LMFDB - Embedded newform 243.3.f.b.188.4

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			188.4
Character	$\chi$	$=$	243.188
Dual form			243.3.f.b.53.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.397073 + 1.09095i) q^{2} +(2.03168 - 1.70478i) q^{4} +(-5.30122 + 0.934749i) q^{5} +(-8.06979 - 6.77136i) q^{7} +(6.68824 + 3.86146i) q^{8} +O(q^{10})$	\(q+(0.397073 + 1.09095i) q^{2} +(2.03168 - 1.70478i) q^{4} +(-5.30122 + 0.934749i) q^{5} +(-8.06979 - 6.77136i) q^{7} +(6.68824 + 3.86146i) q^{8} +(-3.12473 - 5.41219i) q^{10} +(-11.5656 - 2.03932i) q^{11} +(-10.5554 - 3.84187i) q^{13} +(4.18291 - 11.4924i) q^{14} +(0.285244 - 1.61770i) q^{16} +(-2.73630 + 1.57980i) q^{17} +(2.26051 - 3.91532i) q^{19} +(-9.17683 + 10.9365i) q^{20} +(-2.36757 - 13.4272i) q^{22} +(-12.7964 - 15.2501i) q^{23} +(3.73689 - 1.36012i) q^{25} -13.0409i q^{26} -27.9389 q^{28} +(8.67353 + 23.8303i) q^{29} +(16.9460 - 14.2194i) q^{31} +(32.3004 - 5.69544i) q^{32} +(-2.80999 - 2.35786i) q^{34} +(49.1093 + 28.3533i) q^{35} +(-8.82807 - 15.2907i) q^{37} +(5.16899 + 0.911433i) q^{38} +(-39.0653 - 14.2186i) q^{40} +(-4.25636 + 11.6943i) q^{41} +(6.32921 - 35.8947i) q^{43} +(-26.9741 + 15.5735i) q^{44} +(11.5560 - 20.0156i) q^{46} +(7.97030 - 9.49863i) q^{47} +(10.7615 + 61.0314i) q^{49} +(2.96764 + 3.53669i) q^{50} +(-27.9948 + 10.1893i) q^{52} -84.6210i q^{53} +63.2178 q^{55} +(-27.8254 - 76.4496i) q^{56} +(-22.5536 + 18.9247i) q^{58} +(-67.2363 + 11.8556i) q^{59} +(59.8066 + 50.1837i) q^{61} +(22.2414 + 12.8411i) q^{62} +(15.7537 + 27.2863i) q^{64} +(59.5480 + 10.4999i) q^{65} +(91.2665 + 33.2183i) q^{67} +(-2.86606 + 7.87443i) q^{68} +(-11.4320 + 64.8340i) q^{70} +(-105.364 + 60.8322i) q^{71} +(-45.5705 + 78.9304i) q^{73} +(13.1759 - 15.7025i) q^{74} +(-2.08213 - 11.8083i) q^{76} +(79.5227 + 94.7714i) q^{77} +(19.1583 - 6.97307i) q^{79} +8.84240i q^{80} -14.4479 q^{82} +(10.8085 + 29.6962i) q^{83} +(13.0290 - 10.9326i) q^{85} +(41.6724 - 7.34797i) q^{86} +(-69.4785 - 58.2994i) q^{88} +(-59.7756 - 34.5114i) q^{89} +(59.1656 + 102.478i) q^{91} +(-51.9962 - 9.16833i) q^{92} +(13.5273 + 4.92353i) q^{94} +(-8.32363 + 22.8690i) q^{95} +(-13.8579 + 78.5918i) q^{97} +(-62.3089 + 35.9741i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{2} + 3 q^{4} + 6 q^{5} + 3 q^{7} + 9 q^{8}+O(q^{10}) $ 30 * q - 3 * q^2 + 3 * q^4 + 6 * q^5 + 3 * q^7 + 9 * q^8	$ 30 q - 3 q^{2} + 3 q^{4} + 6 q^{5} + 3 q^{7} + 9 q^{8} - 3 q^{10} + 51 q^{11} + 3 q^{13} - 129 q^{14} - 9 q^{16} + 9 q^{17} - 3 q^{19} + 30 q^{20} - 33 q^{22} + 168 q^{23} - 6 q^{25} - 12 q^{28} - 246 q^{29} + 48 q^{31} - 117 q^{32} + 99 q^{34} + 252 q^{35} - 3 q^{37} + 237 q^{38} + 201 q^{40} - 129 q^{41} + 183 q^{43} - 639 q^{44} - 3 q^{46} + 348 q^{47} + 147 q^{49} + 471 q^{50} + 45 q^{52} - 12 q^{55} - 570 q^{56} - 267 q^{58} - 426 q^{59} - 285 q^{61} + 900 q^{62} - 51 q^{64} + 213 q^{65} - 366 q^{67} - 378 q^{68} - 483 q^{70} - 315 q^{71} - 66 q^{73} - 159 q^{74} - 201 q^{76} + 654 q^{77} - 15 q^{79} - 12 q^{82} - 624 q^{83} + 18 q^{85} + 411 q^{86} + 51 q^{88} - 72 q^{89} + 96 q^{91} + 561 q^{92} - 96 q^{94} + 75 q^{95} - 114 q^{97} - 882 q^{98}+O(q^{100}) $ 30 * q - 3 * q^2 + 3 * q^4 + 6 * q^5 + 3 * q^7 + 9 * q^8 - 3 * q^10 + 51 * q^11 + 3 * q^13 - 129 * q^14 - 9 * q^16 + 9 * q^17 - 3 * q^19 + 30 * q^20 - 33 * q^22 + 168 * q^23 - 6 * q^25 - 12 * q^28 - 246 * q^29 + 48 * q^31 - 117 * q^32 + 99 * q^34 + 252 * q^35 - 3 * q^37 + 237 * q^38 + 201 * q^40 - 129 * q^41 + 183 * q^43 - 639 * q^44 - 3 * q^46 + 348 * q^47 + 147 * q^49 + 471 * q^50 + 45 * q^52 - 12 * q^55 - 570 * q^56 - 267 * q^58 - 426 * q^59 - 285 * q^61 + 900 * q^62 - 51 * q^64 + 213 * q^65 - 366 * q^67 - 378 * q^68 - 483 * q^70 - 315 * q^71 - 66 * q^73 - 159 * q^74 - 201 * q^76 + 654 * q^77 - 15 * q^79 - 12 * q^82 - 624 * q^83 + 18 * q^85 + 411 * q^86 + 51 * q^88 - 72 * q^89 + 96 * q^91 + 561 * q^92 - 96 * q^94 + 75 * q^95 - 114 * q^97 - 882 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{18}\right)$

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 $

$2$	0.397073	+	1.09095i	0.198536	+	0.545474i	0.998510	−	0.0545605i	$-0.0173758\pi$
$2$	0.397073	+	1.09095i	0.198536	+	0.545474i	−0.799974	+	0.600034i	$0.795154\pi$
$3$		0			0
$3$		0			0
$4$	2.03168	−	1.70478i	0.507919	−	0.426195i
$5$	−5.30122	+	0.934749i	−1.06024	+	0.186950i	−0.676465	−	0.736475i	$-0.736489\pi$
$5$	−5.30122	+	0.934749i	−1.06024	+	0.186950i	−0.383780	+	0.923425i	$0.625378\pi$
$6$		0			0
$7$	−8.06979	−	6.77136i	−1.15283	−	0.967337i	−0.153046	−	0.988219i	$-0.548908\pi$
$7$	−8.06979	−	6.77136i	−1.15283	−	0.967337i	−0.999782	+	0.0208820i	$0.993353\pi$
$8$	6.68824	+	3.86146i	0.836030	+	0.482682i
$9$		0			0
$10$	−3.12473	−	5.41219i	−0.312473	−	0.541219i
$11$	−11.5656	−	2.03932i	−1.05141	−	0.185393i	−0.378870	−	0.925450i	$-0.623687\pi$
$11$	−11.5656	−	2.03932i	−1.05141	−	0.185393i	−0.672544	+	0.740057i	$0.734798\pi$
$12$		0			0
$13$	−10.5554	−	3.84187i	−0.811957	−	0.295528i	−0.0975252	−	0.995233i	$-0.531093\pi$
$13$	−10.5554	−	3.84187i	−0.811957	−	0.295528i	−0.714432	+	0.699705i	$0.753315\pi$
$14$	4.18291	−	11.4924i	0.298779	−	0.820889i
$15$		0			0
$16$	0.285244	−	1.61770i	0.0178277	−	0.101106i
$17$	−2.73630	+	1.57980i	−0.160959	+	0.0929296i	−0.578316	−	0.815813i	$-0.696290\pi$
$17$	−2.73630	+	1.57980i	−0.160959	+	0.0929296i	0.417357	+	0.908743i	$0.362956\pi$
$18$		0			0
$19$	2.26051	−	3.91532i	0.118974	−	0.206069i	−0.800387	−	0.599483i	$-0.795373\pi$
$19$	2.26051	−	3.91532i	0.118974	−	0.206069i	0.919361	+	0.393414i	$0.128706\pi$
$20$	−9.17683	+	10.9365i	−0.458842	+	0.546826i
$21$		0			0
$22$	−2.36757	−	13.4272i	−0.107617	−	0.610326i
$23$	−12.7964	−	15.2501i	−0.556364	−	0.663048i	0.412409	−	0.910999i	$-0.364687\pi$
$23$	−12.7964	−	15.2501i	−0.556364	−	0.663048i	−0.968773	+	0.247950i	$0.920243\pi$
$24$		0			0
$25$	3.73689	−	1.36012i	0.149476	−	0.0544047i
$26$		−	13.0409i		−	0.501575i
$27$		0			0
$28$	−27.9389			−0.997818
$29$	8.67353	+	23.8303i	0.299087	+	0.821735i	0.994653	+	0.103273i	$0.0329315\pi$
$29$	8.67353	+	23.8303i	0.299087	+	0.821735i	−0.695566	+	0.718462i	$0.744846\pi$
$30$		0			0
$31$	16.9460	−	14.2194i	0.546646	−	0.458690i	−0.327158	−	0.944970i	$-0.606091\pi$
$31$	16.9460	−	14.2194i	0.546646	−	0.458690i	0.873803	+	0.486280i	$0.161646\pi$
$32$	32.3004	−	5.69544i	1.00939	−	0.177982i
$33$		0			0
$34$	−2.80999	−	2.35786i	−0.0826468	−	0.0693489i
$35$	49.1093	+	28.3533i	1.40312	+	0.810093i
$36$		0			0
$37$	−8.82807	−	15.2907i	−0.238596	−	0.413261i	0.721715	−	0.692190i	$-0.243354\pi$
$37$	−8.82807	−	15.2907i	−0.238596	−	0.413261i	−0.960312	+	0.278929i	$0.910021\pi$
$38$	5.16899	+	0.911433i	0.136026	+	0.0239851i
$39$		0			0
$40$	−39.0653	−	14.2186i	−0.976634	−	0.355466i
$41$	−4.25636	+	11.6943i	−0.103814	+	0.285226i	−0.980715	−	0.195446i	$-0.937385\pi$
$41$	−4.25636	+	11.6943i	−0.103814	+	0.285226i	0.876901	+	0.480671i	$0.159607\pi$
$42$		0			0
$43$	6.32921	−	35.8947i	0.147191	−	0.834761i	−0.818391	−	0.574662i	$-0.805134\pi$
$43$	6.32921	−	35.8947i	0.147191	−	0.834761i	0.965582	−	0.260099i	$-0.0837552\pi$
$44$	−26.9741	+	15.5735i	−0.613047	+	0.353943i
$45$		0			0
$46$	11.5560	−	20.0156i	0.251217	−	0.435121i
$47$	7.97030	−	9.49863i	0.169581	−	0.202098i	−0.674560	−	0.738220i	$-0.735667\pi$
$47$	7.97030	−	9.49863i	0.169581	−	0.202098i	0.844141	+	0.536121i	$0.180111\pi$
$48$		0			0
$49$	10.7615	+	61.0314i	0.219622	+	1.24554i
$50$	2.96764	+	3.53669i	0.0593527	+	0.0707338i
$51$		0			0
$52$	−27.9948	+	10.1893i	−0.538362	+	0.195948i
$53$		−	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
$56$	−27.8254	−	76.4496i	−0.496882	−	1.36517i
$57$		0			0
$58$	−22.5536	+	18.9247i	−0.388855	+	0.326288i
$59$	−67.2363	+	11.8556i	−1.13960	+	0.200942i	−0.711430	−	0.702757i	$-0.751952\pi$
$59$	−67.2363	+	11.8556i	−1.13960	+	0.200942i	−0.428169	+	0.903699i	$0.640841\pi$
$60$		0			0
$61$	59.8066	+	50.1837i	0.980437	+	0.822684i	0.984155	−	0.177309i	$-0.0567392\pi$
$61$	59.8066	+	50.1837i	0.980437	+	0.822684i	−0.00371858	+	0.999993i	$0.501184\pi$
$62$	22.2414	+	12.8411i	0.358733	+	0.207114i
$63$		0			0
$64$	15.7537	+	27.2863i	0.246152	+	0.426348i
$65$	59.5480	+	10.4999i	0.916122	+	0.161537i
$66$		0			0
$67$	91.2665	+	33.2183i	1.36219	+	0.495795i	0.916730	−	0.399508i	$-0.130819\pi$
$67$	91.2665	+	33.2183i	1.36219	+	0.495795i	0.445457	+	0.895303i	$0.353041\pi$
$68$	−2.86606	+	7.87443i	−0.0421479	+	0.115801i
$69$		0			0
$70$	−11.4320	+	64.8340i	−0.163314	+	0.926200i
$71$	−105.364	+	60.8322i	−1.48401	+	0.856791i	−0.999835	−	0.0181820i	$-0.994212\pi$
$71$	−105.364	+	60.8322i	−1.48401	+	0.856791i	−0.484171	+	0.874973i	$0.660879\pi$
$72$		0			0
$73$	−45.5705	+	78.9304i	−0.624254	+	1.08124i	0.364431	+	0.931230i	$0.381263\pi$
$73$	−45.5705	+	78.9304i	−0.624254	+	1.08124i	−0.988685	+	0.150009i	$0.952070\pi$
$74$	13.1759	−	15.7025i	0.178053	−	0.212195i
$75$		0			0
$76$	−2.08213	−	11.8083i	−0.0273964	−	0.155373i
$77$	79.5227	+	94.7714i	1.03276	+	1.23080i
$78$		0			0
$79$	19.1583	−	6.97307i	0.242511	−	0.0882667i	−0.217905	−	0.975970i	$-0.569922\pi$
$79$	19.1583	−	6.97307i	0.242511	−	0.0882667i	0.460416	+	0.887703i	$0.347700\pi$
$80$			8.84240i			0.110530i
$81$		0			0
$82$	−14.4479			−0.176194
$83$	10.8085	+	29.6962i	0.130223	+	0.357785i	0.987619	−	0.156872i	$-0.0501412\pi$
$83$	10.8085	+	29.6962i	0.130223	+	0.357785i	−0.857396	+	0.514658i	$0.827919\pi$
$84$		0			0
$85$	13.0290	−	10.9326i	0.153282	−	0.128619i
$86$	41.6724	−	7.34797i	0.484563	−	0.0854415i
$87$		0			0
$88$	−69.4785	−	58.2994i	−0.789528	−	0.662493i
$89$	−59.7756	−	34.5114i	−0.671636	−	0.387769i	0.125060	−	0.992149i	$-0.460088\pi$
$89$	−59.7756	−	34.5114i	−0.671636	−	0.387769i	−0.796696	+	0.604380i	$0.793421\pi$
$90$		0			0
$91$	59.1656	+	102.478i	0.650171	+	1.12613i
$92$	−51.9962	−	9.16833i	−0.565176	−	0.0996557i
$93$		0			0
$94$	13.5273	+	4.92353i	0.143907	+	0.0523780i
$95$	−8.32363	+	22.8690i	−0.0876171	+	0.240726i
$96$		0			0
$97$	−13.8579	+	78.5918i	−0.142864	+	0.810224i	0.826193	+	0.563388i	$0.190502\pi$
$97$	−13.8579	+	78.5918i	−0.142864	+	0.810224i	−0.969057	+	0.246837i	$0.920609\pi$
$98$	−62.3089	+	35.9741i	−0.635806	+	0.367083i
$99$		0			0
$100$	5.27346	−	9.13390i	0.0527346	−	0.0913390i
$101$	3.07039	−	3.65915i	0.0303999	−	0.0362292i	−0.750630	−	0.660722i	$-0.770250\pi$
$101$	3.07039	−	3.65915i	0.0303999	−	0.0362292i	0.781030	+	0.624493i	$0.214694\pi$
$102$		0			0
$103$	−12.5535	−	71.1945i	−0.121879	−	0.691209i	−0.983113	−	0.183000i	$-0.941419\pi$
$103$	−12.5535	−	71.1945i	−0.121879	−	0.691209i	0.861234	−	0.508208i	$-0.169692\pi$
$104$	−55.7621	−	66.4547i	−0.536175	−	0.638988i
$105$		0			0
$106$	92.3171	−	33.6007i	0.870916	−	0.316987i
$107$		−	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	$0.527161\pi$
$110$	25.1021	+	68.9674i	0.228201	+	0.626976i
$111$		0			0
$112$	−13.2559	+	11.1230i	−0.118356	+	0.0993124i
$113$	−17.7424	+	3.12847i	−0.157013	+	0.0276856i	−0.251602	−	0.967831i	$-0.580957\pi$
$113$	−17.7424	+	3.12847i	−0.157013	+	0.0276856i	0.0945892	+	0.995516i	$0.469846\pi$
$114$		0			0
$115$	82.0914	+	68.8829i	0.713838	+	0.598981i
$116$	58.2473	+	33.6291i	0.502131	+	0.289906i
$117$		0			0
$118$	−39.6315	−	68.6438i	−0.335860	−	0.581727i
$119$	32.7788	+	5.77978i	0.275452	+	0.0485696i
$120$		0			0
$121$	15.9004	+	5.78728i	0.131408	+	0.0478287i
$122$	−31.0003	+	85.1725i	−0.254100	+	0.698135i
$123$		0			0
$124$	10.1879	−	57.7785i	0.0821605	−	0.465955i
$125$	98.0067	−	56.5842i	0.784054	−	0.452674i
$126$		0			0
$127$	78.1067	−	135.285i	0.615013	−	1.06523i	−0.375369	−	0.926876i	$-0.622484\pi$
$127$	78.1067	−	135.285i	0.615013	−	1.06523i	0.990382	−	0.138359i	$-0.0441827\pi$
$128$	60.8179	−	72.4800i	0.475140	−	0.566250i
$129$		0			0
$130$	12.1900	+	69.1329i	0.0937692	+	0.531792i
$131$	−63.3268	−	75.4699i	−0.483411	−	0.576106i	0.468118	−	0.883666i	$-0.344932\pi$
$131$	−63.3268	−	75.4699i	−0.483411	−	0.576106i	−0.951529	+	0.307559i	$0.900488\pi$
$132$		0			0
$133$	−44.7539	+	16.2891i	−0.336495	+	0.122474i
$134$			112.757i			0.841471i
$135$		0			0
$136$	−24.4014			−0.179422
$137$	−22.4558	−	61.6969i	−0.163911	−	0.450342i	0.830360	−	0.557227i	$-0.188135\pi$
$137$	−22.4558	−	61.6969i	−0.163911	−	0.450342i	−0.994271	+	0.106885i	$0.965912\pi$
$138$		0			0
$139$	−95.9859	+	80.5417i	−0.690546	+	0.579437i	−0.919067	−	0.394102i	$-0.871056\pi$
$139$	−95.9859	+	80.5417i	−0.690546	+	0.579437i	0.228521	+	0.973539i	$0.426611\pi$
$140$	148.110	−	26.1158i	1.05793	−	0.186542i
$141$		0			0
$142$	−108.202	−	90.7923i	−0.761986	−	0.639382i
$143$	114.245	+	65.9593i	0.798915	+	0.461254i
$144$		0			0
$145$	−68.2557	−	118.222i	−0.470729	−	0.815326i
$146$	−104.204	−	18.3739i	−0.713725	−	0.125849i
$147$		0			0
$148$	−44.0030	−	16.0158i	−0.297317	−	0.108215i
$149$	69.0048	−	189.589i	0.463119	−	1.27241i	−0.460008	−	0.887915i	$-0.652153\pi$
$149$	69.0048	−	189.589i	0.463119	−	1.27241i	0.923127	−	0.384495i	$-0.125624\pi$
$150$		0			0
$151$	22.2514	−	126.194i	0.147360	−	0.835720i	−0.818082	−	0.575102i	$-0.804962\pi$
$151$	22.2514	−	126.194i	0.147360	−	0.835720i	0.965442	−	0.260619i	$-0.0839265\pi$
$152$	30.2377	−	17.4577i	0.198932	−	0.114853i
$153$		0			0
$154$	−71.8144	+	124.386i	−0.466327	+	0.807703i
$155$	−76.5431	+	91.2205i	−0.493826	+	0.588519i
$156$		0			0
$157$	−24.1278	−	136.835i	−0.153680	−	0.871563i	−0.959983	−	0.280059i	$-0.909646\pi$
$157$	−24.1278	−	136.835i	−0.153680	−	0.871563i	0.806303	−	0.591503i	$-0.201465\pi$
$158$	15.2145	+	18.1319i	0.0962943	+	0.114759i
$159$		0			0
$160$	−165.908	+	60.3856i	−1.03692	+	0.377410i
$161$			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	$0.460986\pi$
$164$	11.2886	+	31.0151i	0.0688328	+	0.189117i
$165$		0			0
$166$	−28.1052	+	23.5831i	−0.169309	+	0.142067i
$167$	−163.432	+	28.8174i	−0.978633	+	0.172559i	−0.640013	−	0.768364i	$-0.721071\pi$
$167$	−163.432	+	28.8174i	−0.978633	+	0.172559i	−0.338620	+	0.940923i	$0.609960\pi$
$168$		0			0
$169$	−32.8040	−	27.5258i	−0.194107	−	0.162875i
$170$	17.1004	+	9.87292i	0.100591	+	0.0580760i
$171$		0			0
$172$	−48.3337	−	83.7164i	−0.281010	−	0.486723i
$173$	−10.7247	−	1.89106i	−0.0619925	−	0.0109310i	0.142566	−	0.989785i	$-0.454465\pi$
$173$	−10.7247	−	1.89106i	−0.0619925	−	0.0109310i	−0.204558	+	0.978854i	$0.565576\pi$
$174$		0			0
$175$	−39.3658	−	14.3280i	−0.224947	−	0.0818742i
$176$	−6.59800	+	18.1279i	−0.0374886	+	0.102999i
$177$		0			0
$178$	13.9149	−	78.9156i	0.0781739	−	0.443346i
$179$	244.720	−	141.289i	1.36715	−	0.789326i	0.376590	−	0.926380i	$-0.377097\pi$
$179$	244.720	−	141.289i	1.36715	−	0.789326i	0.990564	+	0.137054i	$0.0437633\pi$
$180$		0			0
$181$	54.3996	−	94.2228i	0.300550	−	0.520568i	−0.675711	−	0.737167i	$-0.736163\pi$
$181$	54.3996	−	94.2228i	0.300550	−	0.520568i	0.976261	+	0.216599i	$0.0694964\pi$
$182$	−88.3049	+	105.238i	−0.485192	+	0.578229i
$183$		0			0
$184$	−26.6975	−	151.409i	−0.145095	−	0.822875i
$185$	61.0925	+	72.8072i	0.330230	+	0.393552i
$186$		0			0
$187$	34.8685	−	12.6911i	0.186463	−	0.0678669i
$188$		−	32.8857i		−	0.174924i
$189$		0			0
$190$	−28.2539			−0.148705
$191$	37.1534	+	102.078i	0.194521	+	0.534441i	0.998157	−	0.0606793i	$-0.0193267\pi$
$191$	37.1534	+	102.078i	0.194521	+	0.534441i	−0.803637	+	0.595120i	$0.797104\pi$
$192$		0			0
$193$	153.292	−	128.627i	0.794258	−	0.666461i	−0.152538	−	0.988298i	$-0.548745\pi$
$193$	153.292	−	128.627i	0.794258	−	0.666461i	0.946795	+	0.321836i	$0.104300\pi$
$194$	−91.2421	+	16.0884i	−0.470320	+	0.0829301i
$195$		0			0
$196$	125.909	+	105.650i	0.642392	+	0.539031i
$197$	−253.494	−	146.355i	−1.28677	−	0.742918i	−0.308694	−	0.951161i	$-0.599892\pi$
$197$	−253.494	−	146.355i	−1.28677	−	0.742918i	−0.978077	+	0.208243i	$0.933225\pi$
$198$		0			0
$199$	41.1548	+	71.2822i	0.206808	+	0.358202i	0.950707	−	0.310090i	$-0.100359\pi$
$199$	41.1548	+	71.2822i	0.206808	+	0.358202i	−0.743899	+	0.668292i	$0.767026\pi$
$200$	30.2453	+	5.33306i	0.151226	+	0.0266653i
$201$		0			0
$202$	5.21111	+	1.89669i	0.0257976	+	0.00938956i
$203$	91.3701	−	251.037i	0.450099	−	1.23664i
$204$		0			0
$205$	11.6327	−	65.9725i	0.0567450	−	0.321817i
$206$	72.6848	−	41.9646i	0.352839	−	0.203712i
$207$		0			0
$208$	−9.22585	+	15.9796i	−0.0443550	+	0.0768252i
$209$	−34.1286	+	40.6729i	−0.163295	+	0.194607i
$210$		0			0
$211$	20.1163	+	114.085i	0.0953379	+	0.540688i	0.994643	+	0.103367i	$0.0329616\pi$
$211$	20.1163	+	114.085i	0.0953379	+	0.540688i	−0.899305	+	0.437321i	$0.855927\pi$
$212$	−144.260	−	171.923i	−0.680472	−	0.810955i
$213$		0			0
$214$	172.515	−	62.7902i	0.806143	−	0.293412i
$215$			196.202i			0.912568i
$216$		0			0
$217$	−233.036			−1.07390
$218$	−7.37714	−	20.2685i	−0.0338401	−	0.0929749i
$219$		0			0
$220$	128.438	−	107.772i	0.583810	−	0.489875i
$221$	34.9522	−	6.16302i	0.158155	−	0.0278870i
$222$		0			0
$223$	−151.858	−	127.424i	−0.680976	−	0.571407i	0.235315	−	0.971919i	$-0.424388\pi$
$223$	−151.858	−	127.424i	−0.680976	−	0.571407i	−0.916291	+	0.400512i	$0.868832\pi$
$224$	−299.224	−	172.757i	−1.33582	−	0.771236i
$225$		0			0
$226$	−10.4580	−	18.1138i	−0.0462745	−	0.0801498i
$227$	−5.07359	−	0.894610i	−0.0223506	−	0.00394102i	0.162462	−	0.986715i	$-0.448057\pi$
$227$	−5.07359	−	0.894610i	−0.0223506	−	0.00394102i	−0.184812	+	0.982774i	$0.559168\pi$
$228$		0			0
$229$	−332.038	−	120.852i	−1.44995	−	0.527737i	−0.507370	−	0.861728i	$-0.669382\pi$
$229$	−332.038	−	120.852i	−1.44995	−	0.527737i	−0.942576	+	0.333991i	$0.891604\pi$
$230$	−42.5514	+	116.909i	−0.185006	+	0.508300i
$231$		0			0
$232$	−34.0091	+	192.875i	−0.146591	+	0.831359i
$233$	−121.729	+	70.2803i	−0.522442	+	0.301632i	−0.737933	−	0.674874i	$-0.764198\pi$
$233$	−121.729	+	70.2803i	−0.522442	+	0.301632i	0.215491	+	0.976506i	$0.430865\pi$
$234$		0			0
$235$	−33.3735	+	57.8046i	−0.142015	+	0.245977i
$236$	−116.391	+	138.710i	−0.493184	+	0.587754i
$237$		0			0
$238$	6.71011	+	38.0549i	0.0281937	+	0.159895i
$239$	94.9229	+	113.125i	0.397167	+	0.473325i	0.927154	−	0.374681i	$-0.122248\pi$
$239$	94.9229	+	113.125i	0.397167	+	0.473325i	−0.529987	+	0.848006i	$0.677803\pi$
$240$		0			0
$241$	−286.055	+	104.116i	−1.18695	+	0.432015i	−0.858652	−	0.512559i	$-0.828698\pi$
$241$	−286.055	+	104.116i	−1.18695	+	0.432015i	−0.328299	+	0.944574i	$0.606475\pi$
$242$			19.6445i			0.0811755i
$243$		0			0
$244$	207.060			0.848606
$245$	−114.098	−	313.482i	−0.465706	−	1.27952i
$246$		0			0
$247$	−38.9028	+	32.6433i	−0.157501	+	0.132159i
$248$	168.247	−	29.6664i	0.678414	−	0.119623i
$249$		0			0
$250$	100.646	+	84.4522i	0.402585	+	0.337809i
$251$	108.072	+	62.3955i	0.430567	+	0.248588i	0.699588	−	0.714546i	$-0.253367\pi$
$251$	108.072	+	62.3955i	0.430567	+	0.248588i	−0.269021	+	0.963134i	$0.586700\pi$
$252$		0			0
$253$	116.897	+	202.472i	0.462044	+	0.800284i
$254$	178.603	+	31.4925i	0.703160	+	0.123986i
$255$		0			0
$256$	221.650	+	80.6741i	0.865822	+	0.315133i
$257$	−156.314	+	429.469i	−0.608225	+	1.67109i	0.125876	+	0.992046i	$0.459826\pi$
$257$	−156.314	+	429.469i	−0.608225	+	1.67109i	−0.734102	+	0.679039i	$0.762397\pi$
$258$		0			0
$259$	−32.2979	+	183.170i	−0.124702	+	0.707222i
$260$	138.882	−	80.1837i	0.534163	−	0.308399i
$261$		0			0
$262$	57.1884	−	99.0533i	0.218276	−	0.378066i
$263$	300.790	−	358.468i	1.14369	−	1.36300i	0.222010	−	0.975044i	$-0.428738\pi$
$263$	300.790	−	358.468i	1.14369	−	1.36300i	0.921679	−	0.387952i	$-0.126817\pi$
$264$		0			0
$265$	79.0994	+	448.595i	0.298488	+	1.69281i
$266$	−35.5411	−	42.3562i	−0.133613	−	0.159234i
$267$		0			0
$268$	242.054	−	88.1004i	0.903187	−	0.328733i
$269$			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	$0.431525\pi$
$272$	1.77513	+	4.87713i	0.00652621	+	0.0179306i
$273$		0			0
$274$	58.3915	−	48.9963i	0.213108	−	0.178818i
$275$	−45.9930	+	8.10980i	−0.167247	+	0.0294902i
$276$		0			0
$277$	−88.3295	−	74.1172i	−0.318879	−	0.267571i	0.469271	−	0.883054i	$-0.344517\pi$
$277$	−88.3295	−	74.1172i	−0.318879	−	0.267571i	−0.788150	+	0.615483i	$0.788961\pi$
$278$	−125.980	−	72.7347i	−0.453166	−	0.261635i
$279$		0			0
$280$	218.970	+	379.267i	0.782035	+	1.35452i
$281$	−80.3524	−	14.1683i	−0.285952	−	0.0504210i	0.0288326	−	0.999584i	$-0.490821\pi$
$281$	−80.3524	−	14.1683i	−0.285952	−	0.0504210i	−0.314784	+	0.949163i	$0.601932\pi$
$282$		0			0
$283$	391.983	+	142.670i	1.38510	+	0.504134i	0.923720	−	0.383069i	$-0.125133\pi$
$283$	391.983	+	142.670i	1.38510	+	0.504134i	0.461378	+	0.887204i	$0.347355\pi$
$284$	−110.361	+	303.214i	−0.388595	+	1.06766i
$285$		0			0
$286$	−26.5946	+	150.826i	−0.0929883	+	0.527363i
$287$	113.534	−	65.5489i	0.395589	−	0.228393i
$288$		0			0
$289$	−139.508	+	241.636i	−0.482728	+	0.836110i
$290$	101.872	−	121.406i	0.351282	−	0.418642i
$291$		0			0
$292$	41.9744	+	238.049i	0.143748	+	0.815236i
$293$	222.297	+	264.924i	0.758694	+	0.904176i	0.997765	−	0.0668261i	$-0.0212873\pi$
$293$	222.297	+	264.924i	0.758694	+	0.904176i	−0.239071	+	0.971002i	$0.576843\pi$
$294$		0			0
$295$	345.353	−	125.698i	1.17069	−	0.426095i
$296$		−	136.357i		−	0.460665i
$297$		0			0
$298$	234.232			0.786012
$299$	76.4824	+	210.134i	0.255794	+	0.702788i
$300$		0			0
$301$	−294.131	+	246.806i	−0.977181	+	0.819952i
$302$	146.506	−	25.8330i	0.485120	−	0.0855397i
$303$		0			0
$304$	−5.68900	−	4.77364i	−0.0187138	−	0.0157028i
$305$	−363.957	−	210.131i	−1.19330	−	0.688954i
$306$		0			0
$307$	−288.668	−	499.988i	−0.940286	−	1.62862i	−0.764925	−	0.644120i	$-0.777224\pi$
$307$	−288.668	−	499.988i	−0.940286	−	1.62862i	−0.175362	−	0.984504i	$-0.556110\pi$
$308$	323.129	+	56.9763i	1.04912	+	0.184988i
$309$		0			0
$310$	−129.910	−	47.2833i	−0.419064	−	0.152527i
$311$	153.602	−	422.019i	0.493898	−	1.35697i	−0.403188	−	0.915117i	$-0.632098\pi$
$311$	153.602	−	422.019i	0.493898	−	1.35697i	0.897086	−	0.441856i	$-0.145680\pi$
$312$		0			0
$313$	1.88192	−	10.6729i	0.00601253	−	0.0340988i	−0.981654	−	0.190672i	$-0.938933\pi$
$313$	1.88192	−	10.6729i	0.00601253	−	0.0340988i	0.987666	+	0.156573i	$0.0500446\pi$
$314$	139.700	−	80.6557i	0.444904	−	0.256865i
$315$		0			0
$316$	27.0360	−	46.8278i	0.0855570	−	0.148189i
$317$	140.278	−	167.176i	0.442516	−	0.527370i	−0.497974	−	0.867192i	$-0.665922\pi$
$317$	140.278	−	167.176i	0.442516	−	0.527370i	0.940490	+	0.339822i	$0.110367\pi$
$318$		0			0
$319$	−51.7165	−	293.299i	−0.162121	−	0.919432i
$320$	−109.020	−	129.925i	−0.340687	−	0.406015i
$321$		0			0
$322$	−228.787	+	83.2717i	−0.710519	+	0.258608i
$323$			14.2846i			0.0442249i
$324$		0			0
$325$	−44.6700			−0.137446
$326$	15.8261	+	43.4818i	0.0485463	+	0.133380i
$327$		0			0
$328$	−73.6244	+	61.7782i	−0.224465	+	0.188348i
$329$	−128.637	+	22.6822i	−0.390995	+	0.0689429i
$330$		0			0
$331$	460.146	+	386.109i	1.39017	+	1.16649i	0.965271	+	0.261250i	$0.0841348\pi$
$331$	460.146	+	386.109i	1.39017	+	1.16649i	0.424899	+	0.905241i	$0.360310\pi$
$332$	72.5849	+	41.9069i	0.218629	+	0.126226i
$333$		0			0
$334$	−96.3325	−	166.853i	−0.288421	−	0.499559i
$335$	−514.875	−	90.7863i	−1.53694	−	0.271004i
$336$		0			0
$337$	−422.175	−	153.659i	−1.25274	−	0.455961i	−0.371416	−	0.928467i	$-0.621128\pi$
$337$	−422.175	−	153.659i	−1.25274	−	0.455961i	−0.881328	+	0.472505i	$0.843350\pi$
$338$	17.0037	−	46.7172i	0.0503068	−	0.138217i
$339$		0			0
$340$	7.83300	−	44.4232i	0.0230382	−	0.130656i
$341$	−224.988	+	129.897i	−0.659789	+	0.380929i
$342$		0			0
$343$	68.3305	−	118.352i	0.199214	−	0.345049i
$344$	180.937	−	215.633i	0.525980	−	0.626839i
$345$		0			0
$346$	−2.19544	−	12.4510i	−0.00634522	−	0.0359855i
$347$	151.801	+	180.909i	0.437467	+	0.521353i	0.939061	−	0.343750i	$-0.111697\pi$
$347$	151.801	+	180.909i	0.437467	+	0.521353i	−0.501594	+	0.865103i	$0.667253\pi$
$348$		0			0
$349$	−225.323	+	82.0110i	−0.645625	+	0.234988i	−0.644018	−	0.765010i	$-0.722734\pi$
$349$	−225.323	+	82.0110i	−0.645625	+	0.234988i	−0.00160737	+	0.999999i	$0.500512\pi$
$350$		−	48.6353i		−	0.138958i
$351$		0			0
$352$	−385.187			−1.09428
$353$	8.75255	+	24.0474i	0.0247948	+	0.0681231i	0.951472	−	0.307734i	$-0.0995706\pi$
$353$	8.75255	+	24.0474i	0.0247948	+	0.0681231i	−0.926678	+	0.375857i	$0.877348\pi$
$354$		0			0
$355$	501.697	−	420.974i	1.41323	−	1.18584i
$356$	−180.279	+	31.7881i	−0.506402	+	0.0892923i
$357$		0			0
$358$	251.311	+	210.875i	0.701986	+	0.589037i
$359$	−16.7796	−	9.68773i	−0.0467399	−	0.0269853i	0.476448	−	0.879203i	$-0.341924\pi$
$359$	−16.7796	−	9.68773i	−0.0467399	−	0.0269853i	−0.523188	+	0.852217i	$0.675257\pi$
$360$		0			0
$361$	170.280	+	294.934i	0.471690	+	0.816992i
$362$	124.393	+	21.9338i	0.343626	+	0.0605906i
$363$		0			0
$364$	294.907	+	107.338i	0.810185	+	0.294883i
$365$	167.799	−	461.025i	0.459724	−	1.26308i
$366$		0			0
$367$	67.8469	−	384.779i	0.184869	−	1.04844i	−0.741254	−	0.671224i	$-0.765769\pi$
$367$	67.8469	−	384.779i	0.184869	−	1.04844i	0.926124	−	0.377220i	$-0.123120\pi$
$368$	−28.3201	+	16.3506i	−0.0769569	+	0.0444311i
$369$		0			0
$370$	−55.1707	+	95.5584i	−0.149110	+	0.258266i
$371$	−572.999	+	682.874i	−1.54447	+	1.84063i
$372$		0			0
$373$	−31.0522	−	176.106i	−0.0832500	−	0.472134i	−0.997721	−	0.0674817i	$-0.978504\pi$
$373$	−31.0522	−	176.106i	−0.0832500	−	0.472134i	0.914471	−	0.404653i	$-0.132608\pi$
$374$	27.6907	+	33.0005i	0.0740392	+	0.0882365i
$375$		0			0
$376$	89.9858	−	32.7522i	0.239324	−	0.0871068i
$377$		−	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	$0.498538\pi$
$380$	22.0756	+	60.6523i	0.0580938	+	0.159611i
$381$		0			0
$382$	−96.6094	+	81.0649i	−0.252904	+	0.212212i
$383$	16.9648	−	2.99135i	0.0442945	−	0.00781031i	−0.151457	−	0.988464i	$-0.548397\pi$
$383$	16.9648	−	2.99135i	0.0442945	−	0.00781031i	0.195752	+	0.980654i	$0.437285\pi$
$384$		0			0
$385$	−510.155	−	428.071i	−1.32508	−	1.11187i
$386$	201.193	+	116.159i	0.521226	+	0.300930i
$387$		0			0
$388$	105.827	+	183.298i	0.272750	+	0.472417i
$389$	311.960	+	55.0070i	0.801955	+	0.141406i	0.559580	−	0.828776i	$-0.310963\pi$
$389$	311.960	+	55.0070i	0.801955	+	0.141406i	0.242375	+	0.970183i	$0.422074\pi$
$390$		0			0
$391$	59.1068	+	21.5131i	0.151168	+	0.0550208i
$392$	−163.695	+	449.747i	−0.417588	+	1.14731i
$393$		0			0
$394$	59.0100	−	334.662i	0.149771	−	0.849396i
$395$	−95.0446	+	54.8740i	−0.240619	+	0.138922i
$396$		0			0
$397$	−134.041	+	232.165i	−0.337634	+	0.584800i	−0.983987	−	0.178239i	$-0.942960\pi$
$397$	−134.041	+	232.165i	−0.337634	+	0.584800i	0.646353	+	0.763039i	$0.276293\pi$
$398$	−61.4238	+	73.2020i	−0.154331	+	0.183925i
$399$		0			0
$400$	−1.13433	−	6.43312i	−0.00283583	−	0.0160828i
$401$	−62.6504	−	74.6638i	−0.156235	−	0.186194i	0.682249	−	0.731120i	$-0.261002\pi$
$401$	−62.6504	−	74.6638i	−0.156235	−	0.186194i	−0.838484	+	0.544926i	$0.816558\pi$
$402$		0			0
$403$	−233.502	+	84.9877i	−0.579409	+	0.210888i
$404$		−	12.6686i		−	0.0313578i
$405$		0			0
$406$	310.149			0.763914
$407$	70.9189	+	194.848i	0.174248	+	0.478742i
$408$		0			0
$409$	−310.511	+	260.550i	−0.759196	+	0.637041i	−0.937917	−	0.346859i	$-0.887248\pi$
$409$	−310.511	+	260.550i	−0.759196	+	0.637041i	0.178721	+	0.983900i	$0.442804\pi$
$410$	76.5916	−	13.5052i	0.186809	−	0.0329394i
$411$		0			0
$412$	−146.876	−	123.243i	−0.356494	−	0.299134i
$413$	622.862	+	359.609i	1.50814	+	0.870725i
$414$		0			0
$415$	−85.0569	−	147.323i	−0.204956	−	0.354995i
$416$	−362.827	−	63.9761i	−0.872179	−	0.153789i
$417$		0			0
$418$	−57.9236	−	21.0825i	−0.138573	−	0.0504365i
$419$	40.1309	−	110.259i	0.0957778	−	0.263147i	−0.882547	−	0.470225i	$-0.844173\pi$
$419$	40.1309	−	110.259i	0.0957778	−	0.263147i	0.978325	+	0.207077i	$0.0663951\pi$
$420$		0			0
$421$	−90.5287	+	513.414i	−0.215032	+	1.21951i	0.665818	+	0.746115i	$0.268083\pi$
$421$	−90.5287	+	513.414i	−0.215032	+	1.21951i	−0.880850	+	0.473395i	$0.843028\pi$
$422$	−116.473	+	67.2459i	−0.276003	+	0.159351i
$423$		0			0
$424$	326.760	−	565.966i	0.770661	−	1.33482i
$425$	−8.07654	+	9.62524i	−0.0190036	+	0.0226476i
$426$		0			0
$427$	−142.815	−	809.945i	−0.334462	−	1.89683i
$428$	−269.582	−	321.275i	−0.629863	−	0.750642i
$429$		0			0
$430$	−214.046	+	77.9065i	−0.497782	+	0.181178i
$431$			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	$0.800880\pi$
$434$	−92.5320	−	254.230i	−0.213207	−	0.585782i
$435$		0			0
$436$	−37.7462	+	31.6728i	−0.0865738	+	0.0726440i
$437$	−88.6353	+	15.6288i	−0.202827	+	0.0357638i
$438$		0			0
$439$	−339.293	−	284.700i	−0.772876	−	0.648520i	0.168567	−	0.985690i	$-0.446086\pi$
$439$	−339.293	−	284.700i	−0.772876	−	0.648520i	−0.941444	+	0.337170i	$0.890530\pi$
$440$	422.816	+	244.113i	0.960946	+	0.554802i
$441$		0			0
$442$	20.6021	+	35.6839i	0.0466111	+	0.0807328i
$443$	−597.623	−	105.377i	−1.34904	−	0.237871i	−0.547995	−	0.836482i	$-0.684609\pi$
$443$	−597.623	−	105.377i	−1.34904	−	0.237871i	−0.801040	+	0.598610i	$0.795720\pi$
$444$		0			0
$445$	349.143	+	127.078i	0.784591	+	0.285568i
$446$	78.7141	−	216.265i	0.176489	−	0.484900i
$447$		0			0
$448$	57.6358	−	326.869i	0.128651	−	0.729618i
$449$	−347.745	+	200.771i	−0.774488	+	0.447151i	−0.834473	−	0.551048i	$-0.814228\pi$
$449$	−347.745	+	200.771i	−0.774488	+	0.447151i	0.0599853	+	0.998199i	$0.480895\pi$
$450$		0			0
$451$	73.0755	−	126.570i	0.162030	−	0.280644i
$452$	−30.7136	+	36.6030i	−0.0679504	+	0.0809801i
$453$		0			0
$454$	−1.03861	−	5.89024i	−0.00228769	−	0.0129741i
$455$	−409.441	−	487.953i	−0.899870	−	1.07242i
$456$		0			0
$457$	138.241	−	50.3155i	0.302496	−	0.110099i	−0.186313	−	0.982490i	$-0.559654\pi$
$457$	138.241	−	50.3155i	0.302496	−	0.110099i	0.488809	+	0.872391i	$0.337432\pi$
$458$		−	410.223i		−	0.895683i
$459$		0			0
$460$	284.213			0.617855
$461$	−268.627	−	738.046i	−0.582705	−	1.60097i	−0.783539	−	0.621343i	$-0.786588\pi$
$461$	−268.627	−	738.046i	−0.582705	−	1.60097i	0.200834	−	0.979625i	$-0.435635\pi$
$462$		0			0
$463$	−274.591	+	230.409i	−0.593069	+	0.497644i	−0.889209	−	0.457501i	$-0.848745\pi$
$463$	−274.591	+	230.409i	−0.593069	+	0.497644i	0.296141	+	0.955144i	$0.404300\pi$
$464$	41.0243	−	7.23369i	0.0884144	−	0.0155898i
$465$		0			0
$466$	−125.007	−	104.894i	−0.268256	−	0.225094i
$467$	88.2727	+	50.9643i	0.189021	+	0.109131i	0.591524	−	0.806287i	$-0.298526\pi$
$467$	88.2727	+	50.9643i	0.189021	+	0.109131i	−0.402503	+	0.915419i	$0.631860\pi$
$468$		0			0
$469$	−511.569	−	886.063i	−1.09077	−	1.88926i
$470$	−76.3135	−	13.4561i	−0.162369	−	0.0286300i
$471$		0			0
$472$	−495.473	−	180.337i	−1.04973	−	0.382071i
$473$	−146.402	+	402.235i	−0.309517	+	0.850391i
$474$		0			0
$475$	3.12199	−	17.7057i	0.00657261	−	0.0372751i
$476$	76.4491	−	44.1379i	0.160607	−	0.0927267i
$477$		0			0
$478$	−85.7219	+	148.475i	−0.179334	+	0.310616i
$479$	−81.2290	+	96.8049i	−0.169580	+	0.202098i	−0.844141	−	0.536122i	$-0.819889\pi$
$479$	−81.2290	+	96.8049i	−0.169580	+	0.202098i	0.674560	+	0.738220i	$0.264333\pi$
$480$		0			0
$481$	34.4395	+	195.316i	0.0715997	+	0.406062i
$482$	−227.169	−	270.730i	−0.471306	−	0.561680i
$483$		0			0
$484$	42.1705	−	15.3488i	0.0871292	−	0.0317124i
$485$		−	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	$0.345648\pi$
$488$	206.219	+	566.582i	0.422580	+	1.16103i
$489$		0			0
$490$	296.687	−	248.950i	0.605483	−	0.508061i
$491$	311.285	−	54.8880i	0.633982	−	0.111788i	0.152585	−	0.988290i	$-0.451240\pi$
$491$	311.285	−	54.8880i	0.633982	−	0.111788i	0.481398	+	0.876502i	$0.340129\pi$
$492$		0			0
$493$	−61.3806	−	51.5044i	−0.124504	−	0.104471i
$494$	−51.0594	−	29.4792i	−0.103359	−	0.0596744i
$495$		0			0
$496$	−18.1689	−	31.4695i	−0.0366309	−	0.0634466i
$497$	1262.19	+	222.557i	2.53961	+	0.447802i
$498$		0			0
$499$	−114.898	−	41.8195i	−0.230257	−	0.0838066i	0.224315	−	0.974517i	$-0.427986\pi$
$499$	−114.898	−	41.8195i	−0.230257	−	0.0838066i	−0.454572	+	0.890710i	$0.650208\pi$
$500$	102.654	−	282.041i	0.205309	−	0.564081i
$501$		0			0
$502$	−25.1577	+	142.677i	−0.0501150	+	0.284217i
$503$	391.041	−	225.768i	0.777418	−	0.448843i	−0.0580963	−	0.998311i	$-0.518503\pi$
$503$	391.041	−	225.768i	0.777418	−	0.448843i	0.835515	+	0.549468i	$0.185170\pi$
$504$		0			0
$505$	−12.8565	+	22.2680i	−0.0254583	+	0.0440951i
$506$	−174.470	+	207.925i	−0.344802	+	0.410918i
$507$		0			0
$508$	−71.9431	−	408.010i	−0.141620	−	0.803169i
$509$	321.207	+	382.800i	0.631055	+	0.752063i	0.982929	−	0.183985i	$-0.0588998\pi$
$509$	321.207	+	382.800i	0.631055	+	0.752063i	−0.351874	+	0.936047i	$0.614455\pi$
$510$		0			0
$511$	902.211	−	328.378i	1.76558	−	0.642618i
$512$		−	104.621i		−	0.204338i
$513$		0			0
$514$	−530.596			−1.03229
$515$	133.098	+	365.684i	0.258443	+	0.710065i
$516$		0			0
$517$	−111.552	+	93.6029i	−0.215767	+	0.181050i
$518$	−212.654	+	37.4966i	−0.410529	+	0.0723873i
$519$		0			0
$520$	357.726	+	300.168i	0.687935	+	0.577246i
$521$	595.632	+	343.888i	1.14325	+	0.660054i	0.947233	−	0.320546i	$-0.103867\pi$
$521$	595.632	+	343.888i	1.14325	+	0.660054i	0.196015	+	0.980601i	$0.437200\pi$
$522$		0			0
$523$	260.218	+	450.711i	0.497549	+	0.861780i	0.999996	−	0.00282784i	$-0.000900130\pi$
$523$	260.218	+	450.711i	0.497549	+	0.861780i	−0.502447	+	0.864608i	$0.667567\pi$
$524$	−257.319	−	45.3723i	−0.491067	−	0.0865884i
$525$		0			0
$526$	510.506	+	185.809i	0.970543	+	0.353249i
$527$	−23.9055	+	65.6799i	−0.0453615	+	0.124630i
$528$		0			0
$529$	23.0409	−	130.671i	0.0435555	−	0.247016i
$530$	−457.985	+	264.418i	−0.864123	+	0.498902i
$531$		0			0
$532$	−63.1561	+	109.390i	−0.118715	+	0.205620i
$533$	89.8556	−	107.086i	0.168585	−	0.200911i
$534$		0			0
$535$	147.814	+	838.297i	0.276289	+	1.56691i
$536$	482.141	+	574.594i	0.899518	+	1.07200i
$537$		0			0
$538$	−345.884	+	125.891i	−0.642907	+	0.233999i
$539$		−	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	$0.233756\pi$
$542$	45.9406	+	126.221i	0.0847613	+	0.232880i
$543$		0			0
$544$	−79.3859	+	66.6127i	−0.145930	+	0.122450i
$545$	98.4905	−	17.3665i	0.180717	−	0.0318652i
$546$		0			0
$547$	−52.6185	−	44.1522i	−0.0961947	−	0.0807169i	0.593422	−	0.804891i	$-0.297777\pi$
$547$	−52.6185	−	44.1522i	−0.0961947	−	0.0807169i	−0.689617	+	0.724175i	$0.742221\pi$
$548$	−150.803	−	87.0659i	−0.275187	−	0.158879i
$549$		0			0
$550$	−27.1099	−	46.9557i	−0.0492907	−	0.0853741i
$551$	112.910	+	19.9091i	0.204918	+	0.0361326i
$552$		0			0
$553$	−201.821	−	73.4568i	−0.364957	−	0.132833i
$554$	45.7848	−	125.793i	0.0826441	−	0.227063i
$555$		0			0
$556$	−57.7064	+	327.269i	−0.103789	+	0.588614i
$557$	−575.120	+	332.045i	−1.03253	+	0.596132i	−0.917709	−	0.397254i	$-0.869963\pi$
$557$	−575.120	+	332.045i	−1.03253	+	0.596132i	−0.114822	+	0.993386i	$0.536630\pi$
$558$		0			0
$559$	−204.710	+	354.569i	−0.366208	+	0.634291i
$560$	59.8751	−	71.3563i	0.106920	−	0.127422i
$561$		0			0
$562$	−16.4489	−	93.2861i	−0.0292684	−	0.165990i
$563$	223.468	+	266.319i	0.396924	+	0.473036i	0.927080	−	0.374865i	$-0.122311\pi$
$563$	223.468	+	266.319i	0.396924	+	0.473036i	−0.530155	+	0.847901i	$0.677866\pi$
$564$		0			0
$565$	91.1323	−	33.1694i	0.161296	−	0.0587070i
$566$			484.283i			0.855623i
$567$		0			0
$568$	−939.603			−1.65423
$569$	−133.736	−	367.437i	−0.235037	−	0.645760i	−0.999999	−	0.00168357i	$-0.999464\pi$
$569$	−133.736	−	367.437i	−0.235037	−	0.645760i	0.764961	−	0.644076i	$-0.222758\pi$
$570$		0			0
$571$	655.523	−	550.049i	1.14803	−	0.963309i	0.148355	−	0.988934i	$-0.452602\pi$
$571$	655.523	−	550.049i	1.14803	−	0.963309i	0.999672	+	0.0256252i	$0.00815764\pi$
$572$	344.555	−	60.7543i	0.602368	−	0.106214i
$573$		0			0
$574$	116.592	+	97.8320i	0.203121	+	0.170439i
$575$	−68.5606	−	39.5835i	−0.119236	−	0.0688408i
$576$		0			0
$577$	313.746	+	543.423i	0.543753	+	0.941808i	0.998684	+	0.0512815i	$0.0163306\pi$
$577$	313.746	+	543.423i	0.543753	+	0.941808i	−0.454931	+	0.890527i	$0.650336\pi$
$578$	−319.007	−	56.2495i	−0.551915	−	0.0973175i
$579$		0			0
$580$	−340.216	−	123.829i	−0.586580	−	0.213498i
$581$	113.861	−	312.831i	0.195974	−	0.538435i
$582$		0			0
$583$	−172.569	+	978.689i	−0.296002	+	1.67871i
$584$	−609.573	+	351.937i	−1.04379	+	0.602632i
$585$		0			0
$586$	−200.750	+	347.709i	−0.342576	+	0.593359i
$587$	478.592	−	570.364i	0.815319	−	0.971659i	−0.184619	−	0.982810i	$-0.559105\pi$
$587$	478.592	−	570.364i	0.815319	−	0.971659i	0.999938	+	0.0111512i	$0.00354962\pi$
$588$		0			0
$589$	−17.3668	−	98.4921i	−0.0294853	−	0.167219i
$590$	274.260	+	326.851i	0.464848	+	0.553984i
$591$		0			0
$592$	−27.2538	+	9.91957i	−0.0460368	+	0.0167560i
$593$		−	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
$596$	−183.012	−	502.822i	−0.307067	−	0.843661i
$597$		0			0
$598$	−198.876	+	166.877i	−0.332568	+	0.279058i
$599$	−564.336	+	99.5077i	−0.942130	+	0.166123i	−0.623559	−	0.781776i	$-0.714314\pi$
$599$	−564.336	+	99.5077i	−0.942130	+	0.166123i	−0.318571	+	0.947899i	$0.603203\pi$
$600$		0			0
$601$	866.763	+	727.301i	1.44220	+	1.21015i	0.938033	+	0.346546i	$0.112645\pi$
$601$	866.763	+	727.301i	1.44220	+	1.21015i	0.504169	+	0.863605i	$0.331799\pi$
$602$	−386.043	−	222.882i	−0.641268	−	0.370236i
$603$		0			0
$604$	−169.925	−	294.319i	−0.281333	−	0.487283i
$605$	−89.7013	−	15.8168i	−0.148267	−	0.0261434i
$606$		0			0
$607$	218.454	+	79.5107i	0.359891	+	0.130990i	0.515636	−	0.856808i	$-0.327556\pi$
$607$	218.454	+	79.5107i	0.359891	+	0.130990i	−0.155745	+	0.987797i	$0.549778\pi$
$608$	50.7160	−	139.341i	0.0834144	−	0.229179i
$609$		0			0
$610$	84.7244	−	480.496i	0.138892	−	0.787698i
$611$	−120.623	+	69.6414i	−0.197418	+	0.113979i
$612$		0			0
$613$	533.889	−	924.724i	0.870945	−	1.50852i	0.00992514	−	0.999951i	$-0.496841\pi$
$613$	533.889	−	924.724i	0.870945	−	1.50852i	0.861020	−	0.508571i	$-0.169826\pi$
$614$	430.838	−	513.453i	0.701691	−	0.836243i
$615$		0			0
$616$	165.911	+	940.927i	0.269336	+	1.52748i
$617$	−271.097	−	323.080i	−0.439378	−	0.523631i	0.500225	−	0.865895i	$-0.333251\pi$
$617$	−271.097	−	323.080i	−0.439378	−	0.523631i	−0.939604	+	0.342264i	$0.888806\pi$
$618$		0			0
$619$	−564.604	+	205.499i	−0.912123	+	0.331986i	−0.755100	−	0.655609i	$-0.772412\pi$
$619$	−564.604	+	205.499i	−0.912123	+	0.331986i	−0.157023	+	0.987595i	$0.550190\pi$
$620$			315.820i			0.509386i
$621$		0			0
$622$	521.392			0.838250
$623$	248.687	+	683.262i	0.399177	+	1.09673i
$624$		0			0
$625$	−542.822	+	455.482i	−0.868515	+	0.728771i
$626$	12.3909	−	2.18484i	0.0197937	−	0.00349016i
$627$		0			0
$628$	−282.294	−	236.873i	−0.449513	−	0.377186i
$629$	48.3124	+	27.8932i	0.0768083	+	0.0443453i
$630$		0			0
$631$	554.621	+	960.632i	0.878956	+	1.52240i	0.852488	+	0.522747i	$0.175093\pi$
$631$	554.621	+	960.632i	0.878956	+	1.52240i	0.0264679	+	0.999650i	$0.491574\pi$
$632$	155.062	+	27.3416i	0.245351	+	0.0432620i
$633$		0			0
$634$	238.081	+	86.6545i	0.375522	+	0.136679i
$635$	−287.604	+	790.185i	−0.452919	+	1.24439i
$636$		0			0
$637$	120.882	−	685.557i	0.189768	−	1.07623i
$638$	299.439	−	172.881i	0.469340	−	0.270973i
$639$		0			0
$640$	−254.659	+	441.082i	−0.397904	+	0.689191i
$641$	106.234	−	126.604i	0.165731	−	0.197511i	−0.676787	−	0.736179i	$-0.736628\pi$
$641$	106.234	−	126.604i	0.165731	−	0.197511i	0.842518	+	0.538669i	$0.181072\pi$
$642$		0			0
$643$	137.985	+	782.552i	0.214596	+	1.21703i	0.881607	+	0.471985i	$0.156462\pi$
$643$	137.985	+	782.552i	0.214596	+	1.21703i	−0.667011	+	0.745048i	$0.732427\pi$
$644$	357.516	+	426.071i	0.555149	+	0.661601i
$645$		0			0
$646$	−15.5838	+	5.67204i	−0.0241235	+	0.00878024i
$647$		−	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
$650$	−17.7372	−	48.7326i	−0.0272880	−	0.0749732i
$651$		0			0
$652$	80.9765	−	67.9473i	0.124197	−	0.104214i
$653$	−459.398	+	81.0043i	−0.703520	+	0.124050i	−0.513953	−	0.857818i	$-0.671819\pi$
$653$	−459.398	+	81.0043i	−0.703520	+	0.124050i	−0.189567	+	0.981868i	$0.560708\pi$
$654$		0			0
$655$	406.255	+	340.888i	0.620237	+	0.520440i
$656$	17.7037	+	10.2212i	0.0269873	+	0.0155811i
$657$		0			0
$658$	−75.8234	−	131.330i	−0.115233	−	0.199590i
$659$	−205.109	−	36.1663i	−0.311244	−	0.0548806i	0.0158446	−	0.999874i	$-0.494956\pi$
$659$	−205.109	−	36.1663i	−0.311244	−	0.0548806i	−0.327088	+	0.944994i	$0.606067\pi$
$660$		0			0
$661$	595.560	+	216.766i	0.900999	+	0.327937i	0.750653	−	0.660697i	$-0.229739\pi$
$661$	595.560	+	216.766i	0.900999	+	0.327937i	0.150346	+	0.988633i	$0.451961\pi$
$662$	−238.513	+	655.309i	−0.360291	+	0.989892i
$663$		0			0
$664$	−42.3805	+	240.352i	−0.0638261	+	0.361976i
$665$	222.024	−	128.186i	0.333871	−	0.192760i
$666$		0			0
$667$	252.425	−	437.214i	0.378449	−	0.655493i
$668$	−282.913	+	337.163i	−0.423523	+	0.504735i
$669$		0			0
$670$	−105.400	−	597.750i	−0.157313	−	0.892165i
$671$	−589.356	−	702.367i	−0.878325	−	1.04675i
$672$		0			0
$673$	−103.386	+	37.6293i	−0.153619	+	0.0559128i	−0.417685	−	0.908592i	$-0.637159\pi$
$673$	−103.386	+	37.6293i	−0.153619	+	0.0559128i	0.264066	+	0.964505i	$0.414936\pi$
$674$		−	521.584i		−	0.773864i
$675$		0			0
$676$	−113.573			−0.168007
$677$	−48.9221	−	134.412i	−0.0722631	−	0.198541i	0.898303	−	0.439377i	$-0.144801\pi$
$677$	−48.9221	−	134.412i	−0.0722631	−	0.198541i	−0.970566	+	0.240836i	$0.922579\pi$
$678$		0			0
$679$	644.003	−	540.383i	0.948458	−	0.795851i
$680$	129.357	−	22.8091i	0.190231	−	0.0335429i
$681$		0			0
$682$	−231.047	−	193.872i	−0.338779	−	0.284269i
$683$	−784.050	−	452.671i	−1.14795	−	0.662769i	−0.199563	−	0.979885i	$-0.563952\pi$
$683$	−784.050	−	452.671i	−1.14795	−	0.662769i	−0.948387	+	0.317116i	$0.897286\pi$
$684$		0			0
$685$	176.714	+	306.078i	0.257977	+	0.446830i
$686$	156.248	+	27.5507i	0.227767	+	0.0401614i
$687$		0			0
$688$	−56.2614	−	20.4775i	−0.0817753	−	0.0297638i
$689$	−325.103	+	893.212i	−0.471847	+	1.29639i
$690$		0			0
$691$	92.3826	−	523.928i	0.133694	−	0.758217i	−0.842066	−	0.539374i	$-0.818661\pi$
$691$	92.3826	−	523.928i	0.133694	−	0.758217i	0.975760	−	0.218842i	$-0.0702280\pi$
$692$	−25.0130	+	14.4413i	−0.0361459	+	0.0208689i
$693$		0			0
$694$	−137.087	+	237.441i	−0.197531	+	0.342134i
$695$	433.556	−	516.692i	0.623822	−	0.743442i
$696$		0			0
$697$	−6.82794	−	38.7232i	−0.00979618	−	0.0555569i
$698$	−178.939	−	213.252i	−0.256360	−	0.305518i
$699$		0			0
$700$	−104.405	+	38.0002i	−0.149150	+	0.0542860i
$701$			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
$704$	−126.555	−	347.708i	−0.179766	−	0.493903i
$705$		0			0
$706$	−22.7591	+	19.0972i	−0.0322367	+	0.0270498i
$707$	−49.5549	+	8.73786i	−0.0700918	+	0.0123591i
$708$		0			0
$709$	−278.738	−	233.889i	−0.393142	−	0.329885i	0.424694	−	0.905337i	$-0.360382\pi$
$709$	−278.738	−	233.889i	−0.393142	−	0.329885i	−0.817836	+	0.575452i	$0.804826\pi$
$710$	658.471	+	380.168i	0.927424	+	0.535449i
$711$		0			0
$712$	−266.529	−	461.642i	−0.374338	−	0.648373i
$713$	−433.695	−	76.4721i	−0.608268	−	0.107254i
$714$		0			0
$715$	−667.292	−	242.875i	−0.933276	−	0.339685i
$716$	256.326	−	704.249i	0.357997	−	0.983588i
$717$		0			0
$718$	3.90607	−	22.1524i	0.00544021	−	0.0308530i
$719$	389.328	−	224.778i	0.541485	−	0.312626i	−0.204196	−	0.978930i	$-0.565458\pi$
$719$	389.328	−	224.778i	0.541485	−	0.312626i	0.745680	+	0.666304i	$0.232125\pi$
$720$		0			0
$721$	−380.779	+	659.529i	−0.528127	+	0.914742i
$722$	−254.144	+	302.877i	−0.352000	+	0.419497i
$723$		0			0
$724$	−50.1068	−	284.170i	−0.0692083	−	0.392500i
$725$	64.8241	+	77.2544i	0.0894126	+	0.106558i
$726$		0			0
$727$	−544.426	+	198.155i	−0.748866	+	0.272565i	−0.688129	−	0.725589i	$-0.741568\pi$
$727$	−544.426	+	198.155i	−0.748866	+	0.272565i	−0.0607376	+	0.998154i	$0.519345\pi$
$728$			913.862i			1.25530i
$729$		0			0
$730$	569.582			0.780250
$731$	39.3880	+	108.218i	0.0538823	+	0.148040i
$732$		0			0
$733$	717.264	−	601.856i	0.978532	−	0.821086i	−0.00533530	−	0.999986i	$-0.501698\pi$
$733$	717.264	−	601.856i	0.978532	−	0.821086i	0.983867	+	0.178900i	$0.0572538\pi$
$734$	446.714	−	78.7677i	0.608602	−	0.107313i
$735$		0			0
$736$	−500.184	−	419.704i	−0.679598	−	0.570250i
$737$	−987.805	−	570.310i	−1.34031	−	0.773826i
$738$		0			0
$739$	−263.918	−	457.119i	−0.357128	−	0.618564i	0.630352	−	0.776310i	$-0.282911\pi$
$739$	−263.918	−	457.119i	−0.357128	−	0.618564i	−0.987480	+	0.157746i	$0.949577\pi$
$740$	248.240	+	43.7715i	0.335460	+	0.0591506i
$741$		0			0
$742$	−972.502	−	353.962i	−1.31065	−	0.477037i
$743$	−12.5973	+	34.6108i	−0.0169547	+	0.0465825i	−0.947881	−	0.318624i	$-0.896779\pi$
$743$	−12.5973	+	34.6108i	−0.0169547	+	0.0465825i	0.930927	+	0.365206i	$0.119002\pi$
$744$		0			0
$745$	−188.592	+	1069.56i	−0.253143	+	1.43565i
$746$	179.793	−	103.803i	0.241009	−	0.139146i
$747$		0			0
$748$	49.2061	−	85.2274i	0.0657835	−	0.113940i
$749$	−1070.77	+	1276.10i	−1.42960	+	1.70374i
$750$		0			0
$751$	17.1046	+	97.0050i	0.0227758	+	0.129168i	0.994076	−	0.108691i	$-0.0346657\pi$
$751$	17.1046	+	97.0050i	0.0227758	+	0.129168i	−0.971300	+	0.237858i	$0.923555\pi$
$752$	−13.0924	−	15.6029i	−0.0174101	−	0.0207486i
$753$		0			0
$754$	310.770	−	113.111i	0.412161	−	0.150015i
$755$			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	$0.867697\pi$
$758$	1.38228	+	3.79779i	0.00182359	+	0.00501027i
$759$		0			0
$760$	−143.978	+	120.812i	−0.189445	+	0.158963i
$761$	1432.82	−	252.644i	1.88281	−	0.331990i	0.890419	−	0.455142i	$-0.150411\pi$
$761$	1432.82	−	252.644i	1.88281	−	0.331990i	0.992388	+	0.123152i	$0.0393003\pi$
$762$		0			0
$763$	149.927	+	125.804i	0.196497	+	0.164881i
$764$	249.505	+	144.052i	0.326577	+	0.188549i
$765$		0			0
$766$	9.99966	+	17.3199i	0.0130544	+	0.0226109i
$767$	755.257	+	133.172i	0.984690	+	0.173627i
$768$		0			0
$769$	94.0313	+	34.2246i	0.122277	+	0.0445053i	0.402434	−	0.915449i	$-0.368164\pi$
$769$	94.0313	+	34.2246i	0.122277	+	0.0445053i	−0.280157	+	0.959954i	$0.590386\pi$
$770$	264.434	−	726.527i	0.343421	−	0.943542i
$771$		0			0
$772$	92.1586	−	522.657i	0.119376	−	0.677017i
$773$	547.928	−	316.347i	0.708834	−	0.409245i	−0.101795	−	0.994805i	$-0.532459\pi$
$773$	547.928	−	316.347i	0.708834	−	0.409245i	0.810629	+	0.585560i	$0.199125\pi$
$774$		0			0
$775$	43.9854	−	76.1850i	0.0567554	−	0.0983032i
$776$	−396.163	+	472.129i	−0.510520	+	0.608414i
$777$		0			0
$778$	63.8611	+	362.174i	0.0820837	+	0.465520i
$779$	36.1652	+	43.1000i	0.0464251	+	0.0553273i
$780$		0			0
$781$	1342.65	−	488.686i	1.71915	−	0.625718i
$782$			73.0247i			0.0933820i
$783$		0			0
$784$	101.800			0.129847
$785$	255.813	+	702.841i	0.325877	+	0.895339i
$786$		0			0
$787$	−624.837	+	524.300i	−0.793948	+	0.666201i	−0.946719	−	0.322060i	$-0.895625\pi$
$787$	−624.837	+	524.300i	−0.793948	+	0.666201i	0.152771	+	0.988262i	$0.451180\pi$
$788$	−764.521	+	134.806i	−0.970204	+	0.171073i
$789$		0			0
$790$	−97.6043	−	81.8997i	−0.123550	−	0.103671i
$791$	164.362	+	94.8944i	0.207790	+	0.119968i
$792$		0			0
$793$	−438.486	−	759.481i	−0.552946	−	0.957731i
$794$	−306.504	−	54.0450i	−0.386026	−	0.0680667i
$795$		0			0
$796$	205.134	+	74.6626i	0.257706	+	0.0937973i
$797$	428.448	−	1177.15i	0.537576	−	1.47698i	−0.312295	−	0.949985i	$-0.601098\pi$
$797$	428.448	−	1177.15i	0.537576	−	1.47698i	0.849870	−	0.526992i	$-0.176680\pi$
$798$		0			0
$799$	−6.80315	+	38.5826i	−0.00851458	+	0.0482886i
$800$	112.957	−	65.2156i	0.141196	−	0.0815196i
$801$		0			0
$802$	56.5776	−	97.9952i	0.0705456	−	0.122189i
$803$	688.013	−	819.941i	0.856803	−	1.02110i
$804$		0			0
$805$	−196.030	−	1111.74i	−0.243515	−	1.38104i
$806$	−185.434	−	220.992i	−0.230067	−	0.274184i
$807$		0			0
$808$	34.6652	−	12.6171i	0.0429025	−	0.0156152i
$809$		−	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	$0.572407\pi$
$812$	−242.329	−	665.793i	−0.298434	−	0.819942i
$813$		0			0
$814$	−184.409	+	154.738i	−0.226547	+	0.190095i
$815$	−211.291	+	37.2562i	−0.259252	+	0.0457132i
$816$		0			0
$817$	−126.232	−	105.921i	−0.154507	−	0.129647i
$818$	−407.542	−	235.294i	−0.498217	−	0.287646i
$819$		0			0
$820$	−88.8346	−	153.866i	−0.108335	−	0.187641i
$821$	−9.54867	−	1.68369i	−0.0116305	−	0.00205078i	0.167830	−	0.985816i	$-0.446324\pi$
$821$	−9.54867	−	1.68369i	−0.0116305	−	0.00205078i	−0.179460	+	0.983765i	$0.557435\pi$
$822$		0			0
$823$	−0.839980	−	0.305728i	−0.00102063	−	0.000371480i	0.341510	−	0.939878i	$-0.389062\pi$
$823$	−0.839980	−	0.305728i	−0.00102063	−	0.000371480i	−0.342530	+	0.939507i	$0.611284\pi$
$824$	190.954	−	524.641i	0.231740	−	0.636700i
$825$		0			0
$826$	−144.994	+	822.301i	−0.175537	+	0.995521i
$827$	583.611	−	336.948i	0.705696	−	0.407434i	−0.103769	−	0.994601i	$-0.533090\pi$
$827$	583.611	−	336.948i	0.705696	−	0.407434i	0.809465	+	0.587168i	$0.199757\pi$
$828$		0			0
$829$	−14.4804	+	25.0808i	−0.0174673	+	0.0302542i	−0.874627	−	0.484797i	$-0.838894\pi$
$829$	−14.4804	+	25.0808i	−0.0174673	+	0.0302542i	0.857160	+	0.515051i	$0.172227\pi$
$830$	126.948	−	151.291i	0.152949	−	0.182278i
$831$		0			0
$832$	−61.4574	−	348.542i	−0.0738671	−	0.418921i
$833$	−125.864	−	149.999i	−0.151097	−	0.180071i
$834$		0			0
$835$	839.451	−	305.535i	1.00533	−	0.365910i
$836$			140.816i			0.168440i
$837$		0			0
$838$	136.221			0.162555
$839$	218.453	+	600.196i	0.260374	+	0.715371i	0.999142	+	0.0414115i	$0.0131855\pi$
$839$	218.453	+	600.196i	0.260374	+	0.715371i	−0.738769	+	0.673959i	$0.764592\pi$
$840$		0			0
$841$	151.589	−	127.199i	0.180249	−	0.151247i
$842$	−596.054	+	105.100i	−0.707903	+	0.124822i
$843$		0			0
$844$	235.360	+	197.490i	0.278862	+	0.233993i
$845$	199.631	+	115.257i	0.236250	+	0.136399i
$846$		0			0
$847$	−89.1253	−	154.370i	−0.105225	−	0.182254i
$848$	−136.891	−	24.1376i	−0.161428	−	0.0284641i
$849$		0			0
$850$	−13.7076	−	4.98916i	−0.0161266	−	0.00586960i
$851$	−120.217	+	330.294i	−0.141266	+	0.388124i
$852$		0			0
$853$	134.939	−	765.276i	0.158193	−	0.897158i	−0.797615	−	0.603167i	$-0.793905\pi$
$853$	134.939	−	765.276i	0.158193	−	0.897158i	0.955808	−	0.293991i	$-0.0949836\pi$
$854$	826.899	−	477.410i	0.968266	−	0.559029i
$855$		0			0
$856$	610.623	−	1057.63i	0.713345	−	1.23555i
$857$	−692.170	+	824.896i	−0.807666	+	0.962539i	−0.999823	−	0.0188256i	$-0.994007\pi$
$857$	−692.170	+	824.896i	−0.807666	+	0.962539i	0.192157	+	0.981364i	$0.438452\pi$
$858$		0			0
$859$	−14.0627	−	79.7538i	−0.0163711	−	0.0928449i	0.975527	−	0.219878i	$-0.0705658\pi$
$859$	−14.0627	−	79.7538i	−0.0163711	−	0.0928449i	−0.991899	+	0.127033i	$0.959455\pi$
$860$	334.481	+	398.619i	0.388932	+	0.463511i
$861$		0			0
$862$	−287.552	+	104.660i	−0.333587	+	0.121416i
$863$			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
$866$	−278.750	−	765.860i	−0.321882	−	0.884365i
$867$		0			0
$868$	−473.453	+	397.274i	−0.545453	+	0.457689i
$869$	−235.797	+	41.5774i	−0.271343	+	0.0478451i
$870$		0			0
$871$	−835.738	−	701.268i	−0.959516	−	0.805130i
$872$	−124.260	−	71.7413i	−0.142500	−	0.0822722i
$873$		0			0
$874$	−52.2449	−	90.4908i	−0.0597767	−	0.103536i
$875$	−1174.05	−	207.016i	−1.34177	−	0.236590i
$876$		0			0
$877$	355.751	+	129.483i	0.405646	+	0.147643i	0.536781	−	0.843721i	$-0.319640\pi$
$877$	355.751	+	129.483i	0.405646	+	0.147643i	−0.131135	+	0.991364i	$0.541862\pi$
$878$	175.869	−	483.197i	0.200307	−	0.550339i
$879$		0			0
$880$	18.0325	−	102.267i	0.0204915	−	0.116213i
$881$	1046.81	−	604.374i	1.18820	−	0.686009i	0.230305	−	0.973119i	$-0.426028\pi$
$881$	1046.81	−	604.374i	1.18820	−	0.686009i	0.957898	+	0.287109i	$0.0926943\pi$
$882$		0			0
$883$	298.144	−	516.401i	0.337649	−	0.584826i	−0.646341	−	0.763049i	$-0.723702\pi$
$883$	298.144	−	516.401i	0.337649	−	0.584826i	0.983990	+	0.178223i	$0.0570349\pi$
$884$	60.5051	−	72.1071i	0.0684447	−	0.0815692i
$885$		0			0
$886$	−122.339	−	693.818i	−0.138080	−	0.783090i
$887$	−65.2823	−	77.8005i	−0.0735990	−	0.0877119i	0.727989	−	0.685589i	$-0.240455\pi$
$887$	−65.2823	−	77.8005i	−0.0735990	−	0.0877119i	−0.801588	+	0.597877i	$0.796011\pi$
$888$		0			0
$889$	−1546.37	+	562.831i	−1.73945	+	0.633106i
$890$			431.356i			0.484670i
$891$		0			0
$892$	−525.755			−0.589412
$893$	−19.1732	−	52.6780i	−0.0214706	−	0.0589899i
$894$		0			0
$895$	−1165.25	+	977.759i	−1.30195	+	1.09247i
$896$	−981.576	+	173.078i	−1.09551	+	0.193168i
$897$		0			0
$898$	−357.110	−	299.651i	−0.397673	−	0.333687i
$899$	485.835	+	280.497i	0.540417	+	0.312010i
$900$		0			0
$901$	133.684	+	231.548i	0.148373	+	0.256990i
$902$	167.098	+	29.4639i	0.185253	+	0.0326651i
$903$		0			0
$904$	−130.746	−	47.5877i	−0.144631	−	0.0526413i
$905$	−200.310	+	550.346i	−0.221337	+	0.608117i
$906$		0			0
$907$	299.653	−	1699.41i	0.330378	−	1.87367i	−0.138440	−	0.990371i	$-0.544209\pi$
$907$	299.653	−	1699.41i	0.330378	−	1.87367i	0.468818	−	0.883295i	$-0.344680\pi$
$908$	−11.8330	+	6.83179i	−0.0130319	+	0.00752400i
$909$		0			0
$910$	369.753	−	640.431i	0.406322	−	0.703771i
$911$	−201.005	+	239.549i	−0.220642	+	0.262951i	−0.864999	−	0.501774i	$-0.832681\pi$
$911$	−201.005	+	239.549i	−0.220642	+	0.262951i	0.644356	+	0.764725i	$0.277125\pi$
$912$		0			0
$913$	−64.4466	−	365.495i	−0.0705878	−	0.400323i
$914$	109.783	+	130.834i	0.120113	+	0.143145i
$915$		0			0
$916$	−880.619	+	320.519i	−0.961375	+	0.349912i
$917$			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	$0.465555\pi$
$920$	283.059	+	777.698i	0.307673	+	0.845324i
$921$		0			0
$922$	698.505	−	586.116i	0.757598	−	0.635700i
$923$	1345.88	−	237.315i	1.45816	−	0.257112i
$924$		0			0
$925$	−53.7866	−	45.1324i	−0.0581477	−	0.0487917i
$926$	−360.397	−	208.075i	−0.389197	−	0.224703i
$927$		0			0
$928$	415.883	+	720.330i	0.448149	+	0.776218i
$929$	1309.55	+	230.908i	1.40963	+	0.248556i	0.826095	−	0.563531i	$-0.190558\pi$
$929$	1309.55	+	230.908i	1.40963	+	0.248556i	0.583536	+	0.812087i	$0.301669\pi$
$930$		0			0
$931$	263.284	+	95.8274i	0.282797	+	0.102930i
$932$	−127.502	+	350.308i	−0.136804	+	0.375867i
$933$		0			0
$934$	−20.5487	+	116.537i	−0.0220008	+	0.124772i
$935$	−172.983	+	99.8717i	−0.185008	+	0.106815i
$936$		0			0
$937$	−675.671	+	1170.30i	−0.721100	+	1.24898i	0.239459	+	0.970906i	$0.423030\pi$
$937$	−675.671	+	1170.30i	−0.721100	+	1.24898i	−0.960559	+	0.278076i	$0.910303\pi$
$938$	763.519	−	909.926i	0.813986	−	0.970071i
$939$		0			0
$940$	30.7399	+	174.335i	0.0327020	+	0.185462i
$941$	−499.617	−	595.420i	−0.530942	−	0.632752i	0.432189	−	0.901783i	$-0.357741\pi$
$941$	−499.617	−	595.420i	−0.530942	−	0.632752i	−0.963132	+	0.269031i	$0.913297\pi$
$942$		0			0
$943$	232.805	−	84.7340i	0.246877	−	0.0898557i
$944$			112.150i			0.118803i
$945$		0			0
$946$	−496.949			−0.525316
$947$	−93.8130	−	257.749i	−0.0990634	−	0.272174i	0.880255	−	0.474502i	$-0.157372\pi$
$947$	−93.8130	−	257.749i	−0.0990634	−	0.272174i	−0.979318	+	0.202327i	$0.935150\pi$
$948$		0			0
$949$	784.257	−	658.070i	0.826404	−	0.693435i
$950$	20.5556	−	3.62451i	0.0216375	−	0.00381528i
$951$		0			0
$952$	196.914	+	165.230i	0.206842	+	0.173561i
$953$	−858.313	−	495.548i	−0.900644	−	0.519987i	−0.0232347	−	0.999730i	$-0.507397\pi$
$953$	−858.313	−	495.548i	−0.900644	−	0.519987i	−0.877409	+	0.479743i	$0.840730\pi$
$954$		0			0
$955$	−292.376	−	506.410i	−0.306153	−	0.530272i
$956$	385.705	+	68.0103i	0.403457	+	0.0711404i
$957$		0			0
$958$	−137.863	−	50.1780i	−0.143907	−	0.0523779i
$959$	−236.558	+	649.937i	−0.246671	+	0.677724i
$960$		0			0
$961$	−81.8996	+	464.476i	−0.0852233	+	0.483326i
$962$	−199.405	+	115.126i	−0.207281	+	0.119674i
$963$		0			0
$964$	−403.678	+	699.190i	−0.418753	+	0.725301i
$965$	−692.400	+	825.170i	−0.717512	+	0.855098i
$966$		0			0
$967$	54.2567	+	307.705i	0.0561083	+	0.318206i	0.999925	−	0.0122640i	$-0.00390387\pi$
$967$	54.2567	+	307.705i	0.0561083	+	0.318206i	−0.943817	+	0.330470i	$0.892793\pi$
$968$	83.9984	+	100.105i	0.0867752	+	0.103415i
$969$		0			0
$970$	468.656	−	170.577i	0.483151	−	0.175852i
$971$		−	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
$974$	180.275	+	495.301i	0.185087	+	0.508522i
$975$		0			0
$976$	98.2415	−	82.4344i	0.100657	−	0.0844615i
$977$	−634.038	+	111.798i	−0.648965	+	0.114430i	−0.488434	−	0.872601i	$-0.662432\pi$
$977$	−634.038	+	111.798i	−0.648965	+	0.114430i	−0.160531	+	0.987031i	$0.551321\pi$
$978$		0			0
$979$	620.958	+	521.046i	0.634278	+	0.532222i
$980$	−766.227	−	442.382i	−0.781865	−	0.451410i
$981$		0			0
$982$	183.483	+	317.802i	0.186846	+	0.323627i
$983$	−1516.43	−	267.387i	−1.54265	−	0.272012i	−0.663364	−	0.748297i	$-0.730872\pi$
$983$	−1516.43	−	267.387i	−1.54265	−	0.272012i	−0.879291	+	0.476286i	$0.841983\pi$
$984$		0			0
$985$	1480.63	+	538.906i	1.50318	+	0.547113i
$986$	31.8161	−	87.4140i	0.0322678	−	0.0886551i
$987$		0			0
$988$	−23.3883	+	132.641i	−0.0236723	+	0.134252i
$989$	−628.389	+	362.801i	−0.635378	+	0.366836i
$990$		0			0
$991$	−155.571	+	269.456i	−0.156984	+	0.271903i	−0.933780	−	0.357849i	$-0.883510\pi$
$991$	−155.571	+	269.456i	−0.156984	+	0.271903i	0.776796	+	0.629752i	$0.216844\pi$
$992$	466.378	−	555.808i	0.470139	−	0.560290i
$993$		0			0
$994$	258.381	+	1465.35i	0.259940	+	1.47420i
$995$	−284.802	−	339.414i	−0.286233	−	0.341119i
$996$		0			0
$997$	45.3212	−	16.4956i	0.0454576	−	0.0165452i	−0.319191	−	0.947690i	$-0.603411\pi$
$997$	45.3212	−	16.4956i	0.0454576	−	0.0165452i	0.364649	+	0.931145i	$0.381189\pi$
$998$		−	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.b.188.4		30
3.2	odd	2		243.3.f.c.188.2		30
9.2	odd	6		243.3.f.d.107.2		30
9.4	even	3		81.3.f.a.8.2		30
9.5	odd	6		27.3.f.a.2.4	✓	30
9.7	even	3		243.3.f.a.107.4		30
27.2	odd	18		729.3.b.a.728.19		30
27.4	even	9		243.3.f.c.53.2		30
27.5	odd	18		81.3.f.a.71.2		30
27.13	even	9		243.3.f.d.134.2		30
27.14	odd	18		243.3.f.a.134.4		30
27.22	even	9		27.3.f.a.14.4	yes	30
27.23	odd	18	inner	243.3.f.b.53.4		30
27.25	even	9		729.3.b.a.728.12		30
36.23	even	6		432.3.bc.a.353.3		30
108.103	odd	18		432.3.bc.a.257.3		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.3.f.a.2.4	✓	30	9.5	odd	6
27.3.f.a.14.4	yes	30	27.22	even	9
81.3.f.a.8.2		30	9.4	even	3
81.3.f.a.71.2		30	27.5	odd	18
243.3.f.a.107.4		30	9.7	even	3
243.3.f.a.134.4		30	27.14	odd	18
243.3.f.b.53.4		30	27.23	odd	18	inner
243.3.f.b.188.4		30	1.1	even	1	trivial
243.3.f.c.53.2		30	27.4	even	9
243.3.f.c.188.2		30	3.2	odd	2
243.3.f.d.107.2		30	9.2	odd	6
243.3.f.d.134.2		30	27.13	even	9
432.3.bc.a.257.3		30	108.103	odd	18
432.3.bc.a.353.3		30	36.23	even	6
729.3.b.a.728.12		30	27.25	even	9
729.3.b.a.728.19		30	27.2	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)

\(f(q)\)	\(=\)	\(q+(0.397073 + 1.09095i) q^{2} +(2.03168 - 1.70478i) q^{4} +(-5.30122 + 0.934749i) q^{5} +(-8.06979 - 6.77136i) q^{7} +(6.68824 + 3.86146i) q^{8} +O(q^{10})\)	\(q+(0.397073 + 1.09095i) q^{2} +(2.03168 - 1.70478i) q^{4} +(-5.30122 + 0.934749i) q^{5} +(-8.06979 - 6.77136i) q^{7} +(6.68824 + 3.86146i) q^{8} +(-3.12473 - 5.41219i) q^{10} +(-11.5656 - 2.03932i) q^{11} +(-10.5554 - 3.84187i) q^{13} +(4.18291 - 11.4924i) q^{14} +(0.285244 - 1.61770i) q^{16} +(-2.73630 + 1.57980i) q^{17} +(2.26051 - 3.91532i) q^{19} +(-9.17683 + 10.9365i) q^{20} +(-2.36757 - 13.4272i) q^{22} +(-12.7964 - 15.2501i) q^{23} +(3.73689 - 1.36012i) q^{25} -13.0409i q^{26} -27.9389 q^{28} +(8.67353 + 23.8303i) q^{29} +(16.9460 - 14.2194i) q^{31} +(32.3004 - 5.69544i) q^{32} +(-2.80999 - 2.35786i) q^{34} +(49.1093 + 28.3533i) q^{35} +(-8.82807 - 15.2907i) q^{37} +(5.16899 + 0.911433i) q^{38} +(-39.0653 - 14.2186i) q^{40} +(-4.25636 + 11.6943i) q^{41} +(6.32921 - 35.8947i) q^{43} +(-26.9741 + 15.5735i) q^{44} +(11.5560 - 20.0156i) q^{46} +(7.97030 - 9.49863i) q^{47} +(10.7615 + 61.0314i) q^{49} +(2.96764 + 3.53669i) q^{50} +(-27.9948 + 10.1893i) q^{52} -84.6210i q^{53} +63.2178 q^{55} +(-27.8254 - 76.4496i) q^{56} +(-22.5536 + 18.9247i) q^{58} +(-67.2363 + 11.8556i) q^{59} +(59.8066 + 50.1837i) q^{61} +(22.2414 + 12.8411i) q^{62} +(15.7537 + 27.2863i) q^{64} +(59.5480 + 10.4999i) q^{65} +(91.2665 + 33.2183i) q^{67} +(-2.86606 + 7.87443i) q^{68} +(-11.4320 + 64.8340i) q^{70} +(-105.364 + 60.8322i) q^{71} +(-45.5705 + 78.9304i) q^{73} +(13.1759 - 15.7025i) q^{74} +(-2.08213 - 11.8083i) q^{76} +(79.5227 + 94.7714i) q^{77} +(19.1583 - 6.97307i) q^{79} +8.84240i q^{80} -14.4479 q^{82} +(10.8085 + 29.6962i) q^{83} +(13.0290 - 10.9326i) q^{85} +(41.6724 - 7.34797i) q^{86} +(-69.4785 - 58.2994i) q^{88} +(-59.7756 - 34.5114i) q^{89} +(59.1656 + 102.478i) q^{91} +(-51.9962 - 9.16833i) q^{92} +(13.5273 + 4.92353i) q^{94} +(-8.32363 + 22.8690i) q^{95} +(-13.8579 + 78.5918i) q^{97} +(-62.3089 + 35.9741i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{2} + 3 q^{4} + 6 q^{5} + 3 q^{7} + 9 q^{8}+O(q^{10}) \) 30 * q - 3 * q^2 + 3 * q^4 + 6 * q^5 + 3 * q^7 + 9 * q^8	\( 30 q - 3 q^{2} + 3 q^{4} + 6 q^{5} + 3 q^{7} + 9 q^{8} - 3 q^{10} + 51 q^{11} + 3 q^{13} - 129 q^{14} - 9 q^{16} + 9 q^{17} - 3 q^{19} + 30 q^{20} - 33 q^{22} + 168 q^{23} - 6 q^{25} - 12 q^{28} - 246 q^{29} + 48 q^{31} - 117 q^{32} + 99 q^{34} + 252 q^{35} - 3 q^{37} + 237 q^{38} + 201 q^{40} - 129 q^{41} + 183 q^{43} - 639 q^{44} - 3 q^{46} + 348 q^{47} + 147 q^{49} + 471 q^{50} + 45 q^{52} - 12 q^{55} - 570 q^{56} - 267 q^{58} - 426 q^{59} - 285 q^{61} + 900 q^{62} - 51 q^{64} + 213 q^{65} - 366 q^{67} - 378 q^{68} - 483 q^{70} - 315 q^{71} - 66 q^{73} - 159 q^{74} - 201 q^{76} + 654 q^{77} - 15 q^{79} - 12 q^{82} - 624 q^{83} + 18 q^{85} + 411 q^{86} + 51 q^{88} - 72 q^{89} + 96 q^{91} + 561 q^{92} - 96 q^{94} + 75 q^{95} - 114 q^{97} - 882 q^{98}+O(q^{100}) \) 30 * q - 3 * q^2 + 3 * q^4 + 6 * q^5 + 3 * q^7 + 9 * q^8 - 3 * q^10 + 51 * q^11 + 3 * q^13 - 129 * q^14 - 9 * q^16 + 9 * q^17 - 3 * q^19 + 30 * q^20 - 33 * q^22 + 168 * q^23 - 6 * q^25 - 12 * q^28 - 246 * q^29 + 48 * q^31 - 117 * q^32 + 99 * q^34 + 252 * q^35 - 3 * q^37 + 237 * q^38 + 201 * q^40 - 129 * q^41 + 183 * q^43 - 639 * q^44 - 3 * q^46 + 348 * q^47 + 147 * q^49 + 471 * q^50 + 45 * q^52 - 12 * q^55 - 570 * q^56 - 267 * q^58 - 426 * q^59 - 285 * q^61 + 900 * q^62 - 51 * q^64 + 213 * q^65 - 366 * q^67 - 378 * q^68 - 483 * q^70 - 315 * q^71 - 66 * q^73 - 159 * q^74 - 201 * q^76 + 654 * q^77 - 15 * q^79 - 12 * q^82 - 624 * q^83 + 18 * q^85 + 411 * q^86 + 51 * q^88 - 72 * q^89 + 96 * q^91 + 561 * q^92 - 96 * q^94 + 75 * q^95 - 114 * q^97 - 882 * q^98

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