LMFDB - Embedded newform 243.3.f.b.107.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [243,3,Mod(26,243)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [30,-3,0,3,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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			107.1
Character	$\chi$	$=$	243.107
Dual form			243.3.f.b.134.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

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	0.155244	+	0.987876i	$0.450384\pi$
$2$	−1.68916	+	2.01307i	−0.844582	+	1.00653i	−0.999826	+	0.0186576i	$0.994061\pi$
$3$		0			0
$3$		0			0
$4$	−0.504573	−	2.86157i	−0.126143	−	0.715393i
$5$	2.13801	−	5.87412i	0.427601	−	1.17482i	−0.519663	−	0.854371i	$-0.673943\pi$
$5$	2.13801	−	5.87412i	0.427601	−	1.17482i	0.947264	−	0.320453i	$-0.103835\pi$
$6$		0			0
$7$	−1.40961	+	7.99430i	−0.201373	+	1.14204i	0.701673	+	0.712499i	$0.252437\pi$
$7$	−1.40961	+	7.99430i	−0.201373	+	1.14204i	−0.903046	+	0.429544i	$0.858674\pi$
$8$	−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	−0.999589	−	0.0286605i	$-0.990876\pi$
$11$	−2.77510	−	7.62453i	−0.252282	−	0.693139i	0.747307	−	0.664479i	$-0.231346\pi$
$12$		0			0
$13$	7.43797	−	6.24120i	0.572152	−	0.480092i	−0.310207	−	0.950669i	$-0.600399\pi$
$13$	7.43797	−	6.24120i	0.572152	−	0.480092i	0.882359	+	0.470577i	$0.155954\pi$
$14$	−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	$-0.520940\pi$
$17$	13.0143	−	7.51380i	0.765546	−	0.441988i	0.831284	+	0.555849i	$0.187607\pi$
$18$		0			0
$19$	8.93226	−	15.4711i	0.470119	−	0.814270i	−0.529297	−	0.848437i	$-0.677544\pi$
$19$	8.93226	−	15.4711i	0.470119	−	0.814270i	0.999416	+	0.0341664i	$0.0108776\pi$
$20$	−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	$-0.361542\pi$
$23$	25.9334	−	4.57276i	1.12754	−	0.198816i	0.706149	+	0.708064i	$0.250431\pi$
$24$		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	$-0.862022\pi$
$29$	−9.75225	+	11.6223i	−0.336284	+	0.400768i	0.571229	+	0.820791i	$0.306467\pi$
$30$		0			0
$31$	5.68415	+	32.2364i	0.183360	+	1.03988i	0.928045	+	0.372468i	$0.121488\pi$
$31$	5.68415	+	32.2364i	0.183360	+	1.03988i	−0.744685	+	0.667416i	$0.767400\pi$
$32$	−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	0.569344	−	0.822100i	$-0.307197\pi$
$37$	−15.8096	−	27.3831i	−0.427287	−	0.740083i	−0.996631	+	0.0820163i	$0.973864\pi$
$38$	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	$-0.286792\pi$
$41$	−10.6189	−	12.6551i	−0.258997	−	0.308660i	−0.879836	+	0.475278i	$0.842348\pi$
$42$		0			0
$43$	78.7688	−	28.6695i	1.83183	−	0.666733i	0.839466	−	0.543412i	$-0.182868\pi$
$43$	78.7688	−	28.6695i	1.83183	−	0.666733i	0.992367	−	0.123320i	$-0.0393542\pi$
$44$	−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	$-0.399699\pi$
$47$	12.9701	+	2.28698i	0.275959	+	0.0486591i	−0.0339557	+	0.999423i	$0.510811\pi$
$48$		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	$-0.950538\pi$
$59$	−7.76763	+	21.3414i	−0.131655	+	0.361718i	0.856296	+	0.516485i	$0.172760\pi$
$60$		0			0
$61$	5.91937	−	33.5704i	0.0970388	−	0.550335i	−0.897065	−	0.441899i	$-0.854305\pi$
$61$	5.91937	−	33.5704i	0.0970388	−	0.550335i	0.994104	−	0.108435i	$-0.0345840\pi$
$62$	−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	−0.595280	−	0.803518i	$-0.702959\pi$
$67$	6.20835	−	5.20943i	0.0926620	−	0.0777526i	0.687942	+	0.725766i	$0.258514\pi$
$68$	−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	$-0.760573\pi$
$71$	−35.7557	+	20.6436i	−0.503601	+	0.290754i	0.226598	+	0.973988i	$0.427240\pi$
$72$		0			0
$73$	40.4046	−	69.9827i	0.553487	−	0.958668i	−0.444532	−	0.895763i	$-0.646630\pi$
$73$	40.4046	−	69.9827i	0.553487	−	0.958668i	0.998020	−	0.0629050i	$-0.0200365\pi$
$74$	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	0.498913	−	0.866652i	$-0.333733\pi$
$79$	−21.1671	−	17.7613i	−0.267937	−	0.224826i	−0.766850	+	0.641826i	$0.778177\pi$
$80$		−	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	$-0.743985\pi$
$83$	11.3065	−	13.4746i	0.136223	−	0.162344i	0.829843	+	0.557997i	$0.188430\pi$
$84$		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	$-0.384136\pi$
$89$	−24.4986	−	14.1443i	−0.275265	−	0.158924i	−0.631278	+	0.775557i	$0.717469\pi$
$90$		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	−0.985907	−	0.167294i	$-0.946497\pi$
$97$	−158.461	+	57.6752i	−1.63362	+	0.594590i	−0.647714	+	0.761883i	$0.724275\pi$
$98$	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	$-0.556798\pi$
$101$	−68.7674	−	12.1255i	−0.680865	−	0.120055i	−0.503376	+	0.864068i	$0.667909\pi$
$102$		0			0
$103$	−65.6495	−	23.8945i	−0.637374	−	0.231985i	0.00306387	−	0.999995i	$-0.499025\pi$
$103$	−65.6495	−	23.8945i	−0.637374	−	0.231985i	−0.640438	+	0.768010i	$0.721247\pi$
$104$	−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	−0.596416	−	0.802675i	$-0.703409\pi$
$113$	42.5349	−	116.864i	0.376415	−	1.03419i	0.972831	−	0.231516i	$-0.0743686\pi$
$114$		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	−0.536641	−	0.843811i	$-0.680307\pi$
$127$	58.7300	−	101.723i	0.462441	−	0.800971i	0.999082	+	0.0428396i	$0.0136404\pi$
$128$	−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	$-0.549830\pi$
$131$	4.64121	−	0.818370i	0.0354291	−	0.00624710i	0.191335	+	0.981525i	$0.438718\pi$
$132$		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	−0.0643220	+	0.997929i	$0.520488\pi$
$137$	−141.921	+	169.135i	−1.03592	+	1.23456i	−0.971599	+	0.236633i	$0.923956\pi$
$138$		0			0
$139$	−6.21061	−	35.2221i	−0.0446807	−	0.253397i	0.954283	−	0.298903i	$-0.0966209\pi$
$139$	−6.21061	−	35.2221i	−0.0446807	−	0.253397i	−0.998964	+	0.0455067i	$0.985510\pi$
$140$	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	$-0.0319183\pi$
$149$	107.819	+	128.493i	0.723615	+	0.862371i	−0.271361	+	0.962478i	$0.587474\pi$
$150$		0			0
$151$	78.6693	−	28.6333i	0.520989	−	0.189624i	−0.0681215	−	0.997677i	$-0.521701\pi$
$151$	78.6693	−	28.6333i	0.520989	−	0.189624i	0.589110	+	0.808053i	$0.299478\pi$
$152$	−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	0.555055	−	0.831814i	$-0.312697\pi$
$157$	69.9547	+	25.4614i	0.445571	+	0.162175i	−0.109483	+	0.993989i	$0.534920\pi$
$158$	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	0.664585	+	0.747213i	$0.268608\pi$
$167$	−54.2442	+	149.035i	−0.324816	+	0.892424i	−0.989401	+	0.145211i	$0.953614\pi$
$168$		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	−0.771778	−	0.635892i	$-0.780633\pi$
$173$	−101.950	−	280.105i	−0.589305	−	1.61910i	0.182473	−	0.983211i	$-0.441590\pi$
$174$		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	$-0.692773\pi$
$179$	−25.3997	+	14.6645i	−0.141898	+	0.0819248i	0.427370	+	0.904077i	$0.359440\pi$
$180$		0			0
$181$	−41.7019	+	72.2299i	−0.230397	+	0.399060i	−0.957925	−	0.287018i	$-0.907336\pi$
$181$	−41.7019	+	72.2299i	−0.230397	+	0.399060i	0.727528	+	0.686078i	$0.240669\pi$
$182$	−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	$-0.912550\pi$
$191$	−100.885	+	120.230i	−0.528193	+	0.629476i	0.434305	+	0.900766i	$0.356994\pi$
$192$		0			0
$193$	−7.20107	−	40.8393i	−0.0373112	−	0.211602i	0.960452	−	0.278444i	$-0.0898188\pi$
$193$	−7.20107	−	40.8393i	−0.0373112	−	0.211602i	−0.997764	+	0.0668419i	$0.978708\pi$
$194$	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	$-0.153770\pi$
$197$	182.437	+	105.330i	0.926074	+	0.534669i	0.0405063	+	0.999179i	$0.487103\pi$
$198$		0			0
$199$	87.7654	+	152.014i	0.441032	+	0.763890i	0.997766	−	0.0668004i	$-0.0212791\pi$
$199$	87.7654	+	152.014i	0.441032	+	0.763890i	−0.556734	+	0.830691i	$0.687946\pi$
$200$	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	0.849711	−	0.527249i	$-0.176776\pi$
$211$	245.123	+	89.2173i	1.16172	+	0.422831i	0.312008	+	0.950080i	$0.398999\pi$
$212$	−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	0.329328	+	0.944216i	$0.393178\pi$
$223$	−67.5868	+	383.304i	−0.303080	+	1.71885i	−0.632408	+	0.774636i	$0.717933\pi$
$224$	−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	−0.864912	−	0.501924i	$-0.832626\pi$
$227$	−119.171	−	327.419i	−0.524981	−	1.44237i	0.339930	−	0.940451i	$-0.389596\pi$
$228$		0			0
$229$	−279.242	+	234.311i	−1.21940	+	1.02319i	−0.220539	+	0.975378i	$0.570782\pi$
$229$	−279.242	+	234.311i	−1.21940	+	1.02319i	−0.998856	+	0.0478162i	$0.984774\pi$
$230$	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	$-0.800098\pi$
$233$	−164.260	+	94.8353i	−0.704976	+	0.407018i	0.104222	+	0.994554i	$0.466765\pi$
$234$		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	$-0.776776\pi$
$239$	−301.448	+	53.1535i	−1.26129	+	0.222400i	−0.497272	+	0.867594i	$0.665665\pi$
$240$		0			0
$241$	−225.911	−	189.561i	−0.937388	−	0.786562i	0.0397406	−	0.999210i	$-0.487347\pi$
$241$	−225.911	−	189.561i	−0.937388	−	0.786562i	−0.977129	+	0.212648i	$0.931791\pi$
$242$			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	$-0.452046\pi$
$251$	−158.404	−	91.4547i	−0.631092	−	0.364361i	−0.781175	+	0.624312i	$0.785379\pi$
$252$		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	$-0.0473676\pi$
$257$	172.501	+	205.579i	0.671210	+	0.799918i	−0.317738	+	0.948179i	$0.602923\pi$
$258$		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	$-0.211100\pi$
$263$	346.629	+	61.1200i	1.31798	+	0.232395i	0.529948	+	0.848030i	$0.322211\pi$
$264$		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	−0.900829	−	0.434175i	$-0.857040\pi$
$277$	26.0851	−	147.936i	0.0941700	−	0.534064i	0.994999	−	0.0998895i	$-0.0318489\pi$
$278$	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	0.818018	+	0.575192i	$0.195073\pi$
$281$	157.671	+	433.197i	0.561106	+	1.54163i	−0.256912	+	0.966435i	$0.582705\pi$
$282$		0			0
$283$	−52.7479	+	44.2607i	−0.186388	+	0.156398i	−0.731207	−	0.682155i	$-0.761043\pi$
$283$	−52.7479	+	44.2607i	−0.186388	+	0.156398i	0.544819	+	0.838554i	$0.316598\pi$
$284$	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	$-0.218629\pi$
$293$	503.007	−	88.6936i	1.71675	−	0.302709i	0.943494	+	0.331390i	$0.107518\pi$
$294$		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	0.820005	−	0.572357i	$-0.193971\pi$
$307$	−26.3017	−	45.5559i	−0.0856734	−	0.148391i	−0.905678	+	0.423966i	$0.860637\pi$
$308$	−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	$-0.0289877\pi$
$311$	228.077	+	271.812i	0.733368	+	0.873993i	−0.262489	+	0.964935i	$0.584543\pi$
$312$		0			0
$313$	−158.102	+	57.5444i	−0.505118	+	0.183848i	−0.581995	−	0.813193i	$-0.697728\pi$
$313$	−158.102	+	57.5444i	−0.505118	+	0.183848i	0.0768764	+	0.997041i	$0.475505\pi$
$314$	−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	$-0.146932\pi$
$317$	502.240	+	88.5585i	1.58435	+	0.279365i	0.689015	+	0.724747i	$0.258044\pi$
$318$		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	0.756570	+	0.653912i	$0.226874\pi$
$331$	−58.9261	+	334.186i	−0.178024	+	1.00963i	−0.934595	+	0.355714i	$0.884238\pi$
$332$	−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	−0.717042	−	0.697030i	$-0.754504\pi$
$337$	−52.2733	+	43.8625i	−0.155114	+	0.130156i	0.561928	+	0.827186i	$0.310060\pi$
$338$	−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	$-0.635796\pi$
$347$	−170.468	+	30.0581i	−0.491262	+	0.0866227i	−0.0774708	+	0.996995i	$0.524684\pi$
$348$		0			0
$349$	352.060	+	295.414i	1.00877	+	0.846457i	0.988175	−	0.153331i	$-0.0490000\pi$
$349$	352.060	+	295.414i	1.00877	+	0.846457i	0.0205933	+	0.999788i	$0.493444\pi$
$350$			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	$-0.584814\pi$
$353$	258.561	−	308.141i	0.732468	−	0.872922i	0.995778	+	0.0917895i	$0.0292587\pi$
$354$		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	$-0.230584\pi$
$359$	197.249	+	113.882i	0.549439	+	0.317219i	−0.199457	+	0.979907i	$0.563918\pi$
$360$		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	−0.0224904	−	0.999747i	$-0.507160\pi$
$367$	221.266	−	80.5344i	0.602906	−	0.219440i	0.625396	+	0.780307i	$0.284937\pi$
$368$	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	−0.656655	−	0.754192i	$-0.728029\pi$
$373$	−613.386	−	223.254i	−1.64447	−	0.598537i	−0.987812	+	0.155655i	$0.950251\pi$
$374$	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	$-0.844473\pi$
$383$	36.4387	−	100.114i	0.0951401	−	0.261395i	0.978129	+	0.207998i	$0.0666948\pi$
$384$		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	−0.868359	−	0.495935i	$-0.834825\pi$
$389$	−203.034	−	557.832i	−0.521939	−	1.43401i	0.346421	−	0.938079i	$-0.387397\pi$
$390$		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	−0.999489	−	0.0319623i	$-0.989824\pi$
$397$	−187.410	+	324.603i	−0.472064	+	0.817640i	0.527425	+	0.849602i	$0.323158\pi$
$398$	−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	$-0.666711\pi$
$401$	−270.237	+	47.6500i	−0.673907	+	0.118828i	−0.173786	+	0.984783i	$0.555600\pi$
$402$		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	−0.844421	−	0.535680i	$-0.820055\pi$
$409$	−95.7625	−	543.096i	−0.234138	−	1.32786i	0.610283	−	0.792183i	$-0.291056\pi$
$410$	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	$-0.188892\pi$
$419$	56.3003	+	67.0960i	0.134368	+	0.160134i	−0.694665	+	0.719334i	$0.744447\pi$
$420$		0			0
$421$	−278.393	+	101.327i	−0.661266	+	0.240681i	−0.650783	−	0.759264i	$-0.725559\pi$
$421$	−278.393	+	101.327i	−0.661266	+	0.240681i	−0.0104830	+	0.999945i	$0.503337\pi$
$422$	−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	−0.844474	−	0.535596i	$-0.820087\pi$
$439$	58.0607	−	329.279i	0.132257	−	0.750065i	0.976731	−	0.214469i	$-0.0688021\pi$
$440$	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	0.982783	+	0.184765i	$0.0591523\pi$
$443$	154.471	+	424.404i	0.348692	+	0.958024i	−0.634091	+	0.773259i	$0.718625\pi$
$444$		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	$-0.598438\pi$
$449$	165.422	−	95.5067i	0.368424	−	0.212710i	0.672770	+	0.739852i	$0.265104\pi$
$450$		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	0.259426	−	0.965763i	$-0.416467\pi$
$457$	−295.504	−	247.957i	−0.646616	−	0.542575i	−0.906042	+	0.423188i	$0.860911\pi$
$458$		−	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	$-0.933412\pi$
$461$	−278.361	+	331.738i	−0.603821	+	0.719606i	0.374378	+	0.927276i	$0.377856\pi$
$462$		0			0
$463$	96.0025	+	544.457i	0.207349	+	1.17593i	0.893701	+	0.448664i	$0.148100\pi$
$463$	96.0025	+	544.457i	0.207349	+	1.17593i	−0.686352	+	0.727270i	$0.740789\pi$
$464$	−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	$-0.259288\pi$
$467$	186.467	+	107.657i	0.399286	+	0.230528i	−0.286890	+	0.957964i	$0.592621\pi$
$468$		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	$-0.520418\pi$
$479$	−223.049	−	39.3296i	−0.465656	−	0.0821077i	−0.401553	+	0.915836i	$0.631530\pi$
$480$		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	0.456796	+	0.889571i	$0.348997\pi$
$491$	−228.283	+	627.203i	−0.464935	+	1.27740i	−0.921732	+	0.387828i	$0.873225\pi$
$492$		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	−0.685844	−	0.727748i	$-0.740567\pi$
$499$	−44.0357	+	36.9503i	−0.0882478	+	0.0740487i	0.597597	+	0.801797i	$0.296122\pi$
$500$	−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	$-0.828123\pi$
$503$	−423.202	+	244.336i	−0.841356	+	0.485757i	0.0163686	+	0.999866i	$0.494789\pi$
$504$		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	$-0.465478\pi$
$509$	279.933	−	49.3598i	0.549967	−	0.0969741i	0.441725	+	0.897150i	$0.354367\pi$
$510$		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	$-0.345752\pi$
$521$	−35.1966	−	20.3207i	−0.0675558	−	0.0390033i	−0.533397	+	0.845865i	$0.679085\pi$
$522$		0			0
$523$	−174.951	−	303.024i	−0.334514	−	0.579395i	0.648877	−	0.760893i	$-0.275239\pi$
$523$	−174.951	−	303.024i	−0.334514	−	0.579395i	−0.983391	+	0.181498i	$0.941905\pi$
$524$	−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	−0.805137	−	0.593088i	$-0.797908\pi$
$547$	84.3980	−	478.645i	0.154292	−	0.875036i	0.959430	−	0.281948i	$-0.0909805\pi$
$548$	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	$-0.667600\pi$
$557$	−2.82805	+	1.63278i	−0.00507730	+	0.00293138i	0.497459	+	0.867487i	$0.334266\pi$
$558$		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	$-0.756571\pi$
$563$	−654.650	+	115.432i	−1.16279	+	0.205031i	−0.441236	+	0.897391i	$0.645460\pi$
$564$		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	$-0.799033\pi$
$569$	−48.8101	+	58.1696i	−0.0857822	+	0.102231i	0.721446	+	0.692471i	$0.243478\pi$
$570$		0			0
$571$	−51.0684	−	289.624i	−0.0894369	−	0.507222i	−0.996311	−	0.0858194i	$-0.972649\pi$
$571$	−51.0684	−	289.624i	−0.0894369	−	0.507222i	0.906874	−	0.421402i	$-0.138462\pi$
$572$	−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	−0.803461	−	0.595357i	$-0.797011\pi$
$577$	−529.296	−	916.768i	−0.917325	−	1.58885i	−0.113864	−	0.993496i	$-0.536323\pi$
$578$	−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	$-0.406695\pi$
$587$	136.792	+	24.1200i	0.233035	+	0.0410904i	−0.0559110	+	0.998436i	$0.517806\pi$
$588$		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	$-0.894993\pi$
$599$	−7.85706	+	21.5871i	−0.0131170	+	0.0360386i	0.932961	+	0.359977i	$0.117215\pi$
$600$		0			0
$601$	−161.036	+	913.281i	−0.267947	+	1.51960i	0.492564	+	0.870276i	$0.336060\pi$
$601$	−161.036	+	913.281i	−0.267947	+	1.51960i	−0.760511	+	0.649325i	$0.775051\pi$
$602$	−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	−0.249203	−	0.968451i	$-0.580169\pi$
$607$	401.386	−	336.803i	0.661262	−	0.554865i	0.910465	+	0.413587i	$0.135724\pi$
$608$	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	−0.893223	−	0.449614i	$-0.851562\pi$
$613$	−35.0848	+	60.7687i	−0.0572346	+	0.0991333i	0.835988	+	0.548747i	$0.184895\pi$
$614$	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	$-0.374531\pi$
$617$	654.465	−	115.400i	1.06072	−	0.187034i	0.676676	+	0.736281i	$0.263420\pi$
$618$		0			0
$619$	−743.640	−	623.988i	−1.20136	−	1.00806i	−0.999590	−	0.0286254i	$-0.990887\pi$
$619$	−743.640	−	623.988i	−1.20136	−	1.00806i	−0.201768	−	0.979433i	$-0.564669\pi$
$620$		−	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	0.931232	−	0.364426i	$-0.118735\pi$
$631$	94.6588	+	163.954i	0.150014	+	0.259832i	−0.781218	+	0.624258i	$0.785401\pi$
$632$	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	$-0.626146\pi$
$641$	−682.182	−	120.287i	−1.06425	−	0.187655i	−0.678240	+	0.734841i	$0.737257\pi$
$642$		0			0
$643$	−1000.40	−	364.116i	−1.55583	−	0.566277i	−0.586056	−	0.810271i	$-0.699320\pi$
$643$	−1000.40	−	364.116i	−1.55583	−	0.566277i	−0.969777	+	0.243994i	$0.921542\pi$
$644$	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	−0.754492	−	0.656309i	$-0.772117\pi$
$653$	160.213	−	440.183i	0.245350	−	0.674093i	0.999842	−	0.0177840i	$-0.00566112\pi$
$654$		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	$-0.131881\pi$
$659$	−29.3934	−	80.7577i	−0.0446030	−	0.122546i	−0.959994	+	0.280019i	$0.909659\pi$
$660$		0			0
$661$	94.3093	−	79.1349i	0.142677	−	0.119720i	−0.568656	−	0.822575i	$-0.692536\pi$
$661$	94.3093	−	79.1349i	0.142677	−	0.119720i	0.711333	+	0.702856i	$0.248092\pi$
$662$	−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	0.204034	−	0.978964i	$-0.434595\pi$
$673$	−487.674	−	409.207i	−0.724627	−	0.608035i	−0.928661	+	0.370929i	$0.879039\pi$
$674$		−	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	$-0.816737\pi$
$677$	−106.259	+	126.634i	−0.156955	+	0.187052i	0.681836	+	0.731505i	$0.261182\pi$
$678$		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	0.975468	+	0.220142i	$0.0706522\pi$
$683$	1129.58	+	652.163i	1.65385	+	0.954851i	0.678383	+	0.734709i	$0.262681\pi$
$684$		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	−0.0840729	−	0.996460i	$-0.526793\pi$
$691$	339.997	−	123.749i	0.492035	−	0.179086i	0.576108	+	0.817373i	$0.304571\pi$
$692$	−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	0.775543	+	0.631295i	$0.217476\pi$
$709$	−119.924	+	680.121i	−0.169145	+	0.959268i	−0.944687	+	0.327972i	$0.893635\pi$
$710$	−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	$-0.775489\pi$
$719$	−417.508	+	241.049i	−0.580679	+	0.335255i	0.180724	+	0.983534i	$0.442156\pi$
$720$		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	0.806209	−	0.591631i	$-0.201516\pi$
$727$	264.311	+	221.783i	0.363563	+	0.305066i	−0.442646	+	0.896697i	$0.645960\pi$
$728$		−	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	0.979634	+	0.200793i	$0.0643518\pi$
$733$	93.6439	+	531.081i	0.127754	+	0.724531i	−0.851879	+	0.523738i	$0.824537\pi$
$734$	−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	0.501032	−	0.865429i	$-0.332954\pi$
$739$	−368.737	−	638.671i	−0.498968	−	0.864237i	−0.999999	+	0.00119161i	$0.999621\pi$
$740$	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	0.996940	+	0.0781750i	$0.0249093\pi$
$743$	669.302	+	797.643i	0.900810	+	1.07354i	−0.0961294	+	0.995369i	$0.530646\pi$
$744$		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	0.186789	−	0.982400i	$-0.440192\pi$
$751$	−226.499	−	82.4391i	−0.301597	−	0.109772i	−0.488386	+	0.872628i	$0.662414\pi$
$752$	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	$-0.821600\pi$
$761$	109.225	−	300.094i	0.143529	−	0.394342i	0.990538	+	0.137236i	$0.0438218\pi$
$762$		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	−0.848388	−	0.529375i	$-0.822427\pi$
$769$	−364.796	+	306.100i	−0.474377	+	0.398050i	0.374011	+	0.927424i	$0.377982\pi$
$770$	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	$-0.983223\pi$
$773$	−1122.62	+	648.147i	−1.45229	+	0.838482i	−0.453682	+	0.891164i	$0.649890\pi$
$774$		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	0.919408	+	0.393306i	$0.128669\pi$
$787$	149.503	+	847.873i	0.189966	+	1.07735i	−0.729442	+	0.684043i	$0.760220\pi$
$788$	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	$-0.103652\pi$
$797$	372.897	+	444.402i	0.467876	+	0.557593i	−0.479572	+	0.877503i	$0.659208\pi$
$798$		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	$-0.0816850\pi$
$821$	51.8428	+	142.437i	0.0631460	+	0.173492i	−0.904107	+	0.427306i	$0.859463\pi$
$822$		0			0
$823$	172.223	−	144.512i	0.209263	−	0.175592i	−0.532132	−	0.846661i	$-0.678609\pi$
$823$	172.223	−	144.512i	0.209263	−	0.175592i	0.741395	+	0.671069i	$0.234165\pi$
$824$	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	$-0.732207\pi$
$827$	−292.855	+	169.080i	−0.354117	+	0.204449i	0.312380	+	0.949957i	$0.398874\pi$
$828$		0			0
$829$	401.806	−	695.949i	0.484688	−	0.839504i	−0.515157	−	0.857096i	$-0.672267\pi$
$829$	401.806	−	695.949i	0.484688	−	0.839504i	0.999845	+	0.0175917i	$0.00559990\pi$
$830$	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	$-0.947727\pi$
$839$	−548.904	+	654.158i	−0.654236	+	0.779688i	0.332311	+	0.943170i	$0.392172\pi$
$840$		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	0.137988	−	0.990434i	$-0.455937\pi$
$853$	750.923	−	273.313i	0.880331	−	0.320414i	0.742343	+	0.670020i	$0.233714\pi$
$854$	−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	$-0.0834003\pi$
$857$	1529.66	+	269.721i	1.78490	+	0.314726i	0.819031	+	0.573749i	$0.194511\pi$
$858$		0			0
$859$	26.5482	+	9.66277i	0.0309060	+	0.0112489i	0.357427	−	0.933941i	$-0.383654\pi$
$859$	26.5482	+	9.66277i	0.0309060	+	0.0112489i	−0.326521	+	0.945190i	$0.605876\pi$
$860$	−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	−0.736986	−	0.675908i	$-0.763752\pi$
$877$	−174.806	+	146.679i	−0.199322	+	0.167251i	0.537663	+	0.843160i	$0.319307\pi$
$878$	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	0.525250	−	0.850948i	$-0.323972\pi$
$881$	1343.36	−	775.592i	1.52482	−	0.880354i	0.999568	−	0.0294054i	$-0.00936139\pi$
$882$		0			0
$883$	−781.794	+	1354.11i	−0.885384	+	1.53353i	−0.0401121	+	0.999195i	$0.512772\pi$
$883$	−781.794	+	1354.11i	−0.885384	+	1.53353i	−0.845272	+	0.534336i	$0.820562\pi$
$884$	−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	$-0.426021\pi$
$887$	691.493	−	121.929i	0.779587	−	0.137462i	0.549260	+	0.835651i	$0.314910\pi$
$888$		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	−0.992282	−	0.124000i	$-0.960428\pi$
$907$	−1517.15	+	552.196i	−1.67271	+	0.608816i	−0.680426	+	0.732816i	$0.738205\pi$
$908$	−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	$-0.553662\pi$
$911$	−603.650	−	106.440i	−0.662623	−	0.116838i	−0.494838	+	0.868985i	$0.664773\pi$
$912$		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	0.924350	+	0.381545i	$0.124608\pi$
$929$	428.742	+	1177.96i	0.461509	+	1.26799i	−0.462841	+	0.886441i	$0.653170\pi$
$930$		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	−0.508878	−	0.860839i	$-0.669939\pi$
$937$	460.132	−	796.972i	0.491070	−	0.850557i	0.999947	+	0.0102815i	$0.00327275\pi$
$938$	−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	$-0.673855\pi$
$941$	−673.068	+	118.680i	−0.715269	+	0.126121i	−0.195841	+	0.980636i	$0.562744\pi$
$942$		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	$-0.631178\pi$
$947$	541.088	−	644.844i	0.571371	−	0.680933i	0.971912	+	0.235346i	$0.0756222\pi$
$948$		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	$-0.615056\pi$
$953$	−1277.52	−	737.576i	−1.34052	−	0.773952i	−0.986884	+	0.161430i	$0.948390\pi$
$954$		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	0.179375	−	0.983781i	$-0.442592\pi$
$967$	−305.163	−	111.070i	−0.315577	−	0.114861i	−0.494953	+	0.868920i	$0.664815\pi$
$968$	−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	$-0.857999\pi$
$977$	64.7541	−	177.910i	0.0662785	−	0.182099i	0.968410	+	0.249362i	$0.0802207\pi$
$978$		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	−0.939470	−	0.342630i	$-0.888682\pi$
$983$	−432.552	−	1188.43i	−0.440033	−	1.20898i	0.499437	−	0.866350i	$-0.333540\pi$
$984$		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	−0.263589	−	0.964635i	$-0.584906\pi$
$991$	697.271	−	1207.71i	0.703604	−	1.21868i	0.967193	−	0.254043i	$-0.0817603\pi$
$992$	−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	0.941996	−	0.335625i	$-0.108947\pi$
$997$	772.720	+	648.389i	0.775045	+	0.650340i	−0.166950	+	0.985965i	$0.553392\pi$
$998$		−	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.b.107.1		30
3.2	odd	2		243.3.f.c.107.5		30
9.2	odd	6		243.3.f.d.26.1		30
9.4	even	3		81.3.f.a.62.1		30
9.5	odd	6		27.3.f.a.20.5	✓	30
9.7	even	3		243.3.f.a.26.5		30
27.4	even	9		243.3.f.d.215.1		30
27.5	odd	18	inner	243.3.f.b.134.1		30
27.7	even	9		729.3.b.a.728.26		30
27.13	even	9		27.3.f.a.23.5	yes	30
27.14	odd	18		81.3.f.a.17.1		30
27.20	odd	18		729.3.b.a.728.5		30
27.22	even	9		243.3.f.c.134.5		30
27.23	odd	18		243.3.f.a.215.5		30
36.23	even	6		432.3.bc.a.209.5		30
108.67	odd	18		432.3.bc.a.401.5		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.3.f.a.20.5	✓	30	9.5	odd	6
27.3.f.a.23.5	yes	30	27.13	even	9
81.3.f.a.17.1		30	27.14	odd	18
81.3.f.a.62.1		30	9.4	even	3
243.3.f.a.26.5		30	9.7	even	3
243.3.f.a.215.5		30	27.23	odd	18
243.3.f.b.107.1		30	1.1	even	1	trivial
243.3.f.b.134.1		30	27.5	odd	18	inner
243.3.f.c.107.5		30	3.2	odd	2
243.3.f.c.134.5		30	27.22	even	9
243.3.f.d.26.1		30	9.2	odd	6
243.3.f.d.215.1		30	27.4	even	9
432.3.bc.a.209.5		30	36.23	even	6
432.3.bc.a.401.5		30	108.67	odd	18
729.3.b.a.728.5		30	27.20	odd	18
729.3.b.a.728.26		30	27.7	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-1.68916 + 2.01307i) q^{2} +(-0.504573 - 2.86157i) q^{4} +(2.13801 - 5.87412i) q^{5} +(-1.40961 + 7.99430i) q^{7} +(-2.49037 - 1.43782i) q^{8} +(8.21356 + 14.2263i) q^{10} +(-2.77510 - 7.62453i) q^{11} +(7.43797 - 6.24120i) q^{13} +(-13.7120 - 16.3413i) q^{14} +(18.0230 - 6.55984i) q^{16} +(13.0143 - 7.51380i) q^{17} +(8.93226 - 15.4711i) q^{19} +(-17.8880 - 3.15414i) q^{20} +(20.0363 + 7.29262i) q^{22} +(25.9334 - 4.57276i) q^{23} +(-10.7831 - 9.04812i) q^{25} +25.5156i q^{26} +23.5875 q^{28} +(-9.75225 + 11.6223i) q^{29} +(5.68415 + 32.2364i) q^{31} +(-13.3043 + 36.5533i) q^{32} +(-6.85748 + 38.8907i) q^{34} +(43.9457 + 25.3721i) q^{35} +(-15.8096 - 27.3831i) q^{37} +(16.0564 + 44.1145i) q^{38} +(-13.7704 + 11.5547i) q^{40} +(-10.6189 - 12.6551i) q^{41} +(78.7688 - 28.6695i) q^{43} +(-20.4179 + 11.7883i) q^{44} +(-34.6005 + 59.9298i) q^{46} +(12.9701 + 2.28698i) q^{47} +(-15.8769 - 5.77871i) q^{49} +(36.4290 - 6.42341i) q^{50} +(-21.6126 - 18.1352i) q^{52} -25.7140i q^{53} -50.7206 q^{55} +(15.0048 - 17.8820i) q^{56} +(-6.92328 - 39.2639i) q^{58} +(-7.76763 + 21.3414i) q^{59} +(5.91937 - 33.5704i) q^{61} +(-74.4955 - 43.0100i) q^{62} +(-12.7517 - 22.0867i) q^{64} +(-20.7591 - 57.0353i) q^{65} +(6.20835 - 5.20943i) q^{67} +(-28.0679 - 33.4501i) q^{68} +(-125.307 + 45.6081i) q^{70} +(-35.7557 + 20.6436i) q^{71} +(40.4046 - 69.9827i) q^{73} +(81.8291 + 14.4287i) q^{74} +(-48.7787 - 17.7540i) q^{76} +(64.8646 - 11.4374i) q^{77} +(-21.1671 - 17.7613i) q^{79} -119.894i q^{80} +43.4126 q^{82} +(11.3065 - 13.4746i) q^{83} +(-16.3124 - 92.5121i) q^{85} +(-75.3398 + 206.994i) q^{86} +(-4.05165 + 22.9780i) q^{88} +(-24.4986 - 14.1443i) q^{89} +(39.4094 + 68.2590i) q^{91} +(-26.1706 - 71.9030i) q^{92} +(-26.5124 + 22.2466i) q^{94} +(-71.7821 - 85.5466i) q^{95} +(-158.461 + 57.6752i) q^{97} +(38.4516 - 22.2000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{2} + 3 q^{4} + 6 q^{5} + 3 q^{7} + 9 q^{8} - 3 q^{10} + 51 q^{11} + 3 q^{13} - 129 q^{14} - 9 q^{16} + 9 q^{17} - 3 q^{19} + 30 q^{20} - 33 q^{22} + 168 q^{23} - 6 q^{25} - 12 q^{28} - 246 q^{29}+ \cdots - 882 q^{98}+O(q^{100}) \) 30 * q - 3 * q^2 + 3 * q^4 + 6 * q^5 + 3 * q^7 + 9 * q^8 - 3 * q^10 + 51 * q^11 + 3 * q^13 - 129 * q^14 - 9 * q^16 + 9 * q^17 - 3 * q^19 + 30 * q^20 - 33 * q^22 + 168 * q^23 - 6 * q^25 - 12 * q^28 - 246 * q^29 + 48 * q^31 - 117 * q^32 + 99 * q^34 + 252 * q^35 - 3 * q^37 + 237 * q^38 + 201 * q^40 - 129 * q^41 + 183 * q^43 - 639 * q^44 - 3 * q^46 + 348 * q^47 + 147 * q^49 + 471 * q^50 + 45 * q^52 - 12 * q^55 - 570 * q^56 - 267 * q^58 - 426 * q^59 - 285 * q^61 + 900 * q^62 - 51 * q^64 + 213 * q^65 - 366 * q^67 - 378 * q^68 - 483 * q^70 - 315 * q^71 - 66 * q^73 - 159 * q^74 - 201 * q^76 + 654 * q^77 - 15 * q^79 - 12 * q^82 - 624 * q^83 + 18 * q^85 + 411 * q^86 + 51 * q^88 - 72 * q^89 + 96 * q^91 + 561 * q^92 - 96 * q^94 + 75 * q^95 - 114 * q^97 - 882 * q^98

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