LMFDB - Embedded newform 1008.2.cq.b.431.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(431,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 3, 4]))

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

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

chi := DirichletCharacter("1008.431");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.cq (of order $6$, 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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 28x^{10} + 276x^{8} + 1178x^{6} + 2292x^{4} + 1888x^{2} + 529 $ x^12 + 28x^10 + 276x^8 + 1178x^6 + 2292x^4 + 1888*x^2 + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			431.6
Root			$-3.39892i$ of defining polynomial
Character	$\chi$	$=$	1008.431
Dual form			1008.2.cq.b.863.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.76362 - 1.59558i) q^{5} +(1.75649 - 1.97857i) q^{7} +(0.786690 - 1.36259i) q^{11} +0.670500 q^{13} +(5.12369 + 2.95816i) q^{17} +(-2.84823 + 1.64442i) q^{19} +(-1.97693 - 3.42415i) q^{23} +(2.59174 - 4.48902i) q^{25} +0.585502i q^{29} +(-8.26946 - 4.77438i) q^{31} +(1.69730 - 8.27064i) q^{35} +(-3.84823 - 6.66532i) q^{37} +3.77666i q^{41} +12.3446i q^{43} +(3.67423 + 6.36396i) q^{47} +(-0.829500 - 6.95068i) q^{49} +(11.5615 + 6.67506i) q^{53} -5.02090i q^{55} +(2.48399 - 4.30240i) q^{59} +(-3.25649 - 5.64040i) q^{61} +(1.85301 - 1.06984i) q^{65} +(-4.77521 - 2.75697i) q^{67} +6.85278 q^{71} +(-2.92124 + 5.05973i) q^{73} +(-1.31417 - 3.94989i) q^{77} +(5.26946 - 3.04233i) q^{79} -9.48111 q^{83} +18.8799 q^{85} +(12.8757 - 7.43380i) q^{89} +(1.17773 - 1.32663i) q^{91} +(-5.24761 + 9.08913i) q^{95} -0.183476 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{7} - 4 q^{13} + 18 q^{19} + 2 q^{25} - 30 q^{31} + 6 q^{37} - 22 q^{49} - 16 q^{61} + 30 q^{67} - 18 q^{73} - 6 q^{79} + 64 q^{85} - 26 q^{91} + 56 q^{97}+O(q^{100}) $ 12 * q - 2 * q^7 - 4 * q^13 + 18 * q^19 + 2 * q^25 - 30 * q^31 + 6 * q^37 - 22 * q^49 - 16 * q^61 + 30 * q^67 - 18 * q^73 - 6 * q^79 + 64 * q^85 - 26 * q^91 + 56 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	2.76362	−	1.59558i	1.23593	−	0.713564i	0.267670	−	0.963511i	$-0.413746\pi$
$5$	2.76362	−	1.59558i	1.23593	−	0.713564i	0.968260	+	0.249947i	$0.0804131\pi$
$6$		0			0
$7$	1.75649	−	1.97857i	0.663890	−	0.747830i
$7$	1.75649	−	1.97857i	0.663890	−	0.747830i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.786690	−	1.36259i	0.237196	−	0.410835i	−0.722713	−	0.691149i	$-0.757105\pi$
$11$	0.786690	−	1.36259i	0.237196	−	0.410835i	0.959909	+	0.280313i	$0.0904383\pi$
$12$		0			0
$13$	0.670500			0.185963			0.0929817	−	0.995668i	$-0.470360\pi$
$13$	0.670500			0.185963			0.0929817	+	0.995668i	$0.470360\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	5.12369	+	2.95816i	1.24268	+	0.717460i	0.969639	−	0.244543i	$-0.0786378\pi$
$17$	5.12369	+	2.95816i	1.24268	+	0.717460i	0.273039	+	0.962003i	$0.411971\pi$
$18$		0			0
$19$	−2.84823	+	1.64442i	−0.653428	+	0.377257i	−0.789768	−	0.613405i	$-0.789799\pi$
$19$	−2.84823	+	1.64442i	−0.653428	+	0.377257i	0.136340	+	0.990662i	$0.456466\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.97693	−	3.42415i	−0.412219	−	0.713984i	0.582913	−	0.812534i	$-0.301913\pi$
$23$	−1.97693	−	3.42415i	−0.412219	−	0.713984i	−0.995132	+	0.0985504i	$0.968579\pi$
$24$		0			0
$25$	2.59174	−	4.48902i	0.518348	−	0.897804i
$26$		0			0
$27$		0			0
$28$		0			0
$29$			0.585502i			0.108725i	0.998521	+	0.0543625i	$0.0173127\pi$
$29$			0.585502i			0.108725i	−0.998521	+	0.0543625i	$0.982687\pi$
$30$		0			0
$31$	−8.26946	−	4.77438i	−1.48524	−	0.857503i	−0.485381	−	0.874303i	$-0.661319\pi$
$31$	−8.26946	−	4.77438i	−1.48524	−	0.857503i	−0.999859	+	0.0167994i	$0.994652\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.69730	−	8.27064i	0.286896	−	1.39799i
$36$		0			0
$37$	−3.84823	−	6.66532i	−0.632644	−	1.09577i	−0.987009	−	0.160665i	$-0.948636\pi$
$37$	−3.84823	−	6.66532i	−0.632644	−	1.09577i	0.354364	−	0.935107i	$-0.384697\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$			3.77666i			0.589815i	0.955526	+	0.294907i	$0.0952888\pi$
$41$			3.77666i			0.589815i	−0.955526	+	0.294907i	$0.904711\pi$
$42$		0			0
$43$			12.3446i			1.88253i	0.337672	+	0.941264i	$0.390361\pi$
$43$			12.3446i			1.88253i	−0.337672	+	0.941264i	$0.609639\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.67423	+	6.36396i	0.535942	+	0.928279i	0.999117	+	0.0420122i	$0.0133768\pi$
$47$	3.67423	+	6.36396i	0.535942	+	0.928279i	−0.463175	+	0.886267i	$0.653290\pi$
$48$		0			0
$49$	−0.829500	−	6.95068i	−0.118500	−	0.992954i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	11.5615	+	6.67506i	1.58810	+	0.916890i	0.993620	+	0.112781i	$0.0359757\pi$
$53$	11.5615	+	6.67506i	1.58810	+	0.916890i	0.594481	+	0.804110i	$0.297358\pi$
$54$		0			0
$55$		−	5.02090i		−	0.677018i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.48399	−	4.30240i	0.323388	−	0.560125i	−0.657797	−	0.753196i	$-0.728511\pi$
$59$	2.48399	−	4.30240i	0.323388	−	0.560125i	0.981185	+	0.193071i	$0.0618447\pi$
$60$		0			0
$61$	−3.25649	−	5.64040i	−0.416951	−	0.722180i	0.578680	−	0.815554i	$-0.303568\pi$
$61$	−3.25649	−	5.64040i	−0.416951	−	0.722180i	−0.995631	+	0.0933748i	$0.970235\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.85301	−	1.06984i	0.229838	−	0.132697i
$66$		0			0
$67$	−4.77521	−	2.75697i	−0.583385	−	0.336818i	0.179092	−	0.983832i	$-0.442684\pi$
$67$	−4.77521	−	2.75697i	−0.583385	−	0.336818i	−0.762478	+	0.647015i	$0.776017\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	6.85278			0.813275			0.406638	−	0.913590i	$-0.366701\pi$
$71$	6.85278			0.813275			0.406638	+	0.913590i	$0.366701\pi$
$72$		0			0
$73$	−2.92124	+	5.05973i	−0.341905	+	0.592197i	−0.984786	−	0.173769i	$-0.944405\pi$
$73$	−2.92124	+	5.05973i	−0.341905	+	0.592197i	0.642881	+	0.765966i	$0.277739\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.31417	−	3.94989i	−0.149763	−	0.450132i
$78$		0			0
$79$	5.26946	−	3.04233i	0.592861	−	0.342288i	−0.173367	−	0.984857i	$-0.555465\pi$
$79$	5.26946	−	3.04233i	0.592861	−	0.342288i	0.766228	+	0.642569i	$0.222131\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−9.48111			−1.04069			−0.520343	−	0.853957i	$-0.674196\pi$
$83$	−9.48111			−1.04069			−0.520343	+	0.853957i	$0.674196\pi$
$84$		0			0
$85$	18.8799			2.04782
$86$		0			0
$87$		0			0
$88$		0			0
$89$	12.8757	−	7.43380i	1.36482	−	0.787981i	0.374562	−	0.927202i	$-0.377793\pi$
$89$	12.8757	−	7.43380i	1.36482	−	0.787981i	0.990261	+	0.139221i	$0.0444599\pi$
$90$		0			0
$91$	1.17773	−	1.32663i	0.123459	−	0.139069i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−5.24761	+	9.08913i	−0.538394	+	0.932525i
$96$		0			0
$97$	−0.183476			−0.0186292			−0.00931460	−	0.999957i	$-0.502965\pi$
$97$	−0.183476			−0.0186292			−0.00931460	+	0.999957i	$0.502965\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−3.27068	−	1.88833i	−0.325445	−	0.187896i	0.328372	−	0.944548i	$-0.393500\pi$
$101$	−3.27068	−	1.88833i	−0.325445	−	0.187896i	−0.653817	+	0.756653i	$0.726833\pi$
$102$		0			0
$103$	11.9327	−	6.88937i	1.17577	−	0.678830i	0.220736	−	0.975334i	$-0.429154\pi$
$103$	11.9327	−	6.88937i	1.17577	−	0.678830i	0.955032	+	0.296504i	$0.0958207\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.58462	−	16.6010i	−0.926580	−	1.60488i	−0.789001	−	0.614392i	$-0.789401\pi$
$107$	−9.58462	−	16.6010i	−0.926580	−	1.60488i	−0.137579	−	0.990491i	$-0.543932\pi$
$108$		0			0
$109$	−4.10471	+	7.10957i	−0.393160	+	0.680974i	−0.992864	−	0.119248i	$-0.961952\pi$
$109$	−4.10471	+	7.10957i	−0.393160	+	0.680974i	0.599704	+	0.800222i	$0.295285\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			4.70862i			0.442950i	0.975166	+	0.221475i	$0.0710871\pi$
$113$			4.70862i			0.442950i	−0.975166	+	0.221475i	$0.928913\pi$
$114$		0			0
$115$	−10.9270	−	6.30870i	−1.01895	−	0.588289i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	14.8526	−	4.94161i	1.36154	−	0.452997i
$120$		0			0
$121$	4.26224	+	7.38241i	0.387476	+	0.671129i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	0.585502i		−	0.0523689i
$126$		0			0
$127$			14.3495i			1.27331i	0.771150	+	0.636654i	$0.219682\pi$
$127$			14.3495i			1.27331i	−0.771150	+	0.636654i	$0.780318\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	6.56178	+	11.3653i	0.573305	+	0.992994i	0.996223	+	0.0868261i	$0.0276724\pi$
$131$	6.56178	+	11.3653i	0.573305	+	0.992994i	−0.422918	+	0.906168i	$0.638994\pi$
$132$		0			0
$133$	−1.74926	+	8.52383i	−0.151680	+	0.739110i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−11.0545	−	6.38231i	−0.944449	−	0.545278i	−0.0530966	−	0.998589i	$-0.516909\pi$
$137$	−11.0545	−	6.38231i	−0.944449	−	0.545278i	−0.891352	+	0.453312i	$0.850242\pi$
$138$		0			0
$139$			4.52786i			0.384048i	0.981390	+	0.192024i	$0.0615051\pi$
$139$			4.52786i			0.384048i	−0.981390	+	0.192024i	$0.938495\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.527476	−	0.913615i	0.0441097	−	0.0764003i
$144$		0			0
$145$	0.934214	+	1.61811i	0.0775822	+	0.134376i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−11.0545	+	6.38231i	−0.905619	+	0.522859i	−0.879019	−	0.476787i	$-0.841801\pi$
$149$	−11.0545	+	6.38231i	−0.905619	+	0.522859i	−0.0266000	+	0.999646i	$0.508468\pi$
$150$		0			0
$151$	12.3597	+	7.13589i	1.00582	+	0.580711i	0.909965	−	0.414685i	$-0.136108\pi$
$151$	12.3597	+	7.13589i	1.00582	+	0.580711i	0.0958552	+	0.995395i	$0.469441\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−30.4716			−2.44754
$156$		0			0
$157$	0.512976	−	0.888501i	0.0409399	−	0.0709101i	−0.844829	−	0.535036i	$-0.820298\pi$
$157$	0.512976	−	0.888501i	0.0409399	−	0.0709101i	0.885769	+	0.464126i	$0.153631\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−10.2474	−	2.10297i	−0.807607	−	0.165737i
$162$		0			0
$163$	−10.9270	+	6.30870i	−0.855868	+	0.494135i	−0.862626	−	0.505842i	$-0.831182\pi$
$163$	−10.9270	+	6.30870i	−0.855868	+	0.494135i	0.00675856	+	0.999977i	$0.497849\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	10.8066			0.836243			0.418122	−	0.908391i	$-0.362689\pi$
$167$	10.8066			0.836243			0.418122	+	0.908391i	$0.362689\pi$
$168$		0			0
$169$	−12.5504			−0.965418
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−9.23326	+	5.33083i	−0.701992	+	0.405295i	−0.808089	−	0.589061i	$-0.799498\pi$
$173$	−9.23326	+	5.33083i	−0.701992	+	0.405295i	0.106097	+	0.994356i	$0.466165\pi$
$174$		0			0
$175$	−4.32950	−	13.0129i	−0.327279	−	0.983679i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−5.65117	+	9.78811i	−0.422388	+	0.731598i	−0.996173	−	0.0874088i	$-0.972141\pi$
$179$	−5.65117	+	9.78811i	−0.422388	+	0.731598i	0.573784	+	0.819006i	$0.305475\pi$
$180$		0			0
$181$	−14.5245			−1.07960			−0.539798	−	0.841795i	$-0.681499\pi$
$181$	−14.5245			−1.07960			−0.539798	+	0.841795i	$0.681499\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−21.2701	−	12.2803i	−1.56381	−	0.902865i
$186$		0			0
$187$	8.06151	−	4.65432i	0.589516	−	0.340357i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	12.5039	+	21.6575i	0.904754	+	1.56708i	0.821247	+	0.570572i	$0.193279\pi$
$191$	12.5039	+	21.6575i	0.904754	+	1.56708i	0.0835063	+	0.996507i	$0.473388\pi$
$192$		0			0
$193$	6.85545	−	11.8740i	0.493466	−	0.854709i	−0.506505	−	0.862237i	$-0.669063\pi$
$193$	6.85545	−	11.8740i	0.493466	−	0.854709i	0.999972	+	0.00752821i	$0.00239633\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			3.03494i			0.216230i	0.994138	+	0.108115i	$0.0344815\pi$
$197$			3.03494i			0.216230i	−0.994138	+	0.108115i	$0.965518\pi$
$198$		0			0
$199$	8.69645	+	5.02090i	0.616475	+	0.355922i	0.775495	−	0.631353i	$-0.217500\pi$
$199$	8.69645	+	5.02090i	0.616475	+	0.355922i	−0.159020	+	0.987275i	$0.550834\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	1.15846	+	1.02843i	0.0813078	+	0.0721814i
$204$		0			0
$205$	6.02595	+	10.4373i	0.420871	+	0.728970i
$206$		0			0
$207$		0			0
$208$		0			0
$209$			5.17461i			0.357935i
$210$		0			0
$211$		−	7.46620i		−	0.513994i	−0.966412	−	0.256997i	$-0.917267\pi$
$211$		−	7.46620i		−	0.513994i	0.966412	−	0.256997i	$-0.0827331\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	19.6967	+	34.1157i	1.34330	+	2.32667i
$216$		0			0
$217$	−23.9717	+	7.97560i	−1.62730	+	0.541419i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	3.43544	+	1.98345i	0.231092	+	0.133421i
$222$		0			0
$223$			14.2718i			0.955709i	0.878439	+	0.477855i	$0.158585\pi$
$223$			14.2718i			0.955709i	−0.878439	+	0.477855i	$0.841415\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	8.13516	−	14.0905i	0.539949	−	0.935220i	−0.458957	−	0.888459i	$-0.651777\pi$
$227$	8.13516	−	14.0905i	0.539949	−	0.935220i	0.998906	−	0.0467612i	$-0.0148900\pi$
$228$		0			0
$229$	−3.25074	−	5.63044i	−0.214815	−	0.372070i	0.738400	−	0.674362i	$-0.235581\pi$
$229$	−3.25074	−	5.63044i	−0.214815	−	0.372070i	−0.953215	+	0.302292i	$0.902248\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−14.7287	+	8.50363i	−0.964911	+	0.557091i	−0.897681	−	0.440646i	$-0.854749\pi$
$233$	−14.7287	+	8.50363i	−0.964911	+	0.557091i	−0.0672298	+	0.997738i	$0.521416\pi$
$234$		0			0
$235$	20.3084	+	11.7251i	1.32477	+	0.764858i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−28.3389			−1.83309			−0.916546	−	0.399928i	$-0.869035\pi$
$239$	−28.3389			−1.83309			−0.916546	+	0.399928i	$0.869035\pi$
$240$		0			0
$241$	−11.2752	+	19.5292i	−0.726300	+	1.25799i	0.232136	+	0.972683i	$0.425429\pi$
$241$	−11.2752	+	19.5292i	−0.726300	+	1.25799i	−0.958437	+	0.285306i	$0.907905\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−13.3828	−	17.8855i	−0.854994	−	1.14266i
$246$		0			0
$247$	−1.90974	+	1.10259i	−0.121514	+	0.0701559i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−11.2615			−0.710820			−0.355410	−	0.934711i	$-0.615659\pi$
$251$	−11.2615			−0.710820			−0.355410	+	0.934711i	$0.615659\pi$
$252$		0			0
$253$	−6.22093			−0.391106
$254$		0			0
$255$		0			0
$256$		0			0
$257$	17.9676	−	10.3736i	1.12079	−	0.647088i	0.179187	−	0.983815i	$-0.442653\pi$
$257$	17.9676	−	10.3736i	1.12079	−	0.647088i	0.941602	+	0.336727i	$0.109320\pi$
$258$		0			0
$259$	−19.9472	−	4.09357i	−1.23946	−	0.254362i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	0.155707	−	0.269693i	0.00960133	−	0.0166300i	−0.861185	−	0.508292i	$-0.830277\pi$
$263$	0.155707	−	0.269693i	0.00960133	−	0.0166300i	0.870786	+	0.491662i	$0.163610\pi$
$264$		0			0
$265$	42.6023			2.61704
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−21.1666	−	12.2205i	−1.29055	−	0.745099i	−0.311798	−	0.950149i	$-0.600931\pi$
$269$	−21.1666	−	12.2205i	−1.29055	−	0.745099i	−0.978752	+	0.205050i	$0.934264\pi$
$270$		0			0
$271$	26.8872	−	15.5233i	1.63328	−	0.942974i	0.650205	−	0.759758i	$-0.274683\pi$
$271$	26.8872	−	15.5233i	1.63328	−	0.942974i	0.983073	−	0.183215i	$-0.0586505\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−4.07779	−	7.06294i	−0.245900	−	0.425911i
$276$		0			0
$277$	−5.94719	+	10.3008i	−0.357332	+	0.618917i	−0.987514	−	0.157530i	$-0.949647\pi$
$277$	−5.94719	+	10.3008i	−0.357332	+	0.618917i	0.630182	+	0.776447i	$0.282980\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$			25.5292i			1.52295i	0.648196	+	0.761474i	$0.275524\pi$
$281$			25.5292i			1.52295i	−0.648196	+	0.761474i	$0.724476\pi$
$282$		0			0
$283$	2.54468	+	1.46917i	0.151265	+	0.0873331i	0.573722	−	0.819050i	$-0.305499\pi$
$283$	2.54468	+	1.46917i	0.151265	+	0.0873331i	−0.422457	+	0.906383i	$0.638832\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	7.47239	+	6.63365i	0.441081	+	0.391572i
$288$		0			0
$289$	9.00147	+	15.5910i	0.529499	+	0.917118i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	16.3851i		−	0.957225i	−0.878026	−	0.478613i	$-0.841140\pi$
$293$		−	16.3851i		−	0.957225i	0.878026	−	0.478613i	$-0.158860\pi$
$294$		0			0
$295$		−	15.8536i		−	0.923033i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.32553	−	2.29589i	−0.0766576	−	0.132775i
$300$		0			0
$301$	24.4246	+	21.6831i	1.40781	+	1.24979i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−17.9994	−	10.3920i	−1.03064	−	0.595042i
$306$		0			0
$307$			13.3306i			0.760820i	0.924818	+	0.380410i	$0.124217\pi$
$307$			13.3306i			0.760820i	−0.924818	+	0.380410i	$0.875783\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	15.1323	−	26.2099i	0.858073	−	1.48623i	−0.0156922	−	0.999877i	$-0.504995\pi$
$311$	15.1323	−	26.2099i	0.858073	−	1.48623i	0.873765	−	0.486349i	$-0.161671\pi$
$312$		0			0
$313$	−3.98702	−	6.90573i	−0.225360	−	0.390335i	0.731067	−	0.682305i	$-0.239022\pi$
$313$	−3.98702	−	6.90573i	−0.225360	−	0.390335i	−0.956427	+	0.291970i	$0.905689\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	22.6160	−	13.0574i	1.27024	−	0.733375i	0.295210	−	0.955433i	$-0.404611\pi$
$317$	22.6160	−	13.0574i	1.27024	−	0.733375i	0.975034	+	0.222057i	$0.0712772\pi$
$318$		0			0
$319$	0.797797	+	0.460608i	0.0446681	+	0.0257891i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−19.4579			−1.08267
$324$		0			0
$325$	1.73776	−	3.00989i	0.0963937	−	0.166959i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	19.0453	+	3.90848i	1.05000	+	0.215482i
$330$		0			0
$331$	−16.4717	+	9.50992i	−0.905365	+	0.522713i	−0.878937	−	0.476938i	$-0.841747\pi$
$331$	−16.4717	+	9.50992i	−0.905365	+	0.522713i	−0.0264279	+	0.999651i	$0.508413\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−17.5959			−0.961364
$336$		0			0
$337$	5.02300			0.273620			0.136810	−	0.990597i	$-0.456315\pi$
$337$	5.02300			0.273620			0.136810	+	0.990597i	$0.456315\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−13.0110	+	7.51191i	−0.704585	+	0.406793i
$342$		0			0
$343$	−15.2094	−	10.5676i	−0.821232	−	0.570595i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−11.0545	+	19.1469i	−0.593436	+	1.02786i	0.400330	+	0.916371i	$0.368896\pi$
$347$	−11.0545	+	19.1469i	−0.593436	+	1.02786i	−0.993766	+	0.111490i	$0.964438\pi$
$348$		0			0
$349$	−22.0519			−1.18041			−0.590206	−	0.807253i	$-0.700953\pi$
$349$	−22.0519			−1.18041			−0.590206	+	0.807253i	$0.700953\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.44946	+	0.836844i	0.0771468	+	0.0445407i	0.538077	−	0.842896i	$-0.319151\pi$
$353$	1.44946	+	0.836844i	0.0771468	+	0.0445407i	−0.460930	+	0.887436i	$0.652484\pi$
$354$		0			0
$355$	18.9385	−	10.9341i	1.00515	−	0.580324i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−3.95386	−	6.84829i	−0.208677	−	0.361439i	0.742621	−	0.669712i	$-0.233582\pi$
$359$	−3.95386	−	6.84829i	−0.208677	−	0.361439i	−0.951298	+	0.308273i	$0.900249\pi$
$360$		0			0
$361$	−4.09174	+	7.08710i	−0.215355	+	0.373005i
$362$		0			0
$363$		0			0
$364$		0			0
$365$			18.6443i			0.975885i
$366$		0			0
$367$	7.66237	+	4.42387i	0.399972	+	0.230924i	0.686472	−	0.727156i	$-0.259158\pi$
$367$	7.66237	+	4.42387i	0.399972	+	0.230924i	−0.286500	+	0.958080i	$0.592492\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	33.5148	−	11.1507i	1.74000	−	0.578915i
$372$		0			0
$373$	−3.76371	−	6.51894i	−0.194878	−	0.337538i	0.751983	−	0.659183i	$-0.229098\pi$
$373$	−3.76371	−	6.51894i	−0.194878	−	0.337538i	−0.946860	+	0.321645i	$0.895764\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			0.392579i			0.0202189i
$378$		0			0
$379$			25.1571i			1.29224i	0.763238	+	0.646118i	$0.223608\pi$
$379$			25.1571i			1.29224i	−0.763238	+	0.646118i	$0.776392\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	5.77509	+	10.0027i	0.295093	+	0.511117i	0.975007	−	0.222176i	$-0.0713159\pi$
$383$	5.77509	+	10.0027i	0.295093	+	0.511117i	−0.679913	+	0.733293i	$0.737983\pi$
$384$		0			0
$385$	−9.93421	−	8.81915i	−0.506294	−	0.449465i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	28.2150	+	16.2899i	1.43056	+	0.825933i	0.997163	−	0.0752717i	$-0.0239824\pi$
$389$	28.2150	+	16.2899i	1.43056	+	0.825933i	0.433394	+	0.901204i	$0.357316\pi$
$390$		0			0
$391$		−	23.3924i		−	1.18300i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	9.70854	−	16.8157i	0.488490	−	0.846089i
$396$		0			0
$397$	−17.1422	−	29.6911i	−0.860341	−	1.49015i	−0.871600	−	0.490217i	$-0.836917\pi$
$397$	−17.1422	−	29.6911i	−0.860341	−	1.49015i	0.0112596	−	0.999937i	$-0.496416\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−13.8898	+	8.01930i	−0.693625	+	0.400465i	−0.804969	−	0.593317i	$-0.797818\pi$
$401$	−13.8898	+	8.01930i	−0.693625	+	0.400465i	0.111344	+	0.993782i	$0.464485\pi$
$402$		0			0
$403$	−5.54468	−	3.20122i	−0.276200	−	0.159464i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−12.1094			−0.600243
$408$		0			0
$409$	11.2224	−	19.4378i	0.554912	−	0.961136i	−0.442998	−	0.896523i	$-0.646085\pi$
$409$	11.2224	−	19.4378i	0.554912	−	0.961136i	0.997910	−	0.0646136i	$-0.0205815\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−4.14951	−	12.4719i	−0.204184	−	0.613701i
$414$		0			0
$415$	−26.2022	+	15.1278i	−1.28622	+	0.742597i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	23.8894			1.16707			0.583536	−	0.812087i	$-0.301669\pi$
$419$	23.8894			1.16707			0.583536	+	0.812087i	$0.301669\pi$
$420$		0			0
$421$	16.3555			0.797116			0.398558	−	0.917143i	$-0.369511\pi$
$421$	16.3555			0.797116			0.398558	+	0.917143i	$0.369511\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	26.5585	−	15.3336i	1.28828	−	0.743788i
$426$		0			0
$427$	−16.8799	−	3.46410i	−0.816877	−	0.167640i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−7.22455	+	12.5133i	−0.347994	+	0.602744i	−0.985893	−	0.167377i	$-0.946470\pi$
$431$	−7.22455	+	12.5133i	−0.347994	+	0.602744i	0.637899	+	0.770120i	$0.279804\pi$
$432$		0			0
$433$	−8.20943			−0.394520			−0.197260	−	0.980351i	$-0.563204\pi$
$433$	−8.20943			−0.394520			−0.197260	+	0.980351i	$0.563204\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	11.2615	+	6.50183i	0.538711	+	0.311025i
$438$		0			0
$439$	9.49425	−	5.48151i	0.453136	−	0.261618i	−0.256018	−	0.966672i	$-0.582411\pi$
$439$	9.49425	−	5.48151i	0.453136	−	0.261618i	0.709154	+	0.705054i	$0.249077\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	5.42374	+	9.39419i	0.257690	+	0.446331i	0.965623	−	0.259948i	$-0.0837055\pi$
$443$	5.42374	+	9.39419i	0.257690	+	0.446331i	−0.707933	+	0.706280i	$0.750372\pi$
$444$		0			0
$445$	23.7224	−	41.0884i	1.12455	−	1.94778i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			4.48168i			0.211503i	0.994393	+	0.105752i	$0.0337249\pi$
$449$			4.48168i			0.211503i	−0.994393	+	0.105752i	$0.966275\pi$
$450$		0			0
$451$	5.14602	+	2.97106i	0.242317	+	0.139902i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	1.13804	−	5.54547i	0.0533522	−	0.259976i
$456$		0			0
$457$	−13.7094	−	23.7454i	−0.641300	−	1.11076i	−0.985143	−	0.171737i	$-0.945062\pi$
$457$	−13.7094	−	23.7454i	−0.641300	−	1.11076i	0.343843	−	0.939027i	$-0.388271\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$			22.4943i			1.04766i	0.851821	+	0.523832i	$0.175498\pi$
$461$			22.4943i			1.04766i	−0.851821	+	0.523832i	$0.824502\pi$
$462$		0			0
$463$			2.20517i			0.102483i	0.998686	+	0.0512416i	$0.0163178\pi$
$463$			2.20517i			0.102483i	−0.998686	+	0.0512416i	$0.983682\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	3.51853	+	6.09427i	0.162818	+	0.282009i	0.935878	−	0.352324i	$-0.114608\pi$
$467$	3.51853	+	6.09427i	0.162818	+	0.282009i	−0.773060	+	0.634333i	$0.781275\pi$
$468$		0			0
$469$	−13.8425	+	4.60552i	−0.639186	+	0.212663i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	16.8205	+	9.71134i	0.773409	+	0.446528i
$474$		0			0
$475$			17.0477i			0.782201i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−0.962813	+	1.66764i	−0.0439921	+	0.0761965i	−0.887183	−	0.461418i	$-0.847341\pi$
$479$	−0.962813	+	1.66764i	−0.0439921	+	0.0761965i	0.843191	+	0.537614i	$0.180674\pi$
$480$		0			0
$481$	−2.58024	−	4.46910i	−0.117649	−	0.203774i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−0.507059	+	0.292751i	−0.0230244	+	0.0132931i
$486$		0			0
$487$	−18.1234	−	10.4636i	−0.821251	−	0.474150i	0.0295964	−	0.999562i	$-0.490578\pi$
$487$	−18.1234	−	10.4636i	−0.821251	−	0.474150i	−0.850848	+	0.525412i	$0.823911\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	1.32553			0.0598205			0.0299103	−	0.999553i	$-0.490478\pi$
$491$	1.32553			0.0598205			0.0299103	+	0.999553i	$0.490478\pi$
$492$		0			0
$493$	−1.73201	+	2.99993i	−0.0780058	+	0.135110i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	12.0368	−	13.5587i	0.539925	−	0.608192i
$498$		0			0
$499$	11.9327	−	6.88937i	0.534183	−	0.308411i	−0.208535	−	0.978015i	$-0.566870\pi$
$499$	11.9327	−	6.88937i	0.534183	−	0.308411i	0.742718	+	0.669604i	$0.233536\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	16.7887			0.748573			0.374287	−	0.927313i	$-0.377888\pi$
$503$	16.7887			0.748573			0.374287	+	0.927313i	$0.377888\pi$
$504$		0			0
$505$	−12.0519			−0.536303
$506$		0			0
$507$		0			0
$508$		0			0
$509$	15.9099	−	9.18560i	0.705195	−	0.407144i	−0.104085	−	0.994568i	$-0.533191\pi$
$509$	15.9099	−	9.18560i	0.705195	−	0.407144i	0.809279	+	0.587424i	$0.199858\pi$
$510$		0			0
$511$	4.87993	+	14.6672i	0.215875	+	0.648841i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	21.9851	−	38.0792i	0.968777	−	1.67797i
$516$		0			0
$517$	11.5619			0.508493
$518$		0			0
$519$		0			0
$520$		0			0
$521$	2.28835	+	1.32118i	0.100254	+	0.0578819i	0.549289	−	0.835633i	$-0.314899\pi$
$521$	2.28835	+	1.32118i	0.100254	+	0.0578819i	−0.449035	+	0.893514i	$0.648232\pi$
$522$		0			0
$523$	−5.84823	+	3.37647i	−0.255725	+	0.147643i	−0.622383	−	0.782713i	$-0.713835\pi$
$523$	−5.84823	+	3.37647i	−0.255725	+	0.147643i	0.366658	+	0.930356i	$0.380502\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−28.2468	−	48.9249i	−1.23045	−	2.13120i
$528$		0			0
$529$	3.68348	−	6.37997i	0.160151	−	0.277390i
$530$		0			0
$531$		0			0
$532$		0			0
$533$			2.53225i			0.109684i
$534$		0			0
$535$	−52.9765	−	30.5860i	−2.29037	−	1.32235i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−10.1235	−	4.33776i	−0.436048	−	0.186841i
$540$		0			0
$541$	7.70220	+	13.3406i	0.331144	+	0.573557i	0.982736	−	0.185011i	$-0.0592322\pi$
$541$	7.70220	+	13.3406i	0.331144	+	0.573557i	−0.651593	+	0.758569i	$0.725899\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$			26.1976i			1.12218i
$546$		0			0
$547$			4.15743i			0.177759i	0.996042	+	0.0888794i	$0.0283286\pi$
$547$			4.15743i			0.177759i	−0.996042	+	0.0888794i	$0.971671\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−0.962813	−	1.66764i	−0.0410172	−	0.0710439i
$552$		0			0
$553$	3.23629	−	15.7698i	0.137621	−	0.670601i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	34.2493	+	19.7738i	1.45119	+	0.837845i	0.998549	−	0.0538483i	$-0.0171487\pi$
$557$	34.2493	+	19.7738i	1.45119	+	0.837845i	0.452641	+	0.891693i	$0.350482\pi$
$558$		0			0
$559$			8.27703i			0.350081i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	8.69442	−	15.0592i	0.366426	−	0.634669i	−0.622578	−	0.782558i	$-0.713915\pi$
$563$	8.69442	−	15.0592i	0.366426	−	0.634669i	0.989004	+	0.147889i	$0.0472479\pi$
$564$		0			0
$565$	7.51298	+	13.0129i	0.316073	+	0.547455i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	17.6276	−	10.1773i	0.738989	−	0.426655i	−0.0827126	−	0.996573i	$-0.526358\pi$
$569$	17.6276	−	10.1773i	0.738989	−	0.426655i	0.821702	+	0.569918i	$0.193025\pi$
$570$		0			0
$571$	9.87123	+	5.69916i	0.413098	+	0.238502i	0.692120	−	0.721782i	$-0.256677\pi$
$571$	9.87123	+	5.69916i	0.413098	+	0.238502i	−0.279022	+	0.960285i	$0.590010\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−20.4948			−0.854691
$576$		0			0
$577$	−0.184951	+	0.320345i	−0.00769963	+	0.0133361i	−0.869850	−	0.493317i	$-0.835784\pi$
$577$	−0.184951	+	0.320345i	−0.00769963	+	0.0133361i	0.862150	+	0.506653i	$0.169118\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−16.6535	+	18.7591i	−0.690902	+	0.778257i
$582$		0			0
$583$	18.1907	−	10.5024i	0.753382	−	0.434965i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−42.8924			−1.77036			−0.885180	−	0.465249i	$-0.845965\pi$
$587$	−42.8924			−1.77036			−0.885180	+	0.465249i	$0.845965\pi$
$588$		0			0
$589$	31.4044			1.29400
$590$		0			0
$591$		0			0
$592$		0			0
$593$	26.7973	−	15.4714i	1.10043	−	0.635336i	0.164099	−	0.986444i	$-0.447528\pi$
$593$	26.7973	−	15.4714i	1.10043	−	0.635336i	0.936335	+	0.351108i	$0.114195\pi$
$594$		0			0
$595$	33.1624	−	37.3553i	1.35952	−	1.53142i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−0.807106	+	1.39795i	−0.0329775	+	0.0571186i	−0.882043	−	0.471169i	$-0.843832\pi$
$599$	−0.807106	+	1.39795i	−0.0329775	+	0.0571186i	0.849066	+	0.528287i	$0.177166\pi$
$600$		0			0
$601$	32.6850			1.33325			0.666623	−	0.745395i	$-0.267739\pi$
$601$	32.6850			1.33325			0.666623	+	0.745395i	$0.267739\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	23.5584	+	13.6015i	0.957787	+	0.552978i
$606$		0			0
$607$	−29.2128	+	16.8660i	−1.18571	+	0.684571i	−0.957329	−	0.289001i	$-0.906677\pi$
$607$	−29.2128	+	16.8660i	−1.18571	+	0.684571i	−0.228382	+	0.973572i	$0.573344\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	2.46358	+	4.26704i	0.0996656	+	0.172626i
$612$		0			0
$613$	−2.42846	+	4.20622i	−0.0980847	+	0.169888i	−0.910892	−	0.412645i	$-0.864605\pi$
$613$	−2.42846	+	4.20622i	−0.0980847	+	0.169888i	0.812807	+	0.582533i	$0.197938\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	36.1542i		−	1.45551i	−0.685835	−	0.727757i	$-0.740563\pi$
$617$		−	36.1542i		−	1.45551i	0.685835	−	0.727757i	$-0.259437\pi$
$618$		0			0
$619$	−37.2526	−	21.5078i	−1.49731	−	0.864472i	−0.497315	−	0.867570i	$-0.665680\pi$
$619$	−37.2526	−	21.5078i	−1.49731	−	0.864472i	−0.999995	+	0.00309817i	$0.999014\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	7.90773	−	38.5329i	0.316816	−	1.54379i
$624$		0			0
$625$	12.0245	+	20.8270i	0.480979	+	0.833080i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	45.5347i		−	1.81559i
$630$		0			0
$631$			27.7378i			1.10423i	0.833769	+	0.552113i	$0.186178\pi$
$631$			27.7378i			1.10423i	−0.833769	+	0.552113i	$0.813822\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	22.8957	+	39.6565i	0.908587	+	1.57372i
$636$		0			0
$637$	−0.556180	−	4.66043i	−0.0220366	−	0.184653i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−31.8892	−	18.4113i	−1.25955	−	0.727201i	−0.286562	−	0.958062i	$-0.592513\pi$
$641$	−31.8892	−	18.4113i	−1.25955	−	0.727201i	−0.972987	+	0.230861i	$0.925846\pi$
$642$		0			0
$643$		−	32.3306i		−	1.27499i	−0.770453	−	0.637497i	$-0.779970\pi$
$643$		−	32.3306i		−	1.27499i	0.770453	−	0.637497i	$-0.220030\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	9.96775	−	17.2647i	0.391873	−	0.678744i	−0.600824	−	0.799381i	$-0.705161\pi$
$647$	9.96775	−	17.2647i	0.391873	−	0.678744i	0.992697	+	0.120638i	$0.0384940\pi$
$648$		0			0
$649$	−3.90826	−	6.76931i	−0.153413	−	0.265719i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	11.9333	−	6.88970i	0.466987	−	0.269615i	−0.247991	−	0.968762i	$-0.579770\pi$
$653$	11.9333	−	6.88970i	0.466987	−	0.269615i	0.714977	+	0.699147i	$0.246437\pi$
$654$		0			0
$655$	36.2686	+	20.9397i	1.41713	+	0.818180i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	36.3102			1.41445			0.707223	−	0.706991i	$-0.249948\pi$
$659$	36.3102			1.41445			0.707223	+	0.706991i	$0.249948\pi$
$660$		0			0
$661$	6.36120	−	11.0179i	0.247422	−	0.428548i	−0.715388	−	0.698728i	$-0.753750\pi$
$661$	6.36120	−	11.0179i	0.247422	−	0.428548i	0.962810	+	0.270180i	$0.0870832\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	8.76614	+	26.3477i	0.339936	+	1.02172i
$666$		0			0
$667$	2.00484	−	1.15750i	0.0776279	−	0.0448185i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−10.2474			−0.395596
$672$		0			0
$673$	2.02595			0.0780947			0.0390474	−	0.999237i	$-0.487568\pi$
$673$	2.02595			0.0780947			0.0390474	+	0.999237i	$0.487568\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	7.91910	−	4.57209i	0.304356	−	0.175720i	−0.340042	−	0.940410i	$-0.610441\pi$
$677$	7.91910	−	4.57209i	0.304356	−	0.175720i	0.644398	+	0.764690i	$0.277108\pi$
$678$		0			0
$679$	−0.322274	+	0.363021i	−0.0123677	+	0.0139315i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−10.3917	+	17.9990i	−0.397628	+	0.688712i	−0.993433	−	0.114417i	$-0.963500\pi$
$683$	−10.3917	+	17.9990i	−0.397628	+	0.688712i	0.595805	+	0.803129i	$0.296833\pi$
$684$		0			0
$685$	−40.7339			−1.55636
$686$		0			0
$687$		0			0
$688$		0			0
$689$	7.75202	+	4.47563i	0.295329	+	0.170508i
$690$		0			0
$691$	11.7982	−	6.81170i	0.448825	−	0.259129i	−0.258509	−	0.966009i	$-0.583231\pi$
$691$	11.7982	−	6.81170i	0.448825	−	0.259129i	0.707334	+	0.706880i	$0.249898\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	7.22455	+	12.5133i	0.274043	+	0.474656i
$696$		0			0
$697$	−11.1720	+	19.3504i	−0.423169	+	0.732950i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			24.0118i			0.906912i	0.891279	+	0.453456i	$0.149809\pi$
$701$			24.0118i			0.906912i	−0.891279	+	0.453456i	$0.850191\pi$
$702$		0			0
$703$	21.9212	+	12.6562i	0.826775	+	0.477339i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−9.48111	+	3.15445i	−0.356574	+	0.118635i
$708$		0			0
$709$	−25.0634	−	43.4111i	−0.941276	−	1.63034i	−0.763041	−	0.646350i	$-0.776295\pi$
$709$	−25.0634	−	43.4111i	−0.941276	−	1.63034i	−0.178235	−	0.983988i	$-0.557039\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$			37.7545i			1.41392i
$714$		0			0
$715$		−	3.36651i		−	0.125901i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−12.9588	−	22.4453i	−0.483282	−	0.837069i	0.516534	−	0.856267i	$-0.327222\pi$
$719$	−12.9588	−	22.4453i	−0.483282	−	0.837069i	−0.999816	+	0.0191981i	$0.993889\pi$
$720$		0			0
$721$	7.32859	−	35.7109i	0.272931	−	1.32994i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	2.62833	+	1.51747i	0.0976138	+	0.0563573i
$726$		0			0
$727$			21.2777i			0.789144i	0.918865	+	0.394572i	$0.129107\pi$
$727$			21.2777i			0.789144i	−0.918865	+	0.394572i	$0.870893\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−36.5172	+	63.2497i	−1.35064	+	2.33938i
$732$		0			0
$733$	13.7022	+	23.7329i	0.506102	+	0.876595i	0.999975	+	0.00706086i	$0.00224756\pi$
$733$	13.7022	+	23.7329i	0.506102	+	0.876595i	−0.493873	+	0.869534i	$0.664419\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−7.51322	+	4.33776i	−0.276753	+	0.159784i
$738$		0			0
$739$	−17.4602	−	10.0806i	−0.642283	−	0.370822i	0.143211	−	0.989692i	$-0.454257\pi$
$739$	−17.4602	−	10.0806i	−0.642283	−	0.370822i	−0.785493	+	0.618870i	$0.787591\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	31.7971			1.16652			0.583261	−	0.812285i	$-0.301776\pi$
$743$	31.7971			1.16652			0.583261	+	0.812285i	$0.301776\pi$
$744$		0			0
$745$	−20.3670	+	35.2766i	−0.746187	+	1.29243i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−49.6816	−	10.1957i	−1.81533	−	0.372542i
$750$		0			0
$751$	13.4155	−	7.74544i	0.489538	−	0.282635i	−0.234845	−	0.972033i	$-0.575458\pi$
$751$	13.4155	−	7.74544i	0.489538	−	0.282635i	0.724383	+	0.689398i	$0.242125\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	45.5435			1.65750
$756$		0			0
$757$	9.17198			0.333361			0.166681	−	0.986011i	$-0.446695\pi$
$757$	9.17198			0.333361			0.166681	+	0.986011i	$0.446695\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−23.7972	+	13.7393i	−0.862649	+	0.498051i	−0.864898	−	0.501947i	$-0.832617\pi$
$761$	−23.7972	+	13.7393i	−0.862649	+	0.498051i	0.00224950	+	0.999997i	$0.499284\pi$
$762$		0			0
$763$	6.85693	+	20.6094i	0.248237	+	0.746109i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.66552	−	2.88476i	0.0601384	−	0.104163i
$768$		0			0
$769$	−16.0779			−0.579782			−0.289891	−	0.957060i	$-0.593619\pi$
$769$	−16.0779			−0.579782			−0.289891	+	0.957060i	$0.593619\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−8.05439	−	4.65020i	−0.289696	−	0.167256i	0.348109	−	0.937454i	$-0.386824\pi$
$773$	−8.05439	−	4.65020i	−0.289696	−	0.167256i	−0.637805	+	0.770198i	$0.720157\pi$
$774$		0			0
$775$	−42.8646	+	24.7479i	−1.53974	+	0.888970i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−6.21043	−	10.7568i	−0.222512	−	0.385401i
$780$		0			0
$781$	5.39101	−	9.33750i	0.192906	−	0.334122i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		−	3.27397i		−	0.116853i
$786$		0			0
$787$	−8.74646	−	5.04977i	−0.311778	−	0.180005i	0.335944	−	0.941882i	$-0.390945\pi$
$787$	−8.74646	−	5.04977i	−0.311778	−	0.180005i	−0.647722	+	0.761877i	$0.724278\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	9.31635	+	8.27064i	0.331251	+	0.294070i
$792$		0			0
$793$	−2.18348	−	3.78189i	−0.0775375	−	0.134299i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	39.1184i		−	1.38565i	−0.721108	−	0.692823i	$-0.756367\pi$
$797$		−	39.1184i		−	1.38565i	0.721108	−	0.692823i	$-0.243633\pi$
$798$		0			0
$799$			43.4760i			1.53807i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	4.59622	+	7.96088i	0.162197	+	0.280933i
$804$		0			0
$805$	−31.6753	+	10.5387i	−1.11641	+	0.371440i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−4.28480	−	2.47383i	−0.150646	−	0.0869753i	0.422782	−	0.906231i	$-0.361053\pi$
$809$	−4.28480	−	2.47383i	−0.150646	−	0.0869753i	−0.573428	+	0.819256i	$0.694387\pi$
$810$		0			0
$811$		−	42.8005i		−	1.50293i	−0.659773	−	0.751465i	$-0.729347\pi$
$811$		−	42.8005i		−	1.50293i	0.659773	−	0.751465i	$-0.270653\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−20.1320	+	34.8697i	−0.705195	+	1.22143i
$816$		0			0
$817$	−20.2997	−	35.1601i	−0.710196	−	1.23010i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−39.8401	+	23.0017i	−1.39043	+	0.802765i	−0.993363	−	0.115025i	$-0.963305\pi$
$821$	−39.8401	+	23.0017i	−1.39043	+	0.802765i	−0.397067	+	0.917790i	$0.629972\pi$
$822$		0			0
$823$	−26.0894	−	15.0627i	−0.909418	−	0.525053i	−0.0291740	−	0.999574i	$-0.509288\pi$
$823$	−26.0894	−	15.0627i	−0.909418	−	0.525053i	−0.880244	+	0.474522i	$0.842621\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	7.94856			0.276399			0.138199	−	0.990404i	$-0.455869\pi$
$827$	7.94856			0.276399			0.138199	+	0.990404i	$0.455869\pi$
$828$		0			0
$829$	−10.5706	+	18.3089i	−0.367133	+	0.635893i	−0.989116	−	0.147138i	$-0.952994\pi$
$829$	−10.5706	+	18.3089i	−0.367133	+	0.635893i	0.621983	+	0.783031i	$0.286327\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	16.3112	−	38.0669i	0.565148	−	1.31894i
$834$		0			0
$835$	29.8655	−	17.2428i	1.03354	−	0.596713i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−35.0074			−1.20859			−0.604295	−	0.796760i	$-0.706545\pi$
$839$	−35.0074			−1.20859			−0.604295	+	0.796760i	$0.706545\pi$
$840$		0			0
$841$	28.6572			0.988179
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−34.6846	+	20.0252i	−1.19319	+	0.688887i
$846$		0			0
$847$	22.0932	+	4.53397i	0.759132	+	0.155789i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−15.2154	+	26.3538i	−0.521576	+	0.903396i
$852$		0			0
$853$	6.26133			0.214384			0.107192	−	0.994238i	$-0.465814\pi$
$853$	6.26133			0.214384			0.107192	+	0.994238i	$0.465814\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−30.6681	−	17.7062i	−1.04760	−	0.604834i	−0.125625	−	0.992078i	$-0.540094\pi$
$857$	−30.6681	−	17.7062i	−1.04760	−	0.604834i	−0.921977	+	0.387244i	$0.873427\pi$
$858$		0			0
$859$	24.5438	−	14.1704i	0.837423	−	0.483486i	−0.0189646	−	0.999820i	$-0.506037\pi$
$859$	24.5438	−	14.1704i	0.837423	−	0.483486i	0.856387	+	0.516334i	$0.172704\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−10.3713	−	17.9636i	−0.353043	−	0.611489i	0.633738	−	0.773548i	$-0.281520\pi$
$863$	−10.3713	−	17.9636i	−0.353043	−	0.611489i	−0.986781	+	0.162059i	$0.948187\pi$
$864$		0			0
$865$	−17.0115	+	29.4648i	−0.578408	+	1.00183i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		−	9.57347i		−	0.324758i
$870$		0			0
$871$	−3.20178	−	1.84855i	−0.108488	−	0.0626357i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1.15846	−	1.02843i	−0.0391630	−	0.0347672i
$876$		0			0
$877$	−8.68200	−	15.0377i	−0.293170	−	0.507786i	0.681387	−	0.731923i	$-0.261377\pi$
$877$	−8.68200	−	15.0377i	−0.293170	−	0.507786i	−0.974558	+	0.224137i	$0.928044\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			51.9905i			1.75160i	0.482671	+	0.875802i	$0.339667\pi$
$881$			51.9905i			1.75160i	−0.482671	+	0.875802i	$0.660333\pi$
$882$		0			0
$883$			15.9062i			0.535288i	0.963518	+	0.267644i	$0.0862451\pi$
$883$			15.9062i			0.535288i	−0.963518	+	0.267644i	$0.913755\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−10.7749	−	18.6626i	−0.361784	−	0.626629i	0.626470	−	0.779445i	$-0.284499\pi$
$887$	−10.7749	−	18.6626i	−0.361784	−	0.626629i	−0.988255	+	0.152816i	$0.951166\pi$
$888$		0			0
$889$	28.3914	+	25.2046i	0.952218	+	0.845336i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−20.9301	−	12.0840i	−0.700399	−	0.404376i
$894$		0			0
$895$			36.0675i			1.20560i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	2.79541	−	4.84179i	0.0932320	−	0.161483i
$900$		0			0
$901$	39.4919	+	68.4019i	1.31566	+	2.27880i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−40.1402	+	23.1749i	−1.33430	+	0.770361i
$906$		0			0
$907$	−23.4102	−	13.5159i	−0.777321	−	0.448787i	0.0581587	−	0.998307i	$-0.481477\pi$
$907$	−23.4102	−	13.5159i	−0.777321	−	0.448787i	−0.835480	+	0.549521i	$0.814810\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	3.95386			0.130997			0.0654987	−	0.997853i	$-0.479136\pi$
$911$	3.95386			0.130997			0.0654987	+	0.997853i	$0.479136\pi$
$912$		0			0
$913$	−7.45869	+	12.9188i	−0.246847	+	0.427551i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	34.0128	+	6.98012i	1.12320	+	0.230504i
$918$		0			0
$919$	−21.9212	+	12.6562i	−0.723115	+	0.417491i	−0.815898	−	0.578196i	$-0.803757\pi$
$919$	−21.9212	+	12.6562i	−0.723115	+	0.417491i	0.0927832	+	0.995686i	$0.470424\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	4.59479			0.151239
$924$		0			0
$925$	−39.8944			−1.31172
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−30.2963	+	17.4916i	−0.993991	+	0.573881i	−0.906465	−	0.422282i	$-0.861229\pi$
$929$	−30.2963	+	17.4916i	−0.993991	+	0.573881i	−0.0875258	+	0.996162i	$0.527896\pi$
$930$		0			0
$931$	13.7925	+	18.4331i	0.452030	+	0.604119i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	14.8526	−	25.7255i	0.485733	−	0.841315i
$936$		0			0
$937$	−10.0779			−0.329229			−0.164615	−	0.986358i	$-0.552638\pi$
$937$	−10.0779			−0.329229			−0.164615	+	0.986358i	$0.552638\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−13.5898	−	7.84607i	−0.443014	−	0.255774i	0.261861	−	0.965106i	$-0.415664\pi$
$941$	−13.5898	−	7.84607i	−0.443014	−	0.255774i	−0.704875	+	0.709331i	$0.748997\pi$
$942$		0			0
$943$	12.9318	−	7.46620i	0.421118	−	0.243133i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	19.8524	+	34.3854i	0.645117	+	1.11738i	0.984275	+	0.176646i	$0.0565246\pi$
$947$	19.8524	+	34.3854i	0.645117	+	1.11738i	−0.339158	+	0.940730i	$0.610142\pi$
$948$		0			0
$949$	−1.95869	+	3.39255i	−0.0635818	+	0.110127i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	51.6901i		−	1.67441i	−0.546891	−	0.837203i	$-0.684189\pi$
$953$		−	51.6901i		−	1.67441i	0.546891	−	0.837203i	$-0.315811\pi$
$954$		0			0
$955$	69.1124	+	39.9020i	2.23642	+	1.29120i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−32.0449	+	10.6617i	−1.03479	+	0.344283i
$960$		0			0
$961$	30.0894	+	52.1163i	0.970624	+	1.68117i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		−	43.7536i		−	1.40848i
$966$		0			0
$967$		−	13.9090i		−	0.447285i	−0.974671	−	0.223642i	$-0.928205\pi$
$967$		−	13.9090i		−	0.447285i	0.974671	−	0.223642i	$-0.0717948\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−1.15846	−	2.00651i	−0.0371767	−	0.0643919i	0.846838	−	0.531850i	$-0.178503\pi$
$971$	−1.15846	−	2.00651i	−0.0371767	−	0.0643919i	−0.884015	+	0.467458i	$0.845170\pi$
$972$		0			0
$973$	8.95869	+	7.95312i	0.287202	+	0.254965i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−26.5267	−	15.3152i	−0.848666	−	0.489977i	0.0115346	−	0.999933i	$-0.496328\pi$
$977$	−26.5267	−	15.3152i	−0.848666	−	0.489977i	−0.860200	+	0.509956i	$0.829662\pi$
$978$		0			0
$979$		−	23.3924i		−	0.747623i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−5.77509	+	10.0027i	−0.184197	+	0.319038i	−0.943306	−	0.331926i	$-0.892302\pi$
$983$	−5.77509	+	10.0027i	−0.184197	+	0.319038i	0.759109	+	0.650964i	$0.225635\pi$
$984$		0			0
$985$	4.84248	+	8.38741i	0.154294	+	0.267245i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	42.2696	−	24.4044i	1.34409	−	0.776013i
$990$		0			0
$991$	−17.5730	−	10.1458i	−0.558225	−	0.322291i	0.194208	−	0.980960i	$-0.437786\pi$
$991$	−17.5730	−	10.1458i	−0.558225	−	0.322291i	−0.752433	+	0.658669i	$0.771120\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	32.0449			1.01589
$996$		0			0
$997$	6.25074	−	10.8266i	0.197963	−	0.342882i	−0.749905	−	0.661546i	$-0.769901\pi$
$997$	6.25074	−	10.8266i	0.197963	−	0.342882i	0.947868	+	0.318664i	$0.103234\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.cq.b.431.6	yes	12
3.2	odd	2	inner	1008.2.cq.b.431.1	✓	12
4.3	odd	2		1008.2.cq.c.431.6	yes	12
7.2	even	3		1008.2.cq.c.863.1	yes	12
7.3	odd	6		7056.2.h.o.4607.1		12
7.4	even	3		7056.2.h.n.4607.11		12
12.11	even	2		1008.2.cq.c.431.1	yes	12
21.2	odd	6		1008.2.cq.c.863.6	yes	12
21.11	odd	6		7056.2.h.n.4607.2		12
21.17	even	6		7056.2.h.o.4607.12		12
28.3	even	6		7056.2.h.o.4607.2		12
28.11	odd	6		7056.2.h.n.4607.12		12
28.23	odd	6	inner	1008.2.cq.b.863.1	yes	12
84.11	even	6		7056.2.h.n.4607.1		12
84.23	even	6	inner	1008.2.cq.b.863.6	yes	12
84.59	odd	6		7056.2.h.o.4607.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.cq.b.431.1	✓	12	3.2	odd	2	inner
1008.2.cq.b.431.6	yes	12	1.1	even	1	trivial
1008.2.cq.b.863.1	yes	12	28.23	odd	6	inner
1008.2.cq.b.863.6	yes	12	84.23	even	6	inner
1008.2.cq.c.431.1	yes	12	12.11	even	2
1008.2.cq.c.431.6	yes	12	4.3	odd	2
1008.2.cq.c.863.1	yes	12	7.2	even	3
1008.2.cq.c.863.6	yes	12	21.2	odd	6
7056.2.h.n.4607.1		12	84.11	even	6
7056.2.h.n.4607.2		12	21.11	odd	6
7056.2.h.n.4607.11		12	7.4	even	3
7056.2.h.n.4607.12		12	28.11	odd	6
7056.2.h.o.4607.1		12	7.3	odd	6
7056.2.h.o.4607.2		12	28.3	even	6
7056.2.h.o.4607.11		12	84.59	odd	6
7056.2.h.o.4607.12		12	21.17	even	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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.cq (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.76362 - 1.59558i) q^{5} +(1.75649 - 1.97857i) q^{7} +(0.786690 - 1.36259i) q^{11} +0.670500 q^{13} +(5.12369 + 2.95816i) q^{17} +(-2.84823 + 1.64442i) q^{19} +(-1.97693 - 3.42415i) q^{23} +(2.59174 - 4.48902i) q^{25} +0.585502i q^{29} +(-8.26946 - 4.77438i) q^{31} +(1.69730 - 8.27064i) q^{35} +(-3.84823 - 6.66532i) q^{37} +3.77666i q^{41} +12.3446i q^{43} +(3.67423 + 6.36396i) q^{47} +(-0.829500 - 6.95068i) q^{49} +(11.5615 + 6.67506i) q^{53} -5.02090i q^{55} +(2.48399 - 4.30240i) q^{59} +(-3.25649 - 5.64040i) q^{61} +(1.85301 - 1.06984i) q^{65} +(-4.77521 - 2.75697i) q^{67} +6.85278 q^{71} +(-2.92124 + 5.05973i) q^{73} +(-1.31417 - 3.94989i) q^{77} +(5.26946 - 3.04233i) q^{79} -9.48111 q^{83} +18.8799 q^{85} +(12.8757 - 7.43380i) q^{89} +(1.17773 - 1.32663i) q^{91} +(-5.24761 + 9.08913i) q^{95} -0.183476 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{7} - 4 q^{13} + 18 q^{19} + 2 q^{25} - 30 q^{31} + 6 q^{37} - 22 q^{49} - 16 q^{61} + 30 q^{67} - 18 q^{73} - 6 q^{79} + 64 q^{85} - 26 q^{91} + 56 q^{97}+O(q^{100}) \) 12 * q - 2 * q^7 - 4 * q^13 + 18 * q^19 + 2 * q^25 - 30 * q^31 + 6 * q^37 - 22 * q^49 - 16 * q^61 + 30 * q^67 - 18 * q^73 - 6 * q^79 + 64 * q^85 - 26 * q^91 + 56 * q^97

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