LMFDB - Embedded newform 243.3.f.c.134.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("243.26");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			134.5
Character	$\chi$	$=$	243.134
Dual form			243.3.f.c.107.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.68916 + 2.01307i) q^{2} +(-0.504573 + 2.86157i) q^{4} +(-2.13801 - 5.87412i) q^{5} +(-1.40961 - 7.99430i) q^{7} +(2.49037 - 1.43782i) q^{8} +O(q^{10})$	\(q+(1.68916 + 2.01307i) q^{2} +(-0.504573 + 2.86157i) q^{4} +(-2.13801 - 5.87412i) q^{5} +(-1.40961 - 7.99430i) q^{7} +(2.49037 - 1.43782i) q^{8} +(8.21356 - 14.2263i) q^{10} +(2.77510 - 7.62453i) q^{11} +(7.43797 + 6.24120i) q^{13} +(13.7120 - 16.3413i) q^{14} +(18.0230 + 6.55984i) q^{16} +(-13.0143 - 7.51380i) q^{17} +(8.93226 + 15.4711i) q^{19} +(17.8880 - 3.15414i) q^{20} +(20.0363 - 7.29262i) q^{22} +(-25.9334 - 4.57276i) q^{23} +(-10.7831 + 9.04812i) q^{25} +25.5156i q^{26} +23.5875 q^{28} +(9.75225 + 11.6223i) q^{29} +(5.68415 - 32.2364i) q^{31} +(13.3043 + 36.5533i) q^{32} +(-6.85748 - 38.8907i) q^{34} +(-43.9457 + 25.3721i) q^{35} +(-15.8096 + 27.3831i) q^{37} +(-16.0564 + 44.1145i) q^{38} +(-13.7704 - 11.5547i) q^{40} +(10.6189 - 12.6551i) q^{41} +(78.7688 + 28.6695i) q^{43} +(20.4179 + 11.7883i) q^{44} +(-34.6005 - 59.9298i) q^{46} +(-12.9701 + 2.28698i) q^{47} +(-15.8769 + 5.77871i) q^{49} +(-36.4290 - 6.42341i) q^{50} +(-21.6126 + 18.1352i) q^{52} -25.7140i q^{53} -50.7206 q^{55} +(-15.0048 - 17.8820i) q^{56} +(-6.92328 + 39.2639i) q^{58} +(7.76763 + 21.3414i) q^{59} +(5.91937 + 33.5704i) q^{61} +(74.4955 - 43.0100i) q^{62} +(-12.7517 + 22.0867i) q^{64} +(20.7591 - 57.0353i) q^{65} +(6.20835 + 5.20943i) q^{67} +(28.0679 - 33.4501i) q^{68} +(-125.307 - 45.6081i) q^{70} +(35.7557 + 20.6436i) q^{71} +(40.4046 + 69.9827i) q^{73} +(-81.8291 + 14.4287i) q^{74} +(-48.7787 + 17.7540i) q^{76} +(-64.8646 - 11.4374i) q^{77} +(-21.1671 + 17.7613i) q^{79} -119.894i q^{80} +43.4126 q^{82} +(-11.3065 - 13.4746i) q^{83} +(-16.3124 + 92.5121i) q^{85} +(75.3398 + 206.994i) q^{86} +(-4.05165 - 22.9780i) q^{88} +(24.4986 - 14.1443i) q^{89} +(39.4094 - 68.2590i) q^{91} +(26.1706 - 71.9030i) q^{92} +(-26.5124 - 22.2466i) q^{94} +(71.7821 - 85.5466i) q^{95} +(-158.461 - 57.6752i) q^{97} +(-38.4516 - 22.2000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	1.68916	+	2.01307i	0.844582	+	1.00653i	0.999826	+	0.0186576i	$0.00593925\pi$
$2$	1.68916	+	2.01307i	0.844582	+	1.00653i	−0.155244	+	0.987876i	$0.549616\pi$
$3$		0			0
$3$		0			0
$4$	−0.504573	+	2.86157i	−0.126143	+	0.715393i
$5$	−2.13801	−	5.87412i	−0.427601	−	1.17482i	−0.947264	−	0.320453i	$-0.896165\pi$
$5$	−2.13801	−	5.87412i	−0.427601	−	1.17482i	0.519663	−	0.854371i	$-0.326057\pi$
$6$		0			0
$7$	−1.40961	−	7.99430i	−0.201373	−	1.14204i	−0.903046	−	0.429544i	$-0.858674\pi$
$7$	−1.40961	−	7.99430i	−0.201373	−	1.14204i	0.701673	−	0.712499i	$-0.252437\pi$
$8$	2.49037	−	1.43782i	0.311297	−	0.179727i
$9$		0			0
$10$	8.21356	−	14.2263i	0.821356	−	1.42263i
$11$	2.77510	−	7.62453i	0.252282	−	0.693139i	−0.747307	−	0.664479i	$-0.768654\pi$
$11$	2.77510	−	7.62453i	0.252282	−	0.693139i	0.999589	−	0.0286605i	$-0.00912418\pi$
$12$		0			0
$13$	7.43797	+	6.24120i	0.572152	+	0.480092i	0.882359	−	0.470577i	$-0.155954\pi$
$13$	7.43797	+	6.24120i	0.572152	+	0.480092i	−0.310207	+	0.950669i	$0.600399\pi$
$14$	13.7120	−	16.3413i	0.979429	−	1.16724i
$15$		0			0
$16$	18.0230	+	6.55984i	1.12644	+	0.409990i
$17$	−13.0143	−	7.51380i	−0.765546	−	0.441988i	0.0657372	−	0.997837i	$-0.479060\pi$
$17$	−13.0143	−	7.51380i	−0.765546	−	0.441988i	−0.831284	+	0.555849i	$0.812393\pi$
$18$		0			0
$19$	8.93226	+	15.4711i	0.470119	+	0.814270i	0.999416	−	0.0341664i	$-0.0108776\pi$
$19$	8.93226	+	15.4711i	0.470119	+	0.814270i	−0.529297	+	0.848437i	$0.677544\pi$
$20$	17.8880	−	3.15414i	0.894400	−	0.157707i
$21$		0			0
$22$	20.0363	−	7.29262i	0.910741	−	0.331483i
$23$	−25.9334	−	4.57276i	−1.12754	−	0.198816i	−0.421391	−	0.906879i	$-0.638458\pi$
$23$	−25.9334	−	4.57276i	−1.12754	−	0.198816i	−0.706149	+	0.708064i	$0.749569\pi$
$24$		0			0
$25$	−10.7831	+	9.04812i	−0.431325	+	0.361925i
$26$			25.5156i			0.981367i
$27$		0			0
$28$	23.5875			0.842411
$29$	9.75225	+	11.6223i	0.336284	+	0.400768i	0.907514	−	0.420022i	$-0.137978\pi$
$29$	9.75225	+	11.6223i	0.336284	+	0.400768i	−0.571229	+	0.820791i	$0.693533\pi$
$30$		0			0
$31$	5.68415	−	32.2364i	0.183360	−	1.03988i	−0.744685	−	0.667416i	$-0.767400\pi$
$31$	5.68415	−	32.2364i	0.183360	−	1.03988i	0.928045	−	0.372468i	$-0.121488\pi$
$32$	13.3043	+	36.5533i	0.415760	+	1.14229i
$33$		0			0
$34$	−6.85748	−	38.8907i	−0.201691	−	1.14384i
$35$	−43.9457	+	25.3721i	−1.25559	+	0.724917i
$36$		0			0
$37$	−15.8096	+	27.3831i	−0.427287	+	0.740083i	−0.996631	−	0.0820163i	$-0.973864\pi$
$37$	−15.8096	+	27.3831i	−0.427287	+	0.740083i	0.569344	+	0.822100i	$0.307197\pi$
$38$	−16.0564	+	44.1145i	−0.422536	+	1.16091i
$39$		0			0
$40$	−13.7704	−	11.5547i	−0.344259	−	0.288867i
$41$	10.6189	−	12.6551i	0.258997	−	0.308660i	−0.620839	−	0.783938i	$-0.713208\pi$
$41$	10.6189	−	12.6551i	0.258997	−	0.308660i	0.879836	+	0.475278i	$0.157652\pi$
$42$		0			0
$43$	78.7688	+	28.6695i	1.83183	+	0.666733i	0.992367	+	0.123320i	$0.0393542\pi$
$43$	78.7688	+	28.6695i	1.83183	+	0.666733i	0.839466	+	0.543412i	$0.182868\pi$
$44$	20.4179	+	11.7883i	0.464044	+	0.267916i
$45$		0			0
$46$	−34.6005	−	59.9298i	−0.752185	−	1.30282i
$47$	−12.9701	+	2.28698i	−0.275959	+	0.0486591i	−0.309915	−	0.950764i	$-0.600301\pi$
$47$	−12.9701	+	2.28698i	−0.275959	+	0.0486591i	0.0339557	+	0.999423i	$0.489189\pi$
$48$		0			0
$49$	−15.8769	+	5.77871i	−0.324018	+	0.117933i
$50$	−36.4290	−	6.42341i	−0.728579	−	0.128468i
$51$		0			0
$52$	−21.6126	+	18.1352i	−0.415628	+	0.348753i
$53$		−	25.7140i		−	0.485169i	−0.970130	−	0.242585i	$-0.922005\pi$
$53$		−	25.7140i		−	0.485169i	0.970130	−	0.242585i	$-0.0779952\pi$
$54$		0			0
$55$	−50.7206			−0.922193
$56$	−15.0048	−	17.8820i	−0.267943	−	0.319322i
$57$		0			0
$58$	−6.92328	+	39.2639i	−0.119367	+	0.676963i
$59$	7.76763	+	21.3414i	0.131655	+	0.361718i	0.987951	−	0.154766i	$-0.0494625\pi$
$59$	7.76763	+	21.3414i	0.131655	+	0.361718i	−0.856296	+	0.516485i	$0.827240\pi$
$60$		0			0
$61$	5.91937	+	33.5704i	0.0970388	+	0.550335i	0.994104	+	0.108435i	$0.0345840\pi$
$61$	5.91937	+	33.5704i	0.0970388	+	0.550335i	−0.897065	+	0.441899i	$0.854305\pi$
$62$	74.4955	−	43.0100i	1.20154	−	0.693710i
$63$		0			0
$64$	−12.7517	+	22.0867i	−0.199246	+	0.345104i
$65$	20.7591	−	57.0353i	0.319371	−	0.877466i
$66$		0			0
$67$	6.20835	+	5.20943i	0.0926620	+	0.0777526i	0.687942	−	0.725766i	$-0.258514\pi$
$67$	6.20835	+	5.20943i	0.0926620	+	0.0777526i	−0.595280	+	0.803518i	$0.702959\pi$
$68$	28.0679	−	33.4501i	0.412764	−	0.491913i
$69$		0			0
$70$	−125.307	−	45.6081i	−1.79010	−	0.651545i
$71$	35.7557	+	20.6436i	0.503601	+	0.290754i	0.730199	−	0.683234i	$-0.239427\pi$
$71$	35.7557	+	20.6436i	0.503601	+	0.290754i	−0.226598	+	0.973988i	$0.572760\pi$
$72$		0			0
$73$	40.4046	+	69.9827i	0.553487	+	0.958668i	0.998020	+	0.0629050i	$0.0200365\pi$
$73$	40.4046	+	69.9827i	0.553487	+	0.958668i	−0.444532	+	0.895763i	$0.646630\pi$
$74$	−81.8291	+	14.4287i	−1.10580	+	0.194982i
$75$		0			0
$76$	−48.7787	+	17.7540i	−0.641826	+	0.233605i
$77$	−64.8646	−	11.4374i	−0.842398	−	0.148537i
$78$		0			0
$79$	−21.1671	+	17.7613i	−0.267937	+	0.224826i	−0.766850	−	0.641826i	$-0.778177\pi$
$79$	−21.1671	+	17.7613i	−0.267937	+	0.224826i	0.498913	+	0.866652i	$0.333733\pi$
$80$		−	119.894i		−	1.49868i
$81$		0			0
$82$	43.4126			0.529421
$83$	−11.3065	−	13.4746i	−0.136223	−	0.162344i	0.693620	−	0.720341i	$-0.256015\pi$
$83$	−11.3065	−	13.4746i	−0.136223	−	0.162344i	−0.829843	+	0.557997i	$0.811570\pi$
$84$		0			0
$85$	−16.3124	+	92.5121i	−0.191910	+	1.08838i
$86$	75.3398	+	206.994i	0.876044	+	2.40691i
$87$		0			0
$88$	−4.05165	−	22.9780i	−0.0460414	−	0.261114i
$89$	24.4986	−	14.1443i	0.275265	−	0.158924i	−0.356013	−	0.934481i	$-0.615864\pi$
$89$	24.4986	−	14.1443i	0.275265	−	0.158924i	0.631278	+	0.775557i	$0.282531\pi$
$90$		0			0
$91$	39.4094	−	68.2590i	0.433070	−	0.750099i
$92$	26.1706	−	71.9030i	0.284463	−	0.781555i
$93$		0			0
$94$	−26.5124	−	22.2466i	−0.282047	−	0.236666i
$95$	71.7821	−	85.5466i	0.755601	−	0.900490i
$96$		0			0
$97$	−158.461	−	57.6752i	−1.63362	−	0.594590i	−0.647714	−	0.761883i	$-0.724275\pi$
$97$	−158.461	−	57.6752i	−1.63362	−	0.594590i	−0.985907	+	0.167294i	$0.946497\pi$
$98$	−38.4516	−	22.2000i	−0.392363	−	0.226531i
$99$		0			0
$100$	−20.4510	−	35.4221i	−0.204510	−	0.354221i
$101$	68.7674	−	12.1255i	0.680865	−	0.120055i	0.177490	−	0.984123i	$-0.443202\pi$
$101$	68.7674	−	12.1255i	0.680865	−	0.120055i	0.503376	+	0.864068i	$0.332091\pi$
$102$		0			0
$103$	−65.6495	+	23.8945i	−0.637374	+	0.231985i	−0.640438	−	0.768010i	$-0.721247\pi$
$103$	−65.6495	+	23.8945i	−0.637374	+	0.231985i	0.00306387	+	0.999995i	$0.499025\pi$
$104$	27.4970	+	4.84847i	0.264395	+	0.0466199i
$105$		0			0
$106$	51.7639	−	43.4351i	0.488339	−	0.409765i
$107$			121.432i			1.13488i	0.823416	+	0.567438i	$0.192065\pi$
$107$			121.432i			1.13488i	−0.823416	+	0.567438i	$0.807935\pi$
$108$		0			0
$109$	−119.633			−1.09755			−0.548777	−	0.835969i	$-0.684907\pi$
$109$	−119.633			−1.09755			−0.548777	+	0.835969i	$0.684907\pi$
$110$	−85.6755	−	102.104i	−0.778868	−	0.928218i
$111$		0			0
$112$	27.0359	−	153.328i	0.241392	−	1.36900i
$113$	−42.5349	−	116.864i	−0.376415	−	1.03419i	−0.972831	−	0.231516i	$-0.925631\pi$
$113$	−42.5349	−	116.864i	−0.376415	−	1.03419i	0.596416	−	0.802675i	$-0.296591\pi$
$114$		0			0
$115$	28.5848	+	162.113i	0.248564	+	1.40967i
$116$	−38.1787	+	22.0425i	−0.329127	+	0.190021i
$117$		0			0
$118$	−29.8408	+	51.6859i	−0.252889	+	0.438016i
$119$	−41.7225	+	114.632i	−0.350609	+	0.963291i
$120$		0			0
$121$	42.2591	+	35.4596i	0.349249	+	0.293054i
$122$	−57.5807	+	68.6220i	−0.471973	+	0.562476i
$123$		0			0
$124$	89.3787	+	32.5312i	0.720796	+	0.262348i
$125$	−59.1363	−	34.1424i	−0.473091	−	0.273139i
$126$		0			0
$127$	58.7300	+	101.723i	0.462441	+	0.800971i	0.999082	−	0.0428396i	$-0.0136404\pi$
$127$	58.7300	+	101.723i	0.462441	+	0.800971i	−0.536641	+	0.843811i	$0.680307\pi$
$128$	87.2312	−	15.3812i	0.681494	−	0.120166i
$129$		0			0
$130$	149.881	−	54.5524i	1.15293	−	0.419634i
$131$	−4.64121	−	0.818370i	−0.0354291	−	0.00624710i	0.155906	−	0.987772i	$-0.450170\pi$
$131$	−4.64121	−	0.818370i	−0.0354291	−	0.00624710i	−0.191335	+	0.981525i	$0.561282\pi$
$132$		0			0
$133$	111.090	−	93.2155i	0.835262	−	0.700868i
$134$			21.2974i			0.158936i
$135$		0			0
$136$	−43.2139			−0.317749
$137$	141.921	+	169.135i	1.03592	+	1.23456i	0.971599	+	0.236633i	$0.0760440\pi$
$137$	141.921	+	169.135i	1.03592	+	1.23456i	0.0643220	+	0.997929i	$0.479512\pi$
$138$		0			0
$139$	−6.21061	+	35.2221i	−0.0446807	+	0.253397i	−0.998964	−	0.0455067i	$-0.985510\pi$
$139$	−6.21061	+	35.2221i	−0.0446807	+	0.253397i	0.954283	+	0.298903i	$0.0966209\pi$
$140$	−50.4303	−	138.556i	−0.360216	−	0.989686i
$141$		0			0
$142$	18.8404	+	106.849i	0.132679	+	0.752457i
$143$	68.2274	−	39.3911i	0.477114	−	0.275462i
$144$		0			0
$145$	47.4203	−	82.1344i	0.327037	−	0.566444i
$146$	−72.6301	+	199.549i	−0.497466	+	1.36678i
$147$		0			0
$148$	−70.3816	−	59.0572i	−0.475551	−	0.399035i
$149$	−107.819	+	128.493i	−0.723615	+	0.862371i	−0.994977	−	0.100106i	$-0.968082\pi$
$149$	−107.819	+	128.493i	−0.723615	+	0.862371i	0.271361	+	0.962478i	$0.412526\pi$
$150$		0			0
$151$	78.6693	+	28.6333i	0.520989	+	0.189624i	0.589110	−	0.808053i	$-0.299478\pi$
$151$	78.6693	+	28.6333i	0.520989	+	0.189624i	−0.0681215	+	0.997677i	$0.521701\pi$
$152$	44.4893	+	25.6859i	0.292693	+	0.168986i
$153$		0			0
$154$	−86.5428	−	149.896i	−0.561966	−	0.973354i
$155$	−201.513	+	35.5322i	−1.30009	+	0.229240i
$156$		0			0
$157$	69.9547	−	25.4614i	0.445571	−	0.162175i	−0.109483	−	0.993989i	$-0.534920\pi$
$157$	69.9547	−	25.4614i	0.445571	−	0.162175i	0.555055	+	0.831814i	$0.312697\pi$
$158$	−71.5093	−	12.6090i	−0.452590	−	0.0798039i
$159$		0			0
$160$	186.274	−	156.302i	1.16421	−	0.976890i
$161$			213.765i			1.32773i
$162$		0			0
$163$	254.830			1.56337			0.781687	−	0.623670i	$-0.214359\pi$
$163$	254.830			1.56337			0.781687	+	0.623670i	$0.214359\pi$
$164$	30.8554	+	36.7721i	0.188143	+	0.224220i
$165$		0			0
$166$	8.02667	−	45.5215i	0.0483534	−	0.274226i
$167$	54.2442	+	149.035i	0.324816	+	0.892424i	0.989401	+	0.145211i	$0.0463861\pi$
$167$	54.2442	+	149.035i	0.324816	+	0.892424i	−0.664585	+	0.747213i	$0.731392\pi$
$168$		0			0
$169$	−12.9757	−	73.5888i	−0.0767792	−	0.435437i
$170$	−213.787	+	123.430i	−1.25757	+	0.726060i
$171$		0			0
$172$	−121.784	+	210.937i	−0.708049	+	1.22638i
$173$	101.950	−	280.105i	0.589305	−	1.61910i	−0.182473	−	0.983211i	$-0.558410\pi$
$173$	101.950	−	280.105i	0.589305	−	1.61910i	0.771778	−	0.635892i	$-0.219367\pi$
$174$		0			0
$175$	87.5334	+	73.4492i	0.500191	+	0.419710i
$176$	100.031	−	119.213i	0.568360	−	0.677345i
$177$		0			0
$178$	69.8555	+	25.4253i	0.392446	+	0.142839i
$179$	25.3997	+	14.6645i	0.141898	+	0.0819248i	0.569268	−	0.822152i	$-0.307227\pi$
$179$	25.3997	+	14.6645i	0.141898	+	0.0819248i	−0.427370	+	0.904077i	$0.640560\pi$
$180$		0			0
$181$	−41.7019	−	72.2299i	−0.230397	−	0.399060i	0.727528	−	0.686078i	$-0.240669\pi$
$181$	−41.7019	−	72.2299i	−0.230397	−	0.399060i	−0.957925	+	0.287018i	$0.907336\pi$
$182$	203.979	−	35.9670i	1.12076	−	0.197621i
$183$		0			0
$184$	−71.1587	+	25.8996i	−0.386732	+	0.140759i
$185$	194.653	+	34.3225i	1.05218	+	0.185527i
$186$		0			0
$187$	−93.4052	+	78.3763i	−0.499493	+	0.419124i
$188$		−	38.2688i		−	0.203557i
$189$		0			0
$190$	293.463			1.54454
$191$	100.885	+	120.230i	0.528193	+	0.629476i	0.962498	−	0.271290i	$-0.0874503\pi$
$191$	100.885	+	120.230i	0.528193	+	0.629476i	−0.434305	+	0.900766i	$0.643006\pi$
$192$		0			0
$193$	−7.20107	+	40.8393i	−0.0373112	+	0.211602i	−0.997764	−	0.0668419i	$-0.978708\pi$
$193$	−7.20107	+	40.8393i	−0.0373112	+	0.211602i	0.960452	+	0.278444i	$0.0898188\pi$
$194$	−151.563	−	416.416i	−0.781253	−	2.14648i
$195$		0			0
$196$	−8.52517	−	48.3486i	−0.0434958	−	0.246677i
$197$	−182.437	+	105.330i	−0.926074	+	0.534669i	−0.885568	−	0.464510i	$-0.846230\pi$
$197$	−182.437	+	105.330i	−0.926074	+	0.534669i	−0.0405063	+	0.999179i	$0.512897\pi$
$198$		0			0
$199$	87.7654	−	152.014i	0.441032	−	0.763890i	−0.556734	−	0.830691i	$-0.687946\pi$
$199$	87.7654	−	152.014i	0.441032	−	0.763890i	0.997766	+	0.0668004i	$0.0212791\pi$
$200$	−13.8445	+	38.0374i	−0.0692224	+	0.190187i
$201$		0			0
$202$	140.569	+	117.951i	0.695886	+	0.583918i
$203$	79.1651	−	94.3453i	0.389976	−	0.464755i
$204$		0			0
$205$	−97.0407	−	35.3199i	−0.473369	−	0.172292i
$206$	−158.994	−	91.7952i	−0.771815	−	0.445608i
$207$		0			0
$208$	93.1133	+	161.277i	0.447660	+	0.775370i
$209$	142.748	−	25.1703i	0.683005	−	0.120432i
$210$		0			0
$211$	245.123	−	89.2173i	1.16172	−	0.422831i	0.312008	−	0.950080i	$-0.398999\pi$
$211$	245.123	−	89.2173i	1.16172	−	0.422831i	0.849711	+	0.527249i	$0.176776\pi$
$212$	73.5824	+	12.9746i	0.347087	+	0.0612007i
$213$		0			0
$214$	−244.450	+	205.118i	−1.14229	+	0.958495i
$215$		−	523.993i		−	2.43718i
$216$		0			0
$217$	−265.720			−1.22452
$218$	−202.081	−	240.830i	−0.926975	−	1.10473i
$219$		0			0
$220$	25.5922	−	145.141i	0.116328	−	0.659731i
$221$	−49.9048	−	137.112i	−0.225813	−	0.620417i
$222$		0			0
$223$	−67.5868	−	383.304i	−0.303080	−	1.71885i	−0.632408	−	0.774636i	$-0.717933\pi$
$223$	−67.5868	−	383.304i	−0.303080	−	1.71885i	0.329328	−	0.944216i	$-0.393178\pi$
$224$	273.464	−	157.885i	1.22082	−	0.704842i
$225$		0			0
$226$	163.406	−	283.027i	0.723035	−	1.25233i
$227$	119.171	−	327.419i	0.524981	−	1.44237i	−0.339930	−	0.940451i	$-0.610404\pi$
$227$	119.171	−	327.419i	0.524981	−	1.44237i	0.864912	−	0.501924i	$-0.167374\pi$
$228$		0			0
$229$	−279.242	−	234.311i	−1.21940	−	1.02319i	−0.998856	−	0.0478162i	$-0.984774\pi$
$229$	−279.242	−	234.311i	−1.21940	−	1.02319i	−0.220539	−	0.975378i	$-0.570782\pi$
$230$	−278.059	+	331.378i	−1.20895	+	1.44077i
$231$		0			0
$232$	40.9975	+	14.9219i	0.176713	+	0.0643184i
$233$	164.260	+	94.8353i	0.704976	+	0.407018i	0.809198	−	0.587536i	$-0.199902\pi$
$233$	164.260	+	94.8353i	0.704976	+	0.407018i	−0.104222	+	0.994554i	$0.533235\pi$
$234$		0			0
$235$	41.1641	+	71.2983i	0.175166	+	0.303397i
$236$	−64.9893	+	11.4594i	−0.275378	+	0.0485566i
$237$		0			0
$238$	−301.237	+	109.641i	−1.26570	+	0.460678i
$239$	301.448	+	53.1535i	1.26129	+	0.222400i	0.764018	−	0.645195i	$-0.223224\pi$
$239$	301.448	+	53.1535i	1.26129	+	0.222400i	0.497272	+	0.867594i	$0.334335\pi$
$240$		0			0
$241$	−225.911	+	189.561i	−0.937388	+	0.786562i	−0.977129	−	0.212648i	$-0.931791\pi$
$241$	−225.911	+	189.561i	−0.937388	+	0.786562i	0.0397406	+	0.999210i	$0.487347\pi$
$242$			144.967i			0.599039i
$243$		0			0
$244$	−99.0509			−0.405946
$245$	67.8897	+	80.9078i	0.277101	+	0.330236i
$246$		0			0
$247$	−30.1205	+	170.822i	−0.121945	+	0.691587i
$248$	−32.1944	−	88.4535i	−0.129816	−	0.356667i
$249$		0			0
$250$	−31.1601	−	176.718i	−0.124640	−	0.706870i
$251$	158.404	−	91.4547i	0.631092	−	0.364361i	−0.150083	−	0.988673i	$-0.547954\pi$
$251$	158.404	−	91.4547i	0.631092	−	0.364361i	0.781175	+	0.624312i	$0.214621\pi$
$252$		0			0
$253$	−106.833	+	185.040i	−0.422265	+	0.731384i
$254$	−105.571	+	290.055i	−0.415635	+	1.14195i
$255$		0			0
$256$	256.459	+	215.194i	1.00179	+	0.840603i
$257$	−172.501	+	205.579i	−0.671210	+	0.799918i	−0.988948	−	0.148261i	$-0.952632\pi$
$257$	−172.501	+	205.579i	−0.671210	+	0.799918i	0.317738	+	0.948179i	$0.397077\pi$
$258$		0			0
$259$	241.194	+	87.7874i	0.931251	+	0.338948i
$260$	152.736	+	88.1822i	0.587447	+	0.339162i
$261$		0			0
$262$	−6.19233	−	10.7254i	−0.0236348	−	0.0409368i
$263$	−346.629	+	61.1200i	−1.31798	+	0.232395i	−0.788032	−	0.615634i	$-0.788900\pi$
$263$	−346.629	+	61.1200i	−1.31798	+	0.232395i	−0.529948	+	0.848030i	$0.677789\pi$
$264$		0			0
$265$	−151.047	+	54.9766i	−0.569988	+	0.207459i
$266$	375.298	+	66.1752i	1.41089	+	0.248779i
$267$		0			0
$268$	−18.0397	+	15.1371i	−0.0673124	+	0.0564818i
$269$			164.243i			0.610570i	0.952261	+	0.305285i	$0.0987518\pi$
$269$			164.243i			0.610570i	−0.952261	+	0.305285i	$0.901248\pi$
$270$		0			0
$271$	−128.850			−0.475462			−0.237731	−	0.971331i	$-0.576404\pi$
$271$	−128.850			−0.475462			−0.237731	+	0.971331i	$0.576404\pi$
$272$	−185.267	−	220.793i	−0.681129	−	0.811738i
$273$		0			0
$274$	−100.752	+	571.394i	−0.367709	+	2.08538i
$275$	39.0634	+	107.326i	0.142049	+	0.390276i
$276$		0			0
$277$	26.0851	+	147.936i	0.0941700	+	0.534064i	0.994999	+	0.0998895i	$0.0318489\pi$
$277$	26.0851	+	147.936i	0.0941700	+	0.534064i	−0.900829	+	0.434175i	$0.857040\pi$
$278$	−81.3953	+	46.9936i	−0.292789	+	0.169042i
$279$		0			0
$280$	−72.9609	+	126.372i	−0.260575	+	0.451328i
$281$	−157.671	+	433.197i	−0.561106	+	1.54163i	0.256912	+	0.966435i	$0.417295\pi$
$281$	−157.671	+	433.197i	−0.561106	+	1.54163i	−0.818018	+	0.575192i	$0.804927\pi$
$282$		0			0
$283$	−52.7479	−	44.2607i	−0.186388	−	0.156398i	0.544819	−	0.838554i	$-0.316598\pi$
$283$	−52.7479	−	44.2607i	−0.186388	−	0.156398i	−0.731207	+	0.682155i	$0.761043\pi$
$284$	−77.1144	+	91.9013i	−0.271529	+	0.323596i
$285$		0			0
$286$	194.544	+	70.8083i	0.680224	+	0.247581i
$287$	−116.137	−	67.0517i	−0.404658	−	0.233630i
$288$		0			0
$289$	−31.5856	−	54.7078i	−0.109293	−	0.189300i
$290$	245.443	−	43.2782i	0.846355	−	0.149235i
$291$		0			0
$292$	−220.648	+	80.3092i	−0.755643	+	0.275032i
$293$	−503.007	−	88.6936i	−1.71675	−	0.302709i	−0.773252	−	0.634098i	$-0.781371\pi$
$293$	−503.007	−	88.6936i	−1.71675	−	0.302709i	−0.943494	+	0.331390i	$0.892482\pi$
$294$		0			0
$295$	108.755	−	91.2560i	0.368660	−	0.309342i
$296$			90.9255i			0.307181i
$297$		0			0
$298$	−440.789			−1.47916
$299$	−164.352	−	195.868i	−0.549674	−	0.655076i
$300$		0			0
$301$	118.159	−	670.114i	0.392556	−	2.22629i
$302$	75.2446	+	206.733i	0.249154	+	0.684546i
$303$		0			0
$304$	59.4981	+	337.430i	0.195717	+	1.10997i
$305$	184.541	−	106.545i	0.605053	−	0.349327i
$306$		0			0
$307$	−26.3017	+	45.5559i	−0.0856734	+	0.148391i	−0.905678	−	0.423966i	$-0.860637\pi$
$307$	−26.3017	+	45.5559i	−0.0856734	+	0.148391i	0.820005	+	0.572357i	$0.193971\pi$
$308$	65.4578	−	179.844i	0.212525	−	0.583909i
$309$		0			0
$310$	−411.918	−	345.640i	−1.32877	−	1.11497i
$311$	−228.077	+	271.812i	−0.733368	+	0.873993i	−0.995856	−	0.0909416i	$-0.971012\pi$
$311$	−228.077	+	271.812i	−0.733368	+	0.873993i	0.262489	+	0.964935i	$0.415457\pi$
$312$		0			0
$313$	−158.102	−	57.5444i	−0.505118	−	0.183848i	0.0768764	−	0.997041i	$-0.475505\pi$
$313$	−158.102	−	57.5444i	−0.505118	−	0.183848i	−0.581995	+	0.813193i	$0.697728\pi$
$314$	169.421	+	97.8150i	0.539556	+	0.311513i
$315$		0			0
$316$	−40.1448	−	69.5329i	−0.127041	−	0.220041i
$317$	−502.240	+	88.5585i	−1.58435	+	0.279365i	−0.895340	−	0.445383i	$-0.853068\pi$
$317$	−502.240	+	88.5585i	−1.58435	+	0.279365i	−0.689015	+	0.724747i	$0.741956\pi$
$318$		0			0
$319$	115.678	−	42.1033i	0.362627	−	0.131985i
$320$	157.003	+	27.6839i	0.490635	+	0.0865121i
$321$		0			0
$322$	−430.324	+	361.085i	−1.33641	+	1.12138i
$323$		−	268.461i		−	0.831149i
$324$		0			0
$325$	−136.676			−0.420541
$326$	430.450	+	512.990i	1.32040	+	1.57359i
$327$		0			0
$328$	8.24926	−	46.7839i	0.0251502	−	0.142634i
$329$	36.5655	+	100.463i	0.111141	+	0.305359i
$330$		0			0
$331$	−58.9261	−	334.186i	−0.178024	−	1.00963i	−0.934595	−	0.355714i	$-0.884238\pi$
$331$	−58.9261	−	334.186i	−0.178024	−	1.00963i	0.756570	−	0.653912i	$-0.226874\pi$
$332$	44.2634	−	25.5555i	0.133324	−	0.0769744i
$333$		0			0
$334$	−208.390	+	360.941i	−0.623921	+	1.08066i
$335$	17.3273	−	47.6064i	0.0517233	−	0.142109i
$336$		0			0
$337$	−52.2733	−	43.8625i	−0.155114	−	0.130156i	0.561928	−	0.827186i	$-0.310060\pi$
$337$	−52.2733	−	43.8625i	−0.155114	−	0.130156i	−0.717042	+	0.697030i	$0.754504\pi$
$338$	126.221	−	150.424i	0.373435	−	0.445043i
$339$		0			0
$340$	−256.499	−	93.3581i	−0.754410	−	0.274583i
$341$	−230.013	−	132.798i	−0.674526	−	0.389438i
$342$		0			0
$343$	−130.305	−	225.695i	−0.379897	−	0.658002i
$344$	237.385	−	41.8574i	0.690074	−	0.121679i
$345$		0			0
$346$	736.080	−	267.911i	2.12740	−	0.774310i
$347$	170.468	+	30.0581i	0.491262	+	0.0866227i	0.413791	−	0.910372i	$-0.364204\pi$
$347$	170.468	+	30.0581i	0.491262	+	0.0866227i	0.0774708	+	0.996995i	$0.475316\pi$
$348$		0			0
$349$	352.060	−	295.414i	1.00877	−	0.846457i	0.0205933	−	0.999788i	$-0.493444\pi$
$349$	352.060	−	295.414i	1.00877	−	0.846457i	0.988175	+	0.153331i	$0.0490000\pi$
$350$			300.278i			0.857939i
$351$		0			0
$352$	315.623			0.896655
$353$	−258.561	−	308.141i	−0.732468	−	0.872922i	0.263310	−	0.964711i	$-0.415186\pi$
$353$	−258.561	−	308.141i	−0.732468	−	0.872922i	−0.995778	+	0.0917895i	$0.970741\pi$
$354$		0			0
$355$	44.8169	−	254.169i	0.126245	−	0.715970i
$356$	28.1135	+	77.2413i	0.0789706	+	0.216970i
$357$		0			0
$358$	13.3836	+	75.9022i	0.0373844	+	0.212017i
$359$	−197.249	+	113.882i	−0.549439	+	0.317219i	−0.748896	−	0.662688i	$-0.769416\pi$
$359$	−197.249	+	113.882i	−0.549439	+	0.317219i	0.199457	+	0.979907i	$0.436082\pi$
$360$		0			0
$361$	20.9294	−	36.2507i	0.0579761	−	0.100418i
$362$	74.9622	−	205.957i	0.207078	−	0.568942i
$363$		0			0
$364$	175.443	+	147.214i	0.481987	+	0.404435i
$365$	324.702	−	386.965i	0.889595	−	1.06018i
$366$		0			0
$367$	221.266	+	80.5344i	0.602906	+	0.219440i	0.625396	−	0.780307i	$-0.284937\pi$
$367$	221.266	+	80.5344i	0.602906	+	0.219440i	−0.0224904	+	0.999747i	$0.507160\pi$
$368$	−437.401	−	252.534i	−1.18859	−	0.686233i
$369$		0			0
$370$	259.707	+	449.825i	0.701910	+	1.21574i
$371$	−205.565	+	36.2467i	−0.554084	+	0.0976999i
$372$		0			0
$373$	−613.386	+	223.254i	−1.64447	+	0.598537i	−0.987812	−	0.155655i	$-0.950251\pi$
$373$	−613.386	+	223.254i	−1.64447	+	0.598537i	−0.656655	+	0.754192i	$0.728029\pi$
$374$	−315.553	−	55.6406i	−0.843726	−	0.148772i
$375$		0			0
$376$	−29.0121	+	24.3441i	−0.0771599	+	0.0647448i
$377$			147.312i			0.390748i
$378$		0			0
$379$	625.053			1.64922			0.824608	−	0.565705i	$-0.191396\pi$
$379$	625.053			1.64922			0.824608	+	0.565705i	$0.191396\pi$
$380$	208.578	+	248.574i	0.548891	+	0.654142i
$381$		0			0
$382$	−71.6198	+	406.176i	−0.187486	+	1.06329i
$383$	−36.4387	−	100.114i	−0.0951401	−	0.261395i	0.882989	−	0.469393i	$-0.155527\pi$
$383$	−36.4387	−	100.114i	−0.0951401	−	0.261395i	−0.978129	+	0.207998i	$0.933305\pi$
$384$		0			0
$385$	71.4963	+	405.476i	0.185705	+	1.05318i
$386$	−94.3760	+	54.4880i	−0.244497	+	0.141161i
$387$		0			0
$388$	244.997	−	424.347i	0.631436	−	1.09368i
$389$	203.034	−	557.832i	0.521939	−	1.43401i	−0.346421	−	0.938079i	$-0.612603\pi$
$389$	203.034	−	557.832i	0.521939	−	1.43401i	0.868359	−	0.495935i	$-0.165175\pi$
$390$		0			0
$391$	303.146	+	254.370i	0.775309	+	0.650562i
$392$	−31.2306	+	37.2192i	−0.0796700	+	0.0949470i
$393$		0			0
$394$	−520.201	−	189.338i	−1.32031	−	0.480553i
$395$	149.587	+	86.3642i	0.378702	+	0.218643i
$396$		0			0
$397$	−187.410	−	324.603i	−0.472064	−	0.817640i	0.527425	−	0.849602i	$-0.323158\pi$
$397$	−187.410	−	324.603i	−0.472064	−	0.817640i	−0.999489	+	0.0319623i	$0.989824\pi$
$398$	454.265	−	80.0992i	1.14137	−	0.201254i
$399$		0			0
$400$	−253.699	+	92.3387i	−0.634246	+	0.230847i
$401$	270.237	+	47.6500i	0.673907	+	0.118828i	0.500121	−	0.865955i	$-0.333289\pi$
$401$	270.237	+	47.6500i	0.673907	+	0.118828i	0.173786	+	0.984783i	$0.444400\pi$
$402$		0			0
$403$	243.472	−	204.298i	0.604150	−	0.506942i
$404$			202.901i			0.502231i
$405$		0			0
$406$	323.646			0.797158
$407$	164.910	+	196.532i	0.405184	+	0.482879i
$408$		0			0
$409$	−95.7625	+	543.096i	−0.234138	+	1.32786i	0.610283	+	0.792183i	$0.291056\pi$
$409$	−95.7625	+	543.096i	−0.234138	+	1.32786i	−0.844421	+	0.535680i	$0.820055\pi$
$410$	−92.8163	−	255.011i	−0.226381	−	0.621977i
$411$		0			0
$412$	−35.2508	−	199.917i	−0.0855602	−	0.485236i
$413$	159.660	−	92.1798i	0.386586	−	0.223196i
$414$		0			0
$415$	−54.9779	+	95.2245i	−0.132477	+	0.229457i
$416$	−129.179	+	354.917i	−0.310527	+	0.853167i
$417$		0			0
$418$	291.795	+	244.845i	0.698073	+	0.585753i
$419$	−56.3003	+	67.0960i	−0.134368	+	0.160134i	−0.829033	−	0.559200i	$-0.811108\pi$
$419$	−56.3003	+	67.0960i	−0.134368	+	0.160134i	0.694665	+	0.719334i	$0.255553\pi$
$420$		0			0
$421$	−278.393	−	101.327i	−0.661266	−	0.240681i	−0.0104830	−	0.999945i	$-0.503337\pi$
$421$	−278.393	−	101.327i	−0.661266	−	0.240681i	−0.650783	+	0.759264i	$0.725559\pi$
$422$	593.653	+	342.746i	1.40676	+	0.812194i
$423$		0			0
$424$	−36.9720	−	64.0374i	−0.0871981	−	0.151032i
$425$	208.321	−	36.7325i	0.490166	−	0.0864295i
$426$		0			0
$427$	260.028	−	94.6424i	0.608965	−	0.221645i
$428$	−347.485	−	61.2711i	−0.811882	−	0.143157i
$429$		0			0
$430$	1054.83	−	885.111i	2.45310	−	2.05840i
$431$		−	586.175i		−	1.36003i	−0.733196	−	0.680017i	$-0.761972\pi$
$431$		−	586.175i		−	1.36003i	0.733196	−	0.680017i	$-0.238028\pi$
$432$		0			0
$433$	415.367			0.959277			0.479639	−	0.877466i	$-0.340768\pi$
$433$	415.367			0.959277			0.479639	+	0.877466i	$0.340768\pi$
$434$	−448.844	−	534.912i	−1.03420	−	1.23252i
$435$		0			0
$436$	60.3638	−	342.340i	0.138449	−	0.785183i
$437$	−160.898	−	442.064i	−0.368188	−	1.01159i
$438$		0			0
$439$	58.0607	+	329.279i	0.132257	+	0.750065i	0.976731	+	0.214469i	$0.0688021\pi$
$439$	58.0607	+	329.279i	0.132257	+	0.750065i	−0.844474	+	0.535596i	$0.820087\pi$
$440$	−126.313	+	72.9270i	−0.287076	+	0.165743i
$441$		0			0
$442$	191.719	−	332.067i	0.433753	−	0.751282i
$443$	−154.471	+	424.404i	−0.348692	+	0.958024i	0.634091	+	0.773259i	$0.281375\pi$
$443$	−154.471	+	424.404i	−0.348692	+	0.958024i	−0.982783	+	0.184765i	$0.940848\pi$
$444$		0			0
$445$	−135.463	−	113.667i	−0.304412	−	0.255432i
$446$	657.451	−	783.520i	1.47411	−	1.75677i
$447$		0			0
$448$	194.542	+	70.8077i	0.434247	+	0.158053i
$449$	−165.422	−	95.5067i	−0.368424	−	0.212710i	0.304346	−	0.952562i	$-0.401562\pi$
$449$	−165.422	−	95.5067i	−0.368424	−	0.212710i	−0.672770	+	0.739852i	$0.734896\pi$
$450$		0			0
$451$	−67.0206	−	116.083i	−0.148604	−	0.257390i
$452$	355.876	−	62.7505i	0.787336	−	0.138829i
$453$		0			0
$454$	860.416	−	313.166i	1.89519	−	0.689792i
$455$	−485.219	−	85.5573i	−1.06642	−	0.188038i
$456$		0			0
$457$	−295.504	+	247.957i	−0.646616	+	0.542575i	−0.906042	−	0.423188i	$-0.860911\pi$
$457$	−295.504	+	247.957i	−0.646616	+	0.542575i	0.259426	+	0.965763i	$0.416467\pi$
$458$		−	957.923i		−	2.09153i
$459$		0			0
$460$	−478.320			−1.03983
$461$	278.361	+	331.738i	0.603821	+	0.719606i	0.978199	−	0.207670i	$-0.0665882\pi$
$461$	278.361	+	331.738i	0.603821	+	0.719606i	−0.374378	+	0.927276i	$0.622144\pi$
$462$		0			0
$463$	96.0025	−	544.457i	0.207349	−	1.17593i	−0.686352	−	0.727270i	$-0.740789\pi$
$463$	96.0025	−	544.457i	0.207349	−	1.17593i	0.893701	−	0.448664i	$-0.148100\pi$
$464$	99.5246	+	273.441i	0.214493	+	0.589314i
$465$		0			0
$466$	86.5515	+	490.858i	0.185733	+	1.05334i
$467$	−186.467	+	107.657i	−0.399286	+	0.230528i	−0.686176	−	0.727436i	$-0.740712\pi$
$467$	−186.467	+	107.657i	−0.399286	+	0.230528i	0.286890	+	0.957964i	$0.407379\pi$
$468$		0			0
$469$	32.8943	−	56.9747i	0.0701372	−	0.121481i
$470$	−73.9954	+	203.301i	−0.157437	+	0.432555i
$471$		0			0
$472$	50.0293	+	41.9796i	0.105994	+	0.0889398i
$473$	437.183	−	521.015i	0.924277	−	1.10151i
$474$		0			0
$475$	−236.302	−	86.0070i	−0.497479	−	0.181067i
$476$	−306.975	−	177.232i	−0.644905	−	0.372336i
$477$		0			0
$478$	402.194	+	696.621i	0.841411	+	1.45737i
$479$	223.049	−	39.3296i	0.465656	−	0.0821077i	0.0641024	−	0.997943i	$-0.479582\pi$
$479$	223.049	−	39.3296i	0.465656	−	0.0821077i	0.401553	+	0.915836i	$0.368470\pi$
$480$		0			0
$481$	−288.495	+	105.004i	−0.599781	+	0.218303i
$482$	−763.200	−	134.573i	−1.58340	−	0.279197i
$483$		0			0
$484$	−122.793	+	103.036i	−0.253704	+	0.212883i
$485$			1054.13i			2.17347i
$486$		0			0
$487$	−443.130			−0.909919			−0.454959	−	0.890512i	$-0.650346\pi$
$487$	−443.130			−0.909919			−0.454959	+	0.890512i	$0.650346\pi$
$488$	63.0096	+	75.0919i	0.129118	+	0.153877i
$489$		0			0
$490$	−48.1960	+	273.333i	−0.0983592	+	0.557823i
$491$	228.283	+	627.203i	0.464935	+	1.27740i	0.921732	+	0.387828i	$0.126775\pi$
$491$	228.283	+	627.203i	0.464935	+	1.27740i	−0.456796	+	0.889571i	$0.651003\pi$
$492$		0			0
$493$	−39.5911	−	224.532i	−0.0803064	−	0.455440i
$494$	−394.754	+	227.912i	−0.799098	+	0.461360i
$495$		0			0
$496$	313.911	−	543.710i	0.632885	−	1.09619i
$497$	114.629	−	314.941i	0.230642	−	0.633684i
$498$		0			0
$499$	−44.0357	−	36.9503i	−0.0882478	−	0.0740487i	0.597597	−	0.801797i	$-0.296122\pi$
$499$	−44.0357	−	36.9503i	−0.0882478	−	0.0740487i	−0.685844	+	0.727748i	$0.740567\pi$
$500$	127.540	−	151.996i	0.255079	−	0.303991i
$501$		0			0
$502$	451.675	+	164.396i	0.899751	+	0.327483i
$503$	423.202	+	244.336i	0.841356	+	0.485757i	0.857725	−	0.514109i	$-0.171877\pi$
$503$	423.202	+	244.336i	0.841356	+	0.485757i	−0.0163686	+	0.999866i	$0.505211\pi$
$504$		0			0
$505$	−218.252	−	378.024i	−0.432182	−	0.748562i
$506$	−552.957	+	97.5012i	−1.09280	+	0.192690i
$507$		0			0
$508$	−320.722	+	116.733i	−0.631343	+	0.229790i
$509$	−279.933	−	49.3598i	−0.549967	−	0.0969741i	−0.108242	−	0.994125i	$-0.534522\pi$
$509$	−279.933	−	49.3598i	−0.549967	−	0.0969741i	−0.441725	+	0.897150i	$0.645633\pi$
$510$		0			0
$511$	502.508	−	421.655i	0.983382	−	0.825156i
$512$			525.459i			1.02629i
$513$		0			0
$514$	−705.227			−1.37204
$515$	280.718	+	334.547i	0.545083	+	0.649605i
$516$		0			0
$517$	−18.5562	+	105.237i	−0.0358921	+	0.203554i
$518$	230.694	+	633.827i	0.445356	+	1.22360i
$519$		0			0
$520$	−30.3083	−	171.887i	−0.0582852	−	0.330552i
$521$	35.1966	−	20.3207i	0.0675558	−	0.0390033i	−0.465842	−	0.884868i	$-0.654248\pi$
$521$	35.1966	−	20.3207i	0.0675558	−	0.0390033i	0.533397	+	0.845865i	$0.320915\pi$
$522$		0			0
$523$	−174.951	+	303.024i	−0.334514	+	0.579395i	−0.983391	−	0.181498i	$-0.941905\pi$
$523$	−174.951	+	303.024i	−0.334514	+	0.579395i	0.648877	+	0.760893i	$0.275239\pi$
$524$	4.68365	−	12.8682i	0.00893827	−	0.0245577i
$525$		0			0
$526$	−708.552	−	594.545i	−1.34706	−	1.13031i
$527$	−316.193	+	376.824i	−0.599987	+	0.715036i
$528$		0			0
$529$	154.534	+	56.2458i	0.292125	+	0.106325i
$530$	−365.815	−	211.203i	−0.690216	−	0.398497i
$531$		0			0
$532$	210.690	+	364.926i	0.396034	+	0.685951i
$533$	157.966	−	27.8536i	0.296371	−	0.0522582i
$534$		0			0
$535$	713.304	−	259.622i	1.33328	−	0.485274i
$536$	22.9513	+	4.04694i	0.0428196	+	0.00755026i
$537$		0			0
$538$	−330.633	+	277.434i	−0.614560	+	0.515677i
$539$			137.090i			0.254342i
$540$		0			0
$541$	145.531			0.269003			0.134501	−	0.990913i	$-0.457057\pi$
$541$	145.531			0.269003			0.134501	+	0.990913i	$0.457057\pi$
$542$	−217.649	−	259.384i	−0.401567	−	0.478569i
$543$		0			0
$544$	101.508	−	575.681i	0.186596	−	1.05824i
$545$	255.777	+	702.742i	0.469316	+	1.28943i
$546$		0			0
$547$	84.3980	+	478.645i	0.154292	+	0.875036i	0.959430	+	0.281948i	$0.0909805\pi$
$547$	84.3980	+	478.645i	0.154292	+	0.875036i	−0.805137	+	0.593088i	$0.797908\pi$
$548$	−555.602	+	320.777i	−1.01387	+	0.585359i
$549$		0			0
$550$	−150.070	+	259.928i	−0.272854	+	0.472597i
$551$	−92.7002	+	254.692i	−0.168240	+	0.462235i
$552$		0			0
$553$	171.826	+	144.179i	0.310716	+	0.260722i
$554$	−253.743	+	302.399i	−0.458020	+	0.545847i
$555$		0			0
$556$	−97.6570	−	35.5443i	−0.175642	−	0.0639285i
$557$	2.82805	+	1.63278i	0.00507730	+	0.00293138i	0.502537	−	0.864556i	$-0.332400\pi$
$557$	2.82805	+	1.63278i	0.00507730	+	0.00293138i	−0.497459	+	0.867487i	$0.665734\pi$
$558$		0			0
$559$	406.948	+	704.855i	0.727993	+	1.26092i
$560$	−958.471	+	169.004i	−1.71155	+	0.301793i
$561$		0			0
$562$	−1138.39	+	414.339i	−2.02560	+	0.737258i
$563$	654.650	+	115.432i	1.16279	+	0.205031i	0.721552	−	0.692360i	$-0.243429\pi$
$563$	654.650	+	115.432i	1.16279	+	0.205031i	0.441236	+	0.897391i	$0.354540\pi$
$564$		0			0
$565$	−595.531	+	499.710i	−1.05404	+	0.884443i
$566$		−	180.949i		−	0.319697i
$567$		0			0
$568$	118.727			0.209026
$569$	48.8101	+	58.1696i	0.0857822	+	0.102231i	0.807228	−	0.590239i	$-0.200967\pi$
$569$	48.8101	+	58.1696i	0.0857822	+	0.102231i	−0.721446	+	0.692471i	$0.756522\pi$
$570$		0			0
$571$	−51.0684	+	289.624i	−0.0894369	+	0.507222i	0.906874	+	0.421402i	$0.138462\pi$
$571$	−51.0684	+	289.624i	−0.0894369	+	0.507222i	−0.996311	+	0.0858194i	$0.972649\pi$
$572$	78.2948	+	215.113i	0.136879	+	0.376072i
$573$		0			0
$574$	−61.1948	−	347.053i	−0.106611	−	0.604622i
$575$	321.018	−	185.340i	0.558292	−	0.322330i
$576$		0			0
$577$	−529.296	+	916.768i	−0.917325	+	1.58885i	−0.113864	+	0.993496i	$0.536323\pi$
$577$	−529.296	+	916.768i	−0.917325	+	1.58885i	−0.803461	+	0.595357i	$0.797011\pi$
$578$	56.7773	−	155.994i	0.0982306	−	0.269886i
$579$		0			0
$580$	211.107	+	177.139i	0.363977	+	0.305413i
$581$	−91.7820	+	109.381i	−0.157972	+	0.188264i
$582$		0			0
$583$	−196.057	−	71.3589i	−0.336290	−	0.122399i
$584$	201.245	+	116.189i	0.344597	+	0.198953i
$585$		0			0
$586$	−671.115	−	1162.40i	−1.14525	−	1.98363i
$587$	−136.792	+	24.1200i	−0.233035	+	0.0410904i	−0.288946	−	0.957345i	$-0.593305\pi$
$587$	−136.792	+	24.1200i	−0.233035	+	0.0410904i	0.0559110	+	0.998436i	$0.482194\pi$
$588$		0			0
$589$	549.506	−	200.004i	0.932947	−	0.339565i
$590$	367.409	+	64.7841i	0.622727	+	0.109804i
$591$		0			0
$592$	−464.565	+	389.817i	−0.784739	+	0.658474i
$593$		−	145.309i		−	0.245040i	−0.992466	−	0.122520i	$-0.960902\pi$
$593$		−	145.309i		−	0.245040i	0.992466	−	0.122520i	$-0.0390975\pi$
$594$		0			0
$595$	762.563			1.28162
$596$	−313.291	−	373.365i	−0.525656	−	0.626452i
$597$		0			0
$598$	116.676	−	661.705i	0.195111	−	1.10653i
$599$	7.85706	+	21.5871i	0.0131170	+	0.0360386i	0.946078	−	0.323938i	$-0.105007\pi$
$599$	7.85706	+	21.5871i	0.0131170	+	0.0360386i	−0.932961	+	0.359977i	$0.882785\pi$
$600$		0			0
$601$	−161.036	−	913.281i	−0.267947	−	1.51960i	−0.760511	−	0.649325i	$-0.775051\pi$
$601$	−161.036	−	913.281i	−0.267947	−	1.51960i	0.492564	−	0.870276i	$-0.336060\pi$
$602$	1548.58	−	894.071i	2.57238	−	1.48517i
$603$		0			0
$604$	−121.631	+	210.670i	−0.201375	+	0.348792i
$605$	117.944	−	324.048i	0.194948	−	0.535616i
$606$		0			0
$607$	401.386	+	336.803i	0.661262	+	0.554865i	0.910465	−	0.413587i	$-0.135724\pi$
$607$	401.386	+	336.803i	0.661262	+	0.554865i	−0.249203	+	0.968451i	$0.580169\pi$
$608$	−446.683	+	532.336i	−0.734677	+	0.875553i
$609$		0			0
$610$	526.202	+	191.522i	0.862626	+	0.313970i
$611$	−110.745	−	63.9384i	−0.181251	−	0.104646i
$612$		0			0
$613$	−35.0848	−	60.7687i	−0.0572346	−	0.0991333i	0.835988	−	0.548747i	$-0.184895\pi$
$613$	−35.0848	−	60.7687i	−0.0572346	−	0.0991333i	−0.893223	+	0.449614i	$0.851562\pi$
$614$	−136.135	+	24.0043i	−0.221718	+	0.0390949i
$615$		0			0
$616$	−177.982	+	64.7801i	−0.288932	+	0.105163i
$617$	−654.465	−	115.400i	−1.06072	−	0.187034i	−0.384045	−	0.923314i	$-0.625469\pi$
$617$	−654.465	−	115.400i	−1.06072	−	0.187034i	−0.676676	+	0.736281i	$0.736580\pi$
$618$		0			0
$619$	−743.640	+	623.988i	−1.20136	+	1.00806i	−0.201768	+	0.979433i	$0.564669\pi$
$619$	−743.640	+	623.988i	−1.20136	+	1.00806i	−0.999590	+	0.0286254i	$0.990887\pi$
$620$		−	594.574i		−	0.958990i
$621$		0			0
$622$	−932.436			−1.49909
$623$	−147.607	−	175.911i	−0.236929	−	0.282361i
$624$		0			0
$625$	−135.231	+	766.934i	−0.216370	+	1.22709i
$626$	−151.219	−	415.472i	−0.241565	−	0.663693i
$627$		0			0
$628$	37.5625	+	213.028i	0.0598129	+	0.339216i
$629$	411.502	−	237.581i	0.654216	−	0.377712i
$630$		0			0
$631$	94.6588	−	163.954i	0.150014	−	0.259832i	−0.781218	−	0.624258i	$-0.785401\pi$
$631$	94.6588	−	163.954i	0.150014	−	0.259832i	0.931232	+	0.364426i	$0.118735\pi$
$632$	−27.1764	+	74.6666i	−0.0430006	+	0.118143i
$633$		0			0
$634$	−1026.64	−	861.454i	−1.61931	−	1.35876i
$635$	471.970	−	562.472i	0.743260	−	0.885783i
$636$		0			0
$637$	−154.158	−	56.1089i	−0.242006	−	0.0880830i
$638$	280.156	+	161.748i	0.439116	+	0.253524i
$639$		0			0
$640$	−276.852	−	479.522i	−0.432581	−	0.749253i
$641$	682.182	−	120.287i	1.06425	−	0.187655i	0.386006	−	0.922496i	$-0.373854\pi$
$641$	682.182	−	120.287i	1.06425	−	0.187655i	0.678240	+	0.734841i	$0.262743\pi$
$642$		0			0
$643$	−1000.40	+	364.116i	−1.55583	+	0.566277i	−0.969777	−	0.243994i	$-0.921542\pi$
$643$	−1000.40	+	364.116i	−1.55583	+	0.566277i	−0.586056	+	0.810271i	$0.699320\pi$
$644$	−611.705	−	107.860i	−0.949852	−	0.167485i
$645$		0			0
$646$	540.430	−	453.475i	0.836579	−	0.701973i
$647$		−	352.755i		−	0.545217i	−0.962125	−	0.272608i	$-0.912114\pi$
$647$		−	352.755i		−	0.545217i	0.962125	−	0.272608i	$-0.0878863\pi$
$648$		0			0
$649$	184.274			0.283935
$650$	−230.868	−	275.138i	−0.355181	−	0.423288i
$651$		0			0
$652$	−128.580	+	729.215i	−0.197209	+	1.11843i
$653$	−160.213	−	440.183i	−0.245350	−	0.674093i	−0.999842	−	0.0177840i	$-0.994339\pi$
$653$	−160.213	−	440.183i	−0.245350	−	0.674093i	0.754492	−	0.656309i	$-0.227883\pi$
$654$		0			0
$655$	5.11572	+	29.0127i	0.00781026	+	0.0442942i
$656$	274.399	−	158.424i	0.418291	−	0.241501i
$657$		0			0
$658$	−140.474	+	243.307i	−0.213486	+	0.369768i
$659$	29.3934	−	80.7577i	0.0446030	−	0.122546i	−0.915391	−	0.402565i	$-0.868119\pi$
$659$	29.3934	−	80.7577i	0.0446030	−	0.122546i	0.959994	+	0.280019i	$0.0903409\pi$
$660$		0			0
$661$	94.3093	+	79.1349i	0.142677	+	0.119720i	0.711333	−	0.702856i	$-0.248092\pi$
$661$	94.3093	+	79.1349i	0.142677	+	0.119720i	−0.568656	+	0.822575i	$0.692536\pi$
$662$	573.204	−	683.118i	0.865867	−	1.03190i
$663$		0			0
$664$	−47.5314	−	17.3000i	−0.0715834	−	0.0260542i
$665$	−785.070	−	453.260i	−1.18056	−	0.681594i
$666$		0			0
$667$	−199.763	−	346.000i	−0.299495	−	0.518741i
$668$	−453.844	+	80.0249i	−0.679407	+	0.119798i
$669$		0			0
$670$	125.104	−	45.5340i	0.186722	−	0.0679612i
$671$	272.386	+	48.0289i	0.405940	+	0.0715781i
$672$		0			0
$673$	−487.674	+	409.207i	−0.724627	+	0.608035i	−0.928661	−	0.370929i	$-0.879039\pi$
$673$	−487.674	+	409.207i	−0.724627	+	0.608035i	0.204034	+	0.978964i	$0.434595\pi$
$674$		−	179.321i		−	0.266054i
$675$		0			0
$676$	217.127			0.321194
$677$	106.259	+	126.634i	0.156955	+	0.187052i	0.838791	−	0.544453i	$-0.183263\pi$
$677$	106.259	+	126.634i	0.156955	+	0.187052i	−0.681836	+	0.731505i	$0.738818\pi$
$678$		0			0
$679$	−237.704	+	1348.09i	−0.350080	+	1.98540i
$680$	92.3916	+	253.844i	0.135870	+	0.373300i
$681$		0			0
$682$	−121.198	−	687.351i	−0.177710	−	1.00785i
$683$	−1129.58	+	652.163i	−1.65385	+	0.954851i	−0.678383	+	0.734709i	$0.737319\pi$
$683$	−1129.58	+	652.163i	−1.65385	+	0.954851i	−0.975468	+	0.220142i	$0.929348\pi$
$684$		0			0
$685$	690.092	−	1195.27i	1.00743	−	1.74493i
$686$	234.232	−	643.548i	0.341446	−	0.938116i
$687$		0			0
$688$	1231.58	+	1033.42i	1.79009	+	1.50207i
$689$	160.486	−	191.260i	0.232926	−	0.277590i
$690$		0			0
$691$	339.997	+	123.749i	0.492035	+	0.179086i	0.576108	−	0.817373i	$-0.304571\pi$
$691$	339.997	+	123.749i	0.492035	+	0.179086i	−0.0840729	+	0.996460i	$0.526793\pi$
$692$	750.099	+	433.070i	1.08396	+	0.625824i
$693$		0			0
$694$	227.439	+	393.936i	0.327722	+	0.567632i
$695$	220.178	−	38.8232i	0.316802	−	0.0558608i
$696$		0			0
$697$	−233.285	+	84.9087i	−0.334698	+	0.121820i
$698$	1189.37	+	209.719i	1.70398	+	0.300457i
$699$		0			0
$700$	−254.347	+	213.423i	−0.363353	+	0.304890i
$701$			893.344i			1.27438i	0.770705	+	0.637192i	$0.219904\pi$
$701$			893.344i			1.27438i	−0.770705	+	0.637192i	$0.780096\pi$
$702$		0			0
$703$	−564.863			−0.803504
$704$	133.013	+	158.519i	0.188939	+	0.225169i
$705$		0			0
$706$	183.557	−	1041.00i	0.259996	−	1.47451i
$707$	−193.871	−	532.655i	−0.274216	−	0.753402i
$708$		0			0
$709$	−119.924	−	680.121i	−0.169145	−	0.959268i	−0.944687	−	0.327972i	$-0.893635\pi$
$709$	−119.924	−	680.121i	−0.169145	−	0.959268i	0.775543	−	0.631295i	$-0.217476\pi$
$710$	587.363	−	339.114i	0.827272	−	0.477626i
$711$		0			0
$712$	40.6737	−	70.4490i	0.0571260	−	0.0989452i
$713$	−294.819	+	810.007i	−0.413490	+	1.13606i
$714$		0			0
$715$	−377.259	−	316.557i	−0.527634	−	0.442738i
$716$	−54.7796	+	65.2838i	−0.0765079	+	0.0911785i
$717$		0			0
$718$	−562.436	−	204.710i	−0.783338	−	0.285112i
$719$	417.508	+	241.049i	0.580679	+	0.335255i	0.761403	−	0.648279i	$-0.224511\pi$
$719$	417.508	+	241.049i	0.580679	+	0.335255i	−0.180724	+	0.983534i	$0.557844\pi$
$720$		0			0
$721$	283.560	+	491.140i	0.393287	+	0.681192i
$722$	108.328	−	19.1012i	0.150039	−	0.0264560i
$723$		0			0
$724$	227.733	−	82.8879i	0.314548	−	0.114486i
$725$	−210.320	−	37.0850i	−0.290096	−	0.0511517i
$726$		0			0
$727$	264.311	−	221.783i	0.363563	−	0.305066i	−0.442646	−	0.896697i	$-0.645960\pi$
$727$	264.311	−	221.783i	0.363563	−	0.305066i	0.806209	+	0.591631i	$0.201516\pi$
$728$		−	226.654i		−	0.311338i
$729$		0			0
$730$	1327.46			1.81844
$731$	−809.703	−	964.966i	−1.10766	−	1.32006i
$732$		0			0
$733$	93.6439	−	531.081i	0.127754	−	0.724531i	−0.851879	−	0.523738i	$-0.824537\pi$
$733$	93.6439	−	531.081i	0.127754	−	0.724531i	0.979634	−	0.200793i	$-0.0643518\pi$
$734$	211.634	+	581.460i	0.288330	+	0.792180i
$735$		0			0
$736$	−177.877	−	1008.79i	−0.241680	−	1.37064i
$737$	56.9482	−	32.8791i	0.0772704	−	0.0446121i
$738$		0			0
$739$	−368.737	+	638.671i	−0.498968	+	0.864237i	−0.999999	−	0.00119161i	$-0.999621\pi$
$739$	−368.737	+	638.671i	−0.498968	+	0.864237i	0.501032	+	0.865429i	$0.332954\pi$
$740$	−196.433	+	539.695i	−0.265450	+	0.729317i
$741$		0			0
$742$	−420.200	−	352.590i	−0.566308	−	0.475188i
$743$	−669.302	+	797.643i	−0.900810	+	1.07354i	0.0961294	+	0.995369i	$0.469354\pi$
$743$	−669.302	+	797.643i	−0.900810	+	1.07354i	−0.996940	+	0.0781750i	$0.975091\pi$
$744$		0			0
$745$	985.303	+	358.621i	1.32255	+	0.481370i
$746$	−1485.54	−	857.674i	−1.99133	−	1.14970i
$747$		0			0
$748$	−177.150	−	306.832i	−0.236831	−	0.410204i
$749$	970.761	−	171.171i	1.29608	−	0.228533i
$750$		0			0
$751$	−226.499	+	82.4391i	−0.301597	+	0.109772i	−0.488386	−	0.872628i	$-0.662414\pi$
$751$	−226.499	+	82.4391i	−0.301597	+	0.109772i	0.186789	+	0.982400i	$0.440192\pi$
$752$	−248.762	−	43.8635i	−0.330801	−	0.0583291i
$753$		0			0
$754$	−296.549	+	248.834i	−0.393301	+	0.330019i
$755$		−	523.331i		−	0.693154i
$756$		0			0
$757$	32.7615			0.0432781			0.0216391	−	0.999766i	$-0.493112\pi$
$757$	32.7615			0.0432781			0.0216391	+	0.999766i	$0.493112\pi$
$758$	1055.82	+	1258.27i	1.39290	+	1.65999i
$759$		0			0
$760$	55.7639	−	316.253i	0.0733735	−	0.416122i
$761$	−109.225	−	300.094i	−0.143529	−	0.394342i	0.847010	−	0.531577i	$-0.178400\pi$
$761$	−109.225	−	300.094i	−0.143529	−	0.394342i	−0.990538	+	0.137236i	$0.956178\pi$
$762$		0			0
$763$	168.637	+	956.386i	0.221018	+	1.25345i
$764$	−394.950	+	228.025i	−0.516951	+	0.298462i
$765$		0			0
$766$	139.986	−	242.463i	0.182750	−	0.316531i
$767$	−75.4204	+	207.216i	−0.0983317	+	0.270164i
$768$		0			0
$769$	−364.796	−	306.100i	−0.474377	−	0.398050i	0.374011	−	0.927424i	$-0.377982\pi$
$769$	−364.796	−	306.100i	−0.474377	−	0.398050i	−0.848388	+	0.529375i	$0.822427\pi$
$770$	−695.481	+	828.842i	−0.903222	+	1.07642i
$771$		0			0
$772$	−113.231	−	41.2128i	−0.146672	−	0.0533844i
$773$	1122.62	+	648.147i	1.45229	+	0.838482i	0.998611	−	0.0526817i	$-0.0167769\pi$
$773$	1122.62	+	648.147i	1.45229	+	0.838482i	0.453682	+	0.891164i	$0.350110\pi$
$774$		0			0
$775$	230.386	+	399.040i	0.297272	+	0.514890i
$776$	−477.554	+	84.2057i	−0.615405	+	0.108513i
$777$		0			0
$778$	1465.91	−	533.548i	1.88420	−	0.685794i
$779$	290.639	+	51.2475i	0.373092	+	0.0657863i
$780$		0			0
$781$	256.623	−	215.332i	0.328583	−	0.275714i
$782$			1039.93i			1.32983i
$783$		0			0
$784$	−324.056			−0.413337
$785$	−299.127	−	356.486i	−0.381054	−	0.454122i
$786$		0			0
$787$	149.503	−	847.873i	0.189966	−	1.07735i	−0.729442	−	0.684043i	$-0.760220\pi$
$787$	149.503	−	847.873i	0.189966	−	1.07735i	0.919408	−	0.393306i	$-0.128669\pi$
$788$	−209.356	−	575.202i	−0.265681	−	0.729952i
$789$		0			0
$790$	78.8203	+	447.012i	0.0997725	+	0.565838i
$791$	−874.285	+	504.769i	−1.10529	+	0.638140i
$792$		0			0
$793$	−165.492	+	286.640i	−0.208690	+	0.361462i
$794$	336.882	−	925.576i	0.424285	−	1.16571i
$795$		0			0
$796$	390.716	+	327.849i	0.490849	+	0.411871i
$797$	−372.897	+	444.402i	−0.467876	+	0.557593i	−0.947448	−	0.319909i	$-0.896348\pi$
$797$	−372.897	+	444.402i	−0.467876	+	0.557593i	0.479572	+	0.877503i	$0.340792\pi$
$798$		0			0
$799$	185.980	+	67.6913i	0.232766	+	0.0847200i
$800$	−474.201	−	273.780i	−0.592751	−	0.342225i
$801$		0			0
$802$	360.552	+	624.494i	0.449566	+	0.778671i
$803$	645.713	−	113.857i	0.804125	−	0.141789i
$804$		0			0
$805$	1255.68	−	457.031i	1.55985	−	0.567741i
$806$	822.529	+	145.034i	1.02051	+	0.179943i
$807$		0			0
$808$	153.822	−	129.072i	0.190374	−	0.159743i
$809$		−	661.323i		−	0.817457i	−0.912656	−	0.408729i	$-0.865972\pi$
$809$		−	661.323i		−	0.817457i	0.912656	−	0.408729i	$-0.134028\pi$
$810$		0			0
$811$	−168.725			−0.208045			−0.104023	−	0.994575i	$-0.533171\pi$
$811$	−168.725			−0.208045			−0.104023	+	0.994575i	$0.533171\pi$
$812$	230.031	+	274.141i	0.283290	+	0.337612i
$813$		0			0
$814$	−117.072	+	663.949i	−0.143823	+	0.815663i
$815$	−544.828	−	1496.90i	−0.668501	−	1.83669i
$816$		0			0
$817$	260.034	+	1474.73i	0.318279	+	1.80505i
$818$	−1255.05	+	724.602i	−1.53429	+	0.885822i
$819$		0			0
$820$	150.035	−	259.868i	0.182969	−	0.316912i
$821$	−51.8428	+	142.437i	−0.0631460	+	0.173492i	−0.967253	−	0.253814i	$-0.918315\pi$
$821$	−51.8428	+	142.437i	−0.0631460	+	0.173492i	0.904107	+	0.427306i	$0.140537\pi$
$822$		0			0
$823$	172.223	+	144.512i	0.209263	+	0.175592i	0.741395	−	0.671069i	$-0.234165\pi$
$823$	172.223	+	144.512i	0.209263	+	0.175592i	−0.532132	+	0.846661i	$0.678609\pi$
$824$	−129.136	+	153.898i	−0.156718	+	0.186770i
$825$		0			0
$826$	455.256	+	165.700i	0.551158	+	0.200605i
$827$	292.855	+	169.080i	0.354117	+	0.204449i	0.666497	−	0.745508i	$-0.267793\pi$
$827$	292.855	+	169.080i	0.354117	+	0.204449i	−0.312380	+	0.949957i	$0.601126\pi$
$828$		0			0
$829$	401.806	+	695.949i	0.484688	+	0.839504i	0.999845	−	0.0175917i	$-0.00559990\pi$
$829$	401.806	+	695.949i	0.484688	+	0.839504i	−0.515157	+	0.857096i	$0.672267\pi$
$830$	−284.560	+	50.1756i	−0.342843	+	0.0604525i
$831$		0			0
$832$	−232.694	+	84.6938i	−0.279681	+	0.101795i
$833$	250.046	+	44.0899i	0.300176	+	0.0529291i
$834$		0			0
$835$	759.474	−	637.274i	0.909550	−	0.763203i
$836$			421.184i			0.503809i
$837$		0			0
$838$	−230.169			−0.274665
$839$	548.904	+	654.158i	0.654236	+	0.779688i	0.986546	−	0.163482i	$-0.0522727\pi$
$839$	548.904	+	654.158i	0.654236	+	0.779688i	−0.332311	+	0.943170i	$0.607828\pi$
$840$		0			0
$841$	106.067	−	601.537i	0.126120	−	0.715263i
$842$	−266.274	−	731.581i	−0.316240	−	0.868861i
$843$		0			0
$844$	131.620	+	746.453i	0.155948	+	0.884423i
$845$	−404.527	+	233.554i	−0.478731	+	0.276395i
$846$		0			0
$847$	223.906	−	387.816i	0.264351	−	0.457870i
$848$	168.679	−	463.443i	0.198914	−	0.546513i
$849$		0			0
$850$	425.833	+	357.316i	0.500980	+	0.420372i
$851$	535.214	−	637.843i	0.628923	−	0.749522i
$852$		0			0
$853$	750.923	+	273.313i	0.880331	+	0.320414i	0.742343	−	0.670020i	$-0.233714\pi$
$853$	750.923	+	273.313i	0.880331	+	0.320414i	0.137988	+	0.990434i	$0.455937\pi$
$854$	629.751	+	363.587i	0.737414	+	0.425746i
$855$		0			0
$856$	174.597	+	302.410i	0.203968	+	0.353283i
$857$	−1529.66	+	269.721i	−1.78490	+	0.314726i	−0.965871	−	0.259022i	$-0.916600\pi$
$857$	−1529.66	+	269.721i	−1.78490	+	0.314726i	−0.819031	+	0.573749i	$0.805489\pi$
$858$		0			0
$859$	26.5482	−	9.66277i	0.0309060	−	0.0112489i	−0.326521	−	0.945190i	$-0.605876\pi$
$859$	26.5482	−	9.66277i	0.0309060	−	0.0112489i	0.357427	+	0.933941i	$0.383654\pi$
$860$	1499.44	+	264.393i	1.74354	+	0.307433i
$861$		0			0
$862$	1180.01	−	990.146i	1.36892	−	1.14866i
$863$			951.550i			1.10261i	0.834305	+	0.551304i	$0.185869\pi$
$863$			951.550i			1.10261i	−0.834305	+	0.551304i	$0.814131\pi$
$864$		0			0
$865$	−1863.34			−2.15415
$866$	701.623	+	836.162i	0.810189	+	0.965545i
$867$		0			0
$868$	134.075	−	760.377i	0.154464	−	0.876010i
$869$	76.6806	+	210.678i	0.0882400	+	0.242438i
$870$		0			0
$871$	13.6645	+	77.4951i	0.0156883	+	0.0889726i
$872$	−297.932	+	172.011i	−0.341665	+	0.197260i
$873$		0			0
$874$	618.122	−	1070.62i	0.707233	−	1.22496i
$875$	−189.585	+	520.881i	−0.216669	+	0.595293i
$876$		0			0
$877$	−174.806	−	146.679i	−0.199322	−	0.167251i	0.537663	−	0.843160i	$-0.319307\pi$
$877$	−174.806	−	146.679i	−0.199322	−	0.167251i	−0.736986	+	0.675908i	$0.763752\pi$
$878$	−564.786	+	673.086i	−0.643264	+	0.766613i
$879$		0			0
$880$	−914.138	−	332.719i	−1.03879	−	0.378090i
$881$	−1343.36	−	775.592i	−1.52482	−	0.880354i	−0.999568	−	0.0294054i	$-0.990639\pi$
$881$	−1343.36	−	775.592i	−1.52482	−	0.880354i	−0.525250	−	0.850948i	$-0.676028\pi$
$882$		0			0
$883$	−781.794	−	1354.11i	−0.885384	−	1.53353i	−0.845272	−	0.534336i	$-0.820562\pi$
$883$	−781.794	−	1354.11i	−0.885384	−	1.53353i	−0.0401121	−	0.999195i	$-0.512772\pi$
$884$	417.537	−	73.6231i	0.472327	−	0.0832840i
$885$		0			0
$886$	−1115.28	+	405.929i	−1.25878	+	0.458159i
$887$	−691.493	−	121.929i	−0.779587	−	0.137462i	−0.230326	−	0.973113i	$-0.573979\pi$
$887$	−691.493	−	121.929i	−0.779587	−	0.137462i	−0.549260	+	0.835651i	$0.685090\pi$
$888$		0			0
$889$	730.420	−	612.895i	0.821620	−	0.689421i
$890$		−	464.699i		−	0.522134i
$891$		0			0
$892$	1130.95			1.26789
$893$	−151.234	−	180.234i	−0.169355	−	0.201830i
$894$		0			0
$895$	31.8365	−	180.554i	0.0355715	−	0.201736i
$896$	−245.924	−	675.671i	−0.274469	−	0.754097i
$897$		0			0
$898$	−87.1642	−	494.333i	−0.0970649	−	0.550482i
$899$	430.094	−	248.315i	0.478413	−	0.276212i
$900$		0			0
$901$	−193.210	+	334.649i	−0.214439	+	0.371419i
$902$	120.474	−	331.000i	0.133564	−	0.366963i
$903$		0			0
$904$	−273.956	−	229.877i	−0.303049	−	0.254288i
$905$	−335.128	+	399.390i	−0.370307	+	0.441315i
$906$		0			0
$907$	−1517.15	−	552.196i	−1.67271	−	0.608816i	−0.680426	−	0.732816i	$-0.738205\pi$
$907$	−1517.15	−	552.196i	−1.67271	−	0.608816i	−0.992282	+	0.124000i	$0.960428\pi$
$908$	876.803	+	506.222i	0.965642	+	0.557514i
$909$		0			0
$910$	−647.383	−	1121.30i	−0.711410	−	1.23220i
$911$	603.650	−	106.440i	0.662623	−	0.116838i	0.167785	−	0.985824i	$-0.446338\pi$
$911$	603.650	−	106.440i	0.662623	−	0.116838i	0.494838	+	0.868985i	$0.335227\pi$
$912$		0			0
$913$	−134.114	+	48.8135i	−0.146894	+	0.0534650i
$914$	−998.308	−	176.029i	−1.09224	−	0.192592i
$915$		0			0
$916$	811.397	−	680.843i	0.885805	−	0.743278i
$917$			38.2568i			0.0417195i
$918$		0			0
$919$	628.091			0.683451			0.341725	−	0.939800i	$-0.388989\pi$
$919$	628.091			0.683451			0.341725	+	0.939800i	$0.388989\pi$
$920$	304.275	+	362.621i	0.330734	+	0.394153i
$921$		0			0
$922$	−197.613	+	1120.72i	−0.214331	+	1.21553i
$923$	137.109	+	376.704i	0.148547	+	0.408131i
$924$		0			0
$925$	−77.2881	−	438.323i	−0.0835547	−	0.473862i
$926$	1258.19	−	726.418i	1.35874	−	0.784469i
$927$		0			0
$928$	−295.086	+	511.103i	−0.317980	+	0.550758i
$929$	−428.742	+	1177.96i	−0.461509	+	1.26799i	0.462841	+	0.886441i	$0.346830\pi$
$929$	−428.742	+	1177.96i	−0.461509	+	1.26799i	−0.924350	+	0.381545i	$0.875392\pi$
$930$		0			0
$931$	−231.220	−	194.016i	−0.248356	−	0.208396i
$932$	−354.259	+	422.189i	−0.380106	+	0.452993i
$933$		0			0
$934$	−531.693	−	193.520i	−0.569265	−	0.207195i
$935$	660.093	+	381.105i	0.705981	+	0.407599i
$936$		0			0
$937$	460.132	+	796.972i	0.491070	+	0.850557i	0.999947	−	0.0102815i	$-0.00327275\pi$
$937$	460.132	+	796.972i	0.491070	+	0.850557i	−0.508878	+	0.860839i	$0.669939\pi$
$938$	170.258	−	30.0211i	0.181512	−	0.0320054i
$939$		0			0
$940$	−224.796	+	81.8189i	−0.239144	+	0.0870414i
$941$	673.068	+	118.680i	0.715269	+	0.126121i	0.519428	−	0.854514i	$-0.326145\pi$
$941$	673.068	+	118.680i	0.715269	+	0.126121i	0.195841	+	0.980636i	$0.437256\pi$
$942$		0			0
$943$	−333.252	+	279.632i	−0.353396	+	0.296534i
$944$			435.590i			0.461430i
$945$		0			0
$946$	1787.31			1.88934
$947$	−541.088	−	644.844i	−0.571371	−	0.680933i	0.400541	−	0.916279i	$-0.368822\pi$
$947$	−541.088	−	644.844i	−0.571371	−	0.680933i	−0.971912	+	0.235346i	$0.924378\pi$
$948$		0			0
$949$	−136.248	+	772.703i	−0.143570	+	0.814228i
$950$	−226.016	−	620.973i	−0.237911	−	0.653656i
$951$		0			0
$952$	60.9148	+	345.465i	0.0639861	+	0.362883i
$953$	1277.52	−	737.576i	1.34052	−	0.773952i	0.353640	−	0.935382i	$-0.384944\pi$
$953$	1277.52	−	737.576i	1.34052	−	0.773952i	0.986884	+	0.161430i	$0.0516105\pi$
$954$		0			0
$955$	490.553	−	849.662i	0.513668	−	0.889698i
$956$	−304.205	+	835.797i	−0.318206	+	0.874265i
$957$		0			0
$958$	455.940	+	382.579i	0.475929	+	0.399352i
$959$	1152.06	−	1372.98i	1.20132	−	1.43167i
$960$		0			0
$961$	−103.831	−	37.7915i	−0.108045	−	0.0393252i
$962$	−698.694	−	403.391i	−0.726294	−	0.419326i
$963$		0			0
$964$	−428.456	−	742.107i	−0.444456	−	0.769821i
$965$	255.291	−	45.0147i	0.264550	−	0.0466473i
$966$		0			0
$967$	−305.163	+	111.070i	−0.315577	+	0.114861i	−0.494953	−	0.868920i	$-0.664815\pi$
$967$	−305.163	+	111.070i	−0.315577	+	0.114861i	0.179375	+	0.983781i	$0.442592\pi$
$968$	156.225	+	27.5467i	0.161390	+	0.0284574i
$969$		0			0
$970$	−2122.04	+	1780.60i	−2.18767	+	1.83567i
$971$		−	1203.37i		−	1.23931i	−0.784873	−	0.619657i	$-0.787272\pi$
$971$		−	1203.37i		−	1.23931i	0.784873	−	0.619657i	$-0.212728\pi$
$972$		0			0
$973$	290.331			0.298387
$974$	−748.520	−	892.051i	−0.768501	−	0.915864i
$975$		0			0
$976$	−113.532	+	643.870i	−0.116323	+	0.659702i
$977$	−64.7541	−	177.910i	−0.0662785	−	0.182099i	0.902132	−	0.431460i	$-0.142001\pi$
$977$	−64.7541	−	177.910i	−0.0662785	−	0.182099i	−0.968410	+	0.249362i	$0.919779\pi$
$978$		0			0
$979$	−39.8573	−	226.042i	−0.0407123	−	0.230891i
$980$	−265.779	+	153.448i	−0.271203	+	0.156579i
$981$		0			0
$982$	−876.994	+	1519.00i	−0.893070	+	1.54684i
$983$	432.552	−	1188.43i	0.440033	−	1.20898i	−0.499437	−	0.866350i	$-0.666460\pi$
$983$	432.552	−	1188.43i	0.440033	−	1.20898i	0.939470	−	0.342630i	$-0.111318\pi$
$984$		0			0
$985$	1008.77	+	846.459i	1.02413	+	0.859349i
$986$	385.123	−	458.971i	0.390591	−	0.465488i
$987$		0			0
$988$	−473.621	−	172.384i	−0.479374	−	0.174478i
$989$	−1911.64	−	1103.69i	−1.93291	−	1.11596i
$990$		0			0
$991$	697.271	+	1207.71i	0.703604	+	1.21868i	0.967193	+	0.254043i	$0.0817603\pi$
$991$	697.271	+	1207.71i	0.703604	+	1.21868i	−0.263589	+	0.964635i	$0.584906\pi$
$992$	1253.97	−	221.109i	1.26408	−	0.222892i
$993$		0			0
$994$	827.625	−	301.231i	0.832621	−	0.303049i
$995$	−1080.59	−	190.538i	−1.08602	−	0.191495i
$996$		0			0
$997$	772.720	−	648.389i	0.775045	−	0.650340i	−0.166950	−	0.985965i	$-0.553392\pi$
$997$	772.720	−	648.389i	0.775045	−	0.650340i	0.941996	+	0.335625i	$0.108947\pi$
$998$		−	151.062i		−	0.151365i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.3.f.c.134.5		30
3.2	odd	2		243.3.f.b.134.1		30
9.2	odd	6		81.3.f.a.17.1		30
9.4	even	3		243.3.f.d.215.1		30
9.5	odd	6		243.3.f.a.215.5		30
9.7	even	3		27.3.f.a.23.5	yes	30
27.2	odd	18		27.3.f.a.20.5	✓	30
27.4	even	9		729.3.b.a.728.26		30
27.7	even	9		243.3.f.a.26.5		30
27.11	odd	18	inner	243.3.f.c.107.5		30
27.16	even	9		243.3.f.b.107.1		30
27.20	odd	18		243.3.f.d.26.1		30
27.23	odd	18		729.3.b.a.728.5		30
27.25	even	9		81.3.f.a.62.1		30
36.7	odd	6		432.3.bc.a.401.5		30
108.83	even	18		432.3.bc.a.209.5		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.3.f.a.20.5	✓	30	27.2	odd	18
27.3.f.a.23.5	yes	30	9.7	even	3
81.3.f.a.17.1		30	9.2	odd	6
81.3.f.a.62.1		30	27.25	even	9
243.3.f.a.26.5		30	27.7	even	9
243.3.f.a.215.5		30	9.5	odd	6
243.3.f.b.107.1		30	27.16	even	9
243.3.f.b.134.1		30	3.2	odd	2
243.3.f.c.107.5		30	27.11	odd	18	inner
243.3.f.c.134.5		30	1.1	even	1	trivial
243.3.f.d.26.1		30	27.20	odd	18
243.3.f.d.215.1		30	9.4	even	3
432.3.bc.a.209.5		30	108.83	even	18
432.3.bc.a.401.5		30	36.7	odd	6
729.3.b.a.728.5		30	27.23	odd	18
729.3.b.a.728.26		30	27.4	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)

\(f(q)\)	\(=\)	\(q+(1.68916 + 2.01307i) q^{2} +(-0.504573 + 2.86157i) q^{4} +(-2.13801 - 5.87412i) q^{5} +(-1.40961 - 7.99430i) q^{7} +(2.49037 - 1.43782i) q^{8} +O(q^{10})\)	\(q+(1.68916 + 2.01307i) q^{2} +(-0.504573 + 2.86157i) q^{4} +(-2.13801 - 5.87412i) q^{5} +(-1.40961 - 7.99430i) q^{7} +(2.49037 - 1.43782i) q^{8} +(8.21356 - 14.2263i) q^{10} +(2.77510 - 7.62453i) q^{11} +(7.43797 + 6.24120i) q^{13} +(13.7120 - 16.3413i) q^{14} +(18.0230 + 6.55984i) q^{16} +(-13.0143 - 7.51380i) q^{17} +(8.93226 + 15.4711i) q^{19} +(17.8880 - 3.15414i) q^{20} +(20.0363 - 7.29262i) q^{22} +(-25.9334 - 4.57276i) q^{23} +(-10.7831 + 9.04812i) q^{25} +25.5156i q^{26} +23.5875 q^{28} +(9.75225 + 11.6223i) q^{29} +(5.68415 - 32.2364i) q^{31} +(13.3043 + 36.5533i) q^{32} +(-6.85748 - 38.8907i) q^{34} +(-43.9457 + 25.3721i) q^{35} +(-15.8096 + 27.3831i) q^{37} +(-16.0564 + 44.1145i) q^{38} +(-13.7704 - 11.5547i) q^{40} +(10.6189 - 12.6551i) q^{41} +(78.7688 + 28.6695i) q^{43} +(20.4179 + 11.7883i) q^{44} +(-34.6005 - 59.9298i) q^{46} +(-12.9701 + 2.28698i) q^{47} +(-15.8769 + 5.77871i) q^{49} +(-36.4290 - 6.42341i) q^{50} +(-21.6126 + 18.1352i) q^{52} -25.7140i q^{53} -50.7206 q^{55} +(-15.0048 - 17.8820i) q^{56} +(-6.92328 + 39.2639i) q^{58} +(7.76763 + 21.3414i) q^{59} +(5.91937 + 33.5704i) q^{61} +(74.4955 - 43.0100i) q^{62} +(-12.7517 + 22.0867i) q^{64} +(20.7591 - 57.0353i) q^{65} +(6.20835 + 5.20943i) q^{67} +(28.0679 - 33.4501i) q^{68} +(-125.307 - 45.6081i) q^{70} +(35.7557 + 20.6436i) q^{71} +(40.4046 + 69.9827i) q^{73} +(-81.8291 + 14.4287i) q^{74} +(-48.7787 + 17.7540i) q^{76} +(-64.8646 - 11.4374i) q^{77} +(-21.1671 + 17.7613i) q^{79} -119.894i q^{80} +43.4126 q^{82} +(-11.3065 - 13.4746i) q^{83} +(-16.3124 + 92.5121i) q^{85} +(75.3398 + 206.994i) q^{86} +(-4.05165 - 22.9780i) q^{88} +(24.4986 - 14.1443i) q^{89} +(39.4094 - 68.2590i) q^{91} +(26.1706 - 71.9030i) q^{92} +(-26.5124 - 22.2466i) q^{94} +(71.7821 - 85.5466i) q^{95} +(-158.461 - 57.6752i) q^{97} +(-38.4516 - 22.2000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} + 3 q^{4} - 6 q^{5} + 3 q^{7} - 9 q^{8}+O(q^{10}) \) 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