LMFDB - Embedded newform 567.3.d.g.244.6

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			244.6
Root			$0.460710i$ of defining polynomial
Character	$\chi$	$=$	567.244
Dual form			567.3.d.g.244.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.90488 q^{2} -0.371447 q^{4} +8.23162i q^{5} +(6.18933 - 3.26989i) q^{7} +8.32706 q^{8} +O(q^{10})$	\(q-1.90488 q^{2} -0.371447 q^{4} +8.23162i q^{5} +(6.18933 - 3.26989i) q^{7} +8.32706 q^{8} -15.6802i q^{10} +11.9301 q^{11} -1.58781i q^{13} +(-11.7899 + 6.22874i) q^{14} -14.3762 q^{16} -19.5020i q^{17} -6.69545i q^{19} -3.05761i q^{20} -22.7253 q^{22} +28.1484 q^{23} -42.7595 q^{25} +3.02458i q^{26} +(-2.29901 + 1.21459i) q^{28} +10.9680 q^{29} -31.7080i q^{31} -5.92330 q^{32} +37.1490i q^{34} +(26.9165 + 50.9482i) q^{35} -6.88791 q^{37} +12.7540i q^{38} +68.5452i q^{40} +1.56305i q^{41} +65.0484 q^{43} -4.43138 q^{44} -53.6193 q^{46} +55.2911i q^{47} +(27.6156 - 40.4769i) q^{49} +81.4516 q^{50} +0.589787i q^{52} +33.9256 q^{53} +98.2037i q^{55} +(51.5390 - 27.2286i) q^{56} -20.8927 q^{58} +6.57763i q^{59} -76.1795i q^{61} +60.3999i q^{62} +68.7881 q^{64} +13.0702 q^{65} -23.7171 q^{67} +7.24397i q^{68} +(-51.2726 - 97.0500i) q^{70} +14.0551 q^{71} -40.2281i q^{73} +13.1206 q^{74} +2.48700i q^{76} +(73.8391 - 39.0100i) q^{77} +63.7289 q^{79} -118.340i q^{80} -2.97741i q^{82} -2.24313i q^{83} +160.533 q^{85} -123.909 q^{86} +99.3424 q^{88} +58.4246i q^{89} +(-5.19197 - 9.82748i) q^{91} -10.4556 q^{92} -105.323i q^{94} +55.1144 q^{95} +129.049i q^{97} +(-52.6043 + 77.1034i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.90488			−0.952438			−0.476219	−	0.879327i	$-0.657993\pi$
$2$	−1.90488			−0.952438			−0.476219	+	0.879327i	$0.657993\pi$
$3$		0			0
$3$		0			0
$4$	−0.371447			−0.0928617
$5$			8.23162i			1.64632i	0.567807	+	0.823162i	$0.307792\pi$
$5$			8.23162i			1.64632i	−0.567807	+	0.823162i	$0.692208\pi$
$6$		0			0
$7$	6.18933	−	3.26989i	0.884190	−	0.467127i
$7$	6.18933	−	3.26989i	0.884190	−	0.467127i
$8$	8.32706			1.04088
$9$		0			0
$10$		−	15.6802i		−	1.56802i
$11$	11.9301			1.08455			0.542276	−	0.840201i	$-0.317563\pi$
$11$	11.9301			1.08455			0.542276	+	0.840201i	$0.317563\pi$
$12$		0			0
$13$		−	1.58781i		−	0.122139i	−0.998134	−	0.0610696i	$-0.980549\pi$
$13$		−	1.58781i		−	0.122139i	0.998134	−	0.0610696i	$-0.0194512\pi$
$14$	−11.7899	+	6.22874i	−0.842136	+	0.444910i
$15$		0			0
$16$	−14.3762			−0.898515
$17$		−	19.5020i		−	1.14718i	−0.819143	−	0.573590i	$-0.805550\pi$
$17$		−	19.5020i		−	1.14718i	0.819143	−	0.573590i	$-0.194450\pi$
$18$		0			0
$19$		−	6.69545i		−	0.352392i	−0.984355	−	0.176196i	$-0.943621\pi$
$19$		−	6.69545i		−	0.352392i	0.984355	−	0.176196i	$-0.0563793\pi$
$20$		−	3.05761i		−	0.152880i
$21$		0			0
$22$	−22.7253			−1.03297
$23$	28.1484			1.22384			0.611922	−	0.790918i	$-0.290396\pi$
$23$	28.1484			1.22384			0.611922	+	0.790918i	$0.290396\pi$
$24$		0			0
$25$	−42.7595			−1.71038
$26$			3.02458i			0.116330i
$27$		0			0
$28$	−2.29901	+	1.21459i	−0.0821073	+	0.0433782i
$29$	10.9680			0.378207			0.189104	−	0.981957i	$-0.439442\pi$
$29$	10.9680			0.378207			0.189104	+	0.981957i	$0.439442\pi$
$30$		0			0
$31$		−	31.7080i		−	1.02284i	−0.859331	−	0.511420i	$-0.829120\pi$
$31$		−	31.7080i		−	1.02284i	0.859331	−	0.511420i	$-0.170880\pi$
$32$	−5.92330			−0.185103
$33$		0			0
$34$			37.1490i			1.09262i
$35$	26.9165	+	50.9482i	0.769043	+	1.45566i
$36$		0			0
$37$	−6.88791			−0.186160			−0.0930798	−	0.995659i	$-0.529671\pi$
$37$	−6.88791			−0.186160			−0.0930798	+	0.995659i	$0.529671\pi$
$38$			12.7540i			0.335632i
$39$		0			0
$40$			68.5452i			1.71363i
$41$			1.56305i			0.0381231i	0.999818	+	0.0190615i	$0.00606784\pi$
$41$			1.56305i			0.0381231i	−0.999818	+	0.0190615i	$0.993932\pi$
$42$		0			0
$43$	65.0484			1.51275			0.756377	−	0.654136i	$-0.226968\pi$
$43$	65.0484			1.51275			0.756377	+	0.654136i	$0.226968\pi$
$44$	−4.43138			−0.100713
$45$		0			0
$46$	−53.6193			−1.16564
$47$			55.2911i			1.17641i	0.808713	+	0.588203i	$0.200164\pi$
$47$			55.2911i			1.17641i	−0.808713	+	0.588203i	$0.799836\pi$
$48$		0			0
$49$	27.6156	−	40.4769i	0.563584	−	0.826059i
$50$	81.4516			1.62903
$51$		0			0
$52$			0.589787i			0.0113420i
$53$	33.9256			0.640106			0.320053	−	0.947400i	$-0.396299\pi$
$53$	33.9256			0.640106			0.320053	+	0.947400i	$0.396299\pi$
$54$		0			0
$55$			98.2037i			1.78552i
$56$	51.5390	−	27.2286i	0.920338	−	0.486225i
$57$		0			0
$58$	−20.8927			−0.360219
$59$			6.57763i			0.111485i	0.998445	+	0.0557426i	$0.0177526\pi$
$59$			6.57763i			0.111485i	−0.998445	+	0.0557426i	$0.982247\pi$
$60$		0			0
$61$		−	76.1795i		−	1.24884i	−0.781087	−	0.624422i	$-0.785334\pi$
$61$		−	76.1795i		−	1.24884i	0.781087	−	0.624422i	$-0.214666\pi$
$62$			60.3999i			0.974192i
$63$		0			0
$64$	68.7881			1.07481
$65$	13.0702			0.201081
$66$		0			0
$67$	−23.7171			−0.353987			−0.176993	−	0.984212i	$-0.556637\pi$
$67$	−23.7171			−0.353987			−0.176993	+	0.984212i	$0.556637\pi$
$68$			7.24397i			0.106529i
$69$		0			0
$70$	−51.2726	−	97.0500i	−0.732466	−	1.38643i
$71$	14.0551			0.197960			0.0989798	−	0.995089i	$-0.468442\pi$
$71$	14.0551			0.197960			0.0989798	+	0.995089i	$0.468442\pi$
$72$		0			0
$73$		−	40.2281i		−	0.551070i	−0.961291	−	0.275535i	$-0.911145\pi$
$73$		−	40.2281i		−	0.551070i	0.961291	−	0.275535i	$-0.0888549\pi$
$74$	13.1206			0.177305
$75$		0			0
$76$			2.48700i			0.0327237i
$77$	73.8391	−	39.0100i	0.958949	−	0.506624i
$78$		0			0
$79$	63.7289			0.806695			0.403348	−	0.915047i	$-0.367847\pi$
$79$	63.7289			0.806695			0.403348	+	0.915047i	$0.367847\pi$
$80$		−	118.340i		−	1.47925i
$81$		0			0
$82$		−	2.97741i		−	0.0363099i
$83$		−	2.24313i		−	0.0270257i	−0.999909	−	0.0135129i	$-0.995699\pi$
$83$		−	2.24313i		−	0.0270257i	0.999909	−	0.0135129i	$-0.00430141\pi$
$84$		0			0
$85$	160.533			1.88863
$86$	−123.909			−1.44080
$87$		0			0
$88$	99.3424			1.12889
$89$			58.4246i			0.656456i	0.944599	+	0.328228i	$0.106451\pi$
$89$			58.4246i			0.656456i	−0.944599	+	0.328228i	$0.893549\pi$
$90$		0			0
$91$	−5.19197	−	9.82748i	−0.0570546	−	0.107994i
$92$	−10.4556			−0.113648
$93$		0			0
$94$		−	105.323i		−	1.12045i
$95$	55.1144			0.580152
$96$		0			0
$97$			129.049i			1.33041i	0.746663	+	0.665203i	$0.231655\pi$
$97$			129.049i			1.33041i	−0.746663	+	0.665203i	$0.768345\pi$
$98$	−52.6043	+	77.1034i	−0.536779	+	0.786770i
$99$		0			0
$100$	15.8829			0.158829
$101$			194.507i			1.92581i	0.269844	+	0.962904i	$0.413028\pi$
$101$			194.507i			1.92581i	−0.269844	+	0.962904i	$0.586972\pi$
$102$		0			0
$103$			95.2765i			0.925015i	0.886615	+	0.462507i	$0.153050\pi$
$103$			95.2765i			0.925015i	−0.886615	+	0.462507i	$0.846950\pi$
$104$		−	13.2218i		−	0.127133i
$105$		0			0
$106$	−64.6242			−0.609662
$107$	10.0507			0.0939319			0.0469660	−	0.998896i	$-0.485045\pi$
$107$	10.0507			0.0939319			0.0469660	+	0.998896i	$0.485045\pi$
$108$		0			0
$109$	70.9967			0.651346			0.325673	−	0.945482i	$-0.394409\pi$
$109$	70.9967			0.651346			0.325673	+	0.945482i	$0.394409\pi$
$110$		−	187.066i		−	1.70060i
$111$		0			0
$112$	−88.9793	+	47.0088i	−0.794458	+	0.419721i
$113$	−54.0265			−0.478111			−0.239055	−	0.971006i	$-0.576838\pi$
$113$	−54.0265			−0.478111			−0.239055	+	0.971006i	$0.576838\pi$
$114$		0			0
$115$			231.707i			2.01484i
$116$	−4.07403			−0.0351209
$117$		0			0
$118$		−	12.5296i		−	0.106183i
$119$	−63.7696	−	120.705i	−0.535879	−	1.01432i
$120$		0			0
$121$	21.3264			0.176251
$122$			145.113i			1.18945i
$123$		0			0
$124$			11.7778i			0.0949826i
$125$		−	146.189i		−	1.16952i
$126$		0			0
$127$	50.2162			0.395403			0.197701	−	0.980262i	$-0.436652\pi$
$127$	50.2162			0.395403			0.197701	+	0.980262i	$0.436652\pi$
$128$	−107.340			−0.838591
$129$		0			0
$130$	−24.8972			−0.191517
$131$		−	45.7188i		−	0.348999i	−0.984657	−	0.174499i	$-0.944169\pi$
$131$		−	45.7188i		−	0.348999i	0.984657	−	0.174499i	$-0.0558307\pi$
$132$		0			0
$133$	−21.8934	−	41.4404i	−0.164612	−	0.311582i
$134$	45.1782			0.337151
$135$		0			0
$136$		−	162.395i		−	1.19408i
$137$	−31.4485			−0.229551			−0.114776	−	0.993391i	$-0.536615\pi$
$137$	−31.4485			−0.229551			−0.114776	+	0.993391i	$0.536615\pi$
$138$		0			0
$139$			119.245i			0.857879i	0.903333	+	0.428939i	$0.141113\pi$
$139$			119.245i			0.857879i	−0.903333	+	0.428939i	$0.858887\pi$
$140$	−9.99804	−	18.9245i	−0.0714146	−	0.135175i
$141$		0			0
$142$	−26.7733			−0.188544
$143$		−	18.9427i		−	0.132466i
$144$		0			0
$145$			90.2844i			0.622651i
$146$			76.6295i			0.524860i
$147$		0			0
$148$	2.55849			0.0172871
$149$	−60.1447			−0.403656			−0.201828	−	0.979421i	$-0.564688\pi$
$149$	−60.1447			−0.403656			−0.201828	+	0.979421i	$0.564688\pi$
$150$		0			0
$151$	−207.625			−1.37500			−0.687499	−	0.726185i	$-0.741292\pi$
$151$	−207.625			−1.37500			−0.687499	+	0.726185i	$0.741292\pi$
$152$		−	55.7535i		−	0.366799i
$153$		0			0
$154$	−140.654	+	74.3092i	−0.913340	+	0.482528i
$155$	261.008			1.68392
$156$		0			0
$157$		−	105.909i		−	0.674579i	−0.941401	−	0.337289i	$-0.890490\pi$
$157$		−	105.909i		−	0.674579i	0.941401	−	0.337289i	$-0.109510\pi$
$158$	−121.396			−0.768327
$159$		0			0
$160$		−	48.7583i		−	0.304740i
$161$	174.220	−	92.0423i	1.08211	−	0.571692i
$162$		0			0
$163$	56.2870			0.345319			0.172660	−	0.984982i	$-0.444764\pi$
$163$	56.2870			0.345319			0.172660	+	0.984982i	$0.444764\pi$
$164$		−	0.580588i		−	0.00354017i
$165$		0			0
$166$			4.27289i			0.0257403i
$167$			170.137i			1.01879i	0.860534	+	0.509394i	$0.170130\pi$
$167$			170.137i			1.01879i	−0.860534	+	0.509394i	$0.829870\pi$
$168$		0			0
$169$	166.479			0.985082
$170$	−305.796			−1.79880
$171$		0			0
$172$	−24.1620			−0.140477
$173$		−	95.7158i		−	0.553270i	−0.960975	−	0.276635i	$-0.910781\pi$
$173$		−	95.7158i		−	0.553270i	0.960975	−	0.276635i	$-0.0892194\pi$
$174$		0			0
$175$	−264.653	+	139.819i	−1.51230	+	0.798965i
$176$	−171.509			−0.974485
$177$		0			0
$178$		−	111.292i		−	0.625233i
$179$	−286.056			−1.59808			−0.799040	−	0.601277i	$-0.794659\pi$
$179$	−286.056			−1.59808			−0.799040	+	0.601277i	$0.794659\pi$
$180$		0			0
$181$		−	246.704i		−	1.36300i	−0.731816	−	0.681502i	$-0.761327\pi$
$181$		−	246.704i		−	1.36300i	0.731816	−	0.681502i	$-0.238673\pi$
$182$	9.89005	+	18.7201i	0.0543409	+	0.102858i
$183$		0			0
$184$	234.394			1.27388
$185$		−	56.6986i		−	0.306479i
$186$		0			0
$187$		−	232.661i		−	1.24417i
$188$		−	20.5377i		−	0.109243i
$189$		0			0
$190$	−104.986			−0.552558
$191$	−271.509			−1.42152			−0.710758	−	0.703437i	$-0.751648\pi$
$191$	−271.509			−1.42152			−0.710758	+	0.703437i	$0.751648\pi$
$192$		0			0
$193$	−192.638			−0.998123			−0.499062	−	0.866566i	$-0.666322\pi$
$193$	−192.638			−0.998123			−0.499062	+	0.866566i	$0.666322\pi$
$194$		−	245.823i		−	1.26713i
$195$		0			0
$196$	−10.2577	+	15.0350i	−0.0523353	+	0.0767092i
$197$	163.463			0.829763			0.414882	−	0.909875i	$-0.363823\pi$
$197$	163.463			0.829763			0.414882	+	0.909875i	$0.363823\pi$
$198$		0			0
$199$			297.225i			1.49359i	0.665053	+	0.746796i	$0.268409\pi$
$199$			297.225i			1.49359i	−0.665053	+	0.746796i	$0.731591\pi$
$200$	−356.061			−1.78031
$201$		0			0
$202$		−	370.511i		−	1.83421i
$203$	67.8846	−	35.8642i	0.334407	−	0.176671i
$204$		0			0
$205$	−12.8664			−0.0627629
$206$		−	181.490i		−	0.881019i
$207$		0			0
$208$			22.8267i			0.109744i
$209$		−	79.8772i		−	0.382187i
$210$		0			0
$211$	86.9972			0.412309			0.206155	−	0.978519i	$-0.433905\pi$
$211$	86.9972			0.412309			0.206155	+	0.978519i	$0.433905\pi$
$212$	−12.6016			−0.0594413
$213$		0			0
$214$	−19.1454			−0.0894643
$215$			535.453i			2.49048i
$216$		0			0
$217$	−103.682	−	196.251i	−0.477796	−	0.904385i
$218$	−135.240			−0.620367
$219$		0			0
$220$		−	36.4774i		−	0.165806i
$221$	−30.9655			−0.140116
$222$		0			0
$223$		−	367.533i		−	1.64813i	−0.566496	−	0.824065i	$-0.691701\pi$
$223$		−	367.533i		−	1.64813i	0.566496	−	0.824065i	$-0.308299\pi$
$224$	−36.6613	+	19.3685i	−0.163666	+	0.0864667i
$225$		0			0
$226$	102.914			0.455371
$227$		−	167.443i		−	0.737633i	−0.929502	−	0.368817i	$-0.879763\pi$
$227$		−	167.443i		−	0.737633i	0.929502	−	0.368817i	$-0.120237\pi$
$228$		0			0
$229$		−	437.899i		−	1.91222i	−0.293001	−	0.956112i	$-0.594654\pi$
$229$		−	437.899i		−	1.91222i	0.293001	−	0.956112i	$-0.405346\pi$
$230$		−	441.373i		−	1.91901i
$231$		0			0
$232$	91.3313			0.393669
$233$	−227.581			−0.976740			−0.488370	−	0.872637i	$-0.662408\pi$
$233$	−227.581			−0.976740			−0.488370	+	0.872637i	$0.662408\pi$
$234$		0			0
$235$	−455.135			−1.93675
$236$		−	2.44324i		−	0.0103527i
$237$		0			0
$238$	121.473	+	229.927i	0.510391	+	0.966081i
$239$	355.290			1.48657			0.743285	−	0.668975i	$-0.233267\pi$
$239$	355.290			1.48657			0.743285	+	0.668975i	$0.233267\pi$
$240$		0			0
$241$			255.935i			1.06197i	0.847381	+	0.530985i	$0.178178\pi$
$241$			255.935i			1.06197i	−0.847381	+	0.530985i	$0.821822\pi$
$242$	−40.6241			−0.167868
$243$		0			0
$244$			28.2966i			0.115970i
$245$	333.190	+	227.321i	1.35996	+	0.927841i
$246$		0			0
$247$	−10.6311			−0.0430409
$248$		−	264.035i		−	1.06466i
$249$		0			0
$250$			278.473i			1.11389i
$251$		−	200.521i		−	0.798889i	−0.916757	−	0.399444i	$-0.869203\pi$
$251$		−	200.521i		−	0.798889i	0.916757	−	0.399444i	$-0.130797\pi$
$252$		0			0
$253$	335.813			1.32732
$254$	−95.6556			−0.376597
$255$		0			0
$256$	−70.6837			−0.276108
$257$			151.654i			0.590092i	0.955483	+	0.295046i	$0.0953349\pi$
$257$			151.654i			0.590092i	−0.955483	+	0.295046i	$0.904665\pi$
$258$		0			0
$259$	−42.6315	+	22.5227i	−0.164600	+	0.0869602i
$260$	−4.85490			−0.0186727
$261$		0			0
$262$			87.0887i			0.332400i
$263$	356.262			1.35461			0.677305	−	0.735702i	$-0.263148\pi$
$263$	356.262			1.35461			0.677305	+	0.735702i	$0.263148\pi$
$264$		0			0
$265$			279.263i			1.05382i
$266$	41.7042	+	78.9388i	0.156783	+	0.296762i
$267$		0			0
$268$	8.80965			0.0328718
$269$			199.704i			0.742395i	0.928554	+	0.371198i	$0.121053\pi$
$269$			199.704i			0.742395i	−0.928554	+	0.371198i	$0.878947\pi$
$270$		0			0
$271$			151.831i			0.560262i	0.959962	+	0.280131i	$0.0903779\pi$
$271$			151.831i			0.560262i	−0.959962	+	0.280131i	$0.909622\pi$
$272$			280.366i			1.03076i
$273$		0			0
$274$	59.9055			0.218633
$275$	−510.123			−1.85499
$276$		0			0
$277$	−61.4847			−0.221966			−0.110983	−	0.993822i	$-0.535400\pi$
$277$	−61.4847			−0.221966			−0.110983	+	0.993822i	$0.535400\pi$
$278$		−	227.147i		−	0.817077i
$279$		0			0
$280$	224.135	+	424.249i	0.800484	+	1.51517i
$281$	−121.844			−0.433610			−0.216805	−	0.976215i	$-0.569564\pi$
$281$	−121.844			−0.433610			−0.216805	+	0.976215i	$0.569564\pi$
$282$		0			0
$283$			508.399i			1.79646i	0.439522	+	0.898232i	$0.355148\pi$
$283$			508.399i			1.79646i	−0.439522	+	0.898232i	$0.644852\pi$
$284$	−5.22073			−0.0183829
$285$		0			0
$286$			36.0834i			0.126166i
$287$	5.11099	+	9.67420i	0.0178083	+	0.0337080i
$288$		0			0
$289$	−91.3299			−0.316020
$290$		−	171.981i		−	0.593037i
$291$		0			0
$292$			14.9426i			0.0511732i
$293$			442.511i			1.51028i	0.655565	+	0.755139i	$0.272431\pi$
$293$			442.511i			1.51028i	−0.655565	+	0.755139i	$0.727569\pi$
$294$		0			0
$295$	−54.1445			−0.183541
$296$	−57.3560			−0.193770
$297$		0			0
$298$	114.568			0.384457
$299$		−	44.6944i		−	0.149479i
$300$		0			0
$301$	402.606	−	212.701i	1.33756	−	0.706649i
$302$	395.500			1.30960
$303$		0			0
$304$			96.2554i			0.316630i
$305$	627.081			2.05600
$306$		0			0
$307$		−	378.900i		−	1.23420i	−0.786884	−	0.617101i	$-0.788307\pi$
$307$		−	378.900i		−	1.23420i	0.786884	−	0.617101i	$-0.211693\pi$
$308$	−27.4273	+	14.4901i	−0.0890496	+	0.0470459i
$309$		0			0
$310$	−497.189			−1.60383
$311$		−	76.8776i		−	0.247195i	−0.992332	−	0.123597i	$-0.960557\pi$
$311$		−	76.8776i		−	0.247195i	0.992332	−	0.123597i	$-0.0394432\pi$
$312$		0			0
$313$		−	143.579i		−	0.458719i	−0.973342	−	0.229360i	$-0.926337\pi$
$313$		−	143.579i		−	0.458719i	0.973342	−	0.229360i	$-0.0736632\pi$
$314$			201.743i			0.642495i
$315$		0			0
$316$	−23.6719			−0.0749110
$317$	−94.7835			−0.299002			−0.149501	−	0.988762i	$-0.547767\pi$
$317$	−94.7835			−0.299002			−0.149501	+	0.988762i	$0.547767\pi$
$318$		0			0
$319$	130.849			0.410185
$320$			566.237i			1.76949i
$321$		0			0
$322$	−331.867	+	175.329i	−1.03064	+	0.544501i
$323$	−130.575			−0.404257
$324$		0			0
$325$			67.8940i			0.208904i
$326$	−107.220			−0.328895
$327$		0			0
$328$			13.0156i			0.0396816i
$329$	180.796	+	342.215i	0.549532	+	1.04017i
$330$		0			0
$331$	468.332			1.41490			0.707451	−	0.706762i	$-0.249845\pi$
$331$	468.332			1.41490			0.707451	+	0.706762i	$0.249845\pi$
$332$			0.833205i			0.00250965i
$333$		0			0
$334$		−	324.091i		−	0.970332i
$335$		−	195.230i		−	0.582777i
$336$		0			0
$337$	−331.311			−0.983119			−0.491560	−	0.870844i	$-0.663573\pi$
$337$	−331.311			−0.983119			−0.491560	+	0.870844i	$0.663573\pi$
$338$	−317.122			−0.938230
$339$		0			0
$340$	−59.6296			−0.175381
$341$		−	378.279i		−	1.10932i
$342$		0			0
$343$	38.5671	−	340.825i	0.112441	−	0.993658i
$344$	541.662			1.57460
$345$		0			0
$346$			182.327i			0.526956i
$347$	−372.049			−1.07219			−0.536094	−	0.844158i	$-0.680101\pi$
$347$	−372.049			−1.07219			−0.536094	+	0.844158i	$0.680101\pi$
$348$		0			0
$349$		−	7.82768i		−	0.0224289i	−0.999937	−	0.0112144i	$-0.996430\pi$
$349$		−	7.82768i		−	0.0224289i	0.999937	−	0.0112144i	$-0.00356974\pi$
$350$	504.131	−	266.338i	1.44037	−	0.760965i
$351$		0			0
$352$	−70.6653			−0.200754
$353$		−	78.2312i		−	0.221618i	−0.993842	−	0.110809i	$-0.964656\pi$
$353$		−	78.2312i		−	0.221618i	0.993842	−	0.110809i	$-0.0353442\pi$
$354$		0			0
$355$			115.696i			0.325905i
$356$		−	21.7016i		−	0.0609596i
$357$		0			0
$358$	544.902			1.52207
$359$	265.434			0.739370			0.369685	−	0.929157i	$-0.379466\pi$
$359$	265.434			0.739370			0.369685	+	0.929157i	$0.379466\pi$
$360$		0			0
$361$	316.171			0.875820
$362$			469.940i			1.29818i
$363$		0			0
$364$	1.92854	+	3.65038i	0.00529818	+	0.0100285i
$365$	331.142			0.907239
$366$		0			0
$367$		−	440.261i		−	1.19962i	−0.800142	−	0.599811i	$-0.795243\pi$
$367$		−	440.261i		−	1.19962i	0.800142	−	0.599811i	$-0.204757\pi$
$368$	−404.669			−1.09964
$369$		0			0
$370$			108.004i			0.291902i
$371$	209.977	−	110.933i	0.565976	−	0.299011i
$372$		0			0
$373$	150.712			0.404053			0.202026	−	0.979380i	$-0.435247\pi$
$373$	150.712			0.404053			0.202026	+	0.979380i	$0.435247\pi$
$374$			443.190i			1.18500i
$375$		0			0
$376$			460.413i			1.22450i
$377$		−	17.4151i		−	0.0461939i
$378$		0			0
$379$	313.660			0.827599			0.413800	−	0.910368i	$-0.364201\pi$
$379$	313.660			0.827599			0.413800	+	0.910368i	$0.364201\pi$
$380$	−20.4721			−0.0538738
$381$		0			0
$382$	517.192			1.35391
$383$		−	647.602i		−	1.69087i	−0.534081	−	0.845434i	$-0.679342\pi$
$383$		−	647.602i		−	1.69087i	0.534081	−	0.845434i	$-0.320658\pi$
$384$		0			0
$385$	321.115	+	607.815i	0.834066	+	1.57874i
$386$	366.951			0.950651
$387$		0			0
$388$		−	47.9349i		−	0.123544i
$389$	203.760			0.523806			0.261903	−	0.965094i	$-0.415650\pi$
$389$	203.760			0.523806			0.261903	+	0.965094i	$0.415650\pi$
$390$		0			0
$391$		−	548.952i		−	1.40397i
$392$	229.957	−	337.054i	0.586625	−	0.859831i
$393$		0			0
$394$	−311.378			−0.790298
$395$			524.592i			1.32808i
$396$		0			0
$397$		−	283.582i		−	0.714312i	−0.934045	−	0.357156i	$-0.883746\pi$
$397$		−	283.582i		−	0.714312i	0.934045	−	0.357156i	$-0.116254\pi$
$398$		−	566.177i		−	1.42255i
$399$		0			0
$400$	614.721			1.53680
$401$	624.239			1.55671			0.778353	−	0.627827i	$-0.216055\pi$
$401$	624.239			1.55671			0.778353	+	0.627827i	$0.216055\pi$
$402$		0			0
$403$	−50.3463			−0.124929
$404$		−	72.2488i		−	0.178834i
$405$		0			0
$406$	−129.312	+	68.3169i	−0.318502	+	0.168268i
$407$	−82.1731			−0.201900
$408$		0			0
$409$		−	29.9575i		−	0.0732457i	−0.999329	−	0.0366228i	$-0.988340\pi$
$409$		−	29.9575i		−	0.0732457i	0.999329	−	0.0366228i	$-0.0116600\pi$
$410$	24.5089			0.0597778
$411$		0			0
$412$		−	35.3901i		−	0.0858984i
$413$	21.5081	+	40.7111i	0.0520778	+	0.0985741i
$414$		0			0
$415$	18.4646			0.0444931
$416$			9.40507i			0.0226083i
$417$		0			0
$418$			152.156i			0.364010i
$419$		−	77.0775i		−	0.183956i	−0.995761	−	0.0919779i	$-0.970681\pi$
$419$		−	77.0775i		−	0.183956i	0.995761	−	0.0919779i	$-0.0293189\pi$
$420$		0			0
$421$	−593.516			−1.40978			−0.704888	−	0.709318i	$-0.749003\pi$
$421$	−593.516			−1.40978			−0.704888	+	0.709318i	$0.749003\pi$
$422$	−165.719			−0.392699
$423$		0			0
$424$	282.501			0.666276
$425$			833.898i			1.96211i
$426$		0			0
$427$	−249.099	−	471.500i	−0.583370	−	1.10422i
$428$	−3.73330			−0.00872267
$429$		0			0
$430$		−	1019.97i		−	2.37203i
$431$	−420.280			−0.975128			−0.487564	−	0.873087i	$-0.662114\pi$
$431$	−420.280			−0.975128			−0.487564	+	0.873087i	$0.662114\pi$
$432$		0			0
$433$			686.056i			1.58442i	0.610246	+	0.792212i	$0.291071\pi$
$433$			686.056i			1.58442i	−0.610246	+	0.792212i	$0.708929\pi$
$434$	197.501	+	373.835i	0.455072	+	0.861370i
$435$		0			0
$436$	−26.3715			−0.0604851
$437$		−	188.467i		−	0.431274i
$438$		0			0
$439$			82.9703i			0.188998i	0.995525	+	0.0944992i	$0.0301250\pi$
$439$			82.9703i			0.188998i	−0.995525	+	0.0944992i	$0.969875\pi$
$440$			817.748i			1.85852i
$441$		0			0
$442$	58.9855			0.133451
$443$	−263.765			−0.595405			−0.297703	−	0.954659i	$-0.596220\pi$
$443$	−263.765			−0.595405			−0.297703	+	0.954659i	$0.596220\pi$
$444$		0			0
$445$	−480.929			−1.08074
$446$			700.105i			1.56974i
$447$		0			0
$448$	425.752	−	224.930i	0.950340	−	0.502075i
$449$	781.684			1.74095			0.870473	−	0.492217i	$-0.163813\pi$
$449$	781.684			1.74095			0.870473	+	0.492217i	$0.163813\pi$
$450$		0			0
$451$			18.6472i			0.0413464i
$452$	20.0680			0.0443982
$453$		0			0
$454$			318.958i			0.702550i
$455$	80.8960	−	42.7383i	0.177793	−	0.0939303i
$456$		0			0
$457$	−855.944			−1.87296			−0.936481	−	0.350718i	$-0.885938\pi$
$457$	−855.944			−1.87296			−0.936481	+	0.350718i	$0.885938\pi$
$458$			834.144i			1.82128i
$459$		0			0
$460$		−	86.0668i		−	0.187102i
$461$			440.539i			0.955615i	0.878465	+	0.477808i	$0.158568\pi$
$461$			440.539i			0.955615i	−0.878465	+	0.477808i	$0.841432\pi$
$462$		0			0
$463$	−235.570			−0.508791			−0.254396	−	0.967100i	$-0.581877\pi$
$463$	−235.570			−0.508791			−0.254396	+	0.967100i	$0.581877\pi$
$464$	−157.679			−0.339825
$465$		0			0
$466$	433.513			0.930285
$467$		−	929.249i		−	1.98983i	−0.100735	−	0.994913i	$-0.532120\pi$
$467$		−	929.249i		−	1.98983i	0.100735	−	0.994913i	$-0.467880\pi$
$468$		0			0
$469$	−146.793	+	77.5524i	−0.312992	+	0.165357i
$470$	866.976			1.84463
$471$		0			0
$472$			54.7723i			0.116043i
$473$	776.031			1.64066
$474$		0			0
$475$			286.294i			0.602725i
$476$	23.6870	+	44.8353i	0.0497626	+	0.0941919i
$477$		0			0
$478$	−676.784			−1.41587
$479$			26.6452i			0.0556267i	0.999613	+	0.0278134i	$0.00885441\pi$
$479$			26.6452i			0.0556267i	−0.999613	+	0.0278134i	$0.991146\pi$
$480$		0			0
$481$			10.9367i			0.0227374i
$482$		−	487.524i		−	1.01146i
$483$		0			0
$484$	−7.92161			−0.0163670
$485$	−1062.28			−2.19028
$486$		0			0
$487$	−712.494			−1.46303			−0.731513	−	0.681827i	$-0.761186\pi$
$487$	−712.494			−1.46303			−0.731513	+	0.681827i	$0.761186\pi$
$488$		−	634.352i		−	1.29990i
$489$		0			0
$490$	−634.686	−	433.019i	−1.29528	−	0.883711i
$491$	−355.431			−0.723893			−0.361946	−	0.932199i	$-0.617888\pi$
$491$	−355.431			−0.723893			−0.361946	+	0.932199i	$0.617888\pi$
$492$		0			0
$493$		−	213.899i		−	0.433872i
$494$	20.2509			0.0409938
$495$		0			0
$496$			455.842i			0.919037i
$497$	86.9918	−	45.9588i	0.175034	−	0.0924723i
$498$		0			0
$499$	236.886			0.474722			0.237361	−	0.971422i	$-0.423718\pi$
$499$	236.886			0.474722			0.237361	+	0.971422i	$0.423718\pi$
$500$			54.3016i			0.108603i
$501$		0			0
$502$			381.968i			0.760892i
$503$			471.038i			0.936457i	0.883608	+	0.468228i	$0.155108\pi$
$503$			471.038i			0.936457i	−0.883608	+	0.468228i	$0.844892\pi$
$504$		0			0
$505$	−1601.10			−3.17050
$506$	−639.681			−1.26419
$507$		0			0
$508$	−18.6526			−0.0367178
$509$		−	477.868i		−	0.938837i	−0.882976	−	0.469418i	$-0.844464\pi$
$509$		−	477.868i		−	0.938837i	0.882976	−	0.469418i	$-0.155536\pi$
$510$		0			0
$511$	−131.541	−	248.985i	−0.257420	−	0.487250i
$512$	564.002			1.10157
$513$		0			0
$514$		−	288.881i		−	0.562026i
$515$	−784.280			−1.52287
$516$		0			0
$517$			659.626i			1.27587i
$518$	81.2078	−	42.9030i	0.156772	−	0.0828243i
$519$		0			0
$520$	108.837			0.209301
$521$			85.6568i			0.164408i	0.996616	+	0.0822042i	$0.0261960\pi$
$521$			85.6568i			0.164408i	−0.996616	+	0.0822042i	$0.973804\pi$
$522$		0			0
$523$			575.874i			1.10110i	0.834803	+	0.550548i	$0.185581\pi$
$523$			575.874i			1.10110i	−0.834803	+	0.550548i	$0.814419\pi$
$524$			16.9821i			0.0324086i
$525$		0			0
$526$	−678.636			−1.29018
$527$	−618.372			−1.17338
$528$		0			0
$529$	263.334			0.497797
$530$		−	531.961i		−	1.00370i
$531$		0			0
$532$	8.13223	+	15.3929i	0.0152862	+	0.0289340i
$533$	2.48182			0.00465632
$534$		0			0
$535$			82.7336i			0.154642i
$536$	−197.494			−0.368459
$537$		0			0
$538$		−	380.412i		−	0.707086i
$539$	329.456	−	482.892i	0.611236	−	0.895903i
$540$		0			0
$541$	798.629			1.47621			0.738104	−	0.674687i	$-0.235721\pi$
$541$	798.629			1.47621			0.738104	+	0.674687i	$0.235721\pi$
$542$		−	289.219i		−	0.533615i
$543$		0			0
$544$			115.516i			0.212346i
$545$			584.418i			1.07233i
$546$		0			0
$547$	−273.484			−0.499971			−0.249986	−	0.968250i	$-0.580426\pi$
$547$	−273.484			−0.499971			−0.249986	+	0.968250i	$0.580426\pi$
$548$	11.6814			0.0213165
$549$		0			0
$550$	971.722			1.76677
$551$		−	73.4358i		−	0.133277i
$552$		0			0
$553$	394.439	−	208.387i	0.713272	−	0.376829i
$554$	117.121			0.211409
$555$		0			0
$556$		−	44.2932i		−	0.0796641i
$557$	526.108			0.944538			0.472269	−	0.881455i	$-0.343435\pi$
$557$	526.108			0.944538			0.472269	+	0.881455i	$0.343435\pi$
$558$		0			0
$559$		−	103.284i		−	0.184767i
$560$	−386.958	−	732.443i	−0.690996	−	1.30793i
$561$		0			0
$562$	232.099			0.412987
$563$		−	386.727i		−	0.686904i	−0.939170	−	0.343452i	$-0.888404\pi$
$563$		−	386.727i		−	0.686904i	0.939170	−	0.343452i	$-0.111596\pi$
$564$		0			0
$565$		−	444.726i		−	0.787125i
$566$		−	968.438i		−	1.71102i
$567$		0			0
$568$	117.038			0.206053
$569$	354.691			0.623359			0.311680	−	0.950187i	$-0.399108\pi$
$569$	354.691			0.623359			0.311680	+	0.950187i	$0.399108\pi$
$570$		0			0
$571$	156.414			0.273929			0.136965	−	0.990576i	$-0.456265\pi$
$571$	156.414			0.273929			0.136965	+	0.990576i	$0.456265\pi$
$572$			7.03619i			0.0123010i
$573$		0			0
$574$	−9.73580	−	18.4282i	−0.0169613	−	0.0321048i
$575$	−1203.61			−2.09324
$576$		0			0
$577$			199.310i			0.345425i	0.984972	+	0.172713i	$0.0552532\pi$
$577$			199.310i			0.345425i	−0.984972	+	0.172713i	$0.944747\pi$
$578$	173.972			0.300990
$579$		0			0
$580$		−	33.5358i		−	0.0578204i
$581$	−7.33481	−	13.8835i	−0.0126245	−	0.0238959i
$582$		0			0
$583$	404.735			0.694228
$584$		−	334.982i		−	0.573599i
$585$		0			0
$586$		−	842.929i		−	1.43845i
$587$		−	144.214i		−	0.245680i	−0.992426	−	0.122840i	$-0.960800\pi$
$587$		−	144.214i		−	0.245680i	0.992426	−	0.122840i	$-0.0392002\pi$
$588$		0			0
$589$	−212.300			−0.360441
$590$	103.139			0.174811
$591$		0			0
$592$	99.0222			0.167267
$593$			743.841i			1.25437i	0.778870	+	0.627185i	$0.215793\pi$
$593$			743.841i			1.25437i	−0.778870	+	0.627185i	$0.784207\pi$
$594$		0			0
$595$	993.594	−	524.927i	1.66991	−	0.882230i
$596$	22.3406			0.0374841
$597$		0			0
$598$			85.1372i			0.142370i
$599$	170.846			0.285218			0.142609	−	0.989779i	$-0.454451\pi$
$599$	170.846			0.285218			0.142609	+	0.989779i	$0.454451\pi$
$600$		0			0
$601$			1179.83i			1.96311i	0.191179	+	0.981555i	$0.438769\pi$
$601$			1179.83i			1.96311i	−0.191179	+	0.981555i	$0.561231\pi$
$602$	−766.915	+	405.170i	−1.27394	+	0.673039i
$603$		0			0
$604$	77.1215			0.127685
$605$			175.550i			0.290166i
$606$		0			0
$607$		−	484.623i		−	0.798390i	−0.916866	−	0.399195i	$-0.869290\pi$
$607$		−	484.623i		−	0.798390i	0.916866	−	0.399195i	$-0.130710\pi$
$608$			39.6592i			0.0652289i
$609$		0			0
$610$	−1194.51			−1.95822
$611$	87.7917			0.143685
$612$		0			0
$613$	−201.948			−0.329442			−0.164721	−	0.986340i	$-0.552672\pi$
$613$	−201.948			−0.329442			−0.164721	+	0.986340i	$0.552672\pi$
$614$			721.757i			1.17550i
$615$		0			0
$616$	614.863	−	324.839i	0.998154	−	0.527336i
$617$	−968.557			−1.56979			−0.784893	−	0.619632i	$-0.787282\pi$
$617$	−968.557			−1.56979			−0.784893	+	0.619632i	$0.787282\pi$
$618$		0			0
$619$		−	28.0026i		−	0.0452385i	−0.999744	−	0.0226193i	$-0.992799\pi$
$619$		−	28.0026i		−	0.0452385i	0.999744	−	0.0226193i	$-0.00720055\pi$
$620$	−96.9507			−0.156372
$621$		0			0
$622$			146.442i			0.235438i
$623$	191.042	+	361.609i	0.306648	+	0.580432i
$624$		0			0
$625$	134.387			0.215020
$626$			273.501i			0.436902i
$627$		0			0
$628$			39.3395i			0.0626425i
$629$			134.328i			0.213558i
$630$		0			0
$631$	−322.046			−0.510373			−0.255187	−	0.966892i	$-0.582137\pi$
$631$	−322.046			−0.510373			−0.255187	+	0.966892i	$0.582137\pi$
$632$	530.675			0.839675
$633$		0			0
$634$	180.551			0.284781
$635$			413.360i			0.650961i
$636$		0			0
$637$	−64.2696	−	43.8483i	−0.100894	−	0.0688357i
$638$	−249.251			−0.390676
$639$		0			0
$640$		−	883.579i		−	1.38059i
$641$	−467.164			−0.728804			−0.364402	−	0.931242i	$-0.618727\pi$
$641$	−467.164			−0.728804			−0.364402	+	0.931242i	$0.618727\pi$
$642$		0			0
$643$		−	147.113i		−	0.228791i	−0.993435	−	0.114396i	$-0.963507\pi$
$643$		−	147.113i		−	0.228791i	0.993435	−	0.114396i	$-0.0364932\pi$
$644$	−64.7134	+	34.1888i	−0.100487	+	0.0530882i
$645$		0			0
$646$	248.729			0.385030
$647$		−	688.665i		−	1.06440i	−0.846620	−	0.532198i	$-0.821366\pi$
$647$		−	688.665i		−	1.06440i	0.846620	−	0.532198i	$-0.178634\pi$
$648$		0			0
$649$			78.4715i			0.120911i
$650$		−	129.330i		−	0.198969i
$651$		0			0
$652$	−20.9076			−0.0320669
$653$	−1170.28			−1.79216			−0.896081	−	0.443890i	$-0.853598\pi$
$653$	−1170.28			−1.79216			−0.896081	+	0.443890i	$0.853598\pi$
$654$		0			0
$655$	376.340			0.574565
$656$		−	22.4707i		−	0.0342541i
$657$		0			0
$658$	−344.394	−	651.877i	−0.523395	−	0.990694i
$659$	−1010.50			−1.53339			−0.766694	−	0.642013i	$-0.778100\pi$
$659$	−1010.50			−1.53339			−0.766694	+	0.642013i	$0.778100\pi$
$660$		0			0
$661$		−	553.620i		−	0.837549i	−0.908090	−	0.418774i	$-0.862460\pi$
$661$		−	553.620i		−	0.837549i	0.908090	−	0.418774i	$-0.137540\pi$
$662$	−892.115			−1.34761
$663$		0			0
$664$		−	18.6787i		−	0.0281306i
$665$	341.121	−	180.218i	0.512964	−	0.271005i
$666$		0			0
$667$	308.732			0.462867
$668$		−	63.1970i		−	0.0946063i
$669$		0			0
$670$			371.890i			0.555059i
$671$		−	908.827i		−	1.35444i
$672$		0			0
$673$	−155.458			−0.230993			−0.115496	−	0.993308i	$-0.536846\pi$
$673$	−155.458			−0.230993			−0.115496	+	0.993308i	$0.536846\pi$
$674$	631.107			0.936360
$675$		0			0
$676$	−61.8380			−0.0914763
$677$		−	887.050i		−	1.31027i	−0.755513	−	0.655133i	$-0.772613\pi$
$677$		−	887.050i		−	1.31027i	0.755513	−	0.655133i	$-0.227387\pi$
$678$		0			0
$679$	421.977	+	798.729i	0.621469	+	1.17633i
$680$	1336.77			1.96584
$681$		0			0
$682$			720.574i			1.05656i
$683$	−440.555			−0.645030			−0.322515	−	0.946564i	$-0.604528\pi$
$683$	−440.555			−0.645030			−0.322515	+	0.946564i	$0.604528\pi$
$684$		0			0
$685$		−	258.872i		−	0.377915i
$686$	−73.4656	+	649.229i	−0.107093	+	0.946398i
$687$		0			0
$688$	−935.151			−1.35923
$689$		−	53.8675i		−	0.0781821i
$690$		0			0
$691$			411.654i			0.595736i	0.954607	+	0.297868i	$0.0962756\pi$
$691$			411.654i			0.595736i	−0.954607	+	0.297868i	$0.903724\pi$
$692$			35.5533i			0.0513776i
$693$		0			0
$694$	708.707			1.02119
$695$	−981.580			−1.41235
$696$		0			0
$697$	30.4826			0.0437340
$698$			14.9108i			0.0213621i
$699$		0			0
$700$	98.3043	−	51.9353i	0.140435	−	0.0741932i
$701$	61.6807			0.0879895			0.0439948	−	0.999032i	$-0.485992\pi$
$701$	61.6807			0.0879895			0.0439948	+	0.999032i	$0.485992\pi$
$702$		0			0
$703$			46.1176i			0.0656012i
$704$	820.646			1.16569
$705$		0			0
$706$			149.021i			0.211078i
$707$	636.016	+	1203.87i	0.899598	+	1.70278i
$708$		0			0
$709$	1094.43			1.54363			0.771814	−	0.635849i	$-0.219350\pi$
$709$	1094.43			1.54363			0.771814	+	0.635849i	$0.219350\pi$
$710$		−	220.387i		−	0.310405i
$711$		0			0
$712$			486.505i			0.683294i
$713$		−	892.531i		−	1.25180i
$714$		0			0
$715$	155.929			0.218082
$716$	106.255			0.148400
$717$		0			0
$718$	−505.619			−0.704204
$719$			577.350i			0.802990i	0.915861	+	0.401495i	$0.131509\pi$
$719$			577.350i			0.802990i	−0.915861	+	0.401495i	$0.868491\pi$
$720$		0			0
$721$	311.544	+	589.698i	0.432100	+	0.817889i
$722$	−602.266			−0.834164
$723$		0			0
$724$			91.6373i			0.126571i
$725$	−468.987			−0.646878
$726$		0			0
$727$			89.5790i			0.123217i	0.998100	+	0.0616087i	$0.0196231\pi$
$727$			89.5790i			0.123217i	−0.998100	+	0.0616087i	$0.980377\pi$
$728$	−43.2338	−	81.8340i	−0.0593871	−	0.112409i
$729$		0			0
$730$	−630.785			−0.864089
$731$		−	1268.58i		−	1.73540i
$732$		0			0
$733$		−	191.799i		−	0.261663i	−0.991405	−	0.130832i	$-0.958235\pi$
$733$		−	191.799i		−	0.261663i	0.991405	−	0.130832i	$-0.0417648\pi$
$734$			838.643i			1.14257i
$735$		0			0
$736$	−166.732			−0.226538
$737$	−282.947			−0.383917
$738$		0			0
$739$	1004.93			1.35985			0.679926	−	0.733281i	$-0.262012\pi$
$739$	1004.93			1.35985			0.679926	+	0.733281i	$0.262012\pi$
$740$			21.0605i			0.0284601i
$741$		0			0
$742$	−399.980	+	211.314i	−0.539057	+	0.284790i
$743$	−319.379			−0.429851			−0.214925	−	0.976630i	$-0.568951\pi$
$743$	−319.379			−0.429851			−0.214925	+	0.976630i	$0.568951\pi$
$744$		0			0
$745$		−	495.088i		−	0.664548i
$746$	−287.087			−0.384835
$747$		0			0
$748$			86.4210i			0.115536i
$749$	62.2072	−	32.8647i	0.0830537	−	0.0438782i
$750$		0			0
$751$	328.885			0.437930			0.218965	−	0.975733i	$-0.429732\pi$
$751$	328.885			0.437930			0.218965	+	0.975733i	$0.429732\pi$
$752$		−	794.878i		−	1.05702i
$753$		0			0
$754$			33.1736i			0.0439969i
$755$		−	1709.09i		−	2.26369i
$756$		0			0
$757$	−314.963			−0.416068			−0.208034	−	0.978122i	$-0.566706\pi$
$757$	−314.963			−0.416068			−0.208034	+	0.978122i	$0.566706\pi$
$758$	−597.484			−0.788237
$759$		0			0
$760$	458.941			0.603870
$761$		−	1077.49i		−	1.41589i	−0.706267	−	0.707946i	$-0.749622\pi$
$761$		−	1077.49i		−	1.41589i	0.706267	−	0.707946i	$-0.250378\pi$
$762$		0			0
$763$	439.422	−	232.152i	0.575914	−	0.304262i
$764$	100.851			0.132004
$765$		0			0
$766$			1233.60i			1.61045i
$767$	10.4440			0.0136167
$768$		0			0
$769$			1014.20i			1.31885i	0.751770	+	0.659426i	$0.229200\pi$
$769$			1014.20i			1.31885i	−0.751770	+	0.659426i	$0.770800\pi$
$770$	−611.685	−	1157.81i	−0.794396	−	1.50365i
$771$		0			0
$772$	71.5547			0.0926874
$773$		−	731.810i		−	0.946714i	−0.880871	−	0.473357i	$-0.843042\pi$
$773$		−	731.810i		−	0.946714i	0.880871	−	0.473357i	$-0.156958\pi$
$774$		0			0
$775$			1355.82i			1.74944i
$776$			1074.60i			1.38480i
$777$		0			0
$778$	−388.138			−0.498893
$779$	10.4653			0.0134343
$780$		0			0
$781$	167.679			0.214697
$782$			1045.69i			1.33719i
$783$		0			0
$784$	−397.009	+	581.905i	−0.506389	+	0.742226i
$785$	871.801			1.11057
$786$		0			0
$787$		−	151.096i		−	0.191989i	−0.995382	−	0.0959947i	$-0.969397\pi$
$787$		−	151.096i		−	0.191989i	0.995382	−	0.0959947i	$-0.0306032\pi$
$788$	−60.7179			−0.0770532
$789$		0			0
$790$		−	999.283i		−	1.26491i
$791$	−334.388	+	176.661i	−0.422741	+	0.223339i
$792$		0			0
$793$	−120.959			−0.152533
$794$			540.189i			0.680338i
$795$		0			0
$796$		−	110.403i		−	0.138697i
$797$		−	157.062i		−	0.197066i	−0.995134	−	0.0985330i	$-0.968585\pi$
$797$		−	157.062i		−	0.197066i	0.995134	−	0.0985330i	$-0.0314150\pi$
$798$		0			0
$799$	1078.29			1.34955
$800$	253.277			0.316597
$801$		0			0
$802$	−1189.10			−1.48267
$803$		−	479.923i		−	0.597663i
$804$		0			0
$805$	757.657	+	1434.11i	0.941189	+	1.78151i
$806$	95.9035			0.118987
$807$		0			0
$808$			1619.67i			2.00454i
$809$	−428.194			−0.529288			−0.264644	−	0.964346i	$-0.585254\pi$
$809$	−428.194			−0.529288			−0.264644	+	0.964346i	$0.585254\pi$
$810$		0			0
$811$		−	1167.08i		−	1.43906i	−0.694459	−	0.719532i	$-0.744356\pi$
$811$		−	1167.08i		−	1.43906i	0.694459	−	0.719532i	$-0.255644\pi$
$812$	−25.2155	+	13.3216i	−0.0310536	+	0.0164060i
$813$		0			0
$814$	156.530			0.192297
$815$			463.333i			0.568507i
$816$		0			0
$817$		−	435.529i		−	0.533083i
$818$			57.0653i			0.0697620i
$819$		0			0
$820$	4.77918			0.00582826
$821$	862.850			1.05097			0.525487	−	0.850802i	$-0.323883\pi$
$821$	862.850			1.05097			0.525487	+	0.850802i	$0.323883\pi$
$822$		0			0
$823$	553.430			0.672454			0.336227	−	0.941781i	$-0.390849\pi$
$823$	553.430			0.672454			0.336227	+	0.941781i	$0.390849\pi$
$824$			793.374i			0.962832i
$825$		0			0
$826$	−40.9703	−	77.5496i	−0.0496009	−	0.0938857i
$827$	−726.434			−0.878396			−0.439198	−	0.898390i	$-0.644737\pi$
$827$	−726.434			−0.878396			−0.439198	+	0.898390i	$0.644737\pi$
$828$		0			0
$829$			153.336i			0.184966i	0.995714	+	0.0924828i	$0.0294803\pi$
$829$			153.336i			0.184966i	−0.995714	+	0.0924828i	$0.970520\pi$
$830$	−35.1728			−0.0423769
$831$		0			0
$832$		−	109.222i		−	0.131277i
$833$	−789.382	−	538.561i	−0.947638	−	0.646532i
$834$		0			0
$835$	−1400.51			−1.67725
$836$			29.6701i			0.0354906i
$837$		0			0
$838$			146.823i			0.175207i
$839$			1568.32i			1.86927i	0.355608	+	0.934635i	$0.384274\pi$
$839$			1568.32i			1.86927i	−0.355608	+	0.934635i	$0.615726\pi$
$840$		0			0
$841$	−720.703			−0.856959
$842$	1130.57			1.34272
$843$		0			0
$844$	−32.3148			−0.0382877
$845$			1370.39i			1.62176i
$846$		0			0
$847$	131.996	−	69.7349i	0.155839	−	0.0823317i
$848$	−487.723			−0.575145
$849$		0			0
$850$		−	1588.47i		−	1.86879i
$851$	−193.884			−0.227830
$852$		0			0
$853$		−	932.411i		−	1.09310i	−0.837428	−	0.546548i	$-0.815942\pi$
$853$		−	932.411i		−	1.09310i	0.837428	−	0.546548i	$-0.184058\pi$
$854$	474.503	+	898.150i	0.555624	+	1.05170i
$855$		0			0
$856$	83.6929			0.0977721
$857$			1058.31i			1.23490i	0.786609	+	0.617451i	$0.211835\pi$
$857$			1058.31i			1.23490i	−0.786609	+	0.617451i	$0.788165\pi$
$858$		0			0
$859$		−	64.7528i		−	0.0753816i	−0.999289	−	0.0376908i	$-0.988000\pi$
$859$		−	64.7528i		−	0.0753816i	0.999289	−	0.0376908i	$-0.0120002\pi$
$860$		−	198.892i		−	0.231270i
$861$		0			0
$862$	800.581			0.928749
$863$	−1210.66			−1.40285			−0.701425	−	0.712743i	$-0.747453\pi$
$863$	−1210.66			−1.40285			−0.701425	+	0.712743i	$0.747453\pi$
$864$		0			0
$865$	787.896			0.910862
$866$		−	1306.85i		−	1.50907i
$867$		0			0
$868$	38.5123	+	72.8969i	0.0443690	+	0.0839827i
$869$	760.290			0.874902
$870$		0			0
$871$			37.6583i			0.0432357i
$872$	591.194			0.677975
$873$		0			0
$874$			359.005i			0.410761i
$875$	−478.023	−	904.814i	−0.546313	−	1.03407i
$876$		0			0
$877$	−834.997			−0.952106			−0.476053	−	0.879416i	$-0.657933\pi$
$877$	−834.997			−0.952106			−0.476053	+	0.879416i	$0.657933\pi$
$878$		−	158.048i		−	0.180009i
$879$		0			0
$880$		−	1411.80i		−	1.60432i
$881$			955.525i			1.08459i	0.840188	+	0.542296i	$0.182445\pi$
$881$			955.525i			1.08459i	−0.840188	+	0.542296i	$0.817555\pi$
$882$		0			0
$883$	513.712			0.581780			0.290890	−	0.956757i	$-0.406049\pi$
$883$	513.712			0.581780			0.290890	+	0.956757i	$0.406049\pi$
$884$	11.5020			0.0130114
$885$		0			0
$886$	502.439			0.567087
$887$		−	816.561i		−	0.920587i	−0.887767	−	0.460294i	$-0.847744\pi$
$887$		−	816.561i		−	0.920587i	0.887767	−	0.460294i	$-0.152256\pi$
$888$		0			0
$889$	310.804	−	164.201i	0.349611	−	0.184704i
$890$	916.109			1.02934
$891$		0			0
$892$			136.519i			0.153048i
$893$	370.199			0.414556
$894$		0			0
$895$		−	2354.71i		−	2.63096i
$896$	−664.361	+	350.989i	−0.741474	+	0.391729i
$897$		0			0
$898$	−1489.01			−1.65814
$899$		−	347.774i		−	0.386845i
$900$		0			0
$901$		−	661.620i		−	0.734317i
$902$		−	35.5207i		−	0.0393799i
$903$		0			0
$904$	−449.882			−0.497657
$905$	2030.77			2.24395
$906$		0			0
$907$	−1001.84			−1.10456			−0.552280	−	0.833659i	$-0.686242\pi$
$907$	−1001.84			−1.10456			−0.552280	+	0.833659i	$0.686242\pi$
$908$			62.1960i			0.0684978i
$909$		0			0
$910$	−154.097	+	81.4111i	−0.169337	+	0.0894628i
$911$	−243.326			−0.267098			−0.133549	−	0.991042i	$-0.542637\pi$
$911$	−243.326			−0.267098			−0.133549	+	0.991042i	$0.542637\pi$
$912$		0			0
$913$		−	26.7607i		−	0.0293108i
$914$	1630.47			1.78388
$915$		0			0
$916$			162.656i			0.177572i
$917$	−149.496	−	282.969i	−0.163027	−	0.308581i
$918$		0			0
$919$	−1305.16			−1.42020			−0.710100	−	0.704101i	$-0.751350\pi$
$919$	−1305.16			−1.42020			−0.710100	+	0.704101i	$0.751350\pi$
$920$			1929.44i			2.09722i
$921$		0			0
$922$		−	839.171i		−	0.910164i
$923$		−	22.3169i		−	0.0241786i
$924$		0			0
$925$	294.523			0.318404
$926$	448.732			0.484592
$927$		0			0
$928$	−64.9668			−0.0700073
$929$		−	90.9709i		−	0.0979234i	−0.998801	−	0.0489617i	$-0.984409\pi$
$929$		−	90.9709i		−	0.0979234i	0.998801	−	0.0489617i	$-0.0155912\pi$
$930$		0			0
$931$	−271.011	−	184.899i	−0.291097	−	0.198603i
$932$	84.5340			0.0907017
$933$		0			0
$934$			1770.10i			1.89519i
$935$	1915.17			2.04831
$936$		0			0
$937$		−	1324.34i		−	1.41338i	−0.707523	−	0.706690i	$-0.750188\pi$
$937$		−	1324.34i		−	1.41338i	0.707523	−	0.706690i	$-0.249812\pi$
$938$	279.623	−	147.728i	0.298105	−	0.157492i
$939$		0			0
$940$	169.058			0.179849
$941$			1083.08i			1.15099i	0.817805	+	0.575495i	$0.195191\pi$
$941$			1083.08i			1.15099i	−0.817805	+	0.575495i	$0.804809\pi$
$942$		0			0
$943$			43.9973i			0.0466567i
$944$		−	94.5616i		−	0.100171i
$945$		0			0
$946$	−1478.24			−1.56263
$947$	119.688			0.126386			0.0631931	−	0.998001i	$-0.479872\pi$
$947$	119.688			0.126386			0.0631931	+	0.998001i	$0.479872\pi$
$948$		0			0
$949$	−63.8745			−0.0673072
$950$		−	545.355i		−	0.574058i
$951$		0			0
$952$	−531.014	−	1005.12i	−0.557787	−	1.05579i
$953$	−463.471			−0.486329			−0.243164	−	0.969985i	$-0.578185\pi$
$953$	−463.471			−0.486329			−0.243164	+	0.969985i	$0.578185\pi$
$954$		0			0
$955$		−	2234.96i		−	2.34027i
$956$	−131.971			−0.138045
$957$		0			0
$958$		−	50.7558i		−	0.0529810i
$959$	−194.645	+	102.833i	−0.202967	+	0.107230i
$960$		0			0
$961$	−44.3992			−0.0462011
$962$		−	20.8330i		−	0.0216560i
$963$		0			0
$964$		−	95.0661i		−	0.0986163i
$965$		−	1585.72i		−	1.64323i
$966$		0			0
$967$	−519.927			−0.537670			−0.268835	−	0.963186i	$-0.586639\pi$
$967$	−519.927			−0.537670			−0.268835	+	0.963186i	$0.586639\pi$
$968$	177.586			0.183457
$969$		0			0
$970$	2023.52			2.08610
$971$			50.6835i			0.0521972i	0.999659	+	0.0260986i	$0.00830839\pi$
$971$			50.6835i			0.0521972i	−0.999659	+	0.0260986i	$0.991692\pi$
$972$		0			0
$973$	389.919	+	738.048i	0.400739	+	0.758528i
$974$	1357.21			1.39344
$975$		0			0
$976$			1095.18i			1.12211i
$977$	493.117			0.504726			0.252363	−	0.967633i	$-0.418792\pi$
$977$	493.117			0.504726			0.252363	+	0.967633i	$0.418792\pi$
$978$		0			0
$979$			697.009i			0.711960i
$980$	−123.762	−	84.4377i	−0.126288	−	0.0861609i
$981$		0			0
$982$	677.053			0.689463
$983$			808.577i			0.822561i	0.911509	+	0.411281i	$0.134918\pi$
$983$			808.577i			0.822561i	−0.911509	+	0.411281i	$0.865082\pi$
$984$		0			0
$985$			1345.57i			1.36606i
$986$			407.450i			0.413236i
$987$		0			0
$988$	3.94889			0.00399685
$989$	1831.01			1.85138
$990$		0			0
$991$	−588.956			−0.594305			−0.297152	−	0.954830i	$-0.596037\pi$
$991$	−588.956			−0.594305			−0.297152	+	0.954830i	$0.596037\pi$
$992$			187.816i			0.189331i
$993$		0			0
$994$	−165.709	+	87.5457i	−0.166709	+	0.0880742i
$995$	−2446.64			−2.45894
$996$		0			0
$997$			539.626i			0.541250i	0.962685	+	0.270625i	$0.0872304\pi$
$997$			539.626i			0.541250i	−0.962685	+	0.270625i	$0.912770\pi$
$998$	−451.239			−0.452143
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.3.d.g.244.6		14
3.2	odd	2		567.3.d.h.244.9		14
7.6	odd	2	inner	567.3.d.g.244.5		14
9.2	odd	6		63.3.l.a.13.6	yes	28
9.4	even	3		189.3.l.a.181.10		28
9.5	odd	6		63.3.l.a.34.5	yes	28
9.7	even	3		189.3.l.a.118.9		28
21.20	even	2		567.3.d.h.244.10		14
63.2	odd	6		441.3.k.a.31.6		28
63.5	even	6		441.3.t.b.178.9		28
63.11	odd	6		441.3.t.b.166.9		28
63.13	odd	6		189.3.l.a.181.9		28
63.20	even	6		63.3.l.a.13.5	✓	28
63.23	odd	6		441.3.t.b.178.10		28
63.32	odd	6		441.3.k.a.313.5		28
63.34	odd	6		189.3.l.a.118.10		28
63.38	even	6		441.3.t.b.166.10		28
63.41	even	6		63.3.l.a.34.6	yes	28
63.47	even	6		441.3.k.a.31.5		28
63.59	even	6		441.3.k.a.313.6		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.l.a.13.5	✓	28	63.20	even	6
63.3.l.a.13.6	yes	28	9.2	odd	6
63.3.l.a.34.5	yes	28	9.5	odd	6
63.3.l.a.34.6	yes	28	63.41	even	6
189.3.l.a.118.9		28	9.7	even	3
189.3.l.a.118.10		28	63.34	odd	6
189.3.l.a.181.9		28	63.13	odd	6
189.3.l.a.181.10		28	9.4	even	3
441.3.k.a.31.5		28	63.47	even	6
441.3.k.a.31.6		28	63.2	odd	6
441.3.k.a.313.5		28	63.32	odd	6
441.3.k.a.313.6		28	63.59	even	6
441.3.t.b.166.9		28	63.11	odd	6
441.3.t.b.166.10		28	63.38	even	6
441.3.t.b.178.9		28	63.5	even	6
441.3.t.b.178.10		28	63.23	odd	6
567.3.d.g.244.5		14	7.6	odd	2	inner
567.3.d.g.244.6		14	1.1	even	1	trivial
567.3.d.h.244.9		14	3.2	odd	2
567.3.d.h.244.10		14	21.20	even	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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	567.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.90488 q^{2} -0.371447 q^{4} +8.23162i q^{5} +(6.18933 - 3.26989i) q^{7} +8.32706 q^{8} +O(q^{10})\)	\(q-1.90488 q^{2} -0.371447 q^{4} +8.23162i q^{5} +(6.18933 - 3.26989i) q^{7} +8.32706 q^{8} -15.6802i q^{10} +11.9301 q^{11} -1.58781i q^{13} +(-11.7899 + 6.22874i) q^{14} -14.3762 q^{16} -19.5020i q^{17} -6.69545i q^{19} -3.05761i q^{20} -22.7253 q^{22} +28.1484 q^{23} -42.7595 q^{25} +3.02458i q^{26} +(-2.29901 + 1.21459i) q^{28} +10.9680 q^{29} -31.7080i q^{31} -5.92330 q^{32} +37.1490i q^{34} +(26.9165 + 50.9482i) q^{35} -6.88791 q^{37} +12.7540i q^{38} +68.5452i q^{40} +1.56305i q^{41} +65.0484 q^{43} -4.43138 q^{44} -53.6193 q^{46} +55.2911i q^{47} +(27.6156 - 40.4769i) q^{49} +81.4516 q^{50} +0.589787i q^{52} +33.9256 q^{53} +98.2037i q^{55} +(51.5390 - 27.2286i) q^{56} -20.8927 q^{58} +6.57763i q^{59} -76.1795i q^{61} +60.3999i q^{62} +68.7881 q^{64} +13.0702 q^{65} -23.7171 q^{67} +7.24397i q^{68} +(-51.2726 - 97.0500i) q^{70} +14.0551 q^{71} -40.2281i q^{73} +13.1206 q^{74} +2.48700i q^{76} +(73.8391 - 39.0100i) q^{77} +63.7289 q^{79} -118.340i q^{80} -2.97741i q^{82} -2.24313i q^{83} +160.533 q^{85} -123.909 q^{86} +99.3424 q^{88} +58.4246i q^{89} +(-5.19197 - 9.82748i) q^{91} -10.4556 q^{92} -105.323i q^{94} +55.1144 q^{95} +129.049i q^{97} +(-52.6043 + 77.1034i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} + 26 q^{4} - 4 q^{8}+O(q^{10}) \) 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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