LMFDB - Embedded newform 946.2.a.h.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [946,2,Mod(1,946)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(946, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("946.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 946 = 2 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	946.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:	$7.55384803121$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.13676.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 6x^{2} + 7x + 1 $ x^4 - x^3 - 6x^2 + 7x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.42957$ of defining polynomial
Character	$\chi$	$=$	946.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.956338 q^{3} +1.00000 q^{4} -2.22628 q^{5} -0.956338 q^{6} +1.00000 q^{8} -2.08542 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.956338 q^{3} +1.00000 q^{4} -2.22628 q^{5} -0.956338 q^{6} +1.00000 q^{8} -2.08542 q^{9} -2.22628 q^{10} -1.00000 q^{11} -0.956338 q^{12} +4.85913 q^{13} +2.12908 q^{15} +1.00000 q^{16} +7.40890 q^{17} -2.08542 q^{18} +1.36715 q^{19} -2.22628 q^{20} -1.00000 q^{22} +7.08542 q^{23} -0.956338 q^{24} -0.0436620 q^{25} +4.85913 q^{26} +4.86338 q^{27} +2.95634 q^{29} +2.12908 q^{30} -3.49623 q^{31} +1.00000 q^{32} +0.956338 q^{33} +7.40890 q^{34} -2.08542 q^{36} +10.2680 q^{37} +1.36715 q^{38} -4.64697 q^{39} -2.22628 q^{40} -7.45066 q^{41} -1.00000 q^{43} -1.00000 q^{44} +4.64273 q^{45} +7.08542 q^{46} +7.32158 q^{47} -0.956338 q^{48} -7.00000 q^{49} -0.0436620 q^{50} -7.08542 q^{51} +4.85913 q^{52} +7.91268 q^{53} +4.86338 q^{54} +2.22628 q^{55} -1.30746 q^{57} +2.95634 q^{58} -8.45257 q^{59} +2.12908 q^{60} -10.9051 q^{61} -3.49623 q^{62} +1.00000 q^{64} -10.8178 q^{65} +0.956338 q^{66} -1.89292 q^{67} +7.40890 q^{68} -6.77605 q^{69} +10.0460 q^{71} -2.08542 q^{72} -0.0873239 q^{73} +10.2680 q^{74} +0.0417556 q^{75} +1.36715 q^{76} -4.64697 q^{78} -5.94455 q^{79} -2.22628 q^{80} +1.60522 q^{81} -7.45066 q^{82} +8.25816 q^{83} -16.4943 q^{85} -1.00000 q^{86} -2.82726 q^{87} -1.00000 q^{88} +14.7305 q^{89} +4.64273 q^{90} +7.08542 q^{92} +3.34358 q^{93} +7.32158 q^{94} -3.04366 q^{95} -0.956338 q^{96} +17.9906 q^{97} -7.00000 q^{98} +2.08542 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + q^{3} + 4 q^{4} + q^{5} + q^{6} + 4 q^{8} + 11 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + q^3 + 4 * q^4 + q^5 + q^6 + 4 * q^8 + 11 * q^9	$ 4 q + 4 q^{2} + q^{3} + 4 q^{4} + q^{5} + q^{6} + 4 q^{8} + 11 q^{9} + q^{10} - 4 q^{11} + q^{12} + 10 q^{13} - 6 q^{15} + 4 q^{16} + 5 q^{17} + 11 q^{18} + 5 q^{19} + q^{20} - 4 q^{22} + 9 q^{23} + q^{24} - 5 q^{25} + 10 q^{26} + 4 q^{27} + 7 q^{29} - 6 q^{30} + q^{31} + 4 q^{32} - q^{33} + 5 q^{34} + 11 q^{36} + 7 q^{37} + 5 q^{38} - 8 q^{39} + q^{40} + 19 q^{41} - 4 q^{43} - 4 q^{44} + 14 q^{45} + 9 q^{46} - 5 q^{47} + q^{48} - 28 q^{49} - 5 q^{50} - 9 q^{51} + 10 q^{52} + 22 q^{53} + 4 q^{54} - q^{55} + 18 q^{57} + 7 q^{58} - 14 q^{59} - 6 q^{60} - 4 q^{61} + q^{62} + 4 q^{64} + 6 q^{65} - q^{66} - 8 q^{67} + 5 q^{68} - 2 q^{69} + 10 q^{71} + 11 q^{72} - 10 q^{73} + 7 q^{74} - 24 q^{75} + 5 q^{76} - 8 q^{78} + 5 q^{79} + q^{80} + 20 q^{81} + 19 q^{82} + 4 q^{83} - 22 q^{85} - 4 q^{86} - 21 q^{87} - 4 q^{88} + 14 q^{90} + 9 q^{92} - 35 q^{93} - 5 q^{94} - 17 q^{95} + q^{96} + 13 q^{97} - 28 q^{98} - 11 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + q^3 + 4 * q^4 + q^5 + q^6 + 4 * q^8 + 11 * q^9 + q^10 - 4 * q^11 + q^12 + 10 * q^13 - 6 * q^15 + 4 * q^16 + 5 * q^17 + 11 * q^18 + 5 * q^19 + q^20 - 4 * q^22 + 9 * q^23 + q^24 - 5 * q^25 + 10 * q^26 + 4 * q^27 + 7 * q^29 - 6 * q^30 + q^31 + 4 * q^32 - q^33 + 5 * q^34 + 11 * q^36 + 7 * q^37 + 5 * q^38 - 8 * q^39 + q^40 + 19 * q^41 - 4 * q^43 - 4 * q^44 + 14 * q^45 + 9 * q^46 - 5 * q^47 + q^48 - 28 * q^49 - 5 * q^50 - 9 * q^51 + 10 * q^52 + 22 * q^53 + 4 * q^54 - q^55 + 18 * q^57 + 7 * q^58 - 14 * q^59 - 6 * q^60 - 4 * q^61 + q^62 + 4 * q^64 + 6 * q^65 - q^66 - 8 * q^67 + 5 * q^68 - 2 * q^69 + 10 * q^71 + 11 * q^72 - 10 * q^73 + 7 * q^74 - 24 * q^75 + 5 * q^76 - 8 * q^78 + 5 * q^79 + q^80 + 20 * q^81 + 19 * q^82 + 4 * q^83 - 22 * q^85 - 4 * q^86 - 21 * q^87 - 4 * q^88 + 14 * q^90 + 9 * q^92 - 35 * q^93 - 5 * q^94 - 17 * q^95 + q^96 + 13 * q^97 - 28 * q^98 - 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.956338	−0.552142	−0.276071	−	0.961137i	$-0.589032\pi$
$3$	−0.956338	−0.552142	−0.276071	+	0.961137i	$0.589032\pi$
$4$	1.00000	0.500000
$5$	−2.22628	−0.995624	−0.497812	−	0.867285i	$-0.665863\pi$
$5$	−2.22628	−0.995624	−0.497812	+	0.867285i	$0.665863\pi$
$6$	−0.956338	−0.390423
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	1.00000	0.353553
$9$	−2.08542	−0.695139
$10$	−2.22628	−0.704013
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.956338	−0.276071
$13$	4.85913	1.34768	0.673841	−	0.738877i	$-0.264643\pi$
$13$	4.85913	1.34768	0.673841	+	0.738877i	$0.264643\pi$
$14$	0	0
$15$	2.12908	0.549726
$16$	1.00000	0.250000
$17$	7.40890	1.79692	0.898462	−	0.439052i	$-0.144686\pi$
$17$	7.40890	1.79692	0.898462	+	0.439052i	$0.144686\pi$
$18$	−2.08542	−0.491538
$19$	1.36715	0.313646	0.156823	−	0.987627i	$-0.449875\pi$
$19$	1.36715	0.313646	0.156823	+	0.987627i	$0.449875\pi$
$20$	−2.22628	−0.497812
$21$	0	0
$22$	−1.00000	−0.213201
$23$	7.08542	1.47741	0.738706	−	0.674028i	$-0.235437\pi$
$23$	7.08542	1.47741	0.738706	+	0.674028i	$0.235437\pi$
$24$	−0.956338	−0.195212
$25$	−0.0436620	−0.00873239
$26$	4.85913	0.952955
$27$	4.86338	0.935958
$28$	0	0
$29$	2.95634	0.548978	0.274489	−	0.961590i	$-0.411491\pi$
$29$	2.95634	0.548978	0.274489	+	0.961590i	$0.411491\pi$
$30$	2.12908	0.388715
$31$	−3.49623	−0.627941	−0.313971	−	0.949433i	$-0.601659\pi$
$31$	−3.49623	−0.627941	−0.313971	+	0.949433i	$0.601659\pi$
$32$	1.00000	0.176777
$33$	0.956338	0.166477
$34$	7.40890	1.27062
$35$	0	0
$36$	−2.08542	−0.347570
$37$	10.2680	1.68806	0.844028	−	0.536300i	$-0.180178\pi$
$37$	10.2680	1.68806	0.844028	+	0.536300i	$0.180178\pi$
$38$	1.36715	0.221781
$39$	−4.64697	−0.744111
$40$	−2.22628	−0.352006
$41$	−7.45066	−1.16360	−0.581799	−	0.813333i	$-0.697651\pi$
$41$	−7.45066	−1.16360	−0.581799	+	0.813333i	$0.697651\pi$
$42$	0	0
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−1.00000	−0.150756
$45$	4.64273	0.692097
$46$	7.08542	1.04469
$47$	7.32158	1.06796	0.533981	−	0.845496i	$-0.320695\pi$
$47$	7.32158	1.06796	0.533981	+	0.845496i	$0.320695\pi$
$48$	−0.956338	−0.138036
$49$	−7.00000	−1.00000
$50$	−0.0436620	−0.00617473
$51$	−7.08542	−0.992157
$52$	4.85913	0.673841
$53$	7.91268	1.08689	0.543445	−	0.839445i	$-0.317120\pi$
$53$	7.91268	1.08689	0.543445	+	0.839445i	$0.317120\pi$
$54$	4.86338	0.661822
$55$	2.22628	0.300192
$56$	0	0
$57$	−1.30746	−0.173177
$58$	2.95634	0.388186
$59$	−8.45257	−1.10043	−0.550215	−	0.835023i	$-0.685454\pi$
$59$	−8.45257	−1.10043	−0.550215	+	0.835023i	$0.685454\pi$
$60$	2.12908	0.274863
$61$	−10.9051	−1.39626	−0.698130	−	0.715971i	$-0.745984\pi$
$61$	−10.9051	−1.39626	−0.698130	+	0.715971i	$0.745984\pi$
$62$	−3.49623	−0.444022
$63$	0	0
$64$	1.00000	0.125000
$65$	−10.8178	−1.34178
$66$	0.956338	0.117717
$67$	−1.89292	−0.231257	−0.115628	−	0.993293i	$-0.536888\pi$
$67$	−1.89292	−0.231257	−0.115628	+	0.993293i	$0.536888\pi$
$68$	7.40890	0.898462
$69$	−6.77605	−0.815741
$70$	0	0
$71$	10.0460	1.19224	0.596120	−	0.802895i	$-0.296708\pi$
$71$	10.0460	1.19224	0.596120	+	0.802895i	$0.296708\pi$
$72$	−2.08542	−0.245769
$73$	−0.0873239	−0.0102205	−0.00511025	−	0.999987i	$-0.501627\pi$
$73$	−0.0873239	−0.0102205	−0.00511025	+	0.999987i	$0.501627\pi$
$74$	10.2680	1.19364
$75$	0.0417556	0.00482152
$76$	1.36715	0.156823
$77$	0	0
$78$	−4.64697	−0.526166
$79$	−5.94455	−0.668814	−0.334407	−	0.942429i	$-0.608536\pi$
$79$	−5.94455	−0.668814	−0.334407	+	0.942429i	$0.608536\pi$
$80$	−2.22628	−0.248906
$81$	1.60522	0.178358
$82$	−7.45066	−0.822788
$83$	8.25816	0.906451	0.453225	−	0.891396i	$-0.350273\pi$
$83$	8.25816	0.906451	0.453225	+	0.891396i	$0.350273\pi$
$84$	0	0
$85$	−16.4943	−1.78906
$86$	−1.00000	−0.107833
$87$	−2.82726	−0.303114
$88$	−1.00000	−0.106600
$89$	14.7305	1.56143	0.780714	−	0.624888i	$-0.214855\pi$
$89$	14.7305	1.56143	0.780714	+	0.624888i	$0.214855\pi$
$90$	4.64273	0.489387
$91$	0	0
$92$	7.08542	0.738706
$93$	3.34358	0.346713
$94$	7.32158	0.755163
$95$	−3.04366	−0.312273
$96$	−0.956338	−0.0976058
$97$	17.9906	1.82666	0.913332	−	0.407216i	$-0.133500\pi$
$97$	17.9906	1.82666	0.913332	+	0.407216i	$0.133500\pi$
$98$	−7.00000	−0.707107
$99$	2.08542	0.209592
$100$	−0.0436620	−0.00436620
$101$	15.2244	1.51488	0.757441	−	0.652904i	$-0.226449\pi$
$101$	15.2244	1.51488	0.757441	+	0.652904i	$0.226449\pi$
$102$	−7.08542	−0.701561
$103$	−16.3794	−1.61391	−0.806953	−	0.590615i	$-0.798885\pi$
$103$	−16.3794	−1.61391	−0.806953	+	0.590615i	$0.798885\pi$
$104$	4.85913	0.476477
$105$	0	0
$106$	7.91268	0.768547
$107$	−11.0122	−1.06459	−0.532296	−	0.846559i	$-0.678671\pi$
$107$	−11.0122	−1.06459	−0.532296	+	0.846559i	$0.678671\pi$
$108$	4.86338	0.467979
$109$	−3.14087	−0.300840	−0.150420	−	0.988622i	$-0.548063\pi$
$109$	−3.14087	−0.300840	−0.150420	+	0.988622i	$0.548063\pi$
$110$	2.22628	0.212268
$111$	−9.81972	−0.932046
$112$	0	0
$113$	−12.5597	−1.18151	−0.590756	−	0.806850i	$-0.701171\pi$
$113$	−12.5597	−1.18151	−0.590756	+	0.806850i	$0.701171\pi$
$114$	−1.30746	−0.122455
$115$	−15.7741	−1.47095
$116$	2.95634	0.274489
$117$	−10.1333	−0.936826
$118$	−8.45257	−0.778122
$119$	0	0
$120$	2.12908	0.194357
$121$	1.00000	0.0909091
$122$	−10.9051	−0.987304
$123$	7.12535	0.642471
$124$	−3.49623	−0.313971
$125$	11.2286	1.00432
$126$	0	0
$127$	−5.72815	−0.508291	−0.254145	−	0.967166i	$-0.581794\pi$
$127$	−5.72815	−0.508291	−0.254145	+	0.967166i	$0.581794\pi$
$128$	1.00000	0.0883883
$129$	0.956338	0.0842009
$130$	−10.8178	−0.948785
$131$	3.69064	0.322452	0.161226	−	0.986917i	$-0.448455\pi$
$131$	3.69064	0.322452	0.161226	+	0.986917i	$0.448455\pi$
$132$	0.956338	0.0832385
$133$	0	0
$134$	−1.89292	−0.163523
$135$	−10.8273	−0.931862
$136$	7.40890	0.635308
$137$	−8.36524	−0.714691	−0.357345	−	0.933972i	$-0.616318\pi$
$137$	−8.36524	−0.714691	−0.357345	+	0.933972i	$0.616318\pi$
$138$	−6.77605	−0.576816
$139$	20.9249	1.77483	0.887413	−	0.460975i	$-0.152500\pi$
$139$	20.9249	1.77483	0.887413	+	0.460975i	$0.152500\pi$
$140$	0	0
$141$	−7.00191	−0.589667
$142$	10.0460	0.843042
$143$	−4.85913	−0.406341
$144$	−2.08542	−0.173785
$145$	−6.58165	−0.546576
$146$	−0.0873239	−0.00722698
$147$	6.69437	0.552142
$148$	10.2680	0.844028
$149$	−8.48020	−0.694725	−0.347362	−	0.937731i	$-0.612923\pi$
$149$	−8.48020	−0.694725	−0.347362	+	0.937731i	$0.612923\pi$
$150$	0.0417556	0.00340933
$151$	−18.4488	−1.50134	−0.750669	−	0.660678i	$-0.770269\pi$
$151$	−18.4488	−1.50134	−0.750669	+	0.660678i	$0.770269\pi$
$152$	1.36715	0.110890
$153$	−15.4507	−1.24911
$154$	0	0
$155$	7.78360	0.625194
$156$	−4.64697	−0.372056
$157$	−23.4093	−1.86827	−0.934134	−	0.356922i	$-0.883826\pi$
$157$	−23.4093	−1.86827	−0.934134	+	0.356922i	$0.883826\pi$
$158$	−5.94455	−0.472923
$159$	−7.56719	−0.600117
$160$	−2.22628	−0.176003
$161$	0	0
$162$	1.60522	0.126118
$163$	8.18496	0.641095	0.320548	−	0.947232i	$-0.396133\pi$
$163$	8.18496	0.641095	0.320548	+	0.947232i	$0.396133\pi$
$164$	−7.45066	−0.581799
$165$	−2.12908	−0.165749
$166$	8.25816	0.640957
$167$	8.77181	0.678783	0.339392	−	0.940645i	$-0.389779\pi$
$167$	8.77181	0.678783	0.339392	+	0.940645i	$0.389779\pi$
$168$	0	0
$169$	10.6112	0.816245
$170$	−16.4943	−1.26506
$171$	−2.85108	−0.218027
$172$	−1.00000	−0.0762493
$173$	16.9511	1.28877	0.644385	−	0.764701i	$-0.277113\pi$
$173$	16.9511	1.28877	0.644385	+	0.764701i	$0.277113\pi$
$174$	−2.82726	−0.214334
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	8.08351	0.607594
$178$	14.7305	1.10410
$179$	−1.35866	−0.101551	−0.0507755	−	0.998710i	$-0.516169\pi$
$179$	−1.35866	−0.101551	−0.0507755	+	0.998710i	$0.516169\pi$
$180$	4.64273	0.346049
$181$	17.2704	1.28370	0.641848	−	0.766831i	$-0.278168\pi$
$181$	17.2704	1.28370	0.641848	+	0.766831i	$0.278168\pi$
$182$	0	0
$183$	10.4290	0.770933
$184$	7.08542	0.522344
$185$	−22.8596	−1.68067
$186$	3.34358	0.245163
$187$	−7.40890	−0.541793
$188$	7.32158	0.533981
$189$	0	0
$190$	−3.04366	−0.220810
$191$	−3.13705	−0.226989	−0.113495	−	0.993539i	$-0.536204\pi$
$191$	−3.13705	−0.226989	−0.113495	+	0.993539i	$0.536204\pi$
$192$	−0.956338	−0.0690178
$193$	19.0618	1.37210	0.686051	−	0.727554i	$-0.259343\pi$
$193$	19.0618	1.37210	0.686051	+	0.727554i	$0.259343\pi$
$194$	17.9906	1.29165
$195$	10.3455	0.740855
$196$	−7.00000	−0.500000
$197$	−12.4986	−0.890486	−0.445243	−	0.895410i	$-0.646883\pi$
$197$	−12.4986	−0.890486	−0.445243	+	0.895410i	$0.646883\pi$
$198$	2.08542	0.148204
$199$	−25.2881	−1.79263	−0.896314	−	0.443420i	$-0.853765\pi$
$199$	−25.2881	−1.79263	−0.896314	+	0.443420i	$0.853765\pi$
$200$	−0.0436620	−0.00308737
$201$	1.81027	0.127686
$202$	15.2244	1.07118
$203$	0	0
$204$	−7.08542	−0.496078
$205$	16.5873	1.15851
$206$	−16.3794	−1.14120
$207$	−14.7761	−1.02701
$208$	4.85913	0.336920
$209$	−1.36715	−0.0945677
$210$	0	0
$211$	−11.8850	−0.818200	−0.409100	−	0.912490i	$-0.634157\pi$
$211$	−11.8850	−0.818200	−0.409100	+	0.912490i	$0.634157\pi$
$212$	7.91268	0.543445
$213$	−9.60737	−0.658286
$214$	−11.0122	−0.752780
$215$	2.22628	0.151831
$216$	4.86338	0.330911
$217$	0	0
$218$	−3.14087	−0.212726
$219$	0.0835112	0.00564316
$220$	2.22628	0.150096
$221$	36.0009	2.42168
$222$	−9.81972	−0.659056
$223$	−15.7643	−1.05565	−0.527827	−	0.849352i	$-0.676993\pi$
$223$	−15.7643	−1.05565	−0.527827	+	0.849352i	$0.676993\pi$
$224$	0	0
$225$	0.0910534	0.00607023
$226$	−12.5597	−0.835456
$227$	11.3633	0.754211	0.377106	−	0.926170i	$-0.376919\pi$
$227$	11.3633	0.754211	0.377106	+	0.926170i	$0.376919\pi$
$228$	−1.30746	−0.0865884
$229$	16.7980	1.11005	0.555023	−	0.831835i	$-0.312709\pi$
$229$	16.7980	1.11005	0.555023	+	0.831835i	$0.312709\pi$
$230$	−15.7741	−1.04012
$231$	0	0
$232$	2.95634	0.194093
$233$	−7.73803	−0.506935	−0.253468	−	0.967344i	$-0.581571\pi$
$233$	−7.73803	−0.506935	−0.253468	+	0.967344i	$0.581571\pi$
$234$	−10.1333	−0.662436
$235$	−16.2999	−1.06329
$236$	−8.45257	−0.550215
$237$	5.68500	0.369280
$238$	0	0
$239$	−11.8657	−0.767529	−0.383765	−	0.923431i	$-0.625373\pi$
$239$	−11.8657	−0.767529	−0.383765	+	0.923431i	$0.625373\pi$
$240$	2.12908	0.137431
$241$	−5.61118	−0.361448	−0.180724	−	0.983534i	$-0.557844\pi$
$241$	−5.61118	−0.361448	−0.180724	+	0.983534i	$0.557844\pi$
$242$	1.00000	0.0642824
$243$	−16.1253	−1.03444
$244$	−10.9051	−0.698130
$245$	15.5840	0.995624
$246$	7.12535	0.454296
$247$	6.64316	0.422694
$248$	−3.49623	−0.222011
$249$	−7.89759	−0.500490
$250$	11.2286	0.710160
$251$	−8.53608	−0.538792	−0.269396	−	0.963029i	$-0.586824\pi$
$251$	−8.53608	−0.538792	−0.269396	+	0.963029i	$0.586824\pi$
$252$	0	0
$253$	−7.08542	−0.445456
$254$	−5.72815	−0.359416
$255$	15.7741	0.987815
$256$	1.00000	0.0625000
$257$	14.2582	0.889400	0.444700	−	0.895680i	$-0.353310\pi$
$257$	14.2582	0.889400	0.444700	+	0.895680i	$0.353310\pi$
$258$	0.956338	0.0595390
$259$	0	0
$260$	−10.8178	−0.670892
$261$	−6.16520	−0.381616
$262$	3.69064	0.228008
$263$	−24.9249	−1.53693	−0.768467	−	0.639889i	$-0.778980\pi$
$263$	−24.9249	−1.53693	−0.768467	+	0.639889i	$0.778980\pi$
$264$	0.956338	0.0588585
$265$	−17.6159	−1.08213
$266$	0	0
$267$	−14.0873	−0.862130
$268$	−1.89292	−0.115628
$269$	23.3775	1.42535	0.712674	−	0.701495i	$-0.247484\pi$
$269$	23.3775	1.42535	0.712674	+	0.701495i	$0.247484\pi$
$270$	−10.8273	−0.658926
$271$	−10.5080	−0.638316	−0.319158	−	0.947701i	$-0.603400\pi$
$271$	−10.5080	−0.638316	−0.319158	+	0.947701i	$0.603400\pi$
$272$	7.40890	0.449231
$273$	0	0
$274$	−8.36524	−0.505363
$275$	0.0436620	0.00263292
$276$	−6.77605	−0.407871
$277$	7.81972	0.469841	0.234921	−	0.972015i	$-0.424517\pi$
$277$	7.81972	0.469841	0.234921	+	0.972015i	$0.424517\pi$
$278$	20.9249	1.25499
$279$	7.29110	0.436507
$280$	0	0
$281$	0.396687	0.0236644	0.0118322	−	0.999930i	$-0.496234\pi$
$281$	0.396687	0.0236644	0.0118322	+	0.999930i	$0.496234\pi$
$282$	−7.00191	−0.416957
$283$	23.2704	1.38328	0.691640	−	0.722242i	$-0.256888\pi$
$283$	23.2704	1.38328	0.691640	+	0.722242i	$0.256888\pi$
$284$	10.0460	0.596120
$285$	2.91077	0.172419
$286$	−4.85913	−0.287327
$287$	0	0
$288$	−2.08542	−0.122884
$289$	37.8919	2.22893
$290$	−6.58165	−0.386488
$291$	−17.2050	−1.00858
$292$	−0.0873239	−0.00511025
$293$	−6.04219	−0.352988	−0.176494	−	0.984302i	$-0.556476\pi$
$293$	−6.04219	−0.352988	−0.176494	+	0.984302i	$0.556476\pi$
$294$	6.69437	0.390423
$295$	18.8178	1.09562
$296$	10.2680	0.596818
$297$	−4.86338	−0.282202
$298$	−8.48020	−0.491245
$299$	34.4290	1.99108
$300$	0.0417556	0.00241076
$301$	0	0
$302$	−18.4488	−1.06161
$303$	−14.5597	−0.836430
$304$	1.36715	0.0784114
$305$	24.2779	1.39015
$306$	−15.4507	−0.883255
$307$	−12.0000	−0.684876	−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000	−0.684876	−0.342438	+	0.939540i	$0.611253\pi$
$308$	0	0
$309$	15.6642	0.891106
$310$	7.78360	0.442079
$311$	−20.6910	−1.17328	−0.586639	−	0.809849i	$-0.699549\pi$
$311$	−20.6910	−1.17328	−0.586639	+	0.809849i	$0.699549\pi$
$312$	−4.64697	−0.263083
$313$	−11.8018	−0.667076	−0.333538	−	0.942737i	$-0.608243\pi$
$313$	−11.8018	−0.667076	−0.333538	+	0.942737i	$0.608243\pi$
$314$	−23.4093	−1.32107
$315$	0	0
$316$	−5.94455	−0.334407
$317$	5.17838	0.290847	0.145423	−	0.989370i	$-0.453546\pi$
$317$	5.17838	0.290847	0.145423	+	0.989370i	$0.453546\pi$
$318$	−7.56719	−0.424347
$319$	−2.95634	−0.165523
$320$	−2.22628	−0.124453
$321$	10.5314	0.587806
$322$	0	0
$323$	10.1291	0.563597
$324$	1.60522	0.0891788
$325$	−0.212159	−0.0117685
$326$	8.18496	0.453323
$327$	3.00373	0.166107
$328$	−7.45066	−0.411394
$329$	0	0
$330$	−2.12908	−0.117202
$331$	−30.8376	−1.69499	−0.847493	−	0.530806i	$-0.821889\pi$
$331$	−30.8376	−1.69499	−0.847493	+	0.530806i	$0.821889\pi$
$332$	8.25816	0.453225
$333$	−21.4131	−1.17343
$334$	8.77181	0.479972
$335$	4.21417	0.230245
$336$	0	0
$337$	16.2943	0.887606	0.443803	−	0.896124i	$-0.353629\pi$
$337$	16.2943	0.887606	0.443803	+	0.896124i	$0.353629\pi$
$338$	10.6112	0.577172
$339$	12.0113	0.652363
$340$	−16.4943	−0.894530
$341$	3.49623	0.189331
$342$	−2.85108	−0.154169
$343$	0	0
$344$	−1.00000	−0.0539164
$345$	15.0854	0.812172
$346$	16.9511	0.911299
$347$	−30.8168	−1.65434	−0.827168	−	0.561955i	$-0.810049\pi$
$347$	−30.8168	−1.65434	−0.827168	+	0.561955i	$0.810049\pi$
$348$	−2.82726	−0.151557
$349$	22.3929	1.19866	0.599332	−	0.800501i	$-0.295433\pi$
$349$	22.3929	1.19866	0.599332	+	0.800501i	$0.295433\pi$
$350$	0	0
$351$	23.6318	1.26137
$352$	−1.00000	−0.0533002
$353$	9.82535	0.522951	0.261475	−	0.965210i	$-0.415791\pi$
$353$	9.82535	0.522951	0.261475	+	0.965210i	$0.415791\pi$
$354$	8.08351	0.429634
$355$	−22.3652	−1.18702
$356$	14.7305	0.780714
$357$	0	0
$358$	−1.35866	−0.0718075
$359$	19.1967	1.01317	0.506583	−	0.862191i	$-0.330908\pi$
$359$	19.1967	1.01317	0.506583	+	0.862191i	$0.330908\pi$
$360$	4.64273	0.244693
$361$	−17.1309	−0.901626
$362$	17.2704	0.907711
$363$	−0.956338	−0.0501947
$364$	0	0
$365$	0.194408	0.0101758
$366$	10.4290	0.545132
$367$	31.8577	1.66296	0.831478	−	0.555557i	$-0.187495\pi$
$367$	31.8577	1.66296	0.831478	+	0.555557i	$0.187495\pi$
$368$	7.08542	0.369353
$369$	15.5377	0.808862
$370$	−22.8596	−1.18841
$371$	0	0
$372$	3.34358	0.173356
$373$	8.27228	0.428323	0.214161	−	0.976798i	$-0.431298\pi$
$373$	8.27228	0.428323	0.214161	+	0.976798i	$0.431298\pi$
$374$	−7.40890	−0.383105
$375$	−10.7384	−0.554526
$376$	7.32158	0.377582
$377$	14.3652	0.739848
$378$	0	0
$379$	−19.8891	−1.02163	−0.510817	−	0.859689i	$-0.670657\pi$
$379$	−19.8891	−1.02163	−0.510817	+	0.859689i	$0.670657\pi$
$380$	−3.04366	−0.156137
$381$	5.47805	0.280649
$382$	−3.13705	−0.160506
$383$	−5.41878	−0.276887	−0.138443	−	0.990370i	$-0.544210\pi$
$383$	−5.41878	−0.276887	−0.138443	+	0.990370i	$0.544210\pi$
$384$	−0.956338	−0.0488029
$385$	0	0
$386$	19.0618	0.970222
$387$	2.08542	0.106008
$388$	17.9906	0.913332
$389$	13.2282	0.670696	0.335348	−	0.942094i	$-0.391146\pi$
$389$	13.2282	0.670696	0.335348	+	0.942094i	$0.391146\pi$
$390$	10.3455	0.523864
$391$	52.4952	2.65480
$392$	−7.00000	−0.353553
$393$	−3.52950	−0.178040
$394$	−12.4986	−0.629669
$395$	13.2343	0.665888
$396$	2.08542	0.104796
$397$	25.3539	1.27248	0.636238	−	0.771493i	$-0.280490\pi$
$397$	25.3539	1.27248	0.636238	+	0.771493i	$0.280490\pi$
$398$	−25.2881	−1.26758
$399$	0	0
$400$	−0.0436620	−0.00218310
$401$	−6.72643	−0.335902	−0.167951	−	0.985795i	$-0.553715\pi$
$401$	−6.72643	−0.335902	−0.167951	+	0.985795i	$0.553715\pi$
$402$	1.81027	0.0902879
$403$	−16.9886	−0.846265
$404$	15.2244	0.757441
$405$	−3.57367	−0.177577
$406$	0	0
$407$	−10.2680	−0.508968
$408$	−7.08542	−0.350780
$409$	−10.2977	−0.509187	−0.254594	−	0.967048i	$-0.581942\pi$
$409$	−10.2977	−0.509187	−0.254594	+	0.967048i	$0.581942\pi$
$410$	16.5873	0.819187
$411$	8.00000	0.394611
$412$	−16.3794	−0.806953
$413$	0	0
$414$	−14.7761	−0.726203
$415$	−18.3850	−0.902484
$416$	4.85913	0.238239
$417$	−20.0113	−0.979956
$418$	−1.36715	−0.0668695
$419$	31.7032	1.54880	0.774401	−	0.632695i	$-0.218051\pi$
$419$	31.7032	1.54880	0.774401	+	0.632695i	$0.218051\pi$
$420$	0	0
$421$	−24.6638	−1.20204	−0.601019	−	0.799235i	$-0.705238\pi$
$421$	−24.6638	−1.20204	−0.601019	+	0.799235i	$0.705238\pi$
$422$	−11.8850	−0.578555
$423$	−15.2686	−0.742382
$424$	7.91268	0.384274
$425$	−0.323487	−0.0156914
$426$	−9.60737	−0.465479
$427$	0	0
$428$	−11.0122	−0.532296
$429$	4.64697	0.224358
$430$	2.22628	0.107361
$431$	−35.7526	−1.72214	−0.861071	−	0.508485i	$-0.830206\pi$
$431$	−35.7526	−1.72214	−0.861071	+	0.508485i	$0.830206\pi$
$432$	4.86338	0.233989
$433$	−1.84511	−0.0886704	−0.0443352	−	0.999017i	$-0.514117\pi$
$433$	−1.84511	−0.0886704	−0.0443352	+	0.999017i	$0.514117\pi$
$434$	0	0
$435$	6.29428	0.301788
$436$	−3.14087	−0.150420
$437$	9.68682	0.463384
$438$	0.0835112	0.00399032
$439$	−0.00987998	−0.000471546 0	−0.000235773	−	1.00000i	$-0.500075\pi$
$439$	−0.00987998	−0.000471546 0	−0.000235773		1.00000i	$0.500075\pi$
$440$	2.22628	0.106134
$441$	14.5979	0.695139
$442$	36.0009	1.71239
$443$	−3.79710	−0.180406	−0.0902029	−	0.995923i	$-0.528752\pi$
$443$	−3.79710	−0.180406	−0.0902029	+	0.995923i	$0.528752\pi$
$444$	−9.81972	−0.466023
$445$	−32.7942	−1.55460
$446$	−15.7643	−0.746460
$447$	8.10994	0.383587
$448$	0	0
$449$	15.6348	0.737850	0.368925	−	0.929459i	$-0.379726\pi$
$449$	15.6348	0.737850	0.368925	+	0.929459i	$0.379726\pi$
$450$	0.0910534	0.00429230
$451$	7.45066	0.350838
$452$	−12.5597	−0.590756
$453$	17.6432	0.828952
$454$	11.3633	0.533308
$455$	0	0
$456$	−1.30746	−0.0612273
$457$	−14.2977	−0.668817	−0.334409	−	0.942428i	$-0.608537\pi$
$457$	−14.2977	−0.668817	−0.334409	+	0.942428i	$0.608537\pi$
$458$	16.7980	0.784921
$459$	36.0323	1.68184
$460$	−15.7741	−0.735473
$461$	−28.6458	−1.33417	−0.667085	−	0.744982i	$-0.732458\pi$
$461$	−28.6458	−1.33417	−0.667085	+	0.744982i	$0.732458\pi$
$462$	0	0
$463$	31.3126	1.45522	0.727609	−	0.685992i	$-0.240631\pi$
$463$	31.3126	1.45522	0.727609	+	0.685992i	$0.240631\pi$
$464$	2.95634	0.137245
$465$	−7.44375	−0.345196
$466$	−7.73803	−0.358457
$467$	18.8493	0.872239	0.436120	−	0.899889i	$-0.356352\pi$
$467$	18.8493	0.872239	0.436120	+	0.899889i	$0.356352\pi$
$468$	−10.1333	−0.468413
$469$	0	0
$470$	−16.2999	−0.751859
$471$	22.3872	1.03155
$472$	−8.45257	−0.389061
$473$	1.00000	0.0459800
$474$	5.68500	0.261121
$475$	−0.0596924	−0.00273888
$476$	0	0
$477$	−16.5012	−0.755540
$478$	−11.8657	−0.542725
$479$	4.58685	0.209579	0.104789	−	0.994494i	$-0.466583\pi$
$479$	4.58685	0.209579	0.104789	+	0.994494i	$0.466583\pi$
$480$	2.12908	0.0971787
$481$	49.8938	2.27496
$482$	−5.61118	−0.255582
$483$	0	0
$484$	1.00000	0.0454545
$485$	−40.0521	−1.81867
$486$	−16.1253	−0.731457
$487$	−39.0665	−1.77027	−0.885137	−	0.465331i	$-0.845935\pi$
$487$	−39.0665	−1.77027	−0.885137	+	0.465331i	$0.845935\pi$
$488$	−10.9051	−0.493652
$489$	−7.82759	−0.353976
$490$	15.5840	0.704013
$491$	15.8159	0.713762	0.356881	−	0.934150i	$-0.383840\pi$
$491$	15.8159	0.713762	0.356881	+	0.934150i	$0.383840\pi$
$492$	7.12535	0.321236
$493$	21.9032	0.986472
$494$	6.64316	0.298890
$495$	−4.64273	−0.208675
$496$	−3.49623	−0.156985
$497$	0	0
$498$	−7.89759	−0.353900
$499$	−3.21831	−0.144071	−0.0720357	−	0.997402i	$-0.522950\pi$
$499$	−3.21831	−0.144071	−0.0720357	+	0.997402i	$0.522950\pi$
$500$	11.2286	0.502159
$501$	−8.38882	−0.374785
$502$	−8.53608	−0.380984
$503$	−30.4403	−1.35726	−0.678632	−	0.734478i	$-0.737427\pi$
$503$	−30.4403	−1.35726	−0.678632	+	0.734478i	$0.737427\pi$
$504$	0	0
$505$	−33.8938	−1.50825
$506$	−7.08542	−0.314985
$507$	−10.1479	−0.450683
$508$	−5.72815	−0.254145
$509$	−22.7502	−1.00839	−0.504193	−	0.863591i	$-0.668210\pi$
$509$	−22.7502	−1.00839	−0.504193	+	0.863591i	$0.668210\pi$
$510$	15.7741	0.698491
$511$	0	0
$512$	1.00000	0.0441942
$513$	6.64896	0.293559
$514$	14.2582	0.628900
$515$	36.4651	1.60684
$516$	0.956338	0.0421004
$517$	−7.32158	−0.322003
$518$	0	0
$519$	−16.2110	−0.711585
$520$	−10.8178	−0.474392
$521$	−41.9097	−1.83610	−0.918049	−	0.396466i	$-0.870236\pi$
$521$	−41.9097	−1.83610	−0.918049	+	0.396466i	$0.870236\pi$
$522$	−6.16520	−0.269843
$523$	26.5637	1.16155	0.580775	−	0.814064i	$-0.302750\pi$
$523$	26.5637	1.16155	0.580775	+	0.814064i	$0.302750\pi$
$524$	3.69064	0.161226
$525$	0	0
$526$	−24.9249	−1.08678
$527$	−25.9032	−1.12836
$528$	0.956338	0.0416193
$529$	27.2031	1.18275
$530$	−17.6159	−0.765184
$531$	17.6271	0.764952
$532$	0	0
$533$	−36.2038	−1.56816
$534$	−14.0873	−0.609618
$535$	24.5163	1.05993
$536$	−1.89292	−0.0817615
$537$	1.29934	0.0560706
$538$	23.3775	1.00787
$539$	7.00000	0.301511
$540$	−10.8273	−0.465931
$541$	−3.49102	−0.150091	−0.0750454	−	0.997180i	$-0.523910\pi$
$541$	−3.49102	−0.150091	−0.0750454	+	0.997180i	$0.523910\pi$
$542$	−10.5080	−0.451358
$543$	−16.5163	−0.708783
$544$	7.40890	0.317654
$545$	6.99246	0.299524
$546$	0	0
$547$	34.0244	1.45478	0.727390	−	0.686224i	$-0.240733\pi$
$547$	34.0244	1.45478	0.727390	+	0.686224i	$0.240733\pi$
$548$	−8.36524	−0.357345
$549$	22.7418	0.970595
$550$	0.0436620	0.00186175
$551$	4.04176	0.172185
$552$	−6.77605	−0.288408
$553$	0	0
$554$	7.81972	0.332228
$555$	21.8615	0.927968
$556$	20.9249	0.887413
$557$	−5.60938	−0.237677	−0.118839	−	0.992914i	$-0.537917\pi$
$557$	−5.60938	−0.237677	−0.118839	+	0.992914i	$0.537917\pi$
$558$	7.29110	0.308657
$559$	−4.85913	−0.205519
$560$	0	0
$561$	7.08542	0.299147
$562$	0.396687	0.0167332
$563$	−8.17551	−0.344557	−0.172278	−	0.985048i	$-0.555113\pi$
$563$	−8.17551	−0.344557	−0.172278	+	0.985048i	$0.555113\pi$
$564$	−7.00191	−0.294833
$565$	27.9613	1.17634
$566$	23.2704	0.978127
$567$	0	0
$568$	10.0460	0.421521
$569$	17.5285	0.734834	0.367417	−	0.930056i	$-0.380242\pi$
$569$	17.5285	0.734834	0.367417	+	0.930056i	$0.380242\pi$
$570$	2.91077	0.121919
$571$	7.51599	0.314534	0.157267	−	0.987556i	$-0.449732\pi$
$571$	7.51599	0.314534	0.157267	+	0.987556i	$0.449732\pi$
$572$	−4.85913	−0.203171
$573$	3.00008	0.125330
$574$	0	0
$575$	−0.309363	−0.0129013
$576$	−2.08542	−0.0868924
$577$	5.95285	0.247821	0.123910	−	0.992293i	$-0.460456\pi$
$577$	5.95285	0.247821	0.123910	+	0.992293i	$0.460456\pi$
$578$	37.8919	1.57609
$579$	−18.2296	−0.757595
$580$	−6.58165	−0.273288
$581$	0	0
$582$	−17.2050	−0.713172
$583$	−7.91268	−0.327710
$584$	−0.0873239	−0.00361349
$585$	22.5597	0.932727
$586$	−6.04219	−0.249600
$587$	8.09200	0.333993	0.166996	−	0.985958i	$-0.446593\pi$
$587$	8.09200	0.333993	0.166996	+	0.985958i	$0.446593\pi$
$588$	6.69437	0.276071
$589$	−4.77987	−0.196951
$590$	18.8178	0.774717
$591$	11.9529	0.491675
$592$	10.2680	0.422014
$593$	9.46478	0.388672	0.194336	−	0.980935i	$-0.437745\pi$
$593$	9.46478	0.388672	0.194336	+	0.980935i	$0.437745\pi$
$594$	−4.86338	−0.199547
$595$	0	0
$596$	−8.48020	−0.347362
$597$	24.1840	0.989785
$598$	34.4290	1.40791
$599$	17.8727	0.730261	0.365130	−	0.930956i	$-0.381024\pi$
$599$	17.8727	0.730261	0.365130	+	0.930956i	$0.381024\pi$
$600$	0.0417556	0.00170467
$601$	24.6036	1.00360	0.501802	−	0.864983i	$-0.332671\pi$
$601$	24.6036	1.00360	0.501802	+	0.864983i	$0.332671\pi$
$602$	0	0
$603$	3.94752	0.160755
$604$	−18.4488	−0.750669
$605$	−2.22628	−0.0905113
$606$	−14.5597	−0.591445
$607$	−27.9924	−1.13618	−0.568088	−	0.822968i	$-0.692317\pi$
$607$	−27.9924	−1.13618	−0.568088	+	0.822968i	$0.692317\pi$
$608$	1.36715	0.0554452
$609$	0	0
$610$	24.2779	0.982984
$611$	35.5765	1.43927
$612$	−15.4507	−0.624556
$613$	−38.5783	−1.55816	−0.779081	−	0.626924i	$-0.784314\pi$
$613$	−38.5783	−1.55816	−0.779081	+	0.626924i	$0.784314\pi$
$614$	−12.0000	−0.484281
$615$	−15.8630	−0.639660
$616$	0	0
$617$	−13.2601	−0.533830	−0.266915	−	0.963720i	$-0.586004\pi$
$617$	−13.2601	−0.533830	−0.266915	+	0.963720i	$0.586004\pi$
$618$	15.6642	0.630107
$619$	−42.1519	−1.69423	−0.847115	−	0.531410i	$-0.821662\pi$
$619$	−42.1519	−1.69423	−0.847115	+	0.531410i	$0.821662\pi$
$620$	7.78360	0.312597
$621$	34.4591	1.38279
$622$	−20.6910	−0.829632
$623$	0	0
$624$	−4.64697	−0.186028
$625$	−24.7798	−0.991191
$626$	−11.8018	−0.471694
$627$	1.30746	0.0522148
$628$	−23.4093	−0.934134
$629$	76.0749	3.03331
$630$	0	0
$631$	−24.6883	−0.982826	−0.491413	−	0.870927i	$-0.663519\pi$
$631$	−24.6883	−0.982826	−0.491413	+	0.870927i	$0.663519\pi$
$632$	−5.94455	−0.236462
$633$	11.3661	0.451763
$634$	5.17838	0.205660
$635$	12.7525	0.506067
$636$	−7.56719	−0.300059
$637$	−34.0139	−1.34768
$638$	−2.95634	−0.117043
$639$	−20.9501	−0.828773
$640$	−2.22628	−0.0880016
$641$	−25.5398	−1.00876	−0.504381	−	0.863481i	$-0.668279\pi$
$641$	−25.5398	−1.00876	−0.504381	+	0.863481i	$0.668279\pi$
$642$	10.5314	0.415641
$643$	16.9689	0.669188	0.334594	−	0.942362i	$-0.391401\pi$
$643$	16.9689	0.669188	0.334594	+	0.942362i	$0.391401\pi$
$644$	0	0
$645$	−2.12908	−0.0838324
$646$	10.1291	0.398523
$647$	34.7491	1.36613	0.683064	−	0.730358i	$-0.260647\pi$
$647$	34.7491	1.36613	0.683064	+	0.730358i	$0.260647\pi$
$648$	1.60522	0.0630590
$649$	8.45257	0.331792
$650$	−0.212159	−0.00832157
$651$	0	0
$652$	8.18496	0.320548
$653$	8.11920	0.317729	0.158864	−	0.987300i	$-0.449217\pi$
$653$	8.11920	0.317729	0.158864	+	0.987300i	$0.449217\pi$
$654$	3.00373	0.117455
$655$	−8.21640	−0.321041
$656$	−7.45066	−0.290899
$657$	0.182107	0.00710467
$658$	0	0
$659$	29.6469	1.15488	0.577439	−	0.816434i	$-0.304052\pi$
$659$	29.6469	1.15488	0.577439	+	0.816434i	$0.304052\pi$
$660$	−2.12908	−0.0828743
$661$	−19.0713	−0.741787	−0.370894	−	0.928675i	$-0.620949\pi$
$661$	−19.0713	−0.741787	−0.370894	+	0.928675i	$0.620949\pi$
$662$	−30.8376	−1.19854
$663$	−34.4290	−1.33711
$664$	8.25816	0.320479
$665$	0	0
$666$	−21.4131	−0.829743
$667$	20.9469	0.811067
$668$	8.77181	0.339392
$669$	15.0760	0.582871
$670$	4.21417	0.162808
$671$	10.9051	0.420988
$672$	0	0
$673$	32.0244	1.23445	0.617226	−	0.786786i	$-0.288257\pi$
$673$	32.0244	1.23445	0.617226	+	0.786786i	$0.288257\pi$
$674$	16.2943	0.627632
$675$	−0.212345	−0.00817315
$676$	10.6112	0.408122
$677$	32.9108	1.26486	0.632432	−	0.774616i	$-0.282057\pi$
$677$	32.9108	1.26486	0.632432	+	0.774616i	$0.282057\pi$
$678$	12.0113	0.461290
$679$	0	0
$680$	−16.4943	−0.632528
$681$	−10.8672	−0.416432
$682$	3.49623	0.133878
$683$	37.2270	1.42445	0.712227	−	0.701950i	$-0.247687\pi$
$683$	37.2270	1.42445	0.712227	+	0.701950i	$0.247687\pi$
$684$	−2.85108	−0.109014
$685$	18.6234	0.711564
$686$	0	0
$687$	−16.0646	−0.612903
$688$	−1.00000	−0.0381246
$689$	38.4488	1.46478
$690$	15.0854	0.574292
$691$	−48.0094	−1.82636	−0.913181	−	0.407554i	$-0.866382\pi$
$691$	−48.0094	−1.82636	−0.913181	+	0.407554i	$0.866382\pi$
$692$	16.9511	0.644385
$693$	0	0
$694$	−30.8168	−1.16979
$695$	−46.5847	−1.76706
$696$	−2.82726	−0.107167
$697$	−55.2012	−2.09090
$698$	22.3929	0.847583
$699$	7.40017	0.279900
$700$	0	0
$701$	−12.9511	−0.489158	−0.244579	−	0.969629i	$-0.578650\pi$
$701$	−12.9511	−0.489158	−0.244579	+	0.969629i	$0.578650\pi$
$702$	23.6318	0.891925
$703$	14.0379	0.529451
$704$	−1.00000	−0.0376889
$705$	15.5882	0.587087
$706$	9.82535	0.369782
$707$	0	0
$708$	8.08351	0.303797
$709$	−19.9567	−0.749488	−0.374744	−	0.927128i	$-0.622269\pi$
$709$	−19.9567	−0.749488	−0.374744	+	0.927128i	$0.622269\pi$
$710$	−22.3652	−0.839353
$711$	12.3969	0.464919
$712$	14.7305	0.552048
$713$	−24.7722	−0.927728
$714$	0	0
$715$	10.8178	0.404563
$716$	−1.35866	−0.0507755
$717$	11.3476	0.423785
$718$	19.1967	0.716416
$719$	17.3169	0.645812	0.322906	−	0.946431i	$-0.395340\pi$
$719$	17.3169	0.645812	0.322906	+	0.946431i	$0.395340\pi$
$720$	4.64273	0.173024
$721$	0	0
$722$	−17.1309	−0.637546
$723$	5.36619	0.199571
$724$	17.2704	0.641848
$725$	−0.129080	−0.00479389
$726$	−0.956338	−0.0354930
$727$	0.937970	0.0347874	0.0173937	−	0.999849i	$-0.494463\pi$
$727$	0.937970	0.0347874	0.0173937	+	0.999849i	$0.494463\pi$
$728$	0	0
$729$	10.6055	0.392798
$730$	0.194408	0.00719536
$731$	−7.40890	−0.274028
$732$	10.4290	0.385467
$733$	−45.6444	−1.68591	−0.842956	−	0.537982i	$-0.819187\pi$
$733$	−45.6444	−1.68591	−0.842956	+	0.537982i	$0.819187\pi$
$734$	31.8577	1.17589
$735$	−14.9036	−0.549726
$736$	7.08542	0.261172
$737$	1.89292	0.0697265
$738$	15.5377	0.571952
$739$	−11.4042	−0.419511	−0.209756	−	0.977754i	$-0.567267\pi$
$739$	−11.4042	−0.419511	−0.209756	+	0.977754i	$0.567267\pi$
$740$	−22.8596	−0.840334
$741$	−6.35311	−0.233387
$742$	0	0
$743$	−8.86561	−0.325248	−0.162624	−	0.986688i	$-0.551996\pi$
$743$	−8.86561	−0.325248	−0.162624	+	0.986688i	$0.551996\pi$
$744$	3.34358	0.122581
$745$	18.8793	0.691685
$746$	8.27228	0.302870
$747$	−17.2217	−0.630109
$748$	−7.40890	−0.270896
$749$	0	0
$750$	−10.7384	−0.392109
$751$	−34.5183	−1.25959	−0.629796	−	0.776761i	$-0.716861\pi$
$751$	−34.5183	−1.25959	−0.629796	+	0.776761i	$0.716861\pi$
$752$	7.32158	0.266991
$753$	8.16338	0.297490
$754$	14.3652	0.523151
$755$	41.0722	1.49477
$756$	0	0
$757$	33.7966	1.22836	0.614179	−	0.789167i	$-0.289487\pi$
$757$	33.7966	1.22836	0.614179	+	0.789167i	$0.289487\pi$
$758$	−19.8891	−0.722405
$759$	6.77605	0.245955
$760$	−3.04366	−0.110405
$761$	−48.9848	−1.77570	−0.887849	−	0.460134i	$-0.847801\pi$
$761$	−48.9848	−1.77570	−0.887849	+	0.460134i	$0.847801\pi$
$762$	5.47805	0.198449
$763$	0	0
$764$	−3.13705	−0.113495
$765$	34.3975	1.24365
$766$	−5.41878	−0.195789
$767$	−41.0722	−1.48303
$768$	−0.956338	−0.0345089
$769$	0.376927	0.0135923	0.00679617	−	0.999977i	$-0.497837\pi$
$769$	0.376927	0.0135923	0.00679617	+	0.999977i	$0.497837\pi$
$770$	0	0
$771$	−13.6356	−0.491075
$772$	19.0618	0.686051
$773$	−16.4671	−0.592281	−0.296141	−	0.955144i	$-0.595700\pi$
$773$	−16.4671	−0.592281	−0.296141	+	0.955144i	$0.595700\pi$
$774$	2.08542	0.0749588
$775$	0.152652	0.00548343
$776$	17.9906	0.645823
$777$	0	0
$778$	13.2282	0.474254
$779$	−10.1862	−0.364957
$780$	10.3455	0.370428
$781$	−10.0460	−0.359474
$782$	52.4952	1.87722
$783$	14.3778	0.513820
$784$	−7.00000	−0.250000
$785$	52.1158	1.86009
$786$	−3.52950	−0.125893
$787$	−28.4966	−1.01579	−0.507896	−	0.861418i	$-0.669577\pi$
$787$	−28.4966	−1.01579	−0.507896	+	0.861418i	$0.669577\pi$
$788$	−12.4986	−0.445243
$789$	23.8366	0.848606
$790$	13.2343	0.470854
$791$	0	0
$792$	2.08542	0.0741021
$793$	−52.9895	−1.88171
$794$	25.3539	0.899776
$795$	16.8467	0.597491
$796$	−25.2881	−0.896314
$797$	35.0798	1.24259	0.621295	−	0.783577i	$-0.286607\pi$
$797$	35.0798	1.24259	0.621295	+	0.783577i	$0.286607\pi$
$798$	0	0
$799$	54.2449	1.91905
$800$	−0.0436620	−0.00154368
$801$	−30.7192	−1.08541
$802$	−6.72643	−0.237518
$803$	0.0873239	0.00308159
$804$	1.81027	0.0638432
$805$	0	0
$806$	−16.9886	−0.598399
$807$	−22.3568	−0.786995
$808$	15.2244	0.535592
$809$	−2.75066	−0.0967080	−0.0483540	−	0.998830i	$-0.515398\pi$
$809$	−2.75066	−0.0967080	−0.0483540	+	0.998830i	$0.515398\pi$
$810$	−3.57367	−0.125566
$811$	7.07415	0.248407	0.124203	−	0.992257i	$-0.460362\pi$
$811$	7.07415	0.248407	0.124203	+	0.992257i	$0.460362\pi$
$812$	0	0
$813$	10.0492	0.352441
$814$	−10.2680	−0.359895
$815$	−18.2220	−0.638290
$816$	−7.08542	−0.248039
$817$	−1.36715	−0.0478305
$818$	−10.2977	−0.360050
$819$	0	0
$820$	16.5873	0.579253
$821$	35.8327	1.25057	0.625285	−	0.780397i	$-0.284983\pi$
$821$	35.8327	1.25057	0.625285	+	0.780397i	$0.284983\pi$
$822$	8.00000	0.279032
$823$	−19.0477	−0.663962	−0.331981	−	0.943286i	$-0.607717\pi$
$823$	−19.0477	−0.663962	−0.331981	+	0.943286i	$0.607717\pi$
$824$	−16.3794	−0.570602
$825$	−0.0417556	−0.00145374
$826$	0	0
$827$	7.65919	0.266336	0.133168	−	0.991093i	$-0.457485\pi$
$827$	7.65919	0.266336	0.133168	+	0.991093i	$0.457485\pi$
$828$	−14.7761	−0.513503
$829$	−40.1610	−1.39485	−0.697424	−	0.716659i	$-0.745670\pi$
$829$	−40.1610	−1.39485	−0.697424	+	0.716659i	$0.745670\pi$
$830$	−18.3850	−0.638153
$831$	−7.47829	−0.259419
$832$	4.85913	0.168460
$833$	−51.8623	−1.79692
$834$	−20.0113	−0.692934
$835$	−19.5285	−0.675813
$836$	−1.36715	−0.0472838
$837$	−17.0035	−0.587726
$838$	31.7032	1.09517
$839$	−15.0620	−0.519999	−0.260000	−	0.965609i	$-0.583722\pi$
$839$	−15.0620	−0.519999	−0.260000	+	0.965609i	$0.583722\pi$
$840$	0	0
$841$	−20.2601	−0.698623
$842$	−24.6638	−0.849970
$843$	−0.379367	−0.0130661
$844$	−11.8850	−0.409100
$845$	−23.6235	−0.812673
$846$	−15.2686	−0.524944
$847$	0	0
$848$	7.91268	0.271722
$849$	−22.2543	−0.763767
$850$	−0.323487	−0.0110955
$851$	72.7533	2.49395
$852$	−9.60737	−0.329143
$853$	6.66940	0.228356	0.114178	−	0.993460i	$-0.463577\pi$
$853$	6.66940	0.228356	0.114178	+	0.993460i	$0.463577\pi$
$854$	0	0
$855$	6.34731	0.217073
$856$	−11.0122	−0.376390
$857$	−13.6215	−0.465301	−0.232651	−	0.972560i	$-0.574740\pi$
$857$	−13.6215	−0.465301	−0.232651	+	0.972560i	$0.574740\pi$
$858$	4.64697	0.158645
$859$	−22.1529	−0.755847	−0.377924	−	0.925837i	$-0.623362\pi$
$859$	−22.1529	−0.755847	−0.377924	+	0.925837i	$0.623362\pi$
$860$	2.22628	0.0759156
$861$	0	0
$862$	−35.7526	−1.21774
$863$	24.8723	0.846663	0.423331	−	0.905975i	$-0.360861\pi$
$863$	24.8723	0.846663	0.423331	+	0.905975i	$0.360861\pi$
$864$	4.86338	0.165455
$865$	−37.7380	−1.28313
$866$	−1.84511	−0.0626995
$867$	−36.2374	−1.23069
$868$	0	0
$869$	5.94455	0.201655
$870$	6.29428	0.213396
$871$	−9.19793	−0.311660
$872$	−3.14087	−0.106363
$873$	−37.5178	−1.26979
$874$	9.68682	0.327662
$875$	0	0
$876$	0.0835112	0.00282158
$877$	−28.5623	−0.964481	−0.482240	−	0.876039i	$-0.660177\pi$
$877$	−28.5623	−0.964481	−0.482240	+	0.876039i	$0.660177\pi$
$878$	−0.00987998	−0.000333433 0
$879$	5.77837	0.194900
$880$	2.22628	0.0750480
$881$	−55.2509	−1.86145	−0.930724	−	0.365721i	$-0.880822\pi$
$881$	−55.2509	−1.86145	−0.930724	+	0.365721i	$0.880822\pi$
$882$	14.5979	0.491538
$883$	−16.8140	−0.565836	−0.282918	−	0.959144i	$-0.591302\pi$
$883$	−16.8140	−0.565836	−0.282918	+	0.959144i	$0.591302\pi$
$884$	36.0009	1.21084
$885$	−17.9962	−0.604935
$886$	−3.79710	−0.127566
$887$	−2.75406	−0.0924722	−0.0462361	−	0.998931i	$-0.514723\pi$
$887$	−2.75406	−0.0924722	−0.0462361	+	0.998931i	$0.514723\pi$
$888$	−9.81972	−0.329528
$889$	0	0
$890$	−32.7942	−1.09927
$891$	−1.60522	−0.0537769
$892$	−15.7643	−0.527827
$893$	10.0097	0.334962
$894$	8.10994	0.271237
$895$	3.02476	0.101107
$896$	0	0
$897$	−32.9258	−1.09936
$898$	15.6348	0.521739
$899$	−10.3360	−0.344726
$900$	0.0910534	0.00303511
$901$	58.6243	1.95306
$902$	7.45066	0.248080
$903$	0	0
$904$	−12.5597	−0.417728
$905$	−38.4488	−1.27808
$906$	17.6432	0.586158
$907$	22.3181	0.741060	0.370530	−	0.928820i	$-0.379176\pi$
$907$	22.3181	0.741060	0.370530	+	0.928820i	$0.379176\pi$
$908$	11.3633	0.377106
$909$	−31.7492	−1.05305
$910$	0	0
$911$	−39.3763	−1.30460	−0.652298	−	0.757963i	$-0.726195\pi$
$911$	−39.3763	−1.30460	−0.652298	+	0.757963i	$0.726195\pi$
$912$	−1.30746	−0.0432942
$913$	−8.25816	−0.273305
$914$	−14.2977	−0.472925
$915$	−23.2179	−0.767560
$916$	16.7980	0.555023
$917$	0	0
$918$	36.0323	1.18924
$919$	−36.9675	−1.21945	−0.609723	−	0.792615i	$-0.708719\pi$
$919$	−36.9675	−1.21945	−0.609723	+	0.792615i	$0.708719\pi$
$920$	−15.7741	−0.520058
$921$	11.4761	0.378149
$922$	−28.6458	−0.943400
$923$	48.8149	1.60676
$924$	0	0
$925$	−0.448323	−0.0147408
$926$	31.3126	1.02899
$927$	34.1578	1.12189
$928$	2.95634	0.0970466
$929$	0.376515	0.0123530	0.00617652	−	0.999981i	$-0.498034\pi$
$929$	0.376515	0.0123530	0.00617652	+	0.999981i	$0.498034\pi$
$930$	−7.44375	−0.244090
$931$	−9.57005	−0.313646
$932$	−7.73803	−0.253468
$933$	19.7876	0.647816
$934$	18.8493	0.616766
$935$	16.4943	0.539422
$936$	−10.1333	−0.331218
$937$	−5.22237	−0.170607	−0.0853037	−	0.996355i	$-0.527186\pi$
$937$	−5.22237	−0.170607	−0.0853037	+	0.996355i	$0.527186\pi$
$938$	0	0
$939$	11.2865	0.368321
$940$	−16.2999	−0.531645
$941$	−35.5745	−1.15970	−0.579848	−	0.814724i	$-0.696888\pi$
$941$	−35.5745	−1.15970	−0.579848	+	0.814724i	$0.696888\pi$
$942$	22.3872	0.729416
$943$	−52.7910	−1.71911
$944$	−8.45257	−0.275108
$945$	0	0
$946$	1.00000	0.0325128
$947$	−35.8976	−1.16651	−0.583257	−	0.812287i	$-0.698222\pi$
$947$	−35.8976	−1.16651	−0.583257	+	0.812287i	$0.698222\pi$
$948$	5.68500	0.184640
$949$	−0.424319	−0.0137740
$950$	−0.0596924	−0.00193668
$951$	−4.95228	−0.160589
$952$	0	0
$953$	12.9296	0.418830	0.209415	−	0.977827i	$-0.432844\pi$
$953$	12.9296	0.418830	0.209415	+	0.977827i	$0.432844\pi$
$954$	−16.5012	−0.534247
$955$	6.98397	0.225996
$956$	−11.8657	−0.383765
$957$	2.82726	0.0913923
$958$	4.58685	0.148194
$959$	0	0
$960$	2.12908	0.0687157
$961$	−18.7764	−0.605690
$962$	49.8938	1.60864
$963$	22.9651	0.740039
$964$	−5.61118	−0.180724
$965$	−42.4371	−1.36610
$966$	0	0
$967$	−24.5756	−0.790297	−0.395149	−	0.918617i	$-0.629307\pi$
$967$	−24.5756	−0.790297	−0.395149	+	0.918617i	$0.629307\pi$
$968$	1.00000	0.0321412
$969$	−9.68682	−0.311186
$970$	−40.0521	−1.28599
$971$	47.5012	1.52438	0.762192	−	0.647351i	$-0.224123\pi$
$971$	47.5012	1.52438	0.762192	+	0.647351i	$0.224123\pi$
$972$	−16.1253	−0.517218
$973$	0	0
$974$	−39.0665	−1.25177
$975$	0.202896	0.00649787
$976$	−10.9051	−0.349065
$977$	−8.42494	−0.269538	−0.134769	−	0.990877i	$-0.543029\pi$
$977$	−8.42494	−0.269538	−0.134769	+	0.990877i	$0.543029\pi$
$978$	−7.82759	−0.250299
$979$	−14.7305	−0.470788
$980$	15.5840	0.497812
$981$	6.55002	0.209126
$982$	15.8159	0.504706
$983$	−12.6609	−0.403820	−0.201910	−	0.979404i	$-0.564715\pi$
$983$	−12.6609	−0.403820	−0.201910	+	0.979404i	$0.564715\pi$
$984$	7.12535	0.227148
$985$	27.8254	0.886589
$986$	21.9032	0.697541
$987$	0	0
$988$	6.64316	0.211347
$989$	−7.08542	−0.225303
$990$	−4.64273	−0.147556
$991$	−17.8996	−0.568600	−0.284300	−	0.958735i	$-0.591761\pi$
$991$	−17.8996	−0.568600	−0.284300	+	0.958735i	$0.591761\pi$
$992$	−3.49623	−0.111005
$993$	29.4911	0.935873
$994$	0	0
$995$	56.2985	1.78478
$996$	−7.89759	−0.250245
$997$	−26.8463	−0.850231	−0.425115	−	0.905139i	$-0.639767\pi$
$997$	−26.8463	−0.850231	−0.425115	+	0.905139i	$0.639767\pi$
$998$	−3.21831	−0.101874
$999$	49.9374	1.57995

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	946.2.a.h.1.2	✓	4
3.2	odd	2		8514.2.a.ba.1.4		4
4.3	odd	2		7568.2.a.y.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
946.2.a.h.1.2	✓	4	1.1	even	1	trivial
7568.2.a.y.1.3		4	4.3	odd	2
8514.2.a.ba.1.4		4	3.2	odd	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:	\( N \)	\(=\)	\( 946 = 2 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	946.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.956338 q^{3} +1.00000 q^{4} -2.22628 q^{5} -0.956338 q^{6} +1.00000 q^{8} -2.08542 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.956338 q^{3} +1.00000 q^{4} -2.22628 q^{5} -0.956338 q^{6} +1.00000 q^{8} -2.08542 q^{9} -2.22628 q^{10} -1.00000 q^{11} -0.956338 q^{12} +4.85913 q^{13} +2.12908 q^{15} +1.00000 q^{16} +7.40890 q^{17} -2.08542 q^{18} +1.36715 q^{19} -2.22628 q^{20} -1.00000 q^{22} +7.08542 q^{23} -0.956338 q^{24} -0.0436620 q^{25} +4.85913 q^{26} +4.86338 q^{27} +2.95634 q^{29} +2.12908 q^{30} -3.49623 q^{31} +1.00000 q^{32} +0.956338 q^{33} +7.40890 q^{34} -2.08542 q^{36} +10.2680 q^{37} +1.36715 q^{38} -4.64697 q^{39} -2.22628 q^{40} -7.45066 q^{41} -1.00000 q^{43} -1.00000 q^{44} +4.64273 q^{45} +7.08542 q^{46} +7.32158 q^{47} -0.956338 q^{48} -7.00000 q^{49} -0.0436620 q^{50} -7.08542 q^{51} +4.85913 q^{52} +7.91268 q^{53} +4.86338 q^{54} +2.22628 q^{55} -1.30746 q^{57} +2.95634 q^{58} -8.45257 q^{59} +2.12908 q^{60} -10.9051 q^{61} -3.49623 q^{62} +1.00000 q^{64} -10.8178 q^{65} +0.956338 q^{66} -1.89292 q^{67} +7.40890 q^{68} -6.77605 q^{69} +10.0460 q^{71} -2.08542 q^{72} -0.0873239 q^{73} +10.2680 q^{74} +0.0417556 q^{75} +1.36715 q^{76} -4.64697 q^{78} -5.94455 q^{79} -2.22628 q^{80} +1.60522 q^{81} -7.45066 q^{82} +8.25816 q^{83} -16.4943 q^{85} -1.00000 q^{86} -2.82726 q^{87} -1.00000 q^{88} +14.7305 q^{89} +4.64273 q^{90} +7.08542 q^{92} +3.34358 q^{93} +7.32158 q^{94} -3.04366 q^{95} -0.956338 q^{96} +17.9906 q^{97} -7.00000 q^{98} +2.08542 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + q^{3} + 4 q^{4} + q^{5} + q^{6} + 4 q^{8} + 11 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + q^3 + 4 * q^4 + q^5 + q^6 + 4 * q^8 + 11 * q^9	\( 4 q + 4 q^{2} + q^{3} + 4 q^{4} + q^{5} + q^{6} + 4 q^{8} + 11 q^{9} + q^{10} - 4 q^{11} + q^{12} + 10 q^{13} - 6 q^{15} + 4 q^{16} + 5 q^{17} + 11 q^{18} + 5 q^{19} + q^{20} - 4 q^{22} + 9 q^{23} + q^{24} - 5 q^{25} + 10 q^{26} + 4 q^{27} + 7 q^{29} - 6 q^{30} + q^{31} + 4 q^{32} - q^{33} + 5 q^{34} + 11 q^{36} + 7 q^{37} + 5 q^{38} - 8 q^{39} + q^{40} + 19 q^{41} - 4 q^{43} - 4 q^{44} + 14 q^{45} + 9 q^{46} - 5 q^{47} + q^{48} - 28 q^{49} - 5 q^{50} - 9 q^{51} + 10 q^{52} + 22 q^{53} + 4 q^{54} - q^{55} + 18 q^{57} + 7 q^{58} - 14 q^{59} - 6 q^{60} - 4 q^{61} + q^{62} + 4 q^{64} + 6 q^{65} - q^{66} - 8 q^{67} + 5 q^{68} - 2 q^{69} + 10 q^{71} + 11 q^{72} - 10 q^{73} + 7 q^{74} - 24 q^{75} + 5 q^{76} - 8 q^{78} + 5 q^{79} + q^{80} + 20 q^{81} + 19 q^{82} + 4 q^{83} - 22 q^{85} - 4 q^{86} - 21 q^{87} - 4 q^{88} + 14 q^{90} + 9 q^{92} - 35 q^{93} - 5 q^{94} - 17 q^{95} + q^{96} + 13 q^{97} - 28 q^{98} - 11 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + q^3 + 4 * q^4 + q^5 + q^6 + 4 * q^8 + 11 * q^9 + q^10 - 4 * q^11 + q^12 + 10 * q^13 - 6 * q^15 + 4 * q^16 + 5 * q^17 + 11 * q^18 + 5 * q^19 + q^20 - 4 * q^22 + 9 * q^23 + q^24 - 5 * q^25 + 10 * q^26 + 4 * q^27 + 7 * q^29 - 6 * q^30 + q^31 + 4 * q^32 - q^33 + 5 * q^34 + 11 * q^36 + 7 * q^37 + 5 * q^38 - 8 * q^39 + q^40 + 19 * q^41 - 4 * q^43 - 4 * q^44 + 14 * q^45 + 9 * q^46 - 5 * q^47 + q^48 - 28 * q^49 - 5 * q^50 - 9 * q^51 + 10 * q^52 + 22 * q^53 + 4 * q^54 - q^55 + 18 * q^57 + 7 * q^58 - 14 * q^59 - 6 * q^60 - 4 * q^61 + q^62 + 4 * q^64 + 6 * q^65 - q^66 - 8 * q^67 + 5 * q^68 - 2 * q^69 + 10 * q^71 + 11 * q^72 - 10 * q^73 + 7 * q^74 - 24 * q^75 + 5 * q^76 - 8 * q^78 + 5 * q^79 + q^80 + 20 * q^81 + 19 * q^82 + 4 * q^83 - 22 * q^85 - 4 * q^86 - 21 * q^87 - 4 * q^88 + 14 * q^90 + 9 * q^92 - 35 * q^93 - 5 * q^94 - 17 * q^95 + q^96 + 13 * q^97 - 28 * q^98 - 11 * q^99

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