LMFDB - Embedded newform 648.4.i.s.217.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [648,4,Mod(217,648)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(648, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("648.217");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	648.i (of order $3$, degree $2$, not 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:	$38.2332376837$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{3} $
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			217.2
Root			$1.68614 + 0.396143i$ of defining polynomial
Character	$\chi$	$=$	648.217
Dual form			648.4.i.s.433.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(10.6168 + 18.3889i) q^{5} +(-14.6168 + 25.3171i) q^{7} +O(q^{10})$	$q+(10.6168 + 18.3889i) q^{5} +(-14.6168 + 25.3171i) q^{7} +(0.500000 - 0.866025i) q^{11} +(26.4674 + 45.8428i) q^{13} +96.9348 q^{17} +126.467 q^{19} +(-11.4674 - 19.8621i) q^{23} +(-162.935 + 282.211i) q^{25} +(-66.7663 + 115.643i) q^{29} +(-50.9158 - 88.1887i) q^{31} -620.739 q^{35} +105.065 q^{37} +(8.16844 + 14.1482i) q^{41} +(100.636 - 174.306i) q^{43} +(-125.935 + 218.125i) q^{47} +(-255.804 - 443.066i) q^{49} +148.038 q^{53} +21.2337 q^{55} +(-36.8043 - 63.7468i) q^{59} +(303.739 - 526.091i) q^{61} +(-562.000 + 973.413i) q^{65} +(-380.973 - 659.864i) q^{67} -701.196 q^{71} -287.000 q^{73} +(14.6168 + 25.3171i) q^{77} +(64.2610 - 111.303i) q^{79} +(80.2390 - 138.978i) q^{83} +(1029.14 + 1782.52i) q^{85} -430.206 q^{89} -1547.48 q^{91} +(1342.68 + 2325.60i) q^{95} +(15.5652 - 26.9598i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{5} - 24 q^{7}+O(q^{10}) $ 4 * q + 8 * q^5 - 24 * q^7	$ 4 q + 8 q^{5} - 24 q^{7} + 2 q^{11} - 32 q^{13} + 112 q^{17} + 368 q^{19} + 92 q^{23} - 376 q^{25} - 336 q^{29} - 376 q^{31} - 1380 q^{35} + 696 q^{37} - 312 q^{41} - 80 q^{43} - 228 q^{47} - 196 q^{49} - 304 q^{53} + 16 q^{55} + 680 q^{59} + 112 q^{61} - 2248 q^{65} - 352 q^{67} - 3632 q^{71} - 1148 q^{73} + 24 q^{77} + 1360 q^{79} - 782 q^{83} + 2600 q^{85} - 480 q^{89} - 3984 q^{91} + 1924 q^{95} + 338 q^{97}+O(q^{100}) $ 4 * q + 8 * q^5 - 24 * q^7 + 2 * q^11 - 32 * q^13 + 112 * q^17 + 368 * q^19 + 92 * q^23 - 376 * q^25 - 336 * q^29 - 376 * q^31 - 1380 * q^35 + 696 * q^37 - 312 * q^41 - 80 * q^43 - 228 * q^47 - 196 * q^49 - 304 * q^53 + 16 * q^55 + 680 * q^59 + 112 * q^61 - 2248 * q^65 - 352 * q^67 - 3632 * q^71 - 1148 * q^73 + 24 * q^77 + 1360 * q^79 - 782 * q^83 + 2600 * q^85 - 480 * q^89 - 3984 * q^91 + 1924 * q^95 + 338 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$5$	10.6168	+	18.3889i	0.949599	+	1.64475i	0.746269	+	0.665644i	$0.231843\pi$
$5$	10.6168	+	18.3889i	0.949599	+	1.64475i	0.203330	+	0.979110i	$0.434824\pi$
$6$		0			0
$7$	−14.6168	+	25.3171i	−0.789235	+	1.36700i	0.137201	+	0.990543i	$0.456190\pi$
$7$	−14.6168	+	25.3171i	−0.789235	+	1.36700i	−0.926436	+	0.376453i	$0.877144\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.500000	−	0.866025i	0.0137051	−	0.0237379i	−0.859092	−	0.511822i	$-0.828971\pi$
$11$	0.500000	−	0.866025i	0.0137051	−	0.0237379i	0.872797	+	0.488084i	$0.162304\pi$
$12$		0			0
$13$	26.4674	+	45.8428i	0.564671	+	0.978040i	0.997080	+	0.0763620i	$0.0243305\pi$
$13$	26.4674	+	45.8428i	0.564671	+	0.978040i	−0.432409	+	0.901678i	$0.642336\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	96.9348			1.38295			0.691474	−	0.722401i	$-0.256961\pi$
$17$	96.9348			1.38295			0.691474	+	0.722401i	$0.256961\pi$
$18$		0			0
$19$	126.467			1.52703			0.763516	−	0.645789i	$-0.223471\pi$
$19$	126.467			1.52703			0.763516	+	0.645789i	$0.223471\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−11.4674	−	19.8621i	−0.103961	−	0.180066i	0.809352	−	0.587324i	$-0.199819\pi$
$23$	−11.4674	−	19.8621i	−0.103961	−	0.180066i	−0.913313	+	0.407257i	$0.866485\pi$
$24$		0			0
$25$	−162.935	+	282.211i	−1.30348	+	2.25769i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−66.7663	+	115.643i	−0.427524	+	0.740493i	−0.996652	−	0.0817555i	$-0.973947\pi$
$29$	−66.7663	+	115.643i	−0.427524	+	0.740493i	0.569129	+	0.822249i	$0.307281\pi$
$30$		0			0
$31$	−50.9158	−	88.1887i	−0.294992	−	0.510941i	0.679991	−	0.733220i	$-0.261984\pi$
$31$	−50.9158	−	88.1887i	−0.294992	−	0.510941i	−0.974983	+	0.222280i	$0.928650\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−620.739			−2.99783
$36$		0			0
$37$	105.065			0.466828			0.233414	−	0.972378i	$-0.425010\pi$
$37$	105.065			0.466828			0.233414	+	0.972378i	$0.425010\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	8.16844	+	14.1482i	0.0311145	+	0.0538920i	0.881163	−	0.472812i	$-0.156761\pi$
$41$	8.16844	+	14.1482i	0.0311145	+	0.0538920i	−0.850049	+	0.526704i	$0.823428\pi$
$42$		0			0
$43$	100.636	−	174.306i	0.356903	−	0.618174i	−0.630539	−	0.776158i	$-0.717166\pi$
$43$	100.636	−	174.306i	0.356903	−	0.618174i	0.987442	+	0.157984i	$0.0504994\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−125.935	+	218.125i	−0.390840	+	0.676954i	−0.992561	−	0.121752i	$-0.961149\pi$
$47$	−125.935	+	218.125i	−0.390840	+	0.676954i	0.601721	+	0.798707i	$0.294482\pi$
$48$		0			0
$49$	−255.804	−	443.066i	−0.745785	−	1.29174i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	148.038			0.383671			0.191836	−	0.981427i	$-0.438556\pi$
$53$	148.038			0.383671			0.191836	+	0.981427i	$0.438556\pi$
$54$		0			0
$55$	21.2337			0.0520573
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−36.8043	−	63.7468i	−0.0812120	−	0.140663i	0.822559	−	0.568680i	$-0.192546\pi$
$59$	−36.8043	−	63.7468i	−0.0812120	−	0.140663i	−0.903771	+	0.428017i	$0.859212\pi$
$60$		0			0
$61$	303.739	−	526.091i	0.637538	−	1.10425i	−0.348434	−	0.937333i	$-0.613286\pi$
$61$	303.739	−	526.091i	0.637538	−	1.10425i	0.985971	−	0.166914i	$-0.0533803\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−562.000	+	973.413i	−1.07242	+	1.85749i
$66$		0			0
$67$	−380.973	−	659.864i	−0.694675	−	1.20321i	−0.970290	−	0.241944i	$-0.922215\pi$
$67$	−380.973	−	659.864i	−0.694675	−	1.20321i	0.275615	−	0.961268i	$-0.411118\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−701.196			−1.17207			−0.586033	−	0.810287i	$-0.699311\pi$
$71$	−701.196			−1.17207			−0.586033	+	0.810287i	$0.699311\pi$
$72$		0			0
$73$	−287.000			−0.460148			−0.230074	−	0.973173i	$-0.573897\pi$
$73$	−287.000			−0.460148			−0.230074	+	0.973173i	$0.573897\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	14.6168	+	25.3171i	0.0216330	+	0.0374695i
$78$		0			0
$79$	64.2610	−	111.303i	0.0915181	−	0.158514i	−0.816632	−	0.577159i	$-0.804161\pi$
$79$	64.2610	−	111.303i	0.0915181	−	0.158514i	0.908150	+	0.418645i	$0.137495\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	80.2390	−	138.978i	0.106113	−	0.183793i	−0.808079	−	0.589074i	$-0.799493\pi$
$83$	80.2390	−	138.978i	0.106113	−	0.183793i	0.914192	+	0.405281i	$0.132826\pi$
$84$		0			0
$85$	1029.14	+	1782.52i	1.31325	+	2.27461i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−430.206			−0.512380			−0.256190	−	0.966626i	$-0.582467\pi$
$89$	−430.206			−0.512380			−0.256190	+	0.966626i	$0.582467\pi$
$90$		0			0
$91$	−1547.48			−1.78263
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1342.68	+	2325.60i	1.45007	+	2.51159i
$96$		0			0
$97$	15.5652	−	26.9598i	0.0162929	−	0.0282201i	−0.857764	−	0.514044i	$-0.828147\pi$
$97$	15.5652	−	26.9598i	0.0162929	−	0.0282201i	0.874057	+	0.485824i	$0.161480\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−491.552	+	851.392i	−0.484269	+	0.838779i	−0.999837	−	0.0180698i	$-0.994248\pi$
$101$	−491.552	+	851.392i	−0.484269	+	0.838779i	0.515567	+	0.856849i	$0.327581\pi$
$102$		0			0
$103$	476.076	+	824.588i	0.455429	+	0.788826i	0.998713	−	0.0507234i	$-0.0161527\pi$
$103$	476.076	+	824.588i	0.455429	+	0.788826i	−0.543284	+	0.839549i	$0.682819\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	272.087			0.245828			0.122914	−	0.992417i	$-0.460776\pi$
$107$	272.087			0.245828			0.122914	+	0.992417i	$0.460776\pi$
$108$		0			0
$109$	1355.76			1.19136			0.595680	−	0.803222i	$-0.296883\pi$
$109$	1355.76			1.19136			0.595680	+	0.803222i	$0.296883\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−969.179	−	1678.67i	−0.806838	−	1.39748i	−0.915043	−	0.403356i	$-0.867844\pi$
$113$	−969.179	−	1678.67i	−0.806838	−	1.39748i	0.108205	−	0.994129i	$-0.465490\pi$
$114$		0			0
$115$	243.495	−	421.745i	0.197443	−	0.341982i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1416.88	+	2454.11i	−1.09147	+	1.89049i
$120$		0			0
$121$	665.000	+	1151.81i	0.499624	+	0.865375i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−4265.20			−3.05193
$126$		0			0
$127$	232.375			0.162362			0.0811808	−	0.996699i	$-0.474131\pi$
$127$	232.375			0.162362			0.0811808	+	0.996699i	$0.474131\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−1397.65	−	2420.80i	−0.932163	−	1.61455i	−0.779616	−	0.626258i	$-0.784586\pi$
$131$	−1397.65	−	2420.80i	−0.932163	−	1.61455i	−0.152548	−	0.988296i	$-0.548748\pi$
$132$		0			0
$133$	−1848.55	+	3201.79i	−1.20519	+	2.08745i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−630.766	+	1092.52i	−0.393358	+	0.681315i	−0.992890	−	0.119035i	$-0.962020\pi$
$137$	−630.766	+	1092.52i	−0.393358	+	0.681315i	0.599532	+	0.800351i	$0.295353\pi$
$138$		0			0
$139$	153.684	+	266.189i	0.0937794	+	0.162431i	0.909099	−	0.416581i	$-0.136772\pi$
$139$	153.684	+	266.189i	0.0937794	+	0.162431i	−0.815319	+	0.579012i	$0.803438\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	52.9348			0.0309554
$144$		0			0
$145$	−2835.39			−1.62391
$146$		0			0
$147$		0			0
$148$		0			0
$149$	798.878	+	1383.70i	0.439239	+	0.760784i	0.997631	−	0.0687929i	$-0.0219148\pi$
$149$	798.878	+	1383.70i	0.439239	+	0.760784i	−0.558392	+	0.829577i	$0.688581\pi$
$150$		0			0
$151$	1707.70	−	2957.83i	0.920337	−	1.59407i	0.121444	−	0.992598i	$-0.461248\pi$
$151$	1707.70	−	2957.83i	0.920337	−	1.59407i	0.798893	−	0.601473i	$-0.205419\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1081.13	−	1872.57i	0.560248	−	0.970378i
$156$		0			0
$157$	−238.413	−	412.943i	−0.121194	−	0.209914i	0.799045	−	0.601271i	$-0.205339\pi$
$157$	−238.413	−	412.943i	−0.121194	−	0.209914i	−0.920239	+	0.391358i	$0.872006\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	670.467			0.328200
$162$		0			0
$163$	3304.04			1.58768			0.793842	−	0.608124i	$-0.208078\pi$
$163$	3304.04			1.58768			0.793842	+	0.608124i	$0.208078\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1045.83	+	1811.42i	0.484601	+	0.839354i	0.999844	−	0.0176906i	$-0.00563138\pi$
$167$	1045.83	+	1811.42i	0.484601	+	0.839354i	−0.515242	+	0.857045i	$0.672298\pi$
$168$		0			0
$169$	−302.544	+	524.022i	−0.137708	+	0.238517i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1462.28	−	2532.74i	0.642631	−	1.11307i	−0.342213	−	0.939622i	$-0.611176\pi$
$173$	1462.28	−	2532.74i	0.642631	−	1.11307i	0.984843	−	0.173446i	$-0.0554903\pi$
$174$		0			0
$175$	−4763.18	−	8250.08i	−2.05750	−	3.56370i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	231.913			0.0968381			0.0484191	−	0.998827i	$-0.484582\pi$
$179$	231.913			0.0968381			0.0484191	+	0.998827i	$0.484582\pi$
$180$		0			0
$181$	2291.74			0.941125			0.470562	−	0.882367i	$-0.344051\pi$
$181$	2291.74			0.941125			0.470562	+	0.882367i	$0.344051\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1115.46	+	1932.04i	0.443299	+	0.767817i
$186$		0			0
$187$	48.4674	−	83.9480i	0.0189534	−	0.0328282i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2108.90	+	3652.72i	−0.798925	+	1.38378i	0.121391	+	0.992605i	$0.461264\pi$
$191$	−2108.90	+	3652.72i	−0.798925	+	1.38378i	−0.920316	+	0.391175i	$0.872069\pi$
$192$		0			0
$193$	594.174	+	1029.14i	0.221604	+	0.383829i	0.955295	−	0.295654i	$-0.0955375\pi$
$193$	594.174	+	1029.14i	0.221604	+	0.383829i	−0.733691	+	0.679483i	$0.762204\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	3130.25			1.13209			0.566044	−	0.824375i	$-0.308473\pi$
$197$	3130.25			1.13209			0.566044	+	0.824375i	$0.308473\pi$
$198$		0			0
$199$	−659.146			−0.234802			−0.117401	−	0.993085i	$-0.537456\pi$
$199$	−659.146			−0.234802			−0.117401	+	0.993085i	$0.537456\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1951.83	−	3380.66i	−0.674834	−	1.16885i
$204$		0			0
$205$	−173.446	+	300.417i	−0.0590927	+	0.102352i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	63.2337	−	109.524i	0.0209281	−	0.0362485i
$210$		0			0
$211$	−1806.97	−	3129.77i	−0.589560	−	1.02115i	−0.994290	−	0.106711i	$-0.965968\pi$
$211$	−1806.97	−	3129.77i	−0.589560	−	1.02115i	0.404730	−	0.914436i	$-0.367365\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	4273.74			1.35566
$216$		0			0
$217$	2976.91			0.931272
$218$		0			0
$219$		0			0
$220$		0			0
$221$	2565.61	+	4443.76i	0.780912	+	1.35258i
$222$		0			0
$223$	1027.07	−	1778.93i	0.308419	−	0.534197i	−0.669598	−	0.742724i	$-0.733534\pi$
$223$	1027.07	−	1778.93i	0.308419	−	0.534197i	0.978017	+	0.208527i	$0.0668669\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1076.80	−	1865.08i	0.314846	−	0.545329i	−0.664559	−	0.747236i	$-0.731381\pi$
$227$	1076.80	−	1865.08i	0.314846	−	0.545329i	0.979405	+	0.201907i	$0.0647138\pi$
$228$		0			0
$229$	909.935	+	1576.05i	0.262577	+	0.454797i	0.966926	−	0.255057i	$-0.0820942\pi$
$229$	909.935	+	1576.05i	0.262577	+	0.454797i	−0.704349	+	0.709854i	$0.748761\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3989.68			1.12177			0.560886	−	0.827893i	$-0.310461\pi$
$233$	3989.68			1.12177			0.560886	+	0.827893i	$0.310461\pi$
$234$		0			0
$235$	−5348.12			−1.48457
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−2852.16	−	4940.09i	−0.771929	−	1.33702i	−0.936504	−	0.350656i	$-0.885959\pi$
$239$	−2852.16	−	4940.09i	−0.771929	−	1.33702i	0.164575	−	0.986365i	$-0.447375\pi$
$240$		0			0
$241$	−3111.98	+	5390.10i	−0.831785	+	1.44069i	0.0648372	+	0.997896i	$0.479347\pi$
$241$	−3111.98	+	5390.10i	−0.831785	+	1.44069i	−0.896622	+	0.442797i	$0.853986\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	5431.67	−	9407.92i	1.41639	−	2.45327i
$246$		0			0
$247$	3347.26	+	5797.62i	0.862271	+	1.49350i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−4622.52			−1.16243			−0.581217	−	0.813749i	$-0.697423\pi$
$251$	−4622.52			−1.16243			−0.581217	+	0.813749i	$0.697423\pi$
$252$		0			0
$253$	−22.9348			−0.00569919
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−2452.54	−	4247.93i	−0.595274	−	1.03104i	−0.993508	−	0.113761i	$-0.963710\pi$
$257$	−2452.54	−	4247.93i	−0.595274	−	1.03104i	0.398234	−	0.917284i	$-0.369623\pi$
$258$		0			0
$259$	−1535.72	+	2659.95i	−0.368437	+	0.638151i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	2216.42	−	3838.96i	0.519660	−	0.900077i	−0.480079	−	0.877225i	$-0.659392\pi$
$263$	2216.42	−	3838.96i	0.519660	−	0.900077i	0.999739	−	0.0228519i	$-0.00727463\pi$
$264$		0			0
$265$	1571.70	+	2722.26i	0.364334	+	0.631045i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−4454.81			−1.00972			−0.504860	−	0.863201i	$-0.668456\pi$
$269$	−4454.81			−1.00972			−0.504860	+	0.863201i	$0.668456\pi$
$270$		0			0
$271$	3256.23			0.729897			0.364948	−	0.931028i	$-0.381087\pi$
$271$	3256.23			0.729897			0.364948	+	0.931028i	$0.381087\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	162.935	+	282.211i	0.0357285	+	0.0618836i
$276$		0			0
$277$	1710.80	−	2963.20i	0.371091	−	0.642749i	−0.618642	−	0.785673i	$-0.712317\pi$
$277$	1710.80	−	2963.20i	0.371091	−	0.642749i	0.989734	+	0.142924i	$0.0456504\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−857.554	+	1485.33i	−0.182055	+	0.315328i	−0.942580	−	0.333980i	$-0.891608\pi$
$281$	−857.554	+	1485.33i	−0.182055	+	0.315328i	0.760525	+	0.649308i	$0.224941\pi$
$282$		0			0
$283$	2243.80	+	3886.37i	0.471307	+	0.816328i	0.999461	−	0.0328205i	$-0.0104490\pi$
$283$	2243.80	+	3886.37i	0.471307	+	0.816328i	−0.528154	+	0.849149i	$0.677116\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−477.587			−0.0982268
$288$		0			0
$289$	4483.35			0.912548
$290$		0			0
$291$		0			0
$292$		0			0
$293$	842.657	+	1459.52i	0.168016	+	0.291011i	0.937722	−	0.347386i	$-0.112931\pi$
$293$	842.657	+	1459.52i	0.168016	+	0.291011i	−0.769707	+	0.638398i	$0.779597\pi$
$294$		0			0
$295$	781.490	−	1353.58i	0.154238	−	0.267147i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	607.023	−	1051.39i	0.117408	−	0.203357i
$300$		0			0
$301$	2941.96	+	5095.62i	0.563361	+	0.975769i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	12899.0			2.42162
$306$		0			0
$307$	−8079.07			−1.50194			−0.750972	−	0.660334i	$-0.770415\pi$
$307$	−8079.07			−1.50194			−0.750972	+	0.660334i	$0.770415\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	1278.81	+	2214.97i	0.233167	+	0.403857i	0.958738	−	0.284290i	$-0.0917578\pi$
$311$	1278.81	+	2214.97i	0.233167	+	0.403857i	−0.725571	+	0.688147i	$0.758424\pi$
$312$		0			0
$313$	2040.72	−	3534.63i	0.368524	−	0.638303i	−0.620811	−	0.783961i	$-0.713196\pi$
$313$	2040.72	−	3534.63i	0.368524	−	0.638303i	0.989335	+	0.145658i	$0.0465298\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3850.96	+	6670.06i	−0.682308	+	1.18179i	0.291967	+	0.956428i	$0.405690\pi$
$317$	−3850.96	+	6670.06i	−0.682308	+	1.18179i	−0.974275	+	0.225364i	$0.927643\pi$
$318$		0			0
$319$	66.7663	+	115.643i	0.0117185	+	0.0202970i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	12259.1			2.11181
$324$		0			0
$325$	−17249.8			−2.94415
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−3681.54	−	6376.61i	−0.616929	−	1.06855i
$330$		0			0
$331$	178.657	−	309.443i	0.0296673	−	0.0513853i	−0.850811	−	0.525473i	$-0.823889\pi$
$331$	178.657	−	309.443i	0.0296673	−	0.0513853i	0.880478	+	0.474087i	$0.157222\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	8089.46	−	14011.3i	1.31933	−	2.28514i
$336$		0			0
$337$	3329.54	+	5766.94i	0.538195	+	0.932181i	0.999001	+	0.0446806i	$0.0142270\pi$
$337$	3329.54	+	5766.94i	0.538195	+	0.932181i	−0.460806	+	0.887501i	$0.652440\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−101.832			−0.0161715
$342$		0			0
$343$	4929.05			0.775929
$344$		0			0
$345$		0			0
$346$		0			0
$347$	3947.02	+	6836.44i	0.610626	+	1.05763i	0.991135	+	0.132858i	$0.0424154\pi$
$347$	3947.02	+	6836.44i	0.610626	+	1.05763i	−0.380509	+	0.924777i	$0.624251\pi$
$348$		0			0
$349$	627.228	−	1086.39i	0.0962027	−	0.166628i	−0.813907	−	0.580995i	$-0.802664\pi$
$349$	627.228	−	1086.39i	0.0962027	−	0.166628i	0.910110	+	0.414367i	$0.135997\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	4302.46	−	7452.08i	0.648716	−	1.12361i	−0.334714	−	0.942320i	$-0.608640\pi$
$353$	4302.46	−	7452.08i	0.648716	−	1.12361i	0.983430	−	0.181290i	$-0.0580271\pi$
$354$		0			0
$355$	−7444.49	−	12894.2i	−1.11299	−	1.92776i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	3875.61			0.569768			0.284884	−	0.958562i	$-0.408045\pi$
$359$	3875.61			0.569768			0.284884	+	0.958562i	$0.408045\pi$
$360$		0			0
$361$	9135.00			1.33183
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−3047.03	−	5277.62i	−0.436956	−	0.756831i
$366$		0			0
$367$	5945.05	−	10297.1i	0.845583	−	1.46459i	−0.0395301	−	0.999218i	$-0.512586\pi$
$367$	5945.05	−	10297.1i	0.845583	−	1.46459i	0.885114	−	0.465375i	$-0.154081\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−2163.85	+	3747.89i	−0.302807	+	0.524477i
$372$		0			0
$373$	−6192.25	−	10725.3i	−0.859578	−	1.48883i	−0.872332	−	0.488914i	$-0.837393\pi$
$373$	−6192.25	−	10725.3i	−0.859578	−	1.48883i	0.0127544	−	0.999919i	$-0.495940\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−7068.52			−0.965642
$378$		0			0
$379$	2062.80			0.279576			0.139788	−	0.990181i	$-0.455358\pi$
$379$	2062.80			0.279576			0.139788	+	0.990181i	$0.455358\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	5952.62	+	10310.2i	0.794164	+	1.37553i	0.923369	+	0.383914i	$0.125424\pi$
$383$	5952.62	+	10310.2i	0.794164	+	1.37553i	−0.129205	+	0.991618i	$0.541243\pi$
$384$		0			0
$385$	−310.370	+	537.576i	−0.0410854	+	0.0711621i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	6358.29	−	11012.9i	0.828735	−	1.43541i	−0.0702954	−	0.997526i	$-0.522394\pi$
$389$	6358.29	−	11012.9i	0.828735	−	1.43541i	0.899031	−	0.437886i	$-0.144272\pi$
$390$		0			0
$391$	−1111.59	−	1925.33i	−0.143773	−	0.249023i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	2729.00			0.347622
$396$		0			0
$397$	−4531.59			−0.572881			−0.286441	−	0.958098i	$-0.592472\pi$
$397$	−4531.59			−0.572881			−0.286441	+	0.958098i	$0.592472\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−2414.58	−	4182.17i	−0.300694	−	0.520817i	0.675600	−	0.737269i	$-0.263885\pi$
$401$	−2414.58	−	4182.17i	−0.300694	−	0.520817i	−0.976293	+	0.216452i	$0.930552\pi$
$402$		0			0
$403$	2695.21	−	4668.25i	0.333147	−	0.577027i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	52.5326	−	90.9892i	0.00639790	−	0.0110815i
$408$		0			0
$409$	−5742.46	−	9946.23i	−0.694245	−	1.20247i	−0.970435	−	0.241364i	$-0.922405\pi$
$409$	−5742.46	−	9946.23i	−0.694245	−	1.20247i	0.276190	−	0.961103i	$-0.410928\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	2151.85			0.256381
$414$		0			0
$415$	3407.54			0.403059
$416$		0			0
$417$		0			0
$418$		0			0
$419$	4105.82	+	7111.50i	0.478718	+	0.829163i	0.999702	−	0.0244030i	$-0.00776848\pi$
$419$	4105.82	+	7111.50i	0.478718	+	0.829163i	−0.520985	+	0.853566i	$0.674435\pi$
$420$		0			0
$421$	−4894.06	+	8476.77i	−0.566561	+	0.981312i	0.430342	+	0.902666i	$0.358393\pi$
$421$	−4894.06	+	8476.77i	−0.566561	+	0.981312i	−0.996903	+	0.0786460i	$0.974940\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−15794.0	+	27356.1i	−1.80264	+	3.12227i
$426$		0			0
$427$	8879.41	+	15379.6i	1.00633	+	1.74302i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−11206.3			−1.25241			−0.626207	−	0.779657i	$-0.715394\pi$
$431$	−11206.3			−1.25241			−0.626207	+	0.779657i	$0.715394\pi$
$432$		0			0
$433$	719.306			0.0798329			0.0399165	−	0.999203i	$-0.487291\pi$
$433$	719.306			0.0798329			0.0399165	+	0.999203i	$0.487291\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1450.25	−	2511.90i	−0.158752	−	0.274967i
$438$		0			0
$439$	−4397.50	+	7616.70i	−0.478090	+	0.828075i	−0.999684	−	0.0251179i	$-0.992004\pi$
$439$	−4397.50	+	7616.70i	−0.478090	+	0.828075i	0.521595	+	0.853193i	$0.325337\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	1511.83	−	2618.56i	0.162142	−	0.280839i	−0.773494	−	0.633803i	$-0.781493\pi$
$443$	1511.83	−	2618.56i	0.162142	−	0.280839i	0.935637	+	0.352964i	$0.114826\pi$
$444$		0			0
$445$	−4567.43	−	7911.03i	−0.486555	−	0.842739i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−3137.67			−0.329790			−0.164895	−	0.986311i	$-0.552728\pi$
$449$	−3137.67			−0.329790			−0.164895	+	0.986311i	$0.552728\pi$
$450$		0			0
$451$	16.3369			0.00170571
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−16429.3	−	28456.4i	−1.69279	−	2.93200i
$456$		0			0
$457$	4507.87	−	7807.86i	0.461421	−	0.799204i	−0.537611	−	0.843193i	$-0.680673\pi$
$457$	4507.87	−	7807.86i	0.461421	−	0.799204i	0.999032	+	0.0439888i	$0.0140066\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−6131.30	+	10619.7i	−0.619442	+	1.07291i	0.370145	+	0.928974i	$0.379308\pi$
$461$	−6131.30	+	10619.7i	−0.619442	+	1.07291i	−0.989588	+	0.143932i	$0.954025\pi$
$462$		0			0
$463$	−1736.15	−	3007.10i	−0.174267	−	0.301840i	0.765640	−	0.643269i	$-0.222422\pi$
$463$	−1736.15	−	3007.10i	−0.174267	−	0.301840i	−0.939907	+	0.341429i	$0.889089\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−11825.0			−1.17172			−0.585860	−	0.810412i	$-0.699243\pi$
$467$	−11825.0			−1.17172			−0.585860	+	0.810412i	$0.699243\pi$
$468$		0			0
$469$	22274.5			2.19305
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−100.636	−	174.306i	−0.00978275	−	0.0169442i
$474$		0			0
$475$	−20605.9	+	35690.5i	−1.99045	+	3.44756i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−851.980	+	1475.67i	−0.0812692	+	0.140762i	−0.903795	−	0.427965i	$-0.859231\pi$
$479$	−851.980	+	1475.67i	−0.0812692	+	0.140762i	0.822526	+	0.568727i	$0.192564\pi$
$480$		0			0
$481$	2780.80	+	4816.49i	0.263604	+	0.456576i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	661.015			0.0618869
$486$		0			0
$487$	7721.95			0.718512			0.359256	−	0.933239i	$-0.383031\pi$
$487$	7721.95			0.718512			0.359256	+	0.933239i	$0.383031\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	10111.8	+	17514.2i	0.929410	+	1.60979i	0.784311	+	0.620368i	$0.213017\pi$
$491$	10111.8	+	17514.2i	0.929410	+	1.60979i	0.145099	+	0.989417i	$0.453650\pi$
$492$		0			0
$493$	−6471.98	+	11209.8i	−0.591244	+	1.02406i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	10249.3	−	17752.3i	0.925035	−	1.60221i
$498$		0			0
$499$	6851.20	+	11866.6i	0.614633	+	1.06458i	0.990449	+	0.137881i	$0.0440291\pi$
$499$	6851.20	+	11866.6i	0.614633	+	1.06458i	−0.375816	+	0.926694i	$0.622638\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−13707.6			−1.21509			−0.607546	−	0.794285i	$-0.707846\pi$
$503$	−13707.6			−1.21509			−0.607546	+	0.794285i	$0.707846\pi$
$504$		0			0
$505$	−20874.9			−1.83945
$506$		0			0
$507$		0			0
$508$		0			0
$509$	6169.59	+	10686.0i	0.537254	+	0.930551i	0.999051	+	0.0435650i	$0.0138716\pi$
$509$	6169.59	+	10686.0i	0.537254	+	0.930551i	−0.461797	+	0.886986i	$0.652795\pi$
$510$		0			0
$511$	4195.03	−	7266.01i	0.363165	−	0.629020i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−10108.8	+	17509.0i	−0.864950	+	1.49814i
$516$		0			0
$517$	125.935	+	218.125i	0.0107130	+	0.0185554i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1416.70			−0.119130			−0.0595649	−	0.998224i	$-0.518971\pi$
$521$	−1416.70			−0.119130			−0.0595649	+	0.998224i	$0.518971\pi$
$522$		0			0
$523$	6696.15			0.559851			0.279925	−	0.960022i	$-0.409690\pi$
$523$	6696.15			0.559851			0.279925	+	0.960022i	$0.409690\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−4935.51	−	8548.55i	−0.407958	−	0.706605i
$528$		0			0
$529$	5820.50	−	10081.4i	0.478384	−	0.828585i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−432.394	+	748.929i	−0.0351390	+	0.0608625i
$534$		0			0
$535$	2888.70	+	5003.38i	0.233438	+	0.404327i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−511.609			−0.0408841
$540$		0			0
$541$	7105.69			0.564691			0.282345	−	0.959313i	$-0.408888\pi$
$541$	7105.69			0.564691			0.282345	+	0.959313i	$0.408888\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	14393.9	+	24931.0i	1.13132	+	1.95950i
$546$		0			0
$547$	−6014.01	+	10416.6i	−0.470092	+	0.814224i	−0.999415	−	0.0341968i	$-0.989113\pi$
$547$	−6014.01	+	10416.6i	−0.470092	+	0.814224i	0.529323	+	0.848420i	$0.322446\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−8443.76	+	14625.0i	−0.652843	+	1.13076i
$552$		0			0
$553$	1878.59	+	3253.81i	0.144459	+	0.250210i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−14529.5			−1.10527			−0.552634	−	0.833424i	$-0.686377\pi$
$557$	−14529.5			−1.10527			−0.552634	+	0.833424i	$0.686377\pi$
$558$		0			0
$559$	10654.3			0.806131
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−5116.72	−	8862.42i	−0.383027	−	0.663422i	0.608467	−	0.793579i	$-0.291785\pi$
$563$	−5116.72	−	8862.42i	−0.383027	−	0.663422i	−0.991493	+	0.130158i	$0.958452\pi$
$564$		0			0
$565$	20579.2	−	35644.3i	1.53235	−	2.65410i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	159.730	−	276.660i	0.0117684	−	0.0203835i	−0.860081	−	0.510157i	$-0.829587\pi$
$569$	159.730	−	276.660i	0.0117684	−	0.0203835i	0.871850	+	0.489774i	$0.162921\pi$
$570$		0			0
$571$	3396.98	+	5883.74i	0.248965	+	0.431221i	0.963239	−	0.268646i	$-0.0865761\pi$
$571$	3396.98	+	5883.74i	0.248965	+	0.431221i	−0.714274	+	0.699866i	$0.753243\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	7473.74			0.542046
$576$		0			0
$577$	−11145.6			−0.804156			−0.402078	−	0.915605i	$-0.631712\pi$
$577$	−11145.6			−0.804156			−0.402078	+	0.915605i	$0.631712\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	2345.68	+	4062.84i	0.167496	+	0.290112i
$582$		0			0
$583$	74.0190	−	128.205i	0.00525824	−	0.00910753i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−11908.8	+	20626.6i	−0.837356	+	1.45034i	0.0547416	+	0.998501i	$0.482566\pi$
$587$	−11908.8	+	20626.6i	−0.837356	+	1.45034i	−0.892098	+	0.451843i	$0.850767\pi$
$588$		0			0
$589$	−6439.19	−	11153.0i	−0.450462	−	0.780223i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	16416.2			1.13682			0.568408	−	0.822747i	$-0.307559\pi$
$593$	16416.2			1.13682			0.568408	+	0.822747i	$0.307559\pi$
$594$		0			0
$595$	−60171.2			−4.14585
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−2400.85	−	4158.39i	−0.163766	−	0.283652i	0.772450	−	0.635075i	$-0.219031\pi$
$599$	−2400.85	−	4158.39i	−0.163766	−	0.283652i	−0.936216	+	0.351424i	$0.885698\pi$
$600$		0			0
$601$	−2262.11	+	3918.08i	−0.153533	+	0.265927i	−0.932524	−	0.361108i	$-0.882398\pi$
$601$	−2262.11	+	3918.08i	−0.153533	+	0.265927i	0.778991	+	0.627035i	$0.215732\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−14120.4	+	24457.3i	−0.948886	+	1.64352i
$606$		0			0
$607$	7489.15	+	12971.6i	0.500783	+	0.867382i	1.00000		0.000904500i	$0.000287911\pi$
$607$	7489.15	+	12971.6i	0.500783	+	0.867382i	−0.499216	+	0.866477i	$0.666379\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−13332.6			−0.882784
$612$		0			0
$613$	11651.6			0.767709			0.383854	−	0.923394i	$-0.374596\pi$
$613$	11651.6			0.767709			0.383854	+	0.923394i	$0.374596\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−170.560	−	295.418i	−0.0111288	−	0.0192757i	0.860407	−	0.509607i	$-0.170209\pi$
$617$	−170.560	−	295.418i	−0.0111288	−	0.0192757i	−0.871536	+	0.490331i	$0.836876\pi$
$618$		0			0
$619$	−9207.57	+	15948.0i	−0.597873	+	1.03555i	0.395262	+	0.918569i	$0.370654\pi$
$619$	−9207.57	+	15948.0i	−0.597873	+	1.03555i	−0.993135	+	0.116978i	$0.962679\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	6288.26	−	10891.6i	0.404388	−	0.700421i
$624$		0			0
$625$	−24916.1	−	43156.0i	−1.59463	−	2.76198i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	10184.5			0.645599
$630$		0			0
$631$	13557.6			0.855341			0.427671	−	0.903935i	$-0.359334\pi$
$631$	13557.6			0.855341			0.427671	+	0.903935i	$0.359334\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	2467.09	+	4273.12i	0.154179	+	0.267045i
$636$		0			0
$637$	13540.9	−	23453.6i	0.842247	−	1.45881i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	4841.27	−	8385.33i	0.298313	−	0.516694i	−0.677437	−	0.735581i	$-0.736909\pi$
$641$	4841.27	−	8385.33i	0.298313	−	0.516694i	0.975750	+	0.218887i	$0.0702427\pi$
$642$		0			0
$643$	1629.75	+	2822.81i	0.0999551	+	0.173127i	0.911666	−	0.410932i	$-0.134797\pi$
$643$	1629.75	+	2822.81i	0.0999551	+	0.173127i	−0.811711	+	0.584060i	$0.801463\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	8115.35			0.493118			0.246559	−	0.969128i	$-0.420700\pi$
$647$	8115.35			0.493118			0.246559	+	0.969128i	$0.420700\pi$
$648$		0			0
$649$	−73.6085			−0.00445206
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1713.87	−	2968.51i	−0.102709	−	0.177897i	0.810091	−	0.586304i	$-0.199418\pi$
$653$	−1713.87	−	2968.51i	−0.102709	−	0.177897i	−0.912800	+	0.408407i	$0.866084\pi$
$654$		0			0
$655$	29677.3	−	51402.6i	1.77036	−	3.06636i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−6910.11	+	11968.7i	−0.408467	+	0.707485i	−0.994718	−	0.102644i	$-0.967270\pi$
$659$	−6910.11	+	11968.7i	−0.408467	+	0.707485i	0.586251	+	0.810129i	$0.300603\pi$
$660$		0			0
$661$	11359.8	+	19675.8i	0.668451	+	1.15779i	0.978337	+	0.207018i	$0.0663759\pi$
$661$	11359.8	+	19675.8i	0.668451	+	1.15779i	−0.309886	+	0.950774i	$0.600291\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−78503.2			−4.57778
$666$		0			0
$667$	3062.54			0.177784
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−303.739	−	526.091i	−0.0174750	−	0.0302676i
$672$		0			0
$673$	2566.59	−	4445.46i	0.147005	−	0.254621i	−0.783114	−	0.621878i	$-0.786370\pi$
$673$	2566.59	−	4445.46i	0.147005	−	0.254621i	0.930119	+	0.367257i	$0.119703\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	4647.94	−	8050.46i	0.263862	−	0.457023i	−0.703403	−	0.710792i	$-0.748337\pi$
$677$	4647.94	−	8050.46i	0.263862	−	0.457023i	0.967265	+	0.253769i	$0.0816702\pi$
$678$		0			0
$679$	455.030	+	788.134i	0.0257179	+	0.0445447i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−13824.3			−0.774486			−0.387243	−	0.921978i	$-0.626573\pi$
$683$	−13824.3			−0.774486			−0.387243	+	0.921978i	$0.626573\pi$
$684$		0			0
$685$	−26787.0			−1.49413
$686$		0			0
$687$		0			0
$688$		0			0
$689$	3918.18	+	6786.48i	0.216648	+	0.375246i
$690$		0			0
$691$	5507.61	−	9539.47i	0.303212	−	0.525179i	−0.673650	−	0.739051i	$-0.735274\pi$
$691$	5507.61	−	9539.47i	0.303212	−	0.525179i	0.976862	+	0.213872i	$0.0686076\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−3263.29	+	5652.18i	−0.178106	+	0.308488i
$696$		0			0
$697$	791.806	+	1371.45i	0.0430298	+	0.0745298i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	460.523			0.0248127			0.0124064	−	0.999923i	$-0.496051\pi$
$701$	460.523			0.0248127			0.0124064	+	0.999923i	$0.496051\pi$
$702$		0			0
$703$	13287.3			0.712861
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−14369.9	−	24889.3i	−0.764405	−	1.32399i
$708$		0			0
$709$	−13222.5	+	22902.1i	−0.700398	+	1.21313i	0.267929	+	0.963439i	$0.413661\pi$
$709$	−13222.5	+	22902.1i	−0.700398	+	1.21313i	−0.968327	+	0.249686i	$0.919672\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−1167.74	+	2022.59i	−0.0613355	+	0.106236i
$714$		0			0
$715$	562.000	+	973.413i	0.0293953	+	0.0509141i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−15524.4			−0.805235			−0.402617	−	0.915368i	$-0.631899\pi$
$719$	−15524.4			−0.805235			−0.402617	+	0.915368i	$0.631899\pi$
$720$		0			0
$721$	−27834.9			−1.43776
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−21757.1	−	37684.4i	−1.11454	−	1.93043i
$726$		0			0
$727$	−9467.02	+	16397.4i	−0.482961	+	0.836513i	−0.999809	−	0.0195647i	$-0.993772\pi$
$727$	−9467.02	+	16397.4i	−0.482961	+	0.836513i	0.516848	+	0.856077i	$0.327105\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	9755.11	−	16896.3i	0.493578	−	0.854903i
$732$		0			0
$733$	8389.96	+	14531.8i	0.422770	+	0.732259i	0.996209	−	0.0869891i	$-0.0277245\pi$
$733$	8389.96	+	14531.8i	0.422770	+	0.732259i	−0.573439	+	0.819248i	$0.694391\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−761.945			−0.0380823
$738$		0			0
$739$	30309.0			1.50871			0.754353	−	0.656469i	$-0.227951\pi$
$739$	30309.0			1.50871			0.754353	+	0.656469i	$0.227951\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	16049.4	+	27798.4i	0.792458	+	1.37258i	0.924441	+	0.381325i	$0.124532\pi$
$743$	16049.4	+	27798.4i	0.792458	+	1.37258i	−0.131983	+	0.991252i	$0.542135\pi$
$744$		0			0
$745$	−16963.1	+	29381.0i	−0.834202	+	1.44488i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−3977.05	+	6888.45i	−0.194016	+	0.336046i
$750$		0			0
$751$	−4717.04	−	8170.15i	−0.229197	−	0.396981i	0.728373	−	0.685181i	$-0.240277\pi$
$751$	−4717.04	−	8170.15i	−0.229197	−	0.396981i	−0.957570	+	0.288199i	$0.906943\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	72521.7			3.49581
$756$		0			0
$757$	1280.65			0.0614876			0.0307438	−	0.999527i	$-0.490212\pi$
$757$	1280.65			0.0614876			0.0307438	+	0.999527i	$0.490212\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	9812.37	+	16995.5i	0.467409	+	0.809576i	0.999307	−	0.0372327i	$-0.0118543\pi$
$761$	9812.37	+	16995.5i	0.467409	+	0.809576i	−0.531898	+	0.846809i	$0.678521\pi$
$762$		0			0
$763$	−19816.9	+	34323.9i	−0.940264	+	1.62858i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1948.22	−	3374.42i	0.0917162	−	0.158857i
$768$		0			0
$769$	−8822.44	−	15280.9i	−0.413713	−	0.716572i	0.581580	−	0.813490i	$-0.302435\pi$
$769$	−8822.44	−	15280.9i	−0.413713	−	0.716572i	−0.995292	+	0.0969179i	$0.969102\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	22541.7			1.04886			0.524430	−	0.851454i	$-0.324278\pi$
$773$	22541.7			1.04886			0.524430	+	0.851454i	$0.324278\pi$
$774$		0			0
$775$	33183.8			1.53806
$776$		0			0
$777$		0			0
$778$		0			0
$779$	1033.04	+	1789.28i	0.0475129	+	0.0822947i
$780$		0			0
$781$	−350.598	+	607.253i	−0.0160632	+	0.0278223i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	5062.38	−	8768.30i	0.230171	−	0.398668i
$786$		0			0
$787$	19843.9	+	34370.7i	0.898804	+	1.55677i	0.829025	+	0.559212i	$0.188896\pi$
$787$	19843.9	+	34370.7i	0.898804	+	1.55677i	0.0697798	+	0.997562i	$0.477770\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	56665.4			2.54714
$792$		0			0
$793$	32156.7			1.44000
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−995.984	−	1725.09i	−0.0442654	−	0.0766700i	0.843044	−	0.537845i	$-0.180761\pi$
$797$	−995.984	−	1725.09i	−0.0442654	−	0.0766700i	−0.887309	+	0.461175i	$0.847428\pi$
$798$		0			0
$799$	−12207.5	+	21143.9i	−0.540511	+	0.936193i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−143.500	+	248.549i	−0.00630636	+	0.0109229i
$804$		0			0
$805$	7118.25	+	12329.2i	0.311659	+	0.539809i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	21679.4			0.942160			0.471080	−	0.882090i	$-0.343864\pi$
$809$	21679.4			0.942160			0.471080	+	0.882090i	$0.343864\pi$
$810$		0			0
$811$	−15099.7			−0.653786			−0.326893	−	0.945061i	$-0.606002\pi$
$811$	−15099.7			−0.653786			−0.326893	+	0.945061i	$0.606002\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	35078.5	+	60757.8i	1.50766	+	2.61135i
$816$		0			0
$817$	12727.1	−	22044.1i	0.545002	−	0.943971i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	4951.38	−	8576.05i	0.210480	−	0.364563i	−0.741385	−	0.671080i	$-0.765831\pi$
$821$	4951.38	−	8576.05i	0.210480	−	0.364563i	0.951865	+	0.306518i	$0.0991638\pi$
$822$		0			0
$823$	−5744.36	−	9949.53i	−0.243300	−	0.421408i	0.718352	−	0.695680i	$-0.244897\pi$
$823$	−5744.36	−	9949.53i	−0.243300	−	0.421408i	−0.961652	+	0.274272i	$0.911563\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−36938.8			−1.55319			−0.776594	−	0.630001i	$-0.783055\pi$
$827$	−36938.8			−1.55319			−0.776594	+	0.630001i	$0.783055\pi$
$828$		0			0
$829$	3205.00			0.134275			0.0671376	−	0.997744i	$-0.478613\pi$
$829$	3205.00			0.134275			0.0671376	+	0.997744i	$0.478613\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−24796.3	−	42948.5i	−1.03138	−	1.78641i
$834$		0			0
$835$	−22206.7	+	38463.2i	−0.920354	+	1.59410i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−563.314	+	975.689i	−0.0231797	+	0.0401484i	−0.877383	−	0.479791i	$-0.840712\pi$
$839$	−563.314	+	975.689i	−0.0231797	+	0.0401484i	0.854203	+	0.519940i	$0.174046\pi$
$840$		0			0
$841$	3279.02	+	5679.43i	0.134447	+	0.232868i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−12848.2			−0.523069
$846$		0			0
$847$	−38880.8			−1.57728
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−1204.82	−	2086.81i	−0.0485321	−	0.0840600i
$852$		0			0
$853$	−3127.33	+	5416.69i	−0.125531	+	0.217425i	−0.921940	−	0.387332i	$-0.873397\pi$
$853$	−3127.33	+	5416.69i	−0.125531	+	0.217425i	0.796410	+	0.604758i	$0.206730\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	9534.68	−	16514.6i	0.380045	−	0.658257i	−0.611023	−	0.791613i	$-0.709242\pi$
$857$	9534.68	−	16514.6i	0.380045	−	0.658257i	0.991068	+	0.133355i	$0.0425752\pi$
$858$		0			0
$859$	−13395.1	−	23201.0i	−0.532056	−	0.921547i	−0.999300	−	0.0374190i	$-0.988086\pi$
$859$	−13395.1	−	23201.0i	−0.532056	−	0.921547i	0.467244	−	0.884128i	$-0.345247\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−46056.3			−1.81666			−0.908329	−	0.418256i	$-0.862641\pi$
$863$	−46056.3			−1.81666			−0.908329	+	0.418256i	$0.862641\pi$
$864$		0			0
$865$	62099.2			2.44097
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−64.2610	−	111.303i	−0.00250852	−	0.00434489i
$870$		0			0
$871$	20166.7	−	34929.7i	0.784526	−	1.35884i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	62343.8	−	107983.i	2.40869	−	4.17197i
$876$		0			0
$877$	−18245.1	−	31601.4i	−0.702500	−	1.21677i	−0.967586	−	0.252541i	$-0.918734\pi$
$877$	−18245.1	−	31601.4i	−0.702500	−	1.21677i	0.265086	−	0.964225i	$-0.414600\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	38136.3			1.45839			0.729197	−	0.684303i	$-0.239894\pi$
$881$	38136.3			1.45839			0.729197	+	0.684303i	$0.239894\pi$
$882$		0			0
$883$	−13336.1			−0.508262			−0.254131	−	0.967170i	$-0.581789\pi$
$883$	−13336.1			−0.508262			−0.254131	+	0.967170i	$0.581789\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−14013.6	−	24272.3i	−0.530474	−	0.918808i	−0.999368	−	0.0355536i	$-0.988681\pi$
$887$	−14013.6	−	24272.3i	−0.530474	−	0.918808i	0.468894	−	0.883255i	$-0.344653\pi$
$888$		0			0
$889$	−3396.59	+	5883.06i	−0.128142	+	0.221948i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−15926.6	+	27585.7i	−0.596825	+	1.03373i
$894$		0			0
$895$	2462.19	+	4264.64i	0.0919574	+	0.159275i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	13597.8			0.504464
$900$		0			0
$901$	14350.0			0.530598
$902$		0			0
$903$		0			0
$904$		0			0
$905$	24331.0	+	42142.6i	0.893692	+	1.54792i
$906$		0			0
$907$	22601.7	−	39147.2i	0.827427	−	1.43315i	−0.0726235	−	0.997359i	$-0.523137\pi$
$907$	22601.7	−	39147.2i	0.827427	−	1.43315i	0.900050	−	0.435786i	$-0.143530\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−14911.0	+	25826.6i	−0.542287	+	0.939268i	0.456486	+	0.889731i	$0.349108\pi$
$911$	−14911.0	+	25826.6i	−0.542287	+	0.939268i	−0.998772	+	0.0495373i	$0.984225\pi$
$912$		0			0
$913$	−80.2390	−	138.978i	−0.00290857	−	0.00503779i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	81717.0			2.94279
$918$		0			0
$919$	36967.7			1.32693			0.663467	−	0.748206i	$-0.269084\pi$
$919$	36967.7			1.32693			0.663467	+	0.748206i	$0.269084\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−18558.8	−	32144.8i	−0.661832	−	1.14633i
$924$		0			0
$925$	−17118.8	+	29650.6i	−0.608499	+	1.05395i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	25204.7	−	43655.8i	0.890139	−	1.54177i	0.0504304	−	0.998728i	$-0.483941\pi$
$929$	25204.7	−	43655.8i	0.890139	−	1.54177i	0.839708	−	0.543038i	$-0.182726\pi$
$930$		0			0
$931$	−32350.9	−	56033.4i	−1.13884	−	1.97252i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	2058.28			0.0719925
$936$		0			0
$937$	−30156.5			−1.05141			−0.525705	−	0.850667i	$-0.676198\pi$
$937$	−30156.5			−1.05141			−0.525705	+	0.850667i	$0.676198\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−21110.6	−	36564.6i	−0.731333	−	1.26671i	−0.956313	−	0.292343i	$-0.905565\pi$
$941$	−21110.6	−	36564.6i	−0.731333	−	1.26671i	0.224980	−	0.974363i	$-0.427768\pi$
$942$		0			0
$943$	187.341	−	324.484i	0.00646942	−	0.0112054i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	20082.3	−	34783.6i	0.689111	−	1.19357i	−0.283015	−	0.959115i	$-0.591335\pi$
$947$	20082.3	−	34783.6i	0.689111	−	1.19357i	0.972126	−	0.234459i	$-0.0753320\pi$
$948$		0			0
$949$	−7596.14	−	13156.9i	−0.259832	−	0.450043i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−7132.10			−0.242425			−0.121213	−	0.992627i	$-0.538678\pi$
$953$	−7132.10			−0.242425			−0.121213	+	0.992627i	$0.538678\pi$
$954$		0			0
$955$	−89559.5			−3.03464
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−18439.6	−	31938.4i	−0.620904	−	1.07544i
$960$		0			0
$961$	9710.67	−	16819.4i	0.325960	−	0.564579i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−12616.5	+	21852.4i	−0.420870	+	0.728968i
$966$		0			0
$967$	274.603	+	475.626i	0.00913199	+	0.0158171i	0.870555	−	0.492071i	$-0.163760\pi$
$967$	274.603	+	475.626i	0.00913199	+	0.0158171i	−0.861423	+	0.507888i	$0.830426\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−31024.8			−1.02537			−0.512685	−	0.858577i	$-0.671349\pi$
$971$	−31024.8			−1.02537			−0.512685	+	0.858577i	$0.671349\pi$
$972$		0			0
$973$	−8985.52			−0.296056
$974$		0			0
$975$		0			0
$976$		0			0
$977$	3913.51	+	6778.40i	0.128152	+	0.221966i	0.922961	−	0.384895i	$-0.125762\pi$
$977$	3913.51	+	6778.40i	0.128152	+	0.221966i	−0.794809	+	0.606860i	$0.792429\pi$
$978$		0			0
$979$	−215.103	+	372.570i	−0.00702219	+	0.0121628i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−23710.7	+	41068.2i	−0.769334	+	1.33253i	0.168590	+	0.985686i	$0.446079\pi$
$983$	−23710.7	+	41068.2i	−0.769334	+	1.33253i	−0.937924	+	0.346840i	$0.887255\pi$
$984$		0			0
$985$	33233.4	+	57562.0i	1.07503	+	1.86201i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−4616.11			−0.148416
$990$		0			0
$991$	43260.0			1.38668			0.693339	−	0.720612i	$-0.256139\pi$
$991$	43260.0			1.38668			0.693339	+	0.720612i	$0.256139\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−6998.05	−	12121.0i	−0.222968	−	0.386192i
$996$		0			0
$997$	20104.6	−	34822.1i	0.638634	−	1.10615i	−0.347099	−	0.937828i	$-0.612833\pi$
$997$	20104.6	−	34822.1i	0.638634	−	1.10615i	0.985733	−	0.168317i	$-0.0538333\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.4.i.s.217.2		4
3.2	odd	2		648.4.i.m.217.1		4
9.2	odd	6		216.4.a.h.1.2	yes	2
9.4	even	3	inner	648.4.i.s.433.2		4
9.5	odd	6		648.4.i.m.433.1		4
9.7	even	3		216.4.a.e.1.1	✓	2
36.7	odd	6		432.4.a.o.1.1		2
36.11	even	6		432.4.a.s.1.2		2
72.11	even	6		1728.4.a.bg.1.1		2
72.29	odd	6		1728.4.a.bh.1.1		2
72.43	odd	6		1728.4.a.bs.1.2		2
72.61	even	6		1728.4.a.bt.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.4.a.e.1.1	✓	2	9.7	even	3
216.4.a.h.1.2	yes	2	9.2	odd	6
432.4.a.o.1.1		2	36.7	odd	6
432.4.a.s.1.2		2	36.11	even	6
648.4.i.m.217.1		4	3.2	odd	2
648.4.i.m.433.1		4	9.5	odd	6
648.4.i.s.217.2		4	1.1	even	1	trivial
648.4.i.s.433.2		4	9.4	even	3	inner
1728.4.a.bg.1.1		2	72.11	even	6
1728.4.a.bh.1.1		2	72.29	odd	6
1728.4.a.bs.1.2		2	72.43	odd	6
1728.4.a.bt.1.2		2	72.61	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	648.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(10.6168 + 18.3889i) q^{5} +(-14.6168 + 25.3171i) q^{7} +O(q^{10})\)	\(q+(10.6168 + 18.3889i) q^{5} +(-14.6168 + 25.3171i) q^{7} +(0.500000 - 0.866025i) q^{11} +(26.4674 + 45.8428i) q^{13} +96.9348 q^{17} +126.467 q^{19} +(-11.4674 - 19.8621i) q^{23} +(-162.935 + 282.211i) q^{25} +(-66.7663 + 115.643i) q^{29} +(-50.9158 - 88.1887i) q^{31} -620.739 q^{35} +105.065 q^{37} +(8.16844 + 14.1482i) q^{41} +(100.636 - 174.306i) q^{43} +(-125.935 + 218.125i) q^{47} +(-255.804 - 443.066i) q^{49} +148.038 q^{53} +21.2337 q^{55} +(-36.8043 - 63.7468i) q^{59} +(303.739 - 526.091i) q^{61} +(-562.000 + 973.413i) q^{65} +(-380.973 - 659.864i) q^{67} -701.196 q^{71} -287.000 q^{73} +(14.6168 + 25.3171i) q^{77} +(64.2610 - 111.303i) q^{79} +(80.2390 - 138.978i) q^{83} +(1029.14 + 1782.52i) q^{85} -430.206 q^{89} -1547.48 q^{91} +(1342.68 + 2325.60i) q^{95} +(15.5652 - 26.9598i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{5} - 24 q^{7}+O(q^{10}) \) 4 * q + 8 * q^5 - 24 * q^7	\( 4 q + 8 q^{5} - 24 q^{7} + 2 q^{11} - 32 q^{13} + 112 q^{17} + 368 q^{19} + 92 q^{23} - 376 q^{25} - 336 q^{29} - 376 q^{31} - 1380 q^{35} + 696 q^{37} - 312 q^{41} - 80 q^{43} - 228 q^{47} - 196 q^{49} - 304 q^{53} + 16 q^{55} + 680 q^{59} + 112 q^{61} - 2248 q^{65} - 352 q^{67} - 3632 q^{71} - 1148 q^{73} + 24 q^{77} + 1360 q^{79} - 782 q^{83} + 2600 q^{85} - 480 q^{89} - 3984 q^{91} + 1924 q^{95} + 338 q^{97}+O(q^{100}) \) 4 * q + 8 * q^5 - 24 * q^7 + 2 * q^11 - 32 * q^13 + 112 * q^17 + 368 * q^19 + 92 * q^23 - 376 * q^25 - 336 * q^29 - 376 * q^31 - 1380 * q^35 + 696 * q^37 - 312 * q^41 - 80 * q^43 - 228 * q^47 - 196 * q^49 - 304 * q^53 + 16 * q^55 + 680 * q^59 + 112 * q^61 - 2248 * q^65 - 352 * q^67 - 3632 * q^71 - 1148 * q^73 + 24 * q^77 + 1360 * q^79 - 782 * q^83 + 2600 * q^85 - 480 * q^89 - 3984 * q^91 + 1924 * q^95 + 338 * q^97

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