LMFDB - Embedded newform 3525.2.a.bg.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3525,2,Mod(1,3525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3525, 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("3525.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3525 = 3 \cdot 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3525.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:	$28.1472667125$
Analytic rank:	$1$
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} - 3x^{9} - 9x^{8} + 29x^{7} + 25x^{6} - 91x^{5} - 21x^{4} + 101x^{3} + 6x^{2} - 30x - 4 $ x^10 - 3x^9 - 9x^8 + 29x^7 + 25x^6 - 91x^5 - 21x^4 + 101x^3 + 6x^2 - 30*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 705)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.801361$ of defining polynomial
Character	$\chi$	$=$	3525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.801361 q^{2} -1.00000 q^{3} -1.35782 q^{4} -0.801361 q^{6} -0.0381502 q^{7} -2.69083 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.801361 q^{2} -1.00000 q^{3} -1.35782 q^{4} -0.801361 q^{6} -0.0381502 q^{7} -2.69083 q^{8} +1.00000 q^{9} -4.03032 q^{11} +1.35782 q^{12} +0.306728 q^{13} -0.0305721 q^{14} +0.559317 q^{16} +5.12558 q^{17} +0.801361 q^{18} +6.79994 q^{19} +0.0381502 q^{21} -3.22974 q^{22} -1.52655 q^{23} +2.69083 q^{24} +0.245800 q^{26} -1.00000 q^{27} +0.0518011 q^{28} +2.50807 q^{29} -2.97719 q^{31} +5.82987 q^{32} +4.03032 q^{33} +4.10744 q^{34} -1.35782 q^{36} -0.701046 q^{37} +5.44921 q^{38} -0.306728 q^{39} +0.769758 q^{41} +0.0305721 q^{42} -5.46128 q^{43} +5.47245 q^{44} -1.22332 q^{46} +1.00000 q^{47} -0.559317 q^{48} -6.99854 q^{49} -5.12558 q^{51} -0.416481 q^{52} +0.523119 q^{53} -0.801361 q^{54} +0.102655 q^{56} -6.79994 q^{57} +2.00987 q^{58} -4.87890 q^{59} -6.69121 q^{61} -2.38580 q^{62} -0.0381502 q^{63} +3.55320 q^{64} +3.22974 q^{66} -0.434698 q^{67} -6.95962 q^{68} +1.52655 q^{69} -4.82694 q^{71} -2.69083 q^{72} -3.80618 q^{73} -0.561791 q^{74} -9.23310 q^{76} +0.153757 q^{77} -0.245800 q^{78} -12.1994 q^{79} +1.00000 q^{81} +0.616854 q^{82} +15.1120 q^{83} -0.0518011 q^{84} -4.37646 q^{86} -2.50807 q^{87} +10.8449 q^{88} -2.36384 q^{89} -0.0117017 q^{91} +2.07278 q^{92} +2.97719 q^{93} +0.801361 q^{94} -5.82987 q^{96} +9.37770 q^{97} -5.60836 q^{98} -4.03032 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 3 q^{2} - 10 q^{3} + 7 q^{4} - 3 q^{6} + 9 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 3 * q^2 - 10 * q^3 + 7 * q^4 - 3 * q^6 + 9 * q^8 + 10 * q^9	$ 10 q + 3 q^{2} - 10 q^{3} + 7 q^{4} - 3 q^{6} + 9 q^{8} + 10 q^{9} - 16 q^{11} - 7 q^{12} + q^{13} - 12 q^{14} - 3 q^{16} + 14 q^{17} + 3 q^{18} - 26 q^{19} + 7 q^{23} - 9 q^{24} - 10 q^{26} - 10 q^{27} - 24 q^{28} - 14 q^{29} - 22 q^{31} + 11 q^{32} + 16 q^{33} - 12 q^{34} + 7 q^{36} + 2 q^{37} - 2 q^{38} - q^{39} - 22 q^{41} + 12 q^{42} - 11 q^{43} - 36 q^{44} - 14 q^{46} + 10 q^{47} + 3 q^{48} + 2 q^{49} - 14 q^{51} + 14 q^{52} + 22 q^{53} - 3 q^{54} - 48 q^{56} + 26 q^{57} - 20 q^{58} - 37 q^{59} - 25 q^{61} - 2 q^{62} - 7 q^{64} - 4 q^{67} + 8 q^{68} - 7 q^{69} - 27 q^{71} + 9 q^{72} + q^{73} + 4 q^{74} - 42 q^{76} + 34 q^{77} + 10 q^{78} + 5 q^{79} + 10 q^{81} - 32 q^{82} + 2 q^{83} + 24 q^{84} - 6 q^{86} + 14 q^{87} - 58 q^{88} + 9 q^{89} - 64 q^{91} + 34 q^{92} + 22 q^{93} + 3 q^{94} - 11 q^{96} - 40 q^{97} + 29 q^{98} - 16 q^{99}+O(q^{100}) $ 10 * q + 3 * q^2 - 10 * q^3 + 7 * q^4 - 3 * q^6 + 9 * q^8 + 10 * q^9 - 16 * q^11 - 7 * q^12 + q^13 - 12 * q^14 - 3 * q^16 + 14 * q^17 + 3 * q^18 - 26 * q^19 + 7 * q^23 - 9 * q^24 - 10 * q^26 - 10 * q^27 - 24 * q^28 - 14 * q^29 - 22 * q^31 + 11 * q^32 + 16 * q^33 - 12 * q^34 + 7 * q^36 + 2 * q^37 - 2 * q^38 - q^39 - 22 * q^41 + 12 * q^42 - 11 * q^43 - 36 * q^44 - 14 * q^46 + 10 * q^47 + 3 * q^48 + 2 * q^49 - 14 * q^51 + 14 * q^52 + 22 * q^53 - 3 * q^54 - 48 * q^56 + 26 * q^57 - 20 * q^58 - 37 * q^59 - 25 * q^61 - 2 * q^62 - 7 * q^64 - 4 * q^67 + 8 * q^68 - 7 * q^69 - 27 * q^71 + 9 * q^72 + q^73 + 4 * q^74 - 42 * q^76 + 34 * q^77 + 10 * q^78 + 5 * q^79 + 10 * q^81 - 32 * q^82 + 2 * q^83 + 24 * q^84 - 6 * q^86 + 14 * q^87 - 58 * q^88 + 9 * q^89 - 64 * q^91 + 34 * q^92 + 22 * q^93 + 3 * q^94 - 11 * q^96 - 40 * q^97 + 29 * q^98 - 16 * 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 $

$2$	0.801361	0.566648	0.283324	−	0.959024i	$-0.408563\pi$
$2$	0.801361	0.566648	0.283324	+	0.959024i	$0.408563\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.35782	−0.678910
$5$	0	0
$5$	0	0
$6$	−0.801361	−0.327154
$7$	−0.0381502	−0.0144194	−0.00720970	−	0.999974i	$-0.502295\pi$
$7$	−0.0381502	−0.0144194	−0.00720970	+	0.999974i	$0.502295\pi$
$8$	−2.69083	−0.951351
$9$	1.00000	0.333333
$10$	0	0
$11$	−4.03032	−1.21519	−0.607594	−	0.794248i	$-0.707865\pi$
$11$	−4.03032	−1.21519	−0.607594	+	0.794248i	$0.707865\pi$
$12$	1.35782	0.391969
$13$	0.306728	0.0850709	0.0425355	−	0.999095i	$-0.486456\pi$
$13$	0.306728	0.0850709	0.0425355	+	0.999095i	$0.486456\pi$
$14$	−0.0305721	−0.00817073
$15$	0	0
$16$	0.559317	0.139829
$17$	5.12558	1.24314	0.621568	−	0.783360i	$-0.286496\pi$
$17$	5.12558	1.24314	0.621568	+	0.783360i	$0.286496\pi$
$18$	0.801361	0.188883
$19$	6.79994	1.56001	0.780007	−	0.625771i	$-0.215215\pi$
$19$	6.79994	1.56001	0.780007	+	0.625771i	$0.215215\pi$
$20$	0	0
$21$	0.0381502	0.00832505
$22$	−3.22974	−0.688583
$23$	−1.52655	−0.318308	−0.159154	−	0.987254i	$-0.550877\pi$
$23$	−1.52655	−0.318308	−0.159154	+	0.987254i	$0.550877\pi$
$24$	2.69083	0.549263
$25$	0	0
$26$	0.245800	0.0482053
$27$	−1.00000	−0.192450
$28$	0.0518011	0.00978948
$29$	2.50807	0.465737	0.232869	−	0.972508i	$-0.425189\pi$
$29$	2.50807	0.465737	0.232869	+	0.972508i	$0.425189\pi$
$30$	0	0
$31$	−2.97719	−0.534718	−0.267359	−	0.963597i	$-0.586151\pi$
$31$	−2.97719	−0.534718	−0.267359	+	0.963597i	$0.586151\pi$
$32$	5.82987	1.03058
$33$	4.03032	0.701589
$34$	4.10744	0.704420
$35$	0	0
$36$	−1.35782	−0.226303
$37$	−0.701046	−0.115251	−0.0576257	−	0.998338i	$-0.518353\pi$
$37$	−0.701046	−0.115251	−0.0576257	+	0.998338i	$0.518353\pi$
$38$	5.44921	0.883979
$39$	−0.306728	−0.0491157
$40$	0	0
$41$	0.769758	0.120216	0.0601080	−	0.998192i	$-0.480855\pi$
$41$	0.769758	0.120216	0.0601080	+	0.998192i	$0.480855\pi$
$42$	0.0305721	0.00471737
$43$	−5.46128	−0.832837	−0.416419	−	0.909173i	$-0.636715\pi$
$43$	−5.46128	−0.832837	−0.416419	+	0.909173i	$0.636715\pi$
$44$	5.47245	0.825003
$45$	0	0
$46$	−1.22332	−0.180368
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	−0.559317	−0.0807304
$49$	−6.99854	−0.999792
$50$	0	0
$51$	−5.12558	−0.717725
$52$	−0.416481	−0.0577555
$53$	0.523119	0.0718559	0.0359279	−	0.999354i	$-0.488561\pi$
$53$	0.523119	0.0718559	0.0359279	+	0.999354i	$0.488561\pi$
$54$	−0.801361	−0.109051
$55$	0	0
$56$	0.102655	0.0137179
$57$	−6.79994	−0.900675
$58$	2.00987	0.263909
$59$	−4.87890	−0.635178	−0.317589	−	0.948228i	$-0.602873\pi$
$59$	−4.87890	−0.635178	−0.317589	+	0.948228i	$0.602873\pi$
$60$	0	0
$61$	−6.69121	−0.856722	−0.428361	−	0.903608i	$-0.640909\pi$
$61$	−6.69121	−0.856722	−0.428361	+	0.903608i	$0.640909\pi$
$62$	−2.38580	−0.302997
$63$	−0.0381502	−0.00480647
$64$	3.55320	0.444149
$65$	0	0
$66$	3.22974	0.397554
$67$	−0.434698	−0.0531068	−0.0265534	−	0.999647i	$-0.508453\pi$
$67$	−0.434698	−0.0531068	−0.0265534	+	0.999647i	$0.508453\pi$
$68$	−6.95962	−0.843977
$69$	1.52655	0.183775
$70$	0	0
$71$	−4.82694	−0.572852	−0.286426	−	0.958102i	$-0.592467\pi$
$71$	−4.82694	−0.572852	−0.286426	+	0.958102i	$0.592467\pi$
$72$	−2.69083	−0.317117
$73$	−3.80618	−0.445480	−0.222740	−	0.974878i	$-0.571500\pi$
$73$	−3.80618	−0.445480	−0.222740	+	0.974878i	$0.571500\pi$
$74$	−0.561791	−0.0653069
$75$	0	0
$76$	−9.23310	−1.05911
$77$	0.153757	0.0175223
$78$	−0.245800	−0.0278313
$79$	−12.1994	−1.37254	−0.686268	−	0.727349i	$-0.740752\pi$
$79$	−12.1994	−1.37254	−0.686268	+	0.727349i	$0.740752\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0.616854	0.0681202
$83$	15.1120	1.65875	0.829377	−	0.558689i	$-0.188695\pi$
$83$	15.1120	1.65875	0.829377	+	0.558689i	$0.188695\pi$
$84$	−0.0518011	−0.00565196
$85$	0	0
$86$	−4.37646	−0.471925
$87$	−2.50807	−0.268893
$88$	10.8449	1.15607
$89$	−2.36384	−0.250567	−0.125283	−	0.992121i	$-0.539984\pi$
$89$	−2.36384	−0.250567	−0.125283	+	0.992121i	$0.539984\pi$
$90$	0	0
$91$	−0.0117017	−0.00122667
$92$	2.07278	0.216102
$93$	2.97719	0.308720
$94$	0.801361	0.0826541
$95$	0	0
$96$	−5.82987	−0.595008
$97$	9.37770	0.952161	0.476080	−	0.879402i	$-0.342057\pi$
$97$	9.37770	0.952161	0.476080	+	0.879402i	$0.342057\pi$
$98$	−5.60836	−0.566530
$99$	−4.03032	−0.405062
$100$	0	0
$101$	−1.04436	−0.103917	−0.0519587	−	0.998649i	$-0.516546\pi$
$101$	−1.04436	−0.103917	−0.0519587	+	0.998649i	$0.516546\pi$
$102$	−4.10744	−0.406697
$103$	−14.2742	−1.40648	−0.703241	−	0.710952i	$-0.748264\pi$
$103$	−14.2742	−1.40648	−0.703241	+	0.710952i	$0.748264\pi$
$104$	−0.825351	−0.0809323
$105$	0	0
$106$	0.419207	0.0407170
$107$	−5.23935	−0.506507	−0.253254	−	0.967400i	$-0.581501\pi$
$107$	−5.23935	−0.506507	−0.253254	+	0.967400i	$0.581501\pi$
$108$	1.35782	0.130656
$109$	−9.29670	−0.890463	−0.445231	−	0.895416i	$-0.646879\pi$
$109$	−9.29670	−0.890463	−0.445231	+	0.895416i	$0.646879\pi$
$110$	0	0
$111$	0.701046	0.0665404
$112$	−0.0213380	−0.00201625
$113$	−19.8465	−1.86701	−0.933503	−	0.358571i	$-0.883264\pi$
$113$	−19.8465	−1.86701	−0.933503	+	0.358571i	$0.883264\pi$
$114$	−5.44921	−0.510365
$115$	0	0
$116$	−3.40551	−0.316194
$117$	0.306728	0.0283570
$118$	−3.90976	−0.359923
$119$	−0.195542	−0.0179253
$120$	0	0
$121$	5.24348	0.476680
$122$	−5.36208	−0.485460
$123$	−0.769758	−0.0694068
$124$	4.04248	0.363026
$125$	0	0
$126$	−0.0305721	−0.00272358
$127$	−8.13495	−0.721860	−0.360930	−	0.932593i	$-0.617541\pi$
$127$	−8.13495	−0.721860	−0.360930	+	0.932593i	$0.617541\pi$
$128$	−8.81234	−0.778908
$129$	5.46128	0.480839
$130$	0	0
$131$	−6.00338	−0.524518	−0.262259	−	0.964998i	$-0.584467\pi$
$131$	−6.00338	−0.524518	−0.262259	+	0.964998i	$0.584467\pi$
$132$	−5.47245	−0.476316
$133$	−0.259419	−0.0224945
$134$	−0.348350	−0.0300929
$135$	0	0
$136$	−13.7920	−1.18266
$137$	12.0670	1.03095	0.515475	−	0.856905i	$-0.327616\pi$
$137$	12.0670	1.03095	0.515475	+	0.856905i	$0.327616\pi$
$138$	1.22332	0.104136
$139$	−1.74377	−0.147905	−0.0739523	−	0.997262i	$-0.523561\pi$
$139$	−1.74377	−0.147905	−0.0739523	+	0.997262i	$0.523561\pi$
$140$	0	0
$141$	−1.00000	−0.0842152
$142$	−3.86812	−0.324605
$143$	−1.23621	−0.103377
$144$	0.559317	0.0466097
$145$	0	0
$146$	−3.05013	−0.252430
$147$	6.99854	0.577230
$148$	0.951895	0.0782453
$149$	−12.2975	−1.00745	−0.503726	−	0.863864i	$-0.668038\pi$
$149$	−12.2975	−1.00745	−0.503726	+	0.863864i	$0.668038\pi$
$150$	0	0
$151$	3.92023	0.319024	0.159512	−	0.987196i	$-0.449008\pi$
$151$	3.92023	0.319024	0.159512	+	0.987196i	$0.449008\pi$
$152$	−18.2975	−1.48412
$153$	5.12558	0.414379
$154$	0.123215	0.00992896
$155$	0	0
$156$	0.416481	0.0333452
$157$	21.9997	1.75576	0.877882	−	0.478878i	$-0.158956\pi$
$157$	21.9997	1.75576	0.877882	+	0.478878i	$0.158956\pi$
$158$	−9.77610	−0.777745
$159$	−0.523119	−0.0414860
$160$	0	0
$161$	0.0582381	0.00458981
$162$	0.801361	0.0629609
$163$	−17.6880	−1.38543	−0.692716	−	0.721210i	$-0.743586\pi$
$163$	−17.6880	−1.38543	−0.692716	+	0.721210i	$0.743586\pi$
$164$	−1.04519	−0.0816159
$165$	0	0
$166$	12.1101	0.939930
$167$	−0.709792	−0.0549254	−0.0274627	−	0.999623i	$-0.508743\pi$
$167$	−0.709792	−0.0549254	−0.0274627	+	0.999623i	$0.508743\pi$
$168$	−0.102655	−0.00792004
$169$	−12.9059	−0.992763
$170$	0	0
$171$	6.79994	0.520005
$172$	7.41544	0.565422
$173$	14.4710	1.10021	0.550103	−	0.835097i	$-0.314588\pi$
$173$	14.4710	1.10021	0.550103	+	0.835097i	$0.314588\pi$
$174$	−2.00987	−0.152368
$175$	0	0
$176$	−2.25423	−0.169919
$177$	4.87890	0.366720
$178$	−1.89429	−0.141983
$179$	−23.4352	−1.75163	−0.875814	−	0.482649i	$-0.839675\pi$
$179$	−23.4352	−1.75163	−0.875814	+	0.482649i	$0.839675\pi$
$180$	0	0
$181$	9.32538	0.693150	0.346575	−	0.938022i	$-0.387345\pi$
$181$	9.32538	0.693150	0.346575	+	0.938022i	$0.387345\pi$
$182$	−0.00937729	−0.000695091 0
$183$	6.69121	0.494629
$184$	4.10768	0.302822
$185$	0	0
$186$	2.38580	0.174935
$187$	−20.6577	−1.51064
$188$	−1.35782	−0.0990292
$189$	0.0381502	0.00277502
$190$	0	0
$191$	11.1768	0.808724	0.404362	−	0.914599i	$-0.367494\pi$
$191$	11.1768	0.808724	0.404362	+	0.914599i	$0.367494\pi$
$192$	−3.55320	−0.256430
$193$	6.75407	0.486169	0.243084	−	0.970005i	$-0.421841\pi$
$193$	6.75407	0.486169	0.243084	+	0.970005i	$0.421841\pi$
$194$	7.51492	0.539540
$195$	0	0
$196$	9.50277	0.678769
$197$	8.44689	0.601816	0.300908	−	0.953653i	$-0.402710\pi$
$197$	8.44689	0.601816	0.300908	+	0.953653i	$0.402710\pi$
$198$	−3.22974	−0.229528
$199$	−7.20769	−0.510940	−0.255470	−	0.966817i	$-0.582230\pi$
$199$	−7.20769	−0.510940	−0.255470	+	0.966817i	$0.582230\pi$
$200$	0	0
$201$	0.434698	0.0306613
$202$	−0.836907	−0.0588846
$203$	−0.0956833	−0.00671565
$204$	6.95962	0.487271
$205$	0	0
$206$	−11.4388	−0.796980
$207$	−1.52655	−0.106103
$208$	0.171558	0.0118954
$209$	−27.4060	−1.89571
$210$	0	0
$211$	−16.0987	−1.10828	−0.554140	−	0.832424i	$-0.686953\pi$
$211$	−16.0987	−1.10828	−0.554140	+	0.832424i	$0.686953\pi$
$212$	−0.710301	−0.0487837
$213$	4.82694	0.330736
$214$	−4.19861	−0.287011
$215$	0	0
$216$	2.69083	0.183088
$217$	0.113580	0.00771032
$218$	−7.45002	−0.504579
$219$	3.80618	0.257198
$220$	0	0
$221$	1.57216	0.105755
$222$	0.561791	0.0377050
$223$	24.2888	1.62650	0.813250	−	0.581914i	$-0.197696\pi$
$223$	24.2888	1.62650	0.813250	+	0.581914i	$0.197696\pi$
$224$	−0.222410	−0.0148604
$225$	0	0
$226$	−15.9042	−1.05793
$227$	27.4925	1.82474	0.912371	−	0.409363i	$-0.134249\pi$
$227$	27.4925	1.82474	0.912371	+	0.409363i	$0.134249\pi$
$228$	9.23310	0.611477
$229$	14.7181	0.972600	0.486300	−	0.873792i	$-0.338346\pi$
$229$	14.7181	0.972600	0.486300	+	0.873792i	$0.338346\pi$
$230$	0	0
$231$	−0.153757	−0.0101165
$232$	−6.74878	−0.443079
$233$	8.70527	0.570301	0.285151	−	0.958483i	$-0.407956\pi$
$233$	8.70527	0.570301	0.285151	+	0.958483i	$0.407956\pi$
$234$	0.245800	0.0160684
$235$	0	0
$236$	6.62467	0.431229
$237$	12.1994	0.792434
$238$	−0.156700	−0.0101573
$239$	3.33027	0.215417	0.107709	−	0.994183i	$-0.465649\pi$
$239$	3.33027	0.215417	0.107709	+	0.994183i	$0.465649\pi$
$240$	0	0
$241$	−3.53503	−0.227712	−0.113856	−	0.993497i	$-0.536320\pi$
$241$	−3.53503	−0.227712	−0.113856	+	0.993497i	$0.536320\pi$
$242$	4.20192	0.270110
$243$	−1.00000	−0.0641500
$244$	9.08546	0.581637
$245$	0	0
$246$	−0.616854	−0.0393292
$247$	2.08573	0.132712
$248$	8.01109	0.508705
$249$	−15.1120	−0.957683
$250$	0	0
$251$	−24.2937	−1.53341	−0.766703	−	0.642002i	$-0.778104\pi$
$251$	−24.2937	−1.53341	−0.766703	+	0.642002i	$0.778104\pi$
$252$	0.0518011	0.00326316
$253$	6.15249	0.386804
$254$	−6.51903	−0.409041
$255$	0	0
$256$	−14.1683	−0.885516
$257$	0.973015	0.0606950	0.0303475	−	0.999539i	$-0.490339\pi$
$257$	0.973015	0.0606950	0.0303475	+	0.999539i	$0.490339\pi$
$258$	4.37646	0.272466
$259$	0.0267450	0.00166186
$260$	0	0
$261$	2.50807	0.155246
$262$	−4.81088	−0.297217
$263$	−2.12610	−0.131101	−0.0655504	−	0.997849i	$-0.520880\pi$
$263$	−2.12610	−0.131101	−0.0655504	+	0.997849i	$0.520880\pi$
$264$	−10.8449	−0.667457
$265$	0	0
$266$	−0.207888	−0.0127465
$267$	2.36384	0.144665
$268$	0.590242	0.0360548
$269$	−16.8131	−1.02511	−0.512556	−	0.858654i	$-0.671301\pi$
$269$	−16.8131	−1.02511	−0.512556	+	0.858654i	$0.671301\pi$
$270$	0	0
$271$	−22.6738	−1.37734	−0.688668	−	0.725077i	$-0.741804\pi$
$271$	−22.6738	−1.37734	−0.688668	+	0.725077i	$0.741804\pi$
$272$	2.86682	0.173827
$273$	0.0117017	0.000708220 0
$274$	9.66999	0.584185
$275$	0	0
$276$	−2.07278	−0.124767
$277$	−30.2620	−1.81827	−0.909135	−	0.416502i	$-0.863256\pi$
$277$	−30.2620	−1.81827	−0.909135	+	0.416502i	$0.863256\pi$
$278$	−1.39739	−0.0838099
$279$	−2.97719	−0.178239
$280$	0	0
$281$	−9.60222	−0.572820	−0.286410	−	0.958107i	$-0.592462\pi$
$281$	−9.60222	−0.572820	−0.286410	+	0.958107i	$0.592462\pi$
$282$	−0.801361	−0.0477204
$283$	−25.0562	−1.48943	−0.744717	−	0.667380i	$-0.767416\pi$
$283$	−25.0562	−1.48943	−0.744717	+	0.667380i	$0.767416\pi$
$284$	6.55411	0.388915
$285$	0	0
$286$	−0.990651	−0.0585784
$287$	−0.0293664	−0.00173344
$288$	5.82987	0.343528
$289$	9.27156	0.545386
$290$	0	0
$291$	−9.37770	−0.549730
$292$	5.16811	0.302441
$293$	−2.51938	−0.147184	−0.0735920	−	0.997288i	$-0.523446\pi$
$293$	−2.51938	−0.147184	−0.0735920	+	0.997288i	$0.523446\pi$
$294$	5.60836	0.327086
$295$	0	0
$296$	1.88639	0.109644
$297$	4.03032	0.233863
$298$	−9.85475	−0.570870
$299$	−0.468235	−0.0270787
$300$	0	0
$301$	0.208349	0.0120090
$302$	3.14152	0.180774
$303$	1.04436	0.0599968
$304$	3.80332	0.218136
$305$	0	0
$306$	4.10744	0.234807
$307$	−21.8715	−1.24827	−0.624137	−	0.781315i	$-0.714549\pi$
$307$	−21.8715	−1.24827	−0.624137	+	0.781315i	$0.714549\pi$
$308$	−0.208775	−0.0118961
$309$	14.2742	0.812032
$310$	0	0
$311$	−28.3769	−1.60911	−0.804553	−	0.593880i	$-0.797595\pi$
$311$	−28.3769	−1.60911	−0.804553	+	0.593880i	$0.797595\pi$
$312$	0.825351	0.0467263
$313$	−18.3432	−1.03682	−0.518410	−	0.855132i	$-0.673476\pi$
$313$	−18.3432	−1.03682	−0.518410	+	0.855132i	$0.673476\pi$
$314$	17.6297	0.994900
$315$	0	0
$316$	16.5645	0.931829
$317$	−30.0078	−1.68541	−0.842704	−	0.538377i	$-0.819038\pi$
$317$	−30.0078	−1.68541	−0.842704	+	0.538377i	$0.819038\pi$
$318$	−0.419207	−0.0235080
$319$	−10.1083	−0.565958
$320$	0	0
$321$	5.23935	0.292432
$322$	0.0466698	0.00260081
$323$	34.8537	1.93931
$324$	−1.35782	−0.0754345
$325$	0	0
$326$	−14.1745	−0.785053
$327$	9.29670	0.514109
$328$	−2.07129	−0.114368
$329$	−0.0381502	−0.00210329
$330$	0	0
$331$	−16.7846	−0.922567	−0.461284	−	0.887253i	$-0.652611\pi$
$331$	−16.7846	−0.922567	−0.461284	+	0.887253i	$0.652611\pi$
$332$	−20.5193	−1.12615
$333$	−0.701046	−0.0384171
$334$	−0.568800	−0.0311233
$335$	0	0
$336$	0.0213380	0.00116408
$337$	6.91935	0.376921	0.188460	−	0.982081i	$-0.439650\pi$
$337$	6.91935	0.376921	0.188460	+	0.982081i	$0.439650\pi$
$338$	−10.3423	−0.562547
$339$	19.8465	1.07792
$340$	0	0
$341$	11.9990	0.649783
$342$	5.44921	0.294660
$343$	0.534047	0.0288358
$344$	14.6954	0.792320
$345$	0	0
$346$	11.5965	0.623430
$347$	−18.2454	−0.979465	−0.489732	−	0.871873i	$-0.662905\pi$
$347$	−18.2454	−0.979465	−0.489732	+	0.871873i	$0.662905\pi$
$348$	3.40551	0.182554
$349$	8.97940	0.480656	0.240328	−	0.970692i	$-0.422745\pi$
$349$	8.97940	0.480656	0.240328	+	0.970692i	$0.422745\pi$
$350$	0	0
$351$	−0.306728	−0.0163719
$352$	−23.4962	−1.25235
$353$	30.5679	1.62697	0.813484	−	0.581588i	$-0.197568\pi$
$353$	30.5679	1.62697	0.813484	+	0.581588i	$0.197568\pi$
$354$	3.90976	0.207801
$355$	0	0
$356$	3.20967	0.170112
$357$	0.195542	0.0103492
$358$	−18.7800	−0.992556
$359$	−2.27316	−0.119973	−0.0599864	−	0.998199i	$-0.519106\pi$
$359$	−2.27316	−0.119973	−0.0599864	+	0.998199i	$0.519106\pi$
$360$	0	0
$361$	27.2392	1.43364
$362$	7.47299	0.392772
$363$	−5.24348	−0.275212
$364$	0.0158888	0.000832800 0
$365$	0	0
$366$	5.36208	0.280280
$367$	26.9823	1.40846	0.704231	−	0.709971i	$-0.251292\pi$
$367$	26.9823	1.40846	0.704231	+	0.709971i	$0.251292\pi$
$368$	−0.853825	−0.0445087
$369$	0.769758	0.0400720
$370$	0	0
$371$	−0.0199571	−0.00103612
$372$	−4.04248	−0.209593
$373$	−3.87261	−0.200516	−0.100258	−	0.994961i	$-0.531967\pi$
$373$	−3.87261	−0.200516	−0.100258	+	0.994961i	$0.531967\pi$
$374$	−16.5543	−0.856003
$375$	0	0
$376$	−2.69083	−0.138769
$377$	0.769295	0.0396207
$378$	0.0305721	0.00157246
$379$	23.6806	1.21639	0.608196	−	0.793787i	$-0.291894\pi$
$379$	23.6806	1.21639	0.608196	+	0.793787i	$0.291894\pi$
$380$	0	0
$381$	8.13495	0.416766
$382$	8.95665	0.458262
$383$	30.9167	1.57977	0.789884	−	0.613256i	$-0.210140\pi$
$383$	30.9167	1.57977	0.789884	+	0.613256i	$0.210140\pi$
$384$	8.81234	0.449703
$385$	0	0
$386$	5.41245	0.275486
$387$	−5.46128	−0.277612
$388$	−12.7332	−0.646432
$389$	−27.9871	−1.41900	−0.709500	−	0.704705i	$-0.751079\pi$
$389$	−27.9871	−1.41900	−0.709500	+	0.704705i	$0.751079\pi$
$390$	0	0
$391$	−7.82446	−0.395700
$392$	18.8319	0.951153
$393$	6.00338	0.302831
$394$	6.76901	0.341018
$395$	0	0
$396$	5.47245	0.275001
$397$	−3.06890	−0.154024	−0.0770118	−	0.997030i	$-0.524538\pi$
$397$	−3.06890	−0.154024	−0.0770118	+	0.997030i	$0.524538\pi$
$398$	−5.77596	−0.289523
$399$	0.259419	0.0129872
$400$	0	0
$401$	−36.4231	−1.81888	−0.909441	−	0.415833i	$-0.863490\pi$
$401$	−36.4231	−1.81888	−0.909441	+	0.415833i	$0.863490\pi$
$402$	0.348350	0.0173741
$403$	−0.913185	−0.0454890
$404$	1.41805	0.0705506
$405$	0	0
$406$	−0.0766769	−0.00380541
$407$	2.82544	0.140052
$408$	13.7920	0.682808
$409$	−4.78448	−0.236577	−0.118289	−	0.992979i	$-0.537741\pi$
$409$	−4.78448	−0.236577	−0.118289	+	0.992979i	$0.537741\pi$
$410$	0	0
$411$	−12.0670	−0.595219
$412$	19.3818	0.954874
$413$	0.186131	0.00915890
$414$	−1.22332	−0.0601228
$415$	0	0
$416$	1.78818	0.0876728
$417$	1.74377	0.0853928
$418$	−21.9621	−1.07420
$419$	27.1532	1.32652	0.663260	−	0.748389i	$-0.269172\pi$
$419$	27.1532	1.32652	0.663260	+	0.748389i	$0.269172\pi$
$420$	0	0
$421$	19.3037	0.940802	0.470401	−	0.882453i	$-0.344109\pi$
$421$	19.3037	0.940802	0.470401	+	0.882453i	$0.344109\pi$
$422$	−12.9009	−0.628004
$423$	1.00000	0.0486217
$424$	−1.40762	−0.0683601
$425$	0	0
$426$	3.86812	0.187411
$427$	0.255271	0.0123534
$428$	7.11410	0.343873
$429$	1.23621	0.0596848
$430$	0	0
$431$	−2.88165	−0.138804	−0.0694020	−	0.997589i	$-0.522109\pi$
$431$	−2.88165	−0.138804	−0.0694020	+	0.997589i	$0.522109\pi$
$432$	−0.559317	−0.0269101
$433$	−11.1242	−0.534593	−0.267296	−	0.963614i	$-0.586130\pi$
$433$	−11.1242	−0.534593	−0.267296	+	0.963614i	$0.586130\pi$
$434$	0.0910187	0.00436904
$435$	0	0
$436$	12.6233	0.604544
$437$	−10.3805	−0.496565
$438$	3.05013	0.145741
$439$	14.1860	0.677059	0.338530	−	0.940956i	$-0.390070\pi$
$439$	14.1860	0.677059	0.338530	+	0.940956i	$0.390070\pi$
$440$	0	0
$441$	−6.99854	−0.333264
$442$	1.25987	0.0599257
$443$	26.2976	1.24944	0.624719	−	0.780850i	$-0.285214\pi$
$443$	26.2976	1.24944	0.624719	+	0.780850i	$0.285214\pi$
$444$	−0.951895	−0.0451749
$445$	0	0
$446$	19.4641	0.921653
$447$	12.2975	0.581652
$448$	−0.135555	−0.00640437
$449$	29.7905	1.40590	0.702951	−	0.711238i	$-0.251865\pi$
$449$	29.7905	1.40590	0.702951	+	0.711238i	$0.251865\pi$
$450$	0	0
$451$	−3.10237	−0.146085
$452$	26.9480	1.26753
$453$	−3.92023	−0.184188
$454$	22.0314	1.03399
$455$	0	0
$456$	18.2975	0.856858
$457$	−7.02784	−0.328748	−0.164374	−	0.986398i	$-0.552560\pi$
$457$	−7.02784	−0.328748	−0.164374	+	0.986398i	$0.552560\pi$
$458$	11.7945	0.551122
$459$	−5.12558	−0.239242
$460$	0	0
$461$	28.1756	1.31227	0.656134	−	0.754644i	$-0.272191\pi$
$461$	28.1756	1.31227	0.656134	+	0.754644i	$0.272191\pi$
$462$	−0.123215	−0.00573249
$463$	−28.6547	−1.33170	−0.665848	−	0.746088i	$-0.731930\pi$
$463$	−28.6547	−1.33170	−0.665848	+	0.746088i	$0.731930\pi$
$464$	1.40281	0.0651236
$465$	0	0
$466$	6.97607	0.323160
$467$	−20.7285	−0.959198	−0.479599	−	0.877488i	$-0.659218\pi$
$467$	−20.7285	−0.959198	−0.479599	+	0.877488i	$0.659218\pi$
$468$	−0.416481	−0.0192518
$469$	0.0165838	0.000765769 0
$470$	0	0
$471$	−21.9997	−1.01369
$472$	13.1283	0.604278
$473$	22.0107	1.01205
$474$	9.77610	0.449031
$475$	0	0
$476$	0.265510	0.0121697
$477$	0.523119	0.0239520
$478$	2.66875	0.122066
$479$	1.70304	0.0778139	0.0389069	−	0.999243i	$-0.487612\pi$
$479$	1.70304	0.0778139	0.0389069	+	0.999243i	$0.487612\pi$
$480$	0	0
$481$	−0.215030	−0.00980454
$482$	−2.83284	−0.129032
$483$	−0.0582381	−0.00264993
$484$	−7.11971	−0.323623
$485$	0	0
$486$	−0.801361	−0.0363505
$487$	−0.818498	−0.0370897	−0.0185448	−	0.999828i	$-0.505903\pi$
$487$	−0.818498	−0.0370897	−0.0185448	+	0.999828i	$0.505903\pi$
$488$	18.0049	0.815043
$489$	17.6880	0.799880
$490$	0	0
$491$	16.1961	0.730921	0.365461	−	0.930827i	$-0.380911\pi$
$491$	16.1961	0.730921	0.365461	+	0.930827i	$0.380911\pi$
$492$	1.04519	0.0471210
$493$	12.8553	0.578974
$494$	1.67142	0.0752009
$495$	0	0
$496$	−1.66519	−0.0747692
$497$	0.184148	0.00826019
$498$	−12.1101	−0.542669
$499$	−33.9334	−1.51907	−0.759533	−	0.650468i	$-0.774573\pi$
$499$	−33.9334	−1.51907	−0.759533	+	0.650468i	$0.774573\pi$
$500$	0	0
$501$	0.709792	0.0317112
$502$	−19.4680	−0.868901
$503$	33.0203	1.47230	0.736151	−	0.676817i	$-0.236641\pi$
$503$	33.0203	1.47230	0.736151	+	0.676817i	$0.236641\pi$
$504$	0.102655	0.00457264
$505$	0	0
$506$	4.93036	0.219181
$507$	12.9059	0.573172
$508$	11.0458	0.490078
$509$	−7.37275	−0.326791	−0.163396	−	0.986561i	$-0.552245\pi$
$509$	−7.37275	−0.326791	−0.163396	+	0.986561i	$0.552245\pi$
$510$	0	0
$511$	0.145206	0.00642356
$512$	6.27079	0.277133
$513$	−6.79994	−0.300225
$514$	0.779736	0.0343927
$515$	0	0
$516$	−7.41544	−0.326446
$517$	−4.03032	−0.177253
$518$	0.0214324	0.000941687 0
$519$	−14.4710	−0.635204
$520$	0	0
$521$	29.9778	1.31335	0.656677	−	0.754172i	$-0.271962\pi$
$521$	29.9778	1.31335	0.656677	+	0.754172i	$0.271962\pi$
$522$	2.00987	0.0879696
$523$	−18.5074	−0.809271	−0.404635	−	0.914478i	$-0.632602\pi$
$523$	−18.5074	−0.809271	−0.404635	+	0.914478i	$0.632602\pi$
$524$	8.15152	0.356101
$525$	0	0
$526$	−1.70377	−0.0742880
$527$	−15.2598	−0.664727
$528$	2.25423	0.0981026
$529$	−20.6696	−0.898680
$530$	0	0
$531$	−4.87890	−0.211726
$532$	0.352244	0.0152717
$533$	0.236106	0.0102269
$534$	1.89429	0.0819740
$535$	0	0
$536$	1.16970	0.0505232
$537$	23.4352	1.01130
$538$	−13.4733	−0.580877
$539$	28.2064	1.21493
$540$	0	0
$541$	2.44881	0.105283	0.0526413	−	0.998613i	$-0.483236\pi$
$541$	2.44881	0.105283	0.0526413	+	0.998613i	$0.483236\pi$
$542$	−18.1699	−0.780464
$543$	−9.32538	−0.400190
$544$	29.8815	1.28116
$545$	0	0
$546$	0.00937729	0.000401311 0
$547$	−25.1853	−1.07684	−0.538422	−	0.842675i	$-0.680980\pi$
$547$	−25.1853	−1.07684	−0.538422	+	0.842675i	$0.680980\pi$
$548$	−16.3848	−0.699922
$549$	−6.69121	−0.285574
$550$	0	0
$551$	17.0547	0.726556
$552$	−4.10768	−0.174835
$553$	0.465408	0.0197912
$554$	−24.2508	−1.03032
$555$	0	0
$556$	2.36773	0.100414
$557$	34.1607	1.44743	0.723717	−	0.690097i	$-0.242432\pi$
$557$	34.1607	1.44743	0.723717	+	0.690097i	$0.242432\pi$
$558$	−2.38580	−0.100999
$559$	−1.67513	−0.0708502
$560$	0	0
$561$	20.6577	0.872170
$562$	−7.69484	−0.324587
$563$	9.00162	0.379373	0.189687	−	0.981845i	$-0.439253\pi$
$563$	9.00162	0.379373	0.189687	+	0.981845i	$0.439253\pi$
$564$	1.35782	0.0571746
$565$	0	0
$566$	−20.0790	−0.843985
$567$	−0.0381502	−0.00160216
$568$	12.9885	0.544983
$569$	17.9671	0.753219	0.376610	−	0.926372i	$-0.377090\pi$
$569$	17.9671	0.753219	0.376610	+	0.926372i	$0.377090\pi$
$570$	0	0
$571$	−30.3786	−1.27131	−0.635653	−	0.771975i	$-0.719269\pi$
$571$	−30.3786	−1.27131	−0.635653	+	0.771975i	$0.719269\pi$
$572$	1.67855	0.0701838
$573$	−11.1768	−0.466917
$574$	−0.0235331	−0.000982252 0
$575$	0	0
$576$	3.55320	0.148050
$577$	22.2523	0.926373	0.463187	−	0.886261i	$-0.346706\pi$
$577$	22.2523	0.926373	0.463187	+	0.886261i	$0.346706\pi$
$578$	7.42987	0.309042
$579$	−6.75407	−0.280690
$580$	0	0
$581$	−0.576524	−0.0239183
$582$	−7.51492	−0.311504
$583$	−2.10834	−0.0873183
$584$	10.2418	0.423808
$585$	0	0
$586$	−2.01894	−0.0834015
$587$	−2.13448	−0.0880996	−0.0440498	−	0.999029i	$-0.514026\pi$
$587$	−2.13448	−0.0880996	−0.0440498	+	0.999029i	$0.514026\pi$
$588$	−9.50277	−0.391887
$589$	−20.2447	−0.834168
$590$	0	0
$591$	−8.44689	−0.347459
$592$	−0.392107	−0.0161155
$593$	−32.1103	−1.31861	−0.659306	−	0.751875i	$-0.729150\pi$
$593$	−32.1103	−1.31861	−0.659306	+	0.751875i	$0.729150\pi$
$594$	3.22974	0.132518
$595$	0	0
$596$	16.6978	0.683969
$597$	7.20769	0.294991
$598$	−0.375225	−0.0153441
$599$	−24.1787	−0.987916	−0.493958	−	0.869486i	$-0.664450\pi$
$599$	−24.1787	−0.987916	−0.493958	+	0.869486i	$0.664450\pi$
$600$	0	0
$601$	5.44087	0.221938	0.110969	−	0.993824i	$-0.464605\pi$
$601$	5.44087	0.221938	0.110969	+	0.993824i	$0.464605\pi$
$602$	0.166963	0.00680488
$603$	−0.434698	−0.0177023
$604$	−5.32297	−0.216588
$605$	0	0
$606$	0.836907	0.0339970
$607$	43.9760	1.78493	0.892465	−	0.451116i	$-0.148974\pi$
$607$	43.9760	1.78493	0.892465	+	0.451116i	$0.148974\pi$
$608$	39.6428	1.60773
$609$	0.0956833	0.00387728
$610$	0	0
$611$	0.306728	0.0124089
$612$	−6.95962	−0.281326
$613$	−29.1039	−1.17550	−0.587748	−	0.809044i	$-0.699985\pi$
$613$	−29.1039	−1.17550	−0.587748	+	0.809044i	$0.699985\pi$
$614$	−17.5270	−0.707331
$615$	0	0
$616$	−0.413735	−0.0166698
$617$	10.1720	0.409511	0.204755	−	0.978813i	$-0.434360\pi$
$617$	10.1720	0.409511	0.204755	+	0.978813i	$0.434360\pi$
$618$	11.4388	0.460136
$619$	1.83696	0.0738338	0.0369169	−	0.999318i	$-0.488246\pi$
$619$	1.83696	0.0738338	0.0369169	+	0.999318i	$0.488246\pi$
$620$	0	0
$621$	1.52655	0.0612584
$622$	−22.7402	−0.911797
$623$	0.0901810	0.00361303
$624$	−0.171558	−0.00686781
$625$	0	0
$626$	−14.6995	−0.587512
$627$	27.4060	1.09449
$628$	−29.8716	−1.19201
$629$	−3.59327	−0.143273
$630$	0	0
$631$	37.3501	1.48688	0.743442	−	0.668800i	$-0.233192\pi$
$631$	37.3501	1.48688	0.743442	+	0.668800i	$0.233192\pi$
$632$	32.8264	1.30576
$633$	16.0987	0.639865
$634$	−24.0471	−0.955033
$635$	0	0
$636$	0.710301	0.0281653
$637$	−2.14665	−0.0850532
$638$	−8.10042	−0.320699
$639$	−4.82694	−0.190951
$640$	0	0
$641$	36.4655	1.44030	0.720151	−	0.693817i	$-0.244072\pi$
$641$	36.4655	1.44030	0.720151	+	0.693817i	$0.244072\pi$
$642$	4.19861	0.165706
$643$	19.8029	0.780949	0.390474	−	0.920614i	$-0.372311\pi$
$643$	19.8029	0.780949	0.390474	+	0.920614i	$0.372311\pi$
$644$	−0.0790769	−0.00311607
$645$	0	0
$646$	27.9304	1.09891
$647$	3.14259	0.123548	0.0617740	−	0.998090i	$-0.480324\pi$
$647$	3.14259	0.123548	0.0617740	+	0.998090i	$0.480324\pi$
$648$	−2.69083	−0.105706
$649$	19.6635	0.771861
$650$	0	0
$651$	−0.113580	−0.00445156
$652$	24.0172	0.940584
$653$	−31.4764	−1.23177	−0.615883	−	0.787838i	$-0.711201\pi$
$653$	−31.4764	−1.23177	−0.615883	+	0.787838i	$0.711201\pi$
$654$	7.45002	0.291319
$655$	0	0
$656$	0.430539	0.0168097
$657$	−3.80618	−0.148493
$658$	−0.0305721	−0.00119182
$659$	19.9911	0.778742	0.389371	−	0.921081i	$-0.372692\pi$
$659$	19.9911	0.778742	0.389371	+	0.921081i	$0.372692\pi$
$660$	0	0
$661$	14.2018	0.552388	0.276194	−	0.961102i	$-0.410927\pi$
$661$	14.2018	0.552388	0.276194	+	0.961102i	$0.410927\pi$
$662$	−13.4506	−0.522771
$663$	−1.57216	−0.0610575
$664$	−40.6637	−1.57806
$665$	0	0
$666$	−0.561791	−0.0217690
$667$	−3.82870	−0.148248
$668$	0.963770	0.0372894
$669$	−24.2888	−0.939061
$670$	0	0
$671$	26.9677	1.04108
$672$	0.222410	0.00857967
$673$	20.6151	0.794654	0.397327	−	0.917677i	$-0.369938\pi$
$673$	20.6151	0.794654	0.397327	+	0.917677i	$0.369938\pi$
$674$	5.54490	0.213581
$675$	0	0
$676$	17.5239	0.673997
$677$	25.0415	0.962422	0.481211	−	0.876605i	$-0.340197\pi$
$677$	25.0415	0.962422	0.481211	+	0.876605i	$0.340197\pi$
$678$	15.9042	0.610799
$679$	−0.357761	−0.0137296
$680$	0	0
$681$	−27.4925	−1.05352
$682$	9.61554	0.368198
$683$	−13.5826	−0.519725	−0.259862	−	0.965646i	$-0.583677\pi$
$683$	−13.5826	−0.519725	−0.259862	+	0.965646i	$0.583677\pi$
$684$	−9.23310	−0.353037
$685$	0	0
$686$	0.427964	0.0163398
$687$	−14.7181	−0.561531
$688$	−3.05459	−0.116455
$689$	0.160455	0.00611285
$690$	0	0
$691$	−10.1454	−0.385947	−0.192974	−	0.981204i	$-0.561813\pi$
$691$	−10.1454	−0.385947	−0.192974	+	0.981204i	$0.561813\pi$
$692$	−19.6490	−0.746941
$693$	0.153757	0.00584076
$694$	−14.6212	−0.555011
$695$	0	0
$696$	6.74878	0.255812
$697$	3.94546	0.149445
$698$	7.19574	0.272363
$699$	−8.70527	−0.329264
$700$	0	0
$701$	29.5694	1.11682	0.558411	−	0.829564i	$-0.311411\pi$
$701$	29.5694	1.11682	0.558411	+	0.829564i	$0.311411\pi$
$702$	−0.245800	−0.00927711
$703$	−4.76708	−0.179794
$704$	−14.3205	−0.539725
$705$	0	0
$706$	24.4960	0.921917
$707$	0.0398424	0.00149843
$708$	−6.62467	−0.248970
$709$	−38.2723	−1.43735	−0.718673	−	0.695348i	$-0.755250\pi$
$709$	−38.2723	−1.43735	−0.718673	+	0.695348i	$0.755250\pi$
$710$	0	0
$711$	−12.1994	−0.457512
$712$	6.36069	0.238377
$713$	4.54482	0.170205
$714$	0.156700	0.00586433
$715$	0	0
$716$	31.8208	1.18920
$717$	−3.33027	−0.124371
$718$	−1.82162	−0.0679824
$719$	42.1369	1.57144	0.785721	−	0.618581i	$-0.212292\pi$
$719$	42.1369	1.57144	0.785721	+	0.618581i	$0.212292\pi$
$720$	0	0
$721$	0.544564	0.0202806
$722$	21.8285	0.812372
$723$	3.53503	0.131469
$724$	−12.6622	−0.470586
$725$	0	0
$726$	−4.20192	−0.155948
$727$	−17.3476	−0.643387	−0.321694	−	0.946844i	$-0.604252\pi$
$727$	−17.3476	−0.643387	−0.321694	+	0.946844i	$0.604252\pi$
$728$	0.0314873	0.00116700
$729$	1.00000	0.0370370
$730$	0	0
$731$	−27.9922	−1.03533
$732$	−9.08546	−0.335808
$733$	−30.1397	−1.11323	−0.556617	−	0.830769i	$-0.687901\pi$
$733$	−30.1397	−1.11323	−0.556617	+	0.830769i	$0.687901\pi$
$734$	21.6225	0.798102
$735$	0	0
$736$	−8.89959	−0.328043
$737$	1.75197	0.0645348
$738$	0.616854	0.0227067
$739$	45.2177	1.66336	0.831679	−	0.555256i	$-0.187380\pi$
$739$	45.2177	1.66336	0.831679	+	0.555256i	$0.187380\pi$
$740$	0	0
$741$	−2.08573	−0.0766212
$742$	−0.0159928	−0.000587115 0
$743$	8.82545	0.323774	0.161887	−	0.986809i	$-0.448242\pi$
$743$	8.82545	0.323774	0.161887	+	0.986809i	$0.448242\pi$
$744$	−8.01109	−0.293701
$745$	0	0
$746$	−3.10336	−0.113622
$747$	15.1120	0.552918
$748$	28.0495	1.02559
$749$	0.199882	0.00730353
$750$	0	0
$751$	−21.9445	−0.800765	−0.400383	−	0.916348i	$-0.631123\pi$
$751$	−21.9445	−0.800765	−0.400383	+	0.916348i	$0.631123\pi$
$752$	0.559317	0.0203962
$753$	24.2937	0.885312
$754$	0.616483	0.0224510
$755$	0	0
$756$	−0.0518011	−0.00188399
$757$	−10.5754	−0.384370	−0.192185	−	0.981359i	$-0.561557\pi$
$757$	−10.5754	−0.384370	−0.192185	+	0.981359i	$0.561557\pi$
$758$	18.9767	0.689266
$759$	−6.15249	−0.223321
$760$	0	0
$761$	37.0117	1.34167	0.670836	−	0.741606i	$-0.265936\pi$
$761$	37.0117	1.34167	0.670836	+	0.741606i	$0.265936\pi$
$762$	6.51903	0.236160
$763$	0.354671	0.0128399
$764$	−15.1761	−0.549051
$765$	0	0
$766$	24.7754	0.895173
$767$	−1.49649	−0.0540352
$768$	14.1683	0.511253
$769$	41.0185	1.47916	0.739582	−	0.673067i	$-0.235023\pi$
$769$	41.0185	1.47916	0.739582	+	0.673067i	$0.235023\pi$
$770$	0	0
$771$	−0.973015	−0.0350423
$772$	−9.17082	−0.330065
$773$	−16.6984	−0.600599	−0.300299	−	0.953845i	$-0.597087\pi$
$773$	−16.6984	−0.600599	−0.300299	+	0.953845i	$0.597087\pi$
$774$	−4.37646	−0.157308
$775$	0	0
$776$	−25.2338	−0.905839
$777$	−0.0267450	−0.000959473 0
$778$	−22.4277	−0.804074
$779$	5.23431	0.187539
$780$	0	0
$781$	19.4541	0.696123
$782$	−6.27021	−0.224222
$783$	−2.50807	−0.0896311
$784$	−3.91440	−0.139800
$785$	0	0
$786$	4.81088	0.171598
$787$	−20.1879	−0.719622	−0.359811	−	0.933025i	$-0.617159\pi$
$787$	−20.1879	−0.719622	−0.359811	+	0.933025i	$0.617159\pi$
$788$	−11.4694	−0.408579
$789$	2.12610	0.0756911
$790$	0	0
$791$	0.757149	0.0269211
$792$	10.8449	0.385357
$793$	−2.05238	−0.0728821
$794$	−2.45930	−0.0872772
$795$	0	0
$796$	9.78675	0.346882
$797$	0.989263	0.0350415	0.0175207	−	0.999846i	$-0.494423\pi$
$797$	0.989263	0.0350415	0.0175207	+	0.999846i	$0.494423\pi$
$798$	0.207888	0.00735917
$799$	5.12558	0.181330
$800$	0	0
$801$	−2.36384	−0.0835223
$802$	−29.1880	−1.03067
$803$	15.3401	0.541342
$804$	−0.590242	−0.0208162
$805$	0	0
$806$	−0.731791	−0.0257762
$807$	16.8131	0.591848
$808$	2.81018	0.0988620
$809$	−52.8194	−1.85703	−0.928515	−	0.371295i	$-0.878914\pi$
$809$	−52.8194	−1.85703	−0.928515	+	0.371295i	$0.878914\pi$
$810$	0	0
$811$	−8.06408	−0.283168	−0.141584	−	0.989926i	$-0.545220\pi$
$811$	−8.06408	−0.283168	−0.141584	+	0.989926i	$0.545220\pi$
$812$	0.129921	0.00455932
$813$	22.6738	0.795205
$814$	2.26420	0.0793601
$815$	0	0
$816$	−2.86682	−0.100359
$817$	−37.1364	−1.29924
$818$	−3.83410	−0.134056
$819$	−0.0117017	−0.000408891 0
$820$	0	0
$821$	31.8297	1.11086	0.555432	−	0.831562i	$-0.312553\pi$
$821$	31.8297	1.11086	0.555432	+	0.831562i	$0.312553\pi$
$822$	−9.66999	−0.337279
$823$	−50.1305	−1.74744	−0.873719	−	0.486431i	$-0.838299\pi$
$823$	−50.1305	−1.74744	−0.873719	+	0.486431i	$0.838299\pi$
$824$	38.4095	1.33806
$825$	0	0
$826$	0.149158	0.00518987
$827$	−8.49029	−0.295236	−0.147618	−	0.989044i	$-0.547161\pi$
$827$	−8.49029	−0.295236	−0.147618	+	0.989044i	$0.547161\pi$
$828$	2.07278	0.0720341
$829$	5.42789	0.188518	0.0942592	−	0.995548i	$-0.469952\pi$
$829$	5.42789	0.188518	0.0942592	+	0.995548i	$0.469952\pi$
$830$	0	0
$831$	30.2620	1.04978
$832$	1.08986	0.0377842
$833$	−35.8716	−1.24288
$834$	1.39739	0.0483876
$835$	0	0
$836$	37.2124	1.28702
$837$	2.97719	0.102907
$838$	21.7595	0.751669
$839$	−51.6995	−1.78486	−0.892432	−	0.451182i	$-0.851003\pi$
$839$	−51.6995	−1.78486	−0.892432	+	0.451182i	$0.851003\pi$
$840$	0	0
$841$	−22.7096	−0.783089
$842$	15.4692	0.533104
$843$	9.60222	0.330718
$844$	21.8591	0.752422
$845$	0	0
$846$	0.801361	0.0275514
$847$	−0.200040	−0.00687345
$848$	0.292589	0.0100475
$849$	25.0562	0.859925
$850$	0	0
$851$	1.07018	0.0366854
$852$	−6.55411	−0.224540
$853$	49.5755	1.69743	0.848716	−	0.528849i	$-0.177376\pi$
$853$	49.5755	1.69743	0.848716	+	0.528849i	$0.177376\pi$
$854$	0.204564	0.00700004
$855$	0	0
$856$	14.0982	0.481866
$857$	32.4895	1.10982	0.554910	−	0.831911i	$-0.312753\pi$
$857$	32.4895	1.10982	0.554910	+	0.831911i	$0.312753\pi$
$858$	0.990651	0.0338203
$859$	−26.2076	−0.894192	−0.447096	−	0.894486i	$-0.647542\pi$
$859$	−26.2076	−0.894192	−0.447096	+	0.894486i	$0.647542\pi$
$860$	0	0
$861$	0.0293664	0.00100080
$862$	−2.30924	−0.0786530
$863$	−4.85547	−0.165282	−0.0826410	−	0.996579i	$-0.526335\pi$
$863$	−4.85547	−0.165282	−0.0826410	+	0.996579i	$0.526335\pi$
$864$	−5.82987	−0.198336
$865$	0	0
$866$	−8.91446	−0.302926
$867$	−9.27156	−0.314879
$868$	−0.154221	−0.00523461
$869$	49.1674	1.66789
$870$	0	0
$871$	−0.133334	−0.00451785
$872$	25.0158	0.847142
$873$	9.37770	0.317387
$874$	−8.31850	−0.281377
$875$	0	0
$876$	−5.16811	−0.174614
$877$	−6.07437	−0.205117	−0.102559	−	0.994727i	$-0.532703\pi$
$877$	−6.07437	−0.205117	−0.102559	+	0.994727i	$0.532703\pi$
$878$	11.3681	0.383654
$879$	2.51938	0.0849767
$880$	0	0
$881$	−43.5432	−1.46701	−0.733503	−	0.679686i	$-0.762116\pi$
$881$	−43.5432	−1.46701	−0.733503	+	0.679686i	$0.762116\pi$
$882$	−5.60836	−0.188843
$883$	−45.9298	−1.54566	−0.772831	−	0.634612i	$-0.781160\pi$
$883$	−45.9298	−1.54566	−0.772831	+	0.634612i	$0.781160\pi$
$884$	−2.13471	−0.0717979
$885$	0	0
$886$	21.0739	0.707991
$887$	−9.05211	−0.303940	−0.151970	−	0.988385i	$-0.548562\pi$
$887$	−9.05211	−0.303940	−0.151970	+	0.988385i	$0.548562\pi$
$888$	−1.88639	−0.0633033
$889$	0.310350	0.0104088
$890$	0	0
$891$	−4.03032	−0.135021
$892$	−32.9799	−1.10425
$893$	6.79994	0.227551
$894$	9.85475	0.329592
$895$	0	0
$896$	0.336192	0.0112314
$897$	0.468235	0.0156339
$898$	23.8730	0.796651
$899$	−7.46699	−0.249038
$900$	0	0
$901$	2.68129	0.0893266
$902$	−2.48612	−0.0827788
$903$	−0.208349	−0.00693341
$904$	53.4036	1.77618
$905$	0	0
$906$	−3.14152	−0.104370
$907$	−25.7166	−0.853905	−0.426953	−	0.904274i	$-0.640413\pi$
$907$	−25.7166	−0.853905	−0.426953	+	0.904274i	$0.640413\pi$
$908$	−37.3299	−1.23884
$909$	−1.04436	−0.0346392
$910$	0	0
$911$	21.4777	0.711588	0.355794	−	0.934564i	$-0.384210\pi$
$911$	21.4777	0.711588	0.355794	+	0.934564i	$0.384210\pi$
$912$	−3.80332	−0.125941
$913$	−60.9061	−2.01570
$914$	−5.63184	−0.186285
$915$	0	0
$916$	−19.9846	−0.660308
$917$	0.229030	0.00756324
$918$	−4.10744	−0.135566
$919$	−38.1338	−1.25792	−0.628960	−	0.777438i	$-0.716519\pi$
$919$	−38.1338	−1.25792	−0.628960	+	0.777438i	$0.716519\pi$
$920$	0	0
$921$	21.8715	0.720691
$922$	22.5788	0.743594
$923$	−1.48055	−0.0487331
$924$	0.208775	0.00686819
$925$	0	0
$926$	−22.9627	−0.754602
$927$	−14.2742	−0.468827
$928$	14.6217	0.479982
$929$	40.6443	1.33350	0.666748	−	0.745284i	$-0.267686\pi$
$929$	40.6443	1.33350	0.666748	+	0.745284i	$0.267686\pi$
$930$	0	0
$931$	−47.5897	−1.55969
$932$	−11.8202	−0.387183
$933$	28.3769	0.929018
$934$	−16.6110	−0.543528
$935$	0	0
$936$	−0.825351	−0.0269774
$937$	−48.8197	−1.59487	−0.797435	−	0.603405i	$-0.793810\pi$
$937$	−48.8197	−1.59487	−0.797435	+	0.603405i	$0.793810\pi$
$938$	0.0132896	0.000433921 0
$939$	18.3432	0.598608
$940$	0	0
$941$	12.2527	0.399425	0.199713	−	0.979855i	$-0.435999\pi$
$941$	12.2527	0.399425	0.199713	+	0.979855i	$0.435999\pi$
$942$	−17.6297	−0.574405
$943$	−1.17507	−0.0382657
$944$	−2.72885	−0.0888165
$945$	0	0
$946$	17.6385	0.573478
$947$	−36.5901	−1.18902	−0.594509	−	0.804089i	$-0.702654\pi$
$947$	−36.5901	−1.18902	−0.594509	+	0.804089i	$0.702654\pi$
$948$	−16.5645	−0.537991
$949$	−1.16746	−0.0378974
$950$	0	0
$951$	30.0078	0.973071
$952$	0.526169	0.0170532
$953$	−10.9087	−0.353369	−0.176685	−	0.984268i	$-0.556537\pi$
$953$	−10.9087	−0.353369	−0.176685	+	0.984268i	$0.556537\pi$
$954$	0.419207	0.0135723
$955$	0	0
$956$	−4.52191	−0.146249
$957$	10.1083	0.326756
$958$	1.36475	0.0440931
$959$	−0.460356	−0.0148657
$960$	0	0
$961$	−22.1364	−0.714076
$962$	−0.172317	−0.00555572
$963$	−5.23935	−0.168836
$964$	4.79994	0.154596
$965$	0	0
$966$	−0.0466698	−0.00150158
$967$	51.3871	1.65250	0.826250	−	0.563304i	$-0.190470\pi$
$967$	51.3871	1.65250	0.826250	+	0.563304i	$0.190470\pi$
$968$	−14.1093	−0.453490
$969$	−34.8537	−1.11966
$970$	0	0
$971$	−35.7381	−1.14689	−0.573446	−	0.819244i	$-0.694394\pi$
$971$	−35.7381	−1.14689	−0.573446	+	0.819244i	$0.694394\pi$
$972$	1.35782	0.0435521
$973$	0.0665251	0.00213270
$974$	−0.655913	−0.0210168
$975$	0	0
$976$	−3.74251	−0.119795
$977$	20.1751	0.645458	0.322729	−	0.946491i	$-0.395400\pi$
$977$	20.1751	0.645458	0.322729	+	0.946491i	$0.395400\pi$
$978$	14.1745	0.453250
$979$	9.52705	0.304486
$980$	0	0
$981$	−9.29670	−0.296821
$982$	12.9790	0.414175
$983$	−42.6737	−1.36108	−0.680540	−	0.732711i	$-0.738255\pi$
$983$	−42.6737	−1.36108	−0.680540	+	0.732711i	$0.738255\pi$
$984$	2.07129	0.0660302
$985$	0	0
$986$	10.3018	0.328075
$987$	0.0381502	0.00121433
$988$	−2.83205	−0.0900994
$989$	8.33692	0.265099
$990$	0	0
$991$	50.1507	1.59309	0.796545	−	0.604579i	$-0.206659\pi$
$991$	50.1507	1.59309	0.796545	+	0.604579i	$0.206659\pi$
$992$	−17.3566	−0.551073
$993$	16.7846	0.532645
$994$	0.147569	0.00468062
$995$	0	0
$996$	20.5193	0.650180
$997$	−52.9439	−1.67675	−0.838375	−	0.545093i	$-0.816494\pi$
$997$	−52.9439	−1.67675	−0.838375	+	0.545093i	$0.816494\pi$
$998$	−27.1929	−0.860776
$999$	0.701046	0.0221801

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.bg.1.6		10
5.2	odd	4		705.2.c.b.424.13	yes	20
5.3	odd	4		705.2.c.b.424.8	✓	20
5.4	even	2		3525.2.a.bf.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
705.2.c.b.424.8	✓	20	5.3	odd	4
705.2.c.b.424.13	yes	20	5.2	odd	4
3525.2.a.bf.1.5		10	5.4	even	2
3525.2.a.bg.1.6		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:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3525.a (trivial)

\(f(q)\)	\(=\)	\(q+0.801361 q^{2} -1.00000 q^{3} -1.35782 q^{4} -0.801361 q^{6} -0.0381502 q^{7} -2.69083 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.801361 q^{2} -1.00000 q^{3} -1.35782 q^{4} -0.801361 q^{6} -0.0381502 q^{7} -2.69083 q^{8} +1.00000 q^{9} -4.03032 q^{11} +1.35782 q^{12} +0.306728 q^{13} -0.0305721 q^{14} +0.559317 q^{16} +5.12558 q^{17} +0.801361 q^{18} +6.79994 q^{19} +0.0381502 q^{21} -3.22974 q^{22} -1.52655 q^{23} +2.69083 q^{24} +0.245800 q^{26} -1.00000 q^{27} +0.0518011 q^{28} +2.50807 q^{29} -2.97719 q^{31} +5.82987 q^{32} +4.03032 q^{33} +4.10744 q^{34} -1.35782 q^{36} -0.701046 q^{37} +5.44921 q^{38} -0.306728 q^{39} +0.769758 q^{41} +0.0305721 q^{42} -5.46128 q^{43} +5.47245 q^{44} -1.22332 q^{46} +1.00000 q^{47} -0.559317 q^{48} -6.99854 q^{49} -5.12558 q^{51} -0.416481 q^{52} +0.523119 q^{53} -0.801361 q^{54} +0.102655 q^{56} -6.79994 q^{57} +2.00987 q^{58} -4.87890 q^{59} -6.69121 q^{61} -2.38580 q^{62} -0.0381502 q^{63} +3.55320 q^{64} +3.22974 q^{66} -0.434698 q^{67} -6.95962 q^{68} +1.52655 q^{69} -4.82694 q^{71} -2.69083 q^{72} -3.80618 q^{73} -0.561791 q^{74} -9.23310 q^{76} +0.153757 q^{77} -0.245800 q^{78} -12.1994 q^{79} +1.00000 q^{81} +0.616854 q^{82} +15.1120 q^{83} -0.0518011 q^{84} -4.37646 q^{86} -2.50807 q^{87} +10.8449 q^{88} -2.36384 q^{89} -0.0117017 q^{91} +2.07278 q^{92} +2.97719 q^{93} +0.801361 q^{94} -5.82987 q^{96} +9.37770 q^{97} -5.60836 q^{98} -4.03032 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{2} - 10 q^{3} + 7 q^{4} - 3 q^{6} + 9 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 3 * q^2 - 10 * q^3 + 7 * q^4 - 3 * q^6 + 9 * q^8 + 10 * q^9	\( 10 q + 3 q^{2} - 10 q^{3} + 7 q^{4} - 3 q^{6} + 9 q^{8} + 10 q^{9} - 16 q^{11} - 7 q^{12} + q^{13} - 12 q^{14} - 3 q^{16} + 14 q^{17} + 3 q^{18} - 26 q^{19} + 7 q^{23} - 9 q^{24} - 10 q^{26} - 10 q^{27} - 24 q^{28} - 14 q^{29} - 22 q^{31} + 11 q^{32} + 16 q^{33} - 12 q^{34} + 7 q^{36} + 2 q^{37} - 2 q^{38} - q^{39} - 22 q^{41} + 12 q^{42} - 11 q^{43} - 36 q^{44} - 14 q^{46} + 10 q^{47} + 3 q^{48} + 2 q^{49} - 14 q^{51} + 14 q^{52} + 22 q^{53} - 3 q^{54} - 48 q^{56} + 26 q^{57} - 20 q^{58} - 37 q^{59} - 25 q^{61} - 2 q^{62} - 7 q^{64} - 4 q^{67} + 8 q^{68} - 7 q^{69} - 27 q^{71} + 9 q^{72} + q^{73} + 4 q^{74} - 42 q^{76} + 34 q^{77} + 10 q^{78} + 5 q^{79} + 10 q^{81} - 32 q^{82} + 2 q^{83} + 24 q^{84} - 6 q^{86} + 14 q^{87} - 58 q^{88} + 9 q^{89} - 64 q^{91} + 34 q^{92} + 22 q^{93} + 3 q^{94} - 11 q^{96} - 40 q^{97} + 29 q^{98} - 16 q^{99}+O(q^{100}) \) 10 * q + 3 * q^2 - 10 * q^3 + 7 * q^4 - 3 * q^6 + 9 * q^8 + 10 * q^9 - 16 * q^11 - 7 * q^12 + q^13 - 12 * q^14 - 3 * q^16 + 14 * q^17 + 3 * q^18 - 26 * q^19 + 7 * q^23 - 9 * q^24 - 10 * q^26 - 10 * q^27 - 24 * q^28 - 14 * q^29 - 22 * q^31 + 11 * q^32 + 16 * q^33 - 12 * q^34 + 7 * q^36 + 2 * q^37 - 2 * q^38 - q^39 - 22 * q^41 + 12 * q^42 - 11 * q^43 - 36 * q^44 - 14 * q^46 + 10 * q^47 + 3 * q^48 + 2 * q^49 - 14 * q^51 + 14 * q^52 + 22 * q^53 - 3 * q^54 - 48 * q^56 + 26 * q^57 - 20 * q^58 - 37 * q^59 - 25 * q^61 - 2 * q^62 - 7 * q^64 - 4 * q^67 + 8 * q^68 - 7 * q^69 - 27 * q^71 + 9 * q^72 + q^73 + 4 * q^74 - 42 * q^76 + 34 * q^77 + 10 * q^78 + 5 * q^79 + 10 * q^81 - 32 * q^82 + 2 * q^83 + 24 * q^84 - 6 * q^86 + 14 * q^87 - 58 * q^88 + 9 * q^89 - 64 * q^91 + 34 * q^92 + 22 * q^93 + 3 * q^94 - 11 * q^96 - 40 * q^97 + 29 * q^98 - 16 * q^99

Introduction

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