LMFDB - Embedded newform 975.2.h.d.649.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(649,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("975.649");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.h (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			649.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	975.649
Dual form			975.2.h.d.649.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000i q^{6} -2.00000 q^{7} -3.00000 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000i q^{6} -2.00000 q^{7} -3.00000 q^{8} -1.00000 q^{9} -1.00000i q^{12} +(2.00000 - 3.00000i) q^{13} -2.00000 q^{14} -1.00000 q^{16} -2.00000i q^{17} -1.00000 q^{18} -2.00000i q^{19} -2.00000i q^{21} -8.00000i q^{23} -3.00000i q^{24} +(2.00000 - 3.00000i) q^{26} -1.00000i q^{27} +2.00000 q^{28} -2.00000 q^{29} -2.00000i q^{31} +5.00000 q^{32} -2.00000i q^{34} +1.00000 q^{36} -8.00000 q^{37} -2.00000i q^{38} +(3.00000 + 2.00000i) q^{39} -2.00000i q^{41} -2.00000i q^{42} -4.00000i q^{43} -8.00000i q^{46} -4.00000 q^{47} -1.00000i q^{48} -3.00000 q^{49} +2.00000 q^{51} +(-2.00000 + 3.00000i) q^{52} -6.00000i q^{53} -1.00000i q^{54} +6.00000 q^{56} +2.00000 q^{57} -2.00000 q^{58} +12.0000i q^{59} +10.0000 q^{61} -2.00000i q^{62} +2.00000 q^{63} +7.00000 q^{64} -6.00000 q^{67} +2.00000i q^{68} +8.00000 q^{69} +8.00000i q^{71} +3.00000 q^{72} -16.0000 q^{73} -8.00000 q^{74} +2.00000i q^{76} +(3.00000 + 2.00000i) q^{78} +8.00000 q^{79} +1.00000 q^{81} -2.00000i q^{82} -12.0000 q^{83} +2.00000i q^{84} -4.00000i q^{86} -2.00000i q^{87} -6.00000i q^{89} +(-4.00000 + 6.00000i) q^{91} +8.00000i q^{92} +2.00000 q^{93} -4.00000 q^{94} +5.00000i q^{96} +16.0000 q^{97} -3.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{4} - 4 q^{7} - 6 q^{8} - 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^4 - 4 * q^7 - 6 * q^8 - 2 * q^9	$ 2 q + 2 q^{2} - 2 q^{4} - 4 q^{7} - 6 q^{8} - 2 q^{9} + 4 q^{13} - 4 q^{14} - 2 q^{16} - 2 q^{18} + 4 q^{26} + 4 q^{28} - 4 q^{29} + 10 q^{32} + 2 q^{36} - 16 q^{37} + 6 q^{39} - 8 q^{47} - 6 q^{49} + 4 q^{51} - 4 q^{52} + 12 q^{56} + 4 q^{57} - 4 q^{58} + 20 q^{61} + 4 q^{63} + 14 q^{64} - 12 q^{67} + 16 q^{69} + 6 q^{72} - 32 q^{73} - 16 q^{74} + 6 q^{78} + 16 q^{79} + 2 q^{81} - 24 q^{83} - 8 q^{91} + 4 q^{93} - 8 q^{94} + 32 q^{97} - 6 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^4 - 4 * q^7 - 6 * q^8 - 2 * q^9 + 4 * q^13 - 4 * q^14 - 2 * q^16 - 2 * q^18 + 4 * q^26 + 4 * q^28 - 4 * q^29 + 10 * q^32 + 2 * q^36 - 16 * q^37 + 6 * q^39 - 8 * q^47 - 6 * q^49 + 4 * q^51 - 4 * q^52 + 12 * q^56 + 4 * q^57 - 4 * q^58 + 20 * q^61 + 4 * q^63 + 14 * q^64 - 12 * q^67 + 16 * q^69 + 6 * q^72 - 32 * q^73 - 16 * q^74 + 6 * q^78 + 16 * q^79 + 2 * q^81 - 24 * q^83 - 8 * q^91 + 4 * q^93 - 8 * q^94 + 32 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$-1$	$1$	$-1$

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			0.353553	−	0.935414i	$-0.384973\pi$
$2$	1.00000			0.707107			0.353553	+	0.935414i	$0.384973\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$			1.00000i			0.408248i
$7$	−2.00000			−0.755929			−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000			−0.755929			−0.377964	+	0.925820i	$0.623376\pi$
$8$	−3.00000			−1.06066
$9$	−1.00000			−0.333333
$10$		0			0
$11$		0			0		1.00000			$0$
$11$		0			0		−1.00000			$\pi$
$12$		−	1.00000i		−	0.288675i
$13$	2.00000	−	3.00000i	0.554700	−	0.832050i
$13$	2.00000	−	3.00000i	0.554700	−	0.832050i
$14$	−2.00000			−0.534522
$15$		0			0
$16$	−1.00000			−0.250000
$17$		−	2.00000i		−	0.485071i	−0.970143	−	0.242536i	$-0.922021\pi$
$17$		−	2.00000i		−	0.485071i	0.970143	−	0.242536i	$-0.0779791\pi$
$18$	−1.00000			−0.235702
$19$		−	2.00000i		−	0.458831i	−0.973329	−	0.229416i	$-0.926318\pi$
$19$		−	2.00000i		−	0.458831i	0.973329	−	0.229416i	$-0.0736815\pi$
$20$		0			0
$21$		−	2.00000i		−	0.436436i
$22$		0			0
$23$		−	8.00000i		−	1.66812i	−0.551677	−	0.834058i	$-0.686012\pi$
$23$		−	8.00000i		−	1.66812i	0.551677	−	0.834058i	$-0.313988\pi$
$24$		−	3.00000i		−	0.612372i
$25$		0			0
$26$	2.00000	−	3.00000i	0.392232	−	0.588348i
$27$		−	1.00000i		−	0.192450i
$28$	2.00000			0.377964
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$		0			0
$31$		−	2.00000i		−	0.359211i	−0.983739	−	0.179605i	$-0.942518\pi$
$31$		−	2.00000i		−	0.359211i	0.983739	−	0.179605i	$-0.0574821\pi$
$32$	5.00000			0.883883
$33$		0			0
$34$		−	2.00000i		−	0.342997i
$35$		0			0
$36$	1.00000			0.166667
$37$	−8.00000			−1.31519			−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000			−1.31519			−0.657596	+	0.753371i	$0.728427\pi$
$38$		−	2.00000i		−	0.324443i
$39$	3.00000	+	2.00000i	0.480384	+	0.320256i
$40$		0			0
$41$		−	2.00000i		−	0.312348i	−0.987730	−	0.156174i	$-0.950084\pi$
$41$		−	2.00000i		−	0.312348i	0.987730	−	0.156174i	$-0.0499160\pi$
$42$		−	2.00000i		−	0.308607i
$43$		−	4.00000i		−	0.609994i	−0.952353	−	0.304997i	$-0.901344\pi$
$43$		−	4.00000i		−	0.609994i	0.952353	−	0.304997i	$-0.0986555\pi$
$44$		0			0
$45$		0			0
$46$		−	8.00000i		−	1.17954i
$47$	−4.00000			−0.583460			−0.291730	−	0.956501i	$-0.594231\pi$
$47$	−4.00000			−0.583460			−0.291730	+	0.956501i	$0.594231\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−3.00000			−0.428571
$50$		0			0
$51$	2.00000			0.280056
$52$	−2.00000	+	3.00000i	−0.277350	+	0.416025i
$53$		−	6.00000i		−	0.824163i	−0.911147	−	0.412082i	$-0.864802\pi$
$53$		−	6.00000i		−	0.824163i	0.911147	−	0.412082i	$-0.135198\pi$
$54$		−	1.00000i		−	0.136083i
$55$		0			0
$56$	6.00000			0.801784
$57$	2.00000			0.264906
$58$	−2.00000			−0.262613
$59$			12.0000i			1.56227i	0.624364	+	0.781133i	$0.285358\pi$
$59$			12.0000i			1.56227i	−0.624364	+	0.781133i	$0.714642\pi$
$60$		0			0
$61$	10.0000			1.28037			0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000			1.28037			0.640184	+	0.768221i	$0.278858\pi$
$62$		−	2.00000i		−	0.254000i
$63$	2.00000			0.251976
$64$	7.00000			0.875000
$65$		0			0
$66$		0			0
$67$	−6.00000			−0.733017			−0.366508	−	0.930415i	$-0.619447\pi$
$67$	−6.00000			−0.733017			−0.366508	+	0.930415i	$0.619447\pi$
$68$			2.00000i			0.242536i
$69$	8.00000			0.963087
$70$		0			0
$71$			8.00000i			0.949425i	0.880141	+	0.474713i	$0.157448\pi$
$71$			8.00000i			0.949425i	−0.880141	+	0.474713i	$0.842552\pi$
$72$	3.00000			0.353553
$73$	−16.0000			−1.87266			−0.936329	−	0.351123i	$-0.885800\pi$
$73$	−16.0000			−1.87266			−0.936329	+	0.351123i	$0.885800\pi$
$74$	−8.00000			−0.929981
$75$		0			0
$76$			2.00000i			0.229416i
$77$		0			0
$78$	3.00000	+	2.00000i	0.339683	+	0.226455i
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		−	2.00000i		−	0.220863i
$83$	−12.0000			−1.31717			−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000			−1.31717			−0.658586	+	0.752506i	$0.728845\pi$
$84$			2.00000i			0.218218i
$85$		0			0
$86$		−	4.00000i		−	0.431331i
$87$		−	2.00000i		−	0.214423i
$88$		0			0
$89$		−	6.00000i		−	0.635999i	−0.948091	−	0.317999i	$-0.896989\pi$
$89$		−	6.00000i		−	0.635999i	0.948091	−	0.317999i	$-0.103011\pi$
$90$		0			0
$91$	−4.00000	+	6.00000i	−0.419314	+	0.628971i
$92$			8.00000i			0.834058i
$93$	2.00000			0.207390
$94$	−4.00000			−0.412568
$95$		0			0
$96$			5.00000i			0.510310i
$97$	16.0000			1.62455			0.812277	−	0.583272i	$-0.198228\pi$
$97$	16.0000			1.62455			0.812277	+	0.583272i	$0.198228\pi$
$98$	−3.00000			−0.303046
$99$		0			0
$100$		0			0
$101$	−2.00000			−0.199007			−0.0995037	−	0.995037i	$-0.531726\pi$
$101$	−2.00000			−0.199007			−0.0995037	+	0.995037i	$0.531726\pi$
$102$	2.00000			0.198030
$103$			16.0000i			1.57653i	0.615338	+	0.788263i	$0.289020\pi$
$103$			16.0000i			1.57653i	−0.615338	+	0.788263i	$0.710980\pi$
$104$	−6.00000	+	9.00000i	−0.588348	+	0.882523i
$105$		0			0
$106$		−	6.00000i		−	0.582772i
$107$		−	8.00000i		−	0.773389i	−0.922208	−	0.386695i	$-0.873617\pi$
$107$		−	8.00000i		−	0.773389i	0.922208	−	0.386695i	$-0.126383\pi$
$108$			1.00000i			0.0962250i
$109$		−	16.0000i		−	1.53252i	−0.642529	−	0.766261i	$-0.722115\pi$
$109$		−	16.0000i		−	1.53252i	0.642529	−	0.766261i	$-0.277885\pi$
$110$		0			0
$111$		−	8.00000i		−	0.759326i
$112$	2.00000			0.188982
$113$		−	14.0000i		−	1.31701i	−0.752577	−	0.658505i	$-0.771189\pi$
$113$		−	14.0000i		−	1.31701i	0.752577	−	0.658505i	$-0.228811\pi$
$114$	2.00000			0.187317
$115$		0			0
$116$	2.00000			0.185695
$117$	−2.00000	+	3.00000i	−0.184900	+	0.277350i
$118$			12.0000i			1.10469i
$119$			4.00000i			0.366679i
$120$		0			0
$121$	11.0000			1.00000
$122$	10.0000			0.905357
$123$	2.00000			0.180334
$124$			2.00000i			0.179605i
$125$		0			0
$126$	2.00000			0.178174
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$	−3.00000			−0.265165
$129$	4.00000			0.352180
$130$		0			0
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$		0			0
$133$			4.00000i			0.346844i
$134$	−6.00000			−0.518321
$135$		0			0
$136$			6.00000i			0.514496i
$137$	−6.00000			−0.512615			−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000			−0.512615			−0.256307	+	0.966595i	$0.582506\pi$
$138$	8.00000			0.681005
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$		0			0
$141$		−	4.00000i		−	0.336861i
$142$			8.00000i			0.671345i
$143$		0			0
$144$	1.00000			0.0833333
$145$		0			0
$146$	−16.0000			−1.32417
$147$		−	3.00000i		−	0.247436i
$148$	8.00000			0.657596
$149$			14.0000i			1.14692i	0.819232	+	0.573462i	$0.194400\pi$
$149$			14.0000i			1.14692i	−0.819232	+	0.573462i	$0.805600\pi$
$150$		0			0
$151$			14.0000i			1.13930i	0.821886	+	0.569652i	$0.192922\pi$
$151$			14.0000i			1.13930i	−0.821886	+	0.569652i	$0.807078\pi$
$152$			6.00000i			0.486664i
$153$			2.00000i			0.161690i
$154$		0			0
$155$		0			0
$156$	−3.00000	−	2.00000i	−0.240192	−	0.160128i
$157$		−	14.0000i		−	1.11732i	−0.829396	−	0.558661i	$-0.811315\pi$
$157$		−	14.0000i		−	1.11732i	0.829396	−	0.558661i	$-0.188685\pi$
$158$	8.00000			0.636446
$159$	6.00000			0.475831
$160$		0			0
$161$			16.0000i			1.26098i
$162$	1.00000			0.0785674
$163$	18.0000			1.40987			0.704934	−	0.709273i	$-0.250976\pi$
$163$	18.0000			1.40987			0.704934	+	0.709273i	$0.250976\pi$
$164$			2.00000i			0.156174i
$165$		0			0
$166$	−12.0000			−0.931381
$167$	−20.0000			−1.54765			−0.773823	−	0.633402i	$-0.781658\pi$
$167$	−20.0000			−1.54765			−0.773823	+	0.633402i	$0.781658\pi$
$168$			6.00000i			0.462910i
$169$	−5.00000	−	12.0000i	−0.384615	−	0.923077i
$170$		0			0
$171$			2.00000i			0.152944i
$172$			4.00000i			0.304997i
$173$			10.0000i			0.760286i	0.924928	+	0.380143i	$0.124125\pi$
$173$			10.0000i			0.760286i	−0.924928	+	0.380143i	$0.875875\pi$
$174$		−	2.00000i		−	0.151620i
$175$		0			0
$176$		0			0
$177$	−12.0000			−0.901975
$178$		−	6.00000i		−	0.449719i
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$		0			0
$181$	6.00000			0.445976			0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000			0.445976			0.222988	+	0.974821i	$0.428419\pi$
$182$	−4.00000	+	6.00000i	−0.296500	+	0.444750i
$183$			10.0000i			0.739221i
$184$			24.0000i			1.76930i
$185$		0			0
$186$	2.00000			0.146647
$187$		0			0
$188$	4.00000			0.291730
$189$			2.00000i			0.145479i
$190$		0			0
$191$	−20.0000			−1.44715			−0.723575	−	0.690246i	$-0.757502\pi$
$191$	−20.0000			−1.44715			−0.723575	+	0.690246i	$0.757502\pi$
$192$			7.00000i			0.505181i
$193$	−4.00000			−0.287926			−0.143963	−	0.989583i	$-0.545985\pi$
$193$	−4.00000			−0.287926			−0.143963	+	0.989583i	$0.545985\pi$
$194$	16.0000			1.14873
$195$		0			0
$196$	3.00000			0.214286
$197$	22.0000			1.56744			0.783718	−	0.621117i	$-0.213321\pi$
$197$	22.0000			1.56744			0.783718	+	0.621117i	$0.213321\pi$
$198$		0			0
$199$	24.0000			1.70131			0.850657	−	0.525720i	$-0.176204\pi$
$199$	24.0000			1.70131			0.850657	+	0.525720i	$0.176204\pi$
$200$		0			0
$201$		−	6.00000i		−	0.423207i
$202$	−2.00000			−0.140720
$203$	4.00000			0.280745
$204$	−2.00000			−0.140028
$205$		0			0
$206$			16.0000i			1.11477i
$207$			8.00000i			0.556038i
$208$	−2.00000	+	3.00000i	−0.138675	+	0.208013i
$209$		0			0
$210$		0			0
$211$	−12.0000			−0.826114			−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000			−0.826114			−0.413057	+	0.910705i	$0.635539\pi$
$212$			6.00000i			0.412082i
$213$	−8.00000			−0.548151
$214$		−	8.00000i		−	0.546869i
$215$		0			0
$216$			3.00000i			0.204124i
$217$			4.00000i			0.271538i
$218$		−	16.0000i		−	1.08366i
$219$		−	16.0000i		−	1.08118i
$220$		0			0
$221$	−6.00000	−	4.00000i	−0.403604	−	0.269069i
$222$		−	8.00000i		−	0.536925i
$223$	22.0000			1.47323			0.736614	−	0.676313i	$-0.236423\pi$
$223$	22.0000			1.47323			0.736614	+	0.676313i	$0.236423\pi$
$224$	−10.0000			−0.668153
$225$		0			0
$226$		−	14.0000i		−	0.931266i
$227$		0			0			−	1.00000i	$-0.5\pi$
$227$		0			0				1.00000i	$0.5\pi$
$228$	−2.00000			−0.132453
$229$		−	8.00000i		−	0.528655i	−0.964433	−	0.264327i	$-0.914850\pi$
$229$		−	8.00000i		−	0.528655i	0.964433	−	0.264327i	$-0.0851500\pi$
$230$		0			0
$231$		0			0
$232$	6.00000			0.393919
$233$			14.0000i			0.917170i	0.888650	+	0.458585i	$0.151644\pi$
$233$			14.0000i			0.917170i	−0.888650	+	0.458585i	$0.848356\pi$
$234$	−2.00000	+	3.00000i	−0.130744	+	0.196116i
$235$		0			0
$236$		−	12.0000i		−	0.781133i
$237$			8.00000i			0.519656i
$238$			4.00000i			0.259281i
$239$		−	8.00000i		−	0.517477i	−0.965947	−	0.258738i	$-0.916693\pi$
$239$		−	8.00000i		−	0.517477i	0.965947	−	0.258738i	$-0.0833068\pi$
$240$		0			0
$241$			12.0000i			0.772988i	0.922292	+	0.386494i	$0.126314\pi$
$241$			12.0000i			0.772988i	−0.922292	+	0.386494i	$0.873686\pi$
$242$	11.0000			0.707107
$243$			1.00000i			0.0641500i
$244$	−10.0000			−0.640184
$245$		0			0
$246$	2.00000			0.127515
$247$	−6.00000	−	4.00000i	−0.381771	−	0.254514i
$248$			6.00000i			0.381000i
$249$		−	12.0000i		−	0.760469i
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$	−2.00000			−0.125988
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−17.0000			−1.06250
$257$		−	30.0000i		−	1.87135i	−0.352865	−	0.935674i	$-0.614792\pi$
$257$		−	30.0000i		−	1.87135i	0.352865	−	0.935674i	$-0.385208\pi$
$258$	4.00000			0.249029
$259$	16.0000			0.994192
$260$		0			0
$261$	2.00000			0.123797
$262$	−12.0000			−0.741362
$263$			12.0000i			0.739952i	0.929041	+	0.369976i	$0.120634\pi$
$263$			12.0000i			0.739952i	−0.929041	+	0.369976i	$0.879366\pi$
$264$		0			0
$265$		0			0
$266$			4.00000i			0.245256i
$267$	6.00000			0.367194
$268$	6.00000			0.366508
$269$	−10.0000			−0.609711			−0.304855	−	0.952399i	$-0.598608\pi$
$269$	−10.0000			−0.609711			−0.304855	+	0.952399i	$0.598608\pi$
$270$		0			0
$271$		−	14.0000i		−	0.850439i	−0.905090	−	0.425220i	$-0.860197\pi$
$271$		−	14.0000i		−	0.850439i	0.905090	−	0.425220i	$-0.139803\pi$
$272$			2.00000i			0.121268i
$273$	−6.00000	−	4.00000i	−0.363137	−	0.242091i
$274$	−6.00000			−0.362473
$275$		0			0
$276$	−8.00000			−0.481543
$277$			2.00000i			0.120168i	0.998193	+	0.0600842i	$0.0191369\pi$
$277$			2.00000i			0.120168i	−0.998193	+	0.0600842i	$0.980863\pi$
$278$	−4.00000			−0.239904
$279$			2.00000i			0.119737i
$280$		0			0
$281$		−	6.00000i		−	0.357930i	−0.983855	−	0.178965i	$-0.942725\pi$
$281$		−	6.00000i		−	0.357930i	0.983855	−	0.178965i	$-0.0572749\pi$
$282$		−	4.00000i		−	0.238197i
$283$		−	4.00000i		−	0.237775i	−0.992908	−	0.118888i	$-0.962067\pi$
$283$		−	4.00000i		−	0.237775i	0.992908	−	0.118888i	$-0.0379328\pi$
$284$		−	8.00000i		−	0.474713i
$285$		0			0
$286$		0			0
$287$			4.00000i			0.236113i
$288$	−5.00000			−0.294628
$289$	13.0000			0.764706
$290$		0			0
$291$			16.0000i			0.937937i
$292$	16.0000			0.936329
$293$	18.0000			1.05157			0.525786	−	0.850617i	$-0.323771\pi$
$293$	18.0000			1.05157			0.525786	+	0.850617i	$0.323771\pi$
$294$		−	3.00000i		−	0.174964i
$295$		0			0
$296$	24.0000			1.39497
$297$		0			0
$298$			14.0000i			0.810998i
$299$	−24.0000	−	16.0000i	−1.38796	−	0.925304i
$300$		0			0
$301$			8.00000i			0.461112i
$302$			14.0000i			0.805609i
$303$		−	2.00000i		−	0.114897i
$304$			2.00000i			0.114708i
$305$		0			0
$306$			2.00000i			0.114332i
$307$	26.0000			1.48390			0.741949	−	0.670456i	$-0.233902\pi$
$307$	26.0000			1.48390			0.741949	+	0.670456i	$0.233902\pi$
$308$		0			0
$309$	−16.0000			−0.910208
$310$		0			0
$311$	4.00000			0.226819			0.113410	−	0.993548i	$-0.463823\pi$
$311$	4.00000			0.226819			0.113410	+	0.993548i	$0.463823\pi$
$312$	−9.00000	−	6.00000i	−0.509525	−	0.339683i
$313$		−	10.0000i		−	0.565233i	−0.959233	−	0.282617i	$-0.908798\pi$
$313$		−	10.0000i		−	0.565233i	0.959233	−	0.282617i	$-0.0912024\pi$
$314$		−	14.0000i		−	0.790066i
$315$		0			0
$316$	−8.00000			−0.450035
$317$	−26.0000			−1.46031			−0.730153	−	0.683284i	$-0.760551\pi$
$317$	−26.0000			−1.46031			−0.730153	+	0.683284i	$0.760551\pi$
$318$	6.00000			0.336463
$319$		0			0
$320$		0			0
$321$	8.00000			0.446516
$322$			16.0000i			0.891645i
$323$	−4.00000			−0.222566
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	18.0000			0.996928
$327$	16.0000			0.884802
$328$			6.00000i			0.331295i
$329$	8.00000			0.441054
$330$		0			0
$331$		−	26.0000i		−	1.42909i	−0.699590	−	0.714545i	$-0.746634\pi$
$331$		−	26.0000i		−	1.42909i	0.699590	−	0.714545i	$-0.253366\pi$
$332$	12.0000			0.658586
$333$	8.00000			0.438397
$334$	−20.0000			−1.09435
$335$		0			0
$336$			2.00000i			0.109109i
$337$		−	6.00000i		−	0.326841i	−0.986557	−	0.163420i	$-0.947747\pi$
$337$		−	6.00000i		−	0.326841i	0.986557	−	0.163420i	$-0.0522527\pi$
$338$	−5.00000	−	12.0000i	−0.271964	−	0.652714i
$339$	14.0000			0.760376
$340$		0			0
$341$		0			0
$342$			2.00000i			0.108148i
$343$	20.0000			1.07990
$344$			12.0000i			0.646997i
$345$		0			0
$346$			10.0000i			0.537603i
$347$			20.0000i			1.07366i	0.843692	+	0.536828i	$0.180378\pi$
$347$			20.0000i			1.07366i	−0.843692	+	0.536828i	$0.819622\pi$
$348$			2.00000i			0.107211i
$349$			20.0000i			1.07058i	0.844670	+	0.535288i	$0.179797\pi$
$349$			20.0000i			1.07058i	−0.844670	+	0.535288i	$0.820203\pi$
$350$		0			0
$351$	−3.00000	−	2.00000i	−0.160128	−	0.106752i
$352$		0			0
$353$	−30.0000			−1.59674			−0.798369	−	0.602168i	$-0.794304\pi$
$353$	−30.0000			−1.59674			−0.798369	+	0.602168i	$0.794304\pi$
$354$	−12.0000			−0.637793
$355$		0			0
$356$			6.00000i			0.317999i
$357$	−4.00000			−0.211702
$358$	−12.0000			−0.634220
$359$		−	4.00000i		−	0.211112i	−0.994413	−	0.105556i	$-0.966338\pi$
$359$		−	4.00000i		−	0.211112i	0.994413	−	0.105556i	$-0.0336622\pi$
$360$		0			0
$361$	15.0000			0.789474
$362$	6.00000			0.315353
$363$			11.0000i			0.577350i
$364$	4.00000	−	6.00000i	0.209657	−	0.314485i
$365$		0			0
$366$			10.0000i			0.522708i
$367$		0			0		1.00000			$0$
$367$		0			0		−1.00000			$\pi$
$368$			8.00000i			0.417029i
$369$			2.00000i			0.104116i
$370$		0			0
$371$			12.0000i			0.623009i
$372$	−2.00000			−0.103695
$373$		−	38.0000i		−	1.96757i	−0.179364	−	0.983783i	$-0.557404\pi$
$373$		−	38.0000i		−	1.96757i	0.179364	−	0.983783i	$-0.442596\pi$
$374$		0			0
$375$		0			0
$376$	12.0000			0.618853
$377$	−4.00000	+	6.00000i	−0.206010	+	0.309016i
$378$			2.00000i			0.102869i
$379$			30.0000i			1.54100i	0.637442	+	0.770498i	$0.279993\pi$
$379$			30.0000i			1.54100i	−0.637442	+	0.770498i	$0.720007\pi$
$380$		0			0
$381$		0			0
$382$	−20.0000			−1.02329
$383$	−4.00000			−0.204390			−0.102195	−	0.994764i	$-0.532587\pi$
$383$	−4.00000			−0.204390			−0.102195	+	0.994764i	$0.532587\pi$
$384$		−	3.00000i		−	0.153093i
$385$		0			0
$386$	−4.00000			−0.203595
$387$			4.00000i			0.203331i
$388$	−16.0000			−0.812277
$389$	38.0000			1.92668			0.963338	−	0.268290i	$-0.0864585\pi$
$389$	38.0000			1.92668			0.963338	+	0.268290i	$0.0864585\pi$
$390$		0			0
$391$	−16.0000			−0.809155
$392$	9.00000			0.454569
$393$		−	12.0000i		−	0.605320i
$394$	22.0000			1.10834
$395$		0			0
$396$		0			0
$397$	8.00000			0.401508			0.200754	−	0.979642i	$-0.435661\pi$
$397$	8.00000			0.401508			0.200754	+	0.979642i	$0.435661\pi$
$398$	24.0000			1.20301
$399$	−4.00000			−0.200250
$400$		0			0
$401$		−	10.0000i		−	0.499376i	−0.968326	−	0.249688i	$-0.919672\pi$
$401$		−	10.0000i		−	0.499376i	0.968326	−	0.249688i	$-0.0803281\pi$
$402$		−	6.00000i		−	0.299253i
$403$	−6.00000	−	4.00000i	−0.298881	−	0.199254i
$404$	2.00000			0.0995037
$405$		0			0
$406$	4.00000			0.198517
$407$		0			0
$408$	−6.00000			−0.297044
$409$			12.0000i			0.593362i	0.954977	+	0.296681i	$0.0958798\pi$
$409$			12.0000i			0.593362i	−0.954977	+	0.296681i	$0.904120\pi$
$410$		0			0
$411$		−	6.00000i		−	0.295958i
$412$		−	16.0000i		−	0.788263i
$413$		−	24.0000i		−	1.18096i
$414$			8.00000i			0.393179i
$415$		0			0
$416$	10.0000	−	15.0000i	0.490290	−	0.735436i
$417$		−	4.00000i		−	0.195881i
$418$		0			0
$419$	12.0000			0.586238			0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000			0.586238			0.293119	+	0.956076i	$0.405307\pi$
$420$		0			0
$421$		−	40.0000i		−	1.94948i	−0.223341	−	0.974740i	$-0.571696\pi$
$421$		−	40.0000i		−	1.94948i	0.223341	−	0.974740i	$-0.428304\pi$
$422$	−12.0000			−0.584151
$423$	4.00000			0.194487
$424$			18.0000i			0.874157i
$425$		0			0
$426$	−8.00000			−0.387601
$427$	−20.0000			−0.967868
$428$			8.00000i			0.386695i
$429$		0			0
$430$		0			0
$431$			12.0000i			0.578020i	0.957326	+	0.289010i	$0.0933260\pi$
$431$			12.0000i			0.578020i	−0.957326	+	0.289010i	$0.906674\pi$
$432$			1.00000i			0.0481125i
$433$			14.0000i			0.672797i	0.941720	+	0.336399i	$0.109209\pi$
$433$			14.0000i			0.672797i	−0.941720	+	0.336399i	$0.890791\pi$
$434$			4.00000i			0.192006i
$435$		0			0
$436$			16.0000i			0.766261i
$437$	−16.0000			−0.765384
$438$		−	16.0000i		−	0.764510i
$439$	−16.0000			−0.763638			−0.381819	−	0.924237i	$-0.624702\pi$
$439$	−16.0000			−0.763638			−0.381819	+	0.924237i	$0.624702\pi$
$440$		0			0
$441$	3.00000			0.142857
$442$	−6.00000	−	4.00000i	−0.285391	−	0.190261i
$443$			24.0000i			1.14027i	0.821549	+	0.570137i	$0.193110\pi$
$443$			24.0000i			1.14027i	−0.821549	+	0.570137i	$0.806890\pi$
$444$			8.00000i			0.379663i
$445$		0			0
$446$	22.0000			1.04173
$447$	−14.0000			−0.662177
$448$	−14.0000			−0.661438
$449$		−	6.00000i		−	0.283158i	−0.989927	−	0.141579i	$-0.954782\pi$
$449$		−	6.00000i		−	0.283158i	0.989927	−	0.141579i	$-0.0452178\pi$
$450$		0			0
$451$		0			0
$452$			14.0000i			0.658505i
$453$	−14.0000			−0.657777
$454$		0			0
$455$		0			0
$456$	−6.00000			−0.280976
$457$	8.00000			0.374224			0.187112	−	0.982339i	$-0.440087\pi$
$457$	8.00000			0.374224			0.187112	+	0.982339i	$0.440087\pi$
$458$		−	8.00000i		−	0.373815i
$459$	−2.00000			−0.0933520
$460$		0			0
$461$		−	34.0000i		−	1.58354i	−0.610821	−	0.791769i	$-0.709160\pi$
$461$		−	34.0000i		−	1.58354i	0.610821	−	0.791769i	$-0.290840\pi$
$462$		0			0
$463$	−14.0000			−0.650635			−0.325318	−	0.945605i	$-0.605471\pi$
$463$	−14.0000			−0.650635			−0.325318	+	0.945605i	$0.605471\pi$
$464$	2.00000			0.0928477
$465$		0			0
$466$			14.0000i			0.648537i
$467$		−	36.0000i		−	1.66588i	−0.553362	−	0.832941i	$-0.686655\pi$
$467$		−	36.0000i		−	1.66588i	0.553362	−	0.832941i	$-0.313345\pi$
$468$	2.00000	−	3.00000i	0.0924500	−	0.138675i
$469$	12.0000			0.554109
$470$		0			0
$471$	14.0000			0.645086
$472$		−	36.0000i		−	1.65703i
$473$		0			0
$474$			8.00000i			0.367452i
$475$		0			0
$476$		−	4.00000i		−	0.183340i
$477$			6.00000i			0.274721i
$478$		−	8.00000i		−	0.365911i
$479$		0			0		1.00000			$0$
$479$		0			0		−1.00000			$\pi$
$480$		0			0
$481$	−16.0000	+	24.0000i	−0.729537	+	1.09431i
$482$			12.0000i			0.546585i
$483$	−16.0000			−0.728025
$484$	−11.0000			−0.500000
$485$		0			0
$486$			1.00000i			0.0453609i
$487$	18.0000			0.815658			0.407829	−	0.913058i	$-0.366286\pi$
$487$	18.0000			0.815658			0.407829	+	0.913058i	$0.366286\pi$
$488$	−30.0000			−1.35804
$489$			18.0000i			0.813988i
$490$		0			0
$491$	−40.0000			−1.80517			−0.902587	−	0.430507i	$-0.858335\pi$
$491$	−40.0000			−1.80517			−0.902587	+	0.430507i	$0.858335\pi$
$492$	−2.00000			−0.0901670
$493$			4.00000i			0.180151i
$494$	−6.00000	−	4.00000i	−0.269953	−	0.179969i
$495$		0			0
$496$			2.00000i			0.0898027i
$497$		−	16.0000i		−	0.717698i
$498$		−	12.0000i		−	0.537733i
$499$			10.0000i			0.447661i	0.974628	+	0.223831i	$0.0718563\pi$
$499$			10.0000i			0.447661i	−0.974628	+	0.223831i	$0.928144\pi$
$500$		0			0
$501$		−	20.0000i		−	0.893534i
$502$		0			0
$503$		−	4.00000i		−	0.178351i	−0.996016	−	0.0891756i	$-0.971577\pi$
$503$		−	4.00000i		−	0.178351i	0.996016	−	0.0891756i	$-0.0284232\pi$
$504$	−6.00000			−0.267261
$505$		0			0
$506$		0			0
$507$	12.0000	−	5.00000i	0.532939	−	0.222058i
$508$		0			0
$509$		−	6.00000i		−	0.265945i	−0.991120	−	0.132973i	$-0.957548\pi$
$509$		−	6.00000i		−	0.265945i	0.991120	−	0.132973i	$-0.0424523\pi$
$510$		0			0
$511$	32.0000			1.41560
$512$	−11.0000			−0.486136
$513$	−2.00000			−0.0883022
$514$		−	30.0000i		−	1.32324i
$515$		0			0
$516$	−4.00000			−0.176090
$517$		0			0
$518$	16.0000			0.703000
$519$	−10.0000			−0.438951
$520$		0			0
$521$	22.0000			0.963837			0.481919	−	0.876216i	$-0.339940\pi$
$521$	22.0000			0.963837			0.481919	+	0.876216i	$0.339940\pi$
$522$	2.00000			0.0875376
$523$		−	28.0000i		−	1.22435i	−0.790721	−	0.612177i	$-0.790294\pi$
$523$		−	28.0000i		−	1.22435i	0.790721	−	0.612177i	$-0.209706\pi$
$524$	12.0000			0.524222
$525$		0			0
$526$			12.0000i			0.523225i
$527$	−4.00000			−0.174243
$528$		0			0
$529$	−41.0000			−1.78261
$530$		0			0
$531$		−	12.0000i		−	0.520756i
$532$		−	4.00000i		−	0.173422i
$533$	−6.00000	−	4.00000i	−0.259889	−	0.173259i
$534$	6.00000			0.259645
$535$		0			0
$536$	18.0000			0.777482
$537$		−	12.0000i		−	0.517838i
$538$	−10.0000			−0.431131
$539$		0			0
$540$		0			0
$541$		−	8.00000i		−	0.343947i	−0.985102	−	0.171973i	$-0.944986\pi$
$541$		−	8.00000i		−	0.343947i	0.985102	−	0.171973i	$-0.0550143\pi$
$542$		−	14.0000i		−	0.601351i
$543$			6.00000i			0.257485i
$544$		−	10.0000i		−	0.428746i
$545$		0			0
$546$	−6.00000	−	4.00000i	−0.256776	−	0.171184i
$547$			4.00000i			0.171028i	0.996337	+	0.0855138i	$0.0272532\pi$
$547$			4.00000i			0.171028i	−0.996337	+	0.0855138i	$0.972747\pi$
$548$	6.00000			0.256307
$549$	−10.0000			−0.426790
$550$		0			0
$551$			4.00000i			0.170406i
$552$	−24.0000			−1.02151
$553$	−16.0000			−0.680389
$554$			2.00000i			0.0849719i
$555$		0			0
$556$	4.00000			0.169638
$557$	6.00000			0.254228			0.127114	−	0.991888i	$-0.459429\pi$
$557$	6.00000			0.254228			0.127114	+	0.991888i	$0.459429\pi$
$558$			2.00000i			0.0846668i
$559$	−12.0000	−	8.00000i	−0.507546	−	0.338364i
$560$		0			0
$561$		0			0
$562$		−	6.00000i		−	0.253095i
$563$			24.0000i			1.01148i	0.862686	+	0.505740i	$0.168780\pi$
$563$			24.0000i			1.01148i	−0.862686	+	0.505740i	$0.831220\pi$
$564$			4.00000i			0.168430i
$565$		0			0
$566$		−	4.00000i		−	0.168133i
$567$	−2.00000			−0.0839921
$568$		−	24.0000i		−	1.00702i
$569$	30.0000			1.25767			0.628833	−	0.777541i	$-0.283533\pi$
$569$	30.0000			1.25767			0.628833	+	0.777541i	$0.283533\pi$
$570$		0			0
$571$	−4.00000			−0.167395			−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000			−0.167395			−0.0836974	+	0.996491i	$0.526673\pi$
$572$		0			0
$573$		−	20.0000i		−	0.835512i
$574$			4.00000i			0.166957i
$575$		0			0
$576$	−7.00000			−0.291667
$577$	4.00000			0.166522			0.0832611	−	0.996528i	$-0.473466\pi$
$577$	4.00000			0.166522			0.0832611	+	0.996528i	$0.473466\pi$
$578$	13.0000			0.540729
$579$		−	4.00000i		−	0.166234i
$580$		0			0
$581$	24.0000			0.995688
$582$			16.0000i			0.663221i
$583$		0			0
$584$	48.0000			1.98625
$585$		0			0
$586$	18.0000			0.743573
$587$	28.0000			1.15568			0.577842	−	0.816149i	$-0.303895\pi$
$587$	28.0000			1.15568			0.577842	+	0.816149i	$0.303895\pi$
$588$			3.00000i			0.123718i
$589$	−4.00000			−0.164817
$590$		0			0
$591$			22.0000i			0.904959i
$592$	8.00000			0.328798
$593$	10.0000			0.410651			0.205325	−	0.978694i	$-0.434175\pi$
$593$	10.0000			0.410651			0.205325	+	0.978694i	$0.434175\pi$
$594$		0			0
$595$		0			0
$596$		−	14.0000i		−	0.573462i
$597$			24.0000i			0.982255i
$598$	−24.0000	−	16.0000i	−0.981433	−	0.654289i
$599$	−16.0000			−0.653742			−0.326871	−	0.945069i	$-0.605994\pi$
$599$	−16.0000			−0.653742			−0.326871	+	0.945069i	$0.605994\pi$
$600$		0			0
$601$	38.0000			1.55005			0.775026	−	0.631929i	$-0.217737\pi$
$601$	38.0000			1.55005			0.775026	+	0.631929i	$0.217737\pi$
$602$			8.00000i			0.326056i
$603$	6.00000			0.244339
$604$		−	14.0000i		−	0.569652i
$605$		0			0
$606$		−	2.00000i		−	0.0812444i
$607$			8.00000i			0.324710i	0.986732	+	0.162355i	$0.0519090\pi$
$607$			8.00000i			0.324710i	−0.986732	+	0.162355i	$0.948091\pi$
$608$		−	10.0000i		−	0.405554i
$609$			4.00000i			0.162088i
$610$		0			0
$611$	−8.00000	+	12.0000i	−0.323645	+	0.485468i
$612$		−	2.00000i		−	0.0808452i
$613$	−16.0000			−0.646234			−0.323117	−	0.946359i	$-0.604731\pi$
$613$	−16.0000			−0.646234			−0.323117	+	0.946359i	$0.604731\pi$
$614$	26.0000			1.04927
$615$		0			0
$616$		0			0
$617$	−10.0000			−0.402585			−0.201292	−	0.979531i	$-0.564514\pi$
$617$	−10.0000			−0.402585			−0.201292	+	0.979531i	$0.564514\pi$
$618$	−16.0000			−0.643614
$619$		−	38.0000i		−	1.52735i	−0.645601	−	0.763674i	$-0.723393\pi$
$619$		−	38.0000i		−	1.52735i	0.645601	−	0.763674i	$-0.276607\pi$
$620$		0			0
$621$	−8.00000			−0.321029
$622$	4.00000			0.160385
$623$			12.0000i			0.480770i
$624$	−3.00000	−	2.00000i	−0.120096	−	0.0800641i
$625$		0			0
$626$		−	10.0000i		−	0.399680i
$627$		0			0
$628$			14.0000i			0.558661i
$629$			16.0000i			0.637962i
$630$		0			0
$631$			38.0000i			1.51276i	0.654135	+	0.756378i	$0.273033\pi$
$631$			38.0000i			1.51276i	−0.654135	+	0.756378i	$0.726967\pi$
$632$	−24.0000			−0.954669
$633$		−	12.0000i		−	0.476957i
$634$	−26.0000			−1.03259
$635$		0			0
$636$	−6.00000			−0.237915
$637$	−6.00000	+	9.00000i	−0.237729	+	0.356593i
$638$		0			0
$639$		−	8.00000i		−	0.316475i
$640$		0			0
$641$	−18.0000			−0.710957			−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000			−0.710957			−0.355479	+	0.934684i	$0.615682\pi$
$642$	8.00000			0.315735
$643$	14.0000			0.552106			0.276053	−	0.961142i	$-0.410973\pi$
$643$	14.0000			0.552106			0.276053	+	0.961142i	$0.410973\pi$
$644$		−	16.0000i		−	0.630488i
$645$		0			0
$646$	−4.00000			−0.157378
$647$		−	28.0000i		−	1.10079i	−0.834903	−	0.550397i	$-0.814476\pi$
$647$		−	28.0000i		−	1.10079i	0.834903	−	0.550397i	$-0.185524\pi$
$648$	−3.00000			−0.117851
$649$		0			0
$650$		0			0
$651$	−4.00000			−0.156772
$652$	−18.0000			−0.704934
$653$		−	2.00000i		−	0.0782660i	−0.999234	−	0.0391330i	$-0.987540\pi$
$653$		−	2.00000i		−	0.0782660i	0.999234	−	0.0391330i	$-0.0124596\pi$
$654$	16.0000			0.625650
$655$		0			0
$656$			2.00000i			0.0780869i
$657$	16.0000			0.624219
$658$	8.00000			0.311872
$659$	−48.0000			−1.86981			−0.934907	−	0.354892i	$-0.884518\pi$
$659$	−48.0000			−1.86981			−0.934907	+	0.354892i	$0.884518\pi$
$660$		0			0
$661$		−	4.00000i		−	0.155582i	−0.996970	−	0.0777910i	$-0.975213\pi$
$661$		−	4.00000i		−	0.155582i	0.996970	−	0.0777910i	$-0.0247867\pi$
$662$		−	26.0000i		−	1.01052i
$663$	4.00000	−	6.00000i	0.155347	−	0.233021i
$664$	36.0000			1.39707
$665$		0			0
$666$	8.00000			0.309994
$667$			16.0000i			0.619522i
$668$	20.0000			0.773823
$669$			22.0000i			0.850569i
$670$		0			0
$671$		0			0
$672$		−	10.0000i		−	0.385758i
$673$		−	14.0000i		−	0.539660i	−0.962908	−	0.269830i	$-0.913032\pi$
$673$		−	14.0000i		−	0.539660i	0.962908	−	0.269830i	$-0.0869676\pi$
$674$		−	6.00000i		−	0.231111i
$675$		0			0
$676$	5.00000	+	12.0000i	0.192308	+	0.461538i
$677$			6.00000i			0.230599i	0.993331	+	0.115299i	$0.0367827\pi$
$677$			6.00000i			0.230599i	−0.993331	+	0.115299i	$0.963217\pi$
$678$	14.0000			0.537667
$679$	−32.0000			−1.22805
$680$		0			0
$681$		0			0
$682$		0			0
$683$	16.0000			0.612223			0.306111	−	0.951996i	$-0.400972\pi$
$683$	16.0000			0.612223			0.306111	+	0.951996i	$0.400972\pi$
$684$		−	2.00000i		−	0.0764719i
$685$		0			0
$686$	20.0000			0.763604
$687$	8.00000			0.305219
$688$			4.00000i			0.152499i
$689$	−18.0000	−	12.0000i	−0.685745	−	0.457164i
$690$		0			0
$691$		−	10.0000i		−	0.380418i	−0.981744	−	0.190209i	$-0.939083\pi$
$691$		−	10.0000i		−	0.380418i	0.981744	−	0.190209i	$-0.0609166\pi$
$692$		−	10.0000i		−	0.380143i
$693$		0			0
$694$			20.0000i			0.759190i
$695$		0			0
$696$			6.00000i			0.227429i
$697$	−4.00000			−0.151511
$698$			20.0000i			0.757011i
$699$	−14.0000			−0.529529
$700$		0			0
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$	−3.00000	−	2.00000i	−0.113228	−	0.0754851i
$703$			16.0000i			0.603451i
$704$		0			0
$705$		0			0
$706$	−30.0000			−1.12906
$707$	4.00000			0.150435
$708$	12.0000			0.450988
$709$			32.0000i			1.20179i	0.799330	+	0.600893i	$0.205188\pi$
$709$			32.0000i			1.20179i	−0.799330	+	0.600893i	$0.794812\pi$
$710$		0			0
$711$	−8.00000			−0.300023
$712$			18.0000i			0.674579i
$713$	−16.0000			−0.599205
$714$	−4.00000			−0.149696
$715$		0			0
$716$	12.0000			0.448461
$717$	8.00000			0.298765
$718$		−	4.00000i		−	0.149279i
$719$	36.0000			1.34257			0.671287	−	0.741198i	$-0.265742\pi$
$719$	36.0000			1.34257			0.671287	+	0.741198i	$0.265742\pi$
$720$		0			0
$721$		−	32.0000i		−	1.19174i
$722$	15.0000			0.558242
$723$	−12.0000			−0.446285
$724$	−6.00000			−0.222988
$725$		0			0
$726$			11.0000i			0.408248i
$727$			40.0000i			1.48352i	0.670667	+	0.741759i	$0.266008\pi$
$727$			40.0000i			1.48352i	−0.670667	+	0.741759i	$0.733992\pi$
$728$	12.0000	−	18.0000i	0.444750	−	0.667124i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−8.00000			−0.295891
$732$		−	10.0000i		−	0.369611i
$733$	−12.0000			−0.443230			−0.221615	−	0.975134i	$-0.571133\pi$
$733$	−12.0000			−0.443230			−0.221615	+	0.975134i	$0.571133\pi$
$734$		0			0
$735$		0			0
$736$		−	40.0000i		−	1.47442i
$737$		0			0
$738$			2.00000i			0.0736210i
$739$		−	6.00000i		−	0.220714i	−0.993892	−	0.110357i	$-0.964801\pi$
$739$		−	6.00000i		−	0.220714i	0.993892	−	0.110357i	$-0.0351994\pi$
$740$		0			0
$741$	4.00000	−	6.00000i	0.146944	−	0.220416i
$742$			12.0000i			0.440534i
$743$	8.00000			0.293492			0.146746	−	0.989174i	$-0.453120\pi$
$743$	8.00000			0.293492			0.146746	+	0.989174i	$0.453120\pi$
$744$	−6.00000			−0.219971
$745$		0			0
$746$		−	38.0000i		−	1.39128i
$747$	12.0000			0.439057
$748$		0			0
$749$			16.0000i			0.584627i
$750$		0			0
$751$	−32.0000			−1.16770			−0.583848	−	0.811863i	$-0.698454\pi$
$751$	−32.0000			−1.16770			−0.583848	+	0.811863i	$0.698454\pi$
$752$	4.00000			0.145865
$753$		0			0
$754$	−4.00000	+	6.00000i	−0.145671	+	0.218507i
$755$		0			0
$756$		−	2.00000i		−	0.0727393i
$757$			22.0000i			0.799604i	0.916602	+	0.399802i	$0.130921\pi$
$757$			22.0000i			0.799604i	−0.916602	+	0.399802i	$0.869079\pi$
$758$			30.0000i			1.08965i
$759$		0			0
$760$		0			0
$761$		−	38.0000i		−	1.37750i	−0.724999	−	0.688749i	$-0.758160\pi$
$761$		−	38.0000i		−	1.37750i	0.724999	−	0.688749i	$-0.241840\pi$
$762$		0			0
$763$			32.0000i			1.15848i
$764$	20.0000			0.723575
$765$		0			0
$766$	−4.00000			−0.144526
$767$	36.0000	+	24.0000i	1.29988	+	0.866590i
$768$		−	17.0000i		−	0.613435i
$769$		−	40.0000i		−	1.44244i	−0.692708	−	0.721218i	$-0.743582\pi$
$769$		−	40.0000i		−	1.44244i	0.692708	−	0.721218i	$-0.256418\pi$
$770$		0			0
$771$	30.0000			1.08042
$772$	4.00000			0.143963
$773$	54.0000			1.94225			0.971123	−	0.238581i	$-0.0766824\pi$
$773$	54.0000			1.94225			0.971123	+	0.238581i	$0.0766824\pi$
$774$			4.00000i			0.143777i
$775$		0			0
$776$	−48.0000			−1.72310
$777$			16.0000i			0.573997i
$778$	38.0000			1.36237
$779$	−4.00000			−0.143315
$780$		0			0
$781$		0			0
$782$	−16.0000			−0.572159
$783$			2.00000i			0.0714742i
$784$	3.00000			0.107143
$785$		0			0
$786$		−	12.0000i		−	0.428026i
$787$	−38.0000			−1.35455			−0.677277	−	0.735728i	$-0.736840\pi$
$787$	−38.0000			−1.35455			−0.677277	+	0.735728i	$0.736840\pi$
$788$	−22.0000			−0.783718
$789$	−12.0000			−0.427211
$790$		0			0
$791$			28.0000i			0.995565i
$792$		0			0
$793$	20.0000	−	30.0000i	0.710221	−	1.06533i
$794$	8.00000			0.283909
$795$		0			0
$796$	−24.0000			−0.850657
$797$			50.0000i			1.77109i	0.464553	+	0.885545i	$0.346215\pi$
$797$			50.0000i			1.77109i	−0.464553	+	0.885545i	$0.653785\pi$
$798$	−4.00000			−0.141598
$799$			8.00000i			0.283020i
$800$		0			0
$801$			6.00000i			0.212000i
$802$		−	10.0000i		−	0.353112i
$803$		0			0
$804$			6.00000i			0.211604i
$805$		0			0
$806$	−6.00000	−	4.00000i	−0.211341	−	0.140894i
$807$		−	10.0000i		−	0.352017i
$808$	6.00000			0.211079
$809$	18.0000			0.632846			0.316423	−	0.948618i	$-0.397518\pi$
$809$	18.0000			0.632846			0.316423	+	0.948618i	$0.397518\pi$
$810$		0			0
$811$		−	14.0000i		−	0.491606i	−0.969320	−	0.245803i	$-0.920948\pi$
$811$		−	14.0000i		−	0.491606i	0.969320	−	0.245803i	$-0.0790517\pi$
$812$	−4.00000			−0.140372
$813$	14.0000			0.491001
$814$		0			0
$815$		0			0
$816$	−2.00000			−0.0700140
$817$	−8.00000			−0.279885
$818$			12.0000i			0.419570i
$819$	4.00000	−	6.00000i	0.139771	−	0.209657i
$820$		0			0
$821$			18.0000i			0.628204i	0.949389	+	0.314102i	$0.101703\pi$
$821$			18.0000i			0.628204i	−0.949389	+	0.314102i	$0.898297\pi$
$822$		−	6.00000i		−	0.209274i
$823$			24.0000i			0.836587i	0.908312	+	0.418294i	$0.137372\pi$
$823$			24.0000i			0.836587i	−0.908312	+	0.418294i	$0.862628\pi$
$824$		−	48.0000i		−	1.67216i
$825$		0			0
$826$		−	24.0000i		−	0.835067i
$827$	8.00000			0.278187			0.139094	−	0.990279i	$-0.455581\pi$
$827$	8.00000			0.278187			0.139094	+	0.990279i	$0.455581\pi$
$828$		−	8.00000i		−	0.278019i
$829$	−34.0000			−1.18087			−0.590434	−	0.807086i	$-0.701044\pi$
$829$	−34.0000			−1.18087			−0.590434	+	0.807086i	$0.701044\pi$
$830$		0			0
$831$	−2.00000			−0.0693792
$832$	14.0000	−	21.0000i	0.485363	−	0.728044i
$833$			6.00000i			0.207888i
$834$		−	4.00000i		−	0.138509i
$835$		0			0
$836$		0			0
$837$	−2.00000			−0.0691301
$838$	12.0000			0.414533
$839$		−	24.0000i		−	0.828572i	−0.910147	−	0.414286i	$-0.864031\pi$
$839$		−	24.0000i		−	0.828572i	0.910147	−	0.414286i	$-0.135969\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$		−	40.0000i		−	1.37849i
$843$	6.00000			0.206651
$844$	12.0000			0.413057
$845$		0			0
$846$	4.00000			0.137523
$847$	−22.0000			−0.755929
$848$			6.00000i			0.206041i
$849$	4.00000			0.137280
$850$		0			0
$851$			64.0000i			2.19389i
$852$	8.00000			0.274075
$853$	−24.0000			−0.821744			−0.410872	−	0.911693i	$-0.634776\pi$
$853$	−24.0000			−0.821744			−0.410872	+	0.911693i	$0.634776\pi$
$854$	−20.0000			−0.684386
$855$		0			0
$856$			24.0000i			0.820303i
$857$		−	38.0000i		−	1.29806i	−0.760765	−	0.649028i	$-0.775176\pi$
$857$		−	38.0000i		−	1.29806i	0.760765	−	0.649028i	$-0.224824\pi$
$858$		0			0
$859$	28.0000			0.955348			0.477674	−	0.878537i	$-0.341480\pi$
$859$	28.0000			0.955348			0.477674	+	0.878537i	$0.341480\pi$
$860$		0			0
$861$	−4.00000			−0.136320
$862$			12.0000i			0.408722i
$863$	36.0000			1.22545			0.612727	−	0.790295i	$-0.290072\pi$
$863$	36.0000			1.22545			0.612727	+	0.790295i	$0.290072\pi$
$864$		−	5.00000i		−	0.170103i
$865$		0			0
$866$			14.0000i			0.475739i
$867$			13.0000i			0.441503i
$868$		−	4.00000i		−	0.135769i
$869$		0			0
$870$		0			0
$871$	−12.0000	+	18.0000i	−0.406604	+	0.609907i
$872$			48.0000i			1.62549i
$873$	−16.0000			−0.541518
$874$	−16.0000			−0.541208
$875$		0			0
$876$			16.0000i			0.540590i
$877$	−16.0000			−0.540282			−0.270141	−	0.962821i	$-0.587070\pi$
$877$	−16.0000			−0.540282			−0.270141	+	0.962821i	$0.587070\pi$
$878$	−16.0000			−0.539974
$879$			18.0000i			0.607125i
$880$		0			0
$881$	−30.0000			−1.01073			−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000			−1.01073			−0.505363	+	0.862907i	$0.668641\pi$
$882$	3.00000			0.101015
$883$			28.0000i			0.942275i	0.882060	+	0.471138i	$0.156156\pi$
$883$			28.0000i			0.942275i	−0.882060	+	0.471138i	$0.843844\pi$
$884$	6.00000	+	4.00000i	0.201802	+	0.134535i
$885$		0			0
$886$			24.0000i			0.806296i
$887$			16.0000i			0.537227i	0.963248	+	0.268614i	$0.0865655\pi$
$887$			16.0000i			0.537227i	−0.963248	+	0.268614i	$0.913434\pi$
$888$			24.0000i			0.805387i
$889$		0			0
$890$		0			0
$891$		0			0
$892$	−22.0000			−0.736614
$893$			8.00000i			0.267710i
$894$	−14.0000			−0.468230
$895$		0			0
$896$	6.00000			0.200446
$897$	16.0000	−	24.0000i	0.534224	−	0.801337i
$898$		−	6.00000i		−	0.200223i
$899$			4.00000i			0.133407i
$900$		0			0
$901$	−12.0000			−0.399778
$902$		0			0
$903$	−8.00000			−0.266223
$904$			42.0000i			1.39690i
$905$		0			0
$906$	−14.0000			−0.465119
$907$			44.0000i			1.46100i	0.682915	+	0.730498i	$0.260712\pi$
$907$			44.0000i			1.46100i	−0.682915	+	0.730498i	$0.739288\pi$
$908$		0			0
$909$	2.00000			0.0663358
$910$		0			0
$911$	20.0000			0.662630			0.331315	−	0.943520i	$-0.392508\pi$
$911$	20.0000			0.662630			0.331315	+	0.943520i	$0.392508\pi$
$912$	−2.00000			−0.0662266
$913$		0			0
$914$	8.00000			0.264616
$915$		0			0
$916$			8.00000i			0.264327i
$917$	24.0000			0.792550
$918$	−2.00000			−0.0660098
$919$	32.0000			1.05558			0.527791	−	0.849374i	$-0.323020\pi$
$919$	32.0000			1.05558			0.527791	+	0.849374i	$0.323020\pi$
$920$		0			0
$921$			26.0000i			0.856729i
$922$		−	34.0000i		−	1.11973i
$923$	24.0000	+	16.0000i	0.789970	+	0.526646i
$924$		0			0
$925$		0			0
$926$	−14.0000			−0.460069
$927$		−	16.0000i		−	0.525509i
$928$	−10.0000			−0.328266
$929$		−	22.0000i		−	0.721797i	−0.932605	−	0.360898i	$-0.882470\pi$
$929$		−	22.0000i		−	0.721797i	0.932605	−	0.360898i	$-0.117530\pi$
$930$		0			0
$931$			6.00000i			0.196642i
$932$		−	14.0000i		−	0.458585i
$933$			4.00000i			0.130954i
$934$		−	36.0000i		−	1.17796i
$935$		0			0
$936$	6.00000	−	9.00000i	0.196116	−	0.294174i
$937$		−	38.0000i		−	1.24141i	−0.784046	−	0.620703i	$-0.786847\pi$
$937$		−	38.0000i		−	1.24141i	0.784046	−	0.620703i	$-0.213153\pi$
$938$	12.0000			0.391814
$939$	10.0000			0.326338
$940$		0			0
$941$			50.0000i			1.62995i	0.579494	+	0.814977i	$0.303250\pi$
$941$			50.0000i			1.62995i	−0.579494	+	0.814977i	$0.696750\pi$
$942$	14.0000			0.456145
$943$	−16.0000			−0.521032
$944$		−	12.0000i		−	0.390567i
$945$		0			0
$946$		0			0
$947$	12.0000			0.389948			0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000			0.389948			0.194974	+	0.980808i	$0.437538\pi$
$948$		−	8.00000i		−	0.259828i
$949$	−32.0000	+	48.0000i	−1.03876	+	1.55815i
$950$		0			0
$951$		−	26.0000i		−	0.843108i
$952$		−	12.0000i		−	0.388922i
$953$			30.0000i			0.971795i	0.874016	+	0.485898i	$0.161507\pi$
$953$			30.0000i			0.971795i	−0.874016	+	0.485898i	$0.838493\pi$
$954$			6.00000i			0.194257i
$955$		0			0
$956$			8.00000i			0.258738i
$957$		0			0
$958$		0			0
$959$	12.0000			0.387500
$960$		0			0
$961$	27.0000			0.870968
$962$	−16.0000	+	24.0000i	−0.515861	+	0.773791i
$963$			8.00000i			0.257796i
$964$		−	12.0000i		−	0.386494i
$965$		0			0
$966$	−16.0000			−0.514792
$967$	58.0000			1.86515			0.932577	−	0.360971i	$-0.117555\pi$
$967$	58.0000			1.86515			0.932577	+	0.360971i	$0.117555\pi$
$968$	−33.0000			−1.06066
$969$		−	4.00000i		−	0.128499i
$970$		0			0
$971$		0			0			−	1.00000i	$-0.5\pi$
$971$		0			0				1.00000i	$0.5\pi$
$972$		−	1.00000i		−	0.0320750i
$973$	8.00000			0.256468
$974$	18.0000			0.576757
$975$		0			0
$976$	−10.0000			−0.320092
$977$	−38.0000			−1.21573			−0.607864	−	0.794041i	$-0.707973\pi$
$977$	−38.0000			−1.21573			−0.607864	+	0.794041i	$0.707973\pi$
$978$			18.0000i			0.575577i
$979$		0			0
$980$		0			0
$981$			16.0000i			0.510841i
$982$	−40.0000			−1.27645
$983$	−32.0000			−1.02064			−0.510321	−	0.859984i	$-0.670473\pi$
$983$	−32.0000			−1.02064			−0.510321	+	0.859984i	$0.670473\pi$
$984$	−6.00000			−0.191273
$985$		0			0
$986$			4.00000i			0.127386i
$987$			8.00000i			0.254643i
$988$	6.00000	+	4.00000i	0.190885	+	0.127257i
$989$	−32.0000			−1.01754
$990$		0			0
$991$	16.0000			0.508257			0.254128	−	0.967170i	$-0.418211\pi$
$991$	16.0000			0.508257			0.254128	+	0.967170i	$0.418211\pi$
$992$		−	10.0000i		−	0.317500i
$993$	26.0000			0.825085
$994$		−	16.0000i		−	0.507489i
$995$		0			0
$996$			12.0000i			0.380235i
$997$			42.0000i			1.33015i	0.746775	+	0.665077i	$0.231601\pi$
$997$			42.0000i			1.33015i	−0.746775	+	0.665077i	$0.768399\pi$
$998$			10.0000i			0.316544i
$999$			8.00000i			0.253109i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.h.d.649.2		2
5.2	odd	4		195.2.b.b.181.2	yes	2
5.3	odd	4		975.2.b.b.376.1		2
5.4	even	2		975.2.h.a.649.1		2
13.12	even	2		975.2.h.a.649.2		2
15.2	even	4		585.2.b.a.181.1		2
20.7	even	4		3120.2.g.a.961.2		2
65.12	odd	4		195.2.b.b.181.1	✓	2
65.38	odd	4		975.2.b.b.376.2		2
65.47	even	4		2535.2.a.e.1.1		1
65.57	even	4		2535.2.a.l.1.1		1
65.64	even	2	inner	975.2.h.d.649.1		2
195.47	odd	4		7605.2.a.p.1.1		1
195.77	even	4		585.2.b.a.181.2		2
195.122	odd	4		7605.2.a.d.1.1		1
260.207	even	4		3120.2.g.a.961.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.b.b.181.1	✓	2	65.12	odd	4
195.2.b.b.181.2	yes	2	5.2	odd	4
585.2.b.a.181.1		2	15.2	even	4
585.2.b.a.181.2		2	195.77	even	4
975.2.b.b.376.1		2	5.3	odd	4
975.2.b.b.376.2		2	65.38	odd	4
975.2.h.a.649.1		2	5.4	even	2
975.2.h.a.649.2		2	13.12	even	2
975.2.h.d.649.1		2	65.64	even	2	inner
975.2.h.d.649.2		2	1.1	even	1	trivial
2535.2.a.e.1.1		1	65.47	even	4
2535.2.a.l.1.1		1	65.57	even	4
3120.2.g.a.961.1		2	260.207	even	4
3120.2.g.a.961.2		2	20.7	even	4
7605.2.a.d.1.1		1	195.122	odd	4
7605.2.a.p.1.1		1	195.47	odd	4

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.h (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000i q^{6} -2.00000 q^{7} -3.00000 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000i q^{6} -2.00000 q^{7} -3.00000 q^{8} -1.00000 q^{9} -1.00000i q^{12} +(2.00000 - 3.00000i) q^{13} -2.00000 q^{14} -1.00000 q^{16} -2.00000i q^{17} -1.00000 q^{18} -2.00000i q^{19} -2.00000i q^{21} -8.00000i q^{23} -3.00000i q^{24} +(2.00000 - 3.00000i) q^{26} -1.00000i q^{27} +2.00000 q^{28} -2.00000 q^{29} -2.00000i q^{31} +5.00000 q^{32} -2.00000i q^{34} +1.00000 q^{36} -8.00000 q^{37} -2.00000i q^{38} +(3.00000 + 2.00000i) q^{39} -2.00000i q^{41} -2.00000i q^{42} -4.00000i q^{43} -8.00000i q^{46} -4.00000 q^{47} -1.00000i q^{48} -3.00000 q^{49} +2.00000 q^{51} +(-2.00000 + 3.00000i) q^{52} -6.00000i q^{53} -1.00000i q^{54} +6.00000 q^{56} +2.00000 q^{57} -2.00000 q^{58} +12.0000i q^{59} +10.0000 q^{61} -2.00000i q^{62} +2.00000 q^{63} +7.00000 q^{64} -6.00000 q^{67} +2.00000i q^{68} +8.00000 q^{69} +8.00000i q^{71} +3.00000 q^{72} -16.0000 q^{73} -8.00000 q^{74} +2.00000i q^{76} +(3.00000 + 2.00000i) q^{78} +8.00000 q^{79} +1.00000 q^{81} -2.00000i q^{82} -12.0000 q^{83} +2.00000i q^{84} -4.00000i q^{86} -2.00000i q^{87} -6.00000i q^{89} +(-4.00000 + 6.00000i) q^{91} +8.00000i q^{92} +2.00000 q^{93} -4.00000 q^{94} +5.00000i q^{96} +16.0000 q^{97} -3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{4} - 4 q^{7} - 6 q^{8} - 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^4 - 4 * q^7 - 6 * q^8 - 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{4} - 4 q^{7} - 6 q^{8} - 2 q^{9} + 4 q^{13} - 4 q^{14} - 2 q^{16} - 2 q^{18} + 4 q^{26} + 4 q^{28} - 4 q^{29} + 10 q^{32} + 2 q^{36} - 16 q^{37} + 6 q^{39} - 8 q^{47} - 6 q^{49} + 4 q^{51} - 4 q^{52} + 12 q^{56} + 4 q^{57} - 4 q^{58} + 20 q^{61} + 4 q^{63} + 14 q^{64} - 12 q^{67} + 16 q^{69} + 6 q^{72} - 32 q^{73} - 16 q^{74} + 6 q^{78} + 16 q^{79} + 2 q^{81} - 24 q^{83} - 8 q^{91} + 4 q^{93} - 8 q^{94} + 32 q^{97} - 6 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^4 - 4 * q^7 - 6 * q^8 - 2 * q^9 + 4 * q^13 - 4 * q^14 - 2 * q^16 - 2 * q^18 + 4 * q^26 + 4 * q^28 - 4 * q^29 + 10 * q^32 + 2 * q^36 - 16 * q^37 + 6 * q^39 - 8 * q^47 - 6 * q^49 + 4 * q^51 - 4 * q^52 + 12 * q^56 + 4 * q^57 - 4 * q^58 + 20 * q^61 + 4 * q^63 + 14 * q^64 - 12 * q^67 + 16 * q^69 + 6 * q^72 - 32 * q^73 - 16 * q^74 + 6 * q^78 + 16 * q^79 + 2 * q^81 - 24 * q^83 - 8 * q^91 + 4 * q^93 - 8 * q^94 + 32 * q^97 - 6 * q^98

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