LMFDB - Embedded newform 54.7.d.a.35.6

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			35.6
Root			$-7.20150i$ of defining polynomial
Character	$\chi$	$=$	54.35
Dual form			54.7.d.a.17.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.89898 + 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(39.5602 - 22.8401i) q^{5} +(-245.097 + 424.521i) q^{7} +181.019i q^{8} +O(q^{10})$	\(q+(4.89898 + 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(39.5602 - 22.8401i) q^{5} +(-245.097 + 424.521i) q^{7} +181.019i q^{8} +258.406 q^{10} +(873.336 + 504.221i) q^{11} +(466.801 + 808.523i) q^{13} +(-2401.45 + 1386.48i) q^{14} +(-512.000 + 886.810i) q^{16} +8090.59i q^{17} -7727.36 q^{19} +(1265.93 + 730.884i) q^{20} +(2852.30 + 4940.34i) q^{22} +(11848.0 - 6840.45i) q^{23} +(-6769.16 + 11724.5i) q^{25} +5281.25i q^{26} -15686.2 q^{28} +(1964.70 + 1134.32i) q^{29} +(-17062.6 - 29553.2i) q^{31} +(-5016.55 + 2896.31i) q^{32} +(-22883.6 + 39635.6i) q^{34} +22392.2i q^{35} +92058.0 q^{37} +(-37856.2 - 21856.3i) q^{38} +(4134.50 + 7161.17i) q^{40} +(31021.6 - 17910.3i) q^{41} +(34570.9 - 59878.5i) q^{43} +32270.1i q^{44} +77390.9 q^{46} +(-13211.1 - 7627.46i) q^{47} +(-61321.0 - 106211. i) q^{49} +(-66323.9 + 38292.1i) q^{50} +(-14937.6 + 25872.7i) q^{52} -236591. i q^{53} +46065.9 q^{55} +(-76846.5 - 44367.4i) q^{56} +(6416.70 + 11114.0i) q^{58} +(221890. - 128108. i) q^{59} +(-19919.6 + 34501.8i) q^{61} -193041. i q^{62} -32768.0 q^{64} +(36933.5 + 21323.6i) q^{65} +(-160204. - 277482. i) q^{67} +(-224213. + 129449. i) q^{68} +(-63334.7 + 109699. i) q^{70} +404593. i q^{71} +393719. q^{73} +(450990. + 260379. i) q^{74} +(-123638. - 214147. i) q^{76} +(-428105. + 247167. i) q^{77} +(-449184. + 778010. i) q^{79} +46776.5i q^{80} +202632. q^{82} +(-154916. - 89441.0i) q^{83} +(184790. + 320066. i) q^{85} +(338724. - 195562. i) q^{86} +(-91273.8 + 158091. i) q^{88} +826458. i q^{89} -457647. q^{91} +(379136. + 218894. i) q^{92} +(-43147.4 - 74733.5i) q^{94} +(-305696. + 176494. i) q^{95} +(-317981. + 550760. i) q^{97} -693768. i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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
$5$	39.5602	−	22.8401i	0.316482	−	0.182721i	−0.333341	−	0.942806i	$-0.608176\pi$
$5$	39.5602	−	22.8401i	0.316482	−	0.182721i	0.649823	+	0.760085i	$0.274843\pi$
$6$		0			0
$7$	−245.097	+	424.521i	−0.714570	+	1.23767i	0.248556	+	0.968618i	$0.420044\pi$
$7$	−245.097	+	424.521i	−0.714570	+	1.23767i	−0.963125	+	0.269053i	$0.913289\pi$
$8$			181.019i			0.353553i
$9$		0			0
$10$	258.406			0.258406
$11$	873.336	+	504.221i	0.656151	+	0.378829i	0.790809	−	0.612063i	$-0.209660\pi$
$11$	873.336	+	504.221i	0.656151	+	0.378829i	−0.134658	+	0.990892i	$0.542994\pi$
$12$		0			0
$13$	466.801	+	808.523i	0.212472	+	0.368012i	0.952488	−	0.304577i	$-0.0985152\pi$
$13$	466.801	+	808.523i	0.212472	+	0.368012i	−0.740016	+	0.672590i	$0.765182\pi$
$14$	−2401.45	+	1386.48i	−0.875166	+	0.505277i
$15$		0			0
$16$	−512.000	+	886.810i	−0.125000	+	0.216506i
$17$			8090.59i			1.64677i	0.567482	+	0.823386i	$0.307918\pi$
$17$			8090.59i			1.64677i	−0.567482	+	0.823386i	$0.692082\pi$
$18$		0			0
$19$	−7727.36			−1.12660			−0.563301	−	0.826252i	$-0.690469\pi$
$19$	−7727.36			−1.12660			−0.563301	+	0.826252i	$0.690469\pi$
$20$	1265.93	+	730.884i	0.158241	+	0.0913604i
$21$		0			0
$22$	2852.30	+	4940.34i	0.267872	+	0.463969i
$23$	11848.0	−	6840.45i	0.973782	−	0.562213i	0.0733950	−	0.997303i	$-0.476617\pi$
$23$	11848.0	−	6840.45i	0.973782	−	0.562213i	0.900387	+	0.435090i	$0.143283\pi$
$24$		0			0
$25$	−6769.16	+	11724.5i	−0.433226	+	0.750370i
$26$			5281.25i			0.300481i
$27$		0			0
$28$	−15686.2			−0.714570
$29$	1964.70	+	1134.32i	0.0805570	+	0.0465096i	0.539737	−	0.841833i	$-0.318524\pi$
$29$	1964.70	+	1134.32i	0.0805570	+	0.0465096i	−0.459180	+	0.888343i	$0.651857\pi$
$30$		0			0
$31$	−17062.6	−	29553.2i	−0.572742	−	0.992019i	−0.996283	−	0.0861417i	$-0.972546\pi$
$31$	−17062.6	−	29553.2i	−0.572742	−	0.992019i	0.423541	−	0.905877i	$-0.360787\pi$
$32$	−5016.55	+	2896.31i	−0.153093	+	0.0883883i
$33$		0			0
$34$	−22883.6	+	39635.6i	−0.582222	+	1.00844i
$35$			22392.2i			0.522267i
$36$		0			0
$37$	92058.0			1.81743			0.908713	−	0.417422i	$-0.137066\pi$
$37$	92058.0			1.81743			0.908713	+	0.417422i	$0.137066\pi$
$38$	−37856.2	−	21856.3i	−0.689900	−	0.398314i
$39$		0			0
$40$	4134.50	+	7161.17i	0.0646016	+	0.111893i
$41$	31021.6	−	17910.3i	0.450103	−	0.259867i	−0.257771	−	0.966206i	$-0.582988\pi$
$41$	31021.6	−	17910.3i	0.450103	−	0.259867i	0.707874	+	0.706339i	$0.249655\pi$
$42$		0			0
$43$	34570.9	−	59878.5i	0.434816	−	0.753123i	−0.562465	−	0.826821i	$-0.690147\pi$
$43$	34570.9	−	59878.5i	0.434816	−	0.753123i	0.997281	+	0.0736985i	$0.0234803\pi$
$44$			32270.1i			0.378829i
$45$		0			0
$46$	77390.9			0.795090
$47$	−13211.1	−	7627.46i	−0.127247	−	0.0734659i	0.435025	−	0.900418i	$-0.356739\pi$
$47$	−13211.1	−	7627.46i	−0.127247	−	0.0734659i	−0.562272	+	0.826952i	$0.690073\pi$
$48$		0			0
$49$	−61321.0	−	106211.i	−0.521220	−	0.902779i
$50$	−66323.9	+	38292.1i	−0.530592	+	0.306337i
$51$		0			0
$52$	−14937.6	+	25872.7i	−0.106236	+	0.184006i
$53$		−	236591.i		−	1.58917i	−0.607153	−	0.794585i	$-0.707688\pi$
$53$		−	236591.i		−	1.58917i	0.607153	−	0.794585i	$-0.292312\pi$
$54$		0			0
$55$	46065.9			0.276880
$56$	−76846.5	−	44367.4i	−0.437583	−	0.252639i
$57$		0			0
$58$	6416.70	+	11114.0i	0.0328873	+	0.0569624i
$59$	221890.	−	128108.i	1.08039	−	0.623766i	0.149392	−	0.988778i	$-0.452268\pi$
$59$	221890.	−	128108.i	1.08039	−	0.623766i	0.931003	+	0.365012i	$0.118935\pi$
$60$		0			0
$61$	−19919.6	+	34501.8i	−0.0877589	+	0.152003i	−0.906563	−	0.422069i	$-0.861304\pi$
$61$	−19919.6	+	34501.8i	−0.0877589	+	0.152003i	0.818805	+	0.574072i	$0.194637\pi$
$62$		−	193041.i		−	0.809980i
$63$		0			0
$64$	−32768.0			−0.125000
$65$	36933.5	+	21323.6i	0.134487	+	0.0776462i
$66$		0			0
$67$	−160204.	−	277482.i	−0.532660	−	0.922593i	−0.999273	−	0.0381319i	$-0.987859\pi$
$67$	−160204.	−	277482.i	−0.532660	−	0.922593i	0.466613	−	0.884461i	$-0.345474\pi$
$68$	−224213.	+	129449.i	−0.713073	+	0.411693i
$69$		0			0
$70$	−63334.7	+	109699.i	−0.184649	+	0.319822i
$71$			404593.i			1.13043i	0.824944	+	0.565215i	$0.191207\pi$
$71$			404593.i			1.13043i	−0.824944	+	0.565215i	$0.808793\pi$
$72$		0			0
$73$	393719.			1.01209			0.506044	−	0.862508i	$-0.331107\pi$
$73$	393719.			1.01209			0.506044	+	0.862508i	$0.331107\pi$
$74$	450990.	+	260379.i	1.11294	+	0.642557i
$75$		0			0
$76$	−123638.	−	214147.i	−0.281650	−	0.487833i
$77$	−428105.	+	247167.i	−0.937731	+	0.541399i
$78$		0			0
$79$	−449184.	+	778010.i	−0.911052	+	1.57799i	−0.0984709	+	0.995140i	$0.531395\pi$
$79$	−449184.	+	778010.i	−0.911052	+	1.57799i	−0.812581	+	0.582848i	$0.801938\pi$
$80$			46776.5i			0.0913604i
$81$		0			0
$82$	202632.			0.367508
$83$	−154916.	−	89441.0i	−0.270934	−	0.156424i	0.358378	−	0.933576i	$-0.383330\pi$
$83$	−154916.	−	89441.0i	−0.270934	−	0.156424i	−0.629312	+	0.777153i	$0.716663\pi$
$84$		0			0
$85$	184790.	+	320066.i	0.300900	+	0.521173i
$86$	338724.	−	195562.i	0.532538	−	0.307461i
$87$		0			0
$88$	−91273.8	+	158091.i	−0.133936	+	0.231984i
$89$			826458.i			1.17233i	0.810191	+	0.586166i	$0.199364\pi$
$89$			826458.i			1.17233i	−0.810191	+	0.586166i	$0.800636\pi$
$90$		0			0
$91$	−457647.			−0.607304
$92$	379136.	+	218894.i	0.486891	+	0.281107i
$93$		0			0
$94$	−43147.4	−	74733.5i	−0.0519483	−	0.0899770i
$95$	−305696.	+	176494.i	−0.356549	+	0.205854i
$96$		0			0
$97$	−317981.	+	550760.i	−0.348406	+	0.603458i	−0.985967	−	0.166943i	$-0.946610\pi$
$97$	−317981.	+	550760.i	−0.348406	+	0.603458i	0.637560	+	0.770401i	$0.279944\pi$
$98$		−	693768.i		−	0.737116i
$99$		0			0
$100$	−433226.			−0.433226
$101$	227301.	+	131232.i	0.220616	+	0.127373i	0.606236	−	0.795285i	$-0.292679\pi$
$101$	227301.	+	131232.i	0.220616	+	0.127373i	−0.385619	+	0.922658i	$0.626012\pi$
$102$		0			0
$103$	41238.0	+	71426.3i	0.0377386	+	0.0653652i	0.884278	−	0.466961i	$-0.154651\pi$
$103$	41238.0	+	71426.3i	0.0377386	+	0.0653652i	−0.846539	+	0.532326i	$0.821318\pi$
$104$	−146358.	+	84500.0i	−0.130112	+	0.0751202i
$105$		0			0
$106$	669180.	−	1.15905e6i	0.561857	−	0.973164i
$107$		−	1.03624e6i		−	0.845881i	−0.906158	−	0.422940i	$-0.860998\pi$
$107$		−	1.03624e6i		−	0.845881i	0.906158	−	0.422940i	$-0.139002\pi$
$108$		0			0
$109$	420018.			0.324331			0.162165	−	0.986764i	$-0.448152\pi$
$109$	420018.			0.324331			0.162165	+	0.986764i	$0.448152\pi$
$110$	225676.	+	130294.i	0.169553	+	0.0978918i
$111$		0			0
$112$	−250980.	−	434710.i	−0.178642	−	0.309418i
$113$	1.32478e6	−	764860.i	0.918136	−	0.530086i	0.0350964	−	0.999384i	$-0.488826\pi$
$113$	1.32478e6	−	764860.i	0.918136	−	0.530086i	0.883040	+	0.469298i	$0.155493\pi$
$114$		0			0
$115$	312473.	−	541220.i	0.205456	−	0.355861i
$116$			72596.7i			0.0465096i
$117$		0			0
$118$	1.44938e6			0.882139
$119$	−3.43463e6	−	1.98298e6i	−2.03816	−	1.17673i
$120$		0			0
$121$	−377303.	−	653508.i	−0.212978	−	0.368888i
$122$	−195171.	+	112682.i	−0.107482	+	0.0620549i
$123$		0			0
$124$	546002.	−	945703.i	0.286371	−	0.496009i
$125$			1.33219e6i			0.682080i
$126$		0			0
$127$	−949267.			−0.463422			−0.231711	−	0.972785i	$-0.574432\pi$
$127$	−949267.			−0.463422			−0.231711	+	0.972785i	$0.574432\pi$
$128$	−160530.	−	92681.9i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	120624.	+	208928.i	0.0549041	+	0.0950967i
$131$	794197.	−	458530.i	0.353276	−	0.203964i	−0.312851	−	0.949802i	$-0.601284\pi$
$131$	794197.	−	458530.i	0.353276	−	0.203964i	0.666127	+	0.745838i	$0.267951\pi$
$132$		0			0
$133$	1.89396e6	−	3.28043e6i	0.805035	−	1.39436i
$134$		−	1.81250e6i		−	0.753294i
$135$		0			0
$136$	−1.46455e6			−0.582222
$137$	413272.	+	238603.i	0.160722	+	0.0927926i	0.578204	−	0.815893i	$-0.303754\pi$
$137$	413272.	+	238603.i	0.160722	+	0.0927926i	−0.417482	+	0.908685i	$0.637087\pi$
$138$		0			0
$139$	2.04226e6	+	3.53730e6i	0.760443	+	1.31713i	0.942623	+	0.333860i	$0.108351\pi$
$139$	2.04226e6	+	3.53730e6i	0.760443	+	1.31713i	−0.182180	+	0.983265i	$0.558315\pi$
$140$	−620551.	+	358275.i	−0.226148	+	0.130567i
$141$		0			0
$142$	−1.14436e6	+	1.98209e6i	−0.399667	+	0.692244i
$143$			941484.i			0.321962i
$144$		0			0
$145$	103632.			0.0339931
$146$	1.92882e6	+	1.11361e6i	0.619775	+	0.357827i
$147$		0			0
$148$	1.47293e6	+	2.55119e6i	0.454356	+	0.786968i
$149$	3.18704e6	−	1.84004e6i	0.963449	−	0.556248i	0.0662161	−	0.997805i	$-0.478907\pi$
$149$	3.18704e6	−	1.84004e6i	0.963449	−	0.556248i	0.897233	+	0.441558i	$0.145574\pi$
$150$		0			0
$151$	333742.	−	578059.i	0.0969350	−	0.167896i	−0.813480	−	0.581594i	$-0.802429\pi$
$151$	333742.	−	578059.i	0.0969350	−	0.167896i	0.910415	+	0.413697i	$0.135763\pi$
$152$		−	1.39880e6i		−	0.398314i
$153$		0			0
$154$	−2.79637e6			−0.765654
$155$	−1.35000e6	−	779422.i	−0.362525	−	0.209304i
$156$		0			0
$157$	753580.	+	1.30524e6i	0.194729	+	0.337280i	0.946812	−	0.321788i	$-0.104284\pi$
$157$	753580.	+	1.30524e6i	0.194729	+	0.337280i	−0.752083	+	0.659069i	$0.770951\pi$
$158$	−4.40109e6	+	2.54097e6i	−1.11581	+	0.644211i
$159$		0			0
$160$	−132304.	+	229157.i	−0.0323008	+	0.0559466i
$161$			6.70631e6i			1.60696i
$162$		0			0
$163$	−5.90805e6			−1.36421			−0.682105	−	0.731254i	$-0.738935\pi$
$163$	−5.90805e6			−1.36421			−0.682105	+	0.731254i	$0.738935\pi$
$164$	992690.	+	573130.i	0.225052	+	0.129934i
$165$		0			0
$166$	−505955.	−	876339.i	−0.110608	−	0.191579i
$167$	−2.33113e6	+	1.34588e6i	−0.500515	+	0.288972i	−0.728926	−	0.684592i	$-0.759980\pi$
$167$	−2.33113e6	+	1.34588e6i	−0.500515	+	0.288972i	0.228411	+	0.973565i	$0.426647\pi$
$168$		0			0
$169$	1.97760e6	−	3.42530e6i	0.409711	−	0.709641i
$170$			2.09066e6i			0.425536i
$171$		0			0
$172$	2.21254e6			0.434816
$173$	5.49562e6	+	3.17290e6i	1.06140	+	0.612798i	0.925819	−	0.377968i	$-0.123377\pi$
$173$	5.49562e6	+	3.17290e6i	1.06140	+	0.612798i	0.135579	+	0.990767i	$0.456710\pi$
$174$		0			0
$175$	−3.31821e6	−	5.74730e6i	−0.619141	−	1.07238i
$176$	−894297.	+	516322.i	−0.164038	+	0.0947072i
$177$		0			0
$178$	−2.33758e6	+	4.04880e6i	−0.414482	+	0.717904i
$179$		−	9.31786e6i		−	1.62464i	−0.583212	−	0.812320i	$-0.698204\pi$
$179$		−	9.31786e6i		−	1.62464i	0.583212	−	0.812320i	$-0.301796\pi$
$180$		0			0
$181$	1.28997e6			0.217542			0.108771	−	0.994067i	$-0.465308\pi$
$181$	1.28997e6			0.217542			0.108771	+	0.994067i	$0.465308\pi$
$182$	−2.24200e6	−	1.29442e6i	−0.371896	−	0.214714i
$183$		0			0
$184$	1.23825e6	+	2.14472e6i	0.198772	+	0.344284i
$185$	3.64184e6	−	2.10262e6i	0.575182	−	0.332082i
$186$		0			0
$187$	−4.07944e6	+	7.06580e6i	−0.623844	+	1.08053i
$188$		−	488157.i		−	0.0734659i
$189$		0			0
$190$	−1.99680e6			−0.291121
$191$	6.26560e6	+	3.61745e6i	0.899214	+	0.519161i	0.876945	−	0.480591i	$-0.159578\pi$
$191$	6.26560e6	+	3.61745e6i	0.899214	+	0.519161i	0.0222687	+	0.999752i	$0.492911\pi$
$192$		0			0
$193$	2.33819e6	+	4.04986e6i	0.325243	+	0.563337i	0.981561	−	0.191147i	$-0.0612207\pi$
$193$	2.33819e6	+	4.04986e6i	0.325243	+	0.563337i	−0.656319	+	0.754484i	$0.727887\pi$
$194$	−3.11557e6	+	1.79877e6i	−0.426709	+	0.246361i
$195$		0			0
$196$	1.96227e6	−	3.39875e6i	0.260610	−	0.451389i
$197$			2.50022e6i			0.327024i	0.986541	+	0.163512i	$0.0522822\pi$
$197$			2.50022e6i			0.327024i	−0.986541	+	0.163512i	$0.947718\pi$
$198$		0			0
$199$	−3.28474e6			−0.416814			−0.208407	−	0.978042i	$-0.566828\pi$
$199$	−3.28474e6			−0.416814			−0.208407	+	0.978042i	$0.566828\pi$
$200$	−2.12237e6	−	1.22535e6i	−0.265296	−	0.153169i
$201$		0			0
$202$	742362.	+	1.28581e6i	0.0900662	+	0.155999i
$203$	−963088.	+	556039.i	−0.115127	+	0.0664687i
$204$		0			0
$205$	818147.	−	1.41707e6i	0.0949663	−	0.164486i
$206$			466555.i			0.0533704i
$207$		0			0
$208$	−956008.			−0.106236
$209$	−6.74859e6	−	3.89630e6i	−0.739220	−	0.426789i
$210$		0			0
$211$	−834440.	−	1.44529e6i	−0.0888276	−	0.153854i	0.818188	−	0.574950i	$-0.194979\pi$
$211$	−834440.	−	1.44529e6i	−0.0888276	−	0.153854i	−0.907016	+	0.421097i	$0.861645\pi$
$212$	6.55660e6	−	3.78545e6i	0.688131	−	0.397293i
$213$		0			0
$214$	2.93093e6	−	5.07652e6i	0.299064	−	0.517994i
$215$		−	3.15841e6i		−	0.317800i
$216$		0			0
$217$	1.67280e7			1.63706
$218$	2.05766e6	+	1.18799e6i	0.198611	+	0.114668i
$219$		0			0
$220$	737054.	+	1.27661e6i	0.0692199	+	0.119892i
$221$	−6.54143e6	+	3.77669e6i	−0.606032	+	0.349893i
$222$		0			0
$223$	5.65363e6	−	9.79237e6i	0.509815	−	0.883025i	−0.490121	−	0.871655i	$-0.663047\pi$
$223$	5.65363e6	−	9.79237e6i	0.509815	−	0.883025i	0.999935	−	0.0113705i	$-0.00361941\pi$
$224$		−	2.83951e6i		−	0.252639i
$225$		0			0
$226$	8.65340e6			0.749655
$227$	−1.32731e7	−	7.66322e6i	−1.13473	−	0.655139i	−0.189613	−	0.981859i	$-0.560723\pi$
$227$	−1.32731e7	−	7.66322e6i	−1.13473	−	0.655139i	−0.945121	+	0.326720i	$0.894057\pi$
$228$		0			0
$229$	−635525.	−	1.10076e6i	−0.0529208	−	0.0916615i	0.838351	−	0.545130i	$-0.183520\pi$
$229$	−635525.	−	1.10076e6i	−0.0529208	−	0.0916615i	−0.891272	+	0.453469i	$0.850186\pi$
$230$	3.06160e6	−	1.76762e6i	0.251632	−	0.145280i
$231$		0			0
$232$	−205334.	+	355650.i	−0.0164436	+	0.0284812i
$233$		−	1.45867e6i		−	0.115316i	−0.998336	−	0.0576578i	$-0.981637\pi$
$233$		−	1.45867e6i		−	0.115316i	0.998336	−	0.0576578i	$-0.0183632\pi$
$234$		0			0
$235$	−696848.			−0.0536951
$236$	7.10049e6	+	4.09947e6i	0.540197	+	0.311883i
$237$		0			0
$238$	−1.12174e7	−	1.94292e7i	−0.832076	−	1.44120i
$239$	−4.35188e6	+	2.51256e6i	−0.318774	+	0.184044i	−0.650846	−	0.759210i	$-0.725586\pi$
$239$	−4.35188e6	+	2.51256e6i	−0.318774	+	0.184044i	0.332072	+	0.943254i	$0.392252\pi$
$240$		0			0
$241$	−2.56745e6	+	4.44695e6i	−0.183421	+	0.317695i	−0.943043	−	0.332670i	$-0.892051\pi$
$241$	−2.56745e6	+	4.44695e6i	−0.183421	+	0.317695i	0.759622	+	0.650365i	$0.225384\pi$
$242$		−	4.26869e6i		−	0.301196i
$243$		0			0
$244$	−1.27485e6			−0.0877589
$245$	−4.85174e6	−	2.80116e6i	−0.329913	−	0.190475i
$246$		0			0
$247$	−3.60714e6	−	6.24775e6i	−0.239371	−	0.414603i
$248$	5.34971e6	−	3.08865e6i	0.350732	−	0.202495i
$249$		0			0
$250$	−3.76799e6	+	6.52636e6i	−0.241152	+	0.417687i
$251$			1.72705e6i			0.109216i	0.998508	+	0.0546078i	$0.0173909\pi$
$251$			1.72705e6i			0.109216i	−0.998508	+	0.0546078i	$0.982609\pi$
$252$		0			0
$253$	1.37964e7			0.851930
$254$	−4.65044e6	−	2.68493e6i	−0.283787	−	0.163845i
$255$		0			0
$256$	−524288.	−	908093.i	−0.0312500	−	0.0541266i
$257$	1.14470e7	−	6.60890e6i	0.674358	−	0.389341i	−0.123368	−	0.992361i	$-0.539369\pi$
$257$	1.14470e7	−	6.60890e6i	0.674358	−	0.389341i	0.797726	+	0.603020i	$0.206036\pi$
$258$		0			0
$259$	−2.25632e7	+	3.90806e7i	−1.29868	+	2.24937i
$260$			1.36471e6i			0.0776462i
$261$		0			0
$262$	5.18767e6			0.288449
$263$	1.03590e7	+	5.98077e6i	0.569444	+	0.328768i	0.756927	−	0.653499i	$-0.226700\pi$
$263$	1.03590e7	+	5.98077e6i	0.569444	+	0.328768i	−0.187483	+	0.982268i	$0.560033\pi$
$264$		0			0
$265$	−5.40376e6	−	9.35959e6i	−0.290375	−	0.502944i
$266$	1.85569e7	−	1.07138e7i	0.985963	−	0.569246i
$267$		0			0
$268$	5.12654e6	−	8.87942e6i	0.266330	−	0.461297i
$269$			210238.i			0.0108007i	0.999985	+	0.00540037i	$0.00171900\pi$
$269$			210238.i			0.0108007i	−0.999985	+	0.00540037i	$0.998281\pi$
$270$		0			0
$271$	−1.71422e6			−0.0861309			−0.0430654	−	0.999072i	$-0.513712\pi$
$271$	−1.71422e6			−0.0861309			−0.0430654	+	0.999072i	$0.513712\pi$
$272$	−7.17481e6	−	4.14238e6i	−0.356536	−	0.205846i
$273$		0			0
$274$	1.34974e6	+	2.33782e6i	0.0656143	+	0.113647i
$275$	−1.18235e7	+	6.82630e6i	−0.568523	+	0.328237i
$276$		0			0
$277$	−7.34449e6	+	1.27210e7i	−0.345559	+	0.598526i	−0.985455	−	0.169936i	$-0.945644\pi$
$277$	−7.34449e6	+	1.27210e7i	−0.345559	+	0.598526i	0.639896	+	0.768461i	$0.278977\pi$
$278$			2.31055e7i			1.07543i
$279$		0			0
$280$	−4.05342e6			−0.184649
$281$	1.13328e7	+	6.54299e6i	0.510761	+	0.294888i	0.733147	−	0.680071i	$-0.238051\pi$
$281$	1.13328e7	+	6.54299e6i	0.510761	+	0.294888i	−0.222385	+	0.974959i	$0.571384\pi$
$282$		0			0
$283$	−1.52840e6	−	2.64726e6i	−0.0674338	−	0.116799i	0.830337	−	0.557261i	$-0.188148\pi$
$283$	−1.52840e6	−	2.64726e6i	−0.0674338	−	0.116799i	−0.897771	+	0.440463i	$0.854814\pi$
$284$	−1.12124e7	+	6.47349e6i	−0.489490	+	0.282607i
$285$		0			0
$286$	−2.66292e6	+	4.61231e6i	−0.113831	+	0.197161i
$287$			1.75591e7i			0.742773i
$288$		0			0
$289$	−4.13200e7			−1.71186
$290$	507692.	+	293116.i	0.0208164	+	0.0120184i
$291$		0			0
$292$	6.29951e6	+	1.09111e7i	0.253022	+	0.438247i
$293$	−2.54752e7	+	1.47081e7i	−1.01278	+	0.584729i	−0.912005	−	0.410180i	$-0.865466\pi$
$293$	−2.54752e7	+	1.47081e7i	−1.01278	+	0.584729i	−0.100776	+	0.994909i	$0.532133\pi$
$294$		0			0
$295$	5.85202e6	−	1.01360e7i	0.227950	−	0.394821i
$296$			1.66643e7i			0.642557i
$297$		0			0
$298$	2.08177e7			0.786653
$299$	1.10613e7	+	6.38626e6i	0.413803	+	0.238909i
$300$		0			0
$301$	1.69465e7	+	2.93521e7i	0.621412	+	1.07632i
$302$	3.27000e6	−	1.88793e6i	0.118721	−	0.0685434i
$303$		0			0
$304$	3.95641e6	−	6.85270e6i	0.140825	−	0.243916i
$305$			1.81986e6i			0.0641415i
$306$		0			0
$307$	3.82307e7			1.32129			0.660643	−	0.750700i	$-0.270284\pi$
$307$	3.82307e7			1.32129			0.660643	+	0.750700i	$0.270284\pi$
$308$	−1.36994e7	−	7.90933e6i	−0.468865	−	0.270700i
$309$		0			0
$310$	−4.40908e6	−	7.63674e6i	−0.148000	−	0.256344i
$311$	638095.	−	368404.i	0.0212131	−	0.0122474i	−0.489356	−	0.872084i	$-0.662768\pi$
$311$	638095.	−	368404.i	0.0212131	−	0.0122474i	0.510569	+	0.859837i	$0.329435\pi$
$312$		0			0
$313$	7.12766e6	−	1.23455e7i	0.232442	−	0.402601i	−0.726084	−	0.687605i	$-0.758662\pi$
$313$	7.12766e6	−	1.23455e7i	0.232442	−	0.402601i	0.958526	+	0.285005i	$0.0919952\pi$
$314$			8.52579e6i			0.275388i
$315$		0			0
$316$	−2.87478e7			−0.911052
$317$	4.59946e7	+	2.65550e7i	1.44387	+	0.833621i	0.998105	−	0.0615279i	$-0.0195973\pi$
$317$	4.59946e7	+	2.65550e7i	1.44387	+	0.833621i	0.445768	+	0.895149i	$0.352931\pi$
$318$		0			0
$319$	1.14390e6	+	1.98129e6i	0.0352383	+	0.0610346i
$320$	−1.29631e6	+	748425.i	−0.0395602	+	0.0228401i
$321$		0			0
$322$	−1.89683e7	+	3.28541e7i	−0.568147	+	0.984060i
$323$		−	6.25189e7i		−	1.85526i
$324$		0			0
$325$	−1.26394e7			−0.368194
$326$	−2.89434e7	−	1.67105e7i	−0.835405	−	0.482321i
$327$		0			0
$328$	3.24211e6	+	5.61550e6i	0.0918769	+	0.159135i
$329$	6.47603e6	−	3.73894e6i	0.181853	−	0.104993i
$330$		0			0
$331$	2.54781e7	−	4.41293e7i	0.702559	−	1.21687i	−0.265006	−	0.964247i	$-0.585374\pi$
$331$	2.54781e7	−	4.41293e7i	0.702559	−	1.21687i	0.967565	−	0.252621i	$-0.0812927\pi$
$332$		−	5.72422e6i		−	0.156424i
$333$		0			0
$334$	−1.52269e7			−0.408669
$335$	−1.26754e7	−	7.31817e6i	−0.337154	−	0.194656i
$336$		0			0
$337$	−2.71146e7	−	4.69638e7i	−0.708457	−	1.22708i	−0.965430	−	0.260664i	$-0.916058\pi$
$337$	−2.71146e7	−	4.69638e7i	−0.708457	−	1.22708i	0.256973	−	0.966419i	$-0.417275\pi$
$338$	1.93764e7	−	1.11870e7i	0.501792	−	0.289710i
$339$		0			0
$340$	−5.91328e6	+	1.02421e7i	−0.150450	+	0.260587i
$341$		−	3.44132e7i		−	0.867885i
$342$		0			0
$343$	2.44751e6			0.0606517
$344$	1.08392e7	+	6.25800e6i	0.266269	+	0.153730i
$345$		0			0
$346$	1.79486e7	+	3.10879e7i	0.433314	+	0.750522i
$347$	1.79173e7	−	1.03446e7i	0.428829	−	0.247584i	−0.270019	−	0.962855i	$-0.587030\pi$
$347$	1.79173e7	−	1.03446e7i	0.428829	−	0.247584i	0.698848	+	0.715271i	$0.253697\pi$
$348$		0			0
$349$	1.72770e7	−	2.99246e7i	0.406435	−	0.703967i	−0.588052	−	0.808823i	$-0.700105\pi$
$349$	1.72770e7	−	2.99246e7i	0.406435	−	0.703967i	0.994487	+	0.104857i	$0.0334383\pi$
$350$		−	3.75412e7i		−	0.875597i
$351$		0			0
$352$	−5.84152e6			−0.133936
$353$	−6.98774e7	−	4.03437e7i	−1.58859	−	0.917174i	−0.993539	−	0.113488i	$-0.963798\pi$
$353$	−6.98774e7	−	4.03437e7i	−1.58859	−	0.917174i	−0.595053	−	0.803687i	$-0.702869\pi$
$354$		0			0
$355$	9.24095e6	+	1.60058e7i	0.206553	+	0.357760i
$356$	−2.29035e7	+	1.32233e7i	−0.507635	+	0.293083i
$357$		0			0
$358$	2.63549e7	−	4.56480e7i	0.574397	−	0.994885i
$359$		−	1.64156e7i		−	0.354792i	−0.984140	−	0.177396i	$-0.943233\pi$
$359$		−	1.64156e7i		−	0.354792i	0.984140	−	0.177396i	$-0.0567674\pi$
$360$		0			0
$361$	1.26662e7			0.269231
$362$	6.31954e6	+	3.64859e6i	0.133217	+	0.0769129i
$363$		0			0
$364$	−7.32235e6	−	1.26827e7i	−0.151826	−	0.262970i
$365$	1.55756e7	−	8.99259e6i	0.320307	−	0.184930i
$366$		0			0
$367$	2.52891e7	−	4.38021e7i	0.511606	−	0.886128i	−0.488303	−	0.872674i	$-0.662384\pi$
$367$	2.52891e7	−	4.38021e7i	0.511606	−	0.886128i	0.999909	−	0.0134538i	$-0.00428259\pi$
$368$			1.40092e7i			0.281107i
$369$		0			0
$370$	2.37884e7			0.469634
$371$	1.00438e8	+	5.79878e7i	1.96687	+	1.13557i
$372$		0			0
$373$	−7.01064e6	−	1.21428e7i	−0.135092	−	0.233987i	0.790540	−	0.612410i	$-0.209800\pi$
$373$	−7.01064e6	−	1.21428e7i	−0.135092	−	0.233987i	−0.925633	+	0.378423i	$0.876466\pi$
$374$	−3.99702e7	+	2.30768e7i	−0.764050	+	0.441124i
$375$		0			0
$376$	1.38072e6	−	2.39147e6i	0.0259741	−	0.0449885i
$377$			2.11801e6i			0.0395280i
$378$		0			0
$379$	−1.76705e7			−0.324587			−0.162294	−	0.986743i	$-0.551889\pi$
$379$	−1.76705e7			−0.324587			−0.162294	+	0.986743i	$0.551889\pi$
$380$	−9.78228e6	−	5.64780e6i	−0.178275	−	0.102927i
$381$		0			0
$382$	2.04634e7	+	3.54436e7i	0.367102	+	0.635840i
$383$	−7.86852e7	+	4.54289e7i	−1.40054	+	0.808605i	−0.994448	−	0.105226i	$-0.966444\pi$
$383$	−7.86852e7	+	4.54289e7i	−1.40054	+	0.808605i	−0.406096	+	0.913830i	$0.633110\pi$
$384$		0			0
$385$	−1.12906e7	+	1.95559e7i	−0.197850	+	0.342686i
$386$			2.64536e7i			0.459962i
$387$		0			0
$388$	−2.03508e7			−0.348406
$389$	−7.01566e7	−	4.05049e7i	−1.19184	−	0.688112i	−0.233120	−	0.972448i	$-0.574894\pi$
$389$	−7.01566e7	−	4.05049e7i	−1.19184	−	0.688112i	−0.958725	+	0.284336i	$0.908227\pi$
$390$		0			0
$391$	5.53433e7	+	9.58573e7i	0.925837	+	1.60360i
$392$	1.92263e7	−	1.11003e7i	0.319181	−	0.184279i
$393$		0			0
$394$	−7.07169e6	+	1.22485e7i	−0.115620	+	0.200260i
$395$			4.10377e7i			0.665873i
$396$		0			0
$397$	−5.78058e7			−0.923846			−0.461923	−	0.886920i	$-0.652840\pi$
$397$	−5.78058e7			−0.923846			−0.461923	+	0.886920i	$0.652840\pi$
$398$	−1.60919e7	−	9.29066e6i	−0.255245	−	0.147366i
$399$		0			0
$400$	−6.93162e6	−	1.20059e7i	−0.108307	−	0.187592i
$401$	1.06341e8	−	6.13960e7i	1.64918	−	0.952153i	0.671778	−	0.740753i	$-0.265531\pi$
$401$	1.06341e8	−	6.13960e7i	1.64918	−	0.952153i	0.977400	−	0.211400i	$-0.0678023\pi$
$402$		0			0
$403$	1.59296e7	−	2.75910e7i	0.243383	−	0.421552i
$404$			8.39887e6i			0.127373i
$405$		0			0
$406$	−6.29086e6			−0.0940009
$407$	8.03976e7	+	4.64176e7i	1.19250	+	0.688493i
$408$		0			0
$409$	9.03706e6	+	1.56527e7i	0.132086	+	0.228780i	0.924481	−	0.381229i	$-0.124499\pi$
$409$	9.03706e6	+	1.56527e7i	0.132086	+	0.228780i	−0.792394	+	0.610009i	$0.791166\pi$
$410$	8.01617e6	−	4.62814e6i	0.116309	−	0.0671513i
$411$		0			0
$412$	−1.31962e6	+	2.28564e6i	−0.0188693	+	0.0326826i
$413$			1.25596e8i			1.78290i
$414$		0			0
$415$	−8.17137e6			−0.114327
$416$	−4.68347e6	−	2.70400e6i	−0.0650560	−	0.0375601i
$417$		0			0
$418$	−2.20408e7	−	3.81758e7i	−0.301785	−	0.522708i
$419$	8.72440e6	−	5.03704e6i	0.118602	−	0.0684751i	−0.439525	−	0.898230i	$-0.644853\pi$
$419$	8.72440e6	−	5.03704e6i	0.118602	−	0.0684751i	0.558128	+	0.829755i	$0.311520\pi$
$420$		0			0
$421$	−7.04278e7	+	1.21985e8i	−0.943839	+	1.63478i	−0.185780	+	0.982591i	$0.559481\pi$
$421$	−7.04278e7	+	1.21985e8i	−0.943839	+	1.63478i	−0.758059	+	0.652186i	$0.773852\pi$
$422$		−	9.44061e6i		−	0.125621i
$423$		0			0
$424$	4.28275e7			0.561857
$425$	−9.48583e7	−	5.47665e7i	−1.23569	−	0.713424i
$426$		0			0
$427$	−9.76448e6	−	1.69126e7i	−0.125420	−	0.217233i
$428$	2.87171e7	−	1.65798e7i	0.366277	−	0.211470i
$429$		0			0
$430$	8.93333e6	−	1.54730e7i	0.112359	−	0.194612i
$431$		−	6.81157e6i		−	0.0850777i	−0.999095	−	0.0425388i	$-0.986455\pi$
$431$		−	6.81157e6i		−	0.0850777i	0.999095	−	0.0425388i	$-0.0135446\pi$
$432$		0			0
$433$	−1.17807e8			−1.45113			−0.725566	−	0.688153i	$-0.758422\pi$
$433$	−1.17807e8			−1.45113			−0.725566	+	0.688153i	$0.758422\pi$
$434$	8.19500e7	+	4.73138e7i	1.00249	+	0.578787i
$435$		0			0
$436$	6.72029e6	+	1.16399e7i	0.0810827	+	0.140439i
$437$	−9.15538e7	+	5.28586e7i	−1.09706	+	0.633391i
$438$		0			0
$439$	−3.55152e7	+	6.15142e7i	−0.419780	+	0.727079i	−0.995917	−	0.0902733i	$-0.971226\pi$
$439$	−3.55152e7	+	6.15142e7i	−0.419780	+	0.727079i	0.576137	+	0.817353i	$0.304559\pi$
$440$			8.33881e6i			0.0978918i
$441$		0			0
$442$	−4.27284e7			−0.494823
$443$	−1.83090e7	−	1.05707e7i	−0.210597	−	0.121588i	0.390992	−	0.920394i	$-0.372132\pi$
$443$	−1.83090e7	−	1.05707e7i	−0.210597	−	0.121588i	−0.601589	+	0.798806i	$0.705465\pi$
$444$		0			0
$445$	1.88764e7	+	3.26949e7i	0.214210	+	0.371022i
$446$	5.53940e7	−	3.19817e7i	0.624393	−	0.360493i
$447$		0			0
$448$	8.03135e6	−	1.39107e7i	0.0893212	−	0.154709i
$449$		−	5.48751e7i		−	0.606228i	−0.952954	−	0.303114i	$-0.901974\pi$
$449$		−	5.48751e7i		−	0.606228i	0.952954	−	0.303114i	$-0.0980263\pi$
$450$		0			0
$451$	3.61230e7			0.393780
$452$	4.23928e7	+	2.44755e7i	0.459068	+	0.265043i
$453$		0			0
$454$	−4.33497e7	−	7.50839e7i	−0.463253	−	0.802378i
$455$	−1.81046e7	+	1.04527e7i	−0.192201	+	0.110967i
$456$		0			0
$457$	9.82826e6	−	1.70230e7i	0.102974	−	0.178356i	−0.809935	−	0.586520i	$-0.800497\pi$
$457$	9.82826e6	−	1.70230e7i	0.102974	−	0.178356i	0.912909	+	0.408164i	$0.133831\pi$
$458$		−	7.19015e6i		−	0.0748413i
$459$		0			0
$460$	1.99983e7			0.205456
$461$	−4.97070e7	−	2.86983e7i	−0.507358	−	0.292923i	0.224389	−	0.974500i	$-0.427961\pi$
$461$	−4.97070e7	−	2.86983e7i	−0.507358	−	0.292923i	−0.731747	+	0.681576i	$0.761295\pi$
$462$		0			0
$463$	−5.06076e7	−	8.76549e7i	−0.509885	−	0.883147i	−0.999934	−	0.0114526i	$-0.996354\pi$
$463$	−5.06076e7	−	8.76549e7i	−0.509885	−	0.883147i	0.490049	−	0.871695i	$-0.336979\pi$
$464$	−2.01186e6	+	1.16155e6i	−0.0201392	+	0.0116274i
$465$		0			0
$466$	4.12573e6	−	7.14597e6i	0.0407702	−	0.0706161i
$467$			1.26426e8i			1.24133i	0.784077	+	0.620663i	$0.213137\pi$
$467$			1.26426e8i			1.24133i	−0.784077	+	0.620663i	$0.786863\pi$
$468$		0			0
$469$	1.57063e8			1.52249
$470$	−3.41384e6	−	1.97098e6i	−0.0328814	−	0.0189841i
$471$		0			0
$472$	2.31901e7	+	4.01665e7i	0.220535	+	0.381977i
$473$	6.03840e7	−	3.48627e7i	0.570609	−	0.329441i
$474$		0			0
$475$	5.23077e7	−	9.05997e7i	0.488073	−	0.845368i
$476$		−	1.26911e8i		−	1.17673i
$477$		0			0
$478$	−2.84264e7			−0.260278
$479$	5.77665e7	+	3.33515e7i	0.525617	+	0.303465i	0.739230	−	0.673453i	$-0.235190\pi$
$479$	5.77665e7	+	3.33515e7i	0.525617	+	0.303465i	−0.213613	+	0.976918i	$0.568523\pi$
$480$		0			0
$481$	4.29728e7	+	7.44310e7i	0.386152	+	0.668835i
$482$	−2.51557e7	+	1.45237e7i	−0.224644	+	0.129699i
$483$		0			0
$484$	1.20737e7	−	2.09122e7i	0.106489	−	0.184444i
$485$			2.90509e7i			0.254645i
$486$		0			0
$487$	6.97650e7			0.604019			0.302009	−	0.953305i	$-0.402343\pi$
$487$	6.97650e7			0.604019			0.302009	+	0.953305i	$0.402343\pi$
$488$	−6.24549e6	−	3.60583e6i	−0.0537411	−	0.0310275i
$489$		0			0
$490$	−1.58457e7	−	2.74456e7i	−0.134686	−	0.233284i
$491$	−9.22974e7	+	5.32879e7i	−0.779731	+	0.450178i	−0.836335	−	0.548219i	$-0.815306\pi$
$491$	−9.22974e7	+	5.32879e7i	−0.779731	+	0.450178i	0.0566037	+	0.998397i	$0.481973\pi$
$492$		0			0
$493$	−9.17734e6	+	1.58956e7i	−0.0765907	+	0.132659i
$494$		−	4.08101e7i		−	0.338522i
$495$		0			0
$496$	3.49441e7			0.286371
$497$	−1.71758e8	−	9.91647e7i	−1.39910	−	0.807770i
$498$		0			0
$499$	−6.75572e7	−	1.17012e8i	−0.543713	−	0.941739i	−0.998687	−	0.0512338i	$-0.983685\pi$
$499$	−6.75572e7	−	1.17012e8i	−0.543713	−	0.941739i	0.454974	−	0.890505i	$-0.349649\pi$
$500$	−3.69186e7	+	2.13150e7i	−0.295349	+	0.170520i
$501$		0			0
$502$	−4.88485e6	+	8.46080e6i	−0.0386136	+	0.0668806i
$503$		−	2.31473e8i		−	1.81885i	−0.415869	−	0.909425i	$-0.636523\pi$
$503$		−	2.31473e8i		−	1.81885i	0.415869	−	0.909425i	$-0.363477\pi$
$504$		0			0
$505$	1.19894e7			0.0930947
$506$	6.75883e7	+	3.90221e7i	0.521699	+	0.301203i
$507$		0			0
$508$	−1.51883e7	−	2.63068e7i	−0.115856	−	0.200668i
$509$	1.13698e8	−	6.56433e7i	0.862179	−	0.497780i	−0.00256205	−	0.999997i	$-0.500816\pi$
$509$	1.13698e8	−	6.56433e7i	0.862179	−	0.497780i	0.864742	+	0.502217i	$0.167482\pi$
$510$		0			0
$511$	−9.64996e7	+	1.67142e8i	−0.723207	+	1.25263i
$512$		−	5.93164e6i		−	0.0441942i
$513$		0			0
$514$	7.47712e7			0.550611
$515$	3.26277e6	+	1.88376e6i	0.0238872	+	0.0137913i
$516$		0			0
$517$	−7.69185e6	−	1.33227e7i	−0.0556620	−	0.0964094i
$518$	−2.21073e8	+	1.27637e8i	−1.59055	+	0.918303i
$519$		0			0
$520$	−3.85998e6	+	6.68568e6i	−0.0274521	+	0.0475484i
$521$			1.14057e8i			0.806509i	0.915088	+	0.403255i	$0.132121\pi$
$521$			1.14057e8i			0.806509i	−0.915088	+	0.403255i	$0.867879\pi$
$522$		0			0
$523$	6.52785e7			0.456315			0.228158	−	0.973624i	$-0.426730\pi$
$523$	6.52785e7			0.456315			0.228158	+	0.973624i	$0.426730\pi$
$524$	2.54143e7	+	1.46730e7i	0.176638	+	0.101982i
$525$		0			0
$526$	3.38324e7	+	5.85994e7i	0.232474	+	0.402657i
$527$	2.39103e8	−	1.38046e8i	1.63363	−	0.943176i
$528$		0			0
$529$	1.95656e7	−	3.38886e7i	0.132168	−	0.228922i
$530$		−	6.11366e7i		−	0.410652i
$531$		0			0
$532$	1.21213e8			0.805035
$533$	2.89618e7	+	1.67211e7i	0.191269	+	0.110429i
$534$		0			0
$535$	−2.36678e7	−	4.09939e7i	−0.154560	−	0.267706i
$536$	5.02296e7	−	2.90001e7i	0.326186	−	0.188324i
$537$		0			0
$538$	−594642.	+	1.02995e6i	−0.00381864	+	0.00661408i
$539$		−	1.23677e8i		−	0.789812i
$540$		0			0
$541$	1.71142e8			1.08085			0.540423	−	0.841394i	$-0.318264\pi$
$541$	1.71142e8			1.08085			0.540423	+	0.841394i	$0.318264\pi$
$542$	−8.39793e6	−	4.84855e6i	−0.0527442	−	0.0304519i
$543$		0			0
$544$	−2.34328e7	−	4.05869e7i	−0.145555	−	0.252109i
$545$	1.66160e7	−	9.59326e6i	0.102645	−	0.0592620i
$546$		0			0
$547$	−2.90478e7	+	5.03122e7i	−0.177481	+	0.307405i	−0.941017	−	0.338359i	$-0.890128\pi$
$547$	−2.90478e7	+	5.03122e7i	−0.177481	+	0.307405i	0.763536	+	0.645765i	$0.223461\pi$
$548$			1.52706e7i			0.0927926i
$549$		0			0
$550$	−7.72308e7			−0.464197
$551$	−1.51820e7	−	8.76532e6i	−0.0907557	−	0.0523978i
$552$		0			0
$553$	−2.20188e8	−	3.81376e8i	−1.30202	−	2.25517i
$554$	−7.19610e7	+	4.15467e7i	−0.423221	+	0.244347i
$555$		0			0
$556$	−6.53523e7	+	1.13193e8i	−0.380221	+	0.658563i
$557$			1.36639e8i			0.790696i	0.918532	+	0.395348i	$0.129376\pi$
$557$			1.36639e8i			0.790696i	−0.918532	+	0.395348i	$0.870624\pi$
$558$		0			0
$559$	6.45509e7			0.369544
$560$	−1.98576e7	−	1.14648e7i	−0.113074	−	0.0652834i
$561$		0			0
$562$	3.70127e7	+	6.41079e7i	0.208517	+	0.361163i
$563$	−2.39951e8	+	1.38536e8i	−1.34461	+	0.776311i	−0.987480	−	0.157743i	$-0.949578\pi$
$563$	−2.39951e8	+	1.38536e8i	−1.34461	+	0.776311i	−0.357130	+	0.934055i	$0.616245\pi$
$564$		0			0
$565$	3.49390e7	−	6.05161e7i	0.193716	−	0.335525i
$566$		−	1.72919e7i		−	0.0953657i
$567$		0			0
$568$	−7.32392e7			−0.399667
$569$	2.10766e8	+	1.21686e8i	1.14410	+	0.660546i	0.947443	−	0.319926i	$-0.103658\pi$
$569$	2.10766e8	+	1.21686e8i	1.14410	+	0.660546i	0.196657	+	0.980472i	$0.436991\pi$
$570$		0			0
$571$	6.95310e7	+	1.20431e8i	0.373483	+	0.646891i	0.990099	−	0.140373i	$-0.0448302\pi$
$571$	6.95310e7	+	1.20431e8i	0.373483	+	0.646891i	−0.616616	+	0.787264i	$0.711497\pi$
$572$	−2.60912e7	+	1.50637e7i	−0.139414	+	0.0804905i
$573$		0			0
$574$	−4.96646e7	+	8.60215e7i	−0.262610	+	0.454853i
$575$			1.85216e8i			0.974262i
$576$		0			0
$577$	−3.45574e8			−1.79893			−0.899464	−	0.436994i	$-0.856043\pi$
$577$	−3.45574e8			−1.79893			−0.899464	+	0.436994i	$0.856043\pi$
$578$	−2.02426e8	−	1.16871e8i	−1.04829	−	0.605232i
$579$		0			0
$580$	1.65812e6	+	2.87194e6i	0.00849828	+	0.0147194i
$581$	7.59392e7	−	4.38435e7i	0.387202	−	0.223551i
$582$		0			0
$583$	1.19294e8	−	2.06623e8i	0.602023	−	1.04273i
$584$			7.12708e7i			0.357827i
$585$		0			0
$586$	−1.66404e8			−0.826932
$587$	1.43696e8	+	8.29627e7i	0.710443	+	0.410174i	0.811225	−	0.584734i	$-0.198801\pi$
$587$	1.43696e8	+	8.29627e7i	0.710443	+	0.410174i	−0.100782	+	0.994909i	$0.532134\pi$
$588$		0			0
$589$	1.31849e8	+	2.28369e8i	0.645253	+	1.11761i
$590$	5.73379e7	−	3.31041e7i	0.279181	−	0.161185i
$591$		0			0
$592$	−4.71337e7	+	8.16380e7i	−0.227178	+	0.393484i
$593$		−	2.87880e8i		−	1.38054i	−0.723553	−	0.690268i	$-0.757492\pi$
$593$		−	2.87880e8i		−	1.38054i	0.723553	−	0.690268i	$-0.242508\pi$
$594$		0			0
$595$	−1.81166e8			−0.860055
$596$	1.01985e8	+	5.88812e7i	0.481724	+	0.278124i
$597$		0			0
$598$	3.61261e7	+	6.25723e7i	0.168934	+	0.292603i
$599$	−3.67511e7	+	2.12182e7i	−0.170997	+	0.0987254i	−0.583056	−	0.812432i	$-0.698143\pi$
$599$	−3.67511e7	+	2.12182e7i	−0.170997	+	0.0987254i	0.412059	+	0.911157i	$0.364810\pi$
$600$		0			0
$601$	8.90001e6	−	1.54153e7i	0.0409984	−	0.0710113i	−0.844798	−	0.535085i	$-0.820279\pi$
$601$	8.90001e6	−	1.54153e7i	0.0409984	−	0.0710113i	0.885796	+	0.464074i	$0.153613\pi$
$602$			1.91727e8i			0.878809i
$603$		0			0
$604$	2.13595e7			0.0969350
$605$	−2.98524e7	−	1.72353e7i	−0.134807	−	0.0778309i
$606$		0			0
$607$	1.72485e8	+	2.98753e8i	0.771232	+	1.33581i	0.936888	+	0.349629i	$0.113692\pi$
$607$	1.72485e8	+	2.98753e8i	0.771232	+	1.33581i	−0.165656	+	0.986184i	$0.552974\pi$
$608$	3.87647e7	−	2.23808e7i	0.172475	−	0.0995785i
$609$		0			0
$610$	−5.14735e6	+	8.91547e6i	−0.0226775	+	0.0392785i
$611$		−	1.42420e7i		−	0.0624378i
$612$		0			0
$613$	1.15533e8			0.501562			0.250781	−	0.968044i	$-0.419313\pi$
$613$	1.15533e8			0.501562			0.250781	+	0.968044i	$0.419313\pi$
$614$	1.87291e8	+	1.08133e8i	0.809119	+	0.467145i
$615$		0			0
$616$	−4.47419e7	−	7.74953e7i	−0.191413	−	0.331538i
$617$	1.99692e8	−	1.15292e8i	0.850168	−	0.490845i	−0.0105398	−	0.999944i	$-0.503355\pi$
$617$	1.99692e8	−	1.15292e8i	0.850168	−	0.490845i	0.860707	+	0.509100i	$0.170022\pi$
$618$		0			0
$619$	−1.43315e8	+	2.48228e8i	−0.604253	+	1.04660i	0.387916	+	0.921695i	$0.373195\pi$
$619$	−1.43315e8	+	2.48228e8i	−0.604253	+	1.04660i	−0.992169	+	0.124902i	$0.960138\pi$
$620$		−	4.98830e7i		−	0.209304i
$621$		0			0
$622$	4.16802e6			0.0173204
$623$	−3.50849e8	−	2.02563e8i	−1.45096	−	0.837713i
$624$		0			0
$625$	−7.53408e7	−	1.30494e8i	−0.308596	−	0.534504i
$626$	6.98365e7	−	4.03201e7i	0.284682	−	0.164361i
$627$		0			0
$628$	−2.41146e7	+	4.17677e7i	−0.0973645	+	0.168640i
$629$			7.44804e8i			2.99288i
$630$		0			0
$631$	−2.03780e8			−0.811098			−0.405549	−	0.914073i	$-0.632920\pi$
$631$	−2.03780e8			−0.811098			−0.405549	+	0.914073i	$0.632920\pi$
$632$	−1.40835e8	−	8.13110e7i	−0.557903	−	0.322105i
$633$		0			0
$634$	1.50218e8	+	2.60185e8i	0.589459	+	1.02097i
$635$	−3.75532e7	+	2.16814e7i	−0.146665	+	0.0846770i
$636$		0			0
$637$	5.72494e7	−	9.91588e7i	0.221489	−	0.383631i
$638$			1.29417e7i			0.0498345i
$639$		0			0
$640$	−8.46746e6			−0.0323008
$641$	4.12801e8	+	2.38331e8i	1.56735	+	0.904910i	0.996476	+	0.0838727i	$0.0267289\pi$
$641$	4.12801e8	+	2.38331e8i	1.56735	+	0.904910i	0.570874	+	0.821038i	$0.306604\pi$
$642$		0			0
$643$	−8.05937e7	−	1.39592e8i	−0.303157	−	0.525084i	0.673692	−	0.739012i	$-0.264707\pi$
$643$	−8.05937e7	−	1.39592e8i	−0.303157	−	0.525084i	−0.976849	+	0.213928i	$0.931374\pi$
$644$	−1.85851e8	+	1.07301e8i	−0.695835	+	0.401741i
$645$		0			0
$646$	1.76830e8	−	3.06279e8i	0.655932	−	1.13611i
$647$		−	3.18171e8i		−	1.17476i	−0.809313	−	0.587378i	$-0.800160\pi$
$647$		−	3.18171e8i		−	1.17476i	0.809313	−	0.587378i	$-0.199840\pi$
$648$		0			0
$649$	2.58380e8			0.945202
$650$	−6.19202e7	−	3.57496e7i	−0.225472	−	0.130176i
$651$		0			0
$652$	−9.45288e7	−	1.63729e8i	−0.341053	−	0.590721i
$653$	−1.55040e8	+	8.95121e7i	−0.556805	+	0.321471i	−0.751862	−	0.659321i	$-0.770844\pi$
$653$	−1.55040e8	+	8.95121e7i	−0.556805	+	0.321471i	0.195057	+	0.980792i	$0.437511\pi$
$654$		0			0
$655$	2.09457e7	−	3.62791e7i	0.0745370	−	0.129102i
$656$			3.66803e7i			0.129934i
$657$		0			0
$658$	4.23013e7			0.148483
$659$	−2.74307e8	−	1.58371e8i	−0.958475	−	0.553376i	−0.0627716	−	0.998028i	$-0.519994\pi$
$659$	−2.74307e8	−	1.58371e8i	−0.958475	−	0.553376i	−0.895703	+	0.444652i	$0.853327\pi$
$660$		0			0
$661$	1.88046e8	+	3.25706e8i	0.651119	+	1.12777i	0.982852	+	0.184398i	$0.0590334\pi$
$661$	1.88046e8	+	3.25706e8i	0.651119	+	1.12777i	−0.331733	+	0.943373i	$0.607633\pi$
$662$	2.49633e8	−	1.44126e8i	0.860456	−	0.496784i
$663$		0			0
$664$	1.61906e7	−	2.80429e7i	0.0553041	−	0.0957895i
$665$		−	1.73033e8i		−	0.588387i
$666$		0			0
$667$	3.10371e7			0.104593
$668$	−7.45961e7	−	4.30681e7i	−0.250257	−	0.144486i
$669$		0			0
$670$	−4.13978e7	−	7.17031e7i	−0.137643	−	0.238404i
$671$	−3.47930e7	+	2.00878e7i	−0.115166	+	0.0664912i
$672$		0			0
$673$	1.18840e8	−	2.05836e8i	0.389867	−	0.675269i	−0.602564	−	0.798070i	$-0.705854\pi$
$673$	1.18840e8	−	2.05836e8i	0.389867	−	0.675269i	0.992431	+	0.122801i	$0.0391877\pi$
$674$		−	3.06767e8i		−	1.00191i
$675$		0			0
$676$	1.26566e8			0.409711
$677$	−3.37474e8	−	1.94841e8i	−1.08761	−	0.627933i	−0.154672	−	0.987966i	$-0.549432\pi$
$677$	−3.37474e8	−	1.94841e8i	−1.08761	−	0.627933i	−0.932940	+	0.360033i	$0.882766\pi$
$678$		0			0
$679$	−1.55873e8	−	2.69979e8i	−0.497921	−	0.862425i
$680$	−5.79380e7	+	3.34505e7i	−0.184263	+	0.106384i
$681$		0			0
$682$	9.73353e7	−	1.68590e8i	0.306844	−	0.531469i
$683$		−	3.91877e8i		−	1.22995i	−0.788546	−	0.614975i	$-0.789166\pi$
$683$		−	3.91877e8i		−	1.22995i	0.788546	−	0.614975i	$-0.210834\pi$
$684$		0			0
$685$	2.17988e7			0.0678206
$686$	1.19903e7	+	6.92261e6i	0.0371414	+	0.0214436i
$687$		0			0
$688$	3.54006e7	+	6.13156e7i	0.108704	+	0.188281i
$689$	1.91289e8	−	1.10441e8i	0.584834	−	0.337654i
$690$		0			0
$691$	1.26455e8	−	2.19026e8i	0.383267	−	0.663838i	−0.608260	−	0.793738i	$-0.708132\pi$
$691$	1.26455e8	−	2.19026e8i	0.383267	−	0.663838i	0.991527	+	0.129900i	$0.0414655\pi$
$692$			2.03065e8i			0.612798i
$693$		0			0
$694$	1.17035e8			0.350137
$695$	1.61584e8	+	9.32908e7i	0.481333	+	0.277897i
$696$		0			0
$697$	1.44905e8	+	2.50983e8i	0.427942	+	0.741217i
$698$	1.69279e8	−	9.77333e7i	0.497780	−	0.287393i
$699$		0			0
$700$	1.06183e8	−	1.83914e8i	0.309570	−	0.536191i
$701$			2.15054e8i			0.624299i	0.950033	+	0.312150i	$0.101049\pi$
$701$			2.15054e8i			0.624299i	−0.950033	+	0.312150i	$0.898951\pi$
$702$		0			0
$703$	−7.11366e8			−2.04751
$704$	−2.86175e7	−	1.65223e7i	−0.0820188	−	0.0473536i
$705$		0			0
$706$	−2.28219e8	−	3.95286e8i	−0.648540	−	1.12330i
$707$	−1.11422e8	+	6.43294e7i	−0.315291	+	0.182033i
$708$		0			0
$709$	7.04509e7	−	1.22025e8i	0.197673	−	0.342380i	−0.750100	−	0.661324i	$-0.769995\pi$
$709$	7.04509e7	−	1.22025e8i	0.197673	−	0.342380i	0.947774	+	0.318944i	$0.103328\pi$
$710$			1.04549e8i			0.292110i
$711$		0			0
$712$	−1.49605e8			−0.414482
$713$	−4.04315e8	−	2.33431e8i	−1.11545	−	0.644007i
$714$		0			0
$715$	2.15036e7	+	3.72453e7i	0.0588292	+	0.101895i
$716$	2.58224e8	−	1.49086e8i	0.703490	−	0.406160i
$717$		0			0
$718$	4.64304e7	−	8.04198e7i	0.125438	−	0.217265i
$719$		−	4.59075e8i		−	1.23508i	−0.786538	−	0.617542i	$-0.788128\pi$
$719$		−	4.59075e8i		−	1.23508i	0.786538	−	0.617542i	$-0.211872\pi$
$720$		0			0
$721$	−4.04293e7			−0.107867
$722$	6.20516e7	+	3.58255e7i	0.164870	+	0.0951877i
$723$		0			0
$724$	2.06395e7	+	3.57487e7i	0.0543856	+	0.0941986i
$725$	−2.65988e7	+	1.53568e7i	−0.0697988	+	0.0402984i
$726$		0			0
$727$	−2.26267e8	+	3.91905e8i	−0.588867	+	1.01995i	0.405514	+	0.914089i	$0.367092\pi$
$727$	−2.26267e8	+	3.91905e8i	−0.588867	+	1.01995i	−0.994381	+	0.105859i	$0.966241\pi$
$728$		−	8.28429e7i		−	0.214714i
$729$		0			0
$730$	1.01740e8			0.261530
$731$	4.84452e8	+	2.79699e8i	1.24022	+	0.716042i
$732$		0			0
$733$	2.37788e8	+	4.11861e8i	0.603779	+	1.04578i	0.992243	+	0.124312i	$0.0396725\pi$
$733$	2.37788e8	+	4.11861e8i	0.603779	+	1.04578i	−0.388464	+	0.921464i	$0.626994\pi$
$734$	2.47782e8	−	1.43057e8i	0.626587	−	0.361760i
$735$		0			0
$736$	−3.96241e7	+	6.86310e7i	−0.0993862	+	0.172142i
$737$		−	3.23113e8i		−	0.807147i
$738$		0			0
$739$	8.91913e7			0.220999			0.110499	−	0.993876i	$-0.464755\pi$
$739$	8.91913e7			0.220999			0.110499	+	0.993876i	$0.464755\pi$
$740$	1.16539e8	+	6.72837e7i	0.287591	+	0.166041i
$741$		0			0
$742$	3.28029e8	+	5.68162e8i	0.802971	+	1.39079i
$743$	−6.30917e8	+	3.64260e8i	−1.53818	+	0.888066i	−0.539230	+	0.842158i	$0.681285\pi$
$743$	−6.30917e8	+	3.64260e8i	−1.53818	+	0.888066i	−0.998946	+	0.0459081i	$0.985382\pi$
$744$		0			0
$745$	8.40534e7	−	1.45585e8i	0.203276	−	0.352085i
$746$		−	7.93163e7i		−	0.191049i
$747$		0			0
$748$	−2.61084e8			−0.623844
$749$	4.39906e8	+	2.53980e8i	1.04692	+	0.604441i
$750$		0			0
$751$	1.79422e8	+	3.10769e8i	0.423601	+	0.733698i	0.996289	−	0.0860756i	$-0.0274327\pi$
$751$	1.79422e8	+	3.10769e8i	0.423601	+	0.733698i	−0.572688	+	0.819773i	$0.694099\pi$
$752$	1.35282e7	−	7.81051e6i	0.0318117	−	0.0183665i
$753$		0			0
$754$	−5.99064e6	+	1.03761e7i	−0.0139752	+	0.0242058i
$755$		−	3.04909e7i		−	0.0708482i
$756$		0			0
$757$	3.38232e8			0.779700			0.389850	−	0.920878i	$-0.372527\pi$
$757$	3.38232e8			0.779700			0.389850	+	0.920878i	$0.372527\pi$
$758$	−8.65675e7	−	4.99798e7i	−0.198768	−	0.114759i
$759$		0			0
$760$	−3.19488e7	−	5.53369e7i	−0.0727803	−	0.126059i
$761$	−5.84127e8	+	3.37246e8i	−1.32542	+	0.765232i	−0.984588	−	0.174892i	$-0.944042\pi$
$761$	−5.84127e8	+	3.37246e8i	−1.32542	+	0.765232i	−0.340833	+	0.940124i	$0.610709\pi$
$762$		0			0
$763$	−1.02945e8	+	1.78306e8i	−0.231757	+	0.401415i
$764$			2.31517e8i			0.519161i
$765$		0			0
$766$	−5.13970e8			−1.14354
$767$	2.07157e8	+	1.19602e8i	0.459107	+	0.265066i
$768$		0			0
$769$	−3.81386e8	−	6.60580e8i	−0.838660	−	1.45260i	−0.891016	−	0.453973i	$-0.850006\pi$
$769$	−3.81386e8	−	6.60580e8i	−0.838660	−	1.45260i	0.0523561	−	0.998628i	$-0.483327\pi$
$770$	−1.10625e8	+	6.38694e7i	−0.242316	+	0.139901i
$771$		0			0
$772$	−7.48220e7	+	1.29595e8i	−0.162621	+	0.281668i
$773$			6.42100e8i			1.39016i	0.718933	+	0.695080i	$0.244631\pi$
$773$			6.42100e8i			1.39016i	−0.718933	+	0.695080i	$0.755369\pi$
$774$		0			0
$775$	4.61997e8			0.992508
$776$	−9.96981e7	−	5.75607e7i	−0.213355	−	0.123180i
$777$		0			0
$778$	−2.29131e8	−	3.96866e8i	−0.486569	−	0.842762i
$779$	−2.39715e8	+	1.38399e8i	−0.507087	+	0.292767i
$780$		0			0
$781$	−2.04004e8	+	3.53346e8i	−0.428239	+	0.741732i
$782$			6.26138e8i			1.30933i
$783$		0			0
$784$	1.25585e8			0.260610
$785$	5.96236e7	+	3.44237e7i	0.123256	+	0.0711621i
$786$		0			0
$787$	−1.70763e8	−	2.95770e8i	−0.350323	−	0.606777i	0.635983	−	0.771703i	$-0.280595\pi$
$787$	−1.70763e8	−	2.95770e8i	−0.350323	−	0.606777i	−0.986306	+	0.164926i	$0.947262\pi$
$788$	−6.92881e7	+	4.00035e7i	−0.141606	+	0.0817560i
$789$		0			0
$790$	−1.16072e8	+	2.01043e8i	−0.235422	+	0.407762i
$791$			7.49861e8i			1.51513i
$792$		0			0
$793$	−3.71940e7			−0.0745852
$794$	−2.83189e8	−	1.63499e8i	−0.565738	−	0.326629i
$795$		0			0
$796$	−5.25559e7	−	9.10295e7i	−0.104204	−	0.180486i
$797$	4.58166e8	−	2.64522e8i	0.904998	−	0.522501i	0.0261795	−	0.999657i	$-0.491666\pi$
$797$	4.58166e8	−	2.64522e8i	0.904998	−	0.522501i	0.878818	+	0.477156i	$0.158333\pi$
$798$		0			0
$799$	6.17106e7	−	1.06886e8i	0.120982	−	0.209546i
$800$		−	7.84223e7i		−	0.153169i
$801$		0			0
$802$	6.94616e8			1.34655
$803$	3.43849e8	+	1.98522e8i	0.664082	+	0.383408i
$804$		0			0
$805$	1.53173e8	+	2.65303e8i	0.293626	+	0.508575i
$806$	1.56078e8	−	9.01117e7i	0.298083	−	0.172098i
$807$		0			0
$808$	−2.37556e7	+	4.11459e7i	−0.0450331	+	0.0779996i
$809$		−	7.38055e8i		−	1.39394i	−0.717102	−	0.696968i	$-0.754532\pi$
$809$		−	7.38055e8i		−	1.39394i	0.717102	−	0.696968i	$-0.245468\pi$
$810$		0			0
$811$	−4.57151e8			−0.857031			−0.428516	−	0.903534i	$-0.640963\pi$
$811$	−4.57151e8			−0.857031			−0.428516	+	0.903534i	$0.640963\pi$
$812$	−3.08188e7	−	1.77933e7i	−0.0575636	−	0.0332344i
$813$		0			0
$814$	2.62578e8	+	4.54798e8i	0.486838	+	0.843228i
$815$	−2.33724e8	+	1.34941e8i	−0.431748	+	0.249270i
$816$		0			0
$817$	−2.67142e8	+	4.62703e8i	−0.489864	+	0.848469i
$818$			1.02243e8i			0.186798i
$819$		0			0
$820$	5.23614e7			0.0949663
$821$	1.21939e8	+	7.04014e7i	0.220350	+	0.127219i	0.606112	−	0.795379i	$-0.292728\pi$
$821$	1.21939e8	+	7.04014e7i	0.220350	+	0.127219i	−0.385762	+	0.922598i	$0.626062\pi$
$822$		0			0
$823$	−1.48682e8	−	2.57524e8i	−0.266721	−	0.461975i	0.701292	−	0.712874i	$-0.252607\pi$
$823$	−1.48682e8	−	2.57524e8i	−0.266721	−	0.461975i	−0.968013	+	0.250899i	$0.919274\pi$
$824$	−1.29295e7	+	7.46487e6i	−0.0231101	+	0.0133426i
$825$		0			0
$826$	−3.55240e8	+	6.15293e8i	−0.630350	+	1.09180i
$827$		−	6.71385e8i		−	1.18701i	−0.804830	−	0.593506i	$-0.797743\pi$
$827$		−	6.71385e8i		−	1.18701i	0.804830	−	0.593506i	$-0.202257\pi$
$828$		0			0
$829$	−4.09596e8			−0.718939			−0.359470	−	0.933157i	$-0.617042\pi$
$829$	−4.09596e8			−0.718939			−0.359470	+	0.933157i	$0.617042\pi$
$830$	−4.00314e7	−	2.31121e7i	−0.0700110	−	0.0404209i
$831$		0			0
$832$	−1.52961e7	−	2.64937e7i	−0.0265590	−	0.0460015i
$833$	8.59310e8	−	4.96123e8i	1.48667	−	0.858329i
$834$		0			0
$835$	−6.14800e7	+	1.06487e8i	−0.105603	+	0.182909i
$836$		−	2.49363e8i		−	0.426789i
$837$		0			0
$838$	5.69876e7			0.0968385
$839$	2.60725e8	+	1.50530e8i	0.441466	+	0.254881i	0.704219	−	0.709982i	$-0.251297\pi$
$839$	2.60725e8	+	1.50530e8i	0.441466	+	0.254881i	−0.262753	+	0.964863i	$0.584630\pi$
$840$		0			0
$841$	−2.94838e8	−	5.10675e8i	−0.495674	−	0.858532i
$842$	−6.90049e8	+	3.98400e8i	−1.15596	+	0.667395i
$843$		0			0
$844$	2.67021e7	−	4.62494e7i	0.0444138	−	0.0769269i
$845$		−	1.80674e8i		−	0.299451i
$846$		0			0
$847$	3.69904e8			0.608749
$848$	2.09811e8	+	1.21135e8i	0.344065	+	0.198646i
$849$		0			0
$850$	−3.09806e8	−	5.36600e8i	−0.504467	−	0.873763i
$851$	1.09070e9	−	6.29718e8i	1.76978	−	1.02178i
$852$		0			0
$853$	1.65403e8	−	2.86486e8i	0.266499	−	0.461590i	−0.701456	−	0.712713i	$-0.747466\pi$
$853$	1.65403e8	−	2.86486e8i	0.266499	−	0.461590i	0.967955	+	0.251122i	$0.0807997\pi$
$854$		−	1.10473e8i		−	0.177370i
$855$		0			0
$856$	1.87580e8			0.299064
$857$	−6.31284e8	−	3.64472e8i	−1.00296	−	0.579057i	−0.0938349	−	0.995588i	$-0.529913\pi$
$857$	−6.31284e8	−	3.64472e8i	−1.00296	−	0.579057i	−0.909122	+	0.416530i	$0.863246\pi$
$858$		0			0
$859$	1.68202e7	+	2.91334e7i	0.0265370	+	0.0459634i	0.878989	−	0.476842i	$-0.158219\pi$
$859$	1.68202e7	+	2.91334e7i	0.0265370	+	0.0459634i	−0.852452	+	0.522806i	$0.824885\pi$
$860$	8.75284e7	−	5.05346e7i	0.137611	−	0.0794499i
$861$		0			0
$862$	1.92660e7	−	3.33698e7i	0.0300795	−	0.0520992i
$863$			3.65765e8i			0.569075i	0.958665	+	0.284537i	$0.0918400\pi$
$863$			3.65765e8i			0.569075i	−0.958665	+	0.284537i	$0.908160\pi$
$864$		0			0
$865$	2.89877e8			0.447884
$866$	−5.77133e8	−	3.33208e8i	−0.888633	−	0.513052i
$867$		0			0
$868$	2.67647e8	+	4.63579e8i	0.409264	+	0.708867i
$869$	−7.84578e8	+	4.52976e8i	−1.19557	+	0.690265i
$870$		0			0
$871$	1.49567e8	−	2.59058e8i	0.226350	−	0.392051i
$872$			7.60314e7i			0.114668i
$873$		0			0
$874$	−5.98027e8			−0.895750
$875$	−5.65541e8	−	3.26516e8i	−0.844190	−	0.487393i
$876$		0			0
$877$	−3.66627e8	−	6.35017e8i	−0.543533	−	0.941426i	−0.998698	−	0.0510192i	$-0.983753\pi$
$877$	−3.66627e8	−	6.35017e8i	−0.543533	−	0.941426i	0.455165	−	0.890407i	$-0.349580\pi$
$878$	−3.47977e8	+	2.00905e8i	−0.514123	+	0.296829i
$879$		0			0
$880$	−2.35857e7	+	4.08517e7i	−0.0346100	+	0.0599462i
$881$			1.64762e8i			0.240951i	0.992716	+	0.120475i	$0.0384419\pi$
$881$			1.64762e8i			0.240951i	−0.992716	+	0.120475i	$0.961558\pi$
$882$		0			0
$883$	4.55533e8			0.661665			0.330832	−	0.943690i	$-0.392671\pi$
$883$	4.55533e8			0.661665			0.330832	+	0.943690i	$0.392671\pi$
$884$	−2.09326e8	−	1.20854e8i	−0.303016	−	0.174946i
$885$		0			0
$886$	−5.97969e7	−	1.03571e8i	−0.0859760	−	0.148915i
$887$	9.00541e8	−	5.19928e8i	1.29043	−	0.745027i	0.311696	−	0.950182i	$-0.399103\pi$
$887$	9.00541e8	−	5.19928e8i	1.29043	−	0.745027i	0.978730	+	0.205155i	$0.0657697\pi$
$888$		0			0
$889$	2.32663e8	−	4.02984e8i	0.331148	−	0.573564i
$890$			2.13562e8i			0.302938i
$891$		0			0
$892$	3.61832e8			0.509815
$893$	1.02087e8	+	5.89401e7i	0.143356	+	0.0827669i
$894$		0			0
$895$	−2.12821e8	−	3.68617e8i	−0.296856	−	0.514169i
$896$	7.86909e7	−	4.54322e7i	0.109396	−	0.0631596i
$897$		0			0
$898$	1.55210e8	−	2.68832e8i	0.214334	−	0.371237i
$899$		−	7.74178e7i		−	0.106552i
$900$		0			0
$901$	1.91416e9			2.61700
$902$	1.76966e8	+	1.02171e8i	0.241140	+	0.139222i
$903$		0			0
$904$	1.38454e8	+	2.39810e8i	0.187414	+	0.324610i
$905$	5.10315e7	−	2.94631e7i	0.0688482	−	0.0397495i
$906$		0			0
$907$	3.58121e8	−	6.20284e8i	0.479963	−	0.831321i	−0.519773	−	0.854305i	$-0.673983\pi$
$907$	3.58121e8	−	6.20284e8i	0.479963	−	0.831321i	0.999736	+	0.0229839i	$0.00731665\pi$
$908$		−	4.90446e8i		−	0.655139i
$909$		0			0
$910$	−1.18259e8			−0.156931
$911$	−7.52640e8	−	4.34537e8i	−0.995479	−	0.574740i	−0.0885714	−	0.996070i	$-0.528230\pi$
$911$	−7.52640e8	−	4.34537e8i	−0.995479	−	0.574740i	−0.906907	+	0.421330i	$0.861563\pi$
$912$		0			0
$913$	−9.01961e7	−	1.56224e8i	−0.118516	−	0.205275i
$914$	9.62968e7	−	5.55970e7i	0.126117	−	0.0728137i
$915$		0			0
$916$	2.03368e7	−	3.52244e7i	0.0264604	−	0.0458308i
$917$			4.49538e8i			0.582986i
$918$		0			0
$919$	6.50303e8			0.837855			0.418928	−	0.908020i	$-0.362406\pi$
$919$	6.50303e8			0.837855			0.418928	+	0.908020i	$0.362406\pi$
$920$	9.79712e7	+	5.65637e7i	0.125816	+	0.0726398i
$921$		0			0
$922$	−1.62342e8	−	2.81185e8i	−0.207128	−	0.358756i
$923$	−3.27123e8	+	1.88864e8i	−0.416012	+	0.240185i
$924$		0			0
$925$	−6.23155e8	+	1.07934e9i	−0.787356	+	1.36374i
$926$		−	5.72559e8i		−	0.721087i
$927$		0			0
$928$	−1.31414e7			−0.0164436
$929$	2.94052e8	+	1.69771e8i	0.366755	+	0.211746i	0.672040	−	0.740515i	$-0.265418\pi$
$929$	2.94052e8	+	1.69771e8i	0.366755	+	0.211746i	−0.305285	+	0.952261i	$0.598752\pi$
$930$		0			0
$931$	4.73849e8	+	8.20731e8i	0.587207	+	1.01707i
$932$	4.04237e7	−	2.33387e7i	0.0499331	−	0.0288289i
$933$		0			0
$934$	−3.57587e8	+	6.19359e8i	−0.438875	+	0.760154i
$935$			3.72700e8i			0.455957i
$936$		0			0
$937$	−1.59228e9			−1.93554			−0.967769	−	0.251838i	$-0.918965\pi$
$937$	−1.59228e9			−1.93554			−0.967769	+	0.251838i	$0.918965\pi$
$938$	7.69446e8	+	4.44240e8i	0.932331	+	0.538281i
$939$		0			0
$940$	−1.11496e7	−	1.93116e7i	−0.0134238	−	0.0232506i
$941$	−1.17773e9	+	6.79964e8i	−1.41344	+	0.816051i	−0.995711	−	0.0925206i	$-0.970508\pi$
$941$	−1.17773e9	+	6.79964e8i	−1.41344	+	0.816051i	−0.417730	+	0.908571i	$0.637174\pi$
$942$		0			0
$943$	2.45029e8	−	4.24403e8i	0.292202	−	0.506108i
$944$			2.62366e8i			0.311883i
$945$		0			0
$946$	3.94427e8			0.465900
$947$	−2.77528e8	−	1.60231e8i	−0.326781	−	0.188667i	0.327630	−	0.944806i	$-0.393750\pi$
$947$	−2.77528e8	−	1.60231e8i	−0.326781	−	0.188667i	−0.654411	+	0.756139i	$0.727083\pi$
$948$		0			0
$949$	1.83789e8	+	3.18331e8i	0.215040	+	0.372461i
$950$	5.12509e8	−	2.95897e8i	0.597765	−	0.345120i
$951$		0			0
$952$	3.58958e8	−	6.21734e8i	0.416038	−	0.720599i
$953$		−	6.65905e8i		−	0.769367i	−0.923049	−	0.384683i	$-0.874311\pi$
$953$		−	6.65905e8i		−	0.769367i	0.923049	−	0.384683i	$-0.125689\pi$
$954$		0			0
$955$	3.30492e8			0.379446
$956$	−1.39260e8	−	8.04019e7i	−0.159387	−	0.0920222i
$957$		0			0
$958$	1.88665e8	+	3.26777e8i	0.214582	+	0.371668i
$959$	−2.02584e8	+	1.16962e8i	−0.229694	+	0.132614i
$960$		0			0
$961$	−1.38511e8	+	2.39907e8i	−0.156068	+	0.270317i
$962$			4.86182e8i			0.546101i
$963$		0			0
$964$	−1.64316e8			−0.183421
$965$	1.84998e8	+	1.06809e8i	0.205867	+	0.118857i
$966$		0			0
$967$	−1.79185e8	−	3.10357e8i	−0.198163	−	0.343228i	0.749770	−	0.661698i	$-0.230164\pi$
$967$	−1.79185e8	−	3.10357e8i	−0.198163	−	0.343228i	−0.947933	+	0.318471i	$0.896831\pi$
$968$	1.18298e8	−	6.82991e7i	0.130422	−	0.0752990i
$969$		0			0
$970$	−8.21684e7	+	1.42320e8i	−0.0900304	+	0.155937i
$971$			3.10565e8i			0.339230i	0.985510	+	0.169615i	$0.0542525\pi$
$971$			3.10565e8i			0.339230i	−0.985510	+	0.169615i	$0.945748\pi$
$972$		0			0
$973$	−2.00221e9			−2.17356
$974$	3.41777e8	+	1.97325e8i	0.369884	+	0.213553i
$975$		0			0
$976$	−2.03977e7	−	3.53298e7i	−0.0219397	−	0.0380007i
$977$	1.19157e9	−	6.87955e8i	1.27772	−	0.737694i	0.301295	−	0.953531i	$-0.402581\pi$
$977$	1.19157e9	−	6.87955e8i	1.27772	−	0.737694i	0.976430	+	0.215837i	$0.0692478\pi$
$978$		0			0
$979$	−4.16718e8	+	7.21776e8i	−0.444113	+	0.769227i
$980$		−	1.79274e8i		−	0.190475i
$981$		0			0
$982$	−6.02884e8			−0.636648
$983$	4.88903e8	+	2.82268e8i	0.514709	+	0.297168i	0.734767	−	0.678319i	$-0.237291\pi$
$983$	4.88903e8	+	2.82268e8i	0.514709	+	0.297168i	−0.220058	+	0.975487i	$0.570625\pi$
$984$		0			0
$985$	5.71053e7	+	9.89093e7i	0.0597541	+	0.103497i
$986$	−8.99192e7	+	5.19149e7i	−0.0938040	+	0.0541578i
$987$		0			0
$988$	1.15428e8	−	1.99928e8i	0.119686	−	0.207302i
$989$		−	9.45922e8i		−	0.977836i
$990$		0			0
$991$	1.94100e8			0.199436			0.0997182	−	0.995016i	$-0.468206\pi$
$991$	1.94100e8			0.199436			0.0997182	+	0.995016i	$0.468206\pi$
$992$	1.71191e8	+	9.88369e7i	0.175366	+	0.101248i
$993$		0			0
$994$	−5.60960e8	−	9.71612e8i	−0.571180	−	0.989313i
$995$	−1.29945e8	+	7.50239e7i	−0.131914	+	0.0761606i
$996$		0			0
$997$	−2.08285e7	+	3.60761e7i	−0.0210171	+	0.0364027i	−0.876343	−	0.481688i	$-0.840024\pi$
$997$	−2.08285e7	+	3.60761e7i	−0.0210171	+	0.0364027i	0.855326	+	0.518091i	$0.173357\pi$
$998$		−	7.64322e8i		−	0.768926i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.7.d.a.35.6		12
3.2	odd	2		18.7.d.a.11.2	yes	12
4.3	odd	2		432.7.q.b.305.5		12
9.2	odd	6		162.7.b.c.161.8		12
9.4	even	3		18.7.d.a.5.2	✓	12
9.5	odd	6	inner	54.7.d.a.17.6		12
9.7	even	3		162.7.b.c.161.5		12
12.11	even	2		144.7.q.c.65.3		12
36.23	even	6		432.7.q.b.17.5		12
36.31	odd	6		144.7.q.c.113.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.7.d.a.5.2	✓	12	9.4	even	3
18.7.d.a.11.2	yes	12	3.2	odd	2
54.7.d.a.17.6		12	9.5	odd	6	inner
54.7.d.a.35.6		12	1.1	even	1	trivial
144.7.q.c.65.3		12	12.11	even	2
144.7.q.c.113.3		12	36.31	odd	6
162.7.b.c.161.5		12	9.7	even	3
162.7.b.c.161.8		12	9.2	odd	6
432.7.q.b.17.5		12	36.23	even	6
432.7.q.b.305.5		12	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(4.89898 + 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(39.5602 - 22.8401i) q^{5} +(-245.097 + 424.521i) q^{7} +181.019i q^{8} +O(q^{10})\)	\(q+(4.89898 + 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(39.5602 - 22.8401i) q^{5} +(-245.097 + 424.521i) q^{7} +181.019i q^{8} +258.406 q^{10} +(873.336 + 504.221i) q^{11} +(466.801 + 808.523i) q^{13} +(-2401.45 + 1386.48i) q^{14} +(-512.000 + 886.810i) q^{16} +8090.59i q^{17} -7727.36 q^{19} +(1265.93 + 730.884i) q^{20} +(2852.30 + 4940.34i) q^{22} +(11848.0 - 6840.45i) q^{23} +(-6769.16 + 11724.5i) q^{25} +5281.25i q^{26} -15686.2 q^{28} +(1964.70 + 1134.32i) q^{29} +(-17062.6 - 29553.2i) q^{31} +(-5016.55 + 2896.31i) q^{32} +(-22883.6 + 39635.6i) q^{34} +22392.2i q^{35} +92058.0 q^{37} +(-37856.2 - 21856.3i) q^{38} +(4134.50 + 7161.17i) q^{40} +(31021.6 - 17910.3i) q^{41} +(34570.9 - 59878.5i) q^{43} +32270.1i q^{44} +77390.9 q^{46} +(-13211.1 - 7627.46i) q^{47} +(-61321.0 - 106211. i) q^{49} +(-66323.9 + 38292.1i) q^{50} +(-14937.6 + 25872.7i) q^{52} -236591. i q^{53} +46065.9 q^{55} +(-76846.5 - 44367.4i) q^{56} +(6416.70 + 11114.0i) q^{58} +(221890. - 128108. i) q^{59} +(-19919.6 + 34501.8i) q^{61} -193041. i q^{62} -32768.0 q^{64} +(36933.5 + 21323.6i) q^{65} +(-160204. - 277482. i) q^{67} +(-224213. + 129449. i) q^{68} +(-63334.7 + 109699. i) q^{70} +404593. i q^{71} +393719. q^{73} +(450990. + 260379. i) q^{74} +(-123638. - 214147. i) q^{76} +(-428105. + 247167. i) q^{77} +(-449184. + 778010. i) q^{79} +46776.5i q^{80} +202632. q^{82} +(-154916. - 89441.0i) q^{83} +(184790. + 320066. i) q^{85} +(338724. - 195562. i) q^{86} +(-91273.8 + 158091. i) q^{88} +826458. i q^{89} -457647. q^{91} +(379136. + 218894. i) q^{92} +(-43147.4 - 74733.5i) q^{94} +(-305696. + 176494. i) q^{95} +(-317981. + 550760. i) q^{97} -693768. i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 192 q^{4} - 432 q^{5} + 240 q^{7}+O(q^{10}) \) 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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