LMFDB - Embedded newform 960.3.l.f.641.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,3,Mod(641,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("960.641");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	960.l (of order $2$, degree $1$, 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:	$26.1581053786$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 4x^{2} + 9 $ x^4 - 4*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			641.3
Root			$-1.58114 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	960.641
Dual form			960.3.l.f.641.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.58114 - 1.52896i) q^{3} -2.23607i q^{5} +7.48683 q^{7} +(4.32456 - 7.89292i) q^{9} +O(q^{10})$	\(q+(2.58114 - 1.52896i) q^{3} -2.23607i q^{5} +7.48683 q^{7} +(4.32456 - 7.89292i) q^{9} -8.48528i q^{11} +10.0000 q^{13} +(-3.41886 - 5.77160i) q^{15} +30.3870i q^{17} +26.9737 q^{19} +(19.3246 - 11.4471i) q^{21} +9.17377i q^{23} -5.00000 q^{25} +(-0.905694 - 26.9848i) q^{27} -26.8328i q^{29} -8.00000 q^{31} +(-12.9737 - 21.9017i) q^{33} -16.7411i q^{35} -15.9473 q^{37} +(25.8114 - 15.2896i) q^{39} -47.3575i q^{41} -14.4605 q^{43} +(-17.6491 - 9.67000i) q^{45} +45.8688i q^{47} +7.05267 q^{49} +(46.4605 + 78.4330i) q^{51} -30.3870i q^{53} -18.9737 q^{55} +(69.6228 - 41.2417i) q^{57} +24.0789i q^{59} +53.9473 q^{61} +(32.3772 - 59.0930i) q^{63} -22.3607i q^{65} -110.460 q^{67} +(14.0263 + 23.6788i) q^{69} +15.5936i q^{71} +87.9473 q^{73} +(-12.9057 + 7.64481i) q^{75} -63.5279i q^{77} +46.9737 q^{79} +(-43.5964 - 68.2668i) q^{81} -26.1443i q^{83} +67.9473 q^{85} +(-41.0263 - 69.2592i) q^{87} -60.7739i q^{89} +74.8683 q^{91} +(-20.6491 + 12.2317i) q^{93} -60.3150i q^{95} +36.0527 q^{97} +(-66.9737 - 36.6951i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} - 8 q^{7} - 8 q^{9}+O(q^{10}) $ 4 * q + 4 * q^3 - 8 * q^7 - 8 * q^9	$ 4 q + 4 q^{3} - 8 q^{7} - 8 q^{9} + 40 q^{13} - 20 q^{15} + 32 q^{19} + 52 q^{21} - 20 q^{25} + 28 q^{27} - 32 q^{31} + 24 q^{33} + 88 q^{37} + 40 q^{39} + 56 q^{43} - 20 q^{45} + 180 q^{49} + 72 q^{51} + 152 q^{57} + 64 q^{61} + 256 q^{63} - 328 q^{67} + 132 q^{69} + 200 q^{73} - 20 q^{75} + 112 q^{79} + 28 q^{81} + 120 q^{85} - 240 q^{87} - 80 q^{91} - 32 q^{93} + 296 q^{97} - 192 q^{99}+O(q^{100}) $ 4 * q + 4 * q^3 - 8 * q^7 - 8 * q^9 + 40 * q^13 - 20 * q^15 + 32 * q^19 + 52 * q^21 - 20 * q^25 + 28 * q^27 - 32 * q^31 + 24 * q^33 + 88 * q^37 + 40 * q^39 + 56 * q^43 - 20 * q^45 + 180 * q^49 + 72 * q^51 + 152 * q^57 + 64 * q^61 + 256 * q^63 - 328 * q^67 + 132 * q^69 + 200 * q^73 - 20 * q^75 + 112 * q^79 + 28 * q^81 + 120 * q^85 - 240 * q^87 - 80 * q^91 - 32 * q^93 + 296 * q^97 - 192 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.58114	−	1.52896i	0.860380	−	0.509654i
$3$	2.58114	−	1.52896i	0.860380	−	0.509654i
$4$		0			0
$5$		−	2.23607i		−	0.447214i
$5$		−	2.23607i		−	0.447214i
$6$		0			0
$7$	7.48683			1.06955			0.534774	−	0.844995i	$-0.320397\pi$
$7$	7.48683			1.06955			0.534774	+	0.844995i	$0.320397\pi$
$8$		0			0
$9$	4.32456	−	7.89292i	0.480506	−	0.876991i
$10$		0			0
$11$		−	8.48528i		−	0.771389i	−0.922627	−	0.385695i	$-0.873962\pi$
$11$		−	8.48528i		−	0.771389i	0.922627	−	0.385695i	$-0.126038\pi$
$12$		0			0
$13$	10.0000			0.769231			0.384615	−	0.923077i	$-0.374334\pi$
$13$	10.0000			0.769231			0.384615	+	0.923077i	$0.374334\pi$
$14$		0			0
$15$	−3.41886	−	5.77160i	−0.227924	−	0.384773i
$16$		0			0
$17$			30.3870i			1.78747i	0.448596	+	0.893734i	$0.351924\pi$
$17$			30.3870i			1.78747i	−0.448596	+	0.893734i	$0.648076\pi$
$18$		0			0
$19$	26.9737			1.41967			0.709833	−	0.704370i	$-0.248770\pi$
$19$	26.9737			1.41967			0.709833	+	0.704370i	$0.248770\pi$
$20$		0			0
$21$	19.3246	−	11.4471i	0.920217	−	0.545099i
$22$		0			0
$23$			9.17377i			0.398859i	0.979912	+	0.199430i	$0.0639090\pi$
$23$			9.17377i			0.398859i	−0.979912	+	0.199430i	$0.936091\pi$
$24$		0			0
$25$	−5.00000			−0.200000
$26$		0			0
$27$	−0.905694	−	26.9848i	−0.0335442	−	0.999437i
$28$		0			0
$29$		−	26.8328i		−	0.925270i	−0.886549	−	0.462635i	$-0.846904\pi$
$29$		−	26.8328i		−	0.925270i	0.886549	−	0.462635i	$-0.153096\pi$
$30$		0			0
$31$	−8.00000			−0.258065			−0.129032	−	0.991640i	$-0.541187\pi$
$31$	−8.00000			−0.258065			−0.129032	+	0.991640i	$0.541187\pi$
$32$		0			0
$33$	−12.9737	−	21.9017i	−0.393141	−	0.663688i
$34$		0			0
$35$		−	16.7411i		−	0.478316i
$36$		0			0
$37$	−15.9473			−0.431009			−0.215504	−	0.976503i	$-0.569140\pi$
$37$	−15.9473			−0.431009			−0.215504	+	0.976503i	$0.569140\pi$
$38$		0			0
$39$	25.8114	−	15.2896i	0.661830	−	0.392041i
$40$		0			0
$41$		−	47.3575i		−	1.15506i	−0.816369	−	0.577531i	$-0.804016\pi$
$41$		−	47.3575i		−	1.15506i	0.816369	−	0.577531i	$-0.195984\pi$
$42$		0			0
$43$	−14.4605			−0.336291			−0.168145	−	0.985762i	$-0.553778\pi$
$43$	−14.4605			−0.336291			−0.168145	+	0.985762i	$0.553778\pi$
$44$		0			0
$45$	−17.6491	−	9.67000i	−0.392202	−	0.214889i
$46$		0			0
$47$			45.8688i			0.975933i	0.872862	+	0.487966i	$0.162261\pi$
$47$			45.8688i			0.975933i	−0.872862	+	0.487966i	$0.837739\pi$
$48$		0			0
$49$	7.05267			0.143932
$50$		0			0
$51$	46.4605	+	78.4330i	0.910990	+	1.53790i
$52$		0			0
$53$		−	30.3870i		−	0.573339i	−0.958030	−	0.286670i	$-0.907452\pi$
$53$		−	30.3870i		−	0.573339i	0.958030	−	0.286670i	$-0.0925482\pi$
$54$		0			0
$55$	−18.9737			−0.344976
$56$		0			0
$57$	69.6228	−	41.2417i	1.22145	−	0.723538i
$58$		0			0
$59$			24.0789i			0.408116i	0.978959	+	0.204058i	$0.0654132\pi$
$59$			24.0789i			0.408116i	−0.978959	+	0.204058i	$0.934587\pi$
$60$		0			0
$61$	53.9473			0.884382			0.442191	−	0.896921i	$-0.354201\pi$
$61$	53.9473			0.884382			0.442191	+	0.896921i	$0.354201\pi$
$62$		0			0
$63$	32.3772	−	59.0930i	0.513924	−	0.937984i
$64$		0			0
$65$		−	22.3607i		−	0.344010i
$66$		0			0
$67$	−110.460			−1.64866			−0.824332	−	0.566107i	$-0.808449\pi$
$67$	−110.460			−1.64866			−0.824332	+	0.566107i	$0.808449\pi$
$68$		0			0
$69$	14.0263	+	23.6788i	0.203280	+	0.343171i
$70$		0			0
$71$			15.5936i			0.219628i	0.993952	+	0.109814i	$0.0350255\pi$
$71$			15.5936i			0.219628i	−0.993952	+	0.109814i	$0.964974\pi$
$72$		0			0
$73$	87.9473			1.20476			0.602379	−	0.798210i	$-0.294220\pi$
$73$	87.9473			1.20476			0.602379	+	0.798210i	$0.294220\pi$
$74$		0			0
$75$	−12.9057	+	7.64481i	−0.172076	+	0.101931i
$76$		0			0
$77$		−	63.5279i		−	0.825037i
$78$		0			0
$79$	46.9737			0.594603			0.297302	−	0.954784i	$-0.403913\pi$
$79$	46.9737			0.594603			0.297302	+	0.954784i	$0.403913\pi$
$80$		0			0
$81$	−43.5964	−	68.2668i	−0.538228	−	0.842799i
$82$		0			0
$83$		−	26.1443i		−	0.314992i	−0.987520	−	0.157496i	$-0.949658\pi$
$83$		−	26.1443i		−	0.314992i	0.987520	−	0.157496i	$-0.0503421\pi$
$84$		0			0
$85$	67.9473			0.799380
$86$		0			0
$87$	−41.0263	−	69.2592i	−0.471567	−	0.796083i
$88$		0			0
$89$		−	60.7739i		−	0.682853i	−0.939908	−	0.341427i	$-0.889090\pi$
$89$		−	60.7739i		−	0.682853i	0.939908	−	0.341427i	$-0.110910\pi$
$90$		0			0
$91$	74.8683			0.822729
$92$		0			0
$93$	−20.6491	+	12.2317i	−0.222033	+	0.131524i
$94$		0			0
$95$		−	60.3150i		−	0.634894i
$96$		0			0
$97$	36.0527			0.371677			0.185838	−	0.982580i	$-0.440500\pi$
$97$	36.0527			0.371677			0.185838	+	0.982580i	$0.440500\pi$
$98$		0			0
$99$	−66.9737	−	36.6951i	−0.676502	−	0.370657i
$100$		0			0
$101$		−	48.1577i		−	0.476809i	−0.971166	−	0.238405i	$-0.923376\pi$
$101$		−	48.1577i		−	0.476809i	0.971166	−	0.238405i	$-0.0766245\pi$
$102$		0			0
$103$	−140.408			−1.36318			−0.681591	−	0.731733i	$-0.738712\pi$
$103$	−140.408			−1.36318			−0.681591	+	0.731733i	$0.738712\pi$
$104$		0			0
$105$	−25.5964	−	43.2110i	−0.243776	−	0.411534i
$106$		0			0
$107$			43.1149i			0.402943i	0.979494	+	0.201471i	$0.0645723\pi$
$107$			43.1149i			0.402943i	−0.979494	+	0.201471i	$0.935428\pi$
$108$		0			0
$109$	−133.842			−1.22791			−0.613954	−	0.789342i	$-0.710422\pi$
$109$	−133.842			−1.22791			−0.613954	+	0.789342i	$0.710422\pi$
$110$		0			0
$111$	−41.1623	+	24.3829i	−0.370831	+	0.219665i
$112$		0			0
$113$		−	7.90852i		−	0.0699869i	−0.999388	−	0.0349935i	$-0.988859\pi$
$113$		−	7.90852i		−	0.0699869i	0.999388	−	0.0349935i	$-0.0111410\pi$
$114$		0			0
$115$	20.5132			0.178375
$116$		0			0
$117$	43.2456	−	78.9292i	0.369620	−	0.674609i
$118$		0			0
$119$			227.502i			1.91178i
$120$		0			0
$121$	49.0000			0.404959
$122$		0			0
$123$	−72.4078	−	122.236i	−0.588682	−	0.993792i
$124$		0			0
$125$			11.1803i			0.0894427i
$126$		0			0
$127$	134.460			1.05874			0.529372	−	0.848390i	$-0.322428\pi$
$127$	134.460			1.05874			0.529372	+	0.848390i	$0.322428\pi$
$128$		0			0
$129$	−37.3246	+	22.1095i	−0.289338	+	0.171392i
$130$		0			0
$131$			220.394i			1.68240i	0.540727	+	0.841198i	$0.318149\pi$
$131$			220.394i			1.68240i	−0.540727	+	0.841198i	$0.681851\pi$
$132$		0			0
$133$	201.947			1.51840
$134$		0			0
$135$	−60.3399	+	2.02519i	−0.446962	+	0.0150014i
$136$		0			0
$137$		−	95.5153i		−	0.697192i	−0.937273	−	0.348596i	$-0.886659\pi$
$137$		−	95.5153i		−	0.697192i	0.937273	−	0.348596i	$-0.113341\pi$
$138$		0			0
$139$	−76.8157			−0.552631			−0.276315	−	0.961067i	$-0.589113\pi$
$139$	−76.8157			−0.552631			−0.276315	+	0.961067i	$0.589113\pi$
$140$		0			0
$141$	70.1317	+	118.394i	0.497388	+	0.839673i
$142$		0			0
$143$		−	84.8528i		−	0.593376i
$144$		0			0
$145$	−60.0000			−0.413793
$146$		0			0
$147$	18.2039	−	10.7833i	0.123836	−	0.0733555i
$148$		0			0
$149$		−	276.237i		−	1.85394i	−0.375139	−	0.926969i	$-0.622405\pi$
$149$		−	276.237i		−	1.85394i	0.375139	−	0.926969i	$-0.377595\pi$
$150$		0			0
$151$	−18.0527			−0.119554			−0.0597770	−	0.998212i	$-0.519039\pi$
$151$	−18.0527			−0.119554			−0.0597770	+	0.998212i	$0.519039\pi$
$152$		0			0
$153$	239.842	+	131.410i	1.56759	+	0.858890i
$154$		0			0
$155$			17.8885i			0.115410i
$156$		0			0
$157$	−103.842			−0.661414			−0.330707	−	0.943733i	$-0.607287\pi$
$157$	−103.842			−0.661414			−0.330707	+	0.943733i	$0.607287\pi$
$158$		0			0
$159$	−46.4605	−	78.4330i	−0.292204	−	0.493289i
$160$		0			0
$161$			68.6825i			0.426599i
$162$		0			0
$163$	−11.3815			−0.0698251			−0.0349126	−	0.999390i	$-0.511115\pi$
$163$	−11.3815			−0.0698251			−0.0349126	+	0.999390i	$0.511115\pi$
$164$		0			0
$165$	−48.9737	+	29.0100i	−0.296810	+	0.175818i
$166$		0			0
$167$			252.270i			1.51060i	0.655382	+	0.755298i	$0.272508\pi$
$167$			252.270i			1.51060i	−0.655382	+	0.755298i	$0.727492\pi$
$168$		0			0
$169$	−69.0000			−0.408284
$170$		0			0
$171$	116.649	−	212.901i	0.682159	−	1.24504i
$172$		0			0
$173$			11.8160i			0.0683005i	0.999417	+	0.0341502i	$0.0108725\pi$
$173$			11.8160i			0.0683005i	−0.999417	+	0.0341502i	$0.989128\pi$
$174$		0			0
$175$	−37.4342			−0.213910
$176$		0			0
$177$	36.8157	+	62.1509i	0.207998	+	0.351135i
$178$		0			0
$179$			69.0358i			0.385675i	0.981231	+	0.192837i	$0.0617690\pi$
$179$			69.0358i			0.385675i	−0.981231	+	0.192837i	$0.938231\pi$
$180$		0			0
$181$	189.684			1.04798			0.523989	−	0.851725i	$-0.324443\pi$
$181$	189.684			1.04798			0.523989	+	0.851725i	$0.324443\pi$
$182$		0			0
$183$	139.246	−	82.4834i	0.760905	−	0.450729i
$184$		0			0
$185$			35.6593i			0.192753i
$186$		0			0
$187$	257.842			1.37883
$188$		0			0
$189$	−6.78078	−	202.031i	−0.0358771	−	1.06895i
$190$		0			0
$191$			108.708i			0.569153i	0.958653	+	0.284577i	$0.0918530\pi$
$191$			108.708i			0.569153i	−0.958653	+	0.284577i	$0.908147\pi$
$192$		0			0
$193$	−167.947			−0.870193			−0.435097	−	0.900384i	$-0.643286\pi$
$193$	−167.947			−0.870193			−0.435097	+	0.900384i	$0.643286\pi$
$194$		0			0
$195$	−34.1886	−	57.7160i	−0.175326	−	0.295980i
$196$		0			0
$197$			171.659i			0.871367i	0.900100	+	0.435684i	$0.143493\pi$
$197$			171.659i			0.871367i	−0.900100	+	0.435684i	$0.856507\pi$
$198$		0			0
$199$	−35.0790			−0.176276			−0.0881382	−	0.996108i	$-0.528092\pi$
$199$	−35.0790			−0.176276			−0.0881382	+	0.996108i	$0.528092\pi$
$200$		0			0
$201$	−285.114	+	168.890i	−1.41848	+	0.840248i
$202$		0			0
$203$		−	200.893i		−	0.989620i
$204$		0			0
$205$	−105.895			−0.516559
$206$		0			0
$207$	72.4078	+	39.6725i	0.349796	+	0.191654i
$208$		0			0
$209$		−	228.879i		−	1.09512i
$210$		0			0
$211$	−58.1580			−0.275630			−0.137815	−	0.990458i	$-0.544008\pi$
$211$	−58.1580			−0.275630			−0.137815	+	0.990458i	$0.544008\pi$
$212$		0			0
$213$	23.8420	+	40.2492i	0.111934	+	0.188963i
$214$		0			0
$215$			32.3347i			0.150394i
$216$		0			0
$217$	−59.8947			−0.276012
$218$		0			0
$219$	227.004	−	134.468i	1.03655	−	0.614009i
$220$		0			0
$221$			303.870i			1.37498i
$222$		0			0
$223$	−99.3815			−0.445657			−0.222828	−	0.974858i	$-0.571529\pi$
$223$	−99.3815			−0.445657			−0.222828	+	0.974858i	$0.571529\pi$
$224$		0			0
$225$	−21.6228	+	39.4646i	−0.0961012	+	0.175398i
$226$		0			0
$227$			216.951i			0.955733i	0.878432	+	0.477867i	$0.158590\pi$
$227$			216.951i			0.955733i	−0.878432	+	0.477867i	$0.841410\pi$
$228$		0			0
$229$	−325.684			−1.42220			−0.711100	−	0.703090i	$-0.751803\pi$
$229$	−325.684			−1.42220			−0.711100	+	0.703090i	$0.751803\pi$
$230$		0			0
$231$	−97.1317	−	163.974i	−0.420483	−	0.709845i
$232$		0			0
$233$			51.7119i			0.221939i	0.993824	+	0.110970i	$0.0353957\pi$
$233$			51.7119i			0.221939i	−0.993824	+	0.110970i	$0.964604\pi$
$234$		0			0
$235$	102.566			0.436450
$236$		0			0
$237$	121.246	−	71.8209i	0.511585	−	0.303042i
$238$		0			0
$239$		−	410.047i		−	1.71568i	−0.513917	−	0.857840i	$-0.671806\pi$
$239$		−	410.047i		−	1.71568i	0.513917	−	0.857840i	$-0.328194\pi$
$240$		0			0
$241$	445.526			1.84866			0.924328	−	0.381599i	$-0.124627\pi$
$241$	445.526			1.84866			0.924328	+	0.381599i	$0.124627\pi$
$242$		0			0
$243$	−216.906	−	109.549i	−0.892616	−	0.450818i
$244$		0			0
$245$		−	15.7702i		−	0.0643683i
$246$		0			0
$247$	269.737			1.09205
$248$		0			0
$249$	−39.9737	−	67.4821i	−0.160537	−	0.271013i
$250$		0			0
$251$			237.364i			0.945675i	0.881150	+	0.472838i	$0.156770\pi$
$251$			237.364i			0.945675i	−0.881150	+	0.472838i	$0.843230\pi$
$252$		0			0
$253$	77.8420			0.307676
$254$		0			0
$255$	175.381	−	103.889i	0.687771	−	0.407407i
$256$		0			0
$257$			318.887i			1.24080i	0.784284	+	0.620402i	$0.213030\pi$
$257$			318.887i			1.24080i	−0.784284	+	0.620402i	$0.786970\pi$
$258$		0			0
$259$	−119.395			−0.460985
$260$		0			0
$261$	−211.789	−	116.040i	−0.811453	−	0.444598i
$262$		0			0
$263$		−	36.2300i		−	0.137757i	−0.997625	−	0.0688784i	$-0.978058\pi$
$263$		−	36.2300i		−	0.137757i	0.997625	−	0.0688784i	$-0.0219420\pi$
$264$		0			0
$265$	−67.9473			−0.256405
$266$		0			0
$267$	−92.9210	−	156.866i	−0.348019	−	0.587513i
$268$		0			0
$269$			528.041i			1.96298i	0.191518	+	0.981489i	$0.438659\pi$
$269$			528.041i			1.96298i	−0.191518	+	0.981489i	$0.561341\pi$
$270$		0			0
$271$	475.895			1.75607			0.878034	−	0.478597i	$-0.158855\pi$
$271$	475.895			1.75607			0.878034	+	0.478597i	$0.158855\pi$
$272$		0			0
$273$	193.246	−	114.471i	0.707859	−	0.419307i
$274$		0			0
$275$			42.4264i			0.154278i
$276$		0			0
$277$	−188.158			−0.679271			−0.339635	−	0.940557i	$-0.610304\pi$
$277$	−188.158			−0.679271			−0.339635	+	0.940557i	$0.610304\pi$
$278$		0			0
$279$	−34.5964	+	63.1434i	−0.124002	+	0.226320i
$280$		0			0
$281$			24.4322i			0.0869473i	0.999055	+	0.0434736i	$0.0138424\pi$
$281$			24.4322i			0.0869473i	−0.999055	+	0.0434736i	$0.986158\pi$
$282$		0			0
$283$	198.460			0.701274			0.350637	−	0.936511i	$-0.385965\pi$
$283$	198.460			0.701274			0.350637	+	0.936511i	$0.385965\pi$
$284$		0			0
$285$	−92.2192	−	155.681i	−0.323576	−	0.546250i
$286$		0			0
$287$		−	354.558i		−	1.23539i
$288$		0			0
$289$	−634.368			−2.19504
$290$		0			0
$291$	93.0569	−	55.1231i	0.319783	−	0.189427i
$292$		0			0
$293$			513.825i			1.75367i	0.480794	+	0.876834i	$0.340349\pi$
$293$			513.825i			1.75367i	−0.480794	+	0.876834i	$0.659651\pi$
$294$		0			0
$295$	53.8420			0.182515
$296$		0			0
$297$	−228.974	+	7.68507i	−0.770955	+	0.0258757i
$298$		0			0
$299$			91.7377i			0.306815i
$300$		0			0
$301$	−108.263			−0.359679
$302$		0			0
$303$	−73.6313	−	124.302i	−0.243008	−	0.410237i
$304$		0			0
$305$		−	120.630i		−	0.395508i
$306$		0			0
$307$	−11.3815			−0.0370733			−0.0185366	−	0.999828i	$-0.505901\pi$
$307$	−11.3815			−0.0370733			−0.0185366	+	0.999828i	$0.505901\pi$
$308$		0			0
$309$	−362.412	+	214.678i	−1.17285	+	0.694751i
$310$		0			0
$311$			518.756i			1.66802i	0.551746	+	0.834012i	$0.313962\pi$
$311$			518.756i			1.66802i	−0.551746	+	0.834012i	$0.686038\pi$
$312$		0			0
$313$	−46.3160			−0.147974			−0.0739872	−	0.997259i	$-0.523572\pi$
$313$	−46.3160			−0.147974			−0.0739872	+	0.997259i	$0.523572\pi$
$314$		0			0
$315$	−132.136	−	72.3977i	−0.419479	−	0.229834i
$316$		0			0
$317$		−	39.0957i		−	0.123330i	−0.998097	−	0.0616651i	$-0.980359\pi$
$317$		−	39.0957i		−	0.123330i	0.998097	−	0.0616651i	$-0.0196411\pi$
$318$		0			0
$319$	−227.684			−0.713743
$320$		0			0
$321$	65.9210	+	111.286i	0.205361	+	0.346684i
$322$		0			0
$323$			819.648i			2.53761i
$324$		0			0
$325$	−50.0000			−0.153846
$326$		0			0
$327$	−345.465	+	204.639i	−1.05647	+	0.625808i
$328$		0			0
$329$			343.412i			1.04381i
$330$		0			0
$331$	−445.421			−1.34568			−0.672841	−	0.739787i	$-0.734926\pi$
$331$	−445.421			−1.34568			−0.672841	+	0.739787i	$0.734926\pi$
$332$		0			0
$333$	−68.9651	+	125.871i	−0.207102	+	0.377991i
$334$		0			0
$335$			246.997i			0.737305i
$336$		0			0
$337$	325.684			0.966421			0.483211	−	0.875504i	$-0.339471\pi$
$337$	325.684			0.966421			0.483211	+	0.875504i	$0.339471\pi$
$338$		0			0
$339$	−12.0918	−	20.4130i	−0.0356691	−	0.0602153i
$340$		0			0
$341$			67.8823i			0.199068i
$342$		0			0
$343$	−314.053			−0.915605
$344$		0			0
$345$	52.9473	−	31.3638i	0.153471	−	0.0909097i
$346$		0			0
$347$		−	51.8236i		−	0.149348i	−0.997208	−	0.0746738i	$-0.976208\pi$
$347$		−	51.8236i		−	0.149348i	0.997208	−	0.0746738i	$-0.0237916\pi$
$348$		0			0
$349$	97.5787			0.279595			0.139798	−	0.990180i	$-0.455355\pi$
$349$	97.5787			0.279595			0.139798	+	0.990180i	$0.455355\pi$
$350$		0			0
$351$	−9.05694	−	269.848i	−0.0258033	−	0.768798i
$352$		0			0
$353$			569.797i			1.61416i	0.590445	+	0.807078i	$0.298952\pi$
$353$			569.797i			1.61416i	−0.590445	+	0.807078i	$0.701048\pi$
$354$		0			0
$355$	34.8683			0.0982206
$356$		0			0
$357$	347.842	+	587.215i	0.974347	+	1.64486i
$358$		0			0
$359$			274.283i			0.764019i	0.924158	+	0.382010i	$0.124768\pi$
$359$			274.283i			0.764019i	−0.924158	+	0.382010i	$0.875232\pi$
$360$		0			0
$361$	366.579			1.01545
$362$		0			0
$363$	126.476	−	74.9191i	0.348418	−	0.206389i
$364$		0			0
$365$		−	196.656i		−	0.538784i
$366$		0			0
$367$	−461.828			−1.25839			−0.629194	−	0.777248i	$-0.716615\pi$
$367$	−461.828			−1.25839			−0.629194	+	0.777248i	$0.716615\pi$
$368$		0			0
$369$	−373.789	−	204.800i	−1.01298	−	0.555014i
$370$		0			0
$371$		−	227.502i		−	0.613213i
$372$		0			0
$373$	491.947			1.31889			0.659447	−	0.751751i	$-0.270791\pi$
$373$	491.947			1.31889			0.659447	+	0.751751i	$0.270791\pi$
$374$		0			0
$375$	17.0943	+	28.8580i	0.0455848	+	0.0769547i
$376$		0			0
$377$		−	268.328i		−	0.711746i
$378$		0			0
$379$	−258.763			−0.682752			−0.341376	−	0.939927i	$-0.610893\pi$
$379$	−258.763			−0.682752			−0.341376	+	0.939927i	$0.610893\pi$
$380$		0			0
$381$	347.061	−	205.585i	0.910922	−	0.539593i
$382$		0			0
$383$			522.422i			1.36402i	0.731341	+	0.682012i	$0.238895\pi$
$383$			522.422i			1.36402i	−0.731341	+	0.682012i	$0.761105\pi$
$384$		0			0
$385$	−142.053			−0.368968
$386$		0			0
$387$	−62.5352	+	114.136i	−0.161590	+	0.294924i
$388$		0			0
$389$		−	610.847i		−	1.57030i	−0.619306	−	0.785150i	$-0.712586\pi$
$389$		−	610.847i		−	1.57030i	0.619306	−	0.785150i	$-0.287414\pi$
$390$		0			0
$391$	−278.763			−0.712949
$392$		0			0
$393$	336.974	+	568.867i	0.857439	+	1.44750i
$394$		0			0
$395$		−	105.036i		−	0.265915i
$396$		0			0
$397$	214.000			0.539043			0.269521	−	0.962994i	$-0.413135\pi$
$397$	214.000			0.539043			0.269521	+	0.962994i	$0.413135\pi$
$398$		0			0
$399$	521.254	−	308.770i	1.30640	−	0.773859i
$400$		0			0
$401$			454.557i			1.13356i	0.823869	+	0.566780i	$0.191811\pi$
$401$			454.557i			1.13356i	−0.823869	+	0.566780i	$0.808189\pi$
$402$		0			0
$403$	−80.0000			−0.198511
$404$		0			0
$405$	−152.649	+	97.4846i	−0.376911	+	0.240703i
$406$		0			0
$407$			135.318i			0.332476i
$408$		0			0
$409$	−573.842			−1.40304			−0.701518	−	0.712651i	$-0.747494\pi$
$409$	−573.842			−1.40304			−0.701518	+	0.712651i	$0.747494\pi$
$410$		0			0
$411$	−146.039	−	246.538i	−0.355326	−	0.599850i
$412$		0			0
$413$			180.274i			0.436500i
$414$		0			0
$415$	−58.4605			−0.140869
$416$		0			0
$417$	−198.272	+	117.448i	−0.475472	+	0.281650i
$418$		0			0
$419$			97.9159i			0.233690i	0.993150	+	0.116845i	$0.0372780\pi$
$419$			97.9159i			0.233690i	−0.993150	+	0.116845i	$0.962722\pi$
$420$		0			0
$421$	−717.315			−1.70384			−0.851918	−	0.523675i	$-0.824561\pi$
$421$	−717.315			−1.70384			−0.851918	+	0.523675i	$0.824561\pi$
$422$		0			0
$423$	362.039	+	198.362i	0.855885	+	0.468942i
$424$		0			0
$425$		−	151.935i		−	0.357494i
$426$		0			0
$427$	403.895			0.945889
$428$		0			0
$429$	−129.737	−	219.017i	−0.302416	−	0.510529i
$430$		0			0
$431$		−	293.077i		−	0.679994i	−0.940427	−	0.339997i	$-0.889574\pi$
$431$		−	293.077i		−	0.679994i	0.940427	−	0.339997i	$-0.110426\pi$
$432$		0			0
$433$	487.526			1.12593			0.562963	−	0.826482i	$-0.309661\pi$
$433$	487.526			1.12593			0.562963	+	0.826482i	$0.309661\pi$
$434$		0			0
$435$	−154.868	+	91.7377i	−0.356019	+	0.210891i
$436$		0			0
$437$			247.450i			0.566247i
$438$		0			0
$439$	−257.237			−0.585961			−0.292981	−	0.956118i	$-0.594647\pi$
$439$	−257.237			−0.585961			−0.292981	+	0.956118i	$0.594647\pi$
$440$		0			0
$441$	30.4997	−	55.6662i	0.0691602	−	0.126227i
$442$		0			0
$443$		−	293.096i		−	0.661615i	−0.943698	−	0.330808i	$-0.892679\pi$
$443$		−	293.096i		−	0.661615i	0.943698	−	0.330808i	$-0.107321\pi$
$444$		0			0
$445$	−135.895			−0.305381
$446$		0			0
$447$	−422.355	−	713.005i	−0.944866	−	1.59509i
$448$		0			0
$449$		−	585.614i		−	1.30426i	−0.758106	−	0.652132i	$-0.773875\pi$
$449$		−	585.614i		−	1.30426i	0.758106	−	0.652132i	$-0.226125\pi$
$450$		0			0
$451$	−401.842			−0.891002
$452$		0			0
$453$	−46.5964	+	27.6018i	−0.102862	+	0.0609312i
$454$		0			0
$455$		−	167.411i		−	0.367936i
$456$		0			0
$457$	−813.052			−1.77911			−0.889554	−	0.456831i	$-0.848984\pi$
$457$	−813.052			−1.77911			−0.889554	+	0.456831i	$0.848984\pi$
$458$		0			0
$459$	819.986	−	27.5213i	1.78646	−	0.0599593i
$460$		0			0
$461$		−	554.074i		−	1.20190i	−0.799288	−	0.600948i	$-0.794790\pi$
$461$		−	554.074i		−	1.20190i	0.799288	−	0.600948i	$-0.205210\pi$
$462$		0			0
$463$	449.723			0.971324			0.485662	−	0.874147i	$-0.338579\pi$
$463$	449.723			0.971324			0.485662	+	0.874147i	$0.338579\pi$
$464$		0			0
$465$	27.3509	+	46.1728i	0.0588191	+	0.0992964i
$466$		0			0
$467$		−	30.7221i		−	0.0657862i	−0.999459	−	0.0328931i	$-0.989528\pi$
$467$		−	30.7221i		−	0.0657862i	0.999459	−	0.0328931i	$-0.0104721\pi$
$468$		0			0
$469$	−826.999			−1.76332
$470$		0			0
$471$	−268.031	+	158.770i	−0.569067	+	0.337092i
$472$		0			0
$473$			122.701i			0.259411i
$474$		0			0
$475$	−134.868			−0.283933
$476$		0			0
$477$	−239.842	−	131.410i	−0.502813	−	0.275493i
$478$		0			0
$479$			735.242i			1.53495i	0.641078	+	0.767476i	$0.278488\pi$
$479$			735.242i			1.53495i	−0.641078	+	0.767476i	$0.721512\pi$
$480$		0			0
$481$	−159.473			−0.331545
$482$		0			0
$483$	105.013	+	177.279i	0.217418	+	0.367037i
$484$		0			0
$485$		−	80.6162i		−	0.166219i
$486$		0			0
$487$	92.6185			0.190182			0.0950909	−	0.995469i	$-0.469686\pi$
$487$	92.6185			0.190182			0.0950909	+	0.995469i	$0.469686\pi$
$488$		0			0
$489$	−29.3772	+	17.4019i	−0.0600761	+	0.0355866i
$490$		0			0
$491$		−	898.323i		−	1.82958i	−0.403933	−	0.914789i	$-0.632357\pi$
$491$		−	898.323i		−	1.82958i	0.403933	−	0.914789i	$-0.367643\pi$
$492$		0			0
$493$	815.368			1.65389
$494$		0			0
$495$	−82.0527	+	149.758i	−0.165763	+	0.302541i
$496$		0			0
$497$			116.747i			0.234903i
$498$		0			0
$499$	136.921			0.274391			0.137195	−	0.990544i	$-0.456191\pi$
$499$	136.921			0.274391			0.137195	+	0.990544i	$0.456191\pi$
$500$		0			0
$501$	385.710	+	651.143i	0.769881	+	1.29969i
$502$		0			0
$503$			443.077i			0.880868i	0.897785	+	0.440434i	$0.145175\pi$
$503$			443.077i			0.880868i	−0.897785	+	0.440434i	$0.854825\pi$
$504$		0			0
$505$	−107.684			−0.213236
$506$		0			0
$507$	−178.099	+	105.498i	−0.351279	+	0.208083i
$508$		0			0
$509$		−	213.062i		−	0.418590i	−0.977853	−	0.209295i	$-0.932883\pi$
$509$		−	213.062i		−	0.418590i	0.977853	−	0.209295i	$-0.0671168\pi$
$510$		0			0
$511$	658.447			1.28855
$512$		0			0
$513$	−24.4299	−	727.879i	−0.0476216	−	1.41887i
$514$		0			0
$515$			313.961i			0.609634i
$516$		0			0
$517$	389.210			0.752824
$518$		0			0
$519$	18.0662	+	30.4987i	0.0348096	+	0.0587643i
$520$		0			0
$521$			3.20085i			0.00614366i	0.999995	+	0.00307183i	$0.000977795\pi$
$521$			3.20085i			0.00614366i	−0.999995	+	0.00307183i	$0.999022\pi$
$522$		0			0
$523$	966.644			1.84827			0.924134	−	0.382069i	$-0.124788\pi$
$523$	966.644			1.84827			0.924134	+	0.382069i	$0.124788\pi$
$524$		0			0
$525$	−96.6228	+	57.2354i	−0.184043	+	0.109020i
$526$		0			0
$527$		−	243.096i		−	0.461282i
$528$		0			0
$529$	444.842			0.840911
$530$		0			0
$531$	190.053	+	104.130i	0.357915	+	0.196102i
$532$		0			0
$533$		−	473.575i		−	0.888509i
$534$		0			0
$535$	96.4078			0.180202
$536$		0			0
$537$	105.553	+	178.191i	0.196561	+	0.331827i
$538$		0			0
$539$		−	59.8439i		−	0.111028i
$540$		0			0
$541$	186.105			0.344002			0.172001	−	0.985097i	$-0.444977\pi$
$541$	186.105			0.344002			0.172001	+	0.985097i	$0.444977\pi$
$542$		0			0
$543$	489.601	−	290.019i	0.901659	−	0.534106i
$544$		0			0
$545$			299.280i			0.549137i
$546$		0			0
$547$	−309.434			−0.565693			−0.282847	−	0.959165i	$-0.591279\pi$
$547$	−309.434			−0.565693			−0.282847	+	0.959165i	$0.591279\pi$
$548$		0			0
$549$	233.298	−	425.802i	0.424951	−	0.775596i
$550$		0			0
$551$		−	723.779i		−	1.31357i
$552$		0			0
$553$	351.684			0.635957
$554$		0			0
$555$	54.5217	+	92.0417i	0.0982373	+	0.165841i
$556$		0			0
$557$		−	4.00106i		−	0.00718323i	−0.999994	−	0.00359161i	$-0.998857\pi$
$557$		−	4.00106i		−	0.00718323i	0.999994	−	0.00359161i	$-0.00114325\pi$
$558$		0			0
$559$	−144.605			−0.258685
$560$		0			0
$561$	665.526	−	394.230i	1.18632	−	0.702728i
$562$		0			0
$563$		−	166.970i		−	0.296572i	−0.988945	−	0.148286i	$-0.952624\pi$
$563$		−	166.970i		−	0.296572i	0.988945	−	0.148286i	$-0.0473756\pi$
$564$		0			0
$565$	−17.6840			−0.0312991
$566$		0			0
$567$	−326.399	−	511.102i	−0.575660	−	0.901414i
$568$		0			0
$569$		−	156.289i		−	0.274673i	−0.990524	−	0.137337i	$-0.956146\pi$
$569$		−	156.289i		−	0.274673i	0.990524	−	0.137337i	$-0.0438542\pi$
$570$		0			0
$571$	−144.105			−0.252374			−0.126187	−	0.992006i	$-0.540274\pi$
$571$	−144.105			−0.252374			−0.126187	+	0.992006i	$0.540274\pi$
$572$		0			0
$573$	166.211	+	280.591i	0.290071	+	0.489688i
$574$		0			0
$575$		−	45.8688i		−	0.0797719i
$576$		0			0
$577$	532.947			0.923651			0.461826	−	0.886971i	$-0.347195\pi$
$577$	532.947			0.923651			0.461826	+	0.886971i	$0.347195\pi$
$578$		0			0
$579$	−433.495	+	256.785i	−0.748697	+	0.443497i
$580$		0			0
$581$		−	195.738i		−	0.336899i
$582$		0			0
$583$	−257.842			−0.442268
$584$		0			0
$585$	−176.491	−	96.7000i	−0.301694	−	0.165299i
$586$		0			0
$587$		−	190.342i		−	0.324262i	−0.986769	−	0.162131i	$-0.948163\pi$
$587$		−	190.342i		−	0.324262i	0.986769	−	0.162131i	$-0.0518368\pi$
$588$		0			0
$589$	−215.789			−0.366366
$590$		0			0
$591$	262.460	+	443.077i	0.444096	+	0.749707i
$592$		0			0
$593$		−	345.719i		−	0.583001i	−0.956571	−	0.291500i	$-0.905846\pi$
$593$		−	345.719i		−	0.583001i	0.956571	−	0.291500i	$-0.0941544\pi$
$594$		0			0
$595$	508.710			0.854975
$596$		0			0
$597$	−90.5438	+	53.6344i	−0.151665	+	0.0898399i
$598$		0			0
$599$		−	704.055i		−	1.17538i	−0.809085	−	0.587692i	$-0.800037\pi$
$599$		−	704.055i		−	1.17538i	0.809085	−	0.587692i	$-0.199963\pi$
$600$		0			0
$601$	338.474			0.563185			0.281592	−	0.959534i	$-0.409137\pi$
$601$	338.474			0.563185			0.281592	+	0.959534i	$0.409137\pi$
$602$		0			0
$603$	−477.693	+	871.856i	−0.792193	+	1.44586i
$604$		0			0
$605$		−	109.567i		−	0.181103i
$606$		0			0
$607$	816.513			1.34516			0.672581	−	0.740024i	$-0.265186\pi$
$607$	816.513			1.34516			0.672581	+	0.740024i	$0.265186\pi$
$608$		0			0
$609$	−307.157	−	518.532i	−0.504363	−	0.851449i
$610$		0			0
$611$			458.688i			0.750717i
$612$		0			0
$613$	229.263			0.374001			0.187001	−	0.982360i	$-0.440123\pi$
$613$	229.263			0.374001			0.187001	+	0.982360i	$0.440123\pi$
$614$		0			0
$615$	−273.329	+	161.909i	−0.444437	+	0.263266i
$616$		0			0
$617$		−	1072.25i		−	1.73785i	−0.494945	−	0.868924i	$-0.664812\pi$
$617$		−	1072.25i		−	1.73785i	0.494945	−	0.868924i	$-0.335188\pi$
$618$		0			0
$619$	−80.7103			−0.130388			−0.0651941	−	0.997873i	$-0.520767\pi$
$619$	−80.7103			−0.130388			−0.0651941	+	0.997873i	$0.520767\pi$
$620$		0			0
$621$	247.552	−	8.30863i	0.398635	−	0.0133794i
$622$		0			0
$623$		−	455.004i		−	0.730344i
$624$		0			0
$625$	25.0000			0.0400000
$626$		0			0
$627$	−349.947	−	590.769i	−0.558130	−	0.942215i
$628$		0			0
$629$		−	484.591i		−	0.770415i
$630$		0			0
$631$	−492.894			−0.781131			−0.390566	−	0.920575i	$-0.627721\pi$
$631$	−492.894			−0.781131			−0.390566	+	0.920575i	$0.627721\pi$
$632$		0			0
$633$	−150.114	+	88.9213i	−0.237147	+	0.140476i
$634$		0			0
$635$		−	300.663i		−	0.473485i
$636$		0			0
$637$	70.5267			0.110717
$638$		0			0
$639$	123.079	+	67.4353i	0.192612	+	0.105533i
$640$		0			0
$641$			65.4816i			0.102155i	0.998695	+	0.0510777i	$0.0162656\pi$
$641$			65.4816i			0.102155i	−0.998695	+	0.0510777i	$0.983734\pi$
$642$		0			0
$643$	−428.619			−0.666592			−0.333296	−	0.942822i	$-0.608161\pi$
$643$	−428.619			−0.666592			−0.333296	+	0.942822i	$0.608161\pi$
$644$		0			0
$645$	49.4384	+	83.4602i	0.0766487	+	0.129396i
$646$		0			0
$647$			462.801i			0.715303i	0.933855	+	0.357652i	$0.116422\pi$
$647$			462.801i			0.715303i	−0.933855	+	0.357652i	$0.883578\pi$
$648$		0			0
$649$	204.316			0.314817
$650$		0			0
$651$	−154.596	+	91.5766i	−0.237475	+	0.140671i
$652$		0			0
$653$			425.064i			0.650941i	0.945552	+	0.325470i	$0.105523\pi$
$653$			425.064i			0.650941i	−0.945552	+	0.325470i	$0.894477\pi$
$654$		0			0
$655$	492.816			0.752390
$656$		0			0
$657$	380.333	−	694.161i	0.578894	−	1.05656i
$658$		0			0
$659$			182.769i			0.277343i	0.990338	+	0.138671i	$0.0442831\pi$
$659$			182.769i			0.277343i	−0.990338	+	0.138671i	$0.955717\pi$
$660$		0			0
$661$	482.053			0.729278			0.364639	−	0.931149i	$-0.381192\pi$
$661$	482.053			0.729278			0.364639	+	0.931149i	$0.381192\pi$
$662$		0			0
$663$	464.605	+	784.330i	0.700762	+	1.18300i
$664$		0			0
$665$		−	451.568i		−	0.679050i
$666$		0			0
$667$	246.158			0.369052
$668$		0			0
$669$	−256.517	+	151.950i	−0.383434	+	0.227131i
$670$		0			0
$671$		−	457.758i		−	0.682203i
$672$		0			0
$673$	184.579			0.274264			0.137132	−	0.990553i	$-0.456212\pi$
$673$	184.579			0.274264			0.137132	+	0.990553i	$0.456212\pi$
$674$		0			0
$675$	4.52847	+	134.924i	0.00670885	+	0.199887i
$676$		0			0
$677$		−	1065.85i		−	1.57437i	−0.616715	−	0.787187i	$-0.711537\pi$
$677$		−	1065.85i		−	1.57437i	0.616715	−	0.787187i	$-0.288463\pi$
$678$		0			0
$679$	269.920			0.397526
$680$		0			0
$681$	331.710	+	559.982i	0.487093	+	0.822293i
$682$		0			0
$683$			788.926i			1.15509i	0.816359	+	0.577545i	$0.195989\pi$
$683$			788.926i			1.15509i	−0.816359	+	0.577545i	$0.804011\pi$
$684$		0			0
$685$	−213.579			−0.311794
$686$		0			0
$687$	−840.636	+	497.958i	−1.22363	+	0.724830i
$688$		0			0
$689$		−	303.870i		−	0.441030i
$690$		0			0
$691$	932.000			1.34877			0.674385	−	0.738380i	$-0.264409\pi$
$691$	932.000			1.34877			0.674385	+	0.738380i	$0.264409\pi$
$692$		0			0
$693$	−501.421	−	274.730i	−0.723551	−	0.396436i
$694$		0			0
$695$			171.765i			0.247144i
$696$		0			0
$697$	1439.05			2.06464
$698$		0			0
$699$	79.0655	+	133.476i	0.113112	+	0.190952i
$700$		0			0
$701$			1352.75i			1.92974i	0.262721	+	0.964872i	$0.415380\pi$
$701$			1352.75i			1.92974i	−0.262721	+	0.964872i	$0.584620\pi$
$702$		0			0
$703$	−430.158			−0.611889
$704$		0			0
$705$	264.737	−	156.819i	0.375513	−	0.222439i
$706$		0			0
$707$		−	360.549i		−	0.509970i
$708$		0			0
$709$	269.473			0.380075			0.190038	−	0.981777i	$-0.439139\pi$
$709$	269.473			0.380075			0.190038	+	0.981777i	$0.439139\pi$
$710$		0			0
$711$	203.140	−	370.759i	0.285711	−	0.521462i
$712$		0			0
$713$		−	73.3901i		−	0.102931i
$714$		0			0
$715$	−189.737			−0.265366
$716$		0			0
$717$	−626.947	−	1058.39i	−0.874403	−	1.47614i
$718$		0			0
$719$		−	537.103i		−	0.747014i	−0.927627	−	0.373507i	$-0.878155\pi$
$719$		−	537.103i		−	0.747014i	0.927627	−	0.373507i	$-0.121845\pi$
$720$		0			0
$721$	−1051.21			−1.45799
$722$		0			0
$723$	1149.96	−	681.192i	1.59055	−	0.942174i
$724$		0			0
$725$			134.164i			0.185054i
$726$		0			0
$727$	1117.83			1.53759			0.768795	−	0.639495i	$-0.220856\pi$
$727$	1117.83			1.53759			0.768795	+	0.639495i	$0.220856\pi$
$728$		0			0
$729$	−727.359	+	48.8800i	−0.997750	+	0.0670507i
$730$		0			0
$731$		−	439.411i		−	0.601109i
$732$		0			0
$733$	−7.52599			−0.0102674			−0.00513369	−	0.999987i	$-0.501634\pi$
$733$	−7.52599			−0.0102674			−0.00513369	+	0.999987i	$0.501634\pi$
$734$		0			0
$735$	−24.1121	−	40.7052i	−0.0328056	−	0.0553812i
$736$		0			0
$737$			937.288i			1.27176i
$738$		0			0
$739$	−823.079			−1.11377			−0.556887	−	0.830588i	$-0.688004\pi$
$739$	−823.079			−1.11377			−0.556887	+	0.830588i	$0.688004\pi$
$740$		0			0
$741$	696.228	−	412.417i	0.939579	−	0.556568i
$742$		0			0
$743$		−	3.21898i		−	0.00433241i	−0.999998	−	0.00216620i	$-0.999310\pi$
$743$		−	3.21898i		−	0.00433241i	0.999998	−	0.00216620i	$-0.000689524\pi$
$744$		0			0
$745$	−617.684			−0.829106
$746$		0			0
$747$	−206.355	−	113.063i	−0.276245	−	0.151356i
$748$		0			0
$749$			322.794i			0.430967i
$750$		0			0
$751$	−1185.63			−1.57874			−0.789368	−	0.613920i	$-0.789592\pi$
$751$	−1185.63			−1.57874			−0.789368	+	0.613920i	$0.789592\pi$
$752$		0			0
$753$	362.921	+	612.671i	0.481967	+	0.813639i
$754$		0			0
$755$			40.3670i			0.0534662i
$756$		0			0
$757$	863.315			1.14044			0.570221	−	0.821491i	$-0.306857\pi$
$757$	863.315			1.14044			0.570221	+	0.821491i	$0.306857\pi$
$758$		0			0
$759$	200.921	−	119.017i	0.264718	−	0.156808i
$760$		0			0
$761$		−	570.597i		−	0.749800i	−0.927065	−	0.374900i	$-0.877677\pi$
$761$		−	570.597i		−	0.749800i	0.927065	−	0.374900i	$-0.122323\pi$
$762$		0			0
$763$	−1002.05			−1.31331
$764$		0			0
$765$	293.842	−	536.303i	0.384107	−	0.701050i
$766$		0			0
$767$			240.789i			0.313936i
$768$		0			0
$769$	−741.684			−0.964479			−0.482239	−	0.876040i	$-0.660176\pi$
$769$	−741.684			−0.964479			−0.482239	+	0.876040i	$0.660176\pi$
$770$		0			0
$771$	487.565	+	823.090i	0.632380	+	1.06756i
$772$		0			0
$773$		−	623.203i		−	0.806214i	−0.915153	−	0.403107i	$-0.867930\pi$
$773$		−	623.203i		−	0.806214i	0.915153	−	0.403107i	$-0.132070\pi$
$774$		0			0
$775$	40.0000			0.0516129
$776$		0			0
$777$	−308.175	+	182.550i	−0.396622	+	0.234943i
$778$		0			0
$779$		−	1277.41i		−	1.63980i
$780$		0			0
$781$	132.316			0.169419
$782$		0			0
$783$	−724.078	+	24.3023i	−0.924749	+	0.0310375i
$784$		0			0
$785$			232.198i			0.295793i
$786$		0			0
$787$	335.303			0.426052			0.213026	−	0.977046i	$-0.431668\pi$
$787$	335.303			0.426052			0.213026	+	0.977046i	$0.431668\pi$
$788$		0			0
$789$	−55.3943	−	93.5147i	−0.0702083	−	0.118523i
$790$		0			0
$791$		−	59.2098i		−	0.0748543i
$792$		0			0
$793$	539.473			0.680294
$794$		0			0
$795$	−175.381	+	103.889i	−0.220606	+	0.130678i
$796$		0			0
$797$		−	550.520i		−	0.690740i	−0.938467	−	0.345370i	$-0.887753\pi$
$797$		−	550.520i		−	0.690740i	0.938467	−	0.345370i	$-0.112247\pi$
$798$		0			0
$799$	−1393.81			−1.74445
$800$		0			0
$801$	−479.684	−	262.820i	−0.598856	−	0.328115i
$802$		0			0
$803$		−	746.258i		−	0.929337i
$804$		0			0
$805$	153.579			0.190781
$806$		0			0
$807$	807.354	+	1362.95i	1.00044	+	1.68891i
$808$		0			0
$809$		−	560.288i		−	0.692569i	−0.938130	−	0.346284i	$-0.887443\pi$
$809$		−	560.288i		−	0.692569i	0.938130	−	0.346284i	$-0.112557\pi$
$810$		0			0
$811$	−237.842			−0.293270			−0.146635	−	0.989191i	$-0.546844\pi$
$811$	−237.842			−0.293270			−0.146635	+	0.989191i	$0.546844\pi$
$812$		0			0
$813$	1228.35	−	727.624i	1.51089	−	0.894987i
$814$		0			0
$815$			25.4498i			0.0312267i
$816$		0			0
$817$	−390.053			−0.477421
$818$		0			0
$819$	323.772	−	590.930i	0.395326	−	0.721526i
$820$		0			0
$821$		−	65.4816i		−	0.0797584i	−0.999205	−	0.0398792i	$-0.987303\pi$
$821$		−	65.4816i		−	0.0797584i	0.999205	−	0.0398792i	$-0.0126973\pi$
$822$		0			0
$823$	−521.512			−0.633673			−0.316836	−	0.948480i	$-0.602621\pi$
$823$	−521.512			−0.633673			−0.316836	+	0.948480i	$0.602621\pi$
$824$		0			0
$825$	64.8683	+	109.508i	0.0786283	+	0.132738i
$826$		0			0
$827$			987.512i			1.19409i	0.802208	+	0.597045i	$0.203658\pi$
$827$			987.512i			1.19409i	−0.802208	+	0.597045i	$0.796342\pi$
$828$		0			0
$829$	−333.631			−0.402450			−0.201225	−	0.979545i	$-0.564492\pi$
$829$	−333.631			−0.402450			−0.201225	+	0.979545i	$0.564492\pi$
$830$		0			0
$831$	−485.662	+	287.686i	−0.584431	+	0.346193i
$832$		0			0
$833$			214.309i			0.257274i
$834$		0			0
$835$	564.092			0.675559
$836$		0			0
$837$	7.24555	+	215.878i	0.00865657	+	0.257919i
$838$		0			0
$839$			129.363i			0.154187i	0.997024	+	0.0770934i	$0.0245640\pi$
$839$			129.363i			0.154187i	−0.997024	+	0.0770934i	$0.975436\pi$
$840$		0			0
$841$	121.000			0.143876
$842$		0			0
$843$	37.3559	+	63.0629i	0.0443130	+	0.0748077i
$844$		0			0
$845$			154.289i			0.182590i
$846$		0			0
$847$	366.855			0.433123
$848$		0			0
$849$	512.254	−	303.438i	0.603362	−	0.357407i
$850$		0			0
$851$		−	146.297i		−	0.171912i
$852$		0			0
$853$	−1080.42			−1.26661			−0.633306	−	0.773902i	$-0.718303\pi$
$853$	−1080.42			−1.26661			−0.633306	+	0.773902i	$0.718303\pi$
$854$		0			0
$855$	−476.061	−	260.835i	−0.556797	−	0.305071i
$856$		0			0
$857$			702.548i			0.819776i	0.912136	+	0.409888i	$0.134432\pi$
$857$			702.548i			0.819776i	−0.912136	+	0.409888i	$0.865568\pi$
$858$		0			0
$859$	−281.132			−0.327278			−0.163639	−	0.986520i	$-0.552323\pi$
$859$	−281.132			−0.327278			−0.163639	+	0.986520i	$0.552323\pi$
$860$		0			0
$861$	−542.105	−	915.163i	−0.629623	−	1.06291i
$862$		0			0
$863$		−	419.221i		−	0.485772i	−0.970055	−	0.242886i	$-0.921906\pi$
$863$		−	419.221i		−	0.485772i	0.970055	−	0.242886i	$-0.0780941\pi$
$864$		0			0
$865$	26.4213			0.0305449
$866$		0			0
$867$	−1637.39	+	969.924i	−1.88857	+	1.11871i
$868$		0			0
$869$		−	398.585i		−	0.458671i
$870$		0			0
$871$	−1104.60			−1.26820
$872$		0			0
$873$	155.912	−	284.561i	0.178593	−	0.325958i
$874$		0			0
$875$			83.7053i			0.0956632i
$876$		0			0
$877$	−1079.42			−1.23081			−0.615405	−	0.788211i	$-0.711008\pi$
$877$	−1079.42			−1.23081			−0.615405	+	0.788211i	$0.711008\pi$
$878$		0			0
$879$	785.618	+	1326.25i	0.893763	+	1.50882i
$880$		0			0
$881$		−	748.212i		−	0.849275i	−0.905363	−	0.424638i	$-0.860401\pi$
$881$		−	748.212i		−	0.849275i	0.905363	−	0.424638i	$-0.139599\pi$
$882$		0			0
$883$	−875.749			−0.991788			−0.495894	−	0.868383i	$-0.665160\pi$
$883$	−875.749			−0.991788			−0.495894	+	0.868383i	$0.665160\pi$
$884$		0			0
$885$	138.974	−	82.3223i	0.157032	−	0.0930196i
$886$		0			0
$887$		−	1015.05i		−	1.14436i	−0.820127	−	0.572182i	$-0.806097\pi$
$887$		−	1015.05i		−	1.14436i	0.820127	−	0.572182i	$-0.193903\pi$
$888$		0			0
$889$	1006.68			1.13238
$890$		0			0
$891$	−579.263	+	369.928i	−0.650126	+	0.415183i
$892$		0			0
$893$			1237.25i			1.38550i
$894$		0			0
$895$	154.369			0.172479
$896$		0			0
$897$	140.263	+	236.788i	0.156369	+	0.263977i
$898$		0			0
$899$			214.663i			0.238779i
$900$		0			0
$901$	923.368			1.02483
$902$		0			0
$903$	−279.443	+	165.530i	−0.309460	+	0.183312i
$904$		0			0
$905$		−	424.146i		−	0.468670i
$906$		0			0
$907$	1504.70			1.65898			0.829491	−	0.558520i	$-0.188631\pi$
$907$	1504.70			1.65898			0.829491	+	0.558520i	$0.188631\pi$
$908$		0			0
$909$	−380.105	−	208.261i	−0.418158	−	0.229110i
$910$		0			0
$911$			1002.19i			1.10010i	0.835131	+	0.550051i	$0.185392\pi$
$911$			1002.19i			1.10010i	−0.835131	+	0.550051i	$0.814608\pi$
$912$		0			0
$913$	−221.842			−0.242981
$914$		0			0
$915$	−184.438	−	311.363i	−0.201572	−	0.340287i
$916$		0			0
$917$			1650.05i			1.79940i
$918$		0			0
$919$	780.289			0.849063			0.424532	−	0.905413i	$-0.360439\pi$
$919$	780.289			0.849063			0.424532	+	0.905413i	$0.360439\pi$
$920$		0			0
$921$	−29.3772	+	17.4019i	−0.0318971	+	0.0188945i
$922$		0			0
$923$			155.936i			0.168945i
$924$		0			0
$925$	79.7367			0.0862018
$926$		0			0
$927$	−607.201	+	1108.23i	−0.655018	+	1.19550i
$928$		0			0
$929$			1093.84i			1.17744i	0.808339	+	0.588718i	$0.200367\pi$
$929$			1093.84i			1.17744i	−0.808339	+	0.588718i	$0.799633\pi$
$930$		0			0
$931$	190.236			0.204335
$932$		0			0
$933$	793.157	+	1338.98i	0.850115	+	1.43513i
$934$		0			0
$935$		−	576.552i		−	0.616633i
$936$		0			0
$937$	−407.947			−0.435376			−0.217688	−	0.976018i	$-0.569852\pi$
$937$	−407.947			−0.435376			−0.217688	+	0.976018i	$0.569852\pi$
$938$		0			0
$939$	−119.548	+	70.8154i	−0.127314	+	0.0754157i
$940$		0			0
$941$		−	671.008i		−	0.713079i	−0.934280	−	0.356540i	$-0.883956\pi$
$941$		−	671.008i		−	0.713079i	0.934280	−	0.356540i	$-0.116044\pi$
$942$		0			0
$943$	434.447			0.460707
$944$		0			0
$945$	−451.754	+	15.1623i	−0.478047	+	0.0160447i
$946$		0			0
$947$		−	1608.13i		−	1.69813i	−0.528290	−	0.849064i	$-0.677167\pi$
$947$		−	1608.13i		−	1.69813i	0.528290	−	0.849064i	$-0.322833\pi$
$948$		0			0
$949$	879.473			0.926737
$950$		0			0
$951$	−59.7758	−	100.911i	−0.0628557	−	0.106111i
$952$		0			0
$953$		−	695.440i		−	0.729737i	−0.931059	−	0.364869i	$-0.881114\pi$
$953$		−	695.440i		−	0.729737i	0.931059	−	0.364869i	$-0.118886\pi$
$954$		0			0
$955$	243.079			0.254533
$956$		0			0
$957$	−587.684	+	348.120i	−0.614090	+	0.363762i
$958$		0			0
$959$		−	715.107i		−	0.745680i
$960$		0			0
$961$	−897.000			−0.933403
$962$		0			0
$963$	340.302	+	186.453i	0.353377	+	0.193617i
$964$		0			0
$965$			375.542i			0.389162i
$966$		0			0
$967$	1030.07			1.06522			0.532609	−	0.846361i	$-0.321212\pi$
$967$	1030.07			1.06522			0.532609	+	0.846361i	$0.321212\pi$
$968$		0			0
$969$	1253.21	+	2115.63i	1.29330	+	2.18331i
$970$		0			0
$971$			1165.24i			1.20004i	0.799986	+	0.600019i	$0.204840\pi$
$971$			1165.24i			1.20004i	−0.799986	+	0.600019i	$0.795160\pi$
$972$		0			0
$973$	−575.106			−0.591065
$974$		0			0
$975$	−129.057	+	76.4481i	−0.132366	+	0.0784083i
$976$		0			0
$977$			726.440i			0.743541i	0.928325	+	0.371771i	$0.121249\pi$
$977$			726.440i			0.743541i	−0.928325	+	0.371771i	$0.878751\pi$
$978$		0			0
$979$	−515.684			−0.526746
$980$		0			0
$981$	−578.807	+	1056.40i	−0.590017	+	1.07686i
$982$		0			0
$983$		−	1024.21i		−	1.04192i	−0.853581	−	0.520960i	$-0.825574\pi$
$983$		−	1024.21i		−	1.04192i	0.853581	−	0.520960i	$-0.174426\pi$
$984$		0			0
$985$	383.842			0.389687
$986$		0			0
$987$	525.064	+	886.395i	0.531980	+	0.898070i
$988$		0			0
$989$		−	132.657i		−	0.134133i
$990$		0			0
$991$	1797.89			1.81422			0.907111	−	0.420892i	$-0.138283\pi$
$991$	1797.89			1.81422			0.907111	+	0.420892i	$0.138283\pi$
$992$		0			0
$993$	−1149.69	+	681.031i	−1.15780	+	0.685832i
$994$		0			0
$995$			78.4390i			0.0788332i
$996$		0			0
$997$	−901.368			−0.904080			−0.452040	−	0.891998i	$-0.649304\pi$
$997$	−901.368			−0.904080			−0.452040	+	0.891998i	$0.649304\pi$
$998$		0			0
$999$	14.4434	+	430.336i	0.0144579	+	0.430766i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.3.l.f.641.3		4
3.2	odd	2	inner	960.3.l.f.641.4		4
4.3	odd	2		960.3.l.e.641.2		4
8.3	odd	2		30.3.d.a.11.4	yes	4
8.5	even	2		240.3.l.c.161.2		4
12.11	even	2		960.3.l.e.641.1		4
24.5	odd	2		240.3.l.c.161.1		4
24.11	even	2		30.3.d.a.11.2	✓	4
40.3	even	4		150.3.b.b.149.8		8
40.13	odd	4		1200.3.c.k.449.3		8
40.19	odd	2		150.3.d.c.101.1		4
40.27	even	4		150.3.b.b.149.1		8
40.29	even	2		1200.3.l.u.401.3		4
40.37	odd	4		1200.3.c.k.449.6		8
72.11	even	6		810.3.h.a.701.2		8
72.43	odd	6		810.3.h.a.701.3		8
72.59	even	6		810.3.h.a.431.3		8
72.67	odd	6		810.3.h.a.431.2		8
120.29	odd	2		1200.3.l.u.401.4		4
120.53	even	4		1200.3.c.k.449.5		8
120.59	even	2		150.3.d.c.101.3		4
120.77	even	4		1200.3.c.k.449.4		8
120.83	odd	4		150.3.b.b.149.2		8
120.107	odd	4		150.3.b.b.149.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.3.d.a.11.2	✓	4	24.11	even	2
30.3.d.a.11.4	yes	4	8.3	odd	2
150.3.b.b.149.1		8	40.27	even	4
150.3.b.b.149.2		8	120.83	odd	4
150.3.b.b.149.7		8	120.107	odd	4
150.3.b.b.149.8		8	40.3	even	4
150.3.d.c.101.1		4	40.19	odd	2
150.3.d.c.101.3		4	120.59	even	2
240.3.l.c.161.1		4	24.5	odd	2
240.3.l.c.161.2		4	8.5	even	2
810.3.h.a.431.2		8	72.67	odd	6
810.3.h.a.431.3		8	72.59	even	6
810.3.h.a.701.2		8	72.11	even	6
810.3.h.a.701.3		8	72.43	odd	6
960.3.l.e.641.1		4	12.11	even	2
960.3.l.e.641.2		4	4.3	odd	2
960.3.l.f.641.3		4	1.1	even	1	trivial
960.3.l.f.641.4		4	3.2	odd	2	inner
1200.3.c.k.449.3		8	40.13	odd	4
1200.3.c.k.449.4		8	120.77	even	4
1200.3.c.k.449.5		8	120.53	even	4
1200.3.c.k.449.6		8	40.37	odd	4
1200.3.l.u.401.3		4	40.29	even	2
1200.3.l.u.401.4		4	120.29	odd	2

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:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	960.l (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.58114 - 1.52896i) q^{3} -2.23607i q^{5} +7.48683 q^{7} +(4.32456 - 7.89292i) q^{9} +O(q^{10})\)	\(q+(2.58114 - 1.52896i) q^{3} -2.23607i q^{5} +7.48683 q^{7} +(4.32456 - 7.89292i) q^{9} -8.48528i q^{11} +10.0000 q^{13} +(-3.41886 - 5.77160i) q^{15} +30.3870i q^{17} +26.9737 q^{19} +(19.3246 - 11.4471i) q^{21} +9.17377i q^{23} -5.00000 q^{25} +(-0.905694 - 26.9848i) q^{27} -26.8328i q^{29} -8.00000 q^{31} +(-12.9737 - 21.9017i) q^{33} -16.7411i q^{35} -15.9473 q^{37} +(25.8114 - 15.2896i) q^{39} -47.3575i q^{41} -14.4605 q^{43} +(-17.6491 - 9.67000i) q^{45} +45.8688i q^{47} +7.05267 q^{49} +(46.4605 + 78.4330i) q^{51} -30.3870i q^{53} -18.9737 q^{55} +(69.6228 - 41.2417i) q^{57} +24.0789i q^{59} +53.9473 q^{61} +(32.3772 - 59.0930i) q^{63} -22.3607i q^{65} -110.460 q^{67} +(14.0263 + 23.6788i) q^{69} +15.5936i q^{71} +87.9473 q^{73} +(-12.9057 + 7.64481i) q^{75} -63.5279i q^{77} +46.9737 q^{79} +(-43.5964 - 68.2668i) q^{81} -26.1443i q^{83} +67.9473 q^{85} +(-41.0263 - 69.2592i) q^{87} -60.7739i q^{89} +74.8683 q^{91} +(-20.6491 + 12.2317i) q^{93} -60.3150i q^{95} +36.0527 q^{97} +(-66.9737 - 36.6951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 8 q^{7} - 8 q^{9}+O(q^{10}) \) 4 * q + 4 * q^3 - 8 * q^7 - 8 * q^9	\( 4 q + 4 q^{3} - 8 q^{7} - 8 q^{9} + 40 q^{13} - 20 q^{15} + 32 q^{19} + 52 q^{21} - 20 q^{25} + 28 q^{27} - 32 q^{31} + 24 q^{33} + 88 q^{37} + 40 q^{39} + 56 q^{43} - 20 q^{45} + 180 q^{49} + 72 q^{51} + 152 q^{57} + 64 q^{61} + 256 q^{63} - 328 q^{67} + 132 q^{69} + 200 q^{73} - 20 q^{75} + 112 q^{79} + 28 q^{81} + 120 q^{85} - 240 q^{87} - 80 q^{91} - 32 q^{93} + 296 q^{97} - 192 q^{99}+O(q^{100}) \) 4 * q + 4 * q^3 - 8 * q^7 - 8 * q^9 + 40 * q^13 - 20 * q^15 + 32 * q^19 + 52 * q^21 - 20 * q^25 + 28 * q^27 - 32 * q^31 + 24 * q^33 + 88 * q^37 + 40 * q^39 + 56 * q^43 - 20 * q^45 + 180 * q^49 + 72 * q^51 + 152 * q^57 + 64 * q^61 + 256 * q^63 - 328 * q^67 + 132 * q^69 + 200 * q^73 - 20 * q^75 + 112 * q^79 + 28 * q^81 + 120 * q^85 - 240 * q^87 - 80 * q^91 - 32 * q^93 + 296 * q^97 - 192 * q^99

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