LMFDB - Embedded newform 1400.2.x.b.993.8

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			993.8
Character	$\chi$	$=$	1400.993
Dual form			1400.2.x.b.657.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.730185 - 0.730185i) q^{3} +(-2.41329 - 1.08445i) q^{7} +1.93366i q^{9} +O(q^{10})$	$q+(0.730185 - 0.730185i) q^{3} +(-2.41329 - 1.08445i) q^{7} +1.93366i q^{9} +5.95977 q^{11} +(0.921623 - 0.921623i) q^{13} +(-2.02728 - 2.02728i) q^{17} +3.29475 q^{19} +(-2.55400 + 0.970294i) q^{21} +(-0.0544054 - 0.0544054i) q^{23} +(3.60248 + 3.60248i) q^{27} -3.78901i q^{29} +4.88150i q^{31} +(4.35174 - 4.35174i) q^{33} +(3.20809 - 3.20809i) q^{37} -1.34591i q^{39} -10.6672i q^{41} +(1.60483 + 1.60483i) q^{43} +(-2.64854 - 2.64854i) q^{47} +(4.64792 + 5.23420i) q^{49} -2.96059 q^{51} +(9.16786 + 9.16786i) q^{53} +(2.40577 - 2.40577i) q^{57} +13.3231 q^{59} -11.2091i q^{61} +(2.09697 - 4.66648i) q^{63} +(6.43325 - 6.43325i) q^{67} -0.0794520 q^{69} -8.51221 q^{71} +(8.66633 - 8.66633i) q^{73} +(-14.3826 - 6.46310i) q^{77} -1.76209i q^{79} -0.540019 q^{81} +(2.36897 - 2.36897i) q^{83} +(-2.76668 - 2.76668i) q^{87} -9.73989 q^{89} +(-3.22360 + 1.22468i) q^{91} +(3.56440 + 3.56440i) q^{93} +(2.05040 + 2.05040i) q^{97} +11.5242i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times$.

$n$	$351$	$701$	$801$	$1177$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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
$3$	0.730185	−	0.730185i	0.421573	−	0.421573i	−0.464172	−	0.885745i	$-0.653648\pi$
$3$	0.730185	−	0.730185i	0.421573	−	0.421573i	0.885745	+	0.464172i	$0.153648\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.41329	−	1.08445i	−0.912137	−	0.409885i
$7$	−2.41329	−	1.08445i	−0.912137	−	0.409885i
$8$		0			0
$9$			1.93366i			0.644553i
$10$		0			0
$11$	5.95977			1.79694			0.898470	−	0.439036i	$-0.144680\pi$
$11$	5.95977			1.79694			0.898470	+	0.439036i	$0.144680\pi$
$12$		0			0
$13$	0.921623	−	0.921623i	0.255612	−	0.255612i	−0.567655	−	0.823267i	$-0.692149\pi$
$13$	0.921623	−	0.921623i	0.255612	−	0.255612i	0.823267	+	0.567655i	$0.192149\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.02728	−	2.02728i	−0.491689	−	0.491689i	0.417149	−	0.908838i	$-0.363029\pi$
$17$	−2.02728	−	2.02728i	−0.491689	−	0.491689i	−0.908838	+	0.417149i	$0.863029\pi$
$18$		0			0
$19$	3.29475			0.755867			0.377933	−	0.925833i	$-0.376635\pi$
$19$	3.29475			0.755867			0.377933	+	0.925833i	$0.376635\pi$
$20$		0			0
$21$	−2.55400	+	0.970294i	−0.557328	+	0.211736i
$22$		0			0
$23$	−0.0544054	−	0.0544054i	−0.0113443	−	0.0113443i	0.701412	−	0.712756i	$-0.252553\pi$
$23$	−0.0544054	−	0.0544054i	−0.0113443	−	0.0113443i	−0.712756	+	0.701412i	$0.752553\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	3.60248	+	3.60248i	0.693298	+	0.693298i
$28$		0			0
$29$		−	3.78901i		−	0.703602i	−0.936075	−	0.351801i	$-0.885569\pi$
$29$		−	3.78901i		−	0.703602i	0.936075	−	0.351801i	$-0.114431\pi$
$30$		0			0
$31$			4.88150i			0.876744i	0.898794	+	0.438372i	$0.144445\pi$
$31$			4.88150i			0.876744i	−0.898794	+	0.438372i	$0.855555\pi$
$32$		0			0
$33$	4.35174	−	4.35174i	0.757540	−	0.757540i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.20809	−	3.20809i	0.527406	−	0.527406i	−0.392392	−	0.919798i	$-0.628352\pi$
$37$	3.20809	−	3.20809i	0.527406	−	0.527406i	0.919798	+	0.392392i	$0.128352\pi$
$38$		0			0
$39$		−	1.34591i		−	0.215518i
$40$		0			0
$41$		−	10.6672i		−	1.66593i	−0.553323	−	0.832967i	$-0.686641\pi$
$41$		−	10.6672i		−	1.66593i	0.553323	−	0.832967i	$-0.313359\pi$
$42$		0			0
$43$	1.60483	+	1.60483i	0.244734	+	0.244734i	0.818805	−	0.574071i	$-0.194637\pi$
$43$	1.60483	+	1.60483i	0.244734	+	0.244734i	−0.574071	+	0.818805i	$0.694637\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.64854	−	2.64854i	−0.386329	−	0.386329i	0.487047	−	0.873376i	$-0.338074\pi$
$47$	−2.64854	−	2.64854i	−0.386329	−	0.386329i	−0.873376	+	0.487047i	$0.838074\pi$
$48$		0			0
$49$	4.64792	+	5.23420i	0.663988	+	0.747743i
$50$		0			0
$51$	−2.96059			−0.414565
$52$		0			0
$53$	9.16786	+	9.16786i	1.25930	+	1.25930i	0.951426	+	0.307876i	$0.0996182\pi$
$53$	9.16786	+	9.16786i	1.25930	+	1.25930i	0.307876	+	0.951426i	$0.400382\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	2.40577	−	2.40577i	0.318653	−	0.318653i
$58$		0			0
$59$	13.3231			1.73452			0.867261	−	0.497854i	$-0.165879\pi$
$59$	13.3231			1.73452			0.867261	+	0.497854i	$0.165879\pi$
$60$		0			0
$61$		−	11.2091i		−	1.43518i	−0.696465	−	0.717591i	$-0.745245\pi$
$61$		−	11.2091i		−	1.43518i	0.696465	−	0.717591i	$-0.254755\pi$
$62$		0			0
$63$	2.09697	−	4.66648i	0.264193	−	0.587921i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	6.43325	−	6.43325i	0.785947	−	0.785947i	−0.194880	−	0.980827i	$-0.562432\pi$
$67$	6.43325	−	6.43325i	0.785947	−	0.785947i	0.980827	+	0.194880i	$0.0624318\pi$
$68$		0			0
$69$	−0.0794520			−0.00956489
$70$		0			0
$71$	−8.51221			−1.01021			−0.505107	−	0.863057i	$-0.668547\pi$
$71$	−8.51221			−1.01021			−0.505107	+	0.863057i	$0.668547\pi$
$72$		0			0
$73$	8.66633	−	8.66633i	1.01432	−	1.01432i	0.0144206	−	0.999896i	$-0.495410\pi$
$73$	8.66633	−	8.66633i	1.01432	−	1.01432i	0.999896	−	0.0144206i	$-0.00459039\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−14.3826	−	6.46310i	−1.63905	−	0.736539i
$78$		0			0
$79$		−	1.76209i		−	0.198250i	−0.995075	−	0.0991251i	$-0.968396\pi$
$79$		−	1.76209i		−	0.198250i	0.995075	−	0.0991251i	$-0.0316044\pi$
$80$		0			0
$81$	−0.540019			−0.0600021
$82$		0			0
$83$	2.36897	−	2.36897i	0.260028	−	0.260028i	−0.565037	−	0.825065i	$-0.691138\pi$
$83$	2.36897	−	2.36897i	0.260028	−	0.260028i	0.825065	+	0.565037i	$0.191138\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−2.76668	−	2.76668i	−0.296619	−	0.296619i
$88$		0			0
$89$	−9.73989			−1.03243			−0.516213	−	0.856460i	$-0.672659\pi$
$89$	−9.73989			−1.03243			−0.516213	+	0.856460i	$0.672659\pi$
$90$		0			0
$91$	−3.22360	+	1.22468i	−0.337925	+	0.128382i
$92$		0			0
$93$	3.56440	+	3.56440i	0.369611	+	0.369611i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	2.05040	+	2.05040i	0.208187	+	0.208187i	0.803496	−	0.595310i	$-0.202971\pi$
$97$	2.05040	+	2.05040i	0.208187	+	0.208187i	−0.595310	+	0.803496i	$0.702971\pi$
$98$		0			0
$99$			11.5242i			1.15822i
$100$		0			0
$101$			5.96787i			0.593825i	0.954905	+	0.296912i	$0.0959570\pi$
$101$			5.96787i			0.593825i	−0.954905	+	0.296912i	$0.904043\pi$
$102$		0			0
$103$	−8.07151	+	8.07151i	−0.795309	+	0.795309i	−0.982352	−	0.187043i	$-0.940110\pi$
$103$	−8.07151	+	8.07151i	−0.795309	+	0.795309i	0.187043	+	0.982352i	$0.440110\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.43407	+	3.43407i	−0.331984	+	0.331984i	−0.853339	−	0.521356i	$-0.825426\pi$
$107$	−3.43407	+	3.43407i	−0.331984	+	0.331984i	0.521356	+	0.853339i	$0.325426\pi$
$108$		0			0
$109$			2.47368i			0.236935i	0.992958	+	0.118468i	$0.0377982\pi$
$109$			2.47368i			0.236935i	−0.992958	+	0.118468i	$0.962202\pi$
$110$		0			0
$111$		−	4.68500i		−	0.444680i
$112$		0			0
$113$	−6.51377	−	6.51377i	−0.612764	−	0.612764i	0.330901	−	0.943665i	$-0.392647\pi$
$113$	−6.51377	−	6.51377i	−0.612764	−	0.612764i	−0.943665	+	0.330901i	$0.892647\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	1.78211	+	1.78211i	0.164756	+	0.164756i
$118$		0			0
$119$	2.69392	+	7.09092i	0.246952	+	0.650024i
$120$		0			0
$121$	24.5189			2.22899
$122$		0			0
$123$	−7.78901	−	7.78901i	−0.702312	−	0.702312i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−4.97529	+	4.97529i	−0.441485	+	0.441485i	−0.892511	−	0.451026i	$-0.851058\pi$
$127$	−4.97529	+	4.97529i	−0.441485	+	0.441485i	0.451026	+	0.892511i	$0.351058\pi$
$128$		0			0
$129$	2.34364			0.206346
$130$		0			0
$131$			7.19072i			0.628256i	0.949381	+	0.314128i	$0.101712\pi$
$131$			7.19072i			0.628256i	−0.949381	+	0.314128i	$0.898288\pi$
$132$		0			0
$133$	−7.95117	−	3.57300i	−0.689454	−	0.309819i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−10.9598	+	10.9598i	−0.936357	+	0.936357i	−0.998093	−	0.0617359i	$-0.980336\pi$
$137$	−10.9598	+	10.9598i	−0.936357	+	0.936357i	0.0617359	+	0.998093i	$0.480336\pi$
$138$		0			0
$139$	−16.0473			−1.36112			−0.680559	−	0.732693i	$-0.738263\pi$
$139$	−16.0473			−1.36112			−0.680559	+	0.732693i	$0.738263\pi$
$140$		0			0
$141$	−3.86784			−0.325731
$142$		0			0
$143$	5.49267	−	5.49267i	0.459320	−	0.459320i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	7.21577	+	0.428096i	0.595147	+	0.0353088i
$148$		0			0
$149$		−	18.0802i		−	1.48119i	−0.671954	−	0.740593i	$-0.734545\pi$
$149$		−	18.0802i		−	1.48119i	0.671954	−	0.740593i	$-0.265455\pi$
$150$		0			0
$151$	−4.72625			−0.384617			−0.192308	−	0.981335i	$-0.561597\pi$
$151$	−4.72625			−0.384617			−0.192308	+	0.981335i	$0.561597\pi$
$152$		0			0
$153$	3.92008	−	3.92008i	0.316920	−	0.316920i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−4.46067	−	4.46067i	−0.356000	−	0.356000i	0.506336	−	0.862336i	$-0.331000\pi$
$157$	−4.46067	−	4.46067i	−0.356000	−	0.356000i	−0.862336	+	0.506336i	$0.831000\pi$
$158$		0			0
$159$	13.3885			1.06177
$160$		0			0
$161$	0.0722957	+	0.190296i	0.00569770	+	0.0149974i
$162$		0			0
$163$	12.2914	+	12.2914i	0.962735	+	0.962735i	0.999330	−	0.0365956i	$-0.0116513\pi$
$163$	12.2914	+	12.2914i	0.962735	+	0.962735i	−0.0365956	+	0.999330i	$0.511651\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	13.3128	+	13.3128i	1.03017	+	1.03017i	0.999530	+	0.0306429i	$0.00975545\pi$
$167$	13.3128	+	13.3128i	1.03017	+	1.03017i	0.0306429	+	0.999530i	$0.490245\pi$
$168$		0			0
$169$			11.3012i			0.869325i
$170$		0			0
$171$			6.37092i			0.487196i
$172$		0			0
$173$	6.42769	−	6.42769i	0.488688	−	0.488688i	−0.419204	−	0.907892i	$-0.637691\pi$
$173$	6.42769	−	6.42769i	0.488688	−	0.488688i	0.907892	+	0.419204i	$0.137691\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	9.72834	−	9.72834i	0.731227	−	0.731227i
$178$		0			0
$179$			1.34949i			0.100866i	0.998727	+	0.0504328i	$0.0160601\pi$
$179$			1.34949i			0.100866i	−0.998727	+	0.0504328i	$0.983940\pi$
$180$		0			0
$181$		−	0.167463i		−	0.0124474i	−0.999981	−	0.00622371i	$-0.998019\pi$
$181$		−	0.167463i		−	0.0124474i	0.999981	−	0.00622371i	$-0.00198108\pi$
$182$		0			0
$183$	−8.18474	−	8.18474i	−0.605033	−	0.605033i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−12.0822	−	12.0822i	−0.883535	−	0.883535i
$188$		0			0
$189$	−4.78710	−	12.6006i	−0.348210	−	0.916556i
$190$		0			0
$191$	16.1288			1.16704			0.583521	−	0.812098i	$-0.301675\pi$
$191$	16.1288			1.16704			0.583521	+	0.812098i	$0.301675\pi$
$192$		0			0
$193$	−8.46997	−	8.46997i	−0.609682	−	0.609682i	0.333181	−	0.942863i	$-0.391878\pi$
$193$	−8.46997	−	8.46997i	−0.609682	−	0.609682i	−0.942863	+	0.333181i	$0.891878\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−2.23062	+	2.23062i	−0.158925	+	0.158925i	−0.782090	−	0.623165i	$-0.785846\pi$
$197$	−2.23062	+	2.23062i	−0.158925	+	0.158925i	0.623165	+	0.782090i	$0.285846\pi$
$198$		0			0
$199$	5.47878			0.388380			0.194190	−	0.980964i	$-0.437792\pi$
$199$	5.47878			0.388380			0.194190	+	0.980964i	$0.437792\pi$
$200$		0			0
$201$		−	9.39493i		−	0.662667i
$202$		0			0
$203$	−4.10901	+	9.14398i	−0.288396	+	0.641782i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.105201	−	0.105201i	0.00731201	−	0.00731201i
$208$		0			0
$209$	19.6359			1.35825
$210$		0			0
$211$	−7.22125			−0.497132			−0.248566	−	0.968615i	$-0.579959\pi$
$211$	−7.22125			−0.497132			−0.248566	+	0.968615i	$0.579959\pi$
$212$		0			0
$213$	−6.21549	+	6.21549i	−0.425878	+	0.425878i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	5.29377	−	11.7805i	0.359364	−	0.799711i
$218$		0			0
$219$		−	12.6560i		−	0.855216i
$220$		0			0
$221$	−3.73679			−0.251363
$222$		0			0
$223$	−12.2709	+	12.2709i	−0.821721	+	0.821721i	−0.986355	−	0.164634i	$-0.947356\pi$
$223$	−12.2709	+	12.2709i	−0.821721	+	0.821721i	0.164634	+	0.986355i	$0.447356\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	13.9412	+	13.9412i	0.925307	+	0.925307i	0.997398	−	0.0720910i	$-0.0229672\pi$
$227$	13.9412	+	13.9412i	0.925307	+	0.925307i	−0.0720910	+	0.997398i	$0.522967\pi$
$228$		0			0
$229$	−24.5615			−1.62307			−0.811535	−	0.584304i	$-0.801368\pi$
$229$	−24.5615			−1.62307			−0.811535	+	0.584304i	$0.801368\pi$
$230$		0			0
$231$	−15.2213	+	5.78273i	−1.00149	+	0.380476i
$232$		0			0
$233$	14.4981	+	14.4981i	0.949802	+	0.949802i	0.998799	−	0.0489972i	$-0.0156025\pi$
$233$	14.4981	+	14.4981i	0.949802	+	0.949802i	−0.0489972	+	0.998799i	$0.515603\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−1.28665	−	1.28665i	−0.0835769	−	0.0835769i
$238$		0			0
$239$		−	2.70102i		−	0.174715i	−0.996177	−	0.0873573i	$-0.972158\pi$
$239$		−	2.70102i		−	0.174715i	0.996177	−	0.0873573i	$-0.0278422\pi$
$240$		0			0
$241$		−	6.19167i		−	0.398840i	−0.979914	−	0.199420i	$-0.936094\pi$
$241$		−	6.19167i		−	0.398840i	0.979914	−	0.199420i	$-0.0639059\pi$
$242$		0			0
$243$	−11.2018	+	11.2018i	−0.718594	+	0.718594i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	3.03652	−	3.03652i	0.193209	−	0.193209i
$248$		0			0
$249$		−	3.45957i		−	0.219241i
$250$		0			0
$251$			21.2989i			1.34437i	0.740381	+	0.672187i	$0.234645\pi$
$251$			21.2989i			1.34437i	−0.740381	+	0.672187i	$0.765355\pi$
$252$		0			0
$253$	−0.324244	−	0.324244i	−0.0203850	−	0.0203850i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	13.5045	+	13.5045i	0.842390	+	0.842390i	0.989169	−	0.146779i	$-0.0468907\pi$
$257$	13.5045	+	13.5045i	0.842390	+	0.842390i	−0.146779	+	0.989169i	$0.546891\pi$
$258$		0			0
$259$	−11.2211	+	4.26301i	−0.697243	+	0.264891i
$260$		0			0
$261$	7.32666			0.453509
$262$		0			0
$263$	3.28861	+	3.28861i	0.202784	+	0.202784i	0.801192	−	0.598408i	$-0.204200\pi$
$263$	3.28861	+	3.28861i	0.202784	+	0.202784i	−0.598408	+	0.801192i	$0.704200\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−7.11192	+	7.11192i	−0.435243	+	0.435243i
$268$		0			0
$269$	−27.9298			−1.70291			−0.851454	−	0.524429i	$-0.824279\pi$
$269$	−27.9298			−1.70291			−0.851454	+	0.524429i	$0.824279\pi$
$270$		0			0
$271$		−	6.55143i		−	0.397971i	−0.980002	−	0.198985i	$-0.936235\pi$
$271$		−	6.55143i		−	0.397971i	0.980002	−	0.198985i	$-0.0637647\pi$
$272$		0			0
$273$	−1.45958	+	3.24807i	−0.0883377	+	0.196582i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	10.6137	−	10.6137i	0.637717	−	0.637717i	−0.312275	−	0.949992i	$-0.601091\pi$
$277$	10.6137	−	10.6137i	0.637717	−	0.637717i	0.949992	+	0.312275i	$0.101091\pi$
$278$		0			0
$279$	−9.43917			−0.565108
$280$		0			0
$281$	−23.3116			−1.39065			−0.695326	−	0.718695i	$-0.744740\pi$
$281$	−23.3116			−1.39065			−0.695326	+	0.718695i	$0.744740\pi$
$282$		0			0
$283$	−18.9859	+	18.9859i	−1.12860	+	1.12860i	−0.138190	+	0.990406i	$0.544128\pi$
$283$	−18.9859	+	18.9859i	−1.12860	+	1.12860i	−0.990406	+	0.138190i	$0.955872\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−11.5681	+	25.7430i	−0.682841	+	1.51956i
$288$		0			0
$289$		−	8.78023i		−	0.516484i
$290$		0			0
$291$	2.99434			0.175531
$292$		0			0
$293$	−11.5947	+	11.5947i	−0.677371	+	0.677371i	−0.959405	−	0.282033i	$-0.908991\pi$
$293$	−11.5947	+	11.5947i	−0.677371	+	0.677371i	0.282033	+	0.959405i	$0.408991\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	21.4700	+	21.4700i	1.24582	+	1.24582i
$298$		0			0
$299$	−0.100282			−0.00579949
$300$		0			0
$301$	−2.13255	−	5.61327i	−0.122918	−	0.323543i
$302$		0			0
$303$	4.35765	+	4.35765i	0.250340	+	0.250340i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−16.8061	−	16.8061i	−0.959174	−	0.959174i	0.0400244	−	0.999199i	$-0.487256\pi$
$307$	−16.8061	−	16.8061i	−0.959174	−	0.959174i	−0.999199	+	0.0400244i	$0.987256\pi$
$308$		0			0
$309$			11.7874i			0.670561i
$310$		0			0
$311$			15.1113i			0.856881i	0.903570	+	0.428440i	$0.140937\pi$
$311$			15.1113i			0.856881i	−0.903570	+	0.428440i	$0.859063\pi$
$312$		0			0
$313$	−13.1100	+	13.1100i	−0.741023	+	0.741023i	−0.972775	−	0.231752i	$-0.925554\pi$
$313$	−13.1100	+	13.1100i	−0.741023	+	0.741023i	0.231752	+	0.972775i	$0.425554\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	12.6159	−	12.6159i	0.708578	−	0.708578i	−0.257658	−	0.966236i	$-0.582951\pi$
$317$	12.6159	−	12.6159i	0.708578	−	0.708578i	0.966236	+	0.257658i	$0.0829508\pi$
$318$		0			0
$319$		−	22.5817i		−	1.26433i
$320$		0			0
$321$			5.01501i			0.279910i
$322$		0			0
$323$	−6.67939	−	6.67939i	−0.371651	−	0.371651i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	1.80624	+	1.80624i	0.0998855	+	0.0998855i
$328$		0			0
$329$	3.51946	+	9.26389i	0.194034	+	0.510735i
$330$		0			0
$331$	16.8901			0.928364			0.464182	−	0.885740i	$-0.346348\pi$
$331$	16.8901			0.928364			0.464182	+	0.885740i	$0.346348\pi$
$332$		0			0
$333$	6.20335	+	6.20335i	0.339942	+	0.339942i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−20.8552	+	20.8552i	−1.13606	+	1.13606i	−0.146906	+	0.989150i	$0.546931\pi$
$337$	−20.8552	+	20.8552i	−1.13606	+	1.13606i	−0.989150	+	0.146906i	$0.953069\pi$
$338$		0			0
$339$	−9.51252			−0.516649
$340$		0			0
$341$			29.0927i			1.57546i
$342$		0			0
$343$	−5.54051	−	17.6721i	−0.299159	−	0.954203i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	3.75386	−	3.75386i	0.201518	−	0.201518i	−0.599132	−	0.800650i	$-0.704488\pi$
$347$	3.75386	−	3.75386i	0.201518	−	0.201518i	0.800650	+	0.599132i	$0.204488\pi$
$348$		0			0
$349$	1.12253			0.0600874			0.0300437	−	0.999549i	$-0.490435\pi$
$349$	1.12253			0.0600874			0.0300437	+	0.999549i	$0.490435\pi$
$350$		0			0
$351$	6.64027			0.354431
$352$		0			0
$353$	−2.71896	+	2.71896i	−0.144716	+	0.144716i	−0.775753	−	0.631037i	$-0.782630\pi$
$353$	−2.71896	+	2.71896i	−0.144716	+	0.144716i	0.631037	+	0.775753i	$0.282630\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	7.14475	+	3.21062i	0.378140	+	0.169924i
$358$		0			0
$359$			5.21128i			0.275041i	0.990499	+	0.137520i	$0.0439133\pi$
$359$			5.21128i			0.275041i	−0.990499	+	0.137520i	$0.956087\pi$
$360$		0			0
$361$	−8.14465			−0.428666
$362$		0			0
$363$	17.9033	−	17.9033i	0.939681	−	0.939681i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−0.978681	−	0.978681i	−0.0510867	−	0.0510867i	0.681102	−	0.732189i	$-0.261501\pi$
$367$	−0.978681	−	0.978681i	−0.0510867	−	0.0510867i	−0.732189	+	0.681102i	$0.761501\pi$
$368$		0			0
$369$	20.6267			1.07378
$370$		0			0
$371$	−12.1826	−	32.0668i	−0.632487	−	1.66483i
$372$		0			0
$373$	−18.7892	−	18.7892i	−0.972870	−	0.972870i	0.0267714	−	0.999642i	$-0.491477\pi$
$373$	−18.7892	−	18.7892i	−0.972870	−	0.972870i	−0.999642	+	0.0267714i	$0.991477\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−3.49204	−	3.49204i	−0.179849	−	0.179849i
$378$		0			0
$379$		−	0.517830i		−	0.0265992i	−0.999912	−	0.0132996i	$-0.995766\pi$
$379$		−	0.517830i		−	0.0265992i	0.999912	−	0.0132996i	$-0.00423351\pi$
$380$		0			0
$381$			7.26576i			0.372236i
$382$		0			0
$383$	13.1105	−	13.1105i	0.669917	−	0.669917i	−0.287779	−	0.957697i	$-0.592917\pi$
$383$	13.1105	−	13.1105i	0.669917	−	0.669917i	0.957697	+	0.287779i	$0.0929170\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−3.10319	+	3.10319i	−0.157744	+	0.157744i
$388$		0			0
$389$			14.3932i			0.729766i	0.931053	+	0.364883i	$0.118891\pi$
$389$			14.3932i			0.729766i	−0.931053	+	0.364883i	$0.881109\pi$
$390$		0			0
$391$			0.220590i			0.0111557i
$392$		0			0
$393$	5.25056	+	5.25056i	0.264856	+	0.264856i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−9.94079	−	9.94079i	−0.498914	−	0.498914i	0.412186	−	0.911100i	$-0.364765\pi$
$397$	−9.94079	−	9.94079i	−0.498914	−	0.498914i	−0.911100	+	0.412186i	$0.864765\pi$
$398$		0			0
$399$	−8.41478	+	3.19687i	−0.421266	+	0.160044i
$400$		0			0
$401$	16.7962			0.838763			0.419382	−	0.907810i	$-0.362247\pi$
$401$	16.7962			0.838763			0.419382	+	0.907810i	$0.362247\pi$
$402$		0			0
$403$	4.49891	+	4.49891i	0.224107	+	0.224107i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	19.1195	−	19.1195i	0.947717	−	0.947717i
$408$		0			0
$409$	−1.41163			−0.0698008			−0.0349004	−	0.999391i	$-0.511111\pi$
$409$	−1.41163			−0.0698008			−0.0349004	+	0.999391i	$0.511111\pi$
$410$		0			0
$411$			16.0053i			0.789484i
$412$		0			0
$413$	−32.1525	−	14.4483i	−1.58212	−	0.710955i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−11.7175	+	11.7175i	−0.573810	+	0.573810i
$418$		0			0
$419$	5.68831			0.277892			0.138946	−	0.990300i	$-0.455629\pi$
$419$	5.68831			0.277892			0.138946	+	0.990300i	$0.455629\pi$
$420$		0			0
$421$	−12.1346			−0.591402			−0.295701	−	0.955280i	$-0.595553\pi$
$421$	−12.1346			−0.591402			−0.295701	+	0.955280i	$0.595553\pi$
$422$		0			0
$423$	5.12137	−	5.12137i	0.249009	−	0.249009i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−12.1558	+	27.0509i	−0.588260	+	1.30908i
$428$		0			0
$429$		−	8.02132i		−	0.387273i
$430$		0			0
$431$	32.9391			1.58662			0.793311	−	0.608817i	$-0.208356\pi$
$431$	32.9391			1.58662			0.793311	+	0.608817i	$0.208356\pi$
$432$		0			0
$433$	0.964365	−	0.964365i	0.0463444	−	0.0463444i	−0.683555	−	0.729899i	$-0.739567\pi$
$433$	0.964365	−	0.964365i	0.0463444	−	0.0463444i	0.729899	+	0.683555i	$0.239567\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.179252	−	0.179252i	−0.00857478	−	0.00857478i
$438$		0			0
$439$	−8.75634			−0.417917			−0.208959	−	0.977924i	$-0.567007\pi$
$439$	−8.75634			−0.417917			−0.208959	+	0.977924i	$0.567007\pi$
$440$		0			0
$441$	−10.1212	+	8.98749i	−0.481960	+	0.427976i
$442$		0			0
$443$	−4.24169	−	4.24169i	−0.201529	−	0.201529i	0.599126	−	0.800655i	$-0.295515\pi$
$443$	−4.24169	−	4.24169i	−0.201529	−	0.201529i	−0.800655	+	0.599126i	$0.795515\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−13.2019	−	13.2019i	−0.624428	−	0.624428i
$448$		0			0
$449$			2.36447i			0.111586i	0.998442	+	0.0557931i	$0.0177687\pi$
$449$			2.36447i			0.111586i	−0.998442	+	0.0557931i	$0.982231\pi$
$450$		0			0
$451$		−	63.5740i		−	2.99358i
$452$		0			0
$453$	−3.45104	+	3.45104i	−0.162144	+	0.162144i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−9.06926	+	9.06926i	−0.424242	+	0.424242i	−0.886661	−	0.462419i	$-0.846982\pi$
$457$	−9.06926	+	9.06926i	−0.424242	+	0.424242i	0.462419	+	0.886661i	$0.346982\pi$
$458$		0			0
$459$		−	14.6065i		−	0.681774i
$460$		0			0
$461$			32.6249i			1.51949i	0.650219	+	0.759747i	$0.274677\pi$
$461$			32.6249i			1.51949i	−0.650219	+	0.759747i	$0.725323\pi$
$462$		0			0
$463$	−25.9003	−	25.9003i	−1.20369	−	1.20369i	−0.973036	−	0.230654i	$-0.925913\pi$
$463$	−25.9003	−	25.9003i	−1.20369	−	1.20369i	−0.230654	−	0.973036i	$-0.574087\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	10.7966	+	10.7966i	0.499608	+	0.499608i	0.911316	−	0.411708i	$-0.135068\pi$
$467$	10.7966	+	10.7966i	0.499608	+	0.499608i	−0.411708	+	0.911316i	$0.635068\pi$
$468$		0			0
$469$	−22.5019	+	8.54872i	−1.03904	+	0.394743i
$470$		0			0
$471$	−6.51423			−0.300160
$472$		0			0
$473$	9.56440	+	9.56440i	0.439772	+	0.439772i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−17.7275	+	17.7275i	−0.811688	+	0.811688i
$478$		0			0
$479$	−14.8255			−0.677395			−0.338697	−	0.940895i	$-0.609986\pi$
$479$	−14.8255			−0.677395			−0.338697	+	0.940895i	$0.609986\pi$
$480$		0			0
$481$		−	5.91330i		−	0.269623i
$482$		0			0
$483$	0.191740	+	0.0861620i	0.00872449	+	0.00392051i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	19.4866	−	19.4866i	0.883024	−	0.883024i	−0.110817	−	0.993841i	$-0.535347\pi$
$487$	19.4866	−	19.4866i	0.883024	−	0.883024i	0.993841	+	0.110817i	$0.0353466\pi$
$488$		0			0
$489$	17.9500			0.811725
$490$		0			0
$491$	−18.7117			−0.844446			−0.422223	−	0.906492i	$-0.638750\pi$
$491$	−18.7117			−0.844446			−0.422223	+	0.906492i	$0.638750\pi$
$492$		0			0
$493$	−7.68141	+	7.68141i	−0.345953	+	0.345953i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	20.5424	+	9.23110i	0.921453	+	0.414071i
$498$		0			0
$499$			3.85409i			0.172533i	0.996272	+	0.0862664i	$0.0274936\pi$
$499$			3.85409i			0.172533i	−0.996272	+	0.0862664i	$0.972506\pi$
$500$		0			0
$501$	19.4416			0.868585
$502$		0			0
$503$	−17.3619	+	17.3619i	−0.774129	+	0.774129i	−0.978825	−	0.204697i	$-0.934379\pi$
$503$	−17.3619	+	17.3619i	−0.774129	+	0.774129i	0.204697	+	0.978825i	$0.434379\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	8.25198	+	8.25198i	0.366483	+	0.366483i
$508$		0			0
$509$	−6.19089			−0.274406			−0.137203	−	0.990543i	$-0.543811\pi$
$509$	−6.19089			−0.274406			−0.137203	+	0.990543i	$0.543811\pi$
$510$		0			0
$511$	−30.3126	+	11.5161i	−1.34095	+	0.509442i
$512$		0			0
$513$	11.8693	+	11.8693i	0.524041	+	0.524041i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−15.7847	−	15.7847i	−0.694209	−	0.694209i
$518$		0			0
$519$		−	9.38681i		−	0.412035i
$520$		0			0
$521$		−	23.4163i		−	1.02589i	−0.858422	−	0.512943i	$-0.828555\pi$
$521$		−	23.4163i		−	1.02589i	0.858422	−	0.512943i	$-0.171445\pi$
$522$		0			0
$523$	4.35649	−	4.35649i	0.190496	−	0.190496i	−0.605414	−	0.795910i	$-0.706993\pi$
$523$	4.35649	−	4.35649i	0.190496	−	0.190496i	0.795910	+	0.605414i	$0.206993\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	9.89620	−	9.89620i	0.431085	−	0.431085i
$528$		0			0
$529$		−	22.9941i		−	0.999743i
$530$		0			0
$531$			25.7624i			1.11799i
$532$		0			0
$533$	−9.83112	−	9.83112i	−0.425833	−	0.425833i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.985377	+	0.985377i	0.0425221	+	0.0425221i
$538$		0			0
$539$	27.7005	+	31.1947i	1.19315	+	1.34365i
$540$		0			0
$541$	8.06640			0.346801			0.173401	−	0.984851i	$-0.444524\pi$
$541$	8.06640			0.346801			0.173401	+	0.984851i	$0.444524\pi$
$542$		0			0
$543$	−0.122279	−	0.122279i	−0.00524749	−	0.00524749i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	19.3200	−	19.3200i	0.826063	−	0.826063i	−0.160907	−	0.986970i	$-0.551442\pi$
$547$	19.3200	−	19.3200i	0.826063	−	0.826063i	0.986970	+	0.160907i	$0.0514419\pi$
$548$		0			0
$549$	21.6746			0.925051
$550$		0			0
$551$		−	12.4838i		−	0.531829i
$552$		0			0
$553$	−1.91090	+	4.25242i	−0.0812599	+	0.180831i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−12.4346	+	12.4346i	−0.526872	+	0.526872i	−0.919638	−	0.392767i	$-0.871518\pi$
$557$	−12.4346	+	12.4346i	−0.526872	+	0.526872i	0.392767	+	0.919638i	$0.371518\pi$
$558$		0			0
$559$	2.95809			0.125114
$560$		0			0
$561$	−17.6444			−0.744948
$562$		0			0
$563$	19.6018	−	19.6018i	0.826118	−	0.826118i	−0.160859	−	0.986977i	$-0.551427\pi$
$563$	19.6018	−	19.6018i	0.826118	−	0.826118i	0.986977	+	0.160859i	$0.0514265\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	1.30322	+	0.585626i	0.0547302	+	0.0245940i
$568$		0			0
$569$		−	17.4875i		−	0.733115i	−0.930395	−	0.366558i	$-0.880536\pi$
$569$		−	17.4875i		−	0.733115i	0.930395	−	0.366558i	$-0.119464\pi$
$570$		0			0
$571$	31.0074			1.29762			0.648810	−	0.760950i	$-0.275267\pi$
$571$	31.0074			1.29762			0.648810	+	0.760950i	$0.275267\pi$
$572$		0			0
$573$	11.7770	−	11.7770i	0.491993	−	0.491993i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−19.6961	−	19.6961i	−0.819957	−	0.819957i	0.166144	−	0.986101i	$-0.446868\pi$
$577$	−19.6961	−	19.6961i	−0.819957	−	0.819957i	−0.986101	+	0.166144i	$0.946868\pi$
$578$		0			0
$579$	−12.3693			−0.514050
$580$		0			0
$581$	−8.28603	+	3.14796i	−0.343762	+	0.130599i
$582$		0			0
$583$	54.6384	+	54.6384i	2.26289	+	2.26289i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−18.6924	−	18.6924i	−0.771519	−	0.771519i	0.206853	−	0.978372i	$-0.433678\pi$
$587$	−18.6924	−	18.6924i	−0.771519	−	0.771519i	−0.978372	+	0.206853i	$0.933678\pi$
$588$		0			0
$589$			16.0833i			0.662701i
$590$		0			0
$591$			3.25754i			0.133997i
$592$		0			0
$593$	24.8700	−	24.8700i	1.02129	−	1.02129i	0.0215185	−	0.999768i	$-0.493150\pi$
$593$	24.8700	−	24.8700i	1.02129	−	1.02129i	0.999768	−	0.0215185i	$-0.00685007\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	4.00052	−	4.00052i	0.163730	−	0.163730i
$598$		0			0
$599$			32.1708i			1.31446i	0.753688	+	0.657232i	$0.228273\pi$
$599$			32.1708i			1.31446i	−0.753688	+	0.657232i	$0.771727\pi$
$600$		0			0
$601$		−	11.8081i		−	0.481664i	−0.970567	−	0.240832i	$-0.922580\pi$
$601$		−	11.8081i		−	0.481664i	0.970567	−	0.240832i	$-0.0774204\pi$
$602$		0			0
$603$	12.4397	+	12.4397i	0.506585	+	0.506585i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−6.50201	−	6.50201i	−0.263908	−	0.263908i	0.562731	−	0.826640i	$-0.309751\pi$
$607$	−6.50201	−	6.50201i	−0.263908	−	0.263908i	−0.826640	+	0.562731i	$0.809751\pi$
$608$		0			0
$609$	3.67646	+	9.67714i	0.148978	+	0.392137i
$610$		0			0
$611$	−4.88190			−0.197501
$612$		0			0
$613$	18.1899	+	18.1899i	0.734682	+	0.734682i	0.971543	−	0.236861i	$-0.0761187\pi$
$613$	18.1899	+	18.1899i	0.734682	+	0.734682i	−0.236861	+	0.971543i	$0.576119\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	4.68616	−	4.68616i	0.188658	−	0.188658i	−0.606458	−	0.795116i	$-0.707410\pi$
$617$	4.68616	−	4.68616i	0.188658	−	0.188658i	0.795116	+	0.606458i	$0.207410\pi$
$618$		0			0
$619$	−6.78552			−0.272733			−0.136366	−	0.990658i	$-0.543542\pi$
$619$	−6.78552			−0.272733			−0.136366	+	0.990658i	$0.543542\pi$
$620$		0			0
$621$		−	0.391989i		−	0.0157300i
$622$		0			0
$623$	23.5052	+	10.5625i	0.941714	+	0.423176i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	14.3379	−	14.3379i	0.572599	−	0.572599i
$628$		0			0
$629$	−13.0074			−0.518640
$630$		0			0
$631$	−0.0455199			−0.00181212			−0.000906059	−	1.00000i	$-0.500288\pi$
$631$	−0.0455199			−0.00181212			−0.000906059		1.00000i	$0.500288\pi$
$632$		0			0
$633$	−5.27285	+	5.27285i	−0.209577	+	0.209577i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	9.10759	+	0.540333i	0.360856	+	0.0214088i
$638$		0			0
$639$		−	16.4597i		−	0.651136i
$640$		0			0
$641$	−14.9331			−0.589823			−0.294912	−	0.955524i	$-0.595290\pi$
$641$	−14.9331			−0.589823			−0.294912	+	0.955524i	$0.595290\pi$
$642$		0			0
$643$	14.2308	−	14.2308i	0.561208	−	0.561208i	−0.368443	−	0.929650i	$-0.620109\pi$
$643$	14.2308	−	14.2308i	0.561208	−	0.561208i	0.929650	+	0.368443i	$0.120109\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−10.4339	−	10.4339i	−0.410201	−	0.410201i	0.471608	−	0.881809i	$-0.343674\pi$
$647$	−10.4339	−	10.4339i	−0.410201	−	0.410201i	−0.881809	+	0.471608i	$0.843674\pi$
$648$		0			0
$649$	79.4027			3.11683
$650$		0			0
$651$	−4.73649	−	12.4674i	−0.185638	−	0.488634i
$652$		0			0
$653$	−2.78826	−	2.78826i	−0.109113	−	0.109113i	0.650442	−	0.759556i	$-0.274584\pi$
$653$	−2.78826	−	2.78826i	−0.109113	−	0.109113i	−0.759556	+	0.650442i	$0.774584\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	16.7577	+	16.7577i	0.653781	+	0.653781i
$658$		0			0
$659$			7.73193i			0.301193i	0.988595	+	0.150597i	$0.0481195\pi$
$659$			7.73193i			0.301193i	−0.988595	+	0.150597i	$0.951881\pi$
$660$		0			0
$661$			35.3366i			1.37443i	0.726453	+	0.687217i	$0.241168\pi$
$661$			35.3366i			1.37443i	−0.726453	+	0.687217i	$0.758832\pi$
$662$		0			0
$663$	−2.72855	+	2.72855i	−0.105968	+	0.105968i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.206143	+	0.206143i	−0.00798187	+	0.00798187i
$668$		0			0
$669$			17.9201i			0.692830i
$670$		0			0
$671$		−	66.8039i		−	2.57894i
$672$		0			0
$673$	3.30292	+	3.30292i	0.127318	+	0.127318i	0.767895	−	0.640576i	$-0.221304\pi$
$673$	3.30292	+	3.30292i	0.127318	+	0.127318i	−0.640576	+	0.767895i	$0.721304\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−11.8424	−	11.8424i	−0.455138	−	0.455138i	0.441917	−	0.897056i	$-0.354298\pi$
$677$	−11.8424	−	11.8424i	−0.455138	−	0.455138i	−0.897056	+	0.441917i	$0.854298\pi$
$678$		0			0
$679$	−2.72464	−	7.17177i	−0.104562	−	0.275227i
$680$		0			0
$681$	20.3592			0.780168
$682$		0			0
$683$	−9.37696	−	9.37696i	−0.358799	−	0.358799i	0.504571	−	0.863370i	$-0.331651\pi$
$683$	−9.37696	−	9.37696i	−0.358799	−	0.358799i	−0.863370	+	0.504571i	$0.831651\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−17.9344	+	17.9344i	−0.684242	+	0.684242i
$688$		0			0
$689$	16.8986			0.643787
$690$		0			0
$691$		−	13.1758i		−	0.501233i	−0.968086	−	0.250616i	$-0.919367\pi$
$691$		−	13.1758i		−	0.501233i	0.968086	−	0.250616i	$-0.0806333\pi$
$692$		0			0
$693$	12.4974	−	27.8111i	0.474739	−	1.05646i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−21.6254	+	21.6254i	−0.819121	+	0.819121i
$698$		0			0
$699$	21.1726			0.800821
$700$		0			0
$701$	−19.5277			−0.737550			−0.368775	−	0.929519i	$-0.620223\pi$
$701$	−19.5277			−0.737550			−0.368775	+	0.929519i	$0.620223\pi$
$702$		0			0
$703$	10.5698	−	10.5698i	0.398649	−	0.398649i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	6.47188	−	14.4022i	0.243400	−	0.541650i
$708$		0			0
$709$		−	24.3216i		−	0.913415i	−0.889617	−	0.456708i	$-0.849029\pi$
$709$		−	24.3216i		−	0.913415i	0.889617	−	0.456708i	$-0.150971\pi$
$710$		0			0
$711$	3.40728			0.127783
$712$		0			0
$713$	0.265580	−	0.265580i	0.00994605	−	0.00994605i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−1.97225	−	1.97225i	−0.0736549	−	0.0736549i
$718$		0			0
$719$	−30.5952			−1.14101			−0.570505	−	0.821294i	$-0.693252\pi$
$719$	−30.5952			−1.14101			−0.570505	+	0.821294i	$0.693252\pi$
$720$		0			0
$721$	28.2321	−	10.7257i	1.05142	−	0.399446i
$722$		0			0
$723$	−4.52106	−	4.52106i	−0.168140	−	0.168140i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	2.97003	+	2.97003i	0.110152	+	0.110152i	0.760035	−	0.649882i	$-0.225182\pi$
$727$	2.97003	+	2.97003i	0.110152	+	0.110152i	−0.649882	+	0.760035i	$0.725182\pi$
$728$		0			0
$729$			14.7387i			0.545877i
$730$		0			0
$731$		−	6.50688i		−	0.240666i
$732$		0			0
$733$	−26.7197	+	26.7197i	−0.986914	+	0.986914i	−0.999915	−	0.0130016i	$-0.995861\pi$
$733$	−26.7197	+	26.7197i	−0.986914	+	0.986914i	0.0130016	+	0.999915i	$0.495861\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	38.3407	−	38.3407i	1.41230	−	1.41230i
$738$		0			0
$739$		−	41.5880i		−	1.52984i	−0.644126	−	0.764920i	$-0.722779\pi$
$739$		−	41.5880i		−	1.52984i	0.644126	−	0.764920i	$-0.277221\pi$
$740$		0			0
$741$		−	4.43444i		−	0.162903i
$742$		0			0
$743$	−3.50770	−	3.50770i	−0.128685	−	0.128685i	0.639831	−	0.768516i	$-0.279004\pi$
$743$	−3.50770	−	3.50770i	−0.128685	−	0.128685i	−0.768516	+	0.639831i	$0.779004\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	4.58077	+	4.58077i	0.167602	+	0.167602i
$748$		0			0
$749$	12.0115	−	4.56330i	0.438890	−	0.166739i
$750$		0			0
$751$	49.1334			1.79290			0.896451	−	0.443142i	$-0.146136\pi$
$751$	49.1334			1.79290			0.896451	+	0.443142i	$0.146136\pi$
$752$		0			0
$753$	15.5521	+	15.5521i	0.566751	+	0.566751i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	34.8748	−	34.8748i	1.26755	−	1.26755i	0.320194	−	0.947352i	$-0.396252\pi$
$757$	34.8748	−	34.8748i	1.26755	−	1.26755i	0.947352	−	0.320194i	$-0.103748\pi$
$758$		0			0
$759$	−0.473516			−0.0171875
$760$		0			0
$761$			42.8325i			1.55268i	0.630317	+	0.776338i	$0.282925\pi$
$761$			42.8325i			1.55268i	−0.630317	+	0.776338i	$0.717075\pi$
$762$		0			0
$763$	2.68259	−	5.96970i	0.0971164	−	0.216118i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	12.2789	−	12.2789i	0.443365	−	0.443365i
$768$		0			0
$769$	−10.4385			−0.376422			−0.188211	−	0.982129i	$-0.560269\pi$
$769$	−10.4385			−0.376422			−0.188211	+	0.982129i	$0.560269\pi$
$770$		0			0
$771$	19.7216			0.710257
$772$		0			0
$773$	−11.9124	+	11.9124i	−0.428459	+	0.428459i	−0.888103	−	0.459644i	$-0.847977\pi$
$773$	−11.9124	+	11.9124i	−0.428459	+	0.428459i	0.459644	+	0.888103i	$0.347977\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−5.08066	+	11.3062i	−0.182268	+	0.405609i
$778$		0			0
$779$		−	35.1456i		−	1.25922i
$780$		0			0
$781$	−50.7308			−1.81529
$782$		0			0
$783$	13.6499	−	13.6499i	0.487806	−	0.487806i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−29.0925	−	29.0925i	−1.03704	−	1.03704i	−0.999287	−	0.0377482i	$-0.987982\pi$
$787$	−29.0925	−	29.0925i	−1.03704	−	1.03704i	−0.0377482	−	0.999287i	$-0.512018\pi$
$788$		0			0
$789$	4.80258			0.170976
$790$		0			0
$791$	8.65572	+	22.7835i	0.307762	+	0.810088i
$792$		0			0
$793$	−10.3306	−	10.3306i	−0.366850	−	0.366850i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	14.9404	+	14.9404i	0.529215	+	0.529215i	0.920338	−	0.391123i	$-0.127913\pi$
$797$	14.9404	+	14.9404i	0.529215	+	0.529215i	−0.391123	+	0.920338i	$0.627913\pi$
$798$		0			0
$799$			10.7387i			0.379907i
$800$		0			0
$801$		−	18.8336i		−	0.665454i
$802$		0			0
$803$	51.6493	−	51.6493i	1.82267	−	1.82267i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−20.3939	+	20.3939i	−0.717899	+	0.717899i
$808$		0			0
$809$			40.4535i			1.42227i	0.703055	+	0.711135i	$0.251819\pi$
$809$			40.4535i			1.42227i	−0.703055	+	0.711135i	$0.748181\pi$
$810$		0			0
$811$			19.8652i			0.697561i	0.937204	+	0.348781i	$0.113404\pi$
$811$			19.8652i			0.697561i	−0.937204	+	0.348781i	$0.886596\pi$
$812$		0			0
$813$	−4.78375	−	4.78375i	−0.167774	−	0.167774i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	5.28750	+	5.28750i	0.184986	+	0.184986i
$818$		0			0
$819$	−2.36812	−	6.23335i	−0.0827489	−	0.217811i
$820$		0			0
$821$	42.9378			1.49854			0.749270	−	0.662265i	$-0.230405\pi$
$821$	42.9378			1.49854			0.749270	+	0.662265i	$0.230405\pi$
$822$		0			0
$823$	−30.9666	−	30.9666i	−1.07943	−	1.07943i	−0.996561	−	0.0828668i	$-0.973592\pi$
$823$	−30.9666	−	30.9666i	−1.07943	−	1.07943i	−0.0828668	−	0.996561i	$-0.526408\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−37.0504	+	37.0504i	−1.28837	+	1.28837i	−0.352593	+	0.935777i	$0.614700\pi$
$827$	−37.0504	+	37.0504i	−1.28837	+	1.28837i	−0.935777	+	0.352593i	$0.885300\pi$
$828$		0			0
$829$	−8.08063			−0.280652			−0.140326	−	0.990105i	$-0.544815\pi$
$829$	−8.08063			−0.280652			−0.140326	+	0.990105i	$0.544815\pi$
$830$		0			0
$831$		−	15.5000i		−	0.537688i
$832$		0			0
$833$	1.18857	−	20.0339i	0.0411813	−	0.694132i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−17.5855	+	17.5855i	−0.607845	+	0.607845i
$838$		0			0
$839$	43.3847			1.49781			0.748903	−	0.662680i	$-0.230581\pi$
$839$	43.3847			1.49781			0.748903	+	0.662680i	$0.230581\pi$
$840$		0			0
$841$	14.6434			0.504944
$842$		0			0
$843$	−17.0218	+	17.0218i	−0.586260	+	0.586260i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−59.1712	−	26.5896i	−2.03315	−	0.913630i
$848$		0			0
$849$			27.7265i			0.951570i
$850$		0			0
$851$	−0.349074			−0.0119661
$852$		0			0
$853$	6.16375	−	6.16375i	0.211043	−	0.211043i	−0.593668	−	0.804710i	$-0.702321\pi$
$853$	6.16375	−	6.16375i	0.211043	−	0.211043i	0.804710	+	0.593668i	$0.202321\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−11.6843	−	11.6843i	−0.399127	−	0.399127i	0.478798	−	0.877925i	$-0.341073\pi$
$857$	−11.6843	−	11.6843i	−0.399127	−	0.399127i	−0.877925	+	0.478798i	$0.841073\pi$
$858$		0			0
$859$	2.90599			0.0991510			0.0495755	−	0.998770i	$-0.484213\pi$
$859$	2.90599			0.0991510			0.0495755	+	0.998770i	$0.484213\pi$
$860$		0			0
$861$	10.3503	+	27.2440i	0.352737	+	0.928472i
$862$		0			0
$863$	25.9632	+	25.9632i	0.883796	+	0.883796i	0.993918	−	0.110122i	$-0.0351242\pi$
$863$	25.9632	+	25.9632i	0.883796	+	0.883796i	−0.110122	+	0.993918i	$0.535124\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−6.41119	−	6.41119i	−0.217736	−	0.217736i
$868$		0			0
$869$		−	10.5016i		−	0.356244i
$870$		0			0
$871$		−	11.8581i		−	0.401795i
$872$		0			0
$873$	−3.96478	+	3.96478i	−0.134187	+	0.134187i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	19.3713	−	19.3713i	0.654124	−	0.654124i	−0.299860	−	0.953983i	$-0.596940\pi$
$877$	19.3713	−	19.3713i	0.654124	−	0.654124i	0.953983	+	0.299860i	$0.0969399\pi$
$878$		0			0
$879$			16.9326i			0.571122i
$880$		0			0
$881$		−	18.7603i		−	0.632049i	−0.948751	−	0.316025i	$-0.897652\pi$
$881$		−	18.7603i		−	0.632049i	0.948751	−	0.316025i	$-0.102348\pi$
$882$		0			0
$883$	−1.50802	−	1.50802i	−0.0507488	−	0.0507488i	0.681277	−	0.732026i	$-0.261425\pi$
$883$	−1.50802	−	1.50802i	−0.0507488	−	0.0507488i	−0.732026	+	0.681277i	$0.761425\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	31.6276	+	31.6276i	1.06195	+	1.06195i	0.997950	+	0.0640012i	$0.0203861\pi$
$887$	31.6276	+	31.6276i	1.06195	+	1.06195i	0.0640012	+	0.997950i	$0.479614\pi$
$888$		0			0
$889$	17.4023	−	6.61133i	0.583653	−	0.221737i
$890$		0			0
$891$	−3.21839			−0.107820
$892$		0			0
$893$	−8.72625	−	8.72625i	−0.292013	−	0.292013i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−0.0732248	+	0.0732248i	−0.00244490	+	0.00244490i
$898$		0			0
$899$	18.4961			0.616879
$900$		0			0
$901$		−	37.1717i		−	1.23837i
$902$		0			0
$903$	−5.65588	−	2.54157i	−0.188216	−	0.0845782i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	25.9988	−	25.9988i	0.863278	−	0.863278i	−0.128440	−	0.991717i	$-0.540997\pi$
$907$	25.9988	−	25.9988i	0.863278	−	0.863278i	0.991717	+	0.128440i	$0.0409969\pi$
$908$		0			0
$909$	−11.5398			−0.382752
$910$		0			0
$911$	−20.0015			−0.662679			−0.331340	−	0.943512i	$-0.607501\pi$
$911$	−20.0015			−0.662679			−0.331340	+	0.943512i	$0.607501\pi$
$912$		0			0
$913$	14.1185	−	14.1185i	0.467254	−	0.467254i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	7.79801	−	17.3533i	0.257513	−	0.573056i
$918$		0			0
$919$			51.2652i			1.69108i	0.533910	+	0.845541i	$0.320722\pi$
$919$			51.2652i			1.69108i	−0.533910	+	0.845541i	$0.679278\pi$
$920$		0			0
$921$	−24.5431			−0.808723
$922$		0			0
$923$	−7.84505	+	7.84505i	−0.258223	+	0.258223i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−15.6075	−	15.6075i	−0.512619	−	0.512619i
$928$		0			0
$929$	−31.4773			−1.03274			−0.516368	−	0.856367i	$-0.672716\pi$
$929$	−31.4773			−1.03274			−0.516368	+	0.856367i	$0.672716\pi$
$930$		0			0
$931$	15.3137	+	17.2454i	0.501887	+	0.565194i
$932$		0			0
$933$	11.0340	+	11.0340i	0.361237	+	0.361237i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	24.5073	+	24.5073i	0.800617	+	0.800617i	0.983192	−	0.182575i	$-0.0584431\pi$
$937$	24.5073	+	24.5073i	0.800617	+	0.800617i	−0.182575	+	0.983192i	$0.558443\pi$
$938$		0			0
$939$			19.1455i			0.624790i
$940$		0			0
$941$			24.6191i			0.802559i	0.915956	+	0.401279i	$0.131434\pi$
$941$			24.6191i			0.802559i	−0.915956	+	0.401279i	$0.868566\pi$
$942$		0			0
$943$	−0.580352	+	0.580352i	−0.0188989	+	0.0188989i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−38.8951	+	38.8951i	−1.26392	+	1.26392i	−0.314743	+	0.949177i	$0.601918\pi$
$947$	−38.8951	+	38.8951i	−1.26392	+	1.26392i	−0.949177	+	0.314743i	$0.898082\pi$
$948$		0			0
$949$		−	15.9742i		−	0.518544i
$950$		0			0
$951$		−	18.4238i		−	0.597434i
$952$		0			0
$953$	−9.24379	−	9.24379i	−0.299436	−	0.299436i	0.541357	−	0.840793i	$-0.317911\pi$
$953$	−9.24379	−	9.24379i	−0.299436	−	0.299436i	−0.840793	+	0.541357i	$0.817911\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−16.4888	−	16.4888i	−0.533007	−	0.533007i
$958$		0			0
$959$	38.3345	−	14.5637i	1.23788	−	0.470287i
$960$		0			0
$961$	7.17092			0.231320
$962$		0			0
$963$	−6.64032	−	6.64032i	−0.213981	−	0.213981i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−9.04994	+	9.04994i	−0.291027	+	0.291027i	−0.837486	−	0.546459i	$-0.815975\pi$
$967$	−9.04994	+	9.04994i	−0.291027	+	0.291027i	0.546459	+	0.837486i	$0.315975\pi$
$968$		0			0
$969$	−9.75438			−0.313356
$970$		0			0
$971$		−	7.64554i		−	0.245357i	−0.992446	−	0.122679i	$-0.960852\pi$
$971$		−	7.64554i		−	0.245357i	0.992446	−	0.122679i	$-0.0391484\pi$
$972$		0			0
$973$	38.7269	+	17.4026i	1.24153	+	0.557902i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.25434	+	1.25434i	−0.0401300	+	0.0401300i	−0.726887	−	0.686757i	$-0.759034\pi$
$977$	−1.25434	+	1.25434i	−0.0401300	+	0.0401300i	0.686757	+	0.726887i	$0.259034\pi$
$978$		0			0
$979$	−58.0475			−1.85521
$980$		0			0
$981$	−4.78325			−0.152718
$982$		0			0
$983$	22.3196	−	22.3196i	0.711885	−	0.711885i	−0.255045	−	0.966929i	$-0.582090\pi$
$983$	22.3196	−	22.3196i	0.711885	−	0.711885i	0.966929	+	0.255045i	$0.0820902\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	9.33421	+	4.19450i	0.297111	+	0.133512i
$988$		0			0
$989$		−	0.174622i		−	0.00555267i
$990$		0			0
$991$	9.17736			0.291528			0.145764	−	0.989319i	$-0.453436\pi$
$991$	9.17736			0.291528			0.145764	+	0.989319i	$0.453436\pi$
$992$		0			0
$993$	12.3329	−	12.3329i	0.391373	−	0.391373i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−20.3783	−	20.3783i	−0.645387	−	0.645387i	0.306488	−	0.951875i	$-0.400846\pi$
$997$	−20.3783	−	20.3783i	−0.645387	−	0.645387i	−0.951875	+	0.306488i	$0.900846\pi$
$998$		0			0
$999$	23.1142			0.731300

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1400.2.x.b.993.8		24
5.2	odd	4	inner	1400.2.x.b.657.5		24
5.3	odd	4		280.2.x.a.97.8	yes	24
5.4	even	2		280.2.x.a.153.5	yes	24
7.6	odd	2	inner	1400.2.x.b.993.5		24
20.3	even	4		560.2.bj.d.97.5		24
20.19	odd	2		560.2.bj.d.433.8		24
35.13	even	4		280.2.x.a.97.5	✓	24
35.27	even	4	inner	1400.2.x.b.657.8		24
35.34	odd	2		280.2.x.a.153.8	yes	24
140.83	odd	4		560.2.bj.d.97.8		24
140.139	even	2		560.2.bj.d.433.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.x.a.97.5	✓	24	35.13	even	4
280.2.x.a.97.8	yes	24	5.3	odd	4
280.2.x.a.153.5	yes	24	5.4	even	2
280.2.x.a.153.8	yes	24	35.34	odd	2
560.2.bj.d.97.5		24	20.3	even	4
560.2.bj.d.97.8		24	140.83	odd	4
560.2.bj.d.433.5		24	140.139	even	2
560.2.bj.d.433.8		24	20.19	odd	2
1400.2.x.b.657.5		24	5.2	odd	4	inner
1400.2.x.b.657.8		24	35.27	even	4	inner
1400.2.x.b.993.5		24	7.6	odd	2	inner
1400.2.x.b.993.8		24	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.730185 - 0.730185i) q^{3} +(-2.41329 - 1.08445i) q^{7} +1.93366i q^{9} +O(q^{10})\)	\(q+(0.730185 - 0.730185i) q^{3} +(-2.41329 - 1.08445i) q^{7} +1.93366i q^{9} +5.95977 q^{11} +(0.921623 - 0.921623i) q^{13} +(-2.02728 - 2.02728i) q^{17} +3.29475 q^{19} +(-2.55400 + 0.970294i) q^{21} +(-0.0544054 - 0.0544054i) q^{23} +(3.60248 + 3.60248i) q^{27} -3.78901i q^{29} +4.88150i q^{31} +(4.35174 - 4.35174i) q^{33} +(3.20809 - 3.20809i) q^{37} -1.34591i q^{39} -10.6672i q^{41} +(1.60483 + 1.60483i) q^{43} +(-2.64854 - 2.64854i) q^{47} +(4.64792 + 5.23420i) q^{49} -2.96059 q^{51} +(9.16786 + 9.16786i) q^{53} +(2.40577 - 2.40577i) q^{57} +13.3231 q^{59} -11.2091i q^{61} +(2.09697 - 4.66648i) q^{63} +(6.43325 - 6.43325i) q^{67} -0.0794520 q^{69} -8.51221 q^{71} +(8.66633 - 8.66633i) q^{73} +(-14.3826 - 6.46310i) q^{77} -1.76209i q^{79} -0.540019 q^{81} +(2.36897 - 2.36897i) q^{83} +(-2.76668 - 2.76668i) q^{87} -9.73989 q^{89} +(-3.22360 + 1.22468i) q^{91} +(3.56440 + 3.56440i) q^{93} +(2.05040 + 2.05040i) q^{97} +11.5242i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{7}+O(q^{10}) \) 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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