LMFDB - Embedded newform 54.7.d.a.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,7,Mod(17,54)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("54.17");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	54.d (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.4229205155$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 370x^{10} + 51793x^{8} + 3491832x^{6} + 117603792x^{4} + 1832032512x^{2} + 10453017600 $ x^12 + 370x^10 + 51793x^8 + 3491832x^6 + 117603792x^4 + 1832032512*x^2 + 10453017600
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{18} $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.1
Root			$8.88570i$ of defining polynomial
Character	$\chi$	$=$	54.17
Dual form			54.7.d.a.35.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.89898 + 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(-202.253 - 116.771i) q^{5} +(95.5752 + 165.541i) q^{7} +181.019i q^{8} +O(q^{10})$	\(q+(-4.89898 + 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(-202.253 - 116.771i) q^{5} +(95.5752 + 165.541i) q^{7} +181.019i q^{8} +1321.11 q^{10} +(673.077 - 388.601i) q^{11} +(45.5802 - 78.9472i) q^{13} +(-936.442 - 540.655i) q^{14} +(-512.000 - 886.810i) q^{16} +7047.39i q^{17} +2731.10 q^{19} +(-6472.09 + 3736.66i) q^{20} +(-2198.26 + 3807.50i) q^{22} +(17228.9 + 9947.14i) q^{23} +(19458.3 + 33702.7i) q^{25} +515.681i q^{26} +6116.81 q^{28} +(-27104.3 + 15648.7i) q^{29} +(6174.50 - 10694.6i) q^{31} +(5016.55 + 2896.31i) q^{32} +(-19933.0 - 34525.0i) q^{34} -44641.5i q^{35} -27972.0 q^{37} +(-13379.6 + 7724.70i) q^{38} +(21137.7 - 36611.7i) q^{40} +(37428.2 + 21609.2i) q^{41} +(19256.1 + 33352.5i) q^{43} -24870.5i q^{44} -112539. q^{46} +(143771. - 83006.2i) q^{47} +(40555.3 - 70243.8i) q^{49} +(-190651. - 110073. i) q^{50} +(-1458.57 - 2526.31i) q^{52} -54741.5i q^{53} -181509. q^{55} +(-29966.1 + 17301.0i) q^{56} +(88522.3 - 153325. i) q^{58} +(14102.1 + 8141.84i) q^{59} +(29443.7 + 50998.0i) q^{61} +69856.5i q^{62} -32768.0 q^{64} +(-18437.4 + 10644.9i) q^{65} +(-147998. + 256341. i) q^{67} +(195303. + 112758. i) q^{68} +(126265. + 218698. i) q^{70} +157251. i q^{71} +80297.0 q^{73} +(137034. - 79116.8i) q^{74} +(43697.5 - 75686.3i) q^{76} +(128659. + 74281.3i) q^{77} +(188424. + 326360. i) q^{79} +239146. i q^{80} -244480. q^{82} +(-733992. + 423771. i) q^{83} +(822929. - 1.42535e6i) q^{85} +(-188670. - 108929. i) q^{86} +(70344.3 + 121840. i) q^{88} +1128.91i q^{89} +17425.3 q^{91} +(551326. - 318308. i) q^{92} +(-469554. + 813291. i) q^{94} +(-552371. - 318912. i) q^{95} +(675152. + 1.16940e6i) q^{97} +458831. i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 192 q^{4} - 432 q^{5} + 240 q^{7}+O(q^{10}) $ 12 * q + 192 * q^4 - 432 * q^5 + 240 * q^7	$ 12 q + 192 q^{4} - 432 q^{5} + 240 q^{7} - 378 q^{11} + 1680 q^{13} + 4752 q^{14} - 6144 q^{16} - 2820 q^{19} - 13824 q^{20} - 3600 q^{22} + 76248 q^{23} + 8094 q^{25} + 15360 q^{28} - 97092 q^{29} + 21480 q^{31} - 27360 q^{34} - 25536 q^{37} - 97632 q^{38} + 410562 q^{41} + 71430 q^{43} - 135072 q^{46} - 347652 q^{47} - 135954 q^{49} - 311040 q^{50} - 53760 q^{52} + 580392 q^{55} + 152064 q^{56} + 159264 q^{58} - 369738 q^{59} + 135744 q^{61} - 393216 q^{64} + 753840 q^{65} - 289938 q^{67} - 744768 q^{68} + 155952 q^{70} - 977700 q^{73} + 2197152 q^{74} - 45120 q^{76} + 159192 q^{77} - 764796 q^{79} + 1073088 q^{82} - 396900 q^{83} + 1619568 q^{85} - 3264624 q^{86} + 115200 q^{88} + 355584 q^{91} + 2439936 q^{92} - 736848 q^{94} + 2089260 q^{95} - 38874 q^{97}+O(q^{100}) $ 12 * q + 192 * q^4 - 432 * q^5 + 240 * q^7 - 378 * q^11 + 1680 * q^13 + 4752 * q^14 - 6144 * q^16 - 2820 * q^19 - 13824 * q^20 - 3600 * q^22 + 76248 * q^23 + 8094 * q^25 + 15360 * q^28 - 97092 * q^29 + 21480 * q^31 - 27360 * q^34 - 25536 * q^37 - 97632 * q^38 + 410562 * q^41 + 71430 * q^43 - 135072 * q^46 - 347652 * q^47 - 135954 * q^49 - 311040 * q^50 - 53760 * q^52 + 580392 * q^55 + 152064 * q^56 + 159264 * q^58 - 369738 * q^59 + 135744 * q^61 - 393216 * q^64 + 753840 * q^65 - 289938 * q^67 - 744768 * q^68 + 155952 * q^70 - 977700 * q^73 + 2197152 * q^74 - 45120 * q^76 + 159192 * q^77 - 764796 * q^79 + 1073088 * q^82 - 396900 * q^83 + 1619568 * q^85 - 3264624 * q^86 + 115200 * q^88 + 355584 * q^91 + 2439936 * q^92 - 736848 * q^94 + 2089260 * q^95 - 38874 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−4.89898	+	2.82843i	−0.612372	+	0.353553i
$2$	−4.89898	+	2.82843i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	16.0000	−	27.7128i	0.250000	−	0.433013i
$5$	−202.253	−	116.771i	−1.61802	−	0.934165i	−0.987431	−	0.158050i	$-0.949479\pi$
$5$	−202.253	−	116.771i	−1.61802	−	0.934165i	−0.630591	−	0.776116i	$-0.717187\pi$
$6$		0			0
$7$	95.5752	+	165.541i	0.278645	+	0.482627i	0.971048	−	0.238884i	$-0.0767814\pi$
$7$	95.5752	+	165.541i	0.278645	+	0.482627i	−0.692403	+	0.721511i	$0.743448\pi$
$8$			181.019i			0.353553i
$9$		0			0
$10$	1321.11			1.32111
$11$	673.077	−	388.601i	0.505693	−	0.291962i	−0.225369	−	0.974274i	$-0.572359\pi$
$11$	673.077	−	388.601i	0.505693	−	0.291962i	0.731061	+	0.682312i	$0.239025\pi$
$12$		0			0
$13$	45.5802	−	78.9472i	0.0207466	−	0.0359341i	−0.855466	−	0.517859i	$-0.826729\pi$
$13$	45.5802	−	78.9472i	0.0207466	−	0.0359341i	0.876212	+	0.481925i	$0.160062\pi$
$14$	−936.442	−	540.655i	−0.341269	−	0.197032i
$15$		0			0
$16$	−512.000	−	886.810i	−0.125000	−	0.216506i
$17$			7047.39i			1.43444i	0.696848	+	0.717219i	$0.254585\pi$
$17$			7047.39i			1.43444i	−0.696848	+	0.717219i	$0.745415\pi$
$18$		0			0
$19$	2731.10			0.398177			0.199088	−	0.979982i	$-0.436202\pi$
$19$	2731.10			0.398177			0.199088	+	0.979982i	$0.436202\pi$
$20$	−6472.09	+	3736.66i	−0.809011	+	0.467083i
$21$		0			0
$22$	−2198.26	+	3807.50i	−0.206448	+	0.357579i
$23$	17228.9	+	9947.14i	1.41604	+	0.817550i	0.995948	−	0.0899317i	$-0.0286649\pi$
$23$	17228.9	+	9947.14i	1.41604	+	0.817550i	0.420091	+	0.907482i	$0.361998\pi$
$24$		0			0
$25$	19458.3	+	33702.7i	1.24533	+	2.15697i
$26$			515.681i			0.0293401i
$27$		0			0
$28$	6116.81			0.278645
$29$	−27104.3	+	15648.7i	−1.11133	+	0.641629i	−0.939175	−	0.343440i	$-0.888408\pi$
$29$	−27104.3	+	15648.7i	−1.11133	+	0.641629i	−0.172159	+	0.985069i	$0.555074\pi$
$30$		0			0
$31$	6174.50	−	10694.6i	0.207261	−	0.358986i	−0.743590	−	0.668636i	$-0.766879\pi$
$31$	6174.50	−	10694.6i	0.207261	−	0.358986i	0.950851	+	0.309650i	$0.100212\pi$
$32$	5016.55	+	2896.31i	0.153093	+	0.0883883i
$33$		0			0
$34$	−19933.0	−	34525.0i	−0.507150	−	0.878410i
$35$		−	44641.5i		−	1.04120i
$36$		0			0
$37$	−27972.0			−0.552228			−0.276114	−	0.961125i	$-0.589047\pi$
$37$	−27972.0			−0.552228			−0.276114	+	0.961125i	$0.589047\pi$
$38$	−13379.6	+	7724.70i	−0.243833	+	0.140777i
$39$		0			0
$40$	21137.7	−	36611.7i	0.330277	−	0.572057i
$41$	37428.2	+	21609.2i	0.543059	+	0.313535i	0.746318	−	0.665590i	$-0.231820\pi$
$41$	37428.2	+	21609.2i	0.543059	+	0.313535i	−0.203259	+	0.979125i	$0.565153\pi$
$42$		0			0
$43$	19256.1	+	33352.5i	0.242193	+	0.419491i	0.961339	−	0.275369i	$-0.0887999\pi$
$43$	19256.1	+	33352.5i	0.242193	+	0.419491i	−0.719146	+	0.694860i	$0.755467\pi$
$44$		−	24870.5i		−	0.291962i
$45$		0			0
$46$	−112539.			−1.15619
$47$	143771.	−	83006.2i	1.38477	−	0.799497i	0.392050	−	0.919944i	$-0.371766\pi$
$47$	143771.	−	83006.2i	1.38477	−	0.799497i	0.992720	+	0.120447i	$0.0384327\pi$
$48$		0			0
$49$	40555.3	−	70243.8i	0.344714	−	0.597062i
$50$	−190651.	−	110073.i	−1.52521	−	0.880581i
$51$		0			0
$52$	−1458.57	−	2526.31i	−0.0103733	−	0.0179671i
$53$		−	54741.5i		−	0.367696i	−0.982955	−	0.183848i	$-0.941145\pi$
$53$		−	54741.5i		−	0.367696i	0.982955	−	0.183848i	$-0.0588554\pi$
$54$		0			0
$55$	−181509.			−1.09096
$56$	−29966.1	+	17301.0i	−0.170634	+	0.0985158i
$57$		0			0
$58$	88522.3	−	153325.i	0.453700	−	0.785832i
$59$	14102.1	+	8141.84i	0.0686637	+	0.0396430i	0.533939	−	0.845523i	$-0.320711\pi$
$59$	14102.1	+	8141.84i	0.0686637	+	0.0396430i	−0.465275	+	0.885166i	$0.654045\pi$
$60$		0			0
$61$	29443.7	+	50998.0i	0.129719	+	0.224680i	0.923568	−	0.383436i	$-0.125259\pi$
$61$	29443.7	+	50998.0i	0.129719	+	0.224680i	−0.793849	+	0.608115i	$0.791926\pi$
$62$			69856.5i			0.293111i
$63$		0			0
$64$	−32768.0			−0.125000
$65$	−18437.4	+	10644.9i	−0.0671368	+	0.0387614i
$66$		0			0
$67$	−147998.	+	256341.i	−0.492076	+	0.852301i	−0.999958	−	0.00912565i	$-0.997095\pi$
$67$	−147998.	+	256341.i	−0.492076	+	0.852301i	0.507882	+	0.861427i	$0.330429\pi$
$68$	195303.	+	112758.i	0.621130	+	0.358609i
$69$		0			0
$70$	126265.	+	218698.i	0.368120	+	0.637603i
$71$			157251.i			0.439358i	0.975572	+	0.219679i	$0.0705010\pi$
$71$			157251.i			0.439358i	−0.975572	+	0.219679i	$0.929499\pi$
$72$		0			0
$73$	80297.0			0.206410			0.103205	−	0.994660i	$-0.467090\pi$
$73$	80297.0			0.206410			0.103205	+	0.994660i	$0.467090\pi$
$74$	137034.	−	79116.8i	0.338169	−	0.195242i
$75$		0			0
$76$	43697.5	−	75686.3i	0.0995442	−	0.172416i
$77$	128659.	+	74281.3i	0.281817	+	0.162707i
$78$		0			0
$79$	188424.	+	326360.i	0.382169	+	0.661936i	0.991372	−	0.131078i	$-0.0418438\pi$
$79$	188424.	+	326360.i	0.382169	+	0.661936i	−0.609203	+	0.793014i	$0.708511\pi$
$80$			239146.i			0.467083i
$81$		0			0
$82$	−244480.			−0.443406
$83$	−733992.	+	423771.i	−1.28368	+	0.741134i	−0.977519	−	0.210846i	$-0.932378\pi$
$83$	−733992.	+	423771.i	−1.28368	+	0.741134i	−0.306162	+	0.951980i	$0.599045\pi$
$84$		0			0
$85$	822929.	−	1.42535e6i	1.34000	−	2.32095i
$86$	−188670.	−	108929.i	−0.296625	−	0.171256i
$87$		0			0
$88$	70344.3	+	121840.i	0.103224	+	0.178789i
$89$			1128.91i			0.00160136i	1.00000		0.000800679i	$0.000254864\pi$
$89$			1128.91i			0.00160136i	−1.00000		0.000800679i	$0.999745\pi$
$90$		0			0
$91$	17425.3			0.0231237
$92$	551326.	−	318308.i	0.708019	−	0.408775i
$93$		0			0
$94$	−469554.	+	813291.i	−0.565330	+	0.979180i
$95$	−552371.	−	318912.i	−0.644259	−	0.371963i
$96$		0			0
$97$	675152.	+	1.16940e6i	0.739753	+	1.28129i	0.952607	+	0.304205i	$0.0983908\pi$
$97$	675152.	+	1.16940e6i	0.739753	+	1.28129i	−0.212854	+	0.977084i	$0.568276\pi$
$98$			458831.i			0.487499i
$99$		0			0
$100$	1.24533e6			1.24533
$101$	137557.	−	79418.5i	0.133511	−	0.0770828i	−0.431757	−	0.901990i	$-0.642106\pi$
$101$	137557.	−	79418.5i	0.133511	−	0.0770828i	0.565268	+	0.824907i	$0.308773\pi$
$102$		0			0
$103$	−248614.	+	430612.i	−0.227517	+	0.394071i	−0.957072	−	0.289851i	$-0.906394\pi$
$103$	−248614.	+	430612.i	−0.227517	+	0.394071i	0.729555	+	0.683923i	$0.239727\pi$
$104$	14291.0	+	8250.90i	0.0127046	+	0.00733502i
$105$		0			0
$106$	154832.	+	268177.i	0.130000	+	0.225167i
$107$			207159.i			0.169103i	0.996419	+	0.0845516i	$0.0269458\pi$
$107$			207159.i			0.169103i	−0.996419	+	0.0845516i	$0.973054\pi$
$108$		0			0
$109$	−2.30287e6			−1.77824			−0.889120	−	0.457673i	$-0.848683\pi$
$109$	−2.30287e6			−1.77824			−0.889120	+	0.457673i	$0.848683\pi$
$110$	889208.	−	513385.i	0.668075	−	0.385713i
$111$		0			0
$112$	97869.0	−	169514.i	0.0696612	−	0.120657i
$113$	677545.	+	391181.i	0.469573	+	0.271108i	0.716061	−	0.698038i	$-0.245943\pi$
$113$	677545.	+	391181.i	0.469573	+	0.271108i	−0.246488	+	0.969146i	$0.579277\pi$
$114$		0			0
$115$	−2.32307e6	−	4.02367e6i	−1.52745	−	2.64563i
$116$			1.00152e6i			0.641629i
$117$		0			0
$118$	−92114.4			−0.0560637
$119$	−1.16663e6	+	673556.i	−0.692298	+	0.399699i
$120$		0			0
$121$	−583759.	+	1.01110e6i	−0.329517	+	0.570739i
$122$	−288488.	−	166559.i	−0.158873	−	0.0917251i
$123$		0			0
$124$	−197584.	−	342226.i	−0.103630	−	0.179493i
$125$		−	5.43954e6i		−	2.78504i
$126$		0			0
$127$	1.19415e6			0.582970			0.291485	−	0.956575i	$-0.405851\pi$
$127$	1.19415e6			0.582970			0.291485	+	0.956575i	$0.405851\pi$
$128$	160530.	−	92681.9i	0.0765466	−	0.0441942i
$129$		0			0
$130$	60216.4	−	104298.i	0.0274085	−	0.0474729i
$131$	2.17543e6	+	1.25598e6i	0.967678	+	0.558689i	0.898528	−	0.438917i	$-0.144638\pi$
$131$	2.17543e6	+	1.25598e6i	0.967678	+	0.558689i	0.0691503	+	0.997606i	$0.477971\pi$
$132$		0			0
$133$	261025.	+	452108.i	0.110950	+	0.192171i
$134$		−	1.67441e6i		−	0.695901i
$135$		0			0
$136$	−1.27571e6			−0.507150
$137$	−703636.	+	406244.i	−0.273644	+	0.157989i	−0.630543	−	0.776155i	$-0.717168\pi$
$137$	−703636.	+	406244.i	−0.273644	+	0.157989i	0.356898	+	0.934143i	$0.383834\pi$
$138$		0			0
$139$	−350555.	+	607179.i	−0.130530	+	0.226085i	−0.923881	−	0.382679i	$-0.875001\pi$
$139$	−350555.	+	607179.i	−0.130530	+	0.226085i	0.793351	+	0.608765i	$0.208335\pi$
$140$	−1.23714e6	−	714264.i	−0.450853	−	0.260300i
$141$		0			0
$142$	−444773.	−	770370.i	−0.155336	−	0.269051i
$143$		−	70850.1i		−	0.0242288i
$144$		0			0
$145$	7.30923e6			2.39755
$146$	−393373.	+	227114.i	−0.126400	+	0.0729769i
$147$		0			0
$148$	−447552.	+	775183.i	−0.138057	+	0.239122i
$149$	−265134.	−	153075.i	−0.0801505	−	0.0462749i	0.459389	−	0.888235i	$-0.348068\pi$
$149$	−265134.	−	153075.i	−0.0801505	−	0.0462749i	−0.539540	+	0.841960i	$0.681402\pi$
$150$		0			0
$151$	−923784.	−	1.60004e6i	−0.268312	−	0.464730i	0.700114	−	0.714031i	$-0.253132\pi$
$151$	−923784.	−	1.60004e6i	−0.268312	−	0.464730i	−0.968426	+	0.249301i	$0.919799\pi$
$152$			494381.i			0.140777i
$153$		0			0
$154$	−840396.			−0.230103
$155$	−2.49762e6	+	1.44200e6i	−0.670704	+	0.387231i
$156$		0			0
$157$	−1.57533e6	+	2.72854e6i	−0.407072	+	0.705070i	−0.994560	−	0.104163i	$-0.966784\pi$
$157$	−1.57533e6	+	2.72854e6i	−0.407072	+	0.705070i	0.587488	+	0.809233i	$0.300117\pi$
$158$	−1.84617e6	−	1.06589e6i	−0.468060	−	0.270234i
$159$		0			0
$160$	−676408.	−	1.17157e6i	−0.165139	−	0.286029i
$161$			3.80280e6i			0.911225i
$162$		0			0
$163$	−1.29782e6			−0.299676			−0.149838	−	0.988711i	$-0.547875\pi$
$163$	−1.29782e6			−0.299676			−0.149838	+	0.988711i	$0.547875\pi$
$164$	1.19770e6	−	691493.i	0.271529	−	0.156768i
$165$		0			0
$166$	2.39721e6	−	4.15209e6i	0.524061	−	0.907700i
$167$	1.41556e6	+	817272.i	0.303933	+	0.175476i	0.644208	−	0.764850i	$-0.277187\pi$
$167$	1.41556e6	+	817272.i	0.303933	+	0.175476i	−0.340275	+	0.940326i	$0.610520\pi$
$168$		0			0
$169$	2.40925e6	+	4.17294e6i	0.499139	+	0.864534i
$170$			9.31038e6i			1.89505i
$171$		0			0
$172$	1.23239e6			0.242193
$173$	8.21215e6	−	4.74129e6i	1.58606	−	0.915710i	0.592108	−	0.805859i	$-0.298296\pi$
$173$	8.21215e6	−	4.74129e6i	1.58606	−	0.915710i	0.993948	−	0.109851i	$-0.0350373\pi$
$174$		0			0
$175$	−3.71946e6	+	6.44229e6i	−0.694009	+	1.20206i
$176$	−689231.	−	397928.i	−0.126423	−	0.0729905i
$177$		0			0
$178$	−3193.03	−	5530.50i	−0.000566166	−	0.000980628i
$179$			9.23510e6i			1.61021i	0.593133	+	0.805105i	$0.297891\pi$
$179$			9.23510e6i			1.61021i	−0.593133	+	0.805105i	$0.702109\pi$
$180$		0			0
$181$	4.59474e6			0.774864			0.387432	−	0.921898i	$-0.373362\pi$
$181$	4.59474e6			0.774864			0.387432	+	0.921898i	$0.373362\pi$
$182$	−85366.4	+	49286.3i	−0.0141603	+	0.00817546i
$183$		0			0
$184$	−1.80062e6	+	3.11877e6i	−0.289048	+	0.500645i
$185$	5.65742e6	+	3.26631e6i	0.893517	+	0.515873i
$186$		0			0
$187$	2.73863e6	+	4.74344e6i	0.418801	+	0.725385i
$188$		−	5.31240e6i		−	0.799497i
$189$		0			0
$190$	3.60808e6			0.526035
$191$	−6.79391e6	+	3.92247e6i	−0.975034	+	0.562936i	−0.900767	−	0.434302i	$-0.856995\pi$
$191$	−6.79391e6	+	3.92247e6i	−0.975034	+	0.562936i	−0.0742671	+	0.997238i	$0.523662\pi$
$192$		0			0
$193$	2.71892e6	−	4.70931e6i	0.378203	−	0.655066i	−0.612598	−	0.790395i	$-0.709876\pi$
$193$	2.71892e6	−	4.70931e6i	0.378203	−	0.655066i	0.990801	+	0.135328i	$0.0432089\pi$
$194$	−6.61511e6	−	3.81924e6i	−0.906008	−	0.523084i
$195$		0			0
$196$	−1.29777e6	−	2.24780e6i	−0.172357	−	0.298531i
$197$		−	1.01096e7i		−	1.32232i	−0.750246	−	0.661159i	$-0.770065\pi$
$197$		−	1.01096e7i		−	1.32232i	0.750246	−	0.661159i	$-0.229935\pi$
$198$		0			0
$199$	−6.91799e6			−0.877851			−0.438925	−	0.898523i	$-0.644641\pi$
$199$	−6.91799e6			−0.877851			−0.438925	+	0.898523i	$0.644641\pi$
$200$	−6.10084e6	+	3.52232e6i	−0.762606	+	0.440291i
$201$		0			0
$202$	−449259.	+	778139.i	−0.0545058	+	0.0944068i
$203$	−5.18100e6	−	2.99125e6i	−0.619335	−	0.357573i
$204$		0			0
$205$	−5.04663e6	−	8.74102e6i	−0.585787	−	1.01461i
$206$		−	2.81275e6i		−	0.321758i
$207$		0			0
$208$	−93348.3			−0.0103733
$209$	1.83824e6	−	1.06131e6i	0.201355	−	0.116252i
$210$		0			0
$211$	4.27596e6	−	7.40617e6i	0.455183	−	0.788400i	−0.543516	−	0.839399i	$-0.682907\pi$
$211$	4.27596e6	−	7.40617e6i	0.455183	−	0.788400i	0.998699	+	0.0509990i	$0.0162405\pi$
$212$	−1.51704e6	−	875863.i	−0.159217	−	0.0919240i
$213$		0			0
$214$	−585933.	−	1.01487e6i	−0.0597870	−	0.103554i
$215$		−	8.99417e6i		−	0.904994i
$216$		0			0
$217$	2.36052e6			0.231008
$218$	1.12817e7	−	6.51351e6i	1.08895	−	0.628703i
$219$		0			0
$220$	−2.90414e6	+	5.03012e6i	−0.272741	+	0.472401i
$221$	556372.	+	321222.i	0.0515452	+	0.0297597i
$222$		0			0
$223$	2.62933e6	+	4.55413e6i	0.237099	+	0.410668i	0.959881	−	0.280409i	$-0.0904700\pi$
$223$	2.62933e6	+	4.55413e6i	0.237099	+	0.410668i	−0.722782	+	0.691077i	$0.757137\pi$
$224$			1.10726e6i			0.0985158i
$225$		0			0
$226$	−4.42570e6			−0.383404
$227$	7.00311e6	−	4.04325e6i	0.598706	−	0.345663i	−0.169827	−	0.985474i	$-0.554321\pi$
$227$	7.00311e6	−	4.04325e6i	0.598706	−	0.345663i	0.768532	+	0.639811i	$0.220987\pi$
$228$		0			0
$229$	6.10057e6	−	1.05665e7i	0.508001	−	0.879883i	−0.491957	−	0.870620i	$-0.663718\pi$
$229$	6.10057e6	−	1.05665e7i	0.508001	−	0.879883i	0.999957	−	0.00926306i	$-0.00294857\pi$
$230$	2.27613e7	+	1.31413e7i	1.87074	+	1.08007i
$231$		0			0
$232$	−2.83272e6	−	4.90641e6i	−0.226850	−	0.392916i
$233$		−	5.57473e6i		−	0.440713i	−0.975419	−	0.220357i	$-0.929278\pi$
$233$		−	5.57473e6i		−	0.440713i	0.975419	−	0.220357i	$-0.0707221\pi$
$234$		0			0
$235$	−3.87708e7			−2.98745
$236$	451266.	−	260539.i	0.0343318	−	0.0198215i
$237$		0			0
$238$	3.81021e6	−	6.59947e6i	0.282630	−	0.489529i
$239$	−1.42628e7	−	8.23463e6i	−1.04475	−	0.603185i	−0.123573	−	0.992336i	$-0.539435\pi$
$239$	−1.42628e7	−	8.23463e6i	−1.04475	−	0.603185i	−0.921174	+	0.389151i	$0.872769\pi$
$240$		0			0
$241$	−2.30270e6	−	3.98840e6i	−0.164508	−	0.284936i	0.771972	−	0.635656i	$-0.219270\pi$
$241$	−2.30270e6	−	3.98840e6i	−0.164508	−	0.284936i	−0.936480	+	0.350720i	$0.885937\pi$
$242$		−	6.60448e6i		−	0.466007i
$243$		0			0
$244$	1.88440e6			0.129719
$245$	−1.64048e7	+	9.47133e6i	−1.11551	+	0.644040i
$246$		0			0
$247$	124484.	−	215612.i	0.00826080	−	0.0143081i
$248$	1.93592e6	+	1.11770e6i	0.126921	+	0.0732777i
$249$		0			0
$250$	1.53853e7	+	2.66482e7i	0.984662	+	1.70548i
$251$			1.58119e7i			0.999913i	0.866051	+	0.499956i	$0.166651\pi$
$251$			1.58119e7i			0.999913i	−0.866051	+	0.499956i	$0.833349\pi$
$252$		0			0
$253$	1.54619e7			0.954774
$254$	−5.85010e6	+	3.37756e6i	−0.356995	+	0.206111i
$255$		0			0
$256$	−524288.	+	908093.i	−0.0312500	+	0.0541266i
$257$	−1.62608e7	−	9.38815e6i	−0.957946	−	0.553071i	−0.0624061	−	0.998051i	$-0.519877\pi$
$257$	−1.62608e7	−	9.38815e6i	−0.957946	−	0.553071i	−0.895540	+	0.444980i	$0.853211\pi$
$258$		0			0
$259$	−2.67343e6	−	4.63052e6i	−0.153876	−	0.266520i
$260$			681271.i			0.0387614i
$261$		0			0
$262$	−1.42098e7			−0.790106
$263$	7.38572e6	−	4.26415e6i	0.406000	−	0.234404i	−0.283070	−	0.959099i	$-0.591353\pi$
$263$	7.38572e6	−	4.26415e6i	0.406000	−	0.234404i	0.689069	+	0.724695i	$0.258019\pi$
$264$		0			0
$265$	−6.39220e6	+	1.10716e7i	−0.343489	+	0.594940i
$266$	−2.55751e6	−	1.47658e6i	−0.135885	−	0.0784534i
$267$		0			0
$268$	4.73595e6	+	8.20290e6i	0.246038	+	0.426150i
$269$			1.62898e7i			0.836871i	0.908247	+	0.418436i	$0.137421\pi$
$269$			1.62898e7i			0.836871i	−0.908247	+	0.418436i	$0.862579\pi$
$270$		0			0
$271$	2.43919e7			1.22557			0.612785	−	0.790250i	$-0.290049\pi$
$271$	2.43919e7			1.22557			0.612785	+	0.790250i	$0.290049\pi$
$272$	6.24970e6	−	3.60826e6i	0.310565	−	0.179305i
$273$		0			0
$274$	2.29806e6	−	3.98036e6i	0.111715	−	0.193496i
$275$	2.61938e7	+	1.51230e7i	1.25951	+	0.727177i
$276$		0			0
$277$	1.65615e7	+	2.86854e7i	0.779223	+	1.34965i	0.932390	+	0.361453i	$0.117719\pi$
$277$	1.65615e7	+	2.86854e7i	0.779223	+	1.34965i	−0.153168	+	0.988200i	$0.548947\pi$
$278$		−	3.96608e6i		−	0.184598i
$279$		0			0
$280$	8.08098e6			0.368120
$281$	3.13249e6	−	1.80854e6i	0.141179	−	0.0815098i	−0.427747	−	0.903899i	$-0.640692\pi$
$281$	3.13249e6	−	1.80854e6i	0.141179	−	0.0815098i	0.568926	+	0.822389i	$0.307359\pi$
$282$		0			0
$283$	1.61928e7	−	2.80467e7i	0.714435	−	1.23744i	−0.248742	−	0.968570i	$-0.580017\pi$
$283$	1.61928e7	−	2.80467e7i	0.714435	−	1.23744i	0.963177	−	0.268868i	$-0.0866494\pi$
$284$	4.35787e6	+	2.51602e6i	0.190248	+	0.109839i
$285$		0			0
$286$	200394.	+	347093.i	0.00856618	+	0.0148371i
$287$			8.26120e6i			0.349460i
$288$		0			0
$289$	−2.55282e7			−1.05761
$290$	−3.58078e7	+	2.06736e7i	−1.46819	+	0.847662i
$291$		0			0
$292$	1.28475e6	−	2.22526e6i	0.0516025	−	0.0893781i
$293$	1.44996e7	+	8.37133e6i	0.576437	+	0.332806i	0.759716	−	0.650255i	$-0.225338\pi$
$293$	1.44996e7	+	8.37133e6i	0.576437	+	0.332806i	−0.183279	+	0.983061i	$0.558671\pi$
$294$		0			0
$295$	−1.90146e6	−	3.29342e6i	−0.0740662	−	0.128286i
$296$		−	5.06348e6i		−	0.195242i
$297$		0			0
$298$	1.73185e6			0.0654426
$299$	1.57060e6	−	906785.i	0.0587559	−	0.0339227i
$300$		0			0
$301$	−3.68080e6	+	6.37534e6i	−0.134972	+	0.233778i
$302$	9.05120e6	+	5.22571e6i	0.328613	+	0.189725i
$303$		0			0
$304$	−1.39832e6	−	2.42196e6i	−0.0497721	−	0.0862078i
$305$		−	1.37527e7i		−	0.484716i
$306$		0			0
$307$	1.09311e7			0.377790			0.188895	−	0.981997i	$-0.439509\pi$
$307$	1.09311e7			0.377790			0.188895	+	0.981997i	$0.439509\pi$
$308$	4.11708e6	−	2.37700e6i	0.140909	−	0.0813536i
$309$		0			0
$310$	8.15719e6	−	1.41287e7i	0.273814	−	0.474260i
$311$	−4.40580e7	−	2.54369e7i	−1.46468	−	0.845635i	−0.465461	−	0.885068i	$-0.654112\pi$
$311$	−4.40580e7	−	2.54369e7i	−1.46468	−	0.845635i	−0.999222	+	0.0394328i	$0.987445\pi$
$312$		0			0
$313$	−1.19934e7	−	2.07732e7i	−0.391120	−	0.677440i	0.601478	−	0.798890i	$-0.294579\pi$
$313$	−1.19934e7	−	2.07732e7i	−0.391120	−	0.677440i	−0.992598	+	0.121450i	$0.961246\pi$
$314$		−	1.78228e7i		−	0.575687i
$315$		0			0
$316$	1.20592e7			0.382169
$317$	−1.93571e7	+	1.11758e7i	−0.607662	+	0.350834i	−0.772050	−	0.635562i	$-0.780768\pi$
$317$	−1.93571e7	+	1.11758e7i	−0.607662	+	0.350834i	0.164388	+	0.986396i	$0.447435\pi$
$318$		0			0
$319$	−1.21622e7	+	2.10655e7i	−0.374662	+	0.648934i
$320$	6.62742e6	+	3.82634e6i	0.202253	+	0.116771i
$321$		0			0
$322$	−1.07559e7	−	1.86298e7i	−0.322167	−	0.558009i
$323$			1.92471e7i			0.571160i
$324$		0			0
$325$	3.54765e6			0.103345
$326$	6.35800e6	−	3.67079e6i	0.183513	−	0.105952i
$327$		0			0
$328$	−3.91168e6	+	6.77522e6i	−0.110851	+	0.192000i
$329$	2.74819e7	+	1.58667e7i	0.771718	+	0.445551i
$330$		0			0
$331$	2.20105e7	+	3.81233e7i	0.606941	+	1.05125i	0.991742	+	0.128252i	$0.0409368\pi$
$331$	2.20105e7	+	3.81233e7i	0.606941	+	1.05125i	−0.384801	+	0.923000i	$0.625730\pi$
$332$			2.71213e7i			0.741134i
$333$		0			0
$334$	−9.24638e6			−0.248160
$335$	5.98661e7	−	3.45637e7i	1.59238	−	0.919361i
$336$		0			0
$337$	−2.44378e7	+	4.23275e7i	−0.638516	+	1.10594i	0.347242	+	0.937776i	$0.387118\pi$
$337$	−2.44378e7	+	4.23275e7i	−0.638516	+	1.10594i	−0.985758	+	0.168167i	$0.946215\pi$
$338$	−2.36057e7	−	1.36288e7i	−0.611318	−	0.352945i
$339$		0			0
$340$	−2.63337e7	−	4.56113e7i	−0.670001	−	1.16048i
$341$		−	9.59768e6i		−	0.242049i
$342$		0			0
$343$	3.79930e7			0.941501
$344$	−6.03744e6	+	3.48572e6i	−0.148312	+	0.0856282i
$345$		0			0
$346$	−2.68208e7	+	4.64549e7i	−0.647505	+	1.12151i
$347$	−4.77428e7	−	2.75643e7i	−1.14267	−	0.659719i	−0.195577	−	0.980688i	$-0.562658\pi$
$347$	−4.77428e7	−	2.75643e7i	−1.14267	−	0.659719i	−0.947089	+	0.320970i	$0.895991\pi$
$348$		0			0
$349$	−9.97084e6	−	1.72700e7i	−0.234561	−	0.406271i	0.724584	−	0.689186i	$-0.242032\pi$
$349$	−9.97084e6	−	1.72700e7i	−0.234561	−	0.406271i	−0.959145	+	0.282915i	$0.908699\pi$
$350$		−	4.20808e7i		−	0.981477i
$351$		0			0
$352$	4.50204e6			0.103224
$353$	6.52970e7	−	3.76992e7i	1.48446	−	0.857054i	0.484617	−	0.874726i	$-0.338959\pi$
$353$	6.52970e7	−	3.76992e7i	1.48446	−	0.857054i	0.999844	+	0.0176724i	$0.00562559\pi$
$354$		0			0
$355$	1.83623e7	−	3.18045e7i	0.410433	−	0.710891i
$356$	31285.2	+	18062.5i	0.000693408	+	0.000400340i
$357$		0			0
$358$	−2.61208e7	−	4.52425e7i	−0.569295	−	0.986048i
$359$			5.29978e7i			1.14545i	0.819749	+	0.572723i	$0.194113\pi$
$359$			5.29978e7i			1.14545i	−0.819749	+	0.572723i	$0.805887\pi$
$360$		0			0
$361$	−3.95870e7			−0.841455
$362$	−2.25096e7	+	1.29959e7i	−0.474506	+	0.273956i
$363$		0			0
$364$	278805.	−	482905.i	0.00578092	−	0.0100129i
$365$	−1.62403e7	−	9.37633e6i	−0.333976	−	0.192821i
$366$		0			0
$367$	−2.03953e7	−	3.53257e7i	−0.412602	−	0.714648i	0.582571	−	0.812780i	$-0.302047\pi$
$367$	−2.03953e7	−	3.53257e7i	−0.412602	−	0.714648i	−0.995173	+	0.0981316i	$0.968713\pi$
$368$		−	2.03717e7i		−	0.408775i
$369$		0			0
$370$	−3.69541e7			−0.729554
$371$	9.06196e6	−	5.23192e6i	0.177460	−	0.102457i
$372$		0			0
$373$	2.14508e7	−	3.71539e7i	0.413349	−	0.715941i	−0.581905	−	0.813257i	$-0.697692\pi$
$373$	2.14508e7	−	3.71539e7i	0.413349	−	0.715941i	0.995254	+	0.0973156i	$0.0310256\pi$
$374$	−2.68329e7	−	1.54920e7i	−0.512924	−	0.296137i
$375$		0			0
$376$	1.50257e7	+	2.60253e7i	0.282665	+	0.489590i
$377$			2.85308e6i			0.0532464i
$378$		0			0
$379$	−3.56353e6			−0.0654579			−0.0327290	−	0.999464i	$-0.510420\pi$
$379$	−3.56353e6			−0.0654579			−0.0327290	+	0.999464i	$0.510420\pi$
$380$	−1.76759e7	+	1.02052e7i	−0.322129	+	0.185982i
$381$		0			0
$382$	2.21888e7	−	3.84322e7i	0.398056	−	0.689453i
$383$	5.10154e7	+	2.94538e7i	0.908040	+	0.524257i	0.879800	−	0.475344i	$-0.157676\pi$
$383$	5.10154e7	+	2.94538e7i	0.908040	+	0.524257i	0.0282400	+	0.999601i	$0.491010\pi$
$384$		0			0
$385$	−1.73477e7	−	3.00472e7i	−0.303991	−	0.526528i
$386$			3.07611e7i			0.534860i
$387$		0			0
$388$	4.32097e7			0.739753
$389$	−3.81501e7	+	2.20260e7i	−0.648108	+	0.374185i	−0.787731	−	0.616020i	$-0.788744\pi$
$389$	−3.81501e7	+	2.20260e7i	−0.648108	+	0.374185i	0.139623	+	0.990205i	$0.455411\pi$
$390$		0			0
$391$	−7.01014e7	+	1.21419e8i	−1.17273	+	2.03122i
$392$	1.27155e7	+	7.34129e6i	0.211093	+	0.121875i
$393$		0			0
$394$	2.85943e7	+	4.95268e7i	0.467510	+	0.809751i
$395$		−	8.80097e7i		−	1.42804i
$396$		0			0
$397$	2.93968e6			0.0469818			0.0234909	−	0.999724i	$-0.492522\pi$
$397$	2.93968e6			0.0469818			0.0234909	+	0.999724i	$0.492522\pi$
$398$	3.38911e7	−	1.95670e7i	0.537572	−	0.310367i
$399$		0			0
$400$	1.99253e7	−	3.45116e7i	0.311332	−	0.539244i
$401$	1.38960e7	+	8.02289e6i	0.215505	+	0.124422i	0.603867	−	0.797085i	$-0.293626\pi$
$401$	1.38960e7	+	8.02289e6i	0.215505	+	0.124422i	−0.388362	+	0.921507i	$0.626959\pi$
$402$		0			0
$403$	−562870.	−	974920.i	−0.00859989	−	0.0148955i
$404$		−	5.08278e6i		−	0.0770828i
$405$		0			0
$406$	3.38422e7			0.505685
$407$	−1.88273e7	+	1.08700e7i	−0.279258	+	0.161230i
$408$		0			0
$409$	9.04280e6	−	1.56626e7i	0.132170	−	0.228925i	−0.792343	−	0.610076i	$-0.791139\pi$
$409$	9.04280e6	−	1.56626e7i	0.132170	−	0.228925i	0.924513	+	0.381151i	$0.124472\pi$
$410$	4.94467e7	+	2.85481e7i	0.717440	+	0.414214i
$411$		0			0
$412$	7.95565e6	+	1.37796e7i	0.113759	+	0.197036i
$413$			3.11263e6i			0.0441853i
$414$		0			0
$415$	1.97936e8			2.76937
$416$	457311.	−	264029.i	0.00635231	−	0.00366751i
$417$		0			0
$418$	−6.00366e6	+	1.03986e7i	−0.0822029	+	0.142380i
$419$	6.46244e6	+	3.73109e6i	0.0878525	+	0.0507217i	0.543283	−	0.839550i	$-0.317181\pi$
$419$	6.46244e6	+	3.73109e6i	0.0878525	+	0.0507217i	−0.455430	+	0.890272i	$0.650515\pi$
$420$		0			0
$421$	1.16773e7	+	2.02257e7i	0.156494	+	0.271055i	0.933602	−	0.358312i	$-0.116648\pi$
$421$	1.16773e7	+	2.02257e7i	0.156494	+	0.271055i	−0.777108	+	0.629367i	$0.783314\pi$
$422$			4.83769e7i			0.643726i
$423$		0			0
$424$	9.90926e6			0.130000
$425$	−2.37516e8	+	1.37130e8i	−3.09405	+	1.78635i
$426$		0			0
$427$	−5.62818e6	+	9.74829e6i	−0.0722910	+	0.125212i
$428$	5.74095e6	+	3.31454e6i	0.0732238	+	0.0422758i
$429$		0			0
$430$	2.54394e7	+	4.40623e7i	0.319964	+	0.554193i
$431$		−	7.00387e7i		−	0.874795i	−0.899268	−	0.437397i	$-0.855900\pi$
$431$		−	7.00387e7i		−	0.874795i	0.899268	−	0.437397i	$-0.144100\pi$
$432$		0			0
$433$	−8.83901e7			−1.08878			−0.544390	−	0.838832i	$-0.683239\pi$
$433$	−8.83901e7			−1.08878			−0.544390	+	0.838832i	$0.683239\pi$
$434$	−1.15641e7	+	6.67655e6i	−0.141463	+	0.0816738i
$435$		0			0
$436$	−3.68460e7	+	6.38191e7i	−0.444560	+	0.770001i
$437$	4.70539e7	+	2.71666e7i	0.563834	+	0.325530i
$438$		0			0
$439$	−5.11723e7	−	8.86331e7i	−0.604842	−	1.04762i	−0.992076	−	0.125635i	$-0.959903\pi$
$439$	−5.11723e7	−	8.86331e7i	−0.604842	−	1.04762i	0.387235	−	0.921981i	$-0.373430\pi$
$440$		−	3.28566e7i		−	0.385713i
$441$		0			0
$442$	−3.63421e6			−0.0420865
$443$	1.10522e8	−	6.38100e7i	1.27127	−	0.733969i	0.296045	−	0.955174i	$-0.404332\pi$
$443$	1.10522e8	−	6.38100e7i	1.27127	−	0.733969i	0.975227	+	0.221205i	$0.0709990\pi$
$444$		0			0
$445$	131823.	−	228325.i	0.00149593	−	0.00259103i
$446$	−2.57620e7	−	1.48737e7i	−0.290386	−	0.167654i
$447$		0			0
$448$	−3.13181e6	−	5.42445e6i	−0.0348306	−	0.0603284i
$449$			1.44858e8i			1.60031i	0.599795	+	0.800154i	$0.295249\pi$
$449$			1.44858e8i			1.60031i	−0.599795	+	0.800154i	$0.704751\pi$
$450$		0			0
$451$	3.35894e7			0.366161
$452$	2.16814e7	−	1.25178e7i	0.234786	−	0.135554i
$453$		0			0
$454$	−2.28721e7	+	3.96156e7i	−0.244421	+	0.423349i
$455$	−3.52432e6	−	2.03477e6i	−0.0374146	−	0.0216014i
$456$		0			0
$457$	5.09129e7	+	8.81838e7i	0.533433	+	0.923933i	0.999237	+	0.0390451i	$0.0124316\pi$
$457$	5.09129e7	+	8.81838e7i	0.533433	+	0.923933i	−0.465805	+	0.884888i	$0.654235\pi$
$458$			6.90201e7i			0.718421i
$459$		0			0
$460$	−1.48676e8			−1.52745
$461$	−5.98283e7	+	3.45419e7i	−0.610666	+	0.352568i	−0.773226	−	0.634130i	$-0.781358\pi$
$461$	−5.98283e7	+	3.45419e7i	−0.610666	+	0.352568i	0.162560	+	0.986699i	$0.448025\pi$
$462$		0			0
$463$	6.74662e7	−	1.16855e8i	0.679741	−	1.17735i	−0.295318	−	0.955399i	$-0.595426\pi$
$463$	6.74662e7	−	1.16855e8i	0.679741	−	1.17735i	0.975059	−	0.221947i	$-0.0712411\pi$
$464$	2.77548e7	+	1.60243e7i	0.277833	+	0.160407i
$465$		0			0
$466$	1.57677e7	+	2.73105e7i	0.155816	+	0.269881i
$467$			1.23430e8i			1.21191i	0.795500	+	0.605954i	$0.207208\pi$
$467$			1.23430e8i			1.21191i	−0.795500	+	0.605954i	$0.792792\pi$
$468$		0			0
$469$	−5.65798e7			−0.548458
$470$	1.89937e8	−	1.09660e8i	1.82943	−	1.05622i
$471$		0			0
$472$	−1.47383e6	+	2.55275e6i	−0.0140159	+	0.0242763i
$473$	2.59216e7	+	1.49659e7i	0.244951	+	0.141422i
$474$		0			0
$475$	5.31424e7	+	9.20453e7i	0.495861	+	0.858857i
$476$			4.31076e7i			0.399699i
$477$		0			0
$478$	9.31642e7			0.853032
$479$	6.01036e7	−	3.47008e7i	0.546882	−	0.315743i	−0.200981	−	0.979595i	$-0.564413\pi$
$479$	6.01036e7	−	3.47008e7i	0.546882	−	0.315743i	0.747864	+	0.663852i	$0.231080\pi$
$480$		0			0
$481$	−1.27497e6	+	2.20831e6i	−0.0114568	+	0.0198438i
$482$	2.25618e7	+	1.30261e7i	0.201480	+	0.116325i
$483$		0			0
$484$	1.86803e7	+	3.23552e7i	0.164758	+	0.285370i
$485$		−	3.15352e8i		−	2.76420i
$486$		0			0
$487$	−2.01197e8			−1.74195			−0.870973	−	0.491331i	$-0.836511\pi$
$487$	−2.01197e8			−1.74195			−0.870973	+	0.491331i	$0.836511\pi$
$488$	−9.23163e6	+	5.32988e6i	−0.0794363	+	0.0458626i
$489$		0			0
$490$	5.35779e7	−	9.27997e7i	0.455405	−	0.788785i
$491$	−1.72658e8	−	9.96841e7i	−1.45862	−	0.842135i	−0.459676	−	0.888087i	$-0.652035\pi$
$491$	−1.72658e8	−	9.96841e7i	−1.45862	−	0.842135i	−0.998944	+	0.0459519i	$0.985368\pi$
$492$		0			0
$493$	−1.10282e8	−	1.91015e8i	−0.920377	−	1.59414i
$494$			1.40837e6i			0.0116825i
$495$		0			0
$496$	−1.26454e7			−0.103630
$497$	−2.60315e7	+	1.50293e7i	−0.212046	+	0.122425i
$498$		0			0
$499$	4.38674e7	−	7.59805e7i	0.353053	−	0.611506i	−0.633730	−	0.773555i	$-0.718477\pi$
$499$	4.38674e7	−	7.59805e7i	0.353053	−	0.611506i	0.986783	+	0.162049i	$0.0518102\pi$
$500$	−1.50745e8	−	8.70326e7i	−1.20596	−	0.696261i
$501$		0			0
$502$	−4.47227e7	−	7.74620e7i	−0.353523	−	0.612319i
$503$		−	1.53094e8i		−	1.20297i	−0.798885	−	0.601484i	$-0.794576\pi$
$503$		−	1.53094e8i		−	1.20297i	0.798885	−	0.601484i	$-0.205424\pi$
$504$		0			0
$505$	−3.70950e7			−0.288032
$506$	−7.57474e7	+	4.37328e7i	−0.584677	+	0.337564i
$507$		0			0
$508$	1.91063e7	−	3.30932e7i	0.145743	−	0.252434i
$509$	−1.05471e8	−	6.08939e7i	−0.799799	−	0.461764i	0.0436020	−	0.999049i	$-0.486117\pi$
$509$	−1.05471e8	−	6.08939e7i	−0.799799	−	0.461764i	−0.843401	+	0.537285i	$0.819450\pi$
$510$		0			0
$511$	7.67440e6	+	1.32924e7i	0.0575151	+	0.0996190i
$512$		−	5.93164e6i		−	0.0441942i
$513$		0			0
$514$	1.06215e8			0.782160
$515$	1.00566e8	−	5.80617e7i	0.736255	−	0.425077i
$516$		0			0
$517$	6.45126e7	−	1.11739e8i	0.466845	−	0.808600i
$518$	2.61942e7	+	1.51232e7i	0.188458	+	0.108806i
$519$		0			0
$520$	−1.92693e6	−	3.33753e6i	−0.0137042	−	0.0237364i
$521$			1.44805e8i			1.02393i	0.859006	+	0.511965i	$0.171082\pi$
$521$			1.44805e8i			1.02393i	−0.859006	+	0.511965i	$0.828918\pi$
$522$		0			0
$523$	−2.14387e8			−1.49863			−0.749313	−	0.662216i	$-0.769616\pi$
$523$	−2.14387e8			−1.49863			−0.749313	+	0.662216i	$0.769616\pi$
$524$	6.96137e7	−	4.01915e7i	0.483839	−	0.279345i
$525$		0			0
$526$	−2.41217e7	+	4.17800e7i	−0.165749	+	0.287085i
$527$	7.53687e7	+	4.35141e7i	0.514943	+	0.297302i
$528$		0			0
$529$	1.23873e8	+	2.14554e8i	0.836777	+	1.44934i
$530$		−	7.23194e7i		−	0.485766i
$531$		0			0
$532$	1.67056e7			0.110950
$533$	3.41197e6	−	1.96990e6i	0.0225332	−	0.0130096i
$534$		0			0
$535$	2.41900e7	−	4.18984e7i	0.157970	−	0.273612i
$536$	−4.64026e7	−	2.67906e7i	−0.301334	−	0.173975i
$537$		0			0
$538$	−4.60745e7	−	7.98033e7i	−0.295879	−	0.512477i
$539$		−	6.30393e7i		−	0.402573i
$540$		0			0
$541$	3.66711e7			0.231596			0.115798	−	0.993273i	$-0.463057\pi$
$541$	3.66711e7			0.231596			0.115798	+	0.993273i	$0.463057\pi$
$542$	−1.19496e8	+	6.89908e7i	−0.750505	+	0.433304i
$543$		0			0
$544$	−2.04114e7	+	3.53536e7i	−0.126788	+	0.219603i
$545$	4.65762e8	+	2.68908e8i	2.87723	+	1.66117i
$546$		0			0
$547$	1.50211e8	+	2.60172e8i	0.917780	+	1.58964i	0.802779	+	0.596277i	$0.203354\pi$
$547$	1.50211e8	+	2.60172e8i	0.917780	+	1.58964i	0.115001	+	0.993365i	$0.463313\pi$
$548$			2.59996e7i			0.157989i
$549$		0			0
$550$	−1.71097e8			−1.02838
$551$	−7.40245e7	+	4.27381e7i	−0.442507	+	0.255482i
$552$		0			0
$553$	−3.60174e7	+	6.23839e7i	−0.212979	+	0.368890i
$554$	−1.62269e8	−	9.36863e7i	−0.954349	−	0.550994i
$555$		0			0
$556$	1.12178e7	+	1.94297e7i	0.0652652	+	0.113043i
$557$		−	2.64642e8i		−	1.53141i	−0.643190	−	0.765707i	$-0.722389\pi$
$557$		−	2.64642e8i		−	1.53141i	0.643190	−	0.765707i	$-0.277611\pi$
$558$		0			0
$559$	3.51078e6			0.0200987
$560$	−3.95885e7	+	2.28564e7i	−0.225427	+	0.130150i
$561$		0			0
$562$	−1.02307e7	+	1.77200e7i	−0.0576361	+	0.0998287i
$563$	5.98361e7	+	3.45464e7i	0.335304	+	0.193588i	0.658193	−	0.752849i	$-0.271321\pi$
$563$	5.98361e7	+	3.45464e7i	0.335304	+	0.193588i	−0.322890	+	0.946437i	$0.604654\pi$
$564$		0			0
$565$	−9.13569e7	−	1.58235e8i	−0.506519	−	0.877317i
$566$			1.83201e8i			1.01036i
$567$		0			0
$568$	−2.84655e7			−0.155336
$569$	1.21080e8	−	6.99054e7i	0.657256	−	0.379467i	−0.133975	−	0.990985i	$-0.542774\pi$
$569$	1.21080e8	−	6.99054e7i	0.657256	−	0.379467i	0.791231	+	0.611518i	$0.209441\pi$
$570$		0			0
$571$	−1.02493e8	+	1.77523e8i	−0.550537	+	0.953557i	0.447699	+	0.894184i	$0.352244\pi$
$571$	−1.02493e8	+	1.77523e8i	−0.550537	+	0.953557i	−0.998236	+	0.0593731i	$0.981090\pi$
$572$	−1.96346e6	−	1.13360e6i	−0.0104914	−	0.00605721i
$573$		0			0
$574$	−2.33662e7	−	4.04714e7i	−0.123553	−	0.214000i
$575$			7.74216e8i			4.07248i
$576$		0			0
$577$	1.77665e8			0.924854			0.462427	−	0.886657i	$-0.346979\pi$
$577$	1.77665e8			0.924854			0.462427	+	0.886657i	$0.346979\pi$
$578$	1.25062e8	−	7.22046e7i	0.647652	−	0.373922i
$579$		0			0
$580$	1.16948e8	−	2.02559e8i	0.599387	−	1.03817i
$581$	−1.40303e8	−	8.10039e7i	−0.715382	−	0.413026i
$582$		0			0
$583$	−2.12726e7	−	3.68452e7i	−0.107353	−	0.185941i
$584$			1.45353e7i			0.0729769i
$585$		0			0
$586$	−9.47107e7			−0.470659
$587$	−2.92418e8	+	1.68828e8i	−1.44574	+	0.834698i	−0.998224	−	0.0595787i	$-0.981024\pi$
$587$	−2.92418e8	+	1.68828e8i	−1.44574	+	0.834698i	−0.447515	+	0.894276i	$0.647691\pi$
$588$		0			0
$589$	1.68632e7	−	2.92078e7i	0.0825264	−	0.142940i
$590$	1.86304e7	+	1.07563e7i	0.0907122	+	0.0523727i
$591$		0			0
$592$	1.43217e7	+	2.48059e7i	0.0690285	+	0.119561i
$593$		−	1.84023e8i		−	0.882488i	−0.897387	−	0.441244i	$-0.854537\pi$
$593$		−	1.84023e8i		−	0.882488i	0.897387	−	0.441244i	$-0.145463\pi$
$594$		0			0
$595$	3.14606e8			1.49354
$596$	−8.48428e6	+	4.89840e6i	−0.0400752	+	0.0231375i
$597$		0			0
$598$	−5.12955e6	+	8.88464e6i	−0.0239870	+	0.0415467i
$599$	−1.41355e8	−	8.16115e7i	−0.657705	−	0.379726i	0.133697	−	0.991022i	$-0.457315\pi$
$599$	−1.41355e8	−	8.16115e7i	−0.657705	−	0.379726i	−0.791402	+	0.611296i	$0.790649\pi$
$600$		0			0
$601$	8.57858e7	+	1.48585e8i	0.395177	+	0.684467i	0.993124	−	0.117069i	$-0.0373498\pi$
$601$	8.57858e7	+	1.48585e8i	0.395177	+	0.684467i	−0.597947	+	0.801536i	$0.704017\pi$
$602$		−	4.16435e7i		−	0.190879i
$603$		0			0
$604$	−5.91222e7			−0.268312
$605$	2.36134e8	−	1.36332e8i	1.06633	−	0.615646i
$606$		0			0
$607$	−9.26524e6	+	1.60479e7i	−0.0414277	+	0.0717549i	−0.885996	−	0.463693i	$-0.846524\pi$
$607$	−9.26524e6	+	1.60479e7i	−0.0414277	+	0.0717549i	0.844568	+	0.535448i	$0.179857\pi$
$608$	1.37007e7	+	7.91010e6i	0.0609581	+	0.0351942i
$609$		0			0
$610$	3.88984e7	+	6.73740e7i	0.171373	+	0.296826i
$611$		−	1.51338e7i		−	0.0663473i
$612$		0			0
$613$	3.64689e8			1.58322			0.791609	−	0.611028i	$-0.209244\pi$
$613$	3.64689e8			1.58322			0.791609	+	0.611028i	$0.209244\pi$
$614$	−5.35514e7	+	3.09179e7i	−0.231348	+	0.133569i
$615$		0			0
$616$	−1.34463e7	+	2.32897e7i	−0.0575257	+	0.0996375i
$617$	6.50805e7	+	3.75743e7i	0.277074	+	0.159969i	0.632098	−	0.774888i	$-0.282194\pi$
$617$	6.50805e7	+	3.75743e7i	0.277074	+	0.159969i	−0.355024	+	0.934857i	$0.615527\pi$
$618$		0			0
$619$	1.42862e6	+	2.47445e6i	0.00602345	+	0.0104329i	0.869021	−	0.494774i	$-0.164749\pi$
$619$	1.42862e6	+	2.47445e6i	0.00602345	+	0.0104329i	−0.862998	+	0.505207i	$0.831416\pi$
$620$			9.22881e7i			0.387231i
$621$		0			0
$622$	2.87786e8			1.19591
$623$	−186881.	+	107896.i	−0.000772859	+	0.000446210i
$624$		0			0
$625$	−3.31143e8	+	5.73557e8i	−1.35636	+	2.34929i
$626$	1.17511e8	+	6.78450e7i	0.479022	+	0.276564i
$627$		0			0
$628$	5.04104e7	+	8.73134e7i	0.203536	+	0.352535i
$629$		−	1.97130e8i		−	0.792137i
$630$		0			0
$631$	−9.87283e7			−0.392965			−0.196482	−	0.980507i	$-0.562952\pi$
$631$	−9.87283e7			−0.392965			−0.196482	+	0.980507i	$0.562952\pi$
$632$	−5.90775e7	+	3.41084e7i	−0.234030	+	0.135117i
$633$		0			0
$634$	6.32200e7	−	1.09500e8i	0.248077	−	0.429682i
$635$	−2.41519e8	−	1.39441e8i	−0.943259	−	0.544591i
$636$		0			0
$637$	−3.69704e6	−	6.40345e6i	−0.0143033	−	0.0247740i
$638$		−	1.37600e8i		−	0.529853i
$639$		0			0
$640$	−4.32901e7			−0.165139
$641$	−4.02095e8	+	2.32150e8i	−1.52670	+	0.881442i	−0.527206	+	0.849738i	$0.676760\pi$
$641$	−4.02095e8	+	2.32150e8i	−1.52670	+	0.881442i	−0.999497	+	0.0317046i	$0.989906\pi$
$642$		0			0
$643$	1.98827e8	−	3.44378e8i	0.747897	−	1.29540i	−0.200932	−	0.979605i	$-0.564397\pi$
$643$	1.98827e8	−	3.44378e8i	0.747897	−	1.29540i	0.948829	−	0.315790i	$-0.102270\pi$
$644$	1.05386e8	+	6.08447e7i	0.394572	+	0.227806i
$645$		0			0
$646$	−5.44390e7	−	9.42911e7i	−0.201936	−	0.349763i
$647$		−	1.29737e8i		−	0.479017i	−0.970894	−	0.239509i	$-0.923014\pi$
$647$		−	1.29737e8i		−	0.479017i	0.970894	−	0.239509i	$-0.0769863\pi$
$648$		0			0
$649$	1.26557e7			0.0462970
$650$	−1.73799e7	+	1.00343e7i	−0.0632858	+	0.0365381i
$651$		0			0
$652$	−2.07652e7	+	3.59663e7i	−0.0749191	+	0.129764i
$653$	3.10514e8	+	1.79275e8i	1.11517	+	0.643844i	0.940164	−	0.340723i	$-0.110672\pi$
$653$	3.10514e8	+	1.79275e8i	1.11517	+	0.643844i	0.175007	+	0.984567i	$0.444005\pi$
$654$		0			0
$655$	−2.93324e8	−	5.08052e8i	−1.04382	−	1.80794i
$656$		−	4.42556e7i		−	0.156768i
$657$		0			0
$658$	−1.79511e8			−0.630105
$659$	3.63796e8	−	2.10038e8i	1.27117	−	0.733908i	0.295958	−	0.955201i	$-0.404361\pi$
$659$	3.63796e8	−	2.10038e8i	1.27117	−	0.733908i	0.975207	+	0.221293i	$0.0710278\pi$
$660$		0			0
$661$	2.06107e8	−	3.56988e8i	0.713655	−	1.23609i	−0.249821	−	0.968292i	$-0.580372\pi$
$661$	2.06107e8	−	3.56988e8i	0.713655	−	1.23609i	0.963476	−	0.267794i	$-0.0862948\pi$
$662$	−2.15658e8	−	1.24510e8i	−0.743347	−	0.429172i
$663$		0			0
$664$	−7.67107e7	−	1.32867e8i	−0.262030	−	0.453850i
$665$		−	1.21920e8i		−	0.414582i
$666$		0			0
$667$	−6.22638e8			−2.09826
$668$	4.52978e7	−	2.61527e7i	0.151967	−	0.0877379i
$669$		0			0
$670$	−1.95522e8	+	3.38654e8i	−0.650086	+	1.12598i
$671$	3.96358e7	+	2.28837e7i	0.131196	+	0.0757459i
$672$		0			0
$673$	−2.35837e8	−	4.08482e8i	−0.773690	−	1.34007i	−0.935528	−	0.353252i	$-0.885076\pi$
$673$	−2.35837e8	−	4.08482e8i	−0.773690	−	1.34007i	0.161838	−	0.986817i	$-0.448258\pi$
$674$		−	2.76482e8i		−	0.902999i
$675$		0			0
$676$	1.54192e8			0.499139
$677$	−6.57025e7	+	3.79334e7i	−0.211746	+	0.122252i	−0.602123	−	0.798404i	$-0.705678\pi$
$677$	−6.57025e7	+	3.79334e7i	−0.211746	+	0.122252i	0.390376	+	0.920655i	$0.372345\pi$
$678$		0			0
$679$	−1.29056e8	+	2.23531e8i	−0.412256	+	0.714049i
$680$	2.58017e8	+	1.48966e8i	0.820580	+	0.473762i
$681$		0			0
$682$	2.71463e7	+	4.70188e7i	0.0855772	+	0.148224i
$683$			2.50625e8i			0.786616i	0.919407	+	0.393308i	$0.128669\pi$
$683$			2.50625e8i			0.786616i	−0.919407	+	0.393308i	$0.871331\pi$
$684$		0			0
$685$	1.89750e8			0.590350
$686$	−1.86127e8	+	1.07460e8i	−0.576549	+	0.332871i
$687$		0			0
$688$	1.97182e7	−	3.41529e7i	0.0605483	−	0.104873i
$689$	−4.32169e6	−	2.49513e6i	−0.0132128	−	0.00762843i
$690$		0			0
$691$	−9.23965e7	−	1.60035e8i	−0.280041	−	0.485045i	0.691354	−	0.722516i	$-0.257015\pi$
$691$	−9.23965e7	−	1.60035e8i	−0.280041	−	0.485045i	−0.971394	+	0.237472i	$0.923681\pi$
$692$		−	3.03442e8i		−	0.915710i
$693$		0			0
$694$	3.11855e8			0.932983
$695$	1.41801e8	−	8.18691e7i	0.422402	−	0.243874i
$696$		0			0
$697$	−1.52288e8	+	2.63771e8i	−0.449747	+	0.778984i
$698$	9.76939e7	+	5.64036e7i	0.287277	+	0.165860i
$699$		0			0
$700$	1.19023e8	+	2.06153e8i	0.347005	+	0.601030i
$701$		−	1.48993e8i		−	0.432525i	−0.976335	−	0.216262i	$-0.930613\pi$
$701$		−	1.48993e8i		−	0.432525i	0.976335	−	0.216262i	$-0.0693866\pi$
$702$		0			0
$703$	−7.63942e7			−0.219885
$704$	−2.20554e7	+	1.27337e7i	−0.0632116	+	0.0364952i
$705$		0			0
$706$	−2.13259e8	+	3.69375e8i	−0.606029	+	1.04967i
$707$	2.62940e7	+	1.51809e7i	0.0744045	+	0.0429575i
$708$		0			0
$709$	1.76797e8	+	3.06222e8i	0.496063	+	0.859206i	0.999990	−	0.00454038i	$-0.00144525\pi$
$709$	1.76797e8	+	3.06222e8i	0.496063	+	0.859206i	−0.503927	+	0.863746i	$0.668112\pi$
$710$			2.07746e8i			0.580440i
$711$		0			0
$712$	−204354.			−0.000566166
$713$	2.12760e8	−	1.22837e8i	0.586978	−	0.338892i
$714$		0			0
$715$	−8.27321e6	+	1.43296e7i	−0.0226337	+	0.0392028i
$716$	2.55930e8	+	1.47762e8i	0.697241	+	0.402552i
$717$		0			0
$718$	−1.49900e8	−	2.59635e8i	−0.404976	−	0.701440i
$719$		−	1.15532e8i		−	0.310824i	−0.987850	−	0.155412i	$-0.950330\pi$
$719$		−	1.15532e8i		−	0.310824i	0.987850	−	0.155412i	$-0.0496705\pi$
$720$		0			0
$721$	−9.50453e7			−0.253586
$722$	1.93936e8	−	1.11969e8i	0.515284	−	0.297499i
$723$		0			0
$724$	7.35159e7	−	1.27333e8i	0.193716	−	0.335526i
$725$	−1.05481e9	−	6.08993e8i	−2.76795	−	1.59808i
$726$		0			0
$727$	4.29149e7	+	7.43308e7i	0.111688	+	0.193449i	0.916451	−	0.400147i	$-0.131041\pi$
$727$	4.29149e7	+	7.43308e7i	0.111688	+	0.193449i	−0.804763	+	0.593596i	$0.797708\pi$
$728$			3.15432e6i			0.00817546i
$729$		0			0
$730$	1.06081e8			0.272690
$731$	−2.35048e8	+	1.35705e8i	−0.601734	+	0.347411i
$732$		0			0
$733$	1.65809e8	−	2.87190e8i	0.421014	−	0.729218i	−0.575025	−	0.818136i	$-0.695008\pi$
$733$	1.65809e8	−	2.87190e8i	0.421014	−	0.729218i	0.996039	+	0.0889179i	$0.0283409\pi$
$734$	1.99832e8	+	1.15373e8i	0.505332	+	0.291754i
$735$		0			0
$736$	5.76200e7	+	9.98007e7i	0.144524	+	0.250323i
$737$			2.30049e8i			0.574670i
$738$		0			0
$739$	−4.32705e7			−0.107216			−0.0536079	−	0.998562i	$-0.517072\pi$
$739$	−4.32705e7			−0.107216			−0.0536079	+	0.998562i	$0.517072\pi$
$740$	1.81037e8	−	1.04522e8i	0.446759	−	0.257936i
$741$		0			0
$742$	−2.95962e7	+	5.12622e7i	−0.0724477	+	0.125483i
$743$	−4.91261e8	−	2.83630e8i	−1.19770	−	0.691490i	−0.237654	−	0.971350i	$-0.576379\pi$
$743$	−4.91261e8	−	2.83630e8i	−1.19770	−	0.691490i	−0.960041	+	0.279860i	$0.909712\pi$
$744$		0			0
$745$	3.57493e7	+	6.19197e7i	0.0864568	+	0.149748i
$746$			2.42688e8i			0.584564i
$747$		0			0
$748$	1.75272e8			0.418801
$749$	−3.42932e7	+	1.97992e7i	−0.0816137	+	0.0471197i
$750$		0			0
$751$	3.02087e7	−	5.23230e7i	0.0713202	−	0.123530i	−0.828160	−	0.560492i	$-0.810612\pi$
$751$	3.02087e7	−	5.23230e7i	0.0713202	−	0.123530i	0.899480	+	0.436962i	$0.143945\pi$
$752$	−1.47221e8	−	8.49983e7i	−0.346192	−	0.199874i
$753$		0			0
$754$	−8.06973e6	−	1.39772e7i	−0.0188254	−	0.0326066i
$755$			4.31484e8i			1.00259i
$756$		0			0
$757$	2.57979e8			0.594697			0.297349	−	0.954769i	$-0.403898\pi$
$757$	2.57979e8			0.594697			0.297349	+	0.954769i	$0.403898\pi$
$758$	1.74576e7	−	1.00792e7i	0.0400846	−	0.0231429i
$759$		0			0
$760$	5.77292e7	−	9.99899e7i	0.131509	−	0.227780i
$761$	2.59671e8	+	1.49921e8i	0.589209	+	0.340180i	0.764785	−	0.644286i	$-0.222845\pi$
$761$	2.59671e8	+	1.49921e8i	0.589209	+	0.340180i	−0.175576	+	0.984466i	$0.556179\pi$
$762$		0			0
$763$	−2.20098e8	−	3.81220e8i	−0.495498	−	0.858227i
$764$			2.51038e8i			0.562936i
$765$		0			0
$766$	−3.33231e8			−0.741412
$767$	1.28555e6	−	742213.i	0.00284907	−	0.00164491i
$768$		0			0
$769$	2.17509e8	−	3.76737e8i	0.478299	−	0.828438i	−0.521392	−	0.853317i	$-0.674587\pi$
$769$	2.17509e8	−	3.76737e8i	0.478299	−	0.828438i	0.999690	+	0.0248798i	$0.00792030\pi$
$770$	1.69972e8	+	9.81336e7i	0.372311	+	0.214954i
$771$		0			0
$772$	−8.70055e7	−	1.50698e8i	−0.189101	−	0.327533i
$773$			5.68247e8i			1.23027i	0.788423	+	0.615133i	$0.210898\pi$
$773$			5.68247e8i			1.23027i	−0.788423	+	0.615133i	$0.789102\pi$
$774$		0			0
$775$	4.80581e8			1.03243
$776$	−2.11684e8	+	1.22216e8i	−0.453004	+	0.261542i
$777$		0			0
$778$	1.24598e8	−	2.15810e8i	0.264589	−	0.458281i
$779$	1.02220e8	+	5.90167e7i	0.216233	+	0.124842i
$780$		0			0
$781$	6.11079e7	+	1.05842e8i	0.128276	+	0.222180i
$782$		−	7.93106e8i		−	1.65848i
$783$		0			0
$784$	−8.30572e7			−0.172357
$785$	6.37228e8	−	3.67904e8i	1.31730	−	0.760545i
$786$		0			0
$787$	−4.11256e8	+	7.12316e8i	−0.843700	+	1.46133i	0.0430452	+	0.999073i	$0.486294\pi$
$787$	−4.11256e8	+	7.12316e8i	−0.843700	+	1.46133i	−0.886745	+	0.462258i	$0.847039\pi$
$788$	−2.80166e8	−	1.61754e8i	−0.572580	−	0.330579i
$789$		0			0
$790$	2.48929e8	+	4.31158e8i	0.504887	+	0.874490i
$791$			1.49549e8i			0.302171i
$792$		0			0
$793$	5.36820e6			0.0107649
$794$	−1.44015e7	+	8.31468e6i	−0.0287703	+	0.0166106i
$795$		0			0
$796$	−1.10688e8	+	1.91717e8i	−0.219463	+	0.380121i
$797$	4.33986e8	+	2.50562e8i	0.857236	+	0.494925i	0.863086	−	0.505058i	$-0.168529\pi$
$797$	4.33986e8	+	2.50562e8i	0.857236	+	0.494925i	−0.00584980	+	0.999983i	$0.501862\pi$
$798$		0			0
$799$	5.84977e8	+	1.01321e9i	1.14683	+	1.98637i
$800$			2.25429e8i			0.440291i
$801$		0			0
$802$	−9.07686e7			−0.175959
$803$	5.40461e7	−	3.12035e7i	0.104380	−	0.0602638i
$804$		0			0
$805$	4.44055e8	−	7.69126e8i	0.851234	−	1.47438i
$806$	5.51498e6	+	3.18407e6i	0.0105327	+	0.00608104i
$807$		0			0
$808$	1.43763e7	+	2.49005e7i	0.0272529	+	0.0472034i
$809$			4.25261e8i			0.803174i	0.915821	+	0.401587i	$0.131541\pi$
$809$			4.25261e8i			0.803174i	−0.915821	+	0.401587i	$0.868459\pi$
$810$		0			0
$811$	3.17254e8			0.594763			0.297381	−	0.954759i	$-0.403887\pi$
$811$	3.17254e8			0.594763			0.297381	+	0.954759i	$0.403887\pi$
$812$	−1.65792e8	+	9.57201e7i	−0.309667	+	0.178787i
$813$		0			0
$814$	6.14898e7	−	1.06503e8i	0.114007	−	0.197465i
$815$	2.62488e8	+	1.51548e8i	0.484883	+	0.279947i
$816$		0			0
$817$	5.25901e7	+	9.10888e7i	0.0964357	+	0.167032i
$818$			1.02308e8i			0.186917i
$819$		0			0
$820$	−3.22984e8			−0.585787
$821$	−2.06773e7	+	1.19380e7i	−0.0373649	+	0.0215726i	−0.518566	−	0.855038i	$-0.673534\pi$
$821$	−2.06773e7	+	1.19380e7i	−0.0373649	+	0.0215726i	0.481201	+	0.876610i	$0.340201\pi$
$822$		0			0
$823$	−5.26330e8	+	9.11631e8i	−0.944189	+	1.63538i	−0.186821	+	0.982394i	$0.559818\pi$
$823$	−5.26330e8	+	9.11631e8i	−0.944189	+	1.63538i	−0.757368	+	0.652988i	$0.773515\pi$
$824$	−7.79491e7	−	4.50040e7i	−0.139325	−	0.0804395i
$825$		0			0
$826$	−8.80385e6	−	1.52487e7i	−0.0156218	−	0.0270578i
$827$			1.79106e8i			0.316660i	0.987386	+	0.158330i	$0.0506109\pi$
$827$			1.79106e8i			0.316660i	−0.987386	+	0.158330i	$0.949389\pi$
$828$		0			0
$829$	−1.21964e8			−0.214076			−0.107038	−	0.994255i	$-0.534137\pi$
$829$	−1.21964e8			−0.214076			−0.107038	+	0.994255i	$0.534137\pi$
$830$	−9.69684e8	+	5.59847e8i	−1.69588	+	0.979118i
$831$		0			0
$832$	−1.49357e6	+	2.58694e6i	−0.00259332	+	0.00449176i
$833$	4.95036e8	+	2.85809e8i	0.856449	+	0.494471i
$834$		0			0
$835$	−1.90867e8	−	3.30591e8i	−0.327847	−	0.567848i
$836$		−	6.79236e7i		−	0.116252i
$837$		0			0
$838$	−4.22125e7			−0.0717313
$839$	−4.91209e8	+	2.83600e8i	−0.831727	+	0.480198i	−0.854444	−	0.519544i	$-0.826102\pi$
$839$	−4.91209e8	+	2.83600e8i	−0.831727	+	0.480198i	0.0227168	+	0.999742i	$0.492768\pi$
$840$		0			0
$841$	1.92351e8	−	3.33162e8i	0.323375	−	0.560102i
$842$	−1.14414e8	−	6.60569e7i	−0.191665	−	0.110658i
$843$		0			0
$844$	−1.36831e8	−	2.36998e8i	−0.227591	−	0.394200i
$845$		−	1.12532e9i		−	1.86511i
$846$		0			0
$847$	−2.23171e8			−0.367272
$848$	−4.85453e7	+	2.80276e7i	−0.0796085	+	0.0459620i
$849$		0			0
$850$	7.75725e8	−	1.34360e9i	1.26314	−	2.18782i
$851$	−4.81928e8	−	2.78241e8i	−0.781977	−	0.451474i
$852$		0			0
$853$	4.59944e8	+	7.96646e8i	0.741068	+	1.28357i	0.952010	+	0.306068i	$0.0990135\pi$
$853$	4.59944e8	+	7.96646e8i	0.741068	+	1.28357i	−0.210942	+	0.977499i	$0.567653\pi$
$854$		−	6.36756e7i		−	0.102235i
$855$		0			0
$856$	−3.74997e7			−0.0597870
$857$	−5.10368e8	+	2.94661e8i	−0.810851	+	0.468145i	−0.847251	−	0.531192i	$-0.821744\pi$
$857$	−5.10368e8	+	2.94661e8i	−0.810851	+	0.468145i	0.0364004	+	0.999337i	$0.488411\pi$
$858$		0			0
$859$	5.10737e7	−	8.84623e7i	0.0805783	−	0.139566i	−0.822920	−	0.568157i	$-0.807657\pi$
$859$	5.10737e7	−	8.84623e7i	0.0805783	−	0.139566i	0.903498	+	0.428591i	$0.140990\pi$
$860$	−2.49254e8	−	1.43907e8i	−0.391874	−	0.226249i
$861$		0			0
$862$	1.98099e8	+	3.43118e8i	0.309287	+	0.535700i
$863$		−	8.24326e8i		−	1.28253i	−0.767321	−	0.641264i	$-0.778410\pi$
$863$		−	8.24326e8i		−	1.28253i	0.767321	−	0.641264i	$-0.221590\pi$
$864$		0			0
$865$	−2.21457e9			−3.42170
$866$	4.33021e8	−	2.50005e8i	0.666739	−	0.384942i
$867$		0			0
$868$	3.77683e7	−	6.54165e7i	0.0577521	−	0.100030i
$869$	2.53648e8	+	1.46444e8i	0.386520	+	0.223158i
$870$		0			0
$871$	1.34916e7	+	2.33681e7i	0.0204178	+	0.0353646i
$872$		−	4.16865e8i		−	0.628703i
$873$		0			0
$874$	−3.07355e8			−0.460368
$875$	9.00467e8	−	5.19885e8i	1.34414	−	0.776038i
$876$		0			0
$877$	−3.55715e8	+	6.16116e8i	−0.527355	+	0.913406i	0.472137	+	0.881525i	$0.343483\pi$
$877$	−3.55715e8	+	6.16116e8i	−0.527355	+	0.913406i	−0.999492	+	0.0318803i	$0.989850\pi$
$878$	5.01384e8	+	2.89474e8i	0.740777	+	0.427688i
$879$		0			0
$880$	9.29325e7	+	1.60964e8i	0.136370	+	0.236200i
$881$		−	1.35023e8i		−	0.197460i	−0.995114	−	0.0987302i	$-0.968522\pi$
$881$		−	1.35023e8i		−	0.197460i	0.995114	−	0.0987302i	$-0.0314781\pi$
$882$		0			0
$883$	4.91077e8			0.713293			0.356646	−	0.934239i	$-0.383920\pi$
$883$	4.91077e8			0.713293			0.356646	+	0.934239i	$0.383920\pi$
$884$	1.78039e7	−	1.02791e7i	0.0257726	−	0.0148798i
$885$		0			0
$886$	−3.60964e8	+	6.25208e8i	−0.518995	+	0.898925i
$887$	8.12126e8	+	4.68881e8i	1.16373	+	0.671881i	0.952195	−	0.305490i	$-0.0988201\pi$
$887$	8.12126e8	+	4.68881e8i	1.16373	+	0.671881i	0.211536	+	0.977370i	$0.432153\pi$
$888$		0			0
$889$	1.14131e8	+	1.97680e8i	0.162442	+	0.281357i
$890$			1.49141e6i			0.00211557i
$891$		0			0
$892$	1.68277e8			0.237099
$893$	3.92652e8	−	2.26698e8i	0.551383	−	0.318341i
$894$		0			0
$895$	1.07839e9	−	1.86782e9i	1.50420	−	2.60535i
$896$	3.06853e7	+	1.77162e7i	0.0426586	+	0.0246290i
$897$		0			0
$898$	−4.09720e8	−	7.09656e8i	−0.565794	−	0.979984i
$899$			3.86491e8i			0.531938i
$900$		0			0
$901$	3.85784e8			0.527437
$902$	−1.64554e8	+	9.50051e7i	−0.224227	+	0.129458i
$903$		0			0
$904$	−7.08113e7	+	1.22649e8i	−0.0958511	+	0.166019i
$905$	−9.29300e8	−	5.36531e8i	−1.25375	−	0.723851i
$906$		0			0
$907$	−3.58999e8	−	6.21805e8i	−0.481140	−	0.833360i	0.518625	−	0.855002i	$-0.326444\pi$
$907$	−3.58999e8	−	6.21805e8i	−0.481140	−	0.833360i	−0.999766	+	0.0216419i	$0.993111\pi$
$908$		−	2.58768e8i		−	0.345663i
$909$		0			0
$910$	2.30208e7			0.0305489
$911$	6.57988e8	−	3.79889e8i	0.870287	−	0.502461i	0.00284370	−	0.999996i	$-0.499095\pi$
$911$	6.57988e8	−	3.79889e8i	0.870287	−	0.502461i	0.867444	+	0.497535i	$0.165761\pi$
$912$		0			0
$913$	−3.29355e8	+	5.70460e8i	−0.432765	+	0.749572i
$914$	−4.98843e8	−	2.88007e8i	−0.653319	−	0.377194i
$915$		0			0
$916$	−1.95218e8	−	3.38128e8i	−0.254000	−	0.439941i
$917$			4.80163e8i			0.622703i
$918$		0			0
$919$	−9.15355e8			−1.17935			−0.589676	−	0.807640i	$-0.700744\pi$
$919$	−9.15355e8			−1.17935			−0.589676	+	0.807640i	$0.700744\pi$
$920$	7.28362e8	−	4.20520e8i	0.935371	−	0.540037i
$921$		0			0
$922$	1.95398e8	−	3.38440e8i	0.249303	−	0.431806i
$923$	1.24145e7	+	7.16754e6i	0.0157879	+	0.00911517i
$924$		0			0
$925$	−5.44287e8	−	9.42733e8i	−0.687706	−	1.19114i
$926$			7.63293e8i			0.961299i
$927$		0			0
$928$	−1.81294e8			−0.226850
$929$	−4.28783e8	+	2.47558e8i	−0.534799	+	0.308766i	−0.742968	−	0.669327i	$-0.766583\pi$
$929$	−4.28783e8	+	2.47558e8i	−0.534799	+	0.308766i	0.208170	+	0.978093i	$0.433249\pi$
$930$		0			0
$931$	1.10760e8	−	1.91842e8i	0.137257	−	0.237736i
$932$	−1.54491e8	−	8.91957e7i	−0.190834	−	0.110178i
$933$		0			0
$934$	−3.49112e8	−	6.04680e8i	−0.428474	−	0.742139i
$935$		−	1.27916e9i		−	1.56492i
$936$		0			0
$937$	5.39309e8			0.655570			0.327785	−	0.944752i	$-0.393698\pi$
$937$	5.39309e8			0.655570			0.327785	+	0.944752i	$0.393698\pi$
$938$	2.77184e8	−	1.60032e8i	0.335860	−	0.193909i
$939$		0			0
$940$	−6.20332e8	+	1.07445e9i	−0.746862	+	1.29360i
$941$	−7.63585e8	−	4.40856e8i	−0.916408	−	0.529088i	−0.0339205	−	0.999425i	$-0.510799\pi$
$941$	−7.63585e8	−	4.40856e8i	−0.916408	−	0.529088i	−0.882487	+	0.470336i	$0.844133\pi$
$942$		0			0
$943$	4.29898e8	+	7.44606e8i	0.512662	+	0.887956i
$944$		−	1.66745e7i		−	0.0198215i
$945$		0			0
$946$	−1.69319e8			−0.200001
$947$	−7.71869e8	+	4.45639e8i	−0.908853	+	0.524727i	−0.880062	−	0.474859i	$-0.842499\pi$
$947$	−7.71869e8	+	4.45639e8i	−0.908853	+	0.524727i	−0.0287913	+	0.999585i	$0.509166\pi$
$948$		0			0
$949$	3.65995e6	−	6.33922e6i	0.00428230	−	0.00741716i
$950$	−5.20687e8	−	3.00619e8i	−0.607304	−	0.350627i
$951$		0			0
$952$	−1.21927e8	−	2.11183e8i	−0.141315	−	0.244764i
$953$			2.13491e8i			0.246661i	0.992366	+	0.123331i	$0.0393576\pi$
$953$			2.13491e8i			0.246661i	−0.992366	+	0.123331i	$0.960642\pi$
$954$		0			0
$955$	1.83212e9			2.10350
$956$	−4.56410e8	+	2.63508e8i	−0.522374	+	0.301592i
$957$		0			0
$958$	−1.96298e8	+	3.39997e8i	−0.223264	+	0.386704i
$959$	−1.34500e8	−	7.76537e7i	−0.152499	−	0.0880454i
$960$		0			0
$961$	3.67503e8	+	6.36534e8i	0.414086	+	0.717218i
$962$		−	1.44246e7i		−	0.0162024i
$963$		0			0
$964$	−1.47373e8			−0.164508
$965$	−1.09982e9	+	6.34981e8i	−1.22388	+	0.706608i
$966$		0			0
$967$	6.06482e8	−	1.05046e9i	0.670716	−	1.16171i	−0.306986	−	0.951714i	$-0.599320\pi$
$967$	6.06482e8	−	1.05046e9i	0.670716	−	1.16171i	0.977701	−	0.210000i	$-0.0673463\pi$
$968$	−1.83029e8	−	1.05672e8i	−0.201787	−	0.116502i
$969$		0			0
$970$	8.91950e8	+	1.54490e9i	0.977294	+	1.69272i
$971$		−	4.38734e8i		−	0.479230i	−0.970868	−	0.239615i	$-0.922979\pi$
$971$		−	4.38734e8i		−	0.479230i	0.970868	−	0.239615i	$-0.0770212\pi$
$972$		0			0
$973$	−1.34017e8			−0.145486
$974$	9.85660e8	−	5.69071e8i	1.06672	−	0.615871i
$975$		0			0
$976$	3.01504e7	−	5.22220e7i	0.0324297	−	0.0561699i
$977$	1.03164e9	+	5.95616e8i	1.10623	+	0.638679i	0.937849	−	0.347044i	$-0.112814\pi$
$977$	1.03164e9	+	5.95616e8i	1.10623	+	0.638679i	0.168376	+	0.985723i	$0.446148\pi$
$978$		0			0
$979$	438695.	+	759842.i	0.000467535	+	0.000809795i
$980$			6.06165e8i			0.644040i
$981$		0			0
$982$	1.12780e9			1.19096
$983$	−4.17380e8	+	2.40974e8i	−0.439411	+	0.253694i	−0.703348	−	0.710846i	$-0.748312\pi$
$983$	−4.17380e8	+	2.40974e8i	−0.439411	+	0.253694i	0.263937	+	0.964540i	$0.414979\pi$
$984$		0			0
$985$	−1.18051e9	+	2.04470e9i	−1.23526	+	2.13954i
$986$	1.08054e9	+	6.23852e8i	1.12723	+	0.650805i
$987$		0			0
$988$	−3.98348e6	−	6.89960e6i	−0.00413040	−	0.00715407i
$989$			7.66170e8i			0.792021i
$990$		0			0
$991$	−8.26440e8			−0.849162			−0.424581	−	0.905390i	$-0.639579\pi$
$991$	−8.26440e8			−0.849162			−0.424581	+	0.905390i	$0.639579\pi$
$992$	6.19495e7	−	3.57665e7i	0.0634604	−	0.0366389i
$993$		0			0
$994$	8.50185e7	−	1.47256e8i	0.0865674	−	0.149939i
$995$	1.39918e9	+	8.07818e8i	1.42038	+	0.820058i
$996$		0			0
$997$	−6.50181e8	−	1.12615e9i	−0.656068	−	1.13634i	−0.981625	−	0.190820i	$-0.938885\pi$
$997$	−6.50181e8	−	1.12615e9i	−0.656068	−	1.13634i	0.325557	−	0.945522i	$-0.394448\pi$
$998$			4.96303e8i			0.499292i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.7.d.a.17.1		12
3.2	odd	2		18.7.d.a.5.5	✓	12
4.3	odd	2		432.7.q.b.17.1		12
9.2	odd	6	inner	54.7.d.a.35.1		12
9.4	even	3		162.7.b.c.161.6		12
9.5	odd	6		162.7.b.c.161.7		12
9.7	even	3		18.7.d.a.11.5	yes	12
12.11	even	2		144.7.q.c.113.4		12
36.7	odd	6		144.7.q.c.65.4		12
36.11	even	6		432.7.q.b.305.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.7.d.a.5.5	✓	12	3.2	odd	2
18.7.d.a.11.5	yes	12	9.7	even	3
54.7.d.a.17.1		12	1.1	even	1	trivial
54.7.d.a.35.1		12	9.2	odd	6	inner
144.7.q.c.65.4		12	36.7	odd	6
144.7.q.c.113.4		12	12.11	even	2
162.7.b.c.161.6		12	9.4	even	3
162.7.b.c.161.7		12	9.5	odd	6
432.7.q.b.17.1		12	4.3	odd	2
432.7.q.b.305.1		12	36.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	54.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.89898 + 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(-202.253 - 116.771i) q^{5} +(95.5752 + 165.541i) q^{7} +181.019i q^{8} +O(q^{10})\)	\(q+(-4.89898 + 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(-202.253 - 116.771i) q^{5} +(95.5752 + 165.541i) q^{7} +181.019i q^{8} +1321.11 q^{10} +(673.077 - 388.601i) q^{11} +(45.5802 - 78.9472i) q^{13} +(-936.442 - 540.655i) q^{14} +(-512.000 - 886.810i) q^{16} +7047.39i q^{17} +2731.10 q^{19} +(-6472.09 + 3736.66i) q^{20} +(-2198.26 + 3807.50i) q^{22} +(17228.9 + 9947.14i) q^{23} +(19458.3 + 33702.7i) q^{25} +515.681i q^{26} +6116.81 q^{28} +(-27104.3 + 15648.7i) q^{29} +(6174.50 - 10694.6i) q^{31} +(5016.55 + 2896.31i) q^{32} +(-19933.0 - 34525.0i) q^{34} -44641.5i q^{35} -27972.0 q^{37} +(-13379.6 + 7724.70i) q^{38} +(21137.7 - 36611.7i) q^{40} +(37428.2 + 21609.2i) q^{41} +(19256.1 + 33352.5i) q^{43} -24870.5i q^{44} -112539. q^{46} +(143771. - 83006.2i) q^{47} +(40555.3 - 70243.8i) q^{49} +(-190651. - 110073. i) q^{50} +(-1458.57 - 2526.31i) q^{52} -54741.5i q^{53} -181509. q^{55} +(-29966.1 + 17301.0i) q^{56} +(88522.3 - 153325. i) q^{58} +(14102.1 + 8141.84i) q^{59} +(29443.7 + 50998.0i) q^{61} +69856.5i q^{62} -32768.0 q^{64} +(-18437.4 + 10644.9i) q^{65} +(-147998. + 256341. i) q^{67} +(195303. + 112758. i) q^{68} +(126265. + 218698. i) q^{70} +157251. i q^{71} +80297.0 q^{73} +(137034. - 79116.8i) q^{74} +(43697.5 - 75686.3i) q^{76} +(128659. + 74281.3i) q^{77} +(188424. + 326360. i) q^{79} +239146. i q^{80} -244480. q^{82} +(-733992. + 423771. i) q^{83} +(822929. - 1.42535e6i) q^{85} +(-188670. - 108929. i) q^{86} +(70344.3 + 121840. i) q^{88} +1128.91i q^{89} +17425.3 q^{91} +(551326. - 318308. i) q^{92} +(-469554. + 813291. i) q^{94} +(-552371. - 318912. i) q^{95} +(675152. + 1.16940e6i) q^{97} +458831. i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 192 q^{4} - 432 q^{5} + 240 q^{7}+O(q^{10}) \) 12 * q + 192 * q^4 - 432 * q^5 + 240 * q^7	\( 12 q + 192 q^{4} - 432 q^{5} + 240 q^{7} - 378 q^{11} + 1680 q^{13} + 4752 q^{14} - 6144 q^{16} - 2820 q^{19} - 13824 q^{20} - 3600 q^{22} + 76248 q^{23} + 8094 q^{25} + 15360 q^{28} - 97092 q^{29} + 21480 q^{31} - 27360 q^{34} - 25536 q^{37} - 97632 q^{38} + 410562 q^{41} + 71430 q^{43} - 135072 q^{46} - 347652 q^{47} - 135954 q^{49} - 311040 q^{50} - 53760 q^{52} + 580392 q^{55} + 152064 q^{56} + 159264 q^{58} - 369738 q^{59} + 135744 q^{61} - 393216 q^{64} + 753840 q^{65} - 289938 q^{67} - 744768 q^{68} + 155952 q^{70} - 977700 q^{73} + 2197152 q^{74} - 45120 q^{76} + 159192 q^{77} - 764796 q^{79} + 1073088 q^{82} - 396900 q^{83} + 1619568 q^{85} - 3264624 q^{86} + 115200 q^{88} + 355584 q^{91} + 2439936 q^{92} - 736848 q^{94} + 2089260 q^{95} - 38874 q^{97}+O(q^{100}) \) 12 * q + 192 * q^4 - 432 * q^5 + 240 * q^7 - 378 * q^11 + 1680 * q^13 + 4752 * q^14 - 6144 * q^16 - 2820 * q^19 - 13824 * q^20 - 3600 * q^22 + 76248 * q^23 + 8094 * q^25 + 15360 * q^28 - 97092 * q^29 + 21480 * q^31 - 27360 * q^34 - 25536 * q^37 - 97632 * q^38 + 410562 * q^41 + 71430 * q^43 - 135072 * q^46 - 347652 * q^47 - 135954 * q^49 - 311040 * q^50 - 53760 * q^52 + 580392 * q^55 + 152064 * q^56 + 159264 * q^58 - 369738 * q^59 + 135744 * q^61 - 393216 * q^64 + 753840 * q^65 - 289938 * q^67 - 744768 * q^68 + 155952 * q^70 - 977700 * q^73 + 2197152 * q^74 - 45120 * q^76 + 159192 * q^77 - 764796 * q^79 + 1073088 * q^82 - 396900 * q^83 + 1619568 * q^85 - 3264624 * q^86 + 115200 * q^88 + 355584 * q^91 + 2439936 * q^92 - 736848 * q^94 + 2089260 * q^95 - 38874 * q^97

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