LMFDB - Embedded newform 1400.2.x.b.657.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1400,2,Mod(657,1400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1400, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))

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

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

chi := DirichletCharacter("1400.657");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1400 = 2^{3} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1400.x (of order $4$, 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:	$11.1790562830$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			657.12
Character	$\chi$	$=$	1400.657
Dual form			1400.2.x.b.993.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.16993 + 2.16993i) q^{3} +(1.63589 - 2.07939i) q^{7} +6.41716i q^{9} +O(q^{10})$	$q+(2.16993 + 2.16993i) q^{3} +(1.63589 - 2.07939i) q^{7} +6.41716i q^{9} +2.56986 q^{11} +(-1.35447 - 1.35447i) q^{13} +(-2.10000 + 2.10000i) q^{17} +4.43874 q^{19} +(8.06189 - 0.962346i) q^{21} +(5.78997 - 5.78997i) q^{23} +(-7.41498 + 7.41498i) q^{27} +4.28527i q^{29} +9.70587i q^{31} +(5.57640 + 5.57640i) q^{33} +(-0.183701 - 0.183701i) q^{37} -5.87819i q^{39} +3.81823i q^{41} +(-5.86065 + 5.86065i) q^{43} +(1.83004 - 1.83004i) q^{47} +(-1.64770 - 6.80331i) q^{49} -9.11369 q^{51} +(2.38616 - 2.38616i) q^{53} +(9.63174 + 9.63174i) q^{57} -6.34515 q^{59} -8.62046i q^{61} +(13.3438 + 10.4978i) q^{63} +(-6.68908 - 6.68908i) q^{67} +25.1276 q^{69} -6.04557 q^{71} +(-1.88962 - 1.88962i) q^{73} +(4.20401 - 5.34372i) q^{77} -12.2456i q^{79} -12.9285 q^{81} +(2.08951 + 2.08951i) q^{83} +(-9.29871 + 9.29871i) q^{87} +10.1525 q^{89} +(-5.03222 + 0.600696i) q^{91} +(-21.0610 + 21.0610i) q^{93} +(-7.15926 + 7.15926i) q^{97} +16.4912i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{7}+O(q^{10}) $ 24 * q - 4 * q^7	$ 24 q - 4 q^{7} + 8 q^{11} + 16 q^{21} + 32 q^{23} + 8 q^{37} - 16 q^{43} - 24 q^{51} + 16 q^{53} - 20 q^{63} + 32 q^{67} - 32 q^{71} + 40 q^{77} - 72 q^{81} - 64 q^{91} - 72 q^{93}+O(q^{100}) $ 24 * q - 4 * q^7 + 8 * q^11 + 16 * q^21 + 32 * q^23 + 8 * q^37 - 16 * q^43 - 24 * q^51 + 16 * q^53 - 20 * q^63 + 32 * q^67 - 32 * q^71 + 40 * q^77 - 72 * q^81 - 64 * q^91 - 72 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times$.

$n$	$351$	$701$	$801$	$1177$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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
$3$	2.16993	+	2.16993i	1.25281	+	1.25281i	0.954456	+	0.298351i	$0.0964367\pi$
$3$	2.16993	+	2.16993i	1.25281	+	1.25281i	0.298351	+	0.954456i	$0.403563\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.63589	−	2.07939i	0.618310	−	0.785934i
$7$	1.63589	−	2.07939i	0.618310	−	0.785934i
$8$		0			0
$9$			6.41716i			2.13905i
$10$		0			0
$11$	2.56986			0.774841			0.387420	−	0.921903i	$-0.373366\pi$
$11$	2.56986			0.774841			0.387420	+	0.921903i	$0.373366\pi$
$12$		0			0
$13$	−1.35447	−	1.35447i	−0.375661	−	0.375661i	0.493873	−	0.869534i	$-0.335581\pi$
$13$	−1.35447	−	1.35447i	−0.375661	−	0.375661i	−0.869534	+	0.493873i	$0.835581\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.10000	+	2.10000i	−0.509325	+	0.509325i	−0.914319	−	0.404994i	$-0.867274\pi$
$17$	−2.10000	+	2.10000i	−0.509325	+	0.509325i	0.404994	+	0.914319i	$0.367274\pi$
$18$		0			0
$19$	4.43874			1.01832			0.509159	−	0.860673i	$-0.329957\pi$
$19$	4.43874			1.01832			0.509159	+	0.860673i	$0.329957\pi$
$20$		0			0
$21$	8.06189	−	0.962346i	1.75925	−	0.210001i
$22$		0			0
$23$	5.78997	−	5.78997i	1.20729	−	1.20729i	0.235391	−	0.971901i	$-0.424363\pi$
$23$	5.78997	−	5.78997i	1.20729	−	1.20729i	0.971901	−	0.235391i	$-0.0756370\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−7.41498	+	7.41498i	−1.42701	+	1.42701i
$28$		0			0
$29$			4.28527i			0.795754i	0.917439	+	0.397877i	$0.130253\pi$
$29$			4.28527i			0.795754i	−0.917439	+	0.397877i	$0.869747\pi$
$30$		0			0
$31$			9.70587i			1.74323i	0.490194	+	0.871613i	$0.336926\pi$
$31$			9.70587i			1.74323i	−0.490194	+	0.871613i	$0.663074\pi$
$32$		0			0
$33$	5.57640	+	5.57640i	0.970726	+	0.970726i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−0.183701	−	0.183701i	−0.0302002	−	0.0302002i	0.691845	−	0.722046i	$-0.256798\pi$
$37$	−0.183701	−	0.183701i	−0.0302002	−	0.0302002i	−0.722046	+	0.691845i	$0.756798\pi$
$38$		0			0
$39$		−	5.87819i		−	0.941263i
$40$		0			0
$41$			3.81823i			0.596307i	0.954518	+	0.298153i	$0.0963707\pi$
$41$			3.81823i			0.596307i	−0.954518	+	0.298153i	$0.903629\pi$
$42$		0			0
$43$	−5.86065	+	5.86065i	−0.893741	+	0.893741i	−0.994873	−	0.101132i	$-0.967754\pi$
$43$	−5.86065	+	5.86065i	−0.893741	+	0.893741i	0.101132	+	0.994873i	$0.467754\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.83004	−	1.83004i	0.266939	−	0.266939i	−0.560926	−	0.827866i	$-0.689555\pi$
$47$	1.83004	−	1.83004i	0.266939	−	0.266939i	0.827866	+	0.560926i	$0.189555\pi$
$48$		0			0
$49$	−1.64770	−	6.80331i	−0.235386	−	0.971902i
$50$		0			0
$51$	−9.11369			−1.27617
$52$		0			0
$53$	2.38616	−	2.38616i	0.327764	−	0.327764i	−0.523972	−	0.851736i	$-0.675550\pi$
$53$	2.38616	−	2.38616i	0.327764	−	0.327764i	0.851736	+	0.523972i	$0.175550\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	9.63174	+	9.63174i	1.27576	+	1.27576i
$58$		0			0
$59$	−6.34515			−0.826068			−0.413034	−	0.910716i	$-0.635531\pi$
$59$	−6.34515			−0.826068			−0.413034	+	0.910716i	$0.635531\pi$
$60$		0			0
$61$		−	8.62046i		−	1.10374i	−0.833931	−	0.551868i	$-0.813915\pi$
$61$		−	8.62046i		−	1.10374i	0.833931	−	0.551868i	$-0.186085\pi$
$62$		0			0
$63$	13.3438	+	10.4978i	1.68116	+	1.32260i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−6.68908	−	6.68908i	−0.817201	−	0.817201i	0.168501	−	0.985702i	$-0.446108\pi$
$67$	−6.68908	−	6.68908i	−0.817201	−	0.817201i	−0.985702	+	0.168501i	$0.946108\pi$
$68$		0			0
$69$	25.1276			3.02501
$70$		0			0
$71$	−6.04557			−0.717477			−0.358739	−	0.933438i	$-0.616793\pi$
$71$	−6.04557			−0.717477			−0.358739	+	0.933438i	$0.616793\pi$
$72$		0			0
$73$	−1.88962	−	1.88962i	−0.221164	−	0.221164i	0.587825	−	0.808988i	$-0.299985\pi$
$73$	−1.88962	−	1.88962i	−0.221164	−	0.221164i	−0.808988	+	0.587825i	$0.799985\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	4.20401	−	5.34372i	0.479092	−	0.608974i
$78$		0			0
$79$		−	12.2456i		−	1.37774i	−0.724887	−	0.688868i	$-0.758108\pi$
$79$		−	12.2456i		−	1.37774i	0.724887	−	0.688868i	$-0.241892\pi$
$80$		0			0
$81$	−12.9285			−1.43650
$82$		0			0
$83$	2.08951	+	2.08951i	0.229354	+	0.229354i	0.812423	−	0.583069i	$-0.198148\pi$
$83$	2.08951	+	2.08951i	0.229354	+	0.229354i	−0.583069	+	0.812423i	$0.698148\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−9.29871	+	9.29871i	−0.996927	+	0.996927i
$88$		0			0
$89$	10.1525			1.07616			0.538081	−	0.842893i	$-0.319150\pi$
$89$	10.1525			1.07616			0.538081	+	0.842893i	$0.319150\pi$
$90$		0			0
$91$	−5.03222	+	0.600696i	−0.527520	+	0.0629700i
$92$		0			0
$93$	−21.0610	+	21.0610i	−2.18393	+	2.18393i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−7.15926	+	7.15926i	−0.726913	+	0.726913i	−0.970004	−	0.243091i	$-0.921839\pi$
$97$	−7.15926	+	7.15926i	−0.726913	+	0.726913i	0.243091	+	0.970004i	$0.421839\pi$
$98$		0			0
$99$			16.4912i			1.65743i
$100$		0			0
$101$			1.12506i			0.111947i	0.998432	+	0.0559737i	$0.0178263\pi$
$101$			1.12506i			0.111947i	−0.998432	+	0.0559737i	$0.982174\pi$
$102$		0			0
$103$	1.56743	+	1.56743i	0.154443	+	0.154443i	0.780099	−	0.625656i	$-0.215169\pi$
$103$	1.56743	+	1.56743i	0.154443	+	0.154443i	−0.625656	+	0.780099i	$0.715169\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.145240	+	0.145240i	0.0140409	+	0.0140409i	0.714092	−	0.700051i	$-0.246840\pi$
$107$	0.145240	+	0.145240i	0.0140409	+	0.0140409i	−0.700051	+	0.714092i	$0.746840\pi$
$108$		0			0
$109$		−	6.51130i		−	0.623669i	−0.950136	−	0.311835i	$-0.899057\pi$
$109$		−	6.51130i		−	0.623669i	0.950136	−	0.311835i	$-0.100943\pi$
$110$		0			0
$111$		−	0.797233i		−	0.0756700i
$112$		0			0
$113$	7.49203	−	7.49203i	0.704791	−	0.704791i	−0.260644	−	0.965435i	$-0.583935\pi$
$113$	7.49203	−	7.49203i	0.704791	−	0.704791i	0.965435	+	0.260644i	$0.0839349\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	8.69183	−	8.69183i	0.803560	−	0.803560i
$118$		0			0
$119$	0.931334	+	7.80209i	0.0853753	+	0.715217i
$120$		0			0
$121$	−4.39584			−0.399622
$122$		0			0
$123$	−8.28527	+	8.28527i	−0.747057	+	0.747057i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−6.78578	−	6.78578i	−0.602141	−	0.602141i	0.338740	−	0.940880i	$-0.389999\pi$
$127$	−6.78578	−	6.78578i	−0.602141	−	0.602141i	−0.940880	+	0.338740i	$0.889999\pi$
$128$		0			0
$129$	−25.4344			−2.23937
$130$		0			0
$131$			8.37853i			0.732036i	0.930608	+	0.366018i	$0.119279\pi$
$131$			8.37853i			0.732036i	−0.930608	+	0.366018i	$0.880721\pi$
$132$		0			0
$133$	7.26131	−	9.22986i	0.629636	−	0.800330i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−7.56986	−	7.56986i	−0.646736	−	0.646736i	0.305466	−	0.952203i	$-0.401188\pi$
$137$	−7.56986	−	7.56986i	−0.646736	−	0.646736i	−0.952203	+	0.305466i	$0.901188\pi$
$138$		0			0
$139$	−11.2432			−0.953636			−0.476818	−	0.879002i	$-0.658210\pi$
$139$	−11.2432			−0.953636			−0.476818	+	0.879002i	$0.658210\pi$
$140$		0			0
$141$	7.94212			0.668847
$142$		0			0
$143$	−3.48078	−	3.48078i	−0.291078	−	0.291078i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	11.1873	−	18.3381i	0.922713	−	1.51250i
$148$		0			0
$149$		−	18.0067i		−	1.47516i	−0.675258	−	0.737581i	$-0.735968\pi$
$149$		−	18.0067i		−	1.47516i	0.675258	−	0.737581i	$-0.264032\pi$
$150$		0			0
$151$	12.1231			0.986563			0.493282	−	0.869870i	$-0.335797\pi$
$151$	12.1231			0.986563			0.493282	+	0.869870i	$0.335797\pi$
$152$		0			0
$153$	−13.4760	−	13.4760i	−1.08947	−	1.08947i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−11.6764	+	11.6764i	−0.931876	+	0.931876i	−0.997823	−	0.0659475i	$-0.978993\pi$
$157$	−11.6764	+	11.6764i	−0.931876	+	0.931876i	0.0659475	+	0.997823i	$0.478993\pi$
$158$		0			0
$159$	10.3556			0.821249
$160$		0			0
$161$	−2.56781	−	21.5114i	−0.202371	−	1.69533i
$162$		0			0
$163$	−10.5217	+	10.5217i	−0.824123	+	0.824123i	−0.986696	−	0.162574i	$-0.948020\pi$
$163$	−10.5217	+	10.5217i	−0.824123	+	0.824123i	0.162574	+	0.986696i	$0.448020\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−9.06283	+	9.06283i	−0.701303	+	0.701303i	−0.964690	−	0.263387i	$-0.915160\pi$
$167$	−9.06283	+	9.06283i	−0.701303	+	0.701303i	0.263387	+	0.964690i	$0.415160\pi$
$168$		0			0
$169$		−	9.33084i		−	0.717757i
$170$		0			0
$171$			28.4841i			2.17823i
$172$		0			0
$173$	9.99321	+	9.99321i	0.759770	+	0.759770i	0.976280	−	0.216511i	$-0.0694676\pi$
$173$	9.99321	+	9.99321i	0.759770	+	0.759770i	−0.216511	+	0.976280i	$0.569468\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−13.7685	−	13.7685i	−1.03490	−	1.03490i
$178$		0			0
$179$			14.8694i			1.11139i	0.831386	+	0.555695i	$0.187548\pi$
$179$			14.8694i			1.11139i	−0.831386	+	0.555695i	$0.812452\pi$
$180$		0			0
$181$			14.2095i			1.05618i	0.849188	+	0.528090i	$0.177092\pi$
$181$			14.2095i			1.05618i	−0.849188	+	0.528090i	$0.822908\pi$
$182$		0			0
$183$	18.7058	−	18.7058i	1.38277	−	1.38277i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−5.39670	+	5.39670i	−0.394646	+	0.394646i
$188$		0			0
$189$	3.28849	+	27.5488i	0.239202	+	2.00388i
$190$		0			0
$191$	−1.04143			−0.0753549			−0.0376775	−	0.999290i	$-0.511996\pi$
$191$	−1.04143			−0.0753549			−0.0376775	+	0.999290i	$0.511996\pi$
$192$		0			0
$193$	−0.0690260	+	0.0690260i	−0.00496860	+	0.00496860i	−0.709587	−	0.704618i	$-0.751118\pi$
$193$	−0.0690260	+	0.0690260i	−0.00496860	+	0.00496860i	0.704618	+	0.709587i	$0.251118\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−12.7945	−	12.7945i	−0.911571	−	0.911571i	0.0848244	−	0.996396i	$-0.472967\pi$
$197$	−12.7945	−	12.7945i	−0.911571	−	0.911571i	−0.996396	+	0.0848244i	$0.972967\pi$
$198$		0			0
$199$	4.09793			0.290494			0.145247	−	0.989395i	$-0.453602\pi$
$199$	4.09793			0.290494			0.145247	+	0.989395i	$0.453602\pi$
$200$		0			0
$201$		−	29.0296i		−	2.04759i
$202$		0			0
$203$	8.91073	+	7.01025i	0.625411	+	0.492023i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	37.1551	+	37.1551i	2.58246	+	2.58246i
$208$		0			0
$209$	11.4069			0.789033
$210$		0			0
$211$	28.7179			1.97702			0.988510	−	0.151154i	$-0.0482988\pi$
$211$	28.7179			1.97702			0.988510	+	0.151154i	$0.0482988\pi$
$212$		0			0
$213$	−13.1184	−	13.1184i	−0.898861	−	0.898861i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	20.1823	+	15.8778i	1.37006	+	1.07785i
$218$		0			0
$219$		−	8.20069i		−	0.554151i
$220$		0			0
$221$	5.68876			0.382668
$222$		0			0
$223$	−3.69411	−	3.69411i	−0.247376	−	0.247376i	0.572517	−	0.819893i	$-0.305967\pi$
$223$	−3.69411	−	3.69411i	−0.247376	−	0.247376i	−0.819893	+	0.572517i	$0.805967\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	7.85781	−	7.85781i	0.521541	−	0.521541i	−0.396495	−	0.918037i	$-0.629774\pi$
$227$	7.85781	−	7.85781i	0.521541	−	0.521541i	0.918037	+	0.396495i	$0.129774\pi$
$228$		0			0
$229$	−9.48513			−0.626795			−0.313397	−	0.949622i	$-0.601467\pi$
$229$	−9.48513			−0.626795			−0.313397	+	0.949622i	$0.601467\pi$
$230$		0			0
$231$	20.7179	−	2.47309i	1.36314	−	0.162717i
$232$		0			0
$233$	13.6024	−	13.6024i	0.891126	−	0.891126i	−0.103503	−	0.994629i	$-0.533005\pi$
$233$	13.6024	−	13.6024i	0.891126	−	0.891126i	0.994629	+	0.103503i	$0.0330053\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	26.5720	−	26.5720i	1.72604	−	1.72604i
$238$		0			0
$239$		−	18.7581i		−	1.21336i	−0.794946	−	0.606680i	$-0.792501\pi$
$239$		−	18.7581i		−	1.21336i	0.794946	−	0.606680i	$-0.207499\pi$
$240$		0			0
$241$		−	2.78395i		−	0.179330i	−0.995972	−	0.0896649i	$-0.971420\pi$
$241$		−	2.78395i		−	0.179330i	0.995972	−	0.0896649i	$-0.0285796\pi$
$242$		0			0
$243$	−5.80885	−	5.80885i	−0.372638	−	0.372638i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−6.01213	−	6.01213i	−0.382543	−	0.382543i
$248$		0			0
$249$			9.06817i			0.574672i
$250$		0			0
$251$		−	28.3562i		−	1.78983i	−0.446241	−	0.894913i	$-0.647237\pi$
$251$		−	28.3562i		−	1.78983i	0.446241	−	0.894913i	$-0.352763\pi$
$252$		0			0
$253$	14.8794	−	14.8794i	0.935458	−	0.935458i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	17.9740	−	17.9740i	1.12119	−	1.12119i	0.129626	−	0.991563i	$-0.458622\pi$
$257$	17.9740	−	17.9740i	1.12119	−	1.12119i	0.991563	−	0.129626i	$-0.0413778\pi$
$258$		0			0
$259$	−0.682499	+	0.0814698i	−0.0424084	+	0.00506229i
$260$		0			0
$261$	−27.4992			−1.70216
$262$		0			0
$263$	−0.986652	+	0.986652i	−0.0608396	+	0.0608396i	−0.736872	−	0.676032i	$-0.763698\pi$
$263$	−0.986652	+	0.986652i	−0.0608396	+	0.0608396i	0.676032	+	0.736872i	$0.263698\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	22.0301	+	22.0301i	1.34822	+	1.34822i
$268$		0			0
$269$	−2.65510			−0.161884			−0.0809422	−	0.996719i	$-0.525793\pi$
$269$	−2.65510			−0.161884			−0.0809422	+	0.996719i	$0.525793\pi$
$270$		0			0
$271$		−	0.573473i		−	0.0348360i	−0.999848	−	0.0174180i	$-0.994455\pi$
$271$		−	0.573473i		−	0.0348360i	0.999848	−	0.0174180i	$-0.00554460\pi$
$272$		0			0
$273$	−12.2230	−	9.61609i	−0.739771	−	0.581992i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−6.98543	−	6.98543i	−0.419714	−	0.419714i	0.465391	−	0.885105i	$-0.345914\pi$
$277$	−6.98543	−	6.98543i	−0.419714	−	0.419714i	−0.885105	+	0.465391i	$0.845914\pi$
$278$		0			0
$279$	−62.2841			−3.72885
$280$		0			0
$281$	23.2936			1.38958			0.694789	−	0.719213i	$-0.255498\pi$
$281$	23.2936			1.38958			0.694789	+	0.719213i	$0.255498\pi$
$282$		0			0
$283$	−9.27105	−	9.27105i	−0.551107	−	0.551107i	0.375653	−	0.926760i	$-0.377418\pi$
$283$	−9.27105	−	9.27105i	−0.551107	−	0.551107i	−0.926760	+	0.375653i	$0.877418\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	7.93957	+	6.24621i	0.468658	+	0.368702i
$288$		0			0
$289$			8.17999i			0.481176i
$290$		0			0
$291$	−31.0701			−1.82136
$292$		0			0
$293$	11.3951	+	11.3951i	0.665707	+	0.665707i	0.956719	−	0.291012i	$-0.0939920\pi$
$293$	11.3951	+	11.3951i	0.665707	+	0.665707i	−0.291012	+	0.956719i	$0.593992\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−19.0554	+	19.0554i	−1.10571	+	1.10571i
$298$		0			0
$299$	−15.6846			−0.907066
$300$		0			0
$301$	2.59915	+	21.7740i	0.149813	+	1.25503i
$302$		0			0
$303$	−2.44129	+	2.44129i	−0.140249	+	0.140249i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−12.7022	+	12.7022i	−0.724953	+	0.724953i	−0.969610	−	0.244657i	$-0.921325\pi$
$307$	−12.7022	+	12.7022i	−0.724953	+	0.724953i	0.244657	+	0.969610i	$0.421325\pi$
$308$		0			0
$309$			6.80241i			0.386976i
$310$		0			0
$311$		−	12.2723i		−	0.695896i	−0.937514	−	0.347948i	$-0.886879\pi$
$311$		−	12.2723i		−	0.695896i	0.937514	−	0.347948i	$-0.113121\pi$
$312$		0			0
$313$	−11.9640	−	11.9640i	−0.676246	−	0.676246i	0.282903	−	0.959149i	$-0.408703\pi$
$313$	−11.9640	−	11.9640i	−0.676246	−	0.676246i	−0.959149	+	0.282903i	$0.908703\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	18.9944	+	18.9944i	1.06683	+	1.06683i	0.997600	+	0.0692338i	$0.0220554\pi$
$317$	18.9944	+	18.9944i	1.06683	+	1.06683i	0.0692338	+	0.997600i	$0.477945\pi$
$318$		0			0
$319$			11.0125i			0.616583i
$320$		0			0
$321$			0.630320i			0.0351811i
$322$		0			0
$323$	−9.32136	+	9.32136i	−0.518654	+	0.518654i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	14.1290	−	14.1290i	0.781337	−	0.781337i
$328$		0			0
$329$	−0.811611	−	6.79913i	−0.0447455	−	0.374848i
$330$		0			0
$331$	−23.8309			−1.30986			−0.654931	−	0.755689i	$-0.727302\pi$
$331$	−23.8309			−1.30986			−0.654931	+	0.755689i	$0.727302\pi$
$332$		0			0
$333$	1.17884	−	1.17884i	0.0645998	−	0.0645998i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−8.26895	−	8.26895i	−0.450439	−	0.450439i	0.445061	−	0.895500i	$-0.353182\pi$
$337$	−8.26895	−	8.26895i	−0.450439	−	0.450439i	−0.895500	+	0.445061i	$0.853182\pi$
$338$		0			0
$339$	32.5143			1.76593
$340$		0			0
$341$			24.9427i			1.35072i
$342$		0			0
$343$	−16.8422	−	7.70330i	−0.909392	−	0.415939i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−12.0104	−	12.0104i	−0.644754	−	0.644754i	0.306966	−	0.951720i	$-0.400686\pi$
$347$	−12.0104	−	12.0104i	−0.644754	−	0.644754i	−0.951720	+	0.306966i	$0.900686\pi$
$348$		0			0
$349$	13.0227			0.697092			0.348546	−	0.937292i	$-0.386676\pi$
$349$	13.0227			0.697092			0.348546	+	0.937292i	$0.386676\pi$
$350$		0			0
$351$	20.0867			1.07215
$352$		0			0
$353$	−9.48642	−	9.48642i	−0.504911	−	0.504911i	0.408049	−	0.912960i	$-0.366209\pi$
$353$	−9.48642	−	9.48642i	−0.504911	−	0.504911i	−0.912960	+	0.408049i	$0.866209\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−14.9090	+	18.9509i	−0.789070	+	1.00299i
$358$		0			0
$359$		−	9.36637i		−	0.494338i	−0.968972	−	0.247169i	$-0.920500\pi$
$359$		−	9.36637i		−	0.494338i	0.968972	−	0.247169i	$-0.0795003\pi$
$360$		0			0
$361$	0.702427			0.0369698
$362$		0			0
$363$	−9.53865	−	9.53865i	−0.500649	−	0.500649i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−1.22951	+	1.22951i	−0.0641798	+	0.0641798i	−0.738468	−	0.674288i	$-0.764451\pi$
$367$	−1.22951	+	1.22951i	−0.0641798	+	0.0641798i	0.674288	+	0.738468i	$0.264451\pi$
$368$		0			0
$369$	−24.5022			−1.27553
$370$		0			0
$371$	−1.05824	−	8.86524i	−0.0549412	−	0.460260i
$372$		0			0
$373$	6.68837	−	6.68837i	0.346311	−	0.346311i	−0.512423	−	0.858733i	$-0.671252\pi$
$373$	6.68837	−	6.68837i	0.346311	−	0.346311i	0.858733	+	0.512423i	$0.171252\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	5.80425	−	5.80425i	0.298934	−	0.298934i
$378$		0			0
$379$			0.0350675i			0.00180130i	1.00000		0.000900649i	$0.000286685\pi$
$379$			0.0350675i			0.00180130i	−1.00000		0.000900649i	$0.999713\pi$
$380$		0			0
$381$		−	29.4493i		−	1.50873i
$382$		0			0
$383$	−20.5450	−	20.5450i	−1.04980	−	1.04980i	−0.998693	−	0.0511048i	$-0.983726\pi$
$383$	−20.5450	−	20.5450i	−1.04980	−	1.04980i	−0.0511048	−	0.998693i	$-0.516274\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−37.6087	−	37.6087i	−1.91176	−	1.91176i
$388$		0			0
$389$		−	11.6510i		−	0.590730i	−0.955385	−	0.295365i	$-0.904559\pi$
$389$		−	11.6510i		−	0.590730i	0.955385	−	0.295365i	$-0.0954412\pi$
$390$		0			0
$391$			24.3179i			1.22981i
$392$		0			0
$393$	−18.1808	+	18.1808i	−0.917100	+	0.917100i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−4.22472	+	4.22472i	−0.212033	+	0.212033i	−0.805131	−	0.593098i	$-0.797905\pi$
$397$	−4.22472	+	4.22472i	−0.212033	+	0.212033i	0.593098	+	0.805131i	$0.297905\pi$
$398$		0			0
$399$	35.7846	−	4.27160i	1.79147	−	0.213848i
$400$		0			0
$401$	−4.26395			−0.212932			−0.106466	−	0.994316i	$-0.533953\pi$
$401$	−4.26395			−0.212932			−0.106466	+	0.994316i	$0.533953\pi$
$402$		0			0
$403$	13.1463	−	13.1463i	0.654863	−	0.654863i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.472084	−	0.472084i	−0.0234003	−	0.0234003i
$408$		0			0
$409$	−25.3610			−1.25402			−0.627011	−	0.779010i	$-0.715722\pi$
$409$	−25.3610			−1.25402			−0.627011	+	0.779010i	$0.715722\pi$
$410$		0			0
$411$		−	32.8521i		−	1.62047i
$412$		0			0
$413$	−10.3800	+	13.1940i	−0.510766	+	0.649235i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−24.3969	−	24.3969i	−1.19472	−	1.19472i
$418$		0			0
$419$	−0.597961			−0.0292123			−0.0146061	−	0.999893i	$-0.504649\pi$
$419$	−0.597961			−0.0292123			−0.0146061	+	0.999893i	$0.504649\pi$
$420$		0			0
$421$	−9.94725			−0.484799			−0.242400	−	0.970176i	$-0.577935\pi$
$421$	−9.94725			−0.484799			−0.242400	+	0.970176i	$0.577935\pi$
$422$		0			0
$423$	11.7437	+	11.7437i	0.570998	+	0.570998i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−17.9253	−	14.1022i	−0.867464	−	0.682451i
$428$		0			0
$429$		−	15.1061i		−	0.729329i
$430$		0			0
$431$	−3.29543			−0.158735			−0.0793677	−	0.996845i	$-0.525290\pi$
$431$	−3.29543			−0.158735			−0.0793677	+	0.996845i	$0.525290\pi$
$432$		0			0
$433$	14.8212	+	14.8212i	0.712260	+	0.712260i	0.967008	−	0.254747i	$-0.0819923\pi$
$433$	14.8212	+	14.8212i	0.712260	+	0.712260i	−0.254747	+	0.967008i	$0.581992\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	25.7002	−	25.7002i	1.22941	−	1.22941i
$438$		0			0
$439$	−3.93710			−0.187907			−0.0939537	−	0.995577i	$-0.529951\pi$
$439$	−3.93710			−0.187907			−0.0939537	+	0.995577i	$0.529951\pi$
$440$		0			0
$441$	43.6580	−	10.5735i	2.07895	−	0.503502i
$442$		0			0
$443$	−23.0246	+	23.0246i	−1.09393	+	1.09393i	−0.0988281	+	0.995105i	$0.531509\pi$
$443$	−23.0246	+	23.0246i	−1.09393	+	1.09393i	−0.995105	+	0.0988281i	$0.968491\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	39.0731	−	39.0731i	1.84810	−	1.84810i
$448$		0			0
$449$			9.44923i			0.445937i	0.974826	+	0.222968i	$0.0715747\pi$
$449$			9.44923i			0.445937i	−0.974826	+	0.222968i	$0.928425\pi$
$450$		0			0
$451$			9.81229i			0.462043i
$452$		0			0
$453$	26.3062	+	26.3062i	1.23597	+	1.23597i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	17.8997	+	17.8997i	0.837313	+	0.837313i	0.988505	−	0.151191i	$-0.0483110\pi$
$457$	17.8997	+	17.8997i	0.837313	+	0.837313i	−0.151191	+	0.988505i	$0.548311\pi$
$458$		0			0
$459$		−	31.1429i		−	1.45363i
$460$		0			0
$461$			8.91063i			0.415009i	0.978234	+	0.207505i	$0.0665342\pi$
$461$			8.91063i			0.415009i	−0.978234	+	0.207505i	$0.933466\pi$
$462$		0			0
$463$	−1.48151	+	1.48151i	−0.0688518	+	0.0688518i	−0.740694	−	0.671842i	$-0.765503\pi$
$463$	−1.48151	+	1.48151i	−0.0688518	+	0.0688518i	0.671842	+	0.740694i	$0.265503\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	0.836995	−	0.836995i	0.0387315	−	0.0387315i	−0.687476	−	0.726207i	$-0.741281\pi$
$467$	0.836995	−	0.836995i	0.0387315	−	0.0387315i	0.726207	+	0.687476i	$0.241281\pi$
$468$		0			0
$469$	−24.8518	+	2.96656i	−1.14755	+	0.136983i
$470$		0			0
$471$	−50.6737			−2.33492
$472$		0			0
$473$	−15.0610	+	15.0610i	−0.692507	+	0.692507i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	15.3123	+	15.3123i	0.701104	+	0.701104i
$478$		0			0
$479$	23.6142			1.07896			0.539479	−	0.841999i	$-0.318621\pi$
$479$	23.6142			1.07896			0.539479	+	0.841999i	$0.318621\pi$
$480$		0			0
$481$			0.497632i			0.0226901i
$482$		0			0
$483$	41.1061	−	52.2500i	1.87039	−	2.37746i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−22.7931	−	22.7931i	−1.03285	−	1.03285i	−0.999442	−	0.0334131i	$-0.989362\pi$
$487$	−22.7931	−	22.7931i	−1.03285	−	1.03285i	−0.0334131	−	0.999442i	$-0.510638\pi$
$488$		0			0
$489$	−45.6626			−2.06493
$490$		0			0
$491$	5.02524			0.226786			0.113393	−	0.993550i	$-0.463828\pi$
$491$	5.02524			0.226786			0.113393	+	0.993550i	$0.463828\pi$
$492$		0			0
$493$	−8.99907	−	8.99907i	−0.405298	−	0.405298i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−9.88992	+	12.5711i	−0.443623	+	0.563890i
$498$		0			0
$499$			10.9254i			0.489089i	0.969638	+	0.244544i	$0.0786384\pi$
$499$			10.9254i			0.489089i	−0.969638	+	0.244544i	$0.921362\pi$
$500$		0			0
$501$	−39.3313			−1.75719
$502$		0			0
$503$	13.4112	+	13.4112i	0.597974	+	0.597974i	0.939773	−	0.341799i	$-0.111036\pi$
$503$	13.4112	+	13.4112i	0.597974	+	0.597974i	−0.341799	+	0.939773i	$0.611036\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	20.2472	−	20.2472i	0.899211	−	0.899211i
$508$		0			0
$509$	40.1376			1.77907			0.889533	−	0.456871i	$-0.151030\pi$
$509$	40.1376			1.77907			0.889533	+	0.456871i	$0.151030\pi$
$510$		0			0
$511$	−7.02049	+	0.838034i	−0.310568	+	0.0370724i
$512$		0			0
$513$	−32.9132	+	32.9132i	−1.45315	+	1.45315i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	4.70295	−	4.70295i	0.206835	−	0.206835i
$518$		0			0
$519$			43.3691i			1.90369i
$520$		0			0
$521$			19.2753i			0.844467i	0.906487	+	0.422234i	$0.138754\pi$
$521$			19.2753i			0.844467i	−0.906487	+	0.422234i	$0.861246\pi$
$522$		0			0
$523$	10.6573	+	10.6573i	0.466013	+	0.466013i	0.900620	−	0.434607i	$-0.143113\pi$
$523$	10.6573	+	10.6573i	0.466013	+	0.466013i	−0.434607	+	0.900620i	$0.643113\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−20.3823	−	20.3823i	−0.887869	−	0.887869i
$528$		0			0
$529$		−	44.0474i		−	1.91511i
$530$		0			0
$531$		−	40.7178i		−	1.76700i
$532$		0			0
$533$	5.17166	−	5.17166i	0.224009	−	0.224009i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−32.2655	+	32.2655i	−1.39236	+	1.39236i
$538$		0			0
$539$	−4.23435	−	17.4835i	−0.182386	−	0.753069i
$540$		0			0
$541$	12.8503			0.552479			0.276240	−	0.961089i	$-0.410912\pi$
$541$	12.8503			0.552479			0.276240	+	0.961089i	$0.410912\pi$
$542$		0			0
$543$	−30.8335	+	30.8335i	−1.32319	+	1.32319i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	26.5300	+	26.5300i	1.13434	+	1.13434i	0.989447	+	0.144895i	$0.0462844\pi$
$547$	26.5300	+	26.5300i	1.13434	+	1.13434i	0.144895	+	0.989447i	$0.453716\pi$
$548$		0			0
$549$	55.3188			2.36095
$550$		0			0
$551$			19.0212i			0.810330i
$552$		0			0
$553$	−25.4633	−	20.0325i	−1.08281	−	0.851868i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	25.9969	+	25.9969i	1.10152	+	1.10152i	0.994227	+	0.107298i	$0.0342198\pi$
$557$	25.9969	+	25.9969i	1.10152	+	1.10152i	0.107298	+	0.994227i	$0.465780\pi$
$558$		0			0
$559$	15.8761			0.671488
$560$		0			0
$561$	−23.4209			−0.988830
$562$		0			0
$563$	−1.11717	−	1.11717i	−0.0470833	−	0.0470833i	0.683173	−	0.730256i	$-0.260599\pi$
$563$	−1.11717	−	1.11717i	−0.0470833	−	0.0470833i	−0.730256	+	0.683173i	$0.760599\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−21.1496	+	26.8833i	−0.888199	+	1.12899i
$568$		0			0
$569$		−	22.9125i		−	0.960543i	−0.877120	−	0.480271i	$-0.840538\pi$
$569$		−	22.9125i		−	0.960543i	0.877120	−	0.480271i	$-0.159462\pi$
$570$		0			0
$571$	33.1839			1.38870			0.694351	−	0.719636i	$-0.255692\pi$
$571$	33.1839			1.38870			0.694351	+	0.719636i	$0.255692\pi$
$572$		0			0
$573$	−2.25982	−	2.25982i	−0.0944052	−	0.0944052i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−29.4941	+	29.4941i	−1.22786	+	1.22786i	−0.263084	+	0.964773i	$0.584740\pi$
$577$	−29.4941	+	29.4941i	−1.22786	+	1.22786i	−0.964773	+	0.263084i	$0.915260\pi$
$578$		0			0
$579$	−0.299563			−0.0124494
$580$		0			0
$581$	7.76312	−	0.926682i	0.322069	−	0.0384452i
$582$		0			0
$583$	6.13207	−	6.13207i	0.253965	−	0.253965i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−14.6733	+	14.6733i	−0.605634	+	0.605634i	−0.941802	−	0.336168i	$-0.890869\pi$
$587$	−14.6733	+	14.6733i	−0.605634	+	0.605634i	0.336168	+	0.941802i	$0.390869\pi$
$588$		0			0
$589$			43.0819i			1.77516i
$590$		0			0
$591$		−	55.5263i		−	2.28405i
$592$		0			0
$593$	−21.3914	−	21.3914i	−0.878439	−	0.878439i	0.114934	−	0.993373i	$-0.463334\pi$
$593$	−21.3914	−	21.3914i	−0.878439	−	0.878439i	−0.993373	+	0.114934i	$0.963334\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	8.89220	+	8.89220i	0.363933	+	0.363933i
$598$		0			0
$599$			13.4975i			0.551494i	0.961230	+	0.275747i	$0.0889252\pi$
$599$			13.4975i			0.551494i	−0.961230	+	0.275747i	$0.911075\pi$
$600$		0			0
$601$			36.3870i			1.48426i	0.670258	+	0.742128i	$0.266183\pi$
$601$			36.3870i			1.48426i	−0.670258	+	0.742128i	$0.733817\pi$
$602$		0			0
$603$	42.9249	−	42.9249i	1.74804	−	1.74804i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−29.3687	+	29.3687i	−1.19204	+	1.19204i	−0.215545	+	0.976494i	$0.569153\pi$
$607$	−29.3687	+	29.3687i	−1.19204	+	1.19204i	−0.976494	+	0.215545i	$0.930847\pi$
$608$		0			0
$609$	4.12391	+	34.5473i	0.167109	+	1.39993i
$610$		0			0
$611$	−4.95747			−0.200558
$612$		0			0
$613$	20.4722	−	20.4722i	0.826863	−	0.826863i	−0.160218	−	0.987082i	$-0.551220\pi$
$613$	20.4722	−	20.4722i	0.826863	−	0.826863i	0.987082	+	0.160218i	$0.0512198\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	5.88024	+	5.88024i	0.236729	+	0.236729i	0.815494	−	0.578765i	$-0.196465\pi$
$617$	5.88024	+	5.88024i	0.236729	+	0.236729i	−0.578765	+	0.815494i	$0.696465\pi$
$618$		0			0
$619$	−22.3760			−0.899368			−0.449684	−	0.893188i	$-0.648463\pi$
$619$	−22.3760			−0.899368			−0.449684	+	0.893188i	$0.648463\pi$
$620$		0			0
$621$			85.8650i			3.44564i
$622$		0			0
$623$	16.6084	−	21.1109i	0.665401	−	0.845792i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	24.7522	+	24.7522i	0.988507	+	0.988507i
$628$		0			0
$629$	0.771543			0.0307634
$630$		0			0
$631$	−42.0404			−1.67360			−0.836802	−	0.547506i	$-0.815577\pi$
$631$	−42.0404			−1.67360			−0.836802	+	0.547506i	$0.815577\pi$
$632$		0			0
$633$	62.3157	+	62.3157i	2.47683	+	2.47683i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−6.98311	+	11.4466i	−0.276681	+	0.453531i
$638$		0			0
$639$		−	38.7954i		−	1.53472i
$640$		0			0
$641$	−1.69064			−0.0667764			−0.0333882	−	0.999442i	$-0.510630\pi$
$641$	−1.69064			−0.0667764			−0.0333882	+	0.999442i	$0.510630\pi$
$642$		0			0
$643$	0.492457	+	0.492457i	0.0194206	+	0.0194206i	0.716750	−	0.697330i	$-0.245629\pi$
$643$	0.492457	+	0.492457i	0.0194206	+	0.0194206i	−0.697330	+	0.716750i	$0.745629\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	6.32851	−	6.32851i	0.248799	−	0.248799i	−0.571678	−	0.820478i	$-0.693707\pi$
$647$	6.32851	−	6.32851i	0.248799	−	0.248799i	0.820478	+	0.571678i	$0.193707\pi$
$648$		0			0
$649$	−16.3061			−0.640071
$650$		0			0
$651$	9.34040	+	78.2476i	0.366079	+	3.06677i
$652$		0			0
$653$	−24.3667	+	24.3667i	−0.953543	+	0.953543i	−0.998968	−	0.0454247i	$-0.985536\pi$
$653$	−24.3667	+	24.3667i	−0.953543	+	0.953543i	0.0454247	+	0.998968i	$0.485536\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	12.1260	−	12.1260i	0.473081	−	0.473081i
$658$		0			0
$659$			10.7004i			0.416829i	0.978041	+	0.208414i	$0.0668303\pi$
$659$			10.7004i			0.416829i	−0.978041	+	0.208414i	$0.933170\pi$
$660$		0			0
$661$		−	34.1408i		−	1.32792i	−0.747766	−	0.663962i	$-0.768874\pi$
$661$		−	34.1408i		−	1.32792i	0.747766	−	0.663962i	$-0.231126\pi$
$662$		0			0
$663$	12.3442	+	12.3442i	0.479409	+	0.479409i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	24.8116	+	24.8116i	0.960707	+	0.960707i
$668$		0			0
$669$		−	16.0319i		−	0.619829i
$670$		0			0
$671$		−	22.1533i		−	0.855220i
$672$		0			0
$673$	11.2267	−	11.2267i	0.432758	−	0.432758i	−0.456808	−	0.889566i	$-0.651007\pi$
$673$	11.2267	−	11.2267i	0.432758	−	0.432758i	0.889566	+	0.456808i	$0.151007\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−2.84843	+	2.84843i	−0.109474	+	0.109474i	−0.759722	−	0.650248i	$-0.774665\pi$
$677$	−2.84843	+	2.84843i	−0.109474	+	0.109474i	0.650248	+	0.759722i	$0.274665\pi$
$678$		0			0
$679$	3.17508	+	26.5987i	0.121848	+	1.02076i
$680$		0			0
$681$	34.1017			1.30678
$682$		0			0
$683$	−22.5165	+	22.5165i	−0.861571	+	0.861571i	−0.991521	−	0.129950i	$-0.958518\pi$
$683$	−22.5165	+	22.5165i	−0.861571	+	0.861571i	0.129950	+	0.991521i	$0.458518\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−20.5820	−	20.5820i	−0.785253	−	0.785253i
$688$		0			0
$689$	−6.46394			−0.246256
$690$		0			0
$691$			7.28794i			0.277246i	0.990345	+	0.138623i	$0.0442677\pi$
$691$			7.28794i			0.277246i	−0.990345	+	0.138623i	$0.955732\pi$
$692$		0			0
$693$	34.2915	+	26.9778i	1.30263	+	1.02480i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−8.01828	−	8.01828i	−0.303714	−	0.303714i
$698$		0			0
$699$	59.0326			2.23282
$700$		0			0
$701$	8.29057			0.313130			0.156565	−	0.987668i	$-0.449958\pi$
$701$	8.29057			0.313130			0.156565	+	0.987668i	$0.449958\pi$
$702$		0			0
$703$	−0.815399	−	0.815399i	−0.0307534	−	0.0307534i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	2.33943	+	1.84048i	0.0879833	+	0.0692182i
$708$		0			0
$709$			15.8960i			0.596987i	0.954412	+	0.298493i	$0.0964841\pi$
$709$			15.8960i			0.596987i	−0.954412	+	0.298493i	$0.903516\pi$
$710$		0			0
$711$	78.5819			2.94705
$712$		0			0
$713$	56.1967	+	56.1967i	2.10458	+	2.10458i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	40.7036	−	40.7036i	1.52011	−	1.52011i
$718$		0			0
$719$	−41.3180			−1.54090			−0.770450	−	0.637500i	$-0.779969\pi$
$719$	−41.3180			−1.54090			−0.770450	+	0.637500i	$0.779969\pi$
$720$		0			0
$721$	5.82344	−	0.695143i	0.216876	−	0.0258885i
$722$		0			0
$723$	6.04096	−	6.04096i	0.224666	−	0.224666i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	2.27196	−	2.27196i	0.0842625	−	0.0842625i	−0.663719	−	0.747982i	$-0.731023\pi$
$727$	2.27196	−	2.27196i	0.0842625	−	0.0842625i	0.747982	+	0.663719i	$0.231023\pi$
$728$		0			0
$729$			13.5758i			0.502809i
$730$		0			0
$731$		−	24.6147i		−	0.910409i
$732$		0			0
$733$	−4.64097	−	4.64097i	−0.171418	−	0.171418i	0.616184	−	0.787602i	$-0.288678\pi$
$733$	−4.64097	−	4.64097i	−0.171418	−	0.171418i	−0.787602	+	0.616184i	$0.788678\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−17.1900	−	17.1900i	−0.633201	−	0.633201i
$738$		0			0
$739$			2.48628i			0.0914592i	0.998954	+	0.0457296i	$0.0145613\pi$
$739$			2.48628i			0.0914592i	−0.998954	+	0.0457296i	$0.985439\pi$
$740$		0			0
$741$		−	26.0917i		−	0.958504i
$742$		0			0
$743$	−11.7230	+	11.7230i	−0.430075	+	0.430075i	−0.888654	−	0.458579i	$-0.848359\pi$
$743$	−11.7230	+	11.7230i	−0.430075	+	0.430075i	0.458579	+	0.888654i	$0.348359\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−13.4087	+	13.4087i	−0.490600	+	0.490600i
$748$		0			0
$749$	0.539608	−	0.0644129i	0.0197168	−	0.00235359i
$750$		0			0
$751$	−18.4627			−0.673714			−0.336857	−	0.941556i	$-0.609364\pi$
$751$	−18.4627			−0.673714			−0.336857	+	0.941556i	$0.609364\pi$
$752$		0			0
$753$	61.5308	−	61.5308i	2.24231	−	2.24231i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	2.72346	+	2.72346i	0.0989857	+	0.0989857i	0.754865	−	0.655880i	$-0.227702\pi$
$757$	2.72346	+	2.72346i	0.0989857	+	0.0989857i	−0.655880	+	0.754865i	$0.727702\pi$
$758$		0			0
$759$	64.5743			2.34390
$760$		0			0
$761$		−	13.4733i		−	0.488406i	−0.969724	−	0.244203i	$-0.921474\pi$
$761$		−	13.4733i		−	0.488406i	0.969724	−	0.244203i	$-0.0785263\pi$
$762$		0			0
$763$	−13.5395	−	10.6518i	−0.490163	−	0.385621i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	8.59429	+	8.59429i	0.310322	+	0.310322i
$768$		0			0
$769$	13.2864			0.479121			0.239561	−	0.970881i	$-0.422997\pi$
$769$	13.2864			0.479121			0.239561	+	0.970881i	$0.422997\pi$
$770$		0			0
$771$	78.0046			2.80927
$772$		0			0
$773$	−0.232304	−	0.232304i	−0.00835541	−	0.00835541i	0.702917	−	0.711272i	$-0.251881\pi$
$773$	−0.232304	−	0.232304i	−0.00835541	−	0.00835541i	−0.711272	+	0.702917i	$0.751881\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−1.65776	−	1.30419i	−0.0594717	−	0.0467875i
$778$		0			0
$779$			16.9481i			0.607229i
$780$		0			0
$781$	−15.5362			−0.555931
$782$		0			0
$783$	−31.7752	−	31.7752i	−1.13555	−	1.13555i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	32.0984	−	32.0984i	1.14419	−	1.14419i	0.156509	−	0.987676i	$-0.449976\pi$
$787$	32.0984	−	32.0984i	1.14419	−	1.14419i	0.987676	−	0.156509i	$-0.0500241\pi$
$788$		0			0
$789$	−4.28192			−0.152441
$790$		0			0
$791$	−3.32266	−	27.8350i	−0.118140	−	0.989699i
$792$		0			0
$793$	−11.6761	+	11.6761i	−0.414631	+	0.414631i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−31.3730	+	31.3730i	−1.11129	+	1.11129i	−0.118313	+	0.992976i	$0.537749\pi$
$797$	−31.3730	+	31.3730i	−1.11129	+	1.11129i	−0.992976	+	0.118313i	$0.962251\pi$
$798$		0			0
$799$			7.68619i			0.271918i
$800$		0			0
$801$			65.1501i			2.30197i
$802$		0			0
$803$	−4.85606	−	4.85606i	−0.171367	−	0.171367i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−5.76138	−	5.76138i	−0.202810	−	0.202810i
$808$		0			0
$809$			43.8681i			1.54232i	0.636642	+	0.771160i	$0.280323\pi$
$809$			43.8681i			1.54232i	−0.636642	+	0.771160i	$0.719677\pi$
$810$		0			0
$811$			20.3680i			0.715217i	0.933872	+	0.357609i	$0.116408\pi$
$811$			20.3680i			0.715217i	−0.933872	+	0.357609i	$0.883592\pi$
$812$		0			0
$813$	1.24439	−	1.24439i	0.0436428	−	0.0436428i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−26.0139	+	26.0139i	−0.910112	+	0.910112i
$818$		0			0
$819$	−3.85476	−	32.2926i	−0.134696	−	1.12839i
$820$		0			0
$821$	2.15818			0.0753209			0.0376604	−	0.999291i	$-0.488009\pi$
$821$	2.15818			0.0753209			0.0376604	+	0.999291i	$0.488009\pi$
$822$		0			0
$823$	−24.0905	+	24.0905i	−0.839741	+	0.839741i	−0.988825	−	0.149083i	$-0.952368\pi$
$823$	−24.0905	+	24.0905i	−0.839741	+	0.839741i	0.149083	+	0.988825i	$0.452368\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	24.0992	+	24.0992i	0.838011	+	0.838011i	0.988597	−	0.150586i	$-0.0481161\pi$
$827$	24.0992	+	24.0992i	0.838011	+	0.838011i	−0.150586	+	0.988597i	$0.548116\pi$
$828$		0			0
$829$	26.8499			0.932536			0.466268	−	0.884643i	$-0.345598\pi$
$829$	26.8499			0.932536			0.466268	+	0.884643i	$0.345598\pi$
$830$		0			0
$831$		−	30.3157i		−	1.05164i
$832$		0			0
$833$	17.7471	+	10.8268i	0.614902	+	0.375126i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−71.9689	−	71.9689i	−2.48761	−	2.48761i
$838$		0			0
$839$	16.1545			0.557717			0.278858	−	0.960332i	$-0.410044\pi$
$839$	16.1545			0.557717			0.278858	+	0.960332i	$0.410044\pi$
$840$		0			0
$841$	10.6365			0.366775
$842$		0			0
$843$	50.5454	+	50.5454i	1.74087	+	1.74087i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−7.19113	+	9.14066i	−0.247090	+	0.314077i
$848$		0			0
$849$		−	40.2350i		−	1.38086i
$850$		0			0
$851$	−2.12724			−0.0729208
$852$		0			0
$853$	2.00773	+	2.00773i	0.0687435	+	0.0687435i	0.740643	−	0.671899i	$-0.234521\pi$
$853$	2.00773	+	2.00773i	0.0687435	+	0.0687435i	−0.671899	+	0.740643i	$0.734521\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	23.9532	−	23.9532i	0.818225	−	0.818225i	−0.167626	−	0.985851i	$-0.553610\pi$
$857$	23.9532	−	23.9532i	0.818225	−	0.818225i	0.985851	+	0.167626i	$0.0536101\pi$
$858$		0			0
$859$	28.0499			0.957049			0.478525	−	0.878074i	$-0.341172\pi$
$859$	28.0499			0.957049			0.478525	+	0.878074i	$0.341172\pi$
$860$		0			0
$861$	3.67445	+	30.7821i	0.125225	+	1.04905i
$862$		0			0
$863$	−0.191578	+	0.191578i	−0.00652139	+	0.00652139i	−0.710360	−	0.703839i	$-0.751468\pi$
$863$	−0.191578	+	0.191578i	−0.00652139	+	0.00652139i	0.703839	+	0.710360i	$0.251468\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−17.7500	+	17.7500i	−0.602821	+	0.602821i
$868$		0			0
$869$		−	31.4694i		−	1.06753i
$870$		0			0
$871$			18.1203i			0.613982i
$872$		0			0
$873$	−45.9421	−	45.9421i	−1.55490	−	1.55490i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−41.2975	−	41.2975i	−1.39452	−	1.39452i	−0.814863	−	0.579653i	$-0.803188\pi$
$877$	−41.2975	−	41.2975i	−1.39452	−	1.39452i	−0.579653	−	0.814863i	$-0.696812\pi$
$878$		0			0
$879$			49.4529i			1.66801i
$880$		0			0
$881$		−	24.7259i		−	0.833037i	−0.909127	−	0.416519i	$-0.863250\pi$
$881$		−	24.7259i		−	0.833037i	0.909127	−	0.416519i	$-0.136750\pi$
$882$		0			0
$883$	−12.2632	+	12.2632i	−0.412688	+	0.412688i	−0.882674	−	0.469986i	$-0.844259\pi$
$883$	−12.2632	+	12.2632i	−0.412688	+	0.412688i	0.469986	+	0.882674i	$0.344259\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	14.0519	−	14.0519i	0.471816	−	0.471816i	−0.430686	−	0.902502i	$-0.641728\pi$
$887$	14.0519	−	14.0519i	0.471816	−	0.471816i	0.902502	+	0.430686i	$0.141728\pi$
$888$		0			0
$889$	−25.2111	+	3.00944i	−0.845553	+	0.100933i
$890$		0			0
$891$	−33.2243			−1.11305
$892$		0			0
$893$	8.12309	−	8.12309i	0.271829	−	0.271829i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−34.0345	−	34.0345i	−1.13638	−	1.13638i
$898$		0			0
$899$	−41.5923			−1.38718
$900$		0			0
$901$			10.0219i			0.333876i
$902$		0			0
$903$	−41.6079	+	52.8879i	−1.38463	+	1.76000i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	30.9592	+	30.9592i	1.02798	+	1.02798i	0.999597	+	0.0283860i	$0.00903674\pi$
$907$	30.9592	+	30.9592i	1.02798	+	1.02798i	0.0283860	+	0.999597i	$0.490963\pi$
$908$		0			0
$909$	−7.21967			−0.239461
$910$		0			0
$911$	22.1629			0.734289			0.367145	−	0.930164i	$-0.380335\pi$
$911$	22.1629			0.734289			0.367145	+	0.930164i	$0.380335\pi$
$912$		0			0
$913$	5.36974	+	5.36974i	0.177712	+	0.177712i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	17.4222	+	13.7064i	0.575332	+	0.452625i
$918$		0			0
$919$			5.60542i			0.184906i	0.995717	+	0.0924529i	$0.0294708\pi$
$919$			5.60542i			0.184906i	−0.995717	+	0.0924529i	$0.970529\pi$
$920$		0			0
$921$	−55.1257			−1.81645
$922$		0			0
$923$	8.18853	+	8.18853i	0.269529	+	0.269529i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−10.0584	+	10.0584i	−0.330363	+	0.330363i
$928$		0			0
$929$	29.8751			0.980170			0.490085	−	0.871675i	$-0.336966\pi$
$929$	29.8751			0.980170			0.490085	+	0.871675i	$0.336966\pi$
$930$		0			0
$931$	−7.31371	−	30.1982i	−0.239697	−	0.989705i
$932$		0			0
$933$	26.6299	−	26.6299i	0.871824	−	0.871824i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−34.6529	+	34.6529i	−1.13206	+	1.13206i	−0.142226	+	0.989834i	$0.545426\pi$
$937$	−34.6529	+	34.6529i	−1.13206	+	1.13206i	−0.989834	+	0.142226i	$0.954574\pi$
$938$		0			0
$939$		−	51.9220i		−	1.69441i
$940$		0			0
$941$		−	21.6170i		−	0.704693i	−0.935870	−	0.352346i	$-0.885384\pi$
$941$		−	21.6170i		−	0.704693i	0.935870	−	0.352346i	$-0.114616\pi$
$942$		0			0
$943$	22.1074	+	22.1074i	0.719916	+	0.719916i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−7.95185	−	7.95185i	−0.258400	−	0.258400i	0.566003	−	0.824403i	$-0.308489\pi$
$947$	−7.95185	−	7.95185i	−0.258400	−	0.258400i	−0.824403	+	0.566003i	$0.808489\pi$
$948$		0			0
$949$			5.11887i			0.166165i
$950$		0			0
$951$			82.4331i			2.67308i
$952$		0			0
$953$	12.7397	−	12.7397i	0.412678	−	0.412678i	−0.469992	−	0.882671i	$-0.655743\pi$
$953$	12.7397	−	12.7397i	0.412678	−	0.412678i	0.882671	+	0.469992i	$0.155743\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−23.8964	+	23.8964i	−0.772459	+	0.772459i
$958$		0			0
$959$	−28.1241	+	3.35717i	−0.908176	+	0.108409i
$960$		0			0
$961$	−63.2040			−2.03884
$962$		0			0
$963$	−0.932029	+	0.932029i	−0.0300342	+	0.0300342i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−11.8492	−	11.8492i	−0.381045	−	0.381045i	0.490434	−	0.871478i	$-0.336838\pi$
$967$	−11.8492	−	11.8492i	−0.381045	−	0.381045i	−0.871478	+	0.490434i	$0.836838\pi$
$968$		0			0
$969$	−40.4533			−1.29955
$970$		0			0
$971$			48.5371i			1.55763i	0.627255	+	0.778814i	$0.284179\pi$
$971$			48.5371i			1.55763i	−0.627255	+	0.778814i	$0.715821\pi$
$972$		0			0
$973$	−18.3927	+	23.3790i	−0.589642	+	0.749495i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	18.9303	+	18.9303i	0.605635	+	0.605635i	0.941802	−	0.336167i	$-0.109131\pi$
$977$	18.9303	+	18.9303i	0.605635	+	0.605635i	−0.336167	+	0.941802i	$0.609131\pi$
$978$		0			0
$979$	26.0904			0.833854
$980$		0			0
$981$	41.7840			1.33406
$982$		0			0
$983$	7.97683	+	7.97683i	0.254421	+	0.254421i	0.822781	−	0.568359i	$-0.192422\pi$
$983$	7.97683	+	7.97683i	0.254421	+	0.254421i	−0.568359	+	0.822781i	$0.692422\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	12.9925	−	16.5147i	0.413555	−	0.525670i
$988$		0			0
$989$			67.8660i			2.15801i
$990$		0			0
$991$	−49.6706			−1.57784			−0.788920	−	0.614496i	$-0.789359\pi$
$991$	−49.6706			−1.57784			−0.788920	+	0.614496i	$0.789359\pi$
$992$		0			0
$993$	−51.7112	−	51.7112i	−1.64100	−	1.64100i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	12.4002	−	12.4002i	0.392718	−	0.392718i	−0.482937	−	0.875655i	$-0.660430\pi$
$997$	12.4002	−	12.4002i	0.392718	−	0.392718i	0.875655	+	0.482937i	$0.160430\pi$
$998$		0			0
$999$	2.72427			0.0861922

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1400.2.x.b.657.12		24
5.2	odd	4		280.2.x.a.153.12	yes	24
5.3	odd	4	inner	1400.2.x.b.993.1		24
5.4	even	2		280.2.x.a.97.1	✓	24
7.6	odd	2	inner	1400.2.x.b.657.1		24
20.7	even	4		560.2.bj.d.433.1		24
20.19	odd	2		560.2.bj.d.97.12		24
35.13	even	4	inner	1400.2.x.b.993.12		24
35.27	even	4		280.2.x.a.153.1	yes	24
35.34	odd	2		280.2.x.a.97.12	yes	24
140.27	odd	4		560.2.bj.d.433.12		24
140.139	even	2		560.2.bj.d.97.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.x.a.97.1	✓	24	5.4	even	2
280.2.x.a.97.12	yes	24	35.34	odd	2
280.2.x.a.153.1	yes	24	35.27	even	4
280.2.x.a.153.12	yes	24	5.2	odd	4
560.2.bj.d.97.1		24	140.139	even	2
560.2.bj.d.97.12		24	20.19	odd	2
560.2.bj.d.433.1		24	20.7	even	4
560.2.bj.d.433.12		24	140.27	odd	4
1400.2.x.b.657.1		24	7.6	odd	2	inner
1400.2.x.b.657.12		24	1.1	even	1	trivial
1400.2.x.b.993.1		24	5.3	odd	4	inner
1400.2.x.b.993.12		24	35.13	even	4	inner

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:	\( N \)	\(=\)	\( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1400.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.16993 + 2.16993i) q^{3} +(1.63589 - 2.07939i) q^{7} +6.41716i q^{9} +O(q^{10})\)	\(q+(2.16993 + 2.16993i) q^{3} +(1.63589 - 2.07939i) q^{7} +6.41716i q^{9} +2.56986 q^{11} +(-1.35447 - 1.35447i) q^{13} +(-2.10000 + 2.10000i) q^{17} +4.43874 q^{19} +(8.06189 - 0.962346i) q^{21} +(5.78997 - 5.78997i) q^{23} +(-7.41498 + 7.41498i) q^{27} +4.28527i q^{29} +9.70587i q^{31} +(5.57640 + 5.57640i) q^{33} +(-0.183701 - 0.183701i) q^{37} -5.87819i q^{39} +3.81823i q^{41} +(-5.86065 + 5.86065i) q^{43} +(1.83004 - 1.83004i) q^{47} +(-1.64770 - 6.80331i) q^{49} -9.11369 q^{51} +(2.38616 - 2.38616i) q^{53} +(9.63174 + 9.63174i) q^{57} -6.34515 q^{59} -8.62046i q^{61} +(13.3438 + 10.4978i) q^{63} +(-6.68908 - 6.68908i) q^{67} +25.1276 q^{69} -6.04557 q^{71} +(-1.88962 - 1.88962i) q^{73} +(4.20401 - 5.34372i) q^{77} -12.2456i q^{79} -12.9285 q^{81} +(2.08951 + 2.08951i) q^{83} +(-9.29871 + 9.29871i) q^{87} +10.1525 q^{89} +(-5.03222 + 0.600696i) q^{91} +(-21.0610 + 21.0610i) q^{93} +(-7.15926 + 7.15926i) q^{97} +16.4912i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{7}+O(q^{10}) \) 24 * q - 4 * q^7	\( 24 q - 4 q^{7} + 8 q^{11} + 16 q^{21} + 32 q^{23} + 8 q^{37} - 16 q^{43} - 24 q^{51} + 16 q^{53} - 20 q^{63} + 32 q^{67} - 32 q^{71} + 40 q^{77} - 72 q^{81} - 64 q^{91} - 72 q^{93}+O(q^{100}) \) 24 * q - 4 * q^7 + 8 * q^11 + 16 * q^21 + 32 * q^23 + 8 * q^37 - 16 * q^43 - 24 * q^51 + 16 * q^53 - 20 * q^63 + 32 * q^67 - 32 * q^71 + 40 * q^77 - 72 * q^81 - 64 * q^91 - 72 * q^93

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