LMFDB - Embedded newform 756.2.b.d.55.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [756,2,Mod(55,756)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(756, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("756.55"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,8,0,0,2,0,0,4,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.60771337450861625344.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{10} + 11x^{8} - 26x^{6} + 44x^{4} - 64x^{2} + 64 $ x^12 - 4x^10 + 11x^8 - 26x^6 + 44x^4 - 64*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.7
Root			$-0.840028 + 1.13770i$ of defining polynomial
Character	$\chi$	$=$	756.55
Dual form			756.2.b.d.55.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.840028 - 1.13770i) q^{2} +(-0.588705 - 1.91139i) q^{4} +2.67907i q^{5} +(0.370556 + 2.61967i) q^{7} +(-2.66911 - 0.935858i) q^{8} +(3.04797 + 2.25049i) q^{10} -1.39642i q^{11} +3.08443i q^{13} +(3.29167 + 1.77902i) q^{14} +(-3.30685 + 2.25049i) q^{16} +5.83343i q^{17} +1.91852 q^{19} +(5.12076 - 1.57718i) q^{20} +(-1.58870 - 1.17303i) q^{22} +1.39642i q^{23} -2.17741 q^{25} +(3.50914 + 2.59101i) q^{26} +(4.78908 - 2.25049i) q^{28} -4.90328 q^{29} +9.53223 q^{31} +(-0.217472 + 5.65267i) q^{32} +(6.63667 + 4.90025i) q^{34} +(-7.01828 + 0.992746i) q^{35} +6.83705 q^{37} +(1.61161 - 2.18270i) q^{38} +(2.50723 - 7.15074i) q^{40} +0.693576i q^{41} +0.678200i q^{43} +(-2.66911 + 0.822081i) q^{44} +(1.58870 + 1.17303i) q^{46} -8.26340 q^{47} +(-6.72538 + 1.94147i) q^{49} +(-1.82909 + 2.47723i) q^{50} +(5.89556 - 1.81582i) q^{52} +10.6765 q^{53} +3.74111 q^{55} +(1.46258 - 7.33899i) q^{56} +(-4.11890 + 5.57845i) q^{58} -12.2196 q^{59} -12.8849i q^{61} +(8.00734 - 10.8448i) q^{62} +(6.24834 + 4.99582i) q^{64} -8.26340 q^{65} -3.08443i q^{67} +(11.1500 - 3.43417i) q^{68} +(-4.76611 + 8.81861i) q^{70} -9.79515i q^{71} +5.91755i q^{73} +(5.74331 - 7.77848i) q^{74} +(-1.12944 - 3.66705i) q^{76} +(3.65817 - 0.517454i) q^{77} -12.0864i q^{79} +(-6.02923 - 8.85929i) q^{80} +(0.789079 + 0.582624i) q^{82} +5.77317 q^{83} -15.6282 q^{85} +(0.771585 + 0.569707i) q^{86} +(-1.30685 + 3.72721i) q^{88} -6.65005i q^{89} +(-8.08020 + 1.14295i) q^{91} +(2.66911 - 0.822081i) q^{92} +(-6.94149 + 9.40123i) q^{94} +5.13985i q^{95} +12.8849i q^{97} +(-3.44070 + 9.28233i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 8 q^{4} + 2 q^{7} + 4 q^{10} - 12 q^{16} - 12 q^{19} - 4 q^{22} + 4 q^{25} + 20 q^{28} + 24 q^{31} + 32 q^{34} + 12 q^{37} - 20 q^{40} + 4 q^{46} - 18 q^{49} + 28 q^{52} + 40 q^{55} + 8 q^{58} + 20 q^{64}+ \cdots - 56 q^{94}+O(q^{100}) $ 12 * q + 8 * q^4 + 2 * q^7 + 4 * q^10 - 12 * q^16 - 12 * q^19 - 4 * q^22 + 4 * q^25 + 20 * q^28 + 24 * q^31 + 32 * q^34 + 12 * q^37 - 20 * q^40 + 4 * q^46 - 18 * q^49 + 28 * q^52 + 40 * q^55 + 8 * q^58 + 20 * q^64 - 12 * q^70 - 16 * q^76 - 28 * q^82 - 32 * q^85 + 12 * q^88 + 26 * q^91 - 56 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	0.840028	−	1.13770i	0.593990	−	0.804473i
$2$	0.840028	−	1.13770i	0.593990	−	0.804473i
$3$		0			0
$3$		0			0
$4$	−0.588705	−	1.91139i	−0.294352	−	0.955697i
$5$			2.67907i			1.19812i	0.800706	+	0.599058i	$0.204458\pi$
$5$			2.67907i			1.19812i	−0.800706	+	0.599058i	$0.795542\pi$
$6$		0			0
$7$	0.370556	+	2.61967i	0.140057	+	0.990143i
$7$	0.370556	+	2.61967i	0.140057	+	0.990143i
$8$	−2.66911	−	0.935858i	−0.943674	−	0.330876i
$9$		0			0
$10$	3.04797	+	2.25049i	0.963852	+	0.711669i
$11$		−	1.39642i		−	0.421037i	−0.977590	−	0.210519i	$-0.932485\pi$
$11$		−	1.39642i		−	0.421037i	0.977590	−	0.210519i	$-0.0675153\pi$
$12$		0			0
$13$			3.08443i			0.855467i	0.903905	+	0.427733i	$0.140688\pi$
$13$			3.08443i			0.855467i	−0.903905	+	0.427733i	$0.859312\pi$
$14$	3.29167	+	1.77902i	0.879736	+	0.475463i
$15$		0			0
$16$	−3.30685	+	2.25049i	−0.826713	+	0.562623i
$17$			5.83343i			1.41481i	0.706806	+	0.707407i	$0.250135\pi$
$17$			5.83343i			1.41481i	−0.706806	+	0.707407i	$0.749865\pi$
$18$		0			0
$19$	1.91852			0.440139			0.220070	−	0.975484i	$-0.429372\pi$
$19$	1.91852			0.440139			0.220070	+	0.975484i	$0.429372\pi$
$20$	5.12076	−	1.57718i	1.14504	−	0.352668i
$21$		0			0
$22$	−1.58870	−	1.17303i	−0.338713	−	0.250092i
$23$			1.39642i			0.291174i	0.989345	+	0.145587i	$0.0465071\pi$
$23$			1.39642i			0.291174i	−0.989345	+	0.145587i	$0.953493\pi$
$24$		0			0
$25$	−2.17741			−0.435482
$26$	3.50914	+	2.59101i	0.688199	+	0.508138i
$27$		0			0
$28$	4.78908	−	2.25049i	0.905051	−	0.425303i
$29$	−4.90328			−0.910517			−0.455258	−	0.890359i	$-0.650453\pi$
$29$	−4.90328			−0.910517			−0.455258	+	0.890359i	$0.650453\pi$
$30$		0			0
$31$	9.53223			1.71204			0.856019	−	0.516944i	$-0.172930\pi$
$31$	9.53223			1.71204			0.856019	+	0.516944i	$0.172930\pi$
$32$	−0.217472	+	5.65267i	−0.0384441	+	0.999261i
$33$		0			0
$34$	6.63667	+	4.90025i	1.13818	+	0.840385i
$35$	−7.01828	+	0.992746i	−1.18631	+	0.167805i
$36$		0			0
$37$	6.83705			1.12400			0.562002	−	0.827136i	$-0.310031\pi$
$37$	6.83705			1.12400			0.562002	+	0.827136i	$0.310031\pi$
$38$	1.61161	−	2.18270i	0.261438	−	0.354080i
$39$		0			0
$40$	2.50723	−	7.15074i	0.396427	−	1.13063i
$41$			0.693576i			0.108318i	0.998532	+	0.0541592i	$0.0172479\pi$
$41$			0.693576i			0.108318i	−0.998532	+	0.0541592i	$0.982752\pi$
$42$		0			0
$43$			0.678200i			0.103424i	0.998662	+	0.0517122i	$0.0164679\pi$
$43$			0.678200i			0.103424i	−0.998662	+	0.0517122i	$0.983532\pi$
$44$	−2.66911	+	0.822081i	−0.402384	+	0.123933i
$45$		0			0
$46$	1.58870	+	1.17303i	0.234242	+	0.172955i
$47$	−8.26340			−1.20534			−0.602670	−	0.797990i	$-0.705897\pi$
$47$	−8.26340			−1.20534			−0.602670	+	0.797990i	$0.705897\pi$
$48$		0			0
$49$	−6.72538	+	1.94147i	−0.960768	+	0.277353i
$50$	−1.82909	+	2.47723i	−0.258672	+	0.350333i
$51$		0			0
$52$	5.89556	−	1.81582i	0.817567	−	0.251809i
$53$	10.6765			1.46652			0.733262	−	0.679946i	$-0.237997\pi$
$53$	10.6765			1.46652			0.733262	+	0.679946i	$0.237997\pi$
$54$		0			0
$55$	3.74111			0.504452
$56$	1.46258	−	7.33899i	0.195446	−	0.980714i
$57$		0			0
$58$	−4.11890	+	5.57845i	−0.540838	+	0.732486i
$59$	−12.2196			−1.59086			−0.795430	−	0.606046i	$-0.792755\pi$
$59$	−12.2196			−1.59086			−0.795430	+	0.606046i	$0.792755\pi$
$60$		0			0
$61$		−	12.8849i		−	1.64975i	−0.565319	−	0.824873i	$-0.691247\pi$
$61$		−	12.8849i		−	1.64975i	0.565319	−	0.824873i	$-0.308753\pi$
$62$	8.00734	−	10.8448i	1.01693	−	1.37729i
$63$		0			0
$64$	6.24834	+	4.99582i	0.781043	+	0.624478i
$65$	−8.26340			−1.02495
$66$		0			0
$67$		−	3.08443i		−	0.376823i	−0.982090	−	0.188411i	$-0.939666\pi$
$67$		−	3.08443i		−	0.376823i	0.982090	−	0.188411i	$-0.0603339\pi$
$68$	11.1500	−	3.43417i	1.35213	−	0.416454i
$69$		0			0
$70$	−4.76611	+	8.81861i	−0.569660	+	1.05403i
$71$		−	9.79515i		−	1.16247i	−0.813736	−	0.581235i	$-0.802570\pi$
$71$		−	9.79515i		−	1.16247i	0.813736	−	0.581235i	$-0.197430\pi$
$72$		0			0
$73$			5.91755i			0.692596i	0.938124	+	0.346298i	$0.112561\pi$
$73$			5.91755i			0.692596i	−0.938124	+	0.346298i	$0.887439\pi$
$74$	5.74331	−	7.77848i	0.667646	−	0.904230i
$75$		0			0
$76$	−1.12944	−	3.66705i	−0.129556	−	0.420640i
$77$	3.65817	−	0.517454i	0.416887	−	0.0589693i
$78$		0			0
$79$		−	12.0864i		−	1.35983i	−0.733293	−	0.679913i	$-0.762017\pi$
$79$		−	12.0864i		−	1.35983i	0.733293	−	0.679913i	$-0.237983\pi$
$80$	−6.02923	−	8.85929i	−0.674088	−	0.990498i
$81$		0			0
$82$	0.789079	+	0.582624i	0.0871392	+	0.0643400i
$83$	5.77317			0.633688			0.316844	−	0.948478i	$-0.397377\pi$
$83$	5.77317			0.633688			0.316844	+	0.948478i	$0.397377\pi$
$84$		0			0
$85$	−15.6282			−1.69511
$86$	0.771585	+	0.569707i	0.0832021	+	0.0614331i
$87$		0			0
$88$	−1.30685	+	3.72721i	−0.139311	+	0.397322i
$89$		−	6.65005i		−	0.704904i	−0.935830	−	0.352452i	$-0.885348\pi$
$89$		−	6.65005i		−	0.704904i	0.935830	−	0.352452i	$-0.114652\pi$
$90$		0			0
$91$	−8.08020	+	1.14295i	−0.847035	+	0.119814i
$92$	2.66911	−	0.822081i	0.278274	−	0.0857079i
$93$		0			0
$94$	−6.94149	+	9.40123i	−0.715960	+	0.969663i
$95$			5.13985i			0.527338i
$96$		0			0
$97$			12.8849i			1.30827i	0.756380	+	0.654133i	$0.226966\pi$
$97$			12.8849i			1.30827i	−0.756380	+	0.654133i	$0.773034\pi$
$98$	−3.44070	+	9.28233i	−0.347563	+	0.937657i
$99$		0			0
$100$	1.28185	+	4.16189i	0.128185	+	0.416189i
$101$			14.1276i			1.40575i	0.711312	+	0.702877i	$0.248101\pi$
$101$			14.1276i			1.40575i	−0.711312	+	0.702877i	$0.751899\pi$
$102$		0			0
$103$	−5.56370			−0.548208			−0.274104	−	0.961700i	$-0.588381\pi$
$103$	−5.56370			−0.548208			−0.274104	+	0.961700i	$0.588381\pi$
$104$	2.88659	−	8.23269i	0.283053	−	0.807282i
$105$		0			0
$106$	8.96853	−	12.1466i	0.871100	−	1.17978i
$107$		−	7.44814i		−	0.720039i	−0.932945	−	0.360019i	$-0.882770\pi$
$107$		−	7.44814i		−	0.720039i	0.932945	−	0.360019i	$-0.117230\pi$
$108$		0			0
$109$	13.3693			1.28054			0.640272	−	0.768148i	$-0.278822\pi$
$109$	13.3693			1.28054			0.640272	+	0.768148i	$0.278822\pi$
$110$	3.14264	−	4.25625i	0.299639	−	0.405817i
$111$		0			0
$112$	−7.12093	−	7.82894i	−0.672865	−	0.739765i
$113$	−3.36011			−0.316093			−0.158046	−	0.987432i	$-0.550520\pi$
$113$	−3.36011			−0.316093			−0.158046	+	0.987432i	$0.550520\pi$
$114$		0			0
$115$	−3.74111			−0.348861
$116$	2.88659	+	9.37211i	0.268013	+	0.870178i
$117$		0			0
$118$	−10.2648	+	13.9022i	−0.944954	+	1.27980i
$119$	−15.2817	+	2.16162i	−1.40087	+	0.198155i
$120$		0			0
$121$	9.05000			0.822728
$122$	−14.6591	−	10.8237i	−1.32717	−	0.979932i
$123$		0			0
$124$	−5.61167	−	18.2198i	−0.503943	−	1.63619i
$125$			7.56191i			0.676358i
$126$		0			0
$127$			15.9694i			1.41705i	0.705685	+	0.708525i	$0.250639\pi$
$127$			15.9694i			1.41705i	−0.705685	+	0.708525i	$0.749361\pi$
$128$	10.9325	−	2.91208i	0.966307	−	0.257394i
$129$		0			0
$130$	−6.94149	+	9.40123i	−0.608809	+	0.824543i
$131$	−1.81694			−0.158747			−0.0793735	−	0.996845i	$-0.525292\pi$
$131$	−1.81694			−0.158747			−0.0793735	+	0.996845i	$0.525292\pi$
$132$		0			0
$133$	0.710921	+	5.02590i	0.0616447	+	0.435801i
$134$	−3.50914	−	2.59101i	−0.303144	−	0.223829i
$135$		0			0
$136$	5.45926	−	15.5701i	0.468128	−	1.33512i
$137$	−18.9399			−1.61814			−0.809070	−	0.587712i	$-0.800029\pi$
$137$	−18.9399			−1.61814			−0.809070	+	0.587712i	$0.800029\pi$
$138$		0			0
$139$	−15.2878			−1.29669			−0.648347	−	0.761345i	$-0.724539\pi$
$139$	−15.2878			−1.29669			−0.648347	+	0.761345i	$0.724539\pi$
$140$	6.02923	+	12.8303i	0.509563	+	1.08436i
$141$		0			0
$142$	−11.1439	−	8.22820i	−0.935175	−	0.690495i
$143$	4.30717			0.360183
$144$		0			0
$145$		−	13.1362i		−	1.09090i
$146$	6.73237	+	4.97091i	0.557175	+	0.411395i
$147$		0			0
$148$	−4.02500	−	13.0683i	−0.330853	−	1.07421i
$149$	17.3967			1.42519			0.712596	−	0.701575i	$-0.247519\pi$
$149$	17.3967			1.42519			0.712596	+	0.701575i	$0.247519\pi$
$150$		0			0
$151$			8.57509i			0.697831i	0.937154	+	0.348915i	$0.113450\pi$
$151$			8.57509i			0.697831i	−0.937154	+	0.348915i	$0.886550\pi$
$152$	−5.12076	−	1.79546i	−0.415348	−	0.145631i
$153$		0			0
$154$	2.48426	−	4.59656i	0.200188	−	0.370402i
$155$			25.5375i			2.05122i
$156$		0			0
$157$		−	18.8025i		−	1.50060i	−0.661097	−	0.750300i	$-0.729909\pi$
$157$		−	18.8025i		−	1.50060i	0.661097	−	0.750300i	$-0.270091\pi$
$158$	−13.7507	−	10.1529i	−1.09394	−	0.807723i
$159$		0			0
$160$	−15.1439	−	0.582624i	−1.19723	−	0.0460605i
$161$	−3.65817	+	0.517454i	−0.288304	+	0.0407810i
$162$		0			0
$163$			0.251311i			0.0196842i	0.999952	+	0.00984211i	$0.00313289\pi$
$163$			0.251311i			0.0196842i	−0.999952	+	0.00984211i	$0.996867\pi$
$164$	1.32570	−	0.408312i	0.103520	−	0.0318838i
$165$		0			0
$166$	4.84963	−	6.56812i	0.376404	−	0.509785i
$167$	14.0366			1.08618			0.543091	−	0.839674i	$-0.317254\pi$
$167$	14.0366			1.08618			0.543091	+	0.839674i	$0.317254\pi$
$168$		0			0
$169$	3.48630			0.268177
$170$	−13.1281	+	17.7801i	−1.00688	+	1.36367i
$171$		0			0
$172$	1.29631	−	0.399259i	0.0988424	−	0.0304432i
$173$		−	14.8212i		−	1.12684i	−0.826172	−	0.563418i	$-0.809486\pi$
$173$		−	14.8212i		−	1.12684i	0.826172	−	0.563418i	$-0.190514\pi$
$174$		0			0
$175$	−0.806853	−	5.70410i	−0.0609924	−	0.431190i
$176$	3.14264	+	4.61777i	0.236885	+	0.348077i
$177$		0			0
$178$	−7.56574	−	5.58623i	−0.567076	−	0.418706i
$179$		−	13.9001i		−	1.03894i	−0.854488	−	0.519471i	$-0.826129\pi$
$179$		−	13.9001i		−	1.03894i	0.854488	−	0.519471i	$-0.173871\pi$
$180$		0			0
$181$		−	5.11903i		−	0.380494i	−0.981736	−	0.190247i	$-0.939071\pi$
$181$		−	5.11903i		−	0.380494i	0.981736	−	0.190247i	$-0.0609289\pi$
$182$	−5.48726	+	10.1529i	−0.406743	+	0.752585i
$183$		0			0
$184$	1.30685	−	3.72721i	0.0963425	−	0.274774i
$185$			18.3169i			1.34669i
$186$		0			0
$187$	8.14594			0.595690
$188$	4.86470	+	15.7946i	0.354795	+	1.15194i
$189$		0			0
$190$	5.84759	+	4.31762i	0.424229	+	0.313233i
$191$			5.34887i			0.387030i	0.981097	+	0.193515i	$0.0619889\pi$
$191$			5.34887i			0.387030i	−0.981097	+	0.193515i	$0.938011\pi$
$192$		0			0
$193$	−2.22334			−0.160039			−0.0800197	−	0.996793i	$-0.525498\pi$
$193$	−2.22334			−0.160039			−0.0800197	+	0.996793i	$0.525498\pi$
$194$	14.6591	+	10.8237i	1.05246	+	0.777096i
$195$		0			0
$196$	7.67018	+	11.7119i	0.547870	+	0.836563i
$197$	23.8431			1.69875			0.849377	−	0.527787i	$-0.176978\pi$
$197$	23.8431			1.69875			0.849377	+	0.527787i	$0.176978\pi$
$198$		0			0
$199$	−17.5467			−1.24385			−0.621926	−	0.783076i	$-0.713649\pi$
$199$	−17.5467			−1.24385			−0.621926	+	0.783076i	$0.713649\pi$
$200$	5.81175	+	2.03775i	0.410953	+	0.144090i
$201$		0			0
$202$	16.0730	+	11.8676i	1.13089	+	0.835003i
$203$	−1.81694	−	12.8450i	−0.127524	−	0.901542i
$204$		0			0
$205$	−1.85814			−0.129778
$206$	−4.67367	+	6.32980i	−0.325630	+	0.441018i
$207$		0			0
$208$	−6.94149	−	10.1998i	−0.481306	−	0.707226i
$209$		−	2.67907i		−	0.185315i
$210$		0			0
$211$		−	3.76263i		−	0.259030i	−0.991577	−	0.129515i	$-0.958658\pi$
$211$		−	3.76263i		−	0.259030i	0.991577	−	0.129515i	$-0.0413420\pi$
$212$	−6.28528	−	20.4069i	−0.431675	−	1.40155i
$213$		0			0
$214$	−8.47372	−	6.25665i	−0.579251	−	0.427696i
$215$	−1.81694			−0.123915
$216$		0			0
$217$	3.53223	+	24.9713i	0.239783	+	1.69516i
$218$	11.2306	−	15.2102i	0.760630	−	1.03016i
$219$		0			0
$220$	−2.20241	−	7.15074i	−0.148487	−	0.482103i
$221$	−17.9928			−1.21033
$222$		0			0
$223$	−10.8056			−0.723595			−0.361797	−	0.932257i	$-0.617837\pi$
$223$	−10.8056			−0.723595			−0.361797	+	0.932257i	$0.617837\pi$
$224$	−14.8887	+	1.52493i	−0.994796	+	0.101889i
$225$		0			0
$226$	−2.82259	+	3.82279i	−0.187756	+	0.254288i
$227$	24.1169			1.60070			0.800348	−	0.599536i	$-0.204648\pi$
$227$	24.1169			1.60070			0.800348	+	0.599536i	$0.204648\pi$
$228$		0			0
$229$		−	22.9367i		−	1.51570i	−0.652428	−	0.757851i	$-0.726249\pi$
$229$		−	22.9367i		−	1.51570i	0.652428	−	0.757851i	$-0.273751\pi$
$230$	−3.14264	+	4.25625i	−0.207220	+	0.280649i
$231$		0			0
$232$	13.0874	+	4.58878i	0.859231	+	0.301268i
$233$	−0.869890			−0.0569884			−0.0284942	−	0.999594i	$-0.509071\pi$
$233$	−0.869890			−0.0569884			−0.0284942	+	0.999594i	$0.509071\pi$
$234$		0			0
$235$		−	22.1382i		−	1.44414i
$236$	7.19375	+	23.3565i	0.468273	+	1.52038i
$237$		0			0
$238$	−10.3778	+	19.2017i	−0.672692	+	1.24466i
$239$		−	21.1005i		−	1.36488i	−0.730943	−	0.682439i	$-0.760919\pi$
$239$		−	21.1005i		−	1.36488i	0.730943	−	0.682439i	$-0.239081\pi$
$240$		0			0
$241$		−	3.08443i		−	0.198686i	−0.995053	−	0.0993428i	$-0.968326\pi$
$241$		−	3.08443i		−	0.198686i	0.995053	−	0.0993428i	$-0.0316740\pi$
$242$	7.60226	−	10.2962i	0.488692	−	0.661862i
$243$		0			0
$244$	−24.6282	+	7.58542i	−1.57666	+	0.485606i
$245$	−5.20134	−	18.0177i	−0.332302	−	1.15111i
$246$		0			0
$247$			5.91755i			0.376524i
$248$	−25.4426	−	8.92081i	−1.61561	−	0.566472i
$249$		0			0
$250$	8.60316	+	6.35222i	0.544112	+	0.401750i
$251$	16.5268			1.04316			0.521581	−	0.853202i	$-0.325342\pi$
$251$	16.5268			1.04316			0.521581	+	0.853202i	$0.325342\pi$
$252$		0			0
$253$	1.95000			0.122595
$254$	18.1683	+	13.4147i	1.13998	+	0.841714i
$255$		0			0
$256$	5.87056	−	14.8841i	0.366910	−	0.930257i
$257$		−	20.1794i		−	1.25875i	−0.777100	−	0.629377i	$-0.783310\pi$
$257$		−	20.1794i		−	1.25875i	0.777100	−	0.629377i	$-0.216690\pi$
$258$		0			0
$259$	2.53351	+	17.9108i	0.157425	+	1.11292i
$260$	4.86470	+	15.7946i	0.301696	+	0.979540i
$261$		0			0
$262$	−1.52628	+	2.06713i	−0.0942941	+	0.127708i
$263$			21.7941i			1.34388i	0.740606	+	0.671940i	$0.234539\pi$
$263$			21.7941i			1.34388i	−0.740606	+	0.671940i	$0.765461\pi$
$264$		0			0
$265$			28.6030i			1.75707i
$266$	6.31514	+	3.41309i	0.387206	+	0.209270i
$267$		0			0
$268$	−5.89556	+	1.81582i	−0.360129	+	0.110919i
$269$			11.4486i			0.698032i	0.937117	+	0.349016i	$0.113484\pi$
$269$			11.4486i			0.698032i	−0.937117	+	0.349016i	$0.886516\pi$
$270$		0			0
$271$	14.6782			0.891635			0.445817	−	0.895124i	$-0.352913\pi$
$271$	14.6782			0.891635			0.445817	+	0.895124i	$0.352913\pi$
$272$	−13.1281	−	19.2903i	−0.796008	−	1.16965i
$273$		0			0
$274$	−15.9100	+	21.5478i	−0.961159	+	1.30175i
$275$			3.04058i			0.183354i
$276$		0			0
$277$	−15.6782			−0.942010			−0.471005	−	0.882131i	$-0.656109\pi$
$277$	−15.6782			−0.942010			−0.471005	+	0.882131i	$0.656109\pi$
$278$	−12.8422	+	17.3929i	−0.770223	+	1.04315i
$279$		0			0
$280$	19.6617	+	3.91836i	1.17501	+	0.234167i
$281$	0.947053			0.0564965			0.0282482	−	0.999601i	$-0.491007\pi$
$281$	0.947053			0.0564965			0.0282482	+	0.999601i	$0.491007\pi$
$282$		0			0
$283$	−9.03555			−0.537108			−0.268554	−	0.963265i	$-0.586546\pi$
$283$	−9.03555			−0.537108			−0.268554	+	0.963265i	$0.586546\pi$
$284$	−18.7224	+	5.76645i	−1.11097	+	0.342176i
$285$		0			0
$286$	3.61814	−	4.90025i	0.213945	−	0.289758i
$287$	−1.81694	+	0.257009i	−0.107251	+	0.0151708i
$288$		0			0
$289$	−17.0289			−1.00170
$290$	−14.9450	−	11.0348i	−0.877603	−	0.647986i
$291$		0			0
$292$	11.3108	−	3.48369i	0.661912	−	0.203867i
$293$		−	7.22058i		−	0.421831i	−0.977504	−	0.210915i	$-0.932356\pi$
$293$		−	7.22058i		−	0.421831i	0.977504	−	0.210915i	$-0.0676445\pi$
$294$		0			0
$295$		−	32.7372i		−	1.90603i
$296$	−18.2489	−	6.39850i	−1.06069	−	0.371905i
$297$		0			0
$298$	14.6137	−	19.7921i	0.846549	−	1.14653i
$299$	−4.30717			−0.249090
$300$		0			0
$301$	−1.77666	+	0.251311i	−0.102405	+	0.0144853i
$302$	9.75584	+	7.20332i	0.561386	+	0.414504i
$303$		0			0
$304$	−6.34427	+	4.31762i	−0.363869	+	0.247633i
$305$	34.5196			1.97659
$306$		0			0
$307$	24.6885			1.40905			0.704525	−	0.709679i	$-0.251160\pi$
$307$	24.6885			1.40905			0.704525	+	0.709679i	$0.251160\pi$
$308$	−3.14264	−	6.68758i	−0.179069	−	0.381060i
$309$		0			0
$310$	29.0539	+	21.4522i	1.65015	+	1.21840i
$311$	32.3803			1.83612			0.918059	−	0.396443i	$-0.129756\pi$
$311$	32.3803			1.83612			0.918059	+	0.396443i	$0.129756\pi$
$312$		0			0
$313$			8.75066i			0.494617i	0.968937	+	0.247308i	$0.0795461\pi$
$313$			8.75066i			0.494617i	−0.968937	+	0.247308i	$0.920454\pi$
$314$	−21.3915	−	15.7946i	−1.20719	−	0.891341i
$315$		0			0
$316$	−23.1019	+	7.11532i	−1.29958	+	0.400268i
$317$	−19.2136			−1.07914			−0.539572	−	0.841939i	$-0.681414\pi$
$317$	−19.2136			−1.07914			−0.539572	+	0.841939i	$0.681414\pi$
$318$		0			0
$319$			6.84706i			0.383362i
$320$	−13.3842	+	16.7397i	−0.748197	+	0.935780i
$321$		0			0
$322$	−2.48426	+	4.59656i	−0.138443	+	0.256156i
$323$			11.1916i			0.622715i
$324$		0			0
$325$		−	6.71606i		−	0.372540i
$326$	0.285916	+	0.211109i	0.0158354	+	0.0116922i
$327$		0			0
$328$	0.649089	−	1.85123i	0.0358399	−	0.102217i
$329$	−3.06205	−	21.6474i	−0.168817	−	1.19346i
$330$		0			0
$331$			6.59575i			0.362535i	0.983434	+	0.181267i	$0.0580200\pi$
$331$			6.59575i			0.362535i	−0.983434	+	0.181267i	$0.941980\pi$
$332$	−3.39870	−	11.0348i	−0.186528	−	0.605614i
$333$		0			0
$334$	11.7911	−	15.9694i	0.645181	−	0.873804i
$335$	8.26340			0.451478
$336$		0			0
$337$	16.6741			0.908296			0.454148	−	0.890926i	$-0.349944\pi$
$337$	16.6741			0.908296			0.454148	+	0.890926i	$0.349944\pi$
$338$	2.92859	−	3.96635i	0.159294	−	0.215741i
$339$		0			0
$340$	9.20037	+	29.8716i	0.498960	+	1.62001i
$341$		−	13.3110i		−	0.720832i
$342$		0			0
$343$	−7.57816	−	16.8989i	−0.409182	−	0.912453i
$344$	0.634698	−	1.81019i	0.0342206	−	0.0975990i
$345$		0			0
$346$	−16.8620	−	12.4502i	−0.906509	−	0.669329i
$347$		−	2.53584i		−	0.136131i	−0.997681	−	0.0680654i	$-0.978317\pi$
$347$		−	2.53584i		−	0.136131i	0.997681	−	0.0680654i	$-0.0216827\pi$
$348$		0			0
$349$		−	9.54918i		−	0.511156i	−0.966788	−	0.255578i	$-0.917734\pi$
$349$		−	9.54918i		−	0.511156i	0.966788	−	0.255578i	$-0.0822658\pi$
$350$	−7.16731	−	3.87365i	−0.383109	−	0.207055i
$351$		0			0
$352$	7.89352	+	0.303684i	0.420726	+	0.0161864i
$353$			3.27741i			0.174439i	0.996189	+	0.0872194i	$0.0277981\pi$
$353$			3.27741i			0.174439i	−0.996189	+	0.0872194i	$0.972202\pi$
$354$		0			0
$355$	26.2419			1.39277
$356$	−12.7109	+	3.91492i	−0.673675	+	0.207490i
$357$		0			0
$358$	−15.8141	−	11.6765i	−0.835800	−	0.617121i
$359$			11.6467i			0.614688i	0.951598	+	0.307344i	$0.0994402\pi$
$359$			11.6467i			0.614688i	−0.951598	+	0.307344i	$0.900560\pi$
$360$		0			0
$361$	−15.3193			−0.806277
$362$	−5.82390	−	4.30013i	−0.306097	−	0.226010i
$363$		0			0
$364$	6.94149	+	14.7716i	0.363833	+	0.774241i
$365$	−15.8535			−0.829811
$366$		0			0
$367$	26.5111			1.38387			0.691935	−	0.721960i	$-0.256758\pi$
$367$	26.5111			1.38387			0.691935	+	0.721960i	$0.256758\pi$
$368$	−3.14264	−	4.61777i	−0.163821	−	0.240718i
$369$		0			0
$370$	20.8391	+	15.3867i	1.08337	+	0.799918i
$371$	3.95623	+	27.9688i	0.205397	+	1.45207i
$372$		0			0
$373$	3.56370			0.184522			0.0922608	−	0.995735i	$-0.470591\pi$
$373$	3.56370			0.184522			0.0922608	+	0.995735i	$0.470591\pi$
$374$	6.84282	−	9.26760i	0.353834	−	0.479216i
$375$		0			0
$376$	22.0559	+	7.73336i	1.13745	+	0.398818i
$377$		−	15.1238i		−	0.778917i
$378$		0			0
$379$			9.37361i			0.481490i	0.970588	+	0.240745i	$0.0773917\pi$
$379$			9.37361i			0.481490i	−0.970588	+	0.240745i	$0.922608\pi$
$380$	9.82429	−	3.02586i	0.503975	−	0.155223i
$381$		0			0
$382$	6.08539	+	4.49320i	0.311355	+	0.229892i
$383$	3.95623			0.202154			0.101077	−	0.994879i	$-0.467771\pi$
$383$	3.95623			0.202154			0.101077	+	0.994879i	$0.467771\pi$
$384$		0			0
$385$	1.38629	+	9.80049i	0.0706521	+	0.499479i
$386$	−1.86767	+	2.52948i	−0.0950618	+	0.128747i
$387$		0			0
$388$	24.6282	−	7.58542i	1.25031	−	0.385091i
$389$	−3.36011			−0.170365			−0.0851823	−	0.996365i	$-0.527147\pi$
$389$	−3.36011			−0.170365			−0.0851823	+	0.996365i	$0.527147\pi$
$390$		0			0
$391$	−8.14594			−0.411958
$392$	19.7677	+	1.11198i	0.998422	+	0.0561635i
$393$		0			0
$394$	20.0289	−	27.1262i	1.00904	−	1.36660i
$395$	32.3803			1.62923
$396$		0			0
$397$		−	25.2672i		−	1.26813i	−0.773282	−	0.634063i	$-0.781386\pi$
$397$		−	25.2672i		−	1.26813i	0.773282	−	0.634063i	$-0.218614\pi$
$398$	−14.7397	+	19.9628i	−0.738835	+	1.00064i
$399$		0			0
$400$	7.20037	−	4.90025i	0.360019	−	0.245012i
$401$	35.7404			1.78479			0.892396	−	0.451254i	$-0.149023\pi$
$401$	35.7404			1.78479			0.892396	+	0.451254i	$0.149023\pi$
$402$		0			0
$403$			29.4015i			1.46459i
$404$	27.0035	−	8.31701i	1.34347	−	0.413787i
$405$		0			0
$406$	−16.1400	−	8.72303i	−0.801014	−	0.432917i
$407$		−	9.54741i		−	0.473247i
$408$		0			0
$409$			16.5166i			0.816691i	0.912827	+	0.408346i	$0.133894\pi$
$409$			16.5166i			0.816691i	−0.912827	+	0.408346i	$0.866106\pi$
$410$	−1.56089	+	2.11400i	−0.0770868	+	0.104403i
$411$		0			0
$412$	3.27538	+	10.6344i	0.161366	+	0.523921i
$413$	−4.52806	−	32.0114i	−0.222811	−	1.57518i
$414$		0			0
$415$			15.4667i			0.759232i
$416$	−17.4353	−	0.670778i	−0.854834	−	0.0328876i
$417$		0			0
$418$	−3.04797	−	2.25049i	−0.149081	−	0.110075i
$419$	−17.9928			−0.879006			−0.439503	−	0.898241i	$-0.644845\pi$
$419$	−17.9928			−0.879006			−0.439503	+	0.898241i	$0.644845\pi$
$420$		0			0
$421$	33.9304			1.65367			0.826834	−	0.562447i	$-0.190140\pi$
$421$	33.9304			1.65367			0.826834	+	0.562447i	$0.190140\pi$
$422$	−4.28073	−	3.16071i	−0.208383	−	0.153861i
$423$		0			0
$424$	−28.4967	−	9.99165i	−1.38392	−	0.485237i
$425$		−	12.7018i		−	0.616126i
$426$		0			0
$427$	33.7543	−	4.77459i	1.63348	−	0.231059i
$428$	−14.2363	+	4.38475i	−0.688139	+	0.211945i
$429$		0			0
$430$	−1.52628	+	2.06713i	−0.0736039	+	0.0996858i
$431$		−	21.0053i		−	1.01179i	−0.862596	−	0.505894i	$-0.831163\pi$
$431$		−	21.0053i		−	1.01179i	0.862596	−	0.505894i	$-0.168837\pi$
$432$		0			0
$433$			13.1362i			0.631287i	0.948878	+	0.315644i	$0.102220\pi$
$433$			13.1362i			0.631287i	−0.948878	+	0.315644i	$0.897780\pi$
$434$	31.3770	+	16.9580i	1.50614	+	0.814011i
$435$		0			0
$436$	−7.87056	−	25.5539i	−0.376931	−	1.22381i
$437$			2.67907i			0.128157i
$438$		0			0
$439$	−6.68073			−0.318854			−0.159427	−	0.987210i	$-0.550965\pi$
$439$	−6.68073			−0.318854			−0.159427	+	0.987210i	$0.550965\pi$
$440$	−9.98546	−	3.50115i	−0.476038	−	0.166911i
$441$		0			0
$442$	−15.1145	+	20.4703i	−0.718922	+	0.973675i
$443$		−	34.6391i		−	1.64575i	−0.568221	−	0.822876i	$-0.692368\pi$
$443$		−	34.6391i		−	1.64575i	0.568221	−	0.822876i	$-0.307632\pi$
$444$		0			0
$445$	17.8160			0.844557
$446$	−9.07699	+	12.2935i	−0.429808	+	0.582112i
$447$		0			0
$448$	−10.7721	+	18.2198i	−0.508932	+	0.860807i
$449$	4.23000			0.199626			0.0998131	−	0.995006i	$-0.468176\pi$
$449$	4.23000			0.199626			0.0998131	+	0.995006i	$0.468176\pi$
$450$		0			0
$451$	0.968526			0.0456061
$452$	1.97811	+	6.42250i	0.0930427	+	0.302089i
$453$		0			0
$454$	20.2589	−	27.4377i	0.950797	−	1.28772i
$455$	−3.06205	−	21.6474i	−0.143551	−	1.01485i
$456$		0			0
$457$	−15.2522			−0.713470			−0.356735	−	0.934206i	$-0.616110\pi$
$457$	−15.2522			−0.713470			−0.356735	+	0.934206i	$0.616110\pi$
$458$	−26.0950	−	19.2675i	−1.21934	−	0.900311i
$459$		0			0
$460$	2.20241	+	7.15074i	0.102688	+	0.333405i
$461$			14.4690i			0.673887i	0.941525	+	0.336944i	$0.109393\pi$
$461$			14.4690i			0.673887i	−0.941525	+	0.336944i	$0.890607\pi$
$462$		0			0
$463$			10.0518i			0.467147i	0.972339	+	0.233573i	$0.0750419\pi$
$463$			10.0518i			0.467147i	−0.972339	+	0.233573i	$0.924958\pi$
$464$	16.2144	−	11.0348i	0.752736	−	0.512278i
$465$		0			0
$466$	−0.730732	+	0.989670i	−0.0338505	+	0.0458456i
$467$	−15.8535			−0.733613			−0.366807	−	0.930297i	$-0.619549\pi$
$467$	−15.8535			−0.733613			−0.366807	+	0.930297i	$0.619549\pi$
$468$		0			0
$469$	8.08020	−	1.14295i	0.373109	−	0.0527768i
$470$	−25.1866	−	18.5967i	−1.16177	−	0.857803i
$471$		0			0
$472$	32.6156	+	11.4358i	1.50125	+	0.526377i
$473$	0.947053			0.0435456
$474$		0			0
$475$	−4.17741			−0.191673
$476$	13.1281	+	27.9368i	0.601725	+	1.28048i
$477$		0			0
$478$	−24.0059	−	17.7250i	−1.09801	−	0.810723i
$479$	3.63389			0.166037			0.0830183	−	0.996548i	$-0.473544\pi$
$479$	3.63389			0.166037			0.0830183	+	0.996548i	$0.473544\pi$
$480$		0			0
$481$			21.0884i			0.961547i
$482$	−3.50914	−	2.59101i	−0.159837	−	0.118017i
$483$		0			0
$484$	−5.32778	−	17.2981i	−0.242172	−	0.786278i
$485$	−34.5196			−1.56745
$486$		0			0
$487$			5.79723i			0.262697i	0.991336	+	0.131349i	$0.0419308\pi$
$487$			5.79723i			0.262697i	−0.991336	+	0.131349i	$0.958069\pi$
$488$	−12.0585	+	34.3913i	−0.545861	+	1.55682i
$489$		0			0
$490$	−24.8680	−	9.21787i	−1.12342	−	0.416421i
$491$			11.2666i			0.508455i	0.967144	+	0.254228i	$0.0818213\pi$
$491$			11.2666i			0.508455i	−0.967144	+	0.254228i	$0.918179\pi$
$492$		0			0
$493$		−	28.6030i		−	1.28821i
$494$	6.73237	+	4.97091i	0.302904	+	0.223652i
$495$		0			0
$496$	−31.5217	+	21.4522i	−1.41537	+	0.963233i
$497$	25.6601	−	3.62965i	1.15101	−	0.162812i
$498$		0			0
$499$			20.6615i			0.924935i	0.886636	+	0.462468i	$0.153036\pi$
$499$			20.6615i			0.924935i	−0.886636	+	0.462468i	$0.846964\pi$
$500$	14.4538	−	4.45174i	0.646393	−	0.199088i
$501$		0			0
$502$	13.8830	−	18.8025i	0.619627	−	0.839195i
$503$	−12.2196			−0.544846			−0.272423	−	0.962178i	$-0.587825\pi$
$503$	−12.2196			−0.544846			−0.272423	+	0.962178i	$0.587825\pi$
$504$		0			0
$505$	−37.8489			−1.68426
$506$	1.63805	−	2.21850i	0.0728203	−	0.0986245i
$507$		0			0
$508$	30.5237	−	9.40123i	1.35427	−	0.417112i
$509$		−	12.8248i		−	0.568450i	−0.958758	−	0.284225i	$-0.908264\pi$
$509$		−	12.8248i		−	0.568450i	0.958758	−	0.284225i	$-0.0917363\pi$
$510$		0			0
$511$	−15.5020	+	2.19278i	−0.685770	+	0.0970031i
$512$	−12.0022	−	19.1820i	−0.530425	−	0.847732i
$513$		0			0
$514$	−22.9580	−	16.9512i	−1.01263	−	0.747687i
$515$		−	14.9055i		−	0.656817i
$516$		0			0
$517$			11.5392i			0.507493i
$518$	22.5053	+	12.1632i	0.988826	+	0.534422i
$519$		0			0
$520$	22.0559	+	7.73336i	0.967217	+	0.339130i
$521$			34.9509i			1.53123i	0.643300	+	0.765614i	$0.277565\pi$
$521$			34.9509i			1.53123i	−0.643300	+	0.765614i	$0.722435\pi$
$522$		0			0
$523$	−7.70964			−0.337119			−0.168559	−	0.985691i	$-0.553912\pi$
$523$	−7.70964			−0.337119			−0.168559	+	0.985691i	$0.553912\pi$
$524$	1.06964	+	3.47289i	0.0467276	+	0.151714i
$525$		0			0
$526$	24.7950	+	18.3076i	1.08111	+	0.798251i
$527$			55.6056i			2.42222i
$528$		0			0
$529$	21.0500			0.915218
$530$	32.5415	+	24.0273i	1.41351	+	1.04368i
$531$		0			0
$532$	9.18796	−	4.31762i	0.398348	−	0.187193i
$533$	−2.13929			−0.0926628
$534$		0			0
$535$	19.9541			0.862690
$536$	−2.88659	+	8.23269i	−0.124682	+	0.355598i
$537$		0			0
$538$	13.0250	+	9.61713i	0.561548	+	0.414624i
$539$	2.71112	+	9.39147i	0.116776	+	0.404519i
$540$		0			0
$541$	−24.7741			−1.06512			−0.532561	−	0.846392i	$-0.678770\pi$
$541$	−24.7741			−1.06512			−0.532561	+	0.846392i	$0.678770\pi$
$542$	12.3301	−	16.6993i	0.529622	−	0.717296i
$543$		0			0
$544$	−32.9745	−	1.26861i	−1.41377	−	0.0543912i
$545$			35.8172i			1.53424i
$546$		0			0
$547$		−	28.5584i		−	1.22107i	−0.791990	−	0.610534i	$-0.790955\pi$
$547$		−	28.5584i		−	1.22107i	0.791990	−	0.610534i	$-0.209045\pi$
$548$	11.1500	+	36.2015i	0.476304	+	1.54645i
$549$		0			0
$550$	3.45926	+	2.55418i	0.147503	+	0.108910i
$551$	−9.40706			−0.400754
$552$		0			0
$553$	31.6624	−	4.47869i	1.34642	−	0.190453i
$554$	−13.1701	+	17.8370i	−0.559544	+	0.757821i
$555$		0			0
$556$	9.00000	+	29.2210i	0.381685	+	1.23925i
$557$	7.31634			0.310003			0.155002	−	0.987914i	$-0.450462\pi$
$557$	7.31634			0.310003			0.155002	+	0.987914i	$0.450462\pi$
$558$		0			0
$559$	−2.09186			−0.0884762
$560$	20.9743	−	19.0775i	0.886325	−	0.806170i
$561$		0			0
$562$	0.795552	−	1.07746i	0.0335583	−	0.0454499i
$563$	38.8268			1.63635			0.818176	−	0.574967i	$-0.194985\pi$
$563$	38.8268			1.63635			0.818176	+	0.574967i	$0.194985\pi$
$564$		0			0
$565$		−	9.00197i		−	0.378716i
$566$	−7.59012	+	10.2797i	−0.319036	+	0.432088i
$567$		0			0
$568$	−9.16686	+	26.1444i	−0.384633	+	1.09699i
$569$	−15.9307			−0.667849			−0.333924	−	0.942600i	$-0.608373\pi$
$569$	−15.9307			−0.667849			−0.333924	+	0.942600i	$0.608373\pi$
$570$		0			0
$571$		−	12.8849i		−	0.539217i	−0.962970	−	0.269609i	$-0.913106\pi$
$571$		−	12.8849i		−	0.539217i	0.962970	−	0.269609i	$-0.0868943\pi$
$572$	−2.53565	−	8.23269i	−0.106021	−	0.344226i
$573$		0			0
$574$	−1.23389	+	2.28302i	−0.0515014	+	0.0952916i
$575$		−	3.04058i		−	0.126801i
$576$		0			0
$577$			15.7180i			0.654351i	0.944964	+	0.327175i	$0.106097\pi$
$577$			15.7180i			0.654351i	−0.944964	+	0.327175i	$0.893903\pi$
$578$	−14.3048	+	19.3737i	−0.595000	+	0.805841i
$579$		0			0
$580$	−25.1085	+	7.73336i	−1.04257	+	0.321110i
$581$	2.13929	+	15.1238i	0.0887526	+	0.627442i
$582$		0			0
$583$		−	14.9088i		−	0.617461i
$584$	5.53798	−	15.7946i	0.229163	−	0.653585i
$585$		0			0
$586$	−8.21483	−	6.06549i	−0.339351	−	0.250563i
$587$	−17.9928			−0.742642			−0.371321	−	0.928504i	$-0.621095\pi$
$587$	−17.9928			−0.742642			−0.371321	+	0.928504i	$0.621095\pi$
$588$		0			0
$589$	18.2878			0.753536
$590$	−37.2450	−	27.5002i	−1.53335	−	1.13216i
$591$		0			0
$592$	−22.6091	+	15.3867i	−0.929228	+	0.632391i
$593$		−	5.49210i		−	0.225534i	−0.993621	−	0.112767i	$-0.964029\pi$
$593$		−	5.49210i		−	0.225534i	0.993621	−	0.112767i	$-0.0359713\pi$
$594$		0			0
$595$	−5.79112	−	40.9407i	−0.237413	−	1.67840i
$596$	−10.2415	−	33.2519i	−0.419509	−	1.36205i
$597$		0			0
$598$	−3.61814	+	4.90025i	−0.147957	+	0.200386i
$599$			38.6101i			1.57756i	0.614673	+	0.788782i	$0.289288\pi$
$599$			38.6101i			1.57756i	−0.614673	+	0.788782i	$0.710712\pi$
$600$		0			0
$601$			15.4667i			0.630901i	0.948942	+	0.315451i	$0.102156\pi$
$601$			15.4667i			0.630901i	−0.948942	+	0.315451i	$0.897844\pi$
$602$	−1.20653	+	2.23241i	−0.0491745	+	0.0909862i
$603$		0			0
$604$	16.3904	−	5.04819i	0.666915	−	0.205408i
$605$			24.2456i			0.985723i
$606$		0			0
$607$	−25.1959			−1.02267			−0.511336	−	0.859381i	$-0.670849\pi$
$607$	−25.1959			−1.02267			−0.511336	+	0.859381i	$0.670849\pi$
$608$	−0.417226	+	10.8448i	−0.0169207	+	0.439814i
$609$		0			0
$610$	28.9974	−	39.2728i	1.17407	−	1.59011i
$611$		−	25.4879i		−	1.03113i
$612$		0			0
$613$	−21.7556			−0.878699			−0.439350	−	0.898316i	$-0.644791\pi$
$613$	−21.7556			−0.878699			−0.439350	+	0.898316i	$0.644791\pi$
$614$	20.7391	−	28.0881i	0.836961	−	1.13354i
$615$		0			0
$616$	−10.2483	−	2.04239i	−0.412917	−	0.0822901i
$617$	−21.7038			−0.873764			−0.436882	−	0.899519i	$-0.643917\pi$
$617$	−21.7038			−0.873764			−0.436882	+	0.899519i	$0.643917\pi$
$618$		0			0
$619$	−25.6385			−1.03050			−0.515250	−	0.857040i	$-0.672301\pi$
$619$	−25.6385			−1.03050			−0.515250	+	0.857040i	$0.672301\pi$
$620$	48.8122	−	15.0340i	1.96035	−	0.603782i
$621$		0			0
$622$	27.2004	−	36.8389i	1.09064	−	1.47711i
$623$	17.4210	−	2.46422i	0.697956	−	0.0987269i
$624$		0			0
$625$	−31.1459			−1.24584
$626$	9.95560	+	7.35081i	0.397906	+	0.293797i
$627$		0			0
$628$	−35.9389	+	11.0691i	−1.43412	+	0.441705i
$629$			39.8834i			1.59026i
$630$		0			0
$631$			30.4513i			1.21225i	0.795370	+	0.606124i	$0.207276\pi$
$631$			30.4513i			1.21225i	−0.795370	+	0.606124i	$0.792724\pi$
$632$	−11.3112	+	32.2600i	−0.449934	+	1.28323i
$633$		0			0
$634$	−16.1400	+	21.8593i	−0.641001	+	0.868142i
$635$	−42.7830			−1.69779
$636$		0			0
$637$	−5.98834	−	20.7439i	−0.237267	−	0.821905i
$638$	7.78987	+	5.75172i	0.308404	+	0.227713i
$639$		0			0
$640$	7.80166	+	29.2889i	0.308388	+	1.15775i
$641$	10.6765			0.421695			0.210847	−	0.977519i	$-0.432378\pi$
$641$	10.6765			0.421695			0.210847	+	0.977519i	$0.432378\pi$
$642$		0			0
$643$	−19.3693			−0.763850			−0.381925	−	0.924193i	$-0.624739\pi$
$643$	−19.3693			−0.763850			−0.381925	+	0.924193i	$0.624739\pi$
$644$	3.14264	+	6.68758i	0.123837	+	0.263528i
$645$		0			0
$646$	12.7326	+	9.40123i	0.500958	+	0.369887i
$647$	13.3633			0.525365			0.262683	−	0.964882i	$-0.415393\pi$
$647$	13.3633			0.525365			0.262683	+	0.964882i	$0.415393\pi$
$648$		0			0
$649$			17.0638i			0.669811i
$650$	−7.64084	−	5.64168i	−0.299698	−	0.221285i
$651$		0			0
$652$	0.480355	−	0.147948i	0.0188121	−	0.00579410i
$653$	15.2574			0.597068			0.298534	−	0.954399i	$-0.403502\pi$
$653$	15.2574			0.597068			0.298534	+	0.954399i	$0.403502\pi$
$654$		0			0
$655$		−	4.86772i		−	0.190197i
$656$	−1.56089	−	2.29356i	−0.0609425	−	0.0895483i
$657$		0			0
$658$	−27.2004	−	14.7007i	−1.06038	−	0.573095i
$659$		−	3.36337i		−	0.131018i	−0.997852	−	0.0655092i	$-0.979133\pi$
$659$		−	3.36337i		−	0.131018i	0.997852	−	0.0655092i	$-0.0208672\pi$
$660$		0			0
$661$		−	0.251311i		−	0.00977487i	−0.999988	−	0.00488744i	$-0.998444\pi$
$661$		−	0.251311i		−	0.00977487i	0.999988	−	0.00488744i	$-0.00155573\pi$
$662$	7.50395	+	5.54061i	0.291649	+	0.215342i
$663$		0			0
$664$	−15.4093	−	5.40287i	−0.597995	−	0.209672i
$665$	−13.4647	+	1.90461i	−0.522140	+	0.0738575i
$666$		0			0
$667$		−	6.84706i		−	0.265119i
$668$	−8.26340	−	26.8294i	−0.319720	−	1.03806i
$669$		0			0
$670$	6.94149	−	9.40123i	0.268173	−	0.363201i
$671$	−17.9928			−0.694604
$672$		0			0
$673$	−11.6767			−0.450102			−0.225051	−	0.974347i	$-0.572255\pi$
$673$	−11.6767			−0.450102			−0.225051	+	0.974347i	$0.572255\pi$
$674$	14.0067	−	18.9700i	0.539518	−	0.730699i
$675$		0			0
$676$	−2.05240	−	6.66369i	−0.0789385	−	0.256296i
$677$		−	12.0082i		−	0.461512i	−0.973012	−	0.230756i	$-0.925880\pi$
$677$		−	12.0082i		−	0.461512i	0.973012	−	0.230756i	$-0.0741200\pi$
$678$		0			0
$679$	−33.7543	+	4.77459i	−1.29537	+	0.183232i
$680$	41.7133	+	14.6257i	1.59963	+	0.560871i
$681$		0			0
$682$	−15.1439	−	11.1816i	−0.579890	−	0.428167i
$683$			20.6345i			0.789556i	0.918777	+	0.394778i	$0.129178\pi$
$683$			20.6345i			0.789556i	−0.918777	+	0.394778i	$0.870822\pi$
$684$		0			0
$685$		−	50.7412i		−	1.93872i
$686$	−25.5916	−	5.57388i	−0.977093	−	0.212812i
$687$		0			0
$688$	−1.52628	−	2.24271i	−0.0581890	−	0.0855024i
$689$			32.9308i			1.25456i
$690$		0			0
$691$	−12.5756			−0.478398			−0.239199	−	0.970971i	$-0.576885\pi$
$691$	−12.5756			−0.478398			−0.239199	+	0.970971i	$0.576885\pi$
$692$	−28.3292	+	8.72533i	−1.07691	+	0.331687i
$693$		0			0
$694$	−2.88501	−	2.13017i	−0.109514	−	0.0808603i
$695$		−	40.9571i		−	1.55359i
$696$		0			0
$697$	−4.04593			−0.153250
$698$	−10.8641	−	8.02158i	−0.411211	−	0.303621i
$699$		0			0
$700$	−10.4278	+	4.90025i	−0.394133	+	0.185212i
$701$	−39.4229			−1.48898			−0.744491	−	0.667633i	$-0.767308\pi$
$701$	−39.4229			−1.48898			−0.744491	+	0.667633i	$0.767308\pi$
$702$		0			0
$703$	13.1170			0.494718
$704$	6.97628	−	8.72533i	0.262928	−	0.328848i
$705$		0			0
$706$	3.72870	+	2.75312i	0.140331	+	0.103615i
$707$	−37.0098	+	5.23509i	−1.39190	+	0.196886i
$708$		0			0
$709$	14.3733			0.539802			0.269901	−	0.962888i	$-0.413009\pi$
$709$	14.3733			0.539802			0.269901	+	0.962888i	$0.413009\pi$
$710$	22.0439	−	29.8553i	0.827293	−	1.12045i
$711$		0			0
$712$	−6.22350	+	17.7498i	−0.233236	+	0.665200i
$713$			13.3110i			0.498502i
$714$		0			0
$715$			11.5392i			0.431541i
$716$	−26.5686	+	8.18305i	−0.992913	+	0.305815i
$717$		0			0
$718$	13.2504	+	9.78354i	0.494500	+	0.365118i
$719$	−38.8268			−1.44799			−0.723997	−	0.689803i	$-0.757697\pi$
$719$	−38.8268			−1.44799			−0.723997	+	0.689803i	$0.757697\pi$
$720$		0			0
$721$	−2.06167	−	14.5751i	−0.0767805	−	0.542805i
$722$	−12.8686	+	17.4287i	−0.478921	+	0.648628i
$723$		0			0
$724$	−9.78448	+	3.01360i	−0.363637	+	0.111999i
$725$	10.6765			0.396514
$726$		0			0
$727$	28.9015			1.07190			0.535949	−	0.844251i	$-0.319954\pi$
$727$	28.9015			1.07190			0.535949	+	0.844251i	$0.319954\pi$
$728$	22.6366	+	4.51124i	0.838968	+	0.167198i
$729$		0			0
$730$	−13.3174	+	18.0365i	−0.492899	+	0.667560i
$731$	−3.95623			−0.146326
$732$		0			0
$733$		−	26.2074i		−	0.967993i	−0.875070	−	0.483996i	$-0.839185\pi$
$733$		−	26.2074i		−	0.967993i	0.875070	−	0.483996i	$-0.160815\pi$
$734$	22.2701	−	30.1616i	0.822005	−	1.11329i
$735$		0			0
$736$	−7.89352	−	0.303684i	−0.290959	−	0.0111939i
$737$	−4.30717			−0.158657
$738$		0			0
$739$		−	42.0351i		−	1.54629i	−0.634232	−	0.773143i	$-0.718684\pi$
$739$		−	42.0351i		−	1.54629i	0.634232	−	0.773143i	$-0.281316\pi$
$740$	35.0108	−	10.7833i	1.28702	−	0.396400i
$741$		0			0
$742$	35.1434	+	18.9936i	1.29015	+	0.697278i
$743$		−	41.3642i		−	1.51750i	−0.651379	−	0.758752i	$-0.725809\pi$
$743$		−	41.3642i		−	1.51750i	0.651379	−	0.758752i	$-0.274191\pi$
$744$		0			0
$745$			46.6069i			1.70755i
$746$	2.99361	−	4.05441i	0.109604	−	0.148443i
$747$		0			0
$748$	−4.79555	−	15.5701i	−0.175343	−	0.569299i
$749$	19.5117	−	2.75996i	0.712941	−	0.100847i
$750$		0			0
$751$		−	19.6117i		−	0.715640i	−0.933791	−	0.357820i	$-0.883520\pi$
$751$		−	19.6117i		−	0.715640i	0.933791	−	0.357820i	$-0.116480\pi$
$752$	27.3258	−	18.5967i	0.996471	−	0.678153i
$753$		0			0
$754$	−17.2063	−	12.7044i	−0.626617	−	0.462669i
$755$	−22.9732			−0.836082
$756$		0			0
$757$	5.86852			0.213295			0.106647	−	0.994297i	$-0.465988\pi$
$757$	5.86852			0.213295			0.106647	+	0.994297i	$0.465988\pi$
$758$	10.6643	+	7.87409i	0.387345	+	0.286000i
$759$		0			0
$760$	4.81017	−	13.7189i	0.174483	−	0.497635i
$761$		−	16.1131i		−	0.584101i	−0.956403	−	0.292050i	$-0.905662\pi$
$761$		−	16.1131i		−	0.584101i	0.956403	−	0.292050i	$-0.0943375\pi$
$762$		0			0
$763$	4.95407	+	35.0231i	0.179349	+	1.26792i
$764$	10.2238	−	3.14890i	0.369884	−	0.113923i
$765$		0			0
$766$	3.32335	−	4.50099i	0.120077	−	0.162627i
$767$		−	37.6906i		−	1.36093i
$768$		0			0
$769$		−	38.3589i		−	1.38326i	−0.722254	−	0.691628i	$-0.756894\pi$
$769$		−	38.3589i		−	1.38326i	0.722254	−	0.691628i	$-0.243106\pi$
$770$	12.3145	+	6.65551i	0.443784	+	0.239848i
$771$		0			0
$772$	1.30889	+	4.24968i	0.0471080	+	0.152949i
$773$		−	8.12153i		−	0.292111i	−0.989276	−	0.146056i	$-0.953342\pi$
$773$		−	8.12153i		−	0.292111i	0.989276	−	0.146056i	$-0.0466578\pi$
$774$		0			0
$775$	−20.7556			−0.745562
$776$	12.0585	−	34.3913i	0.432873	−	1.23458i
$777$		0			0
$778$	−2.82259	+	3.82279i	−0.101195	+	0.137054i
$779$			1.33064i			0.0476752i
$780$		0			0
$781$	−13.6782			−0.489443
$782$	−6.84282	+	9.26760i	−0.244699	+	0.331409i
$783$		0			0
$784$	17.8706	−	21.5556i	0.638234	−	0.769842i
$785$	50.3731			1.79789
$786$		0			0
$787$	−6.54925			−0.233455			−0.116728	−	0.993164i	$-0.537240\pi$
$787$	−6.54925			−0.233455			−0.116728	+	0.993164i	$0.537240\pi$
$788$	−14.0366	−	45.5736i	−0.500032	−	1.62349i
$789$		0			0
$790$	27.2004	−	36.8389i	0.967746	−	1.31067i
$791$	−1.24511	−	8.80240i	−0.0442711	−	0.312977i
$792$		0			0
$793$	39.7426			1.41130
$794$	−28.7464	−	21.2252i	−1.02017	−	0.753254i
$795$		0			0
$796$	10.3298	+	33.5386i	0.366131	+	1.18875i
$797$		−	10.0227i		−	0.355022i	−0.984119	−	0.177511i	$-0.943195\pi$
$797$		−	10.0227i		−	0.355022i	0.984119	−	0.177511i	$-0.0568046\pi$
$798$		0			0
$799$		−	48.2039i		−	1.70533i
$800$	0.473527	−	12.3082i	0.0167417	−	0.435160i
$801$		0			0
$802$	30.0230	−	40.6617i	1.06015	−	1.43582i
$803$	8.26340			0.291609
$804$		0			0
$805$	−1.38629	−	9.80049i	−0.0488604	−	0.345422i
$806$	33.4499	+	24.6981i	1.17822	+	0.869953i
$807$		0			0
$808$	13.2215	−	37.7083i	0.465130	−	1.32657i
$809$	−37.9569			−1.33449			−0.667246	−	0.744837i	$-0.732527\pi$
$809$	−37.9569			−1.33449			−0.667246	+	0.744837i	$0.732527\pi$
$810$		0			0
$811$	−22.8056			−0.800812			−0.400406	−	0.916338i	$-0.631131\pi$
$811$	−22.8056			−0.800812			−0.400406	+	0.916338i	$0.631131\pi$
$812$	−23.4822	+	11.0348i	−0.824064	+	0.387246i
$813$		0			0
$814$	−10.8620	−	8.02009i	−0.380715	−	0.281104i
$815$	−0.673280			−0.0235840
$816$		0			0
$817$			1.30114i			0.0455212i
$818$	18.7908	+	13.8744i	0.657006	+	0.485106i
$819$		0			0
$820$	1.09390	+	3.55163i	0.0382005	+	0.124028i
$821$	29.9387			1.04487			0.522433	−	0.852680i	$-0.325024\pi$
$821$	29.9387			1.04487			0.522433	+	0.852680i	$0.325024\pi$
$822$		0			0
$823$		−	2.28591i		−	0.0796818i	−0.999206	−	0.0398409i	$-0.987315\pi$
$823$		−	2.28591i		−	0.0796818i	0.999206	−	0.0398409i	$-0.0126851\pi$
$824$	14.8502	+	5.20684i	0.517330	+	0.181389i
$825$		0			0
$826$	−40.2230	−	21.7389i	−1.39954	−	0.756395i
$827$			21.3188i			0.741326i	0.928767	+	0.370663i	$0.120870\pi$
$827$			21.3188i			0.741326i	−0.928767	+	0.370663i	$0.879130\pi$
$828$		0			0
$829$		−	2.58181i		−	0.0896698i	−0.998994	−	0.0448349i	$-0.985724\pi$
$829$		−	2.58181i		−	0.0896698i	0.998994	−	0.0448349i	$-0.0142762\pi$
$830$	17.5964	+	12.9925i	0.610781	+	0.450976i
$831$		0			0
$832$	−15.4093	+	19.2726i	−0.534220	+	0.668156i
$833$	−11.3255	−	39.2320i	−0.392404	−	1.35931i
$834$		0			0
$835$			37.6049i			1.30137i
$836$	−5.12076	+	1.57718i	−0.177105	+	0.0545479i
$837$		0			0
$838$	−15.1145	+	20.4703i	−0.522120	+	0.707136i
$839$	−46.7392			−1.61362			−0.806809	−	0.590813i	$-0.798807\pi$
$839$	−46.7392			−1.61362			−0.806809	+	0.590813i	$0.798807\pi$
$840$		0			0
$841$	−4.95781			−0.170959
$842$	28.5025	−	38.6025i	0.982261	−	1.33033i
$843$		0			0
$844$	−7.19186	+	2.21508i	−0.247554	+	0.0762461i
$845$			9.34004i			0.321307i
$846$		0			0
$847$	3.35354	+	23.7081i	0.115229	+	0.814618i
$848$	−35.3055	+	24.0273i	−1.21239	+	0.825101i
$849$		0			0
$850$	−14.4508	−	10.6698i	−0.495657	−	0.365973i
$851$			9.54741i			0.327281i
$852$		0			0
$853$			0.547208i			0.0187360i	0.999956	+	0.00936801i	$0.00298198\pi$
$853$			0.547208i			0.0187360i	−0.999956	+	0.00936801i	$0.997018\pi$
$854$	22.9225	−	42.4129i	0.784393	−	1.45134i
$855$		0			0
$856$	−6.97040	+	19.8799i	−0.238243	+	0.679482i
$857$		−	1.20759i		−	0.0412506i	−0.999787	−	0.0206253i	$-0.993434\pi$
$857$		−	1.20759i		−	0.0412506i	0.999787	−	0.0206253i	$-0.00656571\pi$
$858$		0			0
$859$	−28.0474			−0.956966			−0.478483	−	0.878097i	$-0.658813\pi$
$859$	−28.0474			−0.956966			−0.478483	+	0.878097i	$0.658813\pi$
$860$	1.06964	+	3.47289i	0.0364745	+	0.118425i
$861$		0			0
$862$	−23.8976	−	17.6450i	−0.813955	−	0.600991i
$863$			42.8853i			1.45983i	0.683537	+	0.729916i	$0.260441\pi$
$863$			42.8853i			1.45983i	−0.683537	+	0.729916i	$0.739559\pi$
$864$		0			0
$865$	39.7071			1.35008
$866$	14.9450	+	11.0348i	0.507853	+	0.374978i
$867$		0			0
$868$	45.6506	−	21.4522i	1.54948	−	0.728136i
$869$	−16.8777			−0.572538
$870$		0			0
$871$	9.51370			0.322359
$872$	−35.6841	−	12.5117i	−1.20842	−	0.423701i
$873$		0			0
$874$	3.04797	+	2.25049i	0.103099	+	0.0761241i
$875$	−19.8097	+	2.80212i	−0.669692	+	0.0947288i
$876$		0			0
$877$	18.8330			0.635944			0.317972	−	0.948100i	$-0.396998\pi$
$877$	18.8330			0.635944			0.317972	+	0.948100i	$0.396998\pi$
$878$	−5.61200	+	7.60064i	−0.189396	+	0.256509i
$879$		0			0
$880$	−12.3713	+	8.41935i	−0.417037	+	0.283816i
$881$		−	24.1116i		−	0.812341i	−0.913797	−	0.406171i	$-0.866864\pi$
$881$		−	24.1116i		−	0.812341i	0.913797	−	0.406171i	$-0.133136\pi$
$882$		0			0
$883$			4.26525i			0.143537i	0.997421	+	0.0717686i	$0.0228643\pi$
$883$			4.26525i			0.143537i	−0.997421	+	0.0717686i	$0.977136\pi$
$884$	10.5924	+	34.3913i	0.356263	+	1.15671i
$885$		0			0
$886$	−39.4087	−	29.0978i	−1.32396	−	0.977560i
$887$	−22.3000			−0.748760			−0.374380	−	0.927275i	$-0.622144\pi$
$887$	−22.3000			−0.748760			−0.374380	+	0.927275i	$0.622144\pi$
$888$		0			0
$889$	−41.8345	+	5.91755i	−1.40308	+	0.198468i
$890$	14.9659	−	20.2691i	0.501658	−	0.679423i
$891$		0			0
$892$	6.36129	+	20.6537i	0.212992	+	0.691537i
$893$	−15.8535			−0.530518
$894$		0			0
$895$	37.2393			1.24477
$896$	11.6798	+	27.5605i	0.390195	+	0.920732i
$897$		0			0
$898$	3.55332	−	4.81246i	0.118576	−	0.160594i
$899$	−46.7392			−1.55884
$900$		0			0
$901$			62.2804i			2.07486i
$902$	0.813589	−	1.10189i	0.0270896	−	0.0366889i
$903$		0			0
$904$	8.96853	+	3.14459i	0.298289	+	0.104587i
$905$	13.7142			0.455876
$906$		0			0
$907$			58.1354i			1.93036i	0.261595	+	0.965178i	$0.415751\pi$
$907$			58.1354i			1.93036i	−0.261595	+	0.965178i	$0.584249\pi$
$908$	−14.1977	−	46.0969i	−0.471169	−	1.52978i
$909$		0			0
$910$	−27.2004	−	14.7007i	−0.901684	−	0.487325i
$911$			50.9890i			1.68934i	0.535286	+	0.844671i	$0.320204\pi$
$911$			50.9890i			1.68934i	−0.535286	+	0.844671i	$0.679796\pi$
$912$		0			0
$913$		−	8.06179i		−	0.266806i
$914$	−12.8123	+	17.3524i	−0.423794	+	0.573967i
$915$		0			0
$916$	−43.8411	+	13.5030i	−1.44855	+	0.446150i
$917$	−0.673280	−	4.75980i	−0.0222337	−	0.157182i
$918$		0			0
$919$			27.7492i			0.915361i	0.889117	+	0.457681i	$0.151320\pi$
$919$			27.7492i			0.915361i	−0.889117	+	0.457681i	$0.848680\pi$
$920$	9.98546	+	3.50115i	0.329211	+	0.115429i
$921$		0			0
$922$	16.4613	+	12.1544i	0.542124	+	0.400282i
$923$	30.2124			0.994454
$924$		0			0
$925$	−14.8870			−0.489483
$926$	11.4359	+	8.44380i	0.375807	+	0.277481i
$927$		0			0
$928$	1.06633	−	27.7167i	0.0350040	−	0.909844i
$929$			47.6636i			1.56379i	0.623408	+	0.781896i	$0.285747\pi$
$929$			47.6636i			1.56379i	−0.623408	+	0.781896i	$0.714253\pi$
$930$		0			0
$931$	−12.9028	+	3.72476i	−0.422872	+	0.122074i
$932$	0.512108	+	1.66270i	0.0167747	+	0.0544636i
$933$		0			0
$934$	−13.3174	+	18.0365i	−0.435759	+	0.590172i
$935$			21.8235i			0.713705i
$936$		0			0
$937$			42.7240i			1.39573i	0.716229	+	0.697866i	$0.245867\pi$
$937$			42.7240i			1.39573i	−0.716229	+	0.697866i	$0.754133\pi$
$938$	5.48726	−	10.1529i	0.179165	−	0.331505i
$939$		0			0
$940$	−42.3148	+	13.0329i	−1.38016	+	0.425085i
$941$			25.7449i			0.839259i	0.907696	+	0.419629i	$0.137840\pi$
$941$			25.7449i			0.839259i	−0.907696	+	0.419629i	$0.862160\pi$
$942$		0			0
$943$	−0.968526			−0.0315395
$944$	40.4085	−	27.5002i	1.31519	−	0.895055i
$945$		0			0
$946$	0.795552	−	1.07746i	0.0258656	−	0.0350312i
$947$		−	36.2740i		−	1.17875i	−0.807861	−	0.589373i	$-0.799375\pi$
$947$		−	36.2740i		−	1.17875i	0.807861	−	0.589373i	$-0.200625\pi$
$948$		0			0
$949$	−18.2522			−0.592493
$950$	−3.50914	+	4.75262i	−0.113852	+	0.154195i
$951$		0			0
$952$	42.8115	+	8.53188i	1.38753	+	0.276520i
$953$	18.0700			0.585344			0.292672	−	0.956213i	$-0.405456\pi$
$953$	18.0700			0.585344			0.292672	+	0.956213i	$0.405456\pi$
$954$		0			0
$955$	−14.3300			−0.463707
$956$	−40.3313	+	12.4220i	−1.30441	+	0.401755i
$957$		0			0
$958$	3.05257	−	4.13426i	0.0986240	−	0.133572i
$959$	−7.01828	−	49.6162i	−0.226632	−	1.60219i
$960$		0			0
$961$	59.8634			1.93108
$962$	23.9922	+	17.7148i	0.773538	+	0.571149i
$963$		0			0
$964$	−5.89556	+	1.81582i	−0.189883	+	0.0584836i
$965$		−	5.95648i		−	0.191746i
$966$		0			0
$967$			21.3843i			0.687672i	0.939030	+	0.343836i	$0.111726\pi$
$967$			21.3843i			0.687672i	−0.939030	+	0.343836i	$0.888274\pi$
$968$	−24.1555	−	8.46952i	−0.776387	−	0.272221i
$969$		0			0
$970$	−28.9974	+	39.2728i	−0.931052	+	1.26097i
$971$	7.23918			0.232316			0.116158	−	0.993231i	$-0.462942\pi$
$971$	7.23918			0.232316			0.116158	+	0.993231i	$0.462942\pi$
$972$		0			0
$973$	−5.66499	−	40.0490i	−0.181611	−	1.28391i
$974$	6.59548	+	4.86983i	0.211333	+	0.156040i
$975$		0			0
$976$	28.9974	+	42.6085i	0.928185	+	1.36387i
$977$	−34.2458			−1.09562			−0.547810	−	0.836603i	$-0.684538\pi$
$977$	−34.2458			−1.09562			−0.547810	+	0.836603i	$0.684538\pi$
$978$		0			0
$979$	−9.28629			−0.296791
$980$	−31.3770	+	20.5489i	−1.00230	+	0.656412i
$981$		0			0
$982$	12.8180	+	9.46428i	0.409038	+	0.302017i
$983$	−7.23918			−0.230894			−0.115447	−	0.993314i	$-0.536830\pi$
$983$	−7.23918			−0.230894			−0.115447	+	0.993314i	$0.536830\pi$
$984$		0			0
$985$			63.8774i			2.03530i
$986$	−32.5415	−	24.0273i	−1.03633	−	0.765185i
$987$		0			0
$988$	11.3108	−	3.48369i	0.359843	−	0.110831i
$989$	−0.947053			−0.0301145
$990$		0			0
$991$		−	0.633615i		−	0.0201274i	−0.999949	−	0.0100637i	$-0.996797\pi$
$991$		−	0.633615i		−	0.0201274i	0.999949	−	0.0100637i	$-0.00320343\pi$
$992$	−2.07300	+	53.8826i	−0.0658177	+	1.71077i
$993$		0			0
$994$	17.4258	−	32.2424i	0.552711	−	1.02267i
$995$		−	47.0088i		−	1.49028i
$996$		0			0
$997$			13.9348i			0.441318i	0.975351	+	0.220659i	$0.0708208\pi$
$997$			13.9348i			0.441318i	−0.975351	+	0.220659i	$0.929179\pi$
$998$	23.5065	+	17.3562i	0.744085	+	0.549402i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.b.d.55.7	yes	12
3.2	odd	2	inner	756.2.b.d.55.6	yes	12
4.3	odd	2		756.2.b.c.55.8	yes	12
7.6	odd	2		756.2.b.c.55.7	yes	12
12.11	even	2		756.2.b.c.55.5	✓	12
21.20	even	2		756.2.b.c.55.6	yes	12
28.27	even	2	inner	756.2.b.d.55.8	yes	12
84.83	odd	2	inner	756.2.b.d.55.5	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.b.c.55.5	✓	12	12.11	even	2
756.2.b.c.55.6	yes	12	21.20	even	2
756.2.b.c.55.7	yes	12	7.6	odd	2
756.2.b.c.55.8	yes	12	4.3	odd	2
756.2.b.d.55.5	yes	12	84.83	odd	2	inner
756.2.b.d.55.6	yes	12	3.2	odd	2	inner
756.2.b.d.55.7	yes	12	1.1	even	1	trivial
756.2.b.d.55.8	yes	12	28.27	even	2	inner

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.840028 - 1.13770i) q^{2} +(-0.588705 - 1.91139i) q^{4} +2.67907i q^{5} +(0.370556 + 2.61967i) q^{7} +(-2.66911 - 0.935858i) q^{8} +(3.04797 + 2.25049i) q^{10} -1.39642i q^{11} +3.08443i q^{13} +(3.29167 + 1.77902i) q^{14} +(-3.30685 + 2.25049i) q^{16} +5.83343i q^{17} +1.91852 q^{19} +(5.12076 - 1.57718i) q^{20} +(-1.58870 - 1.17303i) q^{22} +1.39642i q^{23} -2.17741 q^{25} +(3.50914 + 2.59101i) q^{26} +(4.78908 - 2.25049i) q^{28} -4.90328 q^{29} +9.53223 q^{31} +(-0.217472 + 5.65267i) q^{32} +(6.63667 + 4.90025i) q^{34} +(-7.01828 + 0.992746i) q^{35} +6.83705 q^{37} +(1.61161 - 2.18270i) q^{38} +(2.50723 - 7.15074i) q^{40} +0.693576i q^{41} +0.678200i q^{43} +(-2.66911 + 0.822081i) q^{44} +(1.58870 + 1.17303i) q^{46} -8.26340 q^{47} +(-6.72538 + 1.94147i) q^{49} +(-1.82909 + 2.47723i) q^{50} +(5.89556 - 1.81582i) q^{52} +10.6765 q^{53} +3.74111 q^{55} +(1.46258 - 7.33899i) q^{56} +(-4.11890 + 5.57845i) q^{58} -12.2196 q^{59} -12.8849i q^{61} +(8.00734 - 10.8448i) q^{62} +(6.24834 + 4.99582i) q^{64} -8.26340 q^{65} -3.08443i q^{67} +(11.1500 - 3.43417i) q^{68} +(-4.76611 + 8.81861i) q^{70} -9.79515i q^{71} +5.91755i q^{73} +(5.74331 - 7.77848i) q^{74} +(-1.12944 - 3.66705i) q^{76} +(3.65817 - 0.517454i) q^{77} -12.0864i q^{79} +(-6.02923 - 8.85929i) q^{80} +(0.789079 + 0.582624i) q^{82} +5.77317 q^{83} -15.6282 q^{85} +(0.771585 + 0.569707i) q^{86} +(-1.30685 + 3.72721i) q^{88} -6.65005i q^{89} +(-8.08020 + 1.14295i) q^{91} +(2.66911 - 0.822081i) q^{92} +(-6.94149 + 9.40123i) q^{94} +5.13985i q^{95} +12.8849i q^{97} +(-3.44070 + 9.28233i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{4} + 2 q^{7} + 4 q^{10} - 12 q^{16} - 12 q^{19} - 4 q^{22} + 4 q^{25} + 20 q^{28} + 24 q^{31} + 32 q^{34} + 12 q^{37} - 20 q^{40} + 4 q^{46} - 18 q^{49} + 28 q^{52} + 40 q^{55} + 8 q^{58} + 20 q^{64}+ \cdots - 56 q^{94}+O(q^{100}) \) 12 * q + 8 * q^4 + 2 * q^7 + 4 * q^10 - 12 * q^16 - 12 * q^19 - 4 * q^22 + 4 * q^25 + 20 * q^28 + 24 * q^31 + 32 * q^34 + 12 * q^37 - 20 * q^40 + 4 * q^46 - 18 * q^49 + 28 * q^52 + 40 * q^55 + 8 * q^58 + 20 * q^64 - 12 * q^70 - 16 * q^76 - 28 * q^82 - 32 * q^85 + 12 * q^88 + 26 * q^91 - 56 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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