LMFDB - Embedded newform 648.4.i.m.433.1

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			433.1
Root			$1.68614 - 0.396143i$ of defining polynomial
Character	$\chi$	$=$	648.433
Dual form			648.4.i.m.217.1

$q$-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 $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

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

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	−0.203330	+	0.979110i	$0.565176\pi$
$5$	−10.6168	+	18.3889i	−0.949599	+	1.64475i	−0.746269	+	0.665644i	$0.768157\pi$
$6$		0			0
$7$	−14.6168	−	25.3171i	−0.789235	−	1.36700i	−0.926436	−	0.376453i	$-0.877144\pi$
$7$	−14.6168	−	25.3171i	−0.789235	−	1.36700i	0.137201	−	0.990543i	$-0.456190\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.500000	−	0.866025i	−0.0137051	−	0.0237379i	0.859092	−	0.511822i	$-0.171029\pi$
$11$	−0.500000	−	0.866025i	−0.0137051	−	0.0237379i	−0.872797	+	0.488084i	$0.837696\pi$
$12$		0			0
$13$	26.4674	−	45.8428i	0.564671	−	0.978040i	−0.432409	−	0.901678i	$-0.642336\pi$
$13$	26.4674	−	45.8428i	0.564671	−	0.978040i	0.997080	−	0.0763620i	$-0.0243305\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−96.9348			−1.38295			−0.691474	−	0.722401i	$-0.743039\pi$
$17$	−96.9348			−1.38295			−0.691474	+	0.722401i	$0.743039\pi$
$18$		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	$-0.800181\pi$
$23$	11.4674	−	19.8621i	0.103961	−	0.180066i	0.913313	+	0.407257i	$0.133515\pi$
$24$		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	$-0.0260527\pi$
$29$	66.7663	+	115.643i	0.427524	+	0.740493i	−0.569129	+	0.822249i	$0.692719\pi$
$30$		0			0
$31$	−50.9158	+	88.1887i	−0.294992	+	0.510941i	−0.974983	−	0.222280i	$-0.928650\pi$
$31$	−50.9158	+	88.1887i	−0.294992	+	0.510941i	0.679991	+	0.733220i	$0.261984\pi$
$32$		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	$-0.843239\pi$
$41$	−8.16844	+	14.1482i	−0.0311145	+	0.0538920i	0.850049	+	0.526704i	$0.176572\pi$
$42$		0			0
$43$	100.636	+	174.306i	0.356903	+	0.618174i	0.987442	−	0.157984i	$-0.0504994\pi$
$43$	100.636	+	174.306i	0.356903	+	0.618174i	−0.630539	+	0.776158i	$0.717166\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	125.935	+	218.125i	0.390840	+	0.676954i	0.992561	−	0.121752i	$-0.0388513\pi$
$47$	125.935	+	218.125i	0.390840	+	0.676954i	−0.601721	+	0.798707i	$0.705518\pi$
$48$		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	$-0.561444\pi$
$53$	−148.038			−0.383671			−0.191836	+	0.981427i	$0.561444\pi$
$54$		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	$-0.807454\pi$
$59$	36.8043	−	63.7468i	0.0812120	−	0.140663i	0.903771	+	0.428017i	$0.140788\pi$
$60$		0			0
$61$	303.739	+	526.091i	0.637538	+	1.10425i	0.985971	+	0.166914i	$0.0533803\pi$
$61$	303.739	+	526.091i	0.637538	+	1.10425i	−0.348434	+	0.937333i	$0.613286\pi$
$62$		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	0.275615	+	0.961268i	$0.411118\pi$
$67$	−380.973	+	659.864i	−0.694675	+	1.20321i	−0.970290	+	0.241944i	$0.922215\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	701.196			1.17207			0.586033	−	0.810287i	$-0.300689\pi$
$71$	701.196			1.17207			0.586033	+	0.810287i	$0.300689\pi$
$72$		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	0.908150	−	0.418645i	$-0.137495\pi$
$79$	64.2610	+	111.303i	0.0915181	+	0.158514i	−0.816632	+	0.577159i	$0.804161\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−80.2390	−	138.978i	−0.106113	−	0.183793i	0.808079	−	0.589074i	$-0.200507\pi$
$83$	−80.2390	−	138.978i	−0.106113	−	0.183793i	−0.914192	+	0.405281i	$0.867174\pi$
$84$		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	$-0.417533\pi$
$89$	430.206			0.512380			0.256190	+	0.966626i	$0.417533\pi$
$90$		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	0.874057	−	0.485824i	$-0.161480\pi$
$97$	15.5652	+	26.9598i	0.0162929	+	0.0282201i	−0.857764	+	0.514044i	$0.828147\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	491.552	+	851.392i	0.484269	+	0.838779i	0.999837	−	0.0180698i	$-0.00575212\pi$
$101$	491.552	+	851.392i	0.484269	+	0.838779i	−0.515567	+	0.856849i	$0.672419\pi$
$102$		0			0
$103$	476.076	−	824.588i	0.455429	−	0.788826i	−0.543284	−	0.839549i	$-0.682819\pi$
$103$	476.076	−	824.588i	0.455429	−	0.788826i	0.998713	+	0.0507234i	$0.0161527\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−272.087			−0.245828			−0.122914	−	0.992417i	$-0.539224\pi$
$107$	−272.087			−0.245828			−0.122914	+	0.992417i	$0.539224\pi$
$108$		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	−0.108205	−	0.994129i	$-0.534510\pi$
$113$	969.179	−	1678.67i	0.806838	−	1.39748i	0.915043	−	0.403356i	$-0.132156\pi$
$114$		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	0.152548	−	0.988296i	$-0.451252\pi$
$131$	1397.65	−	2420.80i	0.932163	−	1.61455i	0.779616	−	0.626258i	$-0.215414\pi$
$132$		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	$-0.0379801\pi$
$137$	630.766	+	1092.52i	0.393358	+	0.681315i	−0.599532	+	0.800351i	$0.704647\pi$
$138$		0			0
$139$	153.684	−	266.189i	0.0937794	−	0.162431i	−0.815319	−	0.579012i	$-0.803438\pi$
$139$	153.684	−	266.189i	0.0937794	−	0.162431i	0.909099	+	0.416581i	$0.136772\pi$
$140$		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	$-0.978085\pi$
$149$	−798.878	+	1383.70i	−0.439239	+	0.760784i	0.558392	+	0.829577i	$0.311419\pi$
$150$		0			0
$151$	1707.70	+	2957.83i	0.920337	+	1.59407i	0.798893	+	0.601473i	$0.205419\pi$
$151$	1707.70	+	2957.83i	0.920337	+	1.59407i	0.121444	+	0.992598i	$0.461248\pi$
$152$		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	−0.920239	−	0.391358i	$-0.872006\pi$
$157$	−238.413	+	412.943i	−0.121194	+	0.209914i	0.799045	+	0.601271i	$0.205339\pi$
$158$		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	$-0.994369\pi$
$167$	−1045.83	+	1811.42i	−0.484601	+	0.839354i	0.515242	+	0.857045i	$0.327702\pi$
$168$		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	−0.984843	−	0.173446i	$-0.944510\pi$
$173$	−1462.28	−	2532.74i	−0.642631	−	1.11307i	0.342213	−	0.939622i	$-0.388824\pi$
$174$		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	$-0.515418\pi$
$179$	−231.913			−0.0968381			−0.0484191	+	0.998827i	$0.515418\pi$
$180$		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	0.920316	+	0.391175i	$0.127931\pi$
$191$	2108.90	+	3652.72i	0.798925	+	1.38378i	−0.121391	+	0.992605i	$0.538736\pi$
$192$		0			0
$193$	594.174	−	1029.14i	0.221604	−	0.383829i	−0.733691	−	0.679483i	$-0.762204\pi$
$193$	594.174	−	1029.14i	0.221604	−	0.383829i	0.955295	+	0.295654i	$0.0955375\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−3130.25			−1.13209			−0.566044	−	0.824375i	$-0.691527\pi$
$197$	−3130.25			−1.13209			−0.566044	+	0.824375i	$0.691527\pi$
$198$		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	0.404730	+	0.914436i	$0.367365\pi$
$211$	−1806.97	+	3129.77i	−0.589560	+	1.02115i	−0.994290	+	0.106711i	$0.965968\pi$
$212$		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	0.978017	−	0.208527i	$-0.0668669\pi$
$223$	1027.07	+	1778.93i	0.308419	+	0.534197i	−0.669598	+	0.742724i	$0.733534\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1076.80	−	1865.08i	−0.314846	−	0.545329i	0.664559	−	0.747236i	$-0.268619\pi$
$227$	−1076.80	−	1865.08i	−0.314846	−	0.545329i	−0.979405	+	0.201907i	$0.935286\pi$
$228$		0			0
$229$	909.935	−	1576.05i	0.262577	−	0.454797i	−0.704349	−	0.709854i	$-0.748761\pi$
$229$	909.935	−	1576.05i	0.262577	−	0.454797i	0.966926	+	0.255057i	$0.0820942\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3989.68			−1.12177			−0.560886	−	0.827893i	$-0.689539\pi$
$233$	−3989.68			−1.12177			−0.560886	+	0.827893i	$0.689539\pi$
$234$		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	−0.164575	−	0.986365i	$-0.552625\pi$
$239$	2852.16	−	4940.09i	0.771929	−	1.33702i	0.936504	−	0.350656i	$-0.114041\pi$
$240$		0			0
$241$	−3111.98	−	5390.10i	−0.831785	−	1.44069i	−0.896622	−	0.442797i	$-0.853986\pi$
$241$	−3111.98	−	5390.10i	−0.831785	−	1.44069i	0.0648372	−	0.997896i	$-0.479347\pi$
$242$		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	$-0.302577\pi$
$251$	4622.52			1.16243			0.581217	+	0.813749i	$0.302577\pi$
$252$		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	−0.398234	−	0.917284i	$-0.630377\pi$
$257$	2452.54	−	4247.93i	0.595274	−	1.03104i	0.993508	−	0.113761i	$-0.0362899\pi$
$258$		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	−0.999739	−	0.0228519i	$-0.992725\pi$
$263$	−2216.42	−	3838.96i	−0.519660	−	0.900077i	0.480079	−	0.877225i	$-0.340608\pi$
$264$		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	$-0.331544\pi$
$269$	4454.81			1.00972			0.504860	+	0.863201i	$0.331544\pi$
$270$		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	0.989734	−	0.142924i	$-0.0456504\pi$
$277$	1710.80	+	2963.20i	0.371091	+	0.642749i	−0.618642	+	0.785673i	$0.712317\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	857.554	+	1485.33i	0.182055	+	0.315328i	0.942580	−	0.333980i	$-0.108392\pi$
$281$	857.554	+	1485.33i	0.182055	+	0.315328i	−0.760525	+	0.649308i	$0.775059\pi$
$282$		0			0
$283$	2243.80	−	3886.37i	0.471307	−	0.816328i	−0.528154	−	0.849149i	$-0.677116\pi$
$283$	2243.80	−	3886.37i	0.471307	−	0.816328i	0.999461	+	0.0328205i	$0.0104490\pi$
$284$		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	$-0.887069\pi$
$293$	−842.657	+	1459.52i	−0.168016	+	0.291011i	0.769707	+	0.638398i	$0.220403\pi$
$294$		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	$-0.908242\pi$
$311$	−1278.81	+	2214.97i	−0.233167	+	0.403857i	0.725571	+	0.688147i	$0.241576\pi$
$312$		0			0
$313$	2040.72	+	3534.63i	0.368524	+	0.638303i	0.989335	−	0.145658i	$-0.0465298\pi$
$313$	2040.72	+	3534.63i	0.368524	+	0.638303i	−0.620811	+	0.783961i	$0.713196\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3850.96	+	6670.06i	0.682308	+	1.18179i	0.974275	+	0.225364i	$0.0723570\pi$
$317$	3850.96	+	6670.06i	0.682308	+	1.18179i	−0.291967	+	0.956428i	$0.594310\pi$
$318$		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	0.880478	−	0.474087i	$-0.157222\pi$
$331$	178.657	+	309.443i	0.0296673	+	0.0513853i	−0.850811	+	0.525473i	$0.823889\pi$
$332$		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	−0.460806	−	0.887501i	$-0.652440\pi$
$337$	3329.54	−	5766.94i	0.538195	−	0.932181i	0.999001	−	0.0446806i	$-0.0142270\pi$
$338$		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	0.380509	+	0.924777i	$0.375749\pi$
$347$	−3947.02	+	6836.44i	−0.610626	+	1.05763i	−0.991135	+	0.132858i	$0.957585\pi$
$348$		0			0
$349$	627.228	+	1086.39i	0.0962027	+	0.166628i	0.910110	−	0.414367i	$-0.135997\pi$
$349$	627.228	+	1086.39i	0.0962027	+	0.166628i	−0.813907	+	0.580995i	$0.802664\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−4302.46	−	7452.08i	−0.648716	−	1.12361i	−0.983430	−	0.181290i	$-0.941973\pi$
$353$	−4302.46	−	7452.08i	−0.648716	−	1.12361i	0.334714	−	0.942320i	$-0.391360\pi$
$354$		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	$-0.591955\pi$
$359$	−3875.61			−0.569768			−0.284884	+	0.958562i	$0.591955\pi$
$360$		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	0.885114	+	0.465375i	$0.154081\pi$
$367$	5945.05	+	10297.1i	0.845583	+	1.46459i	−0.0395301	+	0.999218i	$0.512586\pi$
$368$		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	0.0127544	+	0.999919i	$0.495940\pi$
$373$	−6192.25	+	10725.3i	−0.859578	+	1.48883i	−0.872332	+	0.488914i	$0.837393\pi$
$374$		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	0.129205	+	0.991618i	$0.458757\pi$
$383$	−5952.62	+	10310.2i	−0.794164	+	1.37553i	−0.923369	+	0.383914i	$0.874576\pi$
$384$		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	−0.899031	−	0.437886i	$-0.855728\pi$
$389$	−6358.29	−	11012.9i	−0.828735	−	1.43541i	0.0702954	−	0.997526i	$-0.477606\pi$
$390$		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	$-0.736115\pi$
$401$	2414.58	−	4182.17i	0.300694	−	0.520817i	0.976293	+	0.216452i	$0.0694485\pi$
$402$		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	0.276190	+	0.961103i	$0.410928\pi$
$409$	−5742.46	+	9946.23i	−0.694245	+	1.20247i	−0.970435	+	0.241364i	$0.922405\pi$
$410$		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	$-0.992232\pi$
$419$	−4105.82	+	7111.50i	−0.478718	+	0.829163i	0.520985	+	0.853566i	$0.325565\pi$
$420$		0			0
$421$	−4894.06	−	8476.77i	−0.566561	−	0.981312i	−0.996903	−	0.0786460i	$-0.974940\pi$
$421$	−4894.06	−	8476.77i	−0.566561	−	0.981312i	0.430342	−	0.902666i	$-0.358393\pi$
$422$		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	$-0.284606\pi$
$431$	11206.3			1.25241			0.626207	+	0.779657i	$0.284606\pi$
$432$		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	0.521595	−	0.853193i	$-0.325337\pi$
$439$	−4397.50	−	7616.70i	−0.478090	−	0.828075i	−0.999684	+	0.0251179i	$0.992004\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−1511.83	−	2618.56i	−0.162142	−	0.280839i	0.773494	−	0.633803i	$-0.218507\pi$
$443$	−1511.83	−	2618.56i	−0.162142	−	0.280839i	−0.935637	+	0.352964i	$0.885174\pi$
$444$		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	$-0.447272\pi$
$449$	3137.67			0.329790			0.164895	+	0.986311i	$0.447272\pi$
$450$		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	0.999032	−	0.0439888i	$-0.0140066\pi$
$457$	4507.87	+	7807.86i	0.461421	+	0.799204i	−0.537611	+	0.843193i	$0.680673\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	6131.30	+	10619.7i	0.619442	+	1.07291i	0.989588	+	0.143932i	$0.0459745\pi$
$461$	6131.30	+	10619.7i	0.619442	+	1.07291i	−0.370145	+	0.928974i	$0.620692\pi$
$462$		0			0
$463$	−1736.15	+	3007.10i	−0.174267	+	0.301840i	−0.939907	−	0.341429i	$-0.889089\pi$
$463$	−1736.15	+	3007.10i	−0.174267	+	0.301840i	0.765640	+	0.643269i	$0.222422\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	11825.0			1.17172			0.585860	−	0.810412i	$-0.300757\pi$
$467$	11825.0			1.17172			0.585860	+	0.810412i	$0.300757\pi$
$468$		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	$-0.140769\pi$
$479$	851.980	+	1475.67i	0.0812692	+	0.140762i	−0.822526	+	0.568727i	$0.807436\pi$
$480$		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	−0.145099	+	0.989417i	$0.546350\pi$
$491$	−10111.8	+	17514.2i	−0.929410	+	1.60979i	−0.784311	+	0.620368i	$0.786983\pi$
$492$		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	−0.375816	−	0.926694i	$-0.622638\pi$
$499$	6851.20	−	11866.6i	0.614633	−	1.06458i	0.990449	−	0.137881i	$-0.0440291\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	13707.6			1.21509			0.607546	−	0.794285i	$-0.292154\pi$
$503$	13707.6			1.21509			0.607546	+	0.794285i	$0.292154\pi$
$504$		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	0.461797	+	0.886986i	$0.347205\pi$
$509$	−6169.59	+	10686.0i	−0.537254	+	0.930551i	−0.999051	+	0.0435650i	$0.986128\pi$
$510$		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	$-0.481029\pi$
$521$	1416.70			0.119130			0.0595649	+	0.998224i	$0.481029\pi$
$522$		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	0.529323	−	0.848420i	$-0.322446\pi$
$547$	−6014.01	−	10416.6i	−0.470092	−	0.814224i	−0.999415	+	0.0341968i	$0.989113\pi$
$548$		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	$-0.313623\pi$
$557$	14529.5			1.10527			0.552634	+	0.833424i	$0.313623\pi$
$558$		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	$-0.708215\pi$
$563$	5116.72	−	8862.42i	0.383027	−	0.663422i	0.991493	+	0.130158i	$0.0415484\pi$
$564$		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	$-0.170413\pi$
$569$	−159.730	−	276.660i	−0.0117684	−	0.0203835i	−0.871850	+	0.489774i	$0.837079\pi$
$570$		0			0
$571$	3396.98	−	5883.74i	0.248965	−	0.431221i	−0.714274	−	0.699866i	$-0.753243\pi$
$571$	3396.98	−	5883.74i	0.248965	−	0.431221i	0.963239	+	0.268646i	$0.0865761\pi$
$572$		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	0.892098	+	0.451843i	$0.149233\pi$
$587$	11908.8	+	20626.6i	0.837356	+	1.45034i	−0.0547416	+	0.998501i	$0.517434\pi$
$588$		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	$-0.692441\pi$
$593$	−16416.2			−1.13682			−0.568408	+	0.822747i	$0.692441\pi$
$594$		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	$-0.780969\pi$
$599$	2400.85	−	4158.39i	0.163766	−	0.283652i	0.936216	+	0.351424i	$0.114302\pi$
$600$		0			0
$601$	−2262.11	−	3918.08i	−0.153533	−	0.265927i	0.778991	−	0.627035i	$-0.215732\pi$
$601$	−2262.11	−	3918.08i	−0.153533	−	0.265927i	−0.932524	+	0.361108i	$0.882398\pi$
$602$		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	−0.499216	−	0.866477i	$-0.666379\pi$
$607$	7489.15	−	12971.6i	0.500783	−	0.867382i	1.00000		0.000904500i	$-0.000287911\pi$
$608$		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	$-0.829791\pi$
$617$	170.560	−	295.418i	0.0111288	−	0.0192757i	0.871536	+	0.490331i	$0.163124\pi$
$618$		0			0
$619$	−9207.57	−	15948.0i	−0.597873	−	1.03555i	−0.993135	−	0.116978i	$-0.962679\pi$
$619$	−9207.57	−	15948.0i	−0.597873	−	1.03555i	0.395262	−	0.918569i	$-0.370654\pi$
$620$		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	$-0.263091\pi$
$641$	−4841.27	−	8385.33i	−0.298313	−	0.516694i	−0.975750	+	0.218887i	$0.929757\pi$
$642$		0			0
$643$	1629.75	−	2822.81i	0.0999551	−	0.173127i	−0.811711	−	0.584060i	$-0.801463\pi$
$643$	1629.75	−	2822.81i	0.0999551	−	0.173127i	0.911666	+	0.410932i	$0.134797\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−8115.35			−0.493118			−0.246559	−	0.969128i	$-0.579300\pi$
$647$	−8115.35			−0.493118			−0.246559	+	0.969128i	$0.579300\pi$
$648$		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	$-0.800582\pi$
$653$	1713.87	−	2968.51i	0.102709	−	0.177897i	0.912800	+	0.408407i	$0.133916\pi$
$654$		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	$-0.0327302\pi$
$659$	6910.11	+	11968.7i	0.408467	+	0.707485i	−0.586251	+	0.810129i	$0.699397\pi$
$660$		0			0
$661$	11359.8	−	19675.8i	0.668451	−	1.15779i	−0.309886	−	0.950774i	$-0.600291\pi$
$661$	11359.8	−	19675.8i	0.668451	−	1.15779i	0.978337	−	0.207018i	$-0.0663759\pi$
$662$		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	0.930119	−	0.367257i	$-0.119703\pi$
$673$	2566.59	+	4445.46i	0.147005	+	0.254621i	−0.783114	+	0.621878i	$0.786370\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−4647.94	−	8050.46i	−0.263862	−	0.457023i	0.703403	−	0.710792i	$-0.251663\pi$
$677$	−4647.94	−	8050.46i	−0.263862	−	0.457023i	−0.967265	+	0.253769i	$0.918330\pi$
$678$		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	$-0.373427\pi$
$683$	13824.3			0.774486			0.387243	+	0.921978i	$0.373427\pi$
$684$		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	0.976862	−	0.213872i	$-0.0686076\pi$
$691$	5507.61	+	9539.47i	0.303212	+	0.525179i	−0.673650	+	0.739051i	$0.735274\pi$
$692$		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	$-0.503949\pi$
$701$	−460.523			−0.0248127			−0.0124064	+	0.999923i	$0.503949\pi$
$702$		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	−0.968327	−	0.249686i	$-0.919672\pi$
$709$	−13222.5	−	22902.1i	−0.700398	−	1.21313i	0.267929	−	0.963439i	$-0.413661\pi$
$710$		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	$-0.368101\pi$
$719$	15524.4			0.805235			0.402617	+	0.915368i	$0.368101\pi$
$720$		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	0.516848	−	0.856077i	$-0.327105\pi$
$727$	−9467.02	−	16397.4i	−0.482961	−	0.836513i	−0.999809	+	0.0195647i	$0.993772\pi$
$728$		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	−0.573439	−	0.819248i	$-0.694391\pi$
$733$	8389.96	−	14531.8i	0.422770	−	0.732259i	0.996209	+	0.0869891i	$0.0277245\pi$
$734$		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	0.131983	+	0.991252i	$0.457865\pi$
$743$	−16049.4	+	27798.4i	−0.792458	+	1.37258i	−0.924441	+	0.381325i	$0.875468\pi$
$744$		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	−0.957570	−	0.288199i	$-0.906943\pi$
$751$	−4717.04	+	8170.15i	−0.229197	+	0.396981i	0.728373	+	0.685181i	$0.240277\pi$
$752$		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	$-0.988146\pi$
$761$	−9812.37	+	16995.5i	−0.467409	+	0.809576i	0.531898	+	0.846809i	$0.321479\pi$
$762$		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	−0.995292	−	0.0969179i	$-0.969102\pi$
$769$	−8822.44	+	15280.9i	−0.413713	+	0.716572i	0.581580	+	0.813490i	$0.302435\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−22541.7			−1.04886			−0.524430	−	0.851454i	$-0.675722\pi$
$773$	−22541.7			−1.04886			−0.524430	+	0.851454i	$0.675722\pi$
$774$		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	0.0697798	−	0.997562i	$-0.477770\pi$
$787$	19843.9	−	34370.7i	0.898804	−	1.55677i	0.829025	−	0.559212i	$-0.188896\pi$
$788$		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	$-0.819239\pi$
$797$	995.984	−	1725.09i	0.0442654	−	0.0766700i	0.887309	+	0.461175i	$0.152572\pi$
$798$		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	$-0.656136\pi$
$809$	−21679.4			−0.942160			−0.471080	+	0.882090i	$0.656136\pi$
$810$		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	$-0.234169\pi$
$821$	−4951.38	−	8576.05i	−0.210480	−	0.364563i	−0.951865	+	0.306518i	$0.900836\pi$
$822$		0			0
$823$	−5744.36	+	9949.53i	−0.243300	+	0.421408i	−0.961652	−	0.274272i	$-0.911563\pi$
$823$	−5744.36	+	9949.53i	−0.243300	+	0.421408i	0.718352	+	0.695680i	$0.244897\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	36938.8			1.55319			0.776594	−	0.630001i	$-0.216945\pi$
$827$	36938.8			1.55319			0.776594	+	0.630001i	$0.216945\pi$
$828$		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	$-0.159288\pi$
$839$	563.314	+	975.689i	0.0231797	+	0.0401484i	−0.854203	+	0.519940i	$0.825954\pi$
$840$		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	0.796410	−	0.604758i	$-0.206730\pi$
$853$	−3127.33	−	5416.69i	−0.125531	−	0.217425i	−0.921940	+	0.387332i	$0.873397\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−9534.68	−	16514.6i	−0.380045	−	0.658257i	0.611023	−	0.791613i	$-0.290758\pi$
$857$	−9534.68	−	16514.6i	−0.380045	−	0.658257i	−0.991068	+	0.133355i	$0.957425\pi$
$858$		0			0
$859$	−13395.1	+	23201.0i	−0.532056	+	0.921547i	0.467244	+	0.884128i	$0.345247\pi$
$859$	−13395.1	+	23201.0i	−0.532056	+	0.921547i	−0.999300	+	0.0374190i	$0.988086\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	46056.3			1.81666			0.908329	−	0.418256i	$-0.137359\pi$
$863$	46056.3			1.81666			0.908329	+	0.418256i	$0.137359\pi$
$864$		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	0.265086	+	0.964225i	$0.414600\pi$
$877$	−18245.1	+	31601.4i	−0.702500	+	1.21677i	−0.967586	+	0.252541i	$0.918734\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−38136.3			−1.45839			−0.729197	−	0.684303i	$-0.760106\pi$
$881$	−38136.3			−1.45839			−0.729197	+	0.684303i	$0.760106\pi$
$882$		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	−0.468894	−	0.883255i	$-0.655347\pi$
$887$	14013.6	−	24272.3i	0.530474	−	0.918808i	0.999368	−	0.0355536i	$-0.0113194\pi$
$888$		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	0.900050	+	0.435786i	$0.143530\pi$
$907$	22601.7	+	39147.2i	0.827427	+	1.43315i	−0.0726235	+	0.997359i	$0.523137\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	14911.0	+	25826.6i	0.542287	+	0.939268i	0.998772	+	0.0495373i	$0.0157747\pi$
$911$	14911.0	+	25826.6i	0.542287	+	0.939268i	−0.456486	+	0.889731i	$0.650892\pi$
$912$		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	−0.839708	−	0.543038i	$-0.817274\pi$
$929$	−25204.7	−	43655.8i	−0.890139	−	1.54177i	−0.0504304	−	0.998728i	$-0.516059\pi$
$930$		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	−0.224980	−	0.974363i	$-0.572232\pi$
$941$	21110.6	−	36564.6i	0.731333	−	1.26671i	0.956313	−	0.292343i	$-0.0944350\pi$
$942$		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	−0.972126	−	0.234459i	$-0.924668\pi$
$947$	−20082.3	−	34783.6i	−0.689111	−	1.19357i	0.283015	−	0.959115i	$-0.408665\pi$
$948$		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	$-0.461322\pi$
$953$	7132.10			0.242425			0.121213	+	0.992627i	$0.461322\pi$
$954$		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	−0.861423	−	0.507888i	$-0.830426\pi$
$967$	274.603	−	475.626i	0.00913199	−	0.0158171i	0.870555	+	0.492071i	$0.163760\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	31024.8			1.02537			0.512685	−	0.858577i	$-0.328651\pi$
$971$	31024.8			1.02537			0.512685	+	0.858577i	$0.328651\pi$
$972$		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	$-0.874238\pi$
$977$	−3913.51	+	6778.40i	−0.128152	+	0.221966i	0.794809	+	0.606860i	$0.207571\pi$
$978$		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	0.937924	+	0.346840i	$0.112745\pi$
$983$	23710.7	+	41068.2i	0.769334	+	1.33253i	−0.168590	+	0.985686i	$0.553921\pi$
$984$		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	0.985733	+	0.168317i	$0.0538333\pi$
$997$	20104.6	+	34822.1i	0.638634	+	1.10615i	−0.347099	+	0.937828i	$0.612833\pi$
$998$		0			0
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.4.a.e.1.1	✓	2	9.5	odd	6
216.4.a.h.1.2	yes	2	9.4	even	3
432.4.a.o.1.1		2	36.23	even	6
432.4.a.s.1.2		2	36.31	odd	6
648.4.i.m.217.1		4	9.7	even	3	inner
648.4.i.m.433.1		4	1.1	even	1	trivial
648.4.i.s.217.2		4	9.2	odd	6
648.4.i.s.433.2		4	3.2	odd	2
1728.4.a.bg.1.1		2	72.67	odd	6
1728.4.a.bh.1.1		2	72.13	even	6
1728.4.a.bs.1.2		2	72.59	even	6
1728.4.a.bt.1.2		2	72.5	odd	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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