LMFDB - Embedded newform 900.3.ba.a.161.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(161,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 8]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("900.161");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	900.ba (of order $10$, degree $4$, 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:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			161.17
Character	$\chi$	$=$	900.161
Dual form			900.3.ba.a.341.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.15240 + 2.78525i) q^{5} -1.13968 q^{7} +O(q^{10})$	$q+(4.15240 + 2.78525i) q^{5} -1.13968 q^{7} +(-1.53818 - 2.11713i) q^{11} +(2.85660 + 2.07544i) q^{13} +(-31.9044 + 10.3664i) q^{17} +(4.93000 + 15.1730i) q^{19} +(17.7682 + 24.4558i) q^{23} +(9.48478 + 23.1309i) q^{25} +(41.4658 + 13.4731i) q^{29} +(-6.90424 - 21.2491i) q^{31} +(-4.73238 - 3.17428i) q^{35} +(-28.9857 - 21.0593i) q^{37} +(-4.28677 + 5.90023i) q^{41} -43.5332 q^{43} +(76.0291 + 24.7034i) q^{47} -47.7011 q^{49} +(-34.7979 - 11.3065i) q^{53} +(-0.490419 - 13.0754i) q^{55} +(-47.9974 + 66.0628i) q^{59} +(-67.3185 + 48.9097i) q^{61} +(6.08111 + 16.5744i) q^{65} +(33.8857 + 104.289i) q^{67} +(103.288 + 33.5604i) q^{71} +(-24.6876 + 17.9366i) q^{73} +(1.75303 + 2.41284i) q^{77} +(39.6322 - 121.975i) q^{79} +(46.7781 - 15.1991i) q^{83} +(-161.353 - 45.8165i) q^{85} +(14.7859 + 20.3511i) q^{89} +(-3.25560 - 2.36533i) q^{91} +(-21.7892 + 76.7355i) q^{95} +(9.39148 - 28.9040i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 16 q^{7}+O(q^{10}) $ 80 * q + 16 * q^7	$ 80 q + 16 q^{7} - 8 q^{13} + 60 q^{19} - 120 q^{25} + 120 q^{31} + 116 q^{37} - 80 q^{43} + 440 q^{49} + 120 q^{55} + 80 q^{61} + 24 q^{67} + 128 q^{73} + 40 q^{79} + 40 q^{85} - 140 q^{91} + 384 q^{97}+O(q^{100}) $ 80 * q + 16 * q^7 - 8 * q^13 + 60 * q^19 - 120 * q^25 + 120 * q^31 + 116 * q^37 - 80 * q^43 + 440 * q^49 + 120 * q^55 + 80 * q^61 + 24 * q^67 + 128 * q^73 + 40 * q^79 + 40 * q^85 - 140 * q^91 + 384 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$-1$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	4.15240	+	2.78525i	0.830479	+	0.557050i
$5$	4.15240	+	2.78525i	0.830479	+	0.557050i
$6$		0			0
$7$	−1.13968			−0.162811			−0.0814054	−	0.996681i	$-0.525941\pi$
$7$	−1.13968			−0.162811			−0.0814054	+	0.996681i	$0.525941\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.53818	−	2.11713i	−0.139835	−	0.192466i	0.733356	−	0.679845i	$-0.237953\pi$
$11$	−1.53818	−	2.11713i	−0.139835	−	0.192466i	−0.873191	+	0.487379i	$0.837953\pi$
$12$		0			0
$13$	2.85660	+	2.07544i	0.219738	+	0.159649i	0.692209	−	0.721697i	$-0.256638\pi$
$13$	2.85660	+	2.07544i	0.219738	+	0.159649i	−0.472470	+	0.881347i	$0.656638\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−31.9044	+	10.3664i	−1.87673	+	0.609787i	−0.888052	+	0.459743i	$0.847941\pi$
$17$	−31.9044	+	10.3664i	−1.87673	+	0.609787i	−0.988679	+	0.150044i	$0.952059\pi$
$18$		0			0
$19$	4.93000	+	15.1730i	0.259474	+	0.798578i	0.992915	+	0.118826i	$0.0379129\pi$
$19$	4.93000	+	15.1730i	0.259474	+	0.798578i	−0.733441	+	0.679753i	$0.762087\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	17.7682	+	24.4558i	0.772529	+	1.06330i	0.996067	+	0.0886001i	$0.0282393\pi$
$23$	17.7682	+	24.4558i	0.772529	+	1.06330i	−0.223538	+	0.974695i	$0.571761\pi$
$24$		0			0
$25$	9.48478	+	23.1309i	0.379391	+	0.925236i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	41.4658	+	13.4731i	1.42986	+	0.464588i	0.918719	−	0.394912i	$-0.129225\pi$
$29$	41.4658	+	13.4731i	1.42986	+	0.464588i	0.511136	+	0.859500i	$0.329225\pi$
$30$		0			0
$31$	−6.90424	−	21.2491i	−0.222717	−	0.685453i	−0.998515	−	0.0544720i	$-0.982652\pi$
$31$	−6.90424	−	21.2491i	−0.222717	−	0.685453i	0.775798	−	0.630981i	$-0.217348\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−4.73238	−	3.17428i	−0.135211	−	0.0906937i
$36$		0			0
$37$	−28.9857	−	21.0593i	−0.783396	−	0.569171i	0.122600	−	0.992456i	$-0.460877\pi$
$37$	−28.9857	−	21.0593i	−0.783396	−	0.569171i	−0.905996	+	0.423285i	$0.860877\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.28677	+	5.90023i	−0.104555	+	0.143908i	−0.858089	−	0.513502i	$-0.828348\pi$
$41$	−4.28677	+	5.90023i	−0.104555	+	0.143908i	0.753533	+	0.657410i	$0.228348\pi$
$42$		0			0
$43$	−43.5332			−1.01240			−0.506199	−	0.862416i	$-0.668950\pi$
$43$	−43.5332			−1.01240			−0.506199	+	0.862416i	$0.668950\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	76.0291	+	24.7034i	1.61764	+	0.525604i	0.971384	−	0.237516i	$-0.0763332\pi$
$47$	76.0291	+	24.7034i	1.61764	+	0.525604i	0.646258	+	0.763119i	$0.276333\pi$
$48$		0			0
$49$	−47.7011			−0.973493
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−34.7979	−	11.3065i	−0.656564	−	0.213330i	−0.0382577	−	0.999268i	$-0.512181\pi$
$53$	−34.7979	−	11.3065i	−0.656564	−	0.213330i	−0.618306	+	0.785937i	$0.712181\pi$
$54$		0			0
$55$	−0.490419	−	13.0754i	−0.00891671	−	0.237734i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−47.9974	+	66.0628i	−0.813516	+	1.11971i	0.177256	+	0.984165i	$0.443278\pi$
$59$	−47.9974	+	66.0628i	−0.813516	+	1.11971i	−0.990771	+	0.135543i	$0.956722\pi$
$60$		0			0
$61$	−67.3185	+	48.9097i	−1.10358	+	0.801799i	−0.981641	−	0.190739i	$-0.938912\pi$
$61$	−67.3185	+	48.9097i	−1.10358	+	0.801799i	−0.121940	+	0.992537i	$0.538912\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	6.08111	+	16.5744i	0.0935556	+	0.254991i
$66$		0			0
$67$	33.8857	+	104.289i	0.505756	+	1.55656i	0.799496	+	0.600672i	$0.205100\pi$
$67$	33.8857	+	104.289i	0.505756	+	1.55656i	−0.293740	+	0.955885i	$0.594900\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	103.288	+	33.5604i	1.45477	+	0.472682i	0.926467	−	0.376377i	$-0.122830\pi$
$71$	103.288	+	33.5604i	1.45477	+	0.472682i	0.528299	+	0.849059i	$0.322830\pi$
$72$		0			0
$73$	−24.6876	+	17.9366i	−0.338187	+	0.245707i	−0.743896	−	0.668295i	$-0.767024\pi$
$73$	−24.6876	+	17.9366i	−0.338187	+	0.245707i	0.405710	+	0.914002i	$0.367024\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.75303	+	2.41284i	0.0227666	+	0.0313356i
$78$		0			0
$79$	39.6322	−	121.975i	0.501673	−	1.54399i	−0.304620	−	0.952474i	$-0.598529\pi$
$79$	39.6322	−	121.975i	0.501673	−	1.54399i	0.806293	−	0.591517i	$-0.201471\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	46.7781	−	15.1991i	0.563592	−	0.183122i	−0.0133450	−	0.999911i	$-0.504248\pi$
$83$	46.7781	−	15.1991i	0.563592	−	0.183122i	0.576937	+	0.816789i	$0.304248\pi$
$84$		0			0
$85$	−161.353	−	45.8165i	−1.89827	−	0.539017i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	14.7859	+	20.3511i	0.166134	+	0.228664i	0.883965	−	0.467554i	$-0.154865\pi$
$89$	14.7859	+	20.3511i	0.166134	+	0.228664i	−0.717830	+	0.696218i	$0.754865\pi$
$90$		0			0
$91$	−3.25560	−	2.36533i	−0.0357758	−	0.0259926i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−21.7892	+	76.7355i	−0.229360	+	0.807742i
$96$		0			0
$97$	9.39148	−	28.9040i	0.0968194	−	0.297980i	−0.890904	−	0.454191i	$-0.849928\pi$
$97$	9.39148	−	28.9040i	0.0968194	−	0.297980i	0.987724	+	0.156212i	$0.0499282\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$			63.1583i			0.625330i	0.949864	+	0.312665i	$0.101222\pi$
$101$			63.1583i			0.625330i	−0.949864	+	0.312665i	$0.898778\pi$
$102$		0			0
$103$	−24.1937	+	74.4605i	−0.234890	+	0.722918i	0.762246	+	0.647288i	$0.224097\pi$
$103$	−24.1937	+	74.4605i	−0.234890	+	0.722918i	−0.997136	+	0.0756299i	$0.975903\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			71.8792i			0.671768i	0.941903	+	0.335884i	$0.109035\pi$
$107$			71.8792i			0.671768i	−0.941903	+	0.335884i	$0.890965\pi$
$108$		0			0
$109$	107.865	+	78.3684i	0.989585	+	0.718976i	0.959830	−	0.280581i	$-0.0905273\pi$
$109$	107.865	+	78.3684i	0.989585	+	0.718976i	0.0297550	+	0.999557i	$0.490527\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−2.57856	+	3.54909i	−0.0228191	+	0.0314079i	−0.820274	−	0.571971i	$-0.806179\pi$
$113$	−2.57856	+	3.54909i	−0.0228191	+	0.0314079i	0.797455	+	0.603378i	$0.206179\pi$
$114$		0			0
$115$	5.66502	+	151.039i	0.0492611	+	1.31338i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	36.3607	−	11.8143i	0.305552	−	0.0992799i
$120$		0			0
$121$	35.2748	−	108.565i	0.291528	−	0.897230i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−25.0408	+	122.466i	−0.200326	+	0.979729i
$126$		0			0
$127$	−44.9479	+	32.6566i	−0.353921	+	0.257139i	−0.750512	−	0.660857i	$-0.770193\pi$
$127$	−44.9479	+	32.6566i	−0.353921	+	0.257139i	0.396591	+	0.917995i	$0.370193\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	4.38366	−	1.42434i	0.0334630	−	0.0108728i	−0.292238	−	0.956346i	$-0.594400\pi$
$131$	4.38366	−	1.42434i	0.0334630	−	0.0108728i	0.325701	+	0.945473i	$0.394400\pi$
$132$		0			0
$133$	−5.61860	−	17.2923i	−0.0422451	−	0.130017i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−77.4328	+	106.577i	−0.565203	+	0.777935i	−0.991976	−	0.126424i	$-0.959650\pi$
$137$	−77.4328	+	106.577i	−0.565203	+	0.777935i	0.426774	+	0.904358i	$0.359650\pi$
$138$		0			0
$139$	−86.7856	+	63.0534i	−0.624357	+	0.453622i	−0.854441	−	0.519549i	$-0.826100\pi$
$139$	−86.7856	+	63.0534i	−0.624357	+	0.453622i	0.230084	+	0.973171i	$0.426100\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	9.24020i		−	0.0646168i
$144$		0			0
$145$	134.657	+	171.438i	0.928666	+	1.18233i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			20.9291i			0.140464i	0.997531	+	0.0702320i	$0.0223740\pi$
$149$			20.9291i			0.140464i	−0.997531	+	0.0702320i	$0.977626\pi$
$150$		0			0
$151$	−126.614			−0.838506			−0.419253	−	0.907869i	$-0.637708\pi$
$151$	−126.614			−0.838506			−0.419253	+	0.907869i	$0.637708\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	30.5148	−	107.465i	0.196870	−	0.693319i
$156$		0			0
$157$	226.029			1.43968			0.719838	−	0.694142i	$-0.244216\pi$
$157$	226.029			1.43968			0.719838	+	0.694142i	$0.244216\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−20.2499	−	27.8717i	−0.125776	−	0.173116i
$162$		0			0
$163$	−118.650	−	86.2045i	−0.727916	−	0.528862i	0.160987	−	0.986956i	$-0.448532\pi$
$163$	−118.650	−	86.2045i	−0.727916	−	0.528862i	−0.888904	+	0.458094i	$0.848532\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−54.0354	+	17.5572i	−0.323565	+	0.105133i	−0.466296	−	0.884629i	$-0.654412\pi$
$167$	−54.0354	+	17.5572i	−0.323565	+	0.105133i	0.142731	+	0.989762i	$0.454412\pi$
$168$		0			0
$169$	−48.3712	−	148.871i	−0.286220	−	0.880894i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−41.5678	−	57.2132i	−0.240276	−	0.330712i	0.671800	−	0.740733i	$-0.265521\pi$
$173$	−41.5678	−	57.2132i	−0.240276	−	0.330712i	−0.912076	+	0.410021i	$0.865521\pi$
$174$		0			0
$175$	−10.8096	−	26.3617i	−0.0617690	−	0.150638i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	303.003	+	98.4515i	1.69275	+	0.550008i	0.987316	−	0.158766i	$-0.0507516\pi$
$179$	303.003	+	98.4515i	1.69275	+	0.550008i	0.705435	+	0.708774i	$0.250752\pi$
$180$		0			0
$181$	−73.5918	−	226.492i	−0.406584	−	1.25134i	−0.919565	−	0.392938i	$-0.871459\pi$
$181$	−73.5918	−	226.492i	−0.406584	−	1.25134i	0.512981	−	0.858400i	$-0.328541\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−61.7045	−	168.179i	−0.333538	−	0.909075i
$186$		0			0
$187$	71.0218	+	51.6004i	0.379796	+	0.275938i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	141.481	−	194.732i	0.740740	−	1.01954i	−0.257835	−	0.966189i	$-0.583009\pi$
$191$	141.481	−	194.732i	0.740740	−	1.01954i	0.998576	−	0.0533528i	$-0.0169908\pi$
$192$		0			0
$193$	−244.117			−1.26485			−0.632426	−	0.774621i	$-0.717941\pi$
$193$	−244.117			−1.26485			−0.632426	+	0.774621i	$0.717941\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−80.6782	−	26.2140i	−0.409534	−	0.133066i	0.0970025	−	0.995284i	$-0.469075\pi$
$197$	−80.6782	−	26.2140i	−0.409534	−	0.133066i	−0.506537	+	0.862218i	$0.669075\pi$
$198$		0			0
$199$	191.282			0.961218			0.480609	−	0.876935i	$-0.340416\pi$
$199$	191.282			0.961218			0.480609	+	0.876935i	$0.340416\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−47.2575	−	15.3549i	−0.232796	−	0.0756399i
$204$		0			0
$205$	−34.2340	+	12.5604i	−0.166995	+	0.0612702i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	24.5399	−	33.7763i	0.117416	−	0.161609i
$210$		0			0
$211$	199.307	−	144.805i	0.944582	−	0.686279i	−0.00493713	−	0.999988i	$-0.501572\pi$
$211$	199.307	−	144.805i	0.944582	−	0.686279i	0.949519	+	0.313709i	$0.101572\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−180.767	−	121.251i	−0.840776	−	0.563957i
$216$		0			0
$217$	7.86859	+	24.2170i	0.0362608	+	0.111599i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−112.653	−	36.6032i	−0.509742	−	0.165625i
$222$		0			0
$223$	−87.5425	+	63.6033i	−0.392567	+	0.285217i	−0.766507	−	0.642236i	$-0.778007\pi$
$223$	−87.5425	+	63.6033i	−0.392567	+	0.285217i	0.373939	+	0.927453i	$0.378007\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−7.60299	−	10.4646i	−0.0334934	−	0.0460997i	0.791942	−	0.610596i	$-0.209070\pi$
$227$	−7.60299	−	10.4646i	−0.0334934	−	0.0460997i	−0.825435	+	0.564497i	$0.809070\pi$
$228$		0			0
$229$	60.9465	−	187.574i	0.266142	−	0.819101i	−0.725286	−	0.688448i	$-0.758292\pi$
$229$	60.9465	−	187.574i	0.266142	−	0.819101i	0.991428	−	0.130654i	$-0.0417075\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−46.7201	+	15.1803i	−0.200515	+	0.0651514i	−0.407553	−	0.913182i	$-0.633618\pi$
$233$	−46.7201	+	15.1803i	−0.200515	+	0.0651514i	0.207037	+	0.978333i	$0.433618\pi$
$234$		0			0
$235$	246.898	+	314.338i	1.05063	+	1.33761i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−35.6685	−	49.0935i	−0.149241	−	0.205412i	0.727851	−	0.685736i	$-0.240519\pi$
$239$	−35.6685	−	49.0935i	−0.149241	−	0.205412i	−0.877092	+	0.480323i	$0.840519\pi$
$240$		0			0
$241$	−84.8074	−	61.6162i	−0.351898	−	0.255669i	0.397767	−	0.917486i	$-0.369785\pi$
$241$	−84.8074	−	61.6162i	−0.351898	−	0.255669i	−0.749665	+	0.661818i	$0.769785\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−198.074	−	132.860i	−0.808465	−	0.542284i
$246$		0			0
$247$	−17.4076	+	53.5751i	−0.0704761	+	0.216903i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	320.087i		−	1.27525i	−0.770348	−	0.637624i	$-0.779917\pi$
$251$		−	320.087i		−	1.27525i	0.770348	−	0.637624i	$-0.220083\pi$
$252$		0			0
$253$	24.4453	−	75.2350i	0.0966219	−	0.297372i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			118.467i			0.460960i	0.973077	+	0.230480i	$0.0740297\pi$
$257$			118.467i			0.460960i	−0.973077	+	0.230480i	$0.925970\pi$
$258$		0			0
$259$	33.0342	+	24.0008i	0.127545	+	0.0926671i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	239.647	−	329.846i	0.911205	−	1.25417i	−0.0555491	−	0.998456i	$-0.517691\pi$
$263$	239.647	−	329.846i	0.911205	−	1.25417i	0.966754	−	0.255710i	$-0.0823091\pi$
$264$		0			0
$265$	−113.003	−	143.870i	−0.426427	−	0.542905i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−290.125	+	94.2672i	−1.07853	+	0.350436i	−0.793804	−	0.608173i	$-0.791902\pi$
$269$	−290.125	+	94.2672i	−1.07853	+	0.350436i	−0.284726	+	0.958609i	$0.591902\pi$
$270$		0			0
$271$	−24.7479	+	76.1663i	−0.0913208	+	0.281056i	−0.986277	−	0.165097i	$-0.947206\pi$
$271$	−24.7479	+	76.1663i	−0.0913208	+	0.281056i	0.894957	+	0.446153i	$0.147206\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	34.3818	−	55.6601i	0.125025	−	0.202400i
$276$		0			0
$277$	200.652	−	145.782i	0.724375	−	0.526289i	−0.163404	−	0.986559i	$-0.552247\pi$
$277$	200.652	−	145.782i	0.724375	−	0.526289i	0.887779	+	0.460270i	$0.152247\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	311.858	−	101.329i	1.10982	−	0.360601i	0.303943	−	0.952690i	$-0.401697\pi$
$281$	311.858	−	101.329i	1.10982	−	0.360601i	0.805873	+	0.592089i	$0.201697\pi$
$282$		0			0
$283$	40.1274	+	123.500i	0.141793	+	0.436394i	0.996585	−	0.0825773i	$-0.0263151\pi$
$283$	40.1274	+	123.500i	0.141793	+	0.436394i	−0.854792	+	0.518971i	$0.826315\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	4.88553	−	6.72435i	0.0170227	−	0.0234298i
$288$		0			0
$289$	676.625	−	491.597i	2.34126	−	1.70103i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	412.201i		−	1.40683i	−0.710780	−	0.703414i	$-0.751658\pi$
$293$		−	412.201i		−	1.40683i	0.710780	−	0.703414i	$-0.248342\pi$
$294$		0			0
$295$	−383.306	+	140.634i	−1.29934	+	0.476726i
$296$		0			0
$297$		0			0
$298$		0			0
$299$			106.737i			0.356981i
$300$		0			0
$301$	49.6137			0.164829
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−415.759	+	15.5939i	−1.36314	+	0.0511275i
$306$		0			0
$307$	484.680			1.57876			0.789381	−	0.613904i	$-0.210402\pi$
$307$	484.680			1.57876			0.789381	+	0.613904i	$0.210402\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	233.864	+	321.886i	0.751973	+	1.03500i	0.997840	+	0.0656983i	$0.0209275\pi$
$311$	233.864	+	321.886i	0.751973	+	1.03500i	−0.245867	+	0.969304i	$0.579073\pi$
$312$		0			0
$313$	−137.153	−	99.6471i	−0.438187	−	0.318361i	0.346727	−	0.937966i	$-0.387293\pi$
$313$	−137.153	−	99.6471i	−0.438187	−	0.318361i	−0.784914	+	0.619605i	$0.787293\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	10.2664	−	3.33576i	0.0323861	−	0.0105229i	−0.292779	−	0.956180i	$-0.594580\pi$
$317$	10.2664	−	3.33576i	0.0323861	−	0.0105229i	0.325165	+	0.945657i	$0.394580\pi$
$318$		0			0
$319$	−35.2578	−	108.512i	−0.110526	−	0.340164i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−314.578	−	432.979i	−0.973925	−	1.34049i
$324$		0			0
$325$	−20.9126	+	85.7609i	−0.0643465	+	0.263880i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−86.6485	−	28.1538i	−0.263369	−	0.0855739i
$330$		0			0
$331$	−54.3241	−	167.192i	−0.164121	−	0.505113i	0.834849	−	0.550479i	$-0.185555\pi$
$331$	−54.3241	−	167.192i	−0.164121	−	0.505113i	−0.998970	+	0.0453655i	$0.985555\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−149.765	+	527.431i	−0.447060	+	1.57442i
$336$		0			0
$337$	474.446	+	344.705i	1.40785	+	1.02286i	0.993630	+	0.112688i	$0.0359462\pi$
$337$	474.446	+	344.705i	1.40785	+	1.02286i	0.414222	+	0.910176i	$0.364054\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−34.3670	+	47.3021i	−0.100783	+	0.138716i
$342$		0			0
$343$	110.208			0.321306
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−366.699	−	119.148i	−1.05677	−	0.343365i	−0.271447	−	0.962453i	$-0.587502\pi$
$347$	−366.699	−	119.148i	−1.05677	−	0.343365i	−0.785321	+	0.619088i	$0.787502\pi$
$348$		0			0
$349$	252.648			0.723920			0.361960	−	0.932194i	$-0.382108\pi$
$349$	252.648			0.723920			0.361960	+	0.932194i	$0.382108\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−543.132	−	176.474i	−1.53862	−	0.499927i	−0.587623	−	0.809135i	$-0.699936\pi$
$353$	−543.132	−	176.474i	−1.53862	−	0.499927i	−0.950995	+	0.309208i	$0.899936\pi$
$354$		0			0
$355$	335.420	+	427.040i	0.944845	+	1.20293i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	228.387	−	314.348i	0.636175	−	0.875620i	−0.362229	−	0.932089i	$-0.617984\pi$
$359$	228.387	−	314.348i	0.636175	−	0.875620i	0.998404	+	0.0564689i	$0.0179842\pi$
$360$		0			0
$361$	86.1405	−	62.5847i	0.238616	−	0.173365i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−152.471	+	5.71873i	−0.417728	+	0.0156678i
$366$		0			0
$367$	67.7793	+	208.603i	0.184685	+	0.568401i	0.999943	−	0.0106969i	$-0.00340498\pi$
$367$	67.7793	+	208.603i	0.184685	+	0.568401i	−0.815258	+	0.579098i	$0.803405\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	39.6583	+	12.8858i	0.106896	+	0.0347325i
$372$		0			0
$373$	−323.516	+	235.048i	−0.867336	+	0.630156i	−0.929871	−	0.367886i	$-0.880082\pi$
$373$	−323.516	+	235.048i	−0.867336	+	0.630156i	0.0625348	+	0.998043i	$0.480082\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	90.4887	+	124.547i	0.240023	+	0.330363i
$378$		0			0
$379$	−40.0206	+	123.171i	−0.105595	+	0.324989i	−0.989870	−	0.141979i	$-0.954654\pi$
$379$	−40.0206	+	123.171i	−0.105595	+	0.324989i	0.884274	+	0.466968i	$0.154654\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	331.736	−	107.788i	0.866152	−	0.281430i	0.157956	−	0.987446i	$-0.449510\pi$
$383$	331.736	−	107.788i	0.866152	−	0.281430i	0.708196	+	0.706016i	$0.249510\pi$
$384$		0			0
$385$	0.558918	+	14.9017i	0.00145174	+	0.0387057i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	267.285	+	367.887i	0.687109	+	0.945724i	0.999992	−	0.00406741i	$-0.00129470\pi$
$389$	267.285	+	367.887i	0.687109	+	0.945724i	−0.312883	+	0.949792i	$0.601295\pi$
$390$		0			0
$391$	−820.401	−	596.057i	−2.09821	−	1.52444i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	504.300	−	396.104i	1.27671	−	1.00280i
$396$		0			0
$397$	−5.02730	+	15.4724i	−0.0126632	+	0.0389734i	−0.957188	−	0.289465i	$-0.906522\pi$
$397$	−5.02730	+	15.4724i	−0.0126632	+	0.0389734i	0.944525	+	0.328439i	$0.106522\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	324.823i		−	0.810033i	−0.914309	−	0.405017i	$-0.867266\pi$
$401$		−	324.823i		−	0.810033i	0.914309	−	0.405017i	$-0.132734\pi$
$402$		0			0
$403$	24.3785	−	75.0294i	0.0604926	−	0.186177i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			93.7595i			0.230367i
$408$		0			0
$409$	−321.193	−	233.360i	−0.785312	−	0.570563i	0.121256	−	0.992621i	$-0.461308\pi$
$409$	−321.193	−	233.360i	−0.785312	−	0.570563i	−0.906569	+	0.422058i	$0.861308\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	54.7015	−	75.2901i	0.132449	−	0.182300i
$414$		0			0
$415$	236.575	+	67.1759i	0.570059	+	0.161870i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	573.463	−	186.329i	1.36865	−	0.444700i	0.469726	−	0.882812i	$-0.344353\pi$
$419$	573.463	−	186.329i	1.36865	−	0.444700i	0.898920	+	0.438112i	$0.144353\pi$
$420$		0			0
$421$	194.806	−	599.550i	0.462721	−	1.42411i	−0.399105	−	0.916905i	$-0.630679\pi$
$421$	194.806	−	599.550i	0.462721	−	1.42411i	0.861826	−	0.507204i	$-0.169321\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−542.390	−	639.656i	−1.27621	−	1.50507i
$426$		0			0
$427$	76.7212	−	55.7412i	0.179675	−	0.130541i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	134.036	−	43.5509i	0.310988	−	0.101046i	−0.149365	−	0.988782i	$-0.547723\pi$
$431$	134.036	−	43.5509i	0.310988	−	0.101046i	0.460353	+	0.887736i	$0.347723\pi$
$432$		0			0
$433$	20.3196	+	62.5372i	0.0469274	+	0.144428i	0.971775	−	0.235911i	$-0.0758074\pi$
$433$	20.3196	+	62.5372i	0.0469274	+	0.144428i	−0.924847	+	0.380339i	$0.875807\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−283.470	+	390.163i	−0.648673	+	0.892822i
$438$		0			0
$439$	307.072	−	223.101i	0.699480	−	0.508202i	−0.180283	−	0.983615i	$-0.557701\pi$
$439$	307.072	−	223.101i	0.699480	−	0.508202i	0.879763	+	0.475413i	$0.157701\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			646.169i			1.45862i	0.684183	+	0.729310i	$0.260159\pi$
$443$			646.169i			1.45862i	−0.684183	+	0.729310i	$0.739841\pi$
$444$		0			0
$445$	4.71420	+	125.688i	0.0105937	+	0.282446i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			581.733i			1.29562i	0.761802	+	0.647810i	$0.224315\pi$
$449$			581.733i			1.29562i	−0.761802	+	0.647810i	$0.775685\pi$
$450$		0			0
$451$	19.0854			0.0423179
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−6.93049	−	18.8894i	−0.0152319	−	0.0415152i
$456$		0			0
$457$	−559.678			−1.22468			−0.612339	−	0.790595i	$-0.709771\pi$
$457$	−559.678			−1.22468			−0.612339	+	0.790595i	$0.709771\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−302.838	−	416.821i	−0.656916	−	0.904167i	0.342459	−	0.939533i	$-0.388740\pi$
$461$	−302.838	−	416.821i	−0.656916	−	0.904167i	−0.999374	+	0.0353659i	$0.988740\pi$
$462$		0			0
$463$	−292.868	−	212.781i	−0.632544	−	0.459570i	0.224737	−	0.974420i	$-0.427848\pi$
$463$	−292.868	−	212.781i	−0.632544	−	0.459570i	−0.857281	+	0.514850i	$0.827848\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−257.839	+	83.7770i	−0.552118	+	0.179394i	−0.571772	−	0.820413i	$-0.693744\pi$
$467$	−257.839	+	83.7770i	−0.552118	+	0.179394i	0.0196536	+	0.999807i	$0.493744\pi$
$468$		0			0
$469$	−38.6186	−	118.856i	−0.0823425	−	0.253424i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	66.9620	+	92.1653i	0.141569	+	0.194853i
$474$		0			0
$475$	−304.205	+	257.948i	−0.640432	+	0.543048i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−49.0112	−	15.9247i	−0.102320	−	0.0332457i	0.257410	−	0.966302i	$-0.417131\pi$
$479$	−49.0112	−	15.9247i	−0.102320	−	0.0332457i	−0.359729	+	0.933057i	$0.617131\pi$
$480$		0			0
$481$	−39.0931	−	120.316i	−0.0812746	−	0.250137i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	119.502	−	93.8633i	0.246396	−	0.193533i
$486$		0			0
$487$	636.187	+	462.217i	1.30634	+	0.949110i	0.999996	−	0.00281161i	$-0.000894963\pi$
$487$	636.187	+	462.217i	1.30634	+	0.949110i	0.306342	+	0.951922i	$0.400895\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	483.282	−	665.181i	0.984282	−	1.35475i	0.0497916	−	0.998760i	$-0.484144\pi$
$491$	483.282	−	665.181i	0.984282	−	1.35475i	0.934490	−	0.355988i	$-0.115856\pi$
$492$		0			0
$493$	−1462.61			−2.96675
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−117.715	−	38.2480i	−0.236851	−	0.0769577i
$498$		0			0
$499$	539.761			1.08169			0.540843	−	0.841124i	$-0.318105\pi$
$499$	539.761			1.08169			0.540843	+	0.841124i	$0.318105\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	192.911	+	62.6805i	0.383520	+	0.124613i	0.494431	−	0.869217i	$-0.335377\pi$
$503$	192.911	+	62.6805i	0.383520	+	0.124613i	−0.110910	+	0.993830i	$0.535377\pi$
$504$		0			0
$505$	−175.912	+	262.258i	−0.348340	+	0.519323i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−27.7334	+	38.1717i	−0.0544860	+	0.0749936i	−0.835391	−	0.549657i	$-0.814759\pi$
$509$	−27.7334	+	38.1717i	−0.0544860	+	0.0749936i	0.780905	+	0.624650i	$0.214759\pi$
$510$		0			0
$511$	28.1359	−	20.4419i	0.0550604	−	0.0400038i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−307.853	+	241.804i	−0.597772	+	0.469522i
$516$		0			0
$517$	−64.6466	−	198.962i	−0.125042	−	0.384839i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	570.556	+	185.385i	1.09512	+	0.355825i	0.800222	−	0.599704i	$-0.204715\pi$
$521$	570.556	+	185.385i	1.09512	+	0.355825i	0.294896	+	0.955529i	$0.404715\pi$
$522$		0			0
$523$	−288.383	+	209.523i	−0.551402	+	0.400617i	−0.828302	−	0.560282i	$-0.810693\pi$
$523$	−288.383	+	209.523i	−0.551402	+	0.400617i	0.276900	+	0.960899i	$0.410693\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	440.552	+	606.367i	0.835961	+	1.15060i
$528$		0			0
$529$	−118.908	+	365.961i	−0.224778	+	0.691797i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−24.4912	+	7.95767i	−0.0459497	+	0.0149300i
$534$		0			0
$535$	−200.201	+	298.471i	−0.374208	+	0.557889i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	73.3731	+	100.989i	0.136128	+	0.187364i
$540$		0			0
$541$	327.786	+	238.151i	0.605889	+	0.440204i	0.847964	−	0.530053i	$-0.177828\pi$
$541$	327.786	+	238.151i	0.605889	+	0.440204i	−0.242075	+	0.970258i	$0.577828\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	229.622	+	625.847i	0.421325	+	1.14834i
$546$		0			0
$547$	−120.369	+	370.459i	−0.220054	+	0.677256i	0.778702	+	0.627394i	$0.215878\pi$
$547$	−120.369	+	370.459i	−0.220054	+	0.677256i	−0.998756	+	0.0498624i	$0.984122\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$			695.582i			1.26240i
$552$		0			0
$553$	−45.1678	+	139.012i	−0.0816778	+	0.251378i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			192.689i			0.345941i	0.984927	+	0.172970i	$0.0553365\pi$
$557$			192.689i			0.345941i	−0.984927	+	0.172970i	$0.944663\pi$
$558$		0			0
$559$	−124.357	−	90.3505i	−0.222463	−	0.161629i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	259.462	−	357.119i	0.460857	−	0.634315i	−0.513830	−	0.857892i	$-0.671774\pi$
$563$	259.462	−	357.119i	0.460857	−	0.634315i	0.974686	+	0.223578i	$0.0717736\pi$
$564$		0			0
$565$	−20.5923	+	7.55528i	−0.0364466	+	0.0133722i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−264.365	+	85.8973i	−0.464613	+	0.150962i	−0.531963	−	0.846767i	$-0.678546\pi$
$569$	−264.365	+	85.8973i	−0.464613	+	0.150962i	0.0673501	+	0.997729i	$0.478546\pi$
$570$		0			0
$571$	50.1640	−	154.389i	0.0878529	−	0.270383i	−0.897472	−	0.441071i	$-0.854599\pi$
$571$	50.1640	−	154.389i	0.0878529	−	0.270383i	0.985325	+	0.170687i	$0.0545988\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−397.157	+	642.952i	−0.690709	+	1.11818i
$576$		0			0
$577$	673.192	−	489.103i	1.16671	−	0.847665i	0.176100	−	0.984372i	$-0.443652\pi$
$577$	673.192	−	489.103i	1.16671	−	0.847665i	0.990612	+	0.136707i	$0.0436519\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−53.3118	+	17.3221i	−0.0917588	+	0.0298142i
$582$		0			0
$583$	29.5882	+	91.0631i	0.0507516	+	0.156197i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−162.852	+	224.146i	−0.277430	+	0.381850i	−0.924881	−	0.380257i	$-0.875835\pi$
$587$	−162.852	+	224.146i	−0.277430	+	0.381850i	0.647450	+	0.762108i	$0.275835\pi$
$588$		0			0
$589$	288.374	−	209.516i	0.489599	−	0.355714i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			83.9758i			0.141612i	0.997490	+	0.0708059i	$0.0225571\pi$
$593$			83.9758i			0.141612i	−0.997490	+	0.0708059i	$0.977443\pi$
$594$		0			0
$595$	183.890	+	52.2159i	0.309058	+	0.0877578i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			790.655i			1.31996i	0.751284	+	0.659979i	$0.229435\pi$
$599$			790.655i			1.31996i	−0.751284	+	0.659979i	$0.770565\pi$
$600$		0			0
$601$	−724.850			−1.20607			−0.603036	−	0.797714i	$-0.706043\pi$
$601$	−724.850			−1.20607			−0.603036	+	0.797714i	$0.706043\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	448.855	−	352.555i	0.741909	−	0.582735i
$606$		0			0
$607$	−363.035			−0.598081			−0.299041	−	0.954240i	$-0.596667\pi$
$607$	−363.035			−0.598081			−0.299041	+	0.954240i	$0.596667\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	165.914	+	228.362i	0.271546	+	0.373751i
$612$		0			0
$613$	842.391	+	612.033i	1.37421	+	0.998423i	0.997395	+	0.0721344i	$0.0229811\pi$
$613$	842.391	+	612.033i	1.37421	+	0.998423i	0.376816	+	0.926288i	$0.377019\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	58.0847	−	18.8729i	0.0941405	−	0.0305881i	−0.261568	−	0.965185i	$-0.584240\pi$
$617$	58.0847	−	18.8729i	0.0941405	−	0.0305881i	0.355709	+	0.934597i	$0.384240\pi$
$618$		0			0
$619$	−262.173	−	806.886i	−0.423543	−	1.30353i	−0.904382	−	0.426723i	$-0.859668\pi$
$619$	−262.173	−	806.886i	−0.423543	−	1.30353i	0.480839	−	0.876809i	$-0.340332\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−16.8512	−	23.1936i	−0.0270484	−	0.0372290i
$624$		0			0
$625$	−445.078	+	438.783i	−0.712125	+	0.702053i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	1143.08	+	371.409i	1.81730	+	0.590476i
$630$		0			0
$631$	−77.0453	−	237.121i	−0.122100	−	0.375786i	0.871261	−	0.490819i	$-0.163303\pi$
$631$	−77.0453	−	237.121i	−0.122100	−	0.375786i	−0.993362	+	0.115033i	$0.963303\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−277.598	+	10.4119i	−0.437163	+	0.0163967i
$636$		0			0
$637$	−136.263	−	99.0009i	−0.213914	−	0.155417i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−599.275	+	824.832i	−0.934907	+	1.28679i	0.0230072	+	0.999735i	$0.492676\pi$
$641$	−599.275	+	824.832i	−0.934907	+	1.28679i	−0.957914	+	0.287054i	$0.907324\pi$
$642$		0			0
$643$	−433.524			−0.674221			−0.337110	−	0.941465i	$-0.609450\pi$
$643$	−433.524			−0.674221			−0.337110	+	0.941465i	$0.609450\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	475.005	+	154.339i	0.734166	+	0.238545i	0.652154	−	0.758086i	$-0.273865\pi$
$647$	475.005	+	154.339i	0.734166	+	0.238545i	0.0820119	+	0.996631i	$0.473865\pi$
$648$		0			0
$649$	213.692			0.329264
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1097.25	−	356.518i	−1.68032	−	0.545969i	−0.695347	−	0.718675i	$-0.744749\pi$
$653$	−1097.25	−	356.518i	−1.68032	−	0.545969i	−0.984974	+	0.172705i	$0.944749\pi$
$654$		0			0
$655$	22.1698	+	6.29517i	0.0338471	+	0.00961095i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	59.4446	−	81.8184i	0.0902042	−	0.124155i	−0.761530	−	0.648130i	$-0.775551\pi$
$659$	59.4446	−	81.8184i	0.0902042	−	0.124155i	0.851734	+	0.523975i	$0.175551\pi$
$660$		0			0
$661$	−1035.45	+	752.299i	−1.56649	+	1.13812i	−0.636071	+	0.771630i	$0.719442\pi$
$661$	−1035.45	+	752.299i	−1.56649	+	1.13812i	−0.930421	+	0.366493i	$0.880558\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	24.8326	−	87.4536i	0.0373423	−	0.131509i
$666$		0			0
$667$	407.277	+	1253.47i	0.610611	+	1.87927i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	207.096	+	67.2897i	0.308638	+	0.100283i
$672$		0			0
$673$	0.0381292	−	0.0277025i	5.66556e−5	−	4.11627e-5i	−0.587757	−	0.809038i	$-0.699989\pi$
$673$	0.0381292	−	0.0277025i	5.66556e−5	−	4.11627e-5i	0.587814	+	0.808996i	$0.299989\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	157.646	+	216.981i	0.232860	+	0.320504i	0.909416	−	0.415887i	$-0.136529\pi$
$677$	157.646	+	216.981i	0.232860	+	0.320504i	−0.676557	+	0.736390i	$0.736529\pi$
$678$		0			0
$679$	−10.7032	+	32.9412i	−0.0157632	+	0.0485143i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	447.684	−	145.461i	0.655467	−	0.212974i	0.0376440	−	0.999291i	$-0.488015\pi$
$683$	447.684	−	145.461i	0.655467	−	0.212974i	0.617823	+	0.786317i	$0.288015\pi$
$684$		0			0
$685$	−618.375	+	226.881i	−0.902737	+	0.331213i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−75.9376	−	104.519i	−0.110214	−	0.151697i
$690$		0			0
$691$	−178.463	−	129.661i	−0.258268	−	0.187643i	0.451115	−	0.892466i	$-0.351026\pi$
$691$	−178.463	−	129.661i	−0.258268	−	0.187643i	−0.709383	+	0.704823i	$0.751026\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−535.987	+	20.1033i	−0.771205	+	0.0289256i
$696$		0			0
$697$	75.6029	−	232.682i	0.108469	−	0.333833i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			407.894i			0.581875i	0.956742	+	0.290937i	$0.0939672\pi$
$701$			407.894i			0.581875i	−0.956742	+	0.290937i	$0.906033\pi$
$702$		0			0
$703$	176.633	−	543.622i	0.251257	−	0.773288i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	71.9799i		−	0.101810i
$708$		0			0
$709$	841.326	+	611.259i	1.18664	+	0.862142i	0.992905	−	0.118912i	$-0.0379407\pi$
$709$	841.326	+	611.259i	1.18664	+	0.862142i	0.193732	+	0.981054i	$0.437941\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	396.987	−	546.405i	0.556784	−	0.766347i
$714$		0			0
$715$	25.7363	−	38.3690i	0.0359948	−	0.0536629i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−703.300	+	228.516i	−0.978164	+	0.317825i	−0.754107	−	0.656751i	$-0.771930\pi$
$719$	−703.300	+	228.516i	−0.978164	+	0.317825i	−0.224057	+	0.974576i	$0.571930\pi$
$720$		0			0
$721$	27.5729	−	84.8608i	0.0382426	−	0.117699i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	81.6500	+	1086.93i	0.112621	+	1.49921i
$726$		0			0
$727$	−458.314	+	332.984i	−0.630418	+	0.458025i	−0.856545	−	0.516073i	$-0.827393\pi$
$727$	−458.314	+	332.984i	−0.630418	+	0.458025i	0.226127	+	0.974098i	$0.427393\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	1388.90	−	451.281i	1.90000	−	0.617348i
$732$		0			0
$733$	−194.561	−	598.796i	−0.265431	−	0.816912i	−0.991594	−	0.129389i	$-0.958698\pi$
$733$	−194.561	−	598.796i	−0.265431	−	0.816912i	0.726163	−	0.687522i	$-0.241302\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	168.672	−	232.156i	0.228862	−	0.315002i
$738$		0			0
$739$	−281.487	+	204.512i	−0.380903	+	0.276742i	−0.761717	−	0.647909i	$-0.775644\pi$
$739$	−281.487	+	204.512i	−0.380903	+	0.276742i	0.380815	+	0.924651i	$0.375644\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			447.693i			0.602548i	0.953538	+	0.301274i	$0.0974118\pi$
$743$			447.693i			0.602548i	−0.953538	+	0.301274i	$0.902588\pi$
$744$		0			0
$745$	−58.2929	+	86.9061i	−0.0782455	+	0.116652i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		−	81.9189i		−	0.109371i
$750$		0			0
$751$	−227.169			−0.302488			−0.151244	−	0.988496i	$-0.548328\pi$
$751$	−227.169			−0.302488			−0.151244	+	0.988496i	$0.548328\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−525.753	−	352.653i	−0.696362	−	0.467090i
$756$		0			0
$757$	1215.69			1.60593			0.802966	−	0.596025i	$-0.203254\pi$
$757$	1215.69			1.60593			0.802966	+	0.596025i	$0.203254\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	23.8013	+	32.7596i	0.0312763	+	0.0430481i	0.824369	−	0.566053i	$-0.191530\pi$
$761$	23.8013	+	32.7596i	0.0312763	+	0.0430481i	−0.793092	+	0.609101i	$0.791530\pi$
$762$		0			0
$763$	−122.931	−	89.3145i	−0.161115	−	0.117057i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−274.219	+	89.0991i	−0.357521	+	0.116166i
$768$		0			0
$769$	−45.7790	−	140.893i	−0.0595306	−	0.183216i	0.916869	−	0.399188i	$-0.130708\pi$
$769$	−45.7790	−	140.893i	−0.0595306	−	0.183216i	−0.976400	+	0.215972i	$0.930708\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−83.1779	−	114.485i	−0.107604	−	0.148104i	0.751819	−	0.659370i	$-0.229177\pi$
$773$	−83.1779	−	114.485i	−0.107604	−	0.148104i	−0.859423	+	0.511266i	$0.829177\pi$
$774$		0			0
$775$	426.025	−	361.244i	0.549709	−	0.466121i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−110.658	−	35.9550i	−0.142051	−	0.0461553i
$780$		0			0
$781$	−87.8247	−	270.297i	−0.112452	−	0.346091i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	938.562	+	629.547i	1.19562	+	0.801971i
$786$		0			0
$787$	−1066.64	−	774.956i	−1.35532	−	0.984696i	−0.998727	−	0.0504355i	$-0.983939\pi$
$787$	−1066.64	−	774.956i	−1.35532	−	0.984696i	−0.356591	−	0.934261i	$-0.616061\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	2.93872	−	4.04481i	0.00371520	−	0.00511354i
$792$		0			0
$793$	−293.811			−0.370506
$794$		0			0
$795$		0			0
$796$		0			0
$797$	506.906	+	164.704i	0.636018	+	0.206655i	0.609239	−	0.792987i	$-0.291475\pi$
$797$	506.906	+	164.704i	0.636018	+	0.206655i	0.0267789	+	0.999641i	$0.491475\pi$
$798$		0			0
$799$	−2681.75			−3.35638
$800$		0			0
$801$		0			0
$802$		0			0
$803$	75.9483	+	24.6771i	0.0945806	+	0.0307311i
$804$		0			0
$805$	−6.45629	−	172.135i	−0.00802023	−	0.213833i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	222.408	−	306.119i	0.274917	−	0.378391i	−0.649125	−	0.760682i	$-0.724865\pi$
$809$	222.408	−	306.119i	0.274917	−	0.378391i	0.924042	+	0.382291i	$0.124865\pi$
$810$		0			0
$811$	962.701	−	699.443i	1.18705	−	0.862446i	0.194105	−	0.980981i	$-0.437820\pi$
$811$	962.701	−	699.443i	1.18705	−	0.862446i	0.992950	+	0.118535i	$0.0378198\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−252.582	−	688.426i	−0.309917	−	0.844695i
$816$		0			0
$817$	−214.619	−	660.528i	−0.262691	−	0.808480i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−72.2296	−	23.4688i	−0.0879775	−	0.0285856i	0.264698	−	0.964331i	$-0.414728\pi$
$821$	−72.2296	−	23.4688i	−0.0879775	−	0.0285856i	−0.352675	+	0.935746i	$0.614728\pi$
$822$		0			0
$823$	156.389	−	113.623i	0.190023	−	0.138060i	−0.488706	−	0.872448i	$-0.662531\pi$
$823$	156.389	−	113.623i	0.190023	−	0.138060i	0.678729	+	0.734389i	$0.262531\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−854.224	−	1175.74i	−1.03292	−	1.42169i	−0.902733	−	0.430201i	$-0.858443\pi$
$827$	−854.224	−	1175.74i	−1.03292	−	1.42169i	−0.130186	−	0.991490i	$-0.541557\pi$
$828$		0			0
$829$	316.162	−	973.046i	0.381377	−	1.17376i	−0.557697	−	0.830045i	$-0.688315\pi$
$829$	316.162	−	973.046i	0.381377	−	1.17376i	0.939074	−	0.343714i	$-0.111685\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1521.88	−	494.488i	1.82698	−	0.593623i
$834$		0			0
$835$	−273.277	−	77.5977i	−0.327278	−	0.0929314i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−217.081	−	298.787i	−0.258738	−	0.356122i	0.659810	−	0.751433i	$-0.270637\pi$
$839$	−217.081	−	298.787i	−0.258738	−	0.356122i	−0.918548	+	0.395311i	$0.870637\pi$
$840$		0			0
$841$	857.506	+	623.015i	1.01963	+	0.740802i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	213.787	−	752.898i	0.253002	−	0.891003i
$846$		0			0
$847$	−40.2019	+	123.729i	−0.0474638	+	0.146079i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		−	1083.05i		−	1.27268i
$852$		0			0
$853$	−209.618	+	645.137i	−0.245742	+	0.756315i	0.749772	+	0.661696i	$0.230163\pi$
$853$	−209.618	+	645.137i	−0.245742	+	0.756315i	−0.995514	+	0.0946189i	$0.969837\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			580.777i			0.677686i	0.940843	+	0.338843i	$0.110035\pi$
$857$			580.777i			0.677686i	−0.940843	+	0.338843i	$0.889965\pi$
$858$		0			0
$859$	828.664	+	602.060i	0.964685	+	0.700885i	0.954234	−	0.299061i	$-0.0966733\pi$
$859$	828.664	+	602.060i	0.964685	+	0.700885i	0.0104509	+	0.999945i	$0.496673\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−823.430	+	1133.35i	−0.954148	+	1.31327i	−0.00448830	+	0.999990i	$0.501429\pi$
$863$	−823.430	+	1133.35i	−0.954148	+	1.31327i	−0.949660	+	0.313283i	$0.898571\pi$
$864$		0			0
$865$	−13.2531	−	353.348i	−0.0153215	−	0.408495i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−319.199	+	103.714i	−0.367317	+	0.119349i
$870$		0			0
$871$	−119.649	+	368.241i	−0.137369	+	0.422779i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	28.5383	−	139.572i	0.0326152	−	0.159510i
$876$		0			0
$877$	−1191.44	+	865.629i	−1.35854	+	0.987034i	−0.360000	+	0.932952i	$0.617223\pi$
$877$	−1191.44	+	865.629i	−1.35854	+	0.987034i	−0.998536	+	0.0540820i	$0.982777\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1305.41	+	424.152i	−1.48173	+	0.481444i	−0.934630	−	0.355622i	$-0.884269\pi$
$881$	−1305.41	+	424.152i	−1.48173	+	0.481444i	−0.547102	+	0.837066i	$0.684269\pi$
$882$		0			0
$883$	256.083	+	788.143i	0.290015	+	0.892574i	0.984851	+	0.173405i	$0.0554771\pi$
$883$	256.083	+	788.143i	0.290015	+	0.892574i	−0.694836	+	0.719168i	$0.744523\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−766.299	+	1054.72i	−0.863922	+	1.18909i	0.116698	+	0.993167i	$0.462769\pi$
$887$	−766.299	+	1054.72i	−0.863922	+	1.18909i	−0.980620	+	0.195920i	$0.937231\pi$
$888$		0			0
$889$	51.2261	−	37.2179i	0.0576221	−	0.0418649i
$890$		0			0
$891$		0			0
$892$		0			0
$893$			1275.38i			1.42819i
$894$		0			0
$895$	983.974	+	1252.75i	1.09941	+	1.39972i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		−	974.130i		−	1.08357i
$900$		0			0
$901$	1227.41			1.36228
$902$		0			0
$903$		0			0
$904$		0			0
$905$	325.255	−	1145.46i	0.359398	−	1.26570i
$906$		0			0
$907$	1345.32			1.48326			0.741631	−	0.670809i	$-0.234053\pi$
$907$	1345.32			1.48326			0.741631	+	0.670809i	$0.234053\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−676.471	−	931.083i	−0.742559	−	1.02205i	−0.998467	−	0.0553439i	$-0.982374\pi$
$911$	−676.471	−	931.083i	−0.742559	−	1.02205i	0.255908	−	0.966701i	$-0.417626\pi$
$912$		0			0
$913$	−104.132	−	75.6562i	−0.114055	−	0.0828655i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−4.99595	+	1.62328i	−0.00544814	+	0.00177021i
$918$		0			0
$919$	259.565	+	798.858i	0.282442	+	0.869268i	0.987154	+	0.159774i	$0.0510766\pi$
$919$	259.565	+	798.858i	0.282442	+	0.869268i	−0.704711	+	0.709494i	$0.748923\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	225.401	+	310.238i	0.244205	+	0.336119i
$924$		0			0
$925$	212.199	−	870.208i	0.229404	−	0.940765i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1154.93	+	375.258i	1.24319	+	0.403938i	0.855477	−	0.517841i	$-0.173264\pi$
$929$	1154.93	+	375.258i	1.24319	+	0.403938i	0.387716	+	0.921779i	$0.373264\pi$
$930$		0			0
$931$	−235.167	−	723.769i	−0.252596	−	0.777410i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	151.191	+	412.079i	0.161701	+	0.440726i
$936$		0			0
$937$	−230.809	−	167.692i	−0.246327	−	0.178967i	0.457770	−	0.889071i	$-0.348648\pi$
$937$	−230.809	−	167.692i	−0.246327	−	0.178967i	−0.704098	+	0.710103i	$0.748648\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	497.862	−	685.249i	0.529078	−	0.728213i	−0.457912	−	0.888998i	$-0.651402\pi$
$941$	497.862	−	685.249i	0.529078	−	0.728213i	0.986990	+	0.160784i	$0.0514024\pi$
$942$		0			0
$943$	−220.463			−0.233789
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−47.1328	−	15.3144i	−0.0497707	−	0.0161715i	0.284026	−	0.958817i	$-0.408330\pi$
$947$	−47.1328	−	15.3144i	−0.0497707	−	0.0161715i	−0.333797	+	0.942645i	$0.608330\pi$
$948$		0			0
$949$	−107.749			−0.113540
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−805.117	−	261.598i	−0.844824	−	0.274500i	−0.145547	−	0.989351i	$-0.546494\pi$
$953$	−805.117	−	261.598i	−0.844824	−	0.274500i	−0.699276	+	0.714851i	$0.746494\pi$
$954$		0			0
$955$	1129.87	−	414.545i	1.18310	−	0.434079i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	88.2482	−	121.463i	0.0920211	−	0.126656i
$960$		0			0
$961$	373.611	−	271.445i	0.388774	−	0.282461i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−1013.67	−	679.925i	−1.05043	−	0.704586i
$966$		0			0
$967$	−253.158	−	779.139i	−0.261797	−	0.805728i	−0.992414	−	0.122941i	$-0.960767\pi$
$967$	−253.158	−	779.139i	−0.261797	−	0.805728i	0.730617	−	0.682788i	$-0.239233\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−259.951	−	84.4632i	−0.267715	−	0.0869858i	0.172084	−	0.985082i	$-0.444950\pi$
$971$	−259.951	−	84.4632i	−0.267715	−	0.0869858i	−0.439798	+	0.898097i	$0.644950\pi$
$972$		0			0
$973$	98.9073	−	71.8604i	0.101652	−	0.0738545i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−367.848	−	506.299i	−0.376508	−	0.518219i	0.578147	−	0.815932i	$-0.303776\pi$
$977$	−367.848	−	506.299i	−0.376508	−	0.518219i	−0.954655	+	0.297714i	$0.903776\pi$
$978$		0			0
$979$	20.3424	−	62.6075i	0.0207788	−	0.0639504i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−809.256	+	262.943i	−0.823251	+	0.267490i	−0.690200	−	0.723619i	$-0.742477\pi$
$983$	−809.256	+	262.943i	−0.823251	+	0.267490i	−0.133051	+	0.991109i	$0.542477\pi$
$984$		0			0
$985$	−261.996	−	333.560i	−0.265985	−	0.338639i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−773.505	−	1064.64i	−0.782108	−	1.07648i
$990$		0			0
$991$	−253.890	−	184.462i	−0.256196	−	0.186137i	0.452272	−	0.891880i	$-0.350613\pi$
$991$	−253.890	−	184.462i	−0.256196	−	0.186137i	−0.708468	+	0.705743i	$0.750613\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	794.280	+	532.769i	0.798271	+	0.535446i
$996$		0			0
$997$	258.459	−	795.456i	0.259237	−	0.797850i	−0.733728	−	0.679443i	$-0.762221\pi$
$997$	258.459	−	795.456i	0.259237	−	0.797850i	0.992965	−	0.118407i	$-0.0377786\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.ba.a.161.17	yes	80
3.2	odd	2	inner	900.3.ba.a.161.4	✓	80
25.16	even	5	inner	900.3.ba.a.341.4	yes	80
75.41	odd	10	inner	900.3.ba.a.341.17	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.3.ba.a.161.4	✓	80	3.2	odd	2	inner
900.3.ba.a.161.17	yes	80	1.1	even	1	trivial
900.3.ba.a.341.4	yes	80	25.16	even	5	inner
900.3.ba.a.341.17	yes	80	75.41	odd	10	inner

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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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.ba (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(4.15240 + 2.78525i) q^{5} -1.13968 q^{7} +O(q^{10})\)	\(q+(4.15240 + 2.78525i) q^{5} -1.13968 q^{7} +(-1.53818 - 2.11713i) q^{11} +(2.85660 + 2.07544i) q^{13} +(-31.9044 + 10.3664i) q^{17} +(4.93000 + 15.1730i) q^{19} +(17.7682 + 24.4558i) q^{23} +(9.48478 + 23.1309i) q^{25} +(41.4658 + 13.4731i) q^{29} +(-6.90424 - 21.2491i) q^{31} +(-4.73238 - 3.17428i) q^{35} +(-28.9857 - 21.0593i) q^{37} +(-4.28677 + 5.90023i) q^{41} -43.5332 q^{43} +(76.0291 + 24.7034i) q^{47} -47.7011 q^{49} +(-34.7979 - 11.3065i) q^{53} +(-0.490419 - 13.0754i) q^{55} +(-47.9974 + 66.0628i) q^{59} +(-67.3185 + 48.9097i) q^{61} +(6.08111 + 16.5744i) q^{65} +(33.8857 + 104.289i) q^{67} +(103.288 + 33.5604i) q^{71} +(-24.6876 + 17.9366i) q^{73} +(1.75303 + 2.41284i) q^{77} +(39.6322 - 121.975i) q^{79} +(46.7781 - 15.1991i) q^{83} +(-161.353 - 45.8165i) q^{85} +(14.7859 + 20.3511i) q^{89} +(-3.25560 - 2.36533i) q^{91} +(-21.7892 + 76.7355i) q^{95} +(9.39148 - 28.9040i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 16 q^{7}+O(q^{10}) \) 80 * q + 16 * q^7	\( 80 q + 16 q^{7} - 8 q^{13} + 60 q^{19} - 120 q^{25} + 120 q^{31} + 116 q^{37} - 80 q^{43} + 440 q^{49} + 120 q^{55} + 80 q^{61} + 24 q^{67} + 128 q^{73} + 40 q^{79} + 40 q^{85} - 140 q^{91} + 384 q^{97}+O(q^{100}) \) 80 * q + 16 * q^7 - 8 * q^13 + 60 * q^19 - 120 * q^25 + 120 * q^31 + 116 * q^37 - 80 * q^43 + 440 * q^49 + 120 * q^55 + 80 * q^61 + 24 * q^67 + 128 * q^73 + 40 * q^79 + 40 * q^85 - 140 * q^91 + 384 * q^97

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