LMFDB - Embedded newform 384.6.f.f.191.13

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			191.13
Root			$4.77687 + 4.77687i$ of defining polynomial
Character	$\chi$	$=$	384.191
Dual form			384.6.f.f.191.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(6.91183 - 13.9723i) q^{3} -56.7417 q^{5} +130.269i q^{7} +(-147.453 - 193.149i) q^{9} +O(q^{10})$	\(q+(6.91183 - 13.9723i) q^{3} -56.7417 q^{5} +130.269i q^{7} +(-147.453 - 193.149i) q^{9} -484.591i q^{11} -555.929i q^{13} +(-392.189 + 792.815i) q^{15} -1110.46i q^{17} +741.084 q^{19} +(1820.17 + 900.400i) q^{21} +459.270 q^{23} +94.6178 q^{25} +(-3717.92 + 725.251i) q^{27} +3061.20 q^{29} +5980.71i q^{31} +(-6770.87 - 3349.41i) q^{33} -7391.70i q^{35} -3466.31i q^{37} +(-7767.63 - 3842.49i) q^{39} +14979.6i q^{41} -16818.5 q^{43} +(8366.73 + 10959.6i) q^{45} -19676.9 q^{47} -163.085 q^{49} +(-15515.8 - 7675.35i) q^{51} -32218.4 q^{53} +27496.5i q^{55} +(5122.25 - 10354.7i) q^{57} +5250.05i q^{59} +53641.2i q^{61} +(25161.4 - 19208.6i) q^{63} +31544.3i q^{65} +66623.4 q^{67} +(3174.40 - 6417.08i) q^{69} +33198.9 q^{71} -80330.2 q^{73} +(653.983 - 1322.03i) q^{75} +63127.3 q^{77} +19463.9i q^{79} +(-15564.2 + 56960.9i) q^{81} +22867.0i q^{83} +63009.6i q^{85} +(21158.5 - 42772.2i) q^{87} +33539.4i q^{89} +72420.4 q^{91} +(83564.6 + 41337.7i) q^{93} -42050.4 q^{95} -146327. q^{97} +(-93598.2 + 71454.4i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	6.91183	−	13.9723i	0.443394	−	0.896327i
$3$	6.91183	−	13.9723i	0.443394	−	0.896327i
$4$		0			0
$5$	−56.7417			−1.01503			−0.507513	−	0.861644i	$-0.669435\pi$
$5$	−56.7417			−1.01503			−0.507513	+	0.861644i	$0.669435\pi$
$6$		0			0
$7$			130.269i			1.00484i	0.864624	+	0.502420i	$0.167557\pi$
$7$			130.269i			1.00484i	−0.864624	+	0.502420i	$0.832443\pi$
$8$		0			0
$9$	−147.453	−	193.149i	−0.606803	−	0.794852i
$10$		0			0
$11$		−	484.591i		−	1.20752i	−0.797167	−	0.603758i	$-0.793669\pi$
$11$		−	484.591i		−	1.20752i	0.797167	−	0.603758i	$-0.206331\pi$
$12$		0			0
$13$		−	555.929i		−	0.912348i	−0.889890	−	0.456174i	$-0.849219\pi$
$13$		−	555.929i		−	0.912348i	0.889890	−	0.456174i	$-0.150781\pi$
$14$		0			0
$15$	−392.189	+	792.815i	−0.450057	+	0.909795i
$16$		0			0
$17$		−	1110.46i		−	0.931928i	−0.884804	−	0.465964i	$-0.845708\pi$
$17$		−	1110.46i		−	0.931928i	0.884804	−	0.465964i	$-0.154292\pi$
$18$		0			0
$19$	741.084			0.470959			0.235480	−	0.971879i	$-0.424334\pi$
$19$	741.084			0.470959			0.235480	+	0.971879i	$0.424334\pi$
$20$		0			0
$21$	1820.17	+	900.400i	0.900665	+	0.445540i
$22$		0			0
$23$	459.270			0.181029			0.0905145	−	0.995895i	$-0.471149\pi$
$23$	459.270			0.181029			0.0905145	+	0.995895i	$0.471149\pi$
$24$		0			0
$25$	94.6178			0.0302777
$26$		0			0
$27$	−3717.92	+	725.251i	−0.981500	+	0.191460i
$28$		0			0
$29$	3061.20			0.675923			0.337962	−	0.941160i	$-0.390263\pi$
$29$	3061.20			0.675923			0.337962	+	0.941160i	$0.390263\pi$
$30$		0			0
$31$			5980.71i			1.11776i	0.829249	+	0.558880i	$0.188769\pi$
$31$			5980.71i			1.11776i	−0.829249	+	0.558880i	$0.811231\pi$
$32$		0			0
$33$	−6770.87	−	3349.41i	−1.08233	−	0.535406i
$34$		0			0
$35$		−	7391.70i		−	1.01994i
$36$		0			0
$37$		−	3466.31i		−	0.416258i	−0.978101	−	0.208129i	$-0.933263\pi$
$37$		−	3466.31i		−	0.416258i	0.978101	−	0.208129i	$-0.0667374\pi$
$38$		0			0
$39$	−7767.63	−	3842.49i	−0.817762	−	0.404530i
$40$		0			0
$41$			14979.6i			1.39168i	0.718195	+	0.695842i	$0.244969\pi$
$41$			14979.6i			1.39168i	−0.718195	+	0.695842i	$0.755031\pi$
$42$		0			0
$43$	−16818.5			−1.38713			−0.693563	−	0.720396i	$-0.743960\pi$
$43$	−16818.5			−1.38713			−0.693563	+	0.720396i	$0.743960\pi$
$44$		0			0
$45$	8366.73	+	10959.6i	0.615921	+	0.806796i
$46$		0			0
$47$	−19676.9			−1.29931			−0.649654	−	0.760230i	$-0.725086\pi$
$47$	−19676.9			−1.29931			−0.649654	+	0.760230i	$0.725086\pi$
$48$		0			0
$49$	−163.085			−0.00970341
$50$		0			0
$51$	−15515.8	−	7675.35i	−0.835312	−	0.413212i
$52$		0			0
$53$	−32218.4			−1.57549			−0.787743	−	0.616004i	$-0.788751\pi$
$53$	−32218.4			−1.57549			−0.787743	+	0.616004i	$0.788751\pi$
$54$		0			0
$55$			27496.5i			1.22566i
$56$		0			0
$57$	5122.25	−	10354.7i	0.208821	−	0.422134i
$58$		0			0
$59$			5250.05i			0.196351i	0.995169	+	0.0981756i	$0.0313007\pi$
$59$			5250.05i			0.196351i	−0.995169	+	0.0981756i	$0.968699\pi$
$60$		0			0
$61$			53641.2i			1.84575i	0.385094	+	0.922877i	$0.374169\pi$
$61$			53641.2i			1.84575i	−0.385094	+	0.922877i	$0.625831\pi$
$62$		0			0
$63$	25161.4	−	19208.6i	0.798699	−	0.609740i
$64$		0			0
$65$			31544.3i			0.926057i
$66$		0			0
$67$	66623.4			1.81317			0.906587	−	0.422019i	$-0.138678\pi$
$67$	66623.4			1.81317			0.906587	+	0.422019i	$0.138678\pi$
$68$		0			0
$69$	3174.40	−	6417.08i	0.0802673	−	0.162261i
$70$		0			0
$71$	33198.9			0.781588			0.390794	−	0.920478i	$-0.372200\pi$
$71$	33198.9			0.781588			0.390794	+	0.920478i	$0.372200\pi$
$72$		0			0
$73$	−80330.2			−1.76430			−0.882149	−	0.470970i	$-0.843904\pi$
$73$	−80330.2			−1.76430			−0.882149	+	0.470970i	$0.843904\pi$
$74$		0			0
$75$	653.983	−	1322.03i	0.0134250	−	0.0271387i
$76$		0			0
$77$	63127.3			1.21336
$78$		0			0
$79$			19463.9i			0.350883i	0.984490	+	0.175442i	$0.0561353\pi$
$79$			19463.9i			0.350883i	−0.984490	+	0.175442i	$0.943865\pi$
$80$		0			0
$81$	−15564.2	+	56960.9i	−0.263581	+	0.964637i
$82$		0			0
$83$			22867.0i			0.364345i	0.983267	+	0.182173i	$0.0583130\pi$
$83$			22867.0i			0.364345i	−0.983267	+	0.182173i	$0.941687\pi$
$84$		0			0
$85$			63009.6i			0.945931i
$86$		0			0
$87$	21158.5	−	42772.2i	0.299701	−	0.605848i
$88$		0			0
$89$			33539.4i			0.448829i	0.974494	+	0.224414i	$0.0720469\pi$
$89$			33539.4i			0.448829i	−0.974494	+	0.224414i	$0.927953\pi$
$90$		0			0
$91$	72420.4			0.916764
$92$		0			0
$93$	83564.6	+	41337.7i	1.00188	+	0.495608i
$94$		0			0
$95$	−42050.4			−0.478036
$96$		0			0
$97$	−146327.			−1.57905			−0.789524	−	0.613719i	$-0.789673\pi$
$97$	−146327.			−1.57905			−0.789524	+	0.613719i	$0.789673\pi$
$98$		0			0
$99$	−93598.2	+	71454.4i	−0.959798	+	0.732725i
$100$		0			0
$101$	113137.			1.10357			0.551786	−	0.833986i	$-0.313947\pi$
$101$	113137.			1.10357			0.551786	+	0.833986i	$0.313947\pi$
$102$		0			0
$103$		−	159779.i		−	1.48398i	−0.670411	−	0.741990i	$-0.733882\pi$
$103$		−	159779.i		−	1.48398i	0.670411	−	0.741990i	$-0.266118\pi$
$104$		0			0
$105$	−103279.	−	51090.2i	−0.914198	−	0.452235i
$106$		0			0
$107$		−	16948.9i		−	0.143114i	−0.997437	−	0.0715571i	$-0.977203\pi$
$107$		−	16948.9i		−	0.143114i	0.997437	−	0.0715571i	$-0.0227968\pi$
$108$		0			0
$109$			152539.i			1.22974i	0.788627	+	0.614872i	$0.210792\pi$
$109$			152539.i			1.22974i	−0.788627	+	0.614872i	$0.789208\pi$
$110$		0			0
$111$	−48432.4	−	23958.5i	−0.373103	−	0.184566i
$112$		0			0
$113$		−	145492.i		−	1.07188i	−0.844258	−	0.535938i	$-0.819958\pi$
$113$		−	145492.i		−	1.07188i	0.844258	−	0.535938i	$-0.180042\pi$
$114$		0			0
$115$	−26059.7			−0.183749
$116$		0			0
$117$	−107377.	+	81973.4i	−0.725182	+	0.553616i
$118$		0			0
$119$	144659.			0.936438
$120$		0			0
$121$	−73777.0			−0.458097
$122$		0			0
$123$	209300.	+	103537.i	1.24740	+	0.617065i
$124$		0			0
$125$	171949.			0.984293
$126$		0			0
$127$			90945.7i			0.500349i	0.968201	+	0.250175i	$0.0804880\pi$
$127$			90945.7i			0.500349i	−0.968201	+	0.250175i	$0.919512\pi$
$128$		0			0
$129$	−116247.	+	234994.i	−0.615044	+	1.24332i
$130$		0			0
$131$		−	40671.9i		−	0.207070i	−0.994626	−	0.103535i	$-0.966985\pi$
$131$		−	40671.9i		−	0.207070i	0.994626	−	0.103535i	$-0.0330153\pi$
$132$		0			0
$133$			96540.5i			0.473239i
$134$		0			0
$135$	210961.	−	41152.0i	0.996248	−	0.194337i
$136$		0			0
$137$			330626.i			1.50499i	0.658595	+	0.752497i	$0.271151\pi$
$137$			330626.i			1.50499i	−0.658595	+	0.752497i	$0.728849\pi$
$138$		0			0
$139$	−176648.			−0.775484			−0.387742	−	0.921768i	$-0.626745\pi$
$139$	−176648.			−0.775484			−0.387742	+	0.921768i	$0.626745\pi$
$140$		0			0
$141$	−136004.	+	274933.i	−0.576106	+	1.16460i
$142$		0			0
$143$	−269398.			−1.10168
$144$		0			0
$145$	−173698.			−0.686079
$146$		0			0
$147$	−1127.22	+	2278.68i	−0.00430244	+	0.00869742i
$148$		0			0
$149$	56218.4			0.207450			0.103725	−	0.994606i	$-0.466924\pi$
$149$	56218.4			0.207450			0.103725	+	0.994606i	$0.466924\pi$
$150$		0			0
$151$			175958.i			0.628010i	0.949421	+	0.314005i	$0.101671\pi$
$151$			175958.i			0.628010i	−0.949421	+	0.314005i	$0.898329\pi$
$152$		0			0
$153$	−214485.	+	163741.i	−0.740745	+	0.565496i
$154$		0			0
$155$		−	339355.i		−	1.13456i
$156$		0			0
$157$			78738.0i			0.254938i	0.991843	+	0.127469i	$0.0406854\pi$
$157$			78738.0i			0.254938i	−0.991843	+	0.127469i	$0.959315\pi$
$158$		0			0
$159$	−222688.	+	450167.i	−0.698562	+	1.41215i
$160$		0			0
$161$			59828.7i			0.181905i
$162$		0			0
$163$	−127815.			−0.376800			−0.188400	−	0.982092i	$-0.560330\pi$
$163$	−127815.			−0.376800			−0.188400	+	0.982092i	$0.560330\pi$
$164$		0			0
$165$	384190.	+	190051.i	1.09859	+	0.543451i
$166$		0			0
$167$	−307401.			−0.852933			−0.426466	−	0.904503i	$-0.640242\pi$
$167$	−307401.			−0.852933			−0.426466	+	0.904503i	$0.640242\pi$
$168$		0			0
$169$	62236.2			0.167620
$170$		0			0
$171$	−109275.	−	143140.i	−0.285780	−	0.374343i
$172$		0			0
$173$	−283267.			−0.719582			−0.359791	−	0.933033i	$-0.617152\pi$
$173$	−283267.			−0.719582			−0.359791	+	0.933033i	$0.617152\pi$
$174$		0			0
$175$			12325.8i			0.0304242i
$176$		0			0
$177$	73355.6	+	36287.5i	0.175995	+	0.0870611i
$178$		0			0
$179$		−	376390.i		−	0.878023i	−0.898481	−	0.439012i	$-0.855329\pi$
$179$		−	376390.i		−	0.878023i	0.898481	−	0.439012i	$-0.144671\pi$
$180$		0			0
$181$			698692.i			1.58522i	0.609730	+	0.792609i	$0.291278\pi$
$181$			698692.i			1.58522i	−0.609730	+	0.792609i	$0.708722\pi$
$182$		0			0
$183$	749494.	+	370759.i	1.65440	+	0.818397i
$184$		0			0
$185$			196684.i			0.422513i
$186$		0			0
$187$	−538120.			−1.12532
$188$		0			0
$189$	−94477.9	−	484331.i	−0.192387	−	0.986251i
$190$		0			0
$191$	−874587.			−1.73468			−0.867340	−	0.497716i	$-0.834172\pi$
$191$	−874587.			−1.73468			−0.867340	+	0.497716i	$0.834172\pi$
$192$		0			0
$193$	−182483.			−0.352637			−0.176319	−	0.984333i	$-0.556419\pi$
$193$	−182483.			−0.352637			−0.176319	+	0.984333i	$0.556419\pi$
$194$		0			0
$195$	440748.	+	218029.i	0.830050	+	0.410609i
$196$		0			0
$197$	288691.			0.529991			0.264995	−	0.964250i	$-0.414630\pi$
$197$	288691.			0.529991			0.264995	+	0.964250i	$0.414630\pi$
$198$		0			0
$199$		−	961761.i		−	1.72161i	−0.508935	−	0.860805i	$-0.669961\pi$
$199$		−	961761.i		−	1.72161i	0.508935	−	0.860805i	$-0.330039\pi$
$200$		0			0
$201$	460490.	−	930885.i	0.803951	−	1.62520i
$202$		0			0
$203$			398781.i			0.679195i
$204$		0			0
$205$		−	849968.i		−	1.41260i
$206$		0			0
$207$	−67720.7	−	88707.6i	−0.109849	−	0.143891i
$208$		0			0
$209$		−	359122.i		−	0.568692i
$210$		0			0
$211$	−191585.			−0.296248			−0.148124	−	0.988969i	$-0.547323\pi$
$211$	−191585.			−0.296248			−0.148124	+	0.988969i	$0.547323\pi$
$212$		0			0
$213$	229465.	−	463867.i	0.346552	−	0.700558i
$214$		0			0
$215$	954309.			1.40797
$216$		0			0
$217$	−779103.			−1.12317
$218$		0			0
$219$	−555229.	+	1.12240e6i	−0.782280	+	1.58139i
$220$		0			0
$221$	−617339.			−0.850243
$222$		0			0
$223$			449203.i			0.604896i	0.953166	+	0.302448i	$0.0978038\pi$
$223$			449203.i			0.604896i	−0.953166	+	0.302448i	$0.902196\pi$
$224$		0			0
$225$	−13951.7	−	18275.4i	−0.0183726	−	0.0240663i
$226$		0			0
$227$		−	578361.i		−	0.744962i	−0.928040	−	0.372481i	$-0.878507\pi$
$227$		−	578361.i		−	0.744962i	0.928040	−	0.372481i	$-0.121493\pi$
$228$		0			0
$229$		−	342423.i		−	0.431494i	−0.976449	−	0.215747i	$-0.930781\pi$
$229$		−	342423.i		−	0.431494i	0.976449	−	0.215747i	$-0.0692186\pi$
$230$		0			0
$231$	436325.	−	882036.i	0.537998	−	1.08757i
$232$		0			0
$233$		−	724022.i		−	0.873699i	−0.899535	−	0.436849i	$-0.856094\pi$
$233$		−	724022.i		−	0.873699i	0.899535	−	0.436849i	$-0.143906\pi$
$234$		0			0
$235$	1.11650e6			1.31883
$236$		0			0
$237$	271957.	+	134531.i	0.314506	+	0.155580i
$238$		0			0
$239$	−1.64343e6			−1.86104			−0.930521	−	0.366238i	$-0.880645\pi$
$239$	−1.64343e6			−1.86104			−0.930521	+	0.366238i	$0.880645\pi$
$240$		0			0
$241$	1.63037e6			1.80819			0.904095	−	0.427331i	$-0.140546\pi$
$241$	1.63037e6			1.80819			0.904095	+	0.427331i	$0.140546\pi$
$242$		0			0
$243$	688300.	+	611172.i	0.747760	+	0.663969i
$244$		0			0
$245$	9253.73			0.00984921
$246$		0			0
$247$		−	411990.i		−	0.429679i
$248$		0			0
$249$	319505.	+	158053.i	0.326572	+	0.161549i
$250$		0			0
$251$		−	1.50508e6i		−	1.50791i	−0.656925	−	0.753956i	$-0.728143\pi$
$251$		−	1.50508e6i		−	1.50791i	0.656925	−	0.753956i	$-0.271857\pi$
$252$		0			0
$253$		−	222558.i		−	0.218596i
$254$		0			0
$255$	880392.	+	435512.i	0.847863	+	0.419420i
$256$		0			0
$257$			1.20632e6i			1.13927i	0.821896	+	0.569637i	$0.192916\pi$
$257$			1.20632e6i			1.13927i	−0.821896	+	0.569637i	$0.807084\pi$
$258$		0			0
$259$	451553.			0.418273
$260$		0			0
$261$	−451384.	−	591269.i	−0.410152	−	0.537259i
$262$		0			0
$263$	1.62597e6			1.44951			0.724757	−	0.689005i	$-0.241952\pi$
$263$	1.62597e6			1.44951			0.724757	+	0.689005i	$0.241952\pi$
$264$		0			0
$265$	1.82813e6			1.59916
$266$		0			0
$267$	468625.	+	231819.i	0.402297	+	0.199008i
$268$		0			0
$269$	−137819.			−0.116126			−0.0580630	−	0.998313i	$-0.518492\pi$
$269$	−137819.			−0.116126			−0.0580630	+	0.998313i	$0.518492\pi$
$270$		0			0
$271$			1.48417e6i			1.22761i	0.789457	+	0.613806i	$0.210362\pi$
$271$			1.48417e6i			1.22761i	−0.789457	+	0.613806i	$0.789638\pi$
$272$		0			0
$273$	500558.	−	1.01188e6i	0.406488	−	0.821720i
$274$		0			0
$275$		−	45850.9i		−	0.0365608i
$276$		0			0
$277$		−	1.61429e6i		−	1.26410i	−0.774927	−	0.632051i	$-0.782214\pi$
$277$		−	1.61429e6i		−	1.26410i	0.774927	−	0.632051i	$-0.217786\pi$
$278$		0			0
$279$	1.15517e6	−	881874.i	0.888454	−	0.678260i
$280$		0			0
$281$			110881.i			0.0837704i	0.999122	+	0.0418852i	$0.0133364\pi$
$281$			110881.i			0.0837704i	−0.999122	+	0.0418852i	$0.986664\pi$
$282$		0			0
$283$	1.24585e6			0.924700			0.462350	−	0.886698i	$-0.347006\pi$
$283$	1.24585e6			0.924700			0.462350	+	0.886698i	$0.347006\pi$
$284$		0			0
$285$	−290645.	+	587542.i	−0.211959	+	0.428476i
$286$		0			0
$287$	−1.95138e6			−1.39842
$288$		0			0
$289$	186726.			0.131511
$290$		0			0
$291$	−1.01139e6	+	2.04453e6i	−0.700141	+	1.41534i
$292$		0			0
$293$	−2.78388e6			−1.89444			−0.947222	−	0.320578i	$-0.896123\pi$
$293$	−2.78388e6			−1.89444			−0.947222	+	0.320578i	$0.896123\pi$
$294$		0			0
$295$		−	297897.i		−	0.199302i
$296$		0			0
$297$	351450.	+	1.80167e6i	0.231192	+	1.18518i
$298$		0			0
$299$		−	255321.i		−	0.165162i
$300$		0			0
$301$		−	2.19093e6i		−	1.39384i
$302$		0			0
$303$	781983.	−	1.58079e6i	0.489317	−	0.989161i
$304$		0			0
$305$		−	3.04369e6i		−	1.87349i
$306$		0			0
$307$	−587991.			−0.356061			−0.178031	−	0.984025i	$-0.556973\pi$
$307$	−587991.			−0.356061			−0.178031	+	0.984025i	$0.556973\pi$
$308$		0			0
$309$	−2.23249e6	−	1.10437e6i	−1.33013	−	0.657988i
$310$		0			0
$311$	−1.26748e6			−0.743086			−0.371543	−	0.928416i	$-0.621171\pi$
$311$	−1.26748e6			−0.743086			−0.371543	+	0.928416i	$0.621171\pi$
$312$		0			0
$313$	2.70854e6			1.56270			0.781348	−	0.624096i	$-0.214533\pi$
$313$	2.70854e6			1.56270			0.781348	+	0.624096i	$0.214533\pi$
$314$		0			0
$315$	−1.42770e6	+	1.08993e6i	−0.810701	+	0.618902i
$316$		0			0
$317$	−264831.			−0.148020			−0.0740100	−	0.997257i	$-0.523580\pi$
$317$	−264831.			−0.148020			−0.0740100	+	0.997257i	$0.523580\pi$
$318$		0			0
$319$		−	1.48343e6i		−	0.816188i
$320$		0			0
$321$	−236816.	−	117148.i	−0.128277	−	0.0634560i
$322$		0			0
$323$		−	822947.i		−	0.438900i
$324$		0			0
$325$		−	52600.8i		−	0.0276238i
$326$		0			0
$327$	2.13133e6	+	1.05432e6i	1.10225	+	0.545261i
$328$		0			0
$329$		−	2.56330e6i		−	1.30560i
$330$		0			0
$331$	534781.			0.268291			0.134145	−	0.990962i	$-0.457171\pi$
$331$	534781.			0.268291			0.134145	+	0.990962i	$0.457171\pi$
$332$		0			0
$333$	−669514.	+	511117.i	−0.330864	+	0.252586i
$334$		0			0
$335$	−3.78032e6			−1.84042
$336$		0			0
$337$	1.31960e6			0.632946			0.316473	−	0.948602i	$-0.397501\pi$
$337$	1.31960e6			0.632946			0.316473	+	0.948602i	$0.397501\pi$
$338$		0			0
$339$	−2.03287e6	−	1.00562e6i	−0.960750	−	0.475263i
$340$		0			0
$341$	2.89819e6			1.34971
$342$		0			0
$343$			2.16819e6i			0.995090i
$344$		0			0
$345$	−180121.	+	364116.i	−0.0814734	+	0.164699i
$346$		0			0
$347$		−	2.91141e6i		−	1.29801i	−0.760783	−	0.649006i	$-0.775185\pi$
$347$		−	2.91141e6i		−	1.29801i	0.760783	−	0.649006i	$-0.224815\pi$
$348$		0			0
$349$		−	1.06388e6i		−	0.467550i	−0.972291	−	0.233775i	$-0.924892\pi$
$349$		−	1.06388e6i		−	0.467550i	0.972291	−	0.233775i	$-0.0751080\pi$
$350$		0			0
$351$	403188.	+	2.06690e6i	0.174679	+	0.895470i
$352$		0			0
$353$			2.38799e6i			1.01999i	0.860178	+	0.509995i	$0.170353\pi$
$353$			2.38799e6i			1.01999i	−0.860178	+	0.509995i	$0.829647\pi$
$354$		0			0
$355$	−1.88376e6			−0.793332
$356$		0			0
$357$	999862.	−	2.02123e6i	0.415212	−	0.839355i
$358$		0			0
$359$	−2.68611e6			−1.09999			−0.549994	−	0.835169i	$-0.685370\pi$
$359$	−2.68611e6			−1.09999			−0.549994	+	0.835169i	$0.685370\pi$
$360$		0			0
$361$	−1.92689e6			−0.778197
$362$		0			0
$363$	−509934.	+	1.03084e6i	−0.203118	+	0.410604i
$364$		0			0
$365$	4.55807e6			1.79081
$366$		0			0
$367$			3.87189e6i			1.50058i	0.661111	+	0.750288i	$0.270085\pi$
$367$			3.87189e6i			1.50058i	−0.661111	+	0.750288i	$0.729915\pi$
$368$		0			0
$369$	2.89330e6	−	2.20879e6i	1.10618	−	0.844478i
$370$		0			0
$371$		−	4.19707e6i		−	1.58311i
$372$		0			0
$373$			206921.i			0.0770074i	0.999258	+	0.0385037i	$0.0122591\pi$
$373$			206921.i			0.0770074i	−0.999258	+	0.0385037i	$0.987741\pi$
$374$		0			0
$375$	1.18848e6	−	2.40253e6i	0.436430	−	0.882248i
$376$		0			0
$377$		−	1.70181e6i		−	0.616677i
$378$		0			0
$379$	−2.05927e6			−0.736404			−0.368202	−	0.929746i	$-0.620027\pi$
$379$	−2.05927e6			−0.736404			−0.368202	+	0.929746i	$0.620027\pi$
$380$		0			0
$381$	1.27073e6	+	628602.i	0.448476	+	0.221852i
$382$		0			0
$383$	−545734.			−0.190101			−0.0950504	−	0.995472i	$-0.530301\pi$
$383$	−545734.			−0.190101			−0.0950504	+	0.995472i	$0.530301\pi$
$384$		0			0
$385$	−3.58195e6			−1.23159
$386$		0			0
$387$	2.47994e6	+	3.24848e6i	0.841712	+	1.10256i
$388$		0			0
$389$	−4.56814e6			−1.53061			−0.765307	−	0.643666i	$-0.777413\pi$
$389$	−4.56814e6			−1.53061			−0.765307	+	0.643666i	$0.777413\pi$
$390$		0			0
$391$		−	510003.i		−	0.168706i
$392$		0			0
$393$	−568282.	−	281118.i	−0.185602	−	0.0918135i
$394$		0			0
$395$		−	1.10442e6i		−	0.356156i
$396$		0			0
$397$			2.08838e6i			0.665019i	0.943100	+	0.332509i	$0.107895\pi$
$397$			2.08838e6i			0.665019i	−0.943100	+	0.332509i	$0.892105\pi$
$398$		0			0
$399$	1.34890e6	+	667272.i	0.424177	+	0.209831i
$400$		0			0
$401$			2.03905e6i			0.633237i	0.948553	+	0.316619i	$0.102548\pi$
$401$			2.03905e6i			0.633237i	−0.948553	+	0.316619i	$0.897452\pi$
$402$		0			0
$403$	3.32485e6			1.01979
$404$		0			0
$405$	883138.	−	3.23206e6i	0.267541	−	0.979132i
$406$		0			0
$407$	−1.67974e6			−0.502638
$408$		0			0
$409$	−2.09607e6			−0.619580			−0.309790	−	0.950805i	$-0.600259\pi$
$409$	−2.09607e6			−0.619580			−0.309790	+	0.950805i	$0.600259\pi$
$410$		0			0
$411$	4.61962e6	+	2.28523e6i	1.34897	+	0.667306i
$412$		0			0
$413$	−683921.			−0.197302
$414$		0			0
$415$		−	1.29751e6i		−	0.369820i
$416$		0			0
$417$	−1.22096e6	+	2.46819e6i	−0.343845	+	0.695087i
$418$		0			0
$419$		−	549636.i		−	0.152947i	−0.997072	−	0.0764733i	$-0.975634\pi$
$419$		−	549636.i		−	0.152947i	0.997072	−	0.0764733i	$-0.0243660\pi$
$420$		0			0
$421$			4.43018e6i			1.21819i	0.793096	+	0.609097i	$0.208468\pi$
$421$			4.43018e6i			1.21819i	−0.793096	+	0.609097i	$0.791532\pi$
$422$		0			0
$423$	2.90142e6	+	3.80058e6i	0.788424	+	1.03276i
$424$		0			0
$425$		−	105070.i		−	0.0282166i
$426$		0			0
$427$	−6.98780e6			−1.85469
$428$		0			0
$429$	−1.86203e6	+	3.76412e6i	−0.488477	+	0.987462i
$430$		0			0
$431$	4.61758e6			1.19735			0.598675	−	0.800992i	$-0.295694\pi$
$431$	4.61758e6			1.19735			0.598675	+	0.800992i	$0.295694\pi$
$432$		0			0
$433$	1.59859e6			0.409747			0.204874	−	0.978788i	$-0.434322\pi$
$433$	1.59859e6			0.409747			0.204874	+	0.978788i	$0.434322\pi$
$434$		0			0
$435$	−1.20057e6	+	2.42697e6i	−0.304204	+	0.614951i
$436$		0			0
$437$	340358.			0.0852573
$438$		0			0
$439$		−	5.04081e6i		−	1.24836i	−0.781281	−	0.624179i	$-0.785434\pi$
$439$		−	5.04081e6i		−	1.24836i	0.781281	−	0.624179i	$-0.214566\pi$
$440$		0			0
$441$	24047.4	+	31499.8i	0.00588806	+	0.00771278i
$442$		0			0
$443$		−	687693.i		−	0.166489i	−0.996529	−	0.0832445i	$-0.973472\pi$
$443$		−	687693.i		−	0.166489i	0.996529	−	0.0832445i	$-0.0265282\pi$
$444$		0			0
$445$		−	1.90308e6i		−	0.455573i
$446$		0			0
$447$	388572.	−	785503.i	0.0919820	−	0.185943i
$448$		0			0
$449$			2.16418e6i			0.506615i	0.967386	+	0.253307i	$0.0815184\pi$
$449$			2.16418e6i			0.506615i	−0.967386	+	0.253307i	$0.918482\pi$
$450$		0			0
$451$	7.25898e6			1.68048
$452$		0			0
$453$	2.45854e6	+	1.21619e6i	0.562902	+	0.278456i
$454$		0			0
$455$	−4.10926e6			−0.930539
$456$		0			0
$457$	−128767.			−0.0288414			−0.0144207	−	0.999896i	$-0.504590\pi$
$457$	−128767.			−0.0288414			−0.0144207	+	0.999896i	$0.504590\pi$
$458$		0			0
$459$	805365.	+	4.12862e6i	0.178427	+	0.914687i
$460$		0			0
$461$	−6.38076e6			−1.39836			−0.699181	−	0.714944i	$-0.746452\pi$
$461$	−6.38076e6			−1.39836			−0.699181	+	0.714944i	$0.746452\pi$
$462$		0			0
$463$		−	5.96689e6i		−	1.29359i	−0.762666	−	0.646793i	$-0.776110\pi$
$463$		−	5.96689e6i		−	1.29359i	0.762666	−	0.646793i	$-0.223890\pi$
$464$		0			0
$465$	−4.74159e6	−	2.34557e6i	−1.01693	−	0.503055i
$466$		0			0
$467$		−	3.67725e6i		−	0.780245i	−0.920763	−	0.390122i	$-0.872433\pi$
$467$		−	3.67725e6i		−	0.780245i	0.920763	−	0.390122i	$-0.127567\pi$
$468$		0			0
$469$			8.67898e6i			1.82195i
$470$		0			0
$471$	1.10015e6	+	544224.i	0.228508	+	0.113038i
$472$		0			0
$473$			8.15008e6i			1.67498i
$474$		0			0
$475$	70119.8			0.0142596
$476$		0			0
$477$	4.75071e6	+	6.22296e6i	0.956010	+	1.25228i
$478$		0			0
$479$	−408276.			−0.0813045			−0.0406523	−	0.999173i	$-0.512944\pi$
$479$	−408276.			−0.0813045			−0.0406523	+	0.999173i	$0.512944\pi$
$480$		0			0
$481$	−1.92702e6			−0.379772
$482$		0			0
$483$	835948.	+	413526.i	0.163046	+	0.0806558i
$484$		0			0
$485$	8.30285e6			1.60278
$486$		0			0
$487$			3.14606e6i			0.601097i	0.953767	+	0.300548i	$0.0971697\pi$
$487$			3.14606e6i			0.601097i	−0.953767	+	0.300548i	$0.902830\pi$
$488$		0			0
$489$	−883433.	+	1.78587e6i	−0.167071	+	0.337736i
$490$		0			0
$491$			566933.i			0.106127i	0.998591	+	0.0530637i	$0.0168986\pi$
$491$			566933.i			0.106127i	−0.998591	+	0.0530637i	$0.983101\pi$
$492$		0			0
$493$		−	3.39936e6i		−	0.629912i
$494$		0			0
$495$	5.31092e6	−	4.05444e6i	0.974220	−	0.743734i
$496$		0			0
$497$			4.32480e6i			0.785371i
$498$		0			0
$499$	−9.53698e6			−1.71459			−0.857293	−	0.514829i	$-0.827856\pi$
$499$	−9.53698e6			−1.71459			−0.857293	+	0.514829i	$0.827856\pi$
$500$		0			0
$501$	−2.12471e6	+	4.29512e6i	−0.378186	+	0.764506i
$502$		0			0
$503$	−9.64354e6			−1.69948			−0.849741	−	0.527200i	$-0.823242\pi$
$503$	−9.64354e6			−1.69948			−0.849741	+	0.527200i	$0.823242\pi$
$504$		0			0
$505$	−6.41957e6			−1.12015
$506$		0			0
$507$	430167.	−	869586.i	0.0743219	−	0.150243i
$508$		0			0
$509$	−3.21318e6			−0.549719			−0.274860	−	0.961484i	$-0.588631\pi$
$509$	−3.21318e6			−0.549719			−0.274860	+	0.961484i	$0.588631\pi$
$510$		0			0
$511$		−	1.04646e7i		−	1.77284i
$512$		0			0
$513$	−2.75529e6	+	537472.i	−0.462247	+	0.0901701i
$514$		0			0
$515$			9.06615e6i			1.50628i
$516$		0			0
$517$			9.53524e6i			1.56894i
$518$		0			0
$519$	−1.95789e6	+	3.95790e6i	−0.319059	+	0.644981i
$520$		0			0
$521$			3.10693e6i			0.501461i	0.968057	+	0.250730i	$0.0806708\pi$
$521$			3.10693e6i			0.501461i	−0.968057	+	0.250730i	$0.919329\pi$
$522$		0			0
$523$	8.71972e6			1.39395			0.696976	−	0.717094i	$-0.254528\pi$
$523$	8.71972e6			1.39395			0.696976	+	0.717094i	$0.254528\pi$
$524$		0			0
$525$	172220.	+	85193.9i	0.0272701	+	0.0134899i
$526$		0			0
$527$	6.64136e6			1.04167
$528$		0			0
$529$	−6.22541e6			−0.967228
$530$		0			0
$531$	1.01404e6	−	774137.i	0.156070	−	0.119147i
$532$		0			0
$533$	8.32760e6			1.26970
$534$		0			0
$535$			961710.i			0.145265i
$536$		0			0
$537$	−5.25906e6	−	2.60155e6i	−0.786996	−	0.389311i
$538$		0			0
$539$			79029.5i			0.0117170i
$540$		0			0
$541$		−	9.33788e6i		−	1.37169i	−0.727749	−	0.685843i	$-0.759433\pi$
$541$		−	9.33788e6i		−	1.37169i	0.727749	−	0.685843i	$-0.240567\pi$
$542$		0			0
$543$	9.76236e6	+	4.82924e6i	1.42087	+	0.702877i
$544$		0			0
$545$		−	8.65532e6i		−	1.24822i
$546$		0			0
$547$	2.94115e6			0.420290			0.210145	−	0.977670i	$-0.432606\pi$
$547$	2.94115e6			0.420290			0.210145	+	0.977670i	$0.432606\pi$
$548$		0			0
$549$	1.03608e7	−	7.90956e6i	1.46710	−	1.12001i
$550$		0			0
$551$	2.26861e6			0.318332
$552$		0			0
$553$	−2.53555e6			−0.352581
$554$		0			0
$555$	2.74814e6	+	1.35945e6i	0.378709	+	0.187340i
$556$		0			0
$557$	9.13152e6			1.24711			0.623555	−	0.781779i	$-0.285688\pi$
$557$	9.13152e6			1.24711			0.623555	+	0.781779i	$0.285688\pi$
$558$		0			0
$559$			9.34988e6i			1.26554i
$560$		0			0
$561$	−3.71940e6	+	7.51881e6i	−0.498960	+	1.00865i
$562$		0			0
$563$		−	1.23038e7i		−	1.63595i	−0.575254	−	0.817975i	$-0.695097\pi$
$563$		−	1.23038e7i		−	1.63595i	0.575254	−	0.817975i	$-0.304903\pi$
$564$		0			0
$565$			8.25548e6i			1.08798i
$566$		0			0
$567$	−7.42025e6	−	2.02753e6i	−0.969306	−	0.264856i
$568$		0			0
$569$		−	482588.i		−	0.0624879i	−0.999512	−	0.0312440i	$-0.990053\pi$
$569$		−	482588.i		−	0.0624879i	0.999512	−	0.0312440i	$-0.00994688\pi$
$570$		0			0
$571$	226475.			0.0290689			0.0145345	−	0.999894i	$-0.495373\pi$
$571$	226475.			0.0290689			0.0145345	+	0.999894i	$0.495373\pi$
$572$		0			0
$573$	−6.04500e6	+	1.22200e7i	−0.769148	+	1.55484i
$574$		0			0
$575$	43455.1			0.00548114
$576$		0			0
$577$	2.54105e6			0.317741			0.158871	−	0.987299i	$-0.449215\pi$
$577$	2.54105e6			0.317741			0.158871	+	0.987299i	$0.449215\pi$
$578$		0			0
$579$	−1.26129e6	+	2.54971e6i	−0.156357	+	0.316078i
$580$		0			0
$581$	−2.97886e6			−0.366109
$582$		0			0
$583$			1.56127e7i			1.90243i
$584$		0			0
$585$	6.09276e6	−	4.65131e6i	0.736079	−	0.561934i
$586$		0			0
$587$		−	6.14425e6i		−	0.735993i	−0.929827	−	0.367997i	$-0.880044\pi$
$587$		−	6.14425e6i		−	0.735993i	0.929827	−	0.367997i	$-0.119956\pi$
$588$		0			0
$589$			4.43221e6i			0.526420i
$590$		0			0
$591$	1.99539e6	−	4.03370e6i	0.234995	−	0.475045i
$592$		0			0
$593$		−	1.36071e7i		−	1.58901i	−0.607255	−	0.794507i	$-0.707729\pi$
$593$		−	1.36071e7i		−	1.58901i	0.607255	−	0.794507i	$-0.292271\pi$
$594$		0			0
$595$	−8.20822e6			−0.950509
$596$		0			0
$597$	−1.34381e7	−	6.64754e6i	−1.54312	−	0.763352i
$598$		0			0
$599$	−6.20455e6			−0.706551			−0.353275	−	0.935519i	$-0.614932\pi$
$599$	−6.20455e6			−0.706551			−0.353275	+	0.935519i	$0.614932\pi$
$600$		0			0
$601$	228374.			0.0257906			0.0128953	−	0.999917i	$-0.495895\pi$
$601$	228374.			0.0257906			0.0128953	+	0.999917i	$0.495895\pi$
$602$		0			0
$603$	−9.82382e6	−	1.28682e7i	−1.10024	−	1.44121i
$604$		0			0
$605$	4.18623e6			0.464980
$606$		0			0
$607$			1.17119e6i			0.129020i	0.997917	+	0.0645101i	$0.0205485\pi$
$607$			1.17119e6i			0.129020i	−0.997917	+	0.0645101i	$0.979452\pi$
$608$		0			0
$609$	5.57191e6	+	2.75631e6i	0.608780	+	0.301151i
$610$		0			0
$611$			1.09390e7i			1.18542i
$612$		0			0
$613$		−	526490.i		−	0.0565899i	−0.999600	−	0.0282950i	$-0.990992\pi$
$613$		−	526490.i		−	0.0565899i	0.999600	−	0.0282950i	$-0.00900777\pi$
$614$		0			0
$615$	−1.18761e7	−	5.87484e6i	−1.26615	−	0.626337i
$616$		0			0
$617$			2.34265e6i			0.247739i	0.992299	+	0.123869i	$0.0395304\pi$
$617$			2.34265e6i			0.247739i	−0.992299	+	0.123869i	$0.960470\pi$
$618$		0			0
$619$	881741.			0.0924942			0.0462471	−	0.998930i	$-0.485274\pi$
$619$	881741.			0.0924942			0.0462471	+	0.998930i	$0.485274\pi$
$620$		0			0
$621$	−1.70753e6	+	333086.i	−0.177680	+	0.0346599i
$622$		0			0
$623$	−4.36916e6			−0.451001
$624$		0			0
$625$	−1.00524e7			−1.02936
$626$		0			0
$627$	−5.01778e6	−	2.48219e6i	−0.509733	−	0.252155i
$628$		0			0
$629$	−3.84921e6			−0.387922
$630$		0			0
$631$			6.37410e6i			0.637302i	0.947872	+	0.318651i	$0.103230\pi$
$631$			6.37410e6i			0.637302i	−0.947872	+	0.318651i	$0.896770\pi$
$632$		0			0
$633$	−1.32420e6	+	2.67689e6i	−0.131355	+	0.265535i
$634$		0			0
$635$		−	5.16041e6i		−	0.507867i
$636$		0			0
$637$			90663.7i			0.00885289i
$638$		0			0
$639$	−4.89528e6	−	6.41234e6i	−0.474270	−	0.621247i
$640$		0			0
$641$			7.98600e6i			0.767687i	0.923398	+	0.383844i	$0.125400\pi$
$641$			7.98600e6i			0.767687i	−0.923398	+	0.383844i	$0.874600\pi$
$642$		0			0
$643$	−7.81890e6			−0.745793			−0.372897	−	0.927873i	$-0.621635\pi$
$643$	−7.81890e6			−0.745793			−0.372897	+	0.927873i	$0.621635\pi$
$644$		0			0
$645$	6.59603e6	−	1.33339e7i	0.624285	−	1.26200i
$646$		0			0
$647$	−8.38044e6			−0.787057			−0.393528	−	0.919313i	$-0.628746\pi$
$647$	−8.38044e6			−0.787057			−0.393528	+	0.919313i	$0.628746\pi$
$648$		0			0
$649$	2.54413e6			0.237097
$650$		0			0
$651$	−5.38503e6	+	1.08859e7i	−0.498007	+	1.00673i
$652$		0			0
$653$	−3.01923e6			−0.277085			−0.138542	−	0.990357i	$-0.544242\pi$
$653$	−3.01923e6			−0.277085			−0.138542	+	0.990357i	$0.544242\pi$
$654$		0			0
$655$			2.30779e6i			0.210181i
$656$		0			0
$657$	1.18449e7	+	1.55157e7i	1.07058	+	1.40236i
$658$		0			0
$659$		−	7.78900e6i		−	0.698664i	−0.936999	−	0.349332i	$-0.886409\pi$
$659$		−	7.78900e6i		−	0.698664i	0.936999	−	0.349332i	$-0.113591\pi$
$660$		0			0
$661$			5.90709e6i			0.525860i	0.964815	+	0.262930i	$0.0846888\pi$
$661$			5.90709e6i			0.525860i	−0.964815	+	0.262930i	$0.915311\pi$
$662$		0			0
$663$	−4.26694e6	+	8.62568e6i	−0.376993	+	0.762095i
$664$		0			0
$665$		−	5.47787e6i		−	0.480350i
$666$		0			0
$667$	1.40592e6			0.122362
$668$		0			0
$669$	6.27642e6	+	3.10482e6i	0.542184	+	0.268207i
$670$		0			0
$671$	2.59940e7			2.22878
$672$		0			0
$673$	8.71964e6			0.742097			0.371049	−	0.928613i	$-0.378998\pi$
$673$	8.71964e6			0.742097			0.371049	+	0.928613i	$0.378998\pi$
$674$		0			0
$675$	−351781.	+	68621.7i	−0.0297176	+	0.00579698i
$676$		0			0
$677$	−1.44508e7			−1.21177			−0.605887	−	0.795551i	$-0.707181\pi$
$677$	−1.44508e7			−1.21177			−0.605887	+	0.795551i	$0.707181\pi$
$678$		0			0
$679$		−	1.90619e7i		−	1.58669i
$680$		0			0
$681$	−8.08106e6	−	3.99754e6i	−0.667730	−	0.330312i
$682$		0			0
$683$			1.40378e7i			1.15145i	0.817642	+	0.575727i	$0.195281\pi$
$683$			1.40378e7i			1.15145i	−0.817642	+	0.575727i	$0.804719\pi$
$684$		0			0
$685$		−	1.87602e7i		−	1.52761i
$686$		0			0
$687$	−4.78446e6	−	2.36677e6i	−0.386759	−	0.191322i
$688$		0			0
$689$			1.79112e7i			1.43739i
$690$		0			0
$691$	1.42291e7			1.13366			0.566828	−	0.823836i	$-0.308170\pi$
$691$	1.42291e7			1.13366			0.566828	+	0.823836i	$0.308170\pi$
$692$		0			0
$693$	−9.30831e6	−	1.21930e7i	−0.736271	−	0.964443i
$694$		0			0
$695$	1.00233e7			0.787136
$696$		0			0
$697$	1.66343e7			1.29695
$698$		0			0
$699$	−1.01163e7	−	5.00432e6i	−0.783119	−	0.387393i
$700$		0			0
$701$	2.47356e6			0.190120			0.0950598	−	0.995472i	$-0.469696\pi$
$701$	2.47356e6			0.190120			0.0950598	+	0.995472i	$0.469696\pi$
$702$		0			0
$703$		−	2.56882e6i		−	0.196041i
$704$		0			0
$705$	7.71707e6	−	1.56001e7i	0.584763	−	1.18210i
$706$		0			0
$707$			1.47383e7i			1.10891i
$708$		0			0
$709$			3.27275e6i			0.244510i	0.992499	+	0.122255i	$0.0390126\pi$
$709$			3.27275e6i			0.244510i	−0.992499	+	0.122255i	$0.960987\pi$
$710$		0			0
$711$	3.75944e6	−	2.87001e6i	0.278900	−	0.212917i
$712$		0			0
$713$			2.74676e6i			0.202347i
$714$		0			0
$715$	1.52861e7			1.11823
$716$		0			0
$717$	−1.13591e7	+	2.29626e7i	−0.825176	+	1.66810i
$718$		0			0
$719$	1.25182e7			0.903067			0.451534	−	0.892254i	$-0.350877\pi$
$719$	1.25182e7			0.903067			0.451534	+	0.892254i	$0.350877\pi$
$720$		0			0
$721$	2.08144e7			1.49116
$722$		0			0
$723$	1.12689e7	−	2.27801e7i	0.801741	−	1.62073i
$724$		0			0
$725$	289644.			0.0204654
$726$		0			0
$727$			2.09674e7i			1.47132i	0.677349	+	0.735661i	$0.263129\pi$
$727$			2.09674e7i			1.47132i	−0.677349	+	0.735661i	$0.736871\pi$
$728$		0			0
$729$	1.32969e7	−	5.39285e6i	0.926686	−	0.375837i
$730$		0			0
$731$			1.86763e7i			1.29270i
$732$		0			0
$733$		−	2.37515e7i		−	1.63279i	−0.577491	−	0.816397i	$-0.695968\pi$
$733$		−	2.37515e7i		−	1.63279i	0.577491	−	0.816397i	$-0.304032\pi$
$734$		0			0
$735$	63960.2	−	129296.i	0.00436709	−	0.00882811i
$736$		0			0
$737$		−	3.22850e7i		−	2.18944i
$738$		0			0
$739$	1.98341e7			1.33598			0.667991	−	0.744170i	$-0.267155\pi$
$739$	1.98341e7			1.33598			0.667991	+	0.744170i	$0.267155\pi$
$740$		0			0
$741$	−5.75647e6	−	2.84761e6i	−0.385133	−	0.190517i
$742$		0			0
$743$	−8.45507e6			−0.561882			−0.280941	−	0.959725i	$-0.590647\pi$
$743$	−8.45507e6			−0.561882			−0.280941	+	0.959725i	$0.590647\pi$
$744$		0			0
$745$	−3.18992e6			−0.210567
$746$		0			0
$747$	4.41673e6	−	3.37180e6i	0.289601	−	0.221086i
$748$		0			0
$749$	2.20792e6			0.143807
$750$		0			0
$751$		−	2.69261e7i		−	1.74210i	−0.491193	−	0.871051i	$-0.663439\pi$
$751$		−	2.69261e7i		−	1.74210i	0.491193	−	0.871051i	$-0.336561\pi$
$752$		0			0
$753$	−2.10295e7	−	1.04029e7i	−1.35158	−	0.668599i
$754$		0			0
$755$		−	9.98414e6i		−	0.637446i
$756$		0			0
$757$		−	2.12014e7i		−	1.34470i	−0.740234	−	0.672350i	$-0.765285\pi$
$757$		−	2.12014e7i		−	1.34470i	0.740234	−	0.672350i	$-0.234715\pi$
$758$		0			0
$759$	−3.10965e6	−	1.53828e6i	−0.195933	−	0.0969241i
$760$		0			0
$761$		−	1.80031e7i		−	1.12690i	−0.826151	−	0.563449i	$-0.809474\pi$
$761$		−	1.80031e7i		−	1.12690i	0.826151	−	0.563449i	$-0.190526\pi$
$762$		0			0
$763$	−1.98711e7			−1.23570
$764$		0			0
$765$	1.21703e7	−	9.29096e6i	0.751875	−	0.573994i
$766$		0			0
$767$	2.91866e6			0.179141
$768$		0			0
$769$	7.91227e6			0.482486			0.241243	−	0.970465i	$-0.422445\pi$
$769$	7.91227e6			0.482486			0.241243	+	0.970465i	$0.422445\pi$
$770$		0			0
$771$	1.68551e7	+	8.33786e6i	1.02116	+	0.505148i
$772$		0			0
$773$	−2.31768e7			−1.39510			−0.697548	−	0.716538i	$-0.745726\pi$
$773$	−2.31768e7			−1.39510			−0.697548	+	0.716538i	$0.745726\pi$
$774$		0			0
$775$			565882.i			0.0338432i
$776$		0			0
$777$	3.12106e6	−	6.30926e6i	0.185460	−	0.374909i
$778$		0			0
$779$			1.11012e7i			0.655427i
$780$		0			0
$781$		−	1.60879e7i		−	0.943781i
$782$		0			0
$783$	−1.13813e7	+	2.22014e6i	−0.663419	+	0.129412i
$784$		0			0
$785$		−	4.46773e6i		−	0.258769i
$786$		0			0
$787$	−2.36874e7			−1.36327			−0.681634	−	0.731693i	$-0.738730\pi$
$787$	−2.36874e7			−1.36327			−0.681634	+	0.731693i	$0.738730\pi$
$788$		0			0
$789$	1.12384e7	−	2.27186e7i	0.642706	−	1.29924i
$790$		0			0
$791$	1.89532e7			1.07706
$792$		0			0
$793$	2.98207e7			1.68397
$794$		0			0
$795$	1.26357e7	−	2.55432e7i	0.709058	−	1.43337i
$796$		0			0
$797$	−1.45597e7			−0.811907			−0.405953	−	0.913894i	$-0.633060\pi$
$797$	−1.45597e7			−0.811907			−0.405953	+	0.913894i	$0.633060\pi$
$798$		0			0
$799$			2.18505e7i			1.21086i
$800$		0			0
$801$	6.47811e6	−	4.94549e6i	0.356753	−	0.272351i
$802$		0			0
$803$			3.89273e7i			2.13042i
$804$		0			0
$805$		−	3.39478e6i		−	0.184639i
$806$		0			0
$807$	−952584.	+	1.92566e6i	−0.0514896	+	0.104087i
$808$		0			0
$809$			3.22475e7i			1.73231i	0.499779	+	0.866153i	$0.333415\pi$
$809$			3.22475e7i			1.73231i	−0.499779	+	0.866153i	$0.666585\pi$
$810$		0			0
$811$	1.06545e7			0.568828			0.284414	−	0.958702i	$-0.408201\pi$
$811$	1.06545e7			0.568828			0.284414	+	0.958702i	$0.408201\pi$
$812$		0			0
$813$	2.07374e7	+	1.02584e7i	1.10034	+	0.544316i
$814$		0			0
$815$	7.25241e6			0.382462
$816$		0			0
$817$	−1.24639e7			−0.653280
$818$		0			0
$819$	−1.06786e7	−	1.39879e7i	−0.556295	−	0.728692i
$820$		0			0
$821$	1.14818e7			0.594498			0.297249	−	0.954800i	$-0.403931\pi$
$821$	1.14818e7			0.594498			0.297249	+	0.954800i	$0.403931\pi$
$822$		0			0
$823$		−	2.52972e7i		−	1.30189i	−0.759126	−	0.650944i	$-0.774373\pi$
$823$		−	2.52972e7i		−	1.30189i	0.759126	−	0.650944i	$-0.225627\pi$
$824$		0			0
$825$	−640645.	−	316914.i	−0.0327704	−	0.0162109i
$826$		0			0
$827$		−	8.83375e6i		−	0.449140i	−0.974458	−	0.224570i	$-0.927902\pi$
$827$		−	8.83375e6i		−	0.449140i	0.974458	−	0.224570i	$-0.0720977\pi$
$828$		0			0
$829$		−	4.86456e6i		−	0.245843i	−0.992416	−	0.122921i	$-0.960774\pi$
$829$		−	4.86456e6i		−	0.245843i	0.992416	−	0.122921i	$-0.0392263\pi$
$830$		0			0
$831$	−2.25554e7	−	1.11577e7i	−1.13305	−	0.560495i
$832$		0			0
$833$			181100.i			0.00904288i
$834$		0			0
$835$	1.74425e7			0.865749
$836$		0			0
$837$	−4.33752e6	−	2.22358e7i	−0.214007	−	1.09708i
$838$		0			0
$839$	2.36695e7			1.16087			0.580436	−	0.814306i	$-0.302882\pi$
$839$	2.36695e7			1.16087			0.580436	+	0.814306i	$0.302882\pi$
$840$		0			0
$841$	−1.11402e7			−0.543128
$842$		0			0
$843$	1.54927e6	+	766390.i	0.0750857	+	0.0371433i
$844$		0			0
$845$	−3.53139e6			−0.170139
$846$		0			0
$847$		−	9.61087e6i		−	0.460314i
$848$		0			0
$849$	8.61113e6	−	1.74075e7i	0.410007	−	0.828833i
$850$		0			0
$851$		−	1.59197e6i		−	0.0753548i
$852$		0			0
$853$			1.69049e7i			0.795498i	0.917494	+	0.397749i	$0.130209\pi$
$853$			1.69049e7i			0.795498i	−0.917494	+	0.397749i	$0.869791\pi$
$854$		0			0
$855$	6.20046e6	+	8.12199e6i	0.290074	+	0.379968i
$856$		0			0
$857$		−	2.33438e7i		−	1.08572i	−0.839822	−	0.542861i	$-0.817341\pi$
$857$		−	2.33438e7i		−	1.08572i	0.839822	−	0.542861i	$-0.182659\pi$
$858$		0			0
$859$	−1.96996e7			−0.910908			−0.455454	−	0.890259i	$-0.650523\pi$
$859$	−1.96996e7			−0.910908			−0.455454	+	0.890259i	$0.650523\pi$
$860$		0			0
$861$	−1.34876e7	+	2.72654e7i	−0.620052	+	1.25344i
$862$		0			0
$863$	−3.42226e6			−0.156418			−0.0782088	−	0.996937i	$-0.524920\pi$
$863$	−3.42226e6			−0.156418			−0.0782088	+	0.996937i	$0.524920\pi$
$864$		0			0
$865$	1.60730e7			0.730395
$866$		0			0
$867$	1.29062e6	−	2.60900e6i	0.0583111	−	0.117876i
$868$		0			0
$869$	9.43203e6			0.423697
$870$		0			0
$871$		−	3.70378e7i		−	1.65425i
$872$		0			0
$873$	2.15764e7	+	2.82630e7i	0.958171	+	1.25511i
$874$		0			0
$875$			2.23997e7i			0.989057i
$876$		0			0
$877$		−	1.82299e7i		−	0.800361i	−0.916436	−	0.400181i	$-0.868947\pi$
$877$		−	1.82299e7i		−	0.800361i	0.916436	−	0.400181i	$-0.131053\pi$
$878$		0			0
$879$	−1.92417e7	+	3.88974e7i	−0.839986	+	1.69804i
$880$		0			0
$881$			3.79378e7i			1.64677i	0.567483	+	0.823385i	$0.307917\pi$
$881$			3.79378e7i			1.64677i	−0.567483	+	0.823385i	$0.692083\pi$
$882$		0			0
$883$	−3.47312e7			−1.49906			−0.749529	−	0.661972i	$-0.769720\pi$
$883$	−3.47312e7			−1.49906			−0.749529	+	0.661972i	$0.769720\pi$
$884$		0			0
$885$	−4.16232e6	−	2.05901e6i	−0.178639	−	0.0883692i
$886$		0			0
$887$	8.89149e6			0.379459			0.189730	−	0.981836i	$-0.439239\pi$
$887$	8.89149e6			0.379459			0.189730	+	0.981836i	$0.439239\pi$
$888$		0			0
$889$	−1.18474e7			−0.502771
$890$		0			0
$891$	2.76027e7	+	7.54225e6i	1.16482	+	0.318278i
$892$		0			0
$893$	−1.45822e7			−0.611922
$894$		0			0
$895$			2.13570e7i			0.891216i
$896$		0			0
$897$	−3.56744e6	−	1.76474e6i	−0.148039	−	0.0732317i
$898$		0			0
$899$			1.83082e7i			0.755520i
$900$		0			0
$901$			3.57774e7i			1.46824i
$902$		0			0
$903$	−3.06125e7	−	1.51434e7i	−1.24934	−	0.618021i
$904$		0			0
$905$		−	3.96449e7i		−	1.60904i
$906$		0			0
$907$	−4.17482e7			−1.68508			−0.842539	−	0.538636i	$-0.818940\pi$
$907$	−4.17482e7			−1.68508			−0.842539	+	0.538636i	$0.818940\pi$
$908$		0			0
$909$	−1.66824e7	−	2.18523e7i	−0.669650	−	0.877176i
$910$		0			0
$911$	−4.26866e6			−0.170410			−0.0852052	−	0.996363i	$-0.527155\pi$
$911$	−4.26866e6			−0.170410			−0.0852052	+	0.996363i	$0.527155\pi$
$912$		0			0
$913$	1.10811e7			0.439953
$914$		0			0
$915$	−4.25275e7	−	2.10375e7i	−1.67926	−	0.830695i
$916$		0			0
$917$	5.29830e6			0.208072
$918$		0			0
$919$			1.88729e7i			0.737138i	0.929600	+	0.368569i	$0.120152\pi$
$919$			1.88729e7i			0.737138i	−0.929600	+	0.368569i	$0.879848\pi$
$920$		0			0
$921$	−4.06410e6	+	8.21562e6i	−0.157876	+	0.319147i
$922$		0			0
$923$		−	1.84562e7i		−	0.713081i
$924$		0			0
$925$		−	327974.i		−	0.0126033i
$926$		0			0
$927$	−3.08613e7	+	2.35600e7i	−1.17954	+	0.900483i
$928$		0			0
$929$			1.24738e7i			0.474197i	0.971486	+	0.237098i	$0.0761964\pi$
$929$			1.24738e7i			0.474197i	−0.971486	+	0.237098i	$0.923804\pi$
$930$		0			0
$931$	−120860.			−0.00456991
$932$		0			0
$933$	−8.76059e6	+	1.77096e7i	−0.329480	+	0.666048i
$934$		0			0
$935$	3.05339e7			1.14223
$936$		0			0
$937$	−2.08166e7			−0.774570			−0.387285	−	0.921960i	$-0.626587\pi$
$937$	−2.08166e7			−0.774570			−0.387285	+	0.921960i	$0.626587\pi$
$938$		0			0
$939$	1.87210e7	−	3.78447e7i	0.692890	−	1.40069i
$940$		0			0
$941$	−1.20794e6			−0.0444703			−0.0222351	−	0.999753i	$-0.507078\pi$
$941$	−1.20794e6			−0.0444703			−0.0222351	+	0.999753i	$0.507078\pi$
$942$		0			0
$943$			6.87968e6i			0.251935i
$944$		0			0
$945$	5.36084e6	+	2.74817e7i	0.195278	+	1.00107i
$946$		0			0
$947$		−	4.75552e7i		−	1.72315i	−0.507631	−	0.861574i	$-0.669479\pi$
$947$		−	4.75552e7i		−	1.72315i	0.507631	−	0.861574i	$-0.330521\pi$
$948$		0			0
$949$			4.46579e7i			1.60965i
$950$		0			0
$951$	−1.83047e6	+	3.70031e6i	−0.0656313	+	0.132674i
$952$		0			0
$953$			2.18909e7i			0.780784i	0.920649	+	0.390392i	$0.127661\pi$
$953$			2.18909e7i			0.780784i	−0.920649	+	0.390392i	$0.872339\pi$
$954$		0			0
$955$	4.96255e7			1.76075
$956$		0			0
$957$	−2.07270e7	−	1.02532e7i	−0.731571	−	0.361893i
$958$		0			0
$959$	−4.30704e7			−1.51228
$960$		0			0
$961$	−7.13973e6			−0.249387
$962$		0			0
$963$	−3.27367e6	+	2.49917e6i	−0.113755	+	0.0868421i
$964$		0			0
$965$	1.03544e7			0.357936
$966$		0			0
$967$			3.28485e7i			1.12967i	0.825205	+	0.564833i	$0.191059\pi$
$967$			3.28485e7i			1.12967i	−0.825205	+	0.564833i	$0.808941\pi$
$968$		0			0
$969$	−1.14985e7	−	5.68808e6i	−0.393398	−	0.194606i
$970$		0			0
$971$			1.25929e7i			0.428624i	0.976765	+	0.214312i	$0.0687509\pi$
$971$			1.25929e7i			0.428624i	−0.976765	+	0.214312i	$0.931249\pi$
$972$		0			0
$973$		−	2.30119e7i		−	0.779237i
$974$		0			0
$975$	−734956.	−	363568.i	−0.0247600	−	0.0122482i
$976$		0			0
$977$			3.98034e6i			0.133408i	0.997773	+	0.0667042i	$0.0212484\pi$
$977$			3.98034e6i			0.133408i	−0.997773	+	0.0667042i	$0.978752\pi$
$978$		0			0
$979$	1.62529e7			0.541968
$980$		0			0
$981$	2.94628e7	−	2.24923e7i	0.977465	−	0.746212i
$982$		0			0
$983$	5.24394e7			1.73091			0.865453	−	0.500989i	$-0.167030\pi$
$983$	5.24394e7			1.73091			0.865453	+	0.500989i	$0.167030\pi$
$984$		0			0
$985$	−1.63808e7			−0.537954
$986$		0			0
$987$	−3.58153e7	−	1.77171e7i	−1.17024	−	0.578895i
$988$		0			0
$989$	−7.72422e6			−0.251110
$990$		0			0
$991$			1.65620e7i			0.535708i	0.963459	+	0.267854i	$0.0863146\pi$
$991$			1.65620e7i			0.535708i	−0.963459	+	0.267854i	$0.913685\pi$
$992$		0			0
$993$	3.69632e6	−	7.47214e6i	0.118959	−	0.240476i
$994$		0			0
$995$			5.45720e7i			1.74748i
$996$		0			0
$997$			1.73906e7i			0.554087i	0.960857	+	0.277043i	$0.0893545\pi$
$997$			1.73906e7i			0.554087i	−0.960857	+	0.277043i	$0.910645\pi$
$998$		0			0
$999$	2.51394e6	+	1.28874e7i	0.0796969	+	0.408557i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.6.f.f.191.13	yes	20
3.2	odd	2		384.6.f.e.191.14	yes	20
4.3	odd	2		384.6.f.e.191.8	yes	20
8.3	odd	2		384.6.f.e.191.13	yes	20
8.5	even	2	inner	384.6.f.f.191.8	yes	20
12.11	even	2	inner	384.6.f.f.191.7	yes	20
24.5	odd	2		384.6.f.e.191.7	✓	20
24.11	even	2	inner	384.6.f.f.191.14	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.6.f.e.191.7	✓	20	24.5	odd	2
384.6.f.e.191.8	yes	20	4.3	odd	2
384.6.f.e.191.13	yes	20	8.3	odd	2
384.6.f.e.191.14	yes	20	3.2	odd	2
384.6.f.f.191.7	yes	20	12.11	even	2	inner
384.6.f.f.191.8	yes	20	8.5	even	2	inner
384.6.f.f.191.13	yes	20	1.1	even	1	trivial
384.6.f.f.191.14	yes	20	24.11	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(6.91183 - 13.9723i) q^{3} -56.7417 q^{5} +130.269i q^{7} +(-147.453 - 193.149i) q^{9} +O(q^{10})\)	\(q+(6.91183 - 13.9723i) q^{3} -56.7417 q^{5} +130.269i q^{7} +(-147.453 - 193.149i) q^{9} -484.591i q^{11} -555.929i q^{13} +(-392.189 + 792.815i) q^{15} -1110.46i q^{17} +741.084 q^{19} +(1820.17 + 900.400i) q^{21} +459.270 q^{23} +94.6178 q^{25} +(-3717.92 + 725.251i) q^{27} +3061.20 q^{29} +5980.71i q^{31} +(-6770.87 - 3349.41i) q^{33} -7391.70i q^{35} -3466.31i q^{37} +(-7767.63 - 3842.49i) q^{39} +14979.6i q^{41} -16818.5 q^{43} +(8366.73 + 10959.6i) q^{45} -19676.9 q^{47} -163.085 q^{49} +(-15515.8 - 7675.35i) q^{51} -32218.4 q^{53} +27496.5i q^{55} +(5122.25 - 10354.7i) q^{57} +5250.05i q^{59} +53641.2i q^{61} +(25161.4 - 19208.6i) q^{63} +31544.3i q^{65} +66623.4 q^{67} +(3174.40 - 6417.08i) q^{69} +33198.9 q^{71} -80330.2 q^{73} +(653.983 - 1322.03i) q^{75} +63127.3 q^{77} +19463.9i q^{79} +(-15564.2 + 56960.9i) q^{81} +22867.0i q^{83} +63009.6i q^{85} +(21158.5 - 42772.2i) q^{87} +33539.4i q^{89} +72420.4 q^{91} +(83564.6 + 41337.7i) q^{93} -42050.4 q^{95} -146327. q^{97} +(-93598.2 + 71454.4i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 44 q^{9}+O(q^{10}) \) 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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