LMFDB - Embedded newform 1260.2.s.f.541.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1260,2,Mod(361,1260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1260, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("1260.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1260.s (of order $3$, degree $2$, 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:	$10.0611506547$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			541.2
Root			$1.32288 + 2.29129i$ of defining polynomial
Character	$\chi$	$=$	1260.541
Dual form			1260.2.s.f.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{5} +(1.32288 - 2.29129i) q^{7} +O(q^{10})$	$q+(0.500000 - 0.866025i) q^{5} +(1.32288 - 2.29129i) q^{7} +(1.82288 + 3.15731i) q^{11} +2.64575 q^{13} +(1.82288 + 3.15731i) q^{17} +(1.14575 - 1.98450i) q^{19} +(-1.82288 + 3.15731i) q^{23} +(-0.500000 - 0.866025i) q^{25} -2.35425 q^{29} +(-3.14575 - 5.44860i) q^{31} +(-1.32288 - 2.29129i) q^{35} +(2.32288 - 4.02334i) q^{37} +10.9373 q^{41} +9.93725 q^{43} +(3.00000 - 5.19615i) q^{47} +(-3.50000 - 6.06218i) q^{49} +(-3.64575 - 6.31463i) q^{53} +3.64575 q^{55} +(-2.46863 - 4.27579i) q^{59} +(-4.00000 + 6.92820i) q^{61} +(1.32288 - 2.29129i) q^{65} +(2.32288 + 4.02334i) q^{67} -8.35425 q^{71} +(6.61438 + 11.4564i) q^{73} +9.64575 q^{77} +(4.14575 - 7.18065i) q^{79} -4.93725 q^{83} +3.64575 q^{85} +(6.11438 - 10.5904i) q^{89} +(3.50000 - 6.06218i) q^{91} +(-1.14575 - 1.98450i) q^{95} +8.00000 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{5}+O(q^{10}) $ 4 * q + 2 * q^5	$ 4 q + 2 q^{5} + 2 q^{11} + 2 q^{17} - 6 q^{19} - 2 q^{23} - 2 q^{25} - 20 q^{29} - 2 q^{31} + 4 q^{37} + 12 q^{41} + 8 q^{43} + 12 q^{47} - 14 q^{49} - 4 q^{53} + 4 q^{55} + 6 q^{59} - 16 q^{61} + 4 q^{67} - 44 q^{71} + 28 q^{77} + 6 q^{79} + 12 q^{83} + 4 q^{85} - 2 q^{89} + 14 q^{91} + 6 q^{95} + 32 q^{97}+O(q^{100}) $ 4 * q + 2 * q^5 + 2 * q^11 + 2 * q^17 - 6 * q^19 - 2 * q^23 - 2 * q^25 - 20 * q^29 - 2 * q^31 + 4 * q^37 + 12 * q^41 + 8 * q^43 + 12 * q^47 - 14 * q^49 - 4 * q^53 + 4 * q^55 + 6 * q^59 - 16 * q^61 + 4 * q^67 - 44 * q^71 + 28 * q^77 + 6 * q^79 + 12 * q^83 + 4 * q^85 - 2 * q^89 + 14 * q^91 + 6 * q^95 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times$.

$n$	$281$	$631$	$757$	$1081$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	1.32288	−	2.29129i	0.500000	−	0.866025i
$7$	1.32288	−	2.29129i	0.500000	−	0.866025i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.82288	+	3.15731i	0.549618	+	0.951966i	0.998301	+	0.0582747i	$0.0185599\pi$
$11$	1.82288	+	3.15731i	0.549618	+	0.951966i	−0.448683	+	0.893691i	$0.648107\pi$
$12$		0			0
$13$	2.64575			0.733799			0.366900	−	0.930261i	$-0.380419\pi$
$13$	2.64575			0.733799			0.366900	+	0.930261i	$0.380419\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.82288	+	3.15731i	0.442112	+	0.765761i	0.997846	−	0.0655994i	$-0.0208959\pi$
$17$	1.82288	+	3.15731i	0.442112	+	0.765761i	−0.555734	+	0.831360i	$0.687563\pi$
$18$		0			0
$19$	1.14575	−	1.98450i	0.262853	−	0.455275i	−0.704146	−	0.710056i	$-0.748670\pi$
$19$	1.14575	−	1.98450i	0.262853	−	0.455275i	0.966999	+	0.254780i	$0.0820031\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.82288	+	3.15731i	−0.380096	+	0.658345i	−0.991076	−	0.133301i	$-0.957442\pi$
$23$	−1.82288	+	3.15731i	−0.380096	+	0.658345i	0.610980	+	0.791646i	$0.290776\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.35425			−0.437173			−0.218587	−	0.975818i	$-0.570145\pi$
$29$	−2.35425			−0.437173			−0.218587	+	0.975818i	$0.570145\pi$
$30$		0			0
$31$	−3.14575	−	5.44860i	−0.564994	−	0.978598i	−0.997050	−	0.0767512i	$-0.975545\pi$
$31$	−3.14575	−	5.44860i	−0.564994	−	0.978598i	0.432057	−	0.901846i	$-0.357788\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.32288	−	2.29129i	−0.223607	−	0.387298i
$36$		0			0
$37$	2.32288	−	4.02334i	0.381878	−	0.661433i	−0.609452	−	0.792823i	$-0.708611\pi$
$37$	2.32288	−	4.02334i	0.381878	−	0.661433i	0.991331	+	0.131390i	$0.0419440\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	10.9373			1.70811			0.854056	−	0.520181i	$-0.174136\pi$
$41$	10.9373			1.70811			0.854056	+	0.520181i	$0.174136\pi$
$42$		0			0
$43$	9.93725			1.51542			0.757709	−	0.652593i	$-0.226319\pi$
$43$	9.93725			1.51542			0.757709	+	0.652593i	$0.226319\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	−0.559908	−	0.828554i	$-0.689164\pi$
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	0.997503	+	0.0706177i	$0.0224970\pi$
$48$		0			0
$49$	−3.50000	−	6.06218i	−0.500000	−	0.866025i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−3.64575	−	6.31463i	−0.500782	−	0.867381i	−1.00000		0.000903738i	$-0.999712\pi$
$53$	−3.64575	−	6.31463i	−0.500782	−	0.867381i	0.499217	−	0.866477i	$-0.333621\pi$
$54$		0			0
$55$	3.64575			0.491593
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.46863	−	4.27579i	−0.321388	−	0.556660i	0.659387	−	0.751804i	$-0.270816\pi$
$59$	−2.46863	−	4.27579i	−0.321388	−	0.556660i	−0.980775	+	0.195144i	$0.937483\pi$
$60$		0			0
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	0.487753	+	0.872982i	$0.337817\pi$
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.32288	−	2.29129i	0.164083	−	0.284199i
$66$		0			0
$67$	2.32288	+	4.02334i	0.283784	+	0.491529i	0.972314	−	0.233680i	$-0.0750767\pi$
$67$	2.32288	+	4.02334i	0.283784	+	0.491529i	−0.688529	+	0.725209i	$0.741743\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−8.35425			−0.991467			−0.495733	−	0.868475i	$-0.665101\pi$
$71$	−8.35425			−0.991467			−0.495733	+	0.868475i	$0.665101\pi$
$72$		0			0
$73$	6.61438	+	11.4564i	0.774154	+	1.34087i	0.935269	+	0.353939i	$0.115158\pi$
$73$	6.61438	+	11.4564i	0.774154	+	1.34087i	−0.161114	+	0.986936i	$0.551509\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	9.64575			1.09924
$78$		0			0
$79$	4.14575	−	7.18065i	0.466433	−	0.807886i	−0.532831	−	0.846221i	$-0.678872\pi$
$79$	4.14575	−	7.18065i	0.466433	−	0.807886i	0.999265	+	0.0383349i	$0.0122054\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.93725			−0.541934			−0.270967	−	0.962589i	$-0.587343\pi$
$83$	−4.93725			−0.541934			−0.270967	+	0.962589i	$0.587343\pi$
$84$		0			0
$85$	3.64575			0.395437
$86$		0			0
$87$		0			0
$88$		0			0
$89$	6.11438	−	10.5904i	0.648123	−	1.12258i	−0.335448	−	0.942059i	$-0.608888\pi$
$89$	6.11438	−	10.5904i	0.648123	−	1.12258i	0.983571	−	0.180523i	$-0.0577790\pi$
$90$		0			0
$91$	3.50000	−	6.06218i	0.366900	−	0.635489i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.14575	−	1.98450i	−0.117552	−	0.203605i
$96$		0			0
$97$	8.00000			0.812277			0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000			0.812277			0.406138	+	0.913812i	$0.366875\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	5.46863	+	9.47194i	0.544149	+	0.942493i	0.998660	+	0.0517522i	$0.0164806\pi$
$101$	5.46863	+	9.47194i	0.544149	+	0.942493i	−0.454511	+	0.890741i	$0.650186\pi$
$102$		0			0
$103$	−7.32288	+	12.6836i	−0.721544	+	1.24975i	0.238836	+	0.971060i	$0.423234\pi$
$103$	−7.32288	+	12.6836i	−0.721544	+	1.24975i	−0.960381	+	0.278692i	$0.910099\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.531373	+	0.920365i	−0.0513698	+	0.0889751i	−0.890567	−	0.454852i	$-0.849692\pi$
$107$	−0.531373	+	0.920365i	−0.0513698	+	0.0889751i	0.839197	+	0.543827i	$0.183025\pi$
$108$		0			0
$109$	6.50000	+	11.2583i	0.622587	+	1.07835i	0.989002	+	0.147901i	$0.0472517\pi$
$109$	6.50000	+	11.2583i	0.622587	+	1.07835i	−0.366415	+	0.930451i	$0.619415\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$		0			0
$115$	1.82288	+	3.15731i	0.169984	+	0.294421i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	9.64575			0.884225
$120$		0			0
$121$	−1.14575	+	1.98450i	−0.104159	+	0.180409i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−17.9373			−1.59167			−0.795837	−	0.605511i	$-0.792969\pi$
$127$	−17.9373			−1.59167			−0.795837	+	0.605511i	$0.792969\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	5.35425	−	9.27383i	0.467803	−	0.810258i	−0.531520	−	0.847046i	$-0.678379\pi$
$131$	5.35425	−	9.27383i	0.467803	−	0.810258i	0.999323	+	0.0367872i	$0.0117124\pi$
$132$		0			0
$133$	−3.03137	−	5.25049i	−0.262853	−	0.455275i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.11438	+	5.39426i	0.266079	+	0.460863i	0.967846	−	0.251544i	$-0.0809384\pi$
$137$	3.11438	+	5.39426i	0.266079	+	0.460863i	−0.701767	+	0.712407i	$0.747605\pi$
$138$		0			0
$139$	5.00000			0.424094			0.212047	−	0.977259i	$-0.431987\pi$
$139$	5.00000			0.424094			0.212047	+	0.977259i	$0.431987\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	4.82288	+	8.35347i	0.403309	+	0.698552i
$144$		0			0
$145$	−1.17712	+	2.03884i	−0.0977549	+	0.169316i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	7.29150	−	12.6293i	0.597343	−	1.03463i	−0.395868	−	0.918307i	$-0.629556\pi$
$149$	7.29150	−	12.6293i	0.597343	−	1.03463i	0.993212	−	0.116321i	$-0.0371103\pi$
$150$		0			0
$151$	−8.29150	−	14.3613i	−0.674753	−	1.16871i	−0.976541	−	0.215331i	$-0.930917\pi$
$151$	−8.29150	−	14.3613i	−0.674753	−	1.16871i	0.301788	−	0.953375i	$-0.402416\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−6.29150			−0.505346
$156$		0			0
$157$	−4.64575	−	8.04668i	−0.370771	−	0.642195i	0.618913	−	0.785459i	$-0.287573\pi$
$157$	−4.64575	−	8.04668i	−0.370771	−	0.642195i	−0.989684	+	0.143265i	$0.954240\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	4.82288	+	8.35347i	0.380096	+	0.658345i
$162$		0			0
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	−0.361619	−	0.932326i	$-0.617776\pi$
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	0.988227	−	0.152992i	$-0.0488907\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−14.3542			−1.11077			−0.555383	−	0.831595i	$-0.687428\pi$
$167$	−14.3542			−1.11077			−0.555383	+	0.831595i	$0.687428\pi$
$168$		0			0
$169$	−6.00000			−0.461538
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−10.9373	+	18.9439i	−0.831544	+	1.44028i	0.0652695	+	0.997868i	$0.479209\pi$
$173$	−10.9373	+	18.9439i	−0.831544	+	1.44028i	−0.896813	+	0.442409i	$0.854124\pi$
$174$		0			0
$175$	−2.64575			−0.200000
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−10.2915	−	17.8254i	−0.769223	−	1.33233i	−0.937985	−	0.346676i	$-0.887310\pi$
$179$	−10.2915	−	17.8254i	−0.769223	−	1.33233i	0.168762	−	0.985657i	$-0.446023\pi$
$180$		0			0
$181$	6.29150			0.467644			0.233822	−	0.972279i	$-0.424877\pi$
$181$	6.29150			0.467644			0.233822	+	0.972279i	$0.424877\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−2.32288	−	4.02334i	−0.170781	−	0.295802i
$186$		0			0
$187$	−6.64575	+	11.5108i	−0.485985	+	0.841752i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−11.5830	+	20.0624i	−0.838117	+	1.45166i	0.0533504	+	0.998576i	$0.483010\pi$
$191$	−11.5830	+	20.0624i	−0.838117	+	1.45166i	−0.891467	+	0.453085i	$0.850323\pi$
$192$		0			0
$193$	11.9686	+	20.7303i	0.861521	+	1.49220i	0.870461	+	0.492237i	$0.163821\pi$
$193$	11.9686	+	20.7303i	0.861521	+	1.49220i	−0.00894034	+	0.999960i	$0.502846\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−10.9373			−0.779247			−0.389624	−	0.920974i	$-0.627395\pi$
$197$	−10.9373			−0.779247			−0.389624	+	0.920974i	$0.627395\pi$
$198$		0			0
$199$	−9.58301	−	16.5983i	−0.679321	−	1.17662i	−0.975186	−	0.221389i	$-0.928941\pi$
$199$	−9.58301	−	16.5983i	−0.679321	−	1.17662i	0.295864	−	0.955230i	$-0.404392\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−3.11438	+	5.39426i	−0.218587	+	0.378603i
$204$		0			0
$205$	5.46863	−	9.47194i	0.381945	−	0.661549i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	8.35425			0.577875
$210$		0			0
$211$	−12.5830			−0.866250			−0.433125	−	0.901334i	$-0.642589\pi$
$211$	−12.5830			−0.866250			−0.433125	+	0.901334i	$0.642589\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	4.96863	−	8.60591i	0.338858	−	0.586918i
$216$		0			0
$217$	−16.6458			−1.12999
$218$		0			0
$219$		0			0
$220$		0			0
$221$	4.82288	+	8.35347i	0.324422	+	0.561915i
$222$		0			0
$223$	−13.8745			−0.929106			−0.464553	−	0.885545i	$-0.653785\pi$
$223$	−13.8745			−0.929106			−0.464553	+	0.885545i	$0.653785\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	7.17712	+	12.4311i	0.476362	+	0.825084i	0.999633	−	0.0270825i	$-0.00862168\pi$
$227$	7.17712	+	12.4311i	0.476362	+	0.825084i	−0.523271	+	0.852167i	$0.675288\pi$
$228$		0			0
$229$	3.50000	−	6.06218i	0.231287	−	0.400600i	−0.726900	−	0.686743i	$-0.759040\pi$
$229$	3.50000	−	6.06218i	0.231287	−	0.400600i	0.958187	+	0.286143i	$0.0923732\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	5.35425	−	9.27383i	0.350768	−	0.607549i	−0.635616	−	0.772006i	$-0.719254\pi$
$233$	5.35425	−	9.27383i	0.350768	−	0.607549i	0.986384	+	0.164457i	$0.0525871\pi$
$234$		0			0
$235$	−3.00000	−	5.19615i	−0.195698	−	0.338960i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$		0			0
$241$	11.6458	+	20.1710i	0.750169	+	1.29933i	0.947741	+	0.319042i	$0.103361\pi$
$241$	11.6458	+	20.1710i	0.750169	+	1.29933i	−0.197572	+	0.980288i	$0.563306\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−7.00000			−0.447214
$246$		0			0
$247$	3.03137	−	5.25049i	0.192882	−	0.334081i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−4.93725			−0.311637			−0.155818	−	0.987786i	$-0.549801\pi$
$251$	−4.93725			−0.311637			−0.155818	+	0.987786i	$0.549801\pi$
$252$		0			0
$253$	−13.2915			−0.835630
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−15.7601	+	27.2973i	−0.983090	+	1.70276i	−0.332955	+	0.942943i	$0.608046\pi$
$257$	−15.7601	+	27.2973i	−0.983090	+	1.70276i	−0.650135	+	0.759819i	$0.725288\pi$
$258$		0			0
$259$	−6.14575	−	10.6448i	−0.381878	−	0.661433i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	12.2288	+	21.1808i	0.754057	+	1.30607i	0.945842	+	0.324629i	$0.105239\pi$
$263$	12.2288	+	21.1808i	0.754057	+	1.30607i	−0.191784	+	0.981437i	$0.561427\pi$
$264$		0			0
$265$	−7.29150			−0.447913
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.93725	−	3.35542i	−0.118116	−	0.204584i	0.800905	−	0.598792i	$-0.204352\pi$
$269$	−1.93725	−	3.35542i	−0.118116	−	0.204584i	−0.919021	+	0.394208i	$0.871019\pi$
$270$		0			0
$271$	−14.2915	+	24.7536i	−0.868147	+	1.50367i	−0.00425882	+	0.999991i	$0.501356\pi$
$271$	−14.2915	+	24.7536i	−0.868147	+	1.50367i	−0.863888	+	0.503684i	$0.831978\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.82288	−	3.15731i	0.109924	−	0.190393i
$276$		0			0
$277$	7.67712	+	13.2972i	0.461274	+	0.798949i	0.999025	−	0.0441542i	$-0.0140593\pi$
$277$	7.67712	+	13.2972i	0.461274	+	0.798949i	−0.537751	+	0.843104i	$0.680726\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−24.0000			−1.43172			−0.715860	−	0.698244i	$-0.753965\pi$
$281$	−24.0000			−1.43172			−0.715860	+	0.698244i	$0.753965\pi$
$282$		0			0
$283$	4.67712	+	8.10102i	0.278026	+	0.481555i	0.970894	−	0.239509i	$-0.0769865\pi$
$283$	4.67712	+	8.10102i	0.278026	+	0.481555i	−0.692868	+	0.721064i	$0.743653\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	14.4686	−	25.0604i	0.854056	−	1.47927i
$288$		0			0
$289$	1.85425	−	3.21165i	0.109073	−	0.188921i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0			−	1.00000i	$-0.5\pi$
$293$		0			0				1.00000i	$0.5\pi$
$294$		0			0
$295$	−4.93725			−0.287458
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−4.82288	+	8.35347i	−0.278914	+	0.483093i
$300$		0			0
$301$	13.1458	−	22.7691i	0.757709	−	1.31239i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	4.00000	+	6.92820i	0.229039	+	0.396708i
$306$		0			0
$307$	12.0627			0.688457			0.344229	−	0.938886i	$-0.388140\pi$
$307$	12.0627			0.688457			0.344229	+	0.938886i	$0.388140\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	4.17712	+	7.23499i	0.236863	+	0.410259i	0.959812	−	0.280642i	$-0.0905474\pi$
$311$	4.17712	+	7.23499i	0.236863	+	0.410259i	−0.722949	+	0.690901i	$0.757214\pi$
$312$		0			0
$313$	−2.61438	+	4.52824i	−0.147773	+	0.255951i	−0.930404	−	0.366535i	$-0.880544\pi$
$313$	−2.61438	+	4.52824i	−0.147773	+	0.255951i	0.782631	+	0.622486i	$0.213877\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−6.76013	+	11.7089i	−0.379687	+	0.657637i	−0.991017	−	0.133739i	$-0.957302\pi$
$317$	−6.76013	+	11.7089i	−0.379687	+	0.657637i	0.611330	+	0.791376i	$0.290635\pi$
$318$		0			0
$319$	−4.29150	−	7.43310i	−0.240278	−	0.416174i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	8.35425			0.464843
$324$		0			0
$325$	−1.32288	−	2.29129i	−0.0733799	−	0.127098i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−7.93725	−	13.7477i	−0.437595	−	0.757937i
$330$		0			0
$331$	−11.0830	+	19.1963i	−0.609177	+	1.05513i	0.382199	+	0.924080i	$0.375167\pi$
$331$	−11.0830	+	19.1963i	−0.609177	+	1.05513i	−0.991376	+	0.131046i	$0.958167\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	4.64575			0.253825
$336$		0			0
$337$	−6.77124			−0.368853			−0.184427	−	0.982846i	$-0.559043\pi$
$337$	−6.77124			−0.368853			−0.184427	+	0.982846i	$0.559043\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	11.4686	−	19.8642i	0.621061	−	1.07571i
$342$		0			0
$343$	−18.5203			−1.00000
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−14.5830	−	25.2585i	−0.782857	−	1.35595i	−0.930271	−	0.366873i	$-0.880428\pi$
$347$	−14.5830	−	25.2585i	−0.782857	−	1.35595i	0.147414	−	0.989075i	$-0.452905\pi$
$348$		0			0
$349$	−10.0000			−0.535288			−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000			−0.535288			−0.267644	+	0.963518i	$0.586245\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	11.0516	+	19.1420i	0.588219	+	1.01883i	0.994466	+	0.105062i	$0.0335040\pi$
$353$	11.0516	+	19.1420i	0.588219	+	1.01883i	−0.406247	+	0.913763i	$0.633163\pi$
$354$		0			0
$355$	−4.17712	+	7.23499i	−0.221699	+	0.383993i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	13.4059	−	23.2197i	0.707535	−	1.22549i	−0.258233	−	0.966083i	$-0.583140\pi$
$359$	13.4059	−	23.2197i	0.707535	−	1.22549i	0.965769	−	0.259405i	$-0.0835263\pi$
$360$		0			0
$361$	6.87451	+	11.9070i	0.361816	+	0.626684i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	13.2288			0.692425
$366$		0			0
$367$	9.61438	+	16.6526i	0.501866	+	0.869258i	0.999998	+	0.00215655i	$0.000686450\pi$
$367$	9.61438	+	16.6526i	0.501866	+	0.869258i	−0.498131	+	0.867102i	$0.665980\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−19.2915			−1.00156
$372$		0			0
$373$	−7.96863	+	13.8021i	−0.412600	+	0.714644i	−0.995173	−	0.0981342i	$-0.968713\pi$
$373$	−7.96863	+	13.8021i	−0.412600	+	0.714644i	0.582573	+	0.812778i	$0.302046\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−6.22876			−0.320797
$378$		0			0
$379$	−26.2915			−1.35050			−0.675252	−	0.737587i	$-0.735965\pi$
$379$	−26.2915			−1.35050			−0.675252	+	0.737587i	$0.735965\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−8.35425	+	14.4700i	−0.426882	+	0.739382i	−0.996594	−	0.0824628i	$-0.973721\pi$
$383$	−8.35425	+	14.4700i	−0.426882	+	0.739382i	0.569712	+	0.821844i	$0.307055\pi$
$384$		0			0
$385$	4.82288	−	8.35347i	0.245797	−	0.425732i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−18.7601	−	32.4935i	−0.951176	−	1.64749i	−0.742885	−	0.669419i	$-0.766543\pi$
$389$	−18.7601	−	32.4935i	−0.951176	−	1.64749i	−0.208291	−	0.978067i	$-0.566790\pi$
$390$		0			0
$391$	−13.2915			−0.672180
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−4.14575	−	7.18065i	−0.208595	−	0.361298i
$396$		0			0
$397$	8.32288	−	14.4156i	0.417713	−	0.723500i	−0.577996	−	0.816040i	$-0.696165\pi$
$397$	8.32288	−	14.4156i	0.417713	−	0.723500i	0.995709	+	0.0925393i	$0.0294984\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	9.64575	−	16.7069i	0.481686	−	0.834304i	−0.518093	−	0.855324i	$-0.673358\pi$
$401$	9.64575	−	16.7069i	0.481686	−	0.834304i	0.999779	+	0.0210198i	$0.00669131\pi$
$402$		0			0
$403$	−8.32288	−	14.4156i	−0.414592	−	0.718094i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	16.9373			0.839549
$408$		0			0
$409$	18.0830	+	31.3207i	0.894147	+	1.54871i	0.834857	+	0.550467i	$0.185550\pi$
$409$	18.0830	+	31.3207i	0.894147	+	1.54871i	0.0592904	+	0.998241i	$0.481116\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−13.0627			−0.642776
$414$		0			0
$415$	−2.46863	+	4.27579i	−0.121180	+	0.209890i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−10.7085			−0.523144			−0.261572	−	0.965184i	$-0.584241\pi$
$419$	−10.7085			−0.523144			−0.261572	+	0.965184i	$0.584241\pi$
$420$		0			0
$421$	1.58301			0.0771510			0.0385755	−	0.999256i	$-0.487718\pi$
$421$	1.58301			0.0771510			0.0385755	+	0.999256i	$0.487718\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.82288	−	3.15731i	0.0884225	−	0.153152i
$426$		0			0
$427$	10.5830	+	18.3303i	0.512148	+	0.887066i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	4.06275	+	7.03688i	0.195696	+	0.338955i	0.947128	−	0.320855i	$-0.103970\pi$
$431$	4.06275	+	7.03688i	0.195696	+	0.338955i	−0.751433	+	0.659810i	$0.770637\pi$
$432$		0			0
$433$	8.64575			0.415488			0.207744	−	0.978183i	$-0.433388\pi$
$433$	8.64575			0.415488			0.207744	+	0.978183i	$0.433388\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	4.17712	+	7.23499i	0.199819	+	0.346097i
$438$		0			0
$439$	2.64575	−	4.58258i	0.126275	−	0.218714i	−0.795956	−	0.605355i	$-0.793031\pi$
$439$	2.64575	−	4.58258i	0.126275	−	0.218714i	0.922231	+	0.386640i	$0.126365\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−10.9373	+	18.9439i	−0.519645	+	0.900051i	0.480095	+	0.877217i	$0.340602\pi$
$443$	−10.9373	+	18.9439i	−0.519645	+	0.900051i	−0.999739	+	0.0228342i	$0.992731\pi$
$444$		0			0
$445$	−6.11438	−	10.5904i	−0.289849	−	0.502034i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−8.58301			−0.405057			−0.202529	−	0.979276i	$-0.564916\pi$
$449$	−8.58301			−0.405057			−0.202529	+	0.979276i	$0.564916\pi$
$450$		0			0
$451$	19.9373	+	34.5323i	0.938809	+	1.62606i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−3.50000	−	6.06218i	−0.164083	−	0.284199i
$456$		0			0
$457$	4.67712	−	8.10102i	0.218787	−	0.378950i	−0.735651	−	0.677361i	$-0.763123\pi$
$457$	4.67712	−	8.10102i	0.218787	−	0.378950i	0.954437	+	0.298412i	$0.0964568\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	14.3542			0.668544			0.334272	−	0.942477i	$-0.391510\pi$
$461$	14.3542			0.668544			0.334272	+	0.942477i	$0.391510\pi$
$462$		0			0
$463$	−26.5203			−1.23250			−0.616250	−	0.787550i	$-0.711349\pi$
$463$	−26.5203			−1.23250			−0.616250	+	0.787550i	$0.711349\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	12.8745	−	22.2993i	0.595761	−	1.03189i	−0.397678	−	0.917525i	$-0.630184\pi$
$467$	12.8745	−	22.2993i	0.595761	−	1.03189i	0.993439	−	0.114363i	$-0.0364829\pi$
$468$		0			0
$469$	12.2915			0.567569
$470$		0			0
$471$		0			0
$472$		0			0
$473$	18.1144	+	31.3750i	0.832900	+	1.44263i
$474$		0			0
$475$	−2.29150			−0.105141
$476$		0			0
$477$		0			0
$478$		0			0
$479$	7.29150	+	12.6293i	0.333157	+	0.577045i	0.983129	−	0.182913i	$-0.0585527\pi$
$479$	7.29150	+	12.6293i	0.333157	+	0.577045i	−0.649972	+	0.759958i	$0.725219\pi$
$480$		0			0
$481$	6.14575	−	10.6448i	0.280222	−	0.485359i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	4.00000	−	6.92820i	0.181631	−	0.314594i
$486$		0			0
$487$	−1.32288	−	2.29129i	−0.0599452	−	0.103828i	0.834495	−	0.551015i	$-0.185759\pi$
$487$	−1.32288	−	2.29129i	−0.0599452	−	0.103828i	−0.894441	+	0.447187i	$0.852426\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−33.8745			−1.52874			−0.764368	−	0.644781i	$-0.776949\pi$
$491$	−33.8745			−1.52874			−0.764368	+	0.644781i	$0.776949\pi$
$492$		0			0
$493$	−4.29150	−	7.43310i	−0.193280	−	0.334770i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−11.0516	+	19.1420i	−0.495733	+	0.858636i
$498$		0			0
$499$	12.7288	−	22.0469i	0.569817	−	0.986953i	−0.426766	−	0.904362i	$-0.640347\pi$
$499$	12.7288	−	22.0469i	0.569817	−	0.986953i	0.996584	−	0.0825907i	$-0.0263194\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	30.4575			1.35803			0.679017	−	0.734123i	$-0.262406\pi$
$503$	30.4575			1.35803			0.679017	+	0.734123i	$0.262406\pi$
$504$		0			0
$505$	10.9373			0.486701
$506$		0			0
$507$		0			0
$508$		0			0
$509$	1.93725	−	3.35542i	0.0858673	−	0.148726i	−0.819893	−	0.572517i	$-0.805967\pi$
$509$	1.93725	−	3.35542i	0.0858673	−	0.148726i	0.905760	+	0.423790i	$0.139301\pi$
$510$		0			0
$511$	35.0000			1.54831
$512$		0			0
$513$		0			0
$514$		0			0
$515$	7.32288	+	12.6836i	0.322684	+	0.558906i
$516$		0			0
$517$	21.8745			0.962040
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−16.9373	−	29.3362i	−0.742035	−	1.28524i	−0.951567	−	0.307440i	$-0.900528\pi$
$521$	−16.9373	−	29.3362i	−0.742035	−	1.28524i	0.209533	−	0.977802i	$-0.432806\pi$
$522$		0			0
$523$	−2.38562	+	4.13202i	−0.104316	+	0.180681i	−0.913459	−	0.406932i	$-0.866599\pi$
$523$	−2.38562	+	4.13202i	−0.104316	+	0.180681i	0.809143	+	0.587612i	$0.199932\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	11.4686	−	19.8642i	0.499581	−	0.865300i
$528$		0			0
$529$	4.85425	+	8.40781i	0.211054	+	0.365557i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	28.9373			1.25341
$534$		0			0
$535$	0.531373	+	0.920365i	0.0229733	+	0.0397909i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	12.7601	−	22.1012i	0.549618	−	0.951966i
$540$		0			0
$541$	13.3745	−	23.1653i	0.575015	−	0.995955i	−0.421025	−	0.907049i	$-0.638330\pi$
$541$	13.3745	−	23.1653i	0.575015	−	0.995955i	0.996040	−	0.0889062i	$-0.0283371\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	13.0000			0.556859
$546$		0			0
$547$	−32.7085			−1.39851			−0.699257	−	0.714870i	$-0.746486\pi$
$547$	−32.7085			−1.39851			−0.699257	+	0.714870i	$0.746486\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−2.69738	+	4.67201i	−0.114912	+	0.199034i
$552$		0			0
$553$	−10.9686	−	18.9982i	−0.466433	−	0.807886i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−9.00000	−	15.5885i	−0.381342	−	0.660504i	0.609912	−	0.792469i	$-0.291205\pi$
$557$	−9.00000	−	15.5885i	−0.381342	−	0.660504i	−0.991254	+	0.131965i	$0.957871\pi$
$558$		0			0
$559$	26.2915			1.11201
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−7.70850	−	13.3515i	−0.324874	−	0.562699i	0.656613	−	0.754228i	$-0.271989\pi$
$563$	−7.70850	−	13.3515i	−0.324874	−	0.562699i	−0.981487	+	0.191529i	$0.938655\pi$
$564$		0			0
$565$	−3.00000	+	5.19615i	−0.126211	+	0.218604i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−15.1144	+	26.1789i	−0.633628	+	1.09748i	0.353176	+	0.935557i	$0.385102\pi$
$569$	−15.1144	+	26.1789i	−0.633628	+	1.09748i	−0.986804	+	0.161919i	$0.948232\pi$
$570$		0			0
$571$	−16.8542	−	29.1924i	−0.705328	−	1.22166i	−0.966573	−	0.256392i	$-0.917466\pi$
$571$	−16.8542	−	29.1924i	−0.705328	−	1.22166i	0.261245	−	0.965273i	$-0.415867\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	3.64575			0.152038
$576$		0			0
$577$	2.73987	+	4.74559i	0.114062	+	0.197562i	0.917405	−	0.397956i	$-0.130280\pi$
$577$	2.73987	+	4.74559i	0.114062	+	0.197562i	−0.803342	+	0.595518i	$0.796947\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−6.53137	+	11.3127i	−0.270967	+	0.469329i
$582$		0			0
$583$	13.2915	−	23.0216i	0.550478	−	0.953456i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−1.06275			−0.0438642			−0.0219321	−	0.999759i	$-0.506982\pi$
$587$	−1.06275			−0.0438642			−0.0219321	+	0.999759i	$0.506982\pi$
$588$		0			0
$589$	−14.4170			−0.594042
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−20.4686	+	35.4527i	−0.840546	+	1.45587i	0.0488882	+	0.998804i	$0.484432\pi$
$593$	−20.4686	+	35.4527i	−0.840546	+	1.45587i	−0.889434	+	0.457064i	$0.848901\pi$
$594$		0			0
$595$	4.82288	−	8.35347i	0.197719	−	0.342459i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	16.9373	+	29.3362i	0.692037	+	1.19864i	0.971169	+	0.238391i	$0.0766200\pi$
$599$	16.9373	+	29.3362i	0.692037	+	1.19864i	−0.279132	+	0.960253i	$0.590047\pi$
$600$		0			0
$601$	−16.4170			−0.669663			−0.334832	−	0.942278i	$-0.608679\pi$
$601$	−16.4170			−0.669663			−0.334832	+	0.942278i	$0.608679\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1.14575	+	1.98450i	0.0465814	+	0.0806814i
$606$		0			0
$607$	21.6144	−	37.4372i	0.877301	−	1.51953i	0.0230088	−	0.999735i	$-0.492675\pi$
$607$	21.6144	−	37.4372i	0.877301	−	1.51953i	0.854292	−	0.519794i	$-0.173991\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	7.93725	−	13.7477i	0.321107	−	0.556174i
$612$		0			0
$613$	−0.583005	−	1.00979i	−0.0235474	−	0.0407852i	0.854012	−	0.520254i	$-0.174163\pi$
$613$	−0.583005	−	1.00979i	−0.0235474	−	0.0407852i	−0.877559	+	0.479469i	$0.840829\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.29150			0.0519939			0.0259970	−	0.999662i	$-0.491724\pi$
$617$	1.29150			0.0519939			0.0259970	+	0.999662i	$0.491724\pi$
$618$		0			0
$619$	9.50000	+	16.4545i	0.381837	+	0.661361i	0.991325	−	0.131434i	$-0.0419582\pi$
$619$	9.50000	+	16.4545i	0.381837	+	0.661361i	−0.609488	+	0.792796i	$0.708625\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−16.1771	−	28.0196i	−0.648123	−	1.12258i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	16.9373			0.675333
$630$		0			0
$631$	27.7490			1.10467			0.552335	−	0.833622i	$-0.313737\pi$
$631$	27.7490			1.10467			0.552335	+	0.833622i	$0.313737\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−8.96863	+	15.5341i	−0.355909	+	0.616453i
$636$		0			0
$637$	−9.26013	−	16.0390i	−0.366900	−	0.635489i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	23.0516	+	39.9266i	0.910485	+	1.57701i	0.813381	+	0.581732i	$0.197625\pi$
$641$	23.0516	+	39.9266i	0.910485	+	1.57701i	0.0971039	+	0.995274i	$0.469042\pi$
$642$		0			0
$643$	25.8118			1.01792			0.508958	−	0.860791i	$-0.330031\pi$
$643$	25.8118			1.01792			0.508958	+	0.860791i	$0.330031\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	3.53137	+	6.11652i	0.138833	+	0.240465i	0.927055	−	0.374925i	$-0.122332\pi$
$647$	3.53137	+	6.11652i	0.138833	+	0.240465i	−0.788222	+	0.615390i	$0.788998\pi$
$648$		0			0
$649$	9.00000	−	15.5885i	0.353281	−	0.611900i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	16.8229	−	29.1381i	0.658330	−	1.14026i	−0.322718	−	0.946495i	$-0.604596\pi$
$653$	16.8229	−	29.1381i	0.658330	−	1.14026i	0.981048	−	0.193766i	$-0.0620702\pi$
$654$		0			0
$655$	−5.35425	−	9.27383i	−0.209208	−	0.362359i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	24.0000			0.934907			0.467454	−	0.884018i	$-0.345171\pi$
$659$	24.0000			0.934907			0.467454	+	0.884018i	$0.345171\pi$
$660$		0			0
$661$	4.56275	+	7.90291i	0.177470	+	0.307387i	0.941013	−	0.338369i	$-0.109875\pi$
$661$	4.56275	+	7.90291i	0.177470	+	0.307387i	−0.763543	+	0.645757i	$0.776542\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−6.06275			−0.235103
$666$		0			0
$667$	4.29150	−	7.43310i	0.166168	−	0.287811i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−29.1660			−1.12594
$672$		0			0
$673$	−10.6458			−0.410364			−0.205182	−	0.978724i	$-0.565779\pi$
$673$	−10.6458			−0.410364			−0.205182	+	0.978724i	$0.565779\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−13.8229	+	23.9419i	−0.531256	+	0.920163i	0.468078	+	0.883687i	$0.344947\pi$
$677$	−13.8229	+	23.9419i	−0.531256	+	0.920163i	−0.999335	+	0.0364758i	$0.988387\pi$
$678$		0			0
$679$	10.5830	−	18.3303i	0.406138	−	0.703452i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−5.46863	−	9.47194i	−0.209251	−	0.362434i	0.742228	−	0.670148i	$-0.233769\pi$
$683$	−5.46863	−	9.47194i	−0.209251	−	0.362434i	−0.951479	+	0.307714i	$0.900436\pi$
$684$		0			0
$685$	6.22876			0.237989
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−9.64575	−	16.7069i	−0.367474	−	0.636483i
$690$		0			0
$691$	−1.20850	+	2.09318i	−0.0459734	+	0.0796283i	−0.888096	−	0.459657i	$-0.847972\pi$
$691$	−1.20850	+	2.09318i	−0.0459734	+	0.0796283i	0.842123	+	0.539285i	$0.181306\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2.50000	−	4.33013i	0.0948304	−	0.164251i
$696$		0			0
$697$	19.9373	+	34.5323i	0.755177	+	1.30801i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−19.0627			−0.719990			−0.359995	−	0.932954i	$-0.617222\pi$
$701$	−19.0627			−0.719990			−0.359995	+	0.932954i	$0.617222\pi$
$702$		0			0
$703$	−5.32288	−	9.21949i	−0.200756	−	0.347720i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	28.9373			1.08830
$708$		0			0
$709$	0.708497	−	1.22715i	0.0266082	−	0.0460867i	−0.852415	−	0.522866i	$-0.824863\pi$
$709$	0.708497	−	1.22715i	0.0266082	−	0.0460867i	0.879023	+	0.476780i	$0.158196\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	22.9373			0.859007
$714$		0			0
$715$	9.64575			0.360731
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−12.6458	+	21.9031i	−0.471607	+	0.816847i	−0.999472	−	0.0324808i	$-0.989659\pi$
$719$	−12.6458	+	21.9031i	−0.471607	+	0.816847i	0.527865	+	0.849328i	$0.322993\pi$
$720$		0			0
$721$	19.3745	+	33.5576i	0.721544	+	1.24975i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1.17712	+	2.03884i	0.0437173	+	0.0757206i
$726$		0			0
$727$	13.8118			0.512250			0.256125	−	0.966644i	$-0.417554\pi$
$727$	13.8118			0.512250			0.256125	+	0.966644i	$0.417554\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	18.1144	+	31.3750i	0.669984	+	1.16045i
$732$		0			0
$733$	9.61438	−	16.6526i	0.355115	−	0.615078i	−0.632023	−	0.774950i	$-0.717775\pi$
$733$	9.61438	−	16.6526i	0.355115	−	0.615078i	0.987138	+	0.159873i	$0.0511083\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−8.46863	+	14.6681i	−0.311946	+	0.540306i
$738$		0			0
$739$	−14.5000	−	25.1147i	−0.533391	−	0.923861i	−0.999239	−	0.0389959i	$-0.987584\pi$
$739$	−14.5000	−	25.1147i	−0.533391	−	0.923861i	0.465848	−	0.884865i	$-0.345749\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	28.9373			1.06160			0.530802	−	0.847496i	$-0.321891\pi$
$743$	28.9373			1.06160			0.530802	+	0.847496i	$0.321891\pi$
$744$		0			0
$745$	−7.29150	−	12.6293i	−0.267140	−	0.462700i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.40588	+	2.43506i	0.0513698	+	0.0889751i
$750$		0			0
$751$	9.08301	−	15.7322i	0.331444	−	0.574077i	−0.651352	−	0.758776i	$-0.725798\pi$
$751$	9.08301	−	15.7322i	0.331444	−	0.574077i	0.982795	+	0.184699i	$0.0591310\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−16.5830			−0.603517
$756$		0			0
$757$	−51.1660			−1.85966			−0.929830	−	0.367989i	$-0.880046\pi$
$757$	−51.1660			−1.85966			−0.929830	+	0.367989i	$0.880046\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	23.0516	−	39.9266i	0.835621	−	1.44734i	−0.0579028	−	0.998322i	$-0.518441\pi$
$761$	23.0516	−	39.9266i	0.835621	−	1.44734i	0.893524	−	0.449016i	$-0.148225\pi$
$762$		0			0
$763$	34.3948			1.24517
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−6.53137	−	11.3127i	−0.235834	−	0.408477i
$768$		0			0
$769$	−14.2915			−0.515365			−0.257682	−	0.966230i	$-0.582959\pi$
$769$	−14.2915			−0.515365			−0.257682	+	0.966230i	$0.582959\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−20.6974	−	35.8489i	−0.744433	−	1.28940i	−0.950459	−	0.310850i	$-0.899386\pi$
$773$	−20.6974	−	35.8489i	−0.744433	−	1.28940i	0.206026	−	0.978547i	$-0.433947\pi$
$774$		0			0
$775$	−3.14575	+	5.44860i	−0.112999	+	0.195720i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	12.5314	−	21.7050i	0.448983	−	0.777661i
$780$		0			0
$781$	−15.2288	−	26.3770i	−0.544928	−	0.943843i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−9.29150			−0.331628
$786$		0			0
$787$	12.9373	+	22.4080i	0.461163	+	0.798758i	0.999019	−	0.0442785i	$-0.0140989\pi$
$787$	12.9373	+	22.4080i	0.461163	+	0.798758i	−0.537856	+	0.843037i	$0.680766\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−7.93725	+	13.7477i	−0.282216	+	0.488813i
$792$		0			0
$793$	−10.5830	+	18.3303i	−0.375814	+	0.650928i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	10.9373			0.387417			0.193709	−	0.981059i	$-0.437948\pi$
$797$	10.9373			0.387417			0.193709	+	0.981059i	$0.437948\pi$
$798$		0			0
$799$	21.8745			0.773864
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−24.1144	+	41.7673i	−0.850978	+	1.47394i
$804$		0			0
$805$	9.64575			0.339968
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−11.5830	−	20.0624i	−0.407237	−	0.705355i	0.587342	−	0.809339i	$-0.300174\pi$
$809$	−11.5830	−	20.0624i	−0.407237	−	0.705355i	−0.994579	+	0.103984i	$0.966841\pi$
$810$		0			0
$811$	6.70850			0.235567			0.117784	−	0.993039i	$-0.462421\pi$
$811$	6.70850			0.235567			0.117784	+	0.993039i	$0.462421\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−8.00000	−	13.8564i	−0.280228	−	0.485369i
$816$		0			0
$817$	11.3856	−	19.7205i	0.398332	−	0.689932i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	18.9889	−	32.8897i	0.662717	−	1.14786i	−0.317182	−	0.948365i	$-0.602737\pi$
$821$	18.9889	−	32.8897i	0.662717	−	1.14786i	0.979899	−	0.199494i	$-0.0639300\pi$
$822$		0			0
$823$	17.2288	+	29.8411i	0.600557	+	1.04019i	0.992737	+	0.120306i	$0.0383877\pi$
$823$	17.2288	+	29.8411i	0.600557	+	1.04019i	−0.392180	+	0.919888i	$0.628279\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	30.4575			1.05911			0.529556	−	0.848275i	$-0.322359\pi$
$827$	30.4575			1.05911			0.529556	+	0.848275i	$0.322359\pi$
$828$		0			0
$829$	−15.1458	−	26.2332i	−0.526034	−	0.911117i	−0.999540	−	0.0303267i	$-0.990345\pi$
$829$	−15.1458	−	26.2332i	−0.526034	−	0.911117i	0.473506	−	0.880790i	$-0.342988\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	12.7601	−	22.1012i	0.442112	−	0.765761i
$834$		0			0
$835$	−7.17712	+	12.4311i	−0.248375	+	0.430197i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−21.6458			−0.747294			−0.373647	−	0.927571i	$-0.621893\pi$
$839$	−21.6458			−0.747294			−0.373647	+	0.927571i	$0.621893\pi$
$840$		0			0
$841$	−23.4575			−0.808880
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−3.00000	+	5.19615i	−0.103203	+	0.178753i
$846$		0			0
$847$	3.03137	+	5.25049i	0.104159	+	0.180409i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	8.46863	+	14.6681i	0.290301	+	0.502816i
$852$		0			0
$853$	16.7712			0.574236			0.287118	−	0.957895i	$-0.407303\pi$
$853$	16.7712			0.574236			0.287118	+	0.957895i	$0.407303\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−4.17712	−	7.23499i	−0.142688	−	0.247143i	0.785820	−	0.618455i	$-0.212241\pi$
$857$	−4.17712	−	7.23499i	−0.142688	−	0.247143i	−0.928508	+	0.371313i	$0.878908\pi$
$858$		0			0
$859$	−13.2288	+	22.9129i	−0.451359	+	0.781777i	−0.998471	−	0.0552825i	$-0.982394\pi$
$859$	−13.2288	+	22.9129i	−0.451359	+	0.781777i	0.547111	+	0.837060i	$0.315727\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	9.22876	−	15.9847i	0.314151	−	0.544125i	−0.665106	−	0.746749i	$-0.731614\pi$
$863$	9.22876	−	15.9847i	0.314151	−	0.544125i	0.979257	+	0.202624i	$0.0649470\pi$
$864$		0			0
$865$	10.9373	+	18.9439i	0.371878	+	0.644111i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	30.2288			1.02544
$870$		0			0
$871$	6.14575	+	10.6448i	0.208241	+	0.360684i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1.32288	+	2.29129i	−0.0447214	+	0.0774597i
$876$		0			0
$877$	−7.00000	+	12.1244i	−0.236373	+	0.409410i	−0.959671	−	0.281126i	$-0.909292\pi$
$877$	−7.00000	+	12.1244i	−0.236373	+	0.409410i	0.723298	+	0.690536i	$0.242625\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	41.1660			1.38692			0.693459	−	0.720496i	$-0.256086\pi$
$881$	41.1660			1.38692			0.693459	+	0.720496i	$0.256086\pi$
$882$		0			0
$883$	25.8118			0.868635			0.434317	−	0.900760i	$-0.356990\pi$
$883$	25.8118			0.868635			0.434317	+	0.900760i	$0.356990\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−7.17712	+	12.4311i	−0.240984	+	0.417397i	−0.960995	−	0.276566i	$-0.910804\pi$
$887$	−7.17712	+	12.4311i	−0.240984	+	0.417397i	0.720011	+	0.693963i	$0.244137\pi$
$888$		0			0
$889$	−23.7288	+	41.0994i	−0.795837	+	1.37843i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−6.87451	−	11.9070i	−0.230047	−	0.398452i
$894$		0			0
$895$	−20.5830			−0.688014
$896$		0			0
$897$		0			0
$898$		0			0
$899$	7.40588	+	12.8274i	0.247000	+	0.427816i
$900$		0			0
$901$	13.2915	−	23.0216i	0.442804	−	0.766959i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	3.14575	−	5.44860i	0.104568	−	0.181118i
$906$		0			0
$907$	7.67712	+	13.2972i	0.254915	+	0.441525i	0.964872	−	0.262719i	$-0.0846193\pi$
$907$	7.67712	+	13.2972i	0.254915	+	0.441525i	−0.709958	+	0.704244i	$0.751286\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−31.5203			−1.04431			−0.522156	−	0.852850i	$-0.674872\pi$
$911$	−31.5203			−1.04431			−0.522156	+	0.852850i	$0.674872\pi$
$912$		0			0
$913$	−9.00000	−	15.5885i	−0.297857	−	0.515903i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−14.1660	−	24.5362i	−0.467803	−	0.810258i
$918$		0			0
$919$	−15.7915	+	27.3517i	−0.520914	+	0.902249i	0.478791	+	0.877929i	$0.341075\pi$
$919$	−15.7915	+	27.3517i	−0.520914	+	0.902249i	−0.999704	+	0.0243197i	$0.992258\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−22.1033			−0.727538
$924$		0			0
$925$	−4.64575			−0.152751
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−0.760130	+	1.31658i	−0.0249390	+	0.0431957i	−0.878226	−	0.478247i	$-0.841273\pi$
$929$	−0.760130	+	1.31658i	−0.0249390	+	0.0431957i	0.853287	+	0.521442i	$0.174606\pi$
$930$		0			0
$931$	−16.0405			−0.525707
$932$		0			0
$933$		0			0
$934$		0			0
$935$	6.64575	+	11.5108i	0.217339	+	0.376443i
$936$		0			0
$937$	−50.9778			−1.66537			−0.832686	−	0.553746i	$-0.813198\pi$
$937$	−50.9778			−1.66537			−0.832686	+	0.553746i	$0.813198\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	2.46863	+	4.27579i	0.0804749	+	0.139387i	0.903454	−	0.428685i	$-0.141023\pi$
$941$	2.46863	+	4.27579i	0.0804749	+	0.139387i	−0.822979	+	0.568072i	$0.807690\pi$
$942$		0			0
$943$	−19.9373	+	34.5323i	−0.649246	+	1.12453i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−22.8229	+	39.5304i	−0.741644	+	1.28456i	0.210103	+	0.977679i	$0.432620\pi$
$947$	−22.8229	+	39.5304i	−0.741644	+	1.28456i	−0.951746	+	0.306885i	$0.900713\pi$
$948$		0			0
$949$	17.5000	+	30.3109i	0.568074	+	0.983933i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−0.457513			−0.0148203			−0.00741015	−	0.999973i	$-0.502359\pi$
$953$	−0.457513			−0.0148203			−0.00741015	+	0.999973i	$0.502359\pi$
$954$		0			0
$955$	11.5830	+	20.0624i	0.374817	+	0.649203i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	16.4797			0.532159
$960$		0			0
$961$	−4.29150	+	7.43310i	−0.138436	+	0.239777i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	23.9373			0.770567
$966$		0			0
$967$	40.3948			1.29901			0.649504	−	0.760358i	$-0.274977\pi$
$967$	40.3948			1.29901			0.649504	+	0.760358i	$0.274977\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	26.5830	−	46.0431i	0.853089	−	1.47759i	−0.0253172	−	0.999679i	$-0.508060\pi$
$971$	26.5830	−	46.0431i	0.853089	−	1.47759i	0.878406	−	0.477914i	$-0.158607\pi$
$972$		0			0
$973$	6.61438	−	11.4564i	0.212047	−	0.367277i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−20.4686	−	35.4527i	−0.654849	−	1.13423i	−0.981932	−	0.189237i	$-0.939399\pi$
$977$	−20.4686	−	35.4527i	−0.654849	−	1.13423i	0.327082	−	0.944996i	$-0.393935\pi$
$978$		0			0
$979$	44.5830			1.42488
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−27.3431	−	47.3597i	−0.872111	−	1.51054i	−0.859809	−	0.510615i	$-0.829418\pi$
$983$	−27.3431	−	47.3597i	−0.872111	−	1.51054i	−0.0123014	−	0.999924i	$-0.503916\pi$
$984$		0			0
$985$	−5.46863	+	9.47194i	−0.174245	+	0.301801i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−18.1144	+	31.3750i	−0.576004	+	0.997668i
$990$		0			0
$991$	−16.8542	−	29.1924i	−0.535393	−	0.927328i	−0.999144	−	0.0413622i	$-0.986830\pi$
$991$	−16.8542	−	29.1924i	−0.535393	−	0.927328i	0.463751	−	0.885965i	$-0.346503\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−19.1660			−0.607603
$996$		0			0
$997$	−8.38562	−	14.5243i	−0.265575	−	0.459990i	0.702139	−	0.712040i	$-0.252229\pi$
$997$	−8.38562	−	14.5243i	−0.265575	−	0.459990i	−0.967714	+	0.252050i	$0.918895\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1260.2.s.f.541.2		4
3.2	odd	2		420.2.q.c.121.2	✓	4
7.2	even	3		8820.2.a.be.1.1		2
7.4	even	3	inner	1260.2.s.f.361.2		4
7.5	odd	6		8820.2.a.bj.1.1		2
12.11	even	2		1680.2.bg.q.961.1		4
15.2	even	4		2100.2.bc.e.1549.2		8
15.8	even	4		2100.2.bc.e.1549.3		8
15.14	odd	2		2100.2.q.h.1801.1		4
21.2	odd	6		2940.2.a.s.1.2		2
21.5	even	6		2940.2.a.m.1.2		2
21.11	odd	6		420.2.q.c.361.2	yes	4
21.17	even	6		2940.2.q.t.361.1		4
21.20	even	2		2940.2.q.t.961.1		4
84.11	even	6		1680.2.bg.q.1201.1		4
105.32	even	12		2100.2.bc.e.949.3		8
105.53	even	12		2100.2.bc.e.949.2		8
105.74	odd	6		2100.2.q.h.1201.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.q.c.121.2	✓	4	3.2	odd	2
420.2.q.c.361.2	yes	4	21.11	odd	6
1260.2.s.f.361.2		4	7.4	even	3	inner
1260.2.s.f.541.2		4	1.1	even	1	trivial
1680.2.bg.q.961.1		4	12.11	even	2
1680.2.bg.q.1201.1		4	84.11	even	6
2100.2.q.h.1201.1		4	105.74	odd	6
2100.2.q.h.1801.1		4	15.14	odd	2
2100.2.bc.e.949.2		8	105.53	even	12
2100.2.bc.e.949.3		8	105.32	even	12
2100.2.bc.e.1549.2		8	15.2	even	4
2100.2.bc.e.1549.3		8	15.8	even	4
2940.2.a.m.1.2		2	21.5	even	6
2940.2.a.s.1.2		2	21.2	odd	6
2940.2.q.t.361.1		4	21.17	even	6
2940.2.q.t.961.1		4	21.20	even	2
8820.2.a.be.1.1		2	7.2	even	3
8820.2.a.bj.1.1		2	7.5	odd	6

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:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{5} +(1.32288 - 2.29129i) q^{7} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{5} +(1.32288 - 2.29129i) q^{7} +(1.82288 + 3.15731i) q^{11} +2.64575 q^{13} +(1.82288 + 3.15731i) q^{17} +(1.14575 - 1.98450i) q^{19} +(-1.82288 + 3.15731i) q^{23} +(-0.500000 - 0.866025i) q^{25} -2.35425 q^{29} +(-3.14575 - 5.44860i) q^{31} +(-1.32288 - 2.29129i) q^{35} +(2.32288 - 4.02334i) q^{37} +10.9373 q^{41} +9.93725 q^{43} +(3.00000 - 5.19615i) q^{47} +(-3.50000 - 6.06218i) q^{49} +(-3.64575 - 6.31463i) q^{53} +3.64575 q^{55} +(-2.46863 - 4.27579i) q^{59} +(-4.00000 + 6.92820i) q^{61} +(1.32288 - 2.29129i) q^{65} +(2.32288 + 4.02334i) q^{67} -8.35425 q^{71} +(6.61438 + 11.4564i) q^{73} +9.64575 q^{77} +(4.14575 - 7.18065i) q^{79} -4.93725 q^{83} +3.64575 q^{85} +(6.11438 - 10.5904i) q^{89} +(3.50000 - 6.06218i) q^{91} +(-1.14575 - 1.98450i) q^{95} +8.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{5}+O(q^{10}) \) 4 * q + 2 * q^5	\( 4 q + 2 q^{5} + 2 q^{11} + 2 q^{17} - 6 q^{19} - 2 q^{23} - 2 q^{25} - 20 q^{29} - 2 q^{31} + 4 q^{37} + 12 q^{41} + 8 q^{43} + 12 q^{47} - 14 q^{49} - 4 q^{53} + 4 q^{55} + 6 q^{59} - 16 q^{61} + 4 q^{67} - 44 q^{71} + 28 q^{77} + 6 q^{79} + 12 q^{83} + 4 q^{85} - 2 q^{89} + 14 q^{91} + 6 q^{95} + 32 q^{97}+O(q^{100}) \) 4 * q + 2 * q^5 + 2 * q^11 + 2 * q^17 - 6 * q^19 - 2 * q^23 - 2 * q^25 - 20 * q^29 - 2 * q^31 + 4 * q^37 + 12 * q^41 + 8 * q^43 + 12 * q^47 - 14 * q^49 - 4 * q^53 + 4 * q^55 + 6 * q^59 - 16 * q^61 + 4 * q^67 - 44 * q^71 + 28 * q^77 + 6 * q^79 + 12 * q^83 + 4 * q^85 - 2 * q^89 + 14 * q^91 + 6 * q^95 + 32 * q^97

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