LMFDB - Embedded newform 54.7.d.a.17.3

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			17.3
Root			$-8.15670i$ of defining polynomial
Character	$\chi$	$=$	54.17
Dual form			54.7.d.a.35.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.89898 + 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(95.8504 + 55.3393i) q^{5} +(-163.169 - 282.617i) q^{7} +181.019i q^{8} +O(q^{10})$	\(q+(-4.89898 + 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(95.8504 + 55.3393i) q^{5} +(-163.169 - 282.617i) q^{7} +181.019i q^{8} -626.092 q^{10} +(-541.817 + 312.818i) q^{11} +(1014.01 - 1756.31i) q^{13} +(1598.72 + 923.023i) q^{14} +(-512.000 - 886.810i) q^{16} -4126.55i q^{17} +12194.5 q^{19} +(3067.21 - 1770.86i) q^{20} +(1769.57 - 3064.98i) q^{22} +(18576.6 + 10725.2i) q^{23} +(-1687.63 - 2923.06i) q^{25} +11472.2i q^{26} -10442.8 q^{28} +(21435.3 - 12375.7i) q^{29} +(20265.9 - 35101.6i) q^{31} +(5016.55 + 2896.31i) q^{32} +(11671.6 + 20215.9i) q^{34} -36118.6i q^{35} -30093.7 q^{37} +(-59740.6 + 34491.3i) q^{38} +(-10017.5 + 17350.8i) q^{40} +(-51294.6 - 29614.9i) q^{41} +(43967.8 + 76154.5i) q^{43} +20020.4i q^{44} -121342. q^{46} +(-112384. + 64885.1i) q^{47} +(5576.24 - 9658.34i) q^{49} +(16535.3 + 9546.68i) q^{50} +(-32448.2 - 56201.9i) q^{52} -165599. i q^{53} -69244.6 q^{55} +(51159.1 - 29536.7i) q^{56} +(-70007.5 + 121257. i) q^{58} +(-46116.0 - 26625.1i) q^{59} +(133491. + 231213. i) q^{61} +229282. i q^{62} -32768.0 q^{64} +(194386. - 112229. i) q^{65} +(203640. - 352715. i) q^{67} +(-114358. - 66024.7i) q^{68} +(102159. + 176944. i) q^{70} +186563. i q^{71} -242102. q^{73} +(147429. - 85117.9i) q^{74} +(195112. - 337944. i) q^{76} +(176816. + 102085. i) q^{77} +(63186.3 + 109442. i) q^{79} -113335. i q^{80} +335055. q^{82} +(59731.2 - 34485.8i) q^{83} +(228360. - 395531. i) q^{85} +(-430795. - 248720. i) q^{86} +(-56626.2 - 98079.4i) q^{88} +413126. i q^{89} -661817. q^{91} +(594452. - 343207. i) q^{92} +(367045. - 635741. i) q^{94} +(1.16885e6 + 674835. i) q^{95} +(-489221. - 847356. i) q^{97} +63088.0i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	95.8504	+	55.3393i	0.766803	+	0.442714i	0.831733	−	0.555176i	$-0.187349\pi$
$5$	95.8504	+	55.3393i	0.766803	+	0.442714i	−0.0649297	+	0.997890i	$0.520682\pi$
$6$		0			0
$7$	−163.169	−	282.617i	−0.475711	−	0.823956i	0.523901	−	0.851779i	$-0.324476\pi$
$7$	−163.169	−	282.617i	−0.475711	−	0.823956i	−0.999613	+	0.0278225i	$0.991143\pi$
$8$			181.019i			0.353553i
$9$		0			0
$10$	−626.092			−0.626092
$11$	−541.817	+	312.818i	−0.407075	+	0.235025i	−0.689532	−	0.724255i	$-0.742184\pi$
$11$	−541.817	+	312.818i	−0.407075	+	0.235025i	0.282457	+	0.959280i	$0.408851\pi$
$12$		0			0
$13$	1014.01	−	1756.31i	0.461541	−	0.799412i	−0.537497	−	0.843266i	$-0.680630\pi$
$13$	1014.01	−	1756.31i	0.461541	−	0.799412i	0.999038	+	0.0438534i	$0.0139635\pi$
$14$	1598.72	+	923.023i	0.582625	+	0.336379i
$15$		0			0
$16$	−512.000	−	886.810i	−0.125000	−	0.216506i
$17$		−	4126.55i		−	0.839924i	−0.907542	−	0.419962i	$-0.862043\pi$
$17$		−	4126.55i		−	0.839924i	0.907542	−	0.419962i	$-0.137957\pi$
$18$		0			0
$19$	12194.5			1.77788			0.888942	−	0.458020i	$-0.151441\pi$
$19$	12194.5			1.77788			0.888942	+	0.458020i	$0.151441\pi$
$20$	3067.21	−	1770.86i	0.383402	−	0.221357i
$21$		0			0
$22$	1769.57	−	3064.98i	0.166188	−	0.287846i
$23$	18576.6	+	10725.2i	1.52680	+	0.881501i	0.999493	+	0.0318293i	$0.0101333\pi$
$23$	18576.6	+	10725.2i	1.52680	+	0.881501i	0.527312	+	0.849672i	$0.323200\pi$
$24$		0			0
$25$	−1687.63	−	2923.06i	−0.108008	−	0.187076i
$26$			11472.2i			0.652717i
$27$		0			0
$28$	−10442.8			−0.475711
$29$	21435.3	−	12375.7i	0.878893	−	0.507429i	0.00859997	−	0.999963i	$-0.497263\pi$
$29$	21435.3	−	12375.7i	0.878893	−	0.507429i	0.870293	+	0.492534i	$0.163929\pi$
$30$		0			0
$31$	20265.9	−	35101.6i	0.680269	−	1.17826i	−0.294630	−	0.955612i	$-0.595196\pi$
$31$	20265.9	−	35101.6i	0.680269	−	1.17826i	0.974899	−	0.222649i	$-0.0714704\pi$
$32$	5016.55	+	2896.31i	0.153093	+	0.0883883i
$33$		0			0
$34$	11671.6	+	20215.9i	0.296958	+	0.514346i
$35$		−	36118.6i		−	0.842417i
$36$		0			0
$37$	−30093.7			−0.594115			−0.297058	−	0.954860i	$-0.596005\pi$
$37$	−30093.7			−0.594115			−0.297058	+	0.954860i	$0.596005\pi$
$38$	−59740.6	+	34491.3i	−1.08873	+	0.628577i
$39$		0			0
$40$	−10017.5	+	17350.8i	−0.156523	+	0.271106i
$41$	−51294.6	−	29614.9i	−0.744252	−	0.429694i	0.0793613	−	0.996846i	$-0.474712\pi$
$41$	−51294.6	−	29614.9i	−0.744252	−	0.429694i	−0.823613	+	0.567152i	$0.808045\pi$
$42$		0			0
$43$	43967.8	+	76154.5i	0.553006	+	0.957834i	0.998056	+	0.0623286i	$0.0198527\pi$
$43$	43967.8	+	76154.5i	0.553006	+	0.957834i	−0.445050	+	0.895506i	$0.646814\pi$
$44$			20020.4i			0.235025i
$45$		0			0
$46$	−121342.			−1.24663
$47$	−112384.	+	64885.1i	−1.08246	+	0.624958i	−0.931559	−	0.363590i	$-0.881551\pi$
$47$	−112384.	+	64885.1i	−1.08246	+	0.624958i	−0.150901	+	0.988549i	$0.548217\pi$
$48$		0			0
$49$	5576.24	−	9658.34i	0.0473973	−	0.0820945i
$50$	16535.3	+	9546.68i	0.132283	+	0.0763734i
$51$		0			0
$52$	−32448.2	−	56201.9i	−0.230770	−	0.399706i
$53$		−	165599.i		−	1.11232i	−0.831074	−	0.556161i	$-0.812274\pi$
$53$		−	165599.i		−	1.11232i	0.831074	−	0.556161i	$-0.187726\pi$
$54$		0			0
$55$	−69244.6			−0.416196
$56$	51159.1	−	29536.7i	0.291313	−	0.168189i
$57$		0			0
$58$	−70007.5	+	121257.i	−0.358807	+	0.621471i
$59$	−46116.0	−	26625.1i	−0.224541	−	0.129639i	0.383510	−	0.923537i	$-0.374715\pi$
$59$	−46116.0	−	26625.1i	−0.224541	−	0.129639i	−0.608051	+	0.793898i	$0.708048\pi$
$60$		0			0
$61$	133491.	+	231213.i	0.588115	+	1.01864i	0.994479	+	0.104933i	$0.0334629\pi$
$61$	133491.	+	231213.i	0.588115	+	1.01864i	−0.406365	+	0.913711i	$0.633204\pi$
$62$			229282.i			0.962046i
$63$		0			0
$64$	−32768.0			−0.125000
$65$	194386.	−	112229.i	0.707822	−	0.408661i
$66$		0			0
$67$	203640.	−	352715.i	0.677079	−	1.17273i	−0.298778	−	0.954323i	$-0.596579\pi$
$67$	203640.	−	352715.i	0.677079	−	1.17273i	0.975857	−	0.218412i	$-0.0700876\pi$
$68$	−114358.	−	66024.7i	−0.363698	−	0.209981i
$69$		0			0
$70$	102159.	+	176944.i	0.297839	+	0.515873i
$71$			186563.i			0.521254i	0.965440	+	0.260627i	$0.0839293\pi$
$71$			186563.i			0.521254i	−0.965440	+	0.260627i	$0.916071\pi$
$72$		0			0
$73$	−242102.			−0.622344			−0.311172	−	0.950354i	$-0.600721\pi$
$73$	−242102.			−0.622344			−0.311172	+	0.950354i	$0.600721\pi$
$74$	147429.	−	85117.9i	0.363820	−	0.210051i
$75$		0			0
$76$	195112.	−	337944.i	0.444471	−	0.769846i
$77$	176816.	+	102085.i	0.387301	+	0.223608i
$78$		0			0
$79$	63186.3	+	109442.i	0.128157	+	0.221974i	0.922963	−	0.384890i	$-0.125761\pi$
$79$	63186.3	+	109442.i	0.128157	+	0.221974i	−0.794806	+	0.606864i	$0.792427\pi$
$80$		−	113335.i		−	0.221357i
$81$		0			0
$82$	335055.			0.607679
$83$	59731.2	−	34485.8i	0.104464	−	0.0603124i	−0.446858	−	0.894605i	$-0.647457\pi$
$83$	59731.2	−	34485.8i	0.104464	−	0.0603124i	0.551322	+	0.834293i	$0.314124\pi$
$84$		0			0
$85$	228360.	−	395531.i	0.371846	−	0.644057i
$86$	−430795.	−	248720.i	−0.677291	−	0.391034i
$87$		0			0
$88$	−56626.2	−	98079.4i	−0.0830939	−	0.143923i
$89$			413126.i			0.586020i	0.956109	+	0.293010i	$0.0946569\pi$
$89$			413126.i			0.586020i	−0.956109	+	0.293010i	$0.905343\pi$
$90$		0			0
$91$	−661817.			−0.878241
$92$	594452.	−	343207.i	0.763402	−	0.440751i
$93$		0			0
$94$	367045.	−	635741.i	0.441912	−	0.765415i
$95$	1.16885e6	+	674835.i	1.36329	+	0.787094i
$96$		0			0
$97$	−489221.	−	847356.i	−0.536031	−	0.928434i	−0.999113	−	0.0421177i	$-0.986590\pi$
$97$	−489221.	−	847356.i	−0.536031	−	0.928434i	0.463081	−	0.886316i	$-0.346744\pi$
$98$			63088.0i			0.0670299i
$99$		0			0
$100$	−108008.			−0.108008
$101$	−975354.	+	563121.i	−0.946669	+	0.546560i	−0.892045	−	0.451947i	$-0.850729\pi$
$101$	−975354.	+	563121.i	−0.946669	+	0.546560i	−0.0546243	+	0.998507i	$0.517396\pi$
$102$		0			0
$103$	−528792.	+	915894.i	−0.483919	+	0.838173i	−0.999829	−	0.0184698i	$-0.994121\pi$
$103$	−528792.	+	915894.i	−0.483919	+	0.838173i	0.515910	+	0.856643i	$0.327454\pi$
$104$	317926.	+	183555.i	0.282635	+	0.163179i
$105$		0			0
$106$	468385.	+	811267.i	0.393265	+	0.681156i
$107$		−	607244.i		−	0.495692i	−0.968799	−	0.247846i	$-0.920277\pi$
$107$		−	607244.i		−	0.495692i	0.968799	−	0.247846i	$-0.0797227\pi$
$108$		0			0
$109$	961305.			0.742303			0.371152	−	0.928572i	$-0.378963\pi$
$109$	961305.			0.742303			0.371152	+	0.928572i	$0.378963\pi$
$110$	339228.	−	195853.i	0.254867	−	0.147147i
$111$		0			0
$112$	−167085.	+	289400.i	−0.118928	+	0.205989i
$113$	−1.15941e6	−	669388.i	−0.803532	−	0.463919i	0.0411727	−	0.999152i	$-0.486891\pi$
$113$	−1.15941e6	−	669388.i	−0.803532	−	0.463919i	−0.844705	+	0.535233i	$0.820224\pi$
$114$		0			0
$115$	1.18705e6	+	2.05603e6i	0.780506	+	1.35188i
$116$		−	792044.i		−	0.507429i
$117$		0			0
$118$	301228.			0.183337
$119$	−1.16623e6	+	673325.i	−0.692061	+	0.399561i
$120$		0			0
$121$	−690070.	+	1.19524e6i	−0.389526	+	0.674679i
$122$	−1.30794e6	−	755138.i	−0.720290	−	0.415860i
$123$		0			0
$124$	−648509.	−	1.12325e6i	−0.340135	−	0.589130i
$125$		−	2.10292e6i		−	1.07670i
$126$		0			0
$127$	−1.62823e6			−0.794885			−0.397443	−	0.917627i	$-0.630102\pi$
$127$	−1.62823e6			−0.794885			−0.397443	+	0.917627i	$0.630102\pi$
$128$	160530.	−	92681.9i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−634861.	+	1.09961e6i	−0.288967	+	0.500506i
$131$	1.19601e6	+	690515.i	0.532010	+	0.307156i	0.741835	−	0.670583i	$-0.233956\pi$
$131$	1.19601e6	+	690515.i	0.532010	+	0.307156i	−0.209824	+	0.977739i	$0.567289\pi$
$132$		0			0
$133$	−1.98977e6	−	3.44637e6i	−0.845760	−	1.46490i
$134$			2.30393e6i			0.957534i
$135$		0			0
$136$	746985.			0.296958
$137$	−3.07236e6	+	1.77383e6i	−1.19484	+	0.689842i	−0.959401	−	0.282046i	$-0.908987\pi$
$137$	−3.07236e6	+	1.77383e6i	−1.19484	+	0.689842i	−0.235441	+	0.971889i	$0.575653\pi$
$138$		0			0
$139$	−1.61016e6	+	2.78888e6i	−0.599548	+	1.03845i	0.393339	+	0.919393i	$0.371320\pi$
$139$	−1.61016e6	+	2.78888e6i	−0.599548	+	1.03845i	−0.992888	+	0.119055i	$0.962014\pi$
$140$	−1.00095e6	−	577898.i	−0.364777	−	0.210604i
$141$		0			0
$142$	−527678.	−	913966.i	−0.184291	−	0.319202i
$143$			1.26880e6i			0.433895i
$144$		0			0
$145$	2.73945e6			0.898585
$146$	1.18605e6	−	684769.i	0.381106	−	0.220032i
$147$		0			0
$148$	−481500.	+	833982.i	−0.148529	+	0.257259i
$149$	791423.	+	456928.i	0.239249	+	0.138130i	0.614832	−	0.788658i	$-0.289224\pi$
$149$	791423.	+	456928.i	0.239249	+	0.138130i	−0.375583	+	0.926789i	$0.622557\pi$
$150$		0			0
$151$	−799451.	−	1.38469e6i	−0.232199	−	0.402181i	0.726256	−	0.687425i	$-0.241259\pi$
$151$	−799451.	−	1.38469e6i	−0.232199	−	0.402181i	−0.958455	+	0.285244i	$0.907925\pi$
$152$			2.20744e6i			0.628577i
$153$		0			0
$154$	−1.15495e6			−0.316230
$155$	3.88499e6	−	2.24300e6i	1.04327	−	0.602329i
$156$		0			0
$157$	2.83537e6	−	4.91100e6i	0.732673	−	1.26903i	−0.223063	−	0.974804i	$-0.571606\pi$
$157$	2.83537e6	−	4.91100e6i	0.732673	−	1.26903i	0.955737	−	0.294224i	$-0.0950611\pi$
$158$	−619097.	−	357436.i	−0.156959	−	0.0906206i
$159$		0			0
$160$	320559.	+	555225.i	0.0782615	+	0.135553i
$161$		−	7.00010e6i		−	1.67736i
$162$		0			0
$163$	5.58510e6			1.28964			0.644820	−	0.764335i	$-0.276932\pi$
$163$	5.58510e6			1.28964			0.644820	+	0.764335i	$0.276932\pi$
$164$	−1.64143e6	+	947678.i	−0.372126	+	0.214847i
$165$		0			0
$166$	−195081.	+	337891.i	−0.0426473	+	0.0738673i
$167$	5.13451e6	+	2.96441e6i	1.10243	+	0.636486i	0.936857	−	0.349712i	$-0.113721\pi$
$167$	5.13451e6	+	2.96441e6i	1.10243	+	0.636486i	0.165569	+	0.986198i	$0.447054\pi$
$168$		0			0
$169$	356991.	+	618327.i	0.0739601	+	0.128103i
$170$			2.58360e6i			0.525870i
$171$		0			0
$172$	2.81394e6			0.553006
$173$	1.94362e6	−	1.12215e6i	0.375382	−	0.216727i	−0.300425	−	0.953805i	$-0.597129\pi$
$173$	1.94362e6	−	1.12215e6i	0.375382	−	0.216727i	0.675807	+	0.737079i	$0.263795\pi$
$174$		0			0
$175$	−550738.	+	953906.i	−0.102762	+	0.177988i
$176$	554821.	+	320326.i	0.101769	+	0.0587563i
$177$		0			0
$178$	−1.16850e6	−	2.02389e6i	−0.207189	−	0.358862i
$179$			777450.i			0.135554i	0.997700	+	0.0677772i	$0.0215907\pi$
$179$			777450.i			0.135554i	−0.997700	+	0.0677772i	$0.978409\pi$
$180$		0			0
$181$	4.10696e6			0.692604			0.346302	−	0.938123i	$-0.387437\pi$
$181$	4.10696e6			0.692604			0.346302	+	0.938123i	$0.387437\pi$
$182$	3.24223e6	−	1.87190e6i	0.537811	−	0.310505i
$183$		0			0
$184$	−1.94147e6	+	3.36273e6i	−0.311658	+	0.539807i
$185$	−2.88450e6	−	1.66536e6i	−0.455570	−	0.263023i
$186$		0			0
$187$	1.29086e6	+	2.23584e6i	0.197403	+	0.341912i
$188$			4.15264e6i			0.624958i
$189$		0			0
$190$	−7.63489e6			−1.11312
$191$	3.69615e6	−	2.13397e6i	0.530456	−	0.306259i	−0.210746	−	0.977541i	$-0.567589\pi$
$191$	3.69615e6	−	2.13397e6i	0.530456	−	0.306259i	0.741202	+	0.671282i	$0.234256\pi$
$192$		0			0
$193$	4.05006e6	−	7.01491e6i	0.563365	−	0.975777i	−0.433835	−	0.900992i	$-0.642840\pi$
$193$	4.05006e6	−	7.01491e6i	0.563365	−	0.975777i	0.997200	−	0.0747842i	$-0.0238268\pi$
$194$	4.79337e6	+	2.76745e6i	0.656502	+	0.379031i
$195$		0			0
$196$	−178440.	−	309067.i	−0.0236986	−	0.0410473i
$197$			4.08228e6i			0.533955i	0.963703	+	0.266977i	$0.0860249\pi$
$197$			4.08228e6i			0.533955i	−0.963703	+	0.266977i	$0.913975\pi$
$198$		0			0
$199$	1.02814e6			0.130464			0.0652322	−	0.997870i	$-0.479221\pi$
$199$	1.02814e6			0.130464			0.0652322	+	0.997870i	$0.479221\pi$
$200$	529131.	−	305494.i	0.0661413	−	0.0381867i
$201$		0			0
$202$	3.18549e6	−	5.51743e6i	0.386476	−	0.669396i
$203$	−6.99516e6	−	4.03866e6i	−0.836199	−	0.482780i
$204$		0			0
$205$	−3.27774e6	−	5.67721e6i	−0.380463	−	0.658982i
$206$		−	5.98260e6i		−	0.684365i
$207$		0			0
$208$	−2.07668e6			−0.230770
$209$	−6.60720e6	+	3.81467e6i	−0.723733	+	0.417847i
$210$		0			0
$211$	−7.72519e6	+	1.33804e7i	−0.822359	+	1.42437i	0.0815616	+	0.996668i	$0.474009\pi$
$211$	−7.72519e6	+	1.33804e7i	−0.822359	+	1.42437i	−0.903921	+	0.427700i	$0.859324\pi$
$212$	−4.58922e6	−	2.64959e6i	−0.481650	−	0.278081i
$213$		0			0
$214$	1.71755e6	+	2.97488e6i	0.175254	+	0.303548i
$215$			9.73259e6i			0.979294i
$216$		0			0
$217$	−1.32271e7			−1.29445
$218$	−4.70941e6	+	2.71898e6i	−0.454566	+	0.262444i
$219$		0			0
$220$	−1.10791e6	+	1.91896e6i	−0.104049	+	0.180218i
$221$	−7.24749e6	−	4.18434e6i	−0.671445	−	0.387659i
$222$		0			0
$223$	1.40565e6	+	2.43465e6i	0.126754	+	0.219544i	0.922417	−	0.386195i	$-0.126211\pi$
$223$	1.40565e6	+	2.43465e6i	0.126754	+	0.219544i	−0.795663	+	0.605739i	$0.792877\pi$
$224$		−	1.89035e6i		−	0.168189i
$225$		0			0
$226$	7.57326e6			0.656081
$227$	−6.45811e6	+	3.72859e6i	−0.552113	+	0.318762i	−0.749974	−	0.661468i	$-0.769934\pi$
$227$	−6.45811e6	+	3.72859e6i	−0.552113	+	0.318762i	0.197861	+	0.980230i	$0.436601\pi$
$228$		0			0
$229$	−6.31232e6	+	1.09333e7i	−0.525633	+	0.910422i	0.473922	+	0.880567i	$0.342838\pi$
$229$	−6.31232e6	+	1.09333e7i	−0.525633	+	0.910422i	−0.999554	+	0.0298554i	$0.990495\pi$
$230$	−1.16307e7	−	6.71498e6i	−0.955921	−	0.551901i
$231$		0			0
$232$	2.24024e6	+	3.88021e6i	0.179403	+	0.310736i
$233$		−	1.64283e7i		−	1.29875i	−0.760469	−	0.649374i	$-0.775031\pi$
$233$		−	1.64283e7i		−	1.29875i	0.760469	−	0.649374i	$-0.224969\pi$
$234$		0			0
$235$	−1.43628e7			−1.10671
$236$	−1.47571e6	+	852002.i	−0.112270	+	0.0648194i
$237$		0			0
$238$	3.80890e6	−	6.59721e6i	0.282533	−	0.489361i
$239$	8.45060e6	+	4.87895e6i	0.619004	+	0.357382i	0.776481	−	0.630140i	$-0.217003\pi$
$239$	8.45060e6	+	4.87895e6i	0.619004	+	0.357382i	−0.157477	+	0.987523i	$0.550336\pi$
$240$		0			0
$241$	7.37017e6	+	1.27655e7i	0.526534	+	0.911984i	0.999522	+	0.0309150i	$0.00984213\pi$
$241$	7.37017e6	+	1.27655e7i	0.526534	+	0.911984i	−0.472988	+	0.881069i	$0.656825\pi$
$242$		−	7.80725e6i		−	0.550873i
$243$		0			0
$244$	8.54341e6			0.588115
$245$	1.06897e6	−	617171.i	0.0726888	−	0.0419669i
$246$		0			0
$247$	1.23653e7	−	2.14173e7i	0.820566	−	1.42126i
$248$	6.35406e6	+	3.66852e6i	0.416578	+	0.240511i
$249$		0			0
$250$	5.94796e6	+	1.03022e7i	0.380669	+	0.659339i
$251$			1.31485e7i			0.831486i	0.909482	+	0.415743i	$0.136478\pi$
$251$			1.31485e7i			0.831486i	−0.909482	+	0.415743i	$0.863522\pi$
$252$		0			0
$253$	−1.34202e7			−0.828700
$254$	7.97666e6	−	4.60533e6i	0.486766	−	0.281034i
$255$		0			0
$256$	−524288.	+	908093.i	−0.0312500	+	0.0541266i
$257$	1.86427e7	+	1.07634e7i	1.09827	+	0.634087i	0.935766	−	0.352621i	$-0.114709\pi$
$257$	1.86427e7	+	1.07634e7i	1.09827	+	0.634087i	0.162505	+	0.986708i	$0.448043\pi$
$258$		0			0
$259$	4.91036e6	+	8.50500e6i	0.282627	+	0.489525i
$260$		−	7.18263e6i		−	0.408661i
$261$		0			0
$262$	−7.81229e6			−0.434385
$263$	−7.35362e6	+	4.24561e6i	−0.404235	+	0.233385i	−0.688310	−	0.725417i	$-0.741647\pi$
$263$	−7.35362e6	+	4.24561e6i	−0.404235	+	0.233385i	0.284075	+	0.958802i	$0.408314\pi$
$264$		0			0
$265$	9.16414e6	−	1.58728e7i	0.492441	−	0.852933i
$266$	1.94956e7	+	1.12558e7i	1.03584	+	0.598042i
$267$		0			0
$268$	−6.51649e6	−	1.12869e7i	−0.338539	−	0.586367i
$269$			883900.i			0.0454094i	0.999742	+	0.0227047i	$0.00722776\pi$
$269$			883900.i			0.0454094i	−0.999742	+	0.0227047i	$0.992772\pi$
$270$		0			0
$271$	−6.17663e6			−0.310345			−0.155172	−	0.987887i	$-0.549593\pi$
$271$	−6.17663e6			−0.310345			−0.155172	+	0.987887i	$0.549593\pi$
$272$	−3.65946e6	+	2.11279e6i	−0.181849	+	0.104991i
$273$		0			0
$274$	1.00343e7	−	1.73799e7i	0.487792	−	0.844881i
$275$	1.82878e6	+	1.05584e6i	0.0879351	+	0.0507693i
$276$		0			0
$277$	2.90287e6	+	5.02791e6i	0.136580	+	0.236564i	0.926200	−	0.377033i	$-0.123056\pi$
$277$	2.90287e6	+	5.02791e6i	0.136580	+	0.236564i	−0.789620	+	0.613596i	$0.789722\pi$
$278$		−	1.82169e7i		−	0.847889i
$279$		0			0
$280$	6.53817e6			0.297839
$281$	1.17606e7	−	6.78998e6i	0.530042	−	0.306020i	−0.210992	−	0.977488i	$-0.567669\pi$
$281$	1.17606e7	−	6.78998e6i	0.530042	−	0.306020i	0.741033	+	0.671468i	$0.234336\pi$
$282$		0			0
$283$	−2.53102e6	+	4.38385e6i	−0.111670	+	0.193418i	−0.916444	−	0.400164i	$-0.868953\pi$
$283$	−2.53102e6	+	4.38385e6i	−0.111670	+	0.193418i	0.804774	+	0.593582i	$0.202287\pi$
$284$	5.17017e6	+	2.98500e6i	0.225710	+	0.130313i
$285$		0			0
$286$	−3.58870e6	−	6.21582e6i	−0.153405	−	0.265705i
$287$			1.93290e7i			0.817642i
$288$		0			0
$289$	7.10918e6			0.294528
$290$	−1.34205e7	+	7.74833e6i	−0.550268	+	0.317698i
$291$		0			0
$292$	−3.87364e6	+	6.70933e6i	−0.155586	+	0.269483i
$293$	−3.26203e7	−	1.88334e7i	−1.29684	−	0.748730i	−0.316981	−	0.948432i	$-0.602669\pi$
$293$	−3.26203e7	−	1.88334e7i	−1.29684	−	0.748730i	−0.979857	+	0.199702i	$0.936003\pi$
$294$		0			0
$295$	−2.94682e6	−	5.10405e6i	−0.114786	−	0.198815i
$296$		−	5.44755e6i		−	0.210051i
$297$		0			0
$298$	−5.16956e6			−0.195346
$299$	3.76736e7	−	2.17509e7i	1.40937	−	0.813698i
$300$		0			0
$301$	1.43484e7	−	2.48521e7i	0.526143	−	0.911306i
$302$	7.83298e6	+	4.52238e6i	0.284385	+	0.164190i
$303$		0			0
$304$	−6.24359e6	−	1.08142e7i	−0.222235	−	0.384923i
$305$			2.95491e7i			1.04147i
$306$		0			0
$307$	4.60441e7			1.59132			0.795662	−	0.605740i	$-0.207123\pi$
$307$	4.60441e7			1.59132			0.795662	+	0.605740i	$0.207123\pi$
$308$	5.65810e6	−	3.26671e6i	0.193650	−	0.111804i
$309$		0			0
$310$	−1.26883e7	+	2.19768e7i	−0.425911	+	0.737700i
$311$	−2.47086e7	−	1.42655e7i	−0.821423	−	0.474249i	0.0294839	−	0.999565i	$-0.490614\pi$
$311$	−2.47086e7	−	1.42655e7i	−0.821423	−	0.474249i	−0.850907	+	0.525316i	$0.823947\pi$
$312$		0			0
$313$	−1.10257e7	−	1.90970e7i	−0.359560	−	0.622776i	0.628327	−	0.777949i	$-0.283740\pi$
$313$	−1.10257e7	−	1.90970e7i	−0.359560	−	0.622776i	−0.987887	+	0.155173i	$0.950407\pi$
$314$			3.20785e7i			1.03616i
$315$		0			0
$316$	4.04392e6			0.128157
$317$	−1.49989e7	+	8.65961e6i	−0.470848	+	0.271844i	−0.716595	−	0.697490i	$-0.754300\pi$
$317$	−1.49989e7	+	8.65961e6i	−0.470848	+	0.271844i	0.245746	+	0.969334i	$0.420967\pi$
$318$		0			0
$319$	−7.74269e6	+	1.34107e7i	−0.238517	+	0.413124i
$320$	−3.14083e6	−	1.81336e6i	−0.0958504	−	0.0553393i
$321$		0			0
$322$	1.97993e7	+	3.42933e7i	0.593037	+	1.02717i
$323$		−	5.03212e7i		−	1.49329i
$324$		0			0
$325$	−6.84506e6			−0.199401
$326$	−2.73613e7	+	1.57971e7i	−0.789740	+	0.455956i
$327$		0			0
$328$	5.36088e6	−	9.28531e6i	0.151920	−	0.263133i
$329$	3.66752e7	+	2.11745e7i	1.02988	+	0.594600i
$330$		0			0
$331$	−7.07998e6	−	1.22629e7i	−0.195231	−	0.338149i	0.751745	−	0.659453i	$-0.229212\pi$
$331$	−7.07998e6	−	1.22629e7i	−0.195231	−	0.338149i	−0.946976	+	0.321304i	$0.895879\pi$
$332$		−	2.20709e6i		−	0.0603124i
$333$		0			0
$334$	−3.35385e7			−0.900127
$335$	3.90380e7	−	2.25386e7i	1.03837	−	0.599505i
$336$		0			0
$337$	−2.40697e7	+	4.16899e7i	−0.628898	+	1.08928i	0.358875	+	0.933386i	$0.383160\pi$
$337$	−2.40697e7	+	4.16899e7i	−0.628898	+	1.08928i	−0.987773	+	0.155898i	$0.950173\pi$
$338$	−3.49779e6	−	2.01945e6i	−0.0905823	−	0.0522977i
$339$		0			0
$340$	−7.30752e6	−	1.26570e7i	−0.185923	−	0.322028i
$341$			2.53582e7i			0.639521i
$342$		0			0
$343$	−4.20328e7			−1.04161
$344$	−1.37854e7	+	7.95903e6i	−0.338646	+	0.195517i
$345$		0			0
$346$	−6.34784e6	+	1.09948e7i	−0.153249	+	0.265435i
$347$	−4.75029e7	−	2.74258e7i	−1.13692	−	0.656404i	−0.191258	−	0.981540i	$-0.561257\pi$
$347$	−4.75029e7	−	2.74258e7i	−1.13692	−	0.656404i	−0.945667	+	0.325136i	$0.894590\pi$
$348$		0			0
$349$	8.59925e6	+	1.48943e7i	0.202295	+	0.350385i	0.949267	−	0.314470i	$-0.101827\pi$
$349$	8.59925e6	+	1.48943e7i	0.202295	+	0.350385i	−0.746973	+	0.664855i	$0.768493\pi$
$350$		−	6.23089e6i		−	0.145327i
$351$		0			0
$352$	−3.62408e6			−0.0830939
$353$	6.25279e6	−	3.61005e6i	0.142151	−	0.0820709i	−0.427238	−	0.904139i	$-0.640513\pi$
$353$	6.25279e6	−	3.61005e6i	0.142151	−	0.0820709i	0.569389	+	0.822068i	$0.307180\pi$
$354$		0			0
$355$	−1.03242e7	+	1.78821e7i	−0.230767	+	0.399699i
$356$	1.14489e7	+	6.61001e6i	0.253754	+	0.146505i
$357$		0			0
$358$	−2.19896e6	−	3.80871e6i	−0.0479257	−	0.0830097i
$359$			1.62223e6i			0.0350614i	0.999846	+	0.0175307i	$0.00558048\pi$
$359$			1.62223e6i			0.0350614i	−0.999846	+	0.0175307i	$0.994420\pi$
$360$		0			0
$361$	1.01660e8			2.16087
$362$	−2.01199e7	+	1.16162e7i	−0.424131	+	0.244872i
$363$		0			0
$364$	−1.05891e7	+	1.83408e7i	−0.219560	+	0.380289i
$365$	−2.32056e7	−	1.33978e7i	−0.477215	−	0.275520i
$366$		0			0
$367$	−1.08645e7	−	1.88180e7i	−0.219793	−	0.380692i	0.734952	−	0.678119i	$-0.237205\pi$
$367$	−1.08645e7	−	1.88180e7i	−0.219793	−	0.380692i	−0.954745	+	0.297427i	$0.903871\pi$
$368$		−	2.19653e7i		−	0.440751i
$369$		0			0
$370$	1.88415e7			0.371971
$371$	−4.68012e7	+	2.70207e7i	−0.916505	+	0.529145i
$372$		0			0
$373$	−3.03671e7	+	5.25974e7i	−0.585163	+	1.01353i	0.409692	+	0.912224i	$0.365636\pi$
$373$	−3.03671e7	+	5.25974e7i	−0.585163	+	1.01353i	−0.994855	+	0.101309i	$0.967697\pi$
$374$	−1.26478e7	−	7.30221e6i	−0.241769	−	0.139585i
$375$		0			0
$376$	−1.17455e7	−	2.03437e7i	−0.220956	−	0.382707i
$377$		−	5.01961e7i		−	0.936797i
$378$		0			0
$379$	2.01121e7			0.369437			0.184719	−	0.982791i	$-0.440863\pi$
$379$	2.01121e7			0.369437			0.184719	+	0.982791i	$0.440863\pi$
$380$	3.74032e7	−	2.15947e7i	0.681644	−	0.393547i
$381$		0			0
$382$	−1.20716e7	+	2.09086e7i	−0.216558	+	0.375089i
$383$	−4.09187e7	−	2.36244e7i	−0.728326	−	0.420499i	0.0894836	−	0.995988i	$-0.471478\pi$
$383$	−4.09187e7	−	2.36244e7i	−0.728326	−	0.420499i	−0.817809	+	0.575489i	$0.804812\pi$
$384$		0			0
$385$	1.12986e7	+	1.95697e7i	0.197989	+	0.342927i
$386$			4.58212e7i			0.796718i
$387$		0			0
$388$	−3.13102e7			−0.536031
$389$	−1.67687e7	+	9.68140e6i	−0.284872	+	0.164471i	−0.635627	−	0.771996i	$-0.719258\pi$
$389$	−1.67687e7	+	9.68140e6i	−0.284872	+	0.164471i	0.350755	+	0.936467i	$0.385925\pi$
$390$		0			0
$391$	4.42581e7	−	7.66574e7i	0.740394	−	1.28240i
$392$	1.74835e6	+	1.00941e6i	0.0290248	+	0.0167575i
$393$		0			0
$394$	−1.15464e7	−	1.99990e7i	−0.188782	−	0.326979i
$395$			1.39867e7i			0.226947i
$396$		0			0
$397$	−3.66656e7			−0.585986			−0.292993	−	0.956115i	$-0.594651\pi$
$397$	−3.66656e7			−0.585986			−0.292993	+	0.956115i	$0.594651\pi$
$398$	−5.03682e6	+	2.90801e6i	−0.0798928	+	0.0461261i
$399$		0			0
$400$	−1.72813e6	+	2.99321e6i	−0.0270021	+	0.0467690i
$401$	1.04853e8	+	6.05366e7i	1.62609	+	0.938826i	0.985243	+	0.171162i	$0.0547520\pi$
$401$	1.04853e8	+	6.05366e7i	1.62609	+	0.938826i	0.640852	+	0.767665i	$0.278581\pi$
$402$		0			0
$403$	−4.10994e7	−	7.11863e7i	−0.627944	−	1.08763i
$404$			3.60397e7i			0.546560i
$405$		0			0
$406$	4.56922e7			0.682754
$407$	1.63053e7	−	9.41387e6i	0.241850	−	0.139632i
$408$		0			0
$409$	−1.99142e7	+	3.44925e7i	−0.291067	+	0.504144i	−0.974062	−	0.226279i	$-0.927344\pi$
$409$	−1.99142e7	+	3.44925e7i	−0.291067	+	0.504144i	0.682995	+	0.730423i	$0.260677\pi$
$410$	3.21152e7	+	1.85417e7i	0.465970	+	0.269028i
$411$		0			0
$412$	1.69213e7	+	2.93086e7i	0.241960	+	0.419086i
$413$			1.73775e7i			0.246683i
$414$		0			0
$415$	7.63369e6			0.106805
$416$	1.01736e7	−	5.87375e6i	0.141317	−	0.0815897i
$417$		0			0
$418$	2.15790e7	−	3.73759e7i	0.295463	−	0.511756i
$419$	−4.69066e7	−	2.70815e7i	−0.637664	−	0.368155i	0.146050	−	0.989277i	$-0.453344\pi$
$419$	−4.69066e7	−	2.70815e7i	−0.637664	−	0.368155i	−0.783714	+	0.621122i	$0.786677\pi$
$420$		0			0
$421$	−2.70636e7	−	4.68755e7i	−0.362693	−	0.628203i	0.625710	−	0.780056i	$-0.284809\pi$
$421$	−2.70636e7	−	4.68755e7i	−0.362693	−	0.628203i	−0.988403	+	0.151853i	$0.951476\pi$
$422$		−	8.74005e7i		−	1.16299i
$423$		0			0
$424$	2.99767e7			0.393265
$425$	−1.20621e7	+	6.96408e6i	−0.157130	+	0.0907188i
$426$		0			0
$427$	4.35631e7	−	7.54536e7i	0.559546	−	0.969161i
$428$	−1.68284e7	−	9.71590e6i	−0.214641	−	0.123923i
$429$		0			0
$430$	−2.75279e7	−	4.76798e7i	−0.346233	−	0.599693i
$431$			8.08186e7i			1.00944i	0.863284	+	0.504719i	$0.168404\pi$
$431$			8.08186e7i			1.00944i	−0.863284	+	0.504719i	$0.831596\pi$
$432$		0			0
$433$	−1.33718e7			−0.164713			−0.0823563	−	0.996603i	$-0.526245\pi$
$433$	−1.33718e7			−0.164713			−0.0823563	+	0.996603i	$0.526245\pi$
$434$	6.47991e7	−	3.74118e7i	0.792684	−	0.457656i
$435$		0			0
$436$	1.53809e7	−	2.66405e7i	0.185576	−	0.321427i
$437$	2.26533e8	+	1.30789e8i	2.71448	+	1.56721i
$438$		0			0
$439$	3.81803e7	+	6.61302e7i	0.451280	+	0.781640i	0.998466	−	0.0553714i	$-0.0176343\pi$
$439$	3.81803e7	+	6.61302e7i	0.451280	+	0.781640i	−0.547186	+	0.837011i	$0.684301\pi$
$440$		−	1.25346e7i		−	0.147147i
$441$		0			0
$442$	4.73404e7			0.548233
$443$	9.63056e7	−	5.56020e7i	1.10775	−	0.639557i	0.169501	−	0.985530i	$-0.445784\pi$
$443$	9.63056e7	−	5.56020e7i	1.10775	−	0.639557i	0.938245	+	0.345973i	$0.112451\pi$
$444$		0			0
$445$	−2.28621e7	+	3.95983e7i	−0.259439	+	0.449362i
$446$	−1.37725e7	−	7.95154e6i	−0.155241	−	0.0896286i
$447$		0			0
$448$	5.34672e6	+	9.26079e6i	0.0594639	+	0.102995i
$449$		−	1.36515e8i		−	1.50814i	−0.656793	−	0.754071i	$-0.728087\pi$
$449$		−	1.36515e8i		−	1.50814i	0.656793	−	0.754071i	$-0.271913\pi$
$450$		0			0
$451$	3.70564e7			0.403956
$452$	−3.71012e7	+	2.14204e7i	−0.401766	+	0.231960i
$453$		0			0
$454$	2.10921e7	−	3.65326e7i	0.225399	−	0.390403i
$455$	−6.34354e7	−	3.66245e7i	−0.673438	−	0.388810i
$456$		0			0
$457$	5.42046e7	+	9.38851e7i	0.567920	+	0.983667i	0.996771	+	0.0802917i	$0.0255852\pi$
$457$	5.42046e7	+	9.38851e7i	0.567920	+	0.983667i	−0.428851	+	0.903375i	$0.641081\pi$
$458$		−	7.14157e7i		−	0.743357i
$459$		0			0
$460$	7.59713e7			0.780506
$461$	−1.42152e8	+	8.20712e7i	−1.45094	+	0.837699i	−0.998535	−	0.0541143i	$-0.982766\pi$
$461$	−1.42152e8	+	8.20712e7i	−1.45094	+	0.837699i	−0.452403	+	0.891814i	$0.649433\pi$
$462$		0			0
$463$	−1.86985e7	+	3.23867e7i	−0.188392	+	0.326305i	−0.944714	−	0.327895i	$-0.893661\pi$
$463$	−1.86985e7	+	3.23867e7i	−0.188392	+	0.326305i	0.756322	+	0.654199i	$0.226994\pi$
$464$	−2.19498e7	−	1.26727e7i	−0.219723	−	0.126857i
$465$		0			0
$466$	4.64663e7	+	8.04820e7i	0.459177	+	0.795318i
$467$			1.45951e8i			1.43304i	0.697569	+	0.716518i	$0.254265\pi$
$467$			1.45951e8i			1.43304i	−0.697569	+	0.716518i	$0.745735\pi$
$468$		0			0
$469$	−1.32911e8			−1.28838
$470$	7.03629e7	−	4.06240e7i	0.677720	−	0.391282i
$471$		0			0
$472$	4.81965e6	−	8.34788e6i	0.0458342	−	0.0793872i
$473$	−4.76451e7	−	2.75079e7i	−0.450230	−	0.259941i
$474$		0			0
$475$	−2.05798e7	−	3.56453e7i	−0.192026	−	0.332599i
$476$			4.30928e7i			0.399561i
$477$		0			0
$478$	−5.51991e7			−0.505415
$479$	−1.15157e8	+	6.64861e7i	−1.04782	+	0.604957i	−0.922037	−	0.387102i	$-0.873476\pi$
$479$	−1.15157e8	+	6.64861e7i	−1.04782	+	0.604957i	−0.125779	+	0.992058i	$0.540143\pi$
$480$		0			0
$481$	−3.05152e7	+	5.28539e7i	−0.274208	+	0.474943i
$482$	−7.22127e7	−	4.16920e7i	−0.644870	−	0.372316i
$483$		0			0
$484$	2.20822e7	+	3.82475e7i	0.194763	+	0.337340i
$485$		−	1.08293e8i		−	0.949235i
$486$		0			0
$487$	−4.62190e7			−0.400160			−0.200080	−	0.979780i	$-0.564120\pi$
$487$	−4.62190e7			−0.400160			−0.200080	+	0.979780i	$0.564120\pi$
$488$	−4.18540e7	+	2.41644e7i	−0.360145	+	0.207930i
$489$		0			0
$490$	−3.49124e6	+	6.04701e6i	−0.0296751	+	0.0513988i
$491$	7.93099e7	+	4.57896e7i	0.670012	+	0.386832i	0.796081	−	0.605190i	$-0.206903\pi$
$491$	7.93099e7	+	4.57896e7i	0.670012	+	0.386832i	−0.126069	+	0.992021i	$0.540236\pi$
$492$		0			0
$493$	−5.10689e7	−	8.84539e7i	−0.426202	−	0.738204i
$494$			1.39897e8i			1.16046i
$495$		0			0
$496$	−4.15046e7			−0.340135
$497$	5.27257e7	−	3.04412e7i	0.429490	−	0.247966i
$498$		0			0
$499$	2.85950e7	−	4.95279e7i	0.230138	−	0.398610i	−0.727711	−	0.685884i	$-0.759416\pi$
$499$	2.85950e7	−	4.95279e7i	0.230138	−	0.398610i	0.957848	+	0.287274i	$0.0927490\pi$
$500$	−5.82779e7	−	3.36467e7i	−0.466223	−	0.269174i
$501$		0			0
$502$	−3.71896e7	−	6.44142e7i	−0.293975	−	0.509179i
$503$		−	1.85206e8i		−	1.45530i	−0.685950	−	0.727649i	$-0.740613\pi$
$503$		−	1.85206e8i		−	1.45530i	0.685950	−	0.727649i	$-0.259387\pi$
$504$		0			0
$505$	−1.24651e8			−0.967879
$506$	6.57453e7	−	3.79580e7i	0.507473	−	0.292990i
$507$		0			0
$508$	−2.60517e7	+	4.51228e7i	−0.198721	+	0.344195i
$509$	−1.08544e8	−	6.26677e7i	−0.823097	−	0.475215i	0.0283864	−	0.999597i	$-0.490963\pi$
$509$	−1.08544e8	−	6.26677e7i	−0.823097	−	0.475215i	−0.851483	+	0.524382i	$0.824296\pi$
$510$		0			0
$511$	3.95036e7	+	6.84222e7i	0.296056	+	0.512784i
$512$		−	5.93164e6i		−	0.0441942i
$513$		0			0
$514$	−1.21774e8			−0.896734
$515$	−1.01370e8	+	5.85259e7i	−0.742142	+	0.428476i
$516$		0			0
$517$	4.05945e7	−	7.03117e7i	0.293762	−	0.508811i
$518$	−4.81115e7	−	2.77772e7i	−0.346146	−	0.199848i
$519$		0			0
$520$	2.03155e7	+	3.51876e7i	0.144484	+	0.250253i
$521$			1.64203e8i			1.16109i	0.814227	+	0.580546i	$0.197161\pi$
$521$			1.64203e8i			1.16109i	−0.814227	+	0.580546i	$0.802839\pi$
$522$		0			0
$523$	−1.39702e8			−0.976559			−0.488280	−	0.872687i	$-0.662375\pi$
$523$	−1.39702e8			−0.976559			−0.488280	+	0.872687i	$0.662375\pi$
$524$	3.82722e7	−	2.20965e7i	0.266005	−	0.153578i
$525$		0			0
$526$	2.40168e7	−	4.15983e7i	0.165028	−	0.285837i
$527$	−1.44848e8	−	8.36282e7i	−0.989649	−	0.571374i
$528$		0			0
$529$	1.56043e8	+	2.70274e8i	1.05409	+	1.82574i
$530$			1.03680e8i			0.696417i
$531$		0			0
$532$	−1.27345e8			−0.845760
$533$	−1.04026e8	+	6.00594e7i	−0.687005	+	0.396643i
$534$		0			0
$535$	3.36044e7	−	5.82046e7i	0.219450	−	0.380098i
$536$	6.38483e7	+	3.68628e7i	0.414624	+	0.239383i
$537$		0			0
$538$	−2.50005e6	−	4.33021e6i	−0.0160547	−	0.0278075i
$539$			6.97741e6i			0.0445582i
$540$		0			0
$541$	1.45535e8			0.919130			0.459565	−	0.888144i	$-0.348005\pi$
$541$	1.45535e8			0.919130			0.459565	+	0.888144i	$0.348005\pi$
$542$	3.02592e7	−	1.74702e7i	0.190046	−	0.109723i
$543$		0			0
$544$	1.19518e7	−	2.07010e7i	0.0742395	−	0.128587i
$545$	9.21415e7	+	5.31979e7i	0.569201	+	0.328628i
$546$		0			0
$547$	4.28578e6	+	7.42318e6i	0.0261859	+	0.0453553i	0.878821	−	0.477151i	$-0.158330\pi$
$547$	4.28578e6	+	7.42318e6i	0.0261859	+	0.0453553i	−0.852635	+	0.522506i	$0.824997\pi$
$548$			1.13525e8i			0.689842i
$549$		0			0
$550$	−1.19455e7			−0.0717987
$551$	2.61393e8	−	1.50915e8i	1.56257	−	0.902150i
$552$		0			0
$553$	2.06201e7	−	3.57151e7i	0.121931	−	0.211191i
$554$	−2.84422e7	−	1.64211e7i	−0.167276	−	0.0965767i
$555$		0			0
$556$	5.15251e7	+	8.92440e7i	0.299774	+	0.519224i
$557$		−	8.68427e7i		−	0.502536i	−0.967918	−	0.251268i	$-0.919152\pi$
$557$		−	8.68427e7i		−	0.502536i	0.967918	−	0.251268i	$-0.0808476\pi$
$558$		0			0
$559$	1.78335e8			1.02094
$560$	−3.20304e7	+	1.84927e7i	−0.182389	+	0.105302i
$561$		0			0
$562$	−3.84099e7	+	6.65279e7i	−0.216389	+	0.374796i
$563$	5.26034e6	+	3.03706e6i	0.0294774	+	0.0170188i	0.514666	−	0.857391i	$-0.327916\pi$
$563$	5.26034e6	+	3.03706e6i	0.0294774	+	0.0170188i	−0.485189	+	0.874409i	$0.661249\pi$
$564$		0			0
$565$	−7.40869e7	−	1.28322e8i	−0.410767	−	0.711470i
$566$		−	2.86352e7i		−	0.157925i
$567$		0			0
$568$	−3.37714e7			−0.184291
$569$	1.35148e8	−	7.80279e7i	0.733624	−	0.423558i	−0.0861225	−	0.996285i	$-0.527448\pi$
$569$	1.35148e8	−	7.80279e7i	0.733624	−	0.423558i	0.819746	+	0.572727i	$0.194114\pi$
$570$		0			0
$571$	−5.10042e7	+	8.83419e7i	−0.273967	+	0.474524i	−0.969874	−	0.243608i	$-0.921669\pi$
$571$	−5.10042e7	+	8.83419e7i	−0.273967	+	0.474524i	0.695907	+	0.718132i	$0.255002\pi$
$572$	3.51620e7	+	2.03008e7i	0.187882	+	0.108474i
$573$		0			0
$574$	−5.46706e7	−	9.46922e7i	−0.289080	−	0.500701i
$575$		−	7.24009e7i		−	0.380838i
$576$		0			0
$577$	2.90791e8			1.51375			0.756874	−	0.653561i	$-0.226726\pi$
$577$	2.90791e8			1.51375			0.756874	+	0.653561i	$0.226726\pi$
$578$	−3.48277e7	+	2.01078e7i	−0.180361	+	0.104131i
$579$		0			0
$580$	4.38312e7	−	7.59178e7i	0.224646	−	0.389099i
$581$	−1.94926e7	−	1.12540e7i	−0.0993896	−	0.0573826i
$582$		0			0
$583$	5.18025e7	+	8.97246e7i	0.261424	+	0.452799i
$584$		−	4.38252e7i		−	0.220032i
$585$		0			0
$586$	2.13075e8			1.05886
$587$	9.36918e7	−	5.40930e7i	0.463220	−	0.267440i	−0.250177	−	0.968200i	$-0.580489\pi$
$587$	9.36918e7	−	5.40930e7i	0.463220	−	0.267440i	0.713397	+	0.700760i	$0.247156\pi$
$588$		0			0
$589$	2.47133e8	−	4.28046e8i	1.20944	−	2.09481i
$590$	2.88729e7	+	1.66698e7i	0.140583	+	0.0811658i
$591$		0			0
$592$	1.54080e7	+	2.66874e7i	0.0742644	+	0.128630i
$593$		−	2.75079e8i		−	1.31915i	−0.751641	−	0.659573i	$-0.770737\pi$
$593$		−	2.75079e8i		−	1.31915i	0.751641	−	0.659573i	$-0.229263\pi$
$594$		0			0
$595$	−1.49045e8			−0.707566
$596$	2.53255e7	−	1.46217e7i	0.119624	−	0.0690652i
$597$		0			0
$598$	−1.23041e8	+	2.13114e8i	−0.575371	+	0.996572i
$599$	2.94213e8	+	1.69864e8i	1.36893	+	0.790351i	0.990791	−	0.135398i	$-0.0432313\pi$
$599$	2.94213e8	+	1.69864e8i	1.36893	+	0.790351i	0.378138	+	0.925749i	$0.376565\pi$
$600$		0			0
$601$	−8.08282e7	−	1.39999e8i	−0.372340	−	0.644911i	0.617585	−	0.786504i	$-0.288111\pi$
$601$	−8.08282e7	−	1.39999e8i	−0.372340	−	0.644911i	−0.989925	+	0.141593i	$0.954778\pi$
$602$			1.62333e8i			0.744078i
$603$		0			0
$604$	−5.11648e7			−0.232199
$605$	−1.32287e8	+	7.63759e7i	−0.597380	+	0.344898i
$606$		0			0
$607$	−1.13595e8	+	1.96752e8i	−0.507916	+	0.879737i	0.492042	+	0.870572i	$0.336251\pi$
$607$	−1.13595e8	+	1.96752e8i	−0.507916	+	0.879737i	−0.999958	+	0.00916513i	$0.997083\pi$
$608$	6.11744e7	+	3.53191e7i	0.272182	+	0.157144i
$609$		0			0
$610$	−8.35776e7	−	1.44761e8i	−0.368214	−	0.637765i
$611$			2.63175e8i			1.15378i
$612$		0			0
$613$	−1.32276e8			−0.574247			−0.287124	−	0.957894i	$-0.592699\pi$
$613$	−1.32276e8			−0.574247			−0.287124	+	0.957894i	$0.592699\pi$
$614$	−2.25569e8	+	1.30232e8i	−0.974483	+	0.562618i
$615$		0			0
$616$	−1.84793e7	+	3.20071e7i	−0.0790575	+	0.136932i
$617$	3.09010e8	+	1.78407e8i	1.31558	+	0.759551i	0.983014	−	0.183528i	$-0.0587519\pi$
$617$	3.09010e8	+	1.78407e8i	1.31558	+	0.759551i	0.332567	+	0.943080i	$0.392085\pi$
$618$		0			0
$619$	−1.56034e8	−	2.70258e8i	−0.657880	−	1.13948i	−0.981163	−	0.193179i	$-0.938120\pi$
$619$	−1.56034e8	−	2.70258e8i	−0.657880	−	1.13948i	0.323284	−	0.946302i	$-0.395213\pi$
$620$		−	1.43552e8i		−	0.602329i
$621$		0			0
$622$	1.61396e8			0.670689
$623$	1.16756e8	−	6.74093e7i	0.482855	−	0.278776i
$624$		0			0
$625$	9.00049e7	−	1.55893e8i	0.368660	−	0.638538i
$626$	1.08029e8	+	6.23705e7i	0.440369	+	0.254247i
$627$		0			0
$628$	−9.07318e7	−	1.57152e8i	−0.366337	−	0.634514i
$629$			1.24183e8i			0.499012i
$630$		0			0
$631$	1.95005e7			0.0776172			0.0388086	−	0.999247i	$-0.487644\pi$
$631$	1.95005e7			0.0776172			0.0388086	+	0.999247i	$0.487644\pi$
$632$	−1.98111e7	+	1.14379e7i	−0.0784797	+	0.0453103i
$633$		0			0
$634$	4.89862e7	−	8.48465e7i	0.192223	−	0.332940i
$635$	−1.56066e8	−	9.01050e7i	−0.609521	−	0.351907i
$636$		0			0
$637$	−1.13087e7	−	1.95872e7i	−0.0437516	−	0.0757799i
$638$		−	8.75985e7i		−	0.337314i
$639$		0			0
$640$	2.05158e7			0.0782615
$641$	−3.70891e8	+	2.14134e8i	−1.40823	+	0.813040i	−0.995217	−	0.0976870i	$-0.968856\pi$
$641$	−3.70891e8	+	2.14134e8i	−1.40823	+	0.813040i	−0.413009	+	0.910727i	$0.635522\pi$
$642$		0			0
$643$	−1.61002e8	+	2.78864e8i	−0.605619	+	1.04896i	0.386334	+	0.922359i	$0.373741\pi$
$643$	−1.61002e8	+	2.78864e8i	−0.605619	+	1.04896i	−0.991953	+	0.126604i	$0.959592\pi$
$644$	−1.93992e8	−	1.12002e8i	−0.726319	−	0.419340i
$645$		0			0
$646$	1.42330e8	+	2.46522e8i	0.527957	+	0.914448i
$647$		−	8.47366e7i		−	0.312866i	−0.987689	−	0.156433i	$-0.950001\pi$
$647$		−	8.47366e7i		−	0.312866i	0.987689	−	0.156433i	$-0.0499995\pi$
$648$		0			0
$649$	3.33153e7			0.121873
$650$	3.35338e7	−	1.93608e7i	0.122108	−	0.0704989i
$651$		0			0
$652$	8.93617e7	−	1.54779e8i	0.322410	−	0.558430i
$653$	−3.79152e8	−	2.18903e8i	−1.36167	−	0.786163i	−0.371828	−	0.928302i	$-0.621269\pi$
$653$	−3.79152e8	−	2.18903e8i	−1.36167	−	0.786163i	−0.989847	+	0.142139i	$0.954602\pi$
$654$		0			0
$655$	7.64252e7	+	1.32372e8i	0.271965	+	0.471057i
$656$			6.06514e7i			0.214847i
$657$		0			0
$658$	−2.39562e8			−0.840891
$659$	2.36172e8	−	1.36354e8i	0.825225	−	0.476444i	−0.0269900	−	0.999636i	$-0.508592\pi$
$659$	2.36172e8	−	1.36354e8i	0.825225	−	0.476444i	0.852215	+	0.523192i	$0.175259\pi$
$660$		0			0
$661$	−1.47145e8	+	2.54862e8i	−0.509495	+	0.882471i	0.490445	+	0.871472i	$0.336834\pi$
$661$	−1.47145e8	+	2.54862e8i	−0.509495	+	0.882471i	−0.999940	+	0.0109985i	$0.996499\pi$
$662$	6.93694e7	+	4.00504e7i	0.239108	+	0.138049i
$663$		0			0
$664$	6.24261e6	+	1.08125e7i	0.0213237	+	0.0369337i
$665$		−	4.40449e8i		−	1.49772i
$666$		0			0
$667$	5.30928e8			1.78920
$668$	1.64304e8	−	9.48611e7i	0.551213	−	0.318243i
$669$		0			0
$670$	−1.27498e8	+	2.20832e8i	−0.423914	+	0.734240i
$671$	−1.44655e8	−	8.35168e7i	−0.478814	−	0.276443i
$672$		0			0
$673$	−1.48525e7	−	2.57254e7i	−0.0487254	−	0.0843949i	0.840634	−	0.541604i	$-0.182183\pi$
$673$	−1.48525e7	−	2.57254e7i	−0.0487254	−	0.0843949i	−0.889359	+	0.457209i	$0.848849\pi$
$674$		−	2.72317e8i		−	0.889396i
$675$		0			0
$676$	2.28475e7			0.0739601
$677$	−4.67116e8	+	2.69690e8i	−1.50542	+	0.869157i	−0.505444	+	0.862859i	$0.668671\pi$
$677$	−4.67116e8	+	2.69690e8i	−1.50542	+	0.869157i	−0.999980	+	0.00629800i	$0.997995\pi$
$678$		0			0
$679$	−1.59652e8	+	2.76525e8i	−0.509992	+	0.883333i
$680$	7.15988e7	+	4.13376e7i	0.227708	+	0.131468i
$681$		0			0
$682$	−7.17238e7	−	1.24229e8i	−0.226105	−	0.391625i
$683$			5.86183e8i			1.83980i	0.392152	+	0.919901i	$0.371731\pi$
$683$			5.86183e8i			1.83980i	−0.392152	+	0.919901i	$0.628269\pi$
$684$		0			0
$685$	−3.92649e8			−1.22161
$686$	2.05918e8	−	1.18887e8i	0.637855	−	0.368266i
$687$		0			0
$688$	4.50231e7	−	7.79823e7i	0.138251	−	0.239459i
$689$	−2.90843e8	−	1.67919e8i	−0.889204	−	0.513382i
$690$		0			0
$691$	2.34528e8	+	4.06214e8i	0.710822	+	1.23118i	0.964549	+	0.263903i	$0.0850100\pi$
$691$	2.34528e8	+	4.06214e8i	0.710822	+	1.23118i	−0.253728	+	0.967276i	$0.581657\pi$
$692$		−	7.18176e7i		−	0.216727i
$693$		0			0
$694$	3.10288e8			0.928295
$695$	−3.08669e8	+	1.78210e8i	−0.919471	+	0.530857i
$696$		0			0
$697$	−1.22207e8	+	2.11670e8i	−0.360910	+	0.625115i
$698$	−8.42551e7	−	4.86447e7i	−0.247759	−	0.143044i
$699$		0			0
$700$	1.76236e7	+	3.05250e7i	0.0513808	+	0.0889942i
$701$		−	5.94604e7i		−	0.172613i	−0.996269	−	0.0863065i	$-0.972494\pi$
$701$		−	5.94604e7i		−	0.172613i	0.996269	−	0.0863065i	$-0.0275064\pi$
$702$		0			0
$703$	−3.66978e8			−1.05627
$704$	1.77543e7	−	1.02504e7i	0.0508844	−	0.0293781i
$705$		0			0
$706$	−2.04215e7	+	3.53711e7i	−0.0580329	+	0.100516i
$707$	3.18295e8	+	1.83768e8i	0.900682	+	0.520009i
$708$		0			0
$709$	−3.34021e8	−	5.78541e8i	−0.937206	−	1.62329i	−0.770652	−	0.637256i	$-0.780070\pi$
$709$	−3.34021e8	−	5.78541e8i	−0.937206	−	1.62329i	−0.166553	−	0.986032i	$-0.553264\pi$
$710$		−	1.16805e8i		−	0.326353i
$711$		0			0
$712$	−7.47838e7			−0.207189
$713$	7.52944e8	−	4.34713e8i	2.07728	−	1.19932i
$714$		0			0
$715$	−7.02144e7	+	1.21615e8i	−0.192091	+	0.332712i
$716$	2.15453e7	+	1.24392e7i	0.0586968	+	0.0338886i
$717$		0			0
$718$	−4.58836e6	−	7.94728e6i	−0.0123961	−	0.0214706i
$719$			6.40752e8i			1.72387i	0.507022	+	0.861933i	$0.330746\pi$
$719$			6.40752e8i			1.72387i	−0.507022	+	0.861933i	$0.669254\pi$
$720$		0			0
$721$	3.45130e8			0.920824
$722$	−4.98031e8	+	2.87538e8i	−1.32326	+	0.763983i
$723$		0			0
$724$	6.57114e7	−	1.13815e8i	0.173151	−	0.299906i
$725$	−7.23498e7	−	4.17712e7i	−0.189856	−	0.109613i
$726$		0			0
$727$	−1.64639e8	−	2.85164e8i	−0.428480	−	0.742149i	0.568259	−	0.822850i	$-0.307617\pi$
$727$	−1.64639e8	−	2.85164e8i	−0.428480	−	0.742149i	−0.996738	+	0.0807013i	$0.974284\pi$
$728$		−	1.19802e8i		−	0.310505i
$729$		0			0
$730$	1.51578e8			0.389645
$731$	3.14255e8	−	1.81435e8i	0.804508	−	0.464483i
$732$		0			0
$733$	−1.81298e8	+	3.14017e8i	−0.460342	+	0.797335i	−0.998978	−	0.0452035i	$-0.985606\pi$
$733$	−1.81298e8	+	3.14017e8i	−0.460342	+	0.797335i	0.538636	+	0.842538i	$0.318940\pi$
$734$	1.06450e8	+	6.14592e7i	0.269190	+	0.155417i
$735$		0			0
$736$	6.21271e7	+	1.07607e8i	0.155829	+	0.269904i
$737$			2.54810e8i			0.636522i
$738$		0			0
$739$	1.76953e7			0.0438454			0.0219227	−	0.999760i	$-0.493021\pi$
$739$	1.76953e7			0.0438454			0.0219227	+	0.999760i	$0.493021\pi$
$740$	−9.23039e7	+	5.32917e7i	−0.227785	+	0.131512i
$741$		0			0
$742$	1.52852e8	−	2.64747e8i	0.374162	−	0.648067i
$743$	−1.11712e8	−	6.44967e7i	−0.272353	−	0.157243i	0.357604	−	0.933873i	$-0.383594\pi$
$743$	−1.11712e8	−	6.44967e7i	−0.272353	−	0.157243i	−0.629956	+	0.776631i	$0.716927\pi$
$744$		0			0
$745$	5.05722e7	+	8.75936e7i	0.122305	+	0.211838i
$746$		−	3.43565e8i		−	0.827546i
$747$		0			0
$748$	8.26150e7			0.197403
$749$	−1.71617e8	+	9.90834e7i	−0.408429	+	0.235806i
$750$		0			0
$751$	1.68815e8	−	2.92395e8i	0.398557	−	0.690321i	−0.594991	−	0.803732i	$-0.702845\pi$
$751$	1.68815e8	−	2.92395e8i	0.398557	−	0.690321i	0.993548	+	0.113411i	$0.0361778\pi$
$752$	1.15081e8	+	6.64423e7i	0.270615	+	0.156240i
$753$		0			0
$754$	1.41976e8	+	2.45910e8i	0.331208	+	0.573669i
$755$		−	1.76964e8i		−	0.411192i
$756$		0			0
$757$	−9.58119e7			−0.220868			−0.110434	−	0.993883i	$-0.535224\pi$
$757$	−9.58119e7			−0.220868			−0.110434	+	0.993883i	$0.535224\pi$
$758$	−9.85290e7	+	5.68857e7i	−0.226233	+	0.130616i
$759$		0			0
$760$	−1.22158e8	+	2.11584e8i	−0.278280	+	0.481995i
$761$	2.89801e8	+	1.67317e8i	0.657575	+	0.379651i	0.791353	−	0.611360i	$-0.209377\pi$
$761$	2.89801e8	+	1.67317e8i	0.657575	+	0.379651i	−0.133777	+	0.991011i	$0.542711\pi$
$762$		0			0
$763$	−1.56855e8	−	2.71681e8i	−0.353122	−	0.611626i
$764$		−	1.36574e8i		−	0.306259i
$765$		0			0
$766$	2.67280e8			0.594676
$767$	−9.35237e7	+	5.39959e7i	−0.207270	+	0.119667i
$768$		0			0
$769$	1.21287e8	−	2.10075e8i	0.266708	−	0.461951i	−0.701302	−	0.712864i	$-0.747398\pi$
$769$	1.21287e8	−	2.10075e8i	0.266708	−	0.461951i	0.968010	+	0.250913i	$0.0807309\pi$
$770$	−1.10703e8	−	6.39144e7i	−0.242486	−	0.139999i
$771$		0			0
$772$	−1.29602e8	−	2.24477e8i	−0.281682	−	0.487888i
$773$		−	2.36476e8i		−	0.511974i	−0.966680	−	0.255987i	$-0.917599\pi$
$773$		−	2.36476e8i		−	0.511974i	0.966680	−	0.255987i	$-0.0824005\pi$
$774$		0			0
$775$	−1.36805e8			−0.293899
$776$	1.53388e8	−	8.85585e7i	0.328251	−	0.189516i
$777$		0			0
$778$	5.47663e7	−	9.48580e7i	0.116299	−	0.201435i
$779$	−6.25512e8	−	3.61140e8i	−1.32319	−	0.763946i
$780$		0			0
$781$	−5.83602e7	−	1.01083e8i	−0.122508	−	0.212190i
$782$			5.00724e8i			1.04708i
$783$		0			0
$784$	−1.14201e7			−0.0236986
$785$	5.43542e8	−	3.13814e8i	1.12363	−	0.648730i
$786$		0			0
$787$	2.48419e8	−	4.30274e8i	0.509636	−	0.882716i	−0.490301	−	0.871553i	$-0.663113\pi$
$787$	2.48419e8	−	4.30274e8i	0.509636	−	0.882716i	0.999938	−	0.0111631i	$-0.00355339\pi$
$788$	1.13132e8	+	6.53165e7i	0.231209	+	0.133489i
$789$		0			0
$790$	−3.95605e7	−	6.85208e7i	−0.0802380	−	0.138976i
$791$			4.36893e8i			0.882767i
$792$		0			0
$793$	5.41442e8			1.08576
$794$	1.79624e8	−	1.03706e8i	0.358842	−	0.207177i
$795$		0			0
$796$	1.64502e7	−	2.84926e7i	0.0326161	−	0.0564927i
$797$	9.18416e7	+	5.30248e7i	0.181411	+	0.104738i	0.587956	−	0.808893i	$-0.299933\pi$
$797$	9.18416e7	+	5.30248e7i	0.181411	+	0.104738i	−0.406544	+	0.913631i	$0.633266\pi$
$798$		0			0
$799$	2.67751e8	+	4.63759e8i	0.524918	+	0.909184i
$800$		−	1.95516e7i		−	0.0381867i
$801$		0			0
$802$	−6.84894e8			−1.32770
$803$	1.31175e8	−	7.57341e7i	0.253341	−	0.146266i
$804$		0			0
$805$	3.87380e8	−	6.70962e8i	0.742591	−	1.28621i
$806$	4.02691e8	+	2.32494e8i	0.769071	+	0.444023i
$807$		0			0
$808$	−1.01936e8	−	1.76558e8i	−0.193238	−	0.334698i
$809$			2.99505e8i			0.565664i	0.959169	+	0.282832i	$0.0912739\pi$
$809$			2.99505e8i			0.565664i	−0.959169	+	0.282832i	$0.908726\pi$
$810$		0			0
$811$	−4.31983e8			−0.809848			−0.404924	−	0.914350i	$-0.632702\pi$
$811$	−4.31983e8			−0.809848			−0.404924	+	0.914350i	$0.632702\pi$
$812$	−2.23845e8	+	1.29237e8i	−0.418100	+	0.241390i
$813$		0			0
$814$	−5.32529e7	+	9.22367e7i	−0.0987348	+	0.171014i
$815$	5.35335e8	+	3.09076e8i	0.988900	+	0.570942i
$816$		0			0
$817$	5.36166e8	+	9.28667e8i	0.983180	+	1.70292i
$818$		−	2.25304e8i		−	0.411632i
$819$		0			0
$820$	−2.09775e8			−0.380463
$821$	−2.29258e8	+	1.32362e8i	−0.414282	+	0.239186i	−0.692628	−	0.721295i	$-0.743547\pi$
$821$	−2.29258e8	+	1.32362e8i	−0.414282	+	0.239186i	0.278346	+	0.960481i	$0.410214\pi$
$822$		0			0
$823$	1.83269e8	−	3.17431e8i	0.328768	−	0.569443i	−0.653499	−	0.756927i	$-0.726700\pi$
$823$	1.83269e8	−	3.17431e8i	0.328768	−	0.569443i	0.982268	+	0.187484i	$0.0600332\pi$
$824$	−1.65795e8	−	9.57215e7i	−0.296339	−	0.171091i
$825$		0			0
$826$	−4.91511e7	−	8.51323e7i	−0.0872154	−	0.151062i
$827$		−	5.77816e8i		−	1.02158i	−0.859705	−	0.510791i	$-0.829353\pi$
$827$		−	5.77816e8i		−	1.02158i	0.859705	−	0.510791i	$-0.170647\pi$
$828$		0			0
$829$	−3.22169e8			−0.565484			−0.282742	−	0.959196i	$-0.591244\pi$
$829$	−3.22169e8			−0.565484			−0.282742	+	0.959196i	$0.591244\pi$
$830$	−3.73973e7	+	2.15913e7i	−0.0654042	+	0.0377611i
$831$		0			0
$832$	−3.32269e7	+	5.75507e7i	−0.0576926	+	0.0999265i
$833$	−3.98556e7	−	2.30106e7i	−0.0689532	−	0.0398101i
$834$		0			0
$835$	3.28097e8	+	5.68280e8i	0.563563	+	0.976119i
$836$			2.44139e8i			0.417847i
$837$		0			0
$838$	3.06393e8			0.520650
$839$	7.64777e8	−	4.41544e8i	1.29494	−	0.747632i	0.315412	−	0.948955i	$-0.397857\pi$
$839$	7.64777e8	−	4.41544e8i	1.29494	−	0.747632i	0.979525	+	0.201322i	$0.0645239\pi$
$840$		0			0
$841$	8.90391e6	−	1.54220e7i	0.0149690	−	0.0259271i
$842$	2.65168e8	+	1.53095e8i	0.444206	+	0.256463i
$843$		0			0
$844$	2.47206e8	+	4.28173e8i	0.411180	+	0.712184i
$845$			7.90226e7i			0.130973i
$846$		0			0
$847$	4.50392e8			0.741209
$848$	−1.46855e8	+	8.47868e7i	−0.240825	+	0.139040i
$849$		0			0
$850$	3.93948e7	−	6.82338e7i	0.0641479	−	0.111107i
$851$	−5.59040e8	−	3.22762e8i	−0.907098	−	0.523713i
$852$		0			0
$853$	−2.30927e8	−	3.99977e8i	−0.372073	−	0.644449i	0.617812	−	0.786326i	$-0.288019\pi$
$853$	−2.30927e8	−	3.99977e8i	−0.372073	−	0.644449i	−0.989884	+	0.141877i	$0.954686\pi$
$854$			4.92861e8i			0.791317i
$855$		0			0
$856$	1.09923e8			0.175254
$857$	3.69032e8	−	2.13061e8i	0.586303	−	0.338502i	−0.177331	−	0.984151i	$-0.556746\pi$
$857$	3.69032e8	−	2.13061e8i	0.586303	−	0.338502i	0.763634	+	0.645649i	$0.223413\pi$
$858$		0			0
$859$	1.54794e8	−	2.68110e8i	0.244216	−	0.422994i	−0.717695	−	0.696357i	$-0.754803\pi$
$859$	1.54794e8	−	2.68110e8i	0.244216	−	0.422994i	0.961911	+	0.273363i	$0.0881362\pi$
$860$	2.69718e8	+	1.55722e8i	0.424047	+	0.244824i
$861$		0			0
$862$	−2.28590e8	−	3.95929e8i	−0.356890	−	0.618152i
$863$		−	3.39614e8i		−	0.528388i	−0.964470	−	0.264194i	$-0.914894\pi$
$863$		−	3.39614e8i		−	0.528388i	0.964470	−	0.264194i	$-0.0851059\pi$
$864$		0			0
$865$	2.48396e8			0.383792
$866$	6.55083e7	−	3.78212e7i	0.100865	−	0.0582347i
$867$		0			0
$868$	−2.11633e8	+	3.66559e8i	−0.323612	+	0.560512i
$869$	−6.84709e7	−	3.95317e7i	−0.104339	−	0.0602402i
$870$		0			0
$871$	−4.12984e8	−	7.15310e8i	−0.624999	−	1.08253i
$872$			1.74015e8i			0.262444i
$873$		0			0
$874$	−1.47971e9			−2.21636
$875$	−5.94321e8	+	3.43132e8i	−0.887150	+	0.512196i
$876$		0			0
$877$	−2.91464e8	+	5.04830e8i	−0.432101	+	0.748422i	−0.997054	−	0.0767016i	$-0.975561\pi$
$877$	−2.91464e8	+	5.04830e8i	−0.432101	+	0.748422i	0.564953	+	0.825123i	$0.308894\pi$
$878$	−3.74089e8	−	2.15980e8i	−0.552703	−	0.319103i
$879$		0			0
$880$	3.54532e7	+	6.14068e7i	0.0520245	+	0.0901090i
$881$		−	5.04493e8i		−	0.737781i	−0.929473	−	0.368890i	$-0.879738\pi$
$881$		−	5.04493e8i		−	0.737781i	0.929473	−	0.368890i	$-0.120262\pi$
$882$		0			0
$883$	−5.92257e8			−0.860256			−0.430128	−	0.902768i	$-0.641532\pi$
$883$	−5.92257e8			−0.860256			−0.430128	+	0.902768i	$0.641532\pi$
$884$	−2.31920e8	+	1.33899e8i	−0.335723	+	0.193830i
$885$		0			0
$886$	−3.14533e8	+	5.44786e8i	−0.452235	+	0.783295i
$887$	−3.30070e8	−	1.90566e8i	−0.472972	−	0.273071i	0.244511	−	0.969647i	$-0.421373\pi$
$887$	−3.30070e8	−	1.90566e8i	−0.472972	−	0.273071i	−0.717483	+	0.696576i	$0.754706\pi$
$888$		0			0
$889$	2.65677e8	+	4.60165e8i	0.378136	+	0.654951i
$890$		−	2.58655e8i		−	0.366903i
$891$		0			0
$892$	8.99614e7			0.126754
$893$	−1.37047e9	+	7.91241e8i	−1.92449	+	1.11110i
$894$		0			0
$895$	−4.30235e7	+	7.45189e7i	−0.0600118	+	0.103944i
$896$	−5.23870e7	−	3.02456e7i	−0.0728281	−	0.0420473i
$897$		0			0
$898$	3.86123e8	+	6.68785e8i	0.533209	+	0.923545i
$899$		−	1.00322e9i		−	1.38075i
$900$		0			0
$901$	−6.83353e8			−0.934267
$902$	−1.81539e8	+	1.04811e8i	−0.247371	+	0.142820i
$903$		0			0
$904$	1.21172e8	−	2.09876e8i	0.164020	−	0.284091i
$905$	3.93654e8	+	2.27276e8i	0.531091	+	0.306625i
$906$		0			0
$907$	6.63839e8	+	1.14980e9i	0.889695	+	1.54100i	0.840237	+	0.542220i	$0.182416\pi$
$907$	6.63839e8	+	1.14980e9i	0.889695	+	1.54100i	0.0494580	+	0.998776i	$0.484251\pi$
$908$			2.38630e8i			0.318762i
$909$		0			0
$910$	4.14359e8			0.549860
$911$	−9.77428e8	+	5.64318e8i	−1.29280	+	0.746396i	−0.979149	−	0.203144i	$-0.934884\pi$
$911$	−9.77428e8	+	5.64318e8i	−1.29280	+	0.746396i	−0.313646	+	0.949540i	$0.601551\pi$
$912$		0			0
$913$	−2.15756e7	+	3.73701e7i	−0.0283499	+	0.0491034i
$914$	−5.31094e8	−	3.06627e8i	−0.695557	−	0.401580i
$915$		0			0
$916$	2.01994e8	+	3.49864e8i	0.262816	+	0.455211i
$917$		−	4.50683e8i		−	0.584471i
$918$		0			0
$919$	−1.60932e8			−0.207347			−0.103673	−	0.994611i	$-0.533060\pi$
$919$	−1.60932e8			−0.207347			−0.103673	+	0.994611i	$0.533060\pi$
$920$	−3.72182e8	+	2.14879e8i	−0.477960	+	0.275951i
$921$		0			0
$922$	4.64265e8	−	8.04131e8i	0.592343	−	1.02597i
$923$	3.27661e8	+	1.89175e8i	0.416697	+	0.240580i
$924$		0			0
$925$	5.07871e7	+	8.79658e7i	0.0641694	+	0.111145i
$926$		−	2.11549e8i		−	0.266427i
$927$		0			0
$928$	1.43375e8			0.179403
$929$	1.99102e8	−	1.14952e8i	0.248330	−	0.143373i	−0.370669	−	0.928765i	$-0.620872\pi$
$929$	1.99102e8	−	1.14952e8i	0.248330	−	0.143373i	0.618999	+	0.785392i	$0.287538\pi$
$930$		0			0
$931$	6.79995e7	−	1.17779e8i	0.0842669	−	0.145955i
$932$	−4.55275e8	−	2.62853e8i	−0.562375	−	0.324687i
$933$		0			0
$934$	−4.12812e8	−	7.15012e8i	−0.506654	−	0.877551i
$935$			2.85741e8i			0.349573i
$936$		0			0
$937$	−7.89016e8			−0.959107			−0.479553	−	0.877513i	$-0.659201\pi$
$937$	−7.89016e8			−0.959107			−0.479553	+	0.877513i	$0.659201\pi$
$938$	6.51129e8	−	3.75929e8i	0.788966	−	0.455510i
$939$		0			0
$940$	−2.29804e8	+	3.98033e8i	−0.276678	+	0.479220i
$941$	−2.11650e8	−	1.22196e8i	−0.254009	−	0.146652i	0.367590	−	0.929988i	$-0.380183\pi$
$941$	−2.11650e8	−	1.22196e8i	−0.254009	−	0.146652i	−0.621599	+	0.783336i	$0.713516\pi$
$942$		0			0
$943$	−6.35254e8	−	1.10029e9i	−0.757552	−	1.31212i
$944$			5.45282e7i			0.0648194i
$945$		0			0
$946$	3.11216e8			0.367612
$947$	4.13601e8	−	2.38793e8i	0.487004	−	0.281172i	−0.236327	−	0.971674i	$-0.575944\pi$
$947$	4.13601e8	−	2.38793e8i	0.487004	−	0.281172i	0.723331	+	0.690502i	$0.242610\pi$
$948$		0			0
$949$	−2.45493e8	+	4.25206e8i	−0.287237	+	0.497509i
$950$	2.01640e8	+	1.16417e8i	0.235183	+	0.135783i
$951$		0			0
$952$	−1.21885e8	−	2.11111e8i	−0.141266	−	0.244680i
$953$			1.14002e9i			1.31715i	0.752517	+	0.658573i	$0.228840\pi$
$953$			1.14002e9i			1.31715i	−0.752517	+	0.658573i	$0.771160\pi$
$954$		0			0
$955$	4.72370e8			0.542341
$956$	2.70419e8	−	1.56127e8i	0.309502	−	0.178691i
$957$		0			0
$958$	3.76102e8	−	6.51428e8i	0.427769	−	0.740917i
$959$	1.00263e9	+	5.78867e8i	1.13680	+	0.656332i
$960$		0			0
$961$	−3.77661e8	−	6.54128e8i	−0.425532	−	0.737043i
$962$		−	3.45240e8i		−	0.387789i
$963$		0			0
$964$	4.71691e8			0.526534
$965$	7.76400e8	−	4.48255e8i	0.863980	−	0.498819i
$966$		0			0
$967$	−1.51397e8	+	2.62227e8i	−0.167431	+	0.290000i	−0.937516	−	0.347942i	$-0.886881\pi$
$967$	−1.51397e8	+	2.62227e8i	−0.167431	+	0.290000i	0.770085	+	0.637942i	$0.220214\pi$
$968$	−2.16361e8	−	1.24916e8i	−0.238535	−	0.137718i
$969$		0			0
$970$	3.06298e8	+	5.30523e8i	0.335605	+	0.581285i
$971$			2.05629e8i			0.224608i	0.993674	+	0.112304i	$0.0358231\pi$
$971$			2.05629e8i			0.224608i	−0.993674	+	0.112304i	$0.964177\pi$
$972$		0			0
$973$	1.05091e9			1.14085
$974$	2.26426e8	−	1.30727e8i	0.245047	−	0.141478i
$975$		0			0
$976$	1.36695e8	−	2.36762e8i	0.147029	−	0.254661i
$977$	5.08949e7	+	2.93842e7i	0.0545746	+	0.0315087i	0.527039	−	0.849841i	$-0.323302\pi$
$977$	5.08949e7	+	2.93842e7i	0.0545746	+	0.0315087i	−0.472464	+	0.881350i	$0.656635\pi$
$978$		0			0
$979$	−1.29233e8	−	2.23839e8i	−0.137729	−	0.238554i
$980$		−	3.94989e7i		−	0.0419669i
$981$		0			0
$982$	−5.18050e8			−0.547063
$983$	−7.03441e7	+	4.06132e7i	−0.0740572	+	0.0427569i	−0.536571	−	0.843855i	$-0.680281\pi$
$983$	−7.03441e7	+	4.06132e7i	−0.0740572	+	0.0427569i	0.462514	+	0.886612i	$0.346947\pi$
$984$		0			0
$985$	−2.25911e8	+	3.91289e8i	−0.236389	+	0.409438i
$986$	5.00371e8	+	2.88889e8i	0.521989	+	0.301370i
$987$		0			0
$988$	−3.95689e8	−	6.85354e8i	−0.410283	−	0.710631i
$989$			1.88626e9i			1.94990i
$990$		0			0
$991$	2.17703e8			0.223688			0.111844	−	0.993726i	$-0.464324\pi$
$991$	2.17703e8			0.223688			0.111844	+	0.993726i	$0.464324\pi$
$992$	2.03330e8	−	1.17393e8i	0.208289	−	0.120256i
$993$		0			0
$994$	−1.72202e8	+	2.98262e8i	−0.175339	+	0.303696i
$995$	9.85474e7	+	5.68964e7i	0.100041	+	0.0577584i
$996$		0			0
$997$	−1.09951e8	−	1.90441e8i	−0.110947	−	0.192166i	0.805205	−	0.592996i	$-0.202055\pi$
$997$	−1.09951e8	−	1.90441e8i	−0.110947	−	0.192166i	−0.916152	+	0.400830i	$0.868722\pi$
$998$			3.23515e8i			0.325464i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.7.d.a.17.3		12
3.2	odd	2		18.7.d.a.5.4	✓	12
4.3	odd	2		432.7.q.b.17.6		12
9.2	odd	6	inner	54.7.d.a.35.3		12
9.4	even	3		162.7.b.c.161.2		12
9.5	odd	6		162.7.b.c.161.11		12
9.7	even	3		18.7.d.a.11.4	yes	12
12.11	even	2		144.7.q.c.113.6		12
36.7	odd	6		144.7.q.c.65.6		12
36.11	even	6		432.7.q.b.305.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.7.d.a.5.4	✓	12	3.2	odd	2
18.7.d.a.11.4	yes	12	9.7	even	3
54.7.d.a.17.3		12	1.1	even	1	trivial
54.7.d.a.35.3		12	9.2	odd	6	inner
144.7.q.c.65.6		12	36.7	odd	6
144.7.q.c.113.6		12	12.11	even	2
162.7.b.c.161.2		12	9.4	even	3
162.7.b.c.161.11		12	9.5	odd	6
432.7.q.b.17.6		12	4.3	odd	2
432.7.q.b.305.6		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)

\(f(q)\)	\(=\)	\(q+(-4.89898 + 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(95.8504 + 55.3393i) q^{5} +(-163.169 - 282.617i) q^{7} +181.019i q^{8} +O(q^{10})\)	\(q+(-4.89898 + 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(95.8504 + 55.3393i) q^{5} +(-163.169 - 282.617i) q^{7} +181.019i q^{8} -626.092 q^{10} +(-541.817 + 312.818i) q^{11} +(1014.01 - 1756.31i) q^{13} +(1598.72 + 923.023i) q^{14} +(-512.000 - 886.810i) q^{16} -4126.55i q^{17} +12194.5 q^{19} +(3067.21 - 1770.86i) q^{20} +(1769.57 - 3064.98i) q^{22} +(18576.6 + 10725.2i) q^{23} +(-1687.63 - 2923.06i) q^{25} +11472.2i q^{26} -10442.8 q^{28} +(21435.3 - 12375.7i) q^{29} +(20265.9 - 35101.6i) q^{31} +(5016.55 + 2896.31i) q^{32} +(11671.6 + 20215.9i) q^{34} -36118.6i q^{35} -30093.7 q^{37} +(-59740.6 + 34491.3i) q^{38} +(-10017.5 + 17350.8i) q^{40} +(-51294.6 - 29614.9i) q^{41} +(43967.8 + 76154.5i) q^{43} +20020.4i q^{44} -121342. q^{46} +(-112384. + 64885.1i) q^{47} +(5576.24 - 9658.34i) q^{49} +(16535.3 + 9546.68i) q^{50} +(-32448.2 - 56201.9i) q^{52} -165599. i q^{53} -69244.6 q^{55} +(51159.1 - 29536.7i) q^{56} +(-70007.5 + 121257. i) q^{58} +(-46116.0 - 26625.1i) q^{59} +(133491. + 231213. i) q^{61} +229282. i q^{62} -32768.0 q^{64} +(194386. - 112229. i) q^{65} +(203640. - 352715. i) q^{67} +(-114358. - 66024.7i) q^{68} +(102159. + 176944. i) q^{70} +186563. i q^{71} -242102. q^{73} +(147429. - 85117.9i) q^{74} +(195112. - 337944. i) q^{76} +(176816. + 102085. i) q^{77} +(63186.3 + 109442. i) q^{79} -113335. i q^{80} +335055. q^{82} +(59731.2 - 34485.8i) q^{83} +(228360. - 395531. i) q^{85} +(-430795. - 248720. i) q^{86} +(-56626.2 - 98079.4i) q^{88} +413126. i q^{89} -661817. q^{91} +(594452. - 343207. i) q^{92} +(367045. - 635741. i) q^{94} +(1.16885e6 + 674835. i) q^{95} +(-489221. - 847356. i) q^{97} +63088.0i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 192 q^{4} - 432 q^{5} + 240 q^{7}+O(q^{10}) \) 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

Introduction

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