LMFDB - Embedded newform 261.3.s.a.253.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,3,Mod(10,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([0, 23]))

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

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

chi := DirichletCharacter("261.10");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	261.s (of order $28$, degree $12$, 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:	$7.11173489980$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{28})$
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			253.1
Character	$\chi$	$=$	261.253
Dual form			261.3.s.a.163.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.929596 + 2.65663i) q^{2} +(-3.06622 - 2.44523i) q^{4} +(-1.35861 - 2.82119i) q^{5} +(2.26277 + 2.83742i) q^{7} +(-0.186254 + 0.117031i) q^{8} +O(q^{10})$	\(q+(-0.929596 + 2.65663i) q^{2} +(-3.06622 - 2.44523i) q^{4} +(-1.35861 - 2.82119i) q^{5} +(2.26277 + 2.83742i) q^{7} +(-0.186254 + 0.117031i) q^{8} +(8.75784 - 0.986771i) q^{10} +(-9.83338 - 6.17872i) q^{11} +(-18.5672 + 4.23785i) q^{13} +(-9.64144 + 3.37369i) q^{14} +(-3.62854 - 15.8977i) q^{16} +(12.3318 - 12.3318i) q^{17} +(-2.90153 - 25.7518i) q^{19} +(-2.73265 + 11.9725i) q^{20} +(25.5557 - 20.3800i) q^{22} +(-9.50107 - 4.57547i) q^{23} +(9.47395 - 11.8800i) q^{25} +(6.00161 - 53.2658i) q^{26} -14.2332i q^{28} +(-14.7201 + 24.9864i) q^{29} +(-8.22632 + 23.5095i) q^{31} +(44.7330 + 5.04020i) q^{32} +(21.2975 + 44.2247i) q^{34} +(4.93068 - 10.2387i) q^{35} +(-25.3173 + 15.9079i) q^{37} +(71.1102 + 16.2304i) q^{38} +(0.583216 + 0.366459i) q^{40} +(-36.7111 - 36.7111i) q^{41} +(37.8059 - 13.2289i) q^{43} +(15.0429 + 42.9902i) q^{44} +(20.9875 - 20.9875i) q^{46} +(-16.7697 + 26.6888i) q^{47} +(7.97269 - 34.9306i) q^{49} +(22.7537 + 36.2124i) q^{50} +(67.2937 + 32.4070i) q^{52} +(47.4028 - 22.8280i) q^{53} +(-4.07159 + 36.1364i) q^{55} +(-0.753518 - 0.263667i) q^{56} +(-52.6958 - 62.3332i) q^{58} -2.51722 q^{59} +(-29.2057 - 3.29069i) q^{61} +(-54.8089 - 43.7086i) q^{62} +(-26.6731 + 55.3872i) q^{64} +(37.1815 + 46.6241i) q^{65} +(-127.279 - 29.0506i) q^{67} +(-67.9662 + 7.65795i) q^{68} +(22.6168 + 22.6168i) q^{70} +(-73.2856 + 16.7270i) q^{71} +(8.81836 + 25.2014i) q^{73} +(-18.7267 - 82.0469i) q^{74} +(-54.0723 + 86.0556i) q^{76} +(-4.71902 - 41.8825i) q^{77} +(51.2212 + 81.5181i) q^{79} +(-39.9206 + 31.8356i) q^{80} +(131.654 - 63.4013i) q^{82} +(-1.49463 + 1.87421i) q^{83} +(-51.5446 - 18.0362i) q^{85} +112.734i q^{86} +2.55462 q^{88} +(28.8259 - 82.3798i) q^{89} +(-54.0378 - 43.0937i) q^{91} +(17.9443 + 37.2617i) q^{92} +(-55.3133 - 69.3607i) q^{94} +(-68.7086 + 43.1725i) q^{95} +(-57.2559 + 6.45119i) q^{97} +(85.3865 + 53.6519i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8}+O(q^{10}) $ 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8	$ 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8} - 20 q^{10} + 8 q^{11} - 14 q^{13} - 26 q^{14} + 18 q^{16} + 26 q^{17} + 2 q^{19} - 46 q^{20} + 154 q^{22} - 56 q^{23} - 34 q^{25} - 110 q^{26} + 170 q^{29} - 88 q^{31} + 132 q^{32} - 224 q^{34} + 210 q^{35} - 56 q^{37} + 294 q^{38} - 492 q^{40} + 34 q^{41} + 176 q^{43} - 126 q^{44} + 744 q^{46} - 208 q^{47} + 506 q^{49} - 732 q^{50} + 690 q^{52} + 14 q^{53} + 284 q^{55} - 332 q^{56} - 508 q^{58} + 44 q^{59} - 30 q^{61} + 504 q^{62} - 896 q^{64} + 554 q^{65} - 574 q^{67} + 796 q^{68} - 1066 q^{70} - 224 q^{71} - 22 q^{73} - 820 q^{74} + 514 q^{76} - 436 q^{77} + 564 q^{79} - 1162 q^{80} - 18 q^{82} + 126 q^{83} + 38 q^{85} - 384 q^{88} + 160 q^{89} - 434 q^{91} + 1022 q^{92} - 2 q^{94} + 642 q^{95} + 604 q^{97} + 102 q^{98}+O(q^{100}) $ 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8 - 20 * q^10 + 8 * q^11 - 14 * q^13 - 26 * q^14 + 18 * q^16 + 26 * q^17 + 2 * q^19 - 46 * q^20 + 154 * q^22 - 56 * q^23 - 34 * q^25 - 110 * q^26 + 170 * q^29 - 88 * q^31 + 132 * q^32 - 224 * q^34 + 210 * q^35 - 56 * q^37 + 294 * q^38 - 492 * q^40 + 34 * q^41 + 176 * q^43 - 126 * q^44 + 744 * q^46 - 208 * q^47 + 506 * q^49 - 732 * q^50 + 690 * q^52 + 14 * q^53 + 284 * q^55 - 332 * q^56 - 508 * q^58 + 44 * q^59 - 30 * q^61 + 504 * q^62 - 896 * q^64 + 554 * q^65 - 574 * q^67 + 796 * q^68 - 1066 * q^70 - 224 * q^71 - 22 * q^73 - 820 * q^74 + 514 * q^76 - 436 * q^77 + 564 * q^79 - 1162 * q^80 - 18 * q^82 + 126 * q^83 + 38 * q^85 - 384 * q^88 + 160 * q^89 - 434 * q^91 + 1022 * q^92 - 2 * q^94 + 642 * q^95 + 604 * q^97 + 102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{17}{28}\right)$	$1$

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 $

$2$	−0.929596	+	2.65663i	−0.464798	+	1.32832i	0.438280	+	0.898839i	$0.355588\pi$
$2$	−0.929596	+	2.65663i	−0.464798	+	1.32832i	−0.903078	+	0.429478i	$0.858698\pi$
$3$		0			0
$3$		0			0
$4$	−3.06622	−	2.44523i	−0.766556	−	0.611308i
$5$	−1.35861	−	2.82119i	−0.271723	−	0.564239i	0.719798	−	0.694183i	$-0.244234\pi$
$5$	−1.35861	−	2.82119i	−0.271723	−	0.564239i	−0.991521	+	0.129945i	$0.958520\pi$
$6$		0			0
$7$	2.26277	+	2.83742i	0.323252	+	0.405346i	0.916732	−	0.399504i	$-0.130817\pi$
$7$	2.26277	+	2.83742i	0.323252	+	0.405346i	−0.593479	+	0.804849i	$0.702246\pi$
$8$	−0.186254	+	0.117031i	−0.0232818	+	0.0146289i
$9$		0			0
$10$	8.75784	−	0.986771i	0.875784	−	0.0986771i
$11$	−9.83338	−	6.17872i	−0.893944	−	0.561702i	0.00489180	−	0.999988i	$-0.498443\pi$
$11$	−9.83338	−	6.17872i	−0.893944	−	0.561702i	−0.898836	+	0.438286i	$0.855586\pi$
$12$		0			0
$13$	−18.5672	+	4.23785i	−1.42825	+	0.325988i	−0.865611	−	0.500717i	$-0.833070\pi$
$13$	−18.5672	+	4.23785i	−1.42825	+	0.325988i	−0.562636	+	0.826705i	$0.690213\pi$
$14$	−9.64144	+	3.37369i	−0.688675	+	0.240978i
$15$		0			0
$16$	−3.62854	−	15.8977i	−0.226784	−	0.993604i
$17$	12.3318	−	12.3318i	0.725401	−	0.725401i	−0.244299	−	0.969700i	$-0.578558\pi$
$17$	12.3318	−	12.3318i	0.725401	−	0.725401i	0.969700	+	0.244299i	$0.0785579\pi$
$18$		0			0
$19$	−2.90153	−	25.7518i	−0.152712	−	1.35536i	−0.803141	−	0.595789i	$-0.796839\pi$
$19$	−2.90153	−	25.7518i	−0.152712	−	1.35536i	0.650429	−	0.759567i	$-0.274589\pi$
$20$	−2.73265	+	11.9725i	−0.136633	+	0.598627i
$21$		0			0
$22$	25.5557	−	20.3800i	1.16162	−	0.926362i
$23$	−9.50107	−	4.57547i	−0.413090	−	0.198934i	0.215784	−	0.976441i	$-0.430769\pi$
$23$	−9.50107	−	4.57547i	−0.413090	−	0.198934i	−0.628874	+	0.777508i	$0.716484\pi$
$24$		0			0
$25$	9.47395	−	11.8800i	0.378958	−	0.475198i
$26$	6.00161	−	53.2658i	0.230831	−	2.04868i
$27$		0			0
$28$		−	14.2332i		−	0.508327i
$29$	−14.7201	+	24.9864i	−0.507590	+	0.861599i
$29$	−14.7201	+	24.9864i	−0.507590	+	0.861599i
$30$		0			0
$31$	−8.22632	+	23.5095i	−0.265365	+	0.758370i	0.731687	+	0.681641i	$0.238733\pi$
$31$	−8.22632	+	23.5095i	−0.265365	+	0.758370i	−0.997052	+	0.0767289i	$0.975552\pi$
$32$	44.7330	+	5.04020i	1.39791	+	0.157506i
$33$		0			0
$34$	21.2975	+	44.2247i	0.626397	+	1.30073i
$35$	4.93068	−	10.2387i	0.140877	−	0.292533i
$36$		0			0
$37$	−25.3173	+	15.9079i	−0.684253	+	0.429944i	−0.828794	−	0.559554i	$-0.810972\pi$
$37$	−25.3173	+	15.9079i	−0.684253	+	0.429944i	0.144541	+	0.989499i	$0.453829\pi$
$38$	71.1102	+	16.2304i	1.87132	+	0.427117i
$39$		0			0
$40$	0.583216	+	0.366459i	0.0145804	+	0.00916148i
$41$	−36.7111	−	36.7111i	−0.895392	−	0.895392i	0.0996326	−	0.995024i	$-0.468233\pi$
$41$	−36.7111	−	36.7111i	−0.895392	−	0.895392i	−0.995024	+	0.0996326i	$0.968233\pi$
$42$		0			0
$43$	37.8059	−	13.2289i	0.879208	−	0.307648i	0.147333	−	0.989087i	$-0.452931\pi$
$43$	37.8059	−	13.2289i	0.879208	−	0.307648i	0.731875	+	0.681439i	$0.238645\pi$
$44$	15.0429	+	42.9902i	0.341885	+	0.977051i
$45$		0			0
$46$	20.9875	−	20.9875i	0.456250	−	0.456250i
$47$	−16.7697	+	26.6888i	−0.356802	+	0.567847i	−0.976103	−	0.217306i	$-0.930273\pi$
$47$	−16.7697	+	26.6888i	−0.356802	+	0.567847i	0.619302	+	0.785153i	$0.287416\pi$
$48$		0			0
$49$	7.97269	−	34.9306i	0.162708	−	0.712870i
$50$	22.7537	+	36.2124i	0.455075	+	0.724247i
$51$		0			0
$52$	67.2937	+	32.4070i	1.29411	+	0.623211i
$53$	47.4028	−	22.8280i	0.894393	−	0.430717i	0.0705326	−	0.997509i	$-0.477530\pi$
$53$	47.4028	−	22.8280i	0.894393	−	0.430717i	0.823861	+	0.566792i	$0.191816\pi$
$54$		0			0
$55$	−4.07159	+	36.1364i	−0.0740289	+	0.657025i
$56$	−0.753518	−	0.263667i	−0.0134557	−	0.00470835i
$57$		0			0
$58$	−52.6958	−	62.3332i	−0.908549	−	1.07471i
$59$	−2.51722			−0.0426647			−0.0213324	−	0.999772i	$-0.506791\pi$
$59$	−2.51722			−0.0426647			−0.0213324	+	0.999772i	$0.506791\pi$
$60$		0			0
$61$	−29.2057	−	3.29069i	−0.478781	−	0.0539457i	−0.130724	−	0.991419i	$-0.541730\pi$
$61$	−29.2057	−	3.29069i	−0.478781	−	0.0539457i	−0.348058	+	0.937473i	$0.613159\pi$
$62$	−54.8089	−	43.7086i	−0.884014	−	0.704977i
$63$		0			0
$64$	−26.6731	+	55.3872i	−0.416766	+	0.865424i
$65$	37.1815	+	46.6241i	0.572023	+	0.717294i
$66$		0			0
$67$	−127.279	−	29.0506i	−1.89969	−	0.433591i	−0.899690	−	0.436529i	$-0.856208\pi$
$67$	−127.279	−	29.0506i	−1.89969	−	0.433591i	−0.999996	+	0.00293826i	$0.999065\pi$
$68$	−67.9662	+	7.65795i	−0.999503	+	0.112617i
$69$		0			0
$70$	22.6168	+	22.6168i	0.323098	+	0.323098i
$71$	−73.2856	+	16.7270i	−1.03219	+	0.235591i	−0.704881	−	0.709326i	$-0.749000\pi$
$71$	−73.2856	+	16.7270i	−1.03219	+	0.235591i	−0.327311	+	0.944917i	$0.606142\pi$
$72$		0			0
$73$	8.81836	+	25.2014i	0.120799	+	0.345225i	0.988366	−	0.152097i	$-0.0486026\pi$
$73$	8.81836	+	25.2014i	0.120799	+	0.345225i	−0.867566	+	0.497322i	$0.834317\pi$
$74$	−18.7267	−	82.0469i	−0.253063	−	1.10874i
$75$		0			0
$76$	−54.0723	+	86.0556i	−0.711477	+	1.13231i
$77$	−4.71902	−	41.8825i	−0.0612860	−	0.543928i
$78$		0			0
$79$	51.2212	+	81.5181i	0.648370	+	1.03188i	0.995564	+	0.0940819i	$0.0299916\pi$
$79$	51.2212	+	81.5181i	0.648370	+	1.03188i	−0.347194	+	0.937793i	$0.612866\pi$
$80$	−39.9206	+	31.8356i	−0.499008	+	0.397945i
$81$		0			0
$82$	131.654	−	63.4013i	1.60554	−	0.773187i
$83$	−1.49463	+	1.87421i	−0.0180076	+	0.0225808i	−0.790754	−	0.612134i	$-0.790311\pi$
$83$	−1.49463	+	1.87421i	−0.0180076	+	0.0225808i	0.772746	+	0.634715i	$0.218883\pi$
$84$		0			0
$85$	−51.5446	−	18.0362i	−0.606407	−	0.212191i
$86$			112.734i			1.31086i
$87$		0			0
$88$	2.55462			0.0290297
$89$	28.8259	−	82.3798i	0.323887	−	0.925615i	−0.660689	−	0.750659i	$-0.729736\pi$
$89$	28.8259	−	82.3798i	0.323887	−	0.925615i	0.984576	−	0.174956i	$-0.0559783\pi$
$90$		0			0
$91$	−54.0378	−	43.0937i	−0.593822	−	0.473558i
$92$	17.9443	+	37.2617i	0.195047	+	0.405019i
$93$		0			0
$94$	−55.3133	−	69.3607i	−0.588440	−	0.737880i
$95$	−68.7086	+	43.1725i	−0.723249	+	0.454447i
$96$		0			0
$97$	−57.2559	+	6.45119i	−0.590267	+	0.0665071i	−0.402046	−	0.915620i	$-0.631701\pi$
$97$	−57.2559	+	6.45119i	−0.590267	+	0.0665071i	−0.188221	+	0.982127i	$0.560272\pi$
$98$	85.3865	+	53.6519i	0.871290	+	0.547468i
$99$		0			0
$100$	−58.0985	+	13.2606i	−0.580985	+	0.132606i
$101$	−172.564	+	60.3829i	−1.70856	+	0.597850i	−0.994736	−	0.102476i	$-0.967324\pi$
$101$	−172.564	+	60.3829i	−1.70856	+	0.597850i	−0.713823	+	0.700326i	$0.753038\pi$
$102$		0			0
$103$	24.0982	+	105.581i	0.233963	+	1.02506i	0.946318	+	0.323238i	$0.104772\pi$
$103$	24.0982	+	105.581i	0.233963	+	1.02506i	−0.712355	+	0.701819i	$0.752371\pi$
$104$	2.96227	−	2.96227i	0.0284833	−	0.0284833i
$105$		0			0
$106$	16.5801	+	147.153i	0.156416	+	1.38823i
$107$	12.9174	−	56.5950i	0.120724	−	0.528925i	−0.878011	−	0.478640i	$-0.841130\pi$
$107$	12.9174	−	56.5950i	0.120724	−	0.528925i	0.998735	−	0.0502849i	$-0.0160129\pi$
$108$		0			0
$109$	−82.1016	+	65.4738i	−0.753225	+	0.600677i	−0.922997	−	0.384806i	$-0.874268\pi$
$109$	−82.1016	+	65.4738i	−0.753225	+	0.600677i	0.169772	+	0.985483i	$0.445697\pi$
$110$	−92.2161	−	44.4089i	−0.838328	−	0.403718i
$111$		0			0
$112$	36.8978	−	46.2684i	0.329445	−	0.413111i
$113$	−13.1858	+	117.027i	−0.116688	+	1.03564i	0.789788	+	0.613380i	$0.210191\pi$
$113$	−13.1858	+	117.027i	−0.116688	+	1.03564i	−0.906476	+	0.422257i	$0.861238\pi$
$114$		0			0
$115$			33.0207i			0.287136i
$116$	106.233	−	40.6197i	0.915798	−	0.350170i
$117$		0			0
$118$	2.34000	−	6.68733i	0.0198305	−	0.0566722i
$119$	62.8945	+	7.08651i	0.528526	+	0.0595505i
$120$		0			0
$121$	6.01884	+	12.4983i	0.0497425	+	0.103291i
$122$	35.8916	−	74.5297i	0.294194	−	0.610899i
$123$		0			0
$124$	82.7098	−	51.9700i	0.667014	−	0.419113i
$125$	−122.707	−	28.0070i	−0.981653	−	0.224056i
$126$		0			0
$127$	158.239	+	99.4283i	1.24598	+	0.782900i	0.983301	−	0.181984i	$-0.0582520\pi$
$127$	158.239	+	99.4283i	1.24598	+	0.782900i	0.262676	+	0.964884i	$0.415395\pi$
$128$	4.97642	+	4.97642i	0.0388783	+	0.0388783i
$129$		0			0
$130$	−158.427	+	55.4360i	−1.21867	+	0.426430i
$131$	40.7754	+	116.530i	0.311263	+	0.889538i	0.988155	+	0.153456i	$0.0490404\pi$
$131$	40.7754	+	116.530i	0.311263	+	0.889538i	−0.676893	+	0.736082i	$0.736674\pi$
$132$		0			0
$133$	66.5031	−	66.5031i	0.500023	−	0.500023i
$134$	195.495	−	311.128i	1.45892	−	2.32185i
$135$		0			0
$136$	−0.853645	+	3.74006i	−0.00627680	+	0.0275005i
$137$	−5.17515	−	8.23621i	−0.0377748	−	0.0601183i	0.827303	−	0.561756i	$-0.189874\pi$
$137$	−5.17515	−	8.23621i	−0.0377748	−	0.0601183i	−0.865078	+	0.501638i	$0.832731\pi$
$138$		0			0
$139$	−140.076	−	67.4569i	−1.00774	−	0.485302i	−0.144181	−	0.989551i	$-0.546055\pi$
$139$	−140.076	−	67.4569i	−1.00774	−	0.485302i	−0.863558	+	0.504250i	$0.831769\pi$
$140$	−40.1545	+	19.3374i	−0.286818	+	0.138124i
$141$		0			0
$142$	23.6886	−	210.242i	0.166821	−	1.48058i
$143$	208.763	+	73.0493i	1.45988	+	0.510835i
$144$		0			0
$145$	90.4903	+	7.58143i	0.624071	+	0.0522858i
$146$	−75.1484			−0.514715
$147$		0			0
$148$	116.527	+	13.1295i	0.787346	+	0.0887126i
$149$	90.7584	+	72.3774i	0.609117	+	0.485754i	0.878797	−	0.477196i	$-0.158347\pi$
$149$	90.7584	+	72.3774i	0.609117	+	0.485754i	−0.269680	+	0.962950i	$0.586918\pi$
$150$		0			0
$151$	69.0723	−	143.430i	0.457432	−	0.949868i	−0.536910	−	0.843640i	$-0.680408\pi$
$151$	69.0723	−	143.430i	0.457432	−	0.949868i	0.994342	−	0.106228i	$-0.0338773\pi$
$152$	3.55419	+	4.45681i	0.0233828	+	0.0293211i
$153$		0			0
$154$	115.653	+	26.3971i	0.750994	+	0.171409i
$155$	77.5011	−	8.73228i	0.500007	−	0.0563373i
$156$		0			0
$157$	−51.5792	−	51.5792i	−0.328530	−	0.328530i	0.523497	−	0.852027i	$-0.324627\pi$
$157$	−51.5792	−	51.5792i	−0.328530	−	0.328530i	−0.852027	+	0.523497i	$0.824627\pi$
$158$	−264.179	+	60.2971i	−1.67202	+	0.381627i
$159$		0			0
$160$	−46.5555	−	133.048i	−0.290972	−	0.831551i
$161$	−8.51617	−	37.3118i	−0.0528954	−	0.231750i
$162$		0			0
$163$	56.0119	−	89.1425i	0.343632	−	0.546886i	−0.629540	−	0.776968i	$-0.716757\pi$
$163$	56.0119	−	89.1425i	0.343632	−	0.546886i	0.973171	+	0.230082i	$0.0738994\pi$
$164$	22.7973	+	202.331i	0.139008	+	1.23373i
$165$		0			0
$166$	−3.58968	−	5.71294i	−0.0216246	−	0.0344153i
$167$	74.9501	−	59.7707i	0.448803	−	0.357908i	−0.372855	−	0.927890i	$-0.621621\pi$
$167$	74.9501	−	59.7707i	0.448803	−	0.357908i	0.821658	+	0.569981i	$0.193050\pi$
$168$		0			0
$169$	174.518	−	84.0437i	1.03265	−	0.497300i
$170$	95.8313	−	120.169i	0.563713	−	0.706874i
$171$		0			0
$172$	−148.269	−	51.8816i	−0.862029	−	0.301637i
$173$		−	296.080i		−	1.71145i	−0.517435	−	0.855723i	$-0.673113\pi$
$173$		−	296.080i		−	1.71145i	0.517435	−	0.855723i	$-0.326887\pi$
$174$		0			0
$175$	55.1458			0.315119
$176$	−62.5465	+	178.748i	−0.355378	+	1.01561i
$177$		0			0
$178$	192.056	+	153.160i	1.07897	+	0.860448i
$179$	74.3652	+	154.421i	0.415448	+	0.862687i	0.998728	+	0.0504158i	$0.0160546\pi$
$179$	74.3652	+	154.421i	0.415448	+	0.862687i	−0.583280	+	0.812271i	$0.698231\pi$
$180$		0			0
$181$	−10.7572	−	13.4891i	−0.0594319	−	0.0745252i	0.751227	−	0.660044i	$-0.229462\pi$
$181$	−10.7572	−	13.4891i	−0.0594319	−	0.0745252i	−0.810659	+	0.585519i	$0.800891\pi$
$182$	164.718	−	103.499i	0.905042	−	0.568675i
$183$		0			0
$184$	2.30509	−	0.259721i	0.0125277	−	0.00141153i
$185$	79.2759	+	49.8123i	0.428518	+	0.269256i
$186$		0			0
$187$	−197.458	+	45.0686i	−1.05593	+	0.241008i
$188$	116.680	−	40.8281i	0.620638	−	0.217171i
$189$		0			0
$190$	−50.8222	−	222.667i	−0.267485	−	1.17193i
$191$	169.220	−	169.220i	0.885969	−	0.885969i	−0.108164	−	0.994133i	$-0.534497\pi$
$191$	169.220	−	169.220i	0.885969	−	0.885969i	0.994133	+	0.108164i	$0.0344973\pi$
$192$		0			0
$193$	23.1678	+	205.620i	0.120040	+	1.06539i	0.898889	+	0.438177i	$0.144376\pi$
$193$	23.1678	+	205.620i	0.120040	+	1.06539i	−0.778848	+	0.627212i	$0.784196\pi$
$194$	36.0864	−	158.105i	0.186012	−	0.814973i
$195$		0			0
$196$	−109.859	+	87.6100i	−0.560508	+	0.446990i
$197$	−80.4002	−	38.7187i	−0.408123	−	0.196542i	0.218547	−	0.975826i	$-0.429868\pi$
$197$	−80.4002	−	38.7187i	−0.408123	−	0.196542i	−0.626670	+	0.779285i	$0.715583\pi$
$198$		0			0
$199$	6.40517	−	8.03183i	0.0321868	−	0.0403609i	−0.765478	−	0.643463i	$-0.777497\pi$
$199$	6.40517	−	8.03183i	0.0321868	−	0.0403609i	0.797664	+	0.603102i	$0.206069\pi$
$200$	−0.374237	+	3.32145i	−0.00187119	+	0.0166072i
$201$		0			0
$202$		−	514.572i		−	2.54739i
$203$	−104.205	+	14.7712i	−0.513325	+	0.0727644i
$204$		0			0
$205$	−53.6928	+	153.445i	−0.261916	+	0.748513i
$206$	−302.891	−	34.1277i	−1.47035	−	0.165668i
$207$		0			0
$208$	134.744	+	279.798i	0.647807	+	1.34518i
$209$	−130.581	+	271.155i	−0.624791	+	1.29739i
$210$		0			0
$211$	11.7610	−	7.38993i	0.0557394	−	0.0350234i	−0.503874	−	0.863777i	$-0.668092\pi$
$211$	11.7610	−	7.38993i	0.0557394	−	0.0350234i	0.559613	+	0.828754i	$0.310950\pi$
$212$	−201.167	−	45.9151i	−0.948903	−	0.216581i
$213$		0			0
$214$	138.344	+	86.9273i	0.646468	+	0.406202i
$215$	−88.6849	−	88.6849i	−0.412488	−	0.412488i
$216$		0			0
$217$	−85.3205	+	29.8549i	−0.393182	+	0.137580i
$218$	−97.6186	−	278.978i	−0.447792	−	1.27972i
$219$		0			0
$220$	100.846	−	100.846i	0.458392	−	0.458392i
$221$	−176.707	+	281.228i	−0.799580	+	1.27252i
$222$		0			0
$223$	23.3723	−	102.401i	0.104808	−	0.459196i	−0.895103	−	0.445860i	$-0.852898\pi$
$223$	23.3723	−	102.401i	0.104808	−	0.459196i	0.999911	−	0.0133356i	$-0.00424497\pi$
$224$	86.9192	+	138.331i	0.388032	+	0.617550i
$225$		0			0
$226$	−298.640	−	143.818i	−1.32142	−	0.636361i
$227$	278.194	−	133.971i	1.22553	−	0.590182i	0.294680	−	0.955596i	$-0.404787\pi$
$227$	278.194	−	133.971i	1.22553	−	0.590182i	0.930845	+	0.365414i	$0.119073\pi$
$228$		0			0
$229$	9.13045	−	81.0350i	0.0398710	−	0.353865i	−0.957898	−	0.287108i	$-0.907306\pi$
$229$	9.13045	−	81.0350i	0.0398710	−	0.353865i	0.997769	−	0.0667570i	$-0.0212652\pi$
$230$	−87.7238	−	30.6959i	−0.381408	−	0.133460i
$231$		0			0
$232$	−0.182503	−	6.37654i	−0.000786651	−	0.0274851i
$233$	155.459			0.667206			0.333603	−	0.942714i	$-0.391735\pi$
$233$	155.459			0.667206			0.333603	+	0.942714i	$0.391735\pi$
$234$		0			0
$235$	98.0778	+	11.0507i	0.417352	+	0.0470243i
$236$	7.71835	+	6.15518i	0.0327049	+	0.0260813i
$237$		0			0
$238$	−77.2928	+	160.500i	−0.324760	+	0.674370i
$239$	−190.666	−	239.088i	−0.797767	−	1.00037i	−0.999780	−	0.0209848i	$-0.993320\pi$
$239$	−190.666	−	239.088i	−0.797767	−	1.00037i	0.202013	−	0.979383i	$-0.435252\pi$
$240$		0			0
$241$	−404.989	−	92.4361i	−1.68045	−	0.383552i	−0.727366	−	0.686250i	$-0.759256\pi$
$241$	−404.989	−	92.4361i	−1.68045	−	0.383552i	−0.953087	+	0.302698i	$0.902113\pi$
$242$	−38.7984	+	4.37153i	−0.160324	+	0.0180642i
$243$		0			0
$244$	81.5046	+	81.5046i	0.334035	+	0.334035i
$245$	−109.378	+	24.9648i	−0.446440	+	0.101897i
$246$		0			0
$247$	163.005	+	465.842i	0.659941	+	1.88600i
$248$	−1.21916	−	5.34148i	−0.00491596	−	0.0215382i
$249$		0			0
$250$	188.472	−	299.951i	0.753887	−	1.19980i
$251$	45.9006	+	407.379i	0.182871	+	1.62302i	0.664944	+	0.746894i	$0.268456\pi$
$251$	45.9006	+	407.379i	0.182871	+	1.62302i	−0.482073	+	0.876131i	$0.660116\pi$
$252$		0			0
$253$	65.1571	+	103.697i	0.257538	+	0.409869i
$254$	−411.243	+	327.955i	−1.61907	+	1.29116i
$255$		0			0
$256$	−239.395	+	115.287i	−0.935138	+	0.450339i
$257$	29.1320	−	36.5304i	0.113354	−	0.142142i	−0.721917	−	0.691979i	$-0.756739\pi$
$257$	29.1320	−	36.5304i	0.113354	−	0.142142i	0.835272	+	0.549838i	$0.185310\pi$
$258$		0			0
$259$	−102.425	−	35.8400i	−0.395463	−	0.138378i
$260$		−	233.877i		−	0.899527i
$261$		0			0
$262$	−347.481			−1.32626
$263$	−9.56028	+	27.3217i	−0.0363509	+	0.103885i	−0.960628	−	0.277836i	$-0.910383\pi$
$263$	−9.56028	+	27.3217i	−0.0363509	+	0.103885i	0.924278	+	0.381721i	$0.124668\pi$
$264$		0			0
$265$	−128.804	−	102.718i	−0.486054	−	0.387615i
$266$	114.853	+	238.495i	0.431779	+	0.896599i
$267$		0			0
$268$	319.230	+	400.302i	1.19116	+	1.49366i
$269$	56.5317	−	35.5212i	0.210155	−	0.132049i	−0.422842	−	0.906203i	$-0.638967\pi$
$269$	56.5317	−	35.5212i	0.210155	−	0.132049i	0.632997	+	0.774154i	$0.281825\pi$
$270$		0			0
$271$	309.195	−	34.8379i	1.14094	−	0.128553i	0.478794	−	0.877927i	$-0.341074\pi$
$271$	309.195	−	34.8379i	1.14094	−	0.128553i	0.662147	+	0.749374i	$0.269646\pi$
$272$	−240.793	−	151.301i	−0.885270	−	0.556252i
$273$		0			0
$274$	26.6914	−	6.09213i	0.0974138	−	0.0222341i
$275$	−166.564	+	58.2833i	−0.605687	+	0.211939i
$276$		0			0
$277$	−55.0697	−	241.276i	−0.198807	−	0.871032i	−0.971648	−	0.236432i	$-0.924022\pi$
$277$	−55.0697	−	241.276i	−0.198807	−	0.871032i	0.772841	−	0.634600i	$-0.218835\pi$
$278$	309.422	−	309.422i	1.11303	−	1.11303i
$279$		0			0
$280$	0.279884	+	2.48404i	0.000999587	+	0.00887158i
$281$	45.2593	−	198.294i	0.161065	−	0.705672i	−0.828308	−	0.560273i	$-0.810696\pi$
$281$	45.2593	−	198.294i	0.161065	−	0.705672i	0.989373	−	0.145399i	$-0.0464466\pi$
$282$		0			0
$283$	231.637	−	184.725i	0.818506	−	0.652737i	−0.121994	−	0.992531i	$-0.538929\pi$
$283$	231.637	−	184.725i	0.818506	−	0.652737i	0.940500	+	0.339794i	$0.110357\pi$
$284$	265.611	+	127.912i	0.935251	+	0.450393i
$285$		0			0
$286$	−388.131	+	486.700i	−1.35710	+	1.70175i
$287$	21.0961	−	187.233i	0.0735057	−	0.652381i
$288$		0			0
$289$		−	15.1471i		−	0.0524120i
$290$	−104.261	+	233.352i	−0.359519	+	0.804661i
$291$		0			0
$292$	34.5842	−	98.8361i	0.118439	−	0.338480i
$293$	−10.2359	−	1.15331i	−0.0349349	−	0.00393622i	0.0944797	−	0.995527i	$-0.469881\pi$
$293$	−10.2359	−	1.15331i	−0.0349349	−	0.00393622i	−0.129415	+	0.991591i	$0.541310\pi$
$294$		0			0
$295$	3.41993	+	7.10156i	0.0115930	+	0.0240731i
$296$	2.85374	−	5.92585i	0.00964101	−	0.0200198i
$297$		0			0
$298$	−276.649	+	173.830i	−0.928352	+	0.583322i
$299$	195.799	+	44.6897i	0.654845	+	0.149464i
$300$		0			0
$301$	123.082	+	77.3375i	0.408910	+	0.256935i
$302$	316.832	+	316.832i	1.04911	+	1.04911i
$303$		0			0
$304$	−398.865	+	139.569i	−1.31206	+	0.459108i
$305$	30.3956	+	86.8656i	0.0996576	+	0.284805i
$306$		0			0
$307$	282.559	−	282.559i	0.920388	−	0.920388i	−0.0766689	−	0.997057i	$-0.524428\pi$
$307$	282.559	−	282.559i	0.920388	−	0.920388i	0.997057	+	0.0766689i	$0.0244284\pi$
$308$	−87.9427	+	139.960i	−0.285528	+	0.454416i
$309$		0			0
$310$	−48.8463	+	214.009i	−0.157569	+	0.690353i
$311$	−19.7419	−	31.4191i	−0.0634788	−	0.101026i	0.813477	−	0.581597i	$-0.197572\pi$
$311$	−19.7419	−	31.4191i	−0.0634788	−	0.101026i	−0.876956	+	0.480572i	$0.840429\pi$
$312$		0			0
$313$	−350.960	−	169.013i	−1.12128	−	0.539979i	−0.220990	−	0.975276i	$-0.570929\pi$
$313$	−350.960	−	169.013i	−1.12128	−	0.539979i	−0.900287	+	0.435297i	$0.856643\pi$
$314$	184.975	−	89.0793i	0.589092	−	0.283692i
$315$		0			0
$316$	42.2749	−	375.201i	0.133781	−	1.18734i
$317$	−95.6338	−	33.4637i	−0.301684	−	0.105564i	0.175192	−	0.984534i	$-0.443945\pi$
$317$	−95.6338	−	33.4637i	−0.301684	−	0.105564i	−0.476876	+	0.878970i	$0.658231\pi$
$318$		0			0
$319$	299.132	−	154.749i	0.937719	−	0.485106i
$320$	192.496			0.601551
$321$		0			0
$322$	107.040	+	12.0605i	0.332423	+	0.0374551i
$323$	−353.347	−	281.785i	−1.09395	−	0.872399i
$324$		0			0
$325$	−125.559	+	260.727i	−0.386337	+	0.802237i
$326$	184.750	+	231.670i	0.566719	+	0.710643i
$327$		0			0
$328$	11.1339	+	2.54125i	0.0339450	+	0.00774772i
$329$	−113.673	+	12.8079i	−0.345512	+	0.0389298i
$330$		0			0
$331$	333.816	+	333.816i	1.00851	+	1.00851i	0.999963	+	0.00854394i	$0.00271965\pi$
$331$	333.816	+	333.816i	1.00851	+	1.00851i	0.00854394	+	0.999963i	$0.497280\pi$
$332$	9.16574	−	2.09202i	0.0276076	−	0.00630126i
$333$		0			0
$334$	89.1155	+	254.677i	0.266813	+	0.762507i
$335$	90.9658	+	398.547i	0.271540	+	1.18969i
$336$		0			0
$337$	55.8513	−	88.8868i	0.165731	−	0.263759i	−0.753525	−	0.657419i	$-0.771648\pi$
$337$	55.8513	−	88.8868i	0.165731	−	0.263759i	0.919256	+	0.393660i	$0.128791\pi$
$338$	61.0415	+	541.758i	0.180596	+	1.60283i
$339$		0			0
$340$	113.944	+	181.342i	0.335131	+	0.533357i
$341$	226.151	−	180.349i	0.663199	−	0.528884i
$342$		0			0
$343$	277.373	−	133.576i	0.808668	−	0.389434i
$344$	−5.49333	+	6.88842i	−0.0159690	+	0.0200245i
$345$		0			0
$346$	786.576	+	275.235i	2.27334	+	0.795476i
$347$		−	402.156i		−	1.15895i	−0.814990	−	0.579475i	$-0.803258\pi$
$347$		−	402.156i		−	1.15895i	0.814990	−	0.579475i	$-0.196742\pi$
$348$		0			0
$349$	−260.433			−0.746226			−0.373113	−	0.927786i	$-0.621710\pi$
$349$	−260.433			−0.746226			−0.373113	+	0.927786i	$0.621710\pi$
$350$	−51.2633	+	146.502i	−0.146467	+	0.418577i
$351$		0			0
$352$	−408.735	−	325.955i	−1.16118	−	0.926009i
$353$	39.7236	+	82.4870i	0.112532	+	0.233674i	0.949627	−	0.313383i	$-0.101462\pi$
$353$	39.7236	+	82.4870i	0.112532	+	0.233674i	−0.837095	+	0.547057i	$0.815748\pi$
$354$		0			0
$355$	146.757	+	184.027i	0.413400	+	0.518387i
$356$	−289.824	+	182.109i	−0.814113	+	0.511541i
$357$		0			0
$358$	−479.369	+	54.0119i	−1.33902	+	0.150871i
$359$	−24.5403	−	15.4197i	−0.0683573	−	0.0429517i	0.497420	−	0.867510i	$-0.334281\pi$
$359$	−24.5403	−	15.4197i	−0.0683573	−	0.0429517i	−0.565777	+	0.824558i	$0.691424\pi$
$360$		0			0
$361$	−302.786	+	69.1088i	−0.838741	+	0.191437i
$362$	45.8353	−	16.0385i	0.126617	−	0.0443052i
$363$		0			0
$364$	60.3179	+	264.270i	0.165709	+	0.726017i
$365$	59.1173	−	59.1173i	0.161965	−	0.161965i
$366$		0			0
$367$	−32.3885	−	287.455i	−0.0882519	−	0.783257i	−0.957412	−	0.288726i	$-0.906768\pi$
$367$	−32.3885	−	287.455i	−0.0882519	−	0.783257i	0.869160	−	0.494531i	$-0.164660\pi$
$368$	−38.2644	+	167.647i	−0.103979	+	0.455563i
$369$		0			0
$370$	−206.028	+	164.302i	−0.556832	+	0.444058i
$371$	172.034	+	82.8473i	0.463704	+	0.223308i
$372$		0			0
$373$	−14.6070	+	18.3167i	−0.0391610	+	0.0491063i	−0.801026	−	0.598629i	$-0.795712\pi$
$373$	−14.6070	+	18.3167i	−0.0391610	+	0.0491063i	0.761865	+	0.647735i	$0.224284\pi$
$374$	63.8258	−	566.470i	0.170657	−	1.51462i
$375$		0			0
$376$		−	6.93349i		−	0.0184401i
$377$	167.423	−	526.309i	0.444093	−	1.39604i
$378$		0			0
$379$	−134.820	+	385.294i	−0.355726	+	1.01661i	0.617463	+	0.786600i	$0.288160\pi$
$379$	−134.820	+	385.294i	−0.355726	+	1.01661i	−0.973189	+	0.230007i	$0.926125\pi$
$380$	316.243	+	35.6320i	0.832218	+	0.0937684i
$381$		0			0
$382$	292.249	+	606.862i	0.765050	+	1.58864i
$383$	38.8770	−	80.7290i	0.101507	−	0.210781i	−0.844030	−	0.536295i	$-0.819823\pi$
$383$	38.8770	−	80.7290i	0.101507	−	0.210781i	0.945537	+	0.325515i	$0.105538\pi$
$384$		0			0
$385$	−111.747	+	70.2154i	−0.290252	+	0.182378i
$386$	−567.794	−	129.595i	−1.47097	−	0.335739i
$387$		0			0
$388$	191.334	+	120.223i	0.493129	+	0.309853i
$389$	76.5479	+	76.5479i	0.196781	+	0.196781i	0.798619	−	0.601837i	$-0.205564\pi$
$389$	76.5479	+	76.5479i	0.196781	+	0.196781i	−0.601837	+	0.798619i	$0.705564\pi$
$390$		0			0
$391$	−173.589	+	60.7415i	−0.443962	+	0.155349i
$392$	2.60303	+	7.43904i	0.00664039	+	0.0189771i
$393$		0			0
$394$	177.601	−	177.601i	0.450764	−	0.450764i
$395$	160.388	−	255.257i	0.406047	−	0.646220i
$396$		0			0
$397$	41.9153	−	183.643i	0.105580	−	0.462576i	−0.894306	−	0.447457i	$-0.852330\pi$
$397$	41.9153	−	183.643i	0.105580	−	0.462576i	0.999886	−	0.0151197i	$-0.00481295\pi$
$398$	15.3834	+	24.4825i	0.0386518	+	0.0615139i
$399$		0			0
$400$	−223.240	−	107.507i	−0.558101	−	0.268767i
$401$	−514.699	+	247.866i	−1.28354	+	0.618120i	−0.946297	−	0.323298i	$-0.895209\pi$
$401$	−514.699	+	247.866i	−1.28354	+	0.618120i	−0.337242	+	0.941418i	$0.609494\pi$
$402$		0			0
$403$	53.1103	−	471.367i	0.131787	−	1.16965i
$404$	676.771	+	236.812i	1.67518	+	0.586169i
$405$		0			0
$406$	57.6270	−	290.566i	0.141938	−	0.715679i
$407$	347.246			0.853184
$408$		0			0
$409$	711.156	+	80.1281i	1.73877	+	0.195912i	0.923612	−	0.383329i	$-0.125222\pi$
$409$	711.156	+	80.1281i	1.73877	+	0.195912i	0.815157	+	0.579241i	$0.196651\pi$
$410$	−357.735	−	285.284i	−0.872524	−	0.695815i
$411$		0			0
$412$	184.279	−	382.660i	0.447280	−	0.928787i
$413$	−5.69588	−	7.14241i	−0.0137915	−	0.0172940i
$414$		0			0
$415$	7.31813	+	1.67031i	0.0176340	+	0.00402485i
$416$	−851.927	+	95.9891i	−2.04790	+	0.230743i
$417$		0			0
$418$	−598.971	−	598.971i	−1.43294	−	1.43294i
$419$	−251.361	+	57.3714i	−0.599906	+	0.136925i	−0.511680	−	0.859176i	$-0.670977\pi$
$419$	−251.361	+	57.3714i	−0.599906	+	0.136925i	−0.0882256	+	0.996101i	$0.528120\pi$
$420$		0			0
$421$	−237.289	−	678.132i	−0.563631	−	1.61077i	−0.774029	−	0.633150i	$-0.781762\pi$
$421$	−237.289	−	678.132i	−0.563631	−	1.61077i	0.210398	−	0.977616i	$-0.432524\pi$
$422$	8.69934	+	38.1143i	0.0206146	+	0.0903183i
$423$		0			0
$424$	−6.15740	+	9.79944i	−0.0145222	+	0.0231119i
$425$	−29.6704	−	263.332i	−0.0698128	−	0.619606i
$426$		0			0
$427$	−56.7485	−	90.3148i	−0.132901	−	0.211510i
$428$	−177.995	+	141.947i	−0.415877	+	0.331651i
$429$		0			0
$430$	318.044	−	153.162i	0.739638	−	0.356191i
$431$	90.8227	−	113.888i	0.210725	−	0.264241i	−0.665224	−	0.746643i	$-0.731664\pi$
$431$	90.8227	−	113.888i	0.210725	−	0.264241i	0.875950	+	0.482402i	$0.160236\pi$
$432$		0			0
$433$	−521.407	−	182.448i	−1.20417	−	0.421359i	−0.347728	−	0.937595i	$-0.613047\pi$
$433$	−521.407	−	182.448i	−1.20417	−	0.421359i	−0.856446	+	0.516237i	$0.827333\pi$
$434$		−	254.418i		−	0.586217i
$435$		0			0
$436$	411.840			0.944588
$437$	−90.2589	+	257.945i	−0.206542	+	0.590264i
$438$		0			0
$439$	113.727	+	90.6945i	0.259060	+	0.206593i	0.744403	−	0.667730i	$-0.232734\pi$
$439$	113.727	+	90.6945i	0.259060	+	0.206593i	−0.485343	+	0.874324i	$0.661305\pi$
$440$	−3.47074	−	7.20707i	−0.00788804	−	0.0163797i
$441$		0			0
$442$	−582.852	−	730.874i	−1.31867	−	1.65356i
$443$	−658.122	+	413.526i	−1.48560	+	0.933467i	−0.487424	+	0.873166i	$0.662063\pi$
$443$	−658.122	+	413.526i	−1.48560	+	0.933467i	−0.998180	+	0.0603010i	$0.980794\pi$
$444$		0			0
$445$	−271.573	+	30.5989i	−0.610275	+	0.0687615i
$446$	250.314	+	157.283i	0.561242	+	0.352652i
$447$		0			0
$448$	−217.512	+	49.6456i	−0.485517	+	0.110816i
$449$	−110.579	+	38.6934i	−0.246279	+	0.0861769i	−0.450596	−	0.892728i	$-0.648788\pi$
$449$	−110.579	+	38.6934i	−0.246279	+	0.0861769i	0.204317	+	0.978905i	$0.434503\pi$
$450$		0			0
$451$	134.166	+	587.821i	0.297486	+	1.30337i
$452$	326.588	−	326.588i	0.722541	−	0.722541i
$453$		0			0
$454$	97.3043	+	863.599i	0.214327	+	1.90220i
$455$	−48.1591	+	210.999i	−0.105844	+	0.463734i
$456$		0			0
$457$	−25.1967	+	20.0937i	−0.0551351	+	0.0439688i	−0.650670	−	0.759361i	$-0.725512\pi$
$457$	−25.1967	+	20.0937i	−0.0551351	+	0.0439688i	0.595535	+	0.803330i	$0.296940\pi$
$458$	206.793	+	99.5861i	0.451512	+	0.217437i
$459$		0			0
$460$	80.7431	−	101.249i	0.175529	−	0.220106i
$461$	73.6762	−	653.894i	0.159818	−	1.41843i	−0.616138	−	0.787638i	$-0.711304\pi$
$461$	73.6762	−	653.894i	0.159818	−	1.41843i	0.775956	−	0.630787i	$-0.217268\pi$
$462$		0			0
$463$		−	467.056i		−	1.00876i	−0.863482	−	0.504380i	$-0.831721\pi$
$463$		−	467.056i		−	1.00876i	0.863482	−	0.504380i	$-0.168279\pi$
$464$	450.637	+	143.352i	0.971201	+	0.308947i
$465$		0			0
$466$	−144.514	+	412.998i	−0.310116	+	0.886261i
$467$	−171.353	−	19.3068i	−0.366922	−	0.0413422i	−0.0734213	−	0.997301i	$-0.523392\pi$
$467$	−171.353	−	19.3068i	−0.366922	−	0.0413422i	−0.293501	+	0.955959i	$0.594820\pi$
$468$		0			0
$469$	−205.574	−	426.879i	−0.438324	−	0.910189i
$470$	−120.530	+	250.284i	−0.256448	+	0.532519i
$471$		0			0
$472$	0.468843	−	0.294594i	0.000993312	−	0.000624139i
$473$	−453.498	−	103.508i	−0.958769	−	0.218833i
$474$		0			0
$475$	−333.419	−	209.501i	−0.701934	−	0.441055i
$476$	−175.521	−	175.521i	−0.368741	−	0.368741i
$477$		0			0
$478$	812.411	−	284.275i	1.69960	−	0.594717i
$479$	18.6715	+	53.3602i	0.0389802	+	0.111399i	0.961729	−	0.274004i	$-0.0883481\pi$
$479$	18.6715	+	53.3602i	0.0389802	+	0.111399i	−0.922748	+	0.385403i	$0.874062\pi$
$480$		0			0
$481$	402.657	−	402.657i	0.837125	−	0.837125i
$482$	622.045	−	989.979i	1.29055	−	2.05390i
$483$		0			0
$484$	12.1060	−	53.0399i	0.0250124	−	0.109587i
$485$	95.9887	+	152.765i	0.197915	+	0.314980i
$486$		0			0
$487$	715.207	+	344.426i	1.46860	+	0.707239i	0.985711	−	0.168443i	$-0.0538740\pi$
$487$	715.207	+	344.426i	1.46860	+	0.707239i	0.482887	+	0.875683i	$0.339588\pi$
$488$	5.82480	−	2.80508i	0.0119361	−	0.00574811i
$489$		0			0
$490$	35.3549	−	313.784i	0.0721530	−	0.640375i
$491$	106.952	+	37.4241i	0.217825	+	0.0762202i	0.436985	−	0.899469i	$-0.356046\pi$
$491$	106.952	+	37.4241i	0.217825	+	0.0762202i	−0.219160	+	0.975689i	$0.570332\pi$
$492$		0			0
$493$	126.601	+	489.653i	0.256798	+	0.993210i
$494$	−1389.10			−2.81195
$495$		0			0
$496$	403.595	+	45.4743i	0.813700	+	0.0916820i
$497$	−213.290	−	170.093i	−0.429154	−	0.342239i
$498$		0			0
$499$	−71.5047	+	148.481i	−0.143296	+	0.297557i	−0.960248	−	0.279148i	$-0.909948\pi$
$499$	−71.5047	+	148.481i	−0.143296	+	0.297557i	0.816952	+	0.576706i	$0.195662\pi$
$500$	307.762	+	385.922i	0.615524	+	0.771843i
$501$		0			0
$502$	−1124.93	−	256.757i	−2.24089	−	0.511468i
$503$	254.483	−	28.6734i	0.505931	−	0.0570048i	0.144690	−	0.989477i	$-0.453782\pi$
$503$	254.483	−	28.6734i	0.505931	−	0.0570048i	0.361241	+	0.932472i	$0.382353\pi$
$504$		0			0
$505$	404.800	+	404.800i	0.801585	+	0.801585i
$506$	−336.054	+	76.7022i	−0.664139	+	0.151585i
$507$		0			0
$508$	−242.072	−	691.801i	−0.476519	−	1.36181i
$509$	−124.011	−	543.329i	−0.243637	−	1.06744i	−0.937677	−	0.347508i	$-0.887028\pi$
$509$	−124.011	−	543.329i	−0.243637	−	1.06744i	0.694040	−	0.719937i	$-0.255829\pi$
$510$		0			0
$511$	−51.5531	+	82.0463i	−0.100887	+	0.160560i
$512$	−80.5816	−	715.181i	−0.157386	−	1.39684i
$513$		0			0
$514$	69.9669	+	111.352i	0.136122	+	0.216637i
$515$	265.124	−	211.429i	0.514804	−	0.410543i
$516$		0			0
$517$	329.806	−	158.826i	0.637922	−	0.307207i
$518$	190.427	−	238.788i	0.367620	−	0.460981i
$519$		0			0
$520$	−12.3817	−	4.33254i	−0.0238110	−	0.00833182i
$521$			656.379i			1.25985i	0.776658	+	0.629923i	$0.216913\pi$
$521$			656.379i			1.25985i	−0.776658	+	0.629923i	$0.783087\pi$
$522$		0			0
$523$	92.0379			0.175981			0.0879903	−	0.996121i	$-0.471956\pi$
$523$	92.0379			0.175981			0.0879903	+	0.996121i	$0.471956\pi$
$524$	159.915	−	457.011i	0.305181	−	0.872158i
$525$		0			0
$526$	−63.6965	−	50.7963i	−0.121096	−	0.0965709i
$527$	188.469	+	391.360i	0.357626	+	0.742618i
$528$		0			0
$529$	−260.491	−	326.645i	−0.492421	−	0.617476i
$530$	392.620	−	246.700i	0.740793	−	0.465471i
$531$		0			0
$532$	−366.529	+	41.2979i	−0.688964	+	0.0776276i
$533$	837.198	+	526.046i	1.57073	+	0.986954i
$534$		0			0
$535$	−177.215	+	40.4482i	−0.331243	+	0.0756041i
$536$	27.1061	−	9.48484i	0.0505711	−	0.0176956i
$537$		0			0
$538$	41.8152	+	183.204i	0.0777234	+	0.340528i
$539$	−294.225	+	294.225i	−0.545872	+	0.545872i
$540$		0			0
$541$	79.9713	+	709.765i	0.147821	+	1.31195i	0.820343	+	0.571872i	$0.193783\pi$
$541$	79.9713	+	709.765i	0.147821	+	1.31195i	−0.672522	+	0.740078i	$0.734789\pi$
$542$	−194.875	+	853.802i	−0.359548	+	1.57528i
$543$		0			0
$544$	613.794	−	489.484i	1.12830	−	0.899787i
$545$	296.259	+	142.671i	0.543594	+	0.261781i
$546$		0			0
$547$	344.538	−	432.037i	0.629868	−	0.789830i	−0.359827	−	0.933019i	$-0.617164\pi$
$547$	344.538	−	432.037i	0.629868	−	0.789830i	0.989695	+	0.143189i	$0.0457357\pi$
$548$	−4.27126	+	37.9085i	−0.00779427	+	0.0691761i
$549$		0			0
$550$		−	496.679i		−	0.903053i
$551$	686.154	+	306.570i	1.24529	+	0.556389i
$552$		0			0
$553$	−115.399	+	329.793i	−0.208679	+	0.596370i
$554$	692.174	+	77.9893i	1.24941	+	0.140775i
$555$		0			0
$556$	264.556	+	549.355i	0.475820	+	0.988049i
$557$	−292.460	+	607.300i	−0.525063	+	1.09030i	0.454792	+	0.890598i	$0.349713\pi$
$557$	−292.460	+	607.300i	−0.525063	+	1.09030i	−0.979856	+	0.199707i	$0.936001\pi$
$558$		0			0
$559$	−645.889	+	405.839i	−1.15544	+	0.726009i
$560$	−180.662	−	41.2349i	−0.322611	−	0.0736338i
$561$		0			0
$562$	484.721	+	304.570i	0.862493	+	0.541940i
$563$	159.823	+	159.823i	0.283878	+	0.283878i	0.834653	−	0.550775i	$-0.185668\pi$
$563$	159.823	+	159.823i	0.283878	+	0.283878i	−0.550775	+	0.834653i	$0.685668\pi$
$564$		0			0
$565$	348.070	−	121.795i	0.616053	−	0.215566i
$566$	275.416	+	787.094i	0.486601	+	1.39063i
$567$		0			0
$568$	11.6922	−	11.6922i	0.0205848	−	0.0205848i
$569$	320.779	−	510.517i	0.563759	−	0.897218i	−0.436237	−	0.899832i	$-0.643689\pi$
$569$	320.779	−	510.517i	0.563759	−	0.897218i	0.999997	+	0.00261377i	$0.000831991\pi$
$570$		0			0
$571$	−159.551	+	699.038i	−0.279424	+	1.22423i	0.619101	+	0.785311i	$0.287497\pi$
$571$	−159.551	+	699.038i	−0.279424	+	1.22423i	−0.898524	+	0.438923i	$0.855360\pi$
$572$	−461.491	−	734.459i	−0.806803	−	1.28402i
$573$		0			0
$574$	477.799	+	230.096i	0.832403	+	0.400864i
$575$	−144.369	+	69.5245i	−0.251077	+	0.120912i
$576$		0			0
$577$	37.7646	−	335.170i	0.0654499	−	0.580884i	−0.917595	−	0.397517i	$-0.869872\pi$
$577$	37.7646	−	335.170i	0.0654499	−	0.580884i	0.983045	−	0.183367i	$-0.0586995\pi$
$578$	40.2402	+	14.0806i	0.0696197	+	0.0243610i
$579$		0			0
$580$	−258.925	−	244.516i	−0.446423	−	0.421579i
$581$	−8.69991			−0.0149740
$582$		0			0
$583$	−607.178	−	68.4125i	−1.04147	−	0.117346i
$584$	−4.59182	−	3.66185i	−0.00786270	−	0.00627029i
$585$		0			0
$586$	12.5792	−	26.1210i	0.0214662	−	0.0445751i
$587$	−309.394	−	387.968i	−0.527077	−	0.660933i	0.445018	−	0.895522i	$-0.353197\pi$
$587$	−309.394	−	387.968i	−0.527077	−	0.660933i	−0.972095	+	0.234588i	$0.924626\pi$
$588$		0			0
$589$	629.279	+	143.629i	1.06839	+	0.243852i
$590$	−22.0454	+	2.48392i	−0.0373651	+	0.00421003i
$591$		0			0
$592$	344.764	+	344.764i	0.582372	+	0.582372i
$593$	319.446	−	72.9114i	0.538694	−	0.122953i	0.0554869	−	0.998459i	$-0.482329\pi$
$593$	319.446	−	72.9114i	0.538694	−	0.122953i	0.483207	+	0.875506i	$0.339472\pi$
$594$		0			0
$595$	−65.4570	−	187.065i	−0.110012	−	0.314396i
$596$	−101.306	−	443.850i	−0.169976	−	0.744715i
$597$		0			0
$598$	−300.738	+	478.622i	−0.502906	+	0.800370i
$599$	55.2829	+	490.650i	0.0922921	+	0.819115i	0.951534	+	0.307545i	$0.0995073\pi$
$599$	55.2829	+	490.650i	0.0922921	+	0.819115i	−0.859242	+	0.511570i	$0.829064\pi$
$600$		0			0
$601$	−327.784	−	521.665i	−0.545397	−	0.867995i	0.454342	−	0.890827i	$-0.349874\pi$
$601$	−327.784	−	521.665i	−0.545397	−	0.867995i	−0.999739	+	0.0228327i	$0.992731\pi$
$602$	−319.874	+	255.091i	−0.531352	+	0.423739i
$603$		0			0
$604$	−562.511	+	270.891i	−0.931309	+	0.448495i
$605$	27.0827	−	33.9606i	0.0447648	−	0.0561333i
$606$		0			0
$607$	−366.644	−	128.294i	−0.604026	−	0.211358i	0.0109025	−	0.999941i	$-0.496530\pi$
$607$	−366.644	−	128.294i	−0.604026	−	0.211358i	−0.614929	+	0.788583i	$0.710815\pi$
$608$		−	1166.58i		−	1.91871i
$609$		0			0
$610$	−259.026			−0.424632
$611$	198.263	−	566.604i	0.324490	−	0.927339i
$612$		0			0
$613$	77.0877	+	61.4754i	0.125755	+	0.100286i	0.684348	−	0.729156i	$-0.260087\pi$
$613$	77.0877	+	61.4754i	0.125755	+	0.100286i	−0.558593	+	0.829442i	$0.688659\pi$
$614$	487.990	+	1013.32i	0.794772	+	1.65036i
$615$		0			0
$616$	5.78050	+	7.24852i	0.00938393	+	0.0117671i
$617$	177.309	−	111.411i	0.287372	−	0.180568i	−0.380629	−	0.924728i	$-0.624293\pi$
$617$	177.309	−	111.411i	0.287372	−	0.180568i	0.668002	+	0.744160i	$0.267150\pi$
$618$		0			0
$619$	376.754	−	42.4500i	0.608650	−	0.0685784i	0.197740	−	0.980254i	$-0.436640\pi$
$619$	376.754	−	42.4500i	0.608650	−	0.0685784i	0.410910	+	0.911676i	$0.365211\pi$
$620$	−258.988	−	162.733i	−0.417723	−	0.262473i
$621$		0			0
$622$	101.821	−	23.2400i	0.163699	−	0.0373633i
$623$	298.972	−	104.615i	0.479892	−	0.167921i
$624$		0			0
$625$	3.16756	+	13.8780i	0.00506809	+	0.0222048i
$626$	775.257	−	775.257i	1.23843	−	1.23843i
$627$		0			0
$628$	32.0303	+	284.277i	0.0510036	+	0.452670i
$629$	−116.035	+	508.382i	−0.184475	+	0.808239i
$630$		0			0
$631$	−479.366	+	382.281i	−0.759692	+	0.605834i	−0.924805	−	0.380441i	$-0.875772\pi$
$631$	−479.366	+	382.281i	−0.759692	+	0.605834i	0.165114	+	0.986275i	$0.447201\pi$
$632$	−19.0804	−	9.18862i	−0.0301905	−	0.0145390i
$633$		0			0
$634$	177.802	−	222.956i	0.280444	−	0.351666i
$635$	65.5202	−	581.508i	0.103181	−	0.915761i
$636$		0			0
$637$			682.351i			1.07120i
$638$	133.039	+	938.539i	0.208525	+	1.47106i
$639$		0			0
$640$	7.27840	−	20.8005i	0.0113725	−	0.0325007i
$641$	−399.518	−	45.0149i	−0.623274	−	0.0702261i	−0.205321	−	0.978695i	$-0.565824\pi$
$641$	−399.518	−	45.0149i	−0.623274	−	0.0702261i	−0.417953	+	0.908469i	$0.637252\pi$
$642$		0			0
$643$	309.674	+	643.044i	0.481607	+	1.00007i	0.990277	+	0.139107i	$0.0444231\pi$
$643$	309.674	+	643.044i	0.481607	+	1.00007i	−0.508670	+	0.860962i	$0.669863\pi$
$644$	−65.1234	+	135.230i	−0.101123	+	0.209985i
$645$		0			0
$646$	1077.07	−	676.767i	1.66729	−	1.04763i
$647$	495.306	+	113.050i	0.765542	+	0.174730i	0.587424	−	0.809279i	$-0.300142\pi$
$647$	495.306	+	113.050i	0.765542	+	0.174730i	0.178118	+	0.984009i	$0.442999\pi$
$648$		0			0
$649$	24.7528	+	15.5532i	0.0381399	+	0.0239649i
$650$	−575.936	−	575.936i	−0.886056	−	0.886056i
$651$		0			0
$652$	−389.719	+	136.369i	−0.597729	+	0.209154i
$653$	−104.338	−	298.181i	−0.159783	−	0.456633i	0.835962	−	0.548788i	$-0.184910\pi$
$653$	−104.338	−	298.181i	−0.159783	−	0.456633i	−0.995745	+	0.0921544i	$0.970625\pi$
$654$		0			0
$655$	273.354	−	273.354i	0.417334	−	0.417334i
$656$	−450.413	+	716.828i	−0.686605	+	1.09273i
$657$		0			0
$658$	71.6443	−	313.894i	0.108882	−	0.477043i
$659$	−209.895	−	334.046i	−0.318505	−	0.506898i	0.648649	−	0.761087i	$-0.275334\pi$
$659$	−209.895	−	334.046i	−0.318505	−	0.506898i	−0.967154	+	0.254189i	$0.918191\pi$
$660$		0			0
$661$	−536.862	−	258.539i	−0.812197	−	0.391134i	−0.0187891	−	0.999823i	$-0.505981\pi$
$661$	−536.862	−	258.539i	−0.812197	−	0.391134i	−0.793408	+	0.608690i	$0.791695\pi$
$662$	−1197.14	+	576.512i	−1.80837	+	0.870865i
$663$		0			0
$664$	0.0590404	−	0.523998i	8.89163e−5	−	0.000789154i
$665$	−277.970	−	97.2660i	−0.418000	−	0.146265i
$666$		0			0
$667$	254.181	−	170.046i	0.381081	−	0.254941i
$668$	−375.967			−0.562824
$669$		0			0
$670$	−1143.35	−	128.825i	−1.70650	−	0.192276i
$671$	266.858	+	212.812i	0.397702	+	0.317157i
$672$		0			0
$673$	−536.353	+	1113.75i	−0.796958	+	1.65490i	−0.0420097	+	0.999117i	$0.513376\pi$
$673$	−536.353	+	1113.75i	−0.796958	+	1.65490i	−0.754949	+	0.655784i	$0.772338\pi$
$674$	184.220	+	231.005i	0.273324	+	0.342738i
$675$		0			0
$676$	−740.619	−	169.041i	−1.09559	−	0.250061i
$677$	−965.383	+	108.773i	−1.42597	+	0.160669i	−0.790976	−	0.611847i	$-0.790427\pi$
$677$	−965.383	+	108.773i	−1.42597	+	0.160669i	−0.634996	+	0.772515i	$0.718998\pi$
$678$		0			0
$679$	−147.861	−	147.861i	−0.217764	−	0.217764i
$680$	11.7112	−	2.67301i	0.0172224	−	0.00393090i
$681$		0			0
$682$	268.893	+	768.452i	0.394271	+	1.12676i
$683$	241.304	+	1057.22i	0.353300	+	1.54791i	0.769506	+	0.638639i	$0.220502\pi$
$683$	241.304	+	1057.22i	0.353300	+	1.54791i	−0.416206	+	0.909270i	$0.636641\pi$
$684$		0			0
$685$	−16.2049	+	25.7899i	−0.0236568	+	0.0376495i
$686$	97.0170	+	861.050i	0.141424	+	1.25517i
$687$		0			0
$688$	−347.489	−	553.025i	−0.505071	−	0.803815i
$689$	−783.397	+	624.738i	−1.13701	+	0.906732i
$690$		0			0
$691$	101.575	−	48.9160i	0.146997	−	0.0707901i	−0.358939	−	0.933361i	$-0.616861\pi$
$691$	101.575	−	48.9160i	0.146997	−	0.0707901i	0.505936	+	0.862571i	$0.331147\pi$
$692$	−723.984	+	907.847i	−1.04622	+	1.31192i
$693$		0			0
$694$	1068.38	+	373.842i	1.53945	+	0.538678i
$695$			486.829i			0.700473i
$696$		0			0
$697$	−905.428			−1.29904
$698$	242.097	−	691.875i	0.346844	−	0.991224i
$699$		0			0
$700$	−169.089	−	134.844i	−0.241556	−	0.192635i
$701$	−358.394	−	744.212i	−0.511261	−	1.06164i	−0.983623	−	0.180239i	$-0.942313\pi$
$701$	−358.394	−	744.212i	−0.511261	−	1.06164i	0.472362	−	0.881405i	$-0.343402\pi$
$702$		0			0
$703$	483.117	+	605.809i	0.687221	+	0.861748i
$704$	604.508	−	379.838i	0.858677	−	0.539542i
$705$		0			0
$706$	−256.064	+	28.8515i	−0.362698	+	0.0408662i
$707$	−561.805	−	353.005i	−0.794632	−	0.499300i
$708$		0			0
$709$	−459.546	+	104.888i	−0.648161	+	0.147938i	−0.533947	−	0.845518i	$-0.679292\pi$
$709$	−459.546	+	104.888i	−0.648161	+	0.147938i	−0.114214	+	0.993456i	$0.536435\pi$
$710$	−625.318	+	218.808i	−0.880729	+	0.308180i
$711$		0			0
$712$	4.27207	+	18.7171i	0.00600009	+	0.0262881i
$713$	185.726	−	185.726i	0.260485	−	0.260485i
$714$		0			0
$715$	−77.5423	−	688.207i	−0.108451	−	0.962527i
$716$	149.575	−	655.329i	0.208903	−	0.915264i
$717$		0			0
$718$	63.7770	−	50.8604i	0.0888258	−	0.0708362i
$719$	−254.261	−	122.446i	−0.353632	−	0.170300i	0.248630	−	0.968598i	$-0.420020\pi$
$719$	−254.261	−	122.446i	−0.353632	−	0.170300i	−0.602262	+	0.798298i	$0.705734\pi$
$720$		0			0
$721$	−245.049	+	307.282i	−0.339874	+	0.426188i
$722$	97.8715	−	868.634i	0.135556	−	1.20309i
$723$		0			0
$724$			67.6643i			0.0934589i
$725$	157.379	+	411.594i	0.217075	+	0.567716i
$726$		0			0
$727$	377.120	−	1077.75i	0.518734	−	1.48246i	−0.325010	−	0.945711i	$-0.605368\pi$
$727$	377.120	−	1077.75i	0.518734	−	1.48246i	0.843744	−	0.536746i	$-0.180347\pi$
$728$	15.1081	+	1.70228i	0.0207529	+	0.00233829i
$729$		0			0
$730$	102.098	+	212.008i	0.139860	+	0.290422i
$731$	303.080	−	629.352i	0.414610	−	0.860946i
$732$		0			0
$733$	−380.609	+	239.152i	−0.519248	+	0.326265i	−0.766029	−	0.642806i	$-0.777770\pi$
$733$	−380.609	+	239.152i	−0.519248	+	0.326265i	0.246781	+	0.969071i	$0.420627\pi$
$734$	793.772	+	181.173i	1.08143	+	0.246830i
$735$		0			0
$736$	−401.950	−	252.562i	−0.546128	−	0.343155i
$737$	1072.09	+	1072.09i	1.45466	+	1.45466i
$738$		0			0
$739$	−316.746	+	110.834i	−0.428614	+	0.149979i	−0.535960	−	0.844243i	$-0.680050\pi$
$739$	−316.746	+	110.834i	−0.428614	+	0.149979i	0.107346	+	0.994222i	$0.465765\pi$
$740$	−121.275	−	346.584i	−0.163885	−	0.468356i
$741$		0			0
$742$	−380.017	+	380.017i	−0.512153	+	0.512153i
$743$	112.744	−	179.430i	0.151741	−	0.241494i	−0.762200	−	0.647342i	$-0.775881\pi$
$743$	112.744	−	179.430i	0.151741	−	0.241494i	0.913941	+	0.405847i	$0.133024\pi$
$744$		0			0
$745$	80.8849	−	354.380i	0.108570	−	0.475678i
$746$	−35.0820	−	55.8327i	−0.0470268	−	0.0748427i
$747$		0			0
$748$	715.654	+	344.641i	0.956757	+	0.460750i
$749$	189.813	−	91.4091i	0.253422	−	0.122041i
$750$		0			0
$751$	−118.630	+	1052.87i	−0.157962	+	1.40195i	0.625360	+	0.780337i	$0.284952\pi$
$751$	−118.630	+	1052.87i	−0.157962	+	1.40195i	−0.783322	+	0.621616i	$0.786476\pi$
$752$	485.139	+	169.758i	0.645132	+	0.225742i
$753$		0			0
$754$	1242.57	+	934.036i	1.64798	+	1.23878i
$755$	−498.486			−0.660247
$756$		0			0
$757$	−483.486	−	54.4758i	−0.638687	−	0.0719627i	−0.213318	−	0.976983i	$-0.568427\pi$
$757$	−483.486	−	54.4758i	−0.638687	−	0.0719627i	−0.425369	+	0.905020i	$0.639856\pi$
$758$	−898.256	−	716.335i	−1.18503	−	0.945033i
$759$		0			0
$760$	7.74475	−	16.0821i	0.0101905	−	0.0211607i
$761$	−229.278	−	287.506i	−0.301286	−	0.377800i	0.608025	−	0.793918i	$-0.291962\pi$
$761$	−229.278	−	287.506i	−0.301286	−	0.377800i	−0.909311	+	0.416117i	$0.863391\pi$
$762$		0			0
$763$	−371.553	−	84.8047i	−0.486964	−	0.111146i
$764$	−932.648	+	105.084i	−1.22074	+	0.137545i
$765$		0			0
$766$	178.327	+	178.327i	0.232803	+	0.232803i
$767$	46.7377	−	10.6676i	0.0609358	−	0.0139082i
$768$		0			0
$769$	−50.1787	−	143.403i	−0.0652519	−	0.186479i	0.906641	−	0.421903i	$-0.138638\pi$
$769$	−50.1787	−	143.403i	−0.0652519	−	0.186479i	−0.971893	+	0.235424i	$0.924352\pi$
$770$	−82.6568	−	362.143i	−0.107346	−	0.470316i
$771$		0			0
$772$	431.751	−	687.127i	0.559263	−	0.890061i
$773$	20.0928	+	178.328i	0.0259933	+	0.230697i	0.999991	+	0.00414067i	$0.00131802\pi$
$773$	20.0928	+	178.328i	0.0259933	+	0.230697i	−0.973998	+	0.226556i	$0.927253\pi$
$774$		0			0
$775$	201.356	+	320.456i	0.259814	+	0.413491i
$776$	9.90917	−	7.90230i	0.0127695	−	0.0101834i
$777$		0			0
$778$	−274.518	+	132.201i	−0.352851	+	0.169924i
$779$	−838.856	+	1051.89i	−1.07684	+	1.35031i
$780$		0			0
$781$	823.997	+	288.329i	1.05505	+	0.369179i
$782$		−	517.628i		−	0.661928i
$783$		0			0
$784$	−584.245			−0.745210
$785$	−75.4387	+	215.591i	−0.0961002	+	0.274639i
$786$		0			0
$787$	−387.718	−	309.195i	−0.492654	−	0.392878i	0.345409	−	0.938452i	$-0.387740\pi$
$787$	−387.718	−	309.195i	−0.492654	−	0.392878i	−0.838063	+	0.545574i	$0.816312\pi$
$788$	151.849	+	315.317i	0.192702	+	0.400149i
$789$		0			0
$790$	529.027	+	663.379i	0.669654	+	0.839720i
$791$	−361.891	+	227.391i	−0.457511	+	0.287473i
$792$		0			0
$793$	556.213	−	62.6702i	0.701404	−	0.0790292i
$794$	448.907	+	282.067i	0.565374	+	0.355248i
$795$		0			0
$796$	−39.2793	+	8.96526i	−0.0493459	+	0.0112629i
$797$	516.674	−	180.792i	0.648274	−	0.226841i	0.0139434	−	0.999903i	$-0.495562\pi$
$797$	516.674	−	180.792i	0.648274	−	0.226841i	0.634331	+	0.773062i	$0.281276\pi$
$798$		0			0
$799$	122.321	+	535.922i	0.153092	+	0.670741i
$800$	483.676	−	483.676i	0.604594	−	0.604594i
$801$		0			0
$802$	−180.027	−	1597.78i	−0.224472	−	1.99225i
$803$	68.9983	−	302.301i	0.0859257	−	0.376465i
$804$		0			0
$805$	−93.6935	+	74.7181i	−0.116389	+	0.0928175i
$806$	1202.88	+	579.276i	1.49240	+	0.718704i
$807$		0			0
$808$	25.0742	−	31.4420i	0.0310324	−	0.0389134i
$809$	19.6700	−	174.576i	0.0243139	−	0.215792i	−0.975680	−	0.219199i	$-0.929656\pi$
$809$	19.6700	−	174.576i	0.0243139	−	0.215792i	0.999994	+	0.00340646i	$0.00108431\pi$
$810$		0			0
$811$		−	1297.41i		−	1.59976i	−0.600160	−	0.799880i	$-0.704896\pi$
$811$		−	1297.41i		−	1.59976i	0.600160	−	0.799880i	$-0.295104\pi$
$812$	355.635	+	209.514i	0.437974	+	0.258022i
$813$		0			0
$814$	−322.798	+	922.505i	−0.396558	+	1.13330i
$815$	−327.587	−	36.9102i	−0.401947	−	0.0452886i
$816$		0			0
$817$	−450.362	−	935.186i	−0.551238	−	1.14466i
$818$	−873.959	+	1814.79i	−1.06841	+	2.21858i
$819$		0			0
$820$	539.843	−	339.206i	0.658345	−	0.413666i
$821$	146.014	+	33.3268i	0.177849	+	0.0405930i	0.310518	−	0.950567i	$-0.399497\pi$
$821$	146.014	+	33.3268i	0.177849	+	0.0405930i	−0.132669	+	0.991160i	$0.542355\pi$
$822$		0			0
$823$	155.485	+	97.6979i	0.188925	+	0.118710i	0.623173	−	0.782084i	$-0.285843\pi$
$823$	155.485	+	97.6979i	0.188925	+	0.118710i	−0.434248	+	0.900793i	$0.642986\pi$
$824$	−16.8447	−	16.8447i	−0.0204426	−	0.0204426i
$825$		0			0
$826$	24.2696	−	8.49231i	0.0293821	−	0.0102812i
$827$	−317.964	−	908.690i	−0.384479	−	1.09878i	−0.959760	−	0.280823i	$-0.909393\pi$
$827$	−317.964	−	908.690i	−0.384479	−	1.09878i	0.575280	−	0.817956i	$-0.304893\pi$
$828$		0			0
$829$	−242.440	+	242.440i	−0.292448	+	0.292448i	−0.838047	−	0.545598i	$-0.816302\pi$
$829$	−242.440	+	242.440i	−0.292448	+	0.292448i	0.545598	+	0.838047i	$0.316302\pi$
$830$	−11.2403	+	17.8889i	−0.0135425	+	0.0215528i
$831$		0			0
$832$	260.522	−	1141.42i	0.313127	−	1.37190i
$833$	−332.440	−	529.075i	−0.399088	−	0.635145i
$834$		0			0
$835$	−270.453	−	130.243i	−0.323896	−	0.155980i
$836$	1063.43	−	512.119i	1.27204	−	0.612583i
$837$		0			0
$838$	81.2490	−	721.105i	0.0969559	−	0.860507i
$839$	488.233	+	170.840i	0.581923	+	0.203624i	0.605156	−	0.796107i	$-0.293111\pi$
$839$	488.233	+	170.840i	0.581923	+	0.203624i	−0.0232339	+	0.999730i	$0.507396\pi$
$840$		0			0
$841$	−407.637	−	735.604i	−0.484705	−	0.874678i
$842$	2022.13			2.40158
$843$		0			0
$844$	−54.1319	−	6.09920i	−0.0641374	−	0.00722655i
$845$	−474.207	−	378.167i	−0.561191	−	0.447535i
$846$		0			0
$847$	−21.8436	+	45.3586i	−0.0257893	+	0.0535521i
$848$	−534.915	−	670.762i	−0.630796	−	0.790993i
$849$		0			0
$850$	727.159	+	165.969i	0.855481	+	0.195258i
$851$	313.328	−	35.3036i	0.368188	−	0.0414849i
$852$		0			0
$853$	462.963	+	462.963i	0.542747	+	0.542747i	0.924333	−	0.381586i	$-0.124622\pi$
$853$	462.963	+	462.963i	0.542747	+	0.542747i	−0.381586	+	0.924333i	$0.624622\pi$
$854$	292.686	−	66.8038i	0.342724	−	0.0782246i
$855$		0			0
$856$	4.21746	+	12.0528i	0.00492694	+	0.0140804i
$857$	−13.0097	−	56.9993i	−0.0151805	−	0.0665103i	0.966770	−	0.255647i	$-0.0822883\pi$
$857$	−13.0097	−	56.9993i	−0.0151805	−	0.0665103i	−0.981951	+	0.189136i	$0.939431\pi$
$858$		0			0
$859$	166.925	−	265.659i	0.194324	−	0.309266i	−0.735322	−	0.677718i	$-0.762969\pi$
$859$	166.925	−	265.659i	0.194324	−	0.309266i	0.929647	+	0.368452i	$0.120112\pi$
$860$	55.0726	+	488.783i	0.0640379	+	0.568352i
$861$		0			0
$862$	218.130	+	347.152i	0.253051	+	0.402729i
$863$	−1042.37	+	831.262i	−1.20784	+	0.963224i	−0.999889	−	0.0149141i	$-0.995253\pi$
$863$	−1042.37	+	831.262i	−1.20784	+	0.963224i	−0.207956	+	0.978138i	$0.566681\pi$
$864$		0			0
$865$	−835.299	+	402.259i	−0.965663	+	0.465039i
$866$	969.397	−	1215.58i	1.11940	−	1.40368i
$867$		0			0
$868$	334.614	+	117.086i	0.385500	+	0.134892i
$869$		−	1118.08i		−	1.28663i
$870$		0			0
$871$	2486.33			2.85457
$872$	7.62929	−	21.8033i	0.00874918	−	0.0250037i
$873$		0			0
$874$	−601.361	−	479.570i	−0.688056	−	0.548707i
$875$	−198.189	−	411.543i	−0.226502	−	0.470335i
$876$		0			0
$877$	−817.856	−	1025.56i	−0.932561	−	1.16939i	−0.985308	−	0.170787i	$-0.945369\pi$
$877$	−817.856	−	1025.56i	−0.932561	−	1.16939i	0.0527468	−	0.998608i	$-0.483202\pi$
$878$	−346.662	+	217.822i	−0.394832	+	0.248089i
$879$		0			0
$880$	589.258	−	66.3934i	0.669611	−	0.0754471i
$881$	548.645	+	344.736i	0.622752	+	0.391301i	0.806128	−	0.591742i	$-0.201559\pi$
$881$	548.645	+	344.736i	0.622752	+	0.391301i	−0.183375	+	0.983043i	$0.558702\pi$
$882$		0			0
$883$	1280.41	−	292.245i	1.45007	−	0.330968i	0.576269	−	0.817260i	$-0.304508\pi$
$883$	1280.41	−	292.245i	1.45007	−	0.330968i	0.873796	+	0.486292i	$0.161651\pi$
$884$	1229.49	−	430.217i	1.39083	−	0.486671i
$885$		0			0
$886$	−486.798	−	2132.80i	−0.549433	−	2.40723i
$887$	86.4254	−	86.4254i	0.0974356	−	0.0974356i	−0.656709	−	0.754144i	$-0.728052\pi$
$887$	86.4254	−	86.4254i	0.0974356	−	0.0974356i	0.754144	+	0.656709i	$0.228052\pi$
$888$		0			0
$889$	75.9387	+	673.974i	0.0854203	+	0.758126i
$890$	171.163	−	749.913i	0.192318	−	0.842599i
$891$		0			0
$892$	−322.058	+	256.833i	−0.361051	+	0.287929i
$893$	735.942	+	354.411i	0.824123	+	0.396877i
$894$		0			0
$895$	334.618	−	419.597i	0.373874	−	0.468824i
$896$	−2.85971	+	25.3807i	−0.00319165	+	0.0283266i
$897$		0			0
$898$		−	329.738i		−	0.367192i
$899$	−466.324	−	551.608i	−0.518714	−	0.613579i
$900$		0			0
$901$	303.052	−	866.073i	0.336351	−	0.961236i
$902$	−1686.35	−	190.006i	−1.86956	−	0.210649i
$903$		0			0
$904$	−11.2399	−	23.3399i	−0.0124335	−	0.0258185i
$905$	−23.4404	+	48.6745i	−0.0259010	+	0.0537840i
$906$		0			0
$907$	−987.442	+	620.451i	−1.08869	+	0.684069i	−0.951862	−	0.306526i	$-0.900833\pi$
$907$	−987.442	+	620.451i	−1.08869	+	0.684069i	−0.136828	+	0.990595i	$0.543691\pi$
$908$	−1180.60	−	269.463i	−1.30022	−	0.296766i
$909$		0			0
$910$	−515.778	−	324.085i	−0.566789	−	0.356137i
$911$	−112.238	−	112.238i	−0.123203	−	0.123203i	0.642817	−	0.766020i	$-0.277766\pi$
$911$	−112.238	−	112.238i	−0.123203	−	0.123203i	−0.766020	+	0.642817i	$0.777766\pi$
$912$		0			0
$913$	26.2775	−	9.19489i	0.0287815	−	0.0100711i
$914$	−29.9589	−	85.6175i	−0.0327778	−	0.0936735i
$915$		0			0
$916$	−226.145	+	226.145i	−0.246884	+	0.246884i
$917$	−238.378	+	379.376i	−0.259954	+	0.413715i
$918$		0			0
$919$	−300.406	+	1316.16i	−0.326883	+	1.43217i	0.498153	+	0.867089i	$0.334012\pi$
$919$	−300.406	+	1316.16i	−0.326883	+	1.43217i	−0.825036	+	0.565080i	$0.808845\pi$
$920$	−3.86446	−	6.15025i	−0.00420049	−	0.00668505i
$921$		0			0
$922$	1668.67	+	803.588i	1.80983	+	0.871570i
$923$	1289.82	−	621.146i	1.39743	−	0.672964i
$924$		0			0
$925$	−50.8696	+	451.480i	−0.0549942	+	0.488087i
$926$	1240.80	+	434.173i	1.33995	+	0.468869i
$927$		0			0
$928$	−784.411	+	1043.52i	−0.845270	+	1.12449i
$929$	761.298			0.819481			0.409741	−	0.912202i	$-0.365619\pi$
$929$	761.298			0.819481			0.409741	+	0.912202i	$0.365619\pi$
$930$		0			0
$931$	−922.658	−	103.959i	−0.991040	−	0.111663i
$932$	−476.672	−	380.133i	−0.511451	−	0.407868i
$933$		0			0
$934$	210.580	−	437.274i	0.225460	−	0.468173i
$935$	395.417	+	495.837i	0.422906	+	0.530307i
$936$		0			0
$937$	1719.59	+	392.486i	1.83521	+	0.418875i	0.992782	−	0.119931i	$-0.0382672\pi$
$937$	1719.59	+	392.486i	1.83521	+	0.418875i	0.842430	+	0.538806i	$0.181124\pi$
$938$	1325.16	−	149.310i	1.41275	−	0.159179i
$939$		0			0
$940$	−273.707	−	273.707i	−0.291178	−	0.291178i
$941$	−1001.33	+	228.548i	−1.06412	+	0.242878i	−0.718520	−	0.695506i	$-0.755180\pi$
$941$	−1001.33	+	228.548i	−1.06412	+	0.242878i	−0.345596	+	0.938384i	$0.612323\pi$
$942$		0			0
$943$	180.824	+	516.765i	0.191754	+	0.548001i
$944$	9.13383	+	40.0179i	0.00967566	+	0.0423919i
$945$		0			0
$946$	696.552	−	1108.56i	0.736313	−	1.17184i
$947$	3.32011	+	29.4668i	0.00350593	+	0.0311160i	0.995343	−	0.0963928i	$-0.0307305\pi$
$947$	3.32011	+	29.4668i	0.00350593	+	0.0311160i	−0.991837	+	0.127509i	$0.959302\pi$
$948$		0			0
$949$	−270.532	−	430.549i	−0.285071	−	0.453687i
$950$	866.512	−	691.020i	0.912118	−	0.727390i
$951$		0			0
$952$	−12.5437	+	6.04074i	−0.0131762	+	0.00634532i
$953$	878.407	−	1101.49i	0.921728	−	1.15581i	−0.0657158	−	0.997838i	$-0.520933\pi$
$953$	878.407	−	1101.49i	0.921728	−	1.15581i	0.987444	−	0.157972i	$-0.0504955\pi$
$954$		0			0
$955$	−707.307	−	247.497i	−0.740636	−	0.259160i
$956$			1199.32i			1.25452i
$957$		0			0
$958$	−159.115			−0.166091
$959$	11.6594	−	33.3207i	0.0121579	−	0.0347453i
$960$		0			0
$961$	266.318	+	212.381i	0.277125	+	0.221000i
$962$	695.404	+	1444.02i	0.722873	+	1.50106i
$963$		0			0
$964$	1015.76	+	1273.72i	1.05369	+	1.32129i
$965$	548.618	−	344.719i	0.568516	−	0.357222i
$966$		0			0
$967$	−1373.11	+	154.713i	−1.41997	+	0.159992i	−0.788323	−	0.615262i	$-0.789050\pi$
$967$	−1373.11	+	154.713i	−1.41997	+	0.159992i	−0.631649	+	0.775254i	$0.717622\pi$
$968$	−2.58373	−	1.62346i	−0.00266914	−	0.00167713i
$969$		0			0
$970$	−495.072	+	112.997i	−0.510383	+	0.116492i
$971$	59.4623	−	20.8068i	0.0612382	−	0.0214282i	−0.299486	−	0.954101i	$-0.596815\pi$
$971$	59.4623	−	20.8068i	0.0612382	−	0.0214282i	0.360724	+	0.932672i	$0.382530\pi$
$972$		0			0
$973$	−125.555	−	550.093i	−0.129039	−	0.565358i
$974$	−1579.87	+	1579.87i	−1.62204	+	1.62204i
$975$		0			0
$976$	53.6596	+	476.242i	0.0549791	+	0.487953i
$977$	−318.680	+	1396.23i	−0.326182	+	1.42910i	0.500162	+	0.865932i	$0.333274\pi$
$977$	−318.680	+	1396.23i	−0.326182	+	1.42910i	−0.826344	+	0.563165i	$0.809584\pi$
$978$		0			0
$979$	−792.458	+	631.964i	−0.809457	+	0.645520i
$980$	396.421	+	190.906i	0.404512	+	0.194803i
$981$		0			0
$982$	−198.844	+	249.343i	−0.202489	+	0.253913i
$983$	−209.502	+	1859.38i	−0.213125	+	1.89153i	0.198379	+	0.980125i	$0.436432\pi$
$983$	−209.502	+	1859.38i	−0.213125	+	1.89153i	−0.411504	+	0.911408i	$0.634996\pi$
$984$		0			0
$985$			279.428i			0.283684i
$986$	−1418.52	−	118.846i	−1.43866	−	0.120533i
$987$		0			0
$988$	639.282	−	1826.96i	0.647046	−	1.84915i
$989$	−419.725	−	47.2917i	−0.424394	−	0.0478177i
$990$		0			0
$991$	−226.286	−	469.889i	−0.228342	−	0.474156i	0.755047	−	0.655671i	$-0.227614\pi$
$991$	−226.286	−	469.889i	−0.228342	−	0.474156i	−0.983388	+	0.181515i	$0.941900\pi$
$992$	−486.480	+	1010.19i	−0.490403	+	1.01833i
$993$		0			0
$994$	650.147	−	408.515i	0.654072	−	0.410981i
$995$	−31.3615	−	7.15806i	−0.0315191	−	0.00719403i
$996$		0			0
$997$	950.882	+	597.479i	0.953744	+	0.599277i	0.916502	−	0.400029i	$-0.131000\pi$
$997$	950.882	+	597.479i	0.953744	+	0.599277i	0.0372414	+	0.999306i	$0.488143\pi$
$998$	−327.989	−	327.989i	−0.328647	−	0.328647i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.3.s.a.253.1		48
3.2	odd	2		29.3.f.a.21.4	yes	48
29.18	odd	28	inner	261.3.s.a.163.1		48
87.47	even	28		29.3.f.a.18.4	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.3.f.a.18.4	✓	48	87.47	even	28
29.3.f.a.21.4	yes	48	3.2	odd	2
261.3.s.a.163.1		48	29.18	odd	28	inner
261.3.s.a.253.1		48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	261.s (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.929596 + 2.65663i) q^{2} +(-3.06622 - 2.44523i) q^{4} +(-1.35861 - 2.82119i) q^{5} +(2.26277 + 2.83742i) q^{7} +(-0.186254 + 0.117031i) q^{8} +O(q^{10})\)	\(q+(-0.929596 + 2.65663i) q^{2} +(-3.06622 - 2.44523i) q^{4} +(-1.35861 - 2.82119i) q^{5} +(2.26277 + 2.83742i) q^{7} +(-0.186254 + 0.117031i) q^{8} +(8.75784 - 0.986771i) q^{10} +(-9.83338 - 6.17872i) q^{11} +(-18.5672 + 4.23785i) q^{13} +(-9.64144 + 3.37369i) q^{14} +(-3.62854 - 15.8977i) q^{16} +(12.3318 - 12.3318i) q^{17} +(-2.90153 - 25.7518i) q^{19} +(-2.73265 + 11.9725i) q^{20} +(25.5557 - 20.3800i) q^{22} +(-9.50107 - 4.57547i) q^{23} +(9.47395 - 11.8800i) q^{25} +(6.00161 - 53.2658i) q^{26} -14.2332i q^{28} +(-14.7201 + 24.9864i) q^{29} +(-8.22632 + 23.5095i) q^{31} +(44.7330 + 5.04020i) q^{32} +(21.2975 + 44.2247i) q^{34} +(4.93068 - 10.2387i) q^{35} +(-25.3173 + 15.9079i) q^{37} +(71.1102 + 16.2304i) q^{38} +(0.583216 + 0.366459i) q^{40} +(-36.7111 - 36.7111i) q^{41} +(37.8059 - 13.2289i) q^{43} +(15.0429 + 42.9902i) q^{44} +(20.9875 - 20.9875i) q^{46} +(-16.7697 + 26.6888i) q^{47} +(7.97269 - 34.9306i) q^{49} +(22.7537 + 36.2124i) q^{50} +(67.2937 + 32.4070i) q^{52} +(47.4028 - 22.8280i) q^{53} +(-4.07159 + 36.1364i) q^{55} +(-0.753518 - 0.263667i) q^{56} +(-52.6958 - 62.3332i) q^{58} -2.51722 q^{59} +(-29.2057 - 3.29069i) q^{61} +(-54.8089 - 43.7086i) q^{62} +(-26.6731 + 55.3872i) q^{64} +(37.1815 + 46.6241i) q^{65} +(-127.279 - 29.0506i) q^{67} +(-67.9662 + 7.65795i) q^{68} +(22.6168 + 22.6168i) q^{70} +(-73.2856 + 16.7270i) q^{71} +(8.81836 + 25.2014i) q^{73} +(-18.7267 - 82.0469i) q^{74} +(-54.0723 + 86.0556i) q^{76} +(-4.71902 - 41.8825i) q^{77} +(51.2212 + 81.5181i) q^{79} +(-39.9206 + 31.8356i) q^{80} +(131.654 - 63.4013i) q^{82} +(-1.49463 + 1.87421i) q^{83} +(-51.5446 - 18.0362i) q^{85} +112.734i q^{86} +2.55462 q^{88} +(28.8259 - 82.3798i) q^{89} +(-54.0378 - 43.0937i) q^{91} +(17.9443 + 37.2617i) q^{92} +(-55.3133 - 69.3607i) q^{94} +(-68.7086 + 43.1725i) q^{95} +(-57.2559 + 6.45119i) q^{97} +(85.3865 + 53.6519i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8}+O(q^{10}) \) 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8	\( 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8} - 20 q^{10} + 8 q^{11} - 14 q^{13} - 26 q^{14} + 18 q^{16} + 26 q^{17} + 2 q^{19} - 46 q^{20} + 154 q^{22} - 56 q^{23} - 34 q^{25} - 110 q^{26} + 170 q^{29} - 88 q^{31} + 132 q^{32} - 224 q^{34} + 210 q^{35} - 56 q^{37} + 294 q^{38} - 492 q^{40} + 34 q^{41} + 176 q^{43} - 126 q^{44} + 744 q^{46} - 208 q^{47} + 506 q^{49} - 732 q^{50} + 690 q^{52} + 14 q^{53} + 284 q^{55} - 332 q^{56} - 508 q^{58} + 44 q^{59} - 30 q^{61} + 504 q^{62} - 896 q^{64} + 554 q^{65} - 574 q^{67} + 796 q^{68} - 1066 q^{70} - 224 q^{71} - 22 q^{73} - 820 q^{74} + 514 q^{76} - 436 q^{77} + 564 q^{79} - 1162 q^{80} - 18 q^{82} + 126 q^{83} + 38 q^{85} - 384 q^{88} + 160 q^{89} - 434 q^{91} + 1022 q^{92} - 2 q^{94} + 642 q^{95} + 604 q^{97} + 102 q^{98}+O(q^{100}) \) 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8 - 20 * q^10 + 8 * q^11 - 14 * q^13 - 26 * q^14 + 18 * q^16 + 26 * q^17 + 2 * q^19 - 46 * q^20 + 154 * q^22 - 56 * q^23 - 34 * q^25 - 110 * q^26 + 170 * q^29 - 88 * q^31 + 132 * q^32 - 224 * q^34 + 210 * q^35 - 56 * q^37 + 294 * q^38 - 492 * q^40 + 34 * q^41 + 176 * q^43 - 126 * q^44 + 744 * q^46 - 208 * q^47 + 506 * q^49 - 732 * q^50 + 690 * q^52 + 14 * q^53 + 284 * q^55 - 332 * q^56 - 508 * q^58 + 44 * q^59 - 30 * q^61 + 504 * q^62 - 896 * q^64 + 554 * q^65 - 574 * q^67 + 796 * q^68 - 1066 * q^70 - 224 * q^71 - 22 * q^73 - 820 * q^74 + 514 * q^76 - 436 * q^77 + 564 * q^79 - 1162 * q^80 - 18 * q^82 + 126 * q^83 + 38 * q^85 - 384 * q^88 + 160 * q^89 - 434 * q^91 + 1022 * q^92 - 2 * q^94 + 642 * q^95 + 604 * q^97 + 102 * q^98

Introduction

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