LMFDB - Embedded newform 528.6.d.b.287.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [528,6,Mod(287,528)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(528, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("528.287");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 528 = 2^{4} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	528.d (of order $2$, degree $1$, 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:	$84.6826568613$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 15 x^{14} + 440 x^{13} - 30788 x^{12} + 421206 x^{11} + 3494011 x^{10} + \cdots + 94\!\cdots\!91 $ x^16 - x^15 + 15x^14 + 440x^13 - 30788x^12 + 421206x^11 + 3494011x^10 + 20989805x^9 + 954917352x^8 + 10008088435x^7 + 94336579421x^6 - 2750414715894x^5 + 58245323176592x^4 + 3790123391809000x^3 + 71789557238409705x^2 + 1216670726903935009x + 9405993299160733691
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{31}\cdot 3^{10}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			287.11
Root			$-8.41804 - 11.5959i$ of defining polynomial
Character	$\chi$	$=$	528.287
Dual form			528.6.d.b.287.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(10.4180 - 11.5959i) q^{3} +49.3758i q^{5} -90.4265i q^{7} +(-25.9288 - 241.613i) q^{9} +O(q^{10})$	\(q+(10.4180 - 11.5959i) q^{3} +49.3758i q^{5} -90.4265i q^{7} +(-25.9288 - 241.613i) q^{9} -121.000 q^{11} +267.559 q^{13} +(572.556 + 514.399i) q^{15} +1466.05i q^{17} +1730.35i q^{19} +(-1048.57 - 942.067i) q^{21} -3528.02 q^{23} +687.033 q^{25} +(-3071.84 - 2216.46i) q^{27} -3193.55i q^{29} +7928.43i q^{31} +(-1260.58 + 1403.10i) q^{33} +4464.88 q^{35} +12916.5 q^{37} +(2787.44 - 3102.58i) q^{39} -15829.5i q^{41} +18023.7i q^{43} +(11929.8 - 1280.25i) q^{45} +7430.56 q^{47} +8630.05 q^{49} +(17000.1 + 15273.4i) q^{51} +13485.6i q^{53} -5974.47i q^{55} +(20064.9 + 18026.8i) q^{57} -45032.2 q^{59} -57152.9 q^{61} +(-21848.2 + 2344.65i) q^{63} +13210.9i q^{65} +16462.3i q^{67} +(-36755.0 + 40910.5i) q^{69} +34702.9 q^{71} +81086.0 q^{73} +(7157.54 - 7966.75i) q^{75} +10941.6i q^{77} +50778.2i q^{79} +(-57704.4 + 12529.5i) q^{81} +72682.1 q^{83} -72387.4 q^{85} +(-37032.0 - 33270.6i) q^{87} -4399.63i q^{89} -24194.4i q^{91} +(91937.1 + 82598.7i) q^{93} -85437.3 q^{95} +103638. q^{97} +(3137.38 + 29235.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 31 q^{3} + 31 q^{9}+O(q^{10}) $ 16 * q + 31 * q^3 + 31 * q^9	$ 16 q + 31 q^{3} + 31 q^{9} - 1936 q^{11} + 444 q^{13} - 979 q^{15} - 3874 q^{21} + 4246 q^{23} - 4194 q^{25} + 1306 q^{27} - 3751 q^{33} - 13964 q^{35} + 35094 q^{37} - 7848 q^{39} - 43369 q^{45} + 18476 q^{47} - 6172 q^{49} + 40886 q^{51} - 27316 q^{57} - 59134 q^{59} + 93580 q^{61} + 52286 q^{63} + 23881 q^{69} + 129154 q^{71} + 63188 q^{73} - 30048 q^{75} + 132223 q^{81} - 46276 q^{83} + 141316 q^{85} - 86304 q^{87} + 228139 q^{93} - 238328 q^{95} - 244198 q^{97} - 3751 q^{99}+O(q^{100}) $ 16 * q + 31 * q^3 + 31 * q^9 - 1936 * q^11 + 444 * q^13 - 979 * q^15 - 3874 * q^21 + 4246 * q^23 - 4194 * q^25 + 1306 * q^27 - 3751 * q^33 - 13964 * q^35 + 35094 * q^37 - 7848 * q^39 - 43369 * q^45 + 18476 * q^47 - 6172 * q^49 + 40886 * q^51 - 27316 * q^57 - 59134 * q^59 + 93580 * q^61 + 52286 * q^63 + 23881 * q^69 + 129154 * q^71 + 63188 * q^73 - 30048 * q^75 + 132223 * q^81 - 46276 * q^83 + 141316 * q^85 - 86304 * q^87 + 228139 * q^93 - 238328 * q^95 - 244198 * q^97 - 3751 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/528\mathbb{Z}\right)^\times$.

$n$	$133$	$145$	$353$	$463$
$\chi(n)$	$1$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	10.4180	−	11.5959i	0.668318	−	0.743876i
$3$	10.4180	−	11.5959i	0.668318	−	0.743876i
$4$		0			0
$5$			49.3758i			0.883261i	0.897197	+	0.441630i	$0.145600\pi$
$5$			49.3758i			0.883261i	−0.897197	+	0.441630i	$0.854400\pi$
$6$		0			0
$7$		−	90.4265i		−	0.697510i	−0.937214	−	0.348755i	$-0.886605\pi$
$7$		−	90.4265i		−	0.697510i	0.937214	−	0.348755i	$-0.113395\pi$
$8$		0			0
$9$	−25.9288	−	241.613i	−0.106703	−	0.994291i
$10$		0			0
$11$	−121.000			−0.301511
$11$	−121.000			−0.301511
$12$		0			0
$13$	267.559			0.439097			0.219549	−	0.975602i	$-0.429542\pi$
$13$	267.559			0.439097			0.219549	+	0.975602i	$0.429542\pi$
$14$		0			0
$15$	572.556	+	514.399i	0.657036	+	0.590299i
$16$		0			0
$17$			1466.05i			1.23034i	0.788393	+	0.615172i	$0.210913\pi$
$17$			1466.05i			1.23034i	−0.788393	+	0.615172i	$0.789087\pi$
$18$		0			0
$19$			1730.35i			1.09964i	0.835284	+	0.549819i	$0.185303\pi$
$19$			1730.35i			1.09964i	−0.835284	+	0.549819i	$0.814697\pi$
$20$		0			0
$21$	−1048.57	−	942.067i	−0.518861	−	0.466158i
$22$		0			0
$23$	−3528.02			−1.39063			−0.695314	−	0.718706i	$-0.744735\pi$
$23$	−3528.02			−1.39063			−0.695314	+	0.718706i	$0.744735\pi$
$24$		0			0
$25$	687.033			0.219850
$26$		0			0
$27$	−3071.84	−	2216.46i	−0.810941	−	0.585129i
$28$		0			0
$29$		−	3193.55i		−	0.705146i	−0.935784	−	0.352573i	$-0.885307\pi$
$29$		−	3193.55i		−	0.705146i	0.935784	−	0.352573i	$-0.114693\pi$
$30$		0			0
$31$			7928.43i			1.48178i	0.671628	+	0.740888i	$0.265595\pi$
$31$			7928.43i			1.48178i	−0.671628	+	0.740888i	$0.734405\pi$
$32$		0			0
$33$	−1260.58	+	1403.10i	−0.201505	+	0.224287i
$34$		0			0
$35$	4464.88			0.616083
$36$		0			0
$37$	12916.5			1.55110			0.775551	−	0.631285i	$-0.217472\pi$
$37$	12916.5			1.55110			0.775551	+	0.631285i	$0.217472\pi$
$38$		0			0
$39$	2787.44	−	3102.58i	0.293456	−	0.326634i
$40$		0			0
$41$		−	15829.5i		−	1.47064i	−0.677718	−	0.735322i	$-0.737031\pi$
$41$		−	15829.5i		−	1.47064i	0.677718	−	0.735322i	$-0.262969\pi$
$42$		0			0
$43$			18023.7i			1.48653i	0.668999	+	0.743263i	$0.266723\pi$
$43$			18023.7i			1.48653i	−0.668999	+	0.743263i	$0.733277\pi$
$44$		0			0
$45$	11929.8	−	1280.25i	0.878218	−	0.0942464i
$46$		0			0
$47$	7430.56			0.490656			0.245328	−	0.969440i	$-0.421104\pi$
$47$	7430.56			0.490656			0.245328	+	0.969440i	$0.421104\pi$
$48$		0			0
$49$	8630.05			0.513480
$50$		0			0
$51$	17000.1	+	15273.4i	0.915223	+	0.822261i
$52$		0			0
$53$			13485.6i			0.659447i	0.944078	+	0.329724i	$0.106956\pi$
$53$			13485.6i			0.659447i	−0.944078	+	0.329724i	$0.893044\pi$
$54$		0			0
$55$		−	5974.47i		−	0.266313i
$56$		0			0
$57$	20064.9	+	18026.8i	0.817994	+	0.734907i
$58$		0			0
$59$	−45032.2			−1.68420			−0.842099	−	0.539323i	$-0.818680\pi$
$59$	−45032.2			−1.68420			−0.842099	+	0.539323i	$0.818680\pi$
$60$		0			0
$61$	−57152.9			−1.96659			−0.983294	−	0.182023i	$-0.941735\pi$
$61$	−57152.9			−1.96659			−0.983294	+	0.182023i	$0.941735\pi$
$62$		0			0
$63$	−21848.2	+	2344.65i	−0.693528	+	0.0744263i
$64$		0			0
$65$			13210.9i			0.387837i
$66$		0			0
$67$			16462.3i			0.448027i	0.974586	+	0.224013i	$0.0719159\pi$
$67$			16462.3i			0.448027i	−0.974586	+	0.224013i	$0.928084\pi$
$68$		0			0
$69$	−36755.0	+	40910.5i	−0.929382	+	1.03445i
$70$		0			0
$71$	34702.9			0.816995			0.408498	−	0.912759i	$-0.366053\pi$
$71$	34702.9			0.816995			0.408498	+	0.912759i	$0.366053\pi$
$72$		0			0
$73$	81086.0			1.78090			0.890449	−	0.455084i	$-0.150391\pi$
$73$	81086.0			1.78090			0.890449	+	0.455084i	$0.150391\pi$
$74$		0			0
$75$	7157.54	−	7966.75i	0.146930	−	0.163541i
$76$		0			0
$77$			10941.6i			0.210307i
$78$		0			0
$79$			50778.2i			0.915397i	0.889108	+	0.457698i	$0.151326\pi$
$79$			50778.2i			0.915397i	−0.889108	+	0.457698i	$0.848674\pi$
$80$		0			0
$81$	−57704.4	+	12529.5i	−0.977229	+	0.212187i
$82$		0			0
$83$	72682.1			1.15806			0.579031	−	0.815305i	$-0.303431\pi$
$83$	72682.1			1.15806			0.579031	+	0.815305i	$0.303431\pi$
$84$		0			0
$85$	−72387.4			−1.08671
$86$		0			0
$87$	−37032.0	−	33270.6i	−0.524541	−	0.471261i
$88$		0			0
$89$		−	4399.63i		−	0.0588764i	−0.999567	−	0.0294382i	$-0.990628\pi$
$89$		−	4399.63i		−	0.0588764i	0.999567	−	0.0294382i	$-0.00937183\pi$
$90$		0			0
$91$		−	24194.4i		−	0.306275i
$92$		0			0
$93$	91937.1	+	82598.7i	1.10226	+	0.990298i
$94$		0			0
$95$	−85437.3			−0.971267
$96$		0			0
$97$	103638.			1.11839			0.559193	−	0.829038i	$-0.311111\pi$
$97$	103638.			1.11839			0.559193	+	0.829038i	$0.311111\pi$
$98$		0			0
$99$	3137.38	+	29235.1i	0.0321721	+	0.299790i
$100$		0			0
$101$			164230.i			1.60195i	0.598695	+	0.800977i	$0.295686\pi$
$101$			164230.i			1.60195i	−0.598695	+	0.800977i	$0.704314\pi$
$102$		0			0
$103$			197566.i			1.83493i	0.397814	+	0.917466i	$0.369769\pi$
$103$			197566.i			1.83493i	−0.397814	+	0.917466i	$0.630231\pi$
$104$		0			0
$105$	46515.3	−	51774.2i	0.411739	−	0.458290i
$106$		0			0
$107$	−125865.			−1.06279			−0.531394	−	0.847125i	$-0.678332\pi$
$107$	−125865.			−1.06279			−0.531394	+	0.847125i	$0.678332\pi$
$108$		0			0
$109$	128685.			1.03744			0.518718	−	0.854946i	$-0.326410\pi$
$109$	128685.			1.03744			0.518718	+	0.854946i	$0.326410\pi$
$110$		0			0
$111$	134565.	−	149778.i	1.03663	−	1.15383i
$112$		0			0
$113$		−	5104.20i		−	0.0376038i	−0.999823	−	0.0188019i	$-0.994015\pi$
$113$		−	5104.20i		−	0.0376038i	0.999823	−	0.0188019i	$-0.00598518\pi$
$114$		0			0
$115$		−	174199.i		−	1.22829i
$116$		0			0
$117$	−6937.47	−	64645.6i	−0.0468529	−	0.436590i
$118$		0			0
$119$	132570.			0.858177
$120$		0			0
$121$	14641.0			0.0909091
$122$		0			0
$123$	−183557.	−	164912.i	−1.09398	−	0.982858i
$124$		0			0
$125$			188222.i			1.07745i
$126$		0			0
$127$		−	101204.i		−	0.556784i	−0.960468	−	0.278392i	$-0.910199\pi$
$127$		−	101204.i		−	0.556784i	0.960468	−	0.278392i	$-0.0898015\pi$
$128$		0			0
$129$	209001.	+	187772.i	1.10579	+	0.993472i
$130$		0			0
$131$	81322.2			0.414029			0.207015	−	0.978338i	$-0.433625\pi$
$131$	81322.2			0.414029			0.207015	+	0.978338i	$0.433625\pi$
$132$		0			0
$133$	156469.			0.767008
$134$		0			0
$135$	109440.	−	151674.i	0.516821	−	0.716272i
$136$		0			0
$137$		−	183147.i		−	0.833679i	−0.908980	−	0.416840i	$-0.863138\pi$
$137$		−	183147.i		−	0.833679i	0.908980	−	0.416840i	$-0.136862\pi$
$138$		0			0
$139$			86376.7i			0.379192i	0.981862	+	0.189596i	$0.0607179\pi$
$139$			86376.7i			0.379192i	−0.981862	+	0.189596i	$0.939282\pi$
$140$		0			0
$141$	77411.9	−	86163.8i	0.327914	−	0.364987i
$142$		0			0
$143$	−32374.6			−0.132393
$144$		0			0
$145$	157684.			0.622828
$146$		0			0
$147$	89908.3	−	100073.i	0.343168	−	0.381965i
$148$		0			0
$149$			377300.i			1.39226i	0.717914	+	0.696132i	$0.245097\pi$
$149$			377300.i			1.39226i	−0.717914	+	0.696132i	$0.754903\pi$
$150$		0			0
$151$		−	67908.0i		−	0.242370i	−0.992630	−	0.121185i	$-0.961331\pi$
$151$		−	67908.0i		−	0.242370i	0.992630	−	0.121185i	$-0.0386694\pi$
$152$		0			0
$153$	354216.	−	38012.9i	1.22332	−	0.131281i
$154$		0			0
$155$	−391472.			−1.30880
$156$		0			0
$157$	359868.			1.16518			0.582591	−	0.812765i	$-0.302039\pi$
$157$	359868.			1.16518			0.582591	+	0.812765i	$0.302039\pi$
$158$		0			0
$159$	156377.	+	140493.i	0.490547	+	0.440720i
$160$		0			0
$161$			319026.i			0.969977i
$162$		0			0
$163$		−	422066.i		−	1.24426i	−0.782914	−	0.622130i	$-0.786268\pi$
$163$		−	422066.i		−	1.24426i	0.782914	−	0.622130i	$-0.213732\pi$
$164$		0			0
$165$	−69279.2	−	62242.3i	−0.198104	−	0.177982i
$166$		0			0
$167$	146704.			0.407054			0.203527	−	0.979069i	$-0.434760\pi$
$167$	146704.			0.407054			0.203527	+	0.979069i	$0.434760\pi$
$168$		0			0
$169$	−299705.			−0.807194
$170$		0			0
$171$	418074.	−	44865.9i	1.09336	−	0.117335i
$172$		0			0
$173$			5642.40i			0.0143334i	0.999974	+	0.00716669i	$0.00228125\pi$
$173$			5642.40i			0.0143334i	−0.999974	+	0.00716669i	$0.997719\pi$
$174$		0			0
$175$		−	62125.9i		−	0.153348i
$176$		0			0
$177$	−469147.	+	522188.i	−1.12558	+	1.25283i
$178$		0			0
$179$	590933.			1.37850			0.689249	−	0.724525i	$-0.257941\pi$
$179$	590933.			1.37850			0.689249	+	0.724525i	$0.257941\pi$
$180$		0			0
$181$	253966.			0.576208			0.288104	−	0.957599i	$-0.406975\pi$
$181$	253966.			0.576208			0.288104	+	0.957599i	$0.406975\pi$
$182$		0			0
$183$	−595421.	+	662738.i	−1.31431	+	1.46290i
$184$		0			0
$185$			637762.i			1.37003i
$186$		0			0
$187$		−	177392.i		−	0.370963i
$188$		0			0
$189$	−200427.	+	277776.i	−0.408133	+	0.565639i
$190$		0			0
$191$	−617421.			−1.22461			−0.612305	−	0.790621i	$-0.709758\pi$
$191$	−617421.			−1.22461			−0.612305	+	0.790621i	$0.709758\pi$
$192$		0			0
$193$	286668.			0.553970			0.276985	−	0.960874i	$-0.410665\pi$
$193$	286668.			0.553970			0.276985	+	0.960874i	$0.410665\pi$
$194$		0			0
$195$	153192.	+	137632.i	0.288503	+	0.259198i
$196$		0			0
$197$			588515.i			1.08042i	0.841531	+	0.540209i	$0.181655\pi$
$197$			588515.i			1.08042i	−0.841531	+	0.540209i	$0.818345\pi$
$198$		0			0
$199$			398737.i			0.713763i	0.934150	+	0.356881i	$0.116160\pi$
$199$			398737.i			0.713763i	−0.934150	+	0.356881i	$0.883840\pi$
$200$		0			0
$201$	190895.	+	171505.i	0.333276	+	0.299424i
$202$		0			0
$203$	−288782.			−0.491846
$204$		0			0
$205$	781594.			1.29896
$206$		0			0
$207$	91477.2	+	852414.i	0.148384	+	1.38269i
$208$		0			0
$209$		−	209372.i		−	0.331553i
$210$		0			0
$211$			388995.i			0.601504i	0.953702	+	0.300752i	$0.0972376\pi$
$211$			388995.i			0.601504i	−0.953702	+	0.300752i	$0.902762\pi$
$212$		0			0
$213$	361536.	−	402410.i	0.546012	−	0.607743i
$214$		0			0
$215$	−889934.			−1.31299
$216$		0			0
$217$	716940.			1.03355
$218$		0			0
$219$	844758.	−	940264.i	1.19021	−	1.32477i
$220$		0			0
$221$			392254.i			0.540240i
$222$		0			0
$223$			219276.i			0.295277i	0.989041	+	0.147638i	$0.0471672\pi$
$223$			219276.i			0.295277i	−0.989041	+	0.147638i	$0.952833\pi$
$224$		0			0
$225$	−17813.9	−	165996.i	−0.0234587	−	0.218595i
$226$		0			0
$227$	−499768.			−0.643730			−0.321865	−	0.946786i	$-0.604310\pi$
$227$	−499768.			−0.643730			−0.321865	+	0.946786i	$0.604310\pi$
$228$		0			0
$229$	−1.00219e6			−1.26288			−0.631438	−	0.775426i	$-0.717535\pi$
$229$	−1.00219e6			−1.26288			−0.631438	+	0.775426i	$0.717535\pi$
$230$		0			0
$231$	126877.	+	113990.i	0.156442	+	0.140552i
$232$		0			0
$233$		−	448893.i		−	0.541692i	−0.962623	−	0.270846i	$-0.912697\pi$
$233$		−	448893.i		−	0.541692i	0.962623	−	0.270846i	$-0.0873034\pi$
$234$		0			0
$235$			366890.i			0.433377i
$236$		0			0
$237$	588818.	+	529009.i	0.680942	+	0.611776i
$238$		0			0
$239$	65551.4			0.0742313			0.0371156	−	0.999311i	$-0.488183\pi$
$239$	65551.4			0.0742313			0.0371156	+	0.999311i	$0.488183\pi$
$240$		0			0
$241$	−648644.			−0.719389			−0.359694	−	0.933070i	$-0.617119\pi$
$241$	−648644.			−0.719389			−0.359694	+	0.933070i	$0.617119\pi$
$242$		0			0
$243$	−455877.	+	799666.i	−0.495258	+	0.868746i
$244$		0			0
$245$			426116.i			0.453537i
$246$		0			0
$247$			462970.i			0.482848i
$248$		0			0
$249$	757205.	−	842812.i	0.773954	−	0.861455i
$250$		0			0
$251$	65771.5			0.0658952			0.0329476	−	0.999457i	$-0.489511\pi$
$251$	65771.5			0.0658952			0.0329476	+	0.999457i	$0.489511\pi$
$252$		0			0
$253$	426890.			0.419290
$254$		0			0
$255$	−754135.	+	839395.i	−0.726271	+	0.808381i
$256$		0			0
$257$			1.69655e6i			1.60227i	0.598486	+	0.801133i	$0.295769\pi$
$257$			1.69655e6i			1.60227i	−0.598486	+	0.801133i	$0.704231\pi$
$258$		0			0
$259$		−	1.16799e6i		−	1.08191i
$260$		0			0
$261$	−771603.	+	82804.9i	−0.701120	+	0.0752411i
$262$		0			0
$263$	1.91412e6			1.70639			0.853197	−	0.521588i	$-0.174660\pi$
$263$	1.91412e6			1.70639			0.853197	+	0.521588i	$0.174660\pi$
$264$		0			0
$265$	−665861.			−0.582464
$266$		0			0
$267$	−51017.6	−	45835.6i	−0.0437968	−	0.0393482i
$268$		0			0
$269$		−	510121.i		−	0.429826i	−0.976633	−	0.214913i	$-0.931053\pi$
$269$		−	510121.i		−	0.429826i	0.976633	−	0.214913i	$-0.0689467\pi$
$270$		0			0
$271$			994071.i			0.822232i	0.911583	+	0.411116i	$0.134861\pi$
$271$			994071.i			0.822232i	−0.911583	+	0.411116i	$0.865139\pi$
$272$		0			0
$273$	−280555.	−	252058.i	−0.227830	−	0.204689i
$274$		0			0
$275$	−83131.0			−0.0662874
$276$		0			0
$277$	52607.8			0.0411956			0.0205978	−	0.999788i	$-0.493443\pi$
$277$	52607.8			0.0411956			0.0205978	+	0.999788i	$0.493443\pi$
$278$		0			0
$279$	1.91561e6	−	205575.i	1.47332	−	0.158110i
$280$		0			0
$281$		−	1.14081e6i		−	0.861881i	−0.902380	−	0.430941i	$-0.858182\pi$
$281$		−	1.14081e6i		−	0.861881i	0.902380	−	0.430941i	$-0.141818\pi$
$282$		0			0
$283$			61412.9i			0.0455820i	0.999740	+	0.0227910i	$0.00725523\pi$
$283$			61412.9i			0.0455820i	−0.999740	+	0.0227910i	$0.992745\pi$
$284$		0			0
$285$	−890090.	+	990721.i	−0.649115	+	0.722502i
$286$		0			0
$287$	−1.43141e6			−1.02579
$288$		0			0
$289$	−729446.			−0.513746
$290$		0			0
$291$	1.07971e6	−	1.20178e6i	0.747437	−	0.831940i
$292$		0			0
$293$		−	1.10576e6i		−	0.752471i	−0.926524	−	0.376236i	$-0.877218\pi$
$293$		−	1.10576e6i		−	0.752471i	0.926524	−	0.376236i	$-0.122782\pi$
$294$		0			0
$295$		−	2.22350e6i		−	1.48759i
$296$		0			0
$297$	371692.	+	268192.i	0.244508	+	0.176423i
$298$		0			0
$299$	−943951.			−0.610621
$300$		0			0
$301$	1.62982e6			1.03687
$302$		0			0
$303$	1.90440e6	+	1.71096e6i	1.19166	+	1.07061i
$304$		0			0
$305$		−	2.82197e6i		−	1.73701i
$306$		0			0
$307$		−	1.38503e6i		−	0.838713i	−0.907822	−	0.419356i	$-0.862256\pi$
$307$		−	1.38503e6i		−	0.838713i	0.907822	−	0.419356i	$-0.137744\pi$
$308$		0			0
$309$	2.29096e6	+	2.05826e6i	1.36496	+	1.22632i
$310$		0			0
$311$	−2.23501e6			−1.31032			−0.655161	−	0.755489i	$-0.727399\pi$
$311$	−2.23501e6			−1.31032			−0.655161	+	0.755489i	$0.727399\pi$
$312$		0			0
$313$	648821.			0.374338			0.187169	−	0.982328i	$-0.440069\pi$
$313$	648821.			0.374338			0.187169	+	0.982328i	$0.440069\pi$
$314$		0			0
$315$	−115769.	−	1.07877e6i	−0.0657378	−	0.612566i
$316$		0			0
$317$		−	2.26536e6i		−	1.26616i	−0.774085	−	0.633082i	$-0.781790\pi$
$317$		−	2.26536e6i		−	1.26616i	0.774085	−	0.633082i	$-0.218210\pi$
$318$		0			0
$319$			386420.i			0.212609i
$320$		0			0
$321$	−1.31127e6	+	1.45952e6i	−0.710281	+	0.790583i
$322$		0			0
$323$	−2.53678e6			−1.35293
$324$		0			0
$325$	183821.			0.0965357
$326$		0			0
$327$	1.34064e6	−	1.49221e6i	0.693336	−	0.771723i
$328$		0			0
$329$		−	671919.i		−	0.342237i
$330$		0			0
$331$			1.57356e6i			0.789430i	0.918804	+	0.394715i	$0.129157\pi$
$331$			1.57356e6i			0.789430i	−0.918804	+	0.394715i	$0.870843\pi$
$332$		0			0
$333$	−334909.	−	3.12079e6i	−0.165507	−	1.54225i
$334$		0			0
$335$	−812839.			−0.395724
$336$		0			0
$337$	−2.26690e6			−1.08732			−0.543660	−	0.839306i	$-0.682962\pi$
$337$	−2.26690e6			−1.08732			−0.543660	+	0.839306i	$0.682962\pi$
$338$		0			0
$339$	−59187.6	−	53175.7i	−0.0279725	−	0.0251313i
$340$		0			0
$341$		−	959340.i		−	0.446772i
$342$		0			0
$343$		−	2.30018e6i		−	1.05567i
$344$		0			0
$345$	−2.01999e6	−	1.81481e6i	−0.913693	−	0.820886i
$346$		0			0
$347$	2.75392e6			1.22780			0.613900	−	0.789384i	$-0.289600\pi$
$347$	2.75392e6			1.22780			0.613900	+	0.789384i	$0.289600\pi$
$348$		0			0
$349$	−2.42583e6			−1.06610			−0.533048	−	0.846085i	$-0.678954\pi$
$349$	−2.42583e6			−1.06610			−0.533048	+	0.846085i	$0.678954\pi$
$350$		0			0
$351$	−821897.	−	593034.i	−0.356082	−	0.256928i
$352$		0			0
$353$		−	1.68972e6i		−	0.721737i	−0.932617	−	0.360868i	$-0.882480\pi$
$353$		−	1.68972e6i		−	0.721737i	0.932617	−	0.360868i	$-0.117520\pi$
$354$		0			0
$355$			1.71348e6i			0.721620i
$356$		0			0
$357$	1.38112e6	−	1.53726e6i	0.573535	−	0.638377i
$358$		0			0
$359$	−3.02071e6			−1.23701			−0.618505	−	0.785781i	$-0.712261\pi$
$359$	−3.02071e6			−1.23701			−0.618505	+	0.785781i	$0.712261\pi$
$360$		0			0
$361$	−518008.			−0.209203
$362$		0			0
$363$	152531.	−	169775.i	0.0607562	−	0.0676251i
$364$		0			0
$365$			4.00369e6i			1.57300i
$366$		0			0
$367$		−	891050.i		−	0.345332i	−0.984980	−	0.172666i	$-0.944762\pi$
$367$		−	891050.i		−	0.345332i	0.984980	−	0.172666i	$-0.0552382\pi$
$368$		0			0
$369$	−3.82461e6	+	410440.i	−1.46225	+	0.156922i
$370$		0			0
$371$	1.21945e6			0.459971
$372$		0			0
$373$	1.97874e6			0.736407			0.368203	−	0.929745i	$-0.379973\pi$
$373$	1.97874e6			0.736407			0.368203	+	0.929745i	$0.379973\pi$
$374$		0			0
$375$	2.18260e6	+	1.96091e6i	0.801486	+	0.720076i
$376$		0			0
$377$		−	854462.i		−	0.309627i
$378$		0			0
$379$		−	1.68153e6i		−	0.601322i	−0.953731	−	0.300661i	$-0.902793\pi$
$379$		−	1.68153e6i		−	0.601322i	0.953731	−	0.300661i	$-0.0972073\pi$
$380$		0			0
$381$	−1.17355e6	−	1.05434e6i	−0.414178	−	0.372109i
$382$		0			0
$383$	344162.			0.119885			0.0599426	−	0.998202i	$-0.480908\pi$
$383$	344162.			0.119885			0.0599426	+	0.998202i	$0.480908\pi$
$384$		0			0
$385$	−540250.			−0.185756
$386$		0			0
$387$	4.35475e6	−	467333.i	1.47804	−	0.158617i
$388$		0			0
$389$			1.45511e6i			0.487554i	0.969831	+	0.243777i	$0.0783865\pi$
$389$			1.45511e6i			0.487554i	−0.969831	+	0.243777i	$0.921614\pi$
$390$		0			0
$391$		−	5.17225e6i		−	1.71095i
$392$		0			0
$393$	847218.	−	943003.i	0.276703	−	0.307986i
$394$		0			0
$395$	−2.50721e6			−0.808534
$396$		0			0
$397$	−5.23469e6			−1.66692			−0.833460	−	0.552580i	$-0.813643\pi$
$397$	−5.23469e6			−1.66692			−0.833460	+	0.552580i	$0.813643\pi$
$398$		0			0
$399$	1.63010e6	−	1.81440e6i	0.512605	−	0.570559i
$400$		0			0
$401$		−	2.31476e6i		−	0.718862i	−0.933172	−	0.359431i	$-0.882971\pi$
$401$		−	2.31476e6i		−	0.718862i	0.933172	−	0.359431i	$-0.117029\pi$
$402$		0			0
$403$			2.12132e6i			0.650644i
$404$		0			0
$405$	−618651.	−	2.84920e6i	−0.187417	−	0.863148i
$406$		0			0
$407$	−1.56289e6			−0.467675
$408$		0			0
$409$	−4.34560e6			−1.28452			−0.642261	−	0.766486i	$-0.722003\pi$
$409$	−4.34560e6			−1.28452			−0.642261	+	0.766486i	$0.722003\pi$
$410$		0			0
$411$	−2.12375e6	−	1.90804e6i	−0.620154	−	0.557163i
$412$		0			0
$413$			4.07210e6i			1.17475i
$414$		0			0
$415$			3.58873e6i			1.02287i
$416$		0			0
$417$	1.00161e6	+	899876.i	0.282072	+	0.253421i
$418$		0			0
$419$	−5.49015e6			−1.52774			−0.763870	−	0.645370i	$-0.776703\pi$
$419$	−5.49015e6			−1.52774			−0.763870	+	0.645370i	$0.776703\pi$
$420$		0			0
$421$	−73995.0			−0.0203468			−0.0101734	−	0.999948i	$-0.503238\pi$
$421$	−73995.0			−0.0203468			−0.0101734	+	0.999948i	$0.503238\pi$
$422$		0			0
$423$	−192665.	−	1.79532e6i	−0.0523544	−	0.487854i
$424$		0			0
$425$			1.00722e6i			0.270492i
$426$		0			0
$427$			5.16813e6i			1.37172i
$428$		0			0
$429$	−337280.	+	375412.i	−0.0884804	+	0.0984838i
$430$		0			0
$431$	−552554.			−0.143279			−0.0716394	−	0.997431i	$-0.522823\pi$
$431$	−552554.			−0.143279			−0.0716394	+	0.997431i	$0.522823\pi$
$432$		0			0
$433$	−5.69741e6			−1.46035			−0.730177	−	0.683258i	$-0.760562\pi$
$433$	−5.69741e6			−1.46035			−0.730177	+	0.683258i	$0.760562\pi$
$434$		0			0
$435$	1.64276e6	−	1.82849e6i	0.416247	−	0.463307i
$436$		0			0
$437$		−	6.10470e6i		−	1.52919i
$438$		0			0
$439$			5.32877e6i			1.31967i	0.751410	+	0.659835i	$0.229374\pi$
$439$			5.32877e6i			1.31967i	−0.751410	+	0.659835i	$0.770626\pi$
$440$		0			0
$441$	−223767.	−	2.08513e6i	−0.0547898	−	0.510548i
$442$		0			0
$443$	−5.06630e6			−1.22654			−0.613270	−	0.789874i	$-0.710146\pi$
$443$	−5.06630e6			−1.22654			−0.613270	+	0.789874i	$0.710146\pi$
$444$		0			0
$445$	217235.			0.0520033
$446$		0			0
$447$	4.37513e6	+	3.93073e6i	1.03567	+	0.930475i
$448$		0			0
$449$		−	8.40296e6i		−	1.96706i	−0.180756	−	0.983528i	$-0.557855\pi$
$449$		−	8.40296e6i		−	1.96706i	0.180756	−	0.983528i	$-0.442145\pi$
$450$		0			0
$451$			1.91537e6i			0.443416i
$452$		0			0
$453$	−787452.	−	707468.i	−0.180293	−	0.161980i
$454$		0			0
$455$	1.19462e6			0.270520
$456$		0			0
$457$	1.96136e6			0.439305			0.219652	−	0.975578i	$-0.429508\pi$
$457$	1.96136e6			0.439305			0.219652	+	0.975578i	$0.429508\pi$
$458$		0			0
$459$	3.24945e6	−	4.50347e6i	0.719909	−	0.997736i
$460$		0			0
$461$			2.70233e6i			0.592225i	0.955153	+	0.296112i	$0.0956903\pi$
$461$			2.70233e6i			0.592225i	−0.955153	+	0.296112i	$0.904310\pi$
$462$		0			0
$463$		−	2.86573e6i		−	0.621274i	−0.950529	−	0.310637i	$-0.899458\pi$
$463$		−	2.86573e6i		−	0.621274i	0.950529	−	0.310637i	$-0.100542\pi$
$464$		0			0
$465$	−4.07837e6	+	4.53946e6i	−0.874691	+	0.973581i
$466$		0			0
$467$	5.04253e6			1.06993			0.534967	−	0.844873i	$-0.320324\pi$
$467$	5.04253e6			1.06993			0.534967	+	0.844873i	$0.320324\pi$
$468$		0			0
$469$	1.48863e6			0.312503
$470$		0			0
$471$	3.74912e6	−	4.17298e6i	0.778712	−	0.866751i
$472$		0			0
$473$		−	2.18087e6i		−	0.448205i
$474$		0			0
$475$			1.18881e6i			0.241756i
$476$		0			0
$477$	3.25829e6	−	349665.i	0.655682	−	0.0703649i
$478$		0			0
$479$	−519165.			−0.103387			−0.0516936	−	0.998663i	$-0.516462\pi$
$479$	−519165.			−0.103387			−0.0516936	+	0.998663i	$0.516462\pi$
$480$		0			0
$481$	3.45592e6			0.681084
$482$		0			0
$483$	3.69939e6	+	3.32363e6i	0.721543	+	0.648253i
$484$		0			0
$485$			5.11723e6i			0.987826i
$486$		0			0
$487$			4.54981e6i			0.869302i	0.900599	+	0.434651i	$0.143128\pi$
$487$			4.54981e6i			0.869302i	−0.900599	+	0.434651i	$0.856872\pi$
$488$		0			0
$489$	−4.89422e6	−	4.39710e6i	−0.925575	−	0.831561i
$490$		0			0
$491$	81176.1			0.0151958			0.00759792	−	0.999971i	$-0.497581\pi$
$491$	81176.1			0.0151958			0.00759792	+	0.999971i	$0.497581\pi$
$492$		0			0
$493$	4.68191e6			0.867572
$494$		0			0
$495$	−1.44351e6	+	154911.i	−0.264793	+	0.0284164i
$496$		0			0
$497$		−	3.13806e6i		−	0.569862i
$498$		0			0
$499$			7.25184e6i			1.30376i	0.758323	+	0.651879i	$0.226019\pi$
$499$			7.25184e6i			1.30376i	−0.758323	+	0.651879i	$0.773981\pi$
$500$		0			0
$501$	1.52837e6	−	1.70116e6i	0.272041	−	0.302797i
$502$		0			0
$503$	−1.34463e6			−0.236964			−0.118482	−	0.992956i	$-0.537803\pi$
$503$	−1.34463e6			−0.236964			−0.118482	+	0.992956i	$0.537803\pi$
$504$		0			0
$505$	−8.10901e6			−1.41494
$506$		0			0
$507$	−3.12234e6	+	3.47535e6i	−0.539462	+	0.600452i
$508$		0			0
$509$		−	1.12166e6i		−	0.191896i	−0.995386	−	0.0959479i	$-0.969412\pi$
$509$		−	1.12166e6i		−	0.191896i	0.995386	−	0.0959479i	$-0.0305882\pi$
$510$		0			0
$511$		−	7.33232e6i		−	1.24219i
$512$		0			0
$513$	3.83526e6	−	5.31535e6i	0.643430	−	0.891741i
$514$		0			0
$515$	−9.75500e6			−1.62072
$516$		0			0
$517$	−899097.			−0.147938
$518$		0			0
$519$	65428.6	+	58782.8i	0.0106623	+	0.00957926i
$520$		0			0
$521$		−	4.69459e6i		−	0.757711i	−0.925456	−	0.378855i	$-0.876318\pi$
$521$		−	4.69459e6i		−	0.757711i	0.925456	−	0.378855i	$-0.123682\pi$
$522$		0			0
$523$			3.14589e6i			0.502909i	0.967869	+	0.251454i	$0.0809088\pi$
$523$			3.14589e6i			0.502909i	−0.967869	+	0.251454i	$0.919091\pi$
$524$		0			0
$525$	−720405.	−	647231.i	−0.114072	−	0.102485i
$526$		0			0
$527$	−1.16235e7			−1.82309
$528$		0			0
$529$	6.01056e6			0.933847
$530$		0			0
$531$	1.16763e6	+	1.08804e7i	0.179709	+	1.67458i
$532$		0			0
$533$		−	4.23532e6i		−	0.645755i
$534$		0			0
$535$		−	6.21470e6i		−	0.938720i
$536$		0			0
$537$	6.15637e6	−	6.85239e6i	0.921274	−	1.02543i
$538$		0			0
$539$	−1.04424e6			−0.154820
$540$		0			0
$541$	1.30526e7			1.91736			0.958680	−	0.284488i	$-0.0918236\pi$
$541$	1.30526e7			1.91736			0.958680	+	0.284488i	$0.0918236\pi$
$542$		0			0
$543$	2.64583e6	−	2.94496e6i	0.385090	−	0.428627i
$544$		0			0
$545$			6.35391e6i			0.916326i
$546$		0			0
$547$		−	1.48958e6i		−	0.212861i	−0.994320	−	0.106431i	$-0.966058\pi$
$547$		−	1.48958e6i		−	0.212861i	0.994320	−	0.106431i	$-0.0339422\pi$
$548$		0			0
$549$	1.48191e6	+	1.38089e7i	0.209841	+	1.95536i
$550$		0			0
$551$	5.52596e6			0.775405
$552$		0			0
$553$	4.59169e6			0.638498
$554$		0			0
$555$	7.39541e6	+	6.64423e6i	1.01913	+	0.915613i
$556$		0			0
$557$			9.60062e6i			1.31118i	0.755118	+	0.655588i	$0.227579\pi$
$557$			9.60062e6i			1.31118i	−0.755118	+	0.655588i	$0.772421\pi$
$558$		0			0
$559$			4.82239e6i			0.652729i
$560$		0			0
$561$	−2.05702e6	−	1.84808e6i	−0.275950	−	0.247921i
$562$		0			0
$563$	−1.01609e7			−1.35101			−0.675507	−	0.737354i	$-0.736075\pi$
$563$	−1.01609e7			−1.35101			−0.675507	+	0.737354i	$0.736075\pi$
$564$		0			0
$565$	252024.			0.0332139
$566$		0			0
$567$	1.13299e6	+	5.21800e6i	0.148003	+	0.681627i
$568$		0			0
$569$		−	5.53882e6i		−	0.717194i	−0.933492	−	0.358597i	$-0.883255\pi$
$569$		−	5.53882e6i		−	0.717194i	0.933492	−	0.358597i	$-0.116745\pi$
$570$		0			0
$571$		−	6.96198e6i		−	0.893598i	−0.894634	−	0.446799i	$-0.852564\pi$
$571$		−	6.96198e6i		−	0.893598i	0.894634	−	0.446799i	$-0.147436\pi$
$572$		0			0
$573$	−6.43232e6	+	7.15954e6i	−0.818429	+	0.910958i
$574$		0			0
$575$	−2.42386e6			−0.305730
$576$		0			0
$577$	−1.41138e7			−1.76483			−0.882417	−	0.470468i	$-0.844085\pi$
$577$	−1.41138e7			−1.76483			−0.882417	+	0.470468i	$0.844085\pi$
$578$		0			0
$579$	2.98652e6	−	3.32417e6i	0.370228	−	0.412085i
$580$		0			0
$581$		−	6.57238e6i		−	0.807760i
$582$		0			0
$583$		−	1.63176e6i		−	0.198831i
$584$		0			0
$585$	3.19192e6	−	342543.i	0.385623	−	0.0413833i
$586$		0			0
$587$	4.93425e6			0.591052			0.295526	−	0.955335i	$-0.404505\pi$
$587$	4.93425e6			0.591052			0.295526	+	0.955335i	$0.404505\pi$
$588$		0			0
$589$	−1.37189e7			−1.62942
$590$		0			0
$591$	6.82434e6	+	6.13117e6i	0.803697	+	0.722062i
$592$		0			0
$593$			1.47329e7i			1.72049i	0.509881	+	0.860245i	$0.329689\pi$
$593$			1.47329e7i			1.72049i	−0.509881	+	0.860245i	$0.670311\pi$
$594$		0			0
$595$			6.54573e6i			0.757994i
$596$		0			0
$597$	4.62371e6	+	4.15406e6i	0.530951	+	0.477020i
$598$		0			0
$599$	−1.36089e7			−1.54973			−0.774863	−	0.632129i	$-0.782181\pi$
$599$	−1.36089e7			−1.54973			−0.774863	+	0.632129i	$0.782181\pi$
$600$		0			0
$601$	−596589.			−0.0673735			−0.0336868	−	0.999432i	$-0.510725\pi$
$601$	−596589.			−0.0673735			−0.0336868	+	0.999432i	$0.510725\pi$
$602$		0			0
$603$	3.97750e6	−	426848.i	0.445469	−	0.0478057i
$604$		0			0
$605$			722911.i			0.0802964i
$606$		0			0
$607$		−	1.03626e7i		−	1.14155i	−0.821106	−	0.570775i	$-0.806643\pi$
$607$		−	1.03626e7i		−	1.14155i	0.821106	−	0.570775i	$-0.193357\pi$
$608$		0			0
$609$	−3.00854e6	+	3.34868e6i	−0.328710	+	0.365873i
$610$		0			0
$611$	1.98811e6			0.215445
$612$		0			0
$613$	8.16913e6			0.878061			0.439031	−	0.898472i	$-0.355322\pi$
$613$	8.16913e6			0.878061			0.439031	+	0.898472i	$0.355322\pi$
$614$		0			0
$615$	8.14268e6	−	9.06327e6i	0.868119	−	0.966267i
$616$		0			0
$617$			9.36584e6i			0.990453i	0.868764	+	0.495226i	$0.164915\pi$
$617$			9.36584e6i			0.990453i	−0.868764	+	0.495226i	$0.835085\pi$
$618$		0			0
$619$		−	1.00892e7i		−	1.05835i	−0.848513	−	0.529174i	$-0.822502\pi$
$619$		−	1.00892e7i		−	1.05835i	0.848513	−	0.529174i	$-0.177498\pi$
$620$		0			0
$621$	1.08375e7	+	7.81972e6i	1.12772	+	0.813696i
$622$		0			0
$623$	−397843.			−0.0410669
$624$		0			0
$625$	−7.14663e6			−0.731815
$626$		0			0
$627$	−2.42785e6	−	2.18125e6i	−0.246635	−	0.221583i
$628$		0			0
$629$			1.89362e7i			1.90839i
$630$		0			0
$631$		−	7.81016e6i		−	0.780884i	−0.920628	−	0.390442i	$-0.872322\pi$
$631$		−	7.81016e6i		−	0.780884i	0.920628	−	0.390442i	$-0.127678\pi$
$632$		0			0
$633$	4.51074e6	+	4.05257e6i	0.447444	+	0.401996i
$634$		0			0
$635$	4.99701e6			0.491786
$636$		0			0
$637$	2.30905e6			0.225467
$638$		0			0
$639$	−899803.	−	8.38465e6i	−0.0871757	−	0.812331i
$640$		0			0
$641$		−	1.98093e7i		−	1.90425i	−0.305707	−	0.952125i	$-0.598893\pi$
$641$		−	1.98093e7i		−	1.90425i	0.305707	−	0.952125i	$-0.401107\pi$
$642$		0			0
$643$		−	1.54294e7i		−	1.47171i	−0.677141	−	0.735853i	$-0.736781\pi$
$643$		−	1.54294e7i		−	1.47171i	0.677141	−	0.735853i	$-0.263219\pi$
$644$		0			0
$645$	−9.27137e6	+	1.03196e7i	−0.877495	+	0.976702i
$646$		0			0
$647$	−8.32198e6			−0.781567			−0.390783	−	0.920483i	$-0.627796\pi$
$647$	−8.32198e6			−0.781567			−0.390783	+	0.920483i	$0.627796\pi$
$648$		0			0
$649$	5.44890e6			0.507805
$650$		0			0
$651$	7.46911e6	−	8.31354e6i	0.690743	−	0.768836i
$652$		0			0
$653$			4.59617e6i			0.421806i	0.977507	+	0.210903i	$0.0676405\pi$
$653$			4.59617e6i			0.421806i	−0.977507	+	0.210903i	$0.932360\pi$
$654$		0			0
$655$			4.01535e6i			0.365696i
$656$		0			0
$657$	−2.10246e6	−	1.95914e7i	−0.190027	−	1.77073i
$658$		0			0
$659$	7.29589e6			0.654432			0.327216	−	0.944950i	$-0.393889\pi$
$659$	7.29589e6			0.654432			0.327216	+	0.944950i	$0.393889\pi$
$660$		0			0
$661$	1.09387e7			0.973785			0.486892	−	0.873462i	$-0.338130\pi$
$661$	1.09387e7			0.973785			0.486892	+	0.873462i	$0.338130\pi$
$662$		0			0
$663$	4.54853e6	+	4.08652e6i	0.401872	+	0.361052i
$664$		0			0
$665$			7.72580e6i			0.677468i
$666$		0			0
$667$			1.12669e7i			0.980596i
$668$		0			0
$669$	2.54270e6	+	2.28443e6i	0.219649	+	0.197339i
$670$		0			0
$671$	6.91550e6			0.592949
$672$		0			0
$673$	−59278.2			−0.00504495			−0.00252248	−	0.999997i	$-0.500803\pi$
$673$	−59278.2			−0.00504495			−0.00252248	+	0.999997i	$0.500803\pi$
$674$		0			0
$675$	−2.11045e6	−	1.52278e6i	−0.178286	−	0.128641i
$676$		0			0
$677$			1.10602e7i			0.927452i	0.885979	+	0.463726i	$0.153488\pi$
$677$			1.10602e7i			0.927452i	−0.885979	+	0.463726i	$0.846512\pi$
$678$		0			0
$679$		−	9.37166e6i		−	0.780085i
$680$		0			0
$681$	−5.20660e6	+	5.79525e6i	−0.430216	+	0.478855i
$682$		0			0
$683$	−1.05020e7			−0.861430			−0.430715	−	0.902488i	$-0.641739\pi$
$683$	−1.05020e7			−0.861430			−0.430715	+	0.902488i	$0.641739\pi$
$684$		0			0
$685$	9.04304e6			0.736356
$686$		0			0
$687$	−1.04408e7	+	1.16213e7i	−0.844002	+	0.939423i
$688$		0			0
$689$			3.60818e6i			0.289561i
$690$		0			0
$691$		−	1.33934e7i		−	1.06708i	−0.845775	−	0.533539i	$-0.820862\pi$
$691$		−	1.33934e7i		−	1.06708i	0.845775	−	0.533539i	$-0.179138\pi$
$692$		0			0
$693$	2.64363e6	−	283703.i	0.209107	−	0.0224404i
$694$		0			0
$695$	−4.26492e6			−0.334926
$696$		0			0
$697$	2.32068e7			1.80940
$698$		0			0
$699$	−5.20530e6	−	4.67658e6i	−0.402952	−	0.362022i
$700$		0			0
$701$			8.35775e6i			0.642383i	0.947014	+	0.321192i	$0.104083\pi$
$701$			8.35775e6i			0.642383i	−0.947014	+	0.321192i	$0.895917\pi$
$702$		0			0
$703$			2.23500e7i			1.70565i
$704$		0			0
$705$	4.25441e6	+	3.82227e6i	0.322379	+	0.289633i
$706$		0			0
$707$	1.48508e7			1.11738
$708$		0			0
$709$	1.45962e7			1.09050			0.545249	−	0.838274i	$-0.316435\pi$
$709$	1.45962e7			1.09050			0.545249	+	0.838274i	$0.316435\pi$
$710$		0			0
$711$	1.22687e7	−	1.31662e6i	0.910171	−	0.0976754i
$712$		0			0
$713$		−	2.79716e7i		−	2.06060i
$714$		0			0
$715$		−	1.59852e6i		−	0.116937i
$716$		0			0
$717$	682917.	−	760126.i	0.0496101	−	0.0552189i
$718$		0			0
$719$	2.70603e6			0.195214			0.0976070	−	0.995225i	$-0.468881\pi$
$719$	2.70603e6			0.195214			0.0976070	+	0.995225i	$0.468881\pi$
$720$		0			0
$721$	1.78652e7			1.27988
$722$		0			0
$723$	−6.75760e6	+	7.52159e6i	−0.480780	+	0.535136i
$724$		0			0
$725$		−	2.19407e6i		−	0.155027i
$726$		0			0
$727$		−	1.43482e7i		−	1.00685i	−0.864040	−	0.503423i	$-0.832074\pi$
$727$		−	1.43482e7i		−	1.00685i	0.864040	−	0.503423i	$-0.167926\pi$
$728$		0			0
$729$	4.52348e6	+	1.36172e7i	0.315249	+	0.949009i
$730$		0			0
$731$	−2.64236e7			−1.82894
$732$		0			0
$733$	−2.95690e6			−0.203272			−0.101636	−	0.994822i	$-0.532408\pi$
$733$	−2.95690e6			−0.203272			−0.101636	+	0.994822i	$0.532408\pi$
$734$		0			0
$735$	4.94118e6	+	4.43929e6i	0.337375	+	0.303106i
$736$		0			0
$737$		−	1.99194e6i		−	0.135085i
$738$		0			0
$739$			6.14861e6i			0.414158i	0.978324	+	0.207079i	$0.0663957\pi$
$739$			6.14861e6i			0.414158i	−0.978324	+	0.207079i	$0.933604\pi$
$740$		0			0
$741$	5.36854e6	+	4.82324e6i	0.359179	+	0.322696i
$742$		0			0
$743$	−8.11409e6			−0.539222			−0.269611	−	0.962969i	$-0.586895\pi$
$743$	−8.11409e6			−0.539222			−0.269611	+	0.962969i	$0.586895\pi$
$744$		0			0
$745$	−1.86295e7			−1.22973
$746$		0			0
$747$	−1.88456e6	−	1.75609e7i	−0.123569	−	1.15145i
$748$		0			0
$749$			1.13816e7i			0.741306i
$750$		0			0
$751$		−	6.47674e6i		−	0.419041i	−0.977804	−	0.209520i	$-0.932810\pi$
$751$		−	6.47674e6i		−	0.419041i	0.977804	−	0.209520i	$-0.0671903\pi$
$752$		0			0
$753$	685211.	−	762679.i	0.0440389	−	0.0490178i
$754$		0			0
$755$	3.35301e6			0.214076
$756$		0			0
$757$	2.78558e7			1.76676			0.883378	−	0.468662i	$-0.155264\pi$
$757$	2.78558e7			1.76676			0.883378	+	0.468662i	$0.155264\pi$
$758$		0			0
$759$	4.44736e6	−	4.95017e6i	0.280219	−	0.311900i
$760$		0			0
$761$			1.53380e7i			0.960078i	0.877247	+	0.480039i	$0.159377\pi$
$761$			1.53380e7i			0.960078i	−0.877247	+	0.480039i	$0.840623\pi$
$762$		0			0
$763$		−	1.16365e7i		−	0.723621i
$764$		0			0
$765$	1.87692e6	+	1.74897e7i	0.115956	+	1.08051i
$766$		0			0
$767$	−1.20488e7			−0.739526
$768$		0			0
$769$	3.85611e6			0.235144			0.117572	−	0.993064i	$-0.462489\pi$
$769$	3.85611e6			0.235144			0.117572	+	0.993064i	$0.462489\pi$
$770$		0			0
$771$	1.96730e7	+	1.76748e7i	1.19189	+	1.07082i
$772$		0			0
$773$		−	4.97015e6i		−	0.299172i	−0.988749	−	0.149586i	$-0.952206\pi$
$773$		−	4.97015e6i		−	0.299172i	0.988749	−	0.149586i	$-0.0477941\pi$
$774$		0			0
$775$			5.44709e6i			0.325769i
$776$		0			0
$777$	−1.35439e7	−	1.21682e7i	−0.804806	−	0.723059i
$778$		0			0
$779$	2.73906e7			1.61718
$780$		0			0
$781$	−4.19905e6			−0.246333
$782$		0			0
$783$	−7.07839e6	+	9.81008e6i	−0.412601	+	0.571831i
$784$		0			0
$785$			1.77688e7i			1.02916i
$786$		0			0
$787$			3.06159e7i			1.76202i	0.473098	+	0.881010i	$0.343136\pi$
$787$			3.06159e7i			1.76202i	−0.473098	+	0.881010i	$0.656864\pi$
$788$		0			0
$789$	1.99414e7	−	2.21959e7i	1.14041	−	1.26935i
$790$		0			0
$791$	−461554.			−0.0262290
$792$		0			0
$793$	−1.52917e7			−0.863523
$794$		0			0
$795$	−6.93697e6	+	7.72124e6i	−0.389271	+	0.433281i
$796$		0			0
$797$			5.80581e6i			0.323755i	0.986811	+	0.161878i	$0.0517550\pi$
$797$			5.80581e6i			0.323755i	−0.986811	+	0.161878i	$0.948245\pi$
$798$		0			0
$799$			1.08936e7i			0.603675i
$800$		0			0
$801$	−1.06301e6	+	114077.i	−0.0585403	+	0.00628229i
$802$		0			0
$803$	−9.81141e6			−0.536961
$804$		0			0
$805$	−1.57522e7			−0.856743
$806$		0			0
$807$	−5.91530e6	−	5.31446e6i	−0.319737	−	0.287260i
$808$		0			0
$809$		−	1.98237e7i		−	1.06491i	−0.846458	−	0.532455i	$-0.821270\pi$
$809$		−	1.98237e7i		−	1.06491i	0.846458	−	0.532455i	$-0.178730\pi$
$810$		0			0
$811$			3.31664e7i			1.77071i	0.464918	+	0.885354i	$0.346084\pi$
$811$			3.31664e7i			1.77071i	−0.464918	+	0.885354i	$0.653916\pi$
$812$		0			0
$813$	1.15271e7	+	1.03563e7i	0.611639	+	0.549512i
$814$		0			0
$815$	2.08398e7			1.09901
$816$		0			0
$817$	−3.11873e7			−1.63464
$818$		0			0
$819$	−5.84567e6	+	627331.i	−0.304526	+	0.0326804i
$820$		0			0
$821$			6.79805e6i			0.351987i	0.984391	+	0.175993i	$0.0563138\pi$
$821$			6.79805e6i			0.351987i	−0.984391	+	0.175993i	$0.943686\pi$
$822$		0			0
$823$			4.93406e6i			0.253924i	0.991908	+	0.126962i	$0.0405227\pi$
$823$			4.93406e6i			0.253924i	−0.991908	+	0.126962i	$0.959477\pi$
$824$		0			0
$825$	−866062.	+	963976.i	−0.0443010	+	0.0493096i
$826$		0			0
$827$	−8.63256e6			−0.438911			−0.219455	−	0.975623i	$-0.570428\pi$
$827$	−8.63256e6			−0.438911			−0.219455	+	0.975623i	$0.570428\pi$
$828$		0			0
$829$	2.02411e6			0.102294			0.0511468	−	0.998691i	$-0.483712\pi$
$829$	2.02411e6			0.102294			0.0511468	+	0.998691i	$0.483712\pi$
$830$		0			0
$831$	548070.	−	610034.i	0.0275318	−	0.0306444i
$832$		0			0
$833$			1.26521e7i			0.631757i
$834$		0			0
$835$			7.24364e6i			0.359534i
$836$		0			0
$837$	1.75731e7	−	2.43548e7i	0.867030	−	1.20163i
$838$		0			0
$839$	9.24944e6			0.453639			0.226820	−	0.973937i	$-0.427167\pi$
$839$	9.24944e6			0.453639			0.226820	+	0.973937i	$0.427167\pi$
$840$		0			0
$841$	1.03124e7			0.502769
$842$		0			0
$843$	−1.32287e7	−	1.18850e7i	−0.641133	−	0.576011i
$844$		0			0
$845$		−	1.47982e7i		−	0.712963i
$846$		0			0
$847$		−	1.32393e6i		−	0.0634100i
$848$		0			0
$849$	712136.	+	639802.i	0.0339073	+	0.0304632i
$850$		0			0
$851$	−4.55696e7			−2.15701
$852$		0			0
$853$	1.31910e7			0.620734			0.310367	−	0.950617i	$-0.399548\pi$
$853$	1.31910e7			0.620734			0.310367	+	0.950617i	$0.399548\pi$
$854$		0			0
$855$	2.21529e6	+	2.06427e7i	0.103637	+	0.965722i
$856$		0			0
$857$			3.19065e7i			1.48398i	0.670411	+	0.741990i	$0.266118\pi$
$857$			3.19065e7i			1.48398i	−0.670411	+	0.741990i	$0.733882\pi$
$858$		0			0
$859$		−	2.48544e7i		−	1.14927i	−0.818411	−	0.574633i	$-0.805145\pi$
$859$		−	2.48544e7i		−	1.14927i	0.818411	−	0.574633i	$-0.194855\pi$
$860$		0			0
$861$	−1.49124e7	+	1.65984e7i	−0.685553	+	0.763060i
$862$		0			0
$863$	1.03873e7			0.474762			0.237381	−	0.971417i	$-0.423711\pi$
$863$	1.03873e7			0.474762			0.237381	+	0.971417i	$0.423711\pi$
$864$		0			0
$865$	−278598.			−0.0126601
$866$		0			0
$867$	−7.59940e6	+	8.45857e6i	−0.343346	+	0.382163i
$868$		0			0
$869$		−	6.14416e6i		−	0.276002i
$870$		0			0
$871$			4.40463e6i			0.196727i
$872$		0			0
$873$	−2.68722e6	−	2.50404e7i	−0.119335	−	1.11200i
$874$		0			0
$875$	1.70203e7			0.751529
$876$		0			0
$877$	2.05588e7			0.902607			0.451303	−	0.892371i	$-0.350959\pi$
$877$	2.05588e7			0.902607			0.451303	+	0.892371i	$0.350959\pi$
$878$		0			0
$879$	−1.28222e7	−	1.15198e7i	−0.559745	−	0.502890i
$880$		0			0
$881$			2.80792e6i			0.121883i	0.998141	+	0.0609417i	$0.0194104\pi$
$881$			2.80792e6i			0.121883i	−0.998141	+	0.0609417i	$0.980590\pi$
$882$		0			0
$883$		−	1.01130e7i		−	0.436495i	−0.975893	−	0.218248i	$-0.929966\pi$
$883$		−	1.01130e7i		−	0.436495i	0.975893	−	0.218248i	$-0.0700341\pi$
$884$		0			0
$885$	−2.57834e7	−	2.31645e7i	−1.10658	−	0.994180i
$886$		0			0
$887$	7.47357e6			0.318947			0.159474	−	0.987202i	$-0.449020\pi$
$887$	7.47357e6			0.318947			0.159474	+	0.987202i	$0.449020\pi$
$888$		0			0
$889$	−9.15149e6			−0.388363
$890$		0			0
$891$	6.98223e6	−	1.51606e6i	0.294646	−	0.0639769i
$892$		0			0
$893$			1.28575e7i			0.539543i
$894$		0			0
$895$			2.91778e7i			1.21757i
$896$		0			0
$897$	−9.83412e6	+	1.09459e7i	−0.408089	+	0.454226i
$898$		0			0
$899$	2.53198e7			1.04487
$900$		0			0
$901$	−1.97705e7			−0.811347
$902$		0			0
$903$	1.69795e7	−	1.88992e7i	0.692957	−	0.771300i
$904$		0			0
$905$			1.25398e7i			0.508942i
$906$		0			0
$907$		−	2.87745e7i		−	1.16142i	−0.814110	−	0.580711i	$-0.802775\pi$
$907$		−	2.87745e7i		−	1.16142i	0.814110	−	0.580711i	$-0.197225\pi$
$908$		0			0
$909$	3.96802e7	−	4.25830e6i	1.59281	−	0.170933i
$910$		0			0
$911$	−2.55554e7			−1.02020			−0.510102	−	0.860114i	$-0.670392\pi$
$911$	−2.55554e7			−1.02020			−0.510102	+	0.860114i	$0.670392\pi$
$912$		0			0
$913$	−8.79453e6			−0.349169
$914$		0			0
$915$	−3.27232e7	−	2.93994e7i	−1.29212	−	1.16087i
$916$		0			0
$917$		−	7.35368e6i		−	0.288790i
$918$		0			0
$919$			1.90504e7i			0.744073i	0.928218	+	0.372036i	$0.121340\pi$
$919$			1.90504e7i			0.744073i	−0.928218	+	0.372036i	$0.878660\pi$
$920$		0			0
$921$	−1.60606e7	−	1.44293e7i	−0.623898	−	0.560527i
$922$		0			0
$923$	9.28505e6			0.358740
$924$		0			0
$925$	8.87405e6			0.341010
$926$		0			0
$927$	4.77346e7	−	5.12266e6i	1.82446	−	0.195793i
$928$		0			0
$929$		−	4.95094e7i		−	1.88213i	−0.338232	−	0.941063i	$-0.609829\pi$
$929$		−	4.95094e7i		−	1.88213i	0.338232	−	0.941063i	$-0.390171\pi$
$930$		0			0
$931$			1.49330e7i			0.564642i
$932$		0			0
$933$	−2.32844e7	+	2.59169e7i	−0.875712	+	0.974717i
$934$		0			0
$935$	8.75887e6			0.327657
$936$		0			0
$937$	−2.62569e7			−0.977000			−0.488500	−	0.872564i	$-0.662456\pi$
$937$	−2.62569e7			−0.977000			−0.488500	+	0.872564i	$0.662456\pi$
$938$		0			0
$939$	6.75945e6	−	7.52365e6i	0.250177	−	0.278461i
$940$		0			0
$941$			2.74328e7i			1.00994i	0.863137	+	0.504970i	$0.168497\pi$
$941$			2.74328e7i			1.00994i	−0.863137	+	0.504970i	$0.831503\pi$
$942$		0			0
$943$			5.58467e7i			2.04512i
$944$		0			0
$945$	−1.37154e7	−	9.89624e6i	−0.499607	−	0.360488i
$946$		0			0
$947$	3.40200e7			1.23270			0.616352	−	0.787470i	$-0.288610\pi$
$947$	3.40200e7			1.23270			0.616352	+	0.787470i	$0.288610\pi$
$948$		0			0
$949$	2.16953e7			0.781987
$950$		0			0
$951$	−2.62689e7	−	2.36006e7i	−0.941868	−	0.846199i
$952$		0			0
$953$		−	1.78317e7i		−	0.636005i	−0.948090	−	0.318002i	$-0.896988\pi$
$953$		−	1.78317e7i		−	0.636005i	0.948090	−	0.318002i	$-0.103012\pi$
$954$		0			0
$955$		−	3.04856e7i		−	1.08165i
$956$		0			0
$957$	4.48088e6	+	4.02574e6i	0.158155	+	0.142091i
$958$		0			0
$959$	−1.65614e7			−0.581500
$960$		0			0
$961$	−3.42308e7			−1.19566
$962$		0			0
$963$	3.26354e6	+	3.04107e7i	0.113403	+	1.05672i
$964$		0			0
$965$			1.41545e7i			0.489300i
$966$		0			0
$967$			2.46276e7i			0.846945i	0.905909	+	0.423472i	$0.139189\pi$
$967$			2.46276e7i			0.846945i	−0.905909	+	0.423472i	$0.860811\pi$
$968$		0			0
$969$	−2.64283e7	+	2.94162e7i	−0.904189	+	1.00641i
$970$		0			0
$971$	4.15710e7			1.41496			0.707478	−	0.706736i	$-0.249833\pi$
$971$	4.15710e7			1.41496			0.707478	+	0.706736i	$0.249833\pi$
$972$		0			0
$973$	7.81074e6			0.264490
$974$		0			0
$975$	1.91506e6	−	2.13157e6i	0.0645165	−	0.0718106i
$976$		0			0
$977$		−	3.43154e7i		−	1.15014i	−0.818103	−	0.575072i	$-0.804974\pi$
$977$		−	3.43154e7i		−	1.15014i	0.818103	−	0.575072i	$-0.195026\pi$
$978$		0			0
$979$			532356.i			0.0177519i
$980$		0			0
$981$	−3.33664e6	−	3.10919e7i	−0.110697	−	1.03151i
$982$		0			0
$983$	−217900.			−0.00719240			−0.00359620	−	0.999994i	$-0.501145\pi$
$983$	−217900.			−0.00719240			−0.00359620	+	0.999994i	$0.501145\pi$
$984$		0			0
$985$	−2.90584e7			−0.954290
$986$		0			0
$987$	−7.79149e6	−	7.00008e6i	−0.254582	−	0.228723i
$988$		0			0
$989$		−	6.35879e7i		−	2.06721i
$990$		0			0
$991$			2.25349e7i			0.728906i	0.931222	+	0.364453i	$0.118744\pi$
$991$			2.25349e7i			0.728906i	−0.931222	+	0.364453i	$0.881256\pi$
$992$		0			0
$993$	1.82468e7	+	1.63934e7i	0.587238	+	0.527590i
$994$		0			0
$995$	−1.96880e7			−0.630439
$996$		0			0
$997$	−1.01901e7			−0.324669			−0.162334	−	0.986736i	$-0.551902\pi$
$997$	−1.01901e7			−0.324669			−0.162334	+	0.986736i	$0.551902\pi$
$998$		0			0
$999$	−3.96774e7	−	2.86289e7i	−1.25785	−	0.907594i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	528.6.d.b.287.11	yes	16
3.2	odd	2		528.6.d.a.287.5	✓	16
4.3	odd	2		528.6.d.a.287.6	yes	16
12.11	even	2	inner	528.6.d.b.287.12	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
528.6.d.a.287.5	✓	16	3.2	odd	2
528.6.d.a.287.6	yes	16	4.3	odd	2
528.6.d.b.287.11	yes	16	1.1	even	1	trivial
528.6.d.b.287.12	yes	16	12.11	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	528.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(10.4180 - 11.5959i) q^{3} +49.3758i q^{5} -90.4265i q^{7} +(-25.9288 - 241.613i) q^{9} +O(q^{10})\)	\(q+(10.4180 - 11.5959i) q^{3} +49.3758i q^{5} -90.4265i q^{7} +(-25.9288 - 241.613i) q^{9} -121.000 q^{11} +267.559 q^{13} +(572.556 + 514.399i) q^{15} +1466.05i q^{17} +1730.35i q^{19} +(-1048.57 - 942.067i) q^{21} -3528.02 q^{23} +687.033 q^{25} +(-3071.84 - 2216.46i) q^{27} -3193.55i q^{29} +7928.43i q^{31} +(-1260.58 + 1403.10i) q^{33} +4464.88 q^{35} +12916.5 q^{37} +(2787.44 - 3102.58i) q^{39} -15829.5i q^{41} +18023.7i q^{43} +(11929.8 - 1280.25i) q^{45} +7430.56 q^{47} +8630.05 q^{49} +(17000.1 + 15273.4i) q^{51} +13485.6i q^{53} -5974.47i q^{55} +(20064.9 + 18026.8i) q^{57} -45032.2 q^{59} -57152.9 q^{61} +(-21848.2 + 2344.65i) q^{63} +13210.9i q^{65} +16462.3i q^{67} +(-36755.0 + 40910.5i) q^{69} +34702.9 q^{71} +81086.0 q^{73} +(7157.54 - 7966.75i) q^{75} +10941.6i q^{77} +50778.2i q^{79} +(-57704.4 + 12529.5i) q^{81} +72682.1 q^{83} -72387.4 q^{85} +(-37032.0 - 33270.6i) q^{87} -4399.63i q^{89} -24194.4i q^{91} +(91937.1 + 82598.7i) q^{93} -85437.3 q^{95} +103638. q^{97} +(3137.38 + 29235.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 31 q^{3} + 31 q^{9}+O(q^{10}) \) 16 * q + 31 * q^3 + 31 * q^9	\( 16 q + 31 q^{3} + 31 q^{9} - 1936 q^{11} + 444 q^{13} - 979 q^{15} - 3874 q^{21} + 4246 q^{23} - 4194 q^{25} + 1306 q^{27} - 3751 q^{33} - 13964 q^{35} + 35094 q^{37} - 7848 q^{39} - 43369 q^{45} + 18476 q^{47} - 6172 q^{49} + 40886 q^{51} - 27316 q^{57} - 59134 q^{59} + 93580 q^{61} + 52286 q^{63} + 23881 q^{69} + 129154 q^{71} + 63188 q^{73} - 30048 q^{75} + 132223 q^{81} - 46276 q^{83} + 141316 q^{85} - 86304 q^{87} + 228139 q^{93} - 238328 q^{95} - 244198 q^{97} - 3751 q^{99}+O(q^{100}) \) 16 * q + 31 * q^3 + 31 * q^9 - 1936 * q^11 + 444 * q^13 - 979 * q^15 - 3874 * q^21 + 4246 * q^23 - 4194 * q^25 + 1306 * q^27 - 3751 * q^33 - 13964 * q^35 + 35094 * q^37 - 7848 * q^39 - 43369 * q^45 + 18476 * q^47 - 6172 * q^49 + 40886 * q^51 - 27316 * q^57 - 59134 * q^59 + 93580 * q^61 + 52286 * q^63 + 23881 * q^69 + 129154 * q^71 + 63188 * q^73 - 30048 * q^75 + 132223 * q^81 - 46276 * q^83 + 141316 * q^85 - 86304 * q^87 + 228139 * q^93 - 238328 * q^95 - 244198 * q^97 - 3751 * q^99

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