LMFDB - Embedded newform 7007.2.a.w.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7007,2,Mod(1,7007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7007, 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("7007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7007 = 7^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7007.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:	$55.9511766963$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - x^{10} - 18x^{9} + 15x^{8} + 117x^{7} - 78x^{6} - 326x^{5} + 167x^{4} + 348x^{3} - 143x^{2} - 74x + 24 $ x^11 - x^10 - 18x^9 + 15x^8 + 117x^7 - 78x^6 - 326x^5 + 167x^4 + 348x^3 - 143x^2 - 74*x + 24
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 1001)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.69905$ of defining polynomial
Character	$\chi$	$=$	7007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69905 q^{2} +3.23405 q^{3} +5.28489 q^{4} +1.09400 q^{5} -8.72887 q^{6} -8.86610 q^{8} +7.45906 q^{9} +O(q^{10})$	\(q-2.69905 q^{2} +3.23405 q^{3} +5.28489 q^{4} +1.09400 q^{5} -8.72887 q^{6} -8.86610 q^{8} +7.45906 q^{9} -2.95277 q^{10} +1.00000 q^{11} +17.0916 q^{12} -1.00000 q^{13} +3.53805 q^{15} +13.3603 q^{16} -5.45836 q^{17} -20.1324 q^{18} -7.90124 q^{19} +5.78168 q^{20} -2.69905 q^{22} -1.74754 q^{23} -28.6734 q^{24} -3.80316 q^{25} +2.69905 q^{26} +14.4208 q^{27} -3.89998 q^{29} -9.54939 q^{30} -6.64408 q^{31} -18.3280 q^{32} +3.23405 q^{33} +14.7324 q^{34} +39.4203 q^{36} -1.89897 q^{37} +21.3259 q^{38} -3.23405 q^{39} -9.69953 q^{40} +10.8879 q^{41} -5.49656 q^{43} +5.28489 q^{44} +8.16022 q^{45} +4.71670 q^{46} -8.58665 q^{47} +43.2078 q^{48} +10.2649 q^{50} -17.6526 q^{51} -5.28489 q^{52} -1.66007 q^{53} -38.9225 q^{54} +1.09400 q^{55} -25.5530 q^{57} +10.5263 q^{58} -10.2796 q^{59} +18.6982 q^{60} +11.6603 q^{61} +17.9327 q^{62} +22.7476 q^{64} -1.09400 q^{65} -8.72887 q^{66} -1.71567 q^{67} -28.8468 q^{68} -5.65163 q^{69} -0.172973 q^{71} -66.1328 q^{72} -16.9234 q^{73} +5.12543 q^{74} -12.2996 q^{75} -41.7572 q^{76} +8.72887 q^{78} +9.86649 q^{79} +14.6162 q^{80} +24.2604 q^{81} -29.3870 q^{82} +0.360529 q^{83} -5.97145 q^{85} +14.8355 q^{86} -12.6127 q^{87} -8.86610 q^{88} +4.17298 q^{89} -22.0249 q^{90} -9.23556 q^{92} -21.4873 q^{93} +23.1758 q^{94} -8.64397 q^{95} -59.2735 q^{96} -8.09496 q^{97} +7.45906 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - q^{2} - 2 q^{3} + 15 q^{4} - 7 q^{5} - 3 q^{6} - 6 q^{8} + 15 q^{9}+O(q^{10}) $ 11 * q - q^2 - 2 * q^3 + 15 * q^4 - 7 * q^5 - 3 * q^6 - 6 * q^8 + 15 * q^9	$ 11 q - q^{2} - 2 q^{3} + 15 q^{4} - 7 q^{5} - 3 q^{6} - 6 q^{8} + 15 q^{9} - q^{10} + 11 q^{11} + 5 q^{12} - 11 q^{13} + 4 q^{15} + 15 q^{16} - 7 q^{17} - 17 q^{18} - 22 q^{19} - 6 q^{20} - q^{22} + 3 q^{23} - 17 q^{24} + 10 q^{25} + q^{26} - 2 q^{27} - 6 q^{29} - 40 q^{30} - 28 q^{31} - 23 q^{32} - 2 q^{33} - 19 q^{34} + 48 q^{36} + q^{37} + 20 q^{38} + 2 q^{39} - 16 q^{40} + 4 q^{41} - 8 q^{43} + 15 q^{44} - 12 q^{45} + 2 q^{46} - 22 q^{47} + 30 q^{48} - 24 q^{50} - 27 q^{51} - 15 q^{52} + 9 q^{53} - 36 q^{54} - 7 q^{55} - 34 q^{57} - 8 q^{58} + 2 q^{59} + 25 q^{60} - 8 q^{62} - 10 q^{64} + 7 q^{65} - 3 q^{66} + 23 q^{67} - 24 q^{68} - 7 q^{69} + 3 q^{71} - 76 q^{72} - 29 q^{73} + 15 q^{74} - 36 q^{75} - 62 q^{76} + 3 q^{78} + 26 q^{79} + 16 q^{80} + 7 q^{81} + 16 q^{82} - 9 q^{83} - 31 q^{85} + 28 q^{86} - 13 q^{87} - 6 q^{88} - 9 q^{89} + 26 q^{90} - 58 q^{92} - 24 q^{93} + 34 q^{94} - 14 q^{95} - 56 q^{96} - 40 q^{97} + 15 q^{99}+O(q^{100}) $ 11 * q - q^2 - 2 * q^3 + 15 * q^4 - 7 * q^5 - 3 * q^6 - 6 * q^8 + 15 * q^9 - q^10 + 11 * q^11 + 5 * q^12 - 11 * q^13 + 4 * q^15 + 15 * q^16 - 7 * q^17 - 17 * q^18 - 22 * q^19 - 6 * q^20 - q^22 + 3 * q^23 - 17 * q^24 + 10 * q^25 + q^26 - 2 * q^27 - 6 * q^29 - 40 * q^30 - 28 * q^31 - 23 * q^32 - 2 * q^33 - 19 * q^34 + 48 * q^36 + q^37 + 20 * q^38 + 2 * q^39 - 16 * q^40 + 4 * q^41 - 8 * q^43 + 15 * q^44 - 12 * q^45 + 2 * q^46 - 22 * q^47 + 30 * q^48 - 24 * q^50 - 27 * q^51 - 15 * q^52 + 9 * q^53 - 36 * q^54 - 7 * q^55 - 34 * q^57 - 8 * q^58 + 2 * q^59 + 25 * q^60 - 8 * q^62 - 10 * q^64 + 7 * q^65 - 3 * q^66 + 23 * q^67 - 24 * q^68 - 7 * q^69 + 3 * q^71 - 76 * q^72 - 29 * q^73 + 15 * q^74 - 36 * q^75 - 62 * q^76 + 3 * q^78 + 26 * q^79 + 16 * q^80 + 7 * q^81 + 16 * q^82 - 9 * q^83 - 31 * q^85 + 28 * q^86 - 13 * q^87 - 6 * q^88 - 9 * q^89 + 26 * q^90 - 58 * q^92 - 24 * q^93 + 34 * q^94 - 14 * q^95 - 56 * q^96 - 40 * q^97 + 15 * 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 $

$2$	−2.69905	−1.90852	−0.954260	−	0.298979i	$-0.903354\pi$
$2$	−2.69905	−1.90852	−0.954260	+	0.298979i	$0.903354\pi$
$3$	3.23405	1.86718	0.933589	−	0.358346i	$-0.116659\pi$
$3$	3.23405	1.86718	0.933589	+	0.358346i	$0.116659\pi$
$4$	5.28489	2.64245
$5$	1.09400	0.489252	0.244626	−	0.969617i	$-0.421335\pi$
$5$	1.09400	0.489252	0.244626	+	0.969617i	$0.421335\pi$
$6$	−8.72887	−3.56354
$7$	0	0
$7$	0	0
$8$	−8.86610	−3.13464
$9$	7.45906	2.48635
$10$	−2.95277	−0.933748
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	17.0916	4.93392
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	3.53805	0.913521
$16$	13.3603	3.34008
$17$	−5.45836	−1.32385	−0.661923	−	0.749572i	$-0.730259\pi$
$17$	−5.45836	−1.32385	−0.661923	+	0.749572i	$0.730259\pi$
$18$	−20.1324	−4.74525
$19$	−7.90124	−1.81267	−0.906335	−	0.422561i	$-0.861131\pi$
$19$	−7.90124	−1.81267	−0.906335	+	0.422561i	$0.861131\pi$
$20$	5.78168	1.29282
$21$	0	0
$22$	−2.69905	−0.575440
$23$	−1.74754	−0.364387	−0.182194	−	0.983263i	$-0.558320\pi$
$23$	−1.74754	−0.364387	−0.182194	+	0.983263i	$0.558320\pi$
$24$	−28.6734	−5.85293
$25$	−3.80316	−0.760632
$26$	2.69905	0.529328
$27$	14.4208	2.77528
$28$	0	0
$29$	−3.89998	−0.724208	−0.362104	−	0.932138i	$-0.617941\pi$
$29$	−3.89998	−0.724208	−0.362104	+	0.932138i	$0.617941\pi$
$30$	−9.54939	−1.74347
$31$	−6.64408	−1.19331	−0.596656	−	0.802497i	$-0.703504\pi$
$31$	−6.64408	−1.19331	−0.596656	+	0.802497i	$0.703504\pi$
$32$	−18.3280	−3.23996
$33$	3.23405	0.562975
$34$	14.7324	2.52659
$35$	0	0
$36$	39.4203	6.57005
$37$	−1.89897	−0.312189	−0.156095	−	0.987742i	$-0.549890\pi$
$37$	−1.89897	−0.312189	−0.156095	+	0.987742i	$0.549890\pi$
$38$	21.3259	3.45951
$39$	−3.23405	−0.517862
$40$	−9.69953	−1.53363
$41$	10.8879	1.70040	0.850202	−	0.526457i	$-0.176480\pi$
$41$	10.8879	1.70040	0.850202	+	0.526457i	$0.176480\pi$
$42$	0	0
$43$	−5.49656	−0.838217	−0.419109	−	0.907936i	$-0.637657\pi$
$43$	−5.49656	−0.838217	−0.419109	+	0.907936i	$0.637657\pi$
$44$	5.28489	0.796727
$45$	8.16022	1.21645
$46$	4.71670	0.695440
$47$	−8.58665	−1.25249	−0.626246	−	0.779626i	$-0.715409\pi$
$47$	−8.58665	−1.25249	−0.626246	+	0.779626i	$0.715409\pi$
$48$	43.2078	6.23651
$49$	0	0
$50$	10.2649	1.45168
$51$	−17.6526	−2.47186
$52$	−5.28489	−0.732883
$53$	−1.66007	−0.228028	−0.114014	−	0.993479i	$-0.536371\pi$
$53$	−1.66007	−0.228028	−0.114014	+	0.993479i	$0.536371\pi$
$54$	−38.9225	−5.29668
$55$	1.09400	0.147515
$56$	0	0
$57$	−25.5530	−3.38458
$58$	10.5263	1.38216
$59$	−10.2796	−1.33829	−0.669145	−	0.743132i	$-0.733339\pi$
$59$	−10.2796	−1.33829	−0.669145	+	0.743132i	$0.733339\pi$
$60$	18.6982	2.41393
$61$	11.6603	1.49295	0.746474	−	0.665414i	$-0.231745\pi$
$61$	11.6603	1.49295	0.746474	+	0.665414i	$0.231745\pi$
$62$	17.9327	2.27746
$63$	0	0
$64$	22.7476	2.84345
$65$	−1.09400	−0.135694
$66$	−8.72887	−1.07445
$67$	−1.71567	−0.209603	−0.104801	−	0.994493i	$-0.533421\pi$
$67$	−1.71567	−0.209603	−0.104801	+	0.994493i	$0.533421\pi$
$68$	−28.8468	−3.49819
$69$	−5.65163	−0.680376
$70$	0	0
$71$	−0.172973	−0.0205282	−0.0102641	−	0.999947i	$-0.503267\pi$
$71$	−0.172973	−0.0205282	−0.0102641	+	0.999947i	$0.503267\pi$
$72$	−66.1328	−7.79382
$73$	−16.9234	−1.98073	−0.990366	−	0.138475i	$-0.955780\pi$
$73$	−16.9234	−1.98073	−0.990366	+	0.138475i	$0.955780\pi$
$74$	5.12543	0.595819
$75$	−12.2996	−1.42024
$76$	−41.7572	−4.78988
$77$	0	0
$78$	8.72887	0.988349
$79$	9.86649	1.11007	0.555033	−	0.831828i	$-0.312705\pi$
$79$	9.86649	1.11007	0.555033	+	0.831828i	$0.312705\pi$
$80$	14.6162	1.63414
$81$	24.2604	2.69560
$82$	−29.3870	−3.24525
$83$	0.360529	0.0395732	0.0197866	−	0.999804i	$-0.493701\pi$
$83$	0.360529	0.0395732	0.0197866	+	0.999804i	$0.493701\pi$
$84$	0	0
$85$	−5.97145	−0.647695
$86$	14.8355	1.59975
$87$	−12.6127	−1.35222
$88$	−8.86610	−0.945130
$89$	4.17298	0.442335	0.221167	−	0.975236i	$-0.429013\pi$
$89$	4.17298	0.442335	0.221167	+	0.975236i	$0.429013\pi$
$90$	−22.0249	−2.32163
$91$	0	0
$92$	−9.23556	−0.962874
$93$	−21.4873	−2.22812
$94$	23.1758	2.39041
$95$	−8.64397	−0.886853
$96$	−59.2735	−6.04958
$97$	−8.09496	−0.821918	−0.410959	−	0.911654i	$-0.634806\pi$
$97$	−8.09496	−0.821918	−0.410959	+	0.911654i	$0.634806\pi$
$98$	0	0
$99$	7.45906	0.749664
$100$	−20.0993	−2.00993
$101$	2.56066	0.254796	0.127398	−	0.991852i	$-0.459338\pi$
$101$	2.56066	0.254796	0.127398	+	0.991852i	$0.459338\pi$
$102$	47.6453	4.71759
$103$	−2.99600	−0.295204	−0.147602	−	0.989047i	$-0.547156\pi$
$103$	−2.99600	−0.295204	−0.147602	+	0.989047i	$0.547156\pi$
$104$	8.86610	0.869393
$105$	0	0
$106$	4.48062	0.435196
$107$	6.00079	0.580118	0.290059	−	0.957009i	$-0.406325\pi$
$107$	6.00079	0.580118	0.290059	+	0.957009i	$0.406325\pi$
$108$	76.2124	7.33354
$109$	−13.8169	−1.32342	−0.661711	−	0.749759i	$-0.730169\pi$
$109$	−13.8169	−1.32342	−0.661711	+	0.749759i	$0.730169\pi$
$110$	−2.95277	−0.281536
$111$	−6.14137	−0.582913
$112$	0	0
$113$	1.63061	0.153395	0.0766975	−	0.997054i	$-0.475562\pi$
$113$	1.63061	0.153395	0.0766975	+	0.997054i	$0.475562\pi$
$114$	68.9689	6.45953
$115$	−1.91181	−0.178277
$116$	−20.6110	−1.91368
$117$	−7.45906	−0.689590
$118$	27.7452	2.55415
$119$	0	0
$120$	−31.3687	−2.86356
$121$	1.00000	0.0909091
$122$	−31.4718	−2.84932
$123$	35.2120	3.17496
$124$	−35.1132	−3.15326
$125$	−9.63067	−0.861394
$126$	0	0
$127$	2.94015	0.260896	0.130448	−	0.991455i	$-0.458358\pi$
$127$	2.94015	0.260896	0.130448	+	0.991455i	$0.458358\pi$
$128$	−24.7410	−2.18682
$129$	−17.7761	−1.56510
$130$	2.95277	0.258975
$131$	0.223641	0.0195396	0.00976980	−	0.999952i	$-0.496890\pi$
$131$	0.223641	0.0195396	0.00976980	+	0.999952i	$0.496890\pi$
$132$	17.0916	1.48763
$133$	0	0
$134$	4.63069	0.400031
$135$	15.7764	1.35781
$136$	48.3944	4.14978
$137$	4.44302	0.379593	0.189796	−	0.981823i	$-0.439217\pi$
$137$	4.44302	0.379593	0.189796	+	0.981823i	$0.439217\pi$
$138$	15.2540	1.29851
$139$	11.2403	0.953393	0.476696	−	0.879068i	$-0.341834\pi$
$139$	11.2403	0.953393	0.476696	+	0.879068i	$0.341834\pi$
$140$	0	0
$141$	−27.7696	−2.33863
$142$	0.466865	0.0391784
$143$	−1.00000	−0.0836242
$144$	99.6553	8.30460
$145$	−4.26658	−0.354320
$146$	45.6771	3.78027
$147$	0	0
$148$	−10.0359	−0.824943
$149$	14.0637	1.15214	0.576071	−	0.817400i	$-0.304585\pi$
$149$	14.0637	1.15214	0.576071	+	0.817400i	$0.304585\pi$
$150$	33.1973	2.71055
$151$	−0.0137347	−0.00111772	−0.000558859	−	1.00000i	$-0.500178\pi$
$151$	−0.0137347	−0.00111772	−0.000558859		1.00000i	$0.500178\pi$
$152$	70.0532	5.68207
$153$	−40.7142	−3.29155
$154$	0	0
$155$	−7.26863	−0.583831
$156$	−17.0916	−1.36842
$157$	−0.913661	−0.0729181	−0.0364590	−	0.999335i	$-0.511608\pi$
$157$	−0.913661	−0.0729181	−0.0364590	+	0.999335i	$0.511608\pi$
$158$	−26.6302	−2.11858
$159$	−5.36875	−0.425769
$160$	−20.0508	−1.58516
$161$	0	0
$162$	−65.4801	−5.14460
$163$	8.51718	0.667117	0.333558	−	0.942729i	$-0.391751\pi$
$163$	8.51718	0.667117	0.333558	+	0.942729i	$0.391751\pi$
$164$	57.5414	4.49323
$165$	3.53805	0.275437
$166$	−0.973088	−0.0755263
$167$	7.00337	0.541937	0.270969	−	0.962588i	$-0.412656\pi$
$167$	7.00337	0.541937	0.270969	+	0.962588i	$0.412656\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	16.1173	1.23614
$171$	−58.9358	−4.50694
$172$	−29.0487	−2.21494
$173$	0.265632	0.0201956	0.0100978	−	0.999949i	$-0.496786\pi$
$173$	0.265632	0.0201956	0.0100978	+	0.999949i	$0.496786\pi$
$174$	34.0424	2.58075
$175$	0	0
$176$	13.3603	1.00707
$177$	−33.2447	−2.49882
$178$	−11.2631	−0.844205
$179$	6.31979	0.472363	0.236182	−	0.971709i	$-0.424104\pi$
$179$	6.31979	0.472363	0.236182	+	0.971709i	$0.424104\pi$
$180$	43.1259	3.21441
$181$	−18.6729	−1.38795	−0.693973	−	0.720001i	$-0.744141\pi$
$181$	−18.6729	−1.38795	−0.693973	+	0.720001i	$0.744141\pi$
$182$	0	0
$183$	37.7100	2.78760
$184$	15.4939	1.14222
$185$	−2.07748	−0.152739
$186$	57.9953	4.25242
$187$	−5.45836	−0.399155
$188$	−45.3795	−3.30964
$189$	0	0
$190$	23.3305	1.69258
$191$	−3.28929	−0.238005	−0.119002	−	0.992894i	$-0.537970\pi$
$191$	−3.28929	−0.238005	−0.119002	+	0.992894i	$0.537970\pi$
$192$	73.5667	5.30922
$193$	−22.1181	−1.59210	−0.796049	−	0.605232i	$-0.793080\pi$
$193$	−22.1181	−1.59210	−0.796049	+	0.605232i	$0.793080\pi$
$194$	21.8487	1.56865
$195$	−3.53805	−0.253365
$196$	0	0
$197$	−4.20099	−0.299308	−0.149654	−	0.988738i	$-0.547816\pi$
$197$	−4.20099	−0.299308	−0.149654	+	0.988738i	$0.547816\pi$
$198$	−20.1324	−1.43075
$199$	−10.4712	−0.742284	−0.371142	−	0.928576i	$-0.621034\pi$
$199$	−10.4712	−0.742284	−0.371142	+	0.928576i	$0.621034\pi$
$200$	33.7192	2.38431
$201$	−5.54857	−0.391366
$202$	−6.91137	−0.486282
$203$	0	0
$204$	−93.2920	−6.53175
$205$	11.9114	0.831927
$206$	8.08635	0.563403
$207$	−13.0350	−0.905995
$208$	−13.3603	−0.926370
$209$	−7.90124	−0.546540
$210$	0	0
$211$	−18.9859	−1.30704	−0.653521	−	0.756909i	$-0.726709\pi$
$211$	−18.9859	−1.30704	−0.653521	+	0.756909i	$0.726709\pi$
$212$	−8.77329	−0.602552
$213$	−0.559404	−0.0383297
$214$	−16.1965	−1.10717
$215$	−6.01324	−0.410100
$216$	−127.856	−8.69952
$217$	0	0
$218$	37.2926	2.52577
$219$	−54.7310	−3.69838
$220$	5.78168	0.389801
$221$	5.45836	0.367169
$222$	16.5759	1.11250
$223$	4.68442	0.313692	0.156846	−	0.987623i	$-0.449867\pi$
$223$	4.68442	0.313692	0.156846	+	0.987623i	$0.449867\pi$
$224$	0	0
$225$	−28.3680	−1.89120
$226$	−4.40111	−0.292757
$227$	1.75847	0.116713	0.0583567	−	0.998296i	$-0.481414\pi$
$227$	1.75847	0.116713	0.0583567	+	0.998296i	$0.481414\pi$
$228$	−135.045	−8.94356
$229$	−23.1084	−1.52705	−0.763524	−	0.645780i	$-0.776532\pi$
$229$	−23.1084	−1.52705	−0.763524	+	0.645780i	$0.776532\pi$
$230$	5.16008	0.340246
$231$	0	0
$232$	34.5776	2.27013
$233$	−12.1317	−0.794777	−0.397388	−	0.917650i	$-0.630083\pi$
$233$	−12.1317	−0.794777	−0.397388	+	0.917650i	$0.630083\pi$
$234$	20.1324	1.31610
$235$	−9.39381	−0.612785
$236$	−54.3266	−3.53636
$237$	31.9087	2.07269
$238$	0	0
$239$	21.2188	1.37253	0.686266	−	0.727351i	$-0.259249\pi$
$239$	21.2188	1.37253	0.686266	+	0.727351i	$0.259249\pi$
$240$	47.2694	3.05123
$241$	24.2579	1.56259	0.781293	−	0.624164i	$-0.214560\pi$
$241$	24.2579	1.56259	0.781293	+	0.624164i	$0.214560\pi$
$242$	−2.69905	−0.173502
$243$	35.1968	2.25787
$244$	61.6235	3.94504
$245$	0	0
$246$	−95.0390	−6.05947
$247$	7.90124	0.502744
$248$	58.9071	3.74060
$249$	1.16597	0.0738903
$250$	25.9937	1.64399
$251$	1.61799	0.102127	0.0510633	−	0.998695i	$-0.483739\pi$
$251$	1.61799	0.102127	0.0510633	+	0.998695i	$0.483739\pi$
$252$	0	0
$253$	−1.74754	−0.109867
$254$	−7.93561	−0.497925
$255$	−19.3120	−1.20936
$256$	21.2821	1.33013
$257$	10.1271	0.631710	0.315855	−	0.948807i	$-0.397709\pi$
$257$	10.1271	0.631710	0.315855	+	0.948807i	$0.397709\pi$
$258$	47.9787	2.98703
$259$	0	0
$260$	−5.78168	−0.358565
$261$	−29.0902	−1.80064
$262$	−0.603619	−0.0372917
$263$	18.6982	1.15298	0.576490	−	0.817104i	$-0.304422\pi$
$263$	18.6982	1.15298	0.576490	+	0.817104i	$0.304422\pi$
$264$	−28.6734	−1.76472
$265$	−1.81612	−0.111563
$266$	0	0
$267$	13.4956	0.825918
$268$	−9.06715	−0.553864
$269$	−6.18853	−0.377321	−0.188661	−	0.982042i	$-0.560415\pi$
$269$	−6.18853	−0.377321	−0.188661	+	0.982042i	$0.560415\pi$
$270$	−42.5813	−2.59142
$271$	−25.9384	−1.57564	−0.787822	−	0.615903i	$-0.788791\pi$
$271$	−25.9384	−1.57564	−0.787822	+	0.615903i	$0.788791\pi$
$272$	−72.9253	−4.42175
$273$	0	0
$274$	−11.9920	−0.724460
$275$	−3.80316	−0.229339
$276$	−29.8682	−1.79786
$277$	7.91414	0.475515	0.237757	−	0.971325i	$-0.423588\pi$
$277$	7.91414	0.475515	0.237757	+	0.971325i	$0.423588\pi$
$278$	−30.3383	−1.81957
$279$	−49.5586	−2.96699
$280$	0	0
$281$	−1.23560	−0.0737096	−0.0368548	−	0.999321i	$-0.511734\pi$
$281$	−1.23560	−0.0737096	−0.0368548	+	0.999321i	$0.511734\pi$
$282$	74.9517	4.46331
$283$	12.0496	0.716277	0.358139	−	0.933668i	$-0.383412\pi$
$283$	12.0496	0.716277	0.358139	+	0.933668i	$0.383412\pi$
$284$	−0.914146	−0.0542446
$285$	−27.9550	−1.65591
$286$	2.69905	0.159598
$287$	0	0
$288$	−136.709	−8.05568
$289$	12.7937	0.752569
$290$	11.5157	0.676227
$291$	−26.1795	−1.53467
$292$	−89.4382	−5.23398
$293$	−22.8536	−1.33512	−0.667562	−	0.744554i	$-0.732662\pi$
$293$	−22.8536	−1.33512	−0.667562	+	0.744554i	$0.732662\pi$
$294$	0	0
$295$	−11.2459	−0.654762
$296$	16.8365	0.978601
$297$	14.4208	0.836780
$298$	−37.9587	−2.19889
$299$	1.74754	0.101063
$300$	−65.0020	−3.75289
$301$	0	0
$302$	0.0370708	0.00213318
$303$	8.28131	0.475749
$304$	−105.563	−6.05445
$305$	12.7564	0.730429
$306$	109.890	6.28198
$307$	6.23831	0.356039	0.178020	−	0.984027i	$-0.443031\pi$
$307$	6.23831	0.356039	0.178020	+	0.984027i	$0.443031\pi$
$308$	0	0
$309$	−9.68919	−0.551199
$310$	19.6184	1.11425
$311$	−19.0653	−1.08110	−0.540548	−	0.841313i	$-0.681783\pi$
$311$	−19.0653	−1.08110	−0.540548	+	0.841313i	$0.681783\pi$
$312$	28.6734	1.62331
$313$	0.473358	0.0267558	0.0133779	−	0.999911i	$-0.495742\pi$
$313$	0.473358	0.0267558	0.0133779	+	0.999911i	$0.495742\pi$
$314$	2.46602	0.139166
$315$	0	0
$316$	52.1433	2.93329
$317$	28.9737	1.62733	0.813663	−	0.581336i	$-0.197470\pi$
$317$	28.9737	1.62733	0.813663	+	0.581336i	$0.197470\pi$
$318$	14.4905	0.812589
$319$	−3.89998	−0.218357
$320$	24.8859	1.39116
$321$	19.4068	1.08318
$322$	0	0
$323$	43.1278	2.39970
$324$	128.213	7.12297
$325$	3.80316	0.210961
$326$	−22.9883	−1.27321
$327$	−44.6846	−2.47106
$328$	−96.5332	−5.33015
$329$	0	0
$330$	−9.54939	−0.525677
$331$	−20.1497	−1.10753	−0.553765	−	0.832673i	$-0.686809\pi$
$331$	−20.1497	−1.10753	−0.553765	+	0.832673i	$0.686809\pi$
$332$	1.90536	0.104570
$333$	−14.1646	−0.776213
$334$	−18.9025	−1.03430
$335$	−1.87695	−0.102549
$336$	0	0
$337$	−4.99966	−0.272349	−0.136175	−	0.990685i	$-0.543481\pi$
$337$	−4.99966	−0.272349	−0.136175	+	0.990685i	$0.543481\pi$
$338$	−2.69905	−0.146809
$339$	5.27347	0.286416
$340$	−31.5585	−1.71150
$341$	−6.64408	−0.359797
$342$	159.071	8.60157
$343$	0	0
$344$	48.7330	2.62751
$345$	−6.18289	−0.332875
$346$	−0.716955	−0.0385438
$347$	21.8453	1.17272	0.586359	−	0.810051i	$-0.300561\pi$
$347$	21.8453	1.17272	0.586359	+	0.810051i	$0.300561\pi$
$348$	−66.6568	−3.57318
$349$	23.9554	1.28230	0.641152	−	0.767414i	$-0.278457\pi$
$349$	23.9554	1.28230	0.641152	+	0.767414i	$0.278457\pi$
$350$	0	0
$351$	−14.4208	−0.769725
$352$	−18.3280	−0.976884
$353$	−27.7334	−1.47610	−0.738049	−	0.674747i	$-0.764253\pi$
$353$	−27.7334	−1.47610	−0.738049	+	0.674747i	$0.764253\pi$
$354$	89.7292	4.76906
$355$	−0.189233	−0.0100435
$356$	22.0537	1.16885
$357$	0	0
$358$	−17.0575	−0.901515
$359$	21.6475	1.14251	0.571255	−	0.820773i	$-0.306457\pi$
$359$	21.6475	1.14251	0.571255	+	0.820773i	$0.306457\pi$
$360$	−72.3494	−3.81315
$361$	43.4296	2.28577
$362$	50.3992	2.64892
$363$	3.23405	0.169743
$364$	0	0
$365$	−18.5142	−0.969078
$366$	−101.781	−5.32019
$367$	−26.2035	−1.36781	−0.683906	−	0.729570i	$-0.739720\pi$
$367$	−26.2035	−1.36781	−0.683906	+	0.729570i	$0.739720\pi$
$368$	−23.3477	−1.21708
$369$	81.2135	4.22780
$370$	5.60723	0.291506
$371$	0	0
$372$	−113.558	−5.88770
$373$	−37.9567	−1.96532	−0.982662	−	0.185408i	$-0.940639\pi$
$373$	−37.9567	−1.96532	−0.982662	+	0.185408i	$0.940639\pi$
$374$	14.7324	0.761794
$375$	−31.1460	−1.60837
$376$	76.1301	3.92611
$377$	3.89998	0.200859
$378$	0	0
$379$	24.0740	1.23660	0.618299	−	0.785943i	$-0.287822\pi$
$379$	24.0740	1.23660	0.618299	+	0.785943i	$0.287822\pi$
$380$	−45.6825	−2.34346
$381$	9.50857	0.487139
$382$	8.87798	0.454237
$383$	31.2996	1.59933	0.799667	−	0.600444i	$-0.205009\pi$
$383$	31.2996	1.59933	0.799667	+	0.600444i	$0.205009\pi$
$384$	−80.0135	−4.08317
$385$	0	0
$386$	59.6981	3.03855
$387$	−40.9992	−2.08410
$388$	−42.7810	−2.17187
$389$	−4.90825	−0.248858	−0.124429	−	0.992228i	$-0.539710\pi$
$389$	−4.90825	−0.248858	−0.124429	+	0.992228i	$0.539710\pi$
$390$	9.54939	0.483552
$391$	9.53870	0.482393
$392$	0	0
$393$	0.723265	0.0364839
$394$	11.3387	0.571235
$395$	10.7940	0.543103
$396$	39.4203	1.98095
$397$	−0.546198	−0.0274129	−0.0137064	−	0.999906i	$-0.504363\pi$
$397$	−0.546198	−0.0274129	−0.0137064	+	0.999906i	$0.504363\pi$
$398$	28.2624	1.41666
$399$	0	0
$400$	−50.8114	−2.54057
$401$	1.16405	0.0581297	0.0290648	−	0.999578i	$-0.490747\pi$
$401$	1.16405	0.0581297	0.0290648	+	0.999578i	$0.490747\pi$
$402$	14.9759	0.746929
$403$	6.64408	0.330965
$404$	13.5328	0.673284
$405$	26.5409	1.31883
$406$	0	0
$407$	−1.89897	−0.0941286
$408$	156.510	7.74838
$409$	−12.1178	−0.599189	−0.299595	−	0.954067i	$-0.596851\pi$
$409$	−12.1178	−0.599189	−0.299595	+	0.954067i	$0.596851\pi$
$410$	−32.1495	−1.58775
$411$	14.3689	0.708768
$412$	−15.8335	−0.780061
$413$	0	0
$414$	35.1822	1.72911
$415$	0.394420	0.0193613
$416$	18.3280	0.898603
$417$	36.3518	1.78015
$418$	21.3259	1.04308
$419$	22.5539	1.10183	0.550915	−	0.834561i	$-0.314279\pi$
$419$	22.5539	1.10183	0.550915	+	0.834561i	$0.314279\pi$
$420$	0	0
$421$	34.7424	1.69324	0.846621	−	0.532197i	$-0.178633\pi$
$421$	34.7424	1.69324	0.846621	+	0.532197i	$0.178633\pi$
$422$	51.2439	2.49451
$423$	−64.0483	−3.11414
$424$	14.7184	0.714786
$425$	20.7590	1.00696
$426$	1.50986	0.0731531
$427$	0	0
$428$	31.7135	1.53293
$429$	−3.23405	−0.156141
$430$	16.2301	0.782684
$431$	−6.46464	−0.311391	−0.155695	−	0.987805i	$-0.549762\pi$
$431$	−6.46464	−0.311391	−0.155695	+	0.987805i	$0.549762\pi$
$432$	192.666	9.26966
$433$	−12.5238	−0.601856	−0.300928	−	0.953647i	$-0.597296\pi$
$433$	−12.5238	−0.601856	−0.300928	+	0.953647i	$0.597296\pi$
$434$	0	0
$435$	−13.7983	−0.661579
$436$	−73.0209	−3.49707
$437$	13.8077	0.660514
$438$	147.722	7.05843
$439$	22.4864	1.07322	0.536609	−	0.843831i	$-0.319705\pi$
$439$	22.4864	1.07322	0.536609	+	0.843831i	$0.319705\pi$
$440$	−9.69953	−0.462407
$441$	0	0
$442$	−14.7324	−0.700749
$443$	17.4883	0.830893	0.415447	−	0.909618i	$-0.363625\pi$
$443$	17.4883	0.830893	0.415447	+	0.909618i	$0.363625\pi$
$444$	−32.4565	−1.54032
$445$	4.56525	0.216413
$446$	−12.6435	−0.598687
$447$	45.4826	2.15125
$448$	0	0
$449$	26.6283	1.25667	0.628335	−	0.777943i	$-0.283737\pi$
$449$	26.6283	1.25667	0.628335	+	0.777943i	$0.283737\pi$
$450$	76.5667	3.60939
$451$	10.8879	0.512691
$452$	8.61761	0.405338
$453$	−0.0444188	−0.00208698
$454$	−4.74619	−0.222750
$455$	0	0
$456$	226.555	10.6094
$457$	27.6267	1.29232	0.646162	−	0.763200i	$-0.276373\pi$
$457$	27.6267	1.29232	0.646162	+	0.763200i	$0.276373\pi$
$458$	62.3709	2.91440
$459$	−78.7139	−3.67405
$460$	−10.1037	−0.471088
$461$	22.3022	1.03872	0.519360	−	0.854556i	$-0.326171\pi$
$461$	22.3022	1.03872	0.519360	+	0.854556i	$0.326171\pi$
$462$	0	0
$463$	−1.70032	−0.0790204	−0.0395102	−	0.999219i	$-0.512580\pi$
$463$	−1.70032	−0.0790204	−0.0395102	+	0.999219i	$0.512580\pi$
$464$	−52.1049	−2.41891
$465$	−23.5071	−1.09012
$466$	32.7442	1.51685
$467$	15.2242	0.704492	0.352246	−	0.935908i	$-0.385418\pi$
$467$	15.2242	0.704492	0.352246	+	0.935908i	$0.385418\pi$
$468$	−39.4203	−1.82220
$469$	0	0
$470$	25.3544	1.16951
$471$	−2.95482	−0.136151
$472$	91.1400	4.19506
$473$	−5.49656	−0.252732
$474$	−86.1233	−3.95577
$475$	30.0497	1.37877
$476$	0	0
$477$	−12.3826	−0.566959
$478$	−57.2708	−2.61950
$479$	−33.4170	−1.52686	−0.763430	−	0.645891i	$-0.776486\pi$
$479$	−33.4170	−1.52686	−0.763430	+	0.645891i	$0.776486\pi$
$480$	−64.8453	−2.95977
$481$	1.89897	0.0865857
$482$	−65.4733	−2.98223
$483$	0	0
$484$	5.28489	0.240222
$485$	−8.85590	−0.402125
$486$	−94.9980	−4.30920
$487$	15.5252	0.703515	0.351757	−	0.936091i	$-0.385584\pi$
$487$	15.5252	0.703515	0.351757	+	0.936091i	$0.385584\pi$
$488$	−103.381	−4.67986
$489$	27.5449	1.24563
$490$	0	0
$491$	−2.13059	−0.0961523	−0.0480761	−	0.998844i	$-0.515309\pi$
$491$	−2.13059	−0.0961523	−0.0480761	+	0.998844i	$0.515309\pi$
$492$	186.091	8.38965
$493$	21.2875	0.958740
$494$	−21.3259	−0.959497
$495$	8.16022	0.366775
$496$	−88.7669	−3.98575
$497$	0	0
$498$	−3.14701	−0.141021
$499$	−25.4753	−1.14043	−0.570215	−	0.821495i	$-0.693140\pi$
$499$	−25.4753	−1.14043	−0.570215	+	0.821495i	$0.693140\pi$
$500$	−50.8971	−2.27619
$501$	22.6492	1.01189
$502$	−4.36705	−0.194911
$503$	1.51953	0.0677526	0.0338763	−	0.999426i	$-0.489215\pi$
$503$	1.51953	0.0677526	0.0338763	+	0.999426i	$0.489215\pi$
$504$	0	0
$505$	2.80137	0.124659
$506$	4.71670	0.209683
$507$	3.23405	0.143629
$508$	15.5384	0.689403
$509$	−24.7256	−1.09594	−0.547970	−	0.836498i	$-0.684599\pi$
$509$	−24.7256	−1.09594	−0.547970	+	0.836498i	$0.684599\pi$
$510$	52.1240	2.30809
$511$	0	0
$512$	−7.95963	−0.351769
$513$	−113.942	−5.03067
$514$	−27.3335	−1.20563
$515$	−3.27762	−0.144429
$516$	−93.9449	−4.13569
$517$	−8.58665	−0.377641
$518$	0	0
$519$	0.859067	0.0377088
$520$	9.69953	0.425353
$521$	6.26803	0.274607	0.137304	−	0.990529i	$-0.456156\pi$
$521$	6.26803	0.274607	0.137304	+	0.990529i	$0.456156\pi$
$522$	78.5159	3.43655
$523$	−39.5261	−1.72835	−0.864177	−	0.503188i	$-0.832160\pi$
$523$	−39.5261	−1.72835	−0.864177	+	0.503188i	$0.832160\pi$
$524$	1.18192	0.0516323
$525$	0	0
$526$	−50.4674	−2.20048
$527$	36.2658	1.57976
$528$	43.2078	1.88038
$529$	−19.9461	−0.867222
$530$	4.90181	0.212921
$531$	−76.6761	−3.32746
$532$	0	0
$533$	−10.8879	−0.471607
$534$	−36.4254	−1.57628
$535$	6.56488	0.283824
$536$	15.2113	0.657029
$537$	20.4385	0.881986
$538$	16.7032	0.720125
$539$	0	0
$540$	83.3765	3.58795
$541$	20.5593	0.883914	0.441957	−	0.897036i	$-0.354284\pi$
$541$	20.5593	0.883914	0.441957	+	0.897036i	$0.354284\pi$
$542$	70.0090	3.00715
$543$	−60.3890	−2.59154
$544$	100.041	4.28921
$545$	−15.1157	−0.647487
$546$	0	0
$547$	−21.8031	−0.932233	−0.466116	−	0.884723i	$-0.654347\pi$
$547$	−21.8031	−0.932233	−0.466116	+	0.884723i	$0.654347\pi$
$548$	23.4809	1.00305
$549$	86.9749	3.71200
$550$	10.2649	0.437698
$551$	30.8147	1.31275
$552$	50.1079	2.13273
$553$	0	0
$554$	−21.3607	−0.907529
$555$	−6.71867	−0.285192
$556$	59.4040	2.51929
$557$	−22.9564	−0.972694	−0.486347	−	0.873766i	$-0.661671\pi$
$557$	−22.9564	−0.972694	−0.486347	+	0.873766i	$0.661671\pi$
$558$	133.761	5.66256
$559$	5.49656	0.232480
$560$	0	0
$561$	−17.6526	−0.745293
$562$	3.33495	0.140676
$563$	−22.3932	−0.943759	−0.471880	−	0.881663i	$-0.656424\pi$
$563$	−22.3932	−0.943759	−0.471880	+	0.881663i	$0.656424\pi$
$564$	−146.760	−6.17969
$565$	1.78389	0.0750489
$566$	−32.5226	−1.36703
$567$	0	0
$568$	1.53360	0.0643484
$569$	−17.5170	−0.734350	−0.367175	−	0.930152i	$-0.619675\pi$
$569$	−17.5170	−0.734350	−0.367175	+	0.930152i	$0.619675\pi$
$570$	75.4521	3.16034
$571$	26.2771	1.09966	0.549830	−	0.835276i	$-0.314692\pi$
$571$	26.2771	1.09966	0.549830	+	0.835276i	$0.314692\pi$
$572$	−5.28489	−0.220972
$573$	−10.6377	−0.444398
$574$	0	0
$575$	6.64617	0.277165
$576$	169.675	7.06981
$577$	25.3847	1.05678	0.528390	−	0.849002i	$-0.322796\pi$
$577$	25.3847	1.05678	0.528390	+	0.849002i	$0.322796\pi$
$578$	−34.5308	−1.43629
$579$	−71.5311	−2.97273
$580$	−22.5484	−0.936273
$581$	0	0
$582$	70.6598	2.92894
$583$	−1.66007	−0.0687531
$584$	150.044	6.20888
$585$	−8.16022	−0.337384
$586$	61.6832	2.54811
$587$	−25.4861	−1.05192	−0.525962	−	0.850508i	$-0.676295\pi$
$587$	−25.4861	−1.05192	−0.525962	+	0.850508i	$0.676295\pi$
$588$	0	0
$589$	52.4965	2.16308
$590$	30.3533	1.24963
$591$	−13.5862	−0.558861
$592$	−25.3709	−1.04274
$593$	−3.59576	−0.147660	−0.0738300	−	0.997271i	$-0.523522\pi$
$593$	−3.59576	−0.147660	−0.0738300	+	0.997271i	$0.523522\pi$
$594$	−38.9225	−1.59701
$595$	0	0
$596$	74.3251	3.04447
$597$	−33.8644	−1.38598
$598$	−4.71670	−0.192880
$599$	24.0909	0.984326	0.492163	−	0.870503i	$-0.336206\pi$
$599$	24.0909	0.984326	0.492163	+	0.870503i	$0.336206\pi$
$600$	109.049	4.45193
$601$	−20.6596	−0.842722	−0.421361	−	0.906893i	$-0.638448\pi$
$601$	−20.6596	−0.842722	−0.421361	+	0.906893i	$0.638448\pi$
$602$	0	0
$603$	−12.7973	−0.521146
$604$	−0.0725866	−0.00295351
$605$	1.09400	0.0444775
$606$	−22.3517	−0.907976
$607$	−10.6545	−0.432453	−0.216226	−	0.976343i	$-0.569375\pi$
$607$	−10.6545	−0.432453	−0.216226	+	0.976343i	$0.569375\pi$
$608$	144.814	5.87297
$609$	0	0
$610$	−34.4302	−1.39404
$611$	8.58665	0.347379
$612$	−215.170	−8.69774
$613$	−12.9288	−0.522188	−0.261094	−	0.965313i	$-0.584083\pi$
$613$	−12.9288	−0.522188	−0.261094	+	0.965313i	$0.584083\pi$
$614$	−16.8375	−0.679508
$615$	38.5220	1.55336
$616$	0	0
$617$	−21.2147	−0.854072	−0.427036	−	0.904235i	$-0.640442\pi$
$617$	−21.2147	−0.854072	−0.427036	+	0.904235i	$0.640442\pi$
$618$	26.1516	1.05197
$619$	28.4470	1.14338	0.571691	−	0.820469i	$-0.306288\pi$
$619$	28.4470	1.14338	0.571691	+	0.820469i	$0.306288\pi$
$620$	−38.4139	−1.54274
$621$	−25.2009	−1.01128
$622$	51.4583	2.06329
$623$	0	0
$624$	−43.2078	−1.72970
$625$	8.47983	0.339193
$626$	−1.27762	−0.0510639
$627$	−25.5530	−1.02049
$628$	−4.82860	−0.192682
$629$	10.3653	0.413291
$630$	0	0
$631$	34.4427	1.37114	0.685571	−	0.728005i	$-0.259552\pi$
$631$	34.4427	1.37114	0.685571	+	0.728005i	$0.259552\pi$
$632$	−87.4773	−3.47966
$633$	−61.4012	−2.44048
$634$	−78.2017	−3.10578
$635$	3.21653	0.127644
$636$	−28.3732	−1.12507
$637$	0	0
$638$	10.5263	0.416738
$639$	−1.29022	−0.0510403
$640$	−27.0667	−1.06991
$641$	1.86343	0.0736009	0.0368004	−	0.999323i	$-0.488283\pi$
$641$	1.86343	0.0736009	0.0368004	+	0.999323i	$0.488283\pi$
$642$	−52.3801	−2.06728
$643$	−8.57510	−0.338169	−0.169084	−	0.985602i	$-0.554081\pi$
$643$	−8.57510	−0.338169	−0.169084	+	0.985602i	$0.554081\pi$
$644$	0	0
$645$	−19.4471	−0.765729
$646$	−116.404	−4.57987
$647$	−6.50644	−0.255794	−0.127897	−	0.991787i	$-0.540823\pi$
$647$	−6.50644	−0.255794	−0.127897	+	0.991787i	$0.540823\pi$
$648$	−215.095	−8.44973
$649$	−10.2796	−0.403510
$650$	−10.2649	−0.402624
$651$	0	0
$652$	45.0124	1.76282
$653$	7.42216	0.290451	0.145226	−	0.989399i	$-0.453609\pi$
$653$	7.42216	0.290451	0.145226	+	0.989399i	$0.453609\pi$
$654$	120.606	4.71607
$655$	0.244664	0.00955980
$656$	145.466	5.67948
$657$	−126.232	−4.92480
$658$	0	0
$659$	−42.9309	−1.67235	−0.836175	−	0.548463i	$-0.815213\pi$
$659$	−42.9309	−1.67235	−0.836175	+	0.548463i	$0.815213\pi$
$660$	18.6982	0.727827
$661$	33.2698	1.29404	0.647022	−	0.762471i	$-0.276014\pi$
$661$	33.2698	1.29404	0.647022	+	0.762471i	$0.276014\pi$
$662$	54.3853	2.11374
$663$	17.6526	0.685570
$664$	−3.19649	−0.124048
$665$	0	0
$666$	38.2309	1.48142
$667$	6.81537	0.263892
$668$	37.0121	1.43204
$669$	15.1496	0.585719
$670$	5.06599	0.195716
$671$	11.6603	0.450141
$672$	0	0
$673$	44.2525	1.70581	0.852905	−	0.522066i	$-0.174839\pi$
$673$	44.2525	1.70581	0.852905	+	0.522066i	$0.174839\pi$
$674$	13.4944	0.519784
$675$	−54.8446	−2.11097
$676$	5.28489	0.203265
$677$	38.8341	1.49252	0.746258	−	0.665657i	$-0.231849\pi$
$677$	38.8341	1.49252	0.746258	+	0.665657i	$0.231849\pi$
$678$	−14.2334	−0.546630
$679$	0	0
$680$	52.9435	2.03029
$681$	5.68696	0.217925
$682$	17.9327	0.686680
$683$	44.5977	1.70648	0.853242	−	0.521515i	$-0.174633\pi$
$683$	44.5977	1.70648	0.853242	+	0.521515i	$0.174633\pi$
$684$	−311.469	−11.9093
$685$	4.86067	0.185717
$686$	0	0
$687$	−74.7337	−2.85127
$688$	−73.4357	−2.79971
$689$	1.66007	0.0632437
$690$	16.6879	0.635299
$691$	37.1335	1.41262	0.706312	−	0.707901i	$-0.250358\pi$
$691$	37.1335	1.41262	0.706312	+	0.707901i	$0.250358\pi$
$692$	1.40384	0.0533659
$693$	0	0
$694$	−58.9617	−2.23816
$695$	12.2969	0.466450
$696$	111.826	4.23874
$697$	−59.4300	−2.25107
$698$	−64.6570	−2.44730
$699$	−39.2346	−1.48399
$700$	0	0
$701$	0.497981	0.0188085	0.00940425	−	0.999956i	$-0.497006\pi$
$701$	0.497981	0.0188085	0.00940425	+	0.999956i	$0.497006\pi$
$702$	38.9225	1.46904
$703$	15.0042	0.565896
$704$	22.7476	0.857332
$705$	−30.3800	−1.14418
$706$	74.8538	2.81716
$707$	0	0
$708$	−175.695	−6.60301
$709$	−35.9108	−1.34866	−0.674329	−	0.738431i	$-0.735567\pi$
$709$	−35.9108	−1.34866	−0.674329	+	0.738431i	$0.735567\pi$
$710$	0.510751	0.0191681
$711$	73.5947	2.76002
$712$	−36.9981	−1.38656
$713$	11.6108	0.434828
$714$	0	0
$715$	−1.09400	−0.0409133
$716$	33.3994	1.24819
$717$	68.6227	2.56276
$718$	−58.4277	−2.18050
$719$	26.3380	0.982242	0.491121	−	0.871091i	$-0.336587\pi$
$719$	26.3380	0.982242	0.491121	+	0.871091i	$0.336587\pi$
$720$	109.023	4.06305
$721$	0	0
$722$	−117.219	−4.36244
$723$	78.4511	2.91763
$724$	−98.6843	−3.66757
$725$	14.8322	0.550856
$726$	−8.72887	−0.323959
$727$	−15.1342	−0.561295	−0.280647	−	0.959811i	$-0.590549\pi$
$727$	−15.1342	−0.561295	−0.280647	+	0.959811i	$0.590549\pi$
$728$	0	0
$729$	41.0469	1.52025
$730$	49.9708	1.84950
$731$	30.0022	1.10967
$732$	199.293	7.36609
$733$	−29.3122	−1.08267	−0.541335	−	0.840807i	$-0.682081\pi$
$733$	−29.3122	−1.08267	−0.541335	+	0.840807i	$0.682081\pi$
$734$	70.7247	2.61050
$735$	0	0
$736$	32.0289	1.18060
$737$	−1.71567	−0.0631976
$738$	−219.200	−8.06885
$739$	−34.9909	−1.28716	−0.643580	−	0.765379i	$-0.722551\pi$
$739$	−34.9909	−1.28716	−0.643580	+	0.765379i	$0.722551\pi$
$740$	−10.9793	−0.403606
$741$	25.5530	0.938712
$742$	0	0
$743$	35.9433	1.31863	0.659316	−	0.751866i	$-0.270846\pi$
$743$	35.9433	1.31863	0.659316	+	0.751866i	$0.270846\pi$
$744$	190.508	6.98437
$745$	15.3857	0.563688
$746$	102.447	3.75086
$747$	2.68921	0.0983930
$748$	−28.8468	−1.05474
$749$	0	0
$750$	84.0649	3.06961
$751$	15.5900	0.568887	0.284444	−	0.958693i	$-0.408191\pi$
$751$	15.5900	0.568887	0.284444	+	0.958693i	$0.408191\pi$
$752$	−114.720	−4.18342
$753$	5.23266	0.190689
$754$	−10.5263	−0.383343
$755$	−0.0150258	−0.000546846 0
$756$	0	0
$757$	3.97685	0.144541	0.0722706	−	0.997385i	$-0.476975\pi$
$757$	3.97685	0.144541	0.0722706	+	0.997385i	$0.476975\pi$
$758$	−64.9770	−2.36007
$759$	−5.65163	−0.205141
$760$	76.6383	2.77996
$761$	−3.75134	−0.135986	−0.0679929	−	0.997686i	$-0.521660\pi$
$761$	−3.75134	−0.135986	−0.0679929	+	0.997686i	$0.521660\pi$
$762$	−25.6641	−0.929714
$763$	0	0
$764$	−17.3836	−0.628915
$765$	−44.5414	−1.61040
$766$	−84.4793	−3.05236
$767$	10.2796	0.371175
$768$	68.8274	2.48360
$769$	−37.0444	−1.33586	−0.667928	−	0.744226i	$-0.732819\pi$
$769$	−37.0444	−1.33586	−0.667928	+	0.744226i	$0.732819\pi$
$770$	0	0
$771$	32.7515	1.17952
$772$	−116.892	−4.20704
$773$	−5.30474	−0.190798	−0.0953990	−	0.995439i	$-0.530413\pi$
$773$	−5.30474	−0.190798	−0.0953990	+	0.995439i	$0.530413\pi$
$774$	110.659	3.97755
$775$	25.2685	0.907671
$776$	71.7707	2.57642
$777$	0	0
$778$	13.2476	0.474951
$779$	−86.0279	−3.08227
$780$	−18.6982	−0.669504
$781$	−0.172973	−0.00618948
$782$	−25.7455	−0.920656
$783$	−56.2408	−2.00988
$784$	0	0
$785$	−0.999546	−0.0356753
$786$	−1.95213	−0.0696302
$787$	−21.0577	−0.750624	−0.375312	−	0.926898i	$-0.622464\pi$
$787$	−21.0577	−0.750624	−0.375312	+	0.926898i	$0.622464\pi$
$788$	−22.2018	−0.790906
$789$	60.4708	2.15282
$790$	−29.1335	−1.03652
$791$	0	0
$792$	−66.1328	−2.34993
$793$	−11.6603	−0.414070
$794$	1.47422	0.0523180
$795$	−5.87342	−0.208309
$796$	−55.3392	−1.96145
$797$	7.96663	0.282193	0.141096	−	0.989996i	$-0.454937\pi$
$797$	7.96663	0.282193	0.141096	+	0.989996i	$0.454937\pi$
$798$	0	0
$799$	46.8690	1.65811
$800$	69.7042	2.46442
$801$	31.1265	1.09980
$802$	−3.14182	−0.110942
$803$	−16.9234	−0.597213
$804$	−29.3236	−1.03416
$805$	0	0
$806$	−17.9327	−0.631653
$807$	−20.0140	−0.704526
$808$	−22.7031	−0.798693
$809$	−49.6420	−1.74532	−0.872659	−	0.488329i	$-0.837606\pi$
$809$	−49.6420	−1.74532	−0.872659	+	0.488329i	$0.837606\pi$
$810$	−71.6353	−2.51701
$811$	−12.9130	−0.453438	−0.226719	−	0.973960i	$-0.572800\pi$
$811$	−12.9130	−0.453438	−0.226719	+	0.973960i	$0.572800\pi$
$812$	0	0
$813$	−83.8859	−2.94201
$814$	5.12543	0.179646
$815$	9.31780	0.326388
$816$	−235.844	−8.25619
$817$	43.4296	1.51941
$818$	32.7067	1.14356
$819$	0	0
$820$	62.9504	2.19832
$821$	28.4338	0.992348	0.496174	−	0.868223i	$-0.334738\pi$
$821$	28.4338	0.992348	0.496174	+	0.868223i	$0.334738\pi$
$822$	−38.7825	−1.35270
$823$	−21.6054	−0.753118	−0.376559	−	0.926393i	$-0.622893\pi$
$823$	−21.6054	−0.753118	−0.376559	+	0.926393i	$0.622893\pi$
$824$	26.5628	0.925359
$825$	−12.2996	−0.428217
$826$	0	0
$827$	27.8739	0.969270	0.484635	−	0.874717i	$-0.338952\pi$
$827$	27.8739	0.969270	0.484635	+	0.874717i	$0.338952\pi$
$828$	−68.8886	−2.39404
$829$	−20.0970	−0.697999	−0.348999	−	0.937123i	$-0.613478\pi$
$829$	−20.0970	−0.697999	−0.348999	+	0.937123i	$0.613478\pi$
$830$	−1.06456	−0.0369514
$831$	25.5947	0.887870
$832$	−22.7476	−0.788630
$833$	0	0
$834$	−98.1154	−3.39746
$835$	7.66170	0.265144
$836$	−41.7572	−1.44420
$837$	−95.8129	−3.31178
$838$	−60.8742	−2.10286
$839$	54.7675	1.89078	0.945392	−	0.325935i	$-0.105679\pi$
$839$	54.7675	1.89078	0.945392	+	0.325935i	$0.105679\pi$
$840$	0	0
$841$	−13.7902	−0.475523
$842$	−93.7716	−3.23158
$843$	−3.99598	−0.137629
$844$	−100.338	−3.45379
$845$	1.09400	0.0376348
$846$	172.870	5.94339
$847$	0	0
$848$	−22.1790	−0.761631
$849$	38.9691	1.33742
$850$	−56.0297	−1.92180
$851$	3.31853	0.113758
$852$	−2.95639	−0.101284
$853$	−17.9625	−0.615023	−0.307511	−	0.951544i	$-0.599496\pi$
$853$	−17.9625	−0.615023	−0.307511	+	0.951544i	$0.599496\pi$
$854$	0	0
$855$	−64.4759	−2.20503
$856$	−53.2036	−1.81846
$857$	−48.3004	−1.64991	−0.824954	−	0.565199i	$-0.808799\pi$
$857$	−48.3004	−1.64991	−0.824954	+	0.565199i	$0.808799\pi$
$858$	8.72887	0.297999
$859$	−14.4503	−0.493040	−0.246520	−	0.969138i	$-0.579287\pi$
$859$	−14.4503	−0.493040	−0.246520	+	0.969138i	$0.579287\pi$
$860$	−31.7794	−1.08367
$861$	0	0
$862$	17.4484	0.594295
$863$	26.3407	0.896647	0.448324	−	0.893871i	$-0.352021\pi$
$863$	26.3407	0.896647	0.448324	+	0.893871i	$0.352021\pi$
$864$	−264.304	−8.99180
$865$	0.290602	0.00988076
$866$	33.8025	1.14865
$867$	41.3753	1.40518
$868$	0	0
$869$	9.86649	0.334698
$870$	37.2424	1.26264
$871$	1.71567	0.0581334
$872$	122.502	4.14845
$873$	−60.3807	−2.04358
$874$	−37.2678	−1.26060
$875$	0	0
$876$	−289.247	−9.77277
$877$	−8.92233	−0.301286	−0.150643	−	0.988588i	$-0.548134\pi$
$877$	−8.92233	−0.301286	−0.150643	+	0.988588i	$0.548134\pi$
$878$	−60.6921	−2.04826
$879$	−73.9097	−2.49291
$880$	14.6162	0.492712
$881$	−51.3994	−1.73169	−0.865845	−	0.500312i	$-0.833219\pi$
$881$	−51.3994	−1.73169	−0.865845	+	0.500312i	$0.833219\pi$
$882$	0	0
$883$	−22.8915	−0.770362	−0.385181	−	0.922841i	$-0.625861\pi$
$883$	−22.8915	−0.770362	−0.385181	+	0.922841i	$0.625861\pi$
$884$	28.8468	0.970224
$885$	−36.3698	−1.22256
$886$	−47.2018	−1.58578
$887$	−52.3315	−1.75712	−0.878561	−	0.477631i	$-0.841496\pi$
$887$	−52.3315	−1.75712	−0.878561	+	0.477631i	$0.841496\pi$
$888$	54.4500	1.82722
$889$	0	0
$890$	−12.3218	−0.413029
$891$	24.2604	0.812753
$892$	24.7567	0.828914
$893$	67.8452	2.27035
$894$	−122.760	−4.10571
$895$	6.91386	0.231105
$896$	0	0
$897$	5.65163	0.188702
$898$	−71.8713	−2.39838
$899$	25.9118	0.864206
$900$	−149.922	−4.99739
$901$	9.06126	0.301874
$902$	−29.3870	−0.978481
$903$	0	0
$904$	−14.4572	−0.480838
$905$	−20.4282	−0.679056
$906$	0.119889	0.00398304
$907$	22.9996	0.763688	0.381844	−	0.924227i	$-0.375289\pi$
$907$	22.9996	0.763688	0.381844	+	0.924227i	$0.375289\pi$
$908$	9.29330	0.308409
$909$	19.1001	0.633512
$910$	0	0
$911$	26.9123	0.891644	0.445822	−	0.895122i	$-0.352911\pi$
$911$	26.9123	0.891644	0.445822	+	0.895122i	$0.352911\pi$
$912$	−341.396	−11.3047
$913$	0.360529	0.0119318
$914$	−74.5660	−2.46643
$915$	41.2548	1.36384
$916$	−122.125	−4.03514
$917$	0	0
$918$	212.453	7.01200
$919$	11.2793	0.372070	0.186035	−	0.982543i	$-0.440436\pi$
$919$	11.2793	0.372070	0.186035	+	0.982543i	$0.440436\pi$
$920$	16.9503	0.558835
$921$	20.1750	0.664789
$922$	−60.1950	−1.98242
$923$	0.172973	0.00569349
$924$	0	0
$925$	7.22210	0.237461
$926$	4.58925	0.150812
$927$	−22.3473	−0.733982
$928$	71.4787	2.34640
$929$	31.8359	1.04450	0.522250	−	0.852792i	$-0.325093\pi$
$929$	31.8359	1.04450	0.522250	+	0.852792i	$0.325093\pi$
$930$	63.4469	2.08051
$931$	0	0
$932$	−64.1149	−2.10015
$933$	−61.6581	−2.01860
$934$	−41.0909	−1.34454
$935$	−5.97145	−0.195287
$936$	66.1328	2.16162
$937$	48.8701	1.59652	0.798259	−	0.602315i	$-0.205755\pi$
$937$	48.8701	1.59652	0.798259	+	0.602315i	$0.205755\pi$
$938$	0	0
$939$	1.53086	0.0499578
$940$	−49.6453	−1.61925
$941$	16.7613	0.546404	0.273202	−	0.961957i	$-0.411917\pi$
$941$	16.7613	0.546404	0.273202	+	0.961957i	$0.411917\pi$
$942$	7.97522	0.259847
$943$	−19.0270	−0.619606
$944$	−137.339	−4.46999
$945$	0	0
$946$	14.8355	0.482344
$947$	−3.49601	−0.113605	−0.0568025	−	0.998385i	$-0.518091\pi$
$947$	−3.49601	−0.113605	−0.0568025	+	0.998385i	$0.518091\pi$
$948$	168.634	5.47698
$949$	16.9234	0.549356
$950$	−81.1057	−2.63142
$951$	93.7024	3.03851
$952$	0	0
$953$	−39.3951	−1.27613	−0.638067	−	0.769981i	$-0.720266\pi$
$953$	−39.3951	−1.27613	−0.638067	+	0.769981i	$0.720266\pi$
$954$	33.4212	1.08205
$955$	−3.59849	−0.116444
$956$	112.139	3.62684
$957$	−12.6127	−0.407711
$958$	90.1942	2.91404
$959$	0	0
$960$	80.4821	2.59755
$961$	13.1438	0.423993
$962$	−5.12543	−0.165251
$963$	44.7603	1.44238
$964$	128.200	4.12905
$965$	−24.1973	−0.778938
$966$	0	0
$967$	−35.1238	−1.12951	−0.564753	−	0.825260i	$-0.691028\pi$
$967$	−35.1238	−1.12951	−0.564753	+	0.825260i	$0.691028\pi$
$968$	−8.86610	−0.284967
$969$	139.477	4.48066
$970$	23.9025	0.767464
$971$	−25.1336	−0.806575	−0.403287	−	0.915073i	$-0.632132\pi$
$971$	−25.1336	−0.806575	−0.403287	+	0.915073i	$0.632132\pi$
$972$	186.011	5.96631
$973$	0	0
$974$	−41.9034	−1.34267
$975$	12.2996	0.393902
$976$	155.785	4.98656
$977$	−10.1838	−0.325809	−0.162905	−	0.986642i	$-0.552086\pi$
$977$	−10.1838	−0.325809	−0.162905	+	0.986642i	$0.552086\pi$
$978$	−74.3453	−2.37730
$979$	4.17298	0.133369
$980$	0	0
$981$	−103.061	−3.29049
$982$	5.75058	0.183508
$983$	6.40516	0.204293	0.102146	−	0.994769i	$-0.467429\pi$
$983$	6.40516	0.204293	0.102146	+	0.994769i	$0.467429\pi$
$984$	−312.193	−9.95235
$985$	−4.59589	−0.146437
$986$	−57.4560	−1.82977
$987$	0	0
$988$	41.7572	1.32847
$989$	9.60546	0.305436
$990$	−22.0249	−0.699997
$991$	49.8551	1.58370	0.791849	−	0.610717i	$-0.209119\pi$
$991$	49.8551	1.58370	0.791849	+	0.610717i	$0.209119\pi$
$992$	121.772	3.86628
$993$	−65.1652	−2.06796
$994$	0	0
$995$	−11.4555	−0.363164
$996$	6.16202	0.195251
$997$	44.7600	1.41756	0.708781	−	0.705429i	$-0.249245\pi$
$997$	44.7600	1.41756	0.708781	+	0.705429i	$0.249245\pi$
$998$	68.7592	2.17653
$999$	−27.3847	−0.866414

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7007.2.a.w.1.1		11
7.6	odd	2		1001.2.a.n.1.1	✓	11
21.20	even	2		9009.2.a.bs.1.11		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1001.2.a.n.1.1	✓	11	7.6	odd	2
7007.2.a.w.1.1		11	1.1	even	1	trivial
9009.2.a.bs.1.11		11	21.20	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:	\( N \)	\(=\)	\( 7007 = 7^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69905 q^{2} +3.23405 q^{3} +5.28489 q^{4} +1.09400 q^{5} -8.72887 q^{6} -8.86610 q^{8} +7.45906 q^{9} +O(q^{10})\)	\(q-2.69905 q^{2} +3.23405 q^{3} +5.28489 q^{4} +1.09400 q^{5} -8.72887 q^{6} -8.86610 q^{8} +7.45906 q^{9} -2.95277 q^{10} +1.00000 q^{11} +17.0916 q^{12} -1.00000 q^{13} +3.53805 q^{15} +13.3603 q^{16} -5.45836 q^{17} -20.1324 q^{18} -7.90124 q^{19} +5.78168 q^{20} -2.69905 q^{22} -1.74754 q^{23} -28.6734 q^{24} -3.80316 q^{25} +2.69905 q^{26} +14.4208 q^{27} -3.89998 q^{29} -9.54939 q^{30} -6.64408 q^{31} -18.3280 q^{32} +3.23405 q^{33} +14.7324 q^{34} +39.4203 q^{36} -1.89897 q^{37} +21.3259 q^{38} -3.23405 q^{39} -9.69953 q^{40} +10.8879 q^{41} -5.49656 q^{43} +5.28489 q^{44} +8.16022 q^{45} +4.71670 q^{46} -8.58665 q^{47} +43.2078 q^{48} +10.2649 q^{50} -17.6526 q^{51} -5.28489 q^{52} -1.66007 q^{53} -38.9225 q^{54} +1.09400 q^{55} -25.5530 q^{57} +10.5263 q^{58} -10.2796 q^{59} +18.6982 q^{60} +11.6603 q^{61} +17.9327 q^{62} +22.7476 q^{64} -1.09400 q^{65} -8.72887 q^{66} -1.71567 q^{67} -28.8468 q^{68} -5.65163 q^{69} -0.172973 q^{71} -66.1328 q^{72} -16.9234 q^{73} +5.12543 q^{74} -12.2996 q^{75} -41.7572 q^{76} +8.72887 q^{78} +9.86649 q^{79} +14.6162 q^{80} +24.2604 q^{81} -29.3870 q^{82} +0.360529 q^{83} -5.97145 q^{85} +14.8355 q^{86} -12.6127 q^{87} -8.86610 q^{88} +4.17298 q^{89} -22.0249 q^{90} -9.23556 q^{92} -21.4873 q^{93} +23.1758 q^{94} -8.64397 q^{95} -59.2735 q^{96} -8.09496 q^{97} +7.45906 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - q^{2} - 2 q^{3} + 15 q^{4} - 7 q^{5} - 3 q^{6} - 6 q^{8} + 15 q^{9}+O(q^{10}) \) 11 * q - q^2 - 2 * q^3 + 15 * q^4 - 7 * q^5 - 3 * q^6 - 6 * q^8 + 15 * q^9	\( 11 q - q^{2} - 2 q^{3} + 15 q^{4} - 7 q^{5} - 3 q^{6} - 6 q^{8} + 15 q^{9} - q^{10} + 11 q^{11} + 5 q^{12} - 11 q^{13} + 4 q^{15} + 15 q^{16} - 7 q^{17} - 17 q^{18} - 22 q^{19} - 6 q^{20} - q^{22} + 3 q^{23} - 17 q^{24} + 10 q^{25} + q^{26} - 2 q^{27} - 6 q^{29} - 40 q^{30} - 28 q^{31} - 23 q^{32} - 2 q^{33} - 19 q^{34} + 48 q^{36} + q^{37} + 20 q^{38} + 2 q^{39} - 16 q^{40} + 4 q^{41} - 8 q^{43} + 15 q^{44} - 12 q^{45} + 2 q^{46} - 22 q^{47} + 30 q^{48} - 24 q^{50} - 27 q^{51} - 15 q^{52} + 9 q^{53} - 36 q^{54} - 7 q^{55} - 34 q^{57} - 8 q^{58} + 2 q^{59} + 25 q^{60} - 8 q^{62} - 10 q^{64} + 7 q^{65} - 3 q^{66} + 23 q^{67} - 24 q^{68} - 7 q^{69} + 3 q^{71} - 76 q^{72} - 29 q^{73} + 15 q^{74} - 36 q^{75} - 62 q^{76} + 3 q^{78} + 26 q^{79} + 16 q^{80} + 7 q^{81} + 16 q^{82} - 9 q^{83} - 31 q^{85} + 28 q^{86} - 13 q^{87} - 6 q^{88} - 9 q^{89} + 26 q^{90} - 58 q^{92} - 24 q^{93} + 34 q^{94} - 14 q^{95} - 56 q^{96} - 40 q^{97} + 15 q^{99}+O(q^{100}) \) 11 * q - q^2 - 2 * q^3 + 15 * q^4 - 7 * q^5 - 3 * q^6 - 6 * q^8 + 15 * q^9 - q^10 + 11 * q^11 + 5 * q^12 - 11 * q^13 + 4 * q^15 + 15 * q^16 - 7 * q^17 - 17 * q^18 - 22 * q^19 - 6 * q^20 - q^22 + 3 * q^23 - 17 * q^24 + 10 * q^25 + q^26 - 2 * q^27 - 6 * q^29 - 40 * q^30 - 28 * q^31 - 23 * q^32 - 2 * q^33 - 19 * q^34 + 48 * q^36 + q^37 + 20 * q^38 + 2 * q^39 - 16 * q^40 + 4 * q^41 - 8 * q^43 + 15 * q^44 - 12 * q^45 + 2 * q^46 - 22 * q^47 + 30 * q^48 - 24 * q^50 - 27 * q^51 - 15 * q^52 + 9 * q^53 - 36 * q^54 - 7 * q^55 - 34 * q^57 - 8 * q^58 + 2 * q^59 + 25 * q^60 - 8 * q^62 - 10 * q^64 + 7 * q^65 - 3 * q^66 + 23 * q^67 - 24 * q^68 - 7 * q^69 + 3 * q^71 - 76 * q^72 - 29 * q^73 + 15 * q^74 - 36 * q^75 - 62 * q^76 + 3 * q^78 + 26 * q^79 + 16 * q^80 + 7 * q^81 + 16 * q^82 - 9 * q^83 - 31 * q^85 + 28 * q^86 - 13 * q^87 - 6 * q^88 - 9 * q^89 + 26 * q^90 - 58 * q^92 - 24 * q^93 + 34 * q^94 - 14 * q^95 - 56 * q^96 - 40 * q^97 + 15 * q^99

Introduction

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