LMFDB - Embedded newform 243.3.f.d.134.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [243,3,Mod(26,243)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(243, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("243.26");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	243.f (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.62127042396$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			134.2
Character	$\chi$	$=$	243.134
Dual form			243.3.f.d.107.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.746252 - 0.889349i) q^{2} +(0.460544 - 2.61187i) q^{4} +(-1.84110 - 5.05837i) q^{5} +(-1.82927 - 10.3743i) q^{7} +(-6.68824 + 3.86146i) q^{8} +O(q^{10})$	\(q+(-0.746252 - 0.889349i) q^{2} +(0.460544 - 2.61187i) q^{4} +(-1.84110 - 5.05837i) q^{5} +(-1.82927 - 10.3743i) q^{7} +(-6.68824 + 3.86146i) q^{8} +(-3.12473 + 5.41219i) q^{10} +(-4.01667 + 11.0357i) q^{11} +(8.60488 + 7.22035i) q^{13} +(-7.86129 + 9.36873i) q^{14} +(-1.54359 - 0.561820i) q^{16} +(2.73630 + 1.57980i) q^{17} +(2.26051 + 3.91532i) q^{19} +(-14.0597 + 2.47911i) q^{20} +(12.8121 - 4.66321i) q^{22} +(-19.6052 - 3.45692i) q^{23} +(-3.04634 + 2.55619i) q^{25} -13.0409i q^{26} -27.9389 q^{28} +(-16.3009 - 19.4267i) q^{29} +(3.84135 - 21.7854i) q^{31} +(11.2178 + 30.8207i) q^{32} +(-0.636973 - 3.61245i) q^{34} +(-49.1093 + 28.3533i) q^{35} +(-8.82807 + 15.2907i) q^{37} +(1.79517 - 4.93220i) q^{38} +(31.8464 + 26.7223i) q^{40} +(7.99934 - 9.53324i) q^{41} +(-34.2503 - 12.4661i) q^{43} +(26.9741 + 15.5735i) q^{44} +(11.5560 + 20.0156i) q^{46} +(12.2112 - 2.15316i) q^{47} +(-58.2355 + 21.1960i) q^{49} +(4.54668 + 0.801703i) q^{50} +(22.8216 - 19.1496i) q^{52} -84.6210i q^{53} +63.2178 q^{55} +(52.2946 + 62.3223i) q^{56} +(-5.11249 + 28.9944i) q^{58} +(-23.3509 - 64.1562i) q^{59} +(13.5571 + 76.8859i) q^{61} +(-22.2414 + 12.8411i) q^{62} +(15.7537 - 27.2863i) q^{64} +(20.6808 - 56.8200i) q^{65} +(-74.4011 - 62.4300i) q^{67} +(5.38643 - 6.41930i) q^{68} +(61.8639 + 22.5166i) q^{70} +(105.364 + 60.8322i) q^{71} +(-45.5705 - 78.9304i) q^{73} +(20.1867 - 3.55946i) q^{74} +(11.2674 - 4.10099i) q^{76} +(121.836 + 21.4829i) q^{77} +(-15.6180 + 13.1051i) q^{79} +8.84240i q^{80} -14.4479 q^{82} +(-20.3134 - 24.2086i) q^{83} +(2.95344 - 16.7498i) q^{85} +(14.4727 + 39.7634i) q^{86} +(-15.7495 - 89.3198i) q^{88} +(59.7756 - 34.5114i) q^{89} +(59.1656 - 102.478i) q^{91} +(-18.0581 + 49.6142i) q^{92} +(-11.0276 - 9.25321i) q^{94} +(15.6433 - 18.6430i) q^{95} +(74.9914 + 27.2946i) q^{97} +(62.3089 + 35.9741i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} + 3 q^{4} + 21 q^{5} + 3 q^{7} - 9 q^{8}+O(q^{10}) $ 30 * q + 3 * q^2 + 3 * q^4 + 21 * q^5 + 3 * q^7 - 9 * q^8	$ 30 q + 3 q^{2} + 3 q^{4} + 21 q^{5} + 3 q^{7} - 9 q^{8} - 3 q^{10} + 57 q^{11} + 3 q^{13} - 114 q^{14} + 27 q^{16} - 9 q^{17} - 3 q^{19} - 183 q^{20} + 75 q^{22} + 48 q^{23} + 21 q^{25} - 12 q^{28} - 78 q^{29} - 87 q^{31} + 243 q^{32} - 153 q^{34} - 252 q^{35} - 3 q^{37} + 321 q^{38} - 168 q^{40} - 357 q^{41} - 87 q^{43} + 639 q^{44} - 3 q^{46} - 51 q^{47} - 69 q^{49} + 168 q^{50} - 36 q^{52} - 12 q^{55} - 177 q^{56} + 138 q^{58} + 48 q^{59} + 147 q^{61} - 900 q^{62} - 51 q^{64} + 624 q^{65} + 12 q^{67} - 477 q^{68} - 6 q^{70} + 315 q^{71} - 66 q^{73} - 480 q^{74} - 57 q^{76} + 453 q^{77} - 15 q^{79} - 12 q^{82} - 591 q^{83} + 243 q^{85} + 669 q^{86} + 591 q^{88} + 72 q^{89} + 96 q^{91} + 564 q^{92} + 957 q^{94} - 606 q^{95} + 696 q^{97} + 882 q^{98}+O(q^{100}) $ 30 * q + 3 * q^2 + 3 * q^4 + 21 * q^5 + 3 * q^7 - 9 * q^8 - 3 * q^10 + 57 * q^11 + 3 * q^13 - 114 * q^14 + 27 * q^16 - 9 * q^17 - 3 * q^19 - 183 * q^20 + 75 * q^22 + 48 * q^23 + 21 * q^25 - 12 * q^28 - 78 * q^29 - 87 * q^31 + 243 * q^32 - 153 * q^34 - 252 * q^35 - 3 * q^37 + 321 * q^38 - 168 * q^40 - 357 * q^41 - 87 * q^43 + 639 * q^44 - 3 * q^46 - 51 * q^47 - 69 * q^49 + 168 * q^50 - 36 * q^52 - 12 * q^55 - 177 * q^56 + 138 * q^58 + 48 * q^59 + 147 * q^61 - 900 * q^62 - 51 * q^64 + 624 * q^65 + 12 * q^67 - 477 * q^68 - 6 * q^70 + 315 * q^71 - 66 * q^73 - 480 * q^74 - 57 * q^76 + 453 * q^77 - 15 * q^79 - 12 * q^82 - 591 * q^83 + 243 * q^85 + 669 * q^86 + 591 * q^88 + 72 * q^89 + 96 * q^91 + 564 * q^92 + 957 * q^94 - 606 * q^95 + 696 * q^97 + 882 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{18}\right)$

Coefficient data

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

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

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

$2$	−0.746252	−	0.889349i	−0.373126	−	0.444674i	0.546506	−	0.837455i	$-0.315958\pi$
$2$	−0.746252	−	0.889349i	−0.373126	−	0.444674i	−0.919632	+	0.392781i	$0.871513\pi$
$3$		0			0
$3$		0			0
$4$	0.460544	−	2.61187i	0.115136	−	0.652969i
$5$	−1.84110	−	5.05837i	−0.368219	−	1.01167i	−0.976038	−	0.217598i	$-0.930178\pi$
$5$	−1.84110	−	5.05837i	−0.368219	−	1.01167i	0.607819	−	0.794075i	$-0.292044\pi$
$6$		0			0
$7$	−1.82927	−	10.3743i	−0.261325	−	1.48205i	−0.779300	−	0.626651i	$-0.784425\pi$
$7$	−1.82927	−	10.3743i	−0.261325	−	1.48205i	0.517975	−	0.855396i	$-0.326686\pi$
$8$	−6.68824	+	3.86146i	−0.836030	+	0.482682i
$9$		0			0
$10$	−3.12473	+	5.41219i	−0.312473	+	0.541219i
$11$	−4.01667	+	11.0357i	−0.365152	+	1.00325i	0.612028	+	0.790836i	$0.290354\pi$
$11$	−4.01667	+	11.0357i	−0.365152	+	1.00325i	−0.977180	+	0.212412i	$0.931868\pi$
$12$		0			0
$13$	8.60488	+	7.22035i	0.661914	+	0.555412i	0.910660	−	0.413157i	$-0.135574\pi$
$13$	8.60488	+	7.22035i	0.661914	+	0.555412i	−0.248746	+	0.968569i	$0.580018\pi$
$14$	−7.86129	+	9.36873i	−0.561521	+	0.669195i
$15$		0			0
$16$	−1.54359	−	0.561820i	−0.0964742	−	0.0351138i
$17$	2.73630	+	1.57980i	0.160959	+	0.0929296i	0.578316	−	0.815813i	$-0.303710\pi$
$17$	2.73630	+	1.57980i	0.160959	+	0.0929296i	−0.417357	+	0.908743i	$0.637044\pi$
$18$		0			0
$19$	2.26051	+	3.91532i	0.118974	+	0.206069i	0.919361	−	0.393414i	$-0.128706\pi$
$19$	2.26051	+	3.91532i	0.118974	+	0.206069i	−0.800387	+	0.599483i	$0.795373\pi$
$20$	−14.0597	+	2.47911i	−0.702986	+	0.123955i
$21$		0			0
$22$	12.8121	−	4.66321i	0.582366	−	0.211964i
$23$	−19.6052	−	3.45692i	−0.852399	−	0.150301i	−0.269655	−	0.962957i	$-0.586910\pi$
$23$	−19.6052	−	3.45692i	−0.852399	−	0.150301i	−0.582744	+	0.812656i	$0.698021\pi$
$24$		0			0
$25$	−3.04634	+	2.55619i	−0.121854	+	0.102247i
$26$		−	13.0409i		−	0.501575i
$27$		0			0
$28$	−27.9389			−0.997818
$29$	−16.3009	−	19.4267i	−0.562100	−	0.669885i	0.407890	−	0.913031i	$-0.366265\pi$
$29$	−16.3009	−	19.4267i	−0.562100	−	0.669885i	−0.969990	+	0.243147i	$0.921820\pi$
$30$		0			0
$31$	3.84135	−	21.7854i	0.123915	−	0.702754i	−0.858032	−	0.513596i	$-0.828313\pi$
$31$	3.84135	−	21.7854i	0.123915	−	0.702754i	0.981947	−	0.189158i	$-0.0605759\pi$
$32$	11.2178	+	30.8207i	0.350557	+	0.963147i
$33$		0			0
$34$	−0.636973	−	3.61245i	−0.0187345	−	0.106249i
$35$	−49.1093	+	28.3533i	−1.40312	+	0.810093i
$36$		0			0
$37$	−8.82807	+	15.2907i	−0.238596	+	0.413261i	−0.960312	−	0.278929i	$-0.910021\pi$
$37$	−8.82807	+	15.2907i	−0.238596	+	0.413261i	0.721715	+	0.692190i	$0.243354\pi$
$38$	1.79517	−	4.93220i	0.0472414	−	0.129795i
$39$		0			0
$40$	31.8464	+	26.7223i	0.796159	+	0.668057i
$41$	7.99934	−	9.53324i	0.195106	−	0.232518i	−0.659618	−	0.751601i	$-0.729282\pi$
$41$	7.99934	−	9.53324i	0.195106	−	0.232518i	0.854724	+	0.519083i	$0.173726\pi$
$42$		0			0
$43$	−34.2503	−	12.4661i	−0.796520	−	0.289909i	−0.0884761	−	0.996078i	$-0.528200\pi$
$43$	−34.2503	−	12.4661i	−0.796520	−	0.289909i	−0.708043	+	0.706169i	$0.750422\pi$
$44$	26.9741	+	15.5735i	0.613047	+	0.353943i
$45$		0			0
$46$	11.5560	+	20.0156i	0.251217	+	0.435121i
$47$	12.2112	−	2.15316i	0.259813	−	0.0458120i	−0.0422244	−	0.999108i	$-0.513444\pi$
$47$	12.2112	−	2.15316i	0.259813	−	0.0458120i	0.302037	+	0.953296i	$0.402333\pi$
$48$		0			0
$49$	−58.2355	+	21.1960i	−1.18848	+	0.432571i
$50$	4.54668	+	0.801703i	0.0909336	+	0.0160341i
$51$		0			0
$52$	22.8216	−	19.1496i	0.438876	−	0.368261i
$53$		−	84.6210i		−	1.59662i	−0.602245	−	0.798311i	$-0.705727\pi$
$53$		−	84.6210i		−	1.59662i	0.602245	−	0.798311i	$-0.294273\pi$
$54$		0			0
$55$	63.2178			1.14942
$56$	52.2946	+	62.3223i	0.933833	+	1.11290i
$57$		0			0
$58$	−5.11249	+	28.9944i	−0.0881464	+	0.499903i
$59$	−23.3509	−	64.1562i	−0.395779	−	1.08739i	−0.964320	−	0.264738i	$-0.914714\pi$
$59$	−23.3509	−	64.1562i	−0.395779	−	1.08739i	0.568542	−	0.822654i	$-0.307508\pi$
$60$		0			0
$61$	13.5571	+	76.8859i	0.222247	+	1.26043i	0.867879	+	0.496776i	$0.165483\pi$
$61$	13.5571	+	76.8859i	0.222247	+	1.26043i	−0.645632	+	0.763649i	$0.723406\pi$
$62$	−22.2414	+	12.8411i	−0.358733	+	0.207114i
$63$		0			0
$64$	15.7537	−	27.2863i	0.246152	−	0.426348i
$65$	20.6808	−	56.8200i	0.318166	−	0.874154i
$66$		0			0
$67$	−74.4011	−	62.4300i	−1.11046	−	0.931791i	−0.112381	−	0.993665i	$-0.535848\pi$
$67$	−74.4011	−	62.4300i	−1.11046	−	0.931791i	−0.998084	+	0.0618745i	$0.980292\pi$
$68$	5.38643	−	6.41930i	0.0792122	−	0.0944014i
$69$		0			0
$70$	61.8639	+	22.5166i	0.883769	+	0.321666i
$71$	105.364	+	60.8322i	1.48401	+	0.856791i	0.999835	−	0.0181820i	$-0.00578784\pi$
$71$	105.364	+	60.8322i	1.48401	+	0.856791i	0.484171	+	0.874973i	$0.339121\pi$
$72$		0			0
$73$	−45.5705	−	78.9304i	−0.624254	−	1.08124i	−0.988685	−	0.150009i	$-0.952070\pi$
$73$	−45.5705	−	78.9304i	−0.624254	−	1.08124i	0.364431	−	0.931230i	$-0.381263\pi$
$74$	20.1867	−	3.55946i	0.272793	−	0.0481008i
$75$		0			0
$76$	11.2674	−	4.10099i	0.148255	−	0.0539604i
$77$	121.836	+	21.4829i	1.58228	+	0.278999i
$78$		0			0
$79$	−15.6180	+	13.1051i	−0.197696	+	0.165887i	−0.736262	−	0.676697i	$-0.763411\pi$
$79$	−15.6180	+	13.1051i	−0.197696	+	0.165887i	0.538566	+	0.842584i	$0.318966\pi$
$80$			8.84240i			0.110530i
$81$		0			0
$82$	−14.4479			−0.176194
$83$	−20.3134	−	24.2086i	−0.244740	−	0.291669i	0.629665	−	0.776867i	$-0.283192\pi$
$83$	−20.3134	−	24.2086i	−0.244740	−	0.291669i	−0.874405	+	0.485197i	$0.838748\pi$
$84$		0			0
$85$	2.95344	−	16.7498i	0.0347463	−	0.197056i
$86$	14.4727	+	39.7634i	0.168287	+	0.462365i
$87$		0			0
$88$	−15.7495	−	89.3198i	−0.178971	−	1.01500i
$89$	59.7756	−	34.5114i	0.671636	−	0.387769i	−0.125060	−	0.992149i	$-0.539912\pi$
$89$	59.7756	−	34.5114i	0.671636	−	0.387769i	0.796696	+	0.604380i	$0.206579\pi$
$90$		0			0
$91$	59.1656	−	102.478i	0.650171	−	1.12613i
$92$	−18.0581	+	49.6142i	−0.196283	+	0.539284i
$93$		0			0
$94$	−11.0276	−	9.25321i	−0.117314	−	0.0984384i
$95$	15.6433	−	18.6430i	0.164666	−	0.196242i
$96$		0			0
$97$	74.9914	+	27.2946i	0.773107	+	0.281388i	0.698295	−	0.715810i	$-0.253942\pi$
$97$	74.9914	+	27.2946i	0.773107	+	0.281388i	0.0748118	+	0.997198i	$0.476164\pi$
$98$	62.3089	+	35.9741i	0.635806	+	0.367083i
$99$		0			0
$100$	5.27346	+	9.13390i	0.0527346	+	0.0913390i
$101$	4.70412	−	0.829463i	0.0465754	−	0.00821250i	−0.150312	−	0.988639i	$-0.548028\pi$
$101$	4.70412	−	0.829463i	0.0465754	−	0.00821250i	0.196887	+	0.980426i	$0.436917\pi$
$102$		0			0
$103$	67.9330	−	24.7256i	0.659544	−	0.240054i	0.00950434	−	0.999955i	$-0.496975\pi$
$103$	67.9330	−	24.7256i	0.659544	−	0.240054i	0.650039	+	0.759901i	$0.274752\pi$
$104$	−85.4326	−	15.0641i	−0.821467	−	0.144847i
$105$		0			0
$106$	−75.2576	+	63.1486i	−0.709977	+	0.595742i
$107$		−	158.133i		−	1.47788i	−0.673773	−	0.738938i	$-0.735328\pi$
$107$		−	158.133i		−	1.47788i	0.673773	−	0.738938i	$-0.264672\pi$
$108$		0			0
$109$	−18.5788			−0.170448			−0.0852240	−	0.996362i	$-0.527161\pi$
$109$	−18.5788			−0.170448			−0.0852240	+	0.996362i	$0.527161\pi$
$110$	−47.1764	−	56.2227i	−0.428877	−	0.511115i
$111$		0			0
$112$	−3.00486	+	17.0414i	−0.0268291	+	0.152155i
$113$	−6.16189	−	16.9296i	−0.0545300	−	0.149820i	0.909437	−	0.415842i	$-0.136513\pi$
$113$	−6.16189	−	16.9296i	−0.0545300	−	0.149820i	−0.963967	+	0.266022i	$0.914291\pi$
$114$		0			0
$115$	18.6086	+	105.535i	0.161814	+	0.917693i
$116$	−58.2473	+	33.6291i	−0.502131	+	0.289906i
$117$		0			0
$118$	−39.6315	+	68.6438i	−0.335860	+	0.581727i
$119$	11.3839	−	31.2771i	0.0956634	−	0.262833i
$120$		0			0
$121$	−12.9621	−	10.8765i	−0.107125	−	0.0898886i
$122$	58.2614	−	69.4333i	0.477553	−	0.569125i
$123$		0			0
$124$	−55.1316	−	20.0662i	−0.444609	−	0.161825i
$125$	−98.0067	−	56.5842i	−0.784054	−	0.452674i
$126$		0			0
$127$	78.1067	+	135.285i	0.615013	+	1.06523i	0.990382	+	0.138359i	$0.0441827\pi$
$127$	78.1067	+	135.285i	0.615013	+	1.06523i	−0.375369	+	0.926876i	$0.622484\pi$
$128$	93.1785	−	16.4299i	0.727957	−	0.128358i
$129$		0			0
$130$	−65.9659	+	24.0096i	−0.507430	+	0.184689i
$131$	−97.0223	−	17.1076i	−0.740628	−	0.130593i	−0.209410	−	0.977828i	$-0.567154\pi$
$131$	−97.0223	−	17.1076i	−0.740628	−	0.130593i	−0.531218	+	0.847235i	$0.678265\pi$
$132$		0			0
$133$	36.4837	−	30.6134i	0.274313	−	0.230176i
$134$			112.757i			0.841471i
$135$		0			0
$136$	−24.4014			−0.179422
$137$	42.2031	+	50.2957i	0.308052	+	0.367122i	0.897753	−	0.440500i	$-0.145199\pi$
$137$	42.2031	+	50.2957i	0.308052	+	0.367122i	−0.589701	+	0.807622i	$0.700754\pi$
$138$		0			0
$139$	−21.7582	+	123.397i	−0.156534	+	0.887749i	0.800836	+	0.598884i	$0.204389\pi$
$139$	−21.7582	+	123.397i	−0.156534	+	0.887749i	−0.957370	+	0.288865i	$0.906722\pi$
$140$	51.4382	+	141.325i	0.367415	+	1.00947i
$141$		0			0
$142$	−24.5274	−	139.102i	−0.172728	−	0.979591i
$143$	−114.245	+	65.9593i	−0.798915	+	0.461254i
$144$		0			0
$145$	−68.2557	+	118.222i	−0.470729	+	0.815326i
$146$	−36.1896	+	99.4301i	−0.247874	+	0.681028i
$147$		0			0
$148$	35.8716	+	30.0998i	0.242375	+	0.203377i
$149$	−129.687	+	154.554i	−0.870380	+	1.03728i	0.128581	+	0.991699i	$0.458958\pi$
$149$	−129.687	+	154.554i	−0.870380	+	1.03728i	−0.998961	+	0.0455791i	$0.985487\pi$
$150$		0			0
$151$	−120.413	−	43.8266i	−0.797435	−	0.290243i	−0.0890119	−	0.996031i	$-0.528371\pi$
$151$	−120.413	−	43.8266i	−0.797435	−	0.290243i	−0.708423	+	0.705788i	$0.750593\pi$
$152$	−30.2377	−	17.4577i	−0.198932	−	0.114853i
$153$		0			0
$154$	−71.8144	−	124.386i	−0.466327	−	0.807703i
$155$	−117.271	+	20.6780i	−0.756586	+	0.133406i
$156$		0			0
$157$	130.567	−	47.5224i	0.831635	−	0.302690i	0.109105	−	0.994030i	$-0.465201\pi$
$157$	130.567	−	47.5224i	0.831635	−	0.302690i	0.722530	+	0.691340i	$0.242979\pi$
$158$	23.3100	+	4.11018i	0.147531	+	0.0260138i
$159$		0			0
$160$	135.249	−	113.488i	0.845309	−	0.709298i
$161$			209.714i			1.30257i
$162$		0			0
$163$	39.8569			0.244521			0.122261	−	0.992498i	$-0.460986\pi$
$163$	39.8569			0.244521			0.122261	+	0.992498i	$0.460986\pi$
$164$	−21.2156	−	25.2837i	−0.129363	−	0.154169i
$165$		0			0
$166$	−6.37094	+	36.1314i	−0.0383791	+	0.217659i
$167$	−56.7592	−	155.945i	−0.339876	−	0.933801i	−0.985429	−	0.170086i	$-0.945596\pi$
$167$	−56.7592	−	155.945i	−0.339876	−	0.933801i	0.645554	−	0.763715i	$-0.276627\pi$
$168$		0			0
$169$	−7.43607	−	42.1720i	−0.0440004	−	0.249539i
$170$	−17.1004	+	9.87292i	−0.100591	+	0.0580760i
$171$		0			0
$172$	−48.3337	+	83.7164i	−0.281010	+	0.486723i
$173$	−3.72465	+	10.2334i	−0.0215298	+	0.0591526i	−0.949992	−	0.312274i	$-0.898909\pi$
$173$	−3.72465	+	10.2334i	−0.0215298	+	0.0591526i	0.928462	+	0.371427i	$0.121131\pi$
$174$		0			0
$175$	32.0913	+	26.9278i	0.183379	+	0.153873i
$176$	12.4002	−	14.7780i	0.0704556	−	0.0839657i
$177$		0			0
$178$	−75.3004	−	27.4071i	−0.423036	−	0.153972i
$179$	−244.720	−	141.289i	−1.36715	−	0.789326i	−0.376590	−	0.926380i	$-0.622903\pi$
$179$	−244.720	−	141.289i	−1.36715	−	0.789326i	−0.990564	+	0.137054i	$0.956237\pi$
$180$		0			0
$181$	54.3996	+	94.2228i	0.300550	+	0.520568i	0.976261	−	0.216599i	$-0.0694964\pi$
$181$	54.3996	+	94.2228i	0.300550	+	0.520568i	−0.675711	+	0.737167i	$0.736163\pi$
$182$	−135.291	+	23.8554i	−0.743357	+	0.131074i
$183$		0			0
$184$	144.473	−	52.5838i	0.785178	−	0.285782i
$185$	93.5991	+	16.5040i	0.505941	+	0.0892110i
$186$		0			0
$187$	−28.4251	+	23.8515i	−0.152006	+	0.127548i
$188$		−	32.8857i		−	0.174924i
$189$		0			0
$190$	−28.2539			−0.148705
$191$	−69.8256	−	83.2149i	−0.365579	−	0.435680i	0.551629	−	0.834090i	$-0.314007\pi$
$191$	−69.8256	−	83.2149i	−0.365579	−	0.435680i	−0.917208	+	0.398410i	$0.869562\pi$
$192$		0			0
$193$	34.7484	−	197.068i	0.180044	−	1.02108i	−0.752116	−	0.659031i	$-0.770967\pi$
$193$	34.7484	−	197.068i	0.180044	−	1.02108i	0.932160	−	0.362047i	$-0.117922\pi$
$194$	−31.6880	−	87.0622i	−0.163340	−	0.448774i
$195$		0			0
$196$	28.5412	+	161.865i	0.145619	+	0.825844i
$197$	253.494	−	146.355i	1.28677	−	0.742918i	0.308694	−	0.951161i	$-0.400108\pi$
$197$	253.494	−	146.355i	1.28677	−	0.742918i	0.978077	+	0.208243i	$0.0667746\pi$
$198$		0			0
$199$	41.1548	−	71.2822i	0.206808	−	0.358202i	−0.743899	−	0.668292i	$-0.767026\pi$
$199$	41.1548	−	71.2822i	0.206808	−	0.358202i	0.950707	+	0.310090i	$0.100359\pi$
$200$	10.5041	−	28.8597i	0.0525204	−	0.144299i
$201$		0			0
$202$	−4.24814	−	3.56461i	−0.0210304	−	0.0176466i
$203$	−171.720	+	204.647i	−0.845910	+	1.00812i
$204$		0			0
$205$	−62.9502	−	22.9120i	−0.307074	−	0.111766i
$206$	−72.6848	−	41.9646i	−0.352839	−	0.203712i
$207$		0			0
$208$	−9.22585	−	15.9796i	−0.0443550	−	0.0768252i
$209$	−52.2881	+	9.21980i	−0.250182	+	0.0441139i
$210$		0			0
$211$	−108.859	+	39.6214i	−0.515919	+	0.187779i	−0.586840	−	0.809703i	$-0.699628\pi$
$211$	−108.859	+	39.6214i	−0.515919	+	0.187779i	0.0709215	+	0.997482i	$0.477406\pi$
$212$	−221.019	−	38.9717i	−1.04254	−	0.183829i
$213$		0			0
$214$	−140.635	+	118.007i	−0.657174	+	0.551434i
$215$			196.202i			0.912568i
$216$		0			0
$217$	−233.036			−1.07390
$218$	13.8645	+	16.5231i	0.0635986	+	0.0757938i
$219$		0			0
$220$	29.1146	−	165.117i	0.132339	−	0.750532i
$221$	12.1388	+	33.3510i	0.0549266	+	0.150910i
$222$		0			0
$223$	−34.4233	−	195.224i	−0.154365	−	0.875446i	−0.959364	−	0.282171i	$-0.908946\pi$
$223$	−34.4233	−	195.224i	−0.154365	−	0.875446i	0.805000	−	0.593275i	$-0.202166\pi$
$224$	299.224	−	172.757i	1.33582	−	0.771236i
$225$		0			0
$226$	−10.4580	+	18.1138i	−0.0462745	+	0.0801498i
$227$	−1.76204	+	4.84116i	−0.00776228	+	0.0213267i	−0.943513	−	0.331335i	$-0.892501\pi$
$227$	−1.76204	+	4.84116i	−0.00776228	+	0.0213267i	0.935751	+	0.352661i	$0.114723\pi$
$228$		0			0
$229$	270.680	+	227.127i	1.18201	+	0.991821i	0.999964	+	0.00853095i	$0.00271552\pi$
$229$	270.680	+	227.127i	1.18201	+	0.991821i	0.182043	+	0.983291i	$0.441729\pi$
$230$	79.9704	−	95.3050i	0.347697	−	0.414370i
$231$		0			0
$232$	184.040	+	66.9849i	0.793274	+	0.288728i
$233$	121.729	+	70.2803i	0.522442	+	0.301632i	0.737933	−	0.674874i	$-0.235802\pi$
$233$	121.729	+	70.2803i	0.522442	+	0.301632i	−0.215491	+	0.976506i	$0.569135\pi$
$234$		0			0
$235$	−33.3735	−	57.8046i	−0.142015	−	0.245977i
$236$	−178.322	+	31.4430i	−0.755602	+	0.133233i
$237$		0			0
$238$	−36.3116	+	13.2163i	−0.152570	+	0.0555308i
$239$	145.430	+	25.6433i	0.608495	+	0.107294i	0.469401	−	0.882985i	$-0.344470\pi$
$239$	145.430	+	25.6433i	0.608495	+	0.107294i	0.139094	+	0.990279i	$0.455581\pi$
$240$		0			0
$241$	233.194	−	195.673i	0.967611	−	0.811922i	−0.0145632	−	0.999894i	$-0.504636\pi$
$241$	233.194	−	195.673i	0.967611	−	0.811922i	0.982174	+	0.187972i	$0.0601913\pi$
$242$			19.6445i			0.0811755i
$243$		0			0
$244$	207.060			0.848606
$245$	214.434	+	255.553i	0.875241	+	1.04307i
$246$		0			0
$247$	−8.81855	+	50.0125i	−0.0357026	+	0.202480i
$248$	58.4314	+	160.539i	0.235611	+	0.647335i
$249$		0			0
$250$	22.8146	+	129.388i	0.0912585	+	0.517553i
$251$	−108.072	+	62.3955i	−0.430567	+	0.248588i	−0.699588	−	0.714546i	$-0.746633\pi$
$251$	−108.072	+	62.3955i	−0.430567	+	0.248588i	0.269021	+	0.963134i	$0.413300\pi$
$252$		0			0
$253$	116.897	−	202.472i	0.462044	−	0.800284i
$254$	62.0280	−	170.421i	0.244205	−	0.670947i
$255$		0			0
$256$	−180.691	−	151.618i	−0.705824	−	0.592257i
$257$	293.774	−	350.106i	1.14309	−	1.36228i	0.221015	−	0.975271i	$-0.429063\pi$
$257$	293.774	−	350.106i	1.14309	−	1.36228i	0.922075	−	0.387011i	$-0.126492\pi$
$258$		0			0
$259$	174.779	+	63.6144i	0.674823	+	0.245616i
$260$	−138.882	−	80.1837i	−0.534163	−	0.308399i
$261$		0			0
$262$	57.1884	+	99.0533i	0.218276	+	0.378066i
$263$	460.838	−	81.2581i	1.75223	−	0.308966i	0.796816	−	0.604222i	$-0.206516\pi$
$263$	460.838	−	81.2581i	1.75223	−	0.308966i	0.955418	+	0.295255i	$0.0954048\pi$
$264$		0			0
$265$	−428.044	+	155.795i	−1.61526	+	0.587907i
$266$	−54.4521	−	9.60137i	−0.204707	−	0.0360954i
$267$		0			0
$268$	−197.324	+	165.575i	−0.736284	+	0.617816i
$269$			317.049i			1.17862i	0.807907	+	0.589310i	$0.200601\pi$
$269$			317.049i			1.17862i	−0.807907	+	0.589310i	$0.799399\pi$
$270$		0			0
$271$	115.698			0.426931			0.213465	−	0.976951i	$-0.431525\pi$
$271$	115.698			0.426931			0.213465	+	0.976951i	$0.431525\pi$
$272$	−3.33615	−	3.97587i	−0.0122653	−	0.0146172i
$273$		0			0
$274$	13.2363	−	75.0666i	0.0483076	−	0.273966i
$275$	−15.9732	−	43.8860i	−0.0580843	−	0.159585i
$276$		0			0
$277$	−20.0227	−	113.554i	−0.0722840	−	0.409943i	−0.999383	−	0.0351261i	$-0.988817\pi$
$277$	−20.0227	−	113.554i	−0.0722840	−	0.409943i	0.927099	−	0.374817i	$-0.122294\pi$
$278$	125.980	−	72.7347i	0.453166	−	0.261635i
$279$		0			0
$280$	218.970	−	379.267i	0.782035	−	1.35452i
$281$	−27.9061	+	76.6714i	−0.0993100	+	0.272852i	−0.979392	−	0.201971i	$-0.935265\pi$
$281$	−27.9061	+	76.6714i	−0.0993100	+	0.272852i	0.880082	+	0.474822i	$0.157488\pi$
$282$		0			0
$283$	−319.547	−	268.132i	−1.12914	−	0.947462i	−0.130112	−	0.991499i	$-0.541534\pi$
$283$	−319.547	−	268.132i	−1.12914	−	0.947462i	−0.999030	+	0.0440369i	$0.985978\pi$
$284$	207.411	−	247.183i	0.730320	−	0.870362i
$285$		0			0
$286$	143.916	+	52.3812i	0.503204	+	0.183151i
$287$	−113.534	−	65.5489i	−0.395589	−	0.228393i
$288$		0			0
$289$	−139.508	−	241.636i	−0.482728	−	0.836110i
$290$	156.077	−	27.5205i	0.538196	−	0.0948984i
$291$		0			0
$292$	−227.144	+	82.6735i	−0.777889	+	0.283128i
$293$	340.579	+	60.0533i	1.16239	+	0.204960i	0.721377	−	0.692542i	$-0.243509\pi$
$293$	340.579	+	60.0533i	1.16239	+	0.204960i	0.441009	+	0.897503i	$0.354621\pi$
$294$		0			0
$295$	−281.534	+	236.235i	−0.954353	+	0.800798i
$296$		−	136.357i		−	0.460665i
$297$		0			0
$298$	234.232			0.786012
$299$	−143.740	−	171.303i	−0.480735	−	0.572918i
$300$		0			0
$301$	−66.6742	+	378.128i	−0.221509	+	1.25624i
$302$	50.8811	+	139.795i	0.168480	+	0.462896i
$303$		0			0
$304$	−1.28959	−	7.31364i	−0.00424208	−	0.0240580i
$305$	363.957	−	210.131i	1.19330	−	0.688954i
$306$		0			0
$307$	−288.668	+	499.988i	−0.940286	+	1.62862i	−0.175362	+	0.984504i	$0.556110\pi$
$307$	−288.668	+	499.988i	−0.940286	+	1.62862i	−0.764925	+	0.644120i	$0.777224\pi$
$308$	112.221	−	308.326i	0.364355	−	1.00106i
$309$		0			0
$310$	105.904	+	88.8636i	0.341624	+	0.286657i
$311$	−288.678	+	344.033i	−0.928224	+	1.10621i	0.0658843	+	0.997827i	$0.479013\pi$
$311$	−288.678	+	344.033i	−0.928224	+	1.10621i	−0.994109	+	0.108388i	$0.965431\pi$
$312$		0			0
$313$	−10.1840	−	3.70667i	−0.0325367	−	0.0118424i	0.325701	−	0.945473i	$-0.394400\pi$
$313$	−10.1840	−	3.70667i	−0.0325367	−	0.0118424i	−0.358237	+	0.933631i	$0.616622\pi$
$314$	−139.700	−	80.6557i	−0.444904	−	0.256865i
$315$		0			0
$316$	27.0360	+	46.8278i	0.0855570	+	0.148189i
$317$	214.918	−	37.8958i	0.677974	−	0.119545i	0.175951	−	0.984399i	$-0.443700\pi$
$317$	214.918	−	37.8958i	0.677974	−	0.119545i	0.502024	+	0.864854i	$0.332589\pi$
$318$		0			0
$319$	279.863	−	101.862i	0.877312	−	0.319316i
$320$	−167.028	−	29.4516i	−0.521963	−	0.0920361i
$321$		0			0
$322$	186.509	−	156.500i	0.579220	−	0.486024i
$323$			14.2846i			0.0442249i
$324$		0			0
$325$	−44.6700			−0.137446
$326$	−29.7433	−	35.4467i	−0.0912372	−	0.108732i
$327$		0			0
$328$	−16.6893	+	94.6497i	−0.0508820	+	0.288566i
$329$	−44.6753	−	122.744i	−0.135791	−	0.373083i
$330$		0			0
$331$	104.307	+	591.553i	0.315126	+	1.78717i	0.571512	+	0.820594i	$0.306357\pi$
$331$	104.307	+	591.553i	0.315126	+	1.78717i	−0.256386	+	0.966574i	$0.582532\pi$
$332$	−72.5849	+	41.9069i	−0.218629	+	0.126226i
$333$		0			0
$334$	−96.3325	+	166.853i	−0.288421	+	0.499559i
$335$	−178.814	+	491.288i	−0.533774	+	1.46653i
$336$		0			0
$337$	344.160	+	288.784i	1.02125	+	0.856927i	0.989784	−	0.142578i	$-0.0455391\pi$
$337$	344.160	+	288.784i	1.02125	+	0.856927i	0.0314624	+	0.999505i	$0.489984\pi$
$338$	−31.9565	+	38.0842i	−0.0945458	+	0.112675i
$339$		0			0
$340$	−42.3881	−	15.4280i	−0.124671	−	0.0453765i
$341$	224.988	+	129.897i	0.659789	+	0.380929i
$342$		0			0
$343$	68.3305	+	118.352i	0.199214	+	0.345049i
$344$	277.212	−	48.8799i	0.805848	−	0.142093i
$345$		0			0
$346$	11.8806	−	4.32418i	0.0343370	−	0.0124976i
$347$	232.573	+	41.0088i	0.670238	+	0.118181i	0.498404	−	0.866945i	$-0.333920\pi$
$347$	232.573	+	41.0088i	0.670238	+	0.118181i	0.171834	+	0.985126i	$0.445031\pi$
$348$		0			0
$349$	183.685	−	154.130i	0.526319	−	0.441634i	−0.340509	−	0.940241i	$-0.610599\pi$
$349$	183.685	−	154.130i	0.526319	−	0.441634i	0.866828	+	0.498607i	$0.166155\pi$
$350$		−	48.6353i		−	0.138958i
$351$		0			0
$352$	−385.187			−1.09428
$353$	−16.4494	−	19.6037i	−0.0465989	−	0.0555344i	0.742242	−	0.670132i	$-0.233763\pi$
$353$	−16.4494	−	19.6037i	−0.0465989	−	0.0555344i	−0.788840	+	0.614598i	$0.789318\pi$
$354$		0			0
$355$	113.726	−	644.970i	0.320354	−	1.81682i
$356$	−62.6103	−	172.020i	−0.175872	−	0.483203i
$357$		0			0
$358$	56.9676	+	323.079i	0.159127	+	0.902456i
$359$	16.7796	−	9.68773i	0.0467399	−	0.0269853i	−0.476448	−	0.879203i	$-0.658076\pi$
$359$	16.7796	−	9.68773i	0.0467399	−	0.0269853i	0.523188	+	0.852217i	$0.324743\pi$
$360$		0			0
$361$	170.280	−	294.934i	0.471690	−	0.816992i
$362$	43.2012	−	118.694i	0.119340	−	0.327885i
$363$		0			0
$364$	−240.411	−	201.729i	−0.660469	−	0.554199i
$365$	−315.360	+	375.831i	−0.863999	+	1.02967i
$366$		0			0
$367$	−367.152	−	133.632i	−1.00041	−	0.364121i	−0.210670	−	0.977557i	$-0.567565\pi$
$367$	−367.152	−	133.632i	−1.00041	−	0.364121i	−0.789744	+	0.613436i	$0.789787\pi$
$368$	28.3201	+	16.3506i	0.0769569	+	0.0444311i
$369$		0			0
$370$	−55.1707	−	95.5584i	−0.149110	−	0.258266i
$371$	−877.886	+	154.795i	−2.36627	+	0.417237i
$372$		0			0
$373$	168.038	−	61.1610i	0.450505	−	0.163970i	−0.106796	−	0.994281i	$-0.534059\pi$
$373$	168.038	−	61.1610i	0.450505	−	0.163970i	0.557301	+	0.830310i	$0.311837\pi$
$374$	42.4246	+	7.48060i	0.113435	+	0.0200016i
$375$		0			0
$376$	−73.3571	+	61.5539i	−0.195099	+	0.163707i
$377$		−	284.862i		−	0.755603i
$378$		0			0
$379$	3.48118			0.00918518			0.00459259	−	0.999989i	$-0.498538\pi$
$379$	3.48118			0.00918518			0.00459259	+	0.999989i	$0.498538\pi$
$380$	−41.4886	−	49.4442i	−0.109181	−	0.130116i
$381$		0			0
$382$	−21.8996	+	124.199i	−0.0573287	+	0.325127i
$383$	5.89181	+	16.1876i	0.0153833	+	0.0422653i	0.947147	−	0.320801i	$-0.103952\pi$
$383$	5.89181	+	16.1876i	0.0153833	+	0.0422653i	−0.931763	+	0.363066i	$0.881730\pi$
$384$		0			0
$385$	−115.643	−	655.842i	−0.300371	−	1.70349i
$386$	−201.193	+	116.159i	−0.521226	+	0.300930i
$387$		0			0
$388$	105.827	−	183.298i	0.272750	−	0.472417i
$389$	108.343	−	297.669i	0.278516	−	0.765216i	−0.719015	−	0.694994i	$-0.755407\pi$
$389$	108.343	−	297.669i	0.278516	−	0.765216i	0.997531	−	0.0702221i	$-0.0223708\pi$
$390$		0			0
$391$	−48.1843	−	40.4315i	−0.123234	−	0.103405i
$392$	307.645	−	366.637i	0.784810	−	0.935300i
$393$		0			0
$394$	−319.331	−	116.227i	−0.810485	−	0.294992i
$395$	95.0446	+	54.8740i	0.240619	+	0.138922i
$396$		0			0
$397$	−134.041	−	232.165i	−0.337634	−	0.584800i	0.646353	−	0.763039i	$-0.276293\pi$
$397$	−134.041	−	232.165i	−0.337634	−	0.584800i	−0.983987	+	0.178239i	$0.942960\pi$
$398$	−94.1067	+	16.5935i	−0.236449	+	0.0416923i
$399$		0			0
$400$	6.13842	−	2.23420i	0.0153460	−	0.00558550i
$401$	−95.9860	−	16.9249i	−0.239366	−	0.0422068i	0.0526778	−	0.998612i	$-0.483224\pi$
$401$	−95.9860	−	16.9249i	−0.239366	−	0.0422068i	−0.292044	+	0.956405i	$0.594335\pi$
$402$		0			0
$403$	190.352	−	159.725i	0.472339	−	0.396339i
$404$		−	12.6686i		−	0.0313578i
$405$		0			0
$406$	310.149			0.763914
$407$	−133.284	−	158.842i	−0.327479	−	0.390274i
$408$		0			0
$409$	−70.3872	+	399.185i	−0.172096	+	0.976003i	0.769347	+	0.638831i	$0.220582\pi$
$409$	−70.3872	+	399.185i	−0.172096	+	0.976003i	−0.941443	+	0.337173i	$0.890529\pi$
$410$	26.6000	+	73.0828i	0.0648780	+	0.178251i
$411$		0			0
$412$	−33.2940	−	188.820i	−0.0808107	−	0.458300i
$413$	−622.862	+	359.609i	−1.50814	+	0.870725i
$414$		0			0
$415$	−85.0569	+	147.323i	−0.204956	+	0.354995i
$416$	−126.008	+	346.205i	−0.302905	+	0.832224i
$417$		0			0
$418$	47.2197	+	39.6221i	0.112966	+	0.0947896i
$419$	−75.4214	+	89.8837i	−0.180003	+	0.214520i	−0.848500	−	0.529196i	$-0.822494\pi$
$419$	−75.4214	+	89.8837i	−0.180003	+	0.214520i	0.668496	+	0.743715i	$0.266938\pi$
$420$		0			0
$421$	489.894	+	178.307i	1.16364	+	0.423531i	0.850397	−	0.526141i	$-0.176362\pi$
$421$	489.894	+	178.307i	1.16364	+	0.423531i	0.313245	+	0.949672i	$0.398584\pi$
$422$	116.473	+	67.2459i	0.276003	+	0.159351i
$423$		0			0
$424$	326.760	+	565.966i	0.770661	+	1.33482i
$425$	−12.3740	+	2.18187i	−0.0291152	+	0.00513380i
$426$		0			0
$427$	772.840	−	281.291i	1.80993	−	0.658761i
$428$	−413.023	−	72.8271i	−0.965007	−	0.170157i
$429$		0			0
$430$	174.492	−	146.416i	0.405796	−	0.340503i
$431$			263.580i			0.611555i	0.952103	+	0.305777i	$0.0989163\pi$
$431$			263.580i			0.611555i	−0.952103	+	0.305777i	$0.901084\pi$
$432$		0			0
$433$	−702.013			−1.62128			−0.810639	−	0.585547i	$-0.800880\pi$
$433$	−702.013			−1.62128			−0.810639	+	0.585547i	$0.800880\pi$
$434$	173.903	+	207.250i	0.400699	+	0.477534i
$435$		0			0
$436$	−8.55636	+	48.5256i	−0.0196247	+	0.111297i
$437$	−30.7827	−	84.5749i	−0.0704410	−	0.193535i
$438$		0			0
$439$	−76.9114	−	436.186i	−0.175197	−	0.993591i	−0.937916	−	0.346861i	$-0.887247\pi$
$439$	−76.9114	−	436.186i	−0.175197	−	0.993591i	0.762720	−	0.646729i	$-0.223864\pi$
$440$	−422.816	+	244.113i	−0.960946	+	0.554802i
$441$		0			0
$442$	20.6021	−	35.6839i	0.0466111	−	0.0807328i
$443$	−207.552	+	570.245i	−0.468515	+	1.28723i	0.450417	+	0.892818i	$0.351275\pi$
$443$	−207.552	+	570.245i	−0.468515	+	1.28723i	−0.918932	+	0.394416i	$0.870947\pi$
$444$		0			0
$445$	−284.624	−	238.828i	−0.639605	−	0.536692i
$446$	−147.934	+	176.301i	−0.331691	+	0.395294i
$447$		0			0
$448$	−311.895	−	113.520i	−0.696193	−	0.253394i
$449$	347.745	+	200.771i	0.774488	+	0.447151i	0.834473	−	0.551048i	$-0.185772\pi$
$449$	347.745	+	200.771i	0.774488	+	0.447151i	−0.0599853	+	0.998199i	$0.519105\pi$
$450$		0			0
$451$	73.0755	+	126.570i	0.162030	+	0.280644i
$452$	−47.0559	+	8.29723i	−0.104106	+	0.0183567i
$453$		0			0
$454$	5.62041	−	2.04566i	0.0123797	−	0.00450586i
$455$	−627.300	−	110.610i	−1.37868	−	0.243099i
$456$		0			0
$457$	−112.695	+	94.5622i	−0.246597	+	0.206919i	−0.757705	−	0.652597i	$-0.773680\pi$
$457$	−112.695	+	94.5622i	−0.246597	+	0.206919i	0.511108	+	0.859516i	$0.329235\pi$
$458$		−	410.223i		−	0.895683i
$459$		0			0
$460$	284.213			0.617855
$461$	504.853	+	601.661i	1.09513	+	1.30512i	0.948798	+	0.315885i	$0.102301\pi$
$461$	504.853	+	601.661i	1.09513	+	1.30512i	0.146329	+	0.989236i	$0.453254\pi$
$462$		0			0
$463$	−62.2447	+	353.007i	−0.134438	+	0.762434i	0.840812	+	0.541328i	$0.182078\pi$
$463$	−62.2447	+	353.007i	−0.134438	+	0.762434i	−0.975250	+	0.221107i	$0.929033\pi$
$464$	14.2476	+	39.1449i	0.0307060	+	0.0843641i
$465$		0			0
$466$	−28.3369	−	160.706i	−0.0608088	−	0.344864i
$467$	−88.2727	+	50.9643i	−0.189021	+	0.109131i	−0.591524	−	0.806287i	$-0.701474\pi$
$467$	−88.2727	+	50.9643i	−0.189021	+	0.109131i	0.402503	+	0.915419i	$0.368140\pi$
$468$		0			0
$469$	−511.569	+	886.063i	−1.09077	+	1.88926i
$470$	−26.5034	+	72.8175i	−0.0563902	+	0.154931i
$471$		0			0
$472$	403.913	+	338.923i	0.855748	+	0.718058i
$473$	275.145	−	327.905i	0.581702	−	0.693245i
$474$		0			0
$475$	−16.8946	−	6.14912i	−0.0355675	−	0.0129455i
$476$	−76.4491	−	44.1379i	−0.160607	−	0.0927267i
$477$		0			0
$478$	−85.7219	−	148.475i	−0.179334	−	0.310616i
$479$	−124.450	+	21.9439i	−0.259812	+	0.0458119i	−0.302037	−	0.953296i	$-0.597667\pi$
$479$	−124.450	+	21.9439i	−0.259812	+	0.0458119i	0.0422247	+	0.999108i	$0.486555\pi$
$480$		0			0
$481$	−186.368	+	67.8325i	−0.387460	+	0.141024i
$482$	−348.044	−	61.3695i	−0.722082	−	0.127323i
$483$		0			0
$484$	−34.3777	+	28.8463i	−0.0710284	+	0.0595999i
$485$		−	429.586i		−	0.885745i
$486$		0			0
$487$	454.010			0.932258			0.466129	−	0.884717i	$-0.345648\pi$
$487$	454.010			0.932258			0.466129	+	0.884717i	$0.345648\pi$
$488$	−387.565	−	461.882i	−0.794190	−	0.946479i
$489$		0			0
$490$	67.2535	−	381.413i	0.137252	−	0.778395i
$491$	108.108	+	297.025i	0.220180	+	0.604939i	0.999772	−	0.0213484i	$-0.00679592\pi$
$491$	108.108	+	297.025i	0.220180	+	0.604939i	−0.779592	+	0.626287i	$0.784574\pi$
$492$		0			0
$493$	−13.9138	−	78.9093i	−0.0282228	−	0.160059i
$494$	51.0594	−	29.4792i	0.103359	−	0.0596744i
$495$		0			0
$496$	−18.1689	+	31.4695i	−0.0366309	+	0.0634466i
$497$	438.352	−	1204.36i	0.881997	−	2.42327i
$498$		0			0
$499$	93.6658	+	78.5949i	0.187707	+	0.157505i	0.731799	−	0.681521i	$-0.238681\pi$
$499$	93.6658	+	78.5949i	0.187707	+	0.157505i	−0.544092	+	0.839026i	$0.683126\pi$
$500$	−192.927	+	229.922i	−0.385854	+	0.459843i
$501$		0			0
$502$	136.141	+	49.5511i	0.271196	+	0.0987074i
$503$	−391.041	−	225.768i	−0.777418	−	0.448843i	0.0580963	−	0.998311i	$-0.481497\pi$
$503$	−391.041	−	225.768i	−0.777418	−	0.448843i	−0.835515	+	0.549468i	$0.814830\pi$
$504$		0			0
$505$	−12.8565	−	22.2680i	−0.0254583	−	0.0440951i
$506$	−267.303	+	47.1327i	−0.528267	+	0.0931477i
$507$		0			0
$508$	389.318	−	141.700i	0.766375	−	0.278938i
$509$	492.118	+	86.7737i	0.966833	+	0.170479i	0.634704	−	0.772755i	$-0.281122\pi$
$509$	492.118	+	86.7737i	0.966833	+	0.170479i	0.332129	+	0.943234i	$0.392233\pi$
$510$		0			0
$511$	−735.489	+	617.149i	−1.43931	+	1.20773i
$512$		−	104.621i		−	0.204338i
$513$		0			0
$514$	−530.596			−1.03229
$515$	−250.142	−	298.108i	−0.485713	−	0.578850i
$516$		0			0
$517$	−25.2867	+	143.408i	−0.0489104	+	0.277385i
$518$	−73.8540	−	202.912i	−0.142575	−	0.391722i
$519$		0			0
$520$	81.0899	+	459.884i	0.155942	+	0.884392i
$521$	−595.632	+	343.888i	−1.14325	+	0.660054i	−0.947233	−	0.320546i	$-0.896133\pi$
$521$	−595.632	+	343.888i	−1.14325	+	0.660054i	−0.196015	+	0.980601i	$0.562800\pi$
$522$		0			0
$523$	260.218	−	450.711i	0.497549	−	0.861780i	−0.502447	−	0.864608i	$-0.667567\pi$
$523$	260.218	−	450.711i	0.497549	−	0.861780i	0.999996	+	0.00282784i	$0.000900130\pi$
$524$	−89.3660	+	245.531i	−0.170546	+	0.468571i
$525$		0			0
$526$	−416.168	−	349.206i	−0.791194	−	0.663890i
$527$	44.9277	−	53.5427i	0.0852518	−	0.101599i
$528$		0			0
$529$	−124.685	−	45.3817i	−0.235700	−	0.0857876i
$530$	457.985	+	264.418i	0.864123	+	0.498902i
$531$		0			0
$532$	−63.1561	−	109.390i	−0.118715	−	0.205620i
$533$	137.667	−	24.2744i	0.258287	−	0.0455429i
$534$		0			0
$535$	−799.894	+	291.138i	−1.49513	+	0.544182i
$536$	738.683	+	130.250i	1.37814	+	0.243003i
$537$		0			0
$538$	281.967	−	236.599i	0.524103	−	0.439774i
$539$		−	727.808i		−	1.35029i
$540$		0			0
$541$	803.120			1.48451			0.742255	−	0.670117i	$-0.233756\pi$
$541$	803.120			1.48451			0.742255	+	0.670117i	$0.233756\pi$
$542$	−86.3401	−	102.896i	−0.159299	−	0.189845i
$543$		0			0
$544$	−17.9953	+	102.057i	−0.0330797	+	0.187604i
$545$	34.2054	+	93.9785i	0.0627622	+	0.172438i
$546$		0			0
$547$	−11.9276	−	67.6450i	−0.0218056	−	0.123665i	0.971962	−	0.235138i	$-0.0755543\pi$
$547$	−11.9276	−	67.6450i	−0.0218056	−	0.123665i	−0.993767	+	0.111473i	$0.964443\pi$
$548$	150.803	−	87.0659i	0.275187	−	0.158879i
$549$		0			0
$550$	−27.1099	+	46.9557i	−0.0492907	+	0.0853741i
$551$	39.2132	−	107.737i	0.0711673	−	0.195531i
$552$		0			0
$553$	164.526	+	138.054i	0.297515	+	0.249645i
$554$	−86.0473	+	102.547i	−0.155320	+	0.185103i
$555$		0			0
$556$	312.277	+	113.660i	0.561649	+	0.204424i
$557$	575.120	+	332.045i	1.03253	+	0.596132i	0.917709	−	0.397254i	$-0.130037\pi$
$557$	575.120	+	332.045i	1.03253	+	0.596132i	0.114822	+	0.993386i	$0.463370\pi$
$558$		0			0
$559$	−204.710	−	354.569i	−0.366208	−	0.634291i
$560$	91.7339	−	16.1752i	0.163811	−	0.0288842i
$561$		0			0
$562$	89.0126	−	32.3979i	0.158385	−	0.0576476i
$563$	342.373	+	60.3696i	0.608123	+	0.107229i	0.469226	−	0.883078i	$-0.344533\pi$
$563$	342.373	+	60.3696i	0.608123	+	0.107229i	0.138897	+	0.990307i	$0.455644\pi$
$564$		0			0
$565$	−74.2917	+	62.3382i	−0.131490	+	0.110333i
$566$			484.283i			0.855623i
$567$		0			0
$568$	−939.603			−1.65423
$569$	251.342	+	299.538i	0.441726	+	0.526428i	0.940267	−	0.340438i	$-0.110575\pi$
$569$	251.342	+	299.538i	0.441726	+	0.526428i	−0.498541	+	0.866866i	$0.666131\pi$
$570$		0			0
$571$	148.595	−	842.725i	0.260237	−	1.47587i	−0.522028	−	0.852928i	$-0.674824\pi$
$571$	148.595	−	842.725i	0.260237	−	1.47587i	0.782264	−	0.622947i	$-0.214065\pi$
$572$	119.663	+	328.770i	0.209200	+	0.574773i
$573$		0			0
$574$	26.4292	+	149.887i	0.0460438	+	0.261128i
$575$	68.5606	−	39.5835i	0.119236	−	0.0688408i
$576$		0			0
$577$	313.746	−	543.423i	0.543753	−	0.941808i	−0.454931	−	0.890527i	$-0.650336\pi$
$577$	313.746	−	543.423i	0.543753	−	0.941808i	0.998684	−	0.0512815i	$-0.0163306\pi$
$578$	−110.790	+	304.393i	−0.191678	+	0.526631i
$579$		0			0
$580$	277.347	+	232.722i	0.478184	+	0.401244i
$581$	−213.989	+	255.022i	−0.368311	+	0.438936i
$582$		0			0
$583$	933.854	+	339.895i	1.60181	+	0.583010i
$584$	609.573	+	351.937i	1.04379	+	0.602632i
$585$		0			0
$586$	−200.750	−	347.709i	−0.342576	−	0.593359i
$587$	733.246	−	129.291i	1.24914	−	0.220257i	0.490312	−	0.871547i	$-0.336883\pi$
$587$	733.246	−	129.291i	1.24914	−	0.220257i	0.758829	+	0.651290i	$0.225772\pi$
$588$		0			0
$589$	93.9801	−	34.2060i	0.159559	−	0.0580746i
$590$	420.191	+	74.0910i	0.712188	+	0.125578i
$591$		0			0
$592$	22.2175	−	18.6427i	0.0375296	−	0.0314910i
$593$		−	625.722i		−	1.05518i	−0.849499	−	0.527591i	$-0.823096\pi$
$593$		−	625.722i		−	1.05518i	0.849499	−	0.527591i	$-0.176904\pi$
$594$		0			0
$595$	−179.170			−0.301126
$596$	343.950	+	409.904i	0.577098	+	0.687759i
$597$		0			0
$598$	−45.0815	+	255.670i	−0.0753871	+	0.427542i
$599$	−195.992	−	538.483i	−0.327198	−	0.898970i	−0.988818	−	0.149130i	$-0.952353\pi$
$599$	−195.992	−	538.483i	−0.327198	−	0.898970i	0.661619	−	0.749840i	$-0.269870\pi$
$600$		0			0
$601$	196.479	+	1114.29i	0.326921	+	1.85406i	0.495820	+	0.868426i	$0.334868\pi$
$601$	196.479	+	1114.29i	0.326921	+	1.85406i	−0.168899	+	0.985633i	$0.554021\pi$
$602$	386.043	−	222.882i	0.641268	−	0.370236i
$603$		0			0
$604$	−169.925	+	294.319i	−0.281333	+	0.487283i
$605$	−31.1529	+	85.5919i	−0.0514924	+	0.141474i
$606$		0			0
$607$	−178.085	−	149.431i	−0.293386	−	0.246180i	0.484199	−	0.874958i	$-0.339111\pi$
$607$	−178.085	−	149.431i	−0.293386	−	0.246180i	−0.777585	+	0.628778i	$0.783556\pi$
$608$	−95.3149	+	113.592i	−0.156768	+	0.186829i
$609$		0			0
$610$	−458.484	−	166.874i	−0.751613	−	0.273565i
$611$	120.623	+	69.6414i	0.197418	+	0.113979i
$612$		0			0
$613$	533.889	+	924.724i	0.870945	+	1.50852i	0.861020	+	0.508571i	$0.169826\pi$
$613$	533.889	+	924.724i	0.870945	+	1.50852i	0.00992514	+	0.999951i	$0.496841\pi$
$614$	660.082	−	116.390i	1.07505	−	0.189561i
$615$		0			0
$616$	−897.822	+	326.781i	−1.45750	+	0.530488i
$617$	−415.344	−	73.2363i	−0.673167	−	0.118697i	−0.173392	−	0.984853i	$-0.555473\pi$
$617$	−415.344	−	73.2363i	−0.673167	−	0.118697i	−0.499775	+	0.866155i	$0.666584\pi$
$618$		0			0
$619$	460.270	−	386.212i	0.743570	−	0.623929i	−0.190224	−	0.981741i	$-0.560921\pi$
$619$	460.270	−	386.212i	0.743570	−	0.623929i	0.933794	+	0.357812i	$0.116477\pi$
$620$			315.820i			0.509386i
$621$		0			0
$622$	521.392			0.838250
$623$	−467.379	−	557.000i	−0.750207	−	0.894062i
$624$		0			0
$625$	−123.048	+	697.838i	−0.196876	+	1.11654i
$626$	4.30330	+	11.8232i	0.00687428	+	0.0188869i
$627$		0			0
$628$	−63.9908	−	362.910i	−0.101896	−	0.577882i
$629$	−48.3124	+	27.8932i	−0.0768083	+	0.0443453i
$630$		0			0
$631$	554.621	−	960.632i	0.878956	−	1.52240i	0.0264679	−	0.999650i	$-0.491574\pi$
$631$	554.621	−	960.632i	0.878956	−	1.52240i	0.852488	−	0.522747i	$-0.175093\pi$
$632$	53.8524	−	147.958i	0.0852095	−	0.234111i
$633$		0			0
$634$	−194.086	−	162.857i	−0.306129	−	0.256872i
$635$	540.518	−	644.165i	0.851210	−	1.01443i
$636$		0			0
$637$	−654.151	−	238.092i	−1.02693	−	0.373770i
$638$	−299.439	−	172.881i	−0.469340	−	0.270973i
$639$		0			0
$640$	−254.659	−	441.082i	−0.397904	−	0.689191i
$641$	162.759	−	28.6989i	0.253915	−	0.0447720i	−0.0452418	−	0.998976i	$-0.514406\pi$
$641$	162.759	−	28.6989i	0.253915	−	0.0447720i	0.299157	+	0.954204i	$0.403295\pi$
$642$		0			0
$643$	−746.702	+	271.777i	−1.16128	+	0.422671i	−0.849554	−	0.527502i	$-0.823129\pi$
$643$	−746.702	+	271.777i	−1.16128	+	0.422671i	−0.311725	+	0.950172i	$0.600907\pi$
$644$	547.747	+	96.5825i	0.850538	+	0.149973i
$645$		0			0
$646$	12.7040	−	10.6599i	0.0196657	−	0.0165015i
$647$		−	222.504i		−	0.343900i	−0.985106	−	0.171950i	$-0.944993\pi$
$647$		−	222.504i		−	0.343900i	0.985106	−	0.171950i	$-0.0550068\pi$
$648$		0			0
$649$	801.803			1.23544
$650$	33.3351	+	39.7272i	0.0512847	+	0.0611188i
$651$		0			0
$652$	18.3559	−	104.101i	0.0281532	−	0.159665i
$653$	−159.547	−	438.353i	−0.244330	−	0.671291i	−0.999869	−	0.0161872i	$-0.994847\pi$
$653$	−159.547	−	438.353i	−0.244330	−	0.671291i	0.755539	−	0.655103i	$-0.227375\pi$
$654$		0			0
$655$	92.0905	+	522.271i	0.140596	+	0.797361i
$656$	−17.7037	+	10.2212i	−0.0269873	+	0.0155811i
$657$		0			0
$658$	−75.8234	+	131.330i	−0.115233	+	0.199590i
$659$	−71.2338	+	195.713i	−0.108094	+	0.296985i	−0.981933	−	0.189230i	$-0.939401\pi$
$659$	−71.2338	+	195.713i	−0.108094	+	0.296985i	0.873839	+	0.486215i	$0.161623\pi$
$660$		0			0
$661$	−485.505	−	407.387i	−0.734501	−	0.616320i	0.196854	−	0.980433i	$-0.436928\pi$
$661$	−485.505	−	407.387i	−0.734501	−	0.616320i	−0.931355	+	0.364113i	$0.881372\pi$
$662$	448.258	−	534.213i	0.677126	−	0.806968i
$663$		0			0
$664$	229.341	+	83.4734i	0.345393	+	0.125713i
$665$	−222.024	−	128.186i	−0.333871	−	0.192760i
$666$		0			0
$667$	252.425	+	437.214i	0.378449	+	0.655493i
$668$	−433.448	+	76.4286i	−0.648874	+	0.114414i
$669$		0			0
$670$	570.367	−	207.597i	0.851294	−	0.309846i
$671$	−902.946	−	159.214i	−1.34567	−	0.237278i
$672$		0			0
$673$	84.2808	−	70.7200i	0.125231	−	0.105082i	−0.578021	−	0.816022i	$-0.696175\pi$
$673$	84.2808	−	70.7200i	0.125231	−	0.105082i	0.703252	+	0.710940i	$0.251730\pi$
$674$		−	521.584i		−	0.773864i
$675$		0			0
$676$	−113.573			−0.168007
$677$	91.9435	+	109.574i	0.135810	+	0.161852i	0.829663	−	0.558265i	$-0.188533\pi$
$677$	91.9435	+	109.574i	0.135810	+	0.161852i	−0.693853	+	0.720117i	$0.744088\pi$
$678$		0			0
$679$	145.984	−	827.915i	0.214998	−	1.21931i
$680$	44.9252	+	123.431i	0.0660665	+	0.181516i
$681$		0			0
$682$	−52.3742	−	297.029i	−0.0767950	−	0.435526i
$683$	784.050	−	452.671i	1.14795	−	0.662769i	0.199563	−	0.979885i	$-0.436048\pi$
$683$	784.050	−	452.671i	1.14795	−	0.662769i	0.948387	+	0.317116i	$0.102714\pi$
$684$		0			0
$685$	176.714	−	306.078i	0.257977	−	0.446830i
$686$	54.2643	−	149.090i	0.0791025	−	0.217332i
$687$		0			0
$688$	45.8647	+	38.4851i	0.0666638	+	0.0559376i
$689$	610.993	−	728.153i	0.886783	−	1.05683i
$690$		0			0
$691$	−499.926	−	181.958i	−0.723482	−	0.263326i	−0.0460786	−	0.998938i	$-0.514672\pi$
$691$	−499.926	−	181.958i	−0.723482	−	0.263326i	−0.677403	+	0.735612i	$0.736895\pi$
$692$	25.0130	+	14.4413i	0.0361459	+	0.0208689i
$693$		0			0
$694$	−137.087	−	237.441i	−0.197531	−	0.342134i
$695$	664.247	−	117.125i	0.955751	−	0.168525i
$696$		0			0
$697$	36.9492	−	13.4484i	0.0530118	−	0.0192947i
$698$	−274.151	−	48.3402i	−0.392767	−	0.0692553i
$699$		0			0
$700$	85.1115	−	71.4170i	0.121588	−	0.102024i
$701$			905.026i			1.29105i	0.763739	+	0.645525i	$0.223361\pi$
$701$			905.026i			1.29105i	−0.763739	+	0.645525i	$0.776639\pi$
$702$		0			0
$703$	−79.8237			−0.113547
$704$	237.846	+	283.454i	0.337850	+	0.402633i
$705$		0			0
$706$	−5.15907	+	29.2585i	−0.00730747	+	0.0414427i
$707$	−17.2102	−	47.2847i	−0.0243426	−	0.0668808i
$708$		0			0
$709$	−63.1847	−	358.338i	−0.0891181	−	0.505414i	−0.996392	−	0.0848731i	$-0.972952\pi$
$709$	−63.1847	−	358.338i	−0.0891181	−	0.505414i	0.907274	−	0.420541i	$-0.138160\pi$
$710$	−658.471	+	380.168i	−0.927424	+	0.535449i
$711$		0			0
$712$	−266.529	+	461.642i	−0.374338	+	0.648373i
$713$	−150.621	+	413.827i	−0.211249	+	0.580402i
$714$		0			0
$715$	543.982	+	456.455i	0.760814	+	0.638398i
$716$	−481.735	+	574.109i	−0.672814	+	0.801828i
$717$		0			0
$718$	−21.1376	−	7.69346i	−0.0294396	−	0.0107151i
$719$	−389.328	−	224.778i	−0.541485	−	0.312626i	0.204196	−	0.978930i	$-0.434542\pi$
$719$	−389.328	−	224.778i	−0.541485	−	0.312626i	−0.745680	+	0.666304i	$0.767875\pi$
$720$		0			0
$721$	−380.779	−	659.529i	−0.528127	−	0.914742i
$722$	−389.371	+	68.6566i	−0.539295	+	0.0950923i
$723$		0			0
$724$	271.152	−	98.6911i	0.374519	−	0.136314i
$725$	99.3163	+	17.5121i	0.136988	+	0.0241547i
$726$		0			0
$727$	443.820	−	372.409i	0.610481	−	0.512255i	−0.284314	−	0.958731i	$-0.591766\pi$
$727$	443.820	−	372.409i	0.610481	−	0.512255i	0.894795	+	0.446477i	$0.147321\pi$
$728$			913.862i			1.25530i
$729$		0			0
$730$	569.582			0.780250
$731$	−74.0252	−	88.2197i	−0.101266	−	0.120684i
$732$		0			0
$733$	162.591	−	922.097i	0.221815	−	1.25798i	−0.646866	−	0.762604i	$-0.723921\pi$
$733$	162.591	−	922.097i	0.221815	−	1.25798i	0.868681	−	0.495372i	$-0.164968\pi$
$734$	155.142	+	426.250i	0.211365	+	0.580722i
$735$		0			0
$736$	−113.383	−	643.024i	−0.154052	−	0.873674i
$737$	987.805	−	570.310i	1.34031	−	0.773826i
$738$		0			0
$739$	−263.918	+	457.119i	−0.357128	+	0.618564i	−0.987480	−	0.157746i	$-0.949577\pi$
$739$	−263.918	+	457.119i	−0.357128	+	0.618564i	0.630352	+	0.776310i	$0.282911\pi$
$740$	86.2130	−	236.868i	0.116504	−	0.320092i
$741$		0			0
$742$	792.791	+	665.230i	1.06845	+	0.896537i
$743$	23.6752	−	28.2150i	0.0318643	−	0.0379744i	−0.749877	−	0.661577i	$-0.769887\pi$
$743$	23.6752	−	28.2150i	0.0318643	−	0.0379744i	0.781741	+	0.623603i	$0.214332\pi$
$744$		0			0
$745$	1020.56	+	371.453i	1.36988	+	0.498595i
$746$	−179.793	−	103.803i	−0.241009	−	0.139146i
$747$		0			0
$748$	49.2061	+	85.2274i	0.0657835	+	0.113940i
$749$	−1640.52	+	289.268i	−2.19028	+	0.386206i
$750$		0			0
$751$	−92.5611	+	33.6895i	−0.123250	+	0.0448595i	−0.402909	−	0.915240i	$-0.632001\pi$
$751$	−92.5611	+	33.6895i	−0.123250	+	0.0448595i	0.279659	+	0.960099i	$0.409779\pi$
$752$	−20.0588	−	3.53690i	−0.0266739	−	0.00470332i
$753$		0			0
$754$	−253.342	+	212.579i	−0.335997	+	0.281935i
$755$			689.781i			0.913617i
$756$		0			0
$757$	−1385.09			−1.82971			−0.914857	−	0.403779i	$-0.867697\pi$
$757$	−1385.09			−1.82971			−0.914857	+	0.403779i	$0.867697\pi$
$758$	−2.59784	−	3.09599i	−0.00342723	−	0.00408441i
$759$		0			0
$760$	−32.6372	+	185.095i	−0.0429436	+	0.243545i
$761$	497.612	+	1367.18i	0.653892	+	1.79655i	0.602847	+	0.797857i	$0.294033\pi$
$761$	497.612	+	1367.18i	0.653892	+	1.79655i	0.0510452	+	0.998696i	$0.483745\pi$
$762$		0			0
$763$	33.9858	+	192.743i	0.0445423	+	0.252612i
$764$	−249.505	+	144.052i	−0.326577	+	0.188549i
$765$		0			0
$766$	9.99966	−	17.3199i	0.0130544	−	0.0226109i
$767$	262.298	−	720.658i	0.341979	−	0.939580i
$768$		0			0
$769$	−76.6550	−	64.3212i	−0.0996814	−	0.0836426i	0.591585	−	0.806243i	$-0.298502\pi$
$769$	−76.6550	−	64.3212i	−0.0996814	−	0.0836426i	−0.691266	+	0.722600i	$0.742947\pi$
$770$	−496.974	+	592.271i	−0.645421	+	0.769182i
$771$		0			0
$772$	−498.714	−	181.517i	−0.646002	−	0.235126i
$773$	−547.928	−	316.347i	−0.708834	−	0.409245i	0.101795	−	0.994805i	$-0.467541\pi$
$773$	−547.928	−	316.347i	−0.708834	−	0.409245i	−0.810629	+	0.585560i	$0.800875\pi$
$774$		0			0
$775$	43.9854	+	76.1850i	0.0567554	+	0.0983032i
$776$	−606.958	+	107.023i	−0.782162	+	0.137916i
$777$		0			0
$778$	−345.583	+	125.782i	−0.444194	+	0.161673i
$779$	55.4083	+	9.76997i	0.0711274	+	0.0125417i
$780$		0			0
$781$	−1094.54	+	918.430i	−1.40146	+	1.17597i
$782$			73.0247i			0.0933820i
$783$		0			0
$784$	101.800			0.129847
$785$	−480.772	−	572.961i	−0.612448	−	0.729887i
$786$		0			0
$787$	−141.639	+	803.275i	−0.179973	+	1.02068i	0.752272	+	0.658853i	$0.228958\pi$
$787$	−141.639	+	803.275i	−0.179973	+	1.02068i	−0.932245	+	0.361827i	$0.882153\pi$
$788$	−265.515	−	729.497i	−0.336948	−	0.925758i
$789$		0			0
$790$	−22.1251	−	125.478i	−0.0280064	−	0.158832i
$791$	−164.362	+	94.8944i	−0.207790	+	0.119968i
$792$		0			0
$793$	−438.486	+	759.481i	−0.552946	+	0.957731i
$794$	−106.448	+	292.463i	−0.134065	+	0.368341i
$795$		0			0
$796$	−167.227	−	140.320i	−0.210084	−	0.176281i
$797$	−805.218	+	959.622i	−1.01031	+	1.20404i	−0.0314530	+	0.999505i	$0.510013\pi$
$797$	−805.218	+	959.622i	−1.01031	+	1.20404i	−0.978859	+	0.204537i	$0.934431\pi$
$798$		0			0
$799$	36.8151	+	13.3996i	0.0460764	+	0.0167704i
$800$	−112.957	−	65.2156i	−0.141196	−	0.0815196i
$801$		0			0
$802$	56.5776	+	97.9952i	0.0705456	+	0.122189i
$803$	1054.10	−	185.866i	1.31270	−	0.231464i
$804$		0			0
$805$	1060.81	−	386.104i	1.31778	−	0.479632i
$806$	−284.102	−	50.0948i	−0.352484	−	0.0621524i
$807$		0			0
$808$	−28.2593	+	23.7124i	−0.0349744	+	0.0293470i
$809$		−	1021.88i		−	1.26313i	−0.775321	−	0.631567i	$-0.782412\pi$
$809$		−	1021.88i		−	1.26313i	0.775321	−	0.631567i	$-0.217588\pi$
$810$		0			0
$811$	−365.788			−0.451034			−0.225517	−	0.974239i	$-0.572407\pi$
$811$	−365.788			−0.451034			−0.225517	+	0.974239i	$0.572407\pi$
$812$	455.429	+	542.759i	0.560873	+	0.668423i
$813$		0			0
$814$	−41.8022	+	237.072i	−0.0513540	+	0.291243i
$815$	−73.3804	−	201.611i	−0.0900374	−	0.247376i
$816$		0			0
$817$	−28.6145	−	162.281i	−0.0350238	−	0.198630i
$818$	407.542	−	235.294i	0.498217	−	0.287646i
$819$		0			0
$820$	−88.8346	+	153.866i	−0.108335	+	0.187641i
$821$	−3.31622	+	9.11124i	−0.00403924	+	0.0110977i	−0.941696	−	0.336465i	$-0.890769\pi$
$821$	−3.31622	+	9.11124i	−0.00403924	+	0.0110977i	0.937657	+	0.347563i	$0.112991\pi$
$822$		0			0
$823$	0.684758	+	0.574580i	0.000832027	+	0.000698153i	0.643204	−	0.765695i	$-0.277605\pi$
$823$	0.684758	+	0.574580i	0.000832027	+	0.000698153i	−0.642372	+	0.766393i	$0.722049\pi$
$824$	−358.875	+	427.691i	−0.435528	+	0.519043i
$825$		0			0
$826$	784.630	+	285.582i	0.949916	+	0.345741i
$827$	−583.611	−	336.948i	−0.705696	−	0.407434i	0.103769	−	0.994601i	$-0.466910\pi$
$827$	−583.611	−	336.948i	−0.705696	−	0.407434i	−0.809465	+	0.587168i	$0.800243\pi$
$828$		0			0
$829$	−14.4804	−	25.0808i	−0.0174673	−	0.0302542i	0.857160	−	0.515051i	$-0.172227\pi$
$829$	−14.4804	−	25.0808i	−0.0174673	−	0.0302542i	−0.874627	+	0.484797i	$0.838894\pi$
$830$	194.495	−	34.2948i	0.234332	−	0.0413190i
$831$		0			0
$832$	332.575	−	121.048i	0.399730	−	0.145490i
$833$	−192.835	−	34.0020i	−0.231495	−	0.0408187i
$834$		0			0
$835$	−684.327	+	574.218i	−0.819553	+	0.687686i
$836$			140.816i			0.168440i
$837$		0			0
$838$	136.221			0.162555
$839$	−410.558	−	489.284i	−0.489342	−	0.583176i	0.463708	−	0.885988i	$-0.346519\pi$
$839$	−410.558	−	489.284i	−0.489342	−	0.583176i	−0.953050	+	0.302813i	$0.902074\pi$
$840$		0			0
$841$	34.3625	−	194.880i	0.0408591	−	0.231724i
$842$	−207.007	−	568.748i	−0.245852	−	0.675473i
$843$		0			0
$844$	53.3518	+	302.573i	0.0632130	+	0.358499i
$845$	−199.631	+	115.257i	−0.236250	+	0.136399i
$846$		0			0
$847$	−89.1253	+	154.370i	−0.105225	+	0.182254i
$848$	−47.5418	+	130.620i	−0.0560634	+	0.154033i
$849$		0			0
$850$	11.1745	+	9.37656i	0.0131465	+	0.0110312i
$851$	225.934	−	269.258i	0.265493	−	0.316402i
$852$		0			0
$853$	−730.218	−	265.777i	−0.856058	−	0.311580i	−0.123550	−	0.992338i	$-0.539428\pi$
$853$	−730.218	−	265.777i	−0.856058	−	0.311580i	−0.732508	+	0.680759i	$0.761650\pi$
$854$	−826.899	−	477.410i	−0.968266	−	0.559029i
$855$		0			0
$856$	610.623	+	1057.63i	0.713345	+	1.23555i
$857$	−1060.47	+	186.989i	−1.23742	+	0.218190i	−0.753808	−	0.657095i	$-0.771785\pi$
$857$	−1060.47	+	186.989i	−1.23742	+	0.218190i	−0.483608	+	0.875285i	$0.660674\pi$
$858$		0			0
$859$	76.1002	−	27.6982i	0.0885916	−	0.0322447i	−0.297344	−	0.954770i	$-0.596101\pi$
$859$	76.1002	−	27.6982i	0.0885916	−	0.0322447i	0.385936	+	0.922526i	$0.373879\pi$
$860$	512.455	+	90.3597i	0.595878	+	0.105069i
$861$		0			0
$862$	234.415	−	196.697i	0.271943	−	0.228187i
$863$			1599.17i			1.85304i	0.376244	+	0.926520i	$0.377215\pi$
$863$			1599.17i			1.85304i	−0.376244	+	0.926520i	$0.622785\pi$
$864$		0			0
$865$	58.6217			0.0677708
$866$	523.879	+	624.335i	0.604941	+	0.720941i
$867$		0			0
$868$	−107.323	+	608.659i	−0.123644	+	0.701221i
$869$	−81.8915	−	224.995i	−0.0942365	−	0.258913i
$870$		0			0
$871$	−189.447	−	1074.40i	−0.217505	−	1.23353i
$872$	124.260	−	71.7413i	0.142500	−	0.0822722i
$873$		0			0
$874$	−52.2449	+	90.4908i	−0.0597767	+	0.103536i
$875$	−407.742	+	1120.26i	−0.465991	+	1.28030i
$876$		0			0
$877$	−290.011	−	243.348i	−0.330686	−	0.277478i	0.462294	−	0.886727i	$-0.347027\pi$
$877$	−290.011	−	243.348i	−0.330686	−	0.277478i	−0.792979	+	0.609249i	$0.791471\pi$
$878$	−330.526	+	393.906i	−0.376454	+	0.448640i
$879$		0			0
$880$	−97.5823	−	35.5170i	−0.110889	−	0.0403603i
$881$	−1046.81	−	604.374i	−1.18820	−	0.686009i	−0.230305	−	0.973119i	$-0.573972\pi$
$881$	−1046.81	−	604.374i	−1.18820	−	0.686009i	−0.957898	+	0.287109i	$0.907306\pi$
$882$		0			0
$883$	298.144	+	516.401i	0.337649	+	0.584826i	0.983990	−	0.178223i	$-0.0570349\pi$
$883$	298.144	+	516.401i	0.337649	+	0.584826i	−0.646341	+	0.763049i	$0.723702\pi$
$884$	92.6992	−	16.3454i	0.104863	−	0.0184902i
$885$		0			0
$886$	662.033	−	240.960i	0.747216	−	0.271964i
$887$	−100.018	−	17.6359i	−0.112760	−	0.0198827i	0.116983	−	0.993134i	$-0.462678\pi$
$887$	−100.018	−	17.6359i	−0.112760	−	0.0198827i	−0.229743	+	0.973251i	$0.573789\pi$
$888$		0			0
$889$	1260.61	−	1057.78i	1.41801	−	1.18985i
$890$			431.356i			0.484670i
$891$		0			0
$892$	−525.755			−0.589412
$893$	36.0339	+	42.9435i	0.0403515	+	0.0480890i
$894$		0			0
$895$	−264.140	+	1498.01i	−0.295129	+	1.67376i
$896$	−340.898	−	936.609i	−0.380466	−	1.04532i
$897$		0			0
$898$	−80.9504	−	459.092i	−0.0901452	−	0.511239i
$899$	−485.835	+	280.497i	−0.540417	+	0.312010i
$900$		0			0
$901$	133.684	−	231.548i	0.148373	−	0.256990i
$902$	58.0325	−	159.443i	0.0643376	−	0.176766i
$903$		0			0
$904$	106.585	+	89.4357i	0.117904	+	0.0989332i
$905$	376.459	−	448.646i	0.415977	−	0.495742i
$906$		0			0
$907$	−1621.56	−	590.201i	−1.78783	−	0.650717i	−0.999365	−	0.0356391i	$-0.988653\pi$
$907$	−1621.56	−	590.201i	−1.78783	−	0.650717i	−0.788466	−	0.615078i	$-0.789124\pi$
$908$	11.8330	+	6.83179i	0.0130319	+	0.00752400i
$909$		0			0
$910$	369.753	+	640.431i	0.406322	+	0.703771i
$911$	−307.958	+	54.3013i	−0.338044	+	0.0596063i	−0.340093	−	0.940392i	$-0.610459\pi$
$911$	−307.958	+	54.3013i	−0.338044	+	0.0596063i	0.00204958	+	0.999998i	$0.499348\pi$
$912$		0			0
$913$	348.751	−	126.935i	0.381984	−	0.139031i
$914$	168.197	+	29.6578i	0.184023	+	0.0324483i
$915$		0			0
$916$	717.887	−	602.379i	0.783720	−	0.657619i
$917$			1037.84i			1.13177i
$918$		0			0
$919$	198.504			0.216000			0.108000	−	0.994151i	$-0.465555\pi$
$919$	198.504			0.216000			0.108000	+	0.994151i	$0.465555\pi$
$920$	−531.977	−	633.985i	−0.578235	−	0.689114i
$921$		0			0
$922$	158.338	−	897.981i	0.171734	−	0.973949i
$923$	467.418	+	1284.22i	0.506412	+	1.39136i
$924$		0			0
$925$	−12.1924	−	69.1468i	−0.0131810	−	0.0747533i
$926$	360.397	−	208.075i	0.389197	−	0.224703i
$927$		0			0
$928$	415.883	−	720.330i	0.448149	−	0.776218i
$929$	454.801	−	1249.56i	0.489560	−	1.34505i	−0.411520	−	0.911401i	$-0.635002\pi$
$929$	454.801	−	1249.56i	0.489560	−	1.34505i	0.901080	−	0.433653i	$-0.142776\pi$
$930$		0			0
$931$	−214.631	−	180.097i	−0.230538	−	0.193444i
$932$	239.625	−	285.574i	0.257108	−	0.306410i
$933$		0			0
$934$	111.199	+	40.4730i	0.119056	+	0.0433330i
$935$	172.983	+	99.8717i	0.185008	+	0.106815i
$936$		0			0
$937$	−675.671	−	1170.30i	−0.721100	−	1.24898i	−0.960559	−	0.278076i	$-0.910303\pi$
$937$	−675.671	−	1170.30i	−0.721100	−	1.24898i	0.239459	−	0.970906i	$-0.423030\pi$
$938$	1169.78	−	206.264i	1.24710	−	0.219897i
$939$		0			0
$940$	−166.348	+	60.5458i	−0.176966	+	0.0644104i
$941$	−765.457	−	134.971i	−0.813451	−	0.143433i	−0.248579	−	0.968612i	$-0.579963\pi$
$941$	−765.457	−	134.971i	−0.813451	−	0.143433i	−0.564872	+	0.825178i	$0.691075\pi$
$942$		0			0
$943$	−189.784	+	159.248i	−0.201256	+	0.168874i
$944$			112.150i			0.118803i
$945$		0			0
$946$	−496.949			−0.525316
$947$	176.311	+	210.119i	0.186178	+	0.221879i	0.851058	−	0.525072i	$-0.175962\pi$
$947$	176.311	+	210.119i	0.186178	+	0.221879i	−0.664880	+	0.746951i	$0.731517\pi$
$948$		0			0
$949$	177.777	−	1008.22i	0.187331	−	1.06240i
$950$	7.13890	+	19.6140i	0.00751463	+	0.0206463i
$951$		0			0
$952$	44.6368	+	253.148i	0.0468874	+	0.265911i
$953$	858.313	−	495.548i	0.900644	−	0.519987i	0.0232347	−	0.999730i	$-0.492603\pi$
$953$	858.313	−	495.548i	0.900644	−	0.519987i	0.877409	+	0.479743i	$0.159270\pi$
$954$		0			0
$955$	−292.376	+	506.410i	−0.306153	+	0.530272i
$956$	133.954	−	368.036i	0.140119	−	0.384975i
$957$		0			0
$958$	112.387	+	94.3038i	0.117314	+	0.0984382i
$959$	444.583	−	529.834i	0.463591	−	0.552486i
$960$		0			0
$961$	443.198	+	161.311i	0.461184	+	0.167857i
$962$	199.405	+	115.126i	0.207281	+	0.119674i
$963$		0			0
$964$	−403.678	−	699.190i	−0.418753	−	0.725301i
$965$	−1060.82	+	187.051i	−1.09929	+	0.193835i
$966$		0			0
$967$	−293.609	+	106.865i	−0.303629	+	0.110512i	−0.489341	−	0.872092i	$-0.662763\pi$
$967$	−293.609	+	106.865i	−0.303629	+	0.110512i	0.185713	+	0.982604i	$0.440541\pi$
$968$	128.693	+	22.6921i	0.132947	+	0.0234422i
$969$		0			0
$970$	−382.052	+	320.580i	−0.393868	+	0.330494i
$971$		−	487.838i		−	0.502407i	−0.967934	−	0.251204i	$-0.919174\pi$
$971$		−	487.838i		−	0.502407i	0.967934	−	0.251204i	$-0.0808264\pi$
$972$		0			0
$973$	1319.96			1.35659
$974$	−338.806	−	403.773i	−0.347850	−	0.414551i
$975$		0			0
$976$	22.2695	−	126.297i	0.0228171	−	0.129402i
$977$	−220.199	−	604.992i	−0.225383	−	0.619235i	0.774528	−	0.632539i	$-0.217987\pi$
$977$	−220.199	−	604.992i	−0.225383	−	0.619235i	−0.999911	+	0.0133043i	$0.995765\pi$
$978$		0			0
$979$	140.760	+	798.288i	0.143779	+	0.815412i
$980$	766.227	−	442.382i	0.781865	−	0.451410i
$981$		0			0
$982$	183.483	−	317.802i	0.186846	−	0.323627i
$983$	−526.650	+	1446.96i	−0.535758	+	1.47198i	0.316363	+	0.948638i	$0.397538\pi$
$983$	−526.650	+	1446.96i	−0.535758	+	1.47198i	−0.852121	+	0.523345i	$0.824684\pi$
$984$		0			0
$985$	−1207.02	−	1012.81i	−1.22540	−	1.02824i
$986$	−59.7947	+	71.2605i	−0.0606437	+	0.0722723i
$987$		0			0
$988$	126.565	+	46.0659i	0.128102	+	0.0466254i
$989$	628.389	+	362.801i	0.635378	+	0.366836i
$990$		0			0
$991$	−155.571	−	269.456i	−0.156984	−	0.271903i	0.776796	−	0.629752i	$-0.216844\pi$
$991$	−155.571	−	269.456i	−0.156984	−	0.271903i	−0.933780	+	0.357849i	$0.883510\pi$
$992$	714.533	−	125.991i	0.720295	−	0.127007i
$993$		0			0
$994$	−1398.22	+	508.911i	−1.40666	+	0.511983i
$995$	−436.342	−	76.9388i	−0.438534	−	0.0773255i
$996$		0			0
$997$	−36.9462	+	31.0015i	−0.0370574	+	0.0310948i	−0.661128	−	0.750273i	$-0.729922\pi$
$997$	−36.9462	+	31.0015i	−0.0370574	+	0.0310948i	0.624071	+	0.781368i	$0.285478\pi$
$998$		−	141.953i		−	0.142238i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.3.f.d.134.2		30
3.2	odd	2		243.3.f.a.134.4		30
9.2	odd	6		243.3.f.b.53.4		30
9.4	even	3		27.3.f.a.14.4	yes	30
9.5	odd	6		81.3.f.a.71.2		30
9.7	even	3		243.3.f.c.53.2		30
27.2	odd	18		243.3.f.c.188.2		30
27.4	even	9		729.3.b.a.728.12		30
27.7	even	9		81.3.f.a.8.2		30
27.11	odd	18	inner	243.3.f.d.107.2		30
27.16	even	9		243.3.f.a.107.4		30
27.20	odd	18		27.3.f.a.2.4	✓	30
27.23	odd	18		729.3.b.a.728.19		30
27.25	even	9		243.3.f.b.188.4		30
36.31	odd	6		432.3.bc.a.257.3		30
108.47	even	18		432.3.bc.a.353.3		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.3.f.a.2.4	✓	30	27.20	odd	18
27.3.f.a.14.4	yes	30	9.4	even	3
81.3.f.a.8.2		30	27.7	even	9
81.3.f.a.71.2		30	9.5	odd	6
243.3.f.a.107.4		30	27.16	even	9
243.3.f.a.134.4		30	3.2	odd	2
243.3.f.b.53.4		30	9.2	odd	6
243.3.f.b.188.4		30	27.25	even	9
243.3.f.c.53.2		30	9.7	even	3
243.3.f.c.188.2		30	27.2	odd	18
243.3.f.d.107.2		30	27.11	odd	18	inner
243.3.f.d.134.2		30	1.1	even	1	trivial
432.3.bc.a.257.3		30	36.31	odd	6
432.3.bc.a.353.3		30	108.47	even	18
729.3.b.a.728.12		30	27.4	even	9
729.3.b.a.728.19		30	27.23	odd	18

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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	243.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.746252 - 0.889349i) q^{2} +(0.460544 - 2.61187i) q^{4} +(-1.84110 - 5.05837i) q^{5} +(-1.82927 - 10.3743i) q^{7} +(-6.68824 + 3.86146i) q^{8} +O(q^{10})\)	\(q+(-0.746252 - 0.889349i) q^{2} +(0.460544 - 2.61187i) q^{4} +(-1.84110 - 5.05837i) q^{5} +(-1.82927 - 10.3743i) q^{7} +(-6.68824 + 3.86146i) q^{8} +(-3.12473 + 5.41219i) q^{10} +(-4.01667 + 11.0357i) q^{11} +(8.60488 + 7.22035i) q^{13} +(-7.86129 + 9.36873i) q^{14} +(-1.54359 - 0.561820i) q^{16} +(2.73630 + 1.57980i) q^{17} +(2.26051 + 3.91532i) q^{19} +(-14.0597 + 2.47911i) q^{20} +(12.8121 - 4.66321i) q^{22} +(-19.6052 - 3.45692i) q^{23} +(-3.04634 + 2.55619i) q^{25} -13.0409i q^{26} -27.9389 q^{28} +(-16.3009 - 19.4267i) q^{29} +(3.84135 - 21.7854i) q^{31} +(11.2178 + 30.8207i) q^{32} +(-0.636973 - 3.61245i) q^{34} +(-49.1093 + 28.3533i) q^{35} +(-8.82807 + 15.2907i) q^{37} +(1.79517 - 4.93220i) q^{38} +(31.8464 + 26.7223i) q^{40} +(7.99934 - 9.53324i) q^{41} +(-34.2503 - 12.4661i) q^{43} +(26.9741 + 15.5735i) q^{44} +(11.5560 + 20.0156i) q^{46} +(12.2112 - 2.15316i) q^{47} +(-58.2355 + 21.1960i) q^{49} +(4.54668 + 0.801703i) q^{50} +(22.8216 - 19.1496i) q^{52} -84.6210i q^{53} +63.2178 q^{55} +(52.2946 + 62.3223i) q^{56} +(-5.11249 + 28.9944i) q^{58} +(-23.3509 - 64.1562i) q^{59} +(13.5571 + 76.8859i) q^{61} +(-22.2414 + 12.8411i) q^{62} +(15.7537 - 27.2863i) q^{64} +(20.6808 - 56.8200i) q^{65} +(-74.4011 - 62.4300i) q^{67} +(5.38643 - 6.41930i) q^{68} +(61.8639 + 22.5166i) q^{70} +(105.364 + 60.8322i) q^{71} +(-45.5705 - 78.9304i) q^{73} +(20.1867 - 3.55946i) q^{74} +(11.2674 - 4.10099i) q^{76} +(121.836 + 21.4829i) q^{77} +(-15.6180 + 13.1051i) q^{79} +8.84240i q^{80} -14.4479 q^{82} +(-20.3134 - 24.2086i) q^{83} +(2.95344 - 16.7498i) q^{85} +(14.4727 + 39.7634i) q^{86} +(-15.7495 - 89.3198i) q^{88} +(59.7756 - 34.5114i) q^{89} +(59.1656 - 102.478i) q^{91} +(-18.0581 + 49.6142i) q^{92} +(-11.0276 - 9.25321i) q^{94} +(15.6433 - 18.6430i) q^{95} +(74.9914 + 27.2946i) q^{97} +(62.3089 + 35.9741i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} + 3 q^{4} + 21 q^{5} + 3 q^{7} - 9 q^{8}+O(q^{10}) \) 30 * q + 3 * q^2 + 3 * q^4 + 21 * q^5 + 3 * q^7 - 9 * q^8	\( 30 q + 3 q^{2} + 3 q^{4} + 21 q^{5} + 3 q^{7} - 9 q^{8} - 3 q^{10} + 57 q^{11} + 3 q^{13} - 114 q^{14} + 27 q^{16} - 9 q^{17} - 3 q^{19} - 183 q^{20} + 75 q^{22} + 48 q^{23} + 21 q^{25} - 12 q^{28} - 78 q^{29} - 87 q^{31} + 243 q^{32} - 153 q^{34} - 252 q^{35} - 3 q^{37} + 321 q^{38} - 168 q^{40} - 357 q^{41} - 87 q^{43} + 639 q^{44} - 3 q^{46} - 51 q^{47} - 69 q^{49} + 168 q^{50} - 36 q^{52} - 12 q^{55} - 177 q^{56} + 138 q^{58} + 48 q^{59} + 147 q^{61} - 900 q^{62} - 51 q^{64} + 624 q^{65} + 12 q^{67} - 477 q^{68} - 6 q^{70} + 315 q^{71} - 66 q^{73} - 480 q^{74} - 57 q^{76} + 453 q^{77} - 15 q^{79} - 12 q^{82} - 591 q^{83} + 243 q^{85} + 669 q^{86} + 591 q^{88} + 72 q^{89} + 96 q^{91} + 564 q^{92} + 957 q^{94} - 606 q^{95} + 696 q^{97} + 882 q^{98}+O(q^{100}) \) 30 * q + 3 * q^2 + 3 * q^4 + 21 * q^5 + 3 * q^7 - 9 * q^8 - 3 * q^10 + 57 * q^11 + 3 * q^13 - 114 * q^14 + 27 * q^16 - 9 * q^17 - 3 * q^19 - 183 * q^20 + 75 * q^22 + 48 * q^23 + 21 * q^25 - 12 * q^28 - 78 * q^29 - 87 * q^31 + 243 * q^32 - 153 * q^34 - 252 * q^35 - 3 * q^37 + 321 * q^38 - 168 * q^40 - 357 * q^41 - 87 * q^43 + 639 * q^44 - 3 * q^46 - 51 * q^47 - 69 * q^49 + 168 * q^50 - 36 * q^52 - 12 * q^55 - 177 * q^56 + 138 * q^58 + 48 * q^59 + 147 * q^61 - 900 * q^62 - 51 * q^64 + 624 * q^65 + 12 * q^67 - 477 * q^68 - 6 * q^70 + 315 * q^71 - 66 * q^73 - 480 * q^74 - 57 * q^76 + 453 * q^77 - 15 * q^79 - 12 * q^82 - 591 * q^83 + 243 * q^85 + 669 * q^86 + 591 * q^88 + 72 * q^89 + 96 * q^91 + 564 * q^92 + 957 * q^94 - 606 * q^95 + 696 * q^97 + 882 * q^98

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