LMFDB - Embedded newform 384.6.f.e.191.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,6,Mod(191,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("384.191");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	384.f (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$61.5873868082$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 5192x^{16} + 8441320x^{12} + 4098006217x^{8} + 8949568544x^{4} + 8386816 $ x^20 + 5192x^16 + 8441320x^12 + 4098006217x^8 + 8949568544x^4 + 8386816
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{87}\cdot 3^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			191.2
Root			$-3.85040 + 3.85040i$ of defining polynomial
Character	$\chi$	$=$	384.191
Dual form			384.6.f.e.191.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-15.4669 + 1.94284i) q^{3} +101.098 q^{5} -200.335i q^{7} +(235.451 - 60.0993i) q^{9} +O(q^{10})$	\(q+(-15.4669 + 1.94284i) q^{3} +101.098 q^{5} -200.335i q^{7} +(235.451 - 60.0993i) q^{9} +350.184i q^{11} +744.475i q^{13} +(-1563.68 + 196.417i) q^{15} +1441.83i q^{17} +1312.68 q^{19} +(389.217 + 3098.56i) q^{21} -2040.14 q^{23} +7095.82 q^{25} +(-3524.93 + 1386.99i) q^{27} -3781.90 q^{29} +1425.86i q^{31} +(-680.350 - 5416.27i) q^{33} -20253.4i q^{35} +2611.15i q^{37} +(-1446.39 - 11514.7i) q^{39} +10839.5i q^{41} +16147.4 q^{43} +(23803.6 - 6075.93i) q^{45} -3411.56 q^{47} -23326.9 q^{49} +(-2801.24 - 22300.6i) q^{51} -539.647 q^{53} +35402.9i q^{55} +(-20303.1 + 2550.32i) q^{57} +33786.7i q^{59} -50481.9i q^{61} +(-12040.0 - 47168.9i) q^{63} +75265.0i q^{65} +15700.1 q^{67} +(31554.7 - 3963.66i) q^{69} -36459.2 q^{71} -37025.8 q^{73} +(-109750. + 13786.0i) q^{75} +70154.0 q^{77} +33204.8i q^{79} +(51825.1 - 28300.9i) q^{81} +75829.2i q^{83} +145766. i q^{85} +(58494.3 - 7347.61i) q^{87} +9734.56i q^{89} +149144. q^{91} +(-2770.21 - 22053.6i) q^{93} +132709. q^{95} +115120. q^{97} +(21045.8 + 82451.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 44 q^{9}+O(q^{10}) $ 20 * q - 44 * q^9	$ 20 q - 44 q^{9} - 3568 q^{15} + 6112 q^{23} + 15228 q^{25} + 7592 q^{33} - 2800 q^{39} + 26112 q^{47} - 81044 q^{49} - 89296 q^{57} - 14816 q^{63} - 72224 q^{71} - 61256 q^{73} + 89588 q^{81} - 145648 q^{87} + 385504 q^{95} + 92808 q^{97}+O(q^{100}) $ 20 * q - 44 * q^9 - 3568 * q^15 + 6112 * q^23 + 15228 * q^25 + 7592 * q^33 - 2800 * q^39 + 26112 * q^47 - 81044 * q^49 - 89296 * q^57 - 14816 * q^63 - 72224 * q^71 - 61256 * q^73 + 89588 * q^81 - 145648 * q^87 + 385504 * q^95 + 92808 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$-1$	$-1$	$-1$

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
$3$	−15.4669	+	1.94284i	−0.992203	+	0.124633i
$3$	−15.4669	+	1.94284i	−0.992203	+	0.124633i
$4$		0			0
$5$	101.098			1.80850			0.904249	−	0.427006i	$-0.140432\pi$
$5$	101.098			1.80850			0.904249	+	0.427006i	$0.140432\pi$
$6$		0			0
$7$		−	200.335i		−	1.54529i	−0.634837	−	0.772646i	$-0.718933\pi$
$7$		−	200.335i		−	1.54529i	0.634837	−	0.772646i	$-0.281067\pi$
$8$		0			0
$9$	235.451	−	60.0993i	0.968933	−	0.247322i
$10$		0			0
$11$			350.184i			0.872599i	0.899802	+	0.436299i	$0.143711\pi$
$11$			350.184i			0.872599i	−0.899802	+	0.436299i	$0.856289\pi$
$12$		0			0
$13$			744.475i			1.22178i	0.791717	+	0.610888i	$0.209188\pi$
$13$			744.475i			1.22178i	−0.791717	+	0.610888i	$0.790812\pi$
$14$		0			0
$15$	−1563.68	+	196.417i	−1.79440	+	0.225398i
$16$		0			0
$17$			1441.83i			1.21002i	0.796219	+	0.605009i	$0.206830\pi$
$17$			1441.83i			1.21002i	−0.796219	+	0.605009i	$0.793170\pi$
$18$		0			0
$19$	1312.68			0.834208			0.417104	−	0.908859i	$-0.363045\pi$
$19$	1312.68			0.834208			0.417104	+	0.908859i	$0.363045\pi$
$20$		0			0
$21$	389.217	+	3098.56i	0.192594	+	1.53324i
$22$		0			0
$23$	−2040.14			−0.804156			−0.402078	−	0.915605i	$-0.631712\pi$
$23$	−2040.14			−0.804156			−0.402078	+	0.915605i	$0.631712\pi$
$24$		0			0
$25$	7095.82			2.27066
$26$		0			0
$27$	−3524.93	+	1386.99i	−0.930554	+	0.366155i
$28$		0			0
$29$	−3781.90			−0.835054			−0.417527	−	0.908664i	$-0.637103\pi$
$29$	−3781.90			−0.835054			−0.417527	+	0.908664i	$0.637103\pi$
$30$		0			0
$31$			1425.86i			0.266484i	0.991084	+	0.133242i	$0.0425388\pi$
$31$			1425.86i			0.266484i	−0.991084	+	0.133242i	$0.957461\pi$
$32$		0			0
$33$	−680.350	−	5416.27i	−0.108755	−	0.865795i
$34$		0			0
$35$		−	20253.4i		−	2.79466i
$36$		0			0
$37$			2611.15i			0.313565i	0.987633	+	0.156783i	$0.0501122\pi$
$37$			2611.15i			0.313565i	−0.987633	+	0.156783i	$0.949888\pi$
$38$		0			0
$39$	−1446.39	−	11514.7i	−0.152274	−	1.21225i
$40$		0			0
$41$			10839.5i			1.00705i	0.863982	+	0.503523i	$0.167963\pi$
$41$			10839.5i			1.00705i	−0.863982	+	0.503523i	$0.832037\pi$
$42$		0			0
$43$	16147.4			1.33178			0.665890	−	0.746050i	$-0.268052\pi$
$43$	16147.4			1.33178			0.665890	+	0.746050i	$0.268052\pi$
$44$		0			0
$45$	23803.6	−	6075.93i	1.75231	−	0.447282i
$46$		0			0
$47$	−3411.56			−0.225273			−0.112636	−	0.993636i	$-0.535930\pi$
$47$	−3411.56			−0.225273			−0.112636	+	0.993636i	$0.535930\pi$
$48$		0			0
$49$	−23326.9			−1.38793
$50$		0			0
$51$	−2801.24	−	22300.6i	−0.150808	−	1.20058i
$52$		0			0
$53$	−539.647			−0.0263888			−0.0131944	−	0.999913i	$-0.504200\pi$
$53$	−539.647			−0.0263888			−0.0131944	+	0.999913i	$0.504200\pi$
$54$		0			0
$55$			35402.9i			1.57809i
$56$		0			0
$57$	−20303.1	+	2550.32i	−0.827703	+	0.103970i
$58$		0			0
$59$			33786.7i			1.26362i	0.775124	+	0.631809i	$0.217687\pi$
$59$			33786.7i			1.26362i	−0.775124	+	0.631809i	$0.782313\pi$
$60$		0			0
$61$		−	50481.9i		−	1.73704i	−0.495651	−	0.868522i	$-0.665070\pi$
$61$		−	50481.9i		−	1.73704i	0.495651	−	0.868522i	$-0.334930\pi$
$62$		0			0
$63$	−12040.0	−	47168.9i	−0.382185	−	1.49729i
$64$		0			0
$65$			75265.0i			2.20958i
$66$		0			0
$67$	15700.1			0.427284			0.213642	−	0.976912i	$-0.431467\pi$
$67$	15700.1			0.427284			0.213642	+	0.976912i	$0.431467\pi$
$68$		0			0
$69$	31554.7	−	3963.66i	0.797886	−	0.100224i
$70$		0			0
$71$	−36459.2			−0.858344			−0.429172	−	0.903223i	$-0.641195\pi$
$71$	−36459.2			−0.858344			−0.429172	+	0.903223i	$0.641195\pi$
$72$		0			0
$73$	−37025.8			−0.813199			−0.406600	−	0.913606i	$-0.633286\pi$
$73$	−37025.8			−0.813199			−0.406600	+	0.913606i	$0.633286\pi$
$74$		0			0
$75$	−109750.	+	13786.0i	−2.25296	+	0.282999i
$76$		0			0
$77$	70154.0			1.34842
$78$		0			0
$79$			33204.8i			0.598596i	0.954160	+	0.299298i	$0.0967524\pi$
$79$			33204.8i			0.598596i	−0.954160	+	0.299298i	$0.903248\pi$
$80$		0			0
$81$	51825.1	−	28300.9i	0.877663	−	0.479278i
$82$		0			0
$83$			75829.2i			1.20821i	0.796906	+	0.604103i	$0.206469\pi$
$83$			75829.2i			1.20821i	−0.796906	+	0.604103i	$0.793531\pi$
$84$		0			0
$85$			145766.i			2.18831i
$86$		0			0
$87$	58494.3	−	7347.61i	0.828543	−	0.104075i
$88$		0			0
$89$			9734.56i			0.130269i	0.997876	+	0.0651345i	$0.0207477\pi$
$89$			9734.56i			0.130269i	−0.997876	+	0.0651345i	$0.979252\pi$
$90$		0			0
$91$	149144.			1.88800
$92$		0			0
$93$	−2770.21	−	22053.6i	−0.0332127	−	0.264407i
$94$		0			0
$95$	132709.			1.50866
$96$		0			0
$97$	115120.			1.24229			0.621143	−	0.783697i	$-0.286669\pi$
$97$	115120.			1.24229			0.621143	+	0.783697i	$0.286669\pi$
$98$		0			0
$99$	21045.8	+	82451.1i	0.215813	+	0.845490i
$100$		0			0
$101$	136541.			1.33187			0.665933	−	0.746012i	$-0.268034\pi$
$101$	136541.			1.33187			0.665933	+	0.746012i	$0.268034\pi$
$102$		0			0
$103$			82338.8i			0.764736i	0.924010	+	0.382368i	$0.124891\pi$
$103$			82338.8i			0.764736i	−0.924010	+	0.382368i	$0.875109\pi$
$104$		0			0
$105$	39349.1	+	313258.i	0.348307	+	2.77287i
$106$		0			0
$107$		−	125914.i		−	1.06320i	−0.846997	−	0.531598i	$-0.821592\pi$
$107$		−	125914.i		−	1.06320i	0.846997	−	0.531598i	$-0.178408\pi$
$108$		0			0
$109$			77223.1i			0.622560i	0.950318	+	0.311280i	$0.100758\pi$
$109$			77223.1i			0.622560i	−0.950318	+	0.311280i	$0.899242\pi$
$110$		0			0
$111$	−5073.04	−	40386.5i	−0.0390806	−	0.311120i
$112$		0			0
$113$			267680.i			1.97206i	0.166572	+	0.986029i	$0.446730\pi$
$113$			267680.i			1.97206i	−0.166572	+	0.986029i	$0.553270\pi$
$114$		0			0
$115$	−206254.			−1.45431
$116$		0			0
$117$	44742.5	+	175287.i	0.302173	+	1.18382i
$118$		0			0
$119$	288848.			1.86983
$120$		0			0
$121$	38422.2			0.238571
$122$		0			0
$123$	−21059.3	−	167653.i	−0.125511	−	0.999193i
$124$		0			0
$125$	401442.			2.29799
$126$		0			0
$127$		−	158232.i		−	0.870535i	−0.900301	−	0.435268i	$-0.856654\pi$
$127$		−	158232.i		−	0.870535i	0.900301	−	0.435268i	$-0.143346\pi$
$128$		0			0
$129$	−249751.	+	31371.8i	−1.32140	+	0.165984i
$130$		0			0
$131$			213698.i			1.08798i	0.839090	+	0.543992i	$0.183088\pi$
$131$			213698.i			1.08798i	−0.839090	+	0.543992i	$0.816912\pi$
$132$		0			0
$133$		−	262975.i		−	1.28910i
$134$		0			0
$135$	−356364.	+	140222.i	−1.68290	+	0.662190i
$136$		0			0
$137$		−	211964.i		−	0.964852i	−0.875937	−	0.482426i	$-0.839756\pi$
$137$		−	211964.i		−	0.964852i	0.875937	−	0.482426i	$-0.160244\pi$
$138$		0			0
$139$	−70467.9			−0.309353			−0.154677	−	0.987965i	$-0.549434\pi$
$139$	−70467.9			−0.309353			−0.154677	+	0.987965i	$0.549434\pi$
$140$		0			0
$141$	52766.3	−	6628.10i	0.223516	−	0.0280764i
$142$		0			0
$143$	−260703.			−1.06612
$144$		0			0
$145$	−382343.			−1.51019
$146$		0			0
$147$	360796.	−	45320.4i	1.37711	−	0.172982i
$148$		0			0
$149$	321079.			1.18480			0.592402	−	0.805643i	$-0.298180\pi$
$149$	321079.			1.18480			0.592402	+	0.805643i	$0.298180\pi$
$150$		0			0
$151$			200683.i			0.716257i	0.933672	+	0.358129i	$0.116585\pi$
$151$			200683.i			0.716257i	−0.933672	+	0.358129i	$0.883415\pi$
$152$		0			0
$153$	86653.0	+	339480.i	0.299264	+	1.17243i
$154$		0			0
$155$			144151.i			0.481936i
$156$		0			0
$157$		−	231866.i		−	0.750737i	−0.926876	−	0.375369i	$-0.877516\pi$
$157$		−	231866.i		−	0.750737i	0.926876	−	0.375369i	$-0.122484\pi$
$158$		0			0
$159$	8346.67	−	1048.44i	0.0261830	−	0.00328891i
$160$		0			0
$161$			408711.i			1.24266i
$162$		0			0
$163$	−79609.6			−0.234691			−0.117346	−	0.993091i	$-0.537438\pi$
$163$	−79609.6			−0.234691			−0.117346	+	0.993091i	$0.537438\pi$
$164$		0			0
$165$	−68782.1	−	547574.i	−0.196682	−	1.56579i
$166$		0			0
$167$	−689402.			−1.91285			−0.956427	−	0.291973i	$-0.905688\pi$
$167$	−689402.			−1.91285			−0.956427	+	0.291973i	$0.905688\pi$
$168$		0			0
$169$	−182950.			−0.492739
$170$		0			0
$171$	309071.	−	78891.1i	0.808292	−	0.206318i
$172$		0			0
$173$	−304555.			−0.773660			−0.386830	−	0.922151i	$-0.626430\pi$
$173$	−304555.			−0.773660			−0.386830	+	0.922151i	$0.626430\pi$
$174$		0			0
$175$		−	1.42154e6i		−	3.50884i
$176$		0			0
$177$	−65642.0	−	522576.i	−0.157488	−	1.25377i
$178$		0			0
$179$		−	514130.i		−	1.19933i	−0.800250	−	0.599667i	$-0.795300\pi$
$179$		−	514130.i		−	1.19933i	0.800250	−	0.599667i	$-0.204700\pi$
$180$		0			0
$181$			123715.i			0.280688i	0.990103	+	0.140344i	$0.0448209\pi$
$181$			123715.i			0.280688i	−0.990103	+	0.140344i	$0.955179\pi$
$182$		0			0
$183$	98078.0	+	780798.i	0.216493	+	1.72350i
$184$		0			0
$185$			263982.i			0.567082i
$186$		0			0
$187$	−504906.			−1.05586
$188$		0			0
$189$	277863.	+	706166.i	0.565817	+	1.43798i
$190$		0			0
$191$	554556.			1.09992			0.549961	−	0.835190i	$-0.314643\pi$
$191$	554556.			1.09992			0.549961	+	0.835190i	$0.314643\pi$
$192$		0			0
$193$	664699.			1.28449			0.642247	−	0.766498i	$-0.278003\pi$
$193$	664699.			1.28449			0.642247	+	0.766498i	$0.278003\pi$
$194$		0			0
$195$	−146228.	−	1.16412e6i	−0.275387	−	2.19235i
$196$		0			0
$197$	207583.			0.381089			0.190544	−	0.981679i	$-0.438975\pi$
$197$	207583.			0.381089			0.190544	+	0.981679i	$0.438975\pi$
$198$		0			0
$199$			486450.i			0.870775i	0.900243	+	0.435387i	$0.143389\pi$
$199$			486450.i			0.870775i	−0.900243	+	0.435387i	$0.856611\pi$
$200$		0			0
$201$	−242833.	+	30502.8i	−0.423952	+	0.0532536i
$202$		0			0
$203$			757645.i			1.29040i
$204$		0			0
$205$			1.09585e6i			1.82124i
$206$		0			0
$207$	−480353.	+	122611.i	−0.779174	+	0.198886i
$208$		0			0
$209$			459679.i			0.727929i
$210$		0			0
$211$	284955.			0.440626			0.220313	−	0.975429i	$-0.429292\pi$
$211$	284955.			0.440626			0.220313	+	0.975429i	$0.429292\pi$
$212$		0			0
$213$	563912.	−	70834.3i	0.851652	−	0.106978i
$214$		0			0
$215$	1.63248e6			2.40852
$216$		0			0
$217$	285648.			0.411796
$218$		0			0
$219$	572674.	−	71935.0i	0.806859	−	0.101351i
$220$		0			0
$221$	−1.07341e6			−1.47837
$222$		0			0
$223$			130981.i			0.176379i	0.996104	+	0.0881893i	$0.0281081\pi$
$223$			130981.i			0.176379i	−0.996104	+	0.0881893i	$0.971892\pi$
$224$		0			0
$225$	1.67072e6	−	426454.i	2.20012	−	0.561586i
$226$		0			0
$227$			409606.i			0.527596i	0.964578	+	0.263798i	$0.0849752\pi$
$227$			409606.i			0.527596i	−0.964578	+	0.263798i	$0.915025\pi$
$228$		0			0
$229$			166764.i			0.210142i	0.994465	+	0.105071i	$0.0335070\pi$
$229$			166764.i			0.210142i	−0.994465	+	0.105071i	$0.966493\pi$
$230$		0			0
$231$	−1.08507e6	+	136298.i	−1.33791	+	0.168058i
$232$		0			0
$233$		−	1.03597e6i		−	1.25013i	−0.780572	−	0.625066i	$-0.785072\pi$
$233$		−	1.03597e6i		−	1.25013i	0.780572	−	0.625066i	$-0.214928\pi$
$234$		0			0
$235$	−344902.			−0.407405
$236$		0			0
$237$	−64511.6	−	513576.i	−0.0746048	−	0.593929i
$238$		0			0
$239$	789687.			0.894253			0.447127	−	0.894471i	$-0.352447\pi$
$239$	789687.			0.894253			0.447127	+	0.894471i	$0.352447\pi$
$240$		0			0
$241$	−413145.			−0.458205			−0.229102	−	0.973402i	$-0.573579\pi$
$241$	−413145.			−0.458205			−0.229102	+	0.973402i	$0.573579\pi$
$242$		0			0
$243$	−746591.	+	538415.i	−0.811086	+	0.584927i
$244$		0			0
$245$	−2.35831e6			−2.51007
$246$		0			0
$247$			977256.i			1.01922i
$248$		0			0
$249$	−147324.	−	1.17284e6i	−0.150582	−	1.19879i
$250$		0			0
$251$			1.34196e6i			1.34448i	0.740333	+	0.672240i	$0.234668\pi$
$251$			1.34196e6i			1.34448i	−0.740333	+	0.672240i	$0.765332\pi$
$252$		0			0
$253$		−	714425.i		−	0.701706i
$254$		0			0
$255$	−283200.	−	2.25455e6i	−0.272736	−	2.17125i
$256$		0			0
$257$		−	1.16583e6i		−	1.10104i	−0.834822	−	0.550521i	$-0.814429\pi$
$257$		−	1.16583e6i		−	1.10104i	0.834822	−	0.550521i	$-0.185571\pi$
$258$		0			0
$259$	523104.			0.484550
$260$		0			0
$261$	−890451.	+	227290.i	−0.809112	+	0.206528i
$262$		0			0
$263$	−259020.			−0.230910			−0.115455	−	0.993313i	$-0.536833\pi$
$263$	−259020.			−0.230910			−0.115455	+	0.993313i	$0.536833\pi$
$264$		0			0
$265$	−54557.2			−0.0477241
$266$		0			0
$267$	−18912.6	−	150564.i	−0.0162358	−	0.129253i
$268$		0			0
$269$	428003.			0.360634			0.180317	−	0.983609i	$-0.442288\pi$
$269$	428003.			0.360634			0.180317	+	0.983609i	$0.442288\pi$
$270$		0			0
$271$		−	662216.i		−	0.547742i	−0.961766	−	0.273871i	$-0.911696\pi$
$271$		−	662216.i		−	0.547742i	0.961766	−	0.273871i	$-0.0883042\pi$
$272$		0			0
$273$	−2.30680e6	+	289763.i	−1.87328	+	0.235307i
$274$		0			0
$275$			2.48484e6i			1.98138i
$276$		0			0
$277$		−	1.71276e6i		−	1.34121i	−0.741815	−	0.670604i	$-0.766035\pi$
$277$		−	1.71276e6i		−	1.34121i	0.741815	−	0.670604i	$-0.233965\pi$
$278$		0			0
$279$	85693.1	+	335719.i	0.0659076	+	0.258206i
$280$		0			0
$281$			193055.i			0.145853i	0.997337	+	0.0729265i	$0.0232338\pi$
$281$			193055.i			0.145853i	−0.997337	+	0.0729265i	$0.976766\pi$
$282$		0			0
$283$	−452871.			−0.336131			−0.168065	−	0.985776i	$-0.553752\pi$
$283$	−452871.			−0.336131			−0.168065	+	0.985776i	$0.553752\pi$
$284$		0			0
$285$	−2.05260e6	+	257832.i	−1.49690	+	0.188029i
$286$		0			0
$287$	2.17152e6			1.55618
$288$		0			0
$289$	−659015.			−0.464142
$290$		0			0
$291$	−1.78055e6	+	223659.i	−1.23260	+	0.154830i
$292$		0			0
$293$	305918.			0.208178			0.104089	−	0.994568i	$-0.466807\pi$
$293$	305918.			0.208178			0.104089	+	0.994568i	$0.466807\pi$
$294$		0			0
$295$			3.41577e6i			2.28525i
$296$		0			0
$297$	−485703.	−	1.23438e6i	−0.319506	−	0.812000i
$298$		0			0
$299$		−	1.51883e6i		−	0.982500i
$300$		0			0
$301$		−	3.23489e6i		−	2.05799i
$302$		0			0
$303$	−2.11187e6	+	265277.i	−1.32148	+	0.165994i
$304$		0			0
$305$		−	5.10362e6i		−	3.14144i
$306$		0			0
$307$	3.11124e6			1.88403			0.942014	−	0.335574i	$-0.108930\pi$
$307$	3.11124e6			1.88403			0.942014	+	0.335574i	$0.108930\pi$
$308$		0			0
$309$	−159971.	−	1.27353e6i	−0.0953113	−	0.758773i
$310$		0			0
$311$	−20084.6			−0.0117751			−0.00588753	−	0.999983i	$-0.501874\pi$
$311$	−20084.6			−0.0117751			−0.00588753	+	0.999983i	$0.501874\pi$
$312$		0			0
$313$	1.18268e6			0.682346			0.341173	−	0.940001i	$-0.389176\pi$
$313$	1.18268e6			0.682346			0.341173	+	0.940001i	$0.389176\pi$
$314$		0			0
$315$	−1.21722e6	−	4.76869e6i	−0.691181	−	2.70784i
$316$		0			0
$317$	−123769.			−0.0691775			−0.0345887	−	0.999402i	$-0.511012\pi$
$317$	−123769.			−0.0691775			−0.0345887	+	0.999402i	$0.511012\pi$
$318$		0			0
$319$		−	1.32436e6i		−	0.728667i
$320$		0			0
$321$	244629.	+	1.94749e6i	0.132509	+	1.05491i
$322$		0			0
$323$			1.89266e6i			1.00941i
$324$		0			0
$325$			5.28266e6i			2.77424i
$326$		0			0
$327$	−150032.	−	1.19440e6i	−0.0775915	−	0.617706i
$328$		0			0
$329$			683454.i			0.348112i
$330$		0			0
$331$	2.79046e6			1.39993			0.699964	−	0.714178i	$-0.253199\pi$
$331$	2.79046e6			1.39993			0.699964	+	0.714178i	$0.253199\pi$
$332$		0			0
$333$	156929.	+	614798.i	0.0775517	+	0.303824i
$334$		0			0
$335$	1.58725e6			0.772741
$336$		0			0
$337$	−306228.			−0.146883			−0.0734414	−	0.997300i	$-0.523398\pi$
$337$	−306228.			−0.146883			−0.0734414	+	0.997300i	$0.523398\pi$
$338$		0			0
$339$	−520058.	−	4.14018e6i	−0.245784	−	1.95668i
$340$		0			0
$341$	−499312.			−0.232534
$342$		0			0
$343$			1.30617e6i			0.599465i
$344$		0			0
$345$	3.19012e6	−	400718.i	1.44298	−	0.181256i
$346$		0			0
$347$			657912.i			0.293322i	0.989187	+	0.146661i	$0.0468526\pi$
$347$			657912.i			0.293322i	−0.989187	+	0.146661i	$0.953147\pi$
$348$		0			0
$349$		−	1.31215e6i		−	0.576661i	−0.957531	−	0.288330i	$-0.906900\pi$
$349$		−	1.31215e6i		−	0.576661i	0.957531	−	0.288330i	$-0.0931001\pi$
$350$		0			0
$351$	−1.03258e6	−	2.62423e6i	−0.447360	−	1.13693i
$352$		0			0
$353$		−	787383.i		−	0.336317i	−0.985760	−	0.168159i	$-0.946218\pi$
$353$		−	787383.i		−	0.336317i	0.985760	−	0.168159i	$-0.0537821\pi$
$354$		0			0
$355$	−3.68596e6			−1.55231
$356$		0			0
$357$	−4.46759e6	+	561185.i	−1.85525	+	0.233043i
$358$		0			0
$359$	2.36201e6			0.967265			0.483632	−	0.875271i	$-0.339317\pi$
$359$	2.36201e6			0.967265			0.483632	+	0.875271i	$0.339317\pi$
$360$		0			0
$361$	−752976.			−0.304098
$362$		0			0
$363$	−594272.	+	74648.0i	−0.236711	+	0.0297339i
$364$		0			0
$365$	−3.74323e6			−1.47067
$366$		0			0
$367$		−	2.15764e6i		−	0.836208i	−0.908399	−	0.418104i	$-0.862695\pi$
$367$		−	2.15764e6i		−	0.836208i	0.908399	−	0.418104i	$-0.137305\pi$
$368$		0			0
$369$	651446.	+	2.55216e6i	0.249065	+	0.975760i
$370$		0			0
$371$			108110.i			0.0407784i
$372$		0			0
$373$			3.35398e6i			1.24821i	0.781340	+	0.624106i	$0.214537\pi$
$373$			3.35398e6i			1.24821i	−0.781340	+	0.624106i	$0.785463\pi$
$374$		0			0
$375$	−6.20908e6	+	779937.i	−2.28007	+	0.286405i
$376$		0			0
$377$		−	2.81553e6i		−	1.02025i
$378$		0			0
$379$	2.84395e6			1.01701			0.508503	−	0.861060i	$-0.330199\pi$
$379$	2.84395e6			1.01701			0.508503	+	0.861060i	$0.330199\pi$
$380$		0			0
$381$	307420.	+	2.44737e6i	0.108497	+	0.863747i
$382$		0			0
$383$	−4.37200e6			−1.52294			−0.761471	−	0.648199i	$-0.775522\pi$
$383$	−4.37200e6			−1.52294			−0.761471	+	0.648199i	$0.775522\pi$
$384$		0			0
$385$	7.09243e6			2.43861
$386$		0			0
$387$	3.80193e6	−	970450.i	1.29041	−	0.329379i
$388$		0			0
$389$	1.31709e6			0.441308			0.220654	−	0.975352i	$-0.429181\pi$
$389$	1.31709e6			0.441308			0.220654	+	0.975352i	$0.429181\pi$
$390$		0			0
$391$		−	2.94153e6i		−	0.973043i
$392$		0			0
$393$	−415180.	−	3.30525e6i	−0.135599	−	1.07950i
$394$		0			0
$395$			3.35695e6i			1.08256i
$396$		0			0
$397$		−	596875.i		−	0.190067i	−0.995474	−	0.0950336i	$-0.969704\pi$
$397$		−	596875.i		−	0.190067i	0.995474	−	0.0950336i	$-0.0302958\pi$
$398$		0			0
$399$	510917.	+	4.06741e6i	0.160664	+	1.27904i
$400$		0			0
$401$			522178.i			0.162165i	0.996707	+	0.0810825i	$0.0258377\pi$
$401$			522178.i			0.162165i	−0.996707	+	0.0810825i	$0.974162\pi$
$402$		0			0
$403$	−1.06152e6			−0.325585
$404$		0			0
$405$	5.23942e6	−	2.86116e6i	1.58725	−	0.866773i
$406$		0			0
$407$	−914384.			−0.273617
$408$		0			0
$409$	−2.75559e6			−0.814530			−0.407265	−	0.913310i	$-0.633517\pi$
$409$	−2.75559e6			−0.814530			−0.407265	+	0.913310i	$0.633517\pi$
$410$		0			0
$411$	411811.	+	3.27843e6i	0.120252	+	0.957329i
$412$		0			0
$413$	6.76865e6			1.95266
$414$		0			0
$415$			7.66619e6i			2.18504i
$416$		0			0
$417$	1.08992e6	−	136908.i	0.306941	−	0.0385556i
$418$		0			0
$419$		−	2.52527e6i		−	0.702703i	−0.936244	−	0.351352i	$-0.885722\pi$
$419$		−	2.52527e6i		−	0.702703i	0.936244	−	0.351352i	$-0.114278\pi$
$420$		0			0
$421$		−	1.48300e6i		−	0.407791i	−0.978993	−	0.203895i	$-0.934640\pi$
$421$		−	1.48300e6i		−	0.407791i	0.978993	−	0.203895i	$-0.0653602\pi$
$422$		0			0
$423$	−803255.	+	205033.i	−0.218274	+	0.0557150i
$424$		0			0
$425$			1.02310e7i			2.74754i
$426$		0			0
$427$	−1.01133e7			−2.68424
$428$		0			0
$429$	4.03228e6	−	506504.i	1.05781	−	0.132874i
$430$		0			0
$431$	4.83581e6			1.25394			0.626969	−	0.779044i	$-0.284295\pi$
$431$	4.83581e6			1.25394			0.626969	+	0.779044i	$0.284295\pi$
$432$		0			0
$433$	−7.25960e6			−1.86077			−0.930386	−	0.366582i	$-0.880528\pi$
$433$	−7.25960e6			−1.86077			−0.930386	+	0.366582i	$0.880528\pi$
$434$		0			0
$435$	5.91366e6	−	742829.i	1.49842	−	0.188220i
$436$		0			0
$437$	−2.67805e6			−0.670834
$438$		0			0
$439$		−	7.32262e6i		−	1.81345i	−0.421724	−	0.906724i	$-0.638575\pi$
$439$		−	7.32262e6i		−	1.81345i	0.421724	−	0.906724i	$-0.361425\pi$
$440$		0			0
$441$	−5.49234e6	+	1.40193e6i	−1.34481	+	0.343266i
$442$		0			0
$443$			7.30040e6i			1.76741i	0.468044	+	0.883705i	$0.344959\pi$
$443$			7.30040e6i			1.76741i	−0.468044	+	0.883705i	$0.655041\pi$
$444$		0			0
$445$			984145.i			0.235591i
$446$		0			0
$447$	−4.96610e6	+	623804.i	−1.17557	+	0.147666i
$448$		0			0
$449$			3.84169e6i			0.899303i	0.893204	+	0.449651i	$0.148452\pi$
$449$			3.84169e6i			0.899303i	−0.893204	+	0.449651i	$0.851548\pi$
$450$		0			0
$451$	−3.79581e6			−0.878746
$452$		0			0
$453$	−389895.	−	3.10395e6i	−0.0892693	−	0.710673i
$454$		0			0
$455$	1.50782e7			3.41445
$456$		0			0
$457$	−4.69416e6			−1.05140			−0.525700	−	0.850670i	$-0.676196\pi$
$457$	−4.69416e6			−1.05140			−0.525700	+	0.850670i	$0.676196\pi$
$458$		0			0
$459$	−1.99981e6	−	5.08235e6i	−0.443054	−	1.12599i
$460$		0			0
$461$	−2.35679e6			−0.516499			−0.258249	−	0.966078i	$-0.583146\pi$
$461$	−2.35679e6			−0.516499			−0.258249	+	0.966078i	$0.583146\pi$
$462$		0			0
$463$		−	8.31332e6i		−	1.80228i	−0.433530	−	0.901139i	$-0.642732\pi$
$463$		−	8.31332e6i		−	1.80228i	0.433530	−	0.901139i	$-0.357268\pi$
$464$		0			0
$465$	−280063.	−	2.22958e6i	−0.0600652	−	0.478179i
$466$		0			0
$467$			627229.i			0.133087i	0.997784	+	0.0665433i	$0.0211970\pi$
$467$			627229.i			0.133087i	−0.997784	+	0.0665433i	$0.978803\pi$
$468$		0			0
$469$		−	3.14528e6i		−	0.660278i
$470$		0			0
$471$	450478.	+	3.58625e6i	0.0935666	+	0.744884i
$472$		0			0
$473$			5.65457e6i			1.16211i
$474$		0			0
$475$	9.31453e6			1.89420
$476$		0			0
$477$	−127060.	+	32432.4i	−0.0255690	+	0.00652654i
$478$		0			0
$479$	8.28840e6			1.65056			0.825282	−	0.564721i	$-0.191016\pi$
$479$	8.28840e6			1.65056			0.825282	+	0.564721i	$0.191016\pi$
$480$		0			0
$481$	−1.94394e6			−0.383107
$482$		0			0
$483$	−794058.	−	6.32149e6i	−0.154876	−	1.23297i
$484$		0			0
$485$	1.16384e7			2.24667
$486$		0			0
$487$			1.20317e6i			0.229881i	0.993372	+	0.114941i	$0.0366678\pi$
$487$			1.20317e6i			0.229881i	−0.993372	+	0.114941i	$0.963332\pi$
$488$		0			0
$489$	1.23132e6	−	154668.i	0.232861	−	0.0292502i
$490$		0			0
$491$			4.06733e6i			0.761387i	0.924701	+	0.380693i	$0.124315\pi$
$491$			4.06733e6i			0.761387i	−0.924701	+	0.380693i	$0.875685\pi$
$492$		0			0
$493$		−	5.45285e6i		−	1.01043i
$494$		0			0
$495$	2.12769e6	+	8.33565e6i	0.390298	+	1.52907i
$496$		0			0
$497$			7.30404e6i			1.32639i
$498$		0			0
$499$	−3.49085e6			−0.627596			−0.313798	−	0.949490i	$-0.601602\pi$
$499$	−3.49085e6			−0.627596			−0.313798	+	0.949490i	$0.601602\pi$
$500$		0			0
$501$	1.06629e7	−	1.33940e6i	1.89794	−	0.238405i
$502$		0			0
$503$	−9.12330e6			−1.60780			−0.803900	−	0.594764i	$-0.797245\pi$
$503$	−9.12330e6			−1.60780			−0.803900	+	0.594764i	$0.797245\pi$
$504$		0			0
$505$	1.38041e7			2.40868
$506$		0			0
$507$	2.82968e6	−	355443.i	0.488897	−	0.0614115i
$508$		0			0
$509$	714234.			0.122193			0.0610964	−	0.998132i	$-0.480540\pi$
$509$	714234.			0.122193			0.0610964	+	0.998132i	$0.480540\pi$
$510$		0			0
$511$			7.41754e6i			1.25663i
$512$		0			0
$513$	−4.62710e6	+	1.82068e6i	−0.776275	+	0.305449i
$514$		0			0
$515$			8.32430e6i			1.38302i
$516$		0			0
$517$		−	1.19467e6i		−	0.196573i
$518$		0			0
$519$	4.71052e6	−	591700.i	0.767628	−	0.0964236i
$520$		0			0
$521$		−	1.10964e7i		−	1.79097i	−0.445097	−	0.895483i	$-0.646831\pi$
$521$		−	1.10964e7i		−	1.79097i	0.445097	−	0.895483i	$-0.353169\pi$
$522$		0			0
$523$	1.49783e6			0.239446			0.119723	−	0.992807i	$-0.461799\pi$
$523$	1.49783e6			0.239446			0.119723	+	0.992807i	$0.461799\pi$
$524$		0			0
$525$	2.76182e6	+	2.19868e7i	0.437317	+	3.48148i
$526$		0			0
$527$	−2.05584e6			−0.322451
$528$		0			0
$529$	−2.27417e6			−0.353332
$530$		0			0
$531$	2.03056e6	+	7.95511e6i	0.312521	+	1.22436i
$532$		0			0
$533$	−8.06973e6			−1.23038
$534$		0			0
$535$		−	1.27296e7i		−	1.92279i
$536$		0			0
$537$	998869.	+	7.95200e6i	0.149477	+	1.18998i
$538$		0			0
$539$		−	8.16872e6i		−	1.21111i
$540$		0			0
$541$			967821.i			0.142168i	0.997470	+	0.0710840i	$0.0226458\pi$
$541$			967821.i			0.142168i	−0.997470	+	0.0710840i	$0.977354\pi$
$542$		0			0
$543$	−240357.	−	1.91348e6i	−0.0349830	−	0.278500i
$544$		0			0
$545$			7.80711e6i			1.12590i
$546$		0			0
$547$	−6.42252e6			−0.917777			−0.458889	−	0.888494i	$-0.651752\pi$
$547$	−6.42252e6			−0.917777			−0.458889	+	0.888494i	$0.651752\pi$
$548$		0			0
$549$	−3.03393e6	−	1.18860e7i	−0.429610	−	1.68308i
$550$		0			0
$551$	−4.96441e6			−0.696609
$552$		0			0
$553$	6.65208e6			0.925006
$554$		0			0
$555$	−512875.	−	4.08299e6i	−0.0706771	−	0.562660i
$556$		0			0
$557$	1.06224e7			1.45072			0.725362	−	0.688368i	$-0.241673\pi$
$557$	1.06224e7			1.45072			0.725362	+	0.688368i	$0.241673\pi$
$558$		0			0
$559$			1.20214e7i			1.62714i
$560$		0			0
$561$	7.80933e6	−	980949.i	1.04763	−	0.131595i
$562$		0			0
$563$			7.61873e6i			1.01301i	0.862238	+	0.506503i	$0.169062\pi$
$563$			7.61873e6i			1.01301i	−0.862238	+	0.506503i	$0.830938\pi$
$564$		0			0
$565$			2.70619e7i			3.56646i
$566$		0			0
$567$	−5.66964e6	−	1.03824e7i	−0.740624	−	1.35625i
$568$		0			0
$569$			4.85750e6i			0.628973i	0.949262	+	0.314486i	$0.101832\pi$
$569$			4.85750e6i			0.628973i	−0.949262	+	0.314486i	$0.898168\pi$
$570$		0			0
$571$	−1.44725e7			−1.85760			−0.928799	−	0.370583i	$-0.879158\pi$
$571$	−1.44725e7			−1.85760			−0.928799	+	0.370583i	$0.879158\pi$
$572$		0			0
$573$	−8.57726e6	+	1.07741e6i	−1.09135	+	0.137086i
$574$		0			0
$575$	−1.44765e7			−1.82597
$576$		0			0
$577$	−1.35271e6			−0.169147			−0.0845736	−	0.996417i	$-0.526953\pi$
$577$	−1.35271e6			−0.169147			−0.0845736	+	0.996417i	$0.526953\pi$
$578$		0			0
$579$	−1.02808e7	+	1.29140e6i	−1.27448	+	0.160090i
$580$		0			0
$581$	1.51912e7			1.86703
$582$		0			0
$583$		−	188976.i		−	0.0230268i
$584$		0			0
$585$	4.52338e6	+	1.77212e7i	0.546479	+	2.14094i
$586$		0			0
$587$		−	8.23231e6i		−	0.986113i	−0.869997	−	0.493056i	$-0.835880\pi$
$587$		−	8.23231e6i		−	0.986113i	0.869997	−	0.493056i	$-0.164120\pi$
$588$		0			0
$589$			1.87169e6i			0.222303i
$590$		0			0
$591$	−3.21067e6	+	403300.i	−0.378117	+	0.0474962i
$592$		0			0
$593$			6.50249e6i			0.759351i	0.925120	+	0.379676i	$0.123964\pi$
$593$			6.50249e6i			0.759351i	−0.925120	+	0.379676i	$0.876036\pi$
$594$		0			0
$595$	2.92020e7			3.38158
$596$		0			0
$597$	−945093.	−	7.52389e6i	−0.108527	−	0.863985i
$598$		0			0
$599$	6.17470e6			0.703151			0.351576	−	0.936159i	$-0.385646\pi$
$599$	6.17470e6			0.703151			0.351576	+	0.936159i	$0.385646\pi$
$600$		0			0
$601$	−1.58108e7			−1.78553			−0.892765	−	0.450523i	$-0.851237\pi$
$601$	−1.58108e7			−1.78553			−0.892765	+	0.450523i	$0.851237\pi$
$602$		0			0
$603$	3.69661e6	−	943568.i	0.414009	−	0.105677i
$604$		0			0
$605$	3.88441e6			0.431456
$606$		0			0
$607$			3.96885e6i			0.437212i	0.975813	+	0.218606i	$0.0701510\pi$
$607$			3.96885e6i			0.437212i	−0.975813	+	0.218606i	$0.929849\pi$
$608$		0			0
$609$	−1.47198e6	−	1.17184e7i	−0.160827	−	1.28034i
$610$		0			0
$611$		−	2.53982e6i		−	0.275233i
$612$		0			0
$613$		−	7.03392e6i		−	0.756042i	−0.925797	−	0.378021i	$-0.876605\pi$
$613$		−	7.03392e6i		−	0.756042i	0.925797	−	0.378021i	$-0.123395\pi$
$614$		0			0
$615$	−2.12906e6	−	1.69494e7i	−0.226986	−	1.80704i
$616$		0			0
$617$		−	8.21076e6i		−	0.868301i	−0.900840	−	0.434151i	$-0.857049\pi$
$617$		−	8.21076e6i		−	0.868301i	0.900840	−	0.434151i	$-0.142951\pi$
$618$		0			0
$619$	1.28591e7			1.34891			0.674455	−	0.738316i	$-0.264379\pi$
$619$	1.28591e7			1.34891			0.674455	+	0.738316i	$0.264379\pi$
$620$		0			0
$621$	7.19136e6	−	2.82966e6i	0.748311	−	0.294446i
$622$		0			0
$623$	1.95017e6			0.201304
$624$		0			0
$625$	1.84106e7			1.88525
$626$		0			0
$627$	−893080.	−	7.10981e6i	−0.0907239	−	0.722253i
$628$		0			0
$629$	−3.76484e6			−0.379419
$630$		0			0
$631$			5.68918e6i			0.568822i	0.958702	+	0.284411i	$0.0917980\pi$
$631$			5.68918e6i			0.568822i	−0.958702	+	0.284411i	$0.908202\pi$
$632$		0			0
$633$	−4.40738e6	+	553621.i	−0.437191	+	0.0549166i
$634$		0			0
$635$		−	1.59970e7i		−	1.57436i
$636$		0			0
$637$		−	1.73663e7i		−	1.69574i
$638$		0			0
$639$	−8.58435e6	+	2.19118e6i	−0.831679	+	0.212288i
$640$		0			0
$641$		−	1.04259e7i		−	1.00223i	−0.865380	−	0.501116i	$-0.832923\pi$
$641$		−	1.04259e7i		−	1.00223i	0.865380	−	0.501116i	$-0.167077\pi$
$642$		0			0
$643$	−4.43058e6			−0.422603			−0.211302	−	0.977421i	$-0.567770\pi$
$643$	−4.43058e6			−0.422603			−0.211302	+	0.977421i	$0.567770\pi$
$644$		0			0
$645$	−2.52493e7	+	3.17163e6i	−2.38974	+	0.300181i
$646$		0			0
$647$	−1.67487e6			−0.157297			−0.0786483	−	0.996902i	$-0.525060\pi$
$647$	−1.67487e6			−0.157297			−0.0786483	+	0.996902i	$0.525060\pi$
$648$		0			0
$649$	−1.18316e7			−1.10263
$650$		0			0
$651$	−4.41810e6	+	554968.i	−0.408586	+	0.0513234i
$652$		0			0
$653$	−9.32316e6			−0.855618			−0.427809	−	0.903869i	$-0.640714\pi$
$653$	−9.32316e6			−0.855618			−0.427809	+	0.903869i	$0.640714\pi$
$654$		0			0
$655$			2.16045e7i			1.96762i
$656$		0			0
$657$	−8.71775e6	+	2.22522e6i	−0.787936	+	0.201122i
$658$		0			0
$659$		−	1.48347e7i		−	1.33066i	−0.746550	−	0.665329i	$-0.768291\pi$
$659$		−	1.48347e7i		−	1.33066i	0.746550	−	0.665329i	$-0.231709\pi$
$660$		0			0
$661$		−	2.00609e6i		−	0.178585i	−0.996005	−	0.0892927i	$-0.971539\pi$
$661$		−	2.00609e6i		−	0.178585i	0.996005	−	0.0892927i	$-0.0284607\pi$
$662$		0			0
$663$	1.66023e7	−	2.08545e6i	1.46684	−	0.184254i
$664$		0			0
$665$		−	2.65862e7i		−	2.33133i
$666$		0			0
$667$	7.71560e6			0.671514
$668$		0			0
$669$	−254475.	−	2.02587e6i	−0.0219826	−	0.175003i
$670$		0			0
$671$	1.76779e7			1.51574
$672$		0			0
$673$	−1.44024e7			−1.22574			−0.612869	−	0.790185i	$-0.709985\pi$
$673$	−1.44024e7			−1.22574			−0.612869	+	0.790185i	$0.709985\pi$
$674$		0			0
$675$	−2.50123e7	+	9.84186e6i	−2.11297	+	0.831415i
$676$		0			0
$677$	2.85454e6			0.239367			0.119683	−	0.992812i	$-0.461812\pi$
$677$	2.85454e6			0.239367			0.119683	+	0.992812i	$0.461812\pi$
$678$		0			0
$679$		−	2.30625e7i		−	1.91970i
$680$		0			0
$681$	−795797.	−	6.33534e6i	−0.0657558	−	0.523482i
$682$		0			0
$683$			1.10530e7i			0.906629i	0.891351	+	0.453315i	$0.149759\pi$
$683$			1.10530e7i			0.906629i	−0.891351	+	0.453315i	$0.850241\pi$
$684$		0			0
$685$		−	2.14291e7i		−	1.74493i
$686$		0			0
$687$	−323995.	−	2.57932e6i	−0.0261906	−	0.208504i
$688$		0			0
$689$		−	401754.i		−	0.0322412i
$690$		0			0
$691$	1.16764e7			0.930283			0.465142	−	0.885236i	$-0.346003\pi$
$691$	1.16764e7			0.930283			0.465142	+	0.885236i	$0.346003\pi$
$692$		0			0
$693$	1.65178e7	−	4.21621e6i	1.30653	−	0.333495i
$694$		0			0
$695$	−7.12417e6			−0.559464
$696$		0			0
$697$	−1.56287e7			−1.21854
$698$		0			0
$699$	2.01271e6	+	1.60232e7i	0.155808	+	1.24039i
$700$		0			0
$701$	−8.27881e6			−0.636316			−0.318158	−	0.948038i	$-0.603064\pi$
$701$	−8.27881e6			−0.636316			−0.318158	+	0.948038i	$0.603064\pi$
$702$		0			0
$703$			3.42760e6i			0.261579i
$704$		0			0
$705$	5.33457e6	−	670088.i	0.404228	−	0.0507761i
$706$		0			0
$707$		−	2.73539e7i		−	2.05812i
$708$		0			0
$709$			2.02599e7i			1.51363i	0.653627	+	0.756817i	$0.273247\pi$
$709$			2.02599e7i			1.51363i	−0.653627	+	0.756817i	$0.726753\pi$
$710$		0			0
$711$	1.99559e6	+	7.81811e6i	0.148046	+	0.579999i
$712$		0			0
$713$		−	2.90895e6i		−	0.214295i
$714$		0			0
$715$	−2.63566e7			−1.92808
$716$		0			0
$717$	−1.22140e7	+	1.53423e6i	−0.887281	+	0.111453i
$718$		0			0
$719$	−1.95355e7			−1.40929			−0.704646	−	0.709559i	$-0.748894\pi$
$719$	−1.95355e7			−1.40929			−0.704646	+	0.709559i	$0.748894\pi$
$720$		0			0
$721$	1.64953e7			1.18174
$722$		0			0
$723$	6.39007e6	−	802672.i	0.454632	−	0.0571074i
$724$		0			0
$725$	−2.68357e7			−1.89613
$726$		0			0
$727$			1.31639e7i			0.923740i	0.886948	+	0.461870i	$0.152821\pi$
$727$			1.31639e7i			0.923740i	−0.886948	+	0.461870i	$0.847179\pi$
$728$		0			0
$729$	1.05014e7	−	9.77812e6i	0.731861	−	0.681454i
$730$		0			0
$731$			2.32819e7i			1.61148i
$732$		0			0
$733$		−	1.12062e7i		−	0.770371i	−0.922839	−	0.385186i	$-0.874137\pi$
$733$		−	1.12062e7i		−	0.770371i	0.922839	−	0.385186i	$-0.125863\pi$
$734$		0			0
$735$	3.64757e7	−	4.58181e6i	2.49050	−	0.312837i
$736$		0			0
$737$			5.49793e6i			0.372847i
$738$		0			0
$739$	−1.59090e6			−0.107160			−0.0535800	−	0.998564i	$-0.517063\pi$
$739$	−1.59090e6			−0.107160			−0.0535800	+	0.998564i	$0.517063\pi$
$740$		0			0
$741$	−1.89865e6	−	1.51151e7i	−0.127028	−	1.01127i
$742$		0			0
$743$	−2.66036e7			−1.76794			−0.883970	−	0.467543i	$-0.845139\pi$
$743$	−2.66036e7			−1.76794			−0.883970	+	0.467543i	$0.845139\pi$
$744$		0			0
$745$	3.24605e7			2.14271
$746$		0			0
$747$	4.55729e6	+	1.78540e7i	0.298817	+	1.17067i
$748$		0			0
$749$	−2.52248e7			−1.64295
$750$		0			0
$751$		−	1.55010e7i		−	1.00291i	−0.865185	−	0.501453i	$-0.832799\pi$
$751$		−	1.55010e7i		−	1.00291i	0.865185	−	0.501453i	$-0.167201\pi$
$752$		0			0
$753$	−2.60720e6	−	2.07559e7i	−0.167567	−	1.33400i
$754$		0			0
$755$			2.02887e7i			1.29535i
$756$		0			0
$757$			2.21393e7i			1.40418i	0.712086	+	0.702092i	$0.247750\pi$
$757$			2.21393e7i			1.40418i	−0.712086	+	0.702092i	$0.752250\pi$
$758$		0			0
$759$	1.38801e6	+	1.10499e7i	0.0874557	+	0.696235i
$760$		0			0
$761$			1.51184e7i			0.946332i	0.880973	+	0.473166i	$0.156889\pi$
$761$			1.51184e7i			0.946332i	−0.880973	+	0.473166i	$0.843111\pi$
$762$		0			0
$763$	1.54705e7			0.962037
$764$		0			0
$765$	8.76045e6	+	3.43208e7i	0.541219	+	2.12033i
$766$		0			0
$767$	−2.51534e7			−1.54386
$768$		0			0
$769$	−1.85995e7			−1.13419			−0.567095	−	0.823653i	$-0.691933\pi$
$769$	−1.85995e7			−1.13419			−0.567095	+	0.823653i	$0.691933\pi$
$770$		0			0
$771$	2.26502e6	+	1.80318e7i	0.137226	+	1.09246i
$772$		0			0
$773$	−1.74518e7			−1.05049			−0.525245	−	0.850951i	$-0.676026\pi$
$773$	−1.74518e7			−1.05049			−0.525245	+	0.850951i	$0.676026\pi$
$774$		0			0
$775$			1.01176e7i			0.605096i
$776$		0			0
$777$	−8.09080e6	+	1.01631e6i	−0.480772	+	0.0603909i
$778$		0			0
$779$			1.42288e7i			0.840085i
$780$		0			0
$781$		−	1.27674e7i		−	0.748990i
$782$		0			0
$783$	1.33309e7	−	5.24547e6i	0.777063	−	0.305759i
$784$		0			0
$785$		−	2.34412e7i		−	1.35771i
$786$		0			0
$787$	6.96713e6			0.400975			0.200488	−	0.979696i	$-0.435747\pi$
$787$	6.96713e6			0.400975			0.200488	+	0.979696i	$0.435747\pi$
$788$		0			0
$789$	4.00624e6	−	503233.i	0.229110	−	0.0287790i
$790$		0			0
$791$	5.36256e7			3.04741
$792$		0			0
$793$	3.75825e7			2.12228
$794$		0			0
$795$	843832.	−	105996.i	0.0473520	−	0.00594799i
$796$		0			0
$797$	1.75254e7			0.977289			0.488645	−	0.872483i	$-0.337491\pi$
$797$	1.75254e7			0.977289			0.488645	+	0.872483i	$0.337491\pi$
$798$		0			0
$799$		−	4.91889e6i		−	0.272584i
$800$		0			0
$801$	585041.	+	2.29201e6i	0.0322185	+	0.126222i
$802$		0			0
$803$		−	1.29658e7i		−	0.709597i
$804$		0			0
$805$			4.13199e7i			2.24734i
$806$		0			0
$807$	−6.61989e6	+	831540.i	−0.357822	+	0.0449468i
$808$		0			0
$809$			1.83843e6i			0.0987587i	0.998780	+	0.0493794i	$0.0157243\pi$
$809$			1.83843e6i			0.0987587i	−0.998780	+	0.0493794i	$0.984276\pi$
$810$		0			0
$811$	−1.97994e7			−1.05706			−0.528530	−	0.848915i	$-0.677257\pi$
$811$	−1.97994e7			−1.05706			−0.528530	+	0.848915i	$0.677257\pi$
$812$		0			0
$813$	1.28658e6	+	1.02424e7i	0.0682668	+	0.543472i
$814$		0			0
$815$	−8.04838e6			−0.424438
$816$		0			0
$817$	2.11964e7			1.11098
$818$		0			0
$819$	3.51161e7	−	8.96346e6i	1.82935	−	0.466945i
$820$		0			0
$821$	−1.93529e7			−1.00205			−0.501025	−	0.865433i	$-0.667043\pi$
$821$	−1.93529e7			−1.00205			−0.501025	+	0.865433i	$0.667043\pi$
$822$		0			0
$823$		−	1.81822e7i		−	0.935722i	−0.883802	−	0.467861i	$-0.845025\pi$
$823$		−	1.81822e7i		−	0.935722i	0.883802	−	0.467861i	$-0.154975\pi$
$824$		0			0
$825$	−4.82764e6	−	3.84329e7i	−0.246945	−	1.96593i
$826$		0			0
$827$		−	2.31170e7i		−	1.17535i	−0.809097	−	0.587674i	$-0.800044\pi$
$827$		−	2.31170e7i		−	1.17535i	0.809097	−	0.587674i	$-0.199956\pi$
$828$		0			0
$829$		−	1.28676e7i		−	0.650298i	−0.945663	−	0.325149i	$-0.894586\pi$
$829$		−	1.28676e7i		−	0.650298i	0.945663	−	0.325149i	$-0.105414\pi$
$830$		0			0
$831$	3.32761e6	+	2.64911e7i	0.167159	+	1.33075i
$832$		0			0
$833$		−	3.36335e7i		−	1.67942i
$834$		0			0
$835$	−6.96973e7			−3.45939
$836$		0			0
$837$	−1.97765e6	−	5.02605e6i	−0.0975746	−	0.247978i
$838$		0			0
$839$	−2.76867e7			−1.35789			−0.678947	−	0.734187i	$-0.737563\pi$
$839$	−2.76867e7			−1.35789			−0.678947	+	0.734187i	$0.737563\pi$
$840$		0			0
$841$	−6.20840e6			−0.302684
$842$		0			0
$843$	−375074.	−	2.98596e6i	−0.0181781	−	0.144716i
$844$		0			0
$845$	−1.84959e7			−0.891117
$846$		0			0
$847$		−	7.69729e6i		−	0.368663i
$848$		0			0
$849$	7.00451e6	−	879854.i	0.333510	−	0.0418930i
$850$		0			0
$851$		−	5.32712e6i		−	0.252155i
$852$		0			0
$853$		−	3.80648e7i		−	1.79123i	−0.444834	−	0.895613i	$-0.646737\pi$
$853$		−	3.80648e7i		−	1.79123i	0.444834	−	0.895613i	$-0.353263\pi$
$854$		0			0
$855$	3.12465e7	−	7.97574e6i	1.46179	−	0.373126i
$856$		0			0
$857$			5.35259e6i			0.248950i	0.992223	+	0.124475i	$0.0397246\pi$
$857$			5.35259e6i			0.248950i	−0.992223	+	0.124475i	$0.960275\pi$
$858$		0			0
$859$	−5.99877e6			−0.277383			−0.138691	−	0.990336i	$-0.544290\pi$
$859$	−5.99877e6			−0.277383			−0.138691	+	0.990336i	$0.544290\pi$
$860$		0			0
$861$	−3.35868e7	+	4.21891e6i	−1.54405	+	0.193951i
$862$		0			0
$863$	2.28810e7			1.04580			0.522900	−	0.852394i	$-0.324850\pi$
$863$	2.28810e7			1.04580			0.522900	+	0.852394i	$0.324850\pi$
$864$		0			0
$865$	−3.07899e7			−1.39916
$866$		0			0
$867$	1.01929e7	−	1.28036e6i	0.460523	−	0.0578474i
$868$		0			0
$869$	−1.16278e7			−0.522334
$870$		0			0
$871$			1.16884e7i			0.522045i
$872$		0			0
$873$	2.71051e7	−	6.91864e6i	1.20369	−	0.307245i
$874$		0			0
$875$		−	8.04228e7i		−	3.55107i
$876$		0			0
$877$		−	2.64785e6i		−	0.116250i	−0.998309	−	0.0581251i	$-0.981488\pi$
$877$		−	2.64785e6i		−	0.116250i	0.998309	−	0.0581251i	$-0.0185122\pi$
$878$		0			0
$879$	−4.73160e6	+	594348.i	−0.206555	+	0.0259459i
$880$		0			0
$881$			3.36236e7i			1.45950i	0.683713	+	0.729751i	$0.260364\pi$
$881$			3.36236e7i			1.45950i	−0.683713	+	0.729751i	$0.739636\pi$
$882$		0			0
$883$	3.25738e7			1.40594			0.702971	−	0.711219i	$-0.251856\pi$
$883$	3.25738e7			1.40594			0.702971	+	0.711219i	$0.251856\pi$
$884$		0			0
$885$	−6.63628e6	−	5.28314e7i	−0.284818	−	2.26743i
$886$		0			0
$887$	−3.13499e7			−1.33791			−0.668955	−	0.743303i	$-0.733258\pi$
$887$	−3.13499e7			−1.33791			−0.668955	+	0.743303i	$0.733258\pi$
$888$		0			0
$889$	−3.16994e7			−1.34523
$890$		0			0
$891$	9.91051e6	+	1.81483e7i	0.418217	+	0.765848i
$892$		0			0
$893$	−4.47828e6			−0.187924
$894$		0			0
$895$		−	5.19775e7i		−	2.16899i
$896$		0			0
$897$	2.95085e6	+	2.34917e7i	0.122452	+	0.974839i
$898$		0			0
$899$		−	5.39245e6i		−	0.222529i
$900$		0			0
$901$		−	778078.i		−	0.0319309i
$902$		0			0
$903$	6.28486e6	+	5.00338e7i	0.256493	+	2.04194i
$904$		0			0
$905$			1.25073e7i			0.507624i
$906$		0			0
$907$	2.44690e7			0.987639			0.493819	−	0.869565i	$-0.335600\pi$
$907$	2.44690e7			0.987639			0.493819	+	0.869565i	$0.335600\pi$
$908$		0			0
$909$	3.21487e7	−	8.20604e6i	1.29049	−	0.329400i
$910$		0			0
$911$	−1.32547e7			−0.529146			−0.264573	−	0.964366i	$-0.585231\pi$
$911$	−1.32547e7			−0.529146			−0.264573	+	0.964366i	$0.585231\pi$
$912$		0			0
$913$	−2.65542e7			−1.05428
$914$		0			0
$915$	9.91549e6	+	7.89372e7i	0.391527	+	3.11694i
$916$		0			0
$917$	4.28111e7			1.68125
$918$		0			0
$919$			1.86148e7i			0.727060i	0.931582	+	0.363530i	$0.118429\pi$
$919$			1.86148e7i			0.727060i	−0.931582	+	0.363530i	$0.881571\pi$
$920$		0			0
$921$	−4.81212e7	+	6.04462e6i	−1.86934	+	0.234812i
$922$		0			0
$923$		−	2.71430e7i		−	1.04871i
$924$		0			0
$925$			1.85283e7i			0.712001i
$926$		0			0
$927$	4.94851e6	+	1.93867e7i	0.189136	+	0.740978i
$928$		0			0
$929$		−	3.92566e7i		−	1.49236i	−0.665745	−	0.746179i	$-0.731886\pi$
$929$		−	3.92566e7i		−	1.49236i	0.665745	−	0.746179i	$-0.268114\pi$
$930$		0			0
$931$	−3.06208e7			−1.15782
$932$		0			0
$933$	310647.	−	39021.2i	0.0116832	−	0.00146756i
$934$		0			0
$935$	−5.10450e7			−1.90952
$936$		0			0
$937$	−4.09078e7			−1.52215			−0.761075	−	0.648664i	$-0.775328\pi$
$937$	−4.09078e7			−1.52215			−0.761075	+	0.648664i	$0.775328\pi$
$938$		0			0
$939$	−1.82923e7	+	2.29774e6i	−0.677026	+	0.0850428i
$940$		0			0
$941$	3.21351e7			1.18306			0.591528	−	0.806285i	$-0.298525\pi$
$941$	3.21351e7			1.18306			0.591528	+	0.806285i	$0.298525\pi$
$942$		0			0
$943$		−	2.21141e7i		−	0.809822i
$944$		0			0
$945$	2.80914e7	+	7.13920e7i	1.02328	+	2.60058i
$946$		0			0
$947$		−	1.93792e7i		−	0.702201i	−0.936338	−	0.351101i	$-0.885807\pi$
$947$		−	1.93792e7i		−	0.702201i	0.936338	−	0.351101i	$-0.114193\pi$
$948$		0			0
$949$		−	2.75648e7i		−	0.993548i
$950$		0			0
$951$	1.91433e6	−	240463.i	0.0686381	−	0.00862179i
$952$		0			0
$953$		−	5.25387e6i		−	0.187390i	−0.995601	−	0.0936952i	$-0.970132\pi$
$953$		−	5.25387e6i		−	0.187390i	0.995601	−	0.0936952i	$-0.0298679\pi$
$954$		0			0
$955$	5.60645e7			1.98921
$956$		0			0
$957$	2.57301e6	+	2.04838e7i	0.0908160	+	0.722986i
$958$		0			0
$959$	−4.24637e7			−1.49098
$960$		0			0
$961$	2.65961e7			0.928986
$962$		0			0
$963$	−7.56732e6	−	2.96464e7i	−0.262952	−	1.03017i
$964$		0			0
$965$	6.71998e7			2.32300
$966$		0			0
$967$		−	1.32467e7i		−	0.455556i	−0.973713	−	0.227778i	$-0.926854\pi$
$967$		−	1.32467e7i		−	0.455556i	0.973713	−	0.227778i	$-0.0731460\pi$
$968$		0			0
$969$	−3.67712e6	−	2.92736e7i	−0.125805	−	1.00154i
$970$		0			0
$971$			376564.i			0.0128171i	0.999979	+	0.00640856i	$0.00203992\pi$
$971$			376564.i			0.0128171i	−0.999979	+	0.00640856i	$0.997960\pi$
$972$		0			0
$973$			1.41172e7i			0.478041i
$974$		0			0
$975$	−1.02633e7	−	8.17065e7i	−0.345762	−	2.75261i
$976$		0			0
$977$		−	5.07648e7i		−	1.70148i	−0.525588	−	0.850739i	$-0.676155\pi$
$977$		−	5.07648e7i		−	1.70148i	0.525588	−	0.850739i	$-0.323845\pi$
$978$		0			0
$979$	−3.40889e6			−0.113673
$980$		0			0
$981$	4.64106e6	+	1.81822e7i	0.153973	+	0.603219i
$982$		0			0
$983$	−1.14328e7			−0.377372			−0.188686	−	0.982038i	$-0.560423\pi$
$983$	−1.14328e7			−0.377372			−0.188686	+	0.982038i	$0.560423\pi$
$984$		0			0
$985$	2.09862e7			0.689198
$986$		0			0
$987$	−1.32784e6	−	1.05709e7i	−0.0433863	−	0.345398i
$988$		0			0
$989$	−3.29430e7			−1.07096
$990$		0			0
$991$		−	2.55463e7i		−	0.826313i	−0.910660	−	0.413156i	$-0.864426\pi$
$991$		−	2.55463e7i		−	0.826313i	0.910660	−	0.413156i	$-0.135574\pi$
$992$		0			0
$993$	−4.31598e7	+	5.42140e6i	−1.38901	+	0.174477i
$994$		0			0
$995$			4.91792e7i			1.57479i
$996$		0			0
$997$			1.08510e7i			0.345725i	0.984946	+	0.172862i	$0.0553016\pi$
$997$			1.08510e7i			0.345725i	−0.984946	+	0.172862i	$0.944698\pi$
$998$		0			0
$999$	−3.62165e6	−	9.20414e6i	−0.114813	−	0.291789i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.6.f.e.191.2	yes	20
3.2	odd	2		384.6.f.f.191.1	yes	20
4.3	odd	2		384.6.f.f.191.19	yes	20
8.3	odd	2		384.6.f.f.191.2	yes	20
8.5	even	2	inner	384.6.f.e.191.19	yes	20
12.11	even	2	inner	384.6.f.e.191.20	yes	20
24.5	odd	2		384.6.f.f.191.20	yes	20
24.11	even	2	inner	384.6.f.e.191.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.6.f.e.191.1	✓	20	24.11	even	2	inner
384.6.f.e.191.2	yes	20	1.1	even	1	trivial
384.6.f.e.191.19	yes	20	8.5	even	2	inner
384.6.f.e.191.20	yes	20	12.11	even	2	inner
384.6.f.f.191.1	yes	20	3.2	odd	2
384.6.f.f.191.2	yes	20	8.3	odd	2
384.6.f.f.191.19	yes	20	4.3	odd	2
384.6.f.f.191.20	yes	20	24.5	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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	384.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-15.4669 + 1.94284i) q^{3} +101.098 q^{5} -200.335i q^{7} +(235.451 - 60.0993i) q^{9} +O(q^{10})\)	\(q+(-15.4669 + 1.94284i) q^{3} +101.098 q^{5} -200.335i q^{7} +(235.451 - 60.0993i) q^{9} +350.184i q^{11} +744.475i q^{13} +(-1563.68 + 196.417i) q^{15} +1441.83i q^{17} +1312.68 q^{19} +(389.217 + 3098.56i) q^{21} -2040.14 q^{23} +7095.82 q^{25} +(-3524.93 + 1386.99i) q^{27} -3781.90 q^{29} +1425.86i q^{31} +(-680.350 - 5416.27i) q^{33} -20253.4i q^{35} +2611.15i q^{37} +(-1446.39 - 11514.7i) q^{39} +10839.5i q^{41} +16147.4 q^{43} +(23803.6 - 6075.93i) q^{45} -3411.56 q^{47} -23326.9 q^{49} +(-2801.24 - 22300.6i) q^{51} -539.647 q^{53} +35402.9i q^{55} +(-20303.1 + 2550.32i) q^{57} +33786.7i q^{59} -50481.9i q^{61} +(-12040.0 - 47168.9i) q^{63} +75265.0i q^{65} +15700.1 q^{67} +(31554.7 - 3963.66i) q^{69} -36459.2 q^{71} -37025.8 q^{73} +(-109750. + 13786.0i) q^{75} +70154.0 q^{77} +33204.8i q^{79} +(51825.1 - 28300.9i) q^{81} +75829.2i q^{83} +145766. i q^{85} +(58494.3 - 7347.61i) q^{87} +9734.56i q^{89} +149144. q^{91} +(-2770.21 - 22053.6i) q^{93} +132709. q^{95} +115120. q^{97} +(21045.8 + 82451.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 44 q^{9}+O(q^{10}) \) 20 * q - 44 * q^9	\( 20 q - 44 q^{9} - 3568 q^{15} + 6112 q^{23} + 15228 q^{25} + 7592 q^{33} - 2800 q^{39} + 26112 q^{47} - 81044 q^{49} - 89296 q^{57} - 14816 q^{63} - 72224 q^{71} - 61256 q^{73} + 89588 q^{81} - 145648 q^{87} + 385504 q^{95} + 92808 q^{97}+O(q^{100}) \) 20 * q - 44 * q^9 - 3568 * q^15 + 6112 * q^23 + 15228 * q^25 + 7592 * q^33 - 2800 * q^39 + 26112 * q^47 - 81044 * q^49 - 89296 * q^57 - 14816 * q^63 - 72224 * q^71 - 61256 * q^73 + 89588 * q^81 - 145648 * q^87 + 385504 * q^95 + 92808 * q^97

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