LMFDB - Embedded newform 243.3.f.b.53.4

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			53.4
Character	$\chi$	$=$	243.53
Dual form			243.3.f.b.188.4

$q$-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 $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{11}{18}\right)$

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	−0.799974	−	0.600034i	$-0.795154\pi$
$2$	0.397073	−	1.09095i	0.198536	−	0.545474i	0.998510	+	0.0545605i	$0.0173758\pi$
$3$		0			0
$3$		0			0
$4$	2.03168	+	1.70478i	0.507919	+	0.426195i
$5$	−5.30122	−	0.934749i	−1.06024	−	0.186950i	−0.383780	−	0.923425i	$-0.625378\pi$
$5$	−5.30122	−	0.934749i	−1.06024	−	0.186950i	−0.676465	+	0.736475i	$0.736489\pi$
$6$		0			0
$7$	−8.06979	+	6.77136i	−1.15283	+	0.967337i	−0.999782	−	0.0208820i	$-0.993353\pi$
$7$	−8.06979	+	6.77136i	−1.15283	+	0.967337i	−0.153046	+	0.988219i	$0.548908\pi$
$8$	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	−0.672544	−	0.740057i	$-0.734798\pi$
$11$	−11.5656	+	2.03932i	−1.05141	+	0.185393i	−0.378870	+	0.925450i	$0.623687\pi$
$12$		0			0
$13$	−10.5554	+	3.84187i	−0.811957	+	0.295528i	−0.714432	−	0.699705i	$-0.753315\pi$
$13$	−10.5554	+	3.84187i	−0.811957	+	0.295528i	−0.0975252	+	0.995233i	$0.531093\pi$
$14$	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	0.417357	−	0.908743i	$-0.362956\pi$
$17$	−2.73630	−	1.57980i	−0.160959	−	0.0929296i	−0.578316	+	0.815813i	$0.696290\pi$
$18$		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	$0.795373\pi$
$20$	−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	−0.968773	−	0.247950i	$-0.920243\pi$
$23$	−12.7964	+	15.2501i	−0.556364	+	0.663048i	0.412409	+	0.910999i	$0.364687\pi$
$24$		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	−0.695566	−	0.718462i	$-0.744846\pi$
$29$	8.67353	−	23.8303i	0.299087	−	0.821735i	0.994653	−	0.103273i	$-0.0329315\pi$
$30$		0			0
$31$	16.9460	+	14.2194i	0.546646	+	0.458690i	0.873803	−	0.486280i	$-0.161646\pi$
$31$	16.9460	+	14.2194i	0.546646	+	0.458690i	−0.327158	+	0.944970i	$0.606091\pi$
$32$	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	−0.960312	−	0.278929i	$-0.910021\pi$
$37$	−8.82807	+	15.2907i	−0.238596	+	0.413261i	0.721715	+	0.692190i	$0.243354\pi$
$38$	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	0.876901	−	0.480671i	$-0.159607\pi$
$41$	−4.25636	−	11.6943i	−0.103814	−	0.285226i	−0.980715	+	0.195446i	$0.937385\pi$
$42$		0			0
$43$	6.32921	+	35.8947i	0.147191	+	0.834761i	0.965582	+	0.260099i	$0.0837552\pi$
$43$	6.32921	+	35.8947i	0.147191	+	0.834761i	−0.818391	+	0.574662i	$0.805134\pi$
$44$	−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	0.844141	−	0.536121i	$-0.180111\pi$
$47$	7.97030	+	9.49863i	0.169581	+	0.202098i	−0.674560	+	0.738220i	$0.735667\pi$
$48$		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	$0.294273\pi$
$53$			84.6210i			1.59662i	−0.602245	+	0.798311i	$0.705727\pi$
$54$		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	−0.428169	−	0.903699i	$-0.640841\pi$
$59$	−67.2363	−	11.8556i	−1.13960	−	0.200942i	−0.711430	+	0.702757i	$0.751952\pi$
$60$		0			0
$61$	59.8066	−	50.1837i	0.980437	−	0.822684i	−0.00371858	−	0.999993i	$-0.501184\pi$
$61$	59.8066	−	50.1837i	0.980437	−	0.822684i	0.984155	+	0.177309i	$0.0567392\pi$
$62$	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	0.445457	−	0.895303i	$-0.353041\pi$
$67$	91.2665	−	33.2183i	1.36219	−	0.495795i	0.916730	+	0.399508i	$0.130819\pi$
$68$	−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	−0.484171	−	0.874973i	$-0.660879\pi$
$71$	−105.364	−	60.8322i	−1.48401	−	0.856791i	−0.999835	+	0.0181820i	$0.994212\pi$
$72$		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	$-0.381263\pi$
$74$	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	0.460416	−	0.887703i	$-0.347700\pi$
$79$	19.1583	+	6.97307i	0.242511	+	0.0882667i	−0.217905	+	0.975970i	$0.569922\pi$
$80$		−	8.84240i		−	0.110530i
$81$		0			0
$82$	−14.4479			−0.176194
$83$	10.8085	−	29.6962i	0.130223	−	0.357785i	−0.857396	−	0.514658i	$-0.827919\pi$
$83$	10.8085	−	29.6962i	0.130223	−	0.357785i	0.987619	+	0.156872i	$0.0501412\pi$
$84$		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	−0.796696	−	0.604380i	$-0.793421\pi$
$89$	−59.7756	+	34.5114i	−0.671636	+	0.387769i	0.125060	+	0.992149i	$0.460088\pi$
$90$		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	−0.969057	−	0.246837i	$-0.920609\pi$
$97$	−13.8579	−	78.5918i	−0.142864	−	0.810224i	0.826193	−	0.563388i	$-0.190502\pi$
$98$	−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	0.781030	−	0.624493i	$-0.214694\pi$
$101$	3.07039	+	3.65915i	0.0303999	+	0.0362292i	−0.750630	+	0.660722i	$0.770250\pi$
$102$		0			0
$103$	−12.5535	+	71.1945i	−0.121879	+	0.691209i	0.861234	+	0.508208i	$0.169692\pi$
$103$	−12.5535	+	71.1945i	−0.121879	+	0.691209i	−0.983113	+	0.183000i	$0.941419\pi$
$104$	−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	$0.264672\pi$
$107$			158.133i			1.47788i	−0.673773	+	0.738938i	$0.735328\pi$
$108$		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	0.0945892	−	0.995516i	$-0.469846\pi$
$113$	−17.7424	−	3.12847i	−0.157013	−	0.0276856i	−0.251602	+	0.967831i	$0.580957\pi$
$114$		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	0.990382	+	0.138359i	$0.0441827\pi$
$127$	78.1067	+	135.285i	0.615013	+	1.06523i	−0.375369	+	0.926876i	$0.622484\pi$
$128$	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	−0.951529	−	0.307559i	$-0.900488\pi$
$131$	−63.3268	+	75.4699i	−0.483411	+	0.576106i	0.468118	+	0.883666i	$0.344932\pi$
$132$		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	−0.994271	−	0.106885i	$-0.965912\pi$
$137$	−22.4558	+	61.6969i	−0.163911	+	0.450342i	0.830360	+	0.557227i	$0.188135\pi$
$138$		0			0
$139$	−95.9859	−	80.5417i	−0.690546	−	0.579437i	0.228521	−	0.973539i	$-0.426611\pi$
$139$	−95.9859	−	80.5417i	−0.690546	−	0.579437i	−0.919067	+	0.394102i	$0.871056\pi$
$140$	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	0.923127	+	0.384495i	$0.125624\pi$
$149$	69.0048	+	189.589i	0.463119	+	1.27241i	−0.460008	+	0.887915i	$0.652153\pi$
$150$		0			0
$151$	22.2514	+	126.194i	0.147360	+	0.835720i	0.965442	+	0.260619i	$0.0839265\pi$
$151$	22.2514	+	126.194i	0.147360	+	0.835720i	−0.818082	+	0.575102i	$0.804962\pi$
$152$	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	0.806303	+	0.591503i	$0.201465\pi$
$157$	−24.1278	+	136.835i	−0.153680	+	0.871563i	−0.959983	+	0.280059i	$0.909646\pi$
$158$	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	−0.338620	−	0.940923i	$-0.609960\pi$
$167$	−163.432	−	28.8174i	−0.978633	−	0.172559i	−0.640013	+	0.768364i	$0.721071\pi$
$168$		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	−0.204558	−	0.978854i	$-0.565576\pi$
$173$	−10.7247	+	1.89106i	−0.0619925	+	0.0109310i	0.142566	+	0.989785i	$0.454465\pi$
$174$		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	0.990564	−	0.137054i	$-0.0437633\pi$
$179$	244.720	+	141.289i	1.36715	+	0.789326i	0.376590	+	0.926380i	$0.377097\pi$
$180$		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	$0.736163\pi$
$182$	−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	−0.803637	−	0.595120i	$-0.797104\pi$
$191$	37.1534	−	102.078i	0.194521	−	0.534441i	0.998157	+	0.0606793i	$0.0193267\pi$
$192$		0			0
$193$	153.292	+	128.627i	0.794258	+	0.666461i	0.946795	−	0.321836i	$-0.104300\pi$
$193$	153.292	+	128.627i	0.794258	+	0.666461i	−0.152538	+	0.988298i	$0.548745\pi$
$194$	−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	−0.978077	−	0.208243i	$-0.933225\pi$
$197$	−253.494	+	146.355i	−1.28677	+	0.742918i	−0.308694	+	0.951161i	$0.599892\pi$
$198$		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	$0.100359\pi$
$200$	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	−0.899305	−	0.437321i	$-0.855927\pi$
$211$	20.1163	−	114.085i	0.0953379	−	0.540688i	0.994643	−	0.103367i	$-0.0329616\pi$
$212$	−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	−0.916291	−	0.400512i	$-0.868832\pi$
$223$	−151.858	+	127.424i	−0.680976	+	0.571407i	0.235315	+	0.971919i	$0.424388\pi$
$224$	−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	−0.184812	−	0.982774i	$-0.559168\pi$
$227$	−5.07359	+	0.894610i	−0.0223506	+	0.00394102i	0.162462	+	0.986715i	$0.448057\pi$
$228$		0			0
$229$	−332.038	+	120.852i	−1.44995	+	0.527737i	−0.942576	−	0.333991i	$-0.891604\pi$
$229$	−332.038	+	120.852i	−1.44995	+	0.527737i	−0.507370	+	0.861728i	$0.669382\pi$
$230$	−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	0.215491	−	0.976506i	$-0.430865\pi$
$233$	−121.729	−	70.2803i	−0.522442	−	0.301632i	−0.737933	+	0.674874i	$0.764198\pi$
$234$		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	−0.529987	−	0.848006i	$-0.677803\pi$
$239$	94.9229	−	113.125i	0.397167	−	0.473325i	0.927154	+	0.374681i	$0.122248\pi$
$240$		0			0
$241$	−286.055	−	104.116i	−1.18695	−	0.432015i	−0.328299	−	0.944574i	$-0.606475\pi$
$241$	−286.055	−	104.116i	−1.18695	−	0.432015i	−0.858652	+	0.512559i	$0.828698\pi$
$242$		−	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	−0.269021	−	0.963134i	$-0.586700\pi$
$251$	108.072	−	62.3955i	0.430567	−	0.248588i	0.699588	+	0.714546i	$0.253367\pi$
$252$		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	−0.734102	−	0.679039i	$-0.762397\pi$
$257$	−156.314	−	429.469i	−0.608225	−	1.67109i	0.125876	−	0.992046i	$-0.459826\pi$
$258$		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	0.921679	+	0.387952i	$0.126817\pi$
$263$	300.790	+	358.468i	1.14369	+	1.36300i	0.222010	+	0.975044i	$0.428738\pi$
$264$		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	$-0.799399\pi$
$269$		−	317.049i		−	1.17862i	0.807907	−	0.589310i	$-0.200601\pi$
$270$		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	−0.788150	−	0.615483i	$-0.788961\pi$
$277$	−88.3295	+	74.1172i	−0.318879	+	0.267571i	0.469271	+	0.883054i	$0.344517\pi$
$278$	−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	−0.314784	−	0.949163i	$-0.601932\pi$
$281$	−80.3524	+	14.1683i	−0.285952	+	0.0504210i	0.0288326	+	0.999584i	$0.490821\pi$
$282$		0			0
$283$	391.983	−	142.670i	1.38510	−	0.504134i	0.461378	−	0.887204i	$-0.347355\pi$
$283$	391.983	−	142.670i	1.38510	−	0.504134i	0.923720	+	0.383069i	$0.125133\pi$
$284$	−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	−0.239071	−	0.971002i	$-0.576843\pi$
$293$	222.297	−	264.924i	0.758694	−	0.904176i	0.997765	+	0.0668261i	$0.0212873\pi$
$294$		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	−0.175362	+	0.984504i	$0.556110\pi$
$307$	−288.668	+	499.988i	−0.940286	+	1.62862i	−0.764925	+	0.644120i	$0.777224\pi$
$308$	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	0.897086	+	0.441856i	$0.145680\pi$
$311$	153.602	+	422.019i	0.493898	+	1.35697i	−0.403188	+	0.915117i	$0.632098\pi$
$312$		0			0
$313$	1.88192	+	10.6729i	0.00601253	+	0.0340988i	0.987666	−	0.156573i	$-0.0500446\pi$
$313$	1.88192	+	10.6729i	0.00601253	+	0.0340988i	−0.981654	+	0.190672i	$0.938933\pi$
$314$	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	0.940490	−	0.339822i	$-0.110367\pi$
$317$	140.278	+	167.176i	0.442516	+	0.527370i	−0.497974	+	0.867192i	$0.665922\pi$
$318$		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	0.424899	−	0.905241i	$-0.360310\pi$
$331$	460.146	−	386.109i	1.39017	−	1.16649i	0.965271	−	0.261250i	$-0.0841348\pi$
$332$	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	−0.881328	−	0.472505i	$-0.843350\pi$
$337$	−422.175	+	153.659i	−1.25274	+	0.455961i	−0.371416	+	0.928467i	$0.621128\pi$
$338$	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	−0.501594	−	0.865103i	$-0.667253\pi$
$347$	151.801	−	180.909i	0.437467	−	0.521353i	0.939061	+	0.343750i	$0.111697\pi$
$348$		0			0
$349$	−225.323	−	82.0110i	−0.645625	−	0.234988i	−0.00160737	−	0.999999i	$-0.500512\pi$
$349$	−225.323	−	82.0110i	−0.645625	−	0.234988i	−0.644018	+	0.765010i	$0.722734\pi$
$350$			48.6353i			0.138958i
$351$		0			0
$352$	−385.187			−1.09428
$353$	8.75255	−	24.0474i	0.0247948	−	0.0681231i	−0.926678	−	0.375857i	$-0.877348\pi$
$353$	8.75255	−	24.0474i	0.0247948	−	0.0681231i	0.951472	+	0.307734i	$0.0995706\pi$
$354$		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	−0.523188	−	0.852217i	$-0.675257\pi$
$359$	−16.7796	+	9.68773i	−0.0467399	+	0.0269853i	0.476448	+	0.879203i	$0.341924\pi$
$360$		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	0.926124	+	0.377220i	$0.123120\pi$
$367$	67.8469	+	384.779i	0.184869	+	1.04844i	−0.741254	+	0.671224i	$0.765769\pi$
$368$	−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	0.914471	+	0.404653i	$0.132608\pi$
$373$	−31.0522	+	176.106i	−0.0832500	+	0.472134i	−0.997721	+	0.0674817i	$0.978504\pi$
$374$	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	0.195752	−	0.980654i	$-0.437285\pi$
$383$	16.9648	+	2.99135i	0.0442945	+	0.00781031i	−0.151457	+	0.988464i	$0.548397\pi$
$384$		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	0.242375	−	0.970183i	$-0.422074\pi$
$389$	311.960	−	55.0070i	0.801955	−	0.141406i	0.559580	+	0.828776i	$0.310963\pi$
$390$		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	0.646353	−	0.763039i	$-0.276293\pi$
$397$	−134.041	−	232.165i	−0.337634	−	0.584800i	−0.983987	+	0.178239i	$0.942960\pi$
$398$	−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	−0.838484	−	0.544926i	$-0.816558\pi$
$401$	−62.6504	+	74.6638i	−0.156235	+	0.186194i	0.682249	+	0.731120i	$0.261002\pi$
$402$		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	0.178721	−	0.983900i	$-0.442804\pi$
$409$	−310.511	−	260.550i	−0.759196	−	0.637041i	−0.937917	+	0.346859i	$0.887248\pi$
$410$	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	0.978325	−	0.207077i	$-0.0663951\pi$
$419$	40.1309	+	110.259i	0.0957778	+	0.263147i	−0.882547	+	0.470225i	$0.844173\pi$
$420$		0			0
$421$	−90.5287	−	513.414i	−0.215032	−	1.21951i	−0.880850	−	0.473395i	$-0.843028\pi$
$421$	−90.5287	−	513.414i	−0.215032	−	1.21951i	0.665818	−	0.746115i	$-0.268083\pi$
$422$	−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	$-0.901084\pi$
$431$		−	263.580i		−	0.611555i	0.952103	−	0.305777i	$-0.0989163\pi$
$432$		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	−0.941444	−	0.337170i	$-0.890530\pi$
$439$	−339.293	+	284.700i	−0.772876	+	0.648520i	0.168567	+	0.985690i	$0.446086\pi$
$440$	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	−0.801040	−	0.598610i	$-0.795720\pi$
$443$	−597.623	+	105.377i	−1.34904	+	0.237871i	−0.547995	+	0.836482i	$0.684609\pi$
$444$		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	0.0599853	−	0.998199i	$-0.480895\pi$
$449$	−347.745	−	200.771i	−0.774488	−	0.447151i	−0.834473	+	0.551048i	$0.814228\pi$
$450$		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	0.488809	−	0.872391i	$-0.337432\pi$
$457$	138.241	+	50.3155i	0.302496	+	0.110099i	−0.186313	+	0.982490i	$0.559654\pi$
$458$			410.223i			0.895683i
$459$		0			0
$460$	284.213			0.617855
$461$	−268.627	+	738.046i	−0.582705	+	1.60097i	0.200834	+	0.979625i	$0.435635\pi$
$461$	−268.627	+	738.046i	−0.582705	+	1.60097i	−0.783539	+	0.621343i	$0.786588\pi$
$462$		0			0
$463$	−274.591	−	230.409i	−0.593069	−	0.497644i	0.296141	−	0.955144i	$-0.404300\pi$
$463$	−274.591	−	230.409i	−0.593069	−	0.497644i	−0.889209	+	0.457501i	$0.848745\pi$
$464$	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	−0.402503	−	0.915419i	$-0.631860\pi$
$467$	88.2727	−	50.9643i	0.189021	−	0.109131i	0.591524	+	0.806287i	$0.298526\pi$
$468$		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	0.674560	−	0.738220i	$-0.264333\pi$
$479$	−81.2290	−	96.8049i	−0.169580	−	0.202098i	−0.844141	+	0.536122i	$0.819889\pi$
$480$		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	0.481398	−	0.876502i	$-0.340129\pi$
$491$	311.285	+	54.8880i	0.633982	+	0.111788i	0.152585	+	0.988290i	$0.451240\pi$
$492$		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	−0.454572	−	0.890710i	$-0.650208\pi$
$499$	−114.898	+	41.8195i	−0.230257	+	0.0838066i	0.224315	+	0.974517i	$0.427986\pi$
$500$	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	0.835515	−	0.549468i	$-0.185170\pi$
$503$	391.041	+	225.768i	0.777418	+	0.448843i	−0.0580963	+	0.998311i	$0.518503\pi$
$504$		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	−0.351874	−	0.936047i	$-0.614455\pi$
$509$	321.207	−	382.800i	0.631055	−	0.752063i	0.982929	+	0.183985i	$0.0588998\pi$
$510$		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	0.196015	−	0.980601i	$-0.437200\pi$
$521$	595.632	−	343.888i	1.14325	−	0.660054i	0.947233	+	0.320546i	$0.103867\pi$
$522$		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	$0.000900130\pi$
$524$	−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	−0.689617	−	0.724175i	$-0.742221\pi$
$547$	−52.6185	+	44.1522i	−0.0961947	+	0.0807169i	0.593422	+	0.804891i	$0.297777\pi$
$548$	−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	−0.114822	−	0.993386i	$-0.536630\pi$
$557$	−575.120	−	332.045i	−1.03253	−	0.596132i	−0.917709	+	0.397254i	$0.869963\pi$
$558$		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	−0.530155	−	0.847901i	$-0.677866\pi$
$563$	223.468	−	266.319i	0.396924	−	0.473036i	0.927080	+	0.374865i	$0.122311\pi$
$564$		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	0.764961	+	0.644076i	$0.222758\pi$
$569$	−133.736	+	367.437i	−0.235037	+	0.645760i	−0.999999	+	0.00168357i	$0.999464\pi$
$570$		0			0
$571$	655.523	+	550.049i	1.14803	+	0.963309i	0.999672	−	0.0256252i	$-0.00815764\pi$
$571$	655.523	+	550.049i	1.14803	+	0.963309i	0.148355	+	0.988934i	$0.452602\pi$
$572$	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	−0.454931	−	0.890527i	$-0.650336\pi$
$577$	313.746	−	543.423i	0.543753	−	0.941808i	0.998684	−	0.0512815i	$-0.0163306\pi$
$578$	−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	0.999938	−	0.0111512i	$-0.00354962\pi$
$587$	478.592	+	570.364i	0.815319	+	0.971659i	−0.184619	+	0.982810i	$0.559105\pi$
$588$		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	$0.176904\pi$
$593$			625.722i			1.05518i	−0.849499	+	0.527591i	$0.823096\pi$
$594$		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	−0.318571	−	0.947899i	$-0.603203\pi$
$599$	−564.336	−	99.5077i	−0.942130	−	0.166123i	−0.623559	+	0.781776i	$0.714314\pi$
$600$		0			0
$601$	866.763	−	727.301i	1.44220	−	1.21015i	0.504169	−	0.863605i	$-0.331799\pi$
$601$	866.763	−	727.301i	1.44220	−	1.21015i	0.938033	−	0.346546i	$-0.112645\pi$
$602$	−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	−0.155745	−	0.987797i	$-0.549778\pi$
$607$	218.454	−	79.5107i	0.359891	−	0.130990i	0.515636	+	0.856808i	$0.327556\pi$
$608$	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	0.861020	+	0.508571i	$0.169826\pi$
$613$	533.889	+	924.724i	0.870945	+	1.50852i	0.00992514	+	0.999951i	$0.496841\pi$
$614$	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	−0.939604	−	0.342264i	$-0.888806\pi$
$617$	−271.097	+	323.080i	−0.439378	+	0.523631i	0.500225	+	0.865895i	$0.333251\pi$
$618$		0			0
$619$	−564.604	−	205.499i	−0.912123	−	0.331986i	−0.157023	−	0.987595i	$-0.550190\pi$
$619$	−564.604	−	205.499i	−0.912123	−	0.331986i	−0.755100	+	0.655609i	$0.772412\pi$
$620$		−	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	0.0264679	−	0.999650i	$-0.491574\pi$
$631$	554.621	−	960.632i	0.878956	−	1.52240i	0.852488	−	0.522747i	$-0.175093\pi$
$632$	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	0.842518	−	0.538669i	$-0.181072\pi$
$641$	106.234	+	126.604i	0.165731	+	0.197511i	−0.676787	+	0.736179i	$0.736628\pi$
$642$		0			0
$643$	137.985	−	782.552i	0.214596	−	1.21703i	−0.667011	−	0.745048i	$-0.732427\pi$
$643$	137.985	−	782.552i	0.214596	−	1.21703i	0.881607	−	0.471985i	$-0.156462\pi$
$644$	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	$0.0550068\pi$
$647$			222.504i			0.343900i	−0.985106	+	0.171950i	$0.944993\pi$
$648$		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	−0.189567	−	0.981868i	$-0.560708\pi$
$653$	−459.398	−	81.0043i	−0.703520	−	0.124050i	−0.513953	+	0.857818i	$0.671819\pi$
$654$		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	−0.327088	−	0.944994i	$-0.606067\pi$
$659$	−205.109	+	36.1663i	−0.311244	+	0.0548806i	0.0158446	+	0.999874i	$0.494956\pi$
$660$		0			0
$661$	595.560	−	216.766i	0.900999	−	0.327937i	0.150346	−	0.988633i	$-0.451961\pi$
$661$	595.560	−	216.766i	0.900999	−	0.327937i	0.750653	+	0.660697i	$0.229739\pi$
$662$	−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	0.264066	−	0.964505i	$-0.414936\pi$
$673$	−103.386	−	37.6293i	−0.153619	−	0.0559128i	−0.417685	+	0.908592i	$0.637159\pi$
$674$			521.584i			0.773864i
$675$		0			0
$676$	−113.573			−0.168007
$677$	−48.9221	+	134.412i	−0.0722631	+	0.198541i	−0.970566	−	0.240836i	$-0.922579\pi$
$677$	−48.9221	+	134.412i	−0.0722631	+	0.198541i	0.898303	+	0.439377i	$0.144801\pi$
$678$		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	−0.948387	−	0.317116i	$-0.897286\pi$
$683$	−784.050	+	452.671i	−1.14795	+	0.662769i	−0.199563	+	0.979885i	$0.563952\pi$
$684$		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	0.975760	+	0.218842i	$0.0702280\pi$
$691$	92.3826	+	523.928i	0.133694	+	0.758217i	−0.842066	+	0.539374i	$0.818661\pi$
$692$	−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	$-0.776639\pi$
$701$		−	905.026i		−	1.29105i	0.763739	−	0.645525i	$-0.223361\pi$
$702$		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	−0.817836	−	0.575452i	$-0.804826\pi$
$709$	−278.738	+	233.889i	−0.393142	+	0.329885i	0.424694	+	0.905337i	$0.360382\pi$
$710$	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	0.745680	−	0.666304i	$-0.232125\pi$
$719$	389.328	+	224.778i	0.541485	+	0.312626i	−0.204196	+	0.978930i	$0.565458\pi$
$720$		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	−0.0607376	−	0.998154i	$-0.519345\pi$
$727$	−544.426	−	198.155i	−0.748866	−	0.272565i	−0.688129	+	0.725589i	$0.741568\pi$
$728$		−	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	0.983867	−	0.178900i	$-0.0572538\pi$
$733$	717.264	+	601.856i	0.978532	+	0.821086i	−0.00533530	+	0.999986i	$0.501698\pi$
$734$	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	−0.987480	−	0.157746i	$-0.949577\pi$
$739$	−263.918	+	457.119i	−0.357128	+	0.618564i	0.630352	+	0.776310i	$0.282911\pi$
$740$	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	0.930927	−	0.365206i	$-0.119002\pi$
$743$	−12.5973	−	34.6108i	−0.0169547	−	0.0465825i	−0.947881	+	0.318624i	$0.896779\pi$
$744$		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	−0.971300	−	0.237858i	$-0.923555\pi$
$751$	17.1046	−	97.0050i	0.0227758	−	0.129168i	0.994076	+	0.108691i	$0.0346657\pi$
$752$	−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	0.992388	−	0.123152i	$-0.0393003\pi$
$761$	1432.82	+	252.644i	1.88281	+	0.331990i	0.890419	+	0.455142i	$0.150411\pi$
$762$		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	−0.280157	−	0.959954i	$-0.590386\pi$
$769$	94.0313	−	34.2246i	0.122277	−	0.0445053i	0.402434	+	0.915449i	$0.368164\pi$
$770$	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	0.810629	−	0.585560i	$-0.199125\pi$
$773$	547.928	+	316.347i	0.708834	+	0.409245i	−0.101795	+	0.994805i	$0.532459\pi$
$774$		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	0.152771	−	0.988262i	$-0.451180\pi$
$787$	−624.837	−	524.300i	−0.793948	−	0.666201i	−0.946719	+	0.322060i	$0.895625\pi$
$788$	−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	0.849870	+	0.526992i	$0.176680\pi$
$797$	428.448	+	1177.15i	0.537576	+	1.47698i	−0.312295	+	0.949985i	$0.601098\pi$
$798$		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	$0.217588\pi$
$809$			1021.88i			1.26313i	−0.775321	+	0.631567i	$0.782412\pi$
$810$		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	−0.179460	−	0.983765i	$-0.557435\pi$
$821$	−9.54867	+	1.68369i	−0.0116305	+	0.00205078i	0.167830	+	0.985816i	$0.446324\pi$
$822$		0			0
$823$	−0.839980	+	0.305728i	−0.00102063	+	0.000371480i	−0.342530	−	0.939507i	$-0.611284\pi$
$823$	−0.839980	+	0.305728i	−0.00102063	+	0.000371480i	0.341510	+	0.939878i	$0.389062\pi$
$824$	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	0.809465	−	0.587168i	$-0.199757\pi$
$827$	583.611	+	336.948i	0.705696	+	0.407434i	−0.103769	+	0.994601i	$0.533090\pi$
$828$		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	$0.838894\pi$
$830$	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	−0.738769	−	0.673959i	$-0.764592\pi$
$839$	218.453	−	600.196i	0.260374	−	0.715371i	0.999142	−	0.0414115i	$-0.0131855\pi$
$840$		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	0.955808	+	0.293991i	$0.0949836\pi$
$853$	134.939	+	765.276i	0.158193	+	0.897158i	−0.797615	+	0.603167i	$0.793905\pi$
$854$	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	0.192157	−	0.981364i	$-0.438452\pi$
$857$	−692.170	−	824.896i	−0.807666	−	0.962539i	−0.999823	+	0.0188256i	$0.994007\pi$
$858$		0			0
$859$	−14.0627	+	79.7538i	−0.0163711	+	0.0928449i	−0.991899	−	0.127033i	$-0.959455\pi$
$859$	−14.0627	+	79.7538i	−0.0163711	+	0.0928449i	0.975527	+	0.219878i	$0.0705658\pi$
$860$	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	$-0.622785\pi$
$863$		−	1599.17i		−	1.85304i	0.376244	−	0.926520i	$-0.377215\pi$
$864$		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	−0.131135	−	0.991364i	$-0.541862\pi$
$877$	355.751	−	129.483i	0.405646	−	0.147643i	0.536781	+	0.843721i	$0.319640\pi$
$878$	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	0.957898	−	0.287109i	$-0.0926943\pi$
$881$	1046.81	+	604.374i	1.18820	+	0.686009i	0.230305	+	0.973119i	$0.426028\pi$
$882$		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	$0.723702\pi$
$884$	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	−0.801588	−	0.597877i	$-0.796011\pi$
$887$	−65.2823	+	77.8005i	−0.0735990	+	0.0877119i	0.727989	+	0.685589i	$0.240455\pi$
$888$		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	0.468818	+	0.883295i	$0.344680\pi$
$907$	299.653	+	1699.41i	0.330378	+	1.87367i	−0.138440	+	0.990371i	$0.544209\pi$
$908$	−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	0.644356	−	0.764725i	$-0.277125\pi$
$911$	−201.005	−	239.549i	−0.220642	−	0.262951i	−0.864999	+	0.501774i	$0.832681\pi$
$912$		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	0.583536	−	0.812087i	$-0.301669\pi$
$929$	1309.55	−	230.908i	1.40963	−	0.248556i	0.826095	+	0.563531i	$0.190558\pi$
$930$		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	−0.960559	−	0.278076i	$-0.910303\pi$
$937$	−675.671	−	1170.30i	−0.721100	−	1.24898i	0.239459	−	0.970906i	$-0.423030\pi$
$938$	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	−0.963132	−	0.269031i	$-0.913297\pi$
$941$	−499.617	+	595.420i	−0.530942	+	0.632752i	0.432189	+	0.901783i	$0.357741\pi$
$942$		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	−0.979318	−	0.202327i	$-0.935150\pi$
$947$	−93.8130	+	257.749i	−0.0990634	+	0.272174i	0.880255	+	0.474502i	$0.157372\pi$
$948$		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	−0.877409	−	0.479743i	$-0.840730\pi$
$953$	−858.313	+	495.548i	−0.900644	+	0.519987i	−0.0232347	+	0.999730i	$0.507397\pi$
$954$		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	−0.943817	−	0.330470i	$-0.892793\pi$
$967$	54.2567	−	307.705i	0.0561083	−	0.318206i	0.999925	+	0.0122640i	$0.00390387\pi$
$968$	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	$0.0808264\pi$
$971$			487.838i			0.502407i	−0.967934	+	0.251204i	$0.919174\pi$
$972$		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	−0.160531	−	0.987031i	$-0.551321\pi$
$977$	−634.038	−	111.798i	−0.648965	−	0.114430i	−0.488434	+	0.872601i	$0.662432\pi$
$978$		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	−0.879291	−	0.476286i	$-0.841983\pi$
$983$	−1516.43	+	267.387i	−1.54265	+	0.272012i	−0.663364	+	0.748297i	$0.730872\pi$
$984$		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	0.776796	−	0.629752i	$-0.216844\pi$
$991$	−155.571	−	269.456i	−0.156984	−	0.271903i	−0.933780	+	0.357849i	$0.883510\pi$
$992$	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	0.364649	−	0.931145i	$-0.381189\pi$
$997$	45.3212	+	16.4956i	0.0454576	+	0.0165452i	−0.319191	+	0.947690i	$0.603411\pi$
$998$			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.53.4		30
3.2	odd	2		243.3.f.c.53.2		30
9.2	odd	6		27.3.f.a.14.4	yes	30
9.4	even	3		243.3.f.a.134.4		30
9.5	odd	6		243.3.f.d.134.2		30
9.7	even	3		81.3.f.a.71.2		30
27.2	odd	18		243.3.f.a.107.4		30
27.7	even	9		243.3.f.c.188.2		30
27.11	odd	18		81.3.f.a.8.2		30
27.13	even	9		729.3.b.a.728.19		30
27.14	odd	18		729.3.b.a.728.12		30
27.16	even	9		27.3.f.a.2.4	✓	30
27.20	odd	18	inner	243.3.f.b.188.4		30
27.25	even	9		243.3.f.d.107.2		30
36.11	even	6		432.3.bc.a.257.3		30
108.43	odd	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	27.16	even	9
27.3.f.a.14.4	yes	30	9.2	odd	6
81.3.f.a.8.2		30	27.11	odd	18
81.3.f.a.71.2		30	9.7	even	3
243.3.f.a.107.4		30	27.2	odd	18
243.3.f.a.134.4		30	9.4	even	3
243.3.f.b.53.4		30	1.1	even	1	trivial
243.3.f.b.188.4		30	27.20	odd	18	inner
243.3.f.c.53.2		30	3.2	odd	2
243.3.f.c.188.2		30	27.7	even	9
243.3.f.d.107.2		30	27.25	even	9
243.3.f.d.134.2		30	9.5	odd	6
432.3.bc.a.257.3		30	36.11	even	6
432.3.bc.a.353.3		30	108.43	odd	18
729.3.b.a.728.12		30	27.14	odd	18
729.3.b.a.728.19		30	27.13	even	9

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more