LMFDB - Embedded newform 252.3.p.a.157.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [252,3,Mod(61,252)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(252, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 5])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("252.61"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	252.p (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.86650266188$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			157.12
Character	$\chi$	$=$	252.157
Dual form			252.3.p.a.61.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.94529 - 2.28383i) q^{3} +0.963344i q^{5} +(6.86265 + 1.37988i) q^{7} +(-1.43172 - 8.88539i) q^{9} +8.27537 q^{11} +(0.385122 + 0.222350i) q^{13} +(2.20011 + 1.87398i) q^{15} +(-4.35489 - 2.51430i) q^{17} +(19.3354 - 11.1633i) q^{19} +(16.5012 - 12.9888i) q^{21} -15.0853 q^{23} +24.0720 q^{25} +(-23.0778 - 14.0148i) q^{27} +(-12.3863 - 21.4537i) q^{29} +(-21.0881 + 12.1752i) q^{31} +(16.0980 - 18.8995i) q^{33} +(-1.32930 + 6.61109i) q^{35} +(-15.1201 - 26.1888i) q^{37} +(1.25698 - 0.447016i) q^{39} +(21.0544 + 12.1558i) q^{41} +(11.5760 + 20.0503i) q^{43} +(8.55969 - 1.37924i) q^{45} +(8.13670 + 4.69773i) q^{47} +(45.1918 + 18.9393i) q^{49} +(-14.2137 + 5.05478i) q^{51} +(-44.7372 + 77.4871i) q^{53} +7.97203i q^{55} +(12.1179 - 65.8745i) q^{57} +(-23.7510 + 13.7127i) q^{59} +(68.9235 + 39.7930i) q^{61} +(2.43544 - 62.9529i) q^{63} +(-0.214200 + 0.371005i) q^{65} +(7.09042 + 12.2810i) q^{67} +(-29.3453 + 34.4522i) q^{69} -133.436 q^{71} +(51.2871 + 29.6106i) q^{73} +(46.8269 - 54.9762i) q^{75} +(56.7910 + 11.4191i) q^{77} +(-9.98363 + 17.2921i) q^{79} +(-76.9004 + 25.4427i) q^{81} +(-101.021 + 58.3246i) q^{83} +(2.42213 - 4.19526i) q^{85} +(-73.0914 - 13.4454i) q^{87} +(-105.064 + 60.6588i) q^{89} +(2.33614 + 2.05734i) q^{91} +(-13.2164 + 71.8460i) q^{93} +(10.7541 + 18.6266i) q^{95} +(-53.2313 + 30.7331i) q^{97} +(-11.8480 - 73.5299i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + q^{7} - 6 q^{9} - 12 q^{11} + 15 q^{13} + 9 q^{15} - 27 q^{17} - 36 q^{21} + 30 q^{23} - 160 q^{25} - 9 q^{27} + 24 q^{29} - 24 q^{31} + 81 q^{33} + 141 q^{35} + 11 q^{37} - 21 q^{39} - 90 q^{41}+ \cdots - 45 q^{99}+O(q^{100}) $ 32 * q + q^7 - 6 * q^9 - 12 * q^11 + 15 * q^13 + 9 * q^15 - 27 * q^17 - 36 * q^21 + 30 * q^23 - 160 * q^25 - 9 * q^27 + 24 * q^29 - 24 * q^31 + 81 * q^33 + 141 * q^35 + 11 * q^37 - 21 * q^39 - 90 * q^41 - 16 * q^43 + 39 * q^45 + 108 * q^47 - 61 * q^49 + 117 * q^51 + 54 * q^53 + 51 * q^57 + 45 * q^59 - 165 * q^61 - 93 * q^63 - 33 * q^65 - 35 * q^67 + 105 * q^69 + 138 * q^71 - 195 * q^75 - 123 * q^77 + 37 * q^79 + 126 * q^81 + 378 * q^83 + 30 * q^85 - 237 * q^87 - 261 * q^89 + 45 * q^91 + 111 * q^93 - 48 * q^95 - 57 * q^97 - 45 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.94529	−	2.28383i	0.648429	−	0.761275i
$3$	1.94529	−	2.28383i	0.648429	−	0.761275i
$4$		0			0
$5$			0.963344i			0.192669i	0.995349	+	0.0963344i	$0.0307118\pi$
$5$			0.963344i			0.192669i	−0.995349	+	0.0963344i	$0.969288\pi$
$6$		0			0
$7$	6.86265	+	1.37988i	0.980378	+	0.197126i
$7$	6.86265	+	1.37988i	0.980378	+	0.197126i
$8$		0			0
$9$	−1.43172	−	8.88539i	−0.159080	−	0.987266i
$10$		0			0
$11$	8.27537			0.752307			0.376153	−	0.926557i	$-0.377247\pi$
$11$	8.27537			0.752307			0.376153	+	0.926557i	$0.377247\pi$
$12$		0			0
$13$	0.385122	+	0.222350i	0.0296248	+	0.0171039i	0.514739	−	0.857347i	$-0.327889\pi$
$13$	0.385122	+	0.222350i	0.0296248	+	0.0171039i	−0.485114	+	0.874451i	$0.661222\pi$
$14$		0			0
$15$	2.20011	+	1.87398i	0.146674	+	0.124932i
$16$		0			0
$17$	−4.35489	−	2.51430i	−0.256170	−	0.147900i	0.366416	−	0.930451i	$-0.380585\pi$
$17$	−4.35489	−	2.51430i	−0.256170	−	0.147900i	−0.622586	+	0.782551i	$0.713918\pi$
$18$		0			0
$19$	19.3354	−	11.1633i	1.01765	−	0.587542i	0.104230	−	0.994553i	$-0.466762\pi$
$19$	19.3354	−	11.1633i	1.01765	−	0.587542i	0.913423	+	0.407011i	$0.133429\pi$
$20$		0			0
$21$	16.5012	−	12.9888i	0.785773	−	0.618515i
$22$		0			0
$23$	−15.0853			−0.655883			−0.327942	−	0.944698i	$-0.606355\pi$
$23$	−15.0853			−0.655883			−0.327942	+	0.944698i	$0.606355\pi$
$24$		0			0
$25$	24.0720			0.962879
$26$		0			0
$27$	−23.0778	−	14.0148i	−0.854733	−	0.519068i
$28$		0			0
$29$	−12.3863	−	21.4537i	−0.427113	−	0.739782i	0.569502	−	0.821990i	$-0.307136\pi$
$29$	−12.3863	−	21.4537i	−0.427113	−	0.739782i	−0.996615	+	0.0822080i	$0.973803\pi$
$30$		0			0
$31$	−21.0881	+	12.1752i	−0.680263	+	0.392750i	−0.799954	−	0.600061i	$-0.795143\pi$
$31$	−21.0881	+	12.1752i	−0.680263	+	0.392750i	0.119691	+	0.992811i	$0.461810\pi$
$32$		0			0
$33$	16.0980	−	18.8995i	0.487817	−	0.572712i
$34$		0			0
$35$	−1.32930	+	6.61109i	−0.0379801	+	0.188888i
$36$		0			0
$37$	−15.1201	−	26.1888i	−0.408652	−	0.707806i	0.586087	−	0.810248i	$-0.300668\pi$
$37$	−15.1201	−	26.1888i	−0.408652	−	0.707806i	−0.994739	+	0.102442i	$0.967334\pi$
$38$		0			0
$39$	1.25698	−	0.447016i	0.0322303	−	0.0114620i
$40$		0			0
$41$	21.0544	+	12.1558i	0.513523	+	0.296483i	0.734281	−	0.678846i	$-0.237520\pi$
$41$	21.0544	+	12.1558i	0.513523	+	0.296483i	−0.220758	+	0.975329i	$0.570853\pi$
$42$		0			0
$43$	11.5760	+	20.0503i	0.269210	+	0.466286i	0.968658	−	0.248398i	$-0.0799041\pi$
$43$	11.5760	+	20.0503i	0.269210	+	0.466286i	−0.699448	+	0.714684i	$0.746571\pi$
$44$		0			0
$45$	8.55969	−	1.37924i	0.190215	−	0.0306497i
$46$		0			0
$47$	8.13670	+	4.69773i	0.173121	+	0.0999517i	0.584057	−	0.811713i	$-0.301465\pi$
$47$	8.13670	+	4.69773i	0.173121	+	0.0999517i	−0.410935	+	0.911664i	$0.634798\pi$
$48$		0			0
$49$	45.1918	+	18.9393i	0.922282	+	0.386517i
$50$		0			0
$51$	−14.2137	+	5.05478i	−0.278700	+	0.0991133i
$52$		0			0
$53$	−44.7372	+	77.4871i	−0.844098	+	1.46202i	0.0423047	+	0.999105i	$0.486530\pi$
$53$	−44.7372	+	77.4871i	−0.844098	+	1.46202i	−0.886402	+	0.462915i	$0.846803\pi$
$54$		0			0
$55$			7.97203i			0.144946i
$56$		0			0
$57$	12.1179	−	65.8745i	0.212594	−	1.15569i
$58$		0			0
$59$	−23.7510	+	13.7127i	−0.402560	+	0.232418i	−0.687588	−	0.726101i	$-0.741330\pi$
$59$	−23.7510	+	13.7127i	−0.402560	+	0.232418i	0.285028	+	0.958519i	$0.407997\pi$
$60$		0			0
$61$	68.9235	+	39.7930i	1.12989	+	0.652344i	0.943908	−	0.330208i	$-0.107119\pi$
$61$	68.9235	+	39.7930i	1.12989	+	0.652344i	0.185985	+	0.982553i	$0.440452\pi$
$62$		0			0
$63$	2.43544	−	62.9529i	0.0386578	−	0.999253i
$64$		0			0
$65$	−0.214200	+	0.371005i	−0.00329538	+	0.00570777i
$66$		0			0
$67$	7.09042	+	12.2810i	0.105827	+	0.183298i	0.914076	−	0.405543i	$-0.132918\pi$
$67$	7.09042	+	12.2810i	0.105827	+	0.183298i	−0.808249	+	0.588841i	$0.799584\pi$
$68$		0			0
$69$	−29.3453	+	34.4522i	−0.425294	+	0.499307i
$70$		0			0
$71$	−133.436			−1.87938			−0.939688	−	0.342032i	$-0.888885\pi$
$71$	−133.436			−1.87938			−0.939688	+	0.342032i	$0.888885\pi$
$72$		0			0
$73$	51.2871	+	29.6106i	0.702563	+	0.405625i	0.808301	−	0.588769i	$-0.200387\pi$
$73$	51.2871	+	29.6106i	0.702563	+	0.405625i	−0.105738	+	0.994394i	$0.533721\pi$
$74$		0			0
$75$	46.8269	−	54.9762i	0.624359	−	0.733016i
$76$		0			0
$77$	56.7910	+	11.4191i	0.737545	+	0.148299i
$78$		0			0
$79$	−9.98363	+	17.2921i	−0.126375	+	0.218888i	−0.922270	−	0.386547i	$-0.873668\pi$
$79$	−9.98363	+	17.2921i	−0.126375	+	0.218888i	0.795895	+	0.605435i	$0.207001\pi$
$80$		0			0
$81$	−76.9004	+	25.4427i	−0.949387	+	0.314108i
$82$		0			0
$83$	−101.021	+	58.3246i	−1.21712	+	0.702705i	−0.964301	−	0.264808i	$-0.914691\pi$
$83$	−101.021	+	58.3246i	−1.21712	+	0.702705i	−0.252820	+	0.967513i	$0.581358\pi$
$84$		0			0
$85$	2.42213	−	4.19526i	0.0284957	−	0.0493559i
$86$		0			0
$87$	−73.0914	−	13.4454i	−0.840130	−	0.154545i
$88$		0			0
$89$	−105.064	+	60.6588i	−1.18050	+	0.681560i	−0.956129	−	0.292945i	$-0.905365\pi$
$89$	−105.064	+	60.6588i	−1.18050	+	0.681560i	−0.224367	+	0.974505i	$0.572031\pi$
$90$		0			0
$91$	2.33614	+	2.05734i	0.0256719	+	0.0226081i
$92$		0			0
$93$	−13.2164	+	71.8460i	−0.142111	+	0.772538i
$94$		0			0
$95$	10.7541	+	18.6266i	0.113201	+	0.196070i
$96$		0			0
$97$	−53.2313	+	30.7331i	−0.548776	+	0.316836i	−0.748628	−	0.662990i	$-0.769287\pi$
$97$	−53.2313	+	30.7331i	−0.548776	+	0.316836i	0.199852	+	0.979826i	$0.435954\pi$
$98$		0			0
$99$	−11.8480	−	73.5299i	−0.119677	−	0.742726i
$100$		0			0
$101$			119.021i			1.17842i	0.807979	+	0.589212i	$0.200562\pi$
$101$			119.021i			1.17842i	−0.807979	+	0.589212i	$0.799438\pi$
$102$		0			0
$103$			97.0278i			0.942018i	0.882129	+	0.471009i	$0.156110\pi$
$103$			97.0278i			0.942018i	−0.882129	+	0.471009i	$0.843890\pi$
$104$		0			0
$105$	12.5127	+	15.8964i	0.119169	+	0.151394i
$106$		0			0
$107$	−38.1581	−	66.0918i	−0.356618	−	0.617681i	0.630775	−	0.775965i	$-0.282737\pi$
$107$	−38.1581	−	66.0918i	−0.356618	−	0.617681i	−0.987394	+	0.158285i	$0.949404\pi$
$108$		0			0
$109$	19.1865	−	33.2320i	0.176023	−	0.304880i	−0.764492	−	0.644633i	$-0.777010\pi$
$109$	19.1865	−	33.2320i	0.176023	−	0.304880i	0.940515	+	0.339753i	$0.110343\pi$
$110$		0			0
$111$	−89.2236	−	16.4130i	−0.803817	−	0.147865i
$112$		0			0
$113$	102.540	−	177.605i	0.907437	−	1.57173i	0.0898260	−	0.995957i	$-0.471369\pi$
$113$	102.540	−	177.605i	0.907437	−	1.57173i	0.817611	−	0.575770i	$-0.195298\pi$
$114$		0			0
$115$		−	14.5323i		−	0.126368i
$116$		0			0
$117$	1.42428	−	3.74030i	0.0121734	−	0.0319684i
$118$		0			0
$119$	−26.4166	−	23.2640i	−0.221988	−	0.195496i
$120$		0			0
$121$	−52.5182			−0.434035
$122$		0			0
$123$	68.7187	−	24.4382i	0.558688	−	0.198684i
$124$		0			0
$125$			47.2732i			0.378185i
$126$		0			0
$127$	−71.8116			−0.565446			−0.282723	−	0.959202i	$-0.591238\pi$
$127$	−71.8116			−0.565446			−0.282723	+	0.959202i	$0.591238\pi$
$128$		0			0
$129$	68.3100	+	12.5659i	0.529535	+	0.0974101i
$130$		0			0
$131$		−	7.55009i		−	0.0576343i	−0.999585	−	0.0288172i	$-0.990826\pi$
$131$		−	7.55009i		−	0.0576343i	0.999585	−	0.0288172i	$-0.00917405\pi$
$132$		0			0
$133$	148.096	−	49.9292i	1.11350	−	0.375407i
$134$		0			0
$135$	13.5011	−	22.2318i	0.100008	−	0.164680i
$136$		0			0
$137$	203.912			1.48841			0.744203	−	0.667954i	$-0.232830\pi$
$137$	203.912			1.48841			0.744203	+	0.667954i	$0.232830\pi$
$138$		0			0
$139$	−77.3785	−	44.6745i	−0.556680	−	0.321399i	0.195132	−	0.980777i	$-0.437486\pi$
$139$	−77.3785	−	44.6745i	−0.556680	−	0.321399i	−0.751812	+	0.659378i	$0.770820\pi$
$140$		0			0
$141$	26.5570	−	9.44438i	0.188348	−	0.0669814i
$142$		0			0
$143$	3.18703	+	1.84003i	0.0222869	+	0.0128674i
$144$		0			0
$145$	20.6673	−	11.9323i	0.142533	−	0.0822914i
$146$		0			0
$147$	131.165	−	66.3679i	0.892280	−	0.451482i
$148$		0			0
$149$	126.472			0.848808			0.424404	−	0.905473i	$-0.360484\pi$
$149$	126.472			0.848808			0.424404	+	0.905473i	$0.360484\pi$
$150$		0			0
$151$	33.9775			0.225017			0.112508	−	0.993651i	$-0.464111\pi$
$151$	33.9775			0.225017			0.112508	+	0.993651i	$0.464111\pi$
$152$		0			0
$153$	−16.1055	+	42.2947i	−0.105265	+	0.276436i
$154$		0			0
$155$	−11.7289	−	20.3151i	−0.0756706	−	0.131065i
$156$		0			0
$157$	39.5383	−	22.8274i	0.251836	−	0.145398i	−0.368769	−	0.929521i	$-0.620220\pi$
$157$	39.5383	−	22.8274i	0.251836	−	0.145398i	0.620605	+	0.784124i	$0.286887\pi$
$158$		0			0
$159$	89.9403	+	252.907i	0.565662	+	1.59061i
$160$		0			0
$161$	−103.525	−	20.8160i	−0.643013	−	0.129292i
$162$		0			0
$163$	65.6487	+	113.707i	0.402753	+	0.697588i	0.994057	−	0.108860i	$-0.0347201\pi$
$163$	65.6487	+	113.707i	0.402753	+	0.697588i	−0.591304	+	0.806449i	$0.701387\pi$
$164$		0			0
$165$	18.2067	+	15.5079i	0.110344	+	0.0939872i
$166$		0			0
$167$	−205.982	−	118.924i	−1.23343	−	0.712118i	−0.265683	−	0.964060i	$-0.585597\pi$
$167$	−205.982	−	118.924i	−1.23343	−	0.712118i	−0.967742	+	0.251942i	$0.918931\pi$
$168$		0			0
$169$	−84.4011	−	146.187i	−0.499415	−	0.865012i
$170$		0			0
$171$	−126.873	−	155.820i	−0.741948	−	0.911228i
$172$		0			0
$173$	268.118	+	154.798i	1.54981	+	0.894785i	0.998155	+	0.0607137i	$0.0193377\pi$
$173$	268.118	+	154.798i	1.54981	+	0.894785i	0.551657	+	0.834071i	$0.313996\pi$
$174$		0			0
$175$	165.197	+	33.2165i	0.943985	+	0.189809i
$176$		0			0
$177$	−14.8852	+	80.9182i	−0.0840974	+	0.457165i
$178$		0			0
$179$	151.419	−	262.266i	0.845917	−	1.46517i	−0.0389054	−	0.999243i	$-0.512387\pi$
$179$	151.419	−	262.266i	0.845917	−	1.46517i	0.884822	−	0.465928i	$-0.154280\pi$
$180$		0			0
$181$		−	205.717i		−	1.13656i	−0.822835	−	0.568280i	$-0.807609\pi$
$181$		−	205.717i		−	1.13656i	0.822835	−	0.568280i	$-0.192391\pi$
$182$		0			0
$183$	224.956	−	80.0004i	1.22927	−	0.437161i
$184$		0			0
$185$	25.2288	−	14.5659i	0.136372	−	0.0787344i
$186$		0			0
$187$	−36.0383	−	20.8067i	−0.192718	−	0.111266i
$188$		0			0
$189$	−139.036	−	128.024i	−0.735639	−	0.677373i
$190$		0			0
$191$	−36.5455	+	63.2987i	−0.191338	+	0.331407i	−0.945694	−	0.325059i	$-0.894616\pi$
$191$	−36.5455	+	63.2987i	−0.191338	+	0.331407i	0.754356	+	0.656465i	$0.227949\pi$
$192$		0			0
$193$	−177.413	−	307.288i	−0.919236	−	1.59216i	−0.800578	−	0.599229i	$-0.795474\pi$
$193$	−177.413	−	307.288i	−0.919236	−	1.59216i	−0.118658	−	0.992935i	$-0.537859\pi$
$194$		0			0
$195$	0.430630	+	1.21091i	0.00220836	+	0.00620977i
$196$		0			0
$197$	−2.81361			−0.0142823			−0.00714113	−	0.999975i	$-0.502273\pi$
$197$	−2.81361			−0.0142823			−0.00714113	+	0.999975i	$0.502273\pi$
$198$		0			0
$199$	92.6937	+	53.5167i	0.465797	+	0.268928i	0.714479	−	0.699657i	$-0.246664\pi$
$199$	92.6937	+	53.5167i	0.465797	+	0.268928i	−0.248681	+	0.968585i	$0.579997\pi$
$200$		0			0
$201$	41.8405	+	7.69672i	0.208161	+	0.0382921i
$202$		0			0
$203$	−55.3991	−	164.321i	−0.272902	−	0.809461i
$204$		0			0
$205$	−11.7102	+	20.2827i	−0.0571230	+	0.0989399i
$206$		0			0
$207$	21.5979	+	134.039i	0.104338	+	0.647531i
$208$		0			0
$209$	160.008	−	92.3805i	0.765587	−	0.442012i
$210$		0			0
$211$	0.310904	−	0.538502i	0.00147348	−	0.00255214i	−0.865288	−	0.501276i	$-0.832864\pi$
$211$	0.310904	−	0.538502i	0.00147348	−	0.00255214i	0.866761	+	0.498723i	$0.166198\pi$
$212$		0			0
$213$	−259.571	+	304.744i	−1.21864	+	1.43072i
$214$		0			0
$215$	−19.3153	+	11.1517i	−0.0898387	+	0.0518684i
$216$		0			0
$217$	−161.521	+	54.4552i	−0.744336	+	0.250946i
$218$		0			0
$219$	167.394	−	59.5296i	0.764354	−	0.271825i
$220$		0			0
$221$	−1.11811	−	1.93662i	−0.00505932	−	0.00876299i
$222$		0			0
$223$	−347.765	+	200.782i	−1.55948	+	0.900368i	−0.562177	+	0.827017i	$0.690036\pi$
$223$	−347.765	+	200.782i	−1.55948	+	0.900368i	−0.997306	+	0.0733508i	$0.976631\pi$
$224$		0			0
$225$	−34.4642	−	213.889i	−0.153174	−	0.950617i
$226$		0			0
$227$			391.807i			1.72602i	0.505187	+	0.863010i	$0.331424\pi$
$227$			391.807i			1.72602i	−0.505187	+	0.863010i	$0.668576\pi$
$228$		0			0
$229$			128.808i			0.562480i	0.959637	+	0.281240i	$0.0907458\pi$
$229$			128.808i			0.562480i	−0.959637	+	0.281240i	$0.909254\pi$
$230$		0			0
$231$	136.554	−	107.487i	0.591142	−	0.465313i
$232$		0			0
$233$	−17.8368	−	30.8942i	−0.0765526	−	0.132593i	0.825208	−	0.564829i	$-0.191058\pi$
$233$	−17.8368	−	30.8942i	−0.0765526	−	0.132593i	−0.901760	+	0.432236i	$0.857725\pi$
$234$		0			0
$235$	−4.52553	+	7.83844i	−0.0192576	+	0.0333551i
$236$		0			0
$237$	20.0712	+	56.4391i	0.0846887	+	0.238139i
$238$		0			0
$239$	142.757	−	247.262i	0.597308	−	1.03457i	−0.395909	−	0.918290i	$-0.629570\pi$
$239$	142.757	−	247.262i	0.597308	−	1.03457i	0.993217	−	0.116278i	$-0.0370963\pi$
$240$		0			0
$241$		−	138.284i		−	0.573792i	−0.957962	−	0.286896i	$-0.907377\pi$
$241$		−	138.284i		−	0.573792i	0.957962	−	0.286896i	$-0.0926234\pi$
$242$		0			0
$243$	−91.4865	+	225.120i	−0.376488	+	0.926422i
$244$		0			0
$245$	−18.2451	+	43.5353i	−0.0744696	+	0.177695i
$246$		0			0
$247$	9.92866			0.0401970
$248$		0			0
$249$	−63.3119	+	344.173i	−0.254265	+	1.38222i
$250$		0			0
$251$		−	29.7450i		−	0.118506i	−0.998243	−	0.0592530i	$-0.981128\pi$
$251$		−	29.7450i		−	0.118506i	0.998243	−	0.0592530i	$-0.0188719\pi$
$252$		0			0
$253$	−124.837			−0.493425
$254$		0			0
$255$	−4.86949	−	13.6927i	−0.0190960	−	0.0536969i
$256$		0			0
$257$		−	289.004i		−	1.12453i	−0.826957	−	0.562265i	$-0.809930\pi$
$257$		−	289.004i		−	1.12453i	0.826957	−	0.562265i	$-0.190070\pi$
$258$		0			0
$259$	−67.6265	−	200.589i	−0.261106	−	0.774473i
$260$		0			0
$261$	−172.891	+	140.773i	−0.662417	+	0.539359i
$262$		0			0
$263$	316.849			1.20475			0.602375	−	0.798213i	$-0.294221\pi$
$263$	316.849			1.20475			0.602375	+	0.798213i	$0.294221\pi$
$264$		0			0
$265$	−74.6467	−	43.0973i	−0.281686	−	0.162631i
$266$		0			0
$267$	−65.8458	+	357.947i	−0.246613	+	1.34063i
$268$		0			0
$269$	154.361	+	89.1206i	0.573834	+	0.331303i	0.758679	−	0.651464i	$-0.225845\pi$
$269$	154.361	+	89.1206i	0.573834	+	0.331303i	−0.184845	+	0.982768i	$0.559178\pi$
$270$		0			0
$271$	−299.052	+	172.658i	−1.10351	+	0.637114i	−0.937142	−	0.348948i	$-0.886539\pi$
$271$	−299.052	+	172.658i	−1.10351	+	0.637114i	−0.166373	+	0.986063i	$0.553205\pi$
$272$		0			0
$273$	9.24305	−	1.33323i	0.0338573	−	0.00488361i
$274$		0			0
$275$	199.204			0.724380
$276$		0			0
$277$	−374.339			−1.35140			−0.675702	−	0.737175i	$-0.736159\pi$
$277$	−374.339			−1.35140			−0.675702	+	0.737175i	$0.736159\pi$
$278$		0			0
$279$	138.374	+	169.945i	0.495964	+	0.609122i
$280$		0			0
$281$	−168.976	−	292.676i	−0.601340	−	1.04155i	−0.992618	−	0.121279i	$-0.961301\pi$
$281$	−168.976	−	292.676i	−0.601340	−	1.04155i	0.391279	−	0.920272i	$-0.372033\pi$
$282$		0			0
$283$	370.026	−	213.634i	1.30751	−	0.754892i	0.325831	−	0.945428i	$-0.394356\pi$
$283$	370.026	−	213.634i	1.30751	−	0.754892i	0.981680	+	0.190536i	$0.0610225\pi$
$284$		0			0
$285$	63.4598	+	11.6737i	0.222666	+	0.0409603i
$286$		0			0
$287$	127.716	+	112.474i	0.445002	+	0.391894i
$288$		0			0
$289$	−131.857	−	228.382i	−0.456251	−	0.790250i
$290$		0			0
$291$	−33.3611	+	181.356i	−0.114643	+	0.623215i
$292$		0			0
$293$	−54.0168	−	31.1866i	−0.184358	−	0.106439i	0.404981	−	0.914325i	$-0.367278\pi$
$293$	−54.0168	−	31.1866i	−0.184358	−	0.106439i	−0.589338	+	0.807886i	$0.700612\pi$
$294$		0			0
$295$	−13.2100	−	22.8804i	−0.0447797	−	0.0775607i
$296$		0			0
$297$	−190.977	−	115.978i	−0.643021	−	0.390498i
$298$		0			0
$299$	−5.80968	−	3.35422i	−0.0194304	−	0.0112181i
$300$		0			0
$301$	51.7752	+	153.572i	0.172011	+	0.510205i
$302$		0			0
$303$	271.823	+	231.530i	0.897104	+	0.764124i
$304$		0			0
$305$	−38.3343	+	66.3970i	−0.125686	+	0.217695i
$306$		0			0
$307$			473.374i			1.54194i	0.636874	+	0.770968i	$0.280227\pi$
$307$			473.374i			1.54194i	−0.636874	+	0.770968i	$0.719773\pi$
$308$		0			0
$309$	221.595	+	188.747i	0.717135	+	0.610832i
$310$		0			0
$311$	−125.112	+	72.2333i	−0.402288	+	0.232261i	−0.687471	−	0.726212i	$-0.741279\pi$
$311$	−125.112	+	72.2333i	−0.402288	+	0.232261i	0.285183	+	0.958473i	$0.407946\pi$
$312$		0			0
$313$	16.2589	+	9.38707i	0.0519453	+	0.0299906i	0.525748	−	0.850641i	$-0.323786\pi$
$313$	16.2589	+	9.38707i	0.0519453	+	0.0299906i	−0.473802	+	0.880631i	$0.657119\pi$
$314$		0			0
$315$	60.6453	+	2.34616i	0.192525	+	0.00744814i
$316$		0			0
$317$	−13.0645	+	22.6284i	−0.0412131	+	0.0713831i	−0.885896	−	0.463884i	$-0.846456\pi$
$317$	−13.0645	+	22.6284i	−0.0412131	+	0.0713831i	0.844683	+	0.535267i	$0.179789\pi$
$318$		0			0
$319$	−102.501	−	177.537i	−0.321320	−	0.556543i
$320$		0			0
$321$	−225.171	−	41.4211i	−0.701466	−	0.129038i
$322$		0			0
$323$	−112.271			−0.347590
$324$		0			0
$325$	9.27064	+	5.35241i	0.0285251	+	0.0164690i
$326$		0			0
$327$	−38.5728	−	108.464i	−0.117960	−	0.331695i
$328$		0			0
$329$	49.3570	+	43.4666i	0.150021	+	0.132117i
$330$		0			0
$331$	−140.657	+	243.624i	−0.424944	+	0.736025i	−0.996415	−	0.0845973i	$-0.973040\pi$
$331$	−140.657	+	243.624i	−0.424944	+	0.736025i	0.571471	+	0.820622i	$0.306373\pi$
$332$		0			0
$333$	−211.050	+	171.843i	−0.633784	+	0.516045i
$334$		0			0
$335$	−11.8308	+	6.83051i	−0.0353158	+	0.0203896i
$336$		0			0
$337$	−94.4669	+	163.621i	−0.280317	+	0.485523i	−0.971463	−	0.237192i	$-0.923773\pi$
$337$	−94.4669	+	163.621i	−0.280317	+	0.485523i	0.691146	+	0.722715i	$0.257106\pi$
$338$		0			0
$339$	−206.149	−	579.678i	−0.608109	−	1.70996i
$340$		0			0
$341$	−174.512	+	100.755i	−0.511766	+	0.295468i
$342$		0			0
$343$	284.002	+	192.333i	0.827993	+	0.560738i
$344$		0			0
$345$	−33.1893	−	28.2696i	−0.0962009	−	0.0819408i
$346$		0			0
$347$	39.7467	+	68.8433i	0.114544	+	0.198396i	0.917597	−	0.397511i	$-0.130126\pi$
$347$	39.7467	+	68.8433i	0.114544	+	0.198396i	−0.803054	+	0.595907i	$0.796793\pi$
$348$		0			0
$349$	256.280	−	147.963i	0.734327	−	0.423964i	−0.0856763	−	0.996323i	$-0.527305\pi$
$349$	256.280	−	147.963i	0.734327	−	0.423964i	0.820003	+	0.572359i	$0.193972\pi$
$350$		0			0
$351$	−5.77156	−	10.5288i	−0.0164432	−	0.0299965i
$352$		0			0
$353$			479.848i			1.35934i	0.733516	+	0.679672i	$0.237878\pi$
$353$			479.848i			1.35934i	−0.733516	+	0.679672i	$0.762122\pi$
$354$		0			0
$355$		−	128.544i		−	0.362097i
$356$		0			0
$357$	−104.519	+	15.0759i	−0.292770	+	0.0422293i
$358$		0			0
$359$	−267.870	−	463.964i	−0.746156	−	1.29238i	−0.949653	−	0.313304i	$-0.898564\pi$
$359$	−267.870	−	463.964i	−0.746156	−	1.29238i	0.203497	−	0.979076i	$-0.434769\pi$
$360$		0			0
$361$	68.7387	−	119.059i	0.190412	−	0.329803i
$362$		0			0
$363$	−102.163	+	119.942i	−0.281441	+	0.330420i
$364$		0			0
$365$	−28.5252	+	49.4071i	−0.0781512	+	0.135362i
$366$		0			0
$367$		−	272.723i		−	0.743115i	−0.928410	−	0.371557i	$-0.878824\pi$
$367$		−	272.723i		−	0.743115i	0.928410	−	0.371557i	$-0.121176\pi$
$368$		0			0
$369$	77.8650	−	204.481i	0.211016	−	0.554148i
$370$		0			0
$371$	−413.939	+	470.034i	−1.11574	+	1.26694i
$372$		0			0
$373$	−671.704			−1.80082			−0.900408	−	0.435047i	$-0.856732\pi$
$373$	−671.704			−1.80082			−0.900408	+	0.435047i	$0.856732\pi$
$374$		0			0
$375$	107.964	+	91.9599i	0.287903	+	0.245226i
$376$		0			0
$377$		−	11.0164i		−	0.0292212i
$378$		0			0
$379$	−140.974			−0.371962			−0.185981	−	0.982553i	$-0.559546\pi$
$379$	−140.974			−0.371962			−0.185981	+	0.982553i	$0.559546\pi$
$380$		0			0
$381$	−139.694	+	164.005i	−0.366651	+	0.430460i
$382$		0			0
$383$		−	397.648i		−	1.03825i	−0.854700	−	0.519123i	$-0.826259\pi$
$383$		−	397.648i		−	1.03825i	0.854700	−	0.519123i	$-0.173741\pi$
$384$		0			0
$385$	−11.0005	+	54.7092i	−0.0285726	+	0.142102i
$386$		0			0
$387$	161.581	−	131.564i	0.417522	−	0.339958i
$388$		0			0
$389$	518.270			1.33231			0.666157	−	0.745812i	$-0.267938\pi$
$389$	518.270			1.33231			0.666157	+	0.745812i	$0.267938\pi$
$390$		0			0
$391$	65.6949	+	37.9289i	0.168018	+	0.0970050i
$392$		0			0
$393$	−17.2431	−	14.6871i	−0.0438756	−	0.0373718i
$394$		0			0
$395$	−16.6583	−	9.61766i	−0.0421729	−	0.0243485i
$396$		0			0
$397$	301.974	−	174.345i	0.760640	−	0.439156i	−0.0688856	−	0.997625i	$-0.521944\pi$
$397$	301.974	−	174.345i	0.760640	−	0.439156i	0.829525	+	0.558469i	$0.188611\pi$
$398$		0			0
$399$	174.060	−	435.352i	0.436240	−	1.09111i
$400$		0			0
$401$	210.523			0.524996			0.262498	−	0.964933i	$-0.415454\pi$
$401$	210.523			0.524996			0.262498	+	0.964933i	$0.415454\pi$
$402$		0			0
$403$	−10.8287			−0.0268702
$404$		0			0
$405$	−24.5101	−	74.0815i	−0.0605188	−	0.182917i
$406$		0			0
$407$	−125.125	−	216.722i	−0.307431	−	0.532487i
$408$		0			0
$409$	464.682	−	268.285i	1.13614	−	0.655952i	0.190670	−	0.981654i	$-0.438934\pi$
$409$	464.682	−	268.285i	1.13614	−	0.655952i	0.945473	+	0.325702i	$0.105601\pi$
$410$		0			0
$411$	396.666	−	465.698i	0.965125	−	1.13309i
$412$		0			0
$413$	−181.917	+	61.3315i	−0.440476	+	0.148502i
$414$		0			0
$415$	−56.1866	−	97.3180i	−0.135389	−	0.234501i
$416$		0			0
$417$	−252.552	+	89.8142i	−0.605640	+	0.215382i
$418$		0			0
$419$	368.723	+	212.882i	0.880007	+	0.508072i	0.870661	−	0.491884i	$-0.163692\pi$
$419$	368.723	+	212.882i	0.880007	+	0.508072i	0.00934643	+	0.999956i	$0.497025\pi$
$420$		0			0
$421$	399.672	+	692.253i	0.949341	+	1.64431i	0.746818	+	0.665029i	$0.231581\pi$
$421$	399.672	+	692.253i	0.949341	+	1.64431i	0.202523	+	0.979277i	$0.435086\pi$
$422$		0			0
$423$	30.0917	−	79.0236i	0.0711388	−	0.186817i
$424$		0			0
$425$	−104.831	−	60.5241i	−0.246661	−	0.142410i
$426$		0			0
$427$	418.088	+	368.192i	0.979129	+	0.862276i
$428$		0			0
$429$	10.4020	−	3.69923i	0.0242471	−	0.00862290i
$430$		0			0
$431$	33.3100	−	57.6946i	0.0772854	−	0.133862i	−0.824792	−	0.565436i	$-0.808708\pi$
$431$	33.3100	−	57.6946i	0.0772854	−	0.133862i	0.902078	+	0.431573i	$0.142041\pi$
$432$		0			0
$433$		−	532.074i		−	1.22881i	−0.788991	−	0.614405i	$-0.789396\pi$
$433$		−	532.074i		−	1.22881i	0.788991	−	0.614405i	$-0.210604\pi$
$434$		0			0
$435$	12.9526	−	70.4121i	0.0297761	−	0.161867i
$436$		0			0
$437$	−291.681	+	168.402i	−0.667461	+	0.385359i
$438$		0			0
$439$	222.308	+	128.350i	0.506397	+	0.292368i	0.731351	−	0.682001i	$-0.238890\pi$
$439$	222.308	+	128.350i	0.506397	+	0.292368i	−0.224955	+	0.974369i	$0.572223\pi$
$440$		0			0
$441$	103.581	−	428.663i	0.234878	−	0.972025i
$442$		0			0
$443$	−45.0204	+	77.9776i	−0.101626	+	0.176022i	−0.912355	−	0.409400i	$-0.865738\pi$
$443$	−45.0204	+	77.9776i	−0.101626	+	0.176022i	0.810729	+	0.585422i	$0.199071\pi$
$444$		0			0
$445$	−58.4353	−	101.213i	−0.131315	−	0.227445i
$446$		0			0
$447$	246.025	−	288.841i	0.550391	−	0.646176i
$448$		0			0
$449$	−238.627			−0.531464			−0.265732	−	0.964047i	$-0.585614\pi$
$449$	−238.627			−0.531464			−0.265732	+	0.964047i	$0.585614\pi$
$450$		0			0
$451$	174.233	+	100.594i	0.386327	+	0.223046i
$452$		0			0
$453$	66.0960	−	77.5987i	0.145907	−	0.171300i
$454$		0			0
$455$	−1.98192	+	2.25050i	−0.00435587	+	0.00494616i
$456$		0			0
$457$	312.577	−	541.400i	0.683977	−	1.18468i	−0.289781	−	0.957093i	$-0.593582\pi$
$457$	312.577	−	541.400i	0.683977	−	1.18468i	0.973757	−	0.227589i	$-0.0730843\pi$
$458$		0			0
$459$	65.2637	+	119.057i	0.142187	+	0.259385i
$460$		0			0
$461$	612.475	−	353.613i	1.32858	−	0.767056i	0.343500	−	0.939153i	$-0.388388\pi$
$461$	612.475	−	353.613i	1.32858	−	0.767056i	0.985080	+	0.172097i	$0.0550542\pi$
$462$		0			0
$463$	−420.069	+	727.582i	−0.907277	+	1.57145i	−0.0894469	+	0.995992i	$0.528510\pi$
$463$	−420.069	+	727.582i	−0.907277	+	1.57145i	−0.817831	+	0.575459i	$0.804823\pi$
$464$		0			0
$465$	−69.2124	−	12.7319i	−0.148844	−	0.0273804i
$466$		0			0
$467$	−37.7190	+	21.7771i	−0.0807688	+	0.0466319i	−0.539840	−	0.841767i	$-0.681515\pi$
$467$	−37.7190	+	21.7771i	−0.0807688	+	0.0466319i	0.459072	+	0.888399i	$0.348182\pi$
$468$		0			0
$469$	31.7127	+	94.0638i	0.0676177	+	0.200563i
$470$		0			0
$471$	24.7794	−	134.704i	0.0526102	−	0.285997i
$472$		0			0
$473$	95.7960	+	165.924i	0.202529	+	0.350790i
$474$		0			0
$475$	465.441	−	268.723i	0.979877	−	0.565732i
$476$		0			0
$477$	752.554	+	286.568i	1.57768	+	0.600771i
$478$		0			0
$479$		−	670.529i		−	1.39985i	−0.714215	−	0.699926i	$-0.753216\pi$
$479$		−	670.529i		−	1.39985i	0.714215	−	0.699926i	$-0.246784\pi$
$480$		0			0
$481$		−	13.4478i		−	0.0279581i
$482$		0			0
$483$	−248.926	+	195.940i	−0.515375	+	0.405674i
$484$		0			0
$485$	−29.6065	−	51.2800i	−0.0610444	−	0.105732i
$486$		0			0
$487$	365.228	−	632.594i	0.749955	−	1.29896i	−0.197888	−	0.980225i	$-0.563408\pi$
$487$	365.228	−	632.594i	0.749955	−	1.29896i	0.947843	−	0.318736i	$-0.103258\pi$
$488$		0			0
$489$	387.392	+	71.2624i	0.792213	+	0.145731i
$490$		0			0
$491$	−256.934	+	445.023i	−0.523287	+	0.906360i	0.476346	+	0.879258i	$0.341961\pi$
$491$	−256.934	+	445.023i	−0.523287	+	0.906360i	−0.999633	+	0.0271018i	$0.991372\pi$
$492$		0			0
$493$			124.571i			0.252680i
$494$		0			0
$495$	70.8346	−	11.4137i	0.143100	−	0.0230580i
$496$		0			0
$497$	−915.722	−	184.126i	−1.84250	−	0.370474i
$498$		0			0
$499$	153.056			0.306724			0.153362	−	0.988170i	$-0.450990\pi$
$499$	153.056			0.306724			0.153362	+	0.988170i	$0.450990\pi$
$500$		0			0
$501$	−672.295	+	239.086i	−1.34191	+	0.477218i
$502$		0			0
$503$			80.5356i			0.160110i	0.996790	+	0.0800552i	$0.0255097\pi$
$503$			80.5356i			0.160110i	−0.996790	+	0.0800552i	$0.974490\pi$
$504$		0			0
$505$	−114.658			−0.227045
$506$		0			0
$507$	−498.050	−	91.6183i	−0.982347	−	0.180707i
$508$		0			0
$509$			66.7632i			0.131165i	0.997847	+	0.0655827i	$0.0208906\pi$
$509$			66.7632i			0.131165i	−0.997847	+	0.0655827i	$0.979109\pi$
$510$		0			0
$511$	311.106	+	273.977i	0.608818	+	0.536159i
$512$		0			0
$513$	−602.670	−	13.3585i	−1.17480	−	0.0260399i
$514$		0			0
$515$	−93.4711			−0.181497
$516$		0			0
$517$	67.3342	+	38.8754i	0.130240	+	0.0751943i
$518$		0			0
$519$	875.097	−	311.208i	1.68612	−	0.599629i
$520$		0			0
$521$	828.396	+	478.274i	1.59001	+	0.917993i	0.993303	+	0.115534i	$0.0368580\pi$
$521$	828.396	+	478.274i	1.59001	+	0.917993i	0.596707	+	0.802459i	$0.296475\pi$
$522$		0			0
$523$	−77.4777	+	44.7318i	−0.148141	+	0.0855292i	−0.572238	−	0.820087i	$-0.693925\pi$
$523$	−77.4777	+	44.7318i	−0.148141	+	0.0855292i	0.424097	+	0.905617i	$0.360591\pi$
$524$		0			0
$525$	397.217	−	312.666i	0.756604	−	0.595555i
$526$		0			0
$527$	122.449			0.232350
$528$		0			0
$529$	−301.433			−0.569817
$530$		0			0
$531$	155.847	+	191.404i	0.293497	+	0.360460i
$532$		0			0
$533$	5.40569	+	9.36293i	0.0101420	+	0.0175665i
$534$		0			0
$535$	63.6691	−	36.7594i	0.119008	−	0.0687092i
$536$		0			0
$537$	−304.415	−	855.997i	−0.566881	−	1.59404i
$538$		0			0
$539$	373.979	+	156.730i	0.693839	+	0.290779i
$540$		0			0
$541$	13.8403	+	23.9722i	0.0255829	+	0.0443109i	0.878533	−	0.477681i	$-0.158522\pi$
$541$	13.8403	+	23.9722i	0.0255829	+	0.0443109i	−0.852951	+	0.521992i	$0.825189\pi$
$542$		0			0
$543$	−469.823	−	400.179i	−0.865235	−	0.736979i
$544$		0			0
$545$	32.0138	+	18.4832i	0.0587409	+	0.0339141i
$546$		0			0
$547$	339.847	+	588.632i	0.621292	+	1.07611i	0.989245	+	0.146265i	$0.0467253\pi$
$547$	339.847	+	588.632i	0.621292	+	1.07611i	−0.367953	+	0.929844i	$0.619941\pi$
$548$		0			0
$549$	254.897	−	669.385i	0.464294	−	1.21928i
$550$		0			0
$551$	−478.988	−	276.544i	−0.869307	−	0.501894i
$552$		0			0
$553$	−92.3753	+	104.894i	−0.167044	+	0.189681i
$554$		0			0
$555$	15.8114	−	85.9530i	0.0284890	−	0.154870i
$556$		0			0
$557$	−172.676	+	299.083i	−0.310010	+	0.536954i	−0.978364	−	0.206890i	$-0.933666\pi$
$557$	−172.676	+	299.083i	−0.310010	+	0.536954i	0.668354	+	0.743843i	$0.266999\pi$
$558$		0			0
$559$			10.2957i			0.0184181i
$560$		0			0
$561$	−117.624	+	41.8302i	−0.209668	+	0.0745636i
$562$		0			0
$563$	−930.283	+	537.099i	−1.65237	+	0.953995i	−0.676273	+	0.736651i	$0.736406\pi$
$563$	−930.283	+	537.099i	−1.65237	+	0.953995i	−0.976095	+	0.217344i	$0.930261\pi$
$564$		0			0
$565$	171.095	+	98.7817i	0.302823	+	0.174835i
$566$		0			0
$567$	−562.848	+	68.4909i	−0.992677	+	0.120795i
$568$		0			0
$569$	307.619	−	532.811i	0.540630	−	0.936399i	−0.458238	−	0.888830i	$-0.651519\pi$
$569$	307.619	−	532.811i	0.540630	−	0.936399i	0.998868	−	0.0475691i	$-0.0151474\pi$
$570$		0			0
$571$	−248.251	−	429.983i	−0.434765	−	0.753035i	0.562512	−	0.826789i	$-0.309835\pi$
$571$	−248.251	−	429.983i	−0.434765	−	0.753035i	−0.997276	+	0.0737547i	$0.976502\pi$
$572$		0			0
$573$	73.4716	+	206.598i	0.128223	+	0.360554i
$574$		0			0
$575$	−363.133			−0.631536
$576$		0			0
$577$	514.284	+	296.922i	0.891306	+	0.514596i	0.874369	−	0.485261i	$-0.161275\pi$
$577$	514.284	+	296.922i	0.891306	+	0.514596i	0.0169365	+	0.999857i	$0.494609\pi$
$578$		0			0
$579$	−1046.91	−	192.583i	−1.80813	−	0.332614i
$580$		0			0
$581$	−773.753	+	260.863i	−1.33176	+	0.448990i
$582$		0			0
$583$	−370.217	+	641.234i	−0.635020	+	1.09989i
$584$		0			0
$585$	3.60320	+	1.37207i	0.00615931	+	0.00234543i
$586$		0			0
$587$	−322.786	+	186.360i	−0.549890	+	0.317479i	−0.749078	−	0.662482i	$-0.769503\pi$
$587$	−322.786	+	186.360i	−0.549890	+	0.317479i	0.199187	+	0.979961i	$0.436170\pi$
$588$		0			0
$589$	−271.832	+	470.827i	−0.461514	+	0.799366i
$590$		0			0
$591$	−5.47327	+	6.42578i	−0.00926103	+	0.0108727i
$592$		0			0
$593$	−857.809	+	495.256i	−1.44656	+	0.835171i	−0.998274	−	0.0587202i	$-0.981298\pi$
$593$	−857.809	+	495.256i	−1.44656	+	0.835171i	−0.448284	+	0.893891i	$0.647965\pi$
$594$		0			0
$595$	22.4112	−	25.4483i	0.0376659	−	0.0427702i
$596$		0			0
$597$	302.539	−	107.591i	0.506765	−	0.180219i
$598$		0			0
$599$	340.110	+	589.088i	0.567796	+	0.983452i	0.996784	+	0.0801414i	$0.0255372\pi$
$599$	340.110	+	589.088i	0.567796	+	0.983452i	−0.428987	+	0.903311i	$0.641129\pi$
$600$		0			0
$601$	132.268	−	76.3649i	0.220080	−	0.127063i	−0.385908	−	0.922537i	$-0.626112\pi$
$601$	132.268	−	76.3649i	0.220080	−	0.127063i	0.605987	+	0.795474i	$0.292778\pi$
$602$		0			0
$603$	98.9697	−	80.5840i	0.164129	−	0.133638i
$604$		0			0
$605$		−	50.5931i		−	0.0836250i
$606$		0			0
$607$			291.769i			0.480674i	0.970690	+	0.240337i	$0.0772579\pi$
$607$			291.769i			0.480674i	−0.970690	+	0.240337i	$0.922742\pi$
$608$		0			0
$609$	−483.047	−	193.129i	−0.793181	−	0.317125i
$610$		0			0
$611$	2.08908	+	3.61840i	0.00341912	+	0.00592209i
$612$		0			0
$613$	−152.238	+	263.684i	−0.248349	+	0.430154i	−0.963068	−	0.269258i	$-0.913221\pi$
$613$	−152.238	+	263.684i	−0.248349	+	0.430154i	0.714719	+	0.699412i	$0.246555\pi$
$614$		0			0
$615$	23.5424	+	66.1997i	0.0382803	+	0.107642i
$616$		0			0
$617$	−42.3876	+	73.4174i	−0.0686995	+	0.118991i	−0.898329	−	0.439323i	$-0.855218\pi$
$617$	−42.3876	+	73.4174i	−0.0686995	+	0.118991i	0.829630	+	0.558314i	$0.188552\pi$
$618$		0			0
$619$		−	649.483i		−	1.04925i	−0.851335	−	0.524623i	$-0.824206\pi$
$619$		−	649.483i		−	1.04925i	0.851335	−	0.524623i	$-0.175794\pi$
$620$		0			0
$621$	348.136	+	211.418i	0.560605	+	0.340448i
$622$		0			0
$623$	−804.720	+	271.304i	−1.29169	+	0.435480i
$624$		0			0
$625$	556.259			0.890014
$626$		0			0
$627$	100.280	−	545.136i	0.159936	−	0.869436i
$628$		0			0
$629$			152.066i			0.241758i
$630$		0			0
$631$	−46.9650			−0.0744295			−0.0372147	−	0.999307i	$-0.511849\pi$
$631$	−46.9650			−0.0744295			−0.0372147	+	0.999307i	$0.511849\pi$
$632$		0			0
$633$	−0.625047	−	1.75759i	−0.000987435	−	0.00277661i
$634$		0			0
$635$		−	69.1793i		−	0.108944i
$636$		0			0
$637$	13.1932	+	17.3424i	0.0207115	+	0.0272251i
$638$		0			0
$639$	191.042	+	1185.63i	0.298971	+	1.85544i
$640$		0			0
$641$	287.551			0.448597			0.224298	−	0.974520i	$-0.427991\pi$
$641$	287.551			0.448597			0.224298	+	0.974520i	$0.427991\pi$
$642$		0			0
$643$	−7.84398	−	4.52872i	−0.0121990	−	0.00704312i	0.493888	−	0.869525i	$-0.335575\pi$
$643$	−7.84398	−	4.52872i	−0.0121990	−	0.00704312i	−0.506087	+	0.862482i	$0.668909\pi$
$644$		0			0
$645$	−12.1053	+	65.8061i	−0.0187679	+	0.102025i
$646$		0			0
$647$	366.328	+	211.499i	0.566194	+	0.326892i	0.755628	−	0.655001i	$-0.227332\pi$
$647$	366.328	+	211.499i	0.566194	+	0.326892i	−0.189434	+	0.981894i	$0.560665\pi$
$648$		0			0
$649$	−196.548	+	113.477i	−0.302848	+	0.174850i
$650$		0			0
$651$	−189.838	+	474.817i	−0.291610	+	0.729365i
$652$		0			0
$653$	361.234			0.553191			0.276596	−	0.960986i	$-0.410794\pi$
$653$	361.234			0.553191			0.276596	+	0.960986i	$0.410794\pi$
$654$		0			0
$655$	7.27333			0.0111043
$656$		0			0
$657$	189.673	−	498.100i	0.288696	−	0.758143i
$658$		0			0
$659$	−271.135	−	469.619i	−0.411433	−	0.712624i	0.583613	−	0.812032i	$-0.301638\pi$
$659$	−271.135	−	469.619i	−0.411433	−	0.712624i	−0.995047	+	0.0994081i	$0.968305\pi$
$660$		0			0
$661$	772.501	−	446.003i	1.16868	−	0.674740i	0.215315	−	0.976545i	$-0.430922\pi$
$661$	772.501	−	446.003i	1.16868	−	0.674740i	0.953370	+	0.301804i	$0.0975889\pi$
$662$		0			0
$663$	−6.59795	−	1.21372i	−0.00995166	−	0.00183065i
$664$		0			0
$665$	48.0990	+	142.667i	0.0723293	+	0.214538i
$666$		0			0
$667$	186.851	+	323.635i	0.280136	+	0.485211i
$668$		0			0
$669$	−217.951	+	1184.81i	−0.325786	+	1.77102i
$670$		0			0
$671$	570.368	+	329.302i	0.850026	+	0.490763i
$672$		0			0
$673$	40.9317	+	70.8958i	0.0608197	+	0.105343i	0.894832	−	0.446403i	$-0.147295\pi$
$673$	40.9317	+	70.8958i	0.0608197	+	0.105343i	−0.834012	+	0.551746i	$0.813962\pi$
$674$		0			0
$675$	−555.528	−	337.365i	−0.823004	−	0.499800i
$676$		0			0
$677$	−452.877	−	261.469i	−0.668946	−	0.386216i	0.126731	−	0.991937i	$-0.459552\pi$
$677$	−452.877	−	261.469i	−0.668946	−	0.386216i	−0.795677	+	0.605721i	$0.792885\pi$
$678$		0			0
$679$	−407.715	+	137.457i	−0.600464	+	0.202441i
$680$		0			0
$681$	894.818	+	762.176i	1.31398	+	1.11920i
$682$		0			0
$683$	466.207	−	807.494i	0.682587	−	1.18228i	−0.291601	−	0.956540i	$-0.594188\pi$
$683$	466.207	−	807.494i	0.682587	−	1.18228i	0.974189	−	0.225736i	$-0.0724786\pi$
$684$		0			0
$685$			196.437i			0.286769i
$686$		0			0
$687$	294.175	+	250.569i	0.428202	+	0.364729i
$688$		0			0
$689$	−34.4585	+	19.8947i	−0.0500124	+	0.0288747i
$690$		0			0
$691$	−978.220	−	564.775i	−1.41566	−	0.817331i	−0.419745	−	0.907642i	$-0.637880\pi$
$691$	−978.220	−	564.775i	−1.41566	−	0.817331i	−0.995914	+	0.0903117i	$0.971214\pi$
$692$		0			0
$693$	20.1542	−	520.959i	0.0290825	−	0.751744i
$694$		0			0
$695$	43.0369	−	74.5421i	0.0619236	−	0.107255i
$696$		0			0
$697$	−61.1265	−	105.874i	−0.0876995	−	0.151900i
$698$		0			0
$699$	−105.255	−	19.3620i	−0.150579	−	0.0276996i
$700$		0			0
$701$	883.655			1.26056			0.630281	−	0.776367i	$-0.282939\pi$
$701$	883.655			1.26056			0.630281	+	0.776367i	$0.282939\pi$
$702$		0			0
$703$	−584.707	−	337.581i	−0.831732	−	0.480200i
$704$		0			0
$705$	9.09818	+	25.5835i	0.0129052	+	0.0362887i
$706$		0			0
$707$	−164.235	+	816.797i	−0.232298	+	1.15530i
$708$		0			0
$709$	118.989	−	206.096i	0.167827	−	0.290685i	−0.769829	−	0.638251i	$-0.779658\pi$
$709$	118.989	−	206.096i	0.167827	−	0.290685i	0.937656	+	0.347566i	$0.112992\pi$
$710$		0			0
$711$	167.941	+	63.9510i	0.236204	+	0.0899451i
$712$		0			0
$713$	318.121	−	183.667i	0.446173	−	0.257598i
$714$		0			0
$715$	−1.77258	+	3.07020i	−0.00247914	+	0.00429399i
$716$		0			0
$717$	−287.000	−	807.026i	−0.400279	−	1.12556i
$718$		0			0
$719$	−54.4638	+	31.4447i	−0.0757494	+	0.0437339i	−0.537396	−	0.843330i	$-0.680592\pi$
$719$	−54.4638	+	31.4447i	−0.0757494	+	0.0437339i	0.461647	+	0.887064i	$0.347259\pi$
$720$		0			0
$721$	−133.887	+	665.868i	−0.185696	+	0.923533i
$722$		0			0
$723$	−315.816	−	269.002i	−0.436813	−	0.372063i
$724$		0			0
$725$	−298.162	−	516.432i	−0.411258	−	0.712321i
$726$		0			0
$727$	245.665	−	141.835i	0.337917	−	0.195096i	−0.321434	−	0.946932i	$-0.604165\pi$
$727$	245.665	−	141.835i	0.337917	−	0.195096i	0.659350	+	0.751836i	$0.270831\pi$
$728$		0			0
$729$	336.168	+	646.863i	0.461136	+	0.887329i
$730$		0			0
$731$		−	116.422i		−	0.159264i
$732$		0			0
$733$			486.378i			0.663544i	0.943360	+	0.331772i	$0.107647\pi$
$733$			486.378i			0.663544i	−0.943360	+	0.331772i	$0.892353\pi$
$734$		0			0
$735$	63.9351	+	126.357i	0.0869865	+	0.171914i
$736$		0			0
$737$	58.6758	+	101.630i	0.0796144	+	0.137896i
$738$		0			0
$739$	378.929	−	656.325i	0.512759	−	0.888125i	−0.487131	−	0.873329i	$-0.661957\pi$
$739$	378.929	−	656.325i	0.512759	−	0.888125i	0.999891	−	0.0147966i	$-0.00471007\pi$
$740$		0			0
$741$	19.3141	−	22.6753i	0.0260649	−	0.0306010i
$742$		0			0
$743$	−181.162	+	313.782i	−0.243825	+	0.422317i	−0.961801	−	0.273751i	$-0.911736\pi$
$743$	−181.162	+	313.782i	−0.243825	+	0.422317i	0.717976	+	0.696068i	$0.245069\pi$
$744$		0			0
$745$			121.836i			0.163539i
$746$		0			0
$747$	662.870	+	814.108i	0.887376	+	1.08984i
$748$		0			0
$749$	−170.667	−	506.219i	−0.227860	−	0.675859i
$750$		0			0
$751$	−1353.58			−1.80236			−0.901182	−	0.433441i	$-0.857299\pi$
$751$	−1353.58			−1.80236			−0.901182	+	0.433441i	$0.857299\pi$
$752$		0			0
$753$	−67.9324	−	57.8626i	−0.0902157	−	0.0768428i
$754$		0			0
$755$			32.7320i			0.0433537i
$756$		0			0
$757$	−160.495			−0.212014			−0.106007	−	0.994365i	$-0.533807\pi$
$757$	−160.495			−0.212014			−0.106007	+	0.994365i	$0.533807\pi$
$758$		0			0
$759$	−242.843	+	285.105i	−0.319951	+	0.375632i
$760$		0			0
$761$		−	619.288i		−	0.813782i	−0.913477	−	0.406891i	$-0.866613\pi$
$761$		−	619.288i		−	0.813782i	0.913477	−	0.406891i	$-0.133387\pi$
$762$		0			0
$763$	177.526	−	201.584i	0.232669	−	0.264199i
$764$		0			0
$765$	−40.7443	−	15.5152i	−0.0532605	−	0.0202813i
$766$		0			0
$767$	−12.1961			−0.0159010
$768$		0			0
$769$	133.828	+	77.2658i	0.174029	+	0.100476i	0.584484	−	0.811405i	$-0.301297\pi$
$769$	133.828	+	77.2658i	0.174029	+	0.100476i	−0.410455	+	0.911881i	$0.634630\pi$
$770$		0			0
$771$	−660.036	−	562.197i	−0.856077	−	0.729179i
$772$		0			0
$773$	554.122	+	319.923i	0.716846	+	0.413871i	0.813591	−	0.581438i	$-0.197510\pi$
$773$	554.122	+	319.923i	0.716846	+	0.413871i	−0.0967447	+	0.995309i	$0.530843\pi$
$774$		0			0
$775$	−507.633	+	293.082i	−0.655011	+	0.378171i
$776$		0			0
$777$	−589.662	−	235.755i	−0.758896	−	0.303417i
$778$		0			0
$779$	542.795			0.696785
$780$		0			0
$781$	−1104.23			−1.41387
$782$		0			0
$783$	−14.8219	+	668.695i	−0.0189297	+	0.854017i
$784$		0			0
$785$	21.9907	+	38.0890i	0.0280136	+	0.0485210i
$786$		0			0
$787$	428.370	−	247.320i	0.544308	−	0.314256i	−0.202515	−	0.979279i	$-0.564911\pi$
$787$	428.370	−	247.320i	0.544308	−	0.314256i	0.746823	+	0.665023i	$0.231578\pi$
$788$		0			0
$789$	616.363	−	723.628i	0.781195	−	0.917146i
$790$		0			0
$791$	948.773	−	1077.35i	1.19946	−	1.36201i
$792$		0			0
$793$	17.6960	+	30.6503i	0.0223152	+	0.0386511i
$794$		0			0
$795$	−243.636	+	86.6434i	−0.306460	+	0.108985i
$796$		0			0
$797$	−933.311	−	538.847i	−1.17103	−	0.676095i	−0.217108	−	0.976148i	$-0.569662\pi$
$797$	−933.311	−	538.847i	−1.17103	−	0.676095i	−0.953923	+	0.300053i	$0.902996\pi$
$798$		0			0
$799$	−23.6230	−	40.9162i	−0.0295657	−	0.0512092i
$800$		0			0
$801$	689.400	+	846.690i	0.860674	+	1.05704i
$802$		0			0
$803$	424.420	+	245.039i	0.528543	+	0.305154i
$804$		0			0
$805$	20.0529	−	99.7303i	0.0249105	−	0.123889i
$806$		0			0
$807$	503.813	−	179.169i	0.624303	−	0.222019i
$808$		0			0
$809$	403.448	−	698.793i	0.498700	−	0.863773i	−0.501299	−	0.865274i	$-0.667144\pi$
$809$	403.448	−	698.793i	0.498700	−	0.863773i	0.999999	+	0.00150078i	$0.000477712\pi$
$810$		0			0
$811$		−	940.287i		−	1.15942i	−0.814824	−	0.579708i	$-0.803167\pi$
$811$		−	940.287i		−	1.15942i	0.814824	−	0.579708i	$-0.196833\pi$
$812$		0			0
$813$	−187.422	+	1018.85i	−0.230531	+	1.25320i
$814$		0			0
$815$	−109.539	+	63.2423i	−0.134403	+	0.0775979i
$816$		0			0
$817$	447.655	+	258.454i	0.547925	+	0.316345i
$818$		0			0
$819$	14.9355	−	23.7030i	0.0182363	−	0.0289414i
$820$		0			0
$821$	−395.018	+	684.191i	−0.481142	+	0.833363i	−0.999766	−	0.0216400i	$-0.993111\pi$
$821$	−395.018	+	684.191i	−0.481142	+	0.833363i	0.518624	+	0.855003i	$0.326445\pi$
$822$		0			0
$823$	−494.196	−	855.972i	−0.600481	−	1.04006i	−0.992748	−	0.120212i	$-0.961642\pi$
$823$	−494.196	−	855.972i	−0.600481	−	1.04006i	0.392267	−	0.919851i	$-0.371691\pi$
$824$		0			0
$825$	387.510	−	454.948i	0.469709	−	0.551452i
$826$		0			0
$827$	1264.20			1.52865			0.764327	−	0.644829i	$-0.223071\pi$
$827$	1264.20			1.52865			0.764327	+	0.644829i	$0.223071\pi$
$828$		0			0
$829$	429.224	+	247.812i	0.517761	+	0.298929i	0.736018	−	0.676962i	$-0.236704\pi$
$829$	429.224	+	247.812i	0.517761	+	0.298929i	−0.218257	+	0.975891i	$0.570037\pi$
$830$		0			0
$831$	−728.197	+	854.925i	−0.876290	+	1.02879i
$832$		0			0
$833$	−149.186	−	196.104i	−0.179095	−	0.235419i
$834$		0			0
$835$	114.564	−	198.431i	0.137203	−	0.237642i
$836$		0			0
$837$	657.302	+	14.5694i	0.785307	+	0.0174067i
$838$		0			0
$839$	1056.00	−	609.684i	1.25865	−	0.726680i	0.285835	−	0.958279i	$-0.407729\pi$
$839$	1056.00	−	609.684i	1.25865	−	0.726680i	0.972811	+	0.231599i	$0.0743958\pi$
$840$		0			0
$841$	113.660	−	196.864i	0.135148	−	0.234084i
$842$		0			0
$843$	−997.128	−	183.426i	−1.18283	−	0.217587i
$844$		0			0
$845$	140.828	−	81.3073i	0.166661	−	0.0962216i
$846$		0			0
$847$	−360.414	−	72.4690i	−0.425518	−	0.0855597i
$848$		0			0
$849$	231.902	−	1260.65i	0.273148	−	1.48487i
$850$		0			0
$851$	228.092	+	395.066i	0.268028	+	0.464238i
$852$		0			0
$853$	−774.869	+	447.371i	−0.908404	+	0.524467i	−0.879917	−	0.475127i	$-0.842402\pi$
$853$	−774.869	+	447.371i	−0.908404	+	0.524467i	−0.0284869	+	0.999594i	$0.509069\pi$
$854$		0			0
$855$	150.108	−	122.222i	0.175565	−	0.142950i
$856$		0			0
$857$			560.997i			0.654605i	0.944920	+	0.327303i	$0.106140\pi$
$857$			560.997i			0.654605i	−0.944920	+	0.327303i	$0.893860\pi$
$858$		0			0
$859$		−	1468.27i		−	1.70928i	−0.519225	−	0.854638i	$-0.673779\pi$
$859$		−	1468.27i		−	1.70928i	0.519225	−	0.854638i	$-0.326221\pi$
$860$		0			0
$861$	505.314	−	72.8869i	0.586892	−	0.0846537i
$862$		0			0
$863$	−723.196	−	1252.61i	−0.838003	−	1.45146i	−0.891562	−	0.452899i	$-0.850390\pi$
$863$	−723.196	−	1252.61i	−0.838003	−	1.45146i	0.0535591	−	0.998565i	$-0.482943\pi$
$864$		0			0
$865$	−149.123	+	258.289i	−0.172397	+	0.298600i
$866$		0			0
$867$	−778.084	−	143.132i	−0.897445	−	0.165089i
$868$		0			0
$869$	−82.6182	+	143.099i	−0.0950727	+	0.164671i
$870$		0			0
$871$			6.30622i			0.00724021i
$872$		0			0
$873$	349.288	+	428.979i	0.400100	+	0.491385i
$874$		0			0
$875$	−65.2315	+	324.419i	−0.0745503	+	0.370765i
$876$		0			0
$877$	1370.01			1.56215			0.781075	−	0.624438i	$-0.214672\pi$
$877$	1370.01			1.56215			0.781075	+	0.624438i	$0.214672\pi$
$878$		0			0
$879$	−176.303	+	62.6980i	−0.200572	+	0.0713288i
$880$		0			0
$881$		−	1155.87i		−	1.31200i	−0.754763	−	0.655998i	$-0.772248\pi$
$881$		−	1155.87i		−	1.31200i	0.754763	−	0.655998i	$-0.227752\pi$
$882$		0			0
$883$	457.894			0.518567			0.259283	−	0.965801i	$-0.416514\pi$
$883$	457.894			0.518567			0.259283	+	0.965801i	$0.416514\pi$
$884$		0			0
$885$	−77.9521	−	14.3396i	−0.0880814	−	0.0162029i
$886$		0			0
$887$			64.4365i			0.0726455i	0.999340	+	0.0363227i	$0.0115644\pi$
$887$			64.4365i			0.0726455i	−0.999340	+	0.0363227i	$0.988436\pi$
$888$		0			0
$889$	−492.818	−	99.0917i	−0.554351	−	0.111464i
$890$		0			0
$891$	−636.379	+	210.548i	−0.714230	+	0.236305i
$892$		0			0
$893$	209.769			0.234903
$894$		0			0
$895$	252.652	+	145.869i	0.282293	+	0.162982i
$896$		0			0
$897$	−18.9620	+	6.74338i	−0.0211393	+	0.00751770i
$898$		0			0
$899$	522.408	+	301.612i	0.581099	+	0.335497i
$900$		0			0
$901$	389.651	−	224.965i	0.432465	−	0.249684i
$902$		0			0
$903$	451.448	+	180.495i	0.499943	+	0.199884i
$904$		0			0
$905$	198.177			0.218980
$906$		0			0
$907$	1027.59			1.13296			0.566480	−	0.824075i	$-0.308305\pi$
$907$	1027.59			1.13296			0.566480	+	0.824075i	$0.308305\pi$
$908$		0			0
$909$	1057.55	−	170.404i	1.16342	−	0.187463i
$910$		0			0
$911$	−838.411	−	1452.17i	−0.920320	−	1.59404i	−0.798921	−	0.601437i	$-0.794595\pi$
$911$	−838.411	−	1452.17i	−0.920320	−	1.59404i	−0.121399	−	0.992604i	$-0.538738\pi$
$912$		0			0
$913$	−835.987	+	482.657i	−0.915648	+	0.528650i
$914$		0			0
$915$	77.0679	+	216.710i	0.0842272	+	0.236842i
$916$		0			0
$917$	10.4183	−	51.8136i	0.0113612	−	0.0565034i
$918$		0			0
$919$	−724.595	−	1255.03i	−0.788460	−	1.36565i	−0.926910	−	0.375283i	$-0.877545\pi$
$919$	−724.595	−	1255.03i	−0.788460	−	1.36565i	0.138450	−	0.990369i	$-0.455788\pi$
$920$		0			0
$921$	1081.10	+	920.849i	1.17384	+	0.999836i
$922$		0			0
$923$	−51.3890	−	29.6695i	−0.0556761	−	0.0321446i
$924$		0			0
$925$	−363.971	−	630.416i	−0.393482	−	0.681531i
$926$		0			0
$927$	862.130	−	138.916i	0.930022	−	0.149856i
$928$		0			0
$929$	1429.67	+	825.418i	1.53893	+	0.888501i	0.998902	+	0.0468537i	$0.0149194\pi$
$929$	1429.67	+	825.418i	1.53893	+	0.888501i	0.540027	+	0.841647i	$0.318414\pi$
$930$		0			0
$931$	1085.23	−	138.291i	1.16566	−	0.148540i
$932$		0			0
$933$	−78.4100	+	426.248i	−0.0840407	+	0.456857i
$934$		0			0
$935$	20.0440	−	34.7173i	0.0214375	−	0.0371308i
$936$		0			0
$937$			1340.89i			1.43105i	0.698588	+	0.715525i	$0.253812\pi$
$937$			1340.89i			1.43105i	−0.698588	+	0.715525i	$0.746188\pi$
$938$		0			0
$939$	53.0666	−	18.8719i	0.0565140	−	0.0200979i
$940$		0			0
$941$	−552.125	+	318.769i	−0.586743	+	0.338756i	−0.763808	−	0.645443i	$-0.776673\pi$
$941$	−552.125	+	318.769i	−0.586743	+	0.338756i	0.177066	+	0.984199i	$0.443339\pi$
$942$		0			0
$943$	−317.613	−	183.374i	−0.336811	−	0.194458i
$944$		0			0
$945$	123.331	−	133.939i	0.130509	−	0.141735i
$946$		0			0
$947$	−506.734	+	877.689i	−0.535094	+	0.926810i	0.464065	+	0.885801i	$0.346391\pi$
$947$	−506.734	+	877.689i	−0.535094	+	0.926810i	−0.999159	+	0.0410089i	$0.986943\pi$
$948$		0			0
$949$	13.1679	+	22.8074i	0.0138755	+	0.0240331i
$950$		0			0
$951$	26.2651	+	73.8560i	0.0276184	+	0.0776614i
$952$		0			0
$953$	81.0381			0.0850347			0.0425173	−	0.999096i	$-0.486462\pi$
$953$	81.0381			0.0850347			0.0425173	+	0.999096i	$0.486462\pi$
$954$		0			0
$955$	−60.9784	−	35.2059i	−0.0638517	−	0.0368648i
$956$		0			0
$957$	−604.858	−	111.266i	−0.632036	−	0.116265i
$958$		0			0
$959$	1399.37	+	281.374i	1.45920	+	0.293404i
$960$		0			0
$961$	−184.027	+	318.744i	−0.191495	+	0.331679i
$962$		0			0
$963$	−532.620	+	433.675i	−0.553084	+	0.450337i
$964$		0			0
$965$	296.024	−	170.909i	0.306760	−	0.177108i
$966$		0			0
$967$	−253.546	+	439.155i	−0.262199	+	0.454142i	−0.966826	−	0.255436i	$-0.917781\pi$
$967$	−253.546	+	439.155i	−0.262199	+	0.454142i	0.704627	+	0.709578i	$0.251114\pi$
$968$		0			0
$969$	−218.400	+	256.408i	−0.225387	+	0.264611i
$970$		0			0
$971$	1301.46	−	751.397i	1.34033	−	0.773839i	0.353473	−	0.935445i	$-0.385001\pi$
$971$	1301.46	−	751.397i	1.34033	−	0.773839i	0.986855	+	0.161606i	$0.0516674\pi$
$972$		0			0
$973$	−469.376	−	413.358i	−0.482400	−	0.424829i
$974$		0			0
$975$	30.2580	−	10.7606i	0.0310339	−	0.0110365i
$976$		0			0
$977$	−310.361	−	537.562i	−0.317668	−	0.550217i	0.662333	−	0.749209i	$-0.269566\pi$
$977$	−310.361	−	537.562i	−0.317668	−	0.550217i	−0.980001	+	0.198993i	$0.936233\pi$
$978$		0			0
$979$	−869.445	+	501.974i	−0.888095	+	0.512742i
$980$		0			0
$981$	−322.749	−	122.901i	−0.329000	−	0.125281i
$982$		0			0
$983$		−	1128.62i		−	1.14814i	−0.818808	−	0.574068i	$-0.805365\pi$
$983$		−	1128.62i		−	1.14814i	0.818808	−	0.574068i	$-0.194635\pi$
$984$		0			0
$985$		−	2.71047i		−	0.00275175i
$986$		0			0
$987$	195.284	−	28.1679i	0.197856	−	0.0285389i
$988$		0			0
$989$	−174.628	−	302.465i	−0.176570	−	0.305829i
$990$		0			0
$991$	−501.599	+	868.795i	−0.506154	+	0.876685i	0.493820	+	0.869564i	$0.335600\pi$
$991$	−501.599	+	868.795i	−0.506154	+	0.876685i	−0.999975	+	0.00712091i	$0.997733\pi$
$992$		0			0
$993$	282.778	+	795.154i	0.284771	+	0.800759i
$994$		0			0
$995$	−51.5550	+	89.2959i	−0.0518141	+	0.0897446i
$996$		0			0
$997$		−	1095.10i		−	1.09839i	−0.835694	−	0.549195i	$-0.814934\pi$
$997$		−	1095.10i		−	1.09839i	0.835694	−	0.549195i	$-0.185066\pi$
$998$		0			0
$999$	−18.0933	+	816.286i	−0.0181114	+	0.817103i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.3.p.a.157.12	yes	32
3.2	odd	2		756.3.p.a.577.8		32
7.5	odd	6		252.3.bd.a.229.7	yes	32
9.2	odd	6		756.3.bd.a.73.9		32
9.7	even	3		252.3.bd.a.241.7	yes	32
21.5	even	6		756.3.bd.a.145.9		32
63.47	even	6		756.3.p.a.397.9		32
63.61	odd	6	inner	252.3.p.a.61.12	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.3.p.a.61.12	✓	32	63.61	odd	6	inner
252.3.p.a.157.12	yes	32	1.1	even	1	trivial
252.3.bd.a.229.7	yes	32	7.5	odd	6
252.3.bd.a.241.7	yes	32	9.7	even	3
756.3.p.a.397.9		32	63.47	even	6
756.3.p.a.577.8		32	3.2	odd	2
756.3.bd.a.73.9		32	9.2	odd	6
756.3.bd.a.145.9		32	21.5	even	6

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	252.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.94529 - 2.28383i) q^{3} +0.963344i q^{5} +(6.86265 + 1.37988i) q^{7} +(-1.43172 - 8.88539i) q^{9} +8.27537 q^{11} +(0.385122 + 0.222350i) q^{13} +(2.20011 + 1.87398i) q^{15} +(-4.35489 - 2.51430i) q^{17} +(19.3354 - 11.1633i) q^{19} +(16.5012 - 12.9888i) q^{21} -15.0853 q^{23} +24.0720 q^{25} +(-23.0778 - 14.0148i) q^{27} +(-12.3863 - 21.4537i) q^{29} +(-21.0881 + 12.1752i) q^{31} +(16.0980 - 18.8995i) q^{33} +(-1.32930 + 6.61109i) q^{35} +(-15.1201 - 26.1888i) q^{37} +(1.25698 - 0.447016i) q^{39} +(21.0544 + 12.1558i) q^{41} +(11.5760 + 20.0503i) q^{43} +(8.55969 - 1.37924i) q^{45} +(8.13670 + 4.69773i) q^{47} +(45.1918 + 18.9393i) q^{49} +(-14.2137 + 5.05478i) q^{51} +(-44.7372 + 77.4871i) q^{53} +7.97203i q^{55} +(12.1179 - 65.8745i) q^{57} +(-23.7510 + 13.7127i) q^{59} +(68.9235 + 39.7930i) q^{61} +(2.43544 - 62.9529i) q^{63} +(-0.214200 + 0.371005i) q^{65} +(7.09042 + 12.2810i) q^{67} +(-29.3453 + 34.4522i) q^{69} -133.436 q^{71} +(51.2871 + 29.6106i) q^{73} +(46.8269 - 54.9762i) q^{75} +(56.7910 + 11.4191i) q^{77} +(-9.98363 + 17.2921i) q^{79} +(-76.9004 + 25.4427i) q^{81} +(-101.021 + 58.3246i) q^{83} +(2.42213 - 4.19526i) q^{85} +(-73.0914 - 13.4454i) q^{87} +(-105.064 + 60.6588i) q^{89} +(2.33614 + 2.05734i) q^{91} +(-13.2164 + 71.8460i) q^{93} +(10.7541 + 18.6266i) q^{95} +(-53.2313 + 30.7331i) q^{97} +(-11.8480 - 73.5299i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + q^{7} - 6 q^{9} - 12 q^{11} + 15 q^{13} + 9 q^{15} - 27 q^{17} - 36 q^{21} + 30 q^{23} - 160 q^{25} - 9 q^{27} + 24 q^{29} - 24 q^{31} + 81 q^{33} + 141 q^{35} + 11 q^{37} - 21 q^{39} - 90 q^{41}+ \cdots - 45 q^{99}+O(q^{100}) \) 32 * q + q^7 - 6 * q^9 - 12 * q^11 + 15 * q^13 + 9 * q^15 - 27 * q^17 - 36 * q^21 + 30 * q^23 - 160 * q^25 - 9 * q^27 + 24 * q^29 - 24 * q^31 + 81 * q^33 + 141 * q^35 + 11 * q^37 - 21 * q^39 - 90 * q^41 - 16 * q^43 + 39 * q^45 + 108 * q^47 - 61 * q^49 + 117 * q^51 + 54 * q^53 + 51 * q^57 + 45 * q^59 - 165 * q^61 - 93 * q^63 - 33 * q^65 - 35 * q^67 + 105 * q^69 + 138 * q^71 - 195 * q^75 - 123 * q^77 + 37 * q^79 + 126 * q^81 + 378 * q^83 + 30 * q^85 - 237 * q^87 - 261 * q^89 + 45 * q^91 + 111 * q^93 - 48 * q^95 - 57 * q^97 - 45 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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