138	0.252631
$13$	−6.61203	−1.83385	−0.916924	−	0.399063i	$-0.869335\pi$
$13$	−6.61203	−1.83385	−0.916924	+	0.399063i	$0.869335\pi$
$14$	0	0
$15$	−0.871357	−0.224983
$16$	−4.98441	−1.24610
$17$	−5.48590	−1.33053	−0.665263	−	0.746609i	$-0.731681\pi$
$17$	−5.48590	−1.33053	−0.665263	+	0.746609i	$0.731681\pi$
$18$	−1.69562	−0.399662
$19$	3.14642	0.721839	0.360920	−	0.932597i	$-0.382463\pi$
$19$	3.14642	0.721839	0.360920	+	0.932597i	$0.382463\pi$
$20$	−0.762557	−0.170513
$21$	0	0
$22$	1.49077	0.317834
$23$	−8.57933	−1.78891	−0.894457	−	0.447154i	$-0.852438\pi$
$23$	−8.57933	−1.78891	−0.894457	+	0.447154i	$0.852438\pi$
$24$	1.90734	0.389335
$25$	−4.24074	−0.848148
$26$	11.2115	2.19876
$27$	1.00000	0.192450
$28$	0	0
$29$	0.898544	0.166855	0.0834277	−	0.996514i	$-0.473413\pi$
$29$	0.898544	0.166855	0.0834277	+	0.996514i	$0.473413\pi$
$30$	1.47749	0.269752
$31$	−9.92346	−1.78231	−0.891153	−	0.453704i	$-0.850103\pi$
$31$	−9.92346	−1.78231	−0.891153	+	0.453704i	$0.850103\pi$
$32$	4.63700	0.819713
$33$	−0.879188	−0.153047
$34$	9.30202	1.59528
$35$	0	0
$36$	0.875138	0.145856
$37$	5.47498	0.900081	0.450040	−	0.893008i	$-0.351410\pi$
$37$	5.47498	0.900081	0.450040	+	0.893008i	$0.351410\pi$
$38$	−5.33515	−0.865476
$39$	−6.61203	−1.05877
$40$	−1.66198	−0.262781
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	1.22541	0.186873	0.0934367	−	0.995625i	$-0.470215\pi$
$43$	1.22541	0.186873	0.0934367	+	0.995625i	$0.470215\pi$
$44$	−0.769411	−0.115993
$45$	−0.871357	−0.129894
$46$	14.5473	2.14488
$47$	−4.45708	−0.650133	−0.325066	−	0.945691i	$-0.605387\pi$
$47$	−4.45708	−0.650133	−0.325066	+	0.945691i	$0.605387\pi$
$48$	−4.98441	−0.719438
$49$	0	0
$50$	7.19069	1.01692
$51$	−5.48590	−0.768180
$52$	−5.78644	−0.802434
$53$	9.34659	1.28385	0.641926	−	0.766766i	$-0.278136\pi$
$53$	9.34659	1.28385	0.641926	+	0.766766i	$0.278136\pi$
$54$	−1.69562	−0.230745
$55$	0.766086	0.103299
$56$	0	0
$57$	3.14642	0.416754
$58$	−1.52359	−0.200057
$59$	−6.59869	−0.859076	−0.429538	−	0.903049i	$-0.641324\pi$
$59$	−6.59869	−0.859076	−0.429538	+	0.903049i	$0.641324\pi$
$60$	−0.762557	−0.0984457
$61$	−4.63726	−0.593740	−0.296870	−	0.954918i	$-0.595943\pi$
$61$	−4.63726	−0.593740	−0.296870	+	0.954918i	$0.595943\pi$
$62$	16.8264	2.13696
$63$	0	0
$64$	2.10622	0.263278
$65$	5.76143	0.714618
$66$	1.49077	0.183501
$67$	−8.87174	−1.08386	−0.541928	−	0.840425i	$-0.682305\pi$
$67$	−8.87174	−1.08386	−0.541928	+	0.840425i	$0.682305\pi$
$68$	−4.80092	−0.582197
$69$	−8.57933	−1.03283
$70$	0	0
$71$	11.3486	1.34683	0.673414	−	0.739266i	$-0.264827\pi$
$71$	11.3486	1.34683	0.673414	+	0.739266i	$0.264827\pi$
$72$	1.90734	0.224782
$73$	0.181676	0.0212636	0.0106318	−	0.999943i	$-0.496616\pi$
$73$	0.181676	0.0212636	0.0106318	+	0.999943i	$0.496616\pi$
$74$	−9.28350	−1.07918
$75$	−4.24074	−0.489678
$76$	2.75356	0.315854
$77$	0	0
$78$	11.2115	1.26945
$79$	10.9094	1.22741	0.613703	−	0.789537i	$-0.289679\pi$
$79$	10.9094	1.22741	0.613703	+	0.789537i	$0.289679\pi$
$80$	4.34320	0.485584
$81$	1.00000	0.111111
$82$	−1.69562	−0.187250
$83$	11.9985	1.31701	0.658505	−	0.752576i	$-0.271189\pi$
$83$	11.9985	1.31701	0.658505	+	0.752576i	$0.271189\pi$
$84$	0	0
$85$	4.78018	0.518483
$86$	−2.07784	−0.224059
$87$	0.898544	0.0963340
$88$	−1.67691	−0.178759
$89$	6.65352	0.705272	0.352636	−	0.935761i	$-0.385285\pi$
$89$	6.65352	0.705272	0.352636	+	0.935761i	$0.385285\pi$
$90$	1.47749	0.155741
$91$	0	0
$92$	−7.50810	−0.782773
$93$	−9.92346	−1.02901
$94$	7.55754	0.779500
$95$	−2.74166	−0.281288
$96$	4.63700	0.473261
$97$	2.66425	0.270513	0.135257	−	0.990811i	$-0.456814\pi$
$97$	2.66425	0.270513	0.135257	+	0.990811i	$0.456814\pi$
$98$	0	0
$99$	−0.879188	−0.0883617
$100$	−3.71123	−0.371123
$101$	12.0803	1.20204	0.601018	−	0.799235i	$-0.294762\pi$
$101$	12.0803	1.20204	0.601018	+	0.799235i	$0.294762\pi$
$102$	9.30202	0.921037
$103$	14.5425	1.43291	0.716456	−	0.697632i	$-0.245763\pi$
$103$	14.5425	1.43291	0.716456	+	0.697632i	$0.245763\pi$
$104$	−12.6114	−1.23665
$105$	0	0
$106$	−15.8483	−1.53932
$107$	−5.63970	−0.545211	−0.272605	−	0.962126i	$-0.587885\pi$
$107$	−5.63970	−0.545211	−0.272605	+	0.962126i	$0.587885\pi$
$108$	0.875138	0.0842102
$109$	11.6710	1.11788	0.558939	−	0.829208i	$-0.311208\pi$
$109$	11.6710	1.11788	0.558939	+	0.829208i	$0.311208\pi$
$110$	−1.29899	−0.123854
$111$	5.47498	0.519662
$112$	0	0
$113$	20.6662	1.94411	0.972056	−	0.234750i	$-0.0754270\pi$
$113$	20.6662	1.94411	0.972056	+	0.234750i	$0.0754270\pi$
$114$	−5.33515	−0.499683
$115$	7.47565	0.697108
$116$	0.786350	0.0730108
$117$	−6.61203	−0.611282
$118$	11.1889	1.03002
$119$	0	0
$120$	−1.66198	−0.151717
$121$	−10.2270	−0.929730
$122$	7.86305	0.711887
$123$	1.00000	0.0901670
$124$	−8.68439	−0.779881
$125$	8.05198	0.720191
$126$	0	0
$127$	−6.90276	−0.612521	−0.306261	−	0.951948i	$-0.599078\pi$
$127$	−6.90276	−0.612521	−0.306261	+	0.951948i	$0.599078\pi$
$128$	−12.8453	−1.13538
$129$	1.22541	0.107891
$130$	−9.76922	−0.856817
$131$	−9.02612	−0.788616	−0.394308	−	0.918978i	$-0.629016\pi$
$131$	−9.02612	−0.788616	−0.394308	+	0.918978i	$0.629016\pi$
$132$	−0.769411	−0.0669686
$133$	0	0
$134$	15.0431	1.29953
$135$	−0.871357	−0.0749944
$136$	−10.4635	−0.897237
$137$	1.87510	0.160201	0.0801005	−	0.996787i	$-0.474476\pi$
$137$	1.87510	0.160201	0.0801005	+	0.996787i	$0.474476\pi$
$138$	14.5473	1.23835
$139$	−12.7080	−1.07787	−0.538937	−	0.842346i	$-0.681174\pi$
$139$	−12.7080	−1.07787	−0.538937	+	0.842346i	$0.681174\pi$
$140$	0	0
$141$	−4.45708	−0.375354
$142$	−19.2429	−1.61483
$143$	5.81322	0.486126
$144$	−4.98441	−0.415367
$145$	−0.782952	−0.0650206
$146$	−0.308054	−0.0254947
$147$	0	0
$148$	4.79136	0.393847
$149$	−16.4295	−1.34595	−0.672977	−	0.739664i	$-0.734985\pi$
$149$	−16.4295	−1.34595	−0.672977	+	0.739664i	$0.734985\pi$
$150$	7.19069	0.587118
$151$	0.339462	0.0276250	0.0138125	−	0.999905i	$-0.495603\pi$
$151$	0.339462	0.0276250	0.0138125	+	0.999905i	$0.495603\pi$
$152$	6.00131	0.486770
$153$	−5.48590	−0.443509
$154$	0	0
$155$	8.64687	0.694533
$156$	−5.78644	−0.463286
$157$	−5.53615	−0.441833	−0.220916	−	0.975293i	$-0.570905\pi$
$157$	−5.53615	−0.441833	−0.220916	+	0.975293i	$0.570905\pi$
$158$	−18.4983	−1.47164
$159$	9.34659	0.741232
$160$	−4.04048	−0.319428
$161$	0	0
$162$	−1.69562	−0.133221
$163$	17.4473	1.36657	0.683287	−	0.730149i	$-0.260550\pi$
$163$	17.4473	1.36657	0.683287	+	0.730149i	$0.260550\pi$
$164$	0.875138	0.0683368
$165$	0.766086	0.0596397
$166$	−20.3450	−1.57908
$167$	14.6921	1.13691	0.568456	−	0.822714i	$-0.307541\pi$
$167$	14.6921	1.13691	0.568456	+	0.822714i	$0.307541\pi$
$168$	0	0
$169$	30.7189	2.36299
$170$	−8.10538	−0.621654
$171$	3.14642	0.240613
$172$	1.07240	0.0817700
$173$	15.4466	1.17439	0.587193	−	0.809447i	$-0.300233\pi$
$173$	15.4466	1.17439	0.587193	+	0.809447i	$0.300233\pi$
$174$	−1.52359	−0.115503
$175$	0	0
$176$	4.38223	0.330323
$177$	−6.59869	−0.495988
$178$	−11.2819	−0.845612
$179$	−25.3116	−1.89188	−0.945938	−	0.324348i	$-0.894855\pi$
$179$	−25.3116	−1.89188	−0.945938	+	0.324348i	$0.894855\pi$
$180$	−0.762557	−0.0568376
$181$	−13.8566	−1.02995	−0.514976	−	0.857204i	$-0.672199\pi$
$181$	−13.8566	−1.02995	−0.514976	+	0.857204i	$0.672199\pi$
$182$	0	0
$183$	−4.63726	−0.342796
$184$	−16.3637	−1.20635
$185$	−4.77066	−0.350746
$186$	16.8264	1.23377
$187$	4.82314	0.352703
$188$	−3.90056	−0.284478
$189$	0	0
$190$	4.64882	0.337261
$191$	0.559263	0.0404668	0.0202334	−	0.999795i	$-0.493559\pi$
$191$	0.559263	0.0404668	0.0202334	+	0.999795i	$0.493559\pi$
$192$	2.10622	0.152003
$193$	−16.6014	−1.19500	−0.597498	−	0.801870i	$-0.703839\pi$
$193$	−16.6014	−1.19500	−0.597498	+	0.801870i	$0.703839\pi$
$194$	−4.51756	−0.324342
$195$	5.76143	0.412585
$196$	0	0
$197$	17.8287	1.27024	0.635120	−	0.772414i	$-0.280951\pi$
$197$	17.8287	1.27024	0.635120	+	0.772414i	$0.280951\pi$
$198$	1.49077	0.105945
$199$	1.69973	0.120491	0.0602455	−	0.998184i	$-0.480812\pi$
$199$	1.69973	0.120491	0.0602455	+	0.998184i	$0.480812\pi$
$200$	−8.08854	−0.571946
$201$	−8.87174	−0.625764
$202$	−20.4837	−1.44123
$203$	0	0
$204$	−4.80092	−0.336132
$205$	−0.871357	−0.0608582
$206$	−24.6585	−1.71804
$207$	−8.57933	−0.596305
$208$	32.9571	2.28516
$209$	−2.76630	−0.191349
$210$	0	0
$211$	4.81896	0.331751	0.165876	−	0.986147i	$-0.446955\pi$
$211$	4.81896	0.331751	0.165876	+	0.986147i	$0.446955\pi$
$212$	8.17955	0.561774
$213$	11.3486	0.777591
$214$	9.56281	0.653701
$215$	−1.06777	−0.0728213
$216$	1.90734	0.129778
$217$	0	0
$218$	−19.7896	−1.34032
$219$	0.181676	0.0122765
$220$	0.670431	0.0452004
$221$	36.2729	2.43998
$222$	−9.28350	−0.623068
$223$	10.4562	0.700197	0.350098	−	0.936713i	$-0.386148\pi$
$223$	10.4562	0.700197	0.350098	+	0.936713i	$0.386148\pi$
$224$	0	0
$225$	−4.24074	−0.282716
$226$	−35.0421	−2.33096
$227$	4.74383	0.314859	0.157430	−	0.987530i	$-0.449679\pi$
$227$	4.74383	0.314859	0.157430	+	0.987530i	$0.449679\pi$
$228$	2.75356	0.182359
$229$	−28.6638	−1.89416	−0.947079	−	0.321001i	$-0.895981\pi$
$229$	−28.6638	−1.89416	−0.947079	+	0.321001i	$0.895981\pi$
$230$	−12.6759	−0.835824
$231$	0	0
$232$	1.71383	0.112519
$233$	22.9428	1.50303	0.751517	−	0.659714i	$-0.229323\pi$
$233$	22.9428	1.50303	0.751517	+	0.659714i	$0.229323\pi$
$234$	11.2115	0.732919
$235$	3.88371	0.253345
$236$	−5.77476	−0.375905
$237$	10.9094	0.708643
$238$	0	0
$239$	−9.26204	−0.599111	−0.299556	−	0.954079i	$-0.596838\pi$
$239$	−9.26204	−0.599111	−0.299556	+	0.954079i	$0.596838\pi$
$240$	4.34320	0.280352
$241$	−25.8703	−1.66645	−0.833226	−	0.552933i	$-0.813509\pi$
$241$	−25.8703	−1.66645	−0.833226	+	0.552933i	$0.813509\pi$
$242$	17.3412	1.11473
$243$	1.00000	0.0641500
$244$	−4.05824	−0.259802
$245$	0	0
$246$	−1.69562	−0.108109
$247$	−20.8043	−1.32374
$248$	−18.9274	−1.20189
$249$	11.9985	0.760376
$250$	−13.6531	−0.863499
$251$	11.0634	0.698316	0.349158	−	0.937064i	$-0.386468\pi$
$251$	11.0634	0.698316	0.349158	+	0.937064i	$0.386468\pi$
$252$	0	0
$253$	7.54284	0.474214
$254$	11.7045	0.734405
$255$	4.78018	0.299346
$256$	17.5684	1.09803
$257$	1.76325	0.109989	0.0549944	−	0.998487i	$-0.482486\pi$
$257$	1.76325	0.109989	0.0549944	+	0.998487i	$0.482486\pi$
$258$	−2.07784	−0.129360
$259$	0	0
$260$	5.04205	0.312695
$261$	0.898544	0.0556185
$262$	15.3049	0.945540
$263$	11.7419	0.724034	0.362017	−	0.932172i	$-0.382088\pi$
$263$	11.7419	0.724034	0.362017	+	0.932172i	$0.382088\pi$
$264$	−1.67691	−0.103207
$265$	−8.14421	−0.500295
$266$	0	0
$267$	6.65352	0.407189
$268$	−7.76400	−0.474262
$269$	24.1277	1.47109	0.735545	−	0.677475i	$-0.236926\pi$
$269$	24.1277	1.47109	0.735545	+	0.677475i	$0.236926\pi$
$270$	1.47749	0.0899173
$271$	−27.3145	−1.65924	−0.829619	−	0.558331i	$-0.811442\pi$
$271$	−27.3145	−1.65924	−0.829619	+	0.558331i	$0.811442\pi$
$272$	27.3440	1.65797
$273$	0	0
$274$	−3.17947	−0.192079
$275$	3.72841	0.224831
$276$	−7.50810	−0.451934
$277$	−20.9432	−1.25835	−0.629177	−	0.777262i	$-0.716608\pi$
$277$	−20.9432	−1.25835	−0.629177	+	0.777262i	$0.716608\pi$
$278$	21.5479	1.29236
$279$	−9.92346	−0.594102
$280$	0	0
$281$	−31.0711	−1.85355	−0.926774	−	0.375620i	$-0.877430\pi$
$281$	−31.0711	−1.85355	−0.926774	+	0.375620i	$0.877430\pi$
$282$	7.55754	0.450045
$283$	13.7139	0.815209	0.407605	−	0.913159i	$-0.366364\pi$
$283$	13.7139	0.815209	0.407605	+	0.913159i	$0.366364\pi$
$284$	9.93157	0.589330
$285$	−2.74166	−0.162402
$286$	−9.85702	−0.582858
$287$	0	0
$288$	4.63700	0.273238
$289$	13.0951	0.770301
$290$	1.32759	0.0779589
$291$	2.66425	0.156181
$292$	0.158991	0.00930427
$293$	2.09423	0.122346	0.0611731	−	0.998127i	$-0.480516\pi$
$293$	2.09423	0.122346	0.0611731	+	0.998127i	$0.480516\pi$
$294$	0	0
$295$	5.74981	0.334767
$296$	10.4427	0.606967
$297$	−0.879188	−0.0510157
$298$	27.8582	1.61378
$299$	56.7268	3.28059
$300$	−3.71123	−0.214268
$301$	0	0
$302$	−0.575600	−0.0331221
$303$	12.0803	0.693996
$304$	−15.6831	−0.899486
$305$	4.04071	0.231370
$306$	9.30202	0.531761
$307$	−22.9961	−1.31246	−0.656229	−	0.754562i	$-0.727850\pi$
$307$	−22.9961	−1.31246	−0.656229	+	0.754562i	$0.727850\pi$
$308$	0	0
$309$	14.5425	0.827292
$310$	−14.6618	−0.832736
$311$	20.6052	1.16841	0.584206	−	0.811605i	$-0.301406\pi$
$311$	20.6052	1.16841	0.584206	+	0.811605i	$0.301406\pi$
$312$	−12.6114	−0.713980
$313$	−12.5390	−0.708747	−0.354374	−	0.935104i	$-0.615306\pi$
$313$	−12.5390	−0.708747	−0.354374	+	0.935104i	$0.615306\pi$
$314$	9.38722	0.529752
$315$	0	0
$316$	9.54725	0.537075
$317$	−18.8666	−1.05965	−0.529827	−	0.848106i	$-0.677743\pi$
$317$	−18.8666	−1.05965	−0.529827	+	0.848106i	$0.677743\pi$
$318$	−15.8483	−0.888728
$319$	−0.789989	−0.0442309
$320$	−1.83527	−0.102595
$321$	−5.63970	−0.314778
$322$	0	0
$323$	−17.2610	−0.960426
$324$	0.875138	0.0486188
$325$	28.0399	1.55537
$326$	−29.5840	−1.63851
$327$	11.6710	0.645408
$328$	1.90734	0.105315
$329$	0	0
$330$	−1.29899	−0.0715072
$331$	2.11679	0.116349	0.0581746	−	0.998306i	$-0.481472\pi$
$331$	2.11679	0.116349	0.0581746	+	0.998306i	$0.481472\pi$
$332$	10.5004	0.576283
$333$	5.47498	0.300027
$334$	−24.9123	−1.36314
$335$	7.73045	0.422360
$336$	0	0
$337$	35.6112	1.93987	0.969933	−	0.243374i	$-0.0782541\pi$
$337$	35.6112	1.93987	0.969933	+	0.243374i	$0.0782541\pi$
$338$	−52.0877	−2.83320
$339$	20.6662	1.12243
$340$	4.18331	0.226872
$341$	8.72458	0.472463
$342$	−5.33515	−0.288492
$343$	0	0
$344$	2.33728	0.126018
$345$	7.47565	0.402476
$346$	−26.1917	−1.40807
$347$	31.8947	1.71220	0.856098	−	0.516813i	$-0.172882\pi$
$347$	31.8947	1.71220	0.856098	+	0.516813i	$0.172882\pi$
$348$	0.786350	0.0421528
$349$	13.2098	0.707104	0.353552	−	0.935415i	$-0.384974\pi$
$349$	13.2098	0.707104	0.353552	+	0.935415i	$0.384974\pi$
$350$	0	0
$351$	−6.61203	−0.352924
$352$	−4.07679	−0.217294
$353$	−13.5106	−0.719095	−0.359547	−	0.933127i	$-0.617069\pi$
$353$	−13.5106	−0.719095	−0.359547	+	0.933127i	$0.617069\pi$
$354$	11.1889	0.594682
$355$	−9.88865	−0.524835
$356$	5.82275	0.308605
$357$	0	0
$358$	42.9189	2.26833
$359$	31.0082	1.63655	0.818275	−	0.574827i	$-0.194931\pi$
$359$	31.0082	1.63655	0.818275	+	0.574827i	$0.194931\pi$
$360$	−1.66198	−0.0875938
$361$	−9.10001	−0.478948
$362$	23.4956	1.23490
$363$	−10.2270	−0.536780
$364$	0	0
$365$	−0.158304	−0.00828603
$366$	7.86305	0.411008
$367$	13.8170	0.721244	0.360622	−	0.932712i	$-0.382564\pi$
$367$	13.8170	0.721244	0.360622	+	0.932712i	$0.382564\pi$
$368$	42.7629	2.22917
$369$	1.00000	0.0520579
$370$	8.08924	0.420539
$371$	0	0
$372$	−8.68439	−0.450265
$373$	20.6893	1.07125	0.535626	−	0.844455i	$-0.320076\pi$
$373$	20.6893	1.07125	0.535626	+	0.844455i	$0.320076\pi$
$374$	−8.17822	−0.422886
$375$	8.05198	0.415802
$376$	−8.50119	−0.438415
$377$	−5.94120	−0.305987
$378$	0	0
$379$	−22.1115	−1.13579	−0.567895	−	0.823101i	$-0.692242\pi$
$379$	−22.1115	−1.13579	−0.567895	+	0.823101i	$0.692242\pi$
$380$	−2.39933	−0.123083
$381$	−6.90276	−0.353639
$382$	−0.948299	−0.0485192
$383$	22.6138	1.15551	0.577757	−	0.816209i	$-0.303928\pi$
$383$	22.6138	1.15551	0.577757	+	0.816209i	$0.303928\pi$
$384$	−12.8453	−0.655512
$385$	0	0
$386$	28.1498	1.43278
$387$	1.22541	0.0622911
$388$	2.33158	0.118368
$389$	−23.0376	−1.16805	−0.584027	−	0.811734i	$-0.698524\pi$
$389$	−23.0376	−1.16805	−0.584027	+	0.811734i	$0.698524\pi$
$390$	−9.76922	−0.494684
$391$	47.0653	2.38020
$392$	0	0
$393$	−9.02612	−0.455308
$394$	−30.2307	−1.52300
$395$	−9.50600	−0.478299
$396$	−0.769411	−0.0386643
$397$	−11.2705	−0.565648	−0.282824	−	0.959172i	$-0.591271\pi$
$397$	−11.2705	−0.565648	−0.282824	+	0.959172i	$0.591271\pi$
$398$	−2.88211	−0.144467
$399$	0	0
$400$	21.1376	1.05688
$401$	−0.777245	−0.0388138	−0.0194069	−	0.999812i	$-0.506178\pi$
$401$	−0.777245	−0.0388138	−0.0194069	+	0.999812i	$0.506178\pi$
$402$	15.0431	0.750283
$403$	65.6142	3.26848
$404$	10.5719	0.525974
$405$	−0.871357	−0.0432981
$406$	0	0
$407$	−4.81353	−0.238598
$408$	−10.4635	−0.518020
$409$	3.01088	0.148879	0.0744393	−	0.997226i	$-0.476283\pi$
$409$	3.01088	0.148879	0.0744393	+	0.997226i	$0.476283\pi$
$410$	1.47749	0.0729681
$411$	1.87510	0.0924921
$412$	12.7267	0.626998
$413$	0	0
$414$	14.5473	0.714961
$415$	−10.4550	−0.513216
$416$	−30.6600	−1.50323
$417$	−12.7080	−0.622311
$418$	4.69060	0.229425
$419$	3.26628	0.159568	0.0797841	−	0.996812i	$-0.474577\pi$
$419$	3.26628	0.159568	0.0797841	+	0.996812i	$0.474577\pi$
$420$	0	0
$421$	−11.7305	−0.571708	−0.285854	−	0.958273i	$-0.592277\pi$
$421$	−11.7305	−0.571708	−0.285854	+	0.958273i	$0.592277\pi$
$422$	−8.17114	−0.397765
$423$	−4.45708	−0.216711
$424$	17.8271	0.865762
$425$	23.2643	1.12848
$426$	−19.2429	−0.932322
$427$	0	0
$428$	−4.93552	−0.238567
$429$	5.81322	0.280665
$430$	1.81054	0.0873118
$431$	13.3053	0.640895	0.320447	−	0.947266i	$-0.396167\pi$
$431$	13.3053	0.640895	0.320447	+	0.947266i	$0.396167\pi$
$432$	−4.98441	−0.239813
$433$	−27.0286	−1.29891	−0.649456	−	0.760399i	$-0.725004\pi$
$433$	−27.0286	−1.29891	−0.649456	+	0.760399i	$0.725004\pi$
$434$	0	0
$435$	−0.782952	−0.0375397
$436$	10.2137	0.489149
$437$	−26.9942	−1.29131
$438$	−0.308054	−0.0147194
$439$	11.1599	0.532635	0.266318	−	0.963885i	$-0.414193\pi$
$439$	11.1599	0.532635	0.266318	+	0.963885i	$0.414193\pi$
$440$	1.46119	0.0696594
$441$	0	0
$442$	−61.5052	−2.92551
$443$	−7.11512	−0.338050	−0.169025	−	0.985612i	$-0.554062\pi$
$443$	−7.11512	−0.338050	−0.169025	+	0.985612i	$0.554062\pi$
$444$	4.79136	0.227388
$445$	−5.79759	−0.274832
$446$	−17.7297	−0.839527
$447$	−16.4295	−0.777086
$448$	0	0
$449$	8.09463	0.382009	0.191005	−	0.981589i	$-0.438825\pi$
$449$	8.09463	0.382009	0.191005	+	0.981589i	$0.438825\pi$
$450$	7.19069	0.338973
$451$	−0.879188	−0.0413993
$452$	18.0858	0.850683
$453$	0.339462	0.0159493
$454$	−8.04376	−0.377512
$455$	0	0
$456$	6.00131	0.281037
$457$	16.1324	0.754641	0.377321	−	0.926083i	$-0.376845\pi$
$457$	16.1324	0.754641	0.377321	+	0.926083i	$0.376845\pi$
$458$	48.6030	2.27107
$459$	−5.48590	−0.256060
$460$	6.54223	0.305033
$461$	−12.1693	−0.566779	−0.283390	−	0.959005i	$-0.591459\pi$
$461$	−12.1693	−0.566779	−0.283390	+	0.959005i	$0.591459\pi$
$462$	0	0
$463$	1.46139	0.0679166	0.0339583	−	0.999423i	$-0.489189\pi$
$463$	1.46139	0.0679166	0.0339583	+	0.999423i	$0.489189\pi$
$464$	−4.47871	−0.207919
$465$	8.64687	0.400989
$466$	−38.9023	−1.80212
$467$	−28.6004	−1.32347	−0.661734	−	0.749739i	$-0.730179\pi$
$467$	−28.6004	−1.32347	−0.661734	+	0.749739i	$0.730179\pi$
$468$	−5.78644	−0.267478
$469$	0	0
$470$	−6.58531	−0.303758
$471$	−5.53615	−0.255092
$472$	−12.5860	−0.579315
$473$	−1.07737	−0.0495374
$474$	−18.4983	−0.849654
$475$	−13.3432	−0.612226
$476$	0	0
$477$	9.34659	0.427951
$478$	15.7049	0.718326
$479$	14.6243	0.668201	0.334100	−	0.942538i	$-0.391568\pi$
$479$	14.6243	0.668201	0.334100	+	0.942538i	$0.391568\pi$
$480$	−4.04048	−0.184422
$481$	−36.2007	−1.65061
$482$	43.8663	1.99805
$483$	0	0
$484$	−8.95006	−0.406821
$485$	−2.32151	−0.105414
$486$	−1.69562	−0.0769150
$487$	11.2976	0.511941	0.255971	−	0.966685i	$-0.417605\pi$
$487$	11.2976	0.511941	0.255971	+	0.966685i	$0.417605\pi$
$488$	−8.84484	−0.400387
$489$	17.4473	0.788992
$490$	0	0
$491$	2.06264	0.0930855	0.0465428	−	0.998916i	$-0.485180\pi$
$491$	2.06264	0.0930855	0.0465428	+	0.998916i	$0.485180\pi$
$492$	0.875138	0.0394543
$493$	−4.92932	−0.222006
$494$	35.2762	1.58715
$495$	0.766086	0.0344330
$496$	49.4626	2.22093
$497$	0	0
$498$	−20.3450	−0.911681
$499$	−15.6805	−0.701957	−0.350979	−	0.936383i	$-0.614151\pi$
$499$	−15.6805	−0.701957	−0.350979	+	0.936383i	$0.614151\pi$
$500$	7.04659	0.315133
$501$	14.6921	0.656396
$502$	−18.7594	−0.837271
$503$	−19.2489	−0.858264	−0.429132	−	0.903242i	$-0.641181\pi$
$503$	−19.2489	−0.858264	−0.429132	+	0.903242i	$0.641181\pi$
$504$	0	0
$505$	−10.5263	−0.468413
$506$	−12.7898	−0.568577
$507$	30.7189	1.36428
$508$	−6.04087	−0.268020
$509$	−19.9986	−0.886421	−0.443211	−	0.896418i	$-0.646161\pi$
$509$	−19.9986	−0.886421	−0.443211	+	0.896418i	$0.646161\pi$
$510$	−8.10538	−0.358912
$511$	0	0
$512$	−4.09873	−0.181140
$513$	3.14642	0.138918
$514$	−2.98981	−0.131875
$515$	−12.6717	−0.558381
$516$	1.07240	0.0472099
$517$	3.91861	0.172340
$518$	0	0
$519$	15.4466	0.678032
$520$	10.9890	0.481901
$521$	−8.14796	−0.356968	−0.178484	−	0.983943i	$-0.557119\pi$
$521$	−8.14796	−0.356968	−0.178484	+	0.983943i	$0.557119\pi$
$522$	−1.52359	−0.0666858
$523$	−37.2224	−1.62762	−0.813811	−	0.581129i	$-0.802611\pi$
$523$	−37.2224	−1.62762	−0.813811	+	0.581129i	$0.802611\pi$
$524$	−7.89910	−0.345074
$525$	0	0
$526$	−19.9098	−0.868107
$527$	54.4391	2.37140
$528$	4.38223	0.190712
$529$	50.6049	2.20021
$530$	13.8095	0.599847
$531$	−6.59869	−0.286359
$532$	0	0
$533$	−6.61203	−0.286399
$534$	−11.2819	−0.488214
$535$	4.91419	0.212459
$536$	−16.9214	−0.730895
$537$	−25.3116	−1.09228
$538$	−40.9115	−1.76382
$539$	0	0
$540$	−0.762557	−0.0328152
$541$	23.6455	1.01660	0.508300	−	0.861180i	$-0.330274\pi$
$541$	23.6455	1.01660	0.508300	+	0.861180i	$0.330274\pi$
$542$	46.3151	1.98940
$543$	−13.8566	−0.594643
$544$	−25.4381	−1.09065
$545$	−10.1696	−0.435618
$546$	0	0
$547$	33.0794	1.41437	0.707187	−	0.707027i	$-0.249964\pi$
$547$	33.0794	1.41437	0.707187	+	0.707027i	$0.249964\pi$
$548$	1.64098	0.0700990
$549$	−4.63726	−0.197913
$550$	−6.32197	−0.269570
$551$	2.82720	0.120443
$552$	−16.3637	−0.696486
$553$	0	0
$554$	35.5118	1.50875
$555$	−4.77066	−0.202503
$556$	−11.1212	−0.471644
$557$	33.2103	1.40717	0.703583	−	0.710613i	$-0.251582\pi$
$557$	33.2103	1.40717	0.703583	+	0.710613i	$0.251582\pi$
$558$	16.8264	0.712320
$559$	−8.10245	−0.342697
$560$	0	0
$561$	4.82314	0.203633
$562$	52.6849	2.22238
$563$	−15.5277	−0.654415	−0.327208	−	0.944952i	$-0.606108\pi$
$563$	−15.5277	−0.654415	−0.327208	+	0.944952i	$0.606108\pi$
$564$	−3.90056	−0.164243
$565$	−18.0076	−0.757586
$566$	−23.2537	−0.977425
$567$	0	0
$568$	21.6456	0.908230
$569$	4.58501	0.192214	0.0961068	−	0.995371i	$-0.469361\pi$
$569$	4.58501	0.192214	0.0961068	+	0.995371i	$0.469361\pi$
$570$	4.64882	0.194718
$571$	12.3228	0.515692	0.257846	−	0.966186i	$-0.416987\pi$
$571$	12.3228	0.515692	0.257846	+	0.966186i	$0.416987\pi$
$572$	5.08737	0.212713
$573$	0.559263	0.0233635
$574$	0	0
$575$	36.3827	1.51726
$576$	2.10622	0.0877593
$577$	−19.6056	−0.816191	−0.408095	−	0.912939i	$-0.633807\pi$
$577$	−19.6056	−0.816191	−0.408095	+	0.912939i	$0.633807\pi$
$578$	−22.2044	−0.923580
$579$	−16.6014	−0.689932
$580$	−0.685191	−0.0284510
$581$	0	0
$582$	−4.51756	−0.187259
$583$	−8.21740	−0.340330
$584$	0.346518	0.0143390
$585$	5.76143	0.238206
$586$	−3.55102	−0.146691
$587$	2.81629	0.116241	0.0581204	−	0.998310i	$-0.481489\pi$
$587$	2.81629	0.116241	0.0581204	+	0.998310i	$0.481489\pi$
$588$	0	0
$589$	−31.2234	−1.28654
$590$	−9.74951	−0.401381
$591$	17.8287	0.733373
$592$	−27.2895	−1.12159
$593$	13.8514	0.568808	0.284404	−	0.958704i	$-0.408204\pi$
$593$	13.8514	0.568808	0.284404	+	0.958704i	$0.408204\pi$
$594$	1.49077	0.0611671
$595$	0	0
$596$	−14.3780	−0.588947
$597$	1.69973	0.0695655
$598$	−96.1872	−3.93339
$599$	2.84666	0.116311	0.0581556	−	0.998308i	$-0.481478\pi$
$599$	2.84666	0.116311	0.0581556	+	0.998308i	$0.481478\pi$
$600$	−8.08854	−0.330213
$601$	−36.8765	−1.50422	−0.752112	−	0.659036i	$-0.770965\pi$
$601$	−36.8765	−1.50422	−0.752112	+	0.659036i	$0.770965\pi$
$602$	0	0
$603$	−8.87174	−0.361285
$604$	0.297076	0.0120879
$605$	8.91139	0.362299
$606$	−20.4837	−0.832092
$607$	37.3095	1.51435	0.757173	−	0.653214i	$-0.226580\pi$
$607$	37.3095	1.51435	0.757173	+	0.653214i	$0.226580\pi$
$608$	14.5900	0.591701
$609$	0	0
$610$	−6.85152	−0.277410
$611$	29.4704	1.19224
$612$	−4.80092	−0.194066
$613$	−37.2080	−1.50282	−0.751408	−	0.659838i	$-0.770625\pi$
$613$	−37.2080	−1.50282	−0.751408	+	0.659838i	$0.770625\pi$
$614$	38.9928	1.57362
$615$	−0.871357	−0.0351365
$616$	0	0
$617$	23.1388	0.931531	0.465766	−	0.884908i	$-0.345779\pi$
$617$	23.1388	0.931531	0.465766	+	0.884908i	$0.345779\pi$
$618$	−24.6585	−0.991912
$619$	−40.3086	−1.62014	−0.810070	−	0.586334i	$-0.800571\pi$
$619$	−40.3086	−1.62014	−0.810070	+	0.586334i	$0.800571\pi$
$620$	7.56720	0.303906
$621$	−8.57933	−0.344277
$622$	−34.9386	−1.40091
$623$	0	0
$624$	32.9571	1.31934
$625$	14.1875	0.567502
$626$	21.2614	0.849778
$627$	−2.76630	−0.110475
$628$	−4.84489	−0.193332
$629$	−30.0352	−1.19758
$630$	0	0
$631$	−37.6695	−1.49960	−0.749799	−	0.661666i	$-0.769850\pi$
$631$	−37.6695	−1.49960	−0.749799	+	0.661666i	$0.769850\pi$
$632$	20.8080	0.827698
$633$	4.81896	0.191537
$634$	31.9906	1.27051
$635$	6.01477	0.238689
$636$	8.17955	0.324340
$637$	0	0
$638$	1.33952	0.0530323
$639$	11.3486	0.448943
$640$	11.1929	0.442437
$641$	9.93607	0.392451	0.196226	−	0.980559i	$-0.437132\pi$
$641$	9.93607	0.392451	0.196226	+	0.980559i	$0.437132\pi$
$642$	9.56281	0.377414
$643$	24.7982	0.977946	0.488973	−	0.872299i	$-0.337372\pi$
$643$	24.7982	0.977946	0.488973	+	0.872299i	$0.337372\pi$
$644$	0	0
$645$	−1.06777	−0.0420434
$646$	29.2681	1.15154
$647$	−28.0631	−1.10328	−0.551638	−	0.834084i	$-0.685997\pi$
$647$	−28.0631	−1.10328	−0.551638	+	0.834084i	$0.685997\pi$
$648$	1.90734	0.0749275
$649$	5.80148	0.227728
$650$	−47.5451	−1.86487
$651$	0	0
$652$	15.2688	0.597971
$653$	30.4801	1.19278	0.596389	−	0.802696i	$-0.296602\pi$
$653$	30.4801	1.19278	0.596389	+	0.802696i	$0.296602\pi$
$654$	−19.7896	−0.773835
$655$	7.86497	0.307310
$656$	−4.98441	−0.194608
$657$	0.181676	0.00708785
$658$	0	0
$659$	−18.2766	−0.711956	−0.355978	−	0.934494i	$-0.615852\pi$
$659$	−18.2766	−0.711956	−0.355978	+	0.934494i	$0.615852\pi$
$660$	0.670431	0.0260965
$661$	33.7328	1.31205	0.656027	−	0.754737i	$-0.272236\pi$
$661$	33.7328	1.31205	0.656027	+	0.754737i	$0.272236\pi$
$662$	−3.58928	−0.139501
$663$	36.2729	1.40872
$664$	22.8853	0.888123
$665$	0	0
$666$	−9.28350	−0.359728
$667$	−7.70891	−0.298490
$668$	12.8576	0.497477
$669$	10.4562	0.404259
$670$	−13.1079	−0.506403
$671$	4.07702	0.157392
$672$	0	0
$673$	−4.15489	−0.160159	−0.0800796	−	0.996788i	$-0.525517\pi$
$673$	−4.15489	−0.160159	−0.0800796	+	0.996788i	$0.525517\pi$
$674$	−60.3832	−2.32587
$675$	−4.24074	−0.163226
$676$	26.8833	1.03397
$677$	8.56758	0.329279	0.164639	−	0.986354i	$-0.447354\pi$
$677$	8.56758	0.329279	0.164639	+	0.986354i	$0.447354\pi$
$678$	−35.0421	−1.34578
$679$	0	0
$680$	9.11743	0.349638
$681$	4.74383	0.181784
$682$	−14.7936	−0.566476
$683$	−34.5199	−1.32087	−0.660434	−	0.750884i	$-0.729628\pi$
$683$	−34.5199	−1.32087	−0.660434	+	0.750884i	$0.729628\pi$
$684$	2.75356	0.105285
$685$	−1.63388	−0.0624275
$686$	0	0
$687$	−28.6638	−1.09359
$688$	−6.10795	−0.232863
$689$	−61.7999	−2.35439
$690$	−12.6759	−0.482563
$691$	7.01425	0.266835	0.133417	−	0.991060i	$-0.457405\pi$
$691$	7.01425	0.266835	0.133417	+	0.991060i	$0.457405\pi$
$692$	13.5179	0.513875
$693$	0	0
$694$	−54.0814	−2.05290
$695$	11.0732	0.420029
$696$	1.71383	0.0649626
$697$	−5.48590	−0.207793
$698$	−22.3988	−0.847808
$699$	22.9428	0.867777
$700$	0	0
$701$	−18.9365	−0.715221	−0.357610	−	0.933871i	$-0.616408\pi$
$701$	−18.9365	−0.715221	−0.357610	+	0.933871i	$0.616408\pi$
$702$	11.2115	0.423151
$703$	17.2266	0.649714
$704$	−1.85176	−0.0697910
$705$	3.88371	0.146269
$706$	22.9088	0.862185
$707$	0	0
$708$	−5.77476	−0.217029
$709$	27.1519	1.01971	0.509855	−	0.860260i	$-0.329699\pi$
$709$	27.1519	1.01971	0.509855	+	0.860260i	$0.329699\pi$
$710$	16.7674	0.629270
$711$	10.9094	0.409135
$712$	12.6905	0.475598
$713$	85.1366	3.18839
$714$	0	0
$715$	−5.06538	−0.189435
$716$	−22.1511	−0.827826
$717$	−9.26204	−0.345897
$718$	−52.5782	−1.96220
$719$	39.6007	1.47686	0.738429	−	0.674331i	$-0.235568\pi$
$719$	39.6007	1.47686	0.738429	+	0.674331i	$0.235568\pi$
$720$	4.34320	0.161861
$721$	0	0
$722$	15.4302	0.574252
$723$	−25.8703	−0.962126
$724$	−12.1264	−0.450675
$725$	−3.81049	−0.141518
$726$	17.3412	0.643592
$727$	25.3854	0.941492	0.470746	−	0.882269i	$-0.343985\pi$
$727$	25.3854	0.941492	0.470746	+	0.882269i	$0.343985\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0.268425	0.00993484
$731$	−6.72248	−0.248640
$732$	−4.05824	−0.149997
$733$	−44.7788	−1.65394	−0.826971	−	0.562245i	$-0.809938\pi$
$733$	−44.7788	−1.65394	−0.826971	+	0.562245i	$0.809938\pi$
$734$	−23.4285	−0.864762
$735$	0	0
$736$	−39.7823	−1.46640
$737$	7.79993	0.287314
$738$	−1.69562	−0.0624168
$739$	36.3218	1.33612	0.668059	−	0.744108i	$-0.267125\pi$
$739$	36.3218	1.33612	0.668059	+	0.744108i	$0.267125\pi$
$740$	−4.17498	−0.153475
$741$	−20.8043	−0.764263
$742$	0	0
$743$	−0.0284860	−0.00104505	−0.000522524	−	1.00000i	$-0.500166\pi$
$743$	−0.0284860	−0.00104505	−0.000522524		1.00000i	$0.500166\pi$
$744$	−18.9274	−0.693913
$745$	14.3159	0.524494
$746$	−35.0813	−1.28442
$747$	11.9985	0.439004
$748$	4.22091	0.154332
$749$	0	0
$750$	−13.6531	−0.498541
$751$	24.9464	0.910307	0.455154	−	0.890413i	$-0.349584\pi$
$751$	24.9464	0.910307	0.455154	+	0.890413i	$0.349584\pi$
$752$	22.2159	0.810132
$753$	11.0634	0.403173
$754$	10.0740	0.366875
$755$	−0.295793	−0.0107650
$756$	0	0
$757$	30.7274	1.11680	0.558402	−	0.829570i	$-0.311415\pi$
$757$	30.7274	1.11680	0.558402	+	0.829570i	$0.311415\pi$
$758$	37.4927	1.36180
$759$	7.54284	0.273788
$760$	−5.22928	−0.189686
$761$	51.3019	1.85969	0.929846	−	0.367949i	$-0.119940\pi$
$761$	51.3019	1.85969	0.929846	+	0.367949i	$0.119940\pi$
$762$	11.7045	0.424009
$763$	0	0
$764$	0.489432	0.0177070
$765$	4.78018	0.172828
$766$	−38.3446	−1.38545
$767$	43.6307	1.57541
$768$	17.5684	0.633946
$769$	−18.8700	−0.680468	−0.340234	−	0.940341i	$-0.610506\pi$
$769$	−18.8700	−0.680468	−0.340234	+	0.940341i	$0.610506\pi$
$770$	0	0
$771$	1.76325	0.0635020
$772$	−14.5285	−0.522893
$773$	36.9531	1.32911	0.664555	−	0.747239i	$-0.268621\pi$
$773$	36.9531	1.32911	0.664555	+	0.747239i	$0.268621\pi$
$774$	−2.07784	−0.0746863
$775$	42.0828	1.51166
$776$	5.08163	0.182420
$777$	0	0
$778$	39.0631	1.40048
$779$	3.14642	0.112732
$780$	5.04205	0.180534
$781$	−9.97753	−0.357024
$782$	−79.8051	−2.85382
$783$	0.898544	0.0321113
$784$	0	0
$785$	4.82396	0.172175
$786$	15.3049	0.545908
$787$	−16.5851	−0.591196	−0.295598	−	0.955312i	$-0.595519\pi$
$787$	−16.5851	−0.591196	−0.295598	+	0.955312i	$0.595519\pi$
$788$	15.6025	0.555817
$789$	11.7419	0.418021
$790$	16.1186	0.573474
$791$	0	0
$792$	−1.67691	−0.0595865
$793$	30.6617	1.08883
$794$	19.1105	0.678205
$795$	−8.14421	−0.288845
$796$	1.48750	0.0527231
$797$	−6.70494	−0.237501	−0.118751	−	0.992924i	$-0.537889\pi$
$797$	−6.70494	−0.237501	−0.118751	+	0.992924i	$0.537889\pi$
$798$	0	0
$799$	24.4511	0.865019
$800$	−19.6643	−0.695237
$801$	6.65352	0.235091
$802$	1.31792	0.0465372
$803$	−0.159727	−0.00563665
$804$	−7.76400	−0.273815
$805$	0	0
$806$	−111.257	−3.91886
$807$	24.1277	0.849335
$808$	23.0413	0.810590
$809$	2.30654	0.0810937	0.0405468	−	0.999178i	$-0.487090\pi$
$809$	2.30654	0.0810937	0.0405468	+	0.999178i	$0.487090\pi$
$810$	1.47749	0.0519138
$811$	24.5837	0.863250	0.431625	−	0.902053i	$-0.357940\pi$
$811$	24.5837	0.863250	0.431625	+	0.902053i	$0.357940\pi$
$812$	0	0
$813$	−27.3145	−0.957961
$814$	8.16194	0.286076
$815$	−15.2028	−0.532530
$816$	27.3440	0.957231
$817$	3.85566	0.134893
$818$	−5.10532	−0.178503
$819$	0	0
$820$	−0.762557	−0.0266296
$821$	15.9030	0.555017	0.277509	−	0.960723i	$-0.410491\pi$
$821$	15.9030	0.555017	0.277509	+	0.960723i	$0.410491\pi$
$822$	−3.17947	−0.110897
$823$	18.0302	0.628495	0.314247	−	0.949341i	$-0.398248\pi$
$823$	18.0302	0.628495	0.314247	+	0.949341i	$0.398248\pi$
$824$	27.7375	0.966280
$825$	3.72841	0.129806
$826$	0	0
$827$	39.9089	1.38777	0.693885	−	0.720086i	$-0.255898\pi$
$827$	39.9089	1.38777	0.693885	+	0.720086i	$0.255898\pi$
$828$	−7.50810	−0.260924
$829$	7.92559	0.275267	0.137634	−	0.990483i	$-0.456050\pi$
$829$	7.92559	0.275267	0.137634	+	0.990483i	$0.456050\pi$
$830$	17.7277	0.615339
$831$	−20.9432	−0.726511
$832$	−13.9264	−0.482811
$833$	0	0
$834$	21.5479	0.746143
$835$	−12.8021	−0.443035
$836$	−2.42089	−0.0837283
$837$	−9.92346	−0.343005
$838$	−5.53838	−0.191320
$839$	6.66949	0.230256	0.115128	−	0.993351i	$-0.463272\pi$
$839$	6.66949	0.230256	0.115128	+	0.993351i	$0.463272\pi$
$840$	0	0
$841$	−28.1926	−0.972159
$842$	19.8904	0.685470
$843$	−31.0711	−1.07015
$844$	4.21726	0.145164
$845$	−26.7671	−0.920818
$846$	7.55754	0.259833
$847$	0	0
$848$	−46.5872	−1.59981
$849$	13.7139	0.470661
$850$	−39.4474	−1.35304
$851$	−46.9716	−1.61017
$852$	9.93157	0.340250
$853$	36.7875	1.25958	0.629790	−	0.776765i	$-0.283141\pi$
$853$	36.7875	1.25958	0.629790	+	0.776765i	$0.283141\pi$
$854$	0	0
$855$	−2.74166	−0.0937627
$856$	−10.7568	−0.367661
$857$	−47.1180	−1.60952	−0.804759	−	0.593601i	$-0.797706\pi$
$857$	−47.1180	−1.60952	−0.804759	+	0.593601i	$0.797706\pi$
$858$	−9.85702	−0.336513
$859$	−50.4429	−1.72109	−0.860544	−	0.509376i	$-0.829876\pi$
$859$	−50.4429	−1.72109	−0.860544	+	0.509376i	$0.829876\pi$
$860$	−0.934446	−0.0318643
$861$	0	0
$862$	−22.5608	−0.768424
$863$	−41.2875	−1.40544	−0.702721	−	0.711466i	$-0.748032\pi$
$863$	−41.2875	−1.40544	−0.702721	+	0.711466i	$0.748032\pi$
$864$	4.63700	0.157754
$865$	−13.4595	−0.457638
$866$	45.8304	1.55738
$867$	13.0951	0.444733
$868$	0	0
$869$	−9.59143	−0.325367
$870$	1.32759	0.0450096
$871$	58.6602	1.98763
$872$	22.2606	0.753839
$873$	2.66425	0.0901711
$874$	45.7720	1.54826
$875$	0	0
$876$	0.158991	0.00537182
$877$	34.3792	1.16090	0.580452	−	0.814294i	$-0.302876\pi$
$877$	34.3792	1.16090	0.580452	+	0.814294i	$0.302876\pi$
$878$	−18.9231	−0.638622
$879$	2.09423	0.0706366
$880$	−3.81849	−0.128721
$881$	6.16673	0.207762	0.103881	−	0.994590i	$-0.466874\pi$
$881$	6.16673	0.207762	0.103881	+	0.994590i	$0.466874\pi$
$882$	0	0
$883$	21.9212	0.737709	0.368854	−	0.929487i	$-0.379750\pi$
$883$	21.9212	0.737709	0.368854	+	0.929487i	$0.379750\pi$
$884$	31.7438	1.06766
$885$	5.74981	0.193278
$886$	12.0646	0.405317
$887$	−2.01792	−0.0677552	−0.0338776	−	0.999426i	$-0.510786\pi$
$887$	−2.01792	−0.0677552	−0.0338776	+	0.999426i	$0.510786\pi$
$888$	10.4427	0.350433
$889$	0	0
$890$	9.83053	0.329520
$891$	−0.879188	−0.0294539
$892$	9.15059	0.306384
$893$	−14.0239	−0.469291
$894$	27.8582	0.931716
$895$	22.0554	0.737231
$896$	0	0
$897$	56.7268	1.89405
$898$	−13.7254	−0.458024
$899$	−8.91666	−0.297387
$900$	−3.71123	−0.123708
$901$	−51.2744	−1.70820
$902$	1.49077	0.0496373
$903$	0	0
$904$	39.4175	1.31101
$905$	12.0740	0.401354
$906$	−0.575600	−0.0191230
$907$	−25.3949	−0.843225	−0.421613	−	0.906776i	$-0.638536\pi$
$907$	−25.3949	−0.843225	−0.421613	+	0.906776i	$0.638536\pi$
$908$	4.15151	0.137773
$909$	12.0803	0.400679
$910$	0	0
$911$	26.8172	0.888494	0.444247	−	0.895904i	$-0.353471\pi$
$911$	26.8172	0.888494	0.444247	+	0.895904i	$0.353471\pi$
$912$	−15.6831	−0.519318
$913$	−10.5490	−0.349120
$914$	−27.3545	−0.904805
$915$	4.04071	0.133582
$916$	−25.0848	−0.828825
$917$	0	0
$918$	9.30202	0.307012
$919$	15.4798	0.510631	0.255315	−	0.966858i	$-0.417821\pi$
$919$	15.4798	0.510631	0.255315	+	0.966858i	$0.417821\pi$
$920$	14.2586	0.470093
$921$	−22.9961	−0.757748
$922$	20.6345	0.679561
$923$	−75.0371	−2.46988
$924$	0	0
$925$	−23.2179	−0.763401
$926$	−2.47797	−0.0814311
$927$	14.5425	0.477637
$928$	4.16654	0.136774
$929$	−5.08006	−0.166671	−0.0833356	−	0.996522i	$-0.526557\pi$
$929$	−5.08006	−0.166671	−0.0833356	+	0.996522i	$0.526557\pi$
$930$	−14.6618	−0.480780
$931$	0	0
$932$	20.0781	0.657681
$933$	20.6052	0.674583
$934$	48.4954	1.58682
$935$	−4.20267	−0.137442
$936$	−12.6114	−0.412217
$937$	59.0986	1.93067	0.965333	−	0.261020i	$-0.0840587\pi$
$937$	59.0986	1.93067	0.965333	+	0.261020i	$0.0840587\pi$
$938$	0	0
$939$	−12.5390	−0.409195
$940$	3.39878	0.110856
$941$	−1.17201	−0.0382065	−0.0191033	−	0.999818i	$-0.506081\pi$
$941$	−1.17201	−0.0382065	−0.0191033	+	0.999818i	$0.506081\pi$
$942$	9.38722	0.305852
$943$	−8.57933	−0.279381
$944$	32.8905	1.07050
$945$	0	0
$946$	1.82681	0.0593946
$947$	10.2959	0.334572	0.167286	−	0.985908i	$-0.446500\pi$
$947$	10.2959	0.334572	0.167286	+	0.985908i	$0.446500\pi$
$948$	9.54725	0.310080
$949$	−1.20125	−0.0389941
$950$	22.6250	0.734051
$951$	−18.8666	−0.611791
$952$	0	0
$953$	−46.6188	−1.51013	−0.755066	−	0.655649i	$-0.772395\pi$
$953$	−46.6188	−1.51013	−0.755066	+	0.655649i	$0.772395\pi$
$954$	−15.8483	−0.513107
$955$	−0.487317	−0.0157692
$956$	−8.10556	−0.262152
$957$	−0.789989	−0.0255367
$958$	−24.7973	−0.801164
$959$	0	0
$960$	−1.83527	−0.0592331
$961$	67.4750	2.17661
$962$	61.3828	1.97906
$963$	−5.63970	−0.181737
$964$	−22.6401	−0.729187
$965$	14.4658	0.465669
$966$	0	0
$967$	5.94014	0.191022	0.0955110	−	0.995428i	$-0.469551\pi$
$967$	5.94014	0.191022	0.0955110	+	0.995428i	$0.469551\pi$
$968$	−19.5064	−0.626961
$969$	−17.2610	−0.554502
$970$	3.93641	0.126390
$971$	−17.9832	−0.577108	−0.288554	−	0.957464i	$-0.593174\pi$
$971$	−17.9832	−0.577108	−0.288554	+	0.957464i	$0.593174\pi$
$972$	0.875138	0.0280701
$973$	0	0
$974$	−19.1564	−0.613811
$975$	28.0399	0.897995
$976$	23.1140	0.739861
$977$	6.77252	0.216672	0.108336	−	0.994114i	$-0.465448\pi$
$977$	6.77252	0.216672	0.108336	+	0.994114i	$0.465448\pi$
$978$	−29.5840	−0.945991
$979$	−5.84970	−0.186957
$980$	0	0
$981$	11.6710	0.372626
$982$	−3.49746	−0.111608
$983$	−32.4471	−1.03490	−0.517451	−	0.855713i	$-0.673119\pi$
$983$	−32.4471	−1.03490	−0.517451	+	0.855713i	$0.673119\pi$
$984$	1.90734	0.0608039
$985$	−15.5351	−0.494990
$986$	8.35828	0.266182
$987$	0	0
$988$	−18.2066	−0.579229
$989$	−10.5132	−0.334300
$990$	−1.29899	−0.0412847
$991$	55.2504	1.75509	0.877543	−	0.479498i	$-0.159181\pi$
$991$	55.2504	1.75509	0.877543	+	0.479498i	$0.159181\pi$
$992$	−46.0150	−1.46098
$993$	2.11679	0.0671743
$994$	0	0
$995$	−1.48107	−0.0469532
$996$	10.5004	0.332717
$997$	−16.2776	−0.515517	−0.257758	−	0.966209i	$-0.582984\pi$
$997$	−16.2776	−0.515517	−0.257758	+	0.966209i	$0.582984\pi$
$998$	26.5883	0.841637
$999$	5.47498	0.173221

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.be.1.2	yes	10
7.6	odd	2		6027.2.a.bd.1.2	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.bd.1.2	✓	10	7.6	odd	2
6027.2.a.be.1.2	yes	10	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q-1.69562 q^{2} +1.00000 q^{3} +0.875138 q^{4} -0.871357 q^{5} -1.69562 q^{6} +1.90734 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.69562 q^{2} +1.00000 q^{3} +0.875138 q^{4} -0.871357 q^{5} -1.69562 q^{6} +1.90734 q^{8} +1.00000 q^{9} +1.47749 q^{10} -0.879188 q^{11} +0.875138 q^{12} -6.61203 q^{13} -0.871357 q^{15} -4.98441 q^{16} -5.48590 q^{17} -1.69562 q^{18} +3.14642 q^{19} -0.762557 q^{20} +1.49077 q^{22} -8.57933 q^{23} +1.90734 q^{24} -4.24074 q^{25} +11.2115 q^{26} +1.00000 q^{27} +0.898544 q^{29} +1.47749 q^{30} -9.92346 q^{31} +4.63700 q^{32} -0.879188 q^{33} +9.30202 q^{34} +0.875138 q^{36} +5.47498 q^{37} -5.33515 q^{38} -6.61203 q^{39} -1.66198 q^{40} +1.00000 q^{41} +1.22541 q^{43} -0.769411 q^{44} -0.871357 q^{45} +14.5473 q^{46} -4.45708 q^{47} -4.98441 q^{48} +7.19069 q^{50} -5.48590 q^{51} -5.78644 q^{52} +9.34659 q^{53} -1.69562 q^{54} +0.766086 q^{55} +3.14642 q^{57} -1.52359 q^{58} -6.59869 q^{59} -0.762557 q^{60} -4.63726 q^{61} +16.8264 q^{62} +2.10622 q^{64} +5.76143 q^{65} +1.49077 q^{66} -8.87174 q^{67} -4.80092 q^{68} -8.57933 q^{69} +11.3486 q^{71} +1.90734 q^{72} +0.181676 q^{73} -9.28350 q^{74} -4.24074 q^{75} +2.75356 q^{76} +11.2115 q^{78} +10.9094 q^{79} +4.34320 q^{80} +1.00000 q^{81} -1.69562 q^{82} +11.9985 q^{83} +4.78018 q^{85} -2.07784 q^{86} +0.898544 q^{87} -1.67691 q^{88} +6.65352 q^{89} +1.47749 q^{90} -7.50810 q^{92} -9.92346 q^{93} +7.55754 q^{94} -2.74166 q^{95} +4.63700 q^{96} +2.66425 q^{97} -0.879188 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + 10 q^{3} + 18 q^{4} + 6 q^{5} + 4 q^{6} + 12 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 + 10 * q^3 + 18 * q^4 + 6 * q^5 + 4 * q^6 + 12 * q^8 + 10 * q^9	\( 10 q + 4 q^{2} + 10 q^{3} + 18 q^{4} + 6 q^{5} + 4 q^{6} + 12 q^{8} + 10 q^{9} + 2 q^{10} - 2 q^{11} + 18 q^{12} + 6 q^{15} + 14 q^{16} + 8 q^{17} + 4 q^{18} + 6 q^{19} + 20 q^{20} + 2 q^{22} + 12 q^{24} + 10 q^{25} + 16 q^{26} + 10 q^{27} + 16 q^{29} + 2 q^{30} + 2 q^{31} + 38 q^{32} - 2 q^{33} - 4 q^{34} + 18 q^{36} + 24 q^{37} - 26 q^{38} + 40 q^{40} + 10 q^{41} + 8 q^{43} - 8 q^{44} + 6 q^{45} + 4 q^{46} - 8 q^{47} + 14 q^{48} + 44 q^{50} + 8 q^{51} - 30 q^{52} + 24 q^{53} + 4 q^{54} + 6 q^{57} - 14 q^{58} + 6 q^{59} + 20 q^{60} - 14 q^{61} - 2 q^{62} + 86 q^{64} + 28 q^{65} + 2 q^{66} + 26 q^{67} - 6 q^{68} + 14 q^{71} + 12 q^{72} - 36 q^{73} + 18 q^{74} + 10 q^{75} - 32 q^{76} + 16 q^{78} + 20 q^{79} + 70 q^{80} + 10 q^{81} + 4 q^{82} + 40 q^{83} + 24 q^{85} - 36 q^{86} + 16 q^{87} + 14 q^{88} + 2 q^{89} + 2 q^{90} + 8 q^{92} + 2 q^{93} - 54 q^{94} - 24 q^{95} + 38 q^{96} + 16 q^{97} - 2 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 + 10 * q^3 + 18 * q^4 + 6 * q^5 + 4 * q^6 + 12 * q^8 + 10 * q^9 + 2 * q^10 - 2 * q^11 + 18 * q^12 + 6 * q^15 + 14 * q^16 + 8 * q^17 + 4 * q^18 + 6 * q^19 + 20 * q^20 + 2 * q^22 + 12 * q^24 + 10 * q^25 + 16 * q^26 + 10 * q^27 + 16 * q^29 + 2 * q^30 + 2 * q^31 + 38 * q^32 - 2 * q^33 - 4 * q^34 + 18 * q^36 + 24 * q^37 - 26 * q^38 + 40 * q^40 + 10 * q^41 + 8 * q^43 - 8 * q^44 + 6 * q^45 + 4 * q^46 - 8 * q^47 + 14 * q^48 + 44 * q^50 + 8 * q^51 - 30 * q^52 + 24 * q^53 + 4 * q^54 + 6 * q^57 - 14 * q^58 + 6 * q^59 + 20 * q^60 - 14 * q^61 - 2 * q^62 + 86 * q^64 + 28 * q^65 + 2 * q^66 + 26 * q^67 - 6 * q^68 + 14 * q^71 + 12 * q^72 - 36 * q^73 + 18 * q^74 + 10 * q^75 - 32 * q^76 + 16 * q^78 + 20 * q^79 + 70 * q^80 + 10 * q^81 + 4 * q^82 + 40 * q^83 + 24 * q^85 - 36 * q^86 + 16 * q^87 + 14 * q^88 + 2 * q^89 + 2 * q^90 + 8 * q^92 + 2 * q^93 - 54 * q^94 - 24 * q^95 + 38 * q^96 + 16 * q^97 - 2 * q^99

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