LMFDB - Embedded newform 900.2.r.f.551.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,2,Mod(551,900)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("900.551"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(900, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.r (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,6,0,0,4,0,0,22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			551.5
Character	$\chi$	$=$	900.551
Dual form			900.2.r.f.851.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.18642 - 0.769686i) q^{2} +(-1.70656 - 0.296046i) q^{3} +(0.815168 + 1.82634i) q^{4} +(1.79683 + 1.66475i) q^{6} +(3.55496 + 2.05246i) q^{7} +(0.438576 - 2.79422i) q^{8} +(2.82471 + 1.01044i) q^{9} +(1.28763 - 2.23023i) q^{11} +(-0.850456 - 3.35808i) q^{12} +(1.23949 + 2.14686i) q^{13} +(-2.63792 - 5.17127i) q^{14} +(-2.67100 + 2.97754i) q^{16} +5.59797i q^{17} +(-2.57356 - 3.37295i) q^{18} +0.255463i q^{19} +(-5.45914 - 4.55508i) q^{21} +(-3.24424 + 1.65492i) q^{22} +(-3.58977 - 6.21767i) q^{23} +(-1.57567 + 4.63867i) q^{24} +(0.181856 - 3.50108i) q^{26} +(-4.52141 - 2.56063i) q^{27} +(-0.850587 + 8.16565i) q^{28} +(4.78623 + 2.76333i) q^{29} +(-8.20219 + 4.73554i) q^{31} +(5.46069 - 1.47677i) q^{32} +(-2.85767 + 3.42484i) q^{33} +(4.30867 - 6.64152i) q^{34} +(0.457209 + 5.98255i) q^{36} +5.63137 q^{37} +(0.196626 - 0.303085i) q^{38} +(-1.47970 - 4.03069i) q^{39} +(-3.64769 + 2.10599i) q^{41} +(2.97084 + 9.60604i) q^{42} +(2.55089 + 1.47276i) q^{43} +(5.12279 + 0.533623i) q^{44} +(-0.526686 + 10.1397i) q^{46} +(-1.96880 + 3.41006i) q^{47} +(5.43972 - 4.29062i) q^{48} +(4.92516 + 8.53062i) q^{49} +(1.65725 - 9.55328i) q^{51} +(-2.91049 + 4.01377i) q^{52} +4.80456i q^{53} +(3.39340 + 6.51804i) q^{54} +(7.29413 - 9.03317i) q^{56} +(0.0756288 - 0.435964i) q^{57} +(-3.55156 - 6.96235i) q^{58} +(0.413974 + 0.717024i) q^{59} +(2.47440 - 4.28578i) q^{61} +(13.3761 + 0.694791i) q^{62} +(7.96785 + 9.38968i) q^{63} +(-7.61530 - 2.45096i) q^{64} +(6.02643 - 1.86378i) q^{66} +(7.51571 - 4.33919i) q^{67} +(-10.2238 + 4.56328i) q^{68} +(4.28546 + 11.6736i) q^{69} +8.80859 q^{71} +(4.06225 - 7.44971i) q^{72} +1.18707 q^{73} +(-6.68115 - 4.33438i) q^{74} +(-0.466561 + 0.208245i) q^{76} +(9.15492 - 5.28559i) q^{77} +(-1.34683 + 5.92098i) q^{78} +(3.87817 + 2.23906i) q^{79} +(6.95801 + 5.70842i) q^{81} +(5.94863 + 0.308988i) q^{82} +(3.65295 - 6.32709i) q^{83} +(3.86899 - 13.6834i) q^{84} +(-1.89286 - 3.71069i) q^{86} +(-7.34992 - 6.13274i) q^{87} +(-5.66704 - 4.57604i) q^{88} +6.33181i q^{89} +10.1760i q^{91} +(8.42928 - 11.6246i) q^{92} +(15.3995 - 5.65327i) q^{93} +(4.96050 - 2.53040i) q^{94} +(-9.75621 + 0.903582i) q^{96} +(-0.431073 + 0.746640i) q^{97} +(0.722612 - 13.9117i) q^{98} +(5.89070 - 4.99870i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{6} + 4 q^{9} + 22 q^{12} - 30 q^{14} + 16 q^{18} - 4 q^{21} - 28 q^{24} - 12 q^{29} + 44 q^{33} - 6 q^{34} + 42 q^{36} - 60 q^{38} - 60 q^{41} + 18 q^{42} - 12 q^{46} + 12 q^{48} + 24 q^{49}+ \cdots + 12 q^{97}+O(q^{100}) $ 48 * q + 6 * q^6 + 4 * q^9 + 22 * q^12 - 30 * q^14 + 16 * q^18 - 4 * q^21 - 28 * q^24 - 12 * q^29 + 44 * q^33 - 6 * q^34 + 42 * q^36 - 60 * q^38 - 60 * q^41 + 18 * q^42 - 12 * q^46 + 12 * q^48 + 24 * q^49 + 18 * q^52 - 32 * q^54 - 42 * q^56 + 12 * q^57 + 18 * q^58 - 48 * q^64 + 16 * q^66 - 48 * q^68 + 36 * q^69 - 60 * q^72 + 24 * q^73 + 84 * q^74 + 6 * q^76 - 48 * q^77 - 38 * q^78 + 36 * q^82 + 50 * q^84 - 54 * q^86 - 60 * q^92 + 32 * q^93 + 18 * q^94 - 18 * q^96 + 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

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 $

$2$	−1.18642	−	0.769686i	−0.838923	−	0.544250i
$2$	−1.18642	−	0.769686i	−0.838923	−	0.544250i
$3$	−1.70656	−	0.296046i	−0.985285	−	0.170922i
$3$	−1.70656	−	0.296046i	−0.985285	−	0.170922i
$4$	0.815168	+	1.82634i	0.407584	+	0.913168i
$5$		0			0
$5$		0			0
$6$	1.79683	+	1.66475i	0.733554	+	0.679632i
$7$	3.55496	+	2.05246i	1.34365	+	0.775756i	0.987341	−	0.158613i	$-0.0507022\pi$
$7$	3.55496	+	2.05246i	1.34365	+	0.775756i	0.356308	+	0.934369i	$0.384036\pi$
$8$	0.438576	−	2.79422i	0.155060	−	0.987905i
$9$	2.82471	+	1.01044i	0.941571	+	0.336814i
$10$		0			0
$11$	1.28763	−	2.23023i	0.388234	−	0.672441i	−0.603978	−	0.797001i	$-0.706419\pi$
$11$	1.28763	−	2.23023i	0.388234	−	0.672441i	0.992212	+	0.124560i	$0.0397519\pi$
$12$	−0.850456	−	3.35808i	−0.245505	−	0.969395i
$13$	1.23949	+	2.14686i	0.343772	+	0.595431i	0.985130	−	0.171811i	$-0.0549618\pi$
$13$	1.23949	+	2.14686i	0.343772	+	0.595431i	−0.641358	+	0.767242i	$0.721628\pi$
$14$	−2.63792	−	5.17127i	−0.705013	−	1.38208i
$15$		0			0
$16$	−2.67100	+	2.97754i	−0.667751	+	0.744385i
$17$			5.59797i			1.35771i	0.734274	+	0.678853i	$0.237523\pi$
$17$			5.59797i			1.35771i	−0.734274	+	0.678853i	$0.762477\pi$
$18$	−2.57356	−	3.37295i	−0.606595	−	0.795011i
$19$			0.255463i			0.0586072i	0.999571	+	0.0293036i	$0.00932896\pi$
$19$			0.255463i			0.0586072i	−0.999571	+	0.0293036i	$0.990671\pi$
$20$		0			0
$21$	−5.45914	−	4.55508i	−1.19128	−	0.993999i
$22$	−3.24424	+	1.65492i	−0.691674	+	0.352830i
$23$	−3.58977	−	6.21767i	−0.748519	−	1.29647i	−0.948532	−	0.316680i	$-0.897432\pi$
$23$	−3.58977	−	6.21767i	−0.748519	−	1.29647i	0.200013	−	0.979793i	$-0.435902\pi$
$24$	−1.57567	+	4.63867i	−0.321633	+	0.946864i
$25$		0			0
$26$	0.181856	−	3.50108i	0.0356649	−	0.686619i
$27$	−4.52141	−	2.56063i	−0.870147	−	0.492793i
$28$	−0.850587	+	8.16565i	−0.160746	+	1.54316i
$29$	4.78623	+	2.76333i	0.888780	+	0.513137i	0.873543	−	0.486747i	$-0.161816\pi$
$29$	4.78623	+	2.76333i	0.888780	+	0.513137i	0.0152367	+	0.999884i	$0.495150\pi$
$30$		0			0
$31$	−8.20219	+	4.73554i	−1.47316	+	0.850527i	−0.999544	−	0.0302057i	$-0.990384\pi$
$31$	−8.20219	+	4.73554i	−1.47316	+	0.850527i	−0.473613	+	0.880733i	$0.657050\pi$
$32$	5.46069	−	1.47677i	0.965323	−	0.261058i
$33$	−2.85767	+	3.42484i	−0.497456	+	0.596188i
$34$	4.30867	−	6.64152i	0.738932	−	1.13901i
$35$		0			0
$36$	0.457209	+	5.98255i	0.0762015	+	0.997092i
$37$	5.63137			0.925791			0.462895	−	0.886413i	$-0.346811\pi$
$37$	5.63137			0.925791			0.462895	+	0.886413i	$0.346811\pi$
$38$	0.196626	−	0.303085i	0.0318970	−	0.0491669i
$39$	−1.47970	−	4.03069i	−0.236941	−	0.645427i
$40$		0			0
$41$	−3.64769	+	2.10599i	−0.569673	+	0.328901i	−0.757019	−	0.653393i	$-0.773345\pi$
$41$	−3.64769	+	2.10599i	−0.569673	+	0.328901i	0.187346	+	0.982294i	$0.440012\pi$
$42$	2.97084	+	9.60604i	0.458410	+	1.48224i
$43$	2.55089	+	1.47276i	0.389007	+	0.224594i	0.681730	−	0.731604i	$-0.261228\pi$
$43$	2.55089	+	1.47276i	0.389007	+	0.224594i	−0.292723	+	0.956197i	$0.594561\pi$
$44$	5.12279	+	0.533623i	0.772289	+	0.0804467i
$45$		0			0
$46$	−0.526686	+	10.1397i	−0.0776556	+	1.49502i
$47$	−1.96880	+	3.41006i	−0.287179	+	0.497409i	−0.973135	−	0.230234i	$-0.926051\pi$
$47$	−1.96880	+	3.41006i	−0.287179	+	0.497409i	0.685956	+	0.727643i	$0.259384\pi$
$48$	5.43972	−	4.29062i	0.785157	−	0.619297i
$49$	4.92516	+	8.53062i	0.703594	+	1.21866i
$50$		0			0
$51$	1.65725	−	9.55328i	0.232062	−	1.33773i
$52$	−2.91049	+	4.01377i	−0.403613	+	0.556610i
$53$			4.80456i			0.659957i	0.943988	+	0.329978i	$0.107041\pi$
$53$			4.80456i			0.659957i	−0.943988	+	0.329978i	$0.892959\pi$
$54$	3.39340	+	6.51804i	0.461783	+	0.886993i
$55$		0			0
$56$	7.29413	−	9.03317i	0.974719	−	1.20711i
$57$	0.0756288	−	0.435964i	0.0100173	−	0.0577448i
$58$	−3.55156	−	6.96235i	−0.466343	−	0.914201i
$59$	0.413974	+	0.717024i	0.0538948	+	0.0933486i	0.891714	−	0.452599i	$-0.149503\pi$
$59$	0.413974	+	0.717024i	0.0538948	+	0.0933486i	−0.837819	+	0.545948i	$0.816170\pi$
$60$		0			0
$61$	2.47440	−	4.28578i	0.316814	−	0.548738i	−0.663007	−	0.748613i	$-0.730720\pi$
$61$	2.47440	−	4.28578i	0.316814	−	0.548738i	0.979821	+	0.199875i	$0.0640535\pi$
$62$	13.3761	+	0.694791i	1.69876	+	0.0882385i
$63$	7.96785	+	9.38968i	1.00386	+	1.18299i
$64$	−7.61530	−	2.45096i	−0.951913	−	0.306369i
$65$		0			0
$66$	6.02643	−	1.86378i	0.741802	−	0.229415i
$67$	7.51571	−	4.33919i	0.918190	−	0.530117i	0.0351325	−	0.999383i	$-0.488815\pi$
$67$	7.51571	−	4.33919i	0.918190	−	0.530117i	0.883057	+	0.469266i	$0.155481\pi$
$68$	−10.2238	+	4.56328i	−1.23981	+	0.553379i
$69$	4.28546	+	11.6736i	0.515909	+	1.40533i
$70$		0			0
$71$	8.80859			1.04539			0.522694	−	0.852521i	$-0.324927\pi$
$71$	8.80859			1.04539			0.522694	+	0.852521i	$0.324927\pi$
$72$	4.06225	−	7.44971i	0.478740	−	0.877957i
$73$	1.18707			0.138936			0.0694679	−	0.997584i	$-0.477870\pi$
$73$	1.18707			0.138936			0.0694679	+	0.997584i	$0.477870\pi$
$74$	−6.68115	−	4.33438i	−0.776667	−	0.503862i
$75$		0			0
$76$	−0.466561	+	0.208245i	−0.0535182	+	0.0238874i
$77$	9.15492	−	5.28559i	1.04330	−	0.602349i
$78$	−1.34683	+	5.92098i	−0.152498	+	0.670419i
$79$	3.87817	+	2.23906i	0.436329	+	0.251914i	0.702039	−	0.712138i	$-0.252273\pi$
$79$	3.87817	+	2.23906i	0.436329	+	0.251914i	−0.265710	+	0.964053i	$0.585607\pi$
$80$		0			0
$81$	6.95801	+	5.70842i	0.773113	+	0.634269i
$82$	5.94863	+	0.308988i	0.656916	+	0.0341220i
$83$	3.65295	−	6.32709i	0.400963	−	0.694488i	−0.592879	−	0.805291i	$-0.702009\pi$
$83$	3.65295	−	6.32709i	0.400963	−	0.694488i	0.993842	+	0.110803i	$0.0353423\pi$
$84$	3.86899	−	13.6834i	0.422141	−	1.49298i
$85$		0			0
$86$	−1.89286	−	3.71069i	−0.204112	−	0.400134i
$87$	−7.34992	−	6.13274i	−0.787995	−	0.657499i
$88$	−5.66704	−	4.57604i	−0.604108	−	0.487807i
$89$			6.33181i			0.671170i	0.942010	+	0.335585i	$0.108934\pi$
$89$			6.33181i			0.671170i	−0.942010	+	0.335585i	$0.891066\pi$
$90$		0			0
$91$			10.1760i			1.06673i
$92$	8.42928	−	11.6246i	0.878814	−	1.21195i
$93$	15.3995	−	5.65327i	1.59685	−	0.586216i
$94$	4.96050	−	2.53040i	0.511636	−	0.260991i
$95$		0			0
$96$	−9.75621	+	0.903582i	−0.995739	+	0.0922214i
$97$	−0.431073	+	0.746640i	−0.0437688	+	0.0758098i	−0.887080	−	0.461616i	$-0.847270\pi$
$97$	−0.431073	+	0.746640i	−0.0437688	+	0.0758098i	0.843311	+	0.537426i	$0.180603\pi$
$98$	0.722612	−	13.9117i	0.0729948	−	1.40529i
$99$	5.89070	−	4.99870i	0.592037	−	0.502388i
$100$		0			0
$101$	4.63376	+	2.67530i	0.461077	+	0.266203i	0.712497	−	0.701675i	$-0.247564\pi$
$101$	4.63376	+	2.67530i	0.461077	+	0.266203i	−0.251420	+	0.967878i	$0.580898\pi$
$102$	−9.31922	+	10.0586i	−0.922740	+	0.995950i
$103$	−14.9069	+	8.60649i	−1.46882	+	0.848023i	−0.999389	−	0.0349474i	$-0.988874\pi$
$103$	−14.9069	+	8.60649i	−1.46882	+	0.848023i	−0.469429	+	0.882970i	$0.655540\pi$
$104$	6.54240	−	2.52184i	0.641535	−	0.247287i
$105$		0			0
$106$	3.69800	−	5.70021i	0.359182	−	0.553653i
$107$	3.83292			0.370543			0.185271	−	0.982687i	$-0.440684\pi$
$107$	3.83292			0.370543			0.185271	+	0.982687i	$0.440684\pi$
$108$	0.990855	−	10.3450i	0.0953450	−	0.995444i
$109$	−1.61725			−0.154904			−0.0774521	−	0.996996i	$-0.524679\pi$
$109$	−1.61725			−0.154904			−0.0774521	+	0.996996i	$0.524679\pi$
$110$		0			0
$111$	−9.61028	−	1.66714i	−0.912168	−	0.158238i
$112$	−15.6066	+	5.10291i	−1.47468	+	0.482180i
$113$	−2.46357	+	1.42234i	−0.231753	+	0.133802i	−0.611380	−	0.791337i	$-0.709385\pi$
$113$	−2.46357	+	1.42234i	−0.231753	+	0.133802i	0.379628	+	0.925139i	$0.376052\pi$
$114$	−0.425282	+	0.459024i	−0.0398313	+	0.0429915i
$115$		0			0
$116$	−1.14519	+	10.9938i	−0.106328	+	1.02075i
$117$	1.33193	+	7.31669i	0.123137	+	0.676428i
$118$	0.0607376	−	1.16932i	0.00559135	−	0.107645i
$119$	−11.4896	+	19.9005i	−1.05325	+	1.82428i
$120$		0			0
$121$	2.18404	+	3.78286i	0.198549	+	0.343897i
$122$	−6.23437	+	3.18021i	−0.564434	+	0.287923i
$123$	6.84848	−	2.51413i	0.617507	−	0.226691i
$124$	−15.3348	−	11.1197i	−1.37711	−	0.998578i
$125$		0			0
$126$	−2.22609	−	17.2728i	−0.198316	−	1.53878i
$127$			18.4907i			1.64078i	0.571804	+	0.820390i	$0.306244\pi$
$127$			18.4907i			1.64078i	−0.571804	+	0.820390i	$0.693756\pi$
$128$	7.14845	+	8.76924i	0.631840	+	0.775099i
$129$	−3.91725	−	3.26854i	−0.344895	−	0.287779i
$130$		0			0
$131$	0.0847534	+	0.146797i	0.00740494	+	0.0128257i	0.869704	−	0.493573i	$-0.164310\pi$
$131$	0.0847534	+	0.146797i	0.00740494	+	0.0128257i	−0.862299	+	0.506399i	$0.830976\pi$
$132$	−8.58438	−	2.42724i	−0.747174	−	0.211264i
$133$	−0.524327	+	0.908160i	−0.0454649	+	0.0787475i
$134$	−12.2566	−	0.636640i	−1.05881	−	0.0549973i
$135$		0			0
$136$	15.6419	+	2.45514i	1.34128	+	0.210526i
$137$	−13.9743	−	8.06808i	−1.19391	−	0.689303i	−0.234717	−	0.972064i	$-0.575416\pi$
$137$	−13.9743	−	8.06808i	−1.19391	−	0.689303i	−0.959190	+	0.282761i	$0.908750\pi$
$138$	3.90065	−	17.1482i	0.332046	−	1.45975i
$139$	13.8868	−	8.01756i	1.17786	−	0.680040i	0.222345	−	0.974968i	$-0.428629\pi$
$139$	13.8868	−	8.01756i	1.17786	−	0.680040i	0.955520	+	0.294928i	$0.0952956\pi$
$140$		0			0
$141$	4.36942	−	5.23663i	0.367971	−	0.441004i
$142$	−10.4507	−	6.77984i	−0.876999	−	0.568952i
$143$	6.38399			0.533856
$144$	−10.5535	+	5.71180i	−0.879454	+	0.475983i
$145$		0			0
$146$	−1.40836	−	0.913669i	−0.116556	−	0.0756158i
$147$	−5.87964	−	16.0161i	−0.484944	−	1.32099i
$148$	4.59051	+	10.2848i	0.377337	+	0.845403i
$149$	−2.57535	+	1.48688i	−0.210981	+	0.121810i	−0.601767	−	0.798672i	$-0.705536\pi$
$149$	−2.57535	+	1.48688i	−0.210981	+	0.121810i	0.390786	+	0.920481i	$0.372203\pi$
$150$		0			0
$151$	18.3549	+	10.5972i	1.49370	+	0.862388i	0.999974	−	0.00723008i	$-0.00230143\pi$
$151$	18.3549	+	10.5972i	1.49370	+	0.862388i	0.493725	+	0.869618i	$0.335635\pi$
$152$	0.713819	+	0.112040i	0.0578984	+	0.00908765i
$153$	−5.65642	+	15.8126i	−0.457294	+	1.27838i
$154$	−14.9298	−	0.775495i	−1.20308	−	0.0624911i
$155$		0			0
$156$	6.15520	−	5.98811i	0.492810	−	0.479433i
$157$	1.61719	+	2.80105i	0.129066	+	0.223548i	0.923315	−	0.384044i	$-0.125469\pi$
$157$	1.61719	+	2.80105i	0.129066	+	0.223548i	−0.794249	+	0.607592i	$0.792136\pi$
$158$	−2.87775	−	5.64144i	−0.228942	−	0.448809i
$159$	1.42237	−	8.19928i	0.112801	−	0.650245i
$160$		0			0
$161$		−	29.4714i		−	2.32267i
$162$	−3.86141	−	12.1280i	−0.303381	−	0.952869i
$163$		−	10.0147i		−	0.784414i	−0.919877	−	0.392207i	$-0.871712\pi$
$163$		−	10.0147i		−	0.784414i	0.919877	−	0.392207i	$-0.128288\pi$
$164$	−6.81973	−	4.94516i	−0.532531	−	0.386152i
$165$		0			0
$166$	−9.20379	+	4.69494i	−0.714352	+	0.364398i
$167$	2.50253	+	4.33451i	0.193652	+	0.335414i	0.946458	−	0.322828i	$-0.104634\pi$
$167$	2.50253	+	4.33451i	0.193652	+	0.335414i	−0.752806	+	0.658242i	$0.771300\pi$
$168$	−15.1221	+	13.2563i	−1.16670	+	1.02274i
$169$	3.42733	−	5.93632i	0.263641	−	0.456640i
$170$		0			0
$171$	−0.258130	+	0.721610i	−0.0197397	+	0.0551829i
$172$	−0.610346	+	5.85933i	−0.0465385	+	0.446770i
$173$	14.6462	+	8.45599i	1.11353	+	0.642897i	0.939741	−	0.341886i	$-0.111066\pi$
$173$	14.6462	+	8.45599i	1.11353	+	0.642897i	0.173788	+	0.984783i	$0.444399\pi$
$174$	3.99979	+	12.9331i	0.303223	+	0.980457i
$175$		0			0
$176$	3.20136	+	9.79092i	0.241311	+	0.738018i
$177$	−0.494201	−	1.34620i	−0.0371464	−	0.101187i
$178$	4.87350	−	7.51216i	0.365285	−	0.563060i
$179$	−22.0170			−1.64563			−0.822815	−	0.568309i	$-0.807598\pi$
$179$	−22.0170			−1.64563			−0.822815	+	0.568309i	$0.807598\pi$
$180$		0			0
$181$	−20.6877			−1.53770			−0.768851	−	0.639428i	$-0.779171\pi$
$181$	−20.6877			−1.53770			−0.768851	+	0.639428i	$0.779171\pi$
$182$	7.83231	−	12.0730i	0.580570	−	0.894907i
$183$	−5.49150	+	6.58142i	−0.405944	+	0.486513i
$184$	−18.9479	+	7.30368i	−1.39686	+	0.538435i
$185$		0			0
$186$	−22.6214	−	5.14564i	−1.65868	−	0.377297i
$187$	12.4848	+	7.20809i	0.912977	+	0.527108i
$188$	−7.83282	−	0.815918i	−0.571267	−	0.0595070i
$189$	−10.8179	−	18.3829i	−0.786884	−	1.33716i
$190$		0			0
$191$	4.13506	−	7.16214i	0.299203	−	0.518234i	−0.676751	−	0.736212i	$-0.736613\pi$
$191$	4.13506	−	7.16214i	0.299203	−	0.518234i	0.975954	+	0.217978i	$0.0699460\pi$
$192$	12.2704	+	6.43719i	0.885540	+	0.464564i
$193$	9.41418	+	16.3058i	0.677648	+	1.17372i	0.975687	+	0.219167i	$0.0703338\pi$
$193$	9.41418	+	16.3058i	0.677648	+	1.17372i	−0.298040	+	0.954553i	$0.596333\pi$
$194$	1.08611	−	0.554035i	0.0779782	−	0.0397774i
$195$		0			0
$196$	−11.5650	+	15.9489i	−0.826068	+	1.13921i
$197$			2.40398i			0.171277i	0.996326	+	0.0856383i	$0.0272929\pi$
$197$			2.40398i			0.171277i	−0.996326	+	0.0856383i	$0.972707\pi$
$198$	−10.8362	+	1.39655i	−0.770099	+	0.0992488i
$199$		−	6.28473i		−	0.445513i	−0.974874	−	0.222756i	$-0.928495\pi$
$199$		−	6.28473i		−	0.445513i	0.974874	−	0.222756i	$-0.0715055\pi$
$200$		0			0
$201$	−14.1106	+	5.18011i	−0.995287	+	0.365377i
$202$	−3.43843	−	6.74057i	−0.241927	−	0.474265i
$203$	11.3432	+	19.6470i	0.796139	+	1.37895i
$204$	18.7984	−	4.76082i	1.31615	−	0.333324i
$205$		0			0
$206$	24.3101	+	1.26273i	1.69376	+	0.0879787i
$207$	−3.85749	−	21.1904i	−0.268114	−	1.47283i
$208$	−9.70303	−	2.04364i	−0.672784	−	0.141701i
$209$	0.569742	+	0.328941i	0.0394099	+	0.0227533i
$210$		0			0
$211$	0.645564	−	0.372717i	0.0444425	−	0.0256589i	−0.477614	−	0.878570i	$-0.658498\pi$
$211$	0.645564	−	0.372717i	0.0444425	−	0.0256589i	0.522057	+	0.852911i	$0.325165\pi$
$212$	−8.77474	+	3.91652i	−0.602651	+	0.268988i
$213$	−15.0324	−	2.60775i	−1.03000	−	0.178680i
$214$	−4.54744	−	2.95015i	−0.310857	−	0.201668i
$215$		0			0
$216$	−9.13794	+	11.5108i	−0.621758	+	0.783210i
$217$	−38.8779			−2.63921
$218$	1.91873	+	1.24477i	0.129953	+	0.0843067i
$219$	−2.02581	−	0.351427i	−0.136891	−	0.0237472i
$220$		0			0
$221$	−12.0180	+	6.93862i	−0.808421	+	0.466742i
$222$	10.1186	+	9.37482i	0.679117	+	0.629197i
$223$	−7.45035	−	4.30146i	−0.498913	−	0.288047i	0.229352	−	0.973344i	$-0.426339\pi$
$223$	−7.45035	−	4.30146i	−0.498913	−	0.288047i	−0.728264	+	0.685296i	$0.759673\pi$
$224$	22.4435	+	5.95798i	1.49957	+	0.398085i
$225$		0			0
$226$	4.01757	+	0.208684i	0.267245	+	0.0138814i
$227$	−11.8245	+	20.4806i	−0.784820	+	1.35935i	0.144287	+	0.989536i	$0.453911\pi$
$227$	−11.8245	+	20.4806i	−0.784820	+	1.35935i	−0.929107	+	0.369812i	$0.879422\pi$
$228$	0.857866	−	0.217260i	0.0568136	−	0.0143884i
$229$	−3.90156	−	6.75769i	−0.257822	−	0.446561i	0.707836	−	0.706377i	$-0.249672\pi$
$229$	−3.90156	−	6.75769i	−0.257822	−	0.446561i	−0.965658	+	0.259816i	$0.916338\pi$
$230$		0			0
$231$	−17.1882	+	6.30992i	−1.13090	+	0.415162i
$232$	9.82047	−	12.1618i	0.644745	−	0.798463i
$233$		−	26.0058i		−	1.70370i	−0.523790	−	0.851848i	$-0.675482\pi$
$233$		−	26.0058i		−	1.70370i	0.523790	−	0.851848i	$-0.324518\pi$
$234$	4.05133	−	9.70581i	0.264844	−	0.634488i
$235$		0			0
$236$	−0.972068	+	1.34055i	−0.0632763	+	0.0872624i
$237$	−5.95548	−	4.96922i	−0.386850	−	0.322786i
$238$	28.9486	−	14.7670i	1.87646	−	0.957200i
$239$	4.50816	+	7.80837i	0.291609	+	0.505081i	0.974190	−	0.225728i	$-0.0724761\pi$
$239$	4.50816	+	7.80837i	0.291609	+	0.505081i	−0.682582	+	0.730809i	$0.739143\pi$
$240$		0			0
$241$	1.34939	−	2.33722i	0.0869220	−	0.150553i	−0.819287	−	0.573384i	$-0.805630\pi$
$241$	1.34939	−	2.33722i	0.0869220	−	0.150553i	0.906209	+	0.422831i	$0.138964\pi$
$242$	0.320439	−	6.16907i	0.0205986	−	0.396563i
$243$	−10.1843	−	11.8017i	−0.653325	−	0.757077i
$244$	9.84433	+	1.02545i	0.630218	+	0.0656477i
$245$		0			0
$246$	−10.0602	−	2.28838i	−0.641417	−	0.145901i
$247$	−0.548443	+	0.316643i	−0.0348966	+	0.0201475i
$248$	9.63483	+	24.9956i	0.611812	+	1.58722i
$249$	−8.10709	+	9.71614i	−0.513766	+	0.615735i
$250$		0			0
$251$	−6.75982			−0.426676			−0.213338	−	0.976978i	$-0.568434\pi$
$251$	−6.75982			−0.426676			−0.213338	+	0.976978i	$0.568434\pi$
$252$	−10.6536	+	22.2061i	−0.671112	+	1.39886i
$253$	−18.4891			−1.16240
$254$	14.2320	−	21.9376i	0.892995	−	1.37649i
$255$		0			0
$256$	−1.73148	−	15.9060i	−0.108217	−	0.994127i
$257$	0.983508	−	0.567828i	0.0613495	−	0.0354202i	−0.469011	−	0.883192i	$-0.655390\pi$
$257$	0.983508	−	0.567828i	0.0613495	−	0.0354202i	0.530361	+	0.847772i	$0.322056\pi$
$258$	2.13175	+	6.89290i	0.132717	+	0.429133i
$259$	20.0193	+	11.5581i	1.24394	+	0.718188i
$260$		0			0
$261$	10.7275	+	12.6418i	0.664018	+	0.782509i
$262$	0.0124349	−	0.239396i	0.000768230	−	0.0147899i
$263$	1.39447	−	2.41530i	0.0859870	−	0.148934i	−0.819824	−	0.572615i	$-0.805929\pi$
$263$	1.39447	−	2.41530i	0.0859870	−	0.148934i	0.905811	+	0.423681i	$0.139262\pi$
$264$	8.31644	+	9.48700i	0.511841	+	0.583884i
$265$		0			0
$266$	1.32107	−	0.673890i	0.0809999	−	0.0413188i
$267$	1.87451	−	10.8056i	0.114718	−	0.661294i
$268$	14.0514	+	10.1890i	0.858325	+	0.622394i
$269$		−	19.1026i		−	1.16471i	−0.812935	−	0.582354i	$-0.802132\pi$
$269$		−	19.1026i		−	1.16471i	0.812935	−	0.582354i	$-0.197868\pi$
$270$		0			0
$271$		−	17.8466i		−	1.08410i	−0.840345	−	0.542052i	$-0.817648\pi$
$271$		−	17.8466i		−	1.08410i	0.840345	−	0.542052i	$-0.182352\pi$
$272$	−16.6682	−	14.9522i	−1.01066	−	0.906609i
$273$	3.01256	−	17.3660i	0.182328	−	1.05104i
$274$	10.3695	+	20.3280i	0.626444	+	1.22806i
$275$		0			0
$276$	−17.8265	+	17.3426i	−1.07303	+	1.04390i
$277$	14.8570	−	25.7332i	0.892673	−	1.54616i	0.0560150	−	0.998430i	$-0.482161\pi$
$277$	14.8570	−	25.7332i	0.892673	−	1.54616i	0.836658	−	0.547725i	$-0.184506\pi$
$278$	−22.6465	−	1.17632i	−1.35825	−	0.0705512i
$279$	−27.9538	+	5.08870i	−1.67355	+	0.304652i
$280$		0			0
$281$	16.8034	+	9.70142i	1.00240	+	0.578738i	0.908959	−	0.416886i	$-0.136879\pi$
$281$	16.8034	+	9.70142i	1.00240	+	0.578738i	0.0934454	+	0.995624i	$0.470212\pi$
$282$	−9.21451	+	2.84975i	−0.548716	+	0.169700i
$283$	13.9024	−	8.02655i	0.826411	−	0.477129i	−0.0262110	−	0.999656i	$-0.508344\pi$
$283$	13.9024	−	8.02655i	0.826411	−	0.477129i	0.852622	+	0.522528i	$0.175011\pi$
$284$	7.18048	+	16.0874i	0.426083	+	0.954614i
$285$		0			0
$286$	−7.57407	−	4.91367i	−0.447864	−	0.290551i
$287$	−17.2898			−1.02059
$288$	16.9171	+	1.34627i	0.996848	+	0.0793295i
$289$	−14.3372			−0.843366
$290$		0			0
$291$	0.956693	−	1.14657i	0.0560823	−	0.0672132i
$292$	0.967659	+	2.16798i	0.0566280	+	0.126872i
$293$	−14.4822	+	8.36129i	−0.846057	+	0.488471i	−0.859319	−	0.511441i	$-0.829112\pi$
$293$	−14.4822	+	8.36129i	−0.846057	+	0.488471i	0.0132612	+	0.999912i	$0.495779\pi$
$294$	−5.35168	+	23.5273i	−0.312117	+	1.37214i
$295$		0			0
$296$	2.46978	−	15.7353i	0.143553	−	0.914594i
$297$	−11.5327	+	6.78668i	−0.669195	+	0.393803i
$298$	4.19986	+	0.218152i	0.243291	+	0.0126372i
$299$	8.89897	−	15.4135i	0.514641	−	0.891384i
$300$		0			0
$301$	6.04555	+	10.4712i	0.348459	+	0.603549i
$302$	−13.6200	−	26.7002i	−0.783744	−	1.53642i
$303$	−7.11580	−	5.93738i	−0.408792	−	0.341094i
$304$	−0.760651	−	0.682342i	−0.0436263	−	0.0391350i
$305$		0			0
$306$	18.8816	−	14.4067i	1.07939	−	0.823577i
$307$		−	4.83690i		−	0.276056i	−0.990428	−	0.138028i	$-0.955924\pi$
$307$		−	4.83690i		−	0.276056i	0.990428	−	0.138028i	$-0.0440765\pi$
$308$	17.1161	+	12.4113i	0.975278	+	0.707200i
$309$	27.9874	−	10.2744i	1.59215	−	0.584490i
$310$		0			0
$311$	3.96739	+	6.87173i	0.224970	+	0.389660i	0.956311	−	0.292353i	$-0.0944382\pi$
$311$	3.96739	+	6.87173i	0.224970	+	0.389660i	−0.731340	+	0.682013i	$0.761105\pi$
$312$	−11.9116	+	2.36683i	−0.674361	+	0.133995i
$313$	16.1572	−	27.9851i	0.913258	−	1.58181i	0.103827	−	0.994595i	$-0.466891\pi$
$313$	16.1572	−	27.9851i	0.913258	−	1.58181i	0.809431	−	0.587214i	$-0.199775\pi$
$314$	0.237272	−	4.56794i	0.0133900	−	0.257784i
$315$		0			0
$316$	−0.927922	+	8.90806i	−0.0521997	+	0.501118i
$317$	−0.0311809	−	0.0180023i	−0.00175129	−	0.00101111i	0.499124	−	0.866531i	$-0.333655\pi$
$317$	−0.0311809	−	0.0180023i	−0.00175129	−	0.00101111i	−0.500875	+	0.865519i	$0.666989\pi$
$318$	−7.99839	+	8.63298i	−0.448528	+	0.484114i
$319$	12.3257	−	7.11627i	0.690109	−	0.398435i
$320$		0			0
$321$	−6.54112	−	1.13472i	−0.365090	−	0.0633339i
$322$	−22.6837	+	34.9654i	−1.26411	+	1.94854i
$323$	−1.43007			−0.0795714
$324$	−4.75354	+	17.3610i	−0.264086	+	0.964499i
$325$		0			0
$326$	−7.70820	+	11.8816i	−0.426918	+	0.658063i
$327$	2.75994	+	0.478780i	0.152625	+	0.0264766i
$328$	4.28481	+	11.1161i	0.236589	+	0.613782i
$329$	−13.9980	+	8.08176i	−0.771736	+	0.445562i
$330$		0			0
$331$	−25.4488	−	14.6929i	−1.39879	−	0.807594i	−0.404528	−	0.914526i	$-0.632564\pi$
$331$	−25.4488	−	14.6929i	−1.39879	−	0.807594i	−0.994266	+	0.106932i	$0.965897\pi$
$332$	14.5332	+	1.51387i	0.797610	+	0.0830843i
$333$	15.9070	+	5.69017i	0.871698	+	0.311819i
$334$	0.367167	−	7.06869i	0.0200905	−	0.386782i
$335$		0			0
$336$	28.1443	−	4.08818i	1.53540	−	0.223028i
$337$	14.6703	+	25.4098i	0.799144	+	1.38416i	0.920174	+	0.391510i	$0.128047\pi$
$337$	14.6703	+	25.4098i	0.799144	+	1.38416i	−0.121029	+	0.992649i	$0.538620\pi$
$338$	−8.63535	+	4.40497i	−0.469701	+	0.239599i
$339$	4.62531	−	1.69798i	0.251212	−	0.0922218i
$340$		0			0
$341$			24.3904i			1.32081i
$342$	0.861663	−	0.657450i	0.0465934	−	0.0355508i
$343$			11.7003i			0.631757i
$344$	5.23397	−	6.48183i	0.282197	−	0.349477i
$345$		0			0
$346$	−10.8680	−	21.3053i	−0.584269	−	1.14538i
$347$	14.1332	+	24.4795i	0.758712	+	1.31413i	0.943508	+	0.331351i	$0.107504\pi$
$347$	14.1332	+	24.4795i	0.758712	+	1.31413i	−0.184796	+	0.982777i	$0.559162\pi$
$348$	5.20902	−	18.4226i	0.279233	−	0.987557i
$349$	0.316602	−	0.548370i	0.0169473	−	0.0293536i	−0.857427	−	0.514605i	$-0.827939\pi$
$349$	0.316602	−	0.548370i	0.0169473	−	0.0293536i	0.874375	+	0.485251i	$0.161272\pi$
$350$		0			0
$351$	−0.106940	−	12.8807i	−0.00570803	−	0.687521i
$352$	3.73779	−	14.0801i	0.199225	−	0.750474i
$353$	−9.99414	−	5.77012i	−0.531934	−	0.307112i	0.209869	−	0.977729i	$-0.432696\pi$
$353$	−9.99414	−	5.77012i	−0.531934	−	0.307112i	−0.741804	+	0.670617i	$0.766029\pi$
$354$	−0.449825	+	1.97754i	−0.0239079	+	0.105105i
$355$		0			0
$356$	−11.5640	+	5.16149i	−0.612891	+	0.273558i
$357$	25.4992	−	30.5601i	1.34956	−	1.61741i
$358$	26.1214	+	16.9462i	1.38056	+	0.895634i
$359$	−6.40458			−0.338021			−0.169010	−	0.985614i	$-0.554057\pi$
$359$	−6.40458			−0.338021			−0.169010	+	0.985614i	$0.554057\pi$
$360$		0			0
$361$	18.9347			0.996565
$362$	24.5442	+	15.9230i	1.29001	+	0.836894i
$363$	−2.60730	−	7.10227i	−0.136848	−	0.372772i
$364$	−18.5848	+	8.29514i	−0.974107	+	0.434783i
$365$		0			0
$366$	11.5808	−	3.58157i	0.605340	−	0.187212i
$367$	20.2411	+	11.6862i	1.05658	+	0.610014i	0.924483	−	0.381223i	$-0.124497\pi$
$367$	20.2411	+	11.6862i	1.05658	+	0.610014i	0.132093	+	0.991237i	$0.457830\pi$
$368$	28.1017	+	5.91873i	1.46490	+	0.308535i
$369$	−12.4317	+	2.26305i	−0.647166	+	0.117810i
$370$		0			0
$371$	−9.86115	+	17.0800i	−0.511965	+	0.886750i
$372$	22.8779	+	23.5163i	1.18617	+	1.21926i
$373$	−16.3788	−	28.3689i	−0.848063	−	1.46889i	−0.882935	−	0.469496i	$-0.844436\pi$
$373$	−16.3788	−	28.3689i	−0.848063	−	1.46889i	0.0348722	−	0.999392i	$-0.488898\pi$
$374$	−9.26418	−	18.1611i	−0.479039	−	0.939090i
$375$		0			0
$376$	8.66499	+	6.99683i	0.446863	+	0.360834i
$377$			13.7005i			0.705610i
$378$	−1.31459	+	30.1362i	−0.0676151	+	1.55004i
$379$			16.9181i			0.869026i	0.900665	+	0.434513i	$0.143080\pi$
$379$			16.9181i			0.869026i	−0.900665	+	0.434513i	$0.856920\pi$
$380$		0			0
$381$	5.47408	−	31.5555i	0.280446	−	1.61664i
$382$	−10.4185	+	5.31458i	−0.533057	+	0.271918i
$383$	−8.29095	−	14.3603i	−0.423648	−	0.733779i	0.572645	−	0.819803i	$-0.305917\pi$
$383$	−8.29095	−	14.3603i	−0.423648	−	0.733779i	−0.996293	+	0.0860238i	$0.972584\pi$
$384$	−9.60319	−	17.0815i	−0.490061	−	0.871688i
$385$		0			0
$386$	1.38123	−	26.5915i	0.0703030	−	1.35347i
$387$	5.71740	+	6.73765i	0.290632	+	0.342494i
$388$	−1.71501	−	0.178647i	−0.0870665	−	0.00906942i
$389$	−0.926451	−	0.534887i	−0.0469729	−	0.0271198i	0.476330	−	0.879267i	$-0.341967\pi$
$389$	−0.926451	−	0.534887i	−0.0469729	−	0.0271198i	−0.523303	+	0.852147i	$0.675300\pi$
$390$		0			0
$391$	34.8063	−	20.0954i	1.76023	−	1.01627i
$392$	25.9965	−	10.0206i	1.31302	−	0.506118i
$393$	−0.101178	−	0.275610i	−0.00510377	−	0.0139027i
$394$	1.85031	−	2.85212i	0.0932173	−	0.143688i
$395$		0			0
$396$	13.9312	+	6.68361i	0.700070	+	0.335864i
$397$	26.6861			1.33934			0.669669	−	0.742660i	$-0.266436\pi$
$397$	26.6861			1.33934			0.669669	+	0.742660i	$0.266436\pi$
$398$	−4.83727	+	7.45631i	−0.242470	+	0.373751i
$399$	1.16365	−	1.39461i	0.0582555	−	0.0698177i
$400$		0			0
$401$	−12.9635	+	7.48451i	−0.647369	+	0.373758i	−0.787447	−	0.616382i	$-0.788598\pi$
$401$	−12.9635	+	7.48451i	−0.647369	+	0.373758i	0.140079	+	0.990140i	$0.455264\pi$
$402$	20.7281	+	4.71497i	1.03383	+	0.235162i
$403$	−20.3330	−	11.7393i	−1.01286	−	0.584776i
$404$	−1.10871	+	10.6436i	−0.0551604	+	0.529540i
$405$		0			0
$406$	1.66426	−	32.0403i	0.0825959	−	1.59013i
$407$	7.25110	−	12.5593i	0.359423	−	0.622540i
$408$	−25.9671	−	8.82057i	−1.28556	−	0.436683i
$409$	−13.3053	−	23.0454i	−0.657903	−	1.13952i	−0.981157	−	0.193210i	$-0.938110\pi$
$409$	−13.3053	−	23.0454i	−0.657903	−	1.13952i	0.323254	−	0.946312i	$-0.395223\pi$
$410$		0			0
$411$	21.4596	+	17.9057i	1.05852	+	0.883225i
$412$	−27.8699	−	20.2092i	−1.37305	−	0.995637i
$413$			3.39865i			0.167237i
$414$	−11.7334	+	28.1097i	−0.576663	+	1.38152i
$415$		0			0
$416$	9.93888	+	9.89289i	0.487294	+	0.485039i
$417$	−26.0723	+	9.57133i	−1.27677	+	0.468710i
$418$	−0.422770	−	0.828783i	−0.0206784	−	0.0405371i
$419$	−1.19855	−	2.07595i	−0.0585530	−	0.101417i	0.835263	−	0.549851i	$-0.185315\pi$
$419$	−1.19855	−	2.07595i	−0.0585530	−	0.101417i	−0.893816	+	0.448434i	$0.851982\pi$
$420$		0			0
$421$	11.7733	−	20.3920i	0.573797	−	0.993845i	−0.422374	−	0.906421i	$-0.638803\pi$
$421$	11.7733	−	20.3920i	0.573797	−	0.993845i	0.996171	−	0.0874237i	$-0.0278634\pi$
$422$	−1.05278	−	0.0546845i	−0.0512487	−	0.00266200i
$423$	−9.00697	+	7.64309i	−0.437934	+	0.371620i
$424$	13.4250	+	2.10717i	0.651975	+	0.102333i
$425$		0			0
$426$	15.8276	+	14.6641i	0.766847	+	0.710478i
$427$	17.5928	−	10.1572i	0.851374	−	0.491541i
$428$	3.12447	+	7.00020i	0.151027	+	0.338368i
$429$	−10.8947	−	1.88996i	−0.526000	−	0.0912479i
$430$		0			0
$431$	−15.1310			−0.728835			−0.364417	−	0.931236i	$-0.618732\pi$
$431$	−15.1310			−0.728835			−0.364417	+	0.931236i	$0.618732\pi$
$432$	19.7011	−	6.62324i	0.947869	−	0.318661i
$433$	−2.72348			−0.130882			−0.0654410	−	0.997856i	$-0.520845\pi$
$433$	−2.72348			−0.130882			−0.0654410	+	0.997856i	$0.520845\pi$
$434$	46.1254	+	29.9238i	2.21409	+	1.43639i
$435$		0			0
$436$	−1.31833	−	2.95364i	−0.0631365	−	0.141454i
$437$	1.58838	−	0.917054i	0.0759827	−	0.0438686i
$438$	2.13296	+	1.97617i	0.101917	+	0.0944252i
$439$	0.994037	+	0.573907i	0.0474428	+	0.0273911i	0.523534	−	0.852005i	$-0.324613\pi$
$439$	0.994037	+	0.573907i	0.0474428	+	0.0273911i	−0.476091	+	0.879396i	$0.657947\pi$
$440$		0			0
$441$	5.29246	+	29.0732i	0.252022	+	1.38444i
$442$	19.5989	+	1.01802i	0.932227	+	0.0484224i
$443$	5.45190	−	9.44296i	0.259027	−	0.448649i	−0.706954	−	0.707259i	$-0.749931\pi$
$443$	5.45190	−	9.44296i	0.259027	−	0.448649i	0.965982	+	0.258611i	$0.0832647\pi$
$444$	−4.78923	−	18.9106i	−0.227287	−	0.897457i
$445$		0			0
$446$	5.52845	+	10.8378i	0.261779	+	0.513183i
$447$	4.83518	−	1.77503i	0.228696	−	0.0839560i
$448$	−22.0416	−	24.3431i	−1.04137	−	1.15010i
$449$		−	21.5098i		−	1.01511i	−0.861620	−	0.507554i	$-0.830550\pi$
$449$		−	21.5098i		−	1.01511i	0.861620	−	0.507554i	$-0.169450\pi$
$450$		0			0
$451$			10.8469i			0.510762i
$452$	−4.60589	−	3.33985i	−0.216643	−	0.157093i
$453$	−28.1865	−	23.5187i	−1.32432	−	1.10500i
$454$	29.7924	−	15.1974i	1.39823	−	0.713250i
$455$		0			0
$456$	−1.18501	−	0.402527i	−0.0554931	−	0.0188500i
$457$	9.04997	−	15.6750i	0.423340	−	0.733246i	−0.572924	−	0.819609i	$-0.694191\pi$
$457$	9.04997	−	15.6750i	0.423340	−	0.733246i	0.996264	+	0.0863623i	$0.0275243\pi$
$458$	−0.572431	+	11.0204i	−0.0267479	+	0.514950i
$459$	14.3343	−	25.3107i	0.669068	−	1.18140i
$460$		0			0
$461$	12.3502	+	7.13038i	0.575205	+	0.332095i	0.759225	−	0.650828i	$-0.225578\pi$
$461$	12.3502	+	7.13038i	0.575205	+	0.332095i	−0.184021	+	0.982922i	$0.558911\pi$
$462$	25.2490	+	5.74333i	1.17469	+	0.267204i
$463$	10.0539	−	5.80459i	0.467242	−	0.269762i	−0.247842	−	0.968800i	$-0.579722\pi$
$463$	10.0539	−	5.80459i	0.467242	−	0.269762i	0.715085	+	0.699038i	$0.246388\pi$
$464$	−21.0119	+	6.87032i	−0.975455	+	0.318946i
$465$		0			0
$466$	−20.0163	+	30.8537i	−0.927236	+	1.42927i
$467$	−36.7596			−1.70103			−0.850516	−	0.525949i	$-0.823710\pi$
$467$	−36.7596			−1.70103			−0.850516	+	0.525949i	$0.823710\pi$
$468$	−12.2770	+	8.39687i	−0.567504	+	0.388146i
$469$	35.6240			1.64497
$470$		0			0
$471$	−1.93059	−	5.25894i	−0.0889571	−	0.242319i
$472$	2.18508	−	0.842264i	0.100576	−	0.0387683i
$473$	6.56919	−	3.79272i	0.302052	−	0.174390i
$474$	3.24094	+	10.4794i	0.148861	+	0.481336i
$475$		0			0
$476$	−45.7110	−	4.76156i	−2.09516	−	0.218246i
$477$	−4.85473	+	13.5715i	−0.222283	+	0.621396i
$478$	0.661431	−	12.7338i	0.0302531	−	0.582432i
$479$	−17.6782	+	30.6195i	−0.807736	+	1.39904i	0.106693	+	0.994292i	$0.465974\pi$
$479$	−17.6782	+	30.6195i	−0.807736	+	1.39904i	−0.914429	+	0.404747i	$0.867360\pi$
$480$		0			0
$481$	6.98002	+	12.0897i	0.318261	+	0.551245i
$482$	−3.39986	+	1.73430i	−0.154860	+	0.0789954i
$483$	−8.72489	+	50.2948i	−0.396996	+	2.28849i
$484$	−5.12842	+	7.07245i	−0.233110	+	0.321475i
$485$		0			0
$486$	2.99929	+	21.8404i	0.136050	+	0.990702i
$487$		−	17.2184i		−	0.780239i	−0.920764	−	0.390119i	$-0.872434\pi$
$487$		−	17.2184i		−	0.780239i	0.920764	−	0.390119i	$-0.127566\pi$
$488$	−10.8902	−	8.79365i	−0.492976	−	0.398070i
$489$	−2.96482	+	17.0908i	−0.134074	+	0.772871i
$490$		0			0
$491$	4.48405	+	7.76660i	0.202362	+	0.350502i	0.949289	−	0.314404i	$-0.101805\pi$
$491$	4.48405	+	7.76660i	0.202362	+	0.350502i	−0.746927	+	0.664906i	$0.768471\pi$
$492$	10.1743	+	10.4582i	0.458693	+	0.471491i
$493$	−15.4690	+	26.7931i	−0.696690	+	1.20670i
$494$	0.894397	+	0.0464575i	0.0402408	+	0.00209022i
$495$		0			0
$496$	7.80783	−	37.0710i	0.350582	−	1.66454i
$497$	31.3142	+	18.0792i	1.40463	+	0.810965i
$498$	17.0968	−	5.28747i	0.766124	−	0.236937i
$499$	−17.8957	+	10.3321i	−0.801121	+	0.462527i	−0.843863	−	0.536559i	$-0.819724\pi$
$499$	−17.8957	+	10.3321i	−0.801121	+	0.462527i	0.0427423	+	0.999086i	$0.486391\pi$
$500$		0			0
$501$	−2.98751	−	8.13798i	−0.133472	−	0.363578i
$502$	8.01997	+	5.20294i	0.357949	+	0.232219i
$503$	4.69790			0.209469			0.104735	−	0.994500i	$-0.466601\pi$
$503$	4.69790			0.209469			0.104735	+	0.994500i	$0.466601\pi$
$504$	29.7313	−	18.1458i	1.32434	−	0.808279i
$505$		0			0
$506$	21.9358	+	14.2308i	0.975166	+	0.632638i
$507$	−7.60638	+	9.11605i	−0.337811	+	0.404858i
$508$	−33.7701	+	15.0730i	−1.49831	+	0.668755i
$509$	24.2945	−	14.0264i	1.07683	−	0.621710i	0.146793	−	0.989167i	$-0.453105\pi$
$509$	24.2945	−	14.0264i	1.07683	−	0.621710i	0.930040	+	0.367458i	$0.119772\pi$
$510$		0			0
$511$	4.21998	+	2.43641i	0.186681	+	0.107780i
$512$	−10.1884	+	20.2039i	−0.450268	+	0.892894i
$513$	0.654145	−	1.15505i	0.0288812	−	0.0509969i
$514$	−1.60390	−	0.0833109i	−0.0707450	−	0.00367469i
$515$		0			0
$516$	2.77622	−	9.81862i	0.122216	−	0.432241i
$517$	5.07016	+	8.78178i	0.222985	+	0.386222i
$518$	−14.8551	−	29.1213i	−0.652694	−	1.27952i
$519$	−22.4913	−	18.7666i	−0.987258	−	0.823763i
$520$		0			0
$521$		−	3.68445i		−	0.161419i	−0.996738	−	0.0807094i	$-0.974281\pi$
$521$		−	3.68445i		−	0.161419i	0.996738	−	0.0807094i	$-0.0257186\pi$
$522$	−2.99710	−	23.2553i	−0.131179	−	1.01786i
$523$			10.6525i			0.465803i	0.972500	+	0.232901i	$0.0748220\pi$
$523$			10.6525i			0.465803i	−0.972500	+	0.232901i	$0.925178\pi$
$524$	−0.199013	+	0.274453i	−0.00869391	+	0.0119895i
$525$		0			0
$526$	−3.51345	+	1.79224i	−0.153194	+	0.0781456i
$527$	−26.5094	−	45.9156i	−1.15477	−	2.00011i
$528$	−2.56475	−	17.6566i	−0.111616	−	0.768404i
$529$	−14.2729	+	24.7215i	−0.620563	+	1.07485i
$530$		0			0
$531$	0.444847	+	2.44368i	0.0193047	+	0.106047i
$532$	−2.08602	−	0.217294i	−0.0904404	−	0.00942087i
$533$	−9.04254	−	5.22071i	−0.391676	−	0.226134i
$534$	−10.5409	+	11.3772i	−0.456149	+	0.492339i
$535$		0			0
$536$	−8.82844	−	22.9036i	−0.381331	−	0.989284i
$537$	37.5734	+	6.51805i	1.62141	+	0.281275i
$538$	−14.7030	+	22.6637i	−0.633892	+	0.977100i
$539$	25.3671			1.09264
$540$		0			0
$541$	−19.2047			−0.825675			−0.412838	−	0.910805i	$-0.635462\pi$
$541$	−19.2047			−0.825675			−0.412838	+	0.910805i	$0.635462\pi$
$542$	−13.7363	+	21.1735i	−0.590024	+	0.909480i
$543$	35.3048	+	6.12450i	1.51507	+	0.262827i
$544$	8.26689	+	30.5688i	0.354440	+	1.31062i
$545$		0			0
$546$	−16.9405	+	18.2845i	−0.724986	+	0.782506i
$547$	−24.6062	−	14.2064i	−1.05208	−	0.607422i	−0.128853	−	0.991664i	$-0.541129\pi$
$547$	−24.6062	−	14.2064i	−1.05208	−	0.607422i	−0.923232	+	0.384242i	$0.874463\pi$
$548$	3.34361	−	32.0987i	0.142832	−	1.37119i
$549$	11.3200	−	9.60587i	0.483126	−	0.409969i
$550$		0			0
$551$	−0.705928	+	1.22270i	−0.0300736	+	0.0520889i
$552$	34.4980	−	6.85474i	1.46833	−	0.291757i
$553$	9.19117	+	15.9196i	0.390848	+	0.676969i
$554$	−37.4331	+	19.0950i	−1.59038	+	0.811268i
$555$		0			0
$556$	25.9628	+	18.8263i	1.10107	+	0.798414i
$557$		−	21.3633i		−	0.905191i	−0.891716	−	0.452596i	$-0.850498\pi$
$557$		−	21.3633i		−	0.905191i	0.891716	−	0.452596i	$-0.149502\pi$
$558$	37.0816	+	15.4783i	1.56979	+	0.655250i
$559$			7.30187i			0.308836i
$560$		0			0
$561$	−19.1721	−	15.9971i	−0.809448	−	0.675399i
$562$	−12.4687	−	24.4432i	−0.525962	−	1.03108i
$563$	−2.28631	−	3.96000i	−0.0963563	−	0.166894i	0.813818	−	0.581120i	$-0.197386\pi$
$563$	−2.28631	−	3.96000i	−0.0963563	−	0.166894i	−0.910174	+	0.414226i	$0.864052\pi$
$564$	13.1257	+	3.71129i	0.552690	+	0.156274i
$565$		0			0
$566$	−22.6719	−	1.17764i	−0.952973	−	0.0495000i
$567$	13.0192	+	34.5742i	0.546754	+	1.45198i
$568$	3.86324	−	24.6131i	0.162098	−	1.03274i
$569$	−11.3437	−	6.54929i	−0.475553	−	0.274561i	0.243009	−	0.970024i	$-0.421866\pi$
$569$	−11.3437	−	6.54929i	−0.475553	−	0.274561i	−0.718561	+	0.695464i	$0.755199\pi$
$570$		0			0
$571$	−11.2935	+	6.52031i	−0.472619	+	0.272866i	−0.717335	−	0.696728i	$-0.754638\pi$
$571$	−11.2935	+	6.52031i	−0.472619	+	0.272866i	0.244717	+	0.969595i	$0.421305\pi$
$572$	5.20402	+	11.6593i	0.217591	+	0.487500i
$573$	−9.17707	+	10.9985i	−0.383377	+	0.459468i
$574$	20.5130	+	13.3077i	0.856194	+	0.555455i
$575$		0			0
$576$	−19.0345	−	14.6181i	−0.793104	−	0.609086i
$577$	−23.2811			−0.969204			−0.484602	−	0.874735i	$-0.661035\pi$
$577$	−23.2811			−0.969204			−0.484602	+	0.874735i	$0.661035\pi$
$578$	17.0099	+	11.0352i	0.707519	+	0.459002i
$579$	−11.2386	−	30.6140i	−0.467061	−	1.27227i
$580$		0			0
$581$	25.9722	−	14.9950i	1.07751	−	0.622099i
$582$	−2.01754	+	0.623958i	−0.0836295	+	0.0258639i
$583$	10.7153	+	6.18648i	0.443782	+	0.256218i
$584$	0.520620	−	3.31693i	0.0215434	−	0.137255i
$585$		0			0
$586$	23.6174	+	1.22676i	0.975628	+	0.0506768i
$587$	−19.3723	+	33.5537i	−0.799579	+	1.38491i	0.120312	+	0.992736i	$0.461610\pi$
$587$	−19.3723	+	33.5537i	−0.799579	+	1.38491i	−0.919891	+	0.392175i	$0.871723\pi$
$588$	24.4579	−	23.7940i	1.00863	−	0.981248i
$589$	−1.20975	−	2.09536i	−0.0498470	−	0.0863376i
$590$		0			0
$591$	0.711689	−	4.10254i	0.0292750	−	0.168756i
$592$	−15.0414	+	16.7676i	−0.618198	+	0.689145i
$593$		−	23.7164i		−	0.973916i	−0.873425	−	0.486958i	$-0.838106\pi$
$593$		−	23.7164i		−	0.973916i	0.873425	−	0.486958i	$-0.161894\pi$
$594$	18.9062	+	0.824718i	0.775730	+	0.0338386i
$595$		0			0
$596$	−4.81488	−	3.49139i	−0.197225	−	0.143013i
$597$	−1.86057	+	10.7253i	−0.0761481	+	0.438957i
$598$	−22.4214	+	11.4374i	−0.916879	+	0.467709i
$599$	4.51043	+	7.81229i	0.184291	+	0.319202i	0.943337	−	0.331835i	$-0.107668\pi$
$599$	4.51043	+	7.81229i	0.184291	+	0.319202i	−0.759046	+	0.651037i	$0.774334\pi$
$600$		0			0
$601$	−0.146733	+	0.254150i	−0.00598538	+	0.0103670i	−0.869003	−	0.494808i	$-0.835239\pi$
$601$	−0.146733	+	0.254150i	−0.00598538	+	0.0103670i	0.863017	+	0.505175i	$0.168572\pi$
$602$	0.886993	−	17.0764i	0.0361512	−	0.695981i
$603$	25.6142	−	4.66280i	1.04309	−	0.189884i
$604$	−4.39173	+	42.1607i	−0.178697	+	1.71549i
$605$		0			0
$606$	3.87238	+	12.5211i	0.157305	+	0.508636i
$607$	17.6674	−	10.2003i	0.717099	−	0.414017i	−0.0965849	−	0.995325i	$-0.530792\pi$
$607$	17.6674	−	10.2003i	0.717099	−	0.414017i	0.813684	+	0.581307i	$0.197459\pi$
$608$	0.377259	+	1.39500i	0.0152999	+	0.0565749i
$609$	−13.5415	−	36.8870i	−0.548729	−	1.49474i
$610$		0			0
$611$	−9.76123			−0.394897
$612$	−33.4901	+	2.55944i	−1.35376	+	0.103459i
$613$	6.97057			0.281539			0.140769	−	0.990042i	$-0.455042\pi$
$613$	6.97057			0.281539			0.140769	+	0.990042i	$0.455042\pi$
$614$	−3.72289	+	5.73857i	−0.150244	+	0.231590i
$615$		0			0
$616$	−10.7540	−	27.8990i	−0.433290	−	1.12408i
$617$	−35.5942	+	20.5503i	−1.43297	+	0.827325i	−0.997346	−	0.0728037i	$-0.976805\pi$
$617$	−35.5942	+	20.5503i	−1.43297	+	0.827325i	−0.435623	+	0.900129i	$0.643472\pi$
$618$	−41.1128	−	9.35182i	−1.65380	−	0.376186i
$619$	−15.8062	−	9.12571i	−0.635305	−	0.366793i	0.147499	−	0.989062i	$-0.452878\pi$
$619$	−15.8062	−	9.12571i	−0.635305	−	0.366793i	−0.782804	+	0.622269i	$0.786211\pi$
$620$		0			0
$621$	0.309716	+	37.3047i	0.0124285	+	1.49699i
$622$	0.582090	−	11.2064i	0.0233397	−	0.449335i
$623$	−12.9958	+	22.5093i	−0.520664	+	0.901817i
$624$	15.9538	+	6.36014i	0.638664	+	0.254609i
$625$		0			0
$626$	−40.7089	+	20.7660i	−1.62705	+	0.829976i
$627$	−0.874919	−	0.730028i	−0.0349409	−	0.0291545i
$628$	−3.79738	+	5.23686i	−0.151532	+	0.208973i
$629$			31.5242i			1.25695i
$630$		0			0
$631$			11.3170i			0.450521i	0.974299	+	0.225260i	$0.0723233\pi$
$631$			11.3170i			0.450521i	−0.974299	+	0.225260i	$0.927677\pi$
$632$	7.95731	−	9.85446i	0.316525	−	0.391989i
$633$	−1.21204	+	0.444948i	−0.0481742	+	0.0176851i
$634$	0.0231374	+	0.0453577i	0.000918905	+	0.00180139i
$635$		0			0
$636$	16.1341	−	4.08606i	0.639759	−	0.162023i
$637$	−12.2094	+	21.1472i	−0.483752	+	0.837884i
$638$	−20.1008	−	1.04409i	−0.795796	−	0.0413359i
$639$	24.8817	+	8.90057i	0.984306	+	0.352101i
$640$		0			0
$641$	−21.6438	−	12.4960i	−0.854877	−	0.493564i	0.00741620	−	0.999972i	$-0.497639\pi$
$641$	−21.6438	−	12.4960i	−0.854877	−	0.493564i	−0.862293	+	0.506409i	$0.830973\pi$
$642$	6.88712	+	6.38086i	0.271813	+	0.251832i
$643$	6.74821	−	3.89608i	0.266123	−	0.153646i	−0.361001	−	0.932565i	$-0.617565\pi$
$643$	6.74821	−	3.89608i	0.266123	−	0.153646i	0.627125	+	0.778919i	$0.284232\pi$
$644$	53.8247	−	24.0241i	2.12099	−	0.946684i
$645$		0			0
$646$	1.69666	+	1.10071i	0.0667543	+	0.0433067i
$647$	22.2643			0.875301			0.437651	−	0.899145i	$-0.355811\pi$
$647$	22.2643			0.875301			0.437651	+	0.899145i	$0.355811\pi$
$648$	19.0022	−	16.9386i	0.746476	−	0.665412i
$649$	2.13218			0.0836952
$650$		0			0
$651$	66.3476	+	11.5097i	2.60037	+	0.451099i
$652$	18.2903	−	8.16369i	0.716302	−	0.319715i
$653$	−16.2273	+	9.36884i	−0.635024	+	0.366631i	−0.782695	−	0.622405i	$-0.786156\pi$
$653$	−16.2273	+	9.36884i	−0.635024	+	0.366631i	0.147671	+	0.989036i	$0.452822\pi$
$654$	−2.90592	−	2.69232i	−0.113631	−	0.105278i
$655$		0			0
$656$	3.47231	−	16.4862i	0.135571	−	0.643680i
$657$	3.35313	+	1.19946i	0.130818	+	0.0467955i
$658$	22.8279	+	1.18574i	0.889924	+	0.0462251i
$659$	7.33504	−	12.7047i	0.285733	−	0.494903i	−0.687054	−	0.726606i	$-0.741096\pi$
$659$	7.33504	−	12.7047i	0.285733	−	0.494903i	0.972787	+	0.231703i	$0.0744297\pi$
$660$		0			0
$661$	14.6723	+	25.4132i	0.570688	+	0.988460i	0.996495	+	0.0836467i	$0.0266567\pi$
$661$	14.6723	+	25.4132i	0.570688	+	0.988460i	−0.425808	+	0.904814i	$0.640010\pi$
$662$	18.8840	+	37.0195i	0.733947	+	1.43880i
$663$	22.5637	−	8.28329i	0.876301	−	0.321696i
$664$	−16.0772	−	12.9820i	−0.623915	−	0.503801i
$665$		0			0
$666$	−14.4927	−	18.9943i	−0.561580	−	0.736014i
$667$		−	39.6789i		−	1.53637i
$668$	−5.87629	+	8.10381i	−0.227360	+	0.313546i
$669$	11.4411	+	9.54636i	0.442337	+	0.369084i
$670$		0			0
$671$	−6.37220	−	11.0370i	−0.245996	−	0.426078i
$672$	−36.5375	−	16.8120i	−1.40946	−	0.648537i
$673$	9.19792	−	15.9313i	0.354554	−	0.614105i	−0.632488	−	0.774570i	$-0.717966\pi$
$673$	9.19792	−	15.9313i	0.354554	−	0.614105i	0.987041	+	0.160465i	$0.0512995\pi$
$674$	2.15241	−	41.4381i	0.0829078	−	1.59614i
$675$		0			0
$676$	13.6356	+	1.42037i	0.524445	+	0.0546296i
$677$	−6.26044	−	3.61447i	−0.240608	−	0.138915i	0.374848	−	0.927086i	$-0.377695\pi$
$677$	−6.26044	−	3.61447i	−0.240608	−	0.138915i	−0.615456	+	0.788171i	$0.711028\pi$
$678$	−6.79445	−	1.54552i	−0.260939	−	0.0593552i
$679$	−3.06489	+	1.76952i	−0.117620	+	0.0679078i
$680$		0			0
$681$	26.2425	−	31.4509i	1.00561	−	1.20520i
$682$	18.7729	−	28.9372i	0.718853	−	1.10806i
$683$	−13.1661			−0.503787			−0.251894	−	0.967755i	$-0.581053\pi$
$683$	−13.1661			−0.503787			−0.251894	+	0.967755i	$0.581053\pi$
$684$	−1.52832	+	0.116800i	−0.0584368	+	0.00446596i
$685$		0			0
$686$	9.00556	−	13.8814i	0.343834	−	0.529995i
$687$	4.65766	+	12.6875i	0.177701	+	0.484057i
$688$	−11.1986	+	3.66164i	−0.426944	+	0.139599i
$689$	−10.3147	+	5.95520i	−0.392959	+	0.226875i
$690$		0			0
$691$	−32.6878	−	18.8723i	−1.24350	−	0.717937i	−0.273698	−	0.961816i	$-0.588247\pi$
$691$	−32.6878	−	18.8723i	−1.24350	−	0.717937i	−0.969806	+	0.243879i	$0.921580\pi$
$692$	−3.50436	+	33.6419i	−0.133216	+	1.27887i
$693$	31.2008	−	5.67978i	1.18522	−	0.215757i
$694$	2.07361	−	39.9210i	0.0787131	−	1.51538i
$695$		0			0
$696$	−20.3597	+	17.8476i	−0.771733	+	0.676512i
$697$	−11.7893	−	20.4196i	−0.446551	−	0.773449i
$698$	−0.797694	+	0.406912i	−0.0301932	+	0.0154018i
$699$	−7.69890	+	44.3805i	−0.291199	+	1.67862i
$700$		0			0
$701$		−	25.2568i		−	0.953934i	−0.878921	−	0.476967i	$-0.841736\pi$
$701$		−	25.2568i		−	0.953934i	0.878921	−	0.476967i	$-0.158264\pi$
$702$	−9.78722	+	15.3642i	−0.369395	+	0.579884i
$703$			1.43861i			0.0542580i
$704$	−15.2719	+	13.8280i	−0.575580	+	0.521162i
$705$		0			0
$706$	7.41603	+	14.5381i	0.279106	+	0.547149i
$707$	10.9819	+	19.0212i	0.413017	+	0.715366i
$708$	2.05576	−	1.99996i	0.0772602	−	0.0751630i
$709$	10.5916	−	18.3453i	0.397777	−	0.688970i	−0.595674	−	0.803226i	$-0.703115\pi$
$709$	10.5916	−	18.3453i	0.397777	−	0.688970i	0.993451	+	0.114256i	$0.0364483\pi$
$710$		0			0
$711$	8.69229	+	10.2434i	0.325986	+	0.384157i
$712$	17.6925	+	2.77698i	0.663053	+	0.104072i
$713$	58.8880	+	33.9990i	2.20537	+	1.27327i
$714$	−53.7743	+	16.6306i	−2.01245	+	0.622386i
$715$		0			0
$716$	−17.9476	−	40.2105i	−0.670732	−	1.50274i
$717$	−5.38183	−	14.6601i	−0.200988	−	0.547491i
$718$	7.59850	+	4.92952i	0.283573	+	0.183968i
$719$	45.3628			1.69175			0.845874	−	0.533382i	$-0.179079\pi$
$719$	45.3628			1.69175			0.845874	+	0.533382i	$0.179079\pi$
$720$		0			0
$721$	−70.6578			−2.63143
$722$	−22.4645	−	14.5738i	−0.836042	−	0.542381i
$723$	−2.99475	+	3.58913i	−0.111376	+	0.133481i
$724$	−16.8639	−	37.7826i	−0.626742	−	1.40418i
$725$		0			0
$726$	−2.37318	+	10.4330i	−0.0880769	+	0.387207i
$727$	8.40168	+	4.85072i	0.311601	+	0.179903i	0.647643	−	0.761944i	$-0.275755\pi$
$727$	8.40168	+	4.85072i	0.311601	+	0.179903i	−0.336042	+	0.941847i	$0.609088\pi$
$728$	28.4339	+	4.46295i	1.05383	+	0.165408i
$729$	13.8864	+	23.1553i	0.514310	+	0.857604i
$730$		0			0
$731$	−8.24445	+	14.2798i	−0.304932	+	0.528158i
$732$	−16.4964	−	4.66437i	−0.609724	−	0.172400i
$733$	−0.831511	−	1.44022i	−0.0307126	−	0.0531957i	0.850261	−	0.526362i	$-0.176444\pi$
$733$	−0.831511	−	1.44022i	−0.0307126	−	0.0531957i	−0.880973	+	0.473166i	$0.843111\pi$
$734$	−15.0197	−	29.4440i	−0.554385	−	1.08680i
$735$		0			0
$736$	−28.7847	−	28.6515i	−1.06102	−	1.05611i
$737$		−	22.3490i		−	0.823238i
$738$	16.4910	+	6.88355i	0.607041	+	0.253387i
$739$		−	6.13631i		−	0.225728i	−0.993610	−	0.112864i	$-0.963998\pi$
$739$		−	6.13631i		−	0.225728i	0.993610	−	0.112864i	$-0.0360024\pi$
$740$		0			0
$741$	1.02969	−	0.378008i	0.0378267	−	0.0138865i
$742$	24.8457	−	12.6740i	0.912113	−	0.465278i
$743$	−13.7603	−	23.8336i	−0.504817	−	0.874368i	−0.999984	−	0.00557094i	$-0.998227\pi$
$743$	−13.7603	−	23.8336i	−0.504817	−	0.874368i	0.495168	−	0.868797i	$-0.335107\pi$
$744$	−9.04260	−	45.5089i	−0.331518	−	1.66844i
$745$		0			0
$746$	−2.40307	+	46.2639i	−0.0879828	+	1.69384i
$747$	16.7117	−	14.1811i	0.611449	−	0.518860i
$748$	−2.98720	+	28.6772i	−0.109223	+	1.04854i
$749$	13.6259	+	7.86691i	0.497879	+	0.287451i
$750$		0			0
$751$	−6.61630	+	3.81992i	−0.241432	+	0.139391i	−0.615835	−	0.787875i	$-0.711181\pi$
$751$	−6.61630	+	3.81992i	−0.241432	+	0.139391i	0.374403	+	0.927266i	$0.377848\pi$
$752$	−4.89492	−	14.9705i	−0.178499	−	0.545917i
$753$	11.5361	+	2.00122i	0.420398	+	0.0729284i
$754$	10.5451	−	16.2545i	0.384028	−	0.591952i
$755$		0			0
$756$	24.7550	−	34.7422i	0.900332	−	1.26356i
$757$	−43.4071			−1.57766			−0.788830	−	0.614612i	$-0.789313\pi$
$757$	−43.4071			−1.57766			−0.788830	+	0.614612i	$0.789313\pi$
$758$	13.0216	−	20.0720i	0.472968	−	0.729046i
$759$	31.5529	+	5.47364i	1.14530	+	0.198680i
$760$		0			0
$761$	−19.9139	+	11.4973i	−0.721877	+	0.416776i	−0.815443	−	0.578837i	$-0.803507\pi$
$761$	−19.9139	+	11.4973i	−0.721877	+	0.416776i	0.0935660	+	0.995613i	$0.470173\pi$
$762$	−30.7823	+	33.2246i	−1.11513	+	1.20360i
$763$	−5.74925	−	3.31933i	−0.208137	−	0.120168i
$764$	16.4512	+	1.71367i	0.595185	+	0.0619984i
$765$		0			0
$766$	−1.21644	+	23.4188i	−0.0439516	+	0.846155i
$767$	−1.02623	+	1.77749i	−0.0370551	+	0.0641813i
$768$	−1.75404	+	27.6572i	−0.0632934	+	0.997995i
$769$	0.0536762	+	0.0929699i	0.00193561	+	0.00335258i	0.866992	−	0.498323i	$-0.166051\pi$
$769$	0.0536762	+	0.0929699i	0.00193561	+	0.00335258i	−0.865056	+	0.501675i	$0.832717\pi$
$770$		0			0
$771$	−1.84652	+	0.677872i	−0.0665008	+	0.0244129i
$772$	−22.1058	+	30.4854i	−0.795605	+	1.09720i
$773$		−	14.1125i		−	0.507591i	−0.967258	−	0.253795i	$-0.918321\pi$
$773$		−	14.1125i		−	0.507591i	0.967258	−	0.253795i	$-0.0816790\pi$
$774$	−1.59735	−	12.3943i	−0.0574155	−	0.445502i
$775$		0			0
$776$	1.89722	+	1.53197i	0.0681061	+	0.0549945i
$777$	−30.7424	−	25.6513i	−1.10288	−	0.920236i
$778$	0.687462	+	1.34767i	0.0246467	+	0.0483165i
$779$	−0.538003	−	0.931849i	−0.0192760	−	0.0333870i
$780$		0			0
$781$	11.3422	−	19.6452i	0.405855	−	0.702961i
$782$	−56.7619	−	2.94837i	−2.02980	−	0.105434i
$783$	−14.5647	−	24.7499i	−0.520498	−	0.884489i
$784$	−38.5554	−	8.12048i	−1.37698	−	0.290017i
$785$		0			0
$786$	−0.0920932	+	0.404863i	−0.00328485	+	0.0144410i
$787$	−23.0881	+	13.3299i	−0.823003	+	0.475161i	−0.851451	−	0.524434i	$-0.824277\pi$
$787$	−23.0881	+	13.3299i	−0.823003	+	0.475161i	0.0284481	+	0.999595i	$0.490943\pi$
$788$	−4.39048	+	1.95965i	−0.156404	+	0.0698095i
$789$	−3.09480	+	3.70903i	−0.110178	+	0.132045i
$790$		0			0
$791$	−11.6772			−0.415192
$792$	−11.3839	−	18.6522i	−0.404511	−	0.662777i
$793$	12.2680			0.435648
$794$	−31.6608	−	20.5399i	−1.12360	−	0.728934i
$795$		0			0
$796$	11.4780	−	5.12311i	0.406828	−	0.181584i
$797$	38.2121	−	22.0618i	1.35354	−	0.781467i	0.364798	−	0.931087i	$-0.381138\pi$
$797$	38.2121	−	22.0618i	1.35354	−	0.781467i	0.988744	+	0.149619i	$0.0478048\pi$
$798$	−2.45399	+	0.758938i	−0.0868702	+	0.0268661i
$799$	−19.0894	−	11.0213i	−0.675335	−	0.389905i
$800$		0			0
$801$	−6.39793	+	17.8855i	−0.226060	+	0.631955i
$802$	21.1409	+	1.09812i	0.746510	+	0.0387758i
$803$	1.52850	−	2.64744i	0.0539396	−	0.0934261i
$804$	−20.9632	−	21.5481i	−0.739313	−	0.759942i
$805$		0			0
$806$	15.0879	+	29.5777i	0.531448	+	1.04183i
$807$	−5.65526	+	32.5998i	−0.199074	+	1.14757i
$808$	9.50764	−	11.7744i	0.334478	−	0.414223i
$809$			41.3252i			1.45292i	0.687210	+	0.726459i	$0.258835\pi$
$809$			41.3252i			1.45292i	−0.687210	+	0.726459i	$0.741165\pi$
$810$		0			0
$811$		−	43.1397i		−	1.51484i	−0.652928	−	0.757420i	$-0.726460\pi$
$811$		−	43.1397i		−	1.51484i	0.652928	−	0.757420i	$-0.273540\pi$
$812$	−26.6355	+	36.7322i	−0.934722	+	1.28905i
$813$	−5.28342	+	30.4564i	−0.185297	+	1.06815i
$814$	−18.2695	+	9.31945i	−0.640346	+	0.326647i
$815$		0			0
$816$	24.0187	+	30.4514i	0.840824	+	1.06601i
$817$	−0.376235	+	0.651658i	−0.0131628	+	0.0227986i
$818$	−1.95213	+	37.5823i	−0.0682546	+	1.31404i
$819$	−10.2822	+	28.7443i	−0.359291	+	1.00441i
$820$		0			0
$821$	−23.1584	−	13.3705i	−0.808235	−	0.466635i	0.0381077	−	0.999274i	$-0.487867\pi$
$821$	−23.1584	−	13.3705i	−0.808235	−	0.466635i	−0.846342	+	0.532639i	$0.821200\pi$
$822$	−11.6782	−	37.7608i	−0.407323	−	1.31706i
$823$	−26.8773	+	15.5176i	−0.936883	+	0.540910i	−0.888982	−	0.457942i	$-0.848587\pi$
$823$	−26.8773	+	15.5176i	−0.936883	+	0.540910i	−0.0479012	+	0.998852i	$0.515253\pi$
$824$	17.5106	+	45.4277i	0.610011	+	1.58255i
$825$		0			0
$826$	2.61590	−	4.03222i	0.0910187	−	0.140299i
$827$	25.6255			0.891086			0.445543	−	0.895260i	$-0.353011\pi$
$827$	25.6255			0.891086			0.445543	+	0.895260i	$0.353011\pi$
$828$	35.5563	−	24.3188i	1.23567	−	0.845136i
$829$	4.43247			0.153946			0.0769731	−	0.997033i	$-0.475474\pi$
$829$	4.43247			0.153946			0.0769731	+	0.997033i	$0.475474\pi$
$830$		0			0
$831$	−32.9727	+	39.5169i	−1.14381	+	1.37083i
$832$	−4.17723	−	19.3869i	−0.144819	−	0.672120i
$833$	−47.7541	+	27.5709i	−1.65458	+	0.955274i
$834$	38.2995	+	8.71189i	1.32620	+	0.301668i
$835$		0			0
$836$	−0.136321	+	1.30868i	−0.00471476	+	0.0452617i
$837$	49.2114	−	0.408570i	1.70100	−	0.0141222i
$838$	−0.175849	+	3.38545i	−0.00607462	+	0.116948i
$839$	18.3303	−	31.7491i	0.632833	−	1.09610i	−0.354136	−	0.935194i	$-0.615225\pi$
$839$	18.3303	−	31.7491i	0.632833	−	1.09610i	0.986970	−	0.160906i	$-0.0514415\pi$
$840$		0			0
$841$	0.771977	+	1.33710i	0.0266199	+	0.0461070i
$842$	−29.6635	+	15.1316i	−1.02227	+	0.521471i
$843$	−25.8039	−	21.5307i	−0.888734	−	0.741555i
$844$	1.20695	+	0.875191i	0.0415449	+	0.0301253i
$845$		0			0
$846$	16.5688	−	2.13535i	0.569647	−	0.0734150i
$847$			17.9306i			0.616102i
$848$	−14.3058	−	12.8330i	−0.491262	−	0.440687i
$849$	−26.1015	+	9.58206i	−0.895802	+	0.328856i
$850$		0			0
$851$	−20.2153	−	35.0140i	−0.692973	−	1.20026i
$852$	−7.49131	−	29.5800i	−0.256648	−	1.01339i
$853$	−16.1002	+	27.8863i	−0.551259	+	0.954809i	0.446925	+	0.894572i	$0.352519\pi$
$853$	−16.1002	+	27.8863i	−0.551259	+	0.954809i	−0.998184	+	0.0602377i	$0.980814\pi$
$854$	−28.6902	−	1.49025i	−0.981758	−	0.0509952i
$855$		0			0
$856$	1.68103	−	10.7100i	0.0574564	−	0.366061i
$857$	−29.4312	−	16.9921i	−1.00535	−	0.580439i	−0.0955233	−	0.995427i	$-0.530452\pi$
$857$	−29.4312	−	16.9921i	−1.00535	−	0.580439i	−0.909827	+	0.414988i	$0.863786\pi$
$858$	11.4710	+	10.6278i	0.391612	+	0.362826i
$859$	−38.2428	+	22.0795i	−1.30483	+	0.753343i	−0.981228	−	0.192852i	$-0.938226\pi$
$859$	−38.2428	+	22.0795i	−1.30483	+	0.753343i	−0.323600	+	0.946194i	$0.604893\pi$
$860$		0			0
$861$	29.5062	+	5.11859i	1.00557	+	0.174441i
$862$	17.9517	+	11.6461i	0.611436	+	0.396668i
$863$	−16.7821			−0.571269			−0.285635	−	0.958339i	$-0.592204\pi$
$863$	−16.7821			−0.571269			−0.285635	+	0.958339i	$0.592204\pi$
$864$	−28.4715	−	7.30572i	−0.968620	−	0.248546i
$865$		0			0
$866$	3.23118	+	2.09622i	0.109800	+	0.0712326i
$867$	24.4674	+	4.24447i	0.830955	+	0.144150i
$868$	−31.6920	−	71.0042i	−1.07570	−	2.41004i
$869$	9.98728	−	5.76616i	0.338795	−	0.195603i
$870$		0			0
$871$	18.6313	+	10.7568i	0.631296	+	0.364479i
$872$	−0.709287	+	4.51894i	−0.0240195	+	0.153031i
$873$	−1.97209	+	1.67347i	−0.0667453	+	0.0566384i
$874$	−2.59033	−	0.134549i	−0.0876192	−	0.00455118i
$875$		0			0
$876$	−1.00955	−	3.98627i	−0.0341095	−	0.134684i
$877$	−1.45455	−	2.51935i	−0.0491165	−	0.0850723i	0.840422	−	0.541933i	$-0.182307\pi$
$877$	−1.45455	−	2.51935i	−0.0491165	−	0.0850723i	−0.889538	+	0.456860i	$0.848974\pi$
$878$	−0.737613	−	1.44599i	−0.0248932	−	0.0487998i
$879$	27.1901	−	9.98167i	0.917098	−	0.336673i
$880$		0			0
$881$			36.0641i			1.21503i	0.794308	+	0.607516i	$0.207834\pi$
$881$			36.0641i			1.21503i	−0.794308	+	0.607516i	$0.792166\pi$
$882$	16.0981	−	38.5664i	0.542052	−	1.29860i
$883$			7.15659i			0.240838i	0.992723	+	0.120419i	$0.0384239\pi$
$883$			7.15659i			0.240838i	−0.992723	+	0.120419i	$0.961576\pi$
$884$	−22.4690	−	16.2928i	−0.755713	−	0.547987i
$885$		0			0
$886$	−13.7363	+	7.00704i	−0.461481	+	0.235406i
$887$	−4.77918	−	8.27778i	−0.160469	−	0.277941i	0.774568	−	0.632491i	$-0.217967\pi$
$887$	−4.77918	−	8.27778i	−0.160469	−	0.277941i	−0.935037	+	0.354550i	$0.884634\pi$
$888$	−8.87320	+	26.1220i	−0.297765	+	0.876598i
$889$	−37.9513	+	65.7335i	−1.27284	+	2.20463i
$890$		0			0
$891$	21.6904	−	8.16769i	0.726657	−	0.273628i
$892$	1.78263	−	17.1133i	0.0596868	−	0.572994i
$893$	−0.871145	−	0.502956i	−0.0291518	−	0.0168308i
$894$	−7.10275	−	1.61564i	−0.237551	−	0.0540352i
$895$		0			0
$896$	7.41397	+	45.8462i	0.247683	+	1.53161i
$897$	−19.7497	+	23.6695i	−0.659425	+	0.790303i
$898$	−16.5558	+	25.5195i	−0.552473	+	0.851598i
$899$	−52.3434			−1.74575
$900$		0			0
$901$	−26.8958			−0.896027
$902$	8.34873	−	12.8690i	0.277982	−	0.428490i
$903$	−7.21715	−	19.6595i	−0.240172	−	0.654227i
$904$	2.89387	+	7.50754i	0.0962485	+	0.249697i
$905$		0			0
$906$	15.3389	+	49.5977i	0.509602	+	1.64777i
$907$	−24.9886	−	14.4272i	−0.829732	−	0.479046i	0.0240286	−	0.999711i	$-0.492351\pi$
$907$	−24.9886	−	14.4272i	−0.829732	−	0.479046i	−0.853761	+	0.520665i	$0.825684\pi$
$908$	−47.0435	−	4.90036i	−1.56119	−	0.162624i
$909$	10.3858	+	12.2391i	0.344476	+	0.405946i
$910$		0			0
$911$	20.0369	−	34.7049i	0.663851	−	1.14982i	−0.315744	−	0.948844i	$-0.602254\pi$
$911$	20.0369	−	34.7049i	0.663851	−	1.14982i	0.979595	−	0.200980i	$-0.0644126\pi$
$912$	1.09609	+	1.38965i	0.0362953	+	0.0460158i
$913$	−9.40726	−	16.2939i	−0.311335	−	0.539248i
$914$	−22.8019	+	11.6315i	−0.754219	+	0.384734i
$915$		0			0
$916$	9.16139	−	12.6342i	0.302701	−	0.417446i
$917$			0.695811i			0.0229777i
$918$	−36.4878	+	18.9961i	−1.20428	+	0.626966i
$919$		−	19.1701i		−	0.632363i	−0.948699	−	0.316181i	$-0.897599\pi$
$919$		−	19.1701i		−	0.632363i	0.948699	−	0.316181i	$-0.102401\pi$
$920$		0			0
$921$	−1.43194	+	8.25447i	−0.0471842	+	0.271994i
$922$	−9.16430	−	17.9653i	−0.301810	−	0.591657i
$923$	10.9181	+	18.9108i	0.359375	+	0.622456i
$924$	−25.5353	−	26.2478i	−0.840050	−	0.863490i
$925$		0			0
$926$	−16.3958	−	0.851641i	−0.538798	−	0.0279867i
$927$	−50.8040	+	9.24834i	−1.66862	+	0.303755i
$928$	30.2169	+	8.02154i	0.991918	+	0.263320i
$929$	−22.6152	−	13.0569i	−0.741980	−	0.428382i	0.0808090	−	0.996730i	$-0.474250\pi$
$929$	−22.6152	−	13.0569i	−0.741980	−	0.428382i	−0.822789	+	0.568347i	$0.807583\pi$
$930$		0			0
$931$	−2.17926	+	1.25820i	−0.0714223	+	0.0412357i
$932$	47.4953	−	21.1991i	1.55576	−	0.694399i
$933$	−4.73626	−	12.9016i	−0.155058	−	0.422378i
$934$	43.6122	+	28.2933i	1.42703	+	0.925787i
$935$		0			0
$936$	21.0286	−	0.512764i	0.687340	−	0.0167602i
$937$	10.2504			0.334865			0.167432	−	0.985884i	$-0.446452\pi$
$937$	10.2504			0.334865			0.167432	+	0.985884i	$0.446452\pi$
$938$	−42.2649	−	27.4193i	−1.38000	−	0.895272i
$939$	−35.8581	+	42.9750i	−1.17019	+	1.40244i
$940$		0			0
$941$	30.8506	−	17.8116i	1.00570	−	0.580642i	0.0957716	−	0.995403i	$-0.469468\pi$
$941$	30.8506	−	17.8116i	1.00570	−	0.580642i	0.909930	+	0.414761i	$0.136135\pi$
$942$	−1.75724	+	7.72524i	−0.0572540	+	0.251702i
$943$	26.1887	+	15.1201i	0.852823	+	0.492377i
$944$	−3.24069	−	0.682550i	−0.105476	−	0.0222151i
$945$		0			0
$946$	−10.7130	−	0.556463i	−0.348310	−	0.0180922i
$947$	26.6819	−	46.2144i	0.867045	−	1.50177i	0.00204212	−	0.999998i	$-0.499350\pi$
$947$	26.6819	−	46.2144i	0.867045	−	1.50177i	0.865003	−	0.501767i	$-0.167317\pi$
$948$	4.22075	−	14.9275i	0.137084	−	0.484821i
$949$	1.47136	+	2.54847i	0.0477623	+	0.0827267i
$950$		0			0
$951$	0.0478827	+	0.0399531i	0.00155270	+	0.00129557i
$952$	50.5674	+	40.8323i	1.63890	+	1.32338i
$953$			16.5663i			0.536636i	0.963330	+	0.268318i	$0.0864677\pi$
$953$			16.5663i			0.536636i	−0.963330	+	0.268318i	$0.913532\pi$
$954$	16.2055	−	12.3648i	0.524673	−	0.400326i
$955$		0			0
$956$	−10.5858	+	14.5985i	−0.342369	+	0.472151i
$957$	−23.1414	+	8.49538i	−0.748055	+	0.274617i
$958$	44.5410	−	22.7208i	1.43906	−	0.734076i
$959$	−33.1188	−	57.3634i	−1.06946	−	1.85236i
$960$		0			0
$961$	29.3506	−	50.8367i	0.946794	−	1.63989i
$962$	1.02410	−	19.7159i	0.0330182	−	0.635666i
$963$	10.8269	+	3.87294i	0.348892	+	0.124804i
$964$	5.36852	+	0.559221i	0.172909	+	0.0180113i
$965$		0			0
$966$	49.0626	−	52.9552i	1.57856	−	1.70380i
$967$	−30.5116	+	17.6159i	−0.981188	+	0.566489i	−0.902629	−	0.430420i	$-0.858365\pi$
$967$	−30.5116	+	17.6159i	−0.981188	+	0.566489i	−0.0785596	+	0.996909i	$0.525032\pi$
$968$	11.5280	−	4.44360i	0.370524	−	0.142823i
$969$	2.44051	+	0.423367i	0.0784004	+	0.0136005i
$970$		0			0
$971$	24.1348			0.774524			0.387262	−	0.921970i	$-0.373421\pi$
$971$	24.1348			0.774524			0.387262	+	0.921970i	$0.373421\pi$
$972$	13.2519	−	28.2203i	0.425054	−	0.905168i
$973$	65.8228			2.11018
$974$	−13.2527	+	20.4282i	−0.424645	+	0.654560i
$975$		0			0
$976$	6.15196	+	18.8150i	0.196919	+	0.602252i
$977$	−12.6750	+	7.31791i	−0.405509	+	0.234121i	−0.688858	−	0.724896i	$-0.741888\pi$
$977$	−12.6750	+	7.31791i	−0.405509	+	0.234121i	0.283349	+	0.959017i	$0.408554\pi$
$978$	16.6720	−	17.9948i	0.533113	−	0.575410i
$979$	14.1214	+	8.15300i	0.451322	+	0.260571i
$980$		0			0
$981$	−4.56826	−	1.63414i	−0.145853	−	0.0521739i
$982$	0.657893	−	12.6657i	0.0209942	−	0.404180i
$983$	17.6027	−	30.4887i	0.561438	−	0.972439i	−0.435933	−	0.899979i	$-0.643582\pi$
$983$	17.6027	−	30.4887i	0.561438	−	0.972439i	0.997371	−	0.0724603i	$-0.0230851\pi$
$984$	−4.02144	−	20.2388i	−0.128199	−	0.645189i
$985$		0			0
$986$	38.9750	−	19.8815i	1.24122	−	0.633157i
$987$	26.2811	−	9.64797i	0.836536	−	0.307098i
$988$	−1.02537	−	0.743523i	−0.0326214	−	0.0236546i
$989$		−	21.1475i		−	0.672450i
$990$		0			0
$991$			33.0695i			1.05049i	0.850952	+	0.525243i	$0.176026\pi$
$991$			33.0695i			1.05049i	−0.850952	+	0.525243i	$0.823974\pi$
$992$	−37.7963	+	37.9720i	−1.20004	+	1.20561i
$993$	39.0802	+	32.6084i	1.24017	+	1.03479i
$994$	−23.2363	−	45.5516i	−0.737011	−	1.44481i
$995$		0			0
$996$	−24.3536	−	6.88599i	−0.771672	−	0.218191i
$997$	25.1550	−	43.5697i	0.796666	−	1.37987i	−0.125111	−	0.992143i	$-0.539929\pi$
$997$	25.1550	−	43.5697i	0.796666	−	1.37987i	0.921776	−	0.387722i	$-0.126738\pi$
$998$	29.1842	+	1.51591i	0.923809	+	0.0479852i
$999$	−25.4617	−	14.4198i	−0.805574	−	0.456223i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.r.f.551.5		48
4.3	odd	2	inner	900.2.r.f.551.4		48
5.2	odd	4		900.2.o.b.299.17		48
5.3	odd	4		900.2.o.c.299.8		48
5.4	even	2		180.2.q.a.11.20	✓	48
9.5	odd	6	inner	900.2.r.f.851.4		48
15.14	odd	2		540.2.q.a.251.5		48
20.3	even	4		900.2.o.c.299.9		48
20.7	even	4		900.2.o.b.299.16		48
20.19	odd	2		180.2.q.a.11.21	yes	48
36.23	even	6	inner	900.2.r.f.851.5		48
45.4	even	6		540.2.q.a.71.4		48
45.14	odd	6		180.2.q.a.131.21	yes	48
45.23	even	12		900.2.o.b.599.16		48
45.29	odd	6		1620.2.e.b.971.24		48
45.32	even	12		900.2.o.c.599.9		48
45.34	even	6		1620.2.e.b.971.25		48
60.59	even	2		540.2.q.a.251.4		48
180.23	odd	12		900.2.o.b.599.17		48
180.59	even	6		180.2.q.a.131.20	yes	48
180.79	odd	6		1620.2.e.b.971.23		48
180.119	even	6		1620.2.e.b.971.26		48
180.139	odd	6		540.2.q.a.71.5		48
180.167	odd	12		900.2.o.c.599.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.q.a.11.20	✓	48	5.4	even	2
180.2.q.a.11.21	yes	48	20.19	odd	2
180.2.q.a.131.20	yes	48	180.59	even	6
180.2.q.a.131.21	yes	48	45.14	odd	6
540.2.q.a.71.4		48	45.4	even	6
540.2.q.a.71.5		48	180.139	odd	6
540.2.q.a.251.4		48	60.59	even	2
540.2.q.a.251.5		48	15.14	odd	2
900.2.o.b.299.16		48	20.7	even	4
900.2.o.b.299.17		48	5.2	odd	4
900.2.o.b.599.16		48	45.23	even	12
900.2.o.b.599.17		48	180.23	odd	12
900.2.o.c.299.8		48	5.3	odd	4
900.2.o.c.299.9		48	20.3	even	4
900.2.o.c.599.8		48	180.167	odd	12
900.2.o.c.599.9		48	45.32	even	12
900.2.r.f.551.4		48	4.3	odd	2	inner
900.2.r.f.551.5		48	1.1	even	1	trivial
900.2.r.f.851.4		48	9.5	odd	6	inner
900.2.r.f.851.5		48	36.23	even	6	inner
1620.2.e.b.971.23		48	180.79	odd	6
1620.2.e.b.971.24		48	45.29	odd	6
1620.2.e.b.971.25		48	45.34	even	6
1620.2.e.b.971.26		48	180.119	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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18642 - 0.769686i) q^{2} +(-1.70656 - 0.296046i) q^{3} +(0.815168 + 1.82634i) q^{4} +(1.79683 + 1.66475i) q^{6} +(3.55496 + 2.05246i) q^{7} +(0.438576 - 2.79422i) q^{8} +(2.82471 + 1.01044i) q^{9} +(1.28763 - 2.23023i) q^{11} +(-0.850456 - 3.35808i) q^{12} +(1.23949 + 2.14686i) q^{13} +(-2.63792 - 5.17127i) q^{14} +(-2.67100 + 2.97754i) q^{16} +5.59797i q^{17} +(-2.57356 - 3.37295i) q^{18} +0.255463i q^{19} +(-5.45914 - 4.55508i) q^{21} +(-3.24424 + 1.65492i) q^{22} +(-3.58977 - 6.21767i) q^{23} +(-1.57567 + 4.63867i) q^{24} +(0.181856 - 3.50108i) q^{26} +(-4.52141 - 2.56063i) q^{27} +(-0.850587 + 8.16565i) q^{28} +(4.78623 + 2.76333i) q^{29} +(-8.20219 + 4.73554i) q^{31} +(5.46069 - 1.47677i) q^{32} +(-2.85767 + 3.42484i) q^{33} +(4.30867 - 6.64152i) q^{34} +(0.457209 + 5.98255i) q^{36} +5.63137 q^{37} +(0.196626 - 0.303085i) q^{38} +(-1.47970 - 4.03069i) q^{39} +(-3.64769 + 2.10599i) q^{41} +(2.97084 + 9.60604i) q^{42} +(2.55089 + 1.47276i) q^{43} +(5.12279 + 0.533623i) q^{44} +(-0.526686 + 10.1397i) q^{46} +(-1.96880 + 3.41006i) q^{47} +(5.43972 - 4.29062i) q^{48} +(4.92516 + 8.53062i) q^{49} +(1.65725 - 9.55328i) q^{51} +(-2.91049 + 4.01377i) q^{52} +4.80456i q^{53} +(3.39340 + 6.51804i) q^{54} +(7.29413 - 9.03317i) q^{56} +(0.0756288 - 0.435964i) q^{57} +(-3.55156 - 6.96235i) q^{58} +(0.413974 + 0.717024i) q^{59} +(2.47440 - 4.28578i) q^{61} +(13.3761 + 0.694791i) q^{62} +(7.96785 + 9.38968i) q^{63} +(-7.61530 - 2.45096i) q^{64} +(6.02643 - 1.86378i) q^{66} +(7.51571 - 4.33919i) q^{67} +(-10.2238 + 4.56328i) q^{68} +(4.28546 + 11.6736i) q^{69} +8.80859 q^{71} +(4.06225 - 7.44971i) q^{72} +1.18707 q^{73} +(-6.68115 - 4.33438i) q^{74} +(-0.466561 + 0.208245i) q^{76} +(9.15492 - 5.28559i) q^{77} +(-1.34683 + 5.92098i) q^{78} +(3.87817 + 2.23906i) q^{79} +(6.95801 + 5.70842i) q^{81} +(5.94863 + 0.308988i) q^{82} +(3.65295 - 6.32709i) q^{83} +(3.86899 - 13.6834i) q^{84} +(-1.89286 - 3.71069i) q^{86} +(-7.34992 - 6.13274i) q^{87} +(-5.66704 - 4.57604i) q^{88} +6.33181i q^{89} +10.1760i q^{91} +(8.42928 - 11.6246i) q^{92} +(15.3995 - 5.65327i) q^{93} +(4.96050 - 2.53040i) q^{94} +(-9.75621 + 0.903582i) q^{96} +(-0.431073 + 0.746640i) q^{97} +(0.722612 - 13.9117i) q^{98} +(5.89070 - 4.99870i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{6} + 4 q^{9} + 22 q^{12} - 30 q^{14} + 16 q^{18} - 4 q^{21} - 28 q^{24} - 12 q^{29} + 44 q^{33} - 6 q^{34} + 42 q^{36} - 60 q^{38} - 60 q^{41} + 18 q^{42} - 12 q^{46} + 12 q^{48} + 24 q^{49}+ \cdots + 12 q^{97}+O(q^{100}) \) 48 * q + 6 * q^6 + 4 * q^9 + 22 * q^12 - 30 * q^14 + 16 * q^18 - 4 * q^21 - 28 * q^24 - 12 * q^29 + 44 * q^33 - 6 * q^34 + 42 * q^36 - 60 * q^38 - 60 * q^41 + 18 * q^42 - 12 * q^46 + 12 * q^48 + 24 * q^49 + 18 * q^52 - 32 * q^54 - 42 * q^56 + 12 * q^57 + 18 * q^58 - 48 * q^64 + 16 * q^66 - 48 * q^68 + 36 * q^69 - 60 * q^72 + 24 * q^73 + 84 * q^74 + 6 * q^76 - 48 * q^77 - 38 * q^78 + 36 * q^82 + 50 * q^84 - 54 * q^86 - 60 * q^92 + 32 * q^93 + 18 * q^94 - 18 * q^96 + 12 * q^97

Introduction

L-functions

Modular forms

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Database

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