LMFDB - Embedded newform 567.3.d.h.244.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,3,Mod(244,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("567.244");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	567.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.4496309892$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 108x^{12} + 4395x^{10} + 83817x^{8} + 766449x^{6} + 3215376x^{4} + 5192667x^{2} + 964467 $ x^14 + 108x^12 + 4395x^10 + 83817x^8 + 766449x^6 + 3215376x^4 + 5192667x^2 + 964467
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			244.3
Root			$2.06788i$ of defining polynomial
Character	$\chi$	$=$	567.244
Dual form			567.3.d.h.244.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.61506 q^{2} +2.83854 q^{4} -3.68512i q^{5} +(-5.61763 - 4.17638i) q^{7} +3.03728 q^{8} +O(q^{10})$	\(q-2.61506 q^{2} +2.83854 q^{4} -3.68512i q^{5} +(-5.61763 - 4.17638i) q^{7} +3.03728 q^{8} +9.63680i q^{10} +13.2613 q^{11} +18.7596i q^{13} +(14.6905 + 10.9215i) q^{14} -19.2968 q^{16} -8.23398i q^{17} +22.6432i q^{19} -10.4604i q^{20} -34.6791 q^{22} -0.738115 q^{23} +11.4199 q^{25} -49.0575i q^{26} +(-15.9459 - 11.8548i) q^{28} +12.2766 q^{29} -33.0617i q^{31} +38.3133 q^{32} +21.5323i q^{34} +(-15.3905 + 20.7016i) q^{35} -9.96860 q^{37} -59.2132i q^{38} -11.1927i q^{40} -26.9933i q^{41} -20.3098 q^{43} +37.6428 q^{44} +1.93021 q^{46} +80.0811i q^{47} +(14.1156 + 46.9228i) q^{49} -29.8638 q^{50} +53.2499i q^{52} +39.0420 q^{53} -48.8695i q^{55} +(-17.0624 - 12.6849i) q^{56} -32.1040 q^{58} -46.5971i q^{59} -40.1315i q^{61} +86.4583i q^{62} -23.0042 q^{64} +69.1313 q^{65} +109.033 q^{67} -23.3725i q^{68} +(40.2470 - 54.1360i) q^{70} +83.8258 q^{71} -37.3200i q^{73} +26.0685 q^{74} +64.2736i q^{76} +(-74.4972 - 55.3844i) q^{77} +98.8329 q^{79} +71.1111i q^{80} +70.5890i q^{82} -143.713i q^{83} -30.3432 q^{85} +53.1113 q^{86} +40.2784 q^{88} -133.114i q^{89} +(78.3474 - 105.385i) q^{91} -2.09517 q^{92} -209.417i q^{94} +83.4427 q^{95} +67.0206i q^{97} +(-36.9132 - 122.706i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{2} + 26 q^{4} + 4 q^{8}+O(q^{10}) $ 14 * q + 2 * q^2 + 26 * q^4 + 4 * q^8	$ 14 q + 2 q^{2} + 26 q^{4} + 4 q^{8} - 4 q^{11} - 34 q^{14} + 42 q^{16} - 14 q^{22} - 4 q^{23} - 28 q^{25} + 10 q^{28} + 38 q^{29} + 168 q^{32} - 132 q^{35} + 18 q^{37} + 66 q^{43} + 54 q^{44} - 20 q^{46} + 38 q^{49} - 196 q^{50} + 260 q^{53} - 332 q^{56} + 34 q^{58} + 36 q^{64} + 102 q^{65} - 68 q^{67} - 102 q^{70} - 166 q^{71} + 616 q^{74} - 334 q^{77} - 146 q^{79} - 78 q^{85} + 340 q^{86} + 74 q^{88} - 192 q^{91} - 606 q^{92} + 360 q^{95} - 538 q^{98}+O(q^{100}) $ 14 * q + 2 * q^2 + 26 * q^4 + 4 * q^8 - 4 * q^11 - 34 * q^14 + 42 * q^16 - 14 * q^22 - 4 * q^23 - 28 * q^25 + 10 * q^28 + 38 * q^29 + 168 * q^32 - 132 * q^35 + 18 * q^37 + 66 * q^43 + 54 * q^44 - 20 * q^46 + 38 * q^49 - 196 * q^50 + 260 * q^53 - 332 * q^56 + 34 * q^58 + 36 * q^64 + 102 * q^65 - 68 * q^67 - 102 * q^70 - 166 * q^71 + 616 * q^74 - 334 * q^77 - 146 * q^79 - 78 * q^85 + 340 * q^86 + 74 * q^88 - 192 * q^91 - 606 * q^92 + 360 * q^95 - 538 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−2.61506			−1.30753			−0.653765	−	0.756698i	$-0.726812\pi$
$2$	−2.61506			−1.30753			−0.653765	+	0.756698i	$0.726812\pi$
$3$		0			0
$3$		0			0
$4$	2.83854			0.709635
$5$		−	3.68512i		−	0.737023i	−0.929623	−	0.368512i	$-0.879868\pi$
$5$		−	3.68512i		−	0.737023i	0.929623	−	0.368512i	$-0.120132\pi$
$6$		0			0
$7$	−5.61763	−	4.17638i	−0.802519	−	0.596626i
$7$	−5.61763	−	4.17638i	−0.802519	−	0.596626i
$8$	3.03728			0.379661
$9$		0			0
$10$			9.63680i			0.963680i
$11$	13.2613			1.20557			0.602787	−	0.797902i	$-0.294057\pi$
$11$	13.2613			1.20557			0.602787	+	0.797902i	$0.294057\pi$
$12$		0			0
$13$			18.7596i			1.44305i	0.692390	+	0.721524i	$0.256558\pi$
$13$			18.7596i			1.44305i	−0.692390	+	0.721524i	$0.743442\pi$
$14$	14.6905	+	10.9215i	1.04932	+	0.780107i
$15$		0			0
$16$	−19.2968			−1.20605
$17$		−	8.23398i		−	0.484352i	−0.970232	−	0.242176i	$-0.922139\pi$
$17$		−	8.23398i		−	0.484352i	0.970232	−	0.242176i	$-0.0778611\pi$
$18$		0			0
$19$			22.6432i			1.19175i	0.803079	+	0.595873i	$0.203194\pi$
$19$			22.6432i			1.19175i	−0.803079	+	0.595873i	$0.796806\pi$
$20$		−	10.4604i		−	0.523018i
$21$		0			0
$22$	−34.6791			−1.57632
$23$	−0.738115			−0.0320919			−0.0160460	−	0.999871i	$-0.505108\pi$
$23$	−0.738115			−0.0320919			−0.0160460	+	0.999871i	$0.505108\pi$
$24$		0			0
$25$	11.4199			0.456797
$26$		−	49.0575i		−	1.88683i
$27$		0			0
$28$	−15.9459	−	11.8548i	−0.569496	−	0.423387i
$29$	12.2766			0.423330			0.211665	−	0.977342i	$-0.432111\pi$
$29$	12.2766			0.423330			0.211665	+	0.977342i	$0.432111\pi$
$30$		0			0
$31$		−	33.0617i		−	1.06651i	−0.845956	−	0.533253i	$-0.820969\pi$
$31$		−	33.0617i		−	1.06651i	0.845956	−	0.533253i	$-0.179031\pi$
$32$	38.3133			1.19729
$33$		0			0
$34$			21.5323i			0.633304i
$35$	−15.3905	+	20.7016i	−0.439727	+	0.591475i
$36$		0			0
$37$	−9.96860			−0.269422			−0.134711	−	0.990885i	$-0.543011\pi$
$37$	−9.96860			−0.269422			−0.134711	+	0.990885i	$0.543011\pi$
$38$		−	59.2132i		−	1.55824i
$39$		0			0
$40$		−	11.1927i		−	0.279819i
$41$		−	26.9933i		−	0.658372i	−0.944265	−	0.329186i	$-0.893226\pi$
$41$		−	26.9933i		−	0.658372i	0.944265	−	0.329186i	$-0.106774\pi$
$42$		0			0
$43$	−20.3098			−0.472321			−0.236160	−	0.971714i	$-0.575889\pi$
$43$	−20.3098			−0.472321			−0.236160	+	0.971714i	$0.575889\pi$
$44$	37.6428			0.855518
$45$		0			0
$46$	1.93021			0.0419612
$47$			80.0811i			1.70385i	0.523661	+	0.851927i	$0.324566\pi$
$47$			80.0811i			1.70385i	−0.523661	+	0.851927i	$0.675434\pi$
$48$		0			0
$49$	14.1156	+	46.9228i	0.288074	+	0.957608i
$50$	−29.8638			−0.597276
$51$		0			0
$52$			53.2499i			1.02404i
$53$	39.0420			0.736641			0.368320	−	0.929699i	$-0.379933\pi$
$53$	39.0420			0.736641			0.368320	+	0.929699i	$0.379933\pi$
$54$		0			0
$55$		−	48.8695i		−	0.888536i
$56$	−17.0624	−	12.6849i	−0.304685	−	0.226516i
$57$		0			0
$58$	−32.1040			−0.553517
$59$		−	46.5971i		−	0.789782i	−0.918728	−	0.394891i	$-0.870782\pi$
$59$		−	46.5971i		−	0.789782i	0.918728	−	0.394891i	$-0.129218\pi$
$60$		0			0
$61$		−	40.1315i		−	0.657894i	−0.944348	−	0.328947i	$-0.893306\pi$
$61$		−	40.1315i		−	0.657894i	0.944348	−	0.328947i	$-0.106694\pi$
$62$			86.4583i			1.39449i
$63$		0			0
$64$	−23.0042			−0.359440
$65$	69.1313			1.06356
$66$		0			0
$67$	109.033			1.62736			0.813682	−	0.581310i	$-0.197460\pi$
$67$	109.033			1.62736			0.813682	+	0.581310i	$0.197460\pi$
$68$		−	23.3725i		−	0.343713i
$69$		0			0
$70$	40.2470	−	54.1360i	0.574957	−	0.773372i
$71$	83.8258			1.18064			0.590322	−	0.807168i	$-0.299001\pi$
$71$	83.8258			1.18064			0.590322	+	0.807168i	$0.299001\pi$
$72$		0			0
$73$		−	37.3200i		−	0.511233i	−0.966778	−	0.255617i	$-0.917722\pi$
$73$		−	37.3200i		−	0.511233i	0.966778	−	0.255617i	$-0.0822785\pi$
$74$	26.0685			0.352277
$75$		0			0
$76$			64.2736i			0.845705i
$77$	−74.4972	−	55.3844i	−0.967496	−	0.719277i
$78$		0			0
$79$	98.8329			1.25105			0.625525	−	0.780204i	$-0.284885\pi$
$79$	98.8329			1.25105			0.625525	+	0.780204i	$0.284885\pi$
$80$			71.1111i			0.888889i
$81$		0			0
$82$			70.5890i			0.860842i
$83$		−	143.713i		−	1.73148i	−0.500494	−	0.865740i	$-0.666848\pi$
$83$		−	143.713i		−	1.73148i	0.500494	−	0.865740i	$-0.333152\pi$
$84$		0			0
$85$	−30.3432			−0.356978
$86$	53.1113			0.617574
$87$		0			0
$88$	40.2784			0.457709
$89$		−	133.114i		−	1.49566i	−0.663887	−	0.747832i	$-0.731095\pi$
$89$		−	133.114i		−	1.49566i	0.663887	−	0.747832i	$-0.268905\pi$
$90$		0			0
$91$	78.3474	−	105.385i	0.860960	−	1.15807i
$92$	−2.09517			−0.0227736
$93$		0			0
$94$		−	209.417i		−	2.22784i
$95$	83.4427			0.878344
$96$		0			0
$97$			67.0206i			0.690934i	0.938431	+	0.345467i	$0.112279\pi$
$97$			67.0206i			0.690934i	−0.938431	+	0.345467i	$0.887721\pi$
$98$	−36.9132	−	122.706i	−0.376665	−	1.25210i
$99$		0			0
$100$	32.4159			0.324159
$101$		−	21.4783i		−	0.212657i	−0.994331	−	0.106328i	$-0.966091\pi$
$101$		−	21.4783i		−	0.212657i	0.994331	−	0.106328i	$-0.0339095\pi$
$102$		0			0
$103$		−	15.0014i		−	0.145644i	−0.997345	−	0.0728222i	$-0.976799\pi$
$103$		−	15.0014i		−	0.145644i	0.997345	−	0.0728222i	$-0.0232006\pi$
$104$			56.9783i			0.547868i
$105$		0			0
$106$	−102.097			−0.963180
$107$	−51.7878			−0.483998			−0.241999	−	0.970276i	$-0.577803\pi$
$107$	−51.7878			−0.483998			−0.241999	+	0.970276i	$0.577803\pi$
$108$		0			0
$109$	141.473			1.29792			0.648960	−	0.760823i	$-0.275204\pi$
$109$	141.473			1.29792			0.648960	+	0.760823i	$0.275204\pi$
$110$			127.797i			1.16179i
$111$		0			0
$112$	108.403	+	80.5911i	0.967881	+	0.719563i
$113$	106.984			0.946760			0.473380	−	0.880858i	$-0.343034\pi$
$113$	106.984			0.946760			0.473380	+	0.880858i	$0.343034\pi$
$114$		0			0
$115$			2.72004i			0.0236525i
$116$	34.8476			0.300410
$117$		0			0
$118$			121.854i			1.03266i
$119$	−34.3883	+	46.2555i	−0.288977	+	0.388701i
$120$		0			0
$121$	54.8625			0.453409
$122$			104.946i			0.860216i
$123$		0			0
$124$		−	93.8469i		−	0.756830i
$125$		−	134.212i		−	1.07369i
$126$		0			0
$127$	−179.059			−1.40991			−0.704956	−	0.709251i	$-0.749033\pi$
$127$	−179.059			−1.40991			−0.704956	+	0.709251i	$0.749033\pi$
$128$	−93.0958			−0.727311
$129$		0			0
$130$	−180.783			−1.39064
$131$			116.644i			0.890411i	0.895428	+	0.445206i	$0.146869\pi$
$131$			116.644i			0.890411i	−0.895428	+	0.445206i	$0.853131\pi$
$132$		0			0
$133$	94.5666	−	127.201i	0.711027	−	0.956399i
$134$	−285.129			−2.12783
$135$		0			0
$136$		−	25.0089i		−	0.183889i
$137$	71.6320			0.522861			0.261430	−	0.965222i	$-0.415806\pi$
$137$	71.6320			0.522861			0.261430	+	0.965222i	$0.415806\pi$
$138$		0			0
$139$		−	217.978i		−	1.56819i	−0.620642	−	0.784094i	$-0.713128\pi$
$139$		−	217.978i		−	1.56819i	0.620642	−	0.784094i	$-0.286872\pi$
$140$	−43.6865	+	58.7624i	−0.312046	+	0.419732i
$141$		0			0
$142$	−219.210			−1.54373
$143$			248.777i			1.73970i
$144$		0			0
$145$		−	45.2406i		−	0.312004i
$146$			97.5941i			0.668453i
$147$		0			0
$148$	−28.2963			−0.191191
$149$	26.4183			0.177304			0.0886520	−	0.996063i	$-0.471744\pi$
$149$	26.4183			0.177304			0.0886520	+	0.996063i	$0.471744\pi$
$150$		0			0
$151$	83.3032			0.551677			0.275838	−	0.961204i	$-0.411045\pi$
$151$	83.3032			0.551677			0.275838	+	0.961204i	$0.411045\pi$
$152$			68.7737i			0.452459i
$153$		0			0
$154$	194.815	+	144.833i	1.26503	+	0.940477i
$155$	−121.836			−0.786039
$156$		0			0
$157$			147.879i			0.941907i	0.882158	+	0.470953i	$0.156090\pi$
$157$			147.879i			0.941907i	−0.882158	+	0.470953i	$0.843910\pi$
$158$	−258.454			−1.63579
$159$		0			0
$160$		−	141.189i		−	0.882431i
$161$	4.14646	+	3.08265i	0.0257544	+	0.0191469i
$162$		0			0
$163$	−80.9615			−0.496696			−0.248348	−	0.968671i	$-0.579888\pi$
$163$	−80.9615			−0.496696			−0.248348	+	0.968671i	$0.579888\pi$
$164$		−	76.6215i		−	0.467204i
$165$		0			0
$166$			375.818i			2.26396i
$167$		−	2.23017i		−	0.0133543i	−0.999978	−	0.00667716i	$-0.997875\pi$
$167$		−	2.23017i		−	0.0133543i	0.999978	−	0.00667716i	$-0.00212542\pi$
$168$		0			0
$169$	−182.923			−1.08238
$170$	79.3492			0.466760
$171$		0			0
$172$	−57.6502			−0.335175
$173$		−	168.938i		−	0.976518i	−0.872699	−	0.488259i	$-0.837632\pi$
$173$		−	168.938i		−	0.976518i	0.872699	−	0.488259i	$-0.162368\pi$
$174$		0			0
$175$	−64.1530	−	47.6940i	−0.366588	−	0.272537i
$176$	−255.902			−1.45399
$177$		0			0
$178$			348.102i			1.95563i
$179$	74.8944			0.418405			0.209202	−	0.977872i	$-0.432913\pi$
$179$	74.8944			0.418405			0.209202	+	0.977872i	$0.432913\pi$
$180$		0			0
$181$		−	1.66857i		−	0.00921864i	−0.999989	−	0.00460932i	$-0.998533\pi$
$181$		−	1.66857i		−	0.00921864i	0.999989	−	0.00460932i	$-0.00146720\pi$
$182$	−204.883	+	275.587i	−1.12573	+	1.51422i
$183$		0			0
$184$	−2.24186			−0.0121840
$185$			36.7354i			0.198570i
$186$		0			0
$187$		−	109.193i		−	0.583922i
$188$			227.314i			1.20911i
$189$		0			0
$190$	−218.208			−1.14846
$191$	120.945			0.633219			0.316609	−	0.948556i	$-0.397456\pi$
$191$	120.945			0.633219			0.316609	+	0.948556i	$0.397456\pi$
$192$		0			0
$193$	202.802			1.05079			0.525393	−	0.850860i	$-0.323918\pi$
$193$	202.802			1.05079			0.525393	+	0.850860i	$0.323918\pi$
$194$		−	175.263i		−	0.903417i
$195$		0			0
$196$	40.0678	+	133.192i	0.204427	+	0.679553i
$197$	−213.013			−1.08129			−0.540643	−	0.841252i	$-0.681819\pi$
$197$	−213.013			−1.08129			−0.540643	+	0.841252i	$0.681819\pi$
$198$		0			0
$199$			200.308i			1.00657i	0.864119	+	0.503287i	$0.167876\pi$
$199$			200.308i			1.00657i	−0.864119	+	0.503287i	$0.832124\pi$
$200$	34.6856			0.173428
$201$		0			0
$202$			56.1671i			0.278055i
$203$	−68.9653	−	51.2717i	−0.339731	−	0.252570i
$204$		0			0
$205$	−99.4733			−0.485236
$206$			39.2295i			0.190434i
$207$		0			0
$208$		−	362.001i		−	1.74039i
$209$			300.278i			1.43674i
$210$		0			0
$211$	−285.767			−1.35435			−0.677173	−	0.735824i	$-0.736795\pi$
$211$	−285.767			−1.35435			−0.677173	+	0.735824i	$0.736795\pi$
$212$	110.822			0.522746
$213$		0			0
$214$	135.428			0.632842
$215$			74.8439i			0.348111i
$216$		0			0
$217$	−138.078	+	185.728i	−0.636306	+	0.855891i
$218$	−369.961			−1.69707
$219$		0			0
$220$		−	138.718i		−	0.630536i
$221$	154.466			0.698942
$222$		0			0
$223$			376.651i			1.68902i	0.535540	+	0.844510i	$0.320108\pi$
$223$			376.651i			1.68902i	−0.535540	+	0.844510i	$0.679892\pi$
$224$	−215.230	−	160.011i	−0.960848	−	0.714335i
$225$		0			0
$226$	−279.769			−1.23792
$227$		−	220.964i		−	0.973409i	−0.873567	−	0.486704i	$-0.838199\pi$
$227$		−	220.964i		−	0.973409i	0.873567	−	0.486704i	$-0.161801\pi$
$228$		0			0
$229$			28.7647i			0.125610i	0.998026	+	0.0628049i	$0.0200046\pi$
$229$			28.7647i			0.125610i	−0.998026	+	0.0628049i	$0.979995\pi$
$230$		−	7.11306i		−	0.0309264i
$231$		0			0
$232$	37.2874			0.160722
$233$	405.664			1.74105			0.870524	−	0.492126i	$-0.163780\pi$
$233$	405.664			1.74105			0.870524	+	0.492126i	$0.163780\pi$
$234$		0			0
$235$	295.108			1.25578
$236$		−	132.268i		−	0.560457i
$237$		0			0
$238$	89.9274	−	120.961i	0.377846	−	0.508239i
$239$	−132.414			−0.554033			−0.277016	−	0.960865i	$-0.589346\pi$
$239$	−132.414			−0.554033			−0.277016	+	0.960865i	$0.589346\pi$
$240$		0			0
$241$		−	82.8584i		−	0.343811i	−0.985113	−	0.171905i	$-0.945008\pi$
$241$		−	82.8584i		−	0.343811i	0.985113	−	0.171905i	$-0.0549923\pi$
$242$	−143.469			−0.592846
$243$		0			0
$244$		−	113.915i		−	0.466865i
$245$	172.916	−	52.0177i	0.705779	−	0.212317i
$246$		0			0
$247$	−424.777			−1.71974
$248$		−	100.418i		−	0.404910i
$249$		0			0
$250$			350.972i			1.40389i
$251$		−	182.888i		−	0.728636i	−0.931275	−	0.364318i	$-0.881302\pi$
$251$		−	182.888i		−	0.728636i	0.931275	−	0.364318i	$-0.118698\pi$
$252$		0			0
$253$	−9.78837			−0.0386892
$254$	468.250			1.84350
$255$		0			0
$256$	335.468			1.31042
$257$			47.5369i			0.184968i	0.995714	+	0.0924842i	$0.0294808\pi$
$257$			47.5369i			0.184968i	−0.995714	+	0.0924842i	$0.970519\pi$
$258$		0			0
$259$	55.9999	+	41.6327i	0.216216	+	0.160744i
$260$	196.232			0.754739
$261$		0			0
$262$		−	305.031i		−	1.16424i
$263$	−409.592			−1.55739			−0.778693	−	0.627406i	$-0.784117\pi$
$263$	−409.592			−1.55739			−0.778693	+	0.627406i	$0.784117\pi$
$264$		0			0
$265$		−	143.874i		−	0.542921i
$266$	−247.297	+	332.638i	−0.929689	+	1.25052i
$267$		0			0
$268$	309.496			1.15484
$269$		−	154.435i		−	0.574108i	−0.957914	−	0.287054i	$-0.907324\pi$
$269$		−	154.435i		−	0.574108i	0.957914	−	0.287054i	$-0.0926759\pi$
$270$		0			0
$271$			62.1999i			0.229520i	0.993393	+	0.114760i	$0.0366099\pi$
$271$			62.1999i			0.229520i	−0.993393	+	0.114760i	$0.963390\pi$
$272$			158.890i			0.584154i
$273$		0			0
$274$	−187.322			−0.683657
$275$	151.443			0.550703
$276$		0			0
$277$	−5.75274			−0.0207680			−0.0103840	−	0.999946i	$-0.503305\pi$
$277$	−5.75274			−0.0207680			−0.0103840	+	0.999946i	$0.503305\pi$
$278$			570.026i			2.05045i
$279$		0			0
$280$	−46.7452	+	62.8767i	−0.166947	+	0.224560i
$281$	252.187			0.897462			0.448731	−	0.893667i	$-0.351876\pi$
$281$	252.187			0.897462			0.448731	+	0.893667i	$0.351876\pi$
$282$		0			0
$283$			135.704i			0.479519i	0.970832	+	0.239760i	$0.0770686\pi$
$283$			135.704i			0.479519i	−0.970832	+	0.239760i	$0.922931\pi$
$284$	237.943			0.837827
$285$		0			0
$286$		−	650.567i		−	2.27471i
$287$	−112.734	+	151.638i	−0.392802	+	0.528356i
$288$		0			0
$289$	221.202			0.765404
$290$			118.307i			0.407955i
$291$		0			0
$292$		−	105.934i		−	0.362789i
$293$			84.1785i			0.287299i	0.989629	+	0.143649i	$0.0458837\pi$
$293$			84.1785i			0.287299i	−0.989629	+	0.143649i	$0.954116\pi$
$294$		0			0
$295$	−171.716			−0.582088
$296$	−30.2775			−0.102289
$297$		0			0
$298$	−69.0854			−0.231830
$299$		−	13.8467i		−	0.0463102i
$300$		0			0
$301$	114.093	+	84.8215i	0.379046	+	0.281799i
$302$	−217.843			−0.721334
$303$		0			0
$304$		−	436.942i		−	1.43731i
$305$	−147.889			−0.484883
$306$		0			0
$307$			155.490i			0.506483i	0.967403	+	0.253242i	$0.0814968\pi$
$307$			155.490i			0.506483i	−0.967403	+	0.253242i	$0.918503\pi$
$308$	−211.463	−	157.211i	−0.686570	−	0.510425i
$309$		0			0
$310$	318.609			1.02777
$311$		−	194.167i		−	0.624331i	−0.950028	−	0.312166i	$-0.898946\pi$
$311$		−	194.167i		−	0.624331i	0.950028	−	0.312166i	$-0.101054\pi$
$312$		0			0
$313$		−	346.766i		−	1.10788i	−0.832557	−	0.553939i	$-0.813124\pi$
$313$		−	346.766i		−	1.10788i	0.832557	−	0.553939i	$-0.186876\pi$
$314$		−	386.713i		−	1.23157i
$315$		0			0
$316$	280.541			0.887789
$317$	69.0607			0.217857			0.108929	−	0.994050i	$-0.465258\pi$
$317$	69.0607			0.217857			0.108929	+	0.994050i	$0.465258\pi$
$318$		0			0
$319$	162.804			0.510356
$320$			84.7730i			0.264916i
$321$		0			0
$322$	−10.8432	−	8.06132i	−0.0336747	−	0.0250352i
$323$	186.443			0.577224
$324$		0			0
$325$			214.233i			0.659180i
$326$	211.719			0.649445
$327$		0			0
$328$		−	81.9862i		−	0.249958i
$329$	334.450	−	449.866i	1.01656	−	1.36737i
$330$		0			0
$331$	−251.642			−0.760246			−0.380123	−	0.924936i	$-0.624118\pi$
$331$	−251.642			−0.760246			−0.380123	+	0.924936i	$0.624118\pi$
$332$		−	407.935i		−	1.22872i
$333$		0			0
$334$			5.83203i			0.0174612i
$335$		−	401.801i		−	1.19940i
$336$		0			0
$337$	281.570			0.835518			0.417759	−	0.908558i	$-0.362816\pi$
$337$	281.570			0.835518			0.417759	+	0.908558i	$0.362816\pi$
$338$	478.355			1.41525
$339$		0			0
$340$	−86.1303			−0.253324
$341$		−	438.441i		−	1.28575i
$342$		0			0
$343$	116.671	−	322.547i	0.340150	−	0.940371i
$344$	−61.6866			−0.179322
$345$		0			0
$346$			441.782i			1.27683i
$347$	−210.142			−0.605596			−0.302798	−	0.953055i	$-0.597921\pi$
$347$	−210.142			−0.605596			−0.302798	+	0.953055i	$0.597921\pi$
$348$		0			0
$349$			73.9547i			0.211905i	0.994371	+	0.105952i	$0.0337891\pi$
$349$			73.9547i			0.211905i	−0.994371	+	0.105952i	$0.966211\pi$
$350$	167.764	+	124.723i	0.479325	+	0.356351i
$351$		0			0
$352$	508.085			1.44342
$353$			324.482i			0.919212i	0.888123	+	0.459606i	$0.152009\pi$
$353$			324.482i			0.919212i	−0.888123	+	0.459606i	$0.847991\pi$
$354$		0			0
$355$		−	308.908i		−	0.870163i
$356$		−	377.850i		−	1.06138i
$357$		0			0
$358$	−195.853			−0.547077
$359$	261.171			0.727495			0.363748	−	0.931498i	$-0.381497\pi$
$359$	261.171			0.727495			0.363748	+	0.931498i	$0.381497\pi$
$360$		0			0
$361$	−151.713			−0.420257
$362$			4.36342i			0.0120537i
$363$		0			0
$364$	222.392	−	299.139i	0.610968	−	0.821809i
$365$	−137.529			−0.376791
$366$		0			0
$367$		−	112.180i		−	0.305668i	−0.988252	−	0.152834i	$-0.951160\pi$
$367$		−	112.180i		−	0.305668i	0.988252	−	0.152834i	$-0.0488399\pi$
$368$	14.2433			0.0387046
$369$		0			0
$370$		−	96.0654i		−	0.259636i
$371$	−219.323	−	163.054i	−0.591168	−	0.439499i
$372$		0			0
$373$	−15.6936			−0.0420740			−0.0210370	−	0.999779i	$-0.506697\pi$
$373$	−15.6936			−0.0420740			−0.0210370	+	0.999779i	$0.506697\pi$
$374$			285.547i			0.763495i
$375$		0			0
$376$			243.229i			0.646886i
$377$			230.304i			0.610885i
$378$		0			0
$379$	197.268			0.520496			0.260248	−	0.965542i	$-0.416196\pi$
$379$	197.268			0.520496			0.260248	+	0.965542i	$0.416196\pi$
$380$	236.855			0.623304
$381$		0			0
$382$	−316.278			−0.827952
$383$			548.135i			1.43116i	0.698530	+	0.715580i	$0.253838\pi$
$383$			548.135i			1.43116i	−0.698530	+	0.715580i	$0.746162\pi$
$384$		0			0
$385$	−204.098	+	274.531i	−0.530124	+	0.713067i
$386$	−530.339			−1.37393
$387$		0			0
$388$			190.241i			0.490311i
$389$	305.510			0.785372			0.392686	−	0.919673i	$-0.371546\pi$
$389$	305.510			0.785372			0.392686	+	0.919673i	$0.371546\pi$
$390$		0			0
$391$			6.07762i			0.0155438i
$392$	42.8731	+	142.518i	0.109370	+	0.363566i
$393$		0			0
$394$	557.043			1.41381
$395$		−	364.211i		−	0.922052i
$396$		0			0
$397$			472.112i			1.18920i	0.804022	+	0.594599i	$0.202689\pi$
$397$			472.112i			1.18920i	−0.804022	+	0.594599i	$0.797311\pi$
$398$		−	523.818i		−	1.31613i
$399$		0			0
$400$	−220.369			−0.550921
$401$	694.513			1.73195			0.865976	−	0.500085i	$-0.166698\pi$
$401$	694.513			1.73195			0.865976	+	0.500085i	$0.166698\pi$
$402$		0			0
$403$	620.224			1.53902
$404$		−	60.9671i		−	0.150909i
$405$		0			0
$406$	180.348	+	134.079i	0.444208	+	0.330243i
$407$	−132.197			−0.324808
$408$		0			0
$409$			295.727i			0.723050i	0.932362	+	0.361525i	$0.117744\pi$
$409$			295.727i			0.723050i	−0.932362	+	0.361525i	$0.882256\pi$
$410$	260.129			0.634460
$411$		0			0
$412$		−	42.5820i		−	0.103354i
$413$	−194.608	+	261.766i	−0.471205	+	0.633815i
$414$		0			0
$415$	−529.598			−1.27614
$416$			718.742i			1.72775i
$417$		0			0
$418$		−	785.245i		−	1.87858i
$419$			220.607i			0.526509i	0.964726	+	0.263254i	$0.0847959\pi$
$419$			220.607i			0.526509i	−0.964726	+	0.263254i	$0.915204\pi$
$420$		0			0
$421$	710.291			1.68715			0.843576	−	0.537010i	$-0.180446\pi$
$421$	710.291			1.68715			0.843576	+	0.537010i	$0.180446\pi$
$422$	747.298			1.77085
$423$		0			0
$424$	118.582			0.279673
$425$		−	94.0314i		−	0.221250i
$426$		0			0
$427$	−167.605	+	225.444i	−0.392517	+	0.527972i
$428$	−147.002			−0.343462
$429$		0			0
$430$		−	195.721i		−	0.455166i
$431$	72.6197			0.168491			0.0842456	−	0.996445i	$-0.473152\pi$
$431$	72.6197			0.168491			0.0842456	+	0.996445i	$0.473152\pi$
$432$		0			0
$433$		−	572.654i		−	1.32253i	−0.750154	−	0.661264i	$-0.770020\pi$
$433$		−	572.654i		−	1.32253i	0.750154	−	0.661264i	$-0.229980\pi$
$434$	361.083	−	485.691i	0.831989	−	1.11910i
$435$		0			0
$436$	401.578			0.921050
$437$		−	16.7133i		−	0.0382454i
$438$		0			0
$439$			446.597i			1.01731i	0.860972	+	0.508653i	$0.169856\pi$
$439$			446.597i			1.01731i	−0.860972	+	0.508653i	$0.830144\pi$
$440$		−	148.430i		−	0.337342i
$441$		0			0
$442$	−403.939			−0.913888
$443$	602.497			1.36004			0.680020	−	0.733194i	$-0.261971\pi$
$443$	602.497			1.36004			0.680020	+	0.733194i	$0.261971\pi$
$444$		0			0
$445$	−490.541			−1.10234
$446$		−	984.966i		−	2.20844i
$447$		0			0
$448$	129.229	+	96.0743i	0.288458	+	0.214452i
$449$	−59.7471			−0.133067			−0.0665335	−	0.997784i	$-0.521194\pi$
$449$	−59.7471			−0.133067			−0.0665335	+	0.997784i	$0.521194\pi$
$450$		0			0
$451$		−	357.966i		−	0.793717i
$452$	303.678			0.671854
$453$		0			0
$454$			577.834i			1.27276i
$455$	−388.355	−	288.719i	−0.853526	−	0.634547i
$456$		0			0
$457$	−711.323			−1.55651			−0.778253	−	0.627951i	$-0.783894\pi$
$457$	−711.323			−1.55651			−0.778253	+	0.627951i	$0.783894\pi$
$458$		−	75.2213i		−	0.164239i
$459$		0			0
$460$			7.72094i			0.0167847i
$461$			1.60977i			0.00349191i	0.999998	+	0.00174596i	$0.000555755\pi$
$461$			1.60977i			0.00349191i	−0.999998	+	0.00174596i	$0.999444\pi$
$462$		0			0
$463$	−42.8502			−0.0925491			−0.0462745	−	0.998929i	$-0.514735\pi$
$463$	−42.8502			−0.0925491			−0.0462745	+	0.998929i	$0.514735\pi$
$464$	−236.899			−0.510559
$465$		0			0
$466$	−1060.84			−2.27647
$467$		−	231.151i		−	0.494969i	−0.968892	−	0.247485i	$-0.920396\pi$
$467$		−	231.151i		−	0.494969i	0.968892	−	0.247485i	$-0.0796040\pi$
$468$		0			0
$469$	−612.510	−	455.365i	−1.30599	−	0.970928i
$470$	−771.726			−1.64197
$471$		0			0
$472$		−	141.529i		−	0.299849i
$473$	−269.335			−0.569418
$474$		0			0
$475$			258.583i			0.544386i
$476$	−97.6125	+	131.298i	−0.205068	+	0.275836i
$477$		0			0
$478$	346.270			0.724415
$479$			246.810i			0.515261i	0.966243	+	0.257631i	$0.0829418\pi$
$479$			246.810i			0.515261i	−0.966243	+	0.257631i	$0.917058\pi$
$480$		0			0
$481$		−	187.007i		−	0.388788i
$482$			216.680i			0.449543i
$483$		0			0
$484$	155.729			0.321755
$485$	246.979			0.509234
$486$		0			0
$487$	−618.473			−1.26996			−0.634982	−	0.772527i	$-0.718993\pi$
$487$	−618.473			−1.26996			−0.634982	+	0.772527i	$0.718993\pi$
$488$		−	121.891i		−	0.249776i
$489$		0			0
$490$	−452.186	+	136.029i	−0.922828	+	0.277611i
$491$	321.323			0.654425			0.327212	−	0.944951i	$-0.393891\pi$
$491$	321.323			0.654425			0.327212	+	0.944951i	$0.393891\pi$
$492$		0			0
$493$		−	101.085i		−	0.205041i
$494$	1110.82			2.24862
$495$		0			0
$496$			637.986i			1.28626i
$497$	−470.903	−	350.089i	−0.947490	−	0.704404i
$498$		0			0
$499$	160.971			0.322587			0.161293	−	0.986906i	$-0.448433\pi$
$499$	160.971			0.322587			0.161293	+	0.986906i	$0.448433\pi$
$500$		−	380.965i		−	0.761931i
$501$		0			0
$502$			478.262i			0.952714i
$503$			941.248i			1.87127i	0.352971	+	0.935634i	$0.385171\pi$
$503$			941.248i			1.87127i	−0.352971	+	0.935634i	$0.614829\pi$
$504$		0			0
$505$	−79.1501			−0.156733
$506$	25.5972			0.0505873
$507$		0			0
$508$	−508.266			−1.00052
$509$		−	474.049i		−	0.931335i	−0.884960	−	0.465667i	$-0.845814\pi$
$509$		−	474.049i		−	0.931335i	0.884960	−	0.465667i	$-0.154186\pi$
$510$		0			0
$511$	−155.863	+	209.650i	−0.305015	+	0.410274i
$512$	−504.886			−0.986105
$513$		0			0
$514$		−	124.312i		−	0.241852i
$515$	−55.2818			−0.107343
$516$		0			0
$517$			1061.98i			2.05412i
$518$	−146.443	−	108.872i	−0.282709	−	0.210178i
$519$		0			0
$520$	209.972			0.403791
$521$		−	179.082i		−	0.343728i	−0.985121	−	0.171864i	$-0.945021\pi$
$521$		−	179.082i		−	0.343728i	0.985121	−	0.171864i	$-0.0549790\pi$
$522$		0			0
$523$			742.307i			1.41932i	0.704542	+	0.709662i	$0.251152\pi$
$523$			742.307i			1.41932i	−0.704542	+	0.709662i	$0.748848\pi$
$524$			331.098i			0.631867i
$525$		0			0
$526$	1071.11			2.03633
$527$	−272.229			−0.516564
$528$		0			0
$529$	−528.455			−0.998970
$530$			376.240i			0.709886i
$531$		0			0
$532$	268.431	−	361.065i	0.504570	−	0.678694i
$533$	506.383			0.950062
$534$		0			0
$535$			190.844i			0.356718i
$536$	331.165			0.617846
$537$		0			0
$538$			403.857i			0.750664i
$539$	187.192	+	622.258i	0.347294	+	1.15447i
$540$		0			0
$541$	−546.499			−1.01016			−0.505082	−	0.863071i	$-0.668538\pi$
$541$	−546.499			−1.01016			−0.505082	+	0.863071i	$0.668538\pi$
$542$		−	162.657i		−	0.300104i
$543$		0			0
$544$		−	315.471i		−	0.579909i
$545$		−	521.345i		−	0.956597i
$546$		0			0
$547$	−384.296			−0.702553			−0.351276	−	0.936272i	$-0.614252\pi$
$547$	−384.296			−0.702553			−0.351276	+	0.936272i	$0.614252\pi$
$548$	203.330			0.371041
$549$		0			0
$550$	−396.033			−0.720060
$551$			277.980i			0.504502i
$552$		0			0
$553$	−555.207	−	412.764i	−1.00399	−	0.746409i
$554$	15.0438			0.0271548
$555$		0			0
$556$		−	618.740i		−	1.11284i
$557$	−314.249			−0.564182			−0.282091	−	0.959388i	$-0.591028\pi$
$557$	−314.249			−0.564182			−0.282091	+	0.959388i	$0.591028\pi$
$558$		0			0
$559$		−	381.004i		−	0.681581i
$560$	296.987	−	399.476i	0.530335	−	0.713350i
$561$		0			0
$562$	−659.484			−1.17346
$563$		−	114.139i		−	0.202734i	−0.994849	−	0.101367i	$-0.967678\pi$
$563$		−	114.139i		−	0.202734i	0.994849	−	0.101367i	$-0.0323216\pi$
$564$		0			0
$565$		−	394.248i		−	0.697784i
$566$		−	354.874i		−	0.626986i
$567$		0			0
$568$	254.603			0.448244
$569$	−356.082			−0.625803			−0.312901	−	0.949786i	$-0.601301\pi$
$569$	−356.082			−0.625803			−0.312901	+	0.949786i	$0.601301\pi$
$570$		0			0
$571$	340.511			0.596342			0.298171	−	0.954512i	$-0.403623\pi$
$571$	340.511			0.596342			0.298171	+	0.954512i	$0.403623\pi$
$572$			706.164i			1.23455i
$573$		0			0
$574$	294.807	−	396.543i	0.513601	−	0.690842i
$575$	−8.42921			−0.0146595
$576$		0			0
$577$			390.835i			0.677356i	0.940902	+	0.338678i	$0.109980\pi$
$577$			390.835i			0.677356i	−0.940902	+	0.338678i	$0.890020\pi$
$578$	−578.456			−1.00079
$579$		0			0
$580$		−	128.417i		−	0.221409i
$581$	−600.200	+	807.326i	−1.03305	+	1.38955i
$582$		0			0
$583$	517.748			0.888075
$584$		−	113.352i		−	0.194095i
$585$		0			0
$586$		−	220.132i		−	0.375652i
$587$			1014.28i			1.72791i	0.503571	+	0.863954i	$0.332019\pi$
$587$			1014.28i			1.72791i	−0.503571	+	0.863954i	$0.667981\pi$
$588$		0			0
$589$	748.621			1.27100
$590$	449.047			0.761097
$591$		0			0
$592$	192.362			0.324937
$593$		−	769.152i		−	1.29705i	−0.761193	−	0.648526i	$-0.775386\pi$
$593$		−	769.152i		−	1.29705i	0.761193	−	0.648526i	$-0.224614\pi$
$594$		0			0
$595$	170.457	+	126.725i	0.286482	+	0.212983i
$596$	74.9894			0.125821
$597$		0			0
$598$			36.2101i			0.0605520i
$599$	−526.826			−0.879509			−0.439754	−	0.898118i	$-0.644934\pi$
$599$	−526.826			−0.879509			−0.439754	+	0.898118i	$0.644934\pi$
$600$		0			0
$601$		−	41.2890i		−	0.0687004i	−0.999410	−	0.0343502i	$-0.989064\pi$
$601$		−	41.2890i		−	0.0687004i	0.999410	−	0.0343502i	$-0.0109362\pi$
$602$	−298.360	−	221.813i	−0.495615	−	0.368461i
$603$		0			0
$604$	236.460			0.391489
$605$		−	202.174i		−	0.334173i
$606$		0			0
$607$			448.326i			0.738592i	0.929312	+	0.369296i	$0.120401\pi$
$607$			448.326i			0.738592i	−0.929312	+	0.369296i	$0.879599\pi$
$608$			867.534i			1.42687i
$609$		0			0
$610$	386.739			0.633999
$611$	−1502.29			−2.45874
$612$		0			0
$613$	1000.80			1.63262			0.816309	−	0.577615i	$-0.196016\pi$
$613$	1000.80			1.63262			0.816309	+	0.577615i	$0.196016\pi$
$614$		−	406.617i		−	0.662242i
$615$		0			0
$616$	−226.269	−	168.218i	−0.367320	−	0.273081i
$617$	177.236			0.287254			0.143627	−	0.989632i	$-0.454123\pi$
$617$	177.236			0.287254			0.143627	+	0.989632i	$0.454123\pi$
$618$		0			0
$619$		−	335.171i		−	0.541472i	−0.962654	−	0.270736i	$-0.912733\pi$
$619$		−	335.171i		−	0.541472i	0.962654	−	0.270736i	$-0.0872670\pi$
$620$	−345.837			−0.557801
$621$		0			0
$622$			507.759i			0.816332i
$623$	−555.936	+	747.787i	−0.892353	+	1.20030i
$624$		0			0
$625$	−209.087			−0.334539
$626$			906.813i			1.44858i
$627$		0			0
$628$			419.762i			0.668410i
$629$			82.0812i			0.130495i
$630$		0			0
$631$	1077.15			1.70705			0.853524	−	0.521053i	$-0.174461\pi$
$631$	1077.15			1.70705			0.853524	+	0.521053i	$0.174461\pi$
$632$	300.184			0.474974
$633$		0			0
$634$	−180.598			−0.284855
$635$			659.853i			1.03914i
$636$		0			0
$637$	−880.254	+	264.804i	−1.38187	+	0.415704i
$638$	−425.741			−0.667306
$639$		0			0
$640$			343.069i			0.536045i
$641$	205.531			0.320641			0.160320	−	0.987065i	$-0.448747\pi$
$641$	205.531			0.320641			0.160320	+	0.987065i	$0.448747\pi$
$642$		0			0
$643$		−	477.945i		−	0.743305i	−0.928372	−	0.371653i	$-0.878791\pi$
$643$		−	477.945i		−	0.743305i	0.928372	−	0.371653i	$-0.121209\pi$
$644$	11.7699	+	8.75023i	0.0182762	+	0.0135873i
$645$		0			0
$646$	−487.561			−0.754738
$647$		−	308.180i		−	0.476322i	−0.971226	−	0.238161i	$-0.923455\pi$
$647$		−	308.180i		−	0.476322i	0.971226	−	0.238161i	$-0.0765446\pi$
$648$		0			0
$649$		−	617.939i		−	0.952141i
$650$		−	560.233i		−	0.861897i
$651$		0			0
$652$	−229.812			−0.352473
$653$	−701.549			−1.07435			−0.537174	−	0.843471i	$-0.680508\pi$
$653$	−701.549			−1.07435			−0.537174	+	0.843471i	$0.680508\pi$
$654$		0			0
$655$	429.846			0.656253
$656$			520.885i			0.794032i
$657$		0			0
$658$	−874.606	+	1176.43i	−1.32919	+	1.78788i
$659$	−725.247			−1.10053			−0.550263	−	0.834991i	$-0.685473\pi$
$659$	−725.247			−1.10053			−0.550263	+	0.834991i	$0.685473\pi$
$660$		0			0
$661$		−	827.849i		−	1.25242i	−0.779655	−	0.626210i	$-0.784605\pi$
$661$		−	827.849i		−	1.25242i	0.779655	−	0.626210i	$-0.215395\pi$
$662$	658.058			0.994045
$663$		0			0
$664$		−	436.497i		−	0.657375i
$665$	−468.750	−	348.489i	−0.704888	−	0.524043i
$666$		0			0
$667$	−9.06152			−0.0135855
$668$		−	6.33043i		−	0.00947670i
$669$		0			0
$670$			1050.73i			1.56826i
$671$		−	532.197i		−	0.793140i
$672$		0			0
$673$	1165.20			1.73136			0.865678	−	0.500601i	$-0.166888\pi$
$673$	1165.20			1.73136			0.865678	+	0.500601i	$0.166888\pi$
$674$	−736.321			−1.09247
$675$		0			0
$676$	−519.235			−0.768099
$677$			295.327i			0.436228i	0.975923	+	0.218114i	$0.0699905\pi$
$677$			295.327i			0.436228i	−0.975923	+	0.218114i	$0.930009\pi$
$678$		0			0
$679$	279.904	−	376.497i	0.412229	−	0.554488i
$680$	−92.1608			−0.135531
$681$		0			0
$682$			1146.55i			1.68116i
$683$	−637.558			−0.933467			−0.466734	−	0.884398i	$-0.654569\pi$
$683$	−637.558			−0.933467			−0.466734	+	0.884398i	$0.654569\pi$
$684$		0			0
$685$		−	263.972i		−	0.385361i
$686$	−305.103	+	843.481i	−0.444756	+	1.22956i
$687$		0			0
$688$	391.915			0.569644
$689$			732.412i			1.06301i
$690$		0			0
$691$		−	734.339i		−	1.06272i	−0.847146	−	0.531360i	$-0.821681\pi$
$691$		−	734.339i		−	1.06272i	0.847146	−	0.531360i	$-0.178319\pi$
$692$		−	479.537i		−	0.692972i
$693$		0			0
$694$	549.534			0.791835
$695$	−803.275			−1.15579
$696$		0			0
$697$	−222.262			−0.318884
$698$		−	193.396i		−	0.277072i
$699$		0			0
$700$	−182.101	−	135.381i	−0.260144	−	0.193402i
$701$	1045.20			1.49101			0.745507	−	0.666498i	$-0.232208\pi$
$701$	1045.20			1.49101			0.745507	+	0.666498i	$0.232208\pi$
$702$		0			0
$703$		−	225.721i		−	0.321082i
$704$	−305.066			−0.433332
$705$		0			0
$706$		−	848.540i		−	1.20190i
$707$	−89.7018	+	120.657i	−0.126877	+	0.170661i
$708$		0			0
$709$	50.1561			0.0707420			0.0353710	−	0.999374i	$-0.488739\pi$
$709$	50.1561			0.0707420			0.0353710	+	0.999374i	$0.488739\pi$
$710$			807.812i			1.13776i
$711$		0			0
$712$		−	404.306i		−	0.567845i
$713$			24.4033i			0.0342262i
$714$		0			0
$715$	916.772			1.28220
$716$	212.591			0.296915
$717$		0			0
$718$	−682.977			−0.951222
$719$			1315.02i			1.82896i	0.404629	+	0.914481i	$0.367401\pi$
$719$			1315.02i			1.82896i	−0.404629	+	0.914481i	$0.632599\pi$
$720$		0			0
$721$	−62.6515	+	84.2722i	−0.0868953	+	0.116882i
$722$	396.738			0.549499
$723$		0			0
$724$		−	4.73632i		−	0.00654187i
$725$	140.198			0.193376
$726$		0			0
$727$		−	810.111i		−	1.11432i	−0.830405	−	0.557160i	$-0.811891\pi$
$727$		−	810.111i		−	1.11432i	0.830405	−	0.557160i	$-0.188109\pi$
$728$	237.963	−	320.083i	0.326873	−	0.439675i
$729$		0			0
$730$	359.646			0.492665
$731$			167.230i			0.228769i
$732$		0			0
$733$		−	100.659i		−	0.137324i	−0.997640	−	0.0686622i	$-0.978127\pi$
$733$		−	100.659i		−	0.137324i	0.997640	−	0.0686622i	$-0.0218731\pi$
$734$			293.358i			0.399670i
$735$		0			0
$736$	−28.2796			−0.0384234
$737$	1445.93			1.96191
$738$		0			0
$739$	422.292			0.571437			0.285719	−	0.958314i	$-0.407768\pi$
$739$	422.292			0.571437			0.285719	+	0.958314i	$0.407768\pi$
$740$			104.275i			0.140912i
$741$		0			0
$742$	573.544	+	426.397i	0.772970	+	0.574659i
$743$	−810.700			−1.09112			−0.545559	−	0.838072i	$-0.683683\pi$
$743$	−810.700			−1.09112			−0.545559	+	0.838072i	$0.683683\pi$
$744$		0			0
$745$		−	97.3544i		−	0.130677i
$746$	41.0397			0.0550130
$747$		0			0
$748$		−	309.950i		−	0.414372i
$749$	290.925	+	216.286i	0.388418	+	0.288766i
$750$		0			0
$751$	398.375			0.530459			0.265230	−	0.964185i	$-0.414552\pi$
$751$	398.375			0.530459			0.265230	+	0.964185i	$0.414552\pi$
$752$		−	1545.31i		−	2.05494i
$753$		0			0
$754$		−	602.258i		−	0.798751i
$755$		−	306.982i		−	0.406599i
$756$		0			0
$757$	730.998			0.965652			0.482826	−	0.875716i	$-0.339610\pi$
$757$	730.998			0.965652			0.482826	+	0.875716i	$0.339610\pi$
$758$	−515.867			−0.680564
$759$		0			0
$760$	253.439			0.333473
$761$			91.5060i			0.120244i	0.998191	+	0.0601222i	$0.0191491\pi$
$761$			91.5060i			0.120244i	−0.998191	+	0.0601222i	$0.980851\pi$
$762$		0			0
$763$	−794.745	−	590.847i	−1.04161	−	0.774373i
$764$	343.307			0.449354
$765$		0			0
$766$		−	1433.40i		−	1.87129i
$767$	874.144			1.13969
$768$		0			0
$769$		−	452.392i		−	0.588286i	−0.955761	−	0.294143i	$-0.904966\pi$
$769$		−	452.392i		−	0.588286i	0.955761	−	0.294143i	$-0.0950341\pi$
$770$	533.728	−	717.915i	0.693153	−	0.932357i
$771$		0			0
$772$	575.661			0.745675
$773$			1138.79i			1.47321i	0.676321	+	0.736607i	$0.263573\pi$
$773$			1138.79i			1.47321i	−0.676321	+	0.736607i	$0.736427\pi$
$774$		0			0
$775$		−	377.562i		−	0.487177i
$776$			203.561i			0.262320i
$777$		0			0
$778$	−798.926			−1.02690
$779$	611.213			0.784612
$780$		0			0
$781$	1111.64			1.42335
$782$		−	15.8933i		−	0.0203240i
$783$		0			0
$784$	−272.387	−	905.462i	−0.347432	−	1.15493i
$785$	544.952			0.694207
$786$		0			0
$787$			291.398i			0.370265i	0.982714	+	0.185132i	$0.0592714\pi$
$787$			291.398i			0.370265i	−0.982714	+	0.185132i	$0.940729\pi$
$788$	−604.647			−0.767319
$789$		0			0
$790$			952.433i			1.20561i
$791$	−600.996	−	446.806i	−0.759793	−	0.564862i
$792$		0			0
$793$	752.852			0.949372
$794$		−	1234.60i		−	1.55491i
$795$		0			0
$796$			568.583i			0.714300i
$797$		−	962.064i		−	1.20711i	−0.797323	−	0.603553i	$-0.793751\pi$
$797$		−	962.064i		−	1.20711i	0.797323	−	0.603553i	$-0.206249\pi$
$798$		0			0
$799$	659.386			0.825264
$800$	437.535			0.546919
$801$		0			0
$802$	−1816.19			−2.26458
$803$		−	494.913i		−	0.616329i
$804$		0			0
$805$	11.3599	−	15.2802i	0.0141117	−	0.0189816i
$806$	−1621.92			−2.01231
$807$		0			0
$808$		−	65.2358i		−	0.0807374i
$809$	681.749			0.842706			0.421353	−	0.906897i	$-0.361555\pi$
$809$	681.749			0.842706			0.421353	+	0.906897i	$0.361555\pi$
$810$		0			0
$811$			1531.25i			1.88810i	0.329801	+	0.944050i	$0.393018\pi$
$811$			1531.25i			1.88810i	−0.329801	+	0.944050i	$0.606982\pi$
$812$	−195.761	−	145.537i	−0.241085	−	0.179233i
$813$		0			0
$814$	345.702			0.424696
$815$			298.352i			0.366076i
$816$		0			0
$817$		−	459.878i		−	0.562886i
$818$		−	773.345i		−	0.945410i
$819$		0			0
$820$	−282.359			−0.344340
$821$	92.6579			0.112860			0.0564299	−	0.998407i	$-0.482028\pi$
$821$	92.6579			0.112860			0.0564299	+	0.998407i	$0.482028\pi$
$822$		0			0
$823$	506.368			0.615271			0.307636	−	0.951504i	$-0.400462\pi$
$823$	506.368			0.615271			0.307636	+	0.951504i	$0.400462\pi$
$824$		−	45.5634i		−	0.0552954i
$825$		0			0
$826$	508.911	−	684.533i	0.616115	−	0.828733i
$827$	−909.882			−1.10022			−0.550110	−	0.835092i	$-0.685414\pi$
$827$	−909.882			−1.10022			−0.550110	+	0.835092i	$0.685414\pi$
$828$		0			0
$829$			162.129i			0.195572i	0.995207	+	0.0977862i	$0.0311761\pi$
$829$			162.129i			0.195572i	−0.995207	+	0.0977862i	$0.968824\pi$
$830$	1384.93			1.66859
$831$		0			0
$832$		−	431.549i		−	0.518689i
$833$	386.361	−	116.228i	0.463819	−	0.139529i
$834$		0			0
$835$	−8.21844			−0.00984244
$836$			852.352i			1.01956i
$837$		0			0
$838$		−	576.901i		−	0.688426i
$839$		−	739.854i		−	0.881828i	−0.897549	−	0.440914i	$-0.854654\pi$
$839$		−	739.854i		−	0.881828i	0.897549	−	0.440914i	$-0.145346\pi$
$840$		0			0
$841$	−690.286			−0.820792
$842$	−1857.45			−2.20600
$843$		0			0
$844$	−811.161			−0.961092
$845$			674.092i			0.797743i
$846$		0			0
$847$	−308.197	−	229.127i	−0.363869	−	0.270516i
$848$	−753.387			−0.888428
$849$		0			0
$850$			245.898i			0.289292i
$851$	7.35797			0.00864626
$852$		0			0
$853$			951.516i			1.11549i	0.830011	+	0.557747i	$0.188334\pi$
$853$			951.516i			1.11549i	−0.830011	+	0.557747i	$0.811666\pi$
$854$	438.296	−	589.550i	0.513228	−	0.690340i
$855$		0			0
$856$	−157.294			−0.183755
$857$		−	1280.77i		−	1.49449i	−0.664551	−	0.747243i	$-0.731377\pi$
$857$		−	1280.77i		−	1.49449i	0.664551	−	0.747243i	$-0.268623\pi$
$858$		0			0
$859$			757.762i			0.882144i	0.897472	+	0.441072i	$0.145402\pi$
$859$			757.762i			0.882144i	−0.897472	+	0.441072i	$0.854598\pi$
$860$			212.448i			0.247032i
$861$		0			0
$862$	−189.905			−0.220307
$863$	−1321.75			−1.53158			−0.765790	−	0.643091i	$-0.777652\pi$
$863$	−1321.75			−1.53158			−0.765790	+	0.643091i	$0.777652\pi$
$864$		0			0
$865$	−622.555			−0.719716
$866$			1497.53i			1.72924i
$867$		0			0
$868$	−391.941	+	527.198i	−0.451545	+	0.607371i
$869$	1310.65			1.50823
$870$		0			0
$871$			2045.42i			2.34836i
$872$	429.694			0.492769
$873$		0			0
$874$			43.7062i			0.0500071i
$875$	−560.519	+	753.952i	−0.640594	+	0.861659i
$876$		0			0
$877$	−483.486			−0.551295			−0.275648	−	0.961259i	$-0.588892\pi$
$877$	−483.486			−0.551295			−0.275648	+	0.961259i	$0.588892\pi$
$878$		−	1167.88i		−	1.33016i
$879$		0			0
$880$			943.027i			1.07162i
$881$			379.667i			0.430950i	0.976509	+	0.215475i	$0.0691299\pi$
$881$			379.667i			0.430950i	−0.976509	+	0.215475i	$0.930870\pi$
$882$		0			0
$883$	−754.801			−0.854814			−0.427407	−	0.904059i	$-0.640573\pi$
$883$	−754.801			−0.854814			−0.427407	+	0.904059i	$0.640573\pi$
$884$	438.459			0.495994
$885$		0			0
$886$	−1575.57			−1.77829
$887$			209.469i			0.236154i	0.993004	+	0.118077i	$0.0376730\pi$
$887$			209.469i			0.236154i	−0.993004	+	0.118077i	$0.962327\pi$
$888$		0			0
$889$	1005.89	+	747.819i	1.13148	+	0.841191i
$890$	1282.79			1.44134
$891$		0			0
$892$			1069.14i			1.19859i
$893$	−1813.29			−2.03056
$894$		0			0
$895$		−	275.995i		−	0.308374i
$896$	522.978	+	388.804i	0.583681	+	0.433933i
$897$		0			0
$898$	156.242			0.173989
$899$		−	405.884i		−	0.451484i
$900$		0			0
$901$		−	321.471i		−	0.356793i
$902$			936.103i			1.03781i
$903$		0			0
$904$	324.940			0.359447
$905$	−6.14889			−0.00679435
$906$		0			0
$907$	−928.747			−1.02398			−0.511988	−	0.858992i	$-0.671091\pi$
$907$	−928.747			−1.02398			−0.511988	+	0.858992i	$0.671091\pi$
$908$		−	627.215i		−	0.690765i
$909$		0			0
$910$	1015.57	+	755.018i	1.11601	+	0.829690i
$911$	315.711			0.346554			0.173277	−	0.984873i	$-0.444564\pi$
$911$	315.711			0.346554			0.173277	+	0.984873i	$0.444564\pi$
$912$		0			0
$913$		−	1905.82i		−	2.08743i
$914$	1860.15			2.03518
$915$		0			0
$916$			81.6497i			0.0891372i
$917$	487.150	−	655.262i	0.531243	−	0.714572i
$918$		0			0
$919$	−374.838			−0.407876			−0.203938	−	0.978984i	$-0.565374\pi$
$919$	−374.838			−0.407876			−0.203938	+	0.978984i	$0.565374\pi$
$920$			8.26153i			0.00897992i
$921$		0			0
$922$		−	4.20965i		−	0.00456578i
$923$			1572.54i			1.70373i
$924$		0			0
$925$	−113.841			−0.123071
$926$	112.056			0.121011
$927$		0			0
$928$	470.356			0.506849
$929$		−	967.865i		−	1.04184i	−0.853607	−	0.520918i	$-0.825590\pi$
$929$		−	967.865i		−	1.04184i	0.853607	−	0.520918i	$-0.174410\pi$
$930$		0			0
$931$	−1062.48	+	319.622i	−1.14123	+	0.343311i
$932$	1151.49			1.23551
$933$		0			0
$934$			604.473i			0.647187i
$935$	−402.390			−0.430364
$936$		0			0
$937$		−	184.891i		−	0.197322i	−0.995121	−	0.0986610i	$-0.968544\pi$
$937$		−	184.891i		−	0.197322i	0.995121	−	0.0986610i	$-0.0314559\pi$
$938$	1601.75	+	1190.81i	1.70762	+	1.26952i
$939$		0			0
$940$	837.677			0.891145
$941$			1260.38i			1.33940i	0.742632	+	0.669700i	$0.233577\pi$
$941$			1260.38i			1.33940i	−0.742632	+	0.669700i	$0.766423\pi$
$942$		0			0
$943$			19.9241i			0.0211284i
$944$			899.178i			0.952519i
$945$		0			0
$946$	704.326			0.744531
$947$	−459.694			−0.485421			−0.242711	−	0.970099i	$-0.578037\pi$
$947$	−459.694			−0.485421			−0.242711	+	0.970099i	$0.578037\pi$
$948$		0			0
$949$	700.109			0.737734
$950$		−	676.211i		−	0.711801i
$951$		0			0
$952$	−104.447	+	140.491i	−0.109713	+	0.147575i
$953$	−278.059			−0.291772			−0.145886	−	0.989301i	$-0.546603\pi$
$953$	−278.059			−0.291772			−0.145886	+	0.989301i	$0.546603\pi$
$954$		0			0
$955$		−	445.695i		−	0.466697i
$956$	−375.862			−0.393161
$957$		0			0
$958$		−	645.424i		−	0.673720i
$959$	−402.402	−	299.163i	−0.419606	−	0.311953i
$960$		0			0
$961$	−132.075			−0.137435
$962$			489.035i			0.508352i
$963$		0			0
$964$		−	235.197i		−	0.243980i
$965$		−	747.347i		−	0.774453i
$966$		0			0
$967$	−479.149			−0.495500			−0.247750	−	0.968824i	$-0.579691\pi$
$967$	−479.149			−0.495500			−0.247750	+	0.968824i	$0.579691\pi$
$968$	166.633			0.172141
$969$		0			0
$970$	−645.864			−0.665839
$971$		−	1621.52i		−	1.66995i	−0.550291	−	0.834973i	$-0.685483\pi$
$971$		−	1621.52i		−	1.66995i	0.550291	−	0.834973i	$-0.314517\pi$
$972$		0			0
$973$	−910.361	+	1224.52i	−0.935623	+	1.25850i
$974$	1617.34			1.66052
$975$		0			0
$976$			774.412i			0.793455i
$977$	−423.533			−0.433504			−0.216752	−	0.976227i	$-0.569546\pi$
$977$	−423.533			−0.433504			−0.216752	+	0.976227i	$0.569546\pi$
$978$		0			0
$979$		−	1765.27i		−	1.80313i
$980$	490.829	−	147.654i	0.500846	−	0.150668i
$981$		0			0
$982$	−840.278			−0.855680
$983$			1574.91i			1.60215i	0.598566	+	0.801073i	$0.295737\pi$
$983$			1574.91i			1.60215i	−0.598566	+	0.801073i	$0.704263\pi$
$984$		0			0
$985$			784.979i			0.796933i
$986$			264.343i			0.268097i
$987$		0			0
$988$	−1205.75			−1.22039
$989$	14.9910			0.0151577
$990$		0			0
$991$	640.630			0.646448			0.323224	−	0.946322i	$-0.395233\pi$
$991$	640.630			0.646448			0.323224	+	0.946322i	$0.395233\pi$
$992$		−	1266.70i		−	1.27692i
$993$		0			0
$994$	1231.44	+	915.503i	1.23887	+	0.921029i
$995$	738.159			0.741868
$996$		0			0
$997$			305.870i			0.306790i	0.988165	+	0.153395i	$0.0490207\pi$
$997$			305.870i			0.306790i	−0.988165	+	0.153395i	$0.950979\pi$
$998$	−420.948			−0.421792
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.3.d.h.244.3		14
3.2	odd	2		567.3.d.g.244.12		14
7.6	odd	2	inner	567.3.d.h.244.4		14
9.2	odd	6		189.3.l.a.118.3		28
9.4	even	3		63.3.l.a.34.11	yes	28
9.5	odd	6		189.3.l.a.181.4		28
9.7	even	3		63.3.l.a.13.12	yes	28
21.20	even	2		567.3.d.g.244.11		14
63.4	even	3		441.3.k.a.313.11		28
63.13	odd	6		63.3.l.a.34.12	yes	28
63.16	even	3		441.3.k.a.31.12		28
63.20	even	6		189.3.l.a.118.4		28
63.25	even	3		441.3.t.b.166.3		28
63.31	odd	6		441.3.k.a.313.12		28
63.34	odd	6		63.3.l.a.13.11	✓	28
63.40	odd	6		441.3.t.b.178.3		28
63.41	even	6		189.3.l.a.181.3		28
63.52	odd	6		441.3.t.b.166.4		28
63.58	even	3		441.3.t.b.178.4		28
63.61	odd	6		441.3.k.a.31.11		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.l.a.13.11	✓	28	63.34	odd	6
63.3.l.a.13.12	yes	28	9.7	even	3
63.3.l.a.34.11	yes	28	9.4	even	3
63.3.l.a.34.12	yes	28	63.13	odd	6
189.3.l.a.118.3		28	9.2	odd	6
189.3.l.a.118.4		28	63.20	even	6
189.3.l.a.181.3		28	63.41	even	6
189.3.l.a.181.4		28	9.5	odd	6
441.3.k.a.31.11		28	63.61	odd	6
441.3.k.a.31.12		28	63.16	even	3
441.3.k.a.313.11		28	63.4	even	3
441.3.k.a.313.12		28	63.31	odd	6
441.3.t.b.166.3		28	63.25	even	3
441.3.t.b.166.4		28	63.52	odd	6
441.3.t.b.178.3		28	63.40	odd	6
441.3.t.b.178.4		28	63.58	even	3
567.3.d.g.244.11		14	21.20	even	2
567.3.d.g.244.12		14	3.2	odd	2
567.3.d.h.244.3		14	1.1	even	1	trivial
567.3.d.h.244.4		14	7.6	odd	2	inner

Overview	Random
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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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	567.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.61506 q^{2} +2.83854 q^{4} -3.68512i q^{5} +(-5.61763 - 4.17638i) q^{7} +3.03728 q^{8} +O(q^{10})\)	\(q-2.61506 q^{2} +2.83854 q^{4} -3.68512i q^{5} +(-5.61763 - 4.17638i) q^{7} +3.03728 q^{8} +9.63680i q^{10} +13.2613 q^{11} +18.7596i q^{13} +(14.6905 + 10.9215i) q^{14} -19.2968 q^{16} -8.23398i q^{17} +22.6432i q^{19} -10.4604i q^{20} -34.6791 q^{22} -0.738115 q^{23} +11.4199 q^{25} -49.0575i q^{26} +(-15.9459 - 11.8548i) q^{28} +12.2766 q^{29} -33.0617i q^{31} +38.3133 q^{32} +21.5323i q^{34} +(-15.3905 + 20.7016i) q^{35} -9.96860 q^{37} -59.2132i q^{38} -11.1927i q^{40} -26.9933i q^{41} -20.3098 q^{43} +37.6428 q^{44} +1.93021 q^{46} +80.0811i q^{47} +(14.1156 + 46.9228i) q^{49} -29.8638 q^{50} +53.2499i q^{52} +39.0420 q^{53} -48.8695i q^{55} +(-17.0624 - 12.6849i) q^{56} -32.1040 q^{58} -46.5971i q^{59} -40.1315i q^{61} +86.4583i q^{62} -23.0042 q^{64} +69.1313 q^{65} +109.033 q^{67} -23.3725i q^{68} +(40.2470 - 54.1360i) q^{70} +83.8258 q^{71} -37.3200i q^{73} +26.0685 q^{74} +64.2736i q^{76} +(-74.4972 - 55.3844i) q^{77} +98.8329 q^{79} +71.1111i q^{80} +70.5890i q^{82} -143.713i q^{83} -30.3432 q^{85} +53.1113 q^{86} +40.2784 q^{88} -133.114i q^{89} +(78.3474 - 105.385i) q^{91} -2.09517 q^{92} -209.417i q^{94} +83.4427 q^{95} +67.0206i q^{97} +(-36.9132 - 122.706i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{2} + 26 q^{4} + 4 q^{8}+O(q^{10}) \) 14 * q + 2 * q^2 + 26 * q^4 + 4 * q^8	\( 14 q + 2 q^{2} + 26 q^{4} + 4 q^{8} - 4 q^{11} - 34 q^{14} + 42 q^{16} - 14 q^{22} - 4 q^{23} - 28 q^{25} + 10 q^{28} + 38 q^{29} + 168 q^{32} - 132 q^{35} + 18 q^{37} + 66 q^{43} + 54 q^{44} - 20 q^{46} + 38 q^{49} - 196 q^{50} + 260 q^{53} - 332 q^{56} + 34 q^{58} + 36 q^{64} + 102 q^{65} - 68 q^{67} - 102 q^{70} - 166 q^{71} + 616 q^{74} - 334 q^{77} - 146 q^{79} - 78 q^{85} + 340 q^{86} + 74 q^{88} - 192 q^{91} - 606 q^{92} + 360 q^{95} - 538 q^{98}+O(q^{100}) \) 14 * q + 2 * q^2 + 26 * q^4 + 4 * q^8 - 4 * q^11 - 34 * q^14 + 42 * q^16 - 14 * q^22 - 4 * q^23 - 28 * q^25 + 10 * q^28 + 38 * q^29 + 168 * q^32 - 132 * q^35 + 18 * q^37 + 66 * q^43 + 54 * q^44 - 20 * q^46 + 38 * q^49 - 196 * q^50 + 260 * q^53 - 332 * q^56 + 34 * q^58 + 36 * q^64 + 102 * q^65 - 68 * q^67 - 102 * q^70 - 166 * q^71 + 616 * q^74 - 334 * q^77 - 146 * q^79 - 78 * q^85 + 340 * q^86 + 74 * q^88 - 192 * q^91 - 606 * q^92 + 360 * q^95 - 538 * q^98

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