LMFDB - Embedded newform 1089.2.e.k.727.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1089,2,Mod(364,1089)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1089, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1089.364");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1089 = 3^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1089.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.69570878012$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 3x^{14} + 5x^{12} + 15x^{10} + 45x^{8} + 60x^{6} + 80x^{4} + 192x^{2} + 256 $ x^16 + 3x^14 + 5x^12 + 15x^10 + 45x^8 + 60x^6 + 80x^4 + 192*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			727.2
Root			$-1.27069 - 0.620769i$ of defining polynomial
Character	$\chi$	$=$	1089.727
Dual form			1089.2.e.k.364.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17295 + 2.03160i) q^{2} +(0.949292 + 1.44874i) q^{3} +(-1.75160 - 3.03386i) q^{4} +(0.779999 + 1.35100i) q^{5} +(-4.05673 + 0.229291i) q^{6} +(-1.95114 + 3.37948i) q^{7} +3.52635 q^{8} +(-1.19769 + 2.75055i) q^{9} +O(q^{10})$	\(q+(-1.17295 + 2.03160i) q^{2} +(0.949292 + 1.44874i) q^{3} +(-1.75160 - 3.03386i) q^{4} +(0.779999 + 1.35100i) q^{5} +(-4.05673 + 0.229291i) q^{6} +(-1.95114 + 3.37948i) q^{7} +3.52635 q^{8} +(-1.19769 + 2.75055i) q^{9} -3.65958 q^{10} +(2.73250 - 5.41764i) q^{12} +(2.71943 + 4.71018i) q^{13} +(-4.57717 - 7.92789i) q^{14} +(-1.21680 + 2.41251i) q^{15} +(-0.633017 + 1.09642i) q^{16} -4.32064 q^{17} +(-4.18320 - 5.65948i) q^{18} +1.61865 q^{19} +(2.73250 - 4.73282i) q^{20} +(-6.74818 + 0.381415i) q^{21} +(3.94929 + 6.84037i) q^{23} +(3.34754 + 5.10877i) q^{24} +(1.28320 - 2.22257i) q^{25} -12.7590 q^{26} +(-5.12179 + 0.875938i) q^{27} +13.6705 q^{28} +(0.742708 - 1.28641i) q^{29} +(-3.47401 - 5.30178i) q^{30} +(-0.729291 - 1.26317i) q^{31} +(2.04137 + 3.53575i) q^{32} +(5.06788 - 8.77782i) q^{34} -6.08755 q^{35} +(10.4427 - 1.18425i) q^{36} +9.31895 q^{37} +(-1.89858 + 3.28844i) q^{38} +(-4.24230 + 8.41108i) q^{39} +(2.75055 + 4.76410i) q^{40} +(-1.76318 - 3.05391i) q^{41} +(7.14037 - 14.1570i) q^{42} +(0.412180 - 0.713916i) q^{43} +(-4.65019 + 0.527352i) q^{45} -18.5292 q^{46} +(2.92698 - 5.06968i) q^{47} +(-2.18934 + 0.123744i) q^{48} +(-4.11391 - 7.12550i) q^{49} +(3.01026 + 5.21392i) q^{50} +(-4.10155 - 6.25948i) q^{51} +(9.52671 - 16.5007i) q^{52} -10.7404 q^{53} +(4.22802 - 11.4329i) q^{54} +(-6.88042 + 11.9172i) q^{56} +(1.53657 + 2.34500i) q^{57} +(1.74231 + 3.01777i) q^{58} +(2.69160 + 4.66200i) q^{59} +(9.45056 - 0.534156i) q^{60} +(6.65480 - 11.5265i) q^{61} +3.42167 q^{62} +(-6.95857 - 9.41428i) q^{63} -12.1097 q^{64} +(-4.24230 + 7.34788i) q^{65} +(-1.69769 - 2.94048i) q^{67} +(7.56805 + 13.1082i) q^{68} +(-6.16089 + 12.2150i) q^{69} +(7.14037 - 12.3675i) q^{70} -6.26216 q^{71} +(-4.22348 + 9.69942i) q^{72} -1.06706 q^{73} +(-10.9306 + 18.9324i) q^{74} +(4.43806 - 0.250844i) q^{75} +(-2.83522 - 4.91075i) q^{76} +(-12.1120 - 18.4844i) q^{78} +(4.95388 - 8.58037i) q^{79} -1.97501 q^{80} +(-6.13108 - 6.58862i) q^{81} +8.27244 q^{82} +(-2.37941 + 4.12126i) q^{83} +(12.9773 + 19.8050i) q^{84} +(-3.37010 - 5.83718i) q^{85} +(0.966929 + 1.67477i) q^{86} +(2.56872 - 0.145187i) q^{87} +3.47075 q^{89} +(4.38305 - 10.0659i) q^{90} -21.2239 q^{91} +(13.8352 - 23.9632i) q^{92} +(1.13769 - 2.25567i) q^{93} +(6.86638 + 11.8929i) q^{94} +(1.26254 + 2.18679i) q^{95} +(-3.18452 + 6.31386i) q^{96} +(-4.63396 + 8.02625i) q^{97} +19.3016 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{3} - 16 q^{4} + 4 q^{5} - 14 q^{9}+O(q^{10}) $ 16 * q - 2 * q^3 - 16 * q^4 + 4 * q^5 - 14 * q^9	$ 16 q - 2 q^{3} - 16 q^{4} + 4 q^{5} - 14 q^{9} - 6 q^{12} + 4 q^{14} - 52 q^{15} - 24 q^{16} - 6 q^{20} + 46 q^{23} - 12 q^{25} - 60 q^{26} - 32 q^{27} + 14 q^{31} + 38 q^{34} + 54 q^{36} - 12 q^{37} + 4 q^{38} - 4 q^{42} - 28 q^{45} + 16 q^{47} + 20 q^{48} - 42 q^{49} - 96 q^{53} + 46 q^{56} + 50 q^{58} + 48 q^{59} + 12 q^{60} - 12 q^{64} - 22 q^{67} - 10 q^{69} - 4 q^{70} + 68 q^{71} - 10 q^{75} - 72 q^{78} - 148 q^{80} - 14 q^{81} + 112 q^{82} + 14 q^{86} - 16 q^{89} - 96 q^{91} + 84 q^{92} + 30 q^{93} - 4 q^{97}+O(q^{100}) $ 16 * q - 2 * q^3 - 16 * q^4 + 4 * q^5 - 14 * q^9 - 6 * q^12 + 4 * q^14 - 52 * q^15 - 24 * q^16 - 6 * q^20 + 46 * q^23 - 12 * q^25 - 60 * q^26 - 32 * q^27 + 14 * q^31 + 38 * q^34 + 54 * q^36 - 12 * q^37 + 4 * q^38 - 4 * q^42 - 28 * q^45 + 16 * q^47 + 20 * q^48 - 42 * q^49 - 96 * q^53 + 46 * q^56 + 50 * q^58 + 48 * q^59 + 12 * q^60 - 12 * q^64 - 22 * q^67 - 10 * q^69 - 4 * q^70 + 68 * q^71 - 10 * q^75 - 72 * q^78 - 148 * q^80 - 14 * q^81 + 112 * q^82 + 14 * q^86 - 16 * q^89 - 96 * q^91 + 84 * q^92 + 30 * q^93 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times$.

$n$	$244$	$848$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.17295	+	2.03160i	−0.829398	+	1.43656i	0.0691136	+	0.997609i	$0.477983\pi$
$2$	−1.17295	+	2.03160i	−0.829398	+	1.43656i	−0.898511	+	0.438950i	$0.855350\pi$
$3$	0.949292	+	1.44874i	0.548074	+	0.836430i
$3$	0.949292	+	1.44874i	0.548074	+	0.836430i
$4$	−1.75160	−	3.03386i	−0.875801	−	1.51693i
$5$	0.779999	+	1.35100i	0.348826	+	0.604184i	0.986041	−	0.166501i	$-0.0532471\pi$
$5$	0.779999	+	1.35100i	0.348826	+	0.604184i	−0.637215	+	0.770686i	$0.719914\pi$
$6$	−4.05673	+	0.229291i	−1.65615	+	0.0936076i
$7$	−1.95114	+	3.37948i	−0.737462	+	1.27732i	0.216172	+	0.976355i	$0.430643\pi$
$7$	−1.95114	+	3.37948i	−0.737462	+	1.27732i	−0.953635	+	0.300967i	$0.902691\pi$
$8$	3.52635			1.24675
$9$	−1.19769	+	2.75055i	−0.399230	+	0.916851i
$10$	−3.65958			−1.15726
$11$		0			0
$11$		0			0
$12$	2.73250	−	5.41764i	0.788804	−	1.56394i
$13$	2.71943	+	4.71018i	0.754233	+	1.30637i	0.945755	+	0.324882i	$0.105324\pi$
$13$	2.71943	+	4.71018i	0.754233	+	1.30637i	−0.191522	+	0.981488i	$0.561342\pi$
$14$	−4.57717	−	7.92789i	−1.22330	−	2.11882i
$15$	−1.21680	+	2.41251i	−0.314175	+	0.622906i
$16$	−0.633017	+	1.09642i	−0.158254	+	0.274105i
$17$	−4.32064			−1.04791			−0.523955	−	0.851746i	$-0.675544\pi$
$17$	−4.32064			−1.04791			−0.523955	+	0.851746i	$0.675544\pi$
$18$	−4.18320	−	5.65948i	−0.985990	−	1.33395i
$19$	1.61865			0.371343			0.185671	−	0.982612i	$-0.440554\pi$
$19$	1.61865			0.371343			0.185671	+	0.982612i	$0.440554\pi$
$20$	2.73250	−	4.73282i	0.611005	−	1.05829i
$21$	−6.74818	+	0.381415i	−1.47257	+	0.0832316i
$22$		0			0
$23$	3.94929	+	6.84037i	0.823484	+	1.42632i	0.903072	+	0.429489i	$0.141306\pi$
$23$	3.94929	+	6.84037i	0.823484	+	1.42632i	−0.0795879	+	0.996828i	$0.525360\pi$
$24$	3.34754	+	5.10877i	0.683314	+	1.04282i
$25$	1.28320	−	2.22257i	0.256641	−	0.444515i
$26$	−12.7590			−2.50224
$27$	−5.12179	+	0.875938i	−0.985689	+	0.168574i
$28$	13.6705			2.58348
$29$	0.742708	−	1.28641i	0.137917	−	0.238880i	−0.788791	−	0.614662i	$-0.789292\pi$
$29$	0.742708	−	1.28641i	0.137917	−	0.238880i	0.926708	+	0.375782i	$0.122626\pi$
$30$	−3.47401	−	5.30178i	−0.634265	−	0.967969i
$31$	−0.729291	−	1.26317i	−0.130984	−	0.226872i	0.793072	−	0.609128i	$-0.208480\pi$
$31$	−0.729291	−	1.26317i	−0.130984	−	0.226872i	−0.924056	+	0.382256i	$0.875147\pi$
$32$	2.04137	+	3.53575i	0.360866	+	0.625038i
$33$		0			0
$34$	5.06788	−	8.77782i	0.869134	−	1.50538i
$35$	−6.08755			−1.02898
$36$	10.4427	−	1.18425i	1.74045	−	0.197375i
$37$	9.31895			1.53203			0.766013	−	0.642825i	$-0.222238\pi$
$37$	9.31895			1.53203			0.766013	+	0.642825i	$0.222238\pi$
$38$	−1.89858	+	3.28844i	−0.307991	+	0.533456i
$39$	−4.24230	+	8.41108i	−0.679311	+	1.34685i
$40$	2.75055	+	4.76410i	0.434901	+	0.753270i
$41$	−1.76318	−	3.05391i	−0.275362	−	0.476941i	0.694864	−	0.719141i	$-0.255464\pi$
$41$	−1.76318	−	3.05391i	−0.275362	−	0.476941i	−0.970226	+	0.242200i	$0.922131\pi$
$42$	7.14037	−	14.1570i	1.10178	−	2.18447i
$43$	0.412180	−	0.713916i	0.0628568	−	0.108871i	−0.832884	−	0.553447i	$-0.813312\pi$
$43$	0.412180	−	0.713916i	0.0628568	−	0.108871i	0.895741	+	0.444576i	$0.146646\pi$
$44$		0			0
$45$	−4.65019	+	0.527352i	−0.693209	+	0.0786130i
$46$	−18.5292			−2.73198
$47$	2.92698	−	5.06968i	0.426944	−	0.739489i	−0.569656	−	0.821883i	$-0.692923\pi$
$47$	2.92698	−	5.06968i	0.426944	−	0.739489i	0.996600	+	0.0823947i	$0.0262568\pi$
$48$	−2.18934	+	0.123744i	−0.316004	+	0.0178609i
$49$	−4.11391	−	7.12550i	−0.587702	−	1.01793i
$50$	3.01026	+	5.21392i	0.425714	+	0.737359i
$51$	−4.10155	−	6.25948i	−0.574332	−	0.876503i
$52$	9.52671	−	16.5007i	1.32112	−	2.28824i
$53$	−10.7404			−1.47530			−0.737652	−	0.675181i	$-0.764065\pi$
$53$	−10.7404			−1.47530			−0.737652	+	0.675181i	$0.764065\pi$
$54$	4.22802	−	11.4329i	0.575361	−	1.55582i
$55$		0			0
$56$	−6.88042	+	11.9172i	−0.919435	+	1.59251i
$57$	1.53657	+	2.34500i	0.203523	+	0.310602i
$58$	1.74231	+	3.01777i	0.228777	+	0.396253i
$59$	2.69160	+	4.66200i	0.350417	+	0.606940i	0.986323	−	0.164827i	$-0.0527065\pi$
$59$	2.69160	+	4.66200i	0.350417	+	0.606940i	−0.635905	+	0.771767i	$0.719373\pi$
$60$	9.45056	−	0.534156i	1.22006	−	0.0689593i
$61$	6.65480	−	11.5265i	0.852060	−	1.47581i	−0.0272853	−	0.999628i	$-0.508686\pi$
$61$	6.65480	−	11.5265i	0.852060	−	1.47581i	0.879346	−	0.476184i	$-0.157980\pi$
$62$	3.42167			0.434553
$63$	−6.95857	−	9.41428i	−0.876697	−	1.18609i
$64$	−12.1097			−1.51371
$65$	−4.24230	+	7.34788i	−0.526192	+	0.911392i
$66$		0			0
$67$	−1.69769	−	2.94048i	−0.207406	−	0.359237i	0.743491	−	0.668746i	$-0.233169\pi$
$67$	−1.69769	−	2.94048i	−0.207406	−	0.359237i	−0.950897	+	0.309509i	$0.899835\pi$
$68$	7.56805	+	13.1082i	0.917760	+	1.58961i
$69$	−6.16089	+	12.2150i	−0.741684	+	1.47051i
$70$	7.14037	−	12.3675i	0.853437	−	1.47820i
$71$	−6.26216			−0.743182			−0.371591	−	0.928397i	$-0.621188\pi$
$71$	−6.26216			−0.743182			−0.371591	+	0.928397i	$0.621188\pi$
$72$	−4.22348	+	9.69942i	−0.497742	+	1.14309i
$73$	−1.06706			−0.124890			−0.0624449	−	0.998048i	$-0.519890\pi$
$73$	−1.06706			−0.124890			−0.0624449	+	0.998048i	$0.519890\pi$
$74$	−10.9306	+	18.9324i	−1.27066	+	2.20085i
$75$	4.43806	−	0.250844i	0.512464	−	0.0289650i
$76$	−2.83522	−	4.91075i	−0.325223	−	0.563302i
$77$		0			0
$78$	−12.1120	−	18.4844i	−1.37141	−	2.09295i
$79$	4.95388	−	8.58037i	0.557355	−	0.965367i	−0.440361	−	0.897821i	$-0.645150\pi$
$79$	4.95388	−	8.58037i	0.557355	−	0.965367i	0.997716	−	0.0675465i	$-0.0215171\pi$
$80$	−1.97501			−0.220813
$81$	−6.13108	−	6.58862i	−0.681231	−	0.732068i
$82$	8.27244			0.913539
$83$	−2.37941	+	4.12126i	−0.261174	+	0.452367i	−0.966554	−	0.256462i	$-0.917443\pi$
$83$	−2.37941	+	4.12126i	−0.261174	+	0.452367i	0.705380	+	0.708829i	$0.250776\pi$
$84$	12.9773	+	19.8050i	1.41594	+	2.16090i
$85$	−3.37010	−	5.83718i	−0.365538	−	0.633131i
$86$	0.966929	+	1.67477i	0.104267	+	0.180595i
$87$	2.56872	−	0.145187i	0.275395	−	0.0155657i
$88$		0			0
$89$	3.47075			0.367899			0.183949	−	0.982936i	$-0.441112\pi$
$89$	3.47075			0.367899			0.183949	+	0.982936i	$0.441112\pi$
$90$	4.38305	−	10.0659i	0.462014	−	1.06104i
$91$	−21.2239			−2.22487
$92$	13.8352	−	23.9632i	1.44242	−	2.49834i
$93$	1.13769	−	2.25567i	0.117973	−	0.233902i
$94$	6.86638	+	11.8929i	0.708213	+	1.22666i
$95$	1.26254	+	2.18679i	0.129534	+	0.224360i
$96$	−3.18452	+	6.31386i	−0.325019	+	0.644406i
$97$	−4.63396	+	8.02625i	−0.470507	+	0.814943i	−0.999431	−	0.0337268i	$-0.989262\pi$
$97$	−4.63396	+	8.02625i	−0.470507	+	0.814943i	0.528924	+	0.848669i	$0.322596\pi$
$98$	19.3016			1.94975
$99$		0			0
$100$	−8.99065			−0.899065
$101$	1.76318	−	3.05391i	0.175443	−	0.303876i	−0.764872	−	0.644183i	$-0.777198\pi$
$101$	1.76318	−	3.05391i	0.175443	−	0.303876i	0.940314	+	0.340307i	$0.110531\pi$
$102$	17.5277	−	0.990683i	1.73550	−	0.0980923i
$103$	4.18179	+	7.24307i	0.412044	+	0.713681i	0.995113	−	0.0987416i	$-0.0314817\pi$
$103$	4.18179	+	7.24307i	0.412044	+	0.713681i	−0.583069	+	0.812422i	$0.698148\pi$
$104$	9.58966	+	16.6098i	0.940344	+	1.62872i
$105$	−5.77887	−	8.81928i	−0.563960	−	0.860673i
$106$	12.5979	−	21.8202i	1.22361	−	2.11936i
$107$	6.81480			0.658811			0.329406	−	0.944188i	$-0.393152\pi$
$107$	6.81480			0.658811			0.329406	+	0.944188i	$0.393152\pi$
$108$	11.6288	+	14.0045i	1.11898	+	1.34759i
$109$	16.3403			1.56512			0.782559	−	0.622576i	$-0.213914\pi$
$109$	16.3403			1.56512			0.782559	+	0.622576i	$0.213914\pi$
$110$		0			0
$111$	8.84641	+	13.5007i	0.839664	+	1.28143i
$112$	−2.47021	−	4.27854i	−0.233413	−	0.404284i
$113$	−1.07622	−	1.86408i	−0.101243	−	0.175357i	0.810954	−	0.585110i	$-0.198949\pi$
$113$	−1.07622	−	1.86408i	−0.101243	−	0.175357i	−0.912197	+	0.409752i	$0.865615\pi$
$114$	−6.56641	+	0.371141i	−0.615000	+	0.0347605i
$115$	−6.16089	+	10.6710i	−0.574506	+	0.995073i
$116$	−5.20372			−0.483153
$117$	−16.2126	+	1.83859i	−1.49886	+	0.169977i
$118$	−12.6284			−1.16254
$119$	8.43019	−	14.6015i	0.772794	−	1.33852i
$120$	−4.29086	+	8.50735i	−0.391700	+	0.776611i
$121$		0			0
$122$	15.6114	+	27.0398i	1.41339	+	2.44807i
$123$	2.75055	−	5.45344i	0.248009	−	0.491720i
$124$	−2.55486	+	4.42514i	−0.229433	+	0.397389i
$125$	11.8036			1.05574
$126$	27.2881	−	3.09459i	2.43102	−	0.275688i
$127$	0.250266			0.0222075			0.0111038	−	0.999938i	$-0.496465\pi$
$127$	0.250266			0.0222075			0.0111038	+	0.999938i	$0.496465\pi$
$128$	10.1213	−	17.5306i	0.894605	−	1.54950i
$129$	1.42556	−	0.0805741i	0.125513	−	0.00709415i
$130$	−9.95197	−	17.2373i	−0.872845	−	1.51181i
$131$	−5.24892	−	9.09140i	−0.458600	−	0.794319i	0.540287	−	0.841481i	$-0.318316\pi$
$131$	−5.24892	−	9.09140i	−0.458600	−	0.794319i	−0.998887	+	0.0471618i	$0.984982\pi$
$132$		0			0
$133$	−3.15821	+	5.47018i	−0.273851	+	0.474325i
$134$	7.96519			0.688088
$135$	−5.17838	−	6.23630i	−0.445684	−	0.536735i
$136$	−15.2361			−1.30649
$137$	−5.49018	+	9.50928i	−0.469058	+	0.812432i	−0.999374	−	0.0353676i	$-0.988740\pi$
$137$	−5.49018	+	9.50928i	−0.469058	+	0.812432i	0.530316	+	0.847800i	$0.322073\pi$
$138$	−17.5896	−	26.8440i	−1.49733	−	2.28511i
$139$	3.92786	+	6.80325i	0.333157	+	0.577044i	0.983129	−	0.182914i	$-0.0585528\pi$
$139$	3.92786	+	6.80325i	0.333157	+	0.577044i	−0.649972	+	0.759958i	$0.725220\pi$
$140$	10.6630	+	18.4688i	0.901186	+	1.56090i
$141$	10.1232	−	0.572175i	0.852527	−	0.0481858i
$142$	7.34517	−	12.7222i	0.616393	−	1.06762i
$143$		0			0
$144$	−2.25760	−	3.05432i	−0.188133	−	0.254526i
$145$	2.31725			0.192437
$146$	1.25160	−	2.16784i	0.103583	−	0.179412i
$147$	6.41769	−	12.7242i	0.529322	−	1.04947i
$148$	−16.3231	−	28.2724i	−1.34175	−	2.32398i
$149$	3.83385	+	6.64043i	0.314082	+	0.544005i	0.979242	−	0.202695i	$-0.0649701\pi$
$149$	3.83385	+	6.64043i	0.314082	+	0.544005i	−0.665160	+	0.746701i	$0.731637\pi$
$150$	−4.69599	+	9.31060i	−0.383426	+	0.760208i
$151$	0.175658	−	0.304248i	0.0142948	−	0.0247594i	−0.858790	−	0.512329i	$-0.828783\pi$
$151$	0.175658	−	0.304248i	0.0142948	−	0.0247594i	0.873084	+	0.487569i	$0.162116\pi$
$152$	5.70792			0.462974
$153$	5.17479	−	11.8842i	0.418357	−	0.960777i
$154$		0			0
$155$	1.13769	−	1.97054i	0.0913816	−	0.158278i
$156$	32.9489	−	1.86231i	2.63802	−	0.149104i
$157$	5.17711	+	8.96702i	0.413179	+	0.715646i	0.995235	−	0.0975018i	$-0.0310852\pi$
$157$	5.17711	+	8.96702i	0.413179	+	0.715646i	−0.582057	+	0.813148i	$0.697752\pi$
$158$	11.6213	+	20.1286i	0.924538	+	1.60135i
$159$	−10.1958	−	15.5600i	−0.808576	−	1.23399i
$160$	−3.18452	+	5.51576i	−0.251759	+	0.436059i
$161$	−30.8225			−2.42915
$162$	20.5769	−	4.72782i	1.61667	−	0.371453i
$163$	21.4071			1.67674			0.838368	−	0.545104i	$-0.183510\pi$
$163$	21.4071			1.67674			0.838368	+	0.545104i	$0.183510\pi$
$164$	−6.17677	+	10.6985i	−0.482325	+	0.835411i
$165$		0			0
$166$	−5.58184	−	9.66803i	−0.433235	−	0.750385i
$167$	7.24882	+	12.5553i	0.560930	+	0.971560i	0.997416	+	0.0718486i	$0.0228898\pi$
$167$	7.24882	+	12.5553i	0.560930	+	0.971560i	−0.436485	+	0.899711i	$0.643777\pi$
$168$	−23.7965	+	1.34500i	−1.83594	+	0.103769i
$169$	−8.29056	+	14.3597i	−0.637735	+	1.10459i
$170$	15.8118			1.21271
$171$	−1.93864	+	4.45217i	−0.148251	+	0.340466i
$172$	−2.88790			−0.220200
$173$	5.06968	−	8.78094i	0.385441	−	0.667603i	−0.606390	−	0.795168i	$-0.707383\pi$
$173$	5.06968	−	8.78094i	0.385441	−	0.667603i	0.991830	+	0.127565i	$0.0407162\pi$
$174$	−2.71800	+	5.38891i	−0.206051	+	0.408532i
$175$	5.00743	+	8.67312i	0.378526	+	0.655626i
$176$		0			0
$177$	−4.19890	+	8.32503i	−0.315608	+	0.625747i
$178$	−4.07100	+	7.05118i	−0.305134	+	0.528508i
$179$	−2.31066			−0.172707			−0.0863533	−	0.996265i	$-0.527521\pi$
$179$	−2.31066			−0.172707			−0.0863533	+	0.996265i	$0.527521\pi$
$180$	9.74519	+	13.1843i	0.726364	+	0.982701i
$181$	−7.72462			−0.574166			−0.287083	−	0.957906i	$-0.592686\pi$
$181$	−7.72462			−0.574166			−0.287083	+	0.957906i	$0.592686\pi$
$182$	24.8945	−	43.1186i	1.84531	−	3.19616i
$183$	23.0162	−	1.30090i	1.70141	−	0.0961653i
$184$	13.9266	+	24.1216i	1.02668	+	1.77827i
$185$	7.26877	+	12.5899i	0.534411	+	0.925626i
$186$	3.24817	+	4.95711i	0.238167	+	0.363473i
$187$		0			0
$188$	−20.5076			−1.49567
$189$	7.03313	−	19.0181i	0.511585	−	1.38336i
$190$	−5.92357			−0.429741
$191$	−9.67377	+	16.7555i	−0.699969	+	1.21238i	0.268508	+	0.963278i	$0.413470\pi$
$191$	−9.67377	+	16.7555i	−0.699969	+	1.21238i	−0.968477	+	0.249104i	$0.919864\pi$
$192$	−11.4957	−	17.5438i	−0.829627	−	1.26612i
$193$	−5.48564	−	9.50141i	−0.394865	−	0.683926i	0.598219	−	0.801333i	$-0.295875\pi$
$193$	−5.48564	−	9.50141i	−0.394865	−	0.683926i	−0.993084	+	0.117406i	$0.962542\pi$
$194$	−10.8708	−	18.8287i	−0.780475	−	1.35182i
$195$	−14.6723	+	0.829297i	−1.05071	+	0.0593872i
$196$	−14.4119	+	24.9621i	−1.02942	+	1.78301i
$197$	−20.7343			−1.47726			−0.738629	−	0.674112i	$-0.764527\pi$
$197$	−20.7343			−1.47726			−0.738629	+	0.674112i	$0.764527\pi$
$198$		0			0
$199$	−4.85396			−0.344088			−0.172044	−	0.985089i	$-0.555037\pi$
$199$	−4.85396			−0.344088			−0.172044	+	0.985089i	$0.555037\pi$
$200$	4.52503	−	7.83758i	0.319968	−	0.554201i
$201$	2.64839	−	5.25089i	0.186803	−	0.370369i
$202$	4.13622	+	7.16415i	0.291024	+	0.504068i
$203$	2.89826	+	5.01993i	0.203418	+	0.352330i
$204$	−11.8061	+	23.4077i	−0.826595	+	1.63886i
$205$	2.75055	−	4.76410i	0.192107	−	0.332739i
$206$	−19.6200			−1.36699
$207$	−23.5448	+	2.67009i	−1.63648	+	0.185584i
$208$	−6.88578			−0.477443
$209$		0			0
$210$	24.6955	−	1.39582i	1.70415	−	0.0963207i
$211$	−2.15989	−	3.74105i	−0.148693	−	0.257544i	0.782052	−	0.623214i	$-0.214173\pi$
$211$	−2.15989	−	3.74105i	−0.148693	−	0.257544i	−0.930745	+	0.365670i	$0.880840\pi$
$212$	18.8129	+	32.5848i	1.29207	+	2.23794i
$213$	−5.94462	−	9.07223i	−0.407318	−	0.621619i
$214$	−7.99339	+	13.8450i	−0.546417	+	0.946422i
$215$	1.28600			0.0877044
$216$	−18.0612	+	3.08887i	−1.22891	+	0.210171i
$217$	5.69180			0.386385
$218$	−19.1663	+	33.1970i	−1.29811	+	2.24838i
$219$	−1.01295	−	1.54589i	−0.0684489	−	0.104462i
$220$		0			0
$221$	−11.7497	−	20.3510i	−0.790368	−	1.36896i
$222$	−37.8045	+	2.13675i	−2.53727	+	0.143409i
$223$	−3.70877	+	6.42378i	−0.248358	+	0.430168i	−0.963070	−	0.269250i	$-0.913224\pi$
$223$	−3.70877	+	6.42378i	−0.248358	+	0.430168i	0.714712	+	0.699418i	$0.246558\pi$
$224$	−15.9320			−1.06450
$225$	4.57643	+	6.19147i	0.305095	+	0.412765i
$226$	5.04941			0.335882
$227$	−1.30996	+	2.26891i	−0.0869450	+	0.150593i	−0.906218	−	0.422810i	$-0.861044\pi$
$227$	−1.30996	+	2.26891i	−0.0869450	+	0.150593i	0.819273	+	0.573403i	$0.194377\pi$
$228$	4.42294	−	8.76924i	0.292917	−	0.580757i
$229$	−5.75481	−	9.96762i	−0.380288	−	0.658679i	0.610815	−	0.791773i	$-0.290842\pi$
$229$	−5.75481	−	9.96762i	−0.380288	−	0.658679i	−0.991103	+	0.133095i	$0.957509\pi$
$230$	−14.4528	−	25.0329i	−0.952987	−	1.65062i
$231$		0			0
$232$	2.61905	−	4.53633i	0.171949	−	0.297825i
$233$	−16.5445			−1.08387			−0.541934	−	0.840421i	$-0.682308\pi$
$233$	−16.5445			−1.08387			−0.541934	+	0.840421i	$0.682308\pi$
$234$	15.2813	−	35.0942i	0.998968	−	2.29418i
$235$	9.13216			0.595717
$236$	9.42924	−	16.3319i	0.613791	−	1.06312i
$237$	17.1334	−	0.968399i	1.11293	−	0.0629043i
$238$	19.7763	+	34.2535i	1.28191	+	2.22033i
$239$	2.57250	+	4.45570i	0.166401	+	0.288215i	0.937152	−	0.348921i	$-0.113452\pi$
$239$	2.57250	+	4.45570i	0.166401	+	0.288215i	−0.770751	+	0.637137i	$0.780119\pi$
$240$	−1.87486	−	2.86128i	−0.121022	−	0.184695i
$241$	−11.5165	+	19.9472i	−0.741843	+	1.28491i	0.209813	+	0.977742i	$0.432715\pi$
$241$	−11.5165	+	19.9472i	−0.741843	+	1.28491i	−0.951655	+	0.307167i	$0.900619\pi$
$242$		0			0
$243$	3.72500	−	15.1369i	0.238959	−	0.971030i
$244$	−46.6263			−2.98494
$245$	6.41769	−	11.1158i	0.410011	−	0.710160i
$246$	7.85297	+	11.9846i	0.500687	+	0.764111i
$247$	4.40179	+	7.62412i	0.280079	+	0.485111i
$248$	−2.57174	−	4.45438i	−0.163306	−	0.282853i
$249$	−8.22939	+	0.465134i	−0.521516	+	0.0294767i
$250$	−13.8450	+	23.9802i	−0.875632	+	1.51664i
$251$	7.91075			0.499322			0.249661	−	0.968333i	$-0.419681\pi$
$251$	7.91075			0.499322			0.249661	+	0.968333i	$0.419681\pi$
$252$	−16.3730	+	37.6014i	−1.03140	+	2.36867i
$253$		0			0
$254$	−0.293548	+	0.508441i	−0.0184189	+	0.0319024i
$255$	5.25734	−	10.4236i	0.329227	−	0.652749i
$256$	11.6338	+	20.1503i	0.727110	+	1.25939i
$257$	−5.21659	−	9.03541i	−0.325402	−	0.563613i	0.656191	−	0.754594i	$-0.272166\pi$
$257$	−5.21659	−	9.03541i	−0.325402	−	0.563613i	−0.981594	+	0.190981i	$0.938833\pi$
$258$	−1.50841	+	2.99067i	−0.0939093	+	0.186191i
$259$	−18.1826	+	31.4932i	−1.12981	+	1.95689i
$260$	29.7233			1.84336
$261$	2.64880	+	3.58358i	0.163957	+	0.221818i
$262$	24.6268			1.52145
$263$	−12.9795	+	22.4812i	−0.800351	+	1.38625i	0.119035	+	0.992890i	$0.462020\pi$
$263$	−12.9795	+	22.4812i	−0.800351	+	1.38625i	−0.919385	+	0.393358i	$0.871313\pi$
$264$		0			0
$265$	−8.37748	−	14.5102i	−0.514624	−	0.891356i
$266$	−7.40881	−	12.8324i	−0.454264	−	0.786808i
$267$	3.29476	+	5.02821i	0.201636	+	0.307722i
$268$	−5.94735	+	10.3011i	−0.363292	+	0.629241i
$269$	−19.9804			−1.21822			−0.609112	−	0.793084i	$-0.708474\pi$
$269$	−19.9804			−1.21822			−0.609112	+	0.793084i	$0.708474\pi$
$270$	18.7436	−	3.20557i	1.14070	−	0.195085i
$271$	−0.296230			−0.0179947			−0.00899734	−	0.999960i	$-0.502864\pi$
$271$	−0.296230			−0.0179947			−0.00899734	+	0.999960i	$0.502864\pi$
$272$	2.73504	−	4.73723i	0.165836	−	0.287237i
$273$	−20.1477	−	30.7480i	−1.21940	−	1.86095i
$274$	−12.8794	−	22.3077i	−0.778071	−	1.34766i
$275$		0			0
$276$	47.8501	−	2.70454i	2.88024	−	0.162794i
$277$	13.2896	−	23.0182i	0.798494	−	1.38303i	−0.122103	−	0.992517i	$-0.538964\pi$
$277$	13.2896	−	23.0182i	0.798494	−	1.38303i	0.920597	−	0.390514i	$-0.127703\pi$
$278$	−18.4287			−1.10528
$279$	4.34788	−	0.493069i	0.260301	−	0.0295193i
$280$	−21.4669			−1.28289
$281$	3.40362	−	5.89524i	0.203043	−	0.351680i	−0.746465	−	0.665425i	$-0.768250\pi$
$281$	3.40362	−	5.89524i	0.203043	−	0.351680i	0.949507	+	0.313745i	$0.101584\pi$
$282$	−10.7115	+	21.2374i	−0.637862	+	1.26467i
$283$	1.03790	+	1.79770i	0.0616967	+	0.106862i	0.895224	−	0.445617i	$-0.147016\pi$
$283$	1.03790	+	1.79770i	0.0616967	+	0.106862i	−0.833527	+	0.552478i	$0.813682\pi$
$284$	10.9688	+	18.9985i	0.650879	+	1.12736i
$285$	−1.96956	+	3.90499i	−0.116667	+	0.231312i
$286$		0			0
$287$	13.7608			0.812277
$288$	−12.1702	+	1.38015i	−0.717135	+	0.0813263i
$289$	1.66794			0.0981143
$290$	−2.71800	+	4.70772i	−0.159607	+	0.276447i
$291$	−16.0269	+	0.905860i	−0.939515	+	0.0531024i
$292$	1.86906	+	3.23731i	0.109379	+	0.189449i
$293$	−1.51851	−	2.63014i	−0.0887123	−	0.153654i	0.818255	−	0.574856i	$-0.194942\pi$
$293$	−1.51851	−	2.63014i	−0.0887123	−	0.153654i	−0.906967	+	0.421202i	$0.861609\pi$
$294$	18.3228	+	27.9629i	1.06861	+	1.63083i
$295$	−4.19890	+	7.27270i	−0.244469	+	0.423433i
$296$	32.8619			1.91006
$297$		0			0
$298$	−17.9876			−1.04199
$299$	−21.4796	+	37.2038i	−1.24220	+	2.15155i
$300$	−8.53475	−	13.0251i	−0.492754	−	0.752005i
$301$	1.60844	+	2.78590i	0.0927091	+	0.160577i
$302$	0.412074	+	0.713733i	0.0237122	+	0.0410707i
$303$	6.09809	−	0.344671i	0.350326	−	0.0198008i
$304$	−1.02463	+	1.77471i	−0.0587666	+	0.101787i
$305$	20.7630			1.18888
$306$	18.0741	+	24.4526i	1.03323	+	1.39786i
$307$	−17.9515			−1.02455			−0.512273	−	0.858823i	$-0.671196\pi$
$307$	−17.9515			−1.02455			−0.512273	+	0.858823i	$0.671196\pi$
$308$		0			0
$309$	−6.52358	+	12.9341i	−0.371113	+	0.735796i
$310$	2.66890	+	4.62267i	0.151583	+	0.262550i
$311$	13.1958	+	22.8557i	0.748262	+	1.29603i	0.948655	+	0.316313i	$0.102445\pi$
$311$	13.1958	+	22.8557i	0.748262	+	1.29603i	−0.200392	+	0.979716i	$0.564222\pi$
$312$	−14.9598	+	29.6604i	−0.846935	+	1.67919i
$313$	4.32409	−	7.48955i	0.244412	−	0.423334i	−0.717554	−	0.696503i	$-0.754738\pi$
$313$	4.32409	−	7.48955i	0.244412	−	0.423334i	0.961966	+	0.273168i	$0.0880716\pi$
$314$	−24.2899			−1.37076
$315$	7.29100	−	16.7441i	0.410801	−	0.943425i
$316$	−34.7089			−1.95253
$317$	3.89806	−	6.75163i	0.218937	−	0.379209i	−0.735546	−	0.677474i	$-0.763075\pi$
$317$	3.89806	−	6.75163i	0.218937	−	0.379209i	0.954483	+	0.298265i	$0.0964079\pi$
$318$	43.5708	−	2.46267i	2.44333	−	0.138100i
$319$		0			0
$320$	−9.44556	−	16.3602i	−0.528023	−	0.914562i
$321$	6.46923	+	9.87286i	0.361077	+	0.551050i
$322$	36.1531	−	62.6191i	2.01474	−	3.48962i
$323$	−6.99359			−0.389134
$324$	−9.24975	+	30.1415i	−0.513875	+	1.67453i
$325$	13.9583			0.774268
$326$	−25.1094	+	43.4908i	−1.39068	+	2.40873i
$327$	15.5117	+	23.6729i	0.857801	+	1.30911i
$328$	−6.21759	−	10.7692i	−0.343309	−	0.594629i
$329$	11.4219	+	19.7833i	0.629710	+	1.09069i
$330$		0			0
$331$	−3.90032	+	6.75555i	−0.214381	+	0.371319i	−0.953081	−	0.302716i	$-0.902107\pi$
$331$	−3.90032	+	6.75555i	−0.214381	+	0.371319i	0.738700	+	0.674034i	$0.235440\pi$
$332$	16.6711			0.914947
$333$	−11.1612	+	25.6323i	−0.611631	+	1.40464i
$334$	−34.0099			−1.86094
$335$	2.64839	−	4.58715i	0.144697	−	0.250623i
$336$	3.85353	−	7.64027i	0.210227	−	0.416811i
$337$	3.55988	+	6.16589i	0.193919	+	0.335877i	0.946546	−	0.322570i	$-0.104547\pi$
$337$	3.55988	+	6.16589i	0.193919	+	0.335877i	−0.752627	+	0.658447i	$0.771214\pi$
$338$	−19.4487	−	33.6862i	−1.05787	−	1.83229i
$339$	1.67891	−	3.32872i	0.0911858	−	0.180791i
$340$	−11.8061	+	20.4488i	−0.640278	+	1.10899i
$341$		0			0
$342$	−6.77112	−	9.16069i	−0.366140	−	0.495353i
$343$	4.79131			0.258706
$344$	1.45349	−	2.51752i	0.0783671	−	0.135736i
$345$	−21.3079	+	1.20435i	−1.14718	+	0.0648399i
$346$	11.8929	+	20.5991i	0.639367	+	1.10742i
$347$	−10.5041	−	18.1937i	−0.563891	−	0.976687i	−0.997152	−	0.0754190i	$-0.975971\pi$
$347$	−10.5041	−	18.1937i	−0.563891	−	0.976687i	0.433261	−	0.901268i	$-0.357363\pi$
$348$	−4.93985	−	7.53883i	−0.264804	−	0.404124i
$349$	−10.4589	+	18.1154i	−0.559853	+	0.969694i	0.437655	+	0.899143i	$0.355809\pi$
$349$	−10.4589	+	18.1154i	−0.559853	+	0.969694i	−0.997508	+	0.0705511i	$0.977524\pi$
$350$	−23.4937			−1.25579
$351$	−18.0542	−	21.7425i	−0.963660	−	1.16053i
$352$		0			0
$353$	12.7877	−	22.1489i	0.680619	−	1.17887i	−0.294173	−	0.955752i	$-0.595044\pi$
$353$	12.7877	−	22.1489i	0.680619	−	1.17887i	0.974792	−	0.223115i	$-0.0716225\pi$
$354$	−11.9881	−	18.2953i	−0.637158	−	0.972384i
$355$	−4.88448	−	8.46016i	−0.259241	−	0.449019i
$356$	−6.07938	−	10.5298i	−0.322206	−	0.558078i
$357$	29.1565	−	1.64796i	1.54312	−	0.0872191i
$358$	2.71028	−	4.69434i	0.143243	−	0.248103i
$359$	35.7137			1.88490			0.942449	−	0.334350i	$-0.108517\pi$
$359$	35.7137			1.88490			0.942449	+	0.334350i	$0.108517\pi$
$360$	−16.3982	+	1.85963i	−0.864261	+	0.0980111i
$361$	−16.3800			−0.862104
$362$	9.06055	−	15.6933i	0.476212	−	0.824824i
$363$		0			0
$364$	37.1759	+	64.3906i	1.94855	+	3.37498i
$365$	−0.832305	−	1.44159i	−0.0435648	−	0.0754565i
$366$	−24.3538	+	48.2856i	−1.27299	+	2.52393i
$367$	2.93712	−	5.08725i	0.153317	−	0.265552i	−0.779128	−	0.626865i	$-0.784338\pi$
$367$	2.93712	−	5.08725i	0.153317	−	0.265552i	0.932445	+	0.361313i	$0.117671\pi$
$368$	−9.99988			−0.521280
$369$	10.5117	−	1.19207i	0.547217	−	0.0620568i
$370$	−34.1035			−1.77296
$371$	20.9560	−	36.2969i	1.08798	−	1.88444i
$372$	−8.83617	+	0.499430i	−0.458134	+	0.0258943i
$373$	9.99046	+	17.3040i	0.517287	+	0.895967i	0.999798	+	0.0200773i	$0.00639122\pi$
$373$	9.99046	+	17.3040i	0.517287	+	0.895967i	−0.482512	+	0.875889i	$0.660275\pi$
$374$		0			0
$375$	11.2050	+	17.1003i	0.578626	+	0.883056i
$376$	10.3216	−	17.8775i	0.532294	−	0.921961i
$377$	8.07896			0.416088
$378$	30.3876	+	36.5956i	1.56297	+	1.88228i
$379$	26.3439			1.35320			0.676599	−	0.736352i	$-0.263453\pi$
$379$	26.3439			1.35320			0.676599	+	0.736352i	$0.263453\pi$
$380$	4.42294	−	7.66076i	0.226892	−	0.392989i
$381$	0.237576	+	0.362570i	0.0121714	+	0.0185750i
$382$	−22.6936	−	39.3065i	−1.16111	−	2.01109i
$383$	0.812128	+	1.40665i	0.0414978	+	0.0718763i	0.886028	−	0.463631i	$-0.153454\pi$
$383$	0.812128	+	1.40665i	0.0414978	+	0.0718763i	−0.844531	+	0.535507i	$0.820120\pi$
$384$	35.0053	−	1.97854i	1.78636	−	0.100967i
$385$		0			0
$386$	25.7374			1.31000
$387$	1.47000	+	1.98877i	0.0747244	+	0.101095i
$388$	32.4674			1.64828
$389$	3.57443	−	6.19109i	0.181231	−	0.313901i	−0.761069	−	0.648671i	$-0.775325\pi$
$389$	3.57443	−	6.19109i	0.181231	−	0.313901i	0.942300	+	0.334770i	$0.108659\pi$
$390$	15.5250	−	30.7811i	0.786141	−	1.55866i
$391$	−17.0635	−	29.5548i	−0.862937	−	1.49465i
$392$	−14.5071	−	25.1270i	−0.732720	−	1.26911i
$393$	8.18830	−	16.2347i	0.413045	−	0.818933i
$394$	24.3202	−	42.1239i	1.22523	−	2.12217i
$395$	15.4561			0.777680
$396$		0			0
$397$	−28.2612			−1.41839			−0.709195	−	0.705012i	$-0.750941\pi$
$397$	−28.2612			−1.41839			−0.709195	+	0.705012i	$0.750941\pi$
$398$	5.69343	−	9.86131i	0.285386	−	0.494303i
$399$	−10.9229	+	0.617376i	−0.546830	+	0.0309074i
$400$	1.62458	+	2.81386i	0.0812290	+	0.140693i
$401$	−2.08005	−	3.60275i	−0.103873	−	0.179913i	0.809404	−	0.587252i	$-0.199790\pi$
$401$	−2.08005	−	3.60275i	−0.103873	−	0.179913i	−0.913277	+	0.407339i	$0.866457\pi$
$402$	7.56129	+	11.5395i	0.377123	+	0.575537i
$403$	3.96650	−	6.87019i	0.197586	−	0.342228i
$404$	−12.3535			−0.614612
$405$	4.11897	−	13.4222i	0.204673	−	0.666954i
$406$	−13.5980			−0.674857
$407$		0			0
$408$	−14.4635	−	22.0732i	−0.716051	−	1.09278i
$409$	13.4436	+	23.2850i	0.664743	+	1.15137i	0.979355	+	0.202149i	$0.0647924\pi$
$409$	13.4436	+	23.2850i	0.664743	+	1.15137i	−0.314612	+	0.949220i	$0.601874\pi$
$410$	6.45250	+	11.1761i	0.318666	+	0.551946i
$411$	−18.9882	+	1.07324i	−0.936621	+	0.0529389i
$412$	14.6497	−	25.3740i	0.721737	−	1.25008i
$413$	−21.0068			−1.03368
$414$	22.1922	−	50.9656i	1.09069	−	2.50482i
$415$	−7.42375			−0.364418
$416$	−11.1027	+	19.2304i	−0.544354	+	0.942848i
$417$	−6.12745	+	12.1487i	−0.300063	+	0.594925i
$418$		0			0
$419$	8.44088	+	14.6200i	0.412364	+	0.714236i	0.995148	−	0.0983917i	$-0.0313698\pi$
$419$	8.44088	+	14.6200i	0.412364	+	0.714236i	−0.582784	+	0.812627i	$0.698036\pi$
$420$	−16.6342	+	32.9802i	−0.811667	+	1.60927i
$421$	16.5021	−	28.5826i	0.804266	−	1.39303i	−0.112520	−	0.993649i	$-0.535892\pi$
$421$	16.5021	−	28.5826i	0.804266	−	1.39303i	0.916786	−	0.399379i	$-0.130774\pi$
$422$	10.1338			0.493303
$423$	10.4388	+	14.1227i	0.507552	+	0.686670i
$424$	−37.8744			−1.83934
$425$	−5.54426	+	9.60295i	−0.268936	+	0.465811i
$426$	25.4039	−	1.43586i	1.23082	−	0.0695674i
$427$	25.9689	+	44.9795i	1.25672	+	2.17671i
$428$	−11.9368	−	20.6752i	−0.576988	−	0.999372i
$429$		0			0
$430$	−1.50841	+	2.61264i	−0.0727418	+	0.125993i
$431$	−11.0594			−0.532713			−0.266356	−	0.963875i	$-0.585820\pi$
$431$	−11.0594			−0.532713			−0.266356	+	0.963875i	$0.585820\pi$
$432$	2.28179	−	6.17011i	0.109783	−	0.296859i
$433$	28.1486			1.35273			0.676367	−	0.736565i	$-0.263553\pi$
$433$	28.1486			1.35273			0.676367	+	0.736565i	$0.263553\pi$
$434$	−6.67617	+	11.5635i	−0.320466	+	0.555064i
$435$	2.19974	+	3.35709i	0.105470	+	0.160960i
$436$	−28.6217	−	49.5743i	−1.37073	−	2.37418i
$437$	6.39251	+	11.0721i	0.305795	+	0.529653i
$438$	4.32877	−	0.244667i	0.206837	−	0.0116906i
$439$	−0.934408	+	1.61844i	−0.0445969	+	0.0772440i	−0.887462	−	0.460881i	$-0.847534\pi$
$439$	−0.934408	+	1.61844i	−0.0445969	+	0.0772440i	0.842865	+	0.538125i	$0.180867\pi$
$440$		0			0
$441$	24.5263	−	2.78139i	1.16792	−	0.132447i
$442$	55.1269			2.62212
$443$	−9.71051	+	16.8191i	−0.461360	+	0.799099i	−0.999029	−	0.0440568i	$-0.985972\pi$
$443$	−9.71051	+	16.8191i	−0.461360	+	0.799099i	0.537669	+	0.843156i	$0.319305\pi$
$444$	25.4640	−	50.4867i	1.20847	−	2.39599i
$445$	2.70718	+	4.68898i	0.128333	+	0.222279i
$446$	−8.70038	−	15.0695i	−0.411975	−	0.713561i
$447$	−5.98080	+	11.8580i	−0.282882	+	0.560862i
$448$	23.6278	−	40.9245i	1.11631	−	1.93350i
$449$	15.6490			0.738520			0.369260	−	0.929326i	$-0.379611\pi$
$449$	15.6490			0.738520			0.369260	+	0.929326i	$0.379611\pi$
$450$	−17.9465	+	2.03521i	−0.846006	+	0.0959409i
$451$		0			0
$452$	−3.77024	+	6.53024i	−0.177337	+	0.307157i
$453$	0.607527	−	0.0343381i	0.0285441	−	0.00161334i
$454$	−3.07302	−	5.32263i	−0.144224	−	0.249803i
$455$	−16.5547	−	28.6735i	−0.776094	−	1.34423i
$456$	5.41848	+	8.26929i	0.253744	+	0.387245i
$457$	−5.42276	+	9.39250i	−0.253666	+	0.439363i	−0.964532	−	0.263965i	$-0.914970\pi$
$457$	−5.42276	+	9.39250i	−0.253666	+	0.439363i	0.710866	+	0.703327i	$0.248303\pi$
$458$	27.0003			1.26164
$459$	22.1294	−	3.78461i	1.03291	−	0.176651i
$460$	43.1657			2.01261
$461$	19.7612	−	34.2274i	0.920371	−	1.59413i	0.121530	−	0.992588i	$-0.461220\pi$
$461$	19.7612	−	34.2274i	0.920371	−	1.59413i	0.798841	−	0.601542i	$-0.205447\pi$
$462$		0			0
$463$	−11.8195	−	20.4719i	−0.549298	−	0.951412i	−0.998323	−	0.0578925i	$-0.981562\pi$
$463$	−11.8195	−	20.4719i	−0.549298	−	0.951412i	0.449025	−	0.893519i	$-0.351771\pi$
$464$	0.940294	+	1.62864i	0.0436521	+	0.0756076i
$465$	3.93480	−	0.222399i	0.182472	−	0.0103135i
$466$	19.4058	−	33.6119i	0.898957	−	1.55704i
$467$	−2.49010			−0.115228			−0.0576140	−	0.998339i	$-0.518349\pi$
$467$	−2.49010			−0.115228			−0.0576140	+	0.998339i	$0.518349\pi$
$468$	33.9761	+	45.9665i	1.57055	+	2.12480i
$469$	13.2497			0.611816
$470$	−10.7115	+	18.5529i	−0.494086	+	0.855782i
$471$	−8.07628	+	16.0126i	−0.372136	+	0.737822i
$472$	9.49155	+	16.4399i	0.436884	+	0.756706i
$473$		0			0
$474$	−18.1291	+	35.9441i	−0.832699	+	1.65097i
$475$	2.07705	−	3.59756i	0.0953017	−	0.165067i
$476$	−59.0653			−2.70726
$477$	12.8636	−	29.5420i	0.588985	−	1.35263i
$478$	−12.0696			−0.552051
$479$	−5.75027	+	9.95976i	−0.262737	+	0.455073i	−0.966968	−	0.254897i	$-0.917958\pi$
$479$	−5.75027	+	9.95976i	−0.262737	+	0.455073i	0.704232	+	0.709970i	$0.251292\pi$
$480$	−11.0139	+	0.622520i	−0.502715	+	0.0284140i
$481$	25.3422	+	43.8940i	1.15550	+	2.00139i
$482$	−27.0164	−	46.7938i	−1.23057	−	2.13140i
$483$	−29.2596	−	44.6538i	−1.33136	−	2.03182i
$484$		0			0
$485$	−14.4579			−0.656501
$486$	26.3828	+	25.3224i	1.19675	+	1.14865i
$487$	−26.7429			−1.21184			−0.605918	−	0.795527i	$-0.707194\pi$
$487$	−26.7429			−1.21184			−0.605918	+	0.795527i	$0.707194\pi$
$488$	23.4672	−	40.6464i	1.06231	−	1.83998i
$489$	20.3216	+	31.0134i	0.918976	+	1.40247i
$490$	15.0552	+	26.0764i	0.680125	+	1.17801i
$491$	5.85088	+	10.1340i	0.264047	+	0.457342i	0.967313	−	0.253584i	$-0.0816094\pi$
$491$	5.85088	+	10.1340i	0.264047	+	0.457342i	−0.703267	+	0.710926i	$0.748276\pi$
$492$	−21.3629	+	1.20745i	−0.963113	+	0.0544362i
$493$	−3.20898	+	5.55811i	−0.144525	+	0.250325i
$494$	−20.6522			−0.929188
$495$		0			0
$496$	1.84661			0.0829155
$497$	12.2184	−	21.1628i	0.548068	−	0.949282i
$498$	8.70766	−	17.2644i	0.390200	−	0.773637i
$499$	12.3613	+	21.4104i	0.553368	+	0.958462i	0.998028	+	0.0627627i	$0.0199911\pi$
$499$	12.3613	+	21.4104i	0.553368	+	0.958462i	−0.444660	+	0.895699i	$0.646676\pi$
$500$	−20.6752	−	35.8105i	−0.924622	−	1.60149i
$501$	−11.3081	+	22.4203i	−0.505210	+	1.00167i
$502$	−9.27888	+	16.0715i	−0.414137	+	0.717306i
$503$	−44.8075			−1.99787			−0.998933	−	0.0461829i	$-0.985294\pi$
$503$	−44.8075			−1.99787			−0.998933	+	0.0461829i	$0.985294\pi$
$504$	−24.5384	−	33.1981i	−1.09303	−	1.47876i
$505$	5.50111			0.244796
$506$		0			0
$507$	−28.6736	+	1.62066i	−1.27344	+	0.0719761i
$508$	−0.438367	−	0.759273i	−0.0194494	−	0.0336873i
$509$	−16.8263	−	29.1440i	−0.745813	−	1.29179i	−0.949814	−	0.312815i	$-0.898728\pi$
$509$	−16.8263	−	29.1440i	−0.745813	−	1.29179i	0.204001	−	0.978971i	$-0.434605\pi$
$510$	15.0100	+	22.9071i	0.664653	+	1.01434i
$511$	2.08198	−	3.60610i	0.0921016	−	0.159525i
$512$	−14.0979			−0.623043
$513$	−8.29037	+	1.41783i	−0.366029	+	0.0625989i
$514$	24.4751			1.07955
$515$	−6.52358	+	11.2992i	−0.287463	+	0.497901i
$516$	−2.74146	−	4.18381i	−0.120686	−	0.184182i
$517$		0			0
$518$	−42.6544	−	73.8796i	−1.87413	−	3.24608i
$519$	17.5339	−	0.991035i	0.769653	−	0.0435016i
$520$	−14.9598	+	25.9112i	−0.656033	+	1.13628i
$521$	−35.7515			−1.56630			−0.783151	−	0.621832i	$-0.786389\pi$
$521$	−35.7515			−1.56630			−0.783151	+	0.621832i	$0.786389\pi$
$522$	−10.3873	+	1.17797i	−0.454640	+	0.0515582i
$523$	30.0048			1.31202			0.656009	−	0.754753i	$-0.272243\pi$
$523$	30.0048			1.31202			0.656009	+	0.754753i	$0.272243\pi$
$524$	−18.3880	+	31.8490i	−0.803285	+	1.39133i
$525$	−7.81157	+	15.4878i	−0.340925	+	0.675942i
$526$	−30.4485	−	52.7384i	−1.32762	−	2.29950i
$527$	3.15100	+	5.45770i	0.137260	+	0.237741i
$528$		0			0
$529$	−19.6938	+	34.1107i	−0.856253	+	1.48307i
$530$	39.3053			1.70731
$531$	−16.0468	+	1.81978i	−0.696371	+	0.0789716i
$532$	22.1277			0.959358
$533$	9.58966	−	16.6098i	0.415374	−	0.719449i
$534$	−14.0799	+	0.795811i	−0.609297	+	0.0344381i
$535$	5.31553	+	9.20678i	0.229811	+	0.398044i
$536$	−5.98666	−	10.3692i	−0.258584	−	0.447881i
$537$	−2.19349	−	3.34754i	−0.0946560	−	0.144457i
$538$	23.4359	−	40.5921i	1.01039	−	1.75005i
$539$		0			0
$540$	−9.84961	+	26.6340i	−0.423860	+	1.14615i
$541$	−4.66677			−0.200640			−0.100320	−	0.994955i	$-0.531987\pi$
$541$	−4.66677			−0.200640			−0.100320	+	0.994955i	$0.531987\pi$
$542$	0.347461	−	0.601821i	0.0149247	−	0.0258504i
$543$	−7.33292	−	11.1910i	−0.314686	−	0.480250i
$544$	−8.82001	−	15.2767i	−0.378155	−	0.654983i
$545$	12.7454	+	22.0757i	0.545954	+	0.945620i
$546$	86.0998	−	4.86646i	3.68473	−	0.208265i
$547$	−10.4912	+	18.1714i	−0.448573	+	0.776951i	−0.998293	−	0.0583977i	$-0.981401\pi$
$547$	−10.4912	+	18.1714i	−0.448573	+	0.776951i	0.549721	+	0.835349i	$0.314734\pi$
$548$	38.4665			1.64321
$549$	23.7337	+	32.1095i	1.01293	+	1.37040i
$550$		0			0
$551$	1.20218	−	2.08224i	0.0512147	−	0.0887064i
$552$	−21.7255	+	43.0744i	−0.924697	+	1.83337i
$553$	19.3314	+	33.4830i	0.822057	+	1.42384i
$554$	31.1759	+	53.9983i	1.32454	+	2.29417i
$555$	−11.3393	+	22.4820i	−0.481325	+	0.954309i
$556$	13.7601	−	23.8332i	0.583558	−	1.01075i
$557$	28.2882			1.19861			0.599304	−	0.800522i	$-0.295444\pi$
$557$	28.2882			1.19861			0.599304	+	0.800522i	$0.295444\pi$
$558$	−4.09810	+	9.41149i	−0.173487	+	0.398420i
$559$	4.48357			0.189635
$560$	3.85353	−	6.67450i	0.162841	−	0.282049i
$561$		0			0
$562$	7.98451	+	13.8296i	0.336806	+	0.583366i
$563$	−5.64908	−	9.78450i	−0.238081	−	0.412368i	0.722083	−	0.691806i	$-0.243185\pi$
$563$	−5.64908	−	9.78450i	−0.238081	−	0.412368i	−0.960163	+	0.279439i	$0.909852\pi$
$564$	−19.4677	−	29.7102i	−0.819739	−	1.25102i
$565$	1.67891	−	2.90795i	0.0706322	−	0.122339i
$566$	−4.86960			−0.204685
$567$	34.2287	−	7.86452i	1.43747	−	0.330279i
$568$	−22.0826			−0.926565
$569$	9.00491	−	15.5970i	0.377505	−	0.653858i	−0.613193	−	0.789933i	$-0.710115\pi$
$569$	9.00491	−	15.5970i	0.377505	−	0.653858i	0.990699	+	0.136075i	$0.0434487\pi$
$570$	−5.62320	−	8.58171i	−0.235530	−	0.359448i
$571$	−1.83865	−	3.18464i	−0.0769452	−	0.133273i	0.824985	−	0.565154i	$-0.191183\pi$
$571$	−1.83865	−	3.18464i	−0.0769452	−	0.133273i	−0.901931	+	0.431881i	$0.857850\pi$
$572$		0			0
$573$	−33.4575	+	1.89106i	−1.39771	+	0.0790000i
$574$	−16.1407	+	27.9565i	−0.673700	+	1.16688i
$575$	20.2710			0.845358
$576$	14.5037	−	33.3084i	0.604320	−	1.38785i
$577$	20.7404			0.863433			0.431717	−	0.902009i	$-0.357908\pi$
$577$	20.7404			0.863433			0.431717	+	0.902009i	$0.357908\pi$
$578$	−1.95641	+	3.38859i	−0.0813758	+	0.140947i
$579$	8.55759	−	16.9669i	0.355641	−	0.705119i
$580$	−4.05889	−	7.03021i	−0.168536	−	0.291914i
$581$	−9.28514	−	16.0823i	−0.385213	−	0.667208i
$582$	16.9584	−	33.6228i	0.702947	−	1.39371i
$583$		0			0
$584$	−3.76283			−0.155707
$585$	−15.1298	−	20.4691i	−0.625539	−	0.846295i
$586$	7.12452			0.294311
$587$	10.0497	−	17.4066i	0.414796	−	0.718448i	−0.580611	−	0.814181i	$-0.697186\pi$
$587$	10.0497	−	17.4066i	0.414796	−	0.718448i	0.995407	+	0.0957333i	$0.0305196\pi$
$588$	−49.8446	+	2.81727i	−2.05556	+	0.116182i
$589$	−1.18046	−	2.04462i	−0.0486402	−	0.0842472i
$590$	−9.85016	−	17.0610i	−0.405524	−	0.702389i
$591$	−19.6829	−	30.0386i	−0.809647	−	1.23562i
$592$	−5.89906	+	10.2175i	−0.242450	+	0.419935i
$593$	−12.9393			−0.531354			−0.265677	−	0.964062i	$-0.585596\pi$
$593$	−12.9393			−0.531354			−0.265677	+	0.964062i	$0.585596\pi$
$594$		0			0
$595$	26.3021			1.07828
$596$	13.4308	−	23.2628i	0.550146	−	0.952881i
$597$	−4.60783	−	7.03212i	−0.188586	−	0.287806i
$598$	−50.3888	−	87.2760i	−2.06055	−	3.56898i
$599$	23.1779	+	40.1453i	0.947024	+	1.64029i	0.751648	+	0.659565i	$0.229259\pi$
$599$	23.1779	+	40.1453i	0.947024	+	1.64029i	0.195376	+	0.980728i	$0.437407\pi$
$600$	15.6502	−	0.884566i	0.638916	−	0.0361123i
$601$	−3.96474	+	6.86713i	−0.161725	+	0.280116i	−0.935487	−	0.353360i	$-0.885039\pi$
$601$	−3.96474	+	6.86713i	−0.161725	+	0.280116i	0.773762	+	0.633476i	$0.218372\pi$
$602$	−7.54646			−0.307571
$603$	10.1213	−	1.14780i	0.412170	−	0.0467419i
$604$	−1.23073			−0.0500777
$605$		0			0
$606$	−6.45250	+	12.7932i	−0.262115	+	0.519687i
$607$	−5.50806	−	9.54024i	−0.223565	−	0.387226i	0.732323	−	0.680958i	$-0.238436\pi$
$607$	−5.50806	−	9.54024i	−0.223565	−	0.387226i	−0.955888	+	0.293731i	$0.905103\pi$
$608$	3.30425	+	5.72313i	0.134005	+	0.232103i
$609$	−4.52128	+	8.96420i	−0.183211	+	0.363248i
$610$	−24.3538	+	42.1820i	−0.986057	+	1.70790i
$611$	31.8388			1.28806
$612$	−45.1191	+	5.11671i	−1.82383	+	0.206831i
$613$	16.8348			0.679951			0.339976	−	0.940434i	$-0.389581\pi$
$613$	16.8348			0.679951			0.339976	+	0.940434i	$0.389581\pi$
$614$	21.0561	−	36.4703i	0.849756	−	1.47182i
$615$	9.51301	−	0.537686i	0.383602	−	0.0216816i
$616$		0			0
$617$	−5.92051	−	10.2546i	−0.238351	−	0.412836i	0.721890	−	0.692007i	$-0.243273\pi$
$617$	−5.92051	−	10.2546i	−0.238351	−	0.412836i	−0.960241	+	0.279172i	$0.909940\pi$
$618$	−18.6251	−	28.4243i	−0.749213	−	1.14339i
$619$	−6.10792	+	10.5792i	−0.245498	+	0.425215i	−0.962271	−	0.272091i	$-0.912285\pi$
$619$	−6.10792	+	10.5792i	−0.245498	+	0.425215i	0.716774	+	0.697306i	$0.245618\pi$
$620$	−7.97114			−0.320129
$621$	−26.2192	−	31.5756i	−1.05214	−	1.26709i
$622$	−61.9116			−2.48243
$623$	−6.77193	+	11.7293i	−0.271312	+	0.469925i
$624$	−6.53661	−	9.97569i	−0.261674	−	0.399347i
$625$	2.79076	+	4.83373i	0.111630	+	0.193349i
$626$	10.1439	+	17.5697i	0.405430	+	0.702225i
$627$		0			0
$628$	18.1365	−	31.4133i	0.723725	−	1.25353i
$629$	−40.2639			−1.60542
$630$	25.4655	+	34.4524i	1.01457	+	1.37262i
$631$	−25.7140			−1.02366			−0.511830	−	0.859087i	$-0.671032\pi$
$631$	−25.7140			−1.02366			−0.511830	+	0.859087i	$0.671032\pi$
$632$	17.4691	−	30.2574i	0.694885	−	1.20358i
$633$	3.36943	−	6.68047i	0.133923	−	0.265525i
$634$	9.14442	+	15.8386i	0.363171	+	0.629031i
$635$	0.195207	+	0.338109i	0.00774656	+	0.0134174i
$636$	−29.3480	+	58.1875i	−1.16373	+	2.30728i
$637$	22.3750	−	38.7546i	0.886528	−	1.53551i
$638$		0			0
$639$	7.50012	−	17.2244i	0.296700	−	0.681387i
$640$	31.5784			1.24825
$641$	18.0588	−	31.2788i	0.713280	−	1.23544i	−0.250340	−	0.968158i	$-0.580542\pi$
$641$	18.0588	−	31.2788i	0.713280	−	1.23544i	0.963619	−	0.267279i	$-0.0861244\pi$
$642$	−27.6458	+	1.56257i	−1.09109	+	0.0616697i
$643$	−13.1004	−	22.6906i	−0.516630	−	0.894830i	−0.999814	−	0.0193105i	$-0.993853\pi$
$643$	−13.1004	−	22.6906i	−0.516630	−	0.894830i	0.483183	−	0.875519i	$-0.339480\pi$
$644$	53.9888	+	93.5113i	2.12746	+	3.68486i
$645$	1.22079	+	1.86308i	0.0480685	+	0.0733586i
$646$	8.20310	−	14.2082i	0.322747	−	0.559014i
$647$	38.2700			1.50455			0.752275	−	0.658849i	$-0.228956\pi$
$647$	38.2700			1.50455			0.752275	+	0.658849i	$0.228956\pi$
$648$	−21.6204	−	23.2338i	−0.849328	−	0.912710i
$649$		0			0
$650$	−16.3723	+	28.3577i	−0.642176	+	1.11228i
$651$	5.40318	+	8.24593i	0.211767	+	0.323184i
$652$	−37.4968	−	64.9464i	−1.46849	−	2.54350i
$653$	0.0125540	+	0.0217442i	0.000491277	+	0.000850916i	0.866271	−	0.499574i	$-0.166510\pi$
$653$	0.0125540	+	0.0217442i	0.000491277	+	0.000850916i	−0.865780	+	0.500425i	$0.833177\pi$
$654$	−66.2882	+	3.74668i	−2.59207	+	0.146507i
$655$	8.18830	−	14.1826i	0.319943	−	0.554158i
$656$	4.46449			0.174309
$657$	1.27801	−	2.93500i	0.0498598	−	0.114505i
$658$	−53.5891			−2.08912
$659$	3.66456	−	6.34720i	0.142751	−	0.247252i	−0.785781	−	0.618505i	$-0.787739\pi$
$659$	3.66456	−	6.34720i	0.142751	−	0.247252i	0.928532	+	0.371253i	$0.121072\pi$
$660$		0			0
$661$	−19.9071	−	34.4802i	−0.774298	−	1.34112i	−0.935188	−	0.354151i	$-0.884770\pi$
$661$	−19.9071	−	34.4802i	−0.774298	−	1.34112i	0.160890	−	0.986972i	$-0.448564\pi$
$662$	−9.14972	−	15.8478i	−0.355614	−	0.615942i
$663$	18.3294	−	36.3413i	0.711857	−	1.41138i
$664$	−8.39065	+	14.5330i	−0.325620	+	0.563991i
$665$	−9.85360			−0.382106
$666$	−38.9831	−	52.7404i	−1.51056	−	2.04365i
$667$	11.7327			0.454292
$668$	25.3941	−	43.9839i	0.982527	−	1.70179i
$669$	−12.8271	+	0.725002i	−0.495924	+	0.0280302i
$670$	6.21284	+	10.7610i	0.240023	+	0.415732i
$671$		0			0
$672$	−15.1241	−	23.0813i	−0.583425	−	0.890379i
$673$	−16.8191	+	29.1316i	−0.648329	+	1.12294i	0.335193	+	0.942150i	$0.391199\pi$
$673$	−16.8191	+	29.1316i	−0.648329	+	1.12294i	−0.983522	+	0.180789i	$0.942135\pi$
$674$	−16.7022			−0.643343
$675$	−4.62546	+	12.5076i	−0.178034	+	0.481416i
$676$	58.0870			2.23412
$677$	−12.8857	+	22.3187i	−0.495238	+	0.857777i	−0.999985	−	0.00549037i	$-0.998252\pi$
$677$	−12.8857	+	22.3187i	−0.495238	+	0.857777i	0.504747	+	0.863267i	$0.331586\pi$
$678$	4.79337	+	7.31528i	0.184088	+	0.280942i
$679$	−18.0830	−	31.3207i	−0.693963	−	1.20198i
$680$	−11.8842	−	20.5840i	−0.455736	−	0.789359i
$681$	−4.53060	+	0.256074i	−0.173613	+	0.00981279i
$682$		0			0
$683$	17.5636			0.672052			0.336026	−	0.941853i	$-0.390917\pi$
$683$	17.5636			0.672052			0.336026	+	0.941853i	$0.390917\pi$
$684$	16.9030	−	1.91688i	0.646303	−	0.0732936i
$685$	−17.1293			−0.654479
$686$	−5.61994	+	9.73402i	−0.214570	+	0.371647i
$687$	8.97749	−	17.7994i	0.342512	−	0.679089i
$688$	0.521834	+	0.903843i	0.0198947	+	0.0344587i
$689$	−29.2077	−	50.5891i	−1.11272	−	1.92729i
$690$	22.5463	−	44.7018i	0.858322	−	1.70177i
$691$	21.6147	−	37.4377i	0.822260	−	1.42420i	−0.0817354	−	0.996654i	$-0.526046\pi$
$691$	21.6147	−	37.4377i	0.822260	−	1.42420i	0.903995	−	0.427542i	$-0.140620\pi$
$692$	−35.5202			−1.35028
$693$		0			0
$694$	49.2830			1.87076
$695$	−6.12745	+	10.6131i	−0.232427	+	0.402576i
$696$	9.05821	−	0.511980i	0.343351	−	0.0194066i
$697$	7.61806	+	13.1949i	0.288555	+	0.499791i
$698$	−24.5355	−	42.4967i	−0.928682	−	1.60852i
$699$	−15.7056	−	23.9687i	−0.594040	−	0.906579i
$700$	17.5420	−	30.3837i	0.663027	−	1.14840i
$701$	46.3884			1.75206			0.876032	−	0.482252i	$-0.160181\pi$
$701$	46.3884			1.75206			0.876032	+	0.482252i	$0.160181\pi$
$702$	65.3487	−	11.1761i	2.46643	−	0.421813i
$703$	15.0841			0.568907
$704$		0			0
$705$	8.66909	+	13.2301i	0.326497	+	0.498275i
$706$	29.9985	+	51.9589i	1.12901	+	1.95550i
$707$	6.88042	+	11.9172i	0.258765	+	0.448194i
$708$	32.6118	−	1.84326i	1.22563	−	0.0692738i
$709$	2.49915	−	4.32865i	0.0938575	−	0.162566i	−0.815274	−	0.579076i	$-0.803414\pi$
$709$	2.49915	−	4.32865i	0.0938575	−	0.162566i	0.909131	+	0.416510i	$0.136747\pi$
$710$	22.9169			0.860056
$711$	17.6676	+	23.9025i	0.662585	+	0.896415i
$712$	12.2391			0.458680
$713$	5.76036	−	9.97724i	0.215727	−	0.373651i
$714$	−30.8510	+	61.1673i	−1.15457	+	2.28913i
$715$		0			0
$716$	4.04735	+	7.01022i	0.151257	+	0.261984i
$717$	−4.01309	+	7.95664i	−0.149872	+	0.297146i
$718$	−41.8902	+	72.5560i	−1.56333	+	2.70777i
$719$	45.0421			1.67979			0.839894	−	0.542751i	$-0.182617\pi$
$719$	45.0421			1.67979			0.839894	+	0.542751i	$0.182617\pi$
$720$	2.36545	−	5.43237i	0.0881551	−	0.202453i
$721$	−32.6370			−1.21547
$722$	19.2128	−	33.2776i	0.715027	−	1.23846i
$723$	−39.8307	+	2.25128i	−1.48132	+	0.0837259i
$724$	13.5305	+	23.4354i	0.502855	+	0.870971i
$725$	−1.90609	−	3.30145i	−0.0707905	−	0.122613i
$726$		0			0
$727$	5.14525	−	8.91183i	0.190827	−	0.330521i	−0.754698	−	0.656073i	$-0.772217\pi$
$727$	5.14525	−	8.91183i	0.190827	−	0.330521i	0.945524	+	0.325551i	$0.105550\pi$
$728$	−74.8432			−2.77387
$729$	25.4655	−	8.97274i	0.943165	−	0.332324i
$730$	3.90499			0.144530
$731$	−1.78088	+	3.08458i	−0.0658683	+	0.114087i
$732$	−44.2620	−	67.5493i	−1.63597	−	2.49669i
$733$	−7.91739	−	13.7133i	−0.292436	−	0.506513i	0.681949	−	0.731399i	$-0.261132\pi$
$733$	−7.91739	−	13.7133i	−0.292436	−	0.506513i	−0.974385	+	0.224886i	$0.927799\pi$
$734$	6.89017	+	11.9341i	0.254321	+	0.440497i
$735$	22.1961	−	1.25455i	0.818716	−	0.0462747i
$736$	−16.1239	+	27.9274i	−0.594335	+	1.02942i
$737$		0			0
$738$	−9.90782	+	22.7538i	−0.364712	+	0.837579i
$739$	37.8681			1.39300			0.696500	−	0.717557i	$-0.254740\pi$
$739$	37.8681			1.39300			0.696500	+	0.717557i	$0.254740\pi$
$740$	25.4640	−	44.1049i	0.936075	−	1.62133i
$741$	−6.86678	+	13.6146i	−0.252257	+	0.500143i
$742$	49.1605	+	85.1485i	1.80474	+	3.12590i
$743$	−8.94538	−	15.4939i	−0.328174	−	0.568414i	0.653975	−	0.756516i	$-0.273100\pi$
$743$	−8.94538	−	15.4939i	−0.328174	−	0.568414i	−0.982150	+	0.188101i	$0.939767\pi$
$744$	4.01191	−	7.95429i	0.147084	−	0.291618i
$745$	−5.98080	+	10.3591i	−0.219120	+	0.379526i
$746$	−46.8731			−1.71615
$747$	−8.48595	−	11.4807i	−0.310485	−	0.420057i
$748$		0			0
$749$	−13.2966	+	23.0305i	−0.485849	+	0.841515i
$750$	−47.8839	+	2.70645i	−1.74847	+	0.0988256i
$751$	18.7341	+	32.4484i	0.683617	+	1.18406i	0.973869	+	0.227109i	$0.0729273\pi$
$751$	18.7341	+	32.4484i	0.683617	+	1.18406i	−0.290253	+	0.956950i	$0.593739\pi$
$752$	3.70566	+	6.41839i	0.135131	+	0.234055i
$753$	7.50961	+	11.4606i	0.273666	+	0.417648i
$754$	−9.47618	+	16.4132i	−0.345102	+	0.597735i
$755$	0.548051			0.0199456
$756$	−70.0174	+	11.9745i	−2.54651	+	0.435509i
$757$	−41.4462			−1.50639			−0.753194	−	0.657799i	$-0.771488\pi$
$757$	−41.4462			−1.50639			−0.753194	+	0.657799i	$0.771488\pi$
$758$	−30.9000	+	53.5204i	−1.12234	+	1.94395i
$759$		0			0
$760$	4.45217	+	7.71139i	0.161497	+	0.279721i
$761$	25.2996	+	43.8202i	0.917111	+	1.58848i	0.803782	+	0.594925i	$0.202818\pi$
$761$	25.2996	+	43.8202i	0.917111	+	1.58848i	0.113329	+	0.993558i	$0.463849\pi$
$762$	−1.01526	+	0.0573837i	−0.0367790	+	0.00207879i
$763$	−31.8823	+	55.2217i	−1.15422	+	1.99916i
$764$	67.7784			2.45214
$765$	20.0918	−	2.27850i	0.726420	−	0.0823793i
$766$	−3.81033			−0.137673
$767$	−14.6392	+	25.3559i	−0.528592	+	0.915549i
$768$	−18.1486	+	35.9828i	−0.654882	+	1.29842i
$769$	−2.68893	−	4.65736i	−0.0969651	−	0.167949i	0.813462	−	0.581618i	$-0.197580\pi$
$769$	−2.68893	−	4.65736i	−0.0969651	−	0.167949i	−0.910427	+	0.413670i	$0.864247\pi$
$770$		0			0
$771$	8.13787	−	16.1347i	0.293078	−	0.581078i
$772$	−19.2173	+	33.2854i	−0.691647	+	1.19797i
$773$	9.31573			0.335063			0.167532	−	0.985867i	$-0.446420\pi$
$773$	9.31573			0.335063			0.167532	+	0.985867i	$0.446420\pi$
$774$	−5.76462	+	0.653734i	−0.207205	+	0.0234980i
$775$	−3.74331			−0.134464
$776$	−16.3410	+	28.3034i	−0.586607	+	1.01603i
$777$	−62.8860	+	3.55439i	−2.25602	+	0.127513i
$778$	8.38522	+	14.5236i	0.300625	+	0.520697i
$779$	−2.85396	−	4.94320i	−0.102254	−	0.177109i
$780$	28.2161	+	43.0613i	1.01030	+	1.54184i
$781$		0			0
$782$	80.0581			2.86287
$783$	−2.67718	+	7.23928i	−0.0956747	+	0.258711i
$784$	10.4167			0.372025
$785$	−8.07628	+	13.9885i	−0.288255	+	0.499272i
$786$	23.3780	+	35.6778i	0.833866	+	1.27258i
$787$	10.0907	+	17.4777i	0.359696	+	0.623012i	0.987910	−	0.155029i	$-0.0495471\pi$
$787$	10.0907	+	17.4777i	0.359696	+	0.623012i	−0.628214	+	0.778041i	$0.716214\pi$
$788$	36.3183	+	62.9051i	1.29378	+	2.24090i
$789$	−44.8907	+	2.53727i	−1.59815	+	0.0903293i
$790$	−18.1291	+	31.4006i	−0.645006	+	1.11718i
$791$	8.39947			0.298651
$792$		0			0
$793$	72.3890			2.57061
$794$	33.1489	−	57.4155i	1.17641	−	2.03760i
$795$	13.0688	−	25.9112i	0.463504	−	0.918976i
$796$	8.50221	+	14.7263i	0.301353	+	0.521958i
$797$	−4.88362	−	8.45869i	−0.172987	−	0.299622i	0.766476	−	0.642273i	$-0.222008\pi$
$797$	−4.88362	−	8.45869i	−0.172987	−	0.299622i	−0.939463	+	0.342651i	$0.888675\pi$
$798$	11.5577	−	22.9152i	0.409139	−	0.811188i
$799$	−12.6464	+	21.9043i	−0.447399	+	0.774917i
$800$	10.4779			0.370451
$801$	−4.15688	+	9.54648i	−0.146876	+	0.337308i
$802$	9.75913			0.344607
$803$		0			0
$804$	−20.5694	+	1.16261i	−0.725427	+	0.0410020i
$805$	−24.0415	−	41.6411i	−0.847353	−	1.46766i
$806$	9.30499	+	16.1167i	0.327754	+	0.567687i
$807$	−18.9672	−	28.9463i	−0.667677	−	1.01896i
$808$	6.21759	−	10.7692i	0.218734	−	0.378858i
$809$	4.69697			0.165137			0.0825683	−	0.996585i	$-0.473688\pi$
$809$	4.69697			0.165137			0.0825683	+	0.996585i	$0.473688\pi$
$810$	22.4372	+	24.1116i	0.788363	+	0.847195i
$811$	36.1706			1.27012			0.635060	−	0.772463i	$-0.280975\pi$
$811$	36.1706			1.27012			0.635060	+	0.772463i	$0.280975\pi$
$812$	10.1532	−	17.5858i	0.356307	−	0.617142i
$813$	−0.281209	−	0.429160i	−0.00986241	−	0.0150513i
$814$		0			0
$815$	16.6975	+	28.9210i	0.584890	+	1.01306i
$816$	9.45936	−	0.534654i	0.331144	−	0.0187166i
$817$	0.667173	−	1.15558i	0.0233414	−	0.0404286i
$818$	−63.0744			−2.20535
$819$	25.4197	−	58.3776i	0.888236	−	2.03988i
$820$	−19.2715			−0.672990
$821$	−6.91422	+	11.9758i	−0.241308	+	0.417958i	−0.961087	−	0.276245i	$-0.910910\pi$
$821$	−6.91422	+	11.9758i	−0.241308	+	0.417958i	0.719779	+	0.694203i	$0.244243\pi$
$822$	20.0918	−	39.8354i	0.700782	−	1.38942i
$823$	22.1891	+	38.4326i	0.773463	+	1.33968i	0.935654	+	0.352917i	$0.114810\pi$
$823$	22.1891	+	38.4326i	0.773463	+	1.33968i	−0.162192	+	0.986759i	$0.551856\pi$
$824$	14.7465	+	25.5416i	0.513718	+	0.889785i
$825$		0			0
$826$	24.6398	−	42.6775i	0.857330	−	1.48494i
$827$	22.5598			0.784483			0.392241	−	0.919862i	$-0.371700\pi$
$827$	22.5598			0.784483			0.392241	+	0.919862i	$0.371700\pi$
$828$	49.3419	+	66.7549i	1.71475	+	2.31989i
$829$	−40.8016			−1.41710			−0.708549	−	0.705662i	$-0.750650\pi$
$829$	−40.8016			−1.41710			−0.708549	+	0.705662i	$0.750650\pi$
$830$	8.70766	−	15.0821i	0.302247	−	0.523508i
$831$	45.9631	−	2.59789i	1.59444	−	0.0901197i
$832$	−32.9315	−	57.0390i	−1.14169	−	1.97747i
$833$	17.7747	+	30.7867i	0.615858	+	1.06670i
$834$	−17.4942	−	26.6983i	−0.605774	−	0.924487i
$835$	−11.3081	+	19.5863i	−0.391334	+	0.677811i
$836$		0			0
$837$	4.84173	+	5.83087i	0.167355	+	0.201544i
$838$	−39.6028			−1.36806
$839$	20.8365	−	36.0899i	0.719357	−	1.24596i	−0.241898	−	0.970302i	$-0.577770\pi$
$839$	20.8365	−	36.0899i	0.719357	−	1.24596i	0.961255	−	0.275661i	$-0.0888967\pi$
$840$	−20.3783	−	31.0999i	−0.703119	−	1.07305i
$841$	13.3968	+	23.2039i	0.461958	+	0.800134i
$842$	38.7122	+	67.0516i	1.33411	+	2.31075i
$843$	11.7717	−	0.665349i	0.405438	−	0.0229158i
$844$	−7.56655	+	13.1056i	−0.260451	+	0.451115i
$845$	−25.8665			−0.889834
$846$	−40.9359	+	4.64231i	−1.40740	+	0.159606i
$847$		0			0
$848$	6.79884	−	11.7759i	0.233473	−	0.404388i
$849$	−1.61912	+	3.21018i	−0.0555681	+	0.110173i
$850$	−13.0062	−	22.5275i	−0.446110	−	0.772686i
$851$	36.8033	+	63.7451i	1.26160	+	2.18515i
$852$	−17.1113	+	33.9261i	−0.586224	+	1.16229i
$853$	5.52310	−	9.56628i	0.189107	−	0.327543i	−0.755846	−	0.654750i	$-0.772774\pi$
$853$	5.52310	−	9.56628i	0.189107	−	0.327543i	0.944953	+	0.327207i	$0.106107\pi$
$854$	−121.841			−4.16930
$855$	−7.52701	+	0.853597i	−0.257418	+	0.0291924i
$856$	24.0314			0.821376
$857$	2.17038	−	3.75922i	0.0741389	−	0.128412i	−0.826573	−	0.562830i	$-0.809713\pi$
$857$	2.17038	−	3.75922i	0.0741389	−	0.128412i	0.900711	+	0.434418i	$0.143046\pi$
$858$		0			0
$859$	21.7145	+	37.6105i	0.740888	+	1.28325i	0.952092	+	0.305813i	$0.0989282\pi$
$859$	21.7145	+	37.6105i	0.740888	+	1.28325i	−0.211204	+	0.977442i	$0.567738\pi$
$860$	−2.25256	−	3.90155i	−0.0768116	−	0.133042i
$861$	13.0631	+	19.9359i	0.445188	+	0.679412i
$862$	12.9721	−	22.4683i	0.441831	−	0.765273i
$863$	−8.21888			−0.279774			−0.139887	−	0.990167i	$-0.544674\pi$
$863$	−8.21888			−0.279774			−0.139887	+	0.990167i	$0.544674\pi$
$864$	−13.5525	−	16.3213i	−0.461067	−	0.555260i
$865$	15.8174			0.537807
$866$	−33.0167	+	57.1867i	−1.12195	+	1.94328i
$867$	1.58336	+	2.41641i	0.0537739	+	0.0820657i
$868$	−9.96977	−	17.2681i	−0.338396	−	0.586119i
$869$		0			0
$870$	−9.40044	+	0.531323i	−0.318705	+	0.0180135i
$871$	9.23348	−	15.9929i	0.312865	−	0.541897i
$872$	57.6218			1.95132
$873$	−16.5266	−	22.3589i	−0.559340	−	0.756734i
$874$	−29.9922			−1.01450
$875$	−23.0305	+	39.8899i	−0.778572	+	1.34853i
$876$	−2.91573	+	5.78094i	−0.0985136	+	0.195320i
$877$	−9.76218	−	16.9086i	−0.329645	−	0.570962i	0.652796	−	0.757534i	$-0.273596\pi$
$877$	−9.76218	−	16.9086i	−0.329645	−	0.570962i	−0.982441	+	0.186571i	$0.940262\pi$
$878$	−2.19202	−	3.79669i	−0.0739771	−	0.128132i
$879$	2.36887	−	4.69669i	0.0799001	−	0.158416i
$880$		0			0
$881$	−31.7440			−1.06948			−0.534742	−	0.845016i	$-0.679591\pi$
$881$	−31.7440			−1.06948			−0.534742	+	0.845016i	$0.679591\pi$
$882$	−23.1173	+	53.0900i	−0.778400	+	1.78763i
$883$	10.5442			0.354842			0.177421	−	0.984135i	$-0.443225\pi$
$883$	10.5442			0.354842			0.177421	+	0.984135i	$0.443225\pi$
$884$	−41.1615	+	71.2938i	−1.38441	+	2.39787i
$885$	−14.5222	+	0.820813i	−0.488159	+	0.0275913i
$886$	−22.7798	−	39.4558i	−0.765302	−	1.32554i
$887$	22.6002	+	39.1447i	0.758841	+	1.31435i	0.943442	+	0.331538i	$0.107567\pi$
$887$	22.6002	+	39.1447i	0.758841	+	1.31435i	−0.184601	+	0.982814i	$0.559099\pi$
$888$	31.1956	+	47.6084i	1.04685	+	1.59763i
$889$	−0.488305	+	0.845768i	−0.0163772	+	0.0283662i
$890$	−12.7015			−0.425755
$891$		0			0
$892$	25.9852			0.870048
$893$	4.73775	−	8.20602i	0.158543	−	0.274604i
$894$	−17.0755	−	26.0593i	−0.571090	−	0.871555i
$895$	−1.80231	−	3.12169i	−0.0602446	−	0.104347i
$896$	39.4962	+	68.4094i	1.31948	+	2.28540i
$897$	−74.2890	+	4.19890i	−2.48044	+	0.140197i
$898$	−18.3554	+	31.7924i	−0.612527	+	1.06093i
$899$	−2.16660			−0.0722602
$900$	10.7680	−	24.7293i	0.358934	−	0.824309i
$901$	46.4053			1.54599
$902$		0			0
$903$	−2.50917	+	4.97485i	−0.0834999	+	0.165553i
$904$	−3.79515	−	6.57339i	−0.126225	−	0.218628i
$905$	−6.02519	−	10.4359i	−0.200284	−	0.346902i
$906$	−0.642835	+	1.27453i	−0.0213567	+	0.0423434i
$907$	−12.7111	+	22.0162i	−0.422064	+	0.731036i	−0.996141	−	0.0877648i	$-0.972028\pi$
$907$	−12.7111	+	22.0162i	−0.422064	+	0.731036i	0.574077	+	0.818801i	$0.305361\pi$
$908$	9.17811			0.304586
$909$	6.28821	+	8.50735i	0.208567	+	0.282171i
$910$	77.6708			2.57476
$911$	−9.48804	+	16.4338i	−0.314353	+	0.544475i	−0.979300	−	0.202416i	$-0.935121\pi$
$911$	−9.48804	+	16.4338i	−0.314353	+	0.544475i	0.664947	+	0.746891i	$0.268454\pi$
$912$	−3.54377	+	0.200298i	−0.117346	+	0.00663252i
$913$		0			0
$914$	−12.7212	−	22.0338i	−0.420780	−	0.728813i
$915$	19.7101	+	30.0801i	0.651596	+	0.994418i
$916$	−20.1603	+	34.9186i	−0.666114	+	1.15374i
$917$	40.9656			1.35280
$918$	−18.2678	+	49.3973i	−0.602926	+	1.63035i
$919$	29.5351			0.974272			0.487136	−	0.873326i	$-0.338042\pi$
$919$	29.5351			0.974272			0.487136	+	0.873326i	$0.338042\pi$
$920$	−21.7255	+	37.6296i	−0.716268	+	1.24061i
$921$	−17.0412	−	26.0070i	−0.561527	−	0.856961i
$922$	46.3576	+	80.2938i	1.52671	+	2.64434i
$923$	−17.0295	−	29.4959i	−0.560532	−	0.970870i
$924$		0			0
$925$	11.9581	−	20.7121i	0.393180	−	0.681008i
$926$	55.4544			1.82235
$927$	−24.9309	+	2.82728i	−0.818839	+	0.0928600i
$928$	6.06456			0.199079
$929$	3.79837	−	6.57896i	0.124620	−	0.215849i	−0.796964	−	0.604027i	$-0.793562\pi$
$929$	3.79837	−	6.57896i	0.124620	−	0.215849i	0.921584	+	0.388178i	$0.126895\pi$
$930$	−4.16348	+	8.25481i	−0.136526	+	0.270686i
$931$	−6.65897	−	11.5337i	−0.218239	−	0.378001i
$932$	28.9794	+	50.1938i	0.949253	+	1.64415i
$933$	−20.5853	+	40.8139i	−0.673934	+	1.33619i
$934$	2.92075	−	5.05889i	0.0955699	−	0.165532i
$935$		0			0
$936$	−57.1715	+	6.48351i	−1.86871	+	0.211920i
$937$	−56.6799			−1.85165			−0.925826	−	0.377949i	$-0.876629\pi$
$937$	−56.6799			−1.85165			−0.925826	+	0.377949i	$0.876629\pi$
$938$	−15.5412	+	26.9182i	−0.507439	+	0.878910i
$939$	14.9552	−	0.845286i	0.488046	−	0.0275849i
$940$	−15.9959	−	27.7057i	−0.521729	−	0.903662i
$941$	−10.8614	−	18.8125i	−0.354072	−	0.613271i	0.632887	−	0.774244i	$-0.281870\pi$
$941$	−10.8614	−	18.8125i	−0.354072	−	0.613271i	−0.986959	+	0.160974i	$0.948537\pi$
$942$	−23.0582	−	35.1897i	−0.751277	−	1.14654i
$943$	13.9266	−	24.1216i	0.453513	−	0.785507i
$944$	−6.81533			−0.221820
$945$	31.1792	−	5.33232i	1.01426	−	0.173460i
$946$		0			0
$947$	21.9773	−	38.0658i	0.714166	−	1.23697i	−0.249115	−	0.968474i	$-0.580140\pi$
$947$	21.9773	−	38.0658i	0.714166	−	1.23697i	0.963280	−	0.268497i	$-0.0865271\pi$
$948$	−32.9489	−	50.2842i	−1.07013	−	1.63315i
$949$	−2.90179	−	5.02605i	−0.0941961	−	0.163152i
$950$	4.87254	+	8.43949i	0.158086	+	0.273813i
$951$	13.4817	−	0.762003i	0.437176	−	0.0247097i
$952$	29.7278	−	51.4901i	0.963484	−	1.66880i
$953$	13.0139			0.421563			0.210781	−	0.977533i	$-0.432399\pi$
$953$	13.0139			0.421563			0.210781	+	0.977533i	$0.432399\pi$
$954$	44.9292	+	60.7849i	1.45464	+	1.96798i
$955$	−30.1821			−0.976670
$956$	9.01200	−	15.6092i	0.291469	−	0.504839i
$957$		0			0
$958$	−13.4895	−	23.3645i	−0.435826	−	0.754873i
$959$	−21.4243	−	37.1079i	−0.691825	−	1.19828i
$960$	14.7351	−	29.2147i	0.475572	−	0.942902i
$961$	14.4363	−	25.0044i	0.465686	−	0.806592i
$962$	−118.900			−3.83349
$963$	−8.16201	+	18.7445i	−0.263017	+	0.604032i
$964$	80.6893			2.59883
$965$	8.55759	−	14.8222i	0.275479	−	0.477143i
$966$	125.039	−	7.06732i	4.02305	−	0.227387i
$967$	−17.3961	−	30.1309i	−0.559420	−	0.968944i	−0.997545	−	0.0700298i	$-0.977691\pi$
$967$	−17.3961	−	30.1309i	−0.559420	−	0.968944i	0.438125	−	0.898914i	$-0.355643\pi$
$968$		0			0
$969$	−6.63896	−	10.1319i	−0.213274	−	0.325483i
$970$	16.9584	−	29.3728i	0.544500	−	0.943102i
$971$	1.24869			0.0400724			0.0200362	−	0.999799i	$-0.493622\pi$
$971$	1.24869			0.0400724			0.0200362	+	0.999799i	$0.493622\pi$
$972$	−52.4479	+	15.2126i	−1.68227	+	0.487945i
$973$	−30.6552			−0.982762
$974$	31.3680	−	54.3309i	1.00509	−	1.74088i
$975$	13.2505	+	20.2219i	0.424356	+	0.647621i
$976$	8.42521	+	14.5929i	0.269684	+	0.467107i
$977$	−7.19890	−	12.4689i	−0.230313	−	0.398914i	0.727587	−	0.686015i	$-0.240642\pi$
$977$	−7.19890	−	12.4689i	−0.230313	−	0.398914i	−0.957900	+	0.287101i	$0.907308\pi$
$978$	−86.8430	+	4.90846i	−2.77693	+	0.156955i
$979$		0			0
$980$	−44.9650			−1.43635
$981$	−19.5706	+	44.9449i	−0.624842	+	1.43498i
$982$	−27.4511			−0.875998
$983$	23.5165	−	40.7318i	0.750060	−	1.29914i	−0.197733	−	0.980256i	$-0.563358\pi$
$983$	23.5165	−	40.7318i	0.750060	−	1.29914i	0.947793	−	0.318886i	$-0.103309\pi$
$984$	9.69942	−	19.2308i	0.309206	−	0.613054i
$985$	−16.1727	−	28.0120i	−0.515306	−	0.892537i
$986$	−7.52791	−	13.0387i	−0.239737	−	0.415237i
$987$	−17.8182	+	35.3275i	−0.567158	+	1.12449i
$988$	15.4204	−	26.7089i	0.490587	−	0.849722i
$989$	6.51127			0.207046
$990$		0			0
$991$	37.6903			1.19727			0.598636	−	0.801022i	$-0.295710\pi$
$991$	37.6903			1.19727			0.598636	+	0.801022i	$0.295710\pi$
$992$	2.97750	−	5.15718i	0.0945356	−	0.163741i
$993$	−13.4896	+	0.762446i	−0.428079	+	0.0241955i
$994$	28.6629	+	49.6457i	0.909133	+	1.57467i
$995$	−3.78608	−	6.55769i	−0.120027	−	0.207893i
$996$	15.8258	+	24.1521i	0.501459	+	0.765289i
$997$	−1.81341	+	3.14093i	−0.0574314	+	0.0994741i	−0.893312	−	0.449438i	$-0.851624\pi$
$997$	−1.81341	+	3.14093i	−0.0574314	+	0.0994741i	0.835880	+	0.548912i	$0.184958\pi$
$998$	−57.9966			−1.83585
$999$	−47.7297	+	8.16282i	−1.51010	+	0.258260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1089.2.e.k.727.2	yes	16
9.2	odd	6		9801.2.a.ca.1.2		8
9.4	even	3	inner	1089.2.e.k.364.2	✓	16
9.7	even	3		9801.2.a.bz.1.7		8
11.10	odd	2	inner	1089.2.e.k.727.7	yes	16
99.43	odd	6		9801.2.a.bz.1.2		8
99.65	even	6		9801.2.a.ca.1.7		8
99.76	odd	6	inner	1089.2.e.k.364.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1089.2.e.k.364.2	✓	16	9.4	even	3	inner
1089.2.e.k.364.7	yes	16	99.76	odd	6	inner
1089.2.e.k.727.2	yes	16	1.1	even	1	trivial
1089.2.e.k.727.7	yes	16	11.10	odd	2	inner
9801.2.a.bz.1.2		8	99.43	odd	6
9801.2.a.bz.1.7		8	9.7	even	3
9801.2.a.ca.1.2		8	9.2	odd	6
9801.2.a.ca.1.7		8	99.65	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1089 = 3^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1089.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17295 + 2.03160i) q^{2} +(0.949292 + 1.44874i) q^{3} +(-1.75160 - 3.03386i) q^{4} +(0.779999 + 1.35100i) q^{5} +(-4.05673 + 0.229291i) q^{6} +(-1.95114 + 3.37948i) q^{7} +3.52635 q^{8} +(-1.19769 + 2.75055i) q^{9} +O(q^{10})\)	\(q+(-1.17295 + 2.03160i) q^{2} +(0.949292 + 1.44874i) q^{3} +(-1.75160 - 3.03386i) q^{4} +(0.779999 + 1.35100i) q^{5} +(-4.05673 + 0.229291i) q^{6} +(-1.95114 + 3.37948i) q^{7} +3.52635 q^{8} +(-1.19769 + 2.75055i) q^{9} -3.65958 q^{10} +(2.73250 - 5.41764i) q^{12} +(2.71943 + 4.71018i) q^{13} +(-4.57717 - 7.92789i) q^{14} +(-1.21680 + 2.41251i) q^{15} +(-0.633017 + 1.09642i) q^{16} -4.32064 q^{17} +(-4.18320 - 5.65948i) q^{18} +1.61865 q^{19} +(2.73250 - 4.73282i) q^{20} +(-6.74818 + 0.381415i) q^{21} +(3.94929 + 6.84037i) q^{23} +(3.34754 + 5.10877i) q^{24} +(1.28320 - 2.22257i) q^{25} -12.7590 q^{26} +(-5.12179 + 0.875938i) q^{27} +13.6705 q^{28} +(0.742708 - 1.28641i) q^{29} +(-3.47401 - 5.30178i) q^{30} +(-0.729291 - 1.26317i) q^{31} +(2.04137 + 3.53575i) q^{32} +(5.06788 - 8.77782i) q^{34} -6.08755 q^{35} +(10.4427 - 1.18425i) q^{36} +9.31895 q^{37} +(-1.89858 + 3.28844i) q^{38} +(-4.24230 + 8.41108i) q^{39} +(2.75055 + 4.76410i) q^{40} +(-1.76318 - 3.05391i) q^{41} +(7.14037 - 14.1570i) q^{42} +(0.412180 - 0.713916i) q^{43} +(-4.65019 + 0.527352i) q^{45} -18.5292 q^{46} +(2.92698 - 5.06968i) q^{47} +(-2.18934 + 0.123744i) q^{48} +(-4.11391 - 7.12550i) q^{49} +(3.01026 + 5.21392i) q^{50} +(-4.10155 - 6.25948i) q^{51} +(9.52671 - 16.5007i) q^{52} -10.7404 q^{53} +(4.22802 - 11.4329i) q^{54} +(-6.88042 + 11.9172i) q^{56} +(1.53657 + 2.34500i) q^{57} +(1.74231 + 3.01777i) q^{58} +(2.69160 + 4.66200i) q^{59} +(9.45056 - 0.534156i) q^{60} +(6.65480 - 11.5265i) q^{61} +3.42167 q^{62} +(-6.95857 - 9.41428i) q^{63} -12.1097 q^{64} +(-4.24230 + 7.34788i) q^{65} +(-1.69769 - 2.94048i) q^{67} +(7.56805 + 13.1082i) q^{68} +(-6.16089 + 12.2150i) q^{69} +(7.14037 - 12.3675i) q^{70} -6.26216 q^{71} +(-4.22348 + 9.69942i) q^{72} -1.06706 q^{73} +(-10.9306 + 18.9324i) q^{74} +(4.43806 - 0.250844i) q^{75} +(-2.83522 - 4.91075i) q^{76} +(-12.1120 - 18.4844i) q^{78} +(4.95388 - 8.58037i) q^{79} -1.97501 q^{80} +(-6.13108 - 6.58862i) q^{81} +8.27244 q^{82} +(-2.37941 + 4.12126i) q^{83} +(12.9773 + 19.8050i) q^{84} +(-3.37010 - 5.83718i) q^{85} +(0.966929 + 1.67477i) q^{86} +(2.56872 - 0.145187i) q^{87} +3.47075 q^{89} +(4.38305 - 10.0659i) q^{90} -21.2239 q^{91} +(13.8352 - 23.9632i) q^{92} +(1.13769 - 2.25567i) q^{93} +(6.86638 + 11.8929i) q^{94} +(1.26254 + 2.18679i) q^{95} +(-3.18452 + 6.31386i) q^{96} +(-4.63396 + 8.02625i) q^{97} +19.3016 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} - 16 q^{4} + 4 q^{5} - 14 q^{9}+O(q^{10}) \) 16 * q - 2 * q^3 - 16 * q^4 + 4 * q^5 - 14 * q^9	\( 16 q - 2 q^{3} - 16 q^{4} + 4 q^{5} - 14 q^{9} - 6 q^{12} + 4 q^{14} - 52 q^{15} - 24 q^{16} - 6 q^{20} + 46 q^{23} - 12 q^{25} - 60 q^{26} - 32 q^{27} + 14 q^{31} + 38 q^{34} + 54 q^{36} - 12 q^{37} + 4 q^{38} - 4 q^{42} - 28 q^{45} + 16 q^{47} + 20 q^{48} - 42 q^{49} - 96 q^{53} + 46 q^{56} + 50 q^{58} + 48 q^{59} + 12 q^{60} - 12 q^{64} - 22 q^{67} - 10 q^{69} - 4 q^{70} + 68 q^{71} - 10 q^{75} - 72 q^{78} - 148 q^{80} - 14 q^{81} + 112 q^{82} + 14 q^{86} - 16 q^{89} - 96 q^{91} + 84 q^{92} + 30 q^{93} - 4 q^{97}+O(q^{100}) \) 16 * q - 2 * q^3 - 16 * q^4 + 4 * q^5 - 14 * q^9 - 6 * q^12 + 4 * q^14 - 52 * q^15 - 24 * q^16 - 6 * q^20 + 46 * q^23 - 12 * q^25 - 60 * q^26 - 32 * q^27 + 14 * q^31 + 38 * q^34 + 54 * q^36 - 12 * q^37 + 4 * q^38 - 4 * q^42 - 28 * q^45 + 16 * q^47 + 20 * q^48 - 42 * q^49 - 96 * q^53 + 46 * q^56 + 50 * q^58 + 48 * q^59 + 12 * q^60 - 12 * q^64 - 22 * q^67 - 10 * q^69 - 4 * q^70 + 68 * q^71 - 10 * q^75 - 72 * q^78 - 148 * q^80 - 14 * q^81 + 112 * q^82 + 14 * q^86 - 16 * q^89 - 96 * q^91 + 84 * q^92 + 30 * q^93 - 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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